LMFDB - Embedded newform 3150.2.bf.f.1601.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.15
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.f.1151.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.07665 + 1.63937i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.07665 + 1.63937i) q^{7} +1.00000i q^{8} +(5.48223 - 3.16517i) q^{11} -1.05290i q^{13} +(-2.61811 + 0.381412i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.31842 - 4.01562i) q^{17} +(-5.35129 - 3.08957i) q^{19} +6.33033 q^{22} +(-6.10091 - 3.52236i) q^{23} +(0.526449 - 0.911836i) q^{26} +(-2.45806 - 0.978745i) q^{28} -2.98101i q^{29} +(5.46948 - 3.15781i) q^{31} +(-0.866025 + 0.500000i) q^{32} -4.63684i q^{34} +(-1.73991 + 3.01361i) q^{37} +(-3.08957 - 5.35129i) q^{38} +6.97007 q^{41} +2.58650 q^{43} +(5.48223 + 3.16517i) q^{44} +(-3.52236 - 6.10091i) q^{46} +(4.07711 - 7.06176i) q^{47} +(1.62493 - 6.80879i) q^{49} +(0.911836 - 0.526449i) q^{52} +(-7.68480 + 4.43682i) q^{53} +(-1.63937 - 2.07665i) q^{56} +(1.49051 - 2.58163i) q^{58} +(0.452296 + 0.783400i) q^{59} +(-8.81047 - 5.08673i) q^{61} +6.31561 q^{62} -1.00000 q^{64} +(-4.91612 - 8.51497i) q^{67} +(2.31842 - 4.01562i) q^{68} +14.4282i q^{71} +(7.24574 - 4.18333i) q^{73} +(-3.01361 + 1.73991i) q^{74} -6.17914i q^{76} +(-6.19578 + 15.5603i) q^{77} +(-2.73283 + 4.73340i) q^{79} +(6.03626 + 3.48504i) q^{82} +14.6297 q^{83} +(2.23997 + 1.29325i) q^{86} +(3.16517 + 5.48223i) q^{88} +(1.91982 - 3.32522i) q^{89} +(1.72609 + 2.18650i) q^{91} -7.04472i q^{92} +(7.06176 - 4.07711i) q^{94} -5.87891i q^{97} +(4.81163 - 5.08412i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.07665	+	1.63937i	−0.784899	+	0.619624i
$7$	−2.07665	+	1.63937i	−0.784899	+	0.619624i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	5.48223	−	3.16517i	1.65295	−	0.954334i	0.677106	−	0.735886i	$-0.263234\pi$
$11$	5.48223	−	3.16517i	1.65295	−	0.954334i	0.975849	−	0.218448i	$-0.0700994\pi$
$12$		0			0
$13$		−	1.05290i		−	0.292021i	−0.989283	−	0.146011i	$-0.953357\pi$
$13$		−	1.05290i		−	0.292021i	0.989283	−	0.146011i	$-0.0466434\pi$
$14$	−2.61811	+	0.381412i	−0.699721	+	0.101937i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.31842	−	4.01562i	−0.562299	−	0.973931i	−0.997295	−	0.0734985i	$-0.976584\pi$
$17$	−2.31842	−	4.01562i	−0.562299	−	0.973931i	0.434996	−	0.900432i	$-0.356750\pi$
$18$		0			0
$19$	−5.35129	−	3.08957i	−1.22767	−	0.708795i	−0.261128	−	0.965304i	$-0.584094\pi$
$19$	−5.35129	−	3.08957i	−1.22767	−	0.708795i	−0.966542	+	0.256509i	$0.917428\pi$
$20$		0			0
$21$		0			0
$22$	6.33033			1.34963
$23$	−6.10091	−	3.52236i	−1.27213	−	0.734463i	−0.296739	−	0.954959i	$-0.595899\pi$
$23$	−6.10091	−	3.52236i	−1.27213	−	0.734463i	−0.975388	+	0.220496i	$0.929232\pi$
$24$		0			0
$25$		0			0
$26$	0.526449	−	0.911836i	0.103245	−	0.178826i
$27$		0			0
$28$	−2.45806	−	0.978745i	−0.464530	−	0.184965i
$29$		−	2.98101i		−	0.553560i	−0.960933	−	0.276780i	$-0.910733\pi$
$29$		−	2.98101i		−	0.553560i	0.960933	−	0.276780i	$-0.0892674\pi$
$30$		0			0
$31$	5.46948	−	3.15781i	0.982348	−	0.567159i	0.0793697	−	0.996845i	$-0.474709\pi$
$31$	5.46948	−	3.15781i	0.982348	−	0.567159i	0.902978	+	0.429686i	$0.141376\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		−	4.63684i		−	0.795211i
$35$		0			0
$36$		0			0
$37$	−1.73991	+	3.01361i	−0.286039	+	0.495434i	−0.972861	−	0.231392i	$-0.925672\pi$
$37$	−1.73991	+	3.01361i	−0.286039	+	0.495434i	0.686821	+	0.726826i	$0.259005\pi$
$38$	−3.08957	−	5.35129i	−0.501194	−	0.868094i
$39$		0			0
$40$		0			0
$41$	6.97007			1.08854			0.544271	−	0.838909i	$-0.316806\pi$
$41$	6.97007			1.08854			0.544271	+	0.838909i	$0.316806\pi$
$42$		0			0
$43$	2.58650			0.394437			0.197218	−	0.980360i	$-0.436809\pi$
$43$	2.58650			0.394437			0.197218	+	0.980360i	$0.436809\pi$
$44$	5.48223	+	3.16517i	0.826477	+	0.477167i
$45$		0			0
$46$	−3.52236	−	6.10091i	−0.519344	−	0.899529i
$47$	4.07711	−	7.06176i	0.594707	−	1.03006i	−0.398881	−	0.917003i	$-0.630601\pi$
$47$	4.07711	−	7.06176i	0.594707	−	1.03006i	0.993588	−	0.113060i	$-0.0360654\pi$
$48$		0			0
$49$	1.62493	−	6.80879i	0.232133	−	0.972684i
$50$		0			0
$51$		0			0
$52$	0.911836	−	0.526449i	0.126449	−	0.0730053i
$53$	−7.68480	+	4.43682i	−1.05559	+	0.609445i	−0.924209	−	0.381887i	$-0.875274\pi$
$53$	−7.68480	+	4.43682i	−1.05559	+	0.609445i	−0.131380	+	0.991332i	$0.541941\pi$
$54$		0			0
$55$		0			0
$56$	−1.63937	−	2.07665i	−0.219070	−	0.277504i
$57$		0			0
$58$	1.49051	−	2.58163i	0.195713	−	0.338985i
$59$	0.452296	+	0.783400i	0.0588839	+	0.101990i	0.893965	−	0.448137i	$-0.147912\pi$
$59$	0.452296	+	0.783400i	0.0588839	+	0.101990i	−0.835081	+	0.550127i	$0.814579\pi$
$60$		0			0
$61$	−8.81047	−	5.08673i	−1.12807	−	0.651289i	−0.184618	−	0.982810i	$-0.559105\pi$
$61$	−8.81047	−	5.08673i	−1.12807	−	0.651289i	−0.943448	+	0.331522i	$0.892438\pi$
$62$	6.31561			0.802084
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−4.91612	−	8.51497i	−0.600600	−	1.04027i	−0.992730	−	0.120360i	$-0.961595\pi$
$67$	−4.91612	−	8.51497i	−0.600600	−	1.04027i	0.392131	−	0.919909i	$-0.371738\pi$
$68$	2.31842	−	4.01562i	0.281150	−	0.486965i
$69$		0			0
$70$		0			0
$71$			14.4282i			1.71232i	0.516713	+	0.856159i	$0.327156\pi$
$71$			14.4282i			1.71232i	−0.516713	+	0.856159i	$0.672844\pi$
$72$		0			0
$73$	7.24574	−	4.18333i	0.848050	−	0.489622i	−0.0119423	−	0.999929i	$-0.503801\pi$
$73$	7.24574	−	4.18333i	0.848050	−	0.489622i	0.859992	+	0.510307i	$0.170468\pi$
$74$	−3.01361	+	1.73991i	−0.350325	+	0.202260i
$75$		0			0
$76$		−	6.17914i		−	0.708795i
$77$	−6.19578	+	15.5603i	−0.706075	+	1.77327i
$78$		0			0
$79$	−2.73283	+	4.73340i	−0.307467	+	0.532549i	−0.977808	−	0.209505i	$-0.932815\pi$
$79$	−2.73283	+	4.73340i	−0.307467	+	0.532549i	0.670340	+	0.742054i	$0.266148\pi$
$80$		0			0
$81$		0			0
$82$	6.03626	+	3.48504i	0.666593	+	0.384858i
$83$	14.6297			1.60581			0.802907	−	0.596105i	$-0.203286\pi$
$83$	14.6297			1.60581			0.802907	+	0.596105i	$0.203286\pi$
$84$		0			0
$85$		0			0
$86$	2.23997	+	1.29325i	0.241542	+	0.139455i
$87$		0			0
$88$	3.16517	+	5.48223i	0.337408	+	0.584408i
$89$	1.91982	−	3.32522i	0.203500	−	0.352473i	−0.746154	−	0.665774i	$-0.768102\pi$
$89$	1.91982	−	3.32522i	0.203500	−	0.352473i	0.949654	+	0.313301i	$0.101435\pi$
$90$		0			0
$91$	1.72609	+	2.18650i	0.180943	+	0.229207i
$92$		−	7.04472i		−	0.734463i
$93$		0			0
$94$	7.06176	−	4.07711i	0.728365	−	0.420522i
$95$		0			0
$96$		0			0
$97$		−	5.87891i		−	0.596913i	−0.954423	−	0.298457i	$-0.903528\pi$
$97$		−	5.87891i		−	0.596913i	0.954423	−	0.298457i	$-0.0964718\pi$
$98$	4.81163	−	5.08412i	0.486048	−	0.513573i
$99$		0			0
$100$		0			0
$101$	−3.35408	−	5.80944i	−0.333744	−	0.578061i	0.649499	−	0.760362i	$-0.274979\pi$
$101$	−3.35408	−	5.80944i	−0.333744	−	0.578061i	−0.983243	+	0.182301i	$0.941645\pi$
$102$		0			0
$103$	−4.30789	−	2.48716i	−0.424469	−	0.245067i	0.272519	−	0.962151i	$-0.412143\pi$
$103$	−4.30789	−	2.48716i	−0.424469	−	0.245067i	−0.696988	+	0.717083i	$0.745477\pi$
$104$	1.05290			0.103245
$105$		0			0
$106$	−8.87365			−0.861885
$107$	6.35602	+	3.66965i	0.614460	+	0.354759i	0.774709	−	0.632318i	$-0.217896\pi$
$107$	6.35602	+	3.66965i	0.614460	+	0.354759i	−0.160249	+	0.987077i	$0.551230\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$		0			0
$112$	−0.381412	−	2.61811i	−0.0360400	−	0.247389i
$113$			0.184551i			0.0173611i	0.999962	+	0.00868054i	$0.00276314\pi$
$113$			0.184551i			0.0173611i	−0.999962	+	0.00868054i	$0.997237\pi$
$114$		0			0
$115$		0			0
$116$	2.58163	−	1.49051i	0.239699	−	0.138390i
$117$		0			0
$118$			0.904592i			0.0832745i
$119$	11.3976	+	4.53828i	1.04482	+	0.416024i
$120$		0			0
$121$	14.5366	−	25.1781i	1.32151	−	2.28891i
$122$	−5.08673	−	8.81047i	−0.460531	−	0.797663i
$123$		0			0
$124$	5.46948	+	3.15781i	0.491174	+	0.283579i
$125$		0			0
$126$		0			0
$127$	6.70276			0.594774			0.297387	−	0.954757i	$-0.403885\pi$
$127$	6.70276			0.594774			0.297387	+	0.954757i	$0.403885\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	2.24116	−	3.88180i	0.195811	−	0.339155i	−0.751355	−	0.659898i	$-0.770599\pi$
$131$	2.24116	−	3.88180i	0.195811	−	0.339155i	0.947166	+	0.320743i	$0.103933\pi$
$132$		0			0
$133$	16.1777	−	2.35680i	1.40278	−	0.204360i
$134$		−	9.83224i		−	0.849376i
$135$		0			0
$136$	4.01562	−	2.31842i	0.344337	−	0.198803i
$137$	−15.2098	+	8.78137i	−1.29946	+	0.750243i	−0.980311	−	0.197461i	$-0.936730\pi$
$137$	−15.2098	+	8.78137i	−1.29946	+	0.750243i	−0.319149	+	0.947705i	$0.603397\pi$
$138$		0			0
$139$		−	6.02268i		−	0.510837i	−0.966831	−	0.255418i	$-0.917787\pi$
$139$		−	6.02268i		−	0.510837i	0.966831	−	0.255418i	$-0.0822132\pi$
$140$		0			0
$141$		0			0
$142$	−7.21412	+	12.4952i	−0.605396	+	1.04858i
$143$	−3.33260	−	5.77223i	−0.278686	−	0.482698i
$144$		0			0
$145$		0			0
$146$	8.36666			0.692430
$147$		0			0
$148$	−3.47982			−0.286039
$149$	6.06548	+	3.50191i	0.496903	+	0.286887i	0.727434	−	0.686178i	$-0.240713\pi$
$149$	6.06548	+	3.50191i	0.496903	+	0.286887i	−0.230530	+	0.973065i	$0.574046\pi$
$150$		0			0
$151$	−6.43540	−	11.1464i	−0.523706	−	0.907085i	−0.999619	−	0.0275929i	$-0.991216\pi$
$151$	−6.43540	−	11.1464i	−0.523706	−	0.907085i	0.475913	−	0.879492i	$-0.342118\pi$
$152$	3.08957	−	5.35129i	0.250597	−	0.434047i
$153$		0			0
$154$	−13.1459	+	10.3778i	−1.05932	+	0.836263i
$155$		0			0
$156$		0			0
$157$	9.56427	−	5.52193i	0.763312	−	0.440698i	−0.0671718	−	0.997741i	$-0.521398\pi$
$157$	9.56427	−	5.52193i	0.763312	−	0.440698i	0.830484	+	0.557043i	$0.188064\pi$
$158$	−4.73340	+	2.73283i	−0.376569	+	0.217412i
$159$		0			0
$160$		0			0
$161$	18.4439	−	2.68694i	1.45358	−	0.211760i
$162$		0			0
$163$	−3.62287	+	6.27500i	−0.283765	+	0.491496i	−0.972309	−	0.233699i	$-0.924917\pi$
$163$	−3.62287	+	6.27500i	−0.283765	+	0.491496i	0.688544	+	0.725195i	$0.258250\pi$
$164$	3.48504	+	6.03626i	0.272136	+	0.471353i
$165$		0			0
$166$	12.6697	+	7.31483i	0.983356	+	0.567741i
$167$	−13.8606			−1.07257			−0.536283	−	0.844038i	$-0.680172\pi$
$167$	−13.8606			−1.07257			−0.536283	+	0.844038i	$0.680172\pi$
$168$		0			0
$169$	11.8914			0.914724
$170$		0			0
$171$		0			0
$172$	1.29325	+	2.23997i	0.0986092	+	0.170796i
$173$	0.479402	−	0.830348i	0.0364482	−	0.0631302i	−0.847226	−	0.531233i	$-0.821729\pi$
$173$	0.479402	−	0.830348i	0.0364482	−	0.0631302i	0.883674	+	0.468103i	$0.155062\pi$
$174$		0			0
$175$		0			0
$176$			6.33033i			0.477167i
$177$		0			0
$178$	3.32522	−	1.91982i	0.249236	−	0.143896i
$179$	20.2531	−	11.6931i	1.51379	−	0.873984i	0.513916	−	0.857841i	$-0.328194\pi$
$179$	20.2531	−	11.6931i	1.51379	−	0.873984i	0.999870	−	0.0161436i	$-0.00513888\pi$
$180$		0			0
$181$		−	19.2865i		−	1.43355i	−0.697303	−	0.716776i	$-0.745617\pi$
$181$		−	19.2865i		−	1.43355i	0.697303	−	0.716776i	$-0.254383\pi$
$182$	0.401588	+	2.75661i	0.0297677	+	0.204333i
$183$		0			0
$184$	3.52236	−	6.10091i	0.259672	−	0.449765i
$185$		0			0
$186$		0			0
$187$	−25.4202	−	14.6764i	−1.85891	−	1.07324i
$188$	8.15421			0.594707
$189$		0			0
$190$		0			0
$191$	2.44949	+	1.41421i	0.177239	+	0.102329i	0.585995	−	0.810315i	$-0.300704\pi$
$191$	2.44949	+	1.41421i	0.177239	+	0.102329i	−0.408756	+	0.912644i	$0.634037\pi$
$192$		0			0
$193$	−4.10862	−	7.11634i	−0.295745	−	0.512246i	0.679413	−	0.733756i	$-0.262235\pi$
$193$	−4.10862	−	7.11634i	−0.295745	−	0.512246i	−0.975158	+	0.221511i	$0.928901\pi$
$194$	2.93946	−	5.09129i	0.211041	−	0.365533i
$195$		0			0
$196$	6.70905	−	1.99716i	0.479218	−	0.142654i
$197$		−	3.51321i		−	0.250306i	−0.992137	−	0.125153i	$-0.960058\pi$
$197$		−	3.51321i		−	0.250306i	0.992137	−	0.125153i	$-0.0399422\pi$
$198$		0			0
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	0.602549	+	0.798082i	$0.294152\pi$
$200$		0			0
$201$		0			0
$202$		−	6.70816i		−	0.471985i
$203$	4.88698	+	6.19052i	0.342999	+	0.434489i
$204$		0			0
$205$		0			0
$206$	−2.48716	−	4.30789i	−0.173289	−	0.300145i
$207$		0			0
$208$	0.911836	+	0.526449i	0.0632245	+	0.0365027i
$209$	−39.1160			−2.70571
$210$		0			0
$211$	−9.96592			−0.686082			−0.343041	−	0.939320i	$-0.611457\pi$
$211$	−9.96592			−0.686082			−0.343041	+	0.939320i	$0.611457\pi$
$212$	−7.68480	−	4.43682i	−0.527795	−	0.304722i
$213$		0			0
$214$	3.66965	+	6.35602i	0.250852	+	0.434489i
$215$		0			0
$216$		0			0
$217$	−6.18138	+	15.5242i	−0.419619	+	1.05385i
$218$			2.00000i			0.135457i
$219$		0			0
$220$		0			0
$221$	−4.22804	+	2.44106i	−0.284408	+	0.164203i
$222$		0			0
$223$			11.1087i			0.743894i	0.928254	+	0.371947i	$0.121310\pi$
$223$			11.1087i			0.743894i	−0.928254	+	0.371947i	$0.878690\pi$
$224$	0.978745	−	2.45806i	0.0653952	−	0.164236i
$225$		0			0
$226$	−0.0922754	+	0.159826i	−0.00613807	+	0.0106314i
$227$	11.7619	+	20.3722i	0.780665	+	1.35215i	0.931555	+	0.363602i	$0.118453\pi$
$227$	11.7619	+	20.3722i	0.780665	+	1.35215i	−0.150889	+	0.988551i	$0.548214\pi$
$228$		0			0
$229$	8.21579	+	4.74339i	0.542915	+	0.313452i	0.746259	−	0.665655i	$-0.231848\pi$
$229$	8.21579	+	4.74339i	0.542915	+	0.313452i	−0.203345	+	0.979107i	$0.565181\pi$
$230$		0			0
$231$		0			0
$232$	2.98101			0.195713
$233$	−8.98361	−	5.18669i	−0.588536	−	0.339791i	0.175982	−	0.984393i	$-0.443690\pi$
$233$	−8.98361	−	5.18669i	−0.588536	−	0.339791i	−0.764518	+	0.644602i	$0.777023\pi$
$234$		0			0
$235$		0			0
$236$	−0.452296	+	0.783400i	−0.0294420	+	0.0509950i
$237$		0			0
$238$	7.60149	+	9.62908i	0.492732	+	0.624161i
$239$			12.3746i			0.800444i	0.916418	+	0.400222i	$0.131067\pi$
$239$			12.3746i			0.800444i	−0.916418	+	0.400222i	$0.868933\pi$
$240$		0			0
$241$	−10.8208	+	6.24737i	−0.697027	+	0.402429i	−0.806239	−	0.591590i	$-0.798501\pi$
$241$	−10.8208	+	6.24737i	−0.697027	+	0.402429i	0.109212	+	0.994018i	$0.465167\pi$
$242$	25.1781	−	14.5366i	1.61851	−	0.934445i
$243$		0			0
$244$		−	10.1735i		−	0.651289i
$245$		0			0
$246$		0			0
$247$	−3.25300	+	5.63436i	−0.206983	+	0.358506i
$248$	3.15781	+	5.46948i	0.200521	+	0.347312i
$249$		0			0
$250$		0			0
$251$	−13.5304			−0.854034			−0.427017	−	0.904244i	$-0.640436\pi$
$251$	−13.5304			−0.854034			−0.427017	+	0.904244i	$0.640436\pi$
$252$		0			0
$253$	−44.5954			−2.80369
$254$	5.80476	+	3.35138i	0.364223	+	0.210284i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.20899	+	3.82609i	−0.137793	+	0.238665i	−0.926661	−	0.375898i	$-0.877334\pi$
$257$	−2.20899	+	3.82609i	−0.137793	+	0.238665i	0.788868	+	0.614563i	$0.210668\pi$
$258$		0			0
$259$	−1.32724	−	9.11056i	−0.0824709	−	0.566103i
$260$		0			0
$261$		0			0
$262$	3.88180	−	2.24116i	0.239819	−	0.138459i
$263$	−5.30558	+	3.06318i	−0.327156	+	0.188884i	−0.654578	−	0.755995i	$-0.727154\pi$
$263$	−5.30558	+	3.06318i	−0.327156	+	0.188884i	0.327422	+	0.944878i	$0.393820\pi$
$264$		0			0
$265$		0			0
$266$	15.1887	+	6.04780i	0.931278	+	0.370814i
$267$		0			0
$268$	4.91612	−	8.51497i	0.300300	−	0.520135i
$269$	2.09370	+	3.62639i	0.127655	+	0.221105i	0.922768	−	0.385357i	$-0.125922\pi$
$269$	2.09370	+	3.62639i	0.127655	+	0.221105i	−0.795113	+	0.606462i	$0.792588\pi$
$270$		0			0
$271$	0.253692	+	0.146469i	0.0154107	+	0.00889737i	0.507686	−	0.861542i	$-0.330501\pi$
$271$	0.253692	+	0.146469i	0.0154107	+	0.00889737i	−0.492275	+	0.870440i	$0.663835\pi$
$272$	4.63684			0.281150
$273$		0			0
$274$	−17.5627			−1.06100
$275$		0			0
$276$		0			0
$277$	7.31099	+	12.6630i	0.439275	+	0.760847i	0.997634	−	0.0687531i	$-0.0219021\pi$
$277$	7.31099	+	12.6630i	0.439275	+	0.760847i	−0.558359	+	0.829600i	$0.688569\pi$
$278$	3.01134	−	5.21579i	0.180608	−	0.312822i
$279$		0			0
$280$		0			0
$281$			18.1691i			1.08388i	0.840419	+	0.541938i	$0.182309\pi$
$281$			18.1691i			1.08388i	−0.840419	+	0.541938i	$0.817691\pi$
$282$		0			0
$283$	−18.3712	+	10.6066i	−1.09206	+	0.630499i	−0.934123	−	0.356951i	$-0.883816\pi$
$283$	−18.3712	+	10.6066i	−1.09206	+	0.630499i	−0.157933	+	0.987450i	$0.550483\pi$
$284$	−12.4952	+	7.21412i	−0.741455	+	0.428079i
$285$		0			0
$286$		−	6.66519i		−	0.394121i
$287$	−14.4744	+	11.4265i	−0.854396	+	0.674486i
$288$		0			0
$289$	−2.25013	+	3.89734i	−0.132361	+	0.229256i
$290$		0			0
$291$		0			0
$292$	7.24574	+	4.18333i	0.424025	+	0.244811i
$293$	−7.64481			−0.446615			−0.223307	−	0.974748i	$-0.571685\pi$
$293$	−7.64481			−0.446615			−0.223307	+	0.974748i	$0.571685\pi$
$294$		0			0
$295$		0			0
$296$	−3.01361	−	1.73991i	−0.175163	−	0.101130i
$297$		0			0
$298$	3.50191	+	6.06548i	0.202860	+	0.351364i
$299$	−3.70868	+	6.42363i	−0.214479	+	0.371488i
$300$		0			0
$301$	−5.37124	+	4.24022i	−0.309593	+	0.244402i
$302$		−	12.8708i		−	0.740632i
$303$		0			0
$304$	5.35129	−	3.08957i	0.306917	−	0.177199i
$305$		0			0
$306$		0			0
$307$		−	13.1561i		−	0.750859i	−0.926851	−	0.375429i	$-0.877495\pi$
$307$		−	13.1561i		−	0.750859i	0.926851	−	0.375429i	$-0.122505\pi$
$308$	−16.5735	+	2.41446i	−0.944365	+	0.137577i
$309$		0			0
$310$		0			0
$311$	3.13043	+	5.42207i	0.177511	+	0.307457i	0.941027	−	0.338331i	$-0.109862\pi$
$311$	3.13043	+	5.42207i	0.177511	+	0.307457i	−0.763517	+	0.645788i	$0.776529\pi$
$312$		0			0
$313$	−15.1392	−	8.74065i	−0.855721	−	0.494051i	0.00685609	−	0.999976i	$-0.497818\pi$
$313$	−15.1392	−	8.74065i	−0.855721	−	0.494051i	−0.862577	+	0.505926i	$0.831151\pi$
$314$	11.0439			0.623241
$315$		0			0
$316$	−5.46566			−0.307467
$317$	−1.32832	−	0.766906i	−0.0746058	−	0.0430737i	0.462233	−	0.886758i	$-0.347048\pi$
$317$	−1.32832	−	0.766906i	−0.0746058	−	0.0430737i	−0.536839	+	0.843685i	$0.680382\pi$
$318$		0			0
$319$	−9.43540	−	16.3426i	−0.528281	−	0.915010i
$320$		0			0
$321$		0			0
$322$	17.3163	+	6.89498i	0.965002	+	0.384242i
$323$			28.6516i			1.59422i
$324$		0			0
$325$		0			0
$326$	−6.27500	+	3.62287i	−0.347540	+	0.200652i
$327$		0			0
$328$			6.97007i			0.384858i
$329$	3.11011	+	21.3487i	0.171466	+	1.17699i
$330$		0			0
$331$	0.756607	−	1.31048i	0.0415869	−	0.0720306i	−0.844483	−	0.535583i	$-0.820092\pi$
$331$	0.756607	−	1.31048i	0.0415869	−	0.0720306i	0.886070	+	0.463552i	$0.153425\pi$
$332$	7.31483	+	12.6697i	0.401453	+	0.695337i
$333$		0			0
$334$	−12.0036	−	6.93030i	−0.656810	−	0.379209i
$335$		0			0
$336$		0			0
$337$	3.14064			0.171082			0.0855408	−	0.996335i	$-0.472738\pi$
$337$	3.14064			0.171082			0.0855408	+	0.996335i	$0.472738\pi$
$338$	10.2983	+	5.94570i	0.560152	+	0.323404i
$339$		0			0
$340$		0			0
$341$	19.9900	−	34.6236i	1.08252	−	1.87498i
$342$		0			0
$343$	7.78771	+	16.8033i	0.420497	+	0.907294i
$344$			2.58650i			0.139455i
$345$		0			0
$346$	0.830348	−	0.479402i	0.0446398	−	0.0257728i
$347$	23.7336	−	13.7026i	1.27408	−	0.735593i	0.298330	−	0.954463i	$-0.403570\pi$
$347$	23.7336	−	13.7026i	1.27408	−	0.735593i	0.975754	+	0.218870i	$0.0702370\pi$
$348$		0			0
$349$		−	19.5594i		−	1.04699i	−0.852028	−	0.523496i	$-0.824627\pi$
$349$		−	19.5594i		−	1.04699i	0.852028	−	0.523496i	$-0.175373\pi$
$350$		0			0
$351$		0			0
$352$	−3.16517	+	5.48223i	−0.168704	+	0.292204i
$353$	7.40515	+	12.8261i	0.394136	+	0.682664i	0.992991	−	0.118194i	$-0.0377105\pi$
$353$	7.40515	+	12.8261i	0.394136	+	0.682664i	−0.598854	+	0.800858i	$0.704377\pi$
$354$		0			0
$355$		0			0
$356$	3.83964			0.203500
$357$		0			0
$358$	23.3862			1.23600
$359$	−14.3492	−	8.28450i	−0.757321	−	0.437239i	0.0710122	−	0.997475i	$-0.477377\pi$
$359$	−14.3492	−	8.28450i	−0.757321	−	0.437239i	−0.828333	+	0.560236i	$0.810710\pi$
$360$		0			0
$361$	9.59086	+	16.6119i	0.504782	+	0.874308i
$362$	9.64324	−	16.7026i	0.506837	−	0.877868i
$363$		0			0
$364$	−1.03052	+	2.58809i	−0.0540138	+	0.135653i
$365$		0			0
$366$		0			0
$367$	−12.1357	+	7.00655i	−0.633479	+	0.365739i	−0.782098	−	0.623155i	$-0.785850\pi$
$367$	−12.1357	+	7.00655i	−0.633479	+	0.365739i	0.148619	+	0.988894i	$0.452517\pi$
$368$	6.10091	−	3.52236i	0.318032	−	0.183616i
$369$		0			0
$370$		0			0
$371$	8.68504	−	21.8120i	0.450905	−	1.13242i
$372$		0			0
$373$	7.31099	−	12.6630i	0.378549	−	0.655666i	−0.612303	−	0.790624i	$-0.709757\pi$
$373$	7.31099	−	12.6630i	0.378549	−	0.655666i	0.990851	+	0.134958i	$0.0430899\pi$
$374$	−14.6764	−	25.4202i	−0.758897	−	1.31445i
$375$		0			0
$376$	7.06176	+	4.07711i	0.364182	+	0.210261i
$377$	−3.13870			−0.161651
$378$		0			0
$379$	4.68145			0.240470			0.120235	−	0.992745i	$-0.461635\pi$
$379$	4.68145			0.240470			0.120235	+	0.992745i	$0.461635\pi$
$380$		0			0
$381$		0			0
$382$	1.41421	+	2.44949i	0.0723575	+	0.125327i
$383$	−5.83621	+	10.1086i	−0.298216	+	0.516526i	−0.975728	−	0.218986i	$-0.929725\pi$
$383$	−5.83621	+	10.1086i	−0.298216	+	0.516526i	0.677511	+	0.735512i	$0.263058\pi$
$384$		0			0
$385$		0			0
$386$		−	8.21725i		−	0.418247i
$387$		0			0
$388$	5.09129	−	2.93946i	0.258471	−	0.149228i
$389$	11.3452	−	6.55018i	0.575226	−	0.332107i	−0.184008	−	0.982925i	$-0.558907\pi$
$389$	11.3452	−	6.55018i	0.575226	−	0.332107i	0.759234	+	0.650818i	$0.225574\pi$
$390$		0			0
$391$			32.6652i			1.65195i
$392$	6.80879	+	1.62493i	0.343896	+	0.0820715i
$393$		0			0
$394$	1.75661	−	3.04253i	0.0884966	−	0.153281i
$395$		0			0
$396$		0			0
$397$	−26.5700	−	15.3402i	−1.33351	−	0.769903i	−0.347675	−	0.937615i	$-0.613029\pi$
$397$	−26.5700	−	15.3402i	−1.33351	−	0.769903i	−0.985836	+	0.167712i	$0.946362\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$		0			0
$401$	−6.88085	−	3.97266i	−0.343613	−	0.198385i	0.318255	−	0.948005i	$-0.396903\pi$
$401$	−6.88085	−	3.97266i	−0.343613	−	0.198385i	−0.661869	+	0.749620i	$0.730236\pi$
$402$		0			0
$403$	−3.32485	−	5.75880i	−0.165622	−	0.286866i
$404$	3.35408	−	5.80944i	0.166872	−	0.289030i
$405$		0			0
$406$	1.13699	+	7.80464i	0.0564281	+	0.387338i
$407$			22.0284i			1.09191i
$408$		0			0
$409$	−34.4957	+	19.9161i	−1.70570	+	0.984789i	−0.765975	+	0.642870i	$0.777744\pi$
$409$	−34.4957	+	19.9161i	−1.70570	+	0.984789i	−0.939729	+	0.341919i	$0.888923\pi$
$410$		0			0
$411$		0			0
$412$		−	4.97432i		−	0.245067i
$413$	−2.22354	−	0.885365i	−0.109413	−	0.0435660i
$414$		0			0
$415$		0			0
$416$	0.526449	+	0.911836i	0.0258113	+	0.0447064i
$417$		0			0
$418$	−33.8754	−	19.5580i	−1.65690	−	0.956613i
$419$	11.0357			0.539131			0.269566	−	0.962982i	$-0.413120\pi$
$419$	11.0357			0.539131			0.269566	+	0.962982i	$0.413120\pi$
$420$		0			0
$421$	−7.78421			−0.379379			−0.189690	−	0.981844i	$-0.560748\pi$
$421$	−7.78421			−0.379379			−0.189690	+	0.981844i	$0.560748\pi$
$422$	−8.63074	−	4.98296i	−0.420138	−	0.242567i
$423$		0			0
$424$	−4.43682	−	7.68480i	−0.215471	−	0.373207i
$425$		0			0
$426$		0			0
$427$	26.6353	−	3.88028i	1.28897	−	0.187780i
$428$			7.33930i			0.354759i
$429$		0			0
$430$		0			0
$431$	8.86273	−	5.11690i	0.426903	−	0.246472i	−0.271124	−	0.962545i	$-0.587395\pi$
$431$	8.86273	−	5.11690i	0.426903	−	0.246472i	0.698026	+	0.716072i	$0.254062\pi$
$432$		0			0
$433$		−	40.3902i		−	1.94103i	−0.241047	−	0.970513i	$-0.577491\pi$
$433$		−	40.3902i		−	1.94103i	0.241047	−	0.970513i	$-0.422509\pi$
$434$	−13.1153	+	10.3536i	−0.629555	+	0.496990i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	21.7651	+	37.6983i	1.04117	+	1.80336i
$438$		0			0
$439$	11.2331	+	6.48543i	0.536126	+	0.309533i	0.743508	−	0.668728i	$-0.233161\pi$
$439$	11.2331	+	6.48543i	0.536126	+	0.309533i	−0.207381	+	0.978260i	$0.566494\pi$
$440$		0			0
$441$		0			0
$442$	−4.88212			−0.232219
$443$	7.49547	+	4.32751i	0.356120	+	0.205606i	0.667378	−	0.744720i	$-0.267417\pi$
$443$	7.49547	+	4.32751i	0.356120	+	0.205606i	−0.311257	+	0.950326i	$0.600750\pi$
$444$		0			0
$445$		0			0
$446$	−5.55435	+	9.62042i	−0.263006	+	0.455540i
$447$		0			0
$448$	2.07665	−	1.63937i	0.0981124	−	0.0774529i
$449$		−	25.4407i		−	1.20062i	−0.799768	−	0.600310i	$-0.795044\pi$
$449$		−	25.4407i		−	1.20062i	0.799768	−	0.600310i	$-0.204956\pi$
$450$		0			0
$451$	38.2115	−	22.0614i	1.79931	−	1.03883i
$452$	−0.159826	+	0.0922754i	−0.00751757	+	0.00434027i
$453$		0			0
$454$			23.5238i			1.10403i
$455$		0			0
$456$		0			0
$457$	−15.2697	+	26.4480i	−0.714289	+	1.23718i	0.248945	+	0.968518i	$0.419916\pi$
$457$	−15.2697	+	26.4480i	−0.714289	+	1.23718i	−0.963233	+	0.268666i	$0.913417\pi$
$458$	4.74339	+	8.21579i	0.221644	+	0.383899i
$459$		0			0
$460$		0			0
$461$	−15.6680			−0.729734			−0.364867	−	0.931060i	$-0.618886\pi$
$461$	−15.6680			−0.729734			−0.364867	+	0.931060i	$0.618886\pi$
$462$		0			0
$463$	32.0462			1.48931			0.744656	−	0.667448i	$-0.232613\pi$
$463$	32.0462			1.48931			0.744656	+	0.667448i	$0.232613\pi$
$464$	2.58163	+	1.49051i	0.119849	+	0.0691950i
$465$		0			0
$466$	−5.18669	−	8.98361i	−0.240269	−	0.416158i
$467$	0.349579	−	0.605489i	0.0161766	−	0.0280187i	−0.857824	−	0.513944i	$-0.828184\pi$
$467$	0.349579	−	0.605489i	0.0161766	−	0.0280187i	0.874000	+	0.485925i	$0.161517\pi$
$468$		0			0
$469$	24.1682	+	9.62326i	1.11599	+	0.444361i
$470$		0			0
$471$		0			0
$472$	−0.783400	+	0.452296i	−0.0360589	+	0.0208186i
$473$	14.1798	−	8.18669i	0.651986	−	0.376424i
$474$		0			0
$475$		0			0
$476$	1.76855	+	12.1398i	0.0810611	+	0.556426i
$477$		0			0
$478$	−6.18728	+	10.7167i	−0.283000	+	0.490170i
$479$	4.27280	+	7.40071i	0.195229	+	0.338147i	0.946976	−	0.321305i	$-0.104122\pi$
$479$	4.27280	+	7.40071i	0.195229	+	0.338147i	−0.751746	+	0.659452i	$0.770788\pi$
$480$		0			0
$481$	3.17302	+	1.83195i	0.144677	+	0.0835295i
$482$	−12.4947			−0.569120
$483$		0			0
$484$	29.0731			1.32151
$485$		0			0
$486$		0			0
$487$	11.9089	+	20.6268i	0.539643	+	0.934689i	0.998923	+	0.0463978i	$0.0147742\pi$
$487$	11.9089	+	20.6268i	0.539643	+	0.934689i	−0.459280	+	0.888292i	$0.651892\pi$
$488$	5.08673	−	8.81047i	0.230265	−	0.398831i
$489$		0			0
$490$		0			0
$491$			12.9104i			0.582638i	0.956626	+	0.291319i	$0.0940941\pi$
$491$			12.9104i			0.582638i	−0.956626	+	0.291319i	$0.905906\pi$
$492$		0			0
$493$	−11.9706	+	6.91124i	−0.539129	+	0.311267i
$494$	−5.63436	+	3.25300i	−0.253502	+	0.146359i
$495$		0			0
$496$			6.31561i			0.283579i
$497$	−23.6532	−	29.9624i	−1.06099	−	1.34400i
$498$		0			0
$499$	−8.16823	+	14.1478i	−0.365660	+	0.633342i	−0.988882	−	0.148703i	$-0.952490\pi$
$499$	−8.16823	+	14.1478i	−0.365660	+	0.633342i	0.623222	+	0.782045i	$0.285823\pi$
$500$		0			0
$501$		0			0
$502$	−11.7177	−	6.76522i	−0.522987	−	0.301947i
$503$	28.3413			1.26368			0.631838	−	0.775100i	$-0.282301\pi$
$503$	28.3413			1.26368			0.631838	+	0.775100i	$0.282301\pi$
$504$		0			0
$505$		0			0
$506$	−38.6208	−	22.2977i	−1.71690	−	0.991254i
$507$		0			0
$508$	3.35138	+	5.80476i	0.148693	+	0.257545i
$509$	1.18911	−	2.05959i	0.0527062	−	0.0912898i	−0.838469	−	0.544950i	$-0.816549\pi$
$509$	1.18911	−	2.05959i	0.0527062	−	0.0912898i	0.891175	+	0.453660i	$0.149882\pi$
$510$		0			0
$511$	−8.18883	+	20.5658i	−0.362253	+	0.909776i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−3.82609	+	2.20899i	−0.168762	+	0.0974346i
$515$		0			0
$516$		0			0
$517$		−	51.6189i		−	2.27020i
$518$	3.40585	−	8.55360i	0.149645	−	0.375824i
$519$		0			0
$520$		0			0
$521$	4.14185	+	7.17389i	0.181458	+	0.314294i	0.942377	−	0.334552i	$-0.108585\pi$
$521$	4.14185	+	7.17389i	0.181458	+	0.314294i	−0.760919	+	0.648846i	$0.775252\pi$
$522$		0			0
$523$	36.2532	+	20.9308i	1.58524	+	0.915239i	0.994076	+	0.108689i	$0.0346653\pi$
$523$	36.2532	+	20.9308i	1.58524	+	0.915239i	0.591166	+	0.806550i	$0.298668\pi$
$524$	4.48232			0.195811
$525$		0			0
$526$	−6.12635			−0.267122
$527$	−25.3611	−	14.6422i	−1.10475	−	0.637826i
$528$		0			0
$529$	13.3140	+	23.0606i	0.578871	+	1.00263i
$530$		0			0
$531$		0			0
$532$	10.1299	+	12.8319i	0.439186	+	0.556333i
$533$		−	7.33877i		−	0.317877i
$534$		0			0
$535$		0			0
$536$	8.51497	−	4.91612i	0.367791	−	0.212344i
$537$		0			0
$538$			4.18740i			0.180531i
$539$	−12.6427	−	42.4705i	−0.544559	−	1.82933i
$540$		0			0
$541$	−22.9652	+	39.7769i	−0.987352	+	1.71014i	−0.356374	+	0.934343i	$0.615987\pi$
$541$	−22.9652	+	39.7769i	−0.987352	+	1.71014i	−0.630978	+	0.775801i	$0.717346\pi$
$542$	0.146469	+	0.253692i	0.00629139	+	0.0108970i
$543$		0			0
$544$	4.01562	+	2.31842i	0.172168	+	0.0994014i
$545$		0			0
$546$		0			0
$547$	4.88688			0.208948			0.104474	−	0.994528i	$-0.466684\pi$
$547$	4.88688			0.208948			0.104474	+	0.994528i	$0.466684\pi$
$548$	−15.2098	−	8.78137i	−0.649730	−	0.375122i
$549$		0			0
$550$		0			0
$551$	−9.21004	+	15.9523i	−0.392361	+	0.679589i
$552$		0			0
$553$	−2.08467	−	14.3097i	−0.0886490	−	0.608511i
$554$			14.6220i			0.621229i
$555$		0			0
$556$	5.21579	−	3.01134i	0.221199	−	0.127709i
$557$	−25.4332	+	14.6839i	−1.07764	+	0.622175i	−0.930258	−	0.366905i	$-0.880417\pi$
$557$	−25.4332	+	14.6839i	−1.07764	+	0.622175i	−0.147380	+	0.989080i	$0.547084\pi$
$558$		0			0
$559$		−	2.72332i		−	0.115184i
$560$		0			0
$561$		0			0
$562$	−9.08453	+	15.7349i	−0.383208	+	0.663735i
$563$	−1.36961	−	2.37223i	−0.0577220	−	0.0999775i	0.835720	−	0.549155i	$-0.185050\pi$
$563$	−1.36961	−	2.37223i	−0.0577220	−	0.0999775i	−0.893442	+	0.449178i	$0.851717\pi$
$564$		0			0
$565$		0			0
$566$	−21.2133			−0.891660
$567$		0			0
$568$	−14.4282			−0.605396
$569$	−0.798865	−	0.461225i	−0.0334902	−	0.0193356i	0.483161	−	0.875531i	$-0.339488\pi$
$569$	−0.798865	−	0.461225i	−0.0334902	−	0.0193356i	−0.516652	+	0.856196i	$0.672822\pi$
$570$		0			0
$571$	12.2761	+	21.2629i	0.513740	+	0.889824i	0.999873	+	0.0159389i	$0.00507372\pi$
$571$	12.2761	+	21.2629i	0.513740	+	0.889824i	−0.486133	+	0.873885i	$0.661593\pi$
$572$	3.33260	−	5.77223i	0.139343	−	0.241349i
$573$		0			0
$574$	−18.2484	+	2.65847i	−0.761675	+	0.110962i
$575$		0			0
$576$		0			0
$577$	23.4982	−	13.5667i	0.978241	−	0.564788i	0.0765024	−	0.997069i	$-0.475625\pi$
$577$	23.4982	−	13.5667i	0.978241	−	0.564788i	0.901739	+	0.432282i	$0.142291\pi$
$578$	−3.89734	+	2.25013i	−0.162108	+	0.0935932i
$579$		0			0
$580$		0			0
$581$	−30.3806	+	23.9834i	−1.26040	+	0.995000i
$582$		0			0
$583$	−28.0866	+	48.6474i	−1.16323	+	2.01477i
$584$	4.18333	+	7.24574i	0.173108	+	0.299831i
$585$		0			0
$586$	−6.62060	−	3.82240i	−0.273494	−	0.157902i
$587$	8.71353			0.359646			0.179823	−	0.983699i	$-0.442448\pi$
$587$	8.71353			0.359646			0.179823	+	0.983699i	$0.442448\pi$
$588$		0			0
$589$	−39.0250			−1.60800
$590$		0			0
$591$		0			0
$592$	−1.73991	−	3.01361i	−0.0715098	−	0.123859i
$593$	−9.13432	+	15.8211i	−0.375102	+	0.649695i	−0.990342	−	0.138644i	$-0.955726\pi$
$593$	−9.13432	+	15.8211i	−0.375102	+	0.649695i	0.615241	+	0.788339i	$0.289059\pi$
$594$		0			0
$595$		0			0
$596$			7.00381i			0.286887i
$597$		0			0
$598$	−6.42363	+	3.70868i	−0.262682	+	0.151659i
$599$	−9.94576	+	5.74219i	−0.406373	+	0.234619i	−0.689230	−	0.724543i	$-0.742051\pi$
$599$	−9.94576	+	5.74219i	−0.406373	+	0.234619i	0.282857	+	0.959162i	$0.408718\pi$
$600$		0			0
$601$		−	34.4022i		−	1.40329i	−0.712525	−	0.701647i	$-0.752448\pi$
$601$		−	34.4022i		−	1.40329i	0.712525	−	0.701647i	$-0.247552\pi$
$602$	−6.77174	+	0.986520i	−0.275996	+	0.0402076i
$603$		0			0
$604$	6.43540	−	11.1464i	0.261853	−	0.453543i
$605$		0			0
$606$		0			0
$607$	−39.4152	−	22.7564i	−1.59981	−	0.923653i	−0.991522	−	0.129941i	$-0.958521\pi$
$607$	−39.4152	−	22.7564i	−1.59981	−	0.923653i	−0.608293	−	0.793713i	$-0.708145\pi$
$608$	6.17914			0.250597
$609$		0			0
$610$		0			0
$611$	−7.43531	−	4.29278i	−0.300800	−	0.173667i
$612$		0			0
$613$	5.85205	+	10.1361i	0.236362	+	0.409391i	0.959668	−	0.281137i	$-0.0907115\pi$
$613$	5.85205	+	10.1361i	0.236362	+	0.409391i	−0.723306	+	0.690528i	$0.757378\pi$
$614$	6.57805	−	11.3935i	0.265469	−	0.459805i
$615$		0			0
$616$	−15.5603	−	6.19578i	−0.626944	−	0.249635i
$617$			24.0582i			0.968547i	0.874917	+	0.484273i	$0.160916\pi$
$617$			24.0582i			0.968547i	−0.874917	+	0.484273i	$0.839084\pi$
$618$		0			0
$619$	−3.32794	+	1.92139i	−0.133761	+	0.0772271i	−0.565387	−	0.824825i	$-0.691273\pi$
$619$	−3.32794	+	1.92139i	−0.133761	+	0.0772271i	0.431626	+	0.902053i	$0.357940\pi$
$620$		0			0
$621$		0			0
$622$			6.26087i			0.251038i
$623$	1.46448	+	10.0526i	0.0586733	+	0.402749i
$624$		0			0
$625$		0			0
$626$	−8.74065	−	15.1392i	−0.349347	−	0.605086i
$627$		0			0
$628$	9.56427	+	5.52193i	0.381656	+	0.220349i
$629$	16.1353			0.643358
$630$		0			0
$631$	−25.4387			−1.01270			−0.506349	−	0.862328i	$-0.669005\pi$
$631$	−25.4387			−1.01270			−0.506349	+	0.862328i	$0.669005\pi$
$632$	−4.73340	−	2.73283i	−0.188284	−	0.108706i
$633$		0			0
$634$	−0.766906	−	1.32832i	−0.0304577	−	0.0527543i
$635$		0			0
$636$		0			0
$637$	−7.16896	−	1.71089i	−0.284044	−	0.0677879i
$638$		−	18.8708i		−	0.747102i
$639$		0			0
$640$		0			0
$641$	−34.2380	+	19.7673i	−1.35232	+	0.780762i	−0.988574	−	0.150737i	$-0.951835\pi$
$641$	−34.2380	+	19.7673i	−1.35232	+	0.780762i	−0.363745	+	0.931499i	$0.618502\pi$
$642$		0			0
$643$		−	12.2816i		−	0.484341i	−0.970234	−	0.242170i	$-0.922141\pi$
$643$		−	12.2816i		−	0.484341i	0.970234	−	0.242170i	$-0.0778593\pi$
$644$	11.5489	+	14.6294i	0.455090	+	0.576479i
$645$		0			0
$646$	−14.3258	+	24.8131i	−0.563642	+	0.976257i
$647$	6.69470	+	11.5956i	0.263196	+	0.455869i	0.967089	−	0.254437i	$-0.0818901\pi$
$647$	6.69470	+	11.5956i	0.263196	+	0.455869i	−0.703893	+	0.710306i	$0.748557\pi$
$648$		0			0
$649$	4.95918	+	2.86319i	0.194665	+	0.112390i
$650$		0			0
$651$		0			0
$652$	−7.24574			−0.283765
$653$	−42.9355	−	24.7888i	−1.68020	−	0.970062i	−0.961527	−	0.274710i	$-0.911418\pi$
$653$	−42.9355	−	24.7888i	−1.68020	−	0.970062i	−0.718670	−	0.695352i	$-0.755249\pi$
$654$		0			0
$655$		0			0
$656$	−3.48504	+	6.03626i	−0.136068	+	0.235676i
$657$		0			0
$658$	−7.98090	+	20.0435i	−0.311128	+	0.781379i
$659$			40.7622i			1.58787i	0.608002	+	0.793936i	$0.291971\pi$
$659$			40.7622i			1.58787i	−0.608002	+	0.793936i	$0.708029\pi$
$660$		0			0
$661$	−30.9652	+	17.8778i	−1.20441	+	0.695365i	−0.961532	−	0.274692i	$-0.911424\pi$
$661$	−30.9652	+	17.8778i	−1.20441	+	0.695365i	−0.242875	+	0.970057i	$0.578091\pi$
$662$	1.31048	−	0.756607i	0.0509333	−	0.0294064i
$663$		0			0
$664$			14.6297i			0.567741i
$665$		0			0
$666$		0			0
$667$	−10.5002	+	18.1869i	−0.406569	+	0.704199i
$668$	−6.93030	−	12.0036i	−0.268141	−	0.464435i
$669$		0			0
$670$		0			0
$671$	−64.4014			−2.48619
$672$		0			0
$673$	35.1987			1.35681			0.678406	−	0.734687i	$-0.262671\pi$
$673$	35.1987			1.35681			0.678406	+	0.734687i	$0.262671\pi$
$674$	2.71987	+	1.57032i	0.104766	+	0.0604865i
$675$		0			0
$676$	5.94570	+	10.2983i	0.228681	+	0.396087i
$677$	19.2211	−	33.2919i	0.738727	−	1.27951i	−0.214341	−	0.976759i	$-0.568761\pi$
$677$	19.2211	−	33.2919i	0.738727	−	1.27951i	0.953069	−	0.302754i	$-0.0979061\pi$
$678$		0			0
$679$	9.63771	+	12.2084i	0.369862	+	0.468517i
$680$		0			0
$681$		0			0
$682$	34.6236	−	19.9900i	1.32581	−	0.765455i
$683$	33.2574	−	19.2012i	1.27256	−	0.734712i	0.297089	−	0.954850i	$-0.403984\pi$
$683$	33.2574	−	19.2012i	1.27256	−	0.734712i	0.975469	+	0.220138i	$0.0706507\pi$
$684$		0			0
$685$		0			0
$686$	−1.65731	+	18.4460i	−0.0632764	+	0.704270i
$687$		0			0
$688$	−1.29325	+	2.23997i	−0.0493046	+	0.0853981i
$689$	4.67152	+	8.09131i	0.177971	+	0.308254i
$690$		0			0
$691$	17.6209	+	10.1735i	0.670332	+	0.387016i	0.796203	−	0.605030i	$-0.206839\pi$
$691$	17.6209	+	10.1735i	0.670332	+	0.387016i	−0.125870	+	0.992047i	$0.540172\pi$
$692$	0.958803			0.0364482
$693$		0			0
$694$	27.4052			1.04029
$695$		0			0
$696$		0			0
$697$	−16.1595	−	27.9892i	−0.612086	−	1.06016i
$698$	9.77972	−	16.9390i	0.370168	−	0.641149i
$699$		0			0
$700$		0			0
$701$			6.98574i			0.263848i	0.991260	+	0.131924i	$0.0421154\pi$
$701$			6.98574i			0.263848i	−0.991260	+	0.131924i	$0.957885\pi$
$702$		0			0
$703$	18.6215	−	10.7511i	0.702323	−	0.405487i
$704$	−5.48223	+	3.16517i	−0.206619	+	0.119292i
$705$		0			0
$706$			14.8103i			0.557393i
$707$	16.4891	+	6.56558i	0.620135	+	0.246924i
$708$		0			0
$709$	6.01348	−	10.4157i	0.225841	−	0.391168i	−0.730730	−	0.682666i	$-0.760820\pi$
$709$	6.01348	−	10.4157i	0.225841	−	0.391168i	0.956571	+	0.291498i	$0.0941537\pi$
$710$		0			0
$711$		0			0
$712$	3.32522	+	1.91982i	0.124618	+	0.0719482i
$713$	−44.4917			−1.66623
$714$		0			0
$715$		0			0
$716$	20.2531	+	11.6931i	0.756893	+	0.436992i
$717$		0			0
$718$	−8.28450	−	14.3492i	−0.309175	−	0.535507i
$719$	−0.835694	+	1.44746i	−0.0311661	+	0.0539813i	−0.881188	−	0.472766i	$-0.843255\pi$
$719$	−0.835694	+	1.44746i	−0.0311661	+	0.0539813i	0.850022	+	0.526748i	$0.176589\pi$
$720$		0			0
$721$	13.0233	−	1.89727i	0.485015	−	0.0706579i
$722$			19.1817i			0.713869i
$723$		0			0
$724$	16.7026	−	9.64324i	0.620746	−	0.358388i
$725$		0			0
$726$		0			0
$727$			42.5043i			1.57640i	0.615422	+	0.788198i	$0.288986\pi$
$727$			42.5043i			1.57640i	−0.615422	+	0.788198i	$0.711014\pi$
$728$	−2.18650	+	1.72609i	−0.0810370	+	0.0639731i
$729$		0			0
$730$		0			0
$731$	−5.99658	−	10.3864i	−0.221792	−	0.384154i
$732$		0			0
$733$	−27.6053	−	15.9379i	−1.01963	−	0.588681i	−0.105630	−	0.994405i	$-0.533686\pi$
$733$	−27.6053	−	15.9379i	−1.01963	−	0.588681i	−0.913996	+	0.405724i	$0.867019\pi$
$734$	−14.0131			−0.517233
$735$		0			0
$736$	7.04472			0.259672
$737$	−53.9026	−	31.1207i	−1.98553	−	1.14634i
$738$		0			0
$739$	8.20932	+	14.2190i	0.301985	+	0.523053i	0.976585	−	0.215130i	$-0.0690176\pi$
$739$	8.20932	+	14.2190i	0.301985	+	0.523053i	−0.674601	+	0.738183i	$0.735684\pi$
$740$		0			0
$741$		0			0
$742$	18.4274	−	14.5472i	0.676493	−	0.534044i
$743$		−	4.52385i		−	0.165964i	−0.996551	−	0.0829821i	$-0.973556\pi$
$743$		−	4.52385i		−	0.165964i	0.996551	−	0.0829821i	$-0.0264444\pi$
$744$		0			0
$745$		0			0
$746$	12.6630	−	7.31099i	0.463626	−	0.267674i
$747$		0			0
$748$		−	29.3527i		−	1.07324i
$749$	−19.2151	+	2.79930i	−0.702106	+	0.102284i
$750$		0			0
$751$	8.69875	−	15.0667i	0.317422	−	0.549791i	−0.662527	−	0.749038i	$-0.730516\pi$
$751$	8.69875	−	15.0667i	0.317422	−	0.549791i	0.979949	+	0.199247i	$0.0638495\pi$
$752$	4.07711	+	7.06176i	0.148677	+	0.257516i
$753$		0			0
$754$	−2.71820	−	1.56935i	−0.0989908	−	0.0571524i
$755$		0			0
$756$		0			0
$757$	5.25454			0.190980			0.0954898	−	0.995430i	$-0.469558\pi$
$757$	5.25454			0.190980			0.0954898	+	0.995430i	$0.469558\pi$
$758$	4.05425	+	2.34072i	0.147257	+	0.0850189i
$759$		0			0
$760$		0			0
$761$	7.31402	−	12.6683i	0.265133	−	0.459224i	−0.702465	−	0.711718i	$-0.747917\pi$
$761$	7.31402	−	12.6683i	0.265133	−	0.459224i	0.967598	+	0.252494i	$0.0812508\pi$
$762$		0			0
$763$	−4.91612	−	1.95749i	−0.177975	−	0.0708659i
$764$			2.82843i			0.102329i
$765$		0			0
$766$	−10.1086	+	5.83621i	−0.365239	+	0.210871i
$767$	0.824840	−	0.476222i	0.0297832	−	0.0171954i
$768$		0			0
$769$			12.4548i			0.449131i	0.974459	+	0.224566i	$0.0720963\pi$
$769$			12.4548i			0.449131i	−0.974459	+	0.224566i	$0.927904\pi$
$770$		0			0
$771$		0			0
$772$	4.10862	−	7.11634i	0.147873	−	0.256123i
$773$	−4.15288	−	7.19300i	−0.149369	−	0.258714i	0.781626	−	0.623748i	$-0.214391\pi$
$773$	−4.15288	−	7.19300i	−0.149369	−	0.258714i	−0.930994	+	0.365034i	$0.881057\pi$
$774$		0			0
$775$		0			0
$776$	5.87891			0.211041
$777$		0			0
$778$	13.1004			0.469670
$779$	−37.2989	−	21.5345i	−1.33637	−	0.771554i
$780$		0			0
$781$	45.6678	+	79.0990i	1.63412	+	2.83038i
$782$	−16.3326	+	28.2889i	−0.584053	+	1.01161i
$783$		0			0
$784$	5.08412	+	4.81163i	0.181576	+	0.171844i
$785$		0			0
$786$		0			0
$787$	43.8271	−	25.3036i	1.56227	−	0.901975i	0.565239	−	0.824927i	$-0.308784\pi$
$787$	43.8271	−	25.3036i	1.56227	−	0.901975i	0.997027	−	0.0770479i	$-0.0245494\pi$
$788$	3.04253	−	1.75661i	0.108386	−	0.0625765i
$789$		0			0
$790$		0			0
$791$	−0.302547	−	0.383247i	−0.0107573	−	0.0136267i
$792$		0			0
$793$	−5.35580	+	9.27652i	−0.190190	+	0.329419i
$794$	−15.3402	−	26.5700i	−0.544404	−	0.942935i
$795$		0			0
$796$	3.00000	+	1.73205i	0.106332	+	0.0613909i
$797$	36.6354			1.29769			0.648846	−	0.760920i	$-0.275252\pi$
$797$	36.6354			1.29769			0.648846	+	0.760920i	$0.275252\pi$
$798$		0			0
$799$	−37.8098			−1.33761
$800$		0			0
$801$		0			0
$802$	−3.97266	−	6.88085i	−0.140280	−	0.242971i
$803$	26.4819	−	45.8680i	0.934525	−	1.61865i
$804$		0			0
$805$		0			0
$806$		−	6.64969i		−	0.234225i
$807$		0			0
$808$	5.80944	−	3.35408i	0.204375	−	0.117996i
$809$	37.7055	−	21.7693i	1.32566	−	0.765368i	0.341031	−	0.940052i	$-0.389224\pi$
$809$	37.7055	−	21.7693i	1.32566	−	0.765368i	0.984624	+	0.174685i	$0.0558906\pi$
$810$		0			0
$811$			13.8915i			0.487795i	0.969801	+	0.243897i	$0.0784260\pi$
$811$			13.8915i			0.487795i	−0.969801	+	0.243897i	$0.921574\pi$
$812$	−2.91765	+	7.32751i	−0.102390	+	0.257145i
$813$		0			0
$814$	−11.0142	+	19.0772i	−0.386048	+	0.668654i
$815$		0			0
$816$		0			0
$817$	−13.8411	−	7.99115i	−0.484238	−	0.279575i
$818$	−39.8323			−1.39270
$819$		0			0
$820$		0			0
$821$	8.26634	+	4.77257i	0.288497	+	0.166564i	0.637264	−	0.770646i	$-0.280066\pi$
$821$	8.26634	+	4.77257i	0.288497	+	0.166564i	−0.348767	+	0.937210i	$0.613399\pi$
$822$		0			0
$823$	5.39798	+	9.34957i	0.188162	+	0.325905i	0.944637	−	0.328116i	$-0.106414\pi$
$823$	5.39798	+	9.34957i	0.188162	+	0.325905i	−0.756476	+	0.654022i	$0.773080\pi$
$824$	2.48716	−	4.30789i	0.0866444	−	0.150072i
$825$		0			0
$826$	−1.48296	−	1.87852i	−0.0515988	−	0.0653621i
$827$		−	10.5599i		−	0.367204i	−0.983001	−	0.183602i	$-0.941224\pi$
$827$		−	10.5599i		−	0.367204i	0.983001	−	0.183602i	$-0.0587757\pi$
$828$		0			0
$829$	30.7288	−	17.7413i	1.06726	−	0.616181i	0.139826	−	0.990176i	$-0.455346\pi$
$829$	30.7288	−	17.7413i	1.06726	−	0.616181i	0.927431	+	0.373995i	$0.122012\pi$
$830$		0			0
$831$		0			0
$832$			1.05290i			0.0365027i
$833$	−31.1088	+	9.26051i	−1.07786	+	0.320858i
$834$		0			0
$835$		0			0
$836$	−19.5580	−	33.8754i	−0.676427	−	1.17161i
$837$		0			0
$838$	9.55723	+	5.51787i	0.330149	+	0.190612i
$839$	−32.5932			−1.12524			−0.562621	−	0.826715i	$-0.690207\pi$
$839$	−32.5932			−1.12524			−0.562621	+	0.826715i	$0.690207\pi$
$840$		0			0
$841$	20.1136			0.693571
$842$	−6.74132	−	3.89211i	−0.232321	−	0.134131i
$843$		0			0
$844$	−4.98296	−	8.63074i	−0.171521	−	0.297082i
$845$		0			0
$846$		0			0
$847$	11.0888	+	76.1168i	0.381017	+	2.61540i
$848$		−	8.87365i		−	0.304722i
$849$		0			0
$850$		0			0
$851$	21.2300	−	12.2572i	0.727756	−	0.420170i
$852$		0			0
$853$			20.2310i			0.692695i	0.938106	+	0.346347i	$0.112578\pi$
$853$			20.2310i			0.692695i	−0.938106	+	0.346347i	$0.887422\pi$
$854$	25.0070	+	9.95722i	0.855721	+	0.340729i
$855$		0			0
$856$	−3.66965	+	6.35602i	−0.125426	+	0.217244i
$857$	−22.4855	−	38.9461i	−0.768091	−	1.33037i	−0.938597	−	0.345016i	$-0.887874\pi$
$857$	−22.4855	−	38.9461i	−0.768091	−	1.33037i	0.170506	−	0.985357i	$-0.445460\pi$
$858$		0			0
$859$	37.8490	+	21.8521i	1.29139	+	0.745585i	0.978901	−	0.204336i	$-0.0655036\pi$
$859$	37.8490	+	21.8521i	1.29139	+	0.745585i	0.312490	+	0.949921i	$0.398837\pi$
$860$		0			0
$861$		0			0
$862$	10.2338			0.348565
$863$	30.8636	+	17.8191i	1.05061	+	0.606569i	0.922819	−	0.385233i	$-0.125879\pi$
$863$	30.8636	+	17.8191i	1.05061	+	0.606569i	0.127788	+	0.991801i	$0.459212\pi$
$864$		0			0
$865$		0			0
$866$	20.1951	−	34.9789i	0.686257	−	1.18863i
$867$		0			0
$868$	−16.5350	+	2.40885i	−0.561235	+	0.0817617i
$869$			34.5994i			1.17371i
$870$		0			0
$871$	−8.96539	+	5.17617i	−0.303781	+	0.175388i
$872$	−1.73205	+	1.00000i	−0.0586546	+	0.0338643i
$873$		0			0
$874$			43.5303i			1.47243i
$875$		0			0
$876$		0			0
$877$	−18.2453	+	31.6018i	−0.616100	+	1.06712i	0.374091	+	0.927392i	$0.377955\pi$
$877$	−18.2453	+	31.6018i	−0.616100	+	1.06712i	−0.990190	+	0.139724i	$0.955378\pi$
$878$	6.48543	+	11.2331i	0.218873	+	0.379099i
$879$		0			0
$880$		0			0
$881$	−0.487935			−0.0164390			−0.00821948	−	0.999966i	$-0.502616\pi$
$881$	−0.487935			−0.0164390			−0.00821948	+	0.999966i	$0.502616\pi$
$882$		0			0
$883$	6.26720			0.210908			0.105454	−	0.994424i	$-0.466370\pi$
$883$	6.26720			0.210908			0.105454	+	0.994424i	$0.466370\pi$
$884$	−4.22804	−	2.44106i	−0.142204	−	0.0821017i
$885$		0			0
$886$	4.32751	+	7.49547i	0.145386	+	0.251815i
$887$	28.4598	−	49.2939i	0.955588	−	1.65513i	0.222571	−	0.974917i	$-0.428555\pi$
$887$	28.4598	−	49.2939i	0.955588	−	1.65513i	0.733017	−	0.680210i	$-0.238112\pi$
$888$		0			0
$889$	−13.9193	+	10.9883i	−0.466838	+	0.368536i
$890$		0			0
$891$		0			0
$892$	−9.62042	+	5.55435i	−0.322115	+	0.185973i
$893$	−43.6356	+	25.1930i	−1.46021	+	0.843052i
$894$		0			0
$895$		0			0
$896$	2.61811	−	0.381412i	0.0874651	−	0.0127421i
$897$		0			0
$898$	12.7203	−	22.0323i	0.424483	−	0.735226i
$899$	−9.41346	−	16.3046i	−0.313957	−	0.543789i
$900$		0			0
$901$	35.6332	+	20.5728i	1.18711	+	0.685380i
$902$	44.1229			1.46913
$903$		0			0
$904$	−0.184551			−0.00613807
$905$		0			0
$906$		0			0
$907$	−8.33031	−	14.4285i	−0.276603	−	0.479091i	0.693935	−	0.720038i	$-0.255876\pi$
$907$	−8.33031	−	14.4285i	−0.276603	−	0.479091i	−0.970538	+	0.240946i	$0.922542\pi$
$908$	−11.7619	+	20.3722i	−0.390333	+	0.676076i
$909$		0			0
$910$		0			0
$911$		−	8.02653i		−	0.265931i	−0.991121	−	0.132965i	$-0.957550\pi$
$911$		−	8.02653i		−	0.265931i	0.991121	−	0.132965i	$-0.0424499\pi$
$912$		0			0
$913$	80.2031	−	46.3053i	2.65434	−	1.53248i
$914$	−26.4480	+	15.2697i	−0.874821	+	0.505078i
$915$		0			0
$916$			9.48678i			0.313452i
$917$	1.70961	+	11.7352i	0.0564563	+	0.387532i
$918$		0			0
$919$	6.85733	−	11.8772i	0.226202	−	0.391794i	−0.730477	−	0.682937i	$-0.760702\pi$
$919$	6.85733	−	11.8772i	0.226202	−	0.391794i	0.956680	+	0.291143i	$0.0940356\pi$
$920$		0			0
$921$		0			0
$922$	−13.5689	−	7.83402i	−0.446869	−	0.258000i
$923$	15.1915			0.500033
$924$		0			0
$925$		0			0
$926$	27.7528	+	16.0231i	0.912014	+	0.526551i
$927$		0			0
$928$	1.49051	+	2.58163i	0.0489283	+	0.0847463i
$929$	−22.9480	+	39.7470i	−0.752898	+	1.30406i	0.193515	+	0.981097i	$0.438011\pi$
$929$	−22.9480	+	39.7470i	−0.752898	+	1.30406i	−0.946413	+	0.322960i	$0.895322\pi$
$930$		0			0
$931$	−29.7317	+	31.4154i	−0.974417	+	1.02960i
$932$		−	10.3734i		−	0.339791i
$933$		0			0
$934$	0.605489	−	0.349579i	0.0198122	−	0.0114386i
$935$		0			0
$936$		0			0
$937$			6.17552i			0.201746i	0.994899	+	0.100873i	$0.0321635\pi$
$937$			6.17552i			0.201746i	−0.994899	+	0.100873i	$0.967836\pi$
$938$	16.1187	+	20.4181i	0.526293	+	0.666675i
$939$		0			0
$940$		0			0
$941$	−16.7048	−	28.9335i	−0.544560	−	0.943206i	−0.998634	−	0.0522424i	$-0.983363\pi$
$941$	−16.7048	−	28.9335i	−0.544560	−	0.943206i	0.454074	−	0.890964i	$-0.349970\pi$
$942$		0			0
$943$	−42.5237	−	24.5511i	−1.38476	−	0.799494i
$944$	−0.904592			−0.0294420
$945$		0			0
$946$	16.3734			0.532345
$947$	−5.67563	−	3.27683i	−0.184433	−	0.106483i	0.404941	−	0.914343i	$-0.367292\pi$
$947$	−5.67563	−	3.27683i	−0.184433	−	0.106483i	−0.589374	+	0.807860i	$0.700625\pi$
$948$		0			0
$949$	−4.40462	−	7.62903i	−0.142980	−	0.247649i
$950$		0			0
$951$		0			0
$952$	−4.53828	+	11.3976i	−0.147087	+	0.369399i
$953$		−	46.5253i		−	1.50710i	−0.657389	−	0.753551i	$-0.728339\pi$
$953$		−	46.5253i		−	1.50710i	0.657389	−	0.753551i	$-0.271661\pi$
$954$		0			0
$955$		0			0
$956$	−10.7167	+	6.18728i	−0.346602	+	0.200111i
$957$		0			0
$958$			8.54561i			0.276096i
$959$	17.1894	−	43.1703i	0.555076	−	1.39404i
$960$		0			0
$961$	4.44349	−	7.69635i	0.143338	−	0.248269i
$962$	1.83195	+	3.17302i	0.0590643	+	0.102302i
$963$		0			0
$964$	−10.8208	−	6.24737i	−0.348514	−	0.201214i
$965$		0			0
$966$		0			0
$967$	5.93169			0.190750			0.0953752	−	0.995441i	$-0.469595\pi$
$967$	5.93169			0.190750			0.0953752	+	0.995441i	$0.469595\pi$
$968$	25.1781	+	14.5366i	0.809253	+	0.467223i
$969$		0			0
$970$		0			0
$971$	−0.170069	+	0.294568i	−0.00545777	+	0.00945314i	−0.868741	−	0.495266i	$-0.835071\pi$
$971$	−0.170069	+	0.294568i	−0.00545777	+	0.00945314i	0.863284	+	0.504719i	$0.168404\pi$
$972$		0			0
$973$	9.87339	+	12.5070i	0.316526	+	0.400955i
$974$			23.8178i			0.763171i
$975$		0			0
$976$	8.81047	−	5.08673i	0.282016	−	0.162822i
$977$	17.9168	−	10.3443i	0.573210	−	0.330943i	−0.185220	−	0.982697i	$-0.559300\pi$
$977$	17.9168	−	10.3443i	0.573210	−	0.330943i	0.758430	+	0.651754i	$0.225967\pi$
$978$		0			0
$979$		−	24.3062i		−	0.776829i
$980$		0			0
$981$		0			0
$982$	−6.45520	+	11.1807i	−0.205994	+	0.356791i
$983$	10.6129	+	18.3821i	0.338499	+	0.586297i	0.984151	−	0.177335i	$-0.0567476\pi$
$983$	10.6129	+	18.3821i	0.338499	+	0.586297i	−0.645652	+	0.763632i	$0.723414\pi$
$984$		0			0
$985$		0			0
$986$	−13.8225			−0.440197
$987$		0			0
$988$	−6.50600			−0.206983
$989$	−15.7800	−	9.11057i	−0.501774	−	0.289699i
$990$		0			0
$991$	−29.1034	−	50.4085i	−0.924499	−	1.60128i	−0.792365	−	0.610048i	$-0.791150\pi$
$991$	−29.1034	−	50.4085i	−0.924499	−	1.60128i	−0.132134	−	0.991232i	$-0.542183\pi$
$992$	−3.15781	+	5.46948i	−0.100260	+	0.173656i
$993$		0			0
$994$	−5.50310	−	37.7748i	−0.174548	−	1.19814i
$995$		0			0
$996$		0			0
$997$	33.1542	−	19.1416i	1.05000	−	0.606220i	0.127354	−	0.991857i	$-0.459352\pi$
$997$	33.1542	−	19.1416i	1.05000	−	0.606220i	0.922651	+	0.385637i	$0.126018\pi$
$998$	−14.1478	+	8.16823i	−0.447841	+	0.258561i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.f.1601.15		32
3.2	odd	2	inner	3150.2.bf.f.1601.3		32
5.2	odd	4		630.2.bo.a.89.6	✓	16
5.3	odd	4		630.2.bo.b.89.1	yes	16
5.4	even	2	inner	3150.2.bf.f.1601.4		32
7.3	odd	6	inner	3150.2.bf.f.1151.3		32
15.2	even	4		630.2.bo.b.89.3	yes	16
15.8	even	4		630.2.bo.a.89.8	yes	16
15.14	odd	2	inner	3150.2.bf.f.1601.16		32
21.17	even	6	inner	3150.2.bf.f.1151.13		32
35.2	odd	12		4410.2.d.b.4409.11		16
35.3	even	12		630.2.bo.b.269.3	yes	16
35.12	even	12		4410.2.d.b.4409.6		16
35.17	even	12		630.2.bo.a.269.8	yes	16
35.23	odd	12		4410.2.d.a.4409.12		16
35.24	odd	6	inner	3150.2.bf.f.1151.14		32
35.33	even	12		4410.2.d.a.4409.5		16
105.2	even	12		4410.2.d.a.4409.6		16
105.17	odd	12		630.2.bo.b.269.1	yes	16
105.23	even	12		4410.2.d.b.4409.5		16
105.38	odd	12		630.2.bo.a.269.6	yes	16
105.47	odd	12		4410.2.d.a.4409.11		16
105.59	even	6	inner	3150.2.bf.f.1151.4		32
105.68	odd	12		4410.2.d.b.4409.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.6	✓	16	5.2	odd	4
630.2.bo.a.89.8	yes	16	15.8	even	4
630.2.bo.a.269.6	yes	16	105.38	odd	12
630.2.bo.a.269.8	yes	16	35.17	even	12
630.2.bo.b.89.1	yes	16	5.3	odd	4
630.2.bo.b.89.3	yes	16	15.2	even	4
630.2.bo.b.269.1	yes	16	105.17	odd	12
630.2.bo.b.269.3	yes	16	35.3	even	12
3150.2.bf.f.1151.3		32	7.3	odd	6	inner
3150.2.bf.f.1151.4		32	105.59	even	6	inner
3150.2.bf.f.1151.13		32	21.17	even	6	inner
3150.2.bf.f.1151.14		32	35.24	odd	6	inner
3150.2.bf.f.1601.3		32	3.2	odd	2	inner
3150.2.bf.f.1601.4		32	5.4	even	2	inner
3150.2.bf.f.1601.15		32	1.1	even	1	trivial
3150.2.bf.f.1601.16		32	15.14	odd	2	inner
4410.2.d.a.4409.5		16	35.33	even	12
4410.2.d.a.4409.6		16	105.2	even	12
4410.2.d.a.4409.11		16	105.47	odd	12
4410.2.d.a.4409.12		16	35.23	odd	12
4410.2.d.b.4409.5		16	105.23	even	12
4410.2.d.b.4409.6		16	35.12	even	12
4410.2.d.b.4409.11		16	35.2	odd	12
4410.2.d.b.4409.12		16	105.68	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.07665 + 1.63937i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.07665 + 1.63937i) q^{7} +1.00000i q^{8} +(5.48223 - 3.16517i) q^{11} -1.05290i q^{13} +(-2.61811 + 0.381412i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.31842 - 4.01562i) q^{17} +(-5.35129 - 3.08957i) q^{19} +6.33033 q^{22} +(-6.10091 - 3.52236i) q^{23} +(0.526449 - 0.911836i) q^{26} +(-2.45806 - 0.978745i) q^{28} -2.98101i q^{29} +(5.46948 - 3.15781i) q^{31} +(-0.866025 + 0.500000i) q^{32} -4.63684i q^{34} +(-1.73991 + 3.01361i) q^{37} +(-3.08957 - 5.35129i) q^{38} +6.97007 q^{41} +2.58650 q^{43} +(5.48223 + 3.16517i) q^{44} +(-3.52236 - 6.10091i) q^{46} +(4.07711 - 7.06176i) q^{47} +(1.62493 - 6.80879i) q^{49} +(0.911836 - 0.526449i) q^{52} +(-7.68480 + 4.43682i) q^{53} +(-1.63937 - 2.07665i) q^{56} +(1.49051 - 2.58163i) q^{58} +(0.452296 + 0.783400i) q^{59} +(-8.81047 - 5.08673i) q^{61} +6.31561 q^{62} -1.00000 q^{64} +(-4.91612 - 8.51497i) q^{67} +(2.31842 - 4.01562i) q^{68} +14.4282i q^{71} +(7.24574 - 4.18333i) q^{73} +(-3.01361 + 1.73991i) q^{74} -6.17914i q^{76} +(-6.19578 + 15.5603i) q^{77} +(-2.73283 + 4.73340i) q^{79} +(6.03626 + 3.48504i) q^{82} +14.6297 q^{83} +(2.23997 + 1.29325i) q^{86} +(3.16517 + 5.48223i) q^{88} +(1.91982 - 3.32522i) q^{89} +(1.72609 + 2.18650i) q^{91} -7.04472i q^{92} +(7.06176 - 4.07711i) q^{94} -5.87891i q^{97} +(4.81163 - 5.08412i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Introduction

L-functions

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Database

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