LMFDB - Embedded newform 780.2.g.d.131.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(131,780)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("780.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.15
Character	$\chi$	$=$	780.131
Dual form			780.2.g.d.131.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.508677 - 1.31956i) q^{2} +(1.38682 + 1.03766i) q^{3} +(-1.48250 + 1.34246i) q^{4} -1.00000i q^{5} +(0.663812 - 2.35783i) q^{6} -3.45974i q^{7} +(2.52558 + 1.27337i) q^{8} +(0.846536 + 2.87809i) q^{9} +(-1.31956 + 0.508677i) q^{10} +1.38443 q^{11} +(-3.44897 + 0.323431i) q^{12} +1.00000 q^{13} +(-4.56535 + 1.75989i) q^{14} +(1.03766 - 1.38682i) q^{15} +(0.395589 - 3.98039i) q^{16} +1.21024i q^{17} +(3.36720 - 2.58107i) q^{18} -6.79078i q^{19} +(1.34246 + 1.48250i) q^{20} +(3.59002 - 4.79804i) q^{21} +(-0.704225 - 1.82684i) q^{22} +2.54649 q^{23} +(2.18120 + 4.38661i) q^{24} -1.00000 q^{25} +(-0.508677 - 1.31956i) q^{26} +(-1.81247 + 4.86980i) q^{27} +(4.64457 + 5.12905i) q^{28} +2.34480i q^{29} +(-2.35783 - 0.663812i) q^{30} -3.03026i q^{31} +(-5.45361 + 1.50273i) q^{32} +(1.91995 + 1.43656i) q^{33} +(1.59699 - 0.615623i) q^{34} -3.45974 q^{35} +(-5.11871 - 3.13031i) q^{36} +1.49033 q^{37} +(-8.96086 + 3.45431i) q^{38} +(1.38682 + 1.03766i) q^{39} +(1.27337 - 2.52558i) q^{40} -9.51887i q^{41} +(-8.15747 - 2.29662i) q^{42} -4.80835i q^{43} +(-2.05241 + 1.85854i) q^{44} +(2.87809 - 0.846536i) q^{45} +(-1.29534 - 3.36025i) q^{46} +11.4074 q^{47} +(4.67889 - 5.10960i) q^{48} -4.96980 q^{49} +(0.508677 + 1.31956i) q^{50} +(-1.25582 + 1.67839i) q^{51} +(-1.48250 + 1.34246i) q^{52} +1.56155i q^{53} +(7.34797 - 0.0854803i) q^{54} -1.38443i q^{55} +(4.40552 - 8.73784i) q^{56} +(7.04650 - 9.41758i) q^{57} +(3.09412 - 1.19275i) q^{58} -4.10481 q^{59} +(0.323431 + 3.44897i) q^{60} +13.5929 q^{61} +(-3.99862 + 1.54142i) q^{62} +(9.95743 - 2.92880i) q^{63} +(4.75706 + 6.43198i) q^{64} -1.00000i q^{65} +(0.918998 - 3.26424i) q^{66} +0.680909i q^{67} +(-1.62471 - 1.79418i) q^{68} +(3.53152 + 2.64238i) q^{69} +(1.75989 + 4.56535i) q^{70} +0.298499 q^{71} +(-1.52687 + 8.34678i) q^{72} -9.83828 q^{73} +(-0.758095 - 1.96658i) q^{74} +(-1.38682 - 1.03766i) q^{75} +(9.11636 + 10.0673i) q^{76} -4.78976i q^{77} +(0.663812 - 2.35783i) q^{78} -15.6146i q^{79} +(-3.98039 - 0.395589i) q^{80} +(-7.56675 + 4.87281i) q^{81} +(-12.5608 + 4.84203i) q^{82} +0.226603 q^{83} +(1.11899 + 11.9325i) q^{84} +1.21024 q^{85} +(-6.34492 + 2.44589i) q^{86} +(-2.43310 + 3.25182i) q^{87} +(3.49647 + 1.76289i) q^{88} +16.5358i q^{89} +(-2.58107 - 3.36720i) q^{90} -3.45974i q^{91} +(-3.77516 + 3.41856i) q^{92} +(3.14437 - 4.20243i) q^{93} +(-5.80267 - 15.0528i) q^{94} -6.79078 q^{95} +(-9.12248 - 3.57496i) q^{96} -11.0094 q^{97} +(2.52802 + 6.55797i) q^{98} +(1.17197 + 3.98450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) $ 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−0.508677	−	1.31956i	−0.359689	−	0.933072i
$2$	−0.508677	−	1.31956i	−0.359689	−	0.933072i
$3$	1.38682	+	1.03766i	0.800681	+	0.599092i
$3$	1.38682	+	1.03766i	0.800681	+	0.599092i
$4$	−1.48250	+	1.34246i	−0.741248	+	0.671231i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.663812	−	2.35783i	0.271000	−	0.962579i
$7$		−	3.45974i		−	1.30766i	−0.756642	−	0.653829i	$-0.773161\pi$
$7$		−	3.45974i		−	1.30766i	0.756642	−	0.653829i	$-0.226839\pi$
$8$	2.52558	+	1.27337i	0.892926	+	0.450204i
$9$	0.846536	+	2.87809i	0.282179	+	0.959362i
$10$	−1.31956	+	0.508677i	−0.417283	+	0.160858i
$11$	1.38443			0.417420			0.208710	−	0.977978i	$-0.433073\pi$
$11$	1.38443			0.417420			0.208710	+	0.977978i	$0.433073\pi$
$12$	−3.44897	+	0.323431i	−0.995632	+	0.0933664i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−4.56535	+	1.75989i	−1.22014	+	0.470350i
$15$	1.03766	−	1.38682i	0.267922	−	0.358075i
$16$	0.395589	−	3.98039i	0.0988974	−	0.995098i
$17$			1.21024i			0.293527i	0.989172	+	0.146764i	$0.0468857\pi$
$17$			1.21024i			0.293527i	−0.989172	+	0.146764i	$0.953114\pi$
$18$	3.36720	−	2.58107i	0.793658	−	0.608365i
$19$		−	6.79078i		−	1.55791i	−0.627079	−	0.778955i	$-0.715750\pi$
$19$		−	6.79078i		−	1.55791i	0.627079	−	0.778955i	$-0.284250\pi$
$20$	1.34246	+	1.48250i	0.300184	+	0.331496i
$21$	3.59002	−	4.79804i	0.783407	−	1.04702i
$22$	−0.704225	−	1.82684i	−0.150141	−	0.389483i
$23$	2.54649			0.530979			0.265489	−	0.964114i	$-0.414466\pi$
$23$	2.54649			0.530979			0.265489	+	0.964114i	$0.414466\pi$
$24$	2.18120	+	4.38661i	0.445235	+	0.895414i
$25$	−1.00000			−0.200000
$26$	−0.508677	−	1.31956i	−0.0997597	−	0.258788i
$27$	−1.81247	+	4.86980i	−0.348811	+	0.937193i
$28$	4.64457	+	5.12905i	0.877741	+	0.969300i
$29$			2.34480i			0.435419i	0.976014	+	0.217709i	$0.0698585\pi$
$29$			2.34480i			0.435419i	−0.976014	+	0.217709i	$0.930141\pi$
$30$	−2.35783	−	0.663812i	−0.430479	−	0.121195i
$31$		−	3.03026i		−	0.544251i	−0.962262	−	0.272125i	$-0.912273\pi$
$31$		−	3.03026i		−	0.544251i	0.962262	−	0.272125i	$-0.0877266\pi$
$32$	−5.45361	+	1.50273i	−0.964070	+	0.265647i
$33$	1.91995	+	1.43656i	0.334220	+	0.250073i
$34$	1.59699	−	0.615623i	0.273882	−	0.105578i
$35$	−3.45974			−0.584803
$36$	−5.11871	−	3.13031i	−0.853118	−	0.521718i
$37$	1.49033			0.245008			0.122504	−	0.992468i	$-0.460907\pi$
$37$	1.49033			0.245008			0.122504	+	0.992468i	$0.460907\pi$
$38$	−8.96086	+	3.45431i	−1.45364	+	0.560363i
$39$	1.38682	+	1.03766i	0.222069	+	0.166158i
$40$	1.27337	−	2.52558i	0.201337	−	0.399329i
$41$		−	9.51887i		−	1.48660i	−0.668959	−	0.743299i	$-0.733260\pi$
$41$		−	9.51887i		−	1.48660i	0.668959	−	0.743299i	$-0.266740\pi$
$42$	−8.15747	−	2.29662i	−1.25873	−	0.354376i
$43$		−	4.80835i		−	0.733266i	−0.930366	−	0.366633i	$-0.880511\pi$
$43$		−	4.80835i		−	0.733266i	0.930366	−	0.366633i	$-0.119489\pi$
$44$	−2.05241	+	1.85854i	−0.309412	+	0.280186i
$45$	2.87809	−	0.846536i	0.429040	−	0.126194i
$46$	−1.29534	−	3.36025i	−0.190987	−	0.495442i
$47$	11.4074			1.66394			0.831969	−	0.554822i	$-0.187214\pi$
$47$	11.4074			1.66394			0.831969	+	0.554822i	$0.187214\pi$
$48$	4.67889	−	5.10960i	0.675340	−	0.737507i
$49$	−4.96980			−0.709972
$50$	0.508677	+	1.31956i	0.0719377	+	0.186614i
$51$	−1.25582	+	1.67839i	−0.175850	+	0.235021i
$52$	−1.48250	+	1.34246i	−0.205585	+	0.186166i
$53$			1.56155i			0.214495i	0.994232	+	0.107248i	$0.0342038\pi$
$53$			1.56155i			0.214495i	−0.994232	+	0.107248i	$0.965796\pi$
$54$	7.34797	−	0.0854803i	0.999932	−	0.0116324i
$55$		−	1.38443i		−	0.186676i
$56$	4.40552	−	8.73784i	0.588713	−	1.16764i
$57$	7.04650	−	9.41758i	0.933331	−	1.24739i
$58$	3.09412	−	1.19275i	0.406277	−	0.156615i
$59$	−4.10481			−0.534401			−0.267201	−	0.963641i	$-0.586099\pi$
$59$	−4.10481			−0.534401			−0.267201	+	0.963641i	$0.586099\pi$
$60$	0.323431	+	3.44897i	0.0417547	+	0.445260i
$61$	13.5929			1.74039			0.870194	−	0.492710i	$-0.163994\pi$
$61$	13.5929			1.74039			0.870194	+	0.492710i	$0.163994\pi$
$62$	−3.99862	+	1.54142i	−0.507826	+	0.195761i
$63$	9.95743	−	2.92880i	1.25452	−	0.368994i
$64$	4.75706	+	6.43198i	0.594633	+	0.803997i
$65$		−	1.00000i		−	0.124035i
$66$	0.918998	−	3.26424i	0.113121	−	0.401800i
$67$			0.680909i			0.0831863i	0.999135	+	0.0415932i	$0.0132433\pi$
$67$			0.680909i			0.0831863i	−0.999135	+	0.0415932i	$0.986757\pi$
$68$	−1.62471	−	1.79418i	−0.197025	−	0.217576i
$69$	3.53152	+	2.64238i	0.425145	+	0.318105i
$70$	1.75989	+	4.56535i	0.210347	+	0.545663i
$71$	0.298499			0.0354253			0.0177127	−	0.999843i	$-0.494362\pi$
$71$	0.298499			0.0354253			0.0177127	+	0.999843i	$0.494362\pi$
$72$	−1.52687	+	8.34678i	−0.179944	+	0.983677i
$73$	−9.83828			−1.15148			−0.575742	−	0.817632i	$-0.695287\pi$
$73$	−9.83828			−1.15148			−0.575742	+	0.817632i	$0.695287\pi$
$74$	−0.758095	−	1.96658i	−0.0881268	−	0.228611i
$75$	−1.38682	−	1.03766i	−0.160136	−	0.119818i
$76$	9.11636	+	10.0673i	1.04572	+	1.15480i
$77$		−	4.78976i		−	0.545843i
$78$	0.663812	−	2.35783i	0.0751619	−	0.266971i
$79$		−	15.6146i		−	1.75678i	−0.477943	−	0.878391i	$-0.658617\pi$
$79$		−	15.6146i		−	1.75678i	0.477943	−	0.878391i	$-0.341383\pi$
$80$	−3.98039	−	0.395589i	−0.445021	−	0.0442282i
$81$	−7.56675	+	4.87281i	−0.840750	+	0.541423i
$82$	−12.5608	+	4.84203i	−1.38710	+	0.534713i
$83$	0.226603			0.0248729			0.0124365	−	0.999923i	$-0.496041\pi$
$83$	0.226603			0.0248729			0.0124365	+	0.999923i	$0.496041\pi$
$84$	1.11899	+	11.9325i	0.122091	+	1.30195i
$85$	1.21024			0.131269
$86$	−6.34492	+	2.44589i	−0.684190	+	0.263747i
$87$	−2.43310	+	3.25182i	−0.260856	+	0.348631i
$88$	3.49647	+	1.76289i	0.372725	+	0.187924i
$89$			16.5358i			1.75279i	0.481589	+	0.876397i	$0.340060\pi$
$89$			16.5358i			1.75279i	−0.481589	+	0.876397i	$0.659940\pi$
$90$	−2.58107	−	3.36720i	−0.272069	−	0.354934i
$91$		−	3.45974i		−	0.362679i
$92$	−3.77516	+	3.41856i	−0.393587	+	0.356410i
$93$	3.14437	−	4.20243i	0.326056	−	0.435771i
$94$	−5.80267	−	15.0528i	−0.598500	−	1.55257i
$95$	−6.79078			−0.696719
$96$	−9.12248	−	3.57496i	−0.931059	−	0.364868i
$97$	−11.0094			−1.11783			−0.558916	−	0.829225i	$-0.688782\pi$
$97$	−11.0094			−1.11783			−0.558916	+	0.829225i	$0.688782\pi$
$98$	2.52802	+	6.55797i	0.255369	+	0.662455i
$99$	1.17197	+	3.98450i	0.117787	+	0.400457i
$100$	1.48250	−	1.34246i	0.148250	−	0.134246i
$101$			17.7812i			1.76929i	0.466262	+	0.884647i	$0.345601\pi$
$101$			17.7812i			1.76929i	−0.466262	+	0.884647i	$0.654399\pi$
$102$	2.85355	+	0.803374i	0.282543	+	0.0795458i
$103$			2.53384i			0.249667i	0.992178	+	0.124833i	$0.0398396\pi$
$103$			2.53384i			0.249667i	−0.992178	+	0.124833i	$0.960160\pi$
$104$	2.52558	+	1.27337i	0.247653	+	0.124864i
$105$	−4.79804	−	3.59002i	−0.468240	−	0.350350i
$106$	2.06056	−	0.794323i	0.200140	−	0.0771515i
$107$	−1.15376			−0.111538			−0.0557692	−	0.998444i	$-0.517761\pi$
$107$	−1.15376			−0.111538			−0.0557692	+	0.998444i	$0.517761\pi$
$108$	−3.85054	−	9.65263i	−0.370518	−	0.928825i
$109$	1.77381			0.169900			0.0849501	−	0.996385i	$-0.472927\pi$
$109$	1.77381			0.169900			0.0849501	+	0.996385i	$0.472927\pi$
$110$	−1.82684	+	0.704225i	−0.174182	+	0.0671453i
$111$	2.06682	+	1.54645i	0.196174	+	0.146782i
$112$	−13.7711	−	1.36864i	−1.30125	−	0.129324i
$113$			16.8066i			1.58103i	0.612440	+	0.790517i	$0.290188\pi$
$113$			16.8066i			1.58103i	−0.612440	+	0.790517i	$0.709812\pi$
$114$	−16.0115	−	4.50780i	−1.49961	−	0.422194i
$115$		−	2.54649i		−	0.237461i
$116$	−3.14781	−	3.47616i	−0.292267	−	0.322753i
$117$	0.846536	+	2.87809i	0.0782623	+	0.266079i
$118$	2.08802	+	5.41656i	0.192218	+	0.498635i
$119$	4.18713			0.383833
$120$	4.38661	−	2.18120i	0.400441	−	0.199115i
$121$	−9.08336			−0.825760
$122$	−6.91437	−	17.9366i	−0.625998	−	1.62391i
$123$	9.87732	−	13.2010i	0.890608	−	1.19029i
$124$	4.06801	+	4.49235i	0.365318	+	0.403425i
$125$			1.00000i			0.0894427i
$126$	−8.92984	−	11.6497i	−0.795534	−	1.03783i
$127$			19.9650i			1.77161i	0.464061	+	0.885803i	$0.346392\pi$
$127$			19.9650i			1.77161i	−0.464061	+	0.885803i	$0.653608\pi$
$128$	6.06760	−	9.54905i	0.536305	−	0.844024i
$129$	4.98941	−	6.66831i	0.439293	−	0.587112i
$130$	−1.31956	+	0.508677i	−0.115733	+	0.0446139i
$131$	−10.3844			−0.907293			−0.453647	−	0.891182i	$-0.649877\pi$
$131$	−10.3844			−0.907293			−0.453647	+	0.891182i	$0.649877\pi$
$132$	−4.77485	+	0.447766i	−0.415597	+	0.0389730i
$133$	−23.4943			−2.03722
$134$	0.898503	−	0.346363i	0.0776188	−	0.0299212i
$135$	4.86980	+	1.81247i	0.419126	+	0.155993i
$136$	−1.54109	+	3.05656i	−0.132147	+	0.262098i
$137$			14.2655i			1.21878i	0.792871	+	0.609390i	$0.208586\pi$
$137$			14.2655i			1.21878i	−0.792871	+	0.609390i	$0.791414\pi$
$138$	1.69039	−	6.00418i	0.143895	−	0.511109i
$139$		−	14.1649i		−	1.20145i	−0.799456	−	0.600724i	$-0.794879\pi$
$139$		−	14.1649i		−	1.20145i	0.799456	−	0.600724i	$-0.205121\pi$
$140$	5.12905	−	4.64457i	0.433484	−	0.392538i
$141$	15.8200	+	11.8370i	1.33228	+	0.996851i
$142$	−0.151840	−	0.393889i	−0.0127421	−	0.0330544i
$143$	1.38443			0.115772
$144$	11.7908	−	2.23100i	0.982565	−	0.185917i
$145$	2.34480			0.194725
$146$	5.00450	+	12.9822i	0.414176	+	1.07442i
$147$	−6.89222	−	5.15695i	−0.568461	−	0.425338i
$148$	−2.20941	+	2.00071i	−0.181612	+	0.164457i
$149$		−	6.43749i		−	0.527380i	−0.964607	−	0.263690i	$-0.915060\pi$
$149$		−	6.43749i		−	0.527380i	0.964607	−	0.263690i	$-0.0849396\pi$
$150$	−0.663812	+	2.35783i	−0.0542000	+	0.192516i
$151$			11.4507i			0.931843i	0.884826	+	0.465922i	$0.154277\pi$
$151$			11.4507i			0.931843i	−0.884826	+	0.465922i	$0.845723\pi$
$152$	8.64716	−	17.1506i	0.701377	−	1.39110i
$153$	−3.48318	+	1.02451i	−0.281599	+	0.0828271i
$154$	−6.32039	+	2.43644i	−0.509311	+	0.196334i
$155$	−3.03026			−0.243396
$156$	−3.44897	+	0.323431i	−0.276139	+	0.0258952i
$157$	−16.7386			−1.33589			−0.667944	−	0.744211i	$-0.732826\pi$
$157$	−16.7386			−1.33589			−0.667944	+	0.744211i	$0.732826\pi$
$158$	−20.6045	+	7.94279i	−1.63920	+	0.631895i
$159$	−1.62035	+	2.16559i	−0.128502	+	0.171742i
$160$	1.50273	+	5.45361i	0.118801	+	0.431145i
$161$		−	8.81018i		−	0.694339i
$162$	10.2790	+	7.50613i	0.807595	+	0.589737i
$163$			19.6769i			1.54121i	0.637313	+	0.770605i	$0.280046\pi$
$163$			19.6769i			1.54121i	−0.637313	+	0.770605i	$0.719954\pi$
$164$	12.7787	+	14.1117i	0.997851	+	1.10194i
$165$	1.43656	−	1.91995i	0.111836	−	0.149468i
$166$	−0.115268	−	0.299017i	−0.00894651	−	0.0232082i
$167$	−11.3891			−0.881317			−0.440659	−	0.897675i	$-0.645255\pi$
$167$	−11.3891			−0.881317			−0.440659	+	0.897675i	$0.645255\pi$
$168$	15.1765	−	7.54638i	1.17090	−	0.582216i
$169$	1.00000			0.0769231
$170$	−0.615623	−	1.59699i	−0.0472161	−	0.122484i
$171$	19.5444	−	5.74864i	1.49460	−	0.439609i
$172$	6.45502	+	7.12835i	0.492191	+	0.543532i
$173$		−	20.6240i		−	1.56801i	−0.620753	−	0.784007i	$-0.713173\pi$
$173$		−	20.6240i		−	1.56801i	0.620753	−	0.784007i	$-0.286827\pi$
$174$	5.52864	+	1.55651i	0.419125	+	0.117999i
$175$			3.45974i			0.261532i
$176$	0.547665	−	5.51056i	0.0412818	−	0.415374i
$177$	−5.69264	−	4.25939i	−0.427885	−	0.320155i
$178$	21.8201	−	8.41139i	1.63548	−	0.630460i
$179$	9.70558			0.725429			0.362715	−	0.931900i	$-0.381850\pi$
$179$	9.70558			0.725429			0.362715	+	0.931900i	$0.381850\pi$
$180$	−3.13031	+	5.11871i	−0.233319	+	0.381526i
$181$	23.4173			1.74059			0.870296	−	0.492530i	$-0.163928\pi$
$181$	23.4173			1.74059			0.870296	+	0.492530i	$0.163928\pi$
$182$	−4.56535	+	1.75989i	−0.338406	+	0.130452i
$183$	18.8508	+	14.1047i	1.39349	+	1.04265i
$184$	6.43134	+	3.24262i	0.474125	+	0.239049i
$185$		−	1.49033i		−	0.109571i
$186$	−7.14484	−	2.01152i	−0.523885	−	0.147492i
$187$			1.67549i			0.122524i
$188$	−16.9114	+	15.3140i	−1.23339	+	1.11689i
$189$	16.8482	+	6.27068i	1.22553	+	0.456125i
$190$	3.45431	+	8.96086i	0.250602	+	0.650089i
$191$	19.1176			1.38330			0.691651	−	0.722232i	$-0.256884\pi$
$191$	19.1176			1.38330			0.691651	+	0.722232i	$0.256884\pi$
$192$	−0.0769961	+	13.8562i	−0.00555671	+	0.999985i
$193$	−10.3671			−0.746244			−0.373122	−	0.927782i	$-0.621713\pi$
$193$	−10.3671			−0.746244			−0.373122	+	0.927782i	$0.621713\pi$
$194$	5.60020	+	14.5276i	0.402071	+	1.04302i
$195$	1.03766	−	1.38682i	0.0743082	−	0.0993122i
$196$	7.36771	−	6.67177i	0.526265	−	0.476555i
$197$			15.7570i			1.12264i	0.827598	+	0.561321i	$0.189707\pi$
$197$			15.7570i			1.12264i	−0.827598	+	0.561321i	$0.810293\pi$
$198$	4.66165	−	3.57331i	0.331289	−	0.253944i
$199$		−	10.0605i		−	0.713170i	−0.934263	−	0.356585i	$-0.883941\pi$
$199$		−	10.0605i		−	0.713170i	0.934263	−	0.356585i	$-0.116059\pi$
$200$	−2.52558	−	1.27337i	−0.178585	−	0.0900408i
$201$	−0.706550	+	0.944298i	−0.0498362	+	0.0666057i
$202$	23.4634	−	9.04487i	1.65088	−	0.636395i
$203$	8.11241			0.569379
$204$	−0.391430	−	4.17409i	−0.0274056	−	0.292245i
$205$	−9.51887			−0.664827
$206$	3.34357	−	1.28891i	0.232957	−	0.0898023i
$207$	2.15569	+	7.32900i	0.149831	+	0.509401i
$208$	0.395589	−	3.98039i	0.0274292	−	0.275990i
$209$		−	9.40133i		−	0.650304i
$210$	−2.29662	+	8.15747i	−0.158482	+	0.562919i
$211$			19.6214i			1.35079i	0.737456	+	0.675395i	$0.236027\pi$
$211$			19.6214i			1.35079i	−0.737456	+	0.675395i	$0.763973\pi$
$212$	−2.09632	−	2.31499i	−0.143976	−	0.158994i
$213$	0.413964	+	0.309740i	0.0283644	+	0.0212230i
$214$	0.586891	+	1.52246i	0.0401191	+	0.104073i
$215$	−4.80835			−0.327926
$216$	−10.7786	+	9.99110i	−0.733390	+	0.679808i
$217$	−10.4839			−0.711695
$218$	−0.902296	−	2.34066i	−0.0611112	−	0.158529i
$219$	−13.6439	−	10.2088i	−0.921971	−	0.689844i
$220$	1.85854	+	2.05241i	0.125303	+	0.138373i
$221$			1.21024i			0.0814098i
$222$	0.989297	−	3.51394i	0.0663973	−	0.235840i
$223$			11.4776i			0.768598i	0.923209	+	0.384299i	$0.125557\pi$
$223$			11.4776i			0.768598i	−0.923209	+	0.384299i	$0.874443\pi$
$224$	5.19904	+	18.8681i	0.347376	+	1.26068i
$225$	−0.846536	−	2.87809i	−0.0564357	−	0.191872i
$226$	22.1774	−	8.54913i	1.47522	−	0.568680i
$227$	−6.06016			−0.402227			−0.201113	−	0.979568i	$-0.564456\pi$
$227$	−6.06016			−0.402227			−0.201113	+	0.979568i	$0.564456\pi$
$228$	2.19634	+	23.4212i	0.145456	+	1.55111i
$229$	8.00430			0.528939			0.264469	−	0.964394i	$-0.414803\pi$
$229$	8.00430			0.528939			0.264469	+	0.964394i	$0.414803\pi$
$230$	−3.36025	+	1.29534i	−0.221568	+	0.0854121i
$231$	4.97012	−	6.64253i	0.327010	−	0.437046i
$232$	−2.98580	+	5.92198i	−0.196027	+	0.388797i
$233$			9.96081i			0.652554i	0.945274	+	0.326277i	$0.105794\pi$
$233$			9.96081i			0.652554i	−0.945274	+	0.326277i	$0.894206\pi$
$234$	3.36720	−	2.58107i	0.220121	−	0.168730i
$235$		−	11.4074i		−	0.744136i
$236$	6.08537	−	5.51056i	0.396124	−	0.358707i
$237$	16.2026	−	21.6547i	1.05247	−	1.40662i
$238$	−2.12989	−	5.52518i	−0.138061	−	0.358144i
$239$	−3.19418			−0.206614			−0.103307	−	0.994649i	$-0.532942\pi$
$239$	−3.19418			−0.206614			−0.103307	+	0.994649i	$0.532942\pi$
$240$	−5.10960	−	4.67889i	−0.329823	−	0.302021i
$241$	5.12470			0.330111			0.165056	−	0.986284i	$-0.447220\pi$
$241$	5.12470			0.330111			0.165056	+	0.986284i	$0.447220\pi$
$242$	4.62049	+	11.9861i	0.297017	+	0.770494i
$243$	−15.5500	−	1.09399i	−0.997534	−	0.0701795i
$244$	−20.1514	+	18.2479i	−1.29006	+	1.16820i
$245$			4.96980i			0.317509i
$246$	−22.4439	−	6.31874i	−1.43097	−	0.402868i
$247$		−	6.79078i		−	0.432087i
$248$	3.85864	−	7.65315i	0.245024	−	0.485976i
$249$	0.314258	+	0.235136i	0.0199153	+	0.0149012i
$250$	1.31956	−	0.508677i	0.0834565	−	0.0321715i
$251$	−3.84674			−0.242804			−0.121402	−	0.992603i	$-0.538739\pi$
$251$	−3.84674			−0.242804			−0.121402	+	0.992603i	$0.538739\pi$
$252$	−10.8301	+	17.7094i	−0.682229	+	1.11559i
$253$	3.52542			0.221641
$254$	26.3451	−	10.1557i	1.65304	−	0.637227i
$255$	1.67839	+	1.25582i	0.105105	+	0.0786423i
$256$	−15.6870	−	3.14920i	−0.980439	−	0.196825i
$257$			0.131199i			0.00818398i	0.999992	+	0.00409199i	$0.00130252\pi$
$257$			0.131199i			0.00818398i	−0.999992	+	0.00409199i	$0.998697\pi$
$258$	−11.3373	−	3.19184i	−0.705827	−	0.198715i
$259$		−	5.15615i		−	0.320387i
$260$	1.34246	+	1.48250i	0.0832560	+	0.0919405i
$261$	−6.74854	+	1.98496i	−0.417724	+	0.122866i
$262$	5.28233	+	13.7029i	0.326343	+	0.846570i
$263$	−6.78828			−0.418583			−0.209292	−	0.977853i	$-0.567116\pi$
$263$	−6.78828			−0.418583			−0.209292	+	0.977853i	$0.567116\pi$
$264$	3.01971	+	6.07294i	0.185850	+	0.373764i
$265$	1.56155			0.0959252
$266$	11.9510	+	31.0023i	0.732764	+	1.90087i
$267$	−17.1585	+	22.9322i	−1.05008	+	1.40343i
$268$	−0.914095	−	1.00945i	−0.0558372	−	0.0616617i
$269$			4.80080i			0.292710i	0.989232	+	0.146355i	$0.0467542\pi$
$269$			4.80080i			0.292710i	−0.989232	+	0.146355i	$0.953246\pi$
$270$	−0.0854803	−	7.34797i	−0.00520217	−	0.447183i
$271$			5.15632i			0.313224i	0.987660	+	0.156612i	$0.0500572\pi$
$271$			5.15632i			0.313224i	−0.987660	+	0.156612i	$0.949943\pi$
$272$	4.81724	+	0.478760i	0.292088	+	0.0290291i
$273$	3.59002	−	4.79804i	0.217278	−	0.290390i
$274$	18.8242	−	7.25651i	1.13721	−	0.438382i
$275$	−1.38443			−0.0834841
$276$	−8.78275	+	0.823611i	−0.528660	+	0.0495756i
$277$	−15.2008			−0.913328			−0.456664	−	0.889639i	$-0.650956\pi$
$277$	−15.2008			−0.913328			−0.456664	+	0.889639i	$0.650956\pi$
$278$	−18.6915	+	7.20534i	−1.12104	+	0.432148i
$279$	8.72135	−	2.56523i	0.522134	−	0.153576i
$280$	−8.73784	−	4.40552i	−0.522186	−	0.263280i
$281$		−	8.54887i		−	0.509983i	−0.966943	−	0.254991i	$-0.917927\pi$
$281$		−	8.54887i		−	0.509983i	0.966943	−	0.254991i	$-0.0820726\pi$
$282$	7.57235	−	26.8967i	0.450927	−	1.60167i
$283$		−	4.72559i		−	0.280907i	−0.990087	−	0.140454i	$-0.955144\pi$
$283$		−	4.72559i		−	0.280907i	0.990087	−	0.140454i	$-0.0448561\pi$
$284$	−0.442524	+	0.400724i	−0.0262590	+	0.0237786i
$285$	−9.41758	−	7.04650i	−0.557849	−	0.417398i
$286$	−0.704225	−	1.82684i	−0.0416417	−	0.108023i
$287$	−32.9328			−1.94396
$288$	−8.94165	−	14.4238i	−0.526892	−	0.849932i
$289$	15.5353			0.913842
$290$	−1.19275	−	3.09412i	−0.0700405	−	0.181693i
$291$	−15.2680	−	11.4239i	−0.895026	−	0.669683i
$292$	14.5852	−	13.2075i	0.853535	−	0.772912i
$293$		−	2.09135i		−	0.122178i	−0.998132	−	0.0610890i	$-0.980543\pi$
$293$		−	2.09135i		−	0.122178i	0.998132	−	0.0610890i	$-0.0194574\pi$
$294$	−3.29901	+	11.7179i	−0.192402	+	0.683404i
$295$			4.10481i			0.238992i
$296$	3.76394	+	1.89774i	0.218774	+	0.110304i
$297$	−2.50924	+	6.74188i	−0.145601	+	0.391204i
$298$	−8.49468	+	3.27460i	−0.492084	+	0.189693i
$299$	2.54649			0.147267
$300$	3.44897	−	0.323431i	0.199126	−	0.0186733i
$301$	−16.6356			−0.958862
$302$	15.1099	−	5.82469i	0.869477	−	0.335174i
$303$	−18.4508	+	24.6593i	−1.05997	+	1.41664i
$304$	−27.0299	−	2.68636i	−1.55027	−	0.154073i
$305$		−	13.5929i		−	0.778325i
$306$	3.12373	+	4.07514i	0.178572	+	0.232960i
$307$		−	19.0109i		−	1.08501i	−0.840053	−	0.542504i	$-0.817476\pi$
$307$		−	19.0109i		−	1.08501i	0.840053	−	0.542504i	$-0.182524\pi$
$308$	6.43007	+	7.10080i	0.366387	+	0.404605i
$309$	−2.62926	+	3.51398i	−0.149573	+	0.199903i
$310$	1.54142	+	3.99862i	0.0875470	+	0.227106i
$311$	−4.52893			−0.256812			−0.128406	−	0.991722i	$-0.540986\pi$
$311$	−4.52893			−0.256812			−0.128406	+	0.991722i	$0.540986\pi$
$312$	2.18120	+	4.38661i	0.123486	+	0.248343i
$313$	3.80338			0.214980			0.107490	−	0.994206i	$-0.465719\pi$
$313$	3.80338			0.214980			0.107490	+	0.994206i	$0.465719\pi$
$314$	8.51455	+	22.0877i	0.480504	+	1.24648i
$315$	−2.92880	−	9.95743i	−0.165019	−	0.561038i
$316$	20.9620	+	23.1486i	1.17921	+	1.30221i
$317$		−	21.6248i		−	1.21457i	−0.794484	−	0.607285i	$-0.792259\pi$
$317$		−	21.6248i		−	1.21457i	0.794484	−	0.607285i	$-0.207741\pi$
$318$	3.68186	+	1.03657i	0.206469	+	0.0581282i
$319$			3.24621i			0.181753i
$320$	6.43198	−	4.75706i	0.359558	−	0.265928i
$321$	−1.60006	−	1.19721i	−0.0893066	−	0.0668217i
$322$	−11.6256	+	4.48153i	−0.647869	+	0.249746i
$323$	8.21849			0.457289
$324$	4.67612	−	17.3820i	0.259785	−	0.965667i
$325$	−1.00000			−0.0554700
$326$	25.9649	−	10.0092i	1.43806	−	0.554356i
$327$	2.45996	+	1.84061i	0.136036	+	0.101786i
$328$	12.1210	−	24.0406i	0.669272	−	1.32742i
$329$		−	39.4666i		−	2.17586i
$330$	−3.26424	−	0.918998i	−0.179691	−	0.0505892i
$331$			18.1376i			0.996933i	0.866909	+	0.498466i	$0.166103\pi$
$331$			18.1376i			0.996933i	−0.866909	+	0.498466i	$0.833897\pi$
$332$	−0.335938	+	0.304206i	−0.0184370	+	0.0166955i
$333$	1.26162	+	4.28929i	0.0691362	+	0.235052i
$334$	5.79338	+	15.0287i	0.317000	+	0.822333i
$335$	0.680909			0.0372020
$336$	−17.6779	−	16.1877i	−0.964407	−	0.883114i
$337$	24.8905			1.35587			0.677935	−	0.735122i	$-0.262875\pi$
$337$	24.8905			1.35587			0.677935	+	0.735122i	$0.262875\pi$
$338$	−0.508677	−	1.31956i	−0.0276684	−	0.0717748i
$339$	−17.4395	+	23.3077i	−0.947184	+	1.26590i
$340$	−1.79418	+	1.62471i	−0.0973031	+	0.0881121i
$341$		−	4.19517i		−	0.227181i
$342$	−17.5275	−	22.8659i	−0.947778	−	1.23645i
$343$		−	7.02395i		−	0.379258i
$344$	6.12280	−	12.1438i	0.330119	−	0.654752i
$345$	2.64238	−	3.53152i	0.142261	−	0.190130i
$346$	−27.2147	+	10.4909i	−1.46307	+	0.563997i
$347$	25.3104			1.35873			0.679367	−	0.733799i	$-0.262255\pi$
$347$	25.3104			1.35873			0.679367	+	0.733799i	$0.262255\pi$
$348$	−0.758381	−	8.08715i	−0.0406535	−	0.433517i
$349$	−5.74690			−0.307625			−0.153812	−	0.988100i	$-0.549155\pi$
$349$	−5.74690			−0.307625			−0.153812	+	0.988100i	$0.549155\pi$
$350$	4.56535	−	1.75989i	0.244028	−	0.0940700i
$351$	−1.81247	+	4.86980i	−0.0967426	+	0.259931i
$352$	−7.55012	+	2.08041i	−0.402423	+	0.110886i
$353$			14.9735i			0.796957i	0.917178	+	0.398479i	$0.130462\pi$
$353$			14.9735i			0.796957i	−0.917178	+	0.398479i	$0.869538\pi$
$354$	−2.72482	+	9.67845i	−0.144823	+	0.514404i
$355$		−	0.298499i		−	0.0158427i
$356$	−22.1987	−	24.5143i	−1.17653	−	1.29926i
$357$	5.80679	+	4.34480i	0.307328	+	0.229951i
$358$	−4.93700	−	12.8071i	−0.260929	−	0.676878i
$359$	−2.49644			−0.131757			−0.0658786	−	0.997828i	$-0.520985\pi$
$359$	−2.49644			−0.131757			−0.0658786	+	0.997828i	$0.520985\pi$
$360$	8.34678	+	1.52687i	0.439914	+	0.0804732i
$361$	−27.1146			−1.42709
$362$	−11.9118	−	30.9006i	−0.626071	−	1.62410i
$363$	−12.5970	−	9.42541i	−0.661170	−	0.494706i
$364$	4.64457	+	5.12905i	0.243442	+	0.268835i
$365$			9.83828i			0.514959i
$366$	9.02310	−	32.0496i	0.471645	−	1.67526i
$367$			20.6629i			1.07859i	0.842116	+	0.539296i	$0.181310\pi$
$367$			20.6629i			1.07859i	−0.842116	+	0.539296i	$0.818690\pi$
$368$	1.00736	−	10.1360i	0.0525124	−	0.528376i
$369$	27.3961	−	8.05807i	1.42619	−	0.419486i
$370$	−1.96658	+	0.758095i	−0.102238	+	0.0394115i
$371$	5.40255			0.280487
$372$	0.980079	+	10.4513i	0.0508147	+	0.541874i
$373$	26.3144			1.36251			0.681254	−	0.732048i	$-0.261435\pi$
$373$	26.3144			1.36251			0.681254	+	0.732048i	$0.261435\pi$
$374$	2.21092	−	0.852284i	0.114324	−	0.0440706i
$375$	−1.03766	+	1.38682i	−0.0535844	+	0.0716150i
$376$	28.8102	+	14.5258i	1.48577	+	0.749111i
$377$			2.34480i			0.120763i
$378$	−0.295740	−	25.4221i	−0.0152112	−	1.30757i
$379$		−	5.38855i		−	0.276791i	−0.990377	−	0.138396i	$-0.955805\pi$
$379$		−	5.38855i		−	0.276791i	0.990377	−	0.138396i	$-0.0441946\pi$
$380$	10.0673	−	9.11636i	0.516442	−	0.467660i
$381$	−20.7168	+	27.6878i	−1.06135	+	1.41849i
$382$	−9.72468	−	25.2269i	−0.497558	−	1.29072i
$383$	24.2343			1.23831			0.619156	−	0.785268i	$-0.287475\pi$
$383$	24.2343			1.23831			0.619156	+	0.785268i	$0.287475\pi$
$384$	18.3233	−	6.94672i	0.935057	−	0.354498i
$385$	−4.78976			−0.244109
$386$	5.27353	+	13.6801i	0.268415	+	0.696299i
$387$	13.8388	−	4.07044i	0.703467	−	0.206912i
$388$	16.3213	−	14.7797i	0.828590	−	0.750323i
$389$		−	29.3011i		−	1.48562i	−0.669500	−	0.742812i	$-0.733492\pi$
$389$		−	29.3011i		−	1.48562i	0.669500	−	0.742812i	$-0.266508\pi$
$390$	−2.35783	−	0.663812i	−0.119393	−	0.0336134i
$391$			3.08187i			0.155857i
$392$	−12.5516	−	6.32839i	−0.633952	−	0.319632i
$393$	−14.4014	−	10.7755i	−0.726452	−	0.543552i
$394$	20.7924	−	8.01524i	1.04751	−	0.403802i
$395$	−15.6146			−0.785657
$396$	−7.08648	−	4.33368i	−0.356109	−	0.217776i
$397$	−26.9542			−1.35279			−0.676395	−	0.736539i	$-0.736459\pi$
$397$	−26.9542			−1.35279			−0.676395	+	0.736539i	$0.736459\pi$
$398$	−13.2755	+	5.11754i	−0.665439	+	0.256519i
$399$	−32.5824	−	24.3790i	−1.63116	−	1.22048i
$400$	−0.395589	+	3.98039i	−0.0197795	+	0.199020i
$401$			7.92292i			0.395652i	0.980237	+	0.197826i	$0.0633880\pi$
$401$			7.92292i			0.395652i	−0.980237	+	0.197826i	$0.936612\pi$
$402$	1.60547	+	0.451995i	0.0800734	+	0.0225435i
$403$		−	3.03026i		−	0.150948i
$404$	−23.8706	−	26.3605i	−1.18761	−	1.31149i
$405$	4.87281	+	7.56675i	0.242132	+	0.375995i
$406$	−4.12659	−	10.7048i	−0.204799	−	0.531272i
$407$	2.06325			0.102272
$408$	−5.30887	+	2.63978i	−0.262828	+	0.130689i
$409$	1.73500			0.0857903			0.0428952	−	0.999080i	$-0.486342\pi$
$409$	1.73500			0.0857903			0.0428952	+	0.999080i	$0.486342\pi$
$410$	4.84203	+	12.5608i	0.239131	+	0.620332i
$411$	−14.8027	+	19.7836i	−0.730161	+	0.975854i
$412$	−3.40159	−	3.75641i	−0.167584	−	0.185065i
$413$			14.2016i			0.698815i
$414$	8.57454	−	6.57267i	0.421415	−	0.323029i
$415$		−	0.226603i		−	0.0111235i
$416$	−5.45361	+	1.50273i	−0.267385	+	0.0736772i
$417$	14.6983	−	19.6441i	0.719778	−	0.961977i
$418$	−12.4057	+	4.78224i	−0.606780	+	0.233907i
$419$	−32.7687			−1.60085			−0.800427	−	0.599430i	$-0.795394\pi$
$419$	−32.7687			−1.60085			−0.800427	+	0.599430i	$0.795394\pi$
$420$	11.9325	−	1.11899i	0.582248	−	0.0546009i
$421$	−34.1733			−1.66551			−0.832753	−	0.553644i	$-0.813237\pi$
$421$	−34.1733			−1.66551			−0.832753	+	0.553644i	$0.813237\pi$
$422$	25.8916	−	9.98093i	1.26038	−	0.485864i
$423$	9.65676	+	32.8314i	0.469528	+	1.59632i
$424$	−1.98843	+	3.94381i	−0.0965666	+	0.191528i
$425$		−	1.21024i		−	0.0587054i
$426$	0.198147	−	0.703810i	0.00960026	−	0.0340997i
$427$		−	47.0278i		−	2.27583i
$428$	1.71045	−	1.54888i	0.0826776	−	0.0748680i
$429$	1.91995	+	1.43656i	0.0926960	+	0.0693578i
$430$	2.44589	+	6.34492i	0.117951	+	0.305979i
$431$	−14.9069			−0.718039			−0.359020	−	0.933330i	$-0.616889\pi$
$431$	−14.9069			−0.718039			−0.359020	+	0.933330i	$0.616889\pi$
$432$	18.6667	+	9.14079i	0.898102	+	0.439786i
$433$	31.9487			1.53535			0.767677	−	0.640837i	$-0.221413\pi$
$433$	31.9487			1.53535			0.767677	+	0.640837i	$0.221413\pi$
$434$	5.33292	+	13.8342i	0.255989	+	0.664063i
$435$	3.25182	+	2.43310i	0.155913	+	0.116658i
$436$	−2.62967	+	2.38127i	−0.125938	+	0.114042i
$437$		−	17.2926i		−	0.827218i
$438$	−6.53076	+	23.1970i	−0.312052	+	1.10839i
$439$			5.95393i			0.284166i	0.989855	+	0.142083i	$0.0453800\pi$
$439$			5.95393i			0.284166i	−0.989855	+	0.142083i	$0.954620\pi$
$440$	1.76289	−	3.49647i	0.0840423	−	0.166688i
$441$	−4.20712	−	14.3035i	−0.200339	−	0.681120i
$442$	1.59699	−	0.615623i	0.0759612	−	0.0292822i
$443$	−20.4178			−0.970079			−0.485039	−	0.874492i	$-0.661195\pi$
$443$	−20.4178			−0.970079			−0.485039	+	0.874492i	$0.661195\pi$
$444$	−5.14010	+	0.482018i	−0.243938	+	0.0228755i
$445$	16.5358			0.783874
$446$	15.1454	−	5.83839i	0.717157	−	0.276456i
$447$	6.67991	−	8.92764i	0.315949	−	0.422263i
$448$	22.2530	−	16.4582i	1.05135	−	0.777577i
$449$		−	24.0219i		−	1.13366i	−0.823833	−	0.566832i	$-0.808169\pi$
$449$		−	24.0219i		−	1.13366i	0.823833	−	0.566832i	$-0.191831\pi$
$450$	−3.36720	+	2.58107i	−0.158732	+	0.121673i
$451$		−	13.1782i		−	0.620536i
$452$	−22.5623	−	24.9157i	−1.06124	−	1.17194i
$453$	−11.8819	+	15.8800i	−0.558259	+	0.746109i
$454$	3.08266	+	7.99676i	0.144676	+	0.375307i
$455$	−3.45974			−0.162195
$456$	29.7885	−	14.8120i	1.39497	−	0.693637i
$457$	−10.5052			−0.491413			−0.245706	−	0.969344i	$-0.579020\pi$
$457$	−10.5052			−0.491413			−0.245706	+	0.969344i	$0.579020\pi$
$458$	−4.07160	−	10.5622i	−0.190253	−	0.493538i
$459$	−5.89364	−	2.19353i	−0.275092	−	0.102385i
$460$	3.41856	+	3.77516i	0.159391	+	0.176018i
$461$		−	18.4543i		−	0.859501i	−0.902948	−	0.429750i	$-0.858602\pi$
$461$		−	18.4543i		−	0.859501i	0.902948	−	0.429750i	$-0.141398\pi$
$462$	−11.2934	−	3.17950i	−0.525418	−	0.147924i
$463$			10.1406i			0.471272i	0.971841	+	0.235636i	$0.0757173\pi$
$463$			10.1406i			0.471272i	−0.971841	+	0.235636i	$0.924283\pi$
$464$	9.33323	+	0.927579i	0.433284	+	0.0430618i
$465$	−4.20243	−	3.14437i	−0.194883	−	0.145817i
$466$	13.1439	−	5.06683i	0.608880	−	0.234716i
$467$	−22.5505			−1.04351			−0.521756	−	0.853094i	$-0.674723\pi$
$467$	−22.5505			−1.04351			−0.521756	+	0.853094i	$0.674723\pi$
$468$	−5.11871	−	3.13031i	−0.236612	−	0.144699i
$469$	2.35577			0.108779
$470$	−15.0528	+	5.80267i	−0.694332	+	0.267657i
$471$	−23.2135	−	17.3690i	−1.06962	−	0.800319i
$472$	−10.3670	−	5.22694i	−0.477181	−	0.240589i
$473$		−	6.65680i		−	0.306080i
$474$	−36.8166	−	10.3652i	−1.69104	−	0.476088i
$475$			6.79078i			0.311582i
$476$	−6.20740	+	5.62106i	−0.284516	+	0.257641i
$477$	−4.49427	+	1.32191i	−0.205779	+	0.0605260i
$478$	1.62481	+	4.21493i	0.0743169	+	0.192786i
$479$	31.5977			1.44374			0.721868	−	0.692030i	$-0.243284\pi$
$479$	31.5977			1.44374			0.721868	+	0.692030i	$0.243284\pi$
$480$	−3.57496	+	9.12248i	−0.163174	+	0.416382i
$481$	1.49033			0.0679531
$482$	−2.60682	−	6.76237i	−0.118737	−	0.308018i
$483$	9.14194	−	12.2181i	0.415973	−	0.555944i
$484$	13.4661	−	12.1941i	0.612093	−	0.554276i
$485$			11.0094i			0.499909i
$486$	6.46634	+	21.0757i	0.293319	+	0.956015i
$487$		−	6.55755i		−	0.297151i	−0.988901	−	0.148576i	$-0.952531\pi$
$487$		−	6.55755i		−	0.297151i	0.988901	−	0.148576i	$-0.0474688\pi$
$488$	34.3298	+	17.3087i	1.55404	+	0.783529i
$489$	−20.4178	+	27.2882i	−0.923326	+	1.23402i
$490$	6.55797	−	2.52802i	0.296259	−	0.114204i
$491$	34.3824			1.55166			0.775828	−	0.630944i	$-0.217332\pi$
$491$	34.3824			1.55166			0.775828	+	0.630944i	$0.217332\pi$
$492$	3.07869	+	32.8303i	0.138798	+	1.48010i
$493$	−2.83778			−0.127807
$494$	−8.96086	+	3.45431i	−0.403168	+	0.155417i
$495$	3.98450	−	1.17197i	0.179090	−	0.0526760i
$496$	−12.0616	−	1.19874i	−0.541583	−	0.0538250i
$497$		−	1.03273i		−	0.0463242i
$498$	0.150422	−	0.534291i	0.00674056	−	0.0239422i
$499$		−	26.6127i		−	1.19135i	−0.803226	−	0.595674i	$-0.796885\pi$
$499$		−	26.6127i		−	1.19135i	0.803226	−	0.595674i	$-0.203115\pi$
$500$	−1.34246	−	1.48250i	−0.0600367	−	0.0662992i
$501$	−15.7947	−	11.8180i	−0.705654	−	0.527990i
$502$	1.95675	+	5.07602i	0.0873339	+	0.226554i
$503$	−41.1702			−1.83569			−0.917844	−	0.396942i	$-0.870071\pi$
$503$	−41.1702			−1.83569			−0.917844	+	0.396942i	$0.870071\pi$
$504$	28.8777	+	5.28258i	1.28631	+	0.235305i
$505$	17.7812			0.791252
$506$	−1.79330	−	4.65202i	−0.0797219	−	0.206807i
$507$	1.38682	+	1.03766i	0.0615908	+	0.0460840i
$508$	−26.8023	−	29.5980i	−1.18916	−	1.31320i
$509$			12.3953i			0.549411i	0.961528	+	0.274706i	$0.0885804\pi$
$509$			12.3953i			0.549411i	−0.961528	+	0.274706i	$0.911420\pi$
$510$	0.803374	−	2.85355i	0.0355740	−	0.126357i
$511$			34.0379i			1.50575i
$512$	3.82405	+	22.3019i	0.169001	+	0.985616i
$513$	33.0697	+	12.3081i	1.46006	+	0.543416i
$514$	0.173126	−	0.0667379i	0.00763624	−	0.00294368i
$515$	2.53384			0.111654
$516$	1.55517	+	16.5838i	0.0684624	+	0.730063i
$517$	15.7927			0.694562
$518$	−6.80387	+	2.62281i	−0.298945	+	0.115240i
$519$	21.4006	−	28.6018i	0.939383	−	1.25548i
$520$	1.27337	−	2.52558i	0.0558409	−	0.110754i
$521$			21.1537i			0.926759i	0.886160	+	0.463379i	$0.153363\pi$
$521$			21.1537i			0.926759i	−0.886160	+	0.463379i	$0.846637\pi$
$522$	6.05211	+	7.89543i	0.264894	+	0.345573i
$523$			8.16325i			0.356954i	0.983944	+	0.178477i	$0.0571170\pi$
$523$			8.16325i			0.356954i	−0.983944	+	0.178477i	$0.942883\pi$
$524$	15.3949	−	13.9407i	0.672529	−	0.609004i
$525$	−3.59002	+	4.79804i	−0.156681	+	0.209403i
$526$	3.45304	+	8.95757i	0.150560	+	0.390569i
$527$	3.66735			0.159752
$528$	6.47758	−	7.07386i	0.281901	−	0.307850i
$529$	−16.5154			−0.718061
$530$	−0.794323	−	2.06056i	−0.0345032	−	0.0895051i
$531$	−3.47487	−	11.8140i	−0.150797	−	0.512684i
$532$	34.8302	−	31.5402i	1.51008	−	1.36744i
$533$		−	9.51887i		−	0.412308i
$534$	38.9886	+	10.9767i	1.68720	+	0.475007i
$535$			1.15376i			0.0498814i
$536$	−0.867048	+	1.71969i	−0.0374508	+	0.0742792i
$537$	13.4599	+	10.0711i	0.580837	+	0.434599i
$538$	6.33497	−	2.44206i	0.273120	−	0.105285i
$539$	−6.88033			−0.296357
$540$	−9.65263	+	3.85054i	−0.415383	+	0.165701i
$541$	13.0239			0.559940			0.279970	−	0.960009i	$-0.409676\pi$
$541$	13.0239			0.559940			0.279970	+	0.960009i	$0.409676\pi$
$542$	6.80409	−	2.62290i	0.292261	−	0.112663i
$543$	32.4755	+	24.2991i	1.39366	+	1.04277i
$544$	−1.81866	−	6.60019i	−0.0779746	−	0.282981i
$545$		−	1.77381i		−	0.0759817i
$546$	−8.15747	−	2.29662i	−0.349108	−	0.0982861i
$547$			14.9421i			0.638879i	0.947607	+	0.319439i	$0.103495\pi$
$547$			14.9421i			0.638879i	−0.947607	+	0.319439i	$0.896505\pi$
$548$	−19.1508	−	21.1485i	−0.818083	−	0.903419i
$549$	11.5068	+	39.1214i	0.491100	+	1.66966i
$550$	0.704225	+	1.82684i	0.0300283	+	0.0778967i
$551$	15.9230			0.678344
$552$	5.55439	+	11.1704i	0.236410	+	0.475446i
$553$	−54.0225			−2.29727
$554$	7.73229	+	20.0584i	0.328514	+	0.852201i
$555$	1.54645	−	2.06682i	0.0656431	−	0.0877315i
$556$	19.0158	+	20.9994i	0.806450	+	0.890572i
$557$			0.583745i			0.0247341i	0.999924	+	0.0123670i	$0.00393665\pi$
$557$			0.583745i			0.0247341i	−0.999924	+	0.0123670i	$0.996063\pi$
$558$	−7.82133	−	10.2035i	−0.331103	−	0.431949i
$559$		−	4.80835i		−	0.203371i
$560$	−1.36864	+	13.7711i	−0.0578355	+	0.581936i
$561$	−1.73859	+	2.32361i	−0.0734032	+	0.0981027i
$562$	−11.2808	+	4.34861i	−0.475851	+	0.183435i
$563$	15.0216			0.633083			0.316542	−	0.948579i	$-0.397478\pi$
$563$	15.0216			0.633083			0.316542	+	0.948579i	$0.397478\pi$
$564$	−39.3437	+	3.68950i	−1.65667	+	0.155356i
$565$	16.8066			0.707060
$566$	−6.23572	+	2.40380i	−0.262107	+	0.101039i
$567$	16.8586	+	26.1790i	0.707997	+	1.09941i
$568$	0.753882	+	0.380099i	0.0316322	+	0.0159486i
$569$		−	7.67267i		−	0.321655i	−0.986983	−	0.160828i	$-0.948584\pi$
$569$		−	7.67267i		−	0.321655i	0.986983	−	0.160828i	$-0.0514163\pi$
$570$	−4.50780	+	16.0115i	−0.188811	+	0.670647i
$571$		−	1.58334i		−	0.0662608i	−0.999451	−	0.0331304i	$-0.989452\pi$
$571$		−	1.58334i		−	0.0662608i	0.999451	−	0.0331304i	$-0.0105477\pi$
$572$	−2.05241	+	1.85854i	−0.0858154	+	0.0777095i
$573$	26.5127	+	19.8375i	1.10758	+	0.828724i
$574$	16.7522	+	43.4570i	0.699222	+	1.81386i
$575$	−2.54649			−0.106196
$576$	−14.4848	+	19.1361i	−0.603531	+	0.797339i
$577$	27.4884			1.14436			0.572178	−	0.820129i	$-0.306099\pi$
$577$	27.4884			1.14436			0.572178	+	0.820129i	$0.306099\pi$
$578$	−7.90245	−	20.4998i	−0.328699	−	0.852681i
$579$	−14.3774	−	10.7575i	−0.597503	−	0.447068i
$580$	−3.47616	+	3.14781i	−0.144340	+	0.130706i
$581$		−	0.783988i		−	0.0325253i
$582$	−7.30814	+	25.9582i	−0.302932	+	1.07600i
$583$			2.16185i			0.0895347i
$584$	−24.8473	−	12.5278i	−1.02819	−	0.518402i
$585$	2.87809	−	0.846536i	0.118994	−	0.0350000i
$586$	−2.75967	+	1.06382i	−0.114001	+	0.0439461i
$587$	0.657644			0.0271439			0.0135719	−	0.999908i	$-0.495680\pi$
$587$	0.657644			0.0271439			0.0135719	+	0.999908i	$0.495680\pi$
$588$	17.1407	−	1.60739i	0.706871	−	0.0662875i
$589$	−20.5778			−0.847895
$590$	5.41656	−	2.08802i	0.222996	−	0.0859625i
$591$	−16.3504	+	21.8522i	−0.672566	+	0.898878i
$592$	0.589558	−	5.93209i	0.0242307	−	0.243807i
$593$			20.3317i			0.834924i	0.908694	+	0.417462i	$0.137080\pi$
$593$			20.3317i			0.834924i	−0.908694	+	0.417462i	$0.862920\pi$
$594$	10.1727	−	0.118341i	0.417392	−	0.00485560i
$595$		−	4.18713i		−	0.171656i
$596$	8.64209	+	9.54356i	0.353994	+	0.390919i
$597$	10.4393	−	13.9521i	0.427254	−	0.571021i
$598$	−1.29534	−	3.36025i	−0.0529703	−	0.137411i
$599$	−39.1001			−1.59759			−0.798793	−	0.601606i	$-0.794528\pi$
$599$	−39.1001			−1.59759			−0.798793	+	0.601606i	$0.794528\pi$
$600$	−2.18120	−	4.38661i	−0.0890470	−	0.179083i
$601$	−13.8806			−0.566201			−0.283101	−	0.959090i	$-0.591363\pi$
$601$	−13.8806			−0.566201			−0.283101	+	0.959090i	$0.591363\pi$
$602$	8.46216	+	21.9518i	0.344892	+	0.894687i
$603$	−1.95971	+	0.576414i	−0.0798058	+	0.0234734i
$604$	−15.3721	−	16.9756i	−0.625482	−	0.690727i
$605$			9.08336i			0.369291i
$606$	41.9250	+	11.8034i	1.70309	+	0.479479i
$607$			4.70639i			0.191027i	0.995428	+	0.0955133i	$0.0304493\pi$
$607$			4.70639i			0.191027i	−0.995428	+	0.0955133i	$0.969551\pi$
$608$	10.2047	+	37.0342i	0.413854	+	1.50194i
$609$	11.2504	+	8.41790i	0.455891	+	0.341110i
$610$	−17.9366	+	6.91437i	−0.726233	+	0.279955i
$611$	11.4074			0.461493
$612$	3.78843	−	6.19488i	0.153138	−	0.250413i
$613$	2.92569			0.118168			0.0590838	−	0.998253i	$-0.481182\pi$
$613$	2.92569			0.118168			0.0590838	+	0.998253i	$0.481182\pi$
$614$	−25.0861	+	9.67039i	−1.01239	+	0.390265i
$615$	−13.2010	−	9.87732i	−0.532314	−	0.398292i
$616$	6.09913	−	12.0969i	0.245741	−	0.487398i
$617$			48.3497i			1.94648i	0.229782	+	0.973242i	$0.426199\pi$
$617$			48.3497i			1.94648i	−0.229782	+	0.973242i	$0.573801\pi$
$618$	5.97436	+	1.68199i	0.240324	+	0.0676597i
$619$		−	47.6933i		−	1.91696i	−0.285165	−	0.958478i	$-0.592048\pi$
$619$		−	47.6933i		−	1.91696i	0.285165	−	0.958478i	$-0.407952\pi$
$620$	4.49235	−	4.06801i	0.180417	−	0.163375i
$621$	−4.61544	+	12.4009i	−0.185211	+	0.497630i
$622$	2.30376	+	5.97621i	0.0923724	+	0.239624i
$623$	57.2097			2.29206
$624$	4.67889	−	5.10960i	0.187306	−	0.204548i
$625$	1.00000			0.0400000
$626$	−1.93469	−	5.01880i	−0.0773258	−	0.200592i
$627$	9.75536	−	13.0379i	0.389591	−	0.520686i
$628$	24.8150	−	22.4710i	0.990225	−	0.896690i
$629$			1.80366i			0.0719166i
$630$	−11.6497	+	8.92984i	−0.464133	+	0.355773i
$631$			18.4310i			0.733725i	0.930275	+	0.366862i	$0.119568\pi$
$631$			18.4310i			0.733725i	−0.930275	+	0.366862i	$0.880432\pi$
$632$	19.8832	−	39.4359i	0.790910	−	1.56868i
$633$	−20.3602	+	27.2113i	−0.809247	+	1.08155i
$634$	−28.5353	+	11.0000i	−1.13328	+	0.436867i
$635$	19.9650			0.792287
$636$	−0.505053	−	5.38573i	−0.0200266	−	0.213558i
$637$	−4.96980			−0.196911
$638$	4.28358	−	1.65127i	0.169588	−	0.0653744i
$639$	0.252690	+	0.859106i	0.00999627	+	0.0339857i
$640$	−9.54905	−	6.06760i	−0.377459	−	0.239843i
$641$			15.4544i			0.610410i	0.952287	+	0.305205i	$0.0987250\pi$
$641$			15.4544i			0.610410i	−0.952287	+	0.305205i	$0.901275\pi$
$642$	−0.765880	+	2.72037i	−0.0302269	+	0.107364i
$643$			13.3360i			0.525921i	0.964807	+	0.262961i	$0.0846990\pi$
$643$			13.3360i			0.525921i	−0.964807	+	0.262961i	$0.915301\pi$
$644$	11.8273	+	13.0611i	0.466062	+	0.514678i
$645$	−6.66831	−	4.98941i	−0.262564	−	0.196458i
$646$	−4.18056	−	10.8448i	−0.164482	−	0.426684i
$647$	1.36586			0.0536974			0.0268487	−	0.999640i	$-0.491453\pi$
$647$	1.36586			0.0536974			0.0268487	+	0.999640i	$0.491453\pi$
$648$	−25.3153	+	2.67138i	−0.994478	+	0.104942i
$649$	−5.68281			−0.223070
$650$	0.508677	+	1.31956i	0.0199519	+	0.0517575i
$651$	−14.5393	−	10.8787i	−0.569840	−	0.426370i
$652$	−26.4154	−	29.1709i	−1.03451	−	1.14242i
$653$		−	47.7854i		−	1.86999i	−0.354662	−	0.934994i	$-0.615404\pi$
$653$		−	47.7854i		−	1.86999i	0.354662	−	0.934994i	$-0.384596\pi$
$654$	1.17748	−	4.18234i	0.0460430	−	0.163542i
$655$			10.3844i			0.405754i
$656$	−37.8888	−	3.76557i	−1.47931	−	0.147021i
$657$	−8.32846	−	28.3154i	−0.324924	−	1.10469i
$658$	−52.0787	+	20.0757i	−2.03024	+	0.782634i
$659$	−10.6354			−0.414296			−0.207148	−	0.978310i	$-0.566418\pi$
$659$	−10.6354			−0.414296			−0.207148	+	0.978310i	$0.566418\pi$
$660$	0.447766	+	4.77485i	0.0174293	+	0.185861i
$661$	41.2265			1.60353			0.801763	−	0.597642i	$-0.203896\pi$
$661$	41.2265			1.60353			0.801763	+	0.597642i	$0.203896\pi$
$662$	23.9337	−	9.22617i	0.930210	−	0.358585i
$663$	−1.25582	+	1.67839i	−0.0487719	+	0.0651832i
$664$	0.572303	+	0.288549i	0.0222097	+	0.0111979i
$665$			23.4943i			0.911071i
$666$	5.01824	−	3.84665i	0.194453	−	0.149055i
$667$			5.97101i			0.231198i
$668$	16.8843	−	15.2895i	0.653275	−	0.591568i
$669$	−11.9098	+	15.9174i	−0.460460	+	0.615401i
$670$	−0.346363	−	0.898503i	−0.0133812	−	0.0347122i
$671$	18.8183			0.726473
$672$	−12.3684	+	31.5614i	−0.477123	+	1.21751i
$673$	17.8034			0.686271			0.343136	−	0.939286i	$-0.388511\pi$
$673$	17.8034			0.686271			0.343136	+	0.939286i	$0.388511\pi$
$674$	−12.6612	−	32.8446i	−0.487691	−	1.26513i
$675$	1.81247	−	4.86980i	0.0697621	−	0.187439i
$676$	−1.48250	+	1.34246i	−0.0570191	+	0.0516332i
$677$			14.7237i			0.565879i	0.959138	+	0.282939i	$0.0913095\pi$
$677$			14.7237i			0.565879i	−0.959138	+	0.282939i	$0.908690\pi$
$678$	39.6271	+	11.1564i	1.52187	+	0.428460i
$679$			38.0895i			1.46174i
$680$	3.05656	+	1.54109i	0.117214	+	0.0590979i
$681$	−8.40434	−	6.28836i	−0.322055	−	0.240971i
$682$	−5.53580	+	2.13399i	−0.211977	+	0.0817146i
$683$	−42.3586			−1.62081			−0.810403	−	0.585872i	$-0.800752\pi$
$683$	−42.3586			−1.62081			−0.810403	+	0.585872i	$0.800752\pi$
$684$	−21.2572	+	34.7600i	−0.812790	+	1.32908i
$685$	14.2655			0.545055
$686$	−9.26855	+	3.57292i	−0.353875	+	0.136415i
$687$	11.1005	+	8.30572i	0.423511	+	0.316883i
$688$	−19.1391	−	1.90213i	−0.729671	−	0.0725181i
$689$			1.56155i			0.0594903i
$690$	−6.00418	−	1.69039i	−0.228575	−	0.0643519i
$691$		−	0.957665i		−	0.0364313i	−0.999834	−	0.0182157i	$-0.994201\pi$
$691$		−	0.957665i		−	0.0364313i	0.999834	−	0.0182157i	$-0.00579854\pi$
$692$	27.6869	+	30.5750i	1.05250	+	1.16229i
$693$	13.7853	−	4.05470i	0.523661	−	0.154025i
$694$	−12.8748	−	33.3987i	−0.488721	−	1.26780i
$695$	−14.1649			−0.537304
$696$	−10.2857	+	5.11448i	−0.389880	+	0.193864i
$697$	11.5202			0.436357
$698$	2.92331	+	7.58340i	0.110649	+	0.287036i
$699$	−10.3359	+	13.8138i	−0.390940	+	0.522487i
$700$	−4.64457	−	5.12905i	−0.175548	−	0.193860i
$701$		−	40.9138i		−	1.54529i	−0.634836	−	0.772647i	$-0.718932\pi$
$701$		−	40.9138i		−	1.54529i	0.634836	−	0.772647i	$-0.281068\pi$
$702$	7.34797	−	0.0854803i	0.277331	−	0.00322625i
$703$		−	10.1205i		−	0.381701i
$704$	6.58581	+	8.90460i	0.248212	+	0.335605i
$705$	11.8370	−	15.8200i	0.445805	−	0.595815i
$706$	19.7584	−	7.61665i	0.743619	−	0.286657i
$707$	61.5183			2.31363
$708$	14.1574	−	1.32762i	0.532067	−	0.0498951i
$709$	−51.6170			−1.93852			−0.969259	−	0.246041i	$-0.920870\pi$
$709$	−51.6170			−1.93852			−0.969259	+	0.246041i	$0.920870\pi$
$710$	−0.393889	+	0.151840i	−0.0147824	+	0.00569844i
$711$	44.9402	−	13.2183i	1.68539	−	0.495726i
$712$	−21.0562	+	41.7625i	−0.789115	+	1.56512i
$713$		−	7.71652i		−	0.288986i
$714$	2.77946	−	9.87253i	0.104019	−	0.369470i
$715$		−	1.38443i		−	0.0517746i
$716$	−14.3885	+	13.0294i	−0.537723	+	0.486931i
$717$	−4.42975	−	3.31447i	−0.165432	−	0.123781i
$718$	1.26988	+	3.29421i	0.0473916	+	0.122939i
$719$	32.5567			1.21416			0.607079	−	0.794641i	$-0.292341\pi$
$719$	32.5567			1.21416			0.607079	+	0.794641i	$0.292341\pi$
$720$	−2.23100	−	11.7908i	−0.0831446	−	0.439417i
$721$	8.76643			0.326479
$722$	13.7926	+	35.7795i	0.513307	+	1.33158i
$723$	7.10704	+	5.31768i	0.264314	+	0.197767i
$724$	−34.7160	+	31.4368i	−1.29021	+	1.16834i
$725$		−	2.34480i		−	0.0870838i
$726$	−6.02964	+	21.4170i	−0.223781	+	0.794860i
$727$		−	42.4585i		−	1.57470i	−0.616508	−	0.787349i	$-0.711453\pi$
$727$		−	42.4585i		−	1.57470i	0.616508	−	0.787349i	$-0.288547\pi$
$728$	4.40552	−	8.73784i	0.163280	−	0.323846i
$729$	−20.4299	−	17.6528i	−0.756662	−	0.653806i
$730$	12.9822	−	5.00450i	0.480494	−	0.185225i
$731$	5.81927			0.215233
$732$	−46.8814	+	4.39635i	−1.73279	+	0.162494i
$733$	−17.0969			−0.631490			−0.315745	−	0.948844i	$-0.602254\pi$
$733$	−17.0969			−0.631490			−0.315745	+	0.948844i	$0.602254\pi$
$734$	27.2660	−	10.5107i	1.00641	−	0.387958i
$735$	−5.15695	+	6.89222i	−0.190217	+	0.254223i
$736$	−13.8875	+	3.82667i	−0.511901	+	0.141053i
$737$			0.942669i			0.0347237i
$738$	−24.5689	−	32.0520i	−0.904394	−	1.17985i
$739$			20.0613i			0.737966i	0.929436	+	0.368983i	$0.120294\pi$
$739$			20.0613i			0.737966i	−0.929436	+	0.368983i	$0.879706\pi$
$740$	2.00071	+	2.20941i	0.0735475	+	0.0812194i
$741$	7.04650	−	9.41758i	0.258860	−	0.345963i
$742$	−2.74815	−	7.12901i	−0.100888	−	0.261714i
$743$	46.9323			1.72178			0.860889	−	0.508792i	$-0.169908\pi$
$743$	46.9323			1.72178			0.860889	+	0.508792i	$0.169908\pi$
$744$	13.2926	−	6.60960i	0.487330	−	0.242320i
$745$	−6.43749			−0.235851
$746$	−13.3855	−	34.7235i	−0.490078	−	1.27132i
$747$	0.191828	+	0.652183i	0.00701861	+	0.0238621i
$748$	−2.24929	−	2.48391i	−0.0822421	−	0.0908208i
$749$			3.99171i			0.145854i
$750$	2.35783	+	0.663812i	0.0860957	+	0.0242390i
$751$		−	48.2466i		−	1.76055i	−0.474468	−	0.880273i	$-0.657360\pi$
$751$		−	48.2466i		−	1.76055i	0.474468	−	0.880273i	$-0.342640\pi$
$752$	4.51264	−	45.4058i	0.164559	−	1.65578i
$753$	−5.33473	−	3.99160i	−0.194409	−	0.145462i
$754$	3.09412	−	1.19275i	0.112681	−	0.0434373i
$755$	11.4507			0.416733
$756$	−33.3956	+	13.3219i	−1.21459	+	0.484512i
$757$	13.1637			0.478444			0.239222	−	0.970965i	$-0.423108\pi$
$757$	13.1637			0.478444			0.239222	+	0.970965i	$0.423108\pi$
$758$	−7.11054	+	2.74103i	−0.258266	+	0.0995588i
$759$	4.88912	+	3.65818i	0.177464	+	0.132783i
$760$	−17.1506	−	8.64716i	−0.622118	−	0.313666i
$761$		−	25.9221i		−	0.939674i	−0.882753	−	0.469837i	$-0.844313\pi$
$761$		−	25.9221i		−	0.939674i	0.882753	−	0.469837i	$-0.155687\pi$
$762$	47.0740	+	13.2530i	1.70531	+	0.480105i
$763$		−	6.13693i		−	0.222172i
$764$	−28.3418	+	25.6647i	−1.02537	+	0.928515i
$765$	1.02451	+	3.48318i	0.0370414	+	0.125935i
$766$	−12.3274	−	31.9786i	−0.445407	−	1.15544i
$767$	−4.10481			−0.148216
$768$	−18.4873	−	20.6451i	−0.667102	−	0.744966i
$769$	34.1109			1.23007			0.615035	−	0.788500i	$-0.289142\pi$
$769$	34.1109			1.23007			0.615035	+	0.788500i	$0.289142\pi$
$770$	2.43644	+	6.32039i	0.0878031	+	0.227771i
$771$	−0.136140	+	0.181950i	−0.00490295	+	0.00655275i
$772$	15.3693	−	13.9175i	0.553152	−	0.500902i
$773$		−	1.46514i		−	0.0526974i	−0.999653	−	0.0263487i	$-0.991612\pi$
$773$		−	1.46514i		−	0.0526974i	0.999653	−	0.0263487i	$-0.00838802\pi$
$774$	−12.4107	−	16.1907i	−0.446093	−	0.581962i
$775$			3.03026i			0.108850i
$776$	−27.8050	−	14.0190i	−0.998140	−	0.503252i
$777$	5.35031	−	7.15065i	0.191941	−	0.256528i
$778$	−38.6646	+	14.9048i	−1.38619	+	0.534362i
$779$	−64.6405			−2.31599
$780$	0.323431	+	3.44897i	0.0115807	+	0.123493i
$781$	0.413250			0.0147873
$782$	4.06672	−	1.56767i	0.145426	−	0.0560599i
$783$	−11.4187	−	4.24989i	−0.408072	−	0.151879i
$784$	−1.96600	+	19.7818i	−0.0702144	+	0.706491i
$785$			16.7386i			0.597427i
$786$	−6.89332	+	24.4847i	−0.245876	+	0.873342i
$787$		−	23.5966i		−	0.841130i	−0.907262	−	0.420565i	$-0.861832\pi$
$787$		−	23.5966i		−	0.841130i	0.907262	−	0.420565i	$-0.138168\pi$
$788$	−21.1532	−	23.3597i	−0.753553	−	0.832157i
$789$	−9.41412	−	7.04391i	−0.335152	−	0.250770i
$790$	7.94279	+	20.6045i	0.282592	+	0.733075i
$791$	58.1465			2.06745
$792$	−2.11384	+	11.5555i	−0.0751121	+	0.410607i
$793$	13.5929			0.482697
$794$	13.7109	+	35.5677i	0.486583	+	1.26225i
$795$	2.16559	+	1.62035i	0.0768054	+	0.0574680i
$796$	13.5058	+	14.9147i	0.478702	+	0.528636i
$797$		−	0.986693i		−	0.0349505i	−0.999847	−	0.0174752i	$-0.994437\pi$
$797$		−	0.986693i		−	0.0349505i	0.999847	−	0.0174752i	$-0.00556282\pi$
$798$	−15.5958	+	55.3956i	−0.552086	+	1.96098i
$799$			13.8057i			0.488411i
$800$	5.45361	−	1.50273i	0.192814	−	0.0531294i
$801$	−47.5915	+	13.9982i	−1.68156	+	0.494601i
$802$	10.4548	−	4.03020i	0.369172	−	0.142311i
$803$	−13.6204			−0.480653
$804$	−0.220227	−	2.34844i	−0.00776680	−	0.0828229i
$805$	−8.81018			−0.310518
$806$	−3.99862	+	1.54142i	−0.140845	+	0.0542943i
$807$	−4.98159	+	6.65785i	−0.175360	+	0.234367i
$808$	−22.6420	+	44.9077i	−0.796543	+	1.57985i
$809$			17.7059i			0.622505i	0.950327	+	0.311253i	$0.100749\pi$
$809$			17.7059i			0.622505i	−0.950327	+	0.311253i	$0.899251\pi$
$810$	7.50613	−	10.2790i	0.263738	−	0.361168i
$811$		−	40.4250i		−	1.41951i	−0.704447	−	0.709756i	$-0.748805\pi$
$811$		−	40.4250i		−	1.41951i	0.704447	−	0.709756i	$-0.251195\pi$
$812$	−12.0266	+	10.8906i	−0.422051	+	0.382185i
$813$	−5.35049	+	7.15088i	−0.187650	+	0.250792i
$814$	−1.04953	−	2.72259i	−0.0367859	−	0.0954267i
$815$	19.6769			0.689250
$816$	6.18386	+	5.66260i	0.216478	+	0.198231i
$817$	−32.6524			−1.14236
$818$	−0.882555	−	2.28945i	−0.0308578	−	0.0800486i
$819$	9.95743	−	2.92880i	0.347941	−	0.102340i
$820$	14.1117	−	12.7787i	0.492802	−	0.446253i
$821$		−	5.04075i		−	0.175924i	−0.996124	−	0.0879618i	$-0.971965\pi$
$821$		−	5.04075i		−	0.175924i	0.996124	−	0.0879618i	$-0.0280353\pi$
$822$	33.6355	+	9.46958i	1.17317	+	0.330289i
$823$			3.19720i			0.111447i	0.998446	+	0.0557237i	$0.0177466\pi$
$823$			3.19720i			0.111447i	−0.998446	+	0.0557237i	$0.982253\pi$
$824$	−3.22651	+	6.39941i	−0.112401	+	0.222934i
$825$	−1.91995	−	1.43656i	−0.0668441	−	0.0500146i
$826$	18.7399	−	7.22402i	0.652045	−	0.251356i
$827$	40.1178			1.39503			0.697516	−	0.716569i	$-0.254289\pi$
$827$	40.1178			1.39503			0.697516	+	0.716569i	$0.254289\pi$
$828$	−13.0347	−	7.97128i	−0.452988	−	0.277021i
$829$	−5.12888			−0.178133			−0.0890667	−	0.996026i	$-0.528388\pi$
$829$	−5.12888			−0.178133			−0.0890667	+	0.996026i	$0.528388\pi$
$830$	−0.299017	+	0.115268i	−0.0103790	+	0.00400100i
$831$	−21.0808	−	15.7732i	−0.731284	−	0.547167i
$832$	4.75706	+	6.43198i	0.164922	+	0.222989i
$833$		−	6.01467i		−	0.208396i
$834$	−33.3983	−	9.40281i	−1.15649	−	0.325593i
$835$			11.3891i			0.394137i
$836$	12.6209	+	13.9374i	0.436504	+	0.482036i
$837$	14.7568	+	5.49227i	0.510068	+	0.189840i
$838$	16.6687	+	43.2403i	0.575809	+	1.49371i
$839$	14.8385			0.512283			0.256142	−	0.966639i	$-0.417549\pi$
$839$	14.8385			0.512283			0.256142	+	0.966639i	$0.417549\pi$
$840$	−7.54638	−	15.1765i	−0.260375	−	0.523641i
$841$	23.5019			0.810410
$842$	17.3832	+	45.0939i	0.599064	+	1.55404i
$843$	8.87079	−	11.8557i	0.305526	−	0.408333i
$844$	−26.3409	−	29.0886i	−0.906692	−	1.00127i
$845$		−	1.00000i		−	0.0344010i
$846$	38.4110	−	29.4433i	1.32060	−	1.01228i
$847$			31.4261i			1.07981i
$848$	6.21557	+	0.617732i	0.213444	+	0.0212130i
$849$	4.90354	−	6.55354i	0.168289	−	0.224917i
$850$	−1.59699	+	0.615623i	−0.0547764	+	0.0211157i
$851$	3.79510			0.130094
$852$	−1.02951	+	0.0965437i	−0.0352706	+	0.00330753i
$853$	56.1528			1.92263			0.961317	−	0.275443i	$-0.0888247\pi$
$853$	56.1528			1.92263			0.961317	+	0.275443i	$0.0888247\pi$
$854$	−62.0561	+	23.9219i	−2.12352	+	0.818592i
$855$	−5.74864	−	19.5444i	−0.196599	−	0.668406i
$856$	−2.91391	−	1.46916i	−0.0995954	−	0.0502150i
$857$			31.3063i			1.06940i	0.845041	+	0.534702i	$0.179576\pi$
$857$			31.3063i			1.06940i	−0.845041	+	0.534702i	$0.820424\pi$
$858$	0.918998	−	3.26424i	0.0313741	−	0.111439i
$859$		−	3.94314i		−	0.134538i	−0.997735	−	0.0672691i	$-0.978571\pi$
$859$		−	3.94314i		−	0.134538i	0.997735	−	0.0672691i	$-0.0214286\pi$
$860$	7.12835	−	6.45502i	0.243075	−	0.220114i
$861$	−45.6719	−	34.1730i	−1.55649	−	1.16461i
$862$	7.58278	+	19.6706i	0.258271	+	0.669983i
$863$	15.9367			0.542490			0.271245	−	0.962510i	$-0.412565\pi$
$863$	15.9367			0.542490			0.271245	+	0.962510i	$0.412565\pi$
$864$	2.56653	−	29.2816i	0.0873153	−	0.996181i
$865$	−20.6240			−0.701237
$866$	−16.2515	−	42.1583i	−0.552250	−	1.43260i
$867$	21.5447	+	16.1203i	0.731695	+	0.547475i
$868$	15.5424	−	14.0743i	0.527542	−	0.477712i
$869$		−	21.6173i		−	0.733316i
$870$	1.55651	−	5.52864i	0.0527705	−	0.187439i
$871$			0.680909i			0.0230717i
$872$	4.47989	+	2.25872i	0.151708	+	0.0764897i
$873$	−9.31982	−	31.6859i	−0.315428	−	1.07240i
$874$	−22.8187	+	8.79635i	−0.771854	+	0.297541i
$875$	3.45974			0.116961
$876$	33.9319	−	3.18200i	1.14645	−	0.107510i
$877$	−37.8557			−1.27830			−0.639148	−	0.769083i	$-0.720713\pi$
$877$	−37.8557			−1.27830			−0.639148	+	0.769083i	$0.720713\pi$
$878$	7.85659	−	3.02863i	0.265147	−	0.102211i
$879$	2.17011	−	2.90033i	0.0731958	−	0.0978256i
$880$	−5.51056	−	0.547665i	−0.185761	−	0.0184618i
$881$			53.8762i			1.81513i	0.419907	+	0.907567i	$0.362063\pi$
$881$			53.8762i			1.81513i	−0.419907	+	0.907567i	$0.637937\pi$
$882$	−16.7343	+	12.8274i	−0.563475	+	0.431922i
$883$			54.6628i			1.83955i	0.392447	+	0.919774i	$0.371628\pi$
$883$			54.6628i			1.83955i	−0.392447	+	0.919774i	$0.628372\pi$
$884$	−1.62471	−	1.79418i	−0.0546448	−	0.0603448i
$885$	−4.25939	+	5.69264i	−0.143178	+	0.191356i
$886$	10.3861	+	26.9426i	0.348926	+	0.905153i
$887$	−50.1663			−1.68442			−0.842209	−	0.539150i	$-0.818745\pi$
$887$	−50.1663			−1.68442			−0.842209	+	0.539150i	$0.818745\pi$
$888$	3.25070	+	6.53749i	0.109086	+	0.219384i
$889$	69.0737			2.31666
$890$	−8.41139	−	21.8201i	−0.281950	−	0.731411i
$891$	−10.4756	+	6.74604i	−0.350946	+	0.226001i
$892$	−15.4083	−	17.0155i	−0.515907	−	0.569722i
$893$		−	77.4650i		−	2.59227i
$894$	−15.1785	−	4.27328i	−0.507645	−	0.142920i
$895$		−	9.70558i		−	0.324422i
$896$	−33.0372	−	20.9923i	−1.10370	−	0.701304i
$897$	3.53152	+	2.64238i	0.117914	+	0.0882265i
$898$	−31.6985	+	12.2194i	−1.05779	+	0.407766i
$899$	7.10536			0.236977
$900$	5.11871	+	3.13031i	0.170624	+	0.104344i
$901$	−1.88985			−0.0629602
$902$	−17.3894	+	6.70343i	−0.579005	+	0.223200i
$903$	−23.0706	−	17.2621i	−0.767742	−	0.574446i
$904$	−21.4010	+	42.4464i	−0.711787	+	1.41175i
$905$		−	23.4173i		−	0.778416i
$906$	26.9987	+	7.60110i	0.896973	+	0.252530i
$907$		−	27.5763i		−	0.915657i	−0.889040	−	0.457829i	$-0.848627\pi$
$907$		−	27.5763i		−	0.915657i	0.889040	−	0.457829i	$-0.151373\pi$
$908$	8.98416	−	8.13553i	0.298150	−	0.269987i
$909$	−51.1758	+	15.0524i	−1.69739	+	0.499257i
$910$	1.75989	+	4.56535i	0.0583398	+	0.151340i
$911$	−0.664100			−0.0220026			−0.0110013	−	0.999939i	$-0.503502\pi$
$911$	−0.664100			−0.0220026			−0.0110013	+	0.999939i	$0.503502\pi$
$912$	−34.6981	−	31.7733i	−1.14897	−	1.05212i
$913$	0.313715			0.0103825
$914$	5.34375	+	13.8623i	0.176756	+	0.458523i
$915$	14.1047	−	18.8508i	0.466288	−	0.623190i
$916$	−11.8663	+	10.7455i	−0.392075	+	0.355040i
$917$			35.9275i			1.18643i
$918$	0.103452	+	8.89283i	0.00341443	+	0.293507i
$919$			36.8995i			1.21720i	0.793476	+	0.608602i	$0.208269\pi$
$919$			36.8995i			1.21720i	−0.793476	+	0.608602i	$0.791731\pi$
$920$	3.24262	−	6.43134i	0.106906	−	0.212035i
$921$	19.7268	−	26.3646i	0.650019	−	0.868745i
$922$	−24.3516	+	9.38725i	−0.801976	+	0.309153i
$923$	0.298499			0.00982522
$924$	1.54915	+	16.5197i	0.0509634	+	0.543459i
$925$	−1.49033			−0.0490017
$926$	13.3811	−	5.15827i	0.439731	−	0.169511i
$927$	−7.29261	+	2.14499i	−0.239521	+	0.0704507i
$928$	−3.52360	−	12.7876i	−0.115668	−	0.419774i
$929$		−	42.2152i		−	1.38503i	−0.721401	−	0.692517i	$-0.756502\pi$
$929$		−	42.2152i		−	1.38503i	0.721401	−	0.692517i	$-0.243498\pi$
$930$	−2.01152	+	7.14484i	−0.0659604	+	0.234288i
$931$			33.7488i			1.10607i
$932$	−13.3720	−	14.7669i	−0.438015	−	0.483704i
$933$	−6.28081	−	4.69948i	−0.205624	−	0.153854i
$934$	11.4709	+	29.7568i	0.375340	+	0.973673i
$935$	1.67549			0.0547945
$936$	−1.52687	+	8.34678i	−0.0499074	+	0.272823i
$937$	28.4325			0.928850			0.464425	−	0.885612i	$-0.346261\pi$
$937$	28.4325			0.928850			0.464425	+	0.885612i	$0.346261\pi$
$938$	−1.19832	−	3.10859i	−0.0391267	−	0.101499i
$939$	5.27460	+	3.94660i	0.172130	+	0.128793i
$940$	15.3140	+	16.9114i	0.499487	+	0.551589i
$941$			37.5619i			1.22448i	0.790671	+	0.612241i	$0.209732\pi$
$941$			37.5619i			1.22448i	−0.790671	+	0.612241i	$0.790268\pi$
$942$	−11.1113	+	39.4668i	−0.362026	+	1.28590i
$943$		−	24.2397i		−	0.789352i
$944$	−1.62382	+	16.3388i	−0.0528509	+	0.531781i
$945$	6.27068	−	16.8482i	0.203985	−	0.548073i
$946$	−8.78407	+	3.38616i	−0.285595	+	0.110094i
$947$	−34.0041			−1.10499			−0.552493	−	0.833518i	$-0.686323\pi$
$947$	−34.0041			−1.10499			−0.552493	+	0.833518i	$0.686323\pi$
$948$	5.05024	+	53.8543i	0.164024	+	1.74911i
$949$	−9.83828			−0.319364
$950$	8.96086	−	3.45431i	0.290729	−	0.112073i
$951$	22.4391	−	29.9897i	0.727639	−	0.972483i
$952$	10.5749	+	5.33176i	0.342735	+	0.172803i
$953$		−	20.7594i		−	0.672463i	−0.941779	−	0.336231i	$-0.890848\pi$
$953$		−	20.7594i		−	0.672463i	0.941779	−	0.336231i	$-0.109152\pi$
$954$	4.03047	+	5.25805i	0.130491	+	0.170236i
$955$		−	19.1176i		−	0.618631i
$956$	4.73536	−	4.28807i	0.153153	−	0.138686i
$957$	−3.36845	+	4.50190i	−0.108886	+	0.145526i
$958$	−16.0730	−	41.6952i	−0.519296	−	1.34711i
$959$	49.3548			1.59375
$960$	13.8562	+	0.0769961i	0.447207	+	0.00248504i
$961$	21.8175			0.703791
$962$	−0.758095	−	1.96658i	−0.0244420	−	0.0634052i
$963$	−0.976701	−	3.32062i	−0.0314737	−	0.107006i
$964$	−7.59735	+	6.87972i	−0.244694	+	0.221581i
$965$			10.3671i			0.333730i
$966$	−20.7729	−	5.84830i	−0.668357	−	0.188166i
$967$			1.11319i			0.0357979i	0.999840	+	0.0178990i	$0.00569772\pi$
$967$			1.11319i			0.0357979i	−0.999840	+	0.0178990i	$0.994302\pi$
$968$	−22.9407	−	11.5665i	−0.737343	−	0.371760i
$969$	11.3976	+	8.52798i	0.366143	+	0.273958i
$970$	14.5276	−	5.60020i	0.466452	−	0.179812i
$971$	−32.1217			−1.03084			−0.515418	−	0.856939i	$-0.672363\pi$
$971$	−32.1217			−1.03084			−0.515418	+	0.856939i	$0.672363\pi$
$972$	24.5215	−	19.2535i	0.786527	−	0.617556i
$973$	−49.0068			−1.57109
$974$	−8.65311	+	3.33567i	−0.277263	+	0.106882i
$975$	−1.38682	−	1.03766i	−0.0444138	−	0.0332316i
$976$	5.37719	−	54.1049i	0.172120	−	1.73186i
$977$			44.0839i			1.41037i	0.709024	+	0.705185i	$0.249136\pi$
$977$			44.0839i			1.41037i	−0.709024	+	0.705185i	$0.750864\pi$
$978$	46.3946	+	13.0617i	1.48354	+	0.417668i
$979$			22.8926i			0.731652i
$980$	−6.67177	−	7.36771i	−0.213122	−	0.235353i
$981$	1.50160	+	5.10518i	0.0479422	+	0.162996i
$982$	−17.4895	−	45.3698i	−0.558113	−	1.44781i
$983$	−6.84273			−0.218249			−0.109125	−	0.994028i	$-0.534805\pi$
$983$	−6.84273			−0.218249			−0.109125	+	0.994028i	$0.534805\pi$
$984$	41.7556	−	20.7625i	1.33112	−	0.661886i
$985$	15.7570			0.502061
$986$	1.44351	+	3.74463i	0.0459708	+	0.119253i
$987$	40.9528	−	54.7330i	1.30354	−	1.74217i
$988$	9.11636	+	10.0673i	0.290030	+	0.320283i
$989$		−	12.2444i		−	0.389349i
$990$	−3.57331	−	4.66165i	−0.113567	−	0.148157i
$991$			31.4987i			1.00059i	0.865856	+	0.500294i	$0.166775\pi$
$991$			31.4987i			1.00059i	−0.865856	+	0.500294i	$0.833225\pi$
$992$	4.55365	+	16.5258i	0.144579	+	0.524696i
$993$	−18.8206	+	25.1536i	−0.597254	+	0.798225i
$994$	−1.36275	+	0.525325i	−0.0432239	+	0.0166623i
$995$	−10.0605			−0.318939
$996$	−0.781547	+	0.0732904i	−0.0247643	+	0.00232229i
$997$	−19.6242			−0.621505			−0.310752	−	0.950491i	$-0.600581\pi$
$997$	−19.6242			−0.621505			−0.310752	+	0.950491i	$0.600581\pi$
$998$	−35.1172	+	13.5373i	−1.11161	+	0.428515i
$999$	−2.70118	+	7.25760i	−0.0854615	+	0.229620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.d.131.15	✓	32
3.2	odd	2	inner	780.2.g.d.131.18	yes	32
4.3	odd	2	inner	780.2.g.d.131.17	yes	32
12.11	even	2	inner	780.2.g.d.131.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.d.131.15	✓	32	1.1	even	1	trivial
780.2.g.d.131.16	yes	32	12.11	even	2	inner
780.2.g.d.131.17	yes	32	4.3	odd	2	inner
780.2.g.d.131.18	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.508677 - 1.31956i) q^{2} +(1.38682 + 1.03766i) q^{3} +(-1.48250 + 1.34246i) q^{4} -1.00000i q^{5} +(0.663812 - 2.35783i) q^{6} -3.45974i q^{7} +(2.52558 + 1.27337i) q^{8} +(0.846536 + 2.87809i) q^{9} +(-1.31956 + 0.508677i) q^{10} +1.38443 q^{11} +(-3.44897 + 0.323431i) q^{12} +1.00000 q^{13} +(-4.56535 + 1.75989i) q^{14} +(1.03766 - 1.38682i) q^{15} +(0.395589 - 3.98039i) q^{16} +1.21024i q^{17} +(3.36720 - 2.58107i) q^{18} -6.79078i q^{19} +(1.34246 + 1.48250i) q^{20} +(3.59002 - 4.79804i) q^{21} +(-0.704225 - 1.82684i) q^{22} +2.54649 q^{23} +(2.18120 + 4.38661i) q^{24} -1.00000 q^{25} +(-0.508677 - 1.31956i) q^{26} +(-1.81247 + 4.86980i) q^{27} +(4.64457 + 5.12905i) q^{28} +2.34480i q^{29} +(-2.35783 - 0.663812i) q^{30} -3.03026i q^{31} +(-5.45361 + 1.50273i) q^{32} +(1.91995 + 1.43656i) q^{33} +(1.59699 - 0.615623i) q^{34} -3.45974 q^{35} +(-5.11871 - 3.13031i) q^{36} +1.49033 q^{37} +(-8.96086 + 3.45431i) q^{38} +(1.38682 + 1.03766i) q^{39} +(1.27337 - 2.52558i) q^{40} -9.51887i q^{41} +(-8.15747 - 2.29662i) q^{42} -4.80835i q^{43} +(-2.05241 + 1.85854i) q^{44} +(2.87809 - 0.846536i) q^{45} +(-1.29534 - 3.36025i) q^{46} +11.4074 q^{47} +(4.67889 - 5.10960i) q^{48} -4.96980 q^{49} +(0.508677 + 1.31956i) q^{50} +(-1.25582 + 1.67839i) q^{51} +(-1.48250 + 1.34246i) q^{52} +1.56155i q^{53} +(7.34797 - 0.0854803i) q^{54} -1.38443i q^{55} +(4.40552 - 8.73784i) q^{56} +(7.04650 - 9.41758i) q^{57} +(3.09412 - 1.19275i) q^{58} -4.10481 q^{59} +(0.323431 + 3.44897i) q^{60} +13.5929 q^{61} +(-3.99862 + 1.54142i) q^{62} +(9.95743 - 2.92880i) q^{63} +(4.75706 + 6.43198i) q^{64} -1.00000i q^{65} +(0.918998 - 3.26424i) q^{66} +0.680909i q^{67} +(-1.62471 - 1.79418i) q^{68} +(3.53152 + 2.64238i) q^{69} +(1.75989 + 4.56535i) q^{70} +0.298499 q^{71} +(-1.52687 + 8.34678i) q^{72} -9.83828 q^{73} +(-0.758095 - 1.96658i) q^{74} +(-1.38682 - 1.03766i) q^{75} +(9.11636 + 10.0673i) q^{76} -4.78976i q^{77} +(0.663812 - 2.35783i) q^{78} -15.6146i q^{79} +(-3.98039 - 0.395589i) q^{80} +(-7.56675 + 4.87281i) q^{81} +(-12.5608 + 4.84203i) q^{82} +0.226603 q^{83} +(1.11899 + 11.9325i) q^{84} +1.21024 q^{85} +(-6.34492 + 2.44589i) q^{86} +(-2.43310 + 3.25182i) q^{87} +(3.49647 + 1.76289i) q^{88} +16.5358i q^{89} +(-2.58107 - 3.36720i) q^{90} -3.45974i q^{91} +(-3.77516 + 3.41856i) q^{92} +(3.14437 - 4.20243i) q^{93} +(-5.80267 - 15.0528i) q^{94} -6.79078 q^{95} +(-9.12248 - 3.57496i) q^{96} -11.0094 q^{97} +(2.52802 + 6.55797i) q^{98} +(1.17197 + 3.98450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) \) 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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