LMFDB - Embedded newform 475.2.bb.b.143.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(32,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.7
Character	$\chi$	$=$	475.143
Dual form			475.2.bb.b.382.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06046 - 1.51450i) q^{2} +(-0.101890 + 1.16461i) q^{3} +(-0.485079 - 1.33274i) q^{4} +(1.65575 + 1.38934i) q^{6} +(-1.17582 - 4.38823i) q^{7} +(1.03888 + 0.278366i) q^{8} +(1.60848 + 0.283619i) q^{9} +(-0.761040 - 1.31816i) q^{11} +(1.60156 - 0.429136i) q^{12} +(-0.138155 + 0.0120870i) q^{13} +(-7.89287 - 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(4.15164 + 2.90701i) q^{17} +(2.13527 - 2.13527i) q^{18} +(4.14601 - 1.34559i) q^{19} +(5.23039 - 0.922259i) q^{21} +(-2.80340 - 0.245266i) q^{22} +(-6.70821 - 3.12809i) q^{23} +(-0.430040 + 1.18152i) q^{24} +(-0.128202 + 0.222052i) q^{26} +(-1.40192 + 5.23204i) q^{27} +(-5.27802 + 3.69571i) q^{28} +(0.346487 - 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(-0.590025 - 6.74402i) q^{32} +(1.61269 - 0.752009i) q^{33} +(8.80531 - 3.20487i) q^{34} +(-0.402250 - 2.28127i) q^{36} +(2.05676 + 2.05676i) q^{37} +(2.35879 - 7.70606i) q^{38} -0.162128i q^{39} +(1.05100 + 1.25253i) q^{41} +(4.14987 - 8.89943i) q^{42} +(0.373752 + 0.801514i) q^{43} +(-1.38761 + 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(-1.41793 - 2.02502i) q^{47} +(3.23541 + 4.62065i) q^{48} +(-11.8118 + 6.81954i) q^{49} +(-3.80855 + 4.53886i) q^{51} +(0.0831248 + 0.178262i) q^{52} +(-4.74246 + 10.1702i) q^{53} +(6.43722 + 7.67158i) q^{54} -4.88613i q^{56} +(1.14465 + 4.96560i) q^{57} +(-2.60859 - 2.60859i) q^{58} +(1.86831 + 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-2.09678 + 0.977745i) q^{62} +(-0.646704 - 7.39187i) q^{63} +(-2.48226 - 1.43314i) q^{64} +(0.571280 - 3.23989i) q^{66} +(-11.6415 + 8.15144i) q^{67} +(1.86043 - 6.94321i) q^{68} +(4.32651 - 7.49374i) q^{69} +(-1.79203 + 4.92356i) q^{71} +(1.59206 + 0.742391i) q^{72} +(6.01690 + 0.526410i) q^{73} +(5.29607 - 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 + 4.88954i) q^{77} +(-0.245543 - 0.171931i) q^{78} +(-4.43572 + 3.72201i) q^{79} +(-1.34607 - 0.489931i) q^{81} +(3.01150 - 0.263472i) q^{82} +(-0.458159 + 0.122763i) q^{83} +(-3.76629 - 6.52341i) q^{84} +(1.61024 + 0.283929i) q^{86} +(2.25319 + 0.603740i) q^{87} +(-0.423695 - 1.58125i) q^{88} +(-1.43212 - 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-0.914930 + 10.4577i) q^{92} +(0.839078 - 1.19833i) q^{93} -4.57054 q^{94} +7.91429 q^{96} +(0.682796 - 0.975134i) q^{97} +(-2.19778 + 25.1208i) q^{98} +(-0.850264 - 2.33608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	1.06046	−	1.51450i	0.749860	−	1.07091i	−0.244988	−	0.969526i	$-0.578784\pi$
$2$	1.06046	−	1.51450i	0.749860	−	1.07091i	0.994847	−	0.101384i	$-0.0323272\pi$
$3$	−0.101890	+	1.16461i	−0.0588265	+	0.672390i	0.908338	+	0.418237i	$0.137352\pi$
$3$	−0.101890	+	1.16461i	−0.0588265	+	0.672390i	−0.967164	+	0.254152i	$0.918204\pi$
$4$	−0.485079	−	1.33274i	−0.242540	−	0.666372i
$5$		0			0
$5$		0			0
$6$	1.65575	+	1.38934i	0.675957	+	0.567196i
$7$	−1.17582	−	4.38823i	−0.444419	−	1.65859i	−0.717466	−	0.696593i	$-0.754698\pi$
$7$	−1.17582	−	4.38823i	−0.444419	−	1.65859i	0.273048	−	0.962001i	$-0.411968\pi$
$8$	1.03888	+	0.278366i	0.367298	+	0.0984172i
$9$	1.60848	+	0.283619i	0.536161	+	0.0945396i
$10$		0			0
$11$	−0.761040	−	1.31816i	−0.229462	−	0.397440i	0.728187	−	0.685379i	$-0.240363\pi$
$11$	−0.761040	−	1.31816i	−0.229462	−	0.397440i	−0.957649	+	0.287939i	$0.907030\pi$
$12$	1.60156	−	0.429136i	0.462330	−	0.123881i
$13$	−0.138155	+	0.0120870i	−0.0383172	+	0.00335232i	−0.106298	−	0.994334i	$-0.533900\pi$
$13$	−0.138155	+	0.0120870i	−0.0383172	+	0.00335232i	0.0679810	+	0.997687i	$0.478344\pi$
$14$	−7.89287	−	2.87277i	−2.10946	−	0.767780i
$15$		0			0
$16$	3.69620	−	3.10148i	0.924050	−	0.775370i
$17$	4.15164	+	2.90701i	1.00692	+	0.705054i	0.955915	−	0.293645i	$-0.0948683\pi$
$17$	4.15164	+	2.90701i	1.00692	+	0.705054i	0.0510063	+	0.998698i	$0.483757\pi$
$18$	2.13527	−	2.13527i	0.503289	−	0.503289i
$19$	4.14601	−	1.34559i	0.951160	−	0.308699i
$19$	4.14601	−	1.34559i	0.951160	−	0.308699i
$20$		0			0
$21$	5.23039	−	0.922259i	1.14136	−	0.201253i
$22$	−2.80340	−	0.245266i	−0.597687	−	0.0522909i
$23$	−6.70821	−	3.12809i	−1.39876	−	0.652252i	−0.430589	−	0.902548i	$-0.641694\pi$
$23$	−6.70821	−	3.12809i	−1.39876	−	0.652252i	−0.968169	+	0.250297i	$0.919472\pi$
$24$	−0.430040	+	1.18152i	−0.0877815	+	0.241178i
$25$		0			0
$26$	−0.128202	+	0.222052i	−0.0251425	+	0.0435481i
$27$	−1.40192	+	5.23204i	−0.269800	+	1.00691i
$28$	−5.27802	+	3.69571i	−0.997452	+	0.698423i
$29$	0.346487	−	1.96502i	0.0643410	−	0.364896i	−0.935589	−	0.353090i	$-0.885131\pi$
$29$	0.346487	−	1.96502i	0.0643410	−	0.364896i	0.999930	−	0.0118058i	$-0.00375798\pi$
$30$		0			0
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	0.399515	−	0.916727i	$-0.369179\pi$
$31$	−1.08369	−	0.625668i	−0.194636	−	0.112373i	−0.594151	+	0.804353i	$0.702512\pi$
$32$	−0.590025	−	6.74402i	−0.104303	−	1.19218i
$33$	1.61269	−	0.752009i	0.280733	−	0.130908i
$34$	8.80531	−	3.20487i	1.51010	−	0.549631i
$35$		0			0
$36$	−0.402250	−	2.28127i	−0.0670417	−	0.380212i
$37$	2.05676	+	2.05676i	0.338129	+	0.338129i	0.855663	−	0.517534i	$-0.173150\pi$
$37$	2.05676	+	2.05676i	0.338129	+	0.338129i	−0.517534	+	0.855663i	$0.673150\pi$
$38$	2.35879	−	7.70606i	0.382647	−	1.25009i
$39$		−	0.162128i		−	0.0259613i
$40$		0			0
$41$	1.05100	+	1.25253i	0.164138	+	0.195613i	0.841844	−	0.539721i	$-0.181470\pi$
$41$	1.05100	+	1.25253i	0.164138	+	0.195613i	−0.677706	+	0.735333i	$0.737026\pi$
$42$	4.14987	−	8.89943i	0.640339	−	1.37321i
$43$	0.373752	+	0.801514i	0.0569966	+	0.122230i	0.932743	−	0.360541i	$-0.117408\pi$
$43$	0.373752	+	0.801514i	0.0569966	+	0.122230i	−0.875747	+	0.482771i	$0.839630\pi$
$44$	−1.38761	+	1.65368i	−0.209190	+	0.249302i
$45$		0			0
$46$	−11.8513	+	6.84234i	−1.74738	+	1.00885i
$47$	−1.41793	−	2.02502i	−0.206827	−	0.295379i	0.702315	−	0.711866i	$-0.252150\pi$
$47$	−1.41793	−	2.02502i	−0.206827	−	0.295379i	−0.909141	+	0.416488i	$0.863261\pi$
$48$	3.23541	+	4.62065i	0.466992	+	0.666934i
$49$	−11.8118	+	6.81954i	−1.68740	+	0.974220i
$50$		0			0
$51$	−3.80855	+	4.53886i	−0.533304	+	0.635567i
$52$	0.0831248	+	0.178262i	0.0115273	+	0.0247205i
$53$	−4.74246	+	10.1702i	−0.651427	+	1.39699i	0.251780	+	0.967784i	$0.418984\pi$
$53$	−4.74246	+	10.1702i	−0.651427	+	1.39699i	−0.903207	+	0.429205i	$0.858794\pi$
$54$	6.43722	+	7.67158i	0.875995	+	1.04397i
$55$		0			0
$56$		−	4.88613i		−	0.652936i
$57$	1.14465	+	4.96560i	0.151613	+	0.657710i
$58$	−2.60859	−	2.60859i	−0.342524	−	0.342524i
$59$	1.86831	+	10.5957i	0.243233	+	1.37944i	0.824561	+	0.565773i	$0.191422\pi$
$59$	1.86831	+	10.5957i	0.243233	+	1.37944i	−0.581328	+	0.813669i	$0.697467\pi$
$60$		0			0
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	−0.514502	−	0.857489i	$-0.672023\pi$
$61$	−2.79178	+	1.01612i	−0.357451	+	0.130101i	0.157052	+	0.987590i	$0.449801\pi$
$62$	−2.09678	+	0.977745i	−0.266292	+	0.124174i
$63$	−0.646704	−	7.39187i	−0.0814771	−	0.931288i
$64$	−2.48226	−	1.43314i	−0.310283	−	0.179142i
$65$		0			0
$66$	0.571280	−	3.23989i	0.0703197	−	0.398803i
$67$	−11.6415	+	8.15144i	−1.42223	+	0.995857i	−0.426411	+	0.904530i	$0.640222\pi$
$67$	−11.6415	+	8.15144i	−1.42223	+	0.995857i	−0.995821	+	0.0913279i	$0.970889\pi$
$68$	1.86043	−	6.94321i	0.225610	−	0.841988i
$69$	4.32651	−	7.49374i	0.520851	−	0.902141i
$70$		0			0
$71$	−1.79203	+	4.92356i	−0.212675	+	0.584319i	−0.999458	−	0.0329100i	$-0.989523\pi$
$71$	−1.79203	+	4.92356i	−0.212675	+	0.584319i	0.786784	+	0.617229i	$0.211745\pi$
$72$	1.59206	+	0.742391i	0.187626	+	0.0874916i
$73$	6.01690	+	0.526410i	0.704225	+	0.0616117i	0.433642	−	0.901085i	$-0.357228\pi$
$73$	6.01690	+	0.526410i	0.704225	+	0.0616117i	0.270582	+	0.962697i	$0.412784\pi$
$74$	5.29607	−	0.933839i	0.615655	−	0.108557i
$75$		0			0
$76$	−3.80447	−	4.87285i	−0.436403	−	0.558955i
$77$	−4.88954	+	4.88954i	−0.557215	+	0.557215i
$78$	−0.245543	−	0.171931i	−0.0278022	−	0.0194673i
$79$	−4.43572	+	3.72201i	−0.499058	+	0.418759i	−0.857259	−	0.514885i	$-0.827835\pi$
$79$	−4.43572	+	3.72201i	−0.499058	+	0.418759i	0.358201	+	0.933644i	$0.383390\pi$
$80$		0			0
$81$	−1.34607	−	0.489931i	−0.149564	−	0.0544368i
$82$	3.01150	−	0.263472i	0.332564	−	0.0290956i
$83$	−0.458159	+	0.122763i	−0.0502895	+	0.0134750i	−0.283876	−	0.958861i	$-0.591620\pi$
$83$	−0.458159	+	0.122763i	−0.0502895	+	0.0134750i	0.233587	+	0.972336i	$0.424954\pi$
$84$	−3.76629	−	6.52341i	−0.410936	−	0.711762i
$85$		0			0
$86$	1.61024	+	0.283929i	0.173636	+	0.0306168i
$87$	2.25319	+	0.603740i	0.241567	+	0.0647278i
$88$	−0.423695	−	1.58125i	−0.0451661	−	0.168562i
$89$	−1.43212	−	1.20169i	−0.151805	−	0.127379i	0.563722	−	0.825964i	$-0.309369\pi$
$89$	−1.43212	−	1.20169i	−0.151805	−	0.127379i	−0.715527	+	0.698585i	$0.753813\pi$
$90$		0			0
$91$	0.215486	+	0.592042i	0.0225890	+	0.0620628i
$92$	−0.914930	+	10.4577i	−0.0953881	+	1.09029i
$93$	0.839078	−	1.19833i	0.0870084	−	0.124261i
$94$	−4.57054			−0.471415
$95$		0			0
$96$	7.91429			0.807749
$97$	0.682796	−	0.975134i	0.0693274	−	0.0990098i	−0.782991	−	0.622033i	$-0.786307\pi$
$97$	0.682796	−	0.975134i	0.0693274	−	0.0990098i	0.852318	+	0.523023i	$0.175196\pi$
$98$	−2.19778	+	25.1208i	−0.222010	+	2.53758i
$99$	−0.850264	−	2.33608i	−0.0854548	−	0.234785i
$100$		0			0
$101$	−0.589039	−	0.494263i	−0.0586116	−	0.0491810i	0.613011	−	0.790074i	$-0.289958\pi$
$101$	−0.589039	−	0.494263i	−0.0586116	−	0.0491810i	−0.671623	+	0.740893i	$0.734402\pi$
$102$	2.83526	+	10.5813i	0.280732	+	1.04771i
$103$	3.83402	+	1.02732i	0.377777	+	0.101225i	0.442711	−	0.896665i	$-0.354017\pi$
$103$	3.83402	+	1.02732i	0.377777	+	0.101225i	−0.0649337	+	0.997890i	$0.520684\pi$
$104$	−0.146890	−	0.0259007i	−0.0144038	−	0.00253977i
$105$		0			0
$106$	10.3736	+	17.9676i	1.00757	+	1.74517i
$107$	14.6290	−	3.91983i	1.41424	−	0.378944i	0.530802	−	0.847496i	$-0.321891\pi$
$107$	14.6290	−	3.91983i	1.41424	−	0.378944i	0.883436	+	0.468552i	$0.155224\pi$
$108$	7.65302	−	0.669552i	0.736412	−	0.0644277i
$109$	−8.35240	−	3.04003i	−0.800015	−	0.291182i	−0.0905223	−	0.995894i	$-0.528854\pi$
$109$	−8.35240	−	3.04003i	−0.800015	−	0.291182i	−0.709493	+	0.704713i	$0.751076\pi$
$110$		0			0
$111$	−2.60489	+	2.18576i	−0.247245	+	0.207464i
$112$	−17.9561	−	12.5730i	−1.69669	−	1.18803i
$113$	−3.03272	+	3.03272i	−0.285294	+	0.285294i	−0.835216	−	0.549922i	$-0.814658\pi$
$113$	−3.03272	+	3.03272i	−0.285294	+	0.285294i	0.549922	+	0.835216i	$0.314658\pi$
$114$	8.73424	+	3.53226i	0.818036	+	0.330826i
$115$		0			0
$116$	−2.78695	+	0.491414i	−0.258762	+	0.0456267i
$117$	−0.225647	−	0.0197416i	−0.0208611	−	0.00182511i
$118$	18.0284	+	8.40679i	1.65965	+	0.773907i
$119$	7.87503	−	21.6365i	0.721903	−	1.98341i
$120$		0			0
$121$	4.34164	−	7.51993i	0.394694	−	0.683630i
$122$	−1.42166	+	5.30570i	−0.128711	+	0.480355i
$123$	−1.56580	+	1.09639i	−0.141184	+	0.0988578i
$124$	−0.308181	+	1.74778i	−0.0276754	+	0.156955i
$125$		0			0
$126$	−11.8808	−	6.85936i	−1.05842	−	0.611080i
$127$	−1.16792	−	13.3493i	−0.103636	−	1.18456i	−0.852822	−	0.522202i	$-0.825111\pi$
$127$	−1.16792	−	13.3493i	−0.103636	−	1.18456i	0.749186	−	0.662360i	$-0.230445\pi$
$128$	7.46818	−	3.48247i	0.660100	−	0.307810i
$129$	−0.971535	+	0.353610i	−0.0855389	+	0.0311336i
$130$		0			0
$131$	−1.85946	−	10.5455i	−0.162462	−	0.921369i	−0.951643	−	0.307207i	$-0.900605\pi$
$131$	−1.85946	−	10.5455i	−0.162462	−	0.921369i	0.789180	−	0.614161i	$-0.210506\pi$
$132$	−1.78452	−	1.78452i	−0.155322	−	0.155322i
$133$	−10.7797	−	16.6115i	−0.934720	−	1.44040i
$134$			26.2753i			2.26984i
$135$		0			0
$136$	3.50383	+	4.17570i	0.300451	+	0.358063i
$137$	−8.82158	+	18.9179i	−0.753679	+	1.61627i	0.0334197	+	0.999441i	$0.489360\pi$
$137$	−8.82158	+	18.9179i	−0.753679	+	1.61627i	−0.787098	+	0.616828i	$0.788418\pi$
$138$	−6.76114	−	14.4993i	−0.575547	−	1.23426i
$139$	4.32307	−	5.15204i	0.366678	−	0.436990i	−0.550884	−	0.834582i	$-0.685709\pi$
$139$	4.32307	−	5.15204i	0.366678	−	0.436990i	0.917562	+	0.397592i	$0.130154\pi$
$140$		0			0
$141$	2.50283	−	1.44501i	0.210777	−	0.121692i
$142$	5.55633	+	7.93526i	0.466277	+	0.665913i
$143$	0.121074	+	0.172911i	0.0101247	+	0.0144596i
$144$	6.82490	−	3.94036i	0.568742	−	0.328363i
$145$		0			0
$146$	7.17794	−	8.55433i	0.594050	−	0.707961i
$147$	−6.73862	−	14.4510i	−0.555792	−	1.19190i
$148$	1.74344	−	3.73883i	0.143310	−	0.307330i
$149$	5.56213	+	6.62869i	0.455668	+	0.543043i	0.944144	−	0.329534i	$-0.106892\pi$
$149$	5.56213	+	6.62869i	0.455668	+	0.543043i	−0.488476	+	0.872577i	$0.662447\pi$
$150$		0			0
$151$		−	10.4228i		−	0.848193i	−0.905617	−	0.424097i	$-0.860592\pi$
$151$		−	10.4228i		−	0.848193i	0.905617	−	0.424097i	$-0.139408\pi$
$152$	4.68175	−	0.243792i	0.379740	−	0.0197742i
$153$	5.85336	+	5.85336i	0.473216	+	0.473216i
$154$	2.22002	+	12.5904i	0.178894	+	1.01456i
$155$		0			0
$156$	−0.216076	+	0.0786451i	−0.0172999	+	0.00629665i
$157$	14.7648	−	6.88494i	1.17836	−	0.549478i	0.268049	−	0.963405i	$-0.413621\pi$
$157$	14.7648	−	6.88494i	1.17836	−	0.549478i	0.910310	+	0.413927i	$0.135843\pi$
$158$	0.933061	+	10.6649i	0.0742304	+	0.848457i
$159$	−11.3612	−	6.55938i	−0.901000	−	0.520193i
$160$		0			0
$161$	−5.83910	+	33.1152i	−0.460186	+	2.60984i
$162$	−2.16946	+	1.51907i	−0.170449	+	0.119350i
$163$	−1.53732	+	5.73737i	−0.120413	+	0.449386i	−0.999635	−	0.0270262i	$-0.991396\pi$
$163$	−1.53732	+	5.73737i	−0.120413	+	0.449386i	0.879222	+	0.476412i	$0.158063\pi$
$164$	1.15949	−	2.00829i	0.0905407	−	0.156821i
$165$		0			0
$166$	−0.299935	+	0.824066i	−0.0232795	+	0.0639599i
$167$	13.5351	+	6.31154i	1.04738	+	0.488402i	0.868614	−	0.495490i	$-0.165011\pi$
$167$	13.5351	+	6.31154i	1.04738	+	0.488402i	0.178767	+	0.983891i	$0.442789\pi$
$168$	5.69045	+	0.497850i	0.439028	+	0.0384099i
$169$	−12.7836	+	2.25409i	−0.983351	+	0.173391i
$170$		0			0
$171$	7.05041	−	0.988470i	0.539159	−	0.0755902i
$172$	0.886914	−	0.886914i	0.0676265	−	0.0676265i
$173$	11.2602	+	7.88448i	0.856098	+	0.599446i	0.917085	−	0.398692i	$-0.130536\pi$
$173$	11.2602	+	7.88448i	0.856098	+	0.599446i	−0.0609868	+	0.998139i	$0.519425\pi$
$174$	3.30378	−	2.77220i	0.250459	−	0.210160i
$175$		0			0
$176$	−6.90120	−	2.51183i	−0.520198	−	0.189336i
$177$	−12.5302	+	1.09625i	−0.941831	+	0.0823995i
$178$	−3.33867	+	0.894595i	−0.250244	+	0.0670527i
$179$	2.00568	+	3.47394i	0.149912	+	0.259654i	0.931195	−	0.364523i	$-0.118768\pi$
$179$	2.00568	+	3.47394i	0.149912	+	0.259654i	−0.781283	+	0.624177i	$0.785434\pi$
$180$		0			0
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.732096	−	0.681202i	$-0.761458\pi$
$181$	−22.2392	−	3.92137i	−1.65303	−	0.291473i	−0.920930	+	0.389729i	$0.872569\pi$
$182$	1.12516	+	0.301485i	0.0834023	+	0.0223476i
$183$	−0.898936	−	3.35487i	−0.0664513	−	0.247999i
$184$	−6.09824	−	5.11703i	−0.449568	−	0.377232i
$185$		0			0
$186$	−0.925053	−	2.54156i	−0.0678282	−	0.186356i
$187$	0.672340	−	7.68488i	0.0491664	−	0.561974i
$188$	−2.01102	+	2.87203i	−0.146669	+	0.209465i
$189$	24.6078			1.78995
$190$		0			0
$191$	12.6937			0.918482			0.459241	−	0.888312i	$-0.348121\pi$
$191$	12.6937			0.918482			0.459241	+	0.888312i	$0.348121\pi$
$192$	1.92197	−	2.74485i	0.138706	−	0.198093i
$193$	1.30105	−	14.8711i	0.0936519	−	1.07045i	−0.793376	−	0.608731i	$-0.791679\pi$
$193$	1.30105	−	14.8711i	0.0936519	−	1.07045i	0.887028	−	0.461715i	$-0.152766\pi$
$194$	−0.752757	−	2.06818i	−0.0540448	−	0.148487i
$195$		0			0
$196$	14.8184	+	12.4341i	1.05845	+	0.888149i
$197$	1.63548	+	6.10369i	0.116523	+	0.434870i	0.999396	−	0.0347415i	$-0.0110608\pi$
$197$	1.63548	+	6.10369i	0.116523	+	0.434870i	−0.882873	+	0.469611i	$0.844394\pi$
$198$	−4.43966	−	1.18960i	−0.315513	−	0.0845414i
$199$	−12.5304	−	2.20944i	−0.888254	−	0.156623i	−0.289140	−	0.957287i	$-0.593369\pi$
$199$	−12.5304	−	2.20944i	−0.888254	−	0.156623i	−0.599114	+	0.800664i	$0.704480\pi$
$200$		0			0
$201$	−8.30712	−	14.3884i	−0.585939	−	1.01488i
$202$	−1.37321	+	0.367951i	−0.0966189	+	0.0258890i
$203$	−9.03038	+	0.790056i	−0.633808	+	0.0554510i
$204$	7.89659	+	2.87412i	0.552872	+	0.201229i
$205$		0			0
$206$	5.62170	−	4.71717i	0.391683	−	0.328661i
$207$	−9.90284	−	6.93405i	−0.688295	−	0.481949i
$208$	−0.473160	+	0.473160i	−0.0328077	+	0.0328077i
$209$	−4.92898	−	4.44106i	−0.340945	−	0.307194i
$210$		0			0
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.441756	−	0.897135i	$-0.354356\pi$
$211$	16.9039	−	2.98061i	1.16371	−	0.205193i	0.721953	+	0.691942i	$0.243245\pi$
$212$	15.8548	+	1.38712i	1.08891	+	0.0952675i
$213$	−5.55145	−	2.58868i	−0.380379	−	0.177374i
$214$	9.57692	−	26.3124i	0.654665	−	1.79868i
$215$		0			0
$216$	−2.91284	+	5.04519i	−0.198194	+	0.343282i
$217$	−1.47135	+	5.49114i	−0.0998816	+	0.372763i
$218$	−13.4615	+	9.42585i	−0.911728	+	0.638399i
$219$	−1.22613	+	6.95372i	−0.0828541	+	0.469889i
$220$		0			0
$221$	−0.608705	−	0.351436i	−0.0409460	−	0.0236402i
$222$	0.547943	+	6.26302i	0.0367755	+	0.420346i
$223$	−17.0209	+	7.93699i	−1.13981	+	0.531500i	−0.898511	−	0.438952i	$-0.855350\pi$
$223$	−17.0209	+	7.93699i	−1.13981	+	0.531500i	−0.241295	+	0.970452i	$0.577572\pi$
$224$	−28.9005	+	10.5189i	−1.93100	+	0.702825i
$225$		0			0
$226$	1.37696	+	7.80913i	0.0915940	+	0.519456i
$227$	0.0653385	+	0.0653385i	0.00433667	+	0.00433667i	0.709272	−	0.704935i	$-0.249024\pi$
$227$	0.0653385	+	0.0653385i	0.00433667	+	0.00433667i	−0.704935	+	0.709272i	$0.749024\pi$
$228$	6.06263	−	3.93424i	0.401507	−	0.260551i
$229$			10.2958i			0.680367i	0.940359	+	0.340184i	$0.110489\pi$
$229$			10.2958i			0.680367i	−0.940359	+	0.340184i	$0.889511\pi$
$230$		0			0
$231$	−5.19622	−	6.19262i	−0.341886	−	0.407444i
$232$	0.906952	−	1.94497i	0.0595443	−	0.127693i
$233$	−9.16084	−	19.6455i	−0.600146	−	1.28702i	−0.938266	−	0.345915i	$-0.887569\pi$
$233$	−9.16084	−	19.6455i	−0.600146	−	1.28702i	0.338119	−	0.941103i	$-0.390209\pi$
$234$	−0.269189	+	0.320807i	−0.0175974	+	0.0209718i
$235$		0			0
$236$	13.2151	−	7.62973i	0.860229	−	0.496653i
$237$	−3.88275	−	5.54514i	−0.252212	−	0.360196i
$238$	−24.4172	−	34.8713i	−1.58273	−	2.26037i
$239$	−8.88903	+	5.13208i	−0.574984	+	0.331967i	−0.759137	−	0.650931i	$-0.774379\pi$
$239$	−8.88903	+	5.13208i	−0.574984	+	0.331967i	0.184154	+	0.982897i	$0.441046\pi$
$240$		0			0
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	−0.999977	−	0.00676413i	$-0.997847\pi$
$241$	−12.7247	+	15.1647i	−0.819672	+	0.976847i	0.180306	+	0.983611i	$0.442291\pi$
$242$	−6.78477	−	14.5500i	−0.436142	−	0.935309i
$243$	−6.15974	+	13.2096i	−0.395147	+	0.847396i
$244$	2.70847	+	3.22783i	0.173392	+	0.206640i
$245$		0			0
$246$			3.53408i			0.225324i
$247$	−0.556526	+	0.236012i	−0.0354109	+	0.0150171i
$248$	−0.951653	−	0.951653i	−0.0604300	−	0.0604300i
$249$	−0.0962897	−	0.546086i	−0.00610211	−	0.0346068i
$250$		0			0
$251$	5.76397	−	2.09791i	0.363819	−	0.132419i	−0.153641	−	0.988127i	$-0.549100\pi$
$251$	5.76397	−	2.09791i	0.363819	−	0.132419i	0.517460	+	0.855708i	$0.326878\pi$
$252$	−9.53777	+	4.44753i	−0.600823	+	0.280168i
$253$	0.981894	+	11.2231i	0.0617311	+	0.705590i
$254$	−21.4560	−	12.3877i	−1.34627	−	0.777270i
$255$		0			0
$256$	3.64098	−	20.6490i	0.227561	−	1.29056i
$257$	19.0585	−	13.3449i	1.18883	−	0.832430i	0.199759	−	0.979845i	$-0.435984\pi$
$257$	19.0585	−	13.3449i	1.18883	−	0.832430i	0.989075	+	0.147415i	$0.0470952\pi$
$258$	−0.494735	+	1.84638i	−0.0308008	+	0.114950i
$259$	6.60714	−	11.4439i	0.410548	−	0.711090i
$260$		0			0
$261$	1.11464	−	3.06244i	0.0689942	−	0.189560i
$262$	−17.9431	−	8.36700i	−1.10853	−	0.516915i
$263$	−12.5544	−	1.09837i	−0.774140	−	0.0677285i	−0.306762	−	0.951786i	$-0.599246\pi$
$263$	−12.5544	−	1.09837i	−0.774140	−	0.0677285i	−0.467378	+	0.884058i	$0.654801\pi$
$264$	1.88472	−	0.332326i	0.115996	−	0.0204533i
$265$		0			0
$266$	−36.5895	−	1.28997i	−2.24344	−	0.0790930i
$267$	1.54543	−	1.54543i	0.0945787	−	0.0945787i
$268$	16.5108	+	11.5610i	1.00856	+	0.706201i
$269$	13.4512	−	11.2869i	0.820136	−	0.688176i	−0.132868	−	0.991134i	$-0.542419\pi$
$269$	13.4512	−	11.2869i	0.820136	−	0.688176i	0.953004	+	0.302958i	$0.0979742\pi$
$270$		0			0
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.183998	−	0.982927i	$-0.558904\pi$
$271$	−15.7503	−	5.73264i	−0.956762	−	0.348233i	−0.772764	+	0.634694i	$0.781126\pi$
$272$	24.3613	−	2.13134i	1.47712	−	0.129231i
$273$	−0.711455	+	0.190634i	−0.0430592	+	0.0115377i
$274$	19.2962	+	33.4220i	1.16573	+	2.01910i
$275$		0			0
$276$	−12.0859	−	2.13108i	−0.727489	−	0.128276i
$277$	−29.0963	−	7.79634i	−1.74823	−	0.468437i	−0.763982	−	0.645237i	$-0.776759\pi$
$277$	−29.0963	−	7.79634i	−1.74823	−	0.468437i	−0.984247	+	0.176800i	$0.943425\pi$
$278$	−3.21829	−	12.0108i	−0.193020	−	0.720361i
$279$	−1.56564	−	1.31373i	−0.0937325	−	0.0786509i
$280$		0			0
$281$	9.59450	+	26.3607i	0.572360	+	1.57255i	0.800764	+	0.598980i	$0.204427\pi$
$281$	9.59450	+	26.3607i	0.572360	+	1.57255i	−0.228404	+	0.973566i	$0.573351\pi$
$282$	0.465694	−	5.32291i	0.0277317	−	0.316975i
$283$	11.2068	−	16.0049i	0.666173	−	0.951394i	−0.333789	−	0.942648i	$-0.608327\pi$
$283$	11.2068	−	16.0049i	0.666173	−	0.951394i	0.999962	−	0.00874584i	$-0.00278392\pi$
$284$	7.43112			0.440956
$285$		0			0
$286$	0.390268			0.0230770
$287$	4.26061	−	6.08478i	0.251496	−	0.359173i
$288$	0.963685	−	11.0150i	0.0567857	−	0.649063i
$289$	2.97107	+	8.16296i	0.174769	+	0.480174i
$290$		0			0
$291$	1.06608	+	0.894550i	0.0624949	+	0.0524394i
$292$	−2.21710	−	8.27434i	−0.129746	−	0.484219i
$293$	5.41159	+	1.45003i	0.316148	+	0.0847117i	0.413404	−	0.910548i	$-0.364340\pi$
$293$	5.41159	+	1.45003i	0.316148	+	0.0847117i	−0.0972556	+	0.995259i	$0.531006\pi$
$294$	−29.0321	−	5.11913i	−1.69318	−	0.298554i
$295$		0			0
$296$	1.56418	+	2.70925i	0.0909164	+	0.157472i
$297$	7.96359	−	2.13384i	0.462094	−	0.123818i
$298$	15.9376	−	1.39436i	0.923238	−	0.0807728i
$299$	0.964579	+	0.351078i	0.0557831	+	0.0203034i
$300$		0			0
$301$	3.07776	−	2.58254i	0.177399	−	0.148855i
$302$	−15.7853	−	11.0530i	−0.908339	−	0.636026i
$303$	0.635642	−	0.635642i	0.0365167	−	0.0365167i
$304$	11.1512	−	17.8323i	0.639563	−	1.02275i
$305$		0			0
$306$	15.0721	−	2.65763i	0.861617	−	0.151926i
$307$	16.2726	+	1.42367i	0.928725	+	0.0812529i	0.541470	−	0.840720i	$-0.317868\pi$
$307$	16.2726	+	1.42367i	0.928725	+	0.0812529i	0.387255	+	0.921973i	$0.373423\pi$
$308$	8.88832	+	4.14469i	0.506459	+	0.236166i
$309$	−1.58708	+	4.36047i	−0.0902859	+	0.248059i
$310$		0			0
$311$	0.890255	−	1.54197i	0.0504817	−	0.0874369i	−0.839680	−	0.543081i	$-0.817258\pi$
$311$	0.890255	−	1.54197i	0.0504817	−	0.0874369i	0.890162	+	0.455644i	$0.150591\pi$
$312$	0.0451310	−	0.168431i	0.00255504	−	0.00953553i
$313$	3.59819	−	2.51948i	0.203382	−	0.142409i	−0.467449	−	0.884020i	$-0.654827\pi$
$313$	3.59819	−	2.51948i	0.203382	−	0.142409i	0.670830	+	0.741611i	$0.265938\pi$
$314$	5.23029	−	29.6624i	0.295162	−	1.67395i
$315$		0			0
$316$	7.11217	+	4.10622i	0.400091	+	0.230993i
$317$	−0.800161	−	9.14589i	−0.0449415	−	0.513684i	−0.984986	−	0.172633i	$-0.944773\pi$
$317$	−0.800161	−	9.14589i	−0.0449415	−	0.513684i	0.940045	−	0.341051i	$-0.110783\pi$
$318$	−21.9822	+	10.2505i	−1.23270	+	0.574819i
$319$	−2.85391	+	1.03874i	−0.159788	+	0.0581581i
$320$		0			0
$321$	3.07453	+	17.4365i	0.171603	+	0.973211i
$322$	43.9607	+	43.9607i	2.44983	+	2.44983i
$323$	21.1244	+	6.46609i	1.17539	+	0.359783i
$324$			2.03163i			0.112868i
$325$		0			0
$326$	7.05896	+	8.41254i	0.390959	+	0.465927i
$327$	4.39148	−	9.41757i	0.242850	−	0.520793i
$328$	0.743195	+	1.59379i	0.0410361	+	0.0880021i
$329$	−7.21899	+	8.60326i	−0.397996	+	0.474313i
$330$		0			0
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	−0.203961	−	0.978979i	$-0.565382\pi$
$331$	9.85862	−	5.69188i	0.541879	−	0.312854i	0.745840	+	0.666125i	$0.232048\pi$
$332$	0.385856	+	0.551059i	0.0211766	+	0.0302433i
$333$	2.72492	+	3.89159i	0.149325	+	0.213258i
$334$	23.9123	−	13.8058i	1.30842	−	0.755418i
$335$		0			0
$336$	16.4722	−	19.6308i	0.898632	−	1.07095i
$337$	6.59306	+	14.1389i	0.359147	+	0.770193i	0.999997	+	0.00252652i	$0.000804216\pi$
$337$	6.59306	+	14.1389i	0.359147	+	0.770193i	−0.640850	+	0.767666i	$0.721418\pi$
$338$	−10.1427	+	21.7510i	−0.551688	+	1.18310i
$339$	−3.22294	−	3.84095i	−0.175046	−	0.208612i
$340$		0			0
$341$			1.90463i			0.103142i
$342$	5.97966	−	11.7261i	0.323343	−	0.634073i
$343$	21.3274	+	21.3274i	1.15157	+	1.15157i
$344$	0.165168	+	0.936712i	0.00890524	+	0.0505041i
$345$		0			0
$346$	23.8820	−	8.69235i	1.28391	−	0.467304i
$347$	−12.7342	+	5.93804i	−0.683606	+	0.318770i	−0.733214	−	0.679998i	$-0.761981\pi$
$347$	−12.7342	+	5.93804i	−0.683606	+	0.318770i	0.0496082	+	0.998769i	$0.484203\pi$
$348$	−0.288344	−	3.29579i	−0.0154569	−	0.176673i
$349$	20.6061	+	11.8969i	1.10302	+	0.636829i	0.937012	−	0.349296i	$-0.113579\pi$
$349$	20.6061	+	11.8969i	1.10302	+	0.636829i	0.166007	+	0.986125i	$0.446913\pi$
$350$		0			0
$351$	0.130442	−	0.739776i	0.00696250	−	0.0394863i
$352$	−8.44066	+	5.91022i	−0.449889	+	0.315016i
$353$	−3.32012	+	12.3909i	−0.176712	+	0.659499i	0.819542	+	0.573020i	$0.194228\pi$
$353$	−3.32012	+	12.3909i	−0.176712	+	0.659499i	−0.996254	+	0.0864789i	$0.972438\pi$
$354$	−11.6276	+	20.1395i	−0.617999	+	1.07040i
$355$		0			0
$356$	−0.906858	+	2.49157i	−0.0480634	+	0.132053i
$357$	24.3957	+	11.3759i	1.29116	+	0.602077i
$358$	7.38821	+	0.646385i	0.390479	+	0.0341625i
$359$	−1.62390	+	0.286337i	−0.0857062	+	0.0151123i	−0.216337	−	0.976319i	$-0.569411\pi$
$359$	−1.62390	+	0.286337i	−0.0857062	+	0.0151123i	0.130631	+	0.991431i	$0.458300\pi$
$360$		0			0
$361$	15.3788	−	11.1576i	0.809409	−	0.587245i
$362$	−29.5227	+	29.5227i	−1.55168	+	1.55168i
$363$	8.31544	+	5.82253i	0.436447	+	0.305604i
$364$	0.684513	−	0.574375i	0.0358782	−	0.0301054i
$365$		0			0
$366$	−6.03423	−	2.19628i	−0.315414	−	0.114801i
$367$	−17.6746	+	1.54633i	−0.922606	+	0.0807176i	−0.538551	−	0.842593i	$-0.681028\pi$
$367$	−17.6746	+	1.54633i	−0.922606	+	0.0807176i	−0.384055	+	0.923310i	$0.625473\pi$
$368$	−34.4966	+	9.24333i	−1.79826	+	0.481842i
$369$	1.33527	+	2.31276i	0.0695114	+	0.120397i
$370$		0			0
$371$	50.2056	+	8.85260i	2.60654	+	0.459604i
$372$	−2.00409	−	0.536993i	−0.103907	−	0.0278418i
$373$	3.36965	+	12.5757i	0.174474	+	0.651145i	0.996641	+	0.0818983i	$0.0260983\pi$
$373$	3.36965	+	12.5757i	0.174474	+	0.651145i	−0.822167	+	0.569246i	$0.807235\pi$
$374$	−10.9257	−	9.16778i	−0.564956	−	0.474054i
$375$		0			0
$376$	−0.909359	−	2.49844i	−0.0468966	−	0.128847i
$377$	−0.0241176	+	0.275665i	−0.00124212	+	0.0141975i
$378$	26.0956	−	37.2684i	1.34221	−	1.91688i
$379$	−19.2818			−0.990442			−0.495221	−	0.868767i	$-0.664913\pi$
$379$	−19.2818			−0.990442			−0.495221	+	0.868767i	$0.664913\pi$
$380$		0			0
$381$	15.6658			0.802583
$382$	13.4612	−	19.2245i	0.688733	−	0.983612i
$383$	1.30745	−	14.9442i	0.0668074	−	0.763612i	−0.886720	−	0.462306i	$-0.847022\pi$
$383$	1.30745	−	14.9442i	0.0668074	−	0.763612i	0.953528	−	0.301305i	$-0.0974224\pi$
$384$	3.29479	+	9.05237i	0.168137	+	0.461952i
$385$		0			0
$386$	−21.1425	−	17.7407i	−1.07613	−	0.902977i
$387$	0.373849	+	1.39522i	0.0190038	+	0.0709232i
$388$	−1.63081	−	0.436975i	−0.0827921	−	0.0221841i
$389$	−13.3902	−	2.36105i	−0.678909	−	0.119710i	−0.176448	−	0.984310i	$-0.556461\pi$
$389$	−13.3902	−	2.36105i	−0.678909	−	0.119710i	−0.502461	+	0.864600i	$0.667572\pi$
$390$		0			0
$391$	−18.7567	−	32.4875i	−0.948566	−	1.64297i
$392$	−14.1693	+	3.79666i	−0.715658	+	0.191760i
$393$	12.4709	−	1.09107i	0.629076	−	0.0550370i
$394$	10.9784	+	3.99580i	0.553082	+	0.201306i
$395$		0			0
$396$	−2.70095	+	2.26637i	−0.135728	+	0.113889i
$397$	3.83927	+	2.68829i	0.192687	+	0.134921i	0.665939	−	0.746006i	$-0.268031\pi$
$397$	3.83927	+	2.68829i	0.192687	+	0.134921i	−0.473252	+	0.880927i	$0.656920\pi$
$398$	−16.6342	+	16.6342i	−0.833795	+	0.833795i
$399$	20.4443	−	10.8617i	1.02349	−	0.543763i
$400$		0			0
$401$	−29.5512	+	5.21067i	−1.47572	+	0.260209i	−0.852865	−	0.522132i	$-0.825137\pi$
$401$	−29.5512	+	5.21067i	−1.47572	+	0.260209i	−0.622851	+	0.782340i	$0.714026\pi$
$402$	−30.6005	−	2.67720i	−1.52621	−	0.133526i
$403$	0.157279	+	0.0733404i	0.00783463	+	0.00365335i
$404$	−0.372995	+	1.02480i	−0.0185572	+	0.0509855i
$405$		0			0
$406$	−8.37983	+	14.5143i	−0.415884	+	0.720333i
$407$	1.14586	−	4.27641i	0.0567982	−	0.211974i
$408$	−5.22008	+	3.65514i	−0.258432	+	0.180956i
$409$	5.94508	−	33.7162i	0.293965	−	1.66716i	−0.377414	−	0.926045i	$-0.623187\pi$
$409$	5.94508	−	33.7162i	0.293965	−	1.66716i	0.671379	−	0.741114i	$-0.265702\pi$
$410$		0			0
$411$	−21.1332	−	12.2013i	−1.04243	−	0.601845i
$412$	−0.490645	−	5.60810i	−0.0241723	−	0.276291i
$413$	44.2995	−	20.6572i	2.17984	−	1.01647i
$414$	−21.0032	+	7.64453i	−1.03225	+	0.375708i
$415$		0			0
$416$	0.163029	+	0.924586i	0.00799317	+	0.0453315i
$417$	5.55965	+	5.55965i	0.272257	+	0.272257i
$418$	−11.9530	+	2.75535i	−0.584638	+	0.134769i
$419$		−	7.01480i		−	0.342696i	−0.985211	−	0.171348i	$-0.945188\pi$
$419$		−	7.01480i		−	0.342696i	0.985211	−	0.171348i	$-0.0548122\pi$
$420$		0			0
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	0.709230	−	0.704977i	$-0.249043\pi$
$421$	−2.21994	−	2.64562i	−0.108193	−	0.128939i	−0.817423	+	0.576037i	$0.804598\pi$
$422$	13.4118	−	28.7616i	0.652875	−	1.40009i
$423$	−1.70638	−	3.65935i	−0.0829672	−	0.177924i
$424$	−7.75787	+	9.24547i	−0.376755	+	0.449000i
$425$		0			0
$426$	−9.80765	+	5.66245i	−0.475182	+	0.274347i
$427$	7.74162	+	11.0562i	0.374643	+	0.535046i
$428$	−12.3203	−	17.5953i	−0.595526	−	0.850500i
$429$	−0.213711	+	0.123386i	−0.0103181	+	0.00595714i
$430$		0			0
$431$	−6.73534	+	8.02687i	−0.324430	+	0.386641i	−0.903465	−	0.428662i	$-0.858985\pi$
$431$	−6.73534	+	8.02687i	−0.324430	+	0.386641i	0.579035	+	0.815303i	$0.303429\pi$
$432$	11.0453	+	23.6867i	0.531416	+	1.13963i
$433$	10.0690	−	21.5929i	0.483883	−	1.03769i	−0.501156	−	0.865357i	$-0.667092\pi$
$433$	10.0690	−	21.5929i	0.483883	−	1.03769i	0.985039	−	0.172333i	$-0.0551306\pi$
$434$	6.75601	+	8.05150i	0.324299	+	0.386484i
$435$		0			0
$436$			12.6063i			0.603731i
$437$	−32.0214	−	3.94259i	−1.53179	−	0.188600i
$438$	9.23112	+	9.23112i	0.441080	+	0.441080i
$439$	−0.100282	−	0.568729i	−0.00478621	−	0.0271439i	0.982321	−	0.187204i	$-0.0599424\pi$
$439$	−0.100282	−	0.568729i	−0.00478621	−	0.0271439i	−0.987107	+	0.160060i	$0.948831\pi$
$440$		0			0
$441$	−20.9332	+	7.61906i	−0.996819	+	0.362813i
$442$	−1.17776	+	0.549197i	−0.0560202	+	0.0261227i
$443$	0.740596	+	8.46505i	0.0351868	+	0.402187i	0.993281	+	0.115732i	$0.0369213\pi$
$443$	0.740596	+	8.46505i	0.0351868	+	0.402187i	−0.958094	+	0.286455i	$0.907523\pi$
$444$	4.17664	+	2.41139i	0.198215	+	0.114439i
$445$		0			0
$446$	−6.02950	+	34.1950i	−0.285505	+	1.61918i
$447$	−8.28659	+	5.80233i	−0.391942	+	0.274441i
$448$	−3.37022	+	12.5778i	−0.159228	+	0.594247i
$449$	−4.27636	+	7.40687i	−0.201814	+	0.349552i	−0.949113	−	0.314936i	$-0.898017\pi$
$449$	−4.27636	+	7.40687i	−0.201814	+	0.349552i	0.747299	+	0.664488i	$0.231350\pi$
$450$		0			0
$451$	0.851185	−	2.33861i	0.0400807	−	0.110121i
$452$	5.51295	+	2.57073i	0.259308	+	0.120917i
$453$	12.1385	+	1.06198i	0.570316	+	0.0498962i
$454$	0.168244	−	0.0296659i	0.00789608	−	0.00139229i
$455$		0			0
$456$	−0.193102	+	5.47727i	−0.00904283	+	0.256497i
$457$	−1.00342	+	1.00342i	−0.0469379	+	0.0469379i	−0.730186	−	0.683248i	$-0.760567\pi$
$457$	−1.00342	+	1.00342i	−0.0469379	+	0.0469379i	0.683248	+	0.730186i	$0.260567\pi$
$458$	15.5930	+	10.9183i	0.728612	+	0.510180i
$459$	−21.0299	+	17.6462i	−0.981590	+	0.823652i
$460$		0			0
$461$	−0.708319	−	0.257807i	−0.0329897	−	0.0120073i	0.325473	−	0.945551i	$-0.394477\pi$
$461$	−0.708319	−	0.257807i	−0.0329897	−	0.0120073i	−0.358462	+	0.933544i	$0.616699\pi$
$462$	−14.8891	+	1.30263i	−0.692703	+	0.0606037i
$463$	−21.1144	+	5.65758i	−0.981269	+	0.262930i	−0.713579	−	0.700575i	$-0.752927\pi$
$463$	−21.1144	+	5.65758i	−0.981269	+	0.262930i	−0.267690	+	0.963505i	$0.586260\pi$
$464$	−4.81380	−	8.33774i	−0.223475	−	0.387070i
$465$		0			0
$466$	−39.4677	−	6.95922i	−1.82831	−	0.322380i
$467$	−3.02917	−	0.811663i	−0.140173	−	0.0375593i	0.188050	−	0.982159i	$-0.439783\pi$
$467$	−3.02917	−	0.811663i	−0.140173	−	0.0375593i	−0.328223	+	0.944600i	$0.606450\pi$
$468$	0.0831464	+	0.310306i	0.00384344	+	0.0143439i
$469$	49.4587	+	41.5008i	2.28379	+	1.91633i
$470$		0			0
$471$	6.51390	+	17.8968i	0.300145	+	0.824640i
$472$	−1.00854	+	11.5277i	−0.0464219	+	0.530605i
$473$	0.772083	−	1.10265i	0.0355004	−	0.0506999i
$474$	−12.5156			−0.574860
$475$		0			0
$476$	−32.6559			−1.49678
$477$	−10.5126	+	15.0136i	−0.481340	+	0.687425i
$478$	−1.65395	+	18.9048i	−0.0756501	+	0.864684i
$479$	9.80127	+	26.9288i	0.447831	+	1.23041i	0.934230	+	0.356670i	$0.116088\pi$
$479$	9.80127	+	26.9288i	0.447831	+	1.23041i	−0.486399	+	0.873737i	$0.661690\pi$
$480$		0			0
$481$	−0.309011	−	0.259291i	−0.0140897	−	0.0118226i
$482$	9.47285	+	35.3532i	0.431477	+	1.61029i
$483$	−37.9715	−	10.1744i	−1.72776	−	0.462952i
$484$	−12.1282	−	2.13853i	−0.551281	−	0.0972058i
$485$		0			0
$486$	13.4737	+	23.3372i	0.611181	+	1.05860i
$487$	9.40703	−	2.52061i	0.426273	−	0.114220i	−0.0393029	−	0.999227i	$-0.512514\pi$
$487$	9.40703	−	2.52061i	0.426273	−	0.114220i	0.465576	+	0.885008i	$0.345847\pi$
$488$	−3.18316	+	0.278491i	−0.144095	+	0.0126067i
$489$	−6.52518	−	2.37497i	−0.295079	−	0.107400i
$490$		0			0
$491$	6.63665	−	5.56881i	0.299508	−	0.251317i	−0.480631	−	0.876923i	$-0.659593\pi$
$491$	6.63665	−	5.56881i	0.299508	−	0.251317i	0.780139	+	0.625606i	$0.215148\pi$
$492$	2.22074	+	1.55498i	0.100119	+	0.0701039i
$493$	7.15084	−	7.15084i	0.322057	−	0.322057i
$494$	−0.232735	+	1.09314i	−0.0104713	+	0.0491826i
$495$		0			0
$496$	−5.94602	+	1.04844i	−0.266984	+	0.0470765i
$497$	23.7128	+	2.07460i	1.06366	+	0.0930586i
$498$	−0.929157	−	0.433273i	−0.0416365	−	0.0194154i
$499$	0.511920	−	1.40649i	0.0229167	−	0.0629631i	−0.927707	−	0.373310i	$-0.878223\pi$
$499$	0.511920	−	1.40649i	0.0229167	−	0.0629631i	0.950623	+	0.310347i	$0.100445\pi$
$500$		0			0
$501$	−8.72960	+	15.1201i	−0.390010	+	0.675517i
$502$	2.93519	−	10.9543i	0.131004	−	0.488913i
$503$	−6.48967	+	4.54411i	−0.289360	+	0.202612i	−0.709239	−	0.704968i	$-0.750961\pi$
$503$	−6.48967	+	4.54411i	−0.289360	+	0.202612i	0.419879	+	0.907580i	$0.362072\pi$
$504$	1.38580	−	7.85925i	0.0617283	−	0.350079i
$505$		0			0
$506$	18.0386	+	10.4146i	0.801913	+	0.462985i
$507$	−1.32262	−	15.1176i	−0.0587394	−	0.671395i
$508$	−17.2247	+	8.03202i	−0.764223	+	0.356363i
$509$	31.2055	−	11.3579i	1.38316	−	0.503430i	0.460026	−	0.887905i	$-0.347840\pi$
$509$	31.2055	−	11.3579i	1.38316	−	0.503430i	0.923135	+	0.384476i	$0.125618\pi$
$510$		0			0
$511$	−4.76479	−	27.0225i	−0.210782	−	1.19540i
$512$	−15.7583	−	15.7583i	−0.696424	−	0.696424i
$513$	1.22780	+	23.5785i	0.0542087	+	1.04102i
$514$		−	43.0157i		−	1.89734i
$515$		0			0
$516$	0.942543	+	1.12328i	0.0414931	+	0.0494496i
$517$	−1.59019	+	3.41018i	−0.0699366	+	0.149979i
$518$	−10.3251	−	22.1423i	−0.453660	−	0.972877i
$519$	−10.3297	+	12.3104i	−0.453423	+	0.540368i
$520$		0			0
$521$	26.1470	−	15.0960i	1.14552	−	0.661367i	0.197729	−	0.980257i	$-0.436643\pi$
$521$	26.1470	−	15.0960i	1.14552	−	0.661367i	0.947792	+	0.318890i	$0.103310\pi$
$522$	−3.45602	−	4.93571i	−0.151266	−	0.216030i
$523$	−4.88803	−	6.98083i	−0.213739	−	0.305250i	0.697939	−	0.716158i	$-0.254101\pi$
$523$	−4.88803	−	6.98083i	−0.213739	−	0.305250i	−0.911677	+	0.410907i	$0.865212\pi$
$524$	−13.1525	+	7.59362i	−0.574571	+	0.331729i
$525$		0			0
$526$	−14.9770	+	17.8489i	−0.653028	+	0.778248i
$527$	−2.68026	−	5.74784i	−0.116754	−	0.250380i
$528$	3.62848	−	7.78130i	0.157909	−	0.338637i
$529$	20.4310	+	24.3487i	0.888304	+	1.05864i
$530$		0			0
$531$			17.5729i			0.762598i
$532$	−16.9098	+	22.4245i	−0.733133	+	0.972225i
$533$	−0.160340	−	0.160340i	−0.00694508	−	0.00694508i
$534$	−0.701678	−	3.97941i	−0.0303646	−	0.172206i
$535$		0			0
$536$	−14.3631	+	5.22775i	−0.620392	+	0.225804i
$537$	−4.25015	+	1.98188i	−0.183408	+	0.0855244i
$538$	−2.82949	−	32.3412i	−0.121988	−	1.39433i
$539$	17.9785	+	10.3799i	0.774389	+	0.447094i
$540$		0			0
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	−0.783099	−	0.621897i	$-0.786362\pi$
$541$	3.84885	−	21.8279i	0.165475	−	0.938454i	0.948574	−	0.316557i	$-0.102527\pi$
$542$	−25.3846	+	17.7745i	−1.09036	+	0.763481i
$543$	6.83284	−	25.5005i	0.293225	−	1.09433i
$544$	17.1554	−	29.7139i	0.735530	−	1.27397i
$545$		0			0
$546$	−0.465757	+	1.27966i	−0.0199326	+	0.0547642i
$547$	−28.6999	−	13.3830i	−1.22712	−	0.572216i	−0.302516	−	0.953144i	$-0.597827\pi$
$547$	−28.6999	−	13.3830i	−1.22712	−	0.572216i	−0.924605	+	0.380928i	$0.875604\pi$
$548$	29.4920	+	2.58021i	1.25983	+	0.110221i
$549$	−4.77872	+	0.842616i	−0.203951	+	0.0359620i
$550$		0			0
$551$	−1.20758	−	8.61324i	−0.0514446	−	0.366936i
$552$	6.58071	−	6.58071i	0.280094	−	0.280094i
$553$	21.5487	+	15.0885i	0.916342	+	0.641630i
$554$	−42.6631	+	35.7986i	−1.81258	+	1.52094i
$555$		0			0
$556$	−8.96338	−	3.26240i	−0.380132	−	0.138357i
$557$	0.255505	−	0.0223538i	0.0108261	−	0.000947162i	−0.0817414	−	0.996654i	$-0.526048\pi$
$557$	0.255505	−	0.0223538i	0.0108261	−	0.000947162i	0.0925675	+	0.995706i	$0.470493\pi$
$558$	−3.64994	+	0.977999i	−0.154514	+	0.0414020i
$559$	−0.0613234	−	0.106215i	−0.00259370	−	0.00449243i
$560$		0			0
$561$	8.88141	+	1.56603i	0.374973	+	0.0661179i
$562$	50.0978	+	13.4237i	2.11325	+	0.566243i
$563$	1.38026	+	5.15121i	0.0581711	+	0.217097i	0.988893	−	0.148631i	$-0.0474866\pi$
$563$	1.38026	+	5.15121i	0.0581711	+	0.217097i	−0.930722	+	0.365728i	$0.880820\pi$
$564$	−3.13990	−	2.63469i	−0.132214	−	0.110941i
$565$		0			0
$566$	−12.3550	−	33.9452i	−0.519321	−	1.42682i
$567$	−0.567185	+	6.48295i	−0.0238195	+	0.272258i
$568$	−3.23224	+	4.61612i	−0.135622	+	0.193688i
$569$	−20.8877			−0.875659			−0.437830	−	0.899058i	$-0.644253\pi$
$569$	−20.8877			−0.875659			−0.437830	+	0.899058i	$0.644253\pi$
$570$		0			0
$571$	−14.0563			−0.588237			−0.294118	−	0.955769i	$-0.595026\pi$
$571$	−14.0563			−0.588237			−0.294118	+	0.955769i	$0.595026\pi$
$572$	0.171716	−	0.245236i	0.00717982	−	0.0102538i
$573$	−1.29336	+	14.7832i	−0.0540311	+	0.617578i
$574$	−4.69716	−	12.9053i	−0.196056	−	0.538659i
$575$		0			0
$576$	−3.58621	−	3.00919i	−0.149425	−	0.125383i
$577$	7.13342	+	26.6223i	0.296968	+	1.10830i	0.939642	+	0.342160i	$0.111159\pi$
$577$	7.13342	+	26.6223i	0.296968	+	1.10830i	−0.642673	+	0.766140i	$0.722175\pi$
$578$	15.5135	+	4.15682i	0.645275	+	0.172901i
$579$	17.1865	+	3.03045i	0.714248	+	0.125941i
$580$		0			0
$581$	1.07743	+	1.86616i	0.0446992	+	0.0774212i
$582$	2.48533	−	0.665943i	0.103020	−	0.0276042i
$583$	17.0152	−	1.48864i	0.704698	−	0.0616531i
$584$	6.10427	+	2.22177i	0.252597	+	0.0919376i
$585$		0			0
$586$	7.93484	−	6.65812i	0.327785	−	0.275045i
$587$	13.4922	+	9.44733i	0.556882	+	0.389933i	0.817865	−	0.575410i	$-0.195158\pi$
$587$	13.4922	+	9.44733i	0.556882	+	0.389933i	−0.260983	+	0.965343i	$0.584047\pi$
$588$	−15.9907	+	15.9907i	−0.659447	+	0.659447i
$589$	−5.33487	−	1.13583i	−0.219820	−	0.0468009i
$590$		0			0
$591$	−7.27507	+	1.28279i	−0.299256	+	0.0527670i
$592$	13.9812	+	1.22319i	0.574623	+	0.0502730i
$593$	−17.2159	−	8.02791i	−0.706972	−	0.329667i	0.0356619	−	0.999364i	$-0.488646\pi$
$593$	−17.2159	−	8.02791i	−0.706972	−	0.329667i	−0.742634	+	0.669697i	$0.766424\pi$
$594$	5.21339	−	14.3237i	0.213908	−	0.587707i
$595$		0			0
$596$	6.13628	−	10.6283i	0.251352	−	0.435354i
$597$	3.84987	−	14.3679i	0.157565	−	0.588039i
$598$	1.55461	−	1.08855i	0.0635726	−	0.0445140i
$599$	−6.72471	+	38.1377i	−0.274764	+	1.55826i	0.464946	+	0.885339i	$0.346074\pi$
$599$	−6.72471	+	38.1377i	−0.274764	+	1.55826i	−0.739710	+	0.672926i	$0.765037\pi$
$600$		0			0
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.904667	−	0.426120i	$-0.140120\pi$
$601$	24.2204	+	13.9836i	0.987970	+	0.570405i	0.0833031	+	0.996524i	$0.473453\pi$
$602$	−0.647411	−	7.39994i	−0.0263865	−	0.301599i
$603$	−21.0370	+	9.80971i	−0.856692	+	0.399482i
$604$	−13.8909	+	5.05587i	−0.565213	+	0.205721i
$605$		0			0
$606$	−0.288603	−	1.63675i	−0.0117237	−	0.0664885i
$607$	−31.1811	−	31.1811i	−1.26560	−	1.26560i	−0.948338	−	0.317263i	$-0.897236\pi$
$607$	−31.1811	−	31.1811i	−1.26560	−	1.26560i	−0.317263	−	0.948338i	$-0.602764\pi$
$608$	−11.5209	−	27.1668i	−0.467235	−	1.10176i
$609$		−	10.5974i		−	0.429428i
$610$		0			0
$611$	0.220370	+	0.262627i	0.00891522	+	0.0106247i
$612$	4.96169	−	10.6404i	0.200564	−	0.430112i
$613$	−6.16710	−	13.2254i	−0.249087	−	0.534169i	0.741516	−	0.670935i	$-0.234107\pi$
$613$	−6.16710	−	13.2254i	−0.249087	−	0.534169i	−0.990603	+	0.136766i	$0.956329\pi$
$614$	19.4126	−	23.1350i	0.783428	−	0.933653i
$615$		0			0
$616$	−6.44070	+	3.71854i	−0.259503	+	0.149824i
$617$	−3.52558	−	5.03505i	−0.141935	−	0.202704i	0.741891	−	0.670521i	$-0.233929\pi$
$617$	−3.52558	−	5.03505i	−0.141935	−	0.202704i	−0.883825	+	0.467817i	$0.845040\pi$
$618$	4.92088	+	7.02774i	0.197947	+	0.282697i
$619$	−19.4464	+	11.2274i	−0.781618	+	0.451268i	−0.837003	−	0.547198i	$-0.815695\pi$
$619$	−19.4464	+	11.2274i	−0.781618	+	0.451268i	0.0553852	+	0.998465i	$0.482361\pi$
$620$		0			0
$621$	25.7707	−	30.7123i	1.03414	−	1.23244i
$622$	−1.39122	−	2.98348i	−0.0557829	−	0.119627i
$623$	−3.58938	+	7.69746i	−0.143806	+	0.308392i
$624$	−0.502837	−	0.599258i	−0.0201296	−	0.0239895i
$625$		0			0
$626$		−	8.12126i		−	0.324591i
$627$	5.67433	−	5.28785i	0.226611	−	0.211177i
$628$	−16.3380	−	16.3380i	−0.651956	−	0.651956i
$629$	2.55990	+	14.5179i	0.102070	+	0.578868i
$630$		0			0
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	−0.0701787	−	0.997534i	$-0.522357\pi$
$631$	12.9935	−	4.72926i	0.517264	−	0.188269i	0.587443	+	0.809266i	$0.300135\pi$
$632$	−5.64425	+	2.63196i	−0.224516	+	0.104694i
$633$	1.74891	+	19.9901i	0.0695130	+	0.794537i
$634$	−14.7000	−	8.48702i	−0.583810	−	0.337063i
$635$		0			0
$636$	−3.23090	+	18.3234i	−0.128114	+	0.726569i
$637$	1.54943	−	1.08492i	0.0613905	−	0.0429861i
$638$	−1.45330	+	5.42377i	−0.0575365	+	0.214729i
$639$	−4.27886	+	7.41120i	−0.169269	+	0.293183i
$640$		0			0
$641$	10.3038	−	28.3093i	0.406974	−	1.11815i	−0.551799	−	0.833977i	$-0.686058\pi$
$641$	10.3038	−	28.3093i	0.406974	−	1.11815i	0.958773	−	0.284174i	$-0.0917194\pi$
$642$	29.6679	+	13.8344i	1.17090	+	0.546000i
$643$	25.5226	+	2.23293i	1.00651	+	0.0880584i	0.578473	−	0.815702i	$-0.303649\pi$
$643$	25.5226	+	2.23293i	1.00651	+	0.0880584i	0.428039	+	0.903760i	$0.359205\pi$
$644$	46.9665	−	8.28147i	1.85074	−	0.326336i
$645$		0			0
$646$	32.1945	−	25.1358i	1.26667	−	0.988953i
$647$	5.87443	−	5.87443i	0.230948	−	0.230948i	−0.582141	−	0.813088i	$-0.697785\pi$
$647$	5.87443	−	5.87443i	0.230948	−	0.230948i	0.813088	+	0.582141i	$0.197785\pi$
$648$	−1.26202	−	0.883679i	−0.0495770	−	0.0347142i
$649$	12.5450	−	10.5265i	0.492433	−	0.413200i
$650$		0			0
$651$	−6.24514	−	2.27305i	−0.244766	−	0.0890877i
$652$	8.39218	−	0.734220i	0.328663	−	0.0287543i
$653$	5.27313	−	1.41293i	0.206353	−	0.0552922i	−0.154162	−	0.988046i	$-0.549268\pi$
$653$	5.27313	−	1.41293i	0.206353	−	0.0552922i	0.360515	+	0.932753i	$0.382601\pi$
$654$	−9.60587	−	16.6379i	−0.375619	−	0.650591i
$655$		0			0
$656$	7.76940	+	1.36995i	0.303344	+	0.0534878i
$657$	9.52877	+	2.55323i	0.371753	+	0.0996108i
$658$	5.37414	+	20.0566i	0.209506	+	0.781886i
$659$	−22.7331	−	19.0754i	−0.885557	−	0.743071i	0.0817569	−	0.996652i	$-0.473947\pi$
$659$	−22.7331	−	19.0754i	−0.885557	−	0.743071i	−0.967314	+	0.253582i	$0.918391\pi$
$660$		0			0
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	0.985776	+	0.168064i	$0.0537516\pi$
$661$	8.70685	+	23.9219i	0.338657	+	0.930454i	−0.647119	+	0.762389i	$0.724026\pi$
$662$	1.83436	−	20.9669i	0.0712945	−	0.814900i
$663$	0.471309	−	0.673098i	0.0183041	−	0.0261410i
$664$	−0.510143			−0.0197974
$665$		0			0
$666$	8.78348			0.340353
$667$	−8.47108	+	12.0980i	−0.328001	+	0.468435i
$668$	1.84605	−	21.1005i	0.0714259	−	0.816402i
$669$	−7.50925	−	20.6315i	−0.290324	−	0.797660i
$670$		0			0
$671$	3.46407	+	2.90670i	0.133729	+	0.112212i
$672$	−9.30579	−	34.7297i	−0.358979	−	1.33973i
$673$	−37.3907	−	10.0188i	−1.44131	−	0.386197i	−0.548315	−	0.836272i	$-0.684731\pi$
$673$	−37.3907	−	10.0188i	−1.44131	−	0.386197i	−0.892991	+	0.450075i	$0.851397\pi$
$674$	28.4049	+	5.00855i	1.09412	+	0.192922i
$675$		0			0
$676$	9.20516	+	15.9438i	0.354045	+	0.613224i
$677$	13.0692	−	3.50187i	0.502289	−	0.134588i	0.00122697	−	0.999999i	$-0.499609\pi$
$677$	13.0692	−	3.50187i	0.502289	−	0.134588i	0.501062	+	0.865411i	$0.332943\pi$
$678$	−9.23491	+	0.807950i	−0.354665	+	0.0310291i
$679$	−5.08195	−	1.84968i	−0.195027	−	0.0709842i
$680$		0			0
$681$	−0.0827514	+	0.0694367i	−0.00317104	+	0.00266082i
$682$	2.88456	+	2.01979i	0.110456	+	0.0773418i
$683$	8.52271	−	8.52271i	0.326112	−	0.326112i	−0.524994	−	0.851106i	$-0.675932\pi$
$683$	8.52271	−	8.52271i	0.326112	−	0.326112i	0.851106	+	0.524994i	$0.175932\pi$
$684$	−4.73739	−	8.91691i	−0.181139	−	0.340947i
$685$		0			0
$686$	54.9172	−	9.68339i	2.09675	−	0.369714i
$687$	−11.9906	−	1.04905i	−0.457472	−	0.0400236i
$688$	3.86734	+	1.80337i	0.147441	+	0.0687528i
$689$	0.532265	−	1.46239i	0.0202777	−	0.0557125i
$690$		0			0
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.389504	+	0.921025i	$0.627354\pi$
$691$	−26.0866	+	45.1834i	−0.992383	+	1.71886i	−0.602878	+	0.797833i	$0.705980\pi$
$692$	5.04591	−	18.8316i	0.191817	−	0.715869i
$693$	−9.25150	+	6.47797i	−0.351435	+	0.246078i
$694$	−4.51095	+	25.5829i	−0.171233	+	0.971113i
$695$		0			0
$696$	2.17272	+	1.25442i	0.0823568	+	0.0475487i
$697$	0.722248	+	8.25533i	0.0273571	+	0.312693i
$698$	39.8698	−	18.5916i	1.50910	−	0.703703i
$699$	23.8128	−	8.66714i	0.900682	−	0.327822i
$700$		0			0
$701$	−4.07872	−	23.1316i	−0.154051	−	0.873668i	−0.959648	−	0.281204i	$-0.909266\pi$
$701$	−4.07872	−	23.1316i	−0.154051	−	0.873668i	0.805597	−	0.592464i	$-0.201845\pi$
$702$	−0.982058	−	0.982058i	−0.0370654	−	0.0370654i
$703$	11.2949	+	5.75979i	0.425995	+	0.217234i
$704$			4.36270i			0.164425i
$705$		0			0
$706$	15.2450	+	18.1683i	0.573755	+	0.683774i
$707$	−1.47633	+	3.16600i	−0.0555232	+	0.119070i
$708$	7.53919	+	16.1679i	0.283340	+	0.607625i
$709$	8.49230	−	10.1207i	0.318935	−	0.380092i	−0.582629	−	0.812739i	$-0.697976\pi$
$709$	8.49230	−	10.1207i	0.318935	−	0.380092i	0.901564	+	0.432647i	$0.142420\pi$
$710$		0			0
$711$	−8.19041	+	4.72874i	−0.307164	+	0.177341i
$712$	−1.15329	−	1.64706i	−0.0432213	−	0.0617264i
$713$	5.31246	+	7.58698i	0.198953	+	0.284135i
$714$	43.0995	−	24.8835i	1.61296	−	0.931242i
$715$		0			0
$716$	3.65696	−	4.35819i	0.136667	−	0.162873i
$717$	−5.07118	−	10.8752i	−0.189387	−	0.406141i
$718$	−1.28843	+	2.76304i	−0.0480837	+	0.103116i
$719$	−30.9997	−	36.9440i	−1.15609	−	1.37778i	−0.913092	−	0.407753i	$-0.866313\pi$
$719$	−30.9997	−	36.9440i	−1.15609	−	1.37778i	−0.243001	−	0.970026i	$-0.578132\pi$
$720$		0			0
$721$		−	18.0325i		−	0.671565i
$722$	−0.589612	−	35.1234i	−0.0219431	−	1.30716i
$723$	−16.3645	−	16.3645i	−0.608603	−	0.608603i
$724$	5.56159	+	31.5413i	0.206695	+	1.17222i
$725$		0			0
$726$	17.6364	−	6.41913i	0.654549	−	0.238236i
$727$	5.18618	−	2.41835i	0.192345	−	0.0896918i	−0.324060	−	0.946037i	$-0.605048\pi$
$727$	5.18618	−	2.41835i	0.192345	−	0.0896918i	0.516404	+	0.856345i	$0.327270\pi$
$728$	0.0590585	+	0.675041i	0.00218885	+	0.0250187i
$729$	−18.4781	−	10.6683i	−0.684374	−	0.395124i
$730$		0			0
$731$	−0.778324	+	4.41410i	−0.0287874	+	0.163261i
$732$	−4.03514	+	2.82543i	−0.149143	+	0.104431i
$733$	3.88782	−	14.5096i	0.143600	−	0.535923i	−0.856214	−	0.516622i	$-0.827189\pi$
$733$	3.88782	−	14.5096i	0.143600	−	0.535923i	0.999814	−	0.0193008i	$-0.00614401\pi$
$734$	−16.4013	+	28.4079i	−0.605384	+	1.04856i
$735$		0			0
$736$	−17.1379	+	47.0859i	−0.631710	+	1.73561i
$737$	19.6045	+	9.14175i	0.722142	+	0.336741i
$738$	4.91867	+	0.430327i	0.181059	+	0.0158406i
$739$	37.0848	−	6.53906i	1.36419	−	0.240543i	0.556840	−	0.830620i	$-0.312014\pi$
$739$	37.0848	−	6.53906i	1.36419	−	0.240543i	0.807347	+	0.590077i	$0.200902\pi$
$740$		0			0
$741$	−0.218158	−	0.672185i	−0.00801423	−	0.0246933i
$742$	66.6483	−	66.6483i	2.44674	−	2.44674i
$743$	−5.49028	−	3.84433i	−0.201419	−	0.141035i	0.468516	−	0.883455i	$-0.344789\pi$
$743$	−5.49028	−	3.84433i	−0.201419	−	0.141035i	−0.669934	+	0.742420i	$0.733678\pi$
$744$	1.20527	−	1.01134i	0.0441874	−	0.0370776i
$745$		0			0
$746$	22.6192	+	8.23272i	0.828148	+	0.301421i
$747$	−0.771758	+	0.0675201i	−0.0282372	+	0.00247043i
$748$	−10.5681	+	2.83172i	−0.386409	+	0.103538i
$749$	−34.4022	−	59.5863i	−1.25703	−	2.17724i
$750$		0			0
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.472960	−	0.881084i	$-0.343185\pi$
$751$	16.8825	+	2.97683i	0.616050	+	0.108626i	0.143089	+	0.989710i	$0.454296\pi$
$752$	−11.5215	−	3.08718i	−0.420146	−	0.112578i
$753$	1.85596	+	6.92655i	0.0676351	+	0.252418i
$754$	0.391918	+	0.328858i	0.0142728	+	0.0119763i
$755$		0			0
$756$	−11.9367	−	32.7959i	−0.434135	−	1.19278i
$757$	−0.579501	+	6.62372i	−0.0210623	+	0.240743i	0.978364	+	0.206889i	$0.0663338\pi$
$757$	−0.579501	+	6.62372i	−0.0210623	+	0.240743i	−0.999427	+	0.0338545i	$0.989222\pi$
$758$	−20.4477	+	29.2023i	−0.742692	+	1.06067i
$759$	−13.1706			−0.478063
$760$		0			0
$761$	−46.7690			−1.69538			−0.847688	−	0.530495i	$-0.822006\pi$
$761$	−46.7690			−1.69538			−0.847688	+	0.530495i	$0.822006\pi$
$762$	16.6130	−	23.7258i	0.601825	−	0.859495i
$763$	−3.51938	+	40.2268i	−0.127410	+	1.45631i
$764$	−6.15744	−	16.9174i	−0.222768	−	0.612051i
$765$		0			0
$766$	−21.2464	−	17.8278i	−0.767664	−	0.644146i
$767$	−0.386185	−	1.44126i	−0.0139443	−	0.0520410i
$768$	23.6771	+	6.34427i	0.854375	+	0.228929i
$769$	−48.7943	−	8.60376i	−1.75957	−	0.310259i	−0.801756	−	0.597652i	$-0.796101\pi$
$769$	−48.7943	−	8.60376i	−1.75957	−	0.310259i	−0.957813	+	0.287392i	$0.907212\pi$
$770$		0			0
$771$	13.5997	+	23.5554i	0.489783	+	0.848328i
$772$	−20.4505	+	5.47970i	−0.736030	+	0.197219i
$773$	14.1733	−	1.24000i	0.509778	−	0.0445998i	0.170634	−	0.985334i	$-0.445418\pi$
$773$	14.1733	−	1.24000i	0.509778	−	0.0445998i	0.339144	+	0.940735i	$0.389863\pi$
$774$	2.50951	+	0.913388i	0.0902025	+	0.0328310i
$775$		0			0
$776$	0.980784	−	0.822975i	0.0352081	−	0.0295431i
$777$	12.6545	+	8.86079i	0.453978	+	0.317879i
$778$	−17.7756	+	17.7756i	−0.637285	+	0.637285i
$779$	6.04284	+	3.77880i	0.216507	+	0.135389i
$780$		0			0
$781$	7.85385	−	1.38484i	0.281033	−	0.0495536i
$782$	−69.0930	−	6.04485i	−2.47076	−	0.216163i
$783$	9.79534	+	4.56764i	0.350057	+	0.163234i
$784$	−22.5081	+	61.8404i	−0.803860	+	2.20859i
$785$		0			0
$786$	11.5725	−	20.0442i	0.412779	−	0.714954i
$787$	5.51072	−	20.5663i	0.196436	−	0.733110i	−0.795454	−	0.606014i	$-0.792768\pi$
$787$	5.51072	−	20.5663i	0.196436	−	0.733110i	0.991890	−	0.127096i	$-0.0405656\pi$
$788$	7.34132	−	5.14045i	0.261524	−	0.183121i
$789$	2.55836	−	14.5092i	0.0910799	−	0.516540i
$790$		0			0
$791$	16.8742	+	9.74233i	0.599978	+	0.346397i
$792$	−0.233033	−	2.66358i	−0.00828048	−	0.0946463i
$793$	0.373415	−	0.174126i	0.0132604	−	0.00618341i
$794$	8.14280	−	2.96374i	0.288977	−	0.105179i
$795$		0			0
$796$	3.13360	+	17.7715i	0.111068	+	0.629895i
$797$	2.03401	+	2.03401i	0.0720484	+	0.0720484i	0.742213	−	0.670164i	$-0.233776\pi$
$797$	2.03401	+	2.03401i	0.0720484	+	0.0720484i	−0.670164	+	0.742213i	$0.733776\pi$
$798$	5.23043	−	42.4811i	0.185155	−	1.50382i
$799$		−	12.5291i		−	0.443247i
$800$		0			0
$801$	−1.96272	−	2.33908i	−0.0693493	−	0.0826473i
$802$	−23.4464	+	50.2809i	−0.827920	+	1.77548i
$803$	−3.88521	−	8.33186i	−0.137106	−	0.294025i
$804$	−15.1464	+	18.0508i	−0.534172	+	0.636602i
$805$		0			0
$806$	0.277862	−	0.160424i	0.00978728	−	0.00565069i
$807$	11.7743	+	16.8155i	0.414476	+	0.591934i
$808$	−0.474353	−	0.677446i	−0.0166877	−	0.0238325i
$809$	8.61084	−	4.97147i	0.302741	−	0.174788i	−0.340932	−	0.940088i	$-0.610743\pi$
$809$	8.61084	−	4.97147i	0.302741	−	0.174788i	0.643674	+	0.765300i	$0.277409\pi$
$810$		0			0
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	−0.677126	−	0.735867i	$-0.736775\pi$
$811$	4.70296	−	5.60477i	0.165143	−	0.196810i	0.842269	+	0.539057i	$0.181219\pi$
$812$	5.43339	+	11.6520i	0.190675	+	0.408903i
$813$	8.28111	−	17.7589i	0.290431	−	0.622831i
$814$	−5.26147	−	6.27038i	−0.184414	−	0.219777i
$815$		0			0
$816$			28.5887i			1.00080i
$817$	2.62809	+	2.82017i	0.0919451	+	0.0986651i
$818$	−44.7585	−	44.7585i	−1.56495	−	1.56495i
$819$	0.178690	+	1.01340i	0.00624395	+	0.0354112i
$820$		0			0
$821$	−42.9758	+	15.6419i	−1.49986	+	0.545906i	−0.956025	−	0.293284i	$-0.905252\pi$
$821$	−42.9758	+	15.6419i	−1.49986	+	0.545906i	−0.543839	+	0.839190i	$0.683030\pi$
$822$	−40.8898	+	19.0672i	−1.42620	+	0.665046i
$823$	−4.37934	−	50.0561i	−0.152654	−	1.74485i	−0.557245	−	0.830348i	$-0.688142\pi$
$823$	−4.37934	−	50.0561i	−0.152654	−	1.74485i	0.404591	−	0.914498i	$-0.367414\pi$
$824$	3.69709	+	2.13452i	0.128794	+	0.0743595i
$825$		0			0
$826$	15.6927	−	88.9976i	0.546018	−	3.09662i
$827$	40.0530	−	28.0454i	1.39278	−	0.975234i	0.394364	−	0.918954i	$-0.370965\pi$
$827$	40.0530	−	28.0454i	1.39278	−	0.975234i	0.998415	−	0.0562800i	$-0.0179240\pi$
$828$	−4.43765	+	16.5615i	−0.154219	+	0.575553i
$829$	−17.1185	+	29.6501i	−0.594549	+	1.02979i	0.399061	+	0.916924i	$0.369336\pi$
$829$	−17.1185	+	29.6501i	−0.594549	+	1.02979i	−0.993610	+	0.112865i	$0.963997\pi$
$830$		0			0
$831$	12.0444	−	33.0916i	0.417814	−	1.14793i
$832$	0.360259	+	0.167991i	0.0124897	+	0.00582405i
$833$	−68.8628	−	6.02472i	−2.38596	−	0.208744i
$834$	14.3159	−	2.52427i	0.495718	−	0.0874084i
$835$		0			0
$836$	−3.52785	+	8.72334i	−0.122013	+	0.301703i
$837$	4.79277	−	4.79277i	0.165662	−	0.165662i
$838$	−10.6239	−	7.43893i	−0.366996	−	0.256974i
$839$	20.4137	−	17.1291i	0.704758	−	0.591362i	−0.218365	−	0.975867i	$-0.570072\pi$
$839$	20.4137	−	17.1291i	0.704758	−	0.591362i	0.923123	+	0.384505i	$0.125628\pi$
$840$		0			0
$841$	23.5098	+	8.55687i	0.810683	+	0.295065i
$842$	−6.36093	+	0.556510i	−0.219212	+	0.0191786i
$843$	−31.6776	+	8.48798i	−1.09103	+	0.292342i
$844$	−12.1721	−	21.0827i	−0.418981	−	0.725696i
$845$		0			0
$846$	−7.35163	−	1.29629i	−0.252754	−	0.0445674i
$847$	−38.1042	−	10.2100i	−1.30927	−	0.350819i
$848$	14.0137	+	52.2998i	0.481232	+	1.79598i
$849$	17.4977	+	14.6823i	0.600519	+	0.503895i
$850$		0			0
$851$	−7.36344	−	20.2309i	−0.252415	−	0.693506i
$852$	−0.757160	+	8.65438i	−0.0259399	+	0.296494i
$853$	8.83275	−	12.6145i	0.302427	−	0.431911i	−0.638959	−	0.769241i	$-0.720635\pi$
$853$	8.83275	−	12.6145i	0.302427	−	0.431911i	0.941387	+	0.337329i	$0.109524\pi$
$854$	24.9542			0.853916
$855$		0			0
$856$	16.2888			0.556741
$857$	20.1332	−	28.7532i	0.687737	−	0.982191i	−0.311750	−	0.950164i	$-0.600915\pi$
$857$	20.1332	−	28.7532i	0.687737	−	0.982191i	0.999487	−	0.0320266i	$-0.0101961\pi$
$858$	−0.0397645	+	0.454511i	−0.00135754	+	0.0155167i
$859$	−13.2030	−	36.2749i	−0.450480	−	1.23768i	−0.932387	−	0.361462i	$-0.882278\pi$
$859$	−13.2030	−	36.2749i	−0.450480	−	1.23768i	0.481907	−	0.876223i	$-0.339944\pi$
$860$		0			0
$861$	6.65229	+	5.58194i	0.226710	+	0.190232i
$862$	5.01409	+	18.7128i	0.170781	+	0.637362i
$863$	31.9550	+	8.56232i	1.08776	+	0.291465i	0.757772	−	0.652520i	$-0.226288\pi$
$863$	31.9550	+	8.56232i	1.08776	+	0.291465i	0.329989	+	0.943985i	$0.392955\pi$
$864$	36.1121	+	6.36754i	1.22856	+	0.216628i
$865$		0			0
$866$	−22.0247	−	38.1479i	−0.748429	−	1.29632i
$867$	−9.80941	+	2.62842i	−0.333145	+	0.0892659i
$868$	8.03201	−	0.702710i	0.272624	−	0.0238515i
$869$	8.28198	+	3.01439i	0.280947	+	0.102256i
$870$		0			0
$871$	1.50980	−	1.26687i	0.0511575	−	0.0429263i
$872$	−7.83086	−	5.48323i	−0.265187	−	0.185686i
$873$	1.37483	−	1.37483i	0.0465310	−	0.0465310i
$874$	−39.9285	+	44.3153i	−1.35060	+	1.49899i
$875$		0			0
$876$	9.86230	−	1.73899i	0.333216	−	0.0587550i
$877$	34.7538	+	3.04056i	1.17355	+	0.102672i	0.657208	−	0.753709i	$-0.271737\pi$
$877$	34.7538	+	3.04056i	1.17355	+	0.102672i	0.516343	+	0.856382i	$0.327293\pi$
$878$	−0.967683	−	0.451238i	−0.0326577	−	0.0152285i
$879$	−2.24011	+	6.15466i	−0.0755571	+	0.207591i
$880$		0			0
$881$	−4.01849	+	6.96024i	−0.135387	+	0.234496i	−0.925745	−	0.378148i	$-0.876561\pi$
$881$	−4.01849	+	6.96024i	−0.135387	+	0.234496i	0.790359	+	0.612645i	$0.209894\pi$
$882$	−10.6598	+	39.7830i	−0.358935	+	1.33956i
$883$	−5.32719	+	3.73014i	−0.179274	+	0.125529i	−0.659769	−	0.751468i	$-0.729346\pi$
$883$	−5.32719	+	3.73014i	−0.179274	+	0.125529i	0.480495	+	0.876997i	$0.340457\pi$
$884$	−0.173104	+	0.981724i	−0.00582213	+	0.0330189i
$885$		0			0
$886$	13.6057	+	7.85523i	0.457091	+	0.263902i
$887$	4.17511	+	47.7217i	0.140186	+	1.60234i	0.662151	+	0.749370i	$0.269644\pi$
$887$	4.17511	+	47.7217i	0.140186	+	1.60234i	−0.521965	+	0.852967i	$0.674801\pi$
$888$	−3.31460	+	1.54562i	−0.111231	+	0.0518677i
$889$	−57.2066	+	20.8215i	−1.91865	+	0.698331i
$890$		0			0
$891$	0.378609	+	2.14720i	0.0126839	+	0.0719339i
$892$	18.8345	+	18.8345i	0.630625	+	0.630625i
$893$	−8.60359	−	6.48778i	−0.287908	−	0.217105i
$894$			18.7032i			0.625527i
$895$		0			0
$896$	−24.0631	−	28.6773i	−0.803892	−	0.958041i
$897$	−0.507152	+	1.08759i	−0.0169333	+	0.0363136i
$898$	6.68276	+	14.3312i	0.223007	+	0.478239i
$899$	−1.60494	+	1.91269i	−0.0535276	+	0.0637918i
$900$		0			0
$901$	−49.2540	+	28.4368i	−1.64089	+	0.947367i
$902$	−2.63917	−	3.76913i	−0.0878747	−	0.125498i
$903$	2.69407	+	3.84753i	0.0896531	+	0.128038i
$904$	−3.99483	+	2.30641i	−0.132866	+	0.0767102i
$905$		0			0
$906$	14.4808	−	17.2575i	0.481092	−	0.573343i
$907$	−11.6361	−	24.9537i	−0.386370	−	0.828574i	−0.999262	−	0.0384071i	$-0.987772\pi$
$907$	−11.6361	−	24.9537i	−0.386370	−	0.828574i	0.612892	−	0.790167i	$-0.290006\pi$
$908$	0.0553852	−	0.118774i	0.00183802	−	0.00394165i
$909$	−0.807277	−	0.962075i	−0.0267757	−	0.0319100i
$910$		0			0
$911$			50.4735i			1.67226i	0.548529	+	0.836132i	$0.315188\pi$
$911$			50.4735i			1.67226i	−0.548529	+	0.836132i	$0.684812\pi$
$912$	19.6316	+	14.8037i	0.650066	+	0.490200i
$913$	0.510499	+	0.510499i	0.0168951	+	0.0168951i
$914$	0.455586	+	2.58376i	0.0150694	+	0.0854631i
$915$		0			0
$916$	13.7217	−	4.99429i	0.453378	−	0.165016i
$917$	−44.0898	+	20.5594i	−1.45598	+	0.678932i
$918$	4.42367	+	50.5627i	0.146003	+	1.66882i
$919$	−22.3948	−	12.9296i	−0.738736	−	0.426510i	0.0828733	−	0.996560i	$-0.473590\pi$
$919$	−22.3948	−	12.9296i	−0.738736	−	0.426510i	−0.821610	+	0.570050i	$0.806924\pi$
$920$		0			0
$921$	−3.31604	+	18.8062i	−0.109267	+	0.619685i
$922$	−1.14159	+	0.799352i	−0.0375964	+	0.0263252i
$923$	0.188066	−	0.701873i	0.00619027	−	0.0231024i
$924$	−5.73260	+	9.92915i	−0.188589	+	0.326645i
$925$		0			0
$926$	−13.8226	+	37.9773i	−0.454239	+	1.24801i
$927$	5.87558	+	2.73983i	0.192979	+	0.0899877i
$928$	−13.4566	−	1.17730i	−0.441734	−	0.0386467i
$929$	49.5361	−	8.73454i	1.62523	−	0.286571i	0.714516	−	0.699619i	$-0.246647\pi$
$929$	49.5361	−	8.73454i	1.62523	−	0.286571i	0.910709	+	0.413048i	$0.135536\pi$
$930$		0			0
$931$	−39.7955	+	44.1677i	−1.30424	+	1.44754i
$932$	−21.7387	+	21.7387i	−0.712074	+	0.712074i
$933$	1.70509	+	1.19391i	0.0558220	+	0.0390870i
$934$	−4.44157	+	3.72692i	−0.145333	+	0.121949i
$935$		0			0
$936$	−0.228924	−	0.0833215i	−0.00748262	−	0.00272345i
$937$	−33.6752	+	2.94620i	−1.10012	+	0.0962482i	−0.622726	−	0.782440i	$-0.713975\pi$
$937$	−33.6752	+	2.94620i	−1.10012	+	0.0962482i	−0.477396	+	0.878688i	$0.658419\pi$
$938$	115.302	−	30.8950i	3.76474	−	1.00876i
$939$	2.56760	+	4.44721i	0.0837904	+	0.145129i
$940$		0			0
$941$	−20.3861	−	3.59461i	−0.664567	−	0.117181i	−0.168818	−	0.985647i	$-0.553995\pi$
$941$	−20.3861	−	3.59461i	−0.664567	−	0.117181i	−0.495748	+	0.868466i	$0.665106\pi$
$942$	34.0124	+	9.11358i	1.10818	+	0.296937i
$943$	−3.13229	−	11.6899i	−0.102001	−	0.380674i
$944$	39.7680	+	33.3693i	1.29434	+	1.08608i
$945$		0			0
$946$	−0.851193	−	2.33863i	−0.0276747	−	0.0760355i
$947$	3.20227	−	36.6021i	0.104060	−	1.18941i	−0.747177	−	0.664625i	$-0.768591\pi$
$947$	3.20227	−	36.6021i	0.104060	−	1.18941i	0.851237	−	0.524782i	$-0.175853\pi$
$948$	−5.50681	+	7.86455i	−0.178853	+	0.255429i
$949$	−0.837625			−0.0271905
$950$		0			0
$951$	10.7329			0.348040
$952$	14.2040	−	20.2855i	0.460355	−	0.657455i
$953$	−1.19399	+	13.6473i	−0.0386770	+	0.442080i	0.952024	+	0.306023i	$0.0989986\pi$
$953$	−1.19399	+	13.6473i	−0.0386770	+	0.442080i	−0.990701	+	0.136057i	$0.956557\pi$
$954$	11.5898	+	31.8427i	0.375233	+	1.03094i
$955$		0			0
$956$	11.1516	+	9.35734i	0.360670	+	0.302638i
$957$	−0.918941	−	3.42954i	−0.0297052	−	0.110861i
$958$	51.1774	+	13.7129i	1.65347	+	0.443045i
$959$	93.3888	+	16.4670i	3.01568	+	0.531746i
$960$		0			0
$961$	−14.7171	−	25.4907i	−0.474744	−	0.822282i
$962$	−0.720389	+	0.193028i	−0.0232263	+	0.00622346i
$963$	24.6422	−	2.15591i	0.794083	−	0.0694733i
$964$	26.3832	+	9.60271i	0.849746	+	0.309282i
$965$		0			0
$966$	−55.6764	+	46.7180i	−1.79136	+	1.50313i
$967$	−0.256099	−	0.179322i	−0.00823557	−	0.00576661i	0.569451	−	0.822025i	$-0.307156\pi$
$967$	−0.256099	−	0.179322i	−0.00823557	−	0.00576661i	−0.577687	+	0.816258i	$0.696045\pi$
$968$	6.60371	−	6.60371i	0.212251	−	0.212251i
$969$	−9.68286	+	23.9429i	−0.311058	+	0.769157i
$970$		0			0
$971$	−38.3652	+	6.76482i	−1.23120	+	0.217093i	−0.751140	−	0.660143i	$-0.770496\pi$
$971$	−38.3652	+	6.76482i	−1.23120	+	0.217093i	−0.480058	+	0.877237i	$0.659384\pi$
$972$	20.5930	+	1.80165i	0.660521	+	0.0577881i
$973$	−27.6915	−	12.9127i	−0.887748	−	0.413963i
$974$	6.15835	−	16.9199i	0.197326	−	0.542149i
$975$		0			0
$976$	−7.16748	+	12.4144i	−0.229425	+	0.397376i
$977$	−4.32385	+	16.1368i	−0.138332	+	0.516262i	0.861630	+	0.507537i	$0.169444\pi$
$977$	−4.32385	+	16.1368i	−0.138332	+	0.516262i	−0.999962	+	0.00872521i	$0.997223\pi$
$978$	−10.5166	+	7.36379i	−0.336283	+	0.235468i
$979$	−0.494122	+	2.80231i	−0.0157922	+	0.0895621i
$980$		0			0
$981$	−12.5725	−	7.25872i	−0.401408	−	0.231753i
$982$	−1.39603	−	15.9567i	−0.0445491	−	0.509199i
$983$	−19.8575	+	9.25970i	−0.633355	+	0.295338i	−0.712657	−	0.701512i	$-0.752509\pi$
$983$	−19.8575	+	9.25970i	−0.633355	+	0.295338i	0.0793022	+	0.996851i	$0.474731\pi$
$984$	−1.93187	+	0.703143i	−0.0615857	+	0.0224154i
$985$		0			0
$986$	−3.24673	−	18.4131i	−0.103397	−	0.586393i
$987$	−9.28392	−	9.28392i	−0.295510	−	0.295510i
$988$	0.584503	+	0.627223i	0.0185955	+	0.0199546i
$989$		−	6.54585i		−	0.208146i
$990$		0			0
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	0.985247	−	0.171139i	$-0.0547446\pi$
$991$	20.3243	+	24.2215i	0.645622	+	0.769422i	−0.339625	+	0.940561i	$0.610300\pi$
$992$	−3.58011	+	7.67757i	−0.113669	+	0.243763i
$993$	5.62433	+	12.0614i	0.178483	+	0.382758i
$994$	28.2885	−	33.7129i	0.897256	−	1.06931i
$995$		0			0
$996$	−0.681085	+	0.393225i	−0.0215810	+	0.0124598i
$997$	20.1485	+	28.7750i	0.638109	+	0.911314i	0.999780	−	0.0209919i	$-0.00668241\pi$
$997$	20.1485	+	28.7750i	0.638109	+	0.911314i	−0.361671	+	0.932306i	$0.617794\pi$
$998$	−1.58725	−	2.26683i	−0.0502436	−	0.0717553i
$999$	−13.6445	+	7.87763i	−0.431692	+	0.249237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.143.7		96
5.2	odd	4	inner	475.2.bb.b.257.7		96
5.3	odd	4		95.2.r.a.67.2	yes	96
5.4	even	2		95.2.r.a.48.2	yes	96
15.8	even	4		855.2.dl.a.352.7		96
15.14	odd	2		855.2.dl.a.523.7		96
19.2	odd	18	inner	475.2.bb.b.268.7		96
95.2	even	36	inner	475.2.bb.b.382.7		96
95.59	odd	18		95.2.r.a.78.2	yes	96
95.78	even	36		95.2.r.a.2.2	✓	96
285.59	even	18		855.2.dl.a.838.7		96
285.173	odd	36		855.2.dl.a.667.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.2	✓	96	95.78	even	36
95.2.r.a.48.2	yes	96	5.4	even	2
95.2.r.a.67.2	yes	96	5.3	odd	4
95.2.r.a.78.2	yes	96	95.59	odd	18
475.2.bb.b.143.7		96	1.1	even	1	trivial
475.2.bb.b.257.7		96	5.2	odd	4	inner
475.2.bb.b.268.7		96	19.2	odd	18	inner
475.2.bb.b.382.7		96	95.2	even	36	inner
855.2.dl.a.352.7		96	15.8	even	4
855.2.dl.a.523.7		96	15.14	odd	2
855.2.dl.a.667.7		96	285.173	odd	36
855.2.dl.a.838.7		96	285.59	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06046 - 1.51450i) q^{2} +(-0.101890 + 1.16461i) q^{3} +(-0.485079 - 1.33274i) q^{4} +(1.65575 + 1.38934i) q^{6} +(-1.17582 - 4.38823i) q^{7} +(1.03888 + 0.278366i) q^{8} +(1.60848 + 0.283619i) q^{9} +(-0.761040 - 1.31816i) q^{11} +(1.60156 - 0.429136i) q^{12} +(-0.138155 + 0.0120870i) q^{13} +(-7.89287 - 2.87277i) q^{14} +(3.69620 - 3.10148i) q^{16} +(4.15164 + 2.90701i) q^{17} +(2.13527 - 2.13527i) q^{18} +(4.14601 - 1.34559i) q^{19} +(5.23039 - 0.922259i) q^{21} +(-2.80340 - 0.245266i) q^{22} +(-6.70821 - 3.12809i) q^{23} +(-0.430040 + 1.18152i) q^{24} +(-0.128202 + 0.222052i) q^{26} +(-1.40192 + 5.23204i) q^{27} +(-5.27802 + 3.69571i) q^{28} +(0.346487 - 1.96502i) q^{29} +(-1.08369 - 0.625668i) q^{31} +(-0.590025 - 6.74402i) q^{32} +(1.61269 - 0.752009i) q^{33} +(8.80531 - 3.20487i) q^{34} +(-0.402250 - 2.28127i) q^{36} +(2.05676 + 2.05676i) q^{37} +(2.35879 - 7.70606i) q^{38} -0.162128i q^{39} +(1.05100 + 1.25253i) q^{41} +(4.14987 - 8.89943i) q^{42} +(0.373752 + 0.801514i) q^{43} +(-1.38761 + 1.65368i) q^{44} +(-11.8513 + 6.84234i) q^{46} +(-1.41793 - 2.02502i) q^{47} +(3.23541 + 4.62065i) q^{48} +(-11.8118 + 6.81954i) q^{49} +(-3.80855 + 4.53886i) q^{51} +(0.0831248 + 0.178262i) q^{52} +(-4.74246 + 10.1702i) q^{53} +(6.43722 + 7.67158i) q^{54} -4.88613i q^{56} +(1.14465 + 4.96560i) q^{57} +(-2.60859 - 2.60859i) q^{58} +(1.86831 + 10.5957i) q^{59} +(-2.79178 + 1.01612i) q^{61} +(-2.09678 + 0.977745i) q^{62} +(-0.646704 - 7.39187i) q^{63} +(-2.48226 - 1.43314i) q^{64} +(0.571280 - 3.23989i) q^{66} +(-11.6415 + 8.15144i) q^{67} +(1.86043 - 6.94321i) q^{68} +(4.32651 - 7.49374i) q^{69} +(-1.79203 + 4.92356i) q^{71} +(1.59206 + 0.742391i) q^{72} +(6.01690 + 0.526410i) q^{73} +(5.29607 - 0.933839i) q^{74} +(-3.80447 - 4.87285i) q^{76} +(-4.88954 + 4.88954i) q^{77} +(-0.245543 - 0.171931i) q^{78} +(-4.43572 + 3.72201i) q^{79} +(-1.34607 - 0.489931i) q^{81} +(3.01150 - 0.263472i) q^{82} +(-0.458159 + 0.122763i) q^{83} +(-3.76629 - 6.52341i) q^{84} +(1.61024 + 0.283929i) q^{86} +(2.25319 + 0.603740i) q^{87} +(-0.423695 - 1.58125i) q^{88} +(-1.43212 - 1.20169i) q^{89} +(0.215486 + 0.592042i) q^{91} +(-0.914930 + 10.4577i) q^{92} +(0.839078 - 1.19833i) q^{93} -4.57054 q^{94} +7.91429 q^{96} +(0.682796 - 0.975134i) q^{97} +(-2.19778 + 25.1208i) q^{98} +(-0.850264 - 2.33608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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