LMFDB - Embedded newform 765.2.n.e.188.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(188,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.188"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			188.1
Character	$\chi$	$=$	765.188
Dual form			765.2.n.e.647.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73886 - 1.73886i) q^{2} +4.04726i q^{4} +(-2.10859 - 0.744208i) q^{5} +(-0.649310 + 0.649310i) q^{7} +(3.55991 - 3.55991i) q^{8} +(2.37247 + 4.96062i) q^{10} -3.82089i q^{11} +(-3.86577 - 3.86577i) q^{13} +2.25812 q^{14} -4.28582 q^{16} +(-0.707107 - 0.707107i) q^{17} +0.869466i q^{19} +(3.01201 - 8.53402i) q^{20} +(-6.64399 + 6.64399i) q^{22} +(-4.26701 + 4.26701i) q^{23} +(3.89231 + 3.13846i) q^{25} +13.4441i q^{26} +(-2.62793 - 2.62793i) q^{28} +2.62630 q^{29} +5.98261 q^{31} +(0.332630 + 0.332630i) q^{32} +2.45912i q^{34} +(1.85235 - 0.885907i) q^{35} +(-3.97330 + 3.97330i) q^{37} +(1.51188 - 1.51188i) q^{38} +(-10.1557 + 4.85707i) q^{40} +8.63126i q^{41} +(0.316622 + 0.316622i) q^{43} +15.4642 q^{44} +14.8395 q^{46} +(8.13256 + 8.13256i) q^{47} +6.15679i q^{49} +(-1.31084 - 12.2255i) q^{50} +(15.6458 - 15.6458i) q^{52} +(-3.07625 + 3.07625i) q^{53} +(-2.84354 + 8.05670i) q^{55} +4.62296i q^{56} +(-4.56676 - 4.56676i) q^{58} -9.94824 q^{59} -4.43292 q^{61} +(-10.4029 - 10.4029i) q^{62} +7.41485i q^{64} +(5.27439 + 11.0283i) q^{65} +(6.18239 - 6.18239i) q^{67} +(2.86185 - 2.86185i) q^{68} +(-4.76144 - 1.68051i) q^{70} +8.53402i q^{71} +(-4.00931 - 4.00931i) q^{73} +13.8180 q^{74} -3.51896 q^{76} +(2.48094 + 2.48094i) q^{77} -3.15768i q^{79} +(9.03704 + 3.18954i) q^{80} +(15.0086 - 15.0086i) q^{82} +(-1.06001 + 1.06001i) q^{83} +(0.964764 + 2.01723i) q^{85} -1.10112i q^{86} +(-13.6020 - 13.6020i) q^{88} +11.1735 q^{89} +5.02016 q^{91} +(-17.2697 - 17.2697i) q^{92} -28.2827i q^{94} +(0.647063 - 1.83335i) q^{95} +(9.02016 - 9.02016i) q^{97} +(10.7058 - 10.7058i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{7} - 20 q^{10} - 20 q^{13} - 8 q^{16} - 40 q^{22} - 24 q^{28} + 72 q^{31} + 16 q^{37} - 88 q^{40} + 36 q^{43} + 56 q^{46} + 32 q^{52} - 88 q^{55} - 80 q^{58} - 8 q^{61} + 104 q^{67} - 136 q^{70}+ \cdots + 88 q^{97}+O(q^{100}) $ 24 * q + 8 * q^7 - 20 * q^10 - 20 * q^13 - 8 * q^16 - 40 * q^22 - 24 * q^28 + 72 * q^31 + 16 * q^37 - 88 * q^40 + 36 * q^43 + 56 * q^46 + 32 * q^52 - 88 * q^55 - 80 * q^58 - 8 * q^61 + 104 * q^67 - 136 * q^70 - 136 * q^73 + 136 * q^76 + 16 * q^82 + 8 * q^85 - 64 * q^88 - 8 * q^91 + 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.73886	−	1.73886i	−1.22956	−	1.22956i	−0.964130	−	0.265429i	$-0.914486\pi$
$2$	−1.73886	−	1.73886i	−1.22956	−	1.22956i	−0.265429	−	0.964130i	$-0.585514\pi$
$3$		0			0
$3$		0			0
$4$			4.04726i			2.02363i
$5$	−2.10859	−	0.744208i	−0.942990	−	0.332820i
$5$	−2.10859	−	0.744208i	−0.942990	−	0.332820i
$6$		0			0
$7$	−0.649310	+	0.649310i	−0.245416	+	0.245416i	−0.819086	−	0.573670i	$-0.805519\pi$
$7$	−0.649310	+	0.649310i	−0.245416	+	0.245416i	0.573670	+	0.819086i	$0.305519\pi$
$8$	3.55991	−	3.55991i	1.25862	−	1.25862i
$9$		0			0
$10$	2.37247	+	4.96062i	0.750241	+	1.56868i
$11$		−	3.82089i		−	1.15204i	−0.817435	−	0.576021i	$-0.804605\pi$
$11$		−	3.82089i		−	1.15204i	0.817435	−	0.576021i	$-0.195395\pi$
$12$		0			0
$13$	−3.86577	−	3.86577i	−1.07217	−	1.07217i	−0.997185	−	0.0749867i	$-0.976109\pi$
$13$	−3.86577	−	3.86577i	−1.07217	−	1.07217i	−0.0749867	−	0.997185i	$-0.523891\pi$
$14$	2.25812			0.603507
$15$		0			0
$16$	−4.28582			−1.07146
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$18$		0			0
$19$			0.869466i			0.199469i	0.995014	+	0.0997346i	$0.0317994\pi$
$19$			0.869466i			0.199469i	−0.995014	+	0.0997346i	$0.968201\pi$
$20$	3.01201	−	8.53402i	0.673505	−	1.90827i
$21$		0			0
$22$	−6.64399	+	6.64399i	−1.41650	+	1.41650i
$23$	−4.26701	+	4.26701i	−0.889734	+	0.889734i	−0.994497	−	0.104764i	$-0.966591\pi$
$23$	−4.26701	+	4.26701i	−0.889734	+	0.889734i	0.104764	+	0.994497i	$0.466591\pi$
$24$		0			0
$25$	3.89231	+	3.13846i	0.778462	+	0.627692i
$26$			13.4441i			2.63660i
$27$		0			0
$28$	−2.62793	−	2.62793i	−0.496632	−	0.496632i
$29$	2.62630			0.487691			0.243846	−	0.969814i	$-0.421591\pi$
$29$	2.62630			0.487691			0.243846	+	0.969814i	$0.421591\pi$
$30$		0			0
$31$	5.98261			1.07451			0.537254	−	0.843420i	$-0.319462\pi$
$31$	5.98261			1.07451			0.537254	+	0.843420i	$0.319462\pi$
$32$	0.332630	+	0.332630i	0.0588012	+	0.0588012i
$33$		0			0
$34$			2.45912i			0.421735i
$35$	1.85235	−	0.885907i	0.313104	−	0.149746i
$36$		0			0
$37$	−3.97330	+	3.97330i	−0.653207	+	0.653207i	−0.953764	−	0.300557i	$-0.902827\pi$
$37$	−3.97330	+	3.97330i	−0.653207	+	0.653207i	0.300557	+	0.953764i	$0.402827\pi$
$38$	1.51188	−	1.51188i	0.245259	−	0.245259i
$39$		0			0
$40$	−10.1557	+	4.85707i	−1.60576	+	0.767971i
$41$			8.63126i			1.34798i	0.738742	+	0.673988i	$0.235420\pi$
$41$			8.63126i			1.34798i	−0.738742	+	0.673988i	$0.764580\pi$
$42$		0			0
$43$	0.316622	+	0.316622i	0.0482844	+	0.0482844i	0.730837	−	0.682552i	$-0.239130\pi$
$43$	0.316622	+	0.316622i	0.0482844	+	0.0482844i	−0.682552	+	0.730837i	$0.739130\pi$
$44$	15.4642			2.33131
$45$		0			0
$46$	14.8395			2.18796
$47$	8.13256	+	8.13256i	1.18626	+	1.18626i	0.978095	+	0.208161i	$0.0667476\pi$
$47$	8.13256	+	8.13256i	1.18626	+	1.18626i	0.208161	+	0.978095i	$0.433252\pi$
$48$		0			0
$49$			6.15679i			0.879542i
$50$	−1.31084	−	12.2255i	−0.185381	−	1.72895i
$51$		0			0
$52$	15.6458	−	15.6458i	2.16968	−	2.16968i
$53$	−3.07625	+	3.07625i	−0.422556	+	0.422556i	−0.886083	−	0.463527i	$-0.846584\pi$
$53$	−3.07625	+	3.07625i	−0.422556	+	0.422556i	0.463527	+	0.886083i	$0.346584\pi$
$54$		0			0
$55$	−2.84354	+	8.05670i	−0.383423	+	1.08636i
$56$			4.62296i			0.617769i
$57$		0			0
$58$	−4.56676	−	4.56676i	−0.599646	−	0.599646i
$59$	−9.94824			−1.29515			−0.647575	−	0.762002i	$-0.724217\pi$
$59$	−9.94824			−1.29515			−0.647575	+	0.762002i	$0.724217\pi$
$60$		0			0
$61$	−4.43292			−0.567577			−0.283788	−	0.958887i	$-0.591591\pi$
$61$	−4.43292			−0.567577			−0.283788	+	0.958887i	$0.591591\pi$
$62$	−10.4029	−	10.4029i	−1.32117	−	1.32117i
$63$		0			0
$64$			7.41485i			0.926856i
$65$	5.27439	+	11.0283i	0.654207	+	1.36789i
$66$		0			0
$67$	6.18239	−	6.18239i	0.755299	−	0.755299i	−0.220164	−	0.975463i	$-0.570659\pi$
$67$	6.18239	−	6.18239i	0.755299	−	0.755299i	0.975463	+	0.220164i	$0.0706592\pi$
$68$	2.86185	−	2.86185i	0.347050	−	0.347050i
$69$		0			0
$70$	−4.76144	−	1.68051i	−0.569101	−	0.200859i
$71$			8.53402i			1.01280i	0.862298	+	0.506401i	$0.169024\pi$
$71$			8.53402i			1.01280i	−0.862298	+	0.506401i	$0.830976\pi$
$72$		0			0
$73$	−4.00931	−	4.00931i	−0.469254	−	0.469254i	0.432419	−	0.901673i	$-0.357660\pi$
$73$	−4.00931	−	4.00931i	−0.469254	−	0.469254i	−0.901673	+	0.432419i	$0.857660\pi$
$74$	13.8180			1.60631
$75$		0			0
$76$	−3.51896			−0.403652
$77$	2.48094	+	2.48094i	0.282730	+	0.282730i
$78$		0			0
$79$		−	3.15768i		−	0.355266i	−0.984097	−	0.177633i	$-0.943156\pi$
$79$		−	3.15768i		−	0.355266i	0.984097	−	0.177633i	$-0.0568441\pi$
$80$	9.03704	+	3.18954i	1.01037	+	0.356602i
$81$		0			0
$82$	15.0086	−	15.0086i	1.65742	−	1.65742i
$83$	−1.06001	+	1.06001i	−0.116351	+	0.116351i	−0.762885	−	0.646534i	$-0.776218\pi$
$83$	−1.06001	+	1.06001i	−0.116351	+	0.116351i	0.646534	+	0.762885i	$0.276218\pi$
$84$		0			0
$85$	0.964764	+	2.01723i	0.104643	+	0.218800i
$86$		−	1.10112i		−	0.118737i
$87$		0			0
$88$	−13.6020	−	13.6020i	−1.44998	−	1.44998i
$89$	11.1735			1.18439			0.592194	−	0.805796i	$-0.298262\pi$
$89$	11.1735			1.18439			0.592194	+	0.805796i	$0.298262\pi$
$90$		0			0
$91$	5.02016			0.526256
$92$	−17.2697	−	17.2697i	−1.80049	−	1.80049i
$93$		0			0
$94$		−	28.2827i		−	2.91714i
$95$	0.647063	−	1.83335i	0.0663873	−	0.188098i
$96$		0			0
$97$	9.02016	−	9.02016i	0.915859	−	0.915859i	−0.0808663	−	0.996725i	$-0.525769\pi$
$97$	9.02016	−	9.02016i	0.915859	−	0.915859i	0.996725	+	0.0808663i	$0.0257687\pi$
$98$	10.7058	−	10.7058i	1.08145	−	1.08145i
$99$		0			0
$100$	−12.7022	+	15.7532i	−1.27022	+	1.57532i
$101$		−	10.2972i		−	1.02461i	−0.858803	−	0.512306i	$-0.828792\pi$
$101$		−	10.2972i		−	1.02461i	0.858803	−	0.512306i	$-0.171208\pi$
$102$		0			0
$103$	8.57226	+	8.57226i	0.844649	+	0.844649i	0.989459	−	0.144810i	$-0.0462571\pi$
$103$	8.57226	+	8.57226i	0.844649	+	0.844649i	−0.144810	+	0.989459i	$0.546257\pi$
$104$	−27.5235			−2.69891
$105$		0			0
$106$	10.6983			1.03911
$107$	−8.96698	−	8.96698i	−0.866871	−	0.866871i	0.125254	−	0.992125i	$-0.460025\pi$
$107$	−8.96698	−	8.96698i	−0.866871	−	0.866871i	−0.992125	+	0.125254i	$0.960025\pi$
$108$		0			0
$109$			15.0983i			1.44615i	0.690767	+	0.723077i	$0.257273\pi$
$109$			15.0983i			1.44615i	−0.690767	+	0.723077i	$0.742727\pi$
$110$	18.9540	−	9.06495i	1.80719	−	0.864309i
$111$		0			0
$112$	2.78283	−	2.78283i	0.262952	−	0.262952i
$113$	−8.42372	+	8.42372i	−0.792437	+	0.792437i	−0.981890	−	0.189453i	$-0.939328\pi$
$113$	−8.42372	+	8.42372i	−0.792437	+	0.792437i	0.189453	+	0.981890i	$0.439328\pi$
$114$		0			0
$115$	12.1729	−	5.82184i	1.13513	−	0.542889i
$116$			10.6293i			0.986908i
$117$		0			0
$118$	17.2986	+	17.2986i	1.59246	+	1.59246i
$119$	0.918263			0.0841770
$120$		0			0
$121$	−3.59921			−0.327201
$122$	7.70822	+	7.70822i	0.697870	+	0.697870i
$123$		0			0
$124$			24.2132i			2.17441i
$125$	−5.87162	−	9.51441i	−0.525174	−	0.850995i
$126$		0			0
$127$	−1.10864	+	1.10864i	−0.0983755	+	0.0983755i	−0.754582	−	0.656206i	$-0.772160\pi$
$127$	−1.10864	+	1.10864i	−0.0983755	+	0.0983755i	0.656206	+	0.754582i	$0.272160\pi$
$128$	13.5586	−	13.5586i	1.19843	−	1.19843i
$129$		0			0
$130$	10.0052	−	28.3480i	0.877512	−	2.48629i
$131$			18.4831i			1.61488i	0.589951	+	0.807439i	$0.299147\pi$
$131$			18.4831i			1.61488i	−0.589951	+	0.807439i	$0.700853\pi$
$132$		0			0
$133$	−0.564553	−	0.564553i	−0.0489529	−	0.0489529i
$134$	−21.5006			−1.85737
$135$		0			0
$136$	−5.03447			−0.431702
$137$	−7.14067	−	7.14067i	−0.610068	−	0.610068i	0.332896	−	0.942964i	$-0.391974\pi$
$137$	−7.14067	−	7.14067i	−0.610068	−	0.610068i	−0.942964	+	0.332896i	$0.891974\pi$
$138$		0			0
$139$		−	10.4884i		−	0.889617i	−0.895626	−	0.444808i	$-0.853272\pi$
$139$		−	10.4884i		−	0.889617i	0.895626	−	0.444808i	$-0.146728\pi$
$140$	3.58550	+	7.49695i	0.303030	+	0.633608i
$141$		0			0
$142$	14.8395	−	14.8395i	1.24530	−	1.24530i
$143$	−14.7707	+	14.7707i	−1.23519	+	1.23519i
$144$		0			0
$145$	−5.53779	−	1.95451i	−0.459888	−	0.162313i
$146$			13.9432i			1.15395i
$147$		0			0
$148$	−16.0810	−	16.0810i	−1.32185	−	1.32185i
$149$	13.5851			1.11293			0.556467	−	0.830870i	$-0.312157\pi$
$149$	13.5851			1.11293			0.556467	+	0.830870i	$0.312157\pi$
$150$		0			0
$151$	−19.9261			−1.62156			−0.810782	−	0.585348i	$-0.800958\pi$
$151$	−19.9261			−1.62156			−0.810782	+	0.585348i	$0.800958\pi$
$152$	3.09522	+	3.09522i	0.251055	+	0.251055i
$153$		0			0
$154$		−	8.62802i		−	0.695266i
$155$	−12.6149	−	4.45231i	−1.01325	−	0.357618i
$156$		0			0
$157$	−12.1028	+	12.1028i	−0.965908	+	0.965908i	−0.999438	−	0.0335302i	$-0.989325\pi$
$157$	−12.1028	+	12.1028i	−0.965908	+	0.965908i	0.0335302	+	0.999438i	$0.489325\pi$
$158$	−5.49076	+	5.49076i	−0.436821	+	0.436821i
$159$		0			0
$160$	−0.453835	−	0.948927i	−0.0358788	−	0.0750192i
$161$		−	5.54122i		−	0.436710i
$162$		0			0
$163$	4.85496	+	4.85496i	0.380270	+	0.380270i	0.871199	−	0.490929i	$-0.163343\pi$
$163$	4.85496	+	4.85496i	0.380270	+	0.380270i	−0.490929	+	0.871199i	$0.663343\pi$
$164$	−34.9330			−2.72781
$165$		0			0
$166$	3.68641			0.286121
$167$	14.6455	+	14.6455i	1.13330	+	1.13330i	0.989624	+	0.143678i	$0.0458929\pi$
$167$	14.6455	+	14.6455i	1.13330	+	1.13330i	0.143678	+	0.989624i	$0.454107\pi$
$168$		0			0
$169$			16.8883i			1.29910i
$170$	1.83010	−	5.18527i	0.140362	−	0.397692i
$171$		0			0
$172$	−1.28145	+	1.28145i	−0.0977098	+	0.0977098i
$173$	−9.00560	+	9.00560i	−0.684683	+	0.684683i	−0.961052	−	0.276368i	$-0.910869\pi$
$173$	−9.00560	+	9.00560i	−0.684683	+	0.684683i	0.276368	+	0.961052i	$0.410869\pi$
$174$		0			0
$175$	−4.56515	+	0.489482i	−0.345093	+	0.0370013i
$176$			16.3757i			1.23436i
$177$		0			0
$178$	−19.4291	−	19.4291i	−1.45627	−	1.45627i
$179$	−8.25053			−0.616674			−0.308337	−	0.951277i	$-0.599772\pi$
$179$	−8.25053			−0.616674			−0.308337	+	0.951277i	$0.599772\pi$
$180$		0			0
$181$	−11.0128			−0.818572			−0.409286	−	0.912406i	$-0.634222\pi$
$181$	−11.0128			−0.818572			−0.409286	+	0.912406i	$0.634222\pi$
$182$	−8.72936	−	8.72936i	−0.647063	−	0.647063i
$183$		0			0
$184$			30.3803i			2.23967i
$185$	11.3350	−	5.42111i	0.833368	−	0.398568i
$186$		0			0
$187$	−2.70178	+	2.70178i	−0.197574	+	0.197574i
$188$	−32.9146	+	32.9146i	−2.40054	+	2.40054i
$189$		0			0
$190$	−4.31309	+	2.06278i	−0.312904	+	0.149650i
$191$		−	6.32126i		−	0.457390i	−0.973498	−	0.228695i	$-0.926554\pi$
$191$		−	6.32126i		−	0.457390i	0.973498	−	0.228695i	$-0.0734459\pi$
$192$		0			0
$193$	−4.71723	−	4.71723i	−0.339554	−	0.339554i	0.516646	−	0.856199i	$-0.327180\pi$
$193$	−4.71723	−	4.71723i	−0.339554	−	0.339554i	−0.856199	+	0.516646i	$0.827180\pi$
$194$	−31.3696			−2.25221
$195$		0			0
$196$	−24.9182			−1.77987
$197$	1.78118	+	1.78118i	0.126904	+	0.126904i	0.767706	−	0.640802i	$-0.221398\pi$
$197$	1.78118	+	1.78118i	0.126904	+	0.126904i	−0.640802	+	0.767706i	$0.721398\pi$
$198$		0			0
$199$		−	4.54605i		−	0.322261i	−0.986933	−	0.161130i	$-0.948486\pi$
$199$		−	4.54605i		−	0.322261i	0.986933	−	0.161130i	$-0.0515139\pi$
$200$	25.0289	−	2.68363i	1.76981	−	0.189762i
$201$		0			0
$202$	−17.9054	+	17.9054i	−1.25982	+	1.25982i
$203$	−1.70528	+	1.70528i	−0.119687	+	0.119687i
$204$		0			0
$205$	6.42345	−	18.1998i	0.448633	−	1.27113i
$206$		−	29.8119i		−	2.07709i
$207$		0			0
$208$	16.5680	+	16.5680i	1.14878	+	1.14878i
$209$	3.32214			0.229797
$210$		0			0
$211$	−17.3827			−1.19668			−0.598339	−	0.801243i	$-0.704172\pi$
$211$	−17.3827			−1.19668			−0.598339	+	0.801243i	$0.704172\pi$
$212$	−12.4504	−	12.4504i	−0.855097	−	0.855097i
$213$		0			0
$214$			31.1846i			2.13174i
$215$	−0.431993	−	0.903258i	−0.0294617	−	0.0616017i
$216$		0			0
$217$	−3.88457	+	3.88457i	−0.263702	+	0.263702i
$218$	26.2538	−	26.2538i	1.77813	−	1.77813i
$219$		0			0
$220$	−32.6076	−	11.5086i	−2.19840	−	0.775906i
$221$			5.46702i			0.367752i
$222$		0			0
$223$	−11.6803	−	11.6803i	−0.782169	−	0.782169i	0.198027	−	0.980197i	$-0.436547\pi$
$223$	−11.6803	−	11.6803i	−0.782169	−	0.782169i	−0.980197	+	0.198027i	$0.936547\pi$
$224$	−0.431960			−0.0288615
$225$		0			0
$226$	29.2953			1.94870
$227$	10.4038	+	10.4038i	0.690528	+	0.690528i	0.962348	−	0.271820i	$-0.0876256\pi$
$227$	10.4038	+	10.4038i	0.690528	+	0.690528i	−0.271820	+	0.962348i	$0.587626\pi$
$228$		0			0
$229$			26.4574i			1.74836i	0.485605	+	0.874178i	$0.338599\pi$
$229$			26.4574i			1.74836i	−0.485605	+	0.874178i	$0.661401\pi$
$230$	−31.2904	−	11.0436i	−2.06323	−	0.728197i
$231$		0			0
$232$	9.34937	−	9.34937i	0.613816	−	0.613816i
$233$	3.76032	−	3.76032i	0.246347	−	0.246347i	−0.573123	−	0.819470i	$-0.694268\pi$
$233$	3.76032	−	3.76032i	0.246347	−	0.246347i	0.819470	+	0.573123i	$0.194268\pi$
$234$		0			0
$235$	−11.0959	−	23.2005i	−0.723818	−	1.51344i
$236$		−	40.2632i		−	2.62091i
$237$		0			0
$238$	−1.59673	−	1.59673i	−0.103501	−	0.103501i
$239$	2.48981			0.161052			0.0805262	−	0.996752i	$-0.474340\pi$
$239$	2.48981			0.161052			0.0805262	+	0.996752i	$0.474340\pi$
$240$		0			0
$241$	22.6242			1.45735			0.728676	−	0.684859i	$-0.240136\pi$
$241$	22.6242			1.45735			0.728676	+	0.684859i	$0.240136\pi$
$242$	6.25853	+	6.25853i	0.402313	+	0.402313i
$243$		0			0
$244$		−	17.9412i		−	1.14857i
$245$	4.58193	−	12.9822i	0.292729	−	0.829400i
$246$		0			0
$247$	3.36115	−	3.36115i	0.213865	−	0.213865i
$248$	21.2975	−	21.2975i	1.35239	−	1.35239i
$249$		0			0
$250$	−6.33431	+	26.7542i	−0.400617	+	1.69208i
$251$		−	17.9719i		−	1.13438i	−0.823588	−	0.567188i	$-0.808031\pi$
$251$		−	17.9719i		−	1.13438i	0.823588	−	0.567188i	$-0.191969\pi$
$252$		0			0
$253$	16.3038	+	16.3038i	1.02501	+	1.02501i
$254$	3.85552			0.241917
$255$		0			0
$256$	−32.3234			−2.02022
$257$	19.4055	+	19.4055i	1.21048	+	1.21048i	0.970869	+	0.239611i	$0.0770200\pi$
$257$	19.4055	+	19.4055i	1.21048	+	1.21048i	0.239611	+	0.970869i	$0.422980\pi$
$258$		0			0
$259$		−	5.15981i		−	0.320615i
$260$	−44.6343	+	21.3468i	−2.76810	+	1.32387i
$261$		0			0
$262$	32.1396	−	32.1396i	1.98559	−	1.98559i
$263$	−17.4147	+	17.4147i	−1.07384	+	1.07384i	−0.0767876	+	0.997047i	$0.524466\pi$
$263$	−17.4147	+	17.4147i	−1.07384	+	1.07384i	−0.997047	+	0.0767876i	$0.975534\pi$
$264$		0			0
$265$	8.77592	−	4.19718i	0.539101	−	0.257831i
$266$			1.96336i			0.120381i
$267$		0			0
$268$	25.0218	+	25.0218i	1.52845	+	1.52845i
$269$	−6.09852			−0.371833			−0.185917	−	0.982566i	$-0.559525\pi$
$269$	−6.09852			−0.371833			−0.185917	+	0.982566i	$0.559525\pi$
$270$		0			0
$271$	−19.8536			−1.20602			−0.603009	−	0.797735i	$-0.706032\pi$
$271$	−19.8536			−1.20602			−0.603009	+	0.797735i	$0.706032\pi$
$272$	3.03053	+	3.03053i	0.183753	+	0.183753i
$273$		0			0
$274$			24.8332i			1.50023i
$275$	11.9917	−	14.8721i	0.723128	−	0.896821i
$276$		0			0
$277$	−8.92288	+	8.92288i	−0.536124	+	0.536124i	−0.922388	−	0.386264i	$-0.873765\pi$
$277$	−8.92288	+	8.92288i	−0.536124	+	0.536124i	0.386264	+	0.922388i	$0.373765\pi$
$278$	−18.2379	+	18.2379i	−1.09384	+	1.09384i
$279$		0			0
$280$	3.44044	−	9.74793i	0.205606	−	0.582550i
$281$		−	25.7707i		−	1.53735i	−0.639639	−	0.768676i	$-0.720916\pi$
$281$		−	25.7707i		−	1.53735i	0.639639	−	0.768676i	$-0.279084\pi$
$282$		0			0
$283$	−6.45731	−	6.45731i	−0.383847	−	0.383847i	0.488639	−	0.872486i	$-0.337494\pi$
$283$	−6.45731	−	6.45731i	−0.383847	−	0.383847i	−0.872486	+	0.488639i	$0.837494\pi$
$284$	−34.5395			−2.04954
$285$		0			0
$286$	51.3683			3.03747
$287$	−5.60436	−	5.60436i	−0.330815	−	0.330815i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$	6.23081	+	13.0281i	0.365886	+	0.765034i
$291$		0			0
$292$	16.2267	−	16.2267i	0.949597	−	0.949597i
$293$	1.85274	−	1.85274i	0.108238	−	0.108238i	−0.650914	−	0.759152i	$-0.725614\pi$
$293$	1.85274	−	1.85274i	0.108238	−	0.108238i	0.759152	+	0.650914i	$0.225614\pi$
$294$		0			0
$295$	20.9768	+	7.40356i	1.22131	+	0.431052i
$296$			28.2892i			1.64427i
$297$		0			0
$298$	−23.6226	−	23.6226i	−1.36842	−	1.36842i
$299$	32.9906			1.90789
$300$		0			0
$301$	−0.411171			−0.0236995
$302$	34.6487	+	34.6487i	1.99381	+	1.99381i
$303$		0			0
$304$		−	3.72638i		−	0.213722i
$305$	9.34721	+	3.29901i	0.535220	+	0.188901i
$306$		0			0
$307$	14.9517	−	14.9517i	0.853339	−	0.853339i	−0.137204	−	0.990543i	$-0.543811\pi$
$307$	14.9517	−	14.9517i	0.853339	−	0.853339i	0.990543	+	0.137204i	$0.0438115\pi$
$308$	−10.0410	+	10.0410i	−0.572141	+	0.572141i
$309$		0			0
$310$	14.1936	+	29.6774i	0.806140	+	1.68556i
$311$		−	15.0297i		−	0.852257i	−0.904663	−	0.426128i	$-0.859877\pi$
$311$		−	15.0297i		−	0.852257i	0.904663	−	0.426128i	$-0.140123\pi$
$312$		0			0
$313$	−1.02361	−	1.02361i	−0.0578580	−	0.0578580i	0.677586	−	0.735444i	$-0.263026\pi$
$313$	−1.02361	−	1.02361i	−0.0578580	−	0.0578580i	−0.735444	+	0.677586i	$0.763026\pi$
$314$	42.0901			2.37528
$315$		0			0
$316$	12.7800			0.718928
$317$	22.7909	+	22.7909i	1.28006	+	1.28006i	0.940630	+	0.339434i	$0.110236\pi$
$317$	22.7909	+	22.7909i	1.28006	+	1.28006i	0.339434	+	0.940630i	$0.389764\pi$
$318$		0			0
$319$		−	10.0348i		−	0.561841i
$320$	5.51819	−	15.6349i	0.308476	−	0.874016i
$321$		0			0
$322$	−9.63541	+	9.63541i	−0.536960	+	0.536960i
$323$	0.614805	−	0.614805i	0.0342087	−	0.0342087i
$324$		0			0
$325$	−2.91421	−	27.1793i	−0.161651	−	1.50764i
$326$		−	16.8842i		−	0.935129i
$327$		0			0
$328$	30.7265	+	30.7265i	1.69659	+	1.69659i
$329$	−10.5611			−0.582252
$330$		0			0
$331$	−18.6624			−1.02578			−0.512889	−	0.858455i	$-0.671425\pi$
$331$	−18.6624			−1.02578			−0.512889	+	0.858455i	$0.671425\pi$
$332$	−4.29014	−	4.29014i	−0.235452	−	0.235452i
$333$		0			0
$334$		−	50.9329i		−	2.78693i
$335$	−17.6371	+	8.43515i	−0.963618	+	0.460861i
$336$		0			0
$337$	−25.3545	+	25.3545i	−1.38115	+	1.38115i	−0.538562	+	0.842586i	$0.681032\pi$
$337$	−25.3545	+	25.3545i	−1.38115	+	1.38115i	−0.842586	+	0.538562i	$0.818968\pi$
$338$	29.3664	−	29.3664i	1.59732	−	1.59732i
$339$		0			0
$340$	−8.16428	+	3.90466i	−0.442770	+	0.211760i
$341$		−	22.8589i		−	1.23788i
$342$		0			0
$343$	−8.54283	−	8.54283i	−0.461270	−	0.461270i
$344$	2.25429			0.121543
$345$		0			0
$346$	31.3190			1.68372
$347$	−17.8363	−	17.8363i	−0.957505	−	0.957505i	0.0416278	−	0.999133i	$-0.486746\pi$
$347$	−17.8363	−	17.8363i	−0.957505	−	0.957505i	−0.999133	+	0.0416278i	$0.986746\pi$
$348$		0			0
$349$		−	18.2426i		−	0.976504i	−0.872703	−	0.488252i	$-0.837635\pi$
$349$		−	18.2426i		−	0.976504i	0.872703	−	0.488252i	$-0.162365\pi$
$350$	8.78929	+	7.08701i	0.469807	+	0.378816i
$351$		0			0
$352$	1.27094	−	1.27094i	0.0677415	−	0.0677415i
$353$	16.1617	−	16.1617i	0.860201	−	0.860201i	−0.131160	−	0.991361i	$-0.541870\pi$
$353$	16.1617	−	16.1617i	0.860201	−	0.860201i	0.991361	+	0.131160i	$0.0418702\pi$
$354$		0			0
$355$	6.35109	−	17.9948i	0.337081	−	0.955063i
$356$			45.2221i			2.39676i
$357$		0			0
$358$	14.3465	+	14.3465i	0.758237	+	0.758237i
$359$	−13.0285			−0.687618			−0.343809	−	0.939040i	$-0.611717\pi$
$359$	−13.0285			−0.687618			−0.343809	+	0.939040i	$0.611717\pi$
$360$		0			0
$361$	18.2440			0.960212
$362$	19.1497	+	19.1497i	1.00648	+	1.00648i
$363$		0			0
$364$			20.3179i			1.06495i
$365$	5.47023	+	11.4377i	0.286325	+	0.598679i
$366$		0			0
$367$	−12.0293	+	12.0293i	−0.627923	+	0.627923i	−0.947545	−	0.319622i	$-0.896444\pi$
$367$	−12.0293	+	12.0293i	−0.627923	+	0.627923i	0.319622	+	0.947545i	$0.396444\pi$
$368$	18.2877	−	18.2877i	0.953310	−	0.953310i
$369$		0			0
$370$	−29.1366	−	10.2835i	−1.51474	−	0.534613i
$371$		−	3.99488i		−	0.207404i
$372$		0			0
$373$	−14.9740	−	14.9740i	−0.775324	−	0.775324i	0.203708	−	0.979032i	$-0.434701\pi$
$373$	−14.9740	−	14.9740i	−0.775324	−	0.775324i	−0.979032	+	0.203708i	$0.934701\pi$
$374$	9.39603			0.485857
$375$		0			0
$376$	57.9023			2.98608
$377$	−10.1527	−	10.1527i	−0.522889	−	0.522889i
$378$		0			0
$379$		−	25.3462i		−	1.30195i	−0.759101	−	0.650973i	$-0.774361\pi$
$379$		−	25.3462i		−	1.30195i	0.759101	−	0.650973i	$-0.225639\pi$
$380$	7.42004	+	2.61884i	0.380640	+	0.134343i
$381$		0			0
$382$	−10.9918	+	10.9918i	−0.562388	+	0.562388i
$383$	14.7252	−	14.7252i	0.752421	−	0.752421i	−0.222510	−	0.974930i	$-0.571425\pi$
$383$	14.7252	−	14.7252i	0.752421	−	0.752421i	0.974930	+	0.222510i	$0.0714249\pi$
$384$		0			0
$385$	−3.38495	−	7.07763i	−0.172513	−	0.360709i
$386$			16.4052i			0.835003i
$387$		0			0
$388$	36.5070	+	36.5070i	1.85336	+	1.85336i
$389$	30.1854			1.53046			0.765231	−	0.643756i	$-0.222625\pi$
$389$	30.1854			1.53046			0.765231	+	0.643756i	$0.222625\pi$
$390$		0			0
$391$	6.03447			0.305176
$392$	21.9176	+	21.9176i	1.10701	+	1.10701i
$393$		0			0
$394$		−	6.19446i		−	0.312072i
$395$	−2.34997	+	6.65825i	−0.118240	+	0.335013i
$396$		0			0
$397$	2.81796	−	2.81796i	0.141429	−	0.141429i	−0.632847	−	0.774277i	$-0.718114\pi$
$397$	2.81796	−	2.81796i	0.141429	−	0.141429i	0.774277	+	0.632847i	$0.218114\pi$
$398$	−7.90494	+	7.90494i	−0.396239	+	0.396239i
$399$		0			0
$400$	−16.6817	−	13.4509i	−0.834087	−	0.672544i
$401$			24.7881i			1.23786i	0.785447	+	0.618929i	$0.212433\pi$
$401$			24.7881i			1.23786i	−0.785447	+	0.618929i	$0.787567\pi$
$402$		0			0
$403$	−23.1274	−	23.1274i	−1.15206	−	1.15206i
$404$	41.6755			2.07344
$405$		0			0
$406$	5.93049			0.294325
$407$	15.1816	+	15.1816i	0.752522	+	0.752522i
$408$		0			0
$409$			19.8164i			0.979858i	0.871762	+	0.489929i	$0.162977\pi$
$409$			19.8164i			0.979858i	−0.871762	+	0.489929i	$0.837023\pi$
$410$	−42.8164	+	20.4774i	−2.11455	+	1.01131i
$411$		0			0
$412$	−34.6942	+	34.6942i	−1.70926	+	1.70926i
$413$	6.45949	−	6.45949i	0.317851	−	0.317851i
$414$		0			0
$415$	3.02399	−	1.44626i	0.148442	−	0.0709940i
$416$		−	2.57174i		−	0.126090i
$417$		0			0
$418$	−5.77673	−	5.77673i	−0.282549	−	0.282549i
$419$	−12.8373			−0.627143			−0.313571	−	0.949565i	$-0.601526\pi$
$419$	−12.8373			−0.627143			−0.313571	+	0.949565i	$0.601526\pi$
$420$		0			0
$421$	−8.68896			−0.423474			−0.211737	−	0.977327i	$-0.567912\pi$
$421$	−8.68896			−0.423474			−0.211737	+	0.977327i	$0.567912\pi$
$422$	30.2261	+	30.2261i	1.47139	+	1.47139i
$423$		0			0
$424$			21.9023i			1.06367i
$425$	−0.533052	−	4.97150i	−0.0258568	−	0.241153i
$426$		0			0
$427$	2.87834	−	2.87834i	0.139292	−	0.139292i
$428$	36.2917	−	36.2917i	1.75423	−	1.75423i
$429$		0			0
$430$	−0.819463	+	2.32181i	−0.0395180	+	0.111968i
$431$		−	12.2638i		−	0.590726i	−0.955385	−	0.295363i	$-0.904559\pi$
$431$		−	12.2638i		−	0.590726i	0.955385	−	0.295363i	$-0.0954405\pi$
$432$		0			0
$433$	−8.19584	−	8.19584i	−0.393867	−	0.393867i	0.482196	−	0.876063i	$-0.339839\pi$
$433$	−8.19584	−	8.19584i	−0.393867	−	0.393867i	−0.876063	+	0.482196i	$0.839839\pi$
$434$	13.5094			0.648473
$435$		0			0
$436$	−61.1068			−2.92648
$437$	−3.71002	−	3.71002i	−0.177474	−	0.177474i
$438$		0			0
$439$			17.6171i			0.840818i	0.907335	+	0.420409i	$0.138113\pi$
$439$			17.6171i			0.840818i	−0.907335	+	0.420409i	$0.861887\pi$
$440$	18.5584	+	38.8038i	0.884735	+	1.84990i
$441$		0			0
$442$	9.50638	−	9.50638i	0.452173	−	0.452173i
$443$	−15.6306	+	15.6306i	−0.742630	+	0.742630i	−0.973083	−	0.230453i	$-0.925979\pi$
$443$	−15.6306	+	15.6306i	−0.742630	+	0.742630i	0.230453	+	0.973083i	$0.425979\pi$
$444$		0			0
$445$	−23.5603	−	8.31540i	−1.11687	−	0.394188i
$446$			40.6207i			1.92345i
$447$		0			0
$448$	−4.81453	−	4.81453i	−0.227465	−	0.227465i
$449$	−7.72558			−0.364593			−0.182296	−	0.983244i	$-0.558353\pi$
$449$	−7.72558			−0.364593			−0.182296	+	0.983244i	$0.558353\pi$
$450$		0			0
$451$	32.9791			1.55293
$452$	−34.0930	−	34.0930i	−1.60360	−	1.60360i
$453$		0			0
$454$		−	36.1817i		−	1.69809i
$455$	−10.5855	−	3.73604i	−0.496254	−	0.175148i
$456$		0			0
$457$	10.6218	−	10.6218i	0.496866	−	0.496866i	−0.413595	−	0.910461i	$-0.635727\pi$
$457$	10.6218	−	10.6218i	0.496866	−	0.496866i	0.910461	+	0.413595i	$0.135727\pi$
$458$	46.0058	−	46.0058i	2.14971	−	2.14971i
$459$		0			0
$460$	23.5625	+	49.2671i	1.09861	+	2.29709i
$461$			28.3479i			1.32029i	0.751136	+	0.660147i	$0.229506\pi$
$461$			28.3479i			1.32029i	−0.751136	+	0.660147i	$0.770494\pi$
$462$		0			0
$463$	7.59415	+	7.59415i	0.352930	+	0.352930i	0.861199	−	0.508268i	$-0.169714\pi$
$463$	7.59415	+	7.59415i	0.352930	+	0.352930i	−0.508268	+	0.861199i	$0.669714\pi$
$464$	−11.2558			−0.522540
$465$		0			0
$466$	−13.0773			−0.605796
$467$	2.36748	+	2.36748i	0.109554	+	0.109554i	0.759759	−	0.650205i	$-0.225317\pi$
$467$	2.36748	+	2.36748i	0.109554	+	0.109554i	−0.650205	+	0.759759i	$0.725317\pi$
$468$		0			0
$469$			8.02857i			0.370725i
$470$	−21.0482	+	59.6367i	−0.970883	+	2.75084i
$471$		0			0
$472$	−35.4148	+	35.4148i	−1.63010	+	1.63010i
$473$	1.20978	−	1.20978i	0.0556256	−	0.0556256i
$474$		0			0
$475$	−2.72878	+	3.38423i	−0.125205	+	0.155279i
$476$			3.71645i			0.170343i
$477$		0			0
$478$	−4.32943	−	4.32943i	−0.198023	−	0.198023i
$479$	−19.8593			−0.907395			−0.453698	−	0.891156i	$-0.649895\pi$
$479$	−19.8593			−0.907395			−0.453698	+	0.891156i	$0.649895\pi$
$480$		0			0
$481$	30.7197			1.40070
$482$	−39.3403	−	39.3403i	−1.79190	−	1.79190i
$483$		0			0
$484$		−	14.5670i		−	0.662135i
$485$	−25.7327	+	12.3070i	−1.16846	+	0.558830i
$486$		0			0
$487$	−14.7455	+	14.7455i	−0.668184	+	0.668184i	−0.957295	−	0.289112i	$-0.906640\pi$
$487$	−14.7455	+	14.7455i	−0.668184	+	0.668184i	0.289112	+	0.957295i	$0.406640\pi$
$488$	−15.7808	+	15.7808i	−0.714362	+	0.714362i
$489$		0			0
$490$	−30.5415	+	14.6068i	−1.37972	+	0.659868i
$491$		−	12.7947i		−	0.577418i	−0.957417	−	0.288709i	$-0.906774\pi$
$491$		−	12.7947i		−	0.577418i	0.957417	−	0.288709i	$-0.0932259\pi$
$492$		0			0
$493$	−1.85707	−	1.85707i	−0.0836384	−	0.0836384i
$494$	−11.6891			−0.525920
$495$		0			0
$496$	−25.6404			−1.15129
$497$	−5.54122	−	5.54122i	−0.248558	−	0.248558i
$498$		0			0
$499$			22.3197i			0.999167i	0.866266	+	0.499584i	$0.166514\pi$
$499$			22.3197i			0.999167i	−0.866266	+	0.499584i	$0.833486\pi$
$500$	38.5074	−	23.7640i	1.72210	−	1.06276i
$501$		0			0
$502$	−31.2506	+	31.2506i	−1.39478	+	1.39478i
$503$	−9.77428	+	9.77428i	−0.435814	+	0.435814i	−0.890600	−	0.454787i	$-0.849715\pi$
$503$	−9.77428	+	9.77428i	−0.435814	+	0.435814i	0.454787	+	0.890600i	$0.349715\pi$
$504$		0			0
$505$	−7.66327	+	21.7126i	−0.341011	+	0.966198i
$506$		−	56.7000i		−	2.52062i
$507$		0			0
$508$	−4.48694	−	4.48694i	−0.199076	−	0.199076i
$509$	−25.9268			−1.14919			−0.574593	−	0.818440i	$-0.694839\pi$
$509$	−25.9268			−1.14919			−0.574593	+	0.818440i	$0.694839\pi$
$510$		0			0
$511$	5.20656			0.230325
$512$	29.0886	+	29.0886i	1.28555	+	1.28555i
$513$		0			0
$514$		−	67.4868i		−	2.97671i
$515$	−11.6958	−	24.4549i	−0.515380	−	1.07761i
$516$		0			0
$517$	31.0736	−	31.0736i	1.36662	−	1.36662i
$518$	−8.97218	+	8.97218i	−0.394215	+	0.394215i
$519$		0			0
$520$	58.0359	+	20.4832i	2.54504	+	0.898249i
$521$		−	22.4666i		−	0.984281i	−0.870516	−	0.492140i	$-0.836215\pi$
$521$		−	22.4666i		−	0.984281i	0.870516	−	0.492140i	$-0.163785\pi$
$522$		0			0
$523$	29.3834	+	29.3834i	1.28485	+	1.28485i	0.937876	+	0.346970i	$0.112790\pi$
$523$	29.3834	+	29.3834i	1.28485	+	1.28485i	0.346970	+	0.937876i	$0.387210\pi$
$524$	−74.8061			−3.26792
$525$		0			0
$526$	60.5634			2.64069
$527$	−4.23034	−	4.23034i	−0.184277	−	0.184277i
$528$		0			0
$529$		−	13.4148i		−	0.583252i
$530$	−22.5584	−	7.96179i	−0.979875	−	0.345838i
$531$		0			0
$532$	2.28489	−	2.28489i	0.0990627	−	0.0990627i
$533$	33.3665	−	33.3665i	1.44526	−	1.44526i
$534$		0			0
$535$	12.2344	+	25.5810i	0.528939	+	1.10596i
$536$		−	44.0174i		−	1.90126i
$537$		0			0
$538$	10.6045	+	10.6045i	0.457191	+	0.457191i
$539$	23.5244			1.01327
$540$		0			0
$541$	−27.1753			−1.16836			−0.584178	−	0.811625i	$-0.698583\pi$
$541$	−27.1753			−1.16836			−0.584178	+	0.811625i	$0.698583\pi$
$542$	34.5225	+	34.5225i	1.48287	+	1.48287i
$543$		0			0
$544$		−	0.470410i		−	0.0201687i
$545$	11.2363	−	31.8361i	0.481309	−	1.36371i
$546$		0			0
$547$	−26.9649	+	26.9649i	−1.15294	+	1.15294i	−0.166976	+	0.985961i	$0.553400\pi$
$547$	−26.9649	+	26.9649i	−1.15294	+	1.15294i	−0.985961	+	0.166976i	$0.946600\pi$
$548$	28.9002	−	28.9002i	1.23455	−	1.23455i
$549$		0			0
$550$	−46.7124	+	5.00857i	−1.99182	+	0.213566i
$551$			2.28348i			0.0972794i
$552$		0			0
$553$	2.05031	+	2.05031i	0.0871880	+	0.0871880i
$554$	31.0313			1.31839
$555$		0			0
$556$	42.4494			1.80026
$557$	6.37426	+	6.37426i	0.270086	+	0.270086i	0.829135	−	0.559049i	$-0.188834\pi$
$557$	6.37426	+	6.37426i	0.270086	+	0.270086i	−0.559049	+	0.829135i	$0.688834\pi$
$558$		0			0
$559$		−	2.44797i		−	0.103538i
$560$	−7.93884	+	3.79684i	−0.335477	+	0.160446i
$561$		0			0
$562$	−44.8116	+	44.8116i	−1.89026	+	1.89026i
$563$	18.9785	−	18.9785i	0.799850	−	0.799850i	−0.183221	−	0.983072i	$-0.558653\pi$
$563$	18.9785	−	18.9785i	0.799850	−	0.799850i	0.983072	+	0.183221i	$0.0586525\pi$
$564$		0			0
$565$	24.0312	−	11.4932i	1.01100	−	0.483521i
$566$			22.4567i			0.943925i
$567$		0			0
$568$	30.3803	+	30.3803i	1.27473	+	1.27473i
$569$	31.3158			1.31283			0.656414	−	0.754401i	$-0.272072\pi$
$569$	31.3158			1.31283			0.656414	+	0.754401i	$0.272072\pi$
$570$		0			0
$571$	−30.5581			−1.27882			−0.639408	−	0.768868i	$-0.720820\pi$
$571$	−30.5581			−1.27882			−0.639408	+	0.768868i	$0.720820\pi$
$572$	−59.7809	−	59.7809i	−2.49956	−	2.49956i
$573$		0			0
$574$			19.4904i			0.813513i
$575$	−30.0004	+	3.21669i	−1.25110	+	0.134145i
$576$		0			0
$577$	11.4463	−	11.4463i	0.476516	−	0.476516i	−0.427500	−	0.904015i	$-0.640606\pi$
$577$	11.4463	−	11.4463i	0.476516	−	0.476516i	0.904015	+	0.427500i	$0.140606\pi$
$578$	1.73886	−	1.73886i	0.0723270	−	0.0723270i
$579$		0			0
$580$	7.91043	−	22.4129i	0.328463	−	0.930645i
$581$		−	1.37655i		−	0.0571088i
$582$		0			0
$583$	11.7540	+	11.7540i	0.486802	+	0.486802i
$584$	−28.5455			−1.18122
$585$		0			0
$586$	−6.44329			−0.266170
$587$	−13.3744	−	13.3744i	−0.552021	−	0.552021i	0.375003	−	0.927024i	$-0.377642\pi$
$587$	−13.3744	−	13.3744i	−0.552021	−	0.552021i	−0.927024	+	0.375003i	$0.877642\pi$
$588$		0			0
$589$			5.20168i			0.214331i
$590$	−23.6019	−	49.3494i	−0.971675	−	2.03168i
$591$		0			0
$592$	17.0289	−	17.0289i	0.699882	−	0.699882i
$593$	−18.9208	+	18.9208i	−0.776983	+	0.776983i	−0.979317	−	0.202333i	$-0.935148\pi$
$593$	−18.9208	+	18.9208i	−0.776983	+	0.776983i	0.202333	+	0.979317i	$0.435148\pi$
$594$		0			0
$595$	−1.93624	−	0.683378i	−0.0793781	−	0.0280158i
$596$			54.9825i			2.25217i
$597$		0			0
$598$	−57.3660	−	57.3660i	−2.34587	−	2.34587i
$599$	4.34968			0.177723			0.0888615	−	0.996044i	$-0.471677\pi$
$599$	4.34968			0.177723			0.0888615	+	0.996044i	$0.471677\pi$
$600$		0			0
$601$	−12.5964			−0.513820			−0.256910	−	0.966435i	$-0.582704\pi$
$601$	−12.5964			−0.513820			−0.256910	+	0.966435i	$0.582704\pi$
$602$	0.714969	+	0.714969i	0.0291400	+	0.0291400i
$603$		0			0
$604$		−	80.6463i		−	3.28145i
$605$	7.58927	+	2.67856i	0.308548	+	0.108899i
$606$		0			0
$607$	17.6710	−	17.6710i	0.717242	−	0.717242i	−0.250797	−	0.968040i	$-0.580693\pi$
$607$	17.6710	−	17.6710i	0.717242	−	0.717242i	0.968040	+	0.250797i	$0.0806928\pi$
$608$	−0.289211	+	0.289211i	−0.0117290	+	0.0117290i
$609$		0			0
$610$	−10.5170	−	21.9900i	−0.425819	−	0.890349i
$611$		−	62.8772i		−	2.54374i
$612$		0			0
$613$	18.1592	+	18.1592i	0.733444	+	0.733444i	0.971300	−	0.237856i	$-0.0764448\pi$
$613$	18.1592	+	18.1592i	0.733444	+	0.733444i	−0.237856	+	0.971300i	$0.576445\pi$
$614$	−51.9978			−2.09846
$615$		0			0
$616$	17.6638			0.711696
$617$	25.7870	+	25.7870i	1.03814	+	1.03814i	0.999243	+	0.0389017i	$0.0123859\pi$
$617$	25.7870	+	25.7870i	1.03814	+	1.03814i	0.0389017	+	0.999243i	$0.487614\pi$
$618$		0			0
$619$			9.63641i			0.387320i	0.981069	+	0.193660i	$0.0620359\pi$
$619$			9.63641i			0.387320i	−0.981069	+	0.193660i	$0.937964\pi$
$620$	18.0197	−	51.0557i	0.723687	−	2.05045i
$621$		0			0
$622$	−26.1346	+	26.1346i	−1.04790	+	1.04790i
$623$	−7.25505	+	7.25505i	−0.290668	+	0.290668i
$624$		0			0
$625$	5.30014	+	24.4317i	0.212006	+	0.977268i
$626$			3.55984i			0.142280i
$627$		0			0
$628$	−48.9832	−	48.9832i	−1.95464	−	1.95464i
$629$	5.61910			0.224048
$630$		0			0
$631$	−7.17134			−0.285487			−0.142743	−	0.989760i	$-0.545592\pi$
$631$	−7.17134			−0.285487			−0.142743	+	0.989760i	$0.545592\pi$
$632$	−11.2410	−	11.2410i	−0.447144	−	0.447144i
$633$		0			0
$634$		−	79.2603i		−	3.14783i
$635$	3.16271	−	1.51260i	0.125508	−	0.0600258i
$636$		0			0
$637$	23.8007	−	23.8007i	0.943020	−	0.943020i
$638$	−17.4491	+	17.4491i	−0.690817	+	0.690817i
$639$		0			0
$640$	−38.6801	+	18.4992i	−1.52896	+	0.731244i
$641$			20.3820i			0.805042i	0.915411	+	0.402521i	$0.131866\pi$
$641$			20.3820i			0.805042i	−0.915411	+	0.402521i	$0.868134\pi$
$642$		0			0
$643$	−3.34518	−	3.34518i	−0.131921	−	0.131921i	0.638063	−	0.769984i	$-0.279736\pi$
$643$	−3.34518	−	3.34518i	−0.131921	−	0.131921i	−0.769984	+	0.638063i	$0.779736\pi$
$644$	22.4268			0.883740
$645$		0			0
$646$	−2.13812			−0.0841232
$647$	−28.1923	−	28.1923i	−1.10835	−	1.10835i	−0.993367	−	0.114987i	$-0.963317\pi$
$647$	−28.1923	−	28.1923i	−1.10835	−	1.10835i	−0.114987	−	0.993367i	$-0.536683\pi$
$648$		0			0
$649$			38.0111i			1.49207i
$650$	−42.1936	+	52.3284i	−1.65497	+	2.05249i
$651$		0			0
$652$	−19.6493	+	19.6493i	−0.769527	+	0.769527i
$653$	−18.4412	+	18.4412i	−0.721661	+	0.721661i	−0.968943	−	0.247282i	$-0.920462\pi$
$653$	−18.4412	+	18.4412i	−0.721661	+	0.721661i	0.247282	+	0.968943i	$0.420462\pi$
$654$		0			0
$655$	13.7553	−	38.9734i	0.537464	−	1.52281i
$656$		−	36.9920i		−	1.44430i
$657$		0			0
$658$	18.3643	+	18.3643i	0.715913	+	0.715913i
$659$	−16.9294			−0.659476			−0.329738	−	0.944073i	$-0.606960\pi$
$659$	−16.9294			−0.659476			−0.329738	+	0.944073i	$0.606960\pi$
$660$		0			0
$661$	41.6509			1.62003			0.810016	−	0.586408i	$-0.199458\pi$
$661$	41.6509			1.62003			0.810016	+	0.586408i	$0.199458\pi$
$662$	32.4513	+	32.4513i	1.26126	+	1.26126i
$663$		0			0
$664$			7.54706i			0.292883i
$665$	0.770266	+	1.61055i	0.0298696	+	0.0624546i
$666$		0			0
$667$	−11.2064	+	11.2064i	−0.433915	+	0.433915i
$668$	−59.2742	+	59.2742i	−2.29339	+	2.29339i
$669$		0			0
$670$	45.3360	+	16.0009i	1.75148	+	0.618170i
$671$			16.9377i			0.653873i
$672$		0			0
$673$	2.35245	+	2.35245i	0.0906803	+	0.0906803i	0.750992	−	0.660311i	$-0.229576\pi$
$673$	2.35245	+	2.35245i	0.0906803	+	0.0906803i	−0.660311	+	0.750992i	$0.729576\pi$
$674$	88.1758			3.39641
$675$		0			0
$676$	−68.3515			−2.62891
$677$	10.2959	+	10.2959i	0.395703	+	0.395703i	0.876714	−	0.481012i	$-0.159730\pi$
$677$	10.2959	+	10.2959i	0.395703	+	0.395703i	−0.481012	+	0.876714i	$0.659730\pi$
$678$		0			0
$679$			11.7138i			0.449533i
$680$	10.6156	+	3.74669i	0.407091	+	0.143679i
$681$		0			0
$682$	−39.7484	+	39.7484i	−1.52205	+	1.52205i
$683$	−36.5150	+	36.5150i	−1.39721	+	1.39721i	−0.589280	+	0.807929i	$0.700589\pi$
$683$	−36.5150	+	36.5150i	−1.39721	+	1.39721i	−0.807929	+	0.589280i	$0.799411\pi$
$684$		0			0
$685$	9.74260	+	20.3709i	0.372246	+	0.778331i
$686$			29.7096i			1.13432i
$687$		0			0
$688$	−1.35698	−	1.35698i	−0.0517345	−	0.0517345i
$689$	23.7841			0.906104
$690$		0			0
$691$	12.7061			0.483363			0.241681	−	0.970356i	$-0.422301\pi$
$691$	12.7061			0.483363			0.241681	+	0.970356i	$0.422301\pi$
$692$	−36.4481	−	36.4481i	−1.38555	−	1.38555i
$693$		0			0
$694$			62.0298i			2.35462i
$695$	−7.80557	+	22.1158i	−0.296082	+	0.838900i
$696$		0			0
$697$	6.10322	−	6.10322i	0.231176	−	0.231176i
$698$	−31.7213	+	31.7213i	−1.20067	+	1.20067i
$699$		0			0
$700$	−1.98106	−	18.4764i	−0.0748771	−	0.698341i
$701$		−	25.0952i		−	0.947832i	−0.880570	−	0.473916i	$-0.842840\pi$
$701$		−	25.0952i		−	0.947832i	0.880570	−	0.473916i	$-0.157160\pi$
$702$		0			0
$703$	−3.45465	−	3.45465i	−0.130295	−	0.130295i
$704$	28.3313			1.06778
$705$		0			0
$706$	−56.2059			−2.11534
$707$	6.68608	+	6.68608i	0.251456	+	0.251456i
$708$		0			0
$709$			32.3991i			1.21677i	0.793641	+	0.608387i	$0.208183\pi$
$709$			32.3991i			1.21677i	−0.793641	+	0.608387i	$0.791817\pi$
$710$	−42.3340	+	20.2467i	−1.58877	+	0.759846i
$711$		0			0
$712$	39.7766	−	39.7766i	1.49069	−	1.49069i
$713$	−25.5279	+	25.5279i	−0.956026	+	0.956026i
$714$		0			0
$715$	42.1378	−	20.1529i	1.57586	−	0.753674i
$716$		−	33.3921i		−	1.24792i
$717$		0			0
$718$	22.6547	+	22.6547i	0.845468	+	0.845468i
$719$	−22.6788			−0.845776			−0.422888	−	0.906182i	$-0.638984\pi$
$719$	−22.6788			−0.845776			−0.422888	+	0.906182i	$0.638984\pi$
$720$		0			0
$721$	−11.1321			−0.414581
$722$	−31.7238	−	31.7238i	−1.18064	−	1.18064i
$723$		0			0
$724$		−	44.5716i		−	1.65649i
$725$	10.2224	+	8.24253i	0.379649	+	0.306120i
$726$		0			0
$727$	7.69574	−	7.69574i	0.285419	−	0.285419i	−0.549847	−	0.835266i	$-0.685314\pi$
$727$	7.69574	−	7.69574i	0.285419	−	0.285419i	0.835266	+	0.549847i	$0.185314\pi$
$728$	17.8713	−	17.8713i	0.662354	−	0.662354i
$729$		0			0
$730$	10.3767	−	29.4006i	0.384058	−	1.08816i
$731$		−	0.447771i		−	0.0165614i
$732$		0			0
$733$	25.9797	+	25.9797i	0.959583	+	0.959583i	0.999214	−	0.0396309i	$-0.0126182\pi$
$733$	25.9797	+	25.9797i	0.959583	+	0.959583i	−0.0396309	+	0.999214i	$0.512618\pi$
$734$	41.8344			1.54414
$735$		0			0
$736$	−2.83867			−0.104635
$737$	−23.6222	−	23.6222i	−0.870137	−	0.870137i
$738$		0			0
$739$		−	33.2853i		−	1.22442i	−0.790696	−	0.612210i	$-0.790281\pi$
$739$		−	33.2853i		−	1.22442i	0.790696	−	0.612210i	$-0.209719\pi$
$740$	21.9406	+	45.8759i	0.806554	+	1.68643i
$741$		0			0
$742$	−6.94653	+	6.94653i	−0.255015	+	0.255015i
$743$	−22.9941	+	22.9941i	−0.843573	+	0.843573i	−0.989322	−	0.145748i	$-0.953441\pi$
$743$	−22.9941	+	22.9941i	−0.843573	+	0.843573i	0.145748	+	0.989322i	$0.453441\pi$
$744$		0			0
$745$	−28.6454	−	10.1101i	−1.04949	−	0.370407i
$746$			52.0753i			1.90661i
$747$		0			0
$748$	−10.9348	−	10.9348i	−0.399816	−	0.399816i
$749$	11.6447			0.425488
$750$		0			0
$751$	−24.7035			−0.901443			−0.450722	−	0.892665i	$-0.648833\pi$
$751$	−24.7035			−0.901443			−0.450722	+	0.892665i	$0.648833\pi$
$752$	−34.8547	−	34.8547i	−1.27102	−	1.27102i
$753$		0			0
$754$			35.3081i			1.28585i
$755$	42.0160	+	14.8292i	1.52912	+	0.539689i
$756$		0			0
$757$	−12.7581	+	12.7581i	−0.463700	+	0.463700i	−0.899866	−	0.436166i	$-0.856336\pi$
$757$	−12.7581	+	12.7581i	−0.463700	+	0.463700i	0.436166	+	0.899866i	$0.356336\pi$
$758$	−44.0735	+	44.0735i	−1.60082	+	1.60082i
$759$		0			0
$760$	−4.22306	−	8.83003i	−0.153186	−	0.320299i
$761$		−	20.0598i		−	0.727167i	−0.931562	−	0.363583i	$-0.881553\pi$
$761$		−	20.0598i		−	0.727167i	0.931562	−	0.363583i	$-0.118447\pi$
$762$		0			0
$763$	−9.80347	−	9.80347i	−0.354909	−	0.354909i
$764$	25.5838			0.925590
$765$		0			0
$766$	−51.2100			−1.85029
$767$	38.4576	+	38.4576i	1.38862	+	1.38862i
$768$		0			0
$769$		−	10.1042i		−	0.364366i	−0.983265	−	0.182183i	$-0.941684\pi$
$769$		−	10.1042i		−	0.364366i	0.983265	−	0.182183i	$-0.0583164\pi$
$770$	−6.42104	+	18.1930i	−0.231398	+	0.655629i
$771$		0			0
$772$	19.0919	−	19.0919i	0.687132	−	0.687132i
$773$	14.3793	−	14.3793i	0.517186	−	0.517186i	−0.399533	−	0.916719i	$-0.630828\pi$
$773$	14.3793	−	14.3793i	0.517186	−	0.517186i	0.916719	+	0.399533i	$0.130828\pi$
$774$		0			0
$775$	23.2862	+	18.7762i	0.836464	+	0.674460i
$776$		−	64.2218i		−	2.30543i
$777$		0			0
$778$	−52.4882	−	52.4882i	−1.88179	−	1.88179i
$779$	−7.50459			−0.268880
$780$		0			0
$781$	32.6076			1.16679
$782$	−10.4931	−	10.4931i	−0.375232	−	0.375232i
$783$		0			0
$784$		−	26.3869i		−	0.942390i
$785$	34.5268	−	16.5128i	1.23231	−	0.589368i
$786$		0			0
$787$	−0.250641	+	0.250641i	−0.00893439	+	0.00893439i	−0.711560	−	0.702625i	$-0.752011\pi$
$787$	−0.250641	+	0.250641i	−0.00893439	+	0.00893439i	0.702625	+	0.711560i	$0.252011\pi$
$788$	−7.20892	+	7.20892i	−0.256807	+	0.256807i
$789$		0			0
$790$	15.6640	−	7.49149i	0.557301	−	0.266535i
$791$		−	10.9392i		−	0.388953i
$792$		0			0
$793$	17.1366	+	17.1366i	0.608540	+	0.608540i
$794$	−9.80007			−0.347792
$795$		0			0
$796$	18.3991			0.652137
$797$	16.2653	+	16.2653i	0.576146	+	0.576146i	0.933839	−	0.357693i	$-0.116437\pi$
$797$	16.2653	+	16.2653i	0.576146	+	0.576146i	−0.357693	+	0.933839i	$0.616437\pi$
$798$		0			0
$799$		−	11.5012i		−	0.406882i
$800$	0.250753	+	2.33865i	0.00886546	+	0.0826836i
$801$		0			0
$802$	43.1030	−	43.1030i	1.52202	−	1.52202i
$803$	−15.3191	+	15.3191i	−0.540600	+	0.540600i
$804$		0			0
$805$	−4.12382	+	11.6842i	−0.145346	+	0.411813i
$806$			80.4305i			2.83305i
$807$		0			0
$808$	−36.6571	−	36.6571i	−1.28959	−	1.28959i
$809$	−17.4790			−0.614530			−0.307265	−	0.951624i	$-0.599414\pi$
$809$	−17.4790			−0.614530			−0.307265	+	0.951624i	$0.599414\pi$
$810$		0			0
$811$	16.8640			0.592175			0.296088	−	0.955161i	$-0.404318\pi$
$811$	16.8640			0.592175			0.296088	+	0.955161i	$0.404318\pi$
$812$	−6.90172	−	6.90172i	−0.242203	−	0.242203i
$813$		0			0
$814$		−	52.7972i		−	1.85054i
$815$	−6.62403	−	13.8502i	−0.232030	−	0.485152i
$816$		0			0
$817$	−0.275292	+	0.275292i	−0.00963124	+	0.00963124i
$818$	34.4579	−	34.4579i	1.20479	−	1.20479i
$819$		0			0
$820$	73.6594	+	25.9974i	2.57230	+	0.907869i
$821$		−	23.8629i		−	0.832822i	−0.909177	−	0.416411i	$-0.863288\pi$
$821$		−	23.8629i		−	0.832822i	0.909177	−	0.416411i	$-0.136712\pi$
$822$		0			0
$823$	−24.6480	−	24.6480i	−0.859177	−	0.859177i	0.132065	−	0.991241i	$-0.457839\pi$
$823$	−24.6480	−	24.6480i	−0.859177	−	0.859177i	−0.991241	+	0.132065i	$0.957839\pi$
$824$	61.0328			2.12618
$825$		0			0
$826$	−22.4643			−0.781632
$827$	−22.2053	−	22.2053i	−0.772154	−	0.772154i	0.206329	−	0.978483i	$-0.433848\pi$
$827$	−22.2053	−	22.2053i	−0.772154	−	0.772154i	−0.978483	+	0.206329i	$0.933848\pi$
$828$		0			0
$829$			4.82239i			0.167488i	0.996487	+	0.0837442i	$0.0266879\pi$
$829$			4.82239i			0.167488i	−0.996487	+	0.0837442i	$0.973312\pi$
$830$	−7.77313	−	2.74346i	−0.269809	−	0.0952268i
$831$		0			0
$832$	28.6641	−	28.6641i	0.993748	−	0.993748i
$833$	4.35351	−	4.35351i	0.150840	−	0.150840i
$834$		0			0
$835$	−19.9821	−	41.7806i	−0.691508	−	1.44588i
$836$			13.4456i			0.465024i
$837$		0			0
$838$	22.3223	+	22.3223i	0.771109	+	0.771109i
$839$	−55.8825			−1.92928			−0.964639	−	0.263575i	$-0.915098\pi$
$839$	−55.8825			−1.92928			−0.964639	+	0.263575i	$0.915098\pi$
$840$		0			0
$841$	−22.1026			−0.762157
$842$	15.1089	+	15.1089i	0.520687	+	0.520687i
$843$		0			0
$844$		−	70.3525i		−	2.42163i
$845$	12.5684	−	35.6106i	0.432367	−	1.22504i
$846$		0			0
$847$	2.33700	−	2.33700i	0.0803004	−	0.0803004i
$848$	13.1843	−	13.1843i	0.452749	−	0.452749i
$849$		0			0
$850$	−7.71784	+	9.57165i	−0.264720	+	0.328305i
$851$		−	33.9083i		−	1.16236i
$852$		0			0
$853$	16.5828	+	16.5828i	0.567786	+	0.567786i	0.931508	−	0.363722i	$-0.118494\pi$
$853$	16.5828	+	16.5828i	0.567786	+	0.567786i	−0.363722	+	0.931508i	$0.618494\pi$
$854$	−10.0100			−0.342537
$855$		0			0
$856$	−63.8432			−2.18212
$857$	20.5138	+	20.5138i	0.700740	+	0.700740i	0.964569	−	0.263830i	$-0.0849857\pi$
$857$	20.5138	+	20.5138i	0.700740	+	0.700740i	−0.263830	+	0.964569i	$0.584986\pi$
$858$		0			0
$859$			47.7868i			1.63046i	0.579135	+	0.815232i	$0.303390\pi$
$859$			47.7868i			1.63046i	−0.579135	+	0.815232i	$0.696610\pi$
$860$	3.65572	−	1.74839i	0.124659	−	0.0596196i
$861$		0			0
$862$	−21.3250	+	21.3250i	−0.726332	+	0.726332i
$863$	−9.97081	+	9.97081i	−0.339410	+	0.339410i	−0.856145	−	0.516735i	$-0.827147\pi$
$863$	−9.97081	+	9.97081i	−0.339410	+	0.339410i	0.516735	+	0.856145i	$0.327147\pi$
$864$		0			0
$865$	25.6912	−	12.2871i	0.873526	−	0.417774i
$866$			28.5028i			0.968566i
$867$		0			0
$868$	−15.7219	−	15.7219i	−0.533635	−	0.533635i
$869$	−12.0651			−0.409282
$870$		0			0
$871$	−47.7994			−1.61962
$872$	53.7485	+	53.7485i	1.82015	+	1.82015i
$873$		0			0
$874$			12.9024i			0.436431i
$875$	9.99030	+	2.36530i	0.337734	+	0.0799618i
$876$		0			0
$877$	12.9484	−	12.9484i	0.437237	−	0.437237i	−0.453844	−	0.891081i	$-0.649948\pi$
$877$	12.9484	−	12.9484i	0.437237	−	0.437237i	0.891081	+	0.453844i	$0.149948\pi$
$878$	30.6337	−	30.6337i	1.03384	−	1.03384i
$879$		0			0
$880$	12.1869	−	34.5296i	0.410820	−	1.16399i
$881$			7.07785i			0.238459i	0.992867	+	0.119229i	$0.0380424\pi$
$881$			7.07785i			0.238459i	−0.992867	+	0.119229i	$0.961958\pi$
$882$		0			0
$883$	34.9669	+	34.9669i	1.17673	+	1.17673i	0.980573	+	0.196157i	$0.0628461\pi$
$883$	34.9669	+	34.9669i	1.17673	+	1.17673i	0.196157	+	0.980573i	$0.437154\pi$
$884$	−22.1265			−0.744194
$885$		0			0
$886$	54.3587			1.82622
$887$	1.54998	+	1.54998i	0.0520432	+	0.0520432i	0.732649	−	0.680606i	$-0.238284\pi$
$887$	1.54998	+	1.54998i	0.0520432	+	0.0520432i	−0.680606	+	0.732649i	$0.738284\pi$
$888$		0			0
$889$		−	1.43970i		−	0.0482858i
$890$	26.5088	+	55.4274i	0.888576	+	1.85793i
$891$		0			0
$892$	47.2732	−	47.2732i	1.58282	−	1.58282i
$893$	−7.07098	+	7.07098i	−0.236621	+	0.236621i
$894$		0			0
$895$	17.3970	+	6.14011i	0.581517	+	0.205241i
$896$			17.6075i			0.588226i
$897$		0			0
$898$	13.4337	+	13.4337i	0.448288	+	0.448288i
$899$	15.7121			0.524029
$900$		0			0
$901$	4.35048			0.144935
$902$	−57.3461	−	57.3461i	−1.90941	−	1.90941i
$903$		0			0
$904$			59.9753i			1.99475i
$905$	23.2214	+	8.19579i	0.771906	+	0.272437i
$906$		0			0
$907$	34.2824	−	34.2824i	1.13833	−	1.13833i	0.149578	−	0.988750i	$-0.452209\pi$
$907$	34.2824	−	34.2824i	1.13833	−	1.13833i	0.988750	−	0.149578i	$-0.0477914\pi$
$908$	−42.1071	+	42.1071i	−1.39737	+	1.39737i
$909$		0			0
$910$	11.9102	+	24.9031i	0.394819	+	0.825529i
$911$			0.903005i			0.0299179i	0.999888	+	0.0149590i	$0.00476176\pi$
$911$			0.903005i			0.0299179i	−0.999888	+	0.0149590i	$0.995238\pi$
$912$		0			0
$913$	4.05018	+	4.05018i	0.134041	+	0.134041i
$914$	−36.9396			−1.22185
$915$		0			0
$916$	−107.080			−3.53803
$917$	−12.0013	−	12.0013i	−0.396317	−	0.396317i
$918$		0			0
$919$		−	19.4879i		−	0.642847i	−0.946936	−	0.321424i	$-0.895839\pi$
$919$		−	19.4879i		−	0.642847i	0.946936	−	0.321424i	$-0.104161\pi$
$920$	22.6093	−	64.0597i	0.745406	−	2.11198i
$921$		0			0
$922$	49.2931	−	49.2931i	1.62338	−	1.62338i
$923$	32.9906	−	32.9906i	1.08590	−	1.08590i
$924$		0			0
$925$	−27.9354	+	2.99527i	−0.918509	+	0.0984840i
$926$		−	26.4103i		−	0.867897i
$927$		0			0
$928$	0.873586	+	0.873586i	0.0286769	+	0.0286769i
$929$	−44.4641			−1.45882			−0.729409	−	0.684077i	$-0.760205\pi$
$929$	−44.4641			−1.45882			−0.729409	+	0.684077i	$0.760205\pi$
$930$		0			0
$931$	−5.35312			−0.175442
$932$	15.2190	+	15.2190i	0.498515	+	0.498515i
$933$		0			0
$934$		−	8.23342i		−	0.269406i
$935$	7.70763	−	3.68626i	0.252066	−	0.120554i
$936$		0			0
$937$	8.49121	−	8.49121i	0.277396	−	0.277396i	−0.554673	−	0.832069i	$-0.687157\pi$
$937$	8.49121	−	8.49121i	0.277396	−	0.277396i	0.832069	+	0.554673i	$0.187157\pi$
$938$	13.9606	−	13.9606i	0.455828	−	0.455828i
$939$		0			0
$940$	93.8987	−	44.9081i	3.06264	−	1.46474i
$941$		−	6.55693i		−	0.213750i	−0.994272	−	0.106875i	$-0.965916\pi$
$941$		−	6.55693i		−	0.213750i	0.994272	−	0.106875i	$-0.0340845\pi$
$942$		0			0
$943$	−36.8297	−	36.8297i	−1.19934	−	1.19934i
$944$	42.6364			1.38770
$945$		0			0
$946$	−4.20727			−0.136790
$947$	−19.5533	−	19.5533i	−0.635397	−	0.635397i	0.314019	−	0.949417i	$-0.398324\pi$
$947$	−19.5533	−	19.5533i	−0.635397	−	0.635397i	−0.949417	+	0.314019i	$0.898324\pi$
$948$		0			0
$949$			30.9981i			1.00624i
$950$	10.6297	−	1.13973i	0.344872	−	0.0369777i
$951$		0			0
$952$	3.26893	−	3.26893i	0.105947	−	0.105947i
$953$	39.5904	−	39.5904i	1.28246	−	1.28246i	0.343192	−	0.939265i	$-0.388492\pi$
$953$	39.5904	−	39.5904i	1.28246	−	1.28246i	0.939265	−	0.343192i	$-0.111508\pi$
$954$		0			0
$955$	−4.70433	+	13.3289i	−0.152229	+	0.431315i
$956$			10.0769i			0.325911i
$957$		0			0
$958$	34.5325	+	34.5325i	1.11570	+	1.11570i
$959$	9.27301			0.299441
$960$		0			0
$961$	4.79163			0.154569
$962$	−53.4173	−	53.4173i	−1.72224	−	1.72224i
$963$		0			0
$964$			91.5660i			2.94914i
$965$	6.43611	+	13.4573i	0.207186	+	0.433206i
$966$		0			0
$967$	24.4789	−	24.4789i	0.787187	−	0.787187i	−0.193845	−	0.981032i	$-0.562096\pi$
$967$	24.4789	−	24.4789i	0.787187	−	0.787187i	0.981032	+	0.193845i	$0.0620959\pi$
$968$	−12.8129	+	12.8129i	−0.411821	+	0.411821i
$969$		0			0
$970$	66.1456	+	23.3455i	2.12381	+	0.749579i
$971$			50.6753i			1.62625i	0.582091	+	0.813124i	$0.302235\pi$
$971$			50.6753i			1.62625i	−0.582091	+	0.813124i	$0.697765\pi$
$972$		0			0
$973$	6.81024	+	6.81024i	0.218326	+	0.218326i
$974$	51.2808			1.64314
$975$		0			0
$976$	18.9987			0.608133
$977$	−1.08217	−	1.08217i	−0.0346216	−	0.0346216i	0.689584	−	0.724206i	$-0.257793\pi$
$977$	−1.08217	−	1.08217i	−0.0346216	−	0.0346216i	−0.724206	+	0.689584i	$0.757793\pi$
$978$		0			0
$979$		−	42.6927i		−	1.36446i
$980$	52.5422	+	18.5443i	1.67840	+	0.592376i
$981$		0			0
$982$	−22.2482	+	22.2482i	−0.709969	+	0.709969i
$983$	−21.0209	+	21.0209i	−0.670462	+	0.670462i	−0.957822	−	0.287361i	$-0.907222\pi$
$983$	−21.0209	+	21.0209i	−0.670462	+	0.670462i	0.287361	+	0.957822i	$0.407222\pi$
$984$		0			0
$985$	−2.43022	−	5.08136i	−0.0774332	−	0.161906i
$986$			6.45838i			0.205677i
$987$		0			0
$988$	13.6035	+	13.6035i	0.432784	+	0.432784i
$989$	−2.70206			−0.0859204
$990$		0			0
$991$	22.6540			0.719628			0.359814	−	0.933024i	$-0.382840\pi$
$991$	22.6540			0.719628			0.359814	+	0.933024i	$0.382840\pi$
$992$	1.99000	+	1.99000i	0.0631824	+	0.0631824i
$993$		0			0
$994$			19.2708i			0.611233i
$995$	−3.38320	+	9.58575i	−0.107255	+	0.303889i
$996$		0			0
$997$	−24.1235	+	24.1235i	−0.763999	+	0.763999i	−0.977043	−	0.213044i	$-0.931662\pi$
$997$	−24.1235	+	24.1235i	−0.763999	+	0.763999i	0.213044	+	0.977043i	$0.431662\pi$
$998$	38.8108	−	38.8108i	1.22854	−	1.22854i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.n.e.188.1	✓	24
3.2	odd	2	inner	765.2.n.e.188.12	yes	24
5.2	odd	4	inner	765.2.n.e.647.12	yes	24
15.2	even	4	inner	765.2.n.e.647.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
765.2.n.e.188.1	✓	24	1.1	even	1	trivial
765.2.n.e.188.12	yes	24	3.2	odd	2	inner
765.2.n.e.647.1	yes	24	15.2	even	4	inner
765.2.n.e.647.12	yes	24	5.2	odd	4	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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73886 - 1.73886i) q^{2} +4.04726i q^{4} +(-2.10859 - 0.744208i) q^{5} +(-0.649310 + 0.649310i) q^{7} +(3.55991 - 3.55991i) q^{8} +(2.37247 + 4.96062i) q^{10} -3.82089i q^{11} +(-3.86577 - 3.86577i) q^{13} +2.25812 q^{14} -4.28582 q^{16} +(-0.707107 - 0.707107i) q^{17} +0.869466i q^{19} +(3.01201 - 8.53402i) q^{20} +(-6.64399 + 6.64399i) q^{22} +(-4.26701 + 4.26701i) q^{23} +(3.89231 + 3.13846i) q^{25} +13.4441i q^{26} +(-2.62793 - 2.62793i) q^{28} +2.62630 q^{29} +5.98261 q^{31} +(0.332630 + 0.332630i) q^{32} +2.45912i q^{34} +(1.85235 - 0.885907i) q^{35} +(-3.97330 + 3.97330i) q^{37} +(1.51188 - 1.51188i) q^{38} +(-10.1557 + 4.85707i) q^{40} +8.63126i q^{41} +(0.316622 + 0.316622i) q^{43} +15.4642 q^{44} +14.8395 q^{46} +(8.13256 + 8.13256i) q^{47} +6.15679i q^{49} +(-1.31084 - 12.2255i) q^{50} +(15.6458 - 15.6458i) q^{52} +(-3.07625 + 3.07625i) q^{53} +(-2.84354 + 8.05670i) q^{55} +4.62296i q^{56} +(-4.56676 - 4.56676i) q^{58} -9.94824 q^{59} -4.43292 q^{61} +(-10.4029 - 10.4029i) q^{62} +7.41485i q^{64} +(5.27439 + 11.0283i) q^{65} +(6.18239 - 6.18239i) q^{67} +(2.86185 - 2.86185i) q^{68} +(-4.76144 - 1.68051i) q^{70} +8.53402i q^{71} +(-4.00931 - 4.00931i) q^{73} +13.8180 q^{74} -3.51896 q^{76} +(2.48094 + 2.48094i) q^{77} -3.15768i q^{79} +(9.03704 + 3.18954i) q^{80} +(15.0086 - 15.0086i) q^{82} +(-1.06001 + 1.06001i) q^{83} +(0.964764 + 2.01723i) q^{85} -1.10112i q^{86} +(-13.6020 - 13.6020i) q^{88} +11.1735 q^{89} +5.02016 q^{91} +(-17.2697 - 17.2697i) q^{92} -28.2827i q^{94} +(0.647063 - 1.83335i) q^{95} +(9.02016 - 9.02016i) q^{97} +(10.7058 - 10.7058i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{7} - 20 q^{10} - 20 q^{13} - 8 q^{16} - 40 q^{22} - 24 q^{28} + 72 q^{31} + 16 q^{37} - 88 q^{40} + 36 q^{43} + 56 q^{46} + 32 q^{52} - 88 q^{55} - 80 q^{58} - 8 q^{61} + 104 q^{67} - 136 q^{70}+ \cdots + 88 q^{97}+O(q^{100}) \) 24 * q + 8 * q^7 - 20 * q^10 - 20 * q^13 - 8 * q^16 - 40 * q^22 - 24 * q^28 + 72 * q^31 + 16 * q^37 - 88 * q^40 + 36 * q^43 + 56 * q^46 + 32 * q^52 - 88 * q^55 - 80 * q^58 - 8 * q^61 + 104 * q^67 - 136 * q^70 - 136 * q^73 + 136 * q^76 + 16 * q^82 + 8 * q^85 - 64 * q^88 - 8 * q^91 + 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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