LMFDB - Embedded newform 260.2.o.a.183.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			183.8
Character	$\chi$	$=$	260.183
Dual form			260.2.o.a.27.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18329 + 0.774482i) q^{2} +(2.05925 - 2.05925i) q^{3} +(0.800354 - 1.83288i) q^{4} +(1.34695 - 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(0.845670 + 0.845670i) q^{7} +(0.472478 + 2.78869i) q^{8} -5.48103i q^{9} +O(q^{10})$	\(q+(-1.18329 + 0.774482i) q^{2} +(2.05925 - 2.05925i) q^{3} +(0.800354 - 1.83288i) q^{4} +(1.34695 - 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(0.845670 + 0.845670i) q^{7} +(0.472478 + 2.78869i) q^{8} -5.48103i q^{9} +(-0.211491 + 3.15520i) q^{10} +4.19592i q^{11} +(-2.12622 - 5.42248i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-1.65563 - 0.345717i) q^{14} +(-0.901767 - 6.44918i) q^{15} +(-2.71887 - 2.93390i) q^{16} +(-0.206069 + 0.206069i) q^{17} +(4.24496 + 6.48565i) q^{18} -4.84005 q^{19} +(-2.19339 - 3.89731i) q^{20} +3.48290 q^{21} +(-3.24967 - 4.96499i) q^{22} +(0.389358 - 0.389358i) q^{23} +(6.71555 + 4.76965i) q^{24} +(-1.37145 - 4.80823i) q^{25} +(1.38435 + 0.289071i) q^{26} +(-5.10906 - 5.10906i) q^{27} +(2.22684 - 0.873173i) q^{28} +6.55621i q^{29} +(6.06183 + 6.93286i) q^{30} +5.06902i q^{31} +(5.48946 + 1.36594i) q^{32} +(8.64045 + 8.64045i) q^{33} +(0.0842426 - 0.403436i) q^{34} +(2.64848 - 0.370328i) q^{35} +(-10.0460 - 4.38677i) q^{36} +(8.49149 - 8.49149i) q^{37} +(5.72719 - 3.74853i) q^{38} -2.91222 q^{39} +(5.61382 + 2.91291i) q^{40} -5.61170 q^{41} +(-4.12128 + 2.69744i) q^{42} +(-3.25094 + 3.25094i) q^{43} +(7.69060 + 3.35822i) q^{44} +(-9.78287 - 7.38267i) q^{45} +(-0.159173 + 0.762274i) q^{46} +(8.91159 + 8.91159i) q^{47} +(-11.6405 - 0.442809i) q^{48} -5.56968i q^{49} +(5.34672 + 4.62738i) q^{50} +0.848694i q^{51} +(-1.86197 + 0.730103i) q^{52} +(0.0714058 + 0.0714058i) q^{53} +(10.0024 + 2.08863i) q^{54} +(7.48913 + 5.65169i) q^{55} +(-1.95875 + 2.75787i) q^{56} +(-9.96688 + 9.96688i) q^{57} +(-5.07767 - 7.75790i) q^{58} -10.9539 q^{59} +(-12.5423 - 3.50881i) q^{60} -3.57989 q^{61} +(-3.92586 - 5.99812i) q^{62} +(4.63514 - 4.63514i) q^{63} +(-7.55353 + 2.63518i) q^{64} +(-2.21452 + 0.309649i) q^{65} +(-16.9160 - 3.53229i) q^{66} +(-6.95966 - 6.95966i) q^{67} +(0.212770 + 0.542626i) q^{68} -1.60357i q^{69} +(-2.84711 + 2.48941i) q^{70} +4.61114i q^{71} +(15.2849 - 2.58966i) q^{72} +(2.57559 + 2.57559i) q^{73} +(-3.47140 + 16.6244i) q^{74} +(-12.7255 - 7.07720i) q^{75} +(-3.87376 + 8.87121i) q^{76} +(-3.54836 + 3.54836i) q^{77} +(3.44600 - 2.25546i) q^{78} +2.19111 q^{79} +(-8.89878 + 0.900979i) q^{80} -4.59860 q^{81} +(6.64027 - 4.34616i) q^{82} +(11.1906 - 11.1906i) q^{83} +(2.78755 - 6.38371i) q^{84} +(0.0902396 + 0.645368i) q^{85} +(1.32901 - 6.36460i) q^{86} +(13.5009 + 13.5009i) q^{87} +(-11.7011 + 1.98248i) q^{88} +15.0102i q^{89} +(17.2937 + 1.15919i) q^{90} -1.19596i q^{91} +(-0.402020 - 1.02527i) q^{92} +(10.4384 + 10.4384i) q^{93} +(-17.4469 - 3.64313i) q^{94} +(-6.51931 + 8.63882i) q^{95} +(14.1170 - 8.49136i) q^{96} +(-5.51024 + 5.51024i) q^{97} +(4.31362 + 6.59056i) q^{98} +22.9980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.18329	+	0.774482i	−0.836713	+	0.547642i
$2$	−1.18329	+	0.774482i	−0.836713	+	0.547642i
$3$	2.05925	−	2.05925i	1.18891	−	1.18891i	0.211540	−	0.977369i	$-0.432152\pi$
$3$	2.05925	−	2.05925i	1.18891	−	1.18891i	0.977369	−	0.211540i	$-0.0678478\pi$
$4$	0.800354	−	1.83288i	0.400177	−	0.916438i
$5$	1.34695	−	1.78486i	0.602374	−	0.798214i
$5$	1.34695	−	1.78486i	0.602374	−	0.798214i
$6$	−0.841839	+	4.03155i	−0.343679	+	1.64587i
$7$	0.845670	+	0.845670i	0.319633	+	0.319633i	0.848626	−	0.528993i	$-0.177430\pi$
$7$	0.845670	+	0.845670i	0.319633	+	0.319633i	−0.528993	+	0.848626i	$0.677430\pi$
$8$	0.472478	+	2.78869i	0.167046	+	0.985949i
$9$		−	5.48103i		−	1.82701i
$10$	−0.211491	+	3.15520i	−0.0668793	+	0.997761i
$11$			4.19592i			1.26512i	0.774512	+	0.632559i	$0.217995\pi$
$11$			4.19592i			1.26512i	−0.774512	+	0.632559i	$0.782005\pi$
$12$	−2.12622	−	5.42248i	−0.613787	−	1.56534i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$14$	−1.65563	−	0.345717i	−0.442486	−	0.0923968i
$15$	−0.901767	−	6.44918i	−0.232835	−	1.66517i
$16$	−2.71887	−	2.93390i	−0.679716	−	0.733475i
$17$	−0.206069	+	0.206069i	−0.0499790	+	0.0499790i	−0.731655	−	0.681676i	$-0.761252\pi$
$17$	−0.206069	+	0.206069i	−0.0499790	+	0.0499790i	0.681676	+	0.731655i	$0.261252\pi$
$18$	4.24496	+	6.48565i	1.00055	+	1.52868i
$19$	−4.84005			−1.11038			−0.555192	−	0.831722i	$-0.687355\pi$
$19$	−4.84005			−1.11038			−0.555192	+	0.831722i	$0.687355\pi$
$20$	−2.19339	−	3.89731i	−0.490457	−	0.871466i
$21$	3.48290			0.760030
$22$	−3.24967	−	4.96499i	−0.692831	−	1.05854i
$23$	0.389358	−	0.389358i	0.0811867	−	0.0811867i	−0.665347	−	0.746534i	$-0.731717\pi$
$23$	0.389358	−	0.389358i	0.0811867	−	0.0811867i	0.746534	+	0.665347i	$0.231717\pi$
$24$	6.71555	+	4.76965i	1.37081	+	0.973601i
$25$	−1.37145	−	4.80823i	−0.274290	−	0.961647i
$26$	1.38435	+	0.289071i	0.271494	+	0.0566915i
$27$	−5.10906	−	5.10906i	−0.983240	−	0.983240i
$28$	2.22684	−	0.873173i	0.420834	−	0.165014i
$29$			6.55621i			1.21746i	0.793379	+	0.608728i	$0.208320\pi$
$29$			6.55621i			1.21746i	−0.793379	+	0.608728i	$0.791680\pi$
$30$	6.06183	+	6.93286i	1.10673	+	1.26576i
$31$			5.06902i			0.910423i	0.890383	+	0.455211i	$0.150436\pi$
$31$			5.06902i			0.910423i	−0.890383	+	0.455211i	$0.849564\pi$
$32$	5.48946	+	1.36594i	0.970409	+	0.241467i
$33$	8.64045	+	8.64045i	1.50411	+	1.50411i
$34$	0.0842426	−	0.403436i	0.0144475	−	0.0691887i
$35$	2.64848	−	0.370328i	0.447675	−	0.0625968i
$36$	−10.0460	−	4.38677i	−1.67434	−	0.731128i
$37$	8.49149	−	8.49149i	1.39599	−	1.39599i	0.584856	−	0.811137i	$-0.301151\pi$
$37$	8.49149	−	8.49149i	1.39599	−	1.39599i	0.811137	−	0.584856i	$-0.198849\pi$
$38$	5.72719	−	3.74853i	0.929073	−	0.608093i
$39$	−2.91222			−0.466329
$40$	5.61382	+	2.91291i	0.887622	+	0.460572i
$41$	−5.61170			−0.876400			−0.438200	−	0.898877i	$-0.644384\pi$
$41$	−5.61170			−0.876400			−0.438200	+	0.898877i	$0.644384\pi$
$42$	−4.12128	+	2.69744i	−0.635927	+	0.416224i
$43$	−3.25094	+	3.25094i	−0.495763	+	0.495763i	−0.910116	−	0.414353i	$-0.864008\pi$
$43$	−3.25094	+	3.25094i	−0.495763	+	0.495763i	0.414353	+	0.910116i	$0.364008\pi$
$44$	7.69060	+	3.35822i	1.15940	+	0.506271i
$45$	−9.78287	−	7.38267i	−1.45834	−	1.10054i
$46$	−0.159173	+	0.762274i	−0.0234687	+	0.112391i
$47$	8.91159	+	8.91159i	1.29989	+	1.29989i	0.928462	+	0.371427i	$0.121131\pi$
$47$	8.91159	+	8.91159i	1.29989	+	1.29989i	0.371427	+	0.928462i	$0.378869\pi$
$48$	−11.6405	−	0.442809i	−1.68016	−	0.0639140i
$49$		−	5.56968i		−	0.795669i
$50$	5.34672	+	4.62738i	0.756140	+	0.654410i
$51$			0.848694i			0.118841i
$52$	−1.86197	+	0.730103i	−0.258209	+	0.101247i
$53$	0.0714058	+	0.0714058i	0.00980834	+	0.00980834i	0.711994	−	0.702186i	$-0.247792\pi$
$53$	0.0714058	+	0.0714058i	0.00980834	+	0.00980834i	−0.702186	+	0.711994i	$0.747792\pi$
$54$	10.0024	+	2.08863i	1.36115	+	0.284226i
$55$	7.48913	+	5.65169i	1.00983	+	0.762074i
$56$	−1.95875	+	2.75787i	−0.261749	+	0.368536i
$57$	−9.96688	+	9.96688i	−1.32015	+	1.32015i
$58$	−5.07767	−	7.75790i	−0.666730	−	1.01866i
$59$	−10.9539			−1.42608			−0.713038	−	0.701125i	$-0.752681\pi$
$59$	−10.9539			−1.42608			−0.713038	+	0.701125i	$0.752681\pi$
$60$	−12.5423	−	3.50881i	−1.61920	−	0.452985i
$61$	−3.57989			−0.458357			−0.229179	−	0.973384i	$-0.573604\pi$
$61$	−3.57989			−0.458357			−0.229179	+	0.973384i	$0.573604\pi$
$62$	−3.92586	−	5.99812i	−0.498585	−	0.761762i
$63$	4.63514	−	4.63514i	0.583973	−	0.583973i
$64$	−7.55353	+	2.63518i	−0.944191	+	0.329398i
$65$	−2.21452	+	0.309649i	−0.274678	+	0.0384073i
$66$	−16.9160	−	3.53229i	−2.08222	−	0.434795i
$67$	−6.95966	−	6.95966i	−0.850258	−	0.850258i	0.139907	−	0.990165i	$-0.455320\pi$
$67$	−6.95966	−	6.95966i	−0.850258	−	0.850258i	−0.990165	+	0.139907i	$0.955320\pi$
$68$	0.212770	+	0.542626i	0.0258022	+	0.0658031i
$69$		−	1.60357i		−	0.193047i
$70$	−2.84711	+	2.48941i	−0.340295	+	0.297541i
$71$			4.61114i			0.547241i	0.961838	+	0.273621i	$0.0882213\pi$
$71$			4.61114i			0.547241i	−0.961838	+	0.273621i	$0.911779\pi$
$72$	15.2849	−	2.58966i	1.80134	−	0.305195i
$73$	2.57559	+	2.57559i	0.301450	+	0.301450i	0.841581	−	0.540131i	$-0.181625\pi$
$73$	2.57559	+	2.57559i	0.301450	+	0.301450i	−0.540131	+	0.841581i	$0.681625\pi$
$74$	−3.47140	+	16.6244i	−0.403541	+	1.93255i
$75$	−12.7255	−	7.07720i	−1.46942	−	0.817205i
$76$	−3.87376	+	8.87121i	−0.444350	+	1.01760i
$77$	−3.54836	+	3.54836i	−0.404374	+	0.404374i
$78$	3.44600	−	2.25546i	0.390183	−	0.255381i
$79$	2.19111			0.246519			0.123259	−	0.992374i	$-0.460665\pi$
$79$	2.19111			0.246519			0.123259	+	0.992374i	$0.460665\pi$
$80$	−8.89878	+	0.900979i	−0.994914	+	0.100732i
$81$	−4.59860			−0.510955
$82$	6.64027	−	4.34616i	0.733295	−	0.479953i
$83$	11.1906	−	11.1906i	1.22832	−	1.22832i	0.263725	−	0.964598i	$-0.415049\pi$
$83$	11.1906	−	11.1906i	1.22832	−	1.22832i	0.964598	−	0.263725i	$-0.0849512\pi$
$84$	2.78755	−	6.38371i	0.304147	−	0.696520i
$85$	0.0902396	+	0.645368i	0.00978785	+	0.0700000i
$86$	1.32901	−	6.36460i	0.143311	−	0.686312i
$87$	13.5009	+	13.5009i	1.44745	+	1.44745i
$88$	−11.7011	+	1.98248i	−1.24734	+	0.211333i
$89$			15.0102i			1.59108i	0.605902	+	0.795540i	$0.292812\pi$
$89$			15.0102i			1.59108i	−0.605902	+	0.795540i	$0.707188\pi$
$90$	17.2937	+	1.15919i	1.82292	+	0.122189i
$91$		−	1.19596i		−	0.125371i
$92$	−0.402020	−	1.02527i	−0.0419135	−	0.106892i
$93$	10.4384	+	10.4384i	1.08241	+	1.08241i
$94$	−17.4469	−	3.64313i	−1.79951	−	0.375761i
$95$	−6.51931	+	8.63882i	−0.668867	+	0.886324i
$96$	14.1170	−	8.49136i	1.44081	−	0.866646i
$97$	−5.51024	+	5.51024i	−0.559480	+	0.559480i	−0.929159	−	0.369680i	$-0.879467\pi$
$97$	−5.51024	+	5.51024i	−0.559480	+	0.559480i	0.369680	+	0.929159i	$0.379467\pi$
$98$	4.31362	+	6.59056i	0.435742	+	0.665747i
$99$	22.9980			2.31138
$100$	−9.91054	−	1.33459i	−0.991054	−	0.133459i
$101$	6.35464			0.632310			0.316155	−	0.948708i	$-0.397608\pi$
$101$	6.35464			0.632310			0.316155	+	0.948708i	$0.397608\pi$
$102$	−0.657299	−	1.00425i	−0.0650823	−	0.0994358i
$103$	2.93721	−	2.93721i	0.289412	−	0.289412i	−0.547436	−	0.836848i	$-0.684396\pi$
$103$	2.93721	−	2.93721i	0.289412	−	0.289412i	0.836848	+	0.547436i	$0.184396\pi$
$104$	1.63781	−	2.30599i	0.160600	−	0.226121i
$105$	4.69129	−	6.21648i	0.457823	−	0.606666i
$106$	−0.139796	−	0.0291913i	−0.0135782	−	0.00283531i
$107$	5.50848	+	5.50848i	0.532525	+	0.532525i	0.921323	−	0.388798i	$-0.127110\pi$
$107$	5.50848	+	5.50848i	0.532525	+	0.532525i	−0.388798	+	0.921323i	$0.627110\pi$
$108$	−13.4533	+	5.27522i	−1.29455	+	0.507608i
$109$		−	8.20270i		−	0.785676i	−0.919608	−	0.392838i	$-0.871493\pi$
$109$		−	8.20270i		−	0.785676i	0.919608	−	0.392838i	$-0.128507\pi$
$110$	−13.2390	−	0.887400i	−1.26228	−	0.0846102i
$111$		−	34.9722i		−	3.31942i
$112$	0.181848	−	4.78038i	0.0171830	−	0.451703i
$113$	−6.21691	−	6.21691i	−0.584838	−	0.584838i	0.351391	−	0.936229i	$-0.385709\pi$
$113$	−6.21691	−	6.21691i	−0.584838	−	0.584838i	−0.936229	+	0.351391i	$0.885709\pi$
$114$	4.07455	−	19.5129i	0.381616	−	1.82755i
$115$	−0.170504	−	1.21939i	−0.0158995	−	0.113709i
$116$	12.0167	+	5.24729i	1.11572	+	0.487198i
$117$	−3.87567	+	3.87567i	−0.358306	+	0.358306i
$118$	12.9617	−	8.48360i	1.19322	−	0.780979i
$119$	−0.348532			−0.0319499
$120$	17.5587	−	5.56184i	1.60288	−	0.507724i
$121$	−6.60574			−0.600522
$122$	4.23605	−	2.77256i	0.383514	−	0.251016i
$123$	−11.5559	+	11.5559i	−1.04196	+	1.04196i
$124$	9.29088	+	4.05701i	0.834346	+	0.364330i
$125$	−10.4293	−	4.02860i	−0.932825	−	0.360329i
$126$	−1.89489	+	9.07456i	−0.168810	+	0.808426i
$127$	6.13573	+	6.13573i	0.544458	+	0.544458i	0.924832	−	0.380375i	$-0.124205\pi$
$127$	6.13573	+	6.13573i	0.544458	+	0.544458i	−0.380375	+	0.924832i	$0.624205\pi$
$128$	6.89712	−	8.96826i	0.609625	−	0.792690i
$129$			13.3890i			1.17884i
$130$	2.38061	−	2.08151i	0.208793	−	0.182561i
$131$			2.46129i			0.215043i	0.994203	+	0.107522i	$0.0342915\pi$
$131$			2.46129i			0.215043i	−0.994203	+	0.107522i	$0.965708\pi$
$132$	22.7523	−	8.92145i	1.98033	−	0.776513i
$133$	−4.09309	−	4.09309i	−0.354916	−	0.354916i
$134$	13.6254	+	2.84517i	1.17706	+	0.245785i
$135$	−16.0006	+	2.23731i	−1.37711	+	0.192557i
$136$	−0.672024	−	0.477298i	−0.0576256	−	0.0409280i
$137$	−1.04589	+	1.04589i	−0.0893561	+	0.0893561i	−0.750372	−	0.661016i	$-0.770126\pi$
$137$	−1.04589	+	1.04589i	−0.0893561	+	0.0893561i	0.661016	+	0.750372i	$0.270126\pi$
$138$	1.24194	+	1.89749i	0.105721	+	0.161525i
$139$	−4.32728			−0.367035			−0.183517	−	0.983016i	$-0.558748\pi$
$139$	−4.32728			−0.367035			−0.183517	+	0.983016i	$0.558748\pi$
$140$	1.44096	−	5.15073i	0.121783	−	0.435316i
$141$	36.7024			3.09090
$142$	−3.57124	−	5.45632i	−0.299692	−	0.457884i
$143$	2.96696	−	2.96696i	0.248110	−	0.248110i
$144$	−16.0808	+	14.9022i	−1.34007	+	1.24185i
$145$	11.7019	+	8.83088i	0.971791	+	0.733365i
$146$	−5.04243	−	1.05292i	−0.417314	−	0.0871406i
$147$	−11.4694	−	11.4694i	−0.945978	−	0.945978i
$148$	−8.76765	−	22.3601i	−0.720696	−	1.83799i
$149$			0.356765i			0.0292274i	0.999893	+	0.0146137i	$0.00465185\pi$
$149$			0.356765i			0.0292274i	−0.999893	+	0.0146137i	$0.995348\pi$
$150$	20.5392	−	1.48131i	1.67702	−	0.120948i
$151$			1.46387i			0.119128i	0.998224	+	0.0595642i	$0.0189711\pi$
$151$			1.46387i			0.119128i	−0.998224	+	0.0595642i	$0.981029\pi$
$152$	−2.28682	−	13.4974i	−0.185485	−	1.09478i
$153$	1.12947	+	1.12947i	0.0913121	+	0.0913121i
$154$	1.45060	−	6.94689i	0.116893	−	0.559797i
$155$	9.04749	+	6.82771i	0.726712	+	0.548415i
$156$	−2.33081	+	5.33774i	−0.186614	+	0.427361i
$157$	1.76334	−	1.76334i	0.140730	−	0.140730i	−0.633232	−	0.773962i	$-0.718272\pi$
$157$	1.76334	−	1.76334i	0.140730	−	0.140730i	0.773962	+	0.633232i	$0.218272\pi$
$158$	−2.59272	+	1.69697i	−0.206265	+	0.135004i
$159$	0.294085			0.0233225
$160$	9.83205	−	7.95807i	0.777292	−	0.629140i
$161$	0.658536			0.0518999
$162$	5.44148	−	3.56153i	0.427523	−	0.279821i
$163$	−11.1949	+	11.1949i	−0.876851	+	0.876851i	−0.993207	−	0.116357i	$-0.962878\pi$
$163$	−11.1949	+	11.1949i	−0.876851	+	0.876851i	0.116357	+	0.993207i	$0.462878\pi$
$164$	−4.49135	+	10.2855i	−0.350715	+	0.803166i
$165$	27.0603	−	3.78374i	2.10664	−	0.294564i
$166$	−4.57479	+	21.9086i	−0.355073	+	1.70043i
$167$	−15.3618	−	15.3618i	−1.18873	−	1.18873i	−0.977418	−	0.211315i	$-0.932226\pi$
$167$	−15.3618	−	15.3618i	−1.18873	−	1.18873i	−0.211315	−	0.977418i	$-0.567774\pi$
$168$	1.64559	+	9.71270i	0.126960	+	0.749351i
$169$			1.00000i			0.0769231i
$170$	−0.606606	−	0.693769i	−0.0465245	−	0.0532097i
$171$			26.5285i			2.02868i
$172$	3.35666	+	8.56047i	0.255943	+	0.652730i
$173$	−7.09724	−	7.09724i	−0.539593	−	0.539593i	0.383816	−	0.923410i	$-0.374610\pi$
$173$	−7.09724	−	7.09724i	−0.539593	−	0.539593i	−0.923410	+	0.383816i	$0.874610\pi$
$174$	−26.4316	−	5.51927i	−2.00378	−	0.418415i
$175$	2.90639	−	5.22598i	0.219702	−	0.395047i
$176$	12.3104	−	11.4081i	0.927932	−	0.859921i
$177$	−22.5568	+	22.5568i	−1.69548	+	1.69548i
$178$	−11.6251	−	17.7614i	−0.871341	−	1.33128i
$179$	12.1671			0.909411			0.454705	−	0.890642i	$-0.349745\pi$
$179$	12.1671			0.909411			0.454705	+	0.890642i	$0.349745\pi$
$180$	−21.3613	+	12.0220i	−1.59218	+	0.896069i
$181$	13.0663			0.971209			0.485605	−	0.874179i	$-0.338599\pi$
$181$	13.0663			0.971209			0.485605	+	0.874179i	$0.338599\pi$
$182$	0.926249	+	1.41517i	0.0686581	+	0.104899i
$183$	−7.37188	+	7.37188i	−0.544945	+	0.544945i
$184$	1.26976	+	0.901833i	0.0936078	+	0.0664840i
$185$	−3.71851	−	26.5937i	−0.273390	−	1.95521i
$186$	−20.4360	−	4.26730i	−1.49844	−	0.312894i
$187$	−0.864648	−	0.864648i	−0.0632293	−	0.0632293i
$188$	23.4663	−	9.20141i	1.71145	−	0.671082i
$189$		−	8.64117i		−	0.628552i
$190$	1.02363	−	15.2713i	0.0742618	−	1.10790i
$191$		−	13.9391i		−	1.00860i	−0.863529	−	0.504300i	$-0.831751\pi$
$191$		−	13.9391i		−	1.00860i	0.863529	−	0.504300i	$-0.168249\pi$
$192$	−10.1281	+	20.9811i	−0.730933	+	1.51418i
$193$	4.56547	+	4.56547i	0.328630	+	0.328630i	0.852065	−	0.523435i	$-0.175350\pi$
$193$	4.56547	+	4.56547i	0.328630	+	0.328630i	−0.523435	+	0.852065i	$0.675350\pi$
$194$	2.25263	−	10.7878i	0.161729	−	0.774518i
$195$	−3.92262	+	5.19791i	−0.280904	+	0.372230i
$196$	−10.2085	−	4.45772i	−0.729181	−	0.318409i
$197$	−13.4201	+	13.4201i	−0.956144	+	0.956144i	−0.999078	−	0.0429337i	$-0.986330\pi$
$197$	−13.4201	+	13.4201i	−0.956144	+	0.956144i	0.0429337	+	0.999078i	$0.486330\pi$
$198$	−27.2133	+	17.8115i	−1.93396	+	1.26581i
$199$	−8.20575			−0.581690			−0.290845	−	0.956770i	$-0.593936\pi$
$199$	−8.20575			−0.581690			−0.290845	+	0.956770i	$0.593936\pi$
$200$	12.7607	−	6.09633i	0.902316	−	0.431076i
$201$	−28.6634			−2.02176
$202$	−7.51939	+	4.92156i	−0.529062	+	0.346279i
$203$	−5.54439	+	5.54439i	−0.389140	+	0.389140i
$204$	1.55555	+	0.679256i	0.108910	+	0.0475575i
$205$	−7.55868	+	10.0161i	−0.527921	+	0.699555i
$206$	−1.20076	+	5.75040i	−0.0836608	+	0.400649i
$207$	−2.13408	−	2.13408i	−0.148329	−	0.148329i
$208$	−0.152052	+	3.99711i	−0.0105429	+	0.277150i
$209$		−	20.3085i		−	1.40477i
$210$	−0.736601	+	10.9892i	−0.0508303	+	0.758328i
$211$		−	9.25421i		−	0.637086i	−0.947908	−	0.318543i	$-0.896806\pi$
$211$		−	9.25421i		−	0.637086i	0.947908	−	0.318543i	$-0.103194\pi$
$212$	0.188028	−	0.0737280i	0.0129138	−	0.00506366i
$213$	9.49549	+	9.49549i	0.650620	+	0.650620i
$214$	−10.7843	−	2.25191i	−0.737203	−	0.153938i
$215$	1.42362	+	10.1813i	0.0970900	+	0.694360i
$216$	11.8337	−	16.6615i	0.805178	−	1.13367i
$217$	−4.28672	+	4.28672i	−0.291001	+	0.291001i
$218$	6.35285	+	9.70618i	0.430269	+	0.657385i
$219$	10.6076			0.716794
$220$	16.3528	−	9.20329i	1.10251	−	0.620485i
$221$	0.291425			0.0196034
$222$	27.0854	+	41.3823i	1.81785	+	2.77740i
$223$	−0.454255	+	0.454255i	−0.0304191	+	0.0304191i	−0.722153	−	0.691734i	$-0.756847\pi$
$223$	−0.454255	+	0.454255i	−0.0304191	+	0.0304191i	0.691734	+	0.722153i	$0.256847\pi$
$224$	3.48714	+	5.79741i	0.232994	+	0.387356i
$225$	−26.3541	+	7.51696i	−1.75694	+	0.501131i
$226$	12.1713	+	2.54153i	0.809623	+	0.169060i
$227$	−17.6950	−	17.6950i	−1.17446	−	1.17446i	−0.981134	−	0.193327i	$-0.938072\pi$
$227$	−17.6950	−	17.6950i	−1.17446	−	1.17446i	−0.193327	−	0.981134i	$-0.561928\pi$
$228$	10.2910	+	26.2451i	0.681539	+	1.73812i
$229$			2.81751i			0.186186i	0.995657	+	0.0930932i	$0.0296755\pi$
$229$			2.81751i			0.186186i	−0.995657	+	0.0930932i	$0.970325\pi$
$230$	1.14615	+	1.31085i	0.0755752	+	0.0864346i
$231$			14.6139i			0.961527i
$232$	−18.2832	+	3.09766i	−1.20035	+	0.203371i
$233$	−11.0313	−	11.0313i	−0.722685	−	0.722685i	0.246466	−	0.969151i	$-0.420731\pi$
$233$	−11.0313	−	11.0313i	−0.722685	−	0.722685i	−0.969151	+	0.246466i	$0.920731\pi$
$234$	1.58441	−	7.58769i	0.103576	−	0.496023i
$235$	27.9094	−	3.90248i	1.82061	−	0.254569i
$236$	−8.76700	+	20.0771i	−0.570683	+	1.30691i
$237$	4.51204	−	4.51204i	0.293088	−	0.293088i
$238$	0.412415	−	0.269932i	0.0267329	−	0.0174971i
$239$	0.438609			0.0283713			0.0141856	−	0.999899i	$-0.495484\pi$
$239$	0.438609			0.0283713			0.0141856	+	0.999899i	$0.495484\pi$
$240$	−16.4695	+	20.1802i	−1.06310	+	1.30262i
$241$	−6.48281			−0.417594			−0.208797	−	0.977959i	$-0.566955\pi$
$241$	−6.48281			−0.417594			−0.208797	+	0.977959i	$0.566955\pi$
$242$	7.81652	−	5.11603i	0.502465	−	0.328871i
$243$	5.85752	−	5.85752i	0.375760	−	0.375760i
$244$	−2.86518	+	6.56148i	−0.183424	+	0.420056i
$245$	−9.94111	−	7.50209i	−0.635114	−	0.479291i
$246$	4.72415	−	22.6238i	0.301201	−	1.44244i
$247$	3.42243	+	3.42243i	0.217764	+	0.217764i
$248$	−14.1359	+	2.39500i	−0.897630	+	0.152083i
$249$		−	46.0883i		−	2.92073i
$250$	15.4610	−	3.31030i	0.977838	−	0.209362i
$251$		−	17.3721i		−	1.09652i	−0.836309	−	0.548259i	$-0.815291\pi$
$251$		−	17.3721i		−	1.09652i	0.836309	−	0.548259i	$-0.184709\pi$
$252$	−4.78589	−	12.2054i	−0.301482	−	0.768868i
$253$	1.63371	+	1.63371i	0.102711	+	0.102711i
$254$	−12.0124	−	2.50834i	−0.753722	−	0.157387i
$255$	1.51480	+	1.14315i	0.0948605	+	0.0715868i
$256$	−1.21554	+	15.9538i	−0.0759710	+	0.997110i
$257$	12.8863	−	12.8863i	0.803824	−	0.803824i	−0.179867	−	0.983691i	$-0.557567\pi$
$257$	12.8863	−	12.8863i	0.803824	−	0.803824i	0.983691	+	0.179867i	$0.0575666\pi$
$258$	−10.3695	−	15.8431i	−0.645579	−	0.986347i
$259$	14.3620			0.892412
$260$	−1.20486	+	4.30678i	−0.0747220	+	0.267095i
$261$	35.9348			2.22431
$262$	−1.90622	−	2.91242i	−0.117767	−	0.179930i
$263$	−17.7105	+	17.7105i	−1.09208	+	1.09208i	−0.0967688	+	0.995307i	$0.530851\pi$
$263$	−17.7105	+	17.7105i	−1.09208	+	1.09208i	−0.995307	+	0.0967688i	$0.969149\pi$
$264$	−20.0131	+	28.1779i	−1.23172	+	1.73423i
$265$	0.223629	−	0.0312693i	0.0137374	−	0.00192086i
$266$	8.01334	+	1.67329i	0.491329	+	0.102596i
$267$	30.9098	+	30.9098i	1.89165	+	1.89165i
$268$	−18.3264	+	7.18600i	−1.11946	+	0.438955i
$269$		−	9.90226i		−	0.603752i	−0.953347	−	0.301876i	$-0.902387\pi$
$269$		−	9.90226i		−	0.603752i	0.953347	−	0.301876i	$-0.0976128\pi$
$270$	17.2006	−	15.0396i	1.04680	−	0.915280i
$271$		−	23.2048i		−	1.40959i	−0.709409	−	0.704797i	$-0.751038\pi$
$271$		−	23.2048i		−	1.40959i	0.709409	−	0.704797i	$-0.248962\pi$
$272$	1.16486	+	0.0443118i	0.0706299	+	0.00268680i
$273$	−2.46278	−	2.46278i	−0.149054	−	0.149054i
$274$	0.427567	−	2.04761i	0.0258303	−	0.123701i
$275$	20.1750	−	5.75450i	1.21660	−	0.347009i
$276$	−2.93914	−	1.28342i	−0.176916	−	0.0772530i
$277$	14.8259	−	14.8259i	0.890802	−	0.890802i	−0.103797	−	0.994599i	$-0.533099\pi$
$277$	14.8259	−	14.8259i	0.890802	−	0.890802i	0.994599	+	0.103797i	$0.0330992\pi$
$278$	5.12043	−	3.35140i	0.307103	−	0.201004i
$279$	27.7834			1.66335
$280$	2.28407	+	7.21080i	0.136500	+	0.430928i
$281$	−0.130168			−0.00776516			−0.00388258	−	0.999992i	$-0.501236\pi$
$281$	−0.130168			−0.00776516			−0.00388258	+	0.999992i	$0.501236\pi$
$282$	−43.4296	+	28.4254i	−2.58620	+	1.69271i
$283$	10.2040	−	10.2040i	0.606564	−	0.606564i	−0.335482	−	0.942047i	$-0.608899\pi$
$283$	10.2040	−	10.2040i	0.606564	−	0.606564i	0.942047	+	0.335482i	$0.108899\pi$
$284$	8.45164	+	3.69054i	0.501513	+	0.218994i
$285$	4.36460	+	31.2144i	0.258536	+	1.84898i
$286$	−1.21292	+	5.80864i	−0.0717215	+	0.343472i
$287$	−4.74565	−	4.74565i	−0.280127	−	0.280127i
$288$	7.48678	−	30.0879i	0.441163	−	1.77295i
$289$			16.9151i			0.995004i
$290$	−20.6861	−	1.38658i	−1.21473	−	0.0814227i
$291$			22.6939i			1.33034i
$292$	6.78213	−	2.65935i	0.396894	−	0.155627i
$293$	11.9053	+	11.9053i	0.695514	+	0.695514i	0.963440	−	0.267926i	$-0.0863382\pi$
$293$	11.9053	+	11.9053i	0.695514	+	0.695514i	−0.267926	+	0.963440i	$0.586338\pi$
$294$	22.4544	+	4.68878i	1.30957	+	0.273455i
$295$	−14.7544	+	19.5512i	−0.859032	+	1.13831i
$296$	27.6921	+	19.6681i	1.60957	+	1.14318i
$297$	21.4372	−	21.4372i	1.24391	−	1.24391i
$298$	−0.276309	−	0.422157i	−0.0160061	−	0.0244549i
$299$	−0.550635			−0.0318440
$300$	−23.1566	+	17.6600i	−1.33694	+	1.01960i
$301$	−5.49844			−0.316925
$302$	−1.13374	−	1.73219i	−0.0652397	−	0.0996763i
$303$	13.0858	−	13.0858i	0.751759	−	0.751759i
$304$	13.1595	+	14.2002i	0.754746	+	0.814439i
$305$	−4.82193	+	6.38959i	−0.276103	+	0.365867i
$306$	−2.21124	−	0.461736i	−0.126408	−	0.0263957i
$307$	−24.2442	−	24.2442i	−1.38369	−	1.38369i	−0.837967	−	0.545721i	$-0.816256\pi$
$307$	−24.2442	−	24.2442i	−1.38369	−	1.38369i	−0.545721	−	0.837967i	$-0.683744\pi$
$308$	3.66376	+	9.34366i	0.208762	+	0.532404i
$309$		−	12.0969i		−	0.688170i
$310$	−15.9938	−	1.07205i	−0.908384	−	0.0608885i
$311$		−	11.5941i		−	0.657443i	−0.944427	−	0.328721i	$-0.893382\pi$
$311$		−	11.5941i		−	0.657443i	0.944427	−	0.328721i	$-0.106618\pi$
$312$	−1.37596	−	8.12127i	−0.0778984	−	0.459776i
$313$	22.6331	+	22.6331i	1.27930	+	1.27930i	0.941062	+	0.338235i	$0.109830\pi$
$313$	22.6331	+	22.6331i	1.27930	+	1.27930i	0.338235	+	0.941062i	$0.390170\pi$
$314$	−0.720869	+	3.45222i	−0.0406810	+	0.194820i
$315$	−2.02978	−	14.5164i	−0.114365	−	0.817906i
$316$	1.75366	−	4.01603i	0.0986512	−	0.225919i
$317$	−0.866886	+	0.866886i	−0.0486892	+	0.0486892i	−0.731032	−	0.682343i	$-0.760961\pi$
$317$	−0.866886	+	0.866886i	−0.0486892	+	0.0486892i	0.682343	+	0.731032i	$0.260961\pi$
$318$	−0.347988	+	0.227764i	−0.0195142	+	0.0127724i
$319$	−27.5093			−1.54023
$320$	−5.47079	+	17.0315i	−0.305827	+	0.952087i
$321$	22.6867			1.26625
$322$	−0.779240	+	0.510025i	−0.0434253	+	0.0284226i
$323$	0.997383	−	0.997383i	0.0554959	−	0.0554959i
$324$	−3.68051	+	8.42866i	−0.204473	+	0.468259i
$325$	−2.43017	+	4.36970i	−0.134802	+	0.242387i
$326$	4.57656	−	21.9170i	0.253472	−	1.21387i
$327$	−16.8914	−	16.8914i	−0.934098	−	0.934098i
$328$	−2.65140	−	15.6493i	−0.146399	−	0.864086i
$329$			15.0725i			0.830976i
$330$	−29.0897	+	25.4350i	−1.60134	+	1.40015i
$331$			6.91111i			0.379869i	0.981797	+	0.189935i	$0.0608276\pi$
$331$			6.91111i			0.379869i	−0.981797	+	0.189935i	$0.939172\pi$
$332$	−11.5545	−	29.4673i	−0.634135	−	1.61723i
$333$	−46.5421	−	46.5421i	−2.55049	−	2.55049i
$334$	30.0749	+	6.28004i	1.64563	+	0.343628i
$335$	−21.7963	+	3.04771i	−1.19086	+	0.166514i
$336$	−9.46952	−	10.2185i	−0.516605	−	0.557463i
$337$	−3.31953	+	3.31953i	−0.180826	+	0.180826i	−0.791716	−	0.610889i	$-0.790812\pi$
$337$	−3.31953	+	3.31953i	−0.180826	+	0.180826i	0.610889	+	0.791716i	$0.290812\pi$
$338$	−0.774482	−	1.18329i	−0.0421263	−	0.0643625i
$339$	−25.6044			−1.39064
$340$	1.25510	+	0.351125i	0.0680675	+	0.0190424i
$341$	−21.2692			−1.15179
$342$	−20.5458	−	31.3909i	−1.11099	−	1.69743i
$343$	10.6298	−	10.6298i	0.573956	−	0.573956i
$344$	−10.6018	−	7.52985i	−0.571613	−	0.405982i
$345$	−2.86215	−	2.15993i	−0.154093	−	0.116287i
$346$	13.8948	+	2.90141i	0.746989	+	0.155981i
$347$	−0.298469	−	0.298469i	−0.0160226	−	0.0160226i	0.699050	−	0.715073i	$-0.253606\pi$
$347$	−0.298469	−	0.298469i	−0.0160226	−	0.0160226i	−0.715073	+	0.699050i	$0.753606\pi$
$348$	35.5509	−	13.9399i	1.90573	−	0.747259i
$349$		−	28.4804i		−	1.52452i	−0.647271	−	0.762260i	$-0.724090\pi$
$349$		−	28.4804i		−	1.52452i	0.647271	−	0.762260i	$-0.275910\pi$
$350$	0.608327	+	8.43480i	0.0325164	+	0.450859i
$351$			7.22531i			0.385658i
$352$	−5.73139	+	23.0333i	−0.305484	+	1.22768i
$353$	−12.3525	−	12.3525i	−0.657459	−	0.657459i	0.297320	−	0.954778i	$-0.403907\pi$
$353$	−12.3525	−	12.3525i	−0.657459	−	0.657459i	−0.954778	+	0.297320i	$0.903907\pi$
$354$	9.22143	−	44.1612i	0.490113	−	2.34714i
$355$	8.23024	+	6.21097i	0.436816	+	0.329644i
$356$	27.5118	+	12.0135i	1.45812	+	0.636713i
$357$	−0.717716	+	0.717716i	−0.0379855	+	0.0379855i
$358$	−14.3972	+	9.42319i	−0.760916	+	0.498031i
$359$	−28.4805			−1.50314			−0.751572	−	0.659651i	$-0.770704\pi$
$359$	−28.4805			−1.50314			−0.751572	+	0.659651i	$0.770704\pi$
$360$	15.9658	−	30.7695i	0.841470	−	1.62169i
$361$	4.42610			0.232953
$362$	−15.4612	+	10.1196i	−0.812624	+	0.531875i
$363$	−13.6029	+	13.6029i	−0.713966	+	0.713966i
$364$	−2.19204	−	0.957191i	−0.114894	−	0.0501704i
$365$	8.06627	−	1.12788i	0.422208	−	0.0590358i
$366$	3.01369	−	14.4325i	0.157528	−	0.754398i
$367$	15.7149	+	15.7149i	0.820313	+	0.820313i	0.986153	−	0.165840i	$-0.0530335\pi$
$367$	15.7149	+	15.7149i	0.820313	+	0.820313i	−0.165840	+	0.986153i	$0.553034\pi$
$368$	−2.20095	−	0.0837251i	−0.114732	−	0.00436447i
$369$			30.7579i			1.60119i
$370$	24.9965	+	28.5882i	1.29950	+	1.48623i
$371$			0.120772i			0.00627015i
$372$	27.4867	−	10.7778i	1.42512	−	0.558805i
$373$	4.87930	+	4.87930i	0.252641	+	0.252641i	0.822052	−	0.569412i	$-0.192829\pi$
$373$	4.87930	+	4.87930i	0.252641	+	0.252641i	−0.569412	+	0.822052i	$0.692829\pi$
$374$	1.69278	+	0.353475i	0.0875318	+	0.0182778i
$375$	−29.7725	+	13.1806i	−1.53744	+	0.680646i
$376$	−20.6411	+	29.0622i	−1.06448	+	1.49877i
$377$	4.63594	−	4.63594i	0.238763	−	0.238763i
$378$	6.69243	+	10.2250i	0.344221	+	0.525918i
$379$	−0.333137			−0.0171121			−0.00855604	−	0.999963i	$-0.502724\pi$
$379$	−0.333137			−0.0171121			−0.00855604	+	0.999963i	$0.502724\pi$
$380$	10.6161	+	18.8632i	0.544595	+	0.967661i
$381$	25.2700			1.29462
$382$	10.7956	+	16.4940i	0.552351	+	0.843909i
$383$	−8.70979	+	8.70979i	−0.445050	+	0.445050i	−0.893705	−	0.448655i	$-0.851903\pi$
$383$	−8.70979	+	8.70979i	−0.445050	+	0.445050i	0.448655	+	0.893705i	$0.351903\pi$
$384$	−4.26501	−	32.6708i	−0.217648	−	1.66723i
$385$	1.55386	+	11.1128i	0.0791923	+	0.566361i
$386$	−8.93816	−	1.86641i	−0.454941	−	0.0949975i
$387$	17.8185	+	17.8185i	0.905765	+	0.905765i
$388$	5.68944	+	14.5097i	0.288837	+	0.736619i
$389$			15.7397i			0.798036i	0.916943	+	0.399018i	$0.130649\pi$
$389$			15.7397i			0.798036i	−0.916943	+	0.399018i	$0.869351\pi$
$390$	0.615909	−	9.18863i	0.0311877	−	0.465284i
$391$			0.160469i			0.00811526i
$392$	15.5321	−	2.63155i	0.784489	−	0.132913i
$393$	5.06840	+	5.06840i	0.255667	+	0.255667i
$394$	5.48626	−	26.2736i	0.276394	−	1.32364i
$395$	2.95131	−	3.91082i	0.148497	−	0.196775i
$396$	18.4065	−	42.1524i	0.924962	−	2.11824i
$397$	17.4901	−	17.4901i	0.877805	−	0.877805i	−0.115502	−	0.993307i	$-0.536848\pi$
$397$	17.4901	−	17.4901i	0.877805	−	0.877805i	0.993307	+	0.115502i	$0.0368478\pi$
$398$	9.70979	−	6.35521i	0.486708	−	0.318558i
$399$	−16.8574			−0.843925
$400$	−10.3781	+	17.0966i	−0.518904	+	0.854832i
$401$	1.23996			0.0619204			0.0309602	−	0.999521i	$-0.490143\pi$
$401$	1.23996			0.0619204			0.0309602	+	0.999521i	$0.490143\pi$
$402$	33.9171	−	22.1993i	1.69163	−	1.10720i
$403$	3.58434	−	3.58434i	0.178549	−	0.178549i
$404$	5.08596	−	11.6473i	0.253036	−	0.579473i
$405$	−6.19408	+	8.20786i	−0.307786	+	0.407852i
$406$	2.26659	−	10.8547i	0.112489	−	0.538707i
$407$	35.6296	+	35.6296i	1.76610	+	1.76610i
$408$	−2.36674	+	0.400989i	−0.117171	+	0.0198519i
$409$			13.6662i			0.675749i	0.941191	+	0.337875i	$0.109708\pi$
$409$			13.6662i			0.675749i	−0.941191	+	0.337875i	$0.890292\pi$
$410$	1.18682	−	17.7060i	0.0586131	−	0.874438i
$411$			4.30749i			0.212473i
$412$	−3.03274	−	7.73436i	−0.149412	−	0.381045i
$413$	−9.26339	−	9.26339i	−0.455822	−	0.455822i
$414$	4.17804	+	0.872430i	0.205340	+	0.0428776i
$415$	−4.90046	−	35.0467i	−0.240554	−	1.72037i
$416$	−2.91577	−	4.84750i	−0.142957	−	0.237668i
$417$	−8.91095	+	8.91095i	−0.436371	+	0.436371i
$418$	15.7285	+	24.0308i	0.769309	+	1.17539i
$419$	−30.4429			−1.48723			−0.743617	−	0.668605i	$-0.766892\pi$
$419$	−30.4429			−1.48723			−0.743617	+	0.668605i	$0.766892\pi$
$420$	−7.63934	−	13.5739i	−0.372762	−	0.662340i
$421$	−30.0550			−1.46479			−0.732396	−	0.680878i	$-0.761598\pi$
$421$	−30.0550			−1.46479			−0.732396	+	0.680878i	$0.761598\pi$
$422$	7.16722	+	10.9504i	0.348895	+	0.533058i
$423$	48.8447	−	48.8447i	2.37491	−	2.37491i
$424$	−0.165391	+	0.232866i	−0.00803208	+	0.0113090i
$425$	1.27344	+	0.708214i	0.0617709	+	0.0343534i
$426$	−18.5900	−	3.88184i	−0.900689	−	0.188076i
$427$	−3.02740	−	3.02740i	−0.146506	−	0.146506i
$428$	14.5051	−	5.68762i	0.701130	−	0.274922i
$429$		−	12.2194i		−	0.589960i
$430$	−9.56981	−	10.9449i	−0.461497	−	0.527810i
$431$			29.7403i			1.43254i	0.697822	+	0.716271i	$0.254153\pi$
$431$			29.7403i			1.43254i	−0.697822	+	0.716271i	$0.745847\pi$
$432$	−1.09862	+	28.8803i	−0.0528575	+	1.38951i
$433$	0.932973	+	0.932973i	0.0448358	+	0.0448358i	0.729169	−	0.684333i	$-0.239907\pi$
$433$	0.932973	+	0.932973i	0.0448358	+	0.0448358i	−0.684333	+	0.729169i	$0.739907\pi$
$434$	1.75245	−	8.39242i	0.0841201	−	0.402849i
$435$	42.2822	−	5.91217i	2.02727	−	0.283467i
$436$	−15.0345	−	6.56507i	−0.720023	−	0.314410i
$437$	−1.88451	+	1.88451i	−0.0901484	+	0.0901484i
$438$	−12.5519	+	8.21539i	−0.599751	+	0.392546i
$439$	−18.8341			−0.898901			−0.449450	−	0.893305i	$-0.648380\pi$
$439$	−18.8341			−0.898901			−0.449450	+	0.893305i	$0.648380\pi$
$440$	−12.2223	+	23.5551i	−0.582678	+	1.12295i
$441$	−30.5276			−1.45370
$442$	−0.344841	+	0.225704i	−0.0164024	+	0.0107356i
$443$	−12.6851	+	12.6851i	−0.602687	+	0.602687i	−0.941025	−	0.338338i	$-0.890135\pi$
$443$	−12.6851	+	12.6851i	−0.602687	+	0.602687i	0.338338	+	0.941025i	$0.390135\pi$
$444$	−64.0998	−	27.9902i	−3.04204	−	1.32836i
$445$	26.7911	+	20.2180i	1.27002	+	0.958425i
$446$	0.185703	−	0.889327i	0.00879330	−	0.0421109i
$447$	0.734670	+	0.734670i	0.0347487	+	0.0347487i
$448$	−8.61629	−	4.15930i	−0.407082	−	0.196508i
$449$			15.8773i			0.749297i	0.927167	+	0.374648i	$0.122237\pi$
$449$			15.8773i			0.749297i	−0.927167	+	0.374648i	$0.877763\pi$
$450$	25.3628	−	29.3055i	1.19561	−	1.38148i
$451$		−	23.5462i		−	1.10875i
$452$	−16.3706	+	6.41909i	−0.770006	+	0.301929i
$453$	3.01448	+	3.01448i	0.141633	+	0.141633i
$454$	34.6429	+	7.23389i	1.62587	+	0.339503i
$455$	−2.13462	−	1.61090i	−0.100072	−	0.0755200i
$456$	−32.5036	−	23.0854i	−1.52212	−	1.08107i
$457$	14.5221	−	14.5221i	0.679317	−	0.679317i	−0.280529	−	0.959846i	$-0.590510\pi$
$457$	14.5221	−	14.5221i	0.679317	−	0.679317i	0.959846	+	0.280529i	$0.0905099\pi$
$458$	−2.18211	−	3.33394i	−0.101963	−	0.155785i
$459$	2.10564			0.0982827
$460$	−2.37146	−	0.663435i	−0.110570	−	0.0309328i
$461$	6.30338			0.293578			0.146789	−	0.989168i	$-0.453106\pi$
$461$	6.30338			0.293578			0.146789	+	0.989168i	$0.453106\pi$
$462$	−11.3182	−	17.2926i	−0.526572	−	0.804522i
$463$	−20.4903	+	20.4903i	−0.952265	+	0.952265i	−0.998911	−	0.0466465i	$-0.985147\pi$
$463$	−20.4903	+	20.4903i	−0.952265	+	0.952265i	0.0466465	+	0.998911i	$0.485147\pi$
$464$	19.2352	−	17.8254i	0.892974	−	0.827525i
$465$	32.6910	−	4.57107i	1.51601	−	0.211978i
$466$	21.5968	+	4.50969i	1.00045	+	0.208908i
$467$	11.3954	+	11.3954i	0.527315	+	0.527315i	0.919771	−	0.392456i	$-0.128374\pi$
$467$	11.3954	+	11.3954i	0.527315	+	0.527315i	−0.392456	+	0.919771i	$0.628374\pi$
$468$	4.00172	+	10.2055i	0.184979	+	0.471751i
$469$		−	11.7712i		−	0.543542i
$470$	−30.0026	+	26.2331i	−1.38391	+	1.21004i
$471$		−	7.26233i		−	0.334630i
$472$	−5.17547	−	30.5470i	−0.238221	−	1.40604i
$473$	−13.6407	−	13.6407i	−0.627199	−	0.627199i
$474$	−1.84456	+	8.83355i	−0.0847235	+	0.405738i
$475$	6.63789	+	23.2721i	0.304567	+	1.06780i
$476$	−0.278949	+	0.638817i	−0.0127856	+	0.0292801i
$477$	0.391377	−	0.391377i	0.0179199	−	0.0179199i
$478$	−0.519002	+	0.339695i	−0.0237386	+	0.0155373i
$479$	27.1128			1.23881			0.619407	−	0.785070i	$-0.287373\pi$
$479$	27.1128			1.23881			0.619407	+	0.785070i	$0.287373\pi$
$480$	3.85900	−	36.6343i	0.176139	−	1.67212i
$481$	−12.0088			−0.547554
$482$	7.67105	−	5.02082i	0.349407	−	0.228692i
$483$	1.35609	−	1.35609i	0.0617043	−	0.0617043i
$484$	−5.28694	+	12.1075i	−0.240315	+	0.550341i
$485$	2.41299	+	17.2570i	0.109568	+	0.783601i
$486$	−2.39460	+	11.4677i	−0.108621	+	0.520185i
$487$	6.08398	+	6.08398i	0.275692	+	0.275692i	0.831386	−	0.555695i	$-0.187548\pi$
$487$	6.08398	+	6.08398i	0.275692	+	0.275692i	−0.555695	+	0.831386i	$0.687548\pi$
$488$	−1.69142	−	9.98317i	−0.0765668	−	0.451917i
$489$			46.1061i			2.08499i
$490$	17.5735	+	1.17794i	0.793888	+	0.0532138i
$491$		−	28.1664i		−	1.27113i	−0.772046	−	0.635567i	$-0.780767\pi$
$491$		−	28.1664i		−	1.27113i	0.772046	−	0.635567i	$-0.219233\pi$
$492$	11.9317	+	30.4293i	0.537923	+	1.37186i
$493$	−1.35103	−	1.35103i	−0.0608473	−	0.0608473i
$494$	−6.70035	−	1.39912i	−0.301463	−	0.0629494i
$495$	30.9771	−	41.0481i	1.39232	−	1.84498i
$496$	14.8720	−	13.7820i	0.667772	−	0.618829i
$497$	−3.89950	+	3.89950i	−0.174917	+	0.174917i
$498$	35.6946	+	54.5359i	1.59951	+	2.44381i
$499$	19.3231			0.865023			0.432511	−	0.901629i	$-0.357628\pi$
$499$	19.3231			0.865023			0.432511	+	0.901629i	$0.357628\pi$
$500$	−15.7311	+	15.8913i	−0.703515	+	0.710681i
$501$	−63.2677			−2.82659
$502$	13.4544	+	20.5563i	0.600499	+	0.917471i
$503$	5.39116	−	5.39116i	0.240380	−	0.240380i	−0.576627	−	0.817007i	$-0.695632\pi$
$503$	5.39116	−	5.39116i	0.240380	−	0.240380i	0.817007	+	0.576627i	$0.195632\pi$
$504$	15.1160	+	10.7360i	0.673318	+	0.478217i
$505$	8.55938	−	11.3421i	0.380887	−	0.504719i
$506$	−3.19844	−	0.667876i	−0.142188	−	0.0296907i
$507$	2.05925	+	2.05925i	0.0914546	+	0.0914546i
$508$	16.1568	−	6.33527i	0.716841	−	0.281082i
$509$			14.1691i			0.628033i	0.949417	+	0.314017i	$0.101675\pi$
$509$			14.1691i			0.628033i	−0.949417	+	0.314017i	$0.898325\pi$
$510$	−2.67780	−	0.179491i	−0.118575	−	0.00794801i
$511$			4.35620i			0.192707i
$512$	−10.9176	−	19.8193i	−0.482493	−	0.875900i
$513$	24.7281	+	24.7281i	1.09177	+	1.09177i
$514$	−5.26802	+	25.2284i	−0.232363	+	1.11278i
$515$	−1.28624	−	9.19880i	−0.0566783	−	0.405347i
$516$	24.5404	+	10.7159i	1.08033	+	0.471743i
$517$	−37.3923	+	37.3923i	−1.64451	+	1.64451i
$518$	−16.9944	+	11.1231i	−0.746693	+	0.488722i
$519$	−29.2300			−1.28306
$520$	−1.90983	−	6.02931i	−0.0837515	−	0.264403i
$521$	18.4923			0.810164			0.405082	−	0.914280i	$-0.367243\pi$
$521$	18.4923			0.810164			0.405082	+	0.914280i	$0.367243\pi$
$522$	−42.5213	+	27.8308i	−1.86111	+	1.21812i
$523$	3.63846	−	3.63846i	0.159099	−	0.159099i	−0.623069	−	0.782167i	$-0.714114\pi$
$523$	3.63846	−	3.63846i	0.159099	−	0.159099i	0.782167	+	0.623069i	$0.214114\pi$
$524$	4.51123	+	1.96990i	0.197074	+	0.0860555i
$525$	−4.77662	−	16.7466i	−0.208469	−	0.730881i
$526$	7.24020	−	34.6731i	0.315688	−	1.51182i
$527$	−1.04457	−	1.04457i	−0.0455020	−	0.0455020i
$528$	1.85799	−	48.8425i	0.0808587	−	2.12559i
$529$			22.6968i			0.986817i
$530$	−0.240401	+	0.210198i	−0.0104424	+	0.00913041i
$531$			60.0387i			2.60546i
$532$	−10.7780	+	4.22620i	−0.467287	+	0.183229i
$533$	3.96807	+	3.96807i	0.171876	+	0.171876i
$534$	−60.5144	−	12.6362i	−2.61871	−	0.546821i
$535$	17.2515	−	2.41222i	0.745848	−	0.104289i
$536$	16.1200	−	22.6966i	0.696279	−	0.980344i
$537$	25.0551	−	25.0551i	1.08121	−	1.08121i
$538$	7.66913	+	11.7173i	0.330640	+	0.505167i
$539$	23.3699			1.00661
$540$	−8.70545	+	31.1178i	−0.374623	+	1.33910i
$541$	12.8284			0.551535			0.275767	−	0.961224i	$-0.411068\pi$
$541$	12.8284			0.551535			0.275767	+	0.961224i	$0.411068\pi$
$542$	17.9717	+	27.4581i	0.771952	+	1.17943i
$543$	26.9068	−	26.9068i	1.15468	−	1.15468i
$544$	−1.41268	+	0.849728i	−0.0605684	+	0.0364318i
$545$	−14.6407	−	11.0486i	−0.627138	−	0.473271i
$546$	4.82156	+	1.00680i	0.206344	+	0.0430873i
$547$	−15.8672	−	15.8672i	−0.678431	−	0.678431i	0.281214	−	0.959645i	$-0.409263\pi$
$547$	−15.8672	−	15.8672i	−0.678431	−	0.678431i	−0.959645	+	0.281214i	$0.909263\pi$
$548$	1.07990	+	2.75406i	0.0461310	+	0.117648i
$549$			19.6215i			0.837423i
$550$	−19.4161	+	22.4344i	−0.827905	+	0.956606i
$551$		−	31.7324i		−	1.35184i
$552$	4.47185	−	0.757651i	0.190335	−	0.0322478i
$553$	1.85295	+	1.85295i	0.0787956	+	0.0787956i
$554$	−6.06095	+	29.0257i	−0.257505	+	1.23319i
$555$	−62.4205	−	47.1059i	−2.64960	−	1.99953i
$556$	−3.46336	+	7.93136i	−0.146879	+	0.336365i
$557$	−4.50875	+	4.50875i	−0.191042	+	0.191042i	−0.796146	−	0.605104i	$-0.793131\pi$
$557$	−4.50875	+	4.50875i	−0.191042	+	0.191042i	0.605104	+	0.796146i	$0.293131\pi$
$558$	−32.8759	+	21.5178i	−1.39175	+	0.910920i
$559$	4.59752			0.194454
$560$	−8.28736	−	6.76350i	−0.350205	−	0.285810i
$561$	−3.56105			−0.150348
$562$	0.154026	−	0.100813i	0.00649721	−	0.00425252i
$563$	−7.11349	+	7.11349i	−0.299798	+	0.299798i	−0.840935	−	0.541137i	$-0.817994\pi$
$563$	−7.11349	+	7.11349i	−0.299798	+	0.299798i	0.541137	+	0.840935i	$0.317994\pi$
$564$	29.3749	−	67.2709i	1.23691	−	2.83262i
$565$	−19.4702	+	2.72245i	−0.819117	+	0.114534i
$566$	−4.17148	+	19.9771i	−0.175340	+	0.839700i
$567$	−3.88890	−	3.88890i	−0.163318	−	0.163318i
$568$	−12.8590	+	2.17866i	−0.539552	+	0.0914146i
$569$			18.4963i			0.775404i	0.921785	+	0.387702i	$0.126731\pi$
$569$			18.4963i			0.775404i	−0.921785	+	0.387702i	$0.873269\pi$
$570$	−29.3396	−	33.5554i	−1.22890	−	1.40548i
$571$			31.1985i			1.30562i	0.757523	+	0.652808i	$0.226409\pi$
$571$			31.1985i			1.30562i	−0.757523	+	0.652808i	$0.773591\pi$
$572$	−3.06345	−	7.81270i	−0.128089	−	0.326665i
$573$	−28.7042	−	28.7042i	−1.19913	−	1.19913i
$574$	9.29090	+	1.94006i	0.387795	+	0.0809766i
$575$	−2.40611	−	1.33814i	−0.100342	−	0.0558042i
$576$	14.4435	+	41.4011i	0.601813	+	1.72505i
$577$	21.5066	−	21.5066i	0.895334	−	0.895334i	−0.0996855	−	0.995019i	$-0.531784\pi$
$577$	21.5066	−	21.5066i	0.895334	−	0.895334i	0.995019	+	0.0996855i	$0.0317837\pi$
$578$	−13.1004	−	20.0154i	−0.544906	−	0.832533i
$579$	18.8029			0.781423
$580$	25.5516	−	14.3803i	1.06097	−	0.597110i
$581$	18.9270			0.785226
$582$	−17.5760	−	26.8535i	−0.728550	−	1.11311i
$583$	−0.299613	+	0.299613i	−0.0124087	+	0.0124087i
$584$	−5.96561	+	8.39943i	−0.246859	+	0.347571i
$585$	1.69720	+	12.1379i	0.0701704	+	0.501839i
$586$	−23.3078	−	4.86698i	−0.962838	−	0.201053i
$587$	−2.12698	−	2.12698i	−0.0877898	−	0.0877898i	0.661848	−	0.749638i	$-0.269772\pi$
$587$	−2.12698	−	2.12698i	−0.0877898	−	0.0877898i	−0.749638	+	0.661848i	$0.769772\pi$
$588$	−30.2015	+	11.8424i	−1.24549	+	0.488371i
$589$		−	24.5343i		−	1.01092i
$590$	2.31665	−	34.5617i	0.0953751	−	1.42288i
$591$			55.2708i			2.27354i
$592$	−48.0004	−	1.82596i	−1.97281	−	0.0750465i
$593$	−14.9993	−	14.9993i	−0.615948	−	0.615948i	0.328541	−	0.944490i	$-0.393443\pi$
$593$	−14.9993	−	14.9993i	−0.615948	−	0.615948i	−0.944490	+	0.328541i	$0.893443\pi$
$594$	−8.76372	+	41.9692i	−0.359580	+	1.72202i
$595$	−0.469456	+	0.622082i	−0.0192458	+	0.0255029i
$596$	0.653907	+	0.285539i	0.0267851	+	0.0116961i
$597$	−16.8977	+	16.8977i	−0.691577	+	0.691577i
$598$	0.651561	−	0.426457i	0.0266443	−	0.0174391i
$599$	31.8821			1.30267			0.651334	−	0.758791i	$-0.274210\pi$
$599$	31.8821			1.30267			0.651334	+	0.758791i	$0.274210\pi$
$600$	13.7236	−	38.8313i	0.560262	−	1.58528i
$601$	−36.5855			−1.49236			−0.746178	−	0.665747i	$-0.768113\pi$
$601$	−36.5855			−1.49236			−0.746178	+	0.665747i	$0.768113\pi$
$602$	6.50626	−	4.25845i	0.265175	−	0.173561i
$603$	−38.1461	+	38.1461i	−1.55343	+	1.55343i
$604$	2.68310	+	1.17162i	0.109174	+	0.0476725i
$605$	−8.89761	+	11.7903i	−0.361739	+	0.479345i
$606$	−5.34959	+	25.6190i	−0.217312	+	1.04070i
$607$	8.79118	+	8.79118i	0.356823	+	0.356823i	0.862640	−	0.505818i	$-0.168809\pi$
$607$	8.79118	+	8.79118i	0.356823	+	0.356823i	−0.505818	+	0.862640i	$0.668809\pi$
$608$	−26.5693	−	6.61124i	−1.07753	−	0.268121i
$609$			22.8346i			0.925304i
$610$	0.757114	−	11.2952i	0.0306546	−	0.457331i
$611$		−	12.6029i		−	0.509858i
$612$	2.97415	−	1.16620i	0.120223	−	0.0471409i
$613$	9.74539	+	9.74539i	0.393613	+	0.393613i	0.875973	−	0.482360i	$-0.160220\pi$
$613$	9.74539	+	9.74539i	0.393613	+	0.393613i	−0.482360	+	0.875973i	$0.660220\pi$
$614$	47.4646	+	9.91122i	1.91551	+	0.399984i
$615$	5.06044	+	36.1909i	0.204057	+	1.45936i
$616$	−11.5718	−	8.21875i	−0.466241	−	0.331143i
$617$	15.9154	−	15.9154i	0.640729	−	0.640729i	−0.310005	−	0.950735i	$-0.600331\pi$
$617$	15.9154	−	15.9154i	0.640729	−	0.640729i	0.950735	+	0.310005i	$0.100331\pi$
$618$	9.36885	+	14.3142i	0.376870	+	0.575801i
$619$	6.47284			0.260165			0.130083	−	0.991503i	$-0.458476\pi$
$619$	6.47284			0.260165			0.130083	+	0.991503i	$0.458476\pi$
$620$	19.7555	−	11.1183i	0.793402	−	0.446523i
$621$	−3.97850			−0.159652
$622$	8.97945	+	13.7192i	0.360043	+	0.550091i
$623$	−12.6937	+	12.6937i	−0.508562	+	0.508562i
$624$	7.91794	+	8.54416i	0.316971	+	0.342040i
$625$	−21.2382	+	13.1885i	−0.849530	+	0.527541i
$626$	−44.3104	−	9.25259i	−1.77100	−	0.369808i
$627$	−41.8202	−	41.8202i	−1.67014	−	1.67014i
$628$	−1.82069	−	4.64328i	−0.0726533	−	0.185287i
$629$			3.49966i			0.139541i
$630$	13.6445	+	15.6051i	0.543610	+	0.621722i
$631$			38.0648i			1.51533i	0.652641	+	0.757667i	$0.273661\pi$
$631$			38.0648i			1.51533i	−0.652641	+	0.757667i	$0.726339\pi$
$632$	1.03525	+	6.11031i	0.0411800	+	0.243055i
$633$	−19.0567	−	19.0567i	−0.757438	−	0.757438i
$634$	0.354390	−	1.69717i	0.0140746	−	0.0674031i
$635$	19.2159	−	2.68690i	0.762561	−	0.106626i
$636$	0.235372	−	0.539021i	0.00933312	−	0.0213736i
$637$	−3.93836	+	3.93836i	−0.156044	+	0.156044i
$638$	32.5515	−	21.3055i	1.28873	−	0.843492i
$639$	25.2738			0.999816
$640$	−6.71702	−	24.3902i	−0.265514	−	0.964107i
$641$	2.47864			0.0979003			0.0489501	−	0.998801i	$-0.484412\pi$
$641$	2.47864			0.0979003			0.0489501	+	0.998801i	$0.484412\pi$
$642$	−26.8449	+	17.5704i	−1.05949	+	0.693450i
$643$	22.2075	−	22.2075i	0.875780	−	0.875780i	−0.117315	−	0.993095i	$-0.537429\pi$
$643$	22.2075	−	22.2075i	0.875780	−	0.875780i	0.993095	+	0.117315i	$0.0374287\pi$
$644$	0.527062	−	1.20701i	0.0207692	−	0.0475631i
$645$	23.8975	+	18.0343i	0.940963	+	0.710100i
$646$	−0.407739	+	1.95265i	−0.0160423	+	0.0768260i
$647$	−19.5503	−	19.5503i	−0.768603	−	0.768603i	0.209258	−	0.977861i	$-0.432895\pi$
$647$	−19.5503	−	19.5503i	−0.768603	−	0.768603i	−0.977861	+	0.209258i	$0.932895\pi$
$648$	−2.17274	−	12.8240i	−0.0853531	−	0.503776i
$649$		−	45.9617i		−	1.80415i
$650$	−0.508652	−	7.05275i	−0.0199510	−	0.276632i
$651$			17.6549i			0.691948i
$652$	11.5590	+	29.4787i	0.452683	+	1.15447i
$653$	1.86959	+	1.86959i	0.0731625	+	0.0731625i	0.742741	−	0.669579i	$-0.233525\pi$
$653$	1.86959	+	1.86959i	0.0731625	+	0.0731625i	−0.669579	+	0.742741i	$0.733525\pi$
$654$	33.0696	+	6.90536i	1.29312	+	0.270021i
$655$	4.39305	+	3.31523i	0.171651	+	0.129537i
$656$	15.2575	+	16.4642i	0.595704	+	0.642818i
$657$	14.1169	−	14.1169i	0.550753	−	0.550753i
$658$	−11.6734	−	17.8352i	−0.455077	−	0.695288i
$659$	1.00511			0.0391535			0.0195767	−	0.999808i	$-0.493768\pi$
$659$	1.00511			0.0391535			0.0195767	+	0.999808i	$0.493768\pi$
$660$	14.7227	−	52.6264i	0.573079	−	2.04848i
$661$	−5.91229			−0.229961			−0.114981	−	0.993368i	$-0.536681\pi$
$661$	−5.91229			−0.229961			−0.114981	+	0.993368i	$0.536681\pi$
$662$	−5.35254	−	8.17786i	−0.208032	−	0.317841i
$663$	0.600118	−	0.600118i	0.0233066	−	0.0233066i
$664$	36.4942	+	25.9196i	1.41625	+	1.00588i
$665$	−12.8188	+	1.79240i	−0.497091	+	0.0695065i
$666$	91.1189	+	19.0268i	3.53079	+	0.737274i
$667$	2.55271	+	2.55271i	0.0988412	+	0.0988412i
$668$	−40.4512	+	15.8614i	−1.56510	+	0.613696i
$669$			1.87085i			0.0723312i
$670$	23.4310	−	20.4872i	0.905219	−	0.791490i
$671$		−	15.0209i		−	0.579876i
$672$	19.1192	+	4.75744i	0.737540	+	0.183522i
$673$	22.2258	+	22.2258i	0.856742	+	0.856742i	0.990953	−	0.134211i	$-0.0428498\pi$
$673$	22.2258	+	22.2258i	0.856742	+	0.856742i	−0.134211	+	0.990953i	$0.542850\pi$
$674$	1.35705	−	6.49889i	0.0522717	−	0.250328i
$675$	−17.5587	+	31.5724i	−0.675836	+	1.21522i
$676$	1.83288	+	0.800354i	0.0704952	+	0.0307829i
$677$	13.0165	−	13.0165i	0.500263	−	0.500263i	−0.411256	−	0.911520i	$-0.634910\pi$
$677$	13.0165	−	13.0165i	0.500263	−	0.500263i	0.911520	+	0.411256i	$0.134910\pi$
$678$	30.2974	−	19.8301i	1.16357	−	0.761571i
$679$	−9.31969			−0.357657
$680$	−1.75709	+	0.556572i	−0.0673814	+	0.0213436i
$681$	−72.8771			−2.79266
$682$	25.1676	−	16.4726i	0.963719	−	0.630769i
$683$	−5.53879	+	5.53879i	−0.211936	+	0.211936i	−0.805089	−	0.593153i	$-0.797883\pi$
$683$	−5.53879	+	5.53879i	−0.211936	+	0.211936i	0.593153	+	0.805089i	$0.297883\pi$
$684$	48.6234	+	21.2322i	1.85916	+	0.811832i
$685$	0.458004	+	3.27552i	0.0174994	+	0.125151i
$686$	−4.34556	+	20.8108i	−0.165914	+	0.794558i
$687$	5.80196	+	5.80196i	0.221359	+	0.221359i
$688$	18.3768	+	0.699062i	0.700609	+	0.0266515i
$689$		−	0.100983i		−	0.00384715i
$690$	5.05958	+	0.339141i	0.192615	+	0.0129109i
$691$		−	24.6693i		−	0.938466i	−0.883074	−	0.469233i	$-0.844530\pi$
$691$		−	24.6693i		−	0.938466i	0.883074	−	0.469233i	$-0.155470\pi$
$692$	−18.6887	+	7.32806i	−0.710437	+	0.278571i
$693$	19.4487	+	19.4487i	0.738795	+	0.738795i
$694$	0.584334	+	0.122017i	0.0221810	+	0.00463169i
$695$	−5.82863	+	7.72359i	−0.221092	+	0.292972i
$696$	−31.2708	+	44.0285i	−1.18532	+	1.66890i
$697$	1.15640	−	1.15640i	0.0438016	−	0.0438016i
$698$	22.0575	+	33.7006i	0.834890	+	1.27559i
$699$	−45.4325			−1.71841
$700$	−7.25243	−	9.50968i	−0.274116	−	0.359432i
$701$	−10.8183			−0.408603			−0.204302	−	0.978908i	$-0.565492\pi$
$701$	−10.8183			−0.408603			−0.204302	+	0.978908i	$0.565492\pi$
$702$	−5.59587	−	8.54964i	−0.211203	−	0.322685i
$703$	−41.0993	+	41.0993i	−1.55009	+	1.55009i
$704$	−11.0570	−	31.6940i	−0.416727	−	1.19451i
$705$	49.4363	−	65.5087i	1.86188	−	2.46720i
$706$	24.1834	+	5.04982i	0.910156	+	0.190052i
$707$	5.37393	+	5.37393i	0.202107	+	0.202107i
$708$	23.2904	+	59.3973i	0.875307	+	2.23229i
$709$		−	26.0040i		−	0.976601i	−0.872676	−	0.488300i	$-0.837617\pi$
$709$		−	26.0040i		−	0.976601i	0.872676	−	0.488300i	$-0.162383\pi$
$710$	−14.5491	−	0.975215i	−0.546016	−	0.0365991i
$711$		−	12.0095i		−	0.450392i
$712$	−41.8587	+	7.09199i	−1.56872	+	0.265784i
$713$	1.97366	+	1.97366i	0.0739142	+	0.0739142i
$714$	0.293408	−	1.40512i	0.0109805	−	0.0525855i
$715$	−1.29926	−	9.29197i	−0.0485897	−	0.347500i
$716$	9.73798	−	22.3008i	0.363925	−	0.833418i
$717$	0.903206	−	0.903206i	0.0337308	−	0.0337308i
$718$	33.7007	−	22.0577i	1.25770	−	0.823184i
$719$	30.3758			1.13283			0.566413	−	0.824122i	$-0.308331\pi$
$719$	30.3758			1.13283			0.566413	+	0.824122i	$0.308331\pi$
$720$	4.93829	+	48.7745i	0.184039	+	1.81772i
$721$	4.96783			0.185012
$722$	−5.23736	+	3.42794i	−0.194914	+	0.127575i
$723$	−13.3497	+	13.3497i	−0.496482	+	0.496482i
$724$	10.4577	−	23.9489i	0.388656	−	0.890053i
$725$	31.5238	−	8.99152i	1.17076	−	0.333937i
$726$	5.56098	−	26.6314i	0.206387	−	0.988383i
$727$	0.0125971	+	0.0125971i	0.000467201	+	0.000467201i	0.707340	−	0.706873i	$-0.249895\pi$
$727$	0.0125971	+	0.0125971i	0.000467201	+	0.000467201i	−0.706873	+	0.707340i	$0.749895\pi$
$728$	3.33515	−	0.565064i	0.123609	−	0.0209427i
$729$		−	37.9200i		−	1.40444i
$730$	−8.67122	+	7.58179i	−0.320936	+	0.280615i
$731$		−	1.33983i		−	0.0495555i
$732$	7.61163	+	19.4119i	0.281334	+	0.717483i
$733$	24.1323	+	24.1323i	0.891347	+	0.891347i	0.994650	−	0.103303i	$-0.0329411\pi$
$733$	24.1323	+	24.1323i	0.891347	+	0.891347i	−0.103303	+	0.994650i	$0.532941\pi$
$734$	−30.7663	−	6.42440i	−1.13560	−	0.237129i
$735$	−35.9199	+	5.02256i	−1.32493	+	0.185260i
$736$	2.66920	−	1.60552i	0.0983882	−	0.0591804i
$737$	29.2022	−	29.2022i	1.07568	−	1.07568i
$738$	−23.8214	−	36.3955i	−0.876879	−	1.33974i
$739$	−1.06565			−0.0392006			−0.0196003	−	0.999808i	$-0.506239\pi$
$739$	−1.06565			−0.0392006			−0.0196003	+	0.999808i	$0.506239\pi$
$740$	−51.7192	−	14.4689i	−1.90123	−	0.531886i
$741$	14.0953			0.517804
$742$	−0.0935354	−	0.142908i	−0.00343379	−	0.00524631i
$743$	1.75392	−	1.75392i	0.0643452	−	0.0643452i	−0.674202	−	0.738547i	$-0.735512\pi$
$743$	1.75392	−	1.75392i	0.0643452	−	0.0643452i	0.738547	+	0.674202i	$0.235512\pi$
$744$	−24.1775	+	34.0413i	−0.886388	+	1.24801i
$745$	0.636776	+	0.480545i	0.0233297	+	0.0176058i
$746$	−9.55256	−	1.99470i	−0.349744	−	0.0730311i
$747$	−61.3358	−	61.3358i	−2.24416	−	2.24416i
$748$	−2.27682	+	0.892767i	−0.0832487	+	0.0326428i
$749$			9.31671i			0.340425i
$750$	25.0213	−	38.6548i	0.913649	−	1.41147i
$751$		−	10.4197i		−	0.380220i	−0.981763	−	0.190110i	$-0.939115\pi$
$751$		−	10.4197i		−	0.380220i	0.981763	−	0.190110i	$-0.0608845\pi$
$752$	1.91629	−	50.3751i	0.0698801	−	1.83699i
$753$	−35.7735	−	35.7735i	−1.30366	−	1.30366i
$754$	−1.89521	+	9.07611i	−0.0690195	+	0.330533i
$755$	2.61281	+	1.97177i	0.0950899	+	0.0717599i
$756$	−15.8382	−	6.91600i	−0.576029	−	0.251532i
$757$	1.88156	−	1.88156i	0.0683863	−	0.0683863i	−0.672086	−	0.740473i	$-0.734602\pi$
$757$	1.88156	−	1.88156i	0.0683863	−	0.0683863i	0.740473	+	0.672086i	$0.234602\pi$
$758$	0.394198	−	0.258008i	0.0143179	−	0.00937129i
$759$	6.72845			0.244227
$760$	−27.1712	−	14.0986i	−0.985602	−	0.511412i
$761$	45.0253			1.63216			0.816082	−	0.577935i	$-0.196141\pi$
$761$	45.0253			1.63216			0.816082	+	0.577935i	$0.196141\pi$
$762$	−29.9018	+	19.5712i	−1.08323	+	0.708989i
$763$	6.93678	−	6.93678i	0.251128	−	0.251128i
$764$	−25.5487	−	11.1562i	−0.924319	−	0.403619i
$765$	3.53728	−	0.494606i	0.127891	−	0.0178825i
$766$	3.56064	−	17.0518i	0.128651	−	0.616106i
$767$	7.74558	+	7.74558i	0.279677	+	0.279677i
$768$	30.3497	+	35.3559i	1.09515	+	1.27580i
$769$			40.0379i			1.44380i	0.691996	+	0.721902i	$0.256732\pi$
$769$			40.0379i			1.44380i	−0.691996	+	0.721902i	$0.743268\pi$
$770$	−10.4453	−	11.9462i	−0.376424	−	0.430513i
$771$		−	53.0722i		−	1.91135i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18329 + 0.774482i) q^{2} +(2.05925 - 2.05925i) q^{3} +(0.800354 - 1.83288i) q^{4} +(1.34695 - 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(0.845670 + 0.845670i) q^{7} +(0.472478 + 2.78869i) q^{8} -5.48103i q^{9} +O(q^{10})\)	\(q+(-1.18329 + 0.774482i) q^{2} +(2.05925 - 2.05925i) q^{3} +(0.800354 - 1.83288i) q^{4} +(1.34695 - 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(0.845670 + 0.845670i) q^{7} +(0.472478 + 2.78869i) q^{8} -5.48103i q^{9} +(-0.211491 + 3.15520i) q^{10} +4.19592i q^{11} +(-2.12622 - 5.42248i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-1.65563 - 0.345717i) q^{14} +(-0.901767 - 6.44918i) q^{15} +(-2.71887 - 2.93390i) q^{16} +(-0.206069 + 0.206069i) q^{17} +(4.24496 + 6.48565i) q^{18} -4.84005 q^{19} +(-2.19339 - 3.89731i) q^{20} +3.48290 q^{21} +(-3.24967 - 4.96499i) q^{22} +(0.389358 - 0.389358i) q^{23} +(6.71555 + 4.76965i) q^{24} +(-1.37145 - 4.80823i) q^{25} +(1.38435 + 0.289071i) q^{26} +(-5.10906 - 5.10906i) q^{27} +(2.22684 - 0.873173i) q^{28} +6.55621i q^{29} +(6.06183 + 6.93286i) q^{30} +5.06902i q^{31} +(5.48946 + 1.36594i) q^{32} +(8.64045 + 8.64045i) q^{33} +(0.0842426 - 0.403436i) q^{34} +(2.64848 - 0.370328i) q^{35} +(-10.0460 - 4.38677i) q^{36} +(8.49149 - 8.49149i) q^{37} +(5.72719 - 3.74853i) q^{38} -2.91222 q^{39} +(5.61382 + 2.91291i) q^{40} -5.61170 q^{41} +(-4.12128 + 2.69744i) q^{42} +(-3.25094 + 3.25094i) q^{43} +(7.69060 + 3.35822i) q^{44} +(-9.78287 - 7.38267i) q^{45} +(-0.159173 + 0.762274i) q^{46} +(8.91159 + 8.91159i) q^{47} +(-11.6405 - 0.442809i) q^{48} -5.56968i q^{49} +(5.34672 + 4.62738i) q^{50} +0.848694i q^{51} +(-1.86197 + 0.730103i) q^{52} +(0.0714058 + 0.0714058i) q^{53} +(10.0024 + 2.08863i) q^{54} +(7.48913 + 5.65169i) q^{55} +(-1.95875 + 2.75787i) q^{56} +(-9.96688 + 9.96688i) q^{57} +(-5.07767 - 7.75790i) q^{58} -10.9539 q^{59} +(-12.5423 - 3.50881i) q^{60} -3.57989 q^{61} +(-3.92586 - 5.99812i) q^{62} +(4.63514 - 4.63514i) q^{63} +(-7.55353 + 2.63518i) q^{64} +(-2.21452 + 0.309649i) q^{65} +(-16.9160 - 3.53229i) q^{66} +(-6.95966 - 6.95966i) q^{67} +(0.212770 + 0.542626i) q^{68} -1.60357i q^{69} +(-2.84711 + 2.48941i) q^{70} +4.61114i q^{71} +(15.2849 - 2.58966i) q^{72} +(2.57559 + 2.57559i) q^{73} +(-3.47140 + 16.6244i) q^{74} +(-12.7255 - 7.07720i) q^{75} +(-3.87376 + 8.87121i) q^{76} +(-3.54836 + 3.54836i) q^{77} +(3.44600 - 2.25546i) q^{78} +2.19111 q^{79} +(-8.89878 + 0.900979i) q^{80} -4.59860 q^{81} +(6.64027 - 4.34616i) q^{82} +(11.1906 - 11.1906i) q^{83} +(2.78755 - 6.38371i) q^{84} +(0.0902396 + 0.645368i) q^{85} +(1.32901 - 6.36460i) q^{86} +(13.5009 + 13.5009i) q^{87} +(-11.7011 + 1.98248i) q^{88} +15.0102i q^{89} +(17.2937 + 1.15919i) q^{90} -1.19596i q^{91} +(-0.402020 - 1.02527i) q^{92} +(10.4384 + 10.4384i) q^{93} +(-17.4469 - 3.64313i) q^{94} +(-6.51931 + 8.63882i) q^{95} +(14.1170 - 8.49136i) q^{96} +(-5.51024 + 5.51024i) q^{97} +(4.31362 + 6.59056i) q^{98} +22.9980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

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