LMFDB - Embedded newform 603.2.v.a.8.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(8,603)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("603.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.v (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			8.7
Character	$\chi$	$=$	603.8
Dual form			603.2.v.a.377.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.219912 + 1.52952i) q^{2} +(-0.372079 - 0.109252i) q^{4} +(2.92951 + 1.88268i) q^{5} +(3.47051 + 0.498984i) q^{7} +(-1.03491 + 2.26614i) q^{8} +O(q^{10})$	\(q+(-0.219912 + 1.52952i) q^{2} +(-0.372079 - 0.109252i) q^{4} +(2.92951 + 1.88268i) q^{5} +(3.47051 + 0.498984i) q^{7} +(-1.03491 + 2.26614i) q^{8} +(-3.52383 + 4.06671i) q^{10} +(-3.30595 - 2.12460i) q^{11} +(2.28803 - 1.04491i) q^{13} +(-1.52641 + 5.19847i) q^{14} +(-3.89096 - 2.50057i) q^{16} +(1.54596 + 5.26506i) q^{17} +(-0.790502 - 5.49806i) q^{19} +(-0.884321 - 1.02056i) q^{20} +(3.97663 - 4.58928i) q^{22} +(6.41323 - 5.55710i) q^{23} +(2.96046 + 6.48249i) q^{25} +(1.09504 + 3.72937i) q^{26} +(-1.23679 - 0.564822i) q^{28} -3.46058i q^{29} +(-6.06023 - 2.76762i) q^{31} +(1.41747 - 1.63584i) q^{32} +(-8.39298 + 1.20673i) q^{34} +(9.22746 + 7.99564i) q^{35} -4.08727 q^{37} +8.58322 q^{38} +(-7.29819 + 4.69026i) q^{40} +(-11.9717 + 3.51520i) q^{41} +(-0.891705 - 3.03687i) q^{43} +(0.997955 + 1.15170i) q^{44} +(7.08934 + 11.0312i) q^{46} +(-1.65837 + 1.43699i) q^{47} +(5.07900 + 1.49133i) q^{49} +(-10.5661 + 3.10250i) q^{50} +(-0.965486 + 0.138816i) q^{52} +(-8.06069 - 2.36683i) q^{53} +(-5.68485 - 12.4481i) q^{55} +(-4.72243 + 7.34824i) q^{56} +(5.29302 + 0.761021i) q^{58} +(0.00334597 + 0.00152805i) q^{59} +(4.52145 + 7.03552i) q^{61} +(5.56583 - 8.66061i) q^{62} +(-3.86738 - 4.46319i) q^{64} +(8.67003 + 1.24656i) q^{65} +(4.75197 + 6.66475i) q^{67} -2.12792i q^{68} +(-14.2587 + 12.3552i) q^{70} +(-3.08601 + 10.5100i) q^{71} +(-0.971268 + 0.624196i) q^{73} +(0.898838 - 6.25156i) q^{74} +(-0.306546 + 2.13207i) q^{76} +(-10.4132 - 9.02307i) q^{77} +(1.73171 - 0.790846i) q^{79} +(-6.69083 - 14.6509i) q^{80} +(-2.74386 - 19.0839i) q^{82} +(7.31571 - 11.3835i) q^{83} +(-5.38352 + 18.3346i) q^{85} +(4.84104 - 0.696036i) q^{86} +(8.23599 - 5.29295i) q^{88} +(-4.50783 - 3.90606i) q^{89} +(8.46203 - 2.48467i) q^{91} +(-2.99335 + 1.36702i) q^{92} +(-1.83320 - 2.85252i) q^{94} +(8.03531 - 17.5949i) q^{95} -3.61146i q^{97} +(-3.39794 + 7.44046i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 28 q^{4}+O(q^{10}) $ 240 * q - 28 * q^4	$ 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) $ 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

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 $

$2$	−0.219912	+	1.52952i	−0.155501	+	1.08153i	0.751296	+	0.659965i	$0.229429\pi$
$2$	−0.219912	+	1.52952i	−0.155501	+	1.08153i	−0.906797	+	0.421567i	$0.861480\pi$
$3$		0			0
$3$		0			0
$4$	−0.372079	−	0.109252i	−0.186039	−	0.0546261i
$5$	2.92951	+	1.88268i	1.31012	+	0.841960i	0.994275	−	0.106852i	$-0.0340771\pi$
$5$	2.92951	+	1.88268i	1.31012	+	0.841960i	0.315841	+	0.948812i	$0.397713\pi$
$6$		0			0
$7$	3.47051	+	0.498984i	1.31173	+	0.188598i	0.762454	−	0.647043i	$-0.223995\pi$
$7$	3.47051	+	0.498984i	1.31173	+	0.188598i	0.549276	+	0.835641i	$0.314904\pi$
$8$	−1.03491	+	2.26614i	−0.365896	+	0.801200i
$9$		0			0
$10$	−3.52383	+	4.06671i	−1.11433	+	1.28601i
$11$	−3.30595	−	2.12460i	−0.996780	−	0.640592i	−0.0628411	−	0.998024i	$-0.520016\pi$
$11$	−3.30595	−	2.12460i	−0.996780	−	0.640592i	−0.933939	+	0.357432i	$0.883652\pi$
$12$		0			0
$13$	2.28803	−	1.04491i	0.634586	−	0.289806i	−0.0720307	−	0.997402i	$-0.522948\pi$
$13$	2.28803	−	1.04491i	0.634586	−	0.289806i	0.706616	+	0.707597i	$0.250221\pi$
$14$	−1.52641	+	5.19847i	−0.407950	+	1.38935i
$15$		0			0
$16$	−3.89096	−	2.50057i	−0.972740	−	0.625142i
$17$	1.54596	+	5.26506i	0.374951	+	1.27696i	0.903693	+	0.428182i	$0.140846\pi$
$17$	1.54596	+	5.26506i	0.374951	+	1.27696i	−0.528742	+	0.848783i	$0.677336\pi$
$18$		0			0
$19$	−0.790502	−	5.49806i	−0.181353	−	1.26134i	−0.853567	−	0.520984i	$-0.825565\pi$
$19$	−0.790502	−	5.49806i	−0.181353	−	1.26134i	0.672213	−	0.740358i	$-0.265344\pi$
$20$	−0.884321	−	1.02056i	−0.197740	−	0.228204i
$21$		0			0
$22$	3.97663	−	4.58928i	0.847821	−	0.978438i
$23$	6.41323	−	5.55710i	1.33725	−	1.15874i	0.363379	−	0.931642i	$-0.381623\pi$
$23$	6.41323	−	5.55710i	1.33725	−	1.15874i	0.973873	−	0.227094i	$-0.0729223\pi$
$24$		0			0
$25$	2.96046	+	6.48249i	0.592091	+	1.29650i
$26$	1.09504	+	3.72937i	0.214756	+	0.731390i
$27$		0			0
$28$	−1.23679	−	0.564822i	−0.233731	−	0.106741i
$29$		−	3.46058i		−	0.642613i	−0.946975	−	0.321307i	$-0.895878\pi$
$29$		−	3.46058i		−	0.642613i	0.946975	−	0.321307i	$-0.104122\pi$
$30$		0			0
$31$	−6.06023	−	2.76762i	−1.08845	−	0.497079i	−0.211362	−	0.977408i	$-0.567790\pi$
$31$	−6.06023	−	2.76762i	−1.08845	−	0.497079i	−0.877088	+	0.480329i	$0.840517\pi$
$32$	1.41747	−	1.63584i	0.250575	−	0.289179i
$33$		0			0
$34$	−8.39298	+	1.20673i	−1.43938	+	0.206952i
$35$	9.22746	+	7.99564i	1.55972	+	1.35151i
$36$		0			0
$37$	−4.08727			−0.671943			−0.335972	−	0.941872i	$-0.609065\pi$
$37$	−4.08727			−0.671943			−0.335972	+	0.941872i	$0.609065\pi$
$38$	8.58322			1.39238
$39$		0			0
$40$	−7.29819	+	4.69026i	−1.15394	+	0.741595i
$41$	−11.9717	+	3.51520i	−1.86966	+	0.548983i	−0.871367	+	0.490632i	$0.836766\pi$
$41$	−11.9717	+	3.51520i	−1.86966	+	0.548983i	−0.998296	+	0.0583504i	$0.981416\pi$
$42$		0			0
$43$	−0.891705	−	3.03687i	−0.135984	−	0.463118i	0.863140	−	0.504964i	$-0.168494\pi$
$43$	−0.891705	−	3.03687i	−0.135984	−	0.463118i	−0.999124	+	0.0418461i	$0.986676\pi$
$44$	0.997955	+	1.15170i	0.150447	+	0.173626i
$45$		0			0
$46$	7.08934	+	11.0312i	1.04527	+	1.62647i
$47$	−1.65837	+	1.43699i	−0.241898	+	0.209606i	−0.767369	−	0.641206i	$-0.778435\pi$
$47$	−1.65837	+	1.43699i	−0.241898	+	0.209606i	0.525471	+	0.850811i	$0.323889\pi$
$48$		0			0
$49$	5.07900	+	1.49133i	0.725571	+	0.213047i
$50$	−10.5661	+	3.10250i	−1.49428	+	0.438759i
$51$		0			0
$52$	−0.965486	+	0.138816i	−0.133889	+	0.0192503i
$53$	−8.06069	−	2.36683i	−1.10722	−	0.325109i	−0.323503	−	0.946227i	$-0.604861\pi$
$53$	−8.06069	−	2.36683i	−1.10722	−	0.325109i	−0.783717	+	0.621118i	$0.786679\pi$
$54$		0			0
$55$	−5.68485	−	12.4481i	−0.766545	−	1.67850i
$56$	−4.72243	+	7.34824i	−0.631061	+	0.981950i
$57$		0			0
$58$	5.29302	+	0.761021i	0.695007	+	0.0999270i
$59$	0.00334597	+	0.00152805i	0.000435608	+	0.000198936i	0.415633	−	0.909533i	$-0.363560\pi$
$59$	0.00334597	+	0.00152805i	0.000435608	+	0.000198936i	−0.415197	+	0.909731i	$0.636287\pi$
$60$		0			0
$61$	4.52145	+	7.03552i	0.578913	+	0.900806i	0.999981	−	0.00622321i	$-0.00198092\pi$
$61$	4.52145	+	7.03552i	0.578913	+	0.900806i	−0.421068	+	0.907029i	$0.638345\pi$
$62$	5.56583	−	8.66061i	0.706862	−	1.09990i
$63$		0			0
$64$	−3.86738	−	4.46319i	−0.483423	−	0.557899i
$65$	8.67003	+	1.24656i	1.07539	+	0.154617i
$66$		0			0
$67$	4.75197	+	6.66475i	0.580545	+	0.814228i
$67$	4.75197	+	6.66475i	0.580545	+	0.814228i
$68$		−	2.12792i		−	0.258048i
$69$		0			0
$70$	−14.2587	+	12.3552i	−1.70424	+	1.47673i
$71$	−3.08601	+	10.5100i	−0.366242	+	1.24731i	0.546045	+	0.837756i	$0.316133\pi$
$71$	−3.08601	+	10.5100i	−0.366242	+	1.24731i	−0.912287	+	0.409550i	$0.865686\pi$
$72$		0			0
$73$	−0.971268	+	0.624196i	−0.113678	+	0.0730566i	−0.596245	−	0.802803i	$-0.703341\pi$
$73$	−0.971268	+	0.624196i	−0.113678	+	0.0730566i	0.482566	+	0.875859i	$0.339705\pi$
$74$	0.898838	−	6.25156i	0.104488	−	0.726729i
$75$		0			0
$76$	−0.306546	+	2.13207i	−0.0351632	+	0.244566i
$77$	−10.4132	−	9.02307i	−1.18669	−	1.02827i
$78$		0			0
$79$	1.73171	−	0.790846i	0.194833	−	0.0889771i	−0.315610	−	0.948889i	$-0.602209\pi$
$79$	1.73171	−	0.790846i	0.194833	−	0.0889771i	0.510442	+	0.859912i	$0.329482\pi$
$80$	−6.69083	−	14.6509i	−0.748058	−	1.63802i
$81$		0			0
$82$	−2.74386	−	19.0839i	−0.303008	−	2.10747i
$83$	7.31571	−	11.3835i	0.803004	−	1.24950i	−0.161877	−	0.986811i	$-0.551755\pi$
$83$	7.31571	−	11.3835i	0.803004	−	1.24950i	0.964881	−	0.262687i	$-0.0846088\pi$
$84$		0			0
$85$	−5.38352	+	18.3346i	−0.583925	+	1.98866i
$86$	4.84104	−	0.696036i	0.522023	−	0.0750555i
$87$		0			0
$88$	8.23599	−	5.29295i	0.877960	−	0.564231i
$89$	−4.50783	−	3.90606i	−0.477829	−	0.414041i	0.382363	−	0.924012i	$-0.375111\pi$
$89$	−4.50783	−	3.90606i	−0.477829	−	0.414041i	−0.860191	+	0.509971i	$0.829656\pi$
$90$		0			0
$91$	8.46203	−	2.48467i	0.887061	−	0.260465i
$92$	−2.99335	+	1.36702i	−0.312079	+	0.142522i
$93$		0			0
$94$	−1.83320	−	2.85252i	−0.189080	−	0.294215i
$95$	8.03531	−	17.5949i	0.824405	−	1.80520i
$96$		0			0
$97$		−	3.61146i		−	0.366688i	−0.983049	−	0.183344i	$-0.941308\pi$
$97$		−	3.61146i		−	0.366688i	0.983049	−	0.183344i	$-0.0586922\pi$
$98$	−3.39794	+	7.44046i	−0.343244	+	0.751600i
$99$		0			0
$100$	−0.393296	−	2.73543i	−0.0393296	−	0.273543i
$101$	−2.38674	−	16.6002i	−0.237490	−	1.65178i	−0.664322	−	0.747447i	$-0.731280\pi$
$101$	−2.38674	−	16.6002i	−0.237490	−	1.65178i	0.426832	−	0.904331i	$-0.359630\pi$
$102$		0			0
$103$	−4.09156	+	8.95927i	−0.403154	+	0.882783i	0.593787	+	0.804622i	$0.297632\pi$
$103$	−4.09156	+	8.95927i	−0.403154	+	0.882783i	−0.996941	+	0.0781612i	$0.975095\pi$
$104$			6.26638i			0.614469i
$105$		0			0
$106$	5.39275	−	11.8085i	0.523790	−	1.14694i
$107$	−0.153997	−	0.239624i	−0.0148874	−	0.0231653i	0.833730	−	0.552172i	$-0.186201\pi$
$107$	−0.153997	−	0.239624i	−0.0148874	−	0.0231653i	−0.848618	+	0.529007i	$0.822565\pi$
$108$		0			0
$109$	14.1951	−	6.48268i	1.35964	−	0.620928i	0.403811	−	0.914843i	$-0.367685\pi$
$109$	14.1951	−	6.48268i	1.35964	−	0.620928i	0.955832	+	0.293915i	$0.0949582\pi$
$110$	20.2897	−	5.95760i	1.93455	−	0.568035i
$111$		0			0
$112$	−12.2559	−	10.6198i	−1.15807	−	1.00347i
$113$	−1.29879	+	0.834682i	−0.122180	+	0.0785202i	−0.600303	−	0.799772i	$-0.704953\pi$
$113$	−1.29879	+	0.834682i	−0.122180	+	0.0785202i	0.478124	+	0.878293i	$0.341317\pi$
$114$		0			0
$115$	29.2499	−	4.20549i	2.72756	−	0.392164i
$116$	−0.378076	+	1.28761i	−0.0351035	+	0.119551i
$117$		0			0
$118$	−0.00307300	+	0.00478169i	−0.000282893	+	0.000440190i
$119$	2.73809	+	19.0438i	0.251000	+	1.74575i
$120$		0			0
$121$	1.84578	+	4.04169i	0.167798	+	0.367427i
$122$	−11.7553	+	5.36845i	−1.06427	+	0.486037i
$123$		0			0
$124$	1.95252	+	1.69186i	0.175341	+	0.151934i
$125$	−1.05386	+	7.32977i	−0.0942603	+	0.655595i
$126$		0			0
$127$	−2.87998	+	20.0307i	−0.255557	+	1.77744i	0.308024	+	0.951379i	$0.400332\pi$
$127$	−2.87998	+	20.0307i	−0.255557	+	1.77744i	−0.563581	+	0.826061i	$0.690577\pi$
$128$	11.3189	−	7.27419i	1.00046	−	0.642954i
$129$		0			0
$130$	−3.81328	+	12.9868i	−0.334447	+	1.13902i
$131$	−1.31139	+	1.13632i	−0.114577	+	0.0992812i	−0.710265	−	0.703935i	$-0.751425\pi$
$131$	−1.31139	+	1.13632i	−0.114577	+	0.0992812i	0.595688	+	0.803216i	$0.296879\pi$
$132$		0			0
$133$		−	19.4755i		−	1.68874i
$134$	−11.2389	+	5.80256i	−0.970890	+	0.501265i
$135$		0			0
$136$	−13.5313	−	1.94550i	−1.16030	−	0.166825i
$137$	11.1225	+	12.8361i	0.950260	+	1.09666i	0.995219	+	0.0976696i	$0.0311388\pi$
$137$	11.1225	+	12.8361i	0.950260	+	1.09666i	−0.0449589	+	0.998989i	$0.514316\pi$
$138$		0			0
$139$	1.52375	−	2.37101i	0.129243	−	0.201106i	−0.770601	−	0.637318i	$-0.780044\pi$
$139$	1.52375	−	2.37101i	0.129243	−	0.201106i	0.899844	+	0.436212i	$0.143680\pi$
$140$	−2.55980	−	3.98313i	−0.216343	−	0.336636i
$141$		0			0
$142$	−15.3966	−	7.03138i	−1.29205	−	0.590060i
$143$	−9.78412	−	1.40674i	−0.818190	−	0.117638i
$144$		0			0
$145$	6.51516	−	10.1378i	0.541055	−	0.841898i
$146$	−0.741126	−	1.62284i	−0.0613360	−	0.134307i
$147$		0			0
$148$	1.52079	+	0.446543i	0.125008	+	0.0367056i
$149$	−7.78254	+	1.11896i	−0.637570	+	0.0916688i	−0.453517	−	0.891248i	$-0.649831\pi$
$149$	−7.78254	+	1.11896i	−0.637570	+	0.0916688i	−0.184053	+	0.982916i	$0.558922\pi$
$150$		0			0
$151$	1.32724	−	0.389712i	0.108009	−	0.0317143i	−0.227281	−	0.973829i	$-0.572984\pi$
$151$	1.32724	−	0.389712i	0.108009	−	0.0317143i	0.335290	+	0.942115i	$0.391166\pi$
$152$	13.2774	+	3.89861i	1.07694	+	0.316219i
$153$		0			0
$154$	16.0909	−	13.9429i	1.29664	−	1.12355i
$155$	−12.5430	−	19.5172i	−1.00748	−	1.56766i
$156$		0			0
$157$	−0.121557	−	0.140285i	−0.00970134	−	0.0111959i	0.750878	−	0.660441i	$-0.229631\pi$
$157$	−0.121557	−	0.140285i	−0.00970134	−	0.0111959i	−0.760580	+	0.649245i	$0.775085\pi$
$158$	0.828790	+	2.82260i	0.0659350	+	0.224554i
$159$		0			0
$160$	7.23226	−	2.12358i	0.571760	−	0.167884i
$161$	25.0301	−	16.0859i	1.97265	−	1.26774i
$162$		0			0
$163$	4.85391			0.380188			0.190094	−	0.981766i	$-0.439121\pi$
$163$	4.85391			0.380188			0.190094	+	0.981766i	$0.439121\pi$
$164$	4.83845			0.377820
$165$		0			0
$166$	15.8024	+	13.6929i	1.22651	+	1.06277i
$167$	−12.0428	+	1.73150i	−0.931901	+	0.133987i	−0.591511	−	0.806297i	$-0.701468\pi$
$167$	−12.0428	+	1.73150i	−0.931901	+	0.133987i	−0.340390	+	0.940284i	$0.610559\pi$
$168$		0			0
$169$	−4.36994	+	5.04318i	−0.336149	+	0.387937i
$170$	−26.8592	−	12.2662i	−2.06000	−	0.940773i
$171$		0			0
$172$			1.22737i			0.0935864i
$173$	4.20643	+	1.92101i	0.319809	+	0.146052i	0.568851	−	0.822441i	$-0.307388\pi$
$173$	4.20643	+	1.92101i	0.319809	+	0.146052i	−0.249041	+	0.968493i	$0.580116\pi$
$174$		0			0
$175$	7.03963	+	23.9748i	0.532146	+	1.81232i
$176$	7.55059	+	16.5335i	0.569147	+	1.24626i
$177$		0			0
$178$	6.96571	−	6.03582i	0.522102	−	0.452404i
$179$	13.8633	−	15.9991i	1.03619	−	1.19583i	0.0558695	−	0.998438i	$-0.482207\pi$
$179$	13.8633	−	15.9991i	1.03619	−	1.19583i	0.980324	−	0.197393i	$-0.0632476\pi$
$180$		0			0
$181$	13.9748	+	16.1277i	1.03874	+	1.19876i	0.979692	+	0.200509i	$0.0642597\pi$
$181$	13.9748	+	16.1277i	1.03874	+	1.19876i	0.0590439	+	0.998255i	$0.481195\pi$
$182$	1.93946	+	13.4892i	0.143762	+	0.999888i
$183$		0			0
$184$	5.95602	+	20.2844i	0.439084	+	1.49538i
$185$	−11.9737	−	7.69503i	−0.880323	−	0.565750i
$186$		0			0
$187$	6.07529	−	20.6906i	0.444270	−	1.51304i
$188$	0.774038	−	0.353491i	0.0564525	−	0.0257810i
$189$		0			0
$190$	25.1446	+	16.1595i	1.82418	+	1.17233i
$191$	7.75847	−	8.95375i	0.561383	−	0.647870i	−0.402114	−	0.915590i	$-0.631724\pi$
$191$	7.75847	−	8.95375i	0.561383	−	0.647870i	0.963497	+	0.267719i	$0.0862700\pi$
$192$		0			0
$193$	2.85313	−	6.24748i	0.205373	−	0.449703i	−0.778717	−	0.627375i	$-0.784129\pi$
$193$	2.85313	−	6.24748i	0.205373	−	0.449703i	0.984090	+	0.177672i	$0.0568565\pi$
$194$	5.52379	+	0.794201i	0.396585	+	0.0570203i
$195$		0			0
$196$	−1.72686	−	1.10978i	−0.123347	−	0.0792702i
$197$	−8.01710	−	2.35403i	−0.571195	−	0.167718i	−0.0166348	−	0.999862i	$-0.505295\pi$
$197$	−8.01710	−	2.35403i	−0.571195	−	0.167718i	−0.554560	+	0.832144i	$0.687113\pi$
$198$		0			0
$199$	2.67639	−	18.6147i	0.189724	−	1.31956i	−0.642997	−	0.765869i	$-0.722309\pi$
$199$	2.67639	−	18.6147i	0.189724	−	1.31956i	0.832721	−	0.553693i	$-0.186782\pi$
$200$	−17.7540			−1.25540
$201$		0			0
$202$	25.9151			1.82338
$203$	1.72677	−	12.0100i	0.121196	−	0.842935i
$204$		0			0
$205$	−41.6891	−	12.2410i	−2.91170	−	0.854951i
$206$	−12.8036	−	8.22837i	−0.892068	−	0.573298i
$207$		0			0
$208$	−11.5155	−	1.65568i	−0.798457	−	0.114801i
$209$	−9.06784	+	19.8558i	−0.627235	+	1.37345i
$210$		0			0
$211$	−1.05562	+	1.21825i	−0.0726716	+	0.0838675i	−0.790921	−	0.611918i	$-0.790398\pi$
$211$	−1.05562	+	1.21825i	−0.0726716	+	0.0838675i	0.718250	+	0.695786i	$0.244944\pi$
$212$	2.74063	+	1.76130i	0.188227	+	0.120966i
$213$		0			0
$214$	0.400374	−	0.182845i	0.0273690	−	0.0124990i
$215$	3.10519	−	10.5753i	0.211773	−	0.721231i
$216$		0			0
$217$	−19.6511	−	12.6290i	−1.33400	−	0.857312i
$218$	6.79371	+	23.1373i	0.460128	+	1.56705i
$219$		0			0
$220$	0.755231	+	5.25275i	0.0509177	+	0.354140i
$221$	9.03871	+	10.4312i	0.608010	+	0.701680i
$222$		0			0
$223$	−4.09617	+	4.72723i	−0.274300	+	0.316559i	−0.876139	−	0.482058i	$-0.839889\pi$
$223$	−4.09617	+	4.72723i	−0.274300	+	0.316559i	0.601839	+	0.798617i	$0.294435\pi$
$224$	5.73560	−	4.96992i	0.383226	−	0.332067i
$225$		0			0
$226$	−0.991042	−	2.17008i	−0.0659231	−	0.144351i
$227$	2.20803	+	7.51986i	0.146552	+	0.499110i	0.999747	−	0.0224813i	$-0.00715661\pi$
$227$	2.20803	+	7.51986i	0.146552	+	0.499110i	−0.853195	+	0.521592i	$0.825338\pi$
$228$		0			0
$229$	14.2345	+	6.50069i	0.940644	+	0.429578i	0.825899	−	0.563818i	$-0.190668\pi$
$229$	14.2345	+	6.50069i	0.940644	+	0.429578i	0.114744	+	0.993395i	$0.463395\pi$
$230$			45.6630i			3.01093i
$231$		0			0
$232$	7.84214	+	3.58139i	0.514862	+	0.235130i
$233$	7.50802	−	8.66471i	0.491867	−	0.567644i	−0.454497	−	0.890748i	$-0.650181\pi$
$233$	7.50802	−	8.66471i	0.491867	−	0.567644i	0.946363	+	0.323104i	$0.104726\pi$
$234$		0			0
$235$	−7.56359	+	1.08748i	−0.493394	+	0.0709394i
$236$	−0.00107802		0.000934111i	−7.01732e−5		6.08054e-5i
$237$		0			0
$238$	−29.7300			−1.92711
$239$	−17.1636			−1.11022			−0.555112	−	0.831776i	$-0.687325\pi$
$239$	−17.1636			−1.11022			−0.555112	+	0.831776i	$0.687325\pi$
$240$		0			0
$241$	9.41611	−	6.05137i	0.606545	−	0.389803i	−0.201015	−	0.979588i	$-0.564424\pi$
$241$	9.41611	−	6.05137i	0.606545	−	0.389803i	0.807560	+	0.589785i	$0.200788\pi$
$242$	−6.58775	+	1.93434i	−0.423477	+	0.124344i
$243$		0			0
$244$	−0.913691	−	3.11175i	−0.0584931	−	0.199209i
$245$	12.0713	+	13.9310i	0.771205	+	0.890018i
$246$		0			0
$247$	−7.55366	−	11.7537i	−0.480628	−	0.747872i
$248$	12.5436	−	10.8691i	0.796519	−	0.690187i
$249$		0			0
$250$	−10.9793	−	3.22380i	−0.694390	−	0.203891i
$251$	16.3109	−	4.78930i	1.02953	−	0.302298i	0.277012	−	0.960866i	$-0.410656\pi$
$251$	16.3109	−	4.78930i	1.02953	−	0.302298i	0.752521	+	0.658568i	$0.228838\pi$
$252$		0			0
$253$	−33.0084	+	4.74590i	−2.07522	+	0.298372i
$254$	−30.0040	−	8.80998i	−1.88262	−	0.552787i
$255$		0			0
$256$	3.73026	+	8.16814i	0.233142	+	0.510509i
$257$	−6.44324	+	10.0259i	−0.401918	+	0.625397i	−0.981937	−	0.189206i	$-0.939409\pi$
$257$	−6.44324	+	10.0259i	−0.401918	+	0.625397i	0.580019	+	0.814603i	$0.303045\pi$
$258$		0			0
$259$	−14.1849	−	2.03948i	−0.881408	−	0.126727i
$260$	−3.08975	−	1.41104i	−0.191618	−	0.0875090i
$261$		0			0
$262$	−1.44964	−	2.25568i	−0.0895591	−	0.139357i
$263$	12.8974	−	20.0688i	0.795290	−	1.23750i	−0.172318	−	0.985041i	$-0.555126\pi$
$263$	12.8974	−	20.0688i	0.795290	−	1.23750i	0.967609	−	0.252455i	$-0.0812378\pi$
$264$		0			0
$265$	−19.1579	−	22.1093i	−1.17686	−	1.35817i
$266$	29.7881	+	4.28289i	1.82643	+	0.262601i
$267$		0			0
$268$	−1.03997	−	2.99897i	−0.0635261	−	0.183191i
$269$			22.9098i			1.39684i	0.715691	+	0.698418i	$0.246112\pi$
$269$			22.9098i			1.39684i	−0.715691	+	0.698418i	$0.753888\pi$
$270$		0			0
$271$	1.77280	−	1.53614i	0.107690	−	0.0933138i	−0.599352	−	0.800486i	$-0.704575\pi$
$271$	1.77280	−	1.53614i	0.107690	−	0.0933138i	0.707041	+	0.707172i	$0.250029\pi$
$272$	7.15037	−	24.3519i	0.433555	−	1.47655i
$273$		0			0
$274$	−22.0790	+	14.1893i	−1.33384	+	0.857206i
$275$	3.98562	−	27.7206i	0.240342	−	1.67161i
$276$		0			0
$277$	−3.73421	+	25.9720i	−0.224367	+	1.56051i	0.496875	+	0.867822i	$0.334481\pi$
$277$	−3.73421	+	25.9720i	−0.224367	+	1.56051i	−0.721241	+	0.692684i	$0.756428\pi$
$278$	3.29141	+	2.85202i	0.197406	+	0.171053i
$279$		0			0
$280$	−27.6688	+	12.6359i	−1.65353	+	0.755140i
$281$	−5.26795	−	11.5352i	−0.314259	−	0.688132i	0.684921	−	0.728618i	$-0.259837\pi$
$281$	−5.26795	−	11.5352i	−0.314259	−	0.688132i	−0.999180	+	0.0404856i	$0.987110\pi$
$282$		0			0
$283$	2.17447	+	15.1238i	0.129259	+	0.899014i	0.946497	+	0.322714i	$0.104595\pi$
$283$	2.17447	+	15.1238i	0.129259	+	0.899014i	−0.817238	+	0.576300i	$0.804496\pi$
$284$	2.29648	−	3.57339i	0.136271	−	0.212042i
$285$		0			0
$286$	4.30328	−	14.6556i	0.254458	−	0.866606i
$287$	−43.3019	+	6.22587i	−2.55603	+	0.367501i
$288$		0			0
$289$	−11.0295	+	7.08825i	−0.648796	+	0.416956i
$290$	14.0732	+	12.1945i	0.826406	+	0.716084i
$291$		0			0
$292$	0.429583	−	0.126137i	0.0251394	−	0.00738161i
$293$	−8.02656	+	3.66561i	−0.468916	+	0.214147i	−0.635837	−	0.771823i	$-0.719345\pi$
$293$	−8.02656	+	3.66561i	−0.468916	+	0.214147i	0.166921	+	0.985970i	$0.446618\pi$
$294$		0			0
$295$	0.00692521	+	0.0107758i	0.000403201	+	0.000627394i
$296$	4.22996	−	9.26231i	0.245861	−	0.538361i
$297$		0			0
$298$		−	12.1496i		−	0.703808i
$299$	8.86702	−	19.4161i	0.512793	−	1.12286i
$300$		0			0
$301$	−1.57932	−	10.9844i	−0.0910306	−	0.633132i
$302$	0.304197	+	2.11574i	0.0175046	+	0.121747i
$303$		0			0
$304$	−10.6725	+	23.3694i	−0.612108	+	1.34033i
$305$			29.1231i			1.66758i
$306$		0			0
$307$	0.884250	−	1.93624i	0.0504668	−	0.110507i	−0.882719	−	0.469901i	$-0.844289\pi$
$307$	0.884250	−	1.93624i	0.0504668	−	0.110507i	0.933186	+	0.359395i	$0.117017\pi$
$308$	2.88873	+	4.49495i	0.164601	+	0.256124i
$309$		0			0
$310$	32.6103	−	14.8926i	1.85214	−	0.845845i
$311$	−2.63732	+	0.774388i	−0.149549	+	0.0439115i	−0.355650	−	0.934619i	$-0.615741\pi$
$311$	−2.63732	+	0.774388i	−0.149549	+	0.0439115i	0.206101	+	0.978531i	$0.433922\pi$
$312$		0			0
$313$	−16.7884	−	14.5473i	−0.948939	−	0.822260i	0.0352510	−	0.999378i	$-0.488777\pi$
$313$	−16.7884	−	14.5473i	−0.948939	−	0.822260i	−0.984190	+	0.177119i	$0.943322\pi$
$314$	0.241300	−	0.155074i	0.0136173	−	0.00875134i
$315$		0			0
$316$	−0.730735	+	0.105064i	−0.0411070	+	0.00591030i
$317$	−2.28892	+	7.79533i	−0.128558	+	0.437829i	−0.998465	−	0.0553870i	$-0.982361\pi$
$317$	−2.28892	+	7.79533i	−0.128558	+	0.437829i	0.869907	+	0.493216i	$0.164179\pi$
$318$		0			0
$319$	−7.35236	+	11.4405i	−0.411653	+	0.640544i
$320$	−2.92675	−	20.3560i	−0.163610	−	1.13794i
$321$		0			0
$322$	19.0992	+	41.8214i	1.06436	+	2.33062i
$323$	27.7255	−	12.6618i	1.54269	−	0.704522i
$324$		0			0
$325$	13.5472	+	11.7387i	0.751465	+	0.651148i
$326$	−1.06743	+	7.42415i	−0.0591196	+	0.411186i
$327$		0			0
$328$	4.42368	−	30.7674i	0.244257	−	1.69884i
$329$	−6.47242	+	4.15957i	−0.356836	+	0.229325i
$330$		0			0
$331$	−3.41032	+	11.6145i	−0.187448	+	0.638390i	0.811119	+	0.584881i	$0.198859\pi$
$331$	−3.41032	+	11.6145i	−0.187448	+	0.638390i	−0.998567	+	0.0535092i	$0.982959\pi$
$332$	−3.96569	+	3.43629i	−0.217646	+	0.188591i
$333$		0			0
$334$		−	18.8005i		−	1.02872i
$335$	1.37333	+	28.4709i	0.0750333	+	1.55553i
$336$		0			0
$337$	8.54767	+	1.22897i	0.465621	+	0.0669463i	0.371133	−	0.928580i	$-0.378969\pi$
$337$	8.54767	+	1.22897i	0.465621	+	0.0669463i	0.0944884	+	0.995526i	$0.469878\pi$
$338$	−6.75263	−	7.79295i	−0.367295	−	0.423881i
$339$		0			0
$340$	4.00619	−	6.23375i	0.217266	−	0.338072i
$341$	14.1547	+	22.0252i	0.766521	+	1.19273i
$342$		0			0
$343$	−5.44288	−	2.48568i	−0.293888	−	0.134214i
$344$	7.80479	+	1.12216i	0.420806	+	0.0605028i
$345$		0			0
$346$	−3.86327	+	6.01136i	−0.207691	+	0.323173i
$347$	9.41141	+	20.6081i	0.505231	+	1.10630i	0.974734	+	0.223371i	$0.0717060\pi$
$347$	9.41141	+	20.6081i	0.505231	+	1.10630i	−0.469503	+	0.882931i	$0.655567\pi$
$348$		0			0
$349$	9.48585	+	2.78530i	0.507766	+	0.149094i	0.525574	−	0.850748i	$-0.323851\pi$
$349$	9.48585	+	2.78530i	0.507766	+	0.149094i	−0.0178080	+	0.999841i	$0.505669\pi$
$350$	−38.2180	+	5.49491i	−2.04284	+	0.293715i
$351$		0			0
$352$	−8.16159	+	2.39646i	−0.435014	+	0.127732i
$353$	2.80003	+	0.822163i	0.149031	+	0.0437593i	0.355397	−	0.934715i	$-0.384346\pi$
$353$	2.80003	+	0.822163i	0.149031	+	0.0437593i	−0.206366	+	0.978475i	$0.566164\pi$
$354$		0			0
$355$	−28.8274	+	24.9791i	−1.53000	+	1.32575i
$356$	1.25052	+	1.94585i	0.0662775	+	0.103130i
$357$		0			0
$358$	21.4223	+	24.7226i	1.13220	+	1.30663i
$359$	1.03574	+	3.52742i	0.0546645	+	0.186170i	0.982299	−	0.187318i	$-0.0599796\pi$
$359$	1.03574	+	3.52742i	0.0546645	+	0.186170i	−0.927635	+	0.373489i	$0.878161\pi$
$360$		0			0
$361$	−11.3734	+	3.33953i	−0.598600	+	0.175765i
$362$	−27.7409	+	17.8280i	−1.45803	+	0.937018i
$363$		0			0
$364$	−3.42000			−0.179256
$365$	−4.02050			−0.210443
$366$		0			0
$367$	9.15538	+	7.93318i	0.477907	+	0.414109i	0.860219	−	0.509924i	$-0.170327\pi$
$367$	9.15538	+	7.93318i	0.477907	+	0.414109i	−0.382312	+	0.924033i	$0.624872\pi$
$368$	−38.8496	+	5.58572i	−2.02517	+	0.291176i
$369$		0			0
$370$	14.4028	−	16.6218i	0.748768	−	0.864124i
$371$	−26.7937	−	12.2363i	−1.39106	−	0.635275i
$372$		0			0
$373$			1.79689i			0.0930394i	0.998917	+	0.0465197i	$0.0148130\pi$
$373$			1.79689i			0.0930394i	−0.998917	+	0.0465197i	$0.985187\pi$
$374$	30.3105	+	13.8424i	1.56732	+	0.715772i
$375$		0			0
$376$	−1.54014	−	5.24524i	−0.0794267	−	0.270503i
$377$	−3.61599	−	7.91791i	−0.186233	−	0.407793i
$378$		0			0
$379$	−8.03858	+	6.96547i	−0.412914	+	0.357792i	−0.836408	−	0.548107i	$-0.815349\pi$
$379$	−8.03858	+	6.96547i	−0.412914	+	0.357792i	0.423494	+	0.905899i	$0.360803\pi$
$380$	−4.91204	+	5.66880i	−0.251983	+	0.290803i
$381$		0			0
$382$	11.9887	+	13.8357i	0.613397	+	0.707898i
$383$	0.521216	+	3.62514i	0.0266329	+	0.185236i	0.998795	−	0.0490725i	$-0.0156265\pi$
$383$	0.521216	+	3.62514i	0.0266329	+	0.185236i	−0.972162	+	0.234308i	$0.924717\pi$
$384$		0			0
$385$	−13.5179	−	46.0378i	−0.688937	−	2.34631i
$386$	8.92820	+	5.73780i	0.454433	+	0.292046i
$387$		0			0
$388$	−0.394560	+	1.34375i	−0.0200307	+	0.0682184i
$389$	−9.10151	+	4.15652i	−0.461465	+	0.210744i	−0.632561	−	0.774510i	$-0.717996\pi$
$389$	−9.10151	+	4.15652i	−0.461465	+	0.210744i	0.171096	+	0.985254i	$0.445269\pi$
$390$		0			0
$391$	39.1731	+	25.1750i	1.98107	+	1.27315i
$392$	−8.63586	+	9.96631i	−0.436177	+	0.503375i
$393$		0			0
$394$	5.36359	−	11.7446i	0.270214	−	0.591686i
$395$	6.56197	+	0.943469i	0.330169	+	0.0474711i
$396$		0			0
$397$	−25.4615	−	16.3631i	−1.27788	−	0.821242i	−0.287252	−	0.957855i	$-0.592742\pi$
$397$	−25.4615	−	16.3631i	−1.27788	−	0.821242i	−0.990624	+	0.136613i	$0.956378\pi$
$398$	27.8830	+	8.18718i	1.39765	+	0.410386i
$399$		0			0
$400$	4.69091	−	32.6260i	0.234545	−	1.63130i
$401$	30.1350			1.50487			0.752434	−	0.658668i	$-0.228880\pi$
$401$	30.1350			1.50487			0.752434	+	0.658668i	$0.228880\pi$
$402$		0			0
$403$	−16.7579			−0.834771
$404$	−0.925547	+	6.43732i	−0.0460477	+	0.320269i
$405$		0			0
$406$	17.9897	+	5.28226i	0.892815	+	0.262154i
$407$	13.5123	+	8.68383i	0.669780	+	0.430441i
$408$		0			0
$409$	−21.4169	−	3.07928i	−1.05900	−	0.152261i	−0.409258	−	0.912418i	$-0.634213\pi$
$409$	−21.4169	−	3.07928i	−1.05900	−	0.152261i	−0.649739	+	0.760158i	$0.725122\pi$
$410$	27.8908	−	61.0724i	1.37743	−	3.01615i
$411$		0			0
$412$	2.50120	−	2.88654i	0.123225	−	0.142210i
$413$	0.0108497	+	0.00697271i	0.000533881	+	0.000343105i
$414$		0			0
$415$	42.8629	−	19.5748i	2.10406	−	0.960890i
$416$	1.53390	−	5.22399i	0.0752057	−	0.256127i
$417$		0			0
$418$	−28.3757	−	18.2359i	−1.38790	−	0.891949i
$419$	9.39340	+	31.9910i	0.458898	+	1.56286i	0.786218	+	0.617949i	$0.212036\pi$
$419$	9.39340	+	31.9910i	0.458898	+	1.56286i	−0.327321	+	0.944913i	$0.606146\pi$
$420$		0			0
$421$	5.49072	+	38.1888i	0.267601	+	1.86121i	0.471030	+	0.882117i	$0.343882\pi$
$421$	5.49072	+	38.1888i	0.267601	+	1.86121i	−0.203429	+	0.979090i	$0.565209\pi$
$422$	−1.63119	−	1.88249i	−0.0794049	−	0.0916382i
$423$		0			0
$424$	13.7056	−	15.8172i	0.665605	−	0.768149i
$425$	−29.5540	+	25.6087i	−1.43358	+	1.24220i
$426$		0			0
$427$	12.1811	+	26.6730i	0.589487	+	1.29080i
$428$	0.0311195	+	0.105983i	0.00150422	+	0.00512290i
$429$		0			0
$430$	15.4923	+	7.07509i	0.747104	+	0.341191i
$431$		−	2.25764i		−	0.108747i	−0.998521	−	0.0543734i	$-0.982684\pi$
$431$		−	2.25764i		−	0.108747i	0.998521	−	0.0543734i	$-0.0173161\pi$
$432$		0			0
$433$	−4.47127	−	2.04196i	−0.214876	−	0.0981304i	0.305069	−	0.952330i	$-0.401320\pi$
$433$	−4.47127	−	2.04196i	−0.214876	−	0.0981304i	−0.519945	+	0.854200i	$0.674048\pi$
$434$	23.6378	−	27.2795i	1.13465	−	1.30946i
$435$		0			0
$436$	−5.98994	+	0.861223i	−0.286866	+	0.0412451i
$437$	−35.6229	−	30.8674i	−1.70408	−	1.47659i
$438$		0			0
$439$	−18.2069			−0.868969			−0.434484	−	0.900679i	$-0.643069\pi$
$439$	−18.2069			−0.868969			−0.434484	+	0.900679i	$0.643069\pi$
$440$	34.0923			1.62529
$441$		0			0
$442$	−17.9425	+	11.5309i	−0.853436	+	0.548470i
$443$	9.30467	−	2.73210i	0.442078	−	0.129806i	−0.0531157	−	0.998588i	$-0.516915\pi$
$443$	9.30467	−	2.73210i	0.442078	−	0.129806i	0.495194	+	0.868783i	$0.335097\pi$
$444$		0			0
$445$	−5.85187	−	19.9296i	−0.277405	−	0.944755i
$446$	−6.32959	−	7.30474i	−0.299715	−	0.345889i
$447$		0			0
$448$	−11.1947	−	17.4193i	−0.528901	−	0.822985i
$449$	9.22309	−	7.99185i	0.435264	−	0.377159i	−0.409489	−	0.912315i	$-0.634293\pi$
$449$	9.22309	−	7.99185i	0.435264	−	0.377159i	0.844753	+	0.535157i	$0.179747\pi$
$450$		0			0
$451$	47.0462	+	13.8140i	2.21532	+	0.650476i
$452$	0.574443	−	0.168672i	0.0270195	−	0.00793365i
$453$		0			0
$454$	−11.9873	+	1.72352i	−0.562593	+	0.0808887i
$455$	29.4674	+	8.65241i	1.38145	+	0.405631i
$456$		0			0
$457$	−4.90373	−	10.7377i	−0.229387	−	0.502287i	0.759582	−	0.650412i	$-0.225404\pi$
$457$	−4.90373	−	10.7377i	−0.229387	−	0.502287i	−0.988969	+	0.148125i	$0.952676\pi$
$458$	−13.0733	+	20.3424i	−0.610873	+	0.950537i
$459$		0			0
$460$	−11.3427	−	1.63084i	−0.528857	−	0.0760381i
$461$	−1.33405	−	0.609240i	−0.0621329	−	0.0283751i	0.384106	−	0.923289i	$-0.374510\pi$
$461$	−1.33405	−	0.609240i	−0.0621329	−	0.0283751i	−0.446239	+	0.894914i	$0.647237\pi$
$462$		0			0
$463$	−1.29722	−	2.01852i	−0.0602871	−	0.0938086i	0.809801	−	0.586704i	$-0.199575\pi$
$463$	−1.29722	−	2.01852i	−0.0602871	−	0.0938086i	−0.870089	+	0.492896i	$0.835938\pi$
$464$	−8.65342	+	13.4650i	−0.401725	+	0.625096i
$465$		0			0
$466$	11.6017	+	13.3891i	0.537440	+	0.620239i
$467$	2.26833	+	0.326137i	0.104966	+	0.0150918i	0.194598	−	0.980883i	$-0.437660\pi$
$467$	2.26833	+	0.326137i	0.104966	+	0.0150918i	−0.0896318	+	0.995975i	$0.528569\pi$
$468$		0			0
$469$	13.1661	+	25.5012i	0.607956	+	1.17754i
$470$		−	11.8078i		−	0.544653i
$471$		0			0
$472$	−0.00692556	+	0.00600103i	−0.000318775	+	0.000276220i
$473$	−3.50421	+	11.9342i	−0.161124	+	0.548737i
$474$		0			0
$475$	33.3009	−	21.4012i	1.52795	−	0.981954i
$476$	1.06180	−	7.38495i	0.0486673	−	0.338489i
$477$		0			0
$478$	3.77448	−	26.2521i	0.172641	−	1.20074i
$479$	−19.7752	−	17.1353i	−0.903551	−	0.782932i	0.0731979	−	0.997317i	$-0.476680\pi$
$479$	−19.7752	−	17.1353i	−0.903551	−	0.782932i	−0.976749	+	0.214386i	$0.931225\pi$
$480$		0			0
$481$	−9.35180	+	4.27083i	−0.426406	+	0.194733i
$482$	7.18497	+	15.7329i	0.327266	+	0.716613i
$483$		0			0
$484$	−0.245212	−	1.70548i	−0.0111460	−	0.0775220i
$485$	6.79922	−	10.5798i	0.308737	−	0.480404i
$486$		0			0
$487$	11.5913	−	39.4764i	0.525252	−	1.78885i	−0.0846986	−	0.996407i	$-0.526993\pi$
$487$	11.5913	−	39.4764i	0.525252	−	1.78885i	0.609951	−	0.792439i	$-0.291189\pi$
$488$	−20.6227	+	2.96510i	−0.933548	+	0.134224i
$489$		0			0
$490$	−23.9623	+	15.3996i	−1.08251	+	0.695685i
$491$	−14.2853	−	12.3783i	−0.644686	−	0.558623i	0.269964	−	0.962870i	$-0.412988\pi$
$491$	−14.2853	−	12.3783i	−0.644686	−	0.558623i	−0.914650	+	0.404247i	$0.867534\pi$
$492$		0			0
$493$	18.2201	−	5.34992i	0.820594	−	0.240948i
$494$	19.6387	−	8.96868i	0.883586	−	0.403520i
$495$		0			0
$496$	16.6595	+	25.9227i	0.748035	+	1.16396i
$497$	−15.9543	+	34.9351i	−0.715650	+	1.56706i
$498$		0			0
$499$			18.8284i			0.842874i	0.906858	+	0.421437i	$0.138474\pi$
$499$			18.8284i			0.842874i	−0.906858	+	0.421437i	$0.861526\pi$
$500$	1.19291	−	2.61212i	0.0533487	−	0.116817i
$501$		0			0
$502$	3.73838	+	26.0010i	0.166852	+	1.16048i
$503$	−1.74332	−	12.1251i	−0.0777309	−	0.540630i	−0.991061	−	0.133410i	$-0.957407\pi$
$503$	−1.74332	−	12.1251i	−0.0777309	−	0.540630i	0.913330	−	0.407220i	$-0.133502\pi$
$504$		0			0
$505$	24.2608	−	53.1238i	1.07959	−	2.36398i
$506$		−	51.5307i		−	2.29082i
$507$		0			0
$508$	3.25998	−	7.13836i	0.144638	−	0.316714i
$509$	−7.11384	−	11.0694i	−0.315315	−	0.490640i	0.647032	−	0.762463i	$-0.276010\pi$
$509$	−7.11384	−	11.0694i	−0.315315	−	0.490640i	−0.962347	+	0.271822i	$0.912374\pi$
$510$		0			0
$511$	−3.68226	+	1.68163i	−0.162894	+	0.0743910i
$512$	12.5058	−	3.67205i	0.552685	−	0.162283i
$513$		0			0
$514$	−13.9178	−	12.0599i	−0.613889	−	0.531938i
$515$	−28.8537	+	18.5432i	−1.27145	+	0.817109i
$516$		0			0
$517$	8.53550	−	1.22722i	0.375391	−	0.0539731i
$518$	6.23885	−	21.2476i	0.274119	−	0.933565i
$519$		0			0
$520$	−11.7976	+	18.3574i	−0.517358	+	0.805025i
$521$	4.78889	+	33.3075i	0.209805	+	1.45923i	0.773790	+	0.633442i	$0.218358\pi$
$521$	4.78889	+	33.3075i	0.209805	+	1.45923i	−0.563985	+	0.825785i	$0.690733\pi$
$522$		0			0
$523$	−3.00414	−	6.57814i	−0.131362	−	0.287642i	0.832509	−	0.554011i	$-0.186903\pi$
$523$	−3.00414	−	6.57814i	−0.131362	−	0.287642i	−0.963871	+	0.266369i	$0.914176\pi$
$524$	0.612086	−	0.279530i	0.0267391	−	0.0122113i
$525$		0			0
$526$	27.8593	+	24.1402i	1.21472	+	1.05256i
$527$	5.20278	−	36.1861i	0.226637	−	1.57629i
$528$		0			0
$529$	6.97498	−	48.5120i	0.303260	−	2.10922i
$530$	38.0297	−	24.4402i	1.65190	−	1.06161i
$531$		0			0
$532$	−2.12774	+	7.24642i	−0.0922493	+	0.314172i
$533$	−23.7185	+	20.5522i	−1.02736	+	0.890215i
$534$		0			0
$535$		−	0.991906i		−	0.0428838i
$536$	−20.0211	+	3.87119i	−0.864779	+	0.167210i
$537$		0			0
$538$	−35.0410	−	5.03813i	−1.51072	−	0.217209i
$539$	−13.6224	−	15.7211i	−0.586759	−	0.677156i
$540$		0			0
$541$	−18.1890	+	28.3026i	−0.782005	+	1.21682i	0.189982	+	0.981788i	$0.439157\pi$
$541$	−18.1890	+	28.3026i	−0.782005	+	1.21682i	−0.971987	+	0.235036i	$0.924479\pi$
$542$	1.95969	+	3.04934i	0.0841760	+	0.130980i
$543$		0			0
$544$	10.8042	+	4.93410i	0.463225	+	0.211548i
$545$	53.7894	+	7.73375i	2.30409	+	0.331277i
$546$		0			0
$547$	15.8504	−	24.6638i	0.677716	−	1.05455i	−0.316650	−	0.948543i	$-0.602558\pi$
$547$	15.8504	−	24.6638i	0.677716	−	1.05455i	0.994366	−	0.106004i	$-0.0338057\pi$
$548$	−2.73608	−	5.99118i	−0.116880	−	0.255931i
$549$		0			0
$550$	41.5226	+	12.1921i	1.77053	+	0.519875i
$551$	−19.0265	+	2.73559i	−0.810555	+	0.116540i
$552$		0			0
$553$	6.40454	−	1.88054i	0.272349	−	0.0799688i
$554$	−38.9034	−	11.4231i	−1.65285	−	0.485320i
$555$		0			0
$556$	−0.825995	+	0.715728i	−0.0350300	+	0.0303536i
$557$	1.91900	+	2.98602i	0.0813107	+	0.126522i	0.879527	−	0.475849i	$-0.157859\pi$
$557$	1.91900	+	2.98602i	0.0813107	+	0.126522i	−0.798216	+	0.602371i	$0.794223\pi$
$558$		0			0
$559$	−5.21350	−	6.01670i	−0.220507	−	0.254479i
$560$	−15.9100	−	54.1846i	−0.672322	−	2.28972i
$561$		0			0
$562$	18.8018	−	5.52070i	0.793105	−	0.232877i
$563$	−18.2913	+	11.7551i	−0.770888	+	0.495419i	−0.865998	−	0.500047i	$-0.833316\pi$
$563$	−18.2913	+	11.7551i	−0.770888	+	0.495419i	0.0951104	+	0.995467i	$0.469680\pi$
$564$		0			0
$565$	−5.37625			−0.226181
$566$	−23.6103			−0.992413
$567$		0			0
$568$	−20.6233	−	17.8702i	−0.865335	−	0.749817i
$569$	−13.6648	+	1.96471i	−0.572860	+	0.0823648i	−0.422656	−	0.906290i	$-0.638902\pi$
$569$	−13.6648	+	1.96471i	−0.572860	+	0.0823648i	−0.150204	+	0.988655i	$0.547993\pi$
$570$		0			0
$571$	5.51092	−	6.35994i	0.230625	−	0.266155i	−0.628628	−	0.777706i	$-0.716383\pi$
$571$	5.51092	−	6.35994i	0.230625	−	0.266155i	0.859253	+	0.511551i	$0.170929\pi$
$572$	3.48677	+	1.59236i	0.145789	+	0.0665798i
$573$		0			0
$574$		−	67.6001i		−	2.82158i
$575$	55.0100	+	25.1222i	2.29407	+	1.04767i
$576$		0			0
$577$	3.13615	+	10.6807i	0.130560	+	0.444645i	0.998660	−	0.0517426i	$-0.0164775\pi$
$577$	3.13615	+	10.6807i	0.130560	+	0.444645i	−0.868101	+	0.496388i	$0.834659\pi$
$578$	−8.41609	−	18.4287i	−0.350063	−	0.766531i
$579$		0			0
$580$	−3.53173	+	3.06026i	−0.146647	+	0.127070i
$581$	31.0694	−	35.8560i	1.28898	−	1.48756i
$582$		0			0
$583$	21.6196	+	24.9504i	0.895393	+	1.03334i
$584$	−0.409339	−	2.84701i	−0.0169386	−	0.117810i
$585$		0			0
$586$	−3.84148	−	13.0829i	−0.158690	−	0.540448i
$587$	−7.77439	−	4.99630i	−0.320884	−	0.206219i	0.370276	−	0.928922i	$-0.379263\pi$
$587$	−7.77439	−	4.99630i	−0.320884	−	0.206219i	−0.691159	+	0.722703i	$0.742900\pi$
$588$		0			0
$589$	−10.4259	+	35.5073i	−0.429591	+	1.46305i
$590$	−0.0180048	+	0.00822251i	−0.000741245	+	0.000338515i
$591$		0			0
$592$	15.9034	+	10.2205i	0.653626	+	0.420060i
$593$	−3.36063	+	3.87837i	−0.138004	+	0.159266i	−0.820545	−	0.571582i	$-0.806330\pi$
$593$	−3.36063	+	3.87837i	−0.138004	+	0.159266i	0.682540	+	0.730848i	$0.260875\pi$
$594$		0			0
$595$	−27.8322	+	60.9440i	−1.14101	+	2.49846i
$596$	3.01797	+	0.433918i	0.123621	+	0.0177740i
$597$		0			0
$598$	27.7473	+	17.8321i	1.13467	+	0.729208i
$599$	−1.43367	−	0.420965i	−0.0585784	−	0.0172002i	0.252312	−	0.967646i	$-0.418809\pi$
$599$	−1.43367	−	0.420965i	−0.0585784	−	0.0172002i	−0.310890	+	0.950446i	$0.600627\pi$
$600$		0			0
$601$	−4.94386	+	34.3853i	−0.201664	+	1.40261i	0.597681	+	0.801734i	$0.296089\pi$
$601$	−4.94386	+	34.3853i	−0.201664	+	1.40261i	−0.799345	+	0.600872i	$0.794820\pi$
$602$	17.1482			0.698908
$603$		0			0
$604$	−0.536414			−0.0218264
$605$	−2.20199	+	15.3152i	−0.0895237	+	0.622651i
$606$		0			0
$607$	0.906640	+	0.266213i	0.0367994	+	0.0108053i	0.300080	−	0.953914i	$-0.402986\pi$
$607$	0.906640	+	0.266213i	0.0367994	+	0.0108053i	−0.263281	+	0.964719i	$0.584805\pi$
$608$	−10.1145	−	6.50018i	−0.410196	−	0.263617i
$609$		0			0
$610$	−44.5443	−	6.40450i	−1.80354	−	0.259310i
$611$	−2.29288	+	5.02071i	−0.0927601	+	0.203116i
$612$		0			0
$613$	−3.70888	+	4.28027i	−0.149800	+	0.172879i	−0.825690	−	0.564124i	$-0.809214\pi$
$613$	−3.70888	+	4.28027i	−0.149800	+	0.172879i	0.675890	+	0.737003i	$0.263759\pi$
$614$	2.76705	+	1.77828i	0.111669	+	0.0717654i
$615$		0			0
$616$	31.2242	−	14.2596i	1.25806	−	0.574536i
$617$	−11.5067	+	39.1883i	−0.463243	+	1.57766i	0.314615	+	0.949219i	$0.398125\pi$
$617$	−11.5067	+	39.1883i	−0.463243	+	1.57766i	−0.777858	+	0.628441i	$0.783694\pi$
$618$		0			0
$619$	21.2307	+	13.6441i	0.853334	+	0.548405i	0.892613	−	0.450824i	$-0.148870\pi$
$619$	21.2307	+	13.6441i	0.853334	+	0.548405i	−0.0392788	+	0.999228i	$0.512506\pi$
$620$	2.53467	+	8.63230i	0.101795	+	0.346681i
$621$		0			0
$622$	−0.604463	−	4.20413i	−0.0242368	−	0.168570i
$623$	−13.6954	−	15.8053i	−0.548695	−	0.633227i
$624$		0			0
$625$	6.44741	−	7.44071i	0.257897	−	0.297628i
$626$	25.9423	−	22.4791i	1.03686	−	0.898446i
$627$		0			0
$628$	0.0299025	+	0.0654774i	0.00119324	+	0.00261283i
$629$	−6.31876	−	21.5197i	−0.251945	−	0.858047i
$630$		0			0
$631$	−35.6654	−	16.2878i	−1.41982	−	0.648408i	−0.450175	−	0.892940i	$-0.648638\pi$
$631$	−35.6654	−	16.2878i	−1.41982	−	0.648408i	−0.969641	+	0.244532i	$0.921366\pi$
$632$			4.74275i			0.188656i
$633$		0			0
$634$	−11.4197	−	5.21522i	−0.453536	−	0.207123i
$635$	−46.1484	+	53.2581i	−1.83134	+	2.11348i
$636$		0			0
$637$	13.1792	−	1.89488i	0.522179	−	0.0750780i
$638$	−15.8816	−	13.7615i	−0.628757	−	0.544821i
$639$		0			0
$640$	46.8537			1.85205
$641$	−8.54727			−0.337597			−0.168798	−	0.985651i	$-0.553989\pi$
$641$	−8.54727			−0.337597			−0.168798	+	0.985651i	$0.553989\pi$
$642$		0			0
$643$	−14.6476	+	9.41343i	−0.577645	+	0.371230i	−0.796601	−	0.604505i	$-0.793371\pi$
$643$	−14.6476	+	9.41343i	−0.577645	+	0.371230i	0.218957	+	0.975735i	$0.429735\pi$
$644$	−11.0706	+	3.25062i	−0.436242	+	0.128092i
$645$		0			0
$646$	13.2693	+	45.1912i	0.522074	+	1.77802i
$647$	15.5790	+	17.9791i	0.612473	+	0.706832i	0.974259	−	0.225429i	$-0.0723785\pi$
$647$	15.5790	+	17.9791i	0.612473	+	0.706832i	−0.361786	+	0.932261i	$0.617833\pi$
$648$		0			0
$649$	−0.00781509	−	0.0121605i	−0.000306769	−	0.000477342i
$650$	−20.9338	+	18.1393i	−0.821092	+	0.711480i
$651$		0			0
$652$	−1.80604	−	0.530301i	−0.0707299	−	0.0207682i
$653$	26.8182	−	7.87452i	1.04948	−	0.308154i	0.288870	−	0.957368i	$-0.406720\pi$
$653$	26.8182	−	7.87452i	1.04948	−	0.308154i	0.760605	+	0.649214i	$0.224902\pi$
$654$		0			0
$655$	−5.98106	+	0.859947i	−0.233699	+	0.0336009i
$656$	55.3714	+	16.2585i	2.16189	+	0.634788i
$657$		0			0
$658$	−4.93878	−	10.8144i	−0.192534	−	0.421590i
$659$	17.8622	−	27.7942i	0.695813	−	1.08271i	−0.296022	−	0.955181i	$-0.595660\pi$
$659$	17.8622	−	27.7942i	0.695813	−	1.08271i	0.991835	−	0.127526i	$-0.0407035\pi$
$660$		0			0
$661$	0.468707	+	0.0673899i	0.0182306	+	0.00262116i	0.151424	−	0.988469i	$-0.451614\pi$
$661$	0.468707	+	0.0673899i	0.0182306	+	0.00262116i	−0.133194	+	0.991090i	$0.542523\pi$
$662$	−17.0146	−	7.77031i	−0.661292	−	0.302002i
$663$		0			0
$664$	18.2254	+	28.3593i	0.707282	+	1.10055i
$665$	36.6662	−	57.0537i	1.42185	−	2.21245i
$666$		0			0
$667$	−19.2308	−	22.1935i	−0.744619	−	0.859336i
$668$	4.67005	+	0.671451i	0.180690	+	0.0259792i
$669$		0			0
$670$	−43.8487	−	4.16053i	−1.69402	−	0.160735i
$671$		−	32.8653i		−	1.26875i
$672$		0			0
$673$	14.2321	−	12.3322i	0.548606	−	0.475370i	−0.335901	−	0.941897i	$-0.609041\pi$
$673$	14.2321	−	12.3322i	0.548606	−	0.475370i	0.884507	+	0.466528i	$0.154495\pi$
$674$	−3.75946	+	12.8036i	−0.144809	+	0.493175i
$675$		0			0
$676$	2.17694	−	1.39903i	0.0837284	−	0.0538090i
$677$	5.45774	−	37.9594i	0.209758	−	1.45890i	−0.564188	−	0.825646i	$-0.690811\pi$
$677$	5.45774	−	37.9594i	0.209758	−	1.45890i	0.773946	−	0.633252i	$-0.218280\pi$
$678$		0			0
$679$	1.80206	−	12.5336i	0.0691567	−	0.480995i
$680$	−35.9772	−	31.1744i	−1.37966	−	1.19548i
$681$		0			0
$682$	−36.8007	+	16.8063i	−1.40917	+	0.643547i
$683$	4.80858	+	10.5293i	0.183995	+	0.402893i	0.979043	−	0.203654i	$-0.0652816\pi$
$683$	4.80858	+	10.5293i	0.183995	+	0.402893i	−0.795048	+	0.606547i	$0.792554\pi$
$684$		0			0
$685$	8.41728	+	58.5435i	0.321608	+	2.23683i
$686$	4.99885	−	7.77836i	0.190857	−	0.296979i
$687$		0			0
$688$	−4.12431	+	14.0461i	−0.157238	+	0.535503i
$689$	−20.9162	+	3.00730i	−0.796845	+	0.114569i
$690$		0			0
$691$	−39.7692	+	25.5581i	−1.51289	+	0.972275i	−0.519881	+	0.854239i	$0.674024\pi$
$691$	−39.7692	+	25.5581i	−1.51289	+	0.972275i	−0.993009	+	0.118036i	$0.962340\pi$
$692$	−1.35525	−	1.17433i	−0.0515189	−	0.0446413i
$693$		0			0
$694$	−33.5902	+	9.86296i	−1.27507	+	0.374393i
$695$	8.92770	−	4.07715i	0.338647	−	0.154655i
$696$		0			0
$697$	−37.0155	−	57.5972i	−1.40206	−	2.18165i
$698$	−6.34621	+	13.8963i	−0.240208	+	0.525981i
$699$		0			0
$700$		−	9.68960i		−	0.366232i
$701$	−14.2291	+	31.1573i	−0.537425	+	1.17680i	0.424986	+	0.905200i	$0.360279\pi$
$701$	−14.2291	+	31.1573i	−0.537425	+	1.17680i	−0.962411	+	0.271597i	$0.912448\pi$
$702$		0			0
$703$	3.23099	+	22.4721i	0.121859	+	0.847550i
$704$	3.30284	+	22.9717i	0.124480	+	0.865780i
$705$		0			0
$706$	−1.87327	+	4.10189i	−0.0705015	+	0.154377i
$707$		−	58.8020i		−	2.21148i
$708$		0			0
$709$	21.0127	−	46.0115i	0.789150	−	1.72800i	0.110083	−	0.993922i	$-0.464888\pi$
$709$	21.0127	−	46.0115i	0.789150	−	1.72800i	0.679067	−	0.734076i	$-0.262384\pi$
$710$	−31.8665	−	49.5853i	−1.19593	−	1.86090i
$711$		0			0
$712$	13.5168	−	6.17294i	0.506565	−	0.231341i
$713$	−54.2456	+	15.9279i	−2.03151	+	0.596506i
$714$		0			0
$715$	−26.0142	−	22.5414i	−0.972877	−	0.843002i
$716$	−6.90619	+	4.43834i	−0.258096	+	0.165869i
$717$		0			0
$718$	−5.62303	+	0.808469i	−0.209850	+	0.0301718i
$719$	−7.93083	+	27.0099i	−0.295770	+	1.00730i	0.668793	+	0.743448i	$0.266811\pi$
$719$	−7.93083	+	27.0099i	−0.295770	+	1.00730i	−0.964563	+	0.263851i	$0.915007\pi$
$720$		0			0
$721$	−18.6703	+	29.0516i	−0.695320	+	1.08194i
$722$	−2.60673	−	18.1302i	−0.0970125	−	0.674737i
$723$		0			0
$724$	−3.43772	−	7.52756i	−0.127762	−	0.279760i
$725$	22.4332	−	10.2449i	0.833148	−	0.380486i
$726$		0			0
$727$	−32.1943	−	27.8965i	−1.19402	−	1.03462i	−0.998546	−	0.0539151i	$-0.982830\pi$
$727$	−32.1943	−	27.8965i	−1.19402	−	1.03462i	−0.195474	−	0.980709i	$-0.562625\pi$
$728$	−3.12682	+	21.7475i	−0.115888	+	0.806016i
$729$		0			0
$730$	0.884154	−	6.14943i	0.0327240	−	0.227601i
$731$	14.6107	−	9.38975i	0.540398	−	0.347293i
$732$		0			0
$733$	10.3562	−	35.2701i	0.382516	−	1.30273i	−0.513264	−	0.858231i	$-0.671564\pi$
$733$	10.3562	−	35.2701i	0.382516	−	1.30273i	0.895780	−	0.444498i	$-0.146618\pi$
$734$	−14.1473	+	12.2587i	−0.522187	+	0.452478i
$735$		0			0
$736$		−	18.3681i		−	0.677056i
$737$	−1.54981	−	32.1293i	−0.0570879	−	1.18350i
$738$		0			0
$739$	14.8962	+	2.14176i	0.547967	+	0.0787858i	0.410738	−	0.911754i	$-0.365271\pi$
$739$	14.8962	+	2.14176i	0.547967	+	0.0787858i	0.137229	+	0.990539i	$0.456180\pi$
$740$	3.61446	+	4.17131i	0.132870	+	0.153340i
$741$		0			0
$742$	24.6078	−	38.2905i	0.903382	−	1.40569i
$743$	9.02918	+	14.0497i	0.331248	+	0.515433i	0.966430	−	0.256930i	$-0.0827111\pi$
$743$	9.02918	+	14.0497i	0.331248	+	0.515433i	−0.635181	+	0.772363i	$0.719075\pi$
$744$		0			0
$745$	−24.9057	−	11.3740i	−0.912472	−	0.416712i
$746$	−2.74837	−	0.395157i	−0.100625	−	0.0144677i
$747$		0			0
$748$	−4.52098	+	7.03478i	−0.165303	+	0.257217i
$749$	−0.414879	−	0.908458i	−0.0151593	−	0.0331943i
$750$		0			0
$751$	−21.1900	−	6.22195i	−0.773234	−	0.227042i	−0.128768	−	0.991675i	$-0.541102\pi$
$751$	−21.1900	−	6.22195i	−0.773234	−	0.227042i	−0.644466	+	0.764633i	$0.722920\pi$
$752$	10.0459	−	1.44439i	0.366337	−	0.0526714i
$753$		0			0
$754$	12.9058	−	3.78948i	0.470001	−	0.138005i
$755$	4.62186	+	1.35710i	0.168207	+	0.0493899i
$756$		0			0
$757$	−31.4315	+	27.2355i	−1.14240	+	0.989892i	−0.142396	+	0.989810i	$0.545481\pi$
$757$	−31.4315	+	27.2355i	−1.14240	+	0.989892i	−1.00000		8.22724e-5i	$0.999974\pi$
$758$	−8.88603	−	13.8269i	−0.322755	−	0.502217i
$759$		0			0
$760$	31.5565	+	36.4182i	1.14468	+	1.32103i
$761$	12.2034	+	41.5608i	0.442371	+	1.50658i	0.815477	+	0.578790i	$0.196475\pi$
$761$	12.2034	+	41.5608i	0.442371	+	1.50658i	−0.373106	+	0.927789i	$0.621707\pi$
$762$		0			0
$763$	52.4989	−	15.4151i	1.90059	−	0.558063i
$764$	−3.86498	+	2.48387i	−0.139830	+	0.0898632i
$765$		0			0
$766$	−5.65934			−0.204480
$767$	0.00925236			0.000334083
$768$		0			0
$769$	2.56549	+	2.22301i	0.0925140	+	0.0801638i	0.699890	−	0.714251i	$-0.253232\pi$
$769$	2.56549	+	2.22301i	0.0925140	+	0.0801638i	−0.607376	+	0.794415i	$0.707778\pi$
$770$	73.3884	−	10.5517i	2.64474	−	0.380256i
$771$		0			0
$772$	−1.74414	+	2.01284i	−0.0627729	+	0.0724438i
$773$	40.7607	+	18.6148i	1.46606	+	0.669528i	0.979004	−	0.203842i	$-0.0653430\pi$
$773$	40.7607	+	18.6148i	1.46606	+	0.669528i	0.487057	+	0.873370i	$0.338070\pi$
$774$		0			0
$775$		−	47.4788i		−	1.70549i
$776$	8.18405	+	3.73753i	0.293790	+	0.134170i
$777$		0			0
$778$	−4.35594	−	14.8350i	−0.156168	−	0.531860i
$779$	28.7904	+	63.0422i	1.03152	+	2.25872i
$780$		0			0
$781$	32.5317	−	28.1889i	1.16408	−	1.00868i
$782$	−47.1202	+	54.3796i	−1.68502	+	1.94461i
$783$		0			0
$784$	−16.0330	−	18.5031i	−0.572608	−	0.660825i
$785$	−0.0919921	−	0.639819i	−0.00328334	−	0.0228361i
$786$		0			0
$787$	−1.74837	−	5.95442i	−0.0623228	−	0.212252i	0.922444	−	0.386130i	$-0.126188\pi$
$787$	−1.74837	−	5.95442i	−0.0623228	−	0.212252i	−0.984767	+	0.173878i	$0.944370\pi$
$788$	2.72581	+	1.75177i	0.0971030	+	0.0624043i
$789$		0			0
$790$	−2.88611	+	9.82917i	−0.102683	+	0.349706i
$791$	−4.92396	+	2.24869i	−0.175076	+	0.0799544i
$792$		0			0
$793$	17.6967	+	11.3730i	0.628428	+	0.403866i
$794$	30.6270	−	35.3454i	1.08691	−	1.25436i
$795$		0			0
$796$	−3.02953	+	6.63374i	−0.107379	+	0.235127i
$797$	48.6580	+	6.99596i	1.72355	+	0.247810i	0.931785	−	0.363011i	$-0.118251\pi$
$797$	48.6580	+	6.99596i	1.72355	+	0.247810i	0.791769	+	0.610821i	$0.209161\pi$
$798$		0			0
$799$	−10.1296	−	6.50989i	−0.358359	−	0.230303i
$800$	14.8007	+	4.34588i	0.523284	+	0.153650i
$801$		0			0
$802$	−6.62703	+	46.0920i	−0.234008	+	1.62756i
$803$	4.53713			0.160112
$804$		0			0
$805$	103.610			3.65179
$806$	3.68526	−	25.6315i	0.129808	−	0.902832i
$807$		0			0
$808$	40.0883	+	11.7710i	1.41030	+	0.414102i
$809$	−27.4424	−	17.6362i	−0.964823	−	0.620054i	−0.0394943	−	0.999220i	$-0.512575\pi$
$809$	−27.4424	−	17.6362i	−0.964823	−	0.620054i	−0.925329	+	0.379166i	$0.876211\pi$
$810$		0			0
$811$	−2.37632	−	0.341664i	−0.0834440	−	0.0119974i	0.100466	−	0.994940i	$-0.467967\pi$
$811$	−2.37632	−	0.341664i	−0.0834440	−	0.0119974i	−0.183910	+	0.982943i	$0.558876\pi$
$812$	−1.95461	+	4.28000i	−0.0685934	+	0.150199i
$813$		0			0
$814$	−16.2536	+	18.7576i	−0.569688	+	0.657455i
$815$	14.2196	+	9.13837i	0.498090	+	0.320103i
$816$		0			0
$817$	−15.9920	+	7.30329i	−0.559489	+	0.255510i
$818$	9.41964	−	32.0804i	0.329350	−	1.12166i
$819$		0			0
$820$	14.1743	+	9.10926i	0.494988	+	0.318109i
$821$	−8.09164	−	27.5576i	−0.282400	−	0.961767i	−0.971488	−	0.237089i	$-0.923807\pi$
$821$	−8.09164	−	27.5576i	−0.282400	−	0.961767i	0.689088	−	0.724678i	$-0.258011\pi$
$822$		0			0
$823$	2.01765	+	14.0331i	0.0703309	+	0.489162i	0.994293	+	0.106679i	$0.0340218\pi$
$823$	2.01765	+	14.0331i	0.0703309	+	0.489162i	−0.923963	+	0.382483i	$0.875069\pi$
$824$	−16.0685	−	18.5441i	−0.559774	−	0.646014i
$825$		0			0
$826$	−0.0130509	+	0.0150615i	−0.000454098	+	0.000524057i
$827$	−16.6563	+	14.4328i	−0.579196	+	0.501876i	−0.894472	−	0.447124i	$-0.852448\pi$
$827$	−16.6563	+	14.4328i	−0.579196	+	0.501876i	0.315276	+	0.949000i	$0.397903\pi$
$828$		0			0
$829$	12.5044	+	27.3807i	0.434294	+	0.950972i	0.992611	+	0.121344i	$0.0387204\pi$
$829$	12.5044	+	27.3807i	0.434294	+	0.950972i	−0.558316	+	0.829628i	$0.688552\pi$
$830$	20.5140	+	69.8643i	0.712051	+	2.42502i
$831$		0			0
$832$	−13.5123	−	6.17087i	−0.468455	−	0.213936i
$833$			29.0468i			1.00641i
$834$		0			0
$835$	−38.5394	−	17.6004i	−1.33371	−	0.609085i
$836$	5.54324	−	6.39724i	0.191717	−	0.221253i
$837$		0			0
$838$	−50.9965	+	7.33219i	−1.76165	+	0.253286i
$839$	−28.0701	−	24.3229i	−0.969087	−	0.839718i	0.0180110	−	0.999838i	$-0.494267\pi$
$839$	−28.0701	−	24.3229i	−0.969087	−	0.839718i	−0.987098	+	0.160119i	$0.948812\pi$
$840$		0			0
$841$	17.0244			0.587048
$842$	−59.6179			−2.05457
$843$		0			0
$844$	0.525868	−	0.337955i	0.0181011	−	0.0116329i
$845$	−22.2965	+	6.54683i	−0.767022	+	0.225218i
$846$		0			0
$847$	4.38906	+	14.9478i	0.150810	+	0.513611i
$848$	25.4454	+	29.3656i	0.873798	+	1.00842i
$849$		0			0
$850$	−32.6696	−	50.8350i	−1.12056	−	1.74362i
$851$	−26.2126	+	22.7134i	−0.898557	+	0.778604i
$852$		0			0
$853$	−41.3913	−	12.1536i	−1.41721	−	0.416131i	−0.518653	−	0.854985i	$-0.673566\pi$
$853$	−41.3913	−	12.1536i	−1.41721	−	0.416131i	−0.898558	+	0.438854i	$0.855384\pi$
$854$	−43.4756	+	12.7656i	−1.48770	+	0.436829i
$855$		0			0
$856$	0.702392	−	0.100989i	0.0240073	−	0.00345172i
$857$	22.1941	+	6.51677i	0.758135	+	0.222609i	0.637881	−	0.770135i	$-0.279811\pi$
$857$	22.1941	+	6.51677i	0.758135	+	0.222609i	0.120254	+	0.992743i	$0.461629\pi$
$858$		0			0
$859$	8.22187	+	18.0034i	0.280527	+	0.614268i	0.996475	−	0.0838850i	$-0.0267329\pi$
$859$	8.22187	+	18.0034i	0.280527	+	0.614268i	−0.715949	+	0.698153i	$0.754006\pi$
$860$	−2.31075	+	3.59560i	−0.0787961	+	0.122609i
$861$		0			0
$862$	3.45310	+	0.496481i	0.117613	+	0.0169102i
$863$	−11.3758	−	5.19516i	−0.387237	−	0.176845i	0.212277	−	0.977210i	$-0.431912\pi$
$863$	−11.3758	−	5.19516i	−0.387237	−	0.176845i	−0.599514	+	0.800364i	$0.704639\pi$
$864$		0			0
$865$	8.70613	+	13.5470i	0.296017	+	0.460612i
$866$	4.10650	−	6.38984i	0.139545	−	0.217136i
$867$		0			0
$868$	5.93201	+	6.84591i	0.201346	+	0.232365i
$869$	−7.40518	−	1.06470i	−0.251203	−	0.0361176i
$870$		0			0
$871$	17.8367	+	10.2838i	0.604373	+	0.348452i
$872$			38.8770i			1.31654i
$873$		0			0
$874$	55.0462	−	47.6978i	1.86197	−	1.61340i
$875$	−7.31488	+	24.9122i	−0.247288	+	0.842186i
$876$		0			0
$877$	−30.8311	+	19.8140i	−1.04109	+	0.669070i	−0.945257	−	0.326327i	$-0.894189\pi$
$877$	−30.8311	+	19.8140i	−1.04109	+	0.669070i	−0.0958367	+	0.995397i	$0.530553\pi$
$878$	4.00391	−	27.8478i	0.135125	−	0.939818i
$879$		0			0
$880$	−9.00776	+	62.6504i	−0.303652	+	2.11194i
$881$	15.0012	+	12.9986i	0.505403	+	0.437934i	0.869869	−	0.493282i	$-0.164203\pi$
$881$	15.0012	+	12.9986i	0.505403	+	0.437934i	−0.364466	+	0.931217i	$0.618749\pi$
$882$		0			0
$883$	−25.5589	+	11.6724i	−0.860126	+	0.392807i	−0.796117	−	0.605143i	$-0.793116\pi$
$883$	−25.5589	+	11.6724i	−0.860126	+	0.392807i	−0.0640095	+	0.997949i	$0.520389\pi$
$884$	−2.22348	−	4.86874i	−0.0747837	−	0.163753i
$885$		0			0
$886$	2.13259	+	14.8325i	0.0716457	+	0.498307i
$887$	−5.20724	+	8.10263i	−0.174842	+	0.272060i	−0.917604	−	0.397496i	$-0.869879\pi$
$887$	−5.20724	+	8.10263i	−0.174842	+	0.272060i	0.742762	+	0.669556i	$0.233516\pi$
$888$		0			0
$889$	−19.9900	+	68.0798i	−0.670444	+	2.28332i
$890$	31.7696	−	4.56778i	1.06492	−	0.153112i
$891$		0			0
$892$	2.04056	−	1.31139i	0.0683229	−	0.0439085i
$893$	9.21157	+	7.98187i	0.308254	+	0.267103i
$894$		0			0
$895$	70.7340	−	20.7694i	2.36438	−	0.694244i
$896$	42.9119	−	19.5972i	1.43359	−	0.654697i
$897$		0			0
$898$	10.1954	+	15.8644i	0.340225	+	0.529401i
$899$	−9.57755	+	20.9719i	−0.319429	+	0.699453i
$900$		0			0
$901$		−	46.0990i		−	1.53578i
$902$	−31.4748	+	68.9201i	−1.04799	+	2.29479i
$903$		0			0
$904$	−0.547372	−	3.80705i	−0.0182053	−	0.126621i
$905$	10.5758	+	73.5563i	0.351552	+	2.44509i
$906$		0			0
$907$	19.8303	−	43.4223i	0.658455	−	1.44181i	−0.225500	−	0.974243i	$-0.572402\pi$
$907$	19.8303	−	43.4223i	0.658455	−	1.44181i	0.883955	−	0.467572i	$-0.154871\pi$
$908$		−	3.03921i		−	0.100860i
$909$		0			0
$910$	−19.7143	+	43.1682i	−0.653521	+	1.43101i
$911$	−5.89423	−	9.17160i	−0.195285	−	0.303869i	0.729777	−	0.683685i	$-0.239624\pi$
$911$	−5.89423	−	9.17160i	−0.195285	−	0.303869i	−0.925062	+	0.379816i	$0.875987\pi$
$912$		0			0
$913$	−48.3707	+	22.0902i	−1.60084	+	0.731078i
$914$	17.5018	−	5.13901i	0.578910	−	0.169983i
$915$		0			0
$916$	−4.58615	−	3.97392i	−0.151531	−	0.131302i
$917$	−5.11820	+	3.28926i	−0.169018	+	0.108621i
$918$		0			0
$919$	53.6997	−	7.72084i	1.77139	−	0.254687i	0.822156	−	0.569263i	$-0.192771\pi$
$919$	53.6997	−	7.72084i	1.77139	−	0.254687i	0.949232	+	0.314575i	$0.101862\pi$
$920$	−20.7407	+	70.6365i	−0.683802	+	2.32882i
$921$		0			0
$922$	1.22522	−	1.90647i	0.0403504	−	0.0627864i
$923$	3.92109	+	27.2718i	0.129064	+	0.897661i
$924$		0			0
$925$	−12.1002	−	26.4957i	−0.397852	−	0.871174i
$926$	3.37264	−	1.54023i	0.110832	−	0.0506152i
$927$		0			0
$928$	−5.66097	−	4.90526i	−0.185830	−	0.161023i
$929$	−3.07171	+	21.3642i	−0.100780	+	0.700937i	0.875309	+	0.483564i	$0.160658\pi$
$929$	−3.07171	+	21.3642i	−0.100780	+	0.700937i	−0.976089	+	0.217373i	$0.930251\pi$
$930$		0			0
$931$	4.18446	−	29.1035i	0.137140	−	0.953830i
$932$	−3.74021	+	2.40369i	−0.122515	+	0.0787354i
$933$		0			0
$934$	−0.997664	+	3.39773i	−0.0326446	+	0.111177i
$935$	56.7513	−	49.1753i	1.85597	−	1.60820i
$936$		0			0
$937$			19.3448i			0.631967i	0.948765	+	0.315983i	$0.102334\pi$
$937$			19.3448i			0.631967i	−0.948765	+	0.315983i	$0.897666\pi$
$938$	−41.9000	+	14.5298i	−1.36808	+	0.474416i
$939$		0			0
$940$	2.93306	+	0.421711i	0.0956659	+	0.0137547i
$941$	−12.4604	−	14.3801i	−0.406197	−	0.468777i	0.515386	−	0.856958i	$-0.327649\pi$
$941$	−12.4604	−	14.3801i	−0.406197	−	0.468777i	−0.921583	+	0.388182i	$0.873103\pi$
$942$		0			0
$943$	−57.2429	+	89.0716i	−1.86408	+	2.90057i
$944$	−0.00919804	−	0.0143124i	−0.000299371	−	0.000465830i
$945$		0			0
$946$	−17.4830	−	7.98423i	−0.568422	−	0.259590i
$947$	9.06880	+	1.30390i	0.294697	+	0.0423710i	0.288077	−	0.957607i	$-0.406984\pi$
$947$	9.06880	+	1.30390i	0.294697	+	0.0423710i	0.00661912	+	0.999978i	$0.497893\pi$
$948$		0			0
$949$	−1.57006	+	2.44307i	−0.0509664	+	0.0793053i
$950$	25.4103	+	55.6407i	0.824417	+	1.80522i
$951$		0			0
$952$	−45.9896	−	13.5038i	−1.49053	−	0.437660i
$953$	−32.6100	+	4.68862i	−1.05634	+	0.151879i	−0.648532	−	0.761187i	$-0.724617\pi$
$953$	−32.6100	+	4.68862i	−1.05634	+	0.151879i	−0.407811	+	0.913066i	$0.633708\pi$
$954$		0			0
$955$	39.5855	−	11.6234i	1.28096	−	0.376123i
$956$	6.38623	+	1.87517i	0.206545	+	0.0606472i
$957$		0			0
$958$	30.5575	−	26.4783i	0.987269	−	0.855474i
$959$	32.1958	+	50.0976i	1.03966	+	1.61774i
$960$		0			0
$961$	8.76605	+	10.1166i	0.282776	+	0.326341i
$962$	−4.47574	−	15.2430i	−0.144304	−	0.491453i
$963$		0			0
$964$	−4.16466	+	1.22285i	−0.134135	+	0.0393855i
$965$	20.1203	−	12.9305i	0.647694	−	0.416248i
$966$		0			0
$967$	−15.8657			−0.510205			−0.255103	−	0.966914i	$-0.582109\pi$
$967$	−15.8657			−0.510205			−0.255103	+	0.966914i	$0.582109\pi$
$968$	−11.0692			−0.355779
$969$		0			0
$970$	14.6868	+	12.7261i	0.471563	+	0.408612i
$971$	25.4626	−	3.66096i	0.817133	−	0.117486i	0.278941	−	0.960308i	$-0.410017\pi$
$971$	25.4626	−	3.66096i	0.817133	−	0.117486i	0.538192	+	0.842822i	$0.319108\pi$
$972$		0			0
$973$	6.47130	−	7.46828i	0.207460	−	0.239422i
$974$	57.8308	+	26.4104i	1.85302	+	0.846245i
$975$		0			0
$976$		−	38.6811i		−	1.23815i
$977$	−32.9501	−	15.0478i	−1.05417	−	0.481423i	−0.188517	−	0.982070i	$-0.560368\pi$
$977$	−32.9501	−	15.0478i	−1.05417	−	0.481423i	−0.865651	+	0.500647i	$0.833095\pi$
$978$		0			0
$979$	6.60382	+	22.4906i	0.211059	+	0.718801i
$980$	−2.96947	−	6.50224i	−0.0948563	−	0.207706i
$981$		0			0
$982$	22.0743	−	19.1275i	0.704419	−	0.610382i
$983$	27.9006	−	32.1990i	0.889890	−	1.02699i	−0.109565	−	0.993980i	$-0.534946\pi$
$983$	27.9006	−	32.1990i	0.889890	−	1.02699i	0.999455	−	0.0330086i	$-0.0105089\pi$
$984$		0			0
$985$	−19.0543	−	21.9898i	−0.607120	−	0.700653i
$986$	4.17598	+	29.0446i	0.132990	+	0.924967i
$987$		0			0
$988$	1.52644	+	5.19857i	0.0485624	+	0.165388i
$989$	−22.5949	−	14.5208i	−0.718475	−	0.461736i
$990$		0			0
$991$	−3.06225	+	10.4290i	−0.0972754	+	0.331290i	−0.993724	−	0.111858i	$-0.964320\pi$
$991$	−3.06225	+	10.4290i	−0.0972754	+	0.331290i	0.896449	+	0.443147i	$0.146138\pi$
$992$	−13.1176	+	5.99060i	−0.416483	+	0.190202i
$993$		0			0
$994$	−49.9254	−	32.0851i	−1.58354	−	1.01768i
$995$	42.8861	−	49.4931i	1.35958	−	1.56904i
$996$		0			0
$997$	23.7713	−	52.0518i	0.752843	−	1.64850i	−0.00834446	−	0.999965i	$-0.502656\pi$
$997$	23.7713	−	52.0518i	0.752843	−	1.64850i	0.761188	−	0.648532i	$-0.224617\pi$
$998$	−28.7984	−	4.14058i	−0.911596	−	0.131068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.v.a.8.7	✓	240
3.2	odd	2	inner	603.2.v.a.8.18	yes	240
67.42	odd	22	inner	603.2.v.a.377.18	yes	240
201.176	even	22	inner	603.2.v.a.377.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.v.a.8.7	✓	240	1.1	even	1	trivial
603.2.v.a.8.18	yes	240	3.2	odd	2	inner
603.2.v.a.377.7	yes	240	201.176	even	22	inner
603.2.v.a.377.18	yes	240	67.42	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.219912 + 1.52952i) q^{2} +(-0.372079 - 0.109252i) q^{4} +(2.92951 + 1.88268i) q^{5} +(3.47051 + 0.498984i) q^{7} +(-1.03491 + 2.26614i) q^{8} +O(q^{10})\)	\(q+(-0.219912 + 1.52952i) q^{2} +(-0.372079 - 0.109252i) q^{4} +(2.92951 + 1.88268i) q^{5} +(3.47051 + 0.498984i) q^{7} +(-1.03491 + 2.26614i) q^{8} +(-3.52383 + 4.06671i) q^{10} +(-3.30595 - 2.12460i) q^{11} +(2.28803 - 1.04491i) q^{13} +(-1.52641 + 5.19847i) q^{14} +(-3.89096 - 2.50057i) q^{16} +(1.54596 + 5.26506i) q^{17} +(-0.790502 - 5.49806i) q^{19} +(-0.884321 - 1.02056i) q^{20} +(3.97663 - 4.58928i) q^{22} +(6.41323 - 5.55710i) q^{23} +(2.96046 + 6.48249i) q^{25} +(1.09504 + 3.72937i) q^{26} +(-1.23679 - 0.564822i) q^{28} -3.46058i q^{29} +(-6.06023 - 2.76762i) q^{31} +(1.41747 - 1.63584i) q^{32} +(-8.39298 + 1.20673i) q^{34} +(9.22746 + 7.99564i) q^{35} -4.08727 q^{37} +8.58322 q^{38} +(-7.29819 + 4.69026i) q^{40} +(-11.9717 + 3.51520i) q^{41} +(-0.891705 - 3.03687i) q^{43} +(0.997955 + 1.15170i) q^{44} +(7.08934 + 11.0312i) q^{46} +(-1.65837 + 1.43699i) q^{47} +(5.07900 + 1.49133i) q^{49} +(-10.5661 + 3.10250i) q^{50} +(-0.965486 + 0.138816i) q^{52} +(-8.06069 - 2.36683i) q^{53} +(-5.68485 - 12.4481i) q^{55} +(-4.72243 + 7.34824i) q^{56} +(5.29302 + 0.761021i) q^{58} +(0.00334597 + 0.00152805i) q^{59} +(4.52145 + 7.03552i) q^{61} +(5.56583 - 8.66061i) q^{62} +(-3.86738 - 4.46319i) q^{64} +(8.67003 + 1.24656i) q^{65} +(4.75197 + 6.66475i) q^{67} -2.12792i q^{68} +(-14.2587 + 12.3552i) q^{70} +(-3.08601 + 10.5100i) q^{71} +(-0.971268 + 0.624196i) q^{73} +(0.898838 - 6.25156i) q^{74} +(-0.306546 + 2.13207i) q^{76} +(-10.4132 - 9.02307i) q^{77} +(1.73171 - 0.790846i) q^{79} +(-6.69083 - 14.6509i) q^{80} +(-2.74386 - 19.0839i) q^{82} +(7.31571 - 11.3835i) q^{83} +(-5.38352 + 18.3346i) q^{85} +(4.84104 - 0.696036i) q^{86} +(8.23599 - 5.29295i) q^{88} +(-4.50783 - 3.90606i) q^{89} +(8.46203 - 2.48467i) q^{91} +(-2.99335 + 1.36702i) q^{92} +(-1.83320 - 2.85252i) q^{94} +(8.03531 - 17.5949i) q^{95} -3.61146i q^{97} +(-3.39794 + 7.44046i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 28 q^{4}+O(q^{10}) \) 240 * q - 28 * q^4	\( 240 q - 28 q^{4} - 28 q^{16} - 20 q^{19} + 12 q^{22} - 24 q^{25} + 44 q^{28} - 88 q^{31} + 24 q^{37} + 32 q^{40} + 44 q^{43} - 44 q^{46} + 8 q^{49} - 220 q^{52} + 52 q^{55} - 88 q^{58} - 88 q^{61} - 148 q^{64} + 8 q^{67} - 176 q^{70} - 120 q^{73} - 64 q^{76} - 264 q^{79} + 8 q^{82} + 256 q^{88} + 256 q^{91} - 88 q^{94}+O(q^{100}) \) 240 * q - 28 * q^4 - 28 * q^16 - 20 * q^19 + 12 * q^22 - 24 * q^25 + 44 * q^28 - 88 * q^31 + 24 * q^37 + 32 * q^40 + 44 * q^43 - 44 * q^46 + 8 * q^49 - 220 * q^52 + 52 * q^55 - 88 * q^58 - 88 * q^61 - 148 * q^64 + 8 * q^67 - 176 * q^70 - 120 * q^73 - 64 * q^76 - 264 * q^79 + 8 * q^82 + 256 * q^88 + 256 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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