LMFDB - Embedded newform 260.2.o.a.27.8

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			27.8
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.8

$q$-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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−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	0.977369	+	0.211540i	$0.0678478\pi$
$3$	2.05925	+	2.05925i	1.18891	+	1.18891i	0.211540	+	0.977369i	$0.432152\pi$
$4$	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	−0.528993	−	0.848626i	$-0.677430\pi$
$7$	0.845670	−	0.845670i	0.319633	−	0.319633i	0.848626	+	0.528993i	$0.177430\pi$
$8$	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	$-0.782005\pi$
$11$		−	4.19592i		−	1.26512i	0.774512	−	0.632559i	$-0.217995\pi$
$12$	−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	0.681676	−	0.731655i	$-0.261252\pi$
$17$	−0.206069	−	0.206069i	−0.0499790	−	0.0499790i	−0.731655	+	0.681676i	$0.761252\pi$
$18$	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	0.746534	−	0.665347i	$-0.231717\pi$
$23$	0.389358	+	0.389358i	0.0811867	+	0.0811867i	−0.665347	+	0.746534i	$0.731717\pi$
$24$	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	$-0.791680\pi$
$29$		−	6.55621i		−	1.21746i	0.793379	−	0.608728i	$-0.208320\pi$
$30$	6.06183	−	6.93286i	1.10673	−	1.26576i
$31$		−	5.06902i		−	0.910423i	−0.890383	−	0.455211i	$-0.849564\pi$
$31$		−	5.06902i		−	0.910423i	0.890383	−	0.455211i	$-0.150436\pi$
$32$	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	0.811137	+	0.584856i	$0.198849\pi$
$37$	8.49149	+	8.49149i	1.39599	+	1.39599i	0.584856	+	0.811137i	$0.301151\pi$
$38$	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	0.414353	−	0.910116i	$-0.364008\pi$
$43$	−3.25094	−	3.25094i	−0.495763	−	0.495763i	−0.910116	+	0.414353i	$0.864008\pi$
$44$	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	0.371427	−	0.928462i	$-0.378869\pi$
$47$	8.91159	−	8.91159i	1.29989	−	1.29989i	0.928462	−	0.371427i	$-0.121131\pi$
$48$	−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	−0.702186	−	0.711994i	$-0.747792\pi$
$53$	0.0714058	−	0.0714058i	0.00980834	−	0.00980834i	0.711994	+	0.702186i	$0.247792\pi$
$54$	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	−0.990165	−	0.139907i	$-0.955320\pi$
$67$	−6.95966	+	6.95966i	−0.850258	+	0.850258i	0.139907	+	0.990165i	$0.455320\pi$
$68$	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	$-0.911779\pi$
$71$		−	4.61114i		−	0.547241i	0.961838	−	0.273621i	$-0.0882213\pi$
$72$	15.2849	+	2.58966i	1.80134	+	0.305195i
$73$	2.57559	−	2.57559i	0.301450	−	0.301450i	−0.540131	−	0.841581i	$-0.681625\pi$
$73$	2.57559	−	2.57559i	0.301450	−	0.301450i	0.841581	+	0.540131i	$0.181625\pi$
$74$	−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	0.964598	+	0.263725i	$0.0849512\pi$
$83$	11.1906	+	11.1906i	1.22832	+	1.22832i	0.263725	+	0.964598i	$0.415049\pi$
$84$	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	$-0.707188\pi$
$89$		−	15.0102i		−	1.59108i	0.605902	−	0.795540i	$-0.292812\pi$
$90$	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	0.369680	−	0.929159i	$-0.379467\pi$
$97$	−5.51024	−	5.51024i	−0.559480	−	0.559480i	−0.929159	+	0.369680i	$0.879467\pi$
$98$	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	0.836848	−	0.547436i	$-0.184396\pi$
$103$	2.93721	+	2.93721i	0.289412	+	0.289412i	−0.547436	+	0.836848i	$0.684396\pi$
$104$	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	−0.388798	−	0.921323i	$-0.627110\pi$
$107$	5.50848	−	5.50848i	0.532525	−	0.532525i	0.921323	+	0.388798i	$0.127110\pi$
$108$	−13.4533	−	5.27522i	−1.29455	−	0.507608i
$109$			8.20270i			0.785676i	0.919608	+	0.392838i	$0.128507\pi$
$109$			8.20270i			0.785676i	−0.919608	+	0.392838i	$0.871493\pi$
$110$	−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	−0.936229	−	0.351391i	$-0.885709\pi$
$113$	−6.21691	+	6.21691i	−0.584838	+	0.584838i	0.351391	+	0.936229i	$0.385709\pi$
$114$	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	−0.380375	−	0.924832i	$-0.624205\pi$
$127$	6.13573	−	6.13573i	0.544458	−	0.544458i	0.924832	+	0.380375i	$0.124205\pi$
$128$	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	$-0.965708\pi$
$131$		−	2.46129i		−	0.215043i	0.994203	−	0.107522i	$-0.0342915\pi$
$132$	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	0.661016	−	0.750372i	$-0.270126\pi$
$137$	−1.04589	−	1.04589i	−0.0893561	−	0.0893561i	−0.750372	+	0.661016i	$0.770126\pi$
$138$	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	$-0.995348\pi$
$149$		−	0.356765i		−	0.0292274i	0.999893	−	0.0146137i	$-0.00465185\pi$
$150$	20.5392	+	1.48131i	1.67702	+	0.120948i
$151$		−	1.46387i		−	0.119128i	−0.998224	−	0.0595642i	$-0.981029\pi$
$151$		−	1.46387i		−	0.119128i	0.998224	−	0.0595642i	$-0.0189711\pi$
$152$	−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	0.773962	−	0.633232i	$-0.218272\pi$
$157$	1.76334	+	1.76334i	0.140730	+	0.140730i	−0.633232	+	0.773962i	$0.718272\pi$
$158$	−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	0.116357	−	0.993207i	$-0.462878\pi$
$163$	−11.1949	−	11.1949i	−0.876851	−	0.876851i	−0.993207	+	0.116357i	$0.962878\pi$
$164$	−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	−0.211315	+	0.977418i	$0.567774\pi$
$167$	−15.3618	+	15.3618i	−1.18873	+	1.18873i	−0.977418	+	0.211315i	$0.932226\pi$
$168$	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	−0.923410	−	0.383816i	$-0.874610\pi$
$173$	−7.09724	+	7.09724i	−0.539593	+	0.539593i	0.383816	+	0.923410i	$0.374610\pi$
$174$	−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	$0.168249\pi$
$191$			13.9391i			1.00860i	−0.863529	+	0.504300i	$0.831751\pi$
$192$	−10.1281	−	20.9811i	−0.730933	−	1.51418i
$193$	4.56547	−	4.56547i	0.328630	−	0.328630i	−0.523435	−	0.852065i	$-0.675350\pi$
$193$	4.56547	−	4.56547i	0.328630	−	0.328630i	0.852065	+	0.523435i	$0.175350\pi$
$194$	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	0.0429337	−	0.999078i	$-0.486330\pi$
$197$	−13.4201	−	13.4201i	−0.956144	−	0.956144i	−0.999078	+	0.0429337i	$0.986330\pi$
$198$	−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	$0.103194\pi$
$211$			9.25421i			0.637086i	−0.947908	+	0.318543i	$0.896806\pi$
$212$	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	0.691734	−	0.722153i	$-0.256847\pi$
$223$	−0.454255	−	0.454255i	−0.0304191	−	0.0304191i	−0.722153	+	0.691734i	$0.756847\pi$
$224$	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	−0.193327	+	0.981134i	$0.561928\pi$
$227$	−17.6950	+	17.6950i	−1.17446	+	1.17446i	−0.981134	+	0.193327i	$0.938072\pi$
$228$	10.2910	−	26.2451i	0.681539	−	1.73812i
$229$		−	2.81751i		−	0.186186i	−0.995657	−	0.0930932i	$-0.970325\pi$
$229$		−	2.81751i		−	0.186186i	0.995657	−	0.0930932i	$-0.0296755\pi$
$230$	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	−0.969151	−	0.246466i	$-0.920731\pi$
$233$	−11.0313	+	11.0313i	−0.722685	+	0.722685i	0.246466	+	0.969151i	$0.420731\pi$
$234$	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	$0.184709\pi$
$251$			17.3721i			1.09652i	−0.836309	+	0.548259i	$0.815291\pi$
$252$	−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	0.983691	−	0.179867i	$-0.0575666\pi$
$257$	12.8863	+	12.8863i	0.803824	+	0.803824i	−0.179867	+	0.983691i	$0.557567\pi$
$258$	−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	−0.995307	−	0.0967688i	$-0.969149\pi$
$263$	−17.7105	−	17.7105i	−1.09208	−	1.09208i	−0.0967688	−	0.995307i	$-0.530851\pi$
$264$	−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	$0.0976128\pi$
$269$			9.90226i			0.603752i	−0.953347	+	0.301876i	$0.902387\pi$
$270$	17.2006	+	15.0396i	1.04680	+	0.915280i
$271$			23.2048i			1.40959i	0.709409	+	0.704797i	$0.248962\pi$
$271$			23.2048i			1.40959i	−0.709409	+	0.704797i	$0.751038\pi$
$272$	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	0.994599	−	0.103797i	$-0.0330992\pi$
$277$	14.8259	+	14.8259i	0.890802	+	0.890802i	−0.103797	+	0.994599i	$0.533099\pi$
$278$	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	0.942047	−	0.335482i	$-0.108899\pi$
$283$	10.2040	+	10.2040i	0.606564	+	0.606564i	−0.335482	+	0.942047i	$0.608899\pi$
$284$	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	−0.267926	−	0.963440i	$-0.586338\pi$
$293$	11.9053	−	11.9053i	0.695514	−	0.695514i	0.963440	+	0.267926i	$0.0863382\pi$
$294$	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	−0.545721	+	0.837967i	$0.683744\pi$
$307$	−24.2442	+	24.2442i	−1.38369	+	1.38369i	−0.837967	+	0.545721i	$0.816256\pi$
$308$	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	$0.106618\pi$
$311$			11.5941i			0.657443i	−0.944427	+	0.328721i	$0.893382\pi$
$312$	−1.37596	+	8.12127i	−0.0778984	+	0.459776i
$313$	22.6331	−	22.6331i	1.27930	−	1.27930i	0.338235	−	0.941062i	$-0.390170\pi$
$313$	22.6331	−	22.6331i	1.27930	−	1.27930i	0.941062	−	0.338235i	$-0.109830\pi$
$314$	−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	0.682343	−	0.731032i	$-0.260961\pi$
$317$	−0.866886	−	0.866886i	−0.0486892	−	0.0486892i	−0.731032	+	0.682343i	$0.760961\pi$
$318$	−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	$-0.939172\pi$
$331$		−	6.91111i		−	0.379869i	0.981797	−	0.189935i	$-0.0608276\pi$
$332$	−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	0.610889	−	0.791716i	$-0.290812\pi$
$337$	−3.31953	−	3.31953i	−0.180826	−	0.180826i	−0.791716	+	0.610889i	$0.790812\pi$
$338$	−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	−0.715073	−	0.699050i	$-0.753606\pi$
$347$	−0.298469	+	0.298469i	−0.0160226	+	0.0160226i	0.699050	+	0.715073i	$0.253606\pi$
$348$	35.5509	+	13.9399i	1.90573	+	0.747259i
$349$			28.4804i			1.52452i	0.647271	+	0.762260i	$0.275910\pi$
$349$			28.4804i			1.52452i	−0.647271	+	0.762260i	$0.724090\pi$
$350$	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	−0.954778	−	0.297320i	$-0.903907\pi$
$353$	−12.3525	+	12.3525i	−0.657459	+	0.657459i	0.297320	+	0.954778i	$0.403907\pi$
$354$	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	−0.165840	−	0.986153i	$-0.553034\pi$
$367$	15.7149	−	15.7149i	0.820313	−	0.820313i	0.986153	+	0.165840i	$0.0530335\pi$
$368$	−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	−0.569412	−	0.822052i	$-0.692829\pi$
$373$	4.87930	−	4.87930i	0.252641	−	0.252641i	0.822052	+	0.569412i	$0.192829\pi$
$374$	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	0.448655	−	0.893705i	$-0.351903\pi$
$383$	−8.70979	−	8.70979i	−0.445050	−	0.445050i	−0.893705	+	0.448655i	$0.851903\pi$
$384$	−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	$-0.869351\pi$
$389$		−	15.7397i		−	0.798036i	0.916943	−	0.399018i	$-0.130649\pi$
$390$	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	0.993307	−	0.115502i	$-0.0368478\pi$
$397$	17.4901	+	17.4901i	0.877805	+	0.877805i	−0.115502	+	0.993307i	$0.536848\pi$
$398$	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	$-0.890292\pi$
$409$		−	13.6662i		−	0.675749i	0.941191	−	0.337875i	$-0.109708\pi$
$410$	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	$-0.745847\pi$
$431$		−	29.7403i		−	1.43254i	0.697822	−	0.716271i	$-0.254153\pi$
$432$	−1.09862	−	28.8803i	−0.0528575	−	1.38951i
$433$	0.932973	−	0.932973i	0.0448358	−	0.0448358i	−0.684333	−	0.729169i	$-0.739907\pi$
$433$	0.932973	−	0.932973i	0.0448358	−	0.0448358i	0.729169	+	0.684333i	$0.239907\pi$
$434$	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	0.338338	−	0.941025i	$-0.390135\pi$
$443$	−12.6851	−	12.6851i	−0.602687	−	0.602687i	−0.941025	+	0.338338i	$0.890135\pi$
$444$	−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	$-0.877763\pi$
$449$		−	15.8773i		−	0.749297i	0.927167	−	0.374648i	$-0.122237\pi$
$450$	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	0.959846	−	0.280529i	$-0.0905099\pi$
$457$	14.5221	+	14.5221i	0.679317	+	0.679317i	−0.280529	+	0.959846i	$0.590510\pi$
$458$	−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	0.0466465	−	0.998911i	$-0.485147\pi$
$463$	−20.4903	−	20.4903i	−0.952265	−	0.952265i	−0.998911	+	0.0466465i	$0.985147\pi$
$464$	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	−0.392456	−	0.919771i	$-0.628374\pi$
$467$	11.3954	−	11.3954i	0.527315	−	0.527315i	0.919771	+	0.392456i	$0.128374\pi$
$468$	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	−0.555695	−	0.831386i	$-0.687548\pi$
$487$	6.08398	−	6.08398i	0.275692	−	0.275692i	0.831386	+	0.555695i	$0.187548\pi$
$488$	−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	$0.219233\pi$
$491$			28.1664i			1.27113i	−0.772046	+	0.635567i	$0.780767\pi$
$492$	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	0.817007	−	0.576627i	$-0.195632\pi$
$503$	5.39116	+	5.39116i	0.240380	+	0.240380i	−0.576627	+	0.817007i	$0.695632\pi$
$504$	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	$-0.898325\pi$
$509$		−	14.1691i		−	0.628033i	0.949417	−	0.314017i	$-0.101675\pi$
$510$	−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	0.782167	−	0.623069i	$-0.214114\pi$
$523$	3.63846	+	3.63846i	0.159099	+	0.159099i	−0.623069	+	0.782167i	$0.714114\pi$
$524$	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	−0.959645	−	0.281214i	$-0.909263\pi$
$547$	−15.8672	+	15.8672i	−0.678431	+	0.678431i	0.281214	+	0.959645i	$0.409263\pi$
$548$	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	0.605104	−	0.796146i	$-0.293131\pi$
$557$	−4.50875	−	4.50875i	−0.191042	−	0.191042i	−0.796146	+	0.605104i	$0.793131\pi$
$558$	−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	0.541137	−	0.840935i	$-0.317994\pi$
$563$	−7.11349	−	7.11349i	−0.299798	−	0.299798i	−0.840935	+	0.541137i	$0.817994\pi$
$564$	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	$-0.873269\pi$
$569$		−	18.4963i		−	0.775404i	0.921785	−	0.387702i	$-0.126731\pi$
$570$	−29.3396	+	33.5554i	−1.22890	+	1.40548i
$571$		−	31.1985i		−	1.30562i	−0.757523	−	0.652808i	$-0.773591\pi$
$571$		−	31.1985i		−	1.30562i	0.757523	−	0.652808i	$-0.226409\pi$
$572$	−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	0.995019	−	0.0996855i	$-0.0317837\pi$
$577$	21.5066	+	21.5066i	0.895334	+	0.895334i	−0.0996855	+	0.995019i	$0.531784\pi$
$578$	−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	−0.749638	−	0.661848i	$-0.769772\pi$
$587$	−2.12698	+	2.12698i	−0.0877898	+	0.0877898i	0.661848	+	0.749638i	$0.269772\pi$
$588$	−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	−0.944490	−	0.328541i	$-0.893443\pi$
$593$	−14.9993	+	14.9993i	−0.615948	+	0.615948i	0.328541	+	0.944490i	$0.393443\pi$
$594$	−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	−0.505818	−	0.862640i	$-0.668809\pi$
$607$	8.79118	−	8.79118i	0.356823	−	0.356823i	0.862640	+	0.505818i	$0.168809\pi$
$608$	−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	−0.482360	−	0.875973i	$-0.660220\pi$
$613$	9.74539	−	9.74539i	0.393613	−	0.393613i	0.875973	+	0.482360i	$0.160220\pi$
$614$	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	0.950735	−	0.310005i	$-0.100331\pi$
$617$	15.9154	+	15.9154i	0.640729	+	0.640729i	−0.310005	+	0.950735i	$0.600331\pi$
$618$	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	$-0.726339\pi$
$631$		−	38.0648i		−	1.51533i	0.652641	−	0.757667i	$-0.273661\pi$
$632$	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	0.993095	−	0.117315i	$-0.0374287\pi$
$643$	22.2075	+	22.2075i	0.875780	+	0.875780i	−0.117315	+	0.993095i	$0.537429\pi$
$644$	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	−0.977861	−	0.209258i	$-0.932895\pi$
$647$	−19.5503	+	19.5503i	−0.768603	+	0.768603i	0.209258	+	0.977861i	$0.432895\pi$
$648$	−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	−0.669579	−	0.742741i	$-0.733525\pi$
$653$	1.86959	−	1.86959i	0.0731625	−	0.0731625i	0.742741	+	0.669579i	$0.233525\pi$
$654$	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	−0.134211	−	0.990953i	$-0.542850\pi$
$673$	22.2258	−	22.2258i	0.856742	−	0.856742i	0.990953	+	0.134211i	$0.0428498\pi$
$674$	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	0.911520	−	0.411256i	$-0.134910\pi$
$677$	13.0165	+	13.0165i	0.500263	+	0.500263i	−0.411256	+	0.911520i	$0.634910\pi$
$678$	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	0.593153	−	0.805089i	$-0.297883\pi$
$683$	−5.53879	−	5.53879i	−0.211936	−	0.211936i	−0.805089	+	0.593153i	$0.797883\pi$
$684$	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	$0.155470\pi$
$691$			24.6693i			0.938466i	−0.883074	+	0.469233i	$0.844530\pi$
$692$	−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	$0.162383\pi$
$709$			26.0040i			0.976601i	−0.872676	+	0.488300i	$0.837617\pi$
$710$	−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	−0.706873	−	0.707340i	$-0.749895\pi$
$727$	0.0125971	−	0.0125971i	0.000467201	−	0.000467201i	0.707340	+	0.706873i	$0.249895\pi$
$728$	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	−0.103303	−	0.994650i	$-0.532941\pi$
$733$	24.1323	−	24.1323i	0.891347	−	0.891347i	0.994650	+	0.103303i	$0.0329411\pi$
$734$	−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	0.738547	−	0.674202i	$-0.235512\pi$
$743$	1.75392	+	1.75392i	0.0643452	+	0.0643452i	−0.674202	+	0.738547i	$0.735512\pi$
$744$	−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	$0.0608845\pi$
$751$			10.4197i			0.380220i	−0.981763	+	0.190110i	$0.939115\pi$
$752$	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	0.740473	−	0.672086i	$-0.234602\pi$
$757$	1.88156	+	1.88156i	0.0683863	+	0.0683863i	−0.672086	+	0.740473i	$0.734602\pi$
$758$	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	$-0.743268\pi$
$769$		−	40.0379i		−	1.44380i	0.691996	−	0.721902i	$-0.256732\pi$
$770$	−10.4453	+	11.9462i	−0.376424	+	0.430513i
$771$			53.0722i			1.91135i
$772$	12.0219	+	4.71395i	0.432679	+	0.169659i
$773$	12.8017	−	12.8017i	0.460444	−	0.460444i	−0.438357	−	0.898801i	$-0.644439\pi$
$773$	12.8017	−	12.8017i	0.460444	−	0.460444i	0.898801	+	0.438357i	$0.144439\pi$
$774$	−34.8846	+	7.28435i	−1.25390	+	0.261831i
$775$	24.3730	+	6.95191i	0.875505	+	0.249720i
$776$	−17.9698	+	12.7628i	−0.645077	+	0.458160i
$777$	29.5750	+	29.5750i	1.06100	+	1.06100i
$778$	−12.1901	+	18.6247i	−0.437038	+	0.667727i
$779$	27.1609			0.973141
$780$	6.38763	−	11.3498i	0.228714	−	0.406389i
$781$	−19.3480			−0.692325
$782$	−0.124280	+	0.189881i	−0.00444425	+	0.00679014i
$783$	33.4961	+	33.4961i	1.19705	+	1.19705i
$784$	−16.3409	−	15.1432i	−0.583603	−	0.540829i
$785$	−0.772185	+	5.52245i	−0.0275605	+	0.197105i
$786$	−9.92279	+	2.07201i	−0.353934	+	0.0739060i
$787$	9.51278	−	9.51278i	0.339094	−	0.339094i	−0.516932	−	0.856026i	$-0.672926\pi$
$787$	9.51278	−	9.51278i	0.339094	−	0.339094i	0.856026	+	0.516932i	$0.172926\pi$
$788$	13.8566	−	35.3383i	0.493620	−	1.25887i
$789$		−	72.9407i		−	2.59676i
$790$	−0.463400	−	6.91338i	−0.0164870	−	0.245967i
$791$			10.5149i			0.373867i
$792$	10.8660	−	64.1341i	0.386107	−	2.27891i
$793$	2.53136	−	2.53136i	0.0898913	−	0.0898913i
$794$	−7.15012	−	34.2417i	−0.253748	−	1.21519i
$795$	0.396118	+	0.524901i	0.0140489	+	0.0186163i
$796$	−6.56751	−	15.0401i	−0.232779	−	0.533083i
$797$	−14.9893	−	14.9893i	−0.530947	−	0.530947i	0.389907	−	0.920854i	$-0.372507\pi$
$797$	−14.9893	−	14.9893i	−0.530947	−	0.530947i	−0.920854	+	0.389907i	$0.872507\pi$
$798$	19.9472	+	13.0558i	0.706123	+	0.462169i
$799$	−3.67280			−0.129934
$800$	−0.960754	+	28.2679i	−0.0339678	+	0.999423i
$801$	82.2714			2.90692
$802$	−1.46723	−	0.960324i	−0.0518096	−	0.0339102i
$803$	−10.8070	−	10.8070i	−0.381370	−	0.381370i
$804$	−22.9409	−	52.5364i	−0.809062	−	1.85282i
$805$	0.887015	+	1.17540i	0.0312632	+	0.0414272i
$806$	−1.46531	−	7.01732i	−0.0516133	−	0.247175i
$807$	−20.3912	+	20.3912i	−0.717806	+	0.717806i
$808$	3.00243	−	17.7211i	0.105625	−	0.623426i
$809$			8.36396i			0.294061i	0.989132	+	0.147031i	$0.0469716\pi$
$809$			8.36396i			0.294061i	−0.989132	+	0.147031i	$0.953028\pi$
$810$	0.972563	+	14.5095i	0.0341724	+	0.509811i
$811$			9.53032i			0.334655i	0.985901	+	0.167327i	$0.0535137\pi$
$811$			9.53032i			0.334655i	−0.985901	+	0.167327i	$0.946486\pi$
$812$	5.72470	−	14.5996i	0.200898	−	0.512347i
$813$	−47.7846	+	47.7846i	−1.67588	+	1.67588i
$814$	−69.7547	+	14.5657i	−2.44490	+	0.510527i
$815$	4.90235	−	35.0602i	0.171722	−	1.22811i
$816$	2.48998	+	2.30749i	0.0871669	+	0.0807782i
$817$	15.7347	+	15.7347i	0.550488	+	0.550488i
$818$	−10.5842	+	16.1711i	−0.370068	+	0.565408i
$819$	−6.55508			−0.229053
$820$	12.3086	−	21.8705i	0.429836	−	0.763753i
$821$	26.2559			0.916336			0.458168	−	0.888866i	$-0.348506\pi$
$821$	26.2559			0.916336			0.458168	+	0.888866i	$0.348506\pi$
$822$	−3.33607	+	5.09701i	−0.116359	+	0.177779i
$823$	19.2819	+	19.2819i	0.672125	+	0.672125i	0.958206	−	0.286080i	$-0.0923524\pi$
$823$	19.2819	+	19.2819i	0.672125	+	0.672125i	−0.286080	+	0.958206i	$0.592352\pi$
$824$	9.57873	−	6.80320i	0.333691	−	0.237001i
$825$	29.6954	+	53.3953i	1.03386	+	1.85899i
$826$	18.1356	−	3.78695i	0.631019	−	0.131765i
$827$	−4.99811	+	4.99811i	−0.173801	+	0.173801i	−0.788647	−	0.614846i	$-0.789218\pi$
$827$	−4.99811	+	4.99811i	−0.173801	+	0.173801i	0.614846	+	0.788647i	$0.289218\pi$
$828$	−5.61952	−	2.20348i	−0.195292	−	0.0765763i
$829$			34.6638i			1.20392i	0.798525	+	0.601961i	$0.205614\pi$
$829$			34.6638i			1.20392i	−0.798525	+	0.601961i	$0.794386\pi$
$830$	32.9417	−	37.6751i	1.14342	−	1.30772i
$831$			61.0605i			2.11816i
$832$	7.20451	−	3.47780i	0.249771	−	0.120571i
$833$	1.14774	−	1.14774i	0.0397667	−	0.0397667i
$834$	3.64287	+	17.4456i	0.126142	+	0.604093i
$835$	−48.1103	−	6.72709i	−1.66492	−	0.232801i
$836$	−37.2229	+	16.2540i	−1.28738	+	0.562155i
$837$	25.8979	+	25.8979i	0.895164	+	0.895164i
$838$	36.0228	+	23.5775i	1.24439	+	0.814472i
$839$	−7.85427			−0.271159			−0.135580	−	0.990766i	$-0.543290\pi$
$839$	−7.85427			−0.271159			−0.135580	+	0.990766i	$0.543290\pi$
$840$	19.5523	−	10.1454i	0.674620	−	0.350049i
$841$	−13.9838			−0.482201
$842$	35.5638	+	23.2771i	1.22561	+	0.802182i
$843$	−0.268048	−	0.268048i	−0.00923207	−	0.00923207i
$844$	−16.9618	+	7.40665i	−0.583850	+	0.254947i
$845$	1.78486	−	1.34695i	0.0614011	−	0.0463365i
$846$	−19.9681	−	95.6268i	−0.686518	−	3.28772i
$847$	−5.58628	+	5.58628i	−0.191947	+	0.191947i
$848$	0.0153547	+	0.403640i	0.000527282	+	0.0138611i
$849$			42.0252i			1.44230i
$850$	−2.05535	−	0.148234i	−0.0704979	−	0.00508439i
$851$			6.61245i			0.226672i
$852$	25.0038	+	9.80430i	0.856616	+	0.335890i
$853$	−7.34699	+	7.34699i	−0.251556	+	0.251556i	−0.821608	−	0.570052i	$-0.806923\pi$
$853$	−7.34699	+	7.34699i	−0.251556	+	0.251556i	0.570052	+	0.821608i	$0.306923\pi$
$854$	5.92697	−	1.23763i	0.202817	−	0.0423508i
$855$	47.3496	−	35.7325i	1.61932	−	1.22203i
$856$	−12.7588	−	17.9640i	−0.436086	−	0.613998i
$857$	−31.6922	−	31.6922i	−1.08258	−	1.08258i	−0.996268	−	0.0863156i	$-0.972491\pi$
$857$	−31.6922	−	31.6922i	−1.08258	−	1.08258i	−0.0863156	−	0.996268i	$-0.527509\pi$
$858$	9.46374	−	14.4592i	0.323087	−	0.493627i
$859$	22.1353			0.755245			0.377623	−	0.925960i	$-0.376742\pi$
$859$	22.1353			0.755245			0.377623	+	0.925960i	$0.376742\pi$
$860$	19.8005	−	5.53935i	0.675191	−	0.188890i
$861$	−19.5450			−0.666090
$862$	−23.0334	+	35.1915i	−0.784520	+	1.19863i
$863$	−16.0017	−	16.0017i	−0.544703	−	0.544703i	0.380201	−	0.924904i	$-0.375855\pi$
$863$	−16.0017	−	16.0017i	−0.544703	−	0.544703i	−0.924904	+	0.380201i	$0.875855\pi$
$864$	−21.0673	+	35.0247i	−0.716725	+	1.19156i
$865$	−22.2272	−	3.10795i	−0.755748	−	0.105674i
$866$	−1.82655	+	0.381407i	−0.0620687	+	0.0129607i
$867$	34.8324	−	34.8324i	1.18297	−	1.18297i
$868$	4.42613	−	11.2879i	0.150233	−	0.383137i
$869$		−	9.19371i		−	0.311875i
$870$	−45.4532	−	39.7426i	−1.54101	−	1.34740i
$871$		−	9.84245i		−	0.333499i
$872$	22.8747	+	3.87559i	0.774637	+	0.131244i
$873$	30.2018	−	30.2018i	1.02217	−	1.02217i
$874$	0.770404	+	3.68944i	0.0260593	+	0.124797i
$875$	−5.41288	+	12.2266i	−0.182989	+	0.413335i
$876$	8.48983	+	19.4424i	0.286845	+	0.656897i
$877$	26.3522	+	26.3522i	0.889850	+	0.889850i	0.994508	−	0.104658i	$-0.0333748\pi$
$877$	26.3522	+	26.3522i	0.889850	+	0.889850i	−0.104658	+	0.994508i	$0.533375\pi$
$878$	22.2862	+	14.5867i	0.752122	+	0.492276i
$879$	49.0319			1.65381
$880$	−3.78043	+	37.3386i	−0.127438	+	1.25868i
$881$	−34.0938			−1.14865			−0.574325	−	0.818627i	$-0.694735\pi$
$881$	−34.0938			−1.14865			−0.574325	+	0.818627i	$0.694735\pi$
$882$	36.1230	+	23.6431i	1.21633	+	0.796104i
$883$	3.30206	+	3.30206i	0.111123	+	0.111123i	0.760482	−	0.649359i	$-0.224963\pi$
$883$	3.30206	+	3.30206i	0.111123	+	0.111123i	−0.649359	+	0.760482i	$0.724963\pi$
$884$	0.233243	+	0.534146i	0.00784482	+	0.0179653i
$885$	9.87786	−	70.6437i	0.332041	−	2.37466i
$886$	5.18577	+	24.8345i	0.174219	+	0.834332i
$887$	31.6204	−	31.6204i	1.06171	−	1.06171i	0.0637435	−	0.997966i	$-0.479696\pi$
$887$	31.6204	−	31.6204i	1.06171	−	1.06171i	0.997966	−	0.0637435i	$-0.0203040\pi$
$888$	97.5266	+	16.5236i	3.27278	+	0.554496i
$889$		−	10.3776i		−	0.348054i
$890$	−47.3602	+	3.17453i	−1.58752	+	0.106410i
$891$			19.2954i			0.646419i
$892$	0.469028	−	1.19616i	0.0157042	−	0.0400503i
$893$	−43.1326	+	43.1326i	−1.44338	+	1.44338i
$894$	−1.43832	+	0.300339i	−0.0481045	+	0.0100448i
$895$	16.3885	+	21.7165i	0.547806	+	0.725904i
$896$	13.4169	+	1.75151i	0.448227	+	0.0585137i
$897$	−1.13390	−	1.13390i	−0.0378597	−	0.0378597i
$898$	−12.2967	+	18.7875i	−0.410346	+	0.626946i
$899$	−33.2335			−1.10840
$900$	−7.31494	−	54.3200i	−0.243831	−	1.81067i
$901$	−0.0294290			−0.000980422
$902$	18.2361	−	27.8620i	0.607197	−	0.927705i
$903$	−11.3227	−	11.3227i	−0.376795	−	0.376795i
$904$	14.3997	+	20.2744i	0.478925	+	0.674315i
$905$	17.5996	+	23.3215i	0.585032	+	0.775233i
$906$	−5.90168	+	1.23235i	−0.196070	+	0.0409420i
$907$	19.5515	−	19.5515i	0.649196	−	0.649196i	−0.303603	−	0.952799i	$-0.598190\pi$
$907$	19.5515	−	19.5515i	0.649196	−	0.649196i	0.952799	+	0.303603i	$0.0981895\pi$
$908$	−46.5951	−	18.2705i	−1.54631	−	0.606328i
$909$			34.8300i			1.15524i
$910$	3.77349	−	0.252935i	0.125090	−	0.00838470i
$911$		−	17.5979i		−	0.583043i	−0.956564	−	0.291522i	$-0.905838\pi$
$911$		−	17.5979i		−	0.583043i	0.956564	−	0.291522i	$-0.0941615\pi$
$912$	56.3404	−	2.14322i	1.86562	−	0.0709690i
$913$	46.9547	−	46.9547i	1.55397	−	1.55397i
$914$	−5.93677	−	28.4310i	−0.196371	−	0.940415i
$915$	3.22822	−	23.0873i	0.106722	−	0.763244i
$916$	5.16415	−	2.25501i	0.170628	−	0.0745076i
$917$	−2.08144	−	2.08144i	−0.0687351	−	0.0687351i
$918$	−2.49158	−	1.63078i	−0.0822344	−	0.0538237i
$919$	44.8302			1.47881			0.739407	−	0.673259i	$-0.235106\pi$
$919$	44.8302			1.47881			0.739407	+	0.673259i	$0.235106\pi$
$920$	3.31995	+	1.05162i	0.109455	+	0.0346708i
$921$	−99.8497			−3.29016
$922$	−7.45873	−	4.88186i	−0.245640	−	0.160775i
$923$	3.26057	+	3.26057i	0.107323	+	0.107323i
$924$	26.7855	−	11.6963i	0.881180	−	0.384781i
$925$	−52.4748	+	29.1834i	−1.72536	+	0.959545i
$926$	8.37661	+	40.1154i	0.275272	+	1.31827i
$927$	−16.0990	+	16.0990i	−0.528759	+	0.528759i
$928$	−8.95540	−	35.9900i	−0.293976	−	1.18143i
$929$		−	14.0437i		−	0.460758i	−0.973101	−	0.230379i	$-0.926003\pi$
$929$		−	14.0437i		−	0.460758i	0.973101	−	0.230379i	$-0.0739966\pi$
$930$	−35.1428	−	30.7275i	−1.15238	−	1.00760i
$931$		−	26.9576i		−	0.883498i
$932$	−29.0480	−	11.3901i	−0.951498	−	0.373094i
$933$	−23.8752	+	23.8752i	−0.781639	+	0.781639i
$934$	−22.3096	+	4.65853i	−0.729992	+	0.152432i
$935$	−2.70791	−	0.378638i	−0.0885582	−	0.0123828i
$936$	−12.6392	+	8.97686i	−0.413125	+	0.293418i
$937$	−20.8706	−	20.8706i	−0.681811	−	0.681811i	0.278597	−	0.960408i	$-0.410131\pi$
$937$	−20.8706	−	20.8706i	−0.681811	−	0.681811i	−0.960408	+	0.278597i	$0.910131\pi$
$938$	9.11656	−	13.9287i	0.297666	−	0.454788i
$939$	93.2143			3.04193
$940$	15.1847	+	54.2778i	0.495269	+	1.77035i
$941$	46.8318			1.52667			0.763337	−	0.646001i	$-0.223560\pi$
$941$	46.8318			1.52667			0.763337	+	0.646001i	$0.223560\pi$
$942$	5.62454	−	8.59344i	0.183257	−	0.279989i
$943$	−2.18496	−	2.18496i	−0.0711520	−	0.0711520i
$944$	29.7822	−	32.1376i	0.969328	−	1.04599i
$945$	−15.4233	+	11.6392i	−0.501719	+	0.378624i
$946$	26.7054	−	5.57643i	0.868266	−	0.181305i
$947$	−3.37955	+	3.37955i	−0.109821	+	0.109821i	−0.759882	−	0.650061i	$-0.774743\pi$
$947$	−3.37955	+	3.37955i	−0.109821	+	0.109821i	0.650061	+	0.759882i	$0.274743\pi$
$948$	−4.65878	+	11.8812i	−0.151310	+	0.385885i
$949$			3.64244i			0.118239i
$950$	−25.8784	+	22.3967i	−0.839606	+	0.726646i
$951$		−	3.57027i		−	0.115774i
$952$	−0.164674	+	0.971947i	−0.00533711	+	0.0315010i
$953$	27.3247	−	27.3247i	0.885135	−	0.885135i	−0.108916	−	0.994051i	$-0.534738\pi$
$953$	27.3247	−	27.3247i	0.885135	−	0.885135i	0.994051	+	0.108916i	$0.0347379\pi$
$954$	−0.159998	−	0.766228i	−0.00518014	−	0.0248076i
$955$	−24.8794	+	18.7753i	−0.805078	+	0.607555i
$956$	0.351043	+	0.803916i	0.0113535	+	0.0260005i
$957$	−56.6486	−	56.6486i	−1.83119	−	1.83119i
$958$	−32.0823	−	20.9984i	−1.03653	−	0.678427i
$959$	−1.76895			−0.0571224
$960$	23.8063	−	46.3378i	0.768345	−	1.49555i
$961$	5.30506			0.171131
$962$	14.2099	+	9.30059i	0.458145	+	0.299863i
$963$	30.1921	+	30.1921i	0.972928	+	0.972928i
$964$	−5.18854	−	11.8822i	−0.167112	−	0.382699i
$965$	14.2982	+	1.99927i	0.460275	+	0.0643587i
$966$	−0.554382	−	2.65492i	−0.0178369	−	0.0854206i
$967$	−13.5761	+	13.5761i	−0.436578	+	0.436578i	−0.890859	−	0.454280i	$-0.849896\pi$
$967$	−13.5761	+	13.5761i	−0.436578	+	0.436578i	0.454280	+	0.890859i	$0.349896\pi$
$968$	−3.12107	+	18.4213i	−0.100315	+	0.592084i
$969$			4.10772i			0.131959i
$970$	−16.2205	+	18.5512i	−0.520809	+	0.595645i
$971$		−	8.11728i		−	0.260496i	−0.991481	−	0.130248i	$-0.958423\pi$
$971$		−	8.11728i		−	0.260496i	0.991481	−	0.130248i	$-0.0415773\pi$
$972$	−6.04801	+	15.4242i	−0.193990	+	0.494731i
$973$	−3.65945	+	3.65945i	−0.117317	+	0.117317i
$974$	−11.9111	+	2.48718i	−0.381655	+	0.0796945i
$975$	3.99397	−	14.0026i	0.127909	−	0.448443i
$976$	9.73323	−	10.5030i	0.311553	−	0.336194i
$977$	9.33818	+	9.33818i	0.298755	+	0.298755i	0.840526	−	0.541771i	$-0.182246\pi$
$977$	9.33818	+	9.33818i	0.298755	+	0.298755i	−0.541771	+	0.840526i	$0.682246\pi$
$978$	−35.7084	+	54.5570i	−1.14183	+	1.74454i
$979$	−62.9816			−2.01290
$980$	−21.7068	−	12.2165i	−0.693398	−	0.390241i
$981$	−44.9592			−1.43544
$982$	21.8144	−	33.3291i	0.696126	−	1.06357i
$983$	12.4357	+	12.4357i	0.396638	+	0.396638i	0.877045	−	0.480408i	$-0.159511\pi$
$983$	12.4357	+	12.4357i	0.396638	+	0.396638i	−0.480408	+	0.877045i	$0.659511\pi$
$984$	−37.6857	+	26.7659i	−1.20138	+	0.853264i
$985$	5.87681	−	42.0293i	0.187251	−	1.33916i
$986$	2.64501	−	0.552312i	0.0842342	−	0.0175892i
$987$	31.0381	−	31.0381i	0.987955	−	0.987955i
$988$	9.01205	+	3.53374i	0.286712	+	0.112423i
$989$		−	2.53155i		−	0.0804988i
$990$	−4.86386	−	72.5631i	−0.154584	−	2.30621i
$991$		−	27.4991i		−	0.873539i	−0.899573	−	0.436769i	$-0.856123\pi$
$991$		−	27.4991i		−	0.873539i	0.899573	−	0.436769i	$-0.143877\pi$
$992$	−6.92399	−	27.8262i	−0.219837	−	0.883482i
$993$	14.2317	−	14.2317i	0.451630	−	0.451630i
$994$	1.59415	+	7.63434i	0.0505634	+	0.242147i
$995$	−11.0527	−	14.6461i	−0.350395	−	0.464313i
$996$	−84.4742	+	36.8870i	−2.67667	+	1.16881i
$997$	6.89846	+	6.89846i	0.218476	+	0.218476i	0.807856	−	0.589380i	$-0.200628\pi$
$997$	6.89846	+	6.89846i	0.218476	+	0.218476i	−0.589380	+	0.807856i	$0.700628\pi$
$998$	−22.8649	−	14.9654i	−0.723776	−	0.473722i
$999$	−86.7672			−2.74519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.8	✓	72
4.3	odd	2	inner	260.2.o.a.27.11	yes	72
5.3	odd	4	inner	260.2.o.a.183.11	yes	72
20.3	even	4	inner	260.2.o.a.183.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.8	✓	72	1.1	even	1	trivial
260.2.o.a.27.11	yes	72	4.3	odd	2	inner
260.2.o.a.183.8	yes	72	20.3	even	4	inner
260.2.o.a.183.11	yes	72	5.3	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 $\F_{q}$

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more