LMFDB - Embedded newform 400.2.bi.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	400.127
Dual form			400.2.bi.d.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94483 + 0.990942i) q^{3} +(1.03746 - 1.98083i) q^{5} +(-1.48328 + 1.48328i) q^{7} +(1.03705 - 1.42738i) q^{9} +O(q^{10})$	\(q+(-1.94483 + 0.990942i) q^{3} +(1.03746 - 1.98083i) q^{5} +(-1.48328 + 1.48328i) q^{7} +(1.03705 - 1.42738i) q^{9} +(0.172056 + 0.236815i) q^{11} +(-4.46218 + 0.706740i) q^{13} +(-0.0547938 + 4.88044i) q^{15} +(-1.99756 + 3.92044i) q^{17} +(-0.873586 - 2.68862i) q^{19} +(1.41489 - 4.35458i) q^{21} +(-3.88485 - 0.615300i) q^{23} +(-2.84737 - 4.11005i) q^{25} +(0.421923 - 2.66392i) q^{27} +(-5.50106 - 1.78740i) q^{29} +(-9.13518 + 2.96820i) q^{31} +(-0.569291 - 0.290068i) q^{33} +(1.39929 + 4.47697i) q^{35} +(0.750303 + 4.73723i) q^{37} +(7.97786 - 5.79625i) q^{39} +(5.38745 + 3.91421i) q^{41} +(-5.39252 - 5.39252i) q^{43} +(-1.75150 - 3.53507i) q^{45} +(3.24189 + 6.36258i) q^{47} +2.59975i q^{49} -9.60406i q^{51} +(-3.61868 - 7.10206i) q^{53} +(0.647592 - 0.0951287i) q^{55} +(4.36324 + 4.36324i) q^{57} +(2.43468 + 1.76890i) q^{59} +(9.58818 - 6.96622i) q^{61} +(0.578966 + 3.65545i) q^{63} +(-3.22939 + 9.57203i) q^{65} +(8.32617 + 4.24240i) q^{67} +(8.16512 - 2.65301i) q^{69} +(0.108915 + 0.0353885i) q^{71} +(-0.879144 + 5.55070i) q^{73} +(9.61047 + 5.17178i) q^{75} +(-0.606473 - 0.0960558i) q^{77} +(4.32162 - 13.3006i) q^{79} +(3.45485 + 10.6329i) q^{81} +(-7.48613 + 14.6924i) q^{83} +(5.69333 + 8.02411i) q^{85} +(12.4699 - 1.97503i) q^{87} +(6.38336 + 8.78594i) q^{89} +(5.57038 - 7.66697i) q^{91} +(14.8251 - 14.8251i) q^{93} +(-6.23201 - 1.05890i) q^{95} +(-2.01972 + 1.02910i) q^{97} +0.516457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5}+O(q^{10}) $ 80 * q + 4 * q^5	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$	$-1$

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
$3$	−1.94483	+	0.990942i	−1.12285	+	0.572120i	−0.913954	−	0.405818i	$-0.866987\pi$
$3$	−1.94483	+	0.990942i	−1.12285	+	0.572120i	−0.208895	+	0.977938i	$0.566987\pi$
$4$		0			0
$5$	1.03746	−	1.98083i	0.463965	−	0.885854i
$5$	1.03746	−	1.98083i	0.463965	−	0.885854i
$6$		0			0
$7$	−1.48328	+	1.48328i	−0.560628	+	0.560628i	−0.929486	−	0.368858i	$-0.879749\pi$
$7$	−1.48328	+	1.48328i	−0.560628	+	0.560628i	0.368858	+	0.929486i	$0.379749\pi$
$8$		0			0
$9$	1.03705	−	1.42738i	0.345684	−	0.475793i
$10$		0			0
$11$	0.172056	+	0.236815i	0.0518770	+	0.0714025i	0.834167	−	0.551511i	$-0.185949\pi$
$11$	0.172056	+	0.236815i	0.0518770	+	0.0714025i	−0.782290	+	0.622914i	$0.785949\pi$
$12$		0			0
$13$	−4.46218	+	0.706740i	−1.23759	+	0.196014i	−0.740721	−	0.671813i	$-0.765516\pi$
$13$	−4.46218	+	0.706740i	−1.23759	+	0.196014i	−0.496866	+	0.867827i	$0.665516\pi$
$14$		0			0
$15$	−0.0547938	+	4.88044i	−0.0141477	+	1.26012i
$16$		0			0
$17$	−1.99756	+	3.92044i	−0.484480	+	0.950845i	0.511329	+	0.859385i	$0.329153\pi$
$17$	−1.99756	+	3.92044i	−0.484480	+	0.950845i	−0.995809	+	0.0914603i	$0.970847\pi$
$18$		0			0
$19$	−0.873586	−	2.68862i	−0.200414	−	0.616812i	−0.999871	−	0.0160876i	$-0.994879\pi$
$19$	−0.873586	−	2.68862i	−0.200414	−	0.616812i	0.799456	−	0.600724i	$-0.205121\pi$
$20$		0			0
$21$	1.41489	−	4.35458i	0.308754	−	0.950248i
$22$		0			0
$23$	−3.88485	−	0.615300i	−0.810048	−	0.128299i	−0.262347	−	0.964973i	$-0.584497\pi$
$23$	−3.88485	−	0.615300i	−0.810048	−	0.128299i	−0.547700	+	0.836674i	$0.684497\pi$
$24$		0			0
$25$	−2.84737	−	4.11005i	−0.569473	−	0.822010i
$26$		0			0
$27$	0.421923	−	2.66392i	0.0811992	−	0.512671i
$28$		0			0
$29$	−5.50106	−	1.78740i	−1.02152	−	0.331912i	−0.250089	−	0.968223i	$-0.580460\pi$
$29$	−5.50106	−	1.78740i	−1.02152	−	0.331912i	−0.771433	+	0.636310i	$0.780460\pi$
$30$		0			0
$31$	−9.13518	+	2.96820i	−1.64073	+	0.533104i	−0.976701	−	0.214605i	$-0.931153\pi$
$31$	−9.13518	+	2.96820i	−1.64073	+	0.533104i	−0.664026	+	0.747710i	$0.731153\pi$
$32$		0			0
$33$	−0.569291	−	0.290068i	−0.0991009	−	0.0504944i
$34$		0			0
$35$	1.39929	+	4.47697i	0.236523	+	0.756746i
$36$		0			0
$37$	0.750303	+	4.73723i	0.123349	+	0.778795i	0.969363	+	0.245634i	$0.0789961\pi$
$37$	0.750303	+	4.73723i	0.123349	+	0.778795i	−0.846014	+	0.533161i	$0.821004\pi$
$38$		0			0
$39$	7.97786	−	5.79625i	1.27748	−	0.928143i
$40$		0			0
$41$	5.38745	+	3.91421i	0.841378	+	0.611297i	0.922755	−	0.385387i	$-0.125932\pi$
$41$	5.38745	+	3.91421i	0.841378	+	0.611297i	−0.0813776	+	0.996683i	$0.525932\pi$
$42$		0			0
$43$	−5.39252	−	5.39252i	−0.822352	−	0.822352i	0.164093	−	0.986445i	$-0.447530\pi$
$43$	−5.39252	−	5.39252i	−0.822352	−	0.822352i	−0.986445	+	0.164093i	$0.947530\pi$
$44$		0			0
$45$	−1.75150	−	3.53507i	−0.261098	−	0.526977i
$46$		0			0
$47$	3.24189	+	6.36258i	0.472879	+	0.928077i	0.997071	+	0.0764773i	$0.0243673\pi$
$47$	3.24189	+	6.36258i	0.472879	+	0.928077i	−0.524192	+	0.851600i	$0.675633\pi$
$48$		0			0
$49$			2.59975i			0.371392i
$50$		0			0
$51$		−	9.60406i		−	1.34484i
$52$		0			0
$53$	−3.61868	−	7.10206i	−0.497064	−	0.975543i	−0.994167	−	0.107852i	$-0.965603\pi$
$53$	−3.61868	−	7.10206i	−0.497064	−	0.975543i	0.497103	−	0.867692i	$-0.334397\pi$
$54$		0			0
$55$	0.647592	−	0.0951287i	0.0873213	−	0.0128271i
$56$		0			0
$57$	4.36324	+	4.36324i	0.577926	+	0.577926i
$58$		0			0
$59$	2.43468	+	1.76890i	0.316969	+	0.230291i	0.734881	−	0.678196i	$-0.237238\pi$
$59$	2.43468	+	1.76890i	0.316969	+	0.230291i	−0.417912	+	0.908487i	$0.637238\pi$
$60$		0			0
$61$	9.58818	−	6.96622i	1.22764	−	0.891933i	0.230929	−	0.972971i	$-0.425823\pi$
$61$	9.58818	−	6.96622i	1.22764	−	0.891933i	0.996711	+	0.0810377i	$0.0258234\pi$
$62$		0			0
$63$	0.578966	+	3.65545i	0.0729429	+	0.460543i
$64$		0			0
$65$	−3.22939	+	9.57203i	−0.400556	+	1.18726i
$66$		0			0
$67$	8.32617	+	4.24240i	1.01720	+	0.518291i	0.881363	−	0.472439i	$-0.156626\pi$
$67$	8.32617	+	4.24240i	1.01720	+	0.518291i	0.135841	+	0.990731i	$0.456626\pi$
$68$		0			0
$69$	8.16512	−	2.65301i	0.982964	−	0.319384i
$70$		0			0
$71$	0.108915	+	0.0353885i	0.0129258	+	0.00419984i	0.315473	−	0.948935i	$-0.397837\pi$
$71$	0.108915	+	0.0353885i	0.0129258	+	0.00419984i	−0.302547	+	0.953134i	$0.597837\pi$
$72$		0			0
$73$	−0.879144	+	5.55070i	−0.102896	+	0.649660i	0.881297	+	0.472562i	$0.156671\pi$
$73$	−0.879144	+	5.55070i	−0.102896	+	0.649660i	−0.984193	+	0.177098i	$0.943329\pi$
$74$		0			0
$75$	9.61047	+	5.17178i	1.10972	+	0.597186i
$76$		0			0
$77$	−0.606473	−	0.0960558i	−0.0691140	−	0.0109466i
$78$		0			0
$79$	4.32162	−	13.3006i	0.486221	−	1.49643i	−0.343985	−	0.938975i	$-0.611777\pi$
$79$	4.32162	−	13.3006i	0.486221	−	1.49643i	0.830205	−	0.557458i	$-0.188223\pi$
$80$		0			0
$81$	3.45485	+	10.6329i	0.383872	+	1.18144i
$82$		0			0
$83$	−7.48613	+	14.6924i	−0.821709	+	1.61270i	−0.0317825	+	0.999495i	$0.510118\pi$
$83$	−7.48613	+	14.6924i	−0.821709	+	1.61270i	−0.789927	+	0.613201i	$0.789882\pi$
$84$		0			0
$85$	5.69333	+	8.02411i	0.617528	+	0.870337i
$86$		0			0
$87$	12.4699	−	1.97503i	1.33691	−	0.211746i
$88$		0			0
$89$	6.38336	+	8.78594i	0.676635	+	0.931308i	0.999887	−	0.0150047i	$-0.00477631\pi$
$89$	6.38336	+	8.78594i	0.676635	+	0.931308i	−0.323252	+	0.946313i	$0.604776\pi$
$90$		0			0
$91$	5.57038	−	7.66697i	0.583935	−	0.803717i
$92$		0			0
$93$	14.8251	−	14.8251i	1.53729	−	1.53729i
$94$		0			0
$95$	−6.23201	−	1.05890i	−0.639390	−	0.108641i
$96$		0			0
$97$	−2.01972	+	1.02910i	−0.205071	+	0.104489i	−0.553510	−	0.832843i	$-0.686712\pi$
$97$	−2.01972	+	1.02910i	−0.205071	+	0.104489i	0.348439	+	0.937332i	$0.386712\pi$
$98$		0			0
$99$	0.516457			0.0519059
$100$		0			0
$101$	−17.0895			−1.70047			−0.850235	−	0.526403i	$-0.823540\pi$
$101$	−17.0895			−1.70047			−0.850235	+	0.526403i	$0.823540\pi$
$102$		0			0
$103$	12.7500	−	6.49647i	1.25630	−	0.640116i	0.306171	−	0.951976i	$-0.400952\pi$
$103$	12.7500	−	6.49647i	1.25630	−	0.640116i	0.950128	+	0.311860i	$0.100952\pi$
$104$		0			0
$105$	−7.15780	−	7.32035i	−0.698529	−	0.714393i
$106$		0			0
$107$	8.06319	−	8.06319i	0.779498	−	0.779498i	−0.200247	−	0.979745i	$-0.564175\pi$
$107$	8.06319	−	8.06319i	0.779498	−	0.779498i	0.979745	+	0.200247i	$0.0641746\pi$
$108$		0			0
$109$	−3.12628	+	4.30296i	−0.299443	+	0.412148i	−0.932053	−	0.362323i	$-0.881984\pi$
$109$	−3.12628	+	4.30296i	−0.299443	+	0.412148i	0.632609	+	0.774471i	$0.281984\pi$
$110$		0			0
$111$	−6.15353	−	8.46960i	−0.584067	−	0.803899i
$112$		0			0
$113$	−11.3689	+	1.80066i	−1.06950	+	0.169392i	−0.666273	−	0.745708i	$-0.732111\pi$
$113$	−11.3689	+	1.80066i	−1.06950	+	0.169392i	−0.403227	+	0.915100i	$0.632111\pi$
$114$		0			0
$115$	−5.24917	+	7.05688i	−0.489488	+	0.658058i
$116$		0			0
$117$	−3.61873	+	7.10215i	−0.334551	+	0.656594i
$118$		0			0
$119$	−2.85217	−	8.77806i	−0.261458	−	0.804684i
$120$		0			0
$121$	3.37271	−	10.3801i	0.306610	−	0.943648i
$122$		0			0
$123$	−14.3564	−	2.27383i	−1.29448	−	0.205025i
$124$		0			0
$125$	−11.0953	+	1.37615i	−0.992396	+	0.123086i
$126$		0			0
$127$	−0.443228	+	2.79843i	−0.0393302	+	0.248321i	−0.999518	−	0.0310331i	$-0.990120\pi$
$127$	−0.443228	+	2.79843i	−0.0393302	+	0.248321i	0.960188	+	0.279354i	$0.0901203\pi$
$128$		0			0
$129$	15.8312	+	5.14388i	1.39386	+	0.452893i
$130$		0			0
$131$	0.292008	−	0.0948793i	0.0255129	−	0.00828964i	−0.296233	−	0.955116i	$-0.595730\pi$
$131$	0.292008	−	0.0948793i	0.0255129	−	0.00828964i	0.321746	+	0.946826i	$0.395730\pi$
$132$		0			0
$133$	5.28376	+	2.69221i	0.458160	+	0.233444i
$134$		0			0
$135$	−4.83904	−	3.59946i	−0.416478	−	0.309792i
$136$		0			0
$137$	−2.70290	−	17.0654i	−0.230924	−	1.45800i	−0.781863	−	0.623451i	$-0.785730\pi$
$137$	−2.70290	−	17.0654i	−0.230924	−	1.45800i	0.550939	−	0.834546i	$-0.314270\pi$
$138$		0			0
$139$	1.54443	−	1.12209i	0.130997	−	0.0951747i	−0.520357	−	0.853949i	$-0.674201\pi$
$139$	1.54443	−	1.12209i	0.130997	−	0.0951747i	0.651354	+	0.758774i	$0.274201\pi$
$140$		0			0
$141$	−12.6099	−	9.16162i	−1.06194	−	0.771547i
$142$		0			0
$143$	−0.935114	−	0.935114i	−0.0781982	−	0.0781982i
$144$		0			0
$145$	−9.24765	+	9.04231i	−0.767976	+	0.750923i
$146$		0			0
$147$	−2.57620	−	5.05607i	−0.212481	−	0.417017i
$148$		0			0
$149$			9.05669i			0.741953i	0.928642	+	0.370976i	$0.120977\pi$
$149$			9.05669i			0.741953i	−0.928642	+	0.370976i	$0.879023\pi$
$150$		0			0
$151$		−	17.3662i		−	1.41324i	−0.707591	−	0.706622i	$-0.750218\pi$
$151$		−	17.3662i		−	1.41324i	0.707591	−	0.706622i	$-0.249782\pi$
$152$		0			0
$153$	3.52437	+	6.91697i	0.284929	+	0.559204i
$154$		0			0
$155$	−3.59786	+	21.1746i	−0.288987	+	1.70079i
$156$		0			0
$157$	−4.25488	−	4.25488i	−0.339576	−	0.339576i	0.516631	−	0.856208i	$-0.327186\pi$
$157$	−4.25488	−	4.25488i	−0.339576	−	0.339576i	−0.856208	+	0.516631i	$0.827186\pi$
$158$		0			0
$159$	14.0755	+	10.2264i	1.11626	+	0.811008i
$160$		0			0
$161$	6.67500	−	4.84967i	0.526064	−	0.382208i
$162$		0			0
$163$	0.842317	+	5.31818i	0.0659753	+	0.416552i	0.998467	+	0.0553591i	$0.0176304\pi$
$163$	0.842317	+	5.31818i	0.0659753	+	0.416552i	−0.932491	+	0.361193i	$0.882370\pi$
$164$		0			0
$165$	−1.16519	+	0.826735i	−0.0907100	+	0.0643612i
$166$		0			0
$167$	7.08288	+	3.60891i	0.548090	+	0.279266i	0.706029	−	0.708183i	$-0.250485\pi$
$167$	7.08288	+	3.60891i	0.548090	+	0.279266i	−0.157939	+	0.987449i	$0.550485\pi$
$168$		0			0
$169$	7.04785	−	2.28998i	0.542142	−	0.176153i
$170$		0			0
$171$	−4.74364	−	1.54130i	−0.362755	−	0.117866i
$172$		0			0
$173$	1.93012	−	12.1863i	0.146745	−	0.926509i	−0.798937	−	0.601415i	$-0.794604\pi$
$173$	1.93012	−	12.1863i	0.146745	−	0.926509i	0.945682	−	0.325094i	$-0.105396\pi$
$174$		0			0
$175$	10.3198	+	1.87291i	0.780105	+	0.141579i
$176$		0			0
$177$	−6.48793	−	1.02759i	−0.487663	−	0.0772382i
$178$		0			0
$179$	−7.39147	+	22.7486i	−0.552464	+	1.70031i	0.150083	+	0.988673i	$0.452046\pi$
$179$	−7.39147	+	22.7486i	−0.552464	+	1.70031i	−0.702547	+	0.711637i	$0.747954\pi$
$180$		0			0
$181$	3.64798	+	11.2273i	0.271153	+	0.834522i	0.990212	+	0.139573i	$0.0445730\pi$
$181$	3.64798	+	11.2273i	0.271153	+	0.834522i	−0.719059	+	0.694949i	$0.755427\pi$
$182$		0			0
$183$	−11.7443	+	23.0495i	−0.868162	+	1.70386i
$184$		0			0
$185$	10.1620	+	3.42844i	0.747128	+	0.252064i
$186$		0			0
$187$	−1.27211	+	0.201483i	−0.0930261	+	0.0147339i
$188$		0			0
$189$	3.32551	+	4.57718i	0.241895	+	0.332940i
$190$		0			0
$191$	−12.8134	+	17.6361i	−0.927145	+	1.27611i	0.0338173	+	0.999428i	$0.489234\pi$
$191$	−12.8134	+	17.6361i	−0.927145	+	1.27611i	−0.960963	+	0.276678i	$0.910766\pi$
$192$		0			0
$193$	10.3562	−	10.3562i	0.745457	−	0.745457i	−0.228165	−	0.973622i	$-0.573273\pi$
$193$	10.3562	−	10.3562i	0.745457	−	0.745457i	0.973622	+	0.228165i	$0.0732726\pi$
$194$		0			0
$195$	−3.20470	−	21.8161i	−0.229494	−	1.56229i
$196$		0			0
$197$	0.990061	−	0.504461i	0.0705389	−	0.0359414i	−0.418365	−	0.908279i	$-0.637397\pi$
$197$	0.990061	−	0.504461i	0.0705389	−	0.0359414i	0.488904	+	0.872338i	$0.337397\pi$
$198$		0			0
$199$	−26.4857			−1.87752			−0.938762	−	0.344566i	$-0.888026\pi$
$199$	−26.4857			−1.87752			−0.938762	+	0.344566i	$0.888026\pi$
$200$		0			0
$201$	−20.3970			−1.43869
$202$		0			0
$203$	10.8109	−	5.50841i	0.758773	−	0.386614i
$204$		0			0
$205$	13.3426	−	6.61079i	0.931889	−	0.461717i
$206$		0			0
$207$	−4.90706	+	4.90706i	−0.341064	+	0.341064i
$208$		0			0
$209$	0.486401	−	0.669473i	0.0336450	−	0.0463084i
$210$		0			0
$211$	1.14945	+	1.58209i	0.0791317	+	0.108915i	0.846748	−	0.531994i	$-0.178557\pi$
$211$	1.14945	+	1.58209i	0.0791317	+	0.108915i	−0.767616	+	0.640910i	$0.778557\pi$
$212$		0			0
$213$	−0.246889	+	0.0391033i	−0.0169165	+	0.00267932i
$214$		0			0
$215$	−16.2762	+	5.08716i	−1.11003	+	0.346941i
$216$		0			0
$217$	9.14737	−	17.9527i	0.620964	−	1.21871i
$218$		0			0
$219$	−3.79063	−	11.6664i	−0.256147	−	0.788340i
$220$		0			0
$221$	6.14275	−	18.9055i	0.413206	−	1.27172i
$222$		0			0
$223$	−4.93639	−	0.781847i	−0.330565	−	0.0523564i	−0.0110540	−	0.999939i	$-0.503519\pi$
$223$	−4.93639	−	0.781847i	−0.330565	−	0.0523564i	−0.319511	+	0.947583i	$0.603519\pi$
$224$		0			0
$225$	−8.81947	−	0.198061i	−0.587964	−	0.0132041i
$226$		0			0
$227$	−1.32974	+	8.39567i	−0.0882581	+	0.557240i	0.903446	+	0.428701i	$0.141029\pi$
$227$	−1.32974	+	8.39567i	−0.0882581	+	0.557240i	−0.991704	+	0.128539i	$0.958971\pi$
$228$		0			0
$229$	−18.3596	−	5.96540i	−1.21324	−	0.394205i	−0.368623	−	0.929579i	$-0.620171\pi$
$229$	−18.3596	−	5.96540i	−1.21324	−	0.394205i	−0.844615	+	0.535374i	$0.820171\pi$
$230$		0			0
$231$	1.27467	−	0.414166i	0.0838673	−	0.0272501i
$232$		0			0
$233$	−10.3382	−	5.26759i	−0.677280	−	0.345091i	0.0812830	−	0.996691i	$-0.474098\pi$
$233$	−10.3382	−	5.26759i	−0.677280	−	0.345091i	−0.758563	+	0.651600i	$0.774098\pi$
$234$		0			0
$235$	15.9665	+	0.179259i	1.04154	+	0.0116936i
$236$		0			0
$237$	4.77527	+	30.1499i	0.310187	+	1.95845i
$238$		0			0
$239$	8.82004	−	6.40814i	0.570521	−	0.414508i	−0.264773	−	0.964311i	$-0.585297\pi$
$239$	8.82004	−	6.40814i	0.570521	−	0.414508i	0.835294	+	0.549803i	$0.185297\pi$
$240$		0			0
$241$	13.2530	+	9.62889i	0.853703	+	0.620251i	0.926164	−	0.377120i	$-0.123086\pi$
$241$	13.2530	+	9.62889i	0.853703	+	0.620251i	−0.0724618	+	0.997371i	$0.523086\pi$
$242$		0			0
$243$	−11.5343	−	11.5343i	−0.739923	−	0.739923i
$244$		0			0
$245$	5.14965	+	2.69712i	0.328999	+	0.172313i
$246$		0			0
$247$	5.79826	+	11.3797i	0.368934	+	0.724074i
$248$		0			0
$249$		−	35.9925i		−	2.28093i
$250$		0			0
$251$			10.2316i			0.645812i	0.946431	+	0.322906i	$0.104660\pi$
$251$			10.2316i			0.645812i	−0.946431	+	0.322906i	$0.895340\pi$
$252$		0			0
$253$	−0.522702	−	1.02586i	−0.0328620	−	0.0644952i
$254$		0			0
$255$	−19.0240	−	9.96380i	−1.19133	−	0.623957i
$256$		0			0
$257$	−5.16997	−	5.16997i	−0.322494	−	0.322494i	0.527229	−	0.849723i	$-0.323231\pi$
$257$	−5.16997	−	5.16997i	−0.322494	−	0.322494i	−0.849723	+	0.527229i	$0.823231\pi$
$258$		0			0
$259$	−8.13955	−	5.91373i	−0.505767	−	0.367461i
$260$		0			0
$261$	−8.25619	+	5.99847i	−0.511045	+	0.371296i
$262$		0			0
$263$	1.29971	+	8.20606i	0.0801437	+	0.506007i	0.994806	+	0.101789i	$0.0324565\pi$
$263$	1.29971	+	8.20606i	0.0801437	+	0.506007i	−0.914662	+	0.404219i	$0.867543\pi$
$264$		0			0
$265$	−17.8222	−	0.200094i	−1.09481	−	0.0122917i
$266$		0			0
$267$	−21.1209	−	10.7616i	−1.29258	−	0.658602i
$268$		0			0
$269$	−11.9803	+	3.89262i	−0.730449	+	0.237337i	−0.650548	−	0.759465i	$-0.725461\pi$
$269$	−11.9803	+	3.89262i	−0.730449	+	0.237337i	−0.0799016	+	0.996803i	$0.525461\pi$
$270$		0			0
$271$	11.3792	+	3.69732i	0.691237	+	0.224596i	0.633508	−	0.773736i	$-0.281614\pi$
$271$	11.3792	+	3.69732i	0.691237	+	0.224596i	0.0577285	+	0.998332i	$0.481614\pi$
$272$		0			0
$273$	−3.23594	+	20.4309i	−0.195848	+	1.23653i
$274$		0			0
$275$	0.483415	−	1.38146i	0.0291510	−	0.0833052i
$276$		0			0
$277$	3.22014	+	0.510020i	0.193479	+	0.0306441i	0.252422	−	0.967617i	$-0.418773\pi$
$277$	3.22014	+	0.510020i	0.193479	+	0.0306441i	−0.0589426	+	0.998261i	$0.518773\pi$
$278$		0			0
$279$	−5.23691	+	16.1175i	−0.313525	+	0.964932i
$280$		0			0
$281$	3.75925	+	11.5698i	0.224258	+	0.690195i	0.998366	+	0.0571416i	$0.0181987\pi$
$281$	3.75925	+	11.5698i	0.224258	+	0.690195i	−0.774108	+	0.633053i	$0.781801\pi$
$282$		0			0
$283$	8.82403	−	17.3181i	0.524534	−	1.02946i	−0.465021	−	0.885300i	$-0.653953\pi$
$283$	8.82403	−	17.3181i	0.524534	−	1.02946i	0.989555	−	0.144157i	$-0.0460469\pi$
$284$		0			0
$285$	13.1695	−	4.11616i	0.780095	−	0.243820i
$286$		0			0
$287$	−13.7970	+	2.18523i	−0.814410	+	0.128990i
$288$		0			0
$289$	−1.38722	−	1.90934i	−0.0816010	−	0.112314i
$290$		0			0
$291$	2.90824	−	4.00284i	0.170484	−	0.234651i
$292$		0			0
$293$	−2.12613	+	2.12613i	−0.124210	+	0.124210i	−0.766479	−	0.642269i	$-0.777993\pi$
$293$	−2.12613	+	2.12613i	−0.124210	+	0.124210i	0.642269	+	0.766479i	$0.277993\pi$
$294$		0			0
$295$	6.02977	−	2.98753i	0.351067	−	0.173941i
$296$		0			0
$297$	0.703451	−	0.358426i	0.0408184	−	0.0207980i
$298$		0			0
$299$	17.7698			1.02765
$300$		0			0
$301$	15.9973			0.922067
$302$		0			0
$303$	33.2362	−	16.9347i	1.90937	−	0.972874i
$304$		0			0
$305$	−3.85157	−	26.2197i	−0.220540	−	1.50134i
$306$		0			0
$307$	0.983328	−	0.983328i	0.0561215	−	0.0561215i	−0.678489	−	0.734611i	$-0.737365\pi$
$307$	0.983328	−	0.983328i	0.0561215	−	0.0561215i	0.734611	+	0.678489i	$0.237365\pi$
$308$		0			0
$309$	−18.3591	+	25.2691i	−1.04441	+	1.43751i
$310$		0			0
$311$	13.2102	+	18.1823i	0.749084	+	1.03103i	0.998044	+	0.0625124i	$0.0199113\pi$
$311$	13.2102	+	18.1823i	0.749084	+	1.03103i	−0.248960	+	0.968514i	$0.580089\pi$
$312$		0			0
$313$	−25.7838	+	4.08374i	−1.45738	+	0.230827i	−0.834292	−	0.551322i	$-0.814124\pi$
$313$	−25.7838	+	4.08374i	−1.45738	+	0.230827i	−0.623091	+	0.782149i	$0.714124\pi$
$314$		0			0
$315$	7.84147	+	2.64554i	0.441817	+	0.149059i
$316$		0			0
$317$	1.22410	−	2.40243i	0.0687524	−	0.134934i	−0.854072	−	0.520154i	$-0.825874\pi$
$317$	1.22410	−	2.40243i	0.0687524	−	0.134934i	0.922825	+	0.385220i	$0.125874\pi$
$318$		0			0
$319$	−0.523209	−	1.61027i	−0.0292941	−	0.0901578i
$320$		0			0
$321$	−7.69140	+	23.6717i	−0.429292	+	1.32123i
$322$		0			0
$323$	12.2856	+	1.94585i	0.683590	+	0.108270i
$324$		0			0
$325$	15.6102	+	16.3274i	0.865898	+	0.905683i
$326$		0			0
$327$	1.81611	−	11.4665i	0.100431	−	0.634098i
$328$		0			0
$329$	−14.2461	−	4.62885i	−0.785415	−	0.255197i
$330$		0			0
$331$	−13.8590	+	4.50307i	−0.761761	+	0.247511i	−0.664034	−	0.747702i	$-0.731157\pi$
$331$	−13.8590	+	4.50307i	−0.761761	+	0.247511i	−0.0977269	+	0.995213i	$0.531157\pi$
$332$		0			0
$333$	7.53992	+	3.84178i	0.413185	+	0.210528i
$334$		0			0
$335$	17.0415	−	12.0914i	0.931077	−	0.660625i
$336$		0			0
$337$	−1.47620	−	9.32038i	−0.0804139	−	0.507714i	−0.994715	−	0.102678i	$-0.967259\pi$
$337$	−1.47620	−	9.32038i	−0.0804139	−	0.507714i	0.914301	−	0.405036i	$-0.132741\pi$
$338$		0			0
$339$	20.3263	−	14.7679i	1.10397	−	0.802084i
$340$		0			0
$341$	−2.27468	−	1.65265i	−0.123181	−	0.0894962i
$342$		0			0
$343$	−14.2391	−	14.2391i	−0.768841	−	0.768841i
$344$		0			0
$345$	3.21580	−	18.9261i	0.173133	−	1.01895i
$346$		0			0
$347$	−10.2217	−	20.0612i	−0.548730	−	1.07694i	−0.984253	−	0.176766i	$-0.943437\pi$
$347$	−10.2217	−	20.0612i	−0.548730	−	1.07694i	0.435523	−	0.900178i	$-0.356563\pi$
$348$		0			0
$349$		−	16.7549i		−	0.896869i	−0.893816	−	0.448435i	$-0.851982\pi$
$349$		−	16.7549i		−	0.896869i	0.893816	−	0.448435i	$-0.148018\pi$
$350$		0			0
$351$			12.1851i			0.650391i
$352$		0			0
$353$	10.6150	+	20.8330i	0.564977	+	1.10883i	0.979996	+	0.199017i	$0.0637750\pi$
$353$	10.6150	+	20.8330i	0.564977	+	1.10883i	−0.415019	+	0.909813i	$0.636225\pi$
$354$		0			0
$355$	0.183093	−	0.179027i	0.00971756	−	0.00950178i
$356$		0			0
$357$	14.2455	+	14.2455i	0.753954	+	0.753954i
$358$		0			0
$359$	10.0828	+	7.32560i	0.532151	+	0.386630i	0.821162	−	0.570696i	$-0.193326\pi$
$359$	10.0828	+	7.32560i	0.532151	+	0.386630i	−0.289011	+	0.957326i	$0.593326\pi$
$360$		0			0
$361$	8.90579	−	6.47044i	0.468726	−	0.340549i
$362$		0			0
$363$	3.72675	+	23.5298i	0.195604	+	1.23499i
$364$		0			0
$365$	10.0829	+	7.50005i	0.527764	+	0.392570i
$366$		0			0
$367$	−25.0240	−	12.7504i	−1.30624	−	0.665565i	−0.344313	−	0.938855i	$-0.611888\pi$
$367$	−25.0240	−	12.7504i	−1.30624	−	0.665565i	−0.961932	+	0.273290i	$0.911888\pi$
$368$		0			0
$369$	11.1741	−	3.63069i	0.581701	−	0.189006i
$370$		0			0
$371$	15.9019	+	5.16684i	0.825585	+	0.268249i
$372$		0			0
$373$	−2.68159	+	16.9309i	−0.138847	+	0.876648i	0.815675	+	0.578510i	$0.196366\pi$
$373$	−2.68159	+	16.9309i	−0.138847	+	0.876648i	−0.954523	+	0.298138i	$0.903634\pi$
$374$		0			0
$375$	20.2149	−	13.6712i	1.04389	−	0.705978i
$376$		0			0
$377$	25.8100	+	4.08790i	1.32928	+	0.210537i
$378$		0			0
$379$	−9.94946	+	30.6213i	−0.511069	+	1.57291i	0.279253	+	0.960218i	$0.409913\pi$
$379$	−9.94946	+	30.6213i	−0.511069	+	1.57291i	−0.790322	+	0.612692i	$0.790087\pi$
$380$		0			0
$381$	−1.91108	−	5.88170i	−0.0979076	−	0.301329i
$382$		0			0
$383$	2.36308	−	4.63781i	0.120748	−	0.236981i	−0.822719	−	0.568449i	$-0.807544\pi$
$383$	2.36308	−	4.63781i	0.120748	−	0.236981i	0.943467	+	0.331468i	$0.107544\pi$
$384$		0			0
$385$	−0.819459	+	1.10166i	−0.0417635	+	0.0561460i
$386$		0			0
$387$	−13.2895	+	2.10485i	−0.675543	+	0.106996i
$388$		0			0
$389$	−5.45864	−	7.51318i	−0.276764	−	0.380933i	0.647895	−	0.761730i	$-0.275650\pi$
$389$	−5.45864	−	7.51318i	−0.276764	−	0.380933i	−0.924659	+	0.380797i	$0.875650\pi$
$390$		0			0
$391$	10.1725	−	14.0012i	0.514444	−	0.708072i
$392$		0			0
$393$	−0.473888	+	0.473888i	−0.0239045	+	0.0239045i
$394$		0			0
$395$	−21.8627	−	22.3592i	−1.10003	−	1.12501i
$396$		0			0
$397$	−10.2184	+	5.20654i	−0.512847	+	0.261309i	−0.691207	−	0.722657i	$-0.742921\pi$
$397$	−10.2184	+	5.20654i	−0.512847	+	0.261309i	0.178360	+	0.983965i	$0.442921\pi$
$398$		0			0
$399$	−12.9438			−0.648003
$400$		0			0
$401$	21.5734			1.07733			0.538663	−	0.842521i	$-0.318930\pi$
$401$	21.5734			1.07733			0.538663	+	0.842521i	$0.318930\pi$
$402$		0			0
$403$	38.6651	−	19.7008i	1.92604	−	0.981369i
$404$		0			0
$405$	24.6463	+	4.18774i	1.22468	+	0.208091i
$406$		0			0
$407$	−0.992753	+	0.992753i	−0.0492090	+	0.0492090i
$408$		0			0
$409$	8.63908	−	11.8907i	0.427175	−	0.587956i	−0.540127	−	0.841584i	$-0.681624\pi$
$409$	8.63908	−	11.8907i	0.427175	−	0.587956i	0.967302	+	0.253628i	$0.0816238\pi$
$410$		0			0
$411$	22.1675	+	30.5110i	1.09344	+	1.50499i
$412$		0			0
$413$	−6.23511	+	0.987544i	−0.306809	+	0.0485938i
$414$		0			0
$415$	21.3365	+	30.0714i	1.04737	+	1.47615i
$416$		0			0
$417$	−1.89173	+	3.71272i	−0.0926382	+	0.181813i
$418$		0			0
$419$	−5.13915	−	15.8167i	−0.251064	−	0.772695i	−0.994580	−	0.103977i	$-0.966843\pi$
$419$	−5.13915	−	15.8167i	−0.251064	−	0.772695i	0.743516	−	0.668718i	$-0.233157\pi$
$420$		0			0
$421$	−0.627906	+	1.93250i	−0.0306023	+	0.0941841i	−0.965191	−	0.261546i	$-0.915768\pi$
$421$	−0.627906	+	1.93250i	−0.0306023	+	0.0941841i	0.934589	+	0.355730i	$0.115768\pi$
$422$		0			0
$423$	12.4438	+	1.97091i	0.605039	+	0.0958288i
$424$		0			0
$425$	21.8010	−	2.95284i	1.05750	−	0.143234i
$426$		0			0
$427$	−3.88911	+	24.5548i	−0.188207	+	1.18829i
$428$		0			0
$429$	2.74528	+	0.891997i	0.132544	+	0.0430660i
$430$		0			0
$431$	14.1343	−	4.59251i	0.680825	−	0.221214i	0.0518687	−	0.998654i	$-0.483482\pi$
$431$	14.1343	−	4.59251i	0.680825	−	0.221214i	0.628957	+	0.777440i	$0.283482\pi$
$432$		0			0
$433$	−1.32156	−	0.673367i	−0.0635100	−	0.0323600i	0.421947	−	0.906620i	$-0.361347\pi$
$433$	−1.32156	−	0.673367i	−0.0635100	−	0.0323600i	−0.485457	+	0.874260i	$0.661347\pi$
$434$		0			0
$435$	9.02474	−	26.7497i	0.432703	−	1.28255i
$436$		0			0
$437$	1.73944	+	10.9824i	0.0832089	+	0.525360i
$438$		0			0
$439$	−25.0144	+	18.1740i	−1.19387	+	0.867398i	−0.993668	−	0.112356i	$-0.964160\pi$
$439$	−25.0144	+	18.1740i	−1.19387	+	0.867398i	−0.200204	+	0.979754i	$0.564160\pi$
$440$		0			0
$441$	3.71082	+	2.69607i	0.176706	+	0.128384i
$442$		0			0
$443$	−24.2332	−	24.2332i	−1.15135	−	1.15135i	−0.986282	−	0.165072i	$-0.947214\pi$
$443$	−24.2332	−	24.2332i	−1.15135	−	1.15135i	−0.165072	−	0.986282i	$-0.552786\pi$
$444$		0			0
$445$	24.0259	−	3.52931i	1.13894	−	0.167305i
$446$		0			0
$447$	−8.97465	−	17.6137i	−0.424486	−	0.833101i
$448$		0			0
$449$			13.4902i			0.636643i	0.947983	+	0.318322i	$0.103119\pi$
$449$			13.4902i			0.636643i	−0.947983	+	0.318322i	$0.896881\pi$
$450$		0			0
$451$			1.94929i			0.0917887i
$452$		0			0
$453$	17.2089	+	33.7744i	0.808546	+	1.58686i
$454$		0			0
$455$	−9.40793	−	18.9881i	−0.441051	−	0.890177i
$456$		0			0
$457$	−20.3252	−	20.3252i	−0.950771	−	0.950771i	0.0480729	−	0.998844i	$-0.484692\pi$
$457$	−20.3252	−	20.3252i	−0.950771	−	0.950771i	−0.998844	+	0.0480729i	$0.984692\pi$
$458$		0			0
$459$	9.60090	+	6.97546i	0.448132	+	0.325587i
$460$		0			0
$461$	−32.1072	+	23.3273i	−1.49538	+	1.08646i	−0.523206	+	0.852206i	$0.675264\pi$
$461$	−32.1072	+	23.3273i	−1.49538	+	1.08646i	−0.972176	+	0.234252i	$0.924736\pi$
$462$		0			0
$463$	−1.08867	−	6.87358i	−0.0505947	−	0.319442i	−0.999986	−	0.00534559i	$-0.998298\pi$
$463$	−1.08867	−	6.87358i	−0.0505947	−	0.319442i	0.949391	−	0.314097i	$-0.101702\pi$
$464$		0			0
$465$	−13.9856	−	44.7463i	−0.648565	−	2.07506i
$466$		0			0
$467$	31.6347	+	16.1187i	1.46388	+	0.745884i	0.990825	−	0.135149i	$-0.0431514\pi$
$467$	31.6347	+	16.1187i	1.46388	+	0.745884i	0.473054	+	0.881033i	$0.343151\pi$
$468$		0			0
$469$	−18.6427	+	6.05739i	−0.860842	+	0.279704i
$470$		0			0
$471$	12.4914	+	4.05869i	0.575572	+	0.187015i
$472$		0			0
$473$	0.349214	−	2.20485i	0.0160569	−	0.101379i
$474$		0			0
$475$	−8.56294	+	11.2460i	−0.392895	+	0.516001i
$476$		0			0
$477$	−13.8901	−	2.19998i	−0.635984	−	0.100730i
$478$		0			0
$479$	1.21688	−	3.74517i	0.0556007	−	0.171121i	−0.919400	−	0.393325i	$-0.871325\pi$
$479$	1.21688	−	3.74517i	0.0556007	−	0.171121i	0.975000	+	0.222203i	$0.0713249\pi$
$480$		0			0
$481$	−6.69597	−	20.6081i	−0.305310	−	0.939648i
$482$		0			0
$483$	−8.17601	+	16.0463i	−0.372022	+	0.730133i
$484$		0			0
$485$	−0.0569036	+	5.06836i	−0.00258386	+	0.230142i
$486$		0			0
$487$	−2.81801	+	0.446328i	−0.127696	+	0.0202251i	−0.219955	−	0.975510i	$-0.570591\pi$
$487$	−2.81801	+	0.446328i	−0.127696	+	0.0202251i	0.0922593	+	0.995735i	$0.470591\pi$
$488$		0			0
$489$	−6.90817	−	9.50828i	−0.312398	−	0.429979i
$490$		0			0
$491$	−9.74120	+	13.4076i	−0.439614	+	0.605077i	−0.970126	−	0.242600i	$-0.922000\pi$
$491$	−9.74120	+	13.4076i	−0.439614	+	0.605077i	0.530512	+	0.847677i	$0.322000\pi$
$492$		0			0
$493$	17.9961	−	17.9961i	0.810504	−	0.810504i
$494$		0			0
$495$	0.535802	−	1.02301i	0.0240825	−	0.0459810i
$496$		0			0
$497$	−0.214042	+	0.109060i	−0.00960111	+	0.00489201i
$498$		0			0
$499$	−36.9363			−1.65350			−0.826749	−	0.562571i	$-0.809812\pi$
$499$	−36.9363			−1.65350			−0.826749	+	0.562571i	$0.809812\pi$
$500$		0			0
$501$	−17.3512			−0.775196
$502$		0			0
$503$	−1.62904	+	0.830040i	−0.0726355	+	0.0370096i	−0.489931	−	0.871761i	$-0.662978\pi$
$503$	−1.62904	+	0.830040i	−0.0726355	+	0.0370096i	0.417295	+	0.908771i	$0.362978\pi$
$504$		0			0
$505$	−17.7296	+	33.8514i	−0.788958	+	1.50637i
$506$		0			0
$507$	−11.4376	+	11.4376i	−0.507963	+	0.507963i
$508$		0			0
$509$	−3.74553	+	5.15527i	−0.166017	+	0.228503i	−0.883918	−	0.467643i	$-0.845103\pi$
$509$	−3.74553	+	5.15527i	−0.166017	+	0.228503i	0.717900	+	0.696146i	$0.245103\pi$
$510$		0			0
$511$	−6.92924	−	9.53728i	−0.306531	−	0.421904i
$512$		0			0
$513$	−7.53085	+	1.19277i	−0.332495	+	0.0526621i
$514$		0			0
$515$	0.359220	−	31.9955i	0.0158291	−	1.40989i
$516$		0			0
$517$	−0.948967	+	1.86245i	−0.0417355	+	0.0819106i
$518$		0			0
$519$	8.32217	+	25.6130i	0.365303	+	1.12429i
$520$		0			0
$521$	−9.16031	+	28.1925i	−0.401320	+	1.23514i	0.522608	+	0.852573i	$0.324959\pi$
$521$	−9.16031	+	28.1925i	−0.401320	+	1.23514i	−0.923929	+	0.382564i	$0.875041\pi$
$522$		0			0
$523$	44.1575	+	6.99386i	1.93087	+	0.305820i	0.998455	−	0.0555623i	$-0.0176951\pi$
$523$	44.1575	+	6.99386i	1.93087	+	0.305820i	0.932418	+	0.361382i	$0.117695\pi$
$524$		0			0
$525$	−21.9263	+	6.58383i	−0.956940	+	0.287342i
$526$		0			0
$527$	6.61145	−	41.7430i	0.287999	−	1.81836i
$528$		0			0
$529$	−7.16081	−	2.32669i	−0.311340	−	0.101160i
$530$		0			0
$531$	5.04979	−	1.64078i	0.219142	−	0.0712036i
$532$		0			0
$533$	−26.8061	−	13.6584i	−1.16110	−	0.591610i
$534$		0			0
$535$	−7.60659	−	24.3370i	−0.328862	−	1.05218i
$536$		0			0
$537$	−8.16737	−	51.5667i	−0.352448	−	2.22527i
$538$		0			0
$539$	−0.615660	+	0.447303i	−0.0265183	+	0.0192667i
$540$		0			0
$541$	−12.7673	−	9.27598i	−0.548909	−	0.398805i	0.278474	−	0.960444i	$-0.410171\pi$
$541$	−12.7673	−	9.27598i	−0.548909	−	0.398805i	−0.827383	+	0.561638i	$0.810171\pi$
$542$		0			0
$543$	−18.2204	−	18.2204i	−0.781910	−	0.781910i
$544$		0			0
$545$	5.28004	+	10.6568i	0.226172	+	0.456485i
$546$		0			0
$547$	2.89405	+	5.67989i	0.123741	+	0.242855i	0.944564	−	0.328328i	$-0.106485\pi$
$547$	2.89405	+	5.67989i	0.123741	+	0.242855i	−0.820823	+	0.571182i	$0.806485\pi$
$548$		0			0
$549$		−	20.9103i		−	0.892430i
$550$		0			0
$551$			16.3517i			0.696607i
$552$		0			0
$553$	13.3183	+	26.1387i	0.566353	+	1.11153i
$554$		0			0
$555$	−23.1609	+	3.40224i	−0.983123	+	0.144417i
$556$		0			0
$557$	0.968643	+	0.968643i	0.0410427	+	0.0410427i	0.727330	−	0.686288i	$-0.240761\pi$
$557$	0.968643	+	0.968643i	0.0410427	+	0.0410427i	−0.686288	+	0.727330i	$0.740761\pi$
$558$		0			0
$559$	27.8735	+	20.2513i	1.17892	+	0.856539i
$560$		0			0
$561$	2.27439	−	1.65244i	0.0960248	−	0.0697661i
$562$		0			0
$563$	5.27655	+	33.3148i	0.222380	+	1.40405i	0.805947	+	0.591987i	$0.201657\pi$
$563$	5.27655	+	33.3148i	0.222380	+	1.40405i	−0.583567	+	0.812065i	$0.698343\pi$
$564$		0			0
$565$	−8.22797	+	24.3880i	−0.346153	+	1.02601i
$566$		0			0
$567$	−20.8962	−	10.6471i	−0.877556	−	0.447137i
$568$		0			0
$569$	23.7786	−	7.72614i	0.996852	−	0.323897i	0.235245	−	0.971936i	$-0.424411\pi$
$569$	23.7786	−	7.72614i	0.996852	−	0.323897i	0.761607	+	0.648039i	$0.224411\pi$
$570$		0			0
$571$	−36.5563	−	11.8778i	−1.52983	−	0.497072i	−0.581282	−	0.813702i	$-0.697449\pi$
$571$	−36.5563	−	11.8778i	−1.52983	−	0.497072i	−0.948549	+	0.316629i	$0.897449\pi$
$572$		0			0
$573$	7.44354	−	46.9967i	0.310958	−	1.96331i
$574$		0			0
$575$	8.53269	+	17.7189i	0.355838	+	0.738930i
$576$		0			0
$577$	−8.10469	−	1.28366i	−0.337403	−	0.0534393i	−0.0145656	−	0.999894i	$-0.504637\pi$
$577$	−8.10469	−	1.28366i	−0.337403	−	0.0534393i	−0.322837	+	0.946455i	$0.604637\pi$
$578$		0			0
$579$	−9.87871	+	30.4035i	−0.410545	+	1.26353i
$580$		0			0
$581$	−10.6889	−	32.8970i	−0.443449	−	1.36480i
$582$		0			0
$583$	1.05926	−	2.07891i	0.0438701	−	0.0860999i
$584$		0			0
$585$	10.3139	+	14.5363i	0.426426	+	0.601000i
$586$		0			0
$587$	−32.7350	+	5.18471i	−1.35112	+	0.213996i	−0.789678	−	0.613522i	$-0.789752\pi$
$587$	−32.7350	+	5.18471i	−1.35112	+	0.213996i	−0.561440	+	0.827518i	$0.689752\pi$
$588$		0			0
$589$	15.9607	+	21.9681i	0.657650	+	0.905178i
$590$		0			0
$591$	−1.42561	+	1.96219i	−0.0586418	+	0.0807135i
$592$		0			0
$593$	−1.73763	+	1.73763i	−0.0713558	+	0.0713558i	−0.741884	−	0.670528i	$-0.766068\pi$
$593$	−1.73763	+	1.73763i	−0.0713558	+	0.0713558i	0.670528	+	0.741884i	$0.266068\pi$
$594$		0			0
$595$	−20.3468	−	3.45721i	−0.834139	−	0.141732i
$596$		0			0
$597$	51.5103	−	26.2458i	2.10818	−	1.07417i
$598$		0			0
$599$	−40.6040			−1.65903			−0.829516	−	0.558482i	$-0.811384\pi$
$599$	−40.6040			−1.65903			−0.829516	+	0.558482i	$0.811384\pi$
$600$		0			0
$601$	−5.30837			−0.216533			−0.108267	−	0.994122i	$-0.534530\pi$
$601$	−5.30837			−0.216533			−0.108267	+	0.994122i	$0.534530\pi$
$602$		0			0
$603$	14.6902	−	7.48502i	0.598231	−	0.304814i
$604$		0			0
$605$	−17.0622	−	17.4497i	−0.693678	−	0.709431i
$606$		0			0
$607$	−20.6837	+	20.6837i	−0.839524	+	0.839524i	−0.988796	−	0.149272i	$-0.952307\pi$
$607$	−20.6837	+	20.6837i	−0.839524	+	0.839524i	0.149272	+	0.988796i	$0.452307\pi$
$608$		0			0
$609$	−15.5668	+	21.4259i	−0.630798	+	0.868219i
$610$		0			0
$611$	−18.9626	−	26.0998i	−0.767145	−	1.05588i
$612$		0			0
$613$	42.2860	−	6.69744i	1.70791	−	0.270507i	0.775355	−	0.631526i	$-0.217571\pi$
$613$	42.2860	−	6.69744i	1.70791	−	0.270507i	0.932559	+	0.361019i	$0.117571\pi$
$614$		0			0
$615$	−19.3983	+	26.0786i	−0.782213	+	1.05159i
$616$		0			0
$617$	12.8425	−	25.2049i	0.517021	−	1.01471i	−0.473940	−	0.880557i	$-0.657169\pi$
$617$	12.8425	−	25.2049i	0.517021	−	1.01471i	0.990961	−	0.134153i	$-0.0428314\pi$
$618$		0			0
$619$	−9.51478	−	29.2835i	−0.382431	−	1.17700i	−0.938327	−	0.345750i	$-0.887625\pi$
$619$	−9.51478	−	29.2835i	−0.382431	−	1.17700i	0.555896	−	0.831252i	$-0.312375\pi$
$620$		0			0
$621$	−3.27822	+	10.0893i	−0.131550	+	0.404871i
$622$		0			0
$623$	−22.5004	−	3.56371i	−0.901458	−	0.142777i
$624$		0			0
$625$	−8.78500	+	23.4056i	−0.351400	+	0.936225i
$626$		0			0
$627$	−0.282559	+	1.78401i	−0.0112843	+	0.0712464i
$628$		0			0
$629$	−20.0708	−	6.52139i	−0.800274	−	0.260025i
$630$		0			0
$631$	21.3613	−	6.94071i	0.850381	−	0.276305i	0.148775	−	0.988871i	$-0.452467\pi$
$631$	21.3613	−	6.94071i	0.850381	−	0.276305i	0.701606	+	0.712566i	$0.252467\pi$
$632$		0			0
$633$	−3.80325	−	1.93785i	−0.151166	−	0.0770228i
$634$		0			0
$635$	5.08339	+	3.78121i	0.201728	+	0.150053i
$636$		0			0
$637$	−1.83734	−	11.6005i	−0.0727982	−	0.459630i
$638$		0			0
$639$	0.163463	−	0.118763i	0.00646649	−	0.00469818i
$640$		0			0
$641$	4.20050	+	3.05184i	0.165910	+	0.120541i	0.667642	−	0.744482i	$-0.267304\pi$
$641$	4.20050	+	3.05184i	0.165910	+	0.120541i	−0.501732	+	0.865023i	$0.667304\pi$
$642$		0			0
$643$	22.0996	+	22.0996i	0.871523	+	0.871523i	0.992638	−	0.121116i	$-0.0386472\pi$
$643$	22.0996	+	22.0996i	0.871523	+	0.871523i	−0.121116	+	0.992638i	$0.538647\pi$
$644$		0			0
$645$	26.6134	−	26.0224i	1.04790	−	1.02463i
$646$		0			0
$647$	−2.73785	−	5.37334i	−0.107636	−	0.211248i	0.830906	−	0.556413i	$-0.187823\pi$
$647$	−2.73785	−	5.37334i	−0.107636	−	0.211248i	−0.938542	+	0.345165i	$0.887823\pi$
$648$		0			0
$649$			0.880922i			0.0345792i
$650$		0			0
$651$			43.9796i			1.72369i
$652$		0			0
$653$	2.91386	+	5.71878i	0.114028	+	0.223793i	0.940966	−	0.338500i	$-0.109919\pi$
$653$	2.91386	+	5.71878i	0.114028	+	0.223793i	−0.826938	+	0.562293i	$0.809919\pi$
$654$		0			0
$655$	0.115006	−	0.676852i	0.00449367	−	0.0264468i
$656$		0			0
$657$	7.01124	+	7.01124i	0.273534	+	0.273534i
$658$		0			0
$659$	−3.26603	−	2.37291i	−0.127227	−	0.0924355i	0.522352	−	0.852730i	$-0.325055\pi$
$659$	−3.26603	−	2.37291i	−0.127227	−	0.0924355i	−0.649579	+	0.760294i	$0.725055\pi$
$660$		0			0
$661$	−14.8924	+	10.8199i	−0.579246	+	0.420847i	−0.838452	−	0.544975i	$-0.816539\pi$
$661$	−14.8924	+	10.8199i	−0.579246	+	0.420847i	0.259206	+	0.965822i	$0.416539\pi$
$662$		0			0
$663$	6.78757	+	42.8551i	0.263608	+	1.66435i
$664$		0			0
$665$	10.8145	−	7.67317i	0.419368	−	0.297553i
$666$		0			0
$667$	20.2710	+	10.3286i	0.784897	+	0.399925i
$668$		0			0
$669$	10.3752	−	3.37111i	0.401129	−	0.130335i
$670$		0			0
$671$	3.29942	+	1.07205i	0.127373	+	0.0413858i
$672$		0			0
$673$	2.13206	−	13.4613i	0.0821849	−	0.518895i	−0.911911	−	0.410389i	$-0.865393\pi$
$673$	2.13206	−	13.4613i	0.0821849	−	0.518895i	0.994096	−	0.108507i	$-0.0346069\pi$
$674$		0			0
$675$	−12.1502	+	5.85103i	−0.467662	+	0.225206i
$676$		0			0
$677$	−11.7197	−	1.85622i	−0.450425	−	0.0713403i	−0.0728991	−	0.997339i	$-0.523225\pi$
$677$	−11.7197	−	1.85622i	−0.450425	−	0.0713403i	−0.377526	+	0.925999i	$0.623225\pi$
$678$		0			0
$679$	1.46937	−	4.52225i	0.0563892	−	0.173548i
$680$		0			0
$681$	−5.73349	−	17.6459i	−0.219708	−	0.676191i
$682$		0			0
$683$	0.0518097	−	0.101682i	0.00198244	−	0.00389076i	−0.890013	−	0.455935i	$-0.849305\pi$
$683$	0.0518097	−	0.101682i	0.00198244	−	0.00389076i	0.891996	+	0.452044i	$0.149305\pi$
$684$		0			0
$685$	−36.6078	−	12.3507i	−1.39871	−	0.471894i
$686$		0			0
$687$	41.6177	−	6.59160i	1.58782	−	0.251485i
$688$		0			0
$689$	21.1665	+	29.1332i	0.806380	+	1.10989i
$690$		0			0
$691$	0.903247	−	1.24321i	0.0343611	−	0.0472940i	−0.791491	−	0.611181i	$-0.790695\pi$
$691$	0.903247	−	1.24321i	0.0343611	−	0.0472940i	0.825852	+	0.563887i	$0.190695\pi$
$692$		0			0
$693$	−0.766052	+	0.766052i	−0.0290999	+	0.0290999i
$694$		0			0
$695$	−0.620397	−	4.22337i	−0.0235330	−	0.160202i
$696$		0			0
$697$	−26.1072	+	13.3023i	−0.988879	+	0.503859i
$698$		0			0
$699$	25.3260			0.957917
$700$		0			0
$701$	45.4053			1.71494			0.857468	−	0.514537i	$-0.172036\pi$
$701$	45.4053			1.71494			0.857468	+	0.514537i	$0.172036\pi$
$702$		0			0
$703$	12.0811	−	6.15565i	0.455649	−	0.232165i
$704$		0			0
$705$	−31.2298	+	15.4732i	−1.17618	+	0.582756i
$706$		0			0
$707$	25.3486	−	25.3486i	0.953331	−	0.953331i
$708$		0			0
$709$	13.0550	−	17.9687i	0.490292	−	0.674829i	−0.490150	−	0.871638i	$-0.663058\pi$
$709$	13.0550	−	17.9687i	0.490292	−	0.674829i	0.980442	+	0.196809i	$0.0630578\pi$
$710$		0			0
$711$	−14.5032	−	19.9620i	−0.543914	−	0.748633i
$712$		0			0
$713$	37.3152	−	5.91014i	1.39746	−	0.221337i
$714$		0			0
$715$	−2.82244	+	0.882161i	−0.105553	+	0.0329909i
$716$		0			0
$717$	−10.8034	+	21.2029i	−0.403461	+	0.791837i
$718$		0			0
$719$	2.52166	+	7.76087i	0.0940420	+	0.289431i	0.987003	−	0.160703i	$-0.0513761\pi$
$719$	2.52166	+	7.76087i	0.0940420	+	0.289431i	−0.892961	+	0.450134i	$0.851376\pi$
$720$		0			0
$721$	−9.27582	+	28.5480i	−0.345449	+	1.06318i
$722$		0			0
$723$	−35.3166	−	5.59360i	−1.31344	−	0.208028i
$724$		0			0
$725$	8.31723	+	27.6990i	0.308894	+	1.02872i
$726$		0			0
$727$	−5.27500	+	33.3051i	−0.195639	+	1.23522i	0.672952	+	0.739686i	$0.265026\pi$
$727$	−5.27500	+	33.3051i	−0.195639	+	1.23522i	−0.868591	+	0.495530i	$0.834974\pi$
$728$		0			0
$729$	1.96316	+	0.637869i	0.0727096	+	0.0236248i
$730$		0			0
$731$	31.9129	−	10.3691i	1.18034	−	0.383517i
$732$		0			0
$733$	−10.3199	−	5.25827i	−0.381176	−	0.194219i	0.252895	−	0.967494i	$-0.418617\pi$
$733$	−10.3199	−	5.25827i	−0.381176	−	0.194219i	−0.634071	+	0.773275i	$0.718617\pi$
$734$		0			0
$735$	−12.6879	−	0.142450i	−0.468000	−	0.00525434i
$736$		0			0
$737$	0.427907	+	2.70170i	0.0157622	+	0.0995183i
$738$		0			0
$739$	1.57032	−	1.14091i	0.0577653	−	0.0419690i	−0.558528	−	0.829486i	$-0.688634\pi$
$739$	1.57032	−	1.14091i	0.0577653	−	0.0419690i	0.616293	+	0.787517i	$0.288634\pi$
$740$		0			0
$741$	−22.5533	−	16.3859i	−0.828515	−	0.601951i
$742$		0			0
$743$	−15.8962	−	15.8962i	−0.583175	−	0.583175i	0.352599	−	0.935774i	$-0.385298\pi$
$743$	−15.8962	−	15.8962i	−0.583175	−	0.583175i	−0.935774	+	0.352599i	$0.885298\pi$
$744$		0			0
$745$	17.9397	+	9.39592i	0.657262	+	0.344240i
$746$		0			0
$747$	13.2081	+	25.9223i	0.483258	+	0.948447i
$748$		0			0
$749$			23.9200i			0.874017i
$750$		0			0
$751$			2.49377i			0.0909990i	0.998964	+	0.0454995i	$0.0144879\pi$
$751$			2.49377i			0.0909990i	−0.998964	+	0.0454995i	$0.985512\pi$
$752$		0			0
$753$	−10.1389	−	19.8987i	−0.369482	−	0.725149i
$754$		0			0
$755$	−34.3995	−	18.0167i	−1.25193	−	0.655696i
$756$		0			0
$757$	−22.1040	−	22.1040i	−0.803383	−	0.803383i	0.180240	−	0.983623i	$-0.442313\pi$
$757$	−22.1040	−	22.1040i	−0.803383	−	0.803383i	−0.983623	+	0.180240i	$0.942313\pi$
$758$		0			0
$759$	2.03313	+	1.47716i	0.0737981	+	0.0536174i
$760$		0			0
$761$	−24.5983	+	17.8717i	−0.891686	+	0.647848i	−0.936317	−	0.351156i	$-0.885789\pi$
$761$	−24.5983	+	17.8717i	−0.891686	+	0.647848i	0.0446310	+	0.999004i	$0.485789\pi$
$762$		0			0
$763$	−1.74534	−	11.0197i	−0.0631856	−	0.398938i
$764$		0			0
$765$	17.3577	+	0.194879i	0.627570	+	0.00704587i
$766$		0			0
$767$	−12.1142	−	6.17247i	−0.437417	−	0.222875i
$768$		0			0
$769$	30.9524	−	10.0570i	1.11617	−	0.362666i	0.307866	−	0.951430i	$-0.400385\pi$
$769$	30.9524	−	10.0570i	1.11617	−	0.362666i	0.808305	+	0.588763i	$0.200385\pi$
$770$		0			0
$771$	15.1779	+	4.93159i	0.546617	+	0.177607i
$772$		0			0
$773$	1.91095	−	12.0653i	0.0687322	−	0.433958i	−0.929194	−	0.369592i	$-0.879498\pi$
$773$	1.91095	−	12.0653i	0.0687322	−	0.433958i	0.997926	−	0.0643659i	$-0.0205025\pi$
$774$		0			0
$775$	38.2106	+	29.0945i	1.37257	+	1.04510i
$776$		0			0
$777$	21.6902	+	3.43540i	0.778133	+	0.123244i
$778$		0			0
$779$	5.81743	−	17.9042i	0.208431	−	0.641484i
$780$		0			0
$781$	0.0103589	+	0.0318815i	0.000370671	+	0.00114081i
$782$		0			0
$783$	−7.08252	+	13.9002i	−0.253109	+	0.496754i
$784$		0			0
$785$	−12.8424	+	4.01394i	−0.458367	+	0.143264i
$786$		0			0
$787$	5.58552	−	0.884660i	0.199102	−	0.0315347i	−0.0560867	−	0.998426i	$-0.517862\pi$
$787$	5.58552	−	0.884660i	0.199102	−	0.0315347i	0.255189	+	0.966891i	$0.417862\pi$
$788$		0			0
$789$	−10.6594	−	14.6715i	−0.379486	−	0.522318i
$790$		0			0
$791$	14.1925	−	19.5342i	0.504625	−	0.694557i
$792$		0			0
$793$	−37.8609	+	37.8609i	−1.34448	+	1.34448i
$794$		0			0
$795$	34.8595	−	17.2716i	1.23634	−	0.612561i
$796$		0			0
$797$	−0.236379	+	0.120441i	−0.00837296	+	0.00426624i	−0.458172	−	0.888864i	$-0.651496\pi$
$797$	−0.236379	+	0.120441i	−0.00837296	+	0.00426624i	0.449799	+	0.893130i	$0.351496\pi$
$798$		0			0
$799$	−31.4200			−1.11156
$800$		0			0
$801$	19.1608			0.677012
$802$		0			0
$803$	−1.46575	+	0.746839i	−0.0517253	+	0.0263554i
$804$		0			0
$805$	−2.68135	−	18.2534i	−0.0945050	−	0.643346i
$806$		0			0
$807$	19.4422	−	19.4422i	0.684399	−	0.684399i
$808$		0			0
$809$	9.88518	−	13.6058i	0.347544	−	0.478354i	−0.599082	−	0.800688i	$-0.704468\pi$
$809$	9.88518	−	13.6058i	0.347544	−	0.478354i	0.946626	+	0.322334i	$0.104468\pi$
$810$		0			0
$811$	−29.7282	−	40.9173i	−1.04390	−	1.43680i	−0.893983	−	0.448101i	$-0.852100\pi$
$811$	−29.7282	−	40.9173i	−1.04390	−	1.43680i	−0.149914	−	0.988699i	$-0.547900\pi$
$812$		0			0
$813$	−25.7945	+	4.08544i	−0.904651	+	0.143283i
$814$		0			0
$815$	11.4083	+	3.84890i	0.399614	+	0.134821i
$816$		0			0
$817$	−9.78762	+	19.2093i	−0.342425	+	0.672048i
$818$		0			0
$819$	−5.16690	−	15.9021i	−0.180546	−	0.555664i
$820$		0			0
$821$	9.76922	−	30.0666i	0.340948	−	1.04933i	−0.622769	−	0.782406i	$-0.713992\pi$
$821$	9.76922	−	30.0666i	0.340948	−	1.04933i	0.963717	−	0.266925i	$-0.0860076\pi$
$822$		0			0
$823$	12.8168	+	2.02998i	0.446766	+	0.0707608i	0.375764	−	0.926715i	$-0.377380\pi$
$823$	12.8168	+	2.02998i	0.446766	+	0.0707608i	0.0710020	+	0.997476i	$0.477380\pi$
$824$		0			0
$825$	0.428786	+	3.16575i	0.0149284	+	0.110217i
$826$		0			0
$827$	5.63640	−	35.5868i	0.195997	−	1.23748i	−0.671866	−	0.740672i	$-0.734507\pi$
$827$	5.63640	−	35.5868i	0.195997	−	1.23748i	0.867863	−	0.496803i	$-0.165493\pi$
$828$		0			0
$829$	−7.79556	−	2.53293i	−0.270751	−	0.0879723i	0.170495	−	0.985359i	$-0.445463\pi$
$829$	−7.79556	−	2.53293i	−0.270751	−	0.0879723i	−0.441246	+	0.897386i	$0.645463\pi$
$830$		0			0
$831$	−6.76803	+	2.19907i	−0.234780	+	0.0762848i
$832$		0			0
$833$	−10.1921	−	5.19315i	−0.353137	−	0.179932i
$834$		0			0
$835$	14.4968	−	10.2859i	0.501683	−	0.355958i
$836$		0			0
$837$	4.05270	+	25.5877i	0.140082	+	0.884441i
$838$		0			0
$839$	40.4235	−	29.3694i	1.39557	−	1.01394i	0.400346	−	0.916364i	$-0.368890\pi$
$839$	40.4235	−	29.3694i	1.39557	−	1.01394i	0.995228	−	0.0975791i	$-0.0311099\pi$
$840$		0			0
$841$	3.60538	+	2.61946i	0.124323	+	0.0903263i
$842$		0			0
$843$	−18.7761	−	18.7761i	−0.646683	−	0.646683i
$844$		0			0
$845$	2.77577	−	16.3363i	0.0954894	−	0.561987i
$846$		0			0
$847$	10.3940	+	20.3993i	0.357142	+	0.700930i
$848$		0			0
$849$			42.4250i			1.45602i
$850$		0			0
$851$		−	18.8651i		−	0.646687i
$852$		0			0
$853$	18.2668	+	35.8506i	0.625444	+	1.22750i	0.958634	+	0.284643i	$0.0918750\pi$
$853$	18.2668	+	35.8506i	0.625444	+	1.22750i	−0.333190	+	0.942860i	$0.608125\pi$
$854$		0			0
$855$	−7.97437	+	7.79730i	−0.272718	+	0.266662i
$856$		0			0
$857$	37.2459	+	37.2459i	1.27230	+	1.27230i	0.944881	+	0.327415i	$0.106178\pi$
$857$	37.2459	+	37.2459i	1.27230	+	1.27230i	0.327415	+	0.944881i	$0.393822\pi$
$858$		0			0
$859$	−7.06031	−	5.12962i	−0.240895	−	0.175020i	0.460787	−	0.887511i	$-0.347567\pi$
$859$	−7.06031	−	5.12962i	−0.240895	−	0.175020i	−0.701682	+	0.712490i	$0.747567\pi$
$860$		0			0
$861$	24.6674	−	17.9219i	0.840662	−	0.610777i
$862$		0			0
$863$	−1.24266	−	7.84587i	−0.0423007	−	0.267076i	0.957469	−	0.288536i	$-0.0931686\pi$
$863$	−1.24266	−	7.84587i	−0.0423007	−	0.267076i	−0.999770	+	0.0214599i	$0.993169\pi$
$864$		0			0
$865$	−22.1366	−	16.4660i	−0.752667	−	0.559862i
$866$		0			0
$867$	4.58995	+	2.33870i	0.155883	+	0.0794262i
$868$		0			0
$869$	3.89335	−	1.26502i	0.132073	−	0.0429130i
$870$		0			0
$871$	−40.1512	−	13.0459i	−1.36047	−	0.442044i
$872$		0			0
$873$	−0.625639	+	3.95013i	−0.0211747	+	0.133692i
$874$		0			0
$875$	14.4163	−	18.4987i	0.487359	−	0.625371i
$876$		0			0
$877$	−45.4568	−	7.19964i	−1.53497	−	0.243115i	−0.669017	−	0.743247i	$-0.733285\pi$
$877$	−45.4568	−	7.19964i	−1.53497	−	0.243115i	−0.865949	+	0.500133i	$0.833285\pi$
$878$		0			0
$879$	2.02809	−	6.24183i	0.0684059	−	0.210532i
$880$		0			0
$881$	−2.60328	−	8.01207i	−0.0877067	−	0.269934i	0.897578	−	0.440856i	$-0.145325\pi$
$881$	−2.60328	−	8.01207i	−0.0877067	−	0.269934i	−0.985284	+	0.170923i	$0.945325\pi$
$882$		0			0
$883$	−0.162109	+	0.318157i	−0.00545541	+	0.0107068i	−0.893718	−	0.448629i	$-0.851913\pi$
$883$	−0.162109	+	0.318157i	−0.00545541	+	0.0107068i	0.888263	+	0.459336i	$0.151913\pi$
$884$		0			0
$885$	−8.76642	+	11.7854i	−0.294680	+	0.396162i
$886$		0			0
$887$	16.8861	−	2.67450i	0.566980	−	0.0898008i	0.133638	−	0.991030i	$-0.457334\pi$
$887$	16.8861	−	2.67450i	0.566980	−	0.0898008i	0.433342	+	0.901229i	$0.357334\pi$
$888$		0			0
$889$	−3.49344	−	4.80830i	−0.117166	−	0.161265i
$890$		0			0
$891$	−1.92361	+	2.64763i	−0.0644435	+	0.0886988i
$892$		0			0
$893$	14.2745	−	14.2745i	0.477677	−	0.477677i
$894$		0			0
$895$	37.3928	+	38.2419i	1.24990	+	1.27829i
$896$		0			0
$897$	−34.5592	+	17.6088i	−1.15390	+	0.587941i
$898$		0			0
$899$	55.5586			1.85298
$900$		0			0
$901$	35.0717			1.16841
$902$		0			0
$903$	−31.1120	+	15.8524i	−1.03534	+	0.527534i
$904$		0			0
$905$	26.0241	+	4.42185i	0.865069	+	0.146987i
$906$		0			0
$907$	−10.5183	+	10.5183i	−0.349256	+	0.349256i	−0.859832	−	0.510576i	$-0.829432\pi$
$907$	−10.5183	+	10.5183i	−0.349256	+	0.349256i	0.510576	+	0.859832i	$0.329432\pi$
$908$		0			0
$909$	−17.7227	+	24.3932i	−0.587825	+	0.809072i
$910$		0			0
$911$	14.6644	+	20.1838i	0.485854	+	0.668721i	0.979617	−	0.200876i	$-0.0643788\pi$
$911$	14.6644	+	20.1838i	0.485854	+	0.668721i	−0.493763	+	0.869597i	$0.664379\pi$
$912$		0			0
$913$	−4.76741	+	0.755084i	−0.157778	+	0.0249896i
$914$		0			0
$915$	33.4728	+	47.1762i	1.10658	+	1.55960i
$916$		0			0
$917$	−0.292398	+	0.573864i	−0.00965584	+	0.0189507i
$918$		0			0
$919$	−3.20824	−	9.87395i	−0.105830	−	0.325712i	0.884094	−	0.467309i	$-0.154776\pi$
$919$	−3.20824	−	9.87395i	−0.105830	−	0.325712i	−0.989924	+	0.141597i	$0.954776\pi$
$920$		0			0
$921$	−0.937988	+	2.88683i	−0.0309077	+	0.0951243i
$922$		0			0
$923$	−0.511007	−	0.0809356i	−0.0168200	−	0.00266403i
$924$		0			0
$925$	17.3338	−	16.5724i	0.569933	−	0.544897i
$926$		0			0
$927$	3.94953	−	24.9363i	0.129719	−	0.819017i
$928$		0			0
$929$	−12.6925	−	4.12404i	−0.416427	−	0.135305i	0.0933071	−	0.995637i	$-0.470256\pi$
$929$	−12.6925	−	4.12404i	−0.416427	−	0.135305i	−0.509734	+	0.860332i	$0.670256\pi$
$930$		0			0
$931$	6.98973	−	2.27110i	0.229079	−	0.0744323i
$932$		0			0
$933$	−43.7094	−	22.2710i	−1.43098	−	0.729121i
$934$		0			0
$935$	−0.920659	+	2.72887i	−0.0301088	+	0.0892435i
$936$		0			0
$937$	6.75071	+	42.6223i	0.220536	+	1.39241i	0.810859	+	0.585242i	$0.199001\pi$
$937$	6.75071	+	42.6223i	0.220536	+	1.39241i	−0.590323	+	0.807167i	$0.700999\pi$
$938$		0			0
$939$	46.0983	−	33.4924i	1.50436	−	1.09298i
$940$		0			0
$941$	8.35073	+	6.06716i	0.272226	+	0.197784i	0.715519	−	0.698593i	$-0.246190\pi$
$941$	8.35073	+	6.06716i	0.272226	+	0.197784i	−0.443294	+	0.896377i	$0.646190\pi$
$942$		0			0
$943$	−18.5210	−	18.5210i	−0.603127	−	0.603127i
$944$		0			0
$945$	12.5167	−	1.83865i	0.407168	−	0.0598113i
$946$		0			0
$947$	−6.04256	−	11.8592i	−0.196357	−	0.385372i	0.771744	−	0.635934i	$-0.219385\pi$
$947$	−6.04256	−	11.8592i	−0.196357	−	0.385372i	−0.968101	+	0.250561i	$0.919385\pi$
$948$		0			0
$949$		−	25.3896i		−	0.824180i
$950$		0			0
$951$			5.88534i			0.190845i
$952$		0			0
$953$	18.1121	+	35.5469i	0.586708	+	1.15148i	0.973366	+	0.229255i	$0.0736291\pi$
$953$	18.1121	+	35.5469i	0.586708	+	1.15148i	−0.386659	+	0.922223i	$0.626371\pi$
$954$		0			0
$955$	21.6408	+	43.6779i	0.700280	+	1.41338i
$956$		0			0
$957$	2.61324	+	2.61324i	0.0844740	+	0.0844740i
$958$		0			0
$959$	29.3220	+	21.3037i	0.946856	+	0.687931i
$960$		0			0
$961$	49.5617	−	36.0087i	1.59877	−	1.16157i
$962$		0			0
$963$	−3.14729	−	19.8712i	−0.101420	−	0.640340i
$964$		0			0
$965$	−9.76977	−	31.2580i	−0.314500	−	1.00623i
$966$		0			0
$967$	16.4629	+	8.38824i	0.529410	+	0.269748i	0.698198	−	0.715905i	$-0.253985\pi$
$967$	16.4629	+	8.38824i	0.529410	+	0.269748i	−0.168788	+	0.985652i	$0.553985\pi$
$968$		0			0
$969$	−25.8217	+	8.38997i	−0.829512	+	0.269525i
$970$		0			0
$971$	−33.9656	−	11.0361i	−1.09001	−	0.354165i	−0.291759	−	0.956492i	$-0.594241\pi$
$971$	−33.9656	−	11.0361i	−1.09001	−	0.354165i	−0.798250	+	0.602327i	$0.794241\pi$
$972$		0			0
$973$	−0.626443	+	3.95521i	−0.0200828	+	0.126798i
$974$		0			0
$975$	−46.5388	−	16.2853i	−1.49043	−	0.521548i
$976$		0			0
$977$	46.9231	+	7.43188i	1.50120	+	0.237767i	0.852279	−	0.523087i	$-0.175220\pi$
$977$	46.9231	+	7.43188i	1.50120	+	0.237767i	0.648923	+	0.760854i	$0.275220\pi$
$978$		0			0
$979$	−0.982348	+	3.02336i	−0.0313960	+	0.0966269i
$980$		0			0
$981$	2.89984	+	8.92478i	0.0925846	+	0.284946i
$982$		0			0
$983$	1.59570	−	3.13173i	0.0508948	−	0.0998867i	−0.864158	−	0.503220i	$-0.832149\pi$
$983$	1.59570	−	3.13173i	0.0508948	−	0.0998867i	0.915053	+	0.403333i	$0.132149\pi$
$984$		0			0
$985$	0.0278940	−	2.48450i	0.000888777	−	0.0791627i
$986$		0			0
$987$	32.2933	−	5.11475i	1.02791	−	0.162804i
$988$		0			0
$989$	17.6311	+	24.2672i	0.560638	+	0.771652i
$990$		0			0
$991$	−2.04735	+	2.81794i	−0.0650363	+	0.0895148i	−0.840296	−	0.542128i	$-0.817619\pi$
$991$	−2.04735	+	2.81794i	−0.0650363	+	0.0895148i	0.775260	+	0.631642i	$0.217619\pi$
$992$		0			0
$993$	22.4912	−	22.4912i	0.713737	−	0.713737i
$994$		0			0
$995$	−27.4778	+	52.4637i	−0.871105	+	1.66321i
$996$		0			0
$997$	42.3137	−	21.5599i	1.34009	−	0.682808i	0.370793	−	0.928715i	$-0.379086\pi$
$997$	42.3137	−	21.5599i	1.34009	−	0.682808i	0.969293	+	0.245907i	$0.0790858\pi$
$998$		0			0
$999$	12.9362			0.409282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.127.2	yes	80
4.3	odd	2	inner	400.2.bi.d.127.9	yes	80
25.13	odd	20	inner	400.2.bi.d.63.9	yes	80
100.63	even	20	inner	400.2.bi.d.63.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.63.2	✓	80	100.63	even	20	inner
400.2.bi.d.63.9	yes	80	25.13	odd	20	inner
400.2.bi.d.127.2	yes	80	1.1	even	1	trivial
400.2.bi.d.127.9	yes	80	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94483 + 0.990942i) q^{3} +(1.03746 - 1.98083i) q^{5} +(-1.48328 + 1.48328i) q^{7} +(1.03705 - 1.42738i) q^{9} +O(q^{10})\)	\(q+(-1.94483 + 0.990942i) q^{3} +(1.03746 - 1.98083i) q^{5} +(-1.48328 + 1.48328i) q^{7} +(1.03705 - 1.42738i) q^{9} +(0.172056 + 0.236815i) q^{11} +(-4.46218 + 0.706740i) q^{13} +(-0.0547938 + 4.88044i) q^{15} +(-1.99756 + 3.92044i) q^{17} +(-0.873586 - 2.68862i) q^{19} +(1.41489 - 4.35458i) q^{21} +(-3.88485 - 0.615300i) q^{23} +(-2.84737 - 4.11005i) q^{25} +(0.421923 - 2.66392i) q^{27} +(-5.50106 - 1.78740i) q^{29} +(-9.13518 + 2.96820i) q^{31} +(-0.569291 - 0.290068i) q^{33} +(1.39929 + 4.47697i) q^{35} +(0.750303 + 4.73723i) q^{37} +(7.97786 - 5.79625i) q^{39} +(5.38745 + 3.91421i) q^{41} +(-5.39252 - 5.39252i) q^{43} +(-1.75150 - 3.53507i) q^{45} +(3.24189 + 6.36258i) q^{47} +2.59975i q^{49} -9.60406i q^{51} +(-3.61868 - 7.10206i) q^{53} +(0.647592 - 0.0951287i) q^{55} +(4.36324 + 4.36324i) q^{57} +(2.43468 + 1.76890i) q^{59} +(9.58818 - 6.96622i) q^{61} +(0.578966 + 3.65545i) q^{63} +(-3.22939 + 9.57203i) q^{65} +(8.32617 + 4.24240i) q^{67} +(8.16512 - 2.65301i) q^{69} +(0.108915 + 0.0353885i) q^{71} +(-0.879144 + 5.55070i) q^{73} +(9.61047 + 5.17178i) q^{75} +(-0.606473 - 0.0960558i) q^{77} +(4.32162 - 13.3006i) q^{79} +(3.45485 + 10.6329i) q^{81} +(-7.48613 + 14.6924i) q^{83} +(5.69333 + 8.02411i) q^{85} +(12.4699 - 1.97503i) q^{87} +(6.38336 + 8.78594i) q^{89} +(5.57038 - 7.66697i) q^{91} +(14.8251 - 14.8251i) q^{93} +(-6.23201 - 1.05890i) q^{95} +(-2.01972 + 1.02910i) q^{97} +0.516457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 80 * q + 4 * q^5	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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