LMFDB - Embedded newform 990.2.bh.d.523.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(73,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.9
Character	$\chi$	$=$	990.523
Dual form			990.2.bh.d.937.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.453990 - 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(-1.04130 + 1.97881i) q^{5} +(1.08010 + 0.171071i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.29039 + 1.82617i) q^{10} +(-3.30854 + 0.231505i) q^{11} +(-2.08157 - 1.06061i) q^{13} +(0.642782 - 0.884714i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-2.96964 + 1.51311i) q^{17} +(-4.05531 - 2.94635i) q^{19} +(2.21295 - 0.320687i) q^{20} +(-1.29577 + 3.05303i) q^{22} +(-2.67409 - 2.67409i) q^{23} +(-2.83139 - 4.12107i) q^{25} +(-1.89002 + 1.37318i) q^{26} +(-0.496469 - 0.974375i) q^{28} +(1.72903 - 1.25621i) q^{29} +(-0.615977 - 1.89578i) q^{31} +(0.707107 + 0.707107i) q^{32} +3.33290i q^{34} +(-1.46323 + 1.95918i) q^{35} +(0.392539 - 2.47839i) q^{37} +(-4.46629 + 2.27569i) q^{38} +(0.718926 - 2.11734i) q^{40} +(-3.67243 + 5.05467i) q^{41} +(0.876728 - 0.876728i) q^{43} +(2.13200 + 2.54059i) q^{44} +(-3.59664 + 1.16862i) q^{46} +(-4.68990 + 0.742808i) q^{47} +(-5.52004 - 1.79357i) q^{49} +(-4.95733 + 0.651858i) q^{50} +(0.365462 + 2.30744i) q^{52} +(-3.40646 + 6.68555i) q^{53} +(2.98707 - 6.78803i) q^{55} -1.09357 q^{56} +(-0.334331 - 2.11088i) q^{58} +(-0.531320 - 0.731299i) q^{59} +(6.76905 + 2.19940i) q^{61} +(-1.96880 - 0.311828i) q^{62} +(0.951057 - 0.309017i) q^{64} +(4.26629 - 3.01462i) q^{65} +(0.578715 - 0.578715i) q^{67} +(2.96964 + 1.51311i) q^{68} +(1.08135 + 2.19320i) q^{70} +(-5.17298 + 15.9208i) q^{71} +(-0.870026 + 5.49313i) q^{73} +(-2.03006 - 1.47492i) q^{74} +5.01264i q^{76} +(-3.61316 - 0.315947i) q^{77} +(1.22478 + 3.76949i) q^{79} +(-1.56018 - 1.60182i) q^{80} +(2.83649 + 5.56693i) q^{82} +(-5.34777 - 10.4956i) q^{83} +(0.0981327 - 7.45195i) q^{85} +(-0.383144 - 1.17920i) q^{86} +(3.23159 - 0.746223i) q^{88} +2.76909i q^{89} +(-2.06687 - 1.50167i) q^{91} +(-0.591594 + 3.73518i) q^{92} +(-1.46733 + 4.51596i) q^{94} +(10.0531 - 4.95665i) q^{95} +(12.0797 + 6.15492i) q^{97} +(-4.10413 + 4.10413i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{7} + 24 q^{16} + 4 q^{22} + 8 q^{25} + 20 q^{28} - 16 q^{31} + 64 q^{37} - 40 q^{46} - 40 q^{52} - 36 q^{55} - 12 q^{58} - 80 q^{61} - 48 q^{67} - 52 q^{70} + 20 q^{73} + 48 q^{82} - 160 q^{85}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q - 40 * q^7 + 24 * q^16 + 4 * q^22 + 8 * q^25 + 20 * q^28 - 16 * q^31 + 64 * q^37 - 40 * q^46 - 40 * q^52 - 36 * q^55 - 12 * q^58 - 80 * q^61 - 48 * q^67 - 52 * q^70 + 20 * q^73 + 48 * q^82 - 160 * q^85 + 4 * q^88 + 8 * q^91 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−1.04130	+	1.97881i	−0.465684	+	0.884951i
$5$	−1.04130	+	1.97881i	−0.465684	+	0.884951i
$6$		0			0
$7$	1.08010	+	0.171071i	0.408240	+	0.0646589i	0.357178	−	0.934037i	$-0.383739\pi$
$7$	1.08010	+	0.171071i	0.408240	+	0.0646589i	0.0510629	+	0.998695i	$0.483739\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$		0			0
$10$	1.29039	+	1.82617i	0.408058	+	0.577485i
$11$	−3.30854	+	0.231505i	−0.997561	+	0.0698013i
$11$	−3.30854	+	0.231505i	−0.997561	+	0.0698013i
$12$		0			0
$13$	−2.08157	−	1.06061i	−0.577323	−	0.294161i	0.140844	−	0.990032i	$-0.455019\pi$
$13$	−2.08157	−	1.06061i	−0.577323	−	0.294161i	−0.718167	+	0.695871i	$0.755019\pi$
$14$	0.642782	−	0.884714i	0.171791	−	0.236450i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−2.96964	+	1.51311i	−0.720243	+	0.366982i	−0.775378	−	0.631497i	$-0.782441\pi$
$17$	−2.96964	+	1.51311i	−0.720243	+	0.366982i	0.0551357	+	0.998479i	$0.482441\pi$
$18$		0			0
$19$	−4.05531	−	2.94635i	−0.930352	−	0.675940i	0.0157271	−	0.999876i	$-0.494994\pi$
$19$	−4.05531	−	2.94635i	−0.930352	−	0.675940i	−0.946079	+	0.323936i	$0.894994\pi$
$20$	2.21295	−	0.320687i	0.494831	−	0.0717077i
$21$		0			0
$22$	−1.29577	+	3.05303i	−0.276259	+	0.650908i
$23$	−2.67409	−	2.67409i	−0.557587	−	0.557587i	0.371033	−	0.928620i	$-0.379004\pi$
$23$	−2.67409	−	2.67409i	−0.557587	−	0.557587i	−0.928620	+	0.371033i	$0.879004\pi$
$24$		0			0
$25$	−2.83139	−	4.12107i	−0.566278	−	0.824215i
$26$	−1.89002	+	1.37318i	−0.370664	+	0.269303i
$27$		0			0
$28$	−0.496469	−	0.974375i	−0.0938238	−	0.184139i
$29$	1.72903	−	1.25621i	0.321072	−	0.233272i	−0.415561	−	0.909565i	$-0.636415\pi$
$29$	1.72903	−	1.25621i	0.321072	−	0.233272i	0.736633	+	0.676293i	$0.236415\pi$
$30$		0			0
$31$	−0.615977	−	1.89578i	−0.110633	−	0.340493i	0.880378	−	0.474272i	$-0.157289\pi$
$31$	−0.615977	−	1.89578i	−0.110633	−	0.340493i	−0.991011	+	0.133779i	$0.957289\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			3.33290i			0.571588i
$35$	−1.46323	+	1.95918i	−0.247331	+	0.331162i
$36$		0			0
$37$	0.392539	−	2.47839i	0.0645330	−	0.407446i	−0.934183	−	0.356793i	$-0.883870\pi$
$37$	0.392539	−	2.47839i	0.0645330	−	0.407446i	0.998716	−	0.0506522i	$-0.0161300\pi$
$38$	−4.46629	+	2.27569i	−0.724528	+	0.369166i
$39$		0			0
$40$	0.718926	−	2.11734i	0.113672	−	0.334781i
$41$	−3.67243	+	5.05467i	−0.573537	+	0.789406i	−0.992968	−	0.118381i	$-0.962230\pi$
$41$	−3.67243	+	5.05467i	−0.573537	+	0.789406i	0.419431	+	0.907787i	$0.362230\pi$
$42$		0			0
$43$	0.876728	−	0.876728i	0.133700	−	0.133700i	−0.637090	−	0.770790i	$-0.719862\pi$
$43$	0.876728	−	0.876728i	0.133700	−	0.133700i	0.770790	+	0.637090i	$0.219862\pi$
$44$	2.13200	+	2.54059i	0.321411	+	0.383008i
$45$		0			0
$46$	−3.59664	+	1.16862i	−0.530296	+	0.172304i
$47$	−4.68990	+	0.742808i	−0.684093	+	0.108350i	−0.488801	−	0.872395i	$-0.662566\pi$
$47$	−4.68990	+	0.742808i	−0.684093	+	0.108350i	−0.195292	+	0.980745i	$0.562566\pi$
$48$		0			0
$49$	−5.52004	−	1.79357i	−0.788577	−	0.256224i
$50$	−4.95733	+	0.651858i	−0.701072	+	0.0921866i
$51$		0			0
$52$	0.365462	+	2.30744i	0.0506805	+	0.319984i
$53$	−3.40646	+	6.68555i	−0.467913	+	0.918331i	0.529627	+	0.848231i	$0.322332\pi$
$53$	−3.40646	+	6.68555i	−0.467913	+	0.918331i	−0.997540	+	0.0701006i	$0.977668\pi$
$54$		0			0
$55$	2.98707	−	6.78803i	0.402777	−	0.915298i
$56$	−1.09357			−0.146134
$57$		0			0
$58$	−0.334331	−	2.11088i	−0.0438998	−	0.277172i
$59$	−0.531320	−	0.731299i	−0.0691720	−	0.0952071i	0.773029	−	0.634370i	$-0.218741\pi$
$59$	−0.531320	−	0.731299i	−0.0691720	−	0.0952071i	−0.842201	+	0.539163i	$0.818741\pi$
$60$		0			0
$61$	6.76905	+	2.19940i	0.866689	+	0.281604i	0.708419	−	0.705792i	$-0.249409\pi$
$61$	6.76905	+	2.19940i	0.866689	+	0.281604i	0.158269	+	0.987396i	$0.449409\pi$
$62$	−1.96880	−	0.311828i	−0.250038	−	0.0396022i
$63$		0			0
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	4.26629	−	3.01462i	0.529168	−	0.373917i
$66$		0			0
$67$	0.578715	−	0.578715i	0.0707013	−	0.0707013i	−0.670872	−	0.741573i	$-0.734080\pi$
$67$	0.578715	−	0.578715i	0.0707013	−	0.0707013i	0.741573	+	0.670872i	$0.234080\pi$
$68$	2.96964	+	1.51311i	0.360121	+	0.183491i
$69$		0			0
$70$	1.08135	+	2.19320i	0.129246	+	0.262137i
$71$	−5.17298	+	15.9208i	−0.613920	+	1.88945i	−0.197411	+	0.980321i	$0.563253\pi$
$71$	−5.17298	+	15.9208i	−0.613920	+	1.88945i	−0.416509	+	0.909131i	$0.636747\pi$
$72$		0			0
$73$	−0.870026	+	5.49313i	−0.101829	+	0.642922i	0.882997	+	0.469378i	$0.155522\pi$
$73$	−0.870026	+	5.49313i	−0.101829	+	0.642922i	−0.984826	+	0.173544i	$0.944478\pi$
$74$	−2.03006	−	1.47492i	−0.235989	−	0.171456i
$75$		0			0
$76$			5.01264i			0.574989i
$77$	−3.61316	−	0.315947i	−0.411758	−	0.0360055i
$78$		0			0
$79$	1.22478	+	3.76949i	0.137799	+	0.424101i	0.996015	−	0.0891877i	$-0.0284271\pi$
$79$	1.22478	+	3.76949i	0.137799	+	0.424101i	−0.858216	+	0.513288i	$0.828427\pi$
$80$	−1.56018	−	1.60182i	−0.174434	−	0.179089i
$81$		0			0
$82$	2.83649	+	5.56693i	0.313238	+	0.614764i
$83$	−5.34777	−	10.4956i	−0.586994	−	1.15204i	−0.973272	−	0.229657i	$-0.926239\pi$
$83$	−5.34777	−	10.4956i	−0.586994	−	1.15204i	0.386278	−	0.922382i	$-0.373761\pi$
$84$		0			0
$85$	0.0981327	−	7.45195i	0.0106440	−	0.808277i
$86$	−0.383144	−	1.17920i	−0.0413155	−	0.127156i
$87$		0			0
$88$	3.23159	−	0.746223i	0.344488	−	0.0795477i
$89$			2.76909i			0.293523i	0.989172	+	0.146761i	$0.0468850\pi$
$89$			2.76909i			0.293523i	−0.989172	+	0.146761i	$0.953115\pi$
$90$		0			0
$91$	−2.06687	−	1.50167i	−0.216666	−	0.157417i
$92$	−0.591594	+	3.73518i	−0.0616779	+	0.389419i
$93$		0			0
$94$	−1.46733	+	4.51596i	−0.151343	+	0.465786i
$95$	10.0531	−	4.95665i	1.03142	−	0.508542i
$96$		0			0
$97$	12.0797	+	6.15492i	1.22651	+	0.624938i	0.942604	−	0.333914i	$-0.108370\pi$
$97$	12.0797	+	6.15492i	1.22651	+	0.624938i	0.283906	+	0.958852i	$0.408370\pi$
$98$	−4.10413	+	4.10413i	−0.414580	+	0.414580i
$99$		0			0
$100$	−1.66977	+	4.71295i	−0.166977	+	0.471295i
$101$	10.8280	−	3.51822i	1.07742	−	0.350076i	0.284048	−	0.958810i	$-0.408322\pi$
$101$	10.8280	−	3.51822i	1.07742	−	0.350076i	0.793374	+	0.608734i	$0.208322\pi$
$102$		0			0
$103$	9.42509	+	1.49279i	0.928681	+	0.147089i	0.602409	−	0.798187i	$-0.294207\pi$
$103$	9.42509	+	1.49279i	0.928681	+	0.147089i	0.326272	+	0.945276i	$0.394207\pi$
$104$	2.22186	+	0.721925i	0.217871	+	0.0707906i
$105$		0			0
$106$	4.41037	+	6.07036i	0.428373	+	0.589605i
$107$	−1.31509	−	8.30313i	−0.127134	−	0.802694i	−0.966035	−	0.258410i	$-0.916801\pi$
$107$	−1.31509	−	8.30313i	−0.127134	−	0.802694i	0.838901	−	0.544284i	$-0.183199\pi$
$108$		0			0
$109$	−18.5282			−1.77468			−0.887339	−	0.461117i	$-0.847449\pi$
$109$	−18.5282			−1.77468			−0.887339	+	0.461117i	$0.847449\pi$
$110$	−4.69208	−	5.74320i	−0.447372	−	0.547593i
$111$		0			0
$112$	−0.496469	+	0.974375i	−0.0469119	+	0.0920697i
$113$	−0.314977	−	1.98869i	−0.0296306	−	0.187080i	0.968434	−	0.249271i	$-0.0801911\pi$
$113$	−0.314977	−	1.98869i	−0.0296306	−	0.187080i	−0.998064	+	0.0621913i	$0.980191\pi$
$114$		0			0
$115$	8.07605	−	2.50699i	0.753096	−	0.233778i
$116$	−2.03259	−	0.660429i	−0.188721	−	0.0613193i
$117$		0			0
$118$	−0.892807	+	0.141407i	−0.0821895	+	0.0130175i
$119$	−3.46636	+	1.12629i	−0.317761	+	0.103247i
$120$		0			0
$121$	10.8928	−	1.53188i	0.990256	−	0.139262i
$122$	5.03276	−	5.03276i	0.455645	−	0.455645i
$123$		0			0
$124$	−1.17166	+	1.61265i	−0.105218	+	0.144820i
$125$	11.1032	−	1.31151i	0.993096	−	0.117305i
$126$		0			0
$127$	11.5818	−	5.90124i	1.02772	−	0.523651i	0.142977	−	0.989726i	$-0.454332\pi$
$127$	11.5818	−	5.90124i	1.02772	−	0.523651i	0.884745	+	0.466075i	$0.154332\pi$
$128$	0.156434	−	0.987688i	0.0138270	−	0.0873001i
$129$		0			0
$130$	−0.749188	−	5.16990i	−0.0657081	−	0.453430i
$131$			1.20664i			0.105424i	0.998610	+	0.0527122i	$0.0167866\pi$
$131$			1.20664i			0.105424i	−0.998610	+	0.0527122i	$0.983213\pi$
$132$		0			0
$133$	−3.87611	−	3.87611i	−0.336102	−	0.336102i
$134$	−0.252908	−	0.778370i	−0.0218479	−	0.0672409i
$135$		0			0
$136$	2.69637	−	1.95903i	0.231212	−	0.167985i
$137$	0.357788	+	0.702199i	0.0305679	+	0.0599929i	0.905785	−	0.423737i	$-0.139282\pi$
$137$	0.357788	+	0.702199i	0.0305679	+	0.0599929i	−0.875217	+	0.483730i	$0.839282\pi$
$138$		0			0
$139$	−9.52324	+	6.91904i	−0.807750	+	0.586865i	−0.913178	−	0.407562i	$-0.866379\pi$
$139$	−9.52324	+	6.91904i	−0.807750	+	0.586865i	0.105427	+	0.994427i	$0.466379\pi$
$140$	2.44508	+	0.0321985i	0.206647	+	0.00272127i
$141$		0			0
$142$	11.8371	+	11.8371i	0.993344	+	0.993344i
$143$	7.13248	+	3.02718i	0.596448	+	0.253145i
$144$		0			0
$145$	0.685369	+	4.72951i	0.0569168	+	0.392764i
$146$	4.49943	+	3.26903i	0.372375	+	0.270546i
$147$		0			0
$148$	−2.23579	+	1.13919i	−0.183781	+	0.0936411i
$149$	2.80098	−	8.62053i	0.229465	−	0.706221i	−0.768342	−	0.640039i	$-0.778918\pi$
$149$	2.80098	−	8.62053i	0.229465	−	0.706221i	0.997808	−	0.0661821i	$-0.0210818\pi$
$150$		0			0
$151$	7.70864	−	10.6100i	0.627320	−	0.863432i	−0.370540	−	0.928817i	$-0.620827\pi$
$151$	7.70864	−	10.6100i	0.627320	−	0.863432i	0.997860	+	0.0653842i	$0.0208273\pi$
$152$	4.46629	+	2.27569i	0.362264	+	0.184583i
$153$		0			0
$154$	−1.92185	+	3.07591i	−0.154867	+	0.247864i
$155$	4.39282	+	0.755177i	0.352839	+	0.0606572i
$156$		0			0
$157$	−16.9785	+	2.68914i	−1.35504	+	0.214616i	−0.791345	−	0.611370i	$-0.790619\pi$
$157$	−16.9785	+	2.68914i	−1.35504	+	0.214616i	−0.563690	+	0.825986i	$0.690619\pi$
$158$	3.91468	+	0.620024i	0.311435	+	0.0493265i
$159$		0			0
$160$	−2.13554	+	0.662921i	−0.168829	+	0.0524085i
$161$	−2.43083	−	3.34575i	−0.191576	−	0.263682i
$162$		0			0
$163$	8.03732	−	15.7741i	0.629532	−	1.23553i	−0.327310	−	0.944917i	$-0.606142\pi$
$163$	8.03732	−	15.7741i	0.629532	−	1.23553i	0.956842	−	0.290608i	$-0.0938577\pi$
$164$	6.24791			0.487880
$165$		0			0
$166$	−11.7795			−0.914264
$167$	5.81678	−	11.4161i	0.450116	−	0.883402i	−0.548759	−	0.835981i	$-0.684900\pi$
$167$	5.81678	−	11.4161i	0.450116	−	0.883402i	0.998875	−	0.0474215i	$-0.0151004\pi$
$168$		0			0
$169$	−4.43318	−	6.10175i	−0.341014	−	0.469365i
$170$	−6.59518	−	3.47055i	−0.505827	−	0.266179i
$171$		0			0
$172$	−1.22462	−	0.193960i	−0.0933760	−	0.0147893i
$173$	−1.94142	+	0.307491i	−0.147604	+	0.0233781i	−0.229799	−	0.973238i	$-0.573807\pi$
$173$	−1.94142	+	0.307491i	−0.147604	+	0.0233781i	0.0821952	+	0.996616i	$0.473807\pi$
$174$		0			0
$175$	−2.35319	−	4.93555i	−0.177885	−	0.373093i
$176$	0.802220	−	3.21814i	0.0604696	−	0.242577i
$177$		0			0
$178$	2.46728	+	1.25714i	0.184930	+	0.0942266i
$179$	−12.0420	+	16.5744i	−0.900061	+	1.23883i	0.0703878	+	0.997520i	$0.477576\pi$
$179$	−12.0420	+	16.5744i	−0.900061	+	1.23883i	−0.970449	+	0.241308i	$0.922424\pi$
$180$		0			0
$181$	−7.71475	+	23.7436i	−0.573433	+	1.76485i	0.0680210	+	0.997684i	$0.478331\pi$
$181$	−7.71475	+	23.7436i	−0.573433	+	1.76485i	−0.641454	+	0.767161i	$0.721669\pi$
$182$	−2.27633	+	1.15985i	−0.168733	+	0.0859738i
$183$		0			0
$184$	3.05949	+	2.22285i	0.225548	+	0.163871i
$185$	4.49552	+	3.35751i	0.330518	+	0.246849i
$186$		0			0
$187$	9.47486	−	5.69365i	0.692870	−	0.416361i
$188$	3.35760	+	3.35760i	0.244878	+	0.244878i
$189$		0			0
$190$	0.147590	−	11.2076i	0.0107073	−	0.813087i
$191$	13.6740	−	9.93478i	0.989419	−	0.718855i	0.0296254	−	0.999561i	$-0.490569\pi$
$191$	13.6740	−	9.93478i	0.989419	−	0.718855i	0.959794	+	0.280706i	$0.0905686\pi$
$192$		0			0
$193$	−1.88940	−	3.70815i	−0.136002	−	0.266918i	0.812954	−	0.582328i	$-0.197858\pi$
$193$	−1.88940	−	3.70815i	−0.136002	−	0.266918i	−0.948956	+	0.315410i	$0.897858\pi$
$194$	10.9682	−	7.96883i	0.787468	−	0.572129i
$195$		0			0
$196$	1.79357	+	5.52004i	0.128112	+	0.394289i
$197$	−16.2104	−	16.2104i	−1.15494	−	1.15494i	−0.985548	−	0.169397i	$-0.945818\pi$
$197$	−16.2104	−	16.2104i	−1.15494	−	1.15494i	−0.169397	−	0.985548i	$-0.554182\pi$
$198$		0			0
$199$			3.84089i			0.272274i	0.990690	+	0.136137i	$0.0434687\pi$
$199$			3.84089i			0.272274i	−0.990690	+	0.136137i	$0.956531\pi$
$200$	3.44121	+	3.62741i	0.243330	+	0.256497i
$201$		0			0
$202$	1.78104	−	11.2450i	0.125313	−	0.791197i
$203$	2.08243	−	1.06105i	0.146158	−	0.0744711i
$204$		0			0
$205$	−6.17813	−	12.5305i	−0.431499	−	0.875166i
$206$	5.60898	−	7.72010i	0.390796	−	0.537885i
$207$		0			0
$208$	1.65194	−	1.65194i	0.114542	−	0.114542i
$209$	14.0992	+	8.80930i	0.975264	+	0.609352i
$210$		0			0
$211$	−20.0607	+	6.51811i	−1.38103	+	0.448725i	−0.903009	−	0.429622i	$-0.858647\pi$
$211$	−20.0607	+	6.51811i	−1.38103	+	0.448725i	−0.478024	+	0.878347i	$0.658647\pi$
$212$	7.41099	−	1.17379i	0.508989	−	0.0806160i
$213$		0			0
$214$	−7.99518	−	2.59779i	−0.546540	−	0.177581i
$215$	0.821942	+	2.64782i	0.0560560	+	0.180580i
$216$		0			0
$217$	−0.341004	−	2.15302i	−0.0231489	−	0.146156i
$218$	−8.41162	+	16.5087i	−0.569707	+	1.11811i
$219$		0			0
$220$	−7.24739	+	1.57331i	−0.488619	+	0.106073i
$221$	7.78632			0.523765
$222$		0			0
$223$	−3.99212	−	25.2053i	−0.267332	−	1.68787i	−0.646796	−	0.762663i	$-0.723892\pi$
$223$	−3.99212	−	25.2053i	−0.267332	−	1.68787i	0.379464	−	0.925207i	$-0.376108\pi$
$224$	0.642782	+	0.884714i	0.0429477	+	0.0591124i
$225$		0			0
$226$	−1.91493	−	0.622199i	−0.127379	−	0.0413881i
$227$	−6.73403	−	1.06657i	−0.446953	−	0.0707904i	−0.0710991	−	0.997469i	$-0.522651\pi$
$227$	−6.73403	−	1.06657i	−0.446953	−	0.0707904i	−0.375854	+	0.926679i	$0.622651\pi$
$228$		0			0
$229$	−17.1075	+	5.55855i	−1.13049	+	0.367320i	−0.813763	−	0.581196i	$-0.802585\pi$
$229$	−17.1075	+	5.55855i	−1.13049	+	0.367320i	−0.316730	+	0.948516i	$0.602585\pi$
$230$	1.43271	−	8.33397i	0.0944699	−	0.549525i
$231$		0			0
$232$	−1.51122	+	1.51122i	−0.0992167	+	0.0992167i
$233$	17.6450	+	8.99060i	1.15597	+	0.588994i	0.923495	−	0.383610i	$-0.125319\pi$
$233$	17.6450	+	8.99060i	1.15597	+	0.588994i	0.232470	+	0.972604i	$0.425319\pi$
$234$		0			0
$235$	3.41372	−	10.0539i	0.222687	−	0.655846i
$236$	−0.279331	+	0.859694i	−0.0181829	+	0.0559613i
$237$		0			0
$238$	−0.570164	+	3.59988i	−0.0369583	+	0.233345i
$239$	0.468024	+	0.340039i	0.0302740	+	0.0219953i	0.602819	−	0.797878i	$-0.294044\pi$
$239$	0.468024	+	0.340039i	0.0302740	+	0.0219953i	−0.572545	+	0.819873i	$0.694044\pi$
$240$		0			0
$241$			29.7695i			1.91763i	0.284040	+	0.958813i	$0.408325\pi$
$241$			29.7695i			1.91763i	−0.284040	+	0.958813i	$0.591675\pi$
$242$	3.58032	−	10.4010i	0.230151	−	0.668603i
$243$		0			0
$244$	−2.19940	−	6.76905i	−0.140802	−	0.433344i
$245$	9.29715	−	9.05547i	0.593973	−	0.578533i
$246$		0			0
$247$	5.31646	+	10.4341i	0.338279	+	0.663909i
$248$	0.904960	+	1.77608i	0.0574650	+	0.112781i
$249$		0			0
$250$	3.87216	−	10.4884i	0.244897	−	0.663344i
$251$	−3.62089	−	11.1439i	−0.228548	−	0.703400i	−0.997912	−	0.0645885i	$-0.979427\pi$
$251$	−3.62089	−	11.1439i	−0.228548	−	0.703400i	0.769364	−	0.638811i	$-0.220573\pi$
$252$		0			0
$253$	9.46639	+	8.22826i	0.595147	+	0.517306i
$254$		−	12.9986i		−	0.815605i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.73653	+	10.9640i	−0.108322	+	0.683918i	0.872441	+	0.488719i	$0.162536\pi$
$257$	−1.73653	+	10.9640i	−0.108322	+	0.683918i	−0.980764	+	0.195200i	$0.937464\pi$
$258$		0			0
$259$	0.847965	−	2.60977i	0.0526900	−	0.162163i
$260$	−4.94654	−	1.67955i	−0.306771	−	0.104161i
$261$		0			0
$262$	1.07512	+	0.547802i	0.0664213	+	0.0338433i
$263$	5.16707	−	5.16707i	0.318615	−	0.318615i	−0.529620	−	0.848235i	$-0.677665\pi$
$263$	5.16707	−	5.16707i	0.318615	−	0.318615i	0.848235	+	0.529620i	$0.177665\pi$
$264$		0			0
$265$	−9.68230	−	13.7024i	−0.594779	−	0.841732i
$266$	−5.21336	+	1.69392i	−0.319652	+	0.103861i
$267$		0			0
$268$	−0.808351	−	0.128030i	−0.0493779	−	0.00782069i
$269$	−16.9878	−	5.51966i	−1.03576	−	0.336539i	−0.258696	−	0.965959i	$-0.583293\pi$
$269$	−16.9878	−	5.51966i	−1.03576	−	0.336539i	−0.777066	+	0.629419i	$0.783293\pi$
$270$		0			0
$271$	8.01595	+	11.0330i	0.486934	+	0.670208i	0.979819	−	0.199887i	$-0.0640575\pi$
$271$	8.01595	+	11.0330i	0.486934	+	0.670208i	−0.492885	+	0.870095i	$0.664058\pi$
$272$	−0.521381	−	3.29187i	−0.0316133	−	0.199599i
$273$		0			0
$274$	0.788097			0.0476107
$275$	10.3218	+	12.9792i	0.622428	+	0.782677i
$276$		0			0
$277$	0.136060	−	0.267032i	0.00817504	−	0.0160444i	−0.886883	−	0.461994i	$-0.847134\pi$
$277$	0.136060	−	0.267032i	0.00817504	−	0.0160444i	0.895058	+	0.445950i	$0.147134\pi$
$278$	1.84145	+	11.6264i	0.110443	+	0.697308i
$279$		0			0
$280$	1.13873	−	2.16396i	0.0680522	−	0.129321i
$281$	13.9727	+	4.54000i	0.833540	+	0.270834i	0.694536	−	0.719458i	$-0.255610\pi$
$281$	13.9727	+	4.54000i	0.833540	+	0.270834i	0.139004	+	0.990292i	$0.455610\pi$
$282$		0			0
$283$	31.3103	−	4.95906i	1.86120	−	0.294786i	0.878189	−	0.478314i	$-0.158752\pi$
$283$	31.3103	−	4.95906i	1.86120	−	0.294786i	0.983014	+	0.183528i	$0.0587519\pi$
$284$	15.9208	−	5.17298i	0.944726	−	0.306960i
$285$		0			0
$286$	5.93531	−	4.98077i	0.350962	−	0.294519i
$287$	−4.83131	+	4.83131i	−0.285183	+	0.285183i
$288$		0			0
$289$	−3.46309	+	4.76654i	−0.203711	+	0.280385i
$290$	4.52517	+	1.53648i	0.265727	+	0.0902254i
$291$		0			0
$292$	4.95542	−	2.52491i	0.289994	−	0.147759i
$293$	3.37389	−	21.3019i	0.197104	−	1.24447i	−0.668489	−	0.743722i	$-0.733059\pi$
$293$	3.37389	−	21.3019i	0.197104	−	1.24447i	0.865594	−	0.500747i	$-0.166941\pi$
$294$		0			0
$295$	2.00037	−	0.289880i	0.116466	−	0.0168775i
$296$			2.50929i			0.145849i
$297$		0			0
$298$	−6.40933	−	6.40933i	−0.371282	−	0.371282i
$299$	2.73013	+	8.40248i	0.157887	+	0.485928i
$300$		0			0
$301$	1.09694	−	0.796973i	0.0632265	−	0.0459367i
$302$	−5.95396	−	11.6853i	−0.342612	−	0.672414i
$303$		0			0
$304$	4.05531	−	2.94635i	0.232588	−	0.168985i
$305$	−11.4008	+	11.1044i	−0.652809	+	0.635839i
$306$		0			0
$307$	14.2674	+	14.2674i	0.814282	+	0.814282i	0.985273	−	0.170991i	$-0.0546968\pi$
$307$	14.2674	+	14.2674i	0.814282	+	0.814282i	−0.170991	+	0.985273i	$0.554697\pi$
$308$	1.86816	+	3.10882i	0.106448	+	0.177141i
$309$		0			0
$310$	2.66716	−	3.57118i	0.151485	−	0.202830i
$311$	9.40697	+	6.83456i	0.533420	+	0.387552i	0.821636	−	0.570013i	$-0.193062\pi$
$311$	9.40697	+	6.83456i	0.533420	+	0.387552i	−0.288215	+	0.957566i	$0.593062\pi$
$312$		0			0
$313$	−26.1779	+	13.3383i	−1.47966	+	0.753926i	−0.992826	−	0.119566i	$-0.961850\pi$
$313$	−26.1779	+	13.3383i	−1.47966	+	0.753926i	−0.486838	+	0.873492i	$0.661850\pi$
$314$	−5.31206	+	16.3488i	−0.299777	+	0.922618i
$315$		0			0
$316$	2.32967	−	3.20652i	0.131054	−	0.180381i
$317$	−9.25608	−	4.71621i	−0.519873	−	0.264889i	0.174305	−	0.984692i	$-0.444232\pi$
$317$	−9.25608	−	4.71621i	−0.519873	−	0.264889i	−0.694178	+	0.719803i	$0.744232\pi$
$318$		0			0
$319$	−5.42972	+	4.55649i	−0.304006	+	0.255115i
$320$	−0.378849	+	2.20374i	−0.0211783	+	0.123193i
$321$		0			0
$322$	−4.08466	+	0.646947i	−0.227629	+	0.0360529i
$323$	16.5009	+	2.61349i	0.918137	+	0.145419i
$324$		0			0
$325$	1.52287	+	11.5813i	0.0844736	+	0.642415i
$326$	−10.4060	−	14.3226i	−0.576334	−	0.793256i
$327$		0			0
$328$	2.83649	−	5.56693i	0.156619	−	0.307382i
$329$	−5.19265			−0.286280
$330$		0			0
$331$	−1.46257			−0.0803901			−0.0401951	−	0.999192i	$-0.512798\pi$
$331$	−1.46257			−0.0803901			−0.0401951	+	0.999192i	$0.512798\pi$
$332$	−5.34777	+	10.4956i	−0.293497	+	0.576020i
$333$		0			0
$334$	−7.53103	−	10.3656i	−0.412080	−	0.567179i
$335$	0.542552	+	1.74778i	0.0296428	+	0.0954917i
$336$		0			0
$337$	19.1441	+	3.03213i	1.04285	+	0.165171i	0.654282	−	0.756251i	$-0.272971\pi$
$337$	19.1441	+	3.03213i	1.04285	+	0.165171i	0.388565	+	0.921421i	$0.372971\pi$
$338$	−7.44932	+	1.17986i	−0.405190	+	0.0641757i
$339$		0			0
$340$	−6.08643	+	4.30075i	−0.330083	+	0.233241i
$341$	2.47687	+	6.12967i	0.134130	+	0.331940i
$342$		0			0
$343$	−12.4760	−	6.35684i	−0.673641	−	0.343237i
$344$	−0.728783	+	1.00308i	−0.0392934	+	0.0540827i
$345$		0			0
$346$	−0.607411	+	1.86942i	−0.0326546	+	0.100501i
$347$	31.8605	−	16.2337i	1.71036	−	0.871473i	0.727741	−	0.685853i	$-0.240571\pi$
$347$	31.8605	−	16.2337i	1.71036	−	0.871473i	0.982622	−	0.185620i	$-0.0594295\pi$
$348$		0			0
$349$	−9.79945	−	7.11972i	−0.524553	−	0.381110i	0.293763	−	0.955878i	$-0.405092\pi$
$349$	−9.79945	−	7.11972i	−0.524553	−	0.381110i	−0.818316	+	0.574768i	$0.805092\pi$
$350$	−5.46593	−	0.143984i	−0.292166	−	0.00769626i
$351$		0			0
$352$	−2.50319	−	2.17579i	−0.133420	−	0.115970i
$353$	−23.1648	−	23.1648i	−1.23294	−	1.23294i	−0.962830	−	0.270108i	$-0.912941\pi$
$353$	−23.1648	−	23.1648i	−1.23294	−	1.23294i	−0.270108	−	0.962830i	$-0.587059\pi$
$354$		0			0
$355$	−26.1176	−	26.8147i	−1.38618	−	1.42318i
$356$	2.24024	−	1.62763i	0.118732	−	0.0862642i
$357$		0			0
$358$	9.30093	+	18.2541i	0.491570	+	0.964760i
$359$	1.78802	−	1.29907i	0.0943681	−	0.0685624i	−0.539601	−	0.841921i	$-0.681425\pi$
$359$	1.78802	−	1.29907i	0.0943681	−	0.0685624i	0.633969	+	0.773359i	$0.281425\pi$
$360$		0			0
$361$	1.89321	+	5.82669i	0.0996424	+	0.306668i
$362$	17.6532	+	17.6532i	0.927834	+	0.927834i
$363$		0			0
$364$			2.55479i			0.133907i
$365$	−9.96390	−	7.44161i	−0.521534	−	0.389512i
$366$		0			0
$367$	−3.40825	+	21.5188i	−0.177909	+	1.12327i	0.723506	+	0.690318i	$0.242529\pi$
$367$	−3.40825	+	21.5188i	−0.177909	+	1.12327i	−0.901415	+	0.432955i	$0.857471\pi$
$368$	3.36955	−	1.71687i	0.175650	−	0.0894981i
$369$		0			0
$370$	5.03249	−	2.48126i	0.261627	−	0.128995i
$371$	−4.82303	+	6.63834i	−0.250399	+	0.344645i
$372$		0			0
$373$	−5.83919	+	5.83919i	−0.302342	+	0.302342i	−0.841929	−	0.539588i	$-0.818580\pi$
$373$	−5.83919	+	5.83919i	−0.302342	+	0.302342i	0.539588	+	0.841929i	$0.318580\pi$
$374$	−0.771582	−	11.0270i	−0.0398976	−	0.570194i
$375$		0			0
$376$	4.51596	−	1.46733i	0.232893	−	0.0756715i
$377$	−4.93144	+	0.781063i	−0.253982	+	0.0402268i
$378$		0			0
$379$	19.7939	+	6.43143i	1.01675	+	0.330361i	0.769537	−	0.638602i	$-0.220487\pi$
$379$	19.7939	+	6.43143i	1.01675	+	0.330361i	0.247208	+	0.968962i	$0.420487\pi$
$380$	−9.91907	−	5.21966i	−0.508837	−	0.267763i
$381$		0			0
$382$	−2.64406	−	16.6940i	−0.135282	−	0.854137i
$383$	10.3490	−	20.3110i	0.528807	−	1.03784i	−0.459898	−	0.887972i	$-0.652114\pi$
$383$	10.3490	−	20.3110i	0.528807	−	1.03784i	0.988706	−	0.149871i	$-0.0478858\pi$
$384$		0			0
$385$	4.38758	−	6.82077i	0.223612	−	0.347619i
$386$	−4.16175			−0.211828
$387$		0			0
$388$	−2.12084	−	13.3905i	−0.107669	−	0.679798i
$389$	−14.8071	−	20.3802i	−0.750750	−	1.03332i	−0.997928	−	0.0643483i	$-0.979503\pi$
$389$	−14.8071	−	20.3802i	−0.750750	−	1.03332i	0.247178	−	0.968970i	$-0.420497\pi$
$390$		0			0
$391$	11.9873	+	3.89490i	0.606222	+	0.196973i
$392$	5.73265	+	0.907963i	0.289543	+	0.0458591i
$393$		0			0
$394$	−21.8030	+	7.08421i	−1.09842	+	0.356898i
$395$	−8.73447	−	1.50156i	−0.439479	−	0.0755516i
$396$		0			0
$397$	−16.8124	+	16.8124i	−0.843788	+	0.843788i	−0.989349	−	0.145561i	$-0.953501\pi$
$397$	−16.8124	+	16.8124i	−0.843788	+	0.843788i	0.145561	+	0.989349i	$0.453501\pi$
$398$	3.42226	+	1.74373i	0.171542	+	0.0874052i
$399$		0			0
$400$	4.79432	−	1.41933i	0.239716	−	0.0709664i
$401$	−0.686588	+	2.11310i	−0.0342865	+	0.105523i	−0.966735	−	0.255780i	$-0.917668\pi$
$401$	−0.686588	+	2.11310i	−0.0342865	+	0.105523i	0.932449	+	0.361303i	$0.117668\pi$
$402$		0			0
$403$	−0.728492	+	4.59952i	−0.0362888	+	0.229118i
$404$	−9.21082	−	6.69205i	−0.458255	−	0.332942i
$405$		0			0
$406$		−	2.33716i		−	0.115991i
$407$	−0.724970	+	8.29073i	−0.0359354	+	0.410956i
$408$		0			0
$409$	5.22226	+	16.0725i	0.258224	+	0.794732i	0.993177	+	0.116614i	$0.0372042\pi$
$409$	5.22226	+	16.0725i	0.258224	+	0.794732i	−0.734953	+	0.678118i	$0.762796\pi$
$410$	−13.9695	−	0.183961i	−0.689906	−	0.00908519i
$411$		0			0
$412$	−4.33224	−	8.50249i	−0.213434	−	0.418888i
$413$	−0.448776	−	0.880772i	−0.0220828	−	0.0433400i
$414$		0			0
$415$	26.3374	+	0.346830i	1.29285	+	0.0170252i
$416$	−0.721925	−	2.22186i	−0.0353953	−	0.108935i
$417$		0			0
$418$	14.2501	−	8.56317i	0.696993	−	0.418838i
$419$		−	2.38744i		−	0.116634i	−0.998298	−	0.0583169i	$-0.981427\pi$
$419$		−	2.38744i		−	0.116634i	0.998298	−	0.0583169i	$-0.0185734\pi$
$420$		0			0
$421$	−20.8060	−	15.1165i	−1.01402	−	0.736732i	−0.0489752	−	0.998800i	$-0.515596\pi$
$421$	−20.8060	−	15.1165i	−1.01402	−	0.736732i	−0.965049	+	0.262068i	$0.915596\pi$
$422$	−3.29968	+	20.8333i	−0.160626	+	1.01415i
$423$		0			0
$424$	2.31867	−	7.13613i	0.112605	−	0.346561i
$425$	14.6438	+	7.95390i	0.710329	+	0.385821i
$426$		0			0
$427$	6.93502	+	3.53357i	0.335609	+	0.171001i
$428$	−5.94439	+	5.94439i	−0.287333	+	0.287333i
$429$		0			0
$430$	2.73237	+	0.469727i	0.131767	+	0.0226523i
$431$	−16.8034	+	5.45976i	−0.809393	+	0.262988i	−0.684341	−	0.729163i	$-0.739910\pi$
$431$	−16.8034	+	5.45976i	−0.809393	+	0.262988i	−0.125052	+	0.992150i	$0.539910\pi$
$432$		0			0
$433$	24.4394	+	3.87082i	1.17448	+	0.186020i	0.713022	−	0.701142i	$-0.247326\pi$
$433$	24.4394	+	3.87082i	1.17448	+	0.186020i	0.461459	+	0.887161i	$0.347326\pi$
$434$	−2.07316	−	0.673612i	−0.0995151	−	0.0323344i
$435$		0			0
$436$	10.8906	+	14.9896i	0.521565	+	0.717873i
$437$	2.96545	+	18.7231i	0.141857	+	0.895647i
$438$		0			0
$439$	1.55255			0.0740992			0.0370496	−	0.999313i	$-0.488204\pi$
$439$	1.55255			0.0740992			0.0370496	+	0.999313i	$0.488204\pi$
$440$	−1.88842	+	7.17174i	−0.0900267	+	0.341899i
$441$		0			0
$442$	3.53492	−	6.93766i	0.168139	−	0.329991i
$443$	−2.07371	−	13.0929i	−0.0985252	−	0.622063i	−0.986699	−	0.162556i	$-0.948026\pi$
$443$	−2.07371	−	13.0929i	−0.0985252	−	0.622063i	0.888174	−	0.459507i	$-0.151974\pi$
$444$		0			0
$445$	−5.47950	−	2.88345i	−0.259753	−	0.136689i
$446$	−24.2704	−	7.88594i	−1.14924	−	0.373410i
$447$		0			0
$448$	1.08010	−	0.171071i	0.0510300	−	0.00808237i
$449$	−32.3129	+	10.4991i	−1.52494	+	0.495483i	−0.947174	−	0.320719i	$-0.896076\pi$
$449$	−32.3129	+	10.4991i	−1.52494	+	0.495483i	−0.577766	+	0.816202i	$0.696076\pi$
$450$		0			0
$451$	10.9802	−	17.5737i	0.517037	−	0.827514i
$452$	−1.42374	+	1.42374i	−0.0669673	+	0.0669673i
$453$		0			0
$454$	−4.00750	+	5.51585i	−0.188081	+	0.258872i
$455$	5.12374	−	2.52625i	0.240205	−	0.118433i
$456$		0			0
$457$	7.51784	−	3.83053i	0.351670	−	0.179185i	−0.269228	−	0.963077i	$-0.586768\pi$
$457$	7.51784	−	3.83053i	0.351670	−	0.179185i	0.620897	+	0.783892i	$0.286768\pi$
$458$	−2.81392	+	17.7664i	−0.131486	+	0.830169i
$459$		0			0
$460$	−6.77518	−	5.06009i	−0.315895	−	0.235928i
$461$			22.5506i			1.05028i	0.851014	+	0.525142i	$0.175988\pi$
$461$			22.5506i			1.05028i	−0.851014	+	0.525142i	$0.824012\pi$
$462$		0			0
$463$	−4.94536	−	4.94536i	−0.229830	−	0.229830i	0.582792	−	0.812622i	$-0.301960\pi$
$463$	−4.94536	−	4.94536i	−0.229830	−	0.229830i	−0.812622	+	0.582792i	$0.801960\pi$
$464$	0.660429	+	2.03259i	0.0306596	+	0.0943607i
$465$		0			0
$466$	16.0214	−	11.6402i	0.742175	−	0.539222i
$467$	11.0991	+	21.7833i	0.513606	+	1.00801i	0.991563	+	0.129626i	$0.0413776\pi$
$467$	11.0991	+	21.7833i	0.513606	+	1.00801i	−0.477957	+	0.878383i	$0.658622\pi$
$468$		0			0
$469$	0.724073	−	0.526070i	0.0334346	−	0.0242917i
$470$	−7.40831	−	7.60603i	−0.341720	−	0.350840i
$471$		0			0
$472$	0.639179	+	0.639179i	0.0294206	+	0.0294206i
$473$	−2.69772	+	3.10365i	−0.124041	+	0.142706i
$474$		0			0
$475$	−0.659986	+	25.0545i	−0.0302822	+	1.14958i
$476$	2.94866	+	2.14233i	0.135152	+	0.0981935i
$477$		0			0
$478$	0.515456	−	0.262638i	0.0235764	−	0.0120128i
$479$	−7.00499	+	21.5591i	−0.320066	+	0.985062i	0.653553	+	0.756881i	$0.273278\pi$
$479$	−7.00499	+	21.5591i	−0.320066	+	0.985062i	−0.973619	+	0.228181i	$0.926722\pi$
$480$		0			0
$481$	−3.44571	+	4.74262i	−0.157111	+	0.216245i
$482$	26.5249	+	13.5151i	1.20817	+	0.615596i
$483$		0			0
$484$	−7.64195	−	7.91205i	−0.347361	−	0.359639i
$485$	−24.7580	+	17.4944i	−1.12421	+	0.794378i
$486$		0			0
$487$	−33.4504	+	5.29802i	−1.51578	+	0.240076i	−0.858203	−	0.513310i	$-0.828419\pi$
$487$	−33.4504	+	5.29802i	−1.51578	+	0.240076i	−0.657578	+	0.753387i	$0.728419\pi$
$488$	−7.02978	−	1.11341i	−0.318223	−	0.0504016i
$489$		0			0
$490$	−3.84767	−	12.3949i	−0.173820	−	0.559946i
$491$	−16.2581	−	22.3774i	−0.733718	−	1.00988i	−0.998956	−	0.0456935i	$-0.985450\pi$
$491$	−16.2581	−	22.3774i	−0.733718	−	1.00988i	0.265237	−	0.964183i	$-0.414550\pi$
$492$		0			0
$493$	−3.23380	+	6.34669i	−0.145643	+	0.285840i
$494$	11.7105			0.526881
$495$		0			0
$496$	1.99334			0.0895038
$497$	−8.31095	+	16.3112i	−0.372797	+	0.731655i
$498$		0			0
$499$	9.04686	+	12.4519i	0.404993	+	0.557425i	0.961988	−	0.273090i	$-0.0880458\pi$
$499$	9.04686	+	12.4519i	0.404993	+	0.557425i	−0.556995	+	0.830516i	$0.688046\pi$
$500$	−7.58730	−	8.21175i	−0.339314	−	0.367241i
$501$		0			0
$502$	−11.5732	−	1.83301i	−0.516536	−	0.0818113i
$503$	−18.1534	+	2.87522i	−0.809421	+	0.128200i	−0.547409	−	0.836865i	$-0.684386\pi$
$503$	−18.1534	+	2.87522i	−0.809421	+	0.128200i	−0.262011	+	0.965065i	$0.584386\pi$
$504$		0			0
$505$	−4.31327	+	25.0900i	−0.191938	+	1.11649i
$506$	11.6291	−	4.69906i	0.516976	−	0.208899i
$507$		0			0
$508$	−11.5818	−	5.90124i	−0.513861	−	0.261825i
$509$	−2.72418	+	3.74951i	−0.120747	+	0.166194i	−0.865112	−	0.501579i	$-0.832753\pi$
$509$	−2.72418	+	3.74951i	−0.120747	+	0.166194i	0.744364	+	0.667774i	$0.232753\pi$
$510$		0			0
$511$	−1.87943	+	5.78430i	−0.0831413	+	0.255882i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$		0			0
$514$	8.98066	+	6.52484i	0.396120	+	0.287798i
$515$	−12.7683	+	17.0960i	−0.562638	+	0.753341i
$516$		0			0
$517$	15.3448	−	3.54334i	0.674861	−	0.155836i
$518$	−1.94035	−	1.94035i	−0.0852542	−	0.0852542i
$519$		0			0
$520$	−3.74217	+	3.64489i	−0.164105	+	0.159839i
$521$	−19.0400	+	13.8333i	−0.834156	+	0.606050i	−0.920732	−	0.390196i	$-0.872407\pi$
$521$	−19.0400	+	13.8333i	−0.834156	+	0.606050i	0.0865764	+	0.996245i	$0.472407\pi$
$522$		0			0
$523$	14.5656	+	28.5865i	0.636907	+	1.25000i	0.953487	+	0.301435i	$0.0974657\pi$
$523$	14.5656	+	28.5865i	0.636907	+	1.25000i	−0.316579	+	0.948566i	$0.602534\pi$
$524$	0.976190	−	0.709244i	0.0426451	−	0.0309835i
$525$		0			0
$526$	−2.25809	−	6.94970i	−0.0984576	−	0.303021i
$527$	4.69775	+	4.69775i	0.204637	+	0.204637i
$528$		0			0
$529$		−	8.69847i		−	0.378195i
$530$	−16.6046	+	2.40623i	−0.721258	+	0.104520i
$531$		0			0
$532$	−0.857519	+	5.41416i	−0.0371782	+	0.234734i
$533$	13.0055	−	6.62661i	0.563329	−	0.287030i
$534$		0			0
$535$	17.7997	+	6.04374i	0.769550	+	0.261294i
$536$	−0.481059	+	0.662121i	−0.0207786	+	0.0285993i
$537$		0			0
$538$	−12.6303	+	12.6303i	−0.544532	+	0.544532i
$539$	18.6785	+	4.65617i	0.804538	+	0.200556i
$540$		0			0
$541$	−21.0951	+	6.85421i	−0.906949	+	0.294686i	−0.725102	−	0.688641i	$-0.758208\pi$
$541$	−21.0951	+	6.85421i	−0.906949	+	0.294686i	−0.181847	+	0.983327i	$0.558208\pi$
$542$	13.4696	−	2.13338i	0.578571	−	0.0916366i
$543$		0			0
$544$	−3.16978	−	1.02992i	−0.135903	−	0.0441576i
$545$	19.2934	−	36.6638i	0.826439	−	1.57050i
$546$		0			0
$547$	−3.06685	−	19.3633i	−0.131129	−	0.827915i	−0.962318	−	0.271926i	$-0.912339\pi$
$547$	−3.06685	−	19.3633i	−0.131129	−	0.827915i	0.831189	−	0.555989i	$-0.187661\pi$
$548$	0.357788	−	0.702199i	0.0152840	−	0.0299965i
$549$		0			0
$550$	16.2506	−	3.30434i	0.692927	−	0.140897i
$551$	−10.7130			−0.456388
$552$		0			0
$553$	0.678038	+	4.28096i	0.0288331	+	0.182045i
$554$	−0.176158	−	0.242460i	−0.00748423	−	0.0103012i
$555$		0			0
$556$	11.1952	+	3.63755i	0.474784	+	0.154267i
$557$	−24.2134	−	3.83502i	−1.02595	−	0.162495i	−0.379296	−	0.925276i	$-0.623834\pi$
$557$	−24.2134	−	3.83502i	−1.02595	−	0.162495i	−0.646657	+	0.762781i	$0.723834\pi$
$558$		0			0
$559$	−2.75484	+	0.895101i	−0.116517	+	0.0378587i
$560$	−1.41113	−	1.99703i	−0.0596312	−	0.0843901i
$561$		0			0
$562$	10.3886	−	10.3886i	0.438218	−	0.438218i
$563$	−32.4116	−	16.5145i	−1.36598	−	0.696004i	−0.391441	−	0.920203i	$-0.628023\pi$
$563$	−32.4116	−	16.5145i	−1.36598	−	0.696004i	−0.974543	+	0.224200i	$0.928023\pi$
$564$		0			0
$565$	4.26323	+	1.44754i	0.179355	+	0.0608985i
$566$	9.79602	−	30.1490i	0.411757	−	1.26726i
$567$		0			0
$568$	2.61873	−	16.5340i	0.109880	−	0.693752i
$569$	12.4610	+	9.05343i	0.522391	+	0.379540i	0.817504	−	0.575923i	$-0.195357\pi$
$569$	12.4610	+	9.05343i	0.522391	+	0.379540i	−0.295113	+	0.955462i	$0.595357\pi$
$570$		0			0
$571$			22.4382i			0.939010i	0.882930	+	0.469505i	$0.155568\pi$
$571$			22.4382i			0.939010i	−0.882930	+	0.469505i	$0.844432\pi$
$572$	−1.74333	−	7.54963i	−0.0728921	−	0.315666i
$573$		0			0
$574$	2.11136	+	6.49810i	0.0881264	+	0.271225i
$575$	−3.44873	+	18.5915i	−0.143822	+	0.775320i
$576$		0			0
$577$	12.2008	+	23.9453i	0.507924	+	0.996858i	0.992516	+	0.122117i	$0.0389683\pi$
$577$	12.2008	+	23.9453i	0.507924	+	0.996858i	−0.484591	+	0.874741i	$0.661032\pi$
$578$	2.67481	+	5.24960i	0.111257	+	0.218355i
$579$		0			0
$580$	3.42340	−	3.33441i	0.142149	−	0.138454i
$581$	−3.98064	−	12.2512i	−0.165145	−	0.508264i
$582$		0			0
$583$	9.72266	−	22.9080i	0.402671	−	0.948752i
$584$		−	5.56160i		−	0.230141i
$585$		0			0
$586$	−17.4484	−	12.6770i	−0.720787	−	0.523682i
$587$	−2.65963	+	16.7923i	−0.109775	+	0.693091i	0.870010	+	0.493035i	$0.164112\pi$
$587$	−2.65963	+	16.7923i	−0.109775	+	0.693091i	−0.979784	+	0.200056i	$0.935888\pi$
$588$		0			0
$589$	−3.08767	+	9.50288i	−0.127225	+	0.391559i
$590$	0.649863	−	1.91394i	0.0267544	−	0.0787958i
$591$		0			0
$592$	2.23579	+	1.13919i	0.0918905	+	0.0468205i
$593$	9.90575	−	9.90575i	0.406781	−	0.406781i	−0.473834	−	0.880614i	$-0.657130\pi$
$593$	9.90575	−	9.90575i	0.406781	−	0.406781i	0.880614	+	0.473834i	$0.157130\pi$
$594$		0			0
$595$	1.38081	−	8.03208i	0.0566076	−	0.329283i
$596$	−8.62053	+	2.80098i	−0.353111	+	0.114733i
$597$		0			0
$598$	8.72611	+	1.38208i	0.356837	+	0.0565175i
$599$	−12.7899	−	4.15568i	−0.522580	−	0.169796i	0.0358361	−	0.999358i	$-0.488591\pi$
$599$	−12.7899	−	4.15568i	−0.522580	−	0.169796i	−0.558416	+	0.829561i	$0.688591\pi$
$600$		0			0
$601$	3.15713	+	4.34542i	0.128782	+	0.177253i	0.868539	−	0.495621i	$-0.165059\pi$
$601$	3.15713	+	4.34542i	0.128782	+	0.177253i	−0.739757	+	0.672874i	$0.765059\pi$
$602$	−0.212108	−	1.33920i	−0.00864488	−	0.0545816i
$603$		0			0
$604$	−13.1147			−0.533631
$605$	−8.31138	+	23.1500i	−0.337906	+	0.941180i
$606$		0			0
$607$	10.6923	−	20.9848i	0.433987	−	0.851747i	−0.565646	−	0.824648i	$-0.691373\pi$
$607$	10.6923	−	20.9848i	0.433987	−	0.851747i	0.999633	−	0.0270990i	$-0.00862694\pi$
$608$	−0.784149	−	4.95092i	−0.0318015	−	0.200787i
$609$		0			0
$610$	4.71827	+	15.1995i	0.191037	+	0.615410i
$611$	10.5502	+	3.42796i	0.426815	+	0.138681i
$612$		0			0
$613$	−12.1333	+	1.92172i	−0.490058	+	0.0776176i	−0.396573	−	0.918003i	$-0.629801\pi$
$613$	−12.1333	+	1.92172i	−0.490058	+	0.0776176i	−0.0934849	+	0.995621i	$0.529801\pi$
$614$	19.1896	−	6.23507i	0.774428	−	0.251627i
$615$		0			0
$616$	3.61810	−	0.253166i	0.145777	−	0.0102003i
$617$	−22.4668	+	22.4668i	−0.904481	+	0.904481i	−0.995820	−	0.0913392i	$-0.970885\pi$
$617$	−22.4668	+	22.4668i	−0.904481	+	0.904481i	0.0913392	+	0.995820i	$0.470885\pi$
$618$		0			0
$619$	20.8674	−	28.7215i	0.838730	−	1.15441i	−0.147505	−	0.989061i	$-0.547124\pi$
$619$	20.8674	−	28.7215i	0.838730	−	1.15441i	0.986235	−	0.165351i	$-0.0528758\pi$
$620$	−1.97108	−	3.99774i	−0.0791605	−	0.160553i
$621$		0			0
$622$	10.3603	−	5.27884i	0.415411	−	0.211662i
$623$	−0.473712	+	2.99090i	−0.0189789	+	0.119828i
$624$		0			0
$625$	−8.96648	+	23.3367i	−0.358659	+	0.933469i
$626$			29.3802i			1.17427i
$627$		0			0
$628$	12.1553	+	12.1553i	0.485049	+	0.485049i
$629$	2.58437	+	7.95389i	0.103046	+	0.317142i
$630$		0			0
$631$	24.8174	−	18.0309i	0.987967	−	0.717800i	0.0284919	−	0.999594i	$-0.490930\pi$
$631$	24.8174	−	18.0309i	0.987967	−	0.717800i	0.959475	+	0.281794i	$0.0909295\pi$
$632$	−1.79938	−	3.53148i	−0.0715755	−	0.140475i
$633$		0			0
$634$	−8.40435	+	6.10612i	−0.333779	+	0.242505i
$635$	−0.382726	+	29.0632i	−0.0151880	+	1.15334i
$636$		0			0
$637$	9.58806	+	9.58806i	0.379893	+	0.379893i
$638$	1.59482	+	6.90652i	0.0631397	+	0.273432i
$639$		0			0
$640$	1.79155	+	1.33803i	0.0708174	+	0.0528904i
$641$	7.95986	+	5.78318i	0.314396	+	0.228422i	0.733780	−	0.679387i	$-0.237754\pi$
$641$	7.95986	+	5.78318i	0.314396	+	0.228422i	−0.419385	+	0.907809i	$0.637754\pi$
$642$		0			0
$643$	−1.59593	+	0.813166i	−0.0629373	+	0.0320681i	−0.485176	−	0.874417i	$-0.661244\pi$
$643$	−1.59593	+	0.813166i	−0.0629373	+	0.0320681i	0.422239	+	0.906485i	$0.361244\pi$
$644$	−1.27796	+	3.93317i	−0.0503588	+	0.154989i
$645$		0			0
$646$	9.81991	−	13.5159i	0.386359	−	0.531778i
$647$	−29.1710	−	14.8634i	−1.14683	−	0.584339i	−0.225933	−	0.974143i	$-0.572543\pi$
$647$	−29.1710	−	14.8634i	−1.14683	−	0.584339i	−0.920898	+	0.389804i	$0.872543\pi$
$648$		0			0
$649$	1.92719	+	2.29653i	0.0756488	+	0.0901466i
$650$	11.0104	+	3.90091i	0.431863	+	0.153006i
$651$		0			0
$652$	−17.4858	+	2.76947i	−0.684795	+	0.108461i
$653$	22.3316	+	3.53698i	0.873903	+	0.138413i	0.577245	−	0.816571i	$-0.304128\pi$
$653$	22.3316	+	3.53698i	0.873903	+	0.138413i	0.296658	+	0.954984i	$0.404128\pi$
$654$		0			0
$655$	−2.38771	−	1.25647i	−0.0932955	−	0.0490944i
$656$	−3.67243	−	5.05467i	−0.143384	−	0.197352i
$657$		0			0
$658$	−2.35741	+	4.62669i	−0.0919016	+	0.180367i
$659$	−24.8542			−0.968181			−0.484090	−	0.875018i	$-0.660849\pi$
$659$	−24.8542			−0.968181			−0.484090	+	0.875018i	$0.660849\pi$
$660$		0			0
$661$	−7.73442			−0.300834			−0.150417	−	0.988623i	$-0.548062\pi$
$661$	−7.73442			−0.300834			−0.150417	+	0.988623i	$0.548062\pi$
$662$	−0.663993	+	1.30316i	−0.0258068	+	0.0506487i
$663$		0			0
$664$	6.92380	+	9.52979i	0.268695	+	0.369828i
$665$	11.7063	−	3.63390i	0.453951	−	0.140917i
$666$		0			0
$667$	−7.98279	−	1.26435i	−0.309095	−	0.0489558i
$668$	−12.6548	+	2.00433i	−0.489629	+	0.0775497i
$669$		0			0
$670$	1.80360	+	0.310060i	0.0696792	+	0.0119787i
$671$	−22.9048	−	5.70972i	−0.884231	−	0.220421i
$672$		0			0
$673$	−35.9248	−	18.3046i	−1.38480	−	0.705591i	−0.406668	−	0.913576i	$-0.633309\pi$
$673$	−35.9248	−	18.3046i	−1.38480	−	0.705591i	−0.978132	+	0.207985i	$0.933309\pi$
$674$	11.3929	−	15.6810i	0.438838	−	0.604009i
$675$		0			0
$676$	−2.33066	+	7.17304i	−0.0896408	+	0.275886i
$677$	26.8343	−	13.6728i	1.03133	−	0.525487i	0.145430	−	0.989369i	$-0.453544\pi$
$677$	26.8343	−	13.6728i	1.03133	−	0.525487i	0.885897	+	0.463881i	$0.153544\pi$
$678$		0			0
$679$	11.9944	+	8.71444i	0.460303	+	0.334430i
$680$	1.06882	+	7.37555i	0.0409873	+	0.282840i
$681$		0			0
$682$	6.58605	+	0.575906i	0.252193	+	0.0220526i
$683$	−1.26442	−	1.26442i	−0.0483815	−	0.0483815i	0.682502	−	0.730884i	$-0.260892\pi$
$683$	−1.26442	−	1.26442i	−0.0483815	−	0.0483815i	−0.730884	+	0.682502i	$0.760892\pi$
$684$		0			0
$685$	−1.76208	−	0.0232044i	−0.0673258	−	0.000886595i
$686$	−11.3280	+	8.23025i	−0.432504	+	0.314233i
$687$		0			0
$688$	0.562894	+	1.10474i	0.0214601	+	0.0421179i
$689$	14.1816	−	10.3035i	0.540274	−	0.392532i
$690$		0			0
$691$	−11.1192	−	34.2213i	−0.422994	−	1.30184i	−0.904902	−	0.425619i	$-0.860056\pi$
$691$	−11.1192	−	34.2213i	−0.422994	−	1.30184i	0.481909	−	0.876222i	$-0.339944\pi$
$692$	1.38991	+	1.38991i	0.0528363	+	0.0528363i
$693$		0			0
$694$		−	35.7579i		−	1.35735i
$695$	−3.77492	−	26.0495i	−0.143191	−	0.988113i
$696$		0			0
$697$	3.25754	−	20.5673i	0.123388	−	0.779042i
$698$	−10.7926	+	5.49909i	−0.408505	+	0.208144i
$699$		0			0
$700$	−2.60977	+	4.80482i	−0.0986401	+	0.181605i
$701$	24.1969	−	33.3041i	0.913902	−	1.25788i	−0.0519138	−	0.998652i	$-0.516532\pi$
$701$	24.1969	−	33.3041i	0.913902	−	1.25788i	0.965816	−	0.259227i	$-0.0834679\pi$
$702$		0			0
$703$	−8.89410	+	8.89410i	−0.335447	+	0.335447i
$704$	−3.07507	+	1.24257i	−0.115896	+	0.0468310i
$705$		0			0
$706$	−31.1566	+	10.1234i	−1.17259	+	0.380999i
$707$	12.2972	−	1.94768i	0.462483	−	0.0732501i
$708$		0			0
$709$	−22.3270	−	7.25447i	−0.838507	−	0.272447i	−0.141882	−	0.989884i	$-0.545315\pi$
$709$	−22.3270	−	7.25447i	−0.838507	−	0.272447i	−0.696624	+	0.717436i	$0.745315\pi$
$710$	−35.7492	+	11.0974i	−1.34164	+	0.416477i
$711$		0			0
$712$	−0.433181	−	2.73500i	−0.0162341	−	0.102498i
$713$	−3.42232	+	6.71668i	−0.128167	+	0.251542i
$714$		0			0
$715$	−13.4173	+	10.9616i	−0.501777	+	0.409942i
$716$	20.4871			0.765637
$717$		0			0
$718$	−0.345738	−	2.18290i	−0.0129028	−	0.0814652i
$719$	−24.1755	−	33.2748i	−0.901595	−	1.24094i	−0.969957	−	0.243278i	$-0.921777\pi$
$719$	−24.1755	−	33.2748i	−0.901595	−	1.24094i	0.0683616	−	0.997661i	$-0.478223\pi$
$720$		0			0
$721$	9.92469	+	3.22473i	0.369615	+	0.120095i
$722$	6.05112	+	0.958403i	0.225199	+	0.0356680i
$723$		0			0
$724$	23.7436	−	7.71475i	0.882423	−	0.286717i
$725$	−10.0725	−	3.56862i	−0.374082	−	0.132535i
$726$		0			0
$727$	−25.5963	+	25.5963i	−0.949313	+	0.949313i	−0.998776	−	0.0494633i	$-0.984249\pi$
$727$	−25.5963	+	25.5963i	−0.949313	+	0.949313i	0.0494633	+	0.998776i	$0.484249\pi$
$728$	2.27633	+	1.15985i	0.0843665	+	0.0429869i
$729$		0			0
$730$	−11.1540	+	5.49948i	−0.412829	+	0.203545i
$731$	−1.27698	+	3.93014i	−0.0472309	+	0.145362i
$732$		0			0
$733$	−0.836472	+	5.28127i	−0.0308958	+	0.195068i	−0.998309	−	0.0581357i	$-0.981484\pi$
$733$	−0.836472	+	5.28127i	−0.0308958	+	0.195068i	0.967413	+	0.253204i	$0.0814844\pi$
$734$	17.6261	+	12.8061i	0.650591	+	0.472682i
$735$		0			0
$736$		−	3.78174i		−	0.139397i
$737$	−1.78072	+	2.04867i	−0.0655938	+	0.0754639i
$738$		0			0
$739$	−10.8738	−	33.4662i	−0.400000	−	1.23107i	−0.924999	−	0.379970i	$-0.875934\pi$
$739$	−10.8738	−	33.4662i	−0.400000	−	1.23107i	0.524999	−	0.851103i	$-0.324066\pi$
$740$	0.0738825	−	5.61045i	0.00271598	−	0.206244i
$741$		0			0
$742$	3.72519	+	7.31110i	0.136756	+	0.268399i
$743$	−0.569495	−	1.11770i	−0.0208927	−	0.0410043i	0.880324	−	0.474372i	$-0.157325\pi$
$743$	−0.569495	−	1.11770i	−0.0208927	−	0.0410043i	−0.901217	+	0.433368i	$0.857325\pi$
$744$		0			0
$745$	14.1417	+	14.5192i	0.518113	+	0.531941i
$746$	2.55182	+	7.85370i	0.0934288	+	0.287544i
$747$		0			0
$748$	−10.1754	−	4.31868i	−0.372051	−	0.157907i
$749$		−	9.19321i		−	0.335913i
$750$		0			0
$751$	−29.3251	−	21.3060i	−1.07009	−	0.777466i	−0.0941612	−	0.995557i	$-0.530017\pi$
$751$	−29.3251	−	21.3060i	−1.07009	−	0.777466i	−0.975928	+	0.218091i	$0.930017\pi$
$752$	0.742808	−	4.68990i	0.0270874	−	0.171023i
$753$		0			0
$754$	−1.54289	+	4.74854i	−0.0561889	+	0.172932i
$755$	12.9682	+	26.3022i	0.471963	+	0.957234i
$756$		0			0
$757$	−29.1464	−	14.8508i	−1.05934	−	0.539763i	−0.164608	−	0.986359i	$-0.552636\pi$
$757$	−29.1464	−	14.8508i	−1.05934	−	0.539763i	−0.894736	+	0.446596i	$0.852636\pi$
$758$	14.7167	−	14.7167i	0.534535	−	0.534535i
$759$		0			0
$760$	−9.15391	+	6.46828i	−0.332047	+	0.234629i
$761$	36.9434	−	12.0036i	1.33920	−	0.435131i	0.450152	−	0.892952i	$-0.351370\pi$
$761$	36.9434	−	12.0036i	1.33920	−	0.435131i	0.889045	+	0.457821i	$0.151370\pi$
$762$		0			0
$763$	−20.0123	−	3.16964i	−0.724495	−	0.114749i
$764$	−16.0748	−	5.22302i	−0.581566	−	0.188962i
$765$		0			0
$766$	−13.3989	−	18.4420i	−0.484121	−	0.666336i
$767$	0.330354	+	2.08577i	0.0119284	+	0.0753129i
$768$		0			0
$769$	26.4586			0.954122			0.477061	−	0.878870i	$-0.341702\pi$
$769$	26.4586			0.954122			0.477061	+	0.878870i	$0.341702\pi$
$770$	−4.08543	−	7.00593i	−0.147229	−	0.252476i
$771$		0			0
$772$	−1.88940	+	3.70815i	−0.0680009	+	0.133459i
$773$	−0.0901421	−	0.569135i	−0.00324219	−	0.0204704i	0.986014	−	0.166661i	$-0.0532986\pi$
$773$	−0.0901421	−	0.569135i	−0.00324219	−	0.0204704i	−0.989256	+	0.146191i	$0.953299\pi$
$774$		0			0
$775$	−6.06859	+	7.90619i	−0.217990	+	0.283999i
$776$	−12.8938	−	4.18946i	−0.462862	−	0.150393i
$777$		0			0
$778$	−24.8812	+	3.94079i	−0.892034	+	0.141284i
$779$	29.7857	−	9.67795i	1.06718	−	0.346749i
$780$		0			0
$781$	13.4293	−	53.8721i	0.480537	−	1.92770i
$782$	8.91248	−	8.91248i	0.318710	−	0.318710i
$783$		0			0
$784$	3.41157	−	4.69563i	0.121842	−	0.167701i
$785$	12.3585	−	36.3975i	0.441092	−	1.29908i
$786$		0			0
$787$	−15.3186	+	7.80519i	−0.546047	+	0.278225i	−0.705175	−	0.709033i	$-0.749132\pi$
$787$	−15.3186	+	7.80519i	−0.546047	+	0.278225i	0.159128	+	0.987258i	$0.449132\pi$
$788$	−3.58626	+	22.6428i	−0.127755	+	0.806615i
$789$		0			0
$790$	−5.30327	+	7.10078i	−0.188682	+	0.252634i
$791$		−	2.20187i		−	0.0782895i
$792$		0			0
$793$	−11.7575	−	11.7575i	−0.417522	−	0.417522i
$794$	7.34727	+	22.6126i	0.260745	+	0.802490i
$795$		0			0
$796$	3.10735	−	2.25762i	0.110137	−	0.0800192i
$797$	8.33074	+	16.3500i	0.295090	+	0.579147i	0.990184	−	0.139772i	$-0.0446371\pi$
$797$	8.33074	+	16.3500i	0.295090	+	0.579147i	−0.695094	+	0.718919i	$0.744637\pi$
$798$		0			0
$799$	12.8034	−	9.30219i	0.452951	−	0.329088i
$800$	0.911945	−	4.91613i	0.0322421	−	0.173812i
$801$		0			0
$802$	1.57108	+	1.57108i	0.0554768	+	0.0554768i
$803$	1.60683	−	18.3756i	0.0567037	−	0.648461i
$804$		0			0
$805$	9.15184	−	1.32622i	0.322560	−	0.0467433i
$806$	3.76747	+	2.73723i	0.132703	+	0.0964147i
$807$		0			0
$808$	−10.1443	+	5.16877i	−0.356875	+	0.181837i
$809$	−8.39216	+	25.8284i	−0.295053	+	0.908079i	0.688151	+	0.725567i	$0.258423\pi$
$809$	−8.39216	+	25.8284i	−0.295053	+	0.908079i	−0.983204	+	0.182511i	$0.941577\pi$
$810$		0			0
$811$	3.71141	−	5.10832i	0.130325	−	0.179377i	−0.738868	−	0.673851i	$-0.764639\pi$
$811$	3.71141	−	5.10832i	0.130325	−	0.179377i	0.869193	+	0.494473i	$0.164639\pi$
$812$	−2.08243	−	1.06105i	−0.0730788	−	0.0372355i
$813$		0			0
$814$	7.05797	+	4.40987i	0.247382	+	0.154566i
$815$	22.8448	+	32.3299i	0.800217	+	1.13247i
$816$		0			0
$817$	−6.13855	+	0.972251i	−0.214761	+	0.0340148i
$818$	16.6915	+	2.64368i	0.583606	+	0.0924341i
$819$		0			0
$820$	−6.50595	+	12.3634i	−0.227198	+	0.431750i
$821$	0.638412	+	0.878699i	0.0222807	+	0.0306668i	0.820012	−	0.572346i	$-0.193967\pi$
$821$	0.638412	+	0.878699i	0.0222807	+	0.0306668i	−0.797731	+	0.603013i	$0.793967\pi$
$822$		0			0
$823$	0.916619	−	1.79897i	0.0319513	−	0.0627080i	−0.874479	−	0.485063i	$-0.838797\pi$
$823$	0.916619	−	1.79897i	0.0319513	−	0.0627080i	0.906430	+	0.422355i	$0.138797\pi$
$824$	−9.54257			−0.332431
$825$		0			0
$826$	−0.988513			−0.0343948
$827$	20.3365	−	39.9126i	0.707169	−	1.38790i	−0.205278	−	0.978704i	$-0.565810\pi$
$827$	20.3365	−	39.9126i	0.707169	−	1.38790i	0.912447	−	0.409194i	$-0.134190\pi$
$828$		0			0
$829$	−1.13270	−	1.55903i	−0.0393402	−	0.0541472i	0.788894	−	0.614530i	$-0.210654\pi$
$829$	−1.13270	−	1.55903i	−0.0393402	−	0.0541472i	−0.828234	+	0.560382i	$0.810654\pi$
$830$	12.2660	−	23.3093i	0.425758	−	0.809079i
$831$		0			0
$832$	−2.30744	−	0.365462i	−0.0799960	−	0.0126701i
$833$	19.1064	−	3.02615i	0.661997	−	0.104850i
$834$		0			0
$835$	16.5332	+	23.3979i	0.572156	+	0.809716i
$836$	−1.16045	−	16.5845i	−0.0401350	−	0.573587i
$837$		0			0
$838$	−2.12722	−	1.08387i	−0.0734836	−	0.0374418i
$839$	−13.0989	+	18.0291i	−0.452224	+	0.622433i	−0.972874	−	0.231337i	$-0.925690\pi$
$839$	−13.0989	+	18.0291i	−0.452224	+	0.622433i	0.520649	+	0.853771i	$0.325690\pi$
$840$		0			0
$841$	−7.55003	+	23.2366i	−0.260346	+	0.801262i
$842$	−22.9146	+	11.6756i	−0.789690	+	0.402367i
$843$		0			0
$844$	17.0646	+	12.3982i	0.587389	+	0.426763i
$845$	16.6905	−	2.41868i	0.574170	−	0.0832050i
$846$		0			0
$847$	12.0274	+	0.208858i	0.413267	+	0.00717646i
$848$	−5.30569	−	5.30569i	−0.182198	−	0.182198i
$849$		0			0
$850$	13.7351	−	9.43674i	0.471111	−	0.323677i
$851$	−7.67714	+	5.57777i	−0.263169	+	0.191203i
$852$		0			0
$853$	−10.0188	−	19.6630i	−0.343037	−	0.673247i	0.653453	−	0.756967i	$-0.273320\pi$
$853$	−10.0188	−	19.6630i	−0.343037	−	0.673247i	−0.996489	+	0.0837200i	$0.973320\pi$
$854$	6.29686	−	4.57494i	0.215474	−	0.156551i
$855$		0			0
$856$	2.59779	+	7.99518i	0.0887907	+	0.273270i
$857$	−5.52754	−	5.52754i	−0.188817	−	0.188817i	0.606367	−	0.795185i	$-0.292626\pi$
$857$	−5.52754	−	5.52754i	−0.188817	−	0.188817i	−0.795185	+	0.606367i	$0.792626\pi$
$858$		0			0
$859$			13.0239i			0.444368i	0.975005	+	0.222184i	$0.0713186\pi$
$859$			13.0239i			0.444368i	−0.975005	+	0.222184i	$0.928681\pi$
$860$	1.65900	−	2.22131i	0.0565715	−	0.0757461i
$861$		0			0
$862$	−2.76391	+	17.4506i	−0.0941392	+	0.594371i
$863$	20.1714	−	10.2778i	0.686643	−	0.349862i	−0.0756136	−	0.997137i	$-0.524092\pi$
$863$	20.1714	−	10.2778i	0.686643	−	0.349862i	0.762256	+	0.647275i	$0.224092\pi$
$864$		0			0
$865$	1.41314	−	4.16190i	0.0480481	−	0.141509i
$866$	14.5442	−	20.0183i	0.494231	−	0.680250i
$867$		0			0
$868$	−1.54139	+	1.54139i	−0.0523182	+	0.0523182i
$869$	−4.92489	−	12.1879i	−0.167065	−	0.413448i
$870$		0			0
$871$	−1.81843	+	0.590843i	−0.0616151	+	0.0200199i
$872$	18.3001	−	2.89845i	0.619719	−	0.0981538i
$873$		0			0
$874$	18.0287	+	5.85787i	0.609829	+	0.198145i
$875$	12.2169	+	0.482867i	0.413007	+	0.0163239i
$876$		0			0
$877$	−6.44509	−	40.6927i	−0.217635	−	1.37409i	−0.818391	−	0.574661i	$-0.805134\pi$
$877$	−6.44509	−	40.6927i	−0.217635	−	1.37409i	0.600756	−	0.799432i	$-0.294866\pi$
$878$	0.704843	−	1.38333i	0.0237873	−	0.0466852i
$879$		0			0
$880$	5.53275	+	4.93849i	0.186509	+	0.166477i
$881$	15.9880			0.538648			0.269324	−	0.963050i	$-0.413200\pi$
$881$	15.9880			0.538648			0.269324	+	0.963050i	$0.413200\pi$
$882$		0			0
$883$	4.17298	+	26.3472i	0.140432	+	0.886653i	0.952820	+	0.303536i	$0.0981672\pi$
$883$	4.17298	+	26.3472i	0.140432	+	0.886653i	−0.812388	+	0.583117i	$0.801833\pi$
$884$	−4.57668	−	6.29926i	−0.153931	−	0.211867i
$885$		0			0
$886$	−12.6073	−	4.09637i	−0.423551	−	0.137620i
$887$	21.3194	+	3.37666i	0.715836	+	0.113377i	0.503719	−	0.863867i	$-0.331965\pi$
$887$	21.3194	+	3.37666i	0.715836	+	0.113377i	0.212116	+	0.977244i	$0.431965\pi$
$888$		0			0
$889$	13.5191	−	4.39262i	0.453416	−	0.147324i
$890$	−5.05682	+	3.57321i	−0.169505	+	0.119774i
$891$		0			0
$892$	−18.0450	+	18.0450i	−0.604191	+	0.604191i
$893$	21.2076	+	10.8058i	0.709685	+	0.361603i
$894$		0			0
$895$	−20.2582	−	41.0877i	−0.677158	−	1.37341i
$896$	0.337931	−	1.04004i	0.0112895	−	0.0347454i
$897$		0			0
$898$	−5.31499	+	33.5575i	−0.177363	+	1.11983i
$899$	−3.44654	−	2.50406i	−0.114949	−	0.0835151i
$900$		0			0
$901$		−	25.0080i		−	0.833137i
$902$	−10.6734	−	17.7617i	−0.355385	−	0.591401i
$903$		0			0
$904$	0.622199	+	1.91493i	0.0206940	+	0.0636897i
$905$	−38.9507	−	39.9902i	−1.29476	−	1.32932i
$906$		0			0
$907$	−22.2347	−	43.6380i	−0.738290	−	1.44897i	−0.887807	−	0.460216i	$-0.847772\pi$
$907$	−22.2347	−	43.6380i	−0.738290	−	1.44897i	0.149518	−	0.988759i	$-0.452228\pi$
$908$	3.09529	+	6.07486i	0.102721	+	0.201601i
$909$		0			0
$910$	0.0752222	−	5.71218i	0.00249359	−	0.189357i
$911$	−9.70739	−	29.8763i	−0.321620	−	0.989845i	−0.972943	−	0.231044i	$-0.925786\pi$
$911$	−9.70739	−	29.8763i	−0.321620	−	0.989845i	0.651323	−	0.758801i	$-0.274214\pi$
$912$		0			0
$913$	20.1231	+	33.4870i	0.665976	+	1.10826i
$914$		−	8.43747i		−	0.279087i
$915$		0			0
$916$	14.5525	+	10.5730i	0.480828	+	0.349342i
$917$	−0.206421	+	1.30329i	−0.00681663	+	0.0430385i
$918$		0			0
$919$	−1.01757	+	3.13176i	−0.0335665	+	0.103307i	−0.966436	−	0.256907i	$-0.917296\pi$
$919$	−1.01757	+	3.13176i	−0.0335665	+	0.103307i	0.932870	+	0.360214i	$0.117296\pi$
$920$	−7.58444	+	3.73950i	−0.250052	+	0.123288i
$921$		0			0
$922$	20.0927	+	10.2377i	0.661718	+	0.337162i
$923$	27.6537	−	27.6537i	0.910233	−	0.910233i
$924$		0			0
$925$	−11.3251	+	5.39962i	−0.372366	+	0.177538i
$926$	−6.65149	+	2.16120i	−0.218581	+	0.0710214i
$927$		0			0
$928$	2.11088	+	0.334331i	0.0692931	+	0.0109749i
$929$	34.7596	+	11.2941i	1.14043	+	0.370547i	0.817530	−	0.575887i	$-0.195343\pi$
$929$	34.7596	+	11.2941i	1.14043	+	0.370547i	0.322898	+	0.946434i	$0.395343\pi$
$930$		0			0
$931$	17.1010	+	23.5375i	0.560462	+	0.771410i
$932$	−3.09795	−	19.5597i	−0.101477	−	0.640699i
$933$		0			0
$934$	24.4479			0.799961
$935$	1.40049	+	24.6778i	0.0458008	+	0.807049i
$936$		0			0
$937$	21.8819	−	42.9456i	0.714850	−	1.40297i	−0.191948	−	0.981405i	$-0.561480\pi$
$937$	21.8819	−	42.9456i	0.714850	−	1.40297i	0.906798	−	0.421566i	$-0.138520\pi$
$938$	−0.140009	−	0.883985i	−0.00457147	−	0.0288631i
$939$		0			0
$940$	−10.1403	+	3.14779i	−0.330741	+	0.102670i
$941$	48.9385	+	15.9011i	1.59535	+	0.518360i	0.965952	−	0.258723i	$-0.0833017\pi$
$941$	48.9385	+	15.9011i	1.59535	+	0.518360i	0.629398	+	0.777083i	$0.283302\pi$
$942$		0			0
$943$	23.3370	−	3.69622i	0.759959	−	0.120366i
$944$	0.859694	−	0.279331i	0.0279807	−	0.00909147i
$945$		0			0
$946$	1.54064	+	3.81271i	0.0500904	+	0.123962i
$947$	16.9938	−	16.9938i	0.552226	−	0.552226i	−0.374857	−	0.927083i	$-0.622308\pi$
$947$	16.9938	−	16.9938i	0.552226	−	0.552226i	0.927083	+	0.374857i	$0.122308\pi$
$948$		0			0
$949$	7.63709	−	10.5116i	0.247911	−	0.341220i
$950$	22.0241	+	11.9626i	0.714556	+	0.388117i
$951$		0			0
$952$	3.24749	−	1.65468i	0.105252	−	0.0536285i
$953$	−9.14740	+	57.7544i	−0.296313	+	1.87085i	0.168877	+	0.985637i	$0.445986\pi$
$953$	−9.14740	+	57.7544i	−0.296313	+	1.87085i	−0.465190	+	0.885211i	$0.654014\pi$
$954$		0			0
$955$	5.42026	+	37.4034i	0.175396	+	1.21035i
$956$		−	0.578510i		−	0.0187103i
$957$		0			0
$958$	16.0291	+	16.0291i	0.517878	+	0.517878i
$959$	0.266322	+	0.819655i	0.00859998	+	0.0264680i
$960$		0			0
$961$	21.8650	−	15.8858i	0.705321	−	0.512446i
$962$	2.66138	+	5.22325i	0.0858064	+	0.168404i
$963$		0			0
$964$	24.0841	−	17.4981i	0.775696	−	0.563576i
$965$	9.30515	+	0.122537i	0.299544	+	0.00394461i
$966$		0			0
$967$	5.32123	+	5.32123i	0.171119	+	0.171119i	0.787471	−	0.616352i	$-0.211390\pi$
$967$	5.32123	+	5.32123i	0.171119	+	0.171119i	−0.616352	+	0.787471i	$0.711390\pi$
$968$	−10.5191	+	3.21703i	−0.338096	+	0.103399i
$969$		0			0
$970$	4.34767	+	30.0019i	0.139595	+	0.963302i
$971$	1.30297	+	0.946661i	0.0418142	+	0.0303798i	0.608496	−	0.793557i	$-0.291773\pi$
$971$	1.30297	+	0.946661i	0.0418142	+	0.0303798i	−0.566682	+	0.823937i	$0.691773\pi$
$972$		0			0
$973$	−11.4697	+	5.84411i	−0.367702	+	0.187354i
$974$	−10.4656	+	32.2097i	−0.335339	+	1.03207i
$975$		0			0
$976$	−4.18351	+	5.75810i	−0.133911	+	0.184312i
$977$	−34.7450	−	17.7034i	−1.11159	−	0.566383i	−0.200957	−	0.979600i	$-0.564405\pi$
$977$	−34.7450	−	17.7034i	−1.11159	−	0.566383i	−0.910633	+	0.413217i	$0.864405\pi$
$978$		0			0
$979$	−0.641057	−	9.16163i	−0.0204883	−	0.292807i
$980$	−12.7908	−	2.19888i	−0.408586	−	0.0702407i
$981$		0			0
$982$	−27.3194	+	4.32697i	−0.871798	+	0.138079i
$983$	−12.6800	−	2.00832i	−0.404430	−	0.0640554i	−0.0490940	−	0.998794i	$-0.515633\pi$
$983$	−12.6800	−	2.00832i	−0.404430	−	0.0640554i	−0.355336	+	0.934739i	$0.615633\pi$
$984$		0			0
$985$	48.9573	−	15.1975i	1.55991	−	0.484231i
$986$	4.18683	+	5.76267i	0.133336	+	0.183521i
$987$		0			0
$988$	5.31646	−	10.4341i	0.169139	−	0.331954i
$989$	−4.68890			−0.149098
$990$		0			0
$991$	13.9933			0.444511			0.222256	−	0.974988i	$-0.428658\pi$
$991$	13.9933			0.444511			0.222256	+	0.974988i	$0.428658\pi$
$992$	0.904960	−	1.77608i	0.0287325	−	0.0563907i
$993$		0			0
$994$	10.7603	+	14.8102i	0.341295	+	0.469752i
$995$	−7.60040	−	3.99952i	−0.240949	−	0.126793i
$996$		0			0
$997$	−33.7368	−	5.34338i	−1.06845	−	0.169227i	−0.402651	−	0.915354i	$-0.631911\pi$
$997$	−33.7368	−	5.34338i	−1.06845	−	0.169227i	−0.665804	+	0.746127i	$0.731911\pi$
$998$	15.2019	−	2.40775i	0.481209	−	0.0762161i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.d.523.9	yes	96
3.2	odd	2	inner	990.2.bh.d.523.4	yes	96
5.2	odd	4	inner	990.2.bh.d.127.9	yes	96
11.2	odd	10	inner	990.2.bh.d.343.9	yes	96
15.2	even	4	inner	990.2.bh.d.127.4	✓	96
33.2	even	10	inner	990.2.bh.d.343.4	yes	96
55.2	even	20	inner	990.2.bh.d.937.9	yes	96
165.2	odd	20	inner	990.2.bh.d.937.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bh.d.127.4	✓	96	15.2	even	4	inner
990.2.bh.d.127.9	yes	96	5.2	odd	4	inner
990.2.bh.d.343.4	yes	96	33.2	even	10	inner
990.2.bh.d.343.9	yes	96	11.2	odd	10	inner
990.2.bh.d.523.4	yes	96	3.2	odd	2	inner
990.2.bh.d.523.9	yes	96	1.1	even	1	trivial
990.2.bh.d.937.4	yes	96	165.2	odd	20	inner
990.2.bh.d.937.9	yes	96	55.2	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(-1.04130 + 1.97881i) q^{5} +(1.08010 + 0.171071i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.29039 + 1.82617i) q^{10} +(-3.30854 + 0.231505i) q^{11} +(-2.08157 - 1.06061i) q^{13} +(0.642782 - 0.884714i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-2.96964 + 1.51311i) q^{17} +(-4.05531 - 2.94635i) q^{19} +(2.21295 - 0.320687i) q^{20} +(-1.29577 + 3.05303i) q^{22} +(-2.67409 - 2.67409i) q^{23} +(-2.83139 - 4.12107i) q^{25} +(-1.89002 + 1.37318i) q^{26} +(-0.496469 - 0.974375i) q^{28} +(1.72903 - 1.25621i) q^{29} +(-0.615977 - 1.89578i) q^{31} +(0.707107 + 0.707107i) q^{32} +3.33290i q^{34} +(-1.46323 + 1.95918i) q^{35} +(0.392539 - 2.47839i) q^{37} +(-4.46629 + 2.27569i) q^{38} +(0.718926 - 2.11734i) q^{40} +(-3.67243 + 5.05467i) q^{41} +(0.876728 - 0.876728i) q^{43} +(2.13200 + 2.54059i) q^{44} +(-3.59664 + 1.16862i) q^{46} +(-4.68990 + 0.742808i) q^{47} +(-5.52004 - 1.79357i) q^{49} +(-4.95733 + 0.651858i) q^{50} +(0.365462 + 2.30744i) q^{52} +(-3.40646 + 6.68555i) q^{53} +(2.98707 - 6.78803i) q^{55} -1.09357 q^{56} +(-0.334331 - 2.11088i) q^{58} +(-0.531320 - 0.731299i) q^{59} +(6.76905 + 2.19940i) q^{61} +(-1.96880 - 0.311828i) q^{62} +(0.951057 - 0.309017i) q^{64} +(4.26629 - 3.01462i) q^{65} +(0.578715 - 0.578715i) q^{67} +(2.96964 + 1.51311i) q^{68} +(1.08135 + 2.19320i) q^{70} +(-5.17298 + 15.9208i) q^{71} +(-0.870026 + 5.49313i) q^{73} +(-2.03006 - 1.47492i) q^{74} +5.01264i q^{76} +(-3.61316 - 0.315947i) q^{77} +(1.22478 + 3.76949i) q^{79} +(-1.56018 - 1.60182i) q^{80} +(2.83649 + 5.56693i) q^{82} +(-5.34777 - 10.4956i) q^{83} +(0.0981327 - 7.45195i) q^{85} +(-0.383144 - 1.17920i) q^{86} +(3.23159 - 0.746223i) q^{88} +2.76909i q^{89} +(-2.06687 - 1.50167i) q^{91} +(-0.591594 + 3.73518i) q^{92} +(-1.46733 + 4.51596i) q^{94} +(10.0531 - 4.95665i) q^{95} +(12.0797 + 6.15492i) q^{97} +(-4.10413 + 4.10413i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{7} + 24 q^{16} + 4 q^{22} + 8 q^{25} + 20 q^{28} - 16 q^{31} + 64 q^{37} - 40 q^{46} - 40 q^{52} - 36 q^{55} - 12 q^{58} - 80 q^{61} - 48 q^{67} - 52 q^{70} + 20 q^{73} + 48 q^{82} - 160 q^{85}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q - 40 * q^7 + 24 * q^16 + 4 * q^22 + 8 * q^25 + 20 * q^28 - 16 * q^31 + 64 * q^37 - 40 * q^46 - 40 * q^52 - 36 * q^55 - 12 * q^58 - 80 * q^61 - 48 * q^67 - 52 * q^70 + 20 * q^73 + 48 * q^82 - 160 * q^85 + 4 * q^88 + 8 * q^91 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more