LMFDB - Embedded newform 780.2.g.e.131.9

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 = [40,0,0,4] 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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	780.131
Dual form			780.2.g.e.131.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13428 - 0.844635i) q^{2} +(-0.684863 + 1.59090i) q^{3} +(0.573183 + 1.91611i) q^{4} +1.00000i q^{5} +(2.12056 - 1.22607i) q^{6} +1.35942i q^{7} +(0.968260 - 2.65753i) q^{8} +(-2.06192 - 2.17910i) q^{9} +(0.844635 - 1.13428i) q^{10} -5.65668 q^{11} +(-3.44088 - 0.400393i) q^{12} -1.00000 q^{13} +(1.14821 - 1.54196i) q^{14} +(-1.59090 - 0.684863i) q^{15} +(-3.34292 + 2.19656i) q^{16} -4.77234i q^{17} +(0.498258 + 4.21328i) q^{18} -8.29423i q^{19} +(-1.91611 + 0.573183i) q^{20} +(-2.16269 - 0.931014i) q^{21} +(6.41626 + 4.77783i) q^{22} +3.30446 q^{23} +(3.56474 + 3.36045i) q^{24} -1.00000 q^{25} +(1.13428 + 0.844635i) q^{26} +(4.87886 - 1.78793i) q^{27} +(-2.60478 + 0.779195i) q^{28} +3.90736i q^{29} +(1.22607 + 2.12056i) q^{30} +8.19765i q^{31} +(5.64710 + 0.332035i) q^{32} +(3.87405 - 8.99922i) q^{33} +(-4.03088 + 5.41317i) q^{34} -1.35942 q^{35} +(2.99352 - 5.19989i) q^{36} +3.51765 q^{37} +(-7.00560 + 9.40798i) q^{38} +(0.684863 - 1.59090i) q^{39} +(2.65753 + 0.968260i) q^{40} -1.39380i q^{41} +(1.66673 + 2.88272i) q^{42} -10.0772i q^{43} +(-3.24232 - 10.8388i) q^{44} +(2.17910 - 2.06192i) q^{45} +(-3.74818 - 2.79106i) q^{46} +6.45448 q^{47} +(-1.20506 - 6.82260i) q^{48} +5.15199 q^{49} +(1.13428 + 0.844635i) q^{50} +(7.59231 + 3.26840i) q^{51} +(-0.573183 - 1.91611i) q^{52} -4.68264i q^{53} +(-7.04415 - 2.09284i) q^{54} -5.65668i q^{55} +(3.61269 + 1.31627i) q^{56} +(13.1953 + 5.68042i) q^{57} +(3.30030 - 4.43205i) q^{58} -13.6004 q^{59} +(0.400393 - 3.44088i) q^{60} +0.137755 q^{61} +(6.92402 - 9.29843i) q^{62} +(2.96230 - 2.80301i) q^{63} +(-6.12495 - 5.14636i) q^{64} -1.00000i q^{65} +(-11.9953 + 6.93547i) q^{66} -5.90581i q^{67} +(9.14430 - 2.73542i) q^{68} +(-2.26310 + 5.25706i) q^{69} +(1.54196 + 1.14821i) q^{70} -12.2472 q^{71} +(-7.78750 + 3.36970i) q^{72} -3.48129 q^{73} +(-3.99000 - 2.97113i) q^{74} +(0.684863 - 1.59090i) q^{75} +(15.8926 - 4.75412i) q^{76} -7.68978i q^{77} +(-2.12056 + 1.22607i) q^{78} -12.9548i q^{79} +(-2.19656 - 3.34292i) q^{80} +(-0.496932 + 8.98627i) q^{81} +(-1.17725 + 1.58096i) q^{82} -6.73642 q^{83} +(0.544301 - 4.67759i) q^{84} +4.77234 q^{85} +(-8.51154 + 11.4303i) q^{86} +(-6.21622 - 2.67601i) q^{87} +(-5.47714 + 15.0328i) q^{88} +1.70338i q^{89} +(-4.21328 + 0.498258i) q^{90} -1.35942i q^{91} +(1.89406 + 6.33169i) q^{92} +(-13.0416 - 5.61427i) q^{93} +(-7.32119 - 5.45168i) q^{94} +8.29423 q^{95} +(-4.39573 + 8.75657i) q^{96} +1.74363 q^{97} +(-5.84380 - 4.35155i) q^{98} +(11.6637 + 12.3265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} - 2 q^{6} - 14 q^{12} - 40 q^{13} + 12 q^{16} - 16 q^{18} - 24 q^{21} + 44 q^{22} - 10 q^{24} - 40 q^{25} - 48 q^{28} - 6 q^{30} - 8 q^{33} - 56 q^{34} + 36 q^{36} - 72 q^{37} - 20 q^{42}+ \cdots + 72 q^{97}+O(q^{100}) $ 40 * q + 4 * q^4 - 2 * q^6 - 14 * q^12 - 40 * q^13 + 12 * q^16 - 16 * q^18 - 24 * q^21 + 44 * q^22 - 10 * q^24 - 40 * q^25 - 48 * q^28 - 6 * q^30 - 8 * q^33 - 56 * q^34 + 36 * q^36 - 72 * q^37 - 20 * q^42 + 8 * q^45 + 84 * q^46 + 70 * q^48 - 96 * q^49 - 4 * q^52 - 14 * q^54 + 80 * q^57 + 18 * q^60 + 40 * q^61 + 28 * q^64 - 24 * q^66 - 56 * q^69 + 24 * q^70 + 12 * q^72 - 68 * q^76 + 2 * q^78 + 96 * q^82 - 48 * q^84 + 8 * q^85 - 116 * q^88 - 8 * q^90 - 24 * q^93 - 8 * q^94 - 10 * q^96 + 72 * 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 $

$2$	−1.13428	−	0.844635i	−0.802057	−	0.597247i
$2$	−1.13428	−	0.844635i	−0.802057	−	0.597247i
$3$	−0.684863	+	1.59090i	−0.395406	+	0.918506i
$3$	−0.684863	+	1.59090i	−0.395406	+	0.918506i
$4$	0.573183	+	1.91611i	0.286592	+	0.958053i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	2.12056	−	1.22607i	0.865714	−	0.500540i
$7$			1.35942i			0.513811i	0.966437	+	0.256905i	$0.0827029\pi$
$7$			1.35942i			0.513811i	−0.966437	+	0.256905i	$0.917297\pi$
$8$	0.968260	−	2.65753i	0.342331	−	0.939579i
$9$	−2.06192	−	2.17910i	−0.687308	−	0.726366i
$10$	0.844635	−	1.13428i	0.267097	−	0.358691i
$11$	−5.65668			−1.70555			−0.852777	−	0.522275i	$-0.825083\pi$
$11$	−5.65668			−1.70555			−0.852777	+	0.522275i	$0.825083\pi$
$12$	−3.44088	−	0.400393i	−0.993298	−	0.115584i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	1.14821	−	1.54196i	0.306872	−	0.412106i
$15$	−1.59090	−	0.684863i	−0.410769	−	0.176831i
$16$	−3.34292	+	2.19656i	−0.835730	+	0.549140i
$17$		−	4.77234i		−	1.15746i	−0.815519	−	0.578731i	$-0.803548\pi$
$17$		−	4.77234i		−	1.15746i	0.815519	−	0.578731i	$-0.196452\pi$
$18$	0.498258	+	4.21328i	0.117441	+	0.993080i
$19$		−	8.29423i		−	1.90283i	−0.307915	−	0.951414i	$-0.599631\pi$
$19$		−	8.29423i		−	1.90283i	0.307915	−	0.951414i	$-0.400369\pi$
$20$	−1.91611	+	0.573183i	−0.428454	+	0.128168i
$21$	−2.16269	−	0.931014i	−0.471939	−	0.203164i
$22$	6.41626	+	4.77783i	1.36795	+	1.01864i
$23$	3.30446			0.689027			0.344513	−	0.938781i	$-0.388044\pi$
$23$	3.30446			0.689027			0.344513	+	0.938781i	$0.388044\pi$
$24$	3.56474	+	3.36045i	0.727650	+	0.685949i
$25$	−1.00000			−0.200000
$26$	1.13428	+	0.844635i	0.222451	+	0.165647i
$27$	4.87886	−	1.78793i	0.938938	−	0.344088i
$28$	−2.60478	+	0.779195i	−0.492258	+	0.147254i
$29$			3.90736i			0.725579i	0.931871	+	0.362790i	$0.118176\pi$
$29$			3.90736i			0.725579i	−0.931871	+	0.362790i	$0.881824\pi$
$30$	1.22607	+	2.12056i	0.223848	+	0.387159i
$31$			8.19765i			1.47234i	0.676796	+	0.736171i	$0.263368\pi$
$31$			8.19765i			1.47234i	−0.676796	+	0.736171i	$0.736632\pi$
$32$	5.64710	+	0.332035i	0.998276	+	0.0586961i
$33$	3.87405	−	8.99922i	0.674386	−	1.56656i
$34$	−4.03088	+	5.41317i	−0.691291	+	0.928350i
$35$	−1.35942			−0.229783
$36$	2.99352	−	5.19989i	0.498920	−	0.866648i
$37$	3.51765			0.578297			0.289149	−	0.957284i	$-0.406628\pi$
$37$	3.51765			0.578297			0.289149	+	0.957284i	$0.406628\pi$
$38$	−7.00560	+	9.40798i	−1.13646	+	1.52618i
$39$	0.684863	−	1.59090i	0.109666	−	0.254748i
$40$	2.65753	+	0.968260i	0.420193	+	0.153095i
$41$		−	1.39380i		−	0.217674i	−0.994060	−	0.108837i	$-0.965287\pi$
$41$		−	1.39380i		−	0.217674i	0.994060	−	0.108837i	$-0.0347127\pi$
$42$	1.66673	+	2.88272i	0.257183	+	0.444813i
$43$		−	10.0772i		−	1.53676i	−0.639997	−	0.768378i	$-0.721064\pi$
$43$		−	10.0772i		−	1.53676i	0.639997	−	0.768378i	$-0.278936\pi$
$44$	−3.24232	−	10.8388i	−0.488797	−	1.63401i
$45$	2.17910	−	2.06192i	0.324841	−	0.307374i
$46$	−3.74818	−	2.79106i	−0.552639	−	0.411519i
$47$	6.45448			0.941482			0.470741	−	0.882271i	$-0.343987\pi$
$47$	6.45448			0.941482			0.470741	+	0.882271i	$0.343987\pi$
$48$	−1.20506	−	6.82260i	−0.173936	−	0.984757i
$49$	5.15199			0.735998
$50$	1.13428	+	0.844635i	0.160411	+	0.119449i
$51$	7.59231	+	3.26840i	1.06314	+	0.457667i
$52$	−0.573183	−	1.91611i	−0.0794862	−	0.265716i
$53$		−	4.68264i		−	0.643210i	−0.946874	−	0.321605i	$-0.895778\pi$
$53$		−	4.68264i		−	0.643210i	0.946874	−	0.321605i	$-0.104222\pi$
$54$	−7.04415	−	2.09284i	−0.958587	−	0.284800i
$55$		−	5.65668i		−	0.762747i
$56$	3.61269	+	1.31627i	0.482766	+	0.175894i
$57$	13.1953	+	5.68042i	1.74776	+	0.752389i
$58$	3.30030	−	4.43205i	0.433350	−	0.581956i
$59$	−13.6004			−1.77062			−0.885310	−	0.465000i	$-0.846054\pi$
$59$	−13.6004			−1.77062			−0.885310	+	0.465000i	$0.846054\pi$
$60$	0.400393	−	3.44088i	0.0516905	−	0.444216i
$61$	0.137755			0.0176378			0.00881889	−	0.999961i	$-0.497193\pi$
$61$	0.137755			0.0176378			0.00881889	+	0.999961i	$0.497193\pi$
$62$	6.92402	−	9.29843i	0.879352	−	1.18090i
$63$	2.96230	−	2.80301i	0.373215	−	0.353147i
$64$	−6.12495	−	5.14636i	−0.765618	−	0.643295i
$65$		−	1.00000i		−	0.124035i
$66$	−11.9953	+	6.93547i	−1.47652	+	0.853697i
$67$		−	5.90581i		−	0.721510i	−0.932661	−	0.360755i	$-0.882519\pi$
$67$		−	5.90581i		−	0.721510i	0.932661	−	0.360755i	$-0.117481\pi$
$68$	9.14430	−	2.73542i	1.10891	−	0.331719i
$69$	−2.26310	+	5.25706i	−0.272445	+	0.632875i
$70$	1.54196	+	1.14821i	0.184299	+	0.137237i
$71$	−12.2472			−1.45347			−0.726737	−	0.686915i	$-0.758964\pi$
$71$	−12.2472			−1.45347			−0.726737	+	0.686915i	$0.758964\pi$
$72$	−7.78750	+	3.36970i	−0.917766	+	0.397123i
$73$	−3.48129			−0.407454			−0.203727	−	0.979028i	$-0.565305\pi$
$73$	−3.48129			−0.407454			−0.203727	+	0.979028i	$0.565305\pi$
$74$	−3.99000	−	2.97113i	−0.463828	−	0.345387i
$75$	0.684863	−	1.59090i	0.0790812	−	0.183701i
$76$	15.8926	−	4.75412i	1.82301	−	0.545334i
$77$		−	7.68978i		−	0.876332i
$78$	−2.12056	+	1.22607i	−0.240106	+	0.138825i
$79$		−	12.9548i		−	1.45753i	−0.684766	−	0.728763i	$-0.740096\pi$
$79$		−	12.9548i		−	1.45753i	0.684766	−	0.728763i	$-0.259904\pi$
$80$	−2.19656	−	3.34292i	−0.245583	−	0.373750i
$81$	−0.496932	+	8.98627i	−0.0552147	+	0.998475i
$82$	−1.17725	+	1.58096i	−0.130005	+	0.174587i
$83$	−6.73642			−0.739418			−0.369709	−	0.929148i	$-0.620543\pi$
$83$	−6.73642			−0.739418			−0.369709	+	0.929148i	$0.620543\pi$
$84$	0.544301	−	4.67759i	0.0593881	−	0.510367i
$85$	4.77234			0.517633
$86$	−8.51154	+	11.4303i	−0.917823	+	1.23257i
$87$	−6.21622	−	2.67601i	−0.666449	−	0.286898i
$88$	−5.47714	+	15.0328i	−0.583865	+	1.60250i
$89$			1.70338i			0.180558i	0.995917	+	0.0902791i	$0.0287759\pi$
$89$			1.70338i			0.180558i	−0.995917	+	0.0902791i	$0.971224\pi$
$90$	−4.21328	+	0.498258i	−0.444119	+	0.0525210i
$91$		−	1.35942i		−	0.142506i
$92$	1.89406	+	6.33169i	0.197469	+	0.660124i
$93$	−13.0416	−	5.61427i	−1.35235	−	0.582172i
$94$	−7.32119	−	5.45168i	−0.755123	−	0.562298i
$95$	8.29423			0.850970
$96$	−4.39573	+	8.75657i	−0.448637	+	0.893714i
$97$	1.74363			0.177039			0.0885193	−	0.996074i	$-0.471787\pi$
$97$	1.74363			0.177039			0.0885193	+	0.996074i	$0.471787\pi$
$98$	−5.84380	−	4.35155i	−0.590313	−	0.439573i
$99$	11.6637	+	12.3265i	1.17224	+	1.23886i
$100$	−0.573183	−	1.91611i	−0.0573183	−	0.191611i
$101$		−	10.5717i		−	1.05193i	−0.850507	−	0.525964i	$-0.823705\pi$
$101$		−	10.5717i		−	1.05193i	0.850507	−	0.525964i	$-0.176295\pi$
$102$	−5.85120	−	10.1200i	−0.579355	−	1.00203i
$103$			6.27478i			0.618272i	0.951018	+	0.309136i	$0.100040\pi$
$103$			6.27478i			0.618272i	−0.951018	+	0.309136i	$0.899960\pi$
$104$	−0.968260	+	2.65753i	−0.0949457	+	0.260592i
$105$	0.931014	−	2.16269i	0.0908577	−	0.211057i
$106$	−3.95512	+	5.31143i	−0.384156	+	0.515892i
$107$	2.98999			0.289053			0.144527	−	0.989501i	$-0.453834\pi$
$107$	2.98999			0.289053			0.144527	+	0.989501i	$0.453834\pi$
$108$	6.22235	+	8.32360i	0.598746	+	0.800939i
$109$	−11.6540			−1.11625			−0.558123	−	0.829758i	$-0.688478\pi$
$109$	−11.6540			−1.11625			−0.558123	+	0.829758i	$0.688478\pi$
$110$	−4.77783	+	6.41626i	−0.455548	+	0.611767i
$111$	−2.40911	+	5.59622i	−0.228662	+	0.531170i
$112$	−2.98604	−	4.54442i	−0.282154	−	0.429407i
$113$			10.0075i			0.941425i	0.882287	+	0.470713i	$0.156003\pi$
$113$			10.0075i			0.941425i	−0.882287	+	0.470713i	$0.843997\pi$
$114$	−10.1693	−	17.5884i	−0.952441	−	1.64730i
$115$			3.30446i			0.308142i
$116$	−7.48692	+	2.23964i	−0.695143	+	0.207945i
$117$	2.06192	+	2.17910i	0.190625	+	0.201458i
$118$	15.4267	+	11.4874i	1.42014	+	1.05750i
$119$	6.48759			0.594716
$120$	−3.36045	+	3.56474i	−0.306766	+	0.325415i
$121$	20.9981			1.90891
$122$	−0.156253	−	0.116353i	−0.0141465	−	0.0105341i
$123$	2.21739	+	0.954560i	0.199935	+	0.0860698i
$124$	−15.7076	+	4.69875i	−1.41058	+	0.421961i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.72760	+	0.677340i	−0.510255	+	0.0603423i
$127$			2.40673i			0.213562i	0.994283	+	0.106781i	$0.0340544\pi$
$127$			2.40673i			0.213562i	−0.994283	+	0.106781i	$0.965946\pi$
$128$	2.60061	+	11.0108i	0.229864	+	0.973223i
$129$	16.0318	+	6.90149i	1.41152	+	0.607642i
$130$	−0.844635	+	1.13428i	−0.0740794	+	0.0994830i
$131$	−15.1268			−1.32163			−0.660816	−	0.750548i	$-0.729790\pi$
$131$	−15.1268			−1.32163			−0.660816	+	0.750548i	$0.729790\pi$
$132$	19.4640	+	2.26490i	1.69412	+	0.197134i
$133$	11.2753			0.977694
$134$	−4.98825	+	6.69884i	−0.430920	+	0.578692i
$135$	1.78793	+	4.87886i	0.153881	+	0.419906i
$136$	−12.6826	−	4.62086i	−1.08753	−	0.396236i
$137$		−	15.0055i		−	1.28201i	−0.767538	−	0.641004i	$-0.778518\pi$
$137$		−	15.0055i		−	1.28201i	0.767538	−	0.641004i	$-0.221482\pi$
$138$	7.00728	−	4.05148i	0.596500	−	0.344885i
$139$		−	11.5491i		−	0.979584i	−0.871839	−	0.489792i	$-0.837073\pi$
$139$		−	11.5491i		−	0.979584i	0.871839	−	0.489792i	$-0.162927\pi$
$140$	−0.779195	−	2.60478i	−0.0658540	−	0.220144i
$141$	−4.42043	+	10.2684i	−0.372268	+	0.864758i
$142$	13.8918	+	10.3444i	1.16577	+	0.868084i
$143$	5.65668			0.473036
$144$	11.6794	+	2.75541i	0.973281	+	0.229618i
$145$	−3.90736			−0.324489
$146$	3.94875	+	2.94042i	0.326801	+	0.243351i
$147$	−3.52841	+	8.19630i	−0.291018	+	0.676019i
$148$	2.01626	+	6.74018i	0.165735	+	0.554039i
$149$		−	7.77947i		−	0.637319i	−0.947869	−	0.318659i	$-0.896767\pi$
$149$		−	7.77947i		−	0.637319i	0.947869	−	0.318659i	$-0.103233\pi$
$150$	−2.12056	+	1.22607i	−0.173143	+	0.100108i
$151$		−	14.2684i		−	1.16114i	−0.814209	−	0.580572i	$-0.802829\pi$
$151$		−	14.2684i		−	1.16114i	0.814209	−	0.580572i	$-0.197171\pi$
$152$	−22.0422	−	8.03097i	−1.78786	−	0.651398i
$153$	−10.3994	+	9.84020i	−0.840741	+	0.795533i
$154$	−6.49506	+	8.72237i	−0.523387	+	0.702869i
$155$	−8.19765			−0.658451
$156$	3.44088	+	0.400393i	0.275491	+	0.0320571i
$157$	6.63498			0.529529			0.264764	−	0.964313i	$-0.414706\pi$
$157$	6.63498			0.529529			0.264764	+	0.964313i	$0.414706\pi$
$158$	−10.9421	+	14.6943i	−0.870503	+	1.16902i
$159$	7.44962	+	3.20697i	0.590793	+	0.254329i
$160$	−0.332035	+	5.64710i	−0.0262497	+	0.446443i
$161$			4.49213i			0.354029i
$162$	8.15378	−	9.77322i	0.640621	−	0.767857i
$163$		−	12.2961i		−	0.963106i	−0.876417	−	0.481553i	$-0.840073\pi$
$163$		−	12.2961i		−	0.963106i	0.876417	−	0.481553i	$-0.159927\pi$
$164$	2.67066	−	0.798901i	0.208544	−	0.0623837i
$165$	8.99922	+	3.87405i	0.700588	+	0.301595i
$166$	7.64099	+	5.68982i	0.593056	+	0.441615i
$167$	−11.2076			−0.867272			−0.433636	−	0.901088i	$-0.642770\pi$
$167$	−11.2076			−0.867272			−0.433636	+	0.901088i	$0.642770\pi$
$168$	−4.56825	+	4.84597i	−0.352448	+	0.373874i
$169$	1.00000			0.0769231
$170$	−5.41317	−	4.03088i	−0.415171	−	0.309155i
$171$	−18.0739	+	17.1021i	−1.38215	+	1.30783i
$172$	19.3089	−	5.77607i	1.47229	−	0.440421i
$173$		−	18.4036i		−	1.39920i	−0.714537	−	0.699598i	$-0.753362\pi$
$173$		−	18.4036i		−	1.39920i	0.714537	−	0.699598i	$-0.246638\pi$
$174$	4.79069	+	8.28579i	0.363181	+	0.628144i
$175$		−	1.35942i		−	0.102762i
$176$	18.9098	−	12.4252i	1.42538	−	0.936588i
$177$	9.31441	−	21.6369i	0.700114	−	1.62633i
$178$	1.43874	−	1.93211i	0.107838	−	0.144818i
$179$	13.4896			1.00826			0.504130	−	0.863628i	$-0.331813\pi$
$179$	13.4896			1.00826			0.504130	+	0.863628i	$0.331813\pi$
$180$	5.19989	+	2.99352i	0.387577	+	0.223124i
$181$	−8.44917			−0.628022			−0.314011	−	0.949419i	$-0.601673\pi$
$181$	−8.44917			−0.628022			−0.314011	+	0.949419i	$0.601673\pi$
$182$	−1.14821	+	1.54196i	−0.0851110	+	0.114298i
$183$	−0.0943436	+	0.219155i	−0.00697408	+	0.0162004i
$184$	3.19957	−	8.78169i	0.235875	−	0.647395i
$185$			3.51765i			0.258622i
$186$	10.0509	+	17.3836i	0.736965	+	1.27463i
$187$			26.9956i			1.97411i
$188$	3.69960	+	12.3675i	0.269821	+	0.901990i
$189$	2.43054	+	6.63240i	0.176796	+	0.482436i
$190$	−9.40798	−	7.00560i	−0.682527	−	0.508240i
$191$	4.49024			0.324902			0.162451	−	0.986717i	$-0.448060\pi$
$191$	4.49024			0.324902			0.162451	+	0.986717i	$0.448060\pi$
$192$	12.3821	−	6.21962i	0.893601	−	0.448863i
$193$	−25.9580			−1.86850			−0.934248	−	0.356624i	$-0.883928\pi$
$193$	−25.9580			−1.86850			−0.934248	+	0.356624i	$0.883928\pi$
$194$	−1.97776	−	1.47273i	−0.141995	−	0.105736i
$195$	1.59090	+	0.684863i	0.113927	+	0.0490441i
$196$	2.95303	+	9.87175i	0.210931	+	0.705125i
$197$			18.5921i			1.32463i	0.749225	+	0.662316i	$0.230426\pi$
$197$			18.5921i			1.32463i	−0.749225	+	0.662316i	$0.769574\pi$
$198$	−2.81849	−	23.8332i	−0.200301	−	1.69375i
$199$			24.0803i			1.70701i	0.521085	+	0.853505i	$0.325528\pi$
$199$			24.0803i			1.70701i	−0.521085	+	0.853505i	$0.674472\pi$
$200$	−0.968260	+	2.65753i	−0.0684663	+	0.187916i
$201$	9.39555	+	4.04467i	0.662711	+	0.285289i
$202$	−8.92926	+	11.9913i	−0.628261	+	0.843706i
$203$	−5.31173			−0.372811
$204$	−1.91081	+	16.4211i	−0.133784	+	1.14970i
$205$	1.39380			0.0973470
$206$	5.29990	−	7.11736i	0.369261	−	0.495890i
$207$	−6.81354	−	7.20073i	−0.473574	−	0.500485i
$208$	3.34292	−	2.19656i	0.231790	−	0.152304i
$209$			46.9178i			3.24538i
$210$	−2.88272	+	1.66673i	−0.198926	+	0.115016i
$211$		−	15.3530i		−	1.05694i	−0.848951	−	0.528472i	$-0.822765\pi$
$211$		−	15.3530i		−	1.05694i	0.848951	−	0.528472i	$-0.177235\pi$
$212$	8.97244	−	2.68401i	0.616230	−	0.184339i
$213$	8.38766	−	19.4841i	0.574713	−	1.33503i
$214$	−3.39149	−	2.52545i	−0.231837	−	0.172636i
$215$	10.0772			0.687258
$216$	−0.0274805	−	14.6969i	−0.00186981	−	0.999998i
$217$	−11.1440			−0.756505
$218$	13.2189	+	9.84334i	0.895294	+	0.666675i
$219$	2.38420	−	5.53838i	0.161110	−	0.374249i
$220$	10.8388	−	3.24232i	0.730752	−	0.218597i
$221$			4.77234i			0.321022i
$222$	7.45937	−	4.31287i	0.500640	−	0.289461i
$223$		−	4.22199i		−	0.282725i	−0.989958	−	0.141363i	$-0.954852\pi$
$223$		−	4.22199i		−	0.282725i	0.989958	−	0.141363i	$-0.0451483\pi$
$224$	−0.451374	+	7.67676i	−0.0301587	+	0.512925i
$225$	2.06192	+	2.17910i	0.137462	+	0.145273i
$226$	8.45267	−	11.3513i	0.562263	−	0.755077i
$227$	14.1803			0.941181			0.470591	−	0.882352i	$-0.344041\pi$
$227$	14.1803			0.941181			0.470591	+	0.882352i	$0.344041\pi$
$228$	−3.32095	+	28.5395i	−0.219936	+	1.89007i
$229$	−12.0315			−0.795061			−0.397531	−	0.917589i	$-0.630133\pi$
$229$	−12.0315			−0.795061			−0.397531	+	0.917589i	$0.630133\pi$
$230$	2.79106	−	3.74818i	0.184037	−	0.247148i
$231$	12.2337	+	5.26645i	0.804917	+	0.346507i
$232$	10.3839	+	3.78334i	0.681739	+	0.248389i
$233$			16.9405i			1.10981i	0.831915	+	0.554903i	$0.187245\pi$
$233$			16.9405i			1.10981i	−0.831915	+	0.554903i	$0.812755\pi$
$234$	−0.498258	−	4.21328i	−0.0325722	−	0.275431i
$235$			6.45448i			0.421044i
$236$	−7.79552	−	26.0598i	−0.507445	−	1.69635i
$237$	20.6097	+	8.87225i	1.33875	+	0.576314i
$238$	−7.35875	−	5.47965i	−0.476997	−	0.355193i
$239$	8.12221			0.525382			0.262691	−	0.964880i	$-0.415390\pi$
$239$	8.12221			0.525382			0.262691	+	0.964880i	$0.415390\pi$
$240$	6.82260	−	1.20506i	0.440397	−	0.0777864i
$241$	−13.3860			−0.862270			−0.431135	−	0.902288i	$-0.641887\pi$
$241$	−13.3860			−0.862270			−0.431135	+	0.902288i	$0.641887\pi$
$242$	−23.8177	−	17.7357i	−1.53106	−	1.14009i
$243$	−13.9559	−	6.94494i	−0.895273	−	0.445518i
$244$	0.0789591	+	0.263954i	0.00505484	+	0.0168979i
$245$			5.15199i			0.329148i
$246$	−1.70889	−	2.95562i	−0.108955	−	0.188444i
$247$			8.29423i			0.527749i
$248$	21.7855	+	7.93745i	1.38338	+	0.504029i
$249$	4.61353	−	10.7170i	0.292370	−	0.679160i
$250$	−0.844635	+	1.13428i	−0.0534194	+	0.0717382i
$251$	−5.94055			−0.374964			−0.187482	−	0.982268i	$-0.560033\pi$
$251$	−5.94055			−0.374964			−0.187482	+	0.982268i	$0.560033\pi$
$252$	7.06881	+	4.06944i	0.445293	+	0.256351i
$253$	−18.6923			−1.17517
$254$	2.03281	−	2.72990i	0.127550	−	0.171289i
$255$	−3.26840	+	7.59231i	−0.204675	+	0.475449i
$256$	6.35025	−	14.6859i	0.396891	−	0.917866i
$257$		−	5.13694i		−	0.320434i	−0.987082	−	0.160217i	$-0.948781\pi$
$257$		−	5.13694i		−	0.320434i	0.987082	−	0.160217i	$-0.0512194\pi$
$258$	−12.3553	−	21.3692i	−0.769207	−	1.33039i
$259$			4.78194i			0.297136i
$260$	1.91611	−	0.573183i	0.118832	−	0.0355473i
$261$	8.51453	−	8.05669i	0.527036	−	0.498697i
$262$	17.1580	+	12.7766i	1.06002	+	0.789341i
$263$	−7.66000			−0.472336			−0.236168	−	0.971712i	$-0.575892\pi$
$263$	−7.66000			−0.472336			−0.236168	+	0.971712i	$0.575892\pi$
$264$	−20.1646	−	19.0090i	−1.24105	−	1.16992i
$265$	4.68264			0.287652
$266$	−12.7894	−	9.52353i	−0.784166	−	0.583925i
$267$	−2.70991	−	1.16658i	−0.165844	−	0.0713938i
$268$	11.3162	−	3.38511i	0.691244	−	0.206779i
$269$			21.2926i			1.29824i	0.760688	+	0.649118i	$0.224862\pi$
$269$			21.2926i			1.29824i	−0.760688	+	0.649118i	$0.775138\pi$
$270$	2.09284	−	7.04415i	0.127366	−	0.428693i
$271$		−	16.0089i		−	0.972473i	−0.873827	−	0.486237i	$-0.838369\pi$
$271$		−	16.0089i		−	0.972473i	0.873827	−	0.486237i	$-0.161631\pi$
$272$	10.4827	+	15.9535i	0.635608	+	0.967326i
$273$	2.16269	+	0.931014i	0.130892	+	0.0563475i
$274$	−12.6742	+	17.0205i	−0.765675	+	1.02824i
$275$	5.65668			0.341111
$276$	−11.3702	−	1.32308i	−0.684409	−	0.0796401i
$277$	−21.2760			−1.27835			−0.639176	−	0.769060i	$-0.720725\pi$
$277$	−21.2760			−1.27835			−0.639176	+	0.769060i	$0.720725\pi$
$278$	−9.75480	+	13.0999i	−0.585054	+	0.785682i
$279$	17.8635	−	16.9029i	1.06946	−	1.01195i
$280$	−1.31627	+	3.61269i	−0.0786620	+	0.215900i
$281$		−	10.3372i		−	0.616666i	−0.951278	−	0.308333i	$-0.900229\pi$
$281$		−	10.3372i		−	0.616666i	0.951278	−	0.308333i	$-0.0997712\pi$
$282$	13.6871	−	7.91362i	0.815054	−	0.471249i
$283$			16.6477i			0.989605i	0.869005	+	0.494803i	$0.164760\pi$
$283$			16.6477i			0.989605i	−0.869005	+	0.494803i	$0.835240\pi$
$284$	−7.01989	−	23.4669i	−0.416554	−	1.39251i
$285$	−5.68042	+	13.1953i	−0.336479	+	0.781622i
$286$	−6.41626	−	4.77783i	−0.379402	−	0.282519i
$287$	1.89475			0.111844
$288$	−10.9204	−	12.9902i	−0.643488	−	0.765456i
$289$	−5.77520			−0.339717
$290$	4.43205	+	3.30030i	0.260259	+	0.193800i
$291$	−1.19415	+	2.77394i	−0.0700021	+	0.162611i
$292$	−1.99541	−	6.67051i	−0.116773	−	0.390362i
$293$		−	13.3543i		−	0.780164i	−0.920780	−	0.390082i	$-0.872447\pi$
$293$		−	13.3543i		−	0.780164i	0.920780	−	0.390082i	$-0.127553\pi$
$294$	10.9251	−	6.31668i	0.637164	−	0.368396i
$295$		−	13.6004i		−	0.791846i
$296$	3.40599	−	9.34825i	0.197969	−	0.543356i
$297$	−27.5982	+	10.1138i	−1.60141	+	0.586860i
$298$	−6.57081	+	8.82410i	−0.380637	+	0.511166i
$299$	−3.30446			−0.191102
$300$	3.44088	+	0.400393i	0.198660	+	0.0231167i
$301$	13.6991			0.789602
$302$	−12.0516	+	16.1843i	−0.693490	+	0.931305i
$303$	16.8186	+	7.24019i	0.966202	+	0.415938i
$304$	18.2188	+	27.7270i	1.04492	+	1.59025i
$305$			0.137755i			0.00788785i
$306$	20.1072	−	2.37786i	1.14945	−	0.135933i
$307$		−	0.385659i		−	0.0220107i	−0.999939	−	0.0110053i	$-0.996497\pi$
$307$		−	0.385659i		−	0.0220107i	0.999939	−	0.0110053i	$-0.00350318\pi$
$308$	14.7344	−	4.40766i	0.839573	−	0.251150i
$309$	−9.98255	−	4.29737i	−0.567887	−	0.244469i
$310$	9.29843	+	6.92402i	0.528115	+	0.393258i
$311$	7.86268			0.445852			0.222926	−	0.974835i	$-0.428439\pi$
$311$	7.86268			0.445852			0.222926	+	0.974835i	$0.428439\pi$
$312$	−3.56474	−	3.36045i	−0.201814	−	0.190248i
$313$	−17.2936			−0.977495			−0.488747	−	0.872425i	$-0.662546\pi$
$313$	−17.2936			−0.977495			−0.488747	+	0.872425i	$0.662546\pi$
$314$	−7.52592	−	5.60413i	−0.424712	−	0.316260i
$315$	2.80301	+	2.96230i	0.157932	+	0.166907i
$316$	24.8227	−	7.42546i	1.39639	−	0.417715i
$317$			8.28922i			0.465569i	0.972528	+	0.232785i	$0.0747837\pi$
$317$			8.28922i			0.465569i	−0.972528	+	0.232785i	$0.925216\pi$
$318$	−5.74123	−	9.92981i	−0.321952	−	0.556836i
$319$		−	22.1027i		−	1.23751i
$320$	5.14636	−	6.12495i	0.287690	−	0.342395i
$321$	−2.04773	+	4.75677i	−0.114293	+	0.265497i
$322$	3.79421	−	5.09533i	0.211443	−	0.283952i
$323$	−39.5829			−2.20245
$324$	−17.5035	+	4.19860i	−0.972415	+	0.233256i
$325$	1.00000			0.0554700
$326$	−10.3857	+	13.9472i	−0.575212	+	0.772466i
$327$	7.98137	−	18.5403i	0.441371	−	1.02528i
$328$	−3.70406	−	1.34956i	−0.204522	−	0.0745168i
$329$			8.77432i			0.483744i
$330$	−6.93547	−	11.9953i	−0.381785	−	0.660320i
$331$			6.81354i			0.374506i	0.982312	+	0.187253i	$0.0599584\pi$
$331$			6.81354i			0.374506i	−0.982312	+	0.187253i	$0.940042\pi$
$332$	−3.86120	−	12.9077i	−0.211911	−	0.708402i
$333$	−7.25312	−	7.66529i	−0.397469	−	0.420056i
$334$	12.7126	+	9.46635i	0.695602	+	0.517976i
$335$	5.90581			0.322669
$336$	9.27475	−	1.63818i	0.505979	−	0.0893701i
$337$	28.7934			1.56848			0.784239	−	0.620459i	$-0.213054\pi$
$337$	28.7934			1.56848			0.784239	+	0.620459i	$0.213054\pi$
$338$	−1.13428	−	0.844635i	−0.0616967	−	0.0459421i
$339$	−15.9209	−	6.85376i	−0.864705	−	0.372245i
$340$	2.73542	+	9.14430i	0.148349	+	0.495919i
$341$		−	46.3715i		−	2.51116i
$342$	34.9459	−	4.13267i	1.88966	−	0.223469i
$343$			16.5196i			0.891975i
$344$	−26.7804	−	9.75733i	−1.44390	−	0.526080i
$345$	−5.25706	−	2.26310i	−0.283030	−	0.121841i
$346$	−15.5443	+	20.8748i	−0.835666	+	1.12224i
$347$	−5.74855			−0.308598			−0.154299	−	0.988024i	$-0.549312\pi$
$347$	−5.74855			−0.308598			−0.154299	+	0.988024i	$0.549312\pi$
$348$	1.56448	−	13.4448i	0.0838650	−	0.720716i
$349$	−36.1146			−1.93317			−0.966584	−	0.256348i	$-0.917481\pi$
$349$	−36.1146			−1.93317			−0.966584	+	0.256348i	$0.917481\pi$
$350$	−1.14821	+	1.54196i	−0.0613744	+	0.0824212i
$351$	−4.87886	+	1.78793i	−0.260414	+	0.0954328i
$352$	−31.9439	−	1.87822i	−1.70261	−	0.100109i
$353$		−	10.2793i		−	0.547112i	−0.961856	−	0.273556i	$-0.911800\pi$
$353$		−	10.2793i		−	0.547112i	0.961856	−	0.273556i	$-0.0881999\pi$
$354$	−28.8404	+	16.6750i	−1.53285	+	0.886266i
$355$		−	12.2472i		−	0.650014i
$356$	−3.26386	+	0.976350i	−0.172984	+	0.0517465i
$357$	−4.44311	+	10.3211i	−0.235154	+	0.546251i
$358$	−15.3010	−	11.3938i	−0.808683	−	0.602181i
$359$	−0.828840			−0.0437445			−0.0218722	−	0.999761i	$-0.506963\pi$
$359$	−0.828840			−0.0437445			−0.0218722	+	0.999761i	$0.506963\pi$
$360$	−3.36970	−	7.78750i	−0.177599	−	0.410437i
$361$	−49.7943			−2.62075
$362$	9.58373	+	7.13647i	0.503710	+	0.375084i
$363$	−14.3808	+	33.4058i	−0.754796	+	1.75335i
$364$	2.60478	−	0.779195i	0.136528	−	0.0408409i
$365$		−	3.48129i		−	0.182219i
$366$	0.292118	−	0.168897i	0.0152693	−	0.00882841i
$367$		−	14.8157i		−	0.773374i	−0.922211	−	0.386687i	$-0.873619\pi$
$367$		−	14.8157i		−	0.773374i	0.922211	−	0.386687i	$-0.126381\pi$
$368$	−11.0465	+	7.25843i	−0.575840	+	0.378372i
$369$	−3.03722	+	2.87390i	−0.158111	+	0.149609i
$370$	2.97113	−	3.99000i	0.154462	−	0.207430i
$371$	6.36566			0.330489
$372$	3.28228	−	28.2072i	0.170178	−	1.46247i
$373$	−7.15263			−0.370349			−0.185175	−	0.982706i	$-0.559285\pi$
$373$	−7.15263			−0.370349			−0.185175	+	0.982706i	$0.559285\pi$
$374$	22.8014	−	30.6206i	1.17903	−	1.58335i
$375$	1.59090	+	0.684863i	0.0821537	+	0.0353662i
$376$	6.24961	−	17.1530i	0.322299	−	0.884597i
$377$		−	3.90736i		−	0.201239i
$378$	2.84504	−	9.57593i	0.146333	−	0.492533i
$379$			26.4875i			1.36057i	0.732946	+	0.680287i	$0.238145\pi$
$379$			26.4875i			1.36057i	−0.732946	+	0.680287i	$0.761855\pi$
$380$	4.75412	+	15.8926i	0.243881	+	0.815275i
$381$	−3.82886	−	1.64828i	−0.196158	−	0.0844439i
$382$	−5.09319	−	3.79261i	−0.260590	−	0.194047i
$383$	18.6316			0.952029			0.476015	−	0.879437i	$-0.342081\pi$
$383$	18.6316			0.952029			0.476015	+	0.879437i	$0.342081\pi$
$384$	−19.2981	−	3.40355i	−0.984801	−	0.173687i
$385$	7.68978			0.391908
$386$	29.4436	+	21.9250i	1.49864	+	1.11595i
$387$	−21.9592	+	20.7784i	−1.11625	+	1.05622i
$388$	0.999418	+	3.34097i	0.0507378	+	0.169612i
$389$			8.15991i			0.413724i	0.978370	+	0.206862i	$0.0663251\pi$
$389$			8.15991i			0.413724i	−0.978370	+	0.206862i	$0.933675\pi$
$390$	−1.22607	−	2.12056i	−0.0620843	−	0.107379i
$391$		−	15.7700i		−	0.797522i
$392$	4.98846	−	13.6916i	0.251955	−	0.691529i
$393$	10.3598	−	24.0652i	0.522581	−	1.21393i
$394$	15.7035	−	21.0886i	0.791132	−	1.06243i
$395$	12.9548			0.651825
$396$	−16.9334	+	29.4141i	−0.850935	+	1.47811i
$397$	27.2220			1.36623			0.683115	−	0.730310i	$-0.260625\pi$
$397$	27.2220			1.36623			0.683115	+	0.730310i	$0.260625\pi$
$398$	20.3391	−	27.3139i	1.01951	−	1.36912i
$399$	−7.72205	+	17.9379i	−0.386586	+	0.898018i
$400$	3.34292	−	2.19656i	0.167146	−	0.109828i
$401$			2.22007i			0.110865i	0.998462	+	0.0554325i	$0.0176538\pi$
$401$			2.22007i			0.110865i	−0.998462	+	0.0554325i	$0.982346\pi$
$402$	−7.24092	−	12.5236i	−0.361144	−	0.624621i
$403$		−	8.19765i		−	0.408354i
$404$	20.2566	−	6.05954i	1.00780	−	0.301474i
$405$	−8.98627	−	0.496932i	−0.446531	−	0.0246928i
$406$	6.02499	+	4.48648i	0.299015	+	0.222660i
$407$	−19.8982			−0.986317
$408$	16.0372	−	17.0121i	0.793960	−	0.842227i
$409$	6.75656			0.334090			0.167045	−	0.985949i	$-0.446577\pi$
$409$	6.75656			0.334090			0.167045	+	0.985949i	$0.446577\pi$
$410$	−1.58096	−	1.17725i	−0.0780778	−	0.0581402i
$411$	23.8723	+	10.2767i	1.17753	+	0.506913i
$412$	−12.0231	+	3.59660i	−0.592338	+	0.177192i
$413$		−	18.4886i		−	0.909764i
$414$	1.64647	+	13.9226i	0.0809197	+	0.684258i
$415$		−	6.73642i		−	0.330678i
$416$	−5.64710	−	0.332035i	−0.276872	−	0.0162794i
$417$	18.3735	+	7.90957i	0.899754	+	0.387333i
$418$	39.6285	−	53.2180i	1.93829	−	2.60298i
$419$	29.4908			1.44072			0.720360	−	0.693600i	$-0.243977\pi$
$419$	29.4908			1.44072			0.720360	+	0.693600i	$0.243977\pi$
$420$	4.67759	+	0.544301i	0.228243	+	0.0265592i
$421$	−21.7440			−1.05974			−0.529870	−	0.848079i	$-0.677759\pi$
$421$	−21.7440			−1.05974			−0.529870	+	0.848079i	$0.677759\pi$
$422$	−12.9677	+	17.4146i	−0.631257	+	0.847729i
$423$	−13.3086	−	14.0649i	−0.647089	−	0.683861i
$424$	−12.4443	−	4.53401i	−0.604347	−	0.220191i
$425$			4.77234i			0.231492i
$426$	−25.9709	+	15.0159i	−1.25829	+	0.727522i
$427$			0.187267i			0.00906248i
$428$	1.71381	+	5.72913i	0.0828402	+	0.276928i
$429$	−3.87405	+	8.99922i	−0.187041	+	0.434486i
$430$	−11.4303	−	8.51154i	−0.551220	−	0.410463i
$431$	25.7919			1.24235			0.621177	−	0.783670i	$-0.286655\pi$
$431$	25.7919			1.24235			0.621177	+	0.783670i	$0.286655\pi$
$432$	−12.3824	+	16.6936i	−0.595746	+	0.803173i
$433$	15.1646			0.728763			0.364382	−	0.931250i	$-0.381280\pi$
$433$	15.1646			0.728763			0.364382	+	0.931250i	$0.381280\pi$
$434$	12.6404	+	9.41262i	0.606760	+	0.451820i
$435$	2.67601	−	6.21622i	0.128305	−	0.298045i
$436$	−6.67985	−	22.3302i	−0.319907	−	1.06942i
$437$		−	27.4079i		−	1.31110i
$438$	−7.38226	+	4.26829i	−0.352738	+	0.203947i
$439$		−	6.02706i		−	0.287656i	−0.989603	−	0.143828i	$-0.954059\pi$
$439$		−	6.02706i		−	0.287656i	0.989603	−	0.143828i	$-0.0459412\pi$
$440$	−15.0328	−	5.47714i	−0.716661	−	0.261112i
$441$	−10.6230	−	11.2267i	−0.505858	−	0.534604i
$442$	4.03088	−	5.41317i	0.191730	−	0.257478i
$443$	−10.8589			−0.515921			−0.257961	−	0.966155i	$-0.583050\pi$
$443$	−10.8589			−0.515921			−0.257961	+	0.966155i	$0.583050\pi$
$444$	−12.1038	−	1.40844i	−0.574422	−	0.0668417i
$445$	−1.70338			−0.0807481
$446$	−3.56604	+	4.78891i	−0.168857	+	0.226762i
$447$	12.3764	+	5.32787i	0.585381	+	0.252000i
$448$	6.99605	−	8.32635i	0.330532	−	0.393383i
$449$		−	18.2223i		−	0.859963i	−0.902838	−	0.429981i	$-0.858520\pi$
$449$		−	18.2223i		−	0.859963i	0.902838	−	0.429981i	$-0.141480\pi$
$450$	−0.498258	−	4.21328i	−0.0234881	−	0.198616i
$451$			7.88426i			0.371255i
$452$	−19.1754	+	5.73612i	−0.901935	+	0.269805i
$453$	22.6996	+	9.77189i	1.06652	+	0.459124i
$454$	−16.0845	−	11.9772i	−0.754881	−	0.562118i
$455$	1.35942			0.0637304
$456$	27.8724	−	29.5668i	1.30524	−	1.38459i
$457$	−12.1375			−0.567768			−0.283884	−	0.958859i	$-0.591623\pi$
$457$	−12.1375			−0.567768			−0.283884	+	0.958859i	$0.591623\pi$
$458$	13.6471	+	10.1622i	0.637685	+	0.474848i
$459$	−8.53261	−	23.2836i	−0.398268	−	1.08678i
$460$	−6.33169	+	1.89406i	−0.295216	+	0.0883109i
$461$			17.8100i			0.829493i	0.909937	+	0.414746i	$0.136130\pi$
$461$			17.8100i			0.829493i	−0.909937	+	0.414746i	$0.863870\pi$
$462$	−9.42819	−	16.3066i	−0.438639	−	0.758653i
$463$			12.9656i			0.602564i	0.953535	+	0.301282i	$0.0974145\pi$
$463$			12.9656i			0.602564i	−0.953535	+	0.301282i	$0.902586\pi$
$464$	−8.58276	−	13.0620i	−0.398444	−	0.606389i
$465$	5.61427	−	13.0416i	0.260355	−	0.604791i
$466$	14.3085	−	19.2152i	0.662828	−	0.890128i
$467$	−2.27821			−0.105423			−0.0527116	−	0.998610i	$-0.516786\pi$
$467$	−2.27821			−0.105423			−0.0527116	+	0.998610i	$0.516786\pi$
$468$	−2.99352	+	5.19989i	−0.138376	+	0.240365i
$469$	8.02845			0.370720
$470$	5.45168	−	7.32119i	0.251467	−	0.337701i
$471$	−4.54405	+	10.5556i	−0.209379	+	0.486376i
$472$	−13.1687	+	36.1435i	−0.606139	+	1.66364i
$473$			57.0034i			2.62102i
$474$	−15.8834	−	27.4713i	−0.729549	−	1.26180i
$475$			8.29423i			0.380566i
$476$	3.71858	+	12.4309i	0.170441	+	0.569770i
$477$	−10.2039	+	9.65526i	−0.467206	+	0.442084i
$478$	−9.21286	−	6.86030i	−0.421387	−	0.313783i
$479$	15.4134			0.704257			0.352128	−	0.935952i	$-0.385458\pi$
$479$	15.4134			0.704257			0.352128	+	0.935952i	$0.385458\pi$
$480$	−8.75657	−	4.39573i	−0.399681	−	0.200637i
$481$	−3.51765			−0.160391
$482$	15.1835	+	11.3063i	0.691590	+	0.514988i
$483$	−7.14653	−	3.07649i	−0.325178	−	0.139985i
$484$	12.0357	+	40.2345i	0.547079	+	1.82884i
$485$			1.74363i			0.0791740i
$486$	9.96399	+	19.6652i	0.451976	+	0.892030i
$487$			25.7958i			1.16892i	0.811422	+	0.584460i	$0.198694\pi$
$487$			25.7958i			1.16892i	−0.811422	+	0.584460i	$0.801306\pi$
$488$	0.133383	−	0.366089i	0.00603796	−	0.0165721i
$489$	19.5619	+	8.42115i	0.884619	+	0.380818i
$490$	4.35155	−	5.84380i	0.196583	−	0.263996i
$491$	−1.92741			−0.0869826			−0.0434913	−	0.999054i	$-0.513848\pi$
$491$	−1.92741			−0.0869826			−0.0434913	+	0.999054i	$0.513848\pi$
$492$	−0.558066	+	4.79589i	−0.0251596	+	0.216216i
$493$	18.6473			0.839830
$494$	7.00560	−	9.40798i	0.315197	−	0.423285i
$495$	−12.3265	+	11.6637i	−0.554033	+	0.524242i
$496$	−18.0066	−	27.4041i	−0.808521	−	1.23048i
$497$		−	16.6490i		−	0.746811i
$498$	−14.2850	+	8.25930i	−0.640124	+	0.370108i
$499$		−	4.99764i		−	0.223725i	−0.993724	−	0.111863i	$-0.964318\pi$
$499$		−	4.99764i		−	0.223725i	0.993724	−	0.111863i	$-0.0356817\pi$
$500$	1.91611	−	0.573183i	0.0856909	−	0.0256335i
$501$	7.67569	−	17.8302i	0.342925	−	0.796595i
$502$	6.73824	+	5.01759i	0.300743	+	0.223946i
$503$	7.88807			0.351712			0.175856	−	0.984416i	$-0.443731\pi$
$503$	7.88807			0.351712			0.175856	+	0.984416i	$0.443731\pi$
$504$	−4.58082	−	10.5865i	−0.204046	−	0.471558i
$505$	10.5717			0.470436
$506$	21.2023	+	15.7881i	0.942555	+	0.701868i
$507$	−0.684863	+	1.59090i	−0.0304158	+	0.0706543i
$508$	−4.61154	+	1.37950i	−0.204604	+	0.0612052i
$509$			12.5772i			0.557473i	0.960368	+	0.278737i	$0.0899157\pi$
$509$			12.5772i			0.557473i	−0.960368	+	0.278737i	$0.910084\pi$
$510$	10.1200	−	5.85120i	0.448122	−	0.259096i
$511$		−	4.73252i		−	0.209354i
$512$	−19.6072	+	11.2942i	−0.866522	+	0.499139i
$513$	−14.8295	−	40.4664i	−0.654740	−	1.78664i
$514$	−4.33884	+	5.82673i	−0.191378	+	0.257006i
$515$	−6.27478			−0.276500
$516$	−4.03483	+	34.6744i	−0.177624	+	1.52646i
$517$	−36.5109			−1.60575
$518$	4.03900	−	5.42406i	0.177463	−	0.238320i
$519$	29.2782	+	12.6039i	1.28517	+	0.553251i
$520$	−2.65753	−	0.968260i	−0.116540	−	0.0424610i
$521$		−	0.945921i		−	0.0414416i	−0.999785	−	0.0207208i	$-0.993404\pi$
$521$		−	0.945921i		−	0.0414416i	0.999785	−	0.0207208i	$-0.00659610\pi$
$522$	−16.4628	+	1.94688i	−0.720558	+	0.0852125i
$523$		−	8.61075i		−	0.376522i	−0.982119	−	0.188261i	$-0.939715\pi$
$523$		−	8.61075i		−	0.376522i	0.982119	−	0.188261i	$-0.0602850\pi$
$524$	−8.67041	−	28.9845i	−0.378769	−	1.26619i
$525$	2.16269	+	0.931014i	0.0943877	+	0.0406328i
$526$	8.68859	+	6.46991i	0.378840	+	0.282101i
$527$	39.1219			1.70418
$528$	6.81665	+	38.5933i	0.296657	+	1.67956i
$529$	−12.0806			−0.525242
$530$	−5.31143	−	3.95512i	−0.230714	−	0.171800i
$531$	28.0430	+	29.6366i	1.21696	+	1.28612i
$532$	6.46282	+	21.6047i	0.280199	+	0.936682i
$533$			1.39380i			0.0603720i
$534$	2.08846	+	3.61212i	0.0903765	+	0.156312i
$535$			2.98999i			0.129268i
$536$	−15.6949	−	5.71836i	−0.677915	−	0.246995i
$537$	−9.23854	+	21.4606i	−0.398672	+	0.926094i
$538$	17.9845	−	24.1518i	0.775368	−	1.04126i
$539$	−29.1432			−1.25528
$540$	−8.32360	+	6.22235i	−0.358191	+	0.267767i
$541$	−20.9269			−0.899718			−0.449859	−	0.893100i	$-0.648526\pi$
$541$	−20.9269			−0.899718			−0.449859	+	0.893100i	$0.648526\pi$
$542$	−13.5217	+	18.1586i	−0.580807	+	0.779979i
$543$	5.78653	−	13.4418i	0.248324	−	0.576842i
$544$	1.58458	−	26.9499i	0.0679384	−	1.15547i
$545$		−	11.6540i		−	0.499201i
$546$	−1.66673	−	2.88272i	−0.0713297	−	0.123369i
$547$			6.00845i			0.256903i	0.991716	+	0.128451i	$0.0410006\pi$
$547$			6.00845i			0.256903i	−0.991716	+	0.128451i	$0.958999\pi$
$548$	28.7521	−	8.60091i	1.22823	−	0.367413i
$549$	−0.284041	−	0.300182i	−0.0121226	−	0.0128115i
$550$	−6.41626	−	4.77783i	−0.273590	−	0.203727i
$551$	32.4086			1.38065
$552$	11.7795	+	11.1045i	0.501370	+	0.472637i
$553$	17.6109			0.748893
$554$	24.1330	+	17.9705i	1.02531	+	0.763493i
$555$	−5.59622	−	2.40911i	−0.237546	−	0.102261i
$556$	22.1293	−	6.61977i	0.938493	−	0.280741i
$557$		−	23.8570i		−	1.01085i	−0.862870	−	0.505426i	$-0.831335\pi$
$557$		−	23.8570i		−	1.01085i	0.862870	−	0.505426i	$-0.168665\pi$
$558$	−34.5390	+	4.08455i	−1.46215	+	0.172913i
$559$			10.0772i			0.426219i
$560$	4.54442	−	2.98604i	0.192037	−	0.126183i
$561$	−42.9473	−	18.4883i	−1.81324	−	0.780576i
$562$	−8.73117	+	11.7253i	−0.368302	+	0.494602i
$563$	14.1284			0.595439			0.297720	−	0.954653i	$-0.403774\pi$
$563$	14.1284			0.595439			0.297720	+	0.954653i	$0.403774\pi$
$564$	−22.2091	−	2.58433i	−0.935172	−	0.108820i
$565$	−10.0075			−0.421018
$566$	14.0613	−	18.8832i	0.591039	−	0.793720i
$567$	−12.2161	−	0.675538i	−0.513027	−	0.0283699i
$568$	−11.8585	+	32.5473i	−0.497570	+	1.36565i
$569$			16.8467i			0.706250i	0.935576	+	0.353125i	$0.114881\pi$
$569$			16.8467i			0.706250i	−0.935576	+	0.353125i	$0.885119\pi$
$570$	17.5884	−	10.1693i	0.736697	−	0.425944i
$571$			6.39696i			0.267705i	0.991001	+	0.133852i	$0.0427348\pi$
$571$			6.39696i			0.267705i	−0.991001	+	0.133852i	$0.957265\pi$
$572$	3.24232	+	10.8388i	0.135568	+	0.453193i
$573$	−3.07520	+	7.14352i	−0.128468	+	0.298425i
$574$	−2.14918	−	1.60037i	−0.0897049	−	0.0667982i
$575$	−3.30446			−0.137805
$576$	1.41476	+	23.9583i	0.0589482	+	0.998261i
$577$	15.4704			0.644039			0.322020	−	0.946733i	$-0.395638\pi$
$577$	15.4704			0.644039			0.322020	+	0.946733i	$0.395638\pi$
$578$	6.55069	+	4.87793i	0.272473	+	0.202895i
$579$	17.7777	−	41.2965i	0.738815	−	1.71623i
$580$	−2.23964	−	7.48692i	−0.0929958	−	0.310878i
$581$		−	9.15760i		−	0.379921i
$582$	3.69746	−	2.13780i	0.153265	−	0.0886148i
$583$			26.4882i			1.09703i
$584$	−3.37079	+	9.25163i	−0.139484	+	0.382835i
$585$	−2.17910	+	2.06192i	−0.0900946	+	0.0852501i
$586$	−11.2795	+	15.1475i	−0.465951	+	0.625736i
$587$	29.8379			1.23154			0.615771	−	0.787925i	$-0.288845\pi$
$587$	29.8379			1.23154			0.615771	+	0.787925i	$0.288845\pi$
$588$	−17.7274	−	2.06282i	−0.731065	−	0.0850693i
$589$	67.9932			2.80161
$590$	−11.4874	+	15.4267i	−0.472928	+	0.635106i
$591$	−29.5781	−	12.7330i	−1.21668	−	0.523767i
$592$	−11.7592	+	7.72672i	−0.483301	+	0.317566i
$593$		−	28.8555i		−	1.18495i	−0.805587	−	0.592477i	$-0.798150\pi$
$593$		−	28.8555i		−	1.18495i	0.805587	−	0.592477i	$-0.201850\pi$
$594$	39.8465	+	11.8385i	1.63492	+	0.485741i
$595$			6.48759i			0.265965i
$596$	14.9063	−	4.45906i	0.610585	−	0.182650i
$597$	−38.3094	−	16.4917i	−1.56790	−	0.674962i
$598$	3.74818	+	2.79106i	0.153274	+	0.114135i
$599$	−18.4307			−0.753057			−0.376529	−	0.926405i	$-0.622882\pi$
$599$	−18.4307			−0.753057			−0.376529	+	0.926405i	$0.622882\pi$
$600$	−3.56474	−	3.36045i	−0.145530	−	0.137190i
$601$	44.8850			1.83090			0.915448	−	0.402436i	$-0.131836\pi$
$601$	44.8850			1.83090			0.915448	+	0.402436i	$0.131836\pi$
$602$	−15.5386	−	11.5707i	−0.633306	−	0.471587i
$603$	−12.8693	+	12.1773i	−0.524080	+	0.495900i
$604$	27.3397	−	8.17840i	1.11244	−	0.332774i
$605$			20.9981i			0.853692i
$606$	−12.9617	−	22.4180i	−0.526531	−	0.910668i
$607$		−	37.1886i		−	1.50944i	−0.656047	−	0.754720i	$-0.727773\pi$
$607$		−	37.1886i		−	1.50944i	0.656047	−	0.754720i	$-0.272227\pi$
$608$	2.75398	−	46.8384i	0.111689	−	1.89955i
$609$	3.63781	−	8.45044i	0.147412	−	0.342429i
$610$	0.116353	−	0.156253i	0.00471100	−	0.00632651i
$611$	−6.45448			−0.261120
$612$	−24.8156	−	14.2861i	−1.00311	−	0.577481i
$613$	20.8295			0.841297			0.420648	−	0.907224i	$-0.361803\pi$
$613$	20.8295			0.841297			0.420648	+	0.907224i	$0.361803\pi$
$614$	−0.325741	+	0.437445i	−0.0131458	+	0.0176538i
$615$	−0.954560	+	2.21739i	−0.0384916	+	0.0894138i
$616$	−20.4358	−	7.44571i	−0.823384	−	0.299996i
$617$		−	14.7739i		−	0.594774i	−0.954757	−	0.297387i	$-0.903885\pi$
$617$		−	14.7739i		−	0.594774i	0.954757	−	0.297387i	$-0.0961151\pi$
$618$	7.69330	+	13.3060i	0.309470	+	0.535247i
$619$			22.1422i			0.889969i	0.895538	+	0.444984i	$0.146791\pi$
$619$			22.1422i			0.889969i	−0.895538	+	0.444984i	$0.853209\pi$
$620$	−4.69875	−	15.7076i	−0.188707	−	0.630831i
$621$	16.1220	−	5.90814i	0.646953	−	0.237086i
$622$	−8.91848	−	6.64110i	−0.357599	−	0.266284i
$623$	−2.31561			−0.0927728
$624$	1.20506	+	6.82260i	0.0482411	+	0.273122i
$625$	1.00000			0.0400000
$626$	19.6158	+	14.6068i	0.784007	+	0.583806i
$627$	−74.6416	−	32.1323i	−2.98090	−	1.28324i
$628$	3.80306	+	12.7133i	0.151758	+	0.507316i
$629$		−	16.7874i		−	0.669357i
$630$	−0.677340	−	5.72760i	−0.0269859	−	0.228193i
$631$		−	18.9284i		−	0.753528i	−0.926309	−	0.376764i	$-0.877037\pi$
$631$		−	18.9284i		−	0.753528i	0.926309	−	0.376764i	$-0.122963\pi$
$632$	−34.4277	−	12.5436i	−1.36946	−	0.498957i
$633$	24.4251	+	10.5147i	0.970810	+	0.417922i
$634$	7.00137	−	9.40230i	0.278060	−	0.373413i
$635$	−2.40673			−0.0955080
$636$	−1.87490	+	16.1124i	−0.0743445	+	0.638900i
$637$	−5.15199			−0.204129
$638$	−18.6687	+	25.0707i	−0.739102	+	0.992557i
$639$	25.2528	+	26.6878i	0.998985	+	1.05575i
$640$	−11.0108	+	2.60061i	−0.435238	+	0.102798i
$641$			13.1971i			0.521255i	0.965439	+	0.260628i	$0.0839295\pi$
$641$			13.1971i			0.521255i	−0.965439	+	0.260628i	$0.916071\pi$
$642$	6.34044	−	3.66593i	0.250237	−	0.144683i
$643$			41.2817i			1.62799i	0.580872	+	0.813995i	$0.302712\pi$
$643$			41.2817i			1.62799i	−0.580872	+	0.813995i	$0.697288\pi$
$644$	−8.60739	+	2.57481i	−0.339179	+	0.101462i
$645$	−6.90149	+	16.0318i	−0.271746	+	0.631251i
$646$	44.8981	+	33.4331i	1.76649	+	1.31541i
$647$	27.0997			1.06540			0.532699	−	0.846305i	$-0.321178\pi$
$647$	27.0997			1.06540			0.532699	+	0.846305i	$0.321178\pi$
$648$	23.4001	+	10.0217i	0.919244	+	0.393688i
$649$	76.9331			3.01989
$650$	−1.13428	−	0.844635i	−0.0444901	−	0.0331293i
$651$	7.63213	−	17.7290i	0.299127	−	0.694855i
$652$	23.5606	−	7.04792i	0.922706	−	0.276018i
$653$			29.0058i			1.13508i	0.823345	+	0.567542i	$0.192105\pi$
$653$			29.0058i			1.13508i	−0.823345	+	0.567542i	$0.807895\pi$
$654$	−24.7129	+	14.2885i	−0.966350	+	0.558726i
$655$		−	15.1268i		−	0.591052i
$656$	3.06156	+	4.65935i	0.119534	+	0.181917i
$657$	7.17815	+	7.58606i	0.280046	+	0.295960i
$658$	7.41110	−	9.95254i	0.288915	−	0.387990i
$659$	8.22195			0.320282			0.160141	−	0.987094i	$-0.448805\pi$
$659$	8.22195			0.320282			0.160141	+	0.987094i	$0.448805\pi$
$660$	−2.26490	+	19.4640i	−0.0881610	+	0.757635i
$661$	42.5145			1.65362			0.826812	−	0.562479i	$-0.190152\pi$
$661$	42.5145			1.65362			0.826812	+	0.562479i	$0.190152\pi$
$662$	5.75495	−	7.72846i	0.223673	−	0.300375i
$663$	−7.59231	−	3.26840i	−0.294861	−	0.126934i
$664$	−6.52260	+	17.9022i	−0.253126	+	0.694742i
$665$			11.2753i			0.437238i
$666$	1.75270	+	14.8208i	0.0679156	+	0.574296i
$667$			12.9117i			0.499943i
$668$	−6.42402	−	21.4750i	−0.248553	−	0.830893i
$669$	6.71676	+	2.89148i	0.259685	+	0.111791i
$670$	−6.69884	−	4.98825i	−0.258799	−	0.192713i
$671$	−0.779239			−0.0300822
$672$	−11.9038	−	5.97562i	−0.459200	−	0.230515i
$673$	−23.2736			−0.897131			−0.448566	−	0.893750i	$-0.648065\pi$
$673$	−23.2736			−0.897131			−0.448566	+	0.893750i	$0.648065\pi$
$674$	−32.6598	−	24.3199i	−1.25801	−	0.936769i
$675$	−4.87886	+	1.78793i	−0.187788	+	0.0688175i
$676$	0.573183	+	1.91611i	0.0220455	+	0.0736964i
$677$			1.50184i			0.0577205i	0.999583	+	0.0288603i	$0.00918778\pi$
$677$			1.50184i			0.0577205i	−0.999583	+	0.0288603i	$0.990812\pi$
$678$	12.2698	+	21.2214i	0.471221	+	0.815004i
$679$			2.37032i			0.0909643i
$680$	4.62086	−	12.6826i	0.177202	−	0.486357i
$681$	−9.71158	+	22.5595i	−0.372149	+	0.864481i
$682$	−39.1670	+	52.5983i	−1.49978	+	2.01409i
$683$	−42.6820			−1.63318			−0.816591	−	0.577216i	$-0.804139\pi$
$683$	−42.6820			−1.63318			−0.816591	+	0.577216i	$0.804139\pi$
$684$	−43.1291	−	24.8290i	−1.64908	−	0.949359i
$685$	15.0055			0.573331
$686$	13.9530	−	18.7379i	0.532730	−	0.715415i
$687$	8.23991	−	19.1409i	0.314372	−	0.730269i
$688$	22.1351	+	33.6872i	0.843894	+	1.28431i
$689$			4.68264i			0.178394i
$690$	4.05148	+	7.00728i	0.154237	+	0.266763i
$691$		−	40.1484i		−	1.52732i	−0.645620	−	0.763659i	$-0.723401\pi$
$691$		−	40.1484i		−	1.52732i	0.645620	−	0.763659i	$-0.276599\pi$
$692$	35.2632	−	10.5486i	1.34050	−	0.400998i
$693$	−16.7568	+	15.8558i	−0.636538	+	0.602310i
$694$	6.52047	+	4.85543i	0.247514	+	0.184310i
$695$	11.5491			0.438083
$696$	−13.1305	+	13.9287i	−0.497710	+	0.527968i
$697$	−6.65167			−0.251950
$698$	40.9640	+	30.5036i	1.55051	+	1.15458i
$699$	−26.9506	−	11.6019i	−1.01936	−	0.438824i
$700$	2.60478	−	0.779195i	0.0984516	−	0.0294508i
$701$			36.0655i			1.36217i	0.732202	+	0.681087i	$0.238493\pi$
$701$			36.0655i			1.36217i	−0.732202	+	0.681087i	$0.761507\pi$
$702$	7.04415	+	2.09284i	0.265864	+	0.0789892i
$703$		−	29.1762i		−	1.10040i
$704$	34.6469	+	29.1113i	1.30580	+	1.09717i
$705$	−10.2684	−	4.42043i	−0.386731	−	0.166483i
$706$	−8.68226	+	11.6596i	−0.326761	+	0.438815i
$707$	14.3714			0.540492
$708$	46.7974	+	5.44551i	1.75875	+	0.204655i
$709$	−5.83506			−0.219140			−0.109570	−	0.993979i	$-0.534947\pi$
$709$	−5.83506			−0.219140			−0.109570	+	0.993979i	$0.534947\pi$
$710$	−10.3444	+	13.8918i	−0.388219	+	0.521348i
$711$	−28.2297	+	26.7118i	−1.05870	+	1.00177i
$712$	4.52679	+	1.64932i	0.169649	+	0.0618108i
$713$			27.0888i			1.01448i
$714$	13.7573	−	7.95422i	0.514854	−	0.297679i
$715$			5.65668i			0.211548i
$716$	7.73202	+	25.8475i	0.288959	+	0.965967i
$717$	−5.56260	+	12.9216i	−0.207739	+	0.482567i
$718$	0.940136	+	0.700067i	0.0350856	+	0.0261263i
$719$	−44.1796			−1.64762			−0.823810	−	0.566866i	$-0.808156\pi$
$719$	−44.1796			−1.64762			−0.823810	+	0.566866i	$0.808156\pi$
$720$	−2.75541	+	11.6794i	−0.102688	+	0.435264i
$721$	−8.53004			−0.317675
$722$	56.4807	+	42.0580i	2.10199	+	1.56524i
$723$	9.16760	−	21.2958i	0.340947	−	0.792000i
$724$	−4.84292	−	16.1895i	−0.179986	−	0.601678i
$725$		−	3.90736i		−	0.145116i
$726$	44.5276	−	25.7450i	1.65257	−	0.955487i
$727$		−	46.4424i		−	1.72245i	−0.508222	−	0.861226i	$-0.669697\pi$
$727$		−	46.4424i		−	1.72245i	0.508222	−	0.861226i	$-0.330303\pi$
$728$	−3.61269	−	1.31627i	−0.133895	−	0.0487841i
$729$	20.6066	−	17.4461i	0.763207	−	0.646154i
$730$	−2.94042	+	3.94875i	−0.108830	+	0.146150i
$731$	−48.0917			−1.77874
$732$	−0.474000	−	0.0551563i	−0.0175196	−	0.00203864i
$733$	−12.4268			−0.458993			−0.229496	−	0.973310i	$-0.573708\pi$
$733$	−12.4268			−0.458993			−0.229496	+	0.973310i	$0.573708\pi$
$734$	−12.5139	+	16.8052i	−0.461895	+	0.620290i
$735$	−8.19630	−	3.52841i	−0.302325	−	0.130147i
$736$	18.6606	+	1.09720i	0.687839	+	0.0404431i
$737$			33.4073i			1.23057i
$738$	5.87246	−	0.694471i	0.216168	−	0.0255638i
$739$			0.412709i			0.0151818i	0.999971	+	0.00759088i	$0.00241627\pi$
$739$			0.412709i			0.0151818i	−0.999971	+	0.00759088i	$0.997584\pi$
$740$	−6.74018	+	2.01626i	−0.247774	+	0.0741190i
$741$	−13.1953	−	5.68042i	−0.484741	−	0.208675i
$742$	−7.22044	−	5.37666i	−0.265071	−	0.197383i
$743$	−23.6768			−0.868618			−0.434309	−	0.900764i	$-0.643007\pi$
$743$	−23.6768			−0.868618			−0.434309	+	0.900764i	$0.643007\pi$
$744$	−27.5478	+	29.2225i	−1.00995	+	1.07135i
$745$	7.77947			0.285018
$746$	8.11308	+	6.04136i	0.297041	+	0.221190i
$747$	13.8900	+	14.6793i	0.508208	+	0.537088i
$748$	−51.7264	+	15.4734i	−1.89130	+	0.565764i
$749$			4.06464i			0.148519i
$750$	−1.22607	−	2.12056i	−0.0447696	−	0.0774318i
$751$			15.0756i			0.550116i	0.961428	+	0.275058i	$0.0886970\pi$
$751$			15.0756i			0.550116i	−0.961428	+	0.275058i	$0.911303\pi$
$752$	−21.5768	+	14.1776i	−0.786825	+	0.517005i
$753$	4.06846	−	9.45081i	0.148263	−	0.344407i
$754$	−3.30030	+	4.43205i	−0.120190	+	0.161406i
$755$	14.2684			0.519280
$756$	−11.3152	+	8.45876i	−0.411531	+	0.307642i
$757$	−25.8699			−0.940256			−0.470128	−	0.882598i	$-0.655792\pi$
$757$	−25.8699			−0.940256			−0.470128	+	0.882598i	$0.655792\pi$
$758$	22.3723	−	30.0443i	0.812598	−	1.09126i
$759$	12.8016	−	29.7375i	0.464670	−	1.07940i
$760$	8.03097	−	22.0422i	0.291314	−	0.799554i
$761$		−	26.6769i		−	0.967038i	−0.875334	−	0.483519i	$-0.839358\pi$
$761$		−	26.6769i		−	0.967038i	0.875334	−	0.483519i	$-0.160642\pi$
$762$	2.95081	+	5.10360i	0.106896	+	0.184884i
$763$		−	15.8426i		−	0.573540i
$764$	2.57373	+	8.60377i	0.0931142	+	0.311273i
$765$	−9.84020	−	10.3994i	−0.355773	−	0.375991i
$766$	−21.1334	−	15.7369i	−0.763582	−	0.568597i
$767$	13.6004			0.491082
$768$	19.0147	+	20.1604i	0.686133	+	0.727476i
$769$	−0.463386			−0.0167101			−0.00835507	−	0.999965i	$-0.502660\pi$
$769$	−0.463386			−0.0167101			−0.00835507	+	0.999965i	$0.502660\pi$
$770$	−8.72237	−	6.49506i	−0.314332	−	0.234066i
$771$	8.17236	+	3.51810i	0.294320	+	0.126701i
$772$	−14.8787	−	49.7382i	−0.535495	−	1.79012i
$773$			15.8657i			0.570649i	0.958431	+	0.285324i	$0.0921013\pi$
$773$			15.8657i			0.570649i	−0.958431	+	0.285324i	$0.907899\pi$
$774$	42.4580	−	5.02104i	1.52612	−	0.180478i
$775$		−	8.19765i		−	0.294468i
$776$	1.68828	−	4.63374i	0.0606059	−	0.166342i
$777$	−7.60759	−	3.27498i	−0.272921	−	0.117489i
$778$	6.89215	−	9.25562i	0.247095	−	0.331830i
$779$	−11.5605			−0.414197
$780$	−0.400393	+	3.44088i	−0.0143364	+	0.123203i
$781$	69.2785			2.47898
$782$	−13.3199	+	17.8876i	−0.476318	+	0.639658i
$783$	6.98610	+	19.0635i	0.249663	+	0.681274i
$784$	−17.2227	+	11.3166i	−0.615096	+	0.404166i
$785$			6.63498i			0.236812i
$786$	−32.0772	+	18.5464i	−1.14416	+	0.661529i
$787$			50.9731i			1.81699i	0.417891	+	0.908497i	$0.362769\pi$
$787$			50.9731i			1.81699i	−0.417891	+	0.908497i	$0.637231\pi$
$788$	−35.6244	+	10.6567i	−1.26907	+	0.379628i
$789$	5.24605	−	12.1863i	0.186764	−	0.433844i
$790$	−14.6943	−	10.9421i	−0.522801	−	0.389301i
$791$	−13.6043			−0.483714
$792$	44.0514	−	19.0613i	1.56530	−	0.677314i
$793$	−0.137755			−0.00489184
$794$	−30.8773	−	22.9926i	−1.09580	−	0.815978i
$795$	−3.20697	+	7.44962i	−0.113740	+	0.264211i
$796$	−46.1405	+	13.8024i	−1.63541	+	0.489215i
$797$		−	10.2020i		−	0.361372i	−0.983541	−	0.180686i	$-0.942168\pi$
$797$		−	10.2020i		−	0.361372i	0.983541	−	0.180686i	$-0.0578317\pi$
$798$	23.9099	−	13.8243i	0.846403	−	0.489374i
$799$		−	30.8029i		−	1.08973i
$800$	−5.64710	−	0.332035i	−0.199655	−	0.0117392i
$801$	3.71184	−	3.51225i	0.131151	−	0.124099i
$802$	1.87515	−	2.51818i	0.0662138	−	0.0889201i
$803$	19.6925			0.694934
$804$	−2.36465	+	20.3212i	−0.0833946	+	0.716674i
$805$	−4.49213			−0.158327
$806$	−6.92402	+	9.29843i	−0.243888	+	0.327523i
$807$	−33.8745	−	14.5826i	−1.19244	−	0.513330i
$808$	−28.0947	−	10.2362i	−0.988369	−	0.360108i
$809$		−	8.86947i		−	0.311834i	−0.987770	−	0.155917i	$-0.950167\pi$
$809$		−	8.86947i		−	0.311834i	0.987770	−	0.155917i	$-0.0498332\pi$
$810$	9.77322	+	8.15378i	0.343396	+	0.286495i
$811$		−	6.20238i		−	0.217795i	−0.994053	−	0.108898i	$-0.965268\pi$
$811$		−	6.20238i		−	0.217795i	0.994053	−	0.108898i	$-0.0347321\pi$
$812$	−3.04460	−	10.1778i	−0.106844	−	0.357172i
$813$	25.4686	+	10.9639i	0.893223	+	0.384522i
$814$	22.5701	+	16.8067i	0.791083	+	0.589075i
$815$	12.2961			0.430714
$816$	−32.5597	+	5.75096i	−1.13982	+	0.201324i
$817$	−83.5825			−2.92418
$818$	−7.66383	−	5.70683i	−0.267960	−	0.199535i
$819$	−2.96230	+	2.80301i	−0.103511	+	0.0979452i
$820$	0.798901	+	2.67066i	0.0278988	+	0.0932635i
$821$			5.49575i			0.191803i	0.995391	+	0.0959015i	$0.0305734\pi$
$821$			5.49575i			0.191803i	−0.995391	+	0.0959015i	$0.969427\pi$
$822$	−18.3978	−	31.8200i	−0.641695	−	1.10985i
$823$		−	12.1422i		−	0.423249i	−0.977351	−	0.211625i	$-0.932125\pi$
$823$		−	12.1422i		−	0.423249i	0.977351	−	0.211625i	$-0.0678754\pi$
$824$	16.6754	+	6.07562i	0.580916	+	0.211654i
$825$	−3.87405	+	8.99922i	−0.134877	+	0.313312i
$826$	−15.6161	+	20.9713i	−0.543354	+	0.729683i
$827$	−17.9733			−0.624994			−0.312497	−	0.949919i	$-0.601165\pi$
$827$	−17.9733			−0.624994			−0.312497	+	0.949919i	$0.601165\pi$
$828$	9.89195	−	17.1828i	0.343769	−	0.597143i
$829$	16.3569			0.568099			0.284050	−	0.958810i	$-0.408322\pi$
$829$	16.3569			0.568099			0.284050	+	0.958810i	$0.408322\pi$
$830$	−5.68982	+	7.64099i	−0.197496	+	0.265223i
$831$	14.5712	−	33.8480i	0.505468	−	1.17418i
$832$	6.12495	+	5.14636i	0.212344	+	0.178418i
$833$		−	24.5870i		−	0.851890i
$834$	−14.1600	−	24.4906i	−0.490321	−	0.848039i
$835$		−	11.2076i		−	0.387856i
$836$	−89.8995	+	26.8925i	−3.10924	+	0.930097i
$837$	14.6568	+	39.9952i	0.506614	+	1.38244i
$838$	−33.4508	−	24.9090i	−1.15554	−	0.860466i
$839$	−2.02715			−0.0699851			−0.0349925	−	0.999388i	$-0.511141\pi$
$839$	−2.02715			−0.0699851			−0.0349925	+	0.999388i	$0.511141\pi$
$840$	−4.84597	−	4.56825i	−0.167202	−	0.157620i
$841$	13.7325			0.473535
$842$	24.6638	+	18.3658i	0.849971	+	0.632926i
$843$	16.4455	+	7.07958i	0.566412	+	0.243834i
$844$	29.4180	−	8.80008i	1.01261	−	0.302911i
$845$			1.00000i			0.0344010i
$846$	3.21600	+	27.1945i	0.110568	+	0.934967i
$847$			28.5451i			0.980821i
$848$	10.2857	+	15.6537i	0.353213	+	0.537551i
$849$	−26.4849	−	11.4014i	−0.908959	−	0.391296i
$850$	4.03088	−	5.41317i	0.138258	−	0.185670i
$851$	11.6239			0.398462
$852$	42.1412	+	4.90369i	1.44373	+	0.167998i
$853$	−14.7459			−0.504890			−0.252445	−	0.967611i	$-0.581235\pi$
$853$	−14.7459			−0.504890			−0.252445	+	0.967611i	$0.581235\pi$
$854$	0.158172	−	0.212413i	0.00541254	−	0.00726863i
$855$	−17.1021	−	18.0739i	−0.584879	−	0.618116i
$856$	2.89509	−	7.94599i	0.0989520	−	0.271588i
$857$			18.8795i			0.644910i	0.946585	+	0.322455i	$0.104508\pi$
$857$			18.8795i			0.644910i	−0.946585	+	0.322455i	$0.895492\pi$
$858$	11.9953	−	6.93547i	0.409513	−	0.236773i
$859$			19.5312i			0.666395i	0.942857	+	0.333197i	$0.108128\pi$
$859$			19.5312i			0.666395i	−0.942857	+	0.333197i	$0.891872\pi$
$860$	5.77607	+	19.3089i	0.196962	+	0.658429i
$861$	−1.29764	+	3.01436i	−0.0442236	+	0.102729i
$862$	−29.2553	−	21.7848i	−0.996439	−	0.741993i
$863$	−49.2146			−1.67529			−0.837643	−	0.546218i	$-0.816067\pi$
$863$	−49.2146			−1.67529			−0.837643	+	0.546218i	$0.816067\pi$
$864$	28.1451	−	8.47668i	0.957515	−	0.288383i
$865$	18.4036			0.625740
$866$	−17.2009	−	12.8085i	−0.584510	−	0.435252i
$867$	3.95522	−	9.18776i	0.134326	−	0.312033i
$868$	−6.38756	−	21.3531i	−0.216808	−	0.724772i
$869$			73.2810i			2.48589i
$870$	−8.28579	+	4.79069i	−0.280914	+	0.162420i
$871$			5.90581i			0.200111i
$872$	−11.2841	+	30.9708i	−0.382126	+	1.04880i
$873$	−3.59523	−	3.79953i	−0.121680	−	0.128595i
$874$	−23.1497	+	31.0883i	−0.783050	+	1.05158i
$875$	1.35942			0.0459567
$876$	11.9787	+	1.39388i	0.404723	+	0.0470949i
$877$	58.8302			1.98655			0.993277	−	0.115758i	$-0.0369297\pi$
$877$	58.8302			1.98655			0.993277	+	0.115758i	$0.0369297\pi$
$878$	−5.09067	+	6.83638i	−0.171802	+	0.230717i
$879$	21.2453	+	9.14584i	0.716586	+	0.308482i
$880$	12.4252	+	18.9098i	0.418855	+	0.637451i
$881$		−	25.2912i		−	0.852082i	−0.904704	−	0.426041i	$-0.859908\pi$
$881$		−	25.2912i		−	0.852082i	0.904704	−	0.426041i	$-0.140092\pi$
$882$	2.56702	+	21.7068i	0.0864361	+	0.730905i
$883$		−	22.2071i		−	0.747328i	−0.927564	−	0.373664i	$-0.878101\pi$
$883$		−	22.2071i		−	0.747328i	0.927564	−	0.373664i	$-0.121899\pi$
$884$	−9.14430	+	2.73542i	−0.307556	+	0.0920022i
$885$	21.6369	+	9.31441i	0.727315	+	0.313101i
$886$	12.3170	+	9.17180i	0.413798	+	0.308133i
$887$	−20.3831			−0.684398			−0.342199	−	0.939627i	$-0.611172\pi$
$887$	−20.3831			−0.684398			−0.342199	+	0.939627i	$0.611172\pi$
$888$	12.5395	+	11.8209i	0.420798	+	0.396682i
$889$	−3.27174			−0.109731
$890$	1.93211	+	1.43874i	0.0647646	+	0.0482266i
$891$	2.81099	−	50.8325i	0.0941717	−	1.70295i
$892$	8.08977	−	2.41997i	0.270866	−	0.0810266i
$893$		−	53.5349i		−	1.79148i
$894$	−9.53815	−	16.4968i	−0.319003	−	0.551736i
$895$			13.4896i			0.450908i
$896$	−14.9682	+	3.53531i	−0.500053	+	0.118106i
$897$	2.26310	−	5.25706i	0.0755627	−	0.175528i
$898$	−15.3912	+	20.6692i	−0.513610	+	0.689739i
$899$	−32.0312			−1.06830
$900$	−2.99352	+	5.19989i	−0.0997840	+	0.173330i
$901$	−22.3471			−0.744491
$902$	6.65933	−	8.94296i	0.221731	−	0.297768i
$903$	−9.38200	+	21.7939i	−0.312213	+	0.725254i
$904$	26.5952	+	9.68984i	0.884543	+	0.322279i
$905$		−	8.44917i		−	0.280860i
$906$	−17.4940	−	30.2569i	−0.581199	−	1.00522i
$907$		−	20.4204i		−	0.678048i	−0.940778	−	0.339024i	$-0.889903\pi$
$907$		−	20.4204i		−	0.678048i	0.940778	−	0.339024i	$-0.110097\pi$
$908$	8.12793	+	27.1710i	0.269735	+	0.901701i
$909$	−23.0368	+	21.7981i	−0.764084	+	0.722998i
$910$	−1.54196	−	1.14821i	−0.0511154	−	0.0380628i
$911$	57.9434			1.91975			0.959876	−	0.280425i	$-0.0904754\pi$
$911$	57.9434			1.91975			0.959876	+	0.280425i	$0.0904754\pi$
$912$	−56.5882	+	9.99506i	−1.87382	+	0.330970i
$913$	38.1058			1.26112
$914$	13.7673	+	10.2518i	0.455383	+	0.339098i
$915$	−0.219155	−	0.0943436i	−0.00724504	−	0.00311890i
$916$	−6.89623	−	23.0536i	−0.227858	−	0.761711i
$917$		−	20.5636i		−	0.679069i
$918$	−9.98775	+	33.6170i	−0.329645	+	1.10953i
$919$			32.3596i			1.06745i	0.845660	+	0.533723i	$0.179207\pi$
$919$			32.3596i			1.06745i	−0.845660	+	0.533723i	$0.820793\pi$
$920$	8.78169	+	3.19957i	0.289524	+	0.105487i
$921$	0.613544	+	0.264123i	0.0202170	+	0.00870316i
$922$	15.0429	−	20.2015i	0.495412	−	0.665301i
$923$	12.2472			0.403121
$924$	−3.07894	+	26.4597i	−0.101290	+	0.870459i
$925$	−3.51765			−0.115659
$926$	10.9512	−	14.7067i	0.359879	−	0.483291i
$927$	13.6734	−	12.9381i	0.449092	−	0.424944i
$928$	−1.29738	+	22.0653i	−0.0425886	+	0.724328i
$929$		−	31.1862i		−	1.02319i	−0.859228	−	0.511593i	$-0.829056\pi$
$929$		−	31.1862i		−	1.02319i	0.859228	−	0.511593i	$-0.170944\pi$
$930$	−17.3836	+	10.0509i	−0.570030	+	0.329581i
$931$		−	42.7318i		−	1.40048i
$932$	−32.4597	+	9.70998i	−1.06325	+	0.318061i
$933$	−5.38486	+	12.5087i	−0.176292	+	0.409518i
$934$	2.58413	+	1.92426i	0.0845554	+	0.0629637i
$935$	−26.9956			−0.882850
$936$	7.78750	−	3.36970i	0.254542	−	0.110142i
$937$	−24.9208			−0.814126			−0.407063	−	0.913400i	$-0.633447\pi$
$937$	−24.9208			−0.814126			−0.407063	+	0.913400i	$0.633447\pi$
$938$	−9.10652	−	6.78111i	−0.297338	−	0.221411i
$939$	11.8438	−	27.5125i	0.386507	−	0.897835i
$940$	−12.3675	+	3.69960i	−0.403382	+	0.120668i
$941$		−	15.6493i		−	0.510153i	−0.966921	−	0.255077i	$-0.917899\pi$
$941$		−	15.6493i		−	0.510153i	0.966921	−	0.255077i	$-0.0821007\pi$
$942$	14.0698	−	8.13492i	0.458420	−	0.265050i
$943$		−	4.60574i		−	0.149983i
$944$	45.4651	−	29.8741i	1.47976	−	0.972318i
$945$	−6.63240	+	2.43054i	−0.215752	+	0.0790656i
$946$	48.1471	−	64.6578i	1.56540	−	2.10221i
$947$	35.7664			1.16225			0.581126	−	0.813814i	$-0.302612\pi$
$947$	35.7664			1.16225			0.581126	+	0.813814i	$0.302612\pi$
$948$	−5.18700	+	44.5759i	−0.168466	+	1.44776i
$949$	3.48129			0.113007
$950$	7.00560	−	9.40798i	0.227292	−	0.305235i
$951$	−13.1873	−	5.67698i	−0.427628	−	0.184089i
$952$	6.28167	−	17.2410i	0.203590	−	0.558783i
$953$		−	27.9971i		−	0.906916i	−0.891278	−	0.453458i	$-0.850190\pi$
$953$		−	27.9971i		−	0.906916i	0.891278	−	0.453458i	$-0.149810\pi$
$954$	19.7293	−	2.33317i	0.638759	−	0.0755390i
$955$			4.49024i			0.145301i
$956$	4.65552	+	15.5630i	0.150570	+	0.503344i
$957$	35.1632	+	15.1373i	1.13667	+	0.489321i
$958$	−17.4831	−	13.0187i	−0.564854	−	0.420615i
$959$	20.3987			0.658709
$960$	6.21962	+	12.3821i	0.200738	+	0.399630i
$961$	−36.2014			−1.16779
$962$	3.99000	+	2.97113i	0.128643	+	0.0957930i
$963$	−6.16513	−	6.51548i	−0.198669	−	0.209958i
$964$	−7.67265	−	25.6490i	−0.247119	−	0.826100i
$965$		−	25.9580i		−	0.835617i
$966$	5.50765	+	9.52581i	0.177206	+	0.306488i
$967$		−	13.4284i		−	0.431830i	−0.976412	−	0.215915i	$-0.930727\pi$
$967$		−	13.4284i		−	0.431830i	0.976412	−	0.215915i	$-0.0692734\pi$
$968$	20.3316	−	55.8030i	0.653481	−	1.79358i
$969$	27.1089	−	62.9724i	0.870862	−	2.02296i
$970$	1.47273	−	1.97776i	0.0472865	−	0.0635021i
$971$	−54.3842			−1.74527			−0.872635	−	0.488372i	$-0.837591\pi$
$971$	−54.3842			−1.74527			−0.872635	+	0.488372i	$0.837591\pi$
$972$	5.30793	−	30.7217i	0.170252	−	0.985401i
$973$	15.7001			0.503321
$974$	21.7881	−	29.2597i	0.698134	−	0.937541i
$975$	−0.684863	+	1.59090i	−0.0219332	+	0.0509496i
$976$	−0.460506	+	0.302588i	−0.0147404	+	0.00968560i
$977$			15.8245i			0.506270i	0.967431	+	0.253135i	$0.0814616\pi$
$977$			15.8245i			0.506270i	−0.967431	+	0.253135i	$0.918538\pi$
$978$	−15.0759	−	26.0746i	−0.482073	−	0.833774i
$979$		−	9.63549i		−	0.307952i
$980$	−9.87175	+	2.95303i	−0.315342	+	0.0943312i
$981$	24.0296	+	25.3951i	0.767206	+	0.810804i
$982$	2.18622	+	1.62796i	0.0697651	+	0.0519501i
$983$	60.3547			1.92502			0.962508	−	0.271254i	$-0.0874384\pi$
$983$	60.3547			1.92502			0.962508	+	0.271254i	$0.0874384\pi$
$984$	4.68378	−	4.96852i	0.149314	−	0.158391i
$985$	−18.5921			−0.592393
$986$	−21.1512	−	15.7501i	−0.673592	−	0.501586i
$987$	−13.9591	−	6.00921i	−0.444322	−	0.191275i
$988$	−15.8926	+	4.75412i	−0.505612	+	0.151249i
$989$		−	33.2996i		−	1.05887i
$990$	23.8332	−	2.81849i	0.757469	−	0.0895775i
$991$			11.9648i			0.380076i	0.981777	+	0.190038i	$0.0608611\pi$
$991$			11.9648i			0.380076i	−0.981777	+	0.190038i	$0.939139\pi$
$992$	−2.72191	+	46.2929i	−0.0864206	+	1.46980i
$993$	−10.8397	−	4.66634i	−0.343986	−	0.148082i
$994$	−14.0624	+	18.8847i	−0.446031	+	0.598985i
$995$	−24.0803			−0.763398
$996$	23.1792	+	2.69722i	0.734462	+	0.0854646i
$997$	31.5273			0.998478			0.499239	−	0.866464i	$-0.333613\pi$
$997$	31.5273			0.998478			0.499239	+	0.866464i	$0.333613\pi$
$998$	−4.22118	+	5.66873i	−0.133619	+	0.179440i
$999$	17.1621	−	6.28931i	0.542985	−	0.198985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.e.131.9	✓	40
3.2	odd	2	inner	780.2.g.e.131.32	yes	40
4.3	odd	2	inner	780.2.g.e.131.31	yes	40
12.11	even	2	inner	780.2.g.e.131.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.e.131.9	✓	40	1.1	even	1	trivial
780.2.g.e.131.10	yes	40	12.11	even	2	inner
780.2.g.e.131.31	yes	40	4.3	odd	2	inner
780.2.g.e.131.32	yes	40	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+(-1.13428 - 0.844635i) q^{2} +(-0.684863 + 1.59090i) q^{3} +(0.573183 + 1.91611i) q^{4} +1.00000i q^{5} +(2.12056 - 1.22607i) q^{6} +1.35942i q^{7} +(0.968260 - 2.65753i) q^{8} +(-2.06192 - 2.17910i) q^{9} +(0.844635 - 1.13428i) q^{10} -5.65668 q^{11} +(-3.44088 - 0.400393i) q^{12} -1.00000 q^{13} +(1.14821 - 1.54196i) q^{14} +(-1.59090 - 0.684863i) q^{15} +(-3.34292 + 2.19656i) q^{16} -4.77234i q^{17} +(0.498258 + 4.21328i) q^{18} -8.29423i q^{19} +(-1.91611 + 0.573183i) q^{20} +(-2.16269 - 0.931014i) q^{21} +(6.41626 + 4.77783i) q^{22} +3.30446 q^{23} +(3.56474 + 3.36045i) q^{24} -1.00000 q^{25} +(1.13428 + 0.844635i) q^{26} +(4.87886 - 1.78793i) q^{27} +(-2.60478 + 0.779195i) q^{28} +3.90736i q^{29} +(1.22607 + 2.12056i) q^{30} +8.19765i q^{31} +(5.64710 + 0.332035i) q^{32} +(3.87405 - 8.99922i) q^{33} +(-4.03088 + 5.41317i) q^{34} -1.35942 q^{35} +(2.99352 - 5.19989i) q^{36} +3.51765 q^{37} +(-7.00560 + 9.40798i) q^{38} +(0.684863 - 1.59090i) q^{39} +(2.65753 + 0.968260i) q^{40} -1.39380i q^{41} +(1.66673 + 2.88272i) q^{42} -10.0772i q^{43} +(-3.24232 - 10.8388i) q^{44} +(2.17910 - 2.06192i) q^{45} +(-3.74818 - 2.79106i) q^{46} +6.45448 q^{47} +(-1.20506 - 6.82260i) q^{48} +5.15199 q^{49} +(1.13428 + 0.844635i) q^{50} +(7.59231 + 3.26840i) q^{51} +(-0.573183 - 1.91611i) q^{52} -4.68264i q^{53} +(-7.04415 - 2.09284i) q^{54} -5.65668i q^{55} +(3.61269 + 1.31627i) q^{56} +(13.1953 + 5.68042i) q^{57} +(3.30030 - 4.43205i) q^{58} -13.6004 q^{59} +(0.400393 - 3.44088i) q^{60} +0.137755 q^{61} +(6.92402 - 9.29843i) q^{62} +(2.96230 - 2.80301i) q^{63} +(-6.12495 - 5.14636i) q^{64} -1.00000i q^{65} +(-11.9953 + 6.93547i) q^{66} -5.90581i q^{67} +(9.14430 - 2.73542i) q^{68} +(-2.26310 + 5.25706i) q^{69} +(1.54196 + 1.14821i) q^{70} -12.2472 q^{71} +(-7.78750 + 3.36970i) q^{72} -3.48129 q^{73} +(-3.99000 - 2.97113i) q^{74} +(0.684863 - 1.59090i) q^{75} +(15.8926 - 4.75412i) q^{76} -7.68978i q^{77} +(-2.12056 + 1.22607i) q^{78} -12.9548i q^{79} +(-2.19656 - 3.34292i) q^{80} +(-0.496932 + 8.98627i) q^{81} +(-1.17725 + 1.58096i) q^{82} -6.73642 q^{83} +(0.544301 - 4.67759i) q^{84} +4.77234 q^{85} +(-8.51154 + 11.4303i) q^{86} +(-6.21622 - 2.67601i) q^{87} +(-5.47714 + 15.0328i) q^{88} +1.70338i q^{89} +(-4.21328 + 0.498258i) q^{90} -1.35942i q^{91} +(1.89406 + 6.33169i) q^{92} +(-13.0416 - 5.61427i) q^{93} +(-7.32119 - 5.45168i) q^{94} +8.29423 q^{95} +(-4.39573 + 8.75657i) q^{96} +1.74363 q^{97} +(-5.84380 - 4.35155i) q^{98} +(11.6637 + 12.3265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} - 2 q^{6} - 14 q^{12} - 40 q^{13} + 12 q^{16} - 16 q^{18} - 24 q^{21} + 44 q^{22} - 10 q^{24} - 40 q^{25} - 48 q^{28} - 6 q^{30} - 8 q^{33} - 56 q^{34} + 36 q^{36} - 72 q^{37} - 20 q^{42}+ \cdots + 72 q^{97}+O(q^{100}) \) 40 * q + 4 * q^4 - 2 * q^6 - 14 * q^12 - 40 * q^13 + 12 * q^16 - 16 * q^18 - 24 * q^21 + 44 * q^22 - 10 * q^24 - 40 * q^25 - 48 * q^28 - 6 * q^30 - 8 * q^33 - 56 * q^34 + 36 * q^36 - 72 * q^37 - 20 * q^42 + 8 * q^45 + 84 * q^46 + 70 * q^48 - 96 * q^49 - 4 * q^52 - 14 * q^54 + 80 * q^57 + 18 * q^60 + 40 * q^61 + 28 * q^64 - 24 * q^66 - 56 * q^69 + 24 * q^70 + 12 * q^72 - 68 * q^76 + 2 * q^78 + 96 * q^82 - 48 * q^84 + 8 * q^85 - 116 * q^88 - 8 * q^90 - 24 * q^93 - 8 * q^94 - 10 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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