LMFDB - Embedded newform 920.2.bv.a.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			433.2
Character	$\chi$	$=$	920.433
Dual form			920.2.bv.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.83699 - 1.54911i) q^{3} +(0.823524 + 2.07890i) q^{5} +(-2.50378 + 3.34466i) q^{7} +(4.02684 + 6.26588i) q^{9} +(-2.09151 - 0.955162i) q^{11} +(-3.94512 + 2.95328i) q^{13} +(0.884116 - 7.17354i) q^{15} +(0.306224 - 4.28157i) q^{17} +(3.62640 - 4.18509i) q^{19} +(12.2844 - 5.61012i) q^{21} +(3.71368 + 3.03456i) q^{23} +(-3.64362 + 3.42404i) q^{25} +(-1.02575 - 14.3418i) q^{27} +(4.00107 - 3.46695i) q^{29} +(-7.20387 - 2.11525i) q^{31} +(4.45395 + 5.94977i) q^{33} +(-9.01512 - 2.45069i) q^{35} +(-5.96155 - 1.29686i) q^{37} +(15.7673 - 2.26699i) q^{39} +(2.67857 + 1.72141i) q^{41} +(-0.506766 + 0.928072i) q^{43} +(-9.70992 + 13.5315i) q^{45} +(1.89883 - 1.89883i) q^{47} +(-2.94569 - 10.0321i) q^{49} +(-7.50139 + 11.6724i) q^{51} +(-3.73011 - 2.79232i) q^{53} +(0.263270 - 5.13463i) q^{55} +(-16.7712 + 6.25535i) q^{57} +(-8.23557 - 1.18410i) q^{59} +(3.86637 - 13.1677i) q^{61} +(-31.0395 - 2.21999i) q^{63} +(-9.38847 - 5.76940i) q^{65} +(0.861972 - 2.31104i) q^{67} +(-5.83481 - 14.3619i) q^{69} +(0.667794 + 1.46227i) q^{71} +(7.05309 - 0.504447i) q^{73} +(15.6411 - 4.06960i) q^{75} +(8.43137 - 4.60388i) q^{77} +(-1.31624 + 9.15465i) q^{79} +(-10.0247 + 21.9511i) q^{81} +(0.975600 - 4.48476i) q^{83} +(9.15312 - 2.88937i) q^{85} +(-16.7217 + 3.63758i) q^{87} +(-5.18455 + 1.52232i) q^{89} -20.5895i q^{91} +(17.1606 + 17.1606i) q^{93} +(11.6868 + 4.09239i) q^{95} +(-2.50196 - 11.5013i) q^{97} +(-2.43725 - 16.9514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.83699	−	1.54911i	−1.63794	−	0.894381i	−0.991306	−	0.131579i	$-0.957995\pi$
$3$	−2.83699	−	1.54911i	−1.63794	−	0.894381i	−0.646631	−	0.762803i	$-0.723823\pi$
$4$		0			0
$5$	0.823524	+	2.07890i	0.368291	+	0.929710i
$5$	0.823524	+	2.07890i	0.368291	+	0.929710i
$6$		0			0
$7$	−2.50378	+	3.34466i	−0.946339	+	1.26416i	0.0180943	+	0.999836i	$0.494240\pi$
$7$	−2.50378	+	3.34466i	−0.946339	+	1.26416i	−0.964434	+	0.264325i	$0.914851\pi$
$8$		0			0
$9$	4.02684	+	6.26588i	1.34228	+	2.08863i
$10$		0			0
$11$	−2.09151	−	0.955162i	−0.630615	−	0.287992i	0.0743525	−	0.997232i	$-0.476311\pi$
$11$	−2.09151	−	0.955162i	−0.630615	−	0.287992i	−0.704967	+	0.709240i	$0.749038\pi$
$12$		0			0
$13$	−3.94512	+	2.95328i	−1.09418	+	0.819093i	−0.984589	−	0.174883i	$-0.944045\pi$
$13$	−3.94512	+	2.95328i	−1.09418	+	0.819093i	−0.109591	+	0.993977i	$0.534954\pi$
$14$		0			0
$15$	0.884116	−	7.17354i	0.228278	−	1.85220i
$16$		0			0
$17$	0.306224	−	4.28157i	0.0742702	−	1.03843i	−0.814525	−	0.580128i	$-0.803002\pi$
$17$	0.306224	−	4.28157i	0.0742702	−	1.03843i	0.888795	−	0.458305i	$-0.151543\pi$
$18$		0			0
$19$	3.62640	−	4.18509i	0.831953	−	0.960125i	−0.167716	−	0.985835i	$-0.553639\pi$
$19$	3.62640	−	4.18509i	0.831953	−	0.960125i	0.999669	+	0.0257099i	$0.00818461\pi$
$20$		0			0
$21$	12.2844	−	5.61012i	2.68069	−	1.22423i
$22$		0			0
$23$	3.71368	+	3.03456i	0.774357	+	0.632749i
$23$	3.71368	+	3.03456i	0.774357	+	0.632749i
$24$		0			0
$25$	−3.64362	+	3.42404i	−0.728723	+	0.684809i
$26$		0			0
$27$	−1.02575	−	14.3418i	−0.197406	−	2.76009i
$28$		0			0
$29$	4.00107	−	3.46695i	0.742980	−	0.643796i	−0.198795	−	0.980041i	$-0.563703\pi$
$29$	4.00107	−	3.46695i	0.742980	−	0.643796i	0.941774	+	0.336246i	$0.109157\pi$
$30$		0			0
$31$	−7.20387	−	2.11525i	−1.29385	−	0.379910i	−0.438864	−	0.898554i	$-0.644619\pi$
$31$	−7.20387	−	2.11525i	−1.29385	−	0.379910i	−0.854990	+	0.518644i	$0.826437\pi$
$32$		0			0
$33$	4.45395	+	5.94977i	0.775332	+	1.03572i
$34$		0			0
$35$	−9.01512	−	2.45069i	−1.52383	−	0.414242i
$36$		0			0
$37$	−5.96155	−	1.29686i	−0.980073	−	0.213202i	−0.306133	−	0.951989i	$-0.599035\pi$
$37$	−5.96155	−	1.29686i	−0.980073	−	0.213202i	−0.673939	+	0.738787i	$0.735399\pi$
$38$		0			0
$39$	15.7673	−	2.26699i	2.52478	−	0.363009i
$40$		0			0
$41$	2.67857	+	1.72141i	0.418322	+	0.268839i	0.732825	−	0.680417i	$-0.238201\pi$
$41$	2.67857	+	1.72141i	0.418322	+	0.268839i	−0.314503	+	0.949256i	$0.601838\pi$
$42$		0			0
$43$	−0.506766	+	0.928072i	−0.0772811	+	0.141530i	−0.913462	−	0.406924i	$-0.866601\pi$
$43$	−0.506766	+	0.928072i	−0.0772811	+	0.141530i	0.836181	+	0.548454i	$0.184783\pi$
$44$		0			0
$45$	−9.70992	+	13.5315i	−1.44747	+	2.01715i
$46$		0			0
$47$	1.89883	−	1.89883i	0.276973	−	0.276973i	−0.554926	−	0.831899i	$-0.687254\pi$
$47$	1.89883	−	1.89883i	0.276973	−	0.276973i	0.831899	+	0.554926i	$0.187254\pi$
$48$		0			0
$49$	−2.94569	−	10.0321i	−0.420813	−	1.43316i
$50$		0			0
$51$	−7.50139	+	11.6724i	−1.05041	+	1.63446i
$52$		0			0
$53$	−3.73011	−	2.79232i	−0.512369	−	0.383555i	0.311579	−	0.950220i	$-0.399142\pi$
$53$	−3.73011	−	2.79232i	−0.512369	−	0.383555i	−0.823948	+	0.566665i	$0.808233\pi$
$54$		0			0
$55$	0.263270	−	5.13463i	0.0354993	−	0.692354i
$56$		0			0
$57$	−16.7712	+	6.25535i	−2.22141	+	0.828542i
$58$		0			0
$59$	−8.23557	−	1.18410i	−1.07218	−	0.154156i	−0.416455	−	0.909156i	$-0.636728\pi$
$59$	−8.23557	−	1.18410i	−1.07218	−	0.154156i	−0.655725	+	0.755000i	$0.727637\pi$
$60$		0			0
$61$	3.86637	−	13.1677i	0.495038	−	1.68595i	−0.210764	−	0.977537i	$-0.567595\pi$
$61$	3.86637	−	13.1677i	0.495038	−	1.68595i	0.705802	−	0.708409i	$-0.250587\pi$
$62$		0			0
$63$	−31.0395	−	2.21999i	−3.91061	−	0.279693i
$64$		0			0
$65$	−9.38847	−	5.76940i	−1.16450	−	0.715606i
$66$		0			0
$67$	0.861972	−	2.31104i	0.105307	−	0.282338i	−0.873601	−	0.486644i	$-0.838221\pi$
$67$	0.861972	−	2.31104i	0.105307	−	0.282338i	0.978907	+	0.204306i	$0.0654937\pi$
$68$		0			0
$69$	−5.83481	−	14.3619i	−0.702429	−	1.72897i
$70$		0			0
$71$	0.667794	+	1.46227i	0.0792526	+	0.173539i	0.945110	−	0.326751i	$-0.105954\pi$
$71$	0.667794	+	1.46227i	0.0792526	+	0.173539i	−0.865858	+	0.500290i	$0.833227\pi$
$72$		0			0
$73$	7.05309	−	0.504447i	0.825502	−	0.0590410i	0.347806	−	0.937566i	$-0.386927\pi$
$73$	7.05309	−	0.504447i	0.825502	−	0.0590410i	0.477696	+	0.878525i	$0.341472\pi$
$74$		0			0
$75$	15.6411	−	4.06960i	1.80608	−	0.469917i
$76$		0			0
$77$	8.43137	−	4.60388i	0.960844	−	0.524660i
$78$		0			0
$79$	−1.31624	+	9.15465i	−0.148089	+	1.02998i	0.771256	+	0.636525i	$0.219629\pi$
$79$	−1.31624	+	9.15465i	−0.148089	+	1.02998i	−0.919344	+	0.393454i	$0.871280\pi$
$80$		0			0
$81$	−10.0247	+	21.9511i	−1.11386	+	2.43902i
$82$		0			0
$83$	0.975600	−	4.48476i	0.107086	−	0.492266i	−0.892097	−	0.451844i	$-0.850766\pi$
$83$	0.975600	−	4.48476i	0.107086	−	0.492266i	0.999183	−	0.0404218i	$-0.0128702\pi$
$84$		0			0
$85$	9.15312	−	2.88937i	0.992795	−	0.313396i
$86$		0			0
$87$	−16.7217	+	3.63758i	−1.79275	+	0.389989i
$88$		0			0
$89$	−5.18455	+	1.52232i	−0.549561	+	0.161366i	−0.544713	−	0.838623i	$-0.683361\pi$
$89$	−5.18455	+	1.52232i	−0.549561	+	0.161366i	−0.00484811	+	0.999988i	$0.501543\pi$
$90$		0			0
$91$		−	20.5895i		−	2.15836i
$92$		0			0
$93$	17.1606	+	17.1606i	1.77947	+	1.77947i
$94$		0			0
$95$	11.6868	+	4.09239i	1.19904	+	0.419870i
$96$		0			0
$97$	−2.50196	−	11.5013i	−0.254036	−	1.16778i	−0.910527	−	0.413450i	$-0.864324\pi$
$97$	−2.50196	−	11.5013i	−0.254036	−	1.16778i	0.656491	−	0.754334i	$-0.272040\pi$
$98$		0			0
$99$	−2.43725	−	16.9514i	−0.244953	−	1.70368i
$100$		0			0
$101$	5.13105	−	3.29752i	0.510558	−	0.328116i	−0.259869	−	0.965644i	$-0.583679\pi$
$101$	5.13105	−	3.29752i	0.510558	−	0.328116i	0.770427	+	0.637528i	$0.220043\pi$
$102$		0			0
$103$	5.40218	+	14.4838i	0.532293	+	1.42713i	0.873351	+	0.487091i	$0.161942\pi$
$103$	5.40218	+	14.4838i	0.532293	+	1.42713i	−0.341058	+	0.940042i	$0.610785\pi$
$104$		0			0
$105$	21.7794	+	20.9180i	2.12545	+	2.04139i
$106$		0			0
$107$	−2.73025	−	5.00008i	−0.263943	−	0.483376i	0.711774	−	0.702408i	$-0.247892\pi$
$107$	−2.73025	−	5.00008i	−0.263943	−	0.483376i	−0.975718	+	0.219032i	$0.929710\pi$
$108$		0			0
$109$	8.99848	+	10.3848i	0.861898	+	0.994683i	0.999991	+	0.00426394i	$0.00135726\pi$
$109$	8.99848	+	10.3848i	0.861898	+	0.994683i	−0.138093	+	0.990419i	$0.544097\pi$
$110$		0			0
$111$	14.9039	+	12.9143i	1.41461	+	1.22577i
$112$		0			0
$113$	−14.2265	−	5.30620i	−1.33831	−	0.499165i	−0.424548	−	0.905406i	$-0.639567\pi$
$113$	−14.2265	−	5.30620i	−1.33831	−	0.499165i	−0.913766	+	0.406240i	$0.866840\pi$
$114$		0			0
$115$	−3.25022	+	10.2194i	−0.303085	+	0.952964i
$116$		0			0
$117$	−34.3913	−	12.8273i	−3.17948	−	1.18588i
$118$		0			0
$119$	13.5537	+	11.7443i	1.24246	+	1.07660i
$120$		0			0
$121$	−3.74138	−	4.31778i	−0.340125	−	0.392526i
$122$		0			0
$123$	−4.93241	−	9.03303i	−0.444740	−	0.814481i
$124$		0			0
$125$	−10.1188	−	4.75491i	−0.905056	−	0.425292i
$126$		0			0
$127$	−5.29327	−	14.1918i	−0.469702	−	1.25932i	−0.928684	−	0.370873i	$-0.879059\pi$
$127$	−5.29327	−	14.1918i	−0.469702	−	1.25932i	0.458982	−	0.888446i	$-0.348214\pi$
$128$		0			0
$129$	2.87538	−	1.84789i	0.253163	−	0.162698i
$130$		0			0
$131$	−0.00349255	−	0.0242912i	−0.000305145	−	0.00212233i	0.989668	−	0.143376i	$-0.0457958\pi$
$131$	−0.00349255	−	0.0242912i	−0.000305145	−	0.00212233i	−0.989973	+	0.141254i	$0.954887\pi$
$132$		0			0
$133$	4.91798	+	22.6076i	0.426443	+	1.96033i
$134$		0			0
$135$	28.9705	−	13.9433i	2.49338	−	1.20005i
$136$		0			0
$137$	0.503236	+	0.503236i	0.0429944	+	0.0429944i	0.728277	−	0.685283i	$-0.240321\pi$
$137$	0.503236	+	0.503236i	0.0429944	+	0.0429944i	−0.685283	+	0.728277i	$0.740321\pi$
$138$		0			0
$139$		−	6.91548i		−	0.586564i	−0.956026	−	0.293282i	$-0.905253\pi$
$139$		−	6.91548i		−	0.586564i	0.956026	−	0.293282i	$-0.0947474\pi$
$140$		0			0
$141$	−8.32847	+	2.44546i	−0.701384	+	0.205945i
$142$		0			0
$143$	11.0721	−	2.40860i	0.925899	−	0.201417i
$144$		0			0
$145$	10.5024	+	5.46269i	0.872176	+	0.453652i
$146$		0			0
$147$	−7.18398	+	33.0242i	−0.592524	+	2.72379i
$148$		0			0
$149$	−3.47939	+	7.61881i	−0.285043	+	0.624157i	−0.996944	−	0.0781229i	$-0.975107\pi$
$149$	−3.47939	+	7.61881i	−0.285043	+	0.624157i	0.711901	+	0.702280i	$0.247835\pi$
$150$		0			0
$151$	−0.590028	+	4.10373i	−0.0480158	+	0.333957i	0.951628	+	0.307254i	$0.0994100\pi$
$151$	−0.590028	+	4.10373i	−0.0480158	+	0.333957i	−0.999643	+	0.0267033i	$0.991499\pi$
$152$		0			0
$153$	28.0609	−	15.3224i	2.26859	−	1.23874i
$154$		0			0
$155$	−1.53519	−	16.7181i	−0.123309	−	1.34283i
$156$		0			0
$157$	7.23164	−	0.517217i	0.577148	−	0.0412784i	0.220286	−	0.975435i	$-0.429301\pi$
$157$	7.23164	−	0.517217i	0.577148	−	0.0412784i	0.356862	+	0.934157i	$0.383847\pi$
$158$		0			0
$159$	6.25665	+	13.7002i	0.496185	+	1.08649i
$160$		0			0
$161$	−19.4478	+	4.82314i	−1.53270	+	0.380116i
$162$		0			0
$163$	4.49192	−	12.0433i	0.351834	−	0.943304i	−0.633663	−	0.773610i	$-0.718449\pi$
$163$	4.49192	−	12.0433i	0.351834	−	0.943304i	0.985497	−	0.169694i	$-0.0542781\pi$
$164$		0			0
$165$	−8.70103	+	14.1591i	−0.677374	+	1.10228i
$166$		0			0
$167$	15.7539	+	1.12674i	1.21907	+	0.0871900i	0.666007	−	0.745946i	$-0.268002\pi$
$167$	15.7539	+	1.12674i	1.21907	+	0.0871900i	0.553068	+	0.833136i	$0.313457\pi$
$168$		0			0
$169$	3.17960	−	10.8287i	0.244585	−	0.832979i
$170$		0			0
$171$	40.8262	+	5.86992i	3.12206	+	0.448884i
$172$		0			0
$173$	−4.21759	+	1.57308i	−0.320657	+	0.119599i	−0.504639	−	0.863331i	$-0.668374\pi$
$173$	−4.21759	+	1.57308i	−0.320657	+	0.119599i	0.183981	+	0.982930i	$0.441101\pi$
$174$		0			0
$175$	−2.32944	−	20.7597i	−0.176089	−	1.56928i
$176$		0			0
$177$	21.5299	+	16.1171i	1.61829	+	1.21144i
$178$		0			0
$179$	−5.09858	+	7.93355i	−0.381086	+	0.592981i	−0.977817	−	0.209460i	$-0.932829\pi$
$179$	−5.09858	+	7.93355i	−0.381086	+	0.592981i	0.596731	+	0.802441i	$0.296466\pi$
$180$		0			0
$181$	−5.76781	−	19.6434i	−0.428718	−	1.46008i	−0.836990	−	0.547219i	$-0.815687\pi$
$181$	−5.76781	−	19.6434i	−0.428718	−	1.46008i	0.408272	−	0.912861i	$-0.366132\pi$
$182$		0			0
$183$	−31.3671	+	31.3671i	−2.31872	+	2.31872i
$184$		0			0
$185$	−2.21345	−	13.4614i	−0.162736	−	0.989704i
$186$		0			0
$187$	−4.73006	+	8.66246i	−0.345896	+	0.633462i
$188$		0			0
$189$	50.5368	+	32.4780i	3.67601	+	2.36243i
$190$		0			0
$191$	4.56066	−	0.655723i	0.329997	−	0.0474465i	0.0246751	−	0.999696i	$-0.492145\pi$
$191$	4.56066	−	0.655723i	0.329997	−	0.0474465i	0.305322	+	0.952249i	$0.401236\pi$
$192$		0			0
$193$	2.83082	+	0.615808i	0.203767	+	0.0443268i	0.313290	−	0.949657i	$-0.398569\pi$
$193$	2.83082	+	0.615808i	0.203767	+	0.0443268i	−0.109523	+	0.993984i	$0.534932\pi$
$194$		0			0
$195$	17.6975	+	30.9115i	1.26735	+	2.21362i
$196$		0			0
$197$	−8.75134	−	11.6904i	−0.623507	−	0.832908i	0.371937	−	0.928258i	$-0.378694\pi$
$197$	−8.75134	−	11.6904i	−0.623507	−	0.832908i	−0.995444	+	0.0953500i	$0.969603\pi$
$198$		0			0
$199$	−2.62762	−	0.771540i	−0.186267	−	0.0546930i	0.187269	−	0.982309i	$-0.440037\pi$
$199$	−2.62762	−	0.771540i	−0.186267	−	0.0546930i	−0.373536	+	0.927616i	$0.621855\pi$
$200$		0			0
$201$	−6.02546	+	5.22109i	−0.425003	+	0.368267i
$202$		0			0
$203$	1.57795	+	22.0627i	0.110751	+	1.54850i
$204$		0			0
$205$	−1.37277	+	6.98608i	−0.0958782	+	0.487929i
$206$		0			0
$207$	−4.05978	+	35.4892i	−0.282174	+	2.46667i
$208$		0			0
$209$	−11.5821	+	5.28937i	−0.801151	+	0.365873i
$210$		0			0
$211$	7.34378	−	8.47517i	0.505567	−	0.583455i	−0.444391	−	0.895833i	$-0.646580\pi$
$211$	7.34378	−	8.47517i	0.505567	−	0.583455i	0.949958	+	0.312378i	$0.101125\pi$
$212$		0			0
$213$	0.370690	−	5.18292i	0.0253992	−	0.355128i
$214$		0			0
$215$	−2.34670	−	0.289223i	−0.160044	−	0.0197249i
$216$		0			0
$217$	25.1117	−	18.7984i	1.70469	−	1.27612i
$218$		0			0
$219$	−20.7910	−	9.49493i	−1.40492	−	0.641608i
$220$		0			0
$221$	11.4366	+	17.7957i	0.769309	+	1.19707i
$222$		0			0
$223$	8.65924	−	11.5674i	0.579866	−	0.774610i	−0.410682	−	0.911779i	$-0.634709\pi$
$223$	8.65924	−	11.5674i	0.579866	−	0.774610i	0.990548	+	0.137169i	$0.0438003\pi$
$224$		0			0
$225$	−36.1269	−	9.04240i	−2.40846	−	0.602826i
$226$		0			0
$227$	−4.92676	−	2.69021i	−0.327000	−	0.178556i	0.307360	−	0.951593i	$-0.400555\pi$
$227$	−4.92676	−	2.69021i	−0.327000	−	0.178556i	−0.634360	+	0.773038i	$0.718736\pi$
$228$		0			0
$229$	19.0327			1.25771			0.628857	−	0.777521i	$-0.283523\pi$
$229$	19.0327			1.25771			0.628857	+	0.777521i	$0.283523\pi$
$230$		0			0
$231$	−31.0516			−2.04305
$232$		0			0
$233$	−12.6842	−	6.92611i	−0.830971	−	0.453744i	0.00666235	−	0.999978i	$-0.497879\pi$
$233$	−12.6842	−	6.92611i	−0.830971	−	0.453744i	−0.837633	+	0.546234i	$0.816061\pi$
$234$		0			0
$235$	5.51121	+	2.38374i	0.359511	+	0.155498i
$236$		0			0
$237$	17.9158	−	23.9327i	1.16375	−	1.55459i
$238$		0			0
$239$	6.95690	+	10.8251i	0.450004	+	0.700221i	0.989940	−	0.141486i	$-0.0451879\pi$
$239$	6.95690	+	10.8251i	0.450004	+	0.700221i	−0.539936	+	0.841706i	$0.681552\pi$
$240$		0			0
$241$	−2.91855	−	1.33286i	−0.188000	−	0.0858568i	0.319191	−	0.947690i	$-0.396589\pi$
$241$	−2.91855	−	1.33286i	−0.188000	−	0.0858568i	−0.507191	+	0.861834i	$0.669316\pi$
$242$		0			0
$243$	27.9132	−	20.8956i	1.79063	−	1.34045i
$244$		0			0
$245$	18.4299	−	14.3855i	1.17744	−	0.919054i
$246$		0			0
$247$	−1.94685	+	27.2205i	−0.123875	+	1.73200i
$248$		0			0
$249$	−9.71517	+	11.2119i	−0.615674	+	0.710526i
$250$		0			0
$251$	2.58110	−	1.17875i	0.162918	−	0.0744021i	−0.332287	−	0.943178i	$-0.607820\pi$
$251$	2.58110	−	1.17875i	0.162918	−	0.0744021i	0.495205	+	0.868776i	$0.335093\pi$
$252$		0			0
$253$	−4.86872	−	9.89398i	−0.306094	−	0.622029i
$254$		0			0
$255$	−30.4433	−	5.98211i	−1.90643	−	0.374614i
$256$		0			0
$257$	0.747940	+	10.4576i	0.0466552	+	0.652325i	0.965946	+	0.258745i	$0.0833090\pi$
$257$	0.747940	+	10.4576i	0.0466552	+	0.652325i	−0.919290	+	0.393580i	$0.871236\pi$
$258$		0			0
$259$	19.2639	−	16.6923i	1.19700	−	1.03721i
$260$		0			0
$261$	37.8351	+	11.1094i	2.34194	+	0.687654i
$262$		0			0
$263$	−4.20686	−	5.61971i	−0.259406	−	0.346526i	0.651864	−	0.758336i	$-0.273987\pi$
$263$	−4.20686	−	5.61971i	−0.259406	−	0.346526i	−0.911270	+	0.411810i	$0.864897\pi$
$264$		0			0
$265$	2.73311	−	10.0540i	0.167894	−	0.617615i
$266$		0			0
$267$	17.0668	+	3.71265i	1.04447	+	0.227210i
$268$		0			0
$269$	−28.2928	+	4.06789i	−1.72504	+	0.248024i	−0.932339	−	0.361584i	$-0.882236\pi$
$269$	−28.2928	+	4.06789i	−1.72504	+	0.248024i	−0.792703	+	0.609608i	$0.791327\pi$
$270$		0			0
$271$	−17.5599	−	11.2851i	−1.06669	−	0.685518i	−0.115242	−	0.993337i	$-0.536764\pi$
$271$	−17.5599	−	11.2851i	−1.06669	−	0.685518i	−0.951445	+	0.307819i	$0.900401\pi$
$272$		0			0
$273$	−31.8954	+	58.4121i	−1.93040	+	3.53526i
$274$		0			0
$275$	10.8912	−	3.68119i	0.656763	−	0.221984i
$276$		0			0
$277$	3.14698	−	3.14698i	0.189084	−	0.189084i	−0.606216	−	0.795300i	$-0.707313\pi$
$277$	3.14698	−	3.14698i	0.189084	−	0.189084i	0.795300	+	0.606216i	$0.207313\pi$
$278$		0			0
$279$	−15.7549	−	53.6564i	−0.943223	−	3.21232i
$280$		0			0
$281$	−11.4871	+	17.8743i	−0.685265	+	1.06629i	0.308108	+	0.951351i	$0.400304\pi$
$281$	−11.4871	+	17.8743i	−0.685265	+	1.06629i	−0.993372	+	0.114941i	$0.963332\pi$
$282$		0			0
$283$	−8.07081	−	6.04173i	−0.479760	−	0.359144i	0.331861	−	0.943328i	$-0.392324\pi$
$283$	−8.07081	−	6.04173i	−0.479760	−	0.359144i	−0.811621	+	0.584185i	$0.801414\pi$
$284$		0			0
$285$	−26.8158	−	29.7142i	−1.58843	−	1.76012i
$286$		0			0
$287$	−12.4641	+	4.64885i	−0.735730	+	0.274413i
$288$		0			0
$289$	−1.41110	−	0.202885i	−0.0830058	−	0.0119344i
$290$		0			0
$291$	−10.7188	+	36.5050i	−0.628349	+	2.13996i
$292$		0			0
$293$	7.30962	+	0.522794i	0.427033	+	0.0305420i	0.283202	−	0.959060i	$-0.408603\pi$
$293$	7.30962	+	0.522794i	0.427033	+	0.0305420i	0.143831	+	0.989602i	$0.454058\pi$
$294$		0			0
$295$	−4.32058	−	18.0960i	−0.251554	−	1.05359i
$296$		0			0
$297$	−11.5534	+	30.9759i	−0.670397	+	1.79740i
$298$		0			0
$299$	−23.6129	−	1.00415i	−1.36557	−	0.0580715i
$300$		0			0
$301$	−1.83525	−	4.01865i	−0.105782	−	0.231631i
$302$		0			0
$303$	−19.6650	+	1.40647i	−1.12972	+	0.0807994i
$304$		0			0
$305$	30.5582	−	2.80610i	1.74976	−	0.160677i
$306$		0			0
$307$	−21.5092	+	11.7449i	−1.22759	+	0.670317i	−0.956358	−	0.292196i	$-0.905614\pi$
$307$	−21.5092	+	11.7449i	−1.22759	+	0.670317i	−0.271236	+	0.962513i	$0.587432\pi$
$308$		0			0
$309$	7.11114	−	49.4590i	0.404538	−	2.81363i
$310$		0			0
$311$	−3.86753	+	8.46870i	−0.219307	+	0.480216i	−0.987024	−	0.160574i	$-0.948666\pi$
$311$	−3.86753	+	8.46870i	−0.219307	+	0.480216i	0.767717	+	0.640790i	$0.221393\pi$
$312$		0			0
$313$	−2.87631	+	13.2222i	−0.162579	+	0.747363i	0.821583	+	0.570089i	$0.193091\pi$
$313$	−2.87631	+	13.2222i	−0.162579	+	0.747363i	−0.984162	+	0.177274i	$0.943272\pi$
$314$		0			0
$315$	−20.9467	−	66.3562i	−1.18021	−	3.73875i
$316$		0			0
$317$	−13.2133	+	2.87438i	−0.742133	+	0.161441i	−0.567709	−	0.823230i	$-0.692170\pi$
$317$	−13.2133	+	2.87438i	−0.742133	+	0.161441i	−0.174424	+	0.984671i	$0.555806\pi$
$318$		0			0
$319$	−11.6798	+	3.42949i	−0.653942	+	0.192015i
$320$		0			0
$321$			18.4147i			1.02781i
$322$		0			0
$323$	−16.8083	−	16.8083i	−0.935237	−	0.935237i
$324$		0			0
$325$	4.26235	−	24.2689i	0.236432	−	1.34620i
$326$		0			0
$327$	−9.44136	−	43.4012i	−0.522108	−	2.40009i
$328$		0			0
$329$	1.59669	+	11.1052i	0.0880281	+	0.612249i
$330$		0			0
$331$	−23.5800	+	15.1540i	−1.29608	+	0.832938i	−0.992779	−	0.119959i	$-0.961724\pi$
$331$	−23.5800	+	15.1540i	−1.29608	+	0.832938i	−0.303297	+	0.952896i	$0.598087\pi$
$332$		0			0
$333$	−15.8802	−	42.5766i	−0.870232	−	2.33318i
$334$		0			0
$335$	5.51426	−	0.111245i	0.301276	−	0.00607796i
$336$		0			0
$337$	−9.41546	−	17.2431i	−0.512893	−	0.939293i	−0.997899	−	0.0647826i	$-0.979365\pi$
$337$	−9.41546	−	17.2431i	−0.512893	−	0.939293i	0.485007	−	0.874511i	$-0.338817\pi$
$338$		0			0
$339$	32.1405	+	37.0921i	1.74563	+	2.01456i
$340$		0			0
$341$	13.0466	+	11.3049i	0.706512	+	0.612196i
$342$		0			0
$343$	13.5273	+	5.04543i	0.730407	+	0.272428i
$344$		0			0
$345$	25.0519	−	23.9574i	1.34875	−	1.28982i
$346$		0			0
$347$	19.5750	+	7.30108i	1.05084	+	0.391943i	0.814764	−	0.579792i	$-0.196866\pi$
$347$	19.5750	+	7.30108i	1.05084	+	0.391943i	0.236075	+	0.971735i	$0.424139\pi$
$348$		0			0
$349$	−12.6493	−	10.9607i	−0.677100	−	0.586711i	0.246928	−	0.969034i	$-0.420579\pi$
$349$	−12.6493	−	10.9607i	−0.677100	−	0.586711i	−0.924029	+	0.382323i	$0.875124\pi$
$350$		0			0
$351$	46.4022	+	53.5510i	2.47677	+	2.85834i
$352$		0			0
$353$	6.47038	+	11.8496i	0.344383	+	0.630691i	0.991263	−	0.131901i	$-0.0421082\pi$
$353$	6.47038	+	11.8496i	0.344383	+	0.630691i	−0.646880	+	0.762592i	$0.723926\pi$
$354$		0			0
$355$	−2.48995	+	2.59249i	−0.132153	+	0.137595i
$356$		0			0
$357$	−20.2583	−	54.3147i	−1.07218	−	2.87464i
$358$		0			0
$359$	−19.7419	+	12.6873i	−1.04194	+	0.669611i	−0.945465	−	0.325725i	$-0.894392\pi$
$359$	−19.7419	+	12.6873i	−1.04194	+	0.669611i	−0.0964707	+	0.995336i	$0.530755\pi$
$360$		0			0
$361$	−1.66021	−	11.5470i	−0.0873795	−	0.607738i
$362$		0			0
$363$	3.92552	+	18.0453i	0.206036	+	0.947134i
$364$		0			0
$365$	6.85708	+	14.2472i	0.358916	+	0.745733i
$366$		0			0
$367$	−6.54247	−	6.54247i	−0.341514	−	0.341514i	0.515422	−	0.856936i	$-0.327635\pi$
$367$	−6.54247	−	6.54247i	−0.341514	−	0.341514i	−0.856936	+	0.515422i	$0.827635\pi$
$368$		0			0
$369$			23.7154i			1.23458i
$370$		0			0
$371$	18.6787	−	5.48457i	0.969751	−	0.284745i
$372$		0			0
$373$	5.26408	−	1.14513i	0.272564	−	0.0592926i	−0.0742059	−	0.997243i	$-0.523642\pi$
$373$	5.26408	−	1.14513i	0.272564	−	0.0592926i	0.346770	+	0.937950i	$0.387279\pi$
$374$		0			0
$375$	21.3411	+	29.1649i	1.10205	+	1.50607i
$376$		0			0
$377$	−5.54584	+	25.4938i	−0.285625	+	1.31300i
$378$		0			0
$379$	−12.7747	+	27.9727i	−0.656193	+	1.43686i	0.229834	+	0.973230i	$0.426182\pi$
$379$	−12.7747	+	27.9727i	−0.656193	+	1.43686i	−0.886027	+	0.463633i	$0.846546\pi$
$380$		0			0
$381$	−6.96776	+	48.4619i	−0.356969	+	2.48278i
$382$		0			0
$383$	1.26972	−	0.693322i	0.0648799	−	0.0354271i	−0.446482	−	0.894793i	$-0.647323\pi$
$383$	1.26972	−	0.693322i	0.0648799	−	0.0354271i	0.511361	+	0.859366i	$0.329141\pi$
$384$		0			0
$385$	16.5144	+	13.7365i	0.841653	+	0.700079i
$386$		0			0
$387$	−7.85586	+	0.561862i	−0.399336	+	0.0285610i
$388$		0			0
$389$	14.7804	+	32.3645i	0.749394	+	1.64094i	0.767452	+	0.641107i	$0.221524\pi$
$389$	14.7804	+	32.3645i	0.749394	+	1.64094i	−0.0180581	+	0.999837i	$0.505748\pi$
$390$		0			0
$391$	14.1299	−	14.9711i	0.714579	−	0.757123i
$392$		0			0
$393$	−0.0277215	+	0.0743242i	−0.00139836	+	0.00374916i
$394$		0			0
$395$	−20.1155	+	4.80275i	−1.01212	+	0.241653i
$396$		0			0
$397$	−11.1662	−	0.798620i	−0.560414	−	0.0400816i	−0.211741	−	0.977326i	$-0.567913\pi$
$397$	−11.1662	−	0.798620i	−0.560414	−	0.0400816i	−0.348673	+	0.937244i	$0.613368\pi$
$398$		0			0
$399$	21.0695	−	71.7561i	1.05479	−	3.59230i
$400$		0			0
$401$	2.59697	+	0.373389i	0.129687	+	0.0186461i	0.206852	−	0.978372i	$-0.433678\pi$
$401$	2.59697	+	0.373389i	0.129687	+	0.0186461i	−0.0771658	+	0.997018i	$0.524587\pi$
$402$		0			0
$403$	34.6671	−	12.9302i	1.72689	−	0.644097i
$404$		0			0
$405$	−53.8897	−	2.76311i	−2.67780	−	0.137300i
$406$		0			0
$407$	11.2299	+	8.40663i	0.556648	+	0.416701i
$408$		0			0
$409$	20.8619	−	32.4618i	1.03156	−	1.60513i	0.263600	−	0.964632i	$-0.415090\pi$
$409$	20.8619	−	32.4618i	1.03156	−	1.60513i	0.767957	−	0.640502i	$-0.221274\pi$
$410$		0			0
$411$	−0.648106	−	2.20725i	−0.0319687	−	0.108875i
$412$		0			0
$413$	24.5804	−	24.5804i	1.20952	−	1.20952i
$414$		0			0
$415$	10.1268	−	1.66514i	0.497104	−	0.0817385i
$416$		0			0
$417$	−10.7129	+	19.6192i	−0.524612	+	0.960755i
$418$		0			0
$419$	2.57092	+	1.65223i	0.125598	+	0.0807167i	0.601931	−	0.798548i	$-0.294398\pi$
$419$	2.57092	+	1.65223i	0.125598	+	0.0807167i	−0.476334	+	0.879265i	$0.658035\pi$
$420$		0			0
$421$	−3.89707	+	0.560315i	−0.189932	+	0.0273081i	−0.236624	−	0.971601i	$-0.576041\pi$
$421$	−3.89707	+	0.560315i	−0.189932	+	0.0273081i	0.0466924	+	0.998909i	$0.485132\pi$
$422$		0			0
$423$	19.5441	+	4.25157i	0.950268	+	0.206718i
$424$		0			0
$425$	13.5445	+	16.6489i	0.657005	+	0.807591i
$426$		0			0
$427$	34.3608	+	45.9006i	1.66283	+	2.22129i
$428$		0			0
$429$	−35.1427	−	10.3188i	−1.69671	−	0.498198i
$430$		0			0
$431$	1.14882	−	0.995462i	0.0553369	−	0.0479497i	−0.626753	−	0.779218i	$-0.715617\pi$
$431$	1.14882	−	0.995462i	0.0553369	−	0.0479497i	0.682090	+	0.731268i	$0.261071\pi$
$432$		0			0
$433$	−1.13985	−	15.9372i	−0.0547777	−	0.765893i	−0.948401	−	0.317074i	$-0.897300\pi$
$433$	−1.13985	−	15.9372i	−0.0547777	−	0.765893i	0.893623	−	0.448818i	$-0.148155\pi$
$434$		0			0
$435$	−21.3329	−	31.7670i	−1.02283	−	1.52311i
$436$		0			0
$437$	26.1672	−	4.53758i	1.25175	−	0.217062i
$438$		0			0
$439$	−13.7224	+	6.26682i	−0.654935	+	0.299099i	−0.715030	−	0.699094i	$-0.753587\pi$
$439$	−13.7224	+	6.26682i	−0.654935	+	0.299099i	0.0600948	+	0.998193i	$0.480860\pi$
$440$		0			0
$441$	50.9982	−	58.8550i	2.42848	−	2.80262i
$442$		0			0
$443$	0.705750	−	9.86767i	0.0335312	−	0.468827i	−0.952750	−	0.303755i	$-0.901760\pi$
$443$	0.705750	−	9.86767i	0.0335312	−	0.468827i	0.986281	−	0.165073i	$-0.0527858\pi$
$444$		0			0
$445$	−7.43435	−	9.52447i	−0.352422	−	0.451503i
$446$		0			0
$447$	21.6734	−	16.2245i	1.02512	−	0.767393i
$448$		0			0
$449$	−18.7693	−	8.57166i	−0.885779	−	0.404522i	−0.0800395	−	0.996792i	$-0.525505\pi$
$449$	−18.7693	−	8.57166i	−0.885779	−	0.404522i	−0.805740	+	0.592270i	$0.798232\pi$
$450$		0			0
$451$	−3.95803	−	6.15881i	−0.186376	−	0.290007i
$452$		0			0
$453$	8.03105	−	10.7282i	0.377332	−	0.504056i
$454$		0			0
$455$	42.8033	−	16.9559i	2.00665	−	0.794906i
$456$		0			0
$457$	−8.71660	−	4.75963i	−0.407745	−	0.222646i	0.262268	−	0.964995i	$-0.415530\pi$
$457$	−8.71660	−	4.75963i	−0.407745	−	0.222646i	−0.670013	+	0.742349i	$0.733712\pi$
$458$		0			0
$459$	−61.7197			−2.88083
$460$		0			0
$461$	−14.3758			−0.669549			−0.334775	−	0.942298i	$-0.608660\pi$
$461$	−14.3758			−0.669549			−0.334775	+	0.942298i	$0.608660\pi$
$462$		0			0
$463$	32.8411	+	17.9326i	1.52626	+	0.833399i	0.999858	−	0.0168394i	$-0.00536041\pi$
$463$	32.8411	+	17.9326i	1.52626	+	0.833399i	0.526398	+	0.850238i	$0.323542\pi$
$464$		0			0
$465$	−21.5429	+	49.8072i	−0.999027	+	2.30975i
$466$		0			0
$467$	17.3214	−	23.1387i	0.801538	−	1.07073i	−0.194421	−	0.980918i	$-0.562283\pi$
$467$	17.3214	−	23.1387i	0.801538	−	1.07073i	0.995959	−	0.0898110i	$-0.0286263\pi$
$468$		0			0
$469$	5.57143	+	8.66932i	0.257265	+	0.400312i
$470$		0			0
$471$	−21.3173	−	9.73530i	−0.982250	−	0.448579i
$472$		0			0
$473$	1.94637	−	1.45703i	0.0894940	−	0.0669944i
$474$		0			0
$475$	1.11672	+	27.6658i	0.0512385	+	1.26939i
$476$		0			0
$477$	2.47583	−	34.6166i	0.113360	−	1.58499i
$478$		0			0
$479$	−22.9239	+	26.4556i	−1.04742	+	1.20879i	−0.0699870	+	0.997548i	$0.522296\pi$
$479$	−22.9239	+	26.4556i	−1.04742	+	1.20879i	−0.977434	+	0.211241i	$0.932250\pi$
$480$		0			0
$481$	27.3490	−	12.4899i	1.24701	−	0.569490i
$482$		0			0
$483$	62.6448	+	16.4437i	2.85044	+	0.748213i
$484$		0			0
$485$	21.8497	−	14.6730i	0.992142	−	0.666264i
$486$		0			0
$487$	−2.42589	−	33.9184i	−0.109928	−	1.53699i	−0.690830	−	0.723017i	$-0.742755\pi$
$487$	−2.42589	−	33.9184i	−0.109928	−	1.53699i	0.580903	−	0.813973i	$-0.302700\pi$
$488$		0			0
$489$	−31.4000	+	27.2082i	−1.41996	+	1.23040i
$490$		0			0
$491$	0.209759	+	0.0615907i	0.00946627	+	0.00277955i	0.286462	−	0.958092i	$-0.407521\pi$
$491$	0.209759	+	0.0615907i	0.00946627	+	0.00277955i	−0.276996	+	0.960871i	$0.589339\pi$
$492$		0			0
$493$	−13.6187	−	18.1925i	−0.613357	−	0.819350i
$494$		0			0
$495$	33.2332	−	19.0267i	1.49372	−	0.855187i
$496$		0			0
$497$	−6.56278	−	1.42765i	−0.294381	−	0.0640387i
$498$		0			0
$499$	−34.2383	+	4.92272i	−1.53271	+	0.220371i	−0.856428	−	0.516267i	$-0.827321\pi$
$499$	−34.2383	+	4.92272i	−1.53271	+	0.220371i	−0.676287	+	0.736638i	$0.736412\pi$
$500$		0			0
$501$	−42.9483	−	27.6012i	−1.91879	−	1.23313i
$502$		0			0
$503$	−3.00930	+	5.51113i	−0.134178	+	0.245729i	−0.936126	−	0.351665i	$-0.885616\pi$
$503$	−3.00930	+	5.51113i	−0.134178	+	0.245729i	0.801948	+	0.597394i	$0.203797\pi$
$504$		0			0
$505$	11.0807	+	7.95132i	0.493087	+	0.353829i
$506$		0			0
$507$	−25.7954	+	25.7954i	−1.14562	+	1.14562i
$508$		0			0
$509$	−11.0233	−	37.5420i	−0.488600	−	1.66402i	−0.722198	−	0.691687i	$-0.756868\pi$
$509$	−11.0233	−	37.5420i	−0.488600	−	1.66402i	0.233597	−	0.972333i	$-0.424950\pi$
$510$		0			0
$511$	−15.9722	+	24.8532i	−0.706567	+	1.09944i
$512$		0			0
$513$	−63.7417	−	47.7164i	−2.81426	−	2.10673i
$514$		0			0
$515$	−25.6615	+	23.1584i	−1.13078	+	1.02048i
$516$		0			0
$517$	−5.78512	+	2.15774i	−0.254429	+	0.0948972i
$518$		0			0
$519$	14.4021	+	2.07072i	0.632184	+	0.0908943i
$520$		0			0
$521$	5.72139	−	19.4853i	0.250659	−	0.853666i	−0.733996	−	0.679154i	$-0.762347\pi$
$521$	5.72139	−	19.4853i	0.250659	−	0.853666i	0.984655	−	0.174512i	$-0.0558348\pi$
$522$		0			0
$523$	−4.38571	−	0.313672i	−0.191774	−	0.0137159i	−0.0248781	−	0.999690i	$-0.507920\pi$
$523$	−4.38571	−	0.313672i	−0.191774	−	0.0137159i	−0.166896	+	0.985975i	$0.553374\pi$
$524$		0			0
$525$	−25.5505	+	62.5036i	−1.11512	+	2.72788i
$526$		0			0
$527$	−11.2626	+	30.1961i	−0.490606	+	1.31536i
$528$		0			0
$529$	4.58291	+	22.5388i	0.199257	+	0.979947i
$530$		0			0
$531$	−25.7439	−	56.3713i	−1.11719	−	2.44631i
$532$		0			0
$533$	−15.6511	+	1.11939i	−0.677924	+	0.0484861i
$534$		0			0
$535$	8.14622	−	9.79360i	0.352192	−	0.423414i
$536$		0			0
$537$	26.7546	−	14.6091i	1.15455	−	0.630430i
$538$		0			0
$539$	−3.42133	+	23.7959i	−0.147367	+	1.02496i
$540$		0			0
$541$	−10.5234	+	23.0431i	−0.452437	+	0.990699i	0.536710	+	0.843767i	$0.319667\pi$
$541$	−10.5234	+	23.0431i	−0.452437	+	0.990699i	−0.989147	+	0.146932i	$0.953060\pi$
$542$		0			0
$543$	−14.0666	+	64.6630i	−0.603655	+	2.77496i
$544$		0			0
$545$	−14.1784	+	27.2590i	−0.607338	+	1.16765i
$546$		0			0
$547$	−18.8955	+	4.11046i	−0.807912	+	0.175751i	−0.597507	−	0.801864i	$-0.703842\pi$
$547$	−18.8955	+	4.11046i	−0.807912	+	0.175751i	−0.210405	+	0.977614i	$0.567478\pi$
$548$		0			0
$549$	98.0763	−	28.7978i	4.18579	−	1.22906i
$550$		0			0
$551$		−	29.3174i		−	1.24896i
$552$		0			0
$553$	−27.3236	−	27.3236i	−1.16192	−	1.16192i
$554$		0			0
$555$	−14.5737	+	41.6188i	−0.618621	+	1.76662i
$556$		0			0
$557$	2.03844	+	9.37056i	0.0863715	+	0.397043i	0.999954	−	0.00961040i	$-0.00305913\pi$
$557$	2.03844	+	9.37056i	0.0863715	+	0.397043i	−0.913582	+	0.406654i	$0.866695\pi$
$558$		0			0
$559$	−0.741606	−	5.15798i	−0.0313666	−	0.218159i
$560$		0			0
$561$	26.8383	−	17.2479i	1.13311	−	0.728207i
$562$		0			0
$563$	7.68958	+	20.6166i	0.324077	+	0.868884i	0.992180	+	0.124815i	$0.0398339\pi$
$563$	7.68958	+	20.6166i	0.324077	+	0.868884i	−0.668103	+	0.744069i	$0.732893\pi$
$564$		0			0
$565$	−0.684811	−	33.9451i	−0.0288102	−	1.42808i
$566$		0			0
$567$	−48.3193	−	88.4901i	−2.02922	−	3.71624i
$568$		0			0
$569$	25.7436	+	29.7097i	1.07923	+	1.24549i	0.967799	+	0.251722i	$0.0809970\pi$
$569$	25.7436	+	29.7097i	1.07923	+	1.24549i	0.111428	+	0.993773i	$0.464458\pi$
$570$		0			0
$571$	14.2793	+	12.3731i	0.597570	+	0.517798i	0.900295	−	0.435280i	$-0.143351\pi$
$571$	14.2793	+	12.3731i	0.597570	+	0.517798i	−0.302725	+	0.953078i	$0.597896\pi$
$572$		0			0
$573$	−13.9543	−	5.20469i	−0.582950	−	0.217429i
$574$		0			0
$575$	−23.9217	+	1.65905i	−0.997604	+	0.0691872i
$576$		0			0
$577$	2.07540	+	0.774082i	0.0863998	+	0.0322255i	0.392292	−	0.919841i	$-0.371682\pi$
$577$	2.07540	+	0.774082i	0.0863998	+	0.0322255i	−0.305893	+	0.952066i	$0.598955\pi$
$578$		0			0
$579$	−7.07706	−	6.13231i	−0.294113	−	0.254850i
$580$		0			0
$581$	12.5573	+	14.4919i	0.520964	+	0.601225i
$582$		0			0
$583$	5.13444	+	9.40303i	0.212647	+	0.389434i
$584$		0			0
$585$	−1.65547	−	82.0595i	−0.0684454	−	3.39274i
$586$		0			0
$587$	−0.0480875	−	0.128928i	−0.00198478	−	0.00532141i	0.935954	−	0.352123i	$-0.114540\pi$
$587$	−0.0480875	−	0.128928i	−0.00198478	−	0.00532141i	−0.937938	+	0.346802i	$0.887268\pi$
$588$		0			0
$589$	−34.9766	+	22.4781i	−1.44119	+	0.926195i
$590$		0			0
$591$	6.71767	+	46.7224i	0.276328	+	1.92190i
$592$		0			0
$593$	8.32032	+	38.2479i	0.341675	+	1.57065i	0.752282	+	0.658841i	$0.228953\pi$
$593$	8.32032	+	38.2479i	0.341675	+	1.57065i	−0.410607	+	0.911812i	$0.634683\pi$
$594$		0			0
$595$	−13.2534	+	37.8484i	−0.543338	+	1.55163i
$596$		0			0
$597$	6.25934	+	6.25934i	0.256178	+	0.256178i
$598$		0			0
$599$		−	39.1031i		−	1.59771i	−0.601524	−	0.798855i	$-0.705439\pi$
$599$		−	39.1031i		−	1.59771i	0.601524	−	0.798855i	$-0.294561\pi$
$600$		0			0
$601$	−25.6764	+	7.53926i	−1.04736	+	0.307533i	−0.759751	−	0.650215i	$-0.774679\pi$
$601$	−25.6764	+	7.53926i	−1.04736	+	0.307533i	−0.287610	+	0.957748i	$0.592861\pi$
$602$		0			0
$603$	17.9517	−	3.90515i	0.731049	−	0.159030i
$604$		0			0
$605$	5.89510	−	11.3337i	0.239670	−	0.460782i
$606$		0			0
$607$	8.30081	−	38.1582i	0.336919	−	1.54879i	−0.427464	−	0.904032i	$-0.640593\pi$
$607$	8.30081	−	38.1582i	0.336919	−	1.54879i	0.764384	−	0.644761i	$-0.223043\pi$
$608$		0			0
$609$	29.7009	−	65.0360i	1.20354	−	2.63539i
$610$		0			0
$611$	−1.88334	+	13.0989i	−0.0761917	+	0.529925i
$612$		0			0
$613$	−18.8292	+	10.2815i	−0.760503	+	0.415266i	−0.812187	−	0.583397i	$-0.801723\pi$
$613$	−18.8292	+	10.2815i	−0.760503	+	0.415266i	0.0516836	+	0.998664i	$0.483541\pi$
$614$		0			0
$615$	14.7168	−	17.6929i	0.593437	−	0.713446i
$616$		0			0
$617$	−4.53845	+	0.324597i	−0.182711	+	0.0130678i	−0.162395	−	0.986726i	$-0.551922\pi$
$617$	−4.53845	+	0.324597i	−0.182711	+	0.0130678i	−0.0203163	+	0.999794i	$0.506467\pi$
$618$		0			0
$619$	−10.0698	−	22.0498i	−0.404740	−	0.886256i	−0.996768	−	0.0803389i	$-0.974400\pi$
$619$	−10.0698	−	22.0498i	−0.404740	−	0.886256i	0.592028	−	0.805917i	$-0.298328\pi$
$620$		0			0
$621$	39.7119	−	56.3738i	1.59358	−	2.26220i
$622$		0			0
$623$	7.88932	−	21.1521i	0.316079	−	0.847441i
$624$		0			0
$625$	1.55186	−	24.9518i	0.0620745	−	0.998072i
$626$		0			0
$627$	41.0521	+	2.93611i	1.63946	+	0.117257i
$628$		0			0
$629$	−7.37815	+	25.1277i	−0.294186	+	1.00191i
$630$		0			0
$631$	22.1266	+	3.18133i	0.880847	+	0.126647i	0.567874	−	0.823115i	$-0.307766\pi$
$631$	22.1266	+	3.18133i	0.880847	+	0.126647i	0.312973	+	0.949762i	$0.398675\pi$
$632$		0			0
$633$	−33.9632	+	12.6676i	−1.34992	+	0.503493i
$634$		0			0
$635$	25.1441	−	22.6914i	0.997815	−	0.900482i
$636$		0			0
$637$	41.2488	+	30.8784i	1.63434	+	1.22345i
$638$		0			0
$639$	−6.47328	+	10.0726i	−0.256079	+	0.398467i
$640$		0			0
$641$	−8.14988	−	27.7559i	−0.321901	−	1.09629i	−0.948454	−	0.316915i	$-0.897353\pi$
$641$	−8.14988	−	27.7559i	−0.321901	−	1.09629i	0.626553	−	0.779379i	$-0.284465\pi$
$642$		0			0
$643$	18.1303	−	18.1303i	0.714991	−	0.714991i	−0.252584	−	0.967575i	$-0.581280\pi$
$643$	18.1303	−	18.1303i	0.714991	−	0.714991i	0.967575	+	0.252584i	$0.0812804\pi$
$644$		0			0
$645$	6.20952	+	4.45583i	0.244500	+	0.175448i
$646$		0			0
$647$	−5.40002	+	9.88940i	−0.212297	+	0.388792i	−0.962028	−	0.272950i	$-0.912001\pi$
$647$	−5.40002	+	9.88940i	−0.212297	+	0.388792i	0.749732	+	0.661742i	$0.230183\pi$
$648$		0			0
$649$	16.0938	+	10.3429i	0.631737	+	0.405993i
$650$		0			0
$651$	−100.362	+	14.4299i	−3.93351	+	0.565554i
$652$		0			0
$653$	−36.1320	−	7.86005i	−1.41396	−	0.307587i	−0.560242	−	0.828329i	$-0.689292\pi$
$653$	−36.1320	−	7.86005i	−1.41396	−	0.307587i	−0.853714	+	0.520742i	$0.825655\pi$
$654$		0			0
$655$	0.0476227	−	0.0272650i	0.00186077	−	0.00106533i
$656$		0			0
$657$	31.5624	+	42.1625i	1.23137	+	1.64492i
$658$		0			0
$659$	−34.0520	−	9.99856i	−1.32648	−	0.389489i	−0.459651	−	0.888100i	$-0.652025\pi$
$659$	−34.0520	−	9.99856i	−1.32648	−	0.389489i	−0.866826	+	0.498611i	$0.833844\pi$
$660$		0			0
$661$	2.19716	−	1.90385i	0.0854598	−	0.0740513i	−0.611083	−	0.791566i	$-0.709266\pi$
$661$	2.19716	−	1.90385i	0.0854598	−	0.0740513i	0.696543	+	0.717515i	$0.254721\pi$
$662$		0			0
$663$	−4.87796	−	68.2028i	−0.189444	−	2.64878i
$664$		0			0
$665$	−42.9488	+	28.8419i	−1.66548	+	1.11844i
$666$		0			0
$667$	25.3794	−	0.733665i	0.982693	−	0.0284076i
$668$		0			0
$669$	−42.4854	+	19.4024i	−1.64258	+	0.750141i
$670$		0			0
$671$	−20.6638	+	23.8473i	−0.797718	+	0.920615i
$672$		0			0
$673$	−1.23239	+	17.2311i	−0.0475052	+	0.664210i	0.916788	+	0.399374i	$0.130772\pi$
$673$	−1.23239	+	17.2311i	−0.0475052	+	0.664210i	−0.964293	+	0.264836i	$0.914682\pi$
$674$		0			0
$675$	52.8445	+	48.7440i	2.03399	+	1.87616i
$676$		0			0
$677$	−29.9572	+	22.4257i	−1.15135	+	0.861890i	−0.992113	−	0.125350i	$-0.959994\pi$
$677$	−29.9572	+	22.4257i	−1.15135	+	0.861890i	−0.159238	+	0.987240i	$0.550904\pi$
$678$		0			0
$679$	44.7324	+	20.4286i	1.71667	+	0.783978i
$680$		0			0
$681$	9.80972	+	15.2642i	0.375909	+	0.584926i
$682$		0			0
$683$	−18.8420	+	25.1699i	−0.720968	+	0.963100i	0.279028	+	0.960283i	$0.409988\pi$
$683$	−18.8420	+	25.1699i	−0.720968	+	0.963100i	−0.999996	+	0.00281712i	$0.999103\pi$
$684$		0			0
$685$	−0.631748	+	1.46060i	−0.0241379	+	0.0558068i
$686$		0			0
$687$	−53.9955	−	29.4838i	−2.06006	−	1.12488i
$688$		0			0
$689$	22.9623			0.874792
$690$		0			0
$691$	28.8391			1.09709			0.548546	−	0.836120i	$-0.315182\pi$
$691$	28.8391			1.09709			0.548546	+	0.836120i	$0.315182\pi$
$692$		0			0
$693$	62.7991	+	34.2909i	2.38554	+	1.30260i
$694$		0			0
$695$	14.3766	−	5.69507i	0.545334	−	0.216026i
$696$		0			0
$697$	8.19058	−	10.9413i	0.310240	−	0.414432i
$698$		0			0
$699$	25.2557	+	39.2986i	0.955257	+	1.48641i
$700$		0			0
$701$	8.28667	+	3.78439i	0.312983	+	0.142935i	0.565713	−	0.824602i	$-0.308601\pi$
$701$	8.28667	+	3.78439i	0.312983	+	0.142935i	−0.252730	+	0.967537i	$0.581328\pi$
$702$		0			0
$703$	−27.0464	+	20.2467i	−1.02008	+	0.763619i
$704$		0			0
$705$	−11.9426	−	15.3001i	−0.449783	−	0.576236i
$706$		0			0
$707$	−1.81792	+	25.4179i	−0.0683699	+	0.955937i
$708$		0			0
$709$	14.7992	−	17.0792i	0.555795	−	0.641422i	−0.406428	−	0.913683i	$-0.633226\pi$
$709$	14.7992	−	17.0792i	0.555795	−	0.641422i	0.962223	+	0.272261i	$0.0877714\pi$
$710$		0			0
$711$	−62.6623	+	28.6169i	−2.35002	+	1.07322i
$712$		0			0
$713$	−20.3341	−	29.7159i	−0.761517	−	1.11287i
$714$		0			0
$715$	14.1254	+	21.0343i	0.528260	+	0.786637i
$716$		0			0
$717$	−2.96727	−	41.4879i	−0.110815	−	1.54939i
$718$		0			0
$719$	31.2180	−	27.0506i	1.16424	−	1.00882i	0.164487	−	0.986379i	$-0.447403\pi$
$719$	31.2180	−	27.0506i	1.16424	−	1.00882i	0.999748	−	0.0224362i	$-0.00714225\pi$
$720$		0			0
$721$	−61.9693	−	18.1958i	−2.30786	−	0.677648i
$722$		0			0
$723$	6.21514	+	8.30246i	0.231144	+	0.308772i
$724$		0			0
$725$	−2.70738	+	26.3320i	−0.100550	+	0.977948i
$726$		0			0
$727$	8.78260	+	1.91054i	0.325728	+	0.0708579i	0.372456	−	0.928050i	$-0.378516\pi$
$727$	8.78260	+	1.91054i	0.325728	+	0.0708579i	−0.0467277	+	0.998908i	$0.514879\pi$
$728$		0			0
$729$	−39.9004	+	5.73681i	−1.47779	+	0.212474i
$730$		0			0
$731$	3.81842	+	2.45395i	0.141229	+	0.0907627i
$732$		0			0
$733$	−13.5982	+	24.9032i	−0.502260	+	0.919820i	0.496401	+	0.868093i	$0.334654\pi$
$733$	−13.5982	+	24.9032i	−0.502260	+	0.919820i	−0.998661	+	0.0517271i	$0.983527\pi$
$734$		0			0
$735$	−74.5701	+	12.2615i	−2.75056	+	0.452272i
$736$		0			0
$737$	−4.01024	+	4.01024i	−0.147719	+	0.147719i
$738$		0			0
$739$	−14.1334	−	48.1338i	−0.519904	−	1.77063i	−0.629876	−	0.776696i	$-0.716894\pi$
$739$	−14.1334	−	48.1338i	−0.519904	−	1.77063i	0.109972	−	0.993935i	$-0.464924\pi$
$740$		0			0
$741$	47.6908	−	74.2084i	1.75197	−	2.72611i
$742$		0			0
$743$	11.1238	+	8.32714i	0.408091	+	0.305493i	0.783530	−	0.621354i	$-0.213417\pi$
$743$	11.1238	+	8.32714i	0.408091	+	0.305493i	−0.375439	+	0.926847i	$0.622508\pi$
$744$		0			0
$745$	−18.7041	−	0.959021i	−0.685264	−	0.0351358i
$746$		0			0
$747$	32.0296	−	11.9464i	1.17190	−	0.437096i
$748$		0			0
$749$	23.5595	+	3.38735i	0.860845	+	0.123771i
$750$		0			0
$751$	6.66147	−	22.6869i	0.243080	−	0.827856i	−0.744076	−	0.668096i	$-0.767110\pi$
$751$	6.66147	−	22.6869i	0.243080	−	0.827856i	0.987156	−	0.159760i	$-0.0510721\pi$
$752$		0			0
$753$	−9.14859	−	0.654320i	−0.333393	−	0.0238447i
$754$		0			0
$755$	−9.01714	+	2.15292i	−0.328167	+	0.0783527i
$756$		0			0
$757$	1.42978	−	3.83338i	0.0519661	−	0.139327i	−0.908373	−	0.418160i	$-0.862675\pi$
$757$	1.42978	−	3.83338i	0.0519661	−	0.139327i	0.960339	+	0.278834i	$0.0899478\pi$
$758$		0			0
$759$	−1.51439	+	35.6113i	−0.0549689	+	1.29261i
$760$		0			0
$761$	−15.7521	−	34.4922i	−0.571012	−	1.25034i	−0.946257	−	0.323417i	$-0.895168\pi$
$761$	−15.7521	−	34.4922i	−0.571012	−	1.25034i	0.375244	−	0.926926i	$-0.377559\pi$
$762$		0			0
$763$	−57.2638	+	4.09559i	−2.07309	+	0.148270i
$764$		0			0
$765$	54.9626	+	45.7173i	1.98718	+	1.65291i
$766$		0			0
$767$	35.9873	−	19.6506i	1.29943	−	0.709541i
$768$		0			0
$769$	−0.722968	+	5.02835i	−0.0260709	+	0.181327i	−0.998696	−	0.0510530i	$-0.983742\pi$
$769$	−0.722968	+	5.02835i	−0.0260709	+	0.181327i	0.972625	+	0.232380i	$0.0746513\pi$
$770$		0			0
$771$	14.0781	−	30.8267i	0.507009	−	1.11020i
$772$		0			0
$773$	−2.32974	+	10.7096i	−0.0837950	+	0.385199i	−0.999875	−	0.0157957i	$-0.994972\pi$
$773$	−2.32974	+	10.7096i	−0.0837950	+	0.385199i	0.916080	+	0.400995i	$0.131336\pi$
$774$		0			0
$775$	33.4908	−	16.9592i	1.20303	−	0.609193i
$776$		0			0
$777$	−80.5099	+	17.5138i	−2.88828	+	0.628306i
$778$		0			0
$779$	16.9178	−	4.96752i	0.606144	−	0.177980i
$780$		0			0
$781$		−	3.69620i		−	0.132260i
$782$		0			0
$783$	−53.8265	−	53.8265i	−1.92360	−	1.92360i
$784$		0			0
$785$	7.03067	+	14.6079i	0.250936	+	0.521378i
$786$		0			0
$787$	5.38497	+	24.7543i	0.191953	+	0.882396i	0.967848	+	0.251534i	$0.0809350\pi$
$787$	5.38497	+	24.7543i	0.191953	+	0.882396i	−0.775895	+	0.630862i	$0.782701\pi$
$788$		0			0
$789$	3.22925	+	22.4600i	0.114964	+	0.799596i
$790$		0			0
$791$	53.3673	−	34.2971i	1.89752	−	1.21946i
$792$		0			0
$793$	23.6345	+	63.3665i	0.839286	+	2.25021i
$794$		0			0
$795$	−23.3287	+	24.2893i	−0.827383	+	0.861454i
$796$		0			0
$797$	9.97904	+	18.2752i	0.353476	+	0.647342i	0.992555	−	0.121799i	$-0.0388662\pi$
$797$	9.97904	+	18.2752i	0.353476	+	0.647342i	−0.639079	+	0.769141i	$0.720684\pi$
$798$		0			0
$799$	−7.54851	−	8.71145i	−0.267047	−	0.308189i
$800$		0			0
$801$	−30.4160	−	26.3556i	−1.07470	−	0.931230i
$802$		0			0
$803$	−15.2334	−	5.68178i	−0.537577	−	0.200506i
$804$		0			0
$805$	−26.0425	−	36.4580i	−0.917879	−	1.28497i
$806$		0			0
$807$	86.5680	+	32.2882i	3.04734	+	1.13660i
$808$		0			0
$809$	4.58736	+	3.97497i	0.161283	+	0.139753i	0.731764	−	0.681559i	$-0.238698\pi$
$809$	4.58736	+	3.97497i	0.161283	+	0.139753i	−0.570480	+	0.821311i	$0.693243\pi$
$810$		0			0
$811$	−33.2168	−	38.3343i	−1.16640	−	1.34610i	−0.926948	−	0.375190i	$-0.877577\pi$
$811$	−33.2168	−	38.3343i	−1.16640	−	1.34610i	−0.239453	−	0.970908i	$-0.576968\pi$
$812$		0			0
$813$	32.3354	+	59.2179i	1.13405	+	2.07686i
$814$		0			0
$815$	28.7360	−	0.579721i	1.00658	−	0.0203067i
$816$		0			0
$817$	2.04633	+	5.48642i	0.0715920	+	0.191946i
$818$		0			0
$819$	129.011	−	82.9104i	4.50801	−	2.89712i
$820$		0			0
$821$	1.76169	+	12.2528i	0.0614835	+	0.427627i	0.997194	+	0.0748585i	$0.0238505\pi$
$821$	1.76169	+	12.2528i	0.0614835	+	0.427627i	−0.935711	+	0.352768i	$0.885240\pi$
$822$		0			0
$823$	−2.93089	−	13.4731i	−0.102164	−	0.469642i	−0.999594	−	0.0284846i	$-0.990932\pi$
$823$	−2.93089	−	13.4731i	−0.102164	−	0.469642i	0.897430	−	0.441157i	$-0.145432\pi$
$824$		0			0
$825$	−36.6007	−	6.42819i	−1.27427	−	0.223801i
$826$		0			0
$827$	7.11232	+	7.11232i	0.247320	+	0.247320i	0.819870	−	0.572550i	$-0.194046\pi$
$827$	7.11232	+	7.11232i	0.247320	+	0.247320i	−0.572550	+	0.819870i	$0.694046\pi$
$828$		0			0
$829$			42.7316i			1.48413i	0.670329	+	0.742064i	$0.266153\pi$
$829$			42.7316i			1.48413i	−0.670329	+	0.742064i	$0.733847\pi$
$830$		0			0
$831$	−13.8030	+	4.05292i	−0.478820	+	0.140594i
$832$		0			0
$833$	−43.8552	+	9.54012i	−1.51949	+	0.330545i
$834$		0			0
$835$	10.6314	+	33.6787i	0.367913	+	1.16550i
$836$		0			0
$837$	−22.9472	+	105.487i	−0.793171	+	3.64615i
$838$		0			0
$839$	14.6209	−	32.0152i	0.504769	−	1.10529i	−0.470121	−	0.882602i	$-0.655790\pi$
$839$	14.6209	−	32.0152i	0.504769	−	1.10529i	0.974890	−	0.222687i	$-0.0714828\pi$
$840$		0			0
$841$	−0.138294	+	0.961854i	−0.00476875	+	0.0331674i
$842$		0			0
$843$	60.2782	−	32.9144i	2.07609	−	1.13363i
$844$		0			0
$845$	25.1303	−	2.30766i	0.864508	−	0.0793860i
$846$		0			0
$847$	23.8091	−	1.70286i	0.818090	−	0.0585109i
$848$		0			0
$849$	13.5375	+	29.6429i	0.464605	+	1.01734i
$850$		0			0
$851$	−18.2039	−	22.9068i	−0.624023	−	0.785234i
$852$		0			0
$853$	17.0537	−	45.7228i	0.583909	−	1.56552i	−0.222985	−	0.974822i	$-0.571580\pi$
$853$	17.0537	−	45.7228i	0.583909	−	1.56552i	0.806893	−	0.590698i	$-0.201147\pi$
$854$		0			0
$855$	21.4184	+	89.7074i	0.732495	+	3.06793i
$856$		0			0
$857$	−25.6752	−	1.83633i	−0.877049	−	0.0627278i	−0.374450	−	0.927247i	$-0.622168\pi$
$857$	−25.6752	−	1.83633i	−0.877049	−	0.0627278i	−0.502600	+	0.864519i	$0.667623\pi$
$858$		0			0
$859$	−13.3715	+	45.5390i	−0.456228	+	1.55377i	0.334980	+	0.942225i	$0.391270\pi$
$859$	−13.3715	+	45.5390i	−0.456228	+	1.55377i	−0.791209	+	0.611546i	$0.790548\pi$
$860$		0			0
$861$	42.5620	+	6.11950i	1.45051	+	0.208552i
$862$		0			0
$863$	−0.0886542	+	0.0330663i	−0.00301782	+	0.00112559i	−0.350973	−	0.936386i	$-0.614149\pi$
$863$	−0.0886542	+	0.0330663i	−0.00301782	+	0.00112559i	0.347955	+	0.937511i	$0.386876\pi$
$864$		0			0
$865$	−6.74356	−	7.47246i	−0.229288	−	0.254071i
$866$		0			0
$867$	3.68898	+	2.76154i	0.125284	+	0.0937867i
$868$		0			0
$869$	11.4971	−	17.8898i	0.390013	−	0.606871i
$870$		0			0
$871$	3.42456	+	11.6630i	0.116037	+	0.395185i
$872$		0			0
$873$	61.9910	−	61.9910i	2.09808	−	2.09808i
$874$		0			0
$875$	41.2389	−	21.9388i	1.39413	−	0.741666i
$876$		0			0
$877$	−13.2605	+	24.2848i	−0.447776	+	0.820041i	−0.999906	−	0.0137174i	$-0.995633\pi$
$877$	−13.2605	+	24.2848i	−0.447776	+	0.820041i	0.552130	+	0.833758i	$0.313815\pi$
$878$		0			0
$879$	−19.9275	−	12.8066i	−0.672136	−	0.431956i
$880$		0			0
$881$	17.6335	−	2.53531i	0.594088	−	0.0854169i	0.161288	−	0.986907i	$-0.448435\pi$
$881$	17.6335	−	2.53531i	0.594088	−	0.0854169i	0.432799	+	0.901490i	$0.357526\pi$
$882$		0			0
$883$	22.3469	+	4.86128i	0.752034	+	0.163595i	0.572214	−	0.820104i	$-0.306085\pi$
$883$	22.3469	+	4.86128i	0.752034	+	0.163595i	0.179820	+	0.983699i	$0.442448\pi$
$884$		0			0
$885$	−15.7754	+	58.0313i	−0.530283	+	1.95070i
$886$		0			0
$887$	−30.0775	−	40.1788i	−1.00990	−	1.34907i	−0.936074	−	0.351803i	$-0.885569\pi$
$887$	−30.0775	−	40.1788i	−1.00990	−	1.34907i	−0.0738299	−	0.997271i	$-0.523522\pi$
$888$		0			0
$889$	60.7199	+	17.8290i	2.03648	+	0.597964i
$890$		0			0
$891$	41.9338	−	36.3358i	1.40483	−	1.21730i
$892$		0			0
$893$	−1.06086	−	14.8327i	−0.0355002	−	0.496357i
$894$		0			0
$895$	−20.6918	−	4.06595i	−0.691651	−	0.135910i
$896$		0			0
$897$	65.4339	+	39.4278i	2.18477	+	1.31645i
$898$		0			0
$899$	−36.1566	+	16.5122i	−1.20589	+	0.550712i
$900$		0			0
$901$	−13.0978	+	15.1156i	−0.436350	+	0.503575i
$902$		0			0
$903$	−1.01874	+	14.2439i	−0.0339016	+	0.474006i
$904$		0			0
$905$	36.0866	−	28.1675i	1.19956	−	0.936318i
$906$		0			0
$907$	−12.4912	+	9.35076i	−0.414762	+	0.310487i	−0.786202	−	0.617970i	$-0.787955\pi$
$907$	−12.4912	+	9.35076i	−0.414762	+	0.310487i	0.371439	+	0.928457i	$0.378864\pi$
$908$		0			0
$909$	41.3238	+	18.8719i	1.37062	+	0.625943i
$910$		0			0
$911$	−11.0404	−	17.1791i	−0.365783	−	0.569170i	0.608764	−	0.793351i	$-0.291666\pi$
$911$	−11.0404	−	17.1791i	−0.365783	−	0.569170i	−0.974547	+	0.224181i	$0.928029\pi$
$912$		0			0
$913$	−6.32415	+	8.44807i	−0.209299	+	0.279590i
$914$		0			0
$915$	−91.0404	−	39.3773i	−3.00970	−	1.30177i
$916$		0			0
$917$	0.0899903	+	0.0491384i	0.00297174	+	0.00162269i
$918$		0			0
$919$	22.4132			0.739343			0.369671	−	0.929163i	$-0.379470\pi$
$919$	22.4132			0.739343			0.369671	+	0.929163i	$0.379470\pi$
$920$		0			0
$921$	79.2155			2.61024
$922$		0			0
$923$	−6.95301	−	3.79663i	−0.228861	−	0.124968i
$924$		0			0
$925$	26.1621	−	15.6874i	0.860204	−	0.515797i
$926$		0			0
$927$	−69.0002	+	92.1734i	−2.26626	+	3.02737i
$928$		0			0
$929$	−11.0398	−	17.1783i	−0.362204	−	0.563600i	0.611549	−	0.791206i	$-0.290547\pi$
$929$	−11.0398	−	17.1783i	−0.362204	−	0.563600i	−0.973753	+	0.227606i	$0.926910\pi$
$930$		0			0
$931$	−52.6675	−	24.0525i	−1.72611	−	0.788287i
$932$		0			0
$933$	24.0911	−	18.0344i	0.788708	−	0.590419i
$934$		0			0
$935$	−21.9037	−	2.69956i	−0.716327	−	0.0882849i
$936$		0			0
$937$	1.15364	−	16.1300i	0.0376879	−	0.526946i	−0.943181	−	0.332278i	$-0.892183\pi$
$937$	1.15364	−	16.1300i	0.0376879	−	0.526946i	0.980869	−	0.194667i	$-0.0623627\pi$
$938$		0			0
$939$	28.6428	−	33.0555i	0.934721	−	1.07873i
$940$		0			0
$941$	−51.1471	+	23.3581i	−1.66735	+	0.761452i	−0.667488	+	0.744620i	$0.732631\pi$
$941$	−51.1471	+	23.3581i	−1.66735	+	0.761452i	−0.999858	+	0.0168314i	$0.994642\pi$
$942$		0			0
$943$	4.72363	+	14.5210i	0.153823	+	0.472870i
$944$		0			0
$945$	−25.9002	+	131.807i	−0.842532	+	4.28769i
$946$		0			0
$947$	−0.961725	−	13.4467i	−0.0312519	−	0.436958i	−0.988856	−	0.148872i	$-0.952436\pi$
$947$	−0.961725	−	13.4467i	−0.0312519	−	0.436958i	0.957605	−	0.288086i	$-0.0930189\pi$
$948$		0			0
$949$	−26.3355	+	22.8199i	−0.854888	+	0.740764i
$950$		0			0
$951$	41.9387	+	12.3143i	1.35996	+	0.399319i
$952$		0			0
$953$	30.8133	+	41.1618i	0.998142	+	1.33336i	0.942245	+	0.334925i	$0.108711\pi$
$953$	30.8133	+	41.1618i	0.998142	+	1.33336i	0.0558973	+	0.998437i	$0.482198\pi$
$954$		0			0
$955$	5.11899	+	8.94112i	0.165647	+	0.289328i
$956$		0			0
$957$	38.4481	+	8.36387i	1.24285	+	0.270365i
$958$		0			0
$959$	−2.94314	+	0.423160i	−0.0950391	+	0.0136646i
$960$		0			0
$961$	21.3427	+	13.7161i	0.688473	+	0.442455i
$962$		0			0
$963$	20.3356	−	37.2419i	0.655307	−	1.20011i
$964$		0			0
$965$	1.05105	+	6.39212i	0.0338345	+	0.205770i
$966$		0			0
$967$	−28.5701	+	28.5701i	−0.918753	+	0.918753i	−0.996939	−	0.0781856i	$-0.975087\pi$
$967$	−28.5701	+	28.5701i	−0.918753	+	0.918753i	0.0781856	+	0.996939i	$0.475087\pi$
$968$		0			0
$969$	21.6470	+	73.7228i	0.695401	+	2.36832i
$970$		0			0
$971$	15.9668	−	24.8448i	0.512399	−	0.797308i	−0.484599	−	0.874736i	$-0.661034\pi$
$971$	15.9668	−	24.8448i	0.512399	−	0.797308i	0.996998	+	0.0774281i	$0.0246708\pi$
$972$		0			0
$973$	23.1299	+	17.3148i	0.741511	+	0.555088i
$974$		0			0
$975$	−49.6875	+	62.2478i	−1.59127	+	1.99352i
$976$		0			0
$977$	56.3025	−	20.9997i	1.80128	−	0.671841i	0.804293	−	0.594233i	$-0.202544\pi$
$977$	56.3025	−	20.9997i	1.80128	−	0.671841i	0.996984	−	0.0776081i	$-0.0247283\pi$
$978$		0			0
$979$	12.2976	+	1.76813i	0.393033	+	0.0565097i
$980$		0			0
$981$	−28.8345	+	98.2013i	−0.920615	+	3.13533i
$982$		0			0
$983$	−8.62160	−	0.616629i	−0.274986	−	0.0196674i	−0.0668350	−	0.997764i	$-0.521290\pi$
$983$	−8.62160	−	0.616629i	−0.274986	−	0.0196674i	−0.208151	+	0.978097i	$0.566745\pi$
$984$		0			0
$985$	17.0962	−	27.8205i	0.544731	−	0.886434i
$986$		0			0
$987$	12.6734	−	33.9788i	0.403400	−	1.08156i
$988$		0			0
$989$	−4.69826	+	1.90876i	−0.149396	+	0.0606950i
$990$		0			0
$991$	−18.4846	−	40.4757i	−0.587184	−	1.28575i	−0.937129	−	0.348983i	$-0.886527\pi$
$991$	−18.4846	−	40.4757i	−0.587184	−	1.28575i	0.349945	−	0.936770i	$-0.386200\pi$
$992$		0			0
$993$	90.3716	−	6.46350i	2.86785	−	0.205113i
$994$		0			0
$995$	−0.559961	−	6.09794i	−0.0177520	−	0.193318i
$996$		0			0
$997$	40.7718	−	22.2631i	1.29126	−	0.705080i	0.320982	−	0.947085i	$-0.395987\pi$
$997$	40.7718	−	22.2631i	1.29126	−	0.705080i	0.970275	+	0.242006i	$0.0778053\pi$
$998$		0			0
$999$	−12.4843	+	86.8299i	−0.394984	+	2.74718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.433.2	yes	720
5.2	odd	4	inner	920.2.bv.a.617.2	yes	720
23.17	odd	22	inner	920.2.bv.a.753.2	yes	720
115.17	even	44	inner	920.2.bv.a.17.2	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.2	✓	720	115.17	even	44	inner
920.2.bv.a.433.2	yes	720	1.1	even	1	trivial
920.2.bv.a.617.2	yes	720	5.2	odd	4	inner
920.2.bv.a.753.2	yes	720	23.17	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.83699 - 1.54911i) q^{3} +(0.823524 + 2.07890i) q^{5} +(-2.50378 + 3.34466i) q^{7} +(4.02684 + 6.26588i) q^{9} +(-2.09151 - 0.955162i) q^{11} +(-3.94512 + 2.95328i) q^{13} +(0.884116 - 7.17354i) q^{15} +(0.306224 - 4.28157i) q^{17} +(3.62640 - 4.18509i) q^{19} +(12.2844 - 5.61012i) q^{21} +(3.71368 + 3.03456i) q^{23} +(-3.64362 + 3.42404i) q^{25} +(-1.02575 - 14.3418i) q^{27} +(4.00107 - 3.46695i) q^{29} +(-7.20387 - 2.11525i) q^{31} +(4.45395 + 5.94977i) q^{33} +(-9.01512 - 2.45069i) q^{35} +(-5.96155 - 1.29686i) q^{37} +(15.7673 - 2.26699i) q^{39} +(2.67857 + 1.72141i) q^{41} +(-0.506766 + 0.928072i) q^{43} +(-9.70992 + 13.5315i) q^{45} +(1.89883 - 1.89883i) q^{47} +(-2.94569 - 10.0321i) q^{49} +(-7.50139 + 11.6724i) q^{51} +(-3.73011 - 2.79232i) q^{53} +(0.263270 - 5.13463i) q^{55} +(-16.7712 + 6.25535i) q^{57} +(-8.23557 - 1.18410i) q^{59} +(3.86637 - 13.1677i) q^{61} +(-31.0395 - 2.21999i) q^{63} +(-9.38847 - 5.76940i) q^{65} +(0.861972 - 2.31104i) q^{67} +(-5.83481 - 14.3619i) q^{69} +(0.667794 + 1.46227i) q^{71} +(7.05309 - 0.504447i) q^{73} +(15.6411 - 4.06960i) q^{75} +(8.43137 - 4.60388i) q^{77} +(-1.31624 + 9.15465i) q^{79} +(-10.0247 + 21.9511i) q^{81} +(0.975600 - 4.48476i) q^{83} +(9.15312 - 2.88937i) q^{85} +(-16.7217 + 3.63758i) q^{87} +(-5.18455 + 1.52232i) q^{89} -20.5895i q^{91} +(17.1606 + 17.1606i) q^{93} +(11.6868 + 4.09239i) q^{95} +(-2.50196 - 11.5013i) q^{97} +(-2.43725 - 16.9514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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