LMFDB - Embedded newform 728.2.i.a.701.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(701,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.701"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.i (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.15
Character	$\chi$	$=$	728.701
Dual form			728.2.i.a.701.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13101 - 0.849005i) q^{2} -0.208275i q^{3} +(0.558380 + 1.92047i) q^{4} +3.52272 q^{5} +(-0.176827 + 0.235562i) q^{6} -1.00000i q^{7} +(0.998957 - 2.64615i) q^{8} +2.95662 q^{9} +(-3.98424 - 2.99081i) q^{10} +1.92616 q^{11} +(0.399987 - 0.116297i) q^{12} +(3.39827 + 1.20488i) q^{13} +(-0.849005 + 1.13101i) q^{14} -0.733695i q^{15} +(-3.37642 + 2.14470i) q^{16} -3.54436 q^{17} +(-3.34398 - 2.51019i) q^{18} +0.129878 q^{19} +(1.96701 + 6.76528i) q^{20} -0.208275 q^{21} +(-2.17851 - 1.63532i) q^{22} -5.09962 q^{23} +(-0.551127 - 0.208058i) q^{24} +7.40954 q^{25} +(-2.82054 - 4.24789i) q^{26} -1.24062i q^{27} +(1.92047 - 0.558380i) q^{28} +6.31068i q^{29} +(-0.622911 + 0.829818i) q^{30} -1.15279i q^{31} +(5.63964 + 0.440915i) q^{32} -0.401171i q^{33} +(4.00871 + 3.00918i) q^{34} -3.52272i q^{35} +(1.65092 + 5.67811i) q^{36} -0.300461 q^{37} +(-0.146894 - 0.110267i) q^{38} +(0.250947 - 0.707776i) q^{39} +(3.51904 - 9.32162i) q^{40} +2.93462i q^{41} +(0.235562 + 0.176827i) q^{42} +5.57927i q^{43} +(1.07553 + 3.69913i) q^{44} +10.4153 q^{45} +(5.76773 + 4.32960i) q^{46} -2.30877i q^{47} +(0.446689 + 0.703226i) q^{48} -1.00000 q^{49} +(-8.38028 - 6.29074i) q^{50} +0.738202i q^{51} +(-0.416414 + 7.19907i) q^{52} -11.5827i q^{53} +(-1.05329 + 1.40315i) q^{54} +6.78531 q^{55} +(-2.64615 - 0.998957i) q^{56} -0.0270504i q^{57} +(5.35780 - 7.13746i) q^{58} -7.08922 q^{59} +(1.40904 - 0.409680i) q^{60} +6.22897i q^{61} +(-0.978728 + 1.30382i) q^{62} -2.95662i q^{63} +(-6.00417 - 5.28677i) q^{64} +(11.9712 + 4.24446i) q^{65} +(-0.340596 + 0.453729i) q^{66} -8.04110 q^{67} +(-1.97910 - 6.80684i) q^{68} +1.06212i q^{69} +(-2.99081 + 3.98424i) q^{70} -16.5533i q^{71} +(2.95354 - 7.82365i) q^{72} -11.4665i q^{73} +(0.339825 + 0.255093i) q^{74} -1.54322i q^{75} +(0.0725211 + 0.249427i) q^{76} -1.92616i q^{77} +(-0.884730 + 0.587449i) q^{78} +14.6896 q^{79} +(-11.8942 + 7.55519i) q^{80} +8.61147 q^{81} +(2.49151 - 3.31910i) q^{82} +3.76948 q^{83} +(-0.116297 - 0.399987i) q^{84} -12.4858 q^{85} +(4.73683 - 6.31022i) q^{86} +1.31436 q^{87} +(1.92415 - 5.09689i) q^{88} -0.982458i q^{89} +(-11.7799 - 8.84268i) q^{90} +(1.20488 - 3.39827i) q^{91} +(-2.84752 - 9.79368i) q^{92} -0.240098 q^{93} +(-1.96016 + 2.61125i) q^{94} +0.457523 q^{95} +(0.0918317 - 1.17460i) q^{96} +9.30657i q^{97} +(1.13101 + 0.849005i) q^{98} +5.69492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) $ 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.13101	−	0.849005i	−0.799747	−	0.600337i
$2$	−1.13101	−	0.849005i	−0.799747	−	0.600337i
$3$		−	0.208275i		−	0.120248i	−0.998191	−	0.0601239i	$-0.980850\pi$
$3$		−	0.208275i		−	0.120248i	0.998191	−	0.0601239i	$-0.0191496\pi$
$4$	0.558380	+	1.92047i	0.279190	+	0.960236i
$5$	3.52272			1.57541			0.787704	−	0.616055i	$-0.211270\pi$
$5$	3.52272			1.57541			0.787704	+	0.616055i	$0.211270\pi$
$6$	−0.176827	+	0.235562i	−0.0721893	+	0.0961678i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.998957	−	2.64615i	0.353185	−	0.935554i
$9$	2.95662			0.985540
$10$	−3.98424	−	2.99081i	−1.25993	−	0.945776i
$11$	1.92616			0.580758			0.290379	−	0.956912i	$-0.406219\pi$
$11$	1.92616			0.580758			0.290379	+	0.956912i	$0.406219\pi$
$12$	0.399987	−	0.116297i	0.115466	−	0.0335720i
$13$	3.39827	+	1.20488i	0.942511	+	0.334174i
$13$	3.39827	+	1.20488i	0.942511	+	0.334174i
$14$	−0.849005	+	1.13101i	−0.226906	+	0.302276i
$15$		−	0.733695i		−	0.189439i
$16$	−3.37642	+	2.14470i	−0.844106	+	0.536176i
$17$	−3.54436			−0.859633			−0.429816	−	0.902916i	$-0.641422\pi$
$17$	−3.54436			−0.859633			−0.429816	+	0.902916i	$0.641422\pi$
$18$	−3.34398	−	2.51019i	−0.788183	−	0.591657i
$19$	0.129878			0.0297960			0.0148980	−	0.999889i	$-0.495258\pi$
$19$	0.129878			0.0297960			0.0148980	+	0.999889i	$0.495258\pi$
$20$	1.96701	+	6.76528i	0.439838	+	1.51276i
$21$	−0.208275			−0.0454494
$22$	−2.17851	−	1.63532i	−0.464459	−	0.348651i
$23$	−5.09962			−1.06334			−0.531672	−	0.846950i	$-0.678436\pi$
$23$	−5.09962			−1.06334			−0.531672	+	0.846950i	$0.678436\pi$
$24$	−0.551127	−	0.208058i	−0.112498	−	0.0424697i
$25$	7.40954			1.48191
$26$	−2.82054	−	4.24789i	−0.553153	−	0.833079i
$27$		−	1.24062i		−	0.238757i
$28$	1.92047	−	0.558380i	0.362935	−	0.105524i
$29$			6.31068i			1.17186i	0.810360	+	0.585932i	$0.199271\pi$
$29$			6.31068i			1.17186i	−0.810360	+	0.585932i	$0.800729\pi$
$30$	−0.622911	+	0.829818i	−0.113727	+	0.151503i
$31$		−	1.15279i		−	0.207048i	−0.994627	−	0.103524i	$-0.966988\pi$
$31$		−	1.15279i		−	0.207048i	0.994627	−	0.103524i	$-0.0330118\pi$
$32$	5.63964	+	0.440915i	0.996958	+	0.0779435i
$33$		−	0.401171i		−	0.0698349i
$34$	4.00871	+	3.00918i	0.687489	+	0.516070i
$35$		−	3.52272i		−	0.595448i
$36$	1.65092	+	5.67811i	0.275153	+	0.946351i
$37$	−0.300461			−0.0493954			−0.0246977	−	0.999695i	$-0.507862\pi$
$37$	−0.300461			−0.0493954			−0.0246977	+	0.999695i	$0.507862\pi$
$38$	−0.146894	−	0.110267i	−0.0238293	−	0.0178877i
$39$	0.250947	−	0.707776i	0.0401837	−	0.113335i
$40$	3.51904	−	9.32162i	0.556409	−	1.47388i
$41$			2.93462i			0.458311i	0.973390	+	0.229156i	$0.0735964\pi$
$41$			2.93462i			0.458311i	−0.973390	+	0.229156i	$0.926404\pi$
$42$	0.235562	+	0.176827i	0.0363480	+	0.0272850i
$43$			5.57927i			0.850830i	0.904998	+	0.425415i	$0.139872\pi$
$43$			5.57927i			0.850830i	−0.904998	+	0.425415i	$0.860128\pi$
$44$	1.07553	+	3.69913i	0.162142	+	0.557665i
$45$	10.4153			1.55263
$46$	5.76773	+	4.32960i	0.850406	+	0.638365i
$47$		−	2.30877i		−	0.336769i	−0.985721	−	0.168384i	$-0.946145\pi$
$47$		−	2.30877i		−	0.336769i	0.985721	−	0.168384i	$-0.0538549\pi$
$48$	0.446689	+	0.703226i	0.0644740	+	0.101502i
$49$	−1.00000			−0.142857
$50$	−8.38028	−	6.29074i	−1.18515	−	0.889645i
$51$			0.738202i			0.103369i
$52$	−0.416414	+	7.19907i	−0.0577462	+	0.998331i
$53$		−	11.5827i		−	1.59101i	−0.605946	−	0.795506i	$-0.707205\pi$
$53$		−	11.5827i		−	1.59101i	0.605946	−	0.795506i	$-0.292795\pi$
$54$	−1.05329	+	1.40315i	−0.143335	+	0.190945i
$55$	6.78531			0.914930
$56$	−2.64615	−	0.998957i	−0.353606	−	0.133491i
$57$		−	0.0270504i		−	0.00358291i
$58$	5.35780	−	7.13746i	0.703514	−	0.937195i
$59$	−7.08922			−0.922938			−0.461469	−	0.887156i	$-0.652677\pi$
$59$	−7.08922			−0.922938			−0.461469	+	0.887156i	$0.652677\pi$
$60$	1.40904	−	0.409680i	0.181906	−	0.0528895i
$61$			6.22897i			0.797538i	0.917051	+	0.398769i	$0.130562\pi$
$61$			6.22897i			0.797538i	−0.917051	+	0.398769i	$0.869438\pi$
$62$	−0.978728	+	1.30382i	−0.124299	+	0.165586i
$63$		−	2.95662i		−	0.372499i
$64$	−6.00417	−	5.28677i	−0.750521	−	0.660846i
$65$	11.9712	+	4.24446i	1.48484	+	0.526460i
$66$	−0.340596	+	0.453729i	−0.0419245	+	0.0558502i
$67$	−8.04110			−0.982376			−0.491188	−	0.871053i	$-0.663437\pi$
$67$	−8.04110			−0.982376			−0.491188	+	0.871053i	$0.663437\pi$
$68$	−1.97910	−	6.80684i	−0.240001	−	0.825450i
$69$			1.06212i			0.127865i
$70$	−2.99081	+	3.98424i	−0.357470	+	0.476208i
$71$		−	16.5533i		−	1.96452i	−0.187535	−	0.982258i	$-0.560050\pi$
$71$		−	16.5533i		−	1.96452i	0.187535	−	0.982258i	$-0.439950\pi$
$72$	2.95354	−	7.82365i	0.348078	−	0.922026i
$73$		−	11.4665i		−	1.34205i	−0.741436	−	0.671024i	$-0.765855\pi$
$73$		−	11.4665i		−	1.34205i	0.741436	−	0.671024i	$-0.234145\pi$
$74$	0.339825	+	0.255093i	0.0395038	+	0.0296539i
$75$		−	1.54322i		−	0.178196i
$76$	0.0725211	+	0.249427i	0.00831875	+	0.0286112i
$77$		−	1.92616i		−	0.219506i
$78$	−0.884730	+	0.587449i	−0.100176	+	0.0665155i
$79$	14.6896			1.65271			0.826357	−	0.563147i	$-0.190409\pi$
$79$	14.6896			1.65271			0.826357	+	0.563147i	$0.190409\pi$
$80$	−11.8942	+	7.55519i	−1.32981	+	0.844696i
$81$	8.61147			0.956830
$82$	2.49151	−	3.31910i	0.275141	−	0.366533i
$83$	3.76948			0.413754			0.206877	−	0.978367i	$-0.433670\pi$
$83$	3.76948			0.413754			0.206877	+	0.978367i	$0.433670\pi$
$84$	−0.116297	−	0.399987i	−0.0126890	−	0.0436421i
$85$	−12.4858			−1.35427
$86$	4.73683	−	6.31022i	0.510785	−	0.680449i
$87$	1.31436			0.140914
$88$	1.92415	−	5.09689i	0.205115	−	0.543330i
$89$		−	0.982458i		−	0.104140i	−0.998643	−	0.0520702i	$-0.983418\pi$
$89$		−	0.982458i		−	0.104140i	0.998643	−	0.0520702i	$-0.0165820\pi$
$90$	−11.7799	−	8.84268i	−1.24171	−	0.932100i
$91$	1.20488	−	3.39827i	0.126306	−	0.356236i
$92$	−2.84752	−	9.79368i	−0.296875	−	1.02106i
$93$	−0.240098			−0.0248970
$94$	−1.96016	+	2.61125i	−0.202175	+	0.269330i
$95$	0.457523			0.0469409
$96$	0.0918317	−	1.17460i	0.00937253	−	0.119882i
$97$			9.30657i			0.944939i	0.881347	+	0.472469i	$0.156637\pi$
$97$			9.30657i			0.944939i	−0.881347	+	0.472469i	$0.843363\pi$
$98$	1.13101	+	0.849005i	0.114250	+	0.0857625i
$99$	5.69492			0.572361
$100$	4.13733	+	14.2298i	0.413733	+	1.42298i
$101$		−	9.15160i		−	0.910618i	−0.890333	−	0.455309i	$-0.849529\pi$
$101$		−	9.15160i		−	0.910618i	0.890333	−	0.455309i	$-0.150471\pi$
$102$	0.626738	−	0.834916i	0.0620563	−	0.0826690i
$103$	5.49996			0.541927			0.270964	−	0.962590i	$-0.412658\pi$
$103$	5.49996			0.541927			0.270964	+	0.962590i	$0.412658\pi$
$104$	6.58302	−	7.78870i	0.645518	−	0.763745i
$105$	−0.733695			−0.0716013
$106$	−9.83381	+	13.1002i	−0.955144	+	1.27241i
$107$			6.53885i			0.632134i	0.948737	+	0.316067i	$0.102363\pi$
$107$			6.53885i			0.632134i	−0.948737	+	0.316067i	$0.897637\pi$
$108$	2.38257	−	0.692735i	0.229263	−	0.0666585i
$109$	−12.0875			−1.15778			−0.578888	−	0.815407i	$-0.696513\pi$
$109$	−12.0875			−1.15778			−0.578888	+	0.815407i	$0.696513\pi$
$110$	−7.67427	−	5.76076i	−0.731713	−	0.549267i
$111$			0.0625785i			0.00593969i
$112$	2.14470	+	3.37642i	0.202656	+	0.319042i
$113$	−4.68304			−0.440543			−0.220272	−	0.975439i	$-0.570694\pi$
$113$	−4.68304			−0.440543			−0.220272	+	0.975439i	$0.570694\pi$
$114$	−0.0229659	+	0.0305943i	−0.00215095	+	0.00286542i
$115$	−17.9645			−1.67520
$116$	−12.1195	+	3.52376i	−1.12527	+	0.327172i
$117$	10.0474	+	3.56238i	0.928883	+	0.329342i
$118$	8.01800	+	6.01879i	0.738117	+	0.554074i
$119$			3.54436i			0.324911i
$120$	−1.94146	−	0.732929i	−0.177231	−	0.0669070i
$121$	−7.28992			−0.662720
$122$	5.28843	−	7.04504i	0.478792	−	0.637828i
$123$	0.611209			0.0551109
$124$	2.21391	−	0.643696i	0.198815	−	0.0578056i
$125$	8.48812			0.759200
$126$	−2.51019	+	3.34398i	−0.223625	+	0.297905i
$127$	−14.7640			−1.31009			−0.655045	−	0.755590i	$-0.727350\pi$
$127$	−14.7640			−1.31009			−0.655045	+	0.755590i	$0.727350\pi$
$128$	2.30230	+	11.0770i	0.203496	+	0.979076i
$129$	1.16202			0.102310
$130$	−9.93596	−	14.9641i	−0.871442	−	1.31244i
$131$			15.8504i			1.38486i	0.721487	+	0.692428i	$0.243459\pi$
$131$			15.8504i			1.38486i	−0.721487	+	0.692428i	$0.756541\pi$
$132$	0.770437	−	0.224006i	0.0670580	−	0.0194972i
$133$		−	0.129878i		−	0.0112618i
$134$	9.09458	+	6.82694i	0.785652	+	0.589757i
$135$		−	4.37034i		−	0.376139i
$136$	−3.54066	+	9.37888i	−0.303609	+	0.804233i
$137$			8.39453i			0.717193i	0.933493	+	0.358596i	$0.116745\pi$
$137$			8.39453i			0.717193i	−0.933493	+	0.358596i	$0.883255\pi$
$138$	0.901750	−	1.20128i	0.0767620	−	0.102259i
$139$			13.5249i			1.14716i	0.819149	+	0.573581i	$0.194446\pi$
$139$			13.5249i			1.14716i	−0.819149	+	0.573581i	$0.805554\pi$
$140$	6.76528	−	1.96701i	0.571770	−	0.166243i
$141$	−0.480859			−0.0404957
$142$	−14.0538	+	18.7220i	−1.17937	+	1.57112i
$143$	6.54561	+	2.32079i	0.547371	+	0.194074i
$144$	−9.98281	+	6.34108i	−0.831901	+	0.528423i
$145$			22.2307i			1.84616i
$146$	−9.73509	+	12.9687i	−0.805681	+	1.07330i
$147$			0.208275i			0.0171783i
$148$	−0.167771	−	0.577026i	−0.0137907	−	0.0474312i
$149$	19.3528			1.58545			0.792723	−	0.609582i	$-0.208663\pi$
$149$	19.3528			1.58545			0.792723	+	0.609582i	$0.208663\pi$
$150$	−1.31021	+	1.74541i	−0.106978	+	0.142512i
$151$			5.55900i			0.452385i	0.974083	+	0.226193i	$0.0726279\pi$
$151$			5.55900i			0.452385i	−0.974083	+	0.226193i	$0.927372\pi$
$152$	0.129742	−	0.343676i	0.0105235	−	0.0278758i
$153$	−10.4793			−0.847203
$154$	−1.63532	+	2.17851i	−0.131778	+	0.175549i
$155$		−	4.06096i		−	0.326184i
$156$	1.49939	+	0.0867287i	0.120047	+	0.00694385i
$157$		−	16.1401i		−	1.28812i	−0.764974	−	0.644061i	$-0.777248\pi$
$157$		−	16.1401i		−	1.28812i	0.764974	−	0.644061i	$-0.222752\pi$
$158$	−16.6142	−	12.4716i	−1.32175	−	0.992186i
$159$	−2.41240			−0.191316
$160$	19.8669	+	1.55322i	1.57061	+	0.122793i
$161$			5.09962i			0.401906i
$162$	−9.73969	−	7.31119i	−0.765222	−	0.574421i
$163$	−3.76604			−0.294979			−0.147490	−	0.989064i	$-0.547119\pi$
$163$	−3.76604			−0.294979			−0.147490	+	0.989064i	$0.547119\pi$
$164$	−5.63586	+	1.63863i	−0.440087	+	0.127956i
$165$		−	1.41321i		−	0.110018i
$166$	−4.26333	−	3.20031i	−0.330899	−	0.248392i
$167$		−	23.2916i		−	1.80236i	−0.433449	−	0.901178i	$-0.642704\pi$
$167$		−	23.2916i		−	1.80236i	0.433449	−	0.901178i	$-0.357296\pi$
$168$	−0.208058	+	0.551127i	−0.0160520	+	0.0425203i
$169$	10.0965	+	8.18903i	0.776656	+	0.629925i
$170$	14.1216	+	10.6005i	1.08307	+	0.813020i
$171$	0.384000			0.0293652
$172$	−10.7148	+	3.11535i	−0.816998	+	0.237543i
$173$		−	19.8402i		−	1.50842i	−0.656633	−	0.754210i	$-0.728020\pi$
$173$		−	19.8402i		−	1.50842i	0.656633	−	0.754210i	$-0.271980\pi$
$174$	−1.48656	−	1.11590i	−0.112696	−	0.0845960i
$175$		−	7.40954i		−	0.560108i
$176$	−6.50352	+	4.13104i	−0.490222	+	0.311389i
$177$			1.47651i			0.110981i
$178$	−0.834112	+	1.11117i	−0.0625194	+	0.0832859i
$179$			0.396420i			0.0296298i	0.999890	+	0.0148149i	$0.00471591\pi$
$179$			0.396420i			0.0296298i	−0.999890	+	0.0148149i	$0.995284\pi$
$180$	5.81571	+	20.0024i	0.433478	+	1.49089i
$181$			21.0449i			1.56425i	0.623121	+	0.782126i	$0.285865\pi$
$181$			21.0449i			1.56425i	−0.623121	+	0.782126i	$0.714135\pi$
$182$	−4.24789	+	2.82054i	−0.314874	+	0.209072i
$183$	1.29734			0.0959022
$184$	−5.09430	+	13.4943i	−0.375557	+	0.994816i
$185$	−1.05844			−0.0778179
$186$	0.271554	+	0.203845i	0.0199113	+	0.0149466i
$187$	−6.82699			−0.499239
$188$	4.43393	−	1.28917i	0.323377	−	0.0940223i
$189$	−1.24062			−0.0902416
$190$	−0.517464	−	0.388440i	−0.0375408	−	0.0281804i
$191$	5.37919			0.389225			0.194612	−	0.980880i	$-0.437655\pi$
$191$	5.37919			0.389225			0.194612	+	0.980880i	$0.437655\pi$
$192$	−1.10110	+	1.25052i	−0.0794653	+	0.0902485i
$193$			23.0841i			1.66163i	0.556548	+	0.830816i	$0.312126\pi$
$193$			23.0841i			1.66163i	−0.556548	+	0.830816i	$0.687874\pi$
$194$	7.90133	−	10.5258i	0.567282	−	0.755712i
$195$	0.884015	−	2.49330i	0.0633056	−	0.178549i
$196$	−0.558380	−	1.92047i	−0.0398843	−	0.137177i
$197$	8.31831			0.592655			0.296328	−	0.955086i	$-0.404238\pi$
$197$	8.31831			0.592655			0.296328	+	0.955086i	$0.404238\pi$
$198$	−6.44102	−	4.83502i	−0.457744	−	0.343610i
$199$	−18.8463			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$199$	−18.8463			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$200$	7.40181	−	19.6067i	0.523387	−	1.38640i
$201$			1.67476i			0.118129i
$202$	−7.76976	+	10.3506i	−0.546678	+	0.728264i
$203$	6.31068			0.442923
$204$	−1.41770	+	0.412197i	−0.0992586	+	0.0288596i
$205$			10.3378i			0.722026i
$206$	−6.22053	−	4.66950i	−0.433405	−	0.325339i
$207$	−15.0776			−1.04797
$208$	−14.0581	+	3.22010i	−0.974756	+	0.223274i
$209$	0.250165			0.0173043
$210$	0.829818	+	0.622911i	0.0572629	+	0.0429849i
$211$			19.4654i			1.34005i	0.742337	+	0.670027i	$0.233717\pi$
$211$			19.4654i			1.34005i	−0.742337	+	0.670027i	$0.766283\pi$
$212$	22.2443	−	6.46757i	1.52775	−	0.444194i
$213$	−3.44764			−0.236229
$214$	5.55152	−	7.39552i	0.379494	−	0.505548i
$215$			19.6542i			1.34040i
$216$	−3.28285	−	1.23932i	−0.223370	−	0.0843252i
$217$	−1.15279			−0.0782567
$218$	13.6712	+	10.2624i	0.925928	+	0.695057i
$219$	−2.38818			−0.161378
$220$	3.78878	+	13.0310i	0.255439	+	0.878549i
$221$	−12.0447	−	4.27053i	−0.810214	−	0.287267i
$222$	0.0531295	−	0.0707771i	0.00356582	−	0.00475025i
$223$		−	17.6477i		−	1.18178i	−0.806753	−	0.590889i	$-0.798777\pi$
$223$		−	17.6477i		−	1.18178i	0.806753	−	0.590889i	$-0.201223\pi$
$224$	0.440915	−	5.63964i	0.0294599	−	0.376815i
$225$	21.9072			1.46048
$226$	5.29658	+	3.97593i	0.352323	+	0.264475i
$227$	−18.0842			−1.20029			−0.600144	−	0.799892i	$-0.704890\pi$
$227$	−18.0842			−1.20029			−0.600144	+	0.799892i	$0.704890\pi$
$228$	0.0519494	−	0.0151044i	0.00344044	−	0.00100031i
$229$	−4.25750			−0.281343			−0.140672	−	0.990056i	$-0.544926\pi$
$229$	−4.25750			−0.281343			−0.140672	+	0.990056i	$0.544926\pi$
$230$	20.3181	+	15.2520i	1.33974	+	1.00569i
$231$	−0.401171			−0.0263951
$232$	16.6990	+	6.30410i	1.09634	+	0.413884i
$233$	−12.0468			−0.789210			−0.394605	−	0.918851i	$-0.629119\pi$
$233$	−12.0468			−0.789210			−0.394605	+	0.918851i	$0.629119\pi$
$234$	−8.33927	−	12.5594i	−0.545155	−	0.821033i
$235$		−	8.13314i		−	0.530547i
$236$	−3.95848	−	13.6147i	−0.257675	−	0.886238i
$237$		−	3.05949i		−	0.198735i
$238$	3.00918	−	4.00871i	0.195056	−	0.259846i
$239$		−	1.26186i		−	0.0816230i	−0.999167	−	0.0408115i	$-0.987006\pi$
$239$		−	1.26186i		−	0.0816230i	0.999167	−	0.0408115i	$-0.0129943\pi$
$240$	1.57356	+	2.47727i	0.101573	+	0.159907i
$241$		−	16.9944i		−	1.09471i	−0.836902	−	0.547353i	$-0.815636\pi$
$241$		−	16.9944i		−	1.09471i	0.836902	−	0.547353i	$-0.184364\pi$
$242$	8.24499	+	6.18918i	0.530008	+	0.397856i
$243$		−	5.51541i		−	0.353814i
$244$	−11.9626	+	3.47813i	−0.765825	+	0.222664i
$245$	−3.52272			−0.225058
$246$	−0.691286	−	0.518920i	−0.0440748	−	0.0330851i
$247$	0.441360	+	0.156487i	0.0280831	+	0.00995705i
$248$	−3.05046	−	1.15159i	−0.193704	−	0.0731261i
$249$		−	0.785089i		−	0.0497530i
$250$	−9.60017	−	7.20646i	−0.607168	−	0.455776i
$251$		−	16.4332i		−	1.03725i	−0.855001	−	0.518626i	$-0.826444\pi$
$251$		−	16.4332i		−	1.03725i	0.855001	−	0.518626i	$-0.173556\pi$
$252$	5.67811	−	1.65092i	0.357687	−	0.103998i
$253$	−9.82267			−0.617546
$254$	16.6982	+	12.5347i	1.04774	+	0.786496i
$255$			2.60048i			0.162848i
$256$	6.80049	−	14.4829i	0.425030	−	0.905179i
$257$	−18.6782			−1.16511			−0.582557	−	0.812790i	$-0.697948\pi$
$257$	−18.6782			−1.16511			−0.582557	+	0.812790i	$0.697948\pi$
$258$	−1.31426	−	0.986564i	−0.0818225	−	0.0614208i
$259$			0.300461i			0.0186697i
$260$	−1.46691	+	25.3603i	−0.0909738	+	1.57278i
$261$			18.6583i			1.15492i
$262$	13.4571	−	17.9270i	0.831380	−	1.10753i
$263$	−0.495204			−0.0305356			−0.0152678	−	0.999883i	$-0.504860\pi$
$263$	−0.495204			−0.0305356			−0.0152678	+	0.999883i	$0.504860\pi$
$264$	−1.06156	−	0.400752i	−0.0653343	−	0.0246646i
$265$		−	40.8027i		−	2.50649i
$266$	−0.110267	+	0.146894i	−0.00676090	+	0.00900662i
$267$	−0.204622			−0.0125226
$268$	−4.48998	−	15.4427i	−0.274269	−	0.943313i
$269$		−	10.0263i		−	0.611314i	−0.952142	−	0.305657i	$-0.901124\pi$
$269$		−	10.0263i		−	0.611314i	0.952142	−	0.305657i	$-0.0988760\pi$
$270$	−3.71045	+	4.94291i	−0.225810	+	0.300816i
$271$			19.8983i			1.20874i	0.796705	+	0.604369i	$0.206575\pi$
$271$			19.8983i			1.20874i	−0.796705	+	0.604369i	$0.793425\pi$
$272$	11.9673	−	7.60160i	0.725621	−	0.460915i
$273$	−0.707776	−	0.250947i	−0.0428366	−	0.0151880i
$274$	7.12700	−	9.49432i	0.430558	−	0.573573i
$275$	14.2719			0.860630
$276$	−2.03978	+	0.593069i	−0.122780	+	0.0356985i
$277$			29.0585i			1.74596i	0.487759	+	0.872978i	$0.337814\pi$
$277$			29.0585i			1.74596i	−0.487759	+	0.872978i	$0.662186\pi$
$278$	11.4827	−	15.2968i	0.688685	−	0.917440i
$279$		−	3.40837i		−	0.204054i
$280$	−9.32162	−	3.51904i	−0.557073	−	0.210303i
$281$		−	14.5021i		−	0.865120i	−0.901605	−	0.432560i	$-0.857610\pi$
$281$		−	14.5021i		−	0.865120i	0.901605	−	0.432560i	$-0.142390\pi$
$282$	0.543858	+	0.408252i	0.0323863	+	0.0243111i
$283$		−	5.54760i		−	0.329771i	−0.986313	−	0.164885i	$-0.947275\pi$
$283$		−	5.54760i		−	0.329771i	0.986313	−	0.164885i	$-0.0527254\pi$
$284$	31.7902	−	9.24303i	1.88640	−	0.548473i
$285$		−	0.0952907i		−	0.00564454i
$286$	−5.43280	−	8.18210i	−0.321248	−	0.483818i
$287$	2.93462			0.173225
$288$	16.6743	+	1.30362i	0.982542	+	0.0768164i
$289$	−4.43753			−0.261031
$290$	18.8740	−	25.1433i	1.10832	−	1.47646i
$291$	1.93833			0.113627
$292$	22.0210	−	6.40264i	1.28868	−	0.374686i
$293$	−24.7162			−1.44393			−0.721967	−	0.691928i	$-0.756762\pi$
$293$	−24.7162			−1.44393			−0.721967	+	0.691928i	$0.756762\pi$
$294$	0.176827	−	0.235562i	0.0103128	−	0.0137383i
$295$	−24.9733			−1.45400
$296$	−0.300147	+	0.795062i	−0.0174457	+	0.0462121i
$297$		−	2.38962i		−	0.138660i
$298$	−21.8883	−	16.4307i	−1.26796	−	0.951803i
$299$	−17.3299	−	6.14444i	−1.00221	−	0.355342i
$300$	2.96372	−	0.861704i	0.171110	−	0.0497505i
$301$	5.57927			0.321584
$302$	4.71963	−	6.28731i	0.271584	−	0.361794i
$303$	−1.90605			−0.109500
$304$	−0.438523	+	0.278550i	−0.0251510	+	0.0159759i
$305$			21.9429i			1.25645i
$306$	11.8522	+	8.89700i	0.677548	+	0.508608i
$307$	14.9768			0.854770			0.427385	−	0.904070i	$-0.359435\pi$
$307$	14.9768			0.854770			0.427385	+	0.904070i	$0.359435\pi$
$308$	3.69913	−	1.07553i	0.210777	−	0.0612838i
$309$		−	1.14551i		−	0.0651656i
$310$	−3.44778	+	4.59300i	−0.195821	+	0.260865i
$311$	−22.2304			−1.26057			−0.630284	−	0.776365i	$-0.717061\pi$
$311$	−22.2304			−1.26057			−0.630284	+	0.776365i	$0.717061\pi$
$312$	−1.62219	−	1.37108i	−0.0918387	−	0.0776221i
$313$	8.34646			0.471770			0.235885	−	0.971781i	$-0.424201\pi$
$313$	8.34646			0.471770			0.235885	+	0.971781i	$0.424201\pi$
$314$	−13.7030	+	18.2547i	−0.773308	+	1.03017i
$315$		−	10.4153i		−	0.586838i
$316$	8.20239	+	28.2110i	0.461421	+	1.58700i
$317$	19.6311			1.10260			0.551298	−	0.834309i	$-0.314133\pi$
$317$	19.6311			1.10260			0.551298	+	0.834309i	$0.314133\pi$
$318$	2.72845	+	2.04814i	0.153004	+	0.114854i
$319$			12.1554i			0.680570i
$320$	−21.1510	−	18.6238i	−1.18238	−	1.04110i
$321$	1.36188			0.0760128
$322$	4.32960	−	5.76773i	0.241279	−	0.321423i
$323$	−0.460334			−0.0256136
$324$	4.80847	+	16.5381i	0.267137	+	0.918783i
$325$	25.1796	+	8.92761i	1.39671	+	0.495215i
$326$	4.25944	+	3.19739i	0.235909	+	0.177087i
$327$			2.51754i			0.139220i
$328$	7.76544	+	2.93156i	0.428775	+	0.161868i
$329$	−2.30877			−0.127287
$330$	−1.19982	+	1.59836i	−0.0660482	+	0.0879868i
$331$	−33.6438			−1.84923			−0.924616	−	0.380900i	$-0.875614\pi$
$331$	−33.6438			−1.84923			−0.924616	+	0.380900i	$0.875614\pi$
$332$	2.10480	+	7.23918i	0.115516	+	0.397302i
$333$	−0.888348			−0.0486812
$334$	−19.7747	+	26.3431i	−1.08202	+	1.44143i
$335$	−28.3265			−1.54764
$336$	0.703226	−	0.446689i	0.0383641	−	0.0243689i
$337$	0.0143341			0.000780827			0.000390413	−	1.00000i	$-0.499876\pi$
$337$	0.0143341			0.000780827			0.000390413		1.00000i	$0.499876\pi$
$338$	−4.46677	−	17.8339i	−0.242960	−	0.970036i
$339$			0.975362i			0.0529744i
$340$	−6.97180	−	23.9786i	−0.378099	−	1.30042i
$341$		−	2.22046i		−	0.120245i
$342$	−0.434309	−	0.326018i	−0.0234847	−	0.0176290i
$343$			1.00000i			0.0539949i
$344$	14.7636	+	5.57345i	0.795998	+	0.300500i
$345$			3.74157i			0.201439i
$346$	−16.8444	+	22.4395i	−0.905561	+	1.20635i
$347$		−	3.13277i		−	0.168176i	−0.996458	−	0.0840880i	$-0.973202\pi$
$347$		−	3.13277i		−	0.168176i	0.996458	−	0.0840880i	$-0.0267977\pi$
$348$	0.733911	+	2.52419i	0.0393418	+	0.135311i
$349$	1.24421			0.0666011			0.0333006	−	0.999445i	$-0.489398\pi$
$349$	1.24421			0.0666011			0.0333006	+	0.999445i	$0.489398\pi$
$350$	−6.29074	+	8.38028i	−0.336254	+	0.447945i
$351$	1.49480	−	4.21596i	0.0797863	−	0.225031i
$352$	10.8628	+	0.849271i	0.578991	+	0.0452663i
$353$			7.40604i			0.394184i	0.980385	+	0.197092i	$0.0631497\pi$
$353$			7.40604i			0.394184i	−0.980385	+	0.197092i	$0.936850\pi$
$354$	1.25356	−	1.66995i	0.0666262	−	0.0887569i
$355$		−	58.3126i		−	3.09491i
$356$	1.88678	−	0.548585i	0.0999993	−	0.0290749i
$357$	0.738202			0.0390698
$358$	0.336563	−	0.448356i	0.0177879	−	0.0236964i
$359$			36.1561i			1.90824i	0.299418	+	0.954122i	$0.403208\pi$
$359$			36.1561i			1.90824i	−0.299418	+	0.954122i	$0.596792\pi$
$360$	10.4045	−	27.5605i	0.548364	−	1.45257i
$361$	−18.9831			−0.999112
$362$	17.8672	−	23.8020i	0.939079	−	1.25101i
$363$			1.51831i			0.0796906i
$364$	7.19907	+	0.416414i	0.377334	+	0.0218260i
$365$		−	40.3931i		−	2.11427i
$366$	−1.46731	−	1.10145i	−0.0766974	−	0.0575737i
$367$	8.10201			0.422922			0.211461	−	0.977386i	$-0.432178\pi$
$367$	8.10201			0.422922			0.211461	+	0.977386i	$0.432178\pi$
$368$	17.2185	−	10.9372i	0.897575	−	0.570140i
$369$			8.67657i			0.451684i
$370$	1.19711	+	0.898619i	0.0622346	+	0.0467170i
$371$	−11.5827			−0.601346
$372$	−0.134066	−	0.461102i	−0.00695100	−	0.0239070i
$373$		−	7.73552i		−	0.400530i	−0.979742	−	0.200265i	$-0.935820\pi$
$373$		−	7.73552i		−	0.400530i	0.979742	−	0.200265i	$-0.0641803\pi$
$374$	7.72141	+	5.79615i	0.399265	+	0.299712i
$375$		−	1.76787i		−	0.0912922i
$376$	−6.10934	−	2.30636i	−0.315065	−	0.118941i
$377$	−7.60362	+	21.4454i	−0.391606	+	1.10450i
$378$	1.40315	+	1.05329i	0.0721704	+	0.0541754i
$379$	32.4599			1.66735			0.833675	−	0.552255i	$-0.186232\pi$
$379$	32.4599			1.66735			0.833675	+	0.552255i	$0.186232\pi$
$380$	0.255471	+	0.878660i	0.0131054	+	0.0450743i
$381$			3.07497i			0.157535i
$382$	−6.08394	−	4.56696i	−0.311281	−	0.233666i
$383$		−	35.7865i		−	1.82860i	−0.405032	−	0.914302i	$-0.632740\pi$
$383$		−	35.7865i		−	1.82860i	0.405032	−	0.914302i	$-0.367260\pi$
$384$	2.30706	−	0.479512i	0.117732	−	0.0244700i
$385$		−	6.78531i		−	0.345811i
$386$	19.5985	−	26.1084i	0.997540	−	1.32888i
$387$			16.4958i			0.838528i
$388$	−17.8730	+	5.19660i	−0.907364	+	0.263817i
$389$		−	6.32180i		−	0.320528i	−0.987074	−	0.160264i	$-0.948765\pi$
$389$		−	6.32180i		−	0.320528i	0.987074	−	0.160264i	$-0.0512345\pi$
$390$	−3.11665	+	2.06942i	−0.157818	+	0.104789i
$391$	18.0749			0.914086
$392$	−0.998957	+	2.64615i	−0.0504549	+	0.133651i
$393$	3.30124			0.166526
$394$	−9.40812	−	7.06229i	−0.473974	−	0.355793i
$395$	51.7474			2.60370
$396$	3.17992	+	10.9369i	0.159797	+	0.549601i
$397$	−10.2742			−0.515649			−0.257824	−	0.966192i	$-0.583006\pi$
$397$	−10.2742			−0.515649			−0.257824	+	0.966192i	$0.583006\pi$
$398$	21.3154	+	16.0006i	1.06844	+	0.802038i
$399$	−0.0270504			−0.00135421
$400$	−25.0177	+	15.8913i	−1.25089	+	0.794563i
$401$			1.79881i			0.0898285i	0.998991	+	0.0449142i	$0.0143015\pi$
$401$			1.79881i			0.0898285i	−0.998991	+	0.0449142i	$0.985699\pi$
$402$	1.42188	−	1.89418i	0.0709170	−	0.0944730i
$403$	1.38898	−	3.91751i	0.0691899	−	0.195145i
$404$	17.5754	−	5.11007i	0.874408	−	0.254235i
$405$	30.3358			1.50740
$406$	−7.13746	−	5.35780i	−0.354226	−	0.265903i
$407$	−0.578734			−0.0286868
$408$	1.95339	+	0.737432i	0.0967072	+	0.0365083i
$409$		−	21.9102i		−	1.08339i	−0.840575	−	0.541696i	$-0.817783\pi$
$409$		−	21.9102i		−	1.08339i	0.840575	−	0.541696i	$-0.182217\pi$
$410$	8.77689	−	11.6922i	0.433460	−	0.577438i
$411$	1.74837			0.0862409
$412$	3.07107	+	10.5625i	0.151301	+	0.520378i
$413$			7.08922i			0.348838i
$414$	17.0530	+	12.8010i	0.838110	+	0.629135i
$415$	13.2788			0.651831
$416$	18.6338	+	8.29345i	0.913597	+	0.406620i
$417$	2.81689			0.137944
$418$	−0.282940	−	0.212392i	−0.0138390	−	0.0103884i
$419$		−	18.8887i		−	0.922773i	−0.887199	−	0.461386i	$-0.847352\pi$
$419$		−	18.8887i		−	0.922773i	0.887199	−	0.461386i	$-0.152648\pi$
$420$	−0.409680	−	1.40904i	−0.0199903	−	0.0687541i
$421$	6.34070			0.309027			0.154513	−	0.987991i	$-0.450619\pi$
$421$	6.34070			0.309027			0.154513	+	0.987991i	$0.450619\pi$
$422$	16.5262	−	22.0156i	0.804484	−	1.07170i
$423$		−	6.82615i		−	0.331899i
$424$	−30.6496	−	11.5707i	−1.48848	−	0.561921i
$425$	−26.2620			−1.27390
$426$	3.89933	+	2.92707i	0.188923	+	0.141817i
$427$	6.22897			0.301441
$428$	−12.5577	+	3.65116i	−0.606998	+	0.176485i
$429$	0.483363	−	1.36329i	0.0233370	−	0.0658202i
$430$	16.6865	−	22.2291i	0.804695	−	1.07198i
$431$			27.2674i			1.31342i	0.754141	+	0.656712i	$0.228053\pi$
$431$			27.2674i			1.31342i	−0.754141	+	0.656712i	$0.771947\pi$
$432$	2.66076	+	4.18885i	0.128016	+	0.201536i
$433$	17.8959			0.860023			0.430012	−	0.902823i	$-0.358509\pi$
$433$	17.8959			0.860023			0.430012	+	0.902823i	$0.358509\pi$
$434$	1.30382	+	0.978728i	0.0625855	+	0.0469804i
$435$	4.63012			0.221997
$436$	−6.74944	−	23.2138i	−0.323239	−	1.11174i
$437$	−0.662328			−0.0316834
$438$	2.70106	+	2.02758i	0.129062	+	0.0968814i
$439$	16.4464			0.784944			0.392472	−	0.919764i	$-0.371620\pi$
$439$	16.4464			0.784944			0.392472	+	0.919764i	$0.371620\pi$
$440$	6.77823	−	17.9549i	0.323139	−	0.855967i
$441$	−2.95662			−0.140791
$442$	9.99700	+	15.0560i	0.475509	+	0.716142i
$443$			21.4873i			1.02089i	0.859910	+	0.510446i	$0.170520\pi$
$443$			21.4873i			1.02089i	−0.859910	+	0.510446i	$0.829480\pi$
$444$	−0.120180	+	0.0349426i	−0.00570350	+	0.00165830i
$445$		−	3.46092i		−	0.164063i
$446$	−14.9830	+	19.9598i	−0.709466	+	0.945123i
$447$		−	4.03072i		−	0.190646i
$448$	−5.28677	+	6.00417i	−0.249776	+	0.283670i
$449$		−	11.6297i		−	0.548840i	−0.961610	−	0.274420i	$-0.911514\pi$
$449$		−	11.6297i		−	0.548840i	0.961610	−	0.274420i	$-0.0884858\pi$
$450$	−24.7773	−	18.5993i	−1.16801	−	0.876781i
$451$			5.65254i			0.266168i
$452$	−2.61491	−	8.99365i	−0.122995	−	0.423026i
$453$	1.15780			0.0543983
$454$	20.4534	+	15.3536i	0.959926	+	0.720578i
$455$	4.24446	−	11.9712i	0.198983	−	0.561216i
$456$	−0.0715792	−	0.0270221i	−0.00335200	−	0.00126543i
$457$		−	20.1702i		−	0.943524i	−0.881726	−	0.471762i	$-0.843618\pi$
$457$		−	20.1702i		−	0.943524i	0.881726	−	0.471762i	$-0.156382\pi$
$458$	4.81529	+	3.61464i	0.225004	+	0.168901i
$459$			4.39719i			0.205243i
$460$	−10.0310	−	34.5004i	−0.467699	−	1.60859i
$461$	−15.3054			−0.712845			−0.356423	−	0.934325i	$-0.616004\pi$
$461$	−15.3054			−0.712845			−0.356423	+	0.934325i	$0.616004\pi$
$462$	0.453729	+	0.340596i	0.0211094	+	0.0158460i
$463$			22.3957i			1.04082i	0.853917	+	0.520409i	$0.174220\pi$
$463$			22.3957i			1.04082i	−0.853917	+	0.520409i	$0.825780\pi$
$464$	−13.5345	−	21.3075i	−0.628326	−	0.989178i
$465$	−0.845798			−0.0392230
$466$	13.6250	+	10.2278i	0.631168	+	0.473792i
$467$			10.1198i			0.468287i	0.972202	+	0.234143i	$0.0752285\pi$
$467$			10.1198i			0.468287i	−0.972202	+	0.234143i	$0.924771\pi$
$468$	−1.23118	+	21.2849i	−0.0569112	+	0.983896i
$469$			8.04110i			0.371303i
$470$	−6.90508	+	9.19868i	−0.318508	+	0.424304i
$471$	−3.36159			−0.154894
$472$	−7.08183	+	18.7591i	−0.325967	+	0.863458i
$473$			10.7465i			0.494127i
$474$	−2.59752	+	3.46032i	−0.119308	+	0.158938i
$475$	0.962335			0.0441550
$476$	−6.80684	+	1.97910i	−0.311991	+	0.0907117i
$477$		−	34.2458i		−	1.56801i
$478$	−1.07133	+	1.42718i	−0.0490013	+	0.0652777i
$479$		−	20.1092i		−	0.918811i	−0.888227	−	0.459405i	$-0.848062\pi$
$479$		−	20.1092i		−	0.918811i	0.888227	−	0.459405i	$-0.151938\pi$
$480$	0.323497	−	4.13778i	0.0147655	−	0.188863i
$481$	−1.02105	−	0.362019i	−0.0465557	−	0.0165067i
$482$	−14.4283	+	19.2209i	−0.657193	+	0.875488i
$483$	1.06212			0.0483284
$484$	−4.07054	−	14.0001i	−0.185025	−	0.636368i
$485$			32.7844i			1.48866i
$486$	−4.68261	+	6.23800i	−0.212408	+	0.282961i
$487$			14.2922i			0.647643i	0.946118	+	0.323822i	$0.104968\pi$
$487$			14.2922i			0.647643i	−0.946118	+	0.323822i	$0.895032\pi$
$488$	16.4828	+	6.22247i	0.746139	+	0.281678i
$489$			0.784373i			0.0354706i
$490$	3.98424	+	2.99081i	0.179990	+	0.135111i
$491$			20.8674i			0.941734i	0.882204	+	0.470867i	$0.156059\pi$
$491$			20.8674i			0.941734i	−0.882204	+	0.470867i	$0.843941\pi$
$492$	0.341287	+	1.17381i	0.0153864	+	0.0529195i
$493$		−	22.3673i		−	1.00737i
$494$	−0.366326	−	0.551707i	−0.0164818	−	0.0248225i
$495$	20.0616			0.901701
$496$	2.47240	+	3.89232i	0.111014	+	0.174770i
$497$	−16.5533			−0.742517
$498$	−0.666545	+	0.887946i	−0.0298686	+	0.0397898i
$499$	19.1219			0.856016			0.428008	−	0.903775i	$-0.359216\pi$
$499$	19.1219			0.856016			0.428008	+	0.903775i	$0.359216\pi$
$500$	4.73959	+	16.3012i	0.211961	+	0.729011i
$501$	−4.85106			−0.216729
$502$	−13.9518	+	18.5861i	−0.622701	+	0.829538i
$503$	27.5342			1.22769			0.613844	−	0.789427i	$-0.289622\pi$
$503$	27.5342			1.22769			0.613844	+	0.789427i	$0.289622\pi$
$504$	−7.82365	−	2.95354i	−0.348493	−	0.131561i
$505$		−	32.2385i		−	1.43459i
$506$	11.1096	+	8.33950i	0.493880	+	0.370736i
$507$	1.70557	−	2.10286i	0.0757471	−	0.0933911i
$508$	−8.24390	−	28.3538i	−0.365764	−	1.25800i
$509$	−13.8266			−0.612851			−0.306426	−	0.951895i	$-0.599133\pi$
$509$	−13.8266			−0.612851			−0.306426	+	0.951895i	$0.599133\pi$
$510$	2.20782	−	2.94117i	0.0977639	−	0.130237i
$511$	−11.4665			−0.507246
$512$	−19.9875	+	10.6067i	−0.883330	+	0.468752i
$513$		−	0.161129i		−	0.00711401i
$514$	21.1253	+	15.8579i	0.931797	+	0.699462i
$515$	19.3748			0.853756
$516$	0.648850	+	2.23163i	0.0285640	+	0.0982422i
$517$		−	4.44705i		−	0.195581i
$518$	0.255093	−	0.339825i	0.0112081	−	0.0149310i
$519$	−4.13222			−0.181384
$520$	23.1901	−	27.4374i	1.01695	−	1.20321i
$521$	−4.40236			−0.192871			−0.0964355	−	0.995339i	$-0.530744\pi$
$521$	−4.40236			−0.192871			−0.0964355	+	0.995339i	$0.530744\pi$
$522$	15.8410	−	21.1028i	0.693341	−	0.923643i
$523$		−	5.70151i		−	0.249309i	−0.992200	−	0.124655i	$-0.960218\pi$
$523$		−	5.70151i		−	0.249309i	0.992200	−	0.124655i	$-0.0397823\pi$
$524$	−30.4402	+	8.85053i	−1.32979	+	0.386637i
$525$	−1.54322			−0.0673518
$526$	0.560082	+	0.420431i	0.0244207	+	0.0183317i
$527$			4.08591i			0.177985i
$528$	0.860393	+	1.35452i	0.0374438	+	0.0589481i
$529$	3.00612			0.130701
$530$	−34.6417	+	46.1484i	−1.50474	+	2.00456i
$531$	−20.9601			−0.909593
$532$	0.249427	−	0.0725211i	0.0108140	−	0.00314419i
$533$	−3.53587	+	9.97265i	−0.153156	+	0.431963i
$534$	0.231430	+	0.173725i	0.0100149	+	0.00751782i
$535$			23.0345i			0.995869i
$536$	−8.03271	+	21.2779i	−0.346960	+	0.919066i
$537$	0.0825646			0.00356292
$538$	−8.51238	+	11.3399i	−0.366995	+	0.488896i
$539$	−1.92616			−0.0829654
$540$	8.39312	−	2.44031i	0.361182	−	0.105014i
$541$	−21.6901			−0.932529			−0.466265	−	0.884645i	$-0.654400\pi$
$541$	−21.6901			−0.932529			−0.466265	+	0.884645i	$0.654400\pi$
$542$	16.8938	−	22.5053i	0.725650	−	0.966684i
$543$	4.38312			0.188098
$544$	−19.9889	−	1.56276i	−0.857018	−	0.0670028i
$545$	−42.5810			−1.82397
$546$	0.587449	+	0.884730i	0.0251405	+	0.0378630i
$547$		−	8.57481i		−	0.366632i	−0.983054	−	0.183316i	$-0.941317\pi$
$547$		−	8.57481i		−	0.366632i	0.983054	−	0.183316i	$-0.0586832\pi$
$548$	−16.1215	+	4.68733i	−0.688674	+	0.200233i
$549$			18.4167i			0.786006i
$550$	−16.1417	−	12.1169i	−0.688286	−	0.516668i
$551$			0.819618i			0.0349169i
$552$	2.81054	+	1.06102i	0.119624	+	0.0451599i
$553$		−	14.6896i		−	0.624667i
$554$	24.6708	−	32.8655i	1.04816	−	1.39632i
$555$			0.220446i			0.00935743i
$556$	−25.9741	+	7.55200i	−1.10155	+	0.320276i
$557$	−2.70216			−0.114494			−0.0572471	−	0.998360i	$-0.518232\pi$
$557$	−2.70216			−0.114494			−0.0572471	+	0.998360i	$0.518232\pi$
$558$	−2.89373	+	3.85491i	−0.122501	+	0.163191i
$559$	−6.72235	+	18.9599i	−0.284325	+	0.801917i
$560$	7.55519	+	11.8942i	0.319265	+	0.502621i
$561$			1.42189i			0.0600324i
$562$	−12.3123	+	16.4020i	−0.519364	+	0.691877i
$563$			39.2914i			1.65593i	0.560777	+	0.827967i	$0.310503\pi$
$563$			39.2914i			1.65593i	−0.560777	+	0.827967i	$0.689497\pi$
$564$	−0.268502	−	0.923477i	−0.0113060	−	0.0388854i
$565$	−16.4970			−0.694035
$566$	−4.70994	+	6.27441i	−0.197974	+	0.263733i
$567$		−	8.61147i		−	0.361648i
$568$	−43.8025	−	16.5360i	−1.83791	−	0.693837i
$569$	1.67637			0.0702771			0.0351386	−	0.999382i	$-0.488813\pi$
$569$	1.67637			0.0702771			0.0351386	+	0.999382i	$0.488813\pi$
$570$	−0.0809024	+	0.107775i	−0.00338863	+	0.00451420i
$571$			34.5286i			1.44498i	0.691384	+	0.722488i	$0.257001\pi$
$571$			34.5286i			1.44498i	−0.691384	+	0.722488i	$0.742999\pi$
$572$	−0.802078	+	13.8665i	−0.0335366	+	0.579789i
$573$		−	1.12035i		−	0.0468034i
$574$	−3.31910	−	2.49151i	−0.138536	−	0.103994i
$575$	−37.7858			−1.57578
$576$	−17.7521	−	15.6310i	−0.739669	−	0.651291i
$577$			22.3246i			0.929384i	0.885472	+	0.464692i	$0.153835\pi$
$577$			22.3246i			0.929384i	−0.885472	+	0.464692i	$0.846165\pi$
$578$	5.01891	+	3.76749i	0.208759	+	0.156707i
$579$	4.80785			0.199808
$580$	−42.6935	+	12.4132i	−1.77275	+	0.515430i
$581$		−	3.76948i		−	0.156384i
$582$	−2.19227	−	1.64565i	−0.0908727	−	0.0682144i
$583$		−	22.3102i		−	0.923993i
$584$	−30.3419	−	11.4545i	−1.25556	−	0.473990i
$585$	35.3942	+	12.5492i	1.46337	+	0.518848i
$586$	27.9543	+	20.9842i	1.15478	+	0.866848i
$587$	13.2895			0.548517			0.274259	−	0.961656i	$-0.411568\pi$
$587$	13.2895			0.548517			0.274259	+	0.961656i	$0.411568\pi$
$588$	−0.399987	+	0.116297i	−0.0164952	+	0.00479599i
$589$		−	0.149722i		−	0.00616920i
$590$	28.2451	+	21.2025i	1.16283	+	0.872893i
$591$		−	1.73250i		−	0.0712655i
$592$	1.01448	−	0.644399i	0.0416950	−	0.0264846i
$593$		−	22.1464i		−	0.909444i	−0.890634	−	0.454722i	$-0.849739\pi$
$593$		−	22.1464i		−	0.909444i	0.890634	−	0.454722i	$-0.150261\pi$
$594$	−2.02880	+	2.70269i	−0.0832428	+	0.110893i
$595$			12.4858i			0.511867i
$596$	10.8062	+	37.1666i	0.442640	+	1.52240i
$597$			3.92522i			0.160649i
$598$	14.3837	+	21.6626i	0.588192	+	0.885850i
$599$	23.3029			0.952129			0.476065	−	0.879410i	$-0.342063\pi$
$599$	23.3029			0.952129			0.476065	+	0.879410i	$0.342063\pi$
$600$	−4.08359	−	1.54161i	−0.166712	−	0.0629361i
$601$	−14.8316			−0.604993			−0.302496	−	0.953151i	$-0.597820\pi$
$601$	−14.8316			−0.604993			−0.302496	+	0.953151i	$0.597820\pi$
$602$	−6.31022	−	4.73683i	−0.257186	−	0.193059i
$603$	−23.7745			−0.968172
$604$	−10.6759	+	3.10403i	−0.434397	+	0.126301i
$605$	−25.6803			−1.04405
$606$	2.15577	+	1.61825i	0.0875721	+	0.0657368i
$607$	38.0443			1.54417			0.772085	−	0.635520i	$-0.219214\pi$
$607$	38.0443			1.54417			0.772085	+	0.635520i	$0.219214\pi$
$608$	0.732465	+	0.0572651i	0.0297054	+	0.00232241i
$609$		−	1.31436i		−	0.0532605i
$610$	18.6296	−	24.8177i	0.754292	−	1.00484i
$611$	2.78179	−	7.84583i	0.112539	−	0.317408i
$612$	−5.85144	−	20.1252i	−0.236530	−	0.813515i
$613$	17.0574			0.688941			0.344470	−	0.938797i	$-0.388059\pi$
$613$	17.0574			0.688941			0.344470	+	0.938797i	$0.388059\pi$
$614$	−16.9389	−	12.7154i	−0.683600	−	0.513151i
$615$	2.15312			0.0868221
$616$	−5.09689	−	1.92415i	−0.205360	−	0.0775261i
$617$			7.95481i			0.320249i	0.987097	+	0.160124i	$0.0511895\pi$
$617$			7.95481i			0.320249i	−0.987097	+	0.160124i	$0.948810\pi$
$618$	−0.972541	+	1.29558i	−0.0391213	+	0.0521159i
$619$	27.3721			1.10018			0.550088	−	0.835106i	$-0.314594\pi$
$619$	27.3721			1.10018			0.550088	+	0.835106i	$0.314594\pi$
$620$	7.79897	−	2.26756i	0.313214	−	0.0910674i
$621$			6.32668i			0.253881i
$622$	25.1428	+	18.8737i	1.00813	+	0.756766i
$623$	−0.982458			−0.0393614
$624$	0.670668	+	2.92796i	0.0268482	+	0.117212i
$625$	−7.14645			−0.285858
$626$	−9.43995	−	7.08619i	−0.377296	−	0.283221i
$627$		−	0.0521032i		−	0.00208080i
$628$	30.9966	−	9.01231i	1.23690	−	0.359630i
$629$	1.06494			0.0424619
$630$	−8.84268	+	11.7799i	−0.352301	+	0.469322i
$631$			21.1834i			0.843298i	0.906759	+	0.421649i	$0.138548\pi$
$631$			21.1834i			0.843298i	−0.906759	+	0.421649i	$0.861452\pi$
$632$	14.6743	−	38.8709i	0.583713	−	1.54620i
$633$	4.05416			0.161138
$634$	−22.2031	−	16.6670i	−0.881797	−	0.661929i
$635$	−52.0093			−2.06393
$636$	−1.34703	−	4.63294i	−0.0534134	−	0.183708i
$637$	−3.39827	−	1.20488i	−0.134644	−	0.0477391i
$638$	10.3200	−	13.7479i	0.408571	−	0.544283i
$639$		−	48.9419i		−	1.93611i
$640$	8.11034	+	39.0211i	0.320590	+	1.54244i
$641$	0.478600			0.0189036			0.00945179	−	0.999955i	$-0.496991\pi$
$641$	0.478600			0.0189036			0.00945179	+	0.999955i	$0.496991\pi$
$642$	−1.54030	−	1.15624i	−0.0607910	−	0.0456333i
$643$	−5.62114			−0.221676			−0.110838	−	0.993838i	$-0.535353\pi$
$643$	−5.62114			−0.221676			−0.110838	+	0.993838i	$0.535353\pi$
$644$	−9.79368	+	2.84752i	−0.385925	+	0.112208i
$645$	4.09348			0.161181
$646$	0.520643	+	0.390826i	0.0204844	+	0.0153768i
$647$	−44.2220			−1.73854			−0.869272	−	0.494333i	$-0.835412\pi$
$647$	−44.2220			−1.73854			−0.869272	+	0.494333i	$0.835412\pi$
$648$	8.60249	−	22.7872i	0.337938	−	0.895166i
$649$	−13.6550			−0.536004
$650$	−20.8989	−	31.4749i	−0.819722	−	1.23455i
$651$			0.240098i			0.00941019i
$652$	−2.10288	−	7.23257i	−0.0823551	−	0.283249i
$653$		−	4.90631i		−	0.191999i	−0.995381	−	0.0959994i	$-0.969395\pi$
$653$		−	4.90631i		−	0.191999i	0.995381	−	0.0959994i	$-0.0306047\pi$
$654$	2.13740	−	2.84737i	0.0835791	−	0.111341i
$655$			55.8364i			2.18171i
$656$	−6.29390	−	9.90853i	−0.245735	−	0.386863i
$657$		−	33.9020i		−	1.32264i
$658$	2.61125	+	1.96016i	0.101797	+	0.0764149i
$659$			2.44724i			0.0953310i	0.998863	+	0.0476655i	$0.0151782\pi$
$659$			2.44724i			0.0953310i	−0.998863	+	0.0476655i	$0.984822\pi$
$660$	2.71403	−	0.789108i	0.105644	−	0.0307160i
$661$	−46.9632			−1.82666			−0.913328	−	0.407225i	$-0.866497\pi$
$661$	−46.9632			−1.82666			−0.913328	+	0.407225i	$0.866497\pi$
$662$	38.0516	+	28.5638i	1.47892	+	1.11016i
$663$	−0.889446	+	2.50861i	−0.0345432	+	0.0974264i
$664$	3.76555	−	9.97459i	0.146132	−	0.387089i
$665$		−	0.457523i		−	0.0177420i
$666$	1.00473	+	0.754212i	0.0389326	+	0.0292251i
$667$		−	32.1821i		−	1.24609i
$668$	44.7308	−	13.0055i	1.73069	−	0.503199i
$669$	−3.67558			−0.142106
$670$	32.0376	+	24.0494i	1.23772	+	0.929108i
$671$			11.9980i			0.463177i
$672$	−1.17460	−	0.0918317i	−0.0453111	−	0.00354248i
$673$	42.5580			1.64049			0.820245	−	0.572013i	$-0.193837\pi$
$673$	42.5580			1.64049			0.820245	+	0.572013i	$0.193837\pi$
$674$	−0.0162120	−	0.0121697i	−0.000624464	−	0.000468760i
$675$		−	9.19240i		−	0.353816i
$676$	−10.0891	+	23.9627i	−0.388043	+	0.921641i
$677$			27.1383i			1.04301i	0.853249	+	0.521504i	$0.174629\pi$
$677$			27.1383i			1.04301i	−0.853249	+	0.521504i	$0.825371\pi$
$678$	0.828087	−	1.10315i	0.0318025	−	0.0423661i
$679$	9.30657			0.357153
$680$	−12.4727	+	33.0392i	−0.478308	+	1.26699i
$681$			3.76648i			0.144332i
$682$	−1.88518	+	2.51137i	−0.0721874	+	0.0961653i
$683$	−34.5690			−1.32275			−0.661373	−	0.750057i	$-0.730026\pi$
$683$	−34.5690			−1.32275			−0.661373	+	0.750057i	$0.730026\pi$
$684$	0.214418	+	0.737461i	0.00819846	+	0.0281975i
$685$			29.5715i			1.12987i
$686$	0.849005	−	1.13101i	0.0324152	−	0.0431823i
$687$			0.886732i			0.0338309i
$688$	−11.9659	−	18.8380i	−0.456195	−	0.718191i
$689$	13.9558	−	39.3613i	0.531675	−	1.49955i
$690$	3.17661	−	4.23176i	0.120931	−	0.161100i
$691$	26.6922			1.01542			0.507709	−	0.861529i	$-0.330492\pi$
$691$	26.6922			1.01542			0.507709	+	0.861529i	$0.330492\pi$
$692$	38.1025	−	11.0783i	1.44844	−	0.421136i
$693$		−	5.69492i		−	0.216332i
$694$	−2.65974	+	3.54320i	−0.100962	+	0.134498i
$695$			47.6442i			1.80725i
$696$	1.31299	−	3.47799i	0.0497687	−	0.131833i
$697$		−	10.4014i		−	0.393979i
$698$	−1.40722	−	1.05634i	−0.0532640	−	0.0399831i
$699$			2.50904i			0.0949007i
$700$	14.2298	−	4.13733i	0.537836	−	0.156377i
$701$		−	21.2235i		−	0.801602i	−0.916165	−	0.400801i	$-0.868732\pi$
$701$		−	21.2235i		−	0.801602i	0.916165	−	0.400801i	$-0.131268\pi$
$702$	−5.27000	+	3.49921i	−0.198903	+	0.132069i
$703$	−0.0390232			−0.00147179
$704$	−11.5650	−	10.1831i	−0.435871	−	0.383792i
$705$	−1.69393			−0.0637972
$706$	6.28777	−	8.37633i	0.236643	−	0.315247i
$707$	−9.15160			−0.344181
$708$	−2.83560	+	0.824453i	−0.106568	+	0.0309848i
$709$	−38.7261			−1.45439			−0.727194	−	0.686432i	$-0.759176\pi$
$709$	−38.7261			−1.45439			−0.727194	+	0.686432i	$0.759176\pi$
$710$	−49.5077	+	65.9523i	−1.85799	+	2.47515i
$711$	43.4317			1.62882
$712$	−2.59973	−	0.981433i	−0.0974289	−	0.0367808i
$713$			5.87881i			0.220163i
$714$	−0.834916	−	0.626738i	−0.0312459	−	0.0234551i
$715$	23.0583	+	8.17549i	0.862332	+	0.305746i
$716$	−0.761314	+	0.221353i	−0.0284516	+	0.00827235i
$717$	−0.262814			−0.00981499
$718$	30.6967	−	40.8930i	1.14559	−	1.52611i
$719$	44.9233			1.67536			0.837679	−	0.546163i	$-0.183912\pi$
$719$	44.9233			1.67536			0.837679	+	0.546163i	$0.183912\pi$
$720$	−35.1666	+	22.3378i	−1.31058	+	0.832482i
$721$		−	5.49996i		−	0.204829i
$722$	21.4702	+	16.1168i	0.799037	+	0.599805i
$723$	−3.53951			−0.131636
$724$	−40.4161	+	11.7510i	−1.50205	+	0.436723i
$725$			46.7592i			1.73659i
$726$	1.28905	−	1.71723i	0.0478413	−	0.0637323i
$727$	24.2750			0.900310			0.450155	−	0.892950i	$-0.351369\pi$
$727$	24.2750			0.900310			0.450155	+	0.892950i	$0.351369\pi$
$728$	−7.78870	−	6.58302i	−0.288668	−	0.243983i
$729$	24.6857			0.914285
$730$	−34.2940	+	45.6851i	−1.26928	+	1.69088i
$731$		−	19.7749i		−	0.731402i
$732$	0.724408	+	2.49151i	0.0267749	+	0.0920887i
$733$	−21.7151			−0.802067			−0.401033	−	0.916063i	$-0.631349\pi$
$733$	−21.7151			−0.802067			−0.401033	+	0.916063i	$0.631349\pi$
$734$	−9.16348	−	6.87865i	−0.338230	−	0.253896i
$735$			0.733695i			0.0270627i
$736$	−28.7600	−	2.24850i	−1.06011	−	0.0828807i
$737$	−15.4884			−0.570523
$738$	7.36645	−	9.81331i	0.271163	−	0.361233i
$739$	4.13272			0.152025			0.0760123	−	0.997107i	$-0.475781\pi$
$739$	4.13272			0.152025			0.0760123	+	0.997107i	$0.475781\pi$
$740$	−0.591010	−	2.03270i	−0.0217260	−	0.0747235i
$741$	0.0325925	−	0.0919245i	0.00119731	−	0.00337693i
$742$	13.1002	+	9.83381i	0.480924	+	0.361011i
$743$			20.2682i			0.743567i	0.928319	+	0.371784i	$0.121254\pi$
$743$			20.2682i			0.743567i	−0.928319	+	0.371784i	$0.878746\pi$
$744$	−0.239848	+	0.635335i	−0.00879325	+	0.0232925i
$745$	68.1746			2.49772
$746$	−6.56750	+	8.74897i	−0.240453	+	0.320323i
$747$	11.1449			0.407771
$748$	−3.81205	−	13.1110i	−0.139382	−	0.479387i
$749$	6.53885			0.238924
$750$	−1.50093	+	1.99948i	−0.0548061	+	0.0730106i
$751$	50.2644			1.83417			0.917087	−	0.398687i	$-0.130534\pi$
$751$	50.2644			1.83417			0.917087	+	0.398687i	$0.130534\pi$
$752$	4.95163	+	7.79538i	0.180567	+	0.284268i
$753$	−3.42262			−0.124727
$754$	26.8071	−	17.7995i	0.976256	−	0.648221i
$755$			19.5828i			0.712691i
$756$	−0.692735	−	2.38257i	−0.0251945	−	0.0866532i
$757$			20.4735i			0.744122i	0.928208	+	0.372061i	$0.121349\pi$
$757$			20.4735i			0.744122i	−0.928208	+	0.372061i	$0.878651\pi$
$758$	−36.7125	−	27.5586i	−1.33346	−	1.00097i
$759$			2.04582i			0.0742585i
$760$	0.457046	−	1.21067i	0.0165788	−	0.0439157i
$761$			31.2031i			1.13111i	0.824710	+	0.565556i	$0.191338\pi$
$761$			31.2031i			1.13111i	−0.824710	+	0.565556i	$0.808662\pi$
$762$	2.61067	−	3.47783i	0.0945744	−	0.125988i
$763$			12.0875i			0.437599i
$764$	3.00363	+	10.3306i	0.108668	+	0.373748i
$765$	−36.9157			−1.33469
$766$	−30.3829	+	40.4750i	−1.09778	+	1.46242i
$767$	−24.0911	−	8.54167i	−0.869880	−	0.308422i
$768$	−3.01642	−	1.41637i	−0.108846	−	0.0511090i
$769$		−	32.8772i		−	1.18558i	−0.805356	−	0.592791i	$-0.798026\pi$
$769$		−	32.8772i		−	1.18558i	0.805356	−	0.592791i	$-0.201974\pi$
$770$	−5.76076	+	7.67427i	−0.207603	+	0.276561i
$771$			3.89021i			0.140103i
$772$	−44.3324	+	12.8897i	−1.59556	+	0.463911i
$773$	12.3295			0.443463			0.221731	−	0.975108i	$-0.428829\pi$
$773$	12.3295			0.443463			0.221731	+	0.975108i	$0.428829\pi$
$774$	14.0050	−	18.6569i	0.503400	−	0.670610i
$775$		−	8.54166i		−	0.306826i
$776$	24.6265	+	9.29686i	0.884041	+	0.333738i
$777$	0.0625785			0.00224499
$778$	−5.36724	+	7.15004i	−0.192425	+	0.256341i
$779$			0.381143i			0.0136558i
$780$	5.28192	+	0.305521i	0.189123	+	0.0109394i
$781$		−	31.8843i		−	1.14091i
$782$	−20.4429	−	15.3457i	−0.731037	−	0.548760i
$783$	7.82914			0.279791
$784$	3.37642	−	2.14470i	0.120587	−	0.0765966i
$785$		−	56.8571i		−	2.02932i
$786$	−3.73375	−	2.80277i	−0.133178	−	0.0999717i
$787$	34.8281			1.24149			0.620743	−	0.784014i	$-0.286831\pi$
$787$	34.8281			1.24149			0.620743	+	0.784014i	$0.286831\pi$
$788$	4.64478	+	15.9751i	0.165463	+	0.569089i
$789$			0.103139i			0.00367184i
$790$	−58.5270	−	43.9339i	−2.08230	−	1.56310i
$791$			4.68304i			0.166510i
$792$	5.68897	−	15.0696i	0.202149	−	0.535474i
$793$	−7.50517	+	21.1677i	−0.266516	+	0.751689i
$794$	11.6203	+	8.72288i	0.412388	+	0.309563i
$795$	−8.49820			−0.301400
$796$	−10.5234	−	36.1938i	−0.372992	−	1.28286i
$797$		−	37.3680i		−	1.32364i	−0.749661	−	0.661821i	$-0.769784\pi$
$797$		−	37.3680i		−	1.32364i	0.749661	−	0.661821i	$-0.230216\pi$
$798$	0.0305943	+	0.0229659i	0.00108303	+	0.000812984i
$799$			8.18310i			0.289497i
$800$	41.7872	+	3.26697i	1.47740	+	0.115505i
$801$		−	2.90476i		−	0.102635i
$802$	1.52720	−	2.03448i	0.0539274	−	0.0718400i
$803$		−	22.0862i		−	0.779405i
$804$	−3.21633	+	0.935153i	−0.113431	+	0.0329803i
$805$			17.9645i			0.633166i
$806$	−4.89694	+	3.25150i	−0.172487	+	0.114529i
$807$	−2.08823			−0.0735091
$808$	−24.2165	−	9.14205i	−0.851932	−	0.321616i
$809$	36.3556			1.27819			0.639097	−	0.769126i	$-0.279308\pi$
$809$	36.3556			1.27819			0.639097	+	0.769126i	$0.279308\pi$
$810$	−34.3102	−	25.7552i	−1.20554	−	0.904947i
$811$	−29.4704			−1.03485			−0.517423	−	0.855730i	$-0.673109\pi$
$811$	−29.4704			−1.03485			−0.517423	+	0.855730i	$0.673109\pi$
$812$	3.52376	+	12.1195i	0.123660	+	0.425311i
$813$	4.14433			0.145348
$814$	0.654556	+	0.491348i	0.0229422	+	0.0172218i
$815$	−13.2667			−0.464712
$816$	−1.58323	−	2.49248i	−0.0554240	−	0.0872544i
$817$			0.724623i			0.0253514i
$818$	−18.6019	+	24.7808i	−0.650400	+	0.866439i
$819$	3.56238	−	10.0474i	0.124480	−	0.351085i
$820$	−19.8535	+	5.77244i	−0.693316	+	0.201582i
$821$	8.34090			0.291100			0.145550	−	0.989351i	$-0.453505\pi$
$821$	8.34090			0.291100			0.145550	+	0.989351i	$0.453505\pi$
$822$	−1.97743	−	1.48438i	−0.0689709	−	0.0517736i
$823$	46.3329			1.61506			0.807531	−	0.589825i	$-0.200803\pi$
$823$	46.3329			1.61506			0.807531	+	0.589825i	$0.200803\pi$
$824$	5.49422	−	14.5537i	0.191400	−	0.507002i
$825$		−	2.97249i		−	0.103489i
$826$	6.01879	−	8.01800i	0.209420	−	0.278982i
$827$	36.3252			1.26315			0.631575	−	0.775315i	$-0.282409\pi$
$827$	36.3252			1.26315			0.631575	+	0.775315i	$0.282409\pi$
$828$	−8.41905	−	28.9562i	−0.292582	−	1.00630i
$829$		−	12.3282i		−	0.428175i	−0.976814	−	0.214088i	$-0.931322\pi$
$829$		−	12.3282i		−	0.428175i	0.976814	−	0.214088i	$-0.0686778\pi$
$830$	−15.0185	−	11.2738i	−0.521300	−	0.391319i
$831$	6.05217			0.209947
$832$	−14.0339	−	25.2002i	−0.486537	−	0.873660i
$833$	3.54436			0.122805
$834$	−3.18594	−	2.39156i	−0.110320	−	0.0828128i
$835$		−	82.0496i		−	2.83944i
$836$	0.139687	+	0.480435i	0.00483118	+	0.0166162i
$837$	−1.43017			−0.0494341
$838$	−16.0366	+	21.3633i	−0.553975	+	0.737985i
$839$		−	33.9276i		−	1.17131i	−0.810560	−	0.585656i	$-0.800837\pi$
$839$		−	33.9276i		−	1.17131i	0.810560	−	0.585656i	$-0.199163\pi$
$840$	−0.732929	+	1.94146i	−0.0252885	+	0.0669869i
$841$	−10.8247			−0.373266
$842$	−7.17141	−	5.38329i	−0.247143	−	0.185520i
$843$	−3.02042			−0.104029
$844$	−37.3827	+	10.8691i	−1.28677	+	0.374129i
$845$	35.5672	+	28.8476i	1.22355	+	0.992389i
$846$	−5.79544	+	7.72047i	−0.199251	+	0.265435i
$847$			7.28992i			0.250485i
$848$	24.8416	+	39.1083i	0.853063	+	1.34298i
$849$	−1.15543			−0.0396542
$850$	29.7027	+	22.2966i	1.01879	+	0.764768i
$851$	1.53223			0.0525243
$852$	−1.92509	−	6.62110i	−0.0659526	−	0.226835i
$853$	38.7697			1.32745			0.663725	−	0.747977i	$-0.268974\pi$
$853$	38.7697			1.32745			0.663725	+	0.747977i	$0.268974\pi$
$854$	−7.04504	−	5.28843i	−0.241076	−	0.180966i
$855$	1.35272			0.0462621
$856$	17.3027	+	6.53203i	0.591396	+	0.223260i
$857$	−26.4866			−0.904764			−0.452382	−	0.891824i	$-0.649426\pi$
$857$	−26.4866			−0.904764			−0.452382	+	0.891824i	$0.649426\pi$
$858$	−1.70413	+	1.13152i	−0.0581780	+	0.0386294i
$859$			17.8500i			0.609033i	0.952507	+	0.304517i	$0.0984949\pi$
$859$			17.8500i			0.609033i	−0.952507	+	0.304517i	$0.901505\pi$
$860$	−37.7453	+	10.9745i	−1.28710	+	0.374227i
$861$		−	0.611209i		−	0.0208300i
$862$	23.1502	−	30.8398i	0.788498	−	1.05041i
$863$		−	13.6999i		−	0.466350i	−0.972435	−	0.233175i	$-0.925088\pi$
$863$		−	13.6999i		−	0.466350i	0.972435	−	0.233175i	$-0.0749115\pi$
$864$	0.547006	−	6.99664i	0.0186095	−	0.238031i
$865$		−	69.8913i		−	2.37638i
$866$	−20.2405	−	15.1937i	−0.687801	−	0.516304i
$867$			0.924228i			0.0313884i
$868$	−0.643696	−	2.21391i	−0.0218485	−	0.0751449i
$869$	28.2945			0.959827
$870$	−5.23672	−	3.93099i	−0.177541	−	0.133273i
$871$	−27.3258	−	9.68857i	−0.925901	−	0.328285i
$872$	−12.0749	+	31.9854i	−0.408909	+	1.08316i
$873$			27.5160i			0.931276i
$874$	0.749101	+	0.562320i	0.0253387	+	0.0190208i
$875$		−	8.48812i		−	0.286951i
$876$	−1.33351	−	4.58643i	−0.0450552	−	0.154961i
$877$	1.66862			0.0563452			0.0281726	−	0.999603i	$-0.491031\pi$
$877$	1.66862			0.0563452			0.0281726	+	0.999603i	$0.491031\pi$
$878$	−18.6011	−	13.9631i	−0.627757	−	0.471231i
$879$			5.14777i			0.173630i
$880$	−22.9101	+	14.5525i	−0.772298	+	0.490564i
$881$	−0.959187			−0.0323158			−0.0161579	−	0.999869i	$-0.505143\pi$
$881$	−0.959187			−0.0323158			−0.0161579	+	0.999869i	$0.505143\pi$
$882$	3.34398	+	2.51019i	0.112598	+	0.0845224i
$883$			40.6249i			1.36714i	0.729886	+	0.683569i	$0.239573\pi$
$883$			40.6249i			1.36714i	−0.729886	+	0.683569i	$0.760427\pi$
$884$	1.47592	−	25.5161i	0.0496405	−	0.858198i
$885$			5.20133i			0.174841i
$886$	18.2428	−	24.3024i	0.612879	−	0.816454i
$887$	−58.6312			−1.96864			−0.984322	−	0.176380i	$-0.943561\pi$
$887$	−58.6312			−1.96864			−0.984322	+	0.176380i	$0.943561\pi$
$888$	0.165592	+	0.0625132i	0.00555690	+	0.00209781i
$889$			14.7640i			0.495168i
$890$	−2.93834	+	3.91435i	−0.0984934	+	0.131209i
$891$	16.5870			0.555687
$892$	33.8919	−	9.85412i	1.13479	−	0.329940i
$893$		−	0.299858i		−	0.0100344i
$894$	−3.42210	+	4.55879i	−0.114452	+	0.152469i
$895$			1.39648i			0.0466791i
$896$	11.0770	−	2.30230i	0.370056	−	0.0769144i
$897$	−1.27973	+	3.60939i	−0.0427291	+	0.120514i
$898$	−9.87368	+	13.1533i	−0.329489	+	0.438933i
$899$	7.27491			0.242632
$900$	12.2325	+	42.0722i	0.407751	+	1.40241i
$901$			41.0534i			1.36769i
$902$	4.79904	−	6.39310i	0.159791	−	0.212867i
$903$		−	1.16202i		−	0.0386697i
$904$	−4.67815	+	12.3920i	−0.155593	+	0.412152i
$905$			74.1351i			2.46433i
$906$	−1.30949	−	0.982981i	−0.0435049	−	0.0326574i
$907$		−	16.8426i		−	0.559251i	−0.960109	−	0.279625i	$-0.909790\pi$
$907$		−	16.8426i		−	0.559251i	0.960109	−	0.279625i	$-0.0902103\pi$
$908$	−10.0978	−	34.7301i	−0.335108	−	1.15256i
$909$		−	27.0578i		−	0.897451i
$910$	−14.9641	+	9.93596i	−0.496055	+	0.329374i
$911$	−19.4339			−0.643874			−0.321937	−	0.946761i	$-0.604334\pi$
$911$	−19.4339			−0.643874			−0.321937	+	0.946761i	$0.604334\pi$
$912$	0.0580150	+	0.0913335i	0.00192107	+	0.00302435i
$913$	7.26061			0.240291
$914$	−17.1246	+	22.8128i	−0.566433	+	0.754580i
$915$	4.57016			0.151085
$916$	−2.37730	−	8.17641i	−0.0785482	−	0.270156i
$917$	15.8504			0.523426
$918$	3.73324	−	4.97328i	0.123215	−	0.164143i
$919$	−4.84960			−0.159974			−0.0799868	−	0.996796i	$-0.525488\pi$
$919$	−4.84960			−0.159974			−0.0799868	+	0.996796i	$0.525488\pi$
$920$	−17.9458	+	47.5367i	−0.591655	+	1.56724i
$921$		−	3.11929i		−	0.102784i
$922$	17.3106	+	12.9944i	0.570096	+	0.427948i
$923$	19.9448	−	56.2527i	0.656490	−	1.85158i
$924$	−0.224006	−	0.770437i	−0.00736924	−	0.0253455i
$925$	−2.22627			−0.0731994
$926$	19.0141	−	25.3299i	0.624842	−	0.832391i
$927$	16.2613			0.534091
$928$	−2.78247	+	35.5900i	−0.0913391	+	1.16830i
$929$		−	15.2435i		−	0.500124i	−0.968230	−	0.250062i	$-0.919549\pi$
$929$		−	15.2435i		−	0.500124i	0.968230	−	0.250062i	$-0.0804509\pi$
$930$	0.956609	+	0.718087i	0.0313684	+	0.0235470i
$931$	−0.129878			−0.00425658
$932$	−6.72667	−	23.1355i	−0.220339	−	0.757828i
$933$			4.63003i			0.151580i
$934$	8.59173	−	11.4456i	0.281130	−	0.374511i
$935$	−24.0495			−0.786504
$936$	19.4635	−	23.0282i	0.636184	−	0.752702i
$937$	−58.4300			−1.90883			−0.954413	−	0.298490i	$-0.903517\pi$
$937$	−58.4300			−1.90883			−0.954413	+	0.298490i	$0.903517\pi$
$938$	6.82694	−	9.09458i	0.222907	−	0.296949i
$939$		−	1.73836i		−	0.0567293i
$940$	15.6195	−	4.54138i	0.509451	−	0.148123i
$941$	−22.9904			−0.749467			−0.374733	−	0.927133i	$-0.622266\pi$
$941$	−22.9904			−0.749467			−0.374733	+	0.927133i	$0.622266\pi$
$942$	3.80200	+	2.85401i	0.123876	+	0.0929885i
$943$		−	14.9655i		−	0.487342i
$944$	23.9362	−	15.2043i	0.779058	−	0.494857i
$945$	−4.37034			−0.142167
$946$	9.12388	−	12.1545i	0.296643	−	0.395176i
$947$	−19.1597			−0.622608			−0.311304	−	0.950310i	$-0.600766\pi$
$947$	−19.1597			−0.622608			−0.311304	+	0.950310i	$0.600766\pi$
$948$	5.87566	−	1.70836i	0.190833	−	0.0554848i
$949$	13.8157	−	38.9662i	0.448477	−	1.26490i
$950$	−1.08841	−	0.817028i	−0.0353128	−	0.0265079i
$951$		−	4.08868i		−	0.132585i
$952$	9.37888	+	3.54066i	0.303971	+	0.114753i
$953$	40.8834			1.32434			0.662171	−	0.749353i	$-0.269635\pi$
$953$	40.8834			1.32434			0.662171	+	0.749353i	$0.269635\pi$
$954$	−29.0749	+	38.7324i	−0.941333	+	1.25401i
$955$	18.9494			0.613188
$956$	2.42337	−	0.704597i	0.0783773	−	0.0227883i
$957$	2.53166			0.0818370
$958$	−17.0728	+	22.7437i	−0.551597	+	0.734816i
$959$	8.39453			0.271073
$960$	−3.87888	+	4.40523i	−0.125190	+	0.142178i
$961$	29.6711			0.957131
$962$	0.847461	+	1.27632i	0.0273232	+	0.0411503i
$963$			19.3329i			0.622994i
$964$	32.6373	−	9.48933i	1.05118	−	0.305631i
$965$			81.3188i			2.61775i
$966$	−1.20128	−	0.901750i	−0.0386504	−	0.0290133i
$967$			1.86092i			0.0598431i	0.999552	+	0.0299216i	$0.00952575\pi$
$967$			1.86092i			0.0598431i	−0.999552	+	0.0299216i	$0.990474\pi$
$968$	−7.28231	+	19.2902i	−0.234062	+	0.620010i
$969$			0.0958761i			0.00307998i
$970$	27.8341	−	37.0796i	0.893700	−	1.19055i
$971$			22.8850i			0.734416i	0.930139	+	0.367208i	$0.119686\pi$
$971$			22.8850i			0.734416i	−0.930139	+	0.367208i	$0.880314\pi$
$972$	10.5922	−	3.07969i	0.339745	−	0.0987811i
$973$	13.5249			0.433587
$974$	12.1342	−	16.1647i	0.388805	−	0.517951i
$975$	1.85940	−	5.24430i	0.0595485	−	0.167952i
$976$	−13.3593	−	21.0316i	−0.427621	−	0.673207i
$977$			3.98677i			0.127548i	0.997964	+	0.0637740i	$0.0203137\pi$
$977$			3.98677i			0.127548i	−0.997964	+	0.0637740i	$0.979686\pi$
$978$	0.665937	−	0.887136i	0.0212943	−	0.0283675i
$979$		−	1.89237i		−	0.0604804i
$980$	−1.96701	−	6.76528i	−0.0628339	−	0.216109i
$981$	−35.7383			−1.14104
$982$	17.7166	−	23.6013i	0.565358	−	0.753148i
$983$		−	50.8782i		−	1.62276i	−0.584518	−	0.811381i	$-0.698716\pi$
$983$		−	50.8782i		−	1.62276i	0.584518	−	0.811381i	$-0.301284\pi$
$984$	0.610572	−	1.61735i	0.0194643	−	0.0515592i
$985$	29.3031			0.933673
$986$	−18.9900	+	25.2977i	−0.604764	+	0.805643i
$987$			0.480859i			0.0153059i
$988$	−0.0540829	+	0.935000i	−0.00172061	+	0.0297463i
$989$		−	28.4521i		−	0.904726i
$990$	−22.6899	−	17.0324i	−0.721132	−	0.541325i
$991$	−54.2500			−1.72331			−0.861653	−	0.507497i	$-0.830571\pi$
$991$	−54.2500			−1.72331			−0.861653	+	0.507497i	$0.830571\pi$
$992$	0.508283	−	6.50134i	0.0161380	−	0.206418i
$993$			7.00718i			0.222366i
$994$	18.7220	+	14.0538i	0.593826	+	0.445761i
$995$	−66.3902			−2.10471
$996$	1.50774	−	0.438378i	0.0477746	−	0.0138905i
$997$		−	25.8118i		−	0.817467i	−0.912654	−	0.408734i	$-0.865971\pi$
$997$		−	25.8118i		−	0.817467i	0.912654	−	0.408734i	$-0.134029\pi$
$998$	−21.6272	−	16.2346i	−0.684596	−	0.513898i
$999$			0.372756i			0.0117935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.i.a.701.15	✓	84
4.3	odd	2		2912.2.i.a.337.72		84
8.3	odd	2		2912.2.i.a.337.13		84
8.5	even	2	inner	728.2.i.a.701.69	yes	84
13.12	even	2	inner	728.2.i.a.701.70	yes	84
52.51	odd	2		2912.2.i.a.337.14		84
104.51	odd	2		2912.2.i.a.337.71		84
104.77	even	2	inner	728.2.i.a.701.16	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.i.a.701.15	✓	84	1.1	even	1	trivial
728.2.i.a.701.16	yes	84	104.77	even	2	inner
728.2.i.a.701.69	yes	84	8.5	even	2	inner
728.2.i.a.701.70	yes	84	13.12	even	2	inner
2912.2.i.a.337.13		84	8.3	odd	2
2912.2.i.a.337.14		84	52.51	odd	2
2912.2.i.a.337.71		84	104.51	odd	2
2912.2.i.a.337.72		84	4.3	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13101 - 0.849005i) q^{2} -0.208275i q^{3} +(0.558380 + 1.92047i) q^{4} +3.52272 q^{5} +(-0.176827 + 0.235562i) q^{6} -1.00000i q^{7} +(0.998957 - 2.64615i) q^{8} +2.95662 q^{9} +(-3.98424 - 2.99081i) q^{10} +1.92616 q^{11} +(0.399987 - 0.116297i) q^{12} +(3.39827 + 1.20488i) q^{13} +(-0.849005 + 1.13101i) q^{14} -0.733695i q^{15} +(-3.37642 + 2.14470i) q^{16} -3.54436 q^{17} +(-3.34398 - 2.51019i) q^{18} +0.129878 q^{19} +(1.96701 + 6.76528i) q^{20} -0.208275 q^{21} +(-2.17851 - 1.63532i) q^{22} -5.09962 q^{23} +(-0.551127 - 0.208058i) q^{24} +7.40954 q^{25} +(-2.82054 - 4.24789i) q^{26} -1.24062i q^{27} +(1.92047 - 0.558380i) q^{28} +6.31068i q^{29} +(-0.622911 + 0.829818i) q^{30} -1.15279i q^{31} +(5.63964 + 0.440915i) q^{32} -0.401171i q^{33} +(4.00871 + 3.00918i) q^{34} -3.52272i q^{35} +(1.65092 + 5.67811i) q^{36} -0.300461 q^{37} +(-0.146894 - 0.110267i) q^{38} +(0.250947 - 0.707776i) q^{39} +(3.51904 - 9.32162i) q^{40} +2.93462i q^{41} +(0.235562 + 0.176827i) q^{42} +5.57927i q^{43} +(1.07553 + 3.69913i) q^{44} +10.4153 q^{45} +(5.76773 + 4.32960i) q^{46} -2.30877i q^{47} +(0.446689 + 0.703226i) q^{48} -1.00000 q^{49} +(-8.38028 - 6.29074i) q^{50} +0.738202i q^{51} +(-0.416414 + 7.19907i) q^{52} -11.5827i q^{53} +(-1.05329 + 1.40315i) q^{54} +6.78531 q^{55} +(-2.64615 - 0.998957i) q^{56} -0.0270504i q^{57} +(5.35780 - 7.13746i) q^{58} -7.08922 q^{59} +(1.40904 - 0.409680i) q^{60} +6.22897i q^{61} +(-0.978728 + 1.30382i) q^{62} -2.95662i q^{63} +(-6.00417 - 5.28677i) q^{64} +(11.9712 + 4.24446i) q^{65} +(-0.340596 + 0.453729i) q^{66} -8.04110 q^{67} +(-1.97910 - 6.80684i) q^{68} +1.06212i q^{69} +(-2.99081 + 3.98424i) q^{70} -16.5533i q^{71} +(2.95354 - 7.82365i) q^{72} -11.4665i q^{73} +(0.339825 + 0.255093i) q^{74} -1.54322i q^{75} +(0.0725211 + 0.249427i) q^{76} -1.92616i q^{77} +(-0.884730 + 0.587449i) q^{78} +14.6896 q^{79} +(-11.8942 + 7.55519i) q^{80} +8.61147 q^{81} +(2.49151 - 3.31910i) q^{82} +3.76948 q^{83} +(-0.116297 - 0.399987i) q^{84} -12.4858 q^{85} +(4.73683 - 6.31022i) q^{86} +1.31436 q^{87} +(1.92415 - 5.09689i) q^{88} -0.982458i q^{89} +(-11.7799 - 8.84268i) q^{90} +(1.20488 - 3.39827i) q^{91} +(-2.84752 - 9.79368i) q^{92} -0.240098 q^{93} +(-1.96016 + 2.61125i) q^{94} +0.457523 q^{95} +(0.0918317 - 1.17460i) q^{96} +9.30657i q^{97} +(1.13101 + 0.849005i) q^{98} +5.69492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) \) 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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