LMFDB - Embedded newform 260.2.o.a.27.11

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			27.11
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.774482 - 1.18329i) q^{2} +(-2.05925 - 2.05925i) q^{3} +(-0.800354 + 1.83288i) q^{4} +(1.34695 + 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(-0.845670 + 0.845670i) q^{7} +(2.78869 - 0.472478i) q^{8} +5.48103i q^{9} +O(q^{10})$	\(q+(-0.774482 - 1.18329i) 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} +(2.78869 - 0.472478i) q^{8} +5.48103i q^{9} +(1.06882 - 2.97618i) q^{10} +4.19592i q^{11} +(5.42248 - 2.12622i) 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} +(6.48565 - 4.24496i) q^{18} +4.84005 q^{19} +(-4.34946 + 1.04027i) q^{20} +3.48290 q^{21} +(4.96499 - 3.24967i) 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} +(-0.873173 - 2.22684i) q^{28} -6.55621i q^{29} +(-8.32966 + 3.92773i) q^{30} +5.06902i q^{31} +(-1.36594 + 5.48946i) 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} +(-3.74853 - 5.72719i) q^{38} +2.91222 q^{39} +(4.59953 + 4.34101i) q^{40} -5.61170 q^{41} +(-2.69744 - 4.12128i) 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} +(-0.442809 + 11.6405i) q^{48} +5.56968i q^{49} +(6.75170 - 2.10107i) q^{50} +0.848694i q^{51} +(-0.730103 - 1.86197i) 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} +(-7.75790 + 5.07767i) q^{58} +10.9539 q^{59} +(11.0988 + 6.81446i) q^{60} -3.57989 q^{61} +(5.99812 - 3.92586i) 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} +(0.542626 - 0.212770i) q^{68} +1.60357i q^{69} +(1.61299 + 3.42073i) q^{70} +4.61114i q^{71} +(2.58966 + 15.2849i) 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} +(-2.25546 - 3.44600i) q^{78} -2.19111 q^{79} +(1.57442 - 8.80461i) q^{80} -4.59860 q^{81} +(4.34616 + 6.64027i) 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} +(1.98248 + 11.7011i) q^{88} -15.0102i q^{89} +(16.3125 + 5.85823i) q^{90} -1.19596i q^{91} +(1.02527 - 0.402020i) 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} +(6.59056 - 4.31362i) 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 $

$2$	−0.774482	−	1.18329i	−0.547642	−	0.836713i
$2$	−0.774482	−	1.18329i	−0.547642	−	0.836713i
$3$	−2.05925	−	2.05925i	−1.18891	−	1.18891i	−0.977369	−	0.211540i	$-0.932152\pi$
$3$	−2.05925	−	2.05925i	−1.18891	−	1.18891i	−0.211540	−	0.977369i	$-0.567848\pi$
$4$	−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	$-0.822570\pi$
$7$	−0.845670	+	0.845670i	−0.319633	+	0.319633i	0.528993	+	0.848626i	$0.322570\pi$
$8$	2.78869	−	0.472478i	0.985949	−	0.167046i
$9$			5.48103i			1.82701i
$10$	1.06882	−	2.97618i	0.337990	−	0.941150i
$11$			4.19592i			1.26512i	0.774512	+	0.632559i	$0.217995\pi$
$11$			4.19592i			1.26512i	−0.774512	+	0.632559i	$0.782005\pi$
$12$	5.42248	−	2.12622i	1.56534	−	0.613787i
$13$	−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	$0.761252\pi$
$18$	6.48565	−	4.24496i	1.52868	−	1.00055i
$19$	4.84005			1.11038			0.555192	−	0.831722i	$-0.312645\pi$
$19$	4.84005			1.11038			0.555192	+	0.831722i	$0.312645\pi$
$20$	−4.34946	+	1.04027i	−0.972570	+	0.232612i
$21$	3.48290			0.760030
$22$	4.96499	−	3.24967i	1.05854	−	0.692831i
$23$	−0.389358	−	0.389358i	−0.0811867	−	0.0811867i	0.665347	−	0.746534i	$-0.268283\pi$
$23$	−0.389358	−	0.389358i	−0.0811867	−	0.0811867i	−0.746534	+	0.665347i	$0.768283\pi$
$24$	−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
$28$	−0.873173	−	2.22684i	−0.165014	−	0.420834i
$29$		−	6.55621i		−	1.21746i	−0.793379	−	0.608728i	$-0.791680\pi$
$29$		−	6.55621i		−	1.21746i	0.793379	−	0.608728i	$-0.208320\pi$
$30$	−8.32966	+	3.92773i	−1.52078	+	0.717101i
$31$			5.06902i			0.910423i	0.890383	+	0.455211i	$0.150436\pi$
$31$			5.06902i			0.910423i	−0.890383	+	0.455211i	$0.849564\pi$
$32$	−1.36594	+	5.48946i	−0.241467	+	0.970409i
$33$	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	$0.301151\pi$
$38$	−3.74853	−	5.72719i	−0.608093	−	0.929073i
$39$	2.91222			0.466329
$40$	4.59953	+	4.34101i	0.727249	+	0.686374i
$41$	−5.61170			−0.876400			−0.438200	−	0.898877i	$-0.644384\pi$
$41$	−5.61170			−0.876400			−0.438200	+	0.898877i	$0.644384\pi$
$42$	−2.69744	−	4.12128i	−0.416224	−	0.635927i
$43$	3.25094	+	3.25094i	0.495763	+	0.495763i	0.910116	−	0.414353i	$-0.135992\pi$
$43$	3.25094	+	3.25094i	0.495763	+	0.495763i	−0.414353	+	0.910116i	$0.635992\pi$
$44$	−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	$0.621131\pi$
$47$	−8.91159	+	8.91159i	−1.29989	+	1.29989i	−0.928462	+	0.371427i	$0.878869\pi$
$48$	−0.442809	+	11.6405i	−0.0639140	+	1.68016i
$49$			5.56968i			0.795669i
$50$	6.75170	−	2.10107i	0.954835	−	0.297136i
$51$			0.848694i			0.118841i
$52$	−0.730103	−	1.86197i	−0.101247	−	0.258209i
$53$	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
$58$	−7.75790	+	5.07767i	−1.01866	+	0.666730i
$59$	10.9539			1.42608			0.713038	−	0.701125i	$-0.247319\pi$
$59$	10.9539			1.42608			0.713038	+	0.701125i	$0.247319\pi$
$60$	11.0988	+	6.81446i	1.43285	+	0.879743i
$61$	−3.57989			−0.458357			−0.229179	−	0.973384i	$-0.573604\pi$
$61$	−3.57989			−0.458357			−0.229179	+	0.973384i	$0.573604\pi$
$62$	5.99812	−	3.92586i	0.761762	−	0.498585i
$63$	−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	$-0.544680\pi$
$67$	6.95966	−	6.95966i	0.850258	−	0.850258i	0.990165	+	0.139907i	$0.0446802\pi$
$68$	0.542626	−	0.212770i	0.0658031	−	0.0258022i
$69$			1.60357i			0.193047i
$70$	1.61299	+	3.42073i	0.192790	+	0.408856i
$71$			4.61114i			0.547241i	0.961838	+	0.273621i	$0.0882213\pi$
$71$			4.61114i			0.547241i	−0.961838	+	0.273621i	$0.911779\pi$
$72$	2.58966	+	15.2849i	0.305195	+	1.80134i
$73$	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
$78$	−2.25546	−	3.44600i	−0.255381	−	0.390183i
$79$	−2.19111			−0.246519			−0.123259	−	0.992374i	$-0.539335\pi$
$79$	−2.19111			−0.246519			−0.123259	+	0.992374i	$0.539335\pi$
$80$	1.57442	−	8.80461i	0.176026	−	0.984386i
$81$	−4.59860			−0.510955
$82$	4.34616	+	6.64027i	0.479953	+	0.733295i
$83$	−11.1906	−	11.1906i	−1.22832	−	1.22832i	−0.964598	−	0.263725i	$-0.915049\pi$
$83$	−11.1906	−	11.1906i	−1.22832	−	1.22832i	−0.263725	−	0.964598i	$-0.584951\pi$
$84$	−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
$88$	1.98248	+	11.7011i	0.211333	+	1.24734i
$89$		−	15.0102i		−	1.59108i	−0.605902	−	0.795540i	$-0.707188\pi$
$89$		−	15.0102i		−	1.59108i	0.605902	−	0.795540i	$-0.292812\pi$
$90$	16.3125	+	5.85823i	1.71949	+	0.617512i
$91$		−	1.19596i		−	0.125371i
$92$	1.02527	−	0.402020i	0.106892	−	0.0419135i
$93$	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	$0.879467\pi$
$98$	6.59056	−	4.31362i	0.665747	−	0.435742i
$99$	−22.9980			−2.31138
$100$	−7.71525	−	6.36199i	−0.771525	−	0.636199i
$101$	6.35464			0.632310			0.316155	−	0.948708i	$-0.397608\pi$
$101$	6.35464			0.632310			0.316155	+	0.948708i	$0.397608\pi$
$102$	1.00425	−	0.657299i	0.0994358	−	0.0650823i
$103$	−2.93721	−	2.93721i	−0.289412	−	0.289412i	0.547436	−	0.836848i	$-0.315604\pi$
$103$	−2.93721	−	2.93721i	−0.289412	−	0.289412i	−0.836848	+	0.547436i	$0.815604\pi$
$104$	−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	$-0.872890\pi$
$107$	−5.50848	+	5.50848i	−0.532525	+	0.532525i	0.388798	+	0.921323i	$0.372890\pi$
$108$	5.27522	+	13.4533i	0.507608	+	1.29455i
$109$			8.20270i			0.785676i	0.919608	+	0.392838i	$0.128507\pi$
$109$			8.20270i			0.785676i	−0.919608	+	0.392838i	$0.871493\pi$
$110$	12.4878	+	4.48468i	1.19066	+	0.427598i
$111$		−	34.9722i		−	3.31942i
$112$	4.78038	+	0.181848i	0.451703	+	0.0171830i
$113$	−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
$118$	−8.48360	−	12.9617i	−0.780979	−	1.19322i
$119$	0.348532			0.0319499
$120$	−0.532352	−	18.4108i	−0.0485969	−	1.68067i
$121$	−6.60574			−0.600522
$122$	2.77256	+	4.23605i	0.251016	+	0.383514i
$123$	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	$-0.875795\pi$
$127$	−6.13573	+	6.13573i	−0.544458	+	0.544458i	0.380375	+	0.924832i	$0.375795\pi$
$128$	−8.96826	−	6.89712i	−0.792690	−	0.609625i
$129$		−	13.3890i		−	1.17884i
$130$	1.34870	+	2.86024i	0.118289	+	0.250860i
$131$			2.46129i			0.215043i	0.994203	+	0.107522i	$0.0342915\pi$
$131$			2.46129i			0.215043i	−0.994203	+	0.107522i	$0.965708\pi$
$132$	8.92145	+	22.7523i	0.776513	+	1.98033i
$133$	−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	$0.770126\pi$
$138$	1.89749	−	1.24194i	0.161525	−	0.105721i
$139$	4.32728			0.367035			0.183517	−	0.983016i	$-0.441252\pi$
$139$	4.32728			0.367035			0.183517	+	0.983016i	$0.441252\pi$
$140$	2.79849	−	4.55794i	0.236515	−	0.385216i
$141$	36.7024			3.09090
$142$	5.45632	−	3.57124i	0.457884	−	0.299692i
$143$	−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
$148$	−22.3601	+	8.76765i	−1.83799	+	0.720696i
$149$		−	0.356765i		−	0.0292274i	−0.999893	−	0.0146137i	$-0.995348\pi$
$149$		−	0.356765i		−	0.0292274i	0.999893	−	0.0146137i	$-0.00465185\pi$
$150$	−18.2301	−	9.57683i	−1.48848	−	0.781945i
$151$			1.46387i			0.119128i	0.998224	+	0.0595642i	$0.0189711\pi$
$151$			1.46387i			0.119128i	−0.998224	+	0.0595642i	$0.981029\pi$
$152$	13.4974	−	2.28682i	1.09478	−	0.185485i
$153$	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	$0.718272\pi$
$158$	1.69697	+	2.59272i	0.135004	+	0.206265i
$159$	−0.294085			−0.0233225
$160$	−11.6378	+	4.95601i	−0.920047	+	0.391807i
$161$	0.658536			0.0518999
$162$	3.56153	+	5.44148i	0.279821	+	0.427523i
$163$	11.1949	+	11.1949i	0.876851	+	0.876851i	0.993207	−	0.116357i	$-0.0371216\pi$
$163$	11.1949	+	11.1949i	0.876851	+	0.876851i	−0.116357	+	0.993207i	$0.537122\pi$
$164$	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	$-0.432226\pi$
$167$	15.3618	−	15.3618i	1.18873	−	1.18873i	0.977418	−	0.211315i	$-0.0677745\pi$
$168$	9.71270	−	1.64559i	0.749351	−	0.126960i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.833547	+	0.393047i	−0.0639301	+	0.0301453i
$171$			26.5285i			2.02868i
$172$	−8.56047	+	3.35666i	−0.652730	+	0.255943i
$173$	−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
$178$	−17.7614	+	11.6251i	−1.33128	+	0.871341i
$179$	−12.1671			−0.909411			−0.454705	−	0.890642i	$-0.650255\pi$
$179$	−12.1671			−0.909411			−0.454705	+	0.890642i	$0.650255\pi$
$180$	−5.70176	−	23.8395i	−0.424984	−	1.77689i
$181$	13.0663			0.971209			0.485605	−	0.874179i	$-0.338599\pi$
$181$	13.0663			0.971209			0.485605	+	0.874179i	$0.338599\pi$
$182$	−1.41517	+	0.926249i	−0.104899	+	0.0686581i
$183$	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
$188$	−9.20141	−	23.4663i	−0.671082	−	1.71145i
$189$			8.64117i			0.628552i
$190$	5.17314	−	14.4048i	0.375299	−	1.04504i
$191$		−	13.9391i		−	1.00860i	−0.863529	−	0.504300i	$-0.831751\pi$
$191$		−	13.9391i		−	1.00860i	0.863529	−	0.504300i	$-0.168249\pi$
$192$	−20.9811	−	10.1281i	−1.51418	−	0.730933i
$193$	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	$0.986330\pi$
$198$	17.8115	+	27.2133i	1.26581	+	1.93396i
$199$	8.20575			0.581690			0.290845	−	0.956770i	$-0.406064\pi$
$199$	8.20575			0.581690			0.290845	+	0.956770i	$0.406064\pi$
$200$	−1.55276	+	14.0566i	−0.109797	+	0.993954i
$201$	−28.6634			−2.02176
$202$	−4.92156	−	7.51939i	−0.346279	−	0.529062i
$203$	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
$208$	3.99711	+	0.152052i	0.277150	+	0.0105429i
$209$			20.3085i			1.40477i
$210$	3.72259	−	10.3657i	0.256883	−	0.715302i
$211$		−	9.25421i		−	0.637086i	−0.947908	−	0.318543i	$-0.896806\pi$
$211$		−	9.25421i		−	0.637086i	0.947908	−	0.318543i	$-0.103194\pi$
$212$	0.0737280	+	0.188028i	0.00506366	+	0.0129138i
$213$	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
$218$	9.70618	−	6.35285i	0.657385	−	0.430269i
$219$	−10.6076			−0.716794
$220$	−4.36490	−	18.2500i	−0.294281	−	1.23041i
$221$	0.291425			0.0196034
$222$	−41.3823	+	27.0854i	−2.77740	+	1.81785i
$223$	0.454255	+	0.454255i	0.0304191	+	0.0304191i	0.722153	−	0.691734i	$-0.243153\pi$
$223$	0.454255	+	0.454255i	0.0304191	+	0.0304191i	−0.691734	+	0.722153i	$0.743153\pi$
$224$	−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	$-0.438072\pi$
$227$	17.6950	−	17.6950i	1.17446	−	1.17446i	0.981134	−	0.193327i	$-0.0619279\pi$
$228$	26.2451	−	10.2910i	1.73812	−	0.681539i
$229$		−	2.81751i		−	0.186186i	−0.995657	−	0.0930932i	$-0.970325\pi$
$229$		−	2.81751i		−	0.186186i	0.995657	−	0.0930932i	$-0.0296755\pi$
$230$	−1.57495	+	0.742644i	−0.103849	+	0.0489685i
$231$			14.6139i			0.961527i
$232$	−3.09766	−	18.2832i	−0.203371	−	1.20035i
$233$	−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
$238$	−0.269932	−	0.412415i	−0.0174971	−	0.0267329i
$239$	−0.438609			−0.0283713			−0.0141856	−	0.999899i	$-0.504516\pi$
$239$	−0.438609			−0.0283713			−0.0141856	+	0.999899i	$0.504516\pi$
$240$	−21.3730	+	14.8888i	−1.37962	+	0.961066i
$241$	−6.48281			−0.417594			−0.208797	−	0.977959i	$-0.566955\pi$
$241$	−6.48281			−0.417594			−0.208797	+	0.977959i	$0.566955\pi$
$242$	5.11603	+	7.81652i	0.328871	+	0.502465i
$243$	−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
$248$	2.39500	+	14.1359i	0.152083	+	0.897630i
$249$			46.0883i			2.92073i
$250$	12.8443	+	9.22082i	0.812346	+	0.583176i
$251$		−	17.3721i		−	1.09652i	−0.836309	−	0.548259i	$-0.815291\pi$
$251$		−	17.3721i		−	1.09652i	0.836309	−	0.548259i	$-0.184709\pi$
$252$	12.2054	−	4.78589i	0.768868	−	0.301482i
$253$	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	$0.557567\pi$
$258$	−15.8431	+	10.3695i	−0.986347	+	0.645579i
$259$	−14.3620			−0.892412
$260$	2.33995	−	3.81112i	0.145118	−	0.236356i
$261$	35.9348			2.22431
$262$	2.91242	−	1.90622i	0.179930	−	0.117767i
$263$	17.7105	+	17.7105i	1.09208	+	1.09208i	0.995307	+	0.0967688i	$0.0308507\pi$
$263$	17.7105	+	17.7105i	1.09208	+	1.09208i	0.0967688	+	0.995307i	$0.469149\pi$
$264$	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
$268$	7.18600	+	18.3264i	0.438955	+	1.11946i
$269$			9.90226i			0.603752i	0.953347	+	0.301876i	$0.0976128\pi$
$269$			9.90226i			0.603752i	−0.953347	+	0.301876i	$0.902387\pi$
$270$	−9.74481	−	20.6661i	−0.593050	−	1.25770i
$271$		−	23.2048i		−	1.40959i	−0.709409	−	0.704797i	$-0.751038\pi$
$271$		−	23.2048i		−	1.40959i	0.709409	−	0.704797i	$-0.248962\pi$
$272$	−0.0443118	+	1.16486i	−0.00268680	+	0.0706299i
$273$	−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	$0.533099\pi$
$278$	−3.35140	−	5.12043i	−0.201004	−	0.307103i
$279$	−27.7834			−1.66335
$280$	−7.56075	+	0.218620i	−0.451841	+	0.0130651i
$281$	−0.130168			−0.00776516			−0.00388258	−	0.999992i	$-0.501236\pi$
$281$	−0.130168			−0.00776516			−0.00388258	+	0.999992i	$0.501236\pi$
$282$	−28.4254	−	43.4296i	−1.69271	−	2.58620i
$283$	−10.2040	−	10.2040i	−0.606564	−	0.606564i	0.335482	−	0.942047i	$-0.391101\pi$
$283$	−10.2040	−	10.2040i	−0.606564	−	0.606564i	−0.942047	+	0.335482i	$0.891101\pi$
$284$	−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
$288$	−30.0879	−	7.48678i	−1.77295	−	0.441163i
$289$		−	16.9151i		−	0.995004i
$290$	−19.5124	−	7.00740i	−1.14581	−	0.411489i
$291$			22.6939i			1.33034i
$292$	2.65935	+	6.78213i	0.155627	+	0.396894i
$293$	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
$298$	−0.422157	+	0.276309i	−0.0244549	+	0.0160061i
$299$	0.550635			0.0318440
$300$	2.78670	+	28.9886i	0.160890	+	1.67366i
$301$	−5.49844			−0.316925
$302$	1.73219	−	1.13374i	0.0996763	−	0.0652397i
$303$	−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	$-0.316256\pi$
$307$	24.2442	−	24.2442i	1.38369	−	1.38369i	0.837967	−	0.545721i	$-0.183744\pi$
$308$	9.34366	−	3.66376i	0.532404	−	0.208762i
$309$			12.0969i			0.688170i
$310$	15.0863	+	5.41787i	0.856844	+	0.307714i
$311$		−	11.5941i		−	0.657443i	−0.944427	−	0.328721i	$-0.893382\pi$
$311$		−	11.5941i		−	0.657443i	0.944427	−	0.328721i	$-0.106618\pi$
$312$	8.12127	−	1.37596i	0.459776	−	0.0778984i
$313$	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	$0.760961\pi$
$318$	0.227764	+	0.347988i	0.0127724	+	0.0195142i
$319$	27.5093			1.54023
$320$	14.8777	+	9.93253i	0.831687	+	0.555245i
$321$	22.6867			1.26625
$322$	−0.510025	−	0.779240i	−0.0284226	−	0.0434253i
$323$	−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
$328$	−15.6493	+	2.65140i	−0.864086	+	0.146399i
$329$		−	15.0725i		−	0.830976i
$330$	−16.4804	−	34.9506i	−0.907217	−	1.92397i
$331$			6.91111i			0.379869i	0.981797	+	0.189935i	$0.0608276\pi$
$331$			6.91111i			0.379869i	−0.981797	+	0.189935i	$0.939172\pi$
$332$	29.4673	−	11.5545i	1.61723	−	0.634135i
$333$	−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	$0.790812\pi$
$338$	−1.18329	+	0.774482i	−0.0643625	+	0.0421263i
$339$	25.6044			1.39064
$340$	1.11066	+	0.681921i	0.0602338	+	0.0369824i
$341$	−21.2692			−1.15179
$342$	31.3909	−	20.5458i	1.69743	−	1.11099i
$343$	−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	$-0.746394\pi$
$347$	0.298469	−	0.298469i	0.0160226	−	0.0160226i	0.715073	+	0.699050i	$0.246394\pi$
$348$	−13.9399	−	35.5509i	−0.747259	−	1.90573i
$349$			28.4804i			1.52452i	0.647271	+	0.762260i	$0.275910\pi$
$349$			28.4804i			1.52452i	−0.647271	+	0.762260i	$0.724090\pi$
$350$	−3.93291	+	7.48653i	−0.210223	+	0.400172i
$351$			7.22531i			0.385658i
$352$	−23.0333	−	5.73139i	−1.22768	−	0.305484i
$353$	−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
$358$	9.42319	+	14.3972i	0.498031	+	0.760916i
$359$	28.4805			1.50314			0.751572	−	0.659651i	$-0.229296\pi$
$359$	28.4805			1.50314			0.751572	+	0.659651i	$0.229296\pi$
$360$	−23.7932	+	25.2101i	−1.25401	+	1.32869i
$361$	4.42610			0.232953
$362$	−10.1196	−	15.4612i	−0.531875	−	0.812624i
$363$	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	$-0.946966\pi$
$367$	−15.7149	+	15.7149i	−0.820313	+	0.820313i	0.165840	+	0.986153i	$0.446966\pi$
$368$	−0.0837251	+	2.20095i	−0.00436447	+	0.114732i
$369$		−	30.7579i		−	1.60119i
$370$	34.3481	−	16.1963i	1.78567	−	0.842006i
$371$			0.120772i			0.00627015i
$372$	10.7778	+	27.4867i	0.558805	+	1.42512i
$373$	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
$378$	10.2250	−	6.69243i	0.525918	−	0.344221i
$379$	0.333137			0.0171121			0.00855604	−	0.999963i	$-0.497276\pi$
$379$	0.333137			0.0171121			0.00855604	+	0.999963i	$0.497276\pi$
$380$	−21.0516	+	5.03497i	−1.07993	+	0.258288i
$381$	25.2700			1.29462
$382$	−16.4940	+	10.7956i	−0.843909	+	0.552351i
$383$	8.70979	+	8.70979i	0.445050	+	0.445050i	0.893705	−	0.448655i	$-0.148097\pi$
$383$	8.70979	+	8.70979i	0.445050	+	0.445050i	−0.448655	+	0.893705i	$0.648097\pi$
$384$	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
$388$	14.5097	−	5.68944i	0.736619	−	0.288837i
$389$		−	15.7397i		−	0.798036i	−0.916943	−	0.399018i	$-0.869351\pi$
$389$		−	15.7397i		−	0.798036i	0.916943	−	0.399018i	$-0.130649\pi$
$390$	3.11264	−	8.66728i	0.157615	−	0.438885i
$391$			0.160469i			0.00811526i
$392$	2.63155	+	15.5321i	0.132913	+	0.784489i
$393$	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	$0.536848\pi$
$398$	−6.35521	−	9.70979i	−0.318558	−	0.486708i
$399$	16.8574			0.843925
$400$	17.8357	−	9.04925i	0.891784	−	0.452462i
$401$	1.23996			0.0619204			0.0309602	−	0.999521i	$-0.490143\pi$
$401$	1.23996			0.0619204			0.0309602	+	0.999521i	$0.490143\pi$
$402$	22.1993	+	33.9171i	1.10720	+	1.69163i
$403$	−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
$408$	0.400989	+	2.36674i	0.0198519	+	0.117171i
$409$		−	13.6662i		−	0.675749i	−0.941191	−	0.337875i	$-0.890292\pi$
$409$		−	13.6662i		−	0.675749i	0.941191	−	0.337875i	$-0.109708\pi$
$410$	−5.99789	+	16.7014i	−0.296215	+	0.824824i
$411$			4.30749i			0.212473i
$412$	7.73436	−	3.03274i	0.381045	−	0.149412i
$413$	−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
$418$	24.0308	−	15.7285i	1.17539	−	0.769309i
$419$	30.4429			1.48723			0.743617	−	0.668605i	$-0.233108\pi$
$419$	30.4429			1.48723			0.743617	+	0.668605i	$0.233108\pi$
$420$	−15.1487	+	3.62316i	−0.739182	+	0.176792i
$421$	−30.0550			−1.46479			−0.732396	−	0.680878i	$-0.761598\pi$
$421$	−30.0550			−1.46479			−0.732396	+	0.680878i	$0.761598\pi$
$422$	−10.9504	+	7.16722i	−0.533058	+	0.348895i
$423$	−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
$428$	−5.68762	−	14.5051i	−0.274922	−	0.701130i
$429$			12.2194i			0.589960i
$430$	13.1500	−	6.20070i	0.634151	−	0.299024i
$431$			29.7403i			1.43254i	0.697822	+	0.716271i	$0.254153\pi$
$431$			29.7403i			1.43254i	−0.697822	+	0.716271i	$0.745847\pi$
$432$	−28.8803	−	1.09862i	−1.38951	−	0.0528575i
$433$	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
$438$	8.21539	+	12.5519i	0.392546	+	0.599751i
$439$	18.8341			0.898901			0.449450	−	0.893305i	$-0.351620\pi$
$439$	18.8341			0.898901			0.449450	+	0.893305i	$0.351620\pi$
$440$	−18.2145	+	19.2992i	−0.868343	+	0.920055i
$441$	−30.5276			−1.45370
$442$	−0.225704	−	0.344841i	−0.0107356	−	0.0164024i
$443$	12.6851	+	12.6851i	0.602687	+	0.602687i	0.941025	−	0.338338i	$-0.109865\pi$
$443$	12.6851	+	12.6851i	0.602687	+	0.602687i	−0.338338	+	0.941025i	$0.609865\pi$
$444$	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
$448$	−4.15930	+	8.61629i	−0.196508	+	0.407082i
$449$		−	15.8773i		−	0.749297i	−0.927167	−	0.374648i	$-0.877763\pi$
$449$		−	15.8773i		−	0.749297i	0.927167	−	0.374648i	$-0.122237\pi$
$450$	11.5160	+	37.0063i	0.542870	+	1.74449i
$451$		−	23.5462i		−	1.10875i
$452$	−6.41909	−	16.3706i	−0.301929	−	0.770006i
$453$	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	$0.590510\pi$
$458$	−3.33394	+	2.18211i	−0.155785	+	0.101963i
$459$	−2.10564			−0.0982827
$460$	2.09853	+	1.28846i	0.0978446	+	0.0600747i
$461$	6.30338			0.293578			0.146789	−	0.989168i	$-0.453106\pi$
$461$	6.30338			0.293578			0.146789	+	0.989168i	$0.453106\pi$
$462$	17.2926	−	11.3182i	0.804522	−	0.526572i
$463$	20.4903	+	20.4903i	0.952265	+	0.952265i	0.998911	−	0.0466465i	$-0.0148534\pi$
$463$	20.4903	+	20.4903i	0.952265	+	0.952265i	−0.0466465	+	0.998911i	$0.514853\pi$
$464$	−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	$-0.871626\pi$
$467$	−11.3954	+	11.3954i	−0.527315	+	0.527315i	0.392456	+	0.919771i	$0.371626\pi$
$468$	10.2055	−	4.00172i	0.471751	−	0.184979i
$469$			11.7712i			0.543542i
$470$	16.9976	+	36.0473i	0.784040	+	1.66274i
$471$		−	7.26233i		−	0.334630i
$472$	30.5470	−	5.17547i	1.40604	−	0.238221i
$473$	−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
$478$	0.339695	+	0.519002i	0.0155373	+	0.0237386i
$479$	−27.1128			−1.23881			−0.619407	−	0.785070i	$-0.712627\pi$
$479$	−27.1128			−1.23881			−0.619407	+	0.785070i	$0.712627\pi$
$480$	34.1708	+	13.7594i	1.55968	+	0.628029i
$481$	−12.0088			−0.547554
$482$	5.02082	+	7.67105i	0.228692	+	0.349407i
$483$	−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	$-0.812452\pi$
$487$	−6.08398	+	6.08398i	−0.275692	+	0.275692i	0.555695	+	0.831386i	$0.312452\pi$
$488$	−9.98317	+	1.69142i	−0.451917	+	0.0765668i
$489$		−	46.1061i		−	2.08499i
$490$	16.5764	+	5.95299i	0.748844	+	0.268929i
$491$		−	28.1664i		−	1.27113i	−0.772046	−	0.635567i	$-0.780767\pi$
$491$		−	28.1664i		−	1.27113i	0.772046	−	0.635567i	$-0.219233\pi$
$492$	−30.4293	+	11.9317i	−1.37186	+	0.537923i
$493$	−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
$498$	54.5359	−	35.6946i	2.44381	−	1.59951i
$499$	−19.3231			−0.865023			−0.432511	−	0.901629i	$-0.642372\pi$
$499$	−19.3231			−0.865023			−0.432511	+	0.901629i	$0.642372\pi$
$500$	0.963208	−	22.3399i	0.0430760	−	0.999072i
$501$	−63.2677			−2.82659
$502$	−20.5563	+	13.4544i	−0.917471	+	0.600499i
$503$	−5.39116	−	5.39116i	−0.240380	−	0.240380i	0.576627	−	0.817007i	$-0.304368\pi$
$503$	−5.39116	−	5.39116i	−0.240380	−	0.240380i	−0.817007	+	0.576627i	$0.804368\pi$
$504$	−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
$508$	−6.33527	−	16.1568i	−0.281082	−	0.716841i
$509$		−	14.1691i		−	0.628033i	−0.949417	−	0.314017i	$-0.898325\pi$
$509$		−	14.1691i		−	0.628033i	0.949417	−	0.314017i	$-0.101675\pi$
$510$	2.52586	+	0.907101i	0.111847	+	0.0401671i
$511$			4.35620i			0.192707i
$512$	19.8193	−	10.9176i	0.875900	−	0.482493i
$513$	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
$518$	11.1231	+	16.9944i	0.488722	+	0.746693i
$519$	29.2300			1.28306
$520$	−6.32191	+	0.182799i	−0.277234	+	0.00801628i
$521$	18.4923			0.810164			0.405082	−	0.914280i	$-0.367243\pi$
$521$	18.4923			0.810164			0.405082	+	0.914280i	$0.367243\pi$
$522$	−27.8308	−	42.5213i	−1.21812	−	1.86111i
$523$	−3.63846	−	3.63846i	−0.159099	−	0.159099i	0.623069	−	0.782167i	$-0.285886\pi$
$523$	−3.63846	−	3.63846i	−0.159099	−	0.159099i	−0.782167	+	0.623069i	$0.785886\pi$
$524$	−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
$528$	−48.8425	−	1.85799i	−2.12559	−	0.0808587i
$529$		−	22.6968i		−	0.986817i
$530$	−0.136196	−	0.288836i	−0.00591599	−	0.0125462i
$531$			60.0387i			2.60546i
$532$	−4.22620	−	10.7780i	−0.183229	−	0.467287i
$533$	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
$538$	11.7173	−	7.66913i	0.505167	−	0.330640i
$539$	−23.3699			−1.00661
$540$	−16.9069	+	27.5365i	−0.727556	+	1.18498i
$541$	12.8284			0.551535			0.275767	−	0.961224i	$-0.411068\pi$
$541$	12.8284			0.551535			0.275767	+	0.961224i	$0.411068\pi$
$542$	−27.4581	+	17.9717i	−1.17943	+	0.771952i
$543$	−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	$-0.590737\pi$
$547$	15.8672	−	15.8672i	0.678431	−	0.678431i	0.959645	+	0.281214i	$0.0907370\pi$
$548$	2.75406	−	1.07990i	0.117648	−	0.0461310i
$549$		−	19.6215i		−	0.837423i
$550$	8.81591	+	28.3296i	0.375912	+	1.20798i
$551$		−	31.7324i		−	1.35184i
$552$	0.757651	+	4.47185i	0.0322478	+	0.190335i
$553$	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	$0.793131\pi$
$558$	21.5178	+	32.8759i	0.910920	+	1.39175i
$559$	−4.59752			−0.194454
$560$	6.11435	+	8.77724i	0.258379	+	0.370906i
$561$	−3.56105			−0.150348
$562$	0.100813	+	0.154026i	0.00425252	+	0.00649721i
$563$	7.11349	+	7.11349i	0.299798	+	0.299798i	0.840935	−	0.541137i	$-0.182006\pi$
$563$	7.11349	+	7.11349i	0.299798	+	0.299798i	−0.541137	+	0.840935i	$0.682006\pi$
$564$	−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
$568$	2.17866	+	12.8590i	0.0914146	+	0.539552i
$569$		−	18.4963i		−	0.775404i	−0.921785	−	0.387702i	$-0.873269\pi$
$569$		−	18.4963i		−	0.775404i	0.921785	−	0.387702i	$-0.126731\pi$
$570$	−40.3160	+	19.0104i	−1.68865	+	0.796258i
$571$			31.1985i			1.30562i	0.757523	+	0.652808i	$0.226409\pi$
$571$			31.1985i			1.30562i	−0.757523	+	0.652808i	$0.773591\pi$
$572$	7.81270	−	3.06345i	0.326665	−	0.128089i
$573$	−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	$0.531784\pi$
$578$	−20.0154	+	13.1004i	−0.832533	+	0.544906i
$579$	−18.8029			−0.781423
$580$	6.82023	+	28.5160i	0.283195	+	1.18406i
$581$	18.9270			0.785226
$582$	26.8535	−	17.5760i	1.11311	−	0.728550i
$583$	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	$-0.730228\pi$
$587$	2.12698	−	2.12698i	0.0877898	−	0.0877898i	0.749638	+	0.661848i	$0.230228\pi$
$588$	11.8424	+	30.2015i	0.488371	+	1.24549i
$589$			24.5343i			1.01092i
$590$	11.7077	−	32.6007i	0.482000	−	1.34215i
$591$			55.2708i			2.27354i
$592$	1.82596	−	48.0004i	0.0750465	−	1.97281i
$593$	−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
$598$	−0.426457	−	0.651561i	−0.0174391	−	0.0266443i
$599$	−31.8821			−1.30267			−0.651334	−	0.758791i	$-0.725790\pi$
$599$	−31.8821			−1.30267			−0.651334	+	0.758791i	$0.725790\pi$
$600$	32.1437	−	25.7486i	1.31226	−	1.05118i
$601$	−36.5855			−1.49236			−0.746178	−	0.665747i	$-0.768113\pi$
$601$	−36.5855			−1.49236			−0.746178	+	0.665747i	$0.768113\pi$
$602$	4.25845	+	6.50626i	0.173561	+	0.265175i
$603$	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	$-0.831191\pi$
$607$	−8.79118	+	8.79118i	−0.356823	+	0.356823i	0.505818	+	0.862640i	$0.331191\pi$
$608$	−6.61124	+	26.5693i	−0.268121	+	1.07753i
$609$		−	22.8346i		−	0.925304i
$610$	−3.82625	+	10.6544i	−0.154920	+	0.431383i
$611$		−	12.6029i		−	0.509858i
$612$	1.16620	+	2.97415i	0.0471409	+	0.120223i
$613$	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	$0.600331\pi$
$618$	14.3142	−	9.36885i	0.575801	−	0.376870i
$619$	−6.47284			−0.260165			−0.130083	−	0.991503i	$-0.541524\pi$
$619$	−6.47284			−0.260165			−0.130083	+	0.991503i	$0.541524\pi$
$620$	−5.27315	−	22.0475i	−0.211775	−	0.885449i
$621$	−3.97850			−0.159652
$622$	−13.7192	+	8.97945i	−0.550091	+	0.360043i
$623$	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
$628$	−4.64328	+	1.82069i	−0.185287	+	0.0726533i
$629$		−	3.49966i		−	0.139541i
$630$	−18.7491	+	8.84087i	−0.746984	+	0.352229i
$631$			38.0648i			1.51533i	0.652641	+	0.757667i	$0.273661\pi$
$631$			38.0648i			1.51533i	−0.652641	+	0.757667i	$0.726339\pi$
$632$	−6.11031	+	1.03525i	−0.243055	+	0.0411800i
$633$	−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
$638$	−21.3055	−	32.5515i	−0.843492	−	1.28873i
$639$	−25.2738			−0.999816
$640$	0.230590	−	25.2972i	0.00911488	−	0.999958i
$641$	2.47864			0.0979003			0.0489501	−	0.998801i	$-0.484412\pi$
$641$	2.47864			0.0979003			0.0489501	+	0.998801i	$0.484412\pi$
$642$	−17.5704	−	26.8449i	−0.693450	−	1.05949i
$643$	−22.2075	−	22.2075i	−0.875780	−	0.875780i	0.117315	−	0.993095i	$-0.462571\pi$
$643$	−22.2075	−	22.2075i	−0.875780	−	0.875780i	−0.993095	+	0.117315i	$0.962571\pi$
$644$	−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	$-0.567105\pi$
$647$	19.5503	−	19.5503i	0.768603	−	0.768603i	0.977861	+	0.209258i	$0.0671048\pi$
$648$	−12.8240	+	2.17274i	−0.503776	+	0.0853531i
$649$			45.9617i			1.80415i
$650$	−3.28850	+	6.25986i	−0.128985	+	0.245532i
$651$			17.6549i			0.691948i
$652$	−29.4787	+	11.5590i	−1.15447	+	0.452683i
$653$	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
$658$	−17.8352	+	11.6734i	−0.695288	+	0.455077i
$659$	−1.00511			−0.0391535			−0.0195767	−	0.999808i	$-0.506232\pi$
$659$	−1.00511			−0.0391535			−0.0195767	+	0.999808i	$0.506232\pi$
$660$	−28.5929	+	46.5698i	−1.11298	+	1.81273i
$661$	−5.91229			−0.229961			−0.114981	−	0.993368i	$-0.536681\pi$
$661$	−5.91229			−0.229961			−0.114981	+	0.993368i	$0.536681\pi$
$662$	8.17786	−	5.35254i	0.317841	−	0.208032i
$663$	−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
$668$	15.8614	+	40.4512i	0.613696	+	1.56510i
$669$		−	1.87085i		−	0.0723312i
$670$	−13.2746	−	28.1518i	−0.512841	−	1.08760i
$671$		−	15.0209i		−	0.579876i
$672$	−4.75744	+	19.1192i	−0.183522	+	0.737540i
$673$	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	$0.634910\pi$
$678$	−19.8301	−	30.2974i	−0.761571	−	1.16357i
$679$	9.31969			0.357657
$680$	−0.0532723	−	1.84236i	−0.00204290	−	0.0706515i
$681$	−72.8771			−2.79266
$682$	16.4726	+	25.1676i	0.630769	+	0.963719i
$683$	5.53879	+	5.53879i	0.211936	+	0.211936i	0.805089	−	0.593153i	$-0.202117\pi$
$683$	5.53879	+	5.53879i	0.211936	+	0.211936i	−0.593153	+	0.805089i	$0.702117\pi$
$684$	−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
$688$	0.699062	−	18.3768i	0.0266515	−	0.700609i
$689$			0.100983i			0.00384715i
$690$	4.77251	+	1.71393i	0.181686	+	0.0652481i
$691$		−	24.6693i		−	0.938466i	−0.883074	−	0.469233i	$-0.844530\pi$
$691$		−	24.6693i		−	0.938466i	0.883074	−	0.469233i	$-0.155470\pi$
$692$	−7.32806	−	18.6887i	−0.278571	−	0.710437i
$693$	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
$698$	33.7006	−	22.0575i	1.27559	−	0.834890i
$699$	45.4325			1.71841
$700$	11.9047	−	1.14441i	0.449956	−	0.0432546i
$701$	−10.8183			−0.408603			−0.204302	−	0.978908i	$-0.565492\pi$
$701$	−10.8183			−0.408603			−0.204302	+	0.978908i	$0.565492\pi$
$702$	8.54964	−	5.59587i	0.322685	−	0.211203i
$703$	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
$708$	59.3973	−	23.2904i	2.23229	−	0.875307i
$709$			26.0040i			0.976601i	0.872676	+	0.488300i	$0.162383\pi$
$709$			26.0040i			0.976601i	−0.872676	+	0.488300i	$0.837617\pi$
$710$	13.7236	+	4.92847i	0.515036	+	0.184962i
$711$		−	12.0095i		−	0.450392i
$712$	−7.09199	−	41.8587i	−0.265784	−	1.56872i
$713$	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
$718$	−22.0577	−	33.7007i	−0.823184	−	1.25770i
$719$	−30.3758			−1.13283			−0.566413	−	0.824122i	$-0.691669\pi$
$719$	−30.3758			−1.13283			−0.566413	+	0.824122i	$0.691669\pi$
$720$	48.2583	+	8.62947i	1.79848	+	0.321601i
$721$	4.96783			0.185012
$722$	−3.42794	−	5.23736i	−0.127575	−	0.194914i
$723$	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	$-0.750105\pi$
$727$	−0.0125971	+	0.0125971i	−0.000467201	+	0.000467201i	0.706873	+	0.707340i	$0.250105\pi$
$728$	−0.565064	−	3.33515i	−0.0209427	−	0.123609i
$729$			37.9200i			1.40444i
$730$	−4.91257	−	10.4183i	−0.181823	−	0.385597i
$731$		−	1.33983i		−	0.0495555i
$732$	−19.4119	+	7.61163i	−0.717483	+	0.281334i
$733$	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
$738$	−36.3955	+	23.8214i	−1.33974	+	0.876879i
$739$	1.06565			0.0392006			0.0196003	−	0.999808i	$-0.493761\pi$
$739$	1.06565			0.0392006			0.0196003	+	0.999808i	$0.493761\pi$
$740$	−45.7669	−	28.1000i	−1.68242	−	1.03298i
$741$	14.0953			0.517804
$742$	0.142908	−	0.0935354i	0.00524631	−	0.00343379i
$743$	−1.75392	−	1.75392i	−0.0643452	−	0.0643452i	0.674202	−	0.738547i	$-0.264488\pi$
$743$	−1.75392	−	1.75392i	−0.0643452	−	0.0643452i	−0.738547	+	0.674202i	$0.764488\pi$
$744$	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
$748$	0.892767	+	2.27682i	0.0326428	+	0.0832487i
$749$		−	9.31671i		−	0.340425i
$750$	−7.46170	−	45.4377i	−0.272463	−	1.65915i
$751$		−	10.4197i		−	0.380220i	−0.981763	−	0.190110i	$-0.939115\pi$
$751$		−	10.4197i		−	0.380220i	0.981763	−	0.190110i	$-0.0608845\pi$
$752$	50.3751	+	1.91629i	1.83699	+	0.0698801i
$753$	−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	$0.734602\pi$
$758$	−0.258008	−	0.394198i	−0.00937129	−	0.0143179i
$759$	−6.72845			−0.244227
$760$	22.2619	+	21.0107i	0.807526	+	0.762138i
$761$	45.0253			1.63216			0.816082	−	0.577935i	$-0.196141\pi$
$761$	45.0253			1.63216			0.816082	+	0.577935i	$0.196141\pi$
$762$	−19.5712	−	29.9018i	−0.708989	−	1.08323i
$763$	−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
$768$	35.3559	−	30.3497i	1.27580	−	1.09515i
$769$		−	40.0379i		−	1.44380i	−0.691996	−	0.721902i	$-0.743268\pi$
$769$		−	40.0379i		−	1.44380i	0.691996	−	0.721902i	$-0.256732\pi$
$770$	−14.3531	+	6.76800i	−0.517251	+	0.243902i
$771$		−	53.0722i		−	1.91135i
$772$	4.71395	+	12.0219i	0.169659	+	0.432679i

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)

\(f(q)\)	\(=\)	\(q+(-0.774482 - 1.18329i) q^{2} +(-2.05925 - 2.05925i) q^{3} +(-0.800354 + 1.83288i) q^{4} +(1.34695 + 1.78486i) q^{5} +(-0.841839 + 4.03155i) q^{6} +(-0.845670 + 0.845670i) q^{7} +(2.78869 - 0.472478i) q^{8} +5.48103i q^{9} +O(q^{10})\)	\(q+(-0.774482 - 1.18329i) 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} +(2.78869 - 0.472478i) q^{8} +5.48103i q^{9} +(1.06882 - 2.97618i) q^{10} +4.19592i q^{11} +(5.42248 - 2.12622i) 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} +(6.48565 - 4.24496i) q^{18} +4.84005 q^{19} +(-4.34946 + 1.04027i) q^{20} +3.48290 q^{21} +(4.96499 - 3.24967i) 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} +(-0.873173 - 2.22684i) q^{28} -6.55621i q^{29} +(-8.32966 + 3.92773i) q^{30} +5.06902i q^{31} +(-1.36594 + 5.48946i) 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} +(-3.74853 - 5.72719i) q^{38} +2.91222 q^{39} +(4.59953 + 4.34101i) q^{40} -5.61170 q^{41} +(-2.69744 - 4.12128i) 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} +(-0.442809 + 11.6405i) q^{48} +5.56968i q^{49} +(6.75170 - 2.10107i) q^{50} +0.848694i q^{51} +(-0.730103 - 1.86197i) 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} +(-7.75790 + 5.07767i) q^{58} +10.9539 q^{59} +(11.0988 + 6.81446i) q^{60} -3.57989 q^{61} +(5.99812 - 3.92586i) 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} +(0.542626 - 0.212770i) q^{68} +1.60357i q^{69} +(1.61299 + 3.42073i) q^{70} +4.61114i q^{71} +(2.58966 + 15.2849i) 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} +(-2.25546 - 3.44600i) q^{78} -2.19111 q^{79} +(1.57442 - 8.80461i) q^{80} -4.59860 q^{81} +(4.34616 + 6.64027i) 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} +(1.98248 + 11.7011i) q^{88} -15.0102i q^{89} +(16.3125 + 5.85823i) q^{90} -1.19596i q^{91} +(1.02527 - 0.402020i) 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} +(6.59056 - 4.31362i) 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

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Database

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