LMFDB - Embedded newform 820.2.s.c.583.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] 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:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			583.19
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27523 + 0.611379i) q^{2} +1.22240 q^{3} +(1.25243 - 1.55930i) q^{4} +(1.86406 + 1.23502i) q^{5} +(-1.55885 + 0.747352i) q^{6} -2.99230i q^{7} +(-0.643820 + 2.75418i) q^{8} -1.50573 q^{9} +(-3.13217 - 0.435297i) q^{10} +(-0.0849144 + 0.0849144i) q^{11} +(1.53098 - 1.90609i) q^{12} -6.06762i q^{13} +(1.82943 + 3.81587i) q^{14} +(2.27863 + 1.50970i) q^{15} +(-0.862826 - 3.90583i) q^{16} +6.38170i q^{17} +(1.92015 - 0.920571i) q^{18} +(5.18495 - 5.18495i) q^{19} +(4.26038 - 1.35984i) q^{20} -3.65779i q^{21} +(0.0563707 - 0.160200i) q^{22} +(5.57803 - 5.57803i) q^{23} +(-0.787008 + 3.36672i) q^{24} +(1.94943 + 4.60432i) q^{25} +(3.70961 + 7.73762i) q^{26} -5.50782 q^{27} +(-4.66589 - 3.74765i) q^{28} +(-0.521178 + 0.521178i) q^{29} +(-3.82878 - 0.532109i) q^{30} -1.55018i q^{31} +(3.48825 + 4.45333i) q^{32} +(-0.103800 + 0.103800i) q^{33} +(-3.90163 - 8.13815i) q^{34} +(3.69556 - 5.57782i) q^{35} +(-1.88582 + 2.34788i) q^{36} +(4.51467 - 4.51467i) q^{37} +(-3.44205 + 9.78198i) q^{38} -7.41708i q^{39} +(-4.60159 + 4.33882i) q^{40} +(-2.83201 + 5.74280i) q^{41} +(2.23630 + 4.66454i) q^{42} +(0.300997 + 0.300997i) q^{43} +(0.0260574 + 0.238757i) q^{44} +(-2.80677 - 1.85961i) q^{45} +(-3.70300 + 10.5236i) q^{46} -4.09699 q^{47} +(-1.05472 - 4.77450i) q^{48} -1.95384 q^{49} +(-5.30095 - 4.67973i) q^{50} +7.80101i q^{51} +(-9.46123 - 7.59928i) q^{52} -9.00865i q^{53} +(7.02375 - 3.36736i) q^{54} +(-0.263157 + 0.0534141i) q^{55} +(8.24132 + 1.92650i) q^{56} +(6.33810 - 6.33810i) q^{57} +(0.345986 - 0.983260i) q^{58} -4.12568 q^{59} +(5.20790 - 1.66227i) q^{60} +10.0153i q^{61} +(0.947745 + 1.97683i) q^{62} +4.50559i q^{63} +(-7.17099 - 3.54639i) q^{64} +(7.49365 - 11.3104i) q^{65} +(0.0689078 - 0.195830i) q^{66} +6.34649 q^{67} +(9.95098 + 7.99265i) q^{68} +(6.81861 - 6.81861i) q^{69} +(-1.30254 + 9.37240i) q^{70} +(-2.90660 + 2.90660i) q^{71} +(0.969418 - 4.14705i) q^{72} +(0.672050 - 0.672050i) q^{73} +(-2.99708 + 8.51742i) q^{74} +(2.38299 + 5.62833i) q^{75} +(-1.59109 - 14.5787i) q^{76} +(0.254089 + 0.254089i) q^{77} +(4.53464 + 9.45849i) q^{78} +(9.02289 + 9.02289i) q^{79} +(3.21544 - 8.34631i) q^{80} -2.21559 q^{81} +(0.100438 - 9.05483i) q^{82} +(7.89831 - 7.89831i) q^{83} +(-5.70360 - 4.58114i) q^{84} +(-7.88155 + 11.8959i) q^{85} +(-0.567865 - 0.199818i) q^{86} +(-0.637090 + 0.637090i) q^{87} +(-0.179200 - 0.288539i) q^{88} +(-4.98059 + 4.98059i) q^{89} +(4.71621 + 0.655439i) q^{90} -18.1561 q^{91} +(-1.71171 - 15.6839i) q^{92} -1.89494i q^{93} +(5.22461 - 2.50481i) q^{94} +(16.0686 - 3.26151i) q^{95} +(4.26405 + 5.44377i) q^{96} -7.96240i q^{97} +(2.49160 - 1.19454i) q^{98} +(0.127858 - 0.127858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

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

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

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 $

$2$	−1.27523	+	0.611379i	−0.901725	+	0.432310i
$2$	−1.27523	+	0.611379i	−0.901725	+	0.432310i
$3$	1.22240			0.705755			0.352878	−	0.935670i	$-0.385203\pi$
$3$	1.22240			0.705755			0.352878	+	0.935670i	$0.385203\pi$
$4$	1.25243	−	1.55930i	0.626216	−	0.779649i
$5$	1.86406	+	1.23502i	0.833632	+	0.552320i
$5$	1.86406	+	1.23502i	0.833632	+	0.552320i
$6$	−1.55885	+	0.747352i	−0.636397	+	0.305105i
$7$		−	2.99230i		−	1.13098i	−0.824755	−	0.565491i	$-0.808687\pi$
$7$		−	2.99230i		−	1.13098i	0.824755	−	0.565491i	$-0.191313\pi$
$8$	−0.643820	+	2.75418i	−0.227625	+	0.973749i
$9$	−1.50573			−0.501910
$10$	−3.13217	−	0.435297i	−0.990481	−	0.137653i
$11$	−0.0849144	+	0.0849144i	−0.0256027	+	0.0256027i	−0.719792	−	0.694190i	$-0.755763\pi$
$11$	−0.0849144	+	0.0849144i	−0.0256027	+	0.0256027i	0.694190	+	0.719792i	$0.255763\pi$
$12$	1.53098	−	1.90609i	0.441955	−	0.550242i
$13$		−	6.06762i		−	1.68285i	−0.540371	−	0.841427i	$-0.681716\pi$
$13$		−	6.06762i		−	1.68285i	0.540371	−	0.841427i	$-0.318284\pi$
$14$	1.82943	+	3.81587i	0.488935	+	1.01983i
$15$	2.27863	+	1.50970i	0.588340	+	0.389803i
$16$	−0.862826	−	3.90583i	−0.215707	−	0.976458i
$17$			6.38170i			1.54779i	0.633314	+	0.773895i	$0.281694\pi$
$17$			6.38170i			1.54779i	−0.633314	+	0.773895i	$0.718306\pi$
$18$	1.92015	−	0.920571i	0.452585	−	0.216981i
$19$	5.18495	−	5.18495i	1.18951	−	1.18951i	0.212306	−	0.977203i	$-0.431903\pi$
$19$	5.18495	−	5.18495i	1.18951	−	1.18951i	0.977203	−	0.212306i	$-0.0680975\pi$
$20$	4.26038	−	1.35984i	0.952650	−	0.304069i
$21$		−	3.65779i		−	0.798196i
$22$	0.0563707	−	0.160200i	0.0120183	−	0.0341548i
$23$	5.57803	−	5.57803i	1.16310	−	1.16310i	0.179308	−	0.983793i	$-0.442614\pi$
$23$	5.57803	−	5.57803i	1.16310	−	1.16310i	0.983793	−	0.179308i	$-0.0573857\pi$
$24$	−0.787008	+	3.36672i	−0.160647	+	0.687228i
$25$	1.94943	+	4.60432i	0.389886	+	0.920863i
$26$	3.70961	+	7.73762i	0.727514	+	1.51747i
$27$	−5.50782			−1.05998
$28$	−4.66589	−	3.74765i	−0.881769	−	0.708239i
$29$	−0.521178	+	0.521178i	−0.0967803	+	0.0967803i	−0.753839	−	0.657059i	$-0.771800\pi$
$29$	−0.521178	+	0.521178i	−0.0967803	+	0.0967803i	0.657059	+	0.753839i	$0.271800\pi$
$30$	−3.82878	−	0.532109i	−0.699037	−	0.0971493i
$31$		−	1.55018i		−	0.278420i	−0.990263	−	0.139210i	$-0.955544\pi$
$31$		−	1.55018i		−	0.278420i	0.990263	−	0.139210i	$-0.0444563\pi$
$32$	3.48825	+	4.45333i	0.616641	+	0.787245i
$33$	−0.103800	+	0.103800i	−0.0180692	+	0.0180692i
$34$	−3.90163	−	8.13815i	−0.669125	−	1.39568i
$35$	3.69556	−	5.57782i	0.624664	−	0.942823i
$36$	−1.88582	+	2.34788i	−0.314304	+	0.391314i
$37$	4.51467	−	4.51467i	0.742207	−	0.742207i	−0.230796	−	0.973002i	$-0.574133\pi$
$37$	4.51467	−	4.51467i	0.742207	−	0.742207i	0.973002	+	0.230796i	$0.0741329\pi$
$38$	−3.44205	+	9.78198i	−0.558374	+	1.58685i
$39$		−	7.41708i		−	1.18768i
$40$	−4.60159	+	4.33882i	−0.727576	+	0.686027i
$41$	−2.83201	+	5.74280i	−0.442285	+	0.896875i
$41$	−2.83201	+	5.74280i	−0.442285	+	0.896875i
$42$	2.23630	+	4.66454i	0.345068	+	0.719754i
$43$	0.300997	+	0.300997i	0.0459017	+	0.0459017i	0.729685	−	0.683783i	$-0.239667\pi$
$43$	0.300997	+	0.300997i	0.0459017	+	0.0459017i	−0.683783	+	0.729685i	$0.739667\pi$
$44$	0.0260574	+	0.238757i	0.00392830	+	0.0359939i
$45$	−2.80677	−	1.85961i	−0.418408	−	0.277215i
$46$	−3.70300	+	10.5236i	−0.545977	+	1.55162i
$47$	−4.09699			−0.597607			−0.298804	−	0.954315i	$-0.596588\pi$
$47$	−4.09699			−0.597607			−0.298804	+	0.954315i	$0.596588\pi$
$48$	−1.05472	−	4.77450i	−0.152236	−	0.689140i
$49$	−1.95384			−0.279120
$50$	−5.30095	−	4.67973i	−0.749668	−	0.661814i
$51$			7.80101i			1.09236i
$52$	−9.46123	−	7.59928i	−1.31204	−	1.05383i
$53$		−	9.00865i		−	1.23743i	−0.785614	−	0.618717i	$-0.787653\pi$
$53$		−	9.00865i		−	1.23743i	0.785614	−	0.618717i	$-0.212347\pi$
$54$	7.02375	−	3.36736i	0.955811	−	0.458240i
$55$	−0.263157	+	0.0534141i	−0.0354841	+	0.00720235i
$56$	8.24132	+	1.92650i	1.10129	+	0.257439i
$57$	6.33810	−	6.33810i	0.839502	−	0.839502i
$58$	0.345986	−	0.983260i	0.0454302	−	0.129108i
$59$	−4.12568			−0.537118			−0.268559	−	0.963263i	$-0.586547\pi$
$59$	−4.12568			−0.537118			−0.268559	+	0.963263i	$0.586547\pi$
$60$	5.20790	−	1.66227i	0.672338	−	0.214599i
$61$			10.0153i			1.28233i	0.767404	+	0.641164i	$0.221548\pi$
$61$			10.0153i			1.28233i	−0.767404	+	0.641164i	$0.778452\pi$
$62$	0.947745	+	1.97683i	0.120364	+	0.251058i
$63$			4.50559i			0.567651i
$64$	−7.17099	−	3.54639i	−0.896374	−	0.443298i
$65$	7.49365	−	11.3104i	0.929473	−	1.40288i
$66$	0.0689078	−	0.195830i	0.00848196	−	0.0241050i
$67$	6.34649			0.775347			0.387673	−	0.921797i	$-0.373279\pi$
$67$	6.34649			0.775347			0.387673	+	0.921797i	$0.373279\pi$
$68$	9.95098	+	7.99265i	1.20673	+	0.969251i
$69$	6.81861	−	6.81861i	0.820864	−	0.820864i
$70$	−1.30254	+	9.37240i	−0.155683	+	1.12022i
$71$	−2.90660	+	2.90660i	−0.344949	+	0.344949i	−0.858224	−	0.513275i	$-0.828432\pi$
$71$	−2.90660	+	2.90660i	−0.344949	+	0.344949i	0.513275	+	0.858224i	$0.328432\pi$
$72$	0.969418	−	4.14705i	0.114247	−	0.488734i
$73$	0.672050	−	0.672050i	0.0786575	−	0.0786575i	−0.666683	−	0.745341i	$-0.732287\pi$
$73$	0.672050	−	0.672050i	0.0786575	−	0.0786575i	0.745341	+	0.666683i	$0.232287\pi$
$74$	−2.99708	+	8.51742i	−0.348403	+	0.990130i
$75$	2.38299	+	5.62833i	0.275164	+	0.649904i
$76$	−1.59109	−	14.5787i	−0.182510	−	1.67229i
$77$	0.254089	+	0.254089i	0.0289561	+	0.0289561i
$78$	4.53464	+	9.45849i	0.513447	+	1.07096i
$79$	9.02289	+	9.02289i	1.01515	+	1.01515i	0.999883	+	0.0152716i	$0.00486129\pi$
$79$	9.02289	+	9.02289i	1.01515	+	1.01515i	0.0152716	+	0.999883i	$0.495139\pi$
$80$	3.21544	−	8.34631i	0.359497	−	0.933146i
$81$	−2.21559			−0.246177
$82$	0.100438	−	9.05483i	0.0110915	−	0.999938i
$83$	7.89831	−	7.89831i	0.866952	−	0.866952i	−0.125182	−	0.992134i	$-0.539951\pi$
$83$	7.89831	−	7.89831i	0.866952	−	0.866952i	0.992134	+	0.125182i	$0.0399514\pi$
$84$	−5.70360	−	4.58114i	−0.622313	−	0.499843i
$85$	−7.88155	+	11.8959i	−0.854875	+	1.29029i
$86$	−0.567865	−	0.199818i	−0.0612345	−	0.0215469i
$87$	−0.637090	+	0.637090i	−0.0683032	+	0.0683032i
$88$	−0.179200	−	0.288539i	−0.0191028	−	0.0307584i
$89$	−4.98059	+	4.98059i	−0.527941	+	0.527941i	−0.919958	−	0.392017i	$-0.871778\pi$
$89$	−4.98059	+	4.98059i	−0.527941	+	0.527941i	0.392017	+	0.919958i	$0.371778\pi$
$90$	4.71621	+	0.655439i	0.497132	+	0.0690894i
$91$	−18.1561			−1.90328
$92$	−1.71171	−	15.6839i	−0.178458	−	1.63516i
$93$		−	1.89494i		−	0.196496i
$94$	5.22461	−	2.50481i	0.538877	−	0.258351i
$95$	16.0686	−	3.26151i	1.64860	−	0.334624i
$96$	4.26405	+	5.44377i	0.435197	+	0.555602i
$97$		−	7.96240i		−	0.808459i	−0.914658	−	0.404230i	$-0.867540\pi$
$97$		−	7.96240i		−	0.808459i	0.914658	−	0.404230i	$-0.132460\pi$
$98$	2.49160	−	1.19454i	0.251689	−	0.120666i
$99$	0.127858	−	0.127858i	0.0128502	−	0.0128502i
$100$	9.62103	+	2.72685i	0.962103	+	0.272685i
$101$	−6.43729	+	6.43729i	−0.640534	+	0.640534i	−0.950687	−	0.310153i	$-0.899620\pi$
$101$	−6.43729	+	6.43729i	−0.640534	+	0.640534i	0.310153	+	0.950687i	$0.399620\pi$
$102$	−4.76937	−	9.94810i	−0.472238	−	0.985009i
$103$	−2.37443	−	2.37443i	−0.233960	−	0.233960i	0.580384	−	0.814343i	$-0.302903\pi$
$103$	−2.37443	−	2.37443i	−0.233960	−	0.233960i	−0.814343	+	0.580384i	$0.802903\pi$
$104$	16.7113	+	3.90645i	1.63868	+	0.383059i
$105$	4.51747	−	6.81834i	0.440860	−	0.665402i
$106$	5.50770	+	11.4881i	0.534955	+	1.11582i
$107$	1.04652	+	1.04652i	0.101171	+	0.101171i	0.755881	−	0.654709i	$-0.227209\pi$
$107$	1.04652	+	1.04652i	0.101171	+	0.101171i	−0.654709	+	0.755881i	$0.727209\pi$
$108$	−6.89817	+	8.58834i	−0.663777	+	0.826413i
$109$	8.39521	+	8.39521i	0.804115	+	0.804115i	0.983736	−	0.179621i	$-0.0574871\pi$
$109$	8.39521	+	8.39521i	0.804115	+	0.804115i	−0.179621	+	0.983736i	$0.557487\pi$
$110$	0.302930	−	0.229004i	0.0288832	−	0.0218347i
$111$	5.51875	−	5.51875i	0.523816	−	0.523816i
$112$	−11.6874	+	2.58183i	−1.10436	+	0.243960i
$113$	4.60137	+	4.60137i	0.432860	+	0.432860i	0.889600	−	0.456740i	$-0.150983\pi$
$113$	4.60137	+	4.60137i	0.432860	+	0.432860i	−0.456740	+	0.889600i	$0.650983\pi$
$114$	−4.20757	+	11.9575i	−0.394075	+	1.11993i
$115$	17.2868	−	3.50877i	1.61200	−	0.327195i
$116$	0.159932	+	1.46541i	0.0148493	+	0.136060i
$117$			9.13619i			0.844641i
$118$	5.26120	−	2.52235i	0.484333	−	0.232202i
$119$	19.0959			1.75052
$120$	−5.62501	+	5.30378i	−0.513491	+	0.484167i
$121$			10.9856i			0.998689i
$122$	−6.12314	−	12.7718i	−0.554363	−	1.15631i
$123$	−3.46185	+	7.02002i	−0.312145	+	0.632974i
$124$	−2.41719	−	1.94149i	−0.217070	−	0.174351i
$125$	−2.05259	+	10.9903i	−0.183590	+	0.983003i
$126$	−2.75462	−	5.74567i	−0.245401	−	0.511865i
$127$	2.54647	+	2.54647i	0.225962	+	0.225962i	0.811004	−	0.585041i	$-0.198922\pi$
$127$	2.54647	+	2.54647i	0.225962	+	0.225962i	−0.585041	+	0.811004i	$0.698922\pi$
$128$	11.3129	+	0.138275i	0.999925	+	0.0122219i
$129$	0.367940	+	0.367940i	0.0323953	+	0.0323953i
$130$	−2.64122	+	19.0048i	−0.231650	+	1.66683i
$131$	−7.71661			−0.674204			−0.337102	−	0.941468i	$-0.609447\pi$
$131$	−7.71661			−0.674204			−0.337102	+	0.941468i	$0.609447\pi$
$132$	0.0318527	+	0.291857i	0.00277242	+	0.0254029i
$133$	−15.5149	−	15.5149i	−1.34531	−	1.34531i
$134$	−8.09324	+	3.88011i	−0.699149	+	0.335190i
$135$	−10.2669	−	6.80229i	−0.883634	−	0.585448i
$136$	−17.5763	−	4.10866i	−1.50716	−	0.352315i
$137$		−	16.6471i		−	1.42226i	−0.703063	−	0.711128i	$-0.748185\pi$
$137$		−	16.6471i		−	1.42226i	0.703063	−	0.711128i	$-0.251815\pi$
$138$	−4.52656	+	12.8641i	−0.385326	+	1.09506i
$139$	−1.77163			−0.150268			−0.0751340	−	0.997173i	$-0.523938\pi$
$139$	−1.77163			−0.150268			−0.0751340	+	0.997173i	$0.523938\pi$
$140$	−4.06904	−	12.7483i	−0.343897	−	1.07743i
$141$	−5.00817			−0.421764
$142$	1.92955	−	5.48361i	0.161924	−	0.460175i
$143$	0.515228	+	0.515228i	0.0430855	+	0.0430855i
$144$	1.29918	+	5.88113i	0.108265	+	0.490094i
$145$	−1.61517	+	0.327839i	−0.134133	+	0.0272255i
$146$	−0.446143	+	1.26790i	−0.0369230	+	0.104932i
$147$	−2.38838			−0.196990
$148$	−1.38540	−	12.6940i	−0.113879	−	1.04344i
$149$	−0.868251	−	0.868251i	−0.0711299	−	0.0711299i	0.670647	−	0.741777i	$-0.266017\pi$
$149$	−0.868251	−	0.868251i	−0.0711299	−	0.0711299i	−0.741777	+	0.670647i	$0.766017\pi$
$150$	−6.47991	−	5.72052i	−0.529082	−	0.467079i
$151$	10.2983	−	10.2983i	0.838062	−	0.838062i	−0.150541	−	0.988604i	$-0.548102\pi$
$151$	10.2983	−	10.2983i	0.838062	−	0.838062i	0.988604	+	0.150541i	$0.0481017\pi$
$152$	10.9421	+	17.6185i	0.887522	+	1.42905i
$153$		−	9.60911i		−	0.776850i
$154$	−0.479367	−	0.168678i	−0.0386285	−	0.0135925i
$155$	1.91451	−	2.88962i	0.153777	−	0.232100i
$156$	−11.5654	−	9.28939i	−0.925976	−	0.743746i
$157$	−2.96848			−0.236910			−0.118455	−	0.992959i	$-0.537794\pi$
$157$	−2.96848			−0.236910			−0.118455	+	0.992959i	$0.537794\pi$
$158$	−17.0227	−	5.98988i	−1.35425	−	0.476529i
$159$		−	11.0122i		−	0.873325i
$160$	1.00232	+	12.6093i	0.0792407	+	0.996856i
$161$	−16.6911	−	16.6911i	−1.31545	−	1.31545i
$162$	2.82539	−	1.35457i	0.221984	−	0.106425i
$163$	−14.2695	+	14.2695i	−1.11768	+	1.11768i	−0.125596	+	0.992081i	$0.540084\pi$
$163$	−14.2695	+	14.2695i	−1.11768	+	1.11768i	−0.992081	+	0.125596i	$0.959916\pi$
$164$	5.40785	+	11.6084i	0.422282	+	0.906465i
$165$	−0.321684	+	0.0652935i	−0.0250431	+	0.00508310i
$166$	−5.24332	+	14.9010i	−0.406960	+	1.15654i
$167$			21.6740i			1.67718i	0.544762	+	0.838591i	$0.316620\pi$
$167$			21.6740i			1.67718i	−0.544762	+	0.838591i	$0.683380\pi$
$168$	10.0742	+	2.35496i	0.777243	+	0.181689i
$169$	−23.8160			−1.83200
$170$	2.77793	−	19.9886i	0.213058	−	1.53306i
$171$	−7.80713	+	7.80713i	−0.597026	+	0.597026i
$172$	0.846324	−	0.0923660i	0.0645316	−	0.00704284i
$173$	2.13813	−	2.13813i	0.162559	−	0.162559i	−0.621140	−	0.783699i	$-0.713330\pi$
$173$	2.13813	−	2.13813i	0.162559	−	0.162559i	0.783699	+	0.621140i	$0.213330\pi$
$174$	0.422934	−	1.20194i	0.0320626	−	0.0911189i
$175$	13.7775	−	5.83327i	1.04148	−	0.440954i
$176$	0.404928	+	0.258395i	0.0305226	+	0.0194773i
$177$	−5.04325			−0.379074
$178$	3.30638	−	9.39643i	0.247824	−	0.704292i
$179$	−4.87184	+	4.87184i	−0.364139	+	0.364139i	−0.865334	−	0.501196i	$-0.832894\pi$
$179$	−4.87184	+	4.87184i	−0.364139	+	0.364139i	0.501196	+	0.865334i	$0.332894\pi$
$180$	−6.41498	+	2.04755i	−0.478144	+	0.152615i
$181$	−2.66660	+	2.66660i	−0.198207	+	0.198207i	−0.799231	−	0.601024i	$-0.794760\pi$
$181$	−2.66660	+	2.66660i	−0.198207	+	0.198207i	0.601024	+	0.799231i	$0.294760\pi$
$182$	23.1532	−	11.1003i	1.71623	−	0.822806i
$183$			12.2428i			0.905010i
$184$	11.7717	+	18.9541i	0.867818	+	1.39732i
$185$	13.9913	−	2.83988i	1.02866	−	0.208792i
$186$	1.15853	+	2.41649i	0.0849473	+	0.177186i
$187$	−0.541898	−	0.541898i	−0.0396275	−	0.0396275i
$188$	−5.13120	+	6.38843i	−0.374231	+	0.465924i
$189$			16.4810i			1.19882i
$190$	−18.4972	+	13.9832i	−1.34193	+	1.01445i
$191$	−13.3368	−	13.3368i	−0.965014	−	0.965014i	0.0343946	−	0.999408i	$-0.489050\pi$
$191$	−13.3368	−	13.3368i	−0.965014	−	0.965014i	−0.999408	+	0.0343946i	$0.989050\pi$
$192$	−8.76585	−	4.33512i	−0.632621	−	0.312860i
$193$			7.44894i			0.536187i	0.963393	+	0.268093i	$0.0863936\pi$
$193$			7.44894i			0.536187i	−0.963393	+	0.268093i	$0.913606\pi$
$194$	4.86804	+	10.1539i	0.349505	+	0.729008i
$195$	9.16027	−	13.8259i	0.655981	−	0.990091i
$196$	−2.44705	+	3.04662i	−0.174789	+	0.217616i
$197$	−12.4389	−	12.4389i	−0.886236	−	0.886236i	0.107923	−	0.994159i	$-0.465580\pi$
$197$	−12.4389	−	12.4389i	−0.886236	−	0.886236i	−0.994159	+	0.107923i	$0.965580\pi$
$198$	−0.0848790	+	0.241218i	−0.00603209	+	0.0171426i
$199$	5.55175	−	5.55175i	0.393553	−	0.393553i	−0.482399	−	0.875952i	$-0.660234\pi$
$199$	5.55175	−	5.55175i	0.393553	−	0.393553i	0.875952	+	0.482399i	$0.160234\pi$
$200$	−13.9362	+	2.40472i	−0.985437	+	0.170040i
$201$	7.75797			0.547205
$202$	4.27341	−	12.1447i	0.300676	−	0.854495i
$203$	1.55952	+	1.55952i	0.109457	+	0.109457i
$204$	12.1641	+	9.77024i	0.851658	+	0.684054i
$205$	−12.3715	+	7.20732i	−0.864065	+	0.503381i
$206$	4.47962	+	1.57627i	0.312110	+	0.109824i
$207$	−8.39901	+	8.39901i	−0.583771	+	0.583771i
$208$	−23.6991	+	5.23530i	−1.64324	+	0.363003i
$209$			0.880554i			0.0609092i
$210$	−1.59223	+	11.4569i	−0.109874	+	0.790598i
$211$	10.9195	+	10.9195i	0.751731	+	0.751731i	0.974802	−	0.223071i	$-0.0716082\pi$
$211$	10.9195	+	10.9195i	0.751731	+	0.751731i	−0.223071	+	0.974802i	$0.571608\pi$
$212$	−14.0472	−	11.2827i	−0.964764	−	0.774901i
$213$	−3.55303	+	3.55303i	−0.243450	+	0.243450i
$214$	−1.97438	−	0.694739i	−0.134966	−	0.0474914i
$215$	0.189338	+	0.932816i	0.0129127	+	0.0636175i
$216$	3.54604	−	15.1695i	0.241278	−	1.03215i
$217$	−4.63859			−0.314888
$218$	−15.8385	−	5.57319i	−1.07272	−	0.377464i
$219$	0.821516	−	0.821516i	0.0555129	−	0.0555129i
$220$	−0.246298	+	0.477238i	−0.0166054	+	0.0321754i
$221$	38.7217			2.60470
$222$	−3.66364	+	10.4117i	−0.245887	+	0.698789i
$223$	−18.6804	+	18.6804i	−1.25093	+	1.25093i	−0.295631	+	0.955302i	$0.595530\pi$
$223$	−18.6804	+	18.6804i	−1.25093	+	1.25093i	−0.955302	+	0.295631i	$0.904470\pi$
$224$	13.3257	−	10.4379i	0.890360	−	0.697409i
$225$	−2.93531	−	6.93285i	−0.195687	−	0.462190i
$226$	−8.68099	−	3.05463i	−0.577451	−	0.203191i
$227$	−19.1209			−1.26910			−0.634549	−	0.772882i	$-0.718814\pi$
$227$	−19.1209			−1.26910			−0.634549	+	0.772882i	$0.718814\pi$
$228$	−1.94495	−	17.8210i	−0.128808	−	1.18023i
$229$	−10.3789	−	10.3789i	−0.685859	−	0.685859i	0.275455	−	0.961314i	$-0.411171\pi$
$229$	−10.3789	−	10.3789i	−0.685859	−	0.685859i	−0.961314	+	0.275455i	$0.911171\pi$
$230$	−19.8995	+	15.0433i	−1.31213	+	0.991924i
$231$	0.310600	+	0.310600i	0.0204359	+	0.0204359i
$232$	−1.09987	−	1.77096i	−0.0722102	−	0.116269i
$233$			3.24861i			0.212823i	0.994322	+	0.106412i	$0.0339362\pi$
$233$			3.24861i			0.212823i	−0.994322	+	0.106412i	$0.966064\pi$
$234$	−5.58567	−	11.6508i	−0.365147	−	0.761634i
$235$	−7.63702	−	5.05988i	−0.498185	−	0.330070i
$236$	−5.16714	+	6.43317i	−0.336352	+	0.418764i
$237$	11.0296	+	11.0296i	0.716451	+	0.716451i
$238$	−24.3517	+	11.6748i	−1.57849	+	0.756768i
$239$	2.25701	+	2.25701i	0.145994	+	0.145994i	0.776326	−	0.630332i	$-0.217081\pi$
$239$	2.25701	+	2.25701i	0.145994	+	0.145994i	−0.630332	+	0.776326i	$0.717081\pi$
$240$	3.93057	−	10.2026i	0.253717	−	0.658573i
$241$		−	5.35428i		−	0.344899i	−0.985018	−	0.172450i	$-0.944832\pi$
$241$		−	5.35428i		−	0.344899i	0.985018	−	0.172450i	$-0.0551682\pi$
$242$	−6.71635	−	14.0092i	−0.431743	−	0.900543i
$243$	13.8151			0.886240
$244$	15.6169	+	12.5435i	0.999767	+	0.803015i
$245$	−3.64207	−	2.41304i	−0.232683	−	0.154163i
$246$	0.122776	−	11.0687i	0.00782790	−	0.705712i
$247$	−31.4603	−	31.4603i	−2.00177	−	2.00177i
$248$	4.26946	+	0.998034i	0.271111	+	0.0633752i
$249$	9.65492	−	9.65492i	0.611856	−	0.611856i
$250$	−4.10171	−	15.2701i	−0.259415	−	0.965766i
$251$	−8.76137			−0.553013			−0.276506	−	0.961012i	$-0.589177\pi$
$251$	−8.76137			−0.553013			−0.276506	+	0.961012i	$0.589177\pi$
$252$	7.02556	+	5.64294i	0.442569	+	0.355472i
$253$			0.947311i			0.0595569i
$254$	−4.80419	−	1.69048i	−0.301442	−	0.106070i
$255$	−9.63444	+	14.5415i	−0.603332	+	0.910627i
$256$	−14.5111	+	6.74011i	−0.906941	+	0.421257i
$257$	3.54731			0.221275			0.110638	−	0.993861i	$-0.464711\pi$
$257$	3.54731			0.221275			0.110638	+	0.993861i	$0.464711\pi$
$258$	−0.694160	−	0.244258i	−0.0432165	−	0.0152069i
$259$	−13.5092	−	13.5092i	−0.839422	−	0.839422i
$260$	−8.25098	−	25.8503i	−0.511704	−	1.60317i
$261$	0.784753	−	0.784753i	0.0485750	−	0.0485750i
$262$	9.84047	−	4.71777i	0.607946	−	0.291465i
$263$		−	14.9192i		−	0.919958i	−0.887930	−	0.459979i	$-0.847857\pi$
$263$		−	14.9192i		−	0.919958i	0.887930	−	0.459979i	$-0.152143\pi$
$264$	−0.219055	−	0.352711i	−0.0134819	−	0.0217079i
$265$	11.1259	−	16.7927i	0.683459	−	1.03156i
$266$	29.2706	+	10.2996i	1.79470	+	0.631511i
$267$	−6.08829	+	6.08829i	−0.372597	+	0.372597i
$268$	7.94854	−	9.89607i	0.485535	−	0.604499i
$269$			17.7773i			1.08390i	0.840411	+	0.541950i	$0.182314\pi$
$269$			17.7773i			1.08390i	−0.840411	+	0.541950i	$0.817686\pi$
$270$	17.2515	+	2.39754i	1.04989	+	0.145910i
$271$			14.3294i			0.870447i	0.900322	+	0.435224i	$0.143331\pi$
$271$			14.3294i			0.870447i	−0.900322	+	0.435224i	$0.856669\pi$
$272$	24.9258	−	5.50630i	1.51135	−	0.333868i
$273$	−22.1941			−1.34325
$274$	10.1777	+	21.2289i	0.614855	+	1.28248i
$275$	−0.556507	−	0.225438i	−0.0335587	−	0.0135944i
$276$	−2.09240	−	19.1721i	−0.125948	−	1.15402i
$277$	−22.7281	+	22.7281i	−1.36560	+	1.36560i	−0.498988	+	0.866609i	$0.666295\pi$
$277$	−22.7281	+	22.7281i	−1.36560	+	1.36560i	−0.866609	+	0.498988i	$0.833705\pi$
$278$	2.25924	−	1.08314i	0.135500	−	0.0649623i
$279$			2.33415i			0.139742i
$280$	12.9830	+	13.7693i	0.775884	+	0.822875i
$281$	−15.7185	+	15.7185i	−0.937687	+	0.937687i	−0.998169	−	0.0604822i	$-0.980736\pi$
$281$	−15.7185	+	15.7185i	−0.937687	+	0.937687i	0.0604822	+	0.998169i	$0.480736\pi$
$282$	6.38658	−	3.06189i	0.380315	−	0.182333i
$283$	2.68300	−	2.68300i	0.159488	−	0.159488i	−0.622852	−	0.782340i	$-0.714026\pi$
$283$	2.68300	−	2.68300i	0.159488	−	0.159488i	0.782340	+	0.622852i	$0.214026\pi$
$284$	0.891937	+	8.17257i	0.0529267	+	0.484953i
$285$	19.6423	−	3.98688i	1.16351	−	0.236163i
$286$	−0.972035	−	0.342036i	−0.0574776	−	0.0202250i
$287$	17.1842	+	8.47420i	1.01435	+	0.500216i
$288$	−5.25235	−	6.70551i	−0.309498	−	0.395126i
$289$	−23.7261			−1.39565
$290$	1.85929	−	1.40555i	0.109181	−	0.0825369i
$291$		−	9.73327i		−	0.570574i
$292$	−0.206230	−	1.88962i	−0.0120687	−	0.110582i
$293$	28.3009			1.65336			0.826678	−	0.562675i	$-0.190228\pi$
$293$	28.3009			1.65336			0.826678	+	0.562675i	$0.190228\pi$
$294$	3.04574	−	1.46021i	0.177631	−	0.0851609i
$295$	−7.69052	−	5.09532i	−0.447759	−	0.296661i
$296$	9.52756	+	15.3408i	0.553778	+	0.891667i
$297$	0.467693	−	0.467693i	0.0271383	−	0.0271383i
$298$	1.63805	+	0.576391i	0.0948898	+	0.0333895i
$299$	−33.8454	−	33.8454i	−1.95733	−	1.95733i
$300$	11.7608	+	3.33332i	0.679009	+	0.192449i
$301$	0.900674	−	0.900674i	0.0519140	−	0.0519140i
$302$	−6.83655	+	19.4288i	−0.393399	+	1.11800i
$303$	−7.86897	+	7.86897i	−0.452060	+	0.452060i
$304$	−24.7253	−	15.7778i	−1.41809	−	0.904921i
$305$	−12.3692	+	18.6691i	−0.708256	+	1.06899i
$306$	5.87480	+	12.2538i	0.335840	+	0.700506i
$307$	0.546547	−	0.546547i	0.0311931	−	0.0311931i	−0.691338	−	0.722531i	$-0.742979\pi$
$307$	0.546547	−	0.546547i	0.0311931	−	0.0311931i	0.722531	+	0.691338i	$0.242979\pi$
$308$	0.714430	−	0.0779714i	0.0407084	−	0.00444284i
$309$	−2.90251	−	2.90251i	−0.165118	−	0.165118i
$310$	−0.674787	+	4.85542i	−0.0383254	+	0.275770i
$311$	10.9903	+	10.9903i	0.623205	+	0.623205i	0.946350	−	0.323144i	$-0.104740\pi$
$311$	10.9903	+	10.9903i	0.623205	+	0.623205i	−0.323144	+	0.946350i	$0.604740\pi$
$312$	20.4279	+	4.77526i	1.15650	+	0.270346i
$313$	4.80232			0.271443			0.135722	−	0.990747i	$-0.456665\pi$
$313$	4.80232			0.271443			0.135722	+	0.990747i	$0.456665\pi$
$314$	3.78550	−	1.81486i	0.213628	−	0.102419i
$315$	−5.56451	+	8.39868i	−0.313525	+	0.473212i
$316$	25.3700	−	2.76882i	1.42717	−	0.155759i
$317$	28.9668			1.62694			0.813470	−	0.581608i	$-0.197576\pi$
$317$	28.9668			1.62694			0.813470	+	0.581608i	$0.197576\pi$
$318$	6.73263	+	14.0431i	0.377547	+	0.787499i
$319$		−	0.0885111i		−	0.00495567i
$320$	−8.98727	−	15.4670i	−0.502404	−	0.864633i
$321$	1.27928	+	1.27928i	0.0714022	+	0.0714022i
$322$	31.4897	+	11.0805i	1.75485	+	0.617490i
$323$	33.0888	+	33.0888i	1.84111	+	1.84111i
$324$	−2.77488	+	3.45477i	−0.154160	+	0.191932i
$325$	27.9372	−	11.8284i	1.54968	−	0.656121i
$326$	9.47289	−	26.9211i	0.524655	−	1.49102i
$327$	10.2623	+	10.2623i	0.567508	+	0.567508i
$328$	−13.9934	−	11.4972i	−0.772656	−	0.634825i
$329$			12.2594i			0.675883i
$330$	0.370302	−	0.279935i	0.0203845	−	0.0154099i
$331$	6.14166	−	6.14166i	0.337576	−	0.337576i	−0.517878	−	0.855454i	$-0.673278\pi$
$331$	6.14166	−	6.14166i	0.337576	−	0.337576i	0.855454	+	0.517878i	$0.173278\pi$
$332$	−2.42373	−	22.2079i	−0.133019	−	1.21882i
$333$	−6.79786	+	6.79786i	−0.372521	+	0.372521i
$334$	−13.2510	−	27.6393i	−0.725062	−	1.51236i
$335$	11.8302	+	7.83807i	0.646354	+	0.428239i
$336$	−14.2867	+	3.15604i	−0.779405	+	0.172176i
$337$	−0.0185951	−	0.0185951i	−0.00101294	−	0.00101294i	0.706600	−	0.707613i	$-0.250228\pi$
$337$	−0.0185951	−	0.0185951i	−0.00101294	−	0.00101294i	−0.707613	+	0.706600i	$0.750228\pi$
$338$	30.3709	−	14.5606i	1.65196	−	0.791991i
$339$	5.62473	+	5.62473i	0.305493	+	0.305493i
$340$	8.67809	+	27.1885i	0.470635	+	1.47450i
$341$	0.131632	+	0.131632i	0.00712829	+	0.00712829i
$342$	5.18279	−	14.7290i	0.280253	−	0.796454i
$343$		−	15.0996i		−	0.815302i
$344$	−1.02279	+	0.635212i	−0.0551451	+	0.0342484i
$345$	21.1314	−	4.28914i	1.13768	−	0.230919i
$346$	−1.41941	+	4.03382i	−0.0763078	+	0.216860i
$347$	5.72510			0.307339			0.153670	−	0.988122i	$-0.450891\pi$
$347$	5.72510			0.307339			0.153670	+	0.988122i	$0.450891\pi$
$348$	0.195502	+	1.79133i	0.0104800	+	0.0960252i
$349$	23.7137			1.26937			0.634683	−	0.772773i	$-0.281131\pi$
$349$	23.7137			1.26937			0.634683	+	0.772773i	$0.281131\pi$
$350$	−14.0031	+	15.8620i	−0.748500	+	0.847861i
$351$			33.4193i			1.78379i
$352$	−0.674354	−	0.0819495i	−0.0359432	−	0.00436792i
$353$	3.35104	+	3.35104i	0.178358	+	0.178358i	0.790640	−	0.612282i	$-0.209748\pi$
$353$	3.35104	+	3.35104i	0.178358	+	0.178358i	−0.612282	+	0.790640i	$0.709748\pi$
$354$	6.43132	−	3.08334i	0.341821	−	0.163877i
$355$	−9.00778	+	1.82835i	−0.478083	+	0.0970386i
$356$	1.52838	+	14.0041i	0.0810038	+	0.742215i
$357$	23.3429			1.23544
$358$	3.23419	−	9.19127i	0.170932	−	0.485774i
$359$	−35.7509			−1.88686			−0.943431	−	0.331568i	$-0.892422\pi$
$359$	−35.7509			−1.88686			−0.943431	+	0.331568i	$0.892422\pi$
$360$	6.92876	−	6.53308i	0.365177	−	0.344324i
$361$		−	34.7674i		−	1.82987i
$362$	1.77023	−	5.03083i	0.0930412	−	0.264415i
$363$			13.4288i			0.704830i
$364$	−22.7393	+	28.3108i	−1.19186	+	1.48389i
$365$	2.08274	−	0.422742i	0.109016	−	0.0221273i
$366$	−7.48496	−	15.6123i	−0.391245	−	0.816070i
$367$	−10.9228	+	10.9228i	−0.570165	+	0.570165i	−0.932174	−	0.362009i	$-0.882091\pi$
$367$	−10.9228	+	10.9228i	−0.570165	+	0.570165i	0.362009	+	0.932174i	$0.382091\pi$
$368$	−26.5997	−	16.9740i	−1.38661	−	0.884831i
$369$	4.26423	−	8.64710i	0.221987	−	0.450150i
$370$	−16.1059	+	12.1755i	−0.837308	+	0.632974i
$371$	−26.9566			−1.39951
$372$	−2.95478	−	2.37329i	−0.153198	−	0.123049i
$373$	7.06852	+	7.06852i	0.365994	+	0.365994i	0.866014	−	0.500020i	$-0.166674\pi$
$373$	7.06852	+	7.06852i	0.365994	+	0.365994i	−0.500020	+	0.866014i	$0.666674\pi$
$374$	1.02235	+	0.359741i	0.0528645	+	0.0186018i
$375$	−2.50910	+	13.4346i	−0.129569	+	0.693759i
$376$	2.63772	−	11.2838i	0.136030	−	0.581919i
$377$	3.16231	+	3.16231i	0.162867	+	0.162867i
$378$	−10.0762	−	21.0171i	−0.518261	−	1.08100i
$379$	15.7562			0.809343			0.404672	−	0.914462i	$-0.367386\pi$
$379$	15.7562			0.809343			0.404672	+	0.914462i	$0.367386\pi$
$380$	15.0392	−	29.1406i	0.771493	−	1.49488i
$381$	3.11281	+	3.11281i	0.159474	+	0.159474i
$382$	25.1613	+	8.85365i	1.28736	+	0.452992i
$383$		−	25.0847i		−	1.28177i	−0.767638	−	0.640884i	$-0.778568\pi$
$383$		−	25.0847i		−	1.28177i	0.767638	−	0.640884i	$-0.221432\pi$
$384$	13.8289	+	0.169028i	0.705702	+	0.00862569i
$385$	0.159831	+	0.787443i	0.00814573	+	0.0401318i
$386$	−4.55413	−	9.49913i	−0.231799	−	0.483493i
$387$	−0.453221	−	0.453221i	−0.0230385	−	0.0230385i
$388$	−12.4158	−	9.97237i	−0.630315	−	0.506270i
$389$	31.0343			1.57350			0.786750	−	0.617272i	$-0.211762\pi$
$389$	31.0343			1.57350			0.786750	+	0.617272i	$0.211762\pi$
$390$	−3.22863	+	23.2316i	−0.163488	+	1.17638i
$391$	35.5973	+	35.5973i	1.80023	+	1.80023i
$392$	1.25792	−	5.38122i	0.0635346	−	0.271793i
$393$	−9.43282			−0.475823
$394$	23.4674	+	8.25761i	1.18227	+	0.416013i
$395$	5.67571	+	27.9627i	0.285576	+	1.40696i
$396$	−0.0392354	−	0.359503i	−0.00197165	−	0.0180657i
$397$	−0.746238			−0.0374526			−0.0187263	−	0.999825i	$-0.505961\pi$
$397$	−0.746238			−0.0374526			−0.0187263	+	0.999825i	$0.505961\pi$
$398$	−3.68555	+	10.4740i	−0.184740	+	0.525014i
$399$	−18.9655	−	18.9655i	−0.949462	−	0.949462i
$400$	16.3017	−	11.5869i	0.815084	−	0.579343i
$401$			32.9511i			1.64550i	0.568404	+	0.822749i	$0.307561\pi$
$401$			32.9511i			1.64550i	−0.568404	+	0.822749i	$0.692439\pi$
$402$	−9.89321	+	4.74306i	−0.493428	+	0.236562i
$403$	−9.40588			−0.468540
$404$	1.97539	+	18.0999i	0.0982792	+	0.900505i
$405$	−4.13000	−	2.73631i	−0.205221	−	0.135968i
$406$	−2.94221	−	1.03529i	−0.146019	−	0.0513807i
$407$			0.766721i			0.0380049i
$408$	−21.4854	−	5.02245i	−1.06368	−	0.248648i
$409$			33.1350i			1.63842i	0.573493	+	0.819210i	$0.305588\pi$
$409$			33.1350i			1.63842i	−0.573493	+	0.819210i	$0.694412\pi$
$410$	11.3702	−	16.7547i	0.561532	−	0.827455i
$411$		−	20.3494i		−	1.00376i
$412$	−6.67626	+	0.728633i	−0.328916	+	0.0358972i
$413$			12.3453i			0.607471i
$414$	5.57571	−	15.8457i	0.274031	−	0.778772i
$415$	24.4775	−	4.96830i	1.20155	−	0.243884i
$416$	27.0211	−	21.1653i	1.32482	−	1.03772i
$417$	−2.16565			−0.106052
$418$	−0.538352	−	1.12291i	−0.0263317	−	0.0549234i
$419$		−	10.6241i		−	0.519022i	−0.965740	−	0.259511i	$-0.916439\pi$
$419$		−	10.6241i		−	0.519022i	0.965740	−	0.259511i	$-0.0835613\pi$
$420$	−4.97401	−	15.5836i	−0.242707	−	0.760402i
$421$	−6.44072	−	6.44072i	−0.313902	−	0.313902i	0.532517	−	0.846419i	$-0.321246\pi$
$421$	−6.44072	−	6.44072i	−0.313902	−	0.313902i	−0.846419	+	0.532517i	$0.821246\pi$
$422$	−20.6009	−	7.24896i	−1.00284	−	0.352874i
$423$	6.16895			0.299945
$424$	24.8114	+	5.79995i	1.20495	+	0.281670i
$425$	−29.3834	+	12.4407i	−1.42530	+	0.603461i
$426$	2.35869	−	6.70319i	0.114279	−	0.324771i
$427$	29.9688			1.45029
$428$	2.94255	−	0.321143i	0.142233	−	0.0155230i
$429$	0.629817	+	0.629817i	0.0304078	+	0.0304078i
$430$	−0.811753	−	1.07380i	−0.0391462	−	0.0517832i
$431$	−23.7176			−1.14243			−0.571217	−	0.820799i	$-0.693529\pi$
$431$	−23.7176			−1.14243			−0.571217	+	0.820799i	$0.693529\pi$
$432$	4.75229	+	21.5126i	0.228645	+	1.03503i
$433$	−1.01284	−	1.01284i	−0.0486739	−	0.0486739i	0.682351	−	0.731025i	$-0.260958\pi$
$433$	−1.01284	−	1.01284i	−0.0486739	−	0.0486739i	−0.731025	+	0.682351i	$0.760958\pi$
$434$	5.91528	−	2.83593i	0.283942	−	0.136129i
$435$	−1.97440	+	0.400751i	−0.0946650	+	0.0192146i
$436$	23.6051	−	2.57621i	1.13048	−	0.123378i
$437$		−	57.8437i		−	2.76704i
$438$	−0.545366	+	1.54988i	−0.0260586	+	0.0740562i
$439$	−1.66020	−	1.66020i	−0.0792368	−	0.0792368i	0.666378	−	0.745614i	$-0.267844\pi$
$439$	−1.66020	−	1.66020i	−0.0792368	−	0.0792368i	−0.745614	+	0.666378i	$0.767844\pi$
$440$	0.0223137	−	0.759170i	0.00106377	−	0.0361920i
$441$	2.94195			0.140093
$442$	−49.3791	+	23.6736i	−2.34873	+	1.12604i
$443$	−11.5292	−	11.5292i	−0.547766	−	0.547766i	0.378028	−	0.925794i	$-0.376602\pi$
$443$	−11.5292	−	11.5292i	−0.547766	−	0.547766i	−0.925794	+	0.378028i	$0.876602\pi$
$444$	−1.69352	−	15.5172i	−0.0803708	−	0.736415i
$445$	−15.4353	+	3.13296i	−0.731701	+	0.148517i
$446$	12.4011	−	35.2427i	0.587207	−	1.66879i
$447$	−1.06135	−	1.06135i	−0.0502003	−	0.0502003i
$448$	−10.6118	+	21.4577i	−0.501363	+	1.01378i
$449$	−0.940288			−0.0443750			−0.0221875	−	0.999754i	$-0.507063\pi$
$449$	−0.940288			−0.0443750			−0.0221875	+	0.999754i	$0.507063\pi$
$450$	7.98180	+	7.04641i	0.376266	+	0.332171i
$451$	−0.247168	−	0.728125i	−0.0116387	−	0.0342860i
$452$	12.9378	−	1.41201i	0.608544	−	0.0664152i
$453$	12.5887	−	12.5887i	0.591467	−	0.591467i
$454$	24.3836	−	11.6901i	1.14438	−	0.548644i
$455$	−33.8440	−	22.4232i	−1.58663	−	1.05122i
$456$	13.3757	+	21.5369i	0.626373	+	1.00856i
$457$			15.4487i			0.722658i	0.932438	+	0.361329i	$0.117677\pi$
$457$			15.4487i			0.722658i	−0.932438	+	0.361329i	$0.882323\pi$
$458$	19.5810	+	6.89008i	0.914960	+	0.321953i
$459$		−	35.1492i		−	1.64063i
$460$	16.1793	−	31.3498i	0.754364	−	1.46169i
$461$	26.0100			1.21141			0.605703	−	0.795691i	$-0.292892\pi$
$461$	26.0100			1.21141			0.605703	+	0.795691i	$0.292892\pi$
$462$	−0.585980	−	0.206192i	−0.0272623	−	0.00959294i
$463$	25.3168			1.17657			0.588285	−	0.808654i	$-0.299803\pi$
$463$	25.3168			1.17657			0.588285	+	0.808654i	$0.299803\pi$
$464$	2.48532	+	1.58595i	0.115378	+	0.0736258i
$465$	2.34030	−	3.53228i	0.108529	−	0.163806i
$466$	−1.98613	−	4.14273i	−0.0920057	−	0.191908i
$467$	−29.2849	−	29.2849i	−1.35514	−	1.35514i	−0.879800	−	0.475345i	$-0.842323\pi$
$467$	−29.2849	−	29.2849i	−1.35514	−	1.35514i	−0.475345	−	0.879800i	$-0.657677\pi$
$468$	14.2460	+	11.4425i	0.658524	+	0.528928i
$469$		−	18.9906i		−	0.876903i
$470$	12.8325	+	1.78341i	0.591918	+	0.0822624i
$471$	−3.62868			−0.167201
$472$	2.65620	−	11.3629i	0.122261	−	0.523018i
$473$	−0.0511180			−0.00235041
$474$	−20.8086	−	7.32205i	−0.955771	−	0.336313i
$475$	33.9809	+	13.7655i	1.55915	+	0.631603i
$476$	23.9164	−	29.7763i	1.09621	−	1.36479i
$477$			13.5646i			0.621080i
$478$	−4.25811	−	1.49833i	−0.194761	−	0.0685319i
$479$	9.10303	+	9.10303i	0.415928	+	0.415928i	0.883798	−	0.467869i	$-0.154978\pi$
$479$	9.10303	+	9.10303i	0.415928	+	0.415928i	−0.467869	+	0.883798i	$0.654978\pi$
$480$	1.22524	+	15.4137i	0.0559245	+	0.703536i
$481$	−27.3933	−	27.3933i	−1.24903	−	1.24903i
$482$	3.27349	+	6.82794i	0.149103	+	0.311004i
$483$	−20.4033	−	20.4033i	−0.928383	−	0.928383i
$484$	17.1298	+	13.7587i	0.778627	+	0.625395i
$485$	9.83376	−	14.8424i	0.446528	−	0.673958i
$486$	−17.6175	+	8.44626i	−0.799145	+	0.383130i
$487$	−7.28618	+	7.28618i	−0.330168	+	0.330168i	−0.852650	−	0.522482i	$-0.825006\pi$
$487$	−7.28618	+	7.28618i	−0.330168	+	0.330168i	0.522482	+	0.852650i	$0.325006\pi$
$488$	−27.5839	−	6.44805i	−1.24867	−	0.291890i
$489$	−17.4432	+	17.4432i	−0.788807	+	0.788807i
$490$	6.11977	+	0.850501i	0.276463	+	0.0384217i
$491$		−	33.8248i		−	1.52649i	−0.646108	−	0.763246i	$-0.723604\pi$
$491$		−	33.8248i		−	1.52649i	0.646108	−	0.763246i	$-0.276396\pi$
$492$	6.61057	+	14.1902i	0.298028	+	0.639742i
$493$	−3.32600	−	3.32600i	−0.149796	−	0.149796i
$494$	59.3533	+	20.8850i	2.67043	+	0.939661i
$495$	0.396243	−	0.0804271i	0.0178098	−	0.00361493i
$496$	−6.05473	+	1.33753i	−0.271865	+	0.0600570i
$497$	8.69740	+	8.69740i	0.390132	+	0.390132i
$498$	−6.40945	+	18.2151i	−0.287214	+	0.816237i
$499$	−1.70332	−	1.70332i	−0.0762512	−	0.0762512i	0.667953	−	0.744204i	$-0.267171\pi$
$499$	−1.70332	−	1.70332i	−0.0762512	−	0.0762512i	−0.744204	+	0.667953i	$0.767171\pi$
$500$	14.5664	+	16.9652i	0.651431	+	0.758708i
$501$			26.4943i			1.18368i
$502$	11.1728	−	5.35651i	0.498665	−	0.239073i
$503$	−7.06455			−0.314993			−0.157496	−	0.987520i	$-0.550342\pi$
$503$	−7.06455			−0.314993			−0.157496	+	0.987520i	$0.550342\pi$
$504$	−12.4092	−	2.90079i	−0.552749	−	0.129211i
$505$	−19.9497	+	4.04927i	−0.887750	+	0.180190i
$506$	−0.579166	−	1.20804i	−0.0257471	−	0.0537040i
$507$	−29.1127			−1.29294
$508$	7.15998	−	0.781425i	0.317673	−	0.0346702i
$509$	−18.0402	−	18.0402i	−0.799618	−	0.799618i	0.183417	−	0.983035i	$-0.441284\pi$
$509$	−18.0402	−	18.0402i	−0.799618	−	0.799618i	−0.983035	+	0.183417i	$0.941284\pi$
$510$	3.39576	−	24.4341i	0.150367	−	1.08196i
$511$	−2.01097	−	2.01097i	−0.0889602	−	0.0889602i
$512$	14.3842	−	17.4670i	0.635698	−	0.771938i
$513$	−28.5578	+	28.5578i	−1.26086	+	1.26086i
$514$	−4.52365	+	2.16875i	−0.199530	+	0.0956595i
$515$	−1.49360	−	7.35855i	−0.0658157	−	0.324257i
$516$	1.03455	−	0.112909i	0.0455435	−	0.00497052i
$517$	0.347893	−	0.347893i	0.0153003	−	0.0153003i
$518$	25.4866	+	8.96814i	1.11982	+	0.394037i
$519$	2.61366	−	2.61366i	0.114727	−	0.114727i
$520$	26.3263	+	27.9207i	1.15448	+	1.22440i
$521$	−6.37960	−	6.37960i	−0.279495	−	0.279495i	0.553412	−	0.832908i	$-0.313325\pi$
$521$	−6.37960	−	6.37960i	−0.279495	−	0.279495i	−0.832908	+	0.553412i	$0.813325\pi$
$522$	−0.520961	+	1.48052i	−0.0228018	+	0.0648007i
$523$	−17.6600	+	17.6600i	−0.772217	+	0.772217i	−0.978494	−	0.206277i	$-0.933865\pi$
$523$	−17.6600	+	17.6600i	−0.772217	+	0.772217i	0.206277	+	0.978494i	$0.433865\pi$
$524$	−9.66454	+	12.0325i	−0.422197	+	0.525642i
$525$	16.8416	−	7.13061i	0.735030	−	0.311205i
$526$	9.12129	+	19.0255i	0.397707	+	0.829549i
$527$	9.89276			0.430935
$528$	0.494985	+	0.315863i	0.0215415	+	0.0137462i
$529$		−	39.2289i		−	1.70561i
$530$	−3.92144	+	28.2167i	−0.170336	+	1.22565i
$531$	6.21216			0.269585
$532$	−43.6238	+	4.76101i	−1.89133	+	0.206416i
$533$	34.8451	+	17.1835i	1.50931	+	0.744301i
$534$	4.04173	−	11.4862i	0.174903	−	0.497058i
$535$	0.658300	+	3.24327i	0.0284608	+	0.140219i
$536$	−4.08599	+	17.4794i	−0.176488	+	0.754993i
$537$	−5.95536	+	5.95536i	−0.256993	+	0.256993i
$538$	−10.8686	−	22.6701i	−0.468581	−	0.977379i
$539$	0.165909	−	0.165909i	0.00714621	−	0.00714621i
$540$	−23.4654	+	7.48975i	−1.00979	+	0.322308i
$541$		−	9.75003i		−	0.419187i	−0.977789	−	0.209593i	$-0.932786\pi$
$541$		−	9.75003i		−	0.419187i	0.977789	−	0.209593i	$-0.0672140\pi$
$542$	−8.76067	−	18.2733i	−0.376303	−	0.784904i
$543$	−3.25966	+	3.25966i	−0.139885	+	0.139885i
$544$	−28.4198	+	22.2609i	−1.21849	+	0.954430i
$545$	5.28087	+	26.0174i	0.226208	+	1.11446i
$546$	28.3026	−	13.5690i	1.21124	−	0.580699i
$547$	8.63443			0.369181			0.184591	−	0.982815i	$-0.440904\pi$
$547$	8.63443			0.369181			0.184591	+	0.982815i	$0.440904\pi$
$548$	−25.9578	−	20.8493i	−1.10886	−	0.890639i
$549$		−	15.0803i		−	0.643613i
$550$	0.847504	−	0.0527507i	0.0361377	−	0.00224930i
$551$			5.40457i			0.230242i
$552$	14.3897	+	23.1696i	0.612467	+	0.986165i
$553$	26.9992	−	26.9992i	1.14812	−	1.14812i
$554$	15.0881	−	42.8790i	0.641032	−	1.82175i
$555$	17.1031	−	3.47148i	0.725984	−	0.147356i
$556$	−2.21885	+	2.76250i	−0.0941002	+	0.117156i
$557$			36.8570i			1.56168i	0.624730	+	0.780841i	$0.285209\pi$
$557$			36.8570i			1.56168i	−0.624730	+	0.780841i	$0.714791\pi$
$558$	−1.42705	−	2.97658i	−0.0604117	−	0.126009i
$559$	1.82634	−	1.82634i	0.0772458	−	0.0772458i
$560$	−24.9746	−	9.62155i	−1.05537	−	0.406585i
$561$	−0.662418	−	0.662418i	−0.0279673	−	0.0279673i
$562$	10.4348	−	29.6547i	0.440164	−	1.25091i
$563$	−19.4288			−0.818827			−0.409413	−	0.912349i	$-0.634267\pi$
$563$	−19.4288			−0.818827			−0.409413	+	0.912349i	$0.634267\pi$
$564$	−6.27240	+	7.80924i	−0.264116	+	0.328828i
$565$	2.89442	+	14.2600i	0.121769	+	0.599924i
$566$	−1.78112	+	5.06178i	−0.0748660	+	0.212762i
$567$			6.62971i			0.278422i
$568$	−6.13396	−	9.87661i	−0.257375	−	0.414413i
$569$	−27.0072			−1.13220			−0.566101	−	0.824336i	$-0.691549\pi$
$569$	−27.0072			−1.13220			−0.566101	+	0.824336i	$0.691549\pi$
$570$	−22.6110	+	17.0931i	−0.947071	+	0.715951i
$571$	10.7641	−	10.7641i	0.450463	−	0.450463i	−0.445045	−	0.895508i	$-0.646812\pi$
$571$	10.7641	−	10.7641i	0.450463	−	0.450463i	0.895508	+	0.445045i	$0.146812\pi$
$572$	1.44868	−	0.158106i	0.0605725	−	0.00661075i
$573$	−16.3029	−	16.3029i	−0.681063	−	0.681063i
$574$	−27.0947	−	0.300541i	−1.13091	−	0.0125443i
$575$	36.5570	+	14.8091i	1.52453	+	0.617580i
$576$	10.7976	+	5.33990i	0.449899	+	0.222496i
$577$	37.6090			1.56568			0.782841	−	0.622222i	$-0.213770\pi$
$577$	37.6090			1.56568			0.782841	+	0.622222i	$0.213770\pi$
$578$	30.2563	−	14.5056i	1.25849	−	0.603354i
$579$			9.10562i			0.378417i
$580$	−1.51170	+	2.92914i	−0.0627698	+	0.121626i
$581$	−23.6341	−	23.6341i	−0.980507	−	0.980507i
$582$	5.95071	+	12.4122i	0.246665	+	0.514501i
$583$	0.764964	+	0.764964i	0.0316816	+	0.0316816i
$584$	1.41827	+	2.28362i	0.0586883	+	0.0944970i
$585$	−11.2834	+	17.0304i	−0.466512	+	0.704120i
$586$	−36.0902	+	17.3026i	−1.49087	+	0.714763i
$587$			11.8243i			0.488042i	0.969770	+	0.244021i	$0.0784666\pi$
$587$			11.8243i			0.488042i	−0.969770	+	0.244021i	$0.921533\pi$
$588$	−2.99129	+	3.72420i	−0.123359	+	0.153583i
$589$	−8.03759	−	8.03759i	−0.331183	−	0.331183i
$590$	12.9224	+	1.79590i	0.532005	+	0.0739360i
$591$	−15.2054	−	15.2054i	−0.625466	−	0.625466i
$592$	−21.5289	−	13.7382i	−0.884833	−	0.564635i
$593$	−25.8202			−1.06031			−0.530154	−	0.847901i	$-0.677866\pi$
$593$	−25.8202			−1.06031			−0.530154	+	0.847901i	$0.677866\pi$
$594$	−0.310480	+	0.882355i	−0.0127391	+	0.0362035i
$595$	35.5959	+	23.5840i	1.45929	+	0.966848i
$596$	−2.44129	+	0.266437i	−0.0999991	+	0.0109137i
$597$	6.78648	−	6.78648i	0.277752	−	0.277752i
$598$	63.8530	+	22.4684i	2.61114	+	0.918800i
$599$	−27.9259			−1.14102			−0.570511	−	0.821290i	$-0.693255\pi$
$599$	−27.9259			−1.14102			−0.570511	+	0.821290i	$0.693255\pi$
$600$	−17.0356	+	2.93954i	−0.695477	+	0.120006i
$601$	4.79880	−	4.79880i	0.195747	−	0.195747i	−0.602427	−	0.798174i	$-0.705799\pi$
$601$	4.79880	−	4.79880i	0.195747	−	0.195747i	0.798174	+	0.602427i	$0.205799\pi$
$602$	−0.597915	+	1.69922i	−0.0243692	+	0.0692551i
$603$	−9.55609			−0.389154
$604$	−3.16020	−	28.9560i	−0.128587	−	1.17820i
$605$	−13.5675	+	20.4778i	−0.551596	+	0.832539i
$606$	5.22384	−	14.8457i	0.212204	−	0.603064i
$607$	1.87954	−	1.87954i	0.0762881	−	0.0762881i	−0.667933	−	0.744221i	$-0.732821\pi$
$607$	1.87954	−	1.87954i	0.0762881	−	0.0762881i	0.744221	+	0.667933i	$0.232821\pi$
$608$	41.1767	+	5.00391i	1.66994	+	0.202935i
$609$	1.90636	+	1.90636i	0.0772497	+	0.0772497i
$610$	4.35963	−	31.3697i	0.176516	−	1.27012i
$611$			24.8589i			1.00569i
$612$	−14.9835	−	12.0348i	−0.605671	−	0.486476i
$613$	−7.01226	+	7.01226i	−0.283223	+	0.283223i	−0.834393	−	0.551170i	$-0.814181\pi$
$613$	−7.01226	+	7.01226i	−0.283223	+	0.283223i	0.551170	+	0.834393i	$0.314181\pi$
$614$	−0.362827	+	1.03112i	−0.0146425	+	0.0416127i
$615$	−15.1230	+	8.81025i	−0.609818	+	0.355264i
$616$	−0.863394	+	0.536219i	−0.0347871	+	0.0216049i
$617$	−6.55689	−	6.55689i	−0.263971	−	0.263971i	0.562694	−	0.826665i	$-0.309765\pi$
$617$	−6.55689	−	6.55689i	−0.263971	−	0.263971i	−0.826665	+	0.562694i	$0.809765\pi$
$618$	5.47591	+	1.92684i	0.220273	+	0.0775089i
$619$	25.6716			1.03183			0.515915	−	0.856640i	$-0.327452\pi$
$619$	25.6716			1.03183			0.515915	+	0.856640i	$0.327452\pi$
$620$	−2.10799	−	6.60434i	−0.0846590	−	0.265237i
$621$	−30.7228	+	30.7228i	−1.23286	+	1.23286i
$622$	−20.7345	−	7.29598i	−0.831378	−	0.292542i
$623$	14.9034	+	14.9034i	0.597092	+	0.597092i
$624$	−28.9699	+	6.39965i	−1.15972	+	0.256191i
$625$	−17.3995	+	17.9516i	−0.695978	+	0.718063i
$626$	−6.12408	+	2.93604i	−0.244767	+	0.117348i
$627$			1.07639i			0.0429870i
$628$	−3.71782	+	4.62874i	−0.148357	+	0.184707i
$629$	28.8112	+	28.8112i	1.14878	+	1.14878i
$630$	1.96127	−	14.1123i	0.0781388	−	0.562247i
$631$			14.7234i			0.586131i	0.956092	+	0.293065i	$0.0946753\pi$
$631$			14.7234i			0.586131i	−0.956092	+	0.293065i	$0.905325\pi$
$632$	−30.6598	+	19.0415i	−1.21958	+	0.757432i
$633$	13.3481	+	13.3481i	0.530538	+	0.530538i
$634$	−36.9394	+	17.7097i	−1.46705	+	0.703342i
$635$	1.60181	+	7.89171i	0.0635661	+	0.313173i
$636$	−17.1713	−	13.7920i	−0.680887	−	0.546890i
$637$			11.8551i			0.469718i
$638$	0.0541138	+	0.112872i	0.00214238	+	0.00446865i
$639$	4.37655	−	4.37655i	0.173133	−	0.173133i
$640$	20.9171	+	14.2294i	0.826820	+	0.562467i
$641$	24.3663	−	24.3663i	0.962413	−	0.962413i	−0.0369061	−	0.999319i	$-0.511750\pi$
$641$	24.3663	−	24.3663i	0.962413	−	0.962413i	0.999319	+	0.0369061i	$0.0117502\pi$
$642$	−2.41349	−	0.849251i	−0.0952530	−	0.0335173i
$643$	39.8371			1.57102			0.785510	−	0.618849i	$-0.212401\pi$
$643$	39.8371			1.57102			0.785510	+	0.618849i	$0.212401\pi$
$644$	−46.9310	+	5.12195i	−1.84934	+	0.201833i
$645$	0.231447	+	1.14028i	0.00911322	+	0.0448984i
$646$	−62.4257	−	21.9661i	−2.45611	−	0.864245i
$647$	−6.17681	+	6.17681i	−0.242836	+	0.242836i	−0.818022	−	0.575187i	$-0.804929\pi$
$647$	−6.17681	+	6.17681i	−0.242836	+	0.242836i	0.575187	+	0.818022i	$0.304929\pi$
$648$	1.42644	−	6.10214i	0.0560359	−	0.239715i
$649$	0.350330	−	0.350330i	0.0137517	−	0.0137517i
$650$	−28.3948	+	32.1642i	−1.11374	+	1.26158i
$651$	−5.67023			−0.222234
$652$	4.37885	+	40.1221i	0.171489	+	1.57130i
$653$			33.3829i			1.30637i	0.757196	+	0.653187i	$0.226569\pi$
$653$			33.3829i			1.30637i	−0.757196	+	0.653187i	$0.773431\pi$
$654$	−19.3610	−	6.81268i	−0.757076	−	0.266397i
$655$	−14.3842	−	9.53021i	−0.562038	−	0.372376i
$656$	24.8739	+	6.10630i	0.971164	+	0.238411i
$657$	−1.01193	+	1.01193i	−0.0394790	+	0.0394790i
$658$	−7.49514	−	15.6336i	−0.292191	−	0.609460i
$659$	8.37949	+	8.37949i	0.326419	+	0.326419i	0.851223	−	0.524804i	$-0.175861\pi$
$659$	8.37949	+	8.37949i	0.326419	+	0.326419i	−0.524804	+	0.851223i	$0.675861\pi$
$660$	−0.301075	+	0.583377i	−0.0117193	+	0.0227079i
$661$			12.0784i			0.469794i	0.972020	+	0.234897i	$0.0754753\pi$
$661$			12.0784i			0.469794i	−0.972020	+	0.234897i	$0.924525\pi$
$662$	−4.07716	+	11.5869i	−0.158463	+	0.450338i
$663$	47.3335			1.83828
$664$	16.6683	+	26.8384i	0.646854	+	1.04153i
$665$	−9.75941	−	48.0820i	−0.378454	−	1.86454i
$666$	4.51278	−	12.8249i	0.174867	−	0.496956i
$667$			5.81430i			0.225131i
$668$	33.7962	+	27.1452i	1.30761	+	1.05028i
$669$	−22.8350	+	22.8350i	−0.882853	+	0.882853i
$670$	−19.8783	−	2.76261i	−0.767966	−	0.106729i
$671$	−0.850444	−	0.850444i	−0.0328310	−	0.0328310i
$672$	16.2894	−	12.7593i	0.628376	−	0.492200i
$673$	−20.0873			−0.774308			−0.387154	−	0.922015i	$-0.626542\pi$
$673$	−20.0873			−0.774308			−0.387154	+	0.922015i	$0.626542\pi$
$674$	0.0350817	+	0.0123444i	0.00135130	+	0.000475489i
$675$	−10.7371	−	25.3597i	−0.413271	−	0.976097i
$676$	−29.8279	+	37.1362i	−1.14723	+	1.42832i
$677$	31.3210	+	31.3210i	1.20376	+	1.20376i	0.973013	+	0.230751i	$0.0741182\pi$
$677$	31.3210	+	31.3210i	1.20376	+	1.20376i	0.230751	+	0.973013i	$0.425882\pi$
$678$	−10.6117	−	3.73400i	−0.407539	−	0.143403i
$679$	−23.8259			−0.914353
$680$	−27.6890	−	29.3660i	−1.06183	−	1.12613i
$681$	−23.3735			−0.895673
$682$	−0.248339	−	0.0873846i	−0.00950939	−	0.00334613i
$683$			49.3386i			1.88789i	0.330105	+	0.943944i	$0.392916\pi$
$683$			49.3386i			1.88789i	−0.330105	+	0.943944i	$0.607084\pi$
$684$	2.39575	+	21.9516i	0.0916037	+	0.839339i
$685$	20.5595	−	31.0311i	0.785540	−	1.18564i
$686$	9.23158	+	19.2555i	0.352463	+	0.735178i
$687$	−12.6872	−	12.6872i	−0.484048	−	0.484048i
$688$	0.915937	−	1.43535i	0.0349198	−	0.0547224i
$689$	−54.6610			−2.08242
$690$	−24.3252	+	18.3890i	−0.926045	+	0.700056i
$691$	−26.0891	−	26.0891i	−0.992475	−	0.992475i	0.00749684	−	0.999972i	$-0.497614\pi$
$691$	−26.0891	−	26.0891i	−0.992475	−	0.992475i	−0.999972	+	0.00749684i	$0.997614\pi$
$692$	−0.656121	−	6.01186i	−0.0249420	−	0.228536i
$693$	−0.382589	−	0.382589i	−0.0145334	−	0.0145334i
$694$	−7.30082	+	3.50020i	−0.277135	+	0.132866i
$695$	−3.30243	−	2.18801i	−0.125268	−	0.0829959i
$696$	−1.34449	−	2.16483i	−0.0509627	−	0.0820577i
$697$	−36.6488	−	18.0730i	−1.38817	−	0.684564i
$698$	−30.2405	+	14.4981i	−1.14462	+	0.548759i
$699$			3.97111i			0.150201i
$700$	8.15955	−	28.7890i	0.308402	−	1.08812i
$701$	28.2225			1.06595			0.532975	−	0.846131i	$-0.321074\pi$
$701$	28.2225			1.06595			0.532975	+	0.846131i	$0.321074\pi$
$702$	−20.4319	−	42.6174i	−0.771151	−	1.60849i
$703$		−	46.8167i		−	1.76572i
$704$	0.910060	−	0.307781i	0.0342992	−	0.0115999i
$705$	−9.33553	−	6.18522i	−0.351596	−	0.232949i
$706$	−6.32211	−	2.22460i	−0.237936	−	0.0837240i
$707$	19.2623	+	19.2623i	0.724433	+	0.724433i
$708$	−6.31633	+	7.86394i	−0.237382	+	0.295545i
$709$	28.3919	−	28.3919i	1.06628	−	1.06628i	0.0686385	−	0.997642i	$-0.478135\pi$
$709$	28.3919	−	28.3919i	1.06628	−	1.06628i	0.997642	−	0.0686385i	$-0.0218655\pi$
$710$	10.3692	−	7.83873i	0.389149	−	0.294182i
$711$	−13.5860	−	13.5860i	−0.509516	−	0.509516i
$712$	−10.5108	−	16.9240i	−0.393910	−	0.634255i
$713$	−8.64694	−	8.64694i	−0.323830	−	0.323830i
$714$	−29.7677	+	14.2714i	−1.11403	+	0.534093i
$715$	0.324096	+	1.59673i	0.0121205	+	0.0597145i
$716$	1.49500	+	13.6983i	0.0558710	+	0.511930i
$717$	2.75898	+	2.75898i	0.103036	+	0.103036i
$718$	45.5907	−	21.8574i	1.70143	−	0.815709i
$719$	8.03662	−	8.03662i	0.299715	−	0.299715i	−0.541187	−	0.840902i	$-0.682025\pi$
$719$	8.03662	−	8.03662i	0.299715	−	0.299715i	0.840902	+	0.541187i	$0.182025\pi$
$720$	−4.84158	+	12.5673i	−0.180435	+	0.468355i
$721$	−7.10500	+	7.10500i	−0.264604	+	0.264604i
$722$	21.2561	+	44.3366i	0.791069	+	1.65004i
$723$		−	6.54509i		−	0.243414i
$724$	0.818290	+	7.49776i	0.0304115	+	0.278652i
$725$	−3.41567	−	1.38367i	−0.126855	−	0.0513882i
$726$	−8.21009	−	17.1249i	−0.304705	−	0.635563i
$727$		−	47.1191i		−	1.74755i	−0.486329	−	0.873776i	$-0.661664\pi$
$727$		−	47.1191i		−	1.74755i	0.486329	−	0.873776i	$-0.338336\pi$
$728$	11.6893	−	50.0051i	0.433233	−	1.85331i
$729$	23.5344			0.871645
$730$	−2.39752	+	1.81244i	−0.0887362	+	0.0670813i
$731$	−1.92088	+	1.92088i	−0.0710461	+	0.0710461i
$732$	19.0901	+	15.3332i	0.705591	+	0.566732i
$733$	5.44257	−	5.44257i	0.201026	−	0.201026i	−0.599414	−	0.800439i	$-0.704600\pi$
$733$	5.44257	−	5.44257i	0.201026	−	0.201026i	0.800439	+	0.599414i	$0.204600\pi$
$734$	7.25113	−	20.6071i	0.267644	−	0.760620i
$735$	−4.45208	−	2.94971i	−0.164218	−	0.108802i
$736$	44.2984	+	5.38327i	1.63286	+	0.198430i
$737$	−0.538908	+	0.538908i	−0.0198509	+	0.0198509i
$738$	−0.151233	+	13.6341i	−0.00556695	+	0.501879i
$739$	20.6491			0.759590			0.379795	−	0.925071i	$-0.375995\pi$
$739$	20.6491			0.759590			0.379795	+	0.925071i	$0.375995\pi$
$740$	13.0950	−	25.3734i	0.481381	−	0.932745i
$741$	−38.4572	−	38.4572i	−1.41276	−	1.41276i
$742$	34.3759	−	16.4807i	1.26198	−	0.605024i
$743$	−22.2252	−	22.2252i	−0.815365	−	0.815365i	0.170068	−	0.985432i	$-0.445601\pi$
$743$	−22.2252	−	22.2252i	−0.815365	−	0.815365i	−0.985432	+	0.170068i	$0.945601\pi$
$744$	5.21901	+	1.22000i	0.191338	+	0.0447274i
$745$	−0.546159	−	2.69078i	−0.0200097	−	0.0985826i
$746$	−13.3355	−	4.69246i	−0.488249	−	0.171803i
$747$	−11.8927	+	11.8927i	−0.435132	+	0.435132i
$748$	−1.52367	+	0.166290i	−0.0557110	+	0.00608018i
$749$	3.13151	−	3.13151i	0.114423	−	0.114423i
$750$	−5.01394	−	18.6662i	−0.183083	−	0.681594i
$751$	−19.5898	+	19.5898i	−0.714841	+	0.714841i	−0.967544	−	0.252703i	$-0.918680\pi$
$751$	−19.5898	+	19.5898i	−0.714841	+	0.714841i	0.252703	+	0.967544i	$0.418680\pi$
$752$	3.53499	+	16.0021i	0.128908	+	0.583538i
$753$	−10.7099			−0.390291
$754$	−5.96604	−	2.09931i	−0.217271	−	0.0764523i
$755$	31.9152	−	6.47797i	1.16151	−	0.235757i
$756$	25.6989	+	20.6414i	0.934658	+	0.750720i
$757$			45.3407i			1.64793i	0.566638	+	0.823967i	$0.308244\pi$
$757$			45.3407i			1.64793i	−0.566638	+	0.823967i	$0.691756\pi$
$758$	−20.0929	+	9.63303i	−0.729805	+	0.349887i
$759$			1.15800i			0.0420326i
$760$	−1.36250	+	46.3556i	−0.0494230	+	1.68149i
$761$	17.4506			0.632583			0.316292	−	0.948662i	$-0.397562\pi$
$761$	17.4506			0.632583			0.316292	+	0.948662i	$0.397562\pi$
$762$	−5.87266	−	2.06645i	−0.212744	−	0.0748596i
$763$	25.1210	−	25.1210i	0.909439	−	0.909439i
$764$	−37.4994	+	4.09260i	−1.35668	+	0.148065i
$765$	11.8675	−	17.9119i	0.429070	−	0.647608i
$766$	15.3362	+	31.9888i	0.554121	+	1.15580i
$767$			25.0331i			0.903892i
$768$	−17.7384	+	8.23914i	−0.640079	+	0.297304i
$769$		−	20.3571i		−	0.734095i	−0.930202	−	0.367047i	$-0.880369\pi$
$769$		−	20.3571i		−	0.734095i	0.930202	−	0.367047i	$-0.119631\pi$
$770$	−0.685247	−	0.906456i	−0.0246946	−	0.0326664i
$771$	4.33625			0.156166
$772$	11.6151	+	9.32930i	0.418038	+	0.335769i
$773$	19.2731			0.693207			0.346603	−	0.938012i	$-0.387335\pi$
$773$	19.2731			0.693207			0.346603	+	0.938012i	$0.387335\pi$
$774$	0.855051	+	0.300872i	0.0307342	+	0.0108146i
$775$	7.13750	−	3.02196i	0.256387	−	0.108552i
$776$	21.9299	+	5.12635i	0.787236	+	0.184025i
$777$	−16.5137	−	16.5137i	−0.592427	−	0.592427i
$778$	−39.5759	+	18.9737i	−1.41886	+	0.680240i
$779$	15.0923	+	44.4599i	0.540739	+	1.59294i
$780$	−10.0860	−	31.5996i	−0.361138	−	1.13145i
$781$		−	0.493624i		−	0.0176632i
$782$	−67.1583	−	23.6314i	−2.40158	−	0.845057i
$783$	2.87056	−	2.87056i	0.102585	−	0.102585i
$784$	1.68582	+	7.63137i	0.0602080	+	0.272549i
$785$	−5.53341	−	3.66614i	−0.197496	−	0.130850i
$786$	12.0290	−	5.76702i	0.429061	−	0.205703i
$787$	−8.48524	+	8.48524i	−0.302466	+	0.302466i	−0.841978	−	0.539512i	$-0.818609\pi$
$787$	−8.48524	+	8.48524i	−0.302466	+	0.302466i	0.539512	+	0.841978i	$0.318609\pi$
$788$	−34.9749	+	3.81709i	−1.24593	+	0.135978i
$789$		−	18.2373i		−	0.649265i
$790$	−24.3336	−	32.1889i	−0.865752	−	1.14523i
$791$	13.7687	−	13.7687i	0.489557	−	0.489557i
$792$	0.269826	+	0.434462i	0.00958786	+	0.0154379i
$793$	60.7690			2.15797
$794$	0.951627	−	0.456234i	0.0337720	−	0.0161911i
$795$	13.6003	−	20.5274i	0.482355	−	0.728032i
$796$	−1.70365	−	15.6100i	−0.0603841	−	0.553283i
$797$	22.4119	−	22.4119i	0.793869	−	0.793869i	−0.188252	−	0.982121i	$-0.560282\pi$
$797$	22.4119	−	22.4119i	0.793869	−	0.793869i	0.982121	+	0.188252i	$0.0602821\pi$
$798$	35.7805	+	12.5903i	1.26662	+	0.445692i
$799$		−	26.1457i		−	0.924970i
$800$	−13.7044	+	24.7424i	−0.484525	+	0.874777i
$801$	7.49942	−	7.49942i	0.264979	−	0.264979i
$802$	−20.1456	−	42.0203i	−0.711365	−	1.48379i
$803$			0.114133i			0.00402768i
$804$	9.71633	−	12.0970i	0.342669	−	0.426628i
$805$	−10.4993	−	51.7272i	−0.370051	−	1.82314i
$806$	11.9947	−	5.75055i	0.422494	−	0.202555i
$807$			21.7310i			0.764968i
$808$	−13.5850	−	21.8739i	−0.477918	−	0.769521i
$809$	7.33452	−	7.33452i	0.257868	−	0.257868i	−0.566318	−	0.824187i	$-0.691633\pi$
$809$	7.33452	−	7.33452i	0.257868	−	0.257868i	0.824187	+	0.566318i	$0.191633\pi$
$810$	6.93962	+	0.964441i	0.243834	+	0.0338870i
$811$	−3.31008			−0.116233			−0.0581163	−	0.998310i	$-0.518509\pi$
$811$	−3.31008			−0.116233			−0.0581163	+	0.998310i	$0.518509\pi$
$812$	4.38495	−	0.478564i	0.153882	−	0.0167943i
$813$			17.5163i			0.614323i
$814$	−0.468757	−	0.977746i	−0.0164299	−	0.0342700i
$815$	−44.2225	+	8.97603i	−1.54905	+	0.314417i
$816$	30.4695	−	6.73092i	1.06664	−	0.235629i
$817$	3.12131			0.109201
$818$	−20.2580	−	42.2548i	−0.708306	−	1.47740i
$819$	27.3382			0.955273
$820$	−4.25613	+	28.3176i	−0.148631	+	0.988893i
$821$	23.5312			0.821244			0.410622	−	0.911806i	$-0.365312\pi$
$821$	23.5312			0.821244			0.410622	+	0.911806i	$0.365312\pi$
$822$	12.4412	+	25.9503i	0.433937	+	0.905119i
$823$	44.7289			1.55915			0.779576	−	0.626308i	$-0.215435\pi$
$823$	44.7289			1.55915			0.779576	+	0.626308i	$0.215435\pi$
$824$	8.06831	−	5.01090i	0.281073	−	0.174563i
$825$	−0.680277	−	0.275577i	−0.0236842	−	0.00959434i
$826$	−7.54763	−	15.7431i	−0.262616	−	0.547772i
$827$			45.6089i			1.58598i	0.609238	+	0.792988i	$0.291476\pi$
$827$			45.6089i			1.58598i	−0.609238	+	0.792988i	$0.708524\pi$
$828$	2.57737	+	23.6158i	0.0895700	+	0.820704i
$829$	−49.7820			−1.72900			−0.864499	−	0.502634i	$-0.832364\pi$
$829$	−49.7820			−1.72900			−0.864499	+	0.502634i	$0.832364\pi$
$830$	−28.1770	+	21.3008i	−0.978038	+	0.739360i
$831$	−27.7829	+	27.7829i	−0.963777	+	0.963777i
$832$	−21.5181	+	43.5108i	−0.746007	+	1.50847i
$833$		−	12.4688i		−	0.432019i
$834$	2.76171	−	1.32403i	0.0956301	−	0.0458475i
$835$	−26.7679	+	40.4015i	−0.926341	+	1.39815i
$836$	1.37305	+	1.10283i	0.0474878	+	0.0381423i
$837$			8.53810i			0.295120i
$838$	6.49535	+	13.5482i	0.224378	+	0.468015i
$839$	28.0218	−	28.0218i	0.967420	−	0.967420i	−0.0320657	−	0.999486i	$-0.510209\pi$
$839$	28.0218	−	28.0218i	0.967420	−	0.967420i	0.999486	+	0.0320657i	$0.0102086\pi$
$840$	15.8705	+	16.8317i	0.547584	+	0.580748i
$841$			28.4567i			0.981267i
$842$	12.1511	+	4.27569i	0.418756	+	0.147350i
$843$	−19.2144	+	19.2144i	−0.661777	+	0.661777i
$844$	30.7028	−	3.35084i	1.05683	−	0.115341i
$845$	−44.3943	−	29.4133i	−1.52721	−	1.01185i
$846$	−7.86685	+	3.77157i	−0.270468	+	0.129669i
$847$	32.8721			1.12950
$848$	−35.1863	+	7.77290i	−1.20830	+	0.266922i
$849$	3.27971	−	3.27971i	0.112559	−	0.112559i
$850$	29.8646	−	33.8291i	1.02435	−	1.16033i
$851$		−	50.3659i		−	1.72652i
$852$	1.09031	+	9.99018i	0.0373533	+	0.342258i
$853$	21.5640	−	21.5640i	0.738337	−	0.738337i	−0.233919	−	0.972256i	$-0.575155\pi$
$853$	21.5640	−	21.5640i	0.738337	−	0.738337i	0.972256	+	0.233919i	$0.0751551\pi$
$854$	−38.2171	+	18.3223i	−1.30776	+	0.626975i
$855$	−24.1950	+	4.91095i	−0.827450	+	0.167951i
$856$	−3.55609	+	2.20854i	−0.121545	+	0.0754864i
$857$	11.2827	−	11.2827i	0.385409	−	0.385409i	−0.487637	−	0.873046i	$-0.662141\pi$
$857$	11.2827	−	11.2827i	0.385409	−	0.385409i	0.873046	+	0.487637i	$0.162141\pi$
$858$	−1.18822	−	0.418106i	−0.0405651	−	0.0142739i
$859$		−	7.16423i		−	0.244440i	−0.992503	−	0.122220i	$-0.960999\pi$
$859$		−	7.16423i		−	0.244440i	0.992503	−	0.122220i	$-0.0390014\pi$
$860$	1.69167	+	0.873055i	0.0576855	+	0.0297709i
$861$	21.0060	+	10.3589i	0.715882	+	0.353030i
$862$	30.2454	−	14.5004i	1.03016	−	0.493886i
$863$	−23.4899	−	23.4899i	−0.799604	−	0.799604i	0.183429	−	0.983033i	$-0.441280\pi$
$863$	−23.4899	−	23.4899i	−0.799604	−	0.799604i	−0.983033	+	0.183429i	$0.941280\pi$
$864$	−19.2126	−	24.5281i	−0.653627	−	0.834464i
$865$	6.62625	−	1.34496i	0.225299	−	0.0457300i
$866$	1.91083	+	0.672375i	0.0649326	+	0.0228482i
$867$	−29.0028			−0.984988
$868$	−5.80952	+	7.23295i	−0.197188	+	0.245502i
$869$	−1.53235			−0.0519813
$870$	2.27280	−	1.71815i	0.0770552	−	0.0582509i
$871$		−	38.5080i		−	1.30480i
$872$	−28.5269	+	17.7169i	−0.966043	+	0.599970i
$873$			11.9892i			0.405773i
$874$	35.3644	+	73.7641i	1.19622	+	2.49511i
$875$	32.8863	+	6.14197i	1.11176	+	0.207637i
$876$	−0.252096	−	2.30988i	−0.00851753	−	0.0780437i
$877$	−7.32172	+	7.32172i	−0.247237	+	0.247237i	−0.819836	−	0.572599i	$-0.805935\pi$
$877$	−7.32172	+	7.32172i	−0.247237	+	0.247237i	0.572599	+	0.819836i	$0.305935\pi$
$878$	3.13214	+	1.10213i	0.105705	+	0.0371950i
$879$	34.5951			1.16686
$880$	0.435685	+	0.981760i	0.0146869	+	0.0330951i
$881$			5.45008i			0.183618i	0.995777	+	0.0918090i	$0.0292649\pi$
$881$			5.45008i			0.183618i	−0.995777	+	0.0918090i	$0.970735\pi$
$882$	−3.75167	+	1.79865i	−0.126325	+	0.0605636i
$883$		−	25.4652i		−	0.856973i	−0.903548	−	0.428487i	$-0.859047\pi$
$883$		−	25.4652i		−	0.856973i	0.903548	−	0.428487i	$-0.140953\pi$
$884$	48.4963	−	60.3787i	1.63111	−	2.03076i
$885$	−9.40092	−	6.22854i	−0.316008	−	0.209370i
$886$	21.7510	+	7.65366i	0.730740	+	0.257130i
$887$	41.7993			1.40348			0.701741	−	0.712432i	$-0.252406\pi$
$887$	41.7993			1.40348			0.701741	+	0.712432i	$0.252406\pi$
$888$	11.6465	+	18.7527i	0.390832	+	0.629299i
$889$	7.61979	−	7.61979i	0.255559	−	0.255559i
$890$	17.7681	−	13.4320i	0.595588	−	0.450243i
$891$	0.188136	−	0.188136i	0.00630279	−	0.00630279i
$892$	5.73240	+	52.5243i	0.191935	+	1.75864i
$893$	−21.2427	+	21.2427i	−0.710859	+	0.710859i
$894$	2.00236	+	0.704583i	0.0669690	+	0.0235648i
$895$	−15.0982	+	3.06455i	−0.504679	+	0.102437i
$896$	0.413761	−	33.8514i	0.0138228	−	1.13090i
$897$	−41.3727	−	41.3727i	−1.38139	−	1.38139i
$898$	1.19909	−	0.574872i	0.0400140	−	0.0191837i
$899$	0.807918	+	0.807918i	0.0269456	+	0.0269456i
$900$	−14.4867	−	4.10590i	−0.482889	−	0.136863i
$901$	57.4905			1.91529
$902$	0.760357	+	0.777414i	0.0253171	+	0.0258851i
$903$	1.10099	−	1.10099i	0.0366386	−	0.0366386i
$904$	−15.6354	+	9.71054i	−0.520027	+	0.322968i
$905$	−8.26401	+	1.67738i	−0.274705	+	0.0557580i
$906$	−8.35702	+	23.7499i	−0.277643	+	0.789037i
$907$	−24.3018	+	24.3018i	−0.806927	+	0.806927i	−0.984168	−	0.177241i	$-0.943283\pi$
$907$	−24.3018	+	24.3018i	−0.806927	+	0.806927i	0.177241	+	0.984168i	$0.443283\pi$
$908$	−23.9476	+	29.8152i	−0.794730	+	0.989452i
$909$	9.69281	−	9.69281i	0.321490	−	0.321490i
$910$	56.8681	+	7.90330i	1.88516	+	0.261992i
$911$	41.5568			1.37684			0.688420	−	0.725313i	$-0.258305\pi$
$911$	41.5568			1.37684			0.688420	+	0.725313i	$0.258305\pi$
$912$	−30.2243	−	19.2869i	−1.00083	−	0.638653i
$913$			1.34136i			0.0443926i
$914$	−9.44498	−	19.7006i	−0.312412	−	0.651639i
$915$	−15.1201	+	22.8212i	−0.499855	+	0.754446i
$916$	−29.1828	+	3.18495i	−0.964225	+	0.105234i
$917$			23.0904i			0.762512i
$918$	21.4895	+	44.8234i	0.709259	+	1.47939i
$919$	0.941189	−	0.941189i	0.0310470	−	0.0310470i	−0.691413	−	0.722460i	$-0.743011\pi$
$919$	0.941189	−	0.941189i	0.0310470	−	0.0310470i	0.722460	+	0.691413i	$0.243011\pi$
$920$	−1.46579	+	49.8699i	−0.0483257	+	1.64416i
$921$	0.668101	−	0.668101i	0.0220147	−	0.0220147i
$922$	−33.1688	+	15.9020i	−1.09236	+	0.523703i
$923$	17.6361	+	17.6361i	0.580499	+	0.580499i
$924$	0.873322	−	0.0953126i	0.0287302	−	0.00313555i
$925$	29.5880	+	11.9859i	0.972847	+	0.394095i
$926$	−32.2847	+	15.4781i	−1.06094	+	0.508643i
$927$	3.57525	+	3.57525i	0.117427	+	0.117427i
$928$	−4.13898	−	0.502980i	−0.135869	−	0.0165111i
$929$	−0.152964	−	0.152964i	−0.00501858	−	0.00501858i	0.704593	−	0.709612i	$-0.251130\pi$
$929$	−0.152964	−	0.152964i	−0.00501858	−	0.00501858i	−0.709612	+	0.704593i	$0.751130\pi$
$930$	−0.824863	+	5.93529i	−0.0270483	+	0.194626i
$931$	−10.1306	+	10.1306i	−0.332016	+	0.332016i
$932$	5.06555	+	4.06866i	0.165928	+	0.133274i
$933$	13.4346	+	13.4346i	0.439830	+	0.439830i
$934$	55.2492	+	19.4409i	1.80781	+	0.636125i
$935$	−0.340872	−	1.67939i	−0.0111477	−	0.0549219i
$936$	−25.1627	−	5.88206i	−0.822468	−	0.192261i
$937$		−	19.7190i		−	0.644192i	−0.946707	−	0.322096i	$-0.895613\pi$
$937$		−	19.7190i		−	0.644192i	0.946707	−	0.322096i	$-0.104387\pi$
$938$	11.6104	+	24.2174i	0.379094	+	0.790725i
$939$	5.87038			0.191573
$940$	−17.4547	+	5.57125i	−0.569310	+	0.181714i
$941$		−	10.3700i		−	0.338054i	−0.985611	−	0.169027i	$-0.945938\pi$
$941$		−	10.3700i		−	0.338054i	0.985611	−	0.169027i	$-0.0540624\pi$
$942$	4.62740	−	2.21850i	0.150769	−	0.0722825i
$943$	16.2365	+	47.8306i	0.528734	+	1.55758i
$944$	3.55975	+	16.1142i	0.115860	+	0.524474i
$945$	−20.3545	+	30.7216i	−0.662131	+	0.999374i
$946$	0.0651874	−	0.0312525i	0.00211942	−	0.00101611i
$947$	28.2675	+	28.2675i	0.918569	+	0.918569i	0.996925	−	0.0783563i	$-0.0249672\pi$
$947$	28.2675	+	28.2675i	0.918569	+	0.918569i	−0.0783563	+	0.996925i	$0.524967\pi$
$948$	31.0123	−	3.38462i	1.00723	−	0.109927i
$949$	−4.07774	−	4.07774i	−0.132369	−	0.132369i
$950$	−51.7494	+	3.22101i	−1.67897	+	0.104503i
$951$	35.4092			1.14822
$952$	−12.2943	+	52.5936i	−0.398462	+	1.70457i
$953$	−25.3813	−	25.3813i	−0.822180	−	0.822180i	0.164240	−	0.986420i	$-0.447483\pi$
$953$	−25.3813	−	25.3813i	−0.822180	−	0.822180i	−0.986420	+	0.164240i	$0.947483\pi$
$954$	−8.29310	−	17.2980i	−0.268499	−	0.560043i
$955$	−8.38927	−	41.3317i	−0.271470	−	1.33746i
$956$	6.34612	−	0.692602i	0.205248	−	0.0224004i
$957$		−	0.108196i		−	0.00349749i
$958$	−17.1739	−	6.04308i	−0.554863	−	0.195243i
$959$	−49.8130			−1.60855
$960$	−10.9861	−	18.9070i	−0.354574	−	0.610219i
$961$	28.5970			0.922482
$962$	51.6804	+	18.1851i	1.66624	+	0.586311i
$963$	−1.57578	−	1.57578i	−0.0507789	−	0.0507789i
$964$	−8.34892	−	6.70587i	−0.268901	−	0.215982i
$965$	−9.19963	+	13.8853i	−0.296147	+	0.446983i
$966$	38.4931	+	13.5448i	1.23849	+	0.435797i
$967$	59.7029			1.91991			0.959957	−	0.280146i	$-0.0903830\pi$
$967$	59.7029			1.91991			0.959957	+	0.280146i	$0.0903830\pi$
$968$	−30.2562	−	7.07273i	−0.972472	−	0.227326i
$969$	40.4479	+	40.4479i	1.29937	+	1.29937i
$970$	−3.46601	+	24.9396i	−0.111287	+	0.800763i
$971$	−11.3481	+	11.3481i	−0.364179	+	0.364179i	−0.865349	−	0.501170i	$-0.832903\pi$
$971$	−11.3481	+	11.3481i	−0.364179	+	0.364179i	0.501170	+	0.865349i	$0.332903\pi$
$972$	17.3025	−	21.5419i	0.554978	−	0.690956i
$973$			5.30125i			0.169950i
$974$	4.83696	−	13.7462i	0.154986	−	0.440456i
$975$	34.1506	−	14.4591i	1.09369	−	0.463061i
$976$	39.1181	−	8.64147i	1.25214	−	0.276607i
$977$	4.99974			0.159956			0.0799779	−	0.996797i	$-0.474515\pi$
$977$	4.99974			0.159956			0.0799779	+	0.996797i	$0.474515\pi$
$978$	11.5797	−	32.9084i	0.370278	−	1.05230i
$979$		−	0.845848i		−	0.0270334i
$980$	−8.32410	+	2.65691i	−0.265904	+	0.0848718i
$981$	−12.6409	−	12.6409i	−0.403593	−	0.403593i
$982$	20.6798	+	43.1345i	0.659918	+	1.37648i
$983$	6.49010	−	6.49010i	0.207002	−	0.207002i	−0.595990	−	0.802992i	$-0.703240\pi$
$983$	6.49010	−	6.49010i	0.207002	−	0.207002i	0.802992	+	0.595990i	$0.203240\pi$
$984$	−17.1056	−	14.0542i	−0.545306	−	0.448031i
$985$	−7.82450	−	38.5492i	−0.249309	−	1.22828i
$986$	6.27487	+	2.20798i	0.199833	+	0.0703163i
$987$			14.9859i			0.477008i
$988$	−88.4579	+	9.65411i	−2.81422	+	0.307138i
$989$	3.35795			0.106777
$990$	−0.456130	+	0.344818i	−0.0144968	+	0.0109590i
$991$	23.7557	−	23.7557i	0.754625	−	0.754625i	−0.220713	−	0.975339i	$-0.570839\pi$
$991$	23.7557	−	23.7557i	0.754625	−	0.754625i	0.975339	+	0.220713i	$0.0708385\pi$
$992$	6.90345	−	5.40740i	0.219185	−	0.171685i
$993$	7.50758	−	7.50758i	0.238246	−	0.238246i
$994$	−16.4086	−	5.77379i	−0.520449	−	0.183134i
$995$	17.2053	−	3.49224i	0.545446	−	0.110711i
$996$	−2.96277	−	27.1470i	−0.0938790	−	0.860187i
$997$	−34.9384			−1.10651			−0.553255	−	0.833012i	$-0.686614\pi$
$997$	−34.9384			−1.10651			−0.553255	+	0.833012i	$0.686614\pi$
$998$	3.21351	+	1.13076i	0.101722	+	0.0357935i
$999$	−24.8660	+	24.8660i	−0.786725	+	0.786725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.19	yes	240
4.3	odd	2	inner	820.2.s.c.583.77	yes	240
5.2	odd	4		820.2.j.c.747.44	yes	240
20.7	even	4		820.2.j.c.747.102	yes	240
41.32	even	4		820.2.j.c.483.102	yes	240
164.155	odd	4		820.2.j.c.483.44	✓	240
205.32	odd	4	inner	820.2.s.c.647.77	yes	240
820.647	even	4	inner	820.2.s.c.647.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.44	✓	240	164.155	odd	4
820.2.j.c.483.102	yes	240	41.32	even	4
820.2.j.c.747.44	yes	240	5.2	odd	4
820.2.j.c.747.102	yes	240	20.7	even	4
820.2.s.c.583.19	yes	240	1.1	even	1	trivial
820.2.s.c.583.77	yes	240	4.3	odd	2	inner
820.2.s.c.647.19	yes	240	820.647	even	4	inner
820.2.s.c.647.77	yes	240	205.32	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27523 + 0.611379i) q^{2} +1.22240 q^{3} +(1.25243 - 1.55930i) q^{4} +(1.86406 + 1.23502i) q^{5} +(-1.55885 + 0.747352i) q^{6} -2.99230i q^{7} +(-0.643820 + 2.75418i) q^{8} -1.50573 q^{9} +(-3.13217 - 0.435297i) q^{10} +(-0.0849144 + 0.0849144i) q^{11} +(1.53098 - 1.90609i) q^{12} -6.06762i q^{13} +(1.82943 + 3.81587i) q^{14} +(2.27863 + 1.50970i) q^{15} +(-0.862826 - 3.90583i) q^{16} +6.38170i q^{17} +(1.92015 - 0.920571i) q^{18} +(5.18495 - 5.18495i) q^{19} +(4.26038 - 1.35984i) q^{20} -3.65779i q^{21} +(0.0563707 - 0.160200i) q^{22} +(5.57803 - 5.57803i) q^{23} +(-0.787008 + 3.36672i) q^{24} +(1.94943 + 4.60432i) q^{25} +(3.70961 + 7.73762i) q^{26} -5.50782 q^{27} +(-4.66589 - 3.74765i) q^{28} +(-0.521178 + 0.521178i) q^{29} +(-3.82878 - 0.532109i) q^{30} -1.55018i q^{31} +(3.48825 + 4.45333i) q^{32} +(-0.103800 + 0.103800i) q^{33} +(-3.90163 - 8.13815i) q^{34} +(3.69556 - 5.57782i) q^{35} +(-1.88582 + 2.34788i) q^{36} +(4.51467 - 4.51467i) q^{37} +(-3.44205 + 9.78198i) q^{38} -7.41708i q^{39} +(-4.60159 + 4.33882i) q^{40} +(-2.83201 + 5.74280i) q^{41} +(2.23630 + 4.66454i) q^{42} +(0.300997 + 0.300997i) q^{43} +(0.0260574 + 0.238757i) q^{44} +(-2.80677 - 1.85961i) q^{45} +(-3.70300 + 10.5236i) q^{46} -4.09699 q^{47} +(-1.05472 - 4.77450i) q^{48} -1.95384 q^{49} +(-5.30095 - 4.67973i) q^{50} +7.80101i q^{51} +(-9.46123 - 7.59928i) q^{52} -9.00865i q^{53} +(7.02375 - 3.36736i) q^{54} +(-0.263157 + 0.0534141i) q^{55} +(8.24132 + 1.92650i) q^{56} +(6.33810 - 6.33810i) q^{57} +(0.345986 - 0.983260i) q^{58} -4.12568 q^{59} +(5.20790 - 1.66227i) q^{60} +10.0153i q^{61} +(0.947745 + 1.97683i) q^{62} +4.50559i q^{63} +(-7.17099 - 3.54639i) q^{64} +(7.49365 - 11.3104i) q^{65} +(0.0689078 - 0.195830i) q^{66} +6.34649 q^{67} +(9.95098 + 7.99265i) q^{68} +(6.81861 - 6.81861i) q^{69} +(-1.30254 + 9.37240i) q^{70} +(-2.90660 + 2.90660i) q^{71} +(0.969418 - 4.14705i) q^{72} +(0.672050 - 0.672050i) q^{73} +(-2.99708 + 8.51742i) q^{74} +(2.38299 + 5.62833i) q^{75} +(-1.59109 - 14.5787i) q^{76} +(0.254089 + 0.254089i) q^{77} +(4.53464 + 9.45849i) q^{78} +(9.02289 + 9.02289i) q^{79} +(3.21544 - 8.34631i) q^{80} -2.21559 q^{81} +(0.100438 - 9.05483i) q^{82} +(7.89831 - 7.89831i) q^{83} +(-5.70360 - 4.58114i) q^{84} +(-7.88155 + 11.8959i) q^{85} +(-0.567865 - 0.199818i) q^{86} +(-0.637090 + 0.637090i) q^{87} +(-0.179200 - 0.288539i) q^{88} +(-4.98059 + 4.98059i) q^{89} +(4.71621 + 0.655439i) q^{90} -18.1561 q^{91} +(-1.71171 - 15.6839i) q^{92} -1.89494i q^{93} +(5.22461 - 2.50481i) q^{94} +(16.0686 - 3.26151i) q^{95} +(4.26405 + 5.44377i) q^{96} -7.96240i q^{97} +(2.49160 - 1.19454i) q^{98} +(0.127858 - 0.127858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

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