LMFDB - Embedded newform 245.2.x.a.108.25

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			108.25
Character	$\chi$	$=$	245.108
Dual form			245.2.x.a.152.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91759 - 1.41525i) q^{2} +(-0.435467 + 2.30150i) q^{3} +(1.08472 - 3.51658i) q^{4} +(-0.384482 + 2.20277i) q^{5} +(2.42214 + 5.02963i) q^{6} +(1.41735 + 2.23408i) q^{7} +(-1.32248 - 3.77942i) q^{8} +(-2.31465 - 0.908433i) q^{9} +(2.38018 + 4.76814i) q^{10} +(-1.66178 - 4.23416i) q^{11} +(7.62106 + 4.02785i) q^{12} +(-0.0800136 - 0.710141i) q^{13} +(5.87968 + 2.27814i) q^{14} +(-4.90224 - 1.84412i) q^{15} +(-1.80353 - 1.22963i) q^{16} +(-0.159617 - 4.26586i) q^{17} +(-5.72421 + 1.53380i) q^{18} +(-3.03772 - 5.26149i) q^{19} +(7.32915 + 3.74145i) q^{20} +(-5.75894 + 2.28917i) q^{21} +(-9.17900 - 5.76755i) q^{22} +(7.32477 + 0.274074i) q^{23} +(9.27423 - 1.39787i) q^{24} +(-4.70435 - 1.69385i) q^{25} +(-1.15846 - 1.24852i) q^{26} +(-0.639878 + 1.01836i) q^{27} +(9.39376 - 2.56089i) q^{28} +(2.15468 + 0.491792i) q^{29} +(-12.0104 + 3.40161i) q^{30} +(-0.305778 - 0.176541i) q^{31} +(2.80397 - 0.104917i) q^{32} +(10.4686 - 1.98076i) q^{33} +(-6.34332 - 7.95427i) q^{34} +(-5.46610 + 2.26314i) q^{35} +(-5.70534 + 7.15426i) q^{36} +(-3.92288 + 7.42244i) q^{37} +(-13.2714 - 5.79026i) q^{38} +(1.66923 + 0.125092i) q^{39} +(8.83364 - 1.45999i) q^{40} +(-2.60325 + 5.40570i) q^{41} +(-7.80356 + 12.5400i) q^{42} +(-3.95770 - 1.38486i) q^{43} +(-16.6923 + 1.25092i) q^{44} +(2.89101 - 4.74936i) q^{45} +(14.4338 - 9.84079i) q^{46} +(-1.54431 - 2.09246i) q^{47} +(3.61537 - 3.61537i) q^{48} +(-2.98221 + 6.33296i) q^{49} +(-11.4182 + 3.40971i) q^{50} +(9.88738 + 1.49028i) q^{51} +(-2.58406 - 0.488931i) q^{52} +(-1.40559 - 2.65951i) q^{53} +(0.214206 + 2.85838i) q^{54} +(9.96578 - 2.03256i) q^{55} +(6.56911 - 8.31130i) q^{56} +(13.4321 - 4.70011i) q^{57} +(4.82781 - 2.10635i) q^{58} +(0.936410 - 12.4955i) q^{59} +(-11.8026 + 15.2388i) q^{60} +(0.327108 + 1.06046i) q^{61} +(-0.836207 + 0.0942179i) q^{62} +(-1.25117 - 6.45868i) q^{63} +(8.64158 - 6.89143i) q^{64} +(1.59504 + 0.0967848i) q^{65} +(17.2712 - 18.6139i) q^{66} +(-1.89933 - 7.08840i) q^{67} +(-15.1744 - 4.06597i) q^{68} +(-3.82048 + 16.7386i) q^{69} +(-7.27884 + 12.0756i) q^{70} +(2.59465 + 11.3679i) q^{71} +(-0.372281 + 9.94942i) q^{72} +(0.733111 - 0.993331i) q^{73} +(2.98212 + 19.7851i) q^{74} +(5.94698 - 10.0894i) q^{75} +(-21.7975 + 4.97515i) q^{76} +(7.10410 - 9.71386i) q^{77} +(3.37794 - 2.12250i) q^{78} +(-7.95495 + 4.59279i) q^{79} +(3.40201 - 3.49999i) q^{80} +(-7.53339 - 6.98996i) q^{81} +(2.65843 + 14.0502i) q^{82} +(3.50280 + 0.394670i) q^{83} +(1.80321 + 22.7349i) q^{84} +(9.45805 + 1.28855i) q^{85} +(-9.54916 + 2.94553i) q^{86} +(-2.07015 + 4.74484i) q^{87} +(-13.8050 + 11.8802i) q^{88} +(-4.59104 + 11.6978i) q^{89} +(-1.17774 - 13.1988i) q^{90} +(1.47310 - 1.18528i) q^{91} +(8.90914 - 25.4609i) q^{92} +(0.539466 - 0.626871i) q^{93} +(-5.92271 - 1.82691i) q^{94} +(12.7578 - 4.66844i) q^{95} +(-0.979570 + 6.49902i) q^{96} +(7.13501 + 7.13501i) q^{97} +(3.24404 + 16.3646i) q^{98} +11.3102i 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.91759	−	1.41525i	1.35594	−	1.00073i	0.358194	−	0.933647i	$-0.383393\pi$
$2$	1.91759	−	1.41525i	1.35594	−	1.00073i	0.997747	−	0.0670835i	$-0.0213694\pi$
$3$	−0.435467	+	2.30150i	−0.251417	+	1.32877i	0.598189	+	0.801355i	$0.295887\pi$
$3$	−0.435467	+	2.30150i	−0.251417	+	1.32877i	−0.849607	+	0.527417i	$0.823161\pi$
$4$	1.08472	−	3.51658i	0.542361	−	1.75829i
$5$	−0.384482	+	2.20277i	−0.171945	+	0.985106i
$5$	−0.384482	+	2.20277i	−0.171945	+	0.985106i
$6$	2.42214	+	5.02963i	0.988836	+	2.05334i
$7$	1.41735	+	2.23408i	0.535710	+	0.844402i
$7$	1.41735	+	2.23408i	0.535710	+	0.844402i
$8$	−1.32248	−	3.77942i	−0.467566	−	1.33623i
$9$	−2.31465	−	0.908433i	−0.771550	−	0.302811i
$10$	2.38018	+	4.76814i	0.752678	+	1.50782i
$11$	−1.66178	−	4.23416i	−0.501047	−	1.27665i	−0.928070	−	0.372406i	$-0.878533\pi$
$11$	−1.66178	−	4.23416i	−0.501047	−	1.27665i	0.427023	−	0.904241i	$-0.359562\pi$
$12$	7.62106	+	4.02785i	2.20001	+	1.16274i
$13$	−0.0800136	−	0.710141i	−0.0221918	−	0.196958i	0.977725	−	0.209892i	$-0.0673113\pi$
$13$	−0.0800136	−	0.710141i	−0.0221918	−	0.196958i	−0.999916	+	0.0129345i	$0.995883\pi$
$14$	5.87968	+	2.27814i	1.57141	+	0.608859i
$15$	−4.90224	−	1.84412i	−1.26575	−	0.476149i
$16$	−1.80353	−	1.22963i	−0.450884	−	0.307407i
$17$	−0.159617	−	4.26586i	−0.0387128	−	1.03462i	−0.874336	−	0.485320i	$-0.838703\pi$
$17$	−0.159617	−	4.26586i	−0.0387128	−	1.03462i	0.835624	−	0.549302i	$-0.185106\pi$
$18$	−5.72421	+	1.53380i	−1.34921	+	0.361520i
$19$	−3.03772	−	5.26149i	−0.696901	−	1.20707i	−0.969536	−	0.244950i	$-0.921228\pi$
$19$	−3.03772	−	5.26149i	−0.696901	−	1.20707i	0.272635	−	0.962118i	$-0.412105\pi$
$20$	7.32915	+	3.74145i	1.63885	+	0.836614i
$21$	−5.75894	+	2.28917i	−1.25670	+	0.499539i
$22$	−9.17900	−	5.76755i	−1.95697	−	1.22965i
$23$	7.32477	+	0.274074i	1.52732	+	0.0571483i	0.787777	−	0.615961i	$-0.211232\pi$
$23$	7.32477	+	0.274074i	1.52732	+	0.0571483i	0.739543	+	0.673109i	$0.235042\pi$
$24$	9.27423	−	1.39787i	1.89310	−	0.285338i
$25$	−4.70435	−	1.69385i	−0.940870	−	0.338769i
$26$	−1.15846	−	1.24852i	−0.227192	−	0.244855i
$27$	−0.639878	+	1.01836i	−0.123145	+	0.195983i
$28$	9.39376	−	2.56089i	1.77525	−	0.483963i
$29$	2.15468	+	0.491792i	0.400114	+	0.0913235i	0.417843	−	0.908519i	$-0.362786\pi$
$29$	2.15468	+	0.491792i	0.400114	+	0.0913235i	−0.0177284	+	0.999843i	$0.505643\pi$
$30$	−12.0104	+	3.40161i	−2.19278	+	0.621046i
$31$	−0.305778	−	0.176541i	−0.0549194	−	0.0317077i	0.472289	−	0.881444i	$-0.343428\pi$
$31$	−0.305778	−	0.176541i	−0.0549194	−	0.0317077i	−0.527208	+	0.849736i	$0.676761\pi$
$32$	2.80397	−	0.104917i	0.495676	−	0.0185469i
$33$	10.4686	−	1.98076i	1.82234	−	0.344806i
$34$	−6.34332	−	7.95427i	−1.08787	−	1.36415i
$35$	−5.46610	+	2.26314i	−0.923939	+	0.382540i
$36$	−5.70534	+	7.15426i	−0.950889	+	1.19238i
$37$	−3.92288	+	7.42244i	−0.644917	+	1.22024i	0.317395	+	0.948293i	$0.397192\pi$
$37$	−3.92288	+	7.42244i	−0.644917	+	1.22024i	−0.962312	+	0.271949i	$0.912332\pi$
$38$	−13.2714	−	5.79026i	−2.15291	−	0.939304i
$39$	1.66923	+	0.125092i	0.267291	+	0.0200307i
$40$	8.83364	−	1.45999i	1.39672	−	0.230844i
$41$	−2.60325	+	5.40570i	−0.406559	+	0.844229i	0.592688	+	0.805432i	$0.298067\pi$
$41$	−2.60325	+	5.40570i	−0.406559	+	0.844229i	−0.999247	+	0.0387966i	$0.987648\pi$
$42$	−7.80356	+	12.5400i	−1.20411	+	1.93497i
$43$	−3.95770	−	1.38486i	−0.603543	−	0.211189i	0.0111727	−	0.999938i	$-0.496444\pi$
$43$	−3.95770	−	1.38486i	−0.603543	−	0.211189i	−0.614716	+	0.788749i	$0.710729\pi$
$44$	−16.6923	+	1.25092i	−2.51647	+	0.188583i
$45$	2.89101	−	4.74936i	0.430966	−	0.707992i
$46$	14.4338	−	9.84079i	2.12815	−	1.45095i
$47$	−1.54431	−	2.09246i	−0.225261	−	0.305217i	0.677362	−	0.735650i	$-0.263123\pi$
$47$	−1.54431	−	2.09246i	−0.225261	−	0.305217i	−0.902623	+	0.430432i	$0.858361\pi$
$48$	3.61537	−	3.61537i	0.521834	−	0.521834i
$49$	−2.98221	+	6.33296i	−0.426030	+	0.904709i
$50$	−11.4182	+	3.40971i	−1.61478	+	0.482206i
$51$	9.88738	+	1.49028i	1.38451	+	0.208681i
$52$	−2.58406	−	0.488931i	−0.358345	−	0.0678025i
$53$	−1.40559	−	2.65951i	−0.193073	−	0.365312i	0.768505	−	0.639844i	$-0.221001\pi$
$53$	−1.40559	−	2.65951i	−0.193073	−	0.365312i	−0.961578	+	0.274532i	$0.911477\pi$
$54$	0.214206	+	2.85838i	0.0291498	+	0.388977i
$55$	9.96578	−	2.03256i	1.34379	−	0.274071i
$56$	6.56911	−	8.31130i	0.877834	−	1.11064i
$57$	13.4321	−	4.70011i	1.77913	−	0.622545i
$58$	4.82781	−	2.10635i	0.633922	−	0.276577i
$59$	0.936410	−	12.4955i	0.121910	−	1.62678i	−0.515945	−	0.856622i	$-0.672559\pi$
$59$	0.936410	−	12.4955i	0.121910	−	1.62678i	0.637855	−	0.770156i	$-0.279822\pi$
$60$	−11.8026	+	15.2388i	−1.52370	+	1.96732i
$61$	0.327108	+	1.06046i	0.0418819	+	0.135778i	0.974099	−	0.226121i	$-0.0726046\pi$
$61$	0.327108	+	1.06046i	0.0418819	+	0.135778i	−0.932217	+	0.361899i	$0.882128\pi$
$62$	−0.836207	+	0.0942179i	−0.106198	+	0.0119657i
$63$	−1.25117	−	6.45868i	−0.157632	−	0.813718i
$64$	8.64158	−	6.89143i	1.08020	−	0.861429i
$65$	1.59504	+	0.0967848i	0.197840	+	0.0120047i
$66$	17.2712	−	18.6139i	2.12593	−	2.29121i
$67$	−1.89933	−	7.08840i	−0.232040	−	0.865986i	−0.979461	−	0.201635i	$-0.935375\pi$
$67$	−1.89933	−	7.08840i	−0.232040	−	0.865986i	0.747421	−	0.664351i	$-0.231292\pi$
$68$	−15.1744	−	4.06597i	−1.84016	−	0.493071i
$69$	−3.82048	+	16.7386i	−0.459932	+	2.01509i
$70$	−7.27884	+	12.0756i	−0.869988	+	1.44332i
$71$	2.59465	+	11.3679i	0.307928	+	1.34912i	0.857848	+	0.513903i	$0.171801\pi$
$71$	2.59465	+	11.3679i	0.307928	+	1.34912i	−0.549921	+	0.835217i	$0.685342\pi$
$72$	−0.372281	+	9.94942i	−0.0438737	+	1.17255i
$73$	0.733111	−	0.993331i	0.0858042	−	0.116261i	−0.759593	−	0.650399i	$-0.774602\pi$
$73$	0.733111	−	0.993331i	0.0858042	−	0.116261i	0.845397	+	0.534138i	$0.179364\pi$
$74$	2.98212	+	19.7851i	0.346664	+	2.29997i
$75$	5.94698	−	10.0894i	0.686698	−	1.16503i
$76$	−21.7975	+	4.97515i	−2.50035	+	0.570689i
$77$	7.10410	−	9.71386i	0.809588	−	1.10700i
$78$	3.37794	−	2.12250i	0.382477	−	0.240326i
$79$	−7.95495	+	4.59279i	−0.895001	+	0.516729i	−0.875575	−	0.483082i	$-0.839517\pi$
$79$	−7.95495	+	4.59279i	−0.895001	+	0.516729i	−0.0194263	+	0.999811i	$0.506184\pi$
$80$	3.40201	−	3.49999i	0.380356	−	0.391311i
$81$	−7.53339	−	6.98996i	−0.837043	−	0.776663i
$82$	2.65843	+	14.0502i	0.293575	+	1.55158i
$83$	3.50280	+	0.394670i	0.384482	+	0.0433207i	0.302090	−	0.953279i	$-0.402316\pi$
$83$	3.50280	+	0.394670i	0.384482	+	0.0433207i	0.0823916	+	0.996600i	$0.473744\pi$
$84$	1.80321	+	22.7349i	0.196747	+	2.48058i
$85$	9.45805	+	1.28855i	1.02587	+	0.139762i
$86$	−9.54916	+	2.94553i	−1.02971	+	0.317624i
$87$	−2.07015	+	4.74484i	−0.221944	+	0.508701i
$88$	−13.8050	+	11.8802i	−1.47162	+	1.26643i
$89$	−4.59104	+	11.6978i	−0.486649	+	1.23996i	0.451045	+	0.892501i	$0.351051\pi$
$89$	−4.59104	+	11.6978i	−0.486649	+	1.23996i	−0.937694	+	0.347461i	$0.887044\pi$
$90$	−1.17774	−	13.1988i	−0.124145	−	1.39128i
$91$	1.47310	−	1.18528i	0.154423	−	0.124251i
$92$	8.90914	−	25.4609i	0.928842	−	2.65448i
$93$	0.539466	−	0.626871i	0.0559400	−	0.0650034i
$94$	−5.92271	−	1.82691i	−0.610881	−	0.188432i
$95$	12.7578	−	4.66844i	1.30892	−	0.478972i
$96$	−0.979570	+	6.49902i	−0.0999769	+	0.663303i
$97$	7.13501	+	7.13501i	0.724450	+	0.724450i	0.969508	−	0.245058i	$-0.0788070\pi$
$97$	7.13501	+	7.13501i	0.724450	+	0.724450i	−0.245058	+	0.969508i	$0.578807\pi$
$98$	3.24404	+	16.3646i	0.327697	+	1.65307i
$99$			11.3102i			1.13672i
$100$	−11.0595	+	14.7059i	−1.10595	+	1.47059i
$101$	5.92165	+	8.68547i	0.589226	+	0.864236i	0.998846	−	0.0480199i	$-0.0152911\pi$
$101$	5.92165	+	8.68547i	0.589226	+	0.864236i	−0.409620	+	0.912256i	$0.634339\pi$
$102$	21.0691	−	11.1353i	2.08615	−	1.10256i
$103$	−1.22455	−	1.05381i	−0.120659	−	0.103835i	0.589889	−	0.807485i	$-0.299172\pi$
$103$	−1.22455	−	1.05381i	−0.120659	−	0.103835i	−0.710547	+	0.703649i	$0.751553\pi$
$104$	−2.57810	+	1.24155i	−0.252804	+	0.121744i
$105$	−2.82830	−	13.5657i	−0.276014	−	1.32388i
$106$	−6.45922	−	3.11059i	−0.627375	−	0.302128i
$107$	−3.89179	−	8.92008i	−0.376233	−	0.862336i	−0.996931	−	0.0782861i	$-0.975055\pi$
$107$	−3.89179	−	8.92008i	−0.376233	−	0.862336i	0.620697	−	0.784050i	$-0.286850\pi$
$108$	2.88706	+	3.35482i	0.277807	+	0.322818i
$109$	−3.60822	+	1.41612i	−0.345605	+	0.135640i	−0.531794	−	0.846874i	$-0.678482\pi$
$109$	−3.60822	+	1.41612i	−0.345605	+	0.135640i	0.186188	+	0.982514i	$0.440387\pi$
$110$	16.2337	−	18.0017i	1.54782	−	1.71639i
$111$	−15.3745	−	12.2607i	−1.45928	−	1.16374i
$112$	0.190840	−	5.77206i	0.0180327	−	0.545408i
$113$	0.263152	−	2.33554i	0.0247552	−	0.219709i	−0.975244	−	0.221133i	$-0.929025\pi$
$113$	0.263152	−	2.33554i	0.0247552	−	0.219709i	0.999999	+	0.00142384i	$0.000453222\pi$
$114$	19.1055	−	28.0227i	1.78940	−	2.62456i
$115$	−3.41996	+	16.0294i	−0.318913	+	1.49475i
$116$	4.06666	−	7.04366i	0.377580	−	0.653988i
$117$	−0.459912	+	1.71641i	−0.0425189	+	0.158683i
$118$	−15.8886	−	25.2865i	−1.46266	−	2.32782i
$119$	9.30403	−	6.40283i	0.852899	−	0.586946i
$120$	−0.486603	+	20.9664i	−0.0444206	+	1.91396i
$121$	−7.10299	+	6.59061i	−0.645727	+	0.599147i
$122$	2.12807	+	1.57059i	0.192666	+	0.142194i
$123$	−11.3076	−	8.34538i	−1.01957	−	0.752478i
$124$	−0.952506	+	0.883796i	−0.0855375	+	0.0793672i
$125$	5.53988	−	9.71132i	0.495502	−	0.868607i
$126$	−11.5399	−	10.6144i	−1.02805	−	0.945606i
$127$	3.99532	+	6.35852i	0.354528	+	0.564228i	0.975608	−	0.219519i	$-0.0704488\pi$
$127$	3.99532	+	6.35852i	0.354528	+	0.564228i	−0.621080	+	0.783747i	$0.713306\pi$
$128$	5.36549	−	20.0243i	0.474247	−	1.76991i
$129$	4.91070	−	8.50558i	0.432363	−	0.748874i
$130$	3.19560	−	2.07178i	0.280273	−	0.181707i
$131$	9.72885	−	14.2696i	0.850014	−	1.24674i	−0.117284	−	0.993098i	$-0.537419\pi$
$131$	9.72885	−	14.2696i	0.850014	−	1.24674i	0.967298	−	0.253643i	$-0.0816288\pi$
$132$	4.38998	−	38.9622i	0.382099	−	3.39122i
$133$	7.44905	−	14.2439i	0.645914	−	1.23510i
$134$	−13.6740	−	10.9046i	−1.18125	−	0.942016i
$135$	−1.99719	−	1.80104i	−0.171890	−	0.155009i
$136$	−15.9114	+	6.24476i	−1.36439	+	0.535484i
$137$	10.4540	+	12.1477i	0.893144	+	1.03785i	0.999054	+	0.0434762i	$0.0138433\pi$
$137$	10.4540	+	12.1477i	0.893144	+	1.03785i	−0.105911	+	0.994376i	$0.533776\pi$
$138$	16.3631	+	37.5047i	1.39292	+	3.19261i
$139$	−16.3960	−	7.89591i	−1.39069	−	0.669722i	−0.419442	−	0.907782i	$-0.637774\pi$
$139$	−16.3960	−	7.89591i	−1.39069	−	0.669722i	−0.971250	+	0.238060i	$0.923488\pi$
$140$	2.02931	+	21.6769i	0.171508	+	1.83203i
$141$	5.48830	−	2.64303i	0.462199	−	0.222583i
$142$	21.0638	+	18.1269i	1.76764	+	1.52117i
$143$	−2.87388	+	1.51889i	−0.240326	+	0.127016i
$144$	3.05752	+	4.48455i	0.254793	+	0.373713i
$145$	−1.91174	+	4.55717i	−0.158761	+	0.378453i
$146$		−	2.94234i		−	0.243509i
$147$	−13.2767	−	9.62136i	−1.09504	−	0.793557i
$148$	21.8464	+	21.8464i	1.79576	+	1.79576i
$149$	−1.87110	+	12.4139i	−0.153286	+	1.01699i	0.771425	+	0.636320i	$0.219544\pi$
$149$	−1.87110	+	12.4139i	−0.153286	+	1.01699i	−0.924712	+	0.380668i	$0.875694\pi$
$150$	−2.87518	−	27.7639i	−0.234758	−	2.26691i
$151$	−19.2335	−	5.93275i	−1.56520	−	0.482801i	−0.613466	−	0.789721i	$-0.710225\pi$
$151$	−19.2335	−	5.93275i	−1.56520	−	0.482801i	−0.951735	+	0.306920i	$0.900701\pi$
$152$	−15.8681	+	18.4390i	−1.28707	+	1.49560i
$153$	−3.50579	+	10.0190i	−0.283426	+	0.809986i
$154$	−0.124741	−	28.6813i	−0.0100519	−	2.31120i
$155$	0.506445	−	0.605681i	0.0406786	−	0.0486494i
$156$	2.25055	−	5.73431i	0.180188	−	0.459112i
$157$	−8.04583	+	6.92400i	−0.642127	+	0.552595i	−0.911943	−	0.410317i	$-0.865418\pi$
$157$	−8.04583	+	6.92400i	−0.642127	+	0.552595i	0.269816	+	0.962912i	$0.413037\pi$
$158$	−8.75440	+	20.0653i	−0.696463	+	1.59631i
$159$	6.73296	−	2.07684i	0.533958	−	0.164704i
$160$	−0.846966	+	6.21682i	−0.0669586	+	0.491483i
$161$	9.76949	+	16.7526i	0.769944	+	1.32029i
$162$	−24.3385	−	2.74229i	−1.91221	−	0.215455i
$163$	2.13405	+	11.2787i	0.167151	+	0.883416i	0.961261	+	0.275641i	$0.0888901\pi$
$163$	2.13405	+	11.2787i	0.167151	+	0.883416i	−0.794109	+	0.607775i	$0.792062\pi$
$164$	16.1858	+	15.0182i	1.26390	+	1.17273i
$165$	0.338176	+	23.8214i	0.0263270	+	1.85449i
$166$	7.27549	−	4.20050i	0.564687	−	0.326022i
$167$	4.32525	−	2.71773i	0.334698	−	0.210304i	−0.354188	−	0.935174i	$-0.615243\pi$
$167$	4.32525	−	2.71773i	0.334698	−	0.210304i	0.688886	+	0.724870i	$0.258100\pi$
$168$	16.2678	+	18.7381i	1.25509	+	1.44568i
$169$	12.1762	−	2.77913i	0.936628	−	0.213779i
$170$	19.9603	−	10.9146i	1.53088	−	0.837110i
$171$	2.25155	+	14.9381i	0.172180	+	1.14234i
$172$	−9.16297	+	12.4154i	−0.698670	+	0.946664i
$173$	0.371465	−	9.92760i	0.0282419	−	0.754782i	−0.911178	−	0.412013i	$-0.864826\pi$
$173$	0.371465	−	9.92760i	0.0282419	−	0.754782i	0.939420	−	0.342769i	$-0.111365\pi$
$174$	2.74541	+	12.0284i	0.208129	+	0.911874i
$175$	−2.88354	−	12.9107i	−0.217975	−	0.975954i
$176$	−2.20936	+	9.67983i	−0.166537	+	0.729645i
$177$	28.3507	+	7.59654i	2.13097	+	0.570991i
$178$	7.75151	+	28.9290i	0.581000	+	2.16832i
$179$	−9.35271	+	10.0798i	−0.699054	+	0.753401i	−0.978385	−	0.206794i	$-0.933697\pi$
$179$	−9.35271	+	10.0798i	−0.699054	+	0.753401i	0.279330	+	0.960195i	$0.409888\pi$
$180$	−13.5656	−	15.3182i	−1.01112	−	1.14175i
$181$	8.23648	−	6.56837i	0.612213	−	0.488223i	−0.267609	−	0.963528i	$-0.586233\pi$
$181$	8.23648	−	6.56837i	0.612213	−	0.488223i	0.879821	+	0.475304i	$0.157662\pi$
$182$	1.14735	−	4.35768i	0.0850471	−	0.323013i
$183$	−2.58309	+	0.291044i	−0.190947	+	0.0215146i
$184$	−8.65100	−	28.0458i	−0.637760	−	2.06757i
$185$	−14.8416	−	11.4950i	−1.09118	−	0.845127i
$186$	0.147298	−	1.96556i	0.0108004	−	0.144122i
$187$	−17.7971	+	7.76478i	−1.30145	+	0.567817i
$188$	−9.03347	+	3.16095i	−0.658834	+	0.230536i
$189$	−3.18203	+	0.0138393i	−0.231459	+	0.00100666i
$190$	17.8572	−	27.0075i	1.29550	−	1.95933i
$191$	−0.605127	−	8.07486i	−0.0437854	−	0.584276i	−0.975345	−	0.220687i	$-0.929170\pi$
$191$	−0.605127	−	8.07486i	−0.0437854	−	0.584276i	0.931559	−	0.363589i	$-0.118449\pi$
$192$	12.0975	+	22.8896i	0.873062	+	1.65191i
$193$	−5.18874	−	0.981762i	−0.373494	−	0.0706688i	−0.00422387	−	0.999991i	$-0.501345\pi$
$193$	−5.18874	−	0.981762i	−0.373494	−	0.0706688i	−0.369270	+	0.929322i	$0.620392\pi$
$194$	23.7798	+	3.58423i	1.70729	+	0.257333i
$195$	−0.917337	+	3.62883i	−0.0656919	+	0.259866i
$196$	19.0355	+	17.3567i	1.35968	+	1.23976i
$197$	−2.04515	+	2.04515i	−0.145711	+	0.145711i	−0.776199	−	0.630488i	$-0.782855\pi$
$197$	−2.04515	+	2.04515i	−0.145711	+	0.145711i	0.630488	+	0.776199i	$0.282855\pi$
$198$	16.0067	+	21.6884i	1.13755	+	1.54133i
$199$	−9.75978	+	6.65410i	−0.691852	+	0.471697i	−0.857497	−	0.514488i	$-0.827982\pi$
$199$	−9.75978	+	6.65410i	−0.691852	+	0.471697i	0.165645	+	0.986185i	$0.447029\pi$
$200$	−0.180365	+	20.0198i	−0.0127538	+	1.41561i
$201$	17.1410	−	1.28454i	1.20904	−	0.0906047i
$202$	23.6474	+	8.27458i	1.66382	+	0.582197i
$203$	1.95525	+	5.51077i	0.137231	+	0.386780i
$204$	15.9658	−	33.1533i	1.11783	−	2.32119i
$205$	−10.9066	−	7.81274i	−0.761749	−	0.545665i
$206$	−3.83959	−	0.287738i	−0.267517	−	0.0200476i
$207$	−16.7053	−	7.28845i	−1.16110	−	0.506582i
$208$	−0.728902	+	1.37915i	−0.0505403	+	0.0956269i
$209$	−17.2299	+	21.6056i	−1.19182	+	1.49449i
$210$	−24.6224	−	22.0108i	−1.69911	−	1.51889i
$211$	−3.89438	−	4.88339i	−0.268100	−	0.336187i	0.629498	−	0.777002i	$-0.283261\pi$
$211$	−3.89438	−	4.88339i	−0.268100	−	0.336187i	−0.897598	+	0.440816i	$0.854689\pi$
$212$	−10.8771	+	2.05805i	−0.747040	+	0.141348i
$213$	−27.2931	+	1.02123i	−1.87009	+	0.0699739i
$214$	−20.0870	−	11.5972i	−1.37312	−	0.792769i
$215$	4.57218	−	8.18542i	0.311820	−	0.558241i
$216$	4.69504	+	1.07161i	0.319457	+	0.0729139i
$217$	−0.0389893	−	0.933354i	−0.00264677	−	0.0633602i
$218$	−4.91493	+	7.82207i	−0.332881	+	0.529778i
$219$	1.96690	+	2.11982i	0.132911	+	0.143244i
$220$	3.66242	−	37.2503i	0.246920	−	2.51141i
$221$	−3.01659	+	0.454678i	−0.202918	+	0.0305849i
$222$	−46.8339	−	1.75240i	−3.14329	−	0.117613i
$223$	14.2205	+	8.93533i	0.952275	+	0.598354i	0.916082	−	0.400991i	$-0.131334\pi$
$223$	14.2205	+	8.93533i	0.952275	+	0.598354i	0.0361931	+	0.999345i	$0.488477\pi$
$224$	4.20861	+	6.11558i	0.281199	+	0.408614i
$225$	9.35018	+	8.19425i	0.623345	+	0.546283i
$226$	−2.80074	−	4.85103i	−0.186303	−	0.322686i
$227$	0.253201	−	0.0678450i	0.0168055	−	0.00450303i	−0.250406	−	0.968141i	$-0.580564\pi$
$227$	0.253201	−	0.0678450i	0.0168055	−	0.00450303i	0.267212	+	0.963638i	$0.413898\pi$
$228$	−1.95818	−	52.3336i	−0.129684	−	3.46588i
$229$	−13.2613	−	9.04138i	−0.876330	−	0.597471i	0.0394192	−	0.999223i	$-0.487449\pi$
$229$	−13.2613	−	9.04138i	−0.876330	−	0.597471i	−0.915749	+	0.401751i	$0.868402\pi$
$230$	16.1274	+	35.5779i	1.06341	+	2.34593i
$231$	19.2628	+	20.5802i	1.26740	+	1.35408i
$232$	−0.990827	−	8.79384i	−0.0650510	−	0.577344i
$233$	3.77918	+	1.99735i	0.247582	+	0.130851i	0.586457	−	0.809981i	$-0.300522\pi$
$233$	3.77918	+	1.99735i	0.247582	+	0.130851i	−0.338875	+	0.940832i	$0.610046\pi$
$234$	1.54723	+	3.94227i	0.101145	+	0.257714i
$235$	5.20297	−	2.59724i	0.339404	−	0.169425i
$236$	−42.9258	−	16.8471i	−2.79423	−	1.09665i
$237$	−7.10619	−	20.3083i	−0.461597	−	1.31917i
$238$	8.77974	−	25.4455i	0.569106	−	1.64939i
$239$	−1.40205	−	2.91139i	−0.0906911	−	0.188322i	0.850689	−	0.525669i	$-0.176185\pi$
$239$	−1.40205	−	2.91139i	−0.0906911	−	0.188322i	−0.941380	+	0.337347i	$0.890471\pi$
$240$	6.57377	+	9.35386i	0.424335	+	0.603789i
$241$	−5.63143	+	18.2566i	−0.362752	+	1.17601i	0.571862	+	0.820350i	$0.306221\pi$
$241$	−5.63143	+	18.2566i	−0.362752	+	1.17601i	−0.934614	+	0.355664i	$0.884255\pi$
$242$	−4.29329	+	22.6906i	−0.275983	+	1.45861i
$243$	16.4649	−	12.1516i	1.05622	−	0.779527i
$244$	4.08401			0.261452
$245$	−12.8034	−	9.00402i	−0.817981	−	0.575246i
$246$	−33.4941			−2.13551
$247$	−3.49334	+	2.57820i	−0.222276	+	0.164047i
$248$	−0.262839	+	1.38914i	−0.0166903	+	0.0882102i
$249$	−2.43369	+	7.88982i	−0.154229	+	0.499997i
$250$	−3.12069	−	26.4626i	−0.197370	−	1.67364i
$251$	9.35814	+	19.4324i	0.590681	+	1.22656i	0.955365	+	0.295430i	$0.0954628\pi$
$251$	9.35814	+	19.4324i	0.590681	+	1.22656i	−0.364684	+	0.931131i	$0.618823\pi$
$252$	−24.0697	−	2.60604i	−1.51625	−	0.164165i
$253$	−11.0117	−	31.4697i	−0.692301	−	1.97848i
$254$	16.6603	+	6.53868i	1.04536	+	0.410273i
$255$	−7.08426	+	21.2066i	−0.443634	+	1.32801i
$256$	−9.97425	−	25.4140i	−0.623391	−	1.58837i
$257$	−1.66410	−	0.879501i	−0.103803	−	0.0548617i	0.414561	−	0.910022i	$-0.363935\pi$
$257$	−1.66410	−	0.879501i	−0.103803	−	0.0548617i	−0.518365	+	0.855160i	$0.673459\pi$
$258$	−2.62078	−	23.2601i	−0.163163	−	1.44811i
$259$	−22.1424	+	1.75622i	−1.37586	+	0.109126i
$260$	2.07052	−	5.50410i	0.128408	−	0.341350i
$261$	−4.54058	−	3.09571i	−0.281055	−	0.191620i
$262$	−1.53905	−	41.1320i	−0.0950829	−	2.54114i
$263$	25.7574	−	6.90169i	1.58827	−	0.425576i	0.646798	−	0.762661i	$-0.276108\pi$
$263$	25.7574	−	6.90169i	1.58827	−	0.425576i	0.941474	+	0.337085i	$0.109441\pi$
$264$	−21.3306	−	36.9456i	−1.31281	−	2.27385i
$265$	6.39870	−	2.07366i	0.393069	−	0.127384i
$266$	−5.87440	−	37.8562i	−0.360183	−	2.32111i
$267$	−24.9232	−	15.6603i	−1.52528	−	0.958394i
$268$	−26.9872	−	1.00979i	−1.64851	−	0.0616827i
$269$	2.92952	−	0.441555i	0.178616	−	0.0269221i	−0.0591250	−	0.998251i	$-0.518831\pi$
$269$	2.92952	−	0.441555i	0.178616	−	0.0269221i	0.237741	+	0.971329i	$0.423593\pi$
$270$	−6.37871	−	0.627150i	−0.388196	−	0.0381671i
$271$	14.6852	+	15.8268i	0.892059	+	0.961411i	0.999462	−	0.0328043i	$-0.0104438\pi$
$271$	14.6852	+	15.8268i	0.892059	+	0.961411i	−0.107402	+	0.994216i	$0.534253\pi$
$272$	−4.95755	+	7.88989i	−0.300596	+	0.478395i
$273$	2.08643	+	3.90650i	0.126276	+	0.236432i
$274$	37.2385	+	8.49945i	2.24966	+	0.513470i
$275$	0.645603	+	22.7338i	0.0389313	+	1.37090i
$276$	54.7186	+	31.5918i	3.29367	+	1.90160i
$277$	10.2835	−	0.384783i	0.617877	−	0.0231193i	0.273379	−	0.961906i	$-0.411859\pi$
$277$	10.2835	−	0.384783i	0.617877	−	0.0231193i	0.344498	+	0.938787i	$0.388049\pi$
$278$	−42.6155	+	8.06329i	−2.55591	+	0.483604i
$279$	0.547394	+	0.686410i	0.0327716	+	0.0410943i
$280$	15.7821	+	17.6657i	0.943163	+	1.05573i
$281$	15.1074	−	18.9441i	0.901231	−	1.13011i	−0.0897315	−	0.995966i	$-0.528601\pi$
$281$	15.1074	−	18.9441i	0.901231	−	1.13011i	0.990962	−	0.134142i	$-0.0428277\pi$
$282$	6.78379	−	12.8356i	0.403969	−	0.764346i
$283$	13.9430	+	6.08326i	0.828824	+	0.361612i	0.771095	−	0.636720i	$-0.219709\pi$
$283$	13.9430	+	6.08326i	0.828824	+	0.361612i	0.0577292	+	0.998332i	$0.481614\pi$
$284$	42.7906	+	3.20671i	2.53915	+	0.190283i
$285$	5.18883	+	31.3950i	0.307360	+	1.85968i
$286$	−3.36133	+	6.97986i	−0.198759	+	0.412728i
$287$	−15.7665	+	1.84593i	−0.930666	+	0.108962i
$288$	−6.58551	−	2.30437i	−0.388055	−	0.135786i
$289$	−1.21961	+	0.0913968i	−0.0717415	+	0.00537628i
$290$	2.78359	+	11.4444i	0.163458	+	0.672037i
$291$	−19.5283	+	13.3142i	−1.14477	+	0.780490i
$292$	−2.69791	−	3.65554i	−0.157883	−	0.213924i
$293$	−5.14502	+	5.14502i	−0.300575	+	0.300575i	−0.841239	−	0.540664i	$-0.818173\pi$
$293$	−5.14502	+	5.14502i	−0.300575	+	0.300575i	0.540664	+	0.841239i	$0.318173\pi$
$294$	−39.0758	+	0.339904i	−2.27895	+	0.0198236i
$295$	27.1647	+	6.86699i	1.58159	+	0.399811i
$296$	33.2405	+	5.01019i	1.93206	+	0.291212i
$297$	5.37524	+	1.01705i	0.311903	+	0.0590152i
$298$	13.9808	+	26.4529i	0.809884	+	1.53237i
$299$	−0.391451	−	5.22355i	−0.0226382	−	0.302085i
$300$	−29.0296	−	31.8573i	−1.67602	−	1.83928i
$301$	−2.51558	−	10.8046i	−0.144995	−	0.622769i
$302$	−45.2783	+	15.8436i	−2.60548	+	0.911695i
$303$	−22.5683	+	9.84645i	−1.29651	+	0.565663i
$304$	−0.991043	+	13.2245i	−0.0568402	+	0.758480i
$305$	−2.46171	+	0.312815i	−0.140957	+	0.0179118i
$306$	7.45665	+	24.1739i	0.426268	+	1.38193i
$307$	−13.0823	+	1.47402i	−0.746647	+	0.0841269i	−0.477086	−	0.878856i	$-0.658307\pi$
$307$	−13.0823	+	1.47402i	−0.746647	+	0.0841269i	−0.269561	+	0.962983i	$0.586878\pi$
$308$	−26.4536	−	35.5190i	−1.50733	−	2.02388i
$309$	2.95860	−	2.35941i	0.168309	−	0.134222i
$310$	0.113966	−	1.87819i	0.00647285	−	0.106674i
$311$	1.85707	−	2.00144i	0.105305	−	0.113491i	−0.678200	−	0.734877i	$-0.737240\pi$
$311$	1.85707	−	2.00144i	0.105305	−	0.113491i	0.783505	+	0.621386i	$0.213430\pi$
$312$	−1.73475	−	6.47416i	−0.0982107	−	0.366527i
$313$	−1.97113	−	0.528164i	−0.111415	−	0.0298536i	0.202681	−	0.979245i	$-0.435035\pi$
$313$	−1.97113	−	0.528164i	−0.111415	−	0.0298536i	−0.314096	+	0.949391i	$0.601701\pi$
$314$	−5.62945	+	24.6642i	−0.317688	+	1.39188i
$315$	14.7080	−	0.272785i	0.828703	−	0.0153697i
$316$	7.52202	+	32.9561i	0.423147	+	1.85393i
$317$	−1.01368	+	27.0911i	−0.0569339	+	1.52159i	0.619447	+	0.785038i	$0.287357\pi$
$317$	−1.01368	+	27.0911i	−0.0569339	+	1.52159i	−0.676381	+	0.736552i	$0.736453\pi$
$318$	9.97181	−	13.5113i	0.559191	−	0.757678i
$319$	−1.49829	−	9.94052i	−0.0838882	−	0.556562i
$320$	11.8577	+	21.6850i	0.662864	+	1.21223i
$321$	22.2243	−	5.07255i	1.24044	−	0.283122i
$322$	42.4429	+	18.2983i	2.36525	+	1.01973i
$323$	−21.9599	+	13.7983i	−1.22188	+	0.767759i
$324$	−32.7524	+	18.9096i	−1.81958	+	1.05053i
$325$	−0.826457	+	3.47628i	−0.0458436	+	0.192829i
$326$	20.0544	+	18.6077i	1.11071	+	1.03059i
$327$	−1.68794	−	8.92100i	−0.0933436	−	0.493333i
$328$	23.8732	+	2.68986i	1.31817	+	0.148523i
$329$	2.48590	−	6.41587i	0.137052	−	0.353718i
$330$	34.3616	+	45.2010i	1.89154	+	2.48823i
$331$	−4.52797	+	1.39669i	−0.248880	+	0.0767692i	−0.416685	−	0.909051i	$-0.636808\pi$
$331$	−4.52797	+	1.39669i	−0.248880	+	0.0767692i	0.167805	+	0.985820i	$0.446332\pi$
$332$	5.18745	−	11.8898i	0.284698	−	0.652536i
$333$	15.8229	−	13.6167i	0.867089	−	0.746190i
$334$	4.44779	−	11.3328i	0.243372	−	0.620103i
$335$	16.3443	−	1.45842i	0.892986	−	0.0796820i
$336$	13.2013	+	2.95276i	0.720189	+	0.161086i
$337$	−2.65971	+	7.60101i	−0.144884	+	0.414053i	−0.993341	−	0.115210i	$-0.963246\pi$
$337$	−2.65971	+	7.60101i	−0.144884	+	0.414053i	0.848458	+	0.529263i	$0.177532\pi$
$338$	19.4158	−	22.5615i	1.05608	−	1.22718i
$339$	5.26064	+	1.62269i	0.285719	+	0.0881326i
$340$	14.7906	−	31.8623i	0.802135	−	1.72798i
$341$	−0.239365	+	1.58809i	−0.0129624	+	0.0859997i
$342$	25.4586	+	25.4586i	1.37664	+	1.37664i
$343$	−18.3752	+	2.31355i	−0.992167	+	0.124920i
$344$			16.7892i			0.905215i
$345$	−35.4023	−	14.8513i	−1.90600	−	0.799567i
$346$	−13.3377	−	19.5628i	−0.717039	−	1.05170i
$347$	10.2003	−	5.39104i	0.547583	−	0.289406i	−0.170507	−	0.985356i	$-0.554541\pi$
$347$	10.2003	−	5.39104i	0.547583	−	0.289406i	0.718090	+	0.695950i	$0.245017\pi$
$348$	14.4401	+	12.4267i	0.774070	+	0.666141i
$349$	26.6333	−	12.8259i	1.42565	−	0.686557i	0.447467	−	0.894301i	$-0.352326\pi$
$349$	26.6333	−	12.8259i	1.42565	−	0.686557i	0.978183	+	0.207744i	$0.0666120\pi$
$350$	−23.8012	−	20.6764i	−1.27223	−	1.10520i
$351$	0.774378	+	0.372921i	0.0413332	+	0.0199050i
$352$	−5.10382	−	11.6981i	−0.272035	−	0.623510i
$353$	−1.05472	−	1.22561i	−0.0561371	−	0.0652325i	0.729201	−	0.684299i	$-0.239892\pi$
$353$	−1.05472	−	1.22561i	−0.0561371	−	0.0652325i	−0.785338	+	0.619067i	$0.787511\pi$
$354$	65.1160	−	25.5561i	3.46087	−	1.35829i
$355$	−26.0384	+	1.34465i	−1.38197	+	0.0713667i
$356$	36.1562	+	28.8336i	1.91628	+	1.52818i
$357$	10.6845	+	24.2014i	0.565485	+	1.28088i
$358$	−3.66924	+	32.5654i	−0.193925	+	1.72113i
$359$	17.6587	−	25.9005i	0.931988	−	1.36698i	0.00175801	−	0.999998i	$-0.499440\pi$
$359$	17.6587	−	25.9005i	0.931988	−	1.36698i	0.930230	−	0.366977i	$-0.119607\pi$
$360$	−21.7731	−	4.64542i	−1.14754	−	0.244835i
$361$	−8.95550	+	15.5114i	−0.471342	+	0.816388i
$362$	6.49833	−	24.2521i	0.341545	−	1.27466i
$363$	−12.0752	−	19.2175i	−0.633783	−	1.00866i
$364$	−2.57022	−	6.46599i	−0.134716	−	0.338910i
$365$	1.90621	+	1.99679i	0.0997754	+	0.104517i
$366$	−4.54141	+	4.21381i	−0.237383	+	0.220260i
$367$	−24.0877	−	17.7776i	−1.25737	−	0.927981i	−0.258097	−	0.966119i	$-0.583095\pi$
$367$	−24.0877	−	17.7776i	−1.25737	−	0.927981i	−0.999272	+	0.0381383i	$0.987857\pi$
$368$	−12.8735	−	9.50105i	−0.671076	−	0.495277i
$369$	10.9363	−	10.1474i	0.569323	−	0.528254i
$370$	−44.7284	−	1.03809i	−2.32532	−	0.0539676i
$371$	3.94933	−	6.90967i	0.205039	−	0.358732i
$372$	−1.61927	−	2.57706i	−0.0839553	−	0.133614i
$373$	1.08761	−	4.05903i	0.0563144	−	0.210168i	−0.932035	−	0.362367i	$-0.881969\pi$
$373$	1.08761	−	4.05903i	0.0563144	−	0.210168i	0.988350	+	0.152199i	$0.0486354\pi$
$374$	−23.1384	+	40.0769i	−1.19646	+	2.07233i
$375$	19.9382	+	16.9790i	1.02960	+	0.876792i
$376$	−5.86599	+	8.60383i	−0.302515	+	0.443709i
$377$	0.176838	−	1.56948i	0.00910760	−	0.0808322i
$378$	−6.08225	+	4.52990i	−0.312837	+	0.232993i
$379$	−17.1758	−	13.6972i	−0.882261	−	0.703580i	0.0736346	−	0.997285i	$-0.476540\pi$
$379$	−17.1758	−	13.6972i	−0.882261	−	0.703580i	−0.955896	+	0.293705i	$0.905112\pi$
$380$	−2.57832	−	49.9277i	−0.132265	−	2.56124i
$381$	−16.3740	+	6.42631i	−0.838864	+	0.329230i
$382$	−12.5883	−	14.6279i	−0.644074	−	0.748427i
$383$	−9.54670	−	21.8813i	−0.487814	−	1.11808i	−0.970240	−	0.242144i	$-0.922149\pi$
$383$	−9.54670	−	21.8813i	−0.487814	−	1.11808i	0.482427	−	0.875936i	$-0.339756\pi$
$384$	43.7494	+	21.0686i	2.23258	+	1.07515i
$385$	18.6660	+	19.3835i	0.951305	+	0.987873i
$386$	−11.3393	+	5.46073i	−0.577156	+	0.277944i
$387$	7.90263	+	6.80076i	0.401713	+	0.345702i
$388$	32.8304	−	17.3513i	1.66671	−	0.880881i
$389$	−19.5691	−	28.7026i	−0.992193	−	1.45528i	−0.887518	−	0.460773i	$-0.847572\pi$
$389$	−19.5691	−	28.7026i	−0.992193	−	1.45528i	−0.104675	−	0.994506i	$-0.533380\pi$
$390$	3.37661	+	8.25687i	0.170982	+	0.418103i
$391$		−	31.2902i		−	1.58241i
$392$	27.8788	+	2.89585i	1.40809	+	0.146262i
$393$	28.6049	+	28.6049i	1.44293	+	1.44293i
$394$	−1.02737	+	6.81614i	−0.0517580	+	0.343392i
$395$	−7.05831	−	19.2887i	−0.355142	−	0.970521i
$396$	39.7733	+	12.2684i	1.99868	+	0.616513i
$397$	−20.1314	+	23.3931i	−1.01036	+	1.17406i	−0.0256879	+	0.999670i	$0.508178\pi$
$397$	−20.1314	+	23.3931i	−1.01036	+	1.17406i	−0.984676	+	0.174394i	$0.944203\pi$
$398$	−9.29807	+	26.5723i	−0.466070	+	1.33195i
$399$	29.5385	+	23.3467i	1.47878	+	1.16880i
$400$	6.40165	+	8.83951i	0.320083	+	0.441976i
$401$	5.58920	−	14.2411i	0.279111	−	0.711164i	−0.720728	−	0.693218i	$-0.756192\pi$
$401$	5.58920	−	14.2411i	0.279111	−	0.711164i	0.999839	−	0.0179459i	$-0.00571265\pi$
$402$	31.0516	−	26.7220i	1.54871	−	1.33277i
$403$	−0.100903	+	0.231271i	−0.00502632	+	0.0115204i
$404$	36.9665	−	11.4027i	1.83915	−	0.567304i
$405$	18.2937	−	13.9068i	0.909021	−	0.691033i
$406$	11.5485	+	7.80025i	0.573141	+	0.387120i
$407$	37.9468	+	4.27557i	1.88095	+	0.211932i
$408$	−7.44343	−	39.3394i	−0.368504	−	1.94759i
$409$	1.58128	+	1.46721i	0.0781893	+	0.0725490i	0.718299	−	0.695734i	$-0.244921\pi$
$409$	1.58128	+	1.46721i	0.0781893	+	0.0725490i	−0.640110	+	0.768283i	$0.721111\pi$
$410$	−31.9713	+	0.453876i	−1.57895	+	0.0224154i
$411$	−32.5104	+	18.7699i	−1.60362	+	0.925850i
$412$	−5.03412	+	3.16314i	−0.248013	+	0.155837i
$413$	29.2432	−	15.6186i	1.43896	−	0.768539i
$414$	−42.3489	+	9.66586i	−2.08133	+	0.475051i
$415$	−2.21613	+	7.56409i	−0.108785	+	0.371307i
$416$	−0.298861	−	1.98282i	−0.0146529	−	0.0972156i
$417$	25.3124	−	34.2970i	1.23955	−	1.67953i
$418$	−2.46264	+	65.8154i	−0.120452	+	3.21914i
$419$	−5.14356	−	22.5354i	−0.251279	−	1.10093i	−0.930298	−	0.366806i	$-0.880451\pi$
$419$	−5.14356	−	22.5354i	−0.251279	−	1.10093i	0.679018	−	0.734122i	$-0.262406\pi$
$420$	−50.7730	−	4.76911i	−2.47747	−	0.232709i
$421$	−1.01783	+	4.45940i	−0.0496059	+	0.217338i	−0.993656	−	0.112465i	$-0.964125\pi$
$421$	−1.01783	+	4.45940i	−0.0496059	+	0.217338i	0.944050	+	0.329803i	$0.106982\pi$
$422$	−14.3790	−	3.85285i	−0.699960	−	0.187554i
$423$	1.67367	+	6.24623i	0.0813767	+	0.303702i
$424$	−8.19255	+	8.82947i	−0.397865	+	0.428797i
$425$	−6.47481	+	20.3384i	−0.314074	+	0.986560i
$426$	−50.8917	+	40.5847i	−2.46571	+	1.96634i
$427$	−1.90552	+	2.23383i	−0.0922145	+	0.108103i
$428$	−35.5897	+	4.01000i	−1.72029	+	0.193831i
$429$	−2.24425	−	7.27567i	−0.108353	−	0.351273i
$430$	−2.81682	−	22.1671i	−0.135839	−	1.06899i
$431$	1.90325	−	25.3971i	0.0916763	−	1.22333i	−0.741740	−	0.670688i	$-0.765999\pi$
$431$	1.90325	−	25.3971i	0.0916763	−	1.22333i	0.833416	−	0.552647i	$-0.186382\pi$
$432$	2.40625	−	1.04984i	0.115771	−	0.0505102i
$433$	−5.70999	+	1.99801i	−0.274405	+	0.0960183i	−0.463973	−	0.885849i	$-0.653577\pi$
$433$	−5.70999	+	1.99801i	−0.274405	+	0.0960183i	0.189569	+	0.981867i	$0.439291\pi$
$434$	−1.39569	−	1.73461i	−0.0669953	−	0.0832640i
$435$	−9.65584	−	6.38437i	−0.462962	−	0.306107i
$436$	1.06600	+	14.2247i	0.0510519	+	0.681241i
$437$	−20.8086	−	39.3717i	−0.995409	−	1.88341i
$438$	6.77179	+	1.28129i	0.323568	+	0.0612225i
$439$	27.3149	+	4.11705i	1.30367	+	0.196496i	0.763909	−	0.645324i	$-0.223278\pi$
$439$	27.3149	+	4.11705i	1.30367	+	0.196496i	0.539758	+	0.841820i	$0.318516\pi$
$440$	−20.8614	−	34.9769i	−0.994530	−	1.66746i
$441$	12.6559	−	11.9495i	0.602660	−	0.569022i
$442$	−5.14110	+	5.14110i	−0.244537	+	0.244537i
$443$	22.9114	+	31.0439i	1.08856	+	1.47494i	0.866016	+	0.500017i	$0.166673\pi$
$443$	22.9114	+	31.0439i	1.08856	+	1.47494i	0.222540	+	0.974924i	$0.428565\pi$
$444$	−59.7929	+	40.7661i	−2.83765	+	1.93467i
$445$	−24.0023	−	14.6106i	−1.13782	−	0.692607i
$446$	39.9148	−	2.99120i	1.89002	−	0.141638i
$447$	−27.7558	−	9.71219i	−1.31281	−	0.459371i
$448$	27.6442	+	9.53837i	1.30606	+	0.450646i
$449$	−4.87379	+	10.1205i	−0.230009	+	0.477618i	−0.983748	−	0.179556i	$-0.942534\pi$
$449$	−4.87379	+	10.1205i	−0.230009	+	0.477618i	0.753739	+	0.657174i	$0.228248\pi$
$450$	29.5267	+	2.48041i	1.39190	+	0.116928i
$451$	27.2146	+	2.03945i	1.28149	+	0.0960342i
$452$	−7.92766	−	3.45880i	−0.372886	−	0.162688i
$453$	22.0298	−	41.6824i	1.03505	−	1.95841i
$454$	0.389519	−	0.488441i	0.0182810	−	0.0229237i
$455$	2.04451	+	3.70062i	0.0958480	+	0.173488i
$456$	−35.5274	−	44.5499i	−1.66372	−	2.08624i
$457$	30.1915	−	5.71253i	1.41230	−	0.267221i	0.576876	−	0.816832i	$-0.304272\pi$
$457$	30.1915	−	5.71253i	1.41230	−	0.267221i	0.835421	+	0.549611i	$0.185224\pi$
$458$	−38.2255	+	1.43030i	−1.78616	+	0.0668334i
$459$	4.44632	+	2.56708i	0.207536	+	0.119821i
$460$	52.6589	+	29.4140i	2.45523	+	1.37143i
$461$	23.1658	+	5.28744i	1.07894	+	0.246260i	0.724818	−	0.688940i	$-0.241924\pi$
$461$	23.1658	+	5.28744i	1.07894	+	0.246260i	0.354119	+	0.935200i	$0.384781\pi$
$462$	66.0643	+	12.2027i	3.07359	+	0.567719i
$463$	−3.15169	+	5.01589i	−0.146472	+	0.233108i	−0.911900	−	0.410413i	$-0.865384\pi$
$463$	−3.15169	+	5.01589i	−0.146472	+	0.233108i	0.765428	+	0.643522i	$0.222527\pi$
$464$	−3.28132	−	3.53642i	−0.152332	−	0.164174i
$465$	1.17343	+	1.42934i	0.0544167	+	0.0662839i
$466$	10.0737	−	1.51836i	0.466654	−	0.0703367i
$467$	18.2278	+	0.682037i	0.843483	+	0.0315609i	0.455640	−	0.890164i	$-0.349411\pi$
$467$	18.2278	+	0.682037i	0.843483	+	0.0315609i	0.387844	+	0.921725i	$0.373220\pi$
$468$	5.53704	+	3.47915i	0.255950	+	0.160824i
$469$	13.1440	−	14.2900i	0.606934	−	0.659852i
$470$	6.30143	−	12.3439i	0.290663	−	0.569382i
$471$	−12.4319	−	21.5327i	−0.572831	−	0.992172i
$472$	−48.4642	+	12.9859i	−2.23075	+	0.597727i
$473$	0.713132	+	19.0588i	0.0327898	+	0.876327i
$474$	−42.3681	−	28.8861i	−1.94603	−	1.32678i
$475$	5.37835	+	29.8973i	0.246776	+	1.37178i
$476$	−12.4238	−	39.6637i	−0.569444	−	1.81798i
$477$	0.837467	+	7.43273i	0.0383450	+	0.340321i
$478$	−6.80889	−	3.59860i	−0.311431	−	0.164596i
$479$	4.06657	+	10.3615i	0.185806	+	0.473427i	0.993177	−	0.116618i	$-0.0372053\pi$
$479$	4.06657	+	10.3615i	0.185806	+	0.473427i	−0.807371	+	0.590045i	$0.799110\pi$
$480$	−13.9392	−	4.65652i	−0.636234	−	0.212540i
$481$	5.58486	+	2.19190i	0.254648	+	0.0999419i
$482$	15.0389	+	42.9786i	0.685002	+	1.95762i
$483$	−42.8103	+	15.1893i	−1.94794	+	0.691137i
$484$	15.4717	+	32.1273i	0.703258	+	1.46033i
$485$	−18.4600	+	12.9735i	−0.838227	+	0.589095i
$486$	14.3753	−	46.6037i	0.652078	−	2.11399i
$487$	−3.64879	+	19.2843i	−0.165343	+	0.873857i	0.797403	+	0.603448i	$0.206207\pi$
$487$	−3.64879	+	19.2843i	−0.165343	+	0.873857i	−0.962745	+	0.270410i	$0.912841\pi$
$488$	3.57532	−	2.63871i	0.161847	−	0.119449i
$489$	−26.8872			−1.21588
$490$	−37.2946	+	0.853964i	−1.68480	+	0.0385782i
$491$	−25.8839			−1.16812			−0.584062	−	0.811709i	$-0.698537\pi$
$491$	−25.8839			−1.16812			−0.584062	+	0.811709i	$0.698537\pi$
$492$	−41.6128	+	30.7117i	−1.87605	+	1.38459i
$493$	1.75399	−	9.27007i	0.0789958	−	0.417503i
$494$	−3.05000	+	9.88787i	−0.137226	+	0.444876i
$495$	−24.9138	−	4.34857i	−1.11979	−	0.195454i
$496$	0.334401	+	0.694392i	0.0150151	+	0.0311791i
$497$	−21.7192	+	21.9090i	−0.974240	+	0.982751i
$498$	6.49922	+	18.5737i	0.291237	+	0.832308i
$499$	25.1466	+	9.86929i	1.12571	+	0.441810i	0.853847	−	0.520524i	$-0.174264\pi$
$499$	25.1466	+	9.86929i	1.12571	+	0.441810i	0.271867	+	0.962335i	$0.412359\pi$
$500$	−28.1414	−	30.0155i	−1.25852	−	1.34234i
$501$	4.37136	+	11.1380i	0.195298	+	0.497611i
$502$	45.4467	+	24.0193i	2.02839	+	1.07203i
$503$	−4.58233	−	40.6693i	−0.204316	−	1.81336i	−0.508851	−	0.860854i	$-0.669930\pi$
$503$	−4.58233	−	40.6693i	−0.204316	−	1.81336i	0.304535	−	0.952501i	$-0.401499\pi$
$504$	−22.7554	+	13.2702i	−1.01361	+	0.591100i
$505$	−21.4088	+	9.70460i	−0.952680	+	0.431849i
$506$	−65.6533	−	44.7617i	−2.91865	−	1.98990i
$507$	1.09385	+	29.2337i	0.0485794	+	1.29831i
$508$	26.6941	−	7.15266i	1.18436	−	0.317348i
$509$	−10.1168	−	17.5228i	−0.448418	−	0.776683i	0.549865	−	0.835253i	$-0.314679\pi$
$509$	−10.1168	−	17.5228i	−0.448418	−	0.776683i	−0.998283	+	0.0585704i	$0.981346\pi$
$510$	16.4278	+	50.6916i	0.727437	+	2.24466i
$511$	3.25826	+	0.229927i	0.144137	+	0.0101714i
$512$	−19.9873	−	12.5588i	−0.883322	−	0.555028i
$513$	7.30186	+	0.273216i	0.322385	+	0.0120628i
$514$	−4.43577	+	0.668584i	−0.195653	+	0.0294900i
$515$	2.79212	−	2.29223i	0.123035	−	0.101008i
$516$	−24.5838	−	26.4951i	−1.08224	−	1.16638i
$517$	−6.29352	+	10.0161i	−0.276788	+	0.440506i
$518$	−39.9746	+	34.7047i	−1.75638	+	1.52484i
$519$	22.6866	+	5.17807i	0.995832	+	0.227292i
$520$	−1.74361	−	6.15631i	−0.0764623	−	0.269972i
$521$	−21.0257	−	12.1392i	−0.921153	−	0.531828i	−0.0371502	−	0.999310i	$-0.511828\pi$
$521$	−21.0257	−	12.1392i	−0.921153	−	0.531828i	−0.884003	+	0.467482i	$0.845161\pi$
$522$	−13.0882	+	0.489725i	−0.572853	+	0.0214347i
$523$	12.5789	−	2.38005i	0.550037	−	0.104073i	0.0965376	−	0.995329i	$-0.469223\pi$
$523$	12.5789	−	2.38005i	0.550037	−	0.104073i	0.453499	+	0.891257i	$0.350176\pi$
$524$	−39.6272	−	49.6909i	−1.73112	−	2.17076i
$525$	30.9696	−	1.01431i	1.35162	−	0.0442679i
$526$	39.6247	−	49.6878i	1.72772	−	2.16649i
$527$	−0.704292	+	1.33259i	−0.0306794	+	0.0580483i
$528$	−21.3160	−	9.30009i	−0.927661	−	0.404734i
$529$	30.6414	+	2.29626i	1.33224	+	0.0998373i
$530$	9.33536	−	13.0322i	0.405502	−	0.566081i
$531$	−13.5188	+	28.0721i	−0.586666	+	1.21823i
$532$	−42.0097	−	41.6459i	−1.82135	−	1.80558i
$533$	4.04710	+	1.41614i	0.175300	+	0.0613400i
$534$	−69.9557	+	5.24245i	−3.02728	+	0.226863i
$535$	21.1452	−	5.14309i	0.914185	−	0.222355i
$536$	−24.2782	+	16.5526i	−1.04866	+	0.714964i
$537$	−19.1259	−	25.9147i	−0.825344	−	1.11830i
$538$	4.99272	−	4.99272i	0.215251	−	0.215251i
$539$	31.7706	+	2.10314i	1.36845	+	0.0905888i
$540$	−8.49991	+	5.06964i	−0.365778	+	0.218163i
$541$	−3.55297	−	0.535525i	−0.152754	−	0.0230240i	0.0722199	−	0.997389i	$-0.476992\pi$
$541$	−3.55297	−	0.535525i	−0.152754	−	0.0230240i	−0.224974	+	0.974365i	$0.572230\pi$
$542$	50.5590	+	9.56628i	2.17169	+	0.410907i
$543$	11.5304	+	21.8166i	0.494817	+	0.936239i
$544$	−0.895123	−	11.9446i	−0.0383781	−	0.512120i
$545$	−1.73209	−	8.49254i	−0.0741946	−	0.363781i
$546$	9.52957	+	4.53825i	0.407828	+	0.194219i
$547$	−2.38322	+	0.833924i	−0.101899	+	0.0356560i	−0.380747	−	0.924679i	$-0.624333\pi$
$547$	−2.38322	+	0.833924i	−0.101899	+	0.0356560i	0.278848	+	0.960335i	$0.410047\pi$
$548$	54.0582	−	23.5854i	2.30925	−	1.00752i
$549$	0.206215	−	2.75175i	0.00880104	−	0.117442i
$550$	33.4119	+	42.6804i	1.42469	+	1.81990i
$551$	−3.95777	−	12.8308i	−0.168606	−	0.546609i
$552$	68.3147	−	7.69722i	2.90767	−	0.327616i
$553$	−21.5356	−	11.2624i	−0.915788	−	0.478924i
$554$	19.1750	−	15.2916i	0.814670	−	0.649677i
$555$	32.9187	−	29.1523i	1.39732	−	1.23745i
$556$	−45.5517	+	49.0931i	−1.93182	+	2.08201i
$557$	−3.49856	−	13.0568i	−0.148239	−	0.553234i	−0.999590	−	0.0286381i	$-0.990883\pi$
$557$	−3.49856	−	13.0568i	−0.148239	−	0.553234i	0.851351	−	0.524596i	$-0.175784\pi$
$558$	2.02112	+	0.541557i	0.0855607	+	0.0229259i
$559$	−0.666774	+	2.92133i	−0.0282015	+	0.123559i
$560$	12.6411	+	2.63963i	0.534185	+	0.111545i
$561$	−10.1206	−	44.3413i	−0.427292	−	1.87209i
$562$	2.15927	−	57.7076i	0.0910832	−	2.43425i
$563$	−4.82585	+	6.53879i	−0.203385	+	0.275577i	−0.894404	−	0.447259i	$-0.852400\pi$
$563$	−4.82585	+	6.53879i	−0.203385	+	0.275577i	0.691019	+	0.722836i	$0.257162\pi$
$564$	−3.34114	−	22.1670i	−0.140687	−	0.933400i
$565$	5.04346	+	1.47763i	0.212180	+	0.0621644i
$566$	35.3463	−	8.06755i	1.48571	−	0.339105i
$567$	4.93865	−	26.7374i	0.207404	−	1.12287i
$568$	39.5327	−	24.8400i	1.65875	−	1.04226i
$569$	−8.48853	+	4.90085i	−0.355858	+	0.205454i	−0.667262	−	0.744823i	$-0.732534\pi$
$569$	−8.48853	+	4.90085i	−0.355858	+	0.205454i	0.311405	+	0.950277i	$0.399201\pi$
$570$	54.3817	+	52.8592i	2.27780	+	2.21403i
$571$	−12.8502	−	11.9233i	−0.537765	−	0.498973i	0.363882	−	0.931445i	$-0.381451\pi$
$571$	−12.8502	−	11.9233i	−0.537765	−	0.498973i	−0.901648	+	0.432472i	$0.857642\pi$
$572$	2.22394	+	11.7538i	0.0929877	+	0.491452i
$573$	18.8478	+	2.12364i	0.787378	+	0.0887162i
$574$	−27.6212	+	25.8532i	−1.15289	+	1.07909i
$575$	−33.9940	−	13.6964i	−1.41765	−	0.571178i
$576$	−26.2627	+	8.10095i	−1.09428	+	0.337540i
$577$	1.11567	−	2.55714i	0.0464460	−	0.106455i	−0.891792	−	0.452445i	$-0.850552\pi$
$577$	1.11567	−	2.55714i	0.0464460	−	0.106455i	0.938238	+	0.345989i	$0.112457\pi$
$578$	−2.20936	+	1.90130i	−0.0918971	+	0.0790839i
$579$	4.51905	−	11.5144i	0.187805	−	0.478520i
$580$	13.9520	+	11.6661i	0.579324	+	0.484407i
$581$	4.08298	+	8.38491i	0.169390	+	0.347865i
$582$	−18.6044	+	53.1685i	−0.771179	+	2.20390i
$583$	−8.92500	+	10.3710i	−0.369636	+	0.429524i
$584$	−4.72374	−	1.45708i	−0.195470	−	0.0602944i
$585$	−3.60403	−	1.67301i	−0.149008	−	0.0691704i
$586$	−2.58457	+	17.1475i	−0.106768	+	0.708358i
$587$	17.0186	+	17.0186i	0.702433	+	0.702433i	0.964932	−	0.262499i	$-0.0845467\pi$
$587$	17.0186	+	17.0186i	0.702433	+	0.702433i	−0.262499	+	0.964932i	$0.584547\pi$
$588$	−48.2358	+	36.2520i	−1.98921	+	1.49501i
$589$			2.14513i			0.0883885i
$590$	61.8092	−	25.2766i	2.54464	−	1.04062i
$591$	−3.81631	−	5.59750i	−0.156982	−	0.230250i
$592$	16.2019	−	8.56295i	0.665894	−	0.351935i
$593$	11.5144	+	9.90892i	0.472838	+	0.406910i	0.856165	−	0.516702i	$-0.172841\pi$
$593$	11.5144	+	9.90892i	0.472838	+	0.406910i	−0.383327	+	0.923613i	$0.625222\pi$
$594$	11.7469	−	5.65700i	0.481980	−	0.232110i
$595$	10.5267	+	22.9564i	0.431553	+	0.941119i
$596$	41.6250	+	20.0455i	1.70503	+	0.821097i
$597$	−11.0644	−	25.3598i	−0.452834	−	1.03791i
$598$	−8.14325	−	9.46263i	−0.333002	−	0.386956i
$599$	2.28671	−	0.897468i	0.0934325	−	0.0366696i	−0.318164	−	0.948036i	$-0.603066\pi$
$599$	2.28671	−	0.897468i	0.0934325	−	0.0366696i	0.411597	+	0.911366i	$0.364971\pi$
$600$	−45.9970	−	9.13307i	−1.87782	−	0.372856i
$601$	−26.5302	−	21.1571i	−1.08219	−	0.863016i	−0.0910487	−	0.995846i	$-0.529022\pi$
$601$	−26.5302	−	21.1571i	−1.08219	−	0.863016i	−0.991139	+	0.132831i	$0.957593\pi$
$602$	−20.1151	−	17.1587i	−0.819829	−	0.699337i
$603$	−2.04305	+	18.1326i	−0.0831995	+	0.738416i
$604$	−41.7260	+	61.2009i	−1.69781	+	2.49023i
$605$	−11.7866	−	18.1802i	−0.479194	−	0.739130i
$606$	−29.3416	+	50.8212i	−1.19192	+	2.06447i
$607$	1.46572	−	5.47016i	0.0594919	−	0.222027i	−0.929779	−	0.368117i	$-0.880002\pi$
$607$	1.46572	−	5.47016i	0.0594919	−	0.222027i	0.989271	+	0.146091i	$0.0466691\pi$
$608$	−9.06969	−	14.4343i	−0.367824	−	0.585389i
$609$	−13.5345	+	2.10024i	−0.548445	+	0.0851059i
$610$	−4.27784	+	4.08377i	−0.173205	+	0.165347i
$611$	−1.36238	+	1.26410i	−0.0551159	+	0.0511401i
$612$	31.4298	+	23.1962i	1.27047	+	0.937651i
$613$	1.56507	+	1.15507i	0.0632124	+	0.0466529i	0.624968	−	0.780650i	$-0.285112\pi$
$613$	1.56507	+	1.15507i	0.0632124	+	0.0466529i	−0.561756	+	0.827303i	$0.689874\pi$
$614$	−23.0004	+	21.3413i	−0.928221	+	0.861264i
$615$	22.7305	−	21.6993i	0.916582	−	0.875001i
$616$	−46.1078	−	14.0030i	−1.85774	−	0.564199i
$617$	16.6624	+	26.5180i	0.670803	+	1.06758i	0.992678	+	0.120794i	$0.0385441\pi$
$617$	16.6624	+	26.5180i	0.670803	+	1.06758i	−0.321875	+	0.946782i	$0.604313\pi$
$618$	2.33425	−	8.71152i	0.0938971	−	0.350429i
$619$	14.5536	−	25.2076i	0.584958	−	1.01318i	−0.409922	−	0.912120i	$-0.634444\pi$
$619$	14.5536	−	25.2076i	0.584958	−	1.01318i	0.994881	−	0.101057i	$-0.0322225\pi$
$620$	−1.58057	−	2.43795i	−0.0634774	−	0.0979104i
$621$	−4.96606	+	7.28388i	−0.199281	+	0.292292i
$622$	0.728561	−	6.46616i	0.0292126	−	0.259269i
$623$	−32.6409	+	6.32316i	−1.30773	+	0.253332i
$624$	−2.85670	−	2.27814i	−0.114360	−	0.0911987i
$625$	19.2618	+	15.9369i	0.770471	+	0.637475i
$626$	−4.52731	+	1.77684i	−0.180948	+	0.0710168i
$627$	−42.2223	−	49.0632i	−1.68620	−	1.95940i
$628$	15.6213	+	35.8044i	0.623358	+	1.42875i
$629$	32.2893	+	15.5497i	1.28746	+	0.620007i
$630$	27.8179	−	21.3386i	1.10829	−	0.850149i
$631$	−11.1685	+	5.37846i	−0.444610	+	0.214113i	−0.642774	−	0.766056i	$-0.722217\pi$
$631$	−11.1685	+	5.37846i	−0.444610	+	0.214113i	0.198164	+	0.980169i	$0.436502\pi$
$632$	27.8783	+	23.9912i	1.10894	+	0.954320i
$633$	12.9350	−	6.83635i	0.514120	−	0.271720i
$634$	36.3968	+	53.3843i	1.44550	+	2.12016i
$635$	−15.5425	+	6.35603i	−0.616784	+	0.252231i
$636$		−	25.9298i		−	1.02818i
$637$	4.73591	+	1.61107i	0.187644	+	0.0638328i
$638$	−16.9414	−	16.9414i	−0.670716	−	0.670716i
$639$	4.32127	−	28.6697i	0.170947	−	1.13416i
$640$	42.0459	+	19.5179i	1.66201	+	0.771512i
$641$	−26.0542	−	8.03664i	−1.02908	−	0.317428i	−0.266163	−	0.963928i	$-0.585756\pi$
$641$	−26.0542	−	8.03664i	−1.02908	−	0.317428i	−0.762914	+	0.646500i	$0.776232\pi$
$642$	35.4382	−	41.1800i	1.39863	−	1.62524i
$643$	5.13645	−	14.6791i	0.202562	−	0.578888i	−0.797128	−	0.603811i	$-0.793648\pi$
$643$	5.13645	−	14.6791i	0.202562	−	0.578888i	0.999689	+	0.0249226i	$0.00793392\pi$
$644$	69.5090	−	16.1833i	2.73904	−	0.637713i
$645$	16.8477	+	14.0874i	0.663378	+	0.554689i
$646$	−22.5821	+	57.5382i	−0.888480	+	2.26381i
$647$	−9.28838	+	7.99330i	−0.365164	+	0.314249i	−0.815662	−	0.578528i	$-0.803627\pi$
$647$	−9.28838	+	7.99330i	−0.365164	+	0.314249i	0.450498	+	0.892777i	$0.351246\pi$
$648$	−16.4553	+	37.7159i	−0.646425	+	1.48162i
$649$	−54.4641	+	16.8000i	−2.13790	+	0.659456i
$650$	3.33499	+	7.83572i	0.130809	+	0.307342i
$651$	2.16509	+	0.316711i	0.0848566	+	0.0124129i
$652$	41.9773	+	4.72971i	1.64396	+	0.185230i
$653$	3.58289	+	18.9360i	0.140209	+	0.741024i	0.980136	+	0.198325i	$0.0635500\pi$
$653$	3.58289	+	18.9360i	0.140209	+	0.741024i	−0.839927	+	0.542699i	$0.817402\pi$
$654$	−15.8622	−	14.7180i	−0.620261	−	0.575518i
$655$	27.6920	+	26.9168i	1.08202	+	1.05173i
$656$	11.3421	−	6.54834i	0.442833	−	0.255670i
$657$	−2.59927	+	1.63323i	−0.101407	+	0.0637184i
$658$	−4.31311	−	15.8212i	−0.168142	−	0.616774i
$659$	−29.7970	+	6.80098i	−1.16073	+	0.264928i	−0.759162	−	0.650902i	$-0.774391\pi$
$659$	−29.7970	+	6.80098i	−1.16073	+	0.264928i	−0.401565	+	0.915830i	$0.631534\pi$
$660$	84.1366	+	24.6503i	3.27501	+	0.959513i
$661$	0.300590	+	1.99428i	0.0116916	+	0.0775686i	0.993916	−	0.110143i	$-0.0351310\pi$
$661$	0.300590	+	1.99428i	0.0116916	+	0.0775686i	−0.982224	+	0.187712i	$0.939893\pi$
$662$	−6.70613	+	9.08648i	−0.260641	+	0.353156i
$663$	0.267185	−	7.14068i	0.0103766	−	0.277321i
$664$	−3.14074	−	13.7605i	−0.121884	−	0.534010i
$665$	28.5119	+	21.8850i	1.10565	+	0.848665i
$666$	11.0708	−	48.5045i	0.428987	−	1.87951i
$667$	15.6478	+	4.19281i	0.605884	+	0.162346i
$668$	−4.86544	−	18.1581i	−0.188250	−	0.702557i
$669$	−26.7572	+	28.8374i	−1.03449	+	1.11492i
$670$	29.2777	−	25.9279i	1.13110	−	1.00168i
$671$	3.94656	−	3.14728i	0.152355	−	0.121499i
$672$	−15.9077	+	7.02298i	−0.613653	+	0.270917i
$673$	−31.2317	+	3.51897i	−1.20389	+	0.135646i	−0.691032	−	0.722825i	$-0.742843\pi$
$673$	−31.2317	+	3.51897i	−1.20389	+	0.135646i	−0.512862	+	0.858471i	$0.671415\pi$
$674$	5.65707	+	18.3398i	0.217902	+	0.706422i
$675$	4.73515	−	3.70687i	0.182256	−	0.142677i
$676$	3.43472	−	45.8331i	0.132104	−	1.76281i
$677$	−11.9082	+	5.19549i	−0.457669	+	0.199679i	−0.616063	−	0.787697i	$-0.711273\pi$
$677$	−11.9082	+	5.19549i	−0.457669	+	0.199679i	0.158394	+	0.987376i	$0.449368\pi$
$678$	12.3843	−	4.33344i	0.475615	−	0.166425i
$679$	−5.82733	+	26.0530i	−0.223633	+	0.999822i
$680$	−7.63810	−	37.4500i	−0.292908	−	1.43614i
$681$	0.0458845	+	0.612287i	0.00175830	+	0.0234629i
$682$	1.78853	+	3.38406i	0.0684863	+	0.129582i
$683$	20.4942	+	3.87771i	0.784188	+	0.148376i	0.562562	−	0.826755i	$-0.309816\pi$
$683$	20.4942	+	3.87771i	0.784188	+	0.148376i	0.221626	+	0.975132i	$0.428864\pi$
$684$	54.9733	+	8.28589i	2.10196	+	0.316819i
$685$	−30.7780	+	18.3571i	−1.17597	+	0.701388i
$686$	−31.9618	+	30.4419i	−1.22031	+	1.16228i
$687$	26.5836	−	26.5836i	1.01423	−	1.01423i
$688$	5.43498	+	7.36414i	0.207207	+	0.280755i
$689$	−1.77616	+	1.21097i	−0.0676663	+	0.0461341i
$690$	−88.9054	+	21.6243i	−3.38457	+	0.823223i
$691$	−1.07836	+	0.0808119i	−0.0410227	+	0.00307423i	−0.0952257	−	0.995456i	$-0.530357\pi$
$691$	−1.07836	+	0.0808119i	−0.0410227	+	0.00307423i	0.0542029	+	0.998530i	$0.482738\pi$
$692$	−34.5083	−	12.0750i	−1.31181	−	0.459022i
$693$	−25.2679	+	16.0306i	−0.959849	+	0.608952i
$694$	11.9304	−	24.7738i	0.452873	−	0.940401i
$695$	23.6968	−	33.0807i	0.898871	−	1.25482i
$696$	20.6705	+	1.54904i	0.783513	+	0.0587162i
$697$	23.4755	+	10.2422i	0.889197	+	0.387953i
$698$	32.9200	−	62.2877i	1.24604	−	2.35762i
$699$	−6.24262	+	7.82800i	−0.236118	+	0.296082i
$700$	−48.5293	−	3.86426i	−1.83423	−	0.146055i
$701$	17.8164	+	22.3411i	0.672917	+	0.843811i	0.994680	−	0.103009i	$-0.0328470\pi$
$701$	17.8164	+	22.3411i	0.672917	+	0.843811i	−0.321763	+	0.946820i	$0.604276\pi$
$702$	2.01272	−	0.380826i	0.0759650	−	0.0143734i
$703$	50.9697	−	1.90715i	1.92236	−	0.0719296i
$704$	−43.5399	−	25.1377i	−1.64097	−	0.947414i
$705$	3.71182	+	13.1056i	0.139795	+	0.493587i
$706$	−3.75706	−	0.857524i	−0.141399	−	0.0322733i
$707$	−11.0109	+	25.5398i	−0.414109	+	0.960524i
$708$	57.4665	−	91.4573i	2.15972	−	3.43718i
$709$	−24.5442	−	26.4523i	−0.921777	−	0.993439i	0.0782174	−	0.996936i	$-0.475077\pi$
$709$	−24.5442	−	26.4523i	−0.921777	−	0.993439i	−0.999994	+	0.00349751i	$0.998887\pi$
$710$	−48.0279	+	39.4292i	−1.80246	+	1.47975i
$711$	22.5852	−	3.40417i	0.847010	−	0.127666i
$712$	50.2824	+	1.88143i	1.88441	+	0.0705097i
$713$	−2.19137	−	1.37693i	−0.0820674	−	0.0515664i
$714$	54.7396	+	31.2873i	2.04858	+	1.17090i
$715$	−2.24081	−	6.91447i	−0.0838014	−	0.258587i
$716$	25.3015	+	43.8234i	0.945560	+	1.63776i
$717$	7.31110	−	1.95900i	0.273038	−	0.0731604i
$718$	−2.79350	−	74.6579i	−0.104253	−	2.78621i
$719$	−21.3289	−	14.5418i	−0.795434	−	0.542318i	0.0960464	−	0.995377i	$-0.469380\pi$
$719$	−21.3289	−	14.5418i	−0.795434	−	0.542318i	−0.891480	+	0.453059i	$0.850333\pi$
$720$	−11.0540	+	5.01076i	−0.411957	+	0.186740i
$721$	0.618675	−	4.22937i	0.0230407	−	0.157510i
$722$	4.77944	+	42.4187i	0.177872	+	1.57866i
$723$	−39.5654	−	20.9109i	−1.47145	−	0.777685i
$724$	−14.1639	−	36.0891i	−0.526399	−	1.34124i
$725$	−9.30335	−	5.96326i	−0.345518	−	0.221470i
$726$	−50.3528	−	19.7620i	−1.86877	−	0.733438i
$727$	6.09740	+	17.4254i	0.226140	+	0.646271i	0.999918	+	0.0128142i	$0.00407899\pi$
$727$	6.09740	+	17.4254i	0.226140	+	0.646271i	−0.773778	+	0.633457i	$0.781635\pi$
$728$	−6.42781	−	3.99997i	−0.238230	−	0.148249i
$729$	7.42031	+	15.4084i	0.274826	+	0.570683i
$730$	6.48127	+	1.13127i	0.239883	+	0.0418703i
$731$	−5.27589	+	17.1040i	−0.195136	+	0.632615i
$732$	−1.77845	+	9.39935i	−0.0657335	+	0.347410i
$733$	−6.87966	+	5.07742i	−0.254106	+	0.187539i	−0.713423	−	0.700734i	$-0.752856\pi$
$733$	−6.87966	+	5.07742i	−0.254106	+	0.187539i	0.459317	+	0.888272i	$0.348094\pi$
$734$	−71.3500			−2.63358
$735$	26.2982	−	25.5461i	0.970025	−	0.942283i
$736$	20.5672			0.758116
$737$	−26.8571	+	19.8215i	−0.989295	+	0.730133i
$738$	6.61029	−	34.9362i	0.243328	−	1.28602i
$739$	−8.06933	+	26.1601i	−0.296835	+	0.962316i	0.677177	+	0.735820i	$0.263203\pi$
$739$	−8.06933	+	26.1601i	−0.296835	+	0.962316i	−0.974012	+	0.226496i	$0.927273\pi$
$740$	−56.5221	+	39.7230i	−2.07779	+	1.46025i
$741$	−4.41249	−	9.16264i	−0.162097	−	0.336598i
$742$	−2.20569	−	18.8392i	−0.0809733	−	0.691609i
$743$	7.66419	+	21.9030i	0.281172	+	0.803543i	0.994691	+	0.102907i	$0.0328145\pi$
$743$	7.66419	+	21.9030i	0.281172	+	0.803543i	−0.713519	+	0.700636i	$0.752900\pi$
$744$	−3.08264	−	1.20985i	−0.113015	−	0.0443551i
$745$	−26.6255	−	8.89451i	−0.975485	−	0.325870i
$746$	−3.65893	−	9.32279i	−0.133963	−	0.341332i
$747$	−7.74922	−	4.09558i	−0.283529	−	0.149849i
$748$	8.00063	+	71.0075i	0.292532	+	2.59629i
$749$	14.4121	−	21.3375i	0.526607	−	0.779654i
$750$	62.2627	+	4.34134i	2.27351	+	0.158523i
$751$	34.7112	+	23.6657i	1.26663	+	0.863575i	0.995102	−	0.0988554i	$-0.0315181\pi$
$751$	34.7112	+	23.6657i	1.26663	+	0.863575i	0.271530	+	0.962430i	$0.412471\pi$
$752$	0.212260	+	5.67276i	0.00774031	+	0.206864i
$753$	−48.7988	+	13.0756i	−1.77833	+	0.476501i
$754$	−1.88210	−	3.25989i	−0.0685419	−	0.118718i
$755$	20.4634	−	40.0859i	0.744739	−	1.45887i
$756$	−3.40295	+	11.2049i	−0.123764	+	0.407518i
$757$	7.83349	+	4.92211i	0.284713	+	0.178897i	0.666815	−	0.745223i	$-0.267657\pi$
$757$	7.83349	+	4.92211i	0.284713	+	0.178897i	−0.382102	+	0.924120i	$0.624800\pi$
$758$	−52.3211	−	1.95772i	−1.90039	−	0.0711075i
$759$	77.2227	−	11.6395i	2.80301	−	0.422485i
$760$	−34.5159	−	42.0431i	−1.25202	−	1.52506i
$761$	−10.5494	−	11.3695i	−0.382415	−	0.412145i	0.512283	−	0.858817i	$-0.328800\pi$
$761$	−10.5494	−	11.3695i	−0.382415	−	0.412145i	−0.894698	+	0.446671i	$0.852609\pi$
$762$	−22.3038	+	35.4963i	−0.807981	+	1.28589i
$763$	−8.27786	−	6.05391i	−0.299679	−	0.219166i
$764$	−29.0523	−	6.63100i	−1.05108	−	0.239901i
$765$	−20.7215	−	11.5745i	−0.749189	−	0.418479i
$766$	−49.2741	−	28.4484i	−1.78034	−	1.02788i
$767$	−8.94850	+	0.334829i	−0.323112	+	0.0120900i
$768$	62.8338	−	11.8888i	2.26732	−	0.429000i
$769$	6.92761	+	8.68694i	0.249816	+	0.313259i	0.890889	−	0.454220i	$-0.150082\pi$
$769$	6.92761	+	8.68694i	0.249816	+	0.313259i	−0.641074	+	0.767479i	$0.721511\pi$
$770$	63.2261	+	10.7526i	2.27851	+	0.387498i
$771$	2.74883	−	3.44692i	0.0989967	−	0.124138i
$772$	−9.08079	+	17.1817i	−0.326825	+	0.618383i
$773$	8.50467	+	3.71055i	0.305892	+	0.133459i	0.547231	−	0.836982i	$-0.315682\pi$
$773$	8.50467	+	3.71055i	0.305892	+	0.133459i	−0.241339	+	0.970441i	$0.577587\pi$
$774$	24.7788	+	1.85691i	0.890655	+	0.0667453i
$775$	1.13945	+	1.34845i	0.0409304	+	0.0484378i
$776$	17.5303	−	36.4021i	0.629302	−	1.30676i
$777$	5.60036	−	51.7256i	0.200912	−	1.85564i
$778$	−78.1468	−	27.3448i	−2.80170	−	0.980357i
$779$	36.3500	−	2.72405i	1.30237	−	0.0975994i
$780$	11.7660	+	7.16217i	0.421292	+	0.256447i
$781$	43.8217	−	29.8771i	1.56806	−	1.06909i
$782$	−44.2833	−	60.0018i	−1.58357	−	2.14566i
$783$	−1.87956	+	1.87956i	−0.0671698	+	0.0671698i
$784$	13.1657	−	7.75470i	0.470204	−	0.276954i
$785$	−12.1585	−	20.3852i	−0.433954	−	0.727580i
$786$	95.3355	+	14.3695i	3.40050	+	0.512544i
$787$	27.2854	+	5.16268i	0.972620	+	0.184030i	0.647854	−	0.761765i	$-0.275667\pi$
$787$	27.2854	+	5.16268i	0.972620	+	0.184030i	0.324766	+	0.945794i	$0.394714\pi$
$788$	4.97351	+	9.41034i	0.177174	+	0.335229i
$789$	4.66771	+	62.2862i	0.166175	+	2.21745i
$790$	−40.8333	−	26.9986i	−1.45278	−	0.960568i
$791$	5.59075	−	2.72238i	0.198784	−	0.0967967i
$792$	42.7461	−	14.9575i	1.51892	−	0.531492i
$793$	0.726901	−	0.317144i	0.0258130	−	0.0112621i
$794$	−5.49676	+	73.3492i	−0.195073	+	2.60306i
$795$	1.98610	+	15.6296i	0.0704396	+	0.554326i
$796$	12.8131	+	41.5389i	0.454147	+	1.47231i
$797$	−35.9187	+	4.04706i	−1.27230	+	0.143354i	−0.722166	−	0.691720i	$-0.756853\pi$
$797$	−35.9187	+	4.04706i	−1.27230	+	0.143354i	−0.550138	+	0.835074i	$0.685425\pi$
$798$	89.6842	+	2.96521i	3.17479	+	0.104967i
$799$	−8.67966	+	6.92180i	−0.307064	+	0.244876i
$800$	−13.3685	−	4.25592i	−0.472650	−	0.150470i
$801$	21.2533	−	22.9056i	0.750949	−	0.809331i
$802$	−9.43680	−	35.2186i	−0.333225	−	1.24361i
$803$	−5.42419	−	1.45341i	−0.191416	−	0.0512896i
$804$	14.0761	−	61.6713i	0.496425	−	2.17498i
$805$	−40.6582	+	15.0788i	−1.43301	+	0.531459i
$806$	0.133816	+	0.586286i	0.00471346	+	0.0206510i
$807$	−0.259474	+	6.93458i	−0.00913391	+	0.244109i
$808$	24.9948	−	33.8667i	0.879314	−	1.19143i
$809$	0.704715	+	4.67548i	0.0247764	+	0.164381i	0.997797	−	0.0663360i	$-0.0211309\pi$
$809$	0.704715	+	4.67548i	0.0247764	+	0.164381i	−0.973021	+	0.230717i	$0.925893\pi$
$810$	15.3983	−	52.5576i	0.541042	−	1.84669i
$811$	42.9534	−	9.80382i	1.50830	−	0.344259i	0.613127	−	0.789984i	$-0.289911\pi$
$811$	42.9534	−	9.80382i	1.50830	−	0.344259i	0.895170	+	0.445726i	$0.147054\pi$
$812$	21.5000	−	0.898127i	0.754502	−	0.0315181i
$813$	−42.8204	+	26.9058i	−1.50178	+	0.943628i
$814$	78.8174	−	45.5052i	2.76255	−	1.59496i
$815$	−25.6648	+	0.364347i	−0.899000	+	0.0127625i
$816$	−15.9997	−	14.8456i	−0.560103	−	0.519700i
$817$	4.73596	+	25.0302i	0.165690	+	0.875695i
$818$	5.10872	+	0.575614i	0.178622	+	0.0201259i
$819$	−4.48646	+	1.40529i	−0.156770	+	0.0491048i
$820$	−39.3048	+	29.8793i	−1.37258	+	1.04343i
$821$	−12.0079	+	3.70394i	−0.419078	+	0.129269i	−0.497121	−	0.867682i	$-0.665609\pi$
$821$	−12.0079	+	3.70394i	−0.419078	+	0.129269i	0.0780422	+	0.996950i	$0.475133\pi$
$822$	−35.7776	+	82.0032i	−1.24789	+	2.86019i
$823$	−10.8285	+	9.31866i	−0.377457	+	0.324828i	−0.820473	−	0.571686i	$-0.806290\pi$
$823$	−10.8285	+	9.31866i	−0.377457	+	0.324828i	0.443015	+	0.896514i	$0.353909\pi$
$824$	−2.36336	+	6.02174i	−0.0823315	+	0.209777i
$825$	−52.6029	−	8.41395i	−1.83140	−	0.292936i
$826$	33.9724	−	71.3363i	1.18205	−	2.48211i
$827$	−6.41528	+	18.3338i	−0.223081	+	0.637529i	0.776888	+	0.629639i	$0.216797\pi$
$827$	−6.41528	+	18.3338i	−0.223081	+	0.637529i	−0.999969	+	0.00789020i	$0.997488\pi$
$828$	−43.7511	+	50.8397i	−1.52045	+	1.76680i
$829$	−24.9525	−	7.69681i	−0.866635	−	0.267321i	−0.170609	−	0.985339i	$-0.554574\pi$
$829$	−24.9525	−	7.69681i	−0.866635	−	0.267321i	−0.696025	+	0.718017i	$0.745050\pi$
$830$	6.45543	+	17.6412i	0.224071	+	0.612335i
$831$	−3.59256	+	23.8351i	−0.124625	+	0.826831i
$832$	−5.58533	−	5.58533i	−0.193636	−	0.193636i
$833$	27.4915	+	11.7109i	0.952525	+	0.405757i
$834$		−	101.591i		−	3.51781i
$835$	4.32355	+	10.5724i	0.149623	+	0.365874i
$836$	57.2884	+	84.0266i	1.98136	+	2.90612i
$837$	0.375443	−	0.198427i	0.0129772	−	0.00685866i
$838$	−41.7564	−	35.9343i	−1.44245	−	1.24133i
$839$	−4.87285	+	2.34664i	−0.168230	+	0.0810151i	−0.516103	−	0.856526i	$-0.672618\pi$
$839$	−4.87285	+	2.34664i	−0.168230	+	0.0810151i	0.347874	+	0.937541i	$0.386904\pi$
$840$	−47.5303	+	28.6297i	−1.63995	+	0.987819i
$841$	−21.7273	−	10.4633i	−0.749217	−	0.360804i
$842$	4.35937	+	9.99178i	0.150234	+	0.344340i
$843$	37.0210	+	43.0192i	1.27507	+	1.48166i
$844$	−21.3972	+	8.39777i	−0.736521	+	0.289063i
$845$	1.44026	+	27.8898i	0.0495464	+	0.959437i
$846$	12.0494	+	9.60905i	0.414266	+	0.330366i
$847$	−24.7914	−	6.52741i	−0.851843	−	0.224284i
$848$	−0.735177	+	6.52488i	−0.0252461	+	0.224065i
$849$	−20.0723	+	29.4407i	−0.688881	+	1.01040i
$850$	16.3679	+	48.1643i	0.561414	+	1.65202i
$851$	−30.7685	+	53.2925i	−1.05473	+	1.82684i
$852$	−26.0142	+	97.0861i	−0.891230	+	3.32612i
$853$	16.9538	+	26.9817i	0.580485	+	0.923837i	0.999872	+	0.0160294i	$0.00510252\pi$
$853$	16.9538	+	26.9817i	0.580485	+	0.923837i	−0.419386	+	0.907808i	$0.637755\pi$
$854$	−0.492585	+	6.98035i	−0.0168559	+	0.238863i
$855$	−33.7707	−	0.783774i	−1.15494	−	0.0268045i
$856$	−28.5659	+	26.5053i	−0.976363	+	0.905933i
$857$	7.17396	+	5.29462i	0.245058	+	0.180861i	0.709423	−	0.704783i	$-0.248956\pi$
$857$	7.17396	+	5.29462i	0.245058	+	0.180861i	−0.464365	+	0.885644i	$0.653718\pi$
$858$	−14.6004	−	10.7756i	−0.498450	−	0.367873i
$859$	9.39036	−	8.71298i	0.320395	−	0.297283i	−0.503535	−	0.863975i	$-0.667967\pi$
$859$	9.39036	−	8.71298i	0.320395	−	0.297283i	0.823930	+	0.566692i	$0.191777\pi$
$860$	−23.8252	−	24.9574i	−0.812432	−	0.851039i
$861$	2.61738	−	37.0904i	0.0891999	−	1.26404i
$862$	−32.2935	−	51.3948i	−1.09992	−	1.75051i
$863$	9.33251	−	34.8294i	0.317682	−	1.18561i	−0.603784	−	0.797148i	$-0.706341\pi$
$863$	9.33251	−	34.8294i	0.317682	−	1.18561i	0.921466	−	0.388458i	$-0.126992\pi$
$864$	−1.68735	+	2.92258i	−0.0574049	+	0.0994283i
$865$	21.7254	+	4.63523i	0.738684	+	0.157603i
$866$	−8.12175	+	11.9124i	−0.275988	+	0.404800i
$867$	0.320749	−	2.84672i	0.0108932	−	0.0966798i
$868$	−3.32451	−	0.875320i	−0.112841	−	0.0297103i
$869$	32.6660	+	26.0503i	1.10812	+	0.883695i
$870$	−27.5514	+	1.42279i	−0.934080	+	0.0482370i
$871$	−4.88179	+	1.91596i	−0.165413	+	0.0649198i
$872$	10.1239	+	11.7642i	0.342839	+	0.398386i
$873$	−10.0334	−	22.9967i	−0.339578	−	0.778321i
$874$	−95.6231	−	46.0496i	−3.23450	−	1.55765i
$875$	29.5478	−	1.38786i	0.998899	−	0.0469182i
$876$	9.58807	−	4.61737i	0.323951	−	0.156006i
$877$	17.4270	+	14.9971i	0.588467	+	0.506417i	0.895369	−	0.445324i	$-0.146912\pi$
$877$	17.4270	+	14.9971i	0.588467	+	0.506417i	−0.306903	+	0.951741i	$0.599293\pi$
$878$	58.2054	−	30.7624i	1.96434	−	1.03818i
$879$	−9.60078	−	14.0818i	−0.323826	−	0.474966i
$880$	−20.4729	−	8.58841i	−0.690142	−	0.289515i
$881$		−	14.4563i		−	0.487045i	−0.969895	−	0.243523i	$-0.921697\pi$
$881$		−	14.4563i		−	0.487045i	0.969895	−	0.243523i	$-0.0783030\pi$
$882$	7.35734	−	40.8253i	0.247734	−	1.37466i
$883$	6.01601	+	6.01601i	0.202455	+	0.202455i	0.801051	−	0.598596i	$-0.204275\pi$
$883$	6.01601	+	6.01601i	0.202455	+	0.202455i	−0.598596	+	0.801051i	$0.704275\pi$
$884$	−1.67325	+	11.1013i	−0.0562775	+	0.373377i
$885$	−27.6337	+	59.5291i	−0.928896	+	2.00105i
$886$	87.8696	+	27.1042i	2.95204	+	0.910583i
$887$	21.3347	−	24.7914i	0.716349	−	0.832412i	−0.275303	−	0.961358i	$-0.588778\pi$
$887$	21.3347	−	24.7914i	0.716349	−	0.832412i	0.991652	+	0.128945i	$0.0411591\pi$
$888$	−26.0061	+	74.3211i	−0.872707	+	2.49405i
$889$	−8.54265	+	17.9381i	−0.286511	+	0.601626i
$890$	−66.7042	+	5.95207i	−2.23593	+	0.199514i
$891$	−17.0777	+	43.5134i	−0.572126	+	1.45775i
$892$	46.8471	−	40.3152i	1.56856	−	1.34985i
$893$	−6.31829	+	14.4817i	−0.211434	+	0.484611i
$894$	−66.9695	+	20.6574i	−2.23980	+	0.690885i
$895$	−18.6075	−	24.4773i	−0.621981	−	0.818187i
$896$	52.3406	−	16.3946i	1.74858	−	0.547704i
$897$	12.1925	+	1.37376i	0.407094	+	0.0458685i
$898$	4.97711	+	26.3047i	0.166088	+	0.877798i
$899$	−0.572033	−	0.530769i	−0.0190784	−	0.0177021i
$900$	38.9581	−	23.9922i	1.29860	−	0.799740i
$901$	−11.1207	+	6.42056i	−0.370486	+	0.213900i
$902$	55.0729	−	34.6046i	1.83373	−	1.15221i
$903$	25.9623	−	1.08453i	0.863972	−	0.0360910i
$904$	−9.17499	+	2.09413i	−0.305155	+	0.0696497i
$905$	11.3018	+	20.6684i	0.375685	+	0.687042i
$906$	−16.7468	−	111.107i	−0.556374	−	3.69130i
$907$	12.7992	−	17.3423i	0.424992	−	0.575843i	−0.538822	−	0.842420i	$-0.681131\pi$
$907$	12.7992	−	17.3423i	0.424992	−	0.575843i	0.963814	+	0.266576i	$0.0858924\pi$
$908$	0.0360702	−	0.963996i	0.00119703	−	0.0319913i
$909$	−5.81639	−	25.4832i	−0.192917	−	0.845226i
$910$	9.15781	+	4.20279i	0.303579	+	0.139321i
$911$	−9.85830	+	43.1920i	−0.326620	+	1.43102i	0.498908	+	0.866655i	$0.333734\pi$
$911$	−9.85830	+	43.1920i	−0.326620	+	1.43102i	−0.825528	+	0.564361i	$0.809123\pi$
$912$	−30.0047	−	8.03974i	−0.993556	−	0.266222i
$913$	−4.14980	−	15.4872i	−0.137338	−	0.512553i
$914$	49.8102	−	53.6827i	1.64758	−	1.77566i
$915$	0.352048	−	5.80184i	0.0116384	−	0.191803i
$916$	−46.1796	+	36.8270i	−1.52582	+	1.21680i
$917$	45.6686	+	1.50993i	1.50811	+	0.0498623i
$918$	12.1593	−	1.37002i	0.401316	−	0.0452174i
$919$	−6.92086	−	22.4369i	−0.228298	−	0.740124i	−0.995156	−	0.0983075i	$-0.968657\pi$
$919$	−6.92086	−	22.4369i	−0.228298	−	0.740124i	0.766858	−	0.641817i	$-0.221819\pi$
$920$	65.1046	−	8.27300i	2.14643	−	0.272753i
$921$	2.30446	−	30.7508i	0.0759344	−	1.01327i
$922$	51.9055	−	22.6461i	1.70942	−	0.745811i
$923$	7.86519	−	2.75215i	0.258886	−	0.0905881i
$924$	93.2667	−	45.4156i	3.06825	−	1.49406i
$925$	31.0270	−	28.2730i	1.02016	−	0.929611i
$926$	1.05506	+	14.0789i	0.0346716	+	0.462660i
$927$	1.87709	+	3.55163i	0.0616518	+	0.116651i
$928$	6.09326	+	1.15291i	0.200021	+	0.0378460i
$929$	9.70170	+	1.46230i	0.318303	+	0.0479764i	0.306250	−	0.951951i	$-0.400926\pi$
$929$	9.70170	+	1.46230i	0.318303	+	0.0479764i	0.0120521	+	0.999927i	$0.496164\pi$
$930$	4.27303	+	1.08018i	0.140118	+	0.0354206i
$931$	42.3799	−	3.54689i	1.38895	−	0.116245i
$932$	11.1232	−	11.1232i	0.364353	−	0.364353i
$933$	3.79763	+	5.14560i	0.124329	+	0.168460i
$934$	35.9188	−	24.4890i	1.17530	−	0.801305i
$935$	−10.2613	−	42.1882i	−0.335582	−	1.37970i
$936$	7.09528	−	0.531718i	0.231916	−	0.0173797i
$937$	−34.1432	−	11.9472i	−1.11541	−	0.390299i	−0.291245	−	0.956649i	$-0.594069\pi$
$937$	−34.1432	−	11.9472i	−1.11541	−	0.390299i	−0.824165	+	0.566350i	$0.808355\pi$
$938$	4.98093	−	46.0045i	0.162633	−	1.50210i
$939$	2.07393	−	4.30657i	0.0676803	−	0.140540i
$940$	−3.48962	−	21.1139i	−0.113819	−	0.688661i
$941$	−18.2113	−	1.36475i	−0.593672	−	0.0444896i	−0.225494	−	0.974245i	$-0.572399\pi$
$941$	−18.2113	−	1.36475i	−0.593672	−	0.0444896i	−0.368179	+	0.929755i	$0.620019\pi$
$942$	−54.3133	−	23.6966i	−1.76962	−	0.772078i
$943$	−20.5498	+	38.8820i	−0.669192	+	1.26617i
$944$	−17.0537	+	21.3847i	−0.555051	+	0.696011i
$945$	1.19295	−	7.01459i	0.0388066	−	0.228185i
$946$	28.3405	+	35.5378i	0.921428	+	1.15543i
$947$	−45.3765	+	8.58571i	−1.47454	+	0.278998i	−0.860165	−	0.510016i	$-0.829639\pi$
$947$	−45.3765	+	8.58571i	−1.47454	+	0.278998i	−0.614375	+	0.789014i	$0.710592\pi$
$948$	−79.1242	+	2.96062i	−2.56983	+	0.0961564i
$949$	−0.764063	−	0.441132i	−0.0248025	−	0.0143198i
$950$	52.6255	+	49.7191i	1.70740	+	1.61310i
$951$	−61.9088	−	14.1303i	−2.00753	−	0.458206i
$952$	−36.5034	−	26.6962i	−1.18308	−	0.865230i
$953$	26.8412	−	42.7175i	0.869471	−	1.38375i	−0.0533705	−	0.998575i	$-0.516996\pi$
$953$	26.8412	−	42.7175i	0.869471	−	1.38375i	0.922841	−	0.385180i	$-0.125861\pi$
$954$	12.1251	+	13.0677i	0.392563	+	0.423083i
$955$	18.0197	+	1.77168i	0.583103	+	0.0573303i
$956$	−11.7590	+	1.77238i	−0.380312	+	0.0573229i
$957$	23.5306	+	0.880451i	0.760635	+	0.0284610i
$958$	22.4620	+	14.1138i	0.725715	+	0.455997i
$959$	−12.3220	+	40.5727i	−0.397899	+	1.31016i
$960$	−55.0717	+	17.8473i	−1.77743	+	0.576020i
$961$	−15.4377	−	26.7388i	−0.497989	−	0.862543i
$962$	13.8116	−	3.70080i	0.445303	−	0.119318i
$963$	0.904838	+	24.1823i	0.0291580	+	0.779264i
$964$	58.0925	+	39.6068i	1.87103	+	1.27565i
$965$	4.15757	−	11.0521i	0.133837	−	0.355780i
$966$	−60.5961	+	89.7140i	−1.94965	+	2.88650i
$967$	−5.79179	−	51.4035i	−0.186251	−	1.65303i	−0.644796	−	0.764355i	$-0.723058\pi$
$967$	−5.79179	−	51.4035i	−0.186251	−	1.65303i	0.458544	−	0.888672i	$-0.348371\pi$
$968$	34.3023	+	18.1293i	1.10252	+	0.582697i
$969$	−22.1940	−	56.5494i	−0.712974	−	1.81663i
$970$	−17.0381	+	51.0033i	−0.547061	+	1.63762i
$971$	−9.06373	−	3.55725i	−0.290869	−	0.114158i	0.215420	−	0.976521i	$-0.430888\pi$
$971$	−9.06373	−	3.55725i	−0.290869	−	0.114158i	−0.506289	+	0.862364i	$0.668983\pi$
$972$	−24.8724	−	71.0812i	−0.797782	−	2.27993i
$973$	−5.59889	−	47.8213i	−0.179492	−	1.53308i
$974$	20.2952	+	42.1434i	0.650300	+	1.35036i
$975$	−7.64076	−	3.41590i	−0.244700	−	0.109396i
$976$	0.714019	−	2.31479i	0.0228552	−	0.0740948i
$977$	−6.65028	+	35.1476i	−0.212761	+	1.12447i	0.699429	+	0.714702i	$0.253438\pi$
$977$	−6.65028	+	35.1476i	−0.212761	+	1.12447i	−0.912190	+	0.409768i	$0.865610\pi$
$978$	−51.5587	+	38.0521i	−1.64867	+	1.21677i
$979$	57.1596			1.82683
$980$	−45.5516	+	35.2574i	−1.45509	+	1.12626i
$981$	9.63823			0.307725
$982$	−49.6347	+	36.6321i	−1.58391	+	1.16898i
$983$	−3.71542	+	19.6365i	−0.118504	+	0.626306i	0.872076	+	0.489370i	$0.162773\pi$
$983$	−3.71542	+	19.6365i	−0.118504	+	0.626306i	−0.990580	+	0.136936i	$0.956274\pi$
$984$	−16.5867	+	53.7727i	−0.528764	+	1.71421i
$985$	−3.71865	−	5.29130i	−0.118486	−	0.168595i
$986$	−9.75599	−	20.2585i	−0.310694	−	0.645163i
$987$	13.6836	+	8.51519i	0.435554	+	0.271042i
$988$	5.27716	+	15.0812i	0.167889	+	0.479798i
$989$	−28.6097	−	11.2285i	−0.909734	−	0.357044i
$990$	−53.9287	+	26.9203i	−1.71397	+	0.855584i
$991$	16.4847	+	42.0023i	0.523654	+	1.33425i	0.911035	+	0.412329i	$0.135284\pi$
$991$	16.4847	+	42.0023i	0.523654	+	1.33425i	−0.387381	+	0.921920i	$0.626620\pi$
$992$	−0.875914	−	0.462934i	−0.0278103	−	0.0146982i
$993$	−1.24271	−	11.0293i	−0.0394361	−	0.350005i
$994$	−10.6420	+	72.7505i	−0.337543	+	2.30751i
$995$	−10.9050	−	24.0569i	−0.345711	−	0.762654i
$996$	25.1053	+	17.1165i	0.795493	+	0.542358i
$997$	0.814586	+	21.7703i	0.0257982	+	0.689471i	0.950854	+	0.309640i	$0.100208\pi$
$997$	0.814586	+	21.7703i	0.0257982	+	0.689471i	−0.925056	+	0.379831i	$0.875982\pi$
$998$	62.1883	−	16.6633i	1.96854	−	0.527468i
$999$	−5.04856	−	8.74436i	−0.159729	−	0.276659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.108.25	yes	624
5.2	odd	4	inner	245.2.x.a.157.25	yes	624
49.5	odd	42	inner	245.2.x.a.103.25	✓	624
245.152	even	84	inner	245.2.x.a.152.25	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.25	✓	624	49.5	odd	42	inner
245.2.x.a.108.25	yes	624	1.1	even	1	trivial
245.2.x.a.152.25	yes	624	245.152	even	84	inner
245.2.x.a.157.25	yes	624	5.2	odd	4	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+(1.91759 - 1.41525i) q^{2} +(-0.435467 + 2.30150i) q^{3} +(1.08472 - 3.51658i) q^{4} +(-0.384482 + 2.20277i) q^{5} +(2.42214 + 5.02963i) q^{6} +(1.41735 + 2.23408i) q^{7} +(-1.32248 - 3.77942i) q^{8} +(-2.31465 - 0.908433i) q^{9} +(2.38018 + 4.76814i) q^{10} +(-1.66178 - 4.23416i) q^{11} +(7.62106 + 4.02785i) q^{12} +(-0.0800136 - 0.710141i) q^{13} +(5.87968 + 2.27814i) q^{14} +(-4.90224 - 1.84412i) q^{15} +(-1.80353 - 1.22963i) q^{16} +(-0.159617 - 4.26586i) q^{17} +(-5.72421 + 1.53380i) q^{18} +(-3.03772 - 5.26149i) q^{19} +(7.32915 + 3.74145i) q^{20} +(-5.75894 + 2.28917i) q^{21} +(-9.17900 - 5.76755i) q^{22} +(7.32477 + 0.274074i) q^{23} +(9.27423 - 1.39787i) q^{24} +(-4.70435 - 1.69385i) q^{25} +(-1.15846 - 1.24852i) q^{26} +(-0.639878 + 1.01836i) q^{27} +(9.39376 - 2.56089i) q^{28} +(2.15468 + 0.491792i) q^{29} +(-12.0104 + 3.40161i) q^{30} +(-0.305778 - 0.176541i) q^{31} +(2.80397 - 0.104917i) q^{32} +(10.4686 - 1.98076i) q^{33} +(-6.34332 - 7.95427i) q^{34} +(-5.46610 + 2.26314i) q^{35} +(-5.70534 + 7.15426i) q^{36} +(-3.92288 + 7.42244i) q^{37} +(-13.2714 - 5.79026i) q^{38} +(1.66923 + 0.125092i) q^{39} +(8.83364 - 1.45999i) q^{40} +(-2.60325 + 5.40570i) q^{41} +(-7.80356 + 12.5400i) q^{42} +(-3.95770 - 1.38486i) q^{43} +(-16.6923 + 1.25092i) q^{44} +(2.89101 - 4.74936i) q^{45} +(14.4338 - 9.84079i) q^{46} +(-1.54431 - 2.09246i) q^{47} +(3.61537 - 3.61537i) q^{48} +(-2.98221 + 6.33296i) q^{49} +(-11.4182 + 3.40971i) q^{50} +(9.88738 + 1.49028i) q^{51} +(-2.58406 - 0.488931i) q^{52} +(-1.40559 - 2.65951i) q^{53} +(0.214206 + 2.85838i) q^{54} +(9.96578 - 2.03256i) q^{55} +(6.56911 - 8.31130i) q^{56} +(13.4321 - 4.70011i) q^{57} +(4.82781 - 2.10635i) q^{58} +(0.936410 - 12.4955i) q^{59} +(-11.8026 + 15.2388i) q^{60} +(0.327108 + 1.06046i) q^{61} +(-0.836207 + 0.0942179i) q^{62} +(-1.25117 - 6.45868i) q^{63} +(8.64158 - 6.89143i) q^{64} +(1.59504 + 0.0967848i) q^{65} +(17.2712 - 18.6139i) q^{66} +(-1.89933 - 7.08840i) q^{67} +(-15.1744 - 4.06597i) q^{68} +(-3.82048 + 16.7386i) q^{69} +(-7.27884 + 12.0756i) q^{70} +(2.59465 + 11.3679i) q^{71} +(-0.372281 + 9.94942i) q^{72} +(0.733111 - 0.993331i) q^{73} +(2.98212 + 19.7851i) q^{74} +(5.94698 - 10.0894i) q^{75} +(-21.7975 + 4.97515i) q^{76} +(7.10410 - 9.71386i) q^{77} +(3.37794 - 2.12250i) q^{78} +(-7.95495 + 4.59279i) q^{79} +(3.40201 - 3.49999i) q^{80} +(-7.53339 - 6.98996i) q^{81} +(2.65843 + 14.0502i) q^{82} +(3.50280 + 0.394670i) q^{83} +(1.80321 + 22.7349i) q^{84} +(9.45805 + 1.28855i) q^{85} +(-9.54916 + 2.94553i) q^{86} +(-2.07015 + 4.74484i) q^{87} +(-13.8050 + 11.8802i) q^{88} +(-4.59104 + 11.6978i) q^{89} +(-1.17774 - 13.1988i) q^{90} +(1.47310 - 1.18528i) q^{91} +(8.90914 - 25.4609i) q^{92} +(0.539466 - 0.626871i) q^{93} +(-5.92271 - 1.82691i) q^{94} +(12.7578 - 4.66844i) q^{95} +(-0.979570 + 6.49902i) q^{96} +(7.13501 + 7.13501i) q^{97} +(3.24404 + 16.3646i) q^{98} +11.3102i 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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