LMFDB - Embedded newform 245.2.x.a.103.17

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			103.17
Character	$\chi$	$=$	245.103
Dual form			245.2.x.a.157.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.455643 - 0.617374i) q^{2} +(-1.13331 + 0.214434i) q^{3} +(0.415970 + 1.34854i) q^{4} +(1.85641 + 1.24649i) q^{5} +(-0.384000 + 0.797384i) q^{6} +(-2.62131 + 0.358764i) q^{7} +(2.47059 + 0.864496i) q^{8} +(-1.55421 + 0.609981i) q^{9} +(1.61541 - 0.578147i) q^{10} +(-1.26351 + 3.21938i) q^{11} +(-0.760597 - 1.43912i) q^{12} +(0.908200 + 0.102330i) q^{13} +(-0.972892 + 1.78180i) q^{14} +(-2.37119 - 1.01458i) q^{15} +(-0.672617 + 0.458583i) q^{16} +(7.82562 + 0.292814i) q^{17} +(-0.331576 + 1.23746i) q^{18} +(0.0769953 - 0.133360i) q^{19} +(-0.908729 + 3.02195i) q^{20} +(2.89384 - 0.968691i) q^{21} +(1.41185 + 2.24695i) q^{22} +(-0.280491 - 7.49628i) q^{23} +(-2.98532 - 0.449965i) q^{24} +(1.89253 + 4.62799i) q^{25} +(0.476990 - 0.514073i) q^{26} +(4.56049 - 2.86554i) q^{27} +(-1.57420 - 3.38572i) q^{28} +(-3.21231 + 0.733188i) q^{29} +(-1.70679 + 1.00162i) q^{30} +(3.14854 - 1.81781i) q^{31} +(-0.219097 + 5.85549i) q^{32} +(0.741610 - 3.91950i) q^{33} +(3.74646 - 4.69792i) q^{34} +(-5.31343 - 2.60142i) q^{35} +(-1.46909 - 1.84218i) q^{36} +(0.347461 - 0.183639i) q^{37} +(-0.0472505 - 0.108299i) q^{38} +(-1.05122 + 0.0787778i) q^{39} +(3.50884 + 4.68442i) q^{40} +(1.29664 + 2.69249i) q^{41} +(0.720512 - 2.22796i) q^{42} +(-2.05365 - 5.86900i) q^{43} +(-4.86705 - 0.364735i) q^{44} +(-3.64558 - 0.804924i) q^{45} +(-4.75582 - 3.24246i) q^{46} +(-4.96343 - 3.66318i) 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} +(0.239788 + 1.26731i) q^{52} +(-7.82670 - 4.13653i) q^{53} +(0.308841 - 4.12119i) q^{54} +(-6.35852 + 4.40154i) q^{55} +(-6.78633 - 1.37976i) q^{56} +(-0.0586628 + 0.167649i) q^{57} +(-1.01101 + 2.31727i) q^{58} +(0.326512 + 4.35700i) q^{59} +(0.381865 - 3.61968i) q^{60} +(3.50233 - 11.3543i) q^{61} +(0.312340 - 2.77210i) q^{62} +(3.85522 - 2.15654i) q^{63} +(2.24226 + 1.78815i) q^{64} +(1.55844 + 1.32203i) q^{65} +(-2.08189 - 2.24374i) q^{66} +(8.57181 + 2.29681i) q^{67} +(2.86035 + 10.6750i) q^{68} +(1.92534 + 8.43549i) q^{69} +(-4.02708 + 2.09506i) q^{70} +(-1.76559 + 7.73555i) q^{71} +(-4.36713 + 0.163406i) q^{72} +(-1.29362 + 0.954739i) q^{73} +(0.0449445 - 0.298187i) q^{74} +(-3.13723 - 4.83914i) q^{75} +(0.211869 + 0.0483577i) q^{76} +(2.15707 - 8.89230i) q^{77} +(-0.430344 + 0.684889i) q^{78} +(11.5906 + 6.69184i) q^{79} +(-1.82027 + 0.0129089i) q^{80} +(-0.882233 + 0.818593i) q^{81} +(2.25308 + 0.426306i) q^{82} +(-0.0998227 - 0.885951i) q^{83} +(2.51007 + 3.49951i) q^{84} +(14.1626 + 10.2981i) q^{85} +(-4.55910 - 1.40630i) q^{86} +(3.48333 - 1.51976i) q^{87} +(-5.90475 + 6.86145i) q^{88} +(-5.52892 - 14.0875i) q^{89} +(-2.15802 + 1.88393i) q^{90} +(-2.41739 + 0.0575912i) q^{91} +(9.99237 - 3.49648i) q^{92} +(-3.17848 + 2.73530i) q^{93} +(-4.52311 + 1.39519i) q^{94} +(0.309166 - 0.151597i) q^{95} +(-1.00731 - 6.68308i) q^{96} +(9.86671 + 9.86671i) q^{97} +(1.91101 - 5.01970i) 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.455643	−	0.617374i	0.322188	−	0.436550i	−0.613331	−	0.789826i	$-0.710171\pi$
$2$	0.455643	−	0.617374i	0.322188	−	0.436550i	0.935519	+	0.353277i	$0.114933\pi$
$3$	−1.13331	+	0.214434i	−0.654318	+	0.123804i	−0.502463	−	0.864599i	$-0.667573\pi$
$3$	−1.13331	+	0.214434i	−0.654318	+	0.123804i	−0.151856	+	0.988403i	$0.548525\pi$
$4$	0.415970	+	1.34854i	0.207985	+	0.674271i
$5$	1.85641	+	1.24649i	0.830213	+	0.557447i
$5$	1.85641	+	1.24649i	0.830213	+	0.557447i
$6$	−0.384000	+	0.797384i	−0.156767	+	0.325530i
$7$	−2.62131	+	0.358764i	−0.990764	+	0.135600i
$7$	−2.62131	+	0.358764i	−0.990764	+	0.135600i
$8$	2.47059	+	0.864496i	0.873484	+	0.305645i
$9$	−1.55421	+	0.609981i	−0.518069	+	0.203327i
$10$	1.61541	−	0.578147i	0.510838	−	0.182826i
$11$	−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	$0.944465\pi$
$12$	−0.760597	−	1.43912i	−0.219566	−	0.415438i
$13$	0.908200	+	0.102330i	0.251889	+	0.0283811i	0.237006	−	0.971508i	$-0.423834\pi$
$13$	0.908200	+	0.102330i	0.251889	+	0.0283811i	0.0148831	+	0.999889i	$0.495262\pi$
$14$	−0.972892	+	1.78180i	−0.260016	+	0.476206i
$15$	−2.37119	−	1.01458i	−0.612237	−	0.261964i
$16$	−0.672617	+	0.458583i	−0.168154	+	0.114646i
$17$	7.82562	+	0.292814i	1.89799	+	0.0710178i	0.960710	−	0.277554i	$-0.0895238\pi$
$17$	7.82562	+	0.292814i	1.89799	+	0.0710178i	0.937282	+	0.348572i	$0.113333\pi$
$18$	−0.331576	+	1.23746i	−0.0781533	+	0.291672i
$19$	0.0769953	−	0.133360i	0.0176639	−	0.0305948i	−0.857058	−	0.515219i	$-0.827710\pi$
$19$	0.0769953	−	0.133360i	0.0176639	−	0.0305948i	0.874722	+	0.484625i	$0.161044\pi$
$20$	−0.908729	+	3.02195i	−0.203198	+	0.675729i
$21$	2.89384	−	0.968691i	0.631487	−	0.211386i
$22$	1.41185	+	2.24695i	0.301007	+	0.479051i
$23$	−0.280491	−	7.49628i	−0.0584864	−	1.56308i	−0.651975	−	0.758241i	$-0.726059\pi$
$23$	−0.280491	−	7.49628i	−0.0584864	−	1.56308i	0.593488	−	0.804843i	$-0.297750\pi$
$24$	−2.98532	−	0.449965i	−0.609377	−	0.0918488i
$25$	1.89253	+	4.62799i	0.378507	+	0.925599i
$26$	0.476990	−	0.514073i	0.0935455	−	0.100818i
$27$	4.56049	−	2.86554i	0.877666	−	0.551474i
$28$	−1.57420	−	3.38572i	−0.297495	−	0.639840i
$29$	−3.21231	+	0.733188i	−0.596510	+	0.136150i	−0.510107	−	0.860111i	$-0.670394\pi$
$29$	−3.21231	+	0.733188i	−0.596510	+	0.136150i	−0.0864028	+	0.996260i	$0.527537\pi$
$30$	−1.70679	+	1.00162i	−0.311616	+	0.182870i
$31$	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	$0.227468\pi$
$32$	−0.219097	+	5.85549i	−0.0387312	+	1.03511i
$33$	0.741610	−	3.91950i	0.129098	−	0.682298i
$34$	3.74646	−	4.69792i	0.642513	−	0.805686i
$35$	−5.31343	−	2.60142i	−0.898134	−	0.439721i
$36$	−1.46909	−	1.84218i	−0.244848	−	0.307029i
$37$	0.347461	−	0.183639i	0.0571223	−	0.0301900i	−0.438464	−	0.898749i	$-0.644477\pi$
$37$	0.347461	−	0.183639i	0.0571223	−	0.0301900i	0.495586	+	0.868559i	$0.334953\pi$
$38$	−0.0472505	−	0.108299i	−0.00766505	−	0.0175685i
$39$	−1.05122	+	0.0787778i	−0.168329	+	0.0126145i
$40$	3.50884	+	4.68442i	0.554797	+	0.740672i
$41$	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	$0.782171\pi$
$42$	0.720512	−	2.22796i	0.111177	−	0.343781i
$43$	−2.05365	−	5.86900i	−0.313179	−	0.895014i	−0.987645	−	0.156708i	$-0.949912\pi$
$43$	−2.05365	−	5.86900i	−0.313179	−	0.895014i	0.674466	−	0.738306i	$-0.264374\pi$
$44$	−4.86705	−	0.364735i	−0.733735	−	0.0549858i
$45$	−3.64558	−	0.804924i	−0.543451	−	0.119991i
$46$	−4.75582	−	3.24246i	−0.701207	−	0.478075i
$47$	−4.96343	−	3.66318i	−0.723991	−	0.534330i	0.168330	−	0.985731i	$-0.446163\pi$
$47$	−4.96343	−	3.66318i	−0.723991	−	0.534330i	−0.892321	+	0.451401i	$0.850924\pi$
$48$	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
$52$	0.239788	+	1.26731i	0.0332526	+	0.175744i
$53$	−7.82670	−	4.13653i	−1.07508	−	0.568197i	−0.166558	−	0.986032i	$-0.553265\pi$
$53$	−7.82670	−	4.13653i	−1.07508	−	0.568197i	−0.908523	+	0.417835i	$0.862789\pi$
$54$	0.308841	−	4.12119i	0.0420279	−	0.560823i
$55$	−6.35852	+	4.40154i	−0.857382	+	0.593503i
$56$	−6.78633	−	1.37976i	−0.906862	−	0.184378i
$57$	−0.0586628	+	0.167649i	−0.00777008	+	0.0222056i
$58$	−1.01101	+	2.31727i	−0.132753	+	0.304272i
$59$	0.326512	+	4.35700i	0.0425082	+	0.567233i	0.977276	+	0.211972i	$0.0679887\pi$
$59$	0.326512	+	4.35700i	0.0425082	+	0.567233i	−0.934767	+	0.355260i	$0.884392\pi$
$60$	0.381865	−	3.61968i	0.0492985	−	0.467298i
$61$	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	$-0.179895\pi$
$62$	0.312340	−	2.77210i	0.0396672	−	0.352057i
$63$	3.85522	−	2.15654i	0.485712	−	0.271699i
$64$	2.24226	+	1.78815i	0.280283	+	0.223518i
$65$	1.55844	+	1.32203i	0.193301	+	0.163977i
$66$	−2.08189	−	2.24374i	−0.256263	−	0.276186i
$67$	8.57181	+	2.29681i	1.04721	+	0.280600i	0.741100	−	0.671395i	$-0.234305\pi$
$67$	8.57181	+	2.29681i	1.04721	+	0.280600i	0.306113	+	0.951995i	$0.400971\pi$
$68$	2.86035	+	10.6750i	0.346868	+	1.29453i
$69$	1.92534	+	8.43549i	0.231784	+	1.01551i
$70$	−4.02708	+	2.09506i	−0.481328	+	0.250407i
$71$	−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	$0.915385\pi$
$72$	−4.36713	+	0.163406i	−0.514671	+	0.0192576i
$73$	−1.29362	+	0.954739i	−0.151407	+	0.111744i	−0.666890	−	0.745157i	$-0.732375\pi$
$73$	−1.29362	+	0.954739i	−0.151407	+	0.111744i	0.515482	+	0.856900i	$0.327613\pi$
$74$	0.0449445	−	0.298187i	0.00522469	−	0.0346636i
$75$	−3.13723	−	4.83914i	−0.362256	−	0.558776i
$76$	0.211869	+	0.0483577i	0.0243030	+	0.00554701i
$77$	2.15707	−	8.89230i	0.245821	−	1.01337i
$78$	−0.430344	+	0.684889i	−0.0487269	+	0.0775484i
$79$	11.5906	+	6.69184i	1.30405	+	0.752891i	0.981095	−	0.193524i	$-0.0619919\pi$
$79$	11.5906	+	6.69184i	1.30405	+	0.752891i	0.322951	+	0.946416i	$0.395325\pi$
$80$	−1.82027	+	0.0129089i	−0.203513	+	0.00144326i
$81$	−0.882233	+	0.818593i	−0.0980259	+	0.0909547i
$82$	2.25308	+	0.426306i	0.248811	+	0.0470776i
$83$	−0.0998227	−	0.885951i	−0.0109570	−	0.0972457i	0.987043	−	0.160453i	$-0.0512956\pi$
$83$	−0.0998227	−	0.885951i	−0.0109570	−	0.0972457i	−0.998000	+	0.0632075i	$0.979867\pi$
$84$	2.51007	+	3.49951i	0.273871	+	0.381828i
$85$	14.1626	+	10.2981i	1.53615	+	1.11699i
$86$	−4.55910	−	1.40630i	−0.491621	−	0.151645i
$87$	3.48333	−	1.51976i	0.373452	−	0.162935i
$88$	−5.90475	+	6.86145i	−0.629449	+	0.731433i
$89$	−5.52892	−	14.0875i	−0.586064	−	1.49327i	−0.848967	−	0.528445i	$-0.822775\pi$
$89$	−5.52892	−	14.0875i	−0.586064	−	1.49327i	0.262903	−	0.964822i	$-0.415320\pi$
$90$	−2.15802	+	1.88393i	−0.227476	+	0.198584i
$91$	−2.41739	+	0.0575912i	−0.253411	+	0.00603720i
$92$	9.99237	−	3.49648i	1.04178	−	0.364533i
$93$	−3.17848	+	2.73530i	−0.329593	+	0.283637i
$94$	−4.52311	+	1.39519i	−0.466523	+	0.143903i
$95$	0.309166	−	0.151597i	0.0317198	−	0.0155535i
$96$	−1.00731	−	6.68308i	−0.102808	−	0.682089i
$97$	9.86671	+	9.86671i	1.00181	+	1.00181i	0.999998	+	0.00181471i	$0.000577641\pi$
$97$	9.86671	+	9.86671i	1.00181	+	1.00181i	0.00181471	+	0.999998i	$0.499422\pi$
$98$	1.91101	−	5.01970i	0.193041	−	0.507066i
$99$		−	5.77429i		−	0.580338i
$100$	−5.45380	+	4.47726i	−0.545380	+	0.447726i
$101$	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	$8.15140e-5\pi$
$102$	−3.23852	+	6.12758i	−0.320661	+	0.606721i
$103$	−1.42704	−	1.65825i	−0.140611	−	0.163393i	0.683251	−	0.730184i	$-0.260566\pi$
$103$	−1.42704	−	1.65825i	−0.140611	−	0.163393i	−0.823861	+	0.566791i	$0.808185\pi$
$104$	2.15532	+	1.03795i	0.211347	+	0.101779i
$105$	6.57962	+	1.80884i	0.642105	+	0.176525i
$106$	−6.11997	+	2.94722i	−0.594424	+	0.286260i
$107$	−13.7256	−	5.98841i	−1.32690	−	0.578922i	−0.387542	−	0.921852i	$-0.626676\pi$
$107$	−13.7256	−	5.98841i	−1.32690	−	0.578922i	−0.939361	+	0.342931i	$0.888580\pi$
$108$	5.76133	+	4.95803i	0.554384	+	0.477086i
$109$	1.51313	+	0.593860i	0.144932	+	0.0568815i	0.436698	−	0.899608i	$-0.356148\pi$
$109$	1.51313	+	0.593860i	0.144932	+	0.0568815i	−0.291766	+	0.956490i	$0.594243\pi$
$110$	−0.179817	+	5.93111i	−0.0171449	+	0.565510i
$111$	−0.354404	+	0.282628i	−0.0336385	+	0.0268258i
$112$	1.59862	−	1.44340i	0.151055	−	0.136389i
$113$	12.9148	−	1.45515i	1.21493	−	0.136889i	0.518855	−	0.854862i	$-0.326358\pi$
$113$	12.9148	−	1.45515i	1.21493	−	0.136889i	0.696071	+	0.717973i	$0.254930\pi$
$114$	0.0767727	+	0.112605i	0.00719042	+	0.0105464i
$115$	8.82332	−	14.2658i	0.822779	−	1.33029i
$116$	−2.32496	−	4.02694i	−0.215867	−	0.373892i
$117$	−1.47395	+	0.394943i	−0.136267	+	0.0365125i
$118$	2.83867	+	1.78365i	0.261321	+	0.164199i
$119$	−20.6185	+	2.03999i	−1.89009	+	0.187006i
$120$	−4.98112	−	4.55649i	−0.454712	−	0.415949i
$121$	−0.704356	−	0.653547i	−0.0640324	−	0.0594133i
$122$	−5.41403	−	7.33575i	−0.490163	−	0.664147i
$123$	−2.04686	−	2.77339i	−0.184559	−	0.250068i
$124$	3.76109	+	3.48978i	0.337755	+	0.313391i
$125$	−2.25542	+	10.9505i	−0.201731	+	0.979441i
$126$	0.425210	−	3.36273i	0.0378807	−	0.299576i
$127$	−2.58611	−	1.62496i	−0.229480	−	0.144192i	0.412384	−	0.911010i	$-0.364696\pi$
$127$	−2.58611	−	1.62496i	−0.229480	−	0.144192i	−0.641865	+	0.766818i	$0.721839\pi$
$128$	−9.19422	+	2.46358i	−0.812662	+	0.217752i
$129$	3.58594	+	6.21104i	0.315725	+	0.546851i
$130$	1.52628	−	0.359769i	0.133863	−	0.0315538i
$131$	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	$0.653085\pi$
$132$	5.59410	−	0.630303i	0.486904	−	0.0548609i
$133$	−0.153984	+	0.377201i	−0.0133521	+	0.0327075i
$134$	5.32367	−	4.24549i	0.459895	−	0.366754i
$135$	12.0380	+	0.364964i	1.03607	+	0.0314111i
$136$	19.0807	+	7.48864i	1.63616	+	0.642145i
$137$	−0.236718	−	0.203712i	−0.0202242	−	0.0174043i	0.642117	−	0.766606i	$-0.278056\pi$
$137$	−0.236718	−	0.203712i	−0.0202242	−	0.0174043i	−0.662341	+	0.749202i	$0.730437\pi$
$138$	6.08512	+	2.65491i	0.518000	+	0.226001i
$139$	−10.5367	+	5.07420i	−0.893710	+	0.430388i	−0.823613	−	0.567152i	$-0.808045\pi$
$139$	−10.5367	+	5.07420i	−0.893710	+	0.430388i	−0.0700972	+	0.997540i	$0.522331\pi$
$140$	1.29790	−	8.24750i	0.109693	−	0.697041i
$141$	6.41063	+	3.08720i	0.539873	+	0.259989i
$142$	3.97125	+	4.61468i	0.333260	+	0.387255i
$143$	−1.47696	+	2.79454i	−0.123510	+	0.233691i
$144$	0.765659	−	1.12302i	0.0638049	−	0.0935847i
$145$	−6.87727	−	2.64300i	−0.571126	−	0.219489i
$146$			1.23367i			0.102099i
$147$	−7.23813	+	3.57745i	−0.596991	+	0.295063i
$148$	0.392178	+	0.392178i	0.0322368	+	0.0322368i
$149$	3.41517	+	22.6582i	0.279782	+	1.85623i	0.481048	+	0.876695i	$0.340256\pi$
$149$	3.41517	+	22.6582i	0.279782	+	1.85623i	−0.201266	+	0.979537i	$0.564505\pi$
$150$	−4.41702	−	0.268073i	−0.360648	−	0.0218881i
$151$	−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	$0.463647\pi$
$152$	0.305513	−	0.262915i	0.0247803	−	0.0213252i
$153$	−12.3412	+	4.31839i	−0.997730	+	0.349121i
$154$	−4.50703	−	5.38343i	−0.363186	−	0.433809i
$155$	8.11086	+	0.550012i	0.651480	+	0.0441781i
$156$	−0.543510	−	1.38484i	−0.0435156	−	0.110876i
$157$	2.36319	−	2.74608i	0.188603	−	0.219161i	−0.655707	−	0.755015i	$-0.727629\pi$
$157$	2.36319	−	2.74608i	0.188603	−	0.219161i	0.844310	+	0.535854i	$0.180010\pi$
$158$	9.41255	−	4.10666i	0.748823	−	0.326708i
$159$	9.75712	+	3.00967i	0.773790	+	0.238683i
$160$	−7.70553	+	10.5971i	−0.609176	+	0.837774i
$161$	3.42465	+	19.5495i	0.269900	+	1.54072i
$162$	0.103395	+	0.917654i	0.00812346	+	0.0720977i
$163$	8.19382	+	1.55036i	0.641790	+	0.121433i	0.496612	−	0.867972i	$-0.334577\pi$
$163$	8.19382	+	1.55036i	0.641790	+	0.121433i	0.145177	+	0.989406i	$0.453625\pi$
$164$	−3.09158	+	2.86856i	−0.241412	+	0.223997i
$165$	6.26235	−	6.35180i	0.487523	−	0.494487i
$166$	−0.592447	−	0.342049i	−0.0459828	−	0.0265482i
$167$	3.20087	−	5.09416i	0.247691	−	0.394198i	−0.699619	−	0.714516i	$-0.746647\pi$
$167$	3.20087	−	5.09416i	0.247691	−	0.394198i	0.947310	+	0.320318i	$0.103790\pi$
$168$	7.98691	+	0.108474i	0.616203	+	0.00836898i
$169$	−11.8597	−	2.70690i	−0.912285	−	0.208223i
$170$	12.8109	−	4.05135i	0.982550	−	0.310724i
$171$	−0.0383196	+	0.254234i	−0.00293038	+	0.0194418i
$172$	7.06033	−	5.21076i	0.538345	−	0.397317i
$173$	−6.91794	+	0.258851i	−0.525961	+	0.0196801i	−0.299054	−	0.954236i	$-0.596671\pi$
$173$	−6.91794	+	0.258851i	−0.525961	+	0.0196801i	−0.226907	+	0.973916i	$0.572861\pi$
$174$	0.648892	−	2.84298i	0.0491924	−	0.215526i
$175$	−6.62128	−	11.4525i	−0.500522	−	0.865724i
$176$	−0.626491	−	2.74483i	−0.0472235	−	0.206900i
$177$	−1.30433	−	4.86782i	−0.0980394	−	0.365888i
$178$	−11.2164	−	3.00544i	−0.840708	−	0.225267i
$179$	−9.71955	−	10.4752i	−0.726473	−	0.782952i	0.256531	−	0.966536i	$-0.417421\pi$
$179$	−9.71955	−	10.4752i	−0.726473	−	0.782952i	−0.983004	+	0.183584i	$0.941230\pi$
$180$	−0.430979	−	5.25104i	−0.0321233	−	0.391389i
$181$	−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	$0.822412\pi$
$182$	−1.06591	+	1.51867i	−0.0790106	+	0.112572i
$183$	−1.53449	+	13.6190i	−0.113433	+	1.00674i
$184$	5.78753	−	18.7627i	0.426662	−	1.38320i
$185$	0.873935	+	0.0921975i	0.0642530	+	0.00677849i
$186$	0.240453	+	3.20863i	0.0176309	+	0.235268i
$187$	−10.8304	+	24.8237i	−0.792001	+	1.81529i
$188$	2.87531	−	8.21717i	0.209704	−	0.599299i
$189$	−10.9264	+	9.14763i	−0.794780	+	0.665392i
$190$	0.0472774	−	0.259945i	0.00342987	−	0.0188584i
$191$	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	$-0.0999660\pi$
$192$	−2.92462	−	1.54571i	−0.211067	−	0.111552i
$193$	0.307938	+	1.62749i	0.0221659	+	0.117149i	0.991902	−	0.127006i	$-0.0405368\pi$
$193$	0.307938	+	1.62749i	0.0221659	+	0.117149i	−0.969736	+	0.244156i	$0.921489\pi$
$194$	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	−0.150834	+	0.988559i	$0.548196\pi$
$197$	−15.9921	+	15.9921i	−1.13939	+	1.13939i	−0.988559	+	0.150834i	$0.951804\pi$
$198$	−3.56490	−	2.63102i	−0.253346	−	0.186978i
$199$	10.6694	+	7.27428i	0.756335	+	0.515660i	0.879020	−	0.476785i	$-0.158198\pi$
$199$	10.6694	+	7.27428i	0.756335	+	0.515660i	−0.122685	+	0.992446i	$0.539151\pi$
$200$	0.674787	+	13.0699i	0.0477147	+	0.924185i
$201$	−10.2071	−	0.764913i	−0.719950	−	0.0539528i
$202$	−2.86836	−	8.19730i	−0.201817	−	0.576760i
$203$	8.15742	−	3.07437i	0.572539	−	0.215779i
$204$	−5.53075	−	11.4847i	−0.387230	−	0.804092i
$205$	−0.949070	+	6.61462i	−0.0662859	+	0.461985i
$206$	−1.67398	+	0.125448i	−0.116632	+	0.00874036i
$207$	5.00853	+	11.4797i	0.348117	+	0.797892i
$208$	−0.657798	+	0.347656i	−0.0456101	+	0.0241056i
$209$	0.332051	+	0.416379i	0.0229684	+	0.0288015i
$210$	4.11469	−	3.23790i	0.283941	−	0.223436i
$211$	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	$0.159758\pi$
$212$	2.32261	−	12.2753i	0.159518	−	0.843071i
$213$	0.342197	−	9.14540i	0.0234469	−	0.626632i
$214$	−9.95106	+	5.74525i	−0.680240	+	0.392737i
$215$	3.50322	−	13.4551i	0.238917	−	0.917633i
$216$	13.7443	−	3.13705i	0.935183	−	0.213449i
$217$	−7.60114	+	5.89463i	−0.515999	+	0.400153i
$218$	1.05608	−	0.663580i	0.0715269	−	0.0449433i
$219$	1.26135	−	1.35942i	0.0852343	−	0.0918608i
$220$	−8.58061	−	6.74381i	−0.578504	−	0.454668i
$221$	7.07726	+	1.06673i	0.476068	+	0.0717557i
$222$	0.0130054	+	0.347577i	0.000872867	+	0.0233279i
$223$	−7.89682	−	12.5677i	−0.528810	−	0.841597i	0.470354	−	0.882478i	$-0.344126\pi$
$223$	−7.89682	−	12.5677i	−0.528810	−	0.841597i	−0.999164	+	0.0408812i	$0.986983\pi$
$224$	−1.52641	−	15.4277i	−0.101988	−	1.03080i
$225$	−5.76437	−	6.03844i	−0.384292	−	0.402563i
$226$	4.98618	−	8.63632i	0.331676	−	0.574479i
$227$	−4.96512	+	18.5301i	−0.329547	+	1.22988i	0.580115	+	0.814535i	$0.303008\pi$
$227$	−4.96512	+	18.5301i	−0.329547	+	1.22988i	−0.909662	+	0.415350i	$0.863659\pi$
$228$	−0.250483	−	0.00937242i	−0.0165887	−	0.000620704i
$229$	7.73843	−	5.27598i	0.511370	−	0.348646i	−0.279984	−	0.960005i	$-0.590329\pi$
$229$	7.73843	−	5.27598i	0.511370	−	0.348646i	0.791354	+	0.611359i	$0.209377\pi$
$230$	−4.78707	−	11.9474i	−0.315650	−	0.787789i
$231$	−0.537817	+	10.5403i	−0.0353858	+	0.693501i
$232$	−8.57012	−	0.965620i	−0.562656	−	0.0633961i
$233$	−3.81469	−	7.21775i	−0.249909	−	0.472850i	0.726963	−	0.686677i	$-0.240931\pi$
$233$	−3.81469	−	7.21775i	−0.249909	−	0.472850i	−0.976872	+	0.213826i	$0.931407\pi$
$234$	−0.427766	+	1.08993i	−0.0279640	+	0.0712510i
$235$	−4.64807	−	12.9872i	−0.303206	−	0.847194i
$236$	−5.73977	+	2.25269i	−0.373627	+	0.146638i
$237$	−14.5708	−	5.09853i	−0.946472	−	0.331185i
$238$	−8.13522	+	13.6588i	−0.527328	+	0.885369i
$239$	4.15342	−	8.62467i	0.268662	−	0.557883i	−0.722370	−	0.691507i	$-0.756947\pi$
$239$	4.15342	−	8.62467i	0.268662	−	0.557883i	0.991032	+	0.133624i	$0.0426614\pi$
$240$	2.06017	−	0.404959i	0.132983	−	0.0261400i
$241$	−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	$-0.236364\pi$
$242$	−0.724418	+	0.137067i	−0.0465673	+	0.00881102i
$243$	−8.77070	+	11.8839i	−0.562641	+	0.762351i
$244$	16.7686			1.07350
$245$	14.8615	+	4.91288i	0.949465	+	0.313873i
$246$	−2.64486			−0.168630
$247$	0.0835738	−	0.113238i	0.00531767	−	0.00720519i
$248$	9.35022	−	1.76916i	0.593739	−	0.112342i
$249$	0.303109	+	0.982654i	0.0192087	+	0.0622732i
$250$	5.73288	+	6.38195i	0.362579	+	0.403630i
$251$	−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	$0.187417\pi$
$252$	4.51185	+	4.30187i	0.284220	+	0.270992i
$253$	24.4878	+	8.56864i	1.53953	+	0.538706i
$254$	−2.18155	+	0.856196i	−0.136883	+	0.0537225i
$255$	−18.2589	−	8.63406i	−1.14342	−	0.540686i
$256$	−4.76390	+	12.1382i	−0.297744	+	0.758638i
$257$	−12.9720	−	24.5442i	−0.809170	−	1.53102i	−0.846909	−	0.531737i	$-0.821539\pi$
$257$	−12.9720	−	24.5442i	−0.809170	−	1.53102i	0.0377393	−	0.999288i	$-0.487984\pi$
$258$	5.46845	+	0.616146i	0.340451	+	0.0383596i
$259$	−0.844923	+	0.606031i	−0.0525009	+	0.0376570i
$260$	−1.13454	+	2.65154i	−0.0703613	+	0.164442i
$261$	4.54535	−	3.09897i	0.281350	−	0.191821i
$262$	8.28324	+	0.309937i	0.511740	+	0.0191480i
$263$	2.41869	−	9.02666i	0.149143	−	0.556608i	−0.850393	−	0.526147i	$-0.823636\pi$
$263$	2.41869	−	9.02666i	0.149143	−	0.556608i	0.999536	−	0.0304602i	$-0.00969729\pi$
$264$	5.22060	−	9.04235i	0.321306	−	0.556518i
$265$	−9.37345	−	17.4350i	−0.575806	−	1.07102i
$266$	0.162712	+	0.266935i	0.00997653	+	0.0163668i
$267$	9.28683	+	14.7799i	0.568345	+	0.904515i
$268$	0.468272	+	12.5148i	0.0286043	+	0.764465i
$269$	−10.1739	−	1.53347i	−0.620314	−	0.0934973i	−0.168636	−	0.985678i	$-0.553936\pi$
$269$	−10.1739	−	1.53347i	−0.620314	−	0.0934973i	−0.451678	+	0.892181i	$0.649174\pi$
$270$	5.71036	−	7.26567i	0.347521	−	0.442174i
$271$	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	$0.189916\pi$
$272$	−5.39793	+	3.39174i	−0.327298	+	0.205655i
$273$	2.72731	−	0.583640i	0.165064	−	0.0353235i
$274$	−0.233626	+	0.0533235i	−0.0141138	+	0.00322139i
$275$	−17.2905	+	0.245251i	−1.04266	+	0.0147892i
$276$	−10.5747	+	6.10531i	−0.636523	+	0.367497i
$277$	0.723189	−	19.3276i	0.0434522	−	1.16128i	−0.791574	−	0.611074i	$-0.790738\pi$
$277$	0.723189	−	19.3276i	0.0434522	−	1.16128i	0.835026	−	0.550211i	$-0.185453\pi$
$278$	−1.66829	+	8.81711i	−0.100057	+	0.528815i
$279$	−3.78464	+	4.74579i	−0.226581	+	0.284123i
$280$	−10.8784	−	11.0205i	−0.650108	−	0.658600i
$281$	−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	$-0.472867\pi$
$282$	4.82692	−	2.55110i	0.287439	−	0.151916i
$283$	−11.6751	−	26.7596i	−0.694011	−	1.59069i	−0.802541	−	0.596598i	$-0.796519\pi$
$283$	−11.6751	−	26.7596i	−0.694011	−	1.59069i	0.108529	−	0.994093i	$-0.465386\pi$
$284$	−11.1661	+	0.836786i	−0.662588	+	0.0496541i
$285$	−0.317875	+	0.238103i	−0.0188293	+	0.0141040i
$286$	1.05231	+	2.18515i	0.0622246	+	0.129211i
$287$	−4.36486	−	6.59269i	−0.257650	−	0.389154i
$288$	−3.23121	−	9.23428i	−0.190401	−	0.544135i
$289$	44.2021	+	3.31249i	2.60013	+	0.194853i
$290$	−4.76530	+	3.04159i	−0.279828	+	0.178608i
$291$	−13.2978	−	9.06631i	−0.779533	−	0.531477i
$292$	−1.82561	−	1.34736i	−0.106836	−	0.0788485i
$293$	−11.2183	+	11.2183i	−0.655381	+	0.655381i	−0.954284	−	0.298902i	$-0.903380\pi$
$293$	−11.2183	+	11.2183i	−0.655381	+	0.655381i	0.298902	+	0.954284i	$0.403380\pi$
$294$	−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
$297$	3.46304	+	18.3026i	0.200946	+	1.06202i
$298$	15.5447	+	8.21560i	0.900479	+	0.475917i
$299$	0.512349	−	6.83683i	0.0296299	−	0.395384i
$300$	5.22078	−	6.24362i	0.301422	−	0.360476i
$301$	7.48885	+	14.6477i	0.431650	+	0.844280i
$302$	−1.14563	+	3.27403i	−0.0659237	+	0.188399i
$303$	−5.22051	+	11.9655i	−0.299911	+	0.687403i
$304$	0.00936812	+	0.125009i	0.000537298	+	0.00716975i
$305$	20.6547	−	16.7126i	1.18269	−	0.956961i
$306$	−2.95714	+	9.58680i	−0.169048	+	0.548041i
$307$	1.68820	−	14.9832i	0.0963507	−	0.855136i	−0.848847	−	0.528638i	$-0.822703\pi$
$307$	1.68820	−	14.9832i	0.0963507	−	0.855136i	0.945198	−	0.326498i	$-0.105869\pi$
$308$	12.8889	−	0.790035i	0.734414	−	0.0450164i
$309$	1.97287	+	1.57331i	0.112233	+	0.0895026i
$310$	4.03522	−	4.75683i	0.229185	−	0.270170i
$311$	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	$0.424538\pi$
$312$	−2.66523	−	0.714145i	−0.150889	−	0.0404305i
$313$	3.99897	+	14.9244i	0.226035	+	0.843575i	0.981987	+	0.188948i	$0.0605076\pi$
$313$	3.99897	+	14.9244i	0.226035	+	0.843575i	−0.755952	+	0.654627i	$0.772826\pi$
$314$	−0.618587	−	2.71021i	−0.0349089	−	0.152946i
$315$	9.84499	+	0.802056i	0.554702	+	0.0451907i
$316$	−4.20288	+	18.4140i	−0.236431	+	1.03587i
$317$	−7.09821	+	0.265596i	−0.398675	+	0.0149174i	−0.235977	−	0.971759i	$-0.575829\pi$
$317$	−7.09821	+	0.265596i	−0.398675	+	0.0149174i	−0.162698	+	0.986676i	$0.552020\pi$
$318$	6.30385	−	4.65246i	0.353503	−	0.260897i
$319$	1.69838	−	11.2680i	0.0950910	−	0.630888i
$320$	1.93366	+	6.11449i	0.108095	+	0.341810i
$321$	16.8395	+	3.84351i	0.939889	+	0.214524i
$322$	13.6298	+	6.79329i	0.759557	+	0.378575i
$323$	0.641586	−	1.02108i	0.0356988	−	0.0568143i
$324$	−1.47089	−	0.849218i	−0.0817160	−	0.0471788i
$325$	1.24522	+	4.39680i	0.0690722	+	0.243891i
$326$	4.69061	−	4.35225i	0.259789	−	0.241049i
$327$	−1.84220	−	0.348562i	−0.101874	−	0.0192755i
$328$	0.875804	+	7.77297i	0.0483582	+	0.429191i
$329$	14.3249	+	7.82165i	0.789759	+	0.431221i
$330$	−1.06805	−	6.76037i	−0.0587940	−	0.372146i
$331$	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	$0.256765\pi$
$332$	1.15322	−	0.503144i	0.0632911	−	0.0276136i
$333$	−0.428010	+	0.497357i	−0.0234548	+	0.0272550i
$334$	−1.68655	−	4.29725i	−0.0922838	−	0.235135i
$335$	13.0499	+	14.9485i	0.712990	+	0.816723i
$336$	−1.50222	+	1.97862i	−0.0819528	+	0.107943i
$337$	−26.8409	+	9.39203i	−1.46212	+	0.511616i	−0.939975	−	0.341243i	$-0.889152\pi$
$337$	−26.8409	+	9.39203i	−1.46212	+	0.511616i	−0.522140	+	0.852860i	$0.674866\pi$
$338$	−7.07496	+	6.08850i	−0.384827	+	0.331171i
$339$	−14.3245	+	4.41853i	−0.778001	+	0.239982i
$340$	−7.99624	+	23.3825i	−0.433657	+	1.26810i
$341$	1.87400	+	12.4331i	0.101483	+	0.673293i
$342$	0.139498	+	0.139498i	0.00754316	+	0.00754316i
$343$	−16.9996	+	7.34933i	−0.917894	+	0.396826i
$344$		−	16.2752i		−	0.877502i
$345$	−6.94050	+	18.0597i	−0.373664	+	0.972299i
$346$	−2.99230	+	4.38890i	−0.160867	+	0.235949i
$347$	−6.93468	+	13.1211i	−0.372273	+	0.704376i	−0.997077	−	0.0764066i	$-0.975655\pi$
$347$	−6.93468	+	13.1211i	−0.372273	+	0.704376i	0.624803	+	0.780782i	$0.285179\pi$
$348$	3.49842	+	4.06523i	0.187535	+	0.217919i
$349$	11.6624	+	5.61631i	0.624273	+	0.300634i	0.719150	−	0.694855i	$-0.244531\pi$
$349$	11.6624	+	5.61631i	0.624273	+	0.300634i	−0.0948768	+	0.995489i	$0.530246\pi$
$350$	−10.0874	−	1.13042i	−0.539194	−	0.0604235i
$351$	4.43506	−	2.13581i	0.236726	−	0.114001i
$352$	−18.5742	−	8.10384i	−0.990008	−	0.431936i
$353$	6.69880	+	5.76478i	0.356541	+	0.306828i	0.812260	−	0.583295i	$-0.198237\pi$
$353$	6.69880	+	5.76478i	0.356541	+	0.306828i	−0.455719	+	0.890124i	$0.650618\pi$
$354$	−3.59958	−	1.41273i	−0.191315	−	0.0750858i
$355$	−12.9199	+	12.1596i	−0.685719	+	0.645364i
$356$	16.6977	−	13.3159i	0.884974	−	0.705743i
$357$	22.9297	−	6.73325i	1.21357	−	0.356362i
$358$	−10.8958	+	1.22766i	−0.575858	+	0.0648837i
$359$	−16.8331	−	24.6896i	−0.888416	−	1.30307i	−0.952317	−	0.305111i	$-0.901306\pi$
$359$	−16.8331	−	24.6896i	−0.888416	−	1.30307i	0.0639002	−	0.997956i	$-0.479646\pi$
$360$	−8.31087	−	5.14022i	−0.438021	−	0.270913i
$361$	9.48814	+	16.4339i	0.499376	+	0.864945i
$362$	−6.64479	+	1.78047i	−0.349242	+	0.0935792i
$363$	0.938398	+	0.589635i	0.0492531	+	0.0309478i
$364$	−1.08323	−	3.23599i	−0.0567764	−	0.169612i
$365$	−3.59157	+	0.159900i	−0.187991	+	0.00836955i
$366$	7.70882	+	7.15274i	0.402946	+	0.373880i
$367$	−13.2414	−	17.9414i	−0.691195	−	0.936536i	0.308698	−	0.951160i	$-0.400107\pi$
$367$	−13.2414	−	17.9414i	−0.691195	−	0.936536i	−0.999893	+	0.0146241i	$0.995345\pi$
$368$	3.62633	+	4.91350i	0.189036	+	0.256134i
$369$	−3.65761	−	3.39377i	−0.190408	−	0.176672i
$370$	0.455123	−	0.497536i	0.0236607	−	0.0258657i
$371$	22.0003	+	8.03522i	1.14220	+	0.417168i
$372$	−5.01081	−	3.14850i	−0.259799	−	0.163242i
$373$	3.60684	−	0.966450i	0.186755	−	0.0500409i	−0.164229	−	0.986422i	$-0.552514\pi$
$373$	3.60684	−	0.966450i	0.186755	−	0.0500409i	0.350984	+	0.936381i	$0.385847\pi$
$374$	10.3907	+	17.9972i	0.537289	+	0.930611i
$375$	0.207934	−	12.8940i	0.0107377	−	0.665841i
$376$	−9.09579	−	13.3411i	−0.469080	−	0.688013i
$377$	−2.99244	+	0.337167i	−0.154119	+	0.0173650i
$378$	0.668966	+	10.9137i	0.0344079	+	0.561342i
$379$	−19.9530	+	15.9120i	−1.02491	+	0.817342i	−0.983337	−	0.181793i	$-0.941810\pi$
$379$	−19.9530	+	15.9120i	−1.02491	+	0.817342i	−0.0415778	+	0.999135i	$0.513238\pi$
$380$	0.333039	+	0.353864i	0.0170845	+	0.0181528i
$381$	3.27932	+	1.28704i	0.168005	+	0.0659369i
$382$	−6.09472	−	5.24493i	−0.311833	−	0.268354i
$383$	−3.98049	−	1.73667i	−0.203394	−	0.0887398i	0.295726	−	0.955273i	$-0.404438\pi$
$383$	−3.98049	−	1.73667i	−0.203394	−	0.0887398i	−0.499120	+	0.866533i	$0.666343\pi$
$384$	9.89165	−	4.76357i	0.504781	−	0.243090i
$385$	15.0886	−	13.8190i	0.768984	−	0.704282i
$386$	1.14508	+	0.551442i	0.0582831	+	0.0280676i
$387$	6.77177	+	7.86895i	0.344229	+	0.400001i
$388$	−9.20142	+	17.4099i	−0.467131	+	0.883855i
$389$	−5.14567	+	7.54731i	−0.260896	+	0.382664i	−0.934228	−	0.356676i	$-0.883910\pi$
$389$	−5.14567	+	7.54731i	−0.260896	+	0.382664i	0.673332	+	0.739340i	$0.264862\pi$
$390$	−1.65260	+	0.735017i	−0.0836828	+	0.0372190i
$391$		−	58.7452i		−	2.97087i
$392$	18.2841	+	1.18209i	0.923488	+	0.0597045i
$393$	−8.81063	−	8.81063i	−0.444438	−	0.444438i
$394$	2.58643	+	17.1598i	0.130302	+	0.864500i
$395$	13.1757	+	26.8704i	0.662939	+	1.35200i
$396$	7.78687	−	2.40193i	0.391305	−	0.120702i
$397$	−4.96744	+	4.27483i	−0.249309	+	0.214547i	−0.768060	−	0.640378i	$-0.778778\pi$
$397$	−4.96744	+	4.27483i	−0.249309	+	0.214547i	0.518752	+	0.854925i	$0.326397\pi$
$398$	9.35240	−	3.27255i	0.468793	−	0.164038i
$399$	0.0936275	−	0.460506i	0.00468724	−	0.0230541i
$400$	−3.39527	−	2.24499i	−0.169763	−	0.112249i
$401$	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	$0.869952\pi$
$402$	−5.12301	+	5.95304i	−0.255512	+	0.296911i
$403$	3.04551	−	1.32874i	0.151708	−	0.0661895i
$404$	15.2632	+	4.70809i	0.759375	+	0.234236i
$405$	−2.65815	+	0.419952i	−0.132085	+	0.0208676i
$406$	1.81883	−	6.43700i	0.0902671	−	0.319463i
$407$	0.152180	+	1.35064i	0.00754331	+	0.0669487i
$408$	−23.2303	−	4.39540i	−1.15007	−	0.217605i
$409$	1.04177	−	0.966624i	0.0515124	−	0.0477965i	−0.653997	−	0.756497i	$-0.726909\pi$
$409$	1.04177	−	0.966624i	0.0515124	−	0.0477965i	0.705509	+	0.708701i	$0.250718\pi$
$410$	3.65126	+	3.59984i	0.180323	+	0.177783i
$411$	0.311958	+	0.180109i	0.0153878	+	0.00888413i
$412$	1.64262	−	2.61421i	0.0809259	−	0.128793i
$413$	−2.41902	−	11.3039i	−0.119032	−	0.556229i
$414$	9.36936	+	2.13849i	0.460479	+	0.105101i
$415$	0.919015	−	1.76912i	0.0451127	−	0.0868426i
$416$	−0.798173	+	5.29553i	−0.0391336	+	0.259635i
$417$	10.8533	−	8.01009i	0.531487	−	0.392256i
$418$	0.408358	−	0.0152797i	0.0199734	−	0.000747354i
$419$	−8.35268	+	36.5955i	−0.408055	+	1.78781i	0.185101	+	0.982720i	$0.440739\pi$
$419$	−8.35268	+	36.5955i	−0.408055	+	1.78781i	−0.593156	+	0.805087i	$0.702118\pi$
$420$	0.297621	+	9.62531i	0.0145224	+	0.469667i
$421$	−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	$-0.261317\pi$
$422$	−0.983512	−	3.67052i	−0.0478766	−	0.178678i
$423$	9.94867	+	2.66574i	0.483721	+	0.129613i
$424$	−15.7605	−	16.9858i	−0.765399	−	0.824904i
$425$	13.4551	+	36.7711i	0.652668	+	1.78366i
$426$	−5.49021	−	4.37830i	−0.266002	−	0.212129i
$427$	−5.10721	+	31.0196i	−0.247155	+	1.50115i
$428$	2.36619	−	21.0005i	0.114374	−	1.01510i
$429$	1.07461	−	3.48380i	0.0518827	−	0.168200i
$430$	−6.71064	−	8.29353i	−0.323616	−	0.399950i
$431$	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	$0.898544\pi$
$432$	−1.75337	+	4.01878i	−0.0843593	+	0.193354i
$433$	6.41647	−	18.3372i	0.308356	−	0.881231i	−0.680552	−	0.732700i	$-0.738260\pi$
$433$	6.41647	−	18.3372i	0.308356	−	0.881231i	0.988908	−	0.148531i	$-0.0474545\pi$
$434$	0.175786	+	7.37859i	0.00843798	+	0.354184i
$435$	8.36085	+	1.52063i	0.400872	+	0.0729084i
$436$	−0.171428	+	2.28755i	−0.00820991	+	0.109554i
$437$	−1.02130	−	0.539772i	−0.0488554	−	0.0258208i
$438$	−0.264541	−	1.39813i	−0.0126403	−	0.0668055i
$439$	6.09322	−	0.918406i	0.290814	−	0.0438331i	−0.00201518	−	0.999998i	$-0.500641\pi$
$439$	6.09322	−	0.918406i	0.290814	−	0.0438331i	0.292829	+	0.956165i	$0.405403\pi$
$440$	−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
$443$	17.9221	+	13.2271i	0.851503	+	0.628438i	0.929625	−	0.368506i	$-0.120131\pi$
$443$	17.9221	+	13.2271i	0.851503	+	0.628438i	−0.0781226	+	0.996944i	$0.524893\pi$
$444$	−0.528557	−	0.360364i	−0.0250842	−	0.0171021i
$445$	7.29590	−	33.0439i	0.345859	−	1.56643i
$446$	−11.3571	−	0.851098i	−0.537775	−	0.0403007i
$447$	−8.72915	−	24.9465i	−0.412875	−	1.17993i
$448$	−6.51920	−	3.88285i	−0.308003	−	0.183447i
$449$	−8.14076	−	16.9045i	−0.384186	−	0.797771i	−0.999952	−	0.00984149i	$-0.996867\pi$
$449$	−8.14076	−	16.9045i	−0.384186	−	0.797771i	0.615765	−	0.787930i	$-0.288847\pi$
$450$	−6.35448	+	0.807401i	−0.299553	+	0.0380612i
$451$	−10.3065	+	0.772363i	−0.485313	+	0.0363692i
$452$	7.33452	+	16.8109i	0.344987	+	0.790718i
$453$	4.60990	−	2.43640i	0.216592	−	0.114472i
$454$	9.17767	+	11.5084i	0.430730	+	0.540118i
$455$	−4.55946	−	2.90633i	−0.213751	−	0.136251i
$456$	−0.289863	+	0.363477i	−0.0135741	+	0.0170214i
$457$	5.81333	−	30.7242i	0.271936	−	1.43722i	−0.534135	−	0.845399i	$-0.679363\pi$
$457$	5.81333	−	30.7242i	0.271936	−	1.43722i	0.806072	−	0.591818i	$-0.201590\pi$
$458$	0.268712	−	7.18147i	0.0125561	−	0.335568i
$459$	36.5277	−	21.0893i	1.70497	−	0.984364i
$460$	22.9083	+	5.96446i	1.06810	+	0.278095i
$461$	−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	$0.611127\pi$
$462$	6.26226	+	5.13465i	0.291347	+	0.238886i
$463$	−6.98128	+	4.38663i	−0.324448	+	0.203864i	−0.684400	−	0.729107i	$-0.739936\pi$
$463$	−6.98128	+	4.38663i	−0.324448	+	0.203864i	0.359952	+	0.932971i	$0.382793\pi$
$464$	1.82443	−	1.96626i	0.0846968	−	0.0912815i
$465$	−9.31008	+	1.11591i	−0.431745	+	0.0517491i
$466$	−6.19419	−	0.933624i	−0.286940	−	0.0432493i
$467$	0.967365	+	25.8534i	0.0447643	+	1.19635i	0.822874	+	0.568223i	$0.192369\pi$
$467$	0.967365	+	25.8534i	0.0447643	+	1.19635i	−0.778110	+	0.628128i	$0.783821\pi$
$468$	−1.14572	−	1.82340i	−0.0529607	−	0.0842865i
$469$	−23.2934	−	2.94540i	−1.07559	−	0.136006i
$470$	−10.1358	−	3.04795i	−0.467532	−	0.140591i
$471$	−2.08938	+	3.61892i	−0.0962737	+	0.166751i
$472$	−2.95993	+	11.0466i	−0.136242	+	0.508461i
$473$	21.4893	+	0.804074i	0.988081	+	0.0369714i
$474$	−9.78676	+	6.67250i	−0.449521	+	0.306478i
$475$	0.762904	+	0.103946i	0.0350045	+	0.00476937i
$476$	−11.3277	−	26.9563i	−0.519203	−	1.23554i
$477$	14.6875	+	1.65489i	0.672495	+	0.0757720i
$478$	−3.43217	−	6.49398i	−0.156984	−	0.297028i
$479$	7.03595	−	17.9273i	0.321481	−	0.819120i	−0.675194	−	0.737640i	$-0.735940\pi$
$479$	7.03595	−	17.9273i	0.321481	−	0.819120i	0.996675	−	0.0814796i	$-0.0259646\pi$
$480$	6.46039	−	13.6622i	0.294875	−	0.623589i
$481$	0.334356	−	0.131225i	0.0152453	−	0.00598335i
$482$	−9.64631	−	3.37539i	−0.439377	−	0.153745i
$483$	−8.07328	−	21.4213i	−0.367347	−	0.974704i
$484$	0.588344	−	1.22171i	0.0267429	−	0.0555322i
$485$	6.01794	+	30.6154i	0.273261	+	1.39018i
$486$	3.34049	+	10.8296i	0.151528	+	0.491241i
$487$	−13.0884	+	2.47646i	−0.593093	+	0.112219i	−0.473789	−	0.880638i	$-0.657114\pi$
$487$	−13.0884	+	2.47646i	−0.593093	+	0.112219i	−0.119304	+	0.992858i	$0.538066\pi$
$488$	18.4685	−	25.0240i	0.836031	−	1.13278i
$489$	−9.61861			−0.434969
$490$	9.80462	−	6.93657i	0.442927	−	0.313362i
$491$	−23.9236			−1.07966			−0.539830	−	0.841774i	$-0.681511\pi$
$491$	−23.9236			−1.07966			−0.539830	+	0.841774i	$0.681511\pi$
$492$	2.88860	−	3.91392i	0.130228	−	0.176453i
$493$	−25.3530	+	4.79704i	−1.14184	+	0.216048i
$494$	−0.0318307	−	0.103193i	−0.00143213	−	0.00464285i
$495$	7.19759	−	10.7195i	0.323508	−	0.481804i
$496$	−1.28414	+	2.66655i	−0.0576598	+	0.119732i
$497$	1.85293	−	20.9107i	0.0831152	−	0.937975i
$498$	0.744774	+	0.260608i	0.0333741	+	0.0116781i
$499$	13.5044	−	5.30008i	0.604539	−	0.237264i	−0.0432744	−	0.999063i	$-0.513779\pi$
$499$	13.5044	−	5.30008i	0.604539	−	0.237264i	0.647813	+	0.761799i	$0.275684\pi$
$500$	−15.7054	+	1.51355i	−0.702365	+	0.0676879i
$501$	−2.53523	+	6.45965i	−0.113266	+	0.288596i
$502$	1.58519	+	2.99932i	0.0707504	+	0.133866i
$503$	0.0735115	+	0.00828276i	0.00327772	+	0.000369310i	0.113603	−	0.993526i	$-0.463761\pi$
$503$	0.0735115	+	0.00828276i	0.00327772	+	0.000369310i	−0.110325	+	0.993896i	$0.535189\pi$
$504$	11.3890	−	1.99511i	0.507306	−	0.0888691i
$505$	23.4929	−	9.41310i	1.04542	−	0.418877i
$506$	16.4477	−	11.2139i	0.731191	−	0.498518i
$507$	14.0212	+	0.524637i	0.622704	+	0.0232999i
$508$	1.11558	−	4.16341i	0.0494960	−	0.184721i
$509$	12.8569	−	22.2688i	0.569871	−	0.987046i	−0.426707	−	0.904390i	$-0.640326\pi$
$509$	12.8569	−	22.2688i	0.569871	−	0.987046i	0.996578	−	0.0826561i	$-0.0263403\pi$
$510$	−13.6500	+	7.33854i	−0.604432	+	0.324956i
$511$	3.04847	−	2.96678i	0.134856	−	0.131242i
$512$	−4.80517	−	7.64739i	−0.212361	−	0.337970i
$513$	−0.0310122	−	0.828819i	−0.00136922	−	0.0365933i
$514$	−21.0635	−	3.17482i	−0.929073	−	0.140035i
$515$	−0.582185	−	4.85719i	−0.0256541	−	0.214033i
$516$	−6.88420	+	7.41940i	−0.303060	+	0.326621i
$517$	18.0645	−	11.3507i	0.794477	−	0.499203i
$518$	−0.0108349	+	0.797767i	−0.000476058	+	0.0350519i
$519$	7.78468	−	1.77680i	0.341709	−	0.0779930i
$520$	2.70738	+	4.61345i	0.118726	+	0.202313i
$521$	−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	$0.468871\pi$
$522$	0.157834	−	4.21821i	0.00690821	−	0.184626i
$523$	−2.51067	+	13.2692i	−0.109784	+	0.580222i	0.883869	+	0.467734i	$0.154930\pi$
$523$	−2.51067	+	13.2692i	−0.109784	+	0.580222i	−0.993653	+	0.112488i	$0.964118\pi$
$524$	−9.50526	+	11.9192i	−0.415239	+	0.520694i
$525$	9.95978	+	11.5594i	0.434680	+	0.504493i
$526$	−4.47077	−	5.60617i	−0.194935	−	0.244440i
$527$	25.1715	−	13.3035i	1.09649	−	0.579511i
$528$	1.29860	+	2.97641i	0.0565142	+	0.129532i
$529$	−33.1799	+	2.48649i	−1.44260	+	0.108108i
$530$	−15.0349	−	2.15721i	−0.653073	−	0.0937033i
$531$	−3.16515	−	6.57250i	−0.137356	−	0.285222i
$532$	−0.572724	−	0.0507498i	−0.0248307	−	0.00220028i
$533$	0.902083	+	2.57801i	0.0390736	+	0.111666i
$534$	13.3562	+	1.00091i	0.577980	+	0.0433136i
$535$	−18.0159	−	28.2257i	−0.778893	−	1.22031i
$536$	19.1918	+	13.0848i	0.828960	+	0.565175i
$537$	13.2615	+	9.78745i	0.572277	+	0.422360i
$538$	−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	$0.830419\pi$
$542$	−0.708169	−	3.74276i	−0.0304184	−	0.160765i
$543$	9.14249	+	4.83195i	0.392342	+	0.207359i
$544$	−3.42914	+	45.7587i	−0.147023	+	1.96189i
$545$	2.06876	+	2.98855i	0.0886158	+	0.128015i
$546$	0.882354	−	1.94970i	0.0377613	−	0.0834395i
$547$	1.22917	−	3.51277i	0.0525556	−	0.150195i	−0.914613	−	0.404330i	$-0.867505\pi$
$547$	1.22917	−	3.51277i	0.0525556	−	0.150195i	0.967169	+	0.254134i	$0.0817906\pi$
$548$	0.176247	−	0.403962i	0.00752889	−	0.0172564i
$549$	1.48255	+	19.7832i	0.0632736	+	0.844328i
$550$	−7.72688	+	10.7865i	−0.329475	+	0.459936i
$551$	−0.149555	+	0.484844i	−0.00637124	+	0.0206551i
$552$	−2.53571	+	22.5051i	−0.107927	+	0.957879i
$553$	−32.7834	−	13.3831i	−1.39409	−	0.569109i
$554$	−11.6029	−	9.25297i	−0.492958	−	0.393121i
$555$	−1.01021	+	0.0829131i	−0.0428811	+	0.00351947i
$556$	−11.2257	−	12.0984i	−0.476076	−	0.513088i
$557$	1.67982	+	0.450107i	0.0711763	+	0.0190716i	0.294231	−	0.955734i	$-0.404936\pi$
$557$	1.67982	+	0.450107i	0.0711763	+	0.0190716i	−0.223055	+	0.974806i	$0.571603\pi$
$558$	1.20548	+	4.49893i	0.0510322	+	0.190455i
$559$	−1.26455	−	5.54037i	−0.0534849	−	0.234333i
$560$	4.76688	−	0.686886i	0.201437	−	0.0290262i
$561$	6.95124	−	30.4554i	0.293482	−	1.28583i
$562$	−18.6609	+	0.698241i	−0.787162	+	0.0294535i
$563$	12.3778	−	9.13523i	0.521662	−	0.385004i	−0.300921	−	0.953649i	$-0.597294\pi$
$563$	12.3778	−	9.13523i	0.521662	−	0.385004i	0.822583	+	0.568645i	$0.192532\pi$
$564$	−1.49658	+	9.92919i	−0.0630176	+	0.418094i
$565$	25.7891	+	13.3968i	1.08496	+	0.563609i
$566$	−21.8403	−	4.98491i	−0.918018	−	0.209532i
$567$	2.01893	−	2.46230i	0.0847870	−	0.103407i
$568$	−11.0494	+	17.5850i	−0.463622	+	0.737850i
$569$	−10.6971	−	6.17599i	−0.448447	−	0.258911i	0.258727	−	0.965950i	$-0.416697\pi$
$569$	−10.6971	−	6.17599i	−0.448447	−	0.258911i	−0.707174	+	0.707040i	$0.750030\pi$
$570$	0.00216111	+	0.304737i	9.05191e−5	+	0.0127640i
$571$	−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	$0.309509\pi$
$572$	−4.38293	−	0.829294i	−0.183259	−	0.0346745i
$573$	1.35332	+	12.0110i	0.0565356	+	0.501767i
$574$	−6.05897	−	0.309158i	−0.252897	−	0.0129040i
$575$	34.1619	−	15.4851i	1.42465	−	0.645772i
$576$	−4.57567	−	1.41141i	−0.190653	−	0.0588087i
$577$	42.7269	−	18.6415i	1.77874	−	0.776058i	0.792690	−	0.609625i	$-0.208680\pi$
$577$	42.7269	−	18.6415i	1.77874	−	0.776058i	0.986053	−	0.166433i	$-0.0532250\pi$
$578$	22.1854	−	25.7799i	0.922793	−	1.07230i
$579$	−0.697980	−	1.77842i	−0.0290071	−	0.0739088i
$580$	0.703460	−	10.3737i	0.0292096	−	0.430744i
$581$	0.579514	+	2.28654i	0.0240423	+	0.0948618i
$582$	−11.6564	+	4.07874i	−0.483172	+	0.169069i
$583$	23.2062	−	19.9705i	0.961103	−	0.827096i
$584$	−4.02138	+	1.24043i	−0.166406	+	0.0513294i
$585$	−3.22855	−	1.10408i	−0.133484	−	0.0456482i
$586$	1.81435	+	12.0375i	0.0749503	+	0.497263i
$587$	−0.521127	−	0.521127i	−0.0215092	−	0.0215092i	0.696270	−	0.717780i	$-0.254841\pi$
$587$	−0.521127	−	0.521127i	−0.0215092	−	0.0215092i	−0.717780	+	0.696270i	$0.754841\pi$
$588$	−7.83518	−	8.27280i	−0.323117	−	0.341165i
$589$		−	0.559851i		−	0.0230682i
$590$	3.04644	+	6.84957i	0.125420	+	0.281992i
$591$	14.6948	−	21.5534i	0.604465	−	0.886587i
$592$	−0.149495	+	0.282858i	−0.00614421	+	0.0116254i
$593$	−20.7124	−	24.0682i	−0.850556	−	0.988364i	0.149444	−	0.988770i	$-0.452252\pi$
$593$	−20.7124	−	24.0682i	−0.850556	−	0.988364i	−1.00000		0.000406235i	$0.999871\pi$
$594$	12.8775	+	6.20145i	0.528368	+	0.254449i
$595$	−40.8192	−	21.9136i	−1.67342	−	0.898371i
$596$	−29.1349	+	14.0306i	−1.19341	+	0.574717i
$597$	−13.6516	−	5.95615i	−0.558724	−	0.243769i
$598$	−3.98743	−	3.43146i	−0.163058	−	0.140323i
$599$	−26.7443	−	10.4964i	−1.09274	−	0.428869i	−0.250580	−	0.968096i	$-0.580621\pi$
$599$	−26.7443	−	10.4964i	−1.09274	−	0.428869i	−0.842161	+	0.539226i	$0.818717\pi$
$600$	−3.56739	−	14.6676i	−0.145638	−	0.598804i
$601$	−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	$0.325949\pi$
$602$	12.4554	+	2.05071i	0.507643	+	0.0835805i
$603$	−14.7234	+	1.65892i	−0.599582	+	0.0675566i
$604$	−3.59377	−	5.27109i	−0.146228	−	0.214478i
$605$	−0.492936	−	2.09122i	−0.0200407	−	0.0850203i
$606$	5.00853	+	8.67503i	0.203458	+	0.352399i
$607$	−13.1172	+	3.51474i	−0.532410	+	0.142659i	−0.515001	−	0.857189i	$-0.672209\pi$
$607$	−13.1172	+	3.51474i	−0.532410	+	0.142659i	−0.0174093	+	0.999848i	$0.505542\pi$
$608$	0.764017	+	0.480064i	0.0309850	+	0.0194692i
$609$	−8.58566	+	5.23346i	−0.347908	+	0.212070i
$610$	−0.906743	−	20.3667i	−0.0367130	−	0.824623i
$611$	−4.13294	−	3.83481i	−0.167201	−	0.155140i
$612$	−10.9571	−	14.8463i	−0.442915	−	0.600128i
$613$	−10.4425	−	14.1490i	−0.421767	−	0.571474i	0.541268	−	0.840850i	$-0.317944\pi$
$613$	−10.4425	−	14.1490i	−0.421767	−	0.571474i	−0.963035	+	0.269376i	$0.913182\pi$
$614$	−8.48102	−	7.86924i	−0.342266	−	0.317577i
$615$	−0.342809	−	7.69995i	−0.0138234	−	0.310492i
$616$	13.0166	−	20.1044i	0.524453	−	0.810030i
$617$	20.6605	+	12.9818i	0.831760	+	0.522629i	0.879316	−	0.476239i	$-0.158000\pi$
$617$	20.6605	+	12.9818i	0.831760	+	0.522629i	−0.0475558	+	0.998869i	$0.515143\pi$
$618$	1.87025	−	0.501131i	0.0752324	−	0.0201585i
$619$	11.6637	+	20.2021i	0.468803	+	0.811990i	0.999364	−	0.0356564i	$-0.0113522\pi$
$619$	11.6637	+	20.2021i	0.468803	+	0.811990i	−0.530561	+	0.847647i	$0.678019\pi$
$620$	2.63216	+	11.1666i	0.105710	+	0.448462i
$621$	−22.7601	−	33.3830i	−0.913332	−	1.33961i
$622$	23.4586	−	2.64315i	0.940604	−	0.105981i
$623$	19.5471	+	34.9441i	0.783138	+	1.40000i
$624$	0.670941	−	0.535057i	0.0268591	−	0.0214194i
$625$	−17.8366	+	17.5173i	−0.713465	+	0.700690i
$626$	11.0360	+	4.33132i	0.441088	+	0.173114i
$627$	−0.465603	−	0.400684i	−0.0185944	−	0.0160018i
$628$	4.68622	+	2.04458i	0.187000	+	0.0815875i
$629$	2.77287	−	1.33535i	0.110562	−	0.0532437i
$630$	4.98097	−	5.71259i	0.198447	−	0.227595i
$631$	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	$0.556035\pi$
$632$	22.8505	+	26.5528i	0.908946	+	1.05621i
$633$	−2.66912	+	5.05022i	−0.106088	+	0.200728i
$634$	−3.07028	+	4.50327i	−0.121936	+	0.178848i
$635$	−2.77539	−	6.24015i	−0.110138	−	0.247633i
$636$			14.4098i			0.571386i
$637$	6.31607	−	1.01824i	0.250252	−	0.0403440i
$638$	−6.18273	−	6.18273i	−0.244777	−	0.244777i
$639$	−1.97445	−	13.0996i	−0.0781080	−	0.518213i
$640$	−20.1391	−	6.88706i	−0.796068	−	0.272235i
$641$	−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	$0.558573\pi$
$642$	10.0457	−	8.64501i	0.396471	−	0.341191i
$643$	9.59254	−	3.35658i	0.378293	−	0.132370i	−0.134433	−	0.990923i	$-0.542921\pi$
$643$	9.59254	−	3.35658i	0.378293	−	0.132370i	0.512726	+	0.858552i	$0.328636\pi$
$644$	−24.9387	+	12.7503i	−0.982724	+	0.502431i
$645$	−1.08500	+	16.0001i	−0.0427217	+	0.630003i
$646$	−0.338053	−	0.861345i	−0.0133005	−	0.0338892i
$647$	20.5726	−	23.9058i	0.808794	−	0.939835i	−0.190329	−	0.981720i	$-0.560955\pi$
$647$	20.5726	−	23.9058i	0.808794	−	0.939835i	0.999122	+	0.0418852i	$0.0133364\pi$
$648$	−2.88730	+	1.25972i	−0.113424	+	0.0494864i
$649$	−14.4394	−	4.45395i	−0.566795	−	0.174833i
$650$	3.28185	+	1.23461i	0.128725	+	0.0484253i
$651$	7.35046	−	8.31040i	0.288087	−	0.325710i
$652$	1.31767	+	11.6946i	0.0516038	+	0.457996i
$653$	−8.65690	−	1.63797i	−0.338771	−	0.0640988i	0.0137430	−	0.999906i	$-0.495625\pi$
$653$	−8.65690	−	1.63797i	−0.338771	−	0.0640988i	−0.352514	+	0.935807i	$0.614673\pi$
$654$	−1.05458	+	0.978504i	−0.0412372	+	0.0382625i
$655$	0.171301	+	24.1551i	0.00669329	+	0.943817i
$656$	−2.10687	−	1.21640i	−0.0822595	−	0.0474926i
$657$	1.42819	−	2.27295i	0.0557189	−	0.0886761i
$658$	11.3559	−	5.27997i	0.442701	−	0.205835i
$659$	36.3871	+	8.30511i	1.41744	+	0.323521i	0.861524	−	0.507718i	$-0.169511\pi$
$659$	36.3871	+	8.30511i	1.41744	+	0.323521i	0.555916	+	0.831239i	$0.312368\pi$
$660$	11.1706	+	5.80287i	0.434816	+	0.225877i
$661$	−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	$0.917851\pi$
$662$	19.6335	−	14.4902i	0.763076	−	0.563176i
$663$	−8.24949	+	0.308674i	−0.320384	+	0.0119879i
$664$	0.519280	−	2.27511i	0.0201520	−	0.0882916i
$665$	−0.756035	+	0.508301i	−0.0293178	+	0.0197111i
$666$	0.112036	+	0.490860i	0.00434129	+	0.0190204i
$667$	6.39721	+	23.8747i	0.247701	+	0.924432i
$668$	8.20115	+	2.19749i	0.317312	+	0.0850235i
$669$	11.6445	+	12.5498i	0.450203	+	0.485204i
$670$	15.1749	−	1.24548i	0.586257	−	0.0481170i
$671$	32.1285	+	25.6216i	1.24031	+	0.989111i
$672$	5.03813	+	17.1571i	0.194350	+	0.661848i
$673$	−3.29302	+	29.2263i	−0.126936	+	1.12659i	0.755166	+	0.655534i	$0.227556\pi$
$673$	−3.29302	+	29.2263i	−0.126936	+	1.12659i	−0.882102	+	0.471058i	$0.843872\pi$
$674$	−6.43146	+	20.8503i	−0.247730	+	0.803123i
$675$	21.8926	+	15.6828i	0.842646	+	0.603630i
$676$	−1.28291	−	17.1193i	−0.0493428	−	0.658434i
$677$	7.25246	−	16.6228i	0.278735	−	0.638867i	−0.719730	−	0.694254i	$-0.755734\pi$
$677$	7.25246	−	16.6228i	0.278735	−	0.638867i	0.998465	+	0.0553870i	$0.0176392\pi$
$678$	−3.79898	+	10.8569i	−0.145899	+	0.416955i
$679$	−29.4036	−	22.3239i	−1.12841	−	0.856714i
$680$	26.0872	+	37.6859i	1.00040	+	1.44519i
$681$	1.65355	−	22.0651i	0.0633641	−	0.845535i
$682$	8.52978	+	4.50812i	0.326622	+	0.172625i
$683$	3.81663	+	20.1714i	0.146039	+	0.771836i	0.976626	+	0.214947i	$0.0689577\pi$
$683$	3.81663	+	20.1714i	0.146039	+	0.771836i	−0.830587	+	0.556890i	$0.811995\pi$
$684$	−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
$688$	4.07274	+	3.00582i	0.155272	+	0.114596i
$689$	−6.68492	−	4.55770i	−0.254675	−	0.173635i
$690$	7.98718	+	12.5136i	0.304067	+	0.476386i
$691$	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	$0.393622\pi$
$692$	−3.22672	−	9.22145i	−0.122662	−	0.350547i
$693$	2.07161	+	15.1362i	0.0786938	+	0.574978i
$694$	4.94087	+	10.2598i	0.187553	+	0.389457i
$695$	−25.8854	−	3.71405i	−0.981888	−	0.140882i
$696$	9.91968	−	0.743377i	0.376005	−	0.0281777i
$697$	9.35859	+	21.4501i	0.354482	+	0.812481i
$698$	8.78125	−	4.64102i	0.332375	−	0.175665i
$699$	5.87097	+	7.36196i	0.222060	+	0.278455i
$700$	12.6899	−	13.6929i	0.479631	−	0.517545i
$701$	−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	$0.391546\pi$
$702$	0.702209	−	3.71126i	0.0265032	−	0.140073i
$703$	0.00226288	−	0.0604767i	8.53461e−5	−	0.00228092i
$704$	−8.58984	+	4.95935i	−0.323742	+	0.186912i
$705$	8.05262	+	13.7219i	0.303279	+	0.516797i
$706$	6.61129	−	1.50898i	0.248819	−	0.0567913i
$707$	−13.3581	+	26.8010i	−0.502382	+	1.00796i
$708$	6.02190	−	3.78381i	0.226317	−	0.142204i
$709$	18.1610	−	19.5729i	0.682050	−	0.735076i	−0.293231	−	0.956042i	$-0.594731\pi$
$709$	18.1610	−	19.5729i	0.682050	−	0.735076i	0.975282	+	0.220966i	$0.0709210\pi$
$710$	1.62014	+	13.5169i	0.0608027	+	0.507279i
$711$	−22.0961	−	3.33045i	−0.828668	−	0.124902i
$712$	−1.48113	−	39.5840i	−0.0555077	−	1.48347i
$713$	−14.5099	−	23.0924i	−0.543402	−	0.864819i
$714$	6.29083	−	17.2242i	0.235428	−	0.644599i
$715$	−6.22521	+	3.34681i	−0.232810	+	0.125164i
$716$	10.0832	−	17.4646i	0.376826	−	0.652682i
$717$	−2.85770	+	10.6651i	−0.106723	+	0.398295i
$718$	−22.9126	−	0.857329i	−0.855091	−	0.0319952i
$719$	8.55568	−	5.83316i	0.319073	−	0.217540i	−0.393183	−	0.919460i	$-0.628626\pi$
$719$	8.55568	−	5.83316i	0.319073	−	0.217540i	0.712256	+	0.701920i	$0.247674\pi$
$720$	2.82121	−	1.13039i	0.105140	−	0.0421273i
$721$	4.33565	+	3.83483i	0.161468	+	0.142817i
$722$	14.4691	+	1.63028i	0.538484	+	0.0606726i
$723$	7.17840	+	13.5822i	0.266967	+	0.505127i
$724$	4.62239	−	11.7777i	0.171790	−	0.437713i
$725$	−9.47258	−	13.4789i	−0.351803	−	0.500595i
$726$	0.791600	−	0.310680i	0.0293790	−	0.0115304i
$727$	28.6096	+	10.0109i	1.06107	+	0.371285i	0.803704	−	0.595029i	$-0.202859\pi$
$727$	28.6096	+	10.0109i	1.06107	+	0.371285i	0.257367	+	0.966314i	$0.417145\pi$
$728$	−6.02216	−	1.94754i	−0.223196	−	0.0721806i
$729$	8.95818	−	18.6019i	0.331785	−	0.688958i
$730$	−1.53776	+	2.29020i	−0.0569149	+	0.0847642i
$731$	−14.3526	−	46.5299i	−0.530849	−	1.72097i
$732$	−19.0040	+	3.59576i	−0.702410	+	0.132903i
$733$	11.5655	−	15.6707i	0.427181	−	0.578810i	−0.537157	−	0.843482i	$-0.680502\pi$
$733$	11.5655	−	15.6707i	0.427181	−	0.578810i	0.964338	+	0.264672i	$0.0852638\pi$
$734$	−17.1099			−0.631539
$735$	−17.8962	−	2.38102i	−0.660111	−	0.0878253i
$736$	43.9558			1.62023
$737$	−18.2249	+	24.6938i	−0.671322	+	0.909609i
$738$	−3.76179	+	0.711768i	−0.138473	+	0.0262006i
$739$	15.7634	+	51.1036i	0.579865	+	1.87987i	0.462086	+	0.886835i	$0.347101\pi$
$739$	15.7634	+	51.1036i	0.579865	+	1.87987i	0.117778	+	0.993040i	$0.462423\pi$
$740$	0.239199	+	1.21689i	0.00879312	+	0.0447337i
$741$	−0.0704330	+	0.146256i	−0.00258742	+	0.00537283i
$742$	14.9850	−	9.92122i	0.550117	−	0.364219i
$743$	32.9737	+	11.5380i	1.20969	+	0.423288i	0.858401	−	0.512979i	$-0.171458\pi$
$743$	32.9737	+	11.5380i	1.20969	+	0.423288i	0.351287	+	0.936268i	$0.385744\pi$
$744$	−10.2174	+	4.01002i	−0.374586	+	0.147014i
$745$	−21.9032	+	46.3199i	−0.802471	+	1.69703i
$746$	1.04677	−	2.66713i	0.0383250	−	0.0976504i
$747$	0.695558	+	1.31606i	0.0254491	+	0.0481521i
$748$	−37.9809	−	4.27942i	−1.38872	−	0.156471i
$749$	38.1275	+	10.7733i	1.39315	+	0.393647i
$750$	−7.86566	−	6.00342i	−0.287213	−	0.219214i
$751$	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	$0.190333\pi$
$752$	5.01836	+	0.187774i	0.183001	+	0.00684741i
$753$	1.31986	−	4.92579i	0.0480984	−	0.179506i
$754$	−1.15533	+	2.00108i	−0.0420745	+	0.0728752i
$755$	−9.68013	−	2.91091i	−0.352296	−	0.105939i
$756$	−16.8810	−	10.9296i	−0.613957	−	0.397505i
$757$	−5.78216	−	9.20225i	−0.210156	−	0.334461i	0.724968	−	0.688783i	$-0.241855\pi$
$757$	−5.78216	−	9.20225i	−0.210156	−	0.334461i	−0.935124	+	0.354322i	$0.884712\pi$
$758$	0.732206	+	19.5686i	0.0265949	+	0.710764i
$759$	−29.5897	−	4.45993i	−1.07404	−	0.161885i
$760$	0.894877	−	0.107260i	0.0324606	−	0.00389074i
$761$	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	$0.122094\pi$
$762$	2.28878	−	1.43814i	0.0829138	−	0.0520982i
$763$	−4.17945	−	1.01384i	−0.151306	−	0.0367034i
$764$	14.4180	−	3.29081i	0.521624	−	0.119057i
$765$	−28.2932	−	7.36650i	−1.02294	−	0.266337i
$766$	−2.88586	+	1.66615i	−0.104270	+	0.0602005i
$767$	−0.149312	+	3.99043i	−0.00539133	+	0.144086i
$768$	2.79614	−	14.7779i	0.100897	−	0.533253i
$769$	5.43361	−	6.81353i	0.195941	−	0.245702i	−0.674149	−	0.738596i	$-0.735489\pi$
$769$	5.43361	−	6.81353i	0.195941	−	0.245702i	0.870090	+	0.492893i	$0.164061\pi$
$770$	−1.65651	−	15.6118i	−0.0596965	−	0.562611i
$771$	19.9644	+	25.0346i	0.719001	+	0.901599i
$772$	−2.06665	+	1.09225i	−0.0743802	+	0.0393111i
$773$	−6.48177	−	14.8564i	−0.233133	−	0.534347i	0.760192	−	0.649699i	$-0.225105\pi$
$773$	−6.48177	−	14.8564i	−0.233133	−	0.534347i	−0.993325	+	0.115352i	$0.963200\pi$
$774$	7.94360	−	0.595290i	0.285527	−	0.0213973i
$775$	14.3715	+	11.1311i	0.516240	+	0.399842i
$776$	15.8468	+	32.9063i	0.568868	+	1.18127i
$777$	0.827608	−	0.868003i	0.0296903	−	0.0311394i
$778$	2.31493	+	6.61568i	0.0829942	+	0.237184i
$779$	0.458905	+	0.0343902i	0.0164420	+	0.00123216i
$780$	0.717209	−	3.24831i	0.0256802	−	0.116308i
$781$	−22.6728	−	15.4581i	−0.811297	−	0.553133i
$782$	−36.2678	−	26.7668i	−1.29693	−	0.957180i
$783$	−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
$787$	−7.92217	−	41.8697i	−0.282395	−	1.49249i	−0.780379	−	0.625306i	$-0.784974\pi$
$787$	−7.92217	−	41.8697i	−0.282395	−	1.49249i	0.497984	−	0.867186i	$-0.334074\pi$
$788$	−28.2183	−	14.9138i	−1.00524	−	0.531283i
$789$	−0.805502	+	10.7487i	−0.0286766	+	0.382663i
$790$	22.5925	+	4.10899i	0.803804	+	0.146191i
$791$	−33.3318	+	8.44779i	−1.18514	+	0.300369i
$792$	4.99185	−	14.2659i	0.177378	−	0.506916i
$793$	4.34269	−	9.95356i	0.154214	−	0.353461i
$794$	0.375790	+	5.01456i	0.0133363	+	0.177960i
$795$	14.3617	+	17.7493i	0.509357	+	0.629504i
$796$	−5.37152	+	17.4140i	−0.190388	+	0.617224i
$797$	−0.714568	+	6.34197i	−0.0253113	+	0.224644i	0.974688	+	0.223569i	$0.0717708\pi$
$797$	−0.714568	+	6.34197i	−0.0253113	+	0.224644i	−0.999999	+	0.00107504i	$0.999658\pi$
$798$	−0.241644	−	0.267630i	−0.00855410	−	0.00947398i
$799$	−37.7693	−	30.1200i	−1.33618	−	1.06557i
$800$	−27.5138	+	10.0677i	−0.972760	+	0.355948i
$801$	17.1862	+	18.5223i	0.607243	+	0.654452i
$802$	1.02564	+	0.274821i	0.0362168	+	0.00970425i
$803$	−1.43915	−	5.37099i	−0.0507866	−	0.189538i
$804$	−3.21431	−	14.0828i	−0.113360	−	0.496662i
$805$	−18.0106	+	40.5607i	−0.634792	+	1.42958i
$806$	0.567335	−	2.48566i	0.0199835	−	0.0875535i
$807$	11.8590	−	0.443734i	0.417458	−	0.0156202i
$808$	23.8365	−	17.5922i	0.838567	−	0.618890i
$809$	3.93717	−	26.1214i	0.138424	−	0.918380i	−0.806534	−	0.591188i	$-0.798659\pi$
$809$	3.93717	−	26.1214i	0.138424	−	0.918380i	0.944958	−	0.327193i	$-0.106103\pi$
$810$	−0.951902	+	1.83242i	−0.0334464	+	0.0643848i
$811$	−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	$0.578223\pi$
$812$	7.53916	+	9.72177i	0.264573	+	0.341167i
$813$	−3.04639	+	4.84831i	−0.106842	+	0.170038i
$814$	0.903190	+	0.521457i	0.0316568	+	0.0182771i
$815$	13.2786	+	13.0916i	0.465130	+	0.458579i
$816$	5.39024	−	5.00141i	0.188696	−	0.175084i
$817$	−0.940810	−	0.178011i	−0.0329148	−	0.00622781i
$818$	−0.122092	−	1.08360i	−0.00426886	−	0.0378872i
$819$	3.72199	−	1.56407i	0.130057	−	0.0546530i
$820$	−9.31487	+	1.47162i	−0.325289	+	0.0513913i
$821$	−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	$0.655777\pi$
$822$	0.253336	−	0.110530i	0.00883612	−	0.00385516i
$823$	−7.75814	+	9.01513i	−0.270432	+	0.314248i	−0.876723	−	0.480995i	$-0.840276\pi$
$823$	−7.75814	+	9.01513i	−0.270432	+	0.314248i	0.606292	+	0.795242i	$0.292656\pi$
$824$	−2.09208	−	5.33053i	−0.0728810	−	0.185698i
$825$	19.5429	−	3.98562i	0.680398	−	0.138762i
$826$	−8.08096	−	3.65711i	−0.281172	−	0.127247i
$827$	−12.5014	+	4.37445i	−0.434718	+	0.152114i	−0.538761	−	0.842458i	$-0.681108\pi$
$827$	−12.5014	+	4.37445i	−0.434718	+	0.152114i	0.104044	+	0.994573i	$0.466822\pi$
$828$	−13.3974	+	11.5294i	−0.465592	+	0.400675i
$829$	35.7797	−	11.0366i	1.24268	−	0.383316i	0.397403	−	0.917644i	$-0.369911\pi$
$829$	35.7797	−	11.0366i	1.24268	−	0.383316i	0.845277	+	0.534328i	$0.179435\pi$
$830$	−0.673465	−	1.37346i	−0.0233763	−	0.0476736i
$831$	3.32491	+	22.0593i	0.115340	+	0.765229i
$832$	1.85344	+	1.85344i	0.0642566	+	0.0642566i
$833$	53.3156	−	12.7446i	1.84728	−	0.441575i
$834$		−	10.3503i		−	0.358401i
$835$	12.2919	−	5.46701i	0.425380	−	0.189194i
$836$	−0.423381	+	0.620985i	−0.0146429	+	0.0214772i
$837$	9.14985	−	17.3124i	0.316265	−	0.598403i
$838$	18.7873	+	21.8312i	0.648996	+	0.754147i
$839$	−8.39018	−	4.04050i	−0.289661	−	0.139493i	0.283411	−	0.958999i	$-0.408534\pi$
$839$	−8.39018	−	4.04050i	−0.289661	−	0.139493i	−0.573072	+	0.819505i	$0.694248\pi$
$840$	14.6918	+	10.1570i	0.506914	+	0.350448i
$841$	−16.3468	+	7.87218i	−0.563681	+	0.271455i
$842$	−16.2136	−	7.07392i	−0.558758	−	0.243784i
$843$	21.2768	+	18.3102i	0.732813	+	0.630637i
$844$	6.50587	+	2.55336i	0.223941	+	0.0878904i
$845$	−18.6424	−	19.8081i	−0.641318	−	0.681420i
$846$	6.17880	−	4.92743i	0.212431	−	0.169408i
$847$	2.08081	+	1.46045i	0.0714974	+	0.0501818i
$848$	7.16132	−	0.806887i	0.245921	−	0.0277086i
$849$	18.9697	+	27.8234i	0.651038	+	0.954897i
$850$	28.8322	+	8.44765i	0.988938	+	0.289752i
$851$	−1.47407	−	2.55316i	−0.0505304	−	0.0875212i
$852$	12.4753	−	3.34274i	0.427396	−	0.114521i
$853$	7.66906	+	4.81879i	0.262584	+	0.164992i	0.656889	−	0.753987i	$-0.271872\pi$
$853$	7.66906	+	4.81879i	0.262584	+	0.164992i	−0.394305	+	0.918979i	$0.629015\pi$
$854$	16.8237	+	17.2869i	0.575694	+	0.591547i
$855$	−0.388037	+	0.424199i	−0.0132706	+	0.0145073i
$856$	−28.7333	−	26.6606i	−0.982084	−	0.911240i
$857$	−14.4748	−	19.6126i	−0.494448	−	0.669954i	0.484328	−	0.874887i	$-0.339064\pi$
$857$	−14.4748	−	19.6126i	−0.494448	−	0.669954i	−0.978776	+	0.204933i	$0.934302\pi$
$858$	−1.66117	−	2.25081i	−0.0567114	−	0.0768413i
$859$	−4.41747	−	4.09882i	−0.150722	−	0.139850i	0.601208	−	0.799093i	$-0.294686\pi$
$859$	−4.41747	−	4.09882i	−0.150722	−	0.139850i	−0.751930	+	0.659243i	$0.770877\pi$
$860$	19.6020	−	0.872700i	0.668424	−	0.0297588i
$861$	6.36045	+	6.53560i	0.216764	+	0.222733i
$862$	6.51532	+	4.09385i	0.221913	+	0.139437i
$863$	31.7716	−	8.51318i	1.08152	−	0.289792i	0.326301	−	0.945266i	$-0.394198\pi$
$863$	31.7716	−	8.51318i	1.08152	−	0.289792i	0.755218	+	0.655474i	$0.227531\pi$
$864$	15.7800	+	27.3317i	0.536845	+	0.929844i
$865$	−13.1652	−	8.14259i	−0.447630	−	0.276856i
$866$	−8.39731	−	12.3166i	−0.285352	−	0.418535i
$867$	−50.8052	+	5.72437i	−1.72543	+	0.194410i
$868$	−11.1110	−	7.79846i	−0.377132	−	0.264697i
$869$	−36.1885	+	28.8593i	−1.22761	+	0.978986i
$870$	4.74836	−	4.46891i	0.160984	−	0.151510i
$871$	7.54988	+	2.96311i	0.255818	+	0.100401i
$872$	3.22493	+	2.77528i	0.109210	+	0.0939828i
$873$	−21.3534	−	9.31640i	−0.722703	−	0.315312i
$874$	−0.798589	+	0.384580i	−0.0270127	+	0.0130086i
$875$	1.98352	−	29.5138i	0.0670553	−	0.997749i
$876$	2.35791	+	1.13551i	0.0796665	+	0.0383653i
$877$	1.80928	+	2.10242i	0.0610951	+	0.0709938i	0.787688	−	0.616075i	$-0.211278\pi$
$877$	1.80928	+	2.10242i	0.0610951	+	0.0709938i	−0.726593	+	0.687069i	$0.758897\pi$
$878$	2.20933	−	4.18027i	0.0745614	−	0.141077i
$879$	10.3083	−	15.1195i	0.347689	−	0.509967i
$880$	2.25838	−	5.87646i	0.0761300	−	0.198095i
$881$			26.7987i			0.902872i	0.892304	+	0.451436i	$0.149088\pi$
$881$			26.7987i			0.902872i	−0.892304	+	0.451436i	$0.850912\pi$
$882$	0.0918153	+	8.96732i	0.00309158	+	0.301945i
$883$	18.7649	+	18.7649i	0.631489	+	0.631489i	0.948441	−	0.316953i	$-0.102660\pi$
$883$	18.7649	+	18.7649i	0.631489	+	0.631489i	−0.316953	+	0.948441i	$0.602660\pi$
$884$	1.50540	+	9.98771i	0.0506322	+	0.335923i
$885$	3.64631	−	10.6625i	0.122569	−	0.358417i
$886$	16.3321	−	5.03779i	0.548688	−	0.169248i
$887$	24.4873	−	21.0730i	0.822203	−	0.707563i	−0.136911	−	0.990583i	$-0.543717\pi$
$887$	24.4873	−	21.0730i	0.822203	−	0.707563i	0.959114	+	0.283021i	$0.0913365\pi$
$888$	−1.11992	+	0.391876i	−0.0375819	+	0.0131505i
$889$	7.36198	+	3.33173i	0.246913	+	0.111743i
$890$	−17.0761	−	19.5605i	−0.572392	−	0.655669i
$891$	−1.52065	−	3.87454i	−0.0509436	−	0.129802i
$892$	13.6632	−	15.8770i	0.457479	−	0.531601i
$893$	−0.870682	+	0.379875i	−0.0291363	+	0.0127120i
$894$	−19.3787	−	5.97753i	−0.648120	−	0.199919i
$895$	−4.98630	−	31.5616i	−0.166674	−	1.05499i
$896$	23.2171	−	9.75638i	0.775629	−	0.325938i
$897$	0.885398	+	7.85813i	0.0295626	+	0.262375i
$898$	−14.1457	−	2.67650i	−0.472047	−	0.0893161i
$899$	−8.78126	+	8.14782i	−0.292872	+	0.271745i
$900$	5.74529	−	10.2853i	0.191510	−	0.342844i
$901$	−60.0376	−	34.6627i	−2.00014	−	1.15478i
$902$	−4.21923	+	6.71487i	−0.140485	+	0.223581i
$903$	−11.6282	−	14.9946i	−0.386962	−	0.498988i
$904$	33.1652	+	7.56974i	1.10306	+	0.251766i
$905$	−6.04471	−	19.1141i	−0.200933	−	0.635375i
$906$	0.596295	−	3.95616i	0.0198106	−	0.131435i
$907$	−45.7328	+	33.7524i	−1.51853	+	1.12073i	−0.562761	+	0.826620i	$0.690261\pi$
$907$	−45.7328	+	33.7524i	−1.51853	+	1.12073i	−0.955772	+	0.294109i	$0.904977\pi$
$908$	−27.0539	+	1.01229i	−0.897816	+	0.0335939i
$909$	−4.20505	+	18.4235i	−0.139473	+	0.611070i
$910$	−3.87178	+	1.49064i	−0.128348	+	0.0494143i
$911$	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	$0.817872\pi$
$912$	−0.0374232	−	0.139665i	−0.00123921	−	0.00462478i
$913$	2.97834	+	0.798043i	0.0985686	+	0.0264114i
$914$	−16.3195	−	17.5883i	−0.539802	−	0.581768i
$915$	−19.8245	+	23.3697i	−0.655379	+	0.772578i
$916$	10.3338	+	8.24095i	0.341439	+	0.272289i
$917$	−19.1540	−	21.2137i	−0.632519	−	0.700539i
$918$	3.62361	−	32.1605i	0.119597	−	1.06145i
$919$	6.52199	−	21.1438i	0.215140	−	0.697468i	−0.782095	−	0.623159i	$-0.785849\pi$
$919$	6.52199	−	21.1438i	0.215140	−	0.697468i	0.997235	−	0.0743088i	$-0.0236750\pi$
$920$	34.1315	−	27.6172i	1.12528	−	0.910513i
$921$	1.29965	+	17.3426i	0.0428250	+	0.571460i
$922$	−7.14928	+	16.3863i	−0.235449	+	0.539655i
$923$	−2.39508	+	6.84475i	−0.0788351	+	0.225298i
$924$	−14.4378	+	3.65918i	−0.474967	+	0.120378i
$925$	1.50746	+	1.26051i	0.0495650	+	0.0414452i
$926$	−0.472779	+	6.30880i	−0.0155365	+	0.207320i
$927$	3.22942	+	1.70680i	0.106068	+	0.0560586i
$928$	−3.58936	−	18.9703i	−0.117827	−	0.622729i
$929$	−23.3712	+	3.52264i	−0.766783	+	0.115574i	−0.520775	−	0.853694i	$-0.674357\pi$
$929$	−23.3712	+	3.52264i	−0.766783	+	0.115574i	−0.246008	+	0.969268i	$0.579119\pi$
$930$	−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
$933$	−28.5521	−	21.0724i	−0.934754	−	0.689880i
$934$	16.4020	+	11.1827i	0.536689	+	0.365908i
$935$	−51.0482	+	32.5829i	−1.66945	+	1.06557i
$936$	−3.98294	−	0.298480i	−0.130187	−	0.00975614i
$937$	10.7626	+	30.7577i	0.351599	+	1.00481i	0.974864	+	0.222801i	$0.0715200\pi$
$937$	10.7626	+	30.7577i	0.351599	+	1.00481i	−0.623265	+	0.782011i	$0.714194\pi$
$938$	−12.4319	+	13.0387i	−0.405916	+	0.425729i
$939$	−7.73238	−	16.0564i	−0.252337	−	0.523982i
$940$	15.5804	−	11.6704i	0.508176	−	0.380647i
$941$	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	$0.392334\pi$
$942$	1.28221	+	2.93886i	0.0417768	+	0.0957534i
$943$	19.8200	−	10.4752i	0.645428	−	0.341119i
$944$	−2.21766	−	2.78086i	−0.0721787	−	0.0905093i
$945$	−31.6864	+	3.36212i	−1.03076	+	0.109370i
$946$	10.2879	−	12.9006i	0.334488	−	0.419434i
$947$	1.78688	−	9.44387i	0.0580657	−	0.306885i	−0.941479	−	0.337073i	$-0.890563\pi$
$947$	1.78688	−	9.44387i	0.0580657	−	0.306885i	0.999544	+	0.0301884i	$0.00961071\pi$
$948$	0.814579	−	21.7701i	0.0264563	−	0.707060i
$949$	−1.27257	+	0.734717i	−0.0413093	+	0.0238499i
$950$	0.411785	−	0.423635i	0.0133601	−	0.0137445i
$951$	7.98754	−	1.82310i	0.259014	−	0.0591182i
$952$	−52.7033	−	12.7846i	−1.70812	−	0.414351i
$953$	−35.4171	+	22.2540i	−1.14727	+	0.720879i	−0.964969	−	0.262363i	$-0.915498\pi$
$953$	−35.4171	+	22.2540i	−1.14727	+	0.720879i	−0.182304	+	0.983242i	$0.558355\pi$
$954$	7.71394	−	8.31366i	0.249748	−	0.269165i
$955$	14.4796	−	18.4233i	0.468547	−	0.596164i
$956$	13.3584	+	2.01346i	0.432042	+	0.0651199i
$957$	0.491454	+	13.1344i	0.0158864	+	0.424574i
$958$	−7.86198	−	12.5123i	−0.254009	−	0.404253i
$959$	0.693597	+	0.449068i	0.0223974	+	0.0145012i
$960$	−3.50260	−	6.51498i	−0.113046	−	0.210270i
$961$	−8.89115	+	15.3999i	−0.286811	+	0.496772i
$962$	0.0713320	−	0.266215i	0.00229984	−	0.00858310i
$963$	24.9852	+	0.934880i	0.805137	+	0.0301261i
$964$	15.5303	−	10.5884i	0.500196	−	0.341028i
$965$	−1.45699	+	3.40514i	−0.0469021	+	0.109615i
$966$	−16.9035	−	4.77624i	−0.543861	−	0.153673i
$967$	−28.3023	−	3.18891i	−0.910141	−	0.102548i	−0.355537	−	0.934662i	$-0.615702\pi$
$967$	−28.3023	−	3.18891i	−0.910141	−	0.102548i	−0.554605	+	0.832114i	$0.687130\pi$
$968$	−1.17518	−	2.22356i	−0.0377718	−	0.0714678i
$969$	−0.508163	+	1.29478i	−0.0163246	+	0.0415943i
$970$	21.6432	+	10.2344i	0.694922	+	0.328606i
$971$	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	$-0.0916427\pi$
$972$	−19.6742	−	6.88432i	−0.631052	−	0.220815i
$973$	25.7995	−	17.0813i	0.827095	−	0.547600i
$974$	−4.43474	+	9.20884i	−0.142098	+	0.295070i
$975$	−2.35405	−	4.71594i	−0.0753898	−	0.151031i
$976$	2.85115	+	9.24319i	0.0912630	+	0.295867i
$977$	−8.06460	+	1.52590i	−0.258009	+	0.0488180i	−0.313307	−	0.949652i	$-0.601437\pi$
$977$	−8.06460	+	1.52590i	−0.258009	+	0.0488180i	0.0552976	+	0.998470i	$0.482389\pi$
$978$	−4.38265	+	5.93828i	−0.140142	+	0.189885i
$979$	52.3387			1.67275
$980$	−0.443299	+	22.0849i	−0.0141607	+	0.705477i
$981$	−2.71396			−0.0866501
$982$	−10.9006	+	14.7698i	−0.347853	+	0.471325i
$983$	−26.0807	+	4.93474i	−0.831845	+	0.157394i	−0.584356	−	0.811497i	$-0.698653\pi$
$983$	−26.0807	+	4.93474i	−0.831845	+	0.157394i	−0.247489	+	0.968891i	$0.579605\pi$
$984$	−2.65935	−	8.62141i	−0.0847771	−	0.274840i
$985$	−49.6220	+	9.75399i	−1.58109	+	0.310788i
$986$	−8.59033	+	17.8380i	−0.273572	+	0.568078i
$987$	−17.9119	−	5.79262i	−0.570141	−	0.184381i
$988$	0.187471	+	0.0655989i	0.00596424	+	0.00208698i
$989$	−43.4197	+	17.0410i	−1.38066	+	0.541871i
$990$	−3.33839	−	9.32786i	−0.106101	−	0.296459i
$991$	−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	$0.955266\pi$
$992$	9.95432	+	18.8345i	0.316050	+	0.597996i
$993$	−36.4499	−	4.10692i	−1.15670	−	0.130329i
$994$	−12.0655	−	10.6718i	−0.382694	−	0.338488i
$995$	10.7395	+	26.8034i	0.340466	+	0.849724i
$996$	−1.19907	+	0.817509i	−0.0379938	+	0.0259038i
$997$	25.0013	+	0.935481i	0.791798	+	0.0296270i	0.430231	−	0.902719i	$-0.358432\pi$
$997$	25.0013	+	0.935481i	0.791798	+	0.0296270i	0.361567	+	0.932346i	$0.382242\pi$
$998$	2.88104	−	10.7522i	0.0911978	−	0.340355i
$999$	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.103.17	✓	624
5.2	odd	4	inner	245.2.x.a.152.17	yes	624
49.10	odd	42	inner	245.2.x.a.108.17	yes	624
245.157	even	84	inner	245.2.x.a.157.17	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.17	✓	624	1.1	even	1	trivial
245.2.x.a.108.17	yes	624	49.10	odd	42	inner
245.2.x.a.152.17	yes	624	5.2	odd	4	inner
245.2.x.a.157.17	yes	624	245.157	even	84	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+(0.455643 - 0.617374i) q^{2} +(-1.13331 + 0.214434i) q^{3} +(0.415970 + 1.34854i) q^{4} +(1.85641 + 1.24649i) q^{5} +(-0.384000 + 0.797384i) q^{6} +(-2.62131 + 0.358764i) q^{7} +(2.47059 + 0.864496i) q^{8} +(-1.55421 + 0.609981i) q^{9} +(1.61541 - 0.578147i) q^{10} +(-1.26351 + 3.21938i) q^{11} +(-0.760597 - 1.43912i) q^{12} +(0.908200 + 0.102330i) q^{13} +(-0.972892 + 1.78180i) q^{14} +(-2.37119 - 1.01458i) q^{15} +(-0.672617 + 0.458583i) q^{16} +(7.82562 + 0.292814i) q^{17} +(-0.331576 + 1.23746i) q^{18} +(0.0769953 - 0.133360i) q^{19} +(-0.908729 + 3.02195i) q^{20} +(2.89384 - 0.968691i) q^{21} +(1.41185 + 2.24695i) q^{22} +(-0.280491 - 7.49628i) q^{23} +(-2.98532 - 0.449965i) q^{24} +(1.89253 + 4.62799i) q^{25} +(0.476990 - 0.514073i) q^{26} +(4.56049 - 2.86554i) q^{27} +(-1.57420 - 3.38572i) q^{28} +(-3.21231 + 0.733188i) q^{29} +(-1.70679 + 1.00162i) q^{30} +(3.14854 - 1.81781i) q^{31} +(-0.219097 + 5.85549i) q^{32} +(0.741610 - 3.91950i) q^{33} +(3.74646 - 4.69792i) q^{34} +(-5.31343 - 2.60142i) q^{35} +(-1.46909 - 1.84218i) q^{36} +(0.347461 - 0.183639i) q^{37} +(-0.0472505 - 0.108299i) q^{38} +(-1.05122 + 0.0787778i) q^{39} +(3.50884 + 4.68442i) q^{40} +(1.29664 + 2.69249i) q^{41} +(0.720512 - 2.22796i) q^{42} +(-2.05365 - 5.86900i) q^{43} +(-4.86705 - 0.364735i) q^{44} +(-3.64558 - 0.804924i) q^{45} +(-4.75582 - 3.24246i) q^{46} +(-4.96343 - 3.66318i) 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} +(0.239788 + 1.26731i) q^{52} +(-7.82670 - 4.13653i) q^{53} +(0.308841 - 4.12119i) q^{54} +(-6.35852 + 4.40154i) q^{55} +(-6.78633 - 1.37976i) q^{56} +(-0.0586628 + 0.167649i) q^{57} +(-1.01101 + 2.31727i) q^{58} +(0.326512 + 4.35700i) q^{59} +(0.381865 - 3.61968i) q^{60} +(3.50233 - 11.3543i) q^{61} +(0.312340 - 2.77210i) q^{62} +(3.85522 - 2.15654i) q^{63} +(2.24226 + 1.78815i) q^{64} +(1.55844 + 1.32203i) q^{65} +(-2.08189 - 2.24374i) q^{66} +(8.57181 + 2.29681i) q^{67} +(2.86035 + 10.6750i) q^{68} +(1.92534 + 8.43549i) q^{69} +(-4.02708 + 2.09506i) q^{70} +(-1.76559 + 7.73555i) q^{71} +(-4.36713 + 0.163406i) q^{72} +(-1.29362 + 0.954739i) q^{73} +(0.0449445 - 0.298187i) q^{74} +(-3.13723 - 4.83914i) q^{75} +(0.211869 + 0.0483577i) q^{76} +(2.15707 - 8.89230i) q^{77} +(-0.430344 + 0.684889i) q^{78} +(11.5906 + 6.69184i) q^{79} +(-1.82027 + 0.0129089i) q^{80} +(-0.882233 + 0.818593i) q^{81} +(2.25308 + 0.426306i) q^{82} +(-0.0998227 - 0.885951i) q^{83} +(2.51007 + 3.49951i) q^{84} +(14.1626 + 10.2981i) q^{85} +(-4.55910 - 1.40630i) q^{86} +(3.48333 - 1.51976i) q^{87} +(-5.90475 + 6.86145i) q^{88} +(-5.52892 - 14.0875i) q^{89} +(-2.15802 + 1.88393i) q^{90} +(-2.41739 + 0.0575912i) q^{91} +(9.99237 - 3.49648i) q^{92} +(-3.17848 + 2.73530i) q^{93} +(-4.52311 + 1.39519i) q^{94} +(0.309166 - 0.151597i) q^{95} +(-1.00731 - 6.68308i) q^{96} +(9.86671 + 9.86671i) q^{97} +(1.91101 - 5.01970i) 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

Fields

Representations

Groups

Database

Properties

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