LMFDB - Embedded newform 245.2.x.a.152.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			152.17
Character	$\chi$	$=$	245.152
Dual form			245.2.x.a.108.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.617374 + 0.455643i) q^{2} +(0.214434 + 1.13331i) q^{3} +(-0.415970 - 1.34854i) q^{4} +(2.02146 - 0.955882i) q^{5} +(-0.384000 + 0.797384i) q^{6} +(-0.358764 - 2.62131i) q^{7} +(0.864496 - 2.47059i) q^{8} +(1.55421 - 0.609981i) q^{9} +(1.68354 + 0.330926i) q^{10} +(-1.26351 + 3.21938i) q^{11} +(1.43912 - 0.760597i) q^{12} +(0.102330 - 0.908200i) q^{13} +(0.972892 - 1.78180i) q^{14} +(1.51678 + 2.08597i) q^{15} +(-0.672617 + 0.458583i) q^{16} +(-0.292814 + 7.82562i) q^{17} +(1.23746 + 0.331576i) q^{18} +(-0.0769953 + 0.133360i) q^{19} +(-2.12991 - 2.32840i) q^{20} +(2.89384 - 0.968691i) q^{21} +(-2.24695 + 1.41185i) q^{22} +(-7.49628 + 0.280491i) q^{23} +(2.98532 + 0.449965i) q^{24} +(3.17258 - 3.86455i) q^{25} +(0.476990 - 0.514073i) q^{26} +(2.86554 + 4.56049i) q^{27} +(-3.38572 + 1.57420i) q^{28} +(3.21231 - 0.733188i) q^{29} +(-0.0140341 + 1.97894i) q^{30} +(3.14854 - 1.81781i) q^{31} +(-5.85549 - 0.219097i) q^{32} +(-3.91950 - 0.741610i) q^{33} +(-3.74646 + 4.69792i) q^{34} +(-3.23089 - 4.95594i) q^{35} +(-1.46909 - 1.84218i) q^{36} +(0.183639 + 0.347461i) q^{37} +(-0.108299 + 0.0472505i) q^{38} +(1.05122 - 0.0787778i) q^{39} +(-0.614049 - 5.82054i) q^{40} +(1.29664 + 2.69249i) q^{41} +(2.22796 + 0.720512i) q^{42} +(-5.86900 + 2.05365i) q^{43} +(4.86705 + 0.364735i) q^{44} +(2.55869 - 2.71869i) q^{45} +(-4.75582 - 3.24246i) q^{46} +(3.66318 - 4.96343i) q^{47} +(-0.663950 - 0.663950i) q^{48} +(-6.74258 + 1.88086i) q^{49} +(3.71952 - 0.940311i) q^{50} +(-8.93166 + 1.34623i) q^{51} +(-1.26731 + 0.239788i) q^{52} +(-4.13653 + 7.82670i) q^{53} +(-0.308841 + 4.12119i) q^{54} +(0.523209 + 7.71560i) q^{55} +(-6.78633 - 1.37976i) q^{56} +(-0.167649 - 0.0586628i) q^{57} +(2.31727 + 1.01101i) q^{58} +(-0.326512 - 4.35700i) q^{59} +(2.18208 - 2.91315i) q^{60} +(3.50233 - 11.3543i) q^{61} +(2.77210 + 0.312340i) q^{62} +(-2.15654 - 3.85522i) q^{63} +(-2.24226 - 1.78815i) q^{64} +(-0.661277 - 1.93370i) q^{65} +(-2.08189 - 2.24374i) q^{66} +(-2.29681 + 8.57181i) q^{67} +(10.6750 - 2.86035i) q^{68} +(-1.92534 - 8.43549i) q^{69} +(0.263468 - 4.53180i) q^{70} +(-1.76559 + 7.73555i) q^{71} +(-0.163406 - 4.36713i) q^{72} +(0.954739 + 1.29362i) q^{73} +(-0.0449445 + 0.298187i) q^{74} +(5.06005 + 2.76683i) q^{75} +(0.211869 + 0.0483577i) q^{76} +(8.89230 + 2.15707i) q^{77} +(0.684889 + 0.430344i) q^{78} +(-11.5906 - 6.69184i) q^{79} +(-0.921316 + 1.56995i) q^{80} +(-0.882233 + 0.818593i) q^{81} +(-0.426306 + 2.25308i) q^{82} +(-0.885951 + 0.0998227i) q^{83} +(-2.51007 - 3.49951i) q^{84} +(6.88846 + 16.0991i) q^{85} +(-4.55910 - 1.40630i) q^{86} +(1.51976 + 3.48333i) q^{87} +(6.86145 + 5.90475i) q^{88} +(5.52892 + 14.0875i) q^{89} +(2.81842 - 0.512599i) q^{90} +(-2.41739 + 0.0575912i) q^{91} +(3.49648 + 9.99237i) q^{92} +(2.73530 + 3.17848i) q^{93} +(4.52311 - 1.39519i) q^{94} +(-0.0281665 + 0.343180i) q^{95} +(-1.00731 - 6.68308i) q^{96} +(-9.86671 + 9.86671i) q^{97} +(-5.01970 - 1.91101i) q^{98} +5.77429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.617374	+	0.455643i	0.436550	+	0.322188i	0.789826	−	0.613331i	$-0.210171\pi$
$2$	0.617374	+	0.455643i	0.436550	+	0.322188i	−0.353277	+	0.935519i	$0.614933\pi$
$3$	0.214434	+	1.13331i	0.123804	+	0.654318i	0.988403	+	0.151856i	$0.0485249\pi$
$3$	0.214434	+	1.13331i	0.123804	+	0.654318i	−0.864599	+	0.502463i	$0.832427\pi$
$4$	−0.415970	−	1.34854i	−0.207985	−	0.674271i
$5$	2.02146	−	0.955882i	0.904023	−	0.427484i
$5$	2.02146	−	0.955882i	0.904023	−	0.427484i
$6$	−0.384000	+	0.797384i	−0.156767	+	0.325530i
$7$	−0.358764	−	2.62131i	−0.135600	−	0.990764i
$7$	−0.358764	−	2.62131i	−0.135600	−	0.990764i
$8$	0.864496	−	2.47059i	0.305645	−	0.873484i
$9$	1.55421	−	0.609981i	0.518069	−	0.203327i
$10$	1.68354	+	0.330926i	0.532381	+	0.104648i
$11$	−1.26351	+	3.21938i	−0.380963	+	0.970679i	0.603856	+	0.797094i	$0.293630\pi$
$11$	−1.26351	+	3.21938i	−0.380963	+	0.970679i	−0.984819	+	0.173585i	$0.944465\pi$
$12$	1.43912	−	0.760597i	0.415438	−	0.219566i
$13$	0.102330	−	0.908200i	0.0283811	−	0.251889i	−0.971508	−	0.237006i	$-0.923834\pi$
$13$	0.102330	−	0.908200i	0.0283811	−	0.251889i	0.999889	−	0.0148831i	$-0.00473760\pi$
$14$	0.972892	−	1.78180i	0.260016	−	0.476206i
$15$	1.51678	+	2.08597i	0.391632	+	0.538595i
$16$	−0.672617	+	0.458583i	−0.168154	+	0.114646i
$17$	−0.292814	+	7.82562i	−0.0710178	+	1.89799i	0.277554	+	0.960710i	$0.410476\pi$
$17$	−0.292814	+	7.82562i	−0.0710178	+	1.89799i	−0.348572	+	0.937282i	$0.613333\pi$
$18$	1.23746	+	0.331576i	0.291672	+	0.0781533i
$19$	−0.0769953	+	0.133360i	−0.0176639	+	0.0305948i	−0.874722	−	0.484625i	$-0.838956\pi$
$19$	−0.0769953	+	0.133360i	−0.0176639	+	0.0305948i	0.857058	+	0.515219i	$0.172290\pi$
$20$	−2.12991	−	2.32840i	−0.476263	−	0.520646i
$21$	2.89384	−	0.968691i	0.631487	−	0.211386i
$22$	−2.24695	+	1.41185i	−0.479051	+	0.301007i
$23$	−7.49628	+	0.280491i	−1.56308	+	0.0584864i	−0.804843	−	0.593488i	$-0.797750\pi$
$23$	−7.49628	+	0.280491i	−1.56308	+	0.0584864i	−0.758241	+	0.651975i	$0.773941\pi$
$24$	2.98532	+	0.449965i	0.609377	+	0.0918488i
$25$	3.17258	−	3.86455i	0.634516	−	0.772910i
$26$	0.476990	−	0.514073i	0.0935455	−	0.100818i
$27$	2.86554	+	4.56049i	0.551474	+	0.877666i
$28$	−3.38572	+	1.57420i	−0.639840	+	0.297495i
$29$	3.21231	−	0.733188i	0.596510	−	0.136150i	0.0864028	−	0.996260i	$-0.472463\pi$
$29$	3.21231	−	0.733188i	0.596510	−	0.136150i	0.510107	+	0.860111i	$0.329606\pi$
$30$	−0.0140341	+	1.97894i	−0.00256226	+	0.361302i
$31$	3.14854	−	1.81781i	0.565494	−	0.326488i	−0.189854	−	0.981812i	$-0.560801\pi$
$31$	3.14854	−	1.81781i	0.565494	−	0.326488i	0.755348	+	0.655324i	$0.227468\pi$
$32$	−5.85549	−	0.219097i	−1.03511	−	0.0387312i
$33$	−3.91950	−	0.741610i	−0.682298	−	0.129098i
$34$	−3.74646	+	4.69792i	−0.642513	+	0.805686i
$35$	−3.23089	−	4.95594i	−0.546121	−	0.837707i
$36$	−1.46909	−	1.84218i	−0.244848	−	0.307029i
$37$	0.183639	+	0.347461i	0.0301900	+	0.0571223i	0.898749	−	0.438464i	$-0.144477\pi$
$37$	0.183639	+	0.347461i	0.0301900	+	0.0571223i	−0.868559	+	0.495586i	$0.834953\pi$
$38$	−0.108299	+	0.0472505i	−0.0175685	+	0.00766505i
$39$	1.05122	−	0.0787778i	0.168329	−	0.0126145i
$40$	−0.614049	−	5.82054i	−0.0970897	−	0.920308i
$41$	1.29664	+	2.69249i	0.202501	+	0.420497i	0.977344	−	0.211656i	$-0.0678857\pi$
$41$	1.29664	+	2.69249i	0.202501	+	0.420497i	−0.774844	+	0.632153i	$0.782171\pi$
$42$	2.22796	+	0.720512i	0.343781	+	0.111177i
$43$	−5.86900	+	2.05365i	−0.895014	+	0.313179i	−0.738306	−	0.674466i	$-0.764374\pi$
$43$	−5.86900	+	2.05365i	−0.895014	+	0.313179i	−0.156708	+	0.987645i	$0.550088\pi$
$44$	4.86705	+	0.364735i	0.733735	+	0.0549858i
$45$	2.55869	−	2.71869i	0.381427	−	0.405278i
$46$	−4.75582	−	3.24246i	−0.701207	−	0.478075i
$47$	3.66318	−	4.96343i	0.534330	−	0.723991i	−0.451401	−	0.892321i	$-0.649076\pi$
$47$	3.66318	−	4.96343i	0.534330	−	0.723991i	0.985731	+	0.168330i	$0.0538374\pi$
$48$	−0.663950	−	0.663950i	−0.0958329	−	0.0958329i
$49$	−6.74258	+	1.88086i	−0.963225	+	0.268695i
$50$	3.71952	−	0.940311i	0.526020	−	0.132980i
$51$	−8.93166	+	1.34623i	−1.25068	+	0.188510i
$52$	−1.26731	+	0.239788i	−0.175744	+	0.0332526i
$53$	−4.13653	+	7.82670i	−0.568197	+	1.07508i	0.417835	+	0.908523i	$0.362789\pi$
$53$	−4.13653	+	7.82670i	−0.568197	+	1.07508i	−0.986032	+	0.166558i	$0.946735\pi$
$54$	−0.308841	+	4.12119i	−0.0420279	+	0.560823i
$55$	0.523209	+	7.71560i	0.0705495	+	1.04037i
$56$	−6.78633	−	1.37976i	−0.906862	−	0.184378i
$57$	−0.167649	−	0.0586628i	−0.0222056	−	0.00777008i
$58$	2.31727	+	1.01101i	0.304272	+	0.132753i
$59$	−0.326512	−	4.35700i	−0.0425082	−	0.567233i	−0.977276	−	0.211972i	$-0.932011\pi$
$59$	−0.326512	−	4.35700i	−0.0425082	−	0.567233i	0.934767	−	0.355260i	$-0.115608\pi$
$60$	2.18208	−	2.91315i	0.281705	−	0.376085i
$61$	3.50233	−	11.3543i	0.448428	−	1.45377i	−0.396077	−	0.918217i	$-0.629629\pi$
$61$	3.50233	−	11.3543i	0.448428	−	1.45377i	0.844504	−	0.535549i	$-0.179895\pi$
$62$	2.77210	+	0.312340i	0.352057	+	0.0396672i
$63$	−2.15654	−	3.85522i	−0.271699	−	0.485712i
$64$	−2.24226	−	1.78815i	−0.280283	−	0.223518i
$65$	−0.661277	−	1.93370i	−0.0820213	−	0.239846i
$66$	−2.08189	−	2.24374i	−0.256263	−	0.276186i
$67$	−2.29681	+	8.57181i	−0.280600	+	1.04721i	0.671395	+	0.741100i	$0.265695\pi$
$67$	−2.29681	+	8.57181i	−0.280600	+	1.04721i	−0.951995	+	0.306113i	$0.900971\pi$
$68$	10.6750	−	2.86035i	1.29453	−	0.346868i
$69$	−1.92534	−	8.43549i	−0.231784	−	1.01551i
$70$	0.263468	−	4.53180i	0.0314905	−	0.541654i
$71$	−1.76559	+	7.73555i	−0.209537	+	0.918041i	0.755339	+	0.655334i	$0.227472\pi$
$71$	−1.76559	+	7.73555i	−0.209537	+	0.918041i	−0.964876	+	0.262707i	$0.915385\pi$
$72$	−0.163406	−	4.36713i	−0.0192576	−	0.514671i
$73$	0.954739	+	1.29362i	0.111744	+	0.151407i	0.856900	−	0.515482i	$-0.172387\pi$
$73$	0.954739	+	1.29362i	0.111744	+	0.151407i	−0.745157	+	0.666890i	$0.767625\pi$
$74$	−0.0449445	+	0.298187i	−0.00522469	+	0.0346636i
$75$	5.06005	+	2.76683i	0.584285	+	0.319486i
$76$	0.211869	+	0.0483577i	0.0243030	+	0.00554701i
$77$	8.89230	+	2.15707i	1.01337	+	0.245821i
$78$	0.684889	+	0.430344i	0.0775484	+	0.0487269i
$79$	−11.5906	−	6.69184i	−1.30405	−	0.752891i	−0.322951	−	0.946416i	$-0.604675\pi$
$79$	−11.5906	−	6.69184i	−1.30405	−	0.752891i	−0.981095	+	0.193524i	$0.938008\pi$
$80$	−0.921316	+	1.56995i	−0.103006	+	0.175526i
$81$	−0.882233	+	0.818593i	−0.0980259	+	0.0909547i
$82$	−0.426306	+	2.25308i	−0.0470776	+	0.248811i
$83$	−0.885951	+	0.0998227i	−0.0972457	+	0.0109570i	−0.160453	−	0.987043i	$-0.551296\pi$
$83$	−0.885951	+	0.0998227i	−0.0972457	+	0.0109570i	0.0632075	+	0.998000i	$0.479867\pi$
$84$	−2.51007	−	3.49951i	−0.273871	−	0.381828i
$85$	6.88846	+	16.0991i	0.747159	+	1.74619i
$86$	−4.55910	−	1.40630i	−0.491621	−	0.151645i
$87$	1.51976	+	3.48333i	0.162935	+	0.373452i
$88$	6.86145	+	5.90475i	0.731433	+	0.629449i
$89$	5.52892	+	14.0875i	0.586064	+	1.49327i	0.848967	+	0.528445i	$0.177225\pi$
$89$	5.52892	+	14.0875i	0.586064	+	1.49327i	−0.262903	+	0.964822i	$0.584680\pi$
$90$	2.81842	−	0.512599i	0.297088	−	0.0540326i
$91$	−2.41739	+	0.0575912i	−0.253411	+	0.00603720i
$92$	3.49648	+	9.99237i	0.364533	+	1.04178i
$93$	2.73530	+	3.17848i	0.283637	+	0.329593i
$94$	4.52311	−	1.39519i	0.466523	−	0.143903i
$95$	−0.0281665	+	0.343180i	−0.00288982	+	0.0352095i
$96$	−1.00731	−	6.68308i	−0.102808	−	0.682089i
$97$	−9.86671	+	9.86671i	−1.00181	+	1.00181i	−0.00181471	+	0.999998i	$0.500578\pi$
$97$	−9.86671	+	9.86671i	−1.00181	+	1.00181i	−0.999998	+	0.00181471i	$0.999422\pi$
$98$	−5.01970	−	1.91101i	−0.507066	−	0.193041i
$99$			5.77429i			0.580338i
$100$	−6.53120	−	2.67082i	−0.653120	−	0.267082i
$101$	6.37585	−	9.35165i	0.634421	−	0.930524i	−0.365579	−	0.930780i	$-0.619129\pi$
$101$	6.37585	−	9.35165i	0.634421	−	0.930524i	1.00000		0.000256084i	$8.15140e-5\pi$
$102$	−6.12758	−	3.23852i	−0.606721	−	0.320661i
$103$	−1.65825	+	1.42704i	−0.163393	+	0.140611i	−0.730184	−	0.683251i	$-0.760566\pi$
$103$	−1.65825	+	1.42704i	−0.163393	+	0.140611i	0.566791	+	0.823861i	$0.308185\pi$
$104$	−2.15532	−	1.03795i	−0.211347	−	0.101779i
$105$	4.92381	−	4.72434i	0.480515	−	0.461048i
$106$	−6.11997	+	2.94722i	−0.594424	+	0.286260i
$107$	5.98841	−	13.7256i	0.578922	−	1.32690i	−0.342931	−	0.939361i	$-0.611420\pi$
$107$	5.98841	−	13.7256i	0.578922	−	1.32690i	0.921852	−	0.387542i	$-0.126676\pi$
$108$	4.95803	−	5.76133i	0.477086	−	0.554384i
$109$	−1.51313	−	0.593860i	−0.144932	−	0.0568815i	0.291766	−	0.956490i	$-0.405757\pi$
$109$	−1.51313	−	0.593860i	−0.144932	−	0.0568815i	−0.436698	+	0.899608i	$0.643852\pi$
$110$	−3.19254	+	5.00181i	−0.304397	+	0.476904i
$111$	−0.354404	+	0.282628i	−0.0336385	+	0.0268258i
$112$	1.44340	+	1.59862i	0.136389	+	0.151055i
$113$	−1.45515	−	12.9148i	−0.136889	−	1.21493i	−0.854862	−	0.518855i	$-0.826358\pi$
$113$	−1.45515	−	12.9148i	−0.136889	−	1.21493i	0.717973	−	0.696071i	$-0.245070\pi$
$114$	−0.0767727	−	0.112605i	−0.00719042	−	0.0105464i
$115$	−14.8853	+	7.73257i	−1.38806	+	0.721065i
$116$	−2.32496	−	4.02694i	−0.215867	−	0.373892i
$117$	−0.394943	−	1.47395i	−0.0365125	−	0.136267i
$118$	1.78365	−	2.83867i	0.164199	−	0.261321i
$119$	20.6185	−	2.03999i	1.89009	−	0.187006i
$120$	6.46482	−	1.94403i	0.590155	−	0.177465i
$121$	−0.704356	−	0.653547i	−0.0640324	−	0.0594133i
$122$	7.33575	−	5.41403i	0.664147	−	0.490163i
$123$	−2.77339	+	2.04686i	−0.250068	+	0.184559i
$124$	−3.76109	−	3.48978i	−0.337755	−	0.313391i
$125$	2.71918	−	10.8446i	0.243210	−	0.969974i
$126$	0.425210	−	3.36273i	0.0378807	−	0.299576i
$127$	1.62496	−	2.58611i	0.144192	−	0.229480i	−0.766818	−	0.641865i	$-0.778161\pi$
$127$	1.62496	−	2.58611i	0.144192	−	0.229480i	0.911010	+	0.412384i	$0.135304\pi$
$128$	2.46358	+	9.19422i	0.217752	+	0.812662i
$129$	−3.58594	−	6.21104i	−0.315725	−	0.546851i
$130$	0.472822	−	1.49512i	0.0414692	−	0.131131i
$131$	6.08541	+	8.92565i	0.531684	+	0.779838i	0.994288	−	0.106727i	$-0.0340372\pi$
$131$	6.08541	+	8.92565i	0.531684	+	0.779838i	−0.462604	+	0.886565i	$0.653085\pi$
$132$	0.630303	+	5.59410i	0.0548609	+	0.486904i
$133$	0.377201	+	0.153984i	0.0327075	+	0.0133521i
$134$	−5.32367	+	4.24549i	−0.459895	+	0.366754i
$135$	10.1519	+	6.47971i	0.873733	+	0.557684i
$136$	19.0807	+	7.48864i	1.63616	+	0.642145i
$137$	0.203712	−	0.236718i	0.0174043	−	0.0202242i	−0.749202	−	0.662341i	$-0.769563\pi$
$137$	0.203712	−	0.236718i	0.0174043	−	0.0202242i	0.766606	+	0.642117i	$0.221944\pi$
$138$	2.65491	−	6.08512i	0.226001	−	0.518000i
$139$	10.5367	−	5.07420i	0.893710	−	0.430388i	0.0700972	−	0.997540i	$-0.477669\pi$
$139$	10.5367	−	5.07420i	0.893710	−	0.430388i	0.823613	+	0.567152i	$0.191955\pi$
$140$	−5.33933	+	6.41851i	−0.451256	+	0.542463i
$141$	6.41063	+	3.08720i	0.539873	+	0.259989i
$142$	−4.61468	+	3.97125i	−0.387255	+	0.333260i
$143$	2.79454	+	1.47696i	0.233691	+	0.123510i
$144$	−0.765659	+	1.12302i	−0.0638049	+	0.0935847i
$145$	5.79270	−	4.55269i	0.481057	−	0.378081i
$146$			1.23367i			0.102099i
$147$	−3.57745	−	7.23813i	−0.295063	−	0.596991i
$148$	0.392178	−	0.392178i	0.0322368	−	0.0322368i
$149$	−3.41517	−	22.6582i	−0.279782	−	1.85623i	−0.481048	−	0.876695i	$-0.659744\pi$
$149$	−3.41517	−	22.6582i	−0.279782	−	1.85623i	0.201266	−	0.979537i	$-0.435495\pi$
$150$	1.86326	+	4.01375i	0.152135	+	0.327721i
$151$	−4.31975	+	1.33247i	−0.351536	+	0.108434i	−0.465494	−	0.885051i	$-0.654123\pi$
$151$	−4.31975	+	1.33247i	−0.351536	+	0.108434i	0.113958	+	0.993486i	$0.463647\pi$
$152$	0.262915	+	0.305513i	0.0213252	+	0.0247803i
$153$	4.31839	+	12.3412i	0.349121	+	0.997730i
$154$	4.50703	+	5.38343i	0.363186	+	0.433809i
$155$	4.62702	−	6.68425i	0.371651	−	0.536892i
$156$	−0.543510	−	1.38484i	−0.0435156	−	0.110876i
$157$	2.74608	+	2.36319i	0.219161	+	0.188603i	0.755015	−	0.655707i	$-0.227629\pi$
$157$	2.74608	+	2.36319i	0.219161	+	0.188603i	−0.535854	+	0.844310i	$0.680010\pi$
$158$	−4.10666	−	9.41255i	−0.326708	−	0.748823i
$159$	−9.75712	−	3.00967i	−0.773790	−	0.238683i
$160$	−12.0460	+	5.15426i	−0.952324	+	0.407480i
$161$	3.42465	+	19.5495i	0.269900	+	1.54072i
$162$	−0.917654	+	0.103395i	−0.0720977	+	0.00812346i
$163$	1.55036	−	8.19382i	0.121433	−	0.641790i	−0.867972	−	0.496612i	$-0.834577\pi$
$163$	1.55036	−	8.19382i	0.121433	−	0.641790i	0.989406	−	0.145177i	$-0.0463753\pi$
$164$	3.09158	−	2.86856i	0.241412	−	0.223997i
$165$	−8.63200	+	2.24745i	−0.672000	+	0.174964i
$166$	−0.592447	−	0.342049i	−0.0459828	−	0.0265482i
$167$	5.09416	+	3.20087i	0.394198	+	0.247691i	0.714516	−	0.699619i	$-0.246647\pi$
$167$	5.09416	+	3.20087i	0.394198	+	0.247691i	−0.320318	+	0.947310i	$0.603790\pi$
$168$	0.108474	−	7.98691i	0.00836898	−	0.616203i
$169$	11.8597	+	2.70690i	0.912285	+	0.208223i
$170$	−3.08266	+	13.0778i	−0.236429	+	1.00302i
$171$	−0.0383196	+	0.254234i	−0.00293038	+	0.0194418i
$172$	5.21076	+	7.06033i	0.397317	+	0.538345i
$173$	0.258851	+	6.91794i	0.0196801	+	0.525961i	0.973916	+	0.226907i	$0.0728614\pi$
$173$	0.258851	+	6.91794i	0.0196801	+	0.525961i	−0.954236	+	0.299054i	$0.903329\pi$
$174$	−0.648892	+	2.84298i	−0.0491924	+	0.215526i
$175$	−11.2684	−	6.92986i	−0.851811	−	0.523848i
$176$	−0.626491	−	2.74483i	−0.0472235	−	0.206900i
$177$	4.86782	−	1.30433i	0.365888	−	0.0980394i
$178$	−3.00544	+	11.2164i	−0.225267	+	0.840708i
$179$	9.71955	+	10.4752i	0.726473	+	0.782952i	0.983004	−	0.183584i	$-0.0587700\pi$
$179$	9.71955	+	10.4752i	0.726473	+	0.782952i	−0.256531	+	0.966536i	$0.582579\pi$
$180$	−4.73060	−	2.31961i	−0.352598	−	0.172893i
$181$	−7.00940	−	5.58981i	−0.521005	−	0.415487i	0.327360	−	0.944900i	$-0.393841\pi$
$181$	−7.00940	−	5.58981i	−0.521005	−	0.415487i	−0.848365	+	0.529412i	$0.822412\pi$
$182$	−1.51867	−	1.06591i	−0.112572	−	0.0790106i
$183$	13.6190	+	1.53449i	1.00674	+	0.113433i
$184$	−5.78753	+	18.7627i	−0.426662	+	1.38320i
$185$	0.703350	+	0.526841i	0.0517113	+	0.0387341i
$186$	0.240453	+	3.20863i	0.0176309	+	0.235268i
$187$	−24.8237	−	10.8304i	−1.81529	−	0.792001i
$188$	−8.21717	−	2.87531i	−0.599299	−	0.209704i
$189$	10.9264	−	9.14763i	0.794780	−	0.665392i
$190$	−0.173757	+	0.199036i	−0.0126056	+	0.0144396i
$191$	0.783117	−	10.4500i	0.0566643	−	0.756133i	−0.894425	−	0.447218i	$-0.852415\pi$
$191$	0.783117	−	10.4500i	0.0566643	−	0.756133i	0.951089	−	0.308915i	$-0.0999660\pi$
$192$	1.54571	−	2.92462i	0.111552	−	0.211067i
$193$	1.62749	−	0.307938i	0.117149	−	0.0221659i	−0.127006	−	0.991902i	$-0.540537\pi$
$193$	1.62749	−	0.307938i	0.117149	−	0.0221659i	0.244156	+	0.969736i	$0.421489\pi$
$194$	−10.5872	+	1.59576i	−0.760113	+	0.114569i
$195$	2.04969	−	1.16409i	0.146781	−	0.0833619i
$196$	5.34113	+	8.31026i	0.381509	+	0.593590i
$197$	−15.9921	−	15.9921i	−1.13939	−	1.13939i	−0.988559	−	0.150834i	$-0.951804\pi$
$197$	−15.9921	−	15.9921i	−1.13939	−	1.13939i	−0.150834	−	0.988559i	$-0.548196\pi$
$198$	−2.63102	+	3.56490i	−0.186978	+	0.253346i
$199$	−10.6694	−	7.27428i	−0.756335	−	0.515660i	0.122685	−	0.992446i	$-0.460849\pi$
$199$	−10.6694	−	7.27428i	−0.756335	−	0.515660i	−0.879020	+	0.476785i	$0.841802\pi$
$200$	−6.80503	−	11.1790i	−0.481188	−	0.790476i
$201$	−10.2071	−	0.764913i	−0.719950	−	0.0539528i
$202$	8.19730	−	2.86836i	0.576760	−	0.201817i
$203$	−3.07437	−	8.15742i	−0.215779	−	0.572539i
$204$	5.53075	+	11.4847i	0.387230	+	0.804092i
$205$	5.19480	+	4.20333i	0.362821	+	0.293573i
$206$	−1.67398	+	0.125448i	−0.116632	+	0.00874036i
$207$	−11.4797	+	5.00853i	−0.797892	+	0.348117i
$208$	0.347656	+	0.657798i	0.0241056	+	0.0456101i
$209$	−0.332051	−	0.416379i	−0.0229684	−	0.0288015i
$210$	5.19245	−	0.673182i	0.358313	−	0.0464540i
$211$	3.08776	−	3.87193i	0.212570	−	0.266554i	−0.664103	−	0.747641i	$-0.731186\pi$
$211$	3.08776	−	3.87193i	0.212570	−	0.266554i	0.876673	+	0.481087i	$0.159758\pi$
$212$	12.2753	+	2.32261i	0.843071	+	0.159518i
$213$	−9.14540	−	0.342197i	−0.626632	−	0.0234469i
$214$	9.95106	−	5.74525i	0.680240	−	0.392737i
$215$	−9.90088	+	9.76144i	−0.675235	+	0.665725i
$216$	13.7443	−	3.13705i	0.935183	−	0.213449i
$217$	−5.89463	−	7.60114i	−0.400153	−	0.515999i
$218$	−0.663580	−	1.05608i	−0.0449433	−	0.0715269i
$219$	−1.26135	+	1.35942i	−0.0852343	+	0.0918608i
$220$	10.1872	−	3.91503i	0.686819	−	0.263951i
$221$	7.07726	+	1.06673i	0.476068	+	0.0717557i
$222$	−0.347577	+	0.0130054i	−0.0233279	+	0.000872867i
$223$	−12.5677	+	7.89682i	−0.841597	+	0.528810i	−0.882478	−	0.470354i	$-0.844126\pi$
$223$	−12.5677	+	7.89682i	−0.841597	+	0.528810i	0.0408812	+	0.999164i	$0.486983\pi$
$224$	1.52641	+	15.4277i	0.101988	+	1.03080i
$225$	2.57354	−	7.94152i	0.171569	−	0.529435i
$226$	4.98618	−	8.63632i	0.331676	−	0.574479i
$227$	−18.5301	−	4.96512i	−1.22988	−	0.329547i	−0.415350	−	0.909662i	$-0.636341\pi$
$227$	−18.5301	−	4.96512i	−1.22988	−	0.329547i	−0.814535	+	0.580115i	$0.803008\pi$
$228$	−0.00937242	+	0.250483i	−0.000620704	+	0.0165887i
$229$	−7.73843	+	5.27598i	−0.511370	+	0.348646i	−0.791354	−	0.611359i	$-0.790623\pi$
$229$	−7.73843	+	5.27598i	−0.511370	+	0.348646i	0.279984	+	0.960005i	$0.409671\pi$
$230$	−12.7131	−	2.00849i	−0.838276	−	0.132436i
$231$	−0.537817	+	10.5403i	−0.0353858	+	0.693501i
$232$	0.965620	−	8.57012i	0.0633961	−	0.562656i
$233$	−7.21775	+	3.81469i	−0.472850	+	0.249909i	−0.686677	−	0.726963i	$-0.740931\pi$
$233$	−7.21775	+	3.81469i	−0.472850	+	0.249909i	0.213826	+	0.976872i	$0.431407\pi$
$234$	0.427766	−	1.08993i	0.0279640	−	0.0712510i
$235$	2.66050	−	13.5349i	0.173552	−	0.882922i
$236$	−5.73977	+	2.25269i	−0.373627	+	0.146638i
$237$	5.09853	−	14.5708i	0.331185	−	0.946472i
$238$	13.6588	+	8.13522i	0.885369	+	0.527328i
$239$	−4.15342	+	8.62467i	−0.268662	+	0.557883i	−0.991032	−	0.133624i	$-0.957339\pi$
$239$	−4.15342	+	8.62467i	−0.268662	+	0.557883i	0.722370	+	0.691507i	$0.243053\pi$
$240$	−1.97680	−	0.707488i	−0.127602	−	0.0456682i
$241$	−3.92586	−	12.7273i	−0.252887	−	0.819839i	−0.989627	−	0.143662i	$-0.954112\pi$
$241$	−3.92586	−	12.7273i	−0.252887	−	0.819839i	0.736740	−	0.676176i	$-0.236364\pi$
$242$	−0.137067	−	0.724418i	−0.00881102	−	0.0465673i
$243$	11.8839	+	8.77070i	0.762351	+	0.562641i
$244$	−16.7686			−1.07350
$245$	−11.8319	+	10.2472i	−0.755915	+	0.654669i
$246$	−2.64486			−0.168630
$247$	0.113238	+	0.0835738i	0.00720519	+	0.00531767i
$248$	−1.76916	−	9.35022i	−0.112342	−	0.593739i
$249$	−0.303109	−	0.982654i	−0.0192087	−	0.0622732i
$250$	6.62003	−	5.45622i	0.418687	−	0.345082i
$251$	−1.91830	+	3.98340i	−0.121082	+	0.251430i	−0.952696	−	0.303924i	$-0.901703\pi$
$251$	−1.91830	+	3.98340i	−0.121082	+	0.251430i	0.831614	+	0.555354i	$0.187417\pi$
$252$	−4.30187	+	4.51185i	−0.270992	+	0.284220i
$253$	8.56864	−	24.4878i	0.538706	−	1.53953i
$254$	2.18155	−	0.856196i	0.136883	−	0.0537225i
$255$	−16.7681	+	11.2590i	−1.05006	+	0.705064i
$256$	−4.76390	+	12.1382i	−0.297744	+	0.758638i
$257$	24.5442	−	12.9720i	1.53102	−	0.809170i	0.531737	−	0.846909i	$-0.321539\pi$
$257$	24.5442	−	12.9720i	1.53102	−	0.809170i	0.999288	+	0.0377393i	$0.0120156\pi$
$258$	0.616146	−	5.46845i	0.0383596	−	0.340451i
$259$	0.844923	−	0.606031i	0.0525009	−	0.0376570i
$260$	−2.33261	+	1.69612i	−0.144662	+	0.105189i
$261$	4.54535	−	3.09897i	0.281350	−	0.191821i
$262$	−0.309937	+	8.28324i	−0.0191480	+	0.511740i
$263$	−9.02666	−	2.41869i	−0.556608	−	0.149143i	−0.0304602	−	0.999536i	$-0.509697\pi$
$263$	−9.02666	−	2.41869i	−0.556608	−	0.149143i	−0.526147	+	0.850393i	$0.676364\pi$
$264$	−5.22060	+	9.04235i	−0.321306	+	0.556518i
$265$	−0.880418	+	19.7754i	−0.0540836	+	1.21479i
$266$	0.162712	+	0.266935i	0.00997653	+	0.0163668i
$267$	−14.7799	+	9.28683i	−0.904515	+	0.568345i
$268$	12.5148	−	0.468272i	0.764465	−	0.0286043i
$269$	10.1739	+	1.53347i	0.620314	+	0.0934973i	0.451678	−	0.892181i	$-0.350826\pi$
$269$	10.1739	+	1.53347i	0.620314	+	0.0934973i	0.168636	+	0.985678i	$0.446064\pi$
$270$	3.31507	+	8.62603i	0.201749	+	0.524964i
$271$	3.37660	−	3.63911i	0.205114	−	0.221060i	−0.622114	−	0.782927i	$-0.713726\pi$
$271$	3.37660	−	3.63911i	0.205114	−	0.221060i	0.827228	+	0.561866i	$0.189916\pi$
$272$	−3.39174	−	5.39793i	−0.205655	−	0.327298i
$273$	−0.583640	−	2.72731i	−0.0353235	−	0.165064i
$274$	0.233626	−	0.0533235i	0.0141138	−	0.00322139i
$275$	8.43285	+	15.0966i	0.508520	+	0.910361i
$276$	−10.5747	+	6.10531i	−0.636523	+	0.367497i
$277$	19.3276	+	0.723189i	1.16128	+	0.0434522i	0.611074	−	0.791574i	$-0.290738\pi$
$277$	19.3276	+	0.723189i	1.16128	+	0.0434522i	0.550211	+	0.835026i	$0.314547\pi$
$278$	8.81711	+	1.66829i	0.528815	+	0.100057i
$279$	3.78464	−	4.74579i	0.226581	−	0.284123i
$280$	−15.0372	+	3.69781i	−0.898643	+	0.220987i
$281$	−15.1738	−	19.0274i	−0.905196	−	1.13508i	−0.990333	−	0.138710i	$-0.955704\pi$
$281$	−15.1738	−	19.0274i	−0.905196	−	1.13508i	0.0851375	−	0.996369i	$-0.472867\pi$
$282$	2.55110	+	4.82692i	0.151916	+	0.287439i
$283$	−26.7596	+	11.6751i	−1.59069	+	0.694011i	−0.994093	−	0.108529i	$-0.965386\pi$
$283$	−26.7596	+	11.6751i	−1.59069	+	0.694011i	−0.596598	+	0.802541i	$0.703481\pi$
$284$	11.1661	−	0.836786i	0.662588	−	0.0496541i
$285$	−0.394970	+	0.0416681i	−0.0233960	+	0.00246820i
$286$	1.05231	+	2.18515i	0.0622246	+	0.129211i
$287$	6.59269	−	4.36486i	0.389154	−	0.257650i
$288$	−9.23428	+	3.23121i	−0.544135	+	0.190401i
$289$	−44.2021	−	3.31249i	−2.60013	−	0.194853i
$290$	5.65066	−	0.171315i	0.331818	−	0.0100599i
$291$	−13.2978	−	9.06631i	−0.779533	−	0.531477i
$292$	1.34736	−	1.82561i	0.0788485	−	0.106836i
$293$	11.2183	+	11.2183i	0.655381	+	0.655381i	0.954284	−	0.298902i	$-0.0966205\pi$
$293$	11.2183	+	11.2183i	0.655381	+	0.655381i	−0.298902	+	0.954284i	$0.596620\pi$
$294$	1.08938	−	6.09867i	0.0635337	−	0.355682i
$295$	−4.82481	−	8.49537i	−0.280911	−	0.494620i
$296$	1.01719	−	0.153316i	0.0591229	−	0.00891134i
$297$	−18.3026	+	3.46304i	−1.06202	+	0.200946i
$298$	8.21560	−	15.5447i	0.475917	−	0.900479i
$299$	−0.512349	+	6.83683i	−0.0296299	+	0.395384i
$300$	1.62636	−	7.97461i	0.0938977	−	0.460414i
$301$	7.48885	+	14.6477i	0.431650	+	0.844280i
$302$	−3.27403	−	1.14563i	−0.188399	−	0.0659237i
$303$	11.9655	+	5.22051i	0.687403	+	0.299911i
$304$	−0.00936812	−	0.125009i	−0.000537298	−	0.00716975i
$305$	−3.77354	−	26.3000i	−0.216072	−	1.50593i
$306$	−2.95714	+	9.58680i	−0.169048	+	0.548041i
$307$	14.9832	+	1.68820i	0.855136	+	0.0963507i	0.528638	−	0.848847i	$-0.322703\pi$
$307$	14.9832	+	1.68820i	0.855136	+	0.0963507i	0.326498	+	0.945198i	$0.394131\pi$
$308$	−0.790035	−	12.8889i	−0.0450164	−	0.734414i
$309$	−1.97287	−	1.57331i	−0.112233	−	0.0895026i
$310$	5.90223	−	2.01842i	0.335224	−	0.114638i
$311$	20.9262	+	22.5531i	1.18662	+	1.27887i	0.951761	+	0.306839i	$0.0992713\pi$
$311$	20.9262	+	22.5531i	1.18662	+	1.27887i	0.234856	+	0.972030i	$0.424538\pi$
$312$	0.714145	−	2.66523i	0.0404305	−	0.150889i
$313$	14.9244	−	3.99897i	0.843575	−	0.226035i	0.188948	−	0.981987i	$-0.439492\pi$
$313$	14.9244	−	3.99897i	0.843575	−	0.226035i	0.654627	+	0.755952i	$0.272826\pi$
$314$	0.618587	+	2.71021i	0.0349089	+	0.152946i
$315$	−8.04450	−	5.73177i	−0.453256	−	0.322948i
$316$	−4.20288	+	18.4140i	−0.236431	+	1.03587i
$317$	−0.265596	−	7.09821i	−0.0149174	−	0.398675i	−0.986676	−	0.162698i	$-0.947980\pi$
$317$	−0.265596	−	7.09821i	−0.0149174	−	0.398675i	0.971759	−	0.235977i	$-0.0758291\pi$
$318$	−4.65246	−	6.30385i	−0.260897	−	0.353503i
$319$	−1.69838	+	11.2680i	−0.0950910	+	0.630888i
$320$	−6.24189	−	1.47132i	−0.348933	−	0.0822492i
$321$	16.8395	+	3.84351i	0.939889	+	0.214524i
$322$	−6.79329	+	13.6298i	−0.378575	+	0.759557i
$323$	−1.02108	−	0.641586i	−0.0568143	−	0.0356988i
$324$	1.47089	+	0.849218i	0.0817160	+	0.0471788i
$325$	−3.18513	−	3.27679i	−0.176679	−	0.181764i
$326$	4.69061	−	4.35225i	0.259789	−	0.241049i
$327$	0.348562	−	1.84220i	0.0192755	−	0.101874i
$328$	7.77297	−	0.875804i	0.429191	−	0.0483582i
$329$	−14.3249	−	7.82165i	−0.789759	−	0.431221i
$330$	−6.35321	−	2.54559i	−0.349733	−	0.140130i
$331$	30.3887	+	9.37367i	1.67031	+	0.515224i	0.978394	−	0.206750i	$-0.0662888\pi$
$331$	30.3887	+	9.37367i	1.67031	+	0.515224i	0.691920	+	0.721974i	$0.256765\pi$
$332$	0.503144	+	1.15322i	0.0276136	+	0.0632911i
$333$	0.497357	+	0.428010i	0.0272550	+	0.0234548i
$334$	1.68655	+	4.29725i	0.0922838	+	0.235135i
$335$	3.55074	+	19.5230i	0.193998	+	1.06666i
$336$	−1.50222	+	1.97862i	−0.0819528	+	0.107943i
$337$	−9.39203	−	26.8409i	−0.511616	−	1.46212i	−0.852860	−	0.522140i	$-0.825134\pi$
$337$	−9.39203	−	26.8409i	−0.511616	−	1.46212i	0.341243	−	0.939975i	$-0.389152\pi$
$338$	6.08850	+	7.07496i	0.331171	+	0.384827i
$339$	14.3245	−	4.41853i	0.778001	−	0.239982i
$340$	18.8448	−	15.9861i	1.02201	−	0.866968i
$341$	1.87400	+	12.4331i	0.101483	+	0.673293i
$342$	−0.139498	+	0.139498i	−0.00754316	+	0.00754316i
$343$	7.34933	+	16.9996i	0.396826	+	0.917894i
$344$			16.2752i			0.877502i
$345$	−11.9553	−	15.2116i	−0.643654	−	0.818963i
$346$	−2.99230	+	4.38890i	−0.160867	+	0.235949i
$347$	−13.1211	−	6.93468i	−0.704376	−	0.372273i	0.0764066	−	0.997077i	$-0.475655\pi$
$347$	−13.1211	−	6.93468i	−0.704376	−	0.372273i	−0.780782	+	0.624803i	$0.785179\pi$
$348$	4.06523	−	3.49842i	0.217919	−	0.187535i
$349$	−11.6624	−	5.61631i	−0.624273	−	0.300634i	0.0948768	−	0.995489i	$-0.469754\pi$
$349$	−11.6624	−	5.61631i	−0.624273	−	0.300634i	−0.719150	+	0.694855i	$0.755469\pi$
$350$	−3.79928	−	9.41269i	−0.203080	−	0.503129i
$351$	4.43506	−	2.13581i	0.236726	−	0.114001i
$352$	8.10384	−	18.5742i	0.431936	−	0.990008i
$353$	5.76478	−	6.69880i	0.306828	−	0.356541i	−0.583295	−	0.812260i	$-0.698237\pi$
$353$	5.76478	−	6.69880i	0.306828	−	0.356541i	0.890124	+	0.455719i	$0.150618\pi$
$354$	3.59958	+	1.41273i	0.191315	+	0.0750858i
$355$	3.82521	+	17.3248i	0.203021	+	0.919504i
$356$	16.6977	−	13.3159i	0.884974	−	0.705743i
$357$	6.73325	+	22.9297i	0.356362	+	1.21357i
$358$	1.22766	+	10.8958i	0.0648837	+	0.575858i
$359$	16.8331	+	24.6896i	0.888416	+	1.30307i	0.952317	+	0.305111i	$0.0986937\pi$
$359$	16.8331	+	24.6896i	0.888416	+	1.30307i	−0.0639002	+	0.997956i	$0.520354\pi$
$360$	−4.50478	−	8.67176i	−0.237423	−	0.457042i
$361$	9.48814	+	16.4339i	0.499376	+	0.864945i
$362$	−1.78047	−	6.64479i	−0.0935792	−	0.349242i
$363$	0.589635	−	0.938398i	0.0309478	−	0.0492531i
$364$	1.08323	+	3.23599i	0.0567764	+	0.169612i
$365$	3.16652	+	1.70239i	0.165743	+	0.0891071i
$366$	7.70882	+	7.15274i	0.402946	+	0.373880i
$367$	17.9414	−	13.2414i	0.936536	−	0.691195i	−0.0146241	−	0.999893i	$-0.504655\pi$
$367$	17.9414	−	13.2414i	0.936536	−	0.691195i	0.951160	+	0.308698i	$0.0998932\pi$
$368$	4.91350	−	3.62633i	0.256134	−	0.189036i
$369$	3.65761	+	3.39377i	0.190408	+	0.176672i
$370$	0.194179	+	0.645735i	0.0100949	+	0.0335701i
$371$	22.0003	+	8.03522i	1.14220	+	0.417168i
$372$	3.14850	−	5.01081i	0.163242	−	0.259799i
$373$	−0.966450	−	3.60684i	−0.0500409	−	0.186755i	0.936381	−	0.350984i	$-0.114153\pi$
$373$	−0.966450	−	3.60684i	−0.0500409	−	0.186755i	−0.986422	+	0.164229i	$0.947486\pi$
$374$	−10.3907	−	17.9972i	−0.537289	−	0.930611i
$375$	12.8734	+	0.756214i	0.664782	+	0.0390507i
$376$	−9.09579	−	13.3411i	−0.469080	−	0.688013i
$377$	−0.337167	−	2.99244i	−0.0173650	−	0.154119i
$378$	10.9137	−	0.668966i	0.561342	−	0.0344079i
$379$	19.9530	−	15.9120i	1.02491	−	0.817342i	0.0415778	−	0.999135i	$-0.486762\pi$
$379$	19.9530	−	15.9120i	1.02491	−	0.817342i	0.983337	+	0.181793i	$0.0581901\pi$
$380$	0.474508	−	0.104769i	0.0243418	−	0.00537452i
$381$	3.27932	+	1.28704i	0.168005	+	0.0659369i
$382$	5.24493	−	6.09472i	0.268354	−	0.311833i
$383$	−1.73667	+	3.98049i	−0.0887398	+	0.203394i	−0.955273	−	0.295726i	$-0.904438\pi$
$383$	−1.73667	+	3.98049i	−0.0887398	+	0.203394i	0.866533	+	0.499120i	$0.166343\pi$
$384$	−9.89165	+	4.76357i	−0.504781	+	0.243090i
$385$	20.0373	−	4.13957i	1.02120	−	0.210972i
$386$	1.14508	+	0.551442i	0.0582831	+	0.0280676i
$387$	−7.86895	+	6.77177i	−0.400001	+	0.344229i
$388$	17.4099	+	9.20142i	0.883855	+	0.467131i
$389$	5.14567	−	7.54731i	0.260896	−	0.382664i	−0.673332	−	0.739340i	$-0.735138\pi$
$389$	5.14567	−	7.54731i	0.260896	−	0.382664i	0.934228	+	0.356676i	$0.116090\pi$
$390$	1.79583	+	0.215249i	0.0909355	+	0.0108996i
$391$		−	58.7452i		−	2.97087i
$392$	−1.18209	+	18.2841i	−0.0597045	+	0.923488i
$393$	−8.81063	+	8.81063i	−0.444438	+	0.444438i
$394$	−2.58643	−	17.1598i	−0.130302	−	0.864500i
$395$	−29.8265	−	2.44801i	−1.50074	−	0.123173i
$396$	7.78687	−	2.40193i	0.391305	−	0.120702i
$397$	−4.27483	−	4.96744i	−0.214547	−	0.249309i	0.640378	−	0.768060i	$-0.278778\pi$
$397$	−4.27483	−	4.96744i	−0.214547	−	0.249309i	−0.854925	+	0.518752i	$0.826397\pi$
$398$	−3.27255	−	9.35240i	−0.164038	−	0.468793i
$399$	−0.0936275	+	0.460506i	−0.00468724	+	0.0230541i
$400$	−0.361715	+	4.05425i	−0.0180858	+	0.202713i
$401$	0.505571	+	1.28817i	0.0252470	+	0.0643283i	0.942941	−	0.332959i	$-0.108047\pi$
$401$	0.505571	+	1.28817i	0.0252470	+	0.0643283i	−0.917694	+	0.397287i	$0.869952\pi$
$402$	−5.95304	−	5.12301i	−0.296911	−	0.255512i
$403$	−1.32874	−	3.04551i	−0.0661895	−	0.151708i
$404$	−15.2632	−	4.70809i	−0.759375	−	0.234236i
$405$	−1.00092	+	2.49806i	−0.0497360	+	0.124130i
$406$	1.81883	−	6.43700i	0.0902671	−	0.319463i
$407$	−1.35064	+	0.152180i	−0.0669487	+	0.00754331i
$408$	−4.39540	+	23.2303i	−0.217605	+	1.15007i
$409$	−1.04177	+	0.966624i	−0.0515124	+	0.0477965i	−0.705509	−	0.708701i	$-0.749282\pi$
$409$	−1.04177	+	0.966624i	−0.0515124	+	0.0477965i	0.653997	+	0.756497i	$0.273091\pi$
$410$	1.29192	+	4.96200i	0.0638034	+	0.245056i
$411$	0.311958	+	0.180109i	0.0153878	+	0.00888413i
$412$	2.61421	+	1.64262i	0.128793	+	0.0809259i
$413$	−11.3039	+	2.41902i	−0.556229	+	0.119032i
$414$	−9.36936	−	2.13849i	−0.460479	−	0.105101i
$415$	−1.69549	+	1.04865i	−0.0832285	+	0.0514763i
$416$	−0.798173	+	5.29553i	−0.0391336	+	0.259635i
$417$	8.01009	+	10.8533i	0.392256	+	0.531487i
$418$	−0.0152797	−	0.408358i	−0.000747354	−	0.0199734i
$419$	8.35268	−	36.5955i	0.408055	−	1.78781i	−0.185101	−	0.982720i	$-0.559261\pi$
$419$	8.35268	−	36.5955i	0.408055	−	1.78781i	0.593156	−	0.805087i	$-0.297882\pi$
$420$	−8.41912	−	4.67478i	−0.410811	−	0.228106i
$421$	−5.13002	−	22.4761i	−0.250022	−	1.09542i	−0.931547	−	0.363622i	$-0.881540\pi$
$421$	−5.13002	−	22.4761i	−0.250022	−	1.09542i	0.681525	−	0.731795i	$-0.261317\pi$
$422$	3.67052	−	0.983512i	0.178678	−	0.0478766i
$423$	2.66574	−	9.94867i	0.129613	−	0.483721i
$424$	15.7605	+	16.9858i	0.765399	+	0.824904i
$425$	29.3135	+	25.9590i	1.42192	+	1.25920i
$426$	−5.49021	−	4.37830i	−0.266002	−	0.212129i
$427$	−31.0196	−	5.10721i	−1.50115	−	0.247155i
$428$	−21.0005	−	2.36619i	−1.01510	−	0.114374i
$429$	−1.07461	+	3.48380i	−0.0518827	+	0.168200i
$430$	−10.5603	+	1.51520i	−0.509262	+	0.0730692i
$431$	0.749410	+	10.0002i	0.0360978	+	0.481692i	0.985731	+	0.168328i	$0.0538368\pi$
$431$	0.749410	+	10.0002i	0.0360978	+	0.481692i	−0.949633	+	0.313364i	$0.898544\pi$
$432$	−4.01878	−	1.75337i	−0.193354	−	0.0843593i
$433$	−18.3372	−	6.41647i	−0.881231	−	0.308356i	−0.148531	−	0.988908i	$-0.547454\pi$
$433$	−18.3372	−	6.41647i	−0.881231	−	0.308356i	−0.732700	+	0.680552i	$0.761740\pi$
$434$	−0.175786	−	7.37859i	−0.00843798	−	0.354184i
$435$	6.40178	+	5.58868i	0.306942	+	0.267957i
$436$	−0.171428	+	2.28755i	−0.00820991	+	0.109554i
$437$	0.539772	−	1.02130i	0.0258208	−	0.0488554i
$438$	−1.39813	+	0.264541i	−0.0668055	+	0.0126403i
$439$	−6.09322	+	0.918406i	−0.290814	+	0.0438331i	−0.292829	−	0.956165i	$-0.594597\pi$
$439$	−6.09322	+	0.918406i	−0.290814	+	0.0438331i	0.00201518	+	0.999998i	$0.499359\pi$
$440$	19.5144	+	5.37747i	0.930311	+	0.256361i
$441$	−9.33206	+	7.03609i	−0.444384	+	0.335052i
$442$	3.88327	+	3.88327i	0.184708	+	0.184708i
$443$	13.2271	−	17.9221i	0.628438	−	0.851503i	−0.368506	−	0.929625i	$-0.620131\pi$
$443$	13.2271	−	17.9221i	0.628438	−	0.851503i	0.996944	+	0.0781226i	$0.0248926\pi$
$444$	0.528557	+	0.360364i	0.0250842	+	0.0171021i
$445$	24.6424	+	23.1922i	1.16816	+	1.09942i
$446$	−11.3571	−	0.851098i	−0.537775	−	0.0403007i
$447$	24.9465	−	8.72915i	1.17993	−	0.412875i
$448$	−3.88285	+	6.51920i	−0.183447	+	0.308003i
$449$	8.14076	+	16.9045i	0.384186	+	0.797771i	0.999952	+	0.00984149i	$0.00313269\pi$
$449$	8.14076	+	16.9045i	0.384186	+	0.797771i	−0.615765	+	0.787930i	$0.711153\pi$
$450$	5.20733	−	3.73027i	0.245476	−	0.175847i
$451$	−10.3065	+	0.772363i	−0.485313	+	0.0363692i
$452$	−16.8109	+	7.33452i	−0.790718	+	0.344987i
$453$	−2.43640	−	4.60990i	−0.114472	−	0.216592i
$454$	−9.17767	−	11.5084i	−0.430730	−	0.540118i
$455$	−4.83160	+	2.42716i	−0.226509	+	0.113787i
$456$	−0.289863	+	0.363477i	−0.0135741	+	0.0170214i
$457$	30.7242	+	5.81333i	1.43722	+	0.271936i	0.845399	−	0.534135i	$-0.179363\pi$
$457$	30.7242	+	5.81333i	1.43722	+	0.271936i	0.591818	+	0.806072i	$0.298410\pi$
$458$	−7.18147	−	0.268712i	−0.335568	−	0.0125561i
$459$	−36.5277	+	21.0893i	−1.70497	+	0.984364i
$460$	16.6195	+	16.8569i	0.774889	+	0.785958i
$461$	−22.7155	+	5.18467i	−1.05797	+	0.241474i	−0.715901	−	0.698202i	$-0.753984\pi$
$461$	−22.7155	+	5.18467i	−1.05797	+	0.241474i	−0.342066	+	0.939676i	$0.611127\pi$
$462$	−5.13465	+	6.26226i	−0.238886	+	0.291347i
$463$	4.38663	+	6.98128i	0.203864	+	0.324448i	0.932971	−	0.359952i	$-0.117207\pi$
$463$	4.38663	+	6.98128i	0.203864	+	0.324448i	−0.729107	+	0.684400i	$0.760064\pi$
$464$	−1.82443	+	1.96626i	−0.0846968	+	0.0912815i
$465$	8.56754	+	3.81053i	0.397310	+	0.176709i
$466$	−6.19419	−	0.933624i	−0.286940	−	0.0432493i
$467$	−25.8534	+	0.967365i	−1.19635	+	0.0447643i	−0.628128	−	0.778110i	$-0.716179\pi$
$467$	−25.8534	+	0.967365i	−1.19635	+	0.0447643i	−0.568223	+	0.822874i	$0.692369\pi$
$468$	−1.82340	+	1.14572i	−0.0842865	+	0.0529607i
$469$	23.2934	+	2.94540i	1.07559	+	0.136006i
$470$	7.80963	−	7.14388i	0.360231	−	0.329523i
$471$	−2.08938	+	3.61892i	−0.0962737	+	0.166751i
$472$	−11.0466	−	2.95993i	−0.508461	−	0.136242i
$473$	0.804074	−	21.4893i	0.0369714	−	0.988081i
$474$	9.78676	−	6.67250i	0.449521	−	0.306478i
$475$	0.271102	+	0.720647i	0.0124390	+	0.0330655i
$476$	−11.3277	−	26.9563i	−0.519203	−	1.23554i
$477$	−1.65489	+	14.6875i	−0.0757720	+	0.672495i
$478$	−6.49398	+	3.43217i	−0.297028	+	0.156984i
$479$	−7.03595	+	17.9273i	−0.321481	+	0.819120i	0.675194	+	0.737640i	$0.264060\pi$
$479$	−7.03595	+	17.9273i	−0.321481	+	0.819120i	−0.996675	+	0.0814796i	$0.974035\pi$
$480$	−8.42448	−	12.5467i	−0.384523	−	0.572675i
$481$	0.334356	−	0.131225i	0.0152453	−	0.00598335i
$482$	3.37539	−	9.64631i	0.153745	−	0.439377i
$483$	−21.4213	+	8.07328i	−0.974704	+	0.367347i
$484$	−0.588344	+	1.22171i	−0.0267429	+	0.0555322i
$485$	−10.5137	+	29.3766i	−0.477404	+	1.33392i
$486$	3.34049	+	10.8296i	0.151528	+	0.491241i
$487$	−2.47646	−	13.0884i	−0.112219	−	0.593093i	−0.992858	−	0.119304i	$-0.961934\pi$
$487$	−2.47646	−	13.0884i	−0.112219	−	0.593093i	0.880638	−	0.473789i	$-0.157114\pi$
$488$	−25.0240	−	18.4685i	−1.13278	−	0.836031i
$489$	9.61861			0.434969
$490$	−11.9738	+	0.935214i	−0.540921	+	0.0422486i
$491$	−23.9236			−1.07966			−0.539830	−	0.841774i	$-0.681511\pi$
$491$	−23.9236			−1.07966			−0.539830	+	0.841774i	$0.681511\pi$
$492$	3.91392	+	2.88860i	0.176453	+	0.130228i
$493$	4.79704	+	25.3530i	0.216048	+	1.14184i
$494$	0.0318307	+	0.103193i	0.00143213	+	0.00464285i
$495$	5.51954	+	11.6725i	0.248085	+	0.524639i
$496$	−1.28414	+	2.66655i	−0.0576598	+	0.119732i
$497$	20.9107	+	1.85293i	0.937975	+	0.0831152i
$498$	0.260608	−	0.744774i	0.0116781	−	0.0333741i
$499$	−13.5044	+	5.30008i	−0.604539	+	0.237264i	−0.647813	−	0.761799i	$-0.724316\pi$
$499$	−13.5044	+	5.30008i	−0.604539	+	0.237264i	0.0432744	+	0.999063i	$0.486221\pi$
$500$	−15.7555	+	0.844121i	−0.704609	+	0.0377502i
$501$	−2.53523	+	6.45965i	−0.113266	+	0.288596i
$502$	−2.99932	+	1.58519i	−0.133866	+	0.0707504i
$503$	0.00828276	−	0.0735115i	0.000369310	−	0.00327772i	−0.993526	−	0.113603i	$-0.963761\pi$
$503$	0.00828276	−	0.0735115i	0.000369310	−	0.00327772i	0.993896	+	0.110325i	$0.0351893\pi$
$504$	−11.3890	+	1.99511i	−0.507306	+	0.0888691i
$505$	3.94943	−	24.9985i	0.175747	−	1.11242i
$506$	16.4477	−	11.2139i	0.731191	−	0.498518i
$507$	−0.524637	+	14.0212i	−0.0232999	+	0.622704i
$508$	−4.16341	−	1.11558i	−0.184721	−	0.0494960i
$509$	−12.8569	+	22.2688i	−0.569871	+	0.987046i	0.426707	+	0.904390i	$0.359674\pi$
$509$	−12.8569	+	22.2688i	−0.569871	+	0.987046i	−0.996578	+	0.0826561i	$0.973660\pi$
$510$	−15.4823	−	0.689285i	−0.685567	−	0.0305221i
$511$	3.04847	−	2.96678i	0.134856	−	0.131242i
$512$	7.64739	−	4.80517i	0.337970	−	0.212361i
$513$	−0.828819	+	0.0310122i	−0.0365933	+	0.00136922i
$514$	21.0635	+	3.17482i	0.929073	+	0.140035i
$515$	−1.98800	+	4.46980i	−0.0876019	+	0.196963i
$516$	−6.88420	+	7.41940i	−0.303060	+	0.326621i
$517$	11.3507	+	18.0645i	0.499203	+	0.794477i
$518$	0.797767	+	0.0108349i	0.0350519	+	0.000476058i
$519$	−7.78468	+	1.77680i	−0.341709	+	0.0779930i
$520$	−5.34905	−	0.0379340i	−0.234571	−	0.00166352i
$521$	−16.3300	+	9.42813i	−0.715430	+	0.413054i	−0.813068	−	0.582168i	$-0.802205\pi$
$521$	−16.3300	+	9.42813i	−0.715430	+	0.413054i	0.0976382	+	0.995222i	$0.468871\pi$
$522$	4.21821	+	0.157834i	0.184626	+	0.00690821i
$523$	13.2692	+	2.51067i	0.580222	+	0.109784i	0.467734	−	0.883869i	$-0.345070\pi$
$523$	13.2692	+	2.51067i	0.580222	+	0.109784i	0.112488	+	0.993653i	$0.464118\pi$
$524$	9.50526	−	11.9192i	0.415239	−	0.520694i
$525$	5.43737	−	14.2566i	0.237306	−	0.622210i
$526$	−4.47077	−	5.60617i	−0.194935	−	0.244440i
$527$	13.3035	+	25.1715i	0.579511	+	1.09649i
$528$	2.97641	−	1.29860i	0.129532	−	0.0565142i
$529$	33.1799	−	2.48649i	1.44260	−	0.108108i
$530$	−9.55406	+	11.8077i	−0.415002	+	0.512892i
$531$	−3.16515	−	6.57250i	−0.137356	−	0.285222i
$532$	0.0507498	−	0.572724i	0.00220028	−	0.0248307i
$533$	2.57801	−	0.902083i	0.111666	−	0.0390736i
$534$	−13.3562	−	1.00091i	−0.577980	−	0.0433136i
$535$	−1.01473	−	33.4699i	−0.0438705	−	1.44703i
$536$	19.1918	+	13.0848i	0.828960	+	0.565175i
$537$	−9.78745	+	13.2615i	−0.422360	+	0.572277i
$538$	5.58239	+	5.58239i	0.240674	+	0.240674i
$539$	2.46412	−	24.0834i	0.106137	−	1.03735i
$540$	4.51528	−	16.3856i	0.194307	−	0.705123i
$541$	−42.6638	+	6.43054i	−1.83426	+	0.276470i	−0.972850	−	0.231438i	$-0.925657\pi$
$541$	−42.6638	+	6.43054i	−1.83426	+	0.276470i	−0.861411	+	0.507908i	$0.830419\pi$
$542$	3.74276	−	0.708169i	0.160765	−	0.0304184i
$543$	4.83195	−	9.14249i	0.207359	−	0.392342i
$544$	3.42914	−	45.7587i	0.147023	−	1.96189i
$545$	−3.62639	+	0.245912i	−0.155338	+	0.0105337i
$546$	0.882354	−	1.94970i	0.0377613	−	0.0834395i
$547$	3.51277	+	1.22917i	0.150195	+	0.0525556i	0.404330	−	0.914613i	$-0.367505\pi$
$547$	3.51277	+	1.22917i	0.150195	+	0.0525556i	−0.254134	+	0.967169i	$0.581791\pi$
$548$	−0.403962	−	0.176247i	−0.0172564	−	0.00752889i
$549$	−1.48255	−	19.7832i	−0.0632736	−	0.844328i
$550$	−1.67245	+	13.1626i	−0.0713134	+	0.561257i
$551$	−0.149555	+	0.484844i	−0.00637124	+	0.0206551i
$552$	−22.5051	−	2.53571i	−0.957879	−	0.107927i
$553$	−13.3831	+	32.7834i	−0.569109	+	1.39409i
$554$	11.6029	+	9.25297i	0.492958	+	0.393121i
$555$	−0.446254	+	0.910088i	−0.0189424	+	0.0386311i
$556$	−11.2257	−	12.0984i	−0.476076	−	0.513088i
$557$	−0.450107	+	1.67982i	−0.0190716	+	0.0711763i	−0.974806	−	0.223055i	$-0.928397\pi$
$557$	−0.450107	+	1.67982i	−0.0190716	+	0.0711763i	0.955734	+	0.294231i	$0.0950637\pi$
$558$	4.49893	−	1.20548i	0.190455	−	0.0510322i
$559$	1.26455	+	5.54037i	0.0534849	+	0.234333i
$560$	4.44586	+	1.85182i	0.187872	+	0.0782536i
$561$	6.95124	−	30.4554i	0.293482	−	1.28583i
$562$	−0.698241	−	18.6609i	−0.0294535	−	0.787162i
$563$	−9.13523	−	12.3778i	−0.385004	−	0.521662i	0.568645	−	0.822583i	$-0.307468\pi$
$563$	−9.13523	−	12.3778i	−0.385004	−	0.521662i	−0.953649	+	0.300921i	$0.902706\pi$
$564$	1.49658	−	9.92919i	0.0630176	−	0.418094i
$565$	−15.2866	−	24.7158i	−0.643112	−	1.03980i
$566$	−21.8403	−	4.98491i	−0.918018	−	0.209532i
$567$	2.46230	+	2.01893i	0.103407	+	0.0847870i
$568$	17.5850	+	11.0494i	0.737850	+	0.463622i
$569$	10.6971	+	6.17599i	0.448447	+	0.258911i	0.707174	−	0.707040i	$-0.249970\pi$
$569$	10.6971	+	6.17599i	0.448447	+	0.258911i	−0.258727	+	0.965950i	$0.583303\pi$
$570$	−0.262830	−	0.154240i	−0.0110087	−	0.00646042i
$571$	−5.21984	+	4.84330i	−0.218444	+	0.202686i	−0.781802	−	0.623526i	$-0.785699\pi$
$571$	−5.21984	+	4.84330i	−0.218444	+	0.202686i	0.563359	+	0.826212i	$0.309509\pi$
$572$	0.829294	−	4.38293i	0.0346745	−	0.183259i
$573$	12.0110	−	1.35332i	0.501767	−	0.0565356i
$574$	6.05897	+	0.309158i	0.252897	+	0.0129040i
$575$	−22.6986	+	29.8596i	−0.946596	+	1.24523i
$576$	−4.57567	−	1.41141i	−0.190653	−	0.0588087i
$577$	18.6415	+	42.7269i	0.776058	+	1.77874i	0.609625	+	0.792690i	$0.291320\pi$
$577$	18.6415	+	42.7269i	0.776058	+	1.77874i	0.166433	+	0.986053i	$0.446775\pi$
$578$	−25.7799	−	22.1854i	−1.07230	−	0.922793i
$579$	0.697980	+	1.77842i	0.0290071	+	0.0739088i
$580$	−8.54908	−	5.91791i	−0.354981	−	0.245728i
$581$	0.579514	+	2.28654i	0.0240423	+	0.0948618i
$582$	−4.07874	−	11.6564i	−0.169069	−	0.483172i
$583$	−19.9705	−	23.2062i	−0.827096	−	0.961103i
$584$	4.02138	−	1.24043i	0.166406	−	0.0513294i
$585$	−2.20728	−	2.60200i	−0.0912599	−	0.107580i
$586$	1.81435	+	12.0375i	0.0749503	+	0.497263i
$587$	0.521127	−	0.521127i	0.0215092	−	0.0215092i	−0.696270	−	0.717780i	$-0.745159\pi$
$587$	0.521127	−	0.521127i	0.0215092	−	0.0215092i	0.717780	+	0.696270i	$0.245159\pi$
$588$	−8.27280	+	7.83518i	−0.341165	+	0.323117i
$589$			0.559851i			0.0230682i
$590$	0.892147	−	7.44321i	0.0367291	−	0.306432i
$591$	14.6948	−	21.5534i	0.604465	−	0.886587i
$592$	−0.282858	−	0.149495i	−0.0116254	−	0.00614421i
$593$	−24.0682	+	20.7124i	−0.988364	+	0.850556i	−0.988770	−	0.149444i	$-0.952252\pi$
$593$	−24.0682	+	20.7124i	−0.988364	+	0.850556i	0.000406235		1.00000i	$0.499871\pi$
$594$	−12.8775	−	6.20145i	−0.528368	−	0.254449i
$595$	39.7293	−	23.8326i	1.62874	−	0.977040i
$596$	−29.1349	+	14.0306i	−1.19341	+	0.574717i
$597$	5.95615	−	13.6516i	0.243769	−	0.558724i
$598$	−3.43146	+	3.98743i	−0.140323	+	0.163058i
$599$	26.7443	+	10.4964i	1.09274	+	0.428869i	0.842161	−	0.539226i	$-0.181283\pi$
$599$	26.7443	+	10.4964i	1.09274	+	0.428869i	0.250580	+	0.968096i	$0.419379\pi$
$600$	11.2101	−	10.1094i	0.457650	−	0.412714i
$601$	−4.83258	+	3.85385i	−0.197125	+	0.157202i	−0.717078	−	0.696993i	$-0.754521\pi$
$601$	−4.83258	+	3.85385i	−0.197125	+	0.157202i	0.519953	+	0.854195i	$0.325949\pi$
$602$	−2.05071	+	12.4554i	−0.0835805	+	0.507643i
$603$	1.65892	+	14.7234i	0.0675566	+	0.599582i
$604$	3.59377	+	5.27109i	0.146228	+	0.214478i
$605$	−2.04854	−	0.647835i	−0.0832850	−	0.0263383i
$606$	5.00853	+	8.67503i	0.203458	+	0.352399i
$607$	−3.51474	−	13.1172i	−0.142659	−	0.532410i	−0.999848	−	0.0174093i	$-0.994458\pi$
$607$	−3.51474	−	13.1172i	−0.142659	−	0.532410i	0.857189	−	0.515001i	$-0.172209\pi$
$608$	0.480064	−	0.764017i	0.0194692	−	0.0309850i
$609$	8.58566	−	5.23346i	0.347908	−	0.212070i
$610$	9.65372	−	17.9563i	0.390868	−	0.727031i
$611$	−4.13294	−	3.83481i	−0.167201	−	0.155140i
$612$	14.8463	−	10.9571i	0.600128	−	0.442915i
$613$	−14.1490	+	10.4425i	−0.571474	+	0.421767i	−0.840850	−	0.541268i	$-0.817944\pi$
$613$	−14.1490	+	10.4425i	−0.571474	+	0.421767i	0.269376	+	0.963035i	$0.413182\pi$
$614$	8.48102	+	7.86924i	0.342266	+	0.317577i
$615$	−3.64974	+	6.78867i	−0.147172	+	0.273746i
$616$	13.0166	−	20.1044i	0.524453	−	0.810030i
$617$	−12.9818	+	20.6605i	−0.522629	+	0.831760i	−0.998869	−	0.0475558i	$-0.984857\pi$
$617$	−12.9818	+	20.6605i	−0.522629	+	0.831760i	0.476239	+	0.879316i	$0.342000\pi$
$618$	−0.501131	−	1.87025i	−0.0201585	−	0.0752324i
$619$	−11.6637	−	20.2021i	−0.468803	−	0.811990i	0.530561	−	0.847647i	$-0.321981\pi$
$619$	−11.6637	−	20.2021i	−0.468803	−	0.811990i	−0.999364	+	0.0356564i	$0.988648\pi$
$620$	−10.9387	−	3.45928i	−0.439308	−	0.138928i
$621$	−22.7601	−	33.3830i	−0.913332	−	1.33961i
$622$	2.64315	+	23.4586i	0.105981	+	0.940604i
$623$	34.9441	−	19.5471i	1.40000	−	0.783138i
$624$	−0.670941	+	0.535057i	−0.0268591	+	0.0214194i
$625$	−4.86950	−	24.5212i	−0.194780	−	0.980847i
$626$	11.0360	+	4.33132i	0.441088	+	0.173114i
$627$	0.400684	−	0.465603i	0.0160018	−	0.0185944i
$628$	2.04458	−	4.68622i	0.0815875	−	0.187000i
$629$	−2.77287	+	1.33535i	−0.110562	+	0.0532437i
$630$	−2.35483	−	7.20406i	−0.0938186	−	0.287017i
$631$	12.1937	+	5.87216i	0.485423	+	0.233767i	0.660555	−	0.750778i	$-0.270321\pi$
$631$	12.1937	+	5.87216i	0.485423	+	0.233767i	−0.175132	+	0.984545i	$0.556035\pi$
$632$	−26.5528	+	22.8505i	−1.05621	+	0.908946i
$633$	5.05022	+	2.66912i	0.200728	+	0.106088i
$634$	3.07028	−	4.50327i	0.121936	−	0.178848i
$635$	0.812771	−	6.78098i	0.0322538	−	0.269095i
$636$			14.4098i			0.571386i
$637$	1.01824	+	6.31607i	0.0403440	+	0.250252i
$638$	−6.18273	+	6.18273i	−0.244777	+	0.244777i
$639$	1.97445	+	13.0996i	0.0781080	+	0.518213i
$640$	13.7686	+	16.2308i	0.544253	+	0.641580i
$641$	−22.4815	+	6.93462i	−0.887965	+	0.273901i	−0.704990	−	0.709217i	$-0.749049\pi$
$641$	−22.4815	+	6.93462i	−0.887965	+	0.273901i	−0.182974	+	0.983118i	$0.558573\pi$
$642$	8.64501	+	10.0457i	0.341191	+	0.396471i
$643$	−3.35658	−	9.59254i	−0.132370	−	0.378293i	0.858552	−	0.512726i	$-0.171364\pi$
$643$	−3.35658	−	9.59254i	−0.132370	−	0.378293i	−0.990923	+	0.134433i	$0.957079\pi$
$644$	24.9387	−	12.7503i	0.982724	−	0.502431i
$645$	−13.1859	−	9.12761i	−0.519193	−	0.359399i
$646$	−0.338053	−	0.861345i	−0.0133005	−	0.0338892i
$647$	23.9058	+	20.5726i	0.939835	+	0.808794i	0.981720	−	0.190329i	$-0.0609554\pi$
$647$	23.9058	+	20.5726i	0.939835	+	0.808794i	−0.0418852	+	0.999122i	$0.513336\pi$
$648$	1.25972	+	2.88730i	0.0494864	+	0.113424i
$649$	14.4394	+	4.45395i	0.566795	+	0.174833i
$650$	−0.473373	−	3.47429i	−0.0185672	−	0.136273i
$651$	7.35046	−	8.31040i	0.288087	−	0.325710i
$652$	−11.6946	+	1.31767i	−0.457996	+	0.0516038i
$653$	−1.63797	+	8.65690i	−0.0640988	+	0.338771i	−0.999906	−	0.0137430i	$-0.995625\pi$
$653$	−1.63797	+	8.65690i	−0.0640988	+	0.338771i	0.935807	+	0.352514i	$0.114673\pi$
$654$	1.05458	−	0.978504i	0.0412372	−	0.0382625i
$655$	20.8333	+	12.2259i	0.814023	+	0.477705i
$656$	−2.10687	−	1.21640i	−0.0822595	−	0.0474926i
$657$	2.27295	+	1.42819i	0.0886761	+	0.0557189i
$658$	−5.27997	−	11.3559i	−0.205835	−	0.442701i
$659$	−36.3871	−	8.30511i	−1.41744	−	0.323521i	−0.555916	−	0.831239i	$-0.687632\pi$
$659$	−36.3871	−	8.30511i	−1.41744	−	0.323521i	−0.861524	+	0.507718i	$0.830489\pi$
$660$	6.62143	+	10.7057i	0.257739	+	0.416720i
$661$	−3.03850	+	20.1592i	−0.118184	+	0.784100i	0.848698	+	0.528878i	$0.177387\pi$
$661$	−3.03850	+	20.1592i	−0.118184	+	0.784100i	−0.966882	+	0.255223i	$0.917851\pi$
$662$	14.4902	+	19.6335i	0.563176	+	0.763076i
$663$	0.308674	+	8.24949i	0.0119879	+	0.320384i
$664$	−0.519280	+	2.27511i	−0.0201520	+	0.0882916i
$665$	0.909687	−	0.0492872i	0.0352761	−	0.00191128i
$666$	0.112036	+	0.490860i	0.00434129	+	0.0190204i
$667$	−23.8747	+	6.39721i	−0.924432	+	0.247701i
$668$	2.19749	−	8.20115i	0.0850235	−	0.317312i
$669$	−11.6445	−	12.5498i	−0.450203	−	0.485204i
$670$	−6.70339	+	13.6709i	−0.258975	+	0.528152i
$671$	32.1285	+	25.6216i	1.24031	+	0.989111i
$672$	−17.1571	+	5.03813i	−0.661848	+	0.194350i
$673$	29.2263	+	3.29302i	1.12659	+	0.126936i	0.655534	−	0.755166i	$-0.272444\pi$
$673$	29.2263	+	3.29302i	1.12659	+	0.126936i	0.471058	+	0.882102i	$0.343872\pi$
$674$	6.43146	−	20.8503i	0.247730	−	0.803123i
$675$	26.7154	+	3.39446i	1.02828	+	0.130653i
$676$	−1.28291	−	17.1193i	−0.0493428	−	0.658434i
$677$	16.6228	+	7.25246i	0.638867	+	0.278735i	0.694254	−	0.719730i	$-0.255734\pi$
$677$	16.6228	+	7.25246i	0.638867	+	0.278735i	−0.0553870	+	0.998465i	$0.517639\pi$
$678$	10.8569	+	3.79898i	0.416955	+	0.145899i
$679$	29.4036	+	22.3239i	1.12841	+	0.856714i
$680$	45.7292	−	3.10098i	1.75363	−	0.118917i
$681$	1.65355	−	22.0651i	0.0633641	−	0.845535i
$682$	−4.50812	+	8.52978i	−0.172625	+	0.326622i
$683$	20.1714	−	3.81663i	0.771836	−	0.146039i	0.214947	−	0.976626i	$-0.431042\pi$
$683$	20.1714	−	3.81663i	0.771836	−	0.146039i	0.556890	+	0.830587i	$0.311995\pi$
$684$	0.358785	−	0.0540782i	0.0137185	−	0.00206773i
$685$	0.185521	−	0.673240i	0.00708840	−	0.0257232i
$686$	−3.20847	+	13.8438i	−0.122500	+	0.528559i
$687$	−7.63872	−	7.63872i	−0.291435	−	0.291435i
$688$	3.00582	−	4.07274i	0.114596	−	0.155272i
$689$	6.68492	+	4.55770i	0.254675	+	0.173635i
$690$	−0.449870	−	14.8386i	−0.0171263	−	0.564896i
$691$	20.8495	+	1.56246i	0.793154	+	0.0594386i	0.465143	−	0.885235i	$-0.346003\pi$
$691$	20.8495	+	1.56246i	0.793154	+	0.0594386i	0.328010	+	0.944674i	$0.393622\pi$
$692$	9.22145	−	3.22672i	0.350547	−	0.122662i
$693$	15.1362	−	2.07161i	0.574978	−	0.0786938i
$694$	−4.94087	−	10.2598i	−0.187553	−	0.389457i
$695$	16.4491	−	20.3291i	0.623951	−	0.771127i
$696$	9.91968	−	0.743377i	0.376005	−	0.0281777i
$697$	−21.4501	+	9.35859i	−0.812481	+	0.354482i
$698$	−4.64102	−	8.78125i	−0.175665	−	0.332375i
$699$	−5.87097	−	7.36196i	−0.222060	−	0.278455i
$700$	−4.65789	+	18.0785i	−0.176052	+	0.683304i
$701$	−17.4500	+	21.8816i	−0.659077	+	0.826457i	−0.993242	−	0.116058i	$-0.962974\pi$
$701$	−17.4500	+	21.8816i	−0.659077	+	0.826457i	0.334165	+	0.942514i	$0.391546\pi$
$702$	3.71126	+	0.702209i	0.140073	+	0.0265032i
$703$	−0.0604767	−	0.00226288i	−0.00228092	−	8.53461e-5i
$704$	8.58984	−	4.95935i	0.323742	−	0.186912i
$705$	15.9098	+	0.112828i	0.599199	+	0.00424935i
$706$	6.61129	−	1.50898i	0.248819	−	0.0567913i
$707$	−26.8010	−	13.3581i	−1.00796	−	0.502382i
$708$	−3.78381	−	6.02190i	−0.142204	−	0.226317i
$709$	−18.1610	+	19.5729i	−0.682050	+	0.735076i	−0.975282	−	0.220966i	$-0.929079\pi$
$709$	−18.1610	+	19.5729i	−0.682050	+	0.735076i	0.293231	+	0.956042i	$0.405269\pi$
$710$	−5.53232	+	12.4388i	−0.207624	+	0.466820i
$711$	−22.0961	−	3.33045i	−0.828668	−	0.124902i
$712$	39.5840	−	1.48113i	1.48347	−	0.0555077i
$713$	−23.0924	+	14.5099i	−0.864819	+	0.543402i
$714$	−6.29083	+	17.2242i	−0.235428	+	0.644599i
$715$	7.06085	+	0.314355i	0.264061	+	0.0117562i
$716$	10.0832	−	17.4646i	0.376826	−	0.652682i
$717$	−10.6651	−	2.85770i	−0.398295	−	0.106723i
$718$	−0.857329	+	22.9126i	−0.0319952	+	0.855091i
$719$	−8.55568	+	5.83316i	−0.319073	+	0.217540i	−0.712256	−	0.701920i	$-0.752326\pi$
$719$	−8.55568	+	5.83316i	−0.319073	+	0.217540i	0.393183	+	0.919460i	$0.371374\pi$
$720$	−0.474276	+	3.00201i	−0.0176752	+	0.111878i
$721$	4.33565	+	3.83483i	0.161468	+	0.142817i
$722$	−1.63028	+	14.4691i	−0.0606726	+	0.538484i
$723$	13.5822	−	7.17840i	0.505127	−	0.266967i
$724$	−4.62239	+	11.7777i	−0.171790	+	0.437713i
$725$	7.35785	−	14.7402i	0.273264	−	0.547438i
$726$	0.791600	−	0.310680i	0.0293790	−	0.0115304i
$727$	−10.0109	+	28.6096i	−0.371285	+	1.06107i	0.595029	+	0.803704i	$0.297141\pi$
$727$	−10.0109	+	28.6096i	−0.371285	+	1.06107i	−0.966314	+	0.257367i	$0.917145\pi$
$728$	−1.94754	+	6.02216i	−0.0721806	+	0.223196i
$729$	−8.95818	+	18.6019i	−0.331785	+	0.688958i
$730$	1.17924	+	2.49381i	0.0436458	+	0.0923001i
$731$	−14.3526	−	46.5299i	−0.530849	−	1.72097i
$732$	−3.59576	−	19.0040i	−0.132903	−	0.702410i
$733$	−15.6707	−	11.5655i	−0.578810	−	0.427181i	0.264672	−	0.964338i	$-0.414736\pi$
$733$	−15.6707	−	11.5655i	−0.578810	−	0.427181i	−0.843482	+	0.537157i	$0.819498\pi$
$734$	17.1099			0.631539
$735$	−14.1505	−	11.2119i	−0.521947	−	0.413559i
$736$	43.9558			1.62023
$737$	−24.6938	−	18.2249i	−0.909609	−	0.671322i
$738$	0.711768	+	3.76179i	0.0262006	+	0.138473i
$739$	−15.7634	−	51.1036i	−0.579865	−	1.87987i	−0.462086	−	0.886835i	$-0.652899\pi$
$739$	−15.7634	−	51.1036i	−0.579865	−	1.87987i	−0.117778	−	0.993040i	$-0.537577\pi$
$740$	0.417895	−	1.16765i	0.0153621	−	0.0429235i
$741$	−0.0704330	+	0.146256i	−0.00258742	+	0.00537283i
$742$	9.92122	+	14.9850i	0.364219	+	0.550117i
$743$	11.5380	−	32.9737i	0.423288	−	1.20969i	−0.512979	−	0.858401i	$-0.671458\pi$
$743$	11.5380	−	32.9737i	0.423288	−	1.20969i	0.936268	−	0.351287i	$-0.114256\pi$
$744$	10.2174	−	4.01002i	0.374586	−	0.147014i
$745$	−28.5622	−	42.5381i	−1.04644	−	1.55847i
$746$	1.04677	−	2.66713i	0.0383250	−	0.0976504i
$747$	−1.31606	+	0.695558i	−0.0481521	+	0.0254491i
$748$	−4.27942	+	37.9809i	−0.156471	+	1.38872i
$749$	−38.1275	−	10.7733i	−1.39315	−	0.393647i
$750$	7.60317	+	6.33256i	0.277629	+	0.231232i
$751$	16.5634	−	11.2928i	0.604408	−	0.412079i	−0.222083	−	0.975028i	$-0.571286\pi$
$751$	16.5634	−	11.2928i	0.604408	−	0.412079i	0.826492	+	0.562949i	$0.190333\pi$
$752$	−0.187774	+	5.01836i	−0.00684741	+	0.183001i
$753$	−4.92579	−	1.31986i	−0.179506	−	0.0480984i
$754$	1.15533	−	2.00108i	0.0420745	−	0.0728752i
$755$	−7.45850	+	6.82269i	−0.271443	+	0.248303i
$756$	−16.8810	−	10.9296i	−0.613957	−	0.397505i
$757$	9.20225	−	5.78216i	0.334461	−	0.210156i	−0.354322	−	0.935124i	$-0.615288\pi$
$757$	9.20225	−	5.78216i	0.334461	−	0.210156i	0.688783	+	0.724968i	$0.258145\pi$
$758$	19.5686	−	0.732206i	0.710764	−	0.0265949i
$759$	29.5897	+	4.45993i	1.07404	+	0.161885i
$760$	0.823505	+	0.366265i	0.0298717	+	0.0132858i
$761$	13.3751	−	14.4149i	0.484846	−	0.522540i	−0.442488	−	0.896775i	$-0.645904\pi$
$761$	13.3751	−	14.4149i	0.484846	−	0.522540i	0.927334	+	0.374234i	$0.122094\pi$
$762$	1.43814	+	2.28878i	0.0520982	+	0.0829138i
$763$	−1.01384	+	4.17945i	−0.0367034	+	0.151306i
$764$	−14.4180	+	3.29081i	−0.521624	+	0.119057i
$765$	20.5262	+	20.8194i	0.742126	+	0.752727i
$766$	−2.88586	+	1.66615i	−0.104270	+	0.0602005i
$767$	−3.99043	−	0.149312i	−0.144086	−	0.00539133i
$768$	−14.7779	−	2.79614i	−0.533253	−	0.100897i
$769$	−5.43361	+	6.81353i	−0.195941	+	0.245702i	−0.870090	−	0.492893i	$-0.835939\pi$
$769$	−5.43361	+	6.81353i	−0.195941	+	0.245702i	0.674149	+	0.738596i	$0.264511\pi$
$770$	14.2567	+	6.57419i	0.513775	+	0.236917i
$771$	19.9644	+	25.0346i	0.719001	+	0.901599i
$772$	−1.09225	−	2.06665i	−0.0393111	−	0.0743802i
$773$	−14.8564	+	6.48177i	−0.534347	+	0.233133i	−0.649699	−	0.760192i	$-0.725105\pi$
$773$	−14.8564	+	6.48177i	−0.534347	+	0.233133i	0.115352	+	0.993325i	$0.463200\pi$
$774$	−7.94360	+	0.595290i	−0.285527	+	0.0213973i
$775$	2.96397	−	17.9348i	0.106469	−	0.644238i
$776$	15.8468	+	32.9063i	0.568868	+	1.18127i
$777$	0.868003	+	0.827608i	0.0311394	+	0.0296903i
$778$	6.61568	−	2.31493i	0.237184	−	0.0829942i
$779$	−0.458905	−	0.0343902i	−0.0164420	−	0.00123216i
$780$	−2.42243	−	2.27986i	−0.0867368	−	0.0816322i
$781$	−22.6728	−	15.4581i	−0.811297	−	0.553133i
$782$	26.7668	−	36.2678i	0.957180	−	1.29693i
$783$	12.5487	+	12.5487i	0.448454	+	0.448454i
$784$	3.67264	−	4.35713i	0.131166	−	0.155612i
$785$	7.81002	+	2.15216i	0.278751	+	0.0768140i
$786$	−9.45396	+	1.42496i	−0.337212	+	0.0508265i
$787$	41.8697	−	7.92217i	1.49249	−	0.282395i	0.625306	−	0.780379i	$-0.284974\pi$
$787$	41.8697	−	7.92217i	1.49249	−	0.282395i	0.867186	+	0.497984i	$0.165926\pi$
$788$	−14.9138	+	28.2183i	−0.531283	+	1.00524i
$789$	0.805502	−	10.7487i	0.0286766	−	0.382663i
$790$	−17.2987	−	15.1016i	−0.615461	−	0.537291i
$791$	−33.3318	+	8.44779i	−1.18514	+	0.300369i
$792$	14.2659	+	4.99185i	0.506916	+	0.177378i
$793$	−9.95356	−	4.34269i	−0.353461	−	0.154214i
$794$	−0.375790	−	5.01456i	−0.0133363	−	0.177960i
$795$	−22.6005	+	3.24273i	−0.801557	+	0.115008i
$796$	−5.37152	+	17.4140i	−0.190388	+	0.617224i
$797$	−6.34197	−	0.714568i	−0.224644	−	0.0253113i	−0.00107504	−	0.999999i	$-0.500342\pi$
$797$	−6.34197	−	0.714568i	−0.224644	−	0.0253113i	−0.223569	+	0.974688i	$0.571771\pi$
$798$	−0.267630	+	0.241644i	−0.00947398	+	0.00855410i
$799$	37.7693	+	30.1200i	1.33618	+	1.06557i
$800$	−19.4237	+	21.9337i	−0.686731	+	0.775474i
$801$	17.1862	+	18.5223i	0.607243	+	0.654452i
$802$	−0.274821	+	1.02564i	−0.00970425	+	0.0362168i
$803$	−5.37099	+	1.43915i	−0.189538	+	0.0507866i
$804$	3.21431	+	14.0828i	0.113360	+	0.496662i
$805$	25.6098	+	36.2449i	0.902626	+	1.27746i
$806$	0.567335	−	2.48566i	0.0199835	−	0.0875535i
$807$	0.443734	+	11.8590i	0.0156202	+	0.417458i
$808$	−17.5922	−	23.8365i	−0.618890	−	0.838567i
$809$	−3.93717	+	26.1214i	−0.138424	+	0.918380i	0.806534	+	0.591188i	$0.201341\pi$
$809$	−3.93717	+	26.1214i	−0.138424	+	0.918380i	−0.944958	+	0.327193i	$0.893897\pi$
$810$	−1.75616	+	1.08618i	−0.0617053	+	0.0381644i
$811$	−1.18512	−	0.270497i	−0.0416154	−	0.00949844i	0.201663	−	0.979455i	$-0.435366\pi$
$811$	−1.18512	−	0.270497i	−0.0416154	−	0.00949844i	−0.243278	+	0.969957i	$0.578223\pi$
$812$	−9.72177	+	7.53916i	−0.341167	+	0.264573i
$813$	4.84831	+	3.04639i	0.170038	+	0.106842i
$814$	−0.903190	−	0.521457i	−0.0316568	−	0.0182771i
$815$	−4.69835	−	18.0454i	−0.164576	−	0.632103i
$816$	5.39024	−	5.00141i	0.188696	−	0.175084i
$817$	0.178011	−	0.940810i	0.00622781	−	0.0329148i
$818$	−1.08360	+	0.122092i	−0.0378872	+	0.00426886i
$819$	−3.72199	+	1.56407i	−0.130057	+	0.0546530i
$820$	3.50748	−	8.75386i	0.122487	−	0.305698i
$821$	−10.3521	−	3.19320i	−0.361291	−	0.111444i	0.108795	−	0.994064i	$-0.465301\pi$
$821$	−10.3521	−	3.19320i	−0.361291	−	0.111444i	−0.470086	+	0.882621i	$0.655777\pi$
$822$	0.110530	+	0.253336i	0.00385516	+	0.00883612i
$823$	9.01513	+	7.75814i	0.314248	+	0.270432i	0.795242	−	0.606292i	$-0.207344\pi$
$823$	9.01513	+	7.75814i	0.314248	+	0.270432i	−0.480995	+	0.876723i	$0.659724\pi$
$824$	2.09208	+	5.33053i	0.0728810	+	0.185698i
$825$	−15.3009	+	12.7943i	−0.532709	+	0.445440i
$826$	−8.08096	−	3.65711i	−0.281172	−	0.127247i
$827$	−4.37445	−	12.5014i	−0.152114	−	0.434718i	0.842458	−	0.538761i	$-0.181108\pi$
$827$	−4.37445	−	12.5014i	−0.152114	−	0.434718i	−0.994573	+	0.104044i	$0.966822\pi$
$828$	11.5294	+	13.3974i	0.400675	+	0.465592i
$829$	−35.7797	+	11.0366i	−1.24268	+	0.383316i	−0.845277	−	0.534328i	$-0.820565\pi$
$829$	−35.7797	+	11.0366i	−1.24268	+	0.383316i	−0.397403	+	0.917644i	$0.630089\pi$
$830$	−1.52456	−	0.125129i	−0.0529184	−	0.00434328i
$831$	3.32491	+	22.0593i	0.115340	+	0.765229i
$832$	−1.85344	+	1.85344i	−0.0642566	+	0.0642566i
$833$	−12.7446	−	53.3156i	−0.441575	−	1.84728i
$834$			10.3503i			0.358401i
$835$	13.3573	+	1.60101i	0.462248	+	0.0554052i
$836$	−0.423381	+	0.620985i	−0.0146429	+	0.0214772i
$837$	17.3124	+	9.14985i	0.598403	+	0.316265i
$838$	21.8312	−	18.7873i	0.754147	−	0.648996i
$839$	8.39018	+	4.04050i	0.289661	+	0.139493i	0.573072	−	0.819505i	$-0.305752\pi$
$839$	8.39018	+	4.04050i	0.289661	+	0.139493i	−0.283411	+	0.958999i	$0.591466\pi$
$840$	−7.41527	−	16.2489i	−0.255851	−	0.560639i
$841$	−16.3468	+	7.87218i	−0.563681	+	0.271455i
$842$	7.07392	−	16.2136i	0.243784	−	0.558758i
$843$	18.3102	−	21.2768i	0.630637	−	0.732813i
$844$	−6.50587	−	2.55336i	−0.223941	−	0.0878904i
$845$	26.5614	−	5.86460i	0.913739	−	0.201748i
$846$	6.17880	−	4.92743i	0.212431	−	0.169408i
$847$	−1.46045	+	2.08081i	−0.0501818	+	0.0714974i
$848$	−0.806887	−	7.16132i	−0.0277086	−	0.245921i
$849$	−18.9697	−	27.8234i	−0.651038	−	0.954897i
$850$	6.26939	+	29.3829i	0.215038	+	1.00783i
$851$	−1.47407	−	2.55316i	−0.0505304	−	0.0875212i
$852$	3.34274	+	12.4753i	0.114521	+	0.427396i
$853$	4.81879	−	7.66906i	0.164992	−	0.262584i	−0.753987	−	0.656889i	$-0.771872\pi$
$853$	4.81879	−	7.66906i	0.164992	−	0.262584i	0.918979	+	0.394305i	$0.129015\pi$
$854$	−16.8237	−	17.2869i	−0.575694	−	0.591547i
$855$	0.165556	+	0.550553i	0.00566191	+	0.0188285i
$856$	−28.7333	−	26.6606i	−0.982084	−	0.911240i
$857$	19.6126	−	14.4748i	0.669954	−	0.494448i	−0.204933	−	0.978776i	$-0.565698\pi$
$857$	19.6126	−	14.4748i	0.669954	−	0.494448i	0.874887	+	0.484328i	$0.160936\pi$
$858$	−2.25081	+	1.66117i	−0.0768413	+	0.0567114i
$859$	4.41747	+	4.09882i	0.150722	+	0.139850i	0.751930	−	0.659243i	$-0.229123\pi$
$859$	4.41747	+	4.09882i	0.150722	+	0.139850i	−0.601208	+	0.799093i	$0.705314\pi$
$860$	17.2822	+	9.29128i	0.589317	+	0.316830i
$861$	6.36045	+	6.53560i	0.216764	+	0.222733i
$862$	−4.09385	+	6.51532i	−0.139437	+	0.221913i
$863$	−8.51318	−	31.7716i	−0.289792	−	1.08152i	−0.945266	−	0.326301i	$-0.894198\pi$
$863$	−8.51318	−	31.7716i	−0.289792	−	1.08152i	0.655474	−	0.755218i	$-0.272469\pi$
$864$	−15.7800	−	27.3317i	−0.536845	−	0.929844i
$865$	7.13599	+	13.7369i	0.242631	+	0.467068i
$866$	−8.39731	−	12.3166i	−0.285352	−	0.418535i
$867$	−5.72437	−	50.8052i	−0.194410	−	1.72543i
$868$	−7.79846	+	11.1110i	−0.264697	+	0.377132i
$869$	36.1885	−	28.8593i	1.22761	−	0.978986i
$870$	1.40585	+	6.36723i	0.0476628	+	0.215869i
$871$	7.54988	+	2.96311i	0.255818	+	0.100401i
$872$	−2.77528	+	3.22493i	−0.0939828	+	0.109210i
$873$	−9.31640	+	21.3534i	−0.315312	+	0.722703i
$874$	0.798589	−	0.384580i	0.0270127	−	0.0130086i
$875$	−29.4027	−	3.23715i	−0.993994	−	0.109436i
$876$	2.35791	+	1.13551i	0.0796665	+	0.0383653i
$877$	−2.10242	+	1.80928i	−0.0709938	+	0.0610951i	−0.687069	−	0.726593i	$-0.741103\pi$
$877$	−2.10242	+	1.80928i	−0.0709938	+	0.0610951i	0.616075	+	0.787688i	$0.288722\pi$
$878$	−4.18027	−	2.20933i	−0.141077	−	0.0745614i
$879$	−10.3083	+	15.1195i	−0.347689	+	0.509967i
$880$	−3.89016	−	4.94971i	−0.131137	−	0.166855i
$881$			26.7987i			0.902872i	0.892304	+	0.451436i	$0.149088\pi$
$881$			26.7987i			0.902872i	−0.892304	+	0.451436i	$0.850912\pi$
$882$	−8.96732	+	0.0918153i	−0.301945	+	0.00309158i
$883$	18.7649	−	18.7649i	0.631489	−	0.631489i	−0.316953	−	0.948441i	$-0.602660\pi$
$883$	18.7649	−	18.7649i	0.631489	−	0.631489i	0.948441	+	0.316953i	$0.102660\pi$
$884$	−1.50540	−	9.98771i	−0.0506322	−	0.335923i
$885$	8.59331	−	7.28971i	0.288861	−	0.245041i
$886$	16.3321	−	5.03779i	0.548688	−	0.169248i
$887$	21.0730	+	24.4873i	0.707563	+	0.822203i	0.990583	−	0.136911i	$-0.0437175\pi$
$887$	21.0730	+	24.4873i	0.707563	+	0.822203i	−0.283021	+	0.959114i	$0.591337\pi$
$888$	0.391876	+	1.11992i	0.0131505	+	0.0375819i
$889$	−7.36198	−	3.33173i	−0.246913	−	0.111743i
$890$	4.64624	+	25.5464i	0.155742	+	0.856318i
$891$	−1.52065	−	3.87454i	−0.0509436	−	0.129802i
$892$	15.8770	+	13.6632i	0.531601	+	0.457479i
$893$	0.379875	+	0.870682i	0.0127120	+	0.0291363i
$894$	19.3787	+	5.97753i	0.648120	+	0.199919i
$895$	29.6607	+	11.8844i	0.991448	+	0.397251i
$896$	23.2171	−	9.75638i	0.775629	−	0.325938i
$897$	−7.85813	+	0.885398i	−0.262375	+	0.0295626i
$898$	−2.67650	+	14.1457i	−0.0893161	+	0.472047i
$899$	8.78126	−	8.14782i	0.292872	−	0.271745i
$900$	−11.7800	−	0.167089i	−0.392666	−	0.00556964i
$901$	−60.0376	−	34.6627i	−2.00014	−	1.15478i
$902$	−6.71487	−	4.21923i	−0.223581	−	0.140485i
$903$	−14.9946	+	11.6282i	−0.498988	+	0.386962i
$904$	−33.1652	−	7.56974i	−1.10306	−	0.251766i
$905$	−19.5124	−	4.59940i	−0.648614	−	0.152889i
$906$	0.596295	−	3.95616i	0.0198106	−	0.131435i
$907$	−33.7524	−	45.7328i	−1.12073	−	1.51853i	−0.826620	−	0.562761i	$-0.809739\pi$
$907$	−33.7524	−	45.7328i	−1.12073	−	1.51853i	−0.294109	−	0.955772i	$-0.595023\pi$
$908$	1.01229	+	27.0539i	0.0335939	+	0.897816i
$909$	4.20505	−	18.4235i	0.139473	−	0.611070i
$910$	−4.08882	−	0.703019i	−0.135543	−	0.0233048i
$911$	4.57791	+	20.0571i	0.151673	+	0.664522i	0.992399	+	0.123062i	$0.0392713\pi$
$911$	4.57791	+	20.0571i	0.151673	+	0.664522i	−0.840726	+	0.541461i	$0.817872\pi$
$912$	0.139665	−	0.0374232i	0.00462478	−	0.00123921i
$913$	0.798043	−	2.97834i	0.0264114	−	0.0985686i
$914$	16.3195	+	17.5883i	0.539802	+	0.581768i
$915$	28.9969	−	9.91623i	0.958610	−	0.327820i
$916$	10.3338	+	8.24095i	0.341439	+	0.272289i
$917$	21.2137	−	19.1540i	0.700539	−	0.632519i
$918$	−32.1605	−	3.62361i	−1.06145	−	0.119597i
$919$	−6.52199	+	21.1438i	−0.215140	+	0.697468i	0.782095	+	0.623159i	$0.214151\pi$
$919$	−6.52199	+	21.1438i	−0.215140	+	0.697468i	−0.997235	+	0.0743088i	$0.976325\pi$
$920$	6.23570	+	43.4602i	0.205585	+	1.43284i
$921$	1.29965	+	17.3426i	0.0428250	+	0.571460i
$922$	−16.3863	−	7.14928i	−0.539655	−	0.235449i
$923$	6.84475	+	2.39508i	0.225298	+	0.0788351i
$924$	14.4378	−	3.65918i	0.474967	−	0.120378i
$925$	1.92539	+	0.392667i	0.0633064	+	0.0129108i
$926$	−0.472779	+	6.30880i	−0.0155365	+	0.207320i
$927$	−1.70680	+	3.22942i	−0.0560586	+	0.106068i
$928$	−18.9703	+	3.58936i	−0.622729	+	0.117827i
$929$	23.3712	−	3.52264i	0.766783	−	0.115574i	0.246008	−	0.969268i	$-0.420881\pi$
$929$	23.3712	−	3.52264i	0.766783	−	0.115574i	0.520775	+	0.853694i	$0.325643\pi$
$930$	3.55314	+	6.25626i	0.116512	+	0.205151i
$931$	0.268315	−	1.04401i	0.00879367	−	0.0342159i
$932$	8.14663	+	8.14663i	0.266852	+	0.266852i
$933$	−21.0724	+	28.5521i	−0.689880	+	0.934754i
$934$	−16.4020	−	11.1827i	−0.536689	−	0.365908i
$935$	−60.5326	+	1.83520i	−1.97963	+	0.0600175i
$936$	−3.98294	−	0.298480i	−0.130187	−	0.00975614i
$937$	−30.7577	+	10.7626i	−1.00481	+	0.351599i	−0.782011	−	0.623265i	$-0.785806\pi$
$937$	−30.7577	+	10.7626i	−1.00481	+	0.351599i	−0.222801	+	0.974864i	$0.571520\pi$
$938$	13.0387	+	12.4319i	0.425729	+	0.405916i
$939$	7.73238	+	16.0564i	0.252337	+	0.523982i
$940$	−19.3591	+	2.04233i	−0.631425	+	0.0666134i
$941$	15.9316	−	1.19391i	0.519356	−	0.0389204i	0.187526	−	0.982260i	$-0.439953\pi$
$941$	15.9316	−	1.19391i	0.519356	−	0.0389204i	0.331830	+	0.943339i	$0.392334\pi$
$942$	−2.93886	+	1.28221i	−0.0957534	+	0.0417768i
$943$	−10.4752	−	19.8200i	−0.341119	−	0.645428i
$944$	2.21766	+	2.78086i	0.0721787	+	0.0905093i
$945$	13.3432	−	28.9359i	0.434055	−	0.941285i
$946$	10.2879	−	12.9006i	0.334488	−	0.419434i
$947$	9.44387	+	1.78688i	0.306885	+	0.0580657i	0.337073	−	0.941479i	$-0.390563\pi$
$947$	9.44387	+	1.78688i	0.306885	+	0.0580657i	−0.0301884	+	0.999544i	$0.509611\pi$
$948$	−21.7701	−	0.814579i	−0.707060	−	0.0264563i
$949$	1.27257	−	0.734717i	0.0413093	−	0.0238499i
$950$	−0.160986	+	0.568434i	−0.00522308	+	0.0184424i
$951$	7.98754	−	1.82310i	0.259014	−	0.0591182i
$952$	12.7846	−	52.7033i	0.414351	−	1.70812i
$953$	22.2540	+	35.4171i	0.720879	+	1.14727i	0.983242	+	0.182304i	$0.0583554\pi$
$953$	22.2540	+	35.4171i	0.720879	+	1.14727i	−0.262363	+	0.964969i	$0.584502\pi$
$954$	−7.71394	+	8.31366i	−0.249748	+	0.269165i
$955$	−8.40590	−	21.8727i	−0.272009	−	0.707785i
$956$	13.3584	+	2.01346i	0.432042	+	0.0651199i
$957$	−13.1344	+	0.491454i	−0.424574	+	0.0158864i
$958$	−12.5123	+	7.86198i	−0.404253	+	0.254009i
$959$	−0.693597	−	0.449068i	−0.0223974	−	0.0145012i
$960$	0.328988	−	7.38952i	0.0106180	−	0.238496i
$961$	−8.89115	+	15.3999i	−0.286811	+	0.496772i
$962$	0.266215	+	0.0713320i	0.00858310	+	0.00229984i
$963$	0.934880	−	24.9852i	0.0301261	−	0.805137i
$964$	−15.5303	+	10.5884i	−0.500196	+	0.341028i
$965$	2.99555	−	2.17817i	0.0964302	−	0.0701179i
$966$	−16.9035	−	4.77624i	−0.543861	−	0.153673i
$967$	3.18891	−	28.3023i	0.102548	−	0.910141i	−0.832114	−	0.554605i	$-0.812870\pi$
$967$	3.18891	−	28.3023i	0.102548	−	0.910141i	0.934662	−	0.355537i	$-0.115702\pi$
$968$	−2.22356	+	1.17518i	−0.0714678	+	0.0377718i
$969$	0.508163	−	1.29478i	0.0163246	−	0.0415943i
$970$	−19.8761	+	13.3458i	−0.638184	+	0.428509i
$971$	57.7988	−	22.6844i	1.85485	−	0.727976i	0.896011	−	0.444033i	$-0.146453\pi$
$971$	57.7988	−	22.6844i	1.85485	−	0.727976i	0.958841	−	0.283943i	$-0.0916427\pi$
$972$	6.88432	−	19.6742i	0.220815	−	0.631052i
$973$	−17.0813	−	25.7995i	−0.547600	−	0.827095i
$974$	4.43474	−	9.20884i	0.142098	−	0.295070i
$975$	3.03063	−	4.31241i	0.0970578	−	0.138108i
$976$	2.85115	+	9.24319i	0.0912630	+	0.295867i
$977$	−1.52590	−	8.06460i	−0.0488180	−	0.258009i	0.949652	−	0.313307i	$-0.101437\pi$
$977$	−1.52590	−	8.06460i	−0.0488180	−	0.258009i	−0.998470	+	0.0552976i	$0.982389\pi$
$978$	5.93828	+	4.38265i	0.189885	+	0.140142i
$979$	−52.3387			−1.67275
$980$	18.7405	+	11.6933i	0.598643	+	0.373530i
$981$	−2.71396			−0.0866501
$982$	−14.7698	−	10.9006i	−0.471325	−	0.347853i
$983$	4.93474	+	26.0807i	0.157394	+	0.831845i	0.968891	+	0.247489i	$0.0796054\pi$
$983$	4.93474	+	26.0807i	0.157394	+	0.831845i	−0.811497	+	0.584356i	$0.801347\pi$
$984$	2.65935	+	8.62141i	0.0847771	+	0.274840i
$985$	−47.6140	−	17.0408i	−1.51711	−	0.542966i
$986$	−8.59033	+	17.8380i	−0.273572	+	0.568078i
$987$	5.79262	−	17.9119i	0.184381	−	0.570141i
$988$	0.0655989	−	0.187471i	0.00208698	−	0.00596424i
$989$	43.4197	−	17.0410i	1.38066	−	0.541871i
$990$	−1.91086	+	9.72123i	−0.0607311	+	0.308961i
$991$	−11.3199	+	28.8427i	−0.359590	+	0.916220i	0.630552	+	0.776147i	$0.282829\pi$
$991$	−11.3199	+	28.8427i	−0.359590	+	0.916220i	−0.990141	+	0.140072i	$0.955266\pi$
$992$	−18.8345	+	9.95432i	−0.597996	+	0.316050i
$993$	−4.10692	+	36.4499i	−0.130329	+	1.15670i
$994$	12.0655	+	10.6718i	0.382694	+	0.338488i
$995$	−28.5211	−	4.50595i	−0.904180	−	0.142848i
$996$	−1.19907	+	0.817509i	−0.0379938	+	0.0259038i
$997$	−0.935481	+	25.0013i	−0.0296270	+	0.791798i	0.902719	+	0.430231i	$0.141568\pi$
$997$	−0.935481	+	25.0013i	−0.0296270	+	0.791798i	−0.932346	+	0.361567i	$0.882242\pi$
$998$	−10.7522	−	2.88104i	−0.340355	−	0.0911978i
$999$	−1.05837	+	1.83315i	−0.0334853	+	0.0579982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.152.17	yes	624
5.3	odd	4	inner	245.2.x.a.103.17	✓	624
49.10	odd	42	inner	245.2.x.a.157.17	yes	624
245.108	even	84	inner	245.2.x.a.108.17	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.17	✓	624	5.3	odd	4	inner
245.2.x.a.108.17	yes	624	245.108	even	84	inner
245.2.x.a.152.17	yes	624	1.1	even	1	trivial
245.2.x.a.157.17	yes	624	49.10	odd	42	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.617374 + 0.455643i) q^{2} +(0.214434 + 1.13331i) q^{3} +(-0.415970 - 1.34854i) q^{4} +(2.02146 - 0.955882i) q^{5} +(-0.384000 + 0.797384i) q^{6} +(-0.358764 - 2.62131i) q^{7} +(0.864496 - 2.47059i) q^{8} +(1.55421 - 0.609981i) q^{9} +(1.68354 + 0.330926i) q^{10} +(-1.26351 + 3.21938i) q^{11} +(1.43912 - 0.760597i) q^{12} +(0.102330 - 0.908200i) q^{13} +(0.972892 - 1.78180i) q^{14} +(1.51678 + 2.08597i) q^{15} +(-0.672617 + 0.458583i) q^{16} +(-0.292814 + 7.82562i) q^{17} +(1.23746 + 0.331576i) q^{18} +(-0.0769953 + 0.133360i) q^{19} +(-2.12991 - 2.32840i) q^{20} +(2.89384 - 0.968691i) q^{21} +(-2.24695 + 1.41185i) q^{22} +(-7.49628 + 0.280491i) q^{23} +(2.98532 + 0.449965i) q^{24} +(3.17258 - 3.86455i) q^{25} +(0.476990 - 0.514073i) q^{26} +(2.86554 + 4.56049i) q^{27} +(-3.38572 + 1.57420i) q^{28} +(3.21231 - 0.733188i) q^{29} +(-0.0140341 + 1.97894i) q^{30} +(3.14854 - 1.81781i) q^{31} +(-5.85549 - 0.219097i) q^{32} +(-3.91950 - 0.741610i) q^{33} +(-3.74646 + 4.69792i) q^{34} +(-3.23089 - 4.95594i) q^{35} +(-1.46909 - 1.84218i) q^{36} +(0.183639 + 0.347461i) q^{37} +(-0.108299 + 0.0472505i) q^{38} +(1.05122 - 0.0787778i) q^{39} +(-0.614049 - 5.82054i) q^{40} +(1.29664 + 2.69249i) q^{41} +(2.22796 + 0.720512i) q^{42} +(-5.86900 + 2.05365i) q^{43} +(4.86705 + 0.364735i) q^{44} +(2.55869 - 2.71869i) q^{45} +(-4.75582 - 3.24246i) q^{46} +(3.66318 - 4.96343i) q^{47} +(-0.663950 - 0.663950i) q^{48} +(-6.74258 + 1.88086i) q^{49} +(3.71952 - 0.940311i) q^{50} +(-8.93166 + 1.34623i) q^{51} +(-1.26731 + 0.239788i) q^{52} +(-4.13653 + 7.82670i) q^{53} +(-0.308841 + 4.12119i) q^{54} +(0.523209 + 7.71560i) q^{55} +(-6.78633 - 1.37976i) q^{56} +(-0.167649 - 0.0586628i) q^{57} +(2.31727 + 1.01101i) q^{58} +(-0.326512 - 4.35700i) q^{59} +(2.18208 - 2.91315i) q^{60} +(3.50233 - 11.3543i) q^{61} +(2.77210 + 0.312340i) q^{62} +(-2.15654 - 3.85522i) q^{63} +(-2.24226 - 1.78815i) q^{64} +(-0.661277 - 1.93370i) q^{65} +(-2.08189 - 2.24374i) q^{66} +(-2.29681 + 8.57181i) q^{67} +(10.6750 - 2.86035i) q^{68} +(-1.92534 - 8.43549i) q^{69} +(0.263468 - 4.53180i) q^{70} +(-1.76559 + 7.73555i) q^{71} +(-0.163406 - 4.36713i) q^{72} +(0.954739 + 1.29362i) q^{73} +(-0.0449445 + 0.298187i) q^{74} +(5.06005 + 2.76683i) q^{75} +(0.211869 + 0.0483577i) q^{76} +(8.89230 + 2.15707i) q^{77} +(0.684889 + 0.430344i) q^{78} +(-11.5906 - 6.69184i) q^{79} +(-0.921316 + 1.56995i) q^{80} +(-0.882233 + 0.818593i) q^{81} +(-0.426306 + 2.25308i) q^{82} +(-0.885951 + 0.0998227i) q^{83} +(-2.51007 - 3.49951i) q^{84} +(6.88846 + 16.0991i) q^{85} +(-4.55910 - 1.40630i) q^{86} +(1.51976 + 3.48333i) q^{87} +(6.86145 + 5.90475i) q^{88} +(5.52892 + 14.0875i) q^{89} +(2.81842 - 0.512599i) q^{90} +(-2.41739 + 0.0575912i) q^{91} +(3.49648 + 9.99237i) q^{92} +(2.73530 + 3.17848i) q^{93} +(4.52311 - 1.39519i) q^{94} +(-0.0281665 + 0.343180i) q^{95} +(-1.00731 - 6.68308i) q^{96} +(-9.86671 + 9.86671i) q^{97} +(-5.01970 - 1.91101i) q^{98} +5.77429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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