LMFDB - Embedded newform 1184.2.y.a.529.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(529,1184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1184.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.21
Character	$\chi$	$=$	1184.529
Dual form			1184.2.y.a.1137.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.576079 + 0.332599i) q^{3} +(-1.60874 + 2.78642i) q^{5} +(0.874135 - 1.51405i) q^{7} +(-1.27876 - 2.21487i) q^{9} -3.96429i q^{11} +(0.268480 - 0.465021i) q^{13} +(-1.85352 + 1.07013i) q^{15} +(6.04097 - 3.48776i) q^{17} +(-2.21841 + 3.84239i) q^{19} +(1.00714 - 0.581474i) q^{21} -2.14898i q^{23} +(-2.67607 - 4.63509i) q^{25} -3.69685i q^{27} +3.76282 q^{29} -1.95692i q^{31} +(1.31852 - 2.28375i) q^{33} +(2.81251 + 4.87141i) q^{35} +(0.0791047 - 6.08225i) q^{37} +(0.309331 - 0.178593i) q^{39} +(1.70672 - 2.95613i) q^{41} +7.07866 q^{43} +8.22873 q^{45} -8.02359 q^{47} +(1.97178 + 3.41521i) q^{49} +4.64010 q^{51} +(0.341615 - 0.197231i) q^{53} +(11.0462 + 6.37751i) q^{55} +(-2.55596 + 1.47568i) q^{57} +(4.26642 + 7.38966i) q^{59} +(0.607843 - 1.05282i) q^{61} -4.47122 q^{63} +(0.863828 + 1.49619i) q^{65} +(7.25109 + 4.18642i) q^{67} +(0.714748 - 1.23798i) q^{69} +(2.54377 - 4.40594i) q^{71} +2.30870 q^{73} -3.56024i q^{75} +(-6.00212 - 3.46533i) q^{77} +(2.04786 + 1.18233i) q^{79} +(-2.60670 + 4.51493i) q^{81} +(-1.40655 + 0.812073i) q^{83} +22.4435i q^{85} +(2.16768 + 1.25151i) q^{87} +(13.0089 - 7.51069i) q^{89} +(-0.469376 - 0.812982i) q^{91} +(0.650872 - 1.12734i) q^{93} +(-7.13767 - 12.3628i) q^{95} -16.7828i q^{97} +(-8.78039 + 5.06936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) $ 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	0.576079	+	0.332599i	0.332599	+	0.192026i	0.656995	−	0.753895i	$-0.271827\pi$
$3$	0.576079	+	0.332599i	0.332599	+	0.192026i	−0.324395	+	0.945922i	$0.605161\pi$
$4$		0			0
$5$	−1.60874	+	2.78642i	−0.719449	+	1.24612i	0.241769	+	0.970334i	$0.422272\pi$
$5$	−1.60874	+	2.78642i	−0.719449	+	1.24612i	−0.961218	+	0.275789i	$0.911061\pi$
$6$		0			0
$7$	0.874135	−	1.51405i	0.330392	−	0.572256i	−0.652197	−	0.758050i	$-0.726152\pi$
$7$	0.874135	−	1.51405i	0.330392	−	0.572256i	0.982589	+	0.185794i	$0.0594857\pi$
$8$		0			0
$9$	−1.27876	−	2.21487i	−0.426252	−	0.738290i
$10$		0			0
$11$		−	3.96429i		−	1.19528i	−0.801765	−	0.597640i	$-0.796105\pi$
$11$		−	3.96429i		−	1.19528i	0.801765	−	0.597640i	$-0.203895\pi$
$12$		0			0
$13$	0.268480	−	0.465021i	0.0744630	−	0.128974i	−0.826390	−	0.563099i	$-0.809609\pi$
$13$	0.268480	−	0.465021i	0.0744630	−	0.128974i	0.900853	+	0.434125i	$0.142942\pi$
$14$		0			0
$15$	−1.85352	+	1.07013i	−0.478577	+	0.276306i
$16$		0			0
$17$	6.04097	−	3.48776i	1.46515	−	0.845905i	0.465908	−	0.884833i	$-0.345728\pi$
$17$	6.04097	−	3.48776i	1.46515	−	0.845905i	0.999242	+	0.0389282i	$0.0123943\pi$
$18$		0			0
$19$	−2.21841	+	3.84239i	−0.508938	+	0.881506i	0.491009	+	0.871155i	$0.336628\pi$
$19$	−2.21841	+	3.84239i	−0.508938	+	0.881506i	−0.999946	+	0.0103511i	$0.996705\pi$
$20$		0			0
$21$	1.00714	−	0.581474i	0.219776	−	0.126888i
$22$		0			0
$23$		−	2.14898i		−	0.448093i	−0.974579	−	0.224046i	$-0.928073\pi$
$23$		−	2.14898i		−	0.448093i	0.974579	−	0.224046i	$-0.0719267\pi$
$24$		0			0
$25$	−2.67607	−	4.63509i	−0.535215	−	0.927019i
$26$		0			0
$27$		−	3.69685i		−	0.711459i
$28$		0			0
$29$	3.76282			0.698739			0.349369	−	0.936985i	$-0.386396\pi$
$29$	3.76282			0.698739			0.349369	+	0.936985i	$0.386396\pi$
$30$		0			0
$31$		−	1.95692i		−	0.351474i	−0.984437	−	0.175737i	$-0.943769\pi$
$31$		−	1.95692i		−	0.351474i	0.984437	−	0.175737i	$-0.0562308\pi$
$32$		0			0
$33$	1.31852	−	2.28375i	0.229525	−	0.397549i
$34$		0			0
$35$	2.81251	+	4.87141i	0.475401	+	0.823418i
$36$		0			0
$37$	0.0791047	−	6.08225i	0.0130047	−	0.999915i
$37$	0.0791047	−	6.08225i	0.0130047	−	0.999915i
$38$		0			0
$39$	0.309331	−	0.178593i	0.0495327	−	0.0285977i
$40$		0			0
$41$	1.70672	−	2.95613i	0.266545	−	0.461670i	−0.701422	−	0.712746i	$-0.747451\pi$
$41$	1.70672	−	2.95613i	0.266545	−	0.461670i	0.967967	+	0.251076i	$0.0807846\pi$
$42$		0			0
$43$	7.07866			1.07949			0.539743	−	0.841830i	$-0.318521\pi$
$43$	7.07866			1.07949			0.539743	+	0.841830i	$0.318521\pi$
$44$		0			0
$45$	8.22873			1.22667
$46$		0			0
$47$	−8.02359			−1.17036			−0.585180	−	0.810903i	$-0.698976\pi$
$47$	−8.02359			−1.17036			−0.585180	+	0.810903i	$0.698976\pi$
$48$		0			0
$49$	1.97178	+	3.41521i	0.281682	+	0.487888i
$50$		0			0
$51$	4.64010			0.649744
$52$		0			0
$53$	0.341615	−	0.197231i	0.0469244	−	0.0270918i	−0.476354	−	0.879253i	$-0.658042\pi$
$53$	0.341615	−	0.197231i	0.0469244	−	0.0270918i	0.523279	+	0.852162i	$0.324709\pi$
$54$		0			0
$55$	11.0462	+	6.37751i	1.48946	+	0.859943i
$56$		0			0
$57$	−2.55596	+	1.47568i	−0.338545	+	0.195459i
$58$		0			0
$59$	4.26642	+	7.38966i	0.555441	+	0.962051i	0.997869	+	0.0652477i	$0.0207837\pi$
$59$	4.26642	+	7.38966i	0.555441	+	0.962051i	−0.442428	+	0.896804i	$0.645883\pi$
$60$		0			0
$61$	0.607843	−	1.05282i	0.0778263	−	0.134799i	−0.824486	−	0.565883i	$-0.808535\pi$
$61$	0.607843	−	1.05282i	0.0778263	−	0.134799i	0.902312	+	0.431084i	$0.141869\pi$
$62$		0			0
$63$	−4.47122			−0.563321
$64$		0			0
$65$	0.863828	+	1.49619i	0.107145	+	0.185580i
$66$		0			0
$67$	7.25109	+	4.18642i	0.885861	+	0.511452i	0.872587	−	0.488460i	$-0.162441\pi$
$67$	7.25109	+	4.18642i	0.885861	+	0.511452i	0.0132749	+	0.999912i	$0.495774\pi$
$68$		0			0
$69$	0.714748	−	1.23798i	0.0860456	−	0.149035i
$70$		0			0
$71$	2.54377	−	4.40594i	0.301890	−	0.522889i	−0.674674	−	0.738116i	$-0.735716\pi$
$71$	2.54377	−	4.40594i	0.301890	−	0.522889i	0.976564	+	0.215227i	$0.0690490\pi$
$72$		0			0
$73$	2.30870			0.270213			0.135107	−	0.990831i	$-0.456862\pi$
$73$	2.30870			0.270213			0.135107	+	0.990831i	$0.456862\pi$
$74$		0			0
$75$		−	3.56024i		−	0.411101i
$76$		0			0
$77$	−6.00212	−	3.46533i	−0.684005	−	0.394911i
$78$		0			0
$79$	2.04786	+	1.18233i	0.230402	+	0.133023i	0.610758	−	0.791818i	$-0.290865\pi$
$79$	2.04786	+	1.18233i	0.230402	+	0.133023i	−0.380355	+	0.924840i	$0.624198\pi$
$80$		0			0
$81$	−2.60670	+	4.51493i	−0.289633	+	0.501659i
$82$		0			0
$83$	−1.40655	+	0.812073i	−0.154389	+	0.0891366i	−0.575204	−	0.818010i	$-0.695077\pi$
$83$	−1.40655	+	0.812073i	−0.154389	+	0.0891366i	0.420815	+	0.907146i	$0.361744\pi$
$84$		0			0
$85$			22.4435i			2.43434i
$86$		0			0
$87$	2.16768	+	1.25151i	0.232400	+	0.134176i
$88$		0			0
$89$	13.0089	−	7.51069i	1.37894	−	0.796132i	0.386909	−	0.922118i	$-0.373543\pi$
$89$	13.0089	−	7.51069i	1.37894	−	0.796132i	0.992032	+	0.125986i	$0.0402094\pi$
$90$		0			0
$91$	−0.469376	−	0.812982i	−0.0492039	−	0.0852237i
$92$		0			0
$93$	0.650872	−	1.12734i	0.0674923	−	0.116900i
$94$		0			0
$95$	−7.13767	−	12.3628i	−0.732309	−	1.26840i
$96$		0			0
$97$		−	16.7828i		−	1.70404i	−0.523510	−	0.852019i	$-0.675378\pi$
$97$		−	16.7828i		−	1.70404i	0.523510	−	0.852019i	$-0.324622\pi$
$98$		0			0
$99$	−8.78039	+	5.06936i	−0.882462	+	0.509490i
$100$		0			0
$101$		−	9.43561i		−	0.938879i	−0.882965	−	0.469439i	$-0.844456\pi$
$101$		−	9.43561i		−	0.938879i	0.882965	−	0.469439i	$-0.155544\pi$
$102$		0			0
$103$		−	19.4350i		−	1.91499i	−0.288452	−	0.957494i	$-0.593141\pi$
$103$		−	19.4350i		−	1.91499i	0.288452	−	0.957494i	$-0.406859\pi$
$104$		0			0
$105$			3.74175i			0.365158i
$106$		0			0
$107$	−14.8325	−	8.56353i	−1.43391	−	0.827867i	−0.436492	−	0.899708i	$-0.643779\pi$
$107$	−14.8325	−	8.56353i	−1.43391	−	0.827867i	−0.997416	+	0.0718408i	$0.977113\pi$
$108$		0			0
$109$	6.06885	+	10.5116i	0.581291	+	1.00683i	0.995327	+	0.0965646i	$0.0307854\pi$
$109$	6.06885	+	10.5116i	0.581291	+	1.00683i	−0.414036	+	0.910261i	$0.635881\pi$
$110$		0			0
$111$	2.06852	−	3.47754i	0.196335	−	0.330074i
$112$		0			0
$113$	−17.7214	+	10.2315i	−1.66709	+	0.962496i	−0.697899	+	0.716196i	$0.745881\pi$
$113$	−17.7214	+	10.2315i	−1.66709	+	0.962496i	−0.969194	+	0.246300i	$0.920785\pi$
$114$		0			0
$115$	5.98794	+	3.45714i	0.558378	+	0.322380i
$116$		0			0
$117$	−1.37328			−0.126960
$118$		0			0
$119$		−	12.1951i		−	1.11792i
$120$		0			0
$121$	−4.71561			−0.428692
$122$		0			0
$123$	1.96641	−	1.13531i	0.177305	−	0.102367i
$124$		0			0
$125$	1.13302			0.101340
$126$		0			0
$127$	10.1083	+	17.5081i	0.896966	+	1.55359i	0.831352	+	0.555746i	$0.187567\pi$
$127$	10.1083	+	17.5081i	0.896966	+	1.55359i	0.0656145	+	0.997845i	$0.479099\pi$
$128$		0			0
$129$	4.07787	+	2.35436i	0.359036	+	0.207290i
$130$		0			0
$131$	−10.5939	−	18.3492i	−0.925595	−	1.60318i	−0.790601	−	0.612332i	$-0.790232\pi$
$131$	−10.5939	−	18.3492i	−0.925595	−	1.60318i	−0.134995	−	0.990846i	$-0.543102\pi$
$132$		0			0
$133$	3.87838	+	6.71754i	0.336298	+	0.582485i
$134$		0			0
$135$	10.3010	+	5.94726i	0.886565	+	0.511859i
$136$		0			0
$137$	−13.9717			−1.19368			−0.596842	−	0.802359i	$-0.703578\pi$
$137$	−13.9717			−1.19368			−0.596842	+	0.802359i	$0.703578\pi$
$138$		0			0
$139$	−5.37160	+	3.10130i	−0.455613	+	0.263048i	−0.710198	−	0.704002i	$-0.751395\pi$
$139$	−5.37160	+	3.10130i	−0.455613	+	0.263048i	0.254585	+	0.967050i	$0.418061\pi$
$140$		0			0
$141$	−4.62222	−	2.66864i	−0.389261	−	0.224740i
$142$		0			0
$143$	−1.84348	−	1.06433i	−0.154159	−	0.0890040i
$144$		0			0
$145$	−6.05340	+	10.4848i	−0.502707	+	0.870714i
$146$		0			0
$147$			2.62324i			0.216362i
$148$		0			0
$149$		−	18.5130i		−	1.51664i	−0.651882	−	0.758321i	$-0.726020\pi$
$149$		−	18.5130i		−	1.51664i	0.651882	−	0.758321i	$-0.273980\pi$
$150$		0			0
$151$	−4.09172	+	7.08706i	−0.332979	+	0.576737i	−0.983095	−	0.183099i	$-0.941387\pi$
$151$	−4.09172	+	7.08706i	−0.332979	+	0.576737i	0.650115	+	0.759835i	$0.274721\pi$
$152$		0			0
$153$	−15.4498	−	8.91997i	−1.24905	−	0.721137i
$154$		0			0
$155$	5.45280	+	3.14818i	0.437980	+	0.252868i
$156$		0			0
$157$	−10.6805	+	6.16641i	−0.852400	+	0.492133i	−0.861460	−	0.507826i	$-0.830449\pi$
$157$	−10.6805	+	6.16641i	−0.852400	+	0.492133i	0.00906013	+	0.999959i	$0.497116\pi$
$158$		0			0
$159$	0.262396			0.0208094
$160$		0			0
$161$	−3.25365	−	1.87850i	−0.256424	−	0.148046i
$162$		0			0
$163$	3.15252	+	5.46032i	0.246924	+	0.427685i	0.962671	−	0.270675i	$-0.0872468\pi$
$163$	3.15252	+	5.46032i	0.246924	+	0.427685i	−0.715747	+	0.698360i	$0.753913\pi$
$164$		0			0
$165$	4.24231	+	7.34789i	0.330263	+	0.572033i
$166$		0			0
$167$	8.91537	+	5.14729i	0.689892	+	0.398309i	0.803572	−	0.595208i	$-0.202930\pi$
$167$	8.91537	+	5.14729i	0.689892	+	0.398309i	−0.113680	+	0.993517i	$0.536264\pi$
$168$		0			0
$169$	6.35584	+	11.0086i	0.488911	+	0.846818i
$170$		0			0
$171$	11.3472			0.867742
$172$		0			0
$173$	0.0102715	−	0.00593025i	0.000780928	−	0.000450869i	−0.499609	−	0.866251i	$-0.666523\pi$
$173$	0.0102715	−	0.00593025i	0.000780928	−	0.000450869i	0.500390	+	0.865800i	$0.333190\pi$
$174$		0			0
$175$	−9.35700			−0.707323
$176$		0			0
$177$			5.67603i			0.426637i
$178$		0			0
$179$	−6.51910			−0.487260			−0.243630	−	0.969868i	$-0.578338\pi$
$179$	−6.51910			−0.487260			−0.243630	+	0.969868i	$0.578338\pi$
$180$		0			0
$181$	−10.1065	−	5.83497i	−0.751207	−	0.433710i	0.0749228	−	0.997189i	$-0.476129\pi$
$181$	−10.1065	−	5.83497i	−0.751207	−	0.433710i	−0.826130	+	0.563480i	$0.809462\pi$
$182$		0			0
$183$	0.700331	−	0.404336i	0.0517700	−	0.0298894i
$184$		0			0
$185$	16.8204	+	10.0052i	1.23666	+	0.735594i
$186$		0			0
$187$	−13.8265	−	23.9482i	−1.01109	−	1.75126i
$188$		0			0
$189$	−5.59720	−	3.23155i	−0.407136	−	0.235060i
$190$		0			0
$191$		−	8.67149i		−	0.627447i	−0.949514	−	0.313724i	$-0.898423\pi$
$191$		−	8.67149i		−	0.627447i	0.949514	−	0.313724i	$-0.101577\pi$
$192$		0			0
$193$		−	0.312961i		−	0.0225274i	−0.999937	−	0.0112637i	$-0.996415\pi$
$193$		−	0.312961i		−	0.0225274i	0.999937	−	0.0112637i	$-0.00358542\pi$
$194$		0			0
$195$			1.14923i			0.0822984i
$196$		0			0
$197$	4.59066	−	2.65042i	0.327071	−	0.188834i	−0.327469	−	0.944862i	$-0.606196\pi$
$197$	4.59066	−	2.65042i	0.327071	−	0.188834i	0.654540	+	0.756027i	$0.272862\pi$
$198$		0			0
$199$			1.44071i			0.102129i	0.998695	+	0.0510647i	$0.0162615\pi$
$199$			1.44071i			0.102129i	−0.998695	+	0.0510647i	$0.983739\pi$
$200$		0			0
$201$	2.78480	+	4.82341i	0.196425	+	0.340217i
$202$		0			0
$203$	3.28922	−	5.69709i	0.230858	−	0.399857i
$204$		0			0
$205$	5.49133	+	9.51127i	0.383531	+	0.664296i
$206$		0			0
$207$	−4.75970	+	2.74802i	−0.330822	+	0.191000i
$208$		0			0
$209$	15.2324	+	8.79442i	1.05365	+	0.608322i
$210$		0			0
$211$			15.6762i			1.07920i	0.841923	+	0.539598i	$0.181424\pi$
$211$			15.6762i			1.07920i	−0.841923	+	0.539598i	$0.818576\pi$
$212$		0			0
$213$	2.93083	−	1.69211i	0.200817	−	0.115942i
$214$		0			0
$215$	−11.3877	+	19.7241i	−0.776635	+	1.34517i
$216$		0			0
$217$	−2.96288	−	1.71062i	−0.201133	−	0.116124i
$218$		0			0
$219$	1.32999	+	0.767873i	0.0898727	+	0.0518880i
$220$		0			0
$221$		−	3.74557i		−	0.251954i
$222$		0			0
$223$	28.4767			1.90694			0.953470	−	0.301489i	$-0.0974835\pi$
$223$	28.4767			1.90694			0.953470	+	0.301489i	$0.0974835\pi$
$224$		0			0
$225$	−6.84408	+	11.8543i	−0.456272	+	0.790287i
$226$		0			0
$227$	−3.36734	+	5.83241i	−0.223499	+	0.387111i	−0.955868	−	0.293797i	$-0.905081\pi$
$227$	−3.36734	+	5.83241i	−0.223499	+	0.387111i	0.732369	+	0.680908i	$0.238414\pi$
$228$		0			0
$229$	1.22233	+	0.705713i	0.0807739	+	0.0466348i	0.539843	−	0.841766i	$-0.318484\pi$
$229$	1.22233	+	0.705713i	0.0807739	+	0.0466348i	−0.459069	+	0.888401i	$0.651817\pi$
$230$		0			0
$231$	−2.30513	−	3.99260i	−0.151667	−	0.262694i
$232$		0			0
$233$	14.9990			0.982614			0.491307	−	0.870986i	$-0.336519\pi$
$233$	14.9990			0.982614			0.491307	+	0.870986i	$0.336519\pi$
$234$		0			0
$235$	12.9078	−	22.3570i	0.842015	−	1.45841i
$236$		0			0
$237$	0.786486	+	1.36223i	0.0510878	+	0.0884866i
$238$		0			0
$239$	−16.6264	+	9.59926i	−1.07547	+	0.620925i	−0.929672	−	0.368389i	$-0.879909\pi$
$239$	−16.6264	+	9.59926i	−1.07547	+	0.620925i	−0.145802	+	0.989314i	$0.546576\pi$
$240$		0			0
$241$	−4.33365	−	2.50203i	−0.279155	−	0.161170i	0.353886	−	0.935289i	$-0.384860\pi$
$241$	−4.33365	−	2.50203i	−0.279155	−	0.161170i	−0.633041	+	0.774119i	$0.718193\pi$
$242$		0			0
$243$	−12.6080	+	7.27924i	−0.808805	+	0.466964i
$244$		0			0
$245$	−12.6883			−0.810624
$246$		0			0
$247$	1.19120	+	2.06321i	0.0757940	+	0.131279i
$248$		0			0
$249$	−1.08038			−0.0684663
$250$		0			0
$251$	3.82856			0.241657			0.120828	−	0.992673i	$-0.461445\pi$
$251$	3.82856			0.241657			0.120828	+	0.992673i	$0.461445\pi$
$252$		0			0
$253$	−8.51917			−0.535596
$254$		0			0
$255$	−7.46470	+	12.9292i	−0.467458	+	0.809661i
$256$		0			0
$257$	0.934828	−	0.539723i	0.0583130	−	0.0336670i	−0.470560	−	0.882368i	$-0.655948\pi$
$257$	0.934828	−	0.539723i	0.0583130	−	0.0336670i	0.528873	+	0.848701i	$0.322615\pi$
$258$		0			0
$259$	−9.13966	−	5.43648i	−0.567911	−	0.337806i
$260$		0			0
$261$	−4.81173	−	8.33416i	−0.297839	−	0.515872i
$262$		0			0
$263$	−9.10932	+	15.7778i	−0.561705	+	0.972901i	0.435643	+	0.900119i	$0.356521\pi$
$263$	−9.10932	+	15.7778i	−0.561705	+	0.972901i	−0.997348	+	0.0727817i	$0.976812\pi$
$264$		0			0
$265$			1.26917i			0.0779648i
$266$		0			0
$267$	9.99221			0.611513
$268$		0			0
$269$		−	27.2251i		−	1.65994i	−0.557806	−	0.829971i	$-0.688357\pi$
$269$		−	27.2251i		−	1.65994i	0.557806	−	0.829971i	$-0.311643\pi$
$270$		0			0
$271$	12.7826	+	22.1402i	0.776489	+	1.34492i	0.933954	+	0.357394i	$0.116335\pi$
$271$	12.7826	+	22.1402i	0.776489	+	1.34492i	−0.157465	+	0.987525i	$0.550332\pi$
$272$		0			0
$273$		−	0.624456i		−	0.0377938i
$274$		0			0
$275$	−18.3749	+	10.6087i	−1.10805	+	0.639731i
$276$		0			0
$277$	−5.60469	+	9.70760i	−0.336753	+	0.583273i	−0.983820	−	0.179160i	$-0.942662\pi$
$277$	−5.60469	+	9.70760i	−0.336753	+	0.583273i	0.647067	+	0.762433i	$0.275995\pi$
$278$		0			0
$279$	−4.33433	+	2.50243i	−0.259490	+	0.149816i
$280$		0			0
$281$	−0.725933	+	0.419117i	−0.0433055	+	0.0250024i	−0.521496	−	0.853253i	$-0.674626\pi$
$281$	−0.725933	+	0.419117i	−0.0433055	+	0.0250024i	0.478191	+	0.878256i	$0.341293\pi$
$282$		0			0
$283$	−4.46864	+	7.73991i	−0.265633	+	0.460090i	−0.967729	−	0.251992i	$-0.918914\pi$
$283$	−4.46864	+	7.73991i	−0.265633	+	0.460090i	0.702096	+	0.712082i	$0.252248\pi$
$284$		0			0
$285$		−	9.49594i		−	0.562491i
$286$		0			0
$287$	−2.98381	−	5.16811i	−0.176129	−	0.305064i
$288$		0			0
$289$	15.8289	−	27.4164i	0.931110	−	1.61273i
$290$		0			0
$291$	5.58196	−	9.66824i	0.327220	−	0.566762i
$292$		0			0
$293$	17.2985	+	9.98732i	1.01059	+	0.583465i	0.911365	−	0.411599i	$-0.135030\pi$
$293$	17.2985	+	9.98732i	1.01059	+	0.583465i	0.0992269	+	0.995065i	$0.468363\pi$
$294$		0			0
$295$	−27.4542			−1.59845
$296$		0			0
$297$	−14.6554			−0.850392
$298$		0			0
$299$	−0.999319	−	0.576957i	−0.0577921	−	0.0333663i
$300$		0			0
$301$	6.18771	−	10.7174i	0.356653	−	0.617742i
$302$		0			0
$303$	3.13828	−	5.43566i	0.180289	−	0.312270i
$304$		0			0
$305$	1.95572	+	3.38741i	0.111984	+	0.193962i
$306$		0			0
$307$			18.8004i			1.07300i	0.843902	+	0.536498i	$0.180253\pi$
$307$			18.8004i			1.07300i	−0.843902	+	0.536498i	$0.819747\pi$
$308$		0			0
$309$	6.46407	−	11.1961i	0.367728	−	0.636924i
$310$		0			0
$311$	−7.38592	+	4.26426i	−0.418817	+	0.241804i	−0.694571	−	0.719424i	$-0.744406\pi$
$311$	−7.38592	+	4.26426i	−0.418817	+	0.241804i	0.275754	+	0.961228i	$0.411072\pi$
$312$		0			0
$313$	11.9036	−	6.87255i	0.672832	−	0.388460i	−0.124317	−	0.992243i	$-0.539674\pi$
$313$	11.9036	−	6.87255i	0.672832	−	0.388460i	0.797149	+	0.603783i	$0.206341\pi$
$314$		0			0
$315$	7.19302	−	12.4587i	0.405281	−	0.701967i
$316$		0			0
$317$	−18.3949	+	10.6203i	−1.03316	+	0.596494i	−0.917888	−	0.396840i	$-0.870107\pi$
$317$	−18.3949	+	10.6203i	−1.03316	+	0.596494i	−0.115270	+	0.993334i	$0.536773\pi$
$318$		0			0
$319$		−	14.9169i		−	0.835188i
$320$		0			0
$321$	−5.69645	−	9.86653i	−0.317945	−	0.550696i
$322$		0			0
$323$			30.9490i			1.72205i
$324$		0			0
$325$	−2.87389			−0.159415
$326$		0			0
$327$			8.07399i			0.446492i
$328$		0			0
$329$	−7.01370	+	12.1481i	−0.386678	+	0.669746i
$330$		0			0
$331$	−1.16160	−	2.01196i	−0.0638475	−	0.110587i	0.832335	−	0.554273i	$-0.187004\pi$
$331$	−1.16160	−	2.01196i	−0.0638475	−	0.110587i	−0.896182	+	0.443686i	$0.853670\pi$
$332$		0			0
$333$	−13.5725	+	7.60250i	−0.743771	+	0.416614i
$334$		0			0
$335$	−23.3302	+	13.4697i	−1.27466	+	0.735928i
$336$		0			0
$337$	−11.5021	+	19.9223i	−0.626562	+	1.08524i	0.361675	+	0.932304i	$0.382205\pi$
$337$	−11.5021	+	19.9223i	−0.626562	+	1.08524i	−0.988237	+	0.152932i	$0.951128\pi$
$338$		0			0
$339$	−13.6119			−0.739298
$340$		0			0
$341$	−7.75782			−0.420110
$342$		0			0
$343$	19.1323			1.03305
$344$		0			0
$345$	2.29968	+	3.98317i	0.123811	+	0.214447i
$346$		0			0
$347$	2.24275			0.120397			0.0601985	−	0.998186i	$-0.480827\pi$
$347$	2.24275			0.120397			0.0601985	+	0.998186i	$0.480827\pi$
$348$		0			0
$349$	−5.18368	+	2.99280i	−0.277476	+	0.160201i	−0.632280	−	0.774740i	$-0.717881\pi$
$349$	−5.18368	+	2.99280i	−0.277476	+	0.160201i	0.354804	+	0.934941i	$0.384548\pi$
$350$		0			0
$351$	−1.71911	−	0.992530i	−0.0917594	−	0.0529773i
$352$		0			0
$353$	15.1608	−	8.75311i	0.806929	−	0.465881i	−0.0389590	−	0.999241i	$-0.512404\pi$
$353$	15.1608	−	8.75311i	0.806929	−	0.465881i	0.845888	+	0.533360i	$0.179071\pi$
$354$		0			0
$355$	8.18453	+	14.1760i	0.434390	+	0.752385i
$356$		0			0
$357$	4.05608	−	7.02533i	0.214670	−	0.371820i
$358$		0			0
$359$	−19.4248			−1.02520			−0.512601	−	0.858627i	$-0.671318\pi$
$359$	−19.4248			−1.02520			−0.512601	+	0.858627i	$0.671318\pi$
$360$		0			0
$361$	−0.342662	−	0.593508i	−0.0180348	−	0.0312373i
$362$		0			0
$363$	−2.71657	−	1.56841i	−0.142583	−	0.0823202i
$364$		0			0
$365$	−3.71410	+	6.43300i	−0.194405	+	0.336719i
$366$		0			0
$367$	14.3982	−	24.9385i	0.751582	−	1.30178i	−0.195473	−	0.980709i	$-0.562624\pi$
$367$	14.3982	−	24.9385i	0.751582	−	1.30178i	0.947056	−	0.321070i	$-0.104042\pi$
$368$		0			0
$369$	−8.72991			−0.454461
$370$		0			0
$371$		−	0.689628i		−	0.0358037i
$372$		0			0
$373$	−27.3585	−	15.7955i	−1.41657	−	0.817857i	−0.420575	−	0.907258i	$-0.638172\pi$
$373$	−27.3585	−	15.7955i	−1.41657	−	0.817857i	−0.995996	+	0.0894004i	$0.971505\pi$
$374$		0			0
$375$	0.652708	+	0.376841i	0.0337057	+	0.0194600i
$376$		0			0
$377$	1.01024	−	1.74979i	0.0520302	−	0.0901189i
$378$		0			0
$379$	9.61823	−	5.55309i	0.494055	−	0.285243i	−0.232200	−	0.972668i	$-0.574592\pi$
$379$	9.61823	−	5.55309i	0.494055	−	0.285243i	0.726255	+	0.687425i	$0.241259\pi$
$380$		0			0
$381$			13.4481i			0.688965i
$382$		0			0
$383$	19.6991	+	11.3733i	1.00657	+	0.581146i	0.910187	−	0.414198i	$-0.135938\pi$
$383$	19.6991	+	11.3733i	1.00657	+	0.581146i	0.0963879	+	0.995344i	$0.469271\pi$
$384$		0			0
$385$	19.3117	−	11.1496i	0.984214	−	0.568236i
$386$		0			0
$387$	−9.05188	−	15.6783i	−0.460133	−	0.796973i
$388$		0			0
$389$	−17.6210	+	30.5205i	−0.893422	+	1.54745i	−0.0576756	+	0.998335i	$0.518369\pi$
$389$	−17.6210	+	30.5205i	−0.893422	+	1.54745i	−0.835746	+	0.549116i	$0.814964\pi$
$390$		0			0
$391$	−7.49510	−	12.9819i	−0.379044	−	0.656523i
$392$		0			0
$393$		−	14.0941i		−	0.710955i
$394$		0			0
$395$	−6.58894	+	3.80413i	−0.331526	+	0.191406i
$396$		0			0
$397$		−	12.7424i		−	0.639525i	−0.947498	−	0.319762i	$-0.896397\pi$
$397$		−	12.7424i		−	0.639525i	0.947498	−	0.319762i	$-0.103603\pi$
$398$		0			0
$399$			5.15978i			0.258312i
$400$		0			0
$401$			30.4901i			1.52260i	0.648397	+	0.761302i	$0.275440\pi$
$401$			30.4901i			1.52260i	−0.648397	+	0.761302i	$0.724560\pi$
$402$		0			0
$403$	−0.910011	−	0.525395i	−0.0453309	−	0.0261718i
$404$		0			0
$405$	−8.38698	−	14.5267i	−0.416752	−	0.721836i
$406$		0			0
$407$	−24.1118	−	0.313594i	−1.19518	−	0.0155443i
$408$		0			0
$409$	−15.5770	+	8.99336i	−0.770231	+	0.444693i	−0.832957	−	0.553338i	$-0.813354\pi$
$409$	−15.5770	+	8.99336i	−0.770231	+	0.444693i	0.0627259	+	0.998031i	$0.480021\pi$
$410$		0			0
$411$	−8.04881	−	4.64698i	−0.397019	−	0.229219i
$412$		0			0
$413$	14.9177			0.734053
$414$		0			0
$415$		−	5.22565i		−	0.256517i
$416$		0			0
$417$	−4.12596			−0.202049
$418$		0			0
$419$	−1.87998	+	1.08540i	−0.0918428	+	0.0530255i	−0.545218	−	0.838294i	$-0.683553\pi$
$419$	−1.87998	+	1.08540i	−0.0918428	+	0.0530255i	0.453375	+	0.891320i	$0.350220\pi$
$420$		0			0
$421$	34.8774			1.69982			0.849910	−	0.526928i	$-0.176656\pi$
$421$	34.8774			1.69982			0.849910	+	0.526928i	$0.176656\pi$
$422$		0			0
$423$	10.2602	+	17.7712i	0.498868	+	0.864065i
$424$		0			0
$425$	−32.3321	−	18.6670i	−1.56834	−	0.905481i
$426$		0			0
$427$	−1.06267	−	1.84061i	−0.0514264	−	0.0890731i
$428$		0			0
$429$	−0.707993	−	1.22628i	−0.0341822	−	0.0592053i
$430$		0			0
$431$	19.7952	+	11.4288i	0.953502	+	0.550505i	0.894167	−	0.447733i	$-0.147769\pi$
$431$	19.7952	+	11.4288i	0.953502	+	0.550505i	0.0593350	+	0.998238i	$0.481102\pi$
$432$		0			0
$433$	3.06108			0.147106			0.0735529	−	0.997291i	$-0.476566\pi$
$433$	3.06108			0.147106			0.0735529	+	0.997291i	$0.476566\pi$
$434$		0			0
$435$	−6.97447	+	4.02671i	−0.334400	+	0.193066i
$436$		0			0
$437$	8.25722	+	4.76731i	0.394996	+	0.228051i
$438$		0			0
$439$	−21.7928	−	12.5821i	−1.04011	−	0.600510i	−0.120249	−	0.992744i	$-0.538369\pi$
$439$	−21.7928	−	12.5821i	−1.04011	−	0.600510i	−0.919866	+	0.392233i	$0.871703\pi$
$440$		0			0
$441$	5.04284	−	8.73445i	0.240135	−	0.415926i
$442$		0			0
$443$		−	28.7440i		−	1.36567i	−0.730573	−	0.682835i	$-0.760747\pi$
$443$		−	28.7440i		−	1.36567i	0.730573	−	0.682835i	$-0.239253\pi$
$444$		0			0
$445$			48.3309i			2.29111i
$446$		0			0
$447$	6.15740	−	10.6649i	0.291235	−	0.504434i
$448$		0			0
$449$	−9.07421	−	5.23900i	−0.428238	−	0.247244i	0.270357	−	0.962760i	$-0.412858\pi$
$449$	−9.07421	−	5.23900i	−0.428238	−	0.247244i	−0.698596	+	0.715516i	$0.746191\pi$
$450$		0			0
$451$	−11.7190	−	6.76594i	−0.551824	−	0.318596i
$452$		0			0
$453$	−4.71430	+	2.72180i	−0.221497	+	0.127881i
$454$		0			0
$455$	3.02041			0.141599
$456$		0			0
$457$	17.5624	+	10.1397i	0.821535	+	0.474314i	0.850946	−	0.525254i	$-0.176030\pi$
$457$	17.5624	+	10.1397i	0.821535	+	0.474314i	−0.0294104	+	0.999567i	$0.509363\pi$
$458$		0			0
$459$	−12.8937	−	22.3325i	−0.601827	−	1.04239i
$460$		0			0
$461$	−6.46253	−	11.1934i	−0.300990	−	0.521330i	0.675370	−	0.737479i	$-0.263984\pi$
$461$	−6.46253	−	11.1934i	−0.300990	−	0.521330i	−0.976360	+	0.216149i	$0.930650\pi$
$462$		0			0
$463$	26.4239	+	15.2559i	1.22802	+	0.709000i	0.966616	−	0.256228i	$-0.0824798\pi$
$463$	26.4239	+	15.2559i	1.22802	+	0.709000i	0.261408	+	0.965228i	$0.415813\pi$
$464$		0			0
$465$	2.09416	+	3.62720i	0.0971145	+	0.168207i
$466$		0			0
$467$	17.2988			0.800493			0.400247	−	0.916407i	$-0.368924\pi$
$467$	17.2988			0.800493			0.400247	+	0.916407i	$0.368924\pi$
$468$		0			0
$469$	12.6769	−	7.31899i	0.585363	−	0.337960i
$470$		0			0
$471$	−8.20378			−0.378010
$472$		0			0
$473$		−	28.0619i		−	1.29029i
$474$		0			0
$475$	23.7465			1.08956
$476$		0			0
$477$	−0.873684	−	0.504422i	−0.0400032	−	0.0230959i
$478$		0			0
$479$	7.72894	−	4.46231i	0.353144	−	0.203888i	−0.312925	−	0.949778i	$-0.601309\pi$
$479$	7.72894	−	4.46231i	0.353144	−	0.203888i	0.666069	+	0.745890i	$0.267976\pi$
$480$		0			0
$481$	−2.80713	−	1.66975i	−0.127994	−	0.0761339i
$482$		0			0
$483$	−1.24957	−	2.16432i	−0.0568575	−	0.0984802i
$484$		0			0
$485$	46.7639	+	26.9992i	2.12344	+	1.22597i
$486$		0			0
$487$		−	3.82200i		−	0.173192i	−0.996244	−	0.0865958i	$-0.972401\pi$
$487$		−	3.82200i		−	0.173192i	0.996244	−	0.0865958i	$-0.0275989\pi$
$488$		0			0
$489$			4.19410i			0.189664i
$490$		0			0
$491$		−	15.1520i		−	0.683800i	−0.939736	−	0.341900i	$-0.888930\pi$
$491$		−	15.1520i		−	0.683800i	0.939736	−	0.341900i	$-0.111070\pi$
$492$		0			0
$493$	22.7311	−	13.1238i	1.02376	−	0.591067i
$494$		0			0
$495$		−	32.6211i		−	1.46621i
$496$		0			0
$497$	−4.44720	−	7.70278i	−0.199484	−	0.345517i
$498$		0			0
$499$	−17.5853	+	30.4586i	−0.787224	+	1.36351i	0.140437	+	0.990090i	$0.455149\pi$
$499$	−17.5853	+	30.4586i	−0.787224	+	1.36351i	−0.927661	+	0.373423i	$0.878184\pi$
$500$		0			0
$501$	3.42397	+	5.93049i	0.152972	+	0.264955i
$502$		0			0
$503$	25.9312	−	14.9714i	1.15621	−	0.667540i	0.205820	−	0.978590i	$-0.434014\pi$
$503$	25.9312	−	14.9714i	1.15621	−	0.667540i	0.950394	+	0.311050i	$0.100681\pi$
$504$		0			0
$505$	26.2915	+	15.1794i	1.16996	+	0.675476i
$506$		0			0
$507$			8.45579i			0.375535i
$508$		0			0
$509$	23.3484	−	13.4802i	1.03490	−	0.597498i	0.116514	−	0.993189i	$-0.462828\pi$
$509$	23.3484	−	13.4802i	1.03490	−	0.597498i	0.918384	+	0.395691i	$0.129495\pi$
$510$		0			0
$511$	2.01812	−	3.49548i	0.0892763	−	0.154631i
$512$		0			0
$513$	14.2048	+	8.20112i	0.627155	+	0.362088i
$514$		0			0
$515$	54.1540	+	31.2658i	2.38631	+	1.37774i
$516$		0			0
$517$			31.8078i			1.39891i
$518$		0			0
$519$	0.00788959			0.000346315
$520$		0			0
$521$	−16.2452	+	28.1374i	−0.711713	+	1.23272i	0.252500	+	0.967597i	$0.418747\pi$
$521$	−16.2452	+	28.1374i	−0.711713	+	1.23272i	−0.964214	+	0.265127i	$0.914586\pi$
$522$		0			0
$523$	−2.09888	+	3.63538i	−0.0917778	+	0.158964i	−0.908259	−	0.418408i	$-0.862588\pi$
$523$	−2.09888	+	3.63538i	−0.0917778	+	0.158964i	0.816481	+	0.577372i	$0.195922\pi$
$524$		0			0
$525$	−5.39037	−	3.11213i	−0.235255	−	0.135825i
$526$		0			0
$527$	−6.82527	−	11.8217i	−0.297314	−	0.514962i
$528$		0			0
$529$	18.3819			0.799213
$530$		0			0
$531$	10.9114	−	18.8991i	0.473515	−	0.820152i
$532$		0			0
$533$	−0.916441	−	1.58732i	−0.0396955	−	0.0687546i
$534$		0			0
$535$	47.7231	−	27.5529i	2.06325	−	1.19122i
$536$		0			0
$537$	−3.75552	−	2.16825i	−0.162063	−	0.0935668i
$538$		0			0
$539$	13.5389	−	7.81669i	0.583162	−	0.336689i
$540$		0			0
$541$	6.09226			0.261927			0.130963	−	0.991387i	$-0.458193\pi$
$541$	6.09226			0.261927			0.130963	+	0.991387i	$0.458193\pi$
$542$		0			0
$543$	−3.88141	−	6.72280i	−0.166567	−	0.288503i
$544$		0			0
$545$	−39.0528			−1.67284
$546$		0			0
$547$	18.1398			0.775601			0.387800	−	0.921743i	$-0.373235\pi$
$547$	18.1398			0.775601			0.387800	+	0.921743i	$0.373235\pi$
$548$		0			0
$549$	−3.10913			−0.132694
$550$		0			0
$551$	−8.34748	+	14.4583i	−0.355614	+	0.615942i
$552$		0			0
$553$	3.58021	−	2.06704i	0.152246	−	0.0878994i
$554$		0			0
$555$	6.36217	+	11.3582i	0.270059	+	0.482130i
$556$		0			0
$557$	0.461524	+	0.799383i	0.0195554	+	0.0338709i	0.875637	−	0.482969i	$-0.160442\pi$
$557$	0.461524	+	0.799383i	0.0195554	+	0.0338709i	−0.856082	+	0.516840i	$0.827108\pi$
$558$		0			0
$559$	1.90048	−	3.29173i	0.0803817	−	0.139225i
$560$		0			0
$561$		−	18.3947i		−	0.776625i
$562$		0			0
$563$	18.9829			0.800032			0.400016	−	0.916508i	$-0.369005\pi$
$563$	18.9829			0.800032			0.400016	+	0.916508i	$0.369005\pi$
$564$		0			0
$565$		−	65.8390i		−	2.76987i
$566$		0			0
$567$	4.55721	+	7.89332i	0.191385	+	0.331488i
$568$		0			0
$569$			25.1360i			1.05375i	0.849942	+	0.526877i	$0.176637\pi$
$569$			25.1360i			1.05375i	−0.849942	+	0.526877i	$0.823363\pi$
$570$		0			0
$571$	−27.1520	+	15.6762i	−1.13628	+	0.656030i	−0.945506	−	0.325604i	$-0.894432\pi$
$571$	−27.1520	+	15.6762i	−1.13628	+	0.656030i	−0.190772	+	0.981634i	$0.561099\pi$
$572$		0			0
$573$	2.88413	−	4.99546i	0.120486	−	0.208688i
$574$		0			0
$575$	−9.96071	+	5.75082i	−0.415390	+	0.239826i
$576$		0			0
$577$	−8.55780	+	4.94085i	−0.356266	+	0.205690i	−0.667442	−	0.744662i	$-0.732611\pi$
$577$	−8.55780	+	4.94085i	−0.356266	+	0.205690i	0.311176	+	0.950352i	$0.399277\pi$
$578$		0			0
$579$	0.104091	−	0.180290i	0.00432586	−	0.00749260i
$580$		0			0
$581$			2.83945i			0.117800i
$582$		0			0
$583$	−0.781883	−	1.35426i	−0.0323823	−	0.0560878i
$584$		0			0
$585$	2.20925	−	3.82653i	0.0913412	−	0.158208i
$586$		0			0
$587$	20.2311	−	35.0412i	0.835025	−	1.44631i	−0.0589852	−	0.998259i	$-0.518786\pi$
$587$	20.2311	−	35.0412i	0.835025	−	1.44631i	0.894010	−	0.448047i	$-0.147880\pi$
$588$		0			0
$589$	7.51928	+	4.34126i	0.309826	+	0.178878i
$590$		0			0
$591$	3.52611			0.145045
$592$		0			0
$593$	6.43804			0.264379			0.132189	−	0.991224i	$-0.457799\pi$
$593$	6.43804			0.264379			0.132189	+	0.991224i	$0.457799\pi$
$594$		0			0
$595$	33.9806	+	19.6187i	1.39307	+	0.804287i
$596$		0			0
$597$	−0.479180	+	0.829964i	−0.0196115	+	0.0339682i
$598$		0			0
$599$	7.94878	−	13.7677i	0.324778	−	0.562532i	−0.656689	−	0.754161i	$-0.728044\pi$
$599$	7.94878	−	13.7677i	0.324778	−	0.562532i	0.981467	+	0.191629i	$0.0613770\pi$
$600$		0			0
$601$	−13.9683	−	24.1938i	−0.569778	−	0.986884i	−0.996588	−	0.0825425i	$-0.973696\pi$
$601$	−13.9683	−	24.1938i	−0.569778	−	0.986884i	0.426810	−	0.904341i	$-0.359637\pi$
$602$		0			0
$603$		−	21.4136i		−	0.872030i
$604$		0			0
$605$	7.58618	−	13.1397i	0.308422	−	0.534203i
$606$		0			0
$607$	−8.19892	+	4.73365i	−0.332784	+	0.192133i	−0.657076	−	0.753824i	$-0.728207\pi$
$607$	−8.19892	+	4.73365i	−0.332784	+	0.192133i	0.324292	+	0.945957i	$0.394874\pi$
$608$		0			0
$609$	3.78970	−	2.18798i	0.153566	−	0.0886615i
$610$		0			0
$611$	−2.15417	+	3.73114i	−0.0871485	+	0.150946i
$612$		0			0
$613$	−21.8779	+	12.6312i	−0.883639	+	0.510169i	−0.871857	−	0.489761i	$-0.837084\pi$
$613$	−21.8779	+	12.6312i	−0.883639	+	0.510169i	−0.0117827	+	0.999931i	$0.503751\pi$
$614$		0			0
$615$			7.30565i			0.294592i
$616$		0			0
$617$	−0.354017	−	0.613176i	−0.0142522	−	0.0246855i	0.858811	−	0.512292i	$-0.171203\pi$
$617$	−0.354017	−	0.613176i	−0.0142522	−	0.0246855i	−0.873064	+	0.487606i	$0.837870\pi$
$618$		0			0
$619$			9.27255i			0.372695i	0.982484	+	0.186348i	$0.0596651\pi$
$619$			9.27255i			0.372695i	−0.982484	+	0.186348i	$0.940335\pi$
$620$		0			0
$621$	−7.94444			−0.318799
$622$		0			0
$623$		−	26.2615i		−	1.05214i
$624$		0			0
$625$	11.5576	−	20.0184i	0.462305	−	0.800736i
$626$		0			0
$627$	5.85003	+	10.1326i	0.233628	+	0.404655i
$628$		0			0
$629$	−20.7355	−	37.0186i	−0.826779	−	1.47603i
$630$		0			0
$631$	3.70834	−	2.14101i	0.147627	−	0.0852323i	−0.424367	−	0.905490i	$-0.639503\pi$
$631$	3.70834	−	2.14101i	0.147627	−	0.0852323i	0.571994	+	0.820258i	$0.306170\pi$
$632$		0			0
$633$	−5.21390	+	9.03074i	−0.207234	+	0.358940i
$634$		0			0
$635$	−65.0464			−2.58129
$636$		0			0
$637$	2.11753			0.0838995
$638$		0			0
$639$	−13.0115			−0.514725
$640$		0			0
$641$	0.806106	+	1.39622i	0.0318393	+	0.0551472i	0.881506	−	0.472173i	$-0.156530\pi$
$641$	0.806106	+	1.39622i	0.0318393	+	0.0551472i	−0.849667	+	0.527320i	$0.823197\pi$
$642$		0			0
$643$	−41.7263			−1.64552			−0.822762	−	0.568386i	$-0.807568\pi$
$643$	−41.7263			−1.64552			−0.822762	+	0.568386i	$0.807568\pi$
$644$		0			0
$645$	−13.1204	+	7.57509i	−0.516617	+	0.298269i
$646$		0			0
$647$	−34.4585	−	19.8946i	−1.35471	−	0.782139i	−0.365801	−	0.930693i	$-0.619205\pi$
$647$	−34.4585	−	19.8946i	−1.35471	−	0.782139i	−0.988904	+	0.148554i	$0.952538\pi$
$648$		0			0
$649$	29.2948	−	16.9133i	1.14992	−	0.663907i
$650$		0			0
$651$	−1.13790	−	1.97090i	−0.0445978	−	0.0772457i
$652$		0			0
$653$	−23.0088	+	39.8523i	−0.900402	+	1.55954i	−0.0734292	+	0.997300i	$0.523394\pi$
$653$	−23.0088	+	39.8523i	−0.900402	+	1.55954i	−0.826973	+	0.562242i	$0.809939\pi$
$654$		0			0
$655$	68.1714			2.66368
$656$		0			0
$657$	−2.95227	−	5.11347i	−0.115179	−	0.199496i
$658$		0			0
$659$	14.3355	+	8.27661i	0.558432	+	0.322411i	0.752516	−	0.658574i	$-0.228840\pi$
$659$	14.3355	+	8.27661i	0.558432	+	0.322411i	−0.194084	+	0.980985i	$0.562173\pi$
$660$		0			0
$661$	−3.48320	+	6.03308i	−0.135481	+	0.234660i	−0.925781	−	0.378060i	$-0.876591\pi$
$661$	−3.48320	+	6.03308i	−0.135481	+	0.234660i	0.790300	+	0.612720i	$0.209925\pi$
$662$		0			0
$663$	1.24577	−	2.15774i	0.0483819	−	0.0837998i
$664$		0			0
$665$	−24.9572			−0.967797
$666$		0			0
$667$		−	8.08622i		−	0.313100i
$668$		0			0
$669$	16.4048	+	9.47132i	0.634247	+	0.366183i
$670$		0			0
$671$	−4.17367	−	2.40967i	−0.161123	−	0.0930242i
$672$		0			0
$673$	6.01450	−	10.4174i	0.231842	−	0.401562i	−0.726508	−	0.687158i	$-0.758858\pi$
$673$	6.01450	−	10.4174i	0.231842	−	0.401562i	0.958350	+	0.285596i	$0.0921914\pi$
$674$		0			0
$675$	−17.1352	+	9.89304i	−0.659536	+	0.380783i
$676$		0			0
$677$			8.24618i			0.316926i	0.987365	+	0.158463i	$0.0506539\pi$
$677$			8.24618i			0.316926i	−0.987365	+	0.158463i	$0.949346\pi$
$678$		0			0
$679$	−25.4100	−	14.6705i	−0.975146	−	0.563001i
$680$		0			0
$681$	−3.87971	+	2.23995i	−0.148671	+	0.0858352i
$682$		0			0
$683$	10.9776	+	19.0138i	0.420046	+	0.727542i	0.995944	−	0.0899805i	$-0.0286805\pi$
$683$	10.9776	+	19.0138i	0.420046	+	0.727542i	−0.575897	+	0.817522i	$0.695347\pi$
$684$		0			0
$685$	22.4768	−	38.9310i	0.858795	−	1.48748i
$686$		0			0
$687$	0.469439	+	0.813093i	0.0179102	+	0.0310214i
$688$		0			0
$689$		−	0.211811i		−	0.00806935i
$690$		0			0
$691$	−16.0037	+	9.23977i	−0.608811	+	0.351497i	−0.772500	−	0.635015i	$-0.780994\pi$
$691$	−16.0037	+	9.23977i	−0.608811	+	0.351497i	0.163689	+	0.986512i	$0.447661\pi$
$692$		0			0
$693$			17.7252i			0.673326i
$694$		0			0
$695$		−	19.9567i		−	0.757000i
$696$		0			0
$697$		−	23.8105i		−	0.901887i
$698$		0			0
$699$	8.64058	+	4.98864i	0.326817	+	0.188688i
$700$		0			0
$701$	5.75067	+	9.96046i	0.217200	+	0.376201i	0.953951	−	0.299963i	$-0.0969743\pi$
$701$	5.75067	+	9.96046i	0.217200	+	0.376201i	−0.736751	+	0.676164i	$0.763641\pi$
$702$		0			0
$703$	23.1949	+	13.7969i	0.874813	+	0.520358i
$704$		0			0
$705$	14.8719	−	8.58628i	0.560107	−	0.323378i
$706$		0			0
$707$	−14.2860	−	8.24800i	−0.537279	−	0.310198i
$708$		0			0
$709$	9.52448			0.357699			0.178850	−	0.983876i	$-0.442762\pi$
$709$	9.52448			0.357699			0.178850	+	0.983876i	$0.442762\pi$
$710$		0			0
$711$		−	6.04766i		−	0.226805i
$712$		0			0
$713$	−4.20539			−0.157493
$714$		0			0
$715$	5.93135	−	3.42447i	0.221820	−	0.128068i
$716$		0			0
$717$	−12.7708			−0.476936
$718$		0			0
$719$	−18.9100	−	32.7531i	−0.705224	−	1.22148i	−0.966611	−	0.256250i	$-0.917513\pi$
$719$	−18.9100	−	32.7531i	−0.705224	−	1.22148i	0.261386	−	0.965234i	$-0.415820\pi$
$720$		0			0
$721$	−29.4255	−	16.9888i	−1.09586	−	0.632697i
$722$		0			0
$723$	−1.66435	−	2.88274i	−0.0618978	−	0.107210i
$724$		0			0
$725$	−10.0696	−	17.4410i	−0.373975	−	0.647744i
$726$		0			0
$727$	34.4965	+	19.9165i	1.27940	+	0.738663i	0.976739	−	0.214434i	$-0.0687906\pi$
$727$	34.4965	+	19.9165i	1.27940	+	0.738663i	0.302664	+	0.953097i	$0.402124\pi$
$728$		0			0
$729$	5.95589			0.220589
$730$		0			0
$731$	42.7620	−	24.6886i	1.58161	−	0.913142i
$732$		0			0
$733$	13.9768	+	8.06949i	0.516244	+	0.298053i	0.735396	−	0.677637i	$-0.236996\pi$
$733$	13.9768	+	8.06949i	0.516244	+	0.298053i	−0.219153	+	0.975691i	$0.570329\pi$
$734$		0			0
$735$	−7.30945	−	4.22011i	−0.269613	−	0.155661i
$736$		0			0
$737$	16.5962	−	28.7454i	0.611328	−	1.05885i
$738$		0			0
$739$			31.0229i			1.14120i	0.821230	+	0.570598i	$0.193289\pi$
$739$			31.0229i			1.14120i	−0.821230	+	0.570598i	$0.806711\pi$
$740$		0			0
$741$			1.58476i			0.0582178i
$742$		0			0
$743$	3.30582	−	5.72584i	0.121279	−	0.210061i	−0.798994	−	0.601340i	$-0.794634\pi$
$743$	3.30582	−	5.72584i	0.121279	−	0.210061i	0.920272	+	0.391279i	$0.127967\pi$
$744$		0			0
$745$	51.5848	+	29.7825i	1.88992	+	1.09115i
$746$		0			0
$747$	3.59727	+	2.07689i	0.131617	+	0.0759893i
$748$		0			0
$749$	−25.9312	+	14.9714i	−0.947504	+	0.547042i
$750$		0			0
$751$	−42.5856			−1.55397			−0.776985	−	0.629519i	$-0.783252\pi$
$751$	−42.5856			−1.55397			−0.776985	+	0.629519i	$0.783252\pi$
$752$		0			0
$753$	2.20555	+	1.27338i	0.0803749	+	0.0464045i
$754$		0			0
$755$	−13.1650	−	22.8024i	−0.479123	−	0.829866i
$756$		0			0
$757$	−1.07846	−	1.86794i	−0.0391971	−	0.0678914i	0.845761	−	0.533561i	$-0.179147\pi$
$757$	−1.07846	−	1.86794i	−0.0391971	−	0.0678914i	−0.884958	+	0.465670i	$0.845813\pi$
$758$		0			0
$759$	−4.90772	−	2.83347i	−0.178139	−	0.102848i
$760$		0			0
$761$	8.16322	+	14.1391i	0.295916	+	0.512542i	0.975198	−	0.221336i	$-0.0710417\pi$
$761$	8.16322	+	14.1391i	0.295916	+	0.512542i	−0.679281	+	0.733878i	$0.737708\pi$
$762$		0			0
$763$	21.2200			0.768215
$764$		0			0
$765$	49.7095	−	28.6998i	1.79725	−	1.03764i
$766$		0			0
$767$	4.58179			0.165439
$768$		0			0
$769$			7.06397i			0.254733i	0.991856	+	0.127367i	$0.0406525\pi$
$769$			7.06397i			0.254733i	−0.991856	+	0.127367i	$0.959348\pi$
$770$		0			0
$771$	0.718046			0.0258598
$772$		0			0
$773$	31.8001	+	18.3598i	1.14377	+	0.660356i	0.947361	−	0.320166i	$-0.103739\pi$
$773$	31.8001	+	18.3598i	1.14377	+	0.660356i	0.196409	+	0.980522i	$0.437072\pi$
$774$		0			0
$775$	−9.07053	+	5.23687i	−0.325823	+	0.188114i
$776$		0			0
$777$	−3.45700	−	6.17168i	−0.124019	−	0.221408i
$778$		0			0
$779$	7.57240	+	13.1158i	0.271310	+	0.469922i
$780$		0			0
$781$	−17.4665	−	10.0843i	−0.624999	−	0.360843i
$782$		0			0
$783$		−	13.9106i		−	0.497124i
$784$		0			0
$785$		−	39.6805i		−	1.41626i
$786$		0			0
$787$			16.8047i			0.599023i	0.954093	+	0.299512i	$0.0968237\pi$
$787$			16.8047i			0.599023i	−0.954093	+	0.299512i	$0.903176\pi$
$788$		0			0
$789$	−10.4954	+	6.05951i	−0.373645	+	0.215724i
$790$		0			0
$791$			35.7748i			1.27200i
$792$		0			0
$793$	−0.326387	−	0.565320i	−0.0115904	−	0.0200751i
$794$		0			0
$795$	−0.422127	+	0.731145i	−0.0149713	+	0.0259310i
$796$		0			0
$797$	0.349355	+	0.605100i	0.0123748	+	0.0214338i	0.872146	−	0.489245i	$-0.162728\pi$
$797$	0.349355	+	0.605100i	0.0123748	+	0.0214338i	−0.859772	+	0.510679i	$0.829394\pi$
$798$		0			0
$799$	−48.4702	+	27.9843i	−1.71475	+	0.990014i
$800$		0			0
$801$	−33.2704	−	19.2087i	−1.17555	−	0.678705i
$802$		0			0
$803$		−	9.15237i		−	0.322980i
$804$		0			0
$805$	10.4685	−	6.04401i	0.368968	−	0.213024i
$806$		0			0
$807$	9.05505	−	15.6838i	0.318753	−	0.552096i
$808$		0			0
$809$	26.4968	+	15.2979i	0.931577	+	0.537846i	0.887310	−	0.461174i	$-0.152571\pi$
$809$	26.4968	+	15.2979i	0.931577	+	0.537846i	0.0442669	+	0.999020i	$0.485905\pi$
$810$		0			0
$811$	−6.49251	−	3.74845i	−0.227983	−	0.131626i	0.381658	−	0.924304i	$-0.375353\pi$
$811$	−6.49251	−	3.74845i	−0.227983	−	0.131626i	−0.609641	+	0.792678i	$0.708686\pi$
$812$		0			0
$813$			17.0060i			0.596425i
$814$		0			0
$815$	−20.2863			−0.710598
$816$		0			0
$817$	−15.7034	+	27.1990i	−0.549391	+	0.951573i
$818$		0			0
$819$	−1.20043	+	2.07921i	−0.0419465	+	0.0726535i
$820$		0			0
$821$	−6.79113	−	3.92086i	−0.237012	−	0.136839i	0.376791	−	0.926298i	$-0.377028\pi$
$821$	−6.79113	−	3.92086i	−0.237012	−	0.136839i	−0.613803	+	0.789459i	$0.710361\pi$
$822$		0			0
$823$	−7.27104	−	12.5938i	−0.253453	−	0.438993i	0.711021	−	0.703170i	$-0.248233\pi$
$823$	−7.27104	−	12.5938i	−0.253453	−	0.438993i	−0.964474	+	0.264177i	$0.914900\pi$
$824$		0			0
$825$	−14.1138			−0.491381
$826$		0			0
$827$	10.6385	−	18.4264i	0.369936	−	0.640747i	−0.619620	−	0.784902i	$-0.712713\pi$
$827$	10.6385	−	18.4264i	0.369936	−	0.640747i	0.989555	+	0.144155i	$0.0460464\pi$
$828$		0			0
$829$	14.1711	+	24.5450i	0.492182	+	0.852485i	0.999959	−	0.00900385i	$-0.00286605\pi$
$829$	14.1711	+	24.5450i	0.492182	+	0.852485i	−0.507777	+	0.861488i	$0.669533\pi$
$830$		0			0
$831$	−6.45748	+	3.72823i	−0.224008	+	0.129331i
$832$		0			0
$833$	23.8229	+	13.7541i	0.825413	+	0.476553i
$834$		0			0
$835$	−28.6850	+	16.5613i	−0.992685	+	0.573127i
$836$		0			0
$837$	−7.23445			−0.250059
$838$		0			0
$839$	20.7540	+	35.9470i	0.716507	+	1.24103i	0.962375	+	0.271724i	$0.0875936\pi$
$839$	20.7540	+	35.9470i	0.716507	+	1.24103i	−0.245868	+	0.969303i	$0.579073\pi$
$840$		0			0
$841$	−14.8412			−0.511764
$842$		0			0
$843$	−0.557593			−0.0192045
$844$		0			0
$845$	−40.8995			−1.40699
$846$		0			0
$847$	−4.12208	+	7.13966i	−0.141636	+	0.245322i
$848$		0			0
$849$	−5.14857	+	2.97253i	−0.176699	+	0.102017i
$850$		0			0
$851$	−13.0706	−	0.169994i	−0.448055	−	0.00582732i
$852$		0			0
$853$	26.1730	+	45.3330i	0.896147	+	1.55217i	0.832379	+	0.554207i	$0.186978\pi$
$853$	26.1730	+	45.3330i	0.896147	+	1.55217i	0.0637681	+	0.997965i	$0.479688\pi$
$854$		0			0
$855$	−18.2547	+	31.6180i	−0.624296	+	1.08131i
$856$		0			0
$857$		−	47.2486i		−	1.61398i	−0.590564	−	0.806991i	$-0.701095\pi$
$857$		−	47.2486i		−	1.61398i	0.590564	−	0.806991i	$-0.298905\pi$
$858$		0			0
$859$	15.1220			0.515958			0.257979	−	0.966151i	$-0.416944\pi$
$859$	15.1220			0.515958			0.257979	+	0.966151i	$0.416944\pi$
$860$		0			0
$861$		−	3.96965i		−	0.135285i
$862$		0			0
$863$	22.0511	+	38.1936i	0.750627	+	1.30012i	0.947519	+	0.319699i	$0.103582\pi$
$863$	22.0511	+	38.1936i	0.750627	+	1.30012i	−0.196892	+	0.980425i	$0.563085\pi$
$864$		0			0
$865$			0.0381609i			0.00129751i
$866$		0			0
$867$	18.2374	−	10.5293i	0.619373	−	0.357595i
$868$		0			0
$869$	4.68711	−	8.11832i	0.158999	−	0.275395i
$870$		0			0
$871$	3.89354	−	2.24794i	0.131928	−	0.0761685i
$872$		0			0
$873$	−37.1718	+	21.4611i	−1.25807	+	0.726349i
$874$		0			0
$875$	0.990411	−	1.71544i	0.0334820	−	0.0579925i
$876$		0			0
$877$		−	15.0650i		−	0.508708i	−0.967111	−	0.254354i	$-0.918137\pi$
$877$		−	15.0650i		−	0.508708i	0.967111	−	0.254354i	$-0.0818628\pi$
$878$		0			0
$879$	6.64355	+	11.5070i	0.224081	+	0.388120i
$880$		0			0
$881$	−19.6313	+	34.0025i	−0.661396	+	1.14557i	0.318853	+	0.947804i	$0.396702\pi$
$881$	−19.6313	+	34.0025i	−0.661396	+	1.14557i	−0.980249	+	0.197768i	$0.936631\pi$
$882$		0			0
$883$	13.3227	−	23.0755i	0.448344	−	0.776554i	−0.549935	−	0.835208i	$-0.685347\pi$
$883$	13.3227	−	23.0755i	0.448344	−	0.776554i	0.998278	+	0.0586537i	$0.0186808\pi$
$884$		0			0
$885$	−15.8158	−	9.13125i	−0.531642	−	0.306944i
$886$		0			0
$887$	21.1228			0.709233			0.354617	−	0.935012i	$-0.384611\pi$
$887$	21.1228			0.709233			0.354617	+	0.935012i	$0.384611\pi$
$888$		0			0
$889$	35.3441			1.18540
$890$		0			0
$891$	17.8985	+	10.3337i	0.599623	+	0.346192i
$892$		0			0
$893$	17.7996	−	30.8298i	0.595640	−	1.03168i
$894$		0			0
$895$	10.4875	−	18.1649i	0.350559	−	0.607186i
$896$		0			0
$897$	−0.383791	−	0.664746i	−0.0128144	−	0.0221952i
$898$		0			0
$899$		−	7.36356i		−	0.245589i
$900$		0			0
$901$	1.37579	−	2.38294i	0.0458342	−	0.0793872i
$902$		0			0
$903$	7.12921	−	4.11605i	0.237245	−	0.136974i
$904$		0			0
$905$	32.5173	−	18.7739i	1.08091	−	0.624064i
$906$		0			0
$907$	2.70347	−	4.68254i	0.0897672	−	0.155481i	−0.817645	−	0.575722i	$-0.804721\pi$
$907$	2.70347	−	4.68254i	0.0897672	−	0.155481i	0.907413	+	0.420241i	$0.138054\pi$
$908$		0			0
$909$	−20.8987	+	12.0658i	−0.693165	+	0.400199i
$910$		0			0
$911$		−	7.13798i		−	0.236492i	−0.992984	−	0.118246i	$-0.962273\pi$
$911$		−	7.13798i		−	0.236492i	0.992984	−	0.118246i	$-0.0377271\pi$
$912$		0			0
$913$	3.21930	+	5.57598i	0.106543	+	0.184538i
$914$		0			0
$915$			2.60188i			0.0860157i
$916$		0			0
$917$	−37.0421			−1.22324
$918$		0			0
$919$		−	18.8976i		−	0.623375i	−0.950185	−	0.311688i	$-0.899106\pi$
$919$		−	18.8976i		−	0.623375i	0.950185	−	0.311688i	$-0.100894\pi$
$920$		0			0
$921$	−6.25300	+	10.8305i	−0.206043	+	0.356878i
$922$		0			0
$923$	−1.36590	−	2.36582i	−0.0449593	−	0.0778718i
$924$		0			0
$925$	−28.4035	+	15.9099i	−0.933901	+	0.523114i
$926$		0			0
$927$	−43.0460	+	24.8526i	−1.41382	+	0.816267i
$928$		0			0
$929$	−10.1932	+	17.6551i	−0.334427	+	0.579244i	−0.983375	−	0.181589i	$-0.941876\pi$
$929$	−10.1932	+	17.6551i	−0.334427	+	0.579244i	0.648948	+	0.760833i	$0.275209\pi$
$930$		0			0
$931$	−17.4968			−0.573435
$932$		0			0
$933$	−5.67316			−0.185731
$934$		0			0
$935$	88.9727			2.90972
$936$		0			0
$937$	−4.12749	−	7.14903i	−0.134839	−	0.233549i	0.790697	−	0.612208i	$-0.209718\pi$
$937$	−4.12749	−	7.14903i	−0.134839	−	0.233549i	−0.925536	+	0.378659i	$0.876385\pi$
$938$		0			0
$939$	9.14323			0.298378
$940$		0			0
$941$	41.0244	−	23.6854i	1.33736	−	0.772123i	0.350941	−	0.936398i	$-0.385862\pi$
$941$	41.0244	−	23.6854i	1.33736	−	0.772123i	0.986415	+	0.164275i	$0.0525284\pi$
$942$		0			0
$943$	−6.35265	−	3.66770i	−0.206871	−	0.119437i
$944$		0			0
$945$	18.0089	−	10.3974i	0.585828	−	0.338228i
$946$		0			0
$947$	9.82338	+	17.0146i	0.319217	+	0.552900i	0.980325	−	0.197391i	$-0.0632468\pi$
$947$	9.82338	+	17.0146i	0.319217	+	0.552900i	−0.661108	+	0.750291i	$0.729913\pi$
$948$		0			0
$949$	0.619840	−	1.07359i	0.0201209	−	0.0348504i
$950$		0			0
$951$	−14.1292			−0.458170
$952$		0			0
$953$	−2.08755	−	3.61574i	−0.0676223	−	0.117125i	0.830232	−	0.557418i	$-0.188208\pi$
$953$	−2.08755	−	3.61574i	−0.0676223	−	0.117125i	−0.897854	+	0.440293i	$0.854875\pi$
$954$		0			0
$955$	24.1624	+	13.9502i	0.781876	+	0.451416i
$956$		0			0
$957$	4.96136	−	8.59333i	0.160378	−	0.277783i
$958$		0			0
$959$	−12.2132	+	21.1538i	−0.394384	+	0.683093i
$960$		0			0
$961$	27.1704			0.876466
$962$		0			0
$963$			43.8026i			1.41152i
$964$		0			0
$965$	0.872039	+	0.503472i	0.0280719	+	0.0162073i
$966$		0			0
$967$	−47.1713	−	27.2344i	−1.51693	−	0.875798i	−0.999802	−	0.0198888i	$-0.993669\pi$
$967$	−47.1713	−	27.2344i	−1.51693	−	0.875798i	−0.517125	−	0.855910i	$-0.672998\pi$
$968$		0			0
$969$	−10.2936	+	17.8291i	−0.330679	+	0.572753i
$970$		0			0
$971$	−21.6943	+	12.5252i	−0.696204	+	0.401953i	−0.805932	−	0.592008i	$-0.798335\pi$
$971$	−21.6943	+	12.5252i	−0.696204	+	0.401953i	0.109728	+	0.993962i	$0.465002\pi$
$972$		0			0
$973$			10.8438i			0.347637i
$974$		0			0
$975$	−1.65559	−	0.955853i	−0.0530212	−	0.0306118i
$976$		0			0
$977$	−8.60464	+	4.96789i	−0.275287	+	0.158937i	−0.631288	−	0.775549i	$-0.717473\pi$
$977$	−8.60464	+	4.96789i	−0.275287	+	0.158937i	0.356001	+	0.934486i	$0.384140\pi$
$978$		0			0
$979$	−29.7746	−	51.5711i	−0.951600	−	1.64822i
$980$		0			0
$981$	15.5212	−	26.8834i	0.495552	−	0.858322i
$982$		0			0
$983$	10.8235	+	18.7468i	0.345215	+	0.597930i	0.985393	−	0.170297i	$-0.0544727\pi$
$983$	10.8235	+	18.7468i	0.345215	+	0.597930i	−0.640178	+	0.768227i	$0.721139\pi$
$984$		0			0
$985$			17.0553i			0.543427i
$986$		0			0
$987$	−8.08089	+	4.66550i	−0.257218	+	0.148505i
$988$		0			0
$989$		−	15.2119i		−	0.483710i
$990$		0			0
$991$			44.7931i			1.42290i	0.702736	+	0.711451i	$0.251961\pi$
$991$			44.7931i			1.42290i	−0.702736	+	0.711451i	$0.748039\pi$
$992$		0			0
$993$		−	1.54539i		−	0.0490416i
$994$		0			0
$995$	−4.01442	−	2.31773i	−0.127266	−	0.0734769i
$996$		0			0
$997$	13.7735	+	23.8564i	0.436211	+	0.755539i	0.997394	−	0.0721525i	$-0.0229868\pi$
$997$	13.7735	+	23.8564i	0.436211	+	0.755539i	−0.561183	+	0.827692i	$0.689653\pi$
$998$		0			0
$999$	−22.4852	−	0.292438i	−0.711399	−	0.00925233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.y.a.529.21		72
4.3	odd	2		296.2.q.a.85.33	yes	72
8.3	odd	2		296.2.q.a.85.21	✓	72
8.5	even	2	inner	1184.2.y.a.529.16		72
37.27	even	6	inner	1184.2.y.a.1137.16		72
148.27	odd	6		296.2.q.a.101.21	yes	72
296.27	odd	6		296.2.q.a.101.33	yes	72
296.101	even	6	inner	1184.2.y.a.1137.21		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.21	✓	72	8.3	odd	2
296.2.q.a.85.33	yes	72	4.3	odd	2
296.2.q.a.101.21	yes	72	148.27	odd	6
296.2.q.a.101.33	yes	72	296.27	odd	6
1184.2.y.a.529.16		72	8.5	even	2	inner
1184.2.y.a.529.21		72	1.1	even	1	trivial
1184.2.y.a.1137.16		72	37.27	even	6	inner
1184.2.y.a.1137.21		72	296.101	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.576079 + 0.332599i) q^{3} +(-1.60874 + 2.78642i) q^{5} +(0.874135 - 1.51405i) q^{7} +(-1.27876 - 2.21487i) q^{9} -3.96429i q^{11} +(0.268480 - 0.465021i) q^{13} +(-1.85352 + 1.07013i) q^{15} +(6.04097 - 3.48776i) q^{17} +(-2.21841 + 3.84239i) q^{19} +(1.00714 - 0.581474i) q^{21} -2.14898i q^{23} +(-2.67607 - 4.63509i) q^{25} -3.69685i q^{27} +3.76282 q^{29} -1.95692i q^{31} +(1.31852 - 2.28375i) q^{33} +(2.81251 + 4.87141i) q^{35} +(0.0791047 - 6.08225i) q^{37} +(0.309331 - 0.178593i) q^{39} +(1.70672 - 2.95613i) q^{41} +7.07866 q^{43} +8.22873 q^{45} -8.02359 q^{47} +(1.97178 + 3.41521i) q^{49} +4.64010 q^{51} +(0.341615 - 0.197231i) q^{53} +(11.0462 + 6.37751i) q^{55} +(-2.55596 + 1.47568i) q^{57} +(4.26642 + 7.38966i) q^{59} +(0.607843 - 1.05282i) q^{61} -4.47122 q^{63} +(0.863828 + 1.49619i) q^{65} +(7.25109 + 4.18642i) q^{67} +(0.714748 - 1.23798i) q^{69} +(2.54377 - 4.40594i) q^{71} +2.30870 q^{73} -3.56024i q^{75} +(-6.00212 - 3.46533i) q^{77} +(2.04786 + 1.18233i) q^{79} +(-2.60670 + 4.51493i) q^{81} +(-1.40655 + 0.812073i) q^{83} +22.4435i q^{85} +(2.16768 + 1.25151i) q^{87} +(13.0089 - 7.51069i) q^{89} +(-0.469376 - 0.812982i) q^{91} +(0.650872 - 1.12734i) q^{93} +(-7.13767 - 12.3628i) q^{95} -16.7828i q^{97} +(-8.78039 + 5.06936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) \) 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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