LMFDB - Embedded newform 22.12.c.a.3.1

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			3.1
Root			$180.810 - 556.477i$ of defining polynomial
Character	$\chi$	$=$	22.3
Dual form			22.12.c.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.8885 + 18.8091i) q^{2} +(-176.692 - 543.803i) q^{3} +(316.433 - 973.882i) q^{4} +(3174.43 + 2306.36i) q^{5} +(14802.8 + 10754.8i) q^{6} +(-18336.8 + 56434.7i) q^{7} +(10125.9 + 31164.2i) q^{8} +(-121186. + 88047.0i) q^{9} +O(q^{10})$	\(q+(-25.8885 + 18.8091i) q^{2} +(-176.692 - 543.803i) q^{3} +(316.433 - 973.882i) q^{4} +(3174.43 + 2306.36i) q^{5} +(14802.8 + 10754.8i) q^{6} +(-18336.8 + 56434.7i) q^{7} +(10125.9 + 31164.2i) q^{8} +(-121186. + 88047.0i) q^{9} -125562. q^{10} +(393586. - 361112. i) q^{11} -585511. q^{12} +(-263363. + 191345. i) q^{13} +(-586776. - 1.80591e6i) q^{14} +(693306. - 2.13378e6i) q^{15} +(-848316. - 616338. i) q^{16} +(4.44099e6 + 3.22657e6i) q^{17} +(1.48125e6 - 4.55882e6i) q^{18} +(-378806. - 1.16584e6i) q^{19} +(3.25061e6 - 2.36171e6i) q^{20} +3.39293e7 q^{21} +(-3.39718e6 + 1.67517e7i) q^{22} +3.88448e7 q^{23} +(1.51580e7 - 1.10129e7i) q^{24} +(-1.03310e7 - 3.17956e7i) q^{25} +(3.21907e6 - 9.90727e6i) q^{26} +(-1.26529e7 - 9.19288e6i) q^{27} +(4.91584e7 + 3.57157e7i) q^{28} +(5.53891e7 - 1.70470e8i) q^{29} +(2.21858e7 + 6.82808e7i) q^{30} +(1.14621e8 - 8.32771e7i) q^{31} +3.35544e7 q^{32} +(-2.65917e8 - 1.50228e8i) q^{33} -1.75660e8 q^{34} +(-1.88367e8 + 1.36857e8i) q^{35} +(4.74000e7 + 1.45882e8i) q^{36} +(-3.17854e7 + 9.78253e7i) q^{37} +(3.17352e7 + 2.30570e7i) q^{38} +(1.50588e8 + 1.09409e8i) q^{39} +(-3.97320e7 + 1.22282e8i) q^{40} +(1.73059e8 + 5.32621e8i) q^{41} +(-8.78381e8 + 6.38181e8i) q^{42} +1.21637e9 q^{43} +(-2.27136e8 - 4.97574e8i) q^{44} -5.87764e8 q^{45} +(-1.00564e9 + 7.30637e8i) q^{46} +(-3.44833e8 - 1.06129e9i) q^{47} +(-1.85275e8 + 5.70218e8i) q^{48} +(-1.24895e9 - 9.07416e8i) q^{49} +(8.65502e8 + 6.28824e8i) q^{50} +(9.69929e8 - 2.98513e9i) q^{51} +(1.03010e8 + 3.17033e8i) q^{52} +(-3.42027e9 + 2.48497e9i) q^{53} +5.00476e8 q^{54} +(2.08226e9 - 2.38572e8i) q^{55} -1.94442e9 q^{56} +(-5.67057e8 + 4.11991e8i) q^{57} +(1.77245e9 + 5.45504e9i) q^{58} +(1.17131e9 - 3.60491e9i) q^{59} +(-1.85866e9 - 1.35040e9i) q^{60} +(5.16697e9 + 3.75402e9i) q^{61} +(-1.40100e9 + 4.31184e9i) q^{62} +(-2.74674e9 - 8.45361e9i) q^{63} +(-8.68675e8 + 6.31130e8i) q^{64} -1.27734e9 q^{65} +(9.70986e9 - 1.11249e9i) q^{66} +1.97652e10 q^{67} +(4.54758e9 - 3.30401e9i) q^{68} +(-6.86357e9 - 2.11239e10i) q^{69} +(2.30240e9 - 7.08605e9i) q^{70} +(6.22460e9 + 4.52244e9i) q^{71} +(-3.97103e9 - 2.88512e9i) q^{72} +(4.18619e9 - 1.28838e10i) q^{73} +(-1.01713e9 - 3.13041e9i) q^{74} +(-1.54651e10 + 1.12361e10i) q^{75} -1.25526e9 q^{76} +(1.31621e10 + 2.88335e10i) q^{77} -5.95638e9 q^{78} +(3.96427e8 - 2.88021e8i) q^{79} +(-1.27142e9 - 3.91304e9i) q^{80} +(-1.09634e10 + 3.37419e10i) q^{81} +(-1.44984e10 - 1.05337e10i) q^{82} +(5.62675e10 + 4.08808e10i) q^{83} +(1.07364e10 - 3.30431e10i) q^{84} +(6.65598e9 + 2.04850e10i) q^{85} +(-3.14900e10 + 2.28788e10i) q^{86} -1.02489e11 q^{87} +(1.52392e10 + 8.60924e9i) q^{88} -7.89655e10 q^{89} +(1.52164e10 - 1.10553e10i) q^{90} +(-5.96926e9 - 1.83715e10i) q^{91} +(1.22918e10 - 3.78302e10i) q^{92} +(-6.55389e10 - 4.76168e10i) q^{93} +(2.88891e10 + 2.09892e10i) q^{94} +(1.48636e9 - 4.57454e9i) q^{95} +(-5.92881e9 - 1.82470e10i) q^{96} +(-8.23566e10 + 5.98356e10i) q^{97} +4.94012e10 q^{98} +(-1.59025e10 + 7.84158e10i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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
$3$	−176.692	−	543.803i	−0.419808	−	1.29204i	−0.907879	−	0.419232i	$-0.862299\pi$
$3$	−176.692	−	543.803i	−0.419808	−	1.29204i	0.488072	−	0.872804i	$-0.337701\pi$
$4$	316.433	−	973.882i	0.154508	−	0.475528i
$5$	3174.43	+	2306.36i	0.454287	+	0.330059i	0.791286	−	0.611446i	$-0.209412\pi$
$5$	3174.43	+	2306.36i	0.454287	+	0.330059i	−0.336999	+	0.941505i	$0.609412\pi$
$6$	14802.8	+	10754.8i	0.777161	+	0.564640i
$7$	−18336.8	+	56434.7i	−0.412366	+	1.26913i	0.502219	+	0.864740i	$0.332517\pi$
$7$	−18336.8	+	56434.7i	−0.412366	+	1.26913i	−0.914585	+	0.404393i	$0.867483\pi$
$8$	10125.9	+	31164.2i	0.109254	+	0.336249i
$9$	−121186.	+	88047.0i	−0.684100	+	0.497028i
$10$	−125562.			−0.397061
$11$	393586.	−	361112.i	0.736852	−	0.676054i
$11$	393586.	−	361112.i	0.736852	−	0.676054i
$12$	−585511.			−0.679263
$13$	−263363.	+	191345.i	−0.196728	+	0.142932i	−0.681789	−	0.731549i	$-0.738798\pi$
$13$	−263363.	+	191345.i	−0.196728	+	0.142932i	0.485060	+	0.874481i	$0.338798\pi$
$14$	−586776.	−	1.80591e6i	−0.291587	−	0.897413i
$15$	693306.	−	2.13378e6i	0.235734	−	0.725516i
$16$	−848316.	−	616338.i	−0.202254	−	0.146946i
$17$	4.44099e6	+	3.22657e6i	0.758597	+	0.551153i	0.898480	−	0.439015i	$-0.144673\pi$
$17$	4.44099e6	+	3.22657e6i	0.758597	+	0.551153i	−0.139883	+	0.990168i	$0.544673\pi$
$18$	1.48125e6	−	4.55882e6i	0.184769	−	0.568661i
$19$	−378806.	−	1.16584e6i	−0.0350971	−	0.108018i	0.931973	−	0.362527i	$-0.118086\pi$
$19$	−378806.	−	1.16584e6i	−0.0350971	−	0.108018i	−0.967070	+	0.254509i	$0.918086\pi$
$20$	3.25061e6	−	2.36171e6i	0.227143	−	0.165029i
$21$	3.39293e7			1.81288
$22$	−3.39718e6	+	1.67517e7i	−0.140538	+	0.693000i
$23$	3.88448e7			1.25843			0.629216	−	0.777231i	$-0.283376\pi$
$23$	3.88448e7			1.25843			0.629216	+	0.777231i	$0.283376\pi$
$24$	1.51580e7	−	1.10129e7i	0.388580	−	0.282320i
$25$	−1.03310e7	−	3.17956e7i	−0.211579	−	0.651174i
$26$	3.21907e6	−	9.90727e6i	0.0531345	−	0.163531i
$27$	−1.26529e7	−	9.19288e6i	−0.169703	−	0.123297i
$28$	4.91584e7	+	3.57157e7i	0.539795	+	0.392184i
$29$	5.53891e7	−	1.70470e8i	0.501459	−	1.54333i	−0.305185	−	0.952293i	$-0.598718\pi$
$29$	5.53891e7	−	1.70470e8i	0.501459	−	1.54333i	0.806644	−	0.591038i	$-0.201282\pi$
$30$	2.21858e7	+	6.82808e7i	0.166689	+	0.513017i
$31$	1.14621e8	−	8.32771e7i	0.719076	−	0.522440i	−0.167013	−	0.985955i	$-0.553412\pi$
$31$	1.14621e8	−	8.32771e7i	0.719076	−	0.522440i	0.886089	+	0.463515i	$0.153412\pi$
$32$	3.35544e7			0.176777
$33$	−2.65917e8	−	1.50228e8i	−1.18282	−	0.668226i
$34$	−1.75660e8			−0.663038
$35$	−1.88367e8	+	1.36857e8i	−0.606221	+	0.440446i
$36$	4.74000e7	+	1.45882e8i	0.130651	+	0.402104i
$37$	−3.17854e7	+	9.78253e7i	−0.0753560	+	0.231922i	−0.981639	−	0.190750i	$-0.938908\pi$
$37$	−3.17854e7	+	9.78253e7i	−0.0753560	+	0.231922i	0.906283	+	0.422672i	$0.138908\pi$
$38$	3.17352e7	+	2.30570e7i	0.0649728	+	0.0472055i
$39$	1.50588e8	+	1.09409e8i	0.267261	+	0.194176i
$40$	−3.97320e7	+	1.22282e8i	−0.0613493	+	0.188814i
$41$	1.73059e8	+	5.32621e8i	0.233283	+	0.717972i	0.997345	+	0.0728280i	$0.0232024\pi$
$41$	1.73059e8	+	5.32621e8i	0.233283	+	0.717972i	−0.764061	+	0.645143i	$0.776798\pi$
$42$	−8.78381e8	+	6.38181e8i	−1.03708	+	0.753482i
$43$	1.21637e9			1.26180			0.630898	−	0.775866i	$-0.282687\pi$
$43$	1.21637e9			1.26180			0.630898	+	0.775866i	$0.282687\pi$
$44$	−2.27136e8	−	4.97574e8i	−0.207633	−	0.454850i
$45$	−5.87764e8			−0.474826
$46$	−1.00564e9	+	7.30637e8i	−0.719900	+	0.523038i
$47$	−3.44833e8	−	1.06129e9i	−0.219316	−	0.674985i	−0.998819	−	0.0485868i	$-0.984528\pi$
$47$	−3.44833e8	−	1.06129e9i	−0.219316	−	0.674985i	0.779503	−	0.626399i	$-0.215472\pi$
$48$	−1.85275e8	+	5.70218e8i	−0.104952	+	0.323009i
$49$	−1.24895e9	−	9.07416e8i	−0.631636	−	0.458911i
$50$	8.65502e8	+	6.28824e8i	0.391682	+	0.284573i
$51$	9.69929e8	−	2.98513e9i	0.393644	−	1.21151i
$52$	1.03010e8	+	3.17033e8i	0.0375718	+	0.115634i
$53$	−3.42027e9	+	2.48497e9i	−1.12342	+	0.816215i	−0.984724	−	0.174120i	$-0.944292\pi$
$53$	−3.42027e9	+	2.48497e9i	−1.12342	+	0.816215i	−0.138699	+	0.990335i	$0.544292\pi$
$54$	5.00476e8			0.148326
$55$	2.08226e9	−	2.38572e8i	0.557880	−	0.0639182i
$56$	−1.94442e9			−0.471798
$57$	−5.67057e8	+	4.11991e8i	−0.124829	+	0.0906935i
$58$	1.77245e9	+	5.45504e9i	0.354585	+	1.09130i
$59$	1.17131e9	−	3.60491e9i	0.213297	−	0.656461i	−0.785973	−	0.618261i	$-0.787838\pi$
$59$	1.17131e9	−	3.60491e9i	0.213297	−	0.656461i	0.999270	−	0.0381999i	$-0.0121624\pi$
$60$	−1.85866e9	−	1.35040e9i	−0.308580	−	0.224197i
$61$	5.16697e9	+	3.75402e9i	0.783289	+	0.569092i	0.905964	−	0.423354i	$-0.139147\pi$
$61$	5.16697e9	+	3.75402e9i	0.783289	+	0.569092i	−0.122676	+	0.992447i	$0.539147\pi$
$62$	−1.40100e9	+	4.31184e9i	−0.194216	+	0.597735i
$63$	−2.74674e9	−	8.45361e9i	−0.348695	−	1.07317i
$64$	−8.68675e8	+	6.31130e8i	−0.101127	+	0.0734732i
$65$	−1.27734e9			−0.136547
$66$	9.70986e9	−	1.11249e9i	0.954380	−	0.109347i
$67$	1.97652e10			1.78850			0.894251	−	0.447566i	$-0.147709\pi$
$67$	1.97652e10			1.78850			0.894251	+	0.447566i	$0.147709\pi$
$68$	4.54758e9	−	3.30401e9i	0.379298	−	0.275576i
$69$	−6.86357e9	−	2.11239e10i	−0.528299	−	1.62594i
$70$	2.30240e9	−	7.08605e9i	0.163735	−	0.503924i
$71$	6.22460e9	+	4.52244e9i	0.409440	+	0.297476i	0.773375	−	0.633949i	$-0.218567\pi$
$71$	6.22460e9	+	4.52244e9i	0.409440	+	0.297476i	−0.363935	+	0.931424i	$0.618567\pi$
$72$	−3.97103e9	−	2.88512e9i	−0.241866	−	0.175726i
$73$	4.18619e9	−	1.28838e10i	0.236344	−	0.727391i	−0.760597	−	0.649225i	$-0.775094\pi$
$73$	4.18619e9	−	1.28838e10i	0.236344	−	0.727391i	0.996940	−	0.0781661i	$-0.0249064\pi$
$74$	−1.01713e9	−	3.13041e9i	−0.0532847	−	0.163994i
$75$	−1.54651e10	+	1.12361e10i	−0.752517	+	0.546736i
$76$	−1.25526e9			−0.0567883
$77$	1.31621e10	+	2.88335e10i	0.554150	+	1.21395i
$78$	−5.95638e9			−0.233594
$79$	3.96427e8	−	2.88021e8i	0.0144949	−	0.0105311i	−0.580514	−	0.814250i	$-0.697148\pi$
$79$	3.96427e8	−	2.88021e8i	0.0144949	−	0.0105311i	0.595009	+	0.803719i	$0.297148\pi$
$80$	−1.27142e9	−	3.91304e9i	−0.0433805	−	0.133512i
$81$	−1.09634e10	+	3.37419e10i	−0.349364	+	1.07523i
$82$	−1.44984e10	−	1.05337e10i	−0.431861	−	0.313765i
$83$	5.62675e10	+	4.08808e10i	1.56794	+	1.13917i	0.929100	+	0.369829i	$0.120584\pi$
$83$	5.62675e10	+	4.08808e10i	1.56794	+	1.13917i	0.638836	+	0.769343i	$0.279416\pi$
$84$	1.07364e10	−	3.30431e10i	0.280105	−	0.862076i
$85$	6.65598e9	+	2.04850e10i	0.162708	+	0.500763i
$86$	−3.14900e10	+	2.28788e10i	−0.721824	+	0.524436i
$87$	−1.02489e11			−2.20455
$88$	1.52392e10	+	8.60924e9i	0.307827	+	0.173904i
$89$	−7.89655e10			−1.49897			−0.749484	−	0.662022i	$-0.769698\pi$
$89$	−7.89655e10			−1.49897			−0.749484	+	0.662022i	$0.769698\pi$
$90$	1.52164e10	−	1.10553e10i	0.271630	−	0.197350i
$91$	−5.96926e9	−	1.83715e10i	−0.100275	−	0.308615i
$92$	1.22918e10	−	3.78302e10i	0.194438	−	0.598420i
$93$	−6.55389e10	−	4.76168e10i	−0.976884	−	0.709748i
$94$	2.88891e10	+	2.09892e10i	0.406004	+	0.294979i
$95$	1.48636e9	−	4.57454e9i	0.0197081	−	0.0606552i
$96$	−5.92881e9	−	1.82470e10i	−0.0742122	−	0.228402i
$97$	−8.23566e10	+	5.98356e10i	−0.973765	+	0.707482i	−0.956306	−	0.292366i	$-0.905557\pi$
$97$	−8.23566e10	+	5.98356e10i	−0.973765	+	0.707482i	−0.0174583	+	0.999848i	$0.505557\pi$
$98$	4.94012e10			0.552070
$99$	−1.59025e10	+	7.84158e10i	−0.168063	+	0.828724i
$100$	−3.42342e10			−0.342342
$101$	6.69132e10	−	4.86153e10i	0.633497	−	0.460262i	−0.224113	−	0.974563i	$-0.571948\pi$
$101$	6.69132e10	−	4.86153e10i	0.633497	−	0.460262i	0.857610	+	0.514301i	$0.171948\pi$
$102$	3.10377e10	+	9.55243e10i	0.278348	+	0.856668i
$103$	5.59562e10	−	1.72216e11i	0.475602	−	1.46375i	−0.369542	−	0.929214i	$-0.620485\pi$
$103$	5.59562e10	−	1.72216e11i	0.475602	−	1.46375i	0.845144	−	0.534539i	$-0.179515\pi$
$104$	−8.62989e9	−	6.26998e9i	−0.0695540	−	0.0505339i
$105$	1.07706e11	+	7.82531e10i	0.823568	+	0.598357i
$106$	4.18057e10	−	1.28665e11i	0.303426	−	0.933850i
$107$	3.95224e10	+	1.21637e11i	0.272416	+	0.838410i	0.989892	+	0.141827i	$0.0452975\pi$
$107$	3.95224e10	+	1.21637e11i	0.272416	+	0.838410i	−0.717476	+	0.696584i	$0.754702\pi$
$108$	−1.29566e10	+	9.41351e9i	−0.0848516	+	0.0616483i
$109$	1.81908e11			1.13242			0.566209	−	0.824262i	$-0.308410\pi$
$109$	1.81908e11			1.13242			0.566209	+	0.824262i	$0.308410\pi$
$110$	−4.94194e10	+	4.53418e10i	−0.292575	+	0.268435i
$111$	5.88139e10			0.331286
$112$	5.03382e10	−	3.65728e10i	0.269897	−	0.196092i
$113$	−1.77844e10	−	5.47347e10i	−0.0908046	−	0.279468i	0.895333	−	0.445397i	$-0.146938\pi$
$113$	−1.77844e10	−	5.47347e10i	−0.0908046	−	0.279468i	−0.986138	+	0.165930i	$0.946938\pi$
$114$	6.93109e9	−	2.13317e10i	0.0337151	−	0.103764i
$115$	1.23310e11	+	8.95899e10i	0.571689	+	0.415356i
$116$	−1.48491e11	−	1.07885e11i	−0.656418	−	0.476916i
$117$	1.50687e10	−	4.63767e10i	0.0635409	−	0.195559i
$118$	3.74818e10	+	1.15357e11i	0.150824	+	0.464188i
$119$	−2.63524e11	+	1.91461e11i	−1.01231	+	0.735483i
$120$	7.35178e10			0.269709
$121$	2.45086e10	−	2.84257e11i	0.0859011	−	0.996304i
$122$	−2.04375e11			−0.684619
$123$	2.59063e11	−	1.88220e11i	0.829711	−	0.602820i
$124$	−4.48321e10	−	1.37979e11i	−0.137331	−	0.422663i
$125$	9.97421e10	−	3.06975e11i	0.292330	−	0.899700i
$126$	2.30114e11	+	1.67188e11i	0.645514	+	0.468993i
$127$	4.70482e10	+	3.41825e10i	0.126364	+	0.0918086i	0.649172	−	0.760642i	$-0.275116\pi$
$127$	4.70482e10	+	3.41825e10i	0.126364	+	0.0918086i	−0.522808	+	0.852450i	$0.675116\pi$
$128$	1.06177e10	−	3.26781e10i	0.0273135	−	0.0840623i
$129$	−2.14923e11	−	6.61465e11i	−0.529712	−	1.63028i
$130$	3.30684e10	−	2.40256e10i	0.0781132	−	0.0567526i
$131$	−3.08315e11			−0.698236			−0.349118	−	0.937079i	$-0.613519\pi$
$131$	−3.08315e11			−0.698236			−0.349118	+	0.937079i	$0.613519\pi$
$132$	−2.30449e11	+	2.11435e11i	−0.500516	+	0.459219i
$133$	7.27401e10			0.151562
$134$	−5.11692e11	+	3.71766e11i	−1.02313	+	0.743350i
$135$	−1.89637e10	−	5.83643e10i	−0.0363988	−	0.112024i
$136$	−5.55846e10	+	1.71072e11i	−0.102445	+	0.315293i
$137$	5.73876e11	+	4.16945e11i	1.01591	+	0.738101i	0.965440	−	0.260624i	$-0.0839284\pi$
$137$	5.73876e11	+	4.16945e11i	1.01591	+	0.738101i	0.0504690	+	0.998726i	$0.483928\pi$
$138$	5.75010e11	+	4.17769e11i	0.978003	+	0.710561i
$139$	−2.04935e11	+	6.30725e11i	−0.334992	+	1.03100i	0.631733	+	0.775186i	$0.282344\pi$
$139$	−2.04935e11	+	6.30725e11i	−0.334992	+	1.03100i	−0.966726	+	0.255815i	$0.917656\pi$
$140$	7.36767e10	+	2.26754e11i	0.115778	+	0.356328i
$141$	−5.16201e11	+	3.75042e11i	−0.780035	+	0.566728i
$142$	−2.46209e11			−0.357864
$143$	−3.45594e10	+	1.70414e11i	−0.0483302	+	0.238318i
$144$	1.57071e11			0.211398
$145$	5.68993e11	−	4.13398e11i	0.737196	−	0.535604i
$146$	1.33958e11	+	4.12281e11i	0.167120	+	0.514343i
$147$	−2.72775e11	+	8.39517e11i	−0.327763	+	1.00875i
$148$	8.52124e10	+	6.19104e10i	0.0986423	+	0.0716678i
$149$	−1.14299e12	−	8.30428e11i	−1.27502	−	0.926355i	−0.275627	−	0.961265i	$-0.588886\pi$
$149$	−1.14299e12	−	8.30428e11i	−1.27502	−	0.926355i	−0.999390	+	0.0349098i	$0.988886\pi$
$150$	1.89029e11	−	5.81771e11i	0.203248	−	0.625533i
$151$	−4.65351e11	−	1.43220e12i	−0.482400	−	1.48467i	−0.835711	−	0.549169i	$-0.814944\pi$
$151$	−4.65351e11	−	1.43220e12i	−0.482400	−	1.48467i	0.353311	−	0.935506i	$-0.385056\pi$
$152$	3.24969e10	−	2.36104e10i	0.0324864	−	0.0236028i
$153$	−8.22277e11			−0.792894
$154$	−8.83082e11	−	4.98890e11i	−0.821556	−	0.464132i
$155$	5.55923e11			0.499103
$156$	1.54202e11	−	1.12034e11i	0.133630	−	0.0970881i
$157$	−1.25422e11	−	3.86008e11i	−0.104936	−	0.322960i	0.884779	−	0.466010i	$-0.154309\pi$
$157$	−1.25422e11	−	3.86008e11i	−0.104936	−	0.322960i	−0.989715	+	0.143050i	$0.954309\pi$
$158$	−4.84550e9	+	1.49129e10i	−0.00391493	+	0.0120489i
$159$	1.95567e12	+	1.42088e12i	1.52620	+	1.10885i
$160$	1.06516e11	+	7.73885e10i	0.0803073	+	0.0583467i
$161$	−7.12287e11	+	2.19220e12i	−0.518935	+	1.59712i
$162$	−3.50829e11	−	1.07974e12i	−0.247037	−	0.760303i
$163$	1.31025e12	−	9.51949e11i	0.891910	−	0.648010i	−0.0444656	−	0.999011i	$-0.514159\pi$
$163$	1.31025e12	−	9.51949e11i	0.891910	−	0.648010i	0.936375	+	0.351001i	$0.114159\pi$
$164$	5.73472e11			0.377460
$165$	−4.97656e11	−	1.09019e12i	−0.316787	−	0.693967i
$166$	−2.22562e12			−1.37043
$167$	3.46587e11	−	2.51810e11i	0.206477	−	0.150014i	−0.479741	−	0.877410i	$-0.659269\pi$
$167$	3.46587e11	−	2.51810e11i	0.206477	−	0.150014i	0.686218	+	0.727396i	$0.259269\pi$
$168$	3.43564e11	+	1.05738e12i	0.198064	+	0.609579i
$169$	−5.21061e11	+	1.60366e12i	−0.290744	+	0.894819i
$170$	−5.57619e11	−	4.05134e11i	−0.301209	−	0.218841i
$171$	1.48555e11	+	1.07932e11i	0.0776978	+	0.0564508i
$172$	3.84900e11	−	1.18460e12i	0.194958	−	0.600019i
$173$	−2.51298e11	−	7.73416e11i	−0.123292	−	0.379455i	0.870294	−	0.492533i	$-0.163929\pi$
$173$	−2.51298e11	−	7.73416e11i	−0.123292	−	0.379455i	−0.993586	+	0.113078i	$0.963929\pi$
$174$	2.65329e12	−	1.92773e12i	1.26114	−	0.916272i
$175$	1.98381e12			0.913675
$176$	−5.56452e11	+	6.37546e10i	−0.248375	+	0.0284572i
$177$	−2.16732e12			−0.937714
$178$	2.04430e12	−	1.48527e12i	0.857502	−	0.623012i
$179$	1.01279e12	+	3.11704e12i	0.411933	+	1.26780i	0.914966	+	0.403531i	$0.132217\pi$
$179$	1.01279e12	+	3.11704e12i	0.411933	+	1.26780i	−0.503033	+	0.864267i	$0.667783\pi$
$180$	−1.85988e11	+	5.72413e11i	−0.0733646	+	0.225793i
$181$	7.15323e11	+	5.19713e11i	0.273697	+	0.198853i	0.716164	−	0.697932i	$-0.245896\pi$
$181$	7.15323e11	+	5.19713e11i	0.273697	+	0.198853i	−0.442466	+	0.896785i	$0.645896\pi$
$182$	5.00087e11	+	3.63334e11i	0.185632	+	0.134870i
$183$	1.12848e12	−	3.47312e12i	0.406457	−	1.25095i
$184$	3.93337e11	+	1.21057e12i	0.137489	+	0.423147i
$185$	−3.26520e11	+	2.37231e11i	−0.110781	+	0.0804872i
$186$	2.59234e12			0.853828
$187$	2.91307e12	−	3.33760e11i	0.931583	−	0.106735i
$188$	−1.14268e12			−0.354861
$189$	7.50811e11	−	5.45496e11i	0.226460	−	0.164533i
$190$	4.75635e10	+	1.46385e11i	0.0139357	+	0.0428897i
$191$	−1.10151e12	+	3.39009e12i	−0.313547	+	0.965000i	0.662801	+	0.748796i	$0.269368\pi$
$191$	−1.10151e12	+	3.39009e12i	−0.313547	+	0.965000i	−0.976348	+	0.216204i	$0.930632\pi$
$192$	4.96698e11	+	3.60872e11i	0.137384	+	0.0998152i
$193$	−2.41698e12	−	1.75604e12i	−0.649693	−	0.472029i	0.213474	−	0.976949i	$-0.431522\pi$
$193$	−2.41698e12	−	1.75604e12i	−0.649693	−	0.472029i	−0.863166	+	0.504919i	$0.831522\pi$
$194$	1.00664e12	−	3.09811e12i	0.263005	−	0.809446i
$195$	2.25695e11	+	6.94619e11i	0.0573234	+	0.176423i
$196$	−1.27893e12	+	9.29194e11i	−0.315818	+	0.229455i
$197$	−6.85722e12			−1.64658			−0.823292	−	0.567619i	$-0.807865\pi$
$197$	−6.85722e12			−1.64658			−0.823292	+	0.567619i	$0.807865\pi$
$198$	−1.06324e12	−	2.32918e12i	−0.248298	−	0.543933i
$199$	−7.49122e11			−0.170161			−0.0850806	−	0.996374i	$-0.527115\pi$
$199$	−7.49122e11			−0.170161			−0.0850806	+	0.996374i	$0.527115\pi$
$200$	8.86274e11	−	6.43916e11i	0.195841	−	0.142287i
$201$	−3.49235e12	−	1.07484e13i	−0.750827	−	2.31081i
$202$	−8.17875e11	+	2.51716e12i	−0.171102	+	0.526597i
$203$	8.60478e12	+	6.25174e12i	1.75191	+	1.27284i
$204$	−2.60025e12	−	1.88919e12i	−0.515287	−	0.374378i
$205$	−6.79050e11	+	2.08990e12i	−0.130995	+	0.403162i
$206$	1.79060e12	+	5.51090e12i	0.336302	+	1.03503i
$207$	−4.70745e12	+	3.42017e12i	−0.860893	+	0.625475i
$208$	3.41348e11			0.0607924
$209$	−5.70092e11	−	3.22069e11i	−0.0988873	−	0.0558656i
$210$	−4.26023e12			−0.719824
$211$	−6.54753e12	+	4.75706e12i	−1.07776	+	0.783041i	−0.977292	−	0.211898i	$-0.932035\pi$
$211$	−6.54753e12	+	4.75706e12i	−1.07776	+	0.783041i	−0.100472	+	0.994940i	$0.532035\pi$
$212$	1.33778e12	+	4.11727e12i	0.214555	+	0.660332i
$213$	1.35947e12	−	4.18403e12i	0.212463	−	0.653894i
$214$	−3.31107e12	−	2.40563e12i	−0.504305	−	0.366399i
$215$	3.86127e12	+	2.80538e12i	0.573217	+	0.416467i
$216$	1.58367e11	−	4.87404e11i	0.0229176	−	0.0705332i
$217$	2.59794e12	+	7.99564e12i	0.366523	+	1.12804i
$218$	−4.70934e12	+	3.42154e12i	−0.647812	+	0.470663i
$219$	−7.74590e12			−1.03903
$220$	4.26556e11	−	2.10337e12i	0.0558022	−	0.275163i
$221$	−1.78698e12			−0.228015
$222$	−1.52261e12	+	1.10624e12i	−0.189516	+	0.137692i
$223$	−2.39049e12	−	7.35718e12i	−0.290276	−	0.893377i	−0.984768	−	0.173876i	$-0.944371\pi$
$223$	−2.39049e12	−	7.35718e12i	−0.290276	−	0.893377i	0.694492	−	0.719501i	$-0.255629\pi$
$224$	−6.15279e11	+	1.89364e12i	−0.0728968	+	0.224353i
$225$	4.05148e12	+	2.94357e12i	0.468393	+	0.340307i
$226$	1.48992e12	+	1.08249e12i	0.168100	+	0.122132i
$227$	−3.95226e11	+	1.21638e12i	−0.0435214	+	0.133945i	−0.970456	−	0.241277i	$-0.922434\pi$
$227$	−3.95226e11	+	1.21638e12i	−0.0435214	+	0.133945i	0.926935	+	0.375222i	$0.122434\pi$
$228$	2.21795e11	+	6.82614e11i	0.0238402	+	0.0733725i
$229$	5.27298e12	−	3.83104e12i	0.553300	−	0.401996i	−0.275701	−	0.961244i	$-0.588910\pi$
$229$	5.27298e12	−	3.83104e12i	0.553300	−	0.401996i	0.829001	+	0.559248i	$0.188910\pi$
$230$	−4.87742e12			−0.499675
$231$	1.33541e13	−	1.22523e13i	1.33582	−	1.22561i
$232$	5.87343e12			0.573730
$233$	1.03996e13	−	7.55577e12i	0.992110	−	0.720810i	0.0317279	−	0.999497i	$-0.489899\pi$
$233$	1.03996e13	−	7.55577e12i	0.992110	−	0.720810i	0.960382	+	0.278686i	$0.0898990\pi$
$234$	4.82198e11	+	1.48405e12i	0.0449302	+	0.138281i
$235$	1.35306e12	−	4.16428e12i	0.123152	−	0.379024i
$236$	−3.14012e12	−	2.28143e12i	−0.279209	−	0.202857i
$237$	−2.26672e11	−	1.64687e11i	−0.0196917	−	0.0143068i
$238$	3.22103e12	−	9.91331e12i	0.273415	−	0.841483i
$239$	1.96282e12	+	6.04094e12i	0.162814	+	0.501091i	0.998869	−	0.0475559i	$-0.0151432\pi$
$239$	1.96282e12	+	6.04094e12i	0.162814	+	0.501091i	−0.836054	+	0.548647i	$0.815143\pi$
$240$	−1.90327e12	+	1.38281e12i	−0.154290	+	0.112098i
$241$	−1.61002e13			−1.27567			−0.637835	−	0.770173i	$-0.720170\pi$
$241$	−1.61002e13			−1.27567			−0.637835	+	0.770173i	$0.720170\pi$
$242$	4.71214e12	+	7.81999e12i	0.364950	+	0.605650i
$243$	1.75155e13			1.32614
$244$	5.29098e12	−	3.84412e12i	0.391644	−	0.284546i
$245$	−1.87188e12	−	5.76105e12i	−0.135477	−	0.416954i
$246$	−3.16650e12	+	9.74548e12i	−0.224097	+	0.689700i
$247$	3.22841e11	+	2.34558e11i	0.0223438	+	0.0162337i
$248$	3.75590e12	+	2.72882e12i	0.254232	+	0.184710i
$249$	1.22890e13	−	3.78217e13i	0.813619	−	2.50406i
$250$	3.19175e12	+	9.82319e12i	0.206709	+	0.636184i
$251$	−2.22611e13	+	1.61736e13i	−1.41040	+	1.02471i	−0.417130	+	0.908847i	$0.636964\pi$
$251$	−2.22611e13	+	1.61736e13i	−1.41040	+	1.02471i	−0.993265	+	0.115865i	$0.963036\pi$
$252$	−9.10198e12			−0.564200
$253$	1.52888e13	−	1.40273e13i	0.927278	−	0.850768i
$254$	−1.86095e12			−0.110446
$255$	9.96374e12	−	7.23908e12i	0.578697	−	0.420448i
$256$	3.39768e11	+	1.04570e12i	0.0193136	+	0.0594410i
$257$	−6.95804e12	+	2.14146e13i	−0.387128	+	1.19146i	0.547797	+	0.836611i	$0.315467\pi$
$257$	−6.95804e12	+	2.14146e13i	−0.387128	+	1.19146i	−0.934925	+	0.354846i	$0.884533\pi$
$258$	1.80056e13	+	1.30818e13i	0.980618	+	0.712460i
$259$	−4.93791e12	−	3.58760e12i	−0.263266	−	0.191274i
$260$	−4.04192e11	+	1.24397e12i	−0.0210977	+	0.0649319i
$261$	8.29698e12	+	2.55355e13i	0.424030	+	1.30503i
$262$	7.98182e12	−	5.79913e12i	0.399434	−	0.290206i
$263$	−2.03894e13			−0.999191			−0.499595	−	0.866259i	$-0.666518\pi$
$263$	−2.03894e13			−0.999191			−0.499595	+	0.866259i	$0.666518\pi$
$264$	1.98909e12	−	9.80828e12i	0.0954624	−	0.470729i
$265$	−1.65886e13			−0.779755
$266$	−1.88314e12	+	1.36818e12i	−0.0867027	+	0.0629932i
$267$	1.39526e13	+	4.29417e13i	0.629279	+	1.93672i
$268$	6.25436e12	−	1.92490e13i	0.276339	−	0.850483i
$269$	−1.51083e13	−	1.09768e13i	−0.654000	−	0.475159i	0.210632	−	0.977566i	$-0.432448\pi$
$269$	−1.51083e13	−	1.09768e13i	−0.654000	−	0.475159i	−0.864631	+	0.502407i	$0.832448\pi$
$270$	1.58872e12	+	1.15427e12i	0.0673826	+	0.0489563i
$271$	1.25738e13	−	3.86982e13i	0.522560	−	1.60827i	−0.246532	−	0.969135i	$-0.579291\pi$
$271$	1.25738e13	−	3.86982e13i	0.522560	−	1.60827i	0.769091	−	0.639139i	$-0.220709\pi$
$272$	−1.77871e12	−	5.47430e12i	−0.0724395	−	0.222946i
$273$	−8.93574e12	+	6.49219e12i	−0.356645	+	0.259118i
$274$	−2.26992e13			−0.887937
$275$	−1.55479e13	−	8.78366e12i	−0.596131	−	0.336780i
$276$	−2.27440e13			−0.854806
$277$	5.48543e12	−	3.98540e12i	0.202103	−	0.146836i	−0.482131	−	0.876099i	$-0.660137\pi$
$277$	5.48543e12	−	3.98540e12i	0.202103	−	0.146836i	0.684233	+	0.729263i	$0.260137\pi$
$278$	−6.55792e12	−	2.01832e13i	−0.236875	−	0.729028i
$279$	−6.55820e12	+	2.01841e13i	−0.232253	+	0.714802i
$280$	−6.17242e12	−	4.48452e12i	−0.214332	−	0.155721i
$281$	5.35121e12	+	3.88788e12i	0.182208	+	0.132382i	0.675150	−	0.737680i	$-0.264079\pi$
$281$	5.35121e12	+	3.88788e12i	0.182208	+	0.132382i	−0.492943	+	0.870062i	$0.664079\pi$
$282$	6.30948e12	−	1.94186e13i	0.210680	−	0.648407i
$283$	1.04976e13	+	3.23084e13i	0.343769	+	1.05801i	0.962240	+	0.272204i	$0.0877526\pi$
$283$	1.04976e13	+	3.23084e13i	0.343769	+	1.05801i	−0.618471	+	0.785808i	$0.712247\pi$
$284$	6.37399e12	−	4.63097e12i	0.204720	−	0.148738i
$285$	−2.75028e12			−0.0866423
$286$	−2.31065e12	−	5.06181e12i	−0.0714037	−	0.156420i
$287$	−3.32317e13			−1.00740
$288$	−4.06634e12	+	2.95437e12i	−0.120933	+	0.0878629i
$289$	−1.27894e12	−	3.93617e12i	−0.0373174	−	0.114851i
$290$	−6.95475e12	+	2.14045e13i	−0.199110	+	0.612797i
$291$	4.70905e13	+	3.42133e13i	1.32289	+	0.961132i
$292$	−1.12226e13	−	8.15372e12i	−0.309378	−	0.224776i
$293$	−9.06823e12	+	2.79091e13i	−0.245330	+	0.755048i	0.750252	+	0.661152i	$0.229932\pi$
$293$	−9.06823e12	+	2.79091e13i	−0.245330	+	0.755048i	−0.995582	+	0.0938962i	$0.970068\pi$
$294$	−8.72881e12	−	2.68645e13i	−0.231763	−	0.713295i
$295$	1.20324e13	−	8.74208e12i	0.313569	−	0.227821i
$296$	−3.37050e12			−0.0862165
$297$	−8.29967e12	+	9.50922e11i	−0.208401	+	0.0238773i
$298$	4.52099e13			1.11441
$299$	−1.02303e13	+	7.43274e12i	−0.247569	+	0.179870i
$300$	6.04892e12	+	1.86167e13i	0.143718	+	0.442318i
$301$	−2.23043e13	+	6.86455e13i	−0.520322	+	1.60139i
$302$	3.89857e13	+	2.83248e13i	0.893033	+	0.648827i
$303$	−3.82602e13	−	2.77977e13i	−0.860622	−	0.625279i
$304$	−3.97206e11	+	1.22248e12i	−0.00877428	+	0.0270045i
$305$	7.74405e12	+	2.38337e13i	0.168004	+	0.517063i
$306$	2.12876e13	−	1.54663e13i	0.453584	−	0.329548i
$307$	4.54031e13			0.950221			0.475110	−	0.879926i	$-0.342408\pi$
$307$	4.54031e13			0.950221			0.475110	+	0.879926i	$0.342408\pi$
$308$	3.22454e13	−	3.69447e12i	0.662886	−	0.0759492i
$309$	−1.03538e14			−2.09088
$310$	−1.43920e13	+	1.04564e13i	−0.285517	+	0.207441i
$311$	−1.60234e13	−	4.93148e13i	−0.312300	−	0.961160i	−0.976852	−	0.213918i	$-0.931378\pi$
$311$	−1.60234e13	−	4.93148e13i	−0.312300	−	0.961160i	0.664552	−	0.747242i	$-0.268622\pi$
$312$	−1.88480e12	+	5.80081e12i	−0.0360923	+	0.111081i
$313$	4.46738e13	+	3.24574e13i	0.840541	+	0.610689i	0.922522	−	0.385945i	$-0.126125\pi$
$313$	4.46738e13	+	3.24574e13i	0.840541	+	0.610689i	−0.0819806	+	0.996634i	$0.526125\pi$
$314$	1.05075e13	+	7.63411e12i	0.194261	+	0.141139i
$315$	1.07777e13	−	3.31703e13i	0.195802	−	0.602617i
$316$	−1.55056e11	−	4.77213e11i	−0.00276827	−	0.00851987i
$317$	2.22404e13	−	1.61586e13i	0.390226	−	0.283516i	−0.375322	−	0.926895i	$-0.622468\pi$
$317$	2.22404e13	−	1.61586e13i	0.390226	−	0.283516i	0.765548	+	0.643378i	$0.222468\pi$
$318$	−7.73549e13			−1.33395
$319$	−3.97583e13	−	8.70963e13i	−0.673875	−	1.47622i
$320$	−4.21316e12			−0.0701912
$321$	5.91635e13	−	4.29848e13i	0.968893	−	0.703942i
$322$	−2.27932e13	−	7.01502e13i	−0.366942	−	1.12933i
$323$	2.07940e12	−	6.39975e12i	0.0329098	−	0.101286i
$324$	2.93914e13	+	2.13541e13i	0.457323	+	0.332265i
$325$	8.80473e12	+	6.39701e12i	0.134697	+	0.0978630i
$326$	−1.60150e13	+	4.92891e13i	−0.240897	+	0.741403i
$327$	−3.21418e13	−	9.89222e13i	−0.475398	−	1.46312i
$328$	−1.48463e13	+	1.07865e13i	−0.215930	+	0.156883i
$329$	6.62165e13			0.947085
$330$	3.33890e13	+	1.88629e13i	0.469653	+	0.265327i
$331$	2.97891e13			0.412101			0.206051	−	0.978541i	$-0.433939\pi$
$331$	2.97891e13			0.412101			0.206051	+	0.978541i	$0.433939\pi$
$332$	5.76179e13	−	4.18619e13i	0.783968	−	0.569586i
$333$	−4.76127e12	−	1.46537e13i	−0.0637206	−	0.196112i
$334$	−4.23631e12	+	1.30380e13i	−0.0557676	+	0.171635i
$335$	6.27431e13	+	4.55855e13i	0.812493	+	0.590311i
$336$	−2.87828e13	−	2.09119e13i	−0.366663	−	0.266396i
$337$	−2.07566e13	+	6.38823e13i	−0.260131	+	0.800600i	0.732644	+	0.680612i	$0.238286\pi$
$337$	−2.07566e13	+	6.38823e13i	−0.260131	+	0.800600i	−0.992775	+	0.119989i	$0.961714\pi$
$338$	−1.66739e13	−	5.13171e13i	−0.205587	−	0.632733i
$339$	−2.66225e13	+	1.93424e13i	−0.322962	+	0.234645i
$340$	2.20562e13			0.263267
$341$	1.50410e13	−	7.41677e13i	0.176655	−	0.871095i
$342$	−5.87597e12			−0.0679104
$343$	−2.08125e13	+	1.51212e13i	−0.236705	+	0.171976i
$344$	1.23168e13	+	3.79072e13i	0.137856	+	0.424278i
$345$	2.69313e13	−	8.28861e13i	0.296656	−	0.913012i
$346$	2.10530e13	+	1.52959e13i	0.228242	+	0.165828i
$347$	4.93098e13	+	3.58256e13i	0.526164	+	0.382280i	0.818921	−	0.573907i	$-0.194573\pi$
$347$	4.93098e13	+	3.58256e13i	0.526164	+	0.382280i	−0.292757	+	0.956187i	$0.594573\pi$
$348$	−3.24309e13	+	9.98121e13i	−0.340622	+	1.04833i
$349$	4.59633e13	+	1.41461e14i	0.475195	+	1.46250i	0.845695	+	0.533666i	$0.179186\pi$
$349$	4.59633e13	+	1.41461e14i	0.475195	+	1.46250i	−0.370500	+	0.928832i	$0.620814\pi$
$350$	−5.13580e13	+	3.73138e13i	−0.522678	+	0.379748i
$351$	5.09132e12			0.0510084
$352$	1.32066e13	−	1.21169e13i	0.130258	−	0.119511i
$353$	−3.35959e13			−0.326231			−0.163115	−	0.986607i	$-0.552154\pi$
$353$	−3.35959e13			−0.326231			−0.163115	+	0.986607i	$0.552154\pi$
$354$	5.61088e13	−	4.07654e13i	0.536430	−	0.389739i
$355$	9.32918e12	+	2.87123e13i	0.0878188	+	0.270279i
$356$	−2.49873e13	+	7.69031e13i	−0.231603	+	0.712802i
$357$	1.50680e14	+	1.09475e14i	1.37524	+	0.999174i
$358$	−8.48483e13	−	6.16459e13i	−0.762582	−	0.554048i
$359$	6.21222e13	−	1.91193e14i	0.549829	−	1.69220i	−0.159394	−	0.987215i	$-0.550954\pi$
$359$	6.21222e13	−	1.91193e14i	0.549829	−	1.69220i	0.709223	−	0.704984i	$-0.249046\pi$
$360$	−5.95163e12	−	1.83172e13i	−0.0518766	−	0.159660i
$361$	9.30269e13	−	6.75880e13i	0.798581	−	0.580203i
$362$	−2.82940e13			−0.239220
$363$	−1.58910e14	+	3.68982e13i	−1.32332	+	0.307269i
$364$	−1.97805e13			−0.162248
$365$	4.30034e13	−	3.12438e13i	0.347449	−	0.252437i
$366$	3.61115e13	+	1.11140e14i	0.287409	+	0.884552i
$367$	−6.41818e13	+	1.97531e14i	−0.503209	+	1.54872i	0.300551	+	0.953766i	$0.402829\pi$
$367$	−6.41818e13	+	1.97531e14i	−0.503209	+	1.54872i	−0.803760	+	0.594953i	$0.797171\pi$
$368$	−3.29526e13	−	2.39415e13i	−0.254523	−	0.184922i
$369$	−6.78681e13	−	4.93090e13i	−0.516441	−	0.375216i
$370$	3.99103e12	−	1.22831e13i	0.0299210	−	0.0920872i
$371$	−7.75221e13	−	2.38588e14i	−0.572623	−	1.76235i
$372$	−6.71119e13	+	4.87596e13i	−0.488442	+	0.354874i
$373$	−4.68649e13			−0.336085			−0.168042	−	0.985780i	$-0.553745\pi$
$373$	−4.68649e13			−0.336085			−0.168042	+	0.985780i	$0.553745\pi$
$374$	−6.91373e13	+	6.34328e13i	−0.488561	+	0.448250i
$375$	−1.84557e14			−1.28517
$376$	2.95824e13	−	2.14929e13i	0.203002	−	0.147490i
$377$	1.80311e13	+	5.54940e13i	0.121940	+	0.375291i
$378$	−9.17710e12	+	2.82442e13i	−0.0611647	+	0.188245i
$379$	−1.81089e14	−	1.31569e14i	−1.18953	−	0.864246i	−0.196317	−	0.980540i	$-0.562898\pi$
$379$	−1.81089e14	−	1.31569e14i	−1.18953	−	0.864246i	−0.993215	+	0.116295i	$0.962898\pi$
$380$	−3.98473e12	−	2.89508e12i	−0.0257982	−	0.0187435i
$381$	1.02755e13	−	3.16247e13i	0.0655715	−	0.201808i
$382$	−3.52482e13	−	1.08483e14i	−0.221711	−	0.682358i
$383$	−1.46662e14	+	1.06556e14i	−0.909334	+	0.660670i	−0.940846	−	0.338834i	$-0.889968\pi$
$383$	−1.46662e14	+	1.06556e14i	−0.909334	+	0.660670i	0.0315125	+	0.999503i	$0.489968\pi$
$384$	−1.96465e13			−0.120078
$385$	−2.47182e13	+	1.21887e14i	−0.148930	+	0.734382i
$386$	9.56017e13			0.567852
$387$	−1.47407e14	+	1.07098e14i	−0.863194	+	0.627147i
$388$	3.22124e13	+	9.91396e13i	0.185973	+	0.572365i
$389$	9.27056e13	−	2.85319e14i	0.527695	−	1.62408i	−0.231228	−	0.972900i	$-0.574274\pi$
$389$	9.27056e13	−	2.85319e14i	0.527695	−	1.62408i	0.758923	−	0.651180i	$-0.225726\pi$
$390$	−1.89081e13	−	1.37375e13i	−0.106119	−	0.0770999i
$391$	1.72509e14	+	1.25335e14i	0.954642	+	0.693588i
$392$	1.56322e13	−	4.81110e13i	0.0852996	−	0.262525i
$393$	5.44768e13	+	1.67662e14i	0.293125	+	0.902146i
$394$	1.77523e14	−	1.28978e14i	0.941947	−	0.684364i
$395$	1.92271e12			0.0100607
$396$	7.13357e13	+	4.03005e13i	0.368115	+	0.207963i
$397$	7.58270e13			0.385901			0.192951	−	0.981208i	$-0.438194\pi$
$397$	7.58270e13			0.385901			0.192951	+	0.981208i	$0.438194\pi$
$398$	1.93937e13	−	1.40903e13i	0.0973427	−	0.0707236i
$399$	−1.28526e13	−	3.95563e13i	−0.0636269	−	0.195823i
$400$	−1.08329e13	+	3.33401e13i	−0.0528948	+	0.162793i
$401$	−4.12224e13	−	2.99498e13i	−0.198536	−	0.144245i	0.484076	−	0.875026i	$-0.339156\pi$
$401$	−4.12224e13	−	2.99498e13i	−0.198536	−	0.144245i	−0.682612	+	0.730781i	$0.739156\pi$
$402$	2.92579e14	+	2.12571e14i	1.38995	+	1.00986i
$403$	−1.42524e13	+	4.38643e13i	−0.0667896	+	0.205557i
$404$	−2.61720e13	−	8.05491e13i	−0.120987	−	0.372360i
$405$	−1.12623e14	+	8.18256e13i	−0.513601	+	0.373153i
$406$	−3.40355e14			−1.53122
$407$	2.28156e13	+	4.99808e13i	0.101266	+	0.221837i
$408$	1.02851e14			0.450377
$409$	−2.21827e14	+	1.61167e14i	−0.958378	+	0.696302i	−0.952773	−	0.303682i	$-0.901784\pi$
$409$	−2.21827e14	+	1.61167e14i	−0.958378	+	0.696302i	−0.00560437	+	0.999984i	$0.501784\pi$
$410$	−2.17296e13	−	6.68769e13i	−0.0926277	−	0.285079i
$411$	1.25337e14	−	3.85746e14i	0.527166	−	1.62245i
$412$	−1.50011e14	−	1.08990e14i	−0.622571	−	0.452325i
$413$	1.81964e14	+	1.32205e14i	0.745179	+	0.541405i
$414$	5.75388e13	−	1.77086e14i	0.232519	−	0.715621i
$415$	8.43316e13	+	2.59546e14i	0.336299	+	1.03502i
$416$	−8.83701e12	+	6.42046e12i	−0.0347770	+	0.0252670i
$417$	3.79201e14			1.47272
$418$	2.08167e13	−	2.38504e12i	0.0797889	−	0.00914169i
$419$	2.58171e14			0.976629			0.488315	−	0.872668i	$-0.337612\pi$
$419$	2.58171e14			0.976629			0.488315	+	0.872668i	$0.337612\pi$
$420$	1.10291e14	−	8.01311e13i	0.411784	−	0.299178i
$421$	−1.00574e13	−	3.09536e13i	−0.0370625	−	0.114067i	0.930814	−	0.365494i	$-0.119100\pi$
$421$	−1.00574e13	−	3.09536e13i	−0.0370625	−	0.114067i	−0.967876	+	0.251427i	$0.919100\pi$
$422$	8.00298e13	−	2.46306e14i	0.291094	−	0.895896i
$423$	1.35232e14	+	9.82518e13i	0.485521	+	0.352751i
$424$	−1.12075e14	−	8.14276e13i	−0.397190	−	0.288575i
$425$	5.67107e13	−	1.74538e14i	0.198393	−	0.610591i
$426$	4.35032e13	+	1.33889e14i	0.150234	+	0.462373i
$427$	−3.06603e14	+	2.22760e14i	−1.04526	+	0.759423i
$428$	1.30967e14			0.440778
$429$	9.87781e13	−	1.13173e13i	0.328205	−	0.0376036i
$430$	−1.52730e14			−0.501010
$431$	4.51950e14	−	3.28361e14i	1.46375	−	1.06347i	0.481379	−	0.876513i	$-0.340136\pi$
$431$	4.51950e14	−	3.28361e14i	1.46375	−	1.06347i	0.982367	−	0.186961i	$-0.0598639\pi$
$432$	5.06775e12	+	1.55969e13i	0.0162052	+	0.0498745i
$433$	−9.14480e12	+	2.81448e13i	−0.0288729	+	0.0888617i	−0.964455	−	0.264249i	$-0.914876\pi$
$433$	−9.14480e12	+	2.81448e13i	−0.0288729	+	0.0888617i	0.935582	+	0.353110i	$0.114876\pi$
$434$	−2.17648e14	−	1.58130e14i	−0.678517	−	0.492972i
$435$	−3.25343e14	−	2.36376e14i	−1.00150	−	0.727633i
$436$	5.75618e13	−	1.77157e14i	0.174968	−	0.538497i
$437$	−1.47146e13	−	4.52869e13i	−0.0441673	−	0.135933i
$438$	2.00530e14	−	1.45694e14i	0.594391	−	0.431850i
$439$	1.26853e14			0.371318			0.185659	−	0.982614i	$-0.440558\pi$
$439$	1.26853e14			0.371318			0.185659	+	0.982614i	$0.440558\pi$
$440$	2.85196e13	+	6.24763e13i	0.0824431	+	0.180603i
$441$	2.31251e14			0.660194
$442$	4.62624e13	−	3.36116e13i	0.130438	−	0.0947690i
$443$	−1.28651e14	−	3.95946e14i	−0.358255	−	1.10259i	−0.954098	−	0.299494i	$-0.903182\pi$
$443$	−1.28651e14	−	3.95946e14i	−0.358255	−	1.10259i	0.595844	−	0.803100i	$-0.296818\pi$
$444$	1.86107e13	−	5.72778e13i	0.0511866	−	0.157536i
$445$	−2.50670e14	−	1.82123e14i	−0.680962	−	0.494748i
$446$	2.00269e14	+	1.45504e14i	0.537367	+	0.390420i
$447$	−2.49632e14	+	7.68289e14i	−0.661621	+	2.03626i
$448$	−1.96889e13	−	6.05963e13i	−0.0515458	−	0.158642i
$449$	−3.34265e14	+	2.42858e14i	−0.864442	+	0.628054i	−0.929090	−	0.369854i	$-0.879408\pi$
$449$	−3.34265e14	+	2.42858e14i	−0.864442	+	0.628054i	0.0646474	+	0.997908i	$0.479408\pi$
$450$	−1.60253e14			−0.409390
$451$	2.60449e14	+	1.47139e14i	0.657283	+	0.371327i
$452$	−5.89328e13			−0.146925
$453$	−6.96612e14	+	5.06118e14i	−1.71574	+	1.24656i
$454$	−1.26472e13	−	3.89242e13i	−0.0307743	−	0.0947136i
$455$	2.34222e13	−	7.20861e13i	0.0563074	−	0.173296i
$456$	−1.85813e13	−	1.35001e13i	−0.0441337	−	0.0320650i
$457$	−2.11284e13	−	1.53507e13i	−0.0495825	−	0.0360238i	0.562718	−	0.826649i	$-0.309756\pi$
$457$	−2.11284e13	−	1.53507e13i	−0.0495825	−	0.0360238i	−0.612300	+	0.790625i	$0.709756\pi$
$458$	−6.44511e13	+	1.98360e14i	−0.149441	+	0.459933i
$459$	−2.65300e13	−	8.16510e13i	−0.0607810	−	0.187065i
$460$	1.26269e14	−	9.17401e13i	0.285845	−	0.207678i
$461$	−6.99784e13			−0.156534			−0.0782670	−	0.996932i	$-0.524939\pi$
$461$	−6.99784e13			−0.156534			−0.0782670	+	0.996932i	$0.524939\pi$
$462$	−1.15264e14	+	5.68373e14i	−0.254779	+	1.25633i
$463$	4.58175e14			1.00077			0.500387	−	0.865802i	$-0.333191\pi$
$463$	4.58175e14			1.00077			0.500387	+	0.865802i	$0.333191\pi$
$464$	−1.52055e14	+	1.10474e14i	−0.328209	+	0.238458i
$465$	−9.82272e13	−	3.02312e14i	−0.209527	−	0.644858i
$466$	−1.27114e14	+	3.91216e14i	−0.267960	+	0.824695i
$467$	−5.59144e14	−	4.06242e14i	−1.16488	−	0.846334i	−0.174492	−	0.984659i	$-0.555828\pi$
$467$	−5.59144e14	−	4.06242e14i	−1.16488	−	0.846334i	−0.990387	+	0.138324i	$0.955828\pi$
$468$	−4.03972e13	−	2.93503e13i	−0.0831761	−	0.0604310i
$469$	−3.62429e14	+	1.11544e15i	−0.737518	+	2.26985i
$470$	4.32978e13	+	1.33257e14i	0.0870819	+	0.268011i
$471$	−1.87751e14	+	1.36409e14i	−0.373222	+	0.271162i
$472$	1.24205e14			0.244038
$473$	4.78746e14	−	4.39245e14i	0.929756	−	0.853042i
$474$	8.96584e12			0.0172112
$475$	−3.31552e13	+	2.40887e13i	−0.0629126	+	0.0457087i
$476$	1.03073e14	+	3.17226e14i	0.193333	+	0.595019i
$477$	1.95696e14	−	6.02289e14i	0.362852	−	1.11674i
$478$	−1.64440e14	−	1.19472e14i	−0.301407	−	0.218985i
$479$	−3.30418e14	−	2.40063e14i	−0.598713	−	0.434990i	0.246709	−	0.969090i	$-0.420651\pi$
$479$	−3.30418e14	−	2.40063e14i	−0.598713	−	0.434990i	−0.845422	+	0.534099i	$0.820651\pi$
$480$	2.32635e13	−	7.15977e13i	0.0416724	−	0.128254i
$481$	−1.03473e13	−	3.18456e13i	−0.0183243	−	0.0563964i
$482$	4.16812e14	−	3.02832e14i	0.729762	−	0.530203i
$483$	1.31798e15			2.28139
$484$	−2.69077e14	−	1.13817e14i	−0.460498	−	0.194786i
$485$	−3.99437e14			−0.675879
$486$	−4.53451e14	+	3.29452e14i	−0.758632	+	0.551178i
$487$	−1.71373e14	−	5.27432e14i	−0.283487	−	0.872484i	−0.986848	−	0.161651i	$-0.948318\pi$
$487$	−1.71373e14	−	5.27432e14i	−0.283487	−	0.872484i	0.703361	−	0.710833i	$-0.251682\pi$
$488$	−6.46711e13	+	1.99037e14i	−0.105780	+	0.325556i
$489$	−7.49183e14	−	5.44313e14i	−1.21168	−	0.880339i
$490$	1.56821e14	+	1.13937e14i	0.250798	+	0.182216i
$491$	−5.07573e13	+	1.56215e14i	−0.0802694	+	0.247044i	−0.983136	−	0.182878i	$-0.941459\pi$
$491$	−5.07573e13	+	1.56215e14i	−0.0802694	+	0.247044i	0.902866	+	0.429922i	$0.141459\pi$
$492$	−1.01328e14	−	3.11855e14i	−0.158461	−	0.487692i
$493$	7.96016e14	−	5.78339e14i	1.23102	−	0.894386i
$494$	−1.27697e13			−0.0195292
$495$	−2.31336e14	+	2.12248e14i	−0.349876	+	0.321008i
$496$	−1.48562e14			−0.222207
$497$	−3.69361e14	+	2.68357e14i	−0.546376	+	0.396965i
$498$	3.93249e14	+	1.21030e15i	0.575316	+	1.77064i
$499$	2.57640e13	−	7.92933e13i	0.0372786	−	0.114732i	−0.930686	−	0.365820i	$-0.880789\pi$
$499$	2.57640e13	−	7.92933e13i	0.0372786	−	0.114732i	0.967964	+	0.251088i	$0.0807885\pi$
$500$	−2.67395e14	−	1.94274e14i	−0.382665	−	0.278022i
$501$	−1.98174e14	−	1.43982e14i	−0.280505	−	0.203799i
$502$	2.72095e14	−	8.37423e14i	0.380935	−	1.17240i
$503$	3.47414e14	+	1.06923e15i	0.481087	+	1.48063i	0.837570	+	0.546331i	$0.183976\pi$
$503$	3.47414e14	+	1.06923e15i	0.481087	+	1.48063i	−0.356483	+	0.934302i	$0.616024\pi$
$504$	2.35637e14	−	1.71200e14i	0.322757	−	0.234497i
$505$	3.24535e14			0.439703
$506$	−1.31963e14	+	6.50715e14i	−0.176858	+	0.872093i
$507$	9.64142e14			1.27819
$508$	4.81774e13	−	3.50029e13i	0.0631819	−	0.0459043i
$509$	−1.15566e14	−	3.55675e14i	−0.149928	−	0.461430i	0.847684	−	0.530501i	$-0.177996\pi$
$509$	−1.15566e14	−	3.55675e14i	−0.149928	−	0.461430i	−0.997612	+	0.0690714i	$0.977996\pi$
$510$	−1.21786e14	+	3.74819e14i	−0.156301	+	0.481045i
$511$	6.50332e14	+	4.72494e14i	0.825695	+	0.599903i
$512$	−2.84648e13	−	2.06809e13i	−0.0357538	−	0.0259767i
$513$	−5.92447e12	+	1.82336e13i	−0.00736214	+	0.0226583i
$514$	−2.22657e14	−	6.85268e14i	−0.273741	−	0.842487i
$515$	5.74819e14	−	4.17631e14i	0.699184	−	0.507987i
$516$	−7.12197e14			−0.857091
$517$	−5.18964e14	−	2.93185e14i	−0.617930	−	0.349095i
$518$	1.95315e14			0.230103
$519$	−3.76183e14	+	2.73313e14i	−0.438510	+	0.318596i
$520$	−1.29341e13	−	3.98072e13i	−0.0149183	−	0.0459138i
$521$	−1.89642e13	+	5.83658e13i	−0.0216435	+	0.0666118i	−0.961295	−	0.275522i	$-0.911149\pi$
$521$	−1.89642e13	+	5.83658e13i	−0.0216435	+	0.0666118i	0.939651	+	0.342133i	$0.111149\pi$
$522$	−6.95096e14	−	5.05017e14i	−0.784978	−	0.570320i
$523$	3.53350e14	+	2.56724e14i	0.394863	+	0.286885i	0.767445	−	0.641114i	$-0.221528\pi$
$523$	3.53350e14	+	2.56724e14i	0.394863	+	0.286885i	−0.372582	+	0.927999i	$0.621528\pi$
$524$	−9.75611e13	+	3.00262e14i	−0.107883	+	0.332031i
$525$	−3.50524e14	−	1.07880e15i	−0.383568	−	1.18050i
$526$	5.27853e14	−	3.83507e14i	0.571599	−	0.415291i
$527$	7.77731e14			0.833433
$528$	1.32991e14	+	2.91335e14i	0.141037	+	0.308963i
$529$	5.56108e14			0.583650
$530$	4.29456e14	−	3.12018e14i	0.446068	−	0.324087i
$531$	1.75455e14	+	5.39996e14i	0.180363	+	0.555099i
$532$	2.30174e13	−	7.08403e13i	0.0234176	−	0.0720720i
$533$	−1.47492e14	−	1.07159e14i	−0.148514	−	0.107902i
$534$	−1.16891e15	−	8.49261e14i	−1.16494	−	0.846378i
$535$	−1.55078e14	+	4.77282e14i	−0.152970	+	0.470792i
$536$	2.00140e14	+	6.15967e14i	0.195401	+	0.601383i
$537$	1.51610e15	−	1.10151e15i	1.46511	−	1.06446i
$538$	5.97596e14			0.571617
$539$	−8.19249e14	+	9.38642e13i	−0.775671	+	0.0888713i
$540$	−6.28406e13			−0.0588945
$541$	−1.00487e15	+	7.30084e14i	−0.932237	+	0.677310i	−0.946540	−	0.322588i	$-0.895447\pi$
$541$	−1.00487e15	+	7.30084e14i	−0.932237	+	0.677310i	0.0143022	+	0.999898i	$0.495447\pi$
$542$	4.02362e14	+	1.23834e15i	0.369506	+	1.13722i
$543$	1.56229e14	−	4.80824e14i	0.142024	−	0.437106i
$544$	1.49015e14	+	1.08266e14i	0.134102	+	0.0974310i
$545$	5.77454e14	+	4.19545e14i	0.514442	+	0.373764i
$546$	1.09221e14	−	3.36147e14i	0.0963265	−	0.296462i
$547$	−4.17695e14	−	1.28553e15i	−0.364695	−	1.12241i	−0.950172	−	0.311726i	$-0.899093\pi$
$547$	−4.17695e14	−	1.28553e15i	−0.364695	−	1.12241i	0.585477	−	0.810689i	$-0.300907\pi$
$548$	5.87649e14	−	4.26952e14i	0.507955	−	0.369051i
$549$	−9.56696e14			−0.818702
$550$	5.67726e14	−	6.50463e13i	0.480998	−	0.0551097i
$551$	−2.19723e14			−0.184307
$552$	5.88810e14	−	4.27796e14i	0.489002	−	0.355281i
$553$	8.98521e12	+	2.76536e13i	0.00738823	+	0.0227386i
$554$	−6.70479e13	+	2.06352e14i	−0.0545861	+	0.167999i
$555$	1.86700e14	+	1.35646e14i	0.150499	+	0.109344i
$556$	5.49404e14	+	3.99165e14i	0.438511	+	0.318597i
$557$	−6.03084e14	+	1.85610e15i	−0.476622	+	1.46689i	0.367136	+	0.930167i	$0.380338\pi$
$557$	−6.03084e14	+	1.85610e15i	−0.476622	+	1.46689i	−0.843758	+	0.536724i	$0.819662\pi$
$558$	−2.09862e14	−	6.45890e14i	−0.164228	−	0.505441i
$559$	−3.20347e14	+	2.32746e14i	−0.248231	+	0.180350i
$560$	2.44145e14			0.187333
$561$	−6.96215e14	−	1.52516e15i	−0.528991	−	1.15883i
$562$	−2.11663e14			−0.159255
$563$	−6.34011e14	+	4.60636e14i	−0.472390	+	0.343211i	−0.798372	−	0.602165i	$-0.794305\pi$
$563$	−6.34011e14	+	4.60636e14i	−0.472390	+	0.343211i	0.325982	+	0.945376i	$0.394305\pi$
$564$	2.01903e14	+	6.21395e14i	0.148973	+	0.458493i
$565$	6.97825e13	−	2.14769e14i	0.0509894	−	0.156929i
$566$	−8.79462e14	−	6.38967e14i	−0.636395	−	0.462368i
$567$	−1.70318e15	−	1.23743e15i	−1.22055	−	0.886778i
$568$	−7.79087e13	+	2.39778e14i	−0.0552930	+	0.170174i
$569$	−3.37283e13	−	1.03805e14i	−0.0237070	−	0.0729628i	0.938503	−	0.345271i	$-0.112213\pi$
$569$	−3.37283e13	−	1.03805e14i	−0.0237070	−	0.0729628i	−0.962210	+	0.272308i	$0.912213\pi$
$570$	7.12007e13	−	5.17303e13i	0.0495647	−	0.0360109i
$571$	2.11851e15			1.46060			0.730302	−	0.683124i	$-0.239379\pi$
$571$	2.11851e15			1.46060			0.730302	+	0.683124i	$0.239379\pi$
$572$	1.55028e14	+	8.75815e13i	0.105860	+	0.0598046i
$573$	2.03816e15			1.37844
$574$	8.60320e14	−	6.25059e14i	0.576294	−	0.418702i
$575$	−4.01306e14	−	1.23509e15i	−0.266258	−	0.819458i
$576$	4.97025e13	−	1.52968e14i	0.0326629	−	0.100526i
$577$	3.22647e14	+	2.34417e14i	0.210020	+	0.152589i	0.687823	−	0.725879i	$-0.258567\pi$
$577$	3.22647e14	+	2.34417e14i	0.210020	+	0.152589i	−0.477803	+	0.878467i	$0.658567\pi$
$578$	1.07146e14	+	7.78459e13i	0.0690831	+	0.0501918i
$579$	−5.27877e14	+	1.62464e15i	−0.337133	+	1.03759i
$580$	−2.22552e14	−	6.84945e14i	−0.140792	−	0.433313i
$581$	−3.33886e15	+	2.42582e15i	−2.09233	+	1.52016i
$582$	−1.86263e15			−1.15624
$583$	−4.48820e14	+	2.21315e15i	−0.275991	+	1.36092i
$584$	4.43902e14			0.270406
$585$	1.54796e14	−	1.12466e14i	0.0934117	−	0.0678676i
$586$	−2.90183e14	−	8.93093e14i	−0.173475	−	0.533900i
$587$	−6.54992e14	+	2.01586e15i	−0.387906	+	1.19385i	0.546445	+	0.837495i	$0.315981\pi$
$587$	−6.54992e14	+	2.01586e15i	−0.387906	+	1.19385i	−0.934350	+	0.356356i	$0.884019\pi$
$588$	7.31275e14	+	5.31302e14i	0.429047	+	0.311721i
$589$	−1.40507e14	−	1.02084e14i	−0.0816703	−	0.0593370i
$590$	−1.47071e14	+	4.52639e14i	−0.0846920	+	0.260655i
$591$	1.21162e15	+	3.72897e15i	0.691248	+	2.12744i
$592$	8.72575e13	−	6.33963e13i	0.0493211	−	0.0358339i
$593$	9.70002e14			0.543215			0.271608	−	0.962408i	$-0.412445\pi$
$593$	9.70002e14			0.543215			0.271608	+	0.962408i	$0.412445\pi$
$594$	1.96980e14	−	1.80728e14i	0.109294	−	0.100276i
$595$	−1.27812e15			−0.702630
$596$	−1.17042e15	+	8.50358e14i	−0.637509	+	0.463177i
$597$	1.32364e14	+	4.07375e14i	0.0714350	+	0.219854i
$598$	1.25044e14	−	3.84846e14i	0.0668661	−	0.205793i
$599$	3.61018e14	+	2.62295e14i	0.191285	+	0.138977i	0.679306	−	0.733855i	$-0.262281\pi$
$599$	3.61018e14	+	2.62295e14i	0.191285	+	0.138977i	−0.488021	+	0.872832i	$0.662281\pi$
$600$	−5.06761e14	−	3.68183e14i	−0.266055	−	0.193300i
$601$	1.86390e14	−	5.73649e14i	0.0969645	−	0.298426i	−0.890796	−	0.454403i	$-0.849853\pi$
$601$	1.86390e14	−	5.73649e14i	0.0969645	−	0.298426i	0.987761	+	0.155977i	$0.0498526\pi$
$602$	−7.13737e14	−	2.19666e15i	−0.367923	−	1.13235i
$603$	−2.39527e15	+	1.74026e15i	−1.22351	+	0.888935i
$604$	−1.54205e15			−0.780540
$605$	7.33399e14	−	8.45828e14i	0.367863	−	0.424255i
$606$	1.51335e15			0.752212
$607$	−5.24871e12	+	3.81341e12i	−0.00258532	+	0.00187835i	−0.589077	−	0.808077i	$-0.700509\pi$
$607$	−5.24871e12	+	3.81341e12i	−0.00258532	+	0.00187835i	0.586492	+	0.809955i	$0.300509\pi$
$608$	−1.27106e13	−	3.91192e13i	−0.00620435	−	0.0190950i
$609$	1.87931e15	−	5.78393e15i	0.909084	−	2.79787i
$610$	−6.48774e14	−	4.71362e14i	−0.311014	−	0.225965i
$611$	2.93888e14	+	2.13522e14i	0.139622	+	0.101442i
$612$	−2.60196e14	+	8.00801e14i	−0.122509	+	0.377044i
$613$	3.08608e14	+	9.49798e14i	0.144004	+	0.443199i	0.996882	−	0.0789122i	$-0.0251447\pi$
$613$	3.08608e14	+	9.49798e14i	0.144004	+	0.443199i	−0.852878	+	0.522111i	$0.825145\pi$
$614$	−1.17542e15	+	8.53993e14i	−0.543585	+	0.394937i
$615$	1.25648e15			0.575893
$616$	−7.65297e14	+	7.02152e14i	−0.347645	+	0.318961i
$617$	−2.85807e15			−1.28678			−0.643389	−	0.765539i	$-0.722472\pi$
$617$	−2.85807e15			−1.28678			−0.643389	+	0.765539i	$0.722472\pi$
$618$	2.68046e15	−	1.94747e15i	1.19611	−	0.869027i
$619$	−1.32609e15	−	4.08130e15i	−0.586511	−	1.80509i	−0.593117	−	0.805117i	$-0.702103\pi$
$619$	−1.32609e15	−	4.08130e15i	−0.586511	−	1.80509i	0.00660585	−	0.999978i	$-0.497897\pi$
$620$	1.75912e14	−	5.41403e14i	0.0771156	−	0.237337i
$621$	−4.91500e14	−	3.57096e14i	−0.213560	−	0.155160i
$622$	1.34239e15	+	9.75304e14i	0.578138	+	0.420042i
$623$	1.44797e15	−	4.45640e15i	0.618124	−	1.90239i
$624$	−6.03136e13	−	1.85626e14i	−0.0255211	−	0.0785459i
$625$	−2.96035e14	+	2.15082e14i	−0.124166	+	0.0902119i
$626$	−1.76704e15			−0.734660
$627$	−7.44111e13	+	3.66925e14i	−0.0306666	+	0.151219i
$628$	−4.15614e14			−0.169790
$629$	−4.56799e14	+	3.31884e14i	−0.184989	+	0.134403i
$630$	3.44886e14	+	1.06145e15i	0.138453	+	0.426115i
$631$	5.27473e14	−	1.62339e15i	0.209913	−	0.646045i	−0.789563	−	0.613669i	$-0.789693\pi$
$631$	5.27473e14	−	1.62339e15i	0.209913	−	0.646045i	0.999476	−	0.0323754i	$-0.0103072\pi$
$632$	1.29901e13	+	9.43788e12i	0.00512471	+	0.00372332i
$633$	3.74380e15	+	2.72003e15i	1.46417	+	1.06378i
$634$	−2.71842e14	+	8.36645e14i	−0.105397	+	0.324377i
$635$	7.05140e13	+	2.17020e14i	0.0271032	+	0.0834149i
$636$	2.00261e15	−	1.45498e15i	0.763100	−	0.554425i
$637$	5.02557e14			0.189854
$638$	2.66749e15	+	1.50698e15i	0.999054	+	0.564408i
$639$	−1.15252e15			−0.427952
$640$	1.09072e14	−	7.92458e13i	0.0401537	−	0.0291733i
$641$	7.36573e14	+	2.26694e15i	0.268842	+	0.827409i	0.990783	+	0.135456i	$0.0432498\pi$
$641$	7.36573e14	+	2.26694e15i	0.268842	+	0.827409i	−0.721942	+	0.691954i	$0.756750\pi$
$642$	−7.23150e14	+	2.22563e15i	−0.261689	+	0.805396i
$643$	2.87100e15	+	2.08591e15i	1.03009	+	0.748401i	0.968326	−	0.249690i	$-0.0803288\pi$
$643$	2.87100e15	+	2.08591e15i	1.03009	+	0.748401i	0.0617595	+	0.998091i	$0.480329\pi$
$644$	1.90955e15	+	1.38737e15i	0.679295	+	0.493537i
$645$	8.43316e14	−	2.59546e15i	0.297449	−	0.915453i
$646$	6.65409e13	+	2.04792e14i	0.0232707	+	0.0716199i
$647$	2.33805e15	−	1.69869e15i	0.810738	−	0.589035i	−0.103307	−	0.994650i	$-0.532942\pi$
$647$	2.33805e15	−	1.69869e15i	0.810738	−	0.589035i	0.914044	+	0.405614i	$0.132942\pi$
$648$	−1.16255e15			−0.399715
$649$	−8.40765e14	−	1.84182e15i	−0.286635	−	0.627914i
$650$	−3.48264e14			−0.117729
$651$	3.88901e15	−	2.82553e15i	1.30360	−	0.947120i
$652$	−5.12480e14	−	1.57725e15i	−0.170340	−	0.524251i
$653$	−7.00072e14	+	2.15460e15i	−0.230739	+	0.710140i	0.766920	+	0.641743i	$0.221788\pi$
$653$	−7.00072e14	+	2.15460e15i	−0.230739	+	0.710140i	−0.997658	+	0.0683971i	$0.978212\pi$
$654$	2.69274e15	+	1.95639e15i	0.880070	+	0.639408i
$655$	−9.78723e14	−	7.11084e14i	−0.317199	−	0.230459i
$656$	1.81466e14	−	5.58494e14i	0.0583208	−	0.179493i
$657$	6.27069e14	+	1.92992e15i	0.199851	+	0.615077i
$658$	−1.71425e15	+	1.24548e15i	−0.541791	+	0.393634i
$659$	1.08037e15			0.338611			0.169306	−	0.985564i	$-0.445847\pi$
$659$	1.08037e15			0.338611			0.169306	+	0.985564i	$0.445847\pi$
$660$	−1.21919e15	+	1.39687e14i	−0.378947	+	0.0434173i
$661$	−4.19346e15			−1.29260			−0.646301	−	0.763083i	$-0.723685\pi$
$661$	−4.19346e15			−1.29260			−0.646301	+	0.763083i	$0.723685\pi$
$662$	−7.71197e14	+	5.60307e14i	−0.235747	+	0.171280i
$663$	3.15746e14	+	9.71765e14i	0.0957223	+	0.294603i
$664$	−7.04259e14	+	2.16749e15i	−0.211743	+	0.651676i
$665$	2.30908e14	+	1.67765e14i	0.0688526	+	0.0500243i
$666$	3.98886e14	+	2.89807e14i	0.117961	+	0.0857040i
$667$	2.15158e15	−	6.62187e15i	0.631052	−	1.94218i
$668$	−1.35562e14	−	4.17216e14i	−0.0394336	−	0.121364i
$669$	−3.57847e15	+	2.59991e15i	−1.03241	+	0.750093i
$670$	−2.48175e15			−0.710145
$671$	3.38927e15	−	3.88320e14i	0.961905	−	0.110209i
$672$	1.13848e15			0.320475
$673$	6.88678e14	−	5.00354e14i	0.192280	−	0.139699i	−0.487480	−	0.873134i	$-0.662084\pi$
$673$	6.88678e14	−	5.00354e14i	0.192280	−	0.139699i	0.679760	+	0.733435i	$0.262084\pi$
$674$	−6.64211e14	−	2.04423e15i	−0.183940	−	0.566110i
$675$	−1.61576e14	+	4.97279e14i	−0.0443818	+	0.136593i
$676$	1.39689e15	+	1.01490e15i	0.380589	+	0.276514i
$677$	2.90736e15	+	2.11232e15i	0.785707	+	0.570850i	0.906686	−	0.421805i	$-0.138603\pi$
$677$	2.90736e15	+	2.11232e15i	0.785707	+	0.570850i	−0.120979	+	0.992655i	$0.538603\pi$
$678$	3.25405e14	−	1.00149e15i	0.0872290	−	0.268463i
$679$	−1.86665e15	−	5.74497e15i	−0.496341	−	1.52758i
$680$	−5.71002e14	+	4.14857e14i	−0.150605	+	0.109421i
$681$	7.31304e14			0.191333
$682$	1.00564e15	+	2.20300e15i	0.260993	+	0.571743i
$683$	−3.30784e15			−0.851590			−0.425795	−	0.904820i	$-0.640005\pi$
$683$	−3.30784e15			−0.851590			−0.425795	+	0.904820i	$0.640005\pi$
$684$	1.52120e14	−	1.10522e14i	0.0388489	−	0.0282254i
$685$	8.60103e14	+	2.64712e15i	0.217897	+	0.670620i
$686$	2.54390e14	−	7.82931e14i	0.0639318	−	0.196762i
$687$	−3.01502e15	−	2.19054e15i	−0.751672	−	0.546122i
$688$	−1.03187e15	−	7.49694e14i	−0.255203	−	0.185416i
$689$	4.25288e14	−	1.30890e15i	0.104346	−	0.321145i
$690$	8.61802e14	+	2.65235e15i	0.209767	+	0.645597i
$691$	−5.41695e15	+	3.93564e15i	−1.30805	+	0.950357i	−0.999999	−	0.00101225i	$-0.999678\pi$
$691$	−5.41695e15	+	3.93564e15i	−1.30805	+	0.950357i	−0.308054	+	0.951369i	$0.599678\pi$
$692$	−8.32735e14			−0.199491
$693$	−4.13378e15	−	2.33534e15i	−0.982458	−	0.555032i
$694$	−1.95041e15			−0.459884
$695$	−2.10523e15	+	1.52954e15i	−0.492473	+	0.357803i
$696$	−1.03779e15	−	3.19399e15i	−0.240856	−	0.741280i
$697$	−9.49985e14	+	2.92375e15i	−0.218744	+	0.673225i
$698$	−3.85067e15	−	2.79768e15i	−0.879694	−	0.639135i
$699$	−5.94638e15	−	4.32030e15i	−1.34781	−	0.979240i
$700$	6.27745e14	−	1.93200e15i	0.141170	−	0.434478i
$701$	9.12145e14	+	2.80729e15i	0.203524	+	0.626381i	0.999771	+	0.0214098i	$0.00681547\pi$
$701$	9.12145e14	+	2.80729e15i	0.203524	+	0.626381i	−0.796247	+	0.604971i	$0.793185\pi$
$702$	−1.31807e14	+	9.57634e13i	−0.0291799	+	0.0212005i
$703$	1.26090e14			0.0276965
$704$	−1.13991e14	+	5.62093e14i	−0.0248439	+	0.122506i
$705$	−2.50362e15			−0.541413
$706$	8.69748e14	−	6.31909e14i	0.186624	−	0.135590i
$707$	1.51662e15	+	4.66768e15i	0.322902	+	0.993789i
$708$	−6.85813e14	+	2.11072e15i	−0.144885	+	0.445910i
$709$	1.77648e15	+	1.29069e15i	0.372397	+	0.270563i	0.758204	−	0.652017i	$-0.226077\pi$
$709$	1.77648e15	+	1.29069e15i	0.372397	+	0.270563i	−0.385807	+	0.922580i	$0.626077\pi$
$710$	−7.81572e14	−	5.67845e14i	−0.162573	−	0.118116i
$711$	−2.26821e13	+	6.98084e13i	−0.00468167	+	0.0144087i
$712$	−7.99595e14	−	2.46090e15i	−0.163768	−	0.504027i
$713$	4.45243e15	−	3.23488e15i	0.904909	−	0.657455i
$714$	−5.96002e15			−1.20201
$715$	−5.02742e14	+	4.61261e14i	−0.100615	+	0.0923131i
$716$	3.35610e15			0.666521
$717$	2.93827e15	−	2.13478e15i	0.579076	−	0.420724i
$718$	1.98791e15	+	6.11816e15i	0.388788	+	1.19657i
$719$	−1.31367e15	+	4.04308e15i	−0.254964	+	0.784699i	0.738873	+	0.673845i	$0.235358\pi$
$719$	−1.31367e15	+	4.04308e15i	−0.254964	+	0.784699i	−0.993837	+	0.110854i	$0.964642\pi$
$720$	4.98610e14	+	3.62261e14i	0.0960356	+	0.0697739i
$721$	8.69289e15	+	6.31575e15i	1.66158	+	1.20721i
$722$	−1.13706e15	+	3.49951e15i	−0.215689	+	0.663824i
$723$	2.84479e15	+	8.75535e15i	0.535537	+	1.64821i
$724$	7.32491e14	−	5.32186e14i	0.136849	−	0.0994263i
$725$	−5.99242e15			−1.11107
$726$	3.41993e15	−	3.94420e15i	0.629312	−	0.725785i
$727$	5.19252e15			0.948285			0.474143	−	0.880448i	$-0.342758\pi$
$727$	5.19252e15			0.948285			0.474143	+	0.880448i	$0.342758\pi$
$728$	5.12089e14	−	3.72054e14i	0.0928160	−	0.0674348i
$729$	−1.15272e15	−	3.54771e15i	−0.207359	−	0.638186i
$730$	−5.25626e14	+	1.61771e15i	−0.0938429	+	0.288819i
$731$	5.40189e15	+	3.92470e15i	0.957194	+	0.695442i
$732$	−3.02532e15	−	2.19802e15i	−0.532059	−	0.386564i
$733$	−2.97774e15	+	9.16454e15i	−0.519774	+	1.59970i	0.254649	+	0.967033i	$0.418040\pi$
$733$	−2.97774e15	+	9.16454e15i	−0.519774	+	1.59970i	−0.774424	+	0.632667i	$0.781960\pi$
$734$	−2.05382e15	−	6.32100e15i	−0.355823	−	1.09511i
$735$	−2.80213e15	+	2.03587e15i	−0.481845	+	0.350081i
$736$	1.30341e15			0.222461
$737$	7.77930e15	−	7.13744e15i	1.31786	−	1.20912i
$738$	2.68447e15			0.451386
$739$	−1.10978e15	+	8.06300e14i	−0.185221	+	0.134571i	−0.676532	−	0.736413i	$-0.736518\pi$
$739$	−1.10978e15	+	8.06300e14i	−0.185221	+	0.134571i	0.491311	+	0.870984i	$0.336518\pi$
$740$	1.27713e14	+	3.93060e14i	0.0211573	+	0.0651155i
$741$	7.05097e13	−	2.17007e14i	0.0115944	−	0.0356839i
$742$	6.49458e15	+	4.71859e15i	1.06006	+	0.770177i
$743$	−7.91501e15	−	5.75059e15i	−1.28237	−	0.931696i	−0.282747	−	0.959194i	$-0.591246\pi$
$743$	−7.91501e15	−	5.75059e15i	−1.28237	−	0.931696i	−0.999622	+	0.0274986i	$0.991246\pi$
$744$	8.20302e14	−	2.52463e15i	0.131924	−	0.406019i
$745$	−1.71306e15	−	5.27226e15i	−0.273472	−	0.841662i
$746$	1.21326e15	−	8.81487e14i	0.192261	−	0.139686i
$747$	−1.04183e16			−1.63882
$748$	5.96748e14	−	2.94259e15i	0.0931821	−	0.459485i
$749$	−7.58929e15			−1.17639
$750$	4.77792e15	−	3.47136e15i	0.735194	−	0.534150i
$751$	−3.07756e15	−	9.47176e15i	−0.470097	−	1.44681i	−0.852458	−	0.522796i	$-0.824889\pi$
$751$	−3.07756e15	−	9.47176e15i	−0.470097	−	1.44681i	0.382362	−	0.924013i	$-0.375111\pi$
$752$	−3.61584e14	+	1.11284e15i	−0.0548290	+	0.168746i
$753$	1.27286e16	+	9.24788e15i	1.91606	+	1.39210i
$754$	−1.51059e15	−	1.09751e15i	−0.225738	−	0.164008i
$755$	1.82595e15	−	5.61969e15i	0.270882	−	0.833689i
$756$	−2.93667e14	−	9.03815e14i	−0.0432499	−	0.133110i
$757$	7.61504e15	−	5.53265e15i	1.11338	−	0.808921i	0.130191	−	0.991489i	$-0.458441\pi$
$757$	7.61504e15	−	5.53265e15i	1.11338	−	0.808921i	0.983193	+	0.182568i	$0.0584411\pi$
$758$	7.16282e15			1.03969
$759$	−1.03295e16	−	5.83556e15i	−1.48850	−	0.840917i
$760$	1.57613e14			0.0225485
$761$	4.60723e14	−	3.34735e14i	0.0654371	−	0.0475428i	−0.554586	−	0.832127i	$-0.687123\pi$
$761$	4.60723e14	−	3.34735e14i	0.0654371	−	0.0475428i	0.620023	+	0.784584i	$0.287123\pi$
$762$	3.28816e14	+	1.01199e15i	0.0463661	+	0.142700i
$763$	−3.33561e15	+	1.02659e16i	−0.466971	+	1.43719i
$764$	2.95299e15	+	2.14547e15i	0.410439	+	0.298201i
$765$	−2.61026e15	−	1.89646e15i	−0.360201	−	0.261702i
$766$	1.79263e15	−	5.51716e15i	0.245603	−	0.755887i
$767$	3.81301e14	+	1.17353e15i	0.0518673	+	0.159631i
$768$	5.08619e14	−	3.69533e14i	0.0686919	−	0.0499076i
$769$	8.33188e15			1.11724			0.558622	−	0.829422i	$-0.311330\pi$
$769$	8.33188e15			1.11724			0.558622	+	0.829422i	$0.311330\pi$
$770$	−1.65266e15	−	3.62039e15i	−0.220032	−	0.482011i
$771$	1.28748e16			1.70192
$772$	−2.47499e15	+	1.79818e15i	−0.324846	+	0.236015i
$773$	−2.07493e15	−	6.38598e15i	−0.270406	−	0.832225i	−0.990398	−	0.138243i	$-0.955855\pi$
$773$	−2.07493e15	−	6.38598e15i	−0.270406	−	0.832225i	0.719992	−	0.693982i	$-0.244145\pi$
$774$	1.80175e15	−	5.54520e15i	0.233141	−	0.717533i
$775$	−3.83200e15	−	2.78411e15i	−0.492341	−	0.357706i
$776$	−2.69866e15	−	1.96069e15i	−0.344278	−	0.250133i
$777$	−1.07846e15	+	3.31915e15i	−0.136611	+	0.420447i
$778$	2.96658e15	+	9.13019e15i	0.373137	+	1.14840i
$779$	5.55397e14	−	4.03520e14i	0.0693662	−	0.0503975i
$780$	7.47894e14			0.0927513
$781$	4.08302e15	−	4.67806e14i	0.502806	−	0.0576083i
$782$	−6.82347e15			−0.834388
$783$	−2.26794e15	+	1.64776e15i	−0.275387	+	0.200080i
$784$	5.00231e14	+	1.53955e15i	0.0603159	+	0.185633i
$785$	4.92130e14	−	1.51462e15i	0.0589246	−	0.181351i
$786$	−4.56391e15	−	3.31587e15i	−0.542641	−	0.394252i
$787$	−5.98991e15	−	4.35193e15i	−0.707228	−	0.513831i	0.175050	−	0.984559i	$-0.443991\pi$
$787$	−5.98991e15	−	4.35193e15i	−0.707228	−	0.513831i	−0.882278	+	0.470728i	$0.843991\pi$
$788$	−2.16985e15	+	6.67812e15i	−0.254411	+	0.782997i
$789$	3.60265e15	+	1.10878e16i	0.419468	+	1.29099i
$790$	−4.97761e13	+	3.61645e13i	−0.00575535	+	0.00418151i
$791$	3.41505e15			0.392127
$792$	−2.60479e15	+	2.98440e14i	−0.297019	+	0.0340306i
$793$	−2.07910e15			−0.235436
$794$	−1.96305e15	+	1.42624e15i	−0.220759	+	0.160391i
$795$	2.93108e15	+	9.02094e15i	0.327347	+	1.00747i
$796$	−2.37047e14	+	7.29556e14i	−0.0262914	+	0.0809165i
$797$	8.31360e15	+	6.04019e15i	0.915732	+	0.665318i	0.942458	−	0.334324i	$-0.108508\pi$
$797$	8.31360e15	+	6.04019e15i	0.915732	+	0.665318i	−0.0267257	+	0.999643i	$0.508508\pi$
$798$	1.07675e15	+	7.82308e14i	0.117788	+	0.0855779i
$799$	1.89291e15	−	5.82579e15i	0.205648	−	0.632918i
$800$	−3.46651e14	−	1.06688e15i	−0.0374023	−	0.115112i
$801$	9.56953e15	−	6.95267e15i	1.02544	−	0.745029i
$802$	1.63052e15			0.173527
$803$	−3.00485e15	−	6.58256e15i	−0.317605	−	0.695760i
$804$	−1.15727e16			−1.21486
$805$	−7.31709e15	+	5.31617e15i	−0.762888	+	0.554271i
$806$	−4.56076e14	−	1.40366e15i	−0.0472274	−	0.145351i
$807$	−3.29970e15	+	1.01554e16i	−0.339368	+	1.04447i
$808$	2.19261e15	+	1.59303e15i	0.223975	+	0.162727i
$809$	2.63997e15	+	1.91805e15i	0.267845	+	0.194600i	0.713598	−	0.700555i	$-0.247064\pi$
$809$	2.63997e15	+	1.91805e15i	0.267845	+	0.194600i	−0.445754	+	0.895156i	$0.647064\pi$
$810$	1.37658e15	−	4.23669e15i	0.138719	−	0.426933i
$811$	4.47129e14	+	1.37612e15i	0.0447526	+	0.137734i	0.970936	−	0.239339i	$-0.0769306\pi$
$811$	4.47129e14	+	1.37612e15i	0.0447526	+	0.137734i	−0.926184	+	0.377073i	$0.876931\pi$
$812$	8.81129e15	−	6.40178e15i	0.875954	−	0.636418i
$813$	−2.32659e16			−2.29732
$814$	−1.53076e15	−	8.64788e14i	−0.150132	−	0.0848156i
$815$	6.35481e15			0.619064
$816$	−2.66266e15	+	1.93453e15i	−0.257643	+	0.187189i
$817$	−4.60767e14	−	1.41810e15i	−0.0442854	−	0.136296i
$818$	2.71138e15	−	8.34476e15i	0.258849	−	0.796655i
$819$	2.34094e15	+	1.70080e15i	0.221988	+	0.161284i
$820$	1.82044e15	+	1.32263e15i	0.171475	+	0.124584i
$821$	−2.03121e15	+	6.25143e15i	−0.190050	+	0.584914i	−0.999999	−	0.00158667i	$-0.999495\pi$
$821$	−2.03121e15	+	6.25143e15i	−0.190050	+	0.584914i	0.809949	+	0.586501i	$0.199495\pi$
$822$	4.01077e15	+	1.23439e16i	0.372763	+	1.14725i
$823$	2.91252e15	−	2.11607e15i	0.268887	−	0.195358i	−0.445169	−	0.895447i	$-0.646856\pi$
$823$	2.91252e15	−	2.11607e15i	0.268887	−	0.195358i	0.714056	+	0.700089i	$0.246856\pi$
$824$	5.93357e15			0.544147
$825$	−2.02938e15	+	1.00070e16i	−0.184871	+	0.911605i
$826$	−7.19745e15			−0.651311
$827$	8.89704e15	−	6.46408e15i	0.799770	−	0.581067i	−0.111076	−	0.993812i	$-0.535430\pi$
$827$	8.89704e15	−	6.46408e15i	0.799770	−	0.581067i	0.910847	+	0.412745i	$0.135430\pi$
$828$	1.84124e15	+	5.66676e15i	0.164416	+	0.506020i
$829$	2.21712e15	−	6.82360e15i	0.196671	−	0.605291i	−0.803282	−	0.595599i	$-0.796915\pi$
$829$	2.21712e15	−	6.82360e15i	0.196671	−	0.605291i	0.999953	−	0.00969197i	$-0.00308510\pi$
$830$	−7.06505e15	−	5.13306e15i	−0.622567	−	0.452321i
$831$	−3.13650e15	−	2.27880e15i	−0.274562	−	0.199481i
$832$	1.08014e14	−	3.32433e14i	0.00939294	−	0.0289085i
$833$	−2.61874e15	−	8.05966e15i	−0.226227	−	0.696256i
$834$	−9.81695e15	+	7.13243e15i	−0.842487	+	0.612103i
$835$	1.68098e15			0.143313
$836$	−4.94053e14	+	4.53289e14i	−0.0418446	+	0.0383920i
$837$	−2.21585e15			−0.186445
$838$	−6.68366e15	+	4.85597e15i	−0.558692	+	0.405914i
$839$	−1.46467e15	−	4.50779e15i	−0.121632	−	0.374346i	0.871640	−	0.490146i	$-0.163057\pi$
$839$	−1.46467e15	−	4.50779e15i	−0.121632	−	0.374346i	−0.993272	+	0.115801i	$0.963057\pi$
$840$	−1.34808e15	+	4.14896e15i	−0.111219	+	0.342297i
$841$	−1.61217e16	−	1.17131e16i	−1.32139	−	0.960048i
$842$	8.42581e14	+	6.12171e14i	0.0686113	+	0.0498490i
$843$	1.16872e15	−	3.59696e15i	0.0945496	−	0.290994i
$844$	2.56095e15	+	7.88181e15i	0.205835	+	0.633494i
$845$	−5.35268e15	+	3.88895e15i	−0.427424	+	0.310542i
$846$	−5.34899e15			−0.424361
$847$	1.55926e16	+	6.59549e15i	1.22902	+	0.519862i
$848$	4.43305e15			0.347157
$849$	1.57146e16	−	1.14173e16i	1.22267	−	0.888323i
$850$	1.81474e15	+	5.58521e15i	0.140285	+	0.431753i
$851$	−1.23470e15	+	3.80000e15i	−0.0948304	+	0.291858i
$852$	−3.64457e15	−	2.64794e15i	−0.278118	−	0.202064i
$853$	−1.42462e16	−	1.03505e16i	−1.08014	−	0.784767i	−0.102432	−	0.994740i	$-0.532663\pi$
$853$	−1.42462e16	−	1.03505e16i	−1.08014	−	0.784767i	−0.977707	+	0.209973i	$0.932663\pi$
$854$	3.74758e15	−	1.15339e16i	0.282314	−	0.868873i
$855$	2.22648e14	+	6.85241e14i	0.0166650	+	0.0512897i
$856$	−3.39054e15	+	2.46337e15i	−0.252152	+	0.183199i
$857$	−9.01997e15			−0.666516			−0.333258	−	0.942836i	$-0.608148\pi$
$857$	−9.01997e15			−0.666516			−0.333258	+	0.942836i	$0.608148\pi$
$858$	−2.34435e15	+	2.15092e15i	−0.172124	+	0.157922i
$859$	−5.55282e15			−0.405090			−0.202545	−	0.979273i	$-0.564921\pi$
$859$	−5.55282e15			−0.405090			−0.202545	+	0.979273i	$0.564921\pi$
$860$	3.95395e15	−	2.87271e15i	0.286609	−	0.208233i
$861$	5.87178e15	+	1.80715e16i	0.422914	+	1.30160i
$862$	−5.52415e15	+	1.70016e16i	−0.395344	+	1.21674i
$863$	−7.45936e15	−	5.41954e15i	−0.530447	−	0.385392i	0.290078	−	0.957003i	$-0.406319\pi$
$863$	−7.45936e15	−	5.41954e15i	−0.530447	−	0.385392i	−0.820525	+	0.571611i	$0.806319\pi$
$864$	−4.24561e14	−	3.08462e14i	−0.0299996	−	0.0217960i
$865$	9.86046e14	−	3.03474e15i	0.0692322	−	0.213075i
$866$	−2.92633e14	−	9.00633e14i	−0.0204162	−	0.0628347i
$867$	−1.91452e15	+	1.39098e15i	−0.132726	+	0.0964308i
$868$	8.60888e15			0.593046
$869$	5.20205e13	−	2.56516e14i	0.00356095	−	0.0175592i
$870$	1.28687e16			0.875343
$871$	−5.20543e15	+	3.78196e15i	−0.351849	+	0.255633i
$872$	1.84198e15	+	5.66903e15i	0.123721	+	0.380775i
$873$	4.71215e15	−	1.45025e16i	0.314515	−	0.967976i
$874$	1.23275e15	+	8.95644e14i	0.0817639	+	0.0594049i
$875$	1.54951e16	+	1.12578e16i	1.02129	+	0.742012i
$876$	−2.45106e15	+	7.54359e15i	−0.160539	+	0.494090i
$877$	−2.33747e15	−	7.19399e15i	−0.152142	−	0.468244i	0.845718	−	0.533629i	$-0.179172\pi$
$877$	−2.33747e15	−	7.19399e15i	−0.152142	−	0.468244i	−0.997860	+	0.0653856i	$0.979172\pi$
$878$	−3.28404e15	+	2.38600e15i	−0.212417	+	0.154330i
$879$	1.67794e16			1.07854
$880$	−1.91346e15	−	1.08099e15i	−0.122226	−	0.0690506i
$881$	−9.53039e15			−0.604983			−0.302492	−	0.953152i	$-0.597818\pi$
$881$	−9.53039e15			−0.604983			−0.302492	+	0.953152i	$0.597818\pi$
$882$	−5.98675e15	+	4.34963e15i	−0.377671	+	0.274394i
$883$	−6.65479e15	−	2.04813e16i	−0.417206	−	1.28403i	−0.910263	−	0.414031i	$-0.864121\pi$
$883$	−6.65479e15	−	2.04813e16i	−0.417206	−	1.28403i	0.493057	−	0.869997i	$-0.335879\pi$
$884$	−5.65461e14	+	1.74031e15i	−0.0352302	+	0.108427i
$885$	−6.88000e15	−	4.99861e15i	−0.425991	−	0.309501i
$886$	1.07780e16	+	7.83066e15i	0.663211	+	0.481851i
$887$	−2.59910e15	+	7.99920e15i	−0.158944	+	0.489178i	−0.998539	−	0.0540341i	$-0.982792\pi$
$887$	−2.59910e15	+	7.99920e15i	−0.158944	+	0.489178i	0.839596	+	0.543212i	$0.182792\pi$
$888$	5.95542e14	+	1.83289e15i	0.0361944	+	0.111395i
$889$	−2.79179e15	+	2.02836e15i	−0.168626	+	0.122514i
$890$	9.91505e15			0.595182
$891$	7.86954e15	+	1.72394e16i	0.469485	+	1.02847i
$892$	−7.92146e15			−0.469676
$893$	−1.10667e15	+	8.04042e14i	−0.0652131	+	0.0473801i
$894$	−7.98823e15	−	2.45852e16i	−0.467836	−	1.43985i
$895$	−3.97398e15	+	1.22306e16i	−0.231312	+	0.711906i
$896$	1.64948e15	+	1.19842e15i	0.0954231	+	0.0693290i
$897$	5.84956e15	+	4.24995e15i	0.336329	+	0.244358i
$898$	4.08569e15	−	1.25745e16i	0.233478	−	0.718571i
$899$	−7.84749e15	−	2.41521e16i	−0.445710	−	1.37175i
$900$	4.14872e15	−	3.01422e15i	0.234196	−	0.170154i
$901$	−2.32073e16			−1.30208
$902$	−9.51021e15	+	1.08962e15i	−0.530339	+	0.0607628i
$903$	4.12706e16			2.28748
$904$	1.52568e15	−	1.10847e15i	0.0840500	−	0.0610659i
$905$	1.07210e15	+	3.29958e15i	0.0587040	+	0.180672i
$906$	8.51462e15	−	2.62053e16i	0.463405	−	1.42621i
$907$	−3.98013e15	−	2.89173e15i	−0.215307	−	0.156429i	0.474905	−	0.880037i	$-0.342482\pi$
$907$	−3.98013e15	−	2.89173e15i	−0.215307	−	0.156429i	−0.690211	+	0.723608i	$0.742482\pi$
$908$	1.05955e15	+	7.69807e14i	0.0569703	+	0.0413913i
$909$	−3.82853e15	+	1.17830e16i	−0.204612	+	0.629731i
$910$	7.49511e14	+	2.30676e15i	0.0398153	+	0.122539i
$911$	−1.31068e15	+	9.52268e14i	−0.0692065	+	0.0502815i	−0.621851	−	0.783136i	$-0.713619\pi$
$911$	−1.31068e15	+	9.52268e14i	−0.0692065	+	0.0502815i	0.552644	+	0.833417i	$0.313619\pi$
$912$	7.34969e14			0.0385742
$913$	3.69086e16	−	4.22875e15i	1.92548	−	0.220609i
$914$	8.35718e14			0.0433367
$915$	1.15925e16	−	8.42247e15i	0.597534	−	0.434134i
$916$	−2.06244e15	−	6.34752e15i	−0.105671	−	0.325222i
$917$	5.65349e15	−	1.73997e16i	0.287929	−	0.886155i
$918$	2.22261e15	+	1.61482e15i	0.112520	+	0.0817503i
$919$	1.82911e16	+	1.32893e16i	0.920461	+	0.668754i	0.943639	−	0.330977i	$-0.107378\pi$
$919$	1.82911e16	+	1.32893e16i	0.920461	+	0.668754i	−0.0231777	+	0.999731i	$0.507378\pi$
$920$	−1.54338e15	+	4.75003e15i	−0.0772040	+	0.237609i
$921$	−8.02237e15	−	2.46903e16i	−0.398910	−	1.22772i
$922$	1.81164e15	−	1.31623e15i	0.0895471	−	0.0650598i
$923$	−2.50468e15			−0.123067
$924$	−7.70657e15	−	1.68824e16i	−0.376414	−	0.824588i
$925$	3.43879e15			0.166965
$926$	−1.18615e16	+	8.61787e15i	−0.572504	+	0.415949i
$927$	8.38193e15	+	2.57969e16i	0.402166	+	1.23774i
$928$	1.85855e15	−	5.72003e15i	0.0886462	−	0.272825i
$929$	−1.07759e15	−	7.82916e14i	−0.0510937	−	0.0371218i	0.561945	−	0.827174i	$-0.310053\pi$
$929$	−1.07759e15	−	7.82916e14i	−0.0510937	−	0.0371218i	−0.613039	+	0.790053i	$0.710053\pi$
$930$	8.22919e15	+	5.97885e15i	0.387883	+	0.281813i
$931$	−5.84796e14	+	1.79982e15i	−0.0274019	+	0.0843344i
$932$	−4.06764e15	−	1.25189e16i	−0.189476	−	0.583148i
$933$	−2.39863e16	+	1.74271e16i	−1.11075	+	0.807005i
$934$	2.21165e16			1.01814
$935$	1.00171e16	+	5.65907e15i	0.458434	+	0.258989i
$936$	1.59788e15			0.0726986
$937$	−3.45113e15	+	2.50739e15i	−0.156097	+	0.113411i	−0.663092	−	0.748538i	$-0.730756\pi$
$937$	−3.45113e15	+	2.50739e15i	−0.156097	+	0.113411i	0.506995	+	0.861949i	$0.330756\pi$
$938$	−1.15977e16	−	3.56942e16i	−0.521504	−	1.60502i
$939$	9.75692e15	−	3.00287e16i	0.436166	−	1.34238i
$940$	−3.62737e15	−	2.63544e15i	−0.161209	−	0.117125i
$941$	2.49092e16	+	1.80976e16i	1.10057	+	0.799611i	0.981153	−	0.193233i	$-0.0618974\pi$
$941$	2.49092e16	+	1.80976e16i	1.10057	+	0.799611i	0.119417	+	0.992844i	$0.461897\pi$
$942$	2.29487e15	−	7.06287e15i	0.100804	−	0.310242i
$943$	6.72244e15	+	2.06896e16i	0.293571	+	0.903518i
$944$	−3.21548e15	+	2.33618e15i	−0.139605	+	0.101429i
$945$	3.64150e15			0.157183
$946$	−4.13223e15	+	2.03762e16i	−0.177330	+	0.874424i
$947$	−1.84099e15			−0.0785464			−0.0392732	−	0.999229i	$-0.512504\pi$
$947$	−1.84099e15			−0.0785464			−0.0392732	+	0.999229i	$0.512504\pi$
$948$	−2.32112e14	+	1.68640e14i	−0.00984584	+	0.00715342i
$949$	1.36275e15	+	4.19412e15i	0.0574716	+	0.176879i
$950$	4.05254e14	−	1.24724e15i	0.0169921	−	0.0522963i
$951$	−1.27168e16	−	9.23929e15i	−0.530133	−	0.385164i
$952$	−8.63515e15	−	6.27381e15i	−0.357904	−	0.260033i
$953$	−2.90283e15	+	8.93400e15i	−0.119622	+	0.368159i	−0.992883	−	0.119094i	$-0.962001\pi$
$953$	−2.90283e15	+	8.93400e15i	−0.119622	+	0.368159i	0.873261	+	0.487253i	$0.162001\pi$
$954$	6.26226e15	+	1.92733e16i	0.256575	+	0.789658i
$955$	−1.13154e16	+	8.22111e15i	−0.460947	+	0.334898i
$956$	6.50427e15			0.263439
$957$	−4.03382e16	+	3.70099e16i	−1.62443	+	1.49040i
$958$	1.30694e16			0.523294
$959$	−3.40532e16	+	2.47411e16i	−1.35568	+	0.984956i
$960$	7.44432e14	+	2.29112e15i	0.0294668	+	0.0906895i
$961$	−1.64874e15	+	5.07429e15i	−0.0648892	+	0.199708i
$962$	8.66863e14	+	6.29813e14i	0.0339225	+	0.0246461i
$963$	−1.54994e16	−	1.12610e16i	−0.603073	−	0.438158i
$964$	−5.09465e15	+	1.56797e16i	−0.197102	+	0.606618i
$965$	−3.62248e15	−	1.11488e16i	−0.139349	−	0.428873i
$966$	−3.41205e16	+	2.47900e16i	−1.30509	+	0.948205i
$967$	−2.15595e16			−0.819959			−0.409980	−	0.912095i	$-0.634464\pi$
$967$	−2.15595e16			−0.819959			−0.409980	+	0.912095i	$0.634464\pi$
$968$	9.10682e15	−	2.11456e15i	0.344391	−	0.0799660i
$969$	−3.84761e15			−0.144681
$970$	1.03408e16	−	7.51307e15i	0.386644	−	0.280914i
$971$	4.69148e15	+	1.44389e16i	0.174423	+	0.536819i	0.999607	−	0.0280454i	$-0.00892829\pi$
$971$	4.69148e15	+	1.44389e16i	0.174423	+	0.536819i	−0.825183	+	0.564865i	$0.808928\pi$
$972$	5.54250e15	−	1.70580e16i	0.204900	−	0.630616i
$973$	−3.18370e16	−	2.31309e16i	−1.17034	−	0.850300i
$974$	1.43571e16	+	1.04311e16i	0.524800	+	0.381289i
$975$	1.92298e15	−	5.91834e15i	0.0698957	−	0.215117i
$976$	−2.06948e15	−	6.36919e15i	−0.0747974	−	0.230203i
$977$	2.68185e16	−	1.94848e16i	0.963862	−	0.700287i	0.00981756	−	0.999952i	$-0.496875\pi$
$977$	2.68185e16	−	1.94848e16i	0.963862	−	0.700287i	0.954044	+	0.299665i	$0.0968749\pi$
$978$	2.96333e16			1.05905
$979$	−3.10797e16	+	2.85154e16i	−1.10452	+	1.01338i
$980$	−6.20291e15			−0.219206
$981$	−2.20448e16	+	1.60165e16i	−0.774687	+	0.562843i
$982$	−1.62423e15	−	4.99887e15i	−0.0567590	−	0.174686i
$983$	−9.99757e15	+	3.07694e16i	−0.347416	+	1.06924i	0.612861	+	0.790190i	$0.290018\pi$
$983$	−9.99757e15	+	3.07694e16i	−0.347416	+	1.06924i	−0.960278	+	0.279047i	$0.909982\pi$
$984$	8.48896e15	+	6.16759e15i	0.293347	+	0.213129i
$985$	−2.17677e16	−	1.58152e16i	−0.748021	−	0.543469i
$986$	−9.72963e15	+	2.99447e16i	−0.332486	+	1.02329i
$987$	−1.16999e16	−	3.60087e16i	−0.397594	−	1.22367i
$988$	3.30590e14	−	2.40187e14i	0.0111719	−	0.00811684i
$989$	4.72496e16			1.58788
$990$	1.99674e15	−	9.84603e15i	0.0667311	−	0.329054i
$991$	1.05948e16			0.352117			0.176058	−	0.984380i	$-0.443665\pi$
$991$	1.05948e16			0.352117			0.176058	+	0.984380i	$0.443665\pi$
$992$	3.84604e15	−	2.79431e15i	0.127116	−	0.0923552i
$993$	−5.26351e15	−	1.61994e16i	−0.173003	−	0.532449i
$994$	4.51467e15	−	1.38947e16i	0.147571	−	0.454177i
$995$	−2.37803e15	−	1.72774e15i	−0.0773020	−	0.0561632i
$996$	−3.29452e16	−	2.39361e16i	−1.06504	−	0.773798i
$997$	−1.70810e15	+	5.25699e15i	−0.0549148	+	0.169010i	−0.974752	−	0.223290i	$-0.928320\pi$
$997$	−1.70810e15	+	5.25699e15i	−0.0549148	+	0.169010i	0.919837	+	0.392300i	$0.128320\pi$
$998$	8.24447e14	+	2.53739e15i	0.0263599	+	0.0811276i
$999$	1.30147e15	−	9.45577e14i	0.0413833	−	0.0300668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.3.1	✓	20
11.2	odd	10		242.12.a.m.1.2		10
11.4	even	5	inner	22.12.c.a.15.1	yes	20
11.9	even	5		242.12.a.n.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.3.1	✓	20	1.1	even	1	trivial
22.12.c.a.15.1	yes	20	11.4	even	5	inner
242.12.a.m.1.2		10	11.2	odd	10
242.12.a.n.1.2		10	11.9	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)

\(f(q)\)	\(=\)	\(q+(-25.8885 + 18.8091i) q^{2} +(-176.692 - 543.803i) q^{3} +(316.433 - 973.882i) q^{4} +(3174.43 + 2306.36i) q^{5} +(14802.8 + 10754.8i) q^{6} +(-18336.8 + 56434.7i) q^{7} +(10125.9 + 31164.2i) q^{8} +(-121186. + 88047.0i) q^{9} +O(q^{10})\)	\(q+(-25.8885 + 18.8091i) q^{2} +(-176.692 - 543.803i) q^{3} +(316.433 - 973.882i) q^{4} +(3174.43 + 2306.36i) q^{5} +(14802.8 + 10754.8i) q^{6} +(-18336.8 + 56434.7i) q^{7} +(10125.9 + 31164.2i) q^{8} +(-121186. + 88047.0i) q^{9} -125562. q^{10} +(393586. - 361112. i) q^{11} -585511. q^{12} +(-263363. + 191345. i) q^{13} +(-586776. - 1.80591e6i) q^{14} +(693306. - 2.13378e6i) q^{15} +(-848316. - 616338. i) q^{16} +(4.44099e6 + 3.22657e6i) q^{17} +(1.48125e6 - 4.55882e6i) q^{18} +(-378806. - 1.16584e6i) q^{19} +(3.25061e6 - 2.36171e6i) q^{20} +3.39293e7 q^{21} +(-3.39718e6 + 1.67517e7i) q^{22} +3.88448e7 q^{23} +(1.51580e7 - 1.10129e7i) q^{24} +(-1.03310e7 - 3.17956e7i) q^{25} +(3.21907e6 - 9.90727e6i) q^{26} +(-1.26529e7 - 9.19288e6i) q^{27} +(4.91584e7 + 3.57157e7i) q^{28} +(5.53891e7 - 1.70470e8i) q^{29} +(2.21858e7 + 6.82808e7i) q^{30} +(1.14621e8 - 8.32771e7i) q^{31} +3.35544e7 q^{32} +(-2.65917e8 - 1.50228e8i) q^{33} -1.75660e8 q^{34} +(-1.88367e8 + 1.36857e8i) q^{35} +(4.74000e7 + 1.45882e8i) q^{36} +(-3.17854e7 + 9.78253e7i) q^{37} +(3.17352e7 + 2.30570e7i) q^{38} +(1.50588e8 + 1.09409e8i) q^{39} +(-3.97320e7 + 1.22282e8i) q^{40} +(1.73059e8 + 5.32621e8i) q^{41} +(-8.78381e8 + 6.38181e8i) q^{42} +1.21637e9 q^{43} +(-2.27136e8 - 4.97574e8i) q^{44} -5.87764e8 q^{45} +(-1.00564e9 + 7.30637e8i) q^{46} +(-3.44833e8 - 1.06129e9i) q^{47} +(-1.85275e8 + 5.70218e8i) q^{48} +(-1.24895e9 - 9.07416e8i) q^{49} +(8.65502e8 + 6.28824e8i) q^{50} +(9.69929e8 - 2.98513e9i) q^{51} +(1.03010e8 + 3.17033e8i) q^{52} +(-3.42027e9 + 2.48497e9i) q^{53} +5.00476e8 q^{54} +(2.08226e9 - 2.38572e8i) q^{55} -1.94442e9 q^{56} +(-5.67057e8 + 4.11991e8i) q^{57} +(1.77245e9 + 5.45504e9i) q^{58} +(1.17131e9 - 3.60491e9i) q^{59} +(-1.85866e9 - 1.35040e9i) q^{60} +(5.16697e9 + 3.75402e9i) q^{61} +(-1.40100e9 + 4.31184e9i) q^{62} +(-2.74674e9 - 8.45361e9i) q^{63} +(-8.68675e8 + 6.31130e8i) q^{64} -1.27734e9 q^{65} +(9.70986e9 - 1.11249e9i) q^{66} +1.97652e10 q^{67} +(4.54758e9 - 3.30401e9i) q^{68} +(-6.86357e9 - 2.11239e10i) q^{69} +(2.30240e9 - 7.08605e9i) q^{70} +(6.22460e9 + 4.52244e9i) q^{71} +(-3.97103e9 - 2.88512e9i) q^{72} +(4.18619e9 - 1.28838e10i) q^{73} +(-1.01713e9 - 3.13041e9i) q^{74} +(-1.54651e10 + 1.12361e10i) q^{75} -1.25526e9 q^{76} +(1.31621e10 + 2.88335e10i) q^{77} -5.95638e9 q^{78} +(3.96427e8 - 2.88021e8i) q^{79} +(-1.27142e9 - 3.91304e9i) q^{80} +(-1.09634e10 + 3.37419e10i) q^{81} +(-1.44984e10 - 1.05337e10i) q^{82} +(5.62675e10 + 4.08808e10i) q^{83} +(1.07364e10 - 3.30431e10i) q^{84} +(6.65598e9 + 2.04850e10i) q^{85} +(-3.14900e10 + 2.28788e10i) q^{86} -1.02489e11 q^{87} +(1.52392e10 + 8.60924e9i) q^{88} -7.89655e10 q^{89} +(1.52164e10 - 1.10553e10i) q^{90} +(-5.96926e9 - 1.83715e10i) q^{91} +(1.22918e10 - 3.78302e10i) q^{92} +(-6.55389e10 - 4.76168e10i) q^{93} +(2.88891e10 + 2.09892e10i) q^{94} +(1.48636e9 - 4.57454e9i) q^{95} +(-5.92881e9 - 1.82470e10i) q^{96} +(-8.23566e10 + 5.98356e10i) q^{97} +4.94012e10 q^{98} +(-1.59025e10 + 7.84158e10i) 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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