LMFDB - Embedded newform 104.2.e.c.77.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(77,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.77"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4521217600.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 $ x^8 + x^6 - 2x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.4
Root			$0.273147 + 1.38758i$ of defining polynomial
Character	$\chi$	$=$	104.77
Dual form			104.2.e.c.77.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.273147 + 1.38758i) q^{2} +1.51606i q^{3} +(-1.85078 - 0.758030i) q^{4} -3.11473 q^{5} +(-2.10366 - 0.414108i) q^{6} +2.77517i q^{7} +(1.55737 - 2.36106i) q^{8} +0.701562 q^{9} +(0.850781 - 4.32196i) q^{10} +2.56844 q^{11} +(1.14922 - 2.80590i) q^{12} +(0.546295 + 3.56393i) q^{13} +(-3.85078 - 0.758030i) q^{14} -4.72212i q^{15} +(2.85078 + 2.80590i) q^{16} -5.70156 q^{17} +(-0.191630 + 0.973477i) q^{18} +4.75362 q^{19} +(5.76469 + 2.36106i) q^{20} -4.20732 q^{21} +(-0.701562 + 3.56393i) q^{22} +4.00000 q^{23} +(3.57951 + 2.36106i) q^{24} +4.70156 q^{25} +(-5.09447 - 0.215447i) q^{26} +5.61179i q^{27} +(2.10366 - 5.13623i) q^{28} -7.12785i q^{29} +(6.55234 + 1.28984i) q^{30} -3.60338i q^{31} +(-4.67210 + 3.18928i) q^{32} +3.89391i q^{33} +(1.55737 - 7.91140i) q^{34} -8.64391i q^{35} +(-1.29844 - 0.531805i) q^{36} +4.20732 q^{37} +(-1.29844 + 6.59605i) q^{38} +(-5.40312 + 0.828216i) q^{39} +(-4.85078 + 7.35408i) q^{40} +(1.14922 - 5.83802i) q^{42} +1.51606i q^{43} +(-4.75362 - 1.94695i) q^{44} -2.18518 q^{45} +(-1.09259 + 5.55034i) q^{46} +2.77517i q^{47} +(-4.25391 + 4.32196i) q^{48} -0.701562 q^{49} +(-1.28422 + 6.52381i) q^{50} -8.64391i q^{51} +(1.69049 - 7.01015i) q^{52} -6.06424i q^{53} +(-7.78683 - 1.53285i) q^{54} -8.00000 q^{55} +(6.55234 + 4.32196i) q^{56} +7.20677i q^{57} +(9.89049 + 1.94695i) q^{58} -4.75362 q^{59} +(-3.57951 + 8.73961i) q^{60} +(5.00000 + 0.984255i) q^{62} +1.94695i q^{63} +(-3.14922 - 7.35408i) q^{64} +(-1.70156 - 11.1007i) q^{65} +(-5.40312 - 1.06361i) q^{66} -12.0757 q^{67} +(10.5523 + 4.32196i) q^{68} +6.06424i q^{69} +(11.9942 + 2.36106i) q^{70} +6.66908i q^{71} +(1.09259 - 1.65643i) q^{72} -14.9946i q^{73} +(-1.14922 + 5.83802i) q^{74} +7.12785i q^{75} +(-8.79790 - 3.60338i) q^{76} +7.12785i q^{77} +(0.326630 - 7.72352i) q^{78} +14.8062 q^{79} +(-8.87942 - 8.73961i) q^{80} -6.40312 q^{81} +9.89049 q^{83} +(7.78683 + 3.18928i) q^{84} +17.7588 q^{85} +(-2.10366 - 0.414108i) q^{86} +10.8062 q^{87} +(4.00000 - 6.06424i) q^{88} +14.9946i q^{89} +(0.596876 - 3.03212i) q^{90} +(-9.89049 + 1.51606i) q^{91} +(-7.40312 - 3.03212i) q^{92} +5.46295 q^{93} +(-3.85078 - 0.758030i) q^{94} -14.8062 q^{95} +(-4.83513 - 7.08318i) q^{96} -3.89391i q^{97} +(0.191630 - 0.973477i) q^{98} +1.80192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 20 q^{9} - 6 q^{10} + 22 q^{12} - 18 q^{14} + 10 q^{16} - 20 q^{17} + 20 q^{22} + 32 q^{23} + 12 q^{25} - 14 q^{26} + 14 q^{30} - 36 q^{36} - 36 q^{38} + 8 q^{39} - 26 q^{40} + 22 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 20 * q^9 - 6 * q^10 + 22 * q^12 - 18 * q^14 + 10 * q^16 - 20 * q^17 + 20 * q^22 + 32 * q^23 + 12 * q^25 - 14 * q^26 + 14 * q^30 - 36 * q^36 - 36 * q^38 + 8 * q^39 - 26 * q^40 + 22 * q^42 + 30 * q^48 + 20 * q^49 - 4 * q^52 - 64 * q^55 + 14 * q^56 + 40 * q^62 - 38 * q^64 + 12 * q^65 + 8 * q^66 + 46 * q^68 - 22 * q^74 - 22 * q^78 + 16 * q^79 - 16 * q^87 + 32 * q^88 + 56 * q^90 - 8 * q^92 - 18 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.273147	+	1.38758i	−0.193144	+	0.981170i
$2$	−0.273147	+	1.38758i	−0.193144	+	0.981170i
$3$			1.51606i			0.875298i	0.899146	+	0.437649i	$0.144189\pi$
$3$			1.51606i			0.875298i	−0.899146	+	0.437649i	$0.855811\pi$
$4$	−1.85078	−	0.758030i	−0.925391	−	0.379015i
$5$	−3.11473			−1.39295			−0.696475	−	0.717581i	$-0.745250\pi$
$5$	−3.11473			−1.39295			−0.696475	+	0.717581i	$0.745250\pi$
$6$	−2.10366	−	0.414108i	−0.858816	−	0.169059i
$7$			2.77517i			1.04892i	0.851437	+	0.524458i	$0.175732\pi$
$7$			2.77517i			1.04892i	−0.851437	+	0.524458i	$0.824268\pi$
$8$	1.55737	−	2.36106i	0.550612	−	0.834761i
$9$	0.701562			0.233854
$10$	0.850781	−	4.32196i	0.269041	−	1.36672i
$11$	2.56844			0.774413			0.387207	−	0.921993i	$-0.373440\pi$
$11$	2.56844			0.774413			0.387207	+	0.921993i	$0.373440\pi$
$12$	1.14922	−	2.80590i	0.331751	−	0.809992i
$13$	0.546295	+	3.56393i	0.151515	+	0.988455i
$13$	0.546295	+	3.56393i	0.151515	+	0.988455i
$14$	−3.85078	−	0.758030i	−1.02916	−	0.202592i
$15$		−	4.72212i		−	1.21925i
$16$	2.85078	+	2.80590i	0.712695	+	0.701474i
$17$	−5.70156			−1.38283			−0.691416	−	0.722457i	$-0.743013\pi$
$17$	−5.70156			−1.38283			−0.691416	+	0.722457i	$0.743013\pi$
$18$	−0.191630	+	0.973477i	−0.0451676	+	0.229451i
$19$	4.75362			1.09055			0.545277	−	0.838256i	$-0.316424\pi$
$19$	4.75362			1.09055			0.545277	+	0.838256i	$0.316424\pi$
$20$	5.76469	+	2.36106i	1.28902	+	0.527949i
$21$	−4.20732			−0.918113
$22$	−0.701562	+	3.56393i	−0.149574	+	0.759831i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	3.57951	+	2.36106i	0.730664	+	0.481950i
$25$	4.70156			0.940312
$26$	−5.09447	−	0.215447i	−0.999107	−	0.0422526i
$27$			5.61179i			1.07999i
$28$	2.10366	−	5.13623i	0.397555	−	0.970656i
$29$		−	7.12785i		−	1.32361i	−0.749677	−	0.661804i	$-0.769791\pi$
$29$		−	7.12785i		−	1.32361i	0.749677	−	0.661804i	$-0.230209\pi$
$30$	6.55234	+	1.28984i	1.19629	+	0.235491i
$31$		−	3.60338i		−	0.647187i	−0.946196	−	0.323593i	$-0.895109\pi$
$31$		−	3.60338i		−	0.647187i	0.946196	−	0.323593i	$-0.104891\pi$
$32$	−4.67210	+	3.18928i	−0.825918	+	0.563790i
$33$			3.89391i			0.677842i
$34$	1.55737	−	7.91140i	0.267086	−	1.35679i
$35$		−	8.64391i		−	1.46109i
$36$	−1.29844	−	0.531805i	−0.216406	−	0.0886342i
$37$	4.20732			0.691680			0.345840	−	0.938294i	$-0.387594\pi$
$37$	4.20732			0.691680			0.345840	+	0.938294i	$0.387594\pi$
$38$	−1.29844	+	6.59605i	−0.210634	+	1.07002i
$39$	−5.40312	+	0.828216i	−0.865192	+	0.132621i
$40$	−4.85078	+	7.35408i	−0.766976	+	1.16278i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	1.14922	−	5.83802i	0.177328	−	0.900825i
$43$			1.51606i			0.231197i	0.993296	+	0.115598i	$0.0368786\pi$
$43$			1.51606i			0.231197i	−0.993296	+	0.115598i	$0.963121\pi$
$44$	−4.75362	−	1.94695i	−0.716635	−	0.293514i
$45$	−2.18518			−0.325747
$46$	−1.09259	+	5.55034i	−0.161094	+	0.818353i
$47$			2.77517i			0.404800i	0.979303	+	0.202400i	$0.0648741\pi$
$47$			2.77517i			0.404800i	−0.979303	+	0.202400i	$0.935126\pi$
$48$	−4.25391	+	4.32196i	−0.613998	+	0.623820i
$49$	−0.701562			−0.100223
$50$	−1.28422	+	6.52381i	−0.181616	+	0.922607i
$51$		−	8.64391i		−	1.21039i
$52$	1.69049	−	7.01015i	0.234429	−	0.972133i
$53$		−	6.06424i		−	0.832987i	−0.909139	−	0.416494i	$-0.863259\pi$
$53$		−	6.06424i		−	0.832987i	0.909139	−	0.416494i	$-0.136741\pi$
$54$	−7.78683	−	1.53285i	−1.05965	−	0.208594i
$55$	−8.00000			−1.07872
$56$	6.55234	+	4.32196i	0.875594	+	0.577546i
$57$			7.20677i			0.954560i
$58$	9.89049	+	1.94695i	1.29869	+	0.255647i
$59$	−4.75362			−0.618868			−0.309434	−	0.950921i	$-0.600140\pi$
$59$	−4.75362			−0.618868			−0.309434	+	0.950921i	$0.600140\pi$
$60$	−3.57951	+	8.73961i	−0.462113	+	1.12828i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	5.00000	+	0.984255i	0.635001	+	0.125000i
$63$			1.94695i			0.245293i
$64$	−3.14922	−	7.35408i	−0.393652	−	0.919259i
$65$	−1.70156	−	11.1007i	−0.211053	−	1.37687i
$66$	−5.40312	−	1.06361i	−0.665079	−	0.130921i
$67$	−12.0757			−1.47528			−0.737639	−	0.675195i	$-0.764059\pi$
$67$	−12.0757			−1.47528			−0.737639	+	0.675195i	$0.764059\pi$
$68$	10.5523	+	4.32196i	1.27966	+	0.524114i
$69$			6.06424i			0.730049i
$70$	11.9942	+	2.36106i	1.43358	+	0.282201i
$71$			6.66908i			0.791474i	0.918364	+	0.395737i	$0.129511\pi$
$71$			6.66908i			0.791474i	−0.918364	+	0.395737i	$0.870489\pi$
$72$	1.09259	−	1.65643i	0.128763	−	0.195212i
$73$		−	14.9946i		−	1.75498i	−0.479592	−	0.877492i	$-0.659215\pi$
$73$		−	14.9946i		−	1.75498i	0.479592	−	0.877492i	$-0.340785\pi$
$74$	−1.14922	+	5.83802i	−0.133594	+	0.678655i
$75$			7.12785i			0.823053i
$76$	−8.79790	−	3.60338i	−1.00919	−	0.413337i
$77$			7.12785i			0.812294i
$78$	0.326630	−	7.72352i	0.0369836	−	0.874516i
$79$	14.8062			1.66583			0.832917	−	0.553399i	$-0.186669\pi$
$79$	14.8062			1.66583			0.832917	+	0.553399i	$0.186669\pi$
$80$	−8.87942	−	8.73961i	−0.992750	−	0.977119i
$81$	−6.40312			−0.711458
$82$		0			0
$83$	9.89049			1.08562			0.542811	−	0.839855i	$-0.317360\pi$
$83$	9.89049			1.08562			0.542811	+	0.839855i	$0.317360\pi$
$84$	7.78683	+	3.18928i	0.849613	+	0.347979i
$85$	17.7588			1.92622
$86$	−2.10366	−	0.414108i	−0.226844	−	0.0446544i
$87$	10.8062			1.15855
$88$	4.00000	−	6.06424i	0.426401	−	0.646450i
$89$			14.9946i			1.58942i	0.606988	+	0.794711i	$0.292378\pi$
$89$			14.9946i			1.58942i	−0.606988	+	0.794711i	$0.707622\pi$
$90$	0.596876	−	3.03212i	0.0629162	−	0.319614i
$91$	−9.89049	+	1.51606i	−1.03681	+	0.158926i
$92$	−7.40312	−	3.03212i	−0.771829	−	0.316120i
$93$	5.46295			0.566481
$94$	−3.85078	−	0.758030i	−0.397178	−	0.0781848i
$95$	−14.8062			−1.51909
$96$	−4.83513	−	7.08318i	−0.493484	−	0.722924i
$97$		−	3.89391i		−	0.395366i	−0.980266	−	0.197683i	$-0.936658\pi$
$97$		−	3.89391i		−	0.395366i	0.980266	−	0.197683i	$-0.0633417\pi$
$98$	0.191630	−	0.973477i	0.0193575	−	0.0983360i
$99$	1.80192			0.181100
$100$	−8.70156	−	3.56393i	−0.870156	−	0.356393i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	11.9942	+	2.36106i	1.18760	+	0.233780i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	9.26543	+	4.26050i	0.908550	+	0.417777i
$105$	13.1047			1.27889
$106$	8.41464	+	1.65643i	0.817303	+	0.160887i
$107$			10.1600i			0.982201i	0.871103	+	0.491101i	$0.163405\pi$
$107$			10.1600i			0.982201i	−0.871103	+	0.491101i	$0.836595\pi$
$108$	4.25391	−	10.3862i	0.409332	−	0.999412i
$109$	2.02214			0.193686			0.0968431	−	0.995300i	$-0.469125\pi$
$109$	2.02214			0.193686			0.0968431	+	0.995300i	$0.469125\pi$
$110$	2.18518	−	11.1007i	0.208349	−	1.05841i
$111$			6.37855i			0.605425i
$112$	−7.78683	+	7.91140i	−0.735787	+	0.747557i
$113$	11.4031			1.07272			0.536358	−	0.843991i	$-0.319800\pi$
$113$	11.4031			1.07272			0.536358	+	0.843991i	$0.319800\pi$
$114$	−10.0000	−	1.96851i	−0.936586	−	0.184368i
$115$	−12.4589			−1.16180
$116$	−5.40312	+	13.1921i	−0.501667	+	1.22485i
$117$	0.383260	+	2.50031i	0.0354324	+	0.231154i
$118$	1.29844	−	6.59605i	0.119531	−	0.607215i
$119$		−	15.8228i		−	1.45047i
$120$	−11.1492	−	7.35408i	−1.01778	−	0.671332i
$121$	−4.40312			−0.400284
$122$		0			0
$123$		0			0
$124$	−2.73147	+	6.66908i	−0.245294	+	0.598901i
$125$	0.929554			0.0831419
$126$	−2.70156	−	0.531805i	−0.240674	−	0.0473770i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	11.0646	−	2.36106i	0.977982	−	0.208690i
$129$	−2.29844			−0.202366
$130$	15.8679	+	0.671059i	1.39171	+	0.0588558i
$131$		−	18.8039i		−	1.64290i	−0.570279	−	0.821451i	$-0.693165\pi$
$131$		−	18.8039i		−	1.64290i	0.570279	−	0.821451i	$-0.306835\pi$
$132$	2.95170	−	7.20677i	0.256912	−	0.627269i
$133$			13.1921i			1.14390i
$134$	3.29844	−	16.7560i	0.284942	−	1.44750i
$135$		−	17.4792i		−	1.50437i
$136$	−8.87942	+	13.4617i	−0.761404	+	1.15433i
$137$		−	11.1007i		−	0.948395i	−0.880419	−	0.474197i	$-0.842738\pi$
$137$		−	11.1007i		−	0.948395i	0.880419	−	0.474197i	$-0.157262\pi$
$138$	−8.41464	−	1.65643i	−0.716302	−	0.141005i
$139$			9.70752i			0.823381i	0.911324	+	0.411691i	$0.135062\pi$
$139$			9.70752i			0.823381i	−0.911324	+	0.411691i	$0.864938\pi$
$140$	−6.55234	+	15.9980i	−0.553774	+	1.35208i
$141$	−4.20732			−0.354320
$142$	−9.25391	−	1.82164i	−0.776570	−	0.152869i
$143$	1.40312	+	9.15372i	0.117335	+	0.765473i
$144$	2.00000	+	1.96851i	0.166667	+	0.164042i
$145$			22.2014i			1.84372i
$146$	20.8062	+	4.09573i	1.72194	+	0.338965i
$147$		−	1.06361i		−	0.0877251i
$148$	−7.78683	−	3.18928i	−0.640074	−	0.262157i
$149$	−13.5515			−1.11018			−0.555092	−	0.831789i	$-0.687317\pi$
$149$	−13.5515			−1.11018			−0.555092	+	0.831789i	$0.687317\pi$
$150$	−9.89049	−	1.94695i	−0.807555	−	0.158968i
$151$			13.8758i			1.12920i	0.825365	+	0.564600i	$0.190970\pi$
$151$			13.8758i			1.12920i	−0.825365	+	0.564600i	$0.809030\pi$
$152$	7.40312	−	11.2236i	0.600473	−	0.910353i
$153$	−4.00000			−0.323381
$154$	−9.89049	−	1.94695i	−0.796999	−	0.156890i
$155$			11.2236i			0.901500i
$156$	10.6278	+	2.56288i	0.850906	+	0.205195i
$157$		−	1.06361i		−	0.0848853i	−0.999099	−	0.0424427i	$-0.986486\pi$
$157$		−	1.06361i		−	0.0848853i	0.999099	−	0.0424427i	$-0.0135140\pi$
$158$	−4.04429	+	20.5449i	−0.321746	+	1.63447i
$159$	9.19375			0.729112
$160$	14.5523	−	9.93375i	1.15046	−	0.785332i
$161$			11.1007i			0.874856i
$162$	1.74900	−	8.88488i	0.137414	−	0.698062i
$163$	9.89049			0.774683			0.387342	−	0.921936i	$-0.373393\pi$
$163$	9.89049			0.774683			0.387342	+	0.921936i	$0.373393\pi$
$164$		0			0
$165$		−	12.1285i		−	0.944201i
$166$	−2.70156	+	13.7239i	−0.209682	+	1.06518i
$167$		−	7.49729i		−	0.580158i	−0.957003	−	0.290079i	$-0.906318\pi$
$167$		−	7.49729i		−	0.580158i	0.957003	−	0.290079i	$-0.0936816\pi$
$168$	−6.55234	+	9.93375i	−0.505524	+	0.766405i
$169$	−12.4031	+	3.89391i	−0.954086	+	0.299531i
$170$	−4.85078	+	24.6419i	−0.372038	+	1.88995i
$171$	3.33496			0.255031
$172$	1.14922	−	2.80590i	0.0876271	−	0.213947i
$173$		−	6.06424i		−	0.461056i	−0.973066	−	0.230528i	$-0.925955\pi$
$173$		−	6.06424i		−	0.461056i	0.973066	−	0.230528i	$-0.0740453\pi$
$174$	−2.95170	+	14.9946i	−0.223768	+	1.13674i
$175$			13.0476i			0.986308i
$176$	7.32206	+	7.20677i	0.551921	+	0.543231i
$177$		−	7.20677i		−	0.541694i
$178$	−20.8062	−	4.09573i	−1.55949	−	0.306988i
$179$		−	12.7396i		−	0.952205i	−0.879390	−	0.476103i	$-0.842049\pi$
$179$		−	12.7396i		−	0.952205i	0.879390	−	0.476103i	$-0.157951\pi$
$180$	4.04429	+	1.65643i	0.301443	+	0.123463i
$181$		−	13.1921i		−	0.980560i	−0.871565	−	0.490280i	$-0.836894\pi$
$181$		−	13.1921i		−	0.980560i	0.871565	−	0.490280i	$-0.163106\pi$
$182$	0.597901	−	14.1380i	0.0443194	−	1.04798i
$183$		0			0
$184$	6.22947	−	9.44424i	0.459242	−	0.696239i
$185$	−13.1047			−0.963476
$186$	−1.49219	+	7.58030i	−0.109413	+	0.555815i
$187$	−14.6441			−1.07088
$188$	2.10366	−	5.13623i	0.153425	−	0.374598i
$189$	−15.5737			−1.13282
$190$	4.04429	−	20.5449i	0.293403	−	1.49049i
$191$	−2.80625			−0.203053			−0.101527	−	0.994833i	$-0.532373\pi$
$191$	−2.80625			−0.203053			−0.101527	+	0.994833i	$0.532373\pi$
$192$	11.1492	−	4.77440i	0.804626	−	0.344563i
$193$		−	14.9946i		−	1.07933i	−0.841879	−	0.539667i	$-0.818550\pi$
$193$		−	14.9946i		−	1.07933i	0.841879	−	0.539667i	$-0.181450\pi$
$194$	5.40312	+	1.06361i	0.387922	+	0.0763628i
$195$	16.8293	−	2.57967i	1.20517	−	0.184734i
$196$	1.29844	+	0.531805i	0.0927456	+	0.0379861i
$197$	4.20732			0.299759			0.149880	−	0.988704i	$-0.452111\pi$
$197$	4.20732			0.299759			0.149880	+	0.988704i	$0.452111\pi$
$198$	−0.492189	+	2.50031i	−0.0349784	+	0.177690i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	7.32206	−	11.1007i	0.517748	−	0.784936i
$201$		−	18.3074i		−	1.29131i
$202$		0			0
$203$	19.7810			1.38835
$204$	−6.55234	+	15.9980i	−0.458756	+	1.12008i
$205$		0			0
$206$	−1.09259	+	5.55034i	−0.0761243	+	0.386710i
$207$	2.80625			0.195048
$208$	−8.44263	+	11.6928i	−0.585391	+	0.810751i
$209$	12.2094			0.844540
$210$	−3.57951	+	18.1839i	−0.247010	+	1.25481i
$211$		−	18.8039i		−	1.29451i	−0.762272	−	0.647256i	$-0.775916\pi$
$211$		−	18.8039i		−	1.29451i	0.762272	−	0.647256i	$-0.224084\pi$
$212$	−4.59688	+	11.2236i	−0.315715	+	0.770839i
$213$	−10.1107			−0.692775
$214$	−14.0978	−	2.77517i	−0.963707	−	0.189707i
$215$		−	4.72212i		−	0.322046i
$216$	13.2498	+	8.73961i	0.901533	+	0.594655i
$217$	10.0000			0.678844
$218$	−0.552343	+	2.80590i	−0.0374094	+	0.190039i
$219$	22.7327			1.53613
$220$	14.8062	+	6.06424i	0.998237	+	0.408851i
$221$	−3.11473	−	20.3199i	−0.209520	−	1.36687i
$222$	−8.85078	−	1.74228i	−0.594026	−	0.116935i
$223$		−	15.5323i		−	1.04012i	−0.854130	−	0.520059i	$-0.825910\pi$
$223$		−	15.5323i		−	1.04012i	0.854130	−	0.520059i	$-0.174090\pi$
$224$	−8.85078	−	12.9659i	−0.591368	−	0.866318i
$225$	3.29844			0.219896
$226$	−3.11473	+	15.8228i	−0.207189	+	1.05252i
$227$	6.93880			0.460544			0.230272	−	0.973126i	$-0.426038\pi$
$227$	6.93880			0.460544			0.230272	+	0.973126i	$0.426038\pi$
$228$	5.46295	−	13.3382i	0.361792	−	0.883341i
$229$	−7.48509			−0.494629			−0.247314	−	0.968935i	$-0.579548\pi$
$229$	−7.48509			−0.494629			−0.247314	+	0.968935i	$0.579548\pi$
$230$	3.40312	−	17.2878i	0.224395	−	1.13993i
$231$	−10.8062			−0.710999
$232$	−16.8293	−	11.1007i	−1.10490	−	0.728795i
$233$	−7.10469			−0.465443			−0.232722	−	0.972543i	$-0.574763\pi$
$233$	−7.10469			−0.465443			−0.232722	+	0.972543i	$0.574763\pi$
$234$	−3.57408	−	0.151149i	−0.233645	−	0.00988093i
$235$		−	8.64391i		−	0.563867i
$236$	8.79790	+	3.60338i	0.572695	+	0.234560i
$237$			22.4472i			1.45810i
$238$	21.9555	+	4.32196i	1.42316	+	0.280151i
$239$		−	12.2194i		−	0.790408i	−0.918593	−	0.395204i	$-0.870674\pi$
$239$		−	12.2194i		−	0.790408i	0.918593	−	0.395204i	$-0.129326\pi$
$240$	13.2498	−	13.4617i	0.855270	−	0.868951i
$241$			7.20677i			0.464229i	0.972688	+	0.232114i	$0.0745644\pi$
$241$			7.20677i			0.464229i	−0.972688	+	0.232114i	$0.925436\pi$
$242$	1.20270	−	6.10971i	0.0773126	−	0.392747i
$243$			7.12785i			0.457252i
$244$		0			0
$245$	2.18518			0.139606
$246$		0			0
$247$	2.59688	+	16.9415i	0.165235	+	1.07796i
$248$	−8.50781	−	5.61179i	−0.540247	−	0.356349i
$249$			14.9946i			0.950243i
$250$	−0.253905	+	1.28984i	−0.0160584	+	0.0815763i
$251$			24.4157i			1.54110i	0.637377	+	0.770552i	$0.280019\pi$
$251$			24.4157i			1.54110i	−0.637377	+	0.770552i	$0.719981\pi$
$252$	1.47585	−	3.60338i	0.0929697	−	0.226992i
$253$	10.2738			0.645905
$254$	3.27777	−	16.6510i	0.205665	−	1.04478i
$255$			26.9235i			1.68601i
$256$	0.253905	+	15.9980i	0.0158691	+	0.999874i
$257$	6.50781			0.405946			0.202973	−	0.979184i	$-0.434940\pi$
$257$	6.50781			0.405946			0.202973	+	0.979184i	$0.434940\pi$
$258$	0.627812	−	3.18928i	0.0390859	−	0.198556i
$259$			11.6760i			0.725513i
$260$	−5.26543	+	21.8348i	−0.326548	+	1.35413i
$261$		−	5.00063i		−	0.309531i
$262$	26.0920	+	5.13623i	1.61197	+	0.317317i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$	9.19375	+	6.06424i	0.565836	+	0.373228i
$265$			18.8885i			1.16031i
$266$	−18.3051	−	3.60338i	−1.12236	−	0.220938i
$267$	−22.7327			−1.39122
$268$	22.3494	+	9.15372i	1.36521	+	0.559153i
$269$			19.2563i			1.17408i	0.809558	+	0.587040i	$0.199707\pi$
$269$			19.2563i			1.17408i	−0.809558	+	0.587040i	$0.800293\pi$
$270$	24.2539	+	4.77440i	1.47605	+	0.290561i
$271$		−	27.2140i		−	1.65313i	−0.562839	−	0.826566i	$-0.690291\pi$
$271$		−	27.2140i		−	1.65313i	0.562839	−	0.826566i	$-0.309709\pi$
$272$	−16.2539	−	15.9980i	−0.985538	−	0.970020i
$273$	−2.29844	−	14.9946i	−0.139108	−	0.907513i
$274$	15.4031	+	3.03212i	0.930537	+	0.183177i
$275$	12.0757			0.728190
$276$	4.59688	−	11.2236i	0.276699	−	0.675580i
$277$			12.1285i			0.728730i	0.931256	+	0.364365i	$0.118714\pi$
$277$			12.1285i			0.728730i	−0.931256	+	0.364365i	$0.881286\pi$
$278$	−13.4700	−	2.65158i	−0.807877	−	0.159031i
$279$		−	2.52800i		−	0.151347i
$280$	−20.4088	−	13.4617i	−1.21966	−	0.804493i
$281$		−	7.20677i		−	0.429920i	−0.976623	−	0.214960i	$-0.931038\pi$
$281$		−	7.20677i		−	0.429920i	0.976623	−	0.214960i	$-0.0689621\pi$
$282$	1.14922	−	5.83802i	0.0684350	−	0.347649i
$283$		−	4.09573i		−	0.243466i	−0.992563	−	0.121733i	$-0.961155\pi$
$283$		−	4.09573i		−	0.243466i	0.992563	−	0.121733i	$-0.0388451\pi$
$284$	5.05536	−	12.3430i	0.299980	−	0.732422i
$285$		−	22.4472i		−	1.32966i
$286$	−13.0848	−	0.553362i	−0.773722	−	0.0327210i
$287$		0			0
$288$	−3.27777	+	2.23748i	−0.193144	+	0.131845i
$289$	15.5078			0.912224
$290$	−30.8062	−	6.06424i	−1.80901	−	0.356104i
$291$	5.90340			0.346063
$292$	−11.3663	+	27.7517i	−0.665165	+	1.62404i
$293$	−29.4513			−1.72056			−0.860280	−	0.509821i	$-0.829712\pi$
$293$	−29.4513			−1.72056			−0.860280	+	0.509821i	$0.829712\pi$
$294$	1.47585	+	0.290522i	0.0860733	+	0.0169436i
$295$	14.8062			0.862053
$296$	6.55234	−	9.93375i	0.380847	−	0.577387i
$297$			14.4135i			0.836358i
$298$	3.70156	−	18.8039i	0.214426	−	1.08928i
$299$	2.18518	+	14.2557i	0.126372	+	0.824428i
$300$	5.40312	−	13.1921i	0.311950	−	0.761646i
$301$	−4.20732			−0.242506
$302$	−19.2539	−	3.79015i	−1.10794	−	0.218099i
$303$		0			0
$304$	13.5515	+	13.3382i	0.777233	+	0.764995i
$305$		0			0
$306$	1.09259	−	5.55034i	0.0624592	−	0.317292i
$307$	−29.6715			−1.69344			−0.846720	−	0.532038i	$-0.821426\pi$
$307$	−29.6715			−1.69344			−0.846720	+	0.532038i	$0.821426\pi$
$308$	5.40312	−	13.1921i	0.307872	−	0.751689i
$309$			6.06424i			0.344983i
$310$	−15.5737	−	3.06569i	−0.884525	−	0.174120i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	−6.45918	+	14.0469i	−0.365679	+	0.795251i
$313$	−24.5078			−1.38526			−0.692632	−	0.721291i	$-0.743549\pi$
$313$	−24.5078			−1.38526			−0.692632	+	0.721291i	$0.743549\pi$
$314$	1.47585	+	0.290522i	0.0832870	+	0.0163951i
$315$		−	6.06424i		−	0.341681i
$316$	−27.4031	−	11.2236i	−1.54155	−	0.631376i
$317$	25.2439			1.41784			0.708920	−	0.705289i	$-0.249183\pi$
$317$	25.2439			1.41784			0.708920	+	0.705289i	$0.249183\pi$
$318$	−2.51125	+	12.7571i	−0.140824	+	0.715383i
$319$		−	18.3074i		−	1.02502i
$320$	9.80898	+	22.9060i	0.548338	+	1.28048i
$321$	−15.4031			−0.859719
$322$	−15.4031	−	3.03212i	−0.858383	−	0.168973i
$323$	−27.1030			−1.50805
$324$	11.8508	+	4.85376i	0.658377	+	0.269653i
$325$	2.56844	+	16.7560i	0.142471	+	0.929456i
$326$	−2.70156	+	13.7239i	−0.149626	+	0.760096i
$327$			3.06569i			0.169533i
$328$		0			0
$329$	−7.70156			−0.424601
$330$	16.8293	+	3.31286i	0.926422	+	0.182367i
$331$	−5.52014			−0.303414			−0.151707	−	0.988425i	$-0.548477\pi$
$331$	−5.52014			−0.303414			−0.151707	+	0.988425i	$0.548477\pi$
$332$	−18.3051	−	7.49729i	−1.00463	−	0.411467i
$333$	2.95170			0.161752
$334$	10.4031	+	2.04787i	0.569234	+	0.112054i
$335$	37.6125			2.05499
$336$	−11.9942	−	11.8053i	−0.654335	−	0.644032i
$337$	14.2984			0.778886			0.389443	−	0.921051i	$-0.372668\pi$
$337$	14.2984			0.778886			0.389443	+	0.921051i	$0.372668\pi$
$338$	−2.01524	−	18.2740i	−0.109615	−	0.993974i
$339$			17.2878i			0.938946i
$340$	−32.8677	−	13.4617i	−1.78250	−	0.730065i
$341$		−	9.25507i		−	0.501190i
$342$	−0.910935	+	4.62754i	−0.0492577	+	0.250228i
$343$			17.4792i			0.943790i
$344$	3.57951	+	2.36106i	0.192994	+	0.127300i
$345$		−	18.8885i		−	1.01692i
$346$	8.41464	+	1.65643i	0.452374	+	0.0890503i
$347$		−	6.67540i		−	0.358354i	−0.983817	−	0.179177i	$-0.942656\pi$
$347$		−	6.67540i		−	0.358354i	0.983817	−	0.179177i	$-0.0573435\pi$
$348$	−20.0000	−	8.19146i	−1.07211	−	0.439108i
$349$	3.44080			0.184182			0.0920910	−	0.995751i	$-0.470645\pi$
$349$	3.44080			0.184182			0.0920910	+	0.995751i	$0.470645\pi$
$350$	−18.1047	−	3.56393i	−0.967736	−	0.190500i
$351$	−20.0000	+	3.06569i	−1.06752	+	0.163634i
$352$	−12.0000	+	8.19146i	−0.639602	+	0.436606i
$353$			33.3020i			1.77249i	0.463219	+	0.886244i	$0.346694\pi$
$353$			33.3020i			1.77249i	−0.463219	+	0.886244i	$0.653306\pi$
$354$	10.0000	+	1.96851i	0.531494	+	0.104625i
$355$		−	20.7724i		−	1.10248i
$356$	11.3663	−	27.7517i	0.602415	−	1.47084i
$357$	23.9883			1.26960
$358$	17.6773	+	3.47980i	0.934276	+	0.183913i
$359$			18.5980i			0.981563i	0.871283	+	0.490782i	$0.163289\pi$
$359$			18.5980i			0.981563i	−0.871283	+	0.490782i	$0.836711\pi$
$360$	−3.40312	+	5.15934i	−0.179360	+	0.271921i
$361$	3.59688			0.189309
$362$	18.3051	+	3.60338i	0.962097	+	0.189390i
$363$		−	6.67540i		−	0.350368i
$364$	19.4544	+	4.69140i	1.01969	+	0.245896i
$365$			46.7041i			2.44461i
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	11.4031	+	11.2236i	0.594429	+	0.585070i
$369$		0			0
$370$	3.57951	−	18.1839i	0.186090	−	0.945334i
$371$	16.8293			0.873733
$372$	−10.1107	−	4.14108i	−0.524216	−	0.214705i
$373$		−	19.2563i		−	0.997055i	−0.866874	−	0.498527i	$-0.833874\pi$
$373$		−	19.2563i		−	0.997055i	0.866874	−	0.498527i	$-0.166126\pi$
$374$	4.00000	−	20.3199i	0.206835	−	1.05072i
$375$			1.40926i			0.0727739i
$376$	6.55234	+	4.32196i	0.337911	+	0.222888i
$377$	25.4031	−	3.89391i	1.30833	−	0.200546i
$378$	4.25391	−	21.6098i	0.218797	−	1.11149i
$379$	4.75362			0.244177			0.122088	−	0.992519i	$-0.461041\pi$
$379$	4.75362			0.244177			0.122088	+	0.992519i	$0.461041\pi$
$380$	27.4031	+	11.2236i	1.40575	+	0.575758i
$381$		−	18.1927i		−	0.932041i
$382$	0.766519	−	3.89391i	0.0392185	−	0.199230i
$383$		−	1.11874i		−	0.0571648i	−0.999591	−	0.0285824i	$-0.990901\pi$
$383$		−	1.11874i		−	0.0571648i	0.999591	−	0.0285824i	$-0.00909930\pi$
$384$	3.57951	+	16.7746i	0.182666	+	0.856025i
$385$		−	22.2014i		−	1.13149i
$386$	20.8062	+	4.09573i	1.05901	+	0.208467i
$387$			1.06361i			0.0540663i
$388$	−2.95170	+	7.20677i	−0.149850	+	0.365868i
$389$			15.3193i			0.776720i	0.921508	+	0.388360i	$0.126958\pi$
$389$			15.3193i			0.776720i	−0.921508	+	0.388360i	$0.873042\pi$
$390$	−1.01737	+	24.0567i	−0.0515163	+	1.21816i
$391$	−22.8062			−1.15336
$392$	−1.09259	+	1.65643i	−0.0551841	+	0.0836624i
$393$	28.5078			1.43803
$394$	−1.14922	+	5.83802i	−0.0578968	+	0.294115i
$395$	−46.1175			−2.32042
$396$	−3.33496	−	1.36591i	−0.167588	−	0.0686395i
$397$	6.22947			0.312648			0.156324	−	0.987706i	$-0.450036\pi$
$397$	6.22947			0.312648			0.156324	+	0.987706i	$0.450036\pi$
$398$		0			0
$399$	−20.0000			−1.00125
$400$	13.4031	+	13.1921i	0.670156	+	0.659605i
$401$		−	7.20677i		−	0.359889i	−0.983677	−	0.179944i	$-0.942408\pi$
$401$		−	7.20677i		−	0.359889i	0.983677	−	0.179944i	$-0.0575918\pi$
$402$	25.4031	+	5.00063i	1.26699	+	0.249409i
$403$	12.8422	−	1.96851i	0.639715	−	0.0980585i
$404$		0			0
$405$	19.9440			0.991026
$406$	−5.40312	+	27.4478i	−0.268153	+	1.36221i
$407$	10.8062			0.535646
$408$	−20.4088	−	13.4617i	−1.01039	−	0.666455i
$409$		−	33.3020i		−	1.64668i	−0.567549	−	0.823340i	$-0.692108\pi$
$409$		−	33.3020i		−	1.64668i	0.567549	−	0.823340i	$-0.307892\pi$
$410$		0			0
$411$	16.8293			0.830128
$412$	−7.40312	−	3.03212i	−0.364726	−	0.149382i
$413$		−	13.1921i		−	0.649140i
$414$	−0.766519	+	3.89391i	−0.0376724	+	0.191375i
$415$	−30.8062			−1.51222
$416$	−13.9187	−	14.9087i	−0.682420	−	0.730961i
$417$	−14.7172			−0.720704
$418$	−3.33496	+	16.9415i	−0.163118	+	0.828638i
$419$			13.6445i			0.666579i	0.942824	+	0.333290i	$0.108159\pi$
$419$			13.6445i			0.666579i	−0.942824	+	0.333290i	$0.891841\pi$
$420$	−24.2539	−	9.93375i	−1.18347	−	0.484717i
$421$	36.4472			1.77633			0.888165	−	0.459525i	$-0.151980\pi$
$421$	36.4472			1.77633			0.888165	+	0.459525i	$0.151980\pi$
$422$	26.0920	+	5.13623i	1.27014	+	0.250028i
$423$			1.94695i			0.0946641i
$424$	−14.3180	−	9.44424i	−0.695346	−	0.458653i
$425$	−26.8062			−1.30029
$426$	2.76172	−	14.0295i	0.133806	−	0.679730i
$427$		0			0
$428$	7.70156	−	18.8039i	0.372269	−	0.908920i
$429$	−13.8776	+	2.12722i	−0.670016	+	0.102703i
$430$	6.55234	+	1.28984i	0.315982	+	0.0622014i
$431$		−	0.537693i		−	0.0258998i	−0.999916	−	0.0129499i	$-0.995878\pi$
$431$		−	0.537693i		−	0.0258998i	0.999916	−	0.0129499i	$-0.00412219\pi$
$432$	−15.7461	+	15.9980i	−0.757584	+	0.769703i
$433$	2.50781			0.120518			0.0602588	−	0.998183i	$-0.480807\pi$
$433$	2.50781			0.120518			0.0602588	+	0.998183i	$0.480807\pi$
$434$	−2.73147	+	13.8758i	−0.131115	+	0.666062i
$435$	−33.6586			−1.61381
$436$	−3.74255	−	1.53285i	−0.179235	−	0.0734100i
$437$	19.0145			0.909585
$438$	−6.20937	+	31.5435i	−0.296695	+	1.50721i
$439$	−14.8062			−0.706664			−0.353332	−	0.935498i	$-0.614951\pi$
$439$	−14.8062			−0.706664			−0.353332	+	0.935498i	$0.614951\pi$
$440$	−12.4589	+	18.8885i	−0.593956	+	0.900473i
$441$	−0.492189			−0.0234376
$442$	29.0464	+	1.22838i	1.38160	+	0.0584282i
$443$			1.51606i			0.0720302i	0.999351	+	0.0360151i	$0.0114664\pi$
$443$			1.51606i			0.0720302i	−0.999351	+	0.0360151i	$0.988534\pi$
$444$	4.83513	−	11.8053i	0.229465	−	0.560255i
$445$		−	46.7041i		−	2.21399i
$446$	21.5523	+	4.24260i	1.02053	+	0.200893i
$447$		−	20.5449i		−	0.971741i
$448$	20.4088	−	8.73961i	0.964225	−	0.412908i
$449$		−	11.6817i		−	0.551294i	−0.961259	−	0.275647i	$-0.911108\pi$
$449$		−	11.6817i		−	0.551294i	0.961259	−	0.275647i	$-0.0888922\pi$
$450$	−0.900960	+	4.57686i	−0.0424716	+	0.215755i
$451$		0			0
$452$	−21.1047	−	8.64391i	−0.992681	−	0.406575i
$453$	−21.0366			−0.988386
$454$	−1.89531	+	9.62817i	−0.0889515	+	0.451872i
$455$	30.8062	−	4.72212i	1.44422	−	0.221377i
$456$	17.0156	+	11.2236i	0.796829	+	0.525592i
$457$			3.31286i			0.154969i	0.996994	+	0.0774846i	$0.0246889\pi$
$457$			3.31286i			0.154969i	−0.996994	+	0.0774846i	$0.975311\pi$
$458$	2.04453	−	10.3862i	0.0955347	−	0.485315i
$459$		−	31.9960i		−	1.49344i
$460$	23.0588	+	9.44424i	1.07512	+	0.440340i
$461$	−8.25161			−0.384316			−0.192158	−	0.981364i	$-0.561549\pi$
$461$	−8.25161			−0.384316			−0.192158	+	0.981364i	$0.561549\pi$
$462$	2.95170	−	14.9946i	0.137325	−	0.697611i
$463$		−	11.3912i		−	0.529394i	−0.964332	−	0.264697i	$-0.914728\pi$
$463$		−	11.3912i		−	0.529394i	0.964332	−	0.264697i	$-0.0852719\pi$
$464$	20.0000	−	20.3199i	0.928477	−	0.943330i
$465$	−17.0156			−0.789081
$466$	1.94063	−	9.85835i	0.0898978	−	0.456679i
$467$		−	16.2242i		−	0.750767i	−0.926870	−	0.375383i	$-0.877511\pi$
$467$		−	16.2242i		−	0.750767i	0.926870	−	0.375383i	$-0.122489\pi$
$468$	1.18598	−	4.91806i	0.0548221	−	0.227337i
$469$		−	33.5120i		−	1.54744i
$470$	11.9942	+	2.36106i	0.553249	+	0.108908i
$471$	1.61250			0.0742999
$472$	−7.40312	+	11.2236i	−0.340756	+	0.516607i
$473$			3.89391i			0.179042i
$474$	−31.1473	−	6.13138i	−1.43064	−	0.281624i
$475$	22.3494			1.02546
$476$	−11.9942	+	29.2845i	−0.549751	+	1.34225i
$477$		−	4.25444i		−	0.194797i
$478$	16.9555	+	3.33770i	0.775525	+	0.152663i
$479$			28.8704i			1.31912i	0.751650	+	0.659562i	$0.229258\pi$
$479$			28.8704i			1.31912i	−0.751650	+	0.659562i	$0.770742\pi$
$480$	15.0602	+	22.0622i	0.687399	+	1.00700i
$481$	2.29844	+	14.9946i	0.104800	+	0.683694i
$482$	−10.0000	−	1.96851i	−0.455488	−	0.0896632i
$483$	−16.8293			−0.765759
$484$	8.14922	+	3.33770i	0.370419	+	0.151714i
$485$			12.1285i			0.550726i
$486$	−9.89049	−	1.94695i	−0.448642	−	0.0883156i
$487$			26.3858i			1.19565i	0.801625	+	0.597827i	$0.203969\pi$
$487$			26.3858i			1.19565i	−0.801625	+	0.597827i	$0.796031\pi$
$488$		0			0
$489$			14.9946i			0.678078i
$490$	−0.596876	+	3.03212i	−0.0269641	+	0.136977i
$491$			3.64328i			0.164419i	0.996615	+	0.0822095i	$0.0261977\pi$
$491$			3.64328i			0.164419i	−0.996615	+	0.0822095i	$0.973802\pi$
$492$		0			0
$493$			40.6399i			1.83033i
$494$	−24.2171	−	1.02415i	−1.08958	−	0.0460787i
$495$	−5.61250			−0.252263
$496$	10.1107	−	10.2725i	0.453985	−	0.461247i
$497$	−18.5078			−0.830189
$498$	−20.8062	−	4.09573i	−0.932350	−	0.183534i
$499$	31.8567			1.42610			0.713050	−	0.701113i	$-0.247313\pi$
$499$	31.8567			1.42610			0.713050	+	0.701113i	$0.247313\pi$
$500$	−1.72040	−	0.704630i	−0.0769387	−	0.0315120i
$501$	11.3663			0.507811
$502$	−33.8788	−	6.66908i	−1.51209	−	0.297655i
$503$	−25.6125			−1.14200			−0.571002	−	0.820948i	$-0.693445\pi$
$503$	−25.6125			−1.14200			−0.571002	+	0.820948i	$0.693445\pi$
$504$	4.59688	+	3.03212i	0.204761	+	0.135061i
$505$		0			0
$506$	−2.80625	+	14.2557i	−0.124753	+	0.633743i
$507$	−5.90340	−	18.8039i	−0.262179	−	0.835110i
$508$	22.2094	+	9.09636i	0.985382	+	0.403586i
$509$	−23.0588			−1.02206			−0.511031	−	0.859562i	$-0.670736\pi$
$509$	−23.0588			−1.02206			−0.511031	+	0.859562i	$0.670736\pi$
$510$	−37.3586	−	7.35408i	−1.65427	−	0.325644i
$511$	41.6125			1.84083
$512$	−22.2679	−	4.01749i	−0.984112	−	0.177550i
$513$			26.6763i			1.17779i
$514$	−1.77759	+	9.03014i	−0.0784062	+	0.398302i
$515$	−12.4589			−0.549006
$516$	4.25391	+	1.74228i	0.187268	+	0.0766998i
$517$			7.12785i			0.313482i
$518$	−16.2015	−	3.18928i	−0.711852	−	0.140129i
$519$	9.19375			0.403561
$520$	−28.8593	−	13.2703i	−1.26557	−	0.581942i
$521$	13.1047			0.574127			0.287063	−	0.957912i	$-0.407321\pi$
$521$	13.1047			0.574127			0.287063	+	0.957912i	$0.407321\pi$
$522$	6.93880	+	1.36591i	0.303703	+	0.0597842i
$523$		−	4.09573i		−	0.179094i	−0.995983	−	0.0895469i	$-0.971458\pi$
$523$		−	4.09573i		−	0.179094i	0.995983	−	0.0895469i	$-0.0285419\pi$
$524$	−14.2539	+	34.8019i	−0.622685	+	1.52033i
$525$	−19.7810			−0.863313
$526$	4.37036	−	22.2014i	0.190557	−	0.968025i
$527$			20.5449i			0.894951i
$528$	−10.9259	+	11.1007i	−0.475488	+	0.483095i
$529$	−7.00000			−0.304348
$530$	−26.2094	−	5.15934i	−1.13846	−	0.224107i
$531$	−3.33496			−0.144725
$532$	10.0000	−	24.4157i	0.433555	−	1.05855i
$533$		0			0
$534$	6.20937	−	31.5435i	0.268706	−	1.36502i
$535$		−	31.6456i		−	1.36816i
$536$	−18.8062	+	28.5114i	−0.812306	+	1.23150i
$537$	19.3141			0.833463
$538$	−26.7198	−	5.25982i	−1.15197	−	0.226767i
$539$	−1.80192			−0.0776141
$540$	−13.2498	+	32.3502i	−0.570180	+	1.39213i
$541$	−8.25161			−0.354764			−0.177382	−	0.984142i	$-0.556763\pi$
$541$	−8.25161			−0.354764			−0.177382	+	0.984142i	$0.556763\pi$
$542$	37.7617	+	7.43343i	1.62200	+	0.319293i
$543$	20.0000			0.858282
$544$	26.6383	−	18.1839i	1.14211	−	0.779627i
$545$	−6.29844			−0.269795
$546$	21.4341	+	0.906454i	0.917293	+	0.0387926i
$547$			42.1559i			1.80246i	0.433343	+	0.901229i	$0.357334\pi$
$547$			42.1559i			1.80246i	−0.433343	+	0.901229i	$0.642666\pi$
$548$	−8.41464	+	20.5449i	−0.359456	+	0.877635i
$549$		0			0
$550$	−3.29844	+	16.7560i	−0.140646	+	0.714479i
$551$		−	33.8831i		−	1.44347i
$552$	14.3180	+	9.44424i	0.609416	+	0.401974i
$553$			41.0898i			1.74732i
$554$	−16.8293	−	3.31286i	−0.715008	−	0.140750i
$555$		−	19.8675i		−	0.843328i
$556$	7.35859	−	17.9665i	0.312074	−	0.761949i
$557$	12.2959			0.520994			0.260497	−	0.965475i	$-0.416114\pi$
$557$	12.2959			0.520994			0.260497	+	0.965475i	$0.416114\pi$
$558$	3.50781	+	0.690516i	0.148497	+	0.0292319i
$559$	−5.40312	+	0.828216i	−0.228528	+	0.0350298i
$560$	24.2539	−	24.6419i	1.02491	−	1.04131i
$561$		−	22.2014i		−	0.937342i
$562$	10.0000	+	1.96851i	0.421825	+	0.0830366i
$563$			27.9002i			1.17585i	0.808914	+	0.587927i	$0.200056\pi$
$563$			27.9002i			1.17585i	−0.808914	+	0.587927i	$0.799944\pi$
$564$	7.78683	+	3.18928i	0.327885	+	0.134293i
$565$	−35.5177			−1.49424
$566$	5.68317	+	1.11874i	0.238882	+	0.0470241i
$567$		−	17.7698i		−	0.746259i
$568$	15.7461	+	10.3862i	0.660691	+	0.435795i
$569$	18.5078			0.775888			0.387944	−	0.921683i	$-0.373185\pi$
$569$	18.5078			0.775888			0.387944	+	0.921683i	$0.373185\pi$
$570$	31.1473	+	6.13138i	1.30462	+	0.256815i
$571$		−	18.8039i		−	0.786918i	−0.919342	−	0.393459i	$-0.871278\pi$
$571$		−	18.8039i		−	0.786918i	0.919342	−	0.393459i	$-0.128722\pi$
$572$	4.34192	−	18.0051i	0.181545	−	0.752833i
$573$		−	4.25444i		−	0.177732i
$574$		0			0
$575$	18.8062			0.784275
$576$	−2.20937	−	5.15934i	−0.0920572	−	0.214973i
$577$		−	25.5142i		−	1.06217i	−0.847318	−	0.531085i	$-0.821784\pi$
$577$		−	25.5142i		−	1.06217i	0.847318	−	0.531085i	$-0.178216\pi$
$578$	−4.23592	+	21.5184i	−0.176191	+	0.895047i
$579$	22.7327			0.944738
$580$	16.8293	−	41.0898i	0.698798	−	1.70616i
$581$			27.4478i			1.13873i
$582$	−1.61250	+	8.19146i	−0.0668401	+	0.339547i
$583$		−	15.5756i		−	0.645077i
$584$	−35.4031	−	23.3521i	−1.46499	−	0.966315i
$585$	−1.19375	−	7.78781i	−0.0493556	−	0.321986i
$586$	8.04453	−	40.8661i	0.332317	−	1.68816i
$587$	15.0274			0.620246			0.310123	−	0.950696i	$-0.399630\pi$
$587$	15.0274			0.620246			0.310123	+	0.950696i	$0.399630\pi$
$588$	−0.806248	+	1.96851i	−0.0332491	+	0.0811800i
$589$		−	17.1291i		−	0.705793i
$590$	−4.04429	+	20.5449i	−0.166501	+	0.845821i
$591$			6.37855i			0.262379i
$592$	11.9942	+	11.8053i	0.492957	+	0.485195i
$593$		−	7.78781i		−	0.319807i	−0.987133	−	0.159904i	$-0.948882\pi$
$593$		−	7.78781i		−	0.319807i	0.987133	−	0.159904i	$-0.0511183\pi$
$594$	−20.0000	−	3.93702i	−0.820610	−	0.161538i
$595$			49.2838i			2.02044i
$596$	25.0809	+	10.2725i	1.02735	+	0.420776i
$597$		0			0
$598$	−20.3779	−	0.861787i	−0.833313	−	0.0352411i
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$	16.8293	+	11.1007i	0.687053	+	0.453183i
$601$	−6.89531			−0.281266			−0.140633	−	0.990062i	$-0.544914\pi$
$601$	−6.89531			−0.281266			−0.140633	+	0.990062i	$0.544914\pi$
$602$	1.14922	−	5.83802i	0.0468387	−	0.237940i
$603$	−8.47183			−0.345000
$604$	10.5183	−	25.6811i	0.427984	−	1.04495i
$605$	13.7146			0.557576
$606$		0			0
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$	−22.2094	+	15.1606i	−0.900709	+	0.614844i
$609$			29.9892i			1.21522i
$610$		0			0
$611$	−9.89049	+	1.51606i	−0.400127	+	0.0613332i
$612$	7.40312	+	3.03212i	0.299254	+	0.122566i
$613$	−34.0990			−1.37725			−0.688623	−	0.725119i	$-0.741785\pi$
$613$	−34.0990			−1.37725			−0.688623	+	0.725119i	$0.741785\pi$
$614$	8.10469	−	41.1717i	0.327079	−	1.66155i
$615$		0			0
$616$	16.8293	+	11.1007i	0.678071	+	0.447259i
$617$			10.5196i			0.423504i	0.977323	+	0.211752i	$0.0679170\pi$
$617$			10.5196i			0.423504i	−0.977323	+	0.211752i	$0.932083\pi$
$618$	−8.41464	−	1.65643i	−0.338487	−	0.0666314i
$619$	31.8567			1.28043			0.640214	−	0.768197i	$-0.278846\pi$
$619$	31.8567			1.28043			0.640214	+	0.768197i	$0.278846\pi$
$620$	8.50781	−	20.7724i	0.341682	−	0.834239i
$621$			22.4472i			0.900774i
$622$	−3.27777	+	16.6510i	−0.131427	+	0.667645i
$623$	−41.6125			−1.66717
$624$	−17.7270	−	12.7995i	−0.709648	−	0.512392i
$625$	−26.4031			−1.05612
$626$	6.69424	−	34.0067i	0.267556	−	1.35918i
$627$			18.5101i			0.739224i
$628$	−0.806248	+	1.96851i	−0.0321728	+	0.0785521i
$629$	−23.9883			−0.956477
$630$	8.41464	+	1.65643i	0.335247	+	0.0659938i
$631$		−	0.537693i		−	0.0214052i	−0.999943	−	0.0107026i	$-0.996593\pi$
$631$		−	0.537693i		−	0.0214052i	0.999943	−	0.0107026i	$-0.00340681\pi$
$632$	23.0588	−	34.9585i	0.917228	−	1.39057i
$633$	28.5078			1.13308
$634$	−6.89531	+	35.0281i	−0.273848	+	1.39114i
$635$	37.3768			1.48325
$636$	−17.0156	−	6.96914i	−0.674713	−	0.276344i
$637$	−0.383260	−	2.50031i	−0.0151853	−	0.0990661i
$638$	25.4031	+	5.00063i	1.00572	+	0.197977i
$639$			4.67877i			0.185089i
$640$	−34.4633	+	7.35408i	−1.36228	+	0.290695i
$641$	24.5969			0.971518			0.485759	−	0.874093i	$-0.338543\pi$
$641$	24.5969			0.971518			0.485759	+	0.874093i	$0.338543\pi$
$642$	4.20732	−	21.3731i	0.166050	−	0.843530i
$643$	36.9935			1.45888			0.729441	−	0.684043i	$-0.239780\pi$
$643$	36.9935			1.45888			0.729441	+	0.684043i	$0.239780\pi$
$644$	8.41464	−	20.5449i	0.331583	−	0.809583i
$645$	7.15902			0.281886
$646$	7.40312	−	37.6078i	0.291272	−	1.47966i
$647$	−17.1938			−0.675956			−0.337978	−	0.941154i	$-0.609743\pi$
$647$	−17.1938			−0.675956			−0.337978	+	0.941154i	$0.609743\pi$
$648$	−9.97201	+	15.1182i	−0.391738	+	0.593898i
$649$	−12.2094			−0.479260
$650$	−23.9519	−	1.01294i	−0.939473	−	0.0397306i
$651$			15.1606i			0.594191i
$652$	−18.3051	−	7.49729i	−0.716885	−	0.293617i
$653$		−	19.2563i		−	0.753558i	−0.926303	−	0.376779i	$-0.877032\pi$
$653$		−	19.2563i		−	0.753558i	0.926303	−	0.376779i	$-0.122968\pi$
$654$	−4.25391	−	0.837385i	−0.166341	−	0.0327444i
$655$			58.5691i			2.28848i
$656$		0			0
$657$		−	10.5196i		−	0.410410i
$658$	2.10366	−	10.6866i	0.0820093	−	0.416606i
$659$			8.03275i			0.312912i	0.987685	+	0.156456i	$0.0500069\pi$
$659$			8.03275i			0.312912i	−0.987685	+	0.156456i	$0.949993\pi$
$660$	−9.19375	+	22.4472i	−0.357866	+	0.873755i
$661$	1.85911			0.0723109			0.0361555	−	0.999346i	$-0.488489\pi$
$661$	1.85911			0.0723109			0.0361555	+	0.999346i	$0.488489\pi$
$662$	1.50781	−	7.65966i	0.0586027	−	0.297701i
$663$	30.8062	−	4.72212i	1.19642	−	0.183392i
$664$	15.4031	−	23.3521i	0.597757	−	0.906236i
$665$		−	41.0898i		−	1.59340i
$666$	−0.806248	+	4.09573i	−0.0312415	+	0.158706i
$667$		−	28.5114i		−	1.10397i
$668$	−5.68317	+	13.8758i	−0.219889	+	0.536873i
$669$	23.5479			0.910413
$670$	−10.2738	+	52.1905i	−0.396910	+	2.01630i
$671$		0			0
$672$	19.6570	−	13.4183i	0.758286	−	0.517623i
$673$	−0.0890652			−0.00343321			−0.00171660	−	0.999999i	$-0.500546\pi$
$673$	−0.0890652			−0.00343321			−0.00171660	+	0.999999i	$0.500546\pi$
$674$	−3.90558	+	19.8403i	−0.150437	+	0.764219i
$675$			26.3842i			1.01553i
$676$	25.9072	+	2.19517i	0.996429	+	0.0844297i
$677$		−	18.1927i		−	0.699203i	−0.936898	−	0.349602i	$-0.886317\pi$
$677$		−	18.1927i		−	0.699203i	0.936898	−	0.349602i	$-0.113683\pi$
$678$	−23.9883	−	4.72212i	−0.921266	−	0.181352i
$679$	10.8062			0.414706
$680$	27.6570	−	41.9297i	1.06060	−	1.60793i
$681$			10.5196i			0.403113i
$682$	12.8422	+	2.52800i	0.491753	+	0.0968020i
$683$	−15.7939			−0.604336			−0.302168	−	0.953255i	$-0.597710\pi$
$683$	−15.7939			−0.604336			−0.302168	+	0.953255i	$0.597710\pi$
$684$	−6.17228	−	2.52800i	−0.236003	−	0.0966604i
$685$			34.5756i			1.32107i
$686$	−24.2539	−	4.77440i	−0.926018	−	0.182288i
$687$		−	11.3478i		−	0.432947i
$688$	−4.25391	+	4.32196i	−0.162179	+	0.164773i
$689$	21.6125	−	3.31286i	0.823371	−	0.126210i
$690$	26.2094	+	5.15934i	0.997774	+	0.196413i
$691$	2.56844			0.0977080			0.0488540	−	0.998806i	$-0.484443\pi$
$691$	2.56844			0.0977080			0.0488540	+	0.998806i	$0.484443\pi$
$692$	−4.59688	+	11.2236i	−0.174747	+	0.426657i
$693$			5.00063i			0.189958i
$694$	9.26268	+	1.82337i	0.351607	+	0.0692141i
$695$		−	30.2363i		−	1.14693i
$696$	16.8293	−	25.5142i	0.637913	−	0.967114i
$697$		0			0
$698$	−0.939846	+	4.77440i	−0.0355737	+	0.180714i
$699$		−	10.7711i		−	0.407402i
$700$	9.89049	−	24.1483i	0.373826	−	0.912720i
$701$			13.1921i			0.498258i	0.968470	+	0.249129i	$0.0801444\pi$
$701$			13.1921i			0.498258i	−0.968470	+	0.249129i	$0.919856\pi$
$702$	1.20904	−	28.5891i	0.0456323	−	1.07903i
$703$	20.0000			0.754314
$704$	−8.08857	−	18.8885i	−0.304850	−	0.711887i
$705$	13.1047			0.493551
$706$	−46.2094	−	9.09636i	−1.73911	−	0.342346i
$707$		0			0
$708$	−5.46295	+	13.3382i	−0.205310	+	0.501278i
$709$	−39.2359			−1.47354			−0.736768	−	0.676146i	$-0.763649\pi$
$709$	−39.2359			−1.47354			−0.736768	+	0.676146i	$0.763649\pi$
$710$	28.8234	+	5.67392i	1.08172	+	0.212939i
$711$	10.3875			0.389562
$712$	35.4031	+	23.3521i	1.32679	+	0.875155i
$713$		−	14.4135i		−	0.539791i
$714$	−6.55234	+	33.2858i	−0.245215	+	1.24569i
$715$	−4.37036	−	28.5114i	−0.163442	−	1.06627i
$716$	−9.65703	+	23.5783i	−0.360900	+	0.881162i
$717$	18.5254			0.691842
$718$	−25.8062	−	5.07999i	−0.963081	−	0.189583i
$719$	−5.19375			−0.193694			−0.0968471	−	0.995299i	$-0.530876\pi$
$719$	−5.19375			−0.193694			−0.0968471	+	0.995299i	$0.530876\pi$
$720$	−6.22947	−	6.13138i	−0.232158	−	0.228503i
$721$			11.1007i			0.413411i
$722$	−0.982477	+	4.99097i	−0.0365640	+	0.185745i
$723$	−10.9259			−0.406338
$724$	−10.0000	+	24.4157i	−0.371647	+	0.907401i
$725$		−	33.5120i		−	1.24461i
$726$	9.26268	+	1.82337i	0.343770	+	0.0676715i
$727$	42.8062			1.58760			0.793798	−	0.608182i	$-0.208101\pi$
$727$	42.8062			1.58760			0.793798	+	0.608182i	$0.208101\pi$
$728$	−11.8236	+	25.7131i	−0.438212	+	0.952992i
$729$	−30.0156			−1.11169
$730$	−64.8059	−	12.7571i	−2.39857	−	0.472162i
$731$		−	8.64391i		−	0.319707i
$732$		0			0
$733$	−19.9440			−0.736649			−0.368325	−	0.929697i	$-0.620069\pi$
$733$	−19.9440			−0.736649			−0.368325	+	0.929697i	$0.620069\pi$
$734$	−2.18518	+	11.1007i	−0.0806564	+	0.409733i
$735$			3.31286i			0.122197i
$736$	−18.6884	+	12.7571i	−0.688864	+	0.470233i
$737$	−31.0156			−1.14248
$738$		0			0
$739$	−6.17228			−0.227051			−0.113525	−	0.993535i	$-0.536214\pi$
$739$	−6.17228			−0.227051			−0.113525	+	0.993535i	$0.536214\pi$
$740$	24.2539	+	9.93375i	0.891591	+	0.365172i
$741$	−25.6844	+	3.93702i	−0.943539	+	0.144630i
$742$	−4.59688	+	23.3521i	−0.168757	+	0.857281i
$743$			39.9711i			1.46640i	0.680014	+	0.733199i	$0.261974\pi$
$743$			39.9711i			1.46640i	−0.680014	+	0.733199i	$0.738026\pi$
$744$	8.50781	−	12.8984i	0.311911	−	0.472876i
$745$	42.2094			1.54643
$746$	26.7198	+	5.25982i	0.978281	+	0.192576i
$747$	6.93880			0.253877
$748$	27.1030	+	11.1007i	0.990985	+	0.405881i
$749$	−28.1956			−1.03025
$750$	−1.95547	−	0.384936i	−0.0714036	−	0.0140559i
$751$	−32.4187			−1.18298			−0.591488	−	0.806313i	$-0.701459\pi$
$751$	−32.4187			−1.18298			−0.591488	+	0.806313i	$0.701459\pi$
$752$	−7.78683	+	7.91140i	−0.283957	+	0.288499i
$753$	−37.0156			−1.34892
$754$	−1.53567	+	36.3126i	−0.0559259	+	1.32243i
$755$		−	43.2196i		−	1.57292i
$756$	28.8234	+	11.8053i	1.04830	+	0.429355i
$757$			34.5756i			1.25667i	0.777942	+	0.628337i	$0.216264\pi$
$757$			34.5756i			1.25667i	−0.777942	+	0.628337i	$0.783736\pi$
$758$	−1.29844	+	6.59605i	−0.0471614	+	0.239579i
$759$			15.5756i			0.565359i
$760$	−23.0588	+	34.9585i	−0.836429	+	1.26808i
$761$			26.6763i			0.967015i	0.875340	+	0.483508i	$0.160637\pi$
$761$			26.6763i			0.967015i	−0.875340	+	0.483508i	$0.839363\pi$
$762$	25.2439	+	4.96929i	0.914491	+	0.180018i
$763$			5.61179i			0.203160i
$764$	5.19375	+	2.12722i	0.187903	+	0.0769601i
$765$	12.4589			0.450454
$766$	1.55234	+	0.305580i	0.0560884	+	0.0110411i
$767$	−2.59688	−	16.9415i	−0.0937677	−	0.611723i
$768$	−24.2539	+	0.384936i	−0.875187	+	0.0138902i
$769$		−	26.0953i		−	0.941019i	−0.882395	−	0.470510i	$-0.844070\pi$
$769$		−	26.0953i		−	0.941019i	0.882395	−	0.470510i	$-0.155930\pi$
$770$	30.8062	+	6.06424i	1.11018	+	0.218540i
$771$			9.86623i			0.355324i
$772$	−11.3663	+	27.7517i	−0.409084	+	0.998805i
$773$	42.3506			1.52325			0.761623	−	0.648020i	$-0.224403\pi$
$773$	42.3506			1.52325			0.761623	+	0.648020i	$0.224403\pi$
$774$	−1.47585	−	0.290522i	−0.0530483	−	0.0104426i
$775$		−	16.9415i		−	0.608558i
$776$	−9.19375	−	6.06424i	−0.330036	−	0.217694i
$777$	−17.7016			−0.635040
$778$	−21.2568	−	4.18443i	−0.762095	−	0.150019i
$779$		0			0
$780$	−33.1028	−	7.98270i	−1.18527	−	0.285827i
$781$			17.1291i			0.612928i
$782$	6.22947	−	31.6456i	0.222765	−	1.13164i
$783$	40.0000			1.42948
$784$	−2.00000	−	1.96851i	−0.0714286	−	0.0703039i
$785$			3.31286i			0.118241i
$786$	−7.78683	+	39.5570i	−0.277747	+	1.41095i
$787$	−40.5974			−1.44714			−0.723570	−	0.690251i	$-0.757500\pi$
$787$	−40.5974			−1.44714			−0.723570	+	0.690251i	$0.757500\pi$
$788$	−7.78683	−	3.18928i	−0.277394	−	0.113613i
$789$		−	24.2570i		−	0.863571i
$790$	12.5969	−	63.9919i	0.448177	−	2.27673i
$791$			31.6456i			1.12519i
$792$	2.80625	−	4.25444i	0.0997157	−	0.151175i
$793$		0			0
$794$	−1.70156	+	8.64391i	−0.0603862	+	0.306761i
$795$	−28.6361			−1.01562
$796$		0			0
$797$		−	53.8320i		−	1.90683i	−0.301668	−	0.953413i	$-0.597543\pi$
$797$		−	53.8320i		−	1.90683i	0.301668	−	0.953413i	$-0.402457\pi$
$798$	5.46295	−	27.7517i	0.193386	−	0.982399i
$799$		−	15.8228i		−	0.559770i
$800$	−21.9662	+	14.9946i	−0.776621	+	0.530139i
$801$			10.5196i			0.371693i
$802$	10.0000	+	1.96851i	0.353112	+	0.0695105i
$803$		−	38.5127i		−	1.35908i
$804$	−13.8776	+	33.8831i	−0.489425	+	1.19496i
$805$		−	34.5756i		−	1.21863i
$806$	−0.776337	+	18.3573i	−0.0273453	+	0.646609i
$807$	−29.1938			−1.02767
$808$		0			0
$809$	−8.50781			−0.299119			−0.149559	−	0.988753i	$-0.547786\pi$
$809$	−8.50781			−0.299119			−0.149559	+	0.988753i	$0.547786\pi$
$810$	−5.44766	+	27.6740i	−0.191411	+	0.972366i
$811$	31.0901			1.09172			0.545861	−	0.837876i	$-0.316203\pi$
$811$	31.0901			1.09172			0.545861	+	0.837876i	$0.316203\pi$
$812$	−36.6103	−	14.9946i	−1.28477	−	0.526207i
$813$	41.2580			1.44698
$814$	−2.95170	+	14.9946i	−0.103457	+	0.525560i
$815$	−30.8062			−1.07910
$816$	24.2539	−	24.6419i	0.849057	−	0.862639i
$817$			7.20677i			0.252133i
$818$	46.2094	+	9.09636i	1.61567	+	0.318047i
$819$	−6.93880	+	1.06361i	−0.242461	+	0.0371656i
$820$		0			0
$821$	17.4328			0.608408			0.304204	−	0.952607i	$-0.401610\pi$
$821$	17.4328			0.608408			0.304204	+	0.952607i	$0.401610\pi$
$822$	−4.59688	+	23.3521i	−0.160334	+	0.814497i
$823$	−25.6125			−0.892796			−0.446398	−	0.894835i	$-0.647293\pi$
$823$	−25.6125			−0.892796			−0.446398	+	0.894835i	$0.647293\pi$
$824$	6.22947	−	9.44424i	0.217014	−	0.329006i
$825$			18.3074i			0.637383i
$826$	18.3051	+	3.60338i	0.636917	+	0.125378i
$827$	−48.6860			−1.69298			−0.846488	−	0.532408i	$-0.821287\pi$
$827$	−48.6860			−1.69298			−0.846488	+	0.532408i	$0.821287\pi$
$828$	−5.19375	−	2.12722i	−0.180495	−	0.0739260i
$829$		−	16.3829i		−	0.569002i	−0.958676	−	0.284501i	$-0.908172\pi$
$829$		−	16.3829i		−	0.569002i	0.958676	−	0.284501i	$-0.0918280\pi$
$830$	8.41464	−	42.7463i	0.292077	−	1.48374i
$831$	−18.3875			−0.637855
$832$	24.4890	−	15.2411i	0.849002	−	0.528389i
$833$	4.00000			0.138592
$834$	4.01996	−	20.4213i	0.139200	−	0.707133i
$835$			23.3521i			0.808131i
$836$	−22.5969	−	9.25507i	−0.781529	−	0.320093i
$837$	20.2214			0.698955
$838$	−18.9330	−	3.72697i	−0.654028	−	0.128746i
$839$			18.5980i			0.642073i	0.947067	+	0.321037i	$0.104031\pi$
$839$			18.5980i			0.642073i	−0.947067	+	0.321037i	$0.895969\pi$
$840$	20.4088	−	30.9410i	0.704170	−	1.06756i
$841$	−21.8062			−0.751940
$842$	−9.95547	+	50.5736i	−0.343088	+	1.74288i
$843$	10.9259			0.376308
$844$	−14.2539	+	34.8019i	−0.490640	+	1.19793i
$845$	38.6324	−	12.1285i	1.32900	−	0.417232i
$846$	−2.70156	−	0.531805i	−0.0928816	−	0.0182838i
$847$		−	12.2194i		−	0.419864i
$848$	17.0156	−	17.2878i	0.584319	−	0.593666i
$849$	6.20937			0.213105
$850$	7.32206	−	37.1959i	0.251144	−	1.27581i
$851$	16.8293			0.576901
$852$	18.7127	+	7.66423i	0.641087	+	0.262572i
$853$	−28.0326			−0.959818			−0.479909	−	0.877318i	$-0.659330\pi$
$853$	−28.0326			−0.959818			−0.479909	+	0.877318i	$0.659330\pi$
$854$		0			0
$855$	−10.3875			−0.355245
$856$	23.9883	+	15.8228i	0.819904	+	0.540812i
$857$	12.8062			0.437453			0.218727	−	0.975786i	$-0.429810\pi$
$857$	12.8062			0.437453			0.218727	+	0.975786i	$0.429810\pi$
$858$	0.838929	−	19.8374i	0.0286406	−	0.677237i
$859$		−	18.3514i		−	0.626143i	−0.949730	−	0.313071i	$-0.898642\pi$
$859$		−	18.3514i		−	0.626143i	0.949730	−	0.313071i	$-0.101358\pi$
$860$	−3.57951	+	8.73961i	−0.122060	+	0.298018i
$861$		0			0
$862$	0.746095	+	0.146869i	0.0254121	+	0.00500239i
$863$		−	22.7390i		−	0.774046i	−0.922070	−	0.387023i	$-0.873503\pi$
$863$		−	22.7390i		−	0.774046i	0.922070	−	0.387023i	$-0.126497\pi$
$864$	−17.8976	−	26.2188i	−0.608887	−	0.891983i
$865$			18.8885i			0.642228i
$866$	−0.685002	+	3.47980i	−0.0232773	+	0.118248i
$867$			23.5108i			0.798468i
$868$	−18.5078	−	7.58030i	−0.628196	−	0.257292i
$869$	38.0289			1.29004
$870$	9.19375	−	46.7041i	0.311697	−	1.58342i
$871$	−6.59688	−	43.0368i	−0.223527	−	1.45825i
$872$	3.14922	−	4.77440i	0.106646	−	0.161682i
$873$		−	2.73182i		−	0.0924580i
$874$	−5.19375	+	26.3842i	−0.175681	+	0.892458i
$875$			2.57967i			0.0872088i
$876$	−42.0732	−	17.2321i	−1.42152	−	0.582217i
$877$	−43.3288			−1.46311			−0.731556	−	0.681782i	$-0.761205\pi$
$877$	−43.3288			−1.46311			−0.731556	+	0.681782i	$0.761205\pi$
$878$	4.04429	−	20.5449i	0.136488	−	0.693357i
$879$		−	44.6499i		−	1.50600i
$880$	−22.8062	−	22.4472i	−0.768798	−	0.756694i
$881$	35.7016			1.20282			0.601408	−	0.798942i	$-0.294607\pi$
$881$	35.7016			1.20282			0.601408	+	0.798942i	$0.294607\pi$
$882$	0.134440	−	0.682954i	0.00452684	−	0.0229963i
$883$			23.9632i			0.806427i	0.915106	+	0.403213i	$0.132107\pi$
$883$			23.9632i			0.806427i	−0.915106	+	0.403213i	$0.867893\pi$
$884$	−9.63844	+	39.9688i	−0.324176	+	1.34430i
$885$			22.4472i			0.754553i
$886$	−2.10366	−	0.414108i	−0.0706739	−	0.0139122i
$887$	−51.2250			−1.71997			−0.859983	−	0.510322i	$-0.829526\pi$
$887$	−51.2250			−1.71997			−0.859983	+	0.510322i	$0.829526\pi$
$888$	15.0602	+	9.93375i	0.505386	+	0.333355i
$889$		−	33.3020i		−	1.11691i
$890$	64.8059	+	12.7571i	2.17230	+	0.427619i
$891$	−16.4460			−0.550963
$892$	−11.7739	+	28.7468i	−0.394220	+	0.962515i
$893$			13.1921i			0.441456i
$894$	28.5078	+	5.61179i	0.953444	+	0.187686i
$895$			39.6806i			1.32638i
$896$	6.55234	+	30.7061i	0.218898	+	1.02582i
$897$	−21.6125	+	3.31286i	−0.721620	+	0.110613i
$898$	16.2094	+	3.19083i	0.540914	+	0.106479i
$899$	−25.6844			−0.856622
$900$	−6.10469	−	2.50031i	−0.203490	−	0.0833438i
$901$			34.5756i			1.15188i
$902$		0			0
$903$		−	6.37855i		−	0.212265i
$904$	17.7588	−	26.9235i	0.590650	−	0.895461i
$905$			41.0898i			1.36587i
$906$	5.74609	−	29.1901i	0.190901	−	0.969775i
$907$		−	55.5067i		−	1.84307i	−0.388294	−	0.921536i	$-0.626935\pi$
$907$		−	55.5067i		−	1.84307i	0.388294	−	0.921536i	$-0.373065\pi$
$908$	−12.8422	−	5.25982i	−0.426183	−	0.174553i
$909$		0			0
$910$	−1.86230	+	44.0361i	−0.0617347	+	1.45978i
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$	−20.2214	+	20.5449i	−0.669599	+	0.680310i
$913$	25.4031			0.840721
$914$	−4.59688	−	0.904899i	−0.152051	−	0.0299314i
$915$		0			0
$916$	13.8533	+	5.67392i	0.457725	+	0.187472i
$917$	52.1839			1.72327
$918$	44.3971	+	8.73961i	1.46532	+	0.288450i
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$	−19.4031	+	29.4163i	−0.639702	+	0.969827i
$921$		−	44.9837i		−	1.48226i
$922$	2.25391	−	11.4498i	0.0742284	−	0.377079i
$923$	−23.7681	+	3.64328i	−0.782336	+	0.119920i
$924$	20.0000	+	8.19146i	0.657952	+	0.269479i
$925$	19.7810			0.650395
$926$	15.8062	+	3.11148i	0.519426	+	0.102249i
$927$	2.80625			0.0921693
$928$	22.7327	+	33.3020i	0.746237	+	1.09319i
$929$		−	11.6817i		−	0.383265i	−0.981467	−	0.191632i	$-0.938622\pi$
$929$		−	11.6817i		−	0.383265i	0.981467	−	0.191632i	$-0.0613781\pi$
$930$	4.64777	−	23.6106i	0.152406	−	0.774222i
$931$	−3.33496			−0.109299
$932$	13.1492	+	5.38557i	0.430717	+	0.176410i
$933$			18.1927i			0.595603i
$934$	22.5125	+	4.43160i	0.736630	+	0.145006i
$935$	45.6125			1.49169
$936$	6.50027	+	2.98901i	0.212468	+	0.0976988i
$937$	12.8062			0.418362			0.209181	−	0.977877i	$-0.432920\pi$
$937$	12.8062			0.418362			0.209181	+	0.977877i	$0.432920\pi$
$938$	46.5008	+	9.15372i	1.51830	+	0.298880i
$939$		−	37.1553i		−	1.21252i
$940$	−6.55234	+	15.9980i	−0.213714	+	0.521797i
$941$	−25.8474			−0.842602			−0.421301	−	0.906921i	$-0.638426\pi$
$941$	−25.8474			−0.842602			−0.421301	+	0.906921i	$0.638426\pi$
$942$	−0.440449	+	2.23748i	−0.0143506	+	0.0729009i
$943$		0			0
$944$	−13.5515	−	13.3382i	−0.441064	−	0.434120i
$945$	48.5078			1.57796
$946$	−5.40312	−	1.06361i	−0.175671	−	0.0345810i
$947$	−12.0757			−0.392407			−0.196203	−	0.980563i	$-0.562861\pi$
$947$	−12.0757			−0.392407			−0.196203	+	0.980563i	$0.562861\pi$
$948$	17.0156	−	41.5448i	0.552642	−	1.34931i
$949$	53.4396	−	8.19146i	1.73472	−	0.265906i
$950$	−6.10469	+	31.0117i	−0.198062	+	1.00615i
$951$			38.2713i			1.24103i
$952$	−37.3586	−	24.6419i	−1.21080	−	0.798648i
$953$	−51.5234			−1.66901			−0.834504	−	0.551002i	$-0.814246\pi$
$953$	−51.5234			−1.66901			−0.834504	+	0.551002i	$0.814246\pi$
$954$	5.90340	+	1.16209i	0.191130	+	0.0376240i
$955$	8.74071			0.282843
$956$	−9.26268	+	22.6155i	−0.299577	+	0.731436i
$957$	27.7552			0.897198
$958$	−40.0602	−	7.88588i	−1.29428	−	0.254781i
$959$	30.8062			0.994786
$960$	−34.7268	+	14.8710i	−1.12080	+	0.479959i
$961$	18.0156			0.581149
$962$	−21.4341	−	0.906454i	−0.691062	−	0.0292252i
$963$			7.12785i			0.229692i
$964$	5.46295	−	13.3382i	0.175950	−	0.429593i
$965$			46.7041i			1.50346i
$966$	4.59688	−	23.3521i	0.147902	−	0.751340i
$967$			51.0718i			1.64236i	0.570671	+	0.821179i	$0.306683\pi$
$967$			51.0718i			1.64236i	−0.570671	+	0.821179i	$0.693317\pi$
$968$	−6.85728	+	10.3960i	−0.220401	+	0.334142i
$969$		−	41.0898i		−	1.32000i
$970$	−16.8293	−	3.31286i	−0.540356	−	0.106370i
$971$			30.0275i			0.963627i	0.876274	+	0.481814i	$0.160022\pi$
$971$			30.0275i			0.963627i	−0.876274	+	0.481814i	$0.839978\pi$
$972$	5.40312	−	13.1921i	0.173305	−	0.423136i
$973$	−26.9400			−0.863657
$974$	−36.6125	−	7.20721i	−1.17314	−	0.230934i
$975$	−25.4031	+	3.89391i	−0.813551	+	0.124705i
$976$		0			0
$977$		−	18.3074i		−	0.585707i	−0.956157	−	0.292854i	$-0.905395\pi$
$977$		−	18.3074i		−	0.585707i	0.956157	−	0.292854i	$-0.0946048\pi$
$978$	−20.8062	−	4.09573i	−0.665310	−	0.130967i
$979$			38.5127i			1.23087i
$980$	−4.04429	−	1.65643i	−0.129190	−	0.0529127i
$981$	1.41866			0.0452943
$982$	−5.05536	−	0.995152i	−0.161323	−	0.0317566i
$983$		−	29.9458i		−	0.955123i	−0.878598	−	0.477562i	$-0.841521\pi$
$983$		−	29.9458i		−	0.955123i	0.878598	−	0.477562i	$-0.158479\pi$
$984$		0			0
$985$	−13.1047			−0.417550
$986$	−56.3913	−	11.1007i	−1.79586	−	0.353518i
$987$		−	11.6760i		−	0.371652i
$988$	8.03594	−	33.3236i	0.255657	−	1.06016i
$989$			6.06424i			0.192832i
$990$	1.53304	−	7.78781i	0.0487232	−	0.247513i
$991$	41.6125			1.32186			0.660932	−	0.750446i	$-0.270161\pi$
$991$	41.6125			1.32186			0.660932	+	0.750446i	$0.270161\pi$
$992$	11.4922	+	16.8354i	0.364877	+	0.534524i
$993$		−	8.36886i		−	0.265578i
$994$	5.05536	−	25.6811i	0.160346	−	0.814557i
$995$		0			0
$996$	11.3663	−	27.7517i	0.360156	−	0.879346i
$997$		−	40.6399i		−	1.28708i	−0.765413	−	0.643539i	$-0.777465\pi$
$997$		−	40.6399i		−	1.28708i	0.765413	−	0.643539i	$-0.222535\pi$
$998$	−8.70156	+	44.2038i	−0.275443	+	1.39925i
$999$			23.6106i			0.747007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.e.c.77.4	yes	8
3.2	odd	2		936.2.m.f.181.5		8
4.3	odd	2		416.2.e.c.337.3		8
8.3	odd	2		416.2.e.c.337.6		8
8.5	even	2	inner	104.2.e.c.77.6	yes	8
12.11	even	2		3744.2.m.g.1585.7		8
13.12	even	2	inner	104.2.e.c.77.5	yes	8
24.5	odd	2		936.2.m.f.181.3		8
24.11	even	2		3744.2.m.g.1585.1		8
39.38	odd	2		936.2.m.f.181.4		8
52.51	odd	2		416.2.e.c.337.4		8
104.51	odd	2		416.2.e.c.337.5		8
104.77	even	2	inner	104.2.e.c.77.3	✓	8
156.155	even	2		3744.2.m.g.1585.2		8
312.77	odd	2		936.2.m.f.181.6		8
312.155	even	2		3744.2.m.g.1585.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.e.c.77.3	✓	8	104.77	even	2	inner
104.2.e.c.77.4	yes	8	1.1	even	1	trivial
104.2.e.c.77.5	yes	8	13.12	even	2	inner
104.2.e.c.77.6	yes	8	8.5	even	2	inner
416.2.e.c.337.3		8	4.3	odd	2
416.2.e.c.337.4		8	52.51	odd	2
416.2.e.c.337.5		8	104.51	odd	2
416.2.e.c.337.6		8	8.3	odd	2
936.2.m.f.181.3		8	24.5	odd	2
936.2.m.f.181.4		8	39.38	odd	2
936.2.m.f.181.5		8	3.2	odd	2
936.2.m.f.181.6		8	312.77	odd	2
3744.2.m.g.1585.1		8	24.11	even	2
3744.2.m.g.1585.2		8	156.155	even	2
3744.2.m.g.1585.7		8	12.11	even	2
3744.2.m.g.1585.8		8	312.155	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.273147 + 1.38758i) q^{2} +1.51606i q^{3} +(-1.85078 - 0.758030i) q^{4} -3.11473 q^{5} +(-2.10366 - 0.414108i) q^{6} +2.77517i q^{7} +(1.55737 - 2.36106i) q^{8} +0.701562 q^{9} +(0.850781 - 4.32196i) q^{10} +2.56844 q^{11} +(1.14922 - 2.80590i) q^{12} +(0.546295 + 3.56393i) q^{13} +(-3.85078 - 0.758030i) q^{14} -4.72212i q^{15} +(2.85078 + 2.80590i) q^{16} -5.70156 q^{17} +(-0.191630 + 0.973477i) q^{18} +4.75362 q^{19} +(5.76469 + 2.36106i) q^{20} -4.20732 q^{21} +(-0.701562 + 3.56393i) q^{22} +4.00000 q^{23} +(3.57951 + 2.36106i) q^{24} +4.70156 q^{25} +(-5.09447 - 0.215447i) q^{26} +5.61179i q^{27} +(2.10366 - 5.13623i) q^{28} -7.12785i q^{29} +(6.55234 + 1.28984i) q^{30} -3.60338i q^{31} +(-4.67210 + 3.18928i) q^{32} +3.89391i q^{33} +(1.55737 - 7.91140i) q^{34} -8.64391i q^{35} +(-1.29844 - 0.531805i) q^{36} +4.20732 q^{37} +(-1.29844 + 6.59605i) q^{38} +(-5.40312 + 0.828216i) q^{39} +(-4.85078 + 7.35408i) q^{40} +(1.14922 - 5.83802i) q^{42} +1.51606i q^{43} +(-4.75362 - 1.94695i) q^{44} -2.18518 q^{45} +(-1.09259 + 5.55034i) q^{46} +2.77517i q^{47} +(-4.25391 + 4.32196i) q^{48} -0.701562 q^{49} +(-1.28422 + 6.52381i) q^{50} -8.64391i q^{51} +(1.69049 - 7.01015i) q^{52} -6.06424i q^{53} +(-7.78683 - 1.53285i) q^{54} -8.00000 q^{55} +(6.55234 + 4.32196i) q^{56} +7.20677i q^{57} +(9.89049 + 1.94695i) q^{58} -4.75362 q^{59} +(-3.57951 + 8.73961i) q^{60} +(5.00000 + 0.984255i) q^{62} +1.94695i q^{63} +(-3.14922 - 7.35408i) q^{64} +(-1.70156 - 11.1007i) q^{65} +(-5.40312 - 1.06361i) q^{66} -12.0757 q^{67} +(10.5523 + 4.32196i) q^{68} +6.06424i q^{69} +(11.9942 + 2.36106i) q^{70} +6.66908i q^{71} +(1.09259 - 1.65643i) q^{72} -14.9946i q^{73} +(-1.14922 + 5.83802i) q^{74} +7.12785i q^{75} +(-8.79790 - 3.60338i) q^{76} +7.12785i q^{77} +(0.326630 - 7.72352i) q^{78} +14.8062 q^{79} +(-8.87942 - 8.73961i) q^{80} -6.40312 q^{81} +9.89049 q^{83} +(7.78683 + 3.18928i) q^{84} +17.7588 q^{85} +(-2.10366 - 0.414108i) q^{86} +10.8062 q^{87} +(4.00000 - 6.06424i) q^{88} +14.9946i q^{89} +(0.596876 - 3.03212i) q^{90} +(-9.89049 + 1.51606i) q^{91} +(-7.40312 - 3.03212i) q^{92} +5.46295 q^{93} +(-3.85078 - 0.758030i) q^{94} -14.8062 q^{95} +(-4.83513 - 7.08318i) q^{96} -3.89391i q^{97} +(0.191630 - 0.973477i) q^{98} +1.80192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 20 q^{9} - 6 q^{10} + 22 q^{12} - 18 q^{14} + 10 q^{16} - 20 q^{17} + 20 q^{22} + 32 q^{23} + 12 q^{25} - 14 q^{26} + 14 q^{30} - 36 q^{36} - 36 q^{38} + 8 q^{39} - 26 q^{40} + 22 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 20 * q^9 - 6 * q^10 + 22 * q^12 - 18 * q^14 + 10 * q^16 - 20 * q^17 + 20 * q^22 + 32 * q^23 + 12 * q^25 - 14 * q^26 + 14 * q^30 - 36 * q^36 - 36 * q^38 + 8 * q^39 - 26 * q^40 + 22 * q^42 + 30 * q^48 + 20 * q^49 - 4 * q^52 - 64 * q^55 + 14 * q^56 + 40 * q^62 - 38 * q^64 + 12 * q^65 + 8 * q^66 + 46 * q^68 - 22 * q^74 - 22 * q^78 + 16 * q^79 - 16 * q^87 + 32 * q^88 + 56 * q^90 - 8 * q^92 - 18 * q^94 - 16 * q^95

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