LMFDB - Embedded newform 400.2.bi.d.63.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(47,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,0,4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			63.6
Character	$\chi$	$=$	400.63
Dual form			400.2.bi.d.127.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.192345 + 0.0980047i) q^{3} +(1.96025 - 1.07584i) q^{5} +(3.64023 + 3.64023i) q^{7} +(-1.73596 - 2.38935i) q^{9} +(1.40862 - 1.93880i) q^{11} +(-3.87519 - 0.613769i) q^{13} +(0.482481 - 0.0148199i) q^{15} +(1.70615 + 3.34851i) q^{17} +(-1.33643 + 4.11310i) q^{19} +(0.343420 + 1.05694i) q^{21} +(4.03892 - 0.639702i) q^{23} +(2.68512 - 4.21783i) q^{25} +(-0.201047 - 1.26936i) q^{27} +(6.80076 - 2.20970i) q^{29} +(-4.89500 - 1.59048i) q^{31} +(0.460954 - 0.234868i) q^{33} +(11.0521 + 3.21942i) q^{35} +(1.32726 - 8.37999i) q^{37} +(-0.685221 - 0.497842i) q^{39} +(-3.51583 + 2.55440i) q^{41} +(0.236979 - 0.236979i) q^{43} +(-5.97348 - 2.81609i) q^{45} +(-3.73202 + 7.32450i) q^{47} +19.5025i q^{49} +0.811279i q^{51} +(1.46515 - 2.87552i) q^{53} +(0.675398 - 5.31599i) q^{55} +(-0.660158 + 0.660158i) q^{57} +(-8.27043 + 6.00882i) q^{59} +(-5.77599 - 4.19650i) q^{61} +(2.37847 - 15.0171i) q^{63} +(-8.25664 + 2.96596i) q^{65} +(-3.40155 + 1.73318i) q^{67} +(0.839560 + 0.272790i) q^{69} +(-10.6414 + 3.45761i) q^{71} +(0.176191 + 1.11243i) q^{73} +(0.929837 - 0.548125i) q^{75} +(12.1854 - 1.92998i) q^{77} +(-3.53547 - 10.8811i) q^{79} +(-2.65222 + 8.16269i) q^{81} +(-6.66869 - 13.0880i) q^{83} +(6.94694 + 4.72835i) q^{85} +(1.52465 + 0.241481i) q^{87} +(-0.149113 + 0.205237i) q^{89} +(-11.8723 - 16.3408i) q^{91} +(-0.785654 - 0.785654i) q^{93} +(1.80533 + 9.50047i) q^{95} +(-6.59923 - 3.36248i) q^{97} -7.07780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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			0
$2$		0			0
$3$	0.192345	+	0.0980047i	0.111050	+	0.0565830i	0.508633	−	0.860983i	$-0.330151\pi$
$3$	0.192345	+	0.0980047i	0.111050	+	0.0565830i	−0.397583	+	0.917566i	$0.630151\pi$
$4$		0			0
$5$	1.96025	−	1.07584i	0.876648	−	0.481132i
$5$	1.96025	−	1.07584i	0.876648	−	0.481132i
$6$		0			0
$7$	3.64023	+	3.64023i	1.37588	+	1.37588i	0.851465	+	0.524411i	$0.175715\pi$
$7$	3.64023	+	3.64023i	1.37588	+	1.37588i	0.524411	+	0.851465i	$0.324285\pi$
$8$		0			0
$9$	−1.73596	−	2.38935i	−0.578655	−	0.796450i
$10$		0			0
$11$	1.40862	−	1.93880i	0.424716	−	0.584572i	−0.542014	−	0.840369i	$-0.682338\pi$
$11$	1.40862	−	1.93880i	0.424716	−	0.584572i	0.966730	+	0.255798i	$0.0823381\pi$
$12$		0			0
$13$	−3.87519	−	0.613769i	−1.07478	−	0.170229i	−0.406139	−	0.913811i	$-0.633125\pi$
$13$	−3.87519	−	0.613769i	−1.07478	−	0.170229i	−0.668644	+	0.743582i	$0.733125\pi$
$14$		0			0
$15$	0.482481	−	0.0148199i	0.124576	−	0.00382649i
$16$		0			0
$17$	1.70615	+	3.34851i	0.413802	+	0.812132i	0.999998	+	0.00196314i	$0.000624888\pi$
$17$	1.70615	+	3.34851i	0.413802	+	0.812132i	−0.586196	+	0.810169i	$0.699375\pi$
$18$		0			0
$19$	−1.33643	+	4.11310i	−0.306598	+	0.943610i	0.672479	+	0.740116i	$0.265230\pi$
$19$	−1.33643	+	4.11310i	−0.306598	+	0.943610i	−0.979076	+	0.203494i	$0.934770\pi$
$20$		0			0
$21$	0.343420	+	1.05694i	0.0749404	+	0.230643i
$22$		0			0
$23$	4.03892	−	0.639702i	0.842174	−	0.133387i	0.279582	−	0.960122i	$-0.409804\pi$
$23$	4.03892	−	0.639702i	0.842174	−	0.133387i	0.562592	+	0.826735i	$0.309804\pi$
$24$		0			0
$25$	2.68512	−	4.21783i	0.537024	−	0.843567i
$26$		0			0
$27$	−0.201047	−	1.26936i	−0.0386915	−	0.244288i
$28$		0			0
$29$	6.80076	−	2.20970i	1.26287	−	0.410331i	0.400353	−	0.916361i	$-0.368888\pi$
$29$	6.80076	−	2.20970i	1.26287	−	0.410331i	0.862516	+	0.506030i	$0.168888\pi$
$30$		0			0
$31$	−4.89500	−	1.59048i	−0.879168	−	0.285659i	−0.165556	−	0.986200i	$-0.552942\pi$
$31$	−4.89500	−	1.59048i	−0.879168	−	0.285659i	−0.713612	+	0.700541i	$0.752942\pi$
$32$		0			0
$33$	0.460954	−	0.234868i	0.0802417	−	0.0408852i
$34$		0			0
$35$	11.0521	+	3.21942i	1.86814	+	0.544182i
$36$		0			0
$37$	1.32726	−	8.37999i	0.218200	−	1.37766i	−0.598742	−	0.800942i	$-0.704332\pi$
$37$	1.32726	−	8.37999i	0.218200	−	1.37766i	0.816942	−	0.576720i	$-0.195668\pi$
$38$		0			0
$39$	−0.685221	−	0.497842i	−0.109723	−	0.0797185i
$40$		0			0
$41$	−3.51583	+	2.55440i	−0.549080	+	0.398930i	−0.827446	−	0.561545i	$-0.810207\pi$
$41$	−3.51583	+	2.55440i	−0.549080	+	0.398930i	0.278366	+	0.960475i	$0.410207\pi$
$42$		0			0
$43$	0.236979	−	0.236979i	0.0361389	−	0.0361389i	−0.688806	−	0.724945i	$-0.741865\pi$
$43$	0.236979	−	0.236979i	0.0361389	−	0.0361389i	0.724945	+	0.688806i	$0.241865\pi$
$44$		0			0
$45$	−5.97348	−	2.81609i	−0.890474	−	0.419797i
$46$		0			0
$47$	−3.73202	+	7.32450i	−0.544371	+	1.06839i	0.440927	+	0.897543i	$0.354650\pi$
$47$	−3.73202	+	7.32450i	−0.544371	+	1.06839i	−0.985298	+	0.170846i	$0.945350\pi$
$48$		0			0
$49$			19.5025i			2.78607i
$50$		0			0
$51$			0.811279i			0.113602i
$52$		0			0
$53$	1.46515	−	2.87552i	0.201254	−	0.394982i	−0.768217	−	0.640189i	$-0.778856\pi$
$53$	1.46515	−	2.87552i	0.201254	−	0.394982i	0.969471	+	0.245207i	$0.0788559\pi$
$54$		0			0
$55$	0.675398	−	5.31599i	0.0910707	−	0.716808i
$56$		0			0
$57$	−0.660158	+	0.660158i	−0.0874401	+	0.0874401i
$58$		0			0
$59$	−8.27043	+	6.00882i	−1.07672	+	0.782282i	−0.977108	−	0.212745i	$-0.931760\pi$
$59$	−8.27043	+	6.00882i	−1.07672	+	0.782282i	−0.0996107	+	0.995026i	$0.531760\pi$
$60$		0			0
$61$	−5.77599	−	4.19650i	−0.739540	−	0.537307i	0.153027	−	0.988222i	$-0.451098\pi$
$61$	−5.77599	−	4.19650i	−0.739540	−	0.537307i	−0.892567	+	0.450915i	$0.851098\pi$
$62$		0			0
$63$	2.37847	−	15.0171i	0.299659	−	1.89197i
$64$		0			0
$65$	−8.25664	+	2.96596i	−1.02411	+	0.367882i
$66$		0			0
$67$	−3.40155	+	1.73318i	−0.415566	+	0.211741i	−0.649256	−	0.760570i	$-0.724920\pi$
$67$	−3.40155	+	1.73318i	−0.415566	+	0.211741i	0.233691	+	0.972311i	$0.424920\pi$
$68$		0			0
$69$	0.839560	+	0.272790i	0.101071	+	0.0328400i
$70$		0			0
$71$	−10.6414	+	3.45761i	−1.26291	+	0.410343i	−0.862529	−	0.506008i	$-0.831121\pi$
$71$	−10.6414	+	3.45761i	−1.26291	+	0.410343i	−0.400377	+	0.916351i	$0.631121\pi$
$72$		0			0
$73$	0.176191	+	1.11243i	0.0206216	+	0.130200i	0.995851	−	0.0909945i	$-0.0290046\pi$
$73$	0.176191	+	1.11243i	0.0206216	+	0.130200i	−0.975230	+	0.221194i	$0.929005\pi$
$74$		0			0
$75$	0.929837	−	0.548125i	0.107368	−	0.0632920i
$76$		0			0
$77$	12.1854	−	1.92998i	1.38865	−	0.219941i
$78$		0			0
$79$	−3.53547	−	10.8811i	−0.397772	−	1.22422i	−0.926782	−	0.375601i	$-0.877436\pi$
$79$	−3.53547	−	10.8811i	−0.397772	−	1.22422i	0.529010	−	0.848616i	$-0.322564\pi$
$80$		0			0
$81$	−2.65222	+	8.16269i	−0.294691	+	0.906965i
$82$		0			0
$83$	−6.66869	−	13.0880i	−0.731983	−	1.43660i	−0.893191	−	0.449678i	$-0.851539\pi$
$83$	−6.66869	−	13.0880i	−0.731983	−	1.43660i	0.161207	−	0.986921i	$-0.448461\pi$
$84$		0			0
$85$	6.94694	+	4.72835i	0.753502	+	0.512861i
$86$		0			0
$87$	1.52465	+	0.241481i	0.163460	+	0.0258895i
$88$		0			0
$89$	−0.149113	+	0.205237i	−0.0158060	+	0.0217550i	−0.816847	−	0.576855i	$-0.804280\pi$
$89$	−0.149113	+	0.205237i	−0.0158060	+	0.0217550i	0.801041	+	0.598610i	$0.204280\pi$
$90$		0			0
$91$	−11.8723	−	16.3408i	−1.24456	−	1.71298i
$92$		0			0
$93$	−0.785654	−	0.785654i	−0.0814685	−	0.0814685i
$94$		0			0
$95$	1.80533	+	9.50047i	0.185223	+	0.974728i
$96$		0			0
$97$	−6.59923	−	3.36248i	−0.670050	−	0.341408i	0.0856499	−	0.996325i	$-0.472703\pi$
$97$	−6.59923	−	3.36248i	−0.670050	−	0.341408i	−0.755700	+	0.654918i	$0.772703\pi$
$98$		0			0
$99$	−7.07780			−0.711346
$100$		0			0
$101$	−4.06971			−0.404951			−0.202476	−	0.979287i	$-0.564899\pi$
$101$	−4.06971			−0.404951			−0.202476	+	0.979287i	$0.564899\pi$
$102$		0			0
$103$	6.15037	+	3.13377i	0.606014	+	0.308780i	0.729939	−	0.683512i	$-0.239548\pi$
$103$	6.15037	+	3.13377i	0.606014	+	0.308780i	−0.123925	+	0.992292i	$0.539548\pi$
$104$		0			0
$105$	1.81029	+	1.70239i	0.176666	+	0.166136i
$106$		0			0
$107$	7.29262	+	7.29262i	0.705004	+	0.705004i	0.965480	−	0.260476i	$-0.0838795\pi$
$107$	7.29262	+	7.29262i	0.705004	+	0.705004i	−0.260476	+	0.965480i	$0.583879\pi$
$108$		0			0
$109$	−2.62365	−	3.61114i	−0.251300	−	0.345885i	0.664666	−	0.747141i	$-0.268574\pi$
$109$	−2.62365	−	3.61114i	−0.251300	−	0.345885i	−0.915966	+	0.401256i	$0.868574\pi$
$110$		0			0
$111$	1.07657	−	1.48177i	0.102183	−	0.140644i
$112$		0			0
$113$	−7.03067	−	1.11355i	−0.661390	−	0.104754i	−0.183289	−	0.983059i	$-0.558675\pi$
$113$	−7.03067	−	1.11355i	−0.661390	−	0.104754i	−0.478101	+	0.878305i	$0.658675\pi$
$114$		0			0
$115$	7.22906	−	5.59922i	0.674113	−	0.522130i
$116$		0			0
$117$	5.26068	+	10.3247i	0.486350	+	0.954515i
$118$		0			0
$119$	−5.97856	+	18.4001i	−0.548053	+	1.68673i
$120$		0			0
$121$	1.62445	+	4.99953i	0.147677	+	0.454503i
$122$		0			0
$123$	−0.926595	+	0.146758i	−0.0835483	+	0.0132327i
$124$		0			0
$125$	0.725769	−	11.1568i	0.0649147	−	0.997891i
$126$		0			0
$127$	1.18966	+	7.51122i	0.105565	+	0.666513i	0.982551	+	0.185996i	$0.0595510\pi$
$127$	1.18966	+	7.51122i	0.105565	+	0.666513i	−0.876985	+	0.480517i	$0.840449\pi$
$128$		0			0
$129$	0.0688066	−	0.0223566i	0.00605809	−	0.00196839i
$130$		0			0
$131$	0.536039	+	0.174170i	0.0468340	+	0.0152173i	0.332340	−	0.943160i	$-0.392162\pi$
$131$	0.536039	+	0.174170i	0.0468340	+	0.0152173i	−0.285506	+	0.958377i	$0.592162\pi$
$132$		0			0
$133$	−19.8375	+	10.1077i	−1.72013	+	0.876451i
$134$		0			0
$135$	−1.75973	−	2.27196i	−0.151454	−	0.195539i
$136$		0			0
$137$	−1.04483	+	6.59680i	−0.0892658	+	0.563602i	0.902001	+	0.431733i	$0.142098\pi$
$137$	−1.04483	+	6.59680i	−0.0892658	+	0.563602i	−0.991267	+	0.131869i	$0.957902\pi$
$138$		0			0
$139$	5.29234	+	3.84511i	0.448891	+	0.326138i	0.789158	−	0.614191i	$-0.210517\pi$
$139$	5.29234	+	3.84511i	0.448891	+	0.326138i	−0.340267	+	0.940329i	$0.610517\pi$
$140$		0			0
$141$	−1.43567	+	1.04308i	−0.120905	+	0.0878429i
$142$		0			0
$143$	−6.64866	+	6.64866i	−0.555989	+	0.555989i
$144$		0			0
$145$	10.9539	−	11.6481i	0.909668	−	0.967322i
$146$		0			0
$147$	−1.91134	+	3.75121i	−0.157644	+	0.309394i
$148$		0			0
$149$		−	9.21679i		−	0.755069i	−0.925996	−	0.377534i	$-0.876772\pi$
$149$		−	9.21679i		−	0.755069i	0.925996	−	0.377534i	$-0.123228\pi$
$150$		0			0
$151$		−	20.2132i		−	1.64493i	−0.568817	−	0.822464i	$-0.692599\pi$
$151$		−	20.2132i		−	1.64493i	0.568817	−	0.822464i	$-0.307401\pi$
$152$		0			0
$153$	5.03894	−	9.88948i	0.407374	−	0.799517i
$154$		0			0
$155$	−11.3065	+	2.14852i	−0.908161	+	0.172573i
$156$		0			0
$157$	1.68750	−	1.68750i	0.134677	−	0.134677i	−0.636555	−	0.771232i	$-0.719641\pi$
$157$	1.68750	−	1.68750i	0.134677	−	0.134677i	0.771232	+	0.636555i	$0.219641\pi$
$158$		0			0
$159$	0.563628	−	0.409500i	0.0446986	−	0.0324754i
$160$		0			0
$161$	17.0313	+	12.3739i	1.34225	+	0.975202i
$162$		0			0
$163$	0.858800	−	5.42225i	0.0672664	−	0.424703i	−0.930957	−	0.365128i	$-0.881025\pi$
$163$	0.858800	−	5.42225i	0.0672664	−	0.424703i	0.998224	−	0.0595754i	$-0.0189747\pi$
$164$		0			0
$165$	0.650901	−	0.956312i	0.0506726	−	0.0744488i
$166$		0			0
$167$	5.47332	−	2.78880i	0.423538	−	0.215803i	−0.229212	−	0.973376i	$-0.573615\pi$
$167$	5.47332	−	2.78880i	0.423538	−	0.215803i	0.652750	+	0.757573i	$0.273615\pi$
$168$		0			0
$169$	2.27663	+	0.739721i	0.175125	+	0.0569016i
$170$		0			0
$171$	12.1476	−	3.94700i	0.928952	−	0.301835i
$172$		0			0
$173$	−0.725555	−	4.58098i	−0.0551630	−	0.348285i	−0.999797	−	0.0201588i	$-0.993583\pi$
$173$	−0.725555	−	4.58098i	−0.0551630	−	0.348285i	0.944634	−	0.328126i	$-0.106417\pi$
$174$		0			0
$175$	25.1283	−	5.57942i	1.89952	−	0.421764i
$176$		0			0
$177$	−2.17967	+	0.345226i	−0.163834	+	0.0259487i
$178$		0			0
$179$	−1.85134	−	5.69784i	−0.138376	−	0.425877i	0.857724	−	0.514110i	$-0.171878\pi$
$179$	−1.85134	−	5.69784i	−0.138376	−	0.425877i	−0.996100	+	0.0882335i	$0.971878\pi$
$180$		0			0
$181$	0.667794	−	2.05526i	0.0496367	−	0.152766i	−0.923166	−	0.384402i	$-0.874408\pi$
$181$	0.667794	−	2.05526i	0.0496367	−	0.152766i	0.972803	+	0.231636i	$0.0744077\pi$
$182$		0			0
$183$	−0.699706	−	1.37325i	−0.0517237	−	0.101514i
$184$		0			0
$185$	−6.41380	−	17.8548i	−0.471552	−	1.31271i
$186$		0			0
$187$	8.89543	+	1.40890i	0.650498	+	0.103029i
$188$		0			0
$189$	3.88890	−	5.35261i	0.282876	−	0.389345i
$190$		0			0
$191$	13.4186	+	18.4691i	0.970935	+	1.33638i	0.941573	+	0.336809i	$0.109348\pi$
$191$	13.4186	+	18.4691i	0.970935	+	1.33638i	0.0293620	+	0.999569i	$0.490652\pi$
$192$		0			0
$193$	3.68505	+	3.68505i	0.265256	+	0.265256i	0.827185	−	0.561930i	$-0.189941\pi$
$193$	3.68505	+	3.68505i	0.265256	+	0.265256i	−0.561930	+	0.827185i	$0.689941\pi$
$194$		0			0
$195$	−1.87880	−	0.238702i	−0.134544	−	0.0170938i
$196$		0			0
$197$	15.5814	+	7.93911i	1.11013	+	0.565638i	0.910199	−	0.414172i	$-0.135929\pi$
$197$	15.5814	+	7.93911i	1.11013	+	0.565638i	0.199929	+	0.979810i	$0.435929\pi$
$198$		0			0
$199$	−16.8827			−1.19678			−0.598392	−	0.801203i	$-0.704194\pi$
$199$	−16.8827			−1.19678			−0.598392	+	0.801203i	$0.704194\pi$
$200$		0			0
$201$	−0.824131			−0.0581297
$202$		0			0
$203$	32.8001	+	16.7125i	2.30212	+	1.17299i
$204$		0			0
$205$	−4.14375	+	8.78973i	−0.289412	+	0.613901i
$206$		0			0
$207$	−8.53990	−	8.53990i	−0.593564	−	0.593564i
$208$		0			0
$209$	6.09198	+	8.38488i	0.421391	+	0.579995i
$210$		0			0
$211$	−14.6938	+	20.2242i	−1.01156	+	1.39229i	−0.0936060	+	0.995609i	$0.529839\pi$
$211$	−14.6938	+	20.2242i	−1.01156	+	1.39229i	−0.917955	+	0.396685i	$0.870161\pi$
$212$		0			0
$213$	−2.38569	−	0.377856i	−0.163465	−	0.0258903i
$214$		0			0
$215$	0.209584	−	0.719488i	0.0142935	−	0.0490687i
$216$		0			0
$217$	−12.0292	−	23.6086i	−0.816595	−	1.60266i
$218$		0			0
$219$	−0.0751335	+	0.231237i	−0.00507705	+	0.0156256i
$220$		0			0
$221$	−4.55644	−	14.0233i	−0.306499	−	0.943308i
$222$		0			0
$223$	−5.43272	+	0.860458i	−0.363802	+	0.0576205i	−0.335659	−	0.941983i	$-0.608959\pi$
$223$	−5.43272	+	0.860458i	−0.363802	+	0.0576205i	−0.0281422	+	0.999604i	$0.508959\pi$
$224$		0			0
$225$	−14.7392	+	0.906313i	−0.982610	+	0.0604209i
$226$		0			0
$227$	2.06996	+	13.0692i	0.137388	+	0.867433i	0.956060	+	0.293171i	$0.0947107\pi$
$227$	2.06996	+	13.0692i	0.137388	+	0.867433i	−0.818672	+	0.574261i	$0.805289\pi$
$228$		0			0
$229$	−15.9951	+	5.19713i	−1.05699	+	0.343436i	−0.785407	−	0.618980i	$-0.787546\pi$
$229$	−15.9951	+	5.19713i	−1.05699	+	0.343436i	−0.271580	+	0.962416i	$0.587546\pi$
$230$		0			0
$231$	2.53295	+	0.823004i	0.166656	+	0.0541497i
$232$		0			0
$233$	16.7045	−	8.51136i	1.09435	−	0.557598i	0.188874	−	0.982001i	$-0.439516\pi$
$233$	16.7045	−	8.51136i	1.09435	−	0.557598i	0.905473	+	0.424404i	$0.139516\pi$
$234$		0			0
$235$	0.564343	+	18.3729i	0.0368137	+	1.19852i
$236$		0			0
$237$	0.386365	−	2.43941i	0.0250971	−	0.158457i
$238$		0			0
$239$	16.9738	+	12.3322i	1.09795	+	0.797705i	0.980724	−	0.195400i	$-0.0626006\pi$
$239$	16.9738	+	12.3322i	1.09795	+	0.797705i	0.117223	+	0.993106i	$0.462601\pi$
$240$		0			0
$241$	4.09871	−	2.97788i	0.264021	−	0.191822i	−0.447897	−	0.894085i	$-0.647827\pi$
$241$	4.09871	−	2.97788i	0.264021	−	0.191822i	0.711918	+	0.702263i	$0.247827\pi$
$242$		0			0
$243$	−4.03641	+	4.03641i	−0.258936	+	0.258936i
$244$		0			0
$245$	20.9816	+	38.2297i	1.34047	+	2.44240i
$246$		0			0
$247$	7.70340	−	15.1188i	0.490156	−	0.961985i
$248$		0			0
$249$		−	3.17098i		−	0.200953i
$250$		0			0
$251$			14.5567i			0.918814i	0.888226	+	0.459407i	$0.151938\pi$
$251$			14.5567i			0.918814i	−0.888226	+	0.459407i	$0.848062\pi$
$252$		0			0
$253$	4.44906	−	8.73178i	0.279710	−	0.548962i
$254$		0			0
$255$	0.872810	+	1.59031i	0.0546575	+	0.0995888i
$256$		0			0
$257$	5.24996	−	5.24996i	0.327483	−	0.327483i	−0.524145	−	0.851629i	$-0.675615\pi$
$257$	5.24996	−	5.24996i	0.327483	−	0.327483i	0.851629	+	0.524145i	$0.175615\pi$
$258$		0			0
$259$	35.3366	−	25.6735i	2.19571	−	1.59528i
$260$		0			0
$261$	−17.0856	−	12.4134i	−1.05757	−	0.768372i
$262$		0			0
$263$	2.81939	−	17.8009i	0.173851	−	1.09765i	−0.734244	−	0.678886i	$-0.762463\pi$
$263$	2.81939	−	17.8009i	0.173851	−	1.09765i	0.908095	−	0.418765i	$-0.137537\pi$
$264$		0			0
$265$	−0.221555	−	7.21299i	−0.0136100	−	0.443090i
$266$		0			0
$267$	−0.0487953	+	0.0248624i	−0.00298622	+	0.00152156i
$268$		0			0
$269$	20.7469	+	6.74109i	1.26496	+	0.411012i	0.863261	−	0.504758i	$-0.168418\pi$
$269$	20.7469	+	6.74109i	1.26496	+	0.411012i	0.401703	+	0.915770i	$0.368418\pi$
$270$		0			0
$271$	−5.35164	+	1.73885i	−0.325089	+	0.105628i	−0.467015	−	0.884249i	$-0.654671\pi$
$271$	−5.35164	+	1.73885i	−0.325089	+	0.105628i	0.141926	+	0.989877i	$0.454671\pi$
$272$		0			0
$273$	−0.682101	−	4.30662i	−0.0412826	−	0.260648i
$274$		0			0
$275$	−4.39523	−	11.1473i	−0.265042	−	0.672206i
$276$		0			0
$277$	−11.5798	+	1.83407i	−0.695765	+	0.110198i	−0.494292	−	0.869296i	$-0.664573\pi$
$277$	−11.5798	+	1.83407i	−0.695765	+	0.110198i	−0.201473	+	0.979494i	$0.564573\pi$
$278$		0			0
$279$	4.69733	+	14.4569i	0.281222	+	0.865511i
$280$		0			0
$281$	3.31191	−	10.1930i	0.197572	−	0.608064i	−0.802365	−	0.596834i	$-0.796425\pi$
$281$	3.31191	−	10.1930i	0.197572	−	0.608064i	0.999937	−	0.0112302i	$-0.00357477\pi$
$282$		0			0
$283$	−4.28246	−	8.40481i	−0.254566	−	0.499614i	0.727988	−	0.685590i	$-0.240455\pi$
$283$	−4.28246	−	8.40481i	−0.254566	−	0.499614i	−0.982554	+	0.185975i	$0.940455\pi$
$284$		0			0
$285$	−0.583845	+	2.00430i	−0.0345840	+	0.118724i
$286$		0			0
$287$	−22.0970	−	3.49982i	−1.30435	−	0.206588i
$288$		0			0
$289$	1.69079	−	2.32717i	0.0994583	−	0.136893i
$290$		0			0
$291$	−0.939791	−	1.29351i	−0.0550915	−	0.0758269i
$292$		0			0
$293$	22.1179	+	22.1179i	1.29214	+	1.29214i	0.933461	+	0.358680i	$0.116773\pi$
$293$	22.1179	+	22.1179i	1.29214	+	1.29214i	0.358680	+	0.933461i	$0.383227\pi$
$294$		0			0
$295$	−9.74752	+	20.6765i	−0.567523	+	1.20383i
$296$		0			0
$297$	−2.74424	−	1.39826i	−0.159237	−	0.0811353i
$298$		0			0
$299$	−16.0442			−0.927861
$300$		0			0
$301$	1.72531			0.0994453
$302$		0			0
$303$	−0.782788	−	0.398850i	−0.0449700	−	0.0229134i
$304$		0			0
$305$	−15.8371	−	2.01211i	−0.906832	−	0.115213i
$306$		0			0
$307$	−12.3567	−	12.3567i	−0.705237	−	0.705237i	0.260293	−	0.965530i	$-0.416181\pi$
$307$	−12.3567	−	12.3567i	−0.705237	−	0.705237i	−0.965530	+	0.260293i	$0.916181\pi$
$308$		0			0
$309$	0.875869	+	1.20553i	0.0498265	+	0.0685802i
$310$		0			0
$311$	15.1927	−	20.9110i	0.861500	−	1.18575i	−0.119710	−	0.992809i	$-0.538196\pi$
$311$	15.1927	−	20.9110i	0.861500	−	1.18575i	0.981210	−	0.192944i	$-0.0618036\pi$
$312$		0			0
$313$	19.2520	+	3.04921i	1.08819	+	0.172352i	0.674651	−	0.738136i	$-0.264294\pi$
$313$	19.2520	+	3.04921i	1.08819	+	0.172352i	0.413535	+	0.910488i	$0.364294\pi$
$314$		0			0
$315$	−11.4936	−	31.9960i	−0.647593	−	1.80277i
$316$		0			0
$317$	−5.86511	−	11.5109i	−0.329417	−	0.646518i	0.665590	−	0.746317i	$-0.268180\pi$
$317$	−5.86511	−	11.5109i	−0.329417	−	0.646518i	−0.995008	+	0.0997997i	$0.968180\pi$
$318$		0			0
$319$	5.29553	−	16.2980i	0.296493	−	0.912511i
$320$		0			0
$321$	0.687988	+	2.11741i	0.0383998	+	0.118182i
$322$		0			0
$323$	−16.0529	+	2.54253i	−0.893207	+	0.141470i
$324$		0			0
$325$	−12.9941	+	14.6968i	−0.720784	+	0.815235i
$326$		0			0
$327$	−0.150737	−	0.951715i	−0.00833577	−	0.0526300i
$328$		0			0
$329$	−40.2483	+	13.0775i	−2.21896	+	0.720983i
$330$		0			0
$331$	−1.66611	−	0.541352i	−0.0915778	−	0.0297554i	0.262870	−	0.964831i	$-0.415331\pi$
$331$	−1.66611	−	0.541352i	−0.0915778	−	0.0297554i	−0.354448	+	0.935076i	$0.615331\pi$
$332$		0			0
$333$	−22.3268	+	11.3761i	−1.22350	+	0.623405i
$334$		0			0
$335$	−4.80325	+	7.05699i	−0.262430	+	0.385565i
$336$		0			0
$337$	−3.39221	+	21.4175i	−0.184785	+	1.16669i	0.704625	+	0.709579i	$0.251115\pi$
$337$	−3.39221	+	21.4175i	−0.184785	+	1.16669i	−0.889411	+	0.457109i	$0.848885\pi$
$338$		0			0
$339$	−1.24318	−	0.903224i	−0.0675204	−	0.0490564i
$340$		0			0
$341$	−9.97885	+	7.25006i	−0.540385	+	0.392613i
$342$		0			0
$343$	−45.5119	+	45.5119i	−2.45741	+	2.45741i
$344$		0			0
$345$	1.93922	−	0.368501i	0.104404	−	0.0198394i
$346$		0			0
$347$	2.76263	−	5.42196i	0.148306	−	0.291066i	−0.804888	−	0.593427i	$-0.797775\pi$
$347$	2.76263	−	5.42196i	0.148306	−	0.291066i	0.953194	+	0.302361i	$0.0977747\pi$
$348$		0			0
$349$		−	24.3951i		−	1.30584i	−0.757427	−	0.652920i	$-0.773544\pi$
$349$		−	24.3951i		−	1.30584i	0.757427	−	0.652920i	$-0.226456\pi$
$350$		0			0
$351$			5.04240i			0.269144i
$352$		0			0
$353$	3.10348	−	6.09091i	0.165181	−	0.324187i	−0.793548	−	0.608508i	$-0.791768\pi$
$353$	3.10348	−	6.09091i	0.165181	−	0.324187i	0.958729	+	0.284321i	$0.0917683\pi$
$354$		0			0
$355$	−17.1400	+	18.2263i	−0.909695	+	0.967350i
$356$		0			0
$357$	−2.95324	+	2.95324i	−0.156302	+	0.156302i
$358$		0			0
$359$	24.2946	−	17.6510i	1.28222	−	0.931586i	0.282601	−	0.959238i	$-0.408803\pi$
$359$	24.2946	−	17.6510i	1.28222	−	0.931586i	0.999618	+	0.0276516i	$0.00880290\pi$
$360$		0			0
$361$	0.239760	+	0.174196i	0.0126189	+	0.00916818i
$362$		0			0
$363$	−0.177523	+	1.12084i	−0.00931755	+	0.0588287i
$364$		0			0
$365$	1.54217	+	1.99107i	0.0807210	+	0.104218i
$366$		0			0
$367$	8.52930	−	4.34589i	0.445226	−	0.226854i	−0.216980	−	0.976176i	$-0.569621\pi$
$367$	8.52930	−	4.34589i	0.445226	−	0.226854i	0.662205	+	0.749322i	$0.269621\pi$
$368$		0			0
$369$	12.2067	+	3.96620i	0.635456	+	0.206472i
$370$		0			0
$371$	15.8010	−	5.13406i	0.820347	−	0.266547i
$372$		0			0
$373$	3.95804	+	24.9901i	0.204939	+	1.29394i	0.848767	+	0.528766i	$0.177345\pi$
$373$	3.95804	+	24.9901i	0.204939	+	1.29394i	−0.643828	+	0.765170i	$0.722655\pi$
$374$		0			0
$375$	1.23301	−	2.07482i	0.0636725	−	0.107143i
$376$		0			0
$377$	−27.7105	+	4.38890i	−1.42716	+	0.226040i
$378$		0			0
$379$	−4.30479	−	13.2488i	−0.221122	−	0.680545i	−0.998662	−	0.0517108i	$-0.983533\pi$
$379$	−4.30479	−	13.2488i	−0.221122	−	0.680545i	0.777540	−	0.628834i	$-0.216467\pi$
$380$		0			0
$381$	−0.507309	+	1.56134i	−0.0259902	+	0.0799897i
$382$		0			0
$383$	0.125402	+	0.246115i	0.00640774	+	0.0125759i	0.894188	−	0.447691i	$-0.147754\pi$
$383$	0.125402	+	0.246115i	0.00640774	+	0.0125759i	−0.887780	+	0.460267i	$0.847754\pi$
$384$		0			0
$385$	21.8100	−	16.8928i	1.11154	−	0.860937i
$386$		0			0
$387$	−0.977611	−	0.154838i	−0.0496948	−	0.00787088i
$388$		0			0
$389$	12.0700	−	16.6130i	0.611975	−	0.842311i	−0.384763	−	0.923015i	$-0.625717\pi$
$389$	12.0700	−	16.6130i	0.611975	−	0.842311i	0.996738	+	0.0807040i	$0.0257168\pi$
$390$		0			0
$391$	9.03306	+	12.4329i	0.456821	+	0.628761i
$392$		0			0
$393$	0.0860350	+	0.0860350i	0.00433989	+	0.00433989i
$394$		0			0
$395$	−18.6367	−	17.5260i	−0.937716	−	0.881826i
$396$		0			0
$397$	24.5705	+	12.5193i	1.23316	+	0.628326i	0.944313	−	0.329050i	$-0.106728\pi$
$397$	24.5705	+	12.5193i	1.23316	+	0.628326i	0.288846	+	0.957376i	$0.406728\pi$
$398$		0			0
$399$	−4.80625			−0.240614
$400$		0			0
$401$	18.9289			0.945262			0.472631	−	0.881260i	$-0.343304\pi$
$401$	18.9289			0.945262			0.472631	+	0.881260i	$0.343304\pi$
$402$		0			0
$403$	17.9929	+	9.16782i	0.896288	+	0.456681i
$404$		0			0
$405$	3.58278	+	18.8542i	0.178030	+	0.936875i
$406$		0			0
$407$	−14.3776	−	14.3776i	−0.712669	−	0.712669i
$408$		0			0
$409$	−13.9772	−	19.2380i	−0.691130	−	0.951259i	−1.00000		0.000154984i	$-0.999951\pi$
$409$	−13.9772	−	19.2380i	−0.691130	−	0.951259i	0.308870	−	0.951104i	$-0.400049\pi$
$410$		0			0
$411$	−0.847485	+	1.16646i	−0.0418033	+	0.0575373i
$412$		0			0
$413$	−51.9797	−	8.23278i	−2.55775	−	0.405109i
$414$		0			0
$415$	−27.1529	−	18.4813i	−1.33289	−	0.907211i
$416$		0			0
$417$	0.641117	+	1.25826i	0.0313956	+	0.0616174i
$418$		0			0
$419$	−5.42361	+	16.6922i	−0.264961	+	0.815466i	0.726742	+	0.686911i	$0.241034\pi$
$419$	−5.42361	+	16.6922i	−0.264961	+	0.815466i	−0.991702	+	0.128555i	$0.958966\pi$
$420$		0			0
$421$	4.42860	+	13.6298i	0.215837	+	0.664277i	0.999093	+	0.0425782i	$0.0135572\pi$
$421$	4.42860	+	13.6298i	0.215837	+	0.664277i	−0.783256	+	0.621699i	$0.786443\pi$
$422$		0			0
$423$	23.9795	−	3.79797i	1.16592	−	0.184664i
$424$		0			0
$425$	18.7047	+	1.79490i	0.907310	+	0.0870652i
$426$		0			0
$427$	−5.74969	−	36.3021i	−0.278247	−	1.75678i
$428$		0			0
$429$	−1.93044	+	0.627237i	−0.0932023	+	0.0302833i
$430$		0			0
$431$	2.94359	+	0.956432i	0.141788	+	0.0460697i	0.379051	−	0.925376i	$-0.376250\pi$
$431$	2.94359	+	0.956432i	0.141788	+	0.0460697i	−0.237263	+	0.971445i	$0.576250\pi$
$432$		0			0
$433$	7.55599	−	3.84997i	0.363118	−	0.185018i	−0.262907	−	0.964821i	$-0.584681\pi$
$433$	7.55599	−	3.84997i	0.363118	−	0.185018i	0.626024	+	0.779804i	$0.284681\pi$
$434$		0			0
$435$	3.24849	−	1.16692i	0.155753	−	0.0559498i
$436$		0			0
$437$	−2.76657	+	17.4674i	−0.132343	+	0.835580i
$438$		0			0
$439$	−2.62691	−	1.90856i	−0.125376	−	0.0910908i	0.523330	−	0.852130i	$-0.324689\pi$
$439$	−2.62691	−	1.90856i	−0.125376	−	0.0910908i	−0.648706	+	0.761039i	$0.724689\pi$
$440$		0			0
$441$	46.5983	−	33.8556i	2.21897	−	1.61217i
$442$		0			0
$443$	−20.4205	+	20.4205i	−0.970209	+	0.970209i	−0.999569	−	0.0293598i	$-0.990653\pi$
$443$	−20.4205	+	20.4205i	−0.970209	+	0.970209i	0.0293598	+	0.999569i	$0.490653\pi$
$444$		0			0
$445$	−0.0714958	+	0.562736i	−0.00338923	+	0.0266763i
$446$		0			0
$447$	0.903288	−	1.77280i	0.0427241	−	0.0838507i
$448$		0			0
$449$			2.88201i			0.136010i	0.997685	+	0.0680051i	$0.0216634\pi$
$449$			2.88201i			0.136010i	−0.997685	+	0.0680051i	$0.978337\pi$
$450$		0			0
$451$			10.4147i			0.490409i
$452$		0			0
$453$	1.98099	−	3.88791i	0.0930750	−	0.182670i
$454$		0			0
$455$	−40.8528	−	19.2593i	−1.91521	−	0.902889i
$456$		0			0
$457$	−8.08023	+	8.08023i	−0.377977	+	0.377977i	−0.870372	−	0.492395i	$-0.836122\pi$
$457$	−8.08023	+	8.08023i	−0.377977	+	0.377977i	0.492395	+	0.870372i	$0.336122\pi$
$458$		0			0
$459$	3.90745	−	2.83893i	0.182384	−	0.132510i
$460$		0			0
$461$	7.08182	+	5.14524i	0.329833	+	0.239638i	0.740360	−	0.672211i	$-0.234655\pi$
$461$	7.08182	+	5.14524i	0.329833	+	0.239638i	−0.410527	+	0.911849i	$0.634655\pi$
$462$		0			0
$463$	−1.06603	+	6.73066i	−0.0495427	+	0.312800i	0.950455	+	0.310861i	$0.100617\pi$
$463$	−1.06603	+	6.73066i	−0.0495427	+	0.312800i	−0.999998	+	0.00193947i	$0.999383\pi$
$464$		0			0
$465$	−2.38532	−	0.694834i	−0.110616	−	0.0322221i
$466$		0			0
$467$	−8.40932	+	4.28476i	−0.389137	+	0.198275i	−0.637602	−	0.770366i	$-0.720074\pi$
$467$	−8.40932	+	4.28476i	−0.389137	+	0.198275i	0.248466	+	0.968641i	$0.420074\pi$
$468$		0			0
$469$	−18.6916	−	6.07326i	−0.863097	−	0.280437i
$470$		0			0
$471$	0.489965	−	0.159199i	0.0225764	−	0.00733551i
$472$		0			0
$473$	−0.125641	−	0.793269i	−0.00577700	−	0.0364745i
$474$		0			0
$475$	13.7599	+	16.6810i	0.631348	+	0.765377i
$476$		0			0
$477$	−9.41406	+	1.49104i	−0.431040	+	0.0682700i
$478$		0			0
$479$	−9.45801	−	29.1088i	−0.432147	−	1.33001i	−0.895982	−	0.444091i	$-0.853527\pi$
$479$	−9.45801	−	29.1088i	−0.432147	−	1.33001i	0.463834	−	0.885922i	$-0.346473\pi$
$480$		0			0
$481$	−10.2868	+	31.6594i	−0.469036	+	1.44354i
$482$		0			0
$483$	2.06317	+	4.04921i	0.0938776	+	0.184245i
$484$		0			0
$485$	−16.5536	+	0.508462i	−0.751661	+	0.0230881i
$486$		0			0
$487$	37.7223	+	5.97462i	1.70936	+	0.270736i	0.933084	−	0.359657i	$-0.117106\pi$
$487$	37.7223	+	5.97462i	1.70936	+	0.270736i	0.776276	+	0.630393i	$0.217106\pi$
$488$		0			0
$489$	0.696591	−	0.958776i	0.0315009	−	0.0433573i
$490$		0			0
$491$	5.99777	+	8.25522i	0.270676	+	0.372553i	0.922618	−	0.385716i	$-0.126045\pi$
$491$	5.99777	+	8.25522i	0.270676	+	0.372553i	−0.651942	+	0.758269i	$0.726045\pi$
$492$		0			0
$493$	19.0023	+	19.0023i	0.855821	+	0.855821i
$494$		0			0
$495$	−13.8742	+	7.61461i	−0.623600	+	0.342251i
$496$		0			0
$497$	−51.3237	−	26.1507i	−2.30218	−	1.17302i
$498$		0			0
$499$	4.20384			0.188190			0.0940950	−	0.995563i	$-0.470004\pi$
$499$	4.20384			0.188190			0.0940950	+	0.995563i	$0.470004\pi$
$500$		0			0
$501$	1.32608			0.0592449
$502$		0			0
$503$	23.8597	+	12.1571i	1.06385	+	0.542059i	0.896137	−	0.443777i	$-0.146362\pi$
$503$	23.8597	+	12.1571i	1.06385	+	0.542059i	0.167713	+	0.985836i	$0.446362\pi$
$504$		0			0
$505$	−7.97763	+	4.37837i	−0.355000	+	0.194835i
$506$		0			0
$507$	0.365402	+	0.365402i	0.0162281	+	0.0162281i
$508$		0			0
$509$	−10.7482	−	14.7937i	−0.476407	−	0.655717i	0.501403	−	0.865214i	$-0.332817\pi$
$509$	−10.7482	−	14.7937i	−0.476407	−	0.655717i	−0.977809	+	0.209497i	$0.932817\pi$
$510$		0			0
$511$	−3.40811	+	4.69086i	−0.150766	+	0.207511i
$512$		0			0
$513$	5.48969	+	0.869482i	0.242376	+	0.0383886i
$514$		0			0
$515$	15.4277	−	0.473878i	0.679825	−	0.0208816i
$516$		0			0
$517$	8.94377	+	17.5531i	0.393346	+	0.771986i
$518$		0			0
$519$	0.309400	−	0.952236i	0.0135812	−	0.0417985i
$520$		0			0
$521$	−8.01741	−	24.6751i	−0.351249	−	1.08103i	−0.958153	−	0.286258i	$-0.907589\pi$
$521$	−8.01741	−	24.6751i	−0.351249	−	1.08103i	0.606903	−	0.794776i	$-0.292411\pi$
$522$		0			0
$523$	−23.5597	+	3.73149i	−1.03019	+	0.163167i	−0.648573	−	0.761152i	$-0.724634\pi$
$523$	−23.5597	+	3.73149i	−1.03019	+	0.163167i	−0.381621	+	0.924319i	$0.624634\pi$
$524$		0			0
$525$	5.38012	+	1.38952i	0.234807	+	0.0606436i
$526$		0			0
$527$	−3.02586	−	19.1045i	−0.131809	−	0.832207i
$528$		0			0
$529$	−5.97063	+	1.93997i	−0.259592	+	0.0843467i
$530$		0			0
$531$	28.7143	+	9.32986i	1.24610	+	0.404881i
$532$		0			0
$533$	15.1923	−	7.74087i	0.658052	−	0.335294i
$534$		0			0
$535$	22.1410	+	6.44961i	0.957241	+	0.278841i
$536$		0			0
$537$	0.202319	−	1.27739i	0.00873071	−	0.0551235i
$538$		0			0
$539$	37.8115	+	27.4717i	1.62866	+	1.18329i
$540$		0			0
$541$	−13.7447	+	9.98610i	−0.590930	+	0.429336i	−0.842648	−	0.538465i	$-0.819005\pi$
$541$	−13.7447	+	9.98610i	−0.590930	+	0.429336i	0.251718	+	0.967801i	$0.419005\pi$
$542$		0			0
$543$	0.329872	−	0.329872i	0.0141562	−	0.0141562i
$544$		0			0
$545$	−9.02802	−	4.25609i	−0.386718	−	0.182311i
$546$		0			0
$547$	12.9848	−	25.4840i	0.555188	−	1.08962i	−0.427442	−	0.904043i	$-0.640585\pi$
$547$	12.9848	−	25.4840i	0.555188	−	1.08962i	0.982630	−	0.185576i	$-0.0594150\pi$
$548$		0			0
$549$			21.0858i			0.899921i
$550$		0			0
$551$			30.9253i			1.31746i
$552$		0			0
$553$	26.7396	−	52.4795i	1.13709	−	2.23166i
$554$		0			0
$555$	0.516187	−	4.06286i	0.0219109	−	0.172459i
$556$		0			0
$557$	8.01664	−	8.01664i	0.339676	−	0.339676i	−0.516569	−	0.856245i	$-0.672791\pi$
$557$	8.01664	−	8.01664i	0.339676	−	0.339676i	0.856245	+	0.516569i	$0.172791\pi$
$558$		0			0
$559$	−1.06379	+	0.772886i	−0.0449934	+	0.0326896i
$560$		0			0
$561$	1.57291	+	1.14279i	0.0664084	+	0.0482485i
$562$		0			0
$563$	1.31424	−	8.29781i	0.0553888	−	0.349711i	−0.944393	−	0.328819i	$-0.893349\pi$
$563$	1.31424	−	8.29781i	0.0553888	−	0.349711i	0.999782	−	0.0208919i	$-0.00665058\pi$
$564$		0			0
$565$	−14.9798	+	5.38107i	−0.630207	+	0.226383i
$566$		0			0
$567$	−39.3687	+	20.0594i	−1.65333	+	0.842414i
$568$		0			0
$569$	8.02073	+	2.60609i	0.336247	+	0.109253i	0.472274	−	0.881452i	$-0.343433\pi$
$569$	8.02073	+	2.60609i	0.336247	+	0.109253i	−0.136027	+	0.990705i	$0.543433\pi$
$570$		0			0
$571$	0.524445	−	0.170402i	0.0219473	−	0.00713112i	−0.298023	−	0.954559i	$-0.596327\pi$
$571$	0.524445	−	0.170402i	0.0219473	−	0.00713112i	0.319970	+	0.947428i	$0.396327\pi$
$572$		0			0
$573$	0.770940	+	4.86752i	0.0322065	+	0.203344i
$574$		0			0
$575$	8.14684	−	18.7532i	0.339747	−	0.782062i
$576$		0			0
$577$	35.0943	−	5.55839i	1.46100	−	0.231399i	0.625211	−	0.780456i	$-0.285013\pi$
$577$	35.0943	−	5.55839i	1.46100	−	0.231399i	0.835785	+	0.549057i	$0.185013\pi$
$578$		0			0
$579$	0.347649	+	1.06995i	0.0144478	+	0.0444657i
$580$		0			0
$581$	23.3679	−	71.9189i	0.969463	−	2.98370i
$582$		0			0
$583$	−3.51122	−	6.89116i	−0.145420	−	0.285403i
$584$		0			0
$585$	21.4199	+	14.5792i	0.885605	+	0.602776i
$586$		0			0
$587$	−30.1313	−	4.77233i	−1.24365	−	0.196975i	−0.500287	−	0.865860i	$-0.666772\pi$
$587$	−30.1313	−	4.77233i	−1.24365	−	0.196975i	−0.743366	+	0.668884i	$0.766772\pi$
$588$		0			0
$589$	13.0836	−	18.0081i	0.539101	−	0.742009i
$590$		0			0
$591$	2.21893	+	3.05410i	0.0912746	+	0.125629i
$592$		0			0
$593$	22.0262	+	22.0262i	0.904507	+	0.904507i	0.995822	−	0.0913149i	$-0.0291070\pi$
$593$	22.0262	+	22.0262i	0.904507	+	0.904507i	−0.0913149	+	0.995822i	$0.529107\pi$
$594$		0			0
$595$	8.07619	+	42.5007i	0.331092	+	1.74236i
$596$		0			0
$597$	−3.24731	−	1.65459i	−0.132903	−	0.0677177i
$598$		0			0
$599$	30.5977			1.25019			0.625095	−	0.780549i	$-0.285060\pi$
$599$	30.5977			1.25019			0.625095	+	0.780549i	$0.285060\pi$
$600$		0			0
$601$	−19.1127			−0.779625			−0.389812	−	0.920894i	$-0.627460\pi$
$601$	−19.1127			−0.779625			−0.389812	+	0.920894i	$0.627460\pi$
$602$		0			0
$603$	10.0461	+	5.11876i	0.409110	+	0.208452i
$604$		0			0
$605$	8.56302	+	8.05265i	0.348136	+	0.327387i
$606$		0			0
$607$	33.4013	+	33.4013i	1.35572	+	1.35572i	0.879122	+	0.476596i	$0.158130\pi$
$607$	33.4013	+	33.4013i	1.35572	+	1.35572i	0.476596	+	0.879122i	$0.341870\pi$
$608$		0			0
$609$	4.67103	+	6.42913i	0.189280	+	0.260521i
$610$		0			0
$611$	18.9578	−	26.0932i	0.766952	−	1.05562i
$612$		0			0
$613$	27.6964	+	4.38668i	1.11865	+	0.177176i	0.688257	−	0.725467i	$-0.258376\pi$
$613$	27.6964	+	4.38668i	1.11865	+	0.177176i	0.430390	+	0.902643i	$0.358376\pi$
$614$		0			0
$615$	−1.65846	+	1.28455i	−0.0668757	+	0.0517982i
$616$		0			0
$617$	9.07774	+	17.8161i	0.365456	+	0.717248i	0.998376	−	0.0569694i	$-0.0181438\pi$
$617$	9.07774	+	17.8161i	0.365456	+	0.717248i	−0.632920	+	0.774217i	$0.718144\pi$
$618$		0			0
$619$	3.35008	−	10.3105i	0.134651	−	0.414413i	−0.860885	−	0.508800i	$-0.830089\pi$
$619$	3.35008	−	10.3105i	0.134651	−	0.414413i	0.995536	+	0.0943873i	$0.0300892\pi$
$620$		0			0
$621$	−1.62403	−	4.99824i	−0.0651699	−	0.200572i
$622$		0			0
$623$	−1.28991	+	0.204302i	−0.0516793	+	0.00818519i
$624$		0			0
$625$	−10.5802	−	22.6508i	−0.423210	−	0.906032i
$626$		0			0
$627$	0.350003	+	2.20983i	0.0139778	+	0.0882522i
$628$		0			0
$629$	30.3250	−	9.85318i	1.20914	−	0.392872i
$630$		0			0
$631$	9.50644	+	3.08883i	0.378445	+	0.122964i	0.492062	−	0.870560i	$-0.336243\pi$
$631$	9.50644	+	3.08883i	0.378445	+	0.122964i	−0.113616	+	0.993525i	$0.536243\pi$
$632$		0			0
$633$	−4.80834	+	2.44997i	−0.191114	+	0.0973777i
$634$		0			0
$635$	10.4129	+	13.4439i	0.413224	+	0.533507i
$636$		0			0
$637$	11.9700	−	75.5758i	0.474270	−	2.99442i
$638$		0			0
$639$	26.7346	+	19.4238i	1.05760	+	0.768394i
$640$		0			0
$641$	−34.9762	+	25.4117i	−1.38148	+	1.00370i	−0.384738	+	0.923026i	$0.625708\pi$
$641$	−34.9762	+	25.4117i	−1.38148	+	1.00370i	−0.996740	+	0.0806767i	$0.974292\pi$
$642$		0			0
$643$	−23.5961	+	23.5961i	−0.930540	+	0.930540i	−0.997740	−	0.0672000i	$-0.978593\pi$
$643$	−23.5961	+	23.5961i	−0.930540	+	0.930540i	0.0672000	+	0.997740i	$0.478593\pi$
$644$		0			0
$645$	0.110826	−	0.117850i	0.00436376	−	0.00464033i
$646$		0			0
$647$	−4.12167	+	8.08924i	−0.162040	+	0.318021i	−0.957723	−	0.287692i	$-0.907112\pi$
$647$	−4.12167	+	8.08924i	−0.162040	+	0.318021i	0.795683	+	0.605713i	$0.207112\pi$
$648$		0			0
$649$			24.4989i			0.961667i
$650$		0			0
$651$		−	5.71992i		−	0.224181i
$652$		0			0
$653$	−14.6745	+	28.8003i	−0.574257	+	1.12704i	0.403043	+	0.915181i	$0.367953\pi$
$653$	−14.6745	+	28.8003i	−0.574257	+	1.12704i	−0.977300	+	0.211862i	$0.932047\pi$
$654$		0			0
$655$	1.23815	−	0.235279i	0.0483784	−	0.00919311i
$656$		0			0
$657$	2.35211	−	2.35211i	0.0917647	−	0.0917647i
$658$		0			0
$659$	2.43517	−	1.76925i	0.0948607	−	0.0689204i	−0.539344	−	0.842086i	$-0.681328\pi$
$659$	2.43517	−	1.76925i	0.0948607	−	0.0689204i	0.634205	+	0.773165i	$0.281328\pi$
$660$		0			0
$661$	−19.3982	−	14.0936i	−0.754501	−	0.548177i	0.142718	−	0.989763i	$-0.454416\pi$
$661$	−19.3982	−	14.0936i	−0.754501	−	0.548177i	−0.897219	+	0.441587i	$0.854416\pi$
$662$		0			0
$663$	0.497938	−	3.14386i	0.0193383	−	0.122097i
$664$		0			0
$665$	−28.0121	+	41.1557i	−1.08626	+	1.59595i
$666$		0			0
$667$	26.0542	−	13.2753i	1.00882	−	0.514020i
$668$		0			0
$669$	−1.12928	−	0.366927i	−0.0436607	−	0.0141862i
$670$		0			0
$671$	−16.2724	+	5.28722i	−0.628189	+	0.204111i
$672$		0			0
$673$	0.877205	+	5.53846i	0.0338138	+	0.213492i	0.998810	−	0.0487723i	$-0.0155309\pi$
$673$	0.877205	+	5.53846i	0.0338138	+	0.213492i	−0.964996	+	0.262264i	$0.915531\pi$
$674$		0			0
$675$	−5.89378	−	2.56040i	−0.226852	−	0.0985500i
$676$		0			0
$677$	4.56981	−	0.723787i	0.175632	−	0.0278174i	−0.0679989	−	0.997685i	$-0.521661\pi$
$677$	4.56981	−	0.723787i	0.175632	−	0.0278174i	0.243631	+	0.969868i	$0.421661\pi$
$678$		0			0
$679$	−11.7825	−	36.2629i	−0.452172	−	1.39164i
$680$		0			0
$681$	−0.882696	+	2.71666i	−0.0338250	+	0.104103i
$682$		0			0
$683$	−17.4960	−	34.3379i	−0.669468	−	1.31390i	−0.936653	−	0.350259i	$-0.886094\pi$
$683$	−17.4960	−	34.3379i	−0.669468	−	1.31390i	0.267185	−	0.963645i	$-0.413906\pi$
$684$		0			0
$685$	5.04900	+	14.0554i	0.192912	+	0.537030i
$686$		0			0
$687$	−3.58592	−	0.567954i	−0.136811	−	0.0216688i
$688$		0			0
$689$	−7.44263	+	10.2439i	−0.283542	+	0.390261i
$690$		0			0
$691$	−8.23171	−	11.3300i	−0.313149	−	0.431013i	0.623211	−	0.782054i	$-0.285828\pi$
$691$	−8.23171	−	11.3300i	−0.313149	−	0.431013i	−0.936360	+	0.351041i	$0.885828\pi$
$692$		0			0
$693$	−25.7648	−	25.7648i	−0.978724	−	0.978724i
$694$		0			0
$695$	14.5110	+	1.84363i	0.550435	+	0.0699329i
$696$		0			0
$697$	−14.5520	−	7.41459i	−0.551195	−	0.280848i
$698$		0			0
$699$	4.04718			0.153078
$700$		0			0
$701$	2.47009			0.0932940			0.0466470	−	0.998911i	$-0.485146\pi$
$701$	2.47009			0.0932940			0.0466470	+	0.998911i	$0.485146\pi$
$702$		0			0
$703$	32.6940	+	16.6584i	1.23308	+	0.628284i
$704$		0			0
$705$	−1.69208	+	3.58924i	−0.0637274	+	0.135179i
$706$		0			0
$707$	−14.8147	−	14.8147i	−0.557163	−	0.557163i
$708$		0			0
$709$	−26.4354	−	36.3852i	−0.992802	−	1.36647i	−0.929639	−	0.368472i	$-0.879881\pi$
$709$	−26.4354	−	36.3852i	−0.992802	−	1.36647i	−0.0631631	−	0.998003i	$-0.520119\pi$
$710$		0			0
$711$	−19.8612	+	27.3366i	−0.744854	+	1.02520i
$712$		0			0
$713$	−20.7880	−	3.29249i	−0.778515	−	0.123305i
$714$		0			0
$715$	−5.88009	+	20.1859i	−0.219903	+	0.754911i
$716$		0			0
$717$	2.05622	+	4.03556i	0.0767909	+	0.150711i
$718$		0			0
$719$	−10.6362	+	32.7347i	−0.396661	+	1.22080i	0.530999	+	0.847373i	$0.321817\pi$
$719$	−10.6362	+	32.7347i	−0.396661	+	1.22080i	−0.927660	+	0.373426i	$0.878183\pi$
$720$		0			0
$721$	10.9811	+	33.7964i	0.408958	+	1.25864i
$722$		0			0
$723$	1.08021	−	0.171089i	0.0401735	−	0.00636286i
$724$		0			0
$725$	8.94071	−	34.6178i	0.332050	−	1.28567i
$726$		0			0
$727$	−1.77969	−	11.2365i	−0.0660049	−	0.416738i	−0.998461	−	0.0554556i	$-0.982339\pi$
$727$	−1.77969	−	11.2365i	−0.0660049	−	0.416738i	0.932456	−	0.361283i	$-0.117661\pi$
$728$		0			0
$729$	23.3161	−	7.57586i	0.863559	−	0.280587i
$730$		0			0
$731$	1.19785	+	0.389204i	0.0443039	+	0.0143952i
$732$		0			0
$733$	4.24037	−	2.16058i	0.156622	−	0.0798027i	−0.373923	−	0.927460i	$-0.621988\pi$
$733$	4.24037	−	2.16058i	0.156622	−	0.0798027i	0.530544	+	0.847657i	$0.321988\pi$
$734$		0			0
$735$	0.289025	+	9.40959i	0.0106609	+	0.347078i
$736$		0			0
$737$	−1.43122	+	9.03634i	−0.0527195	+	0.332858i
$738$		0			0
$739$	−17.0602	−	12.3950i	−0.627570	−	0.455957i	0.227987	−	0.973664i	$-0.426786\pi$
$739$	−17.0602	−	12.3950i	−0.627570	−	0.455957i	−0.855558	+	0.517707i	$0.826786\pi$
$740$		0			0
$741$	2.96342	−	2.15305i	0.108864	−	0.0790943i
$742$		0			0
$743$	25.1785	−	25.1785i	0.923710	−	0.923710i	−0.0735796	−	0.997289i	$-0.523442\pi$
$743$	25.1785	−	25.1785i	0.923710	−	0.923710i	0.997289	+	0.0735796i	$0.0234423\pi$
$744$		0			0
$745$	−9.91582	−	18.0672i	−0.363288	−	0.661930i
$746$		0			0
$747$	−19.6953	+	38.6542i	−0.720613	+	1.41428i
$748$		0			0
$749$			53.0936i			1.94000i
$750$		0			0
$751$		−	23.6461i		−	0.862858i	−0.902147	−	0.431429i	$-0.858010\pi$
$751$		−	23.6461i		−	0.862858i	0.902147	−	0.431429i	$-0.141990\pi$
$752$		0			0
$753$	−1.42663	+	2.79992i	−0.0519893	+	0.102035i
$754$		0			0
$755$	−21.7462	−	39.6228i	−0.791427	−	1.44202i
$756$		0			0
$757$	−23.1204	+	23.1204i	−0.840323	+	0.840323i	−0.988901	−	0.148577i	$-0.952531\pi$
$757$	−23.1204	+	23.1204i	−0.840323	+	0.840323i	0.148577	+	0.988901i	$0.452531\pi$
$758$		0			0
$759$	1.71151	−	1.24349i	0.0621239	−	0.0451356i
$760$		0			0
$761$	34.1126	+	24.7842i	1.23658	+	0.898428i	0.997366	−	0.0725391i	$-0.0231102\pi$
$761$	34.1126	+	24.7842i	1.23658	+	0.898428i	0.239214	+	0.970967i	$0.423110\pi$
$762$		0			0
$763$	3.59470	−	22.6961i	0.130137	−	0.821653i
$764$		0			0
$765$	−0.761971	−	24.8069i	−0.0275491	−	0.896896i
$766$		0			0
$767$	35.7375	−	18.2092i	1.29041	−	0.657495i
$768$		0			0
$769$	−10.6684	−	3.46638i	−0.384713	−	0.125001i	0.110274	−	0.993901i	$-0.464827\pi$
$769$	−10.6684	−	3.46638i	−0.384713	−	0.125001i	−0.494987	+	0.868900i	$0.664827\pi$
$770$		0			0
$771$	1.52432	−	0.495283i	0.0548972	−	0.0178372i
$772$		0			0
$773$	−8.18899	−	51.7033i	−0.294538	−	1.85964i	−0.480384	−	0.877059i	$-0.659503\pi$
$773$	−8.18899	−	51.7033i	−0.294538	−	1.85964i	0.185846	−	0.982579i	$-0.440497\pi$
$774$		0			0
$775$	−19.8521	+	16.3757i	−0.713107	+	0.588231i
$776$		0			0
$777$	9.31294	−	1.47503i	0.334100	−	0.0529162i
$778$		0			0
$779$	−5.80785	−	17.8747i	−0.208088	−	0.640429i
$780$		0			0
$781$	−8.28614	+	25.5021i	−0.296502	+	0.912538i
$782$		0			0
$783$	−4.17218	−	8.18836i	−0.149101	−	0.292628i
$784$		0			0
$785$	1.49243	−	5.12340i	0.0532670	−	0.182862i
$786$		0			0
$787$	16.3452	+	2.58883i	0.582644	+	0.0922818i	0.440797	−	0.897607i	$-0.354696\pi$
$787$	16.3452	+	2.58883i	0.582644	+	0.0922818i	0.141847	+	0.989889i	$0.454696\pi$
$788$		0			0
$789$	2.28687	−	3.14760i	0.0814146	−	0.112058i
$790$		0			0
$791$	−21.5397	−	29.6468i	−0.765863	−	1.05412i
$792$		0			0
$793$	19.8074	+	19.8074i	0.703380	+	0.703380i
$794$		0			0
$795$	0.664291	−	1.40909i	0.0235600	−	0.0499754i
$796$		0			0
$797$	48.7783	+	24.8538i	1.72782	+	0.880366i	0.975022	+	0.222109i	$0.0712941\pi$
$797$	48.7783	+	24.8538i	1.72782	+	0.880366i	0.752793	+	0.658257i	$0.228706\pi$
$798$		0			0
$799$	−30.8936			−1.09294
$800$		0			0
$801$	0.749237			0.0264730
$802$		0			0
$803$	2.40496	+	1.22539i	0.0848693	+	0.0432431i
$804$		0			0
$805$	46.6978	+	5.93297i	1.64588	+	0.209110i
$806$		0			0
$807$	3.32991	+	3.32991i	0.117218	+	0.117218i
$808$		0			0
$809$	−10.5113	−	14.4675i	−0.369556	−	0.508650i	0.583224	−	0.812311i	$-0.301791\pi$
$809$	−10.5113	−	14.4675i	−0.369556	−	0.508650i	−0.952780	+	0.303661i	$0.901791\pi$
$810$		0			0
$811$	−10.7812	+	14.8390i	−0.378579	+	0.521069i	−0.955207	−	0.295938i	$-0.904368\pi$
$811$	−10.7812	+	14.8390i	−0.378579	+	0.521069i	0.576629	+	0.817006i	$0.304368\pi$
$812$		0			0
$813$	−1.19978	−	0.190026i	−0.0420780	−	0.00666451i
$814$		0			0
$815$	−4.15003	−	11.5529i	−0.145369	−	0.404679i
$816$		0			0
$817$	0.658012	+	1.29142i	0.0230209	+	0.0451811i
$818$		0			0
$819$	−18.4340	+	56.7342i	−0.644138	+	1.98245i
$820$		0			0
$821$	2.49993	+	7.69400i	0.0872483	+	0.268523i	0.985156	−	0.171661i	$-0.0549134\pi$
$821$	2.49993	+	7.69400i	0.0872483	+	0.268523i	−0.897908	+	0.440184i	$0.854913\pi$
$822$		0			0
$823$	−39.0685	+	6.18784i	−1.36184	+	0.215695i	−0.794238	−	0.607607i	$-0.792130\pi$
$823$	−39.0685	+	6.18784i	−1.36184	+	0.215695i	−0.567604	+	0.823302i	$0.692130\pi$
$824$		0			0
$825$	0.247084	−	2.57487i	0.00860237	−	0.0896456i
$826$		0			0
$827$	5.64845	+	35.6629i	0.196416	+	1.24012i	0.867008	+	0.498294i	$0.166040\pi$
$827$	5.64845	+	35.6629i	0.196416	+	1.24012i	−0.670592	+	0.741826i	$0.733960\pi$
$828$		0			0
$829$	13.9893	−	4.54542i	0.485870	−	0.157869i	−0.0558305	−	0.998440i	$-0.517781\pi$
$829$	13.9893	−	4.54542i	0.485870	−	0.157869i	0.541701	+	0.840571i	$0.317781\pi$
$830$		0			0
$831$	−2.40707	−	0.782104i	−0.0835003	−	0.0271309i
$832$		0			0
$833$	−65.3043	+	33.2742i	−2.26266	+	1.15288i
$834$		0			0
$835$	7.72874	−	11.3552i	0.267464	−	0.392961i
$836$		0			0
$837$	−1.03477	+	6.53328i	−0.0357669	+	0.225823i
$838$		0			0
$839$	−42.8035	−	31.0986i	−1.47774	−	1.07364i	−0.978275	−	0.207309i	$-0.933529\pi$
$839$	−42.8035	−	31.0986i	−1.47774	−	1.07364i	−0.499467	−	0.866333i	$-0.666471\pi$
$840$		0			0
$841$	17.9060	−	13.0095i	0.617449	−	0.448603i
$842$		0			0
$843$	1.63599	−	1.63599i	0.0563465	−	0.0563465i
$844$		0			0
$845$	5.25857	−	0.999260i	0.180900	−	0.0343756i
$846$		0			0
$847$	−12.2861	+	24.1128i	−0.422154	+	0.828525i
$848$		0			0
$849$		−	2.03632i		−	0.0698865i
$850$		0			0
$851$		−	34.6952i		−	1.18934i
$852$		0			0
$853$	3.15524	−	6.19251i	0.108033	−	0.212028i	−0.830660	−	0.556779i	$-0.812037\pi$
$853$	3.15524	−	6.19251i	0.108033	−	0.212028i	0.938694	+	0.344752i	$0.112037\pi$
$854$		0			0
$855$	19.5660	−	20.8060i	0.669142	−	0.711552i
$856$		0			0
$857$	−27.0210	+	27.0210i	−0.923020	+	0.923020i	−0.997242	−	0.0742219i	$-0.976353\pi$
$857$	−27.0210	+	27.0210i	−0.923020	+	0.923020i	0.0742219	+	0.997242i	$0.476353\pi$
$858$		0			0
$859$	−18.5730	+	13.4941i	−0.633703	+	0.460413i	−0.857681	−	0.514182i	$-0.828096\pi$
$859$	−18.5730	+	13.4941i	−0.633703	+	0.460413i	0.223978	+	0.974594i	$0.428096\pi$
$860$		0			0
$861$	−3.90725	−	2.83878i	−0.133159	−	0.0967455i
$862$		0			0
$863$	2.01921	−	12.7488i	0.0687345	−	0.433973i	−0.929191	−	0.369599i	$-0.879495\pi$
$863$	2.01921	−	12.7488i	0.0687345	−	0.433973i	0.997926	−	0.0643737i	$-0.0205050\pi$
$864$		0			0
$865$	−6.35068	−	8.19925i	−0.215930	−	0.278783i
$866$		0			0
$867$	0.553289	−	0.281915i	0.0187907	−	0.00957433i
$868$		0			0
$869$	−26.0764	−	8.47274i	−0.884582	−	0.287418i
$870$		0			0
$871$	14.2454	−	4.62862i	0.482688	−	0.156835i
$872$		0			0
$873$	3.42190	+	21.6050i	0.115814	+	0.731219i
$874$		0			0
$875$	43.2551	−	37.9712i	1.46229	−	1.28366i
$876$		0			0
$877$	−24.8095	+	3.92943i	−0.837756	+	0.132688i	−0.560547	−	0.828122i	$-0.689409\pi$
$877$	−24.8095	+	3.92943i	−0.837756	+	0.132688i	−0.277208	+	0.960810i	$0.589409\pi$
$878$		0			0
$879$	2.08661	+	6.42192i	0.0703795	+	0.216606i
$880$		0			0
$881$	−0.733423	+	2.25725i	−0.0247097	+	0.0760485i	−0.962651	−	0.270746i	$-0.912730\pi$
$881$	−0.733423	+	2.25725i	−0.0247097	+	0.0760485i	0.937941	+	0.346794i	$0.112730\pi$
$882$		0			0
$883$	14.8124	+	29.0710i	0.498478	+	0.978318i	0.993964	+	0.109703i	$0.0349899\pi$
$883$	14.8124	+	29.0710i	0.498478	+	0.978318i	−0.495486	+	0.868616i	$0.665010\pi$
$884$		0			0
$885$	−3.90128	+	3.02171i	−0.131140	+	0.101574i
$886$		0			0
$887$	−43.0953	−	6.82562i	−1.44700	−	0.229182i	−0.617006	−	0.786958i	$-0.711655\pi$
$887$	−43.0953	−	6.82562i	−1.44700	−	0.229182i	−0.829991	+	0.557776i	$0.811655\pi$
$888$		0			0
$889$	−23.0119	+	31.6732i	−0.771795	+	1.06228i
$890$		0			0
$891$	12.0899	+	16.6403i	0.405026	+	0.557471i
$892$		0			0
$893$	−25.1389	−	25.1389i	−0.841240	−	0.841240i
$894$		0			0
$895$	−9.75907	−	9.17742i	−0.326210	−	0.306767i
$896$		0			0
$897$	−3.08602	−	1.57241i	−0.103039	−	0.0525012i
$898$		0			0
$899$	−36.8042			−1.22749
$900$		0			0
$901$	12.1285			0.404057
$902$		0			0
$903$	0.331855	+	0.169089i	0.0110434	+	0.00562691i
$904$		0			0
$905$	−0.902096	−	4.74725i	−0.0299867	−	0.157804i
$906$		0			0
$907$	24.8335	+	24.8335i	0.824583	+	0.824583i	0.986761	−	0.162178i	$-0.0518520\pi$
$907$	24.8335	+	24.8335i	0.824583	+	0.824583i	−0.162178	+	0.986761i	$0.551852\pi$
$908$		0			0
$909$	7.06487	+	9.72396i	0.234327	+	0.322523i
$910$		0			0
$911$	12.3458	−	16.9926i	0.409035	−	0.562989i	−0.553947	−	0.832552i	$-0.686879\pi$
$911$	12.3458	−	16.9926i	0.409035	−	0.562989i	0.962983	+	0.269563i	$0.0868791\pi$
$912$		0			0
$913$	−34.7688	−	5.50684i	−1.15068	−	0.182250i
$914$		0			0
$915$	−2.84900	−	1.93913i	−0.0941849	−	0.0641057i
$916$		0			0
$917$	1.31729	+	2.58532i	0.0435007	+	0.0853748i
$918$		0			0
$919$	−6.73458	+	20.7269i	−0.222153	+	0.683718i	0.776415	+	0.630222i	$0.217036\pi$
$919$	−6.73458	+	20.7269i	−0.222153	+	0.683718i	−0.998568	+	0.0534956i	$0.982964\pi$
$920$		0			0
$921$	−1.16574	−	3.58778i	−0.0384124	−	0.118221i
$922$		0			0
$923$	43.3597	−	6.86750i	1.42720	−	0.226047i
$924$		0			0
$925$	−31.7815	−	28.0995i	−1.04497	−	0.923904i
$926$		0			0
$927$	−3.18915	−	20.1355i	−0.104745	−	0.661337i
$928$		0			0
$929$	31.8479	−	10.3480i	1.04489	−	0.339507i	0.264232	−	0.964459i	$-0.414882\pi$
$929$	31.8479	−	10.3480i	1.04489	−	0.339507i	0.780663	+	0.624952i	$0.214882\pi$
$930$		0			0
$931$	−80.2158	−	26.0637i	−2.62897	−	0.854203i
$932$		0			0
$933$	4.97162	−	2.53316i	0.162763	−	0.0829321i
$934$		0			0
$935$	18.9530	−	6.80830i	0.619828	−	0.222655i
$936$		0			0
$937$	−4.94578	+	31.2265i	−0.161572	+	1.02012i	0.765007	+	0.644022i	$0.222736\pi$
$937$	−4.94578	+	31.2265i	−0.161572	+	1.02012i	−0.926578	+	0.376102i	$0.877264\pi$
$938$		0			0
$939$	3.40418	+	2.47329i	0.111091	+	0.0807126i
$940$		0			0
$941$	−23.2656	+	16.9034i	−0.758437	+	0.551037i	−0.898431	−	0.439116i	$-0.855292\pi$
$941$	−23.2656	+	16.9034i	−0.758437	+	0.551037i	0.139994	+	0.990152i	$0.455292\pi$
$942$		0			0
$943$	−12.5661	+	12.5661i	−0.409209	+	0.409209i
$944$		0			0
$945$	1.86463	−	14.6763i	0.0606563	−	0.477420i
$946$		0			0
$947$	10.1653	−	19.9506i	0.330328	−	0.648306i	−0.664786	−	0.747034i	$-0.731477\pi$
$947$	10.1653	−	19.9506i	0.330328	−	0.648306i	0.995114	+	0.0987277i	$0.0314773\pi$
$948$		0			0
$949$		−	4.41900i		−	0.143447i
$950$		0			0
$951$		−	2.78887i		−	0.0904355i
$952$		0			0
$953$	−4.65277	+	9.13158i	−0.150718	+	0.295801i	−0.954005	−	0.299792i	$-0.903083\pi$
$953$	−4.65277	+	9.13158i	−0.150718	+	0.295801i	0.803287	+	0.595593i	$0.203083\pi$
$954$		0			0
$955$	46.1736	+	21.7677i	1.49414	+	0.704385i
$956$		0			0
$957$	2.61585	−	2.61585i	0.0845583	−	0.0845583i
$958$		0			0
$959$	−27.8173	+	20.2104i	−0.898266	+	0.652628i
$960$		0			0
$961$	−3.64813	−	2.65053i	−0.117682	−	0.0855008i
$962$		0			0
$963$	4.76489	−	30.0844i	0.153547	−	0.969455i
$964$		0			0
$965$	11.1881	+	3.25906i	0.360159	+	0.104913i
$966$		0			0
$967$	−10.3311	+	5.26397i	−0.332226	+	0.169278i	−0.612144	−	0.790746i	$-0.709693\pi$
$967$	−10.3311	+	5.26397i	−0.332226	+	0.169278i	0.279918	+	0.960024i	$0.409693\pi$
$968$		0			0
$969$	−3.33687	−	1.08422i	−0.107196	−	0.0348300i
$970$		0			0
$971$	−42.5120	+	13.8130i	−1.36427	+	0.443279i	−0.897468	−	0.441080i	$-0.854595\pi$
$971$	−42.5120	+	13.8130i	−1.36427	+	0.443279i	−0.466806	+	0.884360i	$0.654595\pi$
$972$		0			0
$973$	5.26825	+	33.2624i	0.168892	+	1.06634i
$974$		0			0
$975$	−3.93971	+	1.55338i	−0.126172	+	0.0497480i
$976$		0			0
$977$	55.6044	−	8.80687i	1.77894	−	0.281757i	0.821464	−	0.570261i	$-0.193158\pi$
$977$	55.6044	−	8.80687i	1.77894	−	0.281757i	0.957479	+	0.288504i	$0.0931579\pi$
$978$		0			0
$979$	0.187869	+	0.578202i	0.00600433	+	0.0184794i
$980$		0			0
$981$	−4.07372	+	12.5376i	−0.130064	+	0.400296i
$982$		0			0
$983$	−22.1249	−	43.4225i	−0.705674	−	1.38496i	−0.913517	−	0.406801i	$-0.866644\pi$
$983$	−22.1249	−	43.4225i	−0.705674	−	1.38496i	0.207843	−	0.978162i	$-0.433356\pi$
$984$		0			0
$985$	39.0846	−	1.20052i	1.24534	−	0.0382519i
$986$		0			0
$987$	−9.02320	−	1.42913i	−0.287212	−	0.0454899i
$988$		0			0
$989$	0.805542	−	1.10873i	0.0256148	−	0.0352557i
$990$		0			0
$991$	−36.6522	−	50.4474i	−1.16429	−	1.60251i	−0.693931	−	0.720041i	$-0.744123\pi$
$991$	−36.6522	−	50.4474i	−1.16429	−	1.60251i	−0.470363	−	0.882473i	$-0.655877\pi$
$992$		0			0
$993$	−0.267413	−	0.267413i	−0.00848610	−	0.00848610i
$994$		0			0
$995$	−33.0943	+	18.1632i	−1.04916	+	0.575811i
$996$		0			0
$997$	−28.8502	−	14.6999i	−0.913696	−	0.465551i	−0.0670752	−	0.997748i	$-0.521367\pi$
$997$	−28.8502	−	14.6999i	−0.913696	−	0.465551i	−0.846621	+	0.532197i	$0.821367\pi$
$998$		0			0
$999$	−10.9041			−0.344989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.63.6	yes	80
4.3	odd	2	inner	400.2.bi.d.63.5	✓	80
25.2	odd	20	inner	400.2.bi.d.127.5	yes	80
100.27	even	20	inner	400.2.bi.d.127.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.63.5	✓	80	4.3	odd	2	inner
400.2.bi.d.63.6	yes	80	1.1	even	1	trivial
400.2.bi.d.127.5	yes	80	25.2	odd	20	inner
400.2.bi.d.127.6	yes	80	100.27	even	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.192345 + 0.0980047i) q^{3} +(1.96025 - 1.07584i) q^{5} +(3.64023 + 3.64023i) q^{7} +(-1.73596 - 2.38935i) q^{9} +(1.40862 - 1.93880i) q^{11} +(-3.87519 - 0.613769i) q^{13} +(0.482481 - 0.0148199i) q^{15} +(1.70615 + 3.34851i) q^{17} +(-1.33643 + 4.11310i) q^{19} +(0.343420 + 1.05694i) q^{21} +(4.03892 - 0.639702i) q^{23} +(2.68512 - 4.21783i) q^{25} +(-0.201047 - 1.26936i) q^{27} +(6.80076 - 2.20970i) q^{29} +(-4.89500 - 1.59048i) q^{31} +(0.460954 - 0.234868i) q^{33} +(11.0521 + 3.21942i) q^{35} +(1.32726 - 8.37999i) q^{37} +(-0.685221 - 0.497842i) q^{39} +(-3.51583 + 2.55440i) q^{41} +(0.236979 - 0.236979i) q^{43} +(-5.97348 - 2.81609i) q^{45} +(-3.73202 + 7.32450i) q^{47} +19.5025i q^{49} +0.811279i q^{51} +(1.46515 - 2.87552i) q^{53} +(0.675398 - 5.31599i) q^{55} +(-0.660158 + 0.660158i) q^{57} +(-8.27043 + 6.00882i) q^{59} +(-5.77599 - 4.19650i) q^{61} +(2.37847 - 15.0171i) q^{63} +(-8.25664 + 2.96596i) q^{65} +(-3.40155 + 1.73318i) q^{67} +(0.839560 + 0.272790i) q^{69} +(-10.6414 + 3.45761i) q^{71} +(0.176191 + 1.11243i) q^{73} +(0.929837 - 0.548125i) q^{75} +(12.1854 - 1.92998i) q^{77} +(-3.53547 - 10.8811i) q^{79} +(-2.65222 + 8.16269i) q^{81} +(-6.66869 - 13.0880i) q^{83} +(6.94694 + 4.72835i) q^{85} +(1.52465 + 0.241481i) q^{87} +(-0.149113 + 0.205237i) q^{89} +(-11.8723 - 16.3408i) q^{91} +(-0.785654 - 0.785654i) q^{93} +(1.80533 + 9.50047i) q^{95} +(-6.59923 - 3.36248i) q^{97} -7.07780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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