LMFDB - Embedded newform 920.2.bv.a.17.2

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			17.2
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.2

$q$-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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	−0.646631	+	0.762803i	$0.723823\pi$
$3$	−2.83699	+	1.54911i	−1.63794	+	0.894381i	−0.991306	+	0.131579i	$0.957995\pi$
$4$		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	−0.964434	−	0.264325i	$-0.914851\pi$
$7$	−2.50378	−	3.34466i	−0.946339	−	1.26416i	0.0180943	−	0.999836i	$-0.494240\pi$
$8$		0			0
$9$	4.02684	−	6.26588i	1.34228	−	2.08863i
$10$		0			0
$11$	−2.09151	+	0.955162i	−0.630615	+	0.287992i	−0.704967	−	0.709240i	$-0.749038\pi$
$11$	−2.09151	+	0.955162i	−0.630615	+	0.287992i	0.0743525	+	0.997232i	$0.476311\pi$
$12$		0			0
$13$	−3.94512	−	2.95328i	−1.09418	−	0.819093i	−0.109591	−	0.993977i	$-0.534954\pi$
$13$	−3.94512	−	2.95328i	−1.09418	−	0.819093i	−0.984589	+	0.174883i	$0.944045\pi$
$14$		0			0
$15$	0.884116	+	7.17354i	0.228278	+	1.85220i
$16$		0			0
$17$	0.306224	+	4.28157i	0.0742702	+	1.03843i	0.888795	+	0.458305i	$0.151543\pi$
$17$	0.306224	+	4.28157i	0.0742702	+	1.03843i	−0.814525	+	0.580128i	$0.803002\pi$
$18$		0			0
$19$	3.62640	+	4.18509i	0.831953	+	0.960125i	0.999669	−	0.0257099i	$-0.00818461\pi$
$19$	3.62640	+	4.18509i	0.831953	+	0.960125i	−0.167716	+	0.985835i	$0.553639\pi$
$20$		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	0.941774	−	0.336246i	$-0.109157\pi$
$29$	4.00107	+	3.46695i	0.742980	+	0.643796i	−0.198795	+	0.980041i	$0.563703\pi$
$30$		0			0
$31$	−7.20387	+	2.11525i	−1.29385	+	0.379910i	−0.854990	−	0.518644i	$-0.826437\pi$
$31$	−7.20387	+	2.11525i	−1.29385	+	0.379910i	−0.438864	+	0.898554i	$0.644619\pi$
$32$		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	−0.673939	−	0.738787i	$-0.735399\pi$
$37$	−5.96155	+	1.29686i	−0.980073	+	0.213202i	−0.306133	+	0.951989i	$0.599035\pi$
$38$		0			0
$39$	15.7673	+	2.26699i	2.52478	+	0.363009i
$40$		0			0
$41$	2.67857	−	1.72141i	0.418322	−	0.268839i	−0.314503	−	0.949256i	$-0.601838\pi$
$41$	2.67857	−	1.72141i	0.418322	−	0.268839i	0.732825	+	0.680417i	$0.238201\pi$
$42$		0			0
$43$	−0.506766	−	0.928072i	−0.0772811	−	0.141530i	0.836181	−	0.548454i	$-0.184783\pi$
$43$	−0.506766	−	0.928072i	−0.0772811	−	0.141530i	−0.913462	+	0.406924i	$0.866601\pi$
$44$		0			0
$45$	−9.70992	−	13.5315i	−1.44747	−	2.01715i
$46$		0			0
$47$	1.89883	+	1.89883i	0.276973	+	0.276973i	0.831899	−	0.554926i	$-0.187254\pi$
$47$	1.89883	+	1.89883i	0.276973	+	0.276973i	−0.554926	+	0.831899i	$0.687254\pi$
$48$		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	−0.823948	−	0.566665i	$-0.808233\pi$
$53$	−3.73011	+	2.79232i	−0.512369	+	0.383555i	0.311579	+	0.950220i	$0.399142\pi$
$54$		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	−0.655725	−	0.755000i	$-0.727637\pi$
$59$	−8.23557	+	1.18410i	−1.07218	+	0.154156i	−0.416455	+	0.909156i	$0.636728\pi$
$60$		0			0
$61$	3.86637	+	13.1677i	0.495038	+	1.68595i	0.705802	+	0.708409i	$0.250587\pi$
$61$	3.86637	+	13.1677i	0.495038	+	1.68595i	−0.210764	+	0.977537i	$0.567595\pi$
$62$		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	0.978907	−	0.204306i	$-0.0654937\pi$
$67$	0.861972	+	2.31104i	0.105307	+	0.282338i	−0.873601	+	0.486644i	$0.838221\pi$
$68$		0			0
$69$	−5.83481	+	14.3619i	−0.702429	+	1.72897i
$70$		0			0
$71$	0.667794	−	1.46227i	0.0792526	−	0.173539i	−0.865858	−	0.500290i	$-0.833227\pi$
$71$	0.667794	−	1.46227i	0.0792526	−	0.173539i	0.945110	+	0.326751i	$0.105954\pi$
$72$		0			0
$73$	7.05309	+	0.504447i	0.825502	+	0.0590410i	0.477696	−	0.878525i	$-0.341472\pi$
$73$	7.05309	+	0.504447i	0.825502	+	0.0590410i	0.347806	+	0.937566i	$0.386927\pi$
$74$		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	−0.919344	−	0.393454i	$-0.871280\pi$
$79$	−1.31624	−	9.15465i	−0.148089	−	1.02998i	0.771256	−	0.636525i	$-0.219629\pi$
$80$		0			0
$81$	−10.0247	−	21.9511i	−1.11386	−	2.43902i
$82$		0			0
$83$	0.975600	+	4.48476i	0.107086	+	0.492266i	0.999183	+	0.0404218i	$0.0128702\pi$
$83$	0.975600	+	4.48476i	0.107086	+	0.492266i	−0.892097	+	0.451844i	$0.850766\pi$
$84$		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	−0.00484811	−	0.999988i	$-0.501543\pi$
$89$	−5.18455	−	1.52232i	−0.549561	−	0.161366i	−0.544713	+	0.838623i	$0.683361\pi$
$90$		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	0.656491	+	0.754334i	$0.272040\pi$
$97$	−2.50196	+	11.5013i	−0.254036	+	1.16778i	−0.910527	+	0.413450i	$0.864324\pi$
$98$		0			0
$99$	−2.43725	+	16.9514i	−0.244953	+	1.70368i
$100$		0			0
$101$	5.13105	+	3.29752i	0.510558	+	0.328116i	0.770427	−	0.637528i	$-0.220043\pi$
$101$	5.13105	+	3.29752i	0.510558	+	0.328116i	−0.259869	+	0.965644i	$0.583679\pi$
$102$		0			0
$103$	5.40218	−	14.4838i	0.532293	−	1.42713i	−0.341058	−	0.940042i	$-0.610785\pi$
$103$	5.40218	−	14.4838i	0.532293	−	1.42713i	0.873351	−	0.487091i	$-0.161942\pi$
$104$		0			0
$105$	21.7794	−	20.9180i	2.12545	−	2.04139i
$106$		0			0
$107$	−2.73025	+	5.00008i	−0.263943	+	0.483376i	−0.975718	−	0.219032i	$-0.929710\pi$
$107$	−2.73025	+	5.00008i	−0.263943	+	0.483376i	0.711774	+	0.702408i	$0.247892\pi$
$108$		0			0
$109$	8.99848	−	10.3848i	0.861898	−	0.994683i	−0.138093	−	0.990419i	$-0.544097\pi$
$109$	8.99848	−	10.3848i	0.861898	−	0.994683i	0.999991	−	0.00426394i	$-0.00135726\pi$
$110$		0			0
$111$	14.9039	−	12.9143i	1.41461	−	1.22577i
$112$		0			0
$113$	−14.2265	+	5.30620i	−1.33831	+	0.499165i	−0.913766	−	0.406240i	$-0.866840\pi$
$113$	−14.2265	+	5.30620i	−1.33831	+	0.499165i	−0.424548	+	0.905406i	$0.639567\pi$
$114$		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	0.458982	+	0.888446i	$0.348214\pi$
$127$	−5.29327	+	14.1918i	−0.469702	+	1.25932i	−0.928684	+	0.370873i	$0.879059\pi$
$128$		0			0
$129$	2.87538	+	1.84789i	0.253163	+	0.162698i
$130$		0			0
$131$	−0.00349255	+	0.0242912i	−0.000305145	+	0.00212233i	−0.989973	−	0.141254i	$-0.954887\pi$
$131$	−0.00349255	+	0.0242912i	−0.000305145	+	0.00212233i	0.989668	+	0.143376i	$0.0457958\pi$
$132$		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	−0.685283	−	0.728277i	$-0.740321\pi$
$137$	0.503236	−	0.503236i	0.0429944	−	0.0429944i	0.728277	+	0.685283i	$0.240321\pi$
$138$		0			0
$139$			6.91548i			0.586564i	0.956026	+	0.293282i	$0.0947474\pi$
$139$			6.91548i			0.586564i	−0.956026	+	0.293282i	$0.905253\pi$
$140$		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	0.711901	−	0.702280i	$-0.247835\pi$
$149$	−3.47939	−	7.61881i	−0.285043	−	0.624157i	−0.996944	+	0.0781229i	$0.975107\pi$
$150$		0			0
$151$	−0.590028	−	4.10373i	−0.0480158	−	0.333957i	−0.999643	−	0.0267033i	$-0.991499\pi$
$151$	−0.590028	−	4.10373i	−0.0480158	−	0.333957i	0.951628	−	0.307254i	$-0.0994100\pi$
$152$		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	0.356862	−	0.934157i	$-0.383847\pi$
$157$	7.23164	+	0.517217i	0.577148	+	0.0412784i	0.220286	+	0.975435i	$0.429301\pi$
$158$		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	0.985497	+	0.169694i	$0.0542781\pi$
$163$	4.49192	+	12.0433i	0.351834	+	0.943304i	−0.633663	+	0.773610i	$0.718449\pi$
$164$		0			0
$165$	−8.70103	−	14.1591i	−0.677374	−	1.10228i
$166$		0			0
$167$	15.7539	−	1.12674i	1.21907	−	0.0871900i	0.553068	−	0.833136i	$-0.313457\pi$
$167$	15.7539	−	1.12674i	1.21907	−	0.0871900i	0.666007	+	0.745946i	$0.268002\pi$
$168$		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	0.183981	−	0.982930i	$-0.441101\pi$
$173$	−4.21759	−	1.57308i	−0.320657	−	0.119599i	−0.504639	+	0.863331i	$0.668374\pi$
$174$		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	0.596731	−	0.802441i	$-0.296466\pi$
$179$	−5.09858	−	7.93355i	−0.381086	−	0.592981i	−0.977817	+	0.209460i	$0.932829\pi$
$180$		0			0
$181$	−5.76781	+	19.6434i	−0.428718	+	1.46008i	0.408272	+	0.912861i	$0.366132\pi$
$181$	−5.76781	+	19.6434i	−0.428718	+	1.46008i	−0.836990	+	0.547219i	$0.815687\pi$
$182$		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	0.305322	−	0.952249i	$-0.401236\pi$
$191$	4.56066	+	0.655723i	0.329997	+	0.0474465i	0.0246751	+	0.999696i	$0.492145\pi$
$192$		0			0
$193$	2.83082	−	0.615808i	0.203767	−	0.0443268i	−0.109523	−	0.993984i	$-0.534932\pi$
$193$	2.83082	−	0.615808i	0.203767	−	0.0443268i	0.313290	+	0.949657i	$0.398569\pi$
$194$		0			0
$195$	17.6975	−	30.9115i	1.26735	−	2.21362i
$196$		0			0
$197$	−8.75134	+	11.6904i	−0.623507	+	0.832908i	−0.995444	−	0.0953500i	$-0.969603\pi$
$197$	−8.75134	+	11.6904i	−0.623507	+	0.832908i	0.371937	+	0.928258i	$0.378694\pi$
$198$		0			0
$199$	−2.62762	+	0.771540i	−0.186267	+	0.0546930i	−0.373536	−	0.927616i	$-0.621855\pi$
$199$	−2.62762	+	0.771540i	−0.186267	+	0.0546930i	0.187269	+	0.982309i	$0.440037\pi$
$200$		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	0.949958	−	0.312378i	$-0.101125\pi$
$211$	7.34378	+	8.47517i	0.505567	+	0.583455i	−0.444391	+	0.895833i	$0.646580\pi$
$212$		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	0.990548	−	0.137169i	$-0.0438003\pi$
$223$	8.65924	+	11.5674i	0.579866	+	0.774610i	−0.410682	+	0.911779i	$0.634709\pi$
$224$		0			0
$225$	−36.1269	+	9.04240i	−2.40846	+	0.602826i
$226$		0			0
$227$	−4.92676	+	2.69021i	−0.327000	+	0.178556i	−0.634360	−	0.773038i	$-0.718736\pi$
$227$	−4.92676	+	2.69021i	−0.327000	+	0.178556i	0.307360	+	0.951593i	$0.400555\pi$
$228$		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	−0.837633	−	0.546234i	$-0.816061\pi$
$233$	−12.6842	+	6.92611i	−0.830971	+	0.453744i	0.00666235	+	0.999978i	$0.497879\pi$
$234$		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	−0.539936	−	0.841706i	$-0.681552\pi$
$239$	6.95690	−	10.8251i	0.450004	−	0.700221i	0.989940	+	0.141486i	$0.0451879\pi$
$240$		0			0
$241$	−2.91855	+	1.33286i	−0.188000	+	0.0858568i	−0.507191	−	0.861834i	$-0.669316\pi$
$241$	−2.91855	+	1.33286i	−0.188000	+	0.0858568i	0.319191	+	0.947690i	$0.396589\pi$
$242$		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	0.495205	−	0.868776i	$-0.335093\pi$
$251$	2.58110	+	1.17875i	0.162918	+	0.0744021i	−0.332287	+	0.943178i	$0.607820\pi$
$252$		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	−0.919290	−	0.393580i	$-0.871236\pi$
$257$	0.747940	−	10.4576i	0.0466552	−	0.652325i	0.965946	−	0.258745i	$-0.0833090\pi$
$258$		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	−0.911270	−	0.411810i	$-0.864897\pi$
$263$	−4.20686	+	5.61971i	−0.259406	+	0.346526i	0.651864	+	0.758336i	$0.273987\pi$
$264$		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	−0.792703	−	0.609608i	$-0.791327\pi$
$269$	−28.2928	−	4.06789i	−1.72504	−	0.248024i	−0.932339	+	0.361584i	$0.882236\pi$
$270$		0			0
$271$	−17.5599	+	11.2851i	−1.06669	+	0.685518i	−0.951445	−	0.307819i	$-0.900401\pi$
$271$	−17.5599	+	11.2851i	−1.06669	+	0.685518i	−0.115242	+	0.993337i	$0.536764\pi$
$272$		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	0.795300	−	0.606216i	$-0.207313\pi$
$277$	3.14698	+	3.14698i	0.189084	+	0.189084i	−0.606216	+	0.795300i	$0.707313\pi$
$278$		0			0
$279$	−15.7549	+	53.6564i	−0.943223	+	3.21232i
$280$		0			0
$281$	−11.4871	−	17.8743i	−0.685265	−	1.06629i	−0.993372	−	0.114941i	$-0.963332\pi$
$281$	−11.4871	−	17.8743i	−0.685265	−	1.06629i	0.308108	−	0.951351i	$-0.400304\pi$
$282$		0			0
$283$	−8.07081	+	6.04173i	−0.479760	+	0.359144i	−0.811621	−	0.584185i	$-0.801414\pi$
$283$	−8.07081	+	6.04173i	−0.479760	+	0.359144i	0.331861	+	0.943328i	$0.392324\pi$
$284$		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	0.143831	−	0.989602i	$-0.454058\pi$
$293$	7.30962	−	0.522794i	0.427033	−	0.0305420i	0.283202	+	0.959060i	$0.408603\pi$
$294$		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	−0.271236	−	0.962513i	$-0.587432\pi$
$307$	−21.5092	−	11.7449i	−1.22759	−	0.670317i	−0.956358	+	0.292196i	$0.905614\pi$
$308$		0			0
$309$	7.11114	+	49.4590i	0.404538	+	2.81363i
$310$		0			0
$311$	−3.86753	−	8.46870i	−0.219307	−	0.480216i	0.767717	−	0.640790i	$-0.221393\pi$
$311$	−3.86753	−	8.46870i	−0.219307	−	0.480216i	−0.987024	+	0.160574i	$0.948666\pi$
$312$		0			0
$313$	−2.87631	−	13.2222i	−0.162579	−	0.747363i	−0.984162	−	0.177274i	$-0.943272\pi$
$313$	−2.87631	−	13.2222i	−0.162579	−	0.747363i	0.821583	−	0.570089i	$-0.193091\pi$
$314$		0			0
$315$	−20.9467	+	66.3562i	−1.18021	+	3.73875i
$316$		0			0
$317$	−13.2133	−	2.87438i	−0.742133	−	0.161441i	−0.174424	−	0.984671i	$-0.555806\pi$
$317$	−13.2133	−	2.87438i	−0.742133	−	0.161441i	−0.567709	+	0.823230i	$0.692170\pi$
$318$		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	−0.303297	−	0.952896i	$-0.598087\pi$
$331$	−23.5800	−	15.1540i	−1.29608	−	0.832938i	−0.992779	+	0.119959i	$0.961724\pi$
$332$		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	0.485007	+	0.874511i	$0.338817\pi$
$337$	−9.41546	+	17.2431i	−0.512893	+	0.939293i	−0.997899	+	0.0647826i	$0.979365\pi$
$338$		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	0.236075	−	0.971735i	$-0.424139\pi$
$347$	19.5750	−	7.30108i	1.05084	−	0.391943i	0.814764	+	0.579792i	$0.196866\pi$
$348$		0			0
$349$	−12.6493	+	10.9607i	−0.677100	+	0.586711i	−0.924029	−	0.382323i	$-0.875124\pi$
$349$	−12.6493	+	10.9607i	−0.677100	+	0.586711i	0.246928	+	0.969034i	$0.420579\pi$
$350$		0			0
$351$	46.4022	−	53.5510i	2.47677	−	2.85834i
$352$		0			0
$353$	6.47038	−	11.8496i	0.344383	−	0.630691i	−0.646880	−	0.762592i	$-0.723926\pi$
$353$	6.47038	−	11.8496i	0.344383	−	0.630691i	0.991263	+	0.131901i	$0.0421082\pi$
$354$		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	−0.0964707	−	0.995336i	$-0.530755\pi$
$359$	−19.7419	−	12.6873i	−1.04194	−	0.669611i	−0.945465	+	0.325725i	$0.894392\pi$
$360$		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	−0.856936	−	0.515422i	$-0.827635\pi$
$367$	−6.54247	+	6.54247i	−0.341514	+	0.341514i	0.515422	+	0.856936i	$0.327635\pi$
$368$		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	0.346770	−	0.937950i	$-0.387279\pi$
$373$	5.26408	+	1.14513i	0.272564	+	0.0592926i	−0.0742059	+	0.997243i	$0.523642\pi$
$374$		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	−0.886027	−	0.463633i	$-0.846546\pi$
$379$	−12.7747	−	27.9727i	−0.656193	−	1.43686i	0.229834	−	0.973230i	$-0.426182\pi$
$380$		0			0
$381$	−6.96776	−	48.4619i	−0.356969	−	2.48278i
$382$		0			0
$383$	1.26972	+	0.693322i	0.0648799	+	0.0354271i	0.511361	−	0.859366i	$-0.329141\pi$
$383$	1.26972	+	0.693322i	0.0648799	+	0.0354271i	−0.446482	+	0.894793i	$0.647323\pi$
$384$		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	−0.0180581	−	0.999837i	$-0.505748\pi$
$389$	14.7804	−	32.3645i	0.749394	−	1.64094i	0.767452	−	0.641107i	$-0.221524\pi$
$390$		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	−0.348673	−	0.937244i	$-0.613368\pi$
$397$	−11.1662	+	0.798620i	−0.560414	+	0.0400816i	−0.211741	+	0.977326i	$0.567913\pi$
$398$		0			0
$399$	21.0695	+	71.7561i	1.05479	+	3.59230i
$400$		0			0
$401$	2.59697	−	0.373389i	0.129687	−	0.0186461i	−0.0771658	−	0.997018i	$-0.524587\pi$
$401$	2.59697	−	0.373389i	0.129687	−	0.0186461i	0.206852	+	0.978372i	$0.433678\pi$
$402$		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	0.767957	+	0.640502i	$0.221274\pi$
$409$	20.8619	+	32.4618i	1.03156	+	1.60513i	0.263600	+	0.964632i	$0.415090\pi$
$410$		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	−0.476334	−	0.879265i	$-0.658035\pi$
$419$	2.57092	−	1.65223i	0.125598	−	0.0807167i	0.601931	+	0.798548i	$0.294398\pi$
$420$		0			0
$421$	−3.89707	−	0.560315i	−0.189932	−	0.0273081i	0.0466924	−	0.998909i	$-0.485132\pi$
$421$	−3.89707	−	0.560315i	−0.189932	−	0.0273081i	−0.236624	+	0.971601i	$0.576041\pi$
$422$		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	0.682090	−	0.731268i	$-0.261071\pi$
$431$	1.14882	+	0.995462i	0.0553369	+	0.0479497i	−0.626753	+	0.779218i	$0.715617\pi$
$432$		0			0
$433$	−1.13985	+	15.9372i	−0.0547777	+	0.765893i	0.893623	+	0.448818i	$0.148155\pi$
$433$	−1.13985	+	15.9372i	−0.0547777	+	0.765893i	−0.948401	+	0.317074i	$0.897300\pi$
$434$		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	0.0600948	−	0.998193i	$-0.480860\pi$
$439$	−13.7224	−	6.26682i	−0.654935	−	0.299099i	−0.715030	+	0.699094i	$0.753587\pi$
$440$		0			0
$441$	50.9982	+	58.8550i	2.42848	+	2.80262i
$442$		0			0
$443$	0.705750	+	9.86767i	0.0335312	+	0.468827i	0.986281	+	0.165073i	$0.0527858\pi$
$443$	0.705750	+	9.86767i	0.0335312	+	0.468827i	−0.952750	+	0.303755i	$0.901760\pi$
$444$		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	−0.805740	−	0.592270i	$-0.798232\pi$
$449$	−18.7693	+	8.57166i	−0.885779	+	0.404522i	−0.0800395	+	0.996792i	$0.525505\pi$
$450$		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	−0.670013	−	0.742349i	$-0.733712\pi$
$457$	−8.71660	+	4.75963i	−0.407745	+	0.222646i	0.262268	+	0.964995i	$0.415530\pi$
$458$		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	0.526398	−	0.850238i	$-0.323542\pi$
$463$	32.8411	−	17.9326i	1.52626	−	0.833399i	0.999858	+	0.0168394i	$0.00536041\pi$
$464$		0			0
$465$	−21.5429	−	49.8072i	−0.999027	−	2.30975i
$466$		0			0
$467$	17.3214	+	23.1387i	0.801538	+	1.07073i	0.995959	+	0.0898110i	$0.0286263\pi$
$467$	17.3214	+	23.1387i	0.801538	+	1.07073i	−0.194421	+	0.980918i	$0.562283\pi$
$468$		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	−0.977434	−	0.211241i	$-0.932250\pi$
$479$	−22.9239	−	26.4556i	−1.04742	−	1.20879i	−0.0699870	−	0.997548i	$-0.522296\pi$
$480$		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	0.580903	+	0.813973i	$0.302700\pi$
$487$	−2.42589	+	33.9184i	−0.109928	+	1.53699i	−0.690830	+	0.723017i	$0.742755\pi$
$488$		0			0
$489$	−31.4000	−	27.2082i	−1.41996	−	1.23040i
$490$		0			0
$491$	0.209759	−	0.0615907i	0.00946627	−	0.00277955i	−0.276996	−	0.960871i	$-0.589339\pi$
$491$	0.209759	−	0.0615907i	0.00946627	−	0.00277955i	0.286462	+	0.958092i	$0.407521\pi$
$492$		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	−0.676287	−	0.736638i	$-0.736412\pi$
$499$	−34.2383	−	4.92272i	−1.53271	−	0.220371i	−0.856428	+	0.516267i	$0.827321\pi$
$500$		0			0
$501$	−42.9483	+	27.6012i	−1.91879	+	1.23313i
$502$		0			0
$503$	−3.00930	−	5.51113i	−0.134178	−	0.245729i	0.801948	−	0.597394i	$-0.203797\pi$
$503$	−3.00930	−	5.51113i	−0.134178	−	0.245729i	−0.936126	+	0.351665i	$0.885616\pi$
$504$		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	0.233597	+	0.972333i	$0.424950\pi$
$509$	−11.0233	+	37.5420i	−0.488600	+	1.66402i	−0.722198	+	0.691687i	$0.756868\pi$
$510$		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	0.984655	+	0.174512i	$0.0558348\pi$
$521$	5.72139	+	19.4853i	0.250659	+	0.853666i	−0.733996	+	0.679154i	$0.762347\pi$
$522$		0			0
$523$	−4.38571	+	0.313672i	−0.191774	+	0.0137159i	−0.166896	−	0.985975i	$-0.553374\pi$
$523$	−4.38571	+	0.313672i	−0.191774	+	0.0137159i	−0.0248781	+	0.999690i	$0.507920\pi$
$524$		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	−0.989147	−	0.146932i	$-0.953060\pi$
$541$	−10.5234	−	23.0431i	−0.452437	−	0.990699i	0.536710	−	0.843767i	$-0.319667\pi$
$542$		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	−0.210405	−	0.977614i	$-0.567478\pi$
$547$	−18.8955	−	4.11046i	−0.807912	−	0.175751i	−0.597507	+	0.801864i	$0.703842\pi$
$548$		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	−0.913582	−	0.406654i	$-0.866695\pi$
$557$	2.03844	−	9.37056i	0.0863715	−	0.397043i	0.999954	+	0.00961040i	$0.00305913\pi$
$558$		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	−0.668103	−	0.744069i	$-0.732893\pi$
$563$	7.68958	−	20.6166i	0.324077	−	0.868884i	0.992180	−	0.124815i	$-0.0398339\pi$
$564$		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	0.111428	−	0.993773i	$-0.464458\pi$
$569$	25.7436	−	29.7097i	1.07923	−	1.24549i	0.967799	−	0.251722i	$-0.0809970\pi$
$570$		0			0
$571$	14.2793	−	12.3731i	0.597570	−	0.517798i	−0.302725	−	0.953078i	$-0.597896\pi$
$571$	14.2793	−	12.3731i	0.597570	−	0.517798i	0.900295	+	0.435280i	$0.143351\pi$
$572$		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	−0.305893	−	0.952066i	$-0.598955\pi$
$577$	2.07540	−	0.774082i	0.0863998	−	0.0322255i	0.392292	+	0.919841i	$0.371682\pi$
$578$		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	−0.937938	−	0.346802i	$-0.887268\pi$
$587$	−0.0480875	+	0.128928i	−0.00198478	+	0.00532141i	0.935954	+	0.352123i	$0.114540\pi$
$588$		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	−0.410607	−	0.911812i	$-0.634683\pi$
$593$	8.32032	−	38.2479i	0.341675	−	1.57065i	0.752282	−	0.658841i	$-0.228953\pi$
$594$		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	$0.294561\pi$
$599$			39.1031i			1.59771i	−0.601524	+	0.798855i	$0.705439\pi$
$600$		0			0
$601$	−25.6764	−	7.53926i	−1.04736	−	0.307533i	−0.287610	−	0.957748i	$-0.592861\pi$
$601$	−25.6764	−	7.53926i	−1.04736	−	0.307533i	−0.759751	+	0.650215i	$0.774679\pi$
$602$		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	0.764384	+	0.644761i	$0.223043\pi$
$607$	8.30081	+	38.1582i	0.336919	+	1.54879i	−0.427464	+	0.904032i	$0.640593\pi$
$608$		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	0.0516836	−	0.998664i	$-0.483541\pi$
$613$	−18.8292	−	10.2815i	−0.760503	−	0.415266i	−0.812187	+	0.583397i	$0.801723\pi$
$614$		0			0
$615$	14.7168	+	17.6929i	0.593437	+	0.713446i
$616$		0			0
$617$	−4.53845	−	0.324597i	−0.182711	−	0.0130678i	−0.0203163	−	0.999794i	$-0.506467\pi$
$617$	−4.53845	−	0.324597i	−0.182711	−	0.0130678i	−0.162395	+	0.986726i	$0.551922\pi$
$618$		0			0
$619$	−10.0698	+	22.0498i	−0.404740	+	0.886256i	0.592028	+	0.805917i	$0.298328\pi$
$619$	−10.0698	+	22.0498i	−0.404740	+	0.886256i	−0.996768	+	0.0803389i	$0.974400\pi$
$620$		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	0.312973	−	0.949762i	$-0.398675\pi$
$631$	22.1266	−	3.18133i	0.880847	−	0.126647i	0.567874	+	0.823115i	$0.307766\pi$
$632$		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	0.626553	+	0.779379i	$0.284465\pi$
$641$	−8.14988	+	27.7559i	−0.321901	+	1.09629i	−0.948454	+	0.316915i	$0.897353\pi$
$642$		0			0
$643$	18.1303	+	18.1303i	0.714991	+	0.714991i	0.967575	−	0.252584i	$-0.0812804\pi$
$643$	18.1303	+	18.1303i	0.714991	+	0.714991i	−0.252584	+	0.967575i	$0.581280\pi$
$644$		0			0
$645$	6.20952	−	4.45583i	0.244500	−	0.175448i
$646$		0			0
$647$	−5.40002	−	9.88940i	−0.212297	−	0.388792i	0.749732	−	0.661742i	$-0.230183\pi$
$647$	−5.40002	−	9.88940i	−0.212297	−	0.388792i	−0.962028	+	0.272950i	$0.912001\pi$
$648$		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	−0.853714	−	0.520742i	$-0.825655\pi$
$653$	−36.1320	+	7.86005i	−1.41396	+	0.307587i	−0.560242	+	0.828329i	$0.689292\pi$
$654$		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	−0.866826	−	0.498611i	$-0.833844\pi$
$659$	−34.0520	+	9.99856i	−1.32648	+	0.389489i	−0.459651	+	0.888100i	$0.652025\pi$
$660$		0			0
$661$	2.19716	+	1.90385i	0.0854598	+	0.0740513i	0.696543	−	0.717515i	$-0.254721\pi$
$661$	2.19716	+	1.90385i	0.0854598	+	0.0740513i	−0.611083	+	0.791566i	$0.709266\pi$
$662$		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	−0.964293	−	0.264836i	$-0.914682\pi$
$673$	−1.23239	−	17.2311i	−0.0475052	−	0.664210i	0.916788	−	0.399374i	$-0.130772\pi$
$674$		0			0
$675$	52.8445	−	48.7440i	2.03399	−	1.87616i
$676$		0			0
$677$	−29.9572	−	22.4257i	−1.15135	−	0.861890i	−0.159238	−	0.987240i	$-0.550904\pi$
$677$	−29.9572	−	22.4257i	−1.15135	−	0.861890i	−0.992113	+	0.125350i	$0.959994\pi$
$678$		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	−0.999996	−	0.00281712i	$-0.999103\pi$
$683$	−18.8420	−	25.1699i	−0.720968	−	0.963100i	0.279028	−	0.960283i	$-0.409988\pi$
$684$		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	−0.252730	−	0.967537i	$-0.581328\pi$
$701$	8.28667	−	3.78439i	0.312983	−	0.142935i	0.565713	+	0.824602i	$0.308601\pi$
$702$		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	0.962223	−	0.272261i	$-0.0877714\pi$
$709$	14.7992	+	17.0792i	0.555795	+	0.641422i	−0.406428	+	0.913683i	$0.633226\pi$
$710$		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	0.999748	+	0.0224362i	$0.00714225\pi$
$719$	31.2180	+	27.0506i	1.16424	+	1.00882i	0.164487	+	0.986379i	$0.447403\pi$
$720$		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	−0.0467277	−	0.998908i	$-0.514879\pi$
$727$	8.78260	−	1.91054i	0.325728	−	0.0708579i	0.372456	+	0.928050i	$0.378516\pi$
$728$		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	−0.998661	−	0.0517271i	$-0.983527\pi$
$733$	−13.5982	−	24.9032i	−0.502260	−	0.919820i	0.496401	−	0.868093i	$-0.334654\pi$
$734$		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	0.109972	+	0.993935i	$0.464924\pi$
$739$	−14.1334	+	48.1338i	−0.519904	+	1.77063i	−0.629876	+	0.776696i	$0.716894\pi$
$740$		0			0
$741$	47.6908	+	74.2084i	1.75197	+	2.72611i
$742$		0			0
$743$	11.1238	−	8.32714i	0.408091	−	0.305493i	−0.375439	−	0.926847i	$-0.622508\pi$
$743$	11.1238	−	8.32714i	0.408091	−	0.305493i	0.783530	+	0.621354i	$0.213417\pi$
$744$		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	0.987156	+	0.159760i	$0.0510721\pi$
$751$	6.66147	+	22.6869i	0.243080	+	0.827856i	−0.744076	+	0.668096i	$0.767110\pi$
$752$		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	0.960339	−	0.278834i	$-0.0899478\pi$
$757$	1.42978	+	3.83338i	0.0519661	+	0.139327i	−0.908373	+	0.418160i	$0.862675\pi$
$758$		0			0
$759$	−1.51439	−	35.6113i	−0.0549689	−	1.29261i
$760$		0			0
$761$	−15.7521	+	34.4922i	−0.571012	+	1.25034i	0.375244	+	0.926926i	$0.377559\pi$
$761$	−15.7521	+	34.4922i	−0.571012	+	1.25034i	−0.946257	+	0.323417i	$0.895168\pi$
$762$		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	0.972625	−	0.232380i	$-0.0746513\pi$
$769$	−0.722968	−	5.02835i	−0.0260709	−	0.181327i	−0.998696	+	0.0510530i	$0.983742\pi$
$770$		0			0
$771$	14.0781	+	30.8267i	0.507009	+	1.11020i
$772$		0			0
$773$	−2.32974	−	10.7096i	−0.0837950	−	0.385199i	0.916080	−	0.400995i	$-0.131336\pi$
$773$	−2.32974	−	10.7096i	−0.0837950	−	0.385199i	−0.999875	+	0.0157957i	$0.994972\pi$
$774$		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	−0.775895	−	0.630862i	$-0.782701\pi$
$787$	5.38497	−	24.7543i	0.191953	−	0.882396i	0.967848	−	0.251534i	$-0.0809350\pi$
$788$		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	−0.639079	−	0.769141i	$-0.720684\pi$
$797$	9.97904	−	18.2752i	0.353476	−	0.647342i	0.992555	+	0.121799i	$0.0388662\pi$
$798$		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	−0.570480	−	0.821311i	$-0.693243\pi$
$809$	4.58736	−	3.97497i	0.161283	−	0.139753i	0.731764	+	0.681559i	$0.238698\pi$
$810$		0			0
$811$	−33.2168	+	38.3343i	−1.16640	+	1.34610i	−0.239453	+	0.970908i	$0.576968\pi$
$811$	−33.2168	+	38.3343i	−1.16640	+	1.34610i	−0.926948	+	0.375190i	$0.877577\pi$
$812$		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	−0.935711	−	0.352768i	$-0.885240\pi$
$821$	1.76169	−	12.2528i	0.0614835	−	0.427627i	0.997194	−	0.0748585i	$-0.0238505\pi$
$822$		0			0
$823$	−2.93089	+	13.4731i	−0.102164	+	0.469642i	0.897430	+	0.441157i	$0.145432\pi$
$823$	−2.93089	+	13.4731i	−0.102164	+	0.469642i	−0.999594	+	0.0284846i	$0.990932\pi$
$824$		0			0
$825$	−36.6007	+	6.42819i	−1.27427	+	0.223801i
$826$		0			0
$827$	7.11232	−	7.11232i	0.247320	−	0.247320i	−0.572550	−	0.819870i	$-0.694046\pi$
$827$	7.11232	−	7.11232i	0.247320	−	0.247320i	0.819870	+	0.572550i	$0.194046\pi$
$828$		0			0
$829$		−	42.7316i		−	1.48413i	−0.670329	−	0.742064i	$-0.733847\pi$
$829$		−	42.7316i		−	1.48413i	0.670329	−	0.742064i	$-0.266153\pi$
$830$		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	0.974890	+	0.222687i	$0.0714828\pi$
$839$	14.6209	+	32.0152i	0.504769	+	1.10529i	−0.470121	+	0.882602i	$0.655790\pi$
$840$		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	0.806893	+	0.590698i	$0.201147\pi$
$853$	17.0537	+	45.7228i	0.583909	+	1.56552i	−0.222985	+	0.974822i	$0.571580\pi$
$854$		0			0
$855$	21.4184	−	89.7074i	0.732495	−	3.06793i
$856$		0			0
$857$	−25.6752	+	1.83633i	−0.877049	+	0.0627278i	−0.502600	−	0.864519i	$-0.667623\pi$
$857$	−25.6752	+	1.83633i	−0.877049	+	0.0627278i	−0.374450	+	0.927247i	$0.622168\pi$
$858$		0			0
$859$	−13.3715	−	45.5390i	−0.456228	−	1.55377i	−0.791209	−	0.611546i	$-0.790548\pi$
$859$	−13.3715	−	45.5390i	−0.456228	−	1.55377i	0.334980	−	0.942225i	$-0.391270\pi$
$860$		0			0
$861$	42.5620	−	6.11950i	1.45051	−	0.208552i
$862$		0			0
$863$	−0.0886542	−	0.0330663i	−0.00301782	−	0.00112559i	0.347955	−	0.937511i	$-0.386876\pi$
$863$	−0.0886542	−	0.0330663i	−0.00301782	−	0.00112559i	−0.350973	+	0.936386i	$0.614149\pi$
$864$		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	0.552130	−	0.833758i	$-0.313815\pi$
$877$	−13.2605	−	24.2848i	−0.447776	−	0.820041i	−0.999906	+	0.0137174i	$0.995633\pi$
$878$		0			0
$879$	−19.9275	+	12.8066i	−0.672136	+	0.431956i
$880$		0			0
$881$	17.6335	+	2.53531i	0.594088	+	0.0854169i	0.432799	−	0.901490i	$-0.357526\pi$
$881$	17.6335	+	2.53531i	0.594088	+	0.0854169i	0.161288	+	0.986907i	$0.448435\pi$
$882$		0			0
$883$	22.3469	−	4.86128i	0.752034	−	0.163595i	0.179820	−	0.983699i	$-0.442448\pi$
$883$	22.3469	−	4.86128i	0.752034	−	0.163595i	0.572214	+	0.820104i	$0.306085\pi$
$884$		0			0
$885$	−15.7754	−	58.0313i	−0.530283	−	1.95070i
$886$		0			0
$887$	−30.0775	+	40.1788i	−1.00990	+	1.34907i	−0.0738299	+	0.997271i	$0.523522\pi$
$887$	−30.0775	+	40.1788i	−1.00990	+	1.34907i	−0.936074	+	0.351803i	$0.885569\pi$
$888$		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	0.371439	−	0.928457i	$-0.378864\pi$
$907$	−12.4912	−	9.35076i	−0.414762	−	0.310487i	−0.786202	+	0.617970i	$0.787955\pi$
$908$		0			0
$909$	41.3238	−	18.8719i	1.37062	−	0.625943i
$910$		0			0
$911$	−11.0404	+	17.1791i	−0.365783	+	0.569170i	−0.974547	−	0.224181i	$-0.928029\pi$
$911$	−11.0404	+	17.1791i	−0.365783	+	0.569170i	0.608764	+	0.793351i	$0.291666\pi$
$912$		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	−0.973753	−	0.227606i	$-0.926910\pi$
$929$	−11.0398	+	17.1783i	−0.362204	+	0.563600i	0.611549	+	0.791206i	$0.290547\pi$
$930$		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	0.980869	+	0.194667i	$0.0623627\pi$
$937$	1.15364	+	16.1300i	0.0376879	+	0.526946i	−0.943181	+	0.332278i	$0.892183\pi$
$938$		0			0
$939$	28.6428	+	33.0555i	0.934721	+	1.07873i
$940$		0			0
$941$	−51.1471	−	23.3581i	−1.66735	−	0.761452i	−0.999858	−	0.0168314i	$-0.994642\pi$
$941$	−51.1471	−	23.3581i	−1.66735	−	0.761452i	−0.667488	−	0.744620i	$-0.732631\pi$
$942$		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	0.957605	+	0.288086i	$0.0930189\pi$
$947$	−0.961725	+	13.4467i	−0.0312519	+	0.436958i	−0.988856	+	0.148872i	$0.952436\pi$
$948$		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	0.0558973	−	0.998437i	$-0.482198\pi$
$953$	30.8133	−	41.1618i	0.998142	−	1.33336i	0.942245	−	0.334925i	$-0.108711\pi$
$954$		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	0.0781856	−	0.996939i	$-0.475087\pi$
$967$	−28.5701	−	28.5701i	−0.918753	−	0.918753i	−0.996939	+	0.0781856i	$0.975087\pi$
$968$		0			0
$969$	21.6470	−	73.7228i	0.695401	−	2.36832i
$970$		0			0
$971$	15.9668	+	24.8448i	0.512399	+	0.797308i	0.996998	−	0.0774281i	$-0.0246708\pi$
$971$	15.9668	+	24.8448i	0.512399	+	0.797308i	−0.484599	+	0.874736i	$0.661034\pi$
$972$		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	0.996984	+	0.0776081i	$0.0247283\pi$
$977$	56.3025	+	20.9997i	1.80128	+	0.671841i	0.804293	+	0.594233i	$0.202544\pi$
$978$		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	−0.208151	−	0.978097i	$-0.566745\pi$
$983$	−8.62160	+	0.616629i	−0.274986	+	0.0196674i	−0.0668350	+	0.997764i	$0.521290\pi$
$984$		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	0.349945	+	0.936770i	$0.386200\pi$
$991$	−18.4846	+	40.4757i	−0.587184	+	1.28575i	−0.937129	+	0.348983i	$0.886527\pi$
$992$		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	0.970275	−	0.242006i	$-0.0778053\pi$
$997$	40.7718	+	22.2631i	1.29126	+	0.705080i	0.320982	+	0.947085i	$0.395987\pi$
$998$		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.17.2	✓	720
5.3	odd	4	inner	920.2.bv.a.753.2	yes	720
23.19	odd	22	inner	920.2.bv.a.617.2	yes	720
115.88	even	44	inner	920.2.bv.a.433.2	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.2	✓	720	1.1	even	1	trivial
920.2.bv.a.433.2	yes	720	115.88	even	44	inner
920.2.bv.a.617.2	yes	720	23.19	odd	22	inner
920.2.bv.a.753.2	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
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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