LMFDB - Embedded newform 990.2.bh.d.343.9

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)

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")

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);

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			343.9
Character	$\chi$	$=$	990.343
Dual form			990.2.bh.d.127.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.891007 - 0.453990i) q^{2} +(0.587785 - 0.809017i) q^{4} +(-0.320687 - 2.21295i) q^{5} +(-0.171071 - 1.08010i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.29039 - 1.82617i) q^{10} +(-3.30854 - 0.231505i) q^{11} +(-1.06061 - 2.08157i) q^{13} +(-0.642782 - 0.884714i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-1.51311 + 2.96964i) q^{17} +(4.05531 - 2.94635i) q^{19} +(-1.97881 - 1.04130i) q^{20} +(-3.05303 + 1.29577i) q^{22} +(-2.67409 - 2.67409i) q^{23} +(-4.79432 + 1.41933i) q^{25} +(-1.89002 - 1.37318i) q^{26} +(-0.974375 - 0.496469i) q^{28} +(-1.72903 - 1.25621i) q^{29} +(-0.615977 + 1.89578i) q^{31} +(-0.707107 - 0.707107i) q^{32} +3.33290i q^{34} +(-2.33536 + 0.724947i) q^{35} +(2.47839 - 0.392539i) q^{37} +(2.27569 - 4.46629i) q^{38} +(-2.23587 - 0.0294436i) q^{40} +(-3.67243 - 5.05467i) q^{41} +(-0.876728 + 0.876728i) q^{43} +(-2.13200 + 2.54059i) q^{44} +(-3.59664 - 1.16862i) q^{46} +(-0.742808 + 4.68990i) q^{47} +(5.52004 - 1.79357i) q^{49} +(-3.62741 + 3.44121i) q^{50} +(-2.30744 - 0.365462i) q^{52} +(6.68555 - 3.40646i) q^{53} +(0.548694 + 7.39587i) q^{55} -1.09357 q^{56} +(-2.11088 - 0.334331i) q^{58} +(0.531320 - 0.731299i) q^{59} +(6.76905 - 2.19940i) q^{61} +(0.311828 + 1.96880i) q^{62} +(-0.951057 - 0.309017i) q^{64} +(-4.26629 + 3.01462i) q^{65} +(0.578715 - 0.578715i) q^{67} +(1.51311 + 2.96964i) q^{68} +(-1.75170 + 1.70616i) q^{70} +(-5.17298 - 15.9208i) q^{71} +(5.49313 - 0.870026i) q^{73} +(2.03006 - 1.47492i) q^{74} -5.01264i q^{76} +(0.315947 + 3.61316i) q^{77} +(-1.22478 + 3.76949i) q^{79} +(-2.00555 + 0.988831i) q^{80} +(-5.56693 - 2.83649i) q^{82} +(-10.4956 - 5.34777i) q^{83} +(7.05690 + 2.39611i) q^{85} +(-0.383144 + 1.17920i) q^{86} +(-0.746223 + 3.23159i) q^{88} +2.76909i q^{89} +(-2.06687 + 1.50167i) q^{91} +(-3.73518 + 0.591594i) q^{92} +(1.46733 + 4.51596i) q^{94} +(-7.82063 - 8.02935i) q^{95} +(-6.15492 - 12.0797i) q^{97} +(4.10413 - 4.10413i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$		0			0
$3$		0			0
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	−0.320687	−	2.21295i	−0.143415	−	0.989663i
$5$	−0.320687	−	2.21295i	−0.143415	−	0.989663i
$6$		0			0
$7$	−0.171071	−	1.08010i	−0.0646589	−	0.408240i	−0.998695	−	0.0510629i	$-0.983739\pi$
$7$	−0.171071	−	1.08010i	−0.0646589	−	0.408240i	0.934037	−	0.357178i	$-0.116261\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$		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
$13$	−1.06061	−	2.08157i	−0.294161	−	0.577323i	0.695871	−	0.718167i	$-0.255019\pi$
$13$	−1.06061	−	2.08157i	−0.294161	−	0.577323i	−0.990032	+	0.140844i	$0.955019\pi$
$14$	−0.642782	−	0.884714i	−0.171791	−	0.236450i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−1.51311	+	2.96964i	−0.366982	+	0.720243i	−0.998479	−	0.0551357i	$-0.982441\pi$
$17$	−1.51311	+	2.96964i	−0.366982	+	0.720243i	0.631497	+	0.775378i	$0.282441\pi$
$18$		0			0
$19$	4.05531	−	2.94635i	0.930352	−	0.675940i	−0.0157271	−	0.999876i	$-0.505006\pi$
$19$	4.05531	−	2.94635i	0.930352	−	0.675940i	0.946079	+	0.323936i	$0.105006\pi$
$20$	−1.97881	−	1.04130i	−0.442476	−	0.232842i
$21$		0			0
$22$	−3.05303	+	1.29577i	−0.650908	+	0.276259i
$23$	−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
$25$	−4.79432	+	1.41933i	−0.958864	+	0.283866i
$26$	−1.89002	−	1.37318i	−0.370664	−	0.269303i
$27$		0			0
$28$	−0.974375	−	0.496469i	−0.184139	−	0.0938238i
$29$	−1.72903	−	1.25621i	−0.321072	−	0.233272i	0.415561	−	0.909565i	$-0.363585\pi$
$29$	−1.72903	−	1.25621i	−0.321072	−	0.233272i	−0.736633	+	0.676293i	$0.763585\pi$
$30$		0			0
$31$	−0.615977	+	1.89578i	−0.110633	+	0.340493i	−0.991011	−	0.133779i	$-0.957289\pi$
$31$	−0.615977	+	1.89578i	−0.110633	+	0.340493i	0.880378	+	0.474272i	$0.157289\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$			3.33290i			0.571588i
$35$	−2.33536	+	0.724947i	−0.394747	+	0.122538i
$36$		0			0
$37$	2.47839	−	0.392539i	0.407446	−	0.0645330i	0.0506522	−	0.998716i	$-0.483870\pi$
$37$	2.47839	−	0.392539i	0.407446	−	0.0645330i	0.356793	+	0.934183i	$0.383870\pi$
$38$	2.27569	−	4.46629i	0.369166	−	0.724528i
$39$		0			0
$40$	−2.23587	−	0.0294436i	−0.353523	−	0.00465545i
$41$	−3.67243	−	5.05467i	−0.573537	−	0.789406i	0.419431	−	0.907787i	$-0.362230\pi$
$41$	−3.67243	−	5.05467i	−0.573537	−	0.789406i	−0.992968	+	0.118381i	$0.962230\pi$
$42$		0			0
$43$	−0.876728	+	0.876728i	−0.133700	+	0.133700i	−0.770790	−	0.637090i	$-0.780138\pi$
$43$	−0.876728	+	0.876728i	−0.133700	+	0.133700i	0.637090	+	0.770790i	$0.280138\pi$
$44$	−2.13200	+	2.54059i	−0.321411	+	0.383008i
$45$		0			0
$46$	−3.59664	−	1.16862i	−0.530296	−	0.172304i
$47$	−0.742808	+	4.68990i	−0.108350	+	0.684093i	0.872395	+	0.488801i	$0.162566\pi$
$47$	−0.742808	+	4.68990i	−0.108350	+	0.684093i	−0.980745	+	0.195292i	$0.937434\pi$
$48$		0			0
$49$	5.52004	−	1.79357i	0.788577	−	0.256224i
$50$	−3.62741	+	3.44121i	−0.512993	+	0.486660i
$51$		0			0
$52$	−2.30744	−	0.365462i	−0.319984	−	0.0506805i
$53$	6.68555	−	3.40646i	0.918331	−	0.467913i	0.0701006	−	0.997540i	$-0.477668\pi$
$53$	6.68555	−	3.40646i	0.918331	−	0.467913i	0.848231	+	0.529627i	$0.177668\pi$
$54$		0			0
$55$	0.548694	+	7.39587i	0.0739859	+	0.997259i
$56$	−1.09357			−0.146134
$57$		0			0
$58$	−2.11088	−	0.334331i	−0.277172	−	0.0438998i
$59$	0.531320	−	0.731299i	0.0691720	−	0.0952071i	−0.773029	−	0.634370i	$-0.781259\pi$
$59$	0.531320	−	0.731299i	0.0691720	−	0.0952071i	0.842201	+	0.539163i	$0.181259\pi$
$60$		0			0
$61$	6.76905	−	2.19940i	0.866689	−	0.281604i	0.158269	−	0.987396i	$-0.449409\pi$
$61$	6.76905	−	2.19940i	0.866689	−	0.281604i	0.708419	+	0.705792i	$0.249409\pi$
$62$	0.311828	+	1.96880i	0.0396022	+	0.250038i
$63$		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	$0.234080\pi$
$68$	1.51311	+	2.96964i	0.183491	+	0.360121i
$69$		0			0
$70$	−1.75170	+	1.70616i	−0.209368	+	0.203925i
$71$	−5.17298	−	15.9208i	−0.613920	−	1.88945i	−0.416509	−	0.909131i	$-0.636747\pi$
$71$	−5.17298	−	15.9208i	−0.613920	−	1.88945i	−0.197411	−	0.980321i	$-0.563253\pi$
$72$		0			0
$73$	5.49313	−	0.870026i	0.642922	−	0.101829i	0.173544	−	0.984826i	$-0.444478\pi$
$73$	5.49313	−	0.870026i	0.642922	−	0.101829i	0.469378	+	0.882997i	$0.344478\pi$
$74$	2.03006	−	1.47492i	0.235989	−	0.171456i
$75$		0			0
$76$		−	5.01264i		−	0.574989i
$77$	0.315947	+	3.61316i	0.0360055	+	0.411758i
$78$		0			0
$79$	−1.22478	+	3.76949i	−0.137799	+	0.424101i	−0.996015	−	0.0891877i	$-0.971573\pi$
$79$	−1.22478	+	3.76949i	−0.137799	+	0.424101i	0.858216	+	0.513288i	$0.171573\pi$
$80$	−2.00555	+	0.988831i	−0.224227	+	0.110555i
$81$		0			0
$82$	−5.56693	−	2.83649i	−0.614764	−	0.313238i
$83$	−10.4956	−	5.34777i	−1.15204	−	0.586994i	−0.229657	−	0.973272i	$-0.573761\pi$
$83$	−10.4956	−	5.34777i	−1.15204	−	0.586994i	−0.922382	+	0.386278i	$0.873761\pi$
$84$		0			0
$85$	7.05690	+	2.39611i	0.765428	+	0.259894i
$86$	−0.383144	+	1.17920i	−0.0413155	+	0.127156i
$87$		0			0
$88$	−0.746223	+	3.23159i	−0.0795477	+	0.344488i
$89$			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
$92$	−3.73518	+	0.591594i	−0.389419	+	0.0616779i
$93$		0			0
$94$	1.46733	+	4.51596i	0.151343	+	0.465786i
$95$	−7.82063	−	8.02935i	−0.802380	−	0.823794i
$96$		0			0
$97$	−6.15492	−	12.0797i	−0.624938	−	1.22651i	−0.958852	−	0.283906i	$-0.908370\pi$
$97$	−6.15492	−	12.0797i	−0.624938	−	1.22651i	0.333914	−	0.942604i	$-0.391630\pi$
$98$	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	0.793374	−	0.608734i	$-0.208322\pi$
$101$	10.8280	+	3.51822i	1.07742	+	0.350076i	0.284048	+	0.958810i	$0.408322\pi$
$102$		0			0
$103$	1.49279	+	9.42509i	0.147089	+	0.928681i	0.945276	+	0.326272i	$0.105793\pi$
$103$	1.49279	+	9.42509i	0.147089	+	0.928681i	−0.798187	+	0.602409i	$0.794207\pi$
$104$	−2.22186	+	0.721925i	−0.217871	+	0.0707906i
$105$		0			0
$106$	4.41037	−	6.07036i	0.428373	−	0.589605i
$107$	8.30313	+	1.31509i	0.802694	+	0.127134i	0.544284	−	0.838901i	$-0.316801\pi$
$107$	8.30313	+	1.31509i	0.802694	+	0.127134i	0.258410	+	0.966035i	$0.416801\pi$
$108$		0			0
$109$	18.5282			1.77468			0.887339	−	0.461117i	$-0.152551\pi$
$109$	18.5282			1.77468			0.887339	+	0.461117i	$0.152551\pi$
$110$	3.84655	+	6.34067i	0.366754	+	0.604559i
$111$		0			0
$112$	−0.974375	+	0.496469i	−0.0920697	+	0.0469119i
$113$	−1.98869	−	0.314977i	−0.187080	−	0.0296306i	0.0621913	−	0.998064i	$-0.480191\pi$
$113$	−1.98869	−	0.314977i	−0.187080	−	0.0296306i	−0.249271	+	0.968434i	$0.580191\pi$
$114$		0			0
$115$	−5.06009	+	6.77518i	−0.471856	+	0.631789i
$116$	−2.03259	+	0.660429i	−0.188721	+	0.0613193i
$117$		0			0
$118$	0.141407	−	0.892807i	0.0130175	−	0.0821895i
$119$	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
$125$	4.67838	+	10.1544i	0.418447	+	0.908241i
$126$		0			0
$127$	5.90124	−	11.5818i	0.523651	−	1.02772i	−0.466075	−	0.884745i	$-0.654332\pi$
$127$	5.90124	−	11.5818i	0.523651	−	1.02772i	0.989726	−	0.142977i	$-0.0456675\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$		0			0
$130$	−2.43268	+	4.62290i	−0.213360	+	0.405455i
$131$		−	1.20664i		−	0.105424i	−0.998610	−	0.0527122i	$-0.983213\pi$
$131$		−	1.20664i		−	0.105424i	0.998610	−	0.0527122i	$-0.0167866\pi$
$132$		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
$137$	−0.702199	−	0.357788i	−0.0599929	−	0.0305679i	0.423737	−	0.905785i	$-0.360718\pi$
$137$	−0.702199	−	0.357788i	−0.0599929	−	0.0305679i	−0.483730	+	0.875217i	$0.660718\pi$
$138$		0			0
$139$	9.52324	+	6.91904i	0.807750	+	0.586865i	0.913178	−	0.407562i	$-0.133621\pi$
$139$	9.52324	+	6.91904i	0.807750	+	0.586865i	−0.105427	+	0.994427i	$0.533621\pi$
$140$	−0.786193	+	2.31546i	−0.0664454	+	0.195692i
$141$		0			0
$142$	−11.8371	−	11.8371i	−0.993344	−	0.993344i
$143$	3.02718	+	7.13248i	0.253145	+	0.596448i
$144$		0			0
$145$	−2.22546	+	4.22910i	−0.184814	+	0.351208i
$146$	4.49943	−	3.26903i	0.372375	−	0.270546i
$147$		0			0
$148$	1.13919	−	2.23579i	0.0936411	−	0.183781i
$149$	−2.80098	−	8.62053i	−0.229465	−	0.706221i	−0.997808	−	0.0661821i	$-0.978918\pi$
$149$	−2.80098	−	8.62053i	−0.229465	−	0.706221i	0.768342	−	0.640039i	$-0.221082\pi$
$150$		0			0
$151$	7.70864	+	10.6100i	0.627320	+	0.863432i	0.997860	−	0.0653842i	$-0.0208273\pi$
$151$	7.70864	+	10.6100i	0.627320	+	0.863432i	−0.370540	+	0.928817i	$0.620827\pi$
$152$	−2.27569	−	4.46629i	−0.184583	−	0.362264i
$153$		0			0
$154$	1.92185	+	3.07591i	0.154867	+	0.247864i
$155$	4.39282	+	0.755177i	0.352839	+	0.0606572i
$156$		0			0
$157$	−2.68914	+	16.9785i	−0.214616	+	1.35504i	0.611370	+	0.791345i	$0.290619\pi$
$157$	−2.68914	+	16.9785i	−0.214616	+	1.35504i	−0.825986	+	0.563690i	$0.809381\pi$
$158$	0.620024	+	3.91468i	0.0493265	+	0.311435i
$159$		0			0
$160$	−1.33803	+	1.79155i	−0.105781	+	0.141635i
$161$	−2.43083	+	3.34575i	−0.191576	+	0.263682i
$162$		0			0
$163$	−15.7741	+	8.03732i	−1.23553	+	0.629532i	−0.944917	−	0.327310i	$-0.893858\pi$
$163$	−15.7741	+	8.03732i	−1.23553	+	0.629532i	−0.290608	+	0.956842i	$0.593858\pi$
$164$	−6.24791			−0.487880
$165$		0			0
$166$	−11.7795			−0.914264
$167$	11.4161	−	5.81678i	0.883402	−	0.450116i	0.0474215	−	0.998875i	$-0.484900\pi$
$167$	11.4161	−	5.81678i	0.883402	−	0.450116i	0.835981	+	0.548759i	$0.184900\pi$
$168$		0			0
$169$	4.43318	−	6.10175i	0.341014	−	0.469365i
$170$	7.37555	−	1.06882i	0.565679	−	0.0819745i
$171$		0			0
$172$	0.193960	+	1.22462i	0.0147893	+	0.0933760i
$173$	0.307491	−	1.94142i	0.0233781	−	0.147604i	−0.973238	−	0.229799i	$-0.926193\pi$
$173$	0.307491	−	1.94142i	0.0233781	−	0.147604i	0.996616	+	0.0821952i	$0.0261931\pi$
$174$		0			0
$175$	2.35319	+	4.93555i	0.177885	+	0.373093i
$176$	0.802220	+	3.21814i	0.0604696	+	0.242577i
$177$		0			0
$178$	1.25714	+	2.46728i	0.0942266	+	0.184930i
$179$	12.0420	+	16.5744i	0.900061	+	1.23883i	0.970449	+	0.241308i	$0.0775763\pi$
$179$	12.0420	+	16.5744i	0.900061	+	1.23883i	−0.0703878	+	0.997520i	$0.522424\pi$
$180$		0			0
$181$	−7.71475	−	23.7436i	−0.573433	−	1.76485i	−0.641454	−	0.767161i	$-0.721669\pi$
$181$	−7.71475	−	23.7436i	−0.573433	−	1.76485i	0.0680210	−	0.997684i	$-0.478331\pi$
$182$	−1.15985	+	2.27633i	−0.0859738	+	0.168733i
$183$		0			0
$184$	−3.05949	+	2.22285i	−0.225548	+	0.163871i
$185$	−1.66346	−	5.35869i	−0.122300	−	0.393979i
$186$		0			0
$187$	5.69365	−	9.47486i	0.416361	−	0.692870i
$188$	3.35760	+	3.35760i	0.244878	+	0.244878i
$189$		0			0
$190$	−10.6135	−	3.60371i	−0.769983	−	0.261441i
$191$	13.6740	+	9.93478i	0.989419	+	0.718855i	0.959794	−	0.280706i	$-0.0905686\pi$
$191$	13.6740	+	9.93478i	0.989419	+	0.718855i	0.0296254	+	0.999561i	$0.490569\pi$
$192$		0			0
$193$	−3.70815	−	1.88940i	−0.266918	−	0.136002i	0.315410	−	0.948956i	$-0.397858\pi$
$193$	−3.70815	−	1.88940i	−0.266918	−	0.136002i	−0.582328	+	0.812954i	$0.697858\pi$
$194$	−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	$0.0541820\pi$
$197$	16.2104	+	16.2104i	1.15494	+	1.15494i	0.169397	+	0.985548i	$0.445818\pi$
$198$		0			0
$199$			3.84089i			0.272274i	0.990690	+	0.136137i	$0.0434687\pi$
$199$			3.84089i			0.272274i	−0.990690	+	0.136137i	$0.956531\pi$
$200$	0.651858	+	4.95733i	0.0460933	+	0.350536i
$201$		0			0
$202$	11.2450	−	1.78104i	0.791197	−	0.125313i
$203$	−1.06105	+	2.08243i	−0.0744711	+	0.146158i
$204$		0			0
$205$	−10.0080	+	9.74788i	−0.698992	+	0.680821i
$206$	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	−0.478024	−	0.878347i	$-0.658647\pi$
$211$	−20.0607	−	6.51811i	−1.38103	−	0.448725i	−0.903009	+	0.429622i	$0.858647\pi$
$212$	1.17379	−	7.41099i	0.0806160	−	0.508989i
$213$		0			0
$214$	7.99518	−	2.59779i	0.546540	−	0.177581i
$215$	2.22131	+	1.65900i	0.151492	+	0.113143i
$216$		0			0
$217$	2.15302	+	0.341004i	0.146156	+	0.0231489i
$218$	16.5087	−	8.41162i	1.11811	−	0.569707i
$219$		0			0
$220$	6.30590	+	3.90328i	0.425144	+	0.263159i
$221$	7.78632			0.523765
$222$		0			0
$223$	−25.2053	−	3.99212i	−1.68787	−	0.267332i	−0.762663	−	0.646796i	$-0.776108\pi$
$223$	−25.2053	−	3.99212i	−1.68787	−	0.267332i	−0.925207	+	0.379464i	$0.876108\pi$
$224$	−0.642782	+	0.884714i	−0.0429477	+	0.0591124i
$225$		0			0
$226$	−1.91493	+	0.622199i	−0.127379	+	0.0413881i
$227$	1.06657	+	6.73403i	0.0707904	+	0.446953i	0.997469	+	0.0710991i	$0.0226507\pi$
$227$	1.06657	+	6.73403i	0.0707904	+	0.446953i	−0.926679	+	0.375854i	$0.877349\pi$
$228$		0			0
$229$	17.1075	+	5.55855i	1.13049	+	0.367320i	0.813763	−	0.581196i	$-0.197415\pi$
$229$	17.1075	+	5.55855i	1.13049	+	0.367320i	0.316730	+	0.948516i	$0.397415\pi$
$230$	−1.43271	+	8.33397i	−0.0944699	+	0.549525i
$231$		0			0
$232$	−1.51122	+	1.51122i	−0.0992167	+	0.0992167i
$233$	8.99060	+	17.6450i	0.588994	+	1.15597i	0.972604	+	0.232470i	$0.0746808\pi$
$233$	8.99060	+	17.6450i	0.588994	+	1.15597i	−0.383610	+	0.923495i	$0.625319\pi$
$234$		0			0
$235$	10.6167	+	0.139809i	0.692560	+	0.00912014i
$236$	−0.279331	−	0.859694i	−0.0181829	−	0.0559613i
$237$		0			0
$238$	3.59988	−	0.570164i	0.233345	−	0.0369583i
$239$	−0.468024	+	0.340039i	−0.0302740	+	0.0219953i	−0.602819	−	0.797878i	$-0.705956\pi$
$239$	−0.468024	+	0.340039i	−0.0302740	+	0.0219953i	0.572545	+	0.819873i	$0.305956\pi$
$240$		0			0
$241$		−	29.7695i		−	1.91763i	−0.284040	−	0.958813i	$-0.591675\pi$
$241$		−	29.7695i		−	1.91763i	0.284040	−	0.958813i	$-0.408325\pi$
$242$	10.4010	−	3.58032i	0.668603	−	0.230151i
$243$		0			0
$244$	2.19940	−	6.76905i	0.140802	−	0.433344i
$245$	−5.73929	−	11.6404i	−0.366670	−	0.743679i
$246$		0			0
$247$	−10.4341	−	5.31646i	−0.663909	−	0.338279i
$248$	1.77608	+	0.904960i	0.112781	+	0.0574650i
$249$		0			0
$250$	8.77849	+	6.92374i	0.555200	+	0.437895i
$251$	−3.62089	+	11.1439i	−0.228548	+	0.703400i	0.769364	+	0.638811i	$0.220573\pi$
$251$	−3.62089	+	11.1439i	−0.228548	+	0.703400i	−0.997912	+	0.0645885i	$0.979427\pi$
$252$		0			0
$253$	8.22826	+	9.46639i	0.517306	+	0.595147i
$254$		−	12.9986i		−	0.815605i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−10.9640	+	1.73653i	−0.683918	+	0.108322i	−0.488719	−	0.872441i	$-0.662536\pi$
$257$	−10.9640	+	1.73653i	−0.683918	+	0.108322i	−0.195200	+	0.980764i	$0.562536\pi$
$258$		0			0
$259$	−0.847965	−	2.60977i	−0.0526900	−	0.162163i
$260$	−0.0687861	+	5.22345i	−0.00426594	+	0.323944i
$261$		0			0
$262$	−0.547802	−	1.07512i	−0.0338433	−	0.0664213i
$263$	−5.16707	+	5.16707i	−0.318615	+	0.318615i	−0.848235	−	0.529620i	$-0.822335\pi$
$263$	−5.16707	+	5.16707i	−0.318615	+	0.318615i	0.529620	+	0.848235i	$0.322335\pi$
$264$		0			0
$265$	−9.68230	−	13.7024i	−0.594779	−	0.841732i
$266$	−5.21336	−	1.69392i	−0.319652	−	0.103861i
$267$		0			0
$268$	−0.128030	−	0.808351i	−0.00782069	−	0.0493779i
$269$	16.9878	−	5.51966i	1.03576	−	0.336539i	0.258696	−	0.965959i	$-0.416707\pi$
$269$	16.9878	−	5.51966i	1.03576	−	0.336539i	0.777066	+	0.629419i	$0.216707\pi$
$270$		0			0
$271$	8.01595	−	11.0330i	0.486934	−	0.670208i	−0.492885	−	0.870095i	$-0.664058\pi$
$271$	8.01595	−	11.0330i	0.486934	−	0.670208i	0.979819	+	0.199887i	$0.0640575\pi$
$272$	3.29187	+	0.521381i	0.199599	+	0.0316133i
$273$		0			0
$274$	−0.788097			−0.0476107
$275$	16.1908	−	3.58599i	0.976339	−	0.216243i
$276$		0			0
$277$	0.267032	−	0.136060i	0.0160444	−	0.00817504i	−0.445950	−	0.895058i	$-0.647134\pi$
$277$	0.267032	−	0.136060i	0.0160444	−	0.00817504i	0.461994	+	0.886883i	$0.347134\pi$
$278$	11.6264	+	1.84145i	0.697308	+	0.110443i
$279$		0			0
$280$	0.350692	+	2.42001i	0.0209579	+	0.144623i
$281$	13.9727	−	4.54000i	0.833540	−	0.270834i	0.139004	−	0.990292i	$-0.455610\pi$
$281$	13.9727	−	4.54000i	0.833540	−	0.270834i	0.694536	+	0.719458i	$0.255610\pi$
$282$		0			0
$283$	−4.95906	+	31.3103i	−0.294786	+	1.86120i	0.183528	+	0.983014i	$0.441248\pi$
$283$	−4.95906	+	31.3103i	−0.294786	+	1.86120i	−0.478314	+	0.878189i	$0.658752\pi$
$284$	−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
$290$	−0.0629267	+	4.77849i	−0.00369518	+	0.280603i
$291$		0			0
$292$	2.52491	−	4.95542i	0.147759	−	0.289994i
$293$	−21.3019	+	3.37389i	−1.24447	+	0.197104i	−0.743722	−	0.668489i	$-0.766941\pi$
$293$	−21.3019	+	3.37389i	−1.24447	+	0.197104i	−0.500747	+	0.865594i	$0.666941\pi$
$294$		0			0
$295$	−1.78872	−	0.941268i	−0.104143	−	0.0548028i
$296$		−	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
$302$	11.6853	+	5.95396i	0.672414	+	0.342612i
$303$		0			0
$304$	−4.05531	−	2.94635i	−0.232588	−	0.168985i
$305$	−7.03791	−	14.2743i	−0.402990	−	0.817343i
$306$		0			0
$307$	−14.2674	−	14.2674i	−0.814282	−	0.814282i	0.170991	−	0.985273i	$-0.445303\pi$
$307$	−14.2674	−	14.2674i	−0.814282	−	0.814282i	−0.985273	+	0.170991i	$0.945303\pi$
$308$	3.10882	+	1.86816i	0.177141	+	0.106448i
$309$		0			0
$310$	4.25687	−	1.32143i	0.241774	−	0.0750521i
$311$	9.40697	−	6.83456i	0.533420	−	0.387552i	−0.288215	−	0.957566i	$-0.593062\pi$
$311$	9.40697	−	6.83456i	0.533420	−	0.387552i	0.821636	+	0.570013i	$0.193062\pi$
$312$		0			0
$313$	13.3383	−	26.1779i	0.753926	−	1.47966i	−0.119566	−	0.992826i	$-0.538150\pi$
$313$	13.3383	−	26.1779i	0.753926	−	1.47966i	0.873492	−	0.486838i	$-0.161850\pi$
$314$	5.31206	+	16.3488i	0.299777	+	0.922618i
$315$		0			0
$316$	2.32967	+	3.20652i	0.131054	+	0.180381i
$317$	4.71621	+	9.25608i	0.264889	+	0.519873i	0.984692	−	0.174305i	$-0.0557679\pi$
$317$	4.71621	+	9.25608i	0.264889	+	0.519873i	−0.719803	+	0.694178i	$0.755768\pi$
$318$		0			0
$319$	5.42972	+	4.55649i	0.304006	+	0.255115i
$320$	−0.378849	+	2.20374i	−0.0211783	+	0.123193i
$321$		0			0
$322$	−0.646947	+	4.08466i	−0.0360529	+	0.227629i
$323$	2.61349	+	16.5009i	0.145419	+	0.918137i
$324$		0			0
$325$	8.03934	+	8.47435i	0.445943	+	0.470072i
$326$	−10.4060	+	14.3226i	−0.576334	+	0.793256i
$327$		0			0
$328$	−5.56693	+	2.83649i	−0.307382	+	0.156619i
$329$	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	$0.512798\pi$
$332$	−10.4956	+	5.34777i	−0.576020	+	0.293497i
$333$		0			0
$334$	7.53103	−	10.3656i	0.412080	−	0.567179i
$335$	−1.46626	−	1.09508i	−0.0801101	−	0.0598308i
$336$		0			0
$337$	−3.03213	−	19.1441i	−0.165171	−	1.04285i	−0.921421	−	0.388565i	$-0.872971\pi$
$337$	−3.03213	−	19.1441i	−0.165171	−	1.04285i	0.756251	−	0.654282i	$-0.227029\pi$
$338$	1.17986	−	7.44932i	0.0641757	−	0.405190i
$339$		0			0
$340$	6.08643	−	4.30075i	0.330083	−	0.233241i
$341$	2.47687	−	6.12967i	0.134130	−	0.331940i
$342$		0			0
$343$	−6.35684	−	12.4760i	−0.343237	−	0.673641i
$344$	0.728783	+	1.00308i	0.0392934	+	0.0540827i
$345$		0			0
$346$	−0.607411	−	1.86942i	−0.0326546	−	0.100501i
$347$	16.2337	−	31.8605i	0.871473	−	1.71036i	0.185620	−	0.982622i	$-0.440571\pi$
$347$	16.2337	−	31.8605i	0.871473	−	1.71036i	0.685853	−	0.727741i	$-0.259429\pi$
$348$		0			0
$349$	9.79945	−	7.11972i	0.524553	−	0.381110i	−0.293763	−	0.955878i	$-0.594908\pi$
$349$	9.79945	−	7.11972i	0.524553	−	0.381110i	0.818316	+	0.574768i	$0.194908\pi$
$350$	4.33740	+	3.32928i	0.231844	+	0.177958i
$351$		0			0
$352$	2.17579	+	2.50319i	0.115970	+	0.133420i
$353$	−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
$355$	−33.5731	+	16.5532i	−1.78187	+	0.878550i
$356$	2.24024	+	1.62763i	0.118732	+	0.0862642i
$357$		0			0
$358$	18.2541	+	9.30093i	0.964760	+	0.491570i
$359$	−1.78802	−	1.29907i	−0.0943681	−	0.0685624i	0.539601	−	0.841921i	$-0.318575\pi$
$359$	−1.78802	−	1.29907i	−0.0943681	−	0.0685624i	−0.633969	+	0.773359i	$0.718575\pi$
$360$		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
$365$	−3.68690	−	11.8770i	−0.192981	−	0.621672i
$366$		0			0
$367$	−21.5188	+	3.40825i	−1.12327	+	0.177909i	−0.690318	−	0.723506i	$-0.742529\pi$
$367$	−21.5188	+	3.40825i	−1.12327	+	0.177909i	−0.432955	+	0.901415i	$0.642529\pi$
$368$	−1.71687	+	3.36955i	−0.0894981	+	0.175650i
$369$		0			0
$370$	−3.91495	−	4.01943i	−0.203528	−	0.208960i
$371$	−4.82303	−	6.63834i	−0.250399	−	0.344645i
$372$		0			0
$373$	5.83919	−	5.83919i	0.302342	−	0.302342i	−0.539588	−	0.841929i	$-0.681420\pi$
$373$	5.83919	−	5.83919i	0.302342	−	0.302342i	0.841929	+	0.539588i	$0.181420\pi$
$374$	0.771582	−	11.0270i	0.0398976	−	0.570194i
$375$		0			0
$376$	4.51596	+	1.46733i	0.232893	+	0.0756715i
$377$	−0.781063	+	4.93144i	−0.0402268	+	0.253982i
$378$		0			0
$379$	−19.7939	+	6.43143i	−1.01675	+	0.330361i	−0.769537	−	0.638602i	$-0.779513\pi$
$379$	−19.7939	+	6.43143i	−1.01675	+	0.330361i	−0.247208	+	0.968962i	$0.579513\pi$
$380$	−11.0927	+	1.60749i	−0.569045	+	0.0824623i
$381$		0			0
$382$	16.6940	+	2.64406i	0.854137	+	0.135282i
$383$	−20.3110	+	10.3490i	−1.03784	+	0.528807i	−0.887972	−	0.459898i	$-0.847886\pi$
$383$	−20.3110	+	10.3490i	−1.03784	+	0.528807i	−0.149871	+	0.988706i	$0.547886\pi$
$384$		0			0
$385$	7.89444	−	1.85787i	0.402338	−	0.0946857i
$386$	−4.16175			−0.211828
$387$		0			0
$388$	−13.3905	−	2.12084i	−0.679798	−	0.107669i
$389$	14.8071	−	20.3802i	0.750750	−	1.03332i	−0.247178	−	0.968970i	$-0.579503\pi$
$389$	14.8071	−	20.3802i	0.750750	−	1.03332i	0.997928	−	0.0643483i	$-0.0204969\pi$
$390$		0			0
$391$	11.9873	−	3.89490i	0.606222	−	0.196973i
$392$	−0.907963	−	5.73265i	−0.0458591	−	0.289543i
$393$		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	$0.453501\pi$
$398$	1.74373	+	3.42226i	0.0874052	+	0.171542i
$399$		0			0
$400$	2.83139	+	4.12107i	0.141569	+	0.206054i
$401$	−0.686588	−	2.11310i	−0.0342865	−	0.105523i	0.932449	−	0.361303i	$-0.117668\pi$
$401$	−0.686588	−	2.11310i	−0.0342865	−	0.105523i	−0.966735	+	0.255780i	$0.917668\pi$
$402$		0			0
$403$	4.59952	−	0.728492i	0.229118	−	0.0362888i
$404$	9.21082	−	6.69205i	0.458255	−	0.332942i
$405$		0			0
$406$			2.33716i			0.115991i
$407$	−8.29073	+	0.724970i	−0.410956	+	0.0359354i
$408$		0			0
$409$	−5.22226	+	16.0725i	−0.258224	+	0.794732i	0.734953	+	0.678118i	$0.237204\pi$
$409$	−5.22226	+	16.0725i	−0.258224	+	0.794732i	−0.993177	+	0.116614i	$0.962796\pi$
$410$	−4.49178	+	13.2290i	−0.221833	+	0.653333i
$411$		0			0
$412$	8.50249	+	4.33224i	0.418888	+	0.213434i
$413$	−0.880772	−	0.448776i	−0.0433400	−	0.0220828i
$414$		0			0
$415$	−8.46856	+	24.9412i	−0.415705	+	1.22431i
$416$	−0.721925	+	2.22186i	−0.0353953	+	0.108935i
$417$		0			0
$418$	−8.56317	+	14.2501i	−0.418838	+	0.696993i
$419$		−	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	−0.965049	−	0.262068i	$-0.915596\pi$
$421$	−20.8060	+	15.1165i	−1.01402	+	0.736732i	−0.0489752	+	0.998800i	$0.515596\pi$
$422$	−20.8333	+	3.29968i	−1.01415	+	0.160626i
$423$		0			0
$424$	−2.31867	−	7.13613i	−0.112605	−	0.346561i
$425$	3.03942	−	16.3850i	0.147434	−	0.794788i
$426$		0			0
$427$	−3.53357	−	6.93502i	−0.171001	−	0.335609i
$428$	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	−0.125052	−	0.992150i	$-0.539910\pi$
$431$	−16.8034	−	5.45976i	−0.809393	−	0.262988i	−0.684341	+	0.729163i	$0.739910\pi$
$432$		0			0
$433$	3.87082	+	24.4394i	0.186020	+	1.17448i	0.887161	+	0.461459i	$0.152674\pi$
$433$	3.87082	+	24.4394i	0.186020	+	1.17448i	−0.701142	+	0.713022i	$0.747326\pi$
$434$	2.07316	−	0.673612i	0.0995151	−	0.0323344i
$435$		0			0
$436$	10.8906	−	14.9896i	0.521565	−	0.717873i
$437$	−18.7231	−	2.96545i	−0.895647	−	0.141857i
$438$		0			0
$439$	−1.55255			−0.0740992			−0.0370496	−	0.999313i	$-0.511796\pi$
$439$	−1.55255			−0.0740992			−0.0370496	+	0.999313i	$0.511796\pi$
$440$	7.39065	+	0.615031i	0.352336	+	0.0293204i
$441$		0			0
$442$	6.93766	−	3.53492i	0.329991	−	0.168139i
$443$	−13.0929	−	2.07371i	−0.622063	−	0.0985252i	−0.162556	−	0.986699i	$-0.551974\pi$
$443$	−13.0929	−	2.07371i	−0.622063	−	0.0985252i	−0.459507	+	0.888174i	$0.651974\pi$
$444$		0			0
$445$	6.12786	−	0.888010i	0.290489	−	0.0420957i
$446$	−24.2704	+	7.88594i	−1.14924	+	0.373410i
$447$		0			0
$448$	−0.171071	+	1.08010i	−0.00808237	+	0.0510300i
$449$	32.3129	+	10.4991i	1.52494	+	0.495483i	0.947174	−	0.320719i	$-0.103924\pi$
$449$	32.3129	+	10.4991i	1.52494	+	0.495483i	0.577766	+	0.816202i	$0.303924\pi$
$450$		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
$455$	3.98593	+	4.09231i	0.186863	+	0.191851i
$456$		0			0
$457$	3.83053	−	7.51784i	0.179185	−	0.351670i	−0.783892	−	0.620897i	$-0.786768\pi$
$457$	3.83053	−	7.51784i	0.179185	−	0.351670i	0.963077	+	0.269228i	$0.0867684\pi$
$458$	17.7664	−	2.81392i	0.830169	−	0.131486i
$459$		0			0
$460$	2.50699	+	8.07605i	0.116889	+	0.376548i
$461$		−	22.5506i		−	1.05028i	−0.851014	−	0.525142i	$-0.824012\pi$
$461$		−	22.5506i		−	1.05028i	0.851014	−	0.525142i	$-0.175988\pi$
$462$		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
$467$	−21.7833	−	11.0991i	−1.00801	−	0.513606i	−0.129626	−	0.991563i	$-0.541378\pi$
$467$	−21.7833	−	11.0991i	−1.00801	−	0.513606i	−0.878383	+	0.477957i	$0.841378\pi$
$468$		0			0
$469$	−0.724073	−	0.526070i	−0.0334346	−	0.0242917i
$470$	9.52306	−	4.69533i	0.439266	−	0.216579i
$471$		0			0
$472$	−0.639179	−	0.639179i	−0.0294206	−	0.0294206i
$473$	3.10365	−	2.69772i	0.142706	−	0.124041i
$474$		0			0
$475$	−15.2606	+	19.8816i	−0.700205	+	0.912230i
$476$	2.94866	−	2.14233i	0.135152	−	0.0981935i
$477$		0			0
$478$	−0.262638	+	0.515456i	−0.0120128	+	0.0235764i
$479$	7.00499	+	21.5591i	0.320066	+	0.985062i	0.973619	+	0.228181i	$0.0732778\pi$
$479$	7.00499	+	21.5591i	0.320066	+	0.985062i	−0.653553	+	0.756881i	$0.726722\pi$
$480$		0			0
$481$	−3.44571	−	4.74262i	−0.157111	−	0.216245i
$482$	−13.5151	−	26.5249i	−0.615596	−	1.20817i
$483$		0			0
$484$	7.64195	−	7.91205i	0.347361	−	0.359639i
$485$	−24.7580	+	17.4944i	−1.12421	+	0.794378i
$486$		0			0
$487$	−5.29802	+	33.4504i	−0.240076	+	1.51578i	0.513310	+	0.858203i	$0.328419\pi$
$487$	−5.29802	+	33.4504i	−0.240076	+	1.51578i	−0.753387	+	0.657578i	$0.771581\pi$
$488$	−1.11341	−	7.02978i	−0.0504016	−	0.318223i
$489$		0			0
$490$	−10.3984	−	7.76610i	−0.469751	−	0.350837i
$491$	−16.2581	+	22.3774i	−0.733718	+	1.00988i	0.265237	+	0.964183i	$0.414550\pi$
$491$	−16.2581	+	22.3774i	−0.733718	+	1.00988i	−0.998956	+	0.0456935i	$0.985450\pi$
$492$		0			0
$493$	6.34669	−	3.23380i	0.285840	−	0.145643i
$494$	−11.7105			−0.526881
$495$		0			0
$496$	1.99334			0.0895038
$497$	−16.3112	+	8.31095i	−0.731655	+	0.372797i
$498$		0			0
$499$	−9.04686	+	12.4519i	−0.404993	+	0.557425i	−0.961988	−	0.273090i	$-0.911954\pi$
$499$	−9.04686	+	12.4519i	−0.404993	+	0.557425i	0.556995	+	0.830516i	$0.311954\pi$
$500$	10.9650	+	2.18374i	0.490370	+	0.0976599i
$501$		0			0
$502$	1.83301	+	11.5732i	0.0818113	+	0.516536i
$503$	2.87522	−	18.1534i	0.128200	−	0.809421i	−0.836865	−	0.547409i	$-0.815614\pi$
$503$	2.87522	−	18.1534i	0.128200	−	0.809421i	0.965065	−	0.262011i	$-0.0843858\pi$
$504$		0			0
$505$	4.31327	−	25.0900i	0.191938	−	1.11649i
$506$	11.6291	+	4.69906i	0.516976	+	0.208899i
$507$		0			0
$508$	−5.90124	−	11.5818i	−0.261825	−	0.513861i
$509$	2.72418	+	3.74951i	0.120747	+	0.166194i	0.865112	−	0.501579i	$-0.167247\pi$
$509$	2.72418	+	3.74951i	0.120747	+	0.166194i	−0.744364	+	0.667774i	$0.767247\pi$
$510$		0			0
$511$	−1.87943	−	5.78430i	−0.0831413	−	0.255882i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$		0			0
$514$	−8.98066	+	6.52484i	−0.396120	+	0.287798i
$515$	20.3786	−	6.32597i	0.897986	−	0.278755i
$516$		0			0
$517$	3.54334	−	15.3448i	0.155836	−	0.674861i
$518$	−1.94035	−	1.94035i	−0.0852542	−	0.0852542i
$519$		0			0
$520$	2.31011	+	4.68535i	0.101305	+	0.205466i
$521$	−19.0400	−	13.8333i	−0.834156	−	0.606050i	0.0865764	−	0.996245i	$-0.472407\pi$
$521$	−19.0400	−	13.8333i	−0.834156	−	0.606050i	−0.920732	+	0.390196i	$0.872407\pi$
$522$		0			0
$523$	28.5865	+	14.5656i	1.25000	+	0.636907i	0.948566	−	0.316579i	$-0.102534\pi$
$523$	28.5865	+	14.5656i	1.25000	+	0.636907i	0.301435	+	0.953487i	$0.402534\pi$
$524$	−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
$530$	−14.8478	−	7.81326i	−0.644945	−	0.339386i
$531$		0			0
$532$	−5.41416	+	0.857519i	−0.234734	+	0.0371782i
$533$	−6.62661	+	13.0055i	−0.287030	+	0.563329i
$534$		0			0
$535$	0.247522	−	18.7962i	0.0107013	−	0.812630i
$536$	−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	−0.181847	−	0.983327i	$-0.558208\pi$
$541$	−21.0951	−	6.85421i	−0.906949	−	0.294686i	−0.725102	+	0.688641i	$0.758208\pi$
$542$	2.13338	−	13.4696i	0.0916366	−	0.578571i
$543$		0			0
$544$	3.16978	−	1.02992i	0.135903	−	0.0441576i
$545$	−5.94174	−	41.0020i	−0.254516	−	1.75633i
$546$		0			0
$547$	19.3633	+	3.06685i	0.827915	+	0.131129i	0.555989	−	0.831189i	$-0.312339\pi$
$547$	19.3633	+	3.06685i	0.827915	+	0.131129i	0.271926	+	0.962318i	$0.412339\pi$
$548$	−0.702199	+	0.357788i	−0.0299965	+	0.0152840i
$549$		0			0
$550$	12.7981	−	10.5456i	0.545711	−	0.449666i
$551$	−10.7130			−0.456388
$552$		0			0
$553$	4.28096	+	0.678038i	0.182045	+	0.0288331i
$554$	0.176158	−	0.242460i	0.00748423	−	0.0103012i
$555$		0			0
$556$	11.1952	−	3.63755i	0.474784	−	0.154267i
$557$	3.83502	+	24.2134i	0.162495	+	1.02595i	0.925276	+	0.379296i	$0.123834\pi$
$557$	3.83502	+	24.2134i	0.162495	+	1.02595i	−0.762781	+	0.646657i	$0.776166\pi$
$558$		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
$563$	−16.5145	−	32.4116i	−0.696004	−	1.36598i	−0.920203	−	0.391441i	$-0.871977\pi$
$563$	−16.5145	−	32.4116i	−0.696004	−	1.36598i	0.224200	−	0.974543i	$-0.428023\pi$
$564$		0			0
$565$	−0.0592841	+	4.50188i	−0.00249410	+	0.189396i
$566$	9.79602	+	30.1490i	0.411757	+	1.26726i
$567$		0			0
$568$	−16.5340	+	2.61873i	−0.693752	+	0.109880i
$569$	−12.4610	+	9.05343i	−0.522391	+	0.379540i	−0.817504	−	0.575923i	$-0.804643\pi$
$569$	−12.4610	+	9.05343i	−0.522391	+	0.379540i	0.295113	+	0.955462i	$0.404643\pi$
$570$		0			0
$571$		−	22.4382i		−	0.939010i	−0.882930	−	0.469505i	$-0.844432\pi$
$571$		−	22.4382i		−	0.939010i	0.882930	−	0.469505i	$-0.155568\pi$
$572$	7.54963	+	1.74333i	0.315666	+	0.0728921i
$573$		0			0
$574$	−2.11136	+	6.49810i	−0.0881264	+	0.271225i
$575$	16.6159	+	9.02503i	0.692929	+	0.376370i
$576$		0			0
$577$	−23.9453	−	12.2008i	−0.996858	−	0.507924i	−0.122117	−	0.992516i	$-0.538968\pi$
$577$	−23.9453	−	12.2008i	−0.996858	−	0.507924i	−0.874741	+	0.484591i	$0.838968\pi$
$578$	5.24960	+	2.67481i	0.218355	+	0.111257i
$579$		0			0
$580$	2.11332	+	4.28624i	0.0877510	+	0.177976i
$581$	−3.98064	+	12.2512i	−0.165145	+	0.508264i
$582$		0			0
$583$	−22.9080	+	9.72266i	−0.948752	+	0.402671i
$584$		−	5.56160i		−	0.230141i
$585$		0			0
$586$	−17.4484	+	12.6770i	−0.720787	+	0.523682i
$587$	−16.7923	+	2.65963i	−0.693091	+	0.109775i	−0.493035	−	0.870010i	$-0.664112\pi$
$587$	−16.7923	+	2.65963i	−0.693091	+	0.109775i	−0.200056	+	0.979784i	$0.564112\pi$
$588$		0			0
$589$	3.08767	+	9.50288i	0.127225	+	0.391559i
$590$	−2.02109	−	0.0266151i	−0.0832068	−	0.00109573i
$591$		0			0
$592$	−1.13919	−	2.23579i	−0.0468205	−	0.0918905i
$593$	−9.90575	+	9.90575i	−0.406781	+	0.406781i	−0.880614	−	0.473834i	$-0.842870\pi$
$593$	−9.90575	+	9.90575i	−0.406781	+	0.406781i	0.473834	+	0.880614i	$0.342870\pi$
$594$		0			0
$595$	1.38081	−	8.03208i	0.0566076	−	0.329283i
$596$	−8.62053	−	2.80098i	−0.353111	−	0.114733i
$597$		0			0
$598$	1.38208	+	8.72611i	0.0565175	+	0.356837i
$599$	12.7899	−	4.15568i	0.522580	−	0.169796i	−0.0358361	−	0.999358i	$-0.511409\pi$
$599$	12.7899	−	4.15568i	0.522580	−	0.169796i	0.558416	+	0.829561i	$0.311409\pi$
$600$		0			0
$601$	3.15713	−	4.34542i	0.128782	−	0.177253i	−0.739757	−	0.672874i	$-0.765059\pi$
$601$	3.15713	−	4.34542i	0.128782	−	0.177253i	0.868539	+	0.495621i	$0.165059\pi$
$602$	1.33920	+	0.212108i	0.0545816	+	0.00864488i
$603$		0			0
$604$	13.1147			0.533631
$605$	−0.103195	−	24.5965i	−0.00419547	−	0.999991i
$606$		0			0
$607$	20.9848	−	10.6923i	0.851747	−	0.433987i	0.0270990	−	0.999633i	$-0.491373\pi$
$607$	20.9848	−	10.6923i	0.851747	−	0.433987i	0.824648	+	0.565646i	$0.191373\pi$
$608$	−4.95092	−	0.784149i	−0.200787	−	0.0318015i
$609$		0			0
$610$	−12.7512	−	9.52333i	−0.516281	−	0.385588i
$611$	10.5502	−	3.42796i	0.426815	−	0.138681i
$612$		0			0
$613$	1.92172	−	12.1333i	0.0776176	−	0.490058i	−0.918003	−	0.396573i	$-0.870199\pi$
$613$	1.92172	−	12.1333i	0.0776176	−	0.490058i	0.995621	−	0.0934849i	$-0.0298007\pi$
$614$	−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	−0.986235	−	0.165351i	$-0.947124\pi$
$619$	−20.8674	−	28.7215i	−0.838730	−	1.15441i	0.147505	−	0.989061i	$-0.452876\pi$
$620$	3.19298	−	3.10998i	0.128233	−	0.124900i
$621$		0			0
$622$	5.27884	−	10.3603i	0.211662	−	0.415411i
$623$	2.99090	−	0.473712i	0.119828	−	0.0189789i
$624$		0			0
$625$	20.9710	−	13.6094i	0.838840	−	0.544377i
$626$		−	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	0.959475	−	0.281794i	$-0.0909295\pi$
$631$	24.8174	+	18.0309i	0.987967	+	0.717800i	0.0284919	+	0.999594i	$0.490930\pi$
$632$	3.53148	+	1.79938i	0.140475	+	0.0715755i
$633$		0			0
$634$	8.40435	+	6.10612i	0.333779	+	0.242505i
$635$	−27.5225	−	9.34503i	−1.09220	−	0.370846i
$636$		0			0
$637$	−9.58806	−	9.58806i	−0.379893	−	0.379893i
$638$	6.90652	+	1.59482i	0.273432	+	0.0631397i
$639$		0			0
$640$	0.662921	+	2.13554i	0.0262042	+	0.0844147i
$641$	7.95986	−	5.78318i	0.314396	−	0.228422i	−0.419385	−	0.907809i	$-0.637754\pi$
$641$	7.95986	−	5.78318i	0.314396	−	0.228422i	0.733780	+	0.679387i	$0.237754\pi$
$642$		0			0
$643$	0.813166	−	1.59593i	0.0320681	−	0.0629373i	−0.874417	−	0.485176i	$-0.838756\pi$
$643$	0.813166	−	1.59593i	0.0320681	−	0.0629373i	0.906485	+	0.422239i	$0.138756\pi$
$644$	1.27796	+	3.93317i	0.0503588	+	0.154989i
$645$		0			0
$646$	9.81991	+	13.5159i	0.386359	+	0.531778i
$647$	14.8634	+	29.1710i	0.584339	+	1.14683i	0.974143	+	0.225933i	$0.0725429\pi$
$647$	14.8634	+	29.1710i	0.584339	+	1.14683i	−0.389804	+	0.920898i	$0.627457\pi$
$648$		0			0
$649$	−1.92719	+	2.29653i	−0.0756488	+	0.0901466i
$650$	11.0104	+	3.90091i	0.431863	+	0.153006i
$651$		0			0
$652$	−2.76947	+	17.4858i	−0.108461	+	0.684795i
$653$	3.53698	+	22.3316i	0.138413	+	0.873903i	0.954984	+	0.296658i	$0.0958721\pi$
$653$	3.53698	+	22.3316i	0.138413	+	0.873903i	−0.816571	+	0.577245i	$0.804128\pi$
$654$		0			0
$655$	−2.67023	+	0.386953i	−0.104335	+	0.0151195i
$656$	−3.67243	+	5.05467i	−0.143384	+	0.197352i
$657$		0			0
$658$	4.62669	−	2.35741i	0.180367	−	0.0919016i
$659$	24.8542			0.968181			0.484090	−	0.875018i	$-0.339151\pi$
$659$	24.8542			0.968181			0.484090	+	0.875018i	$0.339151\pi$
$660$		0			0
$661$	−7.73442			−0.300834			−0.150417	−	0.988623i	$-0.548062\pi$
$661$	−7.73442			−0.300834			−0.150417	+	0.988623i	$0.548062\pi$
$662$	−1.30316	+	0.663993i	−0.0506487	+	0.0258068i
$663$		0			0
$664$	−6.92380	+	9.52979i	−0.268695	+	0.369828i
$665$	−7.33464	+	9.82067i	−0.284425	+	0.380829i
$666$		0			0
$667$	1.26435	+	7.98279i	0.0489558	+	0.309095i
$668$	2.00433	−	12.6548i	0.0775497	−	0.489629i
$669$		0			0
$670$	−1.80360	−	0.310060i	−0.0696792	−	0.0119787i
$671$	−22.9048	+	5.70972i	−0.884231	+	0.220421i
$672$		0			0
$673$	−18.3046	−	35.9248i	−0.705591	−	1.38480i	−0.913576	−	0.406668i	$-0.866691\pi$
$673$	−18.3046	−	35.9248i	−0.705591	−	1.38480i	0.207985	−	0.978132i	$-0.433309\pi$
$674$	−11.3929	−	15.6810i	−0.438838	−	0.604009i
$675$		0			0
$676$	−2.33066	−	7.17304i	−0.0896408	−	0.275886i
$677$	13.6728	−	26.8343i	0.525487	−	1.03133i	−0.463881	−	0.885897i	$-0.653544\pi$
$677$	13.6728	−	26.8343i	0.525487	−	1.03133i	0.989369	−	0.145430i	$-0.0464564\pi$
$678$		0			0
$679$	−11.9944	+	8.71444i	−0.460303	+	0.334430i
$680$	3.47055	−	6.59518i	0.133090	−	0.252914i
$681$		0			0
$682$	−0.575906	−	6.58605i	−0.0220526	−	0.252193i
$683$	−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
$685$	−0.566583	+	1.66867i	−0.0216480	+	0.0637567i
$686$	−11.3280	−	8.23025i	−0.432504	−	0.314233i
$687$		0			0
$688$	1.10474	+	0.562894i	0.0421179	+	0.0214601i
$689$	−14.1816	−	10.3035i	−0.540274	−	0.392532i
$690$		0			0
$691$	−11.1192	+	34.2213i	−0.422994	+	1.30184i	0.481909	+	0.876222i	$0.339944\pi$
$691$	−11.1192	+	34.2213i	−0.422994	+	1.30184i	−0.904902	+	0.425619i	$0.860056\pi$
$692$	−1.38991	−	1.38991i	−0.0528363	−	0.0528363i
$693$		0			0
$694$		−	35.7579i		−	1.35735i
$695$	12.2575	−	23.2933i	0.464954	−	0.883566i
$696$		0			0
$697$	20.5673	−	3.25754i	0.779042	−	0.123388i
$698$	5.49909	−	10.7926i	0.208144	−	0.408505i
$699$		0			0
$700$	5.37612	+	0.997272i	0.203198	+	0.0376933i
$701$	24.1969	+	33.3041i	0.913902	+	1.25788i	0.965816	+	0.259227i	$0.0834679\pi$
$701$	24.1969	+	33.3041i	0.913902	+	1.25788i	−0.0519138	+	0.998652i	$0.516532\pi$
$702$		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
$707$	1.94768	−	12.2972i	0.0732501	−	0.462483i
$708$		0			0
$709$	22.3270	−	7.25447i	0.838507	−	0.272447i	0.141882	−	0.989884i	$-0.454685\pi$
$709$	22.3270	−	7.25447i	0.838507	−	0.272447i	0.696624	+	0.717436i	$0.254685\pi$
$710$	−22.3989	+	29.9908i	−0.840614	+	1.12554i
$711$		0			0
$712$	2.73500	+	0.433181i	0.102498	+	0.0162341i
$713$	6.71668	−	3.42232i	0.251542	−	0.128167i
$714$		0			0
$715$	14.8131	−	8.98630i	0.553977	−	0.336068i
$716$	20.4871			0.765637
$717$		0			0
$718$	−2.18290	−	0.345738i	−0.0814652	−	0.0129028i
$719$	24.1755	−	33.2748i	0.901595	−	1.24094i	−0.0683616	−	0.997661i	$-0.521777\pi$
$719$	24.1755	−	33.2748i	0.901595	−	1.24094i	0.969957	−	0.243278i	$-0.0782228\pi$
$720$		0			0
$721$	9.92469	−	3.22473i	0.369615	−	0.120095i
$722$	−0.958403	−	6.05112i	−0.0356680	−	0.225199i
$723$		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	$0.484249\pi$
$728$	1.15985	+	2.27633i	0.0429869	+	0.0843665i
$729$		0			0
$730$	−8.67711	−	8.90869i	−0.321154	−	0.329725i
$731$	−1.27698	−	3.93014i	−0.0472309	−	0.145362i
$732$		0			0
$733$	5.28127	−	0.836472i	0.195068	−	0.0308958i	−0.0581357	−	0.998309i	$-0.518516\pi$
$733$	5.28127	−	0.836472i	0.195068	−	0.0308958i	0.253204	+	0.967413i	$0.418516\pi$
$734$	−17.6261	+	12.8061i	−0.650591	+	0.472682i
$735$		0			0
$736$			3.78174i			0.139397i
$737$	−2.04867	+	1.78072i	−0.0754639	+	0.0655938i
$738$		0			0
$739$	10.8738	−	33.4662i	0.400000	−	1.23107i	−0.524999	−	0.851103i	$-0.675934\pi$
$739$	10.8738	−	33.4662i	0.400000	−	1.23107i	0.924999	−	0.379970i	$-0.124066\pi$
$740$	−5.31303	−	1.80399i	−0.195311	−	0.0663161i
$741$		0			0
$742$	−7.31110	−	3.72519i	−0.268399	−	0.136756i
$743$	−1.11770	−	0.569495i	−0.0410043	−	0.0208927i	0.433368	−	0.901217i	$-0.357325\pi$
$743$	−1.11770	−	0.569495i	−0.0410043	−	0.0208927i	−0.474372	+	0.880324i	$0.657325\pi$
$744$		0			0
$745$	−18.1786	+	8.96292i	−0.666012	+	0.328376i
$746$	2.55182	−	7.85370i	0.0934288	−	0.287544i
$747$		0			0
$748$	−4.31868	−	10.1754i	−0.157907	−	0.372051i
$749$		−	9.19321i		−	0.335913i
$750$		0			0
$751$	−29.3251	+	21.3060i	−1.07009	+	0.777466i	−0.975928	−	0.218091i	$-0.930017\pi$
$751$	−29.3251	+	21.3060i	−1.07009	+	0.777466i	−0.0941612	+	0.995557i	$0.530017\pi$
$752$	4.68990	−	0.742808i	0.171023	−	0.0270874i
$753$		0			0
$754$	1.54289	+	4.74854i	0.0561889	+	0.172932i
$755$	21.0074	−	20.4614i	0.764539	−	0.744665i
$756$		0			0
$757$	14.8508	+	29.1464i	0.539763	+	1.05934i	0.986359	+	0.164608i	$0.0526360\pi$
$757$	14.8508	+	29.1464i	0.539763	+	1.05934i	−0.446596	+	0.894736i	$0.647364\pi$
$758$	−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	0.889045	−	0.457821i	$-0.151370\pi$
$761$	36.9434	+	12.0036i	1.33920	+	0.435131i	0.450152	+	0.892952i	$0.351370\pi$
$762$		0			0
$763$	−3.16964	−	20.0123i	−0.114749	−	0.724495i
$764$	16.0748	−	5.22302i	0.581566	−	0.188962i
$765$		0			0
$766$	−13.3989	+	18.4420i	−0.484121	+	0.666336i
$767$	−2.08577	−	0.330354i	−0.0753129	−	0.0119284i
$768$		0			0
$769$	−26.4586			−0.954122			−0.477061	−	0.878870i	$-0.658298\pi$
$769$	−26.4586			−0.954122			−0.477061	+	0.878870i	$0.658298\pi$
$770$	6.19054	−	5.23937i	0.223092	−	0.188814i
$771$		0			0
$772$	−3.70815	+	1.88940i	−0.133459	+	0.0680009i
$773$	−0.569135	−	0.0901421i	−0.0204704	−	0.00324219i	0.146191	−	0.989256i	$-0.453299\pi$
$773$	−0.569135	−	0.0901421i	−0.0204704	−	0.00324219i	−0.166661	+	0.986014i	$0.553299\pi$
$774$		0			0
$775$	0.262453	−	9.96327i	0.00942758	−	0.357891i
$776$	−12.8938	+	4.18946i	−0.462862	+	0.150393i
$777$		0			0
$778$	3.94079	−	24.8812i	0.141284	−	0.892034i
$779$	−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
$785$	38.4351	+	0.506141i	1.37181	+	0.0180650i
$786$		0			0
$787$	−7.80519	+	15.3186i	−0.278225	+	0.546047i	−0.987258	−	0.159128i	$-0.949132\pi$
$787$	−7.80519	+	15.3186i	−0.278225	+	0.546047i	0.709033	+	0.705175i	$0.249132\pi$
$788$	22.6428	−	3.58626i	0.806615	−	0.127755i
$789$		0			0
$790$	8.46417	−	2.62747i	0.301142	−	0.0934812i
$791$			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
$797$	−16.3500	−	8.33074i	−0.579147	−	0.295090i	0.139772	−	0.990184i	$-0.455363\pi$
$797$	−16.3500	−	8.33074i	−0.579147	−	0.295090i	−0.718919	+	0.695094i	$0.755363\pi$
$798$		0			0
$799$	−12.8034	−	9.30219i	−0.452951	−	0.329088i
$800$	4.39371	+	2.38648i	0.155341	+	0.0843748i
$801$		0			0
$802$	−1.57108	−	1.57108i	−0.0554768	−	0.0554768i
$803$	−18.3756	+	1.60683i	−0.648461	+	0.0567037i
$804$		0			0
$805$	8.18353	+	4.30638i	0.288431	+	0.151780i
$806$	3.76747	−	2.73723i	0.132703	−	0.0964147i
$807$		0			0
$808$	5.16877	−	10.1443i	0.181837	−	0.356875i
$809$	8.39216	+	25.8284i	0.295053	+	0.908079i	0.983204	+	0.182511i	$0.0584226\pi$
$809$	8.39216	+	25.8284i	0.295053	+	0.908079i	−0.688151	+	0.725567i	$0.741577\pi$
$810$		0			0
$811$	3.71141	+	5.10832i	0.130325	+	0.179377i	0.869193	−	0.494473i	$-0.164639\pi$
$811$	3.71141	+	5.10832i	0.130325	+	0.179377i	−0.738868	+	0.673851i	$0.764639\pi$
$812$	1.06105	+	2.08243i	0.0372355	+	0.0730788i
$813$		0			0
$814$	−7.05797	+	4.40987i	−0.247382	+	0.154566i
$815$	22.8448	+	32.3299i	0.800217	+	1.13247i
$816$		0			0
$817$	−0.972251	+	6.13855i	−0.0340148	+	0.214761i
$818$	2.64368	+	16.6915i	0.0924341	+	0.583606i
$819$		0			0
$820$	2.00362	+	13.8263i	0.0699695	+	0.482836i
$821$	0.638412	−	0.878699i	0.0222807	−	0.0306668i	−0.797731	−	0.603013i	$-0.793967\pi$
$821$	0.638412	−	0.878699i	0.0222807	−	0.0306668i	0.820012	+	0.572346i	$0.193967\pi$
$822$		0			0
$823$	−1.79897	+	0.916619i	−0.0627080	+	0.0319513i	−0.485063	−	0.874479i	$-0.661203\pi$
$823$	−1.79897	+	0.916619i	−0.0627080	+	0.0319513i	0.422355	+	0.906430i	$0.361203\pi$
$824$	9.54257			0.332431
$825$		0			0
$826$	−0.988513			−0.0343948
$827$	39.9126	−	20.3365i	1.38790	−	0.707169i	0.409194	−	0.912447i	$-0.365810\pi$
$827$	39.9126	−	20.3365i	1.38790	−	0.707169i	0.978704	+	0.205278i	$0.0658099\pi$
$828$		0			0
$829$	1.13270	−	1.55903i	0.0393402	−	0.0541472i	−0.788894	−	0.614530i	$-0.789346\pi$
$829$	1.13270	−	1.55903i	0.0393402	−	0.0541472i	0.828234	+	0.560382i	$0.189346\pi$
$830$	3.77752	+	26.0674i	0.131120	+	0.904813i
$831$		0			0
$832$	0.365462	+	2.30744i	0.0126701	+	0.0799960i
$833$	−3.02615	+	19.1064i	−0.104850	+	0.661997i
$834$		0			0
$835$	−16.5332	−	23.3979i	−0.572156	−	0.809716i
$836$	−1.16045	+	16.5845i	−0.0401350	+	0.573587i
$837$		0			0
$838$	−1.08387	−	2.12722i	−0.0374418	−	0.0734836i
$839$	13.0989	+	18.0291i	0.452224	+	0.622433i	0.972874	−	0.231337i	$-0.0743101\pi$
$839$	13.0989	+	18.0291i	0.452224	+	0.622433i	−0.520649	+	0.853771i	$0.674310\pi$
$840$		0			0
$841$	−7.55003	−	23.2366i	−0.260346	−	0.801262i
$842$	−11.6756	+	22.9146i	−0.402367	+	0.789690i
$843$		0			0
$844$	−17.0646	+	12.3982i	−0.587389	+	0.426763i
$845$	−14.9245	−	7.85367i	−0.513420	−	0.270174i
$846$		0			0
$847$	−0.208858	−	12.0274i	−0.00717646	−	0.413267i
$848$	−5.30569	−	5.30569i	−0.182198	−	0.182198i
$849$		0			0
$850$	−4.73048	−	15.9790i	−0.162254	−	0.548075i
$851$	−7.67714	−	5.57777i	−0.263169	−	0.191203i
$852$		0			0
$853$	−19.6630	−	10.0188i	−0.673247	−	0.343037i	0.0837200	−	0.996489i	$-0.473320\pi$
$853$	−19.6630	−	10.0188i	−0.673247	−	0.343037i	−0.756967	+	0.653453i	$0.773320\pi$
$854$	−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	0.795185	−	0.606367i	$-0.207374\pi$
$857$	5.52754	+	5.52754i	0.188817	+	0.188817i	−0.606367	+	0.795185i	$0.707374\pi$
$858$		0			0
$859$			13.0239i			0.444368i	0.975005	+	0.222184i	$0.0713186\pi$
$859$			13.0239i			0.444368i	−0.975005	+	0.222184i	$0.928681\pi$
$860$	2.64782	−	0.821942i	0.0902898	−	0.0280280i
$861$		0			0
$862$	−17.4506	+	2.76391i	−0.594371	+	0.0941392i
$863$	−10.2778	+	20.1714i	−0.349862	+	0.686643i	−0.997137	−	0.0756136i	$-0.975908\pi$
$863$	−10.2778	+	20.1714i	−0.349862	+	0.686643i	0.647275	+	0.762256i	$0.275908\pi$
$864$		0			0
$865$	−4.39489	−	0.0578751i	−0.149431	−	0.00196781i
$866$	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
$872$	2.89845	−	18.3001i	0.0981538	−	0.619719i
$873$		0			0
$874$	−18.0287	+	5.85787i	−0.609829	+	0.198145i
$875$	10.1675	−	6.79027i	0.343724	−	0.229553i
$876$		0			0
$877$	40.6927	+	6.44509i	1.37409	+	0.217635i	0.799432	−	0.600756i	$-0.205134\pi$
$877$	40.6927	+	6.44509i	1.37409	+	0.217635i	0.574661	+	0.818391i	$0.305134\pi$
$878$	−1.38333	+	0.704843i	−0.0466852	+	0.0237873i
$879$		0			0
$880$	6.86434	−	2.80729i	0.231397	−	0.0946337i
$881$	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
$883$	26.3472	+	4.17298i	0.886653	+	0.140432i	0.583117	−	0.812388i	$-0.301833\pi$
$883$	26.3472	+	4.17298i	0.886653	+	0.140432i	0.303536	+	0.952820i	$0.401833\pi$
$884$	4.57668	−	6.29926i	0.153931	−	0.211867i
$885$		0			0
$886$	−12.6073	+	4.09637i	−0.423551	+	0.137620i
$887$	−3.37666	−	21.3194i	−0.113377	−	0.715836i	−0.977244	−	0.212116i	$-0.931965\pi$
$887$	−3.37666	−	21.3194i	−0.113377	−	0.715836i	0.863867	−	0.503719i	$-0.168035\pi$
$888$		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
$893$	10.8058	+	21.2076i	0.361603	+	0.709685i
$894$		0			0
$895$	32.8166	−	31.9635i	1.09694	−	1.06842i
$896$	0.337931	+	1.04004i	0.0112895	+	0.0347454i
$897$		0			0
$898$	33.5575	−	5.31499i	1.11983	−	0.177363i
$899$	3.44654	−	2.50406i	0.114949	−	0.0835151i
$900$		0			0
$901$			25.0080i			0.833137i
$902$	17.7617	+	10.6734i	0.591401	+	0.355385i
$903$		0			0
$904$	−0.622199	+	1.91493i	−0.0206940	+	0.0636897i
$905$	−50.0694	+	24.6866i	−1.66436	+	0.820611i
$906$		0			0
$907$	43.6380	+	22.2347i	1.44897	+	0.738290i	0.988759	−	0.149518i	$-0.0477720\pi$
$907$	43.6380	+	22.2347i	1.44897	+	0.738290i	0.460216	+	0.887807i	$0.347772\pi$
$908$	6.07486	+	3.09529i	0.201601	+	0.102721i
$909$		0			0
$910$	5.40936	+	1.83670i	0.179319	+	0.0608861i
$911$	−9.70739	+	29.8763i	−0.321620	+	0.989845i	0.651323	+	0.758801i	$0.274214\pi$
$911$	−9.70739	+	29.8763i	−0.321620	+	0.989845i	−0.972943	+	0.231044i	$0.925786\pi$
$912$		0			0
$913$	33.4870	+	20.1231i	1.10826	+	0.665976i
$914$		−	8.43747i		−	0.279087i
$915$		0			0
$916$	14.5525	−	10.5730i	0.480828	−	0.349342i
$917$	−1.30329	+	0.206421i	−0.0430385	+	0.00681663i
$918$		0			0
$919$	1.01757	+	3.13176i	0.0335665	+	0.103307i	0.966436	−	0.256907i	$-0.0827035\pi$
$919$	1.01757	+	3.13176i	0.0335665	+	0.103307i	−0.932870	+	0.360214i	$0.882704\pi$
$920$	5.90020	+	6.05767i	0.194524	+	0.199715i
$921$		0			0
$922$	−10.2377	−	20.0927i	−0.337162	−	0.661718i
$923$	−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
$928$	0.334331	+	2.11088i	0.0109749	+	0.0692931i
$929$	−34.7596	+	11.2941i	−1.14043	+	0.370547i	−0.817530	−	0.575887i	$-0.804657\pi$
$929$	−34.7596	+	11.2941i	−1.14043	+	0.370547i	−0.322898	+	0.946434i	$0.604657\pi$
$930$		0			0
$931$	17.1010	−	23.5375i	0.560462	−	0.771410i
$932$	19.5597	+	3.09795i	0.640699	+	0.101477i
$933$		0			0
$934$	−24.4479			−0.799961
$935$	−22.7933	−	9.56131i	−0.745420	−	0.312688i
$936$		0			0
$937$	42.9456	−	21.8819i	1.40297	−	0.714850i	0.421566	−	0.906798i	$-0.361480\pi$
$937$	42.9456	−	21.8819i	1.40297	−	0.714850i	0.981405	+	0.191948i	$0.0614805\pi$
$938$	−0.883985	−	0.140009i	−0.0288631	−	0.00457147i
$939$		0			0
$940$	6.35348	−	8.50695i	0.207228	−	0.277466i
$941$	48.9385	−	15.9011i	1.59535	−	0.518360i	0.629398	−	0.777083i	$-0.283302\pi$
$941$	48.9385	−	15.9011i	1.59535	−	0.518360i	0.965952	+	0.258723i	$0.0833017\pi$
$942$		0			0
$943$	−3.69622	+	23.3370i	−0.120366	+	0.759959i
$944$	−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
$950$	−4.57125	+	24.6428i	−0.148311	+	0.799518i
$951$		0			0
$952$	1.65468	−	3.24749i	0.0536285	−	0.105252i
$953$	57.7544	−	9.14740i	1.87085	−	0.296313i	0.885211	−	0.465190i	$-0.154014\pi$
$953$	57.7544	−	9.14740i	1.87085	−	0.296313i	0.985637	+	0.168877i	$0.0540139\pi$
$954$		0			0
$955$	17.6001	−	33.4460i	0.569526	−	1.08229i
$956$			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
$962$	−5.22325	−	2.66138i	−0.168404	−	0.0858064i
$963$		0			0
$964$	−24.0841	−	17.4981i	−0.775696	−	0.563576i
$965$	−2.99199	+	8.81186i	−0.0963156	+	0.283664i
$966$		0			0
$967$	−5.32123	−	5.32123i	−0.171119	−	0.171119i	0.616352	−	0.787471i	$-0.288610\pi$
$967$	−5.32123	−	5.32123i	−0.171119	−	0.171119i	−0.787471	+	0.616352i	$0.788610\pi$
$968$	3.21703	−	10.5191i	0.103399	−	0.338096i
$969$		0			0
$970$	−14.1173	+	26.8275i	−0.453279	+	0.861379i
$971$	1.30297	−	0.946661i	0.0418142	−	0.0303798i	−0.566682	−	0.823937i	$-0.691773\pi$
$971$	1.30297	−	0.946661i	0.0418142	−	0.0303798i	0.608496	+	0.793557i	$0.291773\pi$
$972$		0			0
$973$	5.84411	−	11.4697i	0.187354	−	0.367702i
$974$	10.4656	+	32.2097i	0.335339	+	1.03207i
$975$		0			0
$976$	−4.18351	−	5.75810i	−0.133911	−	0.184312i
$977$	17.7034	+	34.7450i	0.566383	+	1.11159i	0.979600	+	0.200957i	$0.0644053\pi$
$977$	17.7034	+	34.7450i	0.566383	+	1.11159i	−0.413217	+	0.910633i	$0.635595\pi$
$978$		0			0
$979$	0.641057	−	9.16163i	0.0204883	−	0.292807i
$980$	−12.7908	−	2.19888i	−0.408586	−	0.0702407i
$981$		0			0
$982$	−4.32697	+	27.3194i	−0.138079	+	0.871798i
$983$	−2.00832	−	12.6800i	−0.0640554	−	0.404430i	−0.998794	−	0.0490940i	$-0.984367\pi$
$983$	−2.00832	−	12.6800i	−0.0640554	−	0.404430i	0.934739	−	0.355336i	$-0.115633\pi$
$984$		0			0
$985$	30.6744	−	41.0714i	0.977369	−	1.30864i
$986$	4.18683	−	5.76267i	0.133336	−	0.183521i
$987$		0			0
$988$	−10.4341	+	5.31646i	−0.331954	+	0.169139i
$989$	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	$0.428658\pi$
$992$	1.77608	−	0.904960i	0.0563907	−	0.0287325i
$993$		0			0
$994$	−10.7603	+	14.8102i	−0.341295	+	0.469752i
$995$	8.49971	−	1.23172i	0.269459	−	0.0390482i
$996$		0			0
$997$	5.34338	+	33.7368i	0.169227	+	1.06845i	0.915354	+	0.402651i	$0.131911\pi$
$997$	5.34338	+	33.7368i	0.169227	+	1.06845i	−0.746127	+	0.665804i	$0.768089\pi$
$998$	−2.40775	+	15.2019i	−0.0762161	+	0.481209i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bh.d.127.4	✓	96	165.17	odd	20	inner
990.2.bh.d.127.9	yes	96	55.17	even	20	inner
990.2.bh.d.343.4	yes	96	3.2	odd	2	inner
990.2.bh.d.343.9	yes	96	1.1	even	1	trivial
990.2.bh.d.523.4	yes	96	33.17	even	10	inner
990.2.bh.d.523.9	yes	96	11.6	odd	10	inner
990.2.bh.d.937.4	yes	96	15.2	even	4	inner
990.2.bh.d.937.9	yes	96	5.2	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.587785 - 0.809017i) q^{4} +(-0.320687 - 2.21295i) q^{5} +(-0.171071 - 1.08010i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.29039 - 1.82617i) q^{10} +(-3.30854 - 0.231505i) q^{11} +(-1.06061 - 2.08157i) q^{13} +(-0.642782 - 0.884714i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-1.51311 + 2.96964i) q^{17} +(4.05531 - 2.94635i) q^{19} +(-1.97881 - 1.04130i) q^{20} +(-3.05303 + 1.29577i) q^{22} +(-2.67409 - 2.67409i) q^{23} +(-4.79432 + 1.41933i) q^{25} +(-1.89002 - 1.37318i) q^{26} +(-0.974375 - 0.496469i) q^{28} +(-1.72903 - 1.25621i) q^{29} +(-0.615977 + 1.89578i) q^{31} +(-0.707107 - 0.707107i) q^{32} +3.33290i q^{34} +(-2.33536 + 0.724947i) q^{35} +(2.47839 - 0.392539i) q^{37} +(2.27569 - 4.46629i) q^{38} +(-2.23587 - 0.0294436i) q^{40} +(-3.67243 - 5.05467i) q^{41} +(-0.876728 + 0.876728i) q^{43} +(-2.13200 + 2.54059i) q^{44} +(-3.59664 - 1.16862i) q^{46} +(-0.742808 + 4.68990i) q^{47} +(5.52004 - 1.79357i) q^{49} +(-3.62741 + 3.44121i) q^{50} +(-2.30744 - 0.365462i) q^{52} +(6.68555 - 3.40646i) q^{53} +(0.548694 + 7.39587i) q^{55} -1.09357 q^{56} +(-2.11088 - 0.334331i) q^{58} +(0.531320 - 0.731299i) q^{59} +(6.76905 - 2.19940i) q^{61} +(0.311828 + 1.96880i) q^{62} +(-0.951057 - 0.309017i) q^{64} +(-4.26629 + 3.01462i) q^{65} +(0.578715 - 0.578715i) q^{67} +(1.51311 + 2.96964i) q^{68} +(-1.75170 + 1.70616i) q^{70} +(-5.17298 - 15.9208i) q^{71} +(5.49313 - 0.870026i) q^{73} +(2.03006 - 1.47492i) q^{74} -5.01264i q^{76} +(0.315947 + 3.61316i) q^{77} +(-1.22478 + 3.76949i) q^{79} +(-2.00555 + 0.988831i) q^{80} +(-5.56693 - 2.83649i) q^{82} +(-10.4956 - 5.34777i) q^{83} +(7.05690 + 2.39611i) q^{85} +(-0.383144 + 1.17920i) q^{86} +(-0.746223 + 3.23159i) q^{88} +2.76909i q^{89} +(-2.06687 + 1.50167i) q^{91} +(-3.73518 + 0.591594i) q^{92} +(1.46733 + 4.51596i) q^{94} +(-7.82063 - 8.02935i) q^{95} +(-6.15492 - 12.0797i) q^{97} +(4.10413 - 4.10413i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{7} + 24 q^{16} + 4 q^{22} + 8 q^{25} + 20 q^{28} - 16 q^{31} + 64 q^{37} - 40 q^{46} - 40 q^{52} - 36 q^{55} - 12 q^{58} - 80 q^{61} - 48 q^{67} - 52 q^{70} + 20 q^{73} + 48 q^{82} - 160 q^{85}+ \cdots + 48 q^{97}+O(q^{100}) \) 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

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