LMFDB - Embedded newform 91.8.u.a.30.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(30,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.30");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.u (of order $6$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.4
Character	$\chi$	$=$	91.30
Dual form			91.8.u.a.88.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.4054 + 10.0490i) q^{2} +67.2867 q^{3} +(137.965 - 238.962i) q^{4} +(-13.7956 - 7.96491i) q^{5} +(-1171.15 + 676.165i) q^{6} +(-799.780 + 428.830i) q^{7} +2973.10i q^{8} +2340.51 q^{9} +O(q^{10})$	\(q+(-17.4054 + 10.0490i) q^{2} +67.2867 q^{3} +(137.965 - 238.962i) q^{4} +(-13.7956 - 7.96491i) q^{5} +(-1171.15 + 676.165i) q^{6} +(-799.780 + 428.830i) q^{7} +2973.10i q^{8} +2340.51 q^{9} +320.158 q^{10} +841.033i q^{11} +(9283.22 - 16079.0i) q^{12} +(-15.9735 - 7921.38i) q^{13} +(9611.17 - 15500.9i) q^{14} +(-928.263 - 535.933i) q^{15} +(-12217.2 - 21160.7i) q^{16} +(-1792.63 + 3104.92i) q^{17} +(-40737.4 + 23519.8i) q^{18} +16754.4i q^{19} +(-3806.63 + 2197.76i) q^{20} +(-53814.6 + 28854.6i) q^{21} +(-8451.54 - 14638.5i) q^{22} +(10312.5 + 17861.7i) q^{23} +200050. i q^{24} +(-38935.6 - 67438.5i) q^{25} +(79880.0 + 137714. i) q^{26} +10329.0 q^{27} +(-7867.46 + 250281. i) q^{28} +(19646.4 - 34028.5i) q^{29} +21542.4 q^{30} +(-232772. + 134391. i) q^{31} +(95717.2 + 55262.3i) q^{32} +56590.4i q^{33} -72056.5i q^{34} +(14449.1 + 454.200i) q^{35} +(322908. - 559293. i) q^{36} +(-81172.1 + 46864.7i) q^{37} +(-168365. - 291617. i) q^{38} +(-1074.81 - 533004. i) q^{39} +(23680.5 - 41015.8i) q^{40} +(-709757. - 409778. i) q^{41} +(646704. - 1.04301e6i) q^{42} +(-5244.40 - 9083.58i) q^{43} +(200975. + 116033. i) q^{44} +(-32288.8 - 18641.9i) q^{45} +(-358985. - 207260. i) q^{46} +(390828. + 225645. i) q^{47} +(-822053. - 1.42384e6i) q^{48} +(455753. - 685939. i) q^{49} +(1.35538e6 + 782528. i) q^{50} +(-120620. + 208920. i) q^{51} +(-1.89512e6 - 1.08906e6i) q^{52} +(-278107. - 481696. i) q^{53} +(-179780. + 103796. i) q^{54} +(6698.75 - 11602.6i) q^{55} +(-1.27495e6 - 2.37782e6i) q^{56} +1.12735e6i q^{57} +789706. i q^{58} +(-407322. - 235167. i) q^{59} +(-256136. + 147880. i) q^{60} -3.29897e6 q^{61} +(2.70099e6 - 4.67825e6i) q^{62} +(-1.87189e6 + 1.00368e6i) q^{63} +906268. q^{64} +(-62872.7 + 109408. i) q^{65} +(-568677. - 984977. i) q^{66} -811868. i q^{67} +(494640. + 856742. i) q^{68} +(693892. + 1.20186e6i) q^{69} +(-256056. + 137293. i) q^{70} +(2.22045e6 - 1.28198e6i) q^{71} +6.95856e6i q^{72} +(-3.89641e6 + 2.24959e6i) q^{73} +(941888. - 1.63140e6i) q^{74} +(-2.61985e6 - 4.53772e6i) q^{75} +(4.00367e6 + 2.31152e6i) q^{76} +(-360660. - 672641. i) q^{77} +(5.37487e6 + 9.26634e6i) q^{78} +(-46809.8 + 81077.0i) q^{79} +389235. i q^{80} -4.42369e6 q^{81} +1.64715e7 q^{82} -3.23708e6i q^{83} +(-529376. + 1.68406e7i) q^{84} +(49460.9 - 28556.3i) q^{85} +(182562. + 105402. i) q^{86} +(1.32194e6 - 2.28967e6i) q^{87} -2.50047e6 q^{88} +(7.48920e6 - 4.32389e6i) q^{89} +749331. q^{90} +(3.40970e6 + 6.32851e6i) q^{91} +5.69104e6 q^{92} +(-1.56625e7 + 9.04272e6i) q^{93} -9.07002e6 q^{94} +(133447. - 231138. i) q^{95} +(6.44050e6 + 3.71842e6i) q^{96} +(-8.37938e6 + 4.83783e6i) q^{97} +(-1.03956e6 + 1.65189e7i) q^{98} +1.96844e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) $ 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−17.4054	+	10.0490i	−1.53843	+	0.888215i	−0.539503	+	0.841984i	$0.681388\pi$
$2$	−17.4054	+	10.0490i	−1.53843	+	0.888215i	−0.998931	+	0.0462310i	$0.985279\pi$
$3$	67.2867			1.43882			0.719408	−	0.694588i	$-0.244413\pi$
$3$	67.2867			1.43882			0.719408	+	0.694588i	$0.244413\pi$
$4$	137.965	−	238.962i	1.07785	−	1.86689i
$5$	−13.7956	−	7.96491i	−0.0493568	−	0.0284961i	0.475119	−	0.879922i	$-0.342405\pi$
$5$	−13.7956	−	7.96491i	−0.0493568	−	0.0284961i	−0.524475	+	0.851426i	$0.675738\pi$
$6$	−1171.15	+	676.165i	−2.21352	+	1.27798i
$7$	−799.780	+	428.830i	−0.881307	+	0.472543i
$7$	−799.780	+	428.830i	−0.881307	+	0.472543i
$8$			2973.10i			2.05303i
$9$	2340.51			1.07019
$10$	320.158			0.101243
$11$			841.033i			0.190519i	0.995452	+	0.0952595i	$0.0303681\pi$
$11$			841.033i			0.190519i	−0.995452	+	0.0952595i	$0.969632\pi$
$12$	9283.22	−	16079.0i	1.55083	−	2.68612i
$13$	−15.9735	−	7921.38i	−0.00201651	−	0.999998i
$13$	−15.9735	−	7921.38i	−0.00201651	−	0.999998i
$14$	9611.17	−	15500.9i	0.936113	−	1.50977i
$15$	−928.263	−	535.933i	−0.0710153	−	0.0410007i
$16$	−12217.2	−	21160.7i	−0.745676	−	1.29155i
$17$	−1792.63	+	3104.92i	−0.0884951	+	0.153278i	−0.906875	−	0.421399i	$-0.861539\pi$
$17$	−1792.63	+	3104.92i	−0.0884951	+	0.153278i	0.818380	+	0.574677i	$0.194872\pi$
$18$	−40737.4	+	23519.8i	−1.64642	+	0.950559i
$19$			16754.4i			0.560392i	0.959943	+	0.280196i	$0.0903994\pi$
$19$			16754.4i			0.560392i	−0.959943	+	0.280196i	$0.909601\pi$
$20$	−3806.63	+	2197.76i	−0.106399	+	0.0614292i
$21$	−53814.6	+	28854.6i	−1.26804	+	0.679903i
$22$	−8451.54	−	14638.5i	−0.169222	−	0.293101i
$23$	10312.5	+	17861.7i	0.176732	+	0.306109i	0.940759	−	0.339075i	$-0.110114\pi$
$23$	10312.5	+	17861.7i	0.176732	+	0.306109i	−0.764027	+	0.645184i	$0.776781\pi$
$24$			200050.i			2.95393i
$25$	−38935.6	−	67438.5i	−0.498376	−	0.863212i
$26$	79880.0	+	137714.i	0.891315	+	1.53664i
$27$	10329.0			0.100991
$28$	−7867.46	+	250281.i	−0.0677301	+	2.15464i
$29$	19646.4	−	34028.5i	0.149585	−	0.259090i	−0.781489	−	0.623919i	$-0.785539\pi$
$29$	19646.4	−	34028.5i	0.149585	−	0.259090i	0.931074	+	0.364830i	$0.118873\pi$
$30$	21542.4			0.145670
$31$	−232772.	+	134391.i	−1.40334	+	0.810221i	−0.994734	−	0.102488i	$-0.967320\pi$
$31$	−232772.	+	134391.i	−1.40334	+	0.810221i	−0.408610	+	0.912709i	$0.633986\pi$
$32$	95717.2	+	55262.3i	0.516375	+	0.298129i
$33$			56590.4i			0.274122i
$34$		−	72056.5i		−	0.314411i
$35$	14449.1	+	454.200i	0.0569641	+	0.00179064i
$36$	322908.	−	559293.i	1.15351	−	1.99793i
$37$	−81172.1	+	46864.7i	−0.263452	+	0.152104i	−0.625908	−	0.779897i	$-0.715271\pi$
$37$	−81172.1	+	46864.7i	−0.263452	+	0.152104i	0.362456	+	0.932001i	$0.381938\pi$
$38$	−168365.	−	291617.i	−0.497748	−	0.862125i
$39$	−1074.81	−	533004.i	−0.00290138	−	1.43881i
$40$	23680.5	−	41015.8i	0.0585033	−	0.101331i
$41$	−709757.	−	409778.i	−1.60830	−	0.928551i	−0.989751	−	0.142802i	$-0.954389\pi$
$41$	−709757.	−	409778.i	−1.60830	−	0.928551i	−0.618546	−	0.785749i	$-0.712278\pi$
$42$	646704.	−	1.04301e6i	1.34689	−	2.17228i
$43$	−5244.40	−	9083.58i	−0.0100590	−	0.0174228i	0.860952	−	0.508686i	$-0.169869\pi$
$43$	−5244.40	−	9083.58i	−0.0100590	−	0.0174228i	−0.871011	+	0.491263i	$0.836535\pi$
$44$	200975.	+	116033.i	0.355679	+	0.205351i
$45$	−32288.8	−	18641.9i	−0.0528211	−	0.0304963i
$46$	−358985.	−	207260.i	−0.543781	−	0.313952i
$47$	390828.	+	225645.i	0.549090	+	0.317017i	0.748755	−	0.662847i	$-0.230652\pi$
$47$	390828.	+	225645.i	0.549090	+	0.317017i	−0.199665	+	0.979864i	$0.563985\pi$
$48$	−822053.	−	1.42384e6i	−1.07289	−	1.85830i
$49$	455753.	−	685939.i	0.553405	−	0.832912i
$50$	1.35538e6	+	782528.i	1.53344	+	0.885330i
$51$	−120620.	+	208920.i	−0.127328	+	0.220539i
$52$	−1.89512e6	−	1.08906e6i	−1.86906	−	1.07408i
$53$	−278107.	−	481696.i	−0.256594	−	0.444434i	0.708733	−	0.705477i	$-0.249267\pi$
$53$	−278107.	−	481696.i	−0.256594	−	0.444434i	−0.965327	+	0.261043i	$0.915934\pi$
$54$	−179780.	+	103796.i	−0.155368	+	0.0897019i
$55$	6698.75	−	11602.6i	0.00542906	−	0.00940341i
$56$	−1.27495e6	−	2.37782e6i	−0.970144	−	1.80935i
$57$			1.12735e6i			0.806300i
$58$			789706.i			0.531456i
$59$	−407322.	−	235167.i	−0.258200	−	0.149072i	0.365313	−	0.930885i	$-0.380962\pi$
$59$	−407322.	−	235167.i	−0.258200	−	0.149072i	−0.623513	+	0.781813i	$0.714295\pi$
$60$	−256136.	+	147880.i	−0.153088	+	0.0883853i
$61$	−3.29897e6			−1.86091			−0.930453	−	0.366412i	$-0.880586\pi$
$61$	−3.29897e6			−1.86091			−0.930453	+	0.366412i	$0.880586\pi$
$62$	2.70099e6	−	4.67825e6i	1.43930	−	2.49294i
$63$	−1.87189e6	+	1.00368e6i	−0.943167	+	0.505712i
$64$	906268.			0.432142
$65$	−62872.7	+	109408.i	−0.0283966	+	0.0494141i
$66$	−568677.	−	984977.i	−0.243479	−	0.421718i
$67$		−	811868.i		−	0.329779i	−0.986312	−	0.164890i	$-0.947273\pi$
$67$		−	811868.i		−	0.329779i	0.986312	−	0.164890i	$-0.0527268\pi$
$68$	494640.	+	856742.i	0.190769	+	0.330422i
$69$	693892.	+	1.20186e6i	0.254285	+	0.440434i
$70$	−256056.	+	137293.i	−0.0892260	+	0.0478416i
$71$	2.22045e6	−	1.28198e6i	0.736271	−	0.425086i	−0.0844410	−	0.996428i	$-0.526910\pi$
$71$	2.22045e6	−	1.28198e6i	0.736271	−	0.425086i	0.820712	+	0.571342i	$0.193577\pi$
$72$			6.95856e6i			2.19713i
$73$	−3.89641e6	+	2.24959e6i	−1.17229	+	0.676821i	−0.954218	−	0.299113i	$-0.903309\pi$
$73$	−3.89641e6	+	2.24959e6i	−1.17229	+	0.676821i	−0.218070	+	0.975933i	$0.569976\pi$
$74$	941888.	−	1.63140e6i	0.270202	−	0.468003i
$75$	−2.61985e6	−	4.53772e6i	−0.717071	−	1.24200i
$76$	4.00367e6	+	2.31152e6i	1.04619	+	0.604019i
$77$	−360660.	−	672641.i	−0.0900286	−	0.167906i
$78$	5.37487e6	+	9.26634e6i	1.28244	+	2.21094i
$79$	−46809.8	+	81077.0i	−0.0106817	+	0.0185013i	−0.871317	−	0.490721i	$-0.836734\pi$
$79$	−46809.8	+	81077.0i	−0.0106817	+	0.0185013i	0.860635	+	0.509222i	$0.170067\pi$
$80$			389235.i			0.0849956i
$81$	−4.42369e6			−0.924883
$82$	1.64715e7			3.29901
$83$		−	3.23708e6i		−	0.621412i	−0.950506	−	0.310706i	$-0.899435\pi$
$83$		−	3.23708e6i		−	0.621412i	0.950506	−	0.310706i	$-0.100565\pi$
$84$	−529376.	+	1.68406e7i	−0.0974511	+	3.10013i
$85$	49460.9	−	28556.3i	0.00873566	−	0.00504354i
$86$	182562.	+	105402.i	0.0309503	+	0.0178692i
$87$	1.32194e6	−	2.28967e6i	0.215226	−	0.372782i
$88$	−2.50047e6			−0.391141
$89$	7.48920e6	−	4.32389e6i	1.12608	−	0.650144i	0.183136	−	0.983088i	$-0.441375\pi$
$89$	7.48920e6	−	4.32389e6i	1.12608	−	0.650144i	0.942947	+	0.332944i	$0.108042\pi$
$90$	749331.			0.108349
$91$	3.40970e6	+	6.32851e6i	0.474320	+	0.880353i
$92$	5.69104e6			0.761963
$93$	−1.56625e7	+	9.04272e6i	−2.01915	+	1.16576i
$94$	−9.07002e6			−1.12632
$95$	133447.	−	231138.i	0.0159690	−	0.0276591i
$96$	6.44050e6	+	3.71842e6i	0.742968	+	0.428953i
$97$	−8.37938e6	+	4.83783e6i	−0.932203	+	0.538208i	−0.887508	−	0.460793i	$-0.847565\pi$
$97$	−8.37938e6	+	4.83783e6i	−0.932203	+	0.538208i	−0.0446955	+	0.999001i	$0.514232\pi$
$98$	−1.03956e6	+	1.65189e7i	−0.111572	+	1.77292i
$99$			1.96844e6i			0.203892i
$100$	−2.14870e7			−2.14870
$101$	−1.17500e7			−1.13479			−0.567394	−	0.823446i	$-0.692048\pi$
$101$	−1.17500e7			−1.13479			−0.567394	+	0.823446i	$0.692048\pi$
$102$		−	4.84845e6i		−	0.452379i
$103$	4.69761e6	−	8.13650e6i	0.423591	−	0.733681i	−0.572697	−	0.819767i	$-0.694103\pi$
$103$	4.69761e6	−	8.13650e6i	0.423591	−	0.733681i	0.996288	+	0.0860862i	$0.0274361\pi$
$104$	2.35510e7	−	47490.9i	2.05302	−	0.00413994i
$105$	972231.	+	30561.6i	0.0819609	+	0.00257640i
$106$	9.68112e6	+	5.58940e6i	0.789505	+	0.455821i
$107$	−5.75667e6	−	9.97085e6i	−0.454285	−	0.786845i	0.544362	−	0.838850i	$-0.316772\pi$
$107$	−5.75667e6	−	9.97085e6i	−0.454285	−	0.786845i	−0.998647	+	0.0520060i	$0.983439\pi$
$108$	1.42504e6	−	2.46823e6i	0.108854	−	0.188540i
$109$	7.51286e6	−	4.33755e6i	0.555664	−	0.320813i	−0.195739	−	0.980656i	$-0.562711\pi$
$109$	7.51286e6	−	4.33755e6i	0.555664	−	0.320813i	0.751403	+	0.659843i	$0.229377\pi$
$110$			269263.i			0.0192887i
$111$	−5.46181e6	+	3.15338e6i	−0.379058	+	0.218849i
$112$	1.88454e7	+	1.16849e7i	1.26748	+	0.785887i
$113$	−1.49574e7	−	2.59069e7i	−0.975171	−	1.68904i	−0.679371	−	0.733795i	$-0.737747\pi$
$113$	−1.49574e7	−	2.59069e7i	−0.975171	−	1.68904i	−0.295800	−	0.955250i	$-0.595586\pi$
$114$	−1.13287e7	−	1.96220e7i	−0.716168	−	1.24044i
$115$		−	328552.i		−	0.0201447i
$116$	−5.42102e6	−	9.38949e6i	−0.322462	−	0.558520i
$117$	−37386.2	−	1.85400e7i	−0.00215804	−	1.07019i
$118$	9.45280e6			0.529631
$119$	102225.	−	3.25199e6i	0.00556086	−	0.176903i
$120$	1.59338e6	−	2.75982e6i	0.0841755	−	0.145796i
$121$	1.87798e7			0.963702
$122$	5.74199e7	−	3.31514e7i	2.86288	−	1.65288i
$123$	−4.77572e7	−	2.75727e7i	−2.31404	−	1.33601i
$124$			7.41649e7i			3.49319i
$125$			2.48499e6i			0.113799i
$126$	2.24950e7	−	3.62801e7i	1.00182	−	1.61574i
$127$	−1.29274e7	+	2.23909e7i	−0.560014	+	0.969972i	0.437481	+	0.899228i	$0.355871\pi$
$127$	−1.29274e7	+	2.23909e7i	−0.560014	+	0.969972i	−0.997494	+	0.0707445i	$0.977462\pi$
$128$	−2.80257e7	+	1.61807e7i	−1.18120	+	0.681964i
$129$	−352879.	−	611204.i	−0.0144731	−	0.0250682i
$130$	−5114.05	−	2.53609e6i	−0.000204157	−	0.101243i
$131$	−2.61441e6	+	4.52829e6i	−0.101607	+	0.175989i	−0.912347	−	0.409418i	$-0.865732\pi$
$131$	−2.61441e6	+	4.52829e6i	−0.101607	+	0.175989i	0.810740	+	0.585407i	$0.199065\pi$
$132$	1.35230e7	+	7.80749e6i	0.511756	+	0.295463i
$133$	−7.18479e6	−	1.33998e7i	−0.264809	−	0.493877i
$134$	8.15846e6	+	1.41309e7i	0.292915	+	0.507344i
$135$	−142495.	−	82269.3i	−0.00498460	−	0.00287786i
$136$	−9.23124e6	−	5.32966e6i	−0.314684	−	0.181683i
$137$	1.34978e7	+	7.79299e6i	0.448479	+	0.258930i	0.707188	−	0.707026i	$-0.249964\pi$
$137$	1.34978e7	+	7.79299e6i	0.448479	+	0.258930i	−0.258708	+	0.965955i	$0.583297\pi$
$138$	−2.41549e7	−	1.39459e7i	−0.782400	−	0.451719i
$139$	2.11412e7	+	3.66176e7i	0.667693	+	1.15648i	0.978548	+	0.206021i	$0.0660515\pi$
$139$	2.11412e7	+	3.66176e7i	0.667693	+	1.15648i	−0.310854	+	0.950458i	$0.600615\pi$
$140$	2.10200e6	−	3.39012e6i	0.0647418	−	0.104416i
$141$	2.62975e7	+	1.51829e7i	0.790039	+	0.456129i
$142$	−2.57652e7	+	4.46267e7i	−0.755136	+	1.30793i
$143$	6.66214e6	−	13434.3i	0.190519	−	0.000384183i
$144$	−2.85943e7	−	4.95269e7i	−0.798016	−	1.38220i
$145$	−542068.	+	312963.i	−0.0147661	+	0.00852522i
$146$	4.52123e7	−	7.83100e7i	1.20232	−	2.08249i
$147$	3.06661e7	−	4.61546e7i	0.796248	−	1.19841i
$148$			2.58628e7i			0.655782i
$149$		−	320664.i		−	0.00794143i	−0.999992	−	0.00397071i	$-0.998736\pi$
$149$		−	320664.i		−	0.00794143i	0.999992	−	0.00397071i	$-0.00126392\pi$
$150$	9.11991e7	+	5.26538e7i	2.20633	+	1.27383i
$151$	−4.77214e7	+	2.75520e7i	−1.12796	+	0.651228i	−0.943421	−	0.331597i	$-0.892413\pi$
$151$	−4.77214e7	+	2.75520e7i	−1.12796	+	0.651228i	−0.184539	+	0.982825i	$0.559079\pi$
$152$	−4.98125e7			−1.15050
$153$	−4.19566e6	+	7.26709e6i	−0.0947066	+	0.164037i
$154$	1.30368e7	+	8.08331e6i	0.287639	+	0.178347i
$155$	4.28165e6			0.0923527
$156$	−1.27516e8	−	7.32790e7i	−2.68924	−	1.54541i
$157$	3.17399e7	+	5.49751e7i	0.654571	+	1.13375i	0.982001	+	0.188874i	$0.0604839\pi$
$157$	3.17399e7	+	5.49751e7i	0.654571	+	1.13375i	−0.327431	+	0.944875i	$0.606183\pi$
$158$		−	1.88157e6i		−	0.0379508i
$159$	−1.87129e7	−	3.24117e7i	−0.369191	−	0.639458i
$160$	−880319.	−	1.52476e6i	−0.0169911	−	0.0294294i
$161$	−1.59073e7	−	9.86315e6i	−0.300405	−	0.186262i
$162$	7.69960e7	−	4.44536e7i	1.42287	−	0.821495i
$163$			5.35756e7i			0.968970i	0.874800	+	0.484485i	$0.160993\pi$
$163$			5.35756e7i			0.968970i	−0.874800	+	0.484485i	$0.839007\pi$
$164$	−1.95843e8	+	1.13070e8i	−3.46701	+	2.00168i
$165$	450737.	−	780700.i	0.00781142	−	0.0135298i
$166$	3.25294e7	+	5.63426e7i	0.551947	+	0.956001i
$167$	5.79111e7	+	3.34350e7i	0.962175	+	0.555512i	0.896842	−	0.442351i	$-0.145856\pi$
$167$	5.79111e7	+	3.34350e7i	0.962175	+	0.555512i	0.0653334	+	0.997863i	$0.479189\pi$
$168$	−8.57874e7	−	1.59996e8i	−1.39586	−	2.60332i
$169$	−6.27480e7	+	253065.i	−0.999992	+	0.00403300i
$170$	−573924.	+	994066.i	−0.00895949	+	0.0155183i
$171$			3.92138e7i			0.599726i
$172$	−2.89418e6			−0.0433686
$173$	6.66358e7			0.978467			0.489233	−	0.872153i	$-0.337277\pi$
$173$	6.66358e7			0.978467			0.489233	+	0.872153i	$0.337277\pi$
$174$			5.31367e7i			0.764667i
$175$	6.00596e7	+	3.72392e7i	0.847128	+	0.525251i
$176$	1.77969e7	−	1.02750e7i	0.246065	−	0.142066i
$177$	−2.74074e7	−	1.58237e7i	−0.371502	−	0.214487i
$178$	−8.69016e7	+	1.50518e8i	−1.15494	+	2.00041i
$179$	2.84612e7			0.370910			0.185455	−	0.982653i	$-0.440624\pi$
$179$	2.84612e7			0.370910			0.185455	+	0.982653i	$0.440624\pi$
$180$	−8.90944e6	+	5.14387e6i	−0.113867	+	0.0657410i
$181$	3.31070e7			0.414996			0.207498	−	0.978235i	$-0.433468\pi$
$181$	3.31070e7			0.414996			0.207498	+	0.978235i	$0.433468\pi$
$182$	−1.22942e8	−	7.58861e7i	−1.51165	−	0.933066i
$183$	−2.21977e8			−2.67750
$184$	−5.31046e7	+	3.06600e7i	−0.628449	+	0.362835i
$185$	1.49309e6			0.0173375
$186$	1.81741e8	−	3.14784e8i	2.07089	−	3.58689i
$187$	−2.61134e6	−	1.50766e6i	−0.0292024	−	0.0168600i
$188$	1.07841e8	−	6.22621e7i	1.18367	−	0.683395i
$189$	−8.26090e6	+	4.42937e6i	−0.0890043	+	0.0477227i
$190$			5.36406e6i			0.0567356i
$191$	1.71143e8			1.77723			0.888615	−	0.458655i	$-0.151668\pi$
$191$	1.71143e8			1.77723			0.888615	+	0.458655i	$0.151668\pi$
$192$	6.09798e7			0.621773
$193$		−	1.41001e8i		−	1.41180i	−0.708313	−	0.705898i	$-0.750544\pi$
$193$		−	1.41001e8i		−	1.41180i	0.708313	−	0.705898i	$-0.249456\pi$
$194$	9.72309e7	−	1.68409e8i	0.956088	−	1.65599i
$195$	−4.23050e6	+	7.36169e6i	−0.0408574	+	0.0710978i
$196$	−1.01036e8	−	2.03543e8i	−0.958469	−	1.93090i
$197$	−6.04321e7	−	3.48905e7i	−0.563165	−	0.325144i	0.191250	−	0.981541i	$-0.438746\pi$
$197$	−6.04321e7	−	3.48905e7i	−0.563165	−	0.325144i	−0.754415	+	0.656398i	$0.772079\pi$
$198$	−1.97809e7	−	3.42615e7i	−0.181100	−	0.313674i
$199$	−4.31472e7	+	7.47331e7i	−0.388120	+	0.672244i	−0.992197	−	0.124682i	$-0.960209\pi$
$199$	−4.31472e7	+	7.47331e7i	−0.388120	+	0.672244i	0.604076	+	0.796926i	$0.293542\pi$
$200$	2.00501e8	−	1.15759e8i	1.77220	−	1.02318i
$201$		−	5.46279e7i		−	0.474492i
$202$	2.04514e8	−	1.18076e8i	1.74580	−	1.00794i
$203$	−1.12034e6	+	3.56403e7i	−0.00939966	+	0.299023i
$204$	3.32827e7	+	5.76474e7i	0.274482	+	0.475416i
$205$	6.52770e6	+	1.13063e7i	0.0529202	+	0.0916605i
$206$			1.88825e8i			1.50496i
$207$	2.41364e7	+	4.18055e7i	0.189137	+	0.327595i
$208$	−1.67427e8	+	9.71148e7i	−1.29004	+	0.748279i
$209$	−1.40910e7			−0.106765
$210$	−1.72292e7	+	9.23801e6i	−0.128380	+	0.0688353i
$211$	−1.05749e8	+	1.83162e8i	−0.774972	+	1.34229i	0.159839	+	0.987143i	$0.448903\pi$
$211$	−1.05749e8	+	1.83162e8i	−0.774972	+	1.34229i	−0.934810	+	0.355147i	$0.884431\pi$
$212$	−1.53476e8			−1.10628
$213$	1.49407e8	−	8.62603e7i	1.05936	−	0.611621i
$214$	2.00394e8	+	1.15698e8i	1.39777	+	0.807005i
$215$			167085.i			0.00114658i
$216$			3.07090e7i			0.207337i
$217$	1.28535e8	−	2.07303e8i	0.853913	−	1.37720i
$218$	−8.71762e7	+	1.50994e8i	−0.569902	+	0.987099i
$219$	−2.62176e8	+	1.51368e8i	−1.68671	+	0.973820i
$220$	−1.84839e6	−	3.20150e6i	−0.0117034	−	0.0202710i
$221$	2.46239e7	+	1.41505e7i	0.153456	+	0.0881858i
$222$	6.33766e7	−	1.09771e8i	0.388771	−	0.673370i
$223$	−2.15991e8	−	1.24702e8i	−1.30427	−	0.753022i	−0.323139	−	0.946351i	$-0.604738\pi$
$223$	−2.15991e8	−	1.24702e8i	−1.30427	−	0.753022i	−0.981134	+	0.193329i	$0.938072\pi$
$224$	−1.00251e8	−	3.15134e6i	−0.595964	−	0.0187338i
$225$	−9.11291e7	−	1.57840e8i	−0.533357	−	0.923802i
$226$	5.20678e8	+	3.00613e8i	3.00047	+	1.73232i
$227$	−2.15973e8	−	1.24692e8i	−1.22549	−	0.707535i	−0.259405	−	0.965769i	$-0.583526\pi$
$227$	−2.15973e8	−	1.24692e8i	−1.22549	−	0.707535i	−0.966083	+	0.258233i	$0.916860\pi$
$228$	2.69394e8	+	1.55535e8i	1.50528	+	0.869072i
$229$	−2.05647e7	−	1.18730e7i	−0.113161	−	0.0653336i	0.442351	−	0.896842i	$-0.354144\pi$
$229$	−2.05647e7	−	1.18730e7i	−0.113161	−	0.0653336i	−0.555512	+	0.831508i	$0.687478\pi$
$230$	3.30162e6	+	5.71857e6i	0.0178928	+	0.0309913i
$231$	−2.42676e7	−	4.52598e7i	−0.129534	−	0.241586i
$232$	1.01170e8	+	5.84106e7i	0.531918	+	0.307103i
$233$	−1.74828e8	+	3.02811e8i	−0.905451	+	1.56829i	−0.0851392	+	0.996369i	$0.527134\pi$
$233$	−1.74828e8	+	3.02811e8i	−0.905451	+	1.56829i	−0.820311	+	0.571917i	$0.806200\pi$
$234$	1.86960e8	+	3.22321e8i	0.953877	+	1.64450i
$235$	−3.59448e6	−	6.22582e6i	−0.0180675	−	0.0312939i
$236$	−1.12392e8	+	6.48898e7i	−0.556602	+	0.321354i
$237$	−3.14968e6	+	5.45541e6i	−0.0153691	+	0.0266200i
$238$	3.09000e7	+	5.76294e7i	0.148573	+	0.277092i
$239$			2.77816e8i			1.31633i	0.752874	+	0.658165i	$0.228667\pi$
$239$			2.77816e8i			1.31633i	−0.752874	+	0.658165i	$0.771333\pi$
$240$			2.61903e7i			0.122293i
$241$	5.69232e7	+	3.28646e7i	0.261957	+	0.151241i	0.625227	−	0.780443i	$-0.285006\pi$
$241$	5.69232e7	+	3.28646e7i	0.261957	+	0.151241i	−0.363270	+	0.931684i	$0.618340\pi$
$242$	−3.26870e8	+	1.88719e8i	−1.48259	+	0.855975i
$243$	−3.20245e8			−1.43173
$244$	−4.55143e8	+	7.88331e8i	−2.00578	+	3.47411i
$245$	−1.17508e7	+	5.83293e6i	−0.0510491	+	0.0253399i
$246$	1.10831e9			4.74667
$247$	1.32718e8	−	267627.i	0.560390	−	0.00113003i
$248$	−3.99557e8	−	6.92053e8i	−1.66341	−	2.88110i
$249$		−	2.17812e8i		−	0.894097i
$250$	−2.49717e7	−	4.32523e7i	−0.101078	−	0.175073i
$251$	1.71430e8	+	2.96925e8i	0.684272	+	1.18519i	0.973665	+	0.227983i	$0.0732130\pi$
$251$	1.71430e8	+	2.96925e8i	0.684272	+	1.18519i	−0.289394	+	0.957210i	$0.593454\pi$
$252$	−1.84139e7	+	5.85784e8i	−0.0724841	+	2.30587i
$253$	−1.50223e7	+	8.67312e6i	−0.0583196	+	0.0336708i
$254$		−	5.19631e8i		−	1.98965i
$255$	3.32806e6	−	1.92146e6i	0.0125690	−	0.00725672i
$256$	2.67198e8	−	4.62801e8i	0.995390	−	1.72407i
$257$	−1.20484e8	−	2.08684e8i	−0.442754	−	0.766872i	0.555139	−	0.831758i	$-0.312665\pi$
$257$	−1.20484e8	−	2.08684e8i	−0.442754	−	0.766872i	−0.997893	+	0.0648857i	$0.979332\pi$
$258$	1.22840e7	+	7.09216e6i	0.0445318	+	0.0257105i
$259$	4.48228e7	−	7.22905e7i	0.160306	−	0.258543i
$260$	1.74701e7	+	3.01187e7i	0.0616436	+	0.106274i
$261$	4.59825e7	−	7.96440e7i	0.160085	−	0.277275i
$262$		−	1.05089e8i		−	0.360996i
$263$	−2.54648e8			−0.863169			−0.431584	−	0.902073i	$-0.642045\pi$
$263$	−2.54648e8			−0.863169			−0.431584	+	0.902073i	$0.642045\pi$
$264$	−1.68249e8			−0.562779
$265$			8.86039e6i			0.0292478i
$266$	2.59709e8	+	1.61029e8i	0.846061	+	0.524590i
$267$	5.03924e8	−	2.90940e8i	1.62022	−	0.935437i
$268$	−1.94006e8	−	1.12009e8i	−0.615663	−	0.355453i
$269$	1.44604e8	−	2.50462e8i	0.452947	−	0.784528i	−0.545620	−	0.838033i	$-0.683706\pi$
$269$	1.44604e8	−	2.50462e8i	0.452947	−	0.784528i	0.998568	+	0.0535046i	$0.0170392\pi$
$270$	3.30690e6			0.0102246
$271$	3.00173e8	−	1.73305e8i	0.916177	−	0.528955i	0.0337637	−	0.999430i	$-0.489251\pi$
$271$	3.00173e8	−	1.73305e8i	0.916177	−	0.528955i	0.882413	+	0.470475i	$0.155917\pi$
$272$	8.76033e7			0.263955
$273$	2.29428e8	+	4.25825e8i	0.682459	+	1.26667i
$274$	−3.13247e8			−0.919941
$275$	5.67180e7	−	3.27461e7i	0.164458	−	0.0949501i
$276$	3.82931e8			1.09632
$277$	1.04167e7	−	1.80422e7i	0.0294475	−	0.0510046i	−0.850926	−	0.525285i	$-0.823959\pi$
$277$	1.04167e7	−	1.80422e7i	0.0294475	−	0.0510046i	0.880374	+	0.474281i	$0.157292\pi$
$278$	−7.35940e8	−	4.24895e8i	−2.05440	−	1.18611i
$279$	−5.44804e8	+	3.14543e8i	−1.50185	+	0.867091i
$280$	−1.35038e6	+	4.29585e7i	−0.00367623	+	0.116949i
$281$			4.51050e8i			1.21270i	0.795199	+	0.606348i	$0.207366\pi$
$281$			4.51050e8i			1.21270i	−0.795199	+	0.606348i	$0.792634\pi$
$282$	−6.10292e8			−1.62056
$283$	9.91777e7			0.260113			0.130056	−	0.991507i	$-0.458484\pi$
$283$	9.91777e7			0.260113			0.130056	+	0.991507i	$0.458484\pi$
$284$		−	7.07473e8i		−	1.83272i
$285$	8.97924e6	−	1.55525e7i	0.0229764	−	0.0397964i
$286$	−1.15822e8	+	6.71817e7i	−0.292759	+	0.169813i
$287$	7.43375e8	+	2.33676e7i	1.85618	+	0.0583483i
$288$	2.24027e8	+	1.29342e8i	0.552619	+	0.319055i
$289$	1.98742e8	+	3.44232e8i	0.484337	+	0.838897i
$290$	6.28994e6	−	1.08945e7i	0.0151444	−	0.0262310i
$291$	−5.63821e8	+	3.25522e8i	−1.34127	+	0.774382i
$292$			1.24146e9i			2.91805i
$293$	3.01576e8	−	1.74115e8i	0.700423	−	0.404390i	−0.107082	−	0.994250i	$-0.534151\pi$
$293$	3.01576e8	−	1.74115e8i	0.700423	−	0.404390i	0.807505	+	0.589861i	$0.200817\pi$
$294$	−6.99483e7	+	1.11150e9i	−0.160532	+	2.55091i
$295$	3.74618e6	+	6.48857e6i	0.00849594	+	0.0147154i
$296$	−1.39334e8	−	2.41333e8i	−0.312273	−	0.540873i
$297$			8.68700e6i			0.0192408i
$298$	3.22236e6	+	5.58129e6i	0.00705370	+	0.0122174i
$299$	1.41325e8	−	8.19743e7i	0.305752	−	0.177349i
$300$	−1.44579e9			−3.09158
$301$	8.08968e6	+	5.01591e6i	0.0170981	+	0.0106015i
$302$	5.53739e8	−	9.59105e8i	1.15686	−	2.00374i
$303$	−7.90622e8			−1.63275
$304$	3.54536e8	−	2.04691e8i	0.723773	−	0.417871i
$305$	4.55114e7	+	2.62760e7i	0.0918483	+	0.0530286i
$306$		−	1.68649e8i		−	0.336479i
$307$		−	1.39728e8i		−	0.275612i	−0.990459	−	0.137806i	$-0.955995\pi$
$307$		−	1.39728e8i		−	0.275612i	0.990459	−	0.137806i	$-0.0440051\pi$
$308$	−2.10494e8	−	6.61680e6i	−0.410500	−	0.0129039i
$309$	3.16087e8	−	5.47479e8i	0.609469	−	1.05563i
$310$	−7.45237e7	+	4.30263e7i	−0.142079	+	0.0820291i
$311$	2.26174e8	+	3.91746e8i	0.426366	+	0.738487i	0.996547	−	0.0830320i	$-0.0264604\pi$
$311$	2.26174e8	+	3.91746e8i	0.426366	+	0.738487i	−0.570181	+	0.821519i	$0.693127\pi$
$312$	1.58467e9	−	3.19551e6i	2.95392	−	0.00595661i
$313$	5.76287e7	−	9.98158e7i	0.106227	−	0.183990i	−0.808012	−	0.589166i	$-0.799456\pi$
$313$	5.76287e7	−	9.98158e7i	0.106227	−	0.183990i	0.914239	+	0.405176i	$0.132790\pi$
$314$	−1.10489e9	−	6.37908e8i	−2.01403	−	1.16280i
$315$	3.38181e7	+	1.06306e6i	0.0609625	+	0.00191633i
$316$	1.29162e7	+	2.23716e7i	0.0230267	+	0.0398834i
$317$	3.72370e8	+	2.14988e8i	0.656550	+	0.379059i	0.790961	−	0.611866i	$-0.209581\pi$
$317$	3.72370e8	+	2.14988e8i	0.656550	+	0.379059i	−0.134411	+	0.990926i	$0.542914\pi$
$318$	6.51411e8	+	3.76092e8i	1.13595	+	0.655843i
$319$	2.86191e7	+	1.65232e7i	0.0493615	+	0.0284989i
$320$	−1.25025e7	−	7.21834e6i	−0.0213291	−	0.0123144i
$321$	−3.87348e8	−	6.70906e8i	−0.653632	−	1.13212i
$322$	3.75988e8	+	1.18190e7i	0.627594	+	0.0197281i
$323$	−5.20212e7	−	3.00344e7i	−0.0858957	−	0.0495919i
$324$	−6.10314e8	+	1.05709e9i	−0.996886	+	1.72666i
$325$	−5.33584e8	+	3.09501e8i	−0.862206	+	0.500116i
$326$	−5.38381e8	−	9.32503e8i	−0.860653	−	1.49070i
$327$	5.05516e8	−	2.91860e8i	0.799499	−	0.461591i
$328$	1.21831e9	−	2.11018e9i	1.90634	−	3.30187i
$329$	−4.09340e8	−	1.28674e7i	−0.633721	−	0.0199207i
$330$			1.81178e7i			0.0277529i
$331$		−	1.02813e9i		−	1.55830i	−0.626839	−	0.779149i	$-0.715651\pi$
$331$		−	1.02813e9i		−	1.55830i	0.626839	−	0.779149i	$-0.284349\pi$
$332$	−7.73540e8	−	4.46603e8i	−1.16011	−	0.669790i
$333$	−1.89984e8	+	1.09687e8i	−0.281943	+	0.162780i
$334$	−1.34395e9			−1.97366
$335$	−6.46646e6	+	1.12002e7i	−0.00939744	+	0.0162768i
$336$	1.26805e9	+	7.86236e8i	1.82367	+	1.13075i
$337$	−8.43289e8			−1.20025			−0.600125	−	0.799906i	$-0.704883\pi$
$337$	−8.43289e8			−1.20025			−0.600125	+	0.799906i	$0.704883\pi$
$338$	1.08961e9	−	6.34960e8i	1.53484	−	0.894412i
$339$	−1.00643e9	−	1.74319e9i	−1.40309	−	2.43022i
$340$		−	1.57591e7i		−	0.0217447i
$341$	−1.13027e8	−	1.95769e8i	−0.154363	−	0.267364i
$342$	−3.94060e8	−	6.82532e8i	−0.532685	−	0.922638i
$343$	−7.03512e7	+	7.44041e8i	−0.0941330	+	0.995560i
$344$	2.70064e7	−	1.55921e7i	0.0357694	−	0.0206515i
$345$		−	2.21072e7i		−	0.0289845i
$346$	−1.15982e9	+	6.69623e8i	−1.50531	+	0.869089i
$347$	8.40031e7	−	1.45498e8i	0.107930	−	0.186940i	−0.807002	−	0.590549i	$-0.798911\pi$
$347$	8.40031e7	−	1.45498e8i	0.107930	−	0.186940i	0.914931	+	0.403609i	$0.132244\pi$
$348$	−3.64763e8	−	6.31788e8i	−0.463963	−	0.803608i
$349$	1.22063e9	+	7.04732e8i	1.53708	+	0.887432i	0.999008	+	0.0445323i	$0.0141798\pi$
$349$	1.22063e9	+	7.04732e8i	1.53708	+	0.887432i	0.538070	+	0.842900i	$0.319154\pi$
$350$	−1.41958e9	−	4.46237e7i	−1.76979	−	0.0556324i
$351$	−164990.	−	8.18196e7i	−0.000203649	−	0.100991i
$352$	−4.64774e7	+	8.05013e7i	−0.0567993	+	0.0983792i
$353$		−	1.26930e9i		−	1.53586i	−0.640532	−	0.767931i	$-0.721286\pi$
$353$		−	1.26930e9i		−	1.53586i	0.640532	−	0.767931i	$-0.278714\pi$
$354$	6.36048e8			0.762041
$355$	−4.08434e7			−0.0484533
$356$		−	2.38618e9i		−	2.80303i
$357$	6.87837e6	−	2.18816e8i	0.00800105	−	0.254530i
$358$	−4.95379e8	+	2.86007e8i	−0.570620	+	0.329448i
$359$	9.40484e8	+	5.42989e8i	1.07281	+	0.619384i	0.928947	−	0.370214i	$-0.120716\pi$
$359$	9.40484e8	+	5.42989e8i	1.07281	+	0.619384i	0.143859	+	0.989598i	$0.454049\pi$
$360$	5.54243e7	−	9.59977e7i	0.0626097	−	0.108443i
$361$	6.13161e8			0.685961
$362$	−5.76239e8	+	3.32692e8i	−0.638444	+	0.368606i
$363$	1.26363e9			1.38659
$364$	1.98270e9	+	5.83233e7i	2.15477	+	0.0633851i
$365$	7.16712e7			0.0771471
$366$	3.86360e9	−	2.23065e9i	4.11916	−	2.37820i
$367$	−7.65956e8			−0.808859			−0.404429	−	0.914569i	$-0.632530\pi$
$367$	−7.65956e8			−0.808859			−0.404429	+	0.914569i	$0.632530\pi$
$368$	2.51978e8	−	4.36439e8i	0.263570	−	0.456516i
$369$	−1.66119e9	−	9.59089e8i	−1.72118	−	0.993726i
$370$	−2.59879e7	+	1.50041e7i	−0.0266726	+	0.0153994i
$371$	4.28990e8	+	2.65990e8i	0.436152	+	0.270431i
$372$			4.99032e9i			5.02606i
$373$	−2.11414e8			−0.210937			−0.105468	−	0.994423i	$-0.533634\pi$
$373$	−2.11414e8			−0.210937			−0.105468	+	0.994423i	$0.533634\pi$
$374$	6.06019e7			0.0599012
$375$			1.67207e8i			0.163736i
$376$	−6.70864e8	+	1.16197e9i	−0.650844	+	1.12729i
$377$	−2.69867e8	−	1.55083e8i	−0.259391	−	0.149063i
$378$	9.92734e7	−	1.60109e8i	0.0945391	−	0.152473i
$379$	−1.40928e9	−	8.13651e8i	−1.32972	−	0.767717i	−0.344467	−	0.938798i	$-0.611940\pi$
$379$	−1.40928e9	−	8.13651e8i	−1.32972	−	0.767717i	−0.985257	+	0.171082i	$0.945274\pi$
$380$	−3.68222e7	−	6.37778e7i	−0.0344244	−	0.0596248i
$381$	−8.69844e8	+	1.50661e9i	−0.805757	+	1.39561i
$382$	−2.97882e9	+	1.71982e9i	−2.73415	+	1.57856i
$383$			1.37278e9i			1.24855i	0.781206	+	0.624274i	$0.214605\pi$
$383$			1.37278e9i			1.24855i	−0.781206	+	0.624274i	$0.785395\pi$
$384$	−1.88576e9	+	1.08874e9i	−1.69952	+	0.981221i
$385$	−381997.	+	1.21521e7i	−0.000341152	+	0.0108528i
$386$	1.41692e9	+	2.45418e9i	1.25398	+	2.17196i
$387$	−1.22746e7	−	2.12602e7i	−0.0107651	−	0.0186457i
$388$			2.66981e9i			2.32043i
$389$	4.19126e8	+	7.25947e8i	0.361011	+	0.625290i	0.988128	−	0.153636i	$-0.0490983\pi$
$389$	4.19126e8	+	7.25947e8i	0.361011	+	0.625290i	−0.627116	+	0.778926i	$0.715765\pi$
$390$	−344108.	−	1.70645e8i	−0.000293744	−	0.145669i
$391$	−7.39457e7			−0.0625596
$392$	2.03936e9	+	1.35500e9i	1.70999	+	1.13616i
$393$	−1.75915e8	+	3.04694e8i	−0.146194	+	0.253215i
$394$	1.40246e9			1.15519
$395$	1.29154e6	−	745673.i	0.00105443	−	0.000608777i
$396$	4.70384e8	+	2.71576e8i	0.380644	+	0.219765i
$397$			3.14648e8i			0.252382i	0.992006	+	0.126191i	$0.0402753\pi$
$397$			3.14648e8i			0.252382i	−0.992006	+	0.126191i	$0.959725\pi$
$398$		−	1.73434e9i		−	1.37894i
$399$	−4.83441e8	−	9.01632e8i	−0.381012	−	0.710598i
$400$	−9.51366e8	+	1.64781e9i	−0.743254	+	1.28735i
$401$	−9.76413e7	+	5.63733e7i	−0.0756186	+	0.0436584i	−0.537333	−	0.843370i	$-0.680568\pi$
$401$	−9.76413e7	+	5.63733e7i	−0.0756186	+	0.0436584i	0.461714	+	0.887029i	$0.347235\pi$
$402$	5.48956e8	+	9.50820e8i	0.421451	+	0.729974i
$403$	1.06828e9	+	1.84173e9i	0.813050	+	1.40171i
$404$	−1.62109e9	+	2.80782e9i	−1.22313	+	2.11853i
$405$	6.10276e7	+	3.52343e7i	0.0456492	+	0.0263556i
$406$	−3.38649e8	−	6.31591e8i	−0.251136	−	0.468376i
$407$	−3.94148e7	−	6.82684e7i	−0.0289787	−	0.0501926i
$408$	−6.21140e8	−	3.58616e8i	−0.452772	−	0.261408i
$409$	3.12452e8	+	1.80394e8i	0.225815	+	0.130374i	0.608640	−	0.793447i	$-0.291715\pi$
$409$	3.12452e8	+	1.80394e8i	0.225815	+	0.130374i	−0.382825	+	0.923821i	$0.625049\pi$
$410$	−2.27234e8	−	1.31194e8i	−0.162828	−	0.0940091i
$411$	9.08226e8	+	5.24365e8i	0.645279	+	0.372552i
$412$	−1.29621e9	−	2.24510e9i	−0.913136	−	1.58160i
$413$	4.26615e8	+	1.34104e7i	0.297996	+	0.00936738i
$414$	−8.40207e8	−	4.85093e8i	−0.581949	−	0.335988i
$415$	−2.57830e7	+	4.46575e7i	−0.0177078	+	0.0306709i
$416$	4.36225e8	−	7.59095e8i	0.297087	−	0.516975i
$417$	1.42252e9	+	2.46388e9i	0.960687	+	1.66396i
$418$	2.45259e8	−	1.41601e8i	0.164251	−	0.0948305i
$419$	1.04243e9	−	1.80554e9i	0.692304	−	1.19911i	−0.278777	−	0.960356i	$-0.589929\pi$
$419$	1.04243e9	−	1.80554e9i	0.692304	−	1.19911i	0.971081	−	0.238750i	$-0.0767376\pi$
$420$	1.41437e8	−	2.28110e8i	0.0931516	−	0.150235i
$421$		−	1.51468e9i		−	0.989315i	−0.869088	−	0.494657i	$-0.835294\pi$
$421$		−	1.51468e9i		−	0.989315i	0.869088	−	0.494657i	$-0.164706\pi$
$422$		−	4.25067e9i		−	2.75337i
$423$	9.14736e8	+	5.28123e8i	0.587630	+	0.339269i
$424$	1.43213e9	−	8.26840e8i	0.912434	−	0.526794i
$425$	2.79188e8			0.176415
$426$	−1.73366e9	+	3.00279e9i	−1.08650	+	1.88188i
$427$	2.63845e9	−	1.41470e9i	1.64003	−	0.879359i
$428$	−3.17688e9			−1.95861
$429$	4.48274e8	−	903948.i	0.274121	−	0.000552768i
$430$	−1.67904e6	−	2.90818e6i	−0.00101841	−	0.00176393i
$431$		−	1.30549e9i		−	0.785424i	−0.919662	−	0.392712i	$-0.871537\pi$
$431$		−	1.30549e9i		−	0.785424i	0.919662	−	0.392712i	$-0.128463\pi$
$432$	−1.26191e8	−	2.18569e8i	−0.0753067	−	0.130435i
$433$	3.65228e8	+	6.32594e8i	0.216200	+	0.374470i	0.953643	−	0.300939i	$-0.0973002\pi$
$433$	3.65228e8	+	6.32594e8i	0.216200	+	0.374470i	−0.737443	+	0.675410i	$0.763967\pi$
$434$	−1.54024e8	+	4.89983e9i	−0.0904429	+	2.87718i
$435$	−3.64740e7	+	2.10583e7i	−0.0212457	+	0.0122662i
$436$		−	2.39372e9i		−	1.38316i
$437$	−2.99263e8	+	1.72779e8i	−0.171541	+	0.0990391i
$438$	3.04219e9	−	5.26923e9i	1.72992	−	2.99631i
$439$	1.25258e9	+	2.16954e9i	0.706612	+	1.22389i	0.966107	+	0.258143i	$0.0831107\pi$
$439$	1.25258e9	+	2.16954e9i	0.706612	+	1.22389i	−0.259495	+	0.965745i	$0.583556\pi$
$440$	3.44956e7	+	1.99161e7i	0.0193054	+	0.0111460i
$441$	1.06669e9	−	1.60544e9i	0.592249	−	0.891375i
$442$	−5.70787e8	+	1.15100e6i	−0.314410	+	0.000634010i
$443$	−3.58912e8	+	6.21653e8i	−0.196144	+	0.339731i	−0.947275	−	0.320422i	$-0.896175\pi$
$443$	−3.58912e8	+	6.21653e8i	−0.196144	+	0.339731i	0.751131	+	0.660153i	$0.229509\pi$
$444$			1.74022e9i			0.943549i
$445$	−1.37758e8			−0.0741064
$446$	5.01254e9			2.67538
$447$		−	2.15765e7i		−	0.0114263i
$448$	−7.24815e8	+	3.88635e8i	−0.380850	+	0.204206i
$449$	2.73272e9	−	1.57773e9i	1.42473	−	0.822568i	0.428031	−	0.903764i	$-0.359207\pi$
$449$	2.73272e9	−	1.57773e9i	1.42473	−	0.822568i	0.996698	+	0.0811960i	$0.0258740\pi$
$450$	3.17227e9	+	1.83151e9i	1.64107	+	0.947472i
$451$	3.44637e8	−	5.96929e8i	0.176907	−	0.306411i
$452$	−8.25437e9			−4.20436
$453$	−3.21102e9	+	1.85388e9i	−1.62293	+	0.936997i
$454$	5.01212e9			2.51377
$455$	3.36709e6	−	1.14464e8i	0.00167577	−	0.0569676i
$456$	−3.35172e9			−1.65535
$457$	−2.56203e8	+	1.47919e8i	−0.125567	+	0.0724964i	−0.561468	−	0.827498i	$-0.689763\pi$
$457$	−2.56203e8	+	1.47919e8i	−0.125567	+	0.0724964i	0.435901	+	0.899995i	$0.356430\pi$
$458$	4.77248e8			0.232121
$459$	−1.85160e7	+	3.20706e7i	−0.00893722	+	0.0154797i
$460$	−7.85115e7	−	4.53286e7i	−0.0376080	−	0.0217130i
$461$	−1.96621e9	+	1.13519e9i	−0.934712	+	0.539656i	−0.888299	−	0.459266i	$-0.848112\pi$
$461$	−1.96621e9	+	1.13519e9i	−0.934712	+	0.539656i	−0.0464131	+	0.998922i	$0.514779\pi$
$462$	8.77204e8	+	5.43899e8i	0.413860	+	0.256609i
$463$		−	3.26208e9i		−	1.52743i	−0.645555	−	0.763714i	$-0.723374\pi$
$463$		−	3.26208e9i		−	1.52743i	0.645555	−	0.763714i	$-0.276626\pi$
$464$	−9.60092e8			−0.446169
$465$	2.88098e8			0.132879
$466$		−	7.02738e9i		−	3.21694i
$467$	−7.08742e8	+	1.22758e9i	−0.322017	+	0.557750i	−0.980904	−	0.194492i	$-0.937694\pi$
$467$	−7.08742e8	+	1.22758e9i	−0.322017	+	0.557750i	0.658887	+	0.752242i	$0.271027\pi$
$468$	−4.43553e9	−	2.54894e9i	−2.00025	−	1.14948i
$469$	3.48153e8	+	6.49316e8i	0.155835	+	0.290637i
$470$	1.25127e8	+	7.22419e7i	0.0555914	+	0.0320957i
$471$	2.13567e9	+	3.69909e9i	0.941806	+	1.63126i
$472$	6.99176e8	−	1.21101e9i	0.306048	−	0.530091i
$473$	7.63958e6	−	4.41072e6i	0.00331937	−	0.00191644i
$474$		−	1.26605e8i		−	0.0546041i
$475$	1.12989e9	−	6.52343e8i	0.483737	−	0.279286i
$476$	−7.62999e8	−	4.73088e8i	−0.324265	−	0.201056i
$477$	−6.50911e8	−	1.12741e9i	−0.274604	−	0.475629i
$478$	−2.79178e9	−	4.83550e9i	−1.16918	−	2.02509i
$479$			1.42677e8i			0.0593172i	0.999560	+	0.0296586i	$0.00944202\pi$
$479$			1.42677e8i			0.0593172i	−0.999560	+	0.0296586i	$0.990558\pi$
$480$	−5.92338e7	−	1.02596e8i	−0.0244470	−	0.0423434i
$481$	3.72530e8	+	6.42247e8i	0.152635	+	0.263144i
$482$	−1.32103e9			−0.537338
$483$	−1.07035e9	−	6.63659e8i	−0.432227	−	0.267997i
$484$	2.59096e9	−	4.48767e9i	1.03873	−	1.79913i
$485$	1.54132e8			0.0613474
$486$	5.57399e9	−	3.21814e9i	2.20262	−	1.27168i
$487$	−2.92600e9	−	1.68933e9i	−1.14795	−	0.662770i	−0.199564	−	0.979885i	$-0.563953\pi$
$487$	−2.92600e9	−	1.68933e9i	−1.14795	−	0.662770i	−0.948387	+	0.317115i	$0.897286\pi$
$488$		−	9.80817e9i		−	3.82049i
$489$			3.60493e9i			1.39417i
$490$	1.45913e8	−	2.19609e8i	0.0560283	−	0.0843263i
$491$	2.49679e9	−	4.32457e9i	0.951912	−	1.64876i	0.210630	−	0.977566i	$-0.432448\pi$
$491$	2.49679e9	−	4.32457e9i	0.951912	−	1.64876i	0.741282	−	0.671194i	$-0.234218\pi$
$492$	−1.31777e10	+	7.60812e9i	−4.98839	+	2.88005i
$493$	7.04373e7	+	1.22001e8i	0.0264751	+	0.0458563i
$494$	−2.30732e9	+	1.33834e9i	−0.861120	+	0.499486i
$495$	1.56785e7	−	2.71559e7i	0.00581013	−	0.0100634i
$496$	5.68762e9	+	3.28375e9i	2.09288	+	1.20833i
$497$	−1.22612e9	+	1.97750e9i	−0.448009	+	0.722552i
$498$	2.18880e9	+	3.79111e9i	0.794151	+	1.37551i
$499$	−6.24034e8	−	3.60286e8i	−0.224831	−	0.129806i	0.383354	−	0.923601i	$-0.374769\pi$
$499$	−6.24034e8	−	3.60286e8i	−0.224831	−	0.129806i	−0.608185	+	0.793795i	$0.708102\pi$
$500$	5.93820e8	+	3.42842e8i	0.212451	+	0.122659i
$501$	3.89665e9	+	2.24973e9i	1.38439	+	0.799280i
$502$	−5.96761e9	−	3.44540e9i	−2.10541	−	1.21556i
$503$	8.84974e8	+	1.53282e9i	0.310058	+	0.537036i	0.978375	−	0.206841i	$-0.0663183\pi$
$503$	8.84974e8	+	1.53282e9i	0.310058	+	0.537036i	−0.668317	+	0.743877i	$0.732985\pi$
$504$	−2.98404e9	−	5.56531e9i	−1.03824	−	1.93635i
$505$	1.62099e8	+	9.35881e7i	0.0560095	+	0.0323371i
$506$	1.74312e8	−	3.01918e8i	0.0598138	−	0.103601i
$507$	−4.22211e9	+	1.70279e7i	−1.43880	+	0.00580275i
$508$	3.56706e9	+	6.17833e9i	1.20722	+	2.09097i
$509$	−3.40592e9	+	1.96641e9i	−1.14478	+	0.660939i	−0.947610	−	0.319430i	$-0.896509\pi$
$509$	−3.40592e9	+	1.96641e9i	−1.14478	+	0.660939i	−0.197170	+	0.980369i	$0.563175\pi$
$510$	−3.86175e7	+	6.68874e7i	−0.0128911	+	0.0223280i
$511$	2.15158e9	−	3.47007e9i	0.713319	−	1.15044i
$512$			6.59805e9i			2.17255i
$513$			1.73056e8i			0.0565946i
$514$	4.19413e9	+	2.42148e9i	1.36229	+	0.786521i
$515$	−1.29613e8	+	7.48321e7i	−0.0418142	+	0.0241414i
$516$	−1.94740e8			−0.0623994
$517$	−1.89775e8	+	3.28699e8i	−0.0603978	+	0.104612i
$518$	−5.37112e7	+	1.70867e9i	−0.0169790	+	0.540137i
$519$	4.48370e9			1.40783
$520$	−3.25280e8	−	1.86927e8i	−0.101448	−	0.0582989i
$521$	−2.20764e9	−	3.82374e9i	−0.683904	−	1.18456i	−0.973780	−	0.227493i	$-0.926947\pi$
$521$	−2.20764e9	−	3.82374e9i	−0.683904	−	1.18456i	0.289876	−	0.957064i	$-0.406386\pi$
$522$			1.84831e9i			0.568759i
$523$	8.31593e8	+	1.44036e9i	0.254188	+	0.440266i	0.964675	−	0.263444i	$-0.0848585\pi$
$523$	8.31593e8	+	1.44036e9i	0.254188	+	0.440266i	−0.710487	+	0.703711i	$0.751525\pi$
$524$	7.21395e8	+	1.24949e9i	0.219035	+	0.379380i
$525$	4.04121e9	+	2.50570e9i	1.21886	+	0.755740i
$526$	4.43225e9	−	2.55896e9i	1.32793	−	0.766679i
$527$		−	9.63651e8i		−	0.286802i
$528$	1.19749e9	−	6.91374e8i	0.354042	−	0.204406i
$529$	1.48972e9	−	2.58027e9i	0.437532	−	0.757827i
$530$	−8.90381e7	−	1.54219e8i	−0.0259783	−	0.0449957i
$531$	−9.53340e8	−	5.50411e8i	−0.276323	−	0.159535i
$532$	−4.19331e9	−	1.31815e8i	−1.20744	−	0.0379554i
$533$	−3.23467e9	+	5.62880e9i	−0.925306	+	1.61017i
$534$	−5.84732e9	+	1.01279e10i	−1.66174	+	2.87822i
$535$			1.83406e8i			0.0517815i
$536$	2.41376e9			0.677045
$537$	1.91506e9			0.533671
$538$			5.81251e9i			1.60926i
$539$	5.76897e8	+	3.83303e8i	0.158686	+	0.105434i
$540$	−3.93185e7	+	2.27006e7i	−0.0107453	+	0.00620381i
$541$	−7.93336e8	−	4.58033e8i	−0.215410	−	0.124367i	0.388413	−	0.921485i	$-0.373023\pi$
$541$	−7.93336e8	−	4.58033e8i	−0.215410	−	0.124367i	−0.603823	+	0.797118i	$0.706357\pi$
$542$	−3.48309e9	+	6.03288e9i	−0.939652	+	1.62752i
$543$	2.22766e9			0.597103
$544$	−3.43171e8	+	1.98130e8i	−0.0913932	+	0.0527659i
$545$	−1.38193e8			−0.0365677
$546$	−8.27239e9	−	5.10613e9i	−2.17499	−	1.34251i
$547$	−5.03138e8			−0.131441			−0.0657206	−	0.997838i	$-0.520935\pi$
$547$	−5.03138e8			−0.131441			−0.0657206	+	0.997838i	$0.520935\pi$
$548$	3.72446e9	−	2.15032e9i	0.966788	−	0.558176i
$549$	−7.72127e9			−1.99152
$550$	−6.58132e8	+	1.13992e9i	−0.168672	+	0.292149i
$551$	5.70128e8	+	3.29163e8i	0.145192	+	0.0838264i
$552$	−3.57324e9	+	2.06301e9i	−0.904222	+	0.522053i
$553$	2.66934e6	−	8.49172e7i	0.000671220	−	0.0213530i
$554$			4.18708e8i			0.104623i
$555$	1.00465e8			0.0249455
$556$	1.16670e10			2.87870
$557$			3.50595e9i			0.859632i	0.902916	+	0.429816i	$0.141422\pi$
$557$			3.50595e9i			0.859632i	−0.902916	+	0.429816i	$0.858578\pi$
$558$	6.32168e9	−	1.09495e10i	1.54033	−	2.66792i
$559$	−7.18707e7	+	4.16880e7i	−0.0174025	+	0.0100942i
$560$	−1.66915e8	−	3.11302e8i	−0.0401641	−	0.0749072i
$561$	−1.75709e8	−	1.01445e8i	−0.0420168	−	0.0242584i
$562$	−4.53260e9	−	7.85069e9i	−1.07714	−	1.86565i
$563$	2.70876e9	−	4.69170e9i	0.639721	−	1.10803i	−0.345773	−	0.938318i	$-0.612383\pi$
$563$	2.70876e9	−	4.69170e9i	0.639721	−	1.10803i	0.985494	−	0.169711i	$-0.0542834\pi$
$564$	7.25628e9	−	4.18942e9i	1.70309	−	0.983279i
$565$			4.76537e8i			0.111154i
$566$	−1.72623e9	+	9.96637e8i	−0.400166	+	0.231036i
$567$	3.53798e9	−	1.89701e9i	0.815106	−	0.437047i
$568$	3.81145e9	+	6.60163e9i	0.872713	+	1.51158i
$569$	1.77127e9	+	3.06793e9i	0.403081	+	0.698157i	0.994096	−	0.108504i	$-0.0346060\pi$
$569$	1.77127e9	+	3.06793e9i	0.403081	+	0.698157i	−0.591015	+	0.806660i	$0.701273\pi$
$570$			3.60930e8i			0.0816321i
$571$	−3.19489e9	−	5.53371e9i	−0.718173	−	1.24391i	−0.961723	−	0.274024i	$-0.911645\pi$
$571$	−3.19489e9	−	5.53371e9i	−0.718173	−	1.24391i	0.243550	−	0.969888i	$-0.421688\pi$
$572$	9.15932e8	−	1.59385e9i	0.204634	−	0.356092i
$573$	1.15157e10			2.55711
$574$	−1.31735e10	+	7.06345e9i	−2.90744	+	1.55893i
$575$	8.03044e8	−	1.39091e9i	0.176158	−	0.305114i
$576$	2.12113e9			0.462474
$577$	−5.87939e9	+	3.39447e9i	−1.27414	+	0.735625i	−0.975764	−	0.218824i	$-0.929778\pi$
$577$	−5.87939e9	+	3.39447e9i	−1.27414	+	0.735625i	−0.298375	+	0.954449i	$0.596445\pi$
$578$	−6.91837e9	−	3.99432e9i	−1.49024	−	0.860391i
$579$		−	9.48751e9i		−	2.03132i
$580$			1.72712e8i			0.0367557i
$581$	1.38815e9	+	2.58895e9i	0.293644	+	0.547655i
$582$	6.54235e9	−	1.13317e10i	1.37563	−	2.38267i
$583$	4.05122e8	−	2.33897e8i	0.0846731	−	0.0488861i
$584$	−6.68826e9	−	1.15844e10i	−1.38953	−	2.40674i
$585$	−1.47154e8	+	2.56069e8i	−0.0303897	+	0.0528825i
$586$	−3.49937e9	+	6.06109e9i	−0.718370	+	1.24425i
$587$	2.22017e9	+	1.28182e9i	0.453058	+	0.261573i	0.709121	−	0.705087i	$-0.249092\pi$
$587$	2.22017e9	+	1.28182e9i	0.453058	+	0.261573i	−0.256063	+	0.966660i	$0.582425\pi$
$588$	−6.79836e9	−	1.36958e10i	−1.37906	−	2.77822i
$589$	−2.25164e9	−	3.89995e9i	−0.454041	−	0.786423i
$590$	−1.30407e8	−	7.52907e7i	−0.0261409	−	0.0150924i
$591$	−4.06628e9	−	2.34767e9i	−0.810291	−	0.467822i
$592$	1.98339e9	+	1.14511e9i	0.392899	+	0.226841i
$593$	−5.25853e9	−	3.03602e9i	−1.03556	−	0.597878i	−0.116984	−	0.993134i	$-0.537323\pi$
$593$	−5.25853e9	−	3.03602e9i	−1.03556	−	0.597878i	−0.918571	+	0.395256i	$0.870656\pi$
$594$	−8.72957e7	−	1.51201e8i	−0.0170899	−	0.0296006i
$595$	−2.73121e7	+	4.40490e7i	−0.00531551	+	0.00857288i
$596$	−7.66267e7	−	4.42404e7i	−0.0148258	−	0.00855968i
$597$	−2.90323e9	+	5.02855e9i	−0.558434	+	0.967236i
$598$	−1.63605e9	+	2.84697e9i	−0.312855	+	0.544413i
$599$	2.29555e9	+	3.97601e9i	0.436409	+	0.755882i	0.997409	−	0.0719333i	$-0.0229169\pi$
$599$	2.29555e9	+	3.97601e9i	0.436409	+	0.755882i	−0.561001	+	0.827815i	$0.689584\pi$
$600$	1.34911e10	−	7.78908e9i	2.54987	−	1.47217i
$601$	−6.30432e6	+	1.09194e7i	−0.00118462	+	0.00205181i	−0.866617	−	0.498974i	$-0.833710\pi$
$601$	−6.30432e6	+	1.09194e7i	−0.00118462	+	0.00205181i	0.865432	+	0.501026i	$0.167044\pi$
$602$	−1.91209e8	−	6.01056e6i	−0.0357207	−	0.00112286i
$603$		−	1.90018e9i		−	0.352927i
$604$			1.52048e10i			2.80771i
$605$	−2.59080e8	−	1.49580e8i	−0.0475652	−	0.0274618i
$606$	1.37611e10	−	7.94497e9i	2.51188	−	1.45023i
$607$	−4.06361e8			−0.0737482			−0.0368741	−	0.999320i	$-0.511740\pi$
$607$	−4.06361e8			−0.0737482			−0.0368741	+	0.999320i	$0.511740\pi$
$608$	−9.25888e8	+	1.60368e9i	−0.167069	+	0.289372i
$609$	−7.53838e7	+	2.39812e9i	−0.0135244	+	0.430239i
$610$	−1.05619e9			−0.188403
$611$	1.78117e9	−	3.09950e9i	0.315909	−	0.549728i
$612$	1.15771e9	+	2.00521e9i	0.204159	+	0.353614i
$613$		−	2.03436e9i		−	0.356711i	−0.983966	−	0.178355i	$-0.942922\pi$
$613$		−	2.03436e9i		−	0.356711i	0.983966	−	0.178355i	$-0.0570777\pi$
$614$	1.40412e9	+	2.43201e9i	0.244803	+	0.424011i
$615$	4.39228e8	+	7.60765e8i	0.0761424	+	0.131883i
$616$	1.99983e9	−	1.07228e9i	0.344715	−	0.184831i
$617$	7.61387e9	−	4.39587e9i	1.30499	−	0.753436i	0.323735	−	0.946148i	$-0.395062\pi$
$617$	7.61387e9	−	4.39587e9i	1.30499	−	0.753436i	0.981255	+	0.192712i	$0.0617282\pi$
$618$			1.27054e10i			2.16536i
$619$	−4.70030e9	+	2.71372e9i	−0.796540	+	0.459883i	−0.842260	−	0.539071i	$-0.818775\pi$
$619$	−4.70030e9	+	2.71372e9i	−0.796540	+	0.459883i	0.0457196	+	0.998954i	$0.485442\pi$
$620$	5.90717e8	−	1.02315e9i	0.0995425	−	0.172413i
$621$	1.06517e8	+	1.84493e8i	0.0178484	+	0.0309143i
$622$	−7.87331e9	−	4.54566e9i	−1.31187	−	0.757409i
$623$	−4.13550e9	+	6.66975e9i	−0.685203	+	1.10510i
$624$	−1.12656e10	+	6.53454e9i	−1.85613	+	1.07664i
$625$	−3.02205e9	+	5.23435e9i	−0.495133	+	0.857596i
$626$			2.31644e9i			0.377408i
$627$	−9.48138e8			−0.153616
$628$	1.75160e10			2.82212
$629$		−	3.36044e8i		−	0.0538418i
$630$	−5.99300e8	+	3.21336e8i	−0.0954888	+	0.0511996i
$631$	−6.55031e9	+	3.78182e9i	−1.03791	+	0.599236i	−0.919240	−	0.393698i	$-0.871196\pi$
$631$	−6.55031e9	+	3.78182e9i	−1.03791	+	0.599236i	−0.118668	+	0.992934i	$0.537862\pi$
$632$	−2.41050e8	−	1.39170e8i	−0.0379837	−	0.0219299i
$633$	−7.11548e9	+	1.23244e10i	−1.11504	+	1.93131i
$634$	−8.64167e9			−1.34674
$635$	3.56684e8	−	2.05932e8i	0.0552809	−	0.0319165i
$636$	−1.03269e10			−1.59173
$637$	−5.44086e9	−	3.59924e9i	−0.834026	−	0.551725i
$638$	−6.64169e8			−0.101253
$639$	5.19699e9	−	3.00048e9i	0.787950	−	0.454923i
$640$	5.15510e8			0.0777334
$641$	−4.24426e9	+	7.35127e9i	−0.636500	+	1.10245i	0.349695	+	0.936864i	$0.386285\pi$
$641$	−4.24426e9	+	7.35127e9i	−0.636500	+	1.10245i	−0.986195	+	0.165587i	$0.947048\pi$
$642$	1.34839e10	+	7.78492e9i	2.01114	+	1.16113i
$643$	−2.49769e9	+	1.44204e9i	−0.370511	+	0.213915i	−0.673682	−	0.739022i	$-0.735288\pi$
$643$	−2.49769e9	+	1.44204e9i	−0.370511	+	0.213915i	0.303171	+	0.952936i	$0.401955\pi$
$644$	−4.55158e9	+	2.44049e9i	−0.671524	+	0.360061i
$645$			1.12426e7i			0.00164971i
$646$	1.20726e9			0.176193
$647$	4.52510e9			0.656846			0.328423	−	0.944531i	$-0.393483\pi$
$647$	4.52510e9			0.656846			0.328423	+	0.944531i	$0.393483\pi$
$648$		−	1.31521e10i		−	1.89881i
$649$	1.97784e8	−	3.42571e8i	0.0284010	−	0.0491920i
$650$	6.17706e9	−	1.07490e10i	0.882236	−	1.53522i
$651$	8.64873e9	−	1.39487e10i	1.22862	−	1.98153i
$652$	1.28025e10	+	7.39155e9i	1.80896	+	1.04441i
$653$	2.27385e9	+	3.93843e9i	0.319570	+	0.553511i	0.980398	−	0.197026i	$-0.0631282\pi$
$653$	2.27385e9	+	3.93843e9i	0.319570	+	0.553511i	−0.660828	+	0.750537i	$0.729795\pi$
$654$	−5.86580e9	+	1.01599e10i	−0.819984	+	1.42025i
$655$	7.21349e7	−	4.16471e7i	0.0100300	−	0.00579083i
$656$			2.00253e10i			2.76959i
$657$	−9.11956e9	+	5.26518e9i	−1.25457	+	0.724327i
$658$	7.25402e9	−	3.88949e9i	0.992631	−	0.532234i
$659$	−5.62422e9	−	9.74143e9i	−0.765531	−	1.32594i	−0.939965	−	0.341270i	$-0.889143\pi$
$659$	−5.62422e9	−	9.74143e9i	−0.765531	−	1.32594i	0.174434	−	0.984669i	$-0.444190\pi$
$660$	−1.24372e8	−	2.15419e8i	−0.0168391	−	0.0291662i
$661$		−	1.03533e10i		−	1.39436i	−0.716896	−	0.697180i	$-0.754438\pi$
$661$		−	1.03533e10i		−	1.39436i	0.716896	−	0.697180i	$-0.245562\pi$
$662$	1.03317e10	+	1.78950e10i	1.38410	+	2.39734i
$663$	1.65686e9	+	9.52141e8i	0.220795	+	0.126883i
$664$	9.62415e9			1.27577
$665$	−7.60985e6	+	2.42086e8i	−0.00100346	+	0.0319222i
$666$	2.20450e9	−	3.81830e9i	0.289167	−	0.500853i
$667$	8.10410e8			0.105746
$668$	1.59794e10	−	9.22572e9i	2.07416	−	1.19752i
$669$	−1.45333e10	−	8.39082e9i	−1.87661	−	1.08346i
$670$		−	2.59926e8i		−	0.0333878i
$671$		−	2.77454e9i		−	0.354538i
$672$	−6.74555e9	−	2.12043e8i	−0.857482	−	0.0269546i
$673$	4.49570e8	−	7.78679e8i	0.0568519	−	0.0984704i	−0.836199	−	0.548427i	$-0.815227\pi$
$673$	4.49570e8	−	7.78679e8i	0.0568519	−	0.0984704i	0.893051	+	0.449956i	$0.148560\pi$
$674$	1.46778e10	−	8.47422e9i	1.84650	−	1.06608i
$675$	−4.02165e8	−	6.96569e8i	−0.0503316	−	0.0871769i
$676$	−8.59656e9	+	1.50293e10i	−1.07031	+	1.87123i
$677$	1.45206e9	−	2.51504e9i	0.179856	−	0.311519i	−0.761975	−	0.647606i	$-0.775770\pi$
$677$	1.45206e9	−	2.51504e9i	0.179856	−	0.311519i	0.941831	+	0.336087i	$0.109104\pi$
$678$	3.50347e10	+	2.02273e10i	4.31712	+	2.49249i
$679$	4.62705e9	−	7.46253e9i	0.567231	−	0.914833i
$680$	8.49006e7	+	1.47052e8i	0.0103545	+	0.0179345i
$681$	−1.45321e10	−	8.39012e9i	−1.76325	−	1.01801i
$682$	3.93456e9	+	2.27162e9i	0.474953	+	0.274214i
$683$	−5.96158e9	−	3.44192e9i	−0.715960	−	0.413360i	0.0973040	−	0.995255i	$-0.468978\pi$
$683$	−5.96158e9	−	3.44192e9i	−0.715960	−	0.413360i	−0.813264	+	0.581895i	$0.802311\pi$
$684$	9.37063e9	+	5.41013e9i	1.11962	+	0.646415i
$685$	−1.24141e8	−	2.15018e8i	−0.0147570	−	0.0255599i
$686$	−6.25238e9	−	1.36573e10i	−0.739454	−	1.61521i
$687$	−1.38373e9	−	7.98896e8i	−0.162818	−	0.0940030i
$688$	−1.28143e8	+	2.21951e8i	−0.0150016	+	0.0259835i
$689$	−3.81125e9	+	2.21069e9i	−0.443915	+	0.257490i
$690$	2.22155e8	+	3.84784e8i	0.0257445	+	0.0445908i
$691$	4.72980e9	−	2.73075e9i	0.545343	−	0.314854i	−0.201899	−	0.979406i	$-0.564711\pi$
$691$	4.72980e9	−	2.73075e9i	0.545343	−	0.314854i	0.747242	+	0.664552i	$0.231378\pi$
$692$	9.19340e9	−	1.59234e10i	1.05464	−	1.82669i
$693$	−8.44127e8	−	1.57432e9i	−0.0963477	−	0.179691i
$694$			3.37659e9i			0.383460i
$695$		−	6.73550e8i		−	0.0761067i
$696$	6.80741e9	+	3.93026e9i	0.765331	+	0.441864i
$697$	2.54466e9	−	1.46916e9i	0.284653	−	0.164344i
$698$	−2.83274e10			−3.15292
$699$	−1.17636e10	+	2.03751e10i	−1.30278	+	2.25647i
$700$	1.71849e10	−	9.21427e9i	1.89367	−	1.01535i
$701$	−1.41658e10			−1.55320			−0.776601	−	0.629993i	$-0.783058\pi$
$701$	−1.41658e10			−1.55320			−0.776601	+	0.629993i	$0.783058\pi$
$702$	8.25078e8	+	1.42244e9i	0.0900150	+	0.155187i
$703$	−7.85191e8	−	1.35999e9i	−0.0852377	−	0.147636i
$704$			7.62201e8i			0.0823313i
$705$	−2.41861e8	−	4.18915e8i	−0.0259958	−	0.0450261i
$706$	1.27552e10	+	2.20926e10i	1.36418	+	2.36282i
$707$	9.39745e9	−	5.03877e9i	1.00010	−	0.536237i
$708$	−7.56252e9	+	4.36622e9i	−0.800848	+	0.462370i
$709$		−	8.63263e9i		−	0.909664i	−0.890577	−	0.454832i	$-0.849699\pi$
$709$		−	8.63263e9i		−	0.909664i	0.890577	−	0.454832i	$-0.150301\pi$
$710$	7.10896e8	−	4.10436e8i	0.0745421	−	0.0430369i
$711$	−1.09559e8	+	1.89761e8i	−0.0114315	+	0.0197999i
$712$	1.28553e10	+	2.22661e10i	1.33476	+	2.31188i
$713$	−4.80090e9	−	2.77180e9i	−0.496032	−	0.286384i
$714$	2.07916e9	+	3.87769e9i	0.213769	+	0.398685i
$715$	−9.20155e7	−	5.28780e7i	−0.00941433	−	0.00541009i
$716$	3.92666e9	−	6.80117e9i	0.399786	−	0.692449i
$717$			1.86933e10i			1.89396i
$718$	−2.18260e10			−2.20059
$719$	−7.55880e9			−0.758406			−0.379203	−	0.925313i	$-0.623802\pi$
$719$	−7.55880e9			−0.758406			−0.379203	+	0.925313i	$0.623802\pi$
$720$			9.11006e8i			0.0909615i
$721$	−2.67882e8	+	8.52189e9i	−0.0266176	+	0.846764i
$722$	−1.06723e10	+	6.16166e9i	−1.05531	+	0.609281i
$723$	3.83018e9	+	2.21135e9i	0.376908	+	0.217608i
$724$	4.56760e9	−	7.91132e9i	0.447304	−	0.774754i
$725$	−3.05977e9			−0.298199
$726$	−2.19940e10	+	1.26983e10i	−2.13318	+	1.23159i
$727$	−1.96501e10			−1.89668			−0.948342	−	0.317251i	$-0.897240\pi$
$727$	−1.96501e10			−1.89668			−0.948342	+	0.317251i	$0.897240\pi$
$728$	−1.88153e10	+	1.01374e10i	−1.80739	+	0.973790i
$729$	−1.18736e10			−1.13511
$730$	−1.24746e9	+	7.20224e8i	−0.118686	+	0.0685232i
$731$	3.76051e7			0.00356070
$732$	−3.06251e10	+	5.30442e10i	−2.88595	+	4.99861i
$733$	−1.30880e10	−	7.55637e9i	−1.22747	−	0.708679i	−0.260968	−	0.965347i	$-0.584042\pi$
$733$	−1.30880e10	−	7.55637e9i	−1.22747	−	0.708679i	−0.966499	+	0.256669i	$0.917375\pi$
$734$	1.33318e10	−	7.69710e9i	1.24438	−	0.718441i
$735$	−7.90676e8	+	3.92479e8i	−0.0734502	+	0.0364595i
$736$			2.27956e9i			0.210756i
$737$	6.82807e8			0.0628293
$738$	3.85516e10			3.53057
$739$		−	1.81572e10i		−	1.65498i	−0.561478	−	0.827491i	$-0.689767\pi$
$739$		−	1.81572e10i		−	1.65498i	0.561478	−	0.827491i	$-0.310233\pi$
$740$	2.05995e8	−	3.56793e8i	0.0186872	−	0.0323673i
$741$	8.93017e9	−	1.80078e7i	0.806299	−	0.00162591i
$742$	−1.01397e10	−	3.18736e8i	−0.911192	−	0.0286429i
$743$	3.20332e9	+	1.84944e9i	0.286510	+	0.165416i	0.636367	−	0.771387i	$-0.280437\pi$
$743$	3.20332e9	+	1.84944e9i	0.286510	+	0.165416i	−0.349857	+	0.936803i	$0.613770\pi$
$744$	−2.68849e10	−	4.65660e10i	−2.39333	−	4.14538i
$745$	−2.55406e6	+	4.42377e6i	−0.000226300	+	0.000391963i
$746$	3.67974e9	−	2.12450e9i	0.324512	−	0.187357i
$747$		−	7.57640e9i		−	0.665029i
$748$	−7.20548e8	+	4.16008e8i	−0.0629517	+	0.0363452i
$749$	8.87987e9	+	5.50585e9i	0.772183	+	0.478783i
$750$	−1.68027e9	−	2.91030e9i	−0.145433	−	0.251898i
$751$	6.57333e9	+	1.13853e10i	0.566298	+	0.980858i	0.996928	+	0.0783287i	$0.0249584\pi$
$751$	6.57333e9	+	1.13853e10i	0.566298	+	0.980858i	−0.430629	+	0.902529i	$0.641708\pi$
$752$		−	1.10270e10i		−	0.945568i
$753$	1.15350e10	+	1.99791e10i	0.984541	+	1.70527i
$754$	6.25556e9	−	1.26144e7i	0.531455	−	0.00107168i
$755$	8.77796e8			0.0742299
$756$	−8.12627e7	+	2.58514e9i	−0.00684014	+	0.217600i
$757$	−5.15290e9	+	8.92509e9i	−0.431734	+	0.747786i	−0.997023	−	0.0771076i	$-0.975432\pi$
$757$	−5.15290e9	+	8.92509e9i	−0.431734	+	0.747786i	0.565289	+	0.824893i	$0.308765\pi$
$758$	3.27055e10			2.72759
$759$	−1.01080e9	+	5.83586e8i	−0.0839111	+	0.0484461i
$760$	6.87195e8	+	3.96752e8i	0.0567849	+	0.0327848i
$761$		−	8.80694e9i		−	0.724401i	−0.932100	−	0.362200i	$-0.882026\pi$
$761$		−	8.80694e9i		−	0.724401i	0.932100	−	0.362200i	$-0.117974\pi$
$762$		−	3.49643e10i		−	2.86274i
$763$	−4.14856e9	+	6.69082e9i	−0.338113	+	0.545310i
$764$	2.36118e10	−	4.08968e10i	1.91559	−	3.31790i
$765$	1.15764e8	−	6.68361e7i	0.00934882	−	0.00539754i
$766$	−1.37951e10	−	2.38938e10i	−1.10898	−	1.92081i
$767$	−1.85634e9	+	3.23031e9i	−0.148551	+	0.258500i
$768$	1.79789e10	−	3.11403e10i	1.43218	−	2.48061i
$769$	1.08884e10	+	6.28642e9i	0.863419	+	0.498495i	0.865156	−	0.501503i	$-0.167219\pi$
$769$	1.08884e10	+	6.28642e9i	0.863419	+	0.498495i	−0.00173642	+	0.999998i	$0.500553\pi$
$770$	−1.15468e8	−	2.15351e8i	−0.00911474	−	0.0169993i
$771$	−8.10695e9	−	1.40417e10i	−0.637041	−	1.10339i
$772$	−3.36940e10	−	1.94532e10i	−2.63567	−	1.52171i
$773$	1.78652e10	+	1.03145e10i	1.39116	+	0.803189i	0.993444	−	0.114317i	$-0.0364681\pi$
$773$	1.78652e10	+	1.03145e10i	1.39116	+	0.803189i	0.397720	+	0.917507i	$0.369801\pi$
$774$	4.27287e8	+	2.46694e8i	0.0331228	+	0.0191234i
$775$	1.81262e10	+	1.04652e10i	1.39879	+	0.807590i
$776$	−1.43834e10	−	2.49127e10i	−1.10495	−	1.91384i
$777$	3.01598e9	−	4.86419e9i	0.230651	−	0.371995i
$778$	−1.45901e10	−	8.42359e9i	−1.11078	−	0.641311i
$779$	6.86560e9	−	1.18916e10i	0.520352	−	0.901276i
$780$	1.17551e9	+	2.02659e9i	0.0886938	+	0.152909i
$781$	1.07819e9	+	1.86747e9i	0.0809870	+	0.140274i
$782$	1.28705e9	−	7.43080e8i	0.0962438	−	0.0555664i
$783$	2.02927e8	−	3.51479e8i	0.0151068	−	0.0261658i
$784$	−2.00830e10	−	1.26385e9i	−1.48841	−	0.0936674i
$785$		−	1.01122e9i		−	0.0746109i
$786$		−	7.07109e9i		−	0.519407i
$787$	−1.16143e10	−	6.70554e9i	−0.849343	−	0.490368i	0.0110864	−	0.999939i	$-0.496471\pi$
$787$	−1.16143e10	−	6.70554e9i	−0.849343	−	0.490368i	−0.860429	+	0.509570i	$0.829804\pi$
$788$	−1.66750e10	+	9.62734e9i	−1.21402	+	0.700913i
$789$	−1.71345e10			−1.24194
$790$	−1.49865e7	+	2.59574e7i	−0.00108145	+	0.00187313i
$791$	2.30723e10	+	1.43057e10i	1.65757	+	1.02776i
$792$	−5.85237e9			−0.418595
$793$	5.26963e7	+	2.61324e10i	0.00375253	+	1.86090i
$794$	−3.16190e9	−	5.47658e9i	−0.224170	−	0.388273i
$795$			5.96187e8i			0.0420821i
$796$	1.19056e10	+	2.06211e10i	0.836672	+	1.44916i
$797$	−1.24095e10	−	2.14940e10i	−0.868263	−	1.50388i	−0.863770	−	0.503886i	$-0.831903\pi$
$797$	−1.24095e10	−	2.14940e10i	−0.868263	−	1.50388i	−0.00449346	−	0.999990i	$-0.501430\pi$
$798$	1.74750e10	+	1.08352e10i	1.21733	+	0.754788i
$799$	−1.40122e9	+	8.08994e8i	−0.0971834	+	0.0561089i
$800$		−	8.60669e9i		−	0.594321i
$801$	1.75285e10	−	1.01201e10i	1.20512	−	0.695778i
$802$	1.13299e9	−	1.96240e9i	0.0775561	−	0.134331i
$803$	−1.89198e9	−	3.27700e9i	−0.128947	−	0.223343i
$804$	−1.30540e10	−	7.53674e9i	−0.885826	−	0.511432i
$805$	1.40893e8	+	2.62769e8i	0.00951925	+	0.0177537i
$806$	−3.71013e10	−	2.13208e10i	−2.49584	−	1.43427i
$807$	9.72994e9	−	1.68528e10i	0.651708	−	1.12879i
$808$		−	3.49340e10i		−	2.32975i
$809$	1.75082e10			1.16257			0.581287	−	0.813699i	$-0.302549\pi$
$809$	1.75082e10			1.16257			0.581287	+	0.813699i	$0.302549\pi$
$810$	−1.41628e9			−0.0936377
$811$			5.15934e9i			0.339642i	0.985475	+	0.169821i	$0.0543189\pi$
$811$			5.15934e9i			0.339642i	−0.985475	+	0.169821i	$0.945681\pi$
$812$	8.36212e9	+	5.18483e9i	0.548113	+	0.339851i
$813$	2.01977e10	−	1.16611e10i	1.31821	−	0.761069i
$814$	1.37206e9	+	7.92159e8i	0.0891636	+	0.0514786i
$815$	4.26725e8	−	7.39109e8i	0.0276119	−	0.0478252i
$816$	5.89454e9			0.379782
$817$	1.52190e8	−	8.78669e7i	0.00976357	−	0.00563700i
$818$	−7.25113e9			−0.463201
$819$	7.98042e9	+	1.48119e10i	0.507612	+	0.942145i
$820$	3.60238e9			0.228161
$821$	9.63640e9	−	5.56358e9i	0.607734	−	0.350875i	−0.164344	−	0.986403i	$-0.552551\pi$
$821$	9.63640e9	−	5.56358e9i	0.607734	−	0.350875i	0.772078	+	0.635528i	$0.219217\pi$
$822$	−2.10774e10			−1.32363
$823$	3.27717e9	−	5.67622e9i	0.204927	−	0.354944i	−0.745182	−	0.666861i	$-0.767638\pi$
$823$	3.27717e9	−	5.67622e9i	0.204927	−	0.354944i	0.950109	+	0.311917i	$0.100971\pi$
$824$	2.41906e10	+	1.39665e10i	1.50627	+	0.869643i
$825$	3.81637e9	−	2.20338e9i	0.236625	−	0.136616i
$826$	−7.56016e9	+	4.05364e9i	−0.466768	+	0.250274i
$827$			3.94091e9i			0.242286i	0.992635	+	0.121143i	$0.0386559\pi$
$827$			3.94091e9i			0.242286i	−0.992635	+	0.121143i	$0.961344\pi$
$828$	1.33199e10			0.815446
$829$	−2.70956e9			−0.165180			−0.0825902	−	0.996584i	$-0.526319\pi$
$829$	−2.70956e9			−0.165180			−0.0825902	+	0.996584i	$0.526319\pi$
$830$		−	1.03638e9i		−	0.0629135i
$831$	7.00903e8	−	1.21400e9i	0.0423696	−	0.0733863i
$832$	−1.44763e7	−	7.17889e9i	−0.000871417	−	0.432141i
$833$	1.31279e9	+	2.64471e9i	0.0786934	+	0.158533i
$834$	−4.95190e10	−	2.85898e10i	−2.95591	−	1.70659i
$835$	−5.32614e8	−	9.22514e8i	−0.0316599	−	0.0548366i
$836$	−1.94407e9	+	3.36722e9i	−0.115077	+	0.199319i
$837$	−2.40429e9	+	1.38812e9i	−0.141725	+	0.0818252i
$838$			4.19014e10i			2.45966i
$839$	2.72663e9	−	1.57422e9i	0.159389	−	0.0920233i	−0.418184	−	0.908362i	$-0.637333\pi$
$839$	2.72663e9	−	1.57422e9i	0.159389	−	0.0920233i	0.577573	+	0.816339i	$0.304000\pi$
$840$	−9.08627e7	+	2.89054e9i	−0.00528942	+	0.168268i
$841$	7.85298e9	+	1.36018e10i	0.455248	+	0.788513i
$842$	1.52211e10	+	2.63636e10i	0.878724	+	1.52199i
$843$			3.03497e10i			1.74485i
$844$	2.91792e10	+	5.05399e10i	1.67061	+	2.89358i
$845$	8.67664e8	+	4.96291e8i	0.0494713	+	0.0282969i
$846$	−2.12284e10			−1.20537
$847$	−1.50197e10	+	8.05335e9i	−0.849318	+	0.455391i
$848$	−6.79536e9	+	1.17699e10i	−0.382672	+	0.662808i
$849$	6.67335e9			0.374254
$850$	−4.85938e9	+	2.80557e9i	−0.271403	+	0.156695i
$851$	−1.67417e9	−	9.66582e8i	−0.0931206	−	0.0537632i
$852$		−	4.76036e10i		−	2.63694i
$853$			9.08424e9i			0.501149i	0.968097	+	0.250575i	$0.0806195\pi$
$853$			9.08424e9i			0.501149i	−0.968097	+	0.250575i	$0.919380\pi$
$854$	−3.17070e10	+	5.11372e10i	−1.74202	+	2.80953i
$855$	3.12335e8	−	5.40979e8i	0.0170899	−	0.0296005i
$856$	2.96443e10	−	1.71152e10i	1.61541	−	0.932659i
$857$	3.43657e9	+	5.95231e9i	0.186506	+	0.323037i	0.944083	−	0.329708i	$-0.106950\pi$
$857$	3.43657e9	+	5.95231e9i	0.186506	+	0.323037i	−0.757577	+	0.652746i	$0.773617\pi$
$858$	−7.79329e9	+	4.52044e9i	−0.421226	+	0.244329i
$859$	1.29930e10	−	2.25045e10i	0.699412	−	1.21142i	−0.269259	−	0.963068i	$-0.586779\pi$
$859$	1.29930e10	−	2.25045e10i	0.699412	−	1.21142i	0.968671	−	0.248349i	$-0.0798879\pi$
$860$	3.99270e7	+	2.30519e7i	0.00214053	+	0.00123584i
$861$	5.00193e10	+	1.57233e9i	2.67071	+	0.0839525i
$862$	1.31189e10	+	2.27226e10i	0.697625	+	1.20832i
$863$	9.63080e9	+	5.56035e9i	0.510064	+	0.294486i	0.732860	−	0.680380i	$-0.238185\pi$
$863$	9.63080e9	+	5.56035e9i	0.510064	+	0.294486i	−0.222796	+	0.974865i	$0.571518\pi$
$864$	9.88659e8	+	5.70802e8i	0.0521493	+	0.0301084i
$865$	−9.19283e8	−	5.30748e8i	−0.0482940	−	0.0278825i
$866$	−1.27139e10	−	7.34036e9i	−0.665220	−	0.384065i
$867$	1.33727e10	+	2.31622e10i	0.696872	+	1.20702i
$868$	−3.18041e10	−	5.93156e10i	−1.65069	−	3.07858i
$869$	−6.81884e7	−	3.93686e7i	−0.00352486	−	0.00203508i
$870$	4.23230e8	−	7.33055e8i	0.0217901	−	0.0377415i
$871$	−6.43111e9	+	1.29684e7i	−0.329779	+	0.000665002i
$872$	1.28960e10	+	2.23365e10i	0.658637	+	1.14079i
$873$	−1.96120e10	+	1.13230e10i	−0.997635	+	0.575985i
$874$	3.47252e9	−	6.01458e9i	0.175936	−	0.304730i
$875$	−1.06564e9	−	1.98745e9i	−0.0537752	−	0.100292i
$876$			8.35338e10i			4.19853i
$877$		−	1.88800e10i		−	0.945156i	−0.881289	−	0.472578i	$-0.843323\pi$
$877$		−	1.88800e10i		−	0.945156i	0.881289	−	0.472578i	$-0.156677\pi$
$878$	−4.36034e10	−	2.51744e10i	−2.17415	−	1.25525i
$879$	2.02921e10	−	1.17156e10i	1.00778	−	0.581842i
$880$	−3.27359e8			−0.0161933
$881$	−9.18354e9	+	1.59064e10i	−0.452475	+	0.783710i	−0.998539	−	0.0540336i	$-0.982792\pi$
$881$	−9.18354e9	+	1.59064e10i	−0.452475	+	0.783710i	0.546064	+	0.837743i	$0.316126\pi$
$882$	−2.43309e9	+	3.86626e10i	−0.119404	+	1.89736i
$883$	3.23548e9			0.158152			0.0790762	−	0.996869i	$-0.474803\pi$
$883$	3.23548e9			0.158152			0.0790762	+	0.996869i	$0.474803\pi$
$884$	6.77867e9	−	3.93192e9i	0.330036	−	0.191435i
$885$	2.52068e8	+	4.36595e8i	0.0122241	+	0.0211727i
$886$		−	1.44268e10i		−	0.696871i
$887$	1.04888e10	+	1.81670e10i	0.504651	+	0.874081i	0.999986	+	0.00537879i	$0.00171213\pi$
$887$	1.04888e10	+	1.81670e10i	0.504651	+	0.874081i	−0.495335	+	0.868702i	$0.664955\pi$
$888$	−9.37530e9	−	1.62385e10i	−0.449303	−	0.778216i
$889$	7.37187e8	−	2.34515e10i	0.0351902	−	1.11947i
$890$	2.39772e9	−	1.38433e9i	0.114008	−	0.0658224i
$891$		−	3.72046e9i		−	0.176208i
$892$	−5.95984e10	+	3.44091e10i	−2.81163	+	1.62329i
$893$	−3.78054e9	+	6.54809e9i	−0.177654	+	0.307705i
$894$	2.16822e8	+	3.75547e8i	0.0101490	+	0.0175785i
$895$	−3.92641e8	−	2.26691e8i	−0.0183069	−	0.0105695i
$896$	1.54757e10	−	2.49592e10i	0.718739	−	1.15919i
$897$	9.50928e9	−	5.51578e9i	0.439920	−	0.255172i
$898$	−3.17093e10	+	5.49222e10i	−1.46123	+	2.53093i
$899$			1.05612e10i			0.484789i
$900$	−5.02905e10			−2.29952
$901$	1.99417e9			0.0908292
$902$			1.38530e10i			0.628524i
$903$	5.44328e8	+	3.37504e8i	0.0246010	+	0.0152536i
$904$	7.70238e10	−	4.44697e10i	3.46765	−	2.00205i
$905$	−4.56731e8	−	2.63694e8i	−0.0204829	−	0.0118258i
$906$	3.72593e10	−	6.45350e10i	1.66451	−	2.88302i
$907$	−1.85695e10			−0.826370			−0.413185	−	0.910647i	$-0.635584\pi$
$907$	−1.85695e10			−0.826370			−0.413185	+	0.910647i	$0.635584\pi$
$908$	−5.95934e10	+	3.44063e10i	−2.64179	+	1.52524i
$909$	−2.75011e10			−1.21444
$910$	1.09164e9	+	2.02612e9i	0.0480214	+	0.0891294i
$911$	2.53606e10			1.11133			0.555667	−	0.831405i	$-0.312463\pi$
$911$	2.53606e10			1.11133			0.555667	+	0.831405i	$0.312463\pi$
$912$	2.38556e10	−	1.37730e10i	1.04138	−	0.601239i
$913$	2.72249e9			0.118391
$914$	2.97287e9	−	5.14916e9i	0.128785	−	0.223062i
$915$	3.06232e9	+	1.76803e9i	0.132153	+	0.0762984i
$916$	−5.67441e9	+	3.27612e9i	−0.243942	+	0.140840i
$917$	1.49087e8	−	4.74278e9i	0.00638480	−	0.203114i
$918$		−	7.44269e8i		−	0.0317527i
$919$	−6.97582e9			−0.296477			−0.148239	−	0.988952i	$-0.547360\pi$
$919$	−6.97582e9			−0.296477			−0.148239	+	0.988952i	$0.547360\pi$
$920$	9.76816e8			0.0413576
$921$		−	9.40182e9i		−	0.396555i
$922$	2.28152e10	−	3.95170e10i	0.958661	−	1.66045i
$923$	−1.01905e10	−	1.75686e10i	−0.426570	−	0.735412i
$924$	−1.41635e10	−	4.45223e8i	−0.590634	−	0.0185663i
$925$	6.32097e9	+	3.64942e9i	0.262596	+	0.151610i
$926$	3.27806e10	+	5.67777e10i	1.35668	+	2.34985i
$927$	1.09948e10	−	1.90435e10i	0.453323	−	0.785179i
$928$	3.76099e9	−	2.17141e9i	0.154484	−	0.0891915i
$929$			1.28260e10i			0.524850i	0.964952	+	0.262425i	$0.0845222\pi$
$929$			1.28260e10i			0.524850i	−0.964952	+	0.262425i	$0.915478\pi$
$930$	−5.01446e9	+	2.89510e9i	−0.204425	+	0.118025i
$931$	1.14925e10	+	7.63588e9i	0.466757	+	0.310124i
$932$	4.82402e10	+	8.35545e10i	1.95188	+	3.38076i
$933$	1.52185e10	+	2.63593e10i	0.613462	+	1.06255i
$934$		−	2.84886e10i		−	1.14408i
$935$	2.40167e7	+	4.15982e7i	0.000960890	+	0.00166431i
$936$	5.51214e10	−	1.11153e8i	2.19712	−	0.00443052i
$937$	−4.32888e10			−1.71904			−0.859522	−	0.511099i	$-0.829239\pi$
$937$	−4.32888e10			−1.71904			−0.859522	+	0.511099i	$0.829239\pi$
$938$	−1.25847e10	−	7.80300e9i	−0.497890	−	0.308711i
$939$	3.87765e9	−	6.71628e9i	0.152841	−	0.264728i
$940$	−1.98365e9			−0.0778964
$941$	−3.38473e10	+	1.95418e10i	−1.32422	+	0.764540i	−0.984399	−	0.175949i	$-0.943700\pi$
$941$	−3.38473e10	+	1.95418e10i	−1.32422	+	0.764540i	−0.339823	+	0.940489i	$0.610367\pi$
$942$	−7.43444e10	−	4.29228e10i	−2.89781	−	1.67305i
$943$		−	1.69033e10i		−	0.656418i
$944$			1.14923e10i			0.444637i
$945$	1.49244e8	+	4.69141e6i	0.00575288	+	0.000180839i
$946$	−8.86466e7	+	1.53540e8i	−0.00340442	+	0.00589663i
$947$	2.73095e10	−	1.57672e10i	1.04494	−	0.603294i	0.123708	−	0.992319i	$-0.460521\pi$
$947$	2.73095e10	−	1.57672e10i	1.04494	−	0.603294i	0.921227	+	0.389025i	$0.127188\pi$
$948$	8.69092e8	+	1.50531e9i	0.0331311	+	0.0573848i
$949$	1.78821e10	+	3.08290e10i	0.679183	+	1.17092i
$950$	−1.31108e10	+	2.27086e10i	−0.496131	+	0.859325i
$951$	2.50556e10	+	1.44659e10i	0.944654	+	0.545396i
$952$	9.66848e9	+	3.03924e8i	0.363186	+	0.0114166i
$953$	−1.85288e9	−	3.20928e9i	−0.0693461	−	0.120111i	0.829268	−	0.558852i	$-0.188758\pi$
$953$	−1.85288e9	−	3.20928e9i	−0.0693461	−	0.120111i	−0.898614	+	0.438741i	$0.855425\pi$
$954$	2.26587e10	+	1.30820e10i	0.844921	+	0.487816i
$955$	−2.36103e9	−	1.36314e9i	−0.0877183	−	0.0506442i
$956$	6.63876e10	+	3.83289e10i	2.45745	+	1.41881i
$957$	1.92569e9	+	1.11180e9i	0.0710221	+	0.0410046i
$958$	−1.43377e9	−	2.48336e9i	−0.0526865	−	0.0912556i
$959$	−1.41372e10	−	4.44396e8i	−0.517604	−	0.0162706i
$960$	−8.41255e8	−	4.85699e8i	−0.0306887	−	0.0177181i
$961$	2.23655e10	−	3.87382e10i	0.812917	−	1.40801i
$962$	−1.29380e10	−	7.43499e9i	−0.468547	−	0.269258i
$963$	−1.34735e10	−	2.33368e10i	−0.486171	−	0.842074i
$964$	1.57068e10	−	9.06834e9i	0.564701	−	0.326030i
$965$	−1.12306e9	+	1.94520e9i	−0.0402308	+	0.0696817i
$966$	2.52990e10	+	7.95263e8i	0.902992	+	0.0283851i
$967$		−	2.44941e10i		−	0.871103i	−0.900164	−	0.435551i	$-0.856553\pi$
$967$		−	2.44941e10i		−	0.871103i	0.900164	−	0.435551i	$-0.143447\pi$
$968$			5.58343e10i			1.97851i
$969$	−3.50034e9	−	2.02092e9i	−0.123588	−	0.0713536i
$970$	−2.68272e9	+	1.54887e9i	−0.0943789	+	0.0544897i
$971$	−1.43575e10			−0.503284			−0.251642	−	0.967820i	$-0.580970\pi$
$971$	−1.43575e10			−0.503284			−0.251642	+	0.967820i	$0.580970\pi$
$972$	−4.41826e10	+	7.65265e10i	−1.54319	+	2.67288i
$973$	−3.26110e10	−	2.02200e10i	−1.13493	−	0.703699i
$974$	6.79043e10			2.35473
$975$	−3.59031e10	+	2.08253e10i	−1.24056	+	0.719574i
$976$	4.03041e10	+	6.98087e10i	1.38763	+	2.40345i
$977$			1.24586e10i			0.427403i	0.976899	+	0.213702i	$0.0685520\pi$
$977$			1.24586e10i			0.427403i	−0.976899	+	0.213702i	$0.931448\pi$
$978$	−3.62259e10	−	6.27451e10i	−1.23832	−	2.14484i
$979$	3.63653e9	+	6.29866e9i	0.123865	+	0.214540i
$980$	−2.27355e8	+	3.61275e9i	−0.00771637	+	0.122616i
$981$	1.75839e10	−	1.01521e10i	0.594667	−	0.343331i
$982$			1.00361e11i			3.38201i
$983$	1.15335e9	−	6.65884e8i	0.0387277	−	0.0223595i	−0.480511	−	0.876989i	$-0.659549\pi$
$983$	1.15335e9	−	6.65884e8i	0.0387277	−	0.0223595i	0.519239	+	0.854629i	$0.326215\pi$
$984$	8.19762e10	−	1.41987e11i	2.74287	−	4.75079i
$985$	5.55800e8	+	9.62673e8i	0.0185307	+	0.0320961i
$986$	−2.45198e9	−	1.41565e9i	−0.0814605	−	0.0470312i
$987$	−2.75431e10	−	8.65806e8i	−0.911808	−	0.0286623i
$988$	1.82465e10	−	3.17516e10i	0.601908	−	1.04741i
$989$	1.08165e8	−	1.87348e8i	0.00355551	−	0.00615832i
$990$			6.30212e8i			0.0206426i
$991$	1.31574e9			0.0429450			0.0214725	−	0.999769i	$-0.493165\pi$
$991$	1.31574e9			0.0429450			0.0214725	+	0.999769i	$0.493165\pi$
$992$	−2.97070e10			−0.966202
$993$		−	6.91796e10i		−	2.24210i
$994$	1.46926e9	−	4.67405e10i	0.0474513	−	1.50953i
$995$	1.19048e9	−	6.87327e8i	0.0383127	−	0.0221199i
$996$	−5.20490e10	−	3.00505e10i	−1.66918	−	0.963704i
$997$	2.25409e10	−	3.90420e10i	0.720341	−	1.24767i	−0.240522	−	0.970644i	$-0.577319\pi$
$997$	2.25409e10	−	3.90420e10i	0.720341	−	1.24767i	0.960863	−	0.277024i	$-0.0893481\pi$
$998$	1.44821e10			0.461183
$999$	−8.38424e8	+	4.84064e8i	−0.0266063	+	0.0153611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.u.a.30.4	yes	126
7.4	even	3		91.8.k.a.4.4	✓	126
13.10	even	6		91.8.k.a.23.60	yes	126
91.88	even	6	inner	91.8.u.a.88.4	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.k.a.4.4	✓	126	7.4	even	3
91.8.k.a.23.60	yes	126	13.10	even	6
91.8.u.a.30.4	yes	126	1.1	even	1	trivial
91.8.u.a.88.4	yes	126	91.88	even	6	inner

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.4054 + 10.0490i) q^{2} +67.2867 q^{3} +(137.965 - 238.962i) q^{4} +(-13.7956 - 7.96491i) q^{5} +(-1171.15 + 676.165i) q^{6} +(-799.780 + 428.830i) q^{7} +2973.10i q^{8} +2340.51 q^{9} +O(q^{10})\)	\(q+(-17.4054 + 10.0490i) q^{2} +67.2867 q^{3} +(137.965 - 238.962i) q^{4} +(-13.7956 - 7.96491i) q^{5} +(-1171.15 + 676.165i) q^{6} +(-799.780 + 428.830i) q^{7} +2973.10i q^{8} +2340.51 q^{9} +320.158 q^{10} +841.033i q^{11} +(9283.22 - 16079.0i) q^{12} +(-15.9735 - 7921.38i) q^{13} +(9611.17 - 15500.9i) q^{14} +(-928.263 - 535.933i) q^{15} +(-12217.2 - 21160.7i) q^{16} +(-1792.63 + 3104.92i) q^{17} +(-40737.4 + 23519.8i) q^{18} +16754.4i q^{19} +(-3806.63 + 2197.76i) q^{20} +(-53814.6 + 28854.6i) q^{21} +(-8451.54 - 14638.5i) q^{22} +(10312.5 + 17861.7i) q^{23} +200050. i q^{24} +(-38935.6 - 67438.5i) q^{25} +(79880.0 + 137714. i) q^{26} +10329.0 q^{27} +(-7867.46 + 250281. i) q^{28} +(19646.4 - 34028.5i) q^{29} +21542.4 q^{30} +(-232772. + 134391. i) q^{31} +(95717.2 + 55262.3i) q^{32} +56590.4i q^{33} -72056.5i q^{34} +(14449.1 + 454.200i) q^{35} +(322908. - 559293. i) q^{36} +(-81172.1 + 46864.7i) q^{37} +(-168365. - 291617. i) q^{38} +(-1074.81 - 533004. i) q^{39} +(23680.5 - 41015.8i) q^{40} +(-709757. - 409778. i) q^{41} +(646704. - 1.04301e6i) q^{42} +(-5244.40 - 9083.58i) q^{43} +(200975. + 116033. i) q^{44} +(-32288.8 - 18641.9i) q^{45} +(-358985. - 207260. i) q^{46} +(390828. + 225645. i) q^{47} +(-822053. - 1.42384e6i) q^{48} +(455753. - 685939. i) q^{49} +(1.35538e6 + 782528. i) q^{50} +(-120620. + 208920. i) q^{51} +(-1.89512e6 - 1.08906e6i) q^{52} +(-278107. - 481696. i) q^{53} +(-179780. + 103796. i) q^{54} +(6698.75 - 11602.6i) q^{55} +(-1.27495e6 - 2.37782e6i) q^{56} +1.12735e6i q^{57} +789706. i q^{58} +(-407322. - 235167. i) q^{59} +(-256136. + 147880. i) q^{60} -3.29897e6 q^{61} +(2.70099e6 - 4.67825e6i) q^{62} +(-1.87189e6 + 1.00368e6i) q^{63} +906268. q^{64} +(-62872.7 + 109408. i) q^{65} +(-568677. - 984977. i) q^{66} -811868. i q^{67} +(494640. + 856742. i) q^{68} +(693892. + 1.20186e6i) q^{69} +(-256056. + 137293. i) q^{70} +(2.22045e6 - 1.28198e6i) q^{71} +6.95856e6i q^{72} +(-3.89641e6 + 2.24959e6i) q^{73} +(941888. - 1.63140e6i) q^{74} +(-2.61985e6 - 4.53772e6i) q^{75} +(4.00367e6 + 2.31152e6i) q^{76} +(-360660. - 672641. i) q^{77} +(5.37487e6 + 9.26634e6i) q^{78} +(-46809.8 + 81077.0i) q^{79} +389235. i q^{80} -4.42369e6 q^{81} +1.64715e7 q^{82} -3.23708e6i q^{83} +(-529376. + 1.68406e7i) q^{84} +(49460.9 - 28556.3i) q^{85} +(182562. + 105402. i) q^{86} +(1.32194e6 - 2.28967e6i) q^{87} -2.50047e6 q^{88} +(7.48920e6 - 4.32389e6i) q^{89} +749331. q^{90} +(3.40970e6 + 6.32851e6i) q^{91} +5.69104e6 q^{92} +(-1.56625e7 + 9.04272e6i) q^{93} -9.07002e6 q^{94} +(133447. - 231138. i) q^{95} +(6.44050e6 + 3.71842e6i) q^{96} +(-8.37938e6 + 4.83783e6i) q^{97} +(-1.03956e6 + 1.65189e7i) q^{98} +1.96844e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Introduction

L-functions

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