LMFDB - Embedded newform 416.2.bi.a.99.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(99,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("416.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bi (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			99.12
Character	$\chi$	$=$	416.99
Dual form			416.2.bi.a.395.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21550 + 0.722878i) q^{2} +(1.19450 - 2.88378i) q^{3} +(0.954896 - 1.75732i) q^{4} +(0.304891 - 0.736071i) q^{5} +(0.632701 + 4.36873i) q^{6} -4.22727 q^{7} +(0.109649 + 2.82630i) q^{8} +(-4.76805 - 4.76805i) q^{9} +(0.161494 + 1.11510i) q^{10} +(2.77874 + 1.15099i) q^{11} +(-3.92711 - 4.85283i) q^{12} +(0.156314 - 3.60216i) q^{13} +(5.13827 - 3.05580i) q^{14} +(-1.75848 - 1.75848i) q^{15} +(-2.17635 - 3.35612i) q^{16} -0.425375 q^{17} +(9.24230 + 2.34886i) q^{18} +(0.456748 + 1.10269i) q^{19} +(-1.00237 - 1.23866i) q^{20} +(-5.04949 + 12.1905i) q^{21} +(-4.20959 + 0.609655i) q^{22} +(-6.61604 - 6.61604i) q^{23} +(8.28141 + 3.05982i) q^{24} +(3.08669 + 3.08669i) q^{25} +(2.41392 + 4.49143i) q^{26} +(-10.7941 + 4.47107i) q^{27} +(-4.03661 + 7.42867i) q^{28} +(2.71411 + 1.12422i) q^{29} +(3.40860 + 0.866271i) q^{30} +(-4.65292 + 4.65292i) q^{31} +(5.07142 + 2.50614i) q^{32} +(6.63842 - 6.63842i) q^{33} +(0.517044 - 0.307494i) q^{34} +(-1.28886 + 3.11158i) q^{35} +(-12.9320 + 3.82600i) q^{36} +(-3.17165 - 1.31374i) q^{37} +(-1.35229 - 1.01015i) q^{38} +(-10.2011 - 4.75356i) q^{39} +(2.11379 + 0.781004i) q^{40} -3.36891i q^{41} +(-2.67460 - 18.4678i) q^{42} +(-0.770093 + 0.318983i) q^{43} +(4.67607 - 3.78406i) q^{44} +(-4.96336 + 2.05589i) q^{45} +(12.8244 + 3.25923i) q^{46} +(-0.0766809 + 0.0766809i) q^{47} +(-12.2780 + 2.26723i) q^{48} +10.8698 q^{49} +(-5.98318 - 1.52058i) q^{50} +(-0.508111 + 1.22669i) q^{51} +(-6.18089 - 3.71438i) q^{52} +(11.4243 - 4.73212i) q^{53} +(9.88825 - 13.2374i) q^{54} +(1.69442 - 1.69442i) q^{55} +(-0.463515 - 11.9475i) q^{56} +3.72550 q^{57} +(-4.11168 + 0.595474i) q^{58} +(3.82451 - 9.23318i) q^{59} +(-4.76937 + 1.41105i) q^{60} +(-0.403832 - 0.167272i) q^{61} +(2.29215 - 9.01913i) q^{62} +(20.1559 + 20.1559i) q^{63} +(-7.97595 + 0.619800i) q^{64} +(-2.60379 - 1.21332i) q^{65} +(-3.27025 + 12.8678i) q^{66} +(-2.69242 + 1.11524i) q^{67} +(-0.406188 + 0.747519i) q^{68} +(-26.9821 + 11.1764i) q^{69} +(-0.682679 - 4.71382i) q^{70} -11.6515i q^{71} +(12.9531 - 13.9988i) q^{72} +14.5835 q^{73} +(4.80482 - 0.695859i) q^{74} +(12.5884 - 5.21429i) q^{75} +(2.37392 + 0.250299i) q^{76} +(-11.7465 - 4.86556i) q^{77} +(15.8358 - 1.59620i) q^{78} +6.05804 q^{79} +(-3.13389 + 0.578699i) q^{80} +16.2395i q^{81} +(2.43531 + 4.09492i) q^{82} +(-4.44848 - 10.7396i) q^{83} +(16.6010 + 20.5143i) q^{84} +(-0.129693 + 0.313106i) q^{85} +(0.705465 - 0.944408i) q^{86} +(6.48401 - 6.48401i) q^{87} +(-2.94836 + 7.97976i) q^{88} +12.9696i q^{89} +(4.54682 - 6.08684i) q^{90} +(-0.660781 + 15.2273i) q^{91} +(-17.9441 + 5.30887i) q^{92} +(7.86009 + 18.9759i) q^{93} +(0.0377750 - 0.148637i) q^{94} +0.950915 q^{95} +(13.2850 - 11.6313i) q^{96} +(-6.81783 - 6.81783i) q^{97} +(-13.2123 + 7.85757i) q^{98} +(-7.76118 - 18.7371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.21550	+	0.722878i	−0.859491	+	0.511152i
$2$	−1.21550	+	0.722878i	−0.859491	+	0.511152i
$3$	1.19450	−	2.88378i	0.689646	−	1.66495i	−0.0558467	−	0.998439i	$-0.517786\pi$
$3$	1.19450	−	2.88378i	0.689646	−	1.66495i	0.745493	−	0.666514i	$-0.232214\pi$
$4$	0.954896	−	1.75732i	0.477448	−	0.878660i
$5$	0.304891	−	0.736071i	0.136351	−	0.329181i	−0.840925	−	0.541152i	$-0.817988\pi$
$5$	0.304891	−	0.736071i	0.136351	−	0.329181i	0.977276	+	0.211971i	$0.0679883\pi$
$6$	0.632701	+	4.36873i	0.258299	+	1.78353i
$7$	−4.22727			−1.59776			−0.798880	−	0.601491i	$-0.794574\pi$
$7$	−4.22727			−1.59776			−0.798880	+	0.601491i	$0.794574\pi$
$8$	0.109649	+	2.82630i	0.0387666	+	0.999248i
$9$	−4.76805	−	4.76805i	−1.58935	−	1.58935i
$10$	0.161494	+	1.11510i	0.0510689	+	0.352624i
$11$	2.77874	+	1.15099i	0.837821	+	0.347037i	0.759994	−	0.649930i	$-0.225202\pi$
$11$	2.77874	+	1.15099i	0.837821	+	0.347037i	0.0778271	+	0.996967i	$0.475202\pi$
$12$	−3.92711	−	4.85283i	−1.13366	−	1.40089i
$13$	0.156314	−	3.60216i	0.0433536	−	0.999060i
$13$	0.156314	−	3.60216i	0.0433536	−	0.999060i
$14$	5.13827	−	3.05580i	1.37326	−	0.816697i
$15$	−1.75848	−	1.75848i	−0.454037	−	0.454037i
$16$	−2.17635	−	3.35612i	−0.544087	−	0.839029i
$17$	−0.425375			−0.103168			−0.0515842	−	0.998669i	$-0.516427\pi$
$17$	−0.425375			−0.103168			−0.0515842	+	0.998669i	$0.516427\pi$
$18$	9.24230	+	2.34886i	2.17843	+	0.553632i
$19$	0.456748	+	1.10269i	0.104785	+	0.252974i	0.967573	−	0.252593i	$-0.0812834\pi$
$19$	0.456748	+	1.10269i	0.104785	+	0.252974i	−0.862787	+	0.505567i	$0.831283\pi$
$20$	−1.00237	−	1.23866i	−0.224138	−	0.276973i
$21$	−5.04949	+	12.1905i	−1.10189	+	2.66019i
$22$	−4.20959	+	0.609655i	−0.897488	+	0.129979i
$23$	−6.61604	−	6.61604i	−1.37954	−	1.37954i	−0.845389	−	0.534152i	$-0.820631\pi$
$23$	−6.61604	−	6.61604i	−1.37954	−	1.37954i	−0.534152	−	0.845389i	$-0.679369\pi$
$24$	8.28141	+	3.05982i	1.69044	+	0.624583i
$25$	3.08669	+	3.08669i	0.617338	+	0.617338i
$26$	2.41392	+	4.49143i	0.473409	+	0.880843i
$27$	−10.7941	+	4.47107i	−2.07733	+	0.860458i
$28$	−4.03661	+	7.42867i	−0.762847	+	1.40389i
$29$	2.71411	+	1.12422i	0.503997	+	0.208762i	0.620171	−	0.784467i	$-0.287063\pi$
$29$	2.71411	+	1.12422i	0.503997	+	0.208762i	−0.116174	+	0.993229i	$0.537063\pi$
$30$	3.40860	+	0.866271i	0.622322	+	0.158159i
$31$	−4.65292	+	4.65292i	−0.835689	+	0.835689i	−0.988288	−	0.152599i	$-0.951236\pi$
$31$	−4.65292	+	4.65292i	−0.835689	+	0.835689i	0.152599	+	0.988288i	$0.451236\pi$
$32$	5.07142	+	2.50614i	0.896509	+	0.443026i
$33$	6.63842	−	6.63842i	1.15560	−	1.15560i
$34$	0.517044	−	0.307494i	0.0886723	−	0.0527347i
$35$	−1.28886	+	3.11158i	−0.217857	+	0.525952i
$36$	−12.9320	+	3.82600i	−2.15533	+	0.637667i
$37$	−3.17165	−	1.31374i	−0.521416	−	0.215977i	0.106423	−	0.994321i	$-0.466060\pi$
$37$	−3.17165	−	1.31374i	−0.521416	−	0.215977i	−0.627839	+	0.778344i	$0.716060\pi$
$38$	−1.35229	−	1.01015i	−0.219370	−	0.163868i
$39$	−10.2011	−	4.75356i	−1.63349	−	0.761179i
$40$	2.11379	+	0.781004i	0.334220	+	0.123488i
$41$		−	3.36891i		−	0.526136i	−0.964777	−	0.263068i	$-0.915266\pi$
$41$		−	3.36891i		−	0.526136i	0.964777	−	0.263068i	$-0.0847343\pi$
$42$	−2.67460	−	18.4678i	−0.412700	−	2.84964i
$43$	−0.770093	+	0.318983i	−0.117438	+	0.0486445i	−0.440629	−	0.897689i	$-0.645244\pi$
$43$	−0.770093	+	0.318983i	−0.117438	+	0.0486445i	0.323191	+	0.946334i	$0.395244\pi$
$44$	4.67607	−	3.78406i	0.704943	−	0.570468i
$45$	−4.96336	+	2.05589i	−0.739894	+	0.306474i
$46$	12.8244	+	3.25923i	1.89086	+	0.480547i
$47$	−0.0766809	+	0.0766809i	−0.0111851	+	0.0111851i	−0.712677	−	0.701492i	$-0.752518\pi$
$47$	−0.0766809	+	0.0766809i	−0.0111851	+	0.0111851i	0.701492	+	0.712677i	$0.252518\pi$
$48$	−12.2780	+	2.26723i	−1.77217	+	0.327246i
$49$	10.8698			1.55284
$50$	−5.98318	−	1.52058i	−0.846150	−	0.215043i
$51$	−0.508111	+	1.22669i	−0.0711497	+	0.171771i
$52$	−6.18089	−	3.71438i	−0.857135	−	0.515092i
$53$	11.4243	−	4.73212i	1.56925	−	0.650006i	0.582588	−	0.812768i	$-0.302040\pi$
$53$	11.4243	−	4.73212i	1.56925	−	0.650006i	0.986665	+	0.162761i	$0.0520401\pi$
$54$	9.88825	−	13.2374i	1.34562	−	1.80139i
$55$	1.69442	−	1.69442i	0.228476	−	0.228476i
$56$	−0.463515	−	11.9475i	−0.0619398	−	1.59656i
$57$	3.72550			0.493454
$58$	−4.11168	+	0.595474i	−0.539890	+	0.0781896i
$59$	3.82451	−	9.23318i	0.497909	−	1.20206i	−0.452699	−	0.891663i	$-0.649539\pi$
$59$	3.82451	−	9.23318i	0.497909	−	1.20206i	0.950608	−	0.310395i	$-0.100461\pi$
$60$	−4.76937	+	1.41105i	−0.615723	+	0.182165i
$61$	−0.403832	−	0.167272i	−0.0517053	−	0.0214170i	0.356681	−	0.934226i	$-0.383908\pi$
$61$	−0.403832	−	0.167272i	−0.0517053	−	0.0214170i	−0.408386	+	0.912809i	$0.633908\pi$
$62$	2.29215	−	9.01913i	0.291103	−	1.14543i
$63$	20.1559	+	20.1559i	2.53940	+	2.53940i
$64$	−7.97595	+	0.619800i	−0.996994	+	0.0774750i
$65$	−2.60379	−	1.21332i	−0.322960	−	0.150494i
$66$	−3.27025	+	12.8678i	−0.402540	+	1.58391i
$67$	−2.69242	+	1.11524i	−0.328932	+	0.136248i	−0.541037	−	0.840999i	$-0.681968\pi$
$67$	−2.69242	+	1.11524i	−0.328932	+	0.136248i	0.212105	+	0.977247i	$0.431968\pi$
$68$	−0.406188	+	0.747519i	−0.0492576	+	0.0906500i
$69$	−26.9821	+	11.1764i	−3.24826	+	1.34548i
$70$	−0.682679	−	4.71382i	−0.0815958	−	0.563409i
$71$		−	11.6515i		−	1.38278i	−0.722481	−	0.691390i	$-0.756998\pi$
$71$		−	11.6515i		−	1.38278i	0.722481	−	0.691390i	$-0.243002\pi$
$72$	12.9531	−	13.9988i	1.52654	−	1.64977i
$73$	14.5835			1.70687			0.853436	−	0.521197i	$-0.174514\pi$
$73$	14.5835			1.70687			0.853436	+	0.521197i	$0.174514\pi$
$74$	4.80482	−	0.695859i	0.558549	−	0.0808919i
$75$	12.5884	−	5.21429i	1.45358	−	0.602094i
$76$	2.37392	+	0.250299i	0.272308	+	0.0287113i
$77$	−11.7465	−	4.86556i	−1.33864	−	0.554482i
$78$	15.8358	−	1.59620i	1.79305	−	0.180734i
$79$	6.05804			0.681583			0.340791	−	0.940139i	$-0.389305\pi$
$79$	6.05804			0.681583			0.340791	+	0.940139i	$0.389305\pi$
$80$	−3.13389	+	0.578699i	−0.350379	+	0.0647005i
$81$			16.2395i			1.80439i
$82$	2.43531	+	4.09492i	0.268935	+	0.452209i
$83$	−4.44848	−	10.7396i	−0.488284	−	1.17882i	−0.955583	−	0.294722i	$-0.904773\pi$
$83$	−4.44848	−	10.7396i	−0.488284	−	1.17882i	0.467299	−	0.884099i	$-0.345227\pi$
$84$	16.6010	+	20.5143i	1.81131	+	2.23829i
$85$	−0.129693	+	0.313106i	−0.0140672	+	0.0339611i
$86$	0.705465	−	0.944408i	0.0760723	−	0.101838i
$87$	6.48401	−	6.48401i	0.695159	−	0.695159i
$88$	−2.94836	+	7.97976i	−0.314297	+	0.850645i
$89$			12.9696i			1.37478i	0.726291	+	0.687388i	$0.241243\pi$
$89$			12.9696i			1.37478i	−0.726291	+	0.687388i	$0.758757\pi$
$90$	4.54682	−	6.08684i	0.479277	−	0.641610i
$91$	−0.660781	+	15.2273i	−0.0692687	+	1.59626i
$92$	−17.9441	+	5.30887i	−1.87081	+	0.553488i
$93$	7.86009	+	18.9759i	0.815053	+	1.96771i
$94$	0.0377750	−	0.148637i	0.00389619	−	0.0153307i
$95$	0.950915			0.0975619
$96$	13.2850	−	11.6313i	1.35589	−	1.18711i
$97$	−6.81783	−	6.81783i	−0.692245	−	0.692245i	0.270480	−	0.962726i	$-0.412818\pi$
$97$	−6.81783	−	6.81783i	−0.692245	−	0.692245i	−0.962726	+	0.270480i	$0.912818\pi$
$98$	−13.2123	+	7.85757i	−1.33465	+	0.793735i
$99$	−7.76118	−	18.7371i	−0.780028	−	1.88315i
$100$	8.37177	−	2.47684i	0.837177	−	0.247684i
$101$	1.97445	−	0.817844i	0.196465	−	0.0813786i	−0.282282	−	0.959332i	$-0.591091\pi$
$101$	1.97445	−	0.817844i	0.196465	−	0.0813786i	0.478747	+	0.877953i	$0.341091\pi$
$102$	−0.269135	−	1.85834i	−0.0266483	−	0.184004i
$103$	−6.20897	+	6.20897i	−0.611788	+	0.611788i	−0.943412	−	0.331624i	$-0.892404\pi$
$103$	−6.20897	+	6.20897i	−0.611788	+	0.611788i	0.331624	+	0.943412i	$0.392404\pi$
$104$	10.1979	+	0.0468178i	0.999989	+	0.00459086i
$105$	7.43357	+	7.43357i	0.725442	+	0.725442i
$106$	−10.4656	+	14.0103i	−1.01651	+	1.36080i
$107$	1.67205	+	4.03668i	0.161643	+	0.390240i	0.983862	−	0.178931i	$-0.0572640\pi$
$107$	1.67205	+	4.03668i	0.161643	+	0.390240i	−0.822219	+	0.569172i	$0.807264\pi$
$108$	−2.45016	+	23.2381i	−0.235766	+	2.23609i
$109$	5.83709	−	2.41780i	0.559092	−	0.231584i	−0.0851989	−	0.996364i	$-0.527153\pi$
$109$	5.83709	−	2.41780i	0.559092	−	0.231584i	0.644291	+	0.764780i	$0.277153\pi$
$110$	−0.834716	+	3.28444i	−0.0795871	+	0.313159i
$111$	−7.57708	+	7.57708i	−0.719184	+	0.719184i
$112$	9.20002	+	14.1872i	0.869320	+	1.34057i
$113$		−	12.2878i		−	1.15593i	−0.816060	−	0.577967i	$-0.803846\pi$
$113$		−	12.2878i		−	1.15593i	0.816060	−	0.577967i	$-0.196154\pi$
$114$	−4.52836	+	2.69308i	−0.424119	+	0.252230i
$115$	−6.88705	+	2.85271i	−0.642221	+	0.266017i
$116$	4.56730	−	3.69604i	0.424063	−	0.343169i
$117$	−17.9206	+	16.4300i	−1.65676	+	1.51895i
$118$	2.02576	+	13.9876i	0.186486	+	1.28766i
$119$	1.79817			0.164838
$120$	4.77717	−	5.16280i	0.436094	−	0.471297i
$121$	−1.38157	−	1.38157i	−0.125597	−	0.125597i
$122$	0.611776	−	0.0886005i	0.0553876	−	0.00802152i
$123$	−9.71521	−	4.02417i	−0.875991	−	0.362847i
$124$	3.73362	+	12.6197i	0.335289	+	1.13328i
$125$	6.89349	−	2.85538i	0.616572	−	0.255393i
$126$	−39.0697	−	9.92929i	−3.48061	−	0.884571i
$127$	12.5749			1.11585			0.557923	−	0.829893i	$-0.311599\pi$
$127$	12.5749			1.11585			0.557923	+	0.829893i	$0.311599\pi$
$128$	9.24676	−	6.51901i	0.817306	−	0.576204i
$129$			2.60181i			0.229076i
$130$	4.04200	−	0.407422i	0.354507	−	0.0357333i
$131$	5.98126	−	14.4400i	0.522585	−	1.26163i	−0.413708	−	0.910410i	$-0.635766\pi$
$131$	5.98126	−	14.4400i	0.522585	−	1.26163i	0.936292	−	0.351222i	$-0.114234\pi$
$132$	−5.32683	−	18.0048i	−0.463641	−	1.56712i
$133$	−1.93080	−	4.66136i	−0.167422	−	0.404192i
$134$	2.46647	−	3.30187i	0.213070	−	0.285238i
$135$			9.30843i			0.801142i
$136$	−0.0466417	−	1.20224i	−0.00399949	−	0.103091i
$137$	7.90676			0.675520			0.337760	−	0.941232i	$-0.390331\pi$
$137$	7.90676			0.675520			0.337760	+	0.941232i	$0.390331\pi$
$138$	24.7177	−	33.0897i	2.10411	−	2.81678i
$139$	2.06285	+	4.98017i	0.174969	+	0.422413i	0.986898	−	0.161343i	$-0.0515826\pi$
$139$	2.06285	+	4.98017i	0.174969	+	0.422413i	−0.811929	+	0.583756i	$0.801583\pi$
$140$	4.23731	+	5.23617i	0.358118	+	0.442537i
$141$	0.129536	+	0.312727i	0.0109089	+	0.0263363i
$142$	8.42262	+	14.1625i	0.706811	+	1.18849i
$143$	4.58041	−	9.82955i	0.383033	−	0.821988i
$144$	−5.62519	+	26.3791i	−0.468766	+	2.19825i
$145$	1.65501	−	1.65501i	0.137441	−	0.137441i
$146$	−17.7263	+	10.5421i	−1.46704	+	0.872471i
$147$	12.9841	−	31.3463i	1.07091	−	2.58540i
$148$	−5.33725	+	4.31911i	−0.438719	+	0.355029i
$149$	13.7411	+	5.69173i	1.12571	+	0.466285i	0.866321	−	0.499488i	$-0.166479\pi$
$149$	13.7411	+	5.69173i	1.12571	+	0.466285i	0.259390	+	0.965773i	$0.416479\pi$
$150$	−11.5320	+	15.4379i	−0.941580	+	1.26050i
$151$			4.09540i			0.333279i	0.986018	+	0.166639i	$0.0532916\pi$
$151$			4.09540i			0.333279i	−0.986018	+	0.166639i	$0.946708\pi$
$152$	−3.06645	+	1.41182i	−0.248722	+	0.114513i
$153$	2.02821	+	2.02821i	0.163971	+	0.163971i
$154$	17.7951	−	2.57718i	1.43397	−	0.207675i
$155$	2.00625	+	4.84351i	0.161146	+	0.389040i
$156$	−18.0946	+	13.3875i	−1.44872	+	1.07186i
$157$	−4.14753	−	1.71796i	−0.331009	−	0.137108i	0.210989	−	0.977489i	$-0.432332\pi$
$157$	−4.14753	−	1.71796i	−0.331009	−	0.137108i	−0.541997	+	0.840380i	$0.682332\pi$
$158$	−7.36357	+	4.37922i	−0.585814	+	0.348392i
$159$		−	38.5978i		−	3.06101i
$160$	3.39092	−	2.96883i	0.268076	−	0.234707i
$161$	27.9678	+	27.9678i	2.20417	+	2.20417i
$162$	−11.7392	−	19.7391i	−0.922315	−	1.55085i
$163$	−2.99654	−	7.23428i	−0.234707	−	0.566633i	0.762013	−	0.647562i	$-0.224211\pi$
$163$	−2.99654	−	7.23428i	−0.234707	−	0.566633i	−0.996720	+	0.0809290i	$0.974211\pi$
$164$	−5.92026	−	3.21696i	−0.462294	−	0.251202i
$165$	−2.86236	−	6.91034i	−0.222834	−	0.537969i
$166$	13.1705	+	9.83828i	1.02223	+	0.763599i
$167$	18.5547			1.43581			0.717903	−	0.696143i	$-0.245102\pi$
$167$	18.5547			1.43581			0.717903	+	0.696143i	$0.245102\pi$
$168$	−35.0078	−	12.9347i	−2.70091	−	0.997934i
$169$	−12.9511	−	1.12613i	−0.996241	−	0.0866257i
$170$	−0.0686954	−	0.474333i	−0.00526870	−	0.0363797i
$171$	3.07987	−	7.43547i	0.235524	−	0.568604i
$172$	−0.174803	+	1.65790i	−0.0133286	+	0.126413i
$173$	−0.709043	−	0.293695i	−0.0539075	−	0.0223292i	0.355567	−	0.934651i	$-0.384288\pi$
$173$	−0.709043	−	0.293695i	−0.0539075	−	0.0223292i	−0.409474	+	0.912322i	$0.634288\pi$
$174$	−3.19419	+	12.5685i	−0.242151	+	0.952814i
$175$	−13.0483	−	13.0483i	−0.986358	−	0.986358i
$176$	−2.18464	−	11.8307i	−0.164674	−	0.891774i
$177$	−22.0581	−	22.0581i	−1.65799	−	1.65799i
$178$	−9.37544	−	15.7646i	−0.702719	−	1.18161i
$179$	−4.70177	+	11.3511i	−0.351427	+	0.848420i	0.645017	+	0.764168i	$0.276850\pi$
$179$	−4.70177	+	11.3511i	−0.351427	+	0.848420i	−0.996444	+	0.0842522i	$0.973150\pi$
$180$	−1.12663	+	10.6854i	−0.0839743	+	0.796441i
$181$	−1.71936	−	4.15090i	−0.127799	−	0.308534i	0.847010	−	0.531578i	$-0.178401\pi$
$181$	−1.71936	−	4.15090i	−0.127799	−	0.308534i	−0.974808	+	0.223044i	$0.928401\pi$
$182$	−10.2043	−	18.9865i	−0.756394	−	1.40737i
$183$	−0.964755	+	0.964755i	−0.0713168	+	0.0713168i
$184$	17.9735	−	19.4244i	1.32502	−	1.43198i
$185$	−1.93401	+	1.93401i	−0.142191	+	0.142191i
$186$	−23.2712	−	17.3834i	−1.70633	−	1.27461i
$187$	−1.18200	−	0.489602i	−0.0864367	−	0.0358033i
$188$	0.0615306	+	0.207975i	0.00448758	+	0.0151682i
$189$	45.6297	−	18.9004i	3.31907	−	1.37480i
$190$	−1.15584	+	0.687395i	−0.0838535	+	0.0498689i
$191$			7.42344i			0.537141i	0.963260	+	0.268571i	$0.0865513\pi$
$191$			7.42344i			0.537141i	−0.963260	+	0.268571i	$0.913449\pi$
$192$	−7.73993	+	23.7413i	−0.558581	+	1.71338i
$193$	−15.8252	+	15.8252i	−1.13912	+	1.13912i	−0.150511	+	0.988608i	$0.548092\pi$
$193$	−15.8252	+	15.8252i	−1.13912	+	1.13912i	−0.988608	+	0.150511i	$0.951908\pi$
$194$	13.2155	+	3.35863i	0.948821	+	0.241136i
$195$	−6.60919	+	6.05945i	−0.473294	+	0.433926i
$196$	10.3796	−	19.1018i	0.741398	−	1.36441i
$197$	−2.52936	+	6.10642i	−0.180209	+	0.435064i	−0.988010	−	0.154392i	$-0.950658\pi$
$197$	−2.52936	+	6.10642i	−0.180209	+	0.435064i	0.807800	+	0.589456i	$0.200658\pi$
$198$	22.9784	+	17.1647i	1.63300	+	1.21984i
$199$	2.35910	−	2.35910i	0.167232	−	0.167232i	−0.618529	−	0.785762i	$-0.712271\pi$
$199$	2.35910	−	2.35910i	0.167232	−	0.167232i	0.785762	+	0.618529i	$0.212271\pi$
$200$	−8.38547	+	9.06237i	−0.592942	+	0.640806i
$201$			9.09651i			0.641619i
$202$	−1.80875	+	2.42138i	−0.127263	+	0.170368i
$203$	−11.4733	−	4.75238i	−0.805266	−	0.333552i
$204$	1.67049	+	2.06427i	0.116958	+	0.144528i
$205$	−2.47976	−	1.02715i	−0.173194	−	0.0717393i
$206$	3.05870	−	12.0353i	0.213109	−	0.838542i
$207$			63.0912i			4.38514i
$208$	−12.4295	+	7.31495i	−0.861828	+	0.507201i
$209$			3.58979i			0.248311i
$210$	−14.4091	−	3.66197i	−0.994321	−	0.252700i
$211$	12.4421	+	5.15371i	0.856553	+	0.354796i	0.767358	−	0.641218i	$-0.221571\pi$
$211$	12.4421	+	5.15371i	0.856553	+	0.354796i	0.0891945	+	0.996014i	$0.471571\pi$
$212$	2.59321	−	24.5949i	0.178102	−	1.68918i
$213$	−33.6005	−	13.9178i	−2.30227	−	0.953629i
$214$	−4.95040	−	3.69791i	−0.338402	−	0.252784i
$215$			0.664099i			0.0452912i
$216$	−13.8201	−	30.0172i	−0.940342	−	2.04241i
$217$	19.6692	−	19.6692i	1.33523	−	1.33523i
$218$	−5.34723	+	7.15835i	−0.362160	+	0.484825i
$219$	17.4200	−	42.0557i	1.17714	−	2.84186i
$220$	−1.35965	−	4.59564i	−0.0916674	−	0.309838i
$221$	−0.0664919	+	1.53227i	−0.00447273	+	0.103071i
$222$	3.73266	−	14.6873i	0.250520	−	0.985744i
$223$	−14.2676	+	14.2676i	−0.955430	+	0.955430i	−0.999048	−	0.0436187i	$-0.986111\pi$
$223$	−14.2676	+	14.2676i	−0.955430	+	0.955430i	0.0436187	+	0.999048i	$0.486111\pi$
$224$	−21.4383	−	10.5941i	−1.43241	−	0.707850i
$225$		−	29.4350i		−	1.96233i
$226$	8.88254	+	14.9358i	0.590858	+	0.993515i
$227$	−16.7706	+	6.94663i	−1.11311	+	0.461064i	−0.862006	−	0.506897i	$-0.830792\pi$
$227$	−16.7706	+	6.94663i	−1.11311	+	0.461064i	−0.251100	+	0.967961i	$0.580792\pi$
$228$	3.55746	−	6.54689i	0.235599	−	0.433579i
$229$	7.25665	+	3.00580i	0.479533	+	0.198629i	0.609338	−	0.792911i	$-0.291435\pi$
$229$	7.25665	+	3.00580i	0.479533	+	0.198629i	−0.129805	+	0.991539i	$0.541435\pi$
$230$	6.30907	−	8.44597i	0.416008	−	0.556911i
$231$	−28.0624	+	28.0624i	−1.84637	+	1.84637i
$232$	−2.87978	+	7.79415i	−0.189067	+	0.511711i
$233$	−8.01713	+	8.01713i	−0.525220	+	0.525220i	−0.919143	−	0.393924i	$-0.871117\pi$
$233$	−8.01713	+	8.01713i	−0.525220	+	0.525220i	0.393924	+	0.919143i	$0.371117\pi$
$234$	9.90568	−	32.9251i	0.647555	−	2.15238i
$235$	0.0330633	+	0.0798219i	0.00215681	+	0.00520701i
$236$	−12.5737	−	15.5376i	−0.818475	−	1.01141i
$237$	7.23634	−	17.4701i	0.470051	−	1.13480i
$238$	−2.18569	+	1.29986i	−0.141677	+	0.0842574i
$239$	−1.79523	−	1.79523i	−0.116124	−	0.116124i	0.646657	−	0.762781i	$-0.276166\pi$
$239$	−1.79523	−	1.79523i	−0.116124	−	0.116124i	−0.762781	+	0.646657i	$0.776166\pi$
$240$	−2.07459	+	9.72871i	−0.133914	+	0.627986i
$241$	6.16294	+	6.16294i	0.396990	+	0.396990i	0.877170	−	0.480180i	$-0.159429\pi$
$241$	6.16294	+	6.16294i	0.396990	+	0.396990i	−0.480180	+	0.877170i	$0.659429\pi$
$242$	2.67800	+	0.680595i	0.172148	+	0.0437503i
$243$	14.4488	+	5.98488i	0.926889	+	0.383930i
$244$	−0.679568	+	0.549933i	−0.0435049	+	0.0352059i
$245$	3.31412	−	8.00099i	0.211731	−	0.511164i
$246$	14.7179	−	2.13152i	0.938376	−	0.135900i
$247$	4.04346	−	1.47292i	0.257279	−	0.0937194i
$248$	−13.6607	−	12.6404i	−0.867458	−	0.802664i
$249$	−36.2843			−2.29943
$250$	−6.31497	+	8.45387i	−0.399394	+	0.534669i
$251$	3.39364	+	8.19297i	0.214205	+	0.517136i	0.994061	−	0.108823i	$-0.0347080\pi$
$251$	3.39364	+	8.19297i	0.214205	+	0.517136i	−0.779857	+	0.625958i	$0.784708\pi$
$252$	54.6670	−	16.1735i	3.44370	−	1.01884i
$253$	−10.7692	−	25.9993i	−0.677057	−	1.63456i
$254$	−15.2849	+	9.09014i	−0.959058	+	0.570366i
$255$	0.748012	+	0.748012i	0.0468423	+	0.0468423i
$256$	−6.52702	+	14.6081i	−0.407939	+	0.913009i
$257$		−	12.1508i		−	0.757948i	−0.925407	−	0.378974i	$-0.876277\pi$
$257$		−	12.1508i		−	0.757948i	0.925407	−	0.378974i	$-0.123723\pi$
$258$	−1.88079	−	3.16251i	−0.117093	−	0.196889i
$259$	13.4074	+	5.55354i	0.833097	+	0.345080i
$260$	−4.61855	+	3.41709i	−0.286430	+	0.211919i
$261$	−7.58066	−	18.3013i	−0.469231	−	1.13282i
$262$	3.16814	+	21.8756i	0.195728	+	1.35148i
$263$	14.6189	+	14.6189i	0.901439	+	0.901439i	0.995561	−	0.0941214i	$-0.0300042\pi$
$263$	14.6189	+	14.6189i	0.901439	+	0.901439i	−0.0941214	+	0.995561i	$0.530004\pi$
$264$	19.4901	+	18.0343i	1.19953	+	1.10993i
$265$		−	9.85191i		−	0.605198i
$266$	5.71649	+	4.27017i	0.350500	+	0.261821i
$267$	37.4015	+	15.4922i	2.28894	+	0.948109i
$268$	−0.611153	+	5.79638i	−0.0373321	+	0.354070i
$269$	−3.11480	+	7.51980i	−0.189913	+	0.458490i	−0.989943	−	0.141470i	$-0.954817\pi$
$269$	−3.11480	+	7.51980i	−0.189913	+	0.458490i	0.800030	+	0.599961i	$0.204817\pi$
$270$	−6.72886	−	11.3144i	−0.409505	−	0.688574i
$271$	−12.9175	+	12.9175i	−0.784680	+	0.784680i	−0.980617	−	0.195937i	$-0.937225\pi$
$271$	−12.9175	+	12.9175i	−0.784680	+	0.784680i	0.195937	+	0.980617i	$0.437225\pi$
$272$	0.925763	+	1.42761i	0.0561326	+	0.0865613i
$273$	43.1230	+	20.0946i	2.60992	+	1.21618i
$274$	−9.61069	+	5.71562i	−0.580603	+	0.345293i
$275$	5.02435	+	12.1299i	0.302980	+	0.731458i
$276$	−6.12467	+	58.0885i	−0.368662	+	3.49651i
$277$	7.88803	+	19.0434i	0.473946	+	1.14421i	0.962405	+	0.271619i	$0.0875592\pi$
$277$	7.88803	+	19.0434i	0.473946	+	1.14421i	−0.488459	+	0.872587i	$0.662441\pi$
$278$	−6.10746	−	4.56222i	−0.366301	−	0.273624i
$279$	44.3707			2.65640
$280$	−8.93557	−	3.30152i	−0.534003	−	0.197303i
$281$		−	7.55383i		−	0.450624i	−0.974287	−	0.225312i	$-0.927660\pi$
$281$		−	7.55383i		−	0.450624i	0.974287	−	0.225312i	$-0.0723401\pi$
$282$	−0.383514	−	0.286482i	−0.0228379	−	0.0170597i
$283$	−8.37012	−	20.2073i	−0.497552	−	1.20120i	−0.950798	−	0.309811i	$-0.899734\pi$
$283$	−8.37012	−	20.2073i	−0.497552	−	1.20120i	0.453246	−	0.891385i	$-0.350266\pi$
$284$	−20.4754	−	11.1260i	−1.21499	−	0.660206i
$285$	1.13587	−	2.74223i	0.0672832	−	0.162436i
$286$	1.53806	+	15.2589i	0.0909472	+	0.902279i
$287$			14.2413i			0.840638i
$288$	−12.2314	−	36.1302i	−0.720742	−	2.12899i
$289$	−16.8191			−0.989356
$290$	−0.815301	+	3.20804i	−0.0478761	+	0.188383i
$291$	−27.8050	+	11.5172i	−1.62996	+	0.675152i
$292$	13.9257	−	25.6279i	0.814943	−	1.49976i
$293$	−0.757644	−	0.313826i	−0.0442620	−	0.0183339i	0.360443	−	0.932781i	$-0.382626\pi$
$293$	−0.757644	−	0.313826i	−0.0442620	−	0.0183339i	−0.404705	+	0.914447i	$0.632626\pi$
$294$	6.87737	+	47.4874i	0.401096	+	2.76952i
$295$	−5.63023	−	5.63023i	−0.327804	−	0.327804i
$296$	3.36526	−	9.10808i	0.195602	−	0.529396i
$297$	−35.1402			−2.03904
$298$	−20.8167	+	3.01478i	−1.20588	+	0.174642i
$299$	−24.8662	+	22.7979i	−1.43805	+	1.31844i
$300$	2.85744	−	27.1010i	0.164974	−	1.56467i
$301$	3.25540	−	1.34843i	0.187638	−	0.0777222i
$302$	−2.96047	−	4.97797i	−0.170356	−	0.286450i
$303$		−	6.67081i		−	0.383228i
$304$	2.70670	−	3.93273i	0.155240	−	0.225558i
$305$	−0.246249	+	0.246249i	−0.0141002	+	0.0141002i
$306$	−3.93144	−	0.999146i	−0.224745	−	0.0571174i
$307$	−19.7866	+	8.19588i	−1.12928	+	0.467763i	−0.867536	−	0.497374i	$-0.834298\pi$
$307$	−19.7866	+	8.19588i	−1.12928	+	0.467763i	−0.261744	+	0.965137i	$0.584298\pi$
$308$	−19.7670	+	15.9962i	−1.12633	+	0.911471i
$309$	10.4887	+	25.3219i	0.596681	+	1.44052i
$310$	−5.93987	−	4.43703i	−0.337362	−	0.252007i
$311$	7.04675	+	7.04675i	0.399585	+	0.399585i	0.878087	−	0.478502i	$-0.158820\pi$
$311$	7.04675	+	7.04675i	0.399585	+	0.399585i	−0.478502	+	0.878087i	$0.658820\pi$
$312$	12.3165	−	29.3527i	0.697282	−	1.66177i
$313$	23.6878	−	23.6878i	1.33891	−	1.33891i	0.441797	−	0.897115i	$-0.354341\pi$
$313$	23.6878	−	23.6878i	1.33891	−	1.33891i	0.897115	−	0.441797i	$-0.145659\pi$
$314$	6.28321	−	0.909967i	0.354582	−	0.0513524i
$315$	20.9815	−	8.69081i	1.18217	−	0.489672i
$316$	5.78480	−	10.6459i	0.325420	−	0.598880i
$317$	7.79959	+	18.8299i	0.438069	+	1.05759i	0.976615	+	0.214996i	$0.0689737\pi$
$317$	7.79959	+	18.8299i	0.438069	+	1.05759i	−0.538546	+	0.842596i	$0.681026\pi$
$318$	27.9015	+	46.9158i	1.56464	+	2.63091i
$319$	6.24782	+	6.24782i	0.349811	+	0.349811i
$320$	−1.97558	+	6.05984i	−0.110438	+	0.338756i
$321$	13.6382			0.761208
$322$	−54.2123	−	13.7777i	−3.02113	−	0.767799i
$323$	−0.194289	−	0.469055i	−0.0108105	−	0.0260989i
$324$	28.5380	+	15.5070i	1.58544	+	0.861500i
$325$	11.6013	−	10.6363i	0.643522	−	0.589994i
$326$	8.87181	+	6.62716i	0.491364	+	0.367045i
$327$		−	19.7210i		−	1.09057i
$328$	9.52156	−	0.369397i	0.525740	−	0.0203965i
$329$	0.324151	−	0.324151i	0.0178710	−	0.0178710i
$330$	8.47454	+	6.33041i	0.466508	+	0.348478i
$331$	−1.34702	+	3.25198i	−0.0740387	+	0.178745i	−0.956566	−	0.291516i	$-0.905840\pi$
$331$	−1.34702	+	3.25198i	−0.0740387	+	0.178745i	0.882527	+	0.470261i	$0.155840\pi$
$332$	−23.1207	−	2.43778i	−1.26891	−	0.133790i
$333$	8.85860	+	21.3865i	0.485448	+	1.17198i
$334$	−22.5533	+	13.4128i	−1.23406	+	0.733915i
$335$			2.32184i			0.126856i
$336$	51.9023	−	9.58420i	2.83150	−	0.522861i
$337$	28.0157			1.52611			0.763056	−	0.646333i	$-0.223698\pi$
$337$	28.0157			1.52611			0.763056	+	0.646333i	$0.223698\pi$
$338$	16.5562	−	7.99326i	0.900539	−	0.434776i
$339$	−35.4352	−	14.6777i	−1.92458	−	0.797186i
$340$	0.426384	+	0.526895i	0.0231239	+	0.0285749i
$341$	−18.2847	+	7.57378i	−0.990173	+	0.410143i
$342$	1.63134	+	11.2642i	0.0882128	+	0.609098i
$343$	−16.3589			−0.883298
$344$	−0.985982	−	2.14154i	−0.0531606	−	0.115464i
$345$			23.2683i			1.25272i
$346$	1.07415	−	0.155564i	0.0577466	−	0.00836316i
$347$	−4.51799	+	1.87141i	−0.242538	+	0.100463i	−0.500642	−	0.865655i	$-0.666903\pi$
$347$	−4.51799	+	1.87141i	−0.242538	+	0.100463i	0.258103	+	0.966117i	$0.416903\pi$
$348$	−5.20293	−	17.5860i	−0.278906	−	0.942710i
$349$	−11.2670	+	4.66693i	−0.603107	+	0.249815i	−0.663278	−	0.748373i	$-0.730835\pi$
$349$	−11.2670	+	4.66693i	−0.603107	+	0.249815i	0.0601710	+	0.998188i	$0.480835\pi$
$350$	25.2926	+	6.42792i	1.35194	+	0.343587i
$351$	14.4182	+	39.5810i	0.769589	+	2.11268i
$352$	11.2076	+	12.8011i	0.597367	+	0.682298i
$353$	−15.3248	−	15.3248i	−0.815656	−	0.815656i	0.169820	−	0.985475i	$-0.445682\pi$
$353$	−15.3248	−	15.3248i	−0.815656	−	0.815656i	−0.985475	+	0.169820i	$0.945682\pi$
$354$	42.7570	+	10.8664i	2.27251	+	0.577542i
$355$	−8.57635	−	3.55244i	−0.455185	−	0.188544i
$356$	22.7918	+	12.3846i	1.20796	+	0.656384i
$357$	2.14792	−	5.18555i	0.113680	−	0.274448i
$358$	−2.49043	−	17.1961i	−0.131623	−	0.908842i
$359$	5.27334			0.278316			0.139158	−	0.990270i	$-0.455560\pi$
$359$	5.27334			0.278316			0.139158	+	0.990270i	$0.455560\pi$
$360$	−6.35479	−	13.8025i	−0.334927	−	0.727457i
$361$	12.4277	−	12.4277i	0.654091	−	0.654091i
$362$	5.09048	+	3.80254i	0.267550	+	0.199857i
$363$	−5.63442	+	2.33385i	−0.295730	+	0.122496i
$364$	26.1283	+	15.7017i	1.36950	+	0.822993i
$365$	4.44638	−	10.7345i	0.232734	−	0.561870i
$366$	0.475263	−	1.87006i	0.0248424	−	0.0977498i
$367$	26.5739			1.38715			0.693573	−	0.720386i	$-0.256035\pi$
$367$	26.5739			1.38715			0.693573	+	0.720386i	$0.256035\pi$
$368$	−7.80539	+	36.6030i	−0.406884	+	1.90806i
$369$	−16.0631	+	16.0631i	−0.836214	+	0.836214i
$370$	0.952744	−	3.74885i	0.0495308	−	0.194894i
$371$	−48.2938	+	20.0040i	−2.50729	+	1.03855i
$372$	40.8524	+	4.30735i	2.11810	+	0.223325i
$373$	−23.9353	+	9.91432i	−1.23932	+	0.513344i	−0.903503	−	0.428582i	$-0.859013\pi$
$373$	−23.9353	+	9.91432i	−1.23932	+	0.513344i	−0.335820	+	0.941926i	$0.609013\pi$
$374$	1.79065	−	0.259332i	0.0925925	−	0.0134097i
$375$		−	23.2901i		−	1.20269i
$376$	−0.225131	−	0.208315i	−0.0116103	−	0.0107430i
$377$	4.47387	−	9.60091i	0.230416	−	0.494472i
$378$	−41.8003	+	55.9582i	−2.14998	+	2.87818i
$379$	−13.9012	−	5.75808i	−0.714059	−	0.295773i	−0.00407573	−	0.999992i	$-0.501297\pi$
$379$	−13.9012	−	5.75808i	−0.714059	−	0.295773i	−0.709983	+	0.704219i	$0.751297\pi$
$380$	0.908025	−	1.67106i	0.0465807	−	0.0857237i
$381$	15.0208	−	36.2634i	0.769538	−	1.85783i
$382$	−5.36624	−	9.02322i	−0.274561	−	0.461668i
$383$	12.7806	−	12.7806i	0.653060	−	0.653060i	−0.300669	−	0.953729i	$-0.597210\pi$
$383$	12.7806	−	12.7806i	0.653060	−	0.653060i	0.953729	+	0.300669i	$0.0972099\pi$
$384$	−7.75413	−	34.4526i	−0.395701	−	1.75815i
$385$	−7.16279	+	7.16279i	−0.365050	+	0.365050i
$386$	7.79587	−	30.6752i	0.396800	−	1.56133i
$387$	5.19277	+	2.15092i	0.263963	+	0.109337i
$388$	−18.4914	+	5.47079i	−0.938759	+	0.277737i
$389$	30.6575	−	12.6987i	1.55440	−	0.643852i	0.570291	−	0.821443i	$-0.306830\pi$
$389$	30.6575	−	12.6987i	1.55440	−	0.643852i	0.984104	+	0.177591i	$0.0568305\pi$
$390$	3.65326	−	12.1429i	0.184990	−	0.614880i
$391$	2.81430	+	2.81430i	0.142325	+	0.142325i
$392$	1.19186	+	30.7215i	0.0601982	+	1.55167i
$393$	−34.4973	−	34.4973i	−1.74016	−	1.74016i
$394$	−1.33975	−	9.25079i	−0.0674954	−	0.466048i
$395$	1.84704	−	4.45915i	0.0929347	−	0.224364i
$396$	−40.3383	−	4.25314i	−2.02708	−	0.213729i
$397$	−9.05798	−	21.8679i	−0.454607	−	1.09752i	−0.970551	−	0.240896i	$-0.922559\pi$
$397$	−9.05798	−	21.8679i	−0.454607	−	1.09752i	0.515944	−	0.856622i	$-0.327441\pi$
$398$	−1.16215	+	4.57283i	−0.0582534	+	0.229215i
$399$	−15.7487			−0.788422
$400$	3.64158	−	17.0770i	0.182079	−	0.853850i
$401$	11.5373	+	11.5373i	0.576147	+	0.576147i	0.933840	−	0.357692i	$-0.116436\pi$
$401$	11.5373	+	11.5373i	0.576147	+	0.576147i	−0.357692	+	0.933840i	$0.616436\pi$
$402$	−6.57567	−	11.0568i	−0.327964	−	0.551465i
$403$	16.0332	+	17.4879i	0.798673	+	0.871133i
$404$	0.448181	−	4.25070i	0.0222978	−	0.211480i
$405$	11.9534	+	4.95127i	0.593970	+	0.246030i
$406$	17.3812	−	2.51723i	0.862614	−	0.124928i
$407$	−7.30108	−	7.30108i	−0.361901	−	0.361901i
$408$	−3.52270	−	1.30157i	−0.174400	−	0.0644373i
$409$	−3.00977			−0.148824			−0.0744118	−	0.997228i	$-0.523708\pi$
$409$	−3.00977			−0.148824			−0.0744118	+	0.997228i	$0.523708\pi$
$410$	3.75666	−	0.544059i	0.185528	−	0.0268692i
$411$	9.44464	−	22.8014i	0.465870	−	1.12471i
$412$	4.98223	+	16.8401i	0.245457	+	0.829650i
$413$	−16.1673	+	39.0312i	−0.795538	+	1.92060i
$414$	−45.6073	−	76.6876i	−2.24147	−	3.76899i
$415$	−9.26140			−0.454624
$416$	9.82024	−	17.8763i	0.481477	−	0.876459i
$417$	16.8258			0.823964
$418$	−2.59498	−	4.36341i	−0.126925	−	0.213421i
$419$	−8.33416	+	20.1204i	−0.407151	+	0.982948i	0.578733	+	0.815517i	$0.303547\pi$
$419$	−8.33416	+	20.1204i	−0.407151	+	0.982948i	−0.985884	+	0.167431i	$0.946453\pi$
$420$	20.1614	−	5.96488i	0.983778	−	0.291056i
$421$	−12.6916	+	30.6402i	−0.618549	+	1.49331i	0.234839	+	0.972034i	$0.424544\pi$
$421$	−12.6916	+	30.6402i	−0.618549	+	1.49331i	−0.853389	+	0.521275i	$0.825456\pi$
$422$	−18.8490	+	2.72980i	−0.917554	+	0.132885i
$423$	0.731237			0.0355540
$424$	14.6270	+	31.7697i	0.710352	+	1.54288i
$425$	−1.31300	−	1.31300i	−0.0636898	−	0.0636898i
$426$	50.9023	−	7.37193i	2.46622	−	0.357171i
$427$	1.70711	+	0.707107i	0.0826127	+	0.0342193i
$428$	8.69036	+	0.916285i	0.420064	+	0.0442903i
$429$	−22.8750	−	24.9503i	−1.10441	−	1.20461i
$430$	−0.480062	−	0.807214i	−0.0231507	−	0.0389273i
$431$	−6.41594	−	6.41594i	−0.309045	−	0.309045i	0.535494	−	0.844539i	$-0.320125\pi$
$431$	−6.41594	−	6.41594i	−0.309045	−	0.309045i	−0.844539	+	0.535494i	$0.820125\pi$
$432$	38.4972	+	26.4957i	1.85220	+	1.27477i
$433$	10.3156			0.495735			0.247867	−	0.968794i	$-0.420270\pi$
$433$	10.3156			0.495735			0.247867	+	0.968794i	$0.420270\pi$
$434$	−9.68953	+	38.1263i	−0.465112	+	1.83012i
$435$	−2.79578	−	6.74961i	−0.134047	−	0.323619i
$436$	1.32496	−	12.5664i	0.0634541	−	0.601821i
$437$	4.27356	−	10.3173i	0.204432	−	0.493543i
$438$	9.22701	+	63.7114i	0.440884	+	3.04425i
$439$	−20.0915	−	20.0915i	−0.958915	−	0.958915i	0.0402733	−	0.999189i	$-0.487177\pi$
$439$	−20.0915	−	20.0915i	−0.958915	−	0.958915i	−0.999189	+	0.0402733i	$0.987177\pi$
$440$	4.97474	+	4.60316i	0.237162	+	0.219447i
$441$	−51.8280	−	51.8280i	−2.46800	−	2.46800i
$442$	−1.02682	−	1.91054i	−0.0488409	−	0.0908752i
$443$	11.1029	−	4.59895i	0.527513	−	0.218503i	−0.103001	−	0.994681i	$-0.532844\pi$
$443$	11.1029	−	4.59895i	0.527513	−	0.218503i	0.630513	+	0.776178i	$0.282844\pi$
$444$	6.08003	+	20.5507i	0.288546	+	0.975292i
$445$	9.54656	+	3.95431i	0.452550	+	0.187452i
$446$	7.02859	−	27.6561i	0.332813	−	1.30955i
$447$	32.8274	−	32.8274i	1.55268	−	1.55268i
$448$	33.7165	−	2.62006i	1.59296	−	0.123786i
$449$	−1.62543	+	1.62543i	−0.0767090	+	0.0767090i	−0.744420	−	0.667711i	$-0.767274\pi$
$449$	−1.62543	+	1.62543i	−0.0767090	+	0.0767090i	0.667711	+	0.744420i	$0.267274\pi$
$450$	21.2779	+	35.7783i	1.00305	+	1.68661i
$451$	3.87759	−	9.36133i	0.182589	−	0.440808i
$452$	−21.5935	−	11.7335i	−1.01567	−	0.551899i
$453$	11.8102	+	4.89196i	0.554894	+	0.229845i
$454$	15.3632	−	20.5668i	0.721031	−	0.965246i
$455$	11.0069	+	5.12905i	0.516013	+	0.240454i
$456$	0.408496	+	10.5294i	0.0191296	+	0.493083i
$457$		−	7.31066i		−	0.341978i	−0.985273	−	0.170989i	$-0.945304\pi$
$457$		−	7.31066i		−	0.341978i	0.985273	−	0.170989i	$-0.0546963\pi$
$458$	−10.9933	+	1.59211i	−0.513683	+	0.0743943i
$459$	4.59154	−	1.90188i	0.214315	−	0.0887721i
$460$	−1.56329	+	14.8268i	−0.0728888	+	0.691303i
$461$	0.765222	−	0.316965i	0.0356399	−	0.0147625i	−0.364792	−	0.931089i	$-0.618860\pi$
$461$	0.765222	−	0.316965i	0.0356399	−	0.0147625i	0.400432	+	0.916326i	$0.368860\pi$
$462$	13.8243	−	54.3956i	0.643163	−	2.53071i
$463$	−2.26830	+	2.26830i	−0.105417	+	0.105417i	−0.757848	−	0.652431i	$-0.773749\pi$
$463$	−2.26830	+	2.26830i	−0.105417	+	0.105417i	0.652431	+	0.757848i	$0.273749\pi$
$464$	−2.13383	−	11.5555i	−0.0990605	−	0.536453i
$465$	16.3641			0.758867
$466$	3.94944	−	15.5402i	0.182954	−	0.719888i
$467$	6.05632	−	14.6213i	0.280253	−	0.676591i	−0.719588	−	0.694401i	$-0.755669\pi$
$467$	6.05632	−	14.6213i	0.280253	−	0.676591i	0.999841	+	0.0178101i	$0.00566942\pi$
$468$	11.7604	+	47.1811i	0.543626	+	2.18095i
$469$	11.3816	−	4.71442i	0.525554	−	0.217691i
$470$	−0.0978901	−	0.0731231i	−0.00451533	−	0.00337292i
$471$	−9.90846	+	9.90846i	−0.456558	+	0.456558i
$472$	26.5151	+	9.79681i	1.22046	+	0.450935i
$473$	−2.50704			−0.115274
$474$	3.83293	+	26.4659i	0.176052	+	1.21562i
$475$	−1.99382	+	4.81350i	−0.0914825	+	0.220858i
$476$	1.71707	−	3.15997i	0.0787018	−	0.144837i
$477$	−77.0348	−	31.9089i	−3.52718	−	1.46101i
$478$	3.47984	+	0.884375i	0.159164	+	0.0404504i
$479$	3.74060	+	3.74060i	0.170913	+	0.170913i	0.787380	−	0.616468i	$-0.211437\pi$
$479$	3.74060	+	3.74060i	0.170913	+	0.170913i	−0.616468	+	0.787380i	$0.711437\pi$
$480$	−4.51099	−	13.3250i	−0.205898	−	0.608198i
$481$	−5.22807	+	11.2194i	−0.238380	+	0.511562i
$482$	−11.9461	−	3.03602i	−0.544131	−	0.138287i
$483$	114.061	−	47.2455i	5.18995	−	2.14975i
$484$	−3.74711	+	1.10860i	−0.170323	+	0.0503910i
$485$	−7.09710	+	2.93971i	−0.322263	+	0.133486i
$486$	−21.8889	+	3.17006i	−0.992899	+	0.143797i
$487$		−	31.9176i		−	1.44632i	−0.690678	−	0.723162i	$-0.742688\pi$
$487$		−	31.9176i		−	1.44632i	0.690678	−	0.723162i	$-0.257312\pi$
$488$	0.428483	−	1.15969i	0.0193965	−	0.0524967i
$489$	−24.4415			−1.10528
$490$	1.75541	+	12.1209i	0.0793015	+	0.547568i
$491$	19.1451	−	7.93016i	0.864007	−	0.357883i	0.0937334	−	0.995597i	$-0.470120\pi$
$491$	19.1451	−	7.93016i	0.864007	−	0.357883i	0.770273	+	0.637714i	$0.220120\pi$
$492$	−16.3488	+	13.2301i	−0.737060	+	0.596458i
$493$	−1.15451	−	0.478214i	−0.0519966	−	0.0215377i
$494$	−3.85009	+	4.71326i	−0.173224	+	0.212059i
$495$	−16.1582			−0.726257
$496$	25.7421	+	5.48936i	1.15585	+	0.246480i
$497$			49.2542i			2.20935i
$498$	44.1037	−	26.2291i	1.97633	−	1.17536i
$499$	2.41007	+	5.81843i	0.107890	+	0.260469i	0.968599	−	0.248628i	$-0.0799796\pi$
$499$	2.41007	+	5.81843i	0.107890	+	0.260469i	−0.860709	+	0.509097i	$0.829980\pi$
$500$	1.56475	−	14.8406i	0.0699778	−	0.663694i
$501$	22.1636	−	53.5077i	0.990198	−	2.39055i
$502$	−10.0475	−	7.50539i	−0.448442	−	0.334982i
$503$	−9.95172	+	9.95172i	−0.443725	+	0.443725i	−0.893262	−	0.449537i	$-0.851589\pi$
$503$	−9.95172	+	9.95172i	−0.443725	+	0.443725i	0.449537	+	0.893262i	$0.351589\pi$
$504$	−54.7564	+	59.1766i	−2.43905	+	2.63593i
$505$		−	1.70269i		−	0.0757687i
$506$	31.8843	+	23.8173i	1.41743	+	1.05881i
$507$	−18.7177	+	36.0031i	−0.831281	+	1.59895i
$508$	12.0078	−	22.0982i	0.532758	−	0.980448i
$509$	−5.25643	−	12.6901i	−0.232987	−	0.562480i	0.763539	−	0.645762i	$-0.223460\pi$
$509$	−5.25643	−	12.6901i	−0.232987	−	0.562480i	−0.996526	+	0.0832812i	$0.973460\pi$
$510$	−1.44993	−	0.368490i	−0.0642040	−	0.0163170i
$511$	−61.6486			−2.72717
$512$	−2.62629	−	22.4745i	−0.116067	−	0.993241i
$513$	−9.86039	−	9.86039i	−0.435347	−	0.435347i
$514$	8.78356	+	14.7694i	0.387426	+	0.651449i
$515$	2.67719	+	6.46330i	0.117971	+	0.284807i
$516$	4.57221	+	2.48446i	0.201280	+	0.109372i
$517$	−0.301335	+	0.124817i	−0.0132527	+	0.00548945i
$518$	−20.3113	+	2.94159i	−0.892427	+	0.129246i
$519$	−1.69391	+	1.69391i	−0.0743542	+	0.0743542i
$520$	3.14372	−	7.49213i	0.137861	−	0.328552i
$521$	−1.88714	−	1.88714i	−0.0826770	−	0.0826770i	0.664559	−	0.747236i	$-0.268619\pi$
$521$	−1.88714	−	1.88714i	−0.0826770	−	0.0826770i	−0.747236	+	0.664559i	$0.768619\pi$
$522$	22.4439	+	16.7654i	0.982344	+	0.733803i
$523$	10.5901	+	25.5668i	0.463073	+	1.11796i	0.967129	+	0.254286i	$0.0818405\pi$
$523$	10.5901	+	25.5668i	0.463073	+	1.11796i	−0.504056	+	0.863671i	$0.668160\pi$
$524$	−19.6643	−	24.2997i	−0.859038	−	1.06154i
$525$	−53.2146	+	22.0422i	−2.32248	+	0.962002i
$526$	−28.3370	−	7.20164i	−1.23555	−	0.314006i
$527$	1.97923	−	1.97923i	0.0862168	−	0.0862168i
$528$	−36.7268	−	7.83179i	−1.59833	−	0.340835i
$529$			64.5441i			2.80626i
$530$	7.12172	+	11.9750i	0.309348	+	0.520162i
$531$	−62.2597	+	25.7888i	−2.70184	+	1.11914i
$532$	−10.0352	−	1.05808i	−0.435082	−	0.0458737i
$533$	−12.1354	−	0.526607i	−0.525641	−	0.0228099i
$534$	−56.6607	+	8.20589i	−2.45195	+	0.355104i
$535$	3.48107			0.150500
$536$	−3.44722	−	7.48731i	−0.148897	−	0.323403i
$537$	27.1178	+	27.1178i	1.17022	+	1.17022i
$538$	−1.64984	−	11.3920i	−0.0711298	−	0.491142i
$539$	30.2045	+	12.5111i	1.30100	+	0.538891i
$540$	16.3579	+	8.88858i	0.703932	+	0.382504i
$541$	−24.7678	+	10.2592i	−1.06485	+	0.441075i	−0.845171	−	0.534497i	$-0.820501\pi$
$541$	−24.7678	+	10.2592i	−1.06485	+	0.441075i	−0.219680	+	0.975572i	$0.570501\pi$
$542$	6.36347	−	25.0390i	0.273335	−	1.07552i
$543$	−14.0241			−0.601830
$544$	−2.15725	−	1.06605i	−0.0924914	−	0.0457063i
$545$		−	5.03368i		−	0.215619i
$546$	−66.9421	+	6.74758i	−2.86486	+	0.288770i
$547$	−11.7903	+	28.4642i	−0.504115	+	1.21704i	0.443108	+	0.896468i	$0.353876\pi$
$547$	−11.7903	+	28.4642i	−0.504115	+	1.21704i	−0.947224	+	0.320574i	$0.896124\pi$
$548$	7.55013	−	13.8947i	0.322526	−	0.593553i
$549$	1.12793	+	2.72305i	0.0481387	+	0.116217i
$550$	−14.8755	−	11.1119i	−0.634294	−	0.473813i
$551$			3.50630i			0.149373i
$552$	−34.5463	−	75.0341i	−1.47039	−	3.19366i
$553$	−25.6090			−1.08901
$554$	−23.3540	−	17.4452i	−0.992215	−	0.741176i
$555$	3.26709	+	7.88745i	0.138680	+	0.334804i
$556$	10.7216	+	1.13045i	0.454696	+	0.0479417i
$557$	5.14788	+	12.4281i	0.218123	+	0.526595i	0.994628	−	0.103516i	$-0.0330094\pi$
$557$	5.14788	+	12.4281i	0.218123	+	0.526595i	−0.776505	+	0.630111i	$0.783009\pi$
$558$	−53.9327	+	32.0746i	−2.28315	+	1.35783i
$559$	1.02865	+	2.82386i	0.0435074	+	0.119437i
$560$	13.2478	−	2.44632i	0.559822	−	0.103376i
$561$	−2.82381	+	2.82381i	−0.119222	+	0.119222i
$562$	5.46050	+	9.18171i	0.230337	+	0.387307i
$563$	−14.9590	+	36.1142i	−0.630446	+	1.52203i	0.208616	+	0.977998i	$0.433104\pi$
$563$	−14.9590	+	36.1142i	−0.630446	+	1.52203i	−0.839063	+	0.544035i	$0.816896\pi$
$564$	0.673254	+	0.0709858i	0.0283491	+	0.00298904i
$565$	−9.04466	−	3.74642i	−0.380512	−	0.157613i
$566$	24.7813	+	18.5114i	1.04164	+	0.778093i
$567$		−	68.6487i		−	2.88297i
$568$	32.9307	−	1.27757i	1.38174	−	0.0536058i
$569$	−15.3191	−	15.3191i	−0.642210	−	0.642210i	0.308888	−	0.951098i	$-0.400043\pi$
$569$	−15.3191	−	15.3191i	−0.642210	−	0.642210i	−0.951098	+	0.308888i	$0.900043\pi$
$570$	0.601645	+	4.15429i	0.0252002	+	0.174004i
$571$	10.6527	+	25.7178i	0.445801	+	1.07626i	0.973880	+	0.227063i	$0.0729123\pi$
$571$	10.6527	+	25.7178i	0.445801	+	1.07626i	−0.528080	+	0.849195i	$0.677088\pi$
$572$	−12.8998	−	17.4354i	−0.539370	−	0.729013i
$573$	21.4076	+	8.86732i	0.894315	+	0.370437i
$574$	−10.2947	−	17.3104i	−0.429694	−	0.722521i
$575$		−	40.8434i		−	1.70329i
$576$	40.9850	+	35.0745i	1.70771	+	1.46144i
$577$	2.15039	+	2.15039i	0.0895219	+	0.0895219i	0.750450	−	0.660928i	$-0.229837\pi$
$577$	2.15039	+	2.15039i	0.0895219	+	0.0895219i	−0.660928	+	0.750450i	$0.729837\pi$
$578$	20.4436	−	12.1581i	0.850342	−	0.505711i
$579$	26.7331	+	64.5395i	1.11099	+	2.68217i
$580$	−1.32802	−	4.48875i	−0.0551431	−	0.186385i
$581$	18.8049	+	45.3991i	0.780160	+	1.88347i
$582$	25.4716	−	34.0989i	1.05583	−	1.41344i
$583$	37.1919			1.54033
$584$	1.59906	+	41.2174i	0.0661697	+	1.70559i
$585$	6.62981	+	18.2002i	0.274109	+	0.752485i
$586$	1.14778	−	0.166227i	0.0474142	−	0.00686677i
$587$	9.37425	−	22.6314i	0.386917	−	0.934100i	−0.603673	−	0.797232i	$-0.706297\pi$
$587$	9.37425	−	22.6314i	0.386917	−	0.934100i	0.990589	−	0.136867i	$-0.0437035\pi$
$588$	−42.6870	−	52.7496i	−1.76038	−	2.17536i
$589$	−7.25593	−	3.00550i	−0.298975	−	0.123840i
$590$	10.9135	+	2.77359i	0.449303	+	0.114187i
$591$	14.5883	+	14.5883i	0.600081	+	0.600081i
$592$	2.49355	+	13.5036i	0.102484	+	0.554993i
$593$	−2.49919	−	2.49919i	−0.102629	−	0.102629i	0.653928	−	0.756557i	$-0.273120\pi$
$593$	−2.49919	−	2.49919i	−0.102629	−	0.102629i	−0.756557	+	0.653928i	$0.773120\pi$
$594$	42.7130	−	25.4021i	1.75254	−	1.04226i
$595$	0.548247	−	1.32359i	0.0224759	−	0.0542617i
$596$	23.1235	−	18.7124i	0.947174	−	0.766490i
$597$	−3.98518	−	9.62108i	−0.163103	−	0.393765i
$598$	13.7449	−	45.6861i	0.562071	−	1.86825i
$599$	−7.91143	+	7.91143i	−0.323252	+	0.323252i	−0.850013	−	0.526761i	$-0.823406\pi$
$599$	−7.91143	+	7.91143i	−0.323252	+	0.323252i	0.526761	+	0.850013i	$0.323406\pi$
$600$	16.1175	+	35.0069i	0.657992	+	1.42915i
$601$	28.7278	−	28.7278i	1.17183	−	1.17183i	0.190058	−	0.981773i	$-0.439132\pi$
$601$	28.7278	−	28.7278i	1.17183	−	1.17183i	0.981773	−	0.190058i	$-0.0608676\pi$
$602$	−2.98220	+	3.99227i	−0.121545	+	0.162713i
$603$	18.1551	+	7.52009i	0.739333	+	0.306242i
$604$	7.19693	+	3.91068i	0.292839	+	0.159123i
$605$	−1.43816	+	0.595705i	−0.0584695	+	0.0242188i
$606$	4.82218	+	8.10839i	0.195888	+	0.329381i
$607$		−	20.3138i		−	0.824512i	−0.911068	−	0.412256i	$-0.864741\pi$
$607$		−	20.3138i		−	0.824512i	0.911068	−	0.412256i	$-0.135259\pi$
$608$	−0.447123	+	6.73686i	−0.0181332	+	0.273216i
$609$	−27.4097	+	27.4097i	−1.11070	+	1.11070i
$610$	0.121309	−	0.477324i	0.00491164	−	0.0193263i
$611$	0.264231	+	0.288203i	0.0106896	+	0.0116595i
$612$	5.50093	−	1.62748i	0.222362	−	0.0657871i
$613$	−0.593465	+	1.43275i	−0.0239698	+	0.0578683i	−0.935411	−	0.353562i	$-0.884970\pi$
$613$	−0.593465	+	1.43275i	−0.0239698	+	0.0578683i	0.911441	+	0.411430i	$0.134970\pi$
$614$	18.1261	−	24.2654i	0.731508	−	0.979272i
$615$	−5.92416	+	5.92416i	−0.238885	+	0.238885i
$616$	12.4635	−	33.7326i	0.502170	−	1.35913i
$617$			43.9882i			1.77090i	0.464736	+	0.885449i	$0.346149\pi$
$617$			43.9882i			1.77090i	−0.464736	+	0.885449i	$0.653851\pi$
$618$	−31.0537	−	23.1969i	−1.24916	−	0.933115i
$619$	32.8776	+	13.6183i	1.32146	+	0.547367i	0.928208	−	0.372063i	$-0.121349\pi$
$619$	32.8776	+	13.6183i	1.32146	+	0.547367i	0.393254	+	0.919430i	$0.371349\pi$
$620$	10.4274	+	1.09943i	0.418773	+	0.0441541i
$621$	100.995	+	41.8336i	4.05280	+	1.67872i
$622$	−13.6593	−	3.47141i	−0.547688	−	0.139191i
$623$		−	54.8261i		−	2.19656i
$624$	6.24771	+	44.5816i	0.250109	+	1.78469i
$625$			15.8815i			0.635261i
$626$	−11.6692	+	45.9159i	−0.466395	+	1.83517i
$627$	10.3522	+	4.28802i	0.413427	+	0.171247i
$628$	−6.97947	+	5.64806i	−0.278511	+	0.225382i
$629$	1.34914	+	0.558831i	0.0537936	+	0.0222821i
$630$	−19.2207	+	25.7308i	−0.765770	+	1.02514i
$631$			13.8984i			0.553286i	0.960973	+	0.276643i	$0.0892219\pi$
$631$			13.8984i			0.553286i	−0.960973	+	0.276643i	$0.910778\pi$
$632$	0.664256	+	17.1218i	0.0264227	+	0.681070i
$633$	29.7243	−	29.7243i	1.18144	−	1.18144i
$634$	−23.0921	−	17.2496i	−0.917106	−	0.685070i
$635$	3.83398	−	9.25605i	0.152147	−	0.367315i
$636$	−67.8288	−	36.8569i	−2.68959	−	1.46147i
$637$	1.69911	−	39.1549i	0.0673211	−	1.55138i
$638$	−12.1107	−	3.07784i	−0.479466	−	0.121853i
$639$	−55.5550	+	55.5550i	−2.19772	+	2.19772i
$640$	−1.97920	−	8.79386i	−0.0782349	−	0.347608i
$641$		−	16.5672i		−	0.654364i	−0.944961	−	0.327182i	$-0.893901\pi$
$641$		−	16.5672i		−	0.654364i	0.944961	−	0.327182i	$-0.106099\pi$
$642$	−16.5772	+	9.85872i	−0.654251	+	0.389093i
$643$	13.3686	−	5.53746i	0.527206	−	0.218376i	−0.103173	−	0.994663i	$-0.532899\pi$
$643$	13.3686	−	5.53746i	0.527206	−	0.218376i	0.630379	+	0.776287i	$0.282899\pi$
$644$	75.8548	−	22.4421i	2.98910	−	0.884341i
$645$	1.91512	+	0.793267i	0.0754077	+	0.0312349i
$646$	0.575229	+	0.429691i	0.0226321	+	0.0169060i
$647$	29.9092	−	29.9092i	1.17585	−	1.17585i	0.195059	−	0.980791i	$-0.437510\pi$
$647$	29.9092	−	29.9092i	1.17585	−	1.17585i	0.980791	−	0.195059i	$-0.0624899\pi$
$648$	−45.8976	+	1.78064i	−1.80303	+	0.0699500i
$649$	21.2546	−	21.2546i	0.834317	−	0.834317i
$650$	−6.41264	+	21.3147i	−0.251524	+	0.836031i
$651$	−33.2267	−	80.2165i	−1.30226	−	3.14393i
$652$	−15.5743	−	1.64211i	−0.609938	−	0.0643100i
$653$	−2.39101	+	5.77241i	−0.0935674	+	0.225892i	−0.963733	−	0.266867i	$-0.914012\pi$
$653$	−2.39101	+	5.77241i	−0.0935674	+	0.225892i	0.870166	+	0.492759i	$0.164012\pi$
$654$	14.2559	+	23.9709i	0.557448	+	0.937337i
$655$	−8.80526	−	8.80526i	−0.344050	−	0.344050i
$656$	−11.3065	+	7.33193i	−0.441443	+	0.286264i
$657$	−69.5350	−	69.5350i	−2.71282	−	2.71282i
$658$	−0.159685	+	0.628329i	−0.00622518	+	0.0244948i
$659$	22.4033	+	9.27975i	0.872708	+	0.361488i	0.773664	−	0.633596i	$-0.218422\pi$
$659$	22.4033	+	9.27975i	0.872708	+	0.361488i	0.0990437	+	0.995083i	$0.468422\pi$
$660$	−14.8769	−	1.56858i	−0.579084	−	0.0610568i
$661$	18.8421	−	45.4888i	0.732871	−	1.76931i	0.100088	−	0.994979i	$-0.468088\pi$
$661$	18.8421	−	45.4888i	0.732871	−	1.76931i	0.632783	−	0.774329i	$-0.281912\pi$
$662$	−0.713485	−	4.92653i	−0.0277304	−	0.191475i
$663$	4.33930	+	2.02205i	0.168525	+	0.0785297i
$664$	29.8655	−	13.7503i	1.15901	−	0.533616i
$665$	−4.01978			−0.155880
$666$	−26.2275	−	19.5917i	−1.01630	−	0.759164i
$667$	−10.5188	−	25.3945i	−0.407288	−	0.983280i
$668$	17.7178	−	32.6066i	0.685523	−	1.26159i
$669$	24.1020	+	58.1874i	0.931837	+	2.24965i
$670$	−1.67841	−	2.82220i	−0.0648425	−	0.109031i
$671$	−0.929613	−	0.929613i	−0.0358873	−	0.0358873i
$672$	−56.1592	+	49.1686i	−2.16639	+	1.89672i
$673$			31.5264i			1.21525i	0.794223	+	0.607627i	$0.207878\pi$
$673$			31.5264i			1.21525i	−0.794223	+	0.607627i	$0.792122\pi$
$674$	−34.0531	+	20.2519i	−1.31168	+	0.780074i
$675$	−47.1189	−	19.5173i	−1.81361	−	0.751221i
$676$	−14.3460	+	21.6839i	−0.551768	+	0.833998i
$677$	−5.10611	−	12.3272i	−0.196244	−	0.473775i	0.794872	−	0.606777i	$-0.207538\pi$
$677$	−5.10611	−	12.3272i	−0.196244	−	0.473775i	−0.991116	+	0.133003i	$0.957538\pi$
$678$	53.6818	−	7.77448i	2.06164	−	0.298577i
$679$	28.8208	+	28.8208i	1.10604	+	1.10604i
$680$	−0.899153	−	0.332219i	−0.0344809	−	0.0127400i
$681$			56.6607i			2.17124i
$682$	16.7502	−	22.4236i	0.641399	−	0.858643i
$683$	17.9750	+	7.44549i	0.687795	+	0.284894i	0.699081	−	0.715042i	$-0.253593\pi$
$683$	17.9750	+	7.44549i	0.687795	+	0.284894i	−0.0112864	+	0.999936i	$0.503593\pi$
$684$	−10.1255	−	12.5124i	−0.387160	−	0.478424i
$685$	2.41070	−	5.81994i	0.0921080	−	0.222368i
$686$	19.8843	−	11.8255i	0.759186	−	0.451499i
$687$	17.3362	−	17.3362i	0.661416	−	0.661416i
$688$	2.74654	+	1.89030i	0.104711	+	0.0720672i
$689$	−15.2601	−	41.8920i	−0.581362	−	1.59596i
$690$	−16.8202	−	28.2827i	−0.640332	−	1.07671i
$691$	−9.42566	−	22.7555i	−0.358569	−	0.865662i	−0.995502	−	0.0947426i	$-0.969797\pi$
$691$	−9.42566	−	22.7555i	−0.358569	−	0.865662i	0.636933	−	0.770919i	$-0.280203\pi$
$692$	−1.19318	+	0.965567i	−0.0453578	+	0.0367053i
$693$	32.8086	+	79.2071i	1.24630	+	3.00883i
$694$	4.13883	−	5.54066i	0.157108	−	0.210321i
$695$	4.29471			0.162907
$696$	19.0367	+	17.6148i	0.721585	+	0.667687i
$697$			1.43305i			0.0542806i
$698$	10.3214	−	13.8173i	0.390672	−	0.522993i
$699$	13.5432	+	32.6961i	0.512250	+	1.23668i
$700$	−35.3898	+	10.4703i	−1.33761	+	0.395739i
$701$	−13.0054	+	31.3978i	−0.491206	+	1.18588i	0.462901	+	0.886410i	$0.346809\pi$
$701$	−13.0054	+	31.3978i	−0.491206	+	1.18588i	−0.954107	+	0.299467i	$0.903191\pi$
$702$	−46.1377	−	37.6883i	−1.74135	−	1.42245i
$703$		−	4.09738i		−	0.154536i
$704$	−22.8765	−	7.45799i	−0.862190	−	0.281084i
$705$	0.269683			0.0101569
$706$	29.7053	+	7.54938i	1.11797	+	0.284125i
$707$	−8.34655	+	3.45725i	−0.313904	+	0.130023i
$708$	−59.8264	+	17.7000i	−2.24841	+	0.665205i
$709$	−39.2747	−	16.2681i	−1.47499	−	0.610961i	−0.507000	−	0.861946i	$-0.669246\pi$
$709$	−39.2747	−	16.2681i	−1.47499	−	0.610961i	−0.967991	+	0.250985i	$0.919246\pi$
$710$	12.9926	−	1.88165i	0.487602	−	0.0706170i
$711$	−28.8850	−	28.8850i	−1.08327	−	1.08327i
$712$	−36.6560	+	1.42210i	−1.37374	+	0.0532954i
$713$	61.5678			2.30573
$714$	1.13771	+	7.85573i	0.0425776	+	0.293993i
$715$	−5.83873	−	6.36845i	−0.218356	−	0.238166i
$716$	15.4578	+	19.1016i	0.577685	+	0.713861i
$717$	−7.32145	+	3.03265i	−0.273425	+	0.113256i
$718$	−6.40976	+	3.81198i	−0.239210	+	0.142262i
$719$		−	29.3422i		−	1.09428i	−0.837042	−	0.547139i	$-0.815717\pi$
$719$		−	29.3422i		−	1.09428i	0.837042	−	0.547139i	$-0.184283\pi$
$720$	17.7018	+	12.1833i	0.659707	+	0.454044i
$721$	26.2470	−	26.2470i	0.977490	−	0.977490i
$722$	−6.12222	+	24.0897i	−0.227845	+	0.896525i
$723$	25.1342	−	10.4109i	0.934752	−	0.387187i
$724$	−8.93626	−	0.942212i	−0.332114	−	0.0350170i
$725$	4.90749	+	11.8477i	0.182260	+	0.440013i
$726$	5.16157	−	6.90980i	0.191564	−	0.256447i
$727$	−6.50387	−	6.50387i	−0.241215	−	0.241215i	0.576138	−	0.817353i	$-0.304559\pi$
$727$	−6.50387	−	6.50387i	−0.241215	−	0.241215i	−0.817353	+	0.576138i	$0.804559\pi$
$728$	−43.1095	−	0.197912i	−1.59774	−	0.00733509i
$729$	0.0690450	−	0.0690450i	0.00255722	−	0.00255722i
$730$	2.35515	+	16.2620i	0.0871680	+	0.601885i
$731$	0.327578	−	0.135687i	0.0121159	−	0.00501858i
$732$	0.774143	+	2.61662i	0.0286132	+	0.0967132i
$733$	4.88756	+	11.7996i	0.180526	+	0.435829i	0.988075	−	0.153972i	$-0.0492064\pi$
$733$	4.88756	+	11.7996i	0.180526	+	0.435829i	−0.807549	+	0.589800i	$0.799206\pi$
$734$	−32.3007	+	19.2097i	−1.19224	+	0.709042i
$735$	−19.1144	−	19.1144i	−0.705045	−	0.705045i
$736$	−16.9720	−	50.1334i	−0.625597	−	1.84794i
$737$	−8.76517			−0.322869
$738$	7.91311	−	31.1365i	0.291286	−	1.14615i
$739$	−16.1253	−	38.9300i	−0.593179	−	1.43206i	−0.880416	−	0.474202i	$-0.842737\pi$
$739$	−16.1253	−	38.9300i	−0.593179	−	1.43206i	0.287237	−	0.957860i	$-0.407263\pi$
$740$	1.55190	+	5.24546i	0.0570489	+	0.192827i
$741$	0.582347	−	13.4198i	0.0213930	−	0.492990i
$742$	44.2409	−	59.2254i	1.62413	−	2.17423i
$743$		−	6.99984i		−	0.256799i	−0.991723	−	0.128400i	$-0.959016\pi$
$743$		−	6.99984i		−	0.256799i	0.991723	−	0.128400i	$-0.0409840\pi$
$744$	−52.7698	+	24.2957i	−1.93464	+	0.890722i
$745$	8.37904	−	8.37904i	0.306984	−	0.306984i
$746$	21.9266	−	29.3532i	0.802789	−	1.07470i
$747$	−29.9963	+	72.4174i	−1.09751	+	2.64961i
$748$	−1.98908	+	1.60964i	−0.0727279	+	0.0588543i
$749$	−7.06820	−	17.0641i	−0.258266	−	0.623510i
$750$	16.8359	+	28.3092i	0.614759	+	1.03370i
$751$			25.2844i			0.922643i	0.887233	+	0.461321i	$0.152624\pi$
$751$			25.2844i			0.922643i	−0.887233	+	0.461321i	$0.847376\pi$
$752$	0.424234	+	0.0904656i	0.0154702	+	0.00329894i
$753$	27.6805			1.00873
$754$	1.50228	+	14.9040i	0.0547099	+	0.542772i
$755$	3.01451	+	1.24865i	0.109709	+	0.0454430i
$756$	10.3575	−	98.2339i	0.376698	−	3.57273i
$757$	−27.2914	+	11.3045i	−0.991924	+	0.410868i	−0.818830	−	0.574037i	$-0.805377\pi$
$757$	−27.2914	+	11.3045i	−0.991924	+	0.410868i	−0.173095	+	0.984905i	$0.555377\pi$
$758$	21.0594	−	3.04993i	0.764911	−	0.110778i
$759$	−87.8401			−3.18839
$760$	0.104267	+	2.68757i	0.00378214	+	0.0974885i
$761$			33.4873i			1.21391i	0.794735	+	0.606956i	$0.207610\pi$
$761$			33.4873i			1.21391i	−0.794735	+	0.606956i	$0.792390\pi$
$762$	7.95618	+	54.9365i	0.288222	+	1.99014i
$763$	−24.6750	+	10.2207i	−0.893295	+	0.370015i
$764$	13.0454	+	7.08861i	0.471965	+	0.256457i
$765$	2.11129	−	0.874524i	0.0763337	−	0.0316185i
$766$	−6.29607	+	24.7737i	−0.227486	+	0.895111i
$767$	−32.6616	−	15.2198i	−1.17934	−	0.549554i
$768$	34.3302	+	36.2720i	1.23878	+	1.30885i
$769$	−3.17883	−	3.17883i	−0.114631	−	0.114631i	0.647464	−	0.762096i	$-0.275829\pi$
$769$	−3.17883	−	3.17883i	−0.114631	−	0.114631i	−0.762096	+	0.647464i	$0.775829\pi$
$770$	3.52857	−	13.8842i	0.127161	−	0.500353i
$771$	−35.0404	−	14.5142i	−1.26195	−	0.522716i
$772$	12.6985	+	42.9212i	0.457029	+	1.54477i
$773$	−4.87879	+	11.7784i	−0.175478	+	0.423641i	−0.987008	−	0.160669i	$-0.948635\pi$
$773$	−4.87879	+	11.7784i	−0.175478	+	0.423641i	0.811530	+	0.584310i	$0.198635\pi$
$774$	−7.86668	+	1.13929i	−0.282762	+	0.0409510i
$775$	−28.7242			−1.03181
$776$	18.5217	−	20.0168i	0.664889	−	0.718561i
$777$	32.0304	−	32.0304i	1.14908	−	1.14908i
$778$	−28.0846	+	37.5970i	−1.00688	+	1.34792i
$779$	3.71486	−	1.53874i	0.133099	−	0.0551313i
$780$	4.33729	+	17.4006i	0.155300	+	0.623042i
$781$	13.4108	−	32.3765i	0.479876	−	1.15852i
$782$	−5.45518	−	1.38639i	−0.195077	−	0.0495774i
$783$	−34.3228			−1.22660
$784$	−23.6566	−	36.4805i	−0.844878	−	1.30287i
$785$	−2.52909	+	2.52909i	−0.0902670	+	0.0902670i
$786$	66.8689	+	16.9942i	2.38513	+	0.606165i
$787$	−9.84402	+	4.07753i	−0.350902	+	0.145348i	−0.551170	−	0.834393i	$-0.685819\pi$
$787$	−9.84402	+	4.07753i	−0.350902	+	0.145348i	0.200269	+	0.979741i	$0.435819\pi$
$788$	8.31565	+	10.2759i	0.296233	+	0.366063i
$789$	59.6200	−	24.6954i	2.12253	−	0.879180i
$790$	0.978336	+	6.75530i	0.0348076	+	0.240343i
$791$			51.9437i			1.84691i
$792$	52.1058	−	23.9899i	1.85150	−	0.852445i
$793$	−0.665667	+	1.42852i	−0.0236385	+	0.0507282i
$794$	26.8178	+	20.0327i	0.951729	+	0.710934i
$795$	−28.4108	−	11.7681i	−1.00763	−	0.417372i
$796$	−1.89300	−	6.39839i	−0.0670955	−	0.226785i
$797$	7.94993	−	19.1928i	0.281601	−	0.679845i	−0.718272	−	0.695762i	$-0.755067\pi$
$797$	7.94993	−	19.1928i	0.281601	−	0.679845i	0.999873	+	0.0159171i	$0.00506678\pi$
$798$	19.1426	−	11.3844i	0.677641	−	0.403003i
$799$	0.0326181	−	0.0326181i	0.00115395	−	0.00115395i
$800$	7.91824	+	23.3896i	0.279952	+	0.826946i
$801$	61.8397	−	61.8397i	2.18500	−	2.18500i
$802$	−22.3638	−	5.68359i	−0.789692	−	0.200695i
$803$	40.5238	+	16.7855i	1.43005	+	0.592348i
$804$	15.9855	+	8.68622i	0.563765	+	0.306339i
$805$	29.1135	−	12.0592i	1.02611	−	0.425031i
$806$	−32.1301	−	9.66650i	−1.13173	−	0.340488i
$807$	17.9648	+	17.9648i	0.632392	+	0.632392i
$808$	2.52797	+	5.49072i	0.0889337	+	0.193163i
$809$	−30.7868	−	30.7868i	−1.08241	−	1.08241i	−0.996285	−	0.0861205i	$-0.972553\pi$
$809$	−30.7868	−	30.7868i	−1.08241	−	1.08241i	−0.0861205	−	0.996285i	$-0.527447\pi$
$810$	−18.1086	+	2.62258i	−0.636270	+	0.0921479i
$811$	1.71928	−	4.15071i	0.0603721	−	0.145751i	−0.890815	−	0.454367i	$-0.849866\pi$
$811$	1.71928	−	4.15071i	0.0603721	−	0.145751i	0.951187	+	0.308615i	$0.0998656\pi$
$812$	−19.3072	+	15.6242i	−0.677551	+	0.548301i
$813$	21.8212	+	52.6811i	0.765304	+	1.84761i
$814$	14.1523	+	3.59670i	0.496037	+	0.126064i
$815$	−6.23857			−0.218527
$816$	5.22273	−	0.964421i	0.182832	−	0.0337615i
$817$	−0.703478	−	0.703478i	−0.0246116	−	0.0246116i
$818$	3.65839	−	2.17570i	0.127912	−	0.0760714i
$819$	75.7553	−	69.4540i	2.64710	−	2.42692i
$820$	−4.17294	+	3.37691i	−0.145726	+	0.117927i
$821$	−15.1009	−	6.25499i	−0.527024	−	0.218301i	0.103275	−	0.994653i	$-0.467068\pi$
$821$	−15.1009	−	6.25499i	−0.527024	−	0.218301i	−0.630299	+	0.776352i	$0.717068\pi$
$822$	5.00262	+	34.5425i	0.174486	+	1.20481i
$823$	16.1038	+	16.1038i	0.561343	+	0.561343i	0.929689	−	0.368346i	$-0.120076\pi$
$823$	16.1038	+	16.1038i	0.561343	+	0.561343i	−0.368346	+	0.929689i	$0.620076\pi$
$824$	−18.2292	−	16.8676i	−0.635045	−	0.587611i
$825$	40.9815			1.42679
$826$	−8.56344	−	59.1295i	−0.297960	−	2.05738i
$827$	2.14072	−	5.16816i	0.0744402	−	0.179714i	−0.882279	−	0.470726i	$-0.843992\pi$
$827$	2.14072	−	5.16816i	0.0744402	−	0.179714i	0.956719	+	0.291012i	$0.0939919\pi$
$828$	110.872	+	60.2456i	3.85305	+	2.09368i
$829$	1.81297	−	4.37689i	0.0629670	−	0.152016i	−0.889264	−	0.457394i	$-0.848783\pi$
$829$	1.81297	−	4.37689i	0.0629670	−	0.152016i	0.952231	+	0.305378i	$0.0987829\pi$
$830$	11.2573	−	6.69486i	0.390745	−	0.232382i
$831$	64.3393			2.23190
$832$	0.985868	+	28.8276i	0.0341788	+	0.999416i
$833$	−4.62376			−0.160204
$834$	−20.4518	+	12.1630i	−0.708189	+	0.421170i
$835$	5.65716	−	13.6576i	0.195774	−	0.472640i
$836$	6.30842	+	3.42788i	0.218181	+	0.118556i
$837$	29.4206	−	71.0277i	1.01693	−	2.45508i
$838$	−4.41442	−	30.4810i	−0.152494	−	1.05295i
$839$	10.3186			0.356239			0.178120	−	0.984009i	$-0.442999\pi$
$839$	10.3186			0.356239			0.178120	+	0.984009i	$0.442999\pi$
$840$	−20.1944	+	21.8246i	−0.696774	+	0.753020i
$841$	−14.4036	−	14.4036i	−0.496676	−	0.496676i
$842$	−6.72244	−	46.4176i	−0.231671	−	1.59966i
$843$	−21.7836	−	9.02307i	−0.750268	−	0.310771i
$844$	20.9377	−	16.9436i	0.720704	−	0.583222i
$845$	−4.77760	+	9.18961i	−0.164354	+	0.316132i
$846$	−0.888821	+	0.528595i	−0.0305583	+	0.0181735i
$847$	5.84026	+	5.84026i	0.200674	+	0.200674i
$848$	−40.7449	−	28.0427i	−1.39918	−	0.962989i
$849$	−68.2715			−2.34307
$850$	2.54509	+	0.646817i	0.0872960	+	0.0221856i
$851$	12.2920	+	29.6755i	0.421364	+	1.01726i
$852$	−56.5429	+	45.7567i	−1.93713	+	1.56760i
$853$	−0.403750	+	0.974739i	−0.0138241	+	0.0333744i	−0.930641	−	0.365934i	$-0.880750\pi$
$853$	−0.403750	+	0.974739i	−0.0138241	+	0.0333744i	0.916817	+	0.399308i	$0.130750\pi$
$854$	−2.58615	+	0.374539i	−0.0884961	+	0.0128165i
$855$	−4.53401	−	4.53401i	−0.155060	−	0.155060i
$856$	−11.2255	+	5.16832i	−0.383680	+	0.176650i
$857$	−20.3927	−	20.3927i	−0.696601	−	0.696601i	0.267075	−	0.963676i	$-0.413943\pi$
$857$	−20.3927	−	20.3927i	−0.696601	−	0.696601i	−0.963676	+	0.267075i	$0.913943\pi$
$858$	45.8406	+	13.7914i	1.56497	+	0.470830i
$859$	38.9768	−	16.1447i	1.32987	−	0.550851i	0.399253	−	0.916841i	$-0.369269\pi$
$859$	38.9768	−	16.1447i	1.32987	−	0.550851i	0.930619	+	0.365989i	$0.119269\pi$
$860$	1.16703	+	0.634145i	0.0397955	+	0.0216242i
$861$	41.0689	+	17.0113i	1.39962	+	0.579743i
$862$	12.4365	+	3.16066i	0.423590	+	0.107652i
$863$	36.1448	−	36.1448i	1.23038	−	1.23038i	0.266568	−	0.963816i	$-0.414110\pi$
$863$	36.1448	−	36.1448i	1.23038	−	1.23038i	0.963816	−	0.266568i	$-0.0858896\pi$
$864$	−65.9466	−	4.37685i	−2.24355	−	0.148904i
$865$	−0.432361	+	0.432361i	−0.0147007	+	0.0147007i
$866$	−12.5386	+	7.45690i	−0.426079	+	0.253396i
$867$	−20.0904	+	48.5025i	−0.682306	+	1.64723i
$868$	−15.7830	−	53.3470i	−0.535710	−	1.81072i
$869$	16.8337	+	6.97275i	0.571044	+	0.236534i
$870$	8.27742	+	6.18316i	0.280631	+	0.209629i
$871$	3.59640	+	9.87286i	0.121859	+	0.334529i
$872$	7.47347	+	16.2323i	0.253084	+	0.549694i
$873$			65.0155i			2.20044i
$874$	2.26361	+	15.6300i	0.0765678	+	0.528692i
$875$	−29.1407	+	12.0705i	−0.985134	+	0.408056i
$876$	−57.2710	−	70.7714i	−1.93501	−	2.39115i
$877$	8.31949	−	3.44605i	0.280929	−	0.116365i	−0.237770	−	0.971321i	$-0.576416\pi$
$877$	8.31949	−	3.44605i	0.280929	−	0.116365i	0.518699	+	0.854957i	$0.326416\pi$
$878$	38.9450	+	9.89759i	1.31433	+	0.334027i
$879$	−1.81001	+	1.81001i	−0.0610503	+	0.0610503i
$880$	−9.37434	−	1.99903i	−0.316009	−	0.0673871i
$881$	−4.75672			−0.160258			−0.0801290	−	0.996785i	$-0.525533\pi$
$881$	−4.75672			−0.160258			−0.0801290	+	0.996785i	$0.525533\pi$
$882$	100.462	+	25.5318i	3.38274	+	0.859700i
$883$	−11.9941	+	28.9563i	−0.403633	+	0.974457i	0.583143	+	0.812369i	$0.301823\pi$
$883$	−11.9941	+	28.9563i	−0.403633	+	0.974457i	−0.986776	+	0.162087i	$0.948177\pi$
$884$	2.62919	+	1.58000i	0.0884293	+	0.0531413i
$885$	−22.9617	+	9.51103i	−0.771848	+	0.319710i
$886$	−10.1711	+	13.6160i	−0.341704	+	0.457440i
$887$	0.0537785	−	0.0537785i	0.00180571	−	0.00180571i	−0.706203	−	0.708009i	$-0.749594\pi$
$887$	0.0537785	−	0.0537785i	0.00180571	−	0.00180571i	0.708009	+	0.706203i	$0.249594\pi$
$888$	−22.2459	−	20.5843i	−0.746524	−	0.690763i
$889$	−53.1577			−1.78285
$890$	−14.4624	+	2.09451i	−0.484779	+	0.0702082i
$891$	−18.6915	+	45.1253i	−0.626189	+	1.51175i
$892$	11.4487	+	38.6968i	0.383330	+	1.29567i
$893$	−0.119579	−	0.0495312i	−0.00400156	−	0.00165750i
$894$	−16.1716	+	63.6321i	−0.540860	+	2.12817i
$895$	6.92168	+	6.92168i	0.231366	+	0.231366i
$896$	−39.0886	+	27.5576i	−1.30586	+	0.920636i
$897$	36.0414	+	98.9409i	1.20339	+	3.30354i
$898$	0.800730	−	3.15071i	0.0267207	−	0.105141i
$899$	−17.8594	+	7.39761i	−0.595645	+	0.246724i
$900$	−51.7267	−	28.1074i	−1.72422	−	0.936912i
$901$	−4.85962	+	2.01292i	−0.161898	+	0.0670601i
$902$	2.05387	+	14.1817i	0.0683865	+	0.472200i
$903$		−	10.9986i		−	0.366009i
$904$	34.7289	−	1.34733i	1.15507	−	0.0448117i
$905$	−3.57957			−0.118989
$906$	−17.8917	+	2.59117i	−0.594411	+	0.0860857i
$907$	−6.93273	+	2.87163i	−0.230197	+	0.0953509i	−0.494801	−	0.869006i	$-0.664759\pi$
$907$	−6.93273	+	2.87163i	−0.230197	+	0.0953509i	0.264603	+	0.964357i	$0.414759\pi$
$908$	−3.80677	+	36.1047i	−0.126332	+	1.19818i
$909$	−13.3138	−	5.51476i	−0.441591	−	0.182913i
$910$	−17.0866	+	1.72229i	−0.566417	+	0.0570932i
$911$	44.4175			1.47162			0.735808	−	0.677190i	$-0.236802\pi$
$911$	44.4175			1.47162			0.735808	+	0.677190i	$0.236802\pi$
$912$	−8.10798	−	12.5032i	−0.268482	−	0.414022i
$913$		−	34.9626i		−	1.15709i
$914$	5.28471	+	8.88613i	0.174803	+	0.293927i
$915$	0.415984	+	1.00427i	0.0137520	+	0.0332003i
$916$	12.2115	−	9.88202i	0.403479	−	0.326511i
$917$	−25.2844	+	61.0420i	−0.834965	+	2.01578i
$918$	−4.20621	+	5.63086i	−0.138826	+	0.185846i
$919$	41.3169	−	41.3169i	1.36292	−	1.36292i	0.492745	−	0.870174i	$-0.335994\pi$
$919$	41.3169	−	41.3169i	1.36292	−	1.36292i	0.870174	−	0.492745i	$-0.164006\pi$
$920$	−8.81777	−	19.1521i	−0.290713	−	0.631426i
$921$			66.8502i			2.20279i
$922$	−0.701003	+	0.938434i	−0.0230863	+	0.0309057i
$923$	−41.9706	−	1.82129i	−1.38148	−	0.0599486i
$924$	22.5180	+	76.1113i	0.740787	+	2.50388i
$925$	−5.73479	−	13.8450i	−0.188559	−	0.455221i
$926$	1.11742	−	4.39684i	0.0367209	−	0.144489i
$927$	59.2093			1.94469
$928$	10.9469	+	12.5033i	0.359350	+	0.410441i
$929$	13.0012	+	13.0012i	0.426554	+	0.426554i	0.887453	−	0.460898i	$-0.152473\pi$
$929$	13.0012	+	13.0012i	0.426554	+	0.426554i	−0.460898	+	0.887453i	$0.652473\pi$
$930$	−19.8906	+	11.8292i	−0.652239	+	0.387896i
$931$	4.96478	+	11.9860i	0.162714	+	0.392827i
$932$	6.43314	+	21.7442i	0.210724	+	0.712254i
$933$	28.7387	−	11.9039i	0.940862	−	0.389718i
$934$	3.20790	+	22.1502i	0.104966	+	0.724775i
$935$	−0.720765	+	0.720765i	−0.0235715	+	0.0235715i
$936$	−48.4010	−	48.8475i	−1.58204	−	1.59663i
$937$	−11.9670	−	11.9670i	−0.390945	−	0.390945i	0.484079	−	0.875024i	$-0.339155\pi$
$937$	−11.9670	−	11.9670i	−0.390945	−	0.390945i	−0.875024	+	0.484079i	$0.839155\pi$
$938$	−10.4264	+	13.9579i	−0.340435	+	0.455741i
$939$	−40.0153	−	96.6055i	−1.30585	−	3.15260i
$940$	0.171845	+	0.0181188i	0.00560496	+	0.000590969i
$941$	41.1427	−	17.0419i	1.34121	−	0.555549i	0.407381	−	0.913258i	$-0.366442\pi$
$941$	41.1427	−	17.0419i	1.34121	−	0.555549i	0.933833	+	0.357709i	$0.116442\pi$
$942$	4.88116	−	19.2064i	0.159037	−	0.625778i
$943$	−22.2889	+	22.2889i	−0.725826	+	0.725826i
$944$	−39.3111	+	7.25912i	−1.27947	+	0.236264i
$945$		−	39.3493i		−	1.28003i
$946$	3.04731	−	1.81228i	0.0990766	−	0.0589223i
$947$	11.7455	−	4.86515i	0.381678	−	0.158096i	−0.183591	−	0.983003i	$-0.558772\pi$
$947$	11.7455	−	4.86515i	0.381678	−	0.158096i	0.565269	+	0.824907i	$0.308772\pi$
$948$	−23.7906	−	29.3987i	−0.772681	−	0.954824i
$949$	2.27961	−	52.5322i	0.0739991	−	1.70527i
$950$	−1.05608	−	7.29211i	−0.0342638	−	0.236587i
$951$	63.6179			2.06295
$952$	0.197167	+	5.08218i	0.00639023	+	0.164715i
$953$	−16.9037	−	16.9037i	−0.547566	−	0.547566i	0.378170	−	0.925736i	$-0.376553\pi$
$953$	−16.9037	−	16.9037i	−0.547566	−	0.547566i	−0.925736	+	0.378170i	$0.876553\pi$
$954$	116.702	−	16.9014i	3.77837	−	0.547203i
$955$	5.46418	+	2.26334i	0.176817	+	0.0732399i
$956$	−4.86905	+	1.44053i	−0.157476	+	0.0465902i
$957$	25.4804	−	10.5543i	0.823665	−	0.341173i
$958$	−7.25071	−	1.84272i	−0.234260	−	0.0595355i
$959$	−33.4240			−1.07932
$960$	15.1154	+	12.9356i	0.487849	+	0.417496i
$961$		−	12.2993i		−	0.396752i
$962$	−1.75554	−	17.4165i	−0.0566007	−	0.561531i
$963$	11.2747	−	27.2195i	0.363321	−	0.877135i
$964$	16.7152	−	4.94529i	0.538361	−	0.159277i
$965$	6.82350	+	16.4734i	0.219656	+	0.530297i
$966$	−104.489	+	139.879i	−3.36186	+	4.50054i
$967$			45.6017i			1.46645i	0.679985	+	0.733226i	$0.261986\pi$
$967$			45.6017i			1.46645i	−0.679985	+	0.733226i	$0.738014\pi$
$968$	3.75324	−	4.05621i	0.120634	−	0.130372i
$969$	−1.58473			−0.0509089
$970$	6.50149	−	8.70357i	0.208750	−	0.279455i
$971$	21.4202	+	51.7129i	0.687407	+	1.65955i	0.749941	+	0.661504i	$0.230082\pi$
$971$	21.4202	+	51.7129i	0.687407	+	1.65955i	−0.0625345	+	0.998043i	$0.519918\pi$
$972$	24.3144	−	19.6762i	0.779885	−	0.631114i
$973$	−8.72025	−	21.0525i	−0.279558	−	0.674914i
$974$	23.0725	+	38.7959i	0.739291	+	1.24310i
$975$	−16.8150	−	46.1605i	−0.538510	−	1.47832i
$976$	0.317492	+	1.71935i	0.0101627	+	0.0550350i
$977$	−9.50345	+	9.50345i	−0.304042	+	0.304042i	−0.842593	−	0.538551i	$-0.818972\pi$
$977$	−9.50345	+	9.50345i	−0.304042	+	0.304042i	0.538551	+	0.842593i	$0.318972\pi$
$978$	29.7087	−	17.6682i	0.949979	−	0.564967i
$979$	−14.9279	+	36.0392i	−0.477098	+	1.15182i
$980$	−10.8957	−	13.4641i	−0.348049	−	0.430094i
$981$	−39.3597	−	16.3033i	−1.25666	−	0.520526i
$982$	−17.5384	+	23.4787i	−0.559673	+	0.749236i
$983$		−	25.8431i		−	0.824266i	−0.911124	−	0.412133i	$-0.864784\pi$
$983$		−	25.8431i		−	0.824266i	0.911124	−	0.412133i	$-0.135216\pi$
$984$	10.3083	−	27.8994i	0.328615	−	0.889399i
$985$	3.72358	+	3.72358i	0.118643	+	0.118643i
$986$	1.74900	−	0.253299i	0.0556996	−	0.00806670i
$987$	−0.547583	−	1.32198i	−0.0174297	−	0.0420791i
$988$	1.27269	−	8.51213i	0.0404898	−	0.270807i
$989$	7.20538	+	2.98457i	0.229118	+	0.0949037i
$990$	19.6403	−	11.6804i	0.624211	−	0.371227i
$991$			4.94447i			0.157066i	0.996912	+	0.0785331i	$0.0250236\pi$
$991$			4.94447i			0.157066i	−0.996912	+	0.0785331i	$0.974976\pi$
$992$	−35.2577	+	11.9361i	−1.11943	+	0.378970i
$993$	7.76901	+	7.76901i	0.246542	+	0.246542i
$994$	−35.6047	−	59.8686i	−1.12931	−	1.89892i
$995$	−1.01720	−	2.45573i	−0.0322473	−	0.0778520i
$996$	−34.6478	+	63.7632i	−1.09786	+	2.02041i
$997$	6.96504	+	16.8151i	0.220585	+	0.532539i	0.994970	−	0.100176i	$-0.0319405\pi$
$997$	6.96504	+	16.8151i	0.220585	+	0.532539i	−0.774385	+	0.632715i	$0.781941\pi$
$998$	−7.13546	−	5.33013i	−0.225869	−	0.168722i
$999$	40.1089			1.26899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bi.a.99.12	yes	216
13.5	odd	4		416.2.bd.a.291.37	yes	216
32.11	odd	8		416.2.bd.a.203.37	✓	216
416.395	even	8	inner	416.2.bi.a.395.12	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.203.37	✓	216	32.11	odd	8
416.2.bd.a.291.37	yes	216	13.5	odd	4
416.2.bi.a.99.12	yes	216	1.1	even	1	trivial
416.2.bi.a.395.12	yes	216	416.395	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bi (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21550 + 0.722878i) q^{2} +(1.19450 - 2.88378i) q^{3} +(0.954896 - 1.75732i) q^{4} +(0.304891 - 0.736071i) q^{5} +(0.632701 + 4.36873i) q^{6} -4.22727 q^{7} +(0.109649 + 2.82630i) q^{8} +(-4.76805 - 4.76805i) q^{9} +(0.161494 + 1.11510i) q^{10} +(2.77874 + 1.15099i) q^{11} +(-3.92711 - 4.85283i) q^{12} +(0.156314 - 3.60216i) q^{13} +(5.13827 - 3.05580i) q^{14} +(-1.75848 - 1.75848i) q^{15} +(-2.17635 - 3.35612i) q^{16} -0.425375 q^{17} +(9.24230 + 2.34886i) q^{18} +(0.456748 + 1.10269i) q^{19} +(-1.00237 - 1.23866i) q^{20} +(-5.04949 + 12.1905i) q^{21} +(-4.20959 + 0.609655i) q^{22} +(-6.61604 - 6.61604i) q^{23} +(8.28141 + 3.05982i) q^{24} +(3.08669 + 3.08669i) q^{25} +(2.41392 + 4.49143i) q^{26} +(-10.7941 + 4.47107i) q^{27} +(-4.03661 + 7.42867i) q^{28} +(2.71411 + 1.12422i) q^{29} +(3.40860 + 0.866271i) q^{30} +(-4.65292 + 4.65292i) q^{31} +(5.07142 + 2.50614i) q^{32} +(6.63842 - 6.63842i) q^{33} +(0.517044 - 0.307494i) q^{34} +(-1.28886 + 3.11158i) q^{35} +(-12.9320 + 3.82600i) q^{36} +(-3.17165 - 1.31374i) q^{37} +(-1.35229 - 1.01015i) q^{38} +(-10.2011 - 4.75356i) q^{39} +(2.11379 + 0.781004i) q^{40} -3.36891i q^{41} +(-2.67460 - 18.4678i) q^{42} +(-0.770093 + 0.318983i) q^{43} +(4.67607 - 3.78406i) q^{44} +(-4.96336 + 2.05589i) q^{45} +(12.8244 + 3.25923i) q^{46} +(-0.0766809 + 0.0766809i) q^{47} +(-12.2780 + 2.26723i) q^{48} +10.8698 q^{49} +(-5.98318 - 1.52058i) q^{50} +(-0.508111 + 1.22669i) q^{51} +(-6.18089 - 3.71438i) q^{52} +(11.4243 - 4.73212i) q^{53} +(9.88825 - 13.2374i) q^{54} +(1.69442 - 1.69442i) q^{55} +(-0.463515 - 11.9475i) q^{56} +3.72550 q^{57} +(-4.11168 + 0.595474i) q^{58} +(3.82451 - 9.23318i) q^{59} +(-4.76937 + 1.41105i) q^{60} +(-0.403832 - 0.167272i) q^{61} +(2.29215 - 9.01913i) q^{62} +(20.1559 + 20.1559i) q^{63} +(-7.97595 + 0.619800i) q^{64} +(-2.60379 - 1.21332i) q^{65} +(-3.27025 + 12.8678i) q^{66} +(-2.69242 + 1.11524i) q^{67} +(-0.406188 + 0.747519i) q^{68} +(-26.9821 + 11.1764i) q^{69} +(-0.682679 - 4.71382i) q^{70} -11.6515i q^{71} +(12.9531 - 13.9988i) q^{72} +14.5835 q^{73} +(4.80482 - 0.695859i) q^{74} +(12.5884 - 5.21429i) q^{75} +(2.37392 + 0.250299i) q^{76} +(-11.7465 - 4.86556i) q^{77} +(15.8358 - 1.59620i) q^{78} +6.05804 q^{79} +(-3.13389 + 0.578699i) q^{80} +16.2395i q^{81} +(2.43531 + 4.09492i) q^{82} +(-4.44848 - 10.7396i) q^{83} +(16.6010 + 20.5143i) q^{84} +(-0.129693 + 0.313106i) q^{85} +(0.705465 - 0.944408i) q^{86} +(6.48401 - 6.48401i) q^{87} +(-2.94836 + 7.97976i) q^{88} +12.9696i q^{89} +(4.54682 - 6.08684i) q^{90} +(-0.660781 + 15.2273i) q^{91} +(-17.9441 + 5.30887i) q^{92} +(7.86009 + 18.9759i) q^{93} +(0.0377750 - 0.148637i) q^{94} +0.950915 q^{95} +(13.2850 - 11.6313i) q^{96} +(-6.81783 - 6.81783i) q^{97} +(-13.2123 + 7.85757i) q^{98} +(-7.76118 - 18.7371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

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