LMFDB - Embedded newform 22.12.c.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,12,Mod(3,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.9035499723$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 339028 x^{18} - 38195378 x^{17} + 220926638311 x^{16} - 35915431412664 x^{15} + \cdots + 11\!\cdots\!00 $ x^20 - 4x^19 + 339028x^18 - 38195378x^17 + 220926638311x^16 - 35915431412664x^15 + 115759899998314350x^14 - 27226928185171403384x^13 + 41831014975562739810959x^12 - 3879797201571793549516048x^11 + 3316840467475291520075063190x^10 + 1067427514312498593848752050628x^9 + 750967910898548932251904101148531x^8 + 228128795234897755949671367783663114x^7 + 90326787979451743483651549716111634592x^6 + 21775725237124771428874092537573760059528x^5 + 5115171268695044278298633768429412143699481x^4 + 644893842489460735970879339730837145914702280x^3 + 40307167403308519805773510178453296556136973760x^2 - 118703222270772703791843925527006368174467110400*x + 1158220182319374358886221767374591631314546790400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 5\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.3
Root			$1.61693 + 4.97641i$ of defining polynomial
Character	$\chi$	$=$	22.15
Dual form			22.12.c.a.3.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.8885 - 18.8091i) q^{2} +(2.50110 - 7.69759i) q^{3} +(316.433 + 973.882i) q^{4} +(-10011.6 + 7273.85i) q^{5} +(-209.535 + 152.236i) q^{6} +(-8899.33 - 27389.3i) q^{7} +(10125.9 - 31164.2i) q^{8} +(143262. + 104086. i) q^{9} +O(q^{10})$	\(q+(-25.8885 - 18.8091i) q^{2} +(2.50110 - 7.69759i) q^{3} +(316.433 + 973.882i) q^{4} +(-10011.6 + 7273.85i) q^{5} +(-209.535 + 152.236i) q^{6} +(-8899.33 - 27389.3i) q^{7} +(10125.9 - 31164.2i) q^{8} +(143262. + 104086. i) q^{9} +396000. q^{10} +(-479251. + 235861. i) q^{11} +8287.98 q^{12} +(117747. + 85548.4i) q^{13} +(-284779. + 876458. i) q^{14} +(30951.1 + 95257.8i) q^{15} +(-848316. + 616338. i) q^{16} +(5.91973e6 - 4.30094e6i) q^{17} +(-1.75108e6 - 5.38926e6i) q^{18} +(4.87836e6 - 1.50140e7i) q^{19} +(-1.02519e7 - 7.44842e6i) q^{20} -233090. q^{21} +(1.68434e7 + 2.90819e6i) q^{22} -3.40170e7 q^{23} +(-214564. - 155890. i) q^{24} +(3.22344e7 - 9.92074e7i) q^{25} +(-1.43922e6 - 4.42945e6i) q^{26} +(2.31948e6 - 1.68520e6i) q^{27} +(2.38579e7 - 1.73338e7i) q^{28} +(-4.40818e7 - 1.35670e8i) q^{29} +(990437. - 3.04825e6i) q^{30} +(1.17652e8 + 8.54792e7i) q^{31} +3.35544e7 q^{32} +(616908. + 4.27899e6i) q^{33} -2.34150e8 q^{34} +(2.88322e8 + 2.09478e8i) q^{35} +(-5.60345e7 + 1.72456e8i) q^{36} +(1.83212e7 + 5.63868e7i) q^{37} +(-4.08695e8 + 2.96934e8i) q^{38} +(953015. - 692406. i) q^{39} +(1.25308e8 + 3.85658e8i) q^{40} +(2.58518e8 - 7.95635e8i) q^{41} +(6.03436e6 + 4.38422e6i) q^{42} +9.13904e8 q^{43} +(-3.81352e8 - 3.92099e8i) q^{44} -2.19139e9 q^{45} +(8.80651e8 + 6.39830e8i) q^{46} +(-7.30609e8 + 2.24858e9i) q^{47} +(2.62259e6 + 8.07151e6i) q^{48} +(9.28714e8 - 6.74750e8i) q^{49} +(-2.70051e9 + 1.96203e9i) q^{50} +(-1.83010e7 - 5.63247e7i) q^{51} +(-4.60549e7 + 1.41742e8i) q^{52} +(3.21090e9 + 2.33286e9i) q^{53} -9.17449e7 q^{54} +(3.08245e9 - 5.84734e9i) q^{55} -9.43680e8 q^{56} +(-1.03371e8 - 7.51033e7i) q^{57} +(-1.41062e9 + 4.34143e9i) q^{58} +(1.16590e8 + 3.58828e8i) q^{59} +(-8.29759e7 + 6.02855e7i) q^{60} +(5.49982e9 - 3.99585e9i) q^{61} +(-1.43805e9 - 4.42587e9i) q^{62} +(1.57591e9 - 4.85014e9i) q^{63} +(-8.68675e8 - 6.31130e8i) q^{64} -1.80111e9 q^{65} +(6.45132e7 - 1.22380e8i) q^{66} -1.62958e10 q^{67} +(6.06180e9 + 4.40416e9i) q^{68} +(-8.50799e7 + 2.61849e8i) q^{69} +(-3.52414e9 - 1.08462e10i) q^{70} +(1.22849e10 - 8.92553e9i) q^{71} +(4.69441e9 - 3.41069e9i) q^{72} +(-6.22572e9 - 1.91608e10i) q^{73} +(5.86278e8 - 1.80438e9i) q^{74} +(-6.83037e8 - 4.96255e8i) q^{75} +1.61656e10 q^{76} +(1.07251e10 + 1.10273e10i) q^{77} -3.76957e7 q^{78} +(-1.69851e10 - 1.23404e10i) q^{79} +(4.00985e9 - 1.23410e10i) q^{80} +(9.68652e9 + 2.98121e10i) q^{81} +(-2.16578e10 + 1.57353e10i) q^{82} +(-2.06835e10 + 1.50275e10i) q^{83} +(-7.37575e7 - 2.27002e8i) q^{84} +(-2.79816e10 + 8.61185e10i) q^{85} +(-2.36596e10 - 1.71897e10i) q^{86} -1.15458e9 q^{87} +(2.49759e9 + 1.73238e10i) q^{88} +3.02385e10 q^{89} +(5.67318e10 + 4.12181e10i) q^{90} +(1.29524e9 - 3.98634e9i) q^{91} +(-1.07641e10 - 3.31285e10i) q^{92} +(9.52244e8 - 6.91846e8i) q^{93} +(6.12083e10 - 4.44704e10i) q^{94} +(6.03698e10 + 1.85799e11i) q^{95} +(8.39230e7 - 2.58288e8i) q^{96} +(-5.94108e10 - 4.31645e10i) q^{97} -3.67345e10 q^{98} +(-9.32082e10 - 1.60933e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) $ 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−25.8885	−	18.8091i	−0.572061	−	0.415627i
$2$	−25.8885	−	18.8091i	−0.572061	−	0.415627i
$3$	2.50110	−	7.69759i	0.00594243	−	0.0182889i	−0.948041	−	0.318147i	$-0.896939\pi$
$3$	2.50110	−	7.69759i	0.00594243	−	0.0182889i	0.953984	+	0.299858i	$0.0969394\pi$
$4$	316.433	+	973.882i	0.154508	+	0.475528i
$5$	−10011.6	+	7273.85i	−1.43274	+	1.04095i	−0.443245	+	0.896400i	$0.646173\pi$
$5$	−10011.6	+	7273.85i	−1.43274	+	1.04095i	−0.989498	+	0.144548i	$0.953827\pi$
$6$	−209.535	+	152.236i	−0.0110008	+	0.00799255i
$7$	−8899.33	−	27389.3i	−0.200133	−	0.615945i	−0.999878	−	0.0156060i	$-0.995032\pi$
$7$	−8899.33	−	27389.3i	−0.200133	−	0.615945i	0.799745	−	0.600339i	$-0.204968\pi$
$8$	10125.9	−	31164.2i	0.109254	−	0.336249i
$9$	143262.	+	104086.i	0.808718	+	0.587568i
$10$	396000.			1.25226
$11$	−479251.	+	235861.i	−0.897228	+	0.441567i
$11$	−479251.	+	235861.i	−0.897228	+	0.441567i
$12$	8287.98			0.00961505
$13$	117747.	+	85548.4i	0.0879554	+	0.0639034i	0.630894	−	0.775869i	$-0.282688\pi$
$13$	117747.	+	85548.4i	0.0879554	+	0.0639034i	−0.542938	+	0.839772i	$0.682688\pi$
$14$	−284779.	+	876458.i	−0.141515	+	0.435539i
$15$	30951.1	+	95257.8i	0.0105239	+	0.0323891i
$16$	−848316.	+	616338.i	−0.202254	+	0.146946i
$17$	5.91973e6	−	4.30094e6i	1.01119	−	0.734673i	0.0467318	−	0.998907i	$-0.485119\pi$
$17$	5.91973e6	−	4.30094e6i	1.01119	−	0.734673i	0.964458	+	0.264235i	$0.0851194\pi$
$18$	−1.75108e6	−	5.38926e6i	−0.218427	−	0.672250i
$19$	4.87836e6	−	1.50140e7i	0.451990	−	1.39108i	−0.422642	−	0.906297i	$-0.638897\pi$
$19$	4.87836e6	−	1.50140e7i	0.451990	−	1.39108i	0.874633	−	0.484786i	$-0.161103\pi$
$20$	−1.02519e7	−	7.44842e6i	−0.716372	−	0.520474i
$21$	−233090.			−0.0124542
$22$	1.68434e7	+	2.90819e6i	0.696797	+	0.120309i
$23$	−3.40170e7			−1.10203			−0.551015	−	0.834496i	$-0.685759\pi$
$23$	−3.40170e7			−1.10203			−0.551015	+	0.834496i	$0.685759\pi$
$24$	−214564.	−	155890.i	−0.00550040	−	0.00399628i
$25$	3.22344e7	−	9.92074e7i	0.660161	−	2.03177i
$26$	−1.43922e6	−	4.42945e6i	−0.0237559	−	0.0731133i
$27$	2.31948e6	−	1.68520e6i	0.0311092	−	0.0226022i
$28$	2.38579e7	−	1.73338e7i	0.261977	−	0.190338i
$29$	−4.40818e7	−	1.35670e8i	−0.399089	−	1.22827i	−0.925731	−	0.378183i	$-0.876549\pi$
$29$	−4.40818e7	−	1.35670e8i	−0.399089	−	1.22827i	0.526642	−	0.850087i	$-0.323451\pi$
$30$	990437.	−	3.04825e6i	0.00744149	−	0.0229025i
$31$	1.17652e8	+	8.54792e7i	0.738092	+	0.536255i	0.892113	−	0.451813i	$-0.149222\pi$
$31$	1.17652e8	+	8.54792e7i	0.738092	+	0.536255i	−0.154021	+	0.988068i	$0.549222\pi$
$32$	3.35544e7			0.176777
$33$	616908.	+	4.27899e6i	0.00274406	+	0.0190333i
$34$	−2.34150e8			−0.883813
$35$	2.88322e8	+	2.09478e8i	0.927906	+	0.674163i
$36$	−5.60345e7	+	1.72456e8i	−0.154451	+	0.475352i
$37$	1.83212e7	+	5.63868e7i	0.0434354	+	0.133681i	0.970423	−	0.241413i	$-0.0776107\pi$
$37$	1.83212e7	+	5.63868e7i	0.0434354	+	0.133681i	−0.926987	+	0.375093i	$0.877611\pi$
$38$	−4.08695e8	+	2.96934e8i	−0.836738	+	0.607926i
$39$	953015.	−	692406.i	0.00169139	−	0.00122887i
$40$	1.25308e8	+	3.85658e8i	0.193485	+	0.595487i
$41$	2.58518e8	−	7.95635e8i	0.348481	−	1.07251i	−0.611213	−	0.791466i	$-0.709318\pi$
$41$	2.58518e8	−	7.95635e8i	0.348481	−	1.07251i	0.959694	−	0.281047i	$-0.0906818\pi$
$42$	6.03436e6	+	4.38422e6i	0.00712459	+	0.00517632i
$43$	9.13904e8			0.948034			0.474017	−	0.880516i	$-0.342803\pi$
$43$	9.13904e8			0.948034			0.474017	+	0.880516i	$0.342803\pi$
$44$	−3.81352e8	−	3.92099e8i	−0.348607	−	0.358432i
$45$	−2.19139e9			−1.77031
$46$	8.80651e8	+	6.39830e8i	0.630428	+	0.458033i
$47$	−7.30609e8	+	2.24858e9i	−0.464672	+	1.43011i	0.394722	+	0.918801i	$0.370841\pi$
$47$	−7.30609e8	+	2.24858e9i	−0.464672	+	1.43011i	−0.859394	+	0.511313i	$0.829159\pi$
$48$	2.62259e6	+	8.07151e6i	0.00148561	+	0.00457223i
$49$	9.28714e8	−	6.74750e8i	0.469682	−	0.341244i
$50$	−2.70051e9	+	1.96203e9i	−1.22211	+	0.887915i
$51$	−1.83010e7	−	5.63247e7i	−0.00742744	−	0.0228593i
$52$	−4.60549e7	+	1.41742e8i	−0.0167980	+	0.0516989i
$53$	3.21090e9	+	2.33286e9i	1.05465	+	0.766250i	0.973092	−	0.230418i	$-0.0740095\pi$
$53$	3.21090e9	+	2.33286e9i	1.05465	+	0.766250i	0.0815610	+	0.996668i	$0.474009\pi$
$54$	−9.17449e7			−0.0271905
$55$	3.08245e9	−	5.84734e9i	0.825849	−	1.56662i
$56$	−9.43680e8			−0.228976
$57$	−1.03371e8	−	7.51033e7i	−0.0227555	−	0.0165328i
$58$	−1.41062e9	+	4.34143e9i	−0.282199	+	0.868518i
$59$	1.16590e8	+	3.58828e8i	0.0212313	+	0.0653431i	0.961111	−	0.276163i	$-0.0890630\pi$
$59$	1.16590e8	+	3.58828e8i	0.0212313	+	0.0653431i	−0.939880	+	0.341506i	$0.889063\pi$
$60$	−8.29759e7	+	6.02855e7i	−0.0137759	+	0.0100088i
$61$	5.49982e9	−	3.99585e9i	0.833748	−	0.605753i	−0.0868695	−	0.996220i	$-0.527686\pi$
$61$	5.49982e9	−	3.99585e9i	0.833748	−	0.605753i	0.920617	+	0.390467i	$0.127686\pi$
$62$	−1.43805e9	−	4.42587e9i	−0.199352	−	0.613541i
$63$	1.57591e9	−	4.85014e9i	0.200059	−	0.615717i
$64$	−8.68675e8	−	6.31130e8i	−0.101127	−	0.0734732i
$65$	−1.80111e9			−0.192538
$66$	6.45132e7	−	1.22380e8i	0.00634099	−	0.0120287i
$67$	−1.62958e10			−1.47457			−0.737284	−	0.675583i	$-0.763892\pi$
$67$	−1.62958e10			−1.47457			−0.737284	+	0.675583i	$0.763892\pi$
$68$	6.06180e9	+	4.40416e9i	0.505595	+	0.367336i
$69$	−8.50799e7	+	2.61849e8i	−0.00654873	+	0.0201549i
$70$	−3.52414e9	−	1.08462e10i	−0.250619	−	0.771326i
$71$	1.22849e10	−	8.92553e9i	0.808076	−	0.587101i	−0.105196	−	0.994451i	$-0.533547\pi$
$71$	1.22849e10	−	8.92553e9i	0.808076	−	0.587101i	0.913272	+	0.407350i	$0.133547\pi$
$72$	4.69441e9	−	3.41069e9i	0.285925	−	0.207737i
$73$	−6.22572e9	−	1.91608e10i	−0.351491	−	1.08178i	−0.958016	−	0.286714i	$-0.907437\pi$
$73$	−6.22572e9	−	1.91608e10i	−0.351491	−	1.08178i	0.606525	−	0.795064i	$-0.292563\pi$
$74$	5.86278e8	−	1.80438e9i	0.0307135	−	0.0945264i
$75$	−6.83037e8	−	4.96255e8i	−0.0332359	−	0.0241473i
$76$	1.61656e10			0.731336
$77$	1.07251e10	+	1.10273e10i	0.451546	+	0.464272i
$78$	−3.76957e7			−0.00147833
$79$	−1.69851e10	−	1.23404e10i	−0.621038	−	0.451211i	0.232246	−	0.972657i	$-0.425393\pi$
$79$	−1.69851e10	−	1.23404e10i	−0.621038	−	0.451211i	−0.853284	+	0.521447i	$0.825393\pi$
$80$	4.00985e9	−	1.23410e10i	0.136815	−	0.421073i
$81$	9.68652e9	+	2.98121e10i	0.308674	+	0.950002i
$82$	−2.16578e10	+	1.57353e10i	−0.645118	+	0.468706i
$83$	−2.06835e10	+	1.50275e10i	−0.576362	+	0.418752i	−0.837411	−	0.546574i	$-0.815932\pi$
$83$	−2.06835e10	+	1.50275e10i	−0.576362	+	0.418752i	0.261049	+	0.965326i	$0.415932\pi$
$84$	−7.37575e7	−	2.27002e8i	−0.00192429	−	0.00592235i
$85$	−2.79816e10	+	8.61185e10i	−0.684019	+	2.10519i
$86$	−2.36596e10	−	1.71897e10i	−0.542334	−	0.394029i
$87$	−1.15458e9			−0.0248353
$88$	2.49759e9	+	1.73238e10i	0.0504507	+	0.349935i
$89$	3.02385e10			0.574005			0.287002	−	0.957930i	$-0.407341\pi$
$89$	3.02385e10			0.574005			0.287002	+	0.957930i	$0.407341\pi$
$90$	5.67318e10	+	4.12181e10i	1.01273	+	0.735790i
$91$	1.29524e9	−	3.98634e9i	0.0217582	−	0.0669649i
$92$	−1.07641e10	−	3.31285e10i	−0.170273	−	0.524046i
$93$	9.52244e8	−	6.91846e8i	0.0141936	−	0.0103122i
$94$	6.12083e10	−	4.44704e10i	0.860215	−	0.624983i
$95$	6.03698e10	+	1.85799e11i	0.800460	+	2.46356i
$96$	8.39230e7	−	2.58288e8i	0.00105048	−	0.00323305i
$97$	−5.94108e10	−	4.31645e10i	−0.702459	−	0.510367i	0.178273	−	0.983981i	$-0.442949\pi$
$97$	−5.94108e10	−	4.31645e10i	−0.702459	−	0.510367i	−0.880732	+	0.473615i	$0.842949\pi$
$98$	−3.67345e10			−0.410517
$99$	−9.32082e10	−	1.60933e10i	−0.985055	−	0.170080i
$100$	1.06816e11			1.06816
$101$	−1.02036e11	−	7.41334e10i	−0.966018	−	0.701853i	−0.0114776	−	0.999934i	$-0.503654\pi$
$101$	−1.02036e11	−	7.41334e10i	−0.966018	−	0.701853i	−0.954541	+	0.298081i	$0.903654\pi$
$102$	−5.85633e8	+	1.80239e9i	−0.00525200	+	0.0161640i
$103$	−2.78586e10	−	8.57400e10i	−0.236785	−	0.728751i	−0.996880	−	0.0789377i	$-0.974847\pi$
$103$	−2.78586e10	−	8.57400e10i	−0.236785	−	0.728751i	0.760094	−	0.649813i	$-0.225153\pi$
$104$	3.85834e9	−	2.80325e9i	0.0310969	−	0.0225932i
$105$	2.33360e9	−	1.69546e9i	0.0178437	−	0.0129642i
$106$	−3.92465e10	−	1.20788e11i	−0.284852	−	0.876684i
$107$	−2.86378e10	+	8.81382e10i	−0.197392	+	0.607510i	0.802548	+	0.596587i	$0.203477\pi$
$107$	−2.86378e10	+	8.81382e10i	−0.197392	+	0.607510i	−0.999940	+	0.0109231i	$0.996523\pi$
$108$	2.37514e9	+	1.72564e9i	0.0155546	+	0.0113011i
$109$	9.28577e10			0.578059			0.289029	−	0.957320i	$-0.406667\pi$
$109$	9.28577e10			0.578059			0.289029	+	0.957320i	$0.406667\pi$
$110$	−1.89784e11	+	9.34010e10i	−1.12357	+	0.552958i
$111$	4.79866e8			0.00270298
$112$	2.44305e10	+	1.77498e10i	0.130989	+	0.0951688i
$113$	8.55095e10	−	2.63171e11i	0.436599	−	1.34371i	−0.454839	−	0.890574i	$-0.650303\pi$
$113$	8.55095e10	−	2.63171e11i	0.436599	−	1.34371i	0.891439	−	0.453141i	$-0.149697\pi$
$114$	1.26349e9	+	3.88863e9i	0.00614605	+	0.0189156i
$115$	3.40565e11	−	2.47435e11i	1.57892	−	1.14716i
$116$	1.18177e11	−	8.58609e10i	0.522415	−	0.379556i
$117$	7.96432e9	+	2.45117e10i	0.0335836	+	0.103360i
$118$	3.73089e9	−	1.14825e10i	0.0150128	−	0.0462046i
$119$	−1.70481e11	−	1.23862e11i	−0.654890	−	0.475806i
$120$	3.28204e9			0.0120406
$121$	1.74051e11	−	2.26073e11i	0.610038	−	0.792372i
$122$	−2.17541e11			−0.728722
$123$	−5.47790e9	−	3.97993e9i	−0.0175443	−	0.0127467i
$124$	−4.60176e10	+	1.41628e11i	−0.140963	+	0.433839i
$125$	2.12179e11	+	6.53018e11i	0.621865	+	1.91390i
$126$	−1.32025e11	+	9.59217e10i	−0.370355	+	0.269078i
$127$	4.41276e10	−	3.20606e10i	0.118520	−	0.0861095i	−0.526946	−	0.849898i	$-0.676663\pi$
$127$	4.41276e10	−	3.20606e10i	0.118520	−	0.0861095i	0.645466	+	0.763789i	$0.276663\pi$
$128$	1.06177e10	+	3.26781e10i	0.0273135	+	0.0840623i
$129$	2.28576e9	−	7.03486e9i	0.00563363	−	0.0173385i
$130$	4.66280e10	+	3.38772e10i	0.110143	+	0.0800238i
$131$	−3.82048e11			−0.865220			−0.432610	−	0.901581i	$-0.642407\pi$
$131$	−3.82048e11			−0.865220			−0.432610	+	0.901581i	$0.642407\pi$
$132$	−3.97202e9	+	1.95481e9i	−0.00862690	+	0.00424569i
$133$	−4.54639e11			−0.947289
$134$	4.21875e11	+	3.06510e11i	0.843543	+	0.612870i
$135$	−1.09638e10	+	3.37430e10i	−0.0210438	+	0.0647662i
$136$	−7.40929e10	−	2.28034e11i	−0.136557	−	0.420278i
$137$	5.12415e11	−	3.72291e11i	0.907107	−	0.659052i	−0.0331747	−	0.999450i	$-0.510562\pi$
$137$	5.12415e11	−	3.72291e11i	0.907107	−	0.659052i	0.940281	+	0.340398i	$0.110562\pi$
$138$	7.12775e9	−	5.17861e9i	0.0121232	−	0.00880802i
$139$	−1.95277e11	−	6.01000e11i	−0.319204	−	0.982410i	−0.973989	−	0.226595i	$-0.927241\pi$
$139$	−1.95277e11	−	6.01000e11i	−0.319204	−	0.982410i	0.654785	−	0.755816i	$-0.272759\pi$
$140$	−1.12772e11	+	3.47078e11i	−0.177214	+	0.545410i
$141$	1.54813e10	+	1.12479e10i	0.0233940	+	0.0169967i
$142$	−4.85921e11			−0.706284
$143$	−7.66080e10	−	1.32272e10i	−0.107134	−	0.0184977i
$144$	−1.85683e11			−0.249908
$145$	1.42817e12	+	1.03763e12i	1.85036	+	1.34436i
$146$	−1.99223e11	+	6.13146e11i	−0.248542	+	0.764932i
$147$	−2.87115e9	−	8.83648e9i	−0.00344993	−	0.0106178i
$148$	−4.91167e10	+	3.56853e10i	−0.0568577	+	0.0413096i
$149$	−7.82405e11	+	5.68451e11i	−0.872785	+	0.634116i	−0.931333	−	0.364169i	$-0.881353\pi$
$149$	−7.82405e11	+	5.68451e11i	−0.872785	+	0.634116i	0.0585477	+	0.998285i	$0.481353\pi$
$150$	8.34870e9	+	2.56947e10i	0.00897670	+	0.0276274i
$151$	9.98827e9	−	3.07407e10i	0.0103542	−	0.0318670i	−0.945746	−	0.324907i	$-0.894667\pi$
$151$	9.98827e9	−	3.07407e10i	0.0103542	−	0.0318670i	0.956100	+	0.293040i	$0.0946670\pi$
$152$	−4.18503e11	−	3.04061e11i	−0.418369	−	0.303963i
$153$	1.29574e12			1.24944
$154$	−7.02420e10	−	4.87211e11i	−0.0653481	−	0.453266i
$155$	−1.79965e12			−1.61571
$156$	9.75887e8	+	7.09024e8i	0.000845696	+	0.000614434i
$157$	−1.34961e11	+	4.15367e11i	−0.112917	+	0.347524i	−0.991507	−	0.130054i	$-0.958485\pi$
$157$	−1.34961e11	+	4.15367e11i	−0.112917	+	0.347524i	0.878590	+	0.477577i	$0.158485\pi$
$158$	2.07607e11	+	6.38949e11i	0.167737	+	0.516240i
$159$	2.59881e10	−	1.88815e10i	0.0202811	−	0.0147351i
$160$	−3.35933e11	+	2.44070e11i	−0.253276	+	0.184015i
$161$	3.02729e11	+	9.31703e11i	0.220552	+	0.678790i
$162$	3.09969e11	−	9.53986e11i	0.218266	−	0.671753i
$163$	−4.68910e11	−	3.40683e11i	−0.319196	−	0.231910i	0.416636	−	0.909073i	$-0.363209\pi$
$163$	−4.68910e11	−	3.40683e11i	−0.319196	−	0.231910i	−0.735832	+	0.677164i	$0.763209\pi$
$164$	8.56658e11			0.563854
$165$	−3.73010e10	−	3.83522e10i	−0.0237442	−	0.0244134i
$166$	8.18121e11			0.503759
$167$	−1.17239e11	−	8.51794e10i	−0.0698446	−	0.0507451i	0.552315	−	0.833635i	$-0.313745\pi$
$167$	−1.17239e11	−	8.51794e10i	−0.0698446	−	0.0507451i	−0.622160	+	0.782890i	$0.713745\pi$
$168$	−2.36024e9	+	7.26407e9i	−0.00136068	+	0.00418773i
$169$	−5.47262e11	−	1.68430e12i	−0.305364	−	0.939815i
$170$	2.34422e12	−	1.70317e12i	1.26628	−	0.920004i
$171$	2.26163e12	−	1.64317e12i	1.18289	−	0.859419i
$172$	2.89190e11	+	8.90035e11i	0.146479	+	0.450817i
$173$	−2.89273e11	+	8.90291e11i	−0.141924	+	0.436796i	−0.996603	−	0.0823611i	$-0.973754\pi$
$173$	−2.89273e11	+	8.90291e11i	−0.141924	+	0.436796i	0.854679	+	0.519157i	$0.173754\pi$
$174$	2.98905e10	+	2.17167e10i	0.0142073	+	0.0103222i
$175$	−3.00409e12			−1.38358
$176$	2.61186e11	−	4.95465e11i	0.116582	−	0.221153i
$177$	3.05371e9			0.00132122
$178$	−7.82831e11	−	5.68760e11i	−0.328366	−	0.238572i
$179$	−3.65353e11	+	1.12444e12i	−0.148601	+	0.457346i	−0.997456	−	0.0712787i	$-0.977292\pi$
$179$	−3.65353e11	+	1.12444e12i	−0.148601	+	0.457346i	0.848856	+	0.528624i	$0.177292\pi$
$180$	−6.93428e11	−	2.13415e12i	−0.273528	−	0.841834i
$181$	1.46905e12	−	1.06733e12i	0.562088	−	0.408381i	−0.270135	−	0.962823i	$-0.587068\pi$
$181$	1.46905e12	−	1.06733e12i	0.562088	−	0.408381i	0.832222	+	0.554442i	$0.187068\pi$
$182$	−1.08512e11	+	7.88383e10i	−0.0402794	+	0.0292647i
$183$	−1.70029e10	−	5.23294e10i	−0.00612408	−	0.0188480i
$184$	−3.44452e11	+	1.06011e12i	−0.120401	+	0.370556i
$185$	−5.93574e11	−	4.31257e11i	−0.201386	−	0.146316i
$186$	−3.76652e10			−0.0124056
$187$	−1.82261e12	+	3.45746e12i	−0.582862	+	1.10568i
$188$	−2.42104e12			−0.751855
$189$	−6.67982e10	−	4.85317e10i	−0.0201477	−	0.0146381i
$190$	1.93183e12	−	5.94557e12i	0.566011	−	1.74200i
$191$	−1.25525e12	−	3.86328e12i	−0.357313	−	1.09970i	−0.954656	−	0.297710i	$-0.903777\pi$
$191$	−1.25525e12	−	3.86328e12i	−0.357313	−	1.09970i	0.597344	−	0.801985i	$-0.296223\pi$
$192$	−7.03082e9	+	5.10819e9i	−0.00194469	+	0.00141290i
$193$	3.90938e12	−	2.84033e12i	1.05085	−	0.763491i	0.0784799	−	0.996916i	$-0.474993\pi$
$193$	3.90938e12	−	2.84033e12i	1.05085	−	0.763491i	0.972375	+	0.233425i	$0.0749934\pi$
$194$	7.26174e11	+	2.23493e12i	0.189728	+	0.583922i
$195$	−4.50474e9	+	1.38642e10i	−0.00114414	+	0.00352131i
$196$	9.51003e11	+	6.90944e11i	0.234841	+	0.170622i
$197$	−2.36396e12			−0.567644			−0.283822	−	0.958877i	$-0.591603\pi$
$197$	−2.36396e12			−0.567644			−0.283822	+	0.958877i	$0.591603\pi$
$198$	2.11032e12	+	2.16980e12i	0.492822	+	0.506711i
$199$	3.11147e12			0.706763			0.353382	−	0.935479i	$-0.385032\pi$
$199$	3.11147e12			0.706763			0.353382	+	0.935479i	$0.385032\pi$
$200$	−2.76532e12	−	2.00912e12i	−0.611055	−	0.443958i
$201$	−4.07575e10	+	1.25439e11i	−0.00876252	+	0.0269683i
$202$	1.24718e12	+	3.83841e12i	0.260913	+	0.803006i
$203$	−3.32360e12	+	2.41474e12i	−0.676676	+	0.491634i
$204$	4.90626e10	−	3.56461e10i	0.00972265	−	0.00706392i
$205$	3.19916e12	+	9.84600e12i	0.617148	+	1.89939i
$206$	−8.91476e11	+	2.74368e12i	−0.167433	+	0.515305i
$207$	−4.87334e12	−	3.54069e12i	−0.891231	−	0.647517i
$208$	−1.52614e11			−0.0271797
$209$	1.20327e12	+	8.34611e12i	0.208717	+	1.44770i
$210$	−9.23037e10			−0.0155960
$211$	2.75596e12	+	2.00232e12i	0.453648	+	0.329595i	0.791035	−	0.611772i	$-0.209543\pi$
$211$	2.75596e12	+	2.00232e12i	0.453648	+	0.329595i	−0.337386	+	0.941366i	$0.609543\pi$
$212$	−1.25589e12	+	3.86523e12i	−0.201421	+	0.619909i
$213$	−3.79793e10	−	1.16888e11i	−0.00593552	−	0.0182676i
$214$	2.39920e12	−	1.74312e12i	0.365418	−	0.265492i
$215$	−9.14964e12	+	6.64760e12i	−1.35829	+	0.986855i
$216$	−2.90312e10	−	8.93487e10i	−0.00420116	−	0.0129298i
$217$	1.29419e12	−	3.98312e12i	0.182587	−	0.561946i
$218$	−2.40395e12	−	1.74657e12i	−0.330685	−	0.240257i
$219$	−1.63063e11			−0.0218733
$220$	6.67001e12	+	1.15165e12i	0.872573	+	0.150659i
$221$	1.06497e12			0.135888
$222$	−1.24230e10	−	9.02586e9i	−0.00154627	−	0.00112343i
$223$	1.65322e11	−	5.08808e11i	0.0200749	−	0.0617841i	−0.940517	−	0.339746i	$-0.889659\pi$
$223$	1.65322e11	−	5.08808e11i	0.0200749	−	0.0617841i	0.960592	+	0.277962i	$0.0896589\pi$
$224$	−2.98612e11	−	9.19033e11i	−0.0353788	−	0.108885i
$225$	1.49441e13	−	1.08575e13i	1.72769	−	1.25524i
$226$	−7.16374e12	+	5.20476e12i	−0.808246	+	0.587225i
$227$	−1.43660e12	−	4.42141e12i	−0.158196	−	0.486876i	0.840275	−	0.542160i	$-0.182393\pi$
$227$	−1.43660e12	−	4.42141e12i	−0.158196	−	0.486876i	−0.998471	+	0.0552844i	$0.982393\pi$
$228$	4.04317e10	−	1.24436e11i	0.00434591	−	0.0133753i
$229$	6.99047e12	+	5.07887e12i	0.733519	+	0.532933i	0.890675	−	0.454641i	$-0.150233\pi$
$229$	6.99047e12	+	5.07887e12i	0.733519	+	0.532933i	−0.157156	+	0.987574i	$0.550233\pi$
$230$	−1.34708e13			−1.38003
$231$	1.11709e11	−	5.49768e10i	0.0111743	−	0.00549938i
$232$	−4.67441e12			−0.456607
$233$	8.85106e12	+	6.43067e12i	0.844379	+	0.613477i	0.923590	−	0.383381i	$-0.125240\pi$
$233$	8.85106e12	+	6.43067e12i	0.844379	+	0.613477i	−0.0792114	+	0.996858i	$0.525240\pi$
$234$	2.54858e11	−	7.84373e11i	0.0237472	−	0.0730863i
$235$	−9.04129e12	−	2.78262e13i	−0.822919	−	2.53269i
$236$	−3.12563e11	+	2.27090e11i	−0.0277921	+	0.0201921i
$237$	−1.37473e11	+	9.98796e10i	−0.0119426	+	0.00867683i
$238$	2.08378e12	+	6.41321e12i	0.176880	+	0.544380i
$239$	7.42400e12	−	2.28487e13i	0.615814	−	1.89528i	0.227370	−	0.973808i	$-0.426987\pi$
$239$	7.42400e12	−	2.28487e13i	0.615814	−	1.89528i	0.388444	−	0.921472i	$-0.373013\pi$
$240$	−8.49673e10	−	6.17324e10i	−0.00688795	−	0.00500439i
$241$	−1.40702e13			−1.11483			−0.557413	−	0.830235i	$-0.688206\pi$
$241$	−1.40702e13			−1.11483			−0.557413	+	0.830235i	$0.688206\pi$
$242$	−8.75816e12	+	2.57896e12i	−0.678310	+	0.199738i
$243$	7.61594e11			0.0576619
$244$	5.63182e12	+	4.09176e12i	0.416874	+	0.302877i
$245$	−4.38988e12	+	1.35107e13i	−0.317716	+	0.977829i
$246$	6.69559e10	+	2.06069e11i	0.00473855	+	0.0145838i
$247$	1.85884e12	−	1.35053e12i	0.128650	−	0.0934696i
$248$	3.85522e12	−	2.80098e12i	0.260955	−	0.189595i
$249$	6.39438e10	+	1.96799e11i	0.00423352	+	0.0130294i
$250$	6.78971e12	−	2.08966e13i	0.439725	−	1.35334i
$251$	1.72729e12	+	1.25495e12i	0.109436	+	0.0795097i	0.641157	−	0.767410i	$-0.278455\pi$
$251$	1.72729e12	+	1.25495e12i	0.109436	+	0.0795097i	−0.531721	+	0.846919i	$0.678455\pi$
$252$	5.22214e12			0.323702
$253$	1.63027e13	−	8.02328e12i	0.988772	−	0.486619i
$254$	−1.74543e12			−0.103590
$255$	5.92920e11	+	4.30782e11i	0.0344370	+	0.0250199i
$256$	3.39768e11	−	1.04570e12i	0.0193136	−	0.0594410i
$257$	5.16982e12	+	1.59111e13i	0.287636	+	0.885253i	0.985596	+	0.169116i	$0.0540914\pi$
$257$	5.16982e12	+	1.59111e13i	0.287636	+	0.885253i	−0.697960	+	0.716137i	$0.745909\pi$
$258$	−1.91495e11	+	1.39129e11i	−0.0104291	+	0.00757721i
$259$	1.38135e12	−	1.00361e12i	0.0736470	−	0.0535077i
$260$	−5.69930e11	−	1.75406e12i	−0.0297487	−	0.0915571i
$261$	7.80606e12	−	2.40246e13i	0.398942	−	1.22782i
$262$	9.89068e12	+	7.18600e12i	0.494959	+	0.359609i
$263$	−2.01877e13			−0.989307			−0.494654	−	0.869090i	$-0.664705\pi$
$263$	−2.01877e13			−0.989307			−0.494654	+	0.869090i	$0.664705\pi$
$264$	1.39598e11	+	2.41030e10i	0.00669974	+	0.00115678i
$265$	−4.91151e13			−2.30867
$266$	1.17699e13	+	8.55136e12i	0.541907	+	0.393719i
$267$	7.56296e10	−	2.32764e11i	0.00341098	−	0.0104979i
$268$	−5.15654e12	−	1.58702e13i	−0.227833	−	0.701199i
$269$	3.27048e13	−	2.37614e13i	1.41571	−	1.02857i	0.423249	−	0.906014i	$-0.360890\pi$
$269$	3.27048e13	−	2.37614e13i	1.41571	−	1.02857i	0.992461	−	0.122560i	$-0.0391104\pi$
$270$	9.18513e11	−	6.67339e11i	0.0389569	−	0.0283039i
$271$	1.27826e13	+	3.93407e13i	0.531236	+	1.63498i	0.751644	+	0.659568i	$0.229261\pi$
$271$	1.27826e13	+	3.93407e13i	0.531236	+	1.63498i	−0.220409	+	0.975408i	$0.570739\pi$
$272$	−2.37097e12	+	7.29710e12i	−0.0965601	+	0.297181i
$273$	−2.74457e10	−	1.99405e10i	−0.00109542	−	0.000795868i
$274$	−2.02681e13			−0.792840
$275$	7.95078e12	+	5.51481e13i	0.304845	+	2.11447i
$276$	−2.81932e11			−0.0105961
$277$	−8.63501e12	−	6.27371e12i	−0.318144	−	0.231145i	0.417239	−	0.908797i	$-0.362998\pi$
$277$	−8.63501e12	−	6.27371e12i	−0.318144	−	0.231145i	−0.735383	+	0.677651i	$0.762998\pi$
$278$	−6.24885e12	+	1.92320e13i	−0.225712	+	0.694669i
$279$	7.95788e12	+	2.44918e13i	0.281822	+	0.867358i
$280$	9.44775e12	−	6.86419e12i	0.328064	−	0.238353i
$281$	−3.54246e13	+	2.57375e13i	−1.20620	+	0.876358i	−0.994881	−	0.101058i	$-0.967777\pi$
$281$	−3.54246e13	+	2.57375e13i	−1.20620	+	0.876358i	−0.211323	+	0.977416i	$0.567777\pi$
$282$	−1.89227e11	−	5.82381e11i	−0.00631849	−	0.0194463i
$283$	6.32798e12	−	1.94755e13i	0.207224	−	0.637769i	−0.792391	−	0.610014i	$-0.791164\pi$
$283$	6.32798e12	−	1.94755e13i	0.207224	−	0.637769i	0.999615	−	0.0277558i	$-0.00883607\pi$
$284$	1.25798e13	+	9.13974e12i	0.404038	+	0.293551i
$285$	1.58120e12			0.0498126
$286$	1.73448e12	+	1.78336e12i	0.0535989	+	0.0551095i
$287$	−2.40925e13			−0.730352
$288$	4.80707e12	+	3.49254e12i	0.142962	+	0.103868i
$289$	5.95456e12	−	1.83263e13i	0.173745	−	0.534731i
$290$	−1.74564e13	−	5.37253e13i	−0.499765	−	1.53812i
$291$	−4.80855e11	+	3.49362e11i	−0.0135084	+	0.00981440i
$292$	1.66903e13	−	1.21262e13i	0.460108	−	0.334288i
$293$	7.76100e12	+	2.38859e13i	0.209964	+	0.646204i	0.999473	+	0.0324643i	$0.0103355\pi$
$293$	7.76100e12	+	2.38859e13i	0.209964	+	0.646204i	−0.789509	+	0.613740i	$0.789664\pi$
$294$	−9.18767e10	+	2.82767e11i	−0.00243947	+	0.00750791i
$295$	−3.77731e12	−	2.74438e12i	−0.0984378	−	0.0715193i
$296$	1.94277e12			0.0496955
$297$	−7.14138e11	+	1.35471e12i	−0.0179317	+	0.0340161i
$298$	3.09474e13			0.762842
$299$	−4.00541e12	−	2.91010e12i	−0.0969294	−	0.0704234i
$300$	2.67158e11	−	8.22229e11i	0.00634749	−	0.0195356i
$301$	−8.13313e12	−	2.50312e13i	−0.189733	−	0.583937i
$302$	−8.36788e11	+	6.07962e11i	−0.0191680	+	0.0139264i
$303$	−8.25851e11	+	6.00016e11i	−0.0185766	+	0.0134967i
$304$	5.11533e12	+	1.57434e13i	0.112998	+	0.347771i
$305$	−2.59968e13	+	8.00098e13i	−0.563988	+	1.73578i
$306$	−3.35448e13	−	2.43717e13i	−0.714755	−	0.519300i
$307$	−4.38955e13			−0.918669			−0.459334	−	0.888263i	$-0.651912\pi$
$307$	−4.38955e13			−0.918669			−0.459334	+	0.888263i	$0.651912\pi$
$308$	−7.34556e12	+	1.39344e13i	−0.151007	+	0.286457i
$309$	−7.29669e11			−0.0147351
$310$	4.65903e13	+	3.38498e13i	0.924285	+	0.671532i
$311$	7.64778e12	−	2.35374e13i	0.149057	−	0.458751i	−0.848453	−	0.529271i	$-0.822466\pi$
$311$	7.64778e12	−	2.35374e13i	0.149057	−	0.458751i	0.997510	+	0.0705194i	$0.0224657\pi$
$312$	−1.19282e10	−	3.67112e10i	−0.000228415	−	0.000702988i
$313$	3.35862e13	−	2.44018e13i	0.631927	−	0.459122i	−0.225140	−	0.974326i	$-0.572284\pi$
$313$	3.35862e13	−	2.44018e13i	0.631927	−	0.459122i	0.857067	+	0.515205i	$0.172284\pi$
$314$	1.13066e13	−	8.21476e12i	0.209036	−	0.151873i
$315$	1.95019e13	+	6.00206e13i	0.354298	+	1.09042i
$316$	6.64342e12	−	2.04464e13i	0.118608	−	0.365037i
$317$	−8.34758e13	−	6.06487e13i	−1.46465	−	1.06413i	−0.982120	−	0.188254i	$-0.939717\pi$
$317$	−8.34758e13	−	6.06487e13i	−1.46465	−	1.06413i	−0.482532	−	0.875878i	$-0.660283\pi$
$318$	−1.02794e12			−0.0177263
$319$	5.31254e13	+	5.46226e13i	0.900437	+	0.925815i
$320$	1.32876e13			0.221371
$321$	6.06826e11	+	4.40885e11i	0.00993772	+	0.00722017i
$322$	9.68732e12	−	2.98145e13i	0.155954	−	0.479977i
$323$	−3.56959e13	−	1.09861e14i	−0.564943	−	1.73871i
$324$	−2.59683e13	+	1.88671e13i	−0.404060	+	0.293567i
$325$	1.22826e13	−	8.92380e12i	0.187902	−	0.136518i
$326$	5.73145e12	+	1.76396e13i	0.0862120	+	0.265333i
$327$	2.32246e11	−	7.14780e11i	0.00343507	−	0.0105721i
$328$	−2.21776e13	−	1.61130e13i	−0.322559	−	0.234353i
$329$	6.80891e13			0.973868
$330$	2.44296e11	+	1.69448e12i	0.00343629	+	0.0238347i
$331$	9.96824e13			1.37900			0.689500	−	0.724286i	$-0.257830\pi$
$331$	9.96824e13			1.37900			0.689500	+	0.724286i	$0.257830\pi$
$332$	−2.11800e13	−	1.53881e13i	−0.288181	−	0.209376i
$333$	−3.24434e12	+	9.98506e12i	−0.0434194	+	0.133631i
$334$	1.43301e12	+	4.41034e12i	0.0188644	+	0.0580586i
$335$	1.63147e14	−	1.18533e14i	2.11268	−	1.53495i
$336$	1.97734e11	−	1.43662e11i	0.00251892	−	0.00183011i
$337$	−6.56642e12	−	2.02094e13i	−0.0822933	−	0.253273i	0.901441	−	0.432902i	$-0.142510\pi$
$337$	−6.56642e12	−	2.02094e13i	−0.0822933	−	0.253273i	−0.983734	+	0.179629i	$0.942510\pi$
$338$	−1.75124e13	+	5.38976e13i	−0.215925	+	0.664550i
$339$	−1.81192e12	−	1.31644e12i	−0.0219806	−	0.0159699i
$340$	−9.27235e13			−1.10677
$341$	−7.65461e13	−	1.32165e13i	−0.899029	−	0.155226i
$342$	−8.94571e13			−1.03388
$343$	−7.28151e13	−	5.29033e13i	−0.828140	−	0.601679i
$344$	9.25407e12	−	2.84811e13i	0.103577	−	0.318776i
$345$	−1.05287e12	−	3.24039e12i	−0.0115976	−	0.0356937i
$346$	2.42345e13	−	1.76074e13i	0.262733	−	0.190887i
$347$	6.06992e13	−	4.41006e13i	0.647696	−	0.470579i	−0.214790	−	0.976660i	$-0.568907\pi$
$347$	6.06992e13	−	4.41006e13i	0.647696	−	0.470579i	0.862486	+	0.506082i	$0.168907\pi$
$348$	−3.65349e11	−	1.12443e12i	−0.00383726	−	0.0118099i
$349$	9.46240e12	−	2.91223e13i	0.0978276	−	0.301083i	−0.890153	−	0.455662i	$-0.849402\pi$
$349$	9.46240e12	−	2.91223e13i	0.0978276	−	0.301083i	0.987980	+	0.154580i	$0.0494024\pi$
$350$	7.77715e13	+	5.65043e13i	0.791491	+	0.575052i
$351$	4.17278e11			0.00418058
$352$	−1.60810e13	+	7.91418e12i	−0.158609	+	0.0780587i
$353$	−1.43702e14			−1.39541			−0.697706	−	0.716385i	$-0.745796\pi$
$353$	−1.43702e14			−1.39541			−0.697706	+	0.716385i	$0.745796\pi$
$354$	−7.90562e10	−	5.74377e10i	−0.000755819	−	0.000549135i
$355$	−5.80689e13	+	1.78718e14i	−0.546623	+	1.68233i
$356$	9.56848e12	+	2.94488e13i	0.0886886	+	0.272956i
$357$	−1.37983e12	+	1.00251e12i	−0.0125936	+	0.00914980i
$358$	3.06082e13	−	2.22381e13i	0.275094	−	0.199867i
$359$	−1.47060e13	−	4.52605e13i	−0.130159	−	0.400590i	0.864646	−	0.502381i	$-0.167543\pi$
$359$	−1.47060e13	−	4.52605e13i	−0.130159	−	0.400590i	−0.994806	+	0.101791i	$0.967543\pi$
$360$	−2.21897e13	+	6.82928e13i	−0.193414	+	0.595266i
$361$	−1.07381e14	−	7.80166e13i	−0.921799	−	0.669726i
$362$	−5.81070e13			−0.491283
$363$	−1.30490e12	−	1.90520e12i	−0.0108665	−	0.0158655i
$364$	4.29209e12			0.0352055
$365$	2.01702e14	+	1.46545e14i	1.62967	+	1.18403i
$366$	−5.44092e11	+	1.67454e12i	−0.00433038	+	0.0133275i
$367$	4.87147e13	+	1.49928e14i	0.381941	+	1.17550i	0.938675	+	0.344804i	$0.112055\pi$
$367$	4.87147e13	+	1.49928e14i	0.381941	+	1.17550i	−0.556733	+	0.830691i	$0.687945\pi$
$368$	2.88572e13	−	2.09660e13i	0.222890	−	0.161939i
$369$	1.19850e14	−	8.70762e13i	0.911997	−	0.662605i
$370$	7.25520e12	+	2.23292e13i	0.0543926	+	0.167403i
$371$	3.53205e13	−	1.08705e14i	0.260898	−	0.802960i
$372$	9.75098e11	+	7.08450e11i	0.00709679	+	0.00515612i
$373$	−3.86185e13			−0.276947			−0.138474	−	0.990366i	$-0.544220\pi$
$373$	−3.86185e13			−0.276947			−0.138474	+	0.990366i	$0.544220\pi$
$374$	1.12217e14	−	5.52269e13i	0.792982	−	0.390262i
$375$	5.55735e12			0.0386986
$376$	6.26773e13	+	4.55377e13i	0.430107	+	0.312491i
$377$	6.41582e12	−	1.97459e13i	0.0433885	−	0.133536i
$378$	8.16469e11	+	2.51283e12i	0.00544170	+	0.0167478i
$379$	−1.89832e14	+	1.37921e14i	−1.24696	+	0.905970i	−0.998042	−	0.0625540i	$-0.980075\pi$
$379$	−1.89832e14	+	1.37921e14i	−1.24696	+	0.905970i	−0.248919	+	0.968524i	$0.580075\pi$
$380$	−1.61843e14	+	1.17586e14i	−1.04782	+	0.761283i
$381$	−1.36422e11	−	4.19863e11i	−0.000870555	−	0.00267929i
$382$	−4.01682e13	+	1.23625e14i	−0.252658	+	0.777602i
$383$	2.35419e14	+	1.71042e14i	1.45965	+	1.06050i	0.983455	+	0.181154i	$0.0579832\pi$
$383$	2.35419e14	+	1.71042e14i	1.45965	+	1.06050i	0.476192	+	0.879341i	$0.342017\pi$
$384$	2.78098e11			0.00169972
$385$	−1.87587e14	−	3.23887e13i	−1.13023	−	0.195146i
$386$	−1.54632e14			−0.918481
$387$	1.30928e14	+	9.51245e13i	0.766692	+	0.557035i
$388$	2.32376e13	−	7.15178e13i	0.134158	−	0.412895i
$389$	2.38340e13	+	7.33535e13i	0.135667	+	0.417540i	0.995693	−	0.0927099i	$-0.0295529\pi$
$389$	2.38340e13	+	7.33535e13i	0.135667	+	0.417540i	−0.860026	+	0.510250i	$0.829553\pi$
$390$	3.77394e11	−	2.74193e11i	0.00211807	−	0.00153887i
$391$	−2.01372e14	+	1.46305e14i	−1.11436	+	0.809631i
$392$	−1.16240e13	−	3.57751e13i	−0.0634283	−	0.195212i
$393$	−9.55541e11	+	2.94085e12i	−0.00514151	+	0.0158239i
$394$	6.11995e13	+	4.44641e13i	0.324727	+	0.235928i
$395$	2.59810e14			1.35948
$396$	−1.38212e13	−	9.58662e13i	−0.0713216	−	0.494700i
$397$	−3.07905e14			−1.56700			−0.783500	−	0.621392i	$-0.786568\pi$
$397$	−3.07905e14			−1.56700			−0.783500	+	0.621392i	$0.786568\pi$
$398$	−8.05515e13	−	5.85241e13i	−0.404312	−	0.293750i
$399$	−1.13710e12	+	3.49962e12i	−0.00562920	+	0.0173249i
$400$	3.38003e13	+	1.04027e14i	0.165040	+	0.507942i
$401$	2.69758e14	−	1.95990e14i	1.29921	−	0.943932i	0.299263	−	0.954171i	$-0.403259\pi$
$401$	2.69758e14	−	1.95990e14i	1.29921	−	0.943932i	0.999948	+	0.0102388i	$0.00325916\pi$
$402$	3.41454e12	−	2.48081e12i	0.0162214	−	0.0117856i
$403$	6.54060e12	+	2.01299e13i	0.0306507	+	0.0943331i
$404$	3.99096e13	−	1.22829e14i	0.184493	−	0.567811i
$405$	−3.13826e14	−	2.28008e14i	−1.43115	−	1.03979i
$406$	1.31462e14			0.591437
$407$	−2.20799e13	−	2.27022e13i	−0.0980004	−	0.100762i
$408$	−1.94063e12			−0.00849791
$409$	1.64368e13	+	1.19421e13i	0.0710134	+	0.0515942i	0.622726	−	0.782440i	$-0.286025\pi$
$409$	1.64368e13	+	1.19421e13i	0.0710134	+	0.0515942i	−0.551712	+	0.834035i	$0.686025\pi$
$410$	1.02373e14	−	3.15072e14i	0.436390	−	1.34307i
$411$	−1.58414e12	−	4.87550e12i	−0.00666292	−	0.0205064i
$412$	7.46853e13	−	5.42620e13i	0.309956	−	0.225196i
$413$	8.79048e12	−	6.38665e12i	0.0359987	−	0.0261546i
$414$	5.95664e13	+	1.83327e14i	0.240713	+	0.740839i
$415$	9.77677e13	−	3.00898e14i	0.389880	−	1.19993i
$416$	3.95094e12	+	2.87053e12i	0.0155485	+	0.0112966i
$417$	−5.11466e12			−0.0198641
$418$	1.25832e14	−	2.38701e14i	0.482305	−	0.914924i
$419$	4.07449e14			1.54133			0.770665	−	0.637240i	$-0.219924\pi$
$419$	4.07449e14			1.54133			0.770665	+	0.637240i	$0.219924\pi$
$420$	2.38961e12	+	1.73615e12i	0.00892187	+	0.00648212i
$421$	−1.26599e14	+	3.89631e14i	−0.466528	+	1.43583i	0.390522	+	0.920594i	$0.372295\pi$
$421$	−1.26599e14	+	3.89631e14i	−0.466528	+	1.43583i	−0.857050	+	0.515233i	$0.827705\pi$
$422$	−3.36859e13	−	1.03674e14i	−0.122526	−	0.377097i
$423$	−3.38714e14	+	2.46090e14i	−1.21608	+	0.883532i
$424$	1.05215e14	−	7.64430e13i	0.372876	−	0.270910i
$425$	−2.35866e14	−	7.25919e14i	−0.825136	−	2.53951i
$426$	−1.21534e12	+	3.74042e12i	−0.00419704	+	0.0129172i
$427$	−1.58389e14	−	1.15076e14i	−0.539971	−	0.392312i
$428$	−9.48982e13			−0.319387
$429$	−2.93422e11	+	5.56615e11i	−0.000974938	+	0.00184944i
$430$	3.61906e14			1.18719
$431$	−3.74166e14	−	2.71847e14i	−1.21182	−	0.880440i	−0.216427	−	0.976299i	$-0.569440\pi$
$431$	−3.74166e14	−	2.71847e14i	−1.21182	−	0.880440i	−0.995395	+	0.0958582i	$0.969440\pi$
$432$	−9.28997e11	+	2.85916e12i	−0.00297067	+	0.00914277i
$433$	3.98865e13	+	1.22758e14i	0.125934	+	0.387585i	0.994070	−	0.108741i	$-0.0346821\pi$
$433$	3.98865e13	+	1.22758e14i	0.125934	+	0.387585i	−0.868136	+	0.496326i	$0.834682\pi$
$434$	−1.08424e14	+	7.87745e13i	−0.338011	+	0.245579i
$435$	1.15592e13	−	8.39827e12i	0.0355826	−	0.0258523i
$436$	2.93833e13	+	9.04324e13i	0.0893150	+	0.274883i
$437$	−1.65947e14	+	5.10733e14i	−0.498106	+	1.53301i
$438$	4.22147e12	+	3.06708e12i	0.0125128	+	0.00909112i
$439$	2.62040e14			0.767031			0.383516	−	0.923534i	$-0.374713\pi$
$439$	2.62040e14			0.767031			0.383516	+	0.923534i	$0.374713\pi$
$440$	−1.51015e14	−	1.55272e14i	−0.436548	−	0.448851i
$441$	2.03281e14			0.580344
$442$	−2.75705e13	−	2.00312e13i	−0.0777361	−	0.0564786i
$443$	9.99088e13	−	3.07488e14i	0.278217	−	0.856263i	−0.710134	−	0.704067i	$-0.751365\pi$
$443$	9.99088e13	−	3.07488e14i	0.278217	−	0.856263i	0.988350	−	0.152196i	$-0.0486345\pi$
$444$	1.51846e11	+	4.67333e11i	0.000417634	+	0.00128535i
$445$	−3.02736e14	+	2.19951e14i	−0.822402	+	0.597510i
$446$	−1.38502e13	+	1.00627e13i	−0.0371632	+	0.0270007i
$447$	2.41883e12	+	7.44439e12i	0.00641082	+	0.0197305i
$448$	−9.55558e12	+	2.94091e13i	−0.0250166	+	0.0769932i
$449$	4.03863e14	+	2.93423e14i	1.04443	+	0.758822i	0.971145	−	0.238490i	$-0.0766523\pi$
$449$	4.03863e14	+	2.93423e14i	1.04443	+	0.758822i	0.0732833	+	0.997311i	$0.476652\pi$
$450$	−5.91100e14			−1.51005
$451$	6.37646e13	+	4.42283e14i	0.160919	+	1.11617i
$452$	2.83356e14			0.706433
$453$	−2.11648e11	−	1.53771e11i	−0.000521284	−	0.000378735i
$454$	−4.59713e13	+	1.41485e14i	−0.111861	+	0.344273i
$455$	1.60286e13	+	4.93311e13i	0.0385331	+	0.118593i
$456$	−3.38725e12	+	2.46098e12i	−0.00804528	+	0.00584524i
$457$	5.18910e14	−	3.77010e14i	1.21774	−	0.884737i	0.221826	−	0.975086i	$-0.428798\pi$
$457$	5.18910e14	−	3.77010e14i	1.21774	−	0.884737i	0.995910	+	0.0903493i	$0.0287984\pi$
$458$	−8.54439e13	−	2.62969e14i	−0.198117	−	0.609740i
$459$	6.48274e12	−	1.99518e13i	0.0148521	−	0.0457102i
$460$	3.48738e14	+	2.53373e14i	0.789462	+	0.573578i
$461$	5.86679e14			1.31234			0.656169	−	0.754614i	$-0.272176\pi$
$461$	5.86679e14			1.31234			0.656169	+	0.754614i	$0.272176\pi$
$462$	−3.92604e12	−	6.77870e11i	−0.00867808	−	0.00149836i
$463$	8.53790e13			0.186490			0.0932450	−	0.995643i	$-0.470276\pi$
$463$	8.53790e13			0.186490			0.0932450	+	0.995643i	$0.470276\pi$
$464$	1.21014e14	+	8.79215e13i	0.261207	+	0.189778i
$465$	−4.50110e12	+	1.38530e13i	−0.00960124	+	0.0295496i
$466$	−1.08186e14	−	3.32961e14i	−0.228059	−	0.701893i
$467$	−2.50965e14	+	1.82336e14i	−0.522841	+	0.379866i	−0.817673	−	0.575683i	$-0.804736\pi$
$467$	−2.50965e14	+	1.82336e14i	−0.522841	+	0.379866i	0.294832	+	0.955549i	$0.404736\pi$
$468$	−2.13513e13	+	1.55126e13i	−0.0439614	+	0.0319399i
$469$	1.45022e14	+	4.46331e14i	0.295109	+	0.908253i
$470$	−2.89321e14	+	8.90440e14i	−0.581892	+	1.79088i
$471$	2.85978e12	+	2.07775e12i	0.00568483	+	0.00413027i
$472$	1.23632e13			0.0242912
$473$	−4.37989e14	+	2.15554e14i	−0.850603	+	0.418620i
$474$	5.43761e12			0.0104382
$475$	−1.33225e15	−	9.67939e14i	−2.52797	−	1.83668i
$476$	6.66809e13	−	2.05223e14i	0.125073	−	0.384935i
$477$	2.17182e14	+	6.68419e14i	0.402692	+	1.23936i
$478$	−6.21961e14	+	4.51881e14i	−1.14001	+	0.828268i
$479$	−5.60921e14	+	4.07533e14i	−1.01638	+	0.738444i	−0.965538	−	0.260263i	$-0.916191\pi$
$479$	−5.60921e14	+	4.07533e14i	−1.01638	+	0.738444i	−0.0508426	+	0.998707i	$0.516191\pi$
$480$	1.03855e12	+	3.19632e12i	0.00186037	+	0.00572564i
$481$	−2.66653e12	+	8.20675e12i	−0.00472225	+	0.0145336i
$482$	3.64258e14	+	2.64649e14i	0.637749	+	0.463352i
$483$	7.92902e12			0.0137249
$484$	2.75244e14	+	9.79679e13i	0.471051	+	0.167662i
$485$	9.08770e14			1.53771
$486$	−1.97166e13	−	1.43249e13i	−0.0329861	−	0.0239658i
$487$	−5.13618e13	+	1.58075e14i	−0.0849632	+	0.261490i	−0.984508	−	0.175338i	$-0.943898\pi$
$487$	−5.13618e13	+	1.58075e14i	−0.0849632	+	0.261490i	0.899545	+	0.436828i	$0.143898\pi$
$488$	−6.88372e13	−	2.11859e14i	−0.112594	−	0.346528i
$489$	−3.79523e12	+	2.75740e12i	−0.00613818	+	0.00445965i
$490$	3.67771e14	−	2.67201e14i	0.588165	−	0.427327i
$491$	−1.90837e14	−	5.87335e14i	−0.301796	−	0.928834i	−0.980853	−	0.194748i	$-0.937611\pi$
$491$	−1.90837e14	−	5.87335e14i	−0.301796	−	0.928834i	0.679057	−	0.734086i	$-0.262389\pi$
$492$	2.14259e12	−	6.59421e12i	0.00335066	−	0.0103123i
$493$	−8.44459e14	−	6.13535e14i	−1.30593	−	0.948815i
$494$	−7.35250e13			−0.112444
$495$	1.05022e15	−	5.16862e14i	1.58838	−	0.781711i
$496$	−1.52490e14			−0.228083
$497$	−3.53792e14	−	2.57045e14i	−0.523345	−	0.380232i
$498$	2.04620e12	−	6.29756e12i	0.00299355	−	0.00921321i
$499$	2.09291e14	+	6.44131e14i	0.302829	+	0.932011i	0.980479	+	0.196626i	$0.0629986\pi$
$499$	2.09291e14	+	6.44131e14i	0.302829	+	0.932011i	−0.677650	+	0.735385i	$0.737001\pi$
$500$	−5.68822e14	+	4.13274e14i	−0.814032	+	0.591429i
$501$	−9.48903e11	+	6.89419e11i	−0.00134312	+	0.000975833i
$502$	−2.11125e13	−	6.49776e13i	−0.0295576	−	0.0909689i
$503$	2.92506e14	−	9.00241e14i	0.405052	−	1.24662i	−0.515800	−	0.856709i	$-0.672505\pi$
$503$	2.92506e14	−	9.00241e14i	0.405052	−	1.24662i	0.920852	−	0.389913i	$-0.127495\pi$
$504$	−1.35193e14	−	9.82238e13i	−0.185177	−	0.134539i
$505$	1.56078e15			2.11465
$506$	−5.72964e14	−	9.89280e13i	−0.767890	−	0.132584i
$507$	−1.43338e13			−0.0190028
$508$	4.51867e13	+	3.28300e13i	0.0592598	+	0.0430547i
$509$	1.07758e13	−	3.31646e13i	0.0139799	−	0.0430256i	−0.943823	−	0.330451i	$-0.892799\pi$
$509$	1.07758e13	−	3.31646e13i	0.0139799	−	0.0430256i	0.957803	+	0.287425i	$0.0927992\pi$
$510$	−7.24721e12	−	2.23046e13i	−0.00930111	−	0.0286259i
$511$	−4.69397e14	+	3.41037e14i	−0.595971	+	0.432998i
$512$	−2.84648e13	+	2.06809e13i	−0.0357538	+	0.0259767i
$513$	−1.39864e13	−	4.30457e13i	−0.0173804	−	0.0534915i
$514$	1.65434e14	−	5.09155e14i	0.203390	−	0.625969i
$515$	9.02570e14	+	6.55755e14i	1.09784	+	0.797631i
$516$	7.57442e12			0.00911540
$517$	−1.80208e14	−	1.24996e15i	−0.214574	−	1.48832i
$518$	−5.46382e13			−0.0643699
$519$	6.12960e12	+	4.45341e12i	0.00714515	+	0.00519126i
$520$	−1.82378e13	+	5.61300e13i	−0.0210355	+	0.0647406i
$521$	−1.34296e14	−	4.13319e14i	−0.153269	−	0.471713i	0.844712	−	0.535220i	$-0.179771\pi$
$521$	−1.34296e14	−	4.13319e14i	−0.153269	−	0.471713i	−0.997981	+	0.0635071i	$0.979771\pi$
$522$	−6.53969e14	+	4.75137e14i	−0.738533	+	0.536575i
$523$	−7.74149e14	+	5.62452e14i	−0.865097	+	0.628530i	−0.929267	−	0.369409i	$-0.879560\pi$
$523$	−7.74149e14	+	5.62452e14i	−0.865097	+	0.628530i	0.0641695	+	0.997939i	$0.479560\pi$
$524$	−1.20893e14	−	3.72070e14i	−0.133684	−	0.411436i
$525$	−7.51353e12	+	2.31243e13i	−0.00822181	+	0.0253041i
$526$	5.22631e14	+	3.79714e14i	0.565945	+	0.411183i
$527$	1.06411e15			1.14032
$528$	−3.16063e12	−	3.24971e12i	−0.00335187	−	0.00344634i
$529$	2.04347e14			0.214468
$530$	1.27152e15	+	9.23812e14i	1.32070	+	0.959547i
$531$	−2.06460e13	+	6.35418e13i	−0.0212234	+	0.0653190i
$532$	−1.43863e14	−	4.42764e14i	−0.146364	−	0.450463i
$533$	9.85051e13	−	7.15681e13i	0.0991880	−	0.0720643i
$534$	−6.33603e12	+	4.60339e12i	−0.00631451	+	0.00458776i
$535$	−3.54394e14	−	1.09071e15i	−0.349575	−	1.07588i
$536$	−1.65009e14	+	5.07846e14i	−0.161102	+	0.495822i
$537$	7.74170e12	+	5.62467e12i	0.00748131	+	0.00543549i
$538$	−1.29361e15			−1.23738
$539$	−2.85940e14	+	5.42422e14i	−0.270730	+	0.513569i
$540$	−3.63310e13			−0.0340496
$541$	−2.33358e14	−	1.69544e14i	−0.216490	−	0.157289i	0.474255	−	0.880387i	$-0.342717\pi$
$541$	−2.33358e14	−	1.69544e14i	−0.216490	−	0.157289i	−0.690745	+	0.723098i	$0.742717\pi$
$542$	4.09043e14	−	1.25890e15i	0.375641	−	1.15610i
$543$	−4.54161e12	−	1.39776e13i	−0.00412867	−	0.0127068i
$544$	1.98633e14	−	1.44315e14i	0.178755	−	0.129873i
$545$	−9.29653e14	+	6.75433e14i	−0.828210	+	0.601730i
$546$	3.35467e11	+	1.03246e12i	0.000295862	+	0.000910571i
$547$	5.11168e14	−	1.57321e15i	0.446307	−	1.37359i	−0.434738	−	0.900557i	$-0.643159\pi$
$547$	5.11168e14	−	1.57321e15i	0.446307	−	1.37359i	0.881045	−	0.473033i	$-0.156841\pi$
$548$	5.24713e14	+	3.81226e14i	0.453553	+	0.329526i
$549$	1.20383e15			1.03019
$550$	8.31453e14	−	1.57725e15i	0.704438	−	1.33631i
$551$	−2.25200e15			−1.88901
$552$	7.29882e12	+	5.30290e12i	0.00606160	+	0.00440401i
$553$	−1.86839e14	+	5.75031e14i	−0.153631	+	0.472827i
$554$	1.05545e14	+	3.24834e14i	0.0859279	+	0.264459i
$555$	−4.80422e12	+	3.49047e12i	−0.00387268	+	0.00281367i
$556$	5.23511e14	−	3.80353e14i	0.417844	−	0.303582i
$557$	−1.06071e14	−	3.26453e14i	−0.0838289	−	0.257999i	0.900353	−	0.435161i	$-0.143308\pi$
$557$	−1.06071e14	−	3.26453e14i	−0.0838289	−	0.257999i	−0.984182	+	0.177162i	$0.943308\pi$
$558$	2.54652e14	−	7.83739e14i	0.199278	−	0.613315i
$559$	1.07610e14	+	7.81831e13i	0.0833848	+	0.0605826i
$560$	−3.73698e14			−0.286739
$561$	2.20556e13	+	2.26772e13i	0.0167580	+	0.0172303i
$562$	1.40119e15			1.05426
$563$	−1.14528e15	−	8.32092e14i	−0.853324	−	0.619976i	0.0727363	−	0.997351i	$-0.476827\pi$
$563$	−1.14528e15	−	8.32092e14i	−0.853324	−	0.619976i	−0.926061	+	0.377375i	$0.876827\pi$
$564$	−6.05527e12	+	1.86362e13i	−0.00446785	+	0.0137506i
$565$	1.05818e15	+	3.25675e15i	0.773203	+	2.37968i
$566$	−5.30140e14	+	3.85169e14i	−0.383619	+	0.278715i
$567$	7.30328e14	−	5.30615e14i	0.523373	−	0.380253i
$568$	−1.53762e14	−	4.73229e14i	−0.109127	−	0.335858i
$569$	−2.99445e14	+	9.21597e14i	−0.210475	+	0.647774i	0.788970	+	0.614432i	$0.210615\pi$
$569$	−2.99445e14	+	9.21597e14i	−0.210475	+	0.647774i	−0.999444	+	0.0333416i	$0.989385\pi$
$570$	−4.09349e13	−	2.97409e13i	−0.0284959	−	0.0207035i
$571$	−1.39785e15			−0.963745			−0.481873	−	0.876241i	$-0.660043\pi$
$571$	−1.39785e15			−0.963745			−0.481873	+	0.876241i	$0.660043\pi$
$572$	−1.13597e13	−	7.87927e13i	−0.00775688	−	0.0538032i
$573$	−3.28775e13			−0.0222355
$574$	6.23721e14	+	4.53160e14i	0.417806	+	0.303554i
$575$	−1.09652e15	+	3.37474e15i	−0.727517	+	2.23907i
$576$	−5.87564e13	−	1.80834e14i	−0.0386128	−	0.118838i
$577$	1.22606e13	−	8.90781e12i	0.00798074	−	0.00579835i	−0.583788	−	0.811906i	$-0.698430\pi$
$577$	1.22606e13	−	8.90781e12i	0.00798074	−	0.00579835i	0.591768	+	0.806108i	$0.298430\pi$
$578$	−4.98856e14	+	3.62440e14i	−0.321641	+	0.233686i
$579$	−1.20860e13	−	3.71968e13i	−0.00771879	−	0.0237560i
$580$	−5.58605e14	+	1.71921e15i	−0.353387	+	1.08761i
$581$	5.95662e14	+	4.32774e14i	0.373277	+	0.271202i
$582$	1.90198e13			0.0118067
$583$	−2.08906e15	−	3.60697e14i	−1.28461	−	0.221802i
$584$	−6.60172e14			−0.402149
$585$	−2.58030e14	−	1.87470e14i	−0.155709	−	0.113129i
$586$	2.48352e14	−	7.64349e14i	0.148467	−	0.456935i
$587$	2.12153e14	+	6.52940e14i	0.125643	+	0.386691i	0.994018	−	0.109219i	$-0.0348348\pi$
$587$	2.12153e14	+	6.52940e14i	0.125643	+	0.386691i	−0.868374	+	0.495909i	$0.834835\pi$
$588$	7.69716e12	−	5.59231e12i	0.00451601	−	0.00328108i
$589$	1.85734e15	−	1.34944e15i	1.07959	−	0.784365i
$590$	4.61698e13	+	1.42096e14i	0.0265871	+	0.0818268i
$591$	−5.91250e12	+	1.81968e13i	−0.00337319	+	0.0103816i
$592$	−5.02955e13	−	3.65418e13i	−0.0284289	−	0.0206548i
$593$	6.03897e13			0.0338191			0.0169096	−	0.999857i	$-0.494617\pi$
$593$	6.03897e13			0.0338191			0.0169096	+	0.999857i	$0.494617\pi$
$594$	4.39688e13	−	2.16391e13i	0.0243960	−	0.0120064i
$595$	2.60774e15			1.43358
$596$	−8.01183e14	−	5.82094e14i	−0.436393	−	0.317058i
$597$	7.78210e12	−	2.39509e13i	0.00419989	−	0.0129259i
$598$	4.89578e13	+	1.50677e14i	0.0261797	+	0.0805730i
$599$	9.61702e13	−	6.98718e13i	0.0509557	−	0.0370215i	−0.562016	−	0.827126i	$-0.689974\pi$
$599$	9.61702e13	−	6.98718e13i	0.0509557	−	0.0370215i	0.612972	+	0.790105i	$0.289974\pi$
$600$	−2.23817e13	+	1.62613e13i	−0.0117507	+	0.00853735i
$601$	−2.01074e14	−	6.18841e14i	−0.104603	−	0.321936i	0.885034	−	0.465527i	$-0.154135\pi$
$601$	−2.01074e14	−	6.18841e14i	−0.104603	−	0.321936i	−0.989637	+	0.143591i	$0.954135\pi$
$602$	−2.60260e14	+	8.00999e14i	−0.134161	+	0.412906i
$603$	−2.33457e15	−	1.69616e15i	−1.19251	−	0.866409i
$604$	3.30985e13			0.0167535
$605$	−9.81052e13	+	3.52937e15i	−0.0492082	+	1.77028i
$606$	3.26658e13			0.0162366
$607$	2.32491e15	+	1.68915e15i	1.14517	+	0.832012i	0.987831	−	0.155533i	$-0.0497096\pi$
$607$	2.32491e15	+	1.68915e15i	1.14517	+	0.832012i	0.157336	+	0.987545i	$0.449710\pi$
$608$	1.63691e14	−	5.03788e14i	0.0799013	−	0.245911i
$609$	1.02750e13	+	3.16233e13i	0.00497036	+	0.0152972i
$610$	2.17793e15	−	1.58236e15i	1.04407	−	0.758562i
$611$	−2.78390e14	+	2.02262e14i	−0.132260	+	0.0960922i
$612$	4.10015e14	+	1.26190e15i	0.193049	+	0.594143i
$613$	−4.06007e14	+	1.24956e15i	−0.189453	+	0.583076i	−0.999997	−	0.00260220i	$-0.999172\pi$
$613$	−4.06007e14	+	1.24956e15i	−0.189453	+	0.583076i	0.810544	+	0.585678i	$0.199172\pi$
$614$	1.13639e15	+	8.25636e14i	0.525535	+	0.381824i
$615$	8.37919e13			0.0384051
$616$	4.52260e14	−	2.22577e14i	0.205444	−	0.101108i
$617$	−1.57236e14			−0.0707917			−0.0353959	−	0.999373i	$-0.511269\pi$
$617$	−1.57236e14			−0.0707917			−0.0353959	+	0.999373i	$0.511269\pi$
$618$	1.88901e13	+	1.37244e13i	0.00842941	+	0.00612432i
$619$	2.64085e14	−	8.12770e14i	0.116801	−	0.359475i	−0.875518	−	0.483186i	$-0.839479\pi$
$619$	2.64085e14	−	8.12770e14i	0.116801	−	0.359475i	0.992318	+	0.123711i	$0.0394795\pi$
$620$	−5.69469e14	−	1.75264e15i	−0.249641	−	0.768316i
$621$	−7.89016e13	+	5.73254e13i	−0.0342833	+	0.0249082i
$622$	−6.40709e14	+	4.65502e14i	−0.275939	+	0.200482i
$623$	−2.69103e14	−	8.28213e14i	−0.114877	−	0.353556i
$624$	−3.81702e11	+	1.17476e12i	−0.000161514	+	0.000497088i
$625$	−2.75356e15	−	2.00058e15i	−1.15493	−	0.839102i
$626$	−1.32847e15			−0.552324
$627$	6.72544e13	+	1.16122e13i	0.0277172	+	0.00478566i
$628$	−4.47225e14			−0.182704
$629$	3.50973e14	+	2.54997e14i	0.142133	+	0.103266i
$630$	6.24060e14	−	1.92066e15i	0.250526	−	0.771040i
$631$	−9.03459e14	−	2.78056e15i	−0.359540	−	1.10655i	−0.953330	−	0.301930i	$-0.902369\pi$
$631$	−9.03459e14	−	2.78056e15i	−0.359540	−	1.10655i	0.593790	−	0.804620i	$-0.297631\pi$
$632$	−5.56567e14	+	4.04369e14i	−0.219570	+	0.159527i
$633$	2.23060e13	−	1.62062e13i	0.00872371	−	0.00633814i
$634$	1.02032e15	+	3.14021e15i	0.395589	+	1.21750i
$635$	−2.08584e14	+	6.41955e14i	−0.0801725	+	0.246746i
$636$	2.66119e13	+	1.93347e13i	0.0101405	+	0.00736754i
$637$	1.67077e14			0.0631177
$638$	−3.47935e14	−	2.41334e15i	−0.130312	−	0.903869i
$639$	2.68899e15			0.998467
$640$	−3.43996e14	−	2.49928e14i	−0.126638	−	0.0920077i
$641$	1.52670e15	−	4.69869e15i	0.557229	−	1.71497i	−0.132754	−	0.991149i	$-0.542382\pi$
$641$	1.52670e15	−	4.69869e15i	0.557229	−	1.71497i	0.689983	−	0.723825i	$-0.257618\pi$
$642$	−7.41718e12	−	2.28277e13i	−0.00268409	−	0.00826077i
$643$	1.11721e15	−	8.11702e14i	0.400844	−	0.291230i	−0.369041	−	0.929413i	$-0.620314\pi$
$643$	1.11721e15	−	8.11702e14i	0.400844	−	0.291230i	0.769885	+	0.638183i	$0.220314\pi$
$644$	−8.11575e14	+	5.89644e14i	−0.288706	+	0.209758i
$645$	2.82864e13	+	8.70565e13i	0.00997697	+	0.0307060i
$646$	−1.14227e15	+	3.51554e15i	−0.399475	+	1.22946i
$647$	−3.16324e15	−	2.29823e15i	−1.09688	−	0.796930i	−0.116332	−	0.993210i	$-0.537114\pi$
$647$	−3.16324e15	−	2.29823e15i	−1.09688	−	0.796930i	−0.980548	+	0.196281i	$0.937114\pi$
$648$	1.02715e15			0.353161
$649$	−1.40509e14	−	1.44469e14i	−0.0479027	−	0.0492527i
$650$	−4.85826e14			−0.164232
$651$	−2.74235e13	−	1.99244e13i	−0.00919238	−	0.00667865i
$652$	1.83406e14	−	5.64467e14i	0.0609611	−	0.187619i
$653$	−8.02259e14	−	2.46910e15i	−0.264419	−	0.813797i	−0.991827	−	0.127592i	$-0.959275\pi$
$653$	−8.02259e14	−	2.46910e15i	−0.264419	−	0.813797i	0.727408	−	0.686205i	$-0.240725\pi$
$654$	−1.94569e13	+	1.41363e13i	−0.00635911	+	0.00462016i
$655$	3.82491e15	−	2.77896e15i	1.23964	−	0.900649i
$656$	2.71075e14	+	8.34284e14i	0.0871202	+	0.268128i
$657$	1.10246e15	−	3.39302e15i	0.351361	−	1.08138i
$658$	−1.76273e15	−	1.28070e15i	−0.557112	−	0.404766i
$659$	6.10639e15			1.91388			0.956939	−	0.290288i	$-0.0937509\pi$
$659$	6.10639e15			1.91388			0.956939	+	0.290288i	$0.0937509\pi$
$660$	2.55473e13	−	4.84627e13i	0.00794059	−	0.0150631i
$661$	−3.70308e15			−1.14145			−0.570723	−	0.821143i	$-0.693337\pi$
$661$	−3.70308e15			−1.14145			−0.570723	+	0.821143i	$0.693337\pi$
$662$	−2.58063e15	−	1.87494e15i	−0.788873	−	0.573150i
$663$	2.66360e12	−	8.19771e12i	0.000807503	−	0.00248524i
$664$	2.58881e14	+	7.96753e14i	0.0778351	+	0.239552i
$665$	4.55166e15	−	3.30697e15i	1.35722	−	0.986079i
$666$	2.71802e14	−	1.97475e14i	0.0803792	−	0.0583989i
$667$	1.49953e15	+	4.61508e15i	0.439808	+	1.35359i
$668$	4.58562e13	−	1.41131e14i	0.0133391	−	0.0410536i
$669$	−3.50311e12	−	2.54516e12i	−0.00101067	−	0.000734296i
$670$	−6.45315e15			−1.84655
$671$	−1.69333e15	+	3.21221e15i	−0.480582	+	0.911654i
$672$	−7.82120e12			−0.00220162
$673$	−1.12525e15	−	8.17545e14i	−0.314172	−	0.228259i	0.419512	−	0.907750i	$-0.362201\pi$
$673$	−1.12525e15	−	8.17545e14i	−0.314172	−	0.228259i	−0.733685	+	0.679490i	$0.762201\pi$
$674$	−2.10125e14	+	6.46700e14i	−0.0581901	+	0.179091i
$675$	−9.24171e13	−	2.84431e14i	−0.0253853	−	0.0781278i
$676$	1.46714e15	−	1.06594e15i	0.399727	−	0.290419i
$677$	−2.59226e15	+	1.88339e15i	−0.700553	+	0.508981i	−0.880112	−	0.474766i	$-0.842533\pi$
$677$	−2.59226e15	+	1.88339e15i	−0.700553	+	0.508981i	0.179560	+	0.983747i	$0.442533\pi$
$678$	2.21469e13	+	6.81612e13i	0.00593677	+	0.0182715i
$679$	−6.53530e14	+	2.01136e15i	−0.173773	+	0.534818i
$680$	2.40048e15	+	1.74405e15i	0.633138	+	0.460002i
$681$	−3.76273e13			−0.00984450
$682$	1.73308e15	+	1.78192e15i	0.449784	+	0.462460i
$683$	−5.05914e15			−1.30246			−0.651228	−	0.758883i	$-0.725746\pi$
$683$	−5.05914e15			−1.30246			−0.651228	+	0.758883i	$0.725746\pi$
$684$	2.31591e15	+	1.68261e15i	0.591444	+	0.429709i
$685$	−2.42210e15	+	7.45446e15i	−0.613612	+	1.88850i
$686$	8.90013e14	+	2.73918e15i	0.223673	+	0.688395i
$687$	5.65790e13	−	4.11070e13i	0.0141056	−	0.0102484i
$688$	−7.75279e14	+	5.63273e14i	−0.191744	+	0.139310i
$689$	1.78503e14	+	5.49375e14i	0.0437965	+	0.134792i
$690$	−3.36917e13	+	1.03692e14i	−0.00820074	+	0.0252393i
$691$	4.44136e15	+	3.22684e15i	1.07247	+	0.779198i	0.976355	−	0.216172i	$-0.0693571\pi$
$691$	4.44136e15	+	3.22684e15i	1.07247	+	0.779198i	0.0961190	+	0.995370i	$0.469357\pi$
$692$	−9.58574e14			−0.229637
$693$	3.88705e14	+	2.69613e15i	0.0923820	+	0.640778i
$694$	−2.40091e15			−0.566107
$695$	6.32661e15	+	4.59655e15i	1.47998	+	1.07527i
$696$	−1.16912e13	+	3.59817e13i	−0.00271336	+	0.00835085i
$697$	−1.89162e15	−	5.82181e15i	−0.435566	−	1.34053i
$698$	−7.92733e14	+	5.75954e14i	−0.181101	+	0.131578i
$699$	7.16380e13	−	5.20481e13i	0.0162375	−	0.0117972i
$700$	−9.50594e14	−	2.92563e15i	−0.213774	−	0.657930i
$701$	7.75996e14	−	2.38827e15i	0.173145	−	0.532886i	−0.826399	−	0.563085i	$-0.809614\pi$
$701$	7.75996e14	−	2.38827e15i	0.173145	−	0.532886i	0.999544	+	0.0301993i	$0.00961419\pi$
$702$	−1.08027e13	−	7.84864e12i	−0.00239155	−	0.00173756i
$703$	9.35972e14			0.205593
$704$	5.65172e14	+	9.75827e13i	0.123177	+	0.0212678i
$705$	−2.36808e14			−0.0512102
$706$	3.72024e15	+	2.70291e15i	0.798261	+	0.579970i
$707$	−1.12241e15	+	3.45443e15i	−0.238971	+	0.735478i
$708$	9.66297e11	+	2.97396e12i	0.000204140	+	0.000628278i
$709$	1.14586e15	−	8.32515e14i	0.240202	−	0.174517i	−0.461171	−	0.887311i	$-0.652571\pi$
$709$	1.14586e15	−	8.32515e14i	0.240202	−	0.174517i	0.701373	+	0.712794i	$0.252571\pi$
$710$	4.86484e15	−	3.53451e15i	1.01192	−	0.735206i
$711$	−1.14885e15	−	3.53581e15i	−0.237128	−	0.729804i
$712$	3.06191e14	−	9.42360e14i	0.0627123	−	0.193009i
$713$	−4.00217e15	−	2.90775e15i	−0.813398	−	0.590969i
$714$	5.45780e13			0.0110072
$715$	8.63181e14	−	4.24810e14i	0.172750	−	0.0850182i
$716$	−1.21068e15			−0.240441
$717$	−1.57312e14	−	1.14294e14i	−0.0310032	−	0.0225251i
$718$	−4.70593e14	+	1.44834e15i	−0.0920366	+	0.283260i
$719$	2.36439e15	+	7.27683e15i	0.458891	+	1.41232i	0.866506	+	0.499167i	$0.166361\pi$
$719$	2.36439e15	+	7.27683e15i	0.458891	+	1.41232i	−0.407615	+	0.913154i	$0.633639\pi$
$720$	1.85899e15	−	1.35063e15i	0.358053	−	0.260141i
$721$	−2.10044e15	+	1.52606e15i	−0.401482	+	0.291694i
$722$	1.31250e15	+	4.03947e15i	0.248969	+	0.766249i
$723$	−3.51910e13	+	1.08307e14i	−0.00662478	+	0.0203890i
$724$	1.50431e15	+	1.09294e15i	0.281044	+	0.204190i
$725$	−1.48804e16			−2.75902
$726$	−2.05327e12	+	7.38670e13i	−0.000377828	+	0.0135925i
$727$	−8.67301e15			−1.58391			−0.791955	−	0.610580i	$-0.790936\pi$
$727$	−8.67301e15			−1.58391			−0.791955	+	0.610580i	$0.790936\pi$
$728$	−1.11116e14	−	8.07304e13i	−0.0201397	−	0.0146324i
$729$	−1.71403e15	+	5.27525e15i	−0.308332	+	0.948947i
$730$	−2.46539e15	−	7.58769e15i	−0.440159	−	1.35467i
$731$	5.41007e15	−	3.93064e15i	0.958643	−	0.696495i
$732$	4.55824e13	−	3.31176e13i	0.00801653	−	0.00582435i
$733$	2.39693e15	+	7.37700e15i	0.418393	+	1.28768i	0.909181	+	0.416402i	$0.136709\pi$
$733$	2.39693e15	+	7.37700e15i	0.418393	+	1.28768i	−0.490788	+	0.871279i	$0.663291\pi$
$734$	1.55887e15	−	4.79771e15i	0.270073	−	0.831201i
$735$	9.30200e13	+	6.75830e13i	0.0159954	+	0.0116214i
$736$	−1.14142e15			−0.194813
$737$	7.80978e15	−	3.84355e15i	1.32302	−	0.651120i
$738$	−4.74057e15			−0.797115
$739$	2.04745e15	+	1.48756e15i	0.341718	+	0.248273i	0.745386	−	0.666633i	$-0.232265\pi$
$739$	2.04745e15	+	1.48756e15i	0.341718	+	0.248273i	−0.403668	+	0.914905i	$0.632265\pi$
$740$	2.32166e14	−	7.14535e14i	0.0384614	−	0.118372i
$741$	−5.74667e12	−	1.76864e13i	−0.000944965	−	0.00290830i
$742$	−2.95905e15	+	2.14987e15i	−0.482981	+	0.350906i
$743$	5.84086e13	−	4.24363e13i	0.00946320	−	0.00687542i	−0.583044	−	0.812441i	$-0.698138\pi$
$743$	5.84086e13	−	4.24363e13i	0.00946320	−	0.00687542i	0.592507	+	0.805565i	$0.298138\pi$
$744$	−1.19185e13	−	3.66815e13i	−0.00191678	−	0.00589923i
$745$	3.69830e15	−	1.13822e16i	0.590395	−	1.81705i
$746$	9.99778e14	+	7.26381e14i	0.158431	+	0.115107i
$747$	−4.52731e15			−0.712159
$748$	−3.94389e15	−	6.80953e14i	−0.615838	−	0.106331i
$749$	2.66890e15			0.413698
$750$	−1.43872e14	−	1.04529e14i	−0.0221380	−	0.0160842i
$751$	2.47772e15	−	7.62563e15i	0.378471	−	1.16481i	−0.562636	−	0.826704i	$-0.690213\pi$
$751$	2.47772e15	−	7.62563e15i	0.378471	−	1.16481i	0.941107	−	0.338109i	$-0.109787\pi$
$752$	−7.66099e14	−	2.35781e15i	−0.116168	−	0.357528i
$753$	1.39802e13	−	1.01572e13i	0.00210446	−	0.00152898i
$754$	−5.37499e14	+	3.90516e14i	−0.0803221	+	0.0583574i
$755$	1.23605e14	+	3.80417e14i	0.0183370	+	0.0564354i
$756$	2.61270e13	−	8.04106e13i	0.00384786	−	0.0118425i
$757$	7.33755e15	+	5.33104e15i	1.07281	+	0.779444i	0.976416	−	0.215899i	$-0.0692683\pi$
$757$	7.33755e15	+	5.33104e15i	1.07281	+	0.779444i	0.0963967	+	0.995343i	$0.469268\pi$
$758$	7.50863e15			1.08988
$759$	−2.09854e13	−	1.45558e14i	−0.00302403	−	0.0209753i
$760$	6.40158e15			0.915825
$761$	−5.40423e15	−	3.92641e15i	−0.767571	−	0.557673i	0.133652	−	0.991028i	$-0.457329\pi$
$761$	−5.40423e15	−	3.92641e15i	−0.767571	−	0.557673i	−0.901223	+	0.433355i	$0.857329\pi$
$762$	−4.36550e12	+	1.34356e13i	−0.000615576	+	0.00189455i
$763$	−8.26371e14	−	2.54331e15i	−0.115688	−	0.356053i
$764$	3.36517e15	−	2.44494e15i	0.467728	−	0.339825i
$765$	−1.29724e16	+	9.42501e15i	−1.79012	+	1.30060i
$766$	−2.87750e15	−	8.85604e15i	−0.394237	−	1.21334i
$767$	−1.69690e13	+	5.22251e13i	−0.00230824	+	0.00710403i
$768$	−7.19956e12	−	5.23079e12i	−0.000972343	−	0.000706448i
$769$	6.52555e15			0.875028			0.437514	−	0.899212i	$-0.355859\pi$
$769$	6.52555e15			0.875028			0.437514	+	0.899212i	$0.355859\pi$
$770$	4.24714e15	+	4.36684e15i	0.565454	+	0.581390i
$771$	1.35407e14			0.0178996
$772$	4.00320e15	+	2.90850e15i	0.525427	+	0.381745i
$773$	1.89913e14	−	5.84492e14i	0.0247496	−	0.0761713i	−0.937919	−	0.346855i	$-0.887250\pi$
$773$	1.89913e14	−	5.84492e14i	0.0247496	−	0.0761713i	0.962668	+	0.270683i	$0.0872497\pi$
$774$	−1.60032e15	−	4.92527e15i	−0.207076	−	0.637316i
$775$	1.22726e16	−	8.91658e15i	1.57681	−	1.14562i
$776$	−1.94677e15	+	1.41441e15i	−0.248357	+	0.180442i
$777$	−4.27049e12	−	1.31432e13i	−0.000540956	−	0.00166489i
$778$	7.62688e14	−	2.34731e15i	0.0959310	−	0.295245i
$779$	−1.06846e16	−	7.76279e15i	−1.33445	−	0.969531i
$780$	−1.49275e13			−0.00185126
$781$	−3.78238e15	+	7.17511e15i	−0.465784	+	0.883584i
$782$	7.96508e15			0.973987
$783$	−3.30877e14	−	2.40396e14i	−0.0401769	−	0.0291902i
$784$	−3.71969e14	+	1.14480e15i	−0.0448506	+	0.138036i
$785$	−1.67014e15	−	5.14018e15i	−0.199973	−	0.615453i
$786$	8.00525e13	−	5.81615e13i	0.00951811	−	0.00691531i
$787$	−2.13874e15	+	1.55388e15i	−0.252521	+	0.183467i	−0.706843	−	0.707370i	$-0.749881\pi$
$787$	−2.13874e15	+	1.55388e15i	−0.252521	+	0.183467i	0.454323	+	0.890837i	$0.349881\pi$
$788$	−7.48036e14	−	2.30222e15i	−0.0877059	−	0.269931i
$789$	−5.04916e13	+	1.55397e14i	−0.00587889	+	0.0180934i
$790$	−6.72609e15	−	4.88679e15i	−0.777703	−	0.565034i
$791$	−7.96906e15			−0.915033
$792$	−1.44535e15	+	2.74180e15i	−0.164810	+	0.312642i
$793$	9.89429e14			0.112042
$794$	7.97121e15	+	5.79143e15i	0.896420	+	0.651287i
$795$	−1.22842e14	+	3.78068e14i	−0.0137191	+	0.0422231i
$796$	9.84574e14	+	3.03021e15i	0.109201	+	0.336086i
$797$	−8.64412e15	+	6.28032e15i	−0.952139	+	0.691769i	−0.951312	−	0.308230i	$-0.900263\pi$
$797$	−8.64412e15	+	6.28032e15i	−0.952139	+	0.691769i	−0.000826898		1.00000i	$0.500263\pi$
$798$	9.52627e13	−	6.92124e13i	0.0104209	−	0.00757126i
$799$	5.34600e15	+	1.64533e16i	0.580794	+	1.78750i
$800$	1.08161e15	−	3.32885e15i	0.116701	−	0.359169i
$801$	4.33203e15	+	3.14740e15i	0.464208	+	0.337267i
$802$	−1.06700e16			−1.13555
$803$	7.50297e15	+	7.71443e15i	0.793045	+	0.815395i
$804$	−1.35059e14			−0.0141781
$805$	−9.80786e15	−	7.12583e15i	−1.02258	−	0.742948i
$806$	2.09299e14	−	6.44157e14i	0.0216733	−	0.0667035i
$807$	−1.01108e14	−	3.11178e14i	−0.0103987	−	0.0320040i
$808$	−3.34351e15	+	2.42920e15i	−0.341539	+	0.248143i
$809$	1.49431e16	−	1.08568e16i	1.51609	−	1.10150i	0.552706	−	0.833376i	$-0.313595\pi$
$809$	1.49431e16	−	1.08568e16i	1.51609	−	1.10150i	0.963383	−	0.268127i	$-0.0864048\pi$
$810$	3.83587e15	+	1.18056e16i	0.386541	+	1.18965i
$811$	−6.39748e14	+	1.96894e15i	−0.0640315	+	0.197069i	−0.977954	−	0.208820i	$-0.933038\pi$
$811$	−6.39748e14	+	1.96894e15i	−0.0640315	+	0.197069i	0.913923	+	0.405888i	$0.133038\pi$
$812$	−3.40337e15	−	2.47269e15i	−0.338338	−	0.245817i
$813$	3.34800e14			0.0330588
$814$	1.44608e14	+	1.00303e15i	0.0141827	+	0.0983738i
$815$	7.17262e15			0.698732
$816$	5.02401e13	+	3.65016e13i	0.00486132	+	0.00353196i
$817$	4.45835e15	−	1.37214e16i	0.428502	−	1.31879i
$818$	−2.00906e14	−	6.18325e14i	−0.0191801	−	0.0590301i
$819$	6.00481e14	−	4.36275e14i	0.0569427	−	0.0413713i
$820$	−8.57652e15	+	6.23120e15i	−0.807857	+	0.586943i
$821$	6.73466e14	+	2.07272e15i	0.0630128	+	0.193933i	0.977607	−	0.210440i	$-0.0674896\pi$
$821$	6.73466e14	+	2.07272e15i	0.0630128	+	0.193933i	−0.914594	+	0.404373i	$0.867490\pi$
$822$	−5.06926e13	+	1.56016e14i	−0.00471140	+	0.0145002i
$823$	9.93477e14	+	7.21803e14i	0.0917189	+	0.0666376i	0.632700	−	0.774397i	$-0.281947\pi$
$823$	9.93477e14	+	7.21803e14i	0.0917189	+	0.0666376i	−0.540981	+	0.841035i	$0.681947\pi$
$824$	−2.95411e15			−0.270912
$825$	4.44393e14	+	7.67290e13i	0.0404828	+	0.00698977i
$826$	−3.47700e14			−0.0314640
$827$	−2.41954e15	−	1.75790e15i	−0.217497	−	0.158021i	0.473702	−	0.880685i	$-0.342917\pi$
$827$	−2.41954e15	−	1.75790e15i	−0.217497	−	0.158021i	−0.691199	+	0.722664i	$0.742917\pi$
$828$	1.90613e15	−	5.86645e15i	0.170210	−	0.523852i
$829$	2.01610e15	+	6.20492e15i	0.178839	+	0.550410i	0.999788	−	0.0205919i	$-0.00655507\pi$
$829$	2.01610e15	+	6.20492e15i	0.178839	+	0.550410i	−0.820949	+	0.571001i	$0.806555\pi$
$830$	−8.19069e15	+	5.95089e15i	−0.721757	+	0.524387i
$831$	−6.98895e13	+	5.07777e13i	−0.00611795	+	0.00444495i
$832$	−4.82921e13	−	1.48628e14i	−0.00419950	−	0.0129247i
$833$	2.59568e15	−	7.98868e15i	0.224235	−	0.690124i
$834$	1.32411e14	+	9.62023e13i	0.0113635	+	0.00825605i
$835$	1.79333e15			0.152892
$836$	−7.74737e15	+	3.81283e15i	−0.656175	+	0.322933i
$837$	4.16940e14			0.0350820
$838$	−1.05483e16	−	7.66376e15i	−0.881736	−	0.640619i
$839$	2.97441e15	−	9.15430e15i	0.247008	−	0.760211i	−0.748292	−	0.663369i	$-0.769126\pi$
$839$	2.97441e15	−	9.15430e15i	0.247008	−	0.760211i	0.995300	−	0.0968420i	$-0.0308741\pi$
$840$	−2.92080e13	−	8.98929e13i	−0.00240971	−	0.00741634i
$841$	−6.59265e15	+	4.78984e15i	−0.540359	+	0.392594i
$842$	1.06061e16	−	7.70577e15i	0.863651	−	0.627479i
$843$	1.09516e14	+	3.37056e14i	0.00885986	+	0.0272679i
$844$	−1.07795e15	+	3.31758e15i	−0.0866391	+	0.266648i
$845$	1.77303e16	+	1.28818e16i	1.41581	+	1.02864i
$846$	1.33976e16			1.06289
$847$	−7.74093e15	−	2.75524e15i	−0.610147	−	0.217170i
$848$	−4.16168e15			−0.325906
$849$	−1.34088e14	−	9.74204e13i	−0.0104327	−	0.00757980i
$850$	−7.54770e15	+	2.32294e16i	−0.583459	+	1.79570i
$851$	−6.23232e14	−	1.91811e15i	−0.0478671	−	0.147320i
$852$	1.01817e14	−	7.39746e13i	0.00776969	−	0.00564501i
$853$	−6.22723e15	+	4.52434e15i	−0.472145	+	0.343033i	−0.798276	−	0.602291i	$-0.794255\pi$
$853$	−6.22723e15	+	4.52434e15i	−0.472145	+	0.343033i	0.326132	+	0.945324i	$0.394255\pi$
$854$	1.93597e15	+	5.95830e15i	0.145841	+	0.448853i
$855$	−1.06904e16	+	3.29016e16i	−0.800164	+	2.46265i
$856$	2.45678e15	+	1.78495e15i	0.182709	+	0.132746i
$857$	−2.25453e16			−1.66595			−0.832974	−	0.553312i	$-0.813364\pi$
$857$	−2.25453e16			−1.66595			−0.832974	+	0.553312i	$0.813364\pi$
$858$	1.80657e13	−	8.89095e12i	0.00132640	−	0.000652782i
$859$	3.05649e15			0.222977			0.111489	−	0.993766i	$-0.464438\pi$
$859$	3.05649e15			0.222977			0.111489	+	0.993766i	$0.464438\pi$
$860$	−9.36923e15	−	6.80714e15i	−0.679145	−	0.493428i
$861$	−6.02579e13	+	1.85455e14i	−0.00434007	+	0.0133573i
$862$	4.57339e15	+	1.40755e16i	0.327302	+	1.00733i
$863$	4.37664e15	−	3.17982e15i	0.311230	−	0.226122i	−0.421194	−	0.906971i	$-0.638389\pi$
$863$	4.37664e15	−	3.17982e15i	0.311230	−	0.226122i	0.732424	+	0.680849i	$0.238389\pi$
$864$	7.78287e13	−	5.65458e13i	0.00549938	−	0.00399554i
$865$	−3.57976e15	−	1.10174e16i	−0.251342	−	0.773551i
$866$	1.27637e15	−	3.92826e15i	0.0890487	−	0.274064i
$867$	−1.26175e14	−	9.16716e13i	−0.00874719	−	0.00635521i
$868$	4.28861e15			0.295433
$869$	1.10507e16	+	1.90802e15i	0.756453	+	0.130609i
$870$	−4.57215e14			−0.0311003
$871$	−1.91879e15	−	1.39408e15i	−0.129696	−	0.0942298i
$872$	9.40264e14	−	2.89384e15i	0.0631552	−	0.194372i
$873$	−4.01850e15	−	1.23677e16i	−0.268216	−	0.825485i
$874$	1.39026e16	−	1.01008e16i	0.922109	−	0.669952i
$875$	1.59975e16	−	1.16229e16i	1.05440	−	0.766070i
$876$	−5.15987e13	−	1.58804e14i	−0.00337960	−	0.0104014i
$877$	2.98034e15	−	9.17254e15i	0.193985	−	0.597024i	−0.806002	−	0.591913i	$-0.798373\pi$
$877$	2.98034e15	−	9.17254e15i	0.193985	−	0.597024i	0.999987	−	0.00511120i	$-0.00162695\pi$
$878$	−6.78384e15	−	4.92875e15i	−0.438789	−	0.318799i
$879$	2.03275e14			0.0130661
$880$	9.89048e14	+	6.86022e15i	0.0631775	+	0.438211i
$881$	9.46138e15			0.600602			0.300301	−	0.953844i	$-0.402913\pi$
$881$	9.46138e15			0.600602			0.300301	+	0.953844i	$0.402913\pi$
$882$	−5.26266e15	−	3.82354e15i	−0.331992	−	0.241206i
$883$	−1.68407e15	+	5.18303e15i	−0.105579	+	0.324938i	−0.989866	−	0.142006i	$-0.954645\pi$
$883$	−1.68407e15	+	5.18303e15i	−0.105579	+	0.324938i	0.884287	+	0.466944i	$0.154645\pi$
$884$	3.36992e14	+	1.03716e15i	0.0209958	+	0.0646184i
$885$	−3.05726e13	+	2.22123e13i	−0.00189297	+	0.00137532i
$886$	−8.37007e15	+	6.08121e15i	−0.515043	+	0.374201i
$887$	−5.02319e14	−	1.54598e15i	−0.0307185	−	0.0945418i	0.934522	−	0.355906i	$-0.115828\pi$
$887$	−5.02319e14	−	1.54598e15i	−0.0307185	−	0.0945418i	−0.965240	+	0.261364i	$0.915828\pi$
$888$	4.85906e12	−	1.49546e13i	0.000295312	−	0.000908877i
$889$	−1.27082e15	−	9.23308e14i	−0.0767584	−	0.0557682i
$890$	1.19745e16			0.718805
$891$	−1.16738e16	−	1.20028e16i	−0.696440	−	0.716068i
$892$	5.47832e14			0.0324818
$893$	3.01962e16	+	2.19388e16i	1.77938	+	1.29279i
$894$	7.74025e13	−	2.38221e14i	0.00453314	−	0.0139516i
$895$	−4.52124e15	−	1.39150e16i	−0.263167	−	0.809945i
$896$	8.00539e14	−	5.81626e14i	0.0463115	−	0.0336472i
$897$	−3.24187e13	+	2.35536e13i	−0.00186396	+	0.00135425i
$898$	−4.93638e15	−	1.51926e16i	−0.282090	−	0.868185i
$899$	6.41063e15	−	1.97299e16i	0.364102	−	1.12059i
$900$	1.53027e16	+	1.11181e16i	0.863843	+	0.627619i
$901$	2.90411e16			1.62940
$902$	6.66818e15	−	1.26494e16i	0.371853	−	0.705399i
$903$	−2.13022e14			−0.0118071
$904$	−7.33567e15	−	5.32968e15i	−0.404123	−	0.293612i
$905$	−6.94395e15	+	2.13713e16i	−0.380224	+	1.17021i
$906$	2.58696e12	+	7.96183e12i	0.000140794	+	0.000433319i
$907$	−2.35581e16	+	1.71160e16i	−1.27438	+	0.925894i	−0.999368	−	0.0355462i	$-0.988683\pi$
$907$	−2.35581e16	+	1.71160e16i	−1.27438	+	0.925894i	−0.275015	+	0.961440i	$0.588683\pi$
$908$	3.85134e15	−	2.79816e15i	0.207081	−	0.150453i
$909$	−6.90162e15	−	2.12410e16i	−0.368850	−	1.13520i
$910$	5.12916e14	−	1.57859e15i	0.0272470	−	0.0838577i
$911$	−2.16535e16	−	1.57322e16i	−1.14335	−	0.830690i	−0.155764	−	0.987794i	$-0.549784\pi$
$911$	−2.16535e16	−	1.57322e16i	−1.14335	−	0.830690i	−0.987582	+	0.157104i	$0.949784\pi$
$912$	1.33980e14			0.00703183
$913$	6.36821e15	−	1.20804e16i	0.332222	−	0.630218i
$914$	−2.05251e16			−1.06434
$915$	5.50862e14	+	4.00225e14i	0.0283940	+	0.0206295i
$916$	−2.73420e15	+	8.41502e15i	−0.140090	+	0.431152i
$917$	3.39998e15	+	1.04640e16i	0.173159	+	0.532928i
$918$	−5.43105e14	+	3.94589e14i	−0.0274947	+	0.0199761i
$919$	−1.20578e16	+	8.76048e15i	−0.606780	+	0.440852i	−0.848279	−	0.529549i	$-0.822361\pi$
$919$	−1.20578e16	+	8.76048e15i	−0.606780	+	0.440852i	0.241499	+	0.970401i	$0.422361\pi$
$920$	−4.26260e15	−	1.31189e16i	−0.213226	−	0.656244i
$921$	−1.09787e14	+	3.37890e14i	−0.00545913	+	0.0168015i
$922$	−1.51883e16	−	1.10349e16i	−0.750738	−	0.545443i
$923$	2.21008e15			0.108592
$924$	8.88893e13	+	9.13944e13i	0.00434164	+	0.00446400i
$925$	6.18456e15			0.300282
$926$	−2.21034e15	−	1.60590e15i	−0.106684	−	0.0775102i
$927$	4.93325e15	−	1.51830e16i	0.236698	−	0.728481i
$928$	−1.47914e15	−	4.55232e15i	−0.0705497	−	0.217130i
$929$	−2.58928e16	+	1.88122e16i	−1.22770	+	0.891978i	−0.996716	−	0.0809794i	$-0.974195\pi$
$929$	−2.58928e16	+	1.88122e16i	−1.22770	+	0.891978i	−0.230986	+	0.972957i	$0.574195\pi$
$930$	3.77089e14	−	2.73971e14i	0.0177741	−	0.0129136i
$931$	−5.60013e15	−	1.72354e16i	−0.262407	−	0.807605i
$932$	−3.46194e15	+	1.06548e16i	−0.161262	+	0.496314i
$933$	−1.62054e14	−	1.17739e14i	−0.00750430	−	0.00545219i
$934$	9.92670e15			0.456980
$935$	−6.90179e15	−	4.78721e16i	−0.315862	−	2.19088i
$936$	8.44533e14			0.0384237
$937$	2.98687e16	+	2.17009e16i	1.35098	+	0.981545i	0.998962	+	0.0455514i	$0.0145045\pi$
$937$	2.98687e16	+	2.17009e16i	1.35098	+	0.981545i	0.352018	+	0.935993i	$0.385496\pi$
$938$	4.64070e15	−	1.42826e16i	0.208674	−	0.642232i
$939$	−1.03833e14	−	3.19564e14i	−0.00464166	−	0.0142856i
$940$	2.42385e16	−	1.76103e16i	1.07722	−	0.782643i
$941$	−2.48070e15	+	1.80234e15i	−0.109605	+	0.0796330i	−0.641238	−	0.767342i	$-0.721579\pi$
$941$	−2.48070e15	+	1.80234e15i	−0.109605	+	0.0796330i	0.531632	+	0.846975i	$0.321579\pi$
$942$	−3.49548e13	−	1.07580e14i	−0.00153542	−	0.00472554i
$943$	−8.79399e15	+	2.70651e16i	−0.384036	+	1.18194i
$944$	−3.20064e14	−	2.32540e14i	−0.0138960	−	0.0100961i
$945$	1.02177e15			0.0441040
$946$	1.53933e16	+	2.65781e15i	0.660587	+	0.114057i
$947$	−3.63422e16			−1.55055			−0.775277	−	0.631622i	$-0.782390\pi$
$947$	−3.63422e16			−1.55055			−0.775277	+	0.631622i	$0.782390\pi$
$948$	−1.40772e14	−	1.02277e14i	−0.00597131	−	0.00433841i
$949$	9.06115e14	−	2.78873e15i	0.0382137	−	0.117610i
$950$	1.62840e16	+	5.01171e16i	0.682782	+	2.10139i
$951$	−6.75630e14	+	4.90874e14i	−0.0281654	+	0.0204634i
$952$	−5.58633e15	+	4.05871e15i	−0.231539	+	0.168223i
$953$	9.08976e14	+	2.79754e15i	0.0374577	+	0.115283i	0.968037	−	0.250807i	$-0.0806961\pi$
$953$	9.08976e14	+	2.79754e15i	0.0374577	+	0.115283i	−0.930579	+	0.366090i	$0.880696\pi$
$954$	6.94984e15	−	2.13894e16i	0.284747	−	0.876360i
$955$	4.06680e16	+	2.95470e16i	1.65666	+	1.20364i
$956$	2.46012e16			0.996408
$957$	5.53335e14	−	2.72321e14i	0.0222829	−	0.0109664i
$958$	2.21868e16			0.888349
$959$	−1.47569e16	−	1.07216e16i	−0.587482	−	0.426830i
$960$	3.32335e13	−	1.02282e14i	0.00131548	−	0.00404864i
$961$	−1.31634e15	−	4.05128e15i	−0.0518071	−	0.159446i
$962$	2.23394e14	−	1.62306e14i	0.00874197	−	0.00635141i
$963$	−1.32767e16	+	9.64606e15i	−0.516588	+	0.375323i
$964$	−4.45229e15	−	1.37027e16i	−0.172250	−	0.530132i
$965$	−1.84790e16	+	5.68725e16i	−0.710850	+	2.18777i
$966$	−2.05271e14	−	1.49138e14i	−0.00785151	−	0.00570446i
$967$	6.75106e15			0.256759			0.128380	−	0.991725i	$-0.459022\pi$
$967$	6.75106e15			0.256759			0.128380	+	0.991725i	$0.459022\pi$
$968$	−5.28298e15	−	7.71335e15i	−0.199786	−	0.291695i
$969$	−9.34941e14			−0.0351563
$970$	−2.35267e16	−	1.70932e16i	−0.879664	−	0.639113i
$971$	−3.20110e15	+	9.85197e15i	−0.119013	+	0.366283i	−0.992763	−	0.120092i	$-0.961681\pi$
$971$	−3.20110e15	+	9.85197e15i	−0.119013	+	0.366283i	0.873750	+	0.486375i	$0.161681\pi$
$972$	2.40994e14	+	7.41702e14i	0.00890925	+	0.0274199i
$973$	−1.47231e16	+	1.06970e16i	−0.541228	+	0.393225i
$974$	4.30294e15	−	3.12627e15i	0.157286	−	0.114275i
$975$	−3.79719e13	−	1.16865e14i	−0.00138018	−	0.00424777i
$976$	−2.20279e15	+	6.77949e15i	−0.0796158	+	0.245032i
$977$	5.08094e15	+	3.69152e15i	0.182610	+	0.132674i	0.675335	−	0.737511i	$-0.263999\pi$
$977$	5.08094e15	+	3.69152e15i	0.182610	+	0.132674i	−0.492725	+	0.870185i	$0.663999\pi$
$978$	1.50117e14			0.00536496
$979$	−1.44918e16	+	7.13209e15i	−0.515014	+	0.253461i
$980$	−1.45469e16			−0.514075
$981$	1.33030e16	+	9.66517e15i	0.467486	+	0.339649i
$982$	−6.10678e15	+	1.87947e16i	−0.213402	+	0.656785i
$983$	1.68758e16	+	5.19383e16i	0.586435	+	1.80486i	0.593431	+	0.804885i	$0.297773\pi$
$983$	1.68758e16	+	5.19383e16i	0.586435	+	1.80486i	−0.00699672	+	0.999976i	$0.502227\pi$
$984$	−1.79500e14	+	1.30414e14i	−0.00620284	+	0.00450663i
$985$	2.36670e16	−	1.71951e16i	0.813288	−	0.590889i
$986$	1.03217e16	+	3.17671e16i	0.352720	+	1.08556i
$987$	1.70298e14	−	5.24122e14i	0.00578714	−	0.0178110i
$988$	1.90345e15	+	1.38294e15i	0.0643249	+	0.0467348i
$989$	−3.10883e16			−1.04476
$990$	−3.69105e16	−	6.37297e15i	−1.23355	−	0.212985i
$991$	−2.57955e15			−0.0857310			−0.0428655	−	0.999081i	$-0.513649\pi$
$991$	−2.57955e15			−0.0857310			−0.0428655	+	0.999081i	$0.513649\pi$
$992$	3.94775e15	+	2.86821e15i	0.130477	+	0.0947974i
$993$	2.49316e14	−	7.67314e14i	0.00819461	−	0.0252204i
$994$	4.32437e15	+	1.33090e16i	0.141351	+	0.435032i
$995$	−3.11508e16	+	2.26324e16i	−1.01261	+	0.735705i
$996$	−1.71425e14	+	1.24547e14i	−0.00554175	+	0.00402632i
$997$	1.17338e15	+	3.61129e15i	0.0377238	+	0.116102i	0.968145	−	0.250390i	$-0.0805588\pi$
$997$	1.17338e15	+	3.61129e15i	0.0377238	+	0.116102i	−0.930421	+	0.366492i	$0.880559\pi$
$998$	6.69731e15	−	2.06122e16i	0.214132	−	0.659031i
$999$	1.37518e14	+	9.99130e13i	0.00437271	+	0.00317696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.15.3	yes	20
11.3	even	5	inner	22.12.c.a.3.3	✓	20
11.5	even	5		242.12.a.n.1.6		10
11.6	odd	10		242.12.a.m.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.3.3	✓	20	11.3	even	5	inner
22.12.c.a.15.3	yes	20	1.1	even	1	trivial
242.12.a.m.1.6		10	11.6	odd	10
242.12.a.n.1.6		10	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-25.8885 - 18.8091i) q^{2} +(2.50110 - 7.69759i) q^{3} +(316.433 + 973.882i) q^{4} +(-10011.6 + 7273.85i) q^{5} +(-209.535 + 152.236i) q^{6} +(-8899.33 - 27389.3i) q^{7} +(10125.9 - 31164.2i) q^{8} +(143262. + 104086. i) q^{9} +O(q^{10})\)	\(q+(-25.8885 - 18.8091i) q^{2} +(2.50110 - 7.69759i) q^{3} +(316.433 + 973.882i) q^{4} +(-10011.6 + 7273.85i) q^{5} +(-209.535 + 152.236i) q^{6} +(-8899.33 - 27389.3i) q^{7} +(10125.9 - 31164.2i) q^{8} +(143262. + 104086. i) q^{9} +396000. q^{10} +(-479251. + 235861. i) q^{11} +8287.98 q^{12} +(117747. + 85548.4i) q^{13} +(-284779. + 876458. i) q^{14} +(30951.1 + 95257.8i) q^{15} +(-848316. + 616338. i) q^{16} +(5.91973e6 - 4.30094e6i) q^{17} +(-1.75108e6 - 5.38926e6i) q^{18} +(4.87836e6 - 1.50140e7i) q^{19} +(-1.02519e7 - 7.44842e6i) q^{20} -233090. q^{21} +(1.68434e7 + 2.90819e6i) q^{22} -3.40170e7 q^{23} +(-214564. - 155890. i) q^{24} +(3.22344e7 - 9.92074e7i) q^{25} +(-1.43922e6 - 4.42945e6i) q^{26} +(2.31948e6 - 1.68520e6i) q^{27} +(2.38579e7 - 1.73338e7i) q^{28} +(-4.40818e7 - 1.35670e8i) q^{29} +(990437. - 3.04825e6i) q^{30} +(1.17652e8 + 8.54792e7i) q^{31} +3.35544e7 q^{32} +(616908. + 4.27899e6i) q^{33} -2.34150e8 q^{34} +(2.88322e8 + 2.09478e8i) q^{35} +(-5.60345e7 + 1.72456e8i) q^{36} +(1.83212e7 + 5.63868e7i) q^{37} +(-4.08695e8 + 2.96934e8i) q^{38} +(953015. - 692406. i) q^{39} +(1.25308e8 + 3.85658e8i) q^{40} +(2.58518e8 - 7.95635e8i) q^{41} +(6.03436e6 + 4.38422e6i) q^{42} +9.13904e8 q^{43} +(-3.81352e8 - 3.92099e8i) q^{44} -2.19139e9 q^{45} +(8.80651e8 + 6.39830e8i) q^{46} +(-7.30609e8 + 2.24858e9i) q^{47} +(2.62259e6 + 8.07151e6i) q^{48} +(9.28714e8 - 6.74750e8i) q^{49} +(-2.70051e9 + 1.96203e9i) q^{50} +(-1.83010e7 - 5.63247e7i) q^{51} +(-4.60549e7 + 1.41742e8i) q^{52} +(3.21090e9 + 2.33286e9i) q^{53} -9.17449e7 q^{54} +(3.08245e9 - 5.84734e9i) q^{55} -9.43680e8 q^{56} +(-1.03371e8 - 7.51033e7i) q^{57} +(-1.41062e9 + 4.34143e9i) q^{58} +(1.16590e8 + 3.58828e8i) q^{59} +(-8.29759e7 + 6.02855e7i) q^{60} +(5.49982e9 - 3.99585e9i) q^{61} +(-1.43805e9 - 4.42587e9i) q^{62} +(1.57591e9 - 4.85014e9i) q^{63} +(-8.68675e8 - 6.31130e8i) q^{64} -1.80111e9 q^{65} +(6.45132e7 - 1.22380e8i) q^{66} -1.62958e10 q^{67} +(6.06180e9 + 4.40416e9i) q^{68} +(-8.50799e7 + 2.61849e8i) q^{69} +(-3.52414e9 - 1.08462e10i) q^{70} +(1.22849e10 - 8.92553e9i) q^{71} +(4.69441e9 - 3.41069e9i) q^{72} +(-6.22572e9 - 1.91608e10i) q^{73} +(5.86278e8 - 1.80438e9i) q^{74} +(-6.83037e8 - 4.96255e8i) q^{75} +1.61656e10 q^{76} +(1.07251e10 + 1.10273e10i) q^{77} -3.76957e7 q^{78} +(-1.69851e10 - 1.23404e10i) q^{79} +(4.00985e9 - 1.23410e10i) q^{80} +(9.68652e9 + 2.98121e10i) q^{81} +(-2.16578e10 + 1.57353e10i) q^{82} +(-2.06835e10 + 1.50275e10i) q^{83} +(-7.37575e7 - 2.27002e8i) q^{84} +(-2.79816e10 + 8.61185e10i) q^{85} +(-2.36596e10 - 1.71897e10i) q^{86} -1.15458e9 q^{87} +(2.49759e9 + 1.73238e10i) q^{88} +3.02385e10 q^{89} +(5.67318e10 + 4.12181e10i) q^{90} +(1.29524e9 - 3.98634e9i) q^{91} +(-1.07641e10 - 3.31285e10i) q^{92} +(9.52244e8 - 6.91846e8i) q^{93} +(6.12083e10 - 4.44704e10i) q^{94} +(6.03698e10 + 1.85799e11i) q^{95} +(8.39230e7 - 2.58288e8i) q^{96} +(-5.94108e10 - 4.31645e10i) q^{97} -3.67345e10 q^{98} +(-9.32082e10 - 1.60933e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

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