LMFDB - Embedded newform 400.2.bi.d.127.6

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			127.6
Character	$\chi$	$=$	400.127
Dual form			400.2.bi.d.63.6

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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	−0.397583	−	0.917566i	$-0.630151\pi$
$3$	0.192345	−	0.0980047i	0.111050	−	0.0565830i	0.508633	+	0.860983i	$0.330151\pi$
$4$		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	0.524411	−	0.851465i	$-0.324285\pi$
$7$	3.64023	−	3.64023i	1.37588	−	1.37588i	0.851465	−	0.524411i	$-0.175715\pi$
$8$		0			0
$9$	−1.73596	+	2.38935i	−0.578655	+	0.796450i
$10$		0			0
$11$	1.40862	+	1.93880i	0.424716	+	0.584572i	0.966730	−	0.255798i	$-0.0823381\pi$
$11$	1.40862	+	1.93880i	0.424716	+	0.584572i	−0.542014	+	0.840369i	$0.682338\pi$
$12$		0			0
$13$	−3.87519	+	0.613769i	−1.07478	+	0.170229i	−0.668644	−	0.743582i	$-0.733125\pi$
$13$	−3.87519	+	0.613769i	−1.07478	+	0.170229i	−0.406139	+	0.913811i	$0.633125\pi$
$14$		0			0
$15$	0.482481	+	0.0148199i	0.124576	+	0.00382649i
$16$		0			0
$17$	1.70615	−	3.34851i	0.413802	−	0.812132i	−0.586196	−	0.810169i	$-0.699375\pi$
$17$	1.70615	−	3.34851i	0.413802	−	0.812132i	0.999998	−	0.00196314i	$-0.000624888\pi$
$18$		0			0
$19$	−1.33643	−	4.11310i	−0.306598	−	0.943610i	−0.979076	−	0.203494i	$-0.934770\pi$
$19$	−1.33643	−	4.11310i	−0.306598	−	0.943610i	0.672479	−	0.740116i	$-0.265230\pi$
$20$		0			0
$21$	0.343420	−	1.05694i	0.0749404	−	0.230643i
$22$		0			0
$23$	4.03892	+	0.639702i	0.842174	+	0.133387i	0.562592	−	0.826735i	$-0.309804\pi$
$23$	4.03892	+	0.639702i	0.842174	+	0.133387i	0.279582	+	0.960122i	$0.409804\pi$
$24$		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	0.862516	−	0.506030i	$-0.168888\pi$
$29$	6.80076	+	2.20970i	1.26287	+	0.410331i	0.400353	+	0.916361i	$0.368888\pi$
$30$		0			0
$31$	−4.89500	+	1.59048i	−0.879168	+	0.285659i	−0.713612	−	0.700541i	$-0.752942\pi$
$31$	−4.89500	+	1.59048i	−0.879168	+	0.285659i	−0.165556	+	0.986200i	$0.552942\pi$
$32$		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	0.816942	+	0.576720i	$0.195668\pi$
$37$	1.32726	+	8.37999i	0.218200	+	1.37766i	−0.598742	+	0.800942i	$0.704332\pi$
$38$		0			0
$39$	−0.685221	+	0.497842i	−0.109723	+	0.0797185i
$40$		0			0
$41$	−3.51583	−	2.55440i	−0.549080	−	0.398930i	0.278366	−	0.960475i	$-0.410207\pi$
$41$	−3.51583	−	2.55440i	−0.549080	−	0.398930i	−0.827446	+	0.561545i	$0.810207\pi$
$42$		0			0
$43$	0.236979	+	0.236979i	0.0361389	+	0.0361389i	0.724945	−	0.688806i	$-0.241865\pi$
$43$	0.236979	+	0.236979i	0.0361389	+	0.0361389i	−0.688806	+	0.724945i	$0.741865\pi$
$44$		0			0
$45$	−5.97348	+	2.81609i	−0.890474	+	0.419797i
$46$		0			0
$47$	−3.73202	−	7.32450i	−0.544371	−	1.06839i	−0.985298	−	0.170846i	$-0.945350\pi$
$47$	−3.73202	−	7.32450i	−0.544371	−	1.06839i	0.440927	−	0.897543i	$-0.354650\pi$
$48$		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	0.969471	−	0.245207i	$-0.0788559\pi$
$53$	1.46515	+	2.87552i	0.201254	+	0.394982i	−0.768217	+	0.640189i	$0.778856\pi$
$54$		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	−0.0996107	−	0.995026i	$-0.531760\pi$
$59$	−8.27043	−	6.00882i	−1.07672	−	0.782282i	−0.977108	+	0.212745i	$0.931760\pi$
$60$		0			0
$61$	−5.77599	+	4.19650i	−0.739540	+	0.537307i	−0.892567	−	0.450915i	$-0.851098\pi$
$61$	−5.77599	+	4.19650i	−0.739540	+	0.537307i	0.153027	+	0.988222i	$0.451098\pi$
$62$		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	0.233691	−	0.972311i	$-0.424920\pi$
$67$	−3.40155	−	1.73318i	−0.415566	−	0.211741i	−0.649256	+	0.760570i	$0.724920\pi$
$68$		0			0
$69$	0.839560	−	0.272790i	0.101071	−	0.0328400i
$70$		0			0
$71$	−10.6414	−	3.45761i	−1.26291	−	0.410343i	−0.400377	−	0.916351i	$-0.631121\pi$
$71$	−10.6414	−	3.45761i	−1.26291	−	0.410343i	−0.862529	+	0.506008i	$0.831121\pi$
$72$		0			0
$73$	0.176191	−	1.11243i	0.0206216	−	0.130200i	−0.975230	−	0.221194i	$-0.929005\pi$
$73$	0.176191	−	1.11243i	0.0206216	−	0.130200i	0.995851	+	0.0909945i	$0.0290046\pi$
$74$		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	0.529010	+	0.848616i	$0.322564\pi$
$79$	−3.53547	+	10.8811i	−0.397772	+	1.22422i	−0.926782	+	0.375601i	$0.877436\pi$
$80$		0			0
$81$	−2.65222	−	8.16269i	−0.294691	−	0.906965i
$82$		0			0
$83$	−6.66869	+	13.0880i	−0.731983	+	1.43660i	0.161207	+	0.986921i	$0.448461\pi$
$83$	−6.66869	+	13.0880i	−0.731983	+	1.43660i	−0.893191	+	0.449678i	$0.851539\pi$
$84$		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	0.801041	−	0.598610i	$-0.204280\pi$
$89$	−0.149113	−	0.205237i	−0.0158060	−	0.0217550i	−0.816847	+	0.576855i	$0.804280\pi$
$90$		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	−0.755700	−	0.654918i	$-0.772703\pi$
$97$	−6.59923	+	3.36248i	−0.670050	+	0.341408i	0.0856499	+	0.996325i	$0.472703\pi$
$98$		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	−0.123925	−	0.992292i	$-0.539548\pi$
$103$	6.15037	−	3.13377i	0.606014	−	0.308780i	0.729939	+	0.683512i	$0.239548\pi$
$104$		0			0
$105$	1.81029	−	1.70239i	0.176666	−	0.166136i
$106$		0			0
$107$	7.29262	−	7.29262i	0.705004	−	0.705004i	−0.260476	−	0.965480i	$-0.583879\pi$
$107$	7.29262	−	7.29262i	0.705004	−	0.705004i	0.965480	+	0.260476i	$0.0838795\pi$
$108$		0			0
$109$	−2.62365	+	3.61114i	−0.251300	+	0.345885i	−0.915966	−	0.401256i	$-0.868574\pi$
$109$	−2.62365	+	3.61114i	−0.251300	+	0.345885i	0.664666	+	0.747141i	$0.268574\pi$
$110$		0			0
$111$	1.07657	+	1.48177i	0.102183	+	0.140644i
$112$		0			0
$113$	−7.03067	+	1.11355i	−0.661390	+	0.104754i	−0.478101	−	0.878305i	$-0.658675\pi$
$113$	−7.03067	+	1.11355i	−0.661390	+	0.104754i	−0.183289	+	0.983059i	$0.558675\pi$
$114$		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	−0.876985	−	0.480517i	$-0.840449\pi$
$127$	1.18966	−	7.51122i	0.105565	−	0.666513i	0.982551	−	0.185996i	$-0.0595510\pi$
$128$		0			0
$129$	0.0688066	+	0.0223566i	0.00605809	+	0.00196839i
$130$		0			0
$131$	0.536039	−	0.174170i	0.0468340	−	0.0152173i	−0.285506	−	0.958377i	$-0.592162\pi$
$131$	0.536039	−	0.174170i	0.0468340	−	0.0152173i	0.332340	+	0.943160i	$0.392162\pi$
$132$		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	−0.991267	−	0.131869i	$-0.957902\pi$
$137$	−1.04483	−	6.59680i	−0.0892658	−	0.563602i	0.902001	−	0.431733i	$-0.142098\pi$
$138$		0			0
$139$	5.29234	−	3.84511i	0.448891	−	0.326138i	−0.340267	−	0.940329i	$-0.610517\pi$
$139$	5.29234	−	3.84511i	0.448891	−	0.326138i	0.789158	+	0.614191i	$0.210517\pi$
$140$		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	$0.123228\pi$
$149$			9.21679i			0.755069i	−0.925996	+	0.377534i	$0.876772\pi$
$150$		0			0
$151$			20.2132i			1.64493i	0.568817	+	0.822464i	$0.307401\pi$
$151$			20.2132i			1.64493i	−0.568817	+	0.822464i	$0.692599\pi$
$152$		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	0.771232	−	0.636555i	$-0.219641\pi$
$157$	1.68750	+	1.68750i	0.134677	+	0.134677i	−0.636555	+	0.771232i	$0.719641\pi$
$158$		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	0.998224	+	0.0595754i	$0.0189747\pi$
$163$	0.858800	+	5.42225i	0.0672664	+	0.424703i	−0.930957	+	0.365128i	$0.881025\pi$
$164$		0			0
$165$	0.650901	+	0.956312i	0.0506726	+	0.0744488i
$166$		0			0
$167$	5.47332	+	2.78880i	0.423538	+	0.215803i	0.652750	−	0.757573i	$-0.273615\pi$
$167$	5.47332	+	2.78880i	0.423538	+	0.215803i	−0.229212	+	0.973376i	$0.573615\pi$
$168$		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	0.944634	+	0.328126i	$0.106417\pi$
$173$	−0.725555	+	4.58098i	−0.0551630	+	0.348285i	−0.999797	+	0.0201588i	$0.993583\pi$
$174$		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	−0.996100	−	0.0882335i	$-0.971878\pi$
$179$	−1.85134	+	5.69784i	−0.138376	+	0.425877i	0.857724	+	0.514110i	$0.171878\pi$
$180$		0			0
$181$	0.667794	+	2.05526i	0.0496367	+	0.152766i	0.972803	−	0.231636i	$-0.0744077\pi$
$181$	0.667794	+	2.05526i	0.0496367	+	0.152766i	−0.923166	+	0.384402i	$0.874408\pi$
$182$		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	0.0293620	−	0.999569i	$-0.490652\pi$
$191$	13.4186	−	18.4691i	0.970935	−	1.33638i	0.941573	−	0.336809i	$-0.109348\pi$
$192$		0			0
$193$	3.68505	−	3.68505i	0.265256	−	0.265256i	−0.561930	−	0.827185i	$-0.689941\pi$
$193$	3.68505	−	3.68505i	0.265256	−	0.265256i	0.827185	+	0.561930i	$0.189941\pi$
$194$		0			0
$195$	−1.87880	+	0.238702i	−0.134544	+	0.0170938i
$196$		0			0
$197$	15.5814	−	7.93911i	1.11013	−	0.565638i	0.199929	−	0.979810i	$-0.435929\pi$
$197$	15.5814	−	7.93911i	1.11013	−	0.565638i	0.910199	+	0.414172i	$0.135929\pi$
$198$		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	−0.917955	−	0.396685i	$-0.870161\pi$
$211$	−14.6938	−	20.2242i	−1.01156	−	1.39229i	−0.0936060	−	0.995609i	$-0.529839\pi$
$212$		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	−0.0281422	−	0.999604i	$-0.508959\pi$
$223$	−5.43272	−	0.860458i	−0.363802	−	0.0576205i	−0.335659	+	0.941983i	$0.608959\pi$
$224$		0			0
$225$	−14.7392	−	0.906313i	−0.982610	−	0.0604209i
$226$		0			0
$227$	2.06996	−	13.0692i	0.137388	−	0.867433i	−0.818672	−	0.574261i	$-0.805289\pi$
$227$	2.06996	−	13.0692i	0.137388	−	0.867433i	0.956060	−	0.293171i	$-0.0947107\pi$
$228$		0			0
$229$	−15.9951	−	5.19713i	−1.05699	−	0.343436i	−0.271580	−	0.962416i	$-0.587546\pi$
$229$	−15.9951	−	5.19713i	−1.05699	−	0.343436i	−0.785407	+	0.618980i	$0.787546\pi$
$230$		0			0
$231$	2.53295	−	0.823004i	0.166656	−	0.0541497i
$232$		0			0
$233$	16.7045	+	8.51136i	1.09435	+	0.557598i	0.905473	−	0.424404i	$-0.139516\pi$
$233$	16.7045	+	8.51136i	1.09435	+	0.557598i	0.188874	+	0.982001i	$0.439516\pi$
$234$		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	0.117223	−	0.993106i	$-0.462601\pi$
$239$	16.9738	−	12.3322i	1.09795	−	0.797705i	0.980724	+	0.195400i	$0.0626006\pi$
$240$		0			0
$241$	4.09871	+	2.97788i	0.264021	+	0.191822i	0.711918	−	0.702263i	$-0.247827\pi$
$241$	4.09871	+	2.97788i	0.264021	+	0.191822i	−0.447897	+	0.894085i	$0.647827\pi$
$242$		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	$-0.848062\pi$
$251$		−	14.5567i		−	0.918814i	0.888226	−	0.459407i	$-0.151938\pi$
$252$		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	0.851629	−	0.524145i	$-0.175615\pi$
$257$	5.24996	+	5.24996i	0.327483	+	0.327483i	−0.524145	+	0.851629i	$0.675615\pi$
$258$		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	0.908095	+	0.418765i	$0.137537\pi$
$263$	2.81939	+	17.8009i	0.173851	+	1.09765i	−0.734244	+	0.678886i	$0.762463\pi$
$264$		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	0.401703	−	0.915770i	$-0.368418\pi$
$269$	20.7469	−	6.74109i	1.26496	−	0.411012i	0.863261	+	0.504758i	$0.168418\pi$
$270$		0			0
$271$	−5.35164	−	1.73885i	−0.325089	−	0.105628i	0.141926	−	0.989877i	$-0.454671\pi$
$271$	−5.35164	−	1.73885i	−0.325089	−	0.105628i	−0.467015	+	0.884249i	$0.654671\pi$
$272$		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	−0.201473	−	0.979494i	$-0.564573\pi$
$277$	−11.5798	−	1.83407i	−0.695765	−	0.110198i	−0.494292	+	0.869296i	$0.664573\pi$
$278$		0			0
$279$	4.69733	−	14.4569i	0.281222	−	0.865511i
$280$		0			0
$281$	3.31191	+	10.1930i	0.197572	+	0.608064i	0.999937	+	0.0112302i	$0.00357477\pi$
$281$	3.31191	+	10.1930i	0.197572	+	0.608064i	−0.802365	+	0.596834i	$0.796425\pi$
$282$		0			0
$283$	−4.28246	+	8.40481i	−0.254566	+	0.499614i	−0.982554	−	0.185975i	$-0.940455\pi$
$283$	−4.28246	+	8.40481i	−0.254566	+	0.499614i	0.727988	+	0.685590i	$0.240455\pi$
$284$		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	0.358680	−	0.933461i	$-0.383227\pi$
$293$	22.1179	−	22.1179i	1.29214	−	1.29214i	0.933461	−	0.358680i	$-0.116773\pi$
$294$		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	−0.965530	−	0.260293i	$-0.916181\pi$
$307$	−12.3567	+	12.3567i	−0.705237	+	0.705237i	0.260293	+	0.965530i	$0.416181\pi$
$308$		0			0
$309$	0.875869	−	1.20553i	0.0498265	−	0.0685802i
$310$		0			0
$311$	15.1927	+	20.9110i	0.861500	+	1.18575i	0.981210	+	0.192944i	$0.0618036\pi$
$311$	15.1927	+	20.9110i	0.861500	+	1.18575i	−0.119710	+	0.992809i	$0.538196\pi$
$312$		0			0
$313$	19.2520	−	3.04921i	1.08819	−	0.172352i	0.413535	−	0.910488i	$-0.364294\pi$
$313$	19.2520	−	3.04921i	1.08819	−	0.172352i	0.674651	+	0.738136i	$0.264294\pi$
$314$		0			0
$315$	−11.4936	+	31.9960i	−0.647593	+	1.80277i
$316$		0			0
$317$	−5.86511	+	11.5109i	−0.329417	+	0.646518i	−0.995008	−	0.0997997i	$-0.968180\pi$
$317$	−5.86511	+	11.5109i	−0.329417	+	0.646518i	0.665590	+	0.746317i	$0.268180\pi$
$318$		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	−0.354448	−	0.935076i	$-0.615331\pi$
$331$	−1.66611	+	0.541352i	−0.0915778	+	0.0297554i	0.262870	+	0.964831i	$0.415331\pi$
$332$		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	−0.889411	−	0.457109i	$-0.848885\pi$
$337$	−3.39221	−	21.4175i	−0.184785	−	1.16669i	0.704625	−	0.709579i	$-0.251115\pi$
$338$		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	0.953194	−	0.302361i	$-0.0977747\pi$
$347$	2.76263	+	5.42196i	0.148306	+	0.291066i	−0.804888	+	0.593427i	$0.797775\pi$
$348$		0			0
$349$			24.3951i			1.30584i	0.757427	+	0.652920i	$0.226456\pi$
$349$			24.3951i			1.30584i	−0.757427	+	0.652920i	$0.773544\pi$
$350$		0			0
$351$		−	5.04240i		−	0.269144i
$352$		0			0
$353$	3.10348	+	6.09091i	0.165181	+	0.324187i	0.958729	−	0.284321i	$-0.0917683\pi$
$353$	3.10348	+	6.09091i	0.165181	+	0.324187i	−0.793548	+	0.608508i	$0.791768\pi$
$354$		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	0.999618	−	0.0276516i	$-0.00880290\pi$
$359$	24.2946	+	17.6510i	1.28222	+	0.931586i	0.282601	+	0.959238i	$0.408803\pi$
$360$		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	0.662205	−	0.749322i	$-0.269621\pi$
$367$	8.52930	+	4.34589i	0.445226	+	0.226854i	−0.216980	+	0.976176i	$0.569621\pi$
$368$		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	−0.643828	−	0.765170i	$-0.722655\pi$
$373$	3.95804	−	24.9901i	0.204939	−	1.29394i	0.848767	−	0.528766i	$-0.177345\pi$
$374$		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	0.777540	+	0.628834i	$0.216467\pi$
$379$	−4.30479	+	13.2488i	−0.221122	+	0.680545i	−0.998662	+	0.0517108i	$0.983533\pi$
$380$		0			0
$381$	−0.507309	−	1.56134i	−0.0259902	−	0.0799897i
$382$		0			0
$383$	0.125402	−	0.246115i	0.00640774	−	0.0125759i	−0.887780	−	0.460267i	$-0.847754\pi$
$383$	0.125402	−	0.246115i	0.00640774	−	0.0125759i	0.894188	+	0.447691i	$0.147754\pi$
$384$		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	0.996738	−	0.0807040i	$-0.0257168\pi$
$389$	12.0700	+	16.6130i	0.611975	+	0.842311i	−0.384763	+	0.923015i	$0.625717\pi$
$390$		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	0.288846	−	0.957376i	$-0.406728\pi$
$397$	24.5705	−	12.5193i	1.23316	−	0.628326i	0.944313	+	0.329050i	$0.106728\pi$
$398$		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	0.308870	+	0.951104i	$0.400049\pi$
$409$	−13.9772	+	19.2380i	−0.691130	+	0.951259i	−1.00000		0.000154984i	$0.999951\pi$
$410$		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	−0.991702	−	0.128555i	$-0.958966\pi$
$419$	−5.42361	−	16.6922i	−0.264961	−	0.815466i	0.726742	−	0.686911i	$-0.241034\pi$
$420$		0			0
$421$	4.42860	−	13.6298i	0.215837	−	0.664277i	−0.783256	−	0.621699i	$-0.786443\pi$
$421$	4.42860	−	13.6298i	0.215837	−	0.664277i	0.999093	−	0.0425782i	$-0.0135572\pi$
$422$		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	−0.237263	−	0.971445i	$-0.576250\pi$
$431$	2.94359	−	0.956432i	0.141788	−	0.0460697i	0.379051	+	0.925376i	$0.376250\pi$
$432$		0			0
$433$	7.55599	+	3.84997i	0.363118	+	0.185018i	0.626024	−	0.779804i	$-0.284681\pi$
$433$	7.55599	+	3.84997i	0.363118	+	0.185018i	−0.262907	+	0.964821i	$0.584681\pi$
$434$		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	−0.648706	−	0.761039i	$-0.724689\pi$
$439$	−2.62691	+	1.90856i	−0.125376	+	0.0910908i	0.523330	+	0.852130i	$0.324689\pi$
$440$		0			0
$441$	46.5983	+	33.8556i	2.21897	+	1.61217i
$442$		0			0
$443$	−20.4205	−	20.4205i	−0.970209	−	0.970209i	0.0293598	−	0.999569i	$-0.490653\pi$
$443$	−20.4205	−	20.4205i	−0.970209	−	0.970209i	−0.999569	+	0.0293598i	$0.990653\pi$
$444$		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	$-0.978337\pi$
$449$		−	2.88201i		−	0.136010i	0.997685	−	0.0680051i	$-0.0216634\pi$
$450$		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	0.492395	−	0.870372i	$-0.336122\pi$
$457$	−8.08023	−	8.08023i	−0.377977	−	0.377977i	−0.870372	+	0.492395i	$0.836122\pi$
$458$		0			0
$459$	3.90745	+	2.83893i	0.182384	+	0.132510i
$460$		0			0
$461$	7.08182	−	5.14524i	0.329833	−	0.239638i	−0.410527	−	0.911849i	$-0.634655\pi$
$461$	7.08182	−	5.14524i	0.329833	−	0.239638i	0.740360	+	0.672211i	$0.234655\pi$
$462$		0			0
$463$	−1.06603	−	6.73066i	−0.0495427	−	0.312800i	−0.999998	−	0.00193947i	$-0.999383\pi$
$463$	−1.06603	−	6.73066i	−0.0495427	−	0.312800i	0.950455	−	0.310861i	$-0.100617\pi$
$464$		0			0
$465$	−2.38532	+	0.694834i	−0.110616	+	0.0322221i
$466$		0			0
$467$	−8.40932	−	4.28476i	−0.389137	−	0.198275i	0.248466	−	0.968641i	$-0.420074\pi$
$467$	−8.40932	−	4.28476i	−0.389137	−	0.198275i	−0.637602	+	0.770366i	$0.720074\pi$
$468$		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	0.463834	+	0.885922i	$0.346473\pi$
$479$	−9.45801	+	29.1088i	−0.432147	+	1.33001i	−0.895982	+	0.444091i	$0.853527\pi$
$480$		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	0.776276	−	0.630393i	$-0.217106\pi$
$487$	37.7223	−	5.97462i	1.70936	−	0.270736i	0.933084	+	0.359657i	$0.117106\pi$
$488$		0			0
$489$	0.696591	+	0.958776i	0.0315009	+	0.0433573i
$490$		0			0
$491$	5.99777	−	8.25522i	0.270676	−	0.372553i	−0.651942	−	0.758269i	$-0.726045\pi$
$491$	5.99777	−	8.25522i	0.270676	−	0.372553i	0.922618	+	0.385716i	$0.126045\pi$
$492$		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	0.167713	−	0.985836i	$-0.446362\pi$
$503$	23.8597	−	12.1571i	1.06385	−	0.542059i	0.896137	+	0.443777i	$0.146362\pi$
$504$		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	−0.977809	−	0.209497i	$-0.932817\pi$
$509$	−10.7482	+	14.7937i	−0.476407	+	0.655717i	0.501403	+	0.865214i	$0.332817\pi$
$510$		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	0.606903	+	0.794776i	$0.292411\pi$
$521$	−8.01741	+	24.6751i	−0.351249	+	1.08103i	−0.958153	+	0.286258i	$0.907589\pi$
$522$		0			0
$523$	−23.5597	−	3.73149i	−1.03019	−	0.163167i	−0.381621	−	0.924319i	$-0.624634\pi$
$523$	−23.5597	−	3.73149i	−1.03019	−	0.163167i	−0.648573	+	0.761152i	$0.724634\pi$
$524$		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	0.251718	−	0.967801i	$-0.419005\pi$
$541$	−13.7447	−	9.98610i	−0.590930	−	0.429336i	−0.842648	+	0.538465i	$0.819005\pi$
$542$		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	0.982630	+	0.185576i	$0.0594150\pi$
$547$	12.9848	+	25.4840i	0.555188	+	1.08962i	−0.427442	+	0.904043i	$0.640585\pi$
$548$		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	0.856245	−	0.516569i	$-0.172791\pi$
$557$	8.01664	+	8.01664i	0.339676	+	0.339676i	−0.516569	+	0.856245i	$0.672791\pi$
$558$		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	0.999782	+	0.0208919i	$0.00665058\pi$
$563$	1.31424	+	8.29781i	0.0553888	+	0.349711i	−0.944393	+	0.328819i	$0.893349\pi$
$564$		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	−0.136027	−	0.990705i	$-0.543433\pi$
$569$	8.02073	−	2.60609i	0.336247	−	0.109253i	0.472274	+	0.881452i	$0.343433\pi$
$570$		0			0
$571$	0.524445	+	0.170402i	0.0219473	+	0.00713112i	0.319970	−	0.947428i	$-0.396327\pi$
$571$	0.524445	+	0.170402i	0.0219473	+	0.00713112i	−0.298023	+	0.954559i	$0.596327\pi$
$572$		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	0.835785	−	0.549057i	$-0.185013\pi$
$577$	35.0943	+	5.55839i	1.46100	+	0.231399i	0.625211	+	0.780456i	$0.285013\pi$
$578$		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	−0.743366	−	0.668884i	$-0.766772\pi$
$587$	−30.1313	+	4.77233i	−1.24365	+	0.196975i	−0.500287	+	0.865860i	$0.666772\pi$
$588$		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	−0.0913149	−	0.995822i	$-0.529107\pi$
$593$	22.0262	−	22.0262i	0.904507	−	0.904507i	0.995822	+	0.0913149i	$0.0291070\pi$
$594$		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	0.476596	−	0.879122i	$-0.341870\pi$
$607$	33.4013	−	33.4013i	1.35572	−	1.35572i	0.879122	−	0.476596i	$-0.158130\pi$
$608$		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	0.430390	−	0.902643i	$-0.358376\pi$
$613$	27.6964	−	4.38668i	1.11865	−	0.177176i	0.688257	+	0.725467i	$0.258376\pi$
$614$		0			0
$615$	−1.65846	−	1.28455i	−0.0668757	−	0.0517982i
$616$		0			0
$617$	9.07774	−	17.8161i	0.365456	−	0.717248i	−0.632920	−	0.774217i	$-0.718144\pi$
$617$	9.07774	−	17.8161i	0.365456	−	0.717248i	0.998376	+	0.0569694i	$0.0181438\pi$
$618$		0			0
$619$	3.35008	+	10.3105i	0.134651	+	0.414413i	0.995536	−	0.0943873i	$-0.0300892\pi$
$619$	3.35008	+	10.3105i	0.134651	+	0.414413i	−0.860885	+	0.508800i	$0.830089\pi$
$620$		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	−0.113616	−	0.993525i	$-0.536243\pi$
$631$	9.50644	−	3.08883i	0.378445	−	0.122964i	0.492062	+	0.870560i	$0.336243\pi$
$632$		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	−0.996740	−	0.0806767i	$-0.974292\pi$
$641$	−34.9762	−	25.4117i	−1.38148	−	1.00370i	−0.384738	−	0.923026i	$-0.625708\pi$
$642$		0			0
$643$	−23.5961	−	23.5961i	−0.930540	−	0.930540i	0.0672000	−	0.997740i	$-0.478593\pi$
$643$	−23.5961	−	23.5961i	−0.930540	−	0.930540i	−0.997740	+	0.0672000i	$0.978593\pi$
$644$		0			0
$645$	0.110826	+	0.117850i	0.00436376	+	0.00464033i
$646$		0			0
$647$	−4.12167	−	8.08924i	−0.162040	−	0.318021i	0.795683	−	0.605713i	$-0.207112\pi$
$647$	−4.12167	−	8.08924i	−0.162040	−	0.318021i	−0.957723	+	0.287692i	$0.907112\pi$
$648$		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	−0.977300	−	0.211862i	$-0.932047\pi$
$653$	−14.6745	−	28.8003i	−0.574257	−	1.12704i	0.403043	−	0.915181i	$-0.367953\pi$
$654$		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	0.634205	−	0.773165i	$-0.281328\pi$
$659$	2.43517	+	1.76925i	0.0948607	+	0.0689204i	−0.539344	+	0.842086i	$0.681328\pi$
$660$		0			0
$661$	−19.3982	+	14.0936i	−0.754501	+	0.548177i	−0.897219	−	0.441587i	$-0.854416\pi$
$661$	−19.3982	+	14.0936i	−0.754501	+	0.548177i	0.142718	+	0.989763i	$0.454416\pi$
$662$		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	−0.964996	−	0.262264i	$-0.915531\pi$
$673$	0.877205	−	5.53846i	0.0338138	−	0.213492i	0.998810	+	0.0487723i	$0.0155309\pi$
$674$		0			0
$675$	−5.89378	+	2.56040i	−0.226852	+	0.0985500i
$676$		0			0
$677$	4.56981	+	0.723787i	0.175632	+	0.0278174i	0.243631	−	0.969868i	$-0.421661\pi$
$677$	4.56981	+	0.723787i	0.175632	+	0.0278174i	−0.0679989	+	0.997685i	$0.521661\pi$
$678$		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	0.267185	+	0.963645i	$0.413906\pi$
$683$	−17.4960	+	34.3379i	−0.669468	+	1.31390i	−0.936653	+	0.350259i	$0.886094\pi$
$684$		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	−0.936360	−	0.351041i	$-0.885828\pi$
$691$	−8.23171	+	11.3300i	−0.313149	+	0.431013i	0.623211	+	0.782054i	$0.285828\pi$
$692$		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	−0.0631631	+	0.998003i	$0.520119\pi$
$709$	−26.4354	+	36.3852i	−0.992802	+	1.36647i	−0.929639	+	0.368472i	$0.879881\pi$
$710$		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	−0.927660	−	0.373426i	$-0.878183\pi$
$719$	−10.6362	−	32.7347i	−0.396661	−	1.22080i	0.530999	−	0.847373i	$-0.321817\pi$
$720$		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	0.932456	+	0.361283i	$0.117661\pi$
$727$	−1.77969	+	11.2365i	−0.0660049	+	0.416738i	−0.998461	+	0.0554556i	$0.982339\pi$
$728$		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	0.530544	−	0.847657i	$-0.321988\pi$
$733$	4.24037	+	2.16058i	0.156622	+	0.0798027i	−0.373923	+	0.927460i	$0.621988\pi$
$734$		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	−0.855558	−	0.517707i	$-0.826786\pi$
$739$	−17.0602	+	12.3950i	−0.627570	+	0.455957i	0.227987	+	0.973664i	$0.426786\pi$
$740$		0			0
$741$	2.96342	+	2.15305i	0.108864	+	0.0790943i
$742$		0			0
$743$	25.1785	+	25.1785i	0.923710	+	0.923710i	0.997289	−	0.0735796i	$-0.0234423\pi$
$743$	25.1785	+	25.1785i	0.923710	+	0.923710i	−0.0735796	+	0.997289i	$0.523442\pi$
$744$		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	$0.141990\pi$
$751$			23.6461i			0.862858i	−0.902147	+	0.431429i	$0.858010\pi$
$752$		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	0.148577	−	0.988901i	$-0.452531\pi$
$757$	−23.1204	−	23.1204i	−0.840323	−	0.840323i	−0.988901	+	0.148577i	$0.952531\pi$
$758$		0			0
$759$	1.71151	+	1.24349i	0.0621239	+	0.0451356i
$760$		0			0
$761$	34.1126	−	24.7842i	1.23658	−	0.898428i	0.239214	−	0.970967i	$-0.423110\pi$
$761$	34.1126	−	24.7842i	1.23658	−	0.898428i	0.997366	+	0.0725391i	$0.0231102\pi$
$762$		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	−0.494987	−	0.868900i	$-0.664827\pi$
$769$	−10.6684	+	3.46638i	−0.384713	+	0.125001i	0.110274	+	0.993901i	$0.464827\pi$
$770$		0			0
$771$	1.52432	+	0.495283i	0.0548972	+	0.0178372i
$772$		0			0
$773$	−8.18899	+	51.7033i	−0.294538	+	1.85964i	0.185846	+	0.982579i	$0.440497\pi$
$773$	−8.18899	+	51.7033i	−0.294538	+	1.85964i	−0.480384	+	0.877059i	$0.659503\pi$
$774$		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	0.141847	−	0.989889i	$-0.454696\pi$
$787$	16.3452	−	2.58883i	0.582644	−	0.0922818i	0.440797	+	0.897607i	$0.354696\pi$
$788$		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	0.752793	−	0.658257i	$-0.228706\pi$
$797$	48.7783	−	24.8538i	1.72782	−	0.880366i	0.975022	−	0.222109i	$-0.0712941\pi$
$798$		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	−0.952780	−	0.303661i	$-0.901791\pi$
$809$	−10.5113	+	14.4675i	−0.369556	+	0.508650i	0.583224	+	0.812311i	$0.301791\pi$
$810$		0			0
$811$	−10.7812	−	14.8390i	−0.378579	−	0.521069i	0.576629	−	0.817006i	$-0.304368\pi$
$811$	−10.7812	−	14.8390i	−0.378579	−	0.521069i	−0.955207	+	0.295938i	$0.904368\pi$
$812$		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	−0.897908	−	0.440184i	$-0.854913\pi$
$821$	2.49993	−	7.69400i	0.0872483	−	0.268523i	0.985156	+	0.171661i	$0.0549134\pi$
$822$		0			0
$823$	−39.0685	−	6.18784i	−1.36184	−	0.215695i	−0.567604	−	0.823302i	$-0.692130\pi$
$823$	−39.0685	−	6.18784i	−1.36184	−	0.215695i	−0.794238	+	0.607607i	$0.792130\pi$
$824$		0			0
$825$	0.247084	+	2.57487i	0.00860237	+	0.0896456i
$826$		0			0
$827$	5.64845	−	35.6629i	0.196416	−	1.24012i	−0.670592	−	0.741826i	$-0.733960\pi$
$827$	5.64845	−	35.6629i	0.196416	−	1.24012i	0.867008	−	0.498294i	$-0.166040\pi$
$828$		0			0
$829$	13.9893	+	4.54542i	0.485870	+	0.157869i	0.541701	−	0.840571i	$-0.317781\pi$
$829$	13.9893	+	4.54542i	0.485870	+	0.157869i	−0.0558305	+	0.998440i	$0.517781\pi$
$830$		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	−0.499467	+	0.866333i	$0.666471\pi$
$839$	−42.8035	+	31.0986i	−1.47774	+	1.07364i	−0.978275	+	0.207309i	$0.933529\pi$
$840$		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	0.938694	−	0.344752i	$-0.112037\pi$
$853$	3.15524	+	6.19251i	0.108033	+	0.212028i	−0.830660	+	0.556779i	$0.812037\pi$
$854$		0			0
$855$	19.5660	+	20.8060i	0.669142	+	0.711552i
$856$		0			0
$857$	−27.0210	−	27.0210i	−0.923020	−	0.923020i	0.0742219	−	0.997242i	$-0.476353\pi$
$857$	−27.0210	−	27.0210i	−0.923020	−	0.923020i	−0.997242	+	0.0742219i	$0.976353\pi$
$858$		0			0
$859$	−18.5730	−	13.4941i	−0.633703	−	0.460413i	0.223978	−	0.974594i	$-0.428096\pi$
$859$	−18.5730	−	13.4941i	−0.633703	−	0.460413i	−0.857681	+	0.514182i	$0.828096\pi$
$860$		0			0
$861$	−3.90725	+	2.83878i	−0.133159	+	0.0967455i
$862$		0			0
$863$	2.01921	+	12.7488i	0.0687345	+	0.433973i	0.997926	+	0.0643737i	$0.0205050\pi$
$863$	2.01921	+	12.7488i	0.0687345	+	0.433973i	−0.929191	+	0.369599i	$0.879495\pi$
$864$		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	−0.277208	−	0.960810i	$-0.589409\pi$
$877$	−24.8095	−	3.92943i	−0.837756	−	0.132688i	−0.560547	+	0.828122i	$0.689409\pi$
$878$		0			0
$879$	2.08661	−	6.42192i	0.0703795	−	0.216606i
$880$		0			0
$881$	−0.733423	−	2.25725i	−0.0247097	−	0.0760485i	0.937941	−	0.346794i	$-0.112730\pi$
$881$	−0.733423	−	2.25725i	−0.0247097	−	0.0760485i	−0.962651	+	0.270746i	$0.912730\pi$
$882$		0			0
$883$	14.8124	−	29.0710i	0.498478	−	0.978318i	−0.495486	−	0.868616i	$-0.665010\pi$
$883$	14.8124	−	29.0710i	0.498478	−	0.978318i	0.993964	−	0.109703i	$-0.0349899\pi$
$884$		0			0
$885$	−3.90128	−	3.02171i	−0.131140	−	0.101574i
$886$		0			0
$887$	−43.0953	+	6.82562i	−1.44700	+	0.229182i	−0.829991	−	0.557776i	$-0.811655\pi$
$887$	−43.0953	+	6.82562i	−1.44700	+	0.229182i	−0.617006	+	0.786958i	$0.711655\pi$
$888$		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	−0.162178	−	0.986761i	$-0.551852\pi$
$907$	24.8335	−	24.8335i	0.824583	−	0.824583i	0.986761	+	0.162178i	$0.0518520\pi$
$908$		0			0
$909$	7.06487	−	9.72396i	0.234327	−	0.322523i
$910$		0			0
$911$	12.3458	+	16.9926i	0.409035	+	0.562989i	0.962983	−	0.269563i	$-0.0868791\pi$
$911$	12.3458	+	16.9926i	0.409035	+	0.562989i	−0.553947	+	0.832552i	$0.686879\pi$
$912$		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	−0.998568	−	0.0534956i	$-0.982964\pi$
$919$	−6.73458	−	20.7269i	−0.222153	−	0.683718i	0.776415	−	0.630222i	$-0.217036\pi$
$920$		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	0.780663	−	0.624952i	$-0.214882\pi$
$929$	31.8479	+	10.3480i	1.04489	+	0.339507i	0.264232	+	0.964459i	$0.414882\pi$
$930$		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	−0.926578	−	0.376102i	$-0.877264\pi$
$937$	−4.94578	−	31.2265i	−0.161572	−	1.02012i	0.765007	−	0.644022i	$-0.222736\pi$
$938$		0			0
$939$	3.40418	−	2.47329i	0.111091	−	0.0807126i
$940$		0			0
$941$	−23.2656	−	16.9034i	−0.758437	−	0.551037i	0.139994	−	0.990152i	$-0.455292\pi$
$941$	−23.2656	−	16.9034i	−0.758437	−	0.551037i	−0.898431	+	0.439116i	$0.855292\pi$
$942$		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	0.995114	−	0.0987277i	$-0.0314773\pi$
$947$	10.1653	+	19.9506i	0.330328	+	0.648306i	−0.664786	+	0.747034i	$0.731477\pi$
$948$		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	0.803287	−	0.595593i	$-0.203083\pi$
$953$	−4.65277	−	9.13158i	−0.150718	−	0.295801i	−0.954005	+	0.299792i	$0.903083\pi$
$954$		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	0.279918	−	0.960024i	$-0.409693\pi$
$967$	−10.3311	−	5.26397i	−0.332226	−	0.169278i	−0.612144	+	0.790746i	$0.709693\pi$
$968$		0			0
$969$	−3.33687	+	1.08422i	−0.107196	+	0.0348300i
$970$		0			0
$971$	−42.5120	−	13.8130i	−1.36427	−	0.443279i	−0.466806	−	0.884360i	$-0.654595\pi$
$971$	−42.5120	−	13.8130i	−1.36427	−	0.443279i	−0.897468	+	0.441080i	$0.854595\pi$
$972$		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	0.957479	−	0.288504i	$-0.0931579\pi$
$977$	55.6044	+	8.80687i	1.77894	+	0.281757i	0.821464	+	0.570261i	$0.193158\pi$
$978$		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	0.207843	+	0.978162i	$0.433356\pi$
$983$	−22.1249	+	43.4225i	−0.705674	+	1.38496i	−0.913517	+	0.406801i	$0.866644\pi$
$984$		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	−0.470363	+	0.882473i	$0.655877\pi$
$991$	−36.6522	+	50.4474i	−1.16429	+	1.60251i	−0.693931	+	0.720041i	$0.744123\pi$
$992$		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	−0.846621	−	0.532197i	$-0.821367\pi$
$997$	−28.8502	+	14.6999i	−0.913696	+	0.465551i	−0.0670752	+	0.997748i	$0.521367\pi$
$998$		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.127.6	yes	80
4.3	odd	2	inner	400.2.bi.d.127.5	yes	80
25.13	odd	20	inner	400.2.bi.d.63.5	✓	80
100.63	even	20	inner	400.2.bi.d.63.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.63.5	✓	80	25.13	odd	20	inner
400.2.bi.d.63.6	yes	80	100.63	even	20	inner
400.2.bi.d.127.5	yes	80	4.3	odd	2	inner
400.2.bi.d.127.6	yes	80	1.1	even	1	trivial

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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