LMFDB - Embedded newform 156.2.c.d.131.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(131,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("156.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$156 = 2^{2} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	156.c (of order $2$ , degree $1$ , 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.78003431400411136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{8} - 4x^{6} - 4x^{4} + 64$ x^12 - x^8 - 4x^6 - 4x^4 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{3}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.6
Root			$-0.373981 - 1.36387i$ of defining polynomial
Character	$\chi$	$=$	156.131
Dual form			156.2.c.d.131.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.373981 + 1.36387i) q^{2} +(-1.20432 + 1.24483i) q^{3} +(-1.72028 - 1.02012i) q^{4} +3.32859i q^{5} +(-1.24739 - 2.10808i) q^{6} -0.723623i q^{7} +(2.03467 - 1.96472i) q^{8} +(-0.0992110 - 2.99836i) q^{9} +(-4.53976 - 1.24483i) q^{10} -4.38250 q^{11} +(3.34165 - 0.912896i) q^{12} -1.00000 q^{13} +(0.986927 + 0.270622i) q^{14} +(-4.14354 - 4.00870i) q^{15} +(1.91870 + 3.50979i) q^{16} +0.660466i q^{17} +(4.12647 + 0.986020i) q^{18} +7.29378i q^{19} +(3.39557 - 5.72610i) q^{20} +(0.900789 + 0.871476i) q^{21} +(1.63897 - 5.97716i) q^{22} +5.87843 q^{23} +(-0.00464491 + 4.89898i) q^{24} -6.07953 q^{25} +(0.373981 - 1.36387i) q^{26} +(3.85193 + 3.48749i) q^{27} +(-0.738185 + 1.24483i) q^{28} +(7.01695 - 4.15206i) q^{30} +3.76170i q^{31} +(-5.50444 + 1.30426i) q^{32} +(5.27795 - 5.45547i) q^{33} +(-0.900789 - 0.247002i) q^{34} +2.40865 q^{35} +(-2.88802 + 5.25921i) q^{36} -0.198422 q^{37} +(-9.94776 - 2.72774i) q^{38} +(1.20432 - 1.24483i) q^{39} +(6.53976 + 6.77257i) q^{40} +6.92189i q^{41} +(-1.52546 + 0.902642i) q^{42} +1.04242i q^{43} +(7.53911 + 4.47069i) q^{44} +(9.98031 - 0.330233i) q^{45} +(-2.19842 + 8.01740i) q^{46} -5.73001 q^{47} +(-6.67982 - 1.83846i) q^{48} +6.47637 q^{49} +(2.27363 - 8.29167i) q^{50} +(-0.822169 - 0.795415i) q^{51} +(1.72028 + 1.02012i) q^{52} -1.32093i q^{53} +(-6.19703 + 3.94928i) q^{54} -14.5876i q^{55} +(-1.42172 - 1.47233i) q^{56} +(-9.07953 - 8.78407i) q^{57} +7.37435 q^{59} +(3.03866 + 11.1230i) q^{60} -10.8811 q^{61} +(-5.13046 - 1.40681i) q^{62} +(-2.16968 + 0.0717914i) q^{63} +(0.279724 - 7.99511i) q^{64} -3.32859i q^{65} +(5.46670 + 9.23867i) q^{66} -11.9227i q^{67} +(0.673757 - 1.13618i) q^{68} +(-7.07953 + 7.31765i) q^{69} +(-0.900789 + 3.28508i) q^{70} +0.912721 q^{71} +(-6.09281 - 5.90573i) q^{72} +16.1591 q^{73} +(0.0742062 - 0.270622i) q^{74} +(7.32171 - 7.56798i) q^{75} +(7.44055 - 12.5473i) q^{76} +3.17128i q^{77} +(1.24739 + 2.10808i) q^{78} +1.99566i q^{79} +(-11.6826 + 6.38656i) q^{80} +(-8.98031 + 0.594941i) q^{81} +(-9.44055 - 2.58866i) q^{82} +14.0171 q^{83} +(-0.660592 - 2.41810i) q^{84} -2.19842 q^{85} +(-1.42172 - 0.389844i) q^{86} +(-8.91692 + 8.61040i) q^{88} +6.39248i q^{89} +(-3.28206 + 13.7353i) q^{90} +0.723623i q^{91} +(-10.1125 - 5.99672i) q^{92} +(-4.68268 - 4.53030i) q^{93} +(2.14292 - 7.81499i) q^{94} -24.2780 q^{95} +(5.00555 - 8.42285i) q^{96} -12.1591 q^{97} +(-2.42204 + 8.83292i) q^{98} +(0.434792 + 13.1403i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 5 q^{6} - 2 q^{9} - 14 q^{10} - 5 q^{12} - 12 q^{13} + 4 q^{16} + 9 q^{18} + 10 q^{21} - 20 q^{22} - 29 q^{24} + 8 q^{25} + 30 q^{28} + 19 q^{30} - 16 q^{33} - 10 q^{34} - 19 q^{36} - 4 q^{37} + 38 q^{40}+ \cdots + 16 q^{97}+O(q^{100})$ 12 * q + 5 * q^6 - 2 * q^9 - 14 * q^10 - 5 * q^12 - 12 * q^13 + 4 * q^16 + 9 * q^18 + 10 * q^21 - 20 * q^22 - 29 * q^24 + 8 * q^25 + 30 * q^28 + 19 * q^30 - 16 * q^33 - 10 * q^34 - 19 * q^36 - 4 * q^37 + 38 * q^40 + 25 * q^42 + 38 * q^45 - 28 * q^46 - 33 * q^48 + 24 * q^54 - 28 * q^57 - 9 * q^60 - 48 * q^61 + 24 * q^64 + 48 * q^66 - 4 * q^69 - 10 * q^70 - 29 * q^72 + 32 * q^73 + 48 * q^76 - 5 * q^78 - 26 * q^81 - 72 * q^82 - 19 * q^84 - 28 * q^85 + 12 * q^88 + 5 * q^90 + 28 * q^93 - 18 * q^94 - q^96 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$ .

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.373981	+	1.36387i	−0.264445	+	0.964401i
$2$	−0.373981	+	1.36387i	−0.264445	+	0.964401i
$3$	−1.20432	+	1.24483i	−0.695316	+	0.718704i
$3$	−1.20432	+	1.24483i	−0.695316	+	0.718704i
$4$	−1.72028	−	1.02012i	−0.860138	−	0.510062i
$5$			3.32859i			1.48859i	0.667850	+	0.744296i	$0.267215\pi$
$5$			3.32859i			1.48859i	−0.667850	+	0.744296i	$0.732785\pi$
$6$	−1.24739	−	2.10808i	−0.509246	−	0.860621i
$7$		−	0.723623i		−	0.273504i	−0.990605	−	0.136752i	$-0.956334\pi$
$7$		−	0.723623i		−	0.273504i	0.990605	−	0.136752i	$-0.0436663\pi$
$8$	2.03467	−	1.96472i	0.719363	−	0.694635i
$9$	−0.0992110	−	2.99836i	−0.0330703	−	0.999453i
$10$	−4.53976	−	1.24483i	−1.43560	−	0.393650i
$11$	−4.38250			−1.32137			−0.660687	−	0.750662i	$-0.729735\pi$
$11$	−4.38250			−1.32137			−0.660687	+	0.750662i	$0.729735\pi$
$12$	3.34165	−	0.912896i	0.964651	−	0.263530i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.986927	+	0.270622i	0.263767	+	0.0723267i
$15$	−4.14354	−	4.00870i	−1.06986	−	1.03504i
$16$	1.91870	+	3.50979i	0.479674	+	0.877447i
$17$			0.660466i			0.160187i	0.996787	+	0.0800933i	$0.0255218\pi$
$17$			0.660466i			0.160187i	−0.996787	+	0.0800933i	$0.974478\pi$
$18$	4.12647	+	0.986020i	0.972619	+	0.232407i
$19$			7.29378i			1.67331i	0.547732	+	0.836654i	$0.315491\pi$
$19$			7.29378i			1.67331i	−0.547732	+	0.836654i	$0.684509\pi$
$20$	3.39557	−	5.72610i	0.759273	−	1.28039i
$21$	0.900789	+	0.871476i	0.196568	+	0.190172i
$22$	1.63897	−	5.97716i	0.349430	−	1.27433i
$23$	5.87843			1.22574			0.612868	−	0.790185i	$-0.290016\pi$
$23$	5.87843			1.22574			0.612868	+	0.790185i	$0.290016\pi$
$24$	−0.00464491	+	4.89898i	−0.000948139	+	1.00000i
$25$	−6.07953			−1.21591
$26$	0.373981	−	1.36387i	0.0733438	−	0.267477i
$27$	3.85193	+	3.48749i	0.741305	+	0.671168i
$28$	−0.738185	+	1.24483i	−0.139504	+	0.235251i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	7.01695	−	4.15206i	1.28111	−	0.758059i
$31$			3.76170i			0.675621i	0.941214	+	0.337811i	$0.109686\pi$
$31$			3.76170i			0.675621i	−0.941214	+	0.337811i	$0.890314\pi$
$32$	−5.50444	+	1.30426i	−0.973058	+	0.230562i
$33$	5.27795	−	5.45547i	0.918773	−	0.949676i
$34$	−0.900789	−	0.247002i	−0.154484	−	0.0423605i
$35$	2.40865			0.407136
$36$	−2.88802	+	5.25921i	−0.481337	+	0.876535i
$37$	−0.198422			−0.0326204			−0.0163102	−	0.999867i	$-0.505192\pi$
$37$	−0.198422			−0.0326204			−0.0163102	+	0.999867i	$0.505192\pi$
$38$	−9.94776	−	2.72774i	−1.61374	−	0.442497i
$39$	1.20432	−	1.24483i	0.192846	−	0.199333i
$40$	6.53976	+	6.77257i	1.03403	+	1.07084i
$41$			6.92189i			1.08102i	0.841338	+	0.540509i	$0.181768\pi$
$41$			6.92189i			1.08102i	−0.841338	+	0.540509i	$0.818232\pi$
$42$	−1.52546	+	0.902642i	−0.235383	+	0.139281i
$43$			1.04242i			0.158967i	0.996836	+	0.0794835i	$0.0253271\pi$
$43$			1.04242i			0.158967i	−0.996836	+	0.0794835i	$0.974673\pi$
$44$	7.53911	+	4.47069i	1.13656	+	0.673982i
$45$	9.98031	−	0.330233i	1.48778	−	0.0492282i
$46$	−2.19842	+	8.01740i	−0.324140	+	1.18210i
$47$	−5.73001			−0.835808			−0.417904	−	0.908491i	$-0.637235\pi$
$47$	−5.73001			−0.835808			−0.417904	+	0.908491i	$0.637235\pi$
$48$	−6.67982	−	1.83846i	−0.964150	−	0.265359i
$49$	6.47637			0.925196
$50$	2.27363	−	8.29167i	0.321540	−	1.17262i
$51$	−0.822169	−	0.795415i	−0.115127	−	0.111380i
$52$	1.72028	+	1.02012i	0.238559	+	0.141466i
$53$		−	1.32093i		−	0.181444i	−0.995876	−	0.0907220i	$-0.971083\pi$
$53$		−	1.32093i		−	0.181444i	0.995876	−	0.0907220i	$-0.0289175\pi$
$54$	−6.19703	+	3.94928i	−0.843309	+	0.537428i
$55$		−	14.5876i		−	1.96699i
$56$	−1.42172	−	1.47233i	−0.189985	−	0.196748i
$57$	−9.07953	−	8.78407i	−1.20261	−	1.16348i
$58$		0			0
$59$	7.37435			0.960059			0.480029	−	0.877252i	$-0.340626\pi$
$59$	7.37435			0.960059			0.480029	+	0.877252i	$0.340626\pi$
$60$	3.03866	+	11.1230i	0.392289	+	1.43597i
$61$	−10.8811			−1.39318			−0.696591	−	0.717468i	$-0.745301\pi$
$61$	−10.8811			−1.39318			−0.696591	+	0.717468i	$0.745301\pi$
$62$	−5.13046	−	1.40681i	−0.651570	−	0.178664i
$63$	−2.16968	+	0.0717914i	−0.273354	+	0.00904487i
$64$	0.279724	−	7.99511i	0.0349655	−	0.999389i
$65$		−	3.32859i		−	0.412861i
$66$	5.46670	+	9.23867i	0.672904	+	1.13720i
$67$		−	11.9227i		−	1.45659i	−0.685265	−	0.728294i	$-0.740314\pi$
$67$		−	11.9227i		−	1.45659i	0.685265	−	0.728294i	$-0.259686\pi$
$68$	0.673757	−	1.13618i	0.0817050	−	0.137783i
$69$	−7.07953	+	7.31765i	−0.852275	+	0.880942i
$70$	−0.900789	+	3.28508i	−0.107665	+	0.392642i
$71$	0.912721			0.108320			0.0541600	−	0.998532i	$-0.482752\pi$
$71$	0.912721			0.108320			0.0541600	+	0.998532i	$0.482752\pi$
$72$	−6.09281	−	5.90573i	−0.718044	−	0.695997i
$73$	16.1591			1.89127			0.945637	−	0.325224i	$-0.105440\pi$
$73$	16.1591			1.89127			0.945637	+	0.325224i	$0.105440\pi$
$74$	0.0742062	−	0.270622i	0.00862629	−	0.0314591i
$75$	7.32171	−	7.56798i	0.845439	−	0.873876i
$76$	7.44055	−	12.5473i	0.853490	−	1.43928i
$77$			3.17128i			0.361401i
$78$	1.24739	+	2.10808i	0.141239	+	0.238693i
$79$			1.99566i			0.224529i	0.993678	+	0.112265i	$0.0358104\pi$
$79$			1.99566i			0.224529i	−0.993678	+	0.112265i	$0.964190\pi$
$80$	−11.6826	+	6.38656i	−1.30616	+	0.714039i
$81$	−8.98031	+	0.594941i	−0.997813	+	0.0661045i
$82$	−9.44055	−	2.58866i	−1.04253	−	0.285870i
$83$	14.0171			1.53858			0.769288	−	0.638903i	$-0.220611\pi$
$83$	14.0171			1.53858			0.769288	+	0.638903i	$0.220611\pi$
$84$	−0.660592	−	2.41810i	−0.0720765	−	0.263836i
$85$	−2.19842			−0.238452
$86$	−1.42172	−	0.389844i	−0.153308	−	0.0420380i
$87$		0			0
$88$	−8.91692	+	8.61040i	−0.950547	+	0.917872i
$89$			6.39248i			0.677601i	0.940858	+	0.338801i	$0.110021\pi$
$89$			6.39248i			0.677601i	−0.940858	+	0.338801i	$0.889979\pi$
$90$	−3.28206	+	13.7353i	−0.345959	+	1.44783i
$91$			0.723623i			0.0758563i
$92$	−10.1125	−	5.99672i	−1.05430	−	0.625201i
$93$	−4.68268	−	4.53030i	−0.485571	−	0.469770i
$94$	2.14292	−	7.81499i	0.221025	−	0.806054i
$95$	−24.2780			−2.49087
$96$	5.00555	−	8.42285i	0.510877	−	0.859654i
$97$	−12.1591			−1.23456			−0.617282	−	0.786742i	$-0.711766\pi$
$97$	−12.1591			−1.23456			−0.617282	+	0.786742i	$0.711766\pi$
$98$	−2.42204	+	8.83292i	−0.244663	+	0.892259i
$99$	0.434792	+	13.1403i	0.0436983	+	1.32065i
$100$	10.4585	+	6.20186i	1.04585	+	0.620186i
$101$		−	7.97812i		−	0.793852i	−0.917851	−	0.396926i	$-0.870077\pi$
$101$		−	7.97812i		−	0.793852i	0.917851	−	0.396926i	$-0.129923\pi$
$102$	1.39232	−	0.823860i	0.137860	−	0.0815743i
$103$		−	5.52774i		−	0.544664i	−0.962203	−	0.272332i	$-0.912205\pi$
$103$		−	5.52774i		−	0.544664i	0.962203	−	0.272332i	$-0.0877949\pi$
$104$	−2.03467	+	1.96472i	−0.199515	+	0.192657i
$105$	−2.90079	+	2.99836i	−0.283088	+	0.292610i
$106$	1.80158	+	0.494004i	0.174985	+	0.0479819i
$107$	6.64273			0.642177			0.321089	−	0.947049i	$-0.395951\pi$
$107$	6.64273			0.642177			0.321089	+	0.947049i	$0.395951\pi$
$108$	−3.06872	−	9.92890i	−0.295287	−	0.955408i
$109$	13.9606			1.33719			0.668593	−	0.743629i	$-0.266897\pi$
$109$	13.9606			1.33719			0.668593	+	0.743629i	$0.266897\pi$
$110$	19.8955	+	5.45547i	1.89696	+	0.520159i
$111$	0.238964	−	0.247002i	0.0226815	−	0.0234444i
$112$	2.53976	−	1.38841i	0.239985	−	0.131193i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	15.3759	−	9.09820i	1.44008	−	0.852125i
$115$			19.5669i			1.82462i
$116$		0			0
$117$	0.0992110	+	2.99836i	0.00917206	+	0.277198i
$118$	−2.75787	+	10.0576i	−0.253883	+	0.925882i
$119$	0.477929			0.0438116
$120$	−16.3067	−	0.0154610i	−1.48859	−	0.00141139i
$121$	8.20631			0.746028
$122$	4.06933	−	14.8404i	0.368420	−	1.34359i
$123$	−8.61659	−	8.33620i	−0.776932	−	0.751649i
$124$	3.83740	−	6.47116i	0.344608	−	0.581127i
$125$		−	3.59330i		−	0.321394i
$126$	0.713507	−	2.98601i	0.0635642	−	0.266015i
$127$		−	10.5071i		−	0.932351i	−0.884692	−	0.466176i	$-0.845631\pi$
$127$		−	10.5071i		−	0.932351i	0.884692	−	0.466176i	$-0.154369\pi$
$128$	10.7997	+	3.37153i	0.954565	+	0.298004i
$129$	−1.29763	−	1.25541i	−0.114250	−	0.110532i
$130$	4.53976	+	1.24483i	0.398164	+	0.109179i
$131$	8.28707			0.724045			0.362022	−	0.932169i	$-0.382086\pi$
$131$	8.28707			0.724045			0.362022	+	0.932169i	$0.382086\pi$
$132$	−14.6448	+	4.00077i	−1.27466	+	0.348222i
$133$	5.27795			0.457656
$134$	16.2610	+	4.45886i	1.40473	+	0.385187i
$135$	−11.6084	+	12.8215i	−0.999095	+	1.10350i
$136$	1.29763	+	1.34383i	0.111271	+	0.115232i
$137$			9.32531i			0.796715i	0.917230	+	0.398358i	$0.130420\pi$
$137$			9.32531i			0.796715i	−0.917230	+	0.398358i	$0.869580\pi$
$138$	−7.33270	−	12.3922i	−0.624201	−	1.05489i
$139$		−	2.48966i		−	0.211170i	−0.994410	−	0.105585i	$-0.966328\pi$
$139$		−	2.48966i		−	0.211170i	0.994410	−	0.105585i	$-0.0336716\pi$
$140$	−4.14354	−	2.45712i	−0.350193	−	0.207664i
$141$	6.90079	−	7.13290i	0.581151	−	0.600699i
$142$	−0.341341	+	1.24483i	−0.0286447	+	0.104464i
$143$	4.38250			0.366483
$144$	10.3332	−	6.10115i	0.861104	−	0.508430i
$145$		0			0
$146$	−6.04318	+	22.0388i	−0.500137	+	1.82395i
$147$	−7.79964	+	8.06199i	−0.643304	+	0.664942i
$148$	0.341341	+	0.202415i	0.0280580	+	0.0166384i
$149$			2.13871i			0.175210i	0.996155	+	0.0876050i	$0.0279213\pi$
$149$			2.13871i			0.175210i	−0.996155	+	0.0876050i	$0.972079\pi$
$150$	7.58355	+	12.8161i	0.619195	+	1.04643i
$151$			8.88461i			0.723019i	0.932368	+	0.361510i	$0.117739\pi$
$151$			8.88461i			0.723019i	−0.932368	+	0.361510i	$0.882261\pi$
$152$	14.3303	+	14.8404i	1.16234	+	1.20372i
$153$	1.98031	−	0.0655255i	0.160099	−	0.00529742i
$154$	−4.32521	−	1.18600i	−0.348535	−	0.0955706i
$155$	−12.5212			−1.00572
$156$	−3.34165	+	0.912896i	−0.267546	+	0.0730901i
$157$	−0.722053			−0.0576261			−0.0288130	−	0.999585i	$-0.509173\pi$
$157$	−0.722053			−0.0576261			−0.0288130	+	0.999585i	$0.509173\pi$
$158$	−2.72182	−	0.746339i	−0.216536	−	0.0593756i
$159$	1.64434	+	1.59083i	0.130404	+	0.126161i
$160$	−4.34134	−	18.3221i	−0.343213	−	1.44849i
$161$		−	4.25377i		−	0.335244i
$162$	2.54705	−	12.4705i	0.200115	−	0.979772i
$163$			10.1883i			0.798007i	0.916949	+	0.399003i	$0.130644\pi$
$163$			10.1883i			0.798007i	−0.916949	+	0.399003i	$0.869356\pi$
$164$	7.06118	−	11.9076i	0.551386	−	0.929824i
$165$	18.1591	+	17.5681i	1.41368	+	1.36768i
$166$	−5.24213	+	19.1175i	−0.406868	+	1.48380i
$167$	−1.39065			−0.107612			−0.0538058	−	0.998551i	$-0.517135\pi$
$167$	−1.39065			−0.107612			−0.0538058	+	0.998551i	$0.517135\pi$
$168$	3.54501	+	0.00336117i	0.273504	+	0.000259320i
$169$	1.00000			0.0769231
$170$	0.822169	−	2.99836i	0.0630575	−	0.229964i
$171$	21.8694	−	0.723623i	1.67239	−	0.0553368i
$172$	1.06339	−	1.79324i	0.0810830	−	0.136734i
$173$		−	13.8438i		−	1.05252i	−0.850323	−	0.526262i	$-0.823593\pi$
$173$		−	13.8438i		−	1.05252i	0.850323	−	0.526262i	$-0.176407\pi$
$174$		0			0
$175$			4.39929i			0.332555i
$176$	−8.40869	−	15.3816i	−0.633829	−	1.15943i
$177$	−8.88110	+	9.17983i	−0.667545	+	0.689998i
$178$	−8.71850	−	2.39067i	−0.653479	−	0.179188i
$179$	−6.46163			−0.482965			−0.241482	−	0.970405i	$-0.577634\pi$
$179$	−6.46163			−0.482965			−0.241482	+	0.970405i	$0.577634\pi$
$180$	−17.5058	−	9.61306i	−1.30480	−	0.716515i
$181$	−10.4843			−0.779289			−0.389644	−	0.920965i	$-0.627402\pi$
$181$	−10.4843			−0.779289			−0.389644	+	0.920965i	$0.627402\pi$
$182$	−0.986927	−	0.270622i	−0.0731559	−	0.0200598i
$183$	13.1044	−	13.5451i	0.968703	−	1.00129i
$184$	11.9606	−	11.5495i	0.881749	−	0.851439i
$185$		−	0.660466i		−	0.0485584i
$186$	7.92997	−	4.69231i	0.581454	−	0.344057i
$187$		−	2.89449i		−	0.211666i
$188$	9.85720	+	5.84532i	0.718911	+	0.426314i
$189$	2.52363	−	2.78735i	0.183567	−	0.202750i
$190$	9.07953	−	33.1120i	0.658698	−	2.40220i
$191$	−13.6876			−0.990398			−0.495199	−	0.868780i	$-0.664905\pi$
$191$	−13.6876			−0.990398			−0.495199	+	0.868780i	$0.664905\pi$
$192$	9.61568	+	9.97690i	0.693952	+	0.720021i
$193$	5.60316			0.403324			0.201662	−	0.979455i	$-0.435366\pi$
$193$	5.60316			0.403324			0.201662	+	0.979455i	$0.435366\pi$
$194$	4.54726	−	16.5833i	0.326474	−	1.19062i
$195$	4.14354	+	4.00870i	0.296725	+	0.287069i
$196$	−11.1411	−	6.60669i	−0.795796	−	0.471907i
$197$		−	17.7254i		−	1.26289i	−0.775422	−	0.631443i	$-0.782463\pi$
$197$		−	17.7254i		−	1.26289i	0.775422	−	0.631443i	$-0.217537\pi$
$198$	−18.0843	−	4.32123i	−1.28519	−	0.307097i
$199$			18.6680i			1.32334i	0.749794	+	0.661671i	$0.230153\pi$
$199$			18.6680i			1.32334i	−0.749794	+	0.661671i	$0.769847\pi$
$200$	−12.3698	+	11.9446i	−0.874677	+	0.844610i
$201$	14.8417	+	14.3588i	1.04686	+	1.01279i
$202$	10.8811	+	2.98367i	0.765592	+	0.209930i
$203$		0			0
$204$	0.602937	+	2.20705i	0.0422140	+	0.154524i
$205$	−23.0402			−1.60919
$206$	7.53911	+	2.06727i	0.525275	+	0.144034i
$207$	−0.583205	−	17.6256i	−0.0405355	−	1.22507i
$208$	−1.91870	−	3.50979i	−0.133038	−	0.243360i
$209$		−	31.9650i		−	2.21106i
$210$	−3.00453	−	5.07763i	−0.207332	−	0.350389i
$211$			15.3428i			1.05624i	0.849169	+	0.528121i	$0.177103\pi$
$211$			15.3428i			1.05624i	−0.849169	+	0.528121i	$0.822897\pi$
$212$	−1.34751	+	2.27237i	−0.0925476	+	0.156067i
$213$	−1.09921	+	1.13618i	−0.0753167	+	0.0778500i
$214$	−2.48426	+	9.05982i	−0.169820	+	0.619316i
$215$	−3.46978			−0.236637
$216$	14.6894	−	0.472105i	0.999484	−	0.0321227i
$217$	2.72205			0.184785
$218$	−5.22102	+	19.0405i	−0.353612	+	1.28958i
$219$	−19.4607	+	20.1153i	−1.31503	+	1.35927i
$220$	−14.8811	+	25.0946i	−1.00328	+	1.69188i
$221$		−	0.660466i		−	0.0444278i
$222$	0.247510	+	0.418290i	0.0166118	+	0.0280738i
$223$		−	17.3960i		−	1.16492i	−0.812858	−	0.582462i	$-0.802090\pi$
$223$		−	17.3960i		−	1.16492i	0.812858	−	0.582462i	$-0.197910\pi$
$224$	0.943791	+	3.98314i	0.0630597	+	0.266135i
$225$	0.603156	+	18.2286i	0.0402104	+	1.21524i
$226$		0			0
$227$	−12.1916			−0.809188			−0.404594	−	0.914496i	$-0.632587\pi$
$227$	−12.1916			−0.809188			−0.404594	+	0.914496i	$0.632587\pi$
$228$	6.65846	+	24.3733i	0.440967	+	1.61416i
$229$	−15.1512			−1.00122			−0.500608	−	0.865674i	$-0.666890\pi$
$229$	−15.1512			−1.00122			−0.500608	+	0.865674i	$0.666890\pi$
$230$	−26.6867	−	7.31765i	−1.75967	−	0.482512i
$231$	−3.94771	−	3.81925i	−0.259740	−	0.251288i
$232$		0			0
$233$			23.3264i			1.52816i	0.645119	+	0.764082i	$0.276808\pi$
$233$			23.3264i			1.52816i	−0.645119	+	0.764082i	$0.723192\pi$
$234$	−4.12647	−	0.986020i	−0.269756	−	0.0644581i
$235$		−	19.0729i		−	1.24418i
$236$	−12.6859	−	7.52275i	−0.825783	−	0.489689i
$237$	−2.48426	−	2.40342i	−0.161370	−	0.156119i
$238$	−0.178736	+	0.651832i	−0.0115858	+	0.0422520i
$239$	−14.4950			−0.937605			−0.468802	−	0.883303i	$-0.655314\pi$
$239$	−14.4950			−0.937605			−0.468802	+	0.883303i	$0.655314\pi$
$240$	6.11949	−	22.2344i	0.395011	−	1.43523i
$241$	2.79369			0.179957			0.0899786	−	0.995944i	$-0.471320\pi$
$241$	2.79369			0.179957			0.0899786	+	0.995944i	$0.471320\pi$
$242$	−3.06901	+	11.1923i	−0.197283	+	0.719470i
$243$	10.0746	−	11.8955i	0.646286	−	0.763095i
$244$	18.7185	+	11.1001i	1.19833	+	0.710609i
$245$			21.5572i			1.37724i
$246$	14.5919	−	8.63431i	0.930347	−	0.550504i
$247$		−	7.29378i		−	0.464092i
$248$	7.39070	+	7.65380i	0.469310	+	0.486017i
$249$	−16.8811	+	17.4489i	−1.06980	+	1.10578i
$250$	4.90079	+	1.34383i	0.309953	+	0.0849911i
$251$	−4.92257			−0.310710			−0.155355	−	0.987859i	$-0.549652\pi$
$251$	−4.92257			−0.310710			−0.155355	+	0.987859i	$0.549652\pi$
$252$	3.80569	+	2.08984i	0.239736	+	0.131648i
$253$	−25.7622			−1.61966
$254$	14.3303	+	3.92945i	0.899160	+	0.246555i
$255$	2.64761	−	2.73667i	0.165800	−	0.171377i
$256$	−8.63720	+	13.4684i	−0.539825	+	0.841777i
$257$			7.84707i			0.489486i	0.969588	+	0.244743i	$0.0787037\pi$
$257$			7.84707i			0.489486i	−0.969588	+	0.244743i	$0.921296\pi$
$258$	2.19750	−	1.30030i	0.136810	−	0.0809533i
$259$			0.143583i			0.00892180i
$260$	−3.39557	+	5.72610i	−0.210585	+	0.355117i
$261$		0			0
$262$	−3.09921	+	11.3025i	−0.191470	+	0.698270i
$263$	19.3554			1.19351			0.596754	−	0.802424i	$-0.296457\pi$
$263$	19.3554			1.19351			0.596754	+	0.802424i	$0.296457\pi$
$264$	0.0203563	−	21.4698i	0.00125285	−	1.32137i
$265$	4.39684			0.270096
$266$	−1.97385	+	7.19843i	−0.121025	+	0.441364i
$267$	−7.95756	−	7.69861i	−0.486995	−	0.471147i
$268$	−12.1626	+	20.5103i	−0.742949	+	1.25287i
$269$		−	23.1428i		−	1.41104i	−0.708688	−	0.705522i	$-0.750713\pi$
$269$		−	23.1428i		−	1.41104i	0.708688	−	0.705522i	$-0.249287\pi$
$270$	−13.1455	−	20.6274i	−0.800011	−	1.25534i
$271$		−	23.1850i		−	1.40839i	−0.710007	−	0.704194i	$-0.751308\pi$
$271$		−	23.1850i		−	1.40839i	0.710007	−	0.704194i	$-0.248692\pi$
$272$	−2.31809	+	1.26723i	−0.140555	+	0.0768374i
$273$	−0.900789	−	0.871476i	−0.0545182	−	0.0527441i
$274$	−12.7185	−	3.48749i	−0.768353	−	0.210687i
$275$	26.6435			1.60666
$276$	19.6436	−	5.36639i	1.18241	−	0.323019i
$277$	16.5559			0.994747			0.497374	−	0.867536i	$-0.334298\pi$
$277$	16.5559			0.994747			0.497374	+	0.867536i	$0.334298\pi$
$278$	3.39557	+	0.931088i	0.203653	+	0.0558429i
$279$	11.2789	−	0.373202i	0.675252	−	0.0223430i
$280$	4.90079	−	4.73232i	0.292878	−	0.282810i
$281$		−	14.6616i		−	0.874635i	−0.899307	−	0.437318i	$-0.855929\pi$
$281$		−	14.6616i		−	0.874635i	0.899307	−	0.437318i	$-0.144071\pi$
$282$	7.14758	+	12.0793i	0.425632	+	0.719314i
$283$		−	6.51575i		−	0.387321i	−0.981069	−	0.193660i	$-0.937964\pi$
$283$		−	6.51575i		−	0.387321i	0.981069	−	0.193660i	$-0.0620360\pi$
$284$	−1.57013	−	0.931088i	−0.0931702	−	0.0552499i
$285$	29.2386	−	30.2220i	1.73194	−	1.79020i
$286$	−1.63897	+	5.97716i	−0.0969145	+	0.353437i
$287$	5.00884			0.295663
$288$	4.45673	+	16.3749i	0.262616	+	0.964901i
$289$	16.5638			0.974340
$290$		0			0
$291$	14.6434	−	15.1360i	0.858413	−	0.887286i
$292$	−27.7980	−	16.4842i	−1.62676	−	0.964666i
$293$			9.43270i			0.551065i	0.961292	+	0.275532i	$0.0888541\pi$
$293$			9.43270i			0.551065i	−0.961292	+	0.275532i	$0.911146\pi$
$294$	−8.07857	−	13.6527i	−0.471152	−	0.796243i
$295$			24.5462i			1.42914i
$296$	−0.403722	+	0.389844i	−0.0234659	+	0.0226592i
$297$	−16.8811	−	15.2839i	−0.979541	−	0.886864i
$298$	−2.91692	−	0.799838i	−0.168973	−	0.0463334i
$299$	−5.87843			−0.339958
$300$	−20.3156	+	5.54997i	−1.17292	+	0.320428i
$301$	0.754317			0.0434781
$302$	−12.1174	−	3.32268i	−0.697280	−	0.191199i
$303$	9.93141	+	9.60823i	0.570545	+	0.551978i
$304$	−25.5996	+	13.9946i	−1.46824	+	0.802643i
$305$		−	36.2188i		−	2.07388i
$306$	−0.651233	+	2.72539i	−0.0372285	+	0.155800i
$307$			10.5387i			0.601475i	0.953707	+	0.300737i	$0.0972328\pi$
$307$			10.5387i			0.601475i	−0.953707	+	0.300737i	$0.902767\pi$
$308$	3.23510	−	5.45547i	0.184337	−	0.310855i
$309$	6.88110	+	6.65718i	0.391452	+	0.378714i
$310$	4.68268	−	17.0772i	0.265958	−	0.969921i
$311$	33.2536			1.88564			0.942818	−	0.333307i	$-0.108165\pi$
$311$	33.2536			1.88564			0.942818	+	0.333307i	$0.108165\pi$
$312$	0.00464491	−	4.89898i	0.000262966	−	0.277350i
$313$	0.992110			0.0560774			0.0280387	−	0.999607i	$-0.491074\pi$
$313$	0.992110			0.0560774			0.0280387	+	0.999607i	$0.491074\pi$
$314$	0.270034	−	0.984785i	0.0152389	−	0.0555746i
$315$	−0.238964	−	7.22199i	−0.0134641	−	0.406913i
$316$	2.03582	−	3.43308i	0.114524	−	0.193126i
$317$			26.8934i			1.51049i	0.655445	+	0.755243i	$0.272481\pi$
$317$			26.8934i			1.51049i	−0.655445	+	0.755243i	$0.727519\pi$
$318$	−2.78463	+	1.64772i	−0.156155	+	0.0923996i
$319$		0			0
$320$	26.6125	+	0.931088i	1.48768	+	0.0520494i
$321$	−8.00000	+	8.26909i	−0.446516	+	0.461535i
$322$	5.80158	+	1.59083i	0.323309	+	0.0886534i
$323$	−4.81729			−0.268041
$324$	16.0555	+	8.13756i	0.891974	+	0.452087i
$325$	6.07953			0.337231
$326$	−13.8955	−	3.81022i	−0.769599	−	0.211029i
$327$	−16.8131	+	17.3786i	−0.929767	+	0.961040i
$328$	13.5996	+	14.0837i	0.750912	+	0.777644i
$329$			4.14637i			0.228597i
$330$	−30.7518	+	18.1964i	−1.69283	+	1.00168i
$331$			0.516785i			0.0284051i	0.999899	+	0.0142025i	$0.00452096\pi$
$331$			0.516785i			0.0284051i	−0.999899	+	0.0142025i	$0.995479\pi$
$332$	−24.1133	−	14.2992i	−1.32339	−	0.784768i
$333$	0.0196857	+	0.594941i	0.00107877	+	0.0326025i
$334$	0.520077	−	1.89666i	0.0284573	−	0.103781i
$335$	39.6857			2.16826
$336$	−1.33035	+	4.83368i	−0.0725767	+	0.263699i
$337$	17.9606			0.978378			0.489189	−	0.872178i	$-0.337293\pi$
$337$	17.9606			0.978378			0.489189	+	0.872178i	$0.337293\pi$
$338$	−0.373981	+	1.36387i	−0.0203419	+	0.0741847i
$339$		0			0
$340$	3.78189	+	2.24266i	0.205102	+	0.121625i
$341$		−	16.4856i		−	0.892748i
$342$	−7.19181	+	30.0976i	−0.388889	+	1.62749i
$343$		−	9.75181i		−	0.526548i
$344$	2.04806	+	2.12097i	0.110424	+	0.114355i
$345$	−24.3575	−	23.5649i	−1.31136	−	1.26869i
$346$	18.8811	+	5.17732i	1.01505	+	0.278334i
$347$	−0.286380			−0.0153737			−0.00768684	−	0.999970i	$-0.502447\pi$
$347$	−0.286380			−0.0153737			−0.00768684	+	0.999970i	$0.502447\pi$
$348$		0			0
$349$	9.56378			0.511938			0.255969	−	0.966685i	$-0.417606\pi$
$349$	9.56378			0.511938			0.255969	+	0.966685i	$0.417606\pi$
$350$	−6.00005	−	1.64525i	−0.320716	−	0.0879424i
$351$	−3.85193	−	3.48749i	−0.205601	−	0.186149i
$352$	24.1232	−	5.71591i	1.28577	−	0.304659i
$353$		−	8.48127i		−	0.451412i	−0.974195	−	0.225706i	$-0.927531\pi$
$353$		−	8.48127i		−	0.451412i	0.974195	−	0.225706i	$-0.0724689\pi$
$354$	−9.19871	−	15.5457i	−0.488906	−	0.826247i
$355$			3.03808i			0.161244i
$356$	6.52111	−	10.9968i	0.345618	−	0.582830i
$357$	−0.575580	+	0.594941i	−0.0304629	+	0.0314876i
$358$	2.41653	−	8.81282i	0.127718	−	0.465772i
$359$	−36.6612			−1.93490			−0.967452	−	0.253054i	$-0.918565\pi$
$359$	−36.6612			−1.93490			−0.967452	+	0.253054i	$0.918565\pi$
$360$	19.6578	−	20.2805i	1.03606	−	1.06887i
$361$	−34.1992			−1.79996
$362$	3.92092	−	14.2992i	0.206079	−	0.751547i
$363$	−9.88305	+	10.2155i	−0.518726	+	0.536173i
$364$	0.738185	−	1.24483i	0.0386914	−	0.0652469i
$365$			53.7869i			2.81533i
$366$	13.5730	+	22.9383i	0.709472	+	1.19900i
$367$		−	32.1588i		−	1.67867i	−0.543611	−	0.839337i	$-0.682943\pi$
$367$		−	32.1588i		−	1.67867i	0.543611	−	0.839337i	$-0.317057\pi$
$368$	11.2789	+	20.6320i	0.587955	+	1.07552i
$369$	20.7543	−	0.686728i	1.08043	−	0.0357496i
$370$	0.900789	+	0.247002i	0.0468298	+	0.0128410i
$371$	−0.955857			−0.0496256
$372$	3.43404	+	12.5703i	0.178047	+	0.651739i
$373$	8.15905			0.422460			0.211230	−	0.977436i	$-0.432253\pi$
$373$	8.15905			0.422460			0.211230	+	0.977436i	$0.432253\pi$
$374$	3.94771	+	1.08249i	0.204131	+	0.0559740i
$375$	4.47305	+	4.32749i	0.230987	+	0.223471i
$376$	−11.6587	+	11.2579i	−0.601249	+	0.580581i
$377$		0			0
$378$	2.85779	+	4.48432i	0.146989	+	0.230648i
$379$			0.229619i			0.0117947i	0.999983	+	0.00589737i	$0.00187720\pi$
$379$			0.229619i			0.0117947i	−0.999983	+	0.00589737i	$0.998123\pi$
$380$	41.7649	+	24.7666i	2.14249	+	1.27050i
$381$	13.0795	+	12.6539i	0.670084	+	0.648279i
$382$	5.11890	−	18.6680i	0.261906	−	0.955140i
$383$	8.42504			0.430499			0.215250	−	0.976559i	$-0.430943\pi$
$383$	8.42504			0.430499			0.215250	+	0.976559i	$0.430943\pi$
$384$	−17.2033	+	9.38335i	−0.877901	+	0.478842i
$385$	−10.5559			−0.537978
$386$	−2.09548	+	7.64197i	−0.106657	+	0.388966i
$387$	3.12554	−	0.103419i	0.158880	−	0.00525709i
$388$	20.9169	+	12.4037i	1.06190	+	0.629704i
$389$		−	5.33625i		−	0.270559i	−0.990807	−	0.135279i	$-0.956807\pi$
$389$		−	5.33625i		−	0.270559i	0.990807	−	0.135279i	$-0.0431932\pi$
$390$	−7.01695	+	4.15206i	−0.355317	+	0.210248i
$391$			3.88250i			0.196347i
$392$	13.1772	−	12.7243i	0.665551	−	0.642673i
$393$	−9.98031	+	10.3160i	−0.503440	+	0.520374i
$394$	24.1752	+	6.62899i	1.21793	+	0.333964i
$395$	−6.64273			−0.334232
$396$	12.6568	−	23.0485i	0.636027	−	1.15823i
$397$	−6.79369			−0.340965			−0.170483	−	0.985361i	$-0.554533\pi$
$397$	−6.79369			−0.340965			−0.170483	+	0.985361i	$0.554533\pi$
$398$	−25.4608	−	6.98150i	−1.27623	−	0.349951i
$399$	−6.35635	+	6.57016i	−0.318216	+	0.328919i
$400$	−11.6648	−	21.3378i	−0.583239	−	1.06689i
$401$			7.16034i			0.357570i	0.983888	+	0.178785i	$0.0572167\pi$
$401$			7.16034i			0.357570i	−0.983888	+	0.178785i	$0.942783\pi$
$402$	−25.1340	+	14.8723i	−1.25357	+	0.741761i
$403$		−	3.76170i		−	0.187384i
$404$	−8.13866	+	13.7246i	−0.404913	+	0.682822i
$405$	−1.98031	−	29.8918i	−0.0984026	−	1.48534i
$406$		0			0
$407$	0.869585			0.0431037
$408$	−3.23561	−	0.00306781i	−0.160186	−	0.000151879i
$409$	36.5559			1.80757			0.903786	−	0.427984i	$-0.140776\pi$
$409$	36.5559			1.80757			0.903786	+	0.427984i	$0.140776\pi$
$410$	8.61659	−	31.4237i	0.425543	−	1.55191i
$411$	−11.6084	−	11.2307i	−0.572602	−	0.553969i
$412$	−5.63897	+	9.50924i	−0.277812	+	0.468486i
$413$		−	5.33625i		−	0.262580i
$414$	24.2572	+	5.79624i	1.19217	+	0.284870i
$415$			46.6572i			2.29031i
$416$	5.50444	−	1.30426i	0.269878	−	0.0639465i
$417$	3.09921	+	2.99836i	0.151769	+	0.146830i
$418$	43.5960	+	11.9543i	2.13235	+	0.584704i
$419$	−18.8775			−0.922227			−0.461113	−	0.887341i	$-0.652550\pi$
$419$	−18.8775			−0.922227			−0.461113	+	0.887341i	$0.652550\pi$
$420$	8.04885	−	2.19884i	0.392744	−	0.107293i
$421$	−24.9134			−1.21420			−0.607102	−	0.794624i	$-0.707668\pi$
$421$	−24.9134			−1.21420			−0.607102	+	0.794624i	$0.707668\pi$
$422$	−20.9256	−	5.73792i	−1.01864	−	0.279318i
$423$	0.568481	+	17.1806i	0.0276405	+	0.835351i
$424$	−2.59527	−	2.68765i	−0.126037	−	0.130524i
$425$		−	4.01532i		−	0.194772i
$426$	−1.13852	−	1.92409i	−0.0551615	−	0.0932225i
$427$			7.87382i			0.381041i
$428$	−11.4273	−	6.77641i	−0.552361	−	0.327550i
$429$	−5.27795	+	5.45547i	−0.254822	+	0.263393i
$430$	1.29763	−	4.73232i	0.0625774	−	0.228213i
$431$	−6.59960			−0.317891			−0.158946	−	0.987287i	$-0.550809\pi$
$431$	−6.59960			−0.317891			−0.158946	+	0.987287i	$0.550809\pi$
$432$	−4.84966	+	20.2109i	−0.233329	+	0.972398i
$433$	−20.6827			−0.993946			−0.496973	−	0.867766i	$-0.665555\pi$
$433$	−20.6827			−0.993946			−0.496973	+	0.867766i	$0.665555\pi$
$434$	−1.01800	+	3.71252i	−0.0488654	+	0.178207i
$435$		0			0
$436$	−24.0161	−	14.2416i	−1.15016	−	0.682047i
$437$			42.8759i			2.05103i
$438$	−20.1567	−	34.0646i	−0.963123	−	1.62767i
$439$			40.6702i			1.94108i	0.240936	+	0.970541i	$0.422546\pi$
$439$			40.6702i			1.94108i	−0.240936	+	0.970541i	$0.577454\pi$
$440$	−28.6605	−	29.6808i	−1.36634	−	1.41498i
$441$	−0.642527	−	19.4185i	−0.0305965	−	0.924690i
$442$	0.900789	+	0.247002i	0.0428462	+	0.0117487i
$443$	−24.8612			−1.18119			−0.590596	−	0.806967i	$-0.701107\pi$
$443$	−24.8612			−1.18119			−0.590596	+	0.806967i	$0.701107\pi$
$444$	−0.663057	+	0.181139i	−0.0314673	+	0.00859646i
$445$	−21.2779			−1.00867
$446$	23.7259	+	6.50579i	1.12345	+	0.308058i
$447$	−2.66233	−	2.57570i	−0.125924	−	0.121826i
$448$	−5.78545	−	0.202415i	−0.273337	−	0.00956321i
$449$			21.7956i			1.02860i	0.857610	+	0.514300i	$0.171948\pi$
$449$			21.7956i			1.02860i	−0.857610	+	0.514300i	$0.828052\pi$
$450$	−25.0870	−	5.99453i	−1.18261	−	0.282585i
$451$		−	30.3352i		−	1.42843i
$452$		0			0
$453$	−11.0598	−	10.6999i	−0.519637	−	0.502727i
$454$	4.55945	−	16.6278i	0.213986	−	0.780381i
$455$	−2.40865			−0.112919
$456$	−35.7321	−	0.0338790i	−1.67331	−	0.00158653i
$457$	36.7307			1.71819			0.859095	−	0.511815i	$-0.171027\pi$
$457$	36.7307			1.71819			0.859095	+	0.511815i	$0.171027\pi$
$458$	5.66625	−	20.6642i	0.264767	−	0.965574i
$459$	−2.30337	+	2.54407i	−0.107512	+	0.118747i
$460$	19.9606	−	33.6604i	0.930669	−	1.56943i
$461$			14.0011i			0.652096i	0.945353	+	0.326048i	$0.105717\pi$
$461$			14.0011i			0.652096i	−0.945353	+	0.326048i	$0.894283\pi$
$462$	6.68532	−	3.95583i	0.311029	−	0.184042i
$463$		−	21.2437i		−	0.987281i	−0.869666	−	0.493640i	$-0.835666\pi$
$463$		−	21.2437i		−	0.987281i	0.869666	−	0.493640i	$-0.164334\pi$
$464$		0			0
$465$	15.0795	−	15.5867i	0.699296	−	0.722818i
$466$	−31.8142	−	8.72364i	−1.47376	−	0.404115i
$467$	16.6794			0.771832			0.385916	−	0.922534i	$-0.373886\pi$
$467$	16.6794			0.771832			0.385916	+	0.922534i	$0.373886\pi$
$468$	2.88802	−	5.25921i	0.133499	−	0.243107i
$469$	−8.62753			−0.398382
$470$	26.0129	+	7.13290i	1.19989	+	0.329016i
$471$	0.869585	−	0.898834i	0.0400683	−	0.0414161i
$472$	15.0043	−	14.4886i	0.690631	−	0.666890i
$473$		−	4.56839i		−	0.210055i
$474$	4.20701	−	2.48937i	0.193235	−	0.114341i
$475$		−	44.3427i		−	2.03458i
$476$	−0.822169	−	0.487546i	−0.0376841	−	0.0223466i
$477$	−3.96063	+	0.131051i	−0.181345	+	0.00600041i
$478$	5.42087	−	19.7693i	0.247945	−	0.904227i
$479$	−4.56360			−0.208516			−0.104258	−	0.994550i	$-0.533247\pi$
$479$	−4.56360			−0.208516			−0.104258	+	0.994550i	$0.533247\pi$
$480$	28.0362	+	16.6614i	1.27967	+	0.760487i
$481$	0.198422			0.00904727
$482$	−1.04479	+	3.81022i	−0.0475888	+	0.173551i
$483$	5.29522	+	5.12291i	0.240941	+	0.233100i
$484$	−14.1171	−	8.37145i	−0.641687	−	0.380520i
$485$		−	40.4725i		−	1.83776i
$486$	12.4562	+	18.1891i	0.565023	+	0.825075i
$487$			30.1056i			1.36421i	0.731252	+	0.682107i	$0.238936\pi$
$487$			30.1056i			1.36421i	−0.731252	+	0.682107i	$0.761064\pi$
$488$	−22.1394	+	21.3784i	−1.00220	+	0.967753i
$489$	−12.6827	−	12.2700i	−0.573531	−	0.554867i
$490$	−29.4012	−	8.06199i	−1.32821	−	0.364204i
$491$	−29.2764			−1.32123			−0.660613	−	0.750727i	$-0.729704\pi$
$491$	−29.2764			−1.32123			−0.660613	+	0.750727i	$0.729704\pi$
$492$	6.31896	+	23.1305i	0.284881	+	1.04281i
$493$		0			0
$494$	9.94776	+	2.72774i	0.447571	+	0.122727i
$495$	−43.7387	+	1.44725i	−1.96591	+	0.0650489i
$496$	−13.2028	+	7.21756i	−0.592821	+	0.324078i
$497$		−	0.660466i		−	0.0296260i
$498$	−17.4848	−	29.5492i	−0.783513	−	1.32413i
$499$		−	11.2851i		−	0.505190i	−0.967572	−	0.252595i	$-0.918716\pi$
$499$		−	11.2851i		−	0.505190i	0.967572	−	0.252595i	$-0.0812841\pi$
$500$	−3.66561	+	6.18147i	−0.163931	+	0.276444i
$501$	1.67479	−	1.73112i	0.0748242	−	0.0773409i
$502$	1.84095	−	6.71374i	0.0821656	−	0.299649i
$503$	21.0946			0.940562			0.470281	−	0.882517i	$-0.344153\pi$
$503$	21.0946			0.940562			0.470281	+	0.882517i	$0.344153\pi$
$504$	−4.27353	+	4.40890i	−0.190358	+	0.196388i
$505$	26.5559			1.18172
$506$	9.63459	−	35.1363i	0.428310	−	1.56200i
$507$	−1.20432	+	1.24483i	−0.0534859	+	0.0552849i
$508$	−10.7185	+	18.0750i	−0.475556	+	0.801951i
$509$			31.7003i			1.40509i	0.711639	+	0.702545i	$0.247953\pi$
$509$			31.7003i			1.40509i	−0.711639	+	0.702545i	$0.752047\pi$
$510$	2.74229	+	4.63446i	0.121431	+	0.205217i
$511$		−	11.6931i		−	0.517271i
$512$	−15.1390	−	16.8169i	−0.669057	−	0.743211i
$513$	−25.4370	+	28.0952i	−1.12307	+	1.24043i
$514$	−10.7024	−	2.93466i	−0.472061	−	0.129442i
$515$	18.3996			0.810783
$516$	0.951618	+	3.48339i	0.0418926	+	0.153348i
$517$	25.1118			1.10442
$518$	−0.195828	−	0.0536973i	−0.00860419	−	0.00235932i
$519$	17.2332	+	16.6724i	0.756453	+	0.731837i
$520$	−6.53976	−	6.77257i	−0.286788	−	0.296997i
$521$		−	9.48262i		−	0.415441i	−0.978188	−	0.207721i	$-0.933396\pi$
$521$		−	9.48262i		−	0.415441i	0.978188	−	0.207721i	$-0.0666045\pi$
$522$		0			0
$523$			22.2001i			0.970744i	0.874308	+	0.485372i	$0.161316\pi$
$523$			22.2001i			0.970744i	−0.874308	+	0.485372i	$0.838684\pi$
$524$	−14.2561	−	8.45383i	−0.622778	−	0.369307i
$525$	−5.47637	−	5.29816i	−0.239008	−	0.231231i
$526$	−7.23858	+	26.3983i	−0.315617	+	1.15102i
$527$	−2.48447			−0.108225
$528$	29.2743	+	8.05706i	1.27400	+	0.350638i
$529$	11.5559			0.502430
$530$	−1.64434	+	5.99672i	−0.0714255	+	0.260481i
$531$	−0.731617	−	22.1110i	−0.0317495	−	0.959534i
$532$	−9.07953	−	5.38416i	−0.393647	−	0.233433i
$533$		−	6.92189i		−	0.299820i
$534$	13.4759	−	7.97393i	0.583158	−	0.345066i
$535$			22.1110i			0.955940i
$536$	−23.4248	−	24.2587i	−1.01180	−	1.04781i
$537$	7.78189	−	8.04364i	0.335813	−	0.347109i
$538$	31.5638	+	8.65499i	1.36081	+	0.373143i
$539$	−28.3827			−1.22253
$540$	33.0492	−	10.2145i	1.42221	−	0.439562i
$541$	35.0724			1.50788			0.753941	−	0.656943i	$-0.228151\pi$
$541$	35.0724			1.50788			0.753941	+	0.656943i	$0.228151\pi$
$542$	31.6213	+	8.67076i	1.35825	+	0.372441i
$543$	12.6264	−	13.0511i	0.541852	−	0.560078i
$544$	−0.861418	−	3.63550i	−0.0369330	−	0.155871i
$545$			46.4692i			1.99052i
$546$	1.52546	−	0.902642i	0.0652836	−	0.0386295i
$547$			3.58649i			0.153347i	0.997056	+	0.0766736i	$0.0244299\pi$
$547$			3.58649i			0.153347i	−0.997056	+	0.0766736i	$0.975570\pi$
$548$	9.51296	−	16.0421i	0.406374	−	0.685285i
$549$	1.07953	+	32.6255i	0.0460730	+	1.39242i
$550$	−9.96418	+	36.3383i	−0.424874	+	1.54947i
$551$		0			0
$552$	−0.0273048	+	28.7983i	−0.00116217	+	1.22574i
$553$	1.44411			0.0614096
$554$	−6.19160	+	22.5801i	−0.263056	+	0.959335i
$555$	0.822169	+	0.795415i	0.0348991	+	0.0337635i
$556$	−2.53976	+	4.28291i	−0.107710	+	0.181636i
$557$		−	9.45636i		−	0.400679i	−0.979727	−	0.200339i	$-0.935796\pi$
$557$		−	9.45636i		−	0.400679i	0.979727	−	0.200339i	$-0.0642045\pi$
$558$	−3.70911	+	15.5225i	−0.157019	+	0.657122i
$559$		−	1.04242i		−	0.0440895i
$560$	4.62146	+	8.45383i	0.195293	+	0.357240i
$561$	3.60316	+	3.48591i	0.152125	+	0.147175i
$562$	19.9964	+	5.48315i	0.843499	+	0.231293i
$563$	27.6425			1.16499			0.582497	−	0.812833i	$-0.302076\pi$
$563$	27.6425			1.16499			0.582497	+	0.812833i	$0.302076\pi$
$564$	−19.1477	+	5.23090i	−0.806264	+	0.220261i
$565$		0			0
$566$	8.88662	+	2.43677i	0.373533	+	0.102425i
$567$	0.430513	+	6.49836i	0.0180798	+	0.272906i
$568$	1.85708	−	1.79324i	0.0779214	−	0.0752429i
$569$		−	15.0337i		−	0.630244i	−0.949051	−	0.315122i	$-0.897955\pi$
$569$		−	15.0337i		−	0.630244i	0.949051	−	0.315122i	$-0.102045\pi$
$570$	30.2842	+	51.1801i	1.26847	+	2.14370i
$571$		−	17.7781i		−	0.743989i	−0.928235	−	0.371994i	$-0.878674\pi$
$571$		−	17.7781i		−	0.743989i	0.928235	−	0.371994i	$-0.121326\pi$
$572$	−7.53911	−	4.47069i	−0.315226	−	0.186929i
$573$	16.4843	−	17.0387i	0.688640	−	0.711803i
$574$	−1.87321	+	6.83140i	−0.0781864	+	0.285137i
$575$	−35.7380			−1.49038
$576$	−24.0000	−	0.0455107i	−0.999998	−	0.00189628i
$577$	−17.6032			−0.732829			−0.366414	−	0.930452i	$-0.619415\pi$
$577$	−17.6032			−0.732829			−0.366414	+	0.930452i	$0.619415\pi$
$578$	−6.19455	+	22.5908i	−0.257659	+	0.939655i
$579$	−6.74801	+	6.97499i	−0.280438	+	0.289870i
$580$		0			0
$581$		−	10.1431i		−	0.420806i
$582$	15.1671	+	25.6323i	0.628697	+	1.06249i
$583$			5.78899i			0.239755i
$584$	32.8783	−	31.7481i	1.36051	−	1.31374i
$585$	−9.98031	+	0.330233i	−0.412635	+	0.0136535i
$586$	−12.8650	−	3.52766i	−0.531447	−	0.145726i
$587$	−8.33021			−0.343825			−0.171912	−	0.985112i	$-0.554995\pi$
$587$	−8.33021			−0.343825			−0.171912	+	0.985112i	$0.554995\pi$
$588$	21.6418	−	5.91225i	0.892491	−	0.243817i
$589$	−27.4370			−1.13052
$590$	−33.4778	−	9.17983i	−1.37826	−	0.377927i
$591$	22.0652	+	21.3472i	0.907641	+	0.878105i
$592$	−0.380712	−	0.696419i	−0.0156472	−	0.0286226i
$593$		−	10.8847i		−	0.446981i	−0.974706	−	0.223490i	$-0.928255\pi$
$593$		−	10.8847i		−	0.446981i	0.974706	−	0.223490i	$-0.0717451\pi$
$594$	27.1585	−	17.3077i	1.11433	−	0.710144i
$595$			1.59083i			0.0652176i
$596$	2.18175	−	3.67917i	0.0893679	−	0.150705i
$597$	−23.2386	−	22.4824i	−0.951092	−	0.920142i
$598$	2.19842	−	8.01740i	0.0899002	−	0.327856i
$599$	23.7896			0.972018			0.486009	−	0.873954i	$-0.338452\pi$
$599$	23.7896			0.972018			0.486009	+	0.873954i	$0.338452\pi$
$600$	0.0282389	−	29.7835i	0.00115285	−	1.21590i
$601$	22.3575			0.911980			0.455990	−	0.889985i	$-0.349285\pi$
$601$	22.3575			0.911980			0.455990	+	0.889985i	$0.349285\pi$
$602$	−0.282100	+	1.02879i	−0.0114976	+	0.0419303i
$603$	−35.7485	+	1.18286i	−1.45579	+	0.0481698i
$604$	9.06339	−	15.2840i	0.368784	−	0.621896i
$605$			27.3155i			1.11053i
$606$	−16.8185	+	9.95184i	−0.683206	+	0.404266i
$607$			15.9456i			0.647213i	0.946192	+	0.323607i	$0.104895\pi$
$607$			15.9456i			0.647213i	−0.946192	+	0.323607i	$0.895105\pi$
$608$	−9.51296	−	40.1482i	−0.385802	−	1.62822i
$609$		0			0
$610$	49.3976	+	13.5451i	2.00005	+	0.548427i
$611$	5.73001			0.231812
$612$	−3.47353	−	1.90744i	−0.140409	−	0.0771038i
$613$	10.7937			0.435953			0.217976	−	0.975954i	$-0.430054\pi$
$613$	10.7937			0.435953			0.217976	+	0.975954i	$0.430054\pi$
$614$	−14.3734	−	3.94127i	−0.580063	−	0.159057i
$615$	27.7478	−	28.6811i	1.11890	−	1.15653i
$616$	6.23069	+	6.45249i	0.251042	+	0.259978i
$617$		−	16.2209i		−	0.653030i	−0.945192	−	0.326515i	$-0.894126\pi$
$617$		−	16.2209i		−	0.653030i	0.945192	−	0.326515i	$-0.105874\pi$
$618$	−11.6529	+	6.89526i	−0.468750	+	0.277368i
$619$		−	21.8813i		−	0.879485i	−0.898124	−	0.439743i	$-0.855070\pi$
$619$		−	21.8813i		−	0.879485i	0.898124	−	0.439743i	$-0.144930\pi$
$620$	21.5399	+	12.7731i	0.865061	+	0.512981i
$621$	22.6433	+	20.5010i	0.908645	+	0.822675i
$622$	−12.4362	+	45.3535i	−0.498647	+	1.81851i
$623$	4.62574			0.185327
$624$	6.67982	+	1.83846i	0.267407	+	0.0735974i
$625$	−18.4370			−0.737480
$626$	−0.371031	+	1.35311i	−0.0148294	+	0.0540811i
$627$	39.7910	+	38.4962i	1.58910	+	1.53739i
$628$	1.24213	+	0.736583i	0.0495664	+	0.0293928i
$629$		−	0.131051i		−	0.00522535i
$630$	9.93921	+	2.37497i	0.395988	+	0.0946212i
$631$		−	9.69427i		−	0.385923i	−0.981206	−	0.192961i	$-0.938191\pi$
$631$		−	9.69427i		−	0.385923i	0.981206	−	0.192961i	$-0.0618092\pi$
$632$	3.92092	+	4.06050i	0.155966	+	0.161518i
$633$	−19.0992	−	18.4777i	−0.759125	−	0.734423i
$634$	−36.6791	−	10.0576i	−1.45671	−	0.399440i
$635$	34.9737			1.38789
$636$	−1.20587	−	4.41409i	−0.0478160	−	0.175030i
$637$	−6.47637			−0.256603
$638$		0			0
$639$	−0.0905520	−	2.73667i	−0.00358218	−	0.108261i
$640$	−11.2224	+	35.9477i	−0.443606	+	1.42096i
$641$			2.69439i			0.106422i	0.998583	+	0.0532110i	$0.0169456\pi$
$641$			2.69439i			0.106422i	−0.998583	+	0.0532110i	$0.983054\pi$
$642$	−8.28610	−	14.0034i	−0.327026	−	0.552671i
$643$		−	45.3307i		−	1.78767i	−0.448397	−	0.893835i	$-0.648005\pi$
$643$		−	45.3307i		−	1.78767i	0.448397	−	0.893835i	$-0.351995\pi$
$644$	−4.33936	+	7.31765i	−0.170995	+	0.288356i
$645$	4.17874	−	4.31929i	0.164538	−	0.170072i
$646$	1.80158	−	6.57016i	0.0708821	−	0.258499i
$647$	−7.89542			−0.310401			−0.155200	−	0.987883i	$-0.549602\pi$
$647$	−7.89542			−0.310401			−0.155200	+	0.987883i	$0.549602\pi$
$648$	−17.1030	+	18.8543i	−0.671871	+	0.740668i
$649$	−32.3181			−1.26860
$650$	−2.27363	+	8.29167i	−0.0891791	+	0.325226i
$651$	−3.27823	+	3.38850i	−0.128484	+	0.132806i
$652$	10.3933	−	17.5266i	0.407033	−	0.686396i
$653$		−	47.9737i		−	1.87736i	−0.344793	−	0.938679i	$-0.612051\pi$
$653$		−	47.9737i		−	1.87736i	0.344793	−	0.938679i	$-0.387949\pi$
$654$	−17.4144	−	29.4302i	−0.680956	−	1.15081i
$655$			27.5843i			1.07781i
$656$	−24.2944	+	13.2810i	−0.948535	+	0.518537i
$657$	−1.60316	−	48.4506i	−0.0625451	−	1.89024i
$658$	−5.65511	−	1.55067i	−0.220459	−	0.0604512i
$659$	13.4770			0.524990			0.262495	−	0.964933i	$-0.415455\pi$
$659$	13.4770			0.524990			0.262495	+	0.964933i	$0.415455\pi$
$660$	−13.3169	−	48.7465i	−0.518360	−	1.89746i
$661$	−30.9685			−1.20454			−0.602268	−	0.798294i	$-0.705736\pi$
$661$	−30.9685			−1.20454			−0.602268	+	0.798294i	$0.705736\pi$
$662$	−0.704827	−	0.193268i	−0.0273939	−	0.00751157i
$663$	0.822169	+	0.795415i	0.0319304	+	0.0308913i
$664$	28.5201	−	27.5397i	1.10679	−	1.06875i
$665$			17.5681i			0.681263i
$666$	−0.818783	−	0.195648i	−0.0317272	−	0.00758121i
$667$		0			0
$668$	2.39230	+	1.41863i	0.0925609	+	0.0548886i
$669$	21.6551	+	20.9504i	0.837235	+	0.809990i
$670$	−14.8417	+	54.1262i	−0.573386	+	2.09108i
$671$	47.6864			1.84091
$672$	−6.09497	−	3.62213i	−0.235119	−	0.139727i
$673$	−4.11101			−0.158468			−0.0792338	−	0.996856i	$-0.525247\pi$
$673$	−4.11101			−0.158468			−0.0792338	+	0.996856i	$0.525247\pi$
$674$	−6.71694	+	24.4959i	−0.258727	+	0.943548i
$675$	−23.4179	−	21.2023i	−0.901357	−	0.816077i
$676$	−1.72028	−	1.02012i	−0.0661645	−	0.0392355i
$677$		−	3.70069i		−	0.142229i	−0.997468	−	0.0711146i	$-0.977344\pi$
$677$		−	3.70069i		−	0.142229i	0.997468	−	0.0711146i	$-0.0226556\pi$
$678$		0			0
$679$			8.79857i			0.337658i
$680$	−4.47305	+	4.31929i	−0.171534	+	0.165637i
$681$	14.6827	−	15.1765i	0.562642	−	0.581566i
$682$	22.4843	+	6.16533i	0.860967	+	0.236083i
$683$	24.9044			0.952939			0.476469	−	0.879191i	$-0.341916\pi$
$683$	24.9044			0.952939			0.476469	+	0.879191i	$0.341916\pi$
$684$	−38.3595	−	21.0646i	−1.46671	−	0.805426i
$685$	−31.0402			−1.18598
$686$	13.3002	+	3.64700i	0.507804	+	0.139243i
$687$	18.2469	−	18.8606i	0.696162	−	0.719578i
$688$	−3.65866	+	2.00008i	−0.139485	+	0.0762524i
$689$			1.32093i			0.0503235i
$690$	41.2486	−	24.4076i	1.57031	−	0.929181i
$691$			46.7780i			1.77952i	0.456431	+	0.889759i	$0.349128\pi$
$691$			46.7780i			1.77952i	−0.456431	+	0.889759i	$0.650872\pi$
$692$	−14.1224	+	23.8151i	−0.536852	+	0.905315i
$693$	9.50863	−	0.314626i	0.361203	−	0.0119516i
$694$	0.107101	−	0.390585i	0.00406549	−	0.0148264i
$695$	8.28707			0.314347
$696$		0			0
$697$	−4.57167			−0.173165
$698$	−3.57668	+	13.0437i	−0.135379	+	0.493713i
$699$	−29.0374	−	28.0925i	−1.09830	−	1.06256i
$700$	4.48781	−	7.56798i	0.169623	−	0.286043i
$701$		−	4.01532i		−	0.151657i	−0.997121	−	0.0758283i	$-0.975840\pi$
$701$		−	4.01532i		−	0.151657i	0.997121	−	0.0758283i	$-0.0241601\pi$
$702$	6.19703	−	3.94928i	0.233892	−	0.149056i
$703$		−	1.44725i		−	0.0545839i
$704$	−1.22589	+	35.0386i	−0.0462025	+	1.32057i
$705$	23.7425	+	22.9699i	0.894195	+	0.865097i
$706$	11.5673	+	3.17184i	0.435343	+	0.119374i
$707$	−5.77315			−0.217122
$708$	24.6425	−	6.73201i	0.926122	−	0.253005i
$709$	13.3496			0.501354			0.250677	−	0.968071i	$-0.419347\pi$
$709$	13.3496			0.501354			0.250677	+	0.968071i	$0.419347\pi$
$710$	−4.14354	−	1.13618i	−0.155504	−	0.0426402i
$711$	5.98370	−	0.197991i	0.224406	−	0.00742526i
$712$	12.5594	+	13.0065i	0.470685	+	0.487441i
$713$			22.1129i			0.828133i
$714$	−0.596164	−	1.00751i	−0.0223109	−	0.0377052i
$715$			14.5876i			0.545544i
$716$	11.1158	+	6.59166i	0.415416	+	0.246342i
$717$	17.4567	−	18.0439i	0.651932	−	0.673860i
$718$	13.7106	−	50.0011i	0.511675	−	1.86602i
$719$	30.7102			1.14530			0.572649	−	0.819801i	$-0.305916\pi$
$719$	30.7102			1.14530			0.572649	+	0.819801i	$0.305916\pi$
$720$	20.3083	+	34.3952i	0.756844	+	1.28183i
$721$	−4.00000			−0.148968
$722$	12.7899	−	46.6432i	0.475990	−	1.73588i
$723$	−3.36450	+	3.47767i	−0.125127	+	0.129336i
$724$	18.0358	+	10.6952i	0.670296	+	0.397485i
$725$		0			0
$726$	−10.2365	−	17.2996i	−0.379912	−	0.642048i
$727$		−	30.0107i		−	1.11303i	−0.830836	−	0.556517i	$-0.812137\pi$
$727$		−	30.0107i		−	1.11303i	0.830836	−	0.556517i	$-0.187863\pi$
$728$	1.42172	+	1.47233i	0.0526924	+	0.0545682i
$729$	2.67479	+	26.8672i	0.0990664	+	0.995081i
$730$	−73.3583	−	20.1153i	−2.71511	−	0.744500i
$731$	−0.688481			−0.0254644
$732$	−36.3608	+	9.93331i	−1.34394	+	0.367146i
$733$	−28.5165			−1.05328			−0.526641	−	0.850088i	$-0.676549\pi$
$733$	−28.5165			−1.05328			−0.526641	+	0.850088i	$0.676549\pi$
$734$	43.8604	+	12.0268i	1.61892	+	0.443917i
$735$	−26.8351	−	25.9618i	−0.989827	−	0.957616i
$736$	−32.3575	+	7.66698i	−1.19271	+	0.282609i
$737$			52.2512i			1.92470i
$738$	−6.82512	+	28.5630i	−0.251236	+	1.05142i
$739$		−	28.3079i		−	1.04132i	−0.853763	−	0.520662i	$-0.825685\pi$
$739$		−	28.3079i		−	1.04132i	0.853763	−	0.520662i	$-0.174315\pi$
$740$	−0.673757	+	1.13618i	−0.0247678	+	0.0417669i
$741$	9.07953	+	8.78407i	0.333545	+	0.322691i
$742$	0.357473	−	1.30366i	0.0131232	−	0.0478590i
$743$	−14.4950			−0.531771			−0.265885	−	0.964005i	$-0.585664\pi$
$743$	−14.4950			−0.531771			−0.265885	+	0.964005i	$0.585664\pi$
$744$	−18.4285	−	0.0174728i	−0.675621	−	0.000640583i
$745$	−7.11890			−0.260816
$746$	−3.05133	+	11.1279i	−0.111717	+	0.407420i
$747$	−1.39065	−	42.0283i	−0.0508812	−	1.53773i
$748$	−2.95274	+	4.97933i	−0.107963	+	0.182062i
$749$		−	4.80684i		−	0.175638i
$750$	−7.57497	+	4.48225i	−0.276599	+	0.163669i
$751$		−	17.3929i		−	0.634675i	−0.948313	−	0.317338i	$-0.897211\pi$
$751$		−	17.3929i		−	0.634675i	0.948313	−	0.317338i	$-0.102789\pi$
$752$	−10.9942	−	20.1111i	−0.400916	−	0.733377i
$753$	5.92836	−	6.12777i	0.216042	−	0.223308i
$754$		0			0
$755$	−29.5732			−1.07628
$756$	−7.18478	+	2.22060i	−0.261308	+	0.0807623i
$757$	13.1189			0.476814			0.238407	−	0.971165i	$-0.423375\pi$
$757$	13.1189			0.476814			0.238407	+	0.971165i	$0.423375\pi$
$758$	−0.313170	−	0.0858733i	−0.0113749	−	0.00311906i
$759$	31.0260	−	32.0696i	1.12617	−	1.16405i
$760$	−49.3976	+	47.6996i	−1.79184	+	1.73025i
$761$			0.264708i			0.00959564i	0.999988	+	0.00479782i	$0.00152720\pi$
$761$			0.264708i			0.00959564i	−0.999988	+	0.00479782i	$0.998473\pi$
$762$	−22.1498	+	13.1064i	−0.802401	+	0.474796i
$763$		−	10.1022i		−	0.365725i
$764$	23.5464	+	13.9630i	0.851879	+	0.505164i
$765$	0.218108	+	6.59166i	0.00788570	+	0.238322i
$766$	−3.15081	+	11.4906i	−0.113843	+	0.415174i
$767$	−7.37435			−0.266272
$768$	−6.36396	−	26.9722i	−0.229640	−	0.973276i
$769$	−30.7149			−1.10761			−0.553805	−	0.832647i	$-0.686825\pi$
$769$	−30.7149			−1.10761			−0.553805	+	0.832647i	$0.686825\pi$
$770$	3.94771	−	14.3969i	0.142266	−	0.518827i
$771$	−9.76827	−	9.45040i	−0.351796	−	0.340348i
$772$	−9.63897	−	5.71591i	−0.346914	−	0.205720i
$773$		−	29.7189i		−	1.06891i	−0.845196	−	0.534457i	$-0.820516\pi$
$773$		−	29.7189i		−	1.06891i	0.845196	−	0.534457i	$-0.179484\pi$
$774$	−1.02784	+	4.30150i	−0.0369451	+	0.154614i
$775$		−	22.8693i		−	0.821491i
$776$	−24.7396	+	23.8892i	−0.888100	+	0.857571i
$777$	−0.178736	−	0.172920i	−0.00641213	−	0.00620347i
$778$	7.27795	+	1.99566i	0.260927	+	0.0715478i
$779$	−50.4867			−1.80888
$780$	−3.03866	−	11.1230i	−0.108801	−	0.398267i
$781$	−4.00000			−0.143131
$782$	−5.29522	−	1.45198i	−0.189357	−	0.0519228i
$783$		0			0
$784$	12.4262	+	22.7307i	0.443793	+	0.811810i
$785$		−	2.40342i		−	0.0857817i
$786$	−10.3372	−	17.4698i	−0.368717	−	0.623128i
$787$			49.9596i			1.78087i	0.455112	+	0.890434i	$0.349599\pi$
$787$			49.9596i			1.78087i	−0.455112	+	0.890434i	$0.650401\pi$
$788$	−18.0821	+	30.4927i	−0.644149	+	1.08626i
$789$	−23.3102	+	24.0943i	−0.829866	+	0.857779i
$790$	2.48426	−	9.05982i	0.0883860	−	0.322334i
$791$		0			0
$792$	26.7017	+	25.8819i	0.948805	+	0.919673i
$793$	10.8811			0.386399
$794$	2.54071	−	9.26570i	0.0901665	−	0.328827i
$795$	−5.29522	+	5.47333i	−0.187802	+	0.194119i
$796$	19.0437	−	32.1142i	0.674986	−	1.13826i
$797$		−	40.7346i		−	1.44289i	−0.692469	−	0.721447i	$-0.743477\pi$
$797$		−	40.7346i		−	1.44289i	0.692469	−	0.721447i	$-0.256523\pi$
$798$	−6.58367	−	11.1263i	−0.233059	−	0.393868i
$799$		−	3.78448i		−	0.133885i
$800$	33.4644	−	7.92927i	1.18315	−	0.280342i
$801$	19.1669	−	0.634204i	0.677231	−	0.0224085i
$802$	−9.76576	−	2.67783i	−0.344841	−	0.0945576i
$803$	−70.8171			−2.49908
$804$	−10.8842	−	39.8414i	−0.383855	−	1.40510i
$805$	14.1591			0.499041
$806$	5.13046	+	1.40681i	0.180713	+	0.0495526i
$807$	28.8089	+	27.8715i	1.01412	+	0.981122i
$808$	−15.6748	−	16.2328i	−0.551437	−	0.571068i
$809$		−	23.0118i		−	0.809051i	−0.914527	−	0.404526i	$-0.867437\pi$
$809$		−	23.0118i		−	0.809051i	0.914527	−	0.404526i	$-0.132563\pi$
$810$	41.5091	+	8.47809i	1.45848	+	0.297890i
$811$			15.6268i			0.548732i	0.961625	+	0.274366i	$0.0884680\pi$
$811$			15.6268i			0.548732i	−0.961625	+	0.274366i	$0.911532\pi$
$812$		0			0
$813$	28.8614	+	27.9222i	1.01221	+	0.979275i
$814$	−0.325209	+	1.18600i	−0.0113986	+	0.0415693i
$815$	−33.9126			−1.18791
$816$	1.21424	−	4.41180i	0.0425069	−	0.154444i
$817$	−7.60316			−0.266001
$818$	−13.6712	+	49.8574i	−0.478003	+	1.74322i
$819$	2.16968	−	0.0717914i	0.0758148	−	0.00250859i
$820$	39.6354	+	23.5038i	1.38413	+	0.820788i
$821$		−	34.2636i		−	1.19581i	−0.801568	−	0.597904i	$-0.796000\pi$
$821$		−	34.2636i		−	1.19581i	0.801568	−	0.597904i	$-0.204000\pi$
$822$	19.6585	−	11.6323i	0.685670	−	0.405724i
$823$		−	24.7442i		−	0.862529i	−0.902226	−	0.431264i	$-0.858068\pi$
$823$		−	24.7442i		−	0.862529i	0.902226	−	0.431264i	$-0.141932\pi$
$824$	−10.8605	−	11.2471i	−0.378343	−	0.391811i
$825$	−32.0874	+	33.1667i	−1.11714	+	1.15472i
$826$	7.27795	+	1.99566i	0.253232	+	0.0694379i
$827$	39.3562			1.36855			0.684275	−	0.729224i	$-0.260119\pi$
$827$	39.3562			1.36855			0.684275	+	0.729224i	$0.260119\pi$
$828$	−16.9770	+	30.9159i	−0.589993	+	1.07440i
$829$	22.0874			0.767128			0.383564	−	0.923514i	$-0.374697\pi$
$829$	22.0874			0.767128			0.383564	+	0.923514i	$0.374697\pi$
$830$	−63.6342	−	17.4489i	−2.20878	−	0.605661i
$831$	−19.9386	+	20.6093i	−0.691664	+	0.714929i
$832$	−0.279724	+	7.99511i	−0.00969769	+	0.277181i
$833$			4.27742i			0.148204i
$834$	−5.24842	+	3.10559i	−0.181738	+	0.107538i
$835$		−	4.62890i		−	0.160190i
$836$	−32.6082	+	54.9886i	−1.12778	+	1.90182i
$837$	−13.1189	+	14.4898i	−0.453455	+	0.500841i
$838$	7.05984	−	25.7465i	0.243878	−	0.889396i
$839$	14.0171			0.483924			0.241962	−	0.970286i	$-0.422209\pi$
$839$	14.0171			0.483924			0.241962	+	0.970286i	$0.422209\pi$
$840$	−0.0111880	+	11.7999i	−0.000386021	+	0.407135i
$841$	29.0000			1.00000
$842$	9.31714	−	33.9786i	0.321090	−	1.17098i
$843$	18.2512	+	17.6573i	0.628604	+	0.608148i
$844$	15.6516	−	26.3939i	0.538749	−	0.908514i
$845$			3.32859i			0.114507i
$846$	−23.6447	−	5.64991i	−0.812923	−	0.194248i
$847$		−	5.93828i		−	0.204042i
$848$	4.63619	−	2.53447i	0.159207	−	0.0870340i
$849$	8.11101	+	7.84707i	0.278369	+	0.269311i
$850$	5.47637	+	1.50165i	0.187838	+	0.0515063i
$851$	−1.16641			−0.0399840
$852$	3.04999	−	0.833219i	0.104491	−	0.0285456i
$853$	14.7543			0.505178			0.252589	−	0.967574i	$-0.418718\pi$
$853$	14.7543			0.505178			0.252589	+	0.967574i	$0.418718\pi$
$854$	−10.7389	−	2.94466i	−0.367476	−	0.100764i
$855$	2.40865	+	72.7942i	0.0823740	+	2.48951i
$856$	13.5157	−	13.0511i	0.461959	−	0.446079i
$857$			14.3207i			0.489185i	0.969626	+	0.244592i	$0.0786542\pi$
$857$			14.3207i			0.489185i	−0.969626	+	0.244592i	$0.921346\pi$
$858$	−5.46670	−	9.23867i	−0.186630	−	0.315403i
$859$			52.4721i			1.79032i	0.445741	+	0.895162i	$0.352940\pi$
$859$			52.4721i			1.79032i	−0.445741	+	0.895162i	$0.647060\pi$
$860$	5.96898	+	3.53960i	0.203540	+	0.120699i
$861$	−6.03226	+	6.23516i	−0.205579	+	0.212494i
$862$	2.46813	−	9.00099i	0.0840647	−	0.306575i
$863$	11.5032			0.391572			0.195786	−	0.980647i	$-0.437274\pi$
$863$	11.5032			0.391572			0.195786	+	0.980647i	$0.437274\pi$
$864$	−25.7513	−	14.1728i	−0.876079	−	0.482168i
$865$	46.0803			1.56678
$866$	7.73494	−	28.2085i	0.262844	−	0.958563i
$867$	−19.9482	+	20.6191i	−0.677475	+	0.700262i
$868$	−4.68268	−	2.77683i	−0.158941	−	0.0942517i
$869$		−	8.74598i		−	0.296687i
$870$		0			0
$871$			11.9227i			0.403985i
$872$	28.4052	−	27.4288i	0.961922	−	0.928855i
$873$	1.20631	+	36.4572i	0.0408275	+	1.23389i
$874$	−58.4772	−	16.0348i	−1.97802	−	0.542385i
$875$	−2.60019			−0.0879026
$876$	53.9979	−	14.7515i	1.82442	−	0.498408i
$877$	11.3260			0.382452			0.191226	−	0.981546i	$-0.438754\pi$
$877$	11.3260			0.382452			0.191226	+	0.981546i	$0.438754\pi$
$878$	−55.4688	−	15.2099i	−1.87198	−	0.513309i
$879$	−11.7421	−	11.3600i	−0.396052	−	0.383164i
$880$	51.1992	−	27.9891i	1.72592	−	0.943513i
$881$			30.7751i			1.03684i	0.855126	+	0.518420i	$0.173480\pi$
$881$			30.7751i			1.03684i	−0.855126	+	0.518420i	$0.826520\pi$
$882$	26.7246	+	6.38583i	0.899862	+	0.215022i
$883$			3.12725i			0.105240i	0.998615	+	0.0526202i	$0.0167573\pi$
$883$			3.12725i			0.105240i	−0.998615	+	0.0526202i	$0.983243\pi$
$884$	−0.673757	+	1.13618i	−0.0226609	+	0.0382140i
$885$	−30.5559	−	29.5616i	−1.02713	−	0.993701i
$886$	9.29763	−	33.9074i	0.312360	−	1.13914i
$887$	−14.2603			−0.478815			−0.239408	−	0.970919i	$-0.576953\pi$
$887$	−14.2603			−0.478815			−0.239408	+	0.970919i	$0.576953\pi$
$888$	0.000921653	−	0.972065i	3.09287e−5	−	0.0326204i
$889$	−7.60316			−0.255002
$890$	7.95756	−	29.0203i	0.266738	−	0.972764i
$891$	39.3562	−	2.60733i	1.31848	−	0.0873487i
$892$	−17.7461	+	29.9259i	−0.594183	+	1.00199i
$893$		−	41.7935i		−	1.39856i
$894$	4.50858	−	2.66781i	0.150789	−	0.0892250i
$895$		−	21.5081i		−	0.718938i
$896$	2.43972	−	7.81489i	0.0815052	−	0.261077i
$897$	7.07953	−	7.31765i	0.236378	−	0.244329i
$898$	−29.7264	−	8.15116i	−0.991982	−	0.272008i
$899$		0			0
$900$	17.5578	−	31.9735i	0.585261	−	1.06578i
$901$	0.872431			0.0290649
$902$	41.3732	+	11.3448i	1.37758	+	0.377740i
$903$	−0.908441	+	0.938997i	−0.0302310	+	0.0312479i
$904$		0			0
$905$		−	34.8978i		−	1.16004i
$906$	18.7295	−	11.0826i	0.622246	−	0.368194i
$907$		−	8.10658i		−	0.269174i	−0.990902	−	0.134587i	$-0.957029\pi$
$907$		−	8.10658i		−	0.269174i	0.990902	−	0.134587i	$-0.0429708\pi$
$908$	20.9730	+	12.4370i	0.696013	+	0.412736i
$909$	−23.9213	+	0.791517i	−0.793418	+	0.0262530i
$910$	0.900789	−	3.28508i	0.0298609	−	0.108899i
$911$	−17.3385			−0.574449			−0.287224	−	0.957863i	$-0.592733\pi$
$911$	−17.3385			−0.574449			−0.287224	+	0.957863i	$0.592733\pi$
$912$	13.4093	−	48.7212i	0.444027	−	1.61332i
$913$	−61.4299			−2.03303
$914$	−13.7366	+	50.0959i	−0.454367	+	1.65702i
$915$	45.0862	+	43.6191i	1.49051	+	1.44200i
$916$	26.0642	+	15.4560i	0.861185	+	0.510682i
$917$		−	5.99672i		−	0.198029i
$918$	−2.60836	−	4.09293i	−0.0860888	−	0.135087i
$919$		−	7.26215i		−	0.239556i	−0.992801	−	0.119778i	$-0.961782\pi$
$919$		−	7.26215i		−	0.239556i	0.992801	−	0.119778i	$-0.0382183\pi$
$920$	38.4435	+	39.8121i	1.26745	+	1.31256i
$921$	−13.1189	−	12.6920i	−0.432282	−	0.418215i
$922$	−19.0957	−	5.23615i	−0.628882	−	0.172443i
$923$	−0.912721			−0.0300426
$924$	2.89505	+	10.5973i	0.0952401	+	0.348626i
$925$	1.20631			0.0396633
$926$	28.9737	+	7.94477i	0.952134	+	0.261081i
$927$	−16.5741	+	0.548413i	−0.544366	+	0.0180122i
$928$		0			0
$929$		−	40.2078i		−	1.31918i	−0.751628	−	0.659588i	$-0.770731\pi$
$929$		−	40.2078i		−	1.31918i	0.751628	−	0.659588i	$-0.229269\pi$
$930$	15.6188	+	26.3956i	0.512161	+	0.865547i
$931$			47.2372i			1.54814i
$932$	23.7958	−	40.1279i	0.779458	−	1.31443i
$933$	−40.0480	+	41.3951i	−1.31111	+	1.35521i
$934$	−6.23779	+	22.7485i	−0.204107	+	0.744355i
$935$	9.63459			0.315085
$936$	6.09281	+	5.90573i	0.199150	+	0.193035i
$937$	32.9614			1.07680			0.538401	−	0.842689i	$-0.319029\pi$
$937$	32.9614			1.07680			0.538401	+	0.842689i	$0.319029\pi$
$938$	3.22654	−	11.7668i	0.105350	−	0.384200i
$939$	−1.19482	+	1.23501i	−0.0389915	+	0.0403030i
$940$	−19.4567	+	32.8106i	−0.634607	+	1.07016i
$941$		−	15.0074i		−	0.489227i	−0.969621	−	0.244614i	$-0.921339\pi$
$941$		−	15.0074i		−	0.489227i	0.969621	−	0.244614i	$-0.0786611\pi$
$942$	0.900683	+	1.52215i	0.0293458	+	0.0495942i
$943$			40.6898i			1.32504i
$944$	14.1492	+	25.8824i	0.460516	+	0.842400i
$945$	9.27795	+	8.40014i	0.301812	+	0.273256i
$946$	6.23069	+	1.70849i	0.202577	+	0.0555479i
$947$	59.7918			1.94297			0.971486	−	0.237095i	$-0.0761953\pi$
$947$	59.7918			1.94297			0.971486	+	0.237095i	$0.0761953\pi$
$948$	1.82183	+	6.66879i	0.0591702	+	0.216592i
$949$	−16.1591			−0.524545
$950$	60.4776	+	16.5833i	1.96215	+	0.538035i
$951$	−33.4778	−	32.3884i	−1.08559	−	1.05027i
$952$	0.972425	−	0.938997i	0.0315165	−	0.0304331i
$953$			37.9617i			1.22970i	0.788644	+	0.614850i	$0.210784\pi$
$953$			37.9617i			1.22970i	−0.788644	+	0.614850i	$0.789216\pi$
$954$	1.30247	−	5.45079i	0.0421689	−	0.176476i
$955$		−	45.5603i		−	1.47430i
$956$	24.9354	+	14.7867i	0.806469	+	0.478236i
$957$		0			0
$958$	1.70670	−	6.22416i	0.0551411	−	0.201093i
$959$	6.74801			0.217905
$960$	−33.2090	+	32.0067i	−1.07182	+	1.03301i
$961$	16.8496			0.543536
$962$	−0.0742062	+	0.270622i	−0.00239250	+	0.00872519i
$963$	−0.659033	−	19.9173i	−0.0212370	−	0.641826i
$964$	−4.80591	−	2.84991i	−0.154788	−	0.0917893i
$965$			18.6506i			0.600385i
$966$	−8.96729	+	5.30611i	−0.288518	+	0.170721i
$967$		−	20.9913i		−	0.675036i	−0.941319	−	0.337518i	$-0.890413\pi$
$967$		−	20.9913i		−	0.675036i	0.941319	−	0.337518i	$-0.109587\pi$
$968$	16.6971	−	16.1231i	0.536665	−	0.518217i
$969$	5.80158	−	5.99672i	0.186374	−	0.192642i
$970$	55.1992	+	15.1360i	1.77234	+	0.485987i
$971$	−46.7410			−1.49999			−0.749996	−	0.661443i	$-0.769944\pi$
$971$	−46.7410			−1.49999			−0.749996	+	0.661443i	$0.769944\pi$
$972$	−29.4659	+	10.1862i	−0.945121	+	0.326722i
$973$	−1.80158			−0.0577559
$974$	−41.0601	−	11.2589i	−1.31565	−	0.360759i
$975$	−7.32171	+	7.56798i	−0.234483	+	0.242369i
$976$	−20.8775	−	38.1903i	−0.668274	−	1.22244i
$977$			17.0125i			0.544277i	0.962258	+	0.272138i	$0.0877308\pi$
$977$			17.0125i			0.544277i	−0.962258	+	0.272138i	$0.912269\pi$
$978$	21.4777	−	12.7088i	0.686782	−	0.406382i
$979$		−	28.0150i		−	0.895364i
$980$	21.9910	−	37.0843i	0.702476	−	1.18462i
$981$	−1.38505	−	41.8590i	−0.0442212	−	1.33645i
$982$	10.9488	−	39.9292i	0.349391	−	1.27419i
$983$	−22.8769			−0.729660			−0.364830	−	0.931074i	$-0.618873\pi$
$983$	−22.8769			−0.729660			−0.364830	+	0.931074i	$0.618873\pi$
$984$	−33.9102	−	0.0321516i	−1.08102	−	0.00102496i
$985$	59.0008			1.87992
$986$		0			0
$987$	−5.16153	−	4.99357i	−0.164293	−	0.158947i
$988$	−7.44055	+	12.5473i	−0.236715	+	0.399183i
$989$			6.12777i			0.194852i
$990$	14.3836	−	60.1951i	0.457141	−	1.91313i
$991$			38.3437i			1.21803i	0.793159	+	0.609015i	$0.208435\pi$
$991$			38.3437i			1.21803i	−0.793159	+	0.609015i	$0.791565\pi$
$992$	−4.90622	−	20.7061i	−0.155773	−	0.657418i
$993$	−0.643310	−	0.622376i	−0.0204148	−	0.0197505i
$994$	0.900789	+	0.247002i	0.0285713	+	0.00783443i
$995$	−62.1383			−1.96992
$996$	46.8402	−	12.7961i	1.48419	−	0.405461i
$997$	18.5717			0.588171			0.294085	−	0.955779i	$-0.404985\pi$
$997$	18.5717			0.588171			0.294085	+	0.955779i	$0.404985\pi$
$998$	15.3914	+	4.22042i	0.487206	+	0.133595i
$999$	−0.764309	−	0.691995i	−0.0241817	−	0.0218938i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.c.d.131.6	yes	12
3.2	odd	2	inner	156.2.c.d.131.7	yes	12
4.3	odd	2	inner	156.2.c.d.131.8	yes	12
8.3	odd	2		2496.2.d.o.1535.4		12
8.5	even	2		2496.2.d.o.1535.9		12
12.11	even	2	inner	156.2.c.d.131.5	✓	12
24.5	odd	2		2496.2.d.o.1535.3		12
24.11	even	2		2496.2.d.o.1535.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.c.d.131.5	✓	12	12.11	even	2	inner
156.2.c.d.131.6	yes	12	1.1	even	1	trivial
156.2.c.d.131.7	yes	12	3.2	odd	2	inner
156.2.c.d.131.8	yes	12	4.3	odd	2	inner
2496.2.d.o.1535.3		12	24.5	odd	2
2496.2.d.o.1535.4		12	8.3	odd	2
2496.2.d.o.1535.9		12	8.5	even	2
2496.2.d.o.1535.10		12	24.11	even	2

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

Introduction

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	156.2.c.d.131.6

Level	$156$
Weight	$2$
Character	156.131
Analytic conductor	$1.246$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$