LMFDB - Embedded newform 22.12.c.a.5.2

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			5.2
Root			$396.589 - 288.139i$ of defining polynomial
Character	$\chi$	$=$	22.5
Dual form			22.12.c.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.88854 + 30.4338i) q^{2} +(-394.707 - 286.771i) q^{3} +(-828.433 + 601.892i) q^{4} +(250.688 - 771.537i) q^{5} +(4824.47 - 14848.2i) q^{6} +(37543.0 - 27276.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(18814.2 + 57904.3i) q^{9} +O(q^{10})$	\(q+(9.88854 + 30.4338i) q^{2} +(-394.707 - 286.771i) q^{3} +(-828.433 + 601.892i) q^{4} +(250.688 - 771.537i) q^{5} +(4824.47 - 14848.2i) q^{6} +(37543.0 - 27276.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(18814.2 + 57904.3i) q^{9} +25959.8 q^{10} +(-524601. - 100526. i) q^{11} +499594. q^{12} +(732307. + 2.25381e6i) q^{13} +(1.20138e6 + 872850. i) q^{14} +(-320203. + 232641. i) q^{15} +(324028. - 997255. i) q^{16} +(-2.50305e6 + 7.70359e6i) q^{17} +(-1.57620e6 + 1.14518e6i) q^{18} +(1.91634e6 + 1.39230e6i) q^{19} +(256704. + 790054. i) q^{20} -2.26406e7 q^{21} +(-2.12814e6 - 1.69597e7i) q^{22} -3.24198e7 q^{23} +(4.94025e6 + 1.52045e7i) q^{24} +(3.89704e7 + 2.83136e7i) q^{25} +(-6.13506e7 + 4.45738e7i) q^{26} +(-1.75283e7 + 5.39466e7i) q^{27} +(-1.46843e7 + 4.51937e7i) q^{28} +(6.58473e7 - 4.78409e7i) q^{29} +(-1.02465e7 - 7.44451e6i) q^{30} +(5.63414e7 + 1.73401e8i) q^{31} +3.35544e7 q^{32} +(1.78235e8 + 1.90119e8i) q^{33} -2.59201e8 q^{34} +(-1.16333e7 - 3.58037e7i) q^{35} +(-5.04385e7 - 3.66457e7i) q^{36} +(9.26502e7 - 6.73143e7i) q^{37} +(-2.34232e7 + 7.20892e7i) q^{38} +(3.57281e8 - 1.09960e9i) q^{39} +(-2.15059e7 + 1.56250e7i) q^{40} +(-3.48742e8 - 2.53376e8i) q^{41} +(-2.23883e8 - 6.89040e8i) q^{42} +1.72803e8 q^{43} +(4.95103e8 - 2.32474e8i) q^{44} +4.93918e7 q^{45} +(-3.20585e8 - 9.86658e8i) q^{46} +(8.17485e8 + 5.93938e8i) q^{47} +(-4.13880e8 + 3.00701e8i) q^{48} +(5.44366e7 - 1.67539e8i) q^{49} +(-4.76331e8 + 1.46600e9i) q^{50} +(3.19714e9 - 2.32286e9i) q^{51} +(-1.96322e9 - 1.42636e9i) q^{52} +(7.85453e8 + 2.41738e9i) q^{53} -1.81513e9 q^{54} +(-2.09071e8 + 3.79548e8i) q^{55} -1.52062e9 q^{56} +(-3.57119e8 - 1.09910e9i) q^{57} +(2.10711e9 + 1.53091e9i) q^{58} +(5.26816e9 - 3.82755e9i) q^{59} +(1.25242e8 - 3.85455e8i) q^{60} +(-2.10763e9 + 6.48663e9i) q^{61} +(-4.72012e9 + 3.42937e9i) q^{62} +(2.28577e9 + 1.66071e9i) q^{63} +(3.31804e8 + 1.02119e9i) q^{64} +1.92248e9 q^{65} +(-4.02355e9 + 7.30438e9i) q^{66} -9.75058e9 q^{67} +(-2.56312e9 - 7.88848e9i) q^{68} +(1.27963e10 + 9.29706e9i) q^{69} +(9.74607e8 - 7.08093e8i) q^{70} +(-5.07871e9 + 1.56307e10i) q^{71} +(6.16505e8 - 1.89741e9i) q^{72} +(-2.37647e10 + 1.72661e10i) q^{73} +(2.96481e9 + 2.15406e9i) q^{74} +(-7.26233e9 - 2.23512e10i) q^{75} -2.42557e9 q^{76} +(-2.24371e10 + 1.05353e10i) q^{77} +3.69980e10 q^{78} +(-5.11437e9 - 1.57404e10i) q^{79} +(-6.88190e8 - 4.99999e8i) q^{80} +(3.11145e10 - 2.26060e10i) q^{81} +(4.26264e9 - 1.31191e10i) q^{82} +(1.54242e10 - 4.74709e10i) q^{83} +(1.87562e10 - 1.36272e10i) q^{84} +(5.31612e9 + 3.86239e9i) q^{85} +(1.70877e9 + 5.25905e9i) q^{86} -3.97098e10 q^{87} +(1.19709e10 + 1.27690e10i) q^{88} -7.22371e10 q^{89} +(4.88413e8 + 1.50318e9i) q^{90} +(8.89692e10 + 6.46399e10i) q^{91} +(2.68576e10 - 1.95132e10i) q^{92} +(2.74881e10 - 8.45996e10i) q^{93} +(-9.99205e9 + 3.07524e10i) q^{94} +(1.55461e9 - 1.12949e9i) q^{95} +(-1.32442e10 - 9.62245e9i) q^{96} +(1.63805e10 + 5.04140e10i) q^{97} +5.63713e9 q^{98} +(-4.04906e9 - 3.22680e10i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	9.88854	+	30.4338i	0.218508	+	0.672499i
$2$	9.88854	+	30.4338i	0.218508	+	0.672499i
$3$	−394.707	−	286.771i	−0.937794	−	0.681348i	0.0100943	−	0.999949i	$-0.496787\pi$
$3$	−394.707	−	286.771i	−0.937794	−	0.681348i	−0.947889	+	0.318602i	$0.896787\pi$
$4$	−828.433	+	601.892i	−0.404508	+	0.293893i
$5$	250.688	−	771.537i	0.0358755	−	0.110413i	−0.931515	−	0.363703i	$-0.881512\pi$
$5$	250.688	−	771.537i	0.0358755	−	0.110413i	0.967391	+	0.253289i	$0.0815124\pi$
$6$	4824.47	−	14848.2i	0.253290	−	0.779545i
$7$	37543.0	−	27276.6i	0.844286	−	0.613410i	−0.0792787	−	0.996852i	$-0.525262\pi$
$7$	37543.0	−	27276.6i	0.844286	−	0.613410i	0.923565	+	0.383443i	$0.125262\pi$
$8$	−26509.9	−	19260.5i	−0.286031	−	0.207813i
$9$	18814.2	+	57904.3i	0.106207	+	0.326871i
$10$	25959.8			0.0820919
$11$	−524601.	−	100526.i	−0.982131	−	0.188200i
$11$	−524601.	−	100526.i	−0.982131	−	0.188200i
$12$	499594.			0.579589
$13$	732307.	+	2.25381e6i	0.547022	+	1.68356i	0.716133	+	0.697964i	$0.245910\pi$
$13$	732307.	+	2.25381e6i	0.547022	+	1.68356i	−0.169111	+	0.985597i	$0.554090\pi$
$14$	1.20138e6	+	872850.i	0.597000	+	0.433746i
$15$	−320203.	+	232641.i	−0.108874	+	0.0791014i
$16$	324028.	−	997255.i	0.0772542	−	0.237764i
$17$	−2.50305e6	+	7.70359e6i	−0.427563	+	1.31590i	0.472956	+	0.881086i	$0.343187\pi$
$17$	−2.50305e6	+	7.70359e6i	−0.427563	+	1.31590i	−0.900519	+	0.434817i	$0.856813\pi$
$18$	−1.57620e6	+	1.14518e6i	−0.196613	+	0.142848i
$19$	1.91634e6	+	1.39230e6i	0.177553	+	0.128999i	0.673012	−	0.739632i	$-0.265000\pi$
$19$	1.91634e6	+	1.39230e6i	0.177553	+	0.128999i	−0.495459	+	0.868631i	$0.665000\pi$
$20$	256704.	+	790054.i	0.0179377	+	0.0552067i
$21$	−2.26406e7			−1.20971
$22$	−2.12814e6	−	1.69597e7i	−0.0880390	−	0.701605i
$23$	−3.24198e7			−1.05028			−0.525142	−	0.851014i	$-0.675988\pi$
$23$	−3.24198e7			−1.05028			−0.525142	+	0.851014i	$0.675988\pi$
$24$	4.94025e6	+	1.52045e7i	0.126645	+	0.389773i
$25$	3.89704e7	+	2.83136e7i	0.798113	+	0.579863i
$26$	−6.13506e7	+	4.45738e7i	−1.01266	+	0.735743i
$27$	−1.75283e7	+	5.39466e7i	−0.235093	+	0.723542i
$28$	−1.46843e7	+	4.51937e7i	−0.161244	+	0.496259i
$29$	6.58473e7	−	4.78409e7i	0.596141	−	0.433122i	−0.248366	−	0.968666i	$-0.579894\pi$
$29$	6.58473e7	−	4.78409e7i	0.596141	−	0.433122i	0.844507	+	0.535544i	$0.179894\pi$
$30$	−1.02465e7	−	7.44451e6i	−0.0769854	−	0.0559331i
$31$	5.63414e7	+	1.73401e8i	0.353458	+	1.08783i	0.956898	+	0.290424i	$0.0937965\pi$
$31$	5.63414e7	+	1.73401e8i	0.353458	+	1.08783i	−0.603440	+	0.797409i	$0.706204\pi$
$32$	3.35544e7			0.176777
$33$	1.78235e8	+	1.90119e8i	0.792807	+	0.845665i
$34$	−2.59201e8			−0.978369
$35$	−1.16333e7	−	3.58037e7i	−0.0374395	−	0.115227i
$36$	−5.04385e7	−	3.66457e7i	−0.139027	−	0.101009i
$37$	9.26502e7	−	6.73143e7i	0.219653	−	0.159587i	−0.472518	−	0.881321i	$-0.656655\pi$
$37$	9.26502e7	−	6.73143e7i	0.219653	−	0.159587i	0.692170	+	0.721734i	$0.256655\pi$
$38$	−2.34232e7	+	7.20892e7i	−0.0479553	+	0.147591i
$39$	3.57281e8	−	1.09960e9i	0.634096	−	1.95155i
$40$	−2.15059e7	+	1.56250e7i	−0.0332069	+	0.0241262i
$41$	−3.48742e8	−	2.53376e8i	−0.470103	−	0.341550i	0.327379	−	0.944893i	$-0.393835\pi$
$41$	−3.48742e8	−	2.53376e8i	−0.470103	−	0.341550i	−0.797481	+	0.603344i	$0.793835\pi$
$42$	−2.23883e8	−	6.89040e8i	−0.264332	−	0.813529i
$43$	1.72803e8			0.179256			0.0896282	−	0.995975i	$-0.471432\pi$
$43$	1.72803e8			0.179256			0.0896282	+	0.995975i	$0.471432\pi$
$44$	4.95103e8	−	2.32474e8i	0.452591	−	0.212512i
$45$	4.93918e7			0.0399012
$46$	−3.20585e8	−	9.86658e8i	−0.229496	−	0.706315i
$47$	8.17485e8	+	5.93938e8i	0.519926	+	0.377748i	0.816576	−	0.577238i	$-0.195869\pi$
$47$	8.17485e8	+	5.93938e8i	0.519926	+	0.377748i	−0.296650	+	0.954986i	$0.595869\pi$
$48$	−4.13880e8	+	3.00701e8i	−0.234449	+	0.170337i
$49$	5.44366e7	−	1.67539e8i	0.0275304	−	0.0847298i
$50$	−4.76331e8	+	1.46600e9i	−0.215563	+	0.663434i
$51$	3.19714e9	−	2.32286e9i	1.29755	−	0.942728i
$52$	−1.96322e9	−	1.42636e9i	−0.716061	−	0.520249i
$53$	7.85453e8	+	2.41738e9i	0.257990	+	0.794012i	0.993226	+	0.116200i	$0.0370714\pi$
$53$	7.85453e8	+	2.41738e9i	0.257990	+	0.794012i	−0.735236	+	0.677811i	$0.762929\pi$
$54$	−1.81513e9			−0.537950
$55$	−2.09071e8	+	3.79548e8i	−0.0560143	+	0.101689i
$56$	−1.52062e9			−0.368966
$57$	−3.57119e8	−	1.09910e9i	−0.0786143	−	0.241950i
$58$	2.10711e9	+	1.53091e9i	0.421535	+	0.306263i
$59$	5.26816e9	−	3.82755e9i	0.959342	−	0.697002i	0.00634384	−	0.999980i	$-0.497981\pi$
$59$	5.26816e9	−	3.82755e9i	0.959342	−	0.697002i	0.952998	+	0.302977i	$0.0979807\pi$
$60$	1.25242e8	−	3.85455e8i	0.0207930	−	0.0639944i
$61$	−2.10763e9	+	6.48663e9i	−0.319507	+	0.983342i	0.654352	+	0.756190i	$0.272942\pi$
$61$	−2.10763e9	+	6.48663e9i	−0.319507	+	0.983342i	−0.973859	+	0.227152i	$0.927058\pi$
$62$	−4.72012e9	+	3.42937e9i	−0.654333	+	0.475400i
$63$	2.28577e9	+	1.66071e9i	0.290175	+	0.210824i
$64$	3.31804e8	+	1.02119e9i	0.0386271	+	0.118882i
$65$	1.92248e9			0.205512
$66$	−4.02355e9	+	7.30438e9i	−0.395474	+	0.717946i
$67$	−9.75058e9			−0.882306			−0.441153	−	0.897432i	$-0.645430\pi$
$67$	−9.75058e9			−0.882306			−0.441153	+	0.897432i	$0.645430\pi$
$68$	−2.56312e9	−	7.88848e9i	−0.213782	−	0.657952i
$69$	1.27963e10	+	9.29706e9i	0.984951	+	0.715609i
$70$	9.74607e8	−	7.08093e8i	0.0693091	−	0.0503560i
$71$	−5.07871e9	+	1.56307e10i	−0.334066	+	1.02815i	0.633114	+	0.774059i	$0.281777\pi$
$71$	−5.07871e9	+	1.56307e10i	−0.334066	+	1.02815i	−0.967180	+	0.254092i	$0.918223\pi$
$72$	6.16505e8	−	1.89741e9i	0.0375498	−	0.115566i
$73$	−2.37647e10	+	1.72661e10i	−1.34171	+	0.974806i	−0.342327	+	0.939581i	$0.611215\pi$
$73$	−2.37647e10	+	1.72661e10i	−1.34171	+	0.974806i	−0.999379	+	0.0352254i	$0.988785\pi$
$74$	2.96481e9	+	2.15406e9i	0.155318	+	0.112845i
$75$	−7.26233e9	−	2.23512e10i	−0.353378	−	1.08758i
$76$	−2.42557e9			−0.109733
$77$	−2.24371e10	+	1.05353e10i	−0.944643	+	0.443554i
$78$	3.69980e10			1.45097
$79$	−5.11437e9	−	1.57404e10i	−0.187001	−	0.575529i	0.812976	−	0.582297i	$-0.197846\pi$
$79$	−5.11437e9	−	1.57404e10i	−0.187001	−	0.575529i	−0.999977	+	0.00676759i	$0.997846\pi$
$80$	−6.88190e8	−	4.99999e8i	−0.0234808	−	0.0170598i
$81$	3.11145e10	−	2.26060e10i	0.991505	−	0.720371i
$82$	4.26264e9	−	1.31191e10i	0.126970	−	0.390775i
$83$	1.54242e10	−	4.74709e10i	0.429808	−	1.32281i	−0.468507	−	0.883460i	$-0.655208\pi$
$83$	1.54242e10	−	4.74709e10i	0.429808	−	1.32281i	0.898315	−	0.439353i	$-0.144792\pi$
$84$	1.87562e10	−	1.36272e10i	0.489339	−	0.355525i
$85$	5.31612e9	+	3.86239e9i	0.129954	+	0.0944174i
$86$	1.70877e9	+	5.25905e9i	0.0391689	+	0.120550i
$87$	−3.97098e10			−0.854164
$88$	1.19709e10	+	1.27690e10i	0.241809	+	0.257931i
$89$	−7.22371e10			−1.37125			−0.685623	−	0.727957i	$-0.740470\pi$
$89$	−7.22371e10			−1.37125			−0.685623	+	0.727957i	$0.740470\pi$
$90$	4.88413e8	+	1.50318e9i	0.00871873	+	0.0268335i
$91$	8.89692e10	+	6.46399e10i	1.49456	+	1.08586i
$92$	2.68576e10	−	1.95132e10i	0.424849	−	0.308671i
$93$	2.74881e10	−	8.45996e10i	0.409721	−	1.26099i
$94$	−9.99205e9	+	3.07524e10i	−0.140427	+	0.432190i
$95$	1.55461e9	−	1.12949e9i	0.0206131	−	0.0149763i
$96$	−1.32442e10	−	9.62245e9i	−0.165780	−	0.120446i
$97$	1.63805e10	+	5.04140e10i	0.193679	+	0.596083i	0.999989	+	0.00459007i	$0.00146107\pi$
$97$	1.63805e10	+	5.04140e10i	0.193679	+	0.596083i	−0.806310	+	0.591493i	$0.798539\pi$
$98$	5.63713e9			0.0629963
$99$	−4.04906e9	−	3.22680e10i	−0.0427918	−	0.341018i
$100$	−4.93261e10			−0.493261
$101$	−2.27135e10	−	6.99050e10i	−0.215039	−	0.661821i	−0.999151	−	0.0412019i	$-0.986881\pi$
$101$	−2.27135e10	−	6.99050e10i	−0.215039	−	0.661821i	0.784112	−	0.620619i	$-0.213119\pi$
$102$	1.02308e11	+	7.43314e10i	0.917509	+	0.666609i
$103$	−1.37568e10	+	9.99493e9i	−0.116927	+	0.0849523i	−0.644712	−	0.764426i	$-0.723023\pi$
$103$	−1.37568e10	+	9.99493e9i	−0.116927	+	0.0849523i	0.527785	+	0.849378i	$0.323023\pi$
$104$	2.39962e10	−	7.38528e10i	0.193401	−	0.595229i
$105$	−5.67572e9	+	1.74681e10i	−0.0433990	+	0.133568i
$106$	−6.58030e10	+	4.78086e10i	−0.477599	+	0.346996i
$107$	−6.50775e10	−	4.72816e10i	−0.448560	−	0.325898i	0.340467	−	0.940256i	$-0.389415\pi$
$107$	−6.50775e10	−	4.72816e10i	−0.448560	−	0.325898i	−0.789027	+	0.614359i	$0.789415\pi$
$108$	−1.79490e10	−	5.52413e10i	−0.117546	−	0.361771i
$109$	−2.29722e11			−1.43007			−0.715034	−	0.699089i	$-0.753589\pi$
$109$	−2.29722e11			−1.43007			−0.715034	+	0.699089i	$0.753589\pi$
$110$	−1.36185e10	−	2.60964e9i	−0.0806250	−	0.0154497i
$111$	−5.58735e10			−0.314723
$112$	−1.50367e10	−	4.62783e10i	−0.0806221	−	0.248129i
$113$	1.28006e11	+	9.30016e10i	0.653579	+	0.474853i	0.864488	−	0.502653i	$-0.167643\pi$
$113$	1.28006e11	+	9.30016e10i	0.653579	+	0.474853i	−0.210910	+	0.977506i	$0.567643\pi$
$114$	2.99184e10	−	2.17370e10i	0.145533	−	0.105736i
$115$	−8.12724e9	+	2.50131e10i	−0.0376795	+	0.115966i
$116$	−2.57551e10	+	7.92659e10i	−0.113853	+	0.350403i
$117$	−1.16727e11	+	8.48074e10i	−0.492210	+	0.357612i
$118$	1.68581e11	+	1.22481e11i	0.678357	+	0.492855i
$119$	1.16156e11	+	3.57490e11i	0.446203	+	1.37327i
$120$	1.29693e10			0.0475796
$121$	2.65101e11	+	1.05472e11i	0.929161	+	0.369675i
$122$	−2.18254e11			−0.731111
$123$	6.49899e10	+	2.00018e11i	0.208146	+	0.640607i
$124$	−1.51044e11	−	1.09740e11i	−0.462683	−	0.336159i
$125$	6.36607e10	−	4.62522e10i	0.186581	−	0.135559i
$126$	−2.79388e10	+	8.59868e10i	−0.0783736	+	0.241209i
$127$	−5.62755e10	+	1.73198e11i	−0.151147	+	0.465182i	−0.997750	−	0.0670422i	$-0.978644\pi$
$127$	−5.62755e10	+	1.73198e11i	−0.151147	+	0.465182i	0.846603	+	0.532225i	$0.178644\pi$
$128$	−2.77976e10	+	2.01961e10i	−0.0715077	+	0.0519534i
$129$	−6.82065e10	−	4.95549e10i	−0.168106	−	0.122136i
$130$	1.90105e10	+	5.85083e10i	0.0449061	+	0.138207i
$131$	1.97280e11			0.446777			0.223388	−	0.974730i	$-0.428288\pi$
$131$	1.97280e11			0.446777			0.223388	+	0.974730i	$0.428288\pi$
$132$	−2.62087e11	−	5.02223e10i	−0.569232	−	0.109079i
$133$	1.09922e11			0.229035
$134$	−9.64190e10	−	2.96747e11i	−0.192791	−	0.593349i
$135$	3.72277e10	+	2.70475e10i	0.0714546	+	0.0519148i
$136$	2.14731e11	−	1.56011e11i	0.395759	−	0.287536i
$137$	2.46487e11	−	7.58608e11i	0.436345	−	1.34293i	−0.455356	−	0.890309i	$-0.650488\pi$
$137$	2.46487e11	−	7.58608e11i	0.436345	−	1.34293i	0.891702	−	0.452624i	$-0.149512\pi$
$138$	−1.56408e11	+	4.81375e11i	−0.266026	+	0.818745i
$139$	8.82377e11	−	6.41084e11i	1.44236	−	1.04793i	0.454813	−	0.890587i	$-0.349706\pi$
$139$	8.82377e11	−	6.41084e11i	1.44236	−	1.04793i	0.987543	−	0.157347i	$-0.0502940\pi$
$140$	3.11874e10	+	2.26590e10i	0.0490089	+	0.0356071i
$141$	−1.52343e11	−	4.68862e11i	−0.230206	−	0.708501i
$142$	−5.25922e11			−0.764426
$143$	−1.57602e11	−	1.25597e12i	−0.220400	−	1.75643i
$144$	6.38416e10			0.0859232
$145$	−2.04039e10	−	6.27968e10i	−0.0264356	−	0.0813604i
$146$	−7.60472e11	−	5.52515e11i	−0.948729	−	0.689292i
$147$	−6.95317e10	+	5.05177e10i	−0.0835483	+	0.0607014i
$148$	−3.62386e10	+	1.11531e11i	−0.0419500	+	0.129109i
$149$	−3.72465e11	+	1.14633e12i	−0.415491	+	1.27875i	0.496320	+	0.868140i	$0.334684\pi$
$149$	−3.72465e11	+	1.14633e12i	−0.415491	+	1.27875i	−0.911811	+	0.410610i	$0.865316\pi$
$150$	6.08417e11	−	4.42041e11i	0.654183	−	0.475292i
$151$	2.97044e11	+	2.15815e11i	0.307927	+	0.223722i	0.731007	−	0.682370i	$-0.239051\pi$
$151$	2.97044e11	+	2.15815e11i	0.307927	+	0.223722i	−0.423079	+	0.906093i	$0.639051\pi$
$152$	−2.39854e10	−	7.38194e10i	−0.0239776	−	0.0737956i
$153$	−4.93164e11			−0.475541
$154$	−5.42498e11	−	5.78668e11i	−0.504701	−	0.538351i
$155$	1.47909e11			0.132792
$156$	3.65856e11	+	1.12599e12i	0.317048	+	0.975773i
$157$	1.51704e12	+	1.10219e12i	1.26925	+	0.922166i	0.999173	−	0.0406714i	$-0.0129497\pi$
$157$	1.51704e12	+	1.10219e12i	1.26925	+	0.922166i	0.270081	+	0.962838i	$0.412950\pi$
$158$	4.28467e11	−	3.11300e11i	0.346181	−	0.251515i
$159$	3.83210e11	−	1.17940e12i	0.299056	−	0.920400i
$160$	8.41168e9	−	2.58885e10i	0.00634195	−	0.0195185i
$161$	−1.21714e12	+	8.84301e11i	−0.886741	+	0.644255i
$162$	9.95664e11	+	7.23392e11i	0.701100	+	0.509379i
$163$	−4.14965e11	−	1.27713e12i	−0.282475	−	0.869368i	−0.987144	−	0.159832i	$-0.948905\pi$
$163$	−4.14965e11	−	1.27713e12i	−0.282475	−	0.869368i	0.704669	−	0.709536i	$-0.251095\pi$
$164$	4.41414e11			0.290540
$165$	1.91365e11	−	8.98548e10i	0.121815	−	0.0571978i
$166$	1.59724e12			0.983506
$167$	8.86527e11	+	2.72845e12i	0.528143	+	1.62546i	0.758016	+	0.652236i	$0.226169\pi$
$167$	8.86527e11	+	2.72845e12i	0.528143	+	1.62546i	−0.229873	+	0.973221i	$0.573831\pi$
$168$	6.00199e11	+	4.36070e11i	0.346015	+	0.251394i
$169$	−3.09350e12	+	2.24756e12i	−1.72613	+	1.25410i
$170$	−6.49785e10	+	1.99983e11i	−0.0350995	+	0.108025i
$171$	−4.45657e10	+	1.37159e11i	−0.0233089	+	0.0717374i
$172$	−1.43156e11	+	1.04009e11i	−0.0725107	+	0.0526821i
$173$	−2.78955e12	−	2.02672e12i	−1.36861	−	0.994354i	−0.997844	−	0.0656276i	$-0.979095\pi$
$173$	−2.78955e12	−	2.02672e12i	−1.36861	−	0.994354i	−0.370766	−	0.928726i	$-0.620905\pi$
$174$	−3.92672e11	−	1.20852e12i	−0.186642	−	0.574424i
$175$	2.23536e12			1.02953
$176$	−2.70236e11	+	4.90588e11i	−0.120621	+	0.218976i
$177$	−3.17701e12			−1.37457
$178$	−7.14319e11	−	2.19845e12i	−0.299628	−	0.922160i
$179$	−1.21468e12	−	8.82515e11i	−0.494048	−	0.358947i	0.312691	−	0.949855i	$-0.398770\pi$
$179$	−1.21468e12	−	8.82515e11i	−0.494048	−	0.358947i	−0.806739	+	0.590908i	$0.798770\pi$
$180$	−4.09178e10	+	2.97285e10i	−0.0161404	+	0.0117267i
$181$	−1.33589e12	+	4.11145e12i	−0.511139	+	1.57313i	0.279059	+	0.960274i	$0.409977\pi$
$181$	−1.33589e12	+	4.11145e12i	−0.511139	+	1.57313i	−0.790198	+	0.612851i	$0.790023\pi$
$182$	−1.08746e12	+	3.34687e12i	−0.403666	+	1.24235i
$183$	2.69207e12	−	1.95591e12i	0.969630	−	0.704477i
$184$	8.59444e11	+	6.24423e11i	0.300414	+	0.218263i
$185$	−2.87092e10	−	8.83579e10i	−0.00974041	−	0.0299779i
$186$	2.84651e12			0.937542
$187$	2.08752e12	−	3.78969e12i	0.667576	−	1.21192i
$188$	−1.03472e12			−0.321332
$189$	8.13414e11	+	2.50343e12i	0.245342	+	0.755084i
$190$	4.97476e10	+	3.61437e10i	0.0145756	+	0.0105898i
$191$	−3.05076e12	+	2.21651e12i	−0.868409	+	0.630936i	−0.930159	−	0.367156i	$-0.880332\pi$
$191$	−3.05076e12	+	2.21651e12i	−0.868409	+	0.630936i	0.0617508	+	0.998092i	$0.480332\pi$
$192$	1.61882e11	−	4.98222e11i	0.0447757	−	0.137805i
$193$	7.63435e11	−	2.34961e12i	0.205214	−	0.631583i	−0.794491	−	0.607276i	$-0.792262\pi$
$193$	7.63435e11	−	2.34961e12i	0.205214	−	0.631583i	0.999705	−	0.0243069i	$-0.00773789\pi$
$194$	−1.37231e12	+	9.97042e11i	−0.358544	+	0.260498i
$195$	−7.58815e11	−	5.51311e11i	−0.192728	−	0.140025i
$196$	5.57430e10	+	1.71559e11i	0.0137652	+	0.0423649i
$197$	−3.00903e12			−0.722541			−0.361271	−	0.932461i	$-0.617657\pi$
$197$	−3.00903e12			−0.722541			−0.361271	+	0.932461i	$0.617657\pi$
$198$	9.41997e11	−	4.42311e11i	0.219984	−	0.103293i
$199$	1.80050e12			0.408979			0.204489	−	0.978869i	$-0.434447\pi$
$199$	1.80050e12			0.408979			0.204489	+	0.978869i	$0.434447\pi$
$200$	−4.87763e11	−	1.50118e12i	−0.107781	−	0.331717i
$201$	3.84862e12	+	2.79619e12i	0.827421	+	0.601157i
$202$	1.90287e12	−	1.38252e12i	0.398086	−	0.289226i
$203$	1.16717e12	−	3.59218e12i	0.237632	−	0.731357i
$204$	−1.25051e12	+	3.84866e12i	−0.247811	+	0.762683i
$205$	−2.82914e11	+	2.05549e11i	−0.0545768	+	0.0396524i
$206$	−4.40219e11	−	3.19838e11i	−0.0826797	−	0.0600703i
$207$	−6.09954e11	−	1.87724e12i	−0.111548	−	0.343308i
$208$	2.48491e12			0.442550
$209$	−8.65349e11	−	9.23044e11i	−0.150102	−	0.160110i
$210$	−5.87744e11			−0.0993076
$211$	−2.38566e12	−	7.34231e12i	−0.392695	−	1.20859i	−0.930742	−	0.365676i	$-0.880838\pi$
$211$	−2.38566e12	−	7.34231e12i	−0.392695	−	1.20859i	0.538048	−	0.842914i	$-0.319162\pi$
$212$	−2.10569e12	−	1.52988e12i	−0.337713	−	0.245363i
$213$	6.48703e12	−	4.71310e12i	1.01381	−	0.736579i
$214$	7.95437e11	−	2.44810e12i	0.121152	−	0.372867i
$215$	4.33195e10	−	1.33324e11i	0.00643091	−	0.0197923i
$216$	1.50371e12	−	1.09251e12i	0.217605	−	0.158100i
$217$	6.84501e12	+	4.97319e12i	0.965707	+	0.701627i
$218$	−2.27162e12	−	6.99131e12i	−0.312481	−	0.961719i
$219$	1.43315e13			1.92243
$220$	−5.52459e10	−	4.40269e11i	−0.00722729	−	0.0575961i
$221$	−1.91954e13			−2.44929
$222$	−5.52507e11	−	1.70044e12i	−0.0687696	−	0.211651i
$223$	7.63508e12	+	5.54721e12i	0.927122	+	0.673594i	0.945287	−	0.326241i	$-0.105782\pi$
$223$	7.63508e12	+	5.54721e12i	0.927122	+	0.673594i	−0.0181642	+	0.999835i	$0.505782\pi$
$224$	1.25973e12	−	9.15250e11i	0.149250	−	0.108437i
$225$	−9.06282e11	+	2.78925e12i	−0.104775	+	0.322466i
$226$	−1.56460e12	+	4.81535e12i	−0.176526	+	0.543290i
$227$	−1.11619e13	+	8.10957e12i	−1.22912	+	0.893009i	−0.996824	−	0.0796364i	$-0.974624\pi$
$227$	−1.11619e13	+	8.10957e12i	−1.22912	+	0.893009i	−0.232297	+	0.972645i	$0.574624\pi$
$228$	9.57389e11	+	6.95584e11i	0.102907	+	0.0747666i
$229$	−3.99669e12	−	1.23006e13i	−0.419378	−	1.29071i	−0.908276	−	0.418372i	$-0.862601\pi$
$229$	−3.99669e12	−	1.23006e13i	−0.419378	−	1.29071i	0.488898	−	0.872341i	$-0.337399\pi$
$230$	−8.41610e11			−0.0862199
$231$	1.18773e13	+	2.27598e12i	1.18810	+	0.227668i
$232$	−2.66704e12			−0.260523
$233$	−1.39150e12	−	4.28260e12i	−0.132747	−	0.408554i	0.862485	−	0.506082i	$-0.168907\pi$
$233$	−1.39150e12	−	4.28260e12i	−0.132747	−	0.408554i	−0.995233	+	0.0975274i	$0.968907\pi$
$234$	−3.73528e12	−	2.71384e12i	−0.348045	−	0.252870i
$235$	6.63178e11	−	4.81827e11i	0.0603611	−	0.0438549i
$236$	−2.06055e12	+	6.34173e12i	−0.183218	+	0.563887i
$237$	−2.49522e12	+	7.67950e12i	−0.216767	+	0.667140i
$238$	−9.73118e12	+	7.07012e12i	−0.826023	+	0.600141i
$239$	8.71611e12	+	6.33263e12i	0.722993	+	0.525285i	0.887339	−	0.461117i	$-0.152551\pi$
$239$	8.71611e12	+	6.33263e12i	0.722993	+	0.525285i	−0.164346	+	0.986403i	$0.552551\pi$
$240$	1.28248e11	+	3.94706e11i	0.0103965	+	0.0319972i
$241$	1.37020e13			1.08565			0.542824	−	0.839846i	$-0.317355\pi$
$241$	1.37020e13			1.08565			0.542824	+	0.839846i	$0.317355\pi$
$242$	−5.88470e11	+	9.11099e12i	−0.0455764	+	0.705636i
$243$	−8.71557e12			−0.659874
$244$	−2.15822e12	−	6.64231e12i	−0.159754	−	0.491671i
$245$	−1.15616e11	−	8.39997e10i	−0.00836764	−	0.00607945i
$246$	−5.44466e12	+	3.95578e12i	−0.385326	+	0.279955i
$247$	−1.73463e12	+	5.33865e12i	−0.120053	+	0.369486i
$248$	1.84619e12	−	5.68200e12i	0.124966	−	0.384607i
$249$	−1.97013e13	+	1.43139e13i	−1.30437	+	0.947678i
$250$	2.03714e12	+	1.48007e12i	0.131932	+	0.0958545i
$251$	−4.21548e12	−	1.29739e13i	−0.267080	−	0.821988i	−0.991207	−	0.132321i	$-0.957757\pi$
$251$	−4.21548e12	−	1.29739e13i	−0.267080	−	0.821988i	0.724127	−	0.689667i	$-0.242243\pi$
$252$	−2.89318e12			−0.179338
$253$	1.70075e13	+	3.25904e12i	1.03152	+	0.197664i
$254$	−5.82757e12			−0.345861
$255$	−9.90688e11	−	3.04902e12i	−0.0575394	−	0.177088i
$256$	−8.89524e11	−	6.46277e11i	−0.0505636	−	0.0367366i
$257$	−7.13810e12	+	5.18613e12i	−0.397146	+	0.288544i	−0.768378	−	0.639997i	$-0.778936\pi$
$257$	−7.13810e12	+	5.18613e12i	−0.397146	+	0.288544i	0.371231	+	0.928540i	$0.378936\pi$
$258$	8.33682e11	−	2.56581e12i	0.0454038	−	0.139738i
$259$	1.64226e12	−	5.05436e12i	0.0875575	−	0.269474i
$260$	−1.59265e12	+	1.15712e12i	−0.0831315	+	0.0603986i
$261$	4.00906e12	+	2.91275e12i	0.204889	+	0.148861i
$262$	1.95081e12	+	6.00397e12i	0.0976243	+	0.300457i
$263$	1.61952e13			0.793653			0.396826	−	0.917894i	$-0.370111\pi$
$263$	1.61952e13			0.793653			0.396826	+	0.917894i	$0.370111\pi$
$264$	−1.06320e12	−	8.47294e12i	−0.0510264	−	0.406642i
$265$	2.06200e12			0.0969250
$266$	1.08697e12	+	3.34535e12i	0.0500459	+	0.154025i
$267$	2.85125e13	+	2.07155e13i	1.28595	+	0.934294i
$268$	8.07771e12	−	5.86880e12i	0.356900	−	0.259303i
$269$	5.14402e12	−	1.58317e13i	0.222672	−	0.685314i	−0.775848	−	0.630920i	$-0.782677\pi$
$269$	5.14402e12	−	1.58317e13i	0.222672	−	0.685314i	0.998520	−	0.0543934i	$-0.0173225\pi$
$270$	−4.55031e11	+	1.40044e12i	−0.0192992	+	0.0593969i
$271$	−2.68318e13	+	1.94944e13i	−1.11511	+	0.810176i	−0.983461	−	0.181120i	$-0.942028\pi$
$271$	−2.68318e13	+	1.94944e13i	−1.11511	+	0.810176i	−0.131651	+	0.991296i	$0.542028\pi$
$272$	6.87139e12	+	4.99236e12i	0.279844	+	0.203318i
$273$	−1.65799e13	−	5.10276e13i	−0.661739	−	2.03662i
$274$	2.55247e13			0.998465
$275$	−1.75976e13	−	1.87709e13i	−0.674721	−	0.719706i
$276$	−1.61967e13			−0.608733
$277$	1.05476e13	+	3.24622e13i	0.388611	+	1.19602i	0.933826	+	0.357726i	$0.116448\pi$
$277$	1.05476e13	+	3.24622e13i	0.388611	+	1.19602i	−0.545215	+	0.838296i	$0.683552\pi$
$278$	2.82361e13	+	2.05147e13i	1.01990	+	0.741001i
$279$	−8.98064e12	+	6.52481e12i	−0.318042	+	0.231071i
$280$	−3.81201e11	+	1.17322e12i	−0.0132369	+	0.0407389i
$281$	−8.46364e12	+	2.60484e13i	−0.288186	+	0.886944i	0.697240	+	0.716838i	$0.254411\pi$
$281$	−8.46364e12	+	2.60484e13i	−0.288186	+	0.886944i	−0.985426	+	0.170106i	$0.945589\pi$
$282$	1.27628e13	−	9.27273e12i	0.426164	−	0.309626i
$283$	−2.02205e13	−	1.46910e13i	−0.662164	−	0.481091i	0.205229	−	0.978714i	$-0.434206\pi$
$283$	−2.02205e13	−	1.46910e13i	−0.662164	−	0.481091i	−0.867393	+	0.497623i	$0.834206\pi$
$284$	−5.20060e12	−	1.60058e13i	−0.167033	−	0.514075i
$285$	−9.37522e11			−0.0295348
$286$	3.66654e13	−	1.72161e13i	1.13303	−	0.532012i
$287$	−2.00040e13			−0.606411
$288$	6.31301e11	+	1.94294e12i	0.0187749	+	0.0577832i
$289$	−2.53535e13	−	1.84204e13i	−0.739776	−	0.537478i
$290$	1.70938e12	−	1.24194e12i	0.0489384	−	0.0355558i
$291$	7.99179e12	−	2.45962e13i	0.224508	−	0.690966i
$292$	9.29518e12	−	2.86076e13i	0.256243	−	0.788635i
$293$	1.11208e13	−	8.07976e12i	0.300861	−	0.218588i	−0.427104	−	0.904202i	$-0.640466\pi$
$293$	1.11208e13	−	8.07976e12i	0.300861	−	0.218588i	0.727965	+	0.685614i	$0.240466\pi$
$294$	−2.22501e12	−	1.61657e12i	−0.0590776	−	0.0429224i
$295$	−1.63243e12	−	5.02410e12i	−0.0425416	−	0.130929i
$296$	−3.75265e12			−0.0959918
$297$	1.46184e13	−	2.65384e13i	0.367063	−	0.666368i
$298$	−3.85704e13			−0.950745
$299$	−2.37412e13	−	7.30680e13i	−0.574529	−	1.76822i
$300$	1.94693e13	+	1.41453e13i	0.462577	+	0.336082i
$301$	6.48754e12	−	4.71347e12i	0.151344	−	0.109958i
$302$	−3.63075e12	+	1.11743e13i	−0.0831683	+	0.255966i
$303$	−1.10816e13	+	3.41055e13i	−0.249268	+	0.767168i
$304$	2.00942e12	−	1.45993e12i	0.0443881	−	0.0322499i
$305$	4.47632e12	+	3.25223e12i	0.0971117	+	0.0705558i
$306$	−4.87667e12	−	1.50088e13i	−0.103910	−	0.319801i
$307$	7.76557e13			1.62522			0.812611	−	0.582807i	$-0.198046\pi$
$307$	7.76557e13			1.62522			0.812611	+	0.582807i	$0.198046\pi$
$308$	1.22466e13	−	2.22325e13i	0.251759	−	0.457045i
$309$	8.29617e12			0.167535
$310$	1.46261e12	+	4.50145e12i	0.0290161	+	0.0893023i
$311$	−9.73377e12	−	7.07200e12i	−0.189714	−	0.137835i	0.488874	−	0.872354i	$-0.337408\pi$
$311$	−9.73377e12	−	7.07200e12i	−0.189714	−	0.137835i	−0.678588	+	0.734519i	$0.737408\pi$
$312$	−3.06503e13	+	2.22688e13i	−0.586928	+	0.426428i
$313$	−2.27220e13	+	6.99311e13i	−0.427516	+	1.31576i	0.473048	+	0.881036i	$0.343154\pi$
$313$	−2.27220e13	+	6.99311e13i	−0.427516	+	1.31576i	−0.900564	+	0.434723i	$0.856846\pi$
$314$	−1.85426e13	+	5.70683e13i	−0.342814	+	1.05507i
$315$	1.85432e12	−	1.34724e12i	0.0336880	−	0.0244758i
$316$	1.37110e13	+	9.96159e12i	0.244787	+	0.177848i
$317$	−9.31275e12	−	2.86617e13i	−0.163400	−	0.502893i	0.835515	−	0.549468i	$-0.185170\pi$
$317$	−9.31275e12	−	2.86617e13i	−0.163400	−	0.502893i	−0.998915	+	0.0465745i	$0.985170\pi$
$318$	3.96830e13			0.684314
$319$	−3.93528e13	+	1.84780e13i	−0.667002	+	0.313188i
$320$	8.71065e11			0.0145119
$321$	1.21275e13	+	3.73247e13i	0.198607	+	0.611250i
$322$	−3.89483e13	−	2.82976e13i	−0.627020	−	0.455557i
$323$	−1.55224e13	+	1.12777e13i	−0.245666	+	0.178487i
$324$	−1.21699e13	+	3.74551e13i	−0.189361	+	0.582792i
$325$	−3.52752e13	+	1.08566e14i	−0.539649	+	1.66087i
$326$	3.47646e13	−	2.52579e13i	0.522926	−	0.379928i
$327$	9.06728e13	+	6.58777e13i	1.34111	+	0.974374i
$328$	4.36494e12	+	1.34339e13i	0.0634852	+	0.195387i
$329$	4.68914e13			0.670681
$330$	4.62695e12	+	4.93544e12i	0.0650831	+	0.0694223i
$331$	−4.24931e13			−0.587848			−0.293924	−	0.955829i	$-0.594961\pi$
$331$	−4.24931e13			−0.587848			−0.293924	+	0.955829i	$0.594961\pi$
$332$	1.57944e13	+	4.86102e13i	0.214904	+	0.661406i
$333$	5.64093e12	+	4.09837e12i	0.0754931	+	0.0548489i
$334$	−7.42707e13	+	5.39608e13i	−0.977714	+	0.710351i
$335$	−2.44435e12	+	7.52294e12i	−0.0316532	+	0.0974184i
$336$	−7.33619e12	+	2.25785e13i	−0.0934554	+	0.287626i
$337$	4.45284e13	−	3.23518e13i	0.558050	−	0.405447i	−0.272695	−	0.962101i	$-0.587915\pi$
$337$	4.45284e13	−	3.23518e13i	0.558050	−	0.405447i	0.830745	+	0.556654i	$0.187915\pi$
$338$	−9.89919e13	−	7.19218e13i	−1.22056	−	0.886786i
$339$	−2.38545e13	−	7.34167e13i	−0.289383	−	0.890629i
$340$	−6.72880e12			−0.0803162
$341$	−1.21254e13	−	9.66301e13i	−0.142412	−	1.13492i
$342$	−4.61496e12			−0.0533365
$343$	2.58290e13	+	7.94934e13i	0.293758	+	0.904094i
$344$	−4.58098e12	−	3.32828e12i	−0.0512728	−	0.0372519i
$345$	1.03809e13	−	7.54217e12i	0.114348	−	0.0830790i
$346$	3.40964e13	−	1.04938e14i	0.369649	−	1.13766i
$347$	−4.16164e13	+	1.28082e14i	−0.444071	+	1.36671i	0.439429	+	0.898277i	$0.355181\pi$
$347$	−4.16164e13	+	1.28082e14i	−0.444071	+	1.36671i	−0.883500	+	0.468431i	$0.844819\pi$
$348$	3.28969e13	−	2.39010e13i	0.345517	−	0.251033i
$349$	1.05411e12	+	7.65856e11i	0.0108980	+	0.00791785i	0.593221	−	0.805040i	$-0.297856\pi$
$349$	1.05411e12	+	7.65856e11i	0.0108980	+	0.00791785i	−0.582323	+	0.812958i	$0.697856\pi$
$350$	2.21045e13	+	6.80306e13i	0.224960	+	0.692357i
$351$	−1.34422e14			−1.34673
$352$	−1.76027e13	−	3.37311e12i	−0.173618	−	0.0332694i
$353$	1.40963e14			1.36882			0.684408	−	0.729100i	$-0.260061\pi$
$353$	1.40963e14			1.36882			0.684408	+	0.729100i	$0.260061\pi$
$354$	−3.14160e13	−	9.66885e13i	−0.300354	−	0.924394i
$355$	1.07865e13	+	7.83683e12i	0.101537	+	0.0737708i
$356$	5.98436e13	−	4.34789e13i	0.554680	−	0.402999i
$357$	5.66705e13	−	1.74414e14i	0.517228	−	1.59186i
$358$	1.48469e13	−	4.56941e13i	0.133438	−	0.410680i
$359$	−3.91960e13	+	2.84775e13i	−0.346914	+	0.252048i	−0.747573	−	0.664179i	$-0.768781\pi$
$359$	−3.91960e13	+	2.84775e13i	−0.346914	+	0.252048i	0.400659	+	0.916227i	$0.368781\pi$
$360$	−1.30937e12	−	9.51313e11i	−0.0114130	−	0.00829201i
$361$	−3.42636e13	−	1.05453e14i	−0.294133	−	0.905248i
$362$	−1.38337e14			−1.16961
$363$	−7.43905e13	−	1.17654e14i	−0.619485	−	0.979760i
$364$	−1.12611e14			−0.923686
$365$	7.36391e12	+	2.26638e13i	0.0594973	+	0.183114i
$366$	8.61464e13	+	6.25890e13i	0.685632	+	0.498141i
$367$	2.92494e13	−	2.12509e13i	0.229326	−	0.166615i	−0.467189	−	0.884158i	$-0.654733\pi$
$367$	2.92494e13	−	2.12509e13i	0.229326	−	0.166615i	0.696515	+	0.717543i	$0.254733\pi$
$368$	−1.05049e13	+	3.23308e13i	−0.0811390	+	0.249720i
$369$	8.11023e12	−	2.49607e13i	0.0617146	−	0.189938i
$370$	2.40518e12	−	1.74746e12i	0.0180317	−	0.0131008i
$371$	9.54260e13	+	6.93310e13i	0.704872	+	0.512119i
$372$	2.81478e13	+	8.66300e13i	0.204861	+	0.630496i
$373$	9.30162e13			0.667053			0.333526	−	0.942741i	$-0.391761\pi$
$373$	9.30162e13			0.667053			0.333526	+	0.942741i	$0.391761\pi$
$374$	1.35977e14	+	2.60566e13i	0.960886	+	0.184129i
$375$	−3.83911e13			−0.267337
$376$	−1.02319e13	−	3.14904e13i	−0.0702136	−	0.216095i
$377$	1.56045e14	+	1.13373e14i	1.05529	+	0.766712i
$378$	−6.81454e13	+	4.95105e13i	−0.454184	+	0.329984i
$379$	−2.12431e13	+	6.53796e13i	−0.139541	+	0.429464i	−0.996269	−	0.0863056i	$-0.972494\pi$
$379$	−2.12431e13	+	6.53796e13i	−0.139541	+	0.429464i	0.856727	+	0.515769i	$0.172494\pi$
$380$	−6.08061e11	+	1.87142e12i	−0.00393674	+	0.0121160i
$381$	7.18806e13	−	5.22243e13i	0.458696	−	0.333262i
$382$	−9.76242e13	−	7.09282e13i	−0.614058	−	0.446139i
$383$	2.92627e13	+	9.00614e13i	0.181435	+	0.558400i	0.999869	−	0.0162009i	$-0.00515715\pi$
$383$	2.92627e13	+	9.00614e13i	0.181435	+	0.558400i	−0.818433	+	0.574601i	$0.805157\pi$
$384$	1.67636e13			0.102458
$385$	2.50364e12	+	1.99521e13i	0.0150847	+	0.120214i
$386$	7.90568e13			0.469580
$387$	3.25115e12	+	1.00060e13i	0.0190383	+	0.0585937i
$388$	−4.39139e13	−	3.19053e13i	−0.253529	−	0.184200i
$389$	1.80249e14	−	1.30959e14i	1.02601	−	0.745437i	0.0585012	−	0.998287i	$-0.481368\pi$
$389$	1.80249e14	−	1.30959e14i	1.02601	−	0.745437i	0.967506	+	0.252850i	$0.0813679\pi$
$390$	9.27493e12	−	2.85453e13i	0.0520541	−	0.160206i
$391$	8.11483e13	−	2.49749e14i	0.449063	−	1.38207i
$392$	−4.66999e12	+	3.39295e12i	−0.0254825	+	0.0185141i
$393$	−7.78676e13	−	5.65742e13i	−0.418985	−	0.304410i
$394$	−2.97550e13	−	9.15763e13i	−0.157881	−	0.485908i
$395$	−1.34264e13			−0.0702549
$396$	2.27762e13	+	2.42948e13i	0.117532	+	0.125369i
$397$	−7.25145e13			−0.369043			−0.184521	−	0.982828i	$-0.559074\pi$
$397$	−7.25145e13			−0.369043			−0.184521	+	0.982828i	$0.559074\pi$
$398$	1.78043e13	+	5.47960e13i	0.0893652	+	0.275038i
$399$	−4.33870e13	−	3.15225e13i	−0.214787	−	0.156052i
$400$	4.08634e13	−	2.96890e13i	0.199528	−	0.144966i
$401$	5.44618e13	−	1.67616e14i	0.262300	−	0.807275i	−0.730004	−	0.683443i	$-0.760482\pi$
$401$	5.44618e13	−	1.67616e14i	0.262300	−	0.807275i	0.992303	−	0.123832i	$-0.0395184\pi$
$402$	−4.70413e13	+	1.44778e14i	−0.223479	+	0.687797i
$403$	−3.49554e14	+	2.53966e14i	−1.63808	+	1.19014i
$404$	6.08919e13	+	4.42405e13i	0.281489	+	0.204514i
$405$	−9.64135e12	−	2.96730e13i	−0.0439679	−	0.135319i
$406$	1.20865e14			0.543761
$407$	−5.53712e13	+	2.59994e13i	−0.245762	+	0.115397i
$408$	−1.29495e14			−0.567052
$409$	5.47846e13	+	1.68610e14i	0.236690	+	0.728457i	0.996893	+	0.0787711i	$0.0250996\pi$
$409$	5.47846e13	+	1.68610e14i	0.236690	+	0.728457i	−0.760203	+	0.649686i	$0.774900\pi$
$410$	−9.05325e12	−	6.57757e12i	−0.0385917	−	0.0280385i
$411$	−3.14837e14	+	2.28742e14i	−1.32421	+	0.962092i
$412$	5.38076e12	−	1.65603e13i	0.0223310	−	0.0687278i
$413$	9.33803e13	−	2.87395e14i	0.382411	−	1.17694i
$414$	5.11001e13	−	3.71264e13i	0.206500	−	0.150031i
$415$	−3.27589e13	−	2.38008e13i	−0.130637	−	0.0949131i
$416$	2.45721e13	+	7.56253e13i	0.0967007	+	0.297614i
$417$	−5.32125e14			−2.06664
$418$	1.95347e13	−	3.54634e13i	0.0748751	−	0.135929i
$419$	2.17649e14			0.823341			0.411670	−	0.911333i	$-0.364945\pi$
$419$	2.17649e14			0.823341			0.411670	+	0.911333i	$0.364945\pi$
$420$	−5.81194e12	−	1.78873e13i	−0.0216995	−	0.0667842i
$421$	2.25514e13	+	1.63845e13i	0.0831040	+	0.0603786i	0.628561	−	0.777760i	$-0.283644\pi$
$421$	2.25514e13	+	1.63845e13i	0.0831040	+	0.0603786i	−0.545457	+	0.838139i	$0.683644\pi$
$422$	1.99864e14	−	1.45209e14i	0.726968	−	0.528173i
$423$	−1.90112e13	+	5.85103e13i	−0.0682553	+	0.210068i
$424$	2.57377e13	−	7.92126e13i	0.0912132	−	0.280725i
$425$	−3.15661e14	+	2.29341e14i	−1.10429	+	0.802312i
$426$	2.07585e14	+	1.50819e14i	0.716875	+	0.520840i
$427$	9.78061e13	+	3.01016e14i	0.333436	+	1.02621i
$428$	8.23708e13			0.277225
$429$	−2.97969e14	+	5.40934e14i	−0.990046	+	1.79734i
$430$	4.48592e12			0.0147155
$431$	−3.71628e13	−	1.14375e14i	−0.120360	−	0.370431i	0.872667	−	0.488316i	$-0.162389\pi$
$431$	−3.71628e13	−	1.14375e14i	−0.120360	−	0.370431i	−0.993027	+	0.117885i	$0.962389\pi$
$432$	4.81189e13	+	3.49604e13i	0.153870	+	0.111793i
$433$	3.25636e14	−	2.36588e14i	1.02813	−	0.746982i	0.0601980	−	0.998186i	$-0.480827\pi$
$433$	3.25636e14	−	2.36588e14i	1.02813	−	0.746982i	0.967934	+	0.251205i	$0.0808268\pi$
$434$	−8.36659e13	+	2.57497e14i	−0.260829	+	0.802748i
$435$	−9.95474e12	+	3.06376e13i	−0.0306436	+	0.0943112i
$436$	1.90309e14	−	1.38268e14i	0.578475	−	0.420287i
$437$	−6.21272e13	−	4.51381e13i	−0.186481	−	0.135486i
$438$	1.41718e14	+	4.36163e14i	0.420066	+	1.29283i
$439$	−4.80897e14			−1.40766			−0.703829	−	0.710369i	$-0.748528\pi$
$439$	−4.80897e14			−1.40766			−0.703829	+	0.710369i	$0.748528\pi$
$440$	1.28527e13	−	6.03496e12i	0.0371541	−	0.0174456i
$441$	1.07254e13			0.0306197
$442$	−1.89815e14	−	5.84190e14i	−0.535190	−	1.64714i
$443$	1.33585e14	+	9.70555e13i	0.371996	+	0.270271i	0.758038	−	0.652210i	$-0.226158\pi$
$443$	1.33585e14	+	9.70555e13i	0.371996	+	0.270271i	−0.386042	+	0.922481i	$0.626158\pi$
$444$	4.62874e13	−	3.36298e13i	0.127308	−	0.0924949i
$445$	−1.81089e13	+	5.57336e13i	−0.0491941	+	0.151404i
$446$	−9.33230e13	+	2.87219e14i	−0.250407	+	0.770674i
$447$	4.75749e14	−	3.45652e14i	1.26092	−	0.916110i
$448$	4.03115e13	+	2.92880e13i	0.105536	+	0.0766762i
$449$	9.50012e13	+	2.92384e14i	0.245683	+	0.756133i	0.995523	+	0.0945150i	$0.0301300\pi$
$449$	9.50012e13	+	2.92384e14i	0.245683	+	0.756133i	−0.749841	+	0.661618i	$0.769870\pi$
$450$	−9.38493e13			−0.239752
$451$	1.57479e14	+	1.67979e14i	0.397423	+	0.423920i
$452$	−1.62021e14			−0.403934
$453$	−5.53558e13	−	1.70368e14i	−0.136340	−	0.419611i
$454$	−3.57180e14	−	2.59506e14i	−0.869120	−	0.631452i
$455$	7.21756e13	−	5.24386e13i	0.173511	−	0.126063i
$456$	−1.17021e13	+	3.60153e13i	−0.0277943	+	0.0855422i
$457$	8.20941e13	−	2.52660e14i	0.192652	−	0.592921i	−0.807344	−	0.590081i	$-0.799096\pi$
$457$	8.20941e13	−	2.52660e14i	0.192652	−	0.592921i	0.999996	−	0.00284009i	$-0.000904029\pi$
$458$	3.34831e14	−	2.43269e14i	0.776365	−	0.564062i
$459$	−3.71708e14	−	2.70062e14i	−0.851594	−	0.618719i
$460$	−8.32229e12	−	2.56134e13i	−0.0188397	−	0.0579828i
$461$	4.18670e14			0.936520			0.468260	−	0.883591i	$-0.344881\pi$
$461$	4.18670e14			0.936520			0.468260	+	0.883591i	$0.344881\pi$
$462$	4.81823e13	+	3.83977e14i	0.106502	+	0.848739i
$463$	8.01721e14			1.75117			0.875584	−	0.483067i	$-0.160477\pi$
$463$	8.01721e14			1.75117			0.875584	+	0.483067i	$0.160477\pi$
$464$	−2.63732e13	−	8.11683e13i	−0.0569264	−	0.175201i
$465$	−5.83808e13	−	4.24162e13i	−0.124531	−	0.0904774i
$466$	1.16576e14	−	8.46973e13i	0.245746	−	0.178545i
$467$	1.75877e14	−	5.41295e14i	0.366410	−	1.12769i	−0.582684	−	0.812699i	$-0.697997\pi$
$467$	1.75877e14	−	5.41295e14i	0.366410	−	1.12769i	0.949093	−	0.314995i	$-0.102003\pi$
$468$	4.56559e13	−	1.40515e14i	0.0940038	−	0.289314i
$469$	−3.66066e14	+	2.65962e14i	−0.744918	+	0.541215i
$470$	2.12217e13	+	1.54185e13i	0.0426817	+	0.0310101i
$471$	−2.82708e14	−	8.70085e14i	−0.561983	−	1.72960i
$472$	−2.13379e14			−0.419248
$473$	−9.06526e13	−	1.73712e13i	−0.176053	−	0.0337361i
$474$	−2.58391e14			−0.496016
$475$	3.52592e13	+	1.08517e14i	0.0669049	+	0.205912i
$476$	−3.11398e14	−	2.26244e14i	−0.584087	−	0.424364i
$477$	−1.25199e14	+	9.09621e13i	−0.232139	+	0.168659i
$478$	−1.06536e14	+	3.27885e14i	−0.195274	+	0.600991i
$479$	2.69172e14	−	8.28426e14i	0.487735	−	1.50109i	−0.340244	−	0.940337i	$-0.610510\pi$
$479$	2.69172e14	−	8.28426e14i	0.487735	−	1.50109i	0.827980	−	0.560758i	$-0.189490\pi$
$480$	−1.07442e13	+	7.80613e12i	−0.0192463	+	0.0139833i
$481$	2.19562e14	+	1.59521e14i	0.388830	+	0.282501i
$482$	1.35493e14	+	4.17003e14i	0.237223	+	0.730097i
$483$	7.34004e14			1.27054
$484$	−2.83101e14	+	7.21850e13i	−0.484498	+	0.123537i
$485$	4.30026e13			0.0727638
$486$	−8.61843e13	−	2.65248e14i	−0.144188	−	0.443765i
$487$	−2.53903e14	−	1.84472e14i	−0.420010	−	0.305155i	0.357632	−	0.933863i	$-0.383584\pi$
$487$	−2.53903e14	−	1.84472e14i	−0.420010	−	0.305155i	−0.777642	+	0.628708i	$0.783584\pi$
$488$	1.80809e14	−	1.31365e14i	0.295741	−	0.214868i
$489$	−2.02455e14	+	6.23093e14i	−0.327439	+	1.00775i
$490$	1.41316e12	−	4.34926e12i	0.00226002	−	0.00695563i
$491$	1.44516e14	−	1.04997e14i	0.228543	−	0.166046i	−0.467621	−	0.883929i	$-0.654889\pi$
$491$	1.44516e14	−	1.04997e14i	0.228543	−	0.166046i	0.696164	+	0.717883i	$0.254889\pi$
$492$	−1.74229e14	−	1.26585e14i	−0.272466	−	0.197958i
$493$	2.03727e14	+	6.27009e14i	0.315059	+	0.969651i
$494$	−1.79628e14			−0.274711
$495$	−2.59110e13	−	4.96518e12i	−0.0391882	−	0.00750942i
$496$	1.91181e14			0.285954
$497$	2.35681e14	+	7.25352e14i	0.348630	+	1.07297i
$498$	−6.30443e14	−	4.58044e14i	−0.922326	−	0.670109i
$499$	−7.66293e14	+	5.56744e14i	−1.10877	+	0.805569i	−0.982470	−	0.186423i	$-0.940311\pi$
$499$	−7.66293e14	+	5.56744e14i	−1.10877	+	0.805569i	−0.126301	+	0.991992i	$0.540311\pi$
$500$	−2.48998e13	+	7.66338e13i	−0.0356337	+	0.109669i
$501$	4.32523e14	−	1.33117e15i	0.612211	−	1.88419i
$502$	3.53161e14	−	2.56586e14i	0.494427	−	0.359222i
$503$	−3.39190e14	−	2.46436e14i	−0.469699	−	0.341256i	0.327625	−	0.944808i	$-0.393752\pi$
$503$	−3.39190e14	−	2.46436e14i	−0.469699	−	0.341256i	−0.797324	+	0.603552i	$0.793752\pi$
$504$	−2.86093e13	−	8.80504e13i	−0.0391868	−	0.120605i
$505$	−5.96283e13			−0.0807885
$506$	6.89938e13	+	5.49829e14i	0.0924660	+	0.736885i
$507$	1.86556e15			2.47323
$508$	−5.76262e13	−	1.77355e14i	−0.0755734	−	0.232591i
$509$	−2.67142e14	−	1.94090e14i	−0.346572	−	0.251800i	0.400857	−	0.916141i	$-0.368712\pi$
$509$	−2.67142e14	−	1.94090e14i	−0.346572	−	0.251800i	−0.747430	+	0.664341i	$0.768712\pi$
$510$	8.29969e13	−	6.03008e13i	0.106519	−	0.0773904i
$511$	−4.21239e14	+	1.29644e15i	−0.534828	+	1.64603i
$512$	1.08726e13	−	3.34623e13i	0.0136568	−	0.0420312i
$513$	−1.08700e14	+	7.89752e13i	−0.135078	+	0.0981398i
$514$	−2.28419e14	−	1.65956e14i	−0.280825	−	0.204031i
$515$	4.26279e12	+	1.31195e13i	0.00518506	+	0.0159580i
$516$	8.63312e13			0.103895
$517$	−3.69147e14	−	3.93759e14i	−0.439543	−	0.468848i
$518$	1.70063e14			0.200353
$519$	5.19846e14	+	1.59992e15i	0.605975	+	1.86500i
$520$	−5.09646e13	−	3.70280e13i	−0.0587829	−	0.0427082i
$521$	−1.36558e15	+	9.92153e14i	−1.55851	+	1.13233i	−0.621297	+	0.783575i	$0.713394\pi$
$521$	−1.36558e15	+	9.92153e14i	−1.55851	+	1.13233i	−0.937216	+	0.348750i	$0.886606\pi$
$522$	−4.90023e13	+	1.50814e14i	−0.0553387	+	0.170315i
$523$	2.76653e14	−	8.51449e14i	0.309154	−	0.951479i	−0.668940	−	0.743317i	$-0.733252\pi$
$523$	2.76653e14	−	8.51449e14i	0.309154	−	0.951479i	0.978094	−	0.208163i	$-0.0667484\pi$
$524$	−1.63433e14	+	1.18741e14i	−0.180725	+	0.131304i
$525$	−8.82312e14	−	6.41038e14i	−0.965487	−	0.701467i
$526$	1.60147e14	+	4.92883e14i	0.173419	+	0.533730i
$527$	−1.47684e15			−1.58261
$528$	2.47350e14	−	1.16142e14i	0.262317	−	0.123170i
$529$	9.82331e13			0.103098
$530$	2.03902e13	+	6.27545e13i	0.0211789	+	0.0651820i
$531$	3.20748e14	+	2.33037e14i	0.329719	+	0.239555i
$532$	−9.10632e13	+	6.61613e13i	−0.0926464	+	0.0673116i
$533$	3.15675e14	−	9.71547e14i	0.317863	−	0.978282i
$534$	−3.48505e14	+	1.07259e15i	−0.347322	+	1.06895i
$535$	−5.27936e13	+	3.83568e13i	−0.0520758	+	0.0378353i
$536$	2.58487e14	+	1.87802e14i	0.252367	+	0.183355i
$537$	2.26362e14	+	6.96669e14i	0.218748	+	0.673237i
$538$	5.32685e14			0.509528
$539$	−4.53995e13	+	8.24185e13i	−0.0429846	+	0.0780345i
$540$	−4.71203e13			−0.0441614
$541$	5.00578e14	+	1.54062e15i	0.464395	+	1.42926i	0.859742	+	0.510728i	$0.170624\pi$
$541$	5.00578e14	+	1.54062e15i	0.464395	+	1.42926i	−0.395348	+	0.918532i	$0.629376\pi$
$542$	−8.58617e14	−	6.23822e14i	−0.788503	−	0.572881i
$543$	1.70633e15	−	1.23972e15i	1.55119	−	1.12700i
$544$	−8.39884e13	+	2.58490e14i	−0.0755832	+	0.232621i
$545$	−5.75885e13	+	1.77239e14i	−0.0513044	+	0.157899i
$546$	1.38901e15	−	1.00918e15i	1.22503	−	0.890037i
$547$	1.12465e15	+	8.17108e14i	0.981947	+	0.713426i	0.958143	−	0.286290i	$-0.0924222\pi$
$547$	1.12465e15	+	8.17108e14i	0.981947	+	0.713426i	0.0238042	+	0.999717i	$0.492422\pi$
$548$	2.52402e14	+	7.76815e14i	0.218173	+	0.671466i
$549$	−4.15257e14			−0.355360
$550$	3.97255e14	−	7.21179e14i	0.336570	−	0.611010i
$551$	1.92794e14			0.161719
$552$	−1.60162e14	−	4.92928e14i	−0.133013	−	0.409372i
$553$	−6.21354e14	−	4.51440e14i	−0.510917	−	0.371203i
$554$	−8.83648e14	+	6.42008e14i	−0.719409	+	0.522681i
$555$	−1.40068e13	+	4.31084e13i	−0.0112909	+	0.0347497i
$556$	−3.45127e14	+	1.06219e15i	−0.275466	+	0.847796i
$557$	−2.88392e14	+	2.09529e14i	−0.227919	+	0.165592i	−0.695884	−	0.718154i	$-0.744987\pi$
$557$	−2.88392e14	+	2.09529e14i	−0.227919	+	0.165592i	0.467965	+	0.883747i	$0.344987\pi$
$558$	−2.87380e14	−	2.08794e14i	−0.224889	−	0.163392i
$559$	1.26545e14	+	3.89465e14i	0.0980572	+	0.301789i
$560$	−3.94750e13			−0.0302892
$561$	−1.91073e15	+	8.97176e14i	−1.45179	+	0.681682i
$562$	−8.76445e14			−0.659439
$563$	−3.67039e14	−	1.12963e15i	−0.273474	−	0.841666i	−0.989619	−	0.143715i	$-0.954095\pi$
$563$	−3.67039e14	−	1.12963e15i	−0.273474	−	0.841666i	0.716145	−	0.697951i	$-0.245905\pi$
$564$	4.08410e14	+	2.96727e14i	0.301343	+	0.218939i
$565$	1.03844e14	−	7.54468e13i	0.0758776	−	0.0551283i
$566$	2.47153e14	−	7.60659e14i	0.178845	−	0.550427i
$567$	5.51517e14	−	1.69739e15i	0.395232	−	1.21640i
$568$	4.35691e14	−	3.16548e14i	0.309217	−	0.224659i
$569$	−6.45577e14	−	4.69039e14i	−0.453764	−	0.329679i	0.337316	−	0.941392i	$-0.390481\pi$
$569$	−6.45577e14	−	4.69039e14i	−0.453764	−	0.329679i	−0.791080	+	0.611712i	$0.790481\pi$
$570$	−9.27073e12	−	2.85324e13i	−0.00645360	−	0.0198621i
$571$	−1.74050e15			−1.19998			−0.599991	−	0.800006i	$-0.704829\pi$
$571$	−1.74050e15			−1.19998			−0.599991	+	0.800006i	$0.704829\pi$
$572$	8.86519e14	+	9.45626e14i	0.605355	+	0.645715i
$573$	1.83978e15			1.24428
$574$	−1.97811e14	−	6.08799e14i	−0.132506	−	0.407811i
$575$	−1.26341e15	−	9.17922e14i	−0.838246	−	0.609021i
$576$	−5.28886e13	+	3.84258e13i	−0.0347567	+	0.0252522i
$577$	5.99685e14	−	1.84564e15i	0.390352	−	1.20138i	−0.542171	−	0.840268i	$-0.682398\pi$
$577$	5.99685e14	−	1.84564e15i	0.390352	−	1.20138i	0.932523	−	0.361111i	$-0.117602\pi$
$578$	3.09894e14	−	9.53755e14i	0.199807	−	0.614941i
$579$	−9.75133e14	+	7.08476e14i	−0.622776	+	0.452473i
$580$	5.47001e13	+	3.97420e13i	0.0346047	+	0.0251418i
$581$	−7.15772e14	−	2.20292e15i	−0.448545	−	1.38048i
$582$	8.27583e14			0.513730
$583$	−1.69039e14	−	1.34712e15i	−0.103947	−	0.828377i
$584$	9.62555e14			0.586347
$585$	3.61700e13	+	1.11320e14i	0.0218268	+	0.0671761i
$586$	3.55867e14	+	2.58552e14i	0.212741	+	0.154565i
$587$	2.65852e14	−	1.93153e14i	0.157446	−	0.114391i	−0.506273	−	0.862373i	$-0.668977\pi$
$587$	2.65852e14	−	1.93153e14i	0.157446	−	0.114391i	0.663719	+	0.747982i	$0.268977\pi$
$588$	2.71962e13	−	8.37012e13i	0.0159563	−	0.0491084i
$589$	−1.33457e14	+	4.10739e14i	−0.0775724	+	0.238743i
$590$	1.36760e14	−	9.93621e13i	0.0787542	−	0.0572183i
$591$	1.18769e15	+	8.62904e14i	0.677595	+	0.492302i
$592$	−3.71083e13	−	1.14208e14i	−0.0209750	−	0.0645543i
$593$	1.56804e15			0.878123			0.439061	−	0.898457i	$-0.355311\pi$
$593$	1.56804e15			0.878123			0.439061	+	0.898457i	$0.355311\pi$
$594$	9.52219e14	+	1.82469e14i	0.528338	+	0.101242i
$595$	3.04936e14			0.167635
$596$	−3.81405e14	−	1.17384e15i	−0.207745	−	0.639375i
$597$	−7.10669e14	−	5.16331e14i	−0.383538	−	0.278657i
$598$	1.98897e15	−	1.44507e15i	1.06359	−	0.772740i
$599$	−7.03237e14	+	2.16434e15i	−0.372610	+	1.14678i	0.572467	+	0.819928i	$0.305986\pi$
$599$	−7.03237e14	+	2.16434e15i	−0.372610	+	1.14678i	−0.945077	+	0.326848i	$0.894014\pi$
$600$	−2.37972e14	+	7.32403e14i	−0.124938	+	0.384519i
$601$	1.28480e15	−	9.33465e14i	0.668386	−	0.485611i	−0.201098	−	0.979571i	$-0.564451\pi$
$601$	1.28480e15	−	9.33465e14i	0.668386	−	0.485611i	0.869485	+	0.493960i	$0.164451\pi$
$602$	2.07601e14	+	1.50831e14i	0.107016	+	0.0777517i
$603$	−1.83450e14	−	5.64600e14i	−0.0937069	−	0.288400i
$604$	−3.75979e14			−0.190310
$605$	1.47833e14	−	1.78094e14i	0.0741512	−	0.0893296i
$606$	−1.14754e15			−0.570386
$607$	−1.51118e14	−	4.65093e14i	−0.0744352	−	0.229088i	0.906916	−	0.421312i	$-0.138430\pi$
$607$	−1.51118e14	−	4.65093e14i	−0.0744352	−	0.229088i	−0.981351	+	0.192224i	$0.938430\pi$
$608$	6.43016e13	+	4.67178e13i	0.0313871	+	0.0228041i
$609$	−1.49082e15	+	1.08315e15i	−0.721159	+	0.523953i
$610$	−5.47136e13	+	1.68391e14i	−0.0262290	+	0.0807245i
$611$	−7.39972e14	+	2.27740e15i	−0.351551	+	1.08196i
$612$	4.08553e14	−	2.96831e14i	0.192360	−	0.139758i
$613$	1.12306e15	+	8.15950e14i	0.524047	+	0.380742i	0.818126	−	0.575039i	$-0.195013\pi$
$613$	1.12306e15	+	8.15950e14i	0.524047	+	0.380742i	−0.294079	+	0.955781i	$0.595013\pi$
$614$	7.67902e14	+	2.36336e15i	0.355124	+	1.09296i
$615$	1.70614e14			0.0781989
$616$	7.97719e14	+	1.52863e14i	0.362373	+	0.0694396i
$617$	−2.48142e15			−1.11720			−0.558601	−	0.829436i	$-0.688662\pi$
$617$	−2.48142e15			−1.11720			−0.558601	+	0.829436i	$0.688662\pi$
$618$	8.20371e13	+	2.52484e14i	0.0366078	+	0.112667i
$619$	2.19289e15	+	1.59323e15i	0.969881	+	0.704660i	0.955425	−	0.295235i	$-0.0953981\pi$
$619$	2.19289e15	+	1.59323e15i	0.969881	+	0.704660i	0.0144569	+	0.999895i	$0.495398\pi$
$620$	−1.22533e14	+	8.90255e13i	−0.0537154	+	0.0390266i
$621$	5.68264e14	−	1.74894e15i	0.246915	−	0.759925i
$622$	1.18975e14	−	3.66168e14i	0.0512400	−	0.157700i
$623$	−2.71200e15	+	1.97038e15i	−1.15772	+	0.841135i
$624$	−9.80811e14	−	7.12601e14i	−0.415021	−	0.301530i
$625$	7.07097e14	+	2.17622e15i	0.296578	+	0.912774i
$626$	−2.35296e15			−0.978262
$627$	7.68565e13	+	6.12489e14i	0.0316745	+	0.252422i
$628$	−1.92017e15			−0.784442
$629$	2.86654e14	+	8.82230e14i	0.116086	+	0.357276i
$630$	5.93381e13	+	4.31116e13i	0.0238210	+	0.0173070i
$631$	2.48274e15	−	1.80382e15i	0.988030	−	0.717846i	0.0285413	−	0.999593i	$-0.490914\pi$
$631$	2.48274e15	−	1.80382e15i	0.988030	−	0.717846i	0.959489	+	0.281747i	$0.0909138\pi$
$632$	−1.67588e14	+	5.15782e14i	−0.0661147	+	0.203480i
$633$	−1.16393e15	+	3.58220e15i	−0.455203	+	1.40097i
$634$	7.80195e14	−	5.66845e14i	0.302491	−	0.219772i
$635$	1.19521e14	+	8.68374e13i	0.0459399	+	0.0333773i
$636$	3.92407e14	+	1.20771e15i	0.149528	+	0.460200i
$637$	4.17464e14			0.157707
$638$	−9.51497e14	−	1.01494e15i	−0.356364	−	0.380124i
$639$	−1.00063e15			−0.371553
$640$	8.61356e12	+	2.65098e13i	0.00317098	+	0.00975926i
$641$	3.13336e15	+	2.27652e15i	1.14364	+	0.830905i	0.987623	−	0.156849i	$-0.0501335\pi$
$641$	3.13336e15	+	2.27652e15i	1.14364	+	0.830905i	0.156020	+	0.987754i	$0.450133\pi$
$642$	−1.01601e15	+	7.38174e14i	−0.367667	+	0.267126i
$643$	1.55790e15	−	4.79473e15i	0.558958	−	1.72030i	−0.126296	−	0.991993i	$-0.540309\pi$
$643$	1.55790e15	−	4.79473e15i	0.558958	−	1.72030i	0.685254	−	0.728304i	$-0.259691\pi$
$644$	4.76062e14	−	1.46517e15i	0.169352	−	0.521213i
$645$	−5.53320e13	+	4.02010e13i	−0.0195163	+	0.0141794i
$646$	−4.96716e14	−	3.60886e14i	−0.173712	−	0.126209i
$647$	−6.64093e14	−	2.04387e15i	−0.230280	−	0.708728i	−0.997713	−	0.0675986i	$-0.978466\pi$
$647$	−6.64093e14	−	2.04387e15i	−0.230280	−	0.708728i	0.767433	−	0.641129i	$-0.221534\pi$
$648$	−1.26024e15			−0.433304
$649$	−3.14845e15	+	1.47834e15i	−1.07337	+	0.503999i
$650$	−3.65290e15			−1.23485
$651$	−1.27560e15	−	3.92590e15i	−0.427583	−	1.31596i
$652$	1.11247e15	+	8.08254e14i	0.369764	+	0.268650i
$653$	3.34118e15	−	2.42751e15i	1.10123	−	0.800090i	0.119970	−	0.992778i	$-0.461720\pi$
$653$	3.34118e15	−	2.42751e15i	1.10123	−	0.800090i	0.981260	+	0.192687i	$0.0617202\pi$
$654$	−1.10829e15	+	3.41095e15i	−0.362221	+	1.11480i
$655$	4.94556e13	−	1.52209e14i	0.0160283	−	0.0493301i
$656$	−3.65682e14	+	2.65684e14i	−0.117526	+	0.0853874i
$657$	−1.44690e15	−	1.05123e15i	−0.461135	−	0.335034i
$658$	4.63688e14	+	1.42708e15i	0.146549	+	0.451032i
$659$	−4.41788e15			−1.38466			−0.692332	−	0.721580i	$-0.743416\pi$
$659$	−4.41788e15			−1.38466			−0.692332	+	0.721580i	$0.743416\pi$
$660$	−1.04450e14	+	1.89620e14i	−0.0324652	+	0.0589376i
$661$	−3.03714e14			−0.0936176			−0.0468088	−	0.998904i	$-0.514905\pi$
$661$	−3.03714e14			−0.0936176			−0.0468088	+	0.998904i	$0.514905\pi$
$662$	−4.20195e14	−	1.29323e15i	−0.128449	−	0.395327i
$663$	7.57656e15	+	5.50470e15i	2.29693	+	1.66882i
$664$	−1.32321e15	+	9.61369e14i	−0.397836	+	0.289045i
$665$	2.75561e13	−	8.48090e13i	0.00821673	−	0.0252885i
$666$	−6.89485e13	+	2.12202e14i	−0.0203900	+	0.0627539i
$667$	−2.13476e15	+	1.55099e15i	−0.626118	+	0.454901i
$668$	−2.37666e15	−	1.72675e15i	−0.691348	−	0.502294i
$669$	−1.42284e15	−	4.37904e15i	−0.410499	−	1.26339i
$670$	−2.53123e14			−0.0724302
$671$	1.75774e15	−	3.19102e15i	0.498863	−	0.905639i
$672$	−7.59693e14			−0.213849
$673$	1.51320e15	+	4.65716e15i	0.422488	+	1.30028i	0.905379	+	0.424604i	$0.139587\pi$
$673$	1.51320e15	+	4.65716e15i	0.422488	+	1.30028i	−0.482892	+	0.875680i	$0.660413\pi$
$674$	1.42491e15	+	1.03526e15i	0.394601	+	0.286694i
$675$	−2.21051e15	+	1.60603e15i	−0.607186	+	0.441146i
$676$	1.20997e15	−	3.72390e15i	0.329661	−	1.01459i
$677$	3.26539e14	−	1.00498e15i	0.0882465	−	0.271595i	−0.897188	−	0.441648i	$-0.854394\pi$
$677$	3.26539e14	−	1.00498e15i	0.0882465	−	0.271595i	0.985435	+	0.170053i	$0.0543940\pi$
$678$	1.99846e15	−	1.45197e15i	0.535714	−	0.389219i
$679$	1.99009e15	+	1.44589e15i	0.529163	+	0.384460i
$680$	−6.65380e13	−	2.04783e14i	−0.0175497	−	0.0540125i
$681$	6.73125e15			1.76111
$682$	2.82092e15	−	1.32455e15i	0.732111	−	0.343760i
$683$	6.05665e15			1.55926			0.779630	−	0.626240i	$-0.215407\pi$
$683$	6.05665e15			1.55926			0.779630	+	0.626240i	$0.215407\pi$
$684$	−4.56353e13	−	1.40451e14i	−0.0116545	−	0.0358687i
$685$	−5.23503e14	−	3.80347e14i	−0.132624	−	0.0963568i
$686$	−2.16388e15	+	1.57215e15i	−0.543813	+	0.395104i
$687$	−1.94992e15	+	6.00125e15i	−0.486134	+	1.49617i
$688$	5.59929e13	−	1.72329e14i	0.0138483	−	0.0426207i
$689$	−4.87311e15	+	3.54052e15i	−1.19564	+	0.868684i
$690$	3.32189e14	+	2.41349e14i	0.0808566	+	0.0587457i
$691$	−1.47690e15	−	4.54543e15i	−0.356633	−	1.09760i	−0.955057	−	0.296423i	$-0.904206\pi$
$691$	−1.47690e15	−	4.54543e15i	−0.356633	−	1.09760i	0.598424	−	0.801180i	$-0.295794\pi$
$692$	3.53082e15			0.845848
$693$	−1.03217e15	−	1.10099e15i	−0.245313	−	0.261668i
$694$	−4.30955e15			−1.01614
$695$	−2.73419e14	−	8.41498e14i	−0.0639607	−	0.196851i
$696$	1.05270e15	+	7.64832e14i	0.244317	+	0.177507i
$697$	2.82482e15	−	2.05235e15i	0.650445	−	0.472576i
$698$	−1.28843e13	+	3.96538e13i	−0.00294345	+	0.00905899i
$699$	−6.78892e14	+	2.08941e15i	−0.153878	+	0.473587i
$700$	−1.85185e15	+	1.34545e15i	−0.416453	+	0.302571i
$701$	4.29162e15	+	3.11804e15i	0.957573	+	0.695717i	0.952586	−	0.304270i	$-0.0984126\pi$
$701$	4.29162e15	+	3.11804e15i	0.957573	+	0.695717i	0.00498690	+	0.999988i	$0.498413\pi$
$702$	−1.32923e15	−	4.09096e15i	−0.294271	−	0.905672i
$703$	2.71271e14			0.0595866
$704$	−7.14085e13	−	5.69072e14i	−0.0155632	−	0.124027i
$705$	−3.99935e14			−0.0864867
$706$	1.39392e15	+	4.29005e15i	0.299097	+	0.920526i
$707$	−2.75950e15	−	2.00489e15i	−0.587522	−	0.426859i
$708$	2.63194e15	−	1.91222e15i	0.556024	−	0.403975i
$709$	2.46254e15	−	7.57892e15i	0.516213	−	1.58874i	−0.264850	−	0.964290i	$-0.585322\pi$
$709$	2.46254e15	−	7.57892e15i	0.516213	−	1.58874i	0.781063	−	0.624452i	$-0.214678\pi$
$710$	−1.31842e14	+	4.05768e14i	−0.0274242	+	0.0844029i
$711$	8.15214e14	−	5.92288e14i	0.168263	−	0.122250i
$712$	1.91500e15	+	1.39133e15i	0.392218	+	0.284963i
$713$	−1.82658e15	−	5.62162e15i	−0.371232	−	1.14253i
$714$	5.86847e15			1.18354
$715$	−1.00853e15	−	1.93260e14i	−0.201840	−	0.0386775i
$716$	1.53746e15			0.305339
$717$	−1.62429e15	−	4.99906e15i	−0.320117	−	0.985219i
$718$	−1.25427e15	−	9.11281e14i	−0.245305	−	0.178225i
$719$	−5.40547e15	+	3.92730e15i	−1.04912	+	0.762229i	−0.972045	−	0.234796i	$-0.924558\pi$
$719$	−5.40547e15	+	3.92730e15i	−1.04912	+	0.762229i	−0.0770740	+	0.997025i	$0.524558\pi$
$720$	1.60043e13	−	4.92562e13i	0.00308254	−	0.00948707i
$721$	−2.43845e14	+	7.50479e14i	−0.0466091	+	0.143448i
$722$	2.87051e15	−	2.08555e15i	0.544508	−	0.395608i
$723$	−5.40826e15	−	3.92933e15i	−1.01812	−	0.739704i
$724$	−1.36795e15	−	4.21013e15i	−0.255570	−	0.786563i
$725$	3.92064e15			0.726939
$726$	2.84504e15	−	3.42741e15i	0.523525	−	0.630689i
$727$	−7.54614e15			−1.37811			−0.689057	−	0.724707i	$-0.741975\pi$
$727$	−7.54614e15			−1.37811			−0.689057	+	0.724707i	$0.741975\pi$
$728$	−1.11356e15	−	3.42719e15i	−0.201833	−	0.621177i
$729$	−2.07174e15	−	1.50521e15i	−0.372679	−	0.270767i
$730$	−6.16927e14	+	4.48224e14i	−0.110143	+	0.0800238i
$731$	−4.32534e14	+	1.33120e15i	−0.0766434	+	0.235884i
$732$	−1.05296e15	+	3.24068e15i	−0.185183	+	0.569934i
$733$	4.38404e15	−	3.18519e15i	0.765248	−	0.555985i	−0.135267	−	0.990809i	$-0.543189\pi$
$733$	4.38404e15	−	3.18519e15i	0.765248	−	0.555985i	0.900516	+	0.434824i	$0.143189\pi$
$734$	9.35979e14	+	6.80029e14i	0.162158	+	0.117815i
$735$	2.15456e13	+	6.63105e13i	0.00370491	+	0.0114025i
$736$	−1.08783e15			−0.185666
$737$	5.11516e15	+	9.80191e14i	0.866539	+	0.166050i
$738$	8.39848e14			0.141218
$739$	−1.20843e14	−	3.71916e14i	−0.0201686	−	0.0620727i	0.940466	−	0.339889i	$-0.110389\pi$
$739$	−1.20843e14	−	3.71916e14i	−0.0201686	−	0.0620727i	−0.960634	+	0.277816i	$0.910389\pi$
$740$	7.69656e13	+	5.59188e13i	0.0127504	+	0.00926368i
$741$	2.21564e15	−	1.60976e15i	0.364334	−	0.264704i
$742$	−1.16638e15	+	3.58976e15i	−0.190379	+	0.585927i
$743$	−3.08277e15	+	9.48780e15i	−0.499463	+	1.53719i	0.310422	+	0.950599i	$0.399530\pi$
$743$	−3.08277e15	+	9.48780e15i	−0.499463	+	1.53719i	−0.809884	+	0.586590i	$0.800470\pi$
$744$	−2.35814e15	+	1.71329e15i	−0.379244	+	0.275537i
$745$	7.91064e14	+	5.74742e14i	0.126285	+	0.0917515i
$746$	9.19795e14	+	2.83084e15i	0.145756	+	0.448592i
$747$	3.03896e15			0.478038
$748$	5.51616e14	+	4.39596e15i	0.0861347	+	0.686428i
$749$	−3.73288e15			−0.578621
$750$	−3.79632e14	−	1.16839e15i	−0.0584152	−	0.179784i
$751$	−6.49890e15	−	4.72173e15i	−0.992705	−	0.721243i	−0.0321934	−	0.999482i	$-0.510249\pi$
$751$	−6.49890e15	−	4.72173e15i	−0.992705	−	0.721243i	−0.960512	+	0.278239i	$0.910249\pi$
$752$	8.57195e14	−	6.22789e14i	0.129981	−	0.0944371i
$753$	−2.05667e15	+	6.32977e15i	−0.309593	+	0.952830i
$754$	−1.90732e15	+	5.87013e15i	−0.285024	+	0.877213i
$755$	2.40975e14	−	1.75079e14i	0.0357490	−	0.0259732i
$756$	−2.18065e15	−	1.58434e15i	−0.321157	−	0.233334i
$757$	1.69324e14	+	5.21124e14i	0.0247565	+	0.0761928i	0.962671	−	0.270673i	$-0.0872461\pi$
$757$	1.69324e14	+	5.21124e14i	0.0247565	+	0.0761928i	−0.937915	+	0.346865i	$0.887246\pi$
$758$	−2.19981e15			−0.319305
$759$	−5.77836e15	−	6.16361e15i	−0.832673	−	0.888190i
$760$	−6.29672e13			−0.00900823
$761$	2.89014e15	+	8.89494e15i	0.410491	+	1.26336i	0.916222	+	0.400670i	$0.131223\pi$
$761$	2.89014e15	+	8.89494e15i	0.410491	+	1.26336i	−0.505731	+	0.862691i	$0.668777\pi$
$762$	2.30018e15	+	1.67118e15i	0.324347	+	0.235652i
$763$	−8.62445e15	+	6.26603e15i	−1.20739	+	0.877218i
$764$	1.19325e15	−	3.67245e15i	0.165851	−	0.510438i
$765$	−1.23630e14	+	3.80494e14i	−0.0170603	+	0.0525061i
$766$	−2.45155e15	+	1.78115e15i	−0.335878	+	0.244030i
$767$	1.24845e16	+	9.07050e15i	1.69823	+	1.23383i
$768$	1.65767e14	+	5.10180e14i	0.0223878	+	0.0689027i
$769$	−3.53525e14			−0.0474051			−0.0237026	−	0.999719i	$-0.507545\pi$
$769$	−3.53525e14			−0.0474051			−0.0237026	+	0.999719i	$0.507545\pi$
$770$	−5.82462e14	+	2.73493e14i	−0.0775476	+	0.0364122i
$771$	4.30469e15			0.569040
$772$	7.81757e14	+	2.40600e15i	0.102607	+	0.315792i
$773$	−3.38158e14	−	2.45686e14i	−0.0440689	−	0.0320179i	0.565533	−	0.824726i	$-0.308671\pi$
$773$	−3.38158e14	−	2.45686e14i	−0.0440689	−	0.0320179i	−0.609602	+	0.792708i	$0.708671\pi$
$774$	−2.72372e14	+	1.97890e14i	−0.0352442	+	0.0256064i
$775$	−2.71397e15	+	8.35273e15i	−0.348694	+	1.07317i
$776$	5.36756e14	−	1.65197e15i	0.0684759	−	0.210747i
$777$	−2.09766e15	+	1.52404e15i	−0.265717	+	0.193054i
$778$	5.76797e15	+	4.19068e15i	0.725496	+	0.527104i
$779$	−3.15532e14	−	9.71106e14i	−0.0394082	−	0.121286i
$780$	9.60458e14			0.119113
$781$	4.23559e15	−	7.68932e15i	0.521595	−	0.946907i
$782$	8.40325e15			1.02757
$783$	1.42666e15	+	4.39081e15i	0.173233	+	0.533157i
$784$	−1.49440e14	−	1.08574e14i	−0.0180189	−	0.0130915i
$785$	1.23068e15	−	8.94145e14i	0.147355	−	0.107059i
$786$	9.51769e14	−	2.92925e15i	0.113164	−	0.348283i
$787$	−1.00279e15	+	3.08627e15i	−0.118399	+	0.364396i	−0.992641	−	0.121095i	$-0.961359\pi$
$787$	−1.00279e15	+	3.08627e15i	−0.118399	+	0.364396i	0.874241	+	0.485491i	$0.161359\pi$
$788$	2.49278e15	−	1.81111e15i	0.292274	−	0.212350i
$789$	−6.39237e15	−	4.64433e15i	−0.744283	−	0.540753i
$790$	−1.32768e14	−	4.08617e14i	−0.0153513	−	0.0472463i
$791$	7.34248e15			0.843087
$792$	−5.14158e14	+	9.33406e14i	−0.0586285	+	0.106434i
$793$	−1.61631e16			−1.83029
$794$	−7.17062e14	−	2.20689e15i	−0.0806388	−	0.248181i
$795$	−8.13885e14	−	5.91322e14i	−0.0908958	−	0.0660396i
$796$	−1.49159e15	+	1.08371e15i	−0.165435	+	0.120196i
$797$	2.84745e15	−	8.76354e15i	0.313643	−	0.965293i	−0.662667	−	0.748914i	$-0.730576\pi$
$797$	2.84745e15	−	8.76354e15i	0.313643	−	0.965293i	0.976310	−	0.216378i	$-0.0694245\pi$
$798$	5.30316e14	−	1.63214e15i	0.0580121	−	0.178543i
$799$	−6.62166e15	+	4.81091e15i	−0.719382	+	0.522661i
$800$	1.30763e15	+	9.50048e14i	0.141088	+	0.102506i
$801$	−1.35909e15	−	4.18283e15i	−0.145636	−	0.448221i
$802$	5.63974e15			0.600206
$803$	1.42027e16	−	6.66883e15i	1.50119	−	0.704878i
$804$	−4.87133e15			−0.511374
$805$	3.77150e14	+	1.16075e15i	0.0393221	+	0.121021i
$806$	−1.11857e16	−	8.12690e15i	−1.15830	−	0.841554i
$807$	−6.57045e15	+	4.77371e15i	−0.675757	+	0.490966i
$808$	−7.44276e14	+	2.29065e15i	−0.0760277	+	0.233989i
$809$	1.26896e15	−	3.90546e15i	0.128745	−	0.396237i	−0.865820	−	0.500356i	$-0.833202\pi$
$809$	1.26896e15	−	3.90546e15i	0.128745	−	0.396237i	0.994565	+	0.104119i	$0.0332024\pi$
$810$	8.07724e14	−	5.86846e14i	0.0813946	−	0.0591366i
$811$	−6.18870e15	−	4.49635e15i	−0.619419	−	0.450034i	0.233299	−	0.972405i	$-0.425048\pi$
$811$	−6.18870e15	−	4.49635e15i	−0.619419	−	0.450034i	−0.852719	+	0.522371i	$0.825048\pi$
$812$	1.19518e15	+	3.67839e15i	0.118816	+	0.365679i
$813$	1.61811e16			1.59776
$814$	−1.33880e15	−	1.42806e15i	−0.131305	−	0.140060i
$815$	−1.08938e15			−0.106124
$816$	−1.28052e15	−	3.94103e15i	−0.123905	−	0.381342i
$817$	3.31148e14	+	2.40593e14i	0.0318274	+	0.0231240i
$818$	−4.58969e15	+	3.33461e15i	−0.438168	+	0.318347i
$819$	−2.06904e15	+	6.36785e15i	−0.196204	+	0.603853i
$820$	1.10657e14	−	3.40568e14i	0.0104233	−	0.0320795i
$821$	1.15731e15	−	8.40832e14i	0.108283	−	0.0786723i	−0.532326	−	0.846539i	$-0.678682\pi$
$821$	1.15731e15	−	8.40832e14i	0.108283	−	0.0786723i	0.640609	+	0.767867i	$0.278682\pi$
$822$	−1.00748e16	−	7.31976e15i	−0.936355	−	0.680302i
$823$	−1.35447e15	−	4.16863e15i	−0.125046	−	0.384852i	0.868863	−	0.495052i	$-0.164851\pi$
$823$	−1.35447e15	−	4.16863e15i	−0.125046	−	0.384852i	−0.993909	+	0.110200i	$0.964851\pi$
$824$	5.57200e14			0.0510989
$825$	1.56294e15	+	1.24555e16i	0.142379	+	1.13466i
$826$	9.66992e15			0.875049
$827$	−3.12433e15	−	9.61570e15i	−0.280851	−	0.864372i	−0.987612	−	0.156918i	$-0.949844\pi$
$827$	−3.12433e15	−	9.61570e15i	−0.280851	−	0.864372i	0.706760	−	0.707453i	$-0.250156\pi$
$828$	1.63520e15	+	1.18805e15i	0.146018	+	0.106088i
$829$	5.48853e15	−	3.98765e15i	0.486862	−	0.353726i	−0.317114	−	0.948387i	$-0.602714\pi$
$829$	5.48853e15	−	3.98765e15i	0.486862	−	0.353726i	0.803976	+	0.594661i	$0.202714\pi$
$830$	4.00409e14	−	1.23233e15i	0.0352838	−	0.108592i
$831$	5.14601e15	−	1.58378e16i	0.450470	−	1.38640i
$832$	−2.05858e15	+	1.49565e15i	−0.179015	+	0.130062i
$833$	1.15439e15	+	8.38714e14i	0.0997253	+	0.0724547i
$834$	−5.26194e15	−	1.61946e16i	−0.451578	−	1.38981i
$835$	2.32734e15			0.198420
$836$	1.27246e15	+	2.43834e14i	0.107773	+	0.0206519i
$837$	−1.03420e16			−0.870188
$838$	2.15223e15	+	6.62389e15i	0.179907	+	0.553696i
$839$	2.45004e15	+	1.78006e15i	0.203462	+	0.147824i	0.684851	−	0.728684i	$-0.259867\pi$
$839$	2.45004e15	+	1.78006e15i	0.203462	+	0.147824i	−0.481389	+	0.876507i	$0.659867\pi$
$840$	4.86907e14	−	3.53759e14i	0.0401708	−	0.0291858i
$841$	−1.72305e15	+	5.30299e15i	−0.141227	+	0.434653i
$842$	−2.75644e14	+	8.48344e14i	−0.0224456	+	0.0690805i
$843$	1.08106e16	−	7.85435e15i	0.874576	−	0.635417i
$844$	6.39564e15	+	4.64670e15i	0.514044	+	0.373475i
$845$	9.58572e14	+	2.95018e15i	0.0765443	+	0.235579i
$846$	−1.96868e15			−0.156185
$847$	1.28296e16	−	3.27128e15i	1.01124	−	0.257845i
$848$	2.66525e15			0.208718
$849$	3.76819e15	+	1.15973e16i	0.293184	+	0.902328i
$850$	−1.01012e16	−	7.33892e15i	−0.780849	−	0.567320i
$851$	−3.00370e15	+	2.18232e15i	−0.230698	+	0.167612i
$852$	−2.53729e15	+	7.80899e15i	−0.193621	+	0.595905i
$853$	4.68955e15	−	1.44330e16i	0.355559	−	1.09430i	−0.600126	−	0.799906i	$-0.704883\pi$
$853$	4.68955e15	−	1.44330e16i	0.355559	−	1.09430i	0.955685	−	0.294392i	$-0.0951172\pi$
$854$	−8.19391e15	+	5.95323e15i	−0.617267	+	0.448471i
$855$	9.46512e13	+	6.87682e13i	0.00708456	+	0.00514723i
$856$	8.14527e14	+	2.50686e15i	0.0605759	+	0.186433i
$857$	−7.83077e15			−0.578642			−0.289321	−	0.957232i	$-0.593430\pi$
$857$	−7.83077e15			−0.578642			−0.289321	+	0.957232i	$0.593430\pi$
$858$	−1.94092e16	−	3.71927e15i	−1.42504	−	0.273072i
$859$	1.92536e16			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$859$	1.92536e16			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$860$	4.43592e13	+	1.36524e14i	0.00321545	+	0.00989615i
$861$	7.89573e15	+	5.73658e15i	0.568689	+	0.413177i
$862$	3.11339e15	−	2.26201e15i	0.222815	−	0.161884i
$863$	6.77173e15	−	2.08412e16i	0.481549	−	1.48206i	−0.355369	−	0.934726i	$-0.615645\pi$
$863$	6.77173e15	−	2.08412e16i	0.481549	−	1.48206i	0.836918	−	0.547329i	$-0.184355\pi$
$864$	−5.88153e14	+	1.81015e15i	−0.0415590	+	0.127905i
$865$	−2.26300e15	+	1.64416e15i	−0.158890	+	0.115440i
$866$	1.04203e16	+	7.57083e15i	0.726999	+	0.528196i
$867$	4.72476e15	+	1.45413e16i	0.327548	+	1.00809i
$868$	−8.66396e15			−0.596840
$869$	1.10068e15	+	8.77157e15i	0.0753444	+	0.600438i
$870$	−1.03086e15			−0.0701200
$871$	−7.14042e15	−	2.19760e16i	−0.482641	−	1.48542i
$872$	6.08990e15	+	4.42457e15i	0.409043	+	0.297187i
$873$	−2.61100e15	+	1.89700e15i	−0.174272	+	0.126616i
$874$	7.59375e14	−	2.33712e15i	0.0503667	−	0.155013i
$875$	1.12841e15	−	3.47289e15i	0.0743743	−	0.228901i
$876$	−1.18727e16	+	8.62603e15i	−0.777638	+	0.564987i
$877$	−1.33852e16	−	9.72489e15i	−0.871216	−	0.632976i	0.0596969	−	0.998217i	$-0.480987\pi$
$877$	−1.33852e16	−	9.72489e15i	−0.871216	−	0.632976i	−0.930913	+	0.365241i	$0.880987\pi$
$878$	−4.75537e15	−	1.46355e16i	−0.307585	−	0.946648i
$879$	−6.70651e15			−0.431080
$880$	3.10762e14	+	3.31481e14i	0.0198506	+	0.0211741i
$881$	5.06694e15			0.321646			0.160823	−	0.986983i	$-0.448585\pi$
$881$	5.06694e15			0.321646			0.160823	+	0.986983i	$0.448585\pi$
$882$	1.06058e14	+	3.26414e14i	0.00669064	+	0.0205917i
$883$	1.38977e16	+	1.00973e16i	0.871283	+	0.633024i	0.930931	−	0.365195i	$-0.118998\pi$
$883$	1.38977e16	+	1.00973e16i	0.871283	+	0.633024i	−0.0596478	+	0.998219i	$0.518998\pi$
$884$	1.59021e16	−	1.15536e16i	0.990759	−	0.719828i
$885$	−7.96437e14	+	2.45118e15i	−0.0493132	+	0.151771i
$886$	−1.63280e15	+	5.02525e15i	−0.100473	+	0.309223i
$887$	4.55762e15	−	3.31131e15i	0.278714	−	0.202497i	−0.439642	−	0.898173i	$-0.644895\pi$
$887$	4.55762e15	−	3.31131e15i	0.278714	−	0.202497i	0.718356	+	0.695676i	$0.244895\pi$
$888$	1.48120e15	+	1.07615e15i	0.0900206	+	0.0654038i
$889$	2.61150e15	+	8.03739e15i	0.157736	+	0.485462i
$890$	−1.87526e15			−0.112568
$891$	−1.85952e16	+	8.73130e15i	−1.10936	+	0.520897i
$892$	−9.66398e15			−0.572993
$893$	7.39637e14	+	2.27637e15i	0.0435848	+	0.134140i
$894$	1.52240e16	+	1.10609e16i	0.891604	+	0.647788i
$895$	−9.85398e14	+	7.15934e14i	−0.0573568	+	0.0416722i
$896$	−4.92724e14	+	1.51645e15i	−0.0285042	+	0.0877270i
$897$	−1.15830e16	+	3.56488e16i	−0.665981	+	2.04968i
$898$	−7.95893e15	+	5.78250e15i	−0.454815	+	0.330442i
$899$	1.20056e16	+	8.72257e15i	0.681875	+	0.495411i
$900$	−9.28033e14	−	2.85619e15i	−0.0523877	−	0.161233i
$901$	−2.05885e16			−1.15515
$902$	−3.55500e15	+	6.45376e15i	−0.198246	+	0.359896i
$903$	−3.91236e15			−0.216848
$904$	−1.60215e15	−	4.93092e15i	−0.0882628	−	0.271645i
$905$	2.83725e15	+	2.06138e15i	0.155357	+	0.112873i
$906$	4.63755e15	−	3.36937e15i	0.252396	−	0.183377i
$907$	−5.89206e14	+	1.81339e15i	−0.0318733	+	0.0980959i	−0.965728	−	0.259558i	$-0.916423\pi$
$907$	−5.89206e14	+	1.81339e15i	−0.0318733	+	0.0980959i	0.933854	+	0.357654i	$0.116423\pi$
$908$	4.36578e15	−	1.34365e16i	0.234741	−	0.722459i
$909$	3.62046e15	−	2.63042e15i	0.193492	−	0.140580i
$910$	2.30962e15	+	1.67804e15i	0.122691	+	0.0891402i
$911$	8.42415e15	+	2.59269e16i	0.444811	+	1.36899i	0.882691	+	0.469953i	$0.155729\pi$
$911$	8.42415e15	+	2.59269e16i	0.444811	+	1.36899i	−0.437881	+	0.899033i	$0.644271\pi$
$912$	−1.21180e15			−0.0636003
$913$	−1.28637e16	+	2.33528e16i	−0.671081	+	1.21828i
$914$	8.50118e15			0.440834
$915$	−8.34185e14	−	2.56736e15i	−0.0429978	−	0.132334i
$916$	1.07146e16	+	7.78462e15i	0.548973	+	0.398852i
$917$	7.40647e15	−	5.38112e15i	0.377207	−	0.274057i
$918$	4.54336e15	−	1.39830e16i	0.230008	−	0.707891i
$919$	9.83702e15	−	3.02752e16i	0.495026	−	1.52353i	−0.321889	−	0.946777i	$-0.604318\pi$
$919$	9.83702e15	−	3.02752e16i	0.495026	−	1.52353i	0.816916	−	0.576757i	$-0.195682\pi$
$920$	6.97218e14	−	5.06558e14i	0.0348767	−	0.0253394i
$921$	−3.06512e16	−	2.22694e16i	−1.52412	−	1.10734i
$922$	4.14004e15	+	1.27417e16i	0.204637	+	0.629808i
$923$	−3.89477e16			−1.91370
$924$	−1.12094e16	+	5.26335e15i	−0.547505	+	0.257079i
$925$	5.51652e15			0.267846
$926$	7.92785e15	+	2.43994e16i	0.382644	+	1.17766i
$927$	−8.37573e14	−	6.08533e14i	−0.0401869	−	0.0291975i
$928$	2.20947e15	−	1.60527e15i	0.105384	−	0.0765658i
$929$	−8.47403e15	+	2.60804e16i	−0.401794	+	1.23659i	0.521749	+	0.853099i	$0.325280\pi$
$929$	−8.47403e15	+	2.60804e16i	−0.401794	+	1.23659i	−0.923543	+	0.383496i	$0.874720\pi$
$930$	7.13584e14	−	2.19619e15i	0.0336348	−	0.103517i
$931$	3.37583e14	−	2.45268e14i	0.0158182	−	0.0114926i
$932$	3.73043e15	+	2.71032e15i	0.173769	+	0.126250i
$933$	1.81394e15	+	5.58273e15i	0.0839989	+	0.258522i
$934$	1.82128e16			0.838436
$935$	−2.40057e15	−	2.56062e15i	−0.109863	−	0.117188i
$936$	4.72786e15			0.215104
$937$	−4.32579e15	−	1.33134e16i	−0.195658	−	0.602173i	−0.999968	−	0.00796381i	$-0.997465\pi$
$937$	−4.32579e15	−	1.33134e16i	−0.195658	−	0.602173i	0.804310	−	0.594209i	$-0.202535\pi$
$938$	−1.17141e16	−	8.51080e15i	−0.526737	−	0.382697i
$939$	2.90227e16	−	2.10863e16i	1.29741	−	0.942624i
$940$	−2.59391e14	+	7.98324e14i	−0.0115279	+	0.0354794i
$941$	−6.32718e15	+	1.94731e16i	−0.279555	+	0.860382i	0.708423	+	0.705788i	$0.249407\pi$
$941$	−6.32718e15	+	1.94731e16i	−0.279555	+	0.860382i	−0.987978	+	0.154594i	$0.950593\pi$
$942$	2.36844e16	−	1.72078e16i	1.04036	−	0.755865i
$943$	1.13061e16	+	8.21439e15i	0.493742	+	0.358725i
$944$	−2.11001e15	−	6.49393e15i	−0.0916090	−	0.281943i
$945$	2.13540e15			0.0921732
$946$	−3.67748e14	−	2.93068e15i	−0.0157815	−	0.125767i
$947$	−2.73034e16			−1.16491			−0.582454	−	0.812864i	$-0.697907\pi$
$947$	−2.73034e16			−1.16491			−0.582454	+	0.812864i	$0.697907\pi$
$948$	−2.55511e15	−	7.86381e15i	−0.108384	−	0.333570i
$949$	−5.63176e16	−	4.09171e16i	−2.37509	−	1.72560i
$950$	−2.95392e15	+	2.14615e15i	−0.123856	+	0.0899870i
$951$	−4.54354e15	+	1.39836e16i	−0.189410	+	0.582943i
$952$	3.80619e15	−	1.17142e16i	0.157756	−	0.485524i
$953$	9.52321e15	−	6.91901e15i	0.392439	−	0.285124i	−0.374015	−	0.927423i	$-0.622019\pi$
$953$	9.52321e15	−	6.91901e15i	0.392439	−	0.285124i	0.766454	+	0.642299i	$0.222019\pi$
$954$	−4.00636e15	−	2.91079e15i	−0.164147	−	0.119260i
$955$	9.45329e14	+	2.90942e15i	0.0385092	+	0.118519i
$956$	−1.10323e16			−0.446834
$957$	2.08318e16	+	3.99188e15i	0.838901	+	0.160754i
$958$	2.78739e16			1.11606
$959$	−1.14384e16	−	3.52037e16i	−0.455368	−	1.40148i
$960$	−3.43815e14	−	2.49796e14i	−0.0136092	−	0.00988768i
$961$	−6.33766e15	+	4.60458e15i	−0.249431	+	0.181222i
$962$	−2.68369e15	+	8.25954e15i	−0.105019	+	0.323216i
$963$	1.51342e15	−	4.65783e15i	0.0588864	−	0.181234i
$964$	−1.13512e16	+	8.24711e15i	−0.439154	+	0.319064i
$965$	−1.62143e15	−	1.17804e15i	−0.0623731	−	0.0453167i
$966$	7.25823e15	+	2.23385e16i	0.277624	+	0.854438i
$967$	7.37290e15			0.280409			0.140205	−	0.990123i	$-0.455224\pi$
$967$	7.37290e15			0.280409			0.140205	+	0.990123i	$0.455224\pi$
$968$	−4.99632e15	−	7.90204e15i	−0.188945	−	0.298831i
$969$	9.36090e15			0.351995
$970$	4.25234e14	+	1.30873e15i	0.0158995	+	0.0489336i
$971$	1.87553e16	+	1.36265e16i	0.697296	+	0.506615i	0.879050	−	0.476729i	$-0.158178\pi$
$971$	1.87553e16	+	1.36265e16i	0.697296	+	0.506615i	−0.181754	+	0.983344i	$0.558178\pi$
$972$	7.22027e15	−	5.24583e15i	0.266925	−	0.193932i
$973$	1.56405e16	−	4.81364e16i	0.574949	−	1.76951i
$974$	3.10344e15	−	9.55140e15i	0.113441	−	0.349135i
$975$	4.50570e16	−	3.27358e16i	1.63771	−	1.18987i
$976$	5.78589e15	+	4.20369e15i	0.209120	+	0.151935i
$977$	1.09159e16	+	3.35958e16i	0.392321	+	1.20744i	0.931029	+	0.364946i	$0.118913\pi$
$977$	1.09159e16	+	3.35958e16i	0.392321	+	1.20744i	−0.538708	+	0.842492i	$0.681087\pi$
$978$	−2.09651e16			−0.749260
$979$	3.78956e16	+	7.26173e15i	1.34674	+	0.258069i
$980$	1.46339e14			0.00517149
$981$	−4.32204e15	−	1.33019e16i	−0.151883	−	0.467448i
$982$	4.62451e15	+	3.35990e15i	0.161604	+	0.117412i
$983$	−6.87011e15	+	4.99143e15i	−0.238737	+	0.173452i	−0.700720	−	0.713436i	$-0.747138\pi$
$983$	−6.87011e15	+	4.99143e15i	−0.238737	+	0.173452i	0.461983	+	0.886889i	$0.347138\pi$
$984$	2.12959e15	−	6.55420e15i	0.0735906	−	0.226489i
$985$	−7.54327e14	+	2.32158e15i	−0.0259215	+	0.0797783i
$986$	−1.70677e16	+	1.24004e16i	−0.583246	+	0.423753i
$987$	−1.85084e16	−	1.34471e16i	−0.628961	−	0.456967i
$988$	−1.77626e15	−	5.46677e15i	−0.0600266	−	0.184743i
$989$	−5.60223e15			−0.188270
$990$	−1.05113e14	−	8.37668e14i	−0.00351286	−	0.0279949i
$991$	−8.46216e15			−0.281239			−0.140620	−	0.990064i	$-0.544909\pi$
$991$	−8.46216e15			−0.281239			−0.140620	+	0.990064i	$0.544909\pi$
$992$	1.89050e15	+	5.81837e15i	0.0624832	+	0.192304i
$993$	1.67723e16	+	1.21858e16i	0.551280	+	0.400528i
$994$	−1.97447e16	+	1.43454e16i	−0.645394	+	0.468906i
$995$	4.51363e14	−	1.38915e15i	0.0146723	−	0.0451568i
$996$	7.70585e15	−	2.37162e16i	0.249112	−	0.766687i
$997$	1.31581e16	−	9.55994e15i	0.423030	−	0.307349i	−0.355826	−	0.934552i	$-0.615800\pi$
$997$	1.31581e16	−	9.55994e15i	0.423030	−	0.307349i	0.778856	+	0.627203i	$0.215800\pi$
$998$	−2.45214e16	−	1.78158e16i	−0.784019	−	0.569623i
$999$	2.00738e15	+	6.17807e15i	0.0638291	+	0.196446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.5.2	✓	20
11.3	even	5		242.12.a.n.1.8		10
11.8	odd	10		242.12.a.m.1.8		10
11.9	even	5	inner	22.12.c.a.9.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.5.2	✓	20	1.1	even	1	trivial
22.12.c.a.9.2	yes	20	11.9	even	5	inner
242.12.a.m.1.8		10	11.8	odd	10
242.12.a.n.1.8		10	11.3	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)

\(f(q)\)	\(=\)	\(q+(9.88854 + 30.4338i) q^{2} +(-394.707 - 286.771i) q^{3} +(-828.433 + 601.892i) q^{4} +(250.688 - 771.537i) q^{5} +(4824.47 - 14848.2i) q^{6} +(37543.0 - 27276.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(18814.2 + 57904.3i) q^{9} +O(q^{10})\)	\(q+(9.88854 + 30.4338i) q^{2} +(-394.707 - 286.771i) q^{3} +(-828.433 + 601.892i) q^{4} +(250.688 - 771.537i) q^{5} +(4824.47 - 14848.2i) q^{6} +(37543.0 - 27276.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(18814.2 + 57904.3i) q^{9} +25959.8 q^{10} +(-524601. - 100526. i) q^{11} +499594. q^{12} +(732307. + 2.25381e6i) q^{13} +(1.20138e6 + 872850. i) q^{14} +(-320203. + 232641. i) q^{15} +(324028. - 997255. i) q^{16} +(-2.50305e6 + 7.70359e6i) q^{17} +(-1.57620e6 + 1.14518e6i) q^{18} +(1.91634e6 + 1.39230e6i) q^{19} +(256704. + 790054. i) q^{20} -2.26406e7 q^{21} +(-2.12814e6 - 1.69597e7i) q^{22} -3.24198e7 q^{23} +(4.94025e6 + 1.52045e7i) q^{24} +(3.89704e7 + 2.83136e7i) q^{25} +(-6.13506e7 + 4.45738e7i) q^{26} +(-1.75283e7 + 5.39466e7i) q^{27} +(-1.46843e7 + 4.51937e7i) q^{28} +(6.58473e7 - 4.78409e7i) q^{29} +(-1.02465e7 - 7.44451e6i) q^{30} +(5.63414e7 + 1.73401e8i) q^{31} +3.35544e7 q^{32} +(1.78235e8 + 1.90119e8i) q^{33} -2.59201e8 q^{34} +(-1.16333e7 - 3.58037e7i) q^{35} +(-5.04385e7 - 3.66457e7i) q^{36} +(9.26502e7 - 6.73143e7i) q^{37} +(-2.34232e7 + 7.20892e7i) q^{38} +(3.57281e8 - 1.09960e9i) q^{39} +(-2.15059e7 + 1.56250e7i) q^{40} +(-3.48742e8 - 2.53376e8i) q^{41} +(-2.23883e8 - 6.89040e8i) q^{42} +1.72803e8 q^{43} +(4.95103e8 - 2.32474e8i) q^{44} +4.93918e7 q^{45} +(-3.20585e8 - 9.86658e8i) q^{46} +(8.17485e8 + 5.93938e8i) q^{47} +(-4.13880e8 + 3.00701e8i) q^{48} +(5.44366e7 - 1.67539e8i) q^{49} +(-4.76331e8 + 1.46600e9i) q^{50} +(3.19714e9 - 2.32286e9i) q^{51} +(-1.96322e9 - 1.42636e9i) q^{52} +(7.85453e8 + 2.41738e9i) q^{53} -1.81513e9 q^{54} +(-2.09071e8 + 3.79548e8i) q^{55} -1.52062e9 q^{56} +(-3.57119e8 - 1.09910e9i) q^{57} +(2.10711e9 + 1.53091e9i) q^{58} +(5.26816e9 - 3.82755e9i) q^{59} +(1.25242e8 - 3.85455e8i) q^{60} +(-2.10763e9 + 6.48663e9i) q^{61} +(-4.72012e9 + 3.42937e9i) q^{62} +(2.28577e9 + 1.66071e9i) q^{63} +(3.31804e8 + 1.02119e9i) q^{64} +1.92248e9 q^{65} +(-4.02355e9 + 7.30438e9i) q^{66} -9.75058e9 q^{67} +(-2.56312e9 - 7.88848e9i) q^{68} +(1.27963e10 + 9.29706e9i) q^{69} +(9.74607e8 - 7.08093e8i) q^{70} +(-5.07871e9 + 1.56307e10i) q^{71} +(6.16505e8 - 1.89741e9i) q^{72} +(-2.37647e10 + 1.72661e10i) q^{73} +(2.96481e9 + 2.15406e9i) q^{74} +(-7.26233e9 - 2.23512e10i) q^{75} -2.42557e9 q^{76} +(-2.24371e10 + 1.05353e10i) q^{77} +3.69980e10 q^{78} +(-5.11437e9 - 1.57404e10i) q^{79} +(-6.88190e8 - 4.99999e8i) q^{80} +(3.11145e10 - 2.26060e10i) q^{81} +(4.26264e9 - 1.31191e10i) q^{82} +(1.54242e10 - 4.74709e10i) q^{83} +(1.87562e10 - 1.36272e10i) q^{84} +(5.31612e9 + 3.86239e9i) q^{85} +(1.70877e9 + 5.25905e9i) q^{86} -3.97098e10 q^{87} +(1.19709e10 + 1.27690e10i) q^{88} -7.22371e10 q^{89} +(4.88413e8 + 1.50318e9i) q^{90} +(8.89692e10 + 6.46399e10i) q^{91} +(2.68576e10 - 1.95132e10i) q^{92} +(2.74881e10 - 8.45996e10i) q^{93} +(-9.99205e9 + 3.07524e10i) q^{94} +(1.55461e9 - 1.12949e9i) q^{95} +(-1.32442e10 - 9.62245e9i) q^{96} +(1.63805e10 + 5.04140e10i) q^{97} +5.63713e9 q^{98} +(-4.04906e9 - 3.22680e10i) 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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