LMFDB - Embedded newform 820.2.bv.c.103.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bv (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.11
Character	$\chi$	$=$	820.103
Dual form			820.2.bv.c.207.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37281 + 0.339686i) q^{2} -0.848586 q^{3} +(1.76923 - 0.932650i) q^{4} +(-2.22703 - 0.200823i) q^{5} +(1.16495 - 0.288253i) q^{6} +(-2.45926 + 0.799062i) q^{7} +(-2.11201 + 1.88134i) q^{8} -2.27990 q^{9} +(3.12551 - 0.480799i) q^{10} +(0.280850 - 1.77322i) q^{11} +(-1.50134 + 0.791434i) q^{12} +(-2.08177 - 0.676408i) q^{13} +(3.10467 - 1.93234i) q^{14} +(1.88983 + 0.170416i) q^{15} +(2.26033 - 3.30014i) q^{16} +(3.19795 + 4.40160i) q^{17} +(3.12988 - 0.774451i) q^{18} +(-6.06554 - 3.09055i) q^{19} +(-4.12742 + 1.72174i) q^{20} +(2.08689 - 0.678072i) q^{21} +(0.216783 + 2.52970i) q^{22} +(1.92814 + 3.78420i) q^{23} +(1.79222 - 1.59647i) q^{24} +(4.91934 + 0.894480i) q^{25} +(3.08765 + 0.221433i) q^{26} +4.48045 q^{27} +(-3.60574 + 3.70735i) q^{28} +(2.94682 - 0.466730i) q^{29} +(-2.65227 + 0.407999i) q^{30} +(-3.17243 - 4.36648i) q^{31} +(-1.98199 + 5.29827i) q^{32} +(-0.238326 + 1.50473i) q^{33} +(-5.88535 - 4.95627i) q^{34} +(5.63732 - 1.28566i) q^{35} +(-4.03366 + 2.12635i) q^{36} +(6.60307 - 1.04582i) q^{37} +(9.37666 + 2.18236i) q^{38} +(1.76656 + 0.573990i) q^{39} +(5.08132 - 3.76565i) q^{40} +(6.12880 + 1.85414i) q^{41} +(-2.63458 + 1.63975i) q^{42} +(-10.5365 + 5.36862i) q^{43} +(-1.15691 - 3.39916i) q^{44} +(5.07742 + 0.457858i) q^{45} +(-3.93242 - 4.54003i) q^{46} +(3.87605 - 11.9292i) q^{47} +(-1.91808 + 2.80045i) q^{48} +(-0.253659 + 0.184294i) q^{49} +(-7.05717 + 0.443078i) q^{50} +(-2.71373 - 3.73514i) q^{51} +(-4.31398 + 0.744844i) q^{52} +(0.202706 - 0.279001i) q^{53} +(-6.15082 + 1.52195i) q^{54} +(-0.981566 + 3.89261i) q^{55} +(3.69067 - 6.31432i) q^{56} +(5.14713 + 2.62259i) q^{57} +(-3.88688 + 1.64172i) q^{58} +(0.807500 - 2.48523i) q^{59} +(3.50247 - 1.46104i) q^{60} +(11.1131 - 3.61088i) q^{61} +(5.83839 + 4.91673i) q^{62} +(5.60687 - 1.82178i) q^{63} +(0.921155 - 7.94679i) q^{64} +(4.50033 + 1.92445i) q^{65} +(-0.183959 - 2.14666i) q^{66} +(2.51467 + 1.82702i) q^{67} +(9.76305 + 4.80486i) q^{68} +(-1.63620 - 3.21121i) q^{69} +(-7.30226 + 3.67989i) q^{70} +(-0.786938 + 4.96853i) q^{71} +(4.81517 - 4.28926i) q^{72} +(-5.24712 + 5.24712i) q^{73} +(-8.70953 + 3.67869i) q^{74} +(-4.17448 - 0.759043i) q^{75} +(-13.6137 + 0.189149i) q^{76} +(0.726228 + 4.58522i) q^{77} +(-2.62013 - 0.187905i) q^{78} +(10.3820 + 10.3820i) q^{79} +(-5.69656 + 6.89559i) q^{80} +3.03766 q^{81} +(-9.04351 - 0.463525i) q^{82} +(8.56967 - 8.56967i) q^{83} +(3.05978 - 3.14600i) q^{84} +(-6.23799 - 10.4447i) q^{85} +(12.6410 - 10.9492i) q^{86} +(-2.50063 + 0.396060i) q^{87} +(2.74286 + 4.27343i) q^{88} +(12.3575 + 6.29646i) q^{89} +(-7.12587 + 1.09617i) q^{90} +5.66011 q^{91} +(6.94066 + 4.89682i) q^{92} +(2.69208 + 3.70533i) q^{93} +(-1.26889 + 17.6933i) q^{94} +(12.8875 + 8.10085i) q^{95} +(1.68189 - 4.49604i) q^{96} +(-6.02225 + 8.28892i) q^{97} +(0.285624 - 0.339166i) q^{98} +(-0.640311 + 4.04277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37281	+	0.339686i	−0.970725	+	0.240194i
$2$	−1.37281	+	0.339686i	−0.970725	+	0.240194i
$3$	−0.848586			−0.489931			−0.244966	−	0.969532i	$-0.578777\pi$
$3$	−0.848586			−0.489931			−0.244966	+	0.969532i	$0.578777\pi$
$4$	1.76923	−	0.932650i	0.884613	−	0.466325i
$5$	−2.22703	−	0.200823i	−0.995959	−	0.0898110i
$5$	−2.22703	−	0.200823i	−0.995959	−	0.0898110i
$6$	1.16495	−	0.288253i	0.475588	−	0.117679i
$7$	−2.45926	+	0.799062i	−0.929513	+	0.302017i	−0.734363	−	0.678756i	$-0.762519\pi$
$7$	−2.45926	+	0.799062i	−0.929513	+	0.302017i	−0.195149	+	0.980774i	$0.562519\pi$
$8$	−2.11201	+	1.88134i	−0.746708	+	0.665152i
$9$	−2.27990			−0.759968
$10$	3.12551	−	0.480799i	0.988374	−	0.152042i
$11$	0.280850	−	1.77322i	0.0846796	−	0.534646i	−0.908484	−	0.417919i	$-0.862760\pi$
$11$	0.280850	−	1.77322i	0.0846796	−	0.534646i	0.993164	−	0.116727i	$-0.0372403\pi$
$12$	−1.50134	+	0.791434i	−0.433400	+	0.228467i
$13$	−2.08177	−	0.676408i	−0.577379	−	0.187602i	0.00574701	−	0.999983i	$-0.498171\pi$
$13$	−2.08177	−	0.676408i	−0.577379	−	0.187602i	−0.583126	+	0.812382i	$0.698171\pi$
$14$	3.10467	−	1.93234i	0.829759	−	0.516439i
$15$	1.88983	+	0.170416i	0.487951	+	0.0440012i
$16$	2.26033	−	3.30014i	0.565082	−	0.825035i
$17$	3.19795	+	4.40160i	0.775617	+	1.06755i	0.995752	+	0.0920757i	$0.0293502\pi$
$17$	3.19795	+	4.40160i	0.775617	+	1.06755i	−0.220135	+	0.975469i	$0.570650\pi$
$18$	3.12988	−	0.774451i	0.737719	−	0.182540i
$19$	−6.06554	−	3.09055i	−1.39153	−	0.709020i	−0.412164	−	0.911110i	$-0.635227\pi$
$19$	−6.06554	−	3.09055i	−1.39153	−	0.709020i	−0.979367	+	0.202090i	$0.935227\pi$
$20$	−4.12742	+	1.72174i	−0.922920	+	0.384993i
$21$	2.08689	−	0.678072i	0.455397	−	0.147968i
$22$	0.216783	+	2.52970i	0.0462183	+	0.539333i
$23$	1.92814	+	3.78420i	0.402046	+	0.789060i	0.999922	−	0.0125293i	$-0.00398831\pi$
$23$	1.92814	+	3.78420i	0.402046	+	0.789060i	−0.597876	+	0.801589i	$0.703988\pi$
$24$	1.79222	−	1.59647i	0.365835	−	0.325879i
$25$	4.91934	+	0.894480i	0.983868	+	0.178896i
$26$	3.08765	+	0.221433i	0.605537	+	0.0434266i
$27$	4.48045			0.862263
$28$	−3.60574	+	3.70735i	−0.681421	+	0.700624i
$29$	2.94682	−	0.466730i	0.547210	−	0.0866696i	0.123293	−	0.992370i	$-0.460655\pi$
$29$	2.94682	−	0.466730i	0.547210	−	0.0866696i	0.423918	+	0.905701i	$0.360655\pi$
$30$	−2.65227	+	0.407999i	−0.484235	+	0.0744901i
$31$	−3.17243	−	4.36648i	−0.569786	−	0.784243i	0.422743	−	0.906249i	$-0.361067\pi$
$31$	−3.17243	−	4.36648i	−0.569786	−	0.784243i	−0.992529	+	0.122006i	$0.961067\pi$
$32$	−1.98199	+	5.29827i	−0.350370	+	0.936611i
$33$	−0.238326	+	1.50473i	−0.0414871	+	0.261940i
$34$	−5.88535	−	4.95627i	−1.00933	−	0.849994i
$35$	5.63732	−	1.28566i	0.952881	−	0.217316i
$36$	−4.03366	+	2.12635i	−0.672277	+	0.354392i
$37$	6.60307	−	1.04582i	1.08554	−	0.171932i	0.412073	−	0.911151i	$-0.364805\pi$
$37$	6.60307	−	1.04582i	1.08554	−	0.171932i	0.673466	+	0.739218i	$0.264805\pi$
$38$	9.37666	+	2.18236i	1.52110	+	0.354026i
$39$	1.76656	+	0.573990i	0.282876	+	0.0919120i
$40$	5.08132	−	3.76565i	0.803428	−	0.595402i
$41$	6.12880	+	1.85414i	0.957157	+	0.289569i
$41$	6.12880	+	1.85414i	0.957157	+	0.289569i
$42$	−2.63458	+	1.63975i	−0.406524	+	0.253020i
$43$	−10.5365	+	5.36862i	−1.60680	+	0.818706i	−0.607091	+	0.794632i	$0.707664\pi$
$43$	−10.5365	+	5.36862i	−1.60680	+	0.818706i	−0.999710	+	0.0240742i	$0.992336\pi$
$44$	−1.15691	−	3.39916i	−0.174410	−	0.512443i
$45$	5.07742	+	0.457858i	0.756896	+	0.0682534i
$46$	−3.93242	−	4.54003i	−0.579804	−	0.669391i
$47$	3.87605	−	11.9292i	0.565380	−	1.74006i	−0.101442	−	0.994841i	$-0.532346\pi$
$47$	3.87605	−	11.9292i	0.565380	−	1.74006i	0.666821	−	0.745218i	$-0.267654\pi$
$48$	−1.91808	+	2.80045i	−0.276851	+	0.404210i
$49$	−0.253659	+	0.184294i	−0.0362370	+	0.0263277i
$50$	−7.05717	+	0.443078i	−0.998035	+	0.0626606i
$51$	−2.71373	−	3.73514i	−0.379999	−	0.523024i
$52$	−4.31398	+	0.744844i	−0.598241	+	0.103291i
$53$	0.202706	−	0.279001i	0.0278438	−	0.0383237i	−0.794868	−	0.606782i	$-0.792460\pi$
$53$	0.202706	−	0.279001i	0.0278438	−	0.0383237i	0.822712	+	0.568458i	$0.192460\pi$
$54$	−6.15082	+	1.52195i	−0.837020	+	0.207111i
$55$	−0.981566	+	3.89261i	−0.132354	+	0.524880i
$56$	3.69067	−	6.31432i	0.493187	−	0.843786i
$57$	5.14713	+	2.62259i	0.681754	+	0.347371i
$58$	−3.88688	+	1.64172i	−0.510373	+	0.215569i
$59$	0.807500	−	2.48523i	0.105128	−	0.323549i	−0.884633	−	0.466288i	$-0.845591\pi$
$59$	0.807500	−	2.48523i	0.105128	−	0.323549i	0.989760	+	0.142739i	$0.0455909\pi$
$60$	3.50247	−	1.46104i	0.452167	−	0.188620i
$61$	11.1131	−	3.61088i	1.42289	−	0.462325i	0.506371	−	0.862315i	$-0.330986\pi$
$61$	11.1131	−	3.61088i	1.42289	−	0.462325i	0.916519	+	0.399990i	$0.130986\pi$
$62$	5.83839	+	4.91673i	0.741476	+	0.624425i
$63$	5.60687	−	1.82178i	0.706400	−	0.229523i
$64$	0.921155	−	7.94679i	0.115144	−	0.993349i
$65$	4.50033	+	1.92445i	0.558197	+	0.238699i
$66$	−0.183959	−	2.14666i	−0.0226438	−	0.264236i
$67$	2.51467	+	1.82702i	0.307216	+	0.223206i	0.730701	−	0.682698i	$-0.239193\pi$
$67$	2.51467	+	1.82702i	0.307216	+	0.223206i	−0.423485	+	0.905903i	$0.639193\pi$
$68$	9.76305	+	4.80486i	1.18394	+	0.582675i
$69$	−1.63620	−	3.21121i	−0.196975	−	0.386585i
$70$	−7.30226	+	3.67989i	−0.872787	+	0.439831i
$71$	−0.786938	+	4.96853i	−0.0933924	+	0.589656i	0.895962	+	0.444131i	$0.146487\pi$
$71$	−0.786938	+	4.96853i	−0.0933924	+	0.589656i	−0.989354	+	0.145526i	$0.953513\pi$
$72$	4.81517	−	4.28926i	0.567473	−	0.505494i
$73$	−5.24712	+	5.24712i	−0.614129	+	0.614129i	−0.944019	−	0.329891i	$-0.892988\pi$
$73$	−5.24712	+	5.24712i	−0.614129	+	0.614129i	0.329891	+	0.944019i	$0.392988\pi$
$74$	−8.70953	+	3.67869i	−1.01246	+	0.427639i
$75$	−4.17448	−	0.759043i	−0.482028	−	0.0876467i
$76$	−13.6137	+	0.189149i	−1.56160	+	0.0216969i
$77$	0.726228	+	4.58522i	0.0827614	+	0.522535i
$78$	−2.62013	−	0.187905i	−0.296671	−	0.0212760i
$79$	10.3820	+	10.3820i	1.16807	+	1.16807i	0.982662	+	0.185407i	$0.0593603\pi$
$79$	10.3820	+	10.3820i	1.16807	+	1.16807i	0.185407	+	0.982662i	$0.440640\pi$
$80$	−5.69656	+	6.89559i	−0.636895	+	0.770950i
$81$	3.03766			0.337518
$82$	−9.04351	−	0.463525i	−0.998689	−	0.0511878i
$83$	8.56967	−	8.56967i	0.940643	−	0.940643i	−0.0576914	−	0.998334i	$-0.518374\pi$
$83$	8.56967	−	8.56967i	0.940643	−	0.940643i	0.998334	+	0.0576914i	$0.0183739\pi$
$84$	3.05978	−	3.14600i	0.333850	−	0.343257i
$85$	−6.23799	−	10.4447i	−0.676605	−	1.13289i
$86$	12.6410	−	10.9492i	1.36311	−	1.18068i
$87$	−2.50063	+	0.396060i	−0.268095	+	0.0424621i
$88$	2.74286	+	4.27343i	0.292390	+	0.455549i
$89$	12.3575	+	6.29646i	1.30989	+	0.667424i	0.962751	−	0.270389i	$-0.0871523\pi$
$89$	12.3575	+	6.29646i	1.30989	+	0.667424i	0.347142	+	0.937813i	$0.387152\pi$
$90$	−7.12587	+	1.09617i	−0.751132	+	0.115547i
$91$	5.66011			0.593340
$92$	6.94066	+	4.89682i	0.723614	+	0.510529i
$93$	2.69208	+	3.70533i	0.279156	+	0.384225i
$94$	−1.26889	+	17.6933i	−0.130876	+	1.82492i
$95$	12.8875	+	8.10085i	1.32223	+	0.831130i
$96$	1.68189	−	4.49604i	0.171657	−	0.458875i
$97$	−6.02225	+	8.28892i	−0.611467	+	0.841612i	−0.996697	−	0.0812083i	$-0.974122\pi$
$97$	−6.02225	+	8.28892i	−0.611467	+	0.841612i	0.385230	+	0.922821i	$0.374122\pi$
$98$	0.285624	−	0.339166i	0.0288524	−	0.0342609i
$99$	−0.640311	+	4.04277i	−0.0643537	+	0.406313i
$100$	9.53767	−	3.00549i	0.953767	−	0.300549i
$101$	12.0124	+	6.12064i	1.19528	+	0.609027i	0.934359	−	0.356333i	$-0.115973\pi$
$101$	12.0124	+	6.12064i	1.19528	+	0.609027i	0.260923	+	0.965360i	$0.415973\pi$
$102$	4.99422	+	4.20582i	0.494502	+	0.416438i
$103$	6.42985	−	12.6193i	0.633551	−	1.24341i	−0.321482	−	0.946916i	$-0.604181\pi$
$103$	6.42985	−	12.6193i	0.633551	−	1.24341i	0.955033	−	0.296499i	$-0.0958191\pi$
$104$	5.66926	−	2.48793i	0.555917	−	0.243961i
$105$	−4.78375	+	1.09099i	−0.466846	+	0.106470i
$106$	−0.183505	+	0.451872i	−0.0178235	+	0.0438897i
$107$	−3.59074	+	7.04723i	−0.347130	+	0.681281i	−0.996886	−	0.0788623i	$-0.974871\pi$
$107$	−3.59074	+	7.04723i	−0.347130	+	0.681281i	0.649756	+	0.760143i	$0.274871\pi$
$108$	7.92693	−	4.17869i	0.762769	−	0.402095i
$109$	−6.25654	−	6.25654i	−0.599268	−	0.599268i	0.340850	−	0.940118i	$-0.389285\pi$
$109$	−6.25654	−	6.25654i	−0.599268	−	0.599268i	−0.940118	+	0.340850i	$0.889285\pi$
$110$	0.0252399	−	5.67725i	0.00240653	−	0.541305i
$111$	−5.60327	+	0.887471i	−0.531839	+	0.0842350i
$112$	−2.92172	+	9.92204i	−0.276076	+	0.937545i
$113$	−14.1589	−	2.24255i	−1.33196	−	0.210962i	−0.550456	−	0.834864i	$-0.685546\pi$
$113$	−14.1589	−	2.24255i	−1.33196	−	0.210962i	−0.781502	+	0.623902i	$0.785546\pi$
$114$	−7.95690	−	1.85192i	−0.745232	−	0.173448i
$115$	−3.53408	−	8.81474i	−0.329555	−	0.821979i
$116$	4.77829	−	3.57410i	0.443653	−	0.331847i
$117$	4.74623	+	1.54214i	0.438789	+	0.142571i
$118$	−0.264348	+	3.68605i	−0.0243352	+	0.339328i
$119$	−11.3817	−	8.26932i	−1.04336	−	0.758047i
$120$	−4.31194	+	3.19548i	−0.393624	+	0.291706i
$121$	7.39619	+	2.40317i	0.672381	+	0.218470i
$122$	−14.0297	+	8.73203i	−1.27019	+	0.790561i
$123$	−5.20081	−	1.57340i	−0.468941	−	0.141869i
$124$	−9.68516	−	4.76652i	−0.869753	−	0.428046i
$125$	−10.7759	−	2.97995i	−0.963825	−	0.266535i
$126$	−7.07835	+	4.40554i	−0.630590	+	0.392477i
$127$	−1.28394	−	8.10650i	−0.113931	−	0.719335i	−0.976839	−	0.213974i	$-0.931359\pi$
$127$	−1.28394	−	8.10650i	−0.113931	−	0.719335i	0.862908	−	0.505361i	$-0.168641\pi$
$128$	1.43484	+	11.2224i	0.126823	+	0.991925i
$129$	8.94112	−	4.55573i	0.787222	−	0.401110i
$130$	−6.83182	−	1.11321i	−0.599190	−	0.0976350i
$131$	2.31107	−	1.67909i	0.201919	−	0.146703i	−0.482231	−	0.876044i	$-0.660173\pi$
$131$	2.31107	−	1.67909i	0.201919	−	0.146703i	0.684150	+	0.729341i	$0.260173\pi$
$132$	0.981733	+	2.88448i	0.0854489	+	0.251062i
$133$	17.3863	+	2.75372i	1.50758	+	0.238778i
$134$	−4.07279	−	1.65395i	−0.351835	−	0.142880i
$135$	−9.97810	−	0.899779i	−0.858778	−	0.0774407i
$136$	−15.0350	−	3.27980i	−1.28924	−	0.281240i
$137$			4.93259i			0.421419i	0.977549	+	0.210710i	$0.0675774\pi$
$137$			4.93259i			0.421419i	−0.977549	+	0.210710i	$0.932423\pi$
$138$	3.33699	+	3.85260i	0.284064	+	0.327955i
$139$	2.49100	+	7.66650i	0.211284	+	0.650264i	0.999397	+	0.0347337i	$0.0110583\pi$
$139$	2.49100	+	7.66650i	0.211284	+	0.650264i	−0.788113	+	0.615531i	$0.788942\pi$
$140$	8.77463	−	7.53227i	0.741591	−	0.636593i
$141$	−3.28916	+	10.1230i	−0.276997	+	0.852509i
$142$	−0.607423	−	7.08817i	−0.0509738	−	0.594826i
$143$	−1.78409	+	3.50146i	−0.149193	+	0.292807i
$144$	−5.15333	+	7.52400i	−0.429444	+	0.627000i
$145$	−6.65638	+	0.447632i	−0.552783	+	0.0371738i
$146$	5.42093	−	8.98568i	0.448640	−	0.743660i
$147$	0.215251	−	0.156389i	0.0177536	−	0.0128988i
$148$	10.7069	−	8.00866i	0.880106	−	0.658308i
$149$	0.686330	+	4.33332i	0.0562263	+	0.354999i	0.999721	+	0.0236120i	$0.00751662\pi$
$149$	0.686330	+	4.33332i	0.0562263	+	0.354999i	−0.943495	+	0.331387i	$0.892483\pi$
$150$	5.98861	−	0.375989i	0.488968	−	0.0306994i
$151$	−7.95891	−	15.6202i	−0.647687	−	1.27116i	−0.948289	−	0.317407i	$-0.897188\pi$
$151$	−7.95891	−	15.6202i	−0.647687	−	1.27116i	0.300603	−	0.953749i	$-0.402812\pi$
$152$	18.6248	−	4.88406i	1.51067	−	0.396149i
$153$	−7.29102	−	10.0352i	−0.589444	−	0.811300i
$154$	−2.55451	−	6.04796i	−0.205848	−	0.487359i
$155$	6.18822	+	10.3614i	0.497050	+	0.832247i
$156$	3.66078	−	0.632064i	0.293097	−	0.0506056i
$157$	−7.12339	−	21.9236i	−0.568509	−	1.74969i	−0.657289	−	0.753639i	$-0.728297\pi$
$157$	−7.12339	−	21.9236i	−0.568509	−	1.74969i	0.0887803	−	0.996051i	$-0.471703\pi$
$158$	−17.7792	−	10.7259i	−1.41444	−	0.853310i
$159$	−0.172013	+	0.236756i	−0.0136416	+	0.0187760i
$160$	5.47798	−	11.4014i	0.433072	−	0.901359i
$161$	−7.76562	−	7.76562i	−0.612016	−	0.612016i
$162$	−4.17014	+	1.03185i	−0.327637	+	0.0810699i
$163$	2.66790	−	2.66790i	0.208966	−	0.208966i	−0.594862	−	0.803828i	$-0.702793\pi$
$163$	2.66790	−	2.66790i	0.208966	−	0.208966i	0.803828	+	0.594862i	$0.202793\pi$
$164$	12.5725	−	2.43562i	0.981747	−	0.190190i
$165$	0.832943	−	3.30322i	0.0648445	−	0.257155i
$166$	−8.85355	+	14.6755i	−0.687168	+	1.13904i
$167$			21.1319i			1.63523i	0.575762	+	0.817617i	$0.304705\pi$
$167$			21.1319i			1.63523i	−0.575762	+	0.817617i	$0.695295\pi$
$168$	−3.13185	+	5.35824i	−0.241628	+	0.413397i
$169$	−6.64098	−	4.82496i	−0.510845	−	0.371150i
$170$	12.1115	+	12.2197i	0.928911	+	0.937208i
$171$	13.8288	+	7.04615i	1.05752	+	0.538832i
$172$	−13.6344	+	19.3252i	−1.03961	+	1.47353i
$173$	8.21513	−	8.21513i	0.624585	−	0.624585i	−0.322115	−	0.946700i	$-0.604394\pi$
$173$	8.21513	−	8.21513i	0.624585	−	0.624585i	0.946700	+	0.322115i	$0.104394\pi$
$174$	3.29835	−	1.39314i	0.250048	−	0.105614i
$175$	−12.8127	+	1.73110i	−0.968548	+	0.130859i
$176$	−5.21706	−	4.93490i	−0.393250	−	0.371982i
$177$	−0.685233	+	2.10893i	−0.0515053	+	0.158517i
$178$	−19.1034	−	4.44619i	−1.43186	−	0.333256i
$179$	−3.24001	+	0.513168i	−0.242170	+	0.0383560i	−0.276339	−	0.961060i	$-0.589121\pi$
$179$	−3.24001	+	0.513168i	−0.242170	+	0.0383560i	0.0341695	+	0.999416i	$0.489121\pi$
$180$	9.41012	−	3.92540i	0.701389	−	0.292582i
$181$	0.567190	−	3.58110i	0.0421589	−	0.266181i	−0.957601	−	0.288098i	$-0.906977\pi$
$181$	0.567190	−	3.58110i	0.0421589	−	0.266181i	0.999760	+	0.0219172i	$0.00697702\pi$
$182$	−7.77026	+	1.92266i	−0.575970	+	0.142517i
$183$	−9.43044	+	3.06414i	−0.697118	+	0.226508i
$184$	−11.1916	−	4.36477i	−0.825056	−	0.321775i
$185$	−14.9153	+	1.00303i	−1.09659	+	0.0737443i
$186$	−4.95437	−	4.17226i	−0.363272	−	0.305925i
$187$	8.70315	−	4.43448i	0.636437	−	0.324281i
$188$	−4.26821	−	24.7205i	−0.311291	−	1.80293i
$189$	−11.0186	+	3.58016i	−0.801484	+	0.260418i
$190$	−20.4439	−	6.74324i	−1.48315	−	0.489206i
$191$	−4.00486	−	4.00486i	−0.289781	−	0.289781i	0.547212	−	0.836994i	$-0.315689\pi$
$191$	−4.00486	−	4.00486i	−0.289781	−	0.289781i	−0.836994	+	0.547212i	$0.815689\pi$
$192$	−0.781678	+	6.74353i	−0.0564128	+	0.486672i
$193$	2.15557	−	2.96688i	0.155161	−	0.213561i	−0.724359	−	0.689423i	$-0.757864\pi$
$193$	2.15557	−	2.96688i	0.155161	−	0.213561i	0.879520	+	0.475863i	$0.157864\pi$
$194$	5.45179	−	13.4248i	0.391416	−	0.963845i
$195$	−3.81891	−	1.63306i	−0.273478	−	0.116946i
$196$	−0.276898	+	0.562633i	−0.0197785	+	0.0401881i
$197$	−5.65581	−	0.895792i	−0.402960	−	0.0638225i	−0.0483348	−	0.998831i	$-0.515391\pi$
$197$	−5.65581	−	0.895792i	−0.402960	−	0.0638225i	−0.354625	+	0.935009i	$0.615391\pi$
$198$	−0.494244	−	5.76746i	−0.0351244	−	0.409876i
$199$	−3.02201	−	5.93102i	−0.214224	−	0.420439i	0.758740	−	0.651393i	$-0.225815\pi$
$199$	−3.02201	−	5.93102i	−0.214224	−	0.420439i	−0.972965	+	0.230954i	$0.925815\pi$
$200$	−12.0725	+	7.36578i	−0.853655	+	0.520839i
$201$	−2.13392	−	1.55038i	−0.150515	−	0.109355i
$202$	−18.5699	−	4.32203i	−1.30657	−	0.304097i
$203$	−6.87404	+	3.50250i	−0.482463	+	0.245827i
$204$	−8.28479	−	4.07734i	−0.580051	−	0.285471i
$205$	−13.2767	−	5.36004i	−0.927283	−	0.374362i
$206$	−4.54038	+	19.5080i	−0.316343	+	1.35919i
$207$	−4.39598	−	8.62760i	−0.305542	−	0.599660i
$208$	−6.93772	+	5.34123i	−0.481044	+	0.370348i
$209$	−7.18373	+	9.88755i	−0.496909	+	0.683936i
$210$	6.19659	−	3.12270i	0.427606	−	0.215487i
$211$	−10.5563	+	5.37871i	−0.726727	+	0.370286i	−0.777887	−	0.628405i	$-0.783708\pi$
$211$	−10.5563	+	5.37871i	−0.726727	+	0.370286i	0.0511598	+	0.998690i	$0.483708\pi$
$212$	0.0984227	−	0.682670i	0.00675970	−	0.0468859i
$213$	0.667784	−	4.21622i	0.0457558	−	0.288891i
$214$	2.53557	−	10.8942i	0.173328	−	0.744715i
$215$	24.5433	−	9.84010i	1.67384	−	0.671089i
$216$	−9.46274	+	8.42923i	−0.643858	+	0.573536i
$217$	11.2909	+	8.20334i	0.766478	+	0.556879i
$218$	10.7143	+	6.46380i	0.725665	+	0.437784i
$219$	4.45263	−	4.45263i	0.300881	−	0.300881i
$220$	1.89383	+	7.80237i	0.127682	+	0.526036i
$221$	−3.68012	−	11.3262i	−0.247552	−	0.761885i
$222$	7.39078	−	3.12169i	0.496037	−	0.209514i
$223$	11.5131	+	22.5958i	0.770975	+	1.51312i	0.856132	+	0.516757i	$0.172861\pi$
$223$	11.5131	+	22.5958i	0.770975	+	1.51312i	−0.0851571	+	0.996368i	$0.527139\pi$
$224$	0.640587	−	14.6136i	0.0428010	−	0.976410i
$225$	−11.2156	−	2.03933i	−0.747708	−	0.135955i
$226$	20.1993	−	1.73098i	1.34364	−	0.115143i
$227$	2.68971	+	8.27806i	0.178522	+	0.549434i	0.999777	−	0.0211273i	$-0.00672552\pi$
$227$	2.68971	+	8.27806i	0.178522	+	0.549434i	−0.821255	+	0.570562i	$0.806726\pi$
$228$	11.5524	−	0.160509i	0.765077	−	0.0106300i
$229$	3.61154	+	0.572011i	0.238657	+	0.0377996i	0.274617	−	0.961554i	$-0.411449\pi$
$229$	3.61154	+	0.572011i	0.238657	+	0.0377996i	−0.0359600	+	0.999353i	$0.511449\pi$
$230$	7.84588	+	10.9005i	0.517342	+	0.718758i
$231$	−0.616267	−	3.89095i	−0.0405474	−	0.256006i
$232$	−5.34562	+	6.52969i	−0.350957	+	0.428695i
$233$	−8.19393	−	2.66237i	−0.536802	−	0.174418i	0.0280549	−	0.999606i	$-0.491069\pi$
$233$	−8.19393	−	2.66237i	−0.536802	−	0.174418i	−0.564857	+	0.825189i	$0.691069\pi$
$234$	−7.03953	−	0.504846i	−0.460189	−	0.0330028i
$235$	−11.0278	+	25.7884i	−0.719371	+	1.68225i
$236$	−0.889200	−	5.15005i	−0.0578820	−	0.335240i
$237$	−8.81003	−	8.81003i	−0.572273	−	0.572273i
$238$	18.4340	+	7.48601i	1.19490	+	0.485246i
$239$	−3.83108	+	7.51893i	−0.247812	+	0.486359i	−0.981085	−	0.193575i	$-0.937992\pi$
$239$	−3.83108	+	7.51893i	−0.247812	+	0.486359i	0.733273	+	0.679934i	$0.237992\pi$
$240$	4.83402	−	5.85150i	0.312035	−	0.377713i
$241$	9.71971	−	13.3780i	0.626102	−	0.861755i	−0.371678	−	0.928362i	$-0.621217\pi$
$241$	9.71971	−	13.3780i	0.626102	−	0.861755i	0.997779	+	0.0666069i	$0.0212173\pi$
$242$	−10.9699	−	0.786716i	−0.705172	−	0.0505720i
$243$	−16.0191			−1.02762
$244$	16.2940	−	16.7531i	1.04311	−	1.07251i
$245$	0.601917	−	0.359488i	0.0384551	−	0.0229668i
$246$	7.67420	+	0.393340i	0.489289	+	0.0250785i
$247$	10.5366	+	10.5366i	0.670427	+	0.670427i
$248$	14.9150	+	3.25363i	0.947105	+	0.206606i
$249$	−7.27209	+	7.27209i	−0.460850	+	0.460850i
$250$	15.8055	+	0.430498i	0.999629	+	0.0272271i
$251$	10.2472	+	7.44503i	0.646798	+	0.469926i	0.862179	−	0.506604i	$-0.169099\pi$
$251$	10.2472	+	7.44503i	0.646798	+	0.469926i	−0.215381	+	0.976530i	$0.569099\pi$
$252$	8.22074	−	8.45240i	0.517858	−	0.532451i
$253$	7.25173	−	2.35623i	0.455912	−	0.148135i
$254$	4.51628	+	10.6926i	0.283376	+	0.670911i
$255$	5.29347	+	8.86325i	0.331490	+	0.555038i
$256$	−5.78184	−	14.9188i	−0.361365	−	0.932424i
$257$	−8.61122	+	6.25642i	−0.537153	+	0.390265i	−0.823027	−	0.568003i	$-0.807716\pi$
$257$	−8.61122	+	6.25642i	−0.537153	+	0.390265i	0.285874	+	0.958267i	$0.407716\pi$
$258$	−10.7270	+	9.29134i	−0.667832	+	0.578453i
$259$	−15.4030	+	7.84822i	−0.957096	+	0.487665i
$260$	9.75694	−	0.792444i	0.605100	−	0.0491453i
$261$	−6.71845	+	1.06410i	−0.415862	+	0.0658661i
$262$	−2.60230	+	3.09011i	−0.160770	+	0.190908i
$263$	−8.57775	−	11.8063i	−0.528927	−	0.728005i	0.458040	−	0.888932i	$-0.348552\pi$
$263$	−8.57775	−	11.8063i	−0.528927	−	0.728005i	−0.986966	+	0.160926i	$0.948552\pi$
$264$	−2.32755	−	3.62637i	−0.143251	−	0.223188i
$265$	−0.507463	+	0.580636i	−0.0311732	+	0.0356682i
$266$	−24.8035	+	2.12554i	−1.52080	+	0.130325i
$267$	−10.4864	−	5.34309i	−0.641757	−	0.326992i
$268$	6.15300	+	0.887097i	0.375854	+	0.0541881i
$269$	8.29951	+	2.69667i	0.506030	+	0.164419i	0.550896	−	0.834574i	$-0.314286\pi$
$269$	8.29951	+	2.69667i	0.506030	+	0.164419i	−0.0448661	+	0.998993i	$0.514286\pi$
$270$	14.0037	−	2.15419i	0.852238	−	0.131100i
$271$	−9.24128	+	3.00267i	−0.561368	+	0.182399i	−0.575936	−	0.817494i	$-0.695362\pi$
$271$	−9.24128	+	3.00267i	−0.561368	+	0.182399i	0.0145688	+	0.999894i	$0.495362\pi$
$272$	21.7543	−	0.604626i	1.31905	−	0.0366608i
$273$	−4.80308			−0.290696
$274$	−1.67553	−	6.77151i	−0.101222	−	0.409082i
$275$	2.96771	−	8.47185i	0.178959	−	0.510872i
$276$	−5.88974	−	4.15537i	−0.354521	−	0.250124i
$277$	0.445231	−	2.81108i	0.0267513	−	0.168901i	−0.970696	−	0.240312i	$-0.922750\pi$
$277$	0.445231	−	2.81108i	0.0267513	−	0.168901i	0.997447	+	0.0714109i	$0.0227502\pi$
$278$	−6.02388	−	9.67851i	−0.361288	−	0.580479i
$279$	7.23284	+	9.95515i	0.433019	+	0.595999i
$280$	−9.48731	+	13.3210i	−0.566975	+	0.796083i
$281$	2.99131	+	5.87078i	0.178447	+	0.350221i	0.962853	−	0.270026i	$-0.0870322\pi$
$281$	2.99131	+	5.87078i	0.178447	+	0.350221i	−0.784406	+	0.620247i	$0.787032\pi$
$282$	1.07676	−	15.0142i	0.0641200	−	0.894085i
$283$	28.7984	−	4.56122i	1.71189	−	0.271136i	0.777886	−	0.628406i	$-0.216292\pi$
$283$	28.7984	−	4.56122i	1.71189	−	0.271136i	0.934001	+	0.357270i	$0.116292\pi$
$284$	3.24163	+	9.52440i	0.192355	+	0.565169i
$285$	−10.9361	−	6.87426i	−0.647801	−	0.407196i
$286$	1.25982	−	5.41288i	0.0744945	−	0.320070i
$287$	−16.5539	+	0.337467i	−0.977145	+	0.0199200i
$288$	4.51875	−	12.0795i	0.266270	−	0.711794i
$289$	−3.89392	+	11.9842i	−0.229054	+	0.704956i
$290$	8.98591	−	2.87560i	0.527671	−	0.168861i
$291$	5.11040	−	7.03386i	0.299577	−	0.412332i
$292$	−4.38961	+	14.1771i	−0.256883	+	0.829650i
$293$	8.46335	−	26.0475i	0.494434	−	1.52171i	−0.323403	−	0.946261i	$-0.604827\pi$
$293$	8.46335	−	26.0475i	0.494434	−	1.52171i	0.817837	−	0.575450i	$-0.195173\pi$
$294$	−0.242376	+	0.287811i	−0.0141357	+	0.0167855i
$295$	−2.29742	+	5.37252i	−0.133761	+	0.312800i
$296$	−11.9782	+	14.6314i	−0.696219	+	0.850432i
$297$	1.25834	−	7.94482i	0.0730160	−	0.461005i
$298$	−2.41417	−	5.71569i	−0.139849	−	0.331101i
$299$	−1.45429	−	9.18204i	−0.0841039	−	0.531011i
$300$	−8.09352	+	2.55041i	−0.467280	+	0.147248i
$301$	21.6221	−	21.6221i	1.24628	−	1.24628i
$302$	16.2321	+	18.7401i	0.934050	+	1.07837i
$303$	−10.1936	−	5.19389i	−0.585606	−	0.298381i
$304$	−23.9093	+	13.0315i	−1.37129	+	0.747407i
$305$	−25.4744	+	5.80976i	−1.45866	+	0.332666i
$306$	13.4180	+	11.2998i	0.767057	+	0.645968i
$307$	−21.7226	−	11.0682i	−1.23977	−	0.631696i	−0.293777	−	0.955874i	$-0.594912\pi$
$307$	−21.7226	−	11.0682i	−1.23977	−	0.631696i	−0.945996	+	0.324178i	$0.894912\pi$
$308$	5.56127	+	7.43498i	0.316883	+	0.423648i
$309$	−5.45627	+	10.7085i	−0.310397	+	0.609188i
$310$	−12.0149	−	12.1222i	−0.682400	−	0.688494i
$311$	20.4787	+	3.24350i	1.16124	+	0.183922i	0.707170	−	0.707044i	$-0.249972\pi$
$311$	20.4787	+	3.24350i	1.16124	+	0.183922i	0.454070	+	0.890966i	$0.349972\pi$
$312$	−4.81086	+	2.11122i	−0.272361	+	0.119524i
$313$	23.7566	+	17.2602i	1.34280	+	0.975604i	0.999336	+	0.0364403i	$0.0116019\pi$
$313$	23.7566	+	17.2602i	1.34280	+	0.975604i	0.343468	+	0.939164i	$0.388398\pi$
$314$	17.2262	+	27.6772i	0.972131	+	1.56191i
$315$	−12.8525	+	2.93118i	−0.724159	+	0.165153i
$316$	28.0509	+	8.68536i	1.57799	+	0.488589i
$317$	−4.73156	+	3.43768i	−0.265751	+	0.193080i	−0.712679	−	0.701491i	$-0.752518\pi$
$317$	−4.73156	+	3.43768i	−0.265751	+	0.193080i	0.446927	+	0.894570i	$0.352518\pi$
$318$	0.155719	−	0.383452i	0.00873231	−	0.0215029i
$319$		−	5.35643i		−	0.299903i
$320$	−3.64734	+	17.5128i	−0.203893	+	0.978993i
$321$	3.04705	−	5.98017i	0.170070	−	0.333781i
$322$	13.2986	+	8.02286i	0.741102	+	0.447097i
$323$	−5.79394	−	36.5815i	−0.322384	−	2.03545i
$324$	5.37432	−	2.83308i	0.298573	−	0.157393i
$325$	−9.63590	−	5.18958i	−0.534504	−	0.287866i
$326$	−2.75628	+	4.56878i	−0.152656	+	0.253041i
$327$	5.30921	+	5.30921i	0.293600	+	0.293600i
$328$	−16.4323	+	7.61436i	−0.907324	+	0.420432i
$329$			32.4343i			1.78816i
$330$	−0.0214182	+	4.81763i	−0.00117904	+	0.265202i
$331$	21.7478	−	21.7478i	1.19536	−	1.19536i	0.219826	−	0.975539i	$-0.429451\pi$
$331$	21.7478	−	21.7478i	1.19536	−	1.19536i	0.975539	−	0.219826i	$-0.0705489\pi$
$332$	7.16918	−	23.1542i	0.393460	−	1.27075i
$333$	−15.0544	+	2.38438i	−0.824974	+	0.130663i
$334$	−7.17821	−	29.0101i	−0.392774	−	1.58736i
$335$	−5.23335	−	4.57383i	−0.285928	−	0.249895i
$336$	2.47933	−	8.41970i	0.135258	−	0.459332i
$337$	−0.751472	−	0.751472i	−0.0409353	−	0.0409353i	0.686343	−	0.727278i	$-0.259215\pi$
$337$	−0.751472	−	0.751472i	−0.0409353	−	0.0409353i	−0.727278	+	0.686343i	$0.759215\pi$
$338$	10.7558	+	4.36791i	0.585038	+	0.237583i
$339$	12.0150	+	1.90300i	0.652568	+	0.103357i
$340$	−20.7777	−	12.6612i	−1.12683	−	0.686652i
$341$	−8.63371	+	4.39909i	−0.467541	+	0.238224i
$342$	−21.3779	−	4.97557i	−1.15598	−	0.269048i
$343$	11.1159	−	15.2997i	0.600202	−	0.826107i
$344$	12.1530	−	31.1613i	0.655246	−	1.68010i
$345$	2.99897	+	7.48006i	0.161459	+	0.402713i
$346$	−8.48727	+	14.0684i	−0.456278	+	0.756322i
$347$	6.73410	+	20.7254i	0.361506	+	1.11260i	0.952140	+	0.305661i	$0.0988774\pi$
$347$	6.73410	+	20.7254i	0.361506	+	1.11260i	−0.590635	+	0.806939i	$0.701123\pi$
$348$	−4.05479	+	3.03293i	−0.217359	+	0.162582i
$349$	7.58897	+	23.3564i	0.406228	+	1.25024i	0.919865	+	0.392234i	$0.128298\pi$
$349$	7.58897	+	23.3564i	0.406228	+	1.25024i	−0.513637	+	0.858007i	$0.671702\pi$
$350$	17.0014	−	6.72876i	0.908762	−	0.359667i
$351$	−9.32726	−	3.03061i	−0.497853	−	0.161762i
$352$	8.83836	+	5.00253i	0.471086	+	0.266636i
$353$	3.56031	−	6.98750i	0.189496	−	0.371907i	−0.776638	−	0.629947i	$-0.783077\pi$
$353$	3.56031	−	6.98750i	0.189496	−	0.371907i	0.966134	+	0.258040i	$0.0830766\pi$
$354$	0.224322	−	3.12793i	0.0119226	−	0.166248i
$355$	2.75033	−	10.9070i	0.145973	−	0.578886i
$356$	27.7356	−	0.385359i	1.46999	−	0.0204240i
$357$	9.65838	+	7.01723i	0.511176	+	0.371391i
$358$	4.27361	−	1.80507i	0.225868	−	0.0954009i
$359$	−4.29447	+	3.12011i	−0.226653	+	0.164673i	−0.695317	−	0.718704i	$-0.744736\pi$
$359$	−4.29447	+	3.12011i	−0.226653	+	0.164673i	0.468663	+	0.883377i	$0.344736\pi$
$360$	−11.5849	+	8.58532i	−0.610579	+	0.452486i
$361$	16.0714	+	22.1204i	0.845862	+	1.16423i
$362$	0.437804	+	5.10884i	0.0230104	+	0.268515i
$363$	−6.27630	−	2.03929i	−0.329420	−	0.107035i
$364$	10.0140	−	5.27890i	0.524877	−	0.276690i
$365$	12.7392	−	10.6318i	0.666802	−	0.556491i
$366$	11.9054	−	7.40987i	0.622304	−	0.387320i
$367$	6.20681	+	12.1816i	0.323993	+	0.635872i	0.994348	−	0.106168i	$-0.0338583\pi$
$367$	6.20681	+	12.1816i	0.323993	+	0.635872i	−0.670355	+	0.742040i	$0.733858\pi$
$368$	16.8466	+	2.19038i	0.878191	+	0.114181i
$369$	−13.9731	−	4.22727i	−0.727408	−	0.220063i
$370$	20.1352	−	6.44349i	1.04678	−	0.334981i
$371$	−0.275568	+	0.848110i	−0.0143068	+	0.0440317i
$372$	8.21868	+	4.04480i	0.426119	+	0.209713i
$373$	2.52191	+	15.9227i	0.130579	+	0.824446i	0.962842	+	0.270065i	$0.0870450\pi$
$373$	2.52191	+	15.9227i	0.130579	+	0.824446i	−0.832263	+	0.554381i	$0.812955\pi$
$374$	−10.4415	+	9.04404i	−0.539915	+	0.467656i
$375$	9.14427	+	2.52875i	0.472208	+	0.130584i
$376$	14.2567	+	32.4868i	0.735232	+	1.67538i
$377$	−6.45029	−	1.02163i	−0.332207	−	0.0526164i
$378$	13.9103	−	8.65774i	0.715470	−	0.445306i
$379$	21.4949	−	15.6170i	1.10412	−	0.802190i	0.122392	−	0.992482i	$-0.460944\pi$
$379$	21.4949	−	15.6170i	1.10412	−	0.802190i	0.981727	+	0.190292i	$0.0609436\pi$
$380$	30.3562	+	2.31271i	1.55724	+	0.118640i
$381$	1.08954	+	6.87905i	0.0558186	+	0.352425i
$382$	6.85831	+	4.13752i	0.350902	+	0.211694i
$383$			12.9647i			0.662467i	0.943549	+	0.331233i	$0.107465\pi$
$383$			12.9647i			0.662467i	−0.943549	+	0.331233i	$0.892535\pi$
$384$	−1.21759	−	9.52313i	−0.0621347	−	0.485975i
$385$	−0.696513	−	10.3573i	−0.0354976	−	0.527856i
$386$	−1.95138	+	4.80519i	−0.0993225	+	0.244578i
$387$	24.0222	−	12.2399i	1.22112	−	0.622190i
$388$	−2.92407	+	20.2816i	−0.148447	+	1.02964i
$389$	0.622907	+	1.91711i	0.0315826	+	0.0972014i	0.965605	−	0.260013i	$-0.0837267\pi$
$389$	0.622907	+	1.91711i	0.0315826	+	0.0972014i	−0.934023	+	0.357214i	$0.883727\pi$
$390$	5.79738	+	0.944654i	0.293562	+	0.0478344i
$391$	−10.4904	+	20.5886i	−0.530523	+	1.04121i
$392$	0.189011	−	0.866448i	0.00954649	−	0.0437622i
$393$	−1.96114	+	1.42485i	−0.0989263	+	0.0718742i
$394$	8.06865	−	0.691445i	0.406493	−	0.0348345i
$395$	−21.0361	−	25.2060i	−1.05844	−	1.26825i
$396$	2.63763	+	7.74976i	0.132546	+	0.389440i
$397$	3.89257	−	11.9801i	0.195362	−	0.601264i	−0.804610	−	0.593804i	$-0.797625\pi$
$397$	3.89257	−	11.9801i	0.195362	−	0.601264i	0.999972	−	0.00745975i	$-0.00237453\pi$
$398$	6.16334	+	7.11565i	0.308940	+	0.356675i
$399$	−14.7537	−	2.33676i	−0.738611	−	0.116985i
$400$	14.0712	−	14.2127i	0.703561	−	0.710635i
$401$			15.1450i			0.756305i	0.925743	+	0.378153i	$0.123441\pi$
$401$			15.1450i			0.756305i	−0.925743	+	0.378153i	$0.876559\pi$
$402$	3.45611	+	1.40352i	0.172375	+	0.0700012i
$403$	3.65076	+	11.2359i	0.181857	+	0.559699i
$404$	26.9611	−	0.374598i	1.34137	−	0.0186370i
$405$	−6.76497	−	0.610034i	−0.336154	−	0.0303128i
$406$	8.24702	−	7.14329i	0.409293	−	0.354516i
$407$		−	12.0024i		−	0.594938i
$408$	12.7585	+	2.78319i	0.631638	+	0.137788i
$409$			24.9238i			1.23240i	0.787588	+	0.616202i	$0.211329\pi$
$409$			24.9238i			1.23240i	−0.787588	+	0.616202i	$0.788671\pi$
$410$	20.0471	+	2.84843i	0.990056	+	0.140674i
$411$		−	4.18572i		−	0.206466i
$412$	−0.393522	−	28.3232i	−0.0193875	−	1.39538i
$413$			6.75707i			0.332494i
$414$	8.96553	+	10.3508i	0.440632	+	0.508715i
$415$	−20.8059	+	17.3639i	−1.02132	+	0.852362i
$416$	7.70985	−	9.68915i	0.378006	−	0.475050i
$417$	−2.11382	−	6.50568i	−0.103514	−	0.318585i
$418$	6.50324	−	16.0140i	0.318084	−	0.783269i
$419$		−	20.0228i		−	0.978176i	−0.872234	−	0.489088i	$-0.837330\pi$
$419$		−	20.0228i		−	0.978176i	0.872234	−	0.489088i	$-0.162670\pi$
$420$	−7.44602	+	6.39178i	−0.363329	+	0.311887i
$421$	−8.00995	−	1.26865i	−0.390381	−	0.0618303i	−0.0418413	−	0.999124i	$-0.513322\pi$
$421$	−8.00995	−	1.26865i	−0.390381	−	0.0618303i	−0.348540	+	0.937294i	$0.613322\pi$
$422$	12.6648	−	10.9698i	0.616511	−	0.534001i
$423$	−8.83701	+	27.1975i	−0.429670	+	1.32239i
$424$	0.0967775	+	0.970610i	0.00469993	+	0.0471370i
$425$	11.7947	+	24.5135i	0.572125	+	1.18908i
$426$	0.515450	+	6.01492i	0.0249736	+	0.291424i
$427$	−24.4448	+	17.7602i	−1.18297	+	0.859475i
$428$	0.219762	+	15.8170i	0.0106226	+	0.764546i
$429$	1.51395	−	2.97129i	0.0730941	−	0.143455i
$430$	−30.3508	+	21.8456i	−1.46364	+	1.05349i
$431$	−1.13727	−	3.50016i	−0.0547805	−	0.168597i	0.919923	−	0.392099i	$-0.128251\pi$
$431$	−1.13727	−	3.50016i	−0.0547805	−	0.168597i	−0.974703	+	0.223502i	$0.928251\pi$
$432$	10.1273	−	14.7861i	0.487249	−	0.711397i
$433$	−22.8772	+	11.6565i	−1.09941	+	0.560176i	−0.906996	−	0.421138i	$-0.861631\pi$
$433$	−22.8772	+	11.6565i	−1.09941	+	0.560176i	−0.192411	+	0.981314i	$0.561631\pi$
$434$	−18.2869	−	7.42628i	−0.877799	−	0.356473i
$435$	5.64851	−	0.379854i	0.270825	−	0.0182126i
$436$	−16.9044	−	5.23408i	−0.809574	−	0.250667i
$437$		−	28.9122i		−	1.38306i
$438$	−4.60013	+	7.62512i	−0.219803	+	0.364342i
$439$	4.00446	+	25.2832i	0.191122	+	1.20670i	0.877544	+	0.479496i	$0.159180\pi$
$439$	4.00446	+	25.2832i	0.191122	+	1.20670i	−0.686422	+	0.727204i	$0.740820\pi$
$440$	−5.25024	−	10.0679i	−0.250295	−	0.479968i
$441$	0.578318	−	0.420172i	0.0275389	−	0.0200082i
$442$	8.89948	+	14.2987i	0.423305	+	0.680121i
$443$	27.9636	+	4.42900i	1.32859	+	0.210428i	0.780062	−	0.625703i	$-0.215188\pi$
$443$	27.9636	+	4.42900i	1.32859	+	0.210428i	0.548530	+	0.836131i	$0.315188\pi$
$444$	−9.08576	+	6.79603i	−0.431191	+	0.322525i
$445$	−26.2561	−	16.5041i	−1.24466	−	0.782369i
$446$	−23.4808	−	27.1089i	−1.11185	−	1.28364i
$447$	−0.582410	−	3.67719i	−0.0275470	−	0.173925i
$448$	4.08462	+	20.2793i	0.192980	+	0.958106i
$449$	9.93993	−	30.5920i	0.469094	−	1.44372i	−0.384665	−	0.923056i	$-0.625683\pi$
$449$	9.93993	−	30.5920i	0.469094	−	1.44372i	0.853759	−	0.520668i	$-0.174317\pi$
$450$	16.0897	−	1.01017i	0.758474	−	0.0476200i
$451$	5.00908	−	10.3470i	0.235868	−	0.487219i
$452$	−27.1418	+	9.23773i	−1.27665	+	0.434506i
$453$	6.75381	+	13.2551i	0.317322	+	0.622779i
$454$	−6.50440	−	10.4506i	−0.305267	−	0.490470i
$455$	−12.6052	−	1.13668i	−0.590943	−	0.0532885i
$456$	−15.8048	+	4.14454i	−0.740126	+	0.194086i
$457$	20.7675	+	6.74777i	0.971462	+	0.315647i	0.751406	−	0.659840i	$-0.229376\pi$
$457$	20.7675	+	6.74777i	0.971462	+	0.315647i	0.220056	+	0.975487i	$0.429376\pi$
$458$	−5.15227	+	0.441525i	−0.240750	+	0.0206311i
$459$	14.3283	+	19.7211i	0.668786	+	0.920504i
$460$	−14.4737	−	12.2992i	−0.674838	−	0.573454i
$461$	21.2443	−	15.4349i	0.989445	−	0.718874i	0.0296455	−	0.999560i	$-0.490562\pi$
$461$	21.2443	−	15.4349i	0.989445	−	0.718874i	0.959799	+	0.280687i	$0.0905622\pi$
$462$	2.16772	+	5.13221i	0.100852	+	0.238772i
$463$	9.95730	+	7.23440i	0.462755	+	0.336211i	0.794611	−	0.607119i	$-0.207675\pi$
$463$	9.95730	+	7.23440i	0.462755	+	0.336211i	−0.331856	+	0.943330i	$0.607675\pi$
$464$	5.12049	−	10.7799i	0.237713	−	0.500443i
$465$	−5.25123	−	8.79253i	−0.243520	−	0.407744i
$466$	12.1531	+	0.871569i	0.562981	+	0.0403747i
$467$	6.50111	−	12.7591i	0.300836	−	0.590423i	−0.690262	−	0.723559i	$-0.742505\pi$
$467$	6.50111	−	12.7591i	0.300836	−	0.590423i	0.991098	+	0.133136i	$0.0425048\pi$
$468$	9.83544	−	1.69817i	0.454644	−	0.0784980i
$469$	−7.64414	−	2.48373i	−0.352973	−	0.114688i
$470$	6.37907	−	39.1486i	0.294245	−	1.80579i
$471$	6.04481	+	18.6040i	0.278530	+	0.857227i
$472$	2.97010	+	6.76800i	0.136710	+	0.311523i
$473$	6.56055	+	20.1913i	0.301655	+	0.928397i
$474$	15.0872	+	9.10188i	0.692977	+	0.418063i
$475$	−27.0740	−	20.6290i	−1.24224	−	0.946522i
$476$	−27.8493	−	4.01512i	−1.27647	−	0.184033i
$477$	−0.462150	+	0.636095i	−0.0211604	+	0.0291248i
$478$	2.70529	−	11.6234i	0.123737	−	0.531644i
$479$	11.7246	−	5.97398i	0.535711	−	0.272958i	−0.165135	−	0.986271i	$-0.552806\pi$
$479$	11.7246	−	5.97398i	0.535711	−	0.272958i	0.700846	+	0.713313i	$0.252806\pi$
$480$	−4.64853	+	9.67506i	−0.212176	+	0.441604i
$481$	−14.4535	−	2.28921i	−0.659022	−	0.104379i
$482$	−8.79901	+	21.6672i	−0.400784	+	0.986913i
$483$	6.58979	+	6.58979i	0.299846	+	0.299846i
$484$	15.3269	−	2.64631i	0.696675	−	0.120287i
$485$	15.0764	−	17.2503i	0.684582	−	0.783295i
$486$	21.9912	−	5.44145i	0.997540	−	0.246829i
$487$	4.29755	−	0.680666i	0.194741	−	0.0308439i	−0.0583021	−	0.998299i	$-0.518569\pi$
$487$	4.29755	−	0.680666i	0.194741	−	0.0308439i	0.253043	+	0.967455i	$0.418569\pi$
$488$	−16.6778	+	28.5337i	−0.754967	+	1.29166i
$489$	−2.26395	+	2.26395i	−0.102379	+	0.102379i
$490$	−0.704206	+	0.697972i	−0.0318128	+	0.0315312i
$491$			26.6465i			1.20254i	0.799045	+	0.601271i	$0.205339\pi$
$491$			26.6465i			1.20254i	−0.799045	+	0.601271i	$0.794661\pi$
$492$	−10.6688	+	2.06683i	−0.480989	+	0.0931801i
$493$	11.4781	+	11.4781i	0.516949	+	0.516949i
$494$	−18.0439	−	10.8856i	−0.811833	−	0.489768i
$495$	2.23788	−	8.87478i	0.100585	−	0.398892i
$496$	−21.5807	+	0.599802i	−0.969004	+	0.0269319i
$497$	−2.03488	−	12.8477i	−0.0912768	−	0.576299i
$498$	7.51299	−	12.4535i	0.336665	−	0.558052i
$499$	12.1709	−	23.8867i	0.544844	−	1.06932i	−0.440342	−	0.897830i	$-0.645143\pi$
$499$	12.1709	−	23.8867i	0.544844	−	1.06932i	0.985186	−	0.171487i	$-0.0548572\pi$
$500$	−21.8443	+	4.77792i	−0.976905	+	0.213675i
$501$		−	17.9322i		−	0.801152i
$502$	−16.5965	−	6.73980i	−0.740737	−	0.300812i
$503$	2.55372	−	1.85539i	0.113865	−	0.0827277i	−0.529396	−	0.848375i	$-0.677581\pi$
$503$	2.55372	−	1.85539i	0.113865	−	0.0827277i	0.643260	+	0.765647i	$0.277581\pi$
$504$	−8.41437	+	14.3960i	−0.374806	+	0.641250i
$505$	−25.5229	−	16.0432i	−1.13575	−	0.713915i
$506$	−9.15489	+	5.69797i	−0.406984	+	0.253306i
$507$	5.63544	+	4.09439i	0.250279	+	0.181838i
$508$	−9.83211	−	13.1448i	−0.436229	−	0.583204i
$509$	−14.4361	−	2.28646i	−0.639870	−	0.101345i	−0.171935	−	0.985108i	$-0.555002\pi$
$509$	−14.4361	−	2.28646i	−0.639870	−	0.101345i	−0.467935	+	0.883763i	$0.655002\pi$
$510$	−10.2777	−	10.3695i	−0.455102	−	0.459167i
$511$	8.71125	−	17.0968i	0.385363	−	0.756318i
$512$	13.0051	+	18.5167i	0.574749	+	0.818330i
$513$	−27.1763	−	13.8470i	−1.19987	−	0.611362i
$514$	9.69637	−	11.5140i	0.427688	−	0.507861i
$515$	−16.8537	+	26.8123i	−0.742663	+	1.18149i
$516$	11.5700	−	16.3991i	0.509340	−	0.721928i
$517$	−20.0646	−	10.2234i	−0.882439	−	0.449625i
$518$	18.4795	−	16.0063i	0.811942	−	0.703277i
$519$	−6.97124	+	6.97124i	−0.306004	+	0.306004i
$520$	−13.1253	+	4.40217i	−0.575581	+	0.193048i
$521$	2.47305	+	15.6142i	0.108346	+	0.684071i	0.980747	+	0.195281i	$0.0625617\pi$
$521$	2.47305	+	15.6142i	0.108346	+	0.684071i	−0.872401	+	0.488790i	$0.837438\pi$
$522$	8.86172	−	3.74297i	0.387867	−	0.163825i
$523$	0.912938	−	5.76406i	0.0399200	−	0.252045i	−0.959656	−	0.281178i	$-0.909275\pi$
$523$	0.912938	−	5.76406i	0.0399200	−	0.252045i	0.999576	+	0.0291334i	$0.00927477\pi$
$524$	2.52280	−	5.12610i	0.110209	−	0.223935i
$525$	10.8727	−	1.46898i	0.474522	−	0.0641118i
$526$	15.7861	+	13.2940i	0.688305	+	0.579648i
$527$	9.07422	−	27.9276i	0.395279	−	1.21654i
$528$	4.42712	+	4.18768i	0.192666	+	0.182246i
$529$	2.91666	−	4.01443i	0.126811	−	0.174541i
$530$	0.499417	−	0.969482i	0.0216933	−	0.0421116i
$531$	−1.84102	+	5.66608i	−0.0798935	+	0.245887i
$532$	33.3285	−	11.3434i	1.44498	−	0.491798i
$533$	−11.5046	−	8.00547i	−0.498319	−	0.346755i
$534$	16.2108	+	3.77297i	0.701511	+	0.163272i
$535$	9.41194	−	14.9733i	0.406914	−	0.647352i
$536$	−8.74824	+	0.872269i	−0.377867	+	0.0376763i
$537$	2.74943	−	0.435467i	0.118647	−	0.0187918i
$538$	−12.3097	−	0.882799i	−0.530708	−	0.0380602i
$539$	0.255553	+	0.501552i	0.0110075	+	0.0216034i
$540$	−18.4927	+	7.71417i	−0.795799	+	0.331965i
$541$	−10.2100	−	14.0528i	−0.438960	−	0.604177i	0.531020	−	0.847359i	$-0.321809\pi$
$541$	−10.2100	−	14.0528i	−0.438960	−	0.604177i	−0.969981	+	0.243182i	$0.921809\pi$
$542$	11.6666	−	7.26124i	0.501122	−	0.311897i
$543$	−0.481310	+	3.03887i	−0.0206550	+	0.130410i
$544$	−29.6592	+	8.21967i	−1.27163	+	0.352416i
$545$	12.6771	+	15.1900i	0.543026	+	0.650667i
$546$	6.59373	−	1.63154i	0.282186	−	0.0698235i
$547$	14.5194			0.620804			0.310402	−	0.950605i	$-0.399536\pi$
$547$	14.5194			0.620804			0.310402	+	0.950605i	$0.399536\pi$
$548$	4.60038	+	8.72686i	0.196518	+	0.372793i
$549$	−25.3369	+	8.23245i	−1.08135	+	0.351352i
$550$	−1.19634	+	12.6384i	−0.0510119	+	0.538901i
$551$	−19.3165	−	6.27631i	−0.822910	−	0.267380i
$552$	9.49703	+	3.70388i	0.404220	+	0.157648i
$553$	−33.8280	−	17.2362i	−1.43851	−	0.732958i
$554$	0.343665	+	4.01032i	0.0146009	+	0.170382i
$555$	12.6569	−	0.851158i	0.537255	−	0.0361296i
$556$	11.5573	+	11.2406i	0.490139	+	0.476706i
$557$	−0.506707	−	0.697422i	−0.0214699	−	0.0295507i	0.798147	−	0.602463i	$-0.205814\pi$
$557$	−0.506707	−	0.697422i	−0.0214699	−	0.0295507i	−0.819617	+	0.572912i	$0.805814\pi$
$558$	−13.3110	−	11.2097i	−0.563498	−	0.474543i
$559$	25.5659	−	4.04925i	1.08132	−	0.171265i
$560$	8.49933	−	21.5100i	0.359162	−	0.908962i
$561$	−7.38537	+	3.76303i	−0.311810	+	0.158875i
$562$	−6.10073	−	7.04337i	−0.257344	−	0.297107i
$563$	−2.09632	+	1.52307i	−0.0883494	+	0.0641896i	−0.631083	−	0.775715i	$-0.717389\pi$
$563$	−2.09632	+	1.52307i	−0.0883494	+	0.0641896i	0.542734	+	0.839905i	$0.317389\pi$
$564$	3.62194	+	20.9775i	0.152511	+	0.883312i
$565$	31.0820	+	7.83768i	1.30763	+	0.329733i
$566$	−37.9854	+	16.0441i	−1.59665	+	0.674384i
$567$	−7.47040	+	2.42728i	−0.313727	+	0.101936i
$568$	−7.68546	−	11.9741i	−0.322475	−	0.502421i
$569$	19.5257	+	14.1862i	0.818559	+	0.594718i	0.916300	−	0.400494i	$-0.131161\pi$
$569$	19.5257	+	14.1862i	0.818559	+	0.594718i	−0.0977400	+	0.995212i	$0.531161\pi$
$570$	17.3484	+	5.72222i	0.726643	+	0.239677i
$571$	−9.72633	+	9.72633i	−0.407034	+	0.407034i	−0.880703	−	0.473669i	$-0.842929\pi$
$571$	−9.72633	+	9.72633i	−0.407034	+	0.407034i	0.473669	+	0.880703i	$0.342929\pi$
$572$	0.109190	+	7.85881i	0.00456548	+	0.328593i
$573$	3.39846	+	3.39846i	0.141973	+	0.141973i
$574$	22.6107	−	6.08640i	0.943754	−	0.254041i
$575$	6.10031	+	20.3404i	0.254400	+	0.848255i
$576$	−2.10014	+	18.1179i	−0.0875059	+	0.754913i
$577$	32.3413			1.34639			0.673193	−	0.739467i	$-0.264922\pi$
$577$	32.3413			1.34639			0.673193	+	0.739467i	$0.264922\pi$
$578$	1.27474	−	17.7748i	0.0530220	−	0.739335i
$579$	−1.82918	+	2.51765i	−0.0760182	+	0.104630i
$580$	−11.3592	+	7.00004i	−0.471664	+	0.290661i
$581$	−14.2273	+	27.9227i	−0.590250	+	1.15843i
$582$	−4.62631	+	11.3921i	−0.191767	+	0.472218i
$583$	−0.437800	−	0.437800i	−0.0181318	−	0.0181318i
$584$	1.21037	−	20.9535i	0.0500853	−	0.867064i
$585$	−10.2603	−	4.38756i	−0.424212	−	0.181403i
$586$	−2.77061	+	38.6332i	−0.114453	+	1.59592i
$587$	−17.4988	−	5.68571i	−0.722254	−	0.234674i	−0.0752537	−	0.997164i	$-0.523977\pi$
$587$	−17.4988	−	5.68571i	−0.722254	−	0.234674i	−0.647000	+	0.762490i	$0.723977\pi$
$588$	0.234972	−	0.477442i	0.00969008	−	0.0196894i
$589$	5.74771	+	36.2896i	0.236830	+	1.49529i
$590$	1.32896	−	8.15586i	0.0547123	−	0.335772i
$591$	4.79944	+	0.760156i	0.197422	+	0.0312687i
$592$	11.4737	−	24.1550i	0.471568	−	0.992763i
$593$	−3.33736	−	10.2714i	−0.137049	−	0.421794i	0.858854	−	0.512220i	$-0.171177\pi$
$593$	−3.33736	−	10.2714i	−0.137049	−	0.421794i	−0.995903	+	0.0904266i	$0.971177\pi$
$594$	0.971285	+	11.3342i	0.0398523	+	0.465047i
$595$	23.6868	+	20.7018i	0.971065	+	0.848689i
$596$	5.25574	+	7.02651i	0.215284	+	0.287817i
$597$	2.56443	+	5.03298i	0.104955	+	0.205986i
$598$	5.11548	+	12.1112i	0.209188	+	0.495264i
$599$	4.08458	+	12.5710i	0.166891	+	0.513639i	0.999171	−	0.0407176i	$-0.0129644\pi$
$599$	4.08458	+	12.5710i	0.166891	+	0.513639i	−0.832279	+	0.554357i	$0.812964\pi$
$600$	10.2446	−	6.25049i	0.418232	−	0.255175i
$601$	3.41425	−	3.41425i	0.139270	−	0.139270i	−0.634034	−	0.773305i	$-0.718602\pi$
$601$	3.41425	−	3.41425i	0.139270	−	0.139270i	0.773305	+	0.634034i	$0.218602\pi$
$602$	−22.3384	+	37.0279i	−0.910445	+	1.50914i
$603$	−5.73321	−	4.16542i	−0.233474	−	0.169629i
$604$	−28.6493	−	20.2129i	−1.16572	−	0.822450i
$605$	−15.9889	−	6.83726i	−0.650043	−	0.277974i
$606$	15.7582	+	3.66762i	0.640132	+	0.148987i
$607$	6.11455	−	38.6058i	0.248182	−	1.56696i	−0.477313	−	0.878733i	$-0.658389\pi$
$607$	6.11455	−	38.6058i	0.248182	−	1.56696i	0.725495	−	0.688227i	$-0.241611\pi$
$608$	28.3964	−	26.0115i	1.15163	−	1.05490i
$609$	5.83321	−	2.97217i	0.236374	−	0.120438i
$610$	32.9981	−	16.6290i	1.33606	−	0.673289i
$611$	−16.1381	+	22.2122i	−0.652877	+	0.898608i
$612$	−22.2588	−	10.9546i	−0.899759	−	0.442814i
$613$	−2.33840	−	4.58937i	−0.0944470	−	0.185363i	0.838950	−	0.544209i	$-0.183170\pi$
$613$	−2.33840	−	4.58937i	−0.0944470	−	0.185363i	−0.933397	+	0.358846i	$0.883170\pi$
$614$	33.5808	+	7.81572i	1.35521	+	0.315417i
$615$	11.2664	+	4.54846i	0.454305	+	0.183411i
$616$	−10.1601	−	8.31775i	−0.409364	−	0.335132i
$617$	10.0324	−	5.11178i	0.403890	−	0.205792i	−0.240231	−	0.970716i	$-0.577223\pi$
$617$	10.0324	−	5.11178i	0.403890	−	0.205792i	0.644121	+	0.764923i	$0.277223\pi$
$618$	3.85290	−	16.5542i	0.154986	−	0.665909i
$619$	−1.89332	−	1.37558i	−0.0760991	−	0.0552892i	0.549085	−	0.835766i	$-0.314976\pi$
$619$	−1.89332	−	1.37558i	−0.0760991	−	0.0552892i	−0.625184	+	0.780477i	$0.714976\pi$
$620$	20.6119	+	12.5602i	0.827795	+	0.504430i
$621$	8.63895	+	16.9549i	0.346669	+	0.680377i
$622$	−29.2151	+	2.50360i	−1.17142	+	0.100385i
$623$	−35.4216	−	5.61023i	−1.41914	−	0.224769i
$624$	5.88725	−	4.53249i	0.235679	−	0.181445i
$625$	23.3998	+	8.80051i	0.935992	+	0.352020i
$626$	−38.4764	−	15.6252i	−1.53783	−	0.624510i
$627$	6.09601	−	8.39043i	0.243451	−	0.335082i
$628$	−33.0499	−	32.1441i	−1.31883	−	1.28269i
$629$	25.7196	+	25.7196i	1.02551	+	1.02551i
$630$	16.6484	−	8.38979i	0.663290	−	0.334257i
$631$	1.11304	−	0.361650i	0.0443096	−	0.0143971i	−0.286778	−	0.957997i	$-0.592584\pi$
$631$	1.11304	−	0.361650i	0.0443096	−	0.0143971i	0.331088	+	0.943600i	$0.392584\pi$
$632$	−41.4590	−	2.39485i	−1.64915	−	0.0952619i
$633$	8.95794	−	4.56430i	0.356046	−	0.181415i
$634$	5.32782	−	6.32654i	0.211595	−	0.251259i
$635$	1.23141	+	18.3113i	0.0488669	+	0.726660i
$636$	−0.0835200	+	0.579304i	−0.00331178	+	0.0229709i
$637$	0.652718	−	0.212081i	0.0258616	−	0.00840295i
$638$	1.81951	+	7.35338i	0.0720349	+	0.291123i
$639$	1.79414	−	11.3278i	0.0709752	−	0.448120i
$640$	−0.941726	−	25.2807i	−0.0372250	−	0.999307i
$641$	−17.7440	+	2.81037i	−0.700845	+	0.111003i	−0.496680	−	0.867934i	$-0.665448\pi$
$641$	−17.7440	+	2.81037i	−0.700845	+	0.111003i	−0.204165	+	0.978937i	$0.565448\pi$
$642$	−2.15165	+	9.24470i	−0.0849187	+	0.364859i
$643$	−9.65414	+	29.7124i	−0.380722	+	1.17174i	0.558814	+	0.829293i	$0.311256\pi$
$643$	−9.65414	+	29.7124i	−0.380722	+	1.17174i	−0.939536	+	0.342449i	$0.888744\pi$
$644$	−20.9817	−	6.49653i	−0.826797	−	0.255999i
$645$	−20.8271	+	8.35017i	−0.820065	+	0.328788i
$646$	20.3802	+	48.2514i	0.801849	+	1.89843i
$647$	18.4451	−	18.4451i	0.725153	−	0.725153i	−0.244497	−	0.969650i	$-0.578623\pi$
$647$	18.4451	−	18.4451i	0.725153	−	0.725153i	0.969650	+	0.244497i	$0.0786229\pi$
$648$	−6.41557	+	5.71486i	−0.252027	+	0.224501i
$649$	−4.18007	−	2.12985i	−0.164082	−	0.0836040i
$650$	14.9911	+	3.85114i	0.588000	+	0.151054i
$651$	−9.58132	−	6.96124i	−0.375522	−	0.272832i
$652$	2.23191	−	7.20835i	0.0874082	−	0.282301i
$653$		−	8.46592i		−	0.331297i	−0.986185	−	0.165648i	$-0.947028\pi$
$653$		−	8.46592i		−	0.331297i	0.986185	−	0.165648i	$-0.0529717\pi$
$654$	−9.09202	−	5.48509i	−0.355526	−	0.214484i
$655$	−5.48402	+	3.27527i	−0.214278	+	0.127975i
$656$	19.9720	−	16.0349i	0.779776	−	0.626058i
$657$	11.9629	−	11.9629i	0.466718	−	0.466718i
$658$	−11.0175	−	44.5262i	−0.429506	−	1.73581i
$659$	13.7781	+	13.7781i	0.536719	+	0.536719i	0.922564	−	0.385845i	$-0.126090\pi$
$659$	13.7781	+	13.7781i	0.536719	+	0.536719i	−0.385845	+	0.922564i	$0.626090\pi$
$660$	−1.60708	−	6.62098i	−0.0625555	−	0.257721i
$661$	20.4822	−	28.1913i	0.796665	−	1.09652i	−0.196581	−	0.980488i	$-0.562984\pi$
$661$	20.4822	−	28.1913i	0.796665	−	1.09652i	0.993246	−	0.116028i	$-0.0370163\pi$
$662$	−22.4682	+	37.2430i	−0.873251	+	1.44749i
$663$	3.12290	+	9.61128i	0.121283	+	0.373271i
$664$	−1.97679	+	34.2216i	−0.0767142	+	1.32806i
$665$	−38.1668	−	9.62419i	−1.48004	−	0.373210i
$666$	19.8569	−	8.38706i	0.769438	−	0.324992i
$667$	7.44809	+	10.2514i	0.288391	+	0.396936i
$668$	19.7087	+	37.3871i	0.762551	+	1.44655i
$669$	−9.76986	−	19.1744i	−0.377725	−	0.741327i
$670$	8.73807	+	4.50131i	0.337581	+	0.173901i
$671$	−3.28175	−	20.7201i	−0.126690	−	0.799892i
$672$	−0.543593	+	12.4009i	−0.0209695	+	0.478374i
$673$	17.1026	−	12.4258i	0.659258	−	0.478979i	−0.207155	−	0.978308i	$-0.566420\pi$
$673$	17.1026	−	12.4258i	0.659258	−	0.478979i	0.866412	+	0.499330i	$0.166420\pi$
$674$	1.28689	+	0.776365i	0.0495693	+	0.0299045i
$675$	22.0409	+	4.00767i	0.848353	+	0.154255i
$676$	−16.2494	−	2.34273i	−0.624977	−	0.0901049i
$677$	3.94900	−	7.75036i	0.151773	−	0.297870i	−0.802585	−	0.596538i	$-0.796542\pi$
$677$	3.94900	−	7.75036i	0.151773	−	0.297870i	0.954357	+	0.298668i	$0.0965423\pi$
$678$	−17.1408	+	1.46889i	−0.658290	+	0.0564123i
$679$	8.18692	−	25.1968i	0.314185	−	0.966963i
$680$	32.8247	+	10.3236i	1.25877	+	0.395892i
$681$	−2.28245	−	7.02465i	−0.0874635	−	0.269185i
$682$	10.3581	−	8.97188i	0.396634	−	0.343551i
$683$			0.959444i			0.0367121i	0.999832	+	0.0183561i	$0.00584324\pi$
$683$			0.959444i			0.0367121i	−0.999832	+	0.0183561i	$0.994157\pi$
$684$	31.0380	−	0.431242i	1.18677	−	0.0164889i
$685$	0.990579	−	10.9850i	0.0378481	−	0.419716i
$686$	−10.0629	+	24.7796i	−0.384205	+	0.946088i
$687$	−3.06470	−	0.485401i	−0.116926	−	0.0185192i
$688$	−6.09876	+	46.9068i	−0.232513	+	1.78830i
$689$	−0.610706	+	0.443704i	−0.0232660	+	0.0169038i
$690$	−6.65790	−	9.25001i	−0.253462	−	0.352142i
$691$	−19.8835	+	10.1311i	−0.756403	+	0.385406i	−0.789264	−	0.614054i	$-0.789538\pi$
$691$	−19.8835	+	10.1311i	−0.756403	+	0.385406i	0.0328618	+	0.999460i	$0.489538\pi$
$692$	6.87259	−	22.1963i	0.261257	−	0.843776i
$693$	−1.65573	−	10.4539i	−0.0628960	−	0.397109i
$694$	−16.2848	−	26.1647i	−0.618163	−	0.993197i
$695$	−4.00792	−	17.5738i	−0.152029	−	0.666612i
$696$	4.53622	−	5.54100i	0.171945	−	0.210031i
$697$	11.4384	+	32.9060i	0.433260	+	1.24640i
$698$	−18.3521	−	29.4861i	−0.694637	−	1.11607i
$699$	6.95325	+	2.25925i	0.262996	+	0.0854526i
$700$	−21.0540	+	15.0125i	−0.795768	+	0.567418i
$701$	23.7710	+	17.2706i	0.897818	+	0.652303i	0.937905	−	0.346893i	$-0.112763\pi$
$701$	23.7710	+	17.2706i	0.897818	+	0.652303i	−0.0400869	+	0.999196i	$0.512763\pi$
$702$	13.8340	+	0.992120i	0.522132	+	0.0374451i
$703$	−43.2834	−	14.0636i	−1.63246	−	0.530420i
$704$	−13.8327	−	3.86527i	−0.521339	−	0.145678i
$705$	9.35799	−	21.8837i	0.352442	−	0.824187i
$706$	−2.51408	+	10.8019i	−0.0946187	+	0.406536i
$707$	−34.4325	−	5.45357i	−1.29497	−	0.205103i
$708$	0.754562	+	4.37026i	0.0283582	+	0.164244i
$709$	37.3295	−	5.91240i	1.40194	−	0.222045i	0.590761	−	0.806847i	$-0.298828\pi$
$709$	37.3295	−	5.91240i	1.40194	−	0.222045i	0.811176	+	0.584802i	$0.198828\pi$
$710$	−0.0707219	+	15.9076i	−0.00265415	+	0.597001i
$711$	−23.6700	−	23.6700i	−0.887694	−	0.887694i
$712$	−37.9449	+	9.95043i	−1.42205	+	0.372908i
$713$	10.4067	−	20.4243i	0.389734	−	0.764897i
$714$	−15.6428	−	6.35252i	−0.585417	−	0.237737i
$715$	4.67639	−	7.43959i	0.174887	−	0.278225i
$716$	−5.25371	+	3.92971i	−0.196340	+	0.146860i
$717$	3.25100	−	6.38045i	0.121411	−	0.238282i
$718$	4.83564	−	5.74210i	0.180464	−	0.214293i
$719$	15.7797	+	8.04013i	0.588482	+	0.299846i	0.722762	−	0.691097i	$-0.242872\pi$
$719$	15.7797	+	8.04013i	0.588482	+	0.299846i	−0.134280	+	0.990943i	$0.542872\pi$
$720$	12.9876	−	15.7213i	0.484020	−	0.585897i
$721$	−5.72907	+	36.1719i	−0.213362	+	1.34711i
$722$	−29.5770	−	24.9079i	−1.10074	−	0.926975i
$723$	−8.24801	+	11.3524i	−0.306747	+	0.422201i
$724$	−2.33643	−	6.86477i	−0.0868326	−	0.255127i
$725$	14.9139	+	0.339866i	0.553887	+	0.0126223i
$726$	9.30890	+	0.667596i	0.345486	+	0.0247768i
$727$	13.3339	+	18.3525i	0.494527	+	0.680657i	0.981215	−	0.192918i	$-0.0617952\pi$
$727$	13.3339	+	18.3525i	0.494527	+	0.680657i	−0.486688	+	0.873576i	$0.661795\pi$
$728$	−11.9542	+	10.6486i	−0.443052	+	0.394662i
$729$	4.48056			0.165947
$730$	−13.8771	+	18.9227i	−0.513615	+	0.700362i
$731$	−57.3257	−	29.2089i	−2.12027	−	1.08033i
$732$	−13.8268	+	14.2165i	−0.511054	+	0.525455i
$733$	37.4991	−	5.93927i	1.38506	−	0.219372i	0.580992	−	0.813909i	$-0.302665\pi$
$733$	37.4991	−	5.93927i	1.38506	−	0.219372i	0.804068	+	0.594537i	$0.202665\pi$
$734$	−12.6587	−	14.6146i	−0.467241	−	0.539435i
$735$	−0.510778	+	0.305056i	−0.0188403	+	0.0112522i
$736$	−23.8713	+	2.71559i	−0.879907	+	0.100098i
$737$	3.94595	−	3.94595i	0.145351	−	0.145351i
$738$	20.6183	+	1.05679i	0.758971	+	0.0389010i
$739$	−47.6660			−1.75342			−0.876710	−	0.481019i	$-0.840267\pi$
$739$	−47.6660			−1.75342			−0.876710	+	0.481019i	$0.840267\pi$
$740$	−25.4530	+	15.6853i	−0.935672	+	0.576604i
$741$	−8.94120	−	8.94120i	−0.328463	−	0.328463i
$742$	0.0902116	−	1.25790i	0.00331177	−	0.0461791i
$743$	0.667716	+	4.21580i	0.0244961	+	0.154663i	0.996904	−	0.0786230i	$-0.0250523\pi$
$743$	0.667716	+	4.21580i	0.0244961	+	0.154663i	−0.972408	+	0.233286i	$0.925052\pi$
$744$	−12.6567	−	2.76098i	−0.464016	−	0.101223i
$745$	−0.658247	−	9.78826i	−0.0241163	−	0.358614i
$746$	−8.87082	−	21.0022i	−0.324784	−	0.768946i
$747$	−19.5380	+	19.5380i	−0.714858	+	0.714858i
$748$	11.2620	−	15.9626i	0.411781	−	0.583650i
$749$	3.19939	−	20.2002i	0.116903	−	0.738099i
$750$	−13.4123	−	0.365314i	−0.489749	−	0.0133394i
$751$	11.2443	+	22.0681i	0.410309	+	0.805277i	0.999997	−	0.00235426i	$-0.000749386\pi$
$751$	11.2443	+	22.0681i	0.410309	+	0.805277i	−0.589688	+	0.807631i	$0.700749\pi$
$752$	−30.6070	−	39.7555i	−1.11612	−	1.44973i
$753$	−8.69563	−	6.31775i	−0.316887	−	0.230232i
$754$	9.20207	−	0.788574i	0.335120	−	0.0287182i
$755$	14.5878	+	36.3851i	0.530906	+	1.32419i
$756$	−16.1553	+	16.6106i	−0.587564	+	0.604122i
$757$	−35.9264	+	11.6732i	−1.30577	+	0.424269i	−0.877584	−	0.479423i	$-0.840846\pi$
$757$	−35.9264	+	11.6732i	−1.30577	+	0.424269i	−0.428183	+	0.903692i	$0.640846\pi$
$758$	−24.2036	+	28.7407i	−0.879115	+	1.04391i
$759$	−6.15371	+	1.99946i	−0.223366	+	0.0725759i
$760$	−42.4589	+	7.13665i	−1.54015	+	0.258873i
$761$	0.422502	−	1.30033i	0.0153157	−	0.0471369i	−0.943107	−	0.332491i	$-0.892111\pi$
$761$	0.422502	−	1.30033i	0.0153157	−	0.0471369i	0.958422	+	0.285354i	$0.0921111\pi$
$762$	−3.83245	−	9.07355i	−0.138835	−	0.328700i
$763$	20.3858	+	10.3871i	0.738017	+	0.376038i
$764$	−10.8206	−	3.35037i	−0.391477	−	0.121212i
$765$	14.2220	+	23.8130i	0.514198	+	0.860960i
$766$	−4.40394	−	17.7981i	−0.159121	−	0.643073i
$767$	−3.36206	+	4.62748i	−0.121397	+	0.167089i
$768$	4.90639	+	12.6599i	0.177044	+	0.456824i
$769$	−7.49680	−	10.3185i	−0.270342	−	0.372093i	0.652163	−	0.758078i	$-0.273862\pi$
$769$	−7.49680	−	10.3185i	−0.270342	−	0.372093i	−0.922505	+	0.385985i	$0.873862\pi$
$770$	4.47440	+	13.9820i	0.161246	+	0.503877i
$771$	7.30736	−	5.30910i	0.263168	−	0.191203i
$772$	1.04662	−	7.25947i	0.0376687	−	0.261274i
$773$	7.44676	−	22.9188i	0.267841	−	0.824331i	−0.723184	−	0.690655i	$-0.757322\pi$
$773$	7.44676	−	22.9188i	0.267841	−	0.824331i	0.991025	−	0.133675i	$-0.0426779\pi$
$774$	−28.8202	+	24.9631i	−1.03592	+	0.897281i
$775$	−11.7006	−	24.3179i	−0.420296	−	0.873524i
$776$	−2.87519	−	28.8361i	−0.103213	−	1.03516i
$777$	13.0708	−	6.65989i	0.468911	−	0.238922i
$778$	−1.50635	−	2.42024i	−0.0540053	−	0.0867698i
$779$	−31.4441	−	30.1877i	−1.12660	−	1.08159i
$780$	−8.27960	+	0.672457i	−0.296457	+	0.0240778i
$781$	8.58928	+	2.79083i	0.307349	+	0.0998637i
$782$	7.40771	−	31.8277i	0.264899	−	1.13816i
$783$	13.2031	−	2.09116i	0.471839	−	0.0747319i
$784$	0.0348439	+	1.25367i	0.00124442	+	0.0447741i
$785$	11.4613	+	50.2550i	0.409070	+	1.79368i
$786$	2.20827	−	2.62222i	0.0787664	−	0.0935316i
$787$	−0.204833	+	1.29327i	−0.00730152	+	0.0461000i	−0.991070	−	0.133342i	$-0.957429\pi$
$787$	−0.204833	+	1.29327i	−0.00730152	+	0.0461000i	0.983769	+	0.179442i	$0.0574292\pi$
$788$	−10.8419	+	3.69003i	−0.386226	+	0.131452i
$789$	7.27896	+	10.0186i	0.259138	+	0.356672i
$790$	37.4408	+	27.4575i	1.33208	+	0.976893i
$791$	36.6124	−	5.79883i	1.30179	−	0.206183i
$792$	−6.25346	−	9.74300i	−0.222207	−	0.346202i
$793$	−25.5774			−0.908281
$794$	−1.27429	+	17.7687i	−0.0452230	+	0.630587i
$795$	0.430625	−	0.492719i	0.0152727	−	0.0174749i
$796$	−10.8782	−	7.67485i	−0.385567	−	0.272028i
$797$	−13.3546	−	26.2099i	−0.473045	−	0.928403i	−0.997055	−	0.0766911i	$-0.975564\pi$
$797$	−13.3546	−	26.2099i	−0.473045	−	0.928403i	0.524010	−	0.851712i	$-0.324436\pi$
$798$	21.0479	−	1.80370i	0.745087	−	0.0638504i
$799$	64.9032	−	21.0883i	2.29611	−	0.746051i
$800$	−14.4893	+	24.2912i	−0.512274	+	0.858822i
$801$	−28.1739	−	14.3553i	−0.995476	−	0.507220i
$802$	−5.14454	−	20.7912i	−0.181660	−	0.734164i
$803$	7.83063	+	10.7779i	0.276337	+	0.380345i
$804$	−5.22134	−	0.752778i	−0.184143	−	0.0265484i
$805$	15.7348	+	18.8538i	0.554577	+	0.664509i
$806$	−8.82847	−	14.1846i	−0.310970	−	0.499632i
$807$	−7.04284	−	2.28836i	−0.247920	−	0.0805540i
$808$	−36.8853	+	9.67258i	−1.29762	+	0.340280i
$809$	−0.701398	+	4.42845i	−0.0246598	+	0.155696i	−0.996946	−	0.0780998i	$-0.975115\pi$
$809$	−0.701398	+	4.42845i	−0.0246598	+	0.155696i	0.972286	+	0.233796i	$0.0751147\pi$
$810$	9.49426	−	1.46050i	0.333594	−	0.0513169i
$811$	38.5988			1.35539			0.677693	−	0.735345i	$-0.262980\pi$
$811$	38.5988			1.35539			0.677693	+	0.735345i	$0.262980\pi$
$812$	−8.89513	+	12.6078i	−0.312158	+	0.442447i
$813$	7.84201	−	2.54803i	0.275031	−	0.0893631i
$814$	4.07705	+	16.4771i	0.142901	+	0.577521i
$815$	−6.47729	+	5.40573i	−0.226889	+	0.189354i
$816$	−18.4604	+	0.513077i	−0.646243	+	0.0179613i
$817$	80.5015			2.81639
$818$	−8.46627	−	34.2157i	−0.296016	−	1.19632i
$819$	−12.9045			−0.450919
$820$	−28.4885	+	2.89936i	−0.994861	+	0.101250i
$821$	−36.1567			−1.26188			−0.630939	−	0.775833i	$-0.717330\pi$
$821$	−36.1567			−1.26188			−0.630939	+	0.775833i	$0.717330\pi$
$822$	1.42183	+	5.74621i	0.0495920	+	0.200422i
$823$	−29.9058			−1.04245			−0.521225	−	0.853420i	$-0.674525\pi$
$823$	−29.9058			−1.04245			−0.521225	+	0.853420i	$0.674525\pi$
$824$	10.1612	+	38.7487i	0.353983	+	1.34988i
$825$	−2.51835	+	7.18909i	−0.0876778	+	0.250292i
$826$	−2.29528	−	9.27619i	−0.0798631	−	0.322760i
$827$	−18.2048	+	5.91510i	−0.633043	+	0.205688i	−0.607923	−	0.793996i	$-0.707997\pi$
$827$	−18.2048	+	5.91510i	−0.633043	+	0.205688i	−0.0251204	+	0.999684i	$0.507997\pi$
$828$	−15.8240	−	11.1643i	−0.549923	−	0.387985i
$829$	25.7983			0.896011			0.448005	−	0.894031i	$-0.352135\pi$
$829$	25.7983			0.896011			0.448005	+	0.894031i	$0.352135\pi$
$830$	22.6643	−	30.9049i	0.786690	−	1.07272i
$831$	−0.377817	+	2.38544i	−0.0131063	+	0.0827500i
$832$	−7.29290	+	15.9203i	−0.252836	+	0.551938i
$833$	−1.62238	−	0.527142i	−0.0562121	−	0.0182644i
$834$	5.11177	+	8.21305i	0.177006	+	0.284395i
$835$	4.24378	−	47.0614i	0.146862	−	1.62863i
$836$	−3.48801	+	24.1932i	−0.120635	+	0.836740i
$837$	−14.2139	−	19.5638i	−0.491305	−	0.676224i
$838$	6.80146	+	27.4875i	0.234952	+	0.949540i
$839$	9.80309	+	4.99492i	0.338440	+	0.172444i	0.614948	−	0.788568i	$-0.289177\pi$
$839$	9.80309	+	4.99492i	0.338440	+	0.172444i	−0.276508	+	0.961012i	$0.589177\pi$
$840$	8.05079	−	11.3040i	0.277779	−	0.390026i
$841$	−19.1147	+	6.21076i	−0.659129	+	0.214164i
$842$	11.4271	−	0.979248i	0.393804	−	0.0337471i
$843$	−2.53838	−	4.98186i	−0.0874266	−	0.171584i
$844$	−13.6601	+	19.3615i	−0.470199	+	0.666451i
$845$	13.8207	+	12.0790i	0.475447	+	0.415530i
$846$	2.89294	−	40.3389i	0.0994612	−	1.38688i
$847$	−20.1094			−0.690969
$848$	−0.462560	−	1.29959i	−0.0158844	−	0.0446282i
$849$	−24.4379	+	3.87058i	−0.838707	+	0.132838i
$850$	−24.5187	−	29.6459i	−0.840986	−	1.01685i
$851$	16.6893	+	22.9708i	0.572101	+	0.787430i
$852$	−2.75080	−	8.08227i	−0.0942409	−	0.276894i
$853$	−3.73788	+	23.6001i	−0.127983	+	0.808051i	0.837281	+	0.546773i	$0.184144\pi$
$853$	−3.73788	+	23.6001i	−0.127983	+	0.808051i	−0.965264	+	0.261278i	$0.915856\pi$
$854$	27.5252	−	32.6849i	0.941893	−	1.11845i
$855$	−29.3822	−	18.4691i	−1.00485	−	0.631632i
$856$	−5.67452	−	21.6392i	−0.193951	−	0.739612i
$857$	26.6879	−	4.22695i	0.911642	−	0.144390i	0.317042	−	0.948412i	$-0.397310\pi$
$857$	26.6879	−	4.22695i	0.911642	−	0.144390i	0.594600	+	0.804022i	$0.297310\pi$
$858$	−1.06906	+	4.59329i	−0.0364971	+	0.156812i
$859$	−27.5618	−	8.95536i	−0.940396	−	0.305553i	−0.201589	−	0.979470i	$-0.564610\pi$
$859$	−27.5618	−	8.95536i	−0.940396	−	0.305553i	−0.738807	+	0.673917i	$0.764610\pi$
$860$	34.2452	−	40.2997i	1.16775	−	1.37421i
$861$	14.0474	−	0.286369i	0.478734	−	0.00975944i
$862$	2.75022	+	4.41875i	0.0936728	+	0.150503i
$863$	3.34925	−	1.70653i	0.114010	−	0.0580909i	−0.396056	−	0.918227i	$-0.629621\pi$
$863$	3.34925	−	1.70653i	0.114010	−	0.0580909i	0.510065	+	0.860136i	$0.329621\pi$
$864$	−8.88022	+	23.7386i	−0.302111	+	0.807605i
$865$	−19.9452	+	16.6456i	−0.678155	+	0.565966i
$866$	27.4465	−	23.7733i	0.932671	−	0.807848i
$867$	3.30432	−	10.1697i	0.112221	−	0.345380i
$868$	27.6271	+	3.98308i	0.937724	+	0.135195i
$869$	21.3254	−	15.4938i	0.723414	−	0.525591i
$870$	−7.62531	+	2.44019i	−0.258522	+	0.0827302i
$871$	−3.99916	−	5.50437i	−0.135506	−	0.186509i
$872$	24.9845	+	1.44321i	0.846083	+	0.0488733i
$873$	13.7301	−	18.8979i	0.464695	−	0.639598i
$874$	9.82108	+	39.6911i	0.332203	+	1.34257i
$875$	28.8819	−	1.28212i	0.976386	−	0.0433437i
$876$	3.72496	−	12.0305i	0.125855	−	0.406471i
$877$	−12.7659	−	6.50453i	−0.431072	−	0.219642i	0.224971	−	0.974365i	$-0.427771\pi$
$877$	−12.7659	−	6.50453i	−0.431072	−	0.219642i	−0.656043	+	0.754723i	$0.727771\pi$
$878$	−14.0857	−	33.3488i	−0.475370	−	1.12547i
$879$	−7.18187	+	22.1035i	−0.242239	+	0.745534i
$880$	10.6275	+	12.0379i	0.358253	+	0.405797i
$881$	−49.7461	+	16.1635i	−1.67599	+	0.544562i	−0.984127	−	0.177467i	$-0.943210\pi$
$881$	−49.7461	+	16.1635i	−1.67599	+	0.544562i	−0.691863	+	0.722029i	$0.743210\pi$
$882$	−0.651195	+	0.773264i	−0.0219269	+	0.0260372i
$883$	−6.10370	+	1.98321i	−0.205406	+	0.0667404i	−0.409913	−	0.912125i	$-0.634441\pi$
$883$	−6.10370	+	1.98321i	−0.205406	+	0.0667404i	0.204507	+	0.978865i	$0.434441\pi$
$884$	−17.0744	−	16.6064i	−0.574274	−	0.558535i
$885$	1.94956	−	4.55904i	0.0655337	−	0.153251i
$886$	−39.8933	+	3.41866i	−1.34024	+	0.114852i
$887$	−6.50419	−	4.72557i	−0.218389	−	0.158669i	0.473212	−	0.880949i	$-0.343094\pi$
$887$	−6.50419	−	4.72557i	−0.218389	−	0.158669i	−0.691601	+	0.722279i	$0.743094\pi$
$888$	10.1645	−	12.4160i	0.341099	−	0.416653i
$889$	9.63514	+	18.9100i	0.323152	+	0.634222i
$890$	41.6509	+	13.7382i	1.39614	+	0.460506i
$891$	0.853129	−	5.38644i	0.0285809	−	0.180453i
$892$	41.4433	+	29.2393i	1.38762	+	0.979005i
$893$	−60.3782	+	60.3782i	−2.02048	+	2.02048i
$894$	2.04863	+	4.85025i	0.0685164	+	0.162217i
$895$	7.31867	−	0.492170i	0.244636	−	0.0164514i
$896$	−12.4960	−	26.4522i	−0.417462	−	0.883705i
$897$	1.23409	+	7.79175i	0.0412051	+	0.260159i
$898$	−3.25400	+	45.3735i	−0.108587	+	1.51413i
$899$	−11.3865	−	11.3865i	−0.379763	−	0.379763i
$900$	−21.7449	+	6.85221i	−0.724832	+	0.228407i
$901$	1.87629			0.0625084
$902$	−3.36180	+	15.9059i	−0.111936	+	0.529610i
$903$	−18.3482	+	18.3482i	−0.610591	+	0.610591i
$904$	34.1227	−	21.9014i	1.13491	−	0.728429i
$905$	−1.98232	+	7.86132i	−0.0658945	+	0.261319i
$906$	−13.7743	−	15.9026i	−0.457620	−	0.528328i
$907$	21.9064	−	3.46963i	0.727390	−	0.115207i	0.218252	−	0.975892i	$-0.429964\pi$
$907$	21.9064	−	3.46963i	0.727390	−	0.115207i	0.509138	+	0.860685i	$0.329964\pi$
$908$	12.4792	+	12.1372i	0.414138	+	0.402788i
$909$	−27.3872	−	13.9545i	−0.908375	−	0.462840i
$910$	17.6907	−	2.72137i	0.586442	−	0.0902126i
$911$	36.1229			1.19680			0.598402	−	0.801196i	$-0.295803\pi$
$911$	36.1229			1.19680			0.598402	+	0.801196i	$0.295803\pi$
$912$	20.2891	−	11.0583i	0.671840	−	0.366178i
$913$	−12.7891	−	17.6027i	−0.423258	−	0.582564i
$914$	−30.8020	−	2.20899i	−1.01884	−	0.0730669i
$915$	21.6172	−	4.93008i	0.714644	−	0.162983i
$916$	6.92312	−	2.35628i	0.228746	−	0.0778538i
$917$	−4.34182	+	5.97600i	−0.143379	+	0.197345i
$918$	−26.3690	−	22.2063i	−0.870307	−	0.732918i
$919$	−3.49503	+	22.0667i	−0.115290	+	0.727915i	0.860540	+	0.509384i	$0.170127\pi$
$919$	−3.49503	+	22.0667i	−0.115290	+	0.727915i	−0.975830	+	0.218531i	$0.929873\pi$
$920$	24.0475	+	11.9680i	0.792823	+	0.394574i
$921$	18.4335	+	9.39232i	0.607404	+	0.309488i
$922$	−23.9214	+	28.4056i	−0.787809	+	0.935488i
$923$	4.99898	−	9.81105i	0.164543	−	0.322935i
$924$	−4.71922	−	6.30922i	−0.155251	−	0.207558i
$925$	33.4182	+	0.761555i	1.09878	+	0.0250398i
$926$	−16.1269	−	6.54912i	−0.529964	−	0.215217i
$927$	−14.6594	+	28.7707i	−0.481479	+	0.944955i
$928$	−3.36771	+	16.5381i	−0.110550	+	0.542890i
$929$	−26.1062	−	26.1062i	−0.856518	−	0.856518i	0.134408	−	0.990926i	$-0.457087\pi$
$929$	−26.1062	−	26.1062i	−0.856518	−	0.856518i	−0.990926	+	0.134408i	$0.957087\pi$
$930$	10.1957	+	10.2867i	0.334329	+	0.337315i
$931$	2.10815	−	0.333898i	0.0690918	−	0.0109431i
$932$	−16.9800	+	2.93174i	−0.556198	+	0.0960322i
$933$	−17.3779	−	2.75239i	−0.568927	−	0.0901092i
$934$	−4.59070	+	19.7243i	−0.150212	+	0.645397i
$935$	−20.2727	+	8.12792i	−0.662989	+	0.265811i
$936$	−12.9254	+	5.67223i	−0.422479	+	0.185403i
$937$	−39.5446	−	12.8488i	−1.29187	−	0.419753i	−0.419122	−	0.907930i	$-0.637662\pi$
$937$	−39.5446	−	12.8488i	−1.29187	−	0.419753i	−0.872745	+	0.488177i	$0.837662\pi$
$938$	11.3377	+	0.813089i	0.370187	+	0.0265483i
$939$	−20.1595	−	14.6468i	−0.657882	−	0.477979i
$940$	4.54097	+	55.9106i	0.148110	+	1.82360i
$941$	50.2557	+	16.3291i	1.63829	+	0.532313i	0.976155	−	0.217073i	$-0.0696509\pi$
$941$	50.2557	+	16.3291i	1.63829	+	0.532313i	0.662134	+	0.749385i	$0.269651\pi$
$942$	−14.6179	−	23.4865i	−0.476277	−	0.765231i
$943$	4.80076	+	26.7676i	0.156334	+	0.871674i
$944$	−6.37639	−	8.28230i	−0.207534	−	0.269566i
$945$	25.2577	−	5.76033i	0.821634	−	0.187384i
$946$	−15.8651	−	25.4903i	−0.515819	−	0.828762i
$947$	4.73613	+	29.9027i	0.153904	+	0.971709i	0.936878	+	0.349655i	$0.113701\pi$
$947$	4.73613	+	29.9027i	0.153904	+	0.971709i	−0.782975	+	0.622053i	$0.786299\pi$
$948$	−23.8036	−	7.37027i	−0.773106	−	0.239375i
$949$	14.4725	−	7.37410i	0.469797	−	0.239373i
$950$	44.1749	+	19.1230i	1.43322	+	0.620433i
$951$	4.01514	−	2.91717i	0.130200	−	0.0945957i
$952$	39.5957	−	3.94801i	1.28330	−	0.127956i
$953$	37.1052	+	5.87689i	1.20196	+	0.190371i	0.725121	−	0.688622i	$-0.241784\pi$
$953$	37.1052	+	5.87689i	1.20196	+	0.190371i	0.476835	+	0.878993i	$0.341784\pi$
$954$	0.418373	−	1.03022i	0.0135453	−	0.0333548i
$955$	8.11467	+	9.72321i	0.262585	+	0.314636i
$956$	0.234472	+	16.8757i	0.00758336	+	0.545801i
$957$			4.54539i			0.146932i
$958$	−14.0664	+	12.1838i	−0.454465	+	0.393642i
$959$	−3.94144	−	12.1305i	−0.127276	−	0.391715i
$960$	3.09508	−	14.8611i	0.0998933	−	0.479639i
$961$	0.577708	−	1.77800i	0.0186357	−	0.0573549i
$962$	20.6195	−	1.76700i	0.664800	−	0.0569702i
$963$	8.18654	−	16.0670i	0.263808	−	0.517751i
$964$	4.71935	−	32.7339i	0.152000	−	1.05429i
$965$	−5.39633	+	6.17445i	−0.173714	+	0.198763i
$966$	−11.2850	−	6.80809i	−0.363089	−	0.219047i
$967$	−7.98383	+	5.80059i	−0.256743	+	0.186535i	−0.708710	−	0.705500i	$-0.750722\pi$
$967$	−7.98383	+	5.80059i	−0.256743	+	0.186535i	0.451967	+	0.892035i	$0.350722\pi$
$968$	−20.1420	+	8.83921i	−0.647388	+	0.284103i
$969$	4.91666	+	31.0425i	0.157946	+	0.997230i
$970$	−14.8373	+	28.8026i	−0.476398	+	0.924796i
$971$	17.6639	+	34.6673i	0.566860	+	1.11253i	0.979465	+	0.201615i	$0.0646191\pi$
$971$	17.6639	+	34.6673i	0.566860	+	1.11253i	−0.412605	+	0.910910i	$0.635381\pi$
$972$	−28.3414	+	14.9402i	−0.909049	+	0.479207i
$973$	−12.2520	−	16.8635i	−0.392782	−	0.540618i
$974$	−5.66852	+	2.39424i	−0.181631	+	0.0767166i
$975$	8.17689	+	4.40381i	0.261870	+	0.141035i
$976$	13.2029	−	44.8367i	0.422615	−	1.43519i
$977$	−18.4442	−	56.7655i	−0.590083	−	1.81609i	−0.577819	−	0.816165i	$-0.696096\pi$
$977$	−18.4442	−	56.7655i	−0.590083	−	1.81609i	−0.0122645	−	0.999925i	$-0.503904\pi$
$978$	2.33894	−	3.87700i	0.0747911	−	0.123973i
$979$	14.6356	−	20.1442i	0.467756	−	0.643811i
$980$	0.729651	−	1.19739i	0.0233079	−	0.0382493i
$981$	14.2643	+	14.2643i	0.455424	+	0.455424i
$982$	−9.05146	−	36.5807i	−0.288844	−	1.16734i
$983$	32.7050	−	32.7050i	1.04313	−	1.04313i	0.0441013	−	0.999027i	$-0.485958\pi$
$983$	32.7050	−	32.7050i	1.04313	−	1.04313i	0.999027	−	0.0441013i	$-0.0140424\pi$
$984$	13.9442	−	6.46143i	0.444526	−	0.205983i
$985$	12.4158	+	3.13078i	0.395599	+	0.0997548i
$986$	−19.6563	−	11.8584i	−0.625984	−	0.377647i
$987$		−	27.5233i		−	0.876076i
$988$	28.4686	+	8.81466i	0.905706	+	0.280432i
$989$	−40.6318	−	29.5207i	−1.29202	−	0.938705i
$990$	−0.0575446	+	12.9436i	−0.00182889	+	0.411374i
$991$	−36.9447	−	18.8243i	−1.17359	−	0.597973i	−0.245159	−	0.969483i	$-0.578840\pi$
$991$	−36.9447	−	18.8243i	−1.17359	−	0.597973i	−0.928429	+	0.371510i	$0.878840\pi$
$992$	29.4226	−	8.15409i	0.934167	−	0.258893i
$993$	−18.4548	+	18.4548i	−0.585646	+	0.585646i
$994$	7.15770	+	16.9463i	0.227028	+	0.537504i
$995$	5.53902	+	13.8155i	0.175599	+	0.437980i
$996$	−6.08366	+	19.6483i	−0.192768	+	0.622580i
$997$	−9.83576	+	30.2714i	−0.311502	+	0.958703i	0.665669	+	0.746247i	$0.268146\pi$
$997$	−9.83576	+	30.2714i	−0.311502	+	0.958703i	−0.977171	+	0.212456i	$0.931854\pi$
$998$	−8.59437	+	36.9263i	−0.272050	+	1.16888i
$999$	29.5847	−	4.68576i	0.936020	−	0.148251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bv.c.103.11	yes	960
4.3	odd	2	inner	820.2.bv.c.103.27	yes	960
5.2	odd	4		820.2.bk.c.267.51	yes	960
20.7	even	4		820.2.bk.c.267.36	yes	960
41.2	even	20		820.2.bk.c.43.36	✓	960
164.43	odd	20		820.2.bk.c.43.51	yes	960
205.2	odd	20	inner	820.2.bv.c.207.27	yes	960
820.207	even	20	inner	820.2.bv.c.207.11	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.36	✓	960	41.2	even	20
820.2.bk.c.43.51	yes	960	164.43	odd	20
820.2.bk.c.267.36	yes	960	20.7	even	4
820.2.bk.c.267.51	yes	960	5.2	odd	4
820.2.bv.c.103.11	yes	960	1.1	even	1	trivial
820.2.bv.c.103.27	yes	960	4.3	odd	2	inner
820.2.bv.c.207.11	yes	960	820.207	even	20	inner
820.2.bv.c.207.27	yes	960	205.2	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37281 + 0.339686i) q^{2} -0.848586 q^{3} +(1.76923 - 0.932650i) q^{4} +(-2.22703 - 0.200823i) q^{5} +(1.16495 - 0.288253i) q^{6} +(-2.45926 + 0.799062i) q^{7} +(-2.11201 + 1.88134i) q^{8} -2.27990 q^{9} +(3.12551 - 0.480799i) q^{10} +(0.280850 - 1.77322i) q^{11} +(-1.50134 + 0.791434i) q^{12} +(-2.08177 - 0.676408i) q^{13} +(3.10467 - 1.93234i) q^{14} +(1.88983 + 0.170416i) q^{15} +(2.26033 - 3.30014i) q^{16} +(3.19795 + 4.40160i) q^{17} +(3.12988 - 0.774451i) q^{18} +(-6.06554 - 3.09055i) q^{19} +(-4.12742 + 1.72174i) q^{20} +(2.08689 - 0.678072i) q^{21} +(0.216783 + 2.52970i) q^{22} +(1.92814 + 3.78420i) q^{23} +(1.79222 - 1.59647i) q^{24} +(4.91934 + 0.894480i) q^{25} +(3.08765 + 0.221433i) q^{26} +4.48045 q^{27} +(-3.60574 + 3.70735i) q^{28} +(2.94682 - 0.466730i) q^{29} +(-2.65227 + 0.407999i) q^{30} +(-3.17243 - 4.36648i) q^{31} +(-1.98199 + 5.29827i) q^{32} +(-0.238326 + 1.50473i) q^{33} +(-5.88535 - 4.95627i) q^{34} +(5.63732 - 1.28566i) q^{35} +(-4.03366 + 2.12635i) q^{36} +(6.60307 - 1.04582i) q^{37} +(9.37666 + 2.18236i) q^{38} +(1.76656 + 0.573990i) q^{39} +(5.08132 - 3.76565i) q^{40} +(6.12880 + 1.85414i) q^{41} +(-2.63458 + 1.63975i) q^{42} +(-10.5365 + 5.36862i) q^{43} +(-1.15691 - 3.39916i) q^{44} +(5.07742 + 0.457858i) q^{45} +(-3.93242 - 4.54003i) q^{46} +(3.87605 - 11.9292i) q^{47} +(-1.91808 + 2.80045i) q^{48} +(-0.253659 + 0.184294i) q^{49} +(-7.05717 + 0.443078i) q^{50} +(-2.71373 - 3.73514i) q^{51} +(-4.31398 + 0.744844i) q^{52} +(0.202706 - 0.279001i) q^{53} +(-6.15082 + 1.52195i) q^{54} +(-0.981566 + 3.89261i) q^{55} +(3.69067 - 6.31432i) q^{56} +(5.14713 + 2.62259i) q^{57} +(-3.88688 + 1.64172i) q^{58} +(0.807500 - 2.48523i) q^{59} +(3.50247 - 1.46104i) q^{60} +(11.1131 - 3.61088i) q^{61} +(5.83839 + 4.91673i) q^{62} +(5.60687 - 1.82178i) q^{63} +(0.921155 - 7.94679i) q^{64} +(4.50033 + 1.92445i) q^{65} +(-0.183959 - 2.14666i) q^{66} +(2.51467 + 1.82702i) q^{67} +(9.76305 + 4.80486i) q^{68} +(-1.63620 - 3.21121i) q^{69} +(-7.30226 + 3.67989i) q^{70} +(-0.786938 + 4.96853i) q^{71} +(4.81517 - 4.28926i) q^{72} +(-5.24712 + 5.24712i) q^{73} +(-8.70953 + 3.67869i) q^{74} +(-4.17448 - 0.759043i) q^{75} +(-13.6137 + 0.189149i) q^{76} +(0.726228 + 4.58522i) q^{77} +(-2.62013 - 0.187905i) q^{78} +(10.3820 + 10.3820i) q^{79} +(-5.69656 + 6.89559i) q^{80} +3.03766 q^{81} +(-9.04351 - 0.463525i) q^{82} +(8.56967 - 8.56967i) q^{83} +(3.05978 - 3.14600i) q^{84} +(-6.23799 - 10.4447i) q^{85} +(12.6410 - 10.9492i) q^{86} +(-2.50063 + 0.396060i) q^{87} +(2.74286 + 4.27343i) q^{88} +(12.3575 + 6.29646i) q^{89} +(-7.12587 + 1.09617i) q^{90} +5.66011 q^{91} +(6.94066 + 4.89682i) q^{92} +(2.69208 + 3.70533i) q^{93} +(-1.26889 + 17.6933i) q^{94} +(12.8875 + 8.10085i) q^{95} +(1.68189 - 4.49604i) q^{96} +(-6.02225 + 8.28892i) q^{97} +(0.285624 - 0.339166i) q^{98} +(-0.640311 + 4.04277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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