LMFDB - Embedded newform 920.2.bv.a.297.5

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			297.5
Character	$\chi$	$=$	920.297
Dual form			920.2.bv.a.793.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26284 - 1.69394i) q^{3} +(2.20720 - 0.358144i) q^{5} +(0.137612 + 1.92407i) q^{7} +(1.40582 + 4.78779i) q^{9} +O(q^{10})$	\(q+(-2.26284 - 1.69394i) q^{3} +(2.20720 - 0.358144i) q^{5} +(0.137612 + 1.92407i) q^{7} +(1.40582 + 4.78779i) q^{9} +(-2.53868 - 3.95027i) q^{11} +(4.62358 + 0.330685i) q^{13} +(-5.60123 - 2.92845i) q^{15} +(1.23850 + 3.32054i) q^{17} +(3.07573 + 6.73491i) q^{19} +(2.94787 - 4.58698i) q^{21} +(2.02686 + 4.34648i) q^{23} +(4.74347 - 1.58099i) q^{25} +(1.96566 - 5.27013i) q^{27} +(-4.72051 - 2.15579i) q^{29} +(0.224795 - 1.56349i) q^{31} +(-0.946888 + 13.2392i) q^{33} +(0.992832 + 4.19753i) q^{35} +(1.83672 - 3.36370i) q^{37} +(-9.90229 - 8.58038i) q^{39} +(-4.89607 - 1.43762i) q^{41} +(7.30808 - 9.76246i) q^{43} +(4.81764 + 10.0641i) q^{45} +(8.52072 + 8.52072i) q^{47} +(3.24564 - 0.466652i) q^{49} +(2.82228 - 9.61181i) q^{51} +(-6.22219 + 0.445020i) q^{53} +(-7.01814 - 7.80982i) q^{55} +(4.44866 - 20.4502i) q^{57} +(6.53877 - 5.66587i) q^{59} +(7.32659 + 1.05340i) q^{61} +(-9.01858 + 3.36376i) q^{63} +(10.3236 - 0.926020i) q^{65} +(7.24133 - 1.57525i) q^{67} +(2.77623 - 13.2688i) q^{69} +(-5.94777 - 3.82240i) q^{71} +(4.22252 + 1.57492i) q^{73} +(-13.4118 - 4.45763i) q^{75} +(7.25124 - 5.42821i) q^{77} +(-10.5851 - 12.2159i) q^{79} +(-0.781936 + 0.502520i) q^{81} +(-5.33221 - 2.91161i) q^{83} +(3.92284 + 6.88554i) q^{85} +(7.03001 + 12.8745i) q^{87} +(-0.876298 - 6.09479i) q^{89} +8.94161i q^{91} +(-3.15714 + 3.15714i) q^{93} +(9.20081 + 13.7637i) q^{95} +(-3.19007 + 1.74191i) q^{97} +(15.3441 - 17.7080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{13}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.26284	−	1.69394i	−1.30645	−	0.977999i	−0.999656	−	0.0262244i	$-0.991652\pi$
$3$	−2.26284	−	1.69394i	−1.30645	−	0.977999i	−0.306798	−	0.951775i	$-0.599258\pi$
$4$		0			0
$5$	2.20720	−	0.358144i	0.987090	−	0.160167i
$5$	2.20720	−	0.358144i	0.987090	−	0.160167i
$6$		0			0
$7$	0.137612	+	1.92407i	0.0520126	+	0.727231i	0.954820	+	0.297185i	$0.0960479\pi$
$7$	0.137612	+	1.92407i	0.0520126	+	0.727231i	−0.902807	+	0.430045i	$0.858498\pi$
$8$		0			0
$9$	1.40582	+	4.78779i	0.468607	+	1.59593i
$10$		0			0
$11$	−2.53868	−	3.95027i	−0.765442	−	1.19105i	−0.976907	−	0.213665i	$-0.931460\pi$
$11$	−2.53868	−	3.95027i	−0.765442	−	1.19105i	0.211465	−	0.977385i	$-0.432176\pi$
$12$		0			0
$13$	4.62358	+	0.330685i	1.28235	+	0.0917156i	0.695823	−	0.718213i	$-0.255040\pi$
$13$	4.62358	+	0.330685i	1.28235	+	0.0917156i	0.586528	+	0.809929i	$0.300494\pi$
$14$		0			0
$15$	−5.60123	−	2.92845i	−1.44623	−	0.756123i
$16$		0			0
$17$	1.23850	+	3.32054i	0.300380	+	0.805349i	0.996197	+	0.0871304i	$0.0277697\pi$
$17$	1.23850	+	3.32054i	0.300380	+	0.805349i	−0.695817	+	0.718219i	$0.744958\pi$
$18$		0			0
$19$	3.07573	+	6.73491i	0.705620	+	1.54509i	0.833021	+	0.553242i	$0.186609\pi$
$19$	3.07573	+	6.73491i	0.705620	+	1.54509i	−0.127400	+	0.991851i	$0.540663\pi$
$20$		0			0
$21$	2.94787	−	4.58698i	0.643279	−	1.00096i
$22$		0			0
$23$	2.02686	+	4.34648i	0.422629	+	0.906303i
$23$	2.02686	+	4.34648i	0.422629	+	0.906303i
$24$		0			0
$25$	4.74347	−	1.58099i	0.948693	−	0.316198i
$26$		0			0
$27$	1.96566	−	5.27013i	0.378291	−	1.01424i
$28$		0			0
$29$	−4.72051	−	2.15579i	−0.876577	−	0.400320i	−0.0742754	−	0.997238i	$-0.523664\pi$
$29$	−4.72051	−	2.15579i	−0.876577	−	0.400320i	−0.802302	+	0.596918i	$0.796392\pi$
$30$		0			0
$31$	0.224795	−	1.56349i	0.0403744	−	0.280810i	−0.959625	−	0.281281i	$-0.909241\pi$
$31$	0.224795	−	1.56349i	0.0403744	−	0.280810i	1.00000		0.000470579i	$0.000149790\pi$
$32$		0			0
$33$	−0.946888	+	13.2392i	−0.164832	+	2.30465i
$34$		0			0
$35$	0.992832	+	4.19753i	0.167819	+	0.709511i
$36$		0			0
$37$	1.83672	−	3.36370i	0.301955	−	0.552989i	−0.682012	−	0.731341i	$-0.738895\pi$
$37$	1.83672	−	3.36370i	0.301955	−	0.552989i	0.983967	+	0.178352i	$0.0570766\pi$
$38$		0			0
$39$	−9.90229	−	8.58038i	−1.58564	−	1.37396i
$40$		0			0
$41$	−4.89607	−	1.43762i	−0.764638	−	0.224518i	−0.123918	−	0.992292i	$-0.539546\pi$
$41$	−4.89607	−	1.43762i	−0.764638	−	0.224518i	−0.640720	+	0.767774i	$0.721364\pi$
$42$		0			0
$43$	7.30808	−	9.76246i	1.11447	−	1.48876i	0.262679	−	0.964883i	$-0.415394\pi$
$43$	7.30808	−	9.76246i	1.11447	−	1.48876i	0.851794	−	0.523877i	$-0.175515\pi$
$44$		0			0
$45$	4.81764	+	10.0641i	0.718172	+	1.50027i
$46$		0			0
$47$	8.52072	+	8.52072i	1.24287	+	1.24287i	0.958803	+	0.284071i	$0.0916852\pi$
$47$	8.52072	+	8.52072i	1.24287	+	1.24287i	0.284071	+	0.958803i	$0.408315\pi$
$48$		0			0
$49$	3.24564	−	0.466652i	0.463662	−	0.0666646i
$50$		0			0
$51$	2.82228	−	9.61181i	0.395199	−	1.34592i
$52$		0			0
$53$	−6.22219	+	0.445020i	−0.854683	+	0.0611281i	−0.491802	−	0.870707i	$-0.663662\pi$
$53$	−6.22219	+	0.445020i	−0.854683	+	0.0611281i	−0.362881	+	0.931835i	$0.618207\pi$
$54$		0			0
$55$	−7.01814	−	7.80982i	−0.946326	−	1.05308i
$56$		0			0
$57$	4.44866	−	20.4502i	0.589239	−	2.70869i
$58$		0			0
$59$	6.53877	−	5.66587i	0.851275	−	0.737634i	−0.115488	−	0.993309i	$-0.536843\pi$
$59$	6.53877	−	5.66587i	0.851275	−	0.737634i	0.966763	+	0.255675i	$0.0822977\pi$
$60$		0			0
$61$	7.32659	+	1.05340i	0.938074	+	0.134875i	0.594359	−	0.804200i	$-0.297406\pi$
$61$	7.32659	+	1.05340i	0.938074	+	0.134875i	0.343714	+	0.939074i	$0.388315\pi$
$62$		0			0
$63$	−9.01858	+	3.36376i	−1.13623	+	0.423794i
$64$		0			0
$65$	10.3236	−	0.926020i	1.28049	−	0.114859i
$66$		0			0
$67$	7.24133	−	1.57525i	0.884669	−	0.192448i	0.252796	−	0.967520i	$-0.418650\pi$
$67$	7.24133	−	1.57525i	0.884669	−	0.192448i	0.631873	+	0.775072i	$0.282286\pi$
$68$		0			0
$69$	2.77623	−	13.2688i	0.334219	−	1.59737i
$70$		0			0
$71$	−5.94777	−	3.82240i	−0.705870	−	0.453635i	0.137826	−	0.990456i	$-0.455989\pi$
$71$	−5.94777	−	3.82240i	−0.705870	−	0.453635i	−0.843696	+	0.536821i	$0.819625\pi$
$72$		0			0
$73$	4.22252	+	1.57492i	0.494209	+	0.184330i	0.584196	−	0.811613i	$-0.301410\pi$
$73$	4.22252	+	1.57492i	0.494209	+	0.184330i	−0.0899872	+	0.995943i	$0.528683\pi$
$74$		0			0
$75$	−13.4118	−	4.45763i	−1.54867	−	0.514723i
$76$		0			0
$77$	7.25124	−	5.42821i	0.826356	−	0.618602i
$78$		0			0
$79$	−10.5851	−	12.2159i	−1.19092	−	1.37440i	−0.909970	−	0.414673i	$-0.863896\pi$
$79$	−10.5851	−	12.2159i	−1.19092	−	1.37440i	−0.280950	−	0.959722i	$-0.590650\pi$
$80$		0			0
$81$	−0.781936	+	0.502520i	−0.0868818	+	0.0558355i
$82$		0			0
$83$	−5.33221	−	2.91161i	−0.585286	−	0.319590i	0.159181	−	0.987249i	$-0.449115\pi$
$83$	−5.33221	−	2.91161i	−0.585286	−	0.319590i	−0.744467	+	0.667659i	$0.767296\pi$
$84$		0			0
$85$	3.92284	+	6.88554i	0.425492	+	0.746841i
$86$		0			0
$87$	7.03001	+	12.8745i	0.753696	+	1.38029i
$88$		0			0
$89$	−0.876298	−	6.09479i	−0.0928874	−	0.646046i	−0.982073	−	0.188500i	$-0.939637\pi$
$89$	−0.876298	−	6.09479i	−0.0928874	−	0.646046i	0.889186	−	0.457546i	$-0.151272\pi$
$90$		0			0
$91$			8.94161i			0.937336i
$92$		0			0
$93$	−3.15714	+	3.15714i	−0.327380	+	0.327380i
$94$		0			0
$95$	9.20081	+	13.7637i	0.943984	+	1.41213i
$96$		0			0
$97$	−3.19007	+	1.74191i	−0.323903	+	0.176864i	−0.632971	−	0.774176i	$-0.718165\pi$
$97$	−3.19007	+	1.74191i	−0.323903	+	0.176864i	0.309068	+	0.951040i	$0.399983\pi$
$98$		0			0
$99$	15.3441	−	17.7080i	1.54214	−	1.77972i
$100$		0			0
$101$	−1.76020	+	0.516841i	−0.175146	+	0.0514276i	−0.368130	−	0.929774i	$-0.620002\pi$
$101$	−1.76020	+	0.516841i	−0.175146	+	0.0514276i	0.192983	+	0.981202i	$0.438184\pi$
$102$		0			0
$103$	1.83062	+	0.398227i	0.180376	+	0.0392384i	0.301846	−	0.953357i	$-0.402397\pi$
$103$	1.83062	+	0.398227i	0.180376	+	0.0392384i	−0.121470	+	0.992595i	$0.538761\pi$
$104$		0			0
$105$	4.86375	−	11.1802i	0.474653	−	1.09107i
$106$		0			0
$107$	10.4907	+	14.0140i	1.01418	+	1.35478i	0.933711	+	0.358027i	$0.116550\pi$
$107$	10.4907	+	14.0140i	1.01418	+	1.35478i	0.0804674	+	0.996757i	$0.474359\pi$
$108$		0			0
$109$	−1.32231	+	2.89545i	−0.126654	+	0.277334i	−0.962328	−	0.271893i	$-0.912350\pi$
$109$	−1.32231	+	2.89545i	−0.126654	+	0.277334i	0.835673	+	0.549227i	$0.185078\pi$
$110$		0			0
$111$	−9.85413	+	4.50023i	−0.935313	+	0.427143i
$112$		0			0
$113$	1.66701	+	7.66310i	0.156819	+	0.720884i	0.986648	+	0.162867i	$0.0520740\pi$
$113$	1.66701	+	7.66310i	0.156819	+	0.720884i	−0.829829	+	0.558017i	$0.811562\pi$
$114$		0			0
$115$	6.03034	+	8.86764i	0.562332	+	0.826911i
$116$		0			0
$117$	4.91668	+	22.6016i	0.454547	+	2.08952i
$118$		0			0
$119$	−6.21852	+	2.83990i	−0.570051	+	0.260334i
$120$		0			0
$121$	−4.59014	+	10.0510i	−0.417285	+	0.913727i
$122$		0			0
$123$	8.64381	+	11.5468i	0.779386	+	1.04114i
$124$		0			0
$125$	9.90356	−	5.18841i	0.885801	−	0.464065i
$126$		0			0
$127$	−2.21125	−	0.481029i	−0.196217	−	0.0426844i	0.113383	−	0.993551i	$-0.463831\pi$
$127$	−2.21125	−	0.481029i	−0.196217	−	0.0426844i	−0.309600	+	0.950867i	$0.600195\pi$
$128$		0			0
$129$	−33.0741	+	9.71144i	−2.91201	+	0.855044i
$130$		0			0
$131$	12.0731	−	13.9331i	1.05483	−	1.21734i	0.0794458	−	0.996839i	$-0.474685\pi$
$131$	12.0731	−	13.9331i	1.05483	−	1.21734i	0.975386	−	0.220502i	$-0.0707696\pi$
$132$		0			0
$133$	−12.5352	+	6.84473i	−1.08694	+	0.593513i
$134$		0			0
$135$	2.45113	−	12.3362i	0.210960	−	1.06173i
$136$		0			0
$137$	−2.10740	+	2.10740i	−0.180048	+	0.180048i	−0.791377	−	0.611329i	$-0.790635\pi$
$137$	−2.10740	+	2.10740i	−0.180048	+	0.180048i	0.611329	+	0.791377i	$0.290635\pi$
$138$		0			0
$139$			8.48978i			0.720094i	0.932934	+	0.360047i	$0.117239\pi$
$139$			8.48978i			0.720094i	−0.932934	+	0.360047i	$0.882761\pi$
$140$		0			0
$141$	−4.84744	−	33.7147i	−0.408228	−	2.83929i
$142$		0			0
$143$	−10.4315	−	19.1039i	−0.872327	−	1.59755i
$144$		0			0
$145$	−11.1912	−	3.06763i	−0.929379	−	0.254753i
$146$		0			0
$147$	−8.13485	−	4.44197i	−0.670952	−	0.366367i
$148$		0			0
$149$	−15.7475	+	10.1203i	−1.29009	+	0.829090i	−0.992096	−	0.125478i	$-0.959953\pi$
$149$	−15.7475	+	10.1203i	−1.29009	+	0.829090i	−0.297993	+	0.954568i	$0.596317\pi$
$150$		0			0
$151$	0.874277	+	1.00897i	0.0711477	+	0.0821088i	0.790207	−	0.612839i	$-0.209973\pi$
$151$	0.874277	+	1.00897i	0.0711477	+	0.0821088i	−0.719060	+	0.694948i	$0.755427\pi$
$152$		0			0
$153$	−14.1569	+	10.5977i	−1.14452	+	0.856777i
$154$		0			0
$155$	−0.0637847	−	3.53144i	−0.00512331	−	0.283652i
$156$		0			0
$157$	10.4878	+	3.91176i	0.837021	+	0.312193i	0.731175	−	0.682190i	$-0.238972\pi$
$157$	10.4878	+	3.91176i	0.837021	+	0.312193i	0.105846	+	0.994383i	$0.466245\pi$
$158$		0			0
$159$	14.8337	+	9.53303i	1.17639	+	0.756018i
$160$		0			0
$161$	−8.08401	+	4.49794i	−0.637109	+	0.354488i
$162$		0			0
$163$	−4.55686	+	0.991284i	−0.356921	+	0.0776434i	−0.387451	−	0.921890i	$-0.626644\pi$
$163$	−4.55686	+	0.991284i	−0.356921	+	0.0776434i	0.0305297	+	0.999534i	$0.490281\pi$
$164$		0			0
$165$	2.65158	+	29.5607i	0.206425	+	2.30130i
$166$		0			0
$167$	−14.3134	+	5.33863i	−1.10761	+	0.413115i	−0.835688	−	0.549205i	$-0.814931\pi$
$167$	−14.3134	+	5.33863i	−1.10761	+	0.413115i	−0.271918	+	0.962320i	$0.587658\pi$
$168$		0			0
$169$	8.40050	+	1.20781i	0.646192	+	0.0929084i
$170$		0			0
$171$	−27.9214	+	24.1940i	−2.13520	+	1.85016i
$172$		0			0
$173$	−2.26934	+	10.4320i	−0.172535	+	0.793130i	0.806791	+	0.590838i	$0.201203\pi$
$173$	−2.26934	+	10.4320i	−0.172535	+	0.793130i	−0.979325	+	0.202292i	$0.935161\pi$
$174$		0			0
$175$	3.69470	+	8.90920i	0.279293	+	0.673472i
$176$		0			0
$177$	−24.3939	+	1.74469i	−1.83356	+	0.131139i
$178$		0			0
$179$	−5.13363	+	17.4836i	−0.383706	+	1.30678i	0.510790	+	0.859706i	$0.329353\pi$
$179$	−5.13363	+	17.4836i	−0.383706	+	1.30678i	−0.894496	+	0.447077i	$0.852465\pi$
$180$		0			0
$181$	−3.85549	+	0.554336i	−0.286576	+	0.0412035i	−0.284104	−	0.958793i	$-0.591696\pi$
$181$	−3.85549	+	0.554336i	−0.286576	+	0.0412035i	−0.00247239	+	0.999997i	$0.500787\pi$
$182$		0			0
$183$	−14.7945	−	14.7945i	−1.09364	−	1.09364i
$184$		0			0
$185$	2.84932	−	8.08217i	0.209486	−	0.594213i
$186$		0			0
$187$	9.97287	−	13.3222i	0.729288	−	0.974215i
$188$		0			0
$189$	10.4106	+	3.05683i	0.757260	+	0.222352i
$190$		0			0
$191$	19.9902	+	17.3216i	1.44644	+	1.25335i	0.913279	+	0.407334i	$0.133542\pi$
$191$	19.9902	+	17.3216i	1.44644	+	1.25335i	0.533161	+	0.846014i	$0.321004\pi$
$192$		0			0
$193$	6.36301	−	11.6530i	0.458020	−	0.838800i	−0.541979	−	0.840392i	$-0.682325\pi$
$193$	6.36301	−	11.6530i	0.458020	−	0.838800i	0.999999	+	0.00159166i	$0.000506642\pi$
$194$		0			0
$195$	−24.9293	−	15.3922i	−1.78523	−	1.10226i
$196$		0			0
$197$	−0.107213	+	1.49904i	−0.00763864	+	0.106802i	−0.999841	−	0.0178358i	$-0.994322\pi$
$197$	−0.107213	+	1.49904i	−0.00763864	+	0.106802i	0.992202	+	0.124638i	$0.0397769\pi$
$198$		0			0
$199$	0.804191	−	5.59327i	0.0570076	−	0.396496i	−0.941261	−	0.337679i	$-0.890358\pi$
$199$	0.804191	−	5.59327i	0.0570076	−	0.396496i	0.998269	−	0.0588170i	$-0.0187328\pi$
$200$		0			0
$201$	−19.0544	−	8.70185i	−1.34399	−	0.613781i
$202$		0			0
$203$	3.49829	−	9.37927i	0.245532	−	0.658296i
$204$		0			0
$205$	−11.3215	−	1.41961i	−0.790727	−	0.0991498i
$206$		0			0
$207$	−17.9606	+	15.8145i	−1.24835	+	1.09919i
$208$		0			0
$209$	18.7964	−	29.2477i	1.30017	−	2.02311i
$210$		0			0
$211$	7.22650	+	15.8238i	0.497493	+	1.08936i	0.977276	+	0.211970i	$0.0679880\pi$
$211$	7.22650	+	15.8238i	0.497493	+	1.08936i	−0.479783	+	0.877387i	$0.659285\pi$
$212$		0			0
$213$	6.98394	+	18.7247i	0.478532	+	1.28299i
$214$		0			0
$215$	12.6340	−	24.1650i	0.861634	−	1.64804i
$216$		0			0
$217$	3.03919	+	0.217367i	0.206314	+	0.0147559i
$218$		0			0
$219$	−6.88709	−	10.7165i	−0.465386	−	0.724155i
$220$		0			0
$221$	4.62824	+	15.7624i	0.311329	+	1.06029i
$222$		0			0
$223$	0.272555	+	3.81081i	0.0182516	+	0.255191i	0.998383	+	0.0568424i	$0.0181032\pi$
$223$	0.272555	+	3.81081i	0.0182516	+	0.255191i	−0.980132	+	0.198349i	$0.936442\pi$
$224$		0			0
$225$	14.2379	+	20.4881i	0.949194	+	1.36587i
$226$		0			0
$227$	−5.86528	−	4.39069i	−0.389292	−	0.291421i	0.386647	−	0.922228i	$-0.373633\pi$
$227$	−5.86528	−	4.39069i	−0.389292	−	0.291421i	−0.775940	+	0.630807i	$0.782724\pi$
$228$		0			0
$229$	−1.43813			−0.0950346			−0.0475173	−	0.998870i	$-0.515131\pi$
$229$	−1.43813			−0.0950346			−0.0475173	+	0.998870i	$0.515131\pi$
$230$		0			0
$231$	−25.6035			−1.68459
$232$		0			0
$233$	−2.85927	−	2.14042i	−0.187317	−	0.140224i	0.501504	−	0.865156i	$-0.332780\pi$
$233$	−2.85927	−	2.14042i	−0.187317	−	0.140224i	−0.688821	+	0.724932i	$0.741871\pi$
$234$		0			0
$235$	21.8586	+	15.7553i	1.42590	+	1.02776i
$236$		0			0
$237$	3.25947	+	45.5733i	0.211725	+	2.96030i
$238$		0			0
$239$	−1.46919	−	5.00359i	−0.0950337	−	0.323655i	0.898231	−	0.439524i	$-0.144853\pi$
$239$	−1.46919	−	5.00359i	−0.0950337	−	0.323655i	−0.993265	+	0.115869i	$0.963035\pi$
$240$		0			0
$241$	−4.62207	−	7.19209i	−0.297734	−	0.463283i	0.659866	−	0.751383i	$-0.270613\pi$
$241$	−4.62207	−	7.19209i	−0.297734	−	0.463283i	−0.957600	+	0.288100i	$0.906977\pi$
$242$		0			0
$243$	−14.2107	−	1.01637i	−0.911616	−	0.0652001i
$244$		0			0
$245$	6.99664	−	2.19240i	0.446999	−	0.140067i
$246$		0			0
$247$	11.9938	+	32.1565i	0.763144	+	2.04607i
$248$		0			0
$249$	7.13386	+	15.6210i	0.452090	+	0.989939i
$250$		0			0
$251$	0.851944	−	1.32565i	0.0537742	−	0.0836743i	−0.813325	−	0.581809i	$-0.802345\pi$
$251$	0.851944	−	1.32565i	0.0537742	−	0.0836743i	0.867100	+	0.498135i	$0.165981\pi$
$252$		0			0
$253$	12.0242	−	19.0409i	0.755955	−	1.19709i
$254$		0			0
$255$	2.78693	−	22.2260i	0.174524	−	1.39184i
$256$		0			0
$257$	5.23371	−	14.0321i	0.326470	−	0.875300i	−0.665220	−	0.746648i	$-0.731662\pi$
$257$	5.23371	−	14.0321i	0.326470	−	0.875300i	0.991690	−	0.128653i	$-0.0410652\pi$
$258$		0			0
$259$	6.72476	+	3.07109i	0.417856	+	0.190828i
$260$		0			0
$261$	3.68525	−	25.6315i	0.228111	−	1.58655i
$262$		0			0
$263$	1.28364	−	17.9477i	0.0791528	−	1.10670i	−0.790312	−	0.612705i	$-0.790081\pi$
$263$	1.28364	−	17.9477i	0.0791528	−	1.10670i	0.869464	−	0.493996i	$-0.164464\pi$
$264$		0			0
$265$	−13.5742	+	3.21069i	−0.833858	+	0.197231i
$266$		0			0
$267$	−8.34130	+	15.2760i	−0.510480	+	0.934873i
$268$		0			0
$269$	−19.8123	−	17.1675i	−1.20798	−	1.04672i	−0.997610	−	0.0690972i	$-0.977988\pi$
$269$	−19.8123	−	17.1675i	−1.20798	−	1.04672i	−0.210369	−	0.977622i	$-0.567466\pi$
$270$		0			0
$271$	8.25260	+	2.42318i	0.501310	+	0.147198i	0.522604	−	0.852575i	$-0.324961\pi$
$271$	8.25260	+	2.42318i	0.501310	+	0.147198i	−0.0212945	+	0.999773i	$0.506779\pi$
$272$		0			0
$273$	15.1466	−	20.2335i	0.916713	−	1.22459i
$274$		0			0
$275$	−18.2875	−	14.7243i	−1.10278	−	0.887910i
$276$		0			0
$277$	−7.92806	−	7.92806i	−0.476351	−	0.476351i	0.427612	−	0.903963i	$-0.359355\pi$
$277$	−7.92806	−	7.92806i	−0.476351	−	0.476351i	−0.903963	+	0.427612i	$0.859355\pi$
$278$		0			0
$279$	7.80166	−	1.12171i	0.467073	−	0.0671550i
$280$		0			0
$281$	−5.56543	+	18.9541i	−0.332006	+	1.13071i	0.609240	+	0.792986i	$0.291475\pi$
$281$	−5.56543	+	18.9541i	−0.332006	+	1.13071i	−0.941246	+	0.337722i	$0.890344\pi$
$282$		0			0
$283$	4.42094	−	0.316192i	0.262797	−	0.0187956i	0.0606813	−	0.998157i	$-0.480673\pi$
$283$	4.42094	−	0.316192i	0.262797	−	0.0187956i	0.202116	+	0.979362i	$0.435218\pi$
$284$		0			0
$285$	2.49498	−	46.7308i	0.147790	−	2.76810i
$286$		0			0
$287$	2.09232	−	9.61823i	0.123506	−	0.567746i
$288$		0			0
$289$	3.35563	−	2.90767i	0.197390	−	0.171039i
$290$		0			0
$291$	10.1693	+	1.46213i	0.596137	+	0.0857115i
$292$		0			0
$293$	11.3594	−	4.23685i	0.663626	−	0.247520i	0.00499691	−	0.999988i	$-0.498409\pi$
$293$	11.3594	−	4.23685i	0.663626	−	0.247520i	0.658629	+	0.752468i	$0.271137\pi$
$294$		0			0
$295$	12.4032	−	14.8475i	0.722140	−	0.864457i
$296$		0			0
$297$	−25.8086	+	5.61432i	−1.49757	+	0.325776i
$298$		0			0
$299$	7.93402	+	20.7665i	0.458836	+	1.20096i
$300$		0			0
$301$	19.7893	+	12.7178i	1.14064	+	0.733044i
$302$		0			0
$303$	4.85856	+	1.81215i	0.279117	+	0.104105i
$304$		0			0
$305$	16.5485	−	0.298899i	0.947565	−	0.0171149i
$306$		0			0
$307$	−14.1753	+	10.6115i	−0.809025	+	0.605629i	−0.921656	−	0.388008i	$-0.873163\pi$
$307$	−14.1753	+	10.6115i	−0.809025	+	0.605629i	0.112631	+	0.993637i	$0.464072\pi$
$308$		0			0
$309$	−3.46783	−	4.00209i	−0.197278	−	0.227671i
$310$		0			0
$311$	−16.3959	+	10.5370i	−0.929725	+	0.597498i	−0.915464	−	0.402401i	$-0.868176\pi$
$311$	−16.3959	+	10.5370i	−0.929725	+	0.597498i	−0.0142610	+	0.999898i	$0.504540\pi$
$312$		0			0
$313$	−6.88337	−	3.75860i	−0.389071	−	0.212449i	0.272793	−	0.962073i	$-0.412053\pi$
$313$	−6.88337	−	3.75860i	−0.389071	−	0.212449i	−0.661864	+	0.749624i	$0.730234\pi$
$314$		0			0
$315$	−18.7011	+	10.6544i	−1.05369	+	0.600310i
$316$		0			0
$317$	−11.3600	−	20.8044i	−0.638043	−	1.16849i	−0.973986	−	0.226607i	$-0.927237\pi$
$317$	−11.3600	−	20.8044i	−0.638043	−	1.16849i	0.335943	−	0.941882i	$-0.390945\pi$
$318$		0			0
$319$	3.46795	+	24.1201i	0.194168	+	1.35047i
$320$		0			0
$321$		−	49.4822i		−	2.76183i
$322$		0			0
$323$	−18.5542	+	18.5542i	−1.03239	+	1.03239i
$324$		0			0
$325$	22.4546	−	5.74125i	1.24556	−	0.318467i
$326$		0			0
$327$	7.89692	−	4.31204i	0.436700	−	0.238456i
$328$		0			0
$329$	−15.2219	+	17.5670i	−0.839211	+	0.968501i
$330$		0			0
$331$	−2.56006	+	0.751701i	−0.140714	+	0.0413172i	−0.351331	−	0.936251i	$-0.614271\pi$
$331$	−2.56006	+	0.751701i	−0.140714	+	0.0413172i	0.210617	+	0.977569i	$0.432453\pi$
$332$		0			0
$333$	18.6868	+	4.06506i	1.02403	+	0.222764i
$334$		0			0
$335$	15.4189	−	6.07034i	0.842424	−	0.331658i
$336$		0			0
$337$	18.8216	+	25.1427i	1.02528	+	1.36961i	0.927257	+	0.374425i	$0.122160\pi$
$337$	18.8216	+	25.1427i	1.02528	+	1.36961i	0.0980198	+	0.995184i	$0.468749\pi$
$338$		0			0
$339$	9.20869	−	20.1642i	0.500147	−	1.09517i
$340$		0			0
$341$	−6.74687	+	3.08119i	−0.365364	+	0.166856i
$342$		0			0
$343$	4.21476	+	19.3749i	0.227576	+	1.04615i
$344$		0			0
$345$	1.37556	−	30.2811i	0.0740575	−	1.63028i
$346$		0			0
$347$	−3.82489	−	17.5827i	−0.205331	−	0.943891i	−0.958284	−	0.285817i	$-0.907735\pi$
$347$	−3.82489	−	17.5827i	−0.205331	−	0.943891i	0.752953	−	0.658074i	$-0.228629\pi$
$348$		0			0
$349$	27.3034	−	12.4691i	1.46152	−	0.667454i	0.483382	−	0.875410i	$-0.339408\pi$
$349$	27.3034	−	12.4691i	1.46152	−	0.667454i	0.978138	+	0.207956i	$0.0666811\pi$
$350$		0			0
$351$	10.8311	−	23.7169i	0.578123	−	1.26591i
$352$		0			0
$353$	−13.5908	−	18.1552i	−0.723366	−	0.966303i	−0.999986	−	0.00532401i	$-0.998305\pi$
$353$	−13.5908	−	18.1552i	−0.723366	−	0.966303i	0.276620	−	0.960979i	$-0.410786\pi$
$354$		0			0
$355$	−14.4969	−	6.30664i	−0.769415	−	0.334722i
$356$		0			0
$357$	18.8822	+	4.10757i	0.999352	+	0.217396i
$358$		0			0
$359$	16.1334	−	4.73720i	0.851490	−	0.250020i	0.173266	−	0.984875i	$-0.444568\pi$
$359$	16.1334	−	4.73720i	0.851490	−	0.250020i	0.678224	+	0.734855i	$0.262750\pi$
$360$		0			0
$361$	−23.4565	+	27.0702i	−1.23455	+	1.42475i
$362$		0			0
$363$	27.4126	−	14.9684i	1.43879	−	0.785638i
$364$		0			0
$365$	9.88400	+	1.96389i	0.517352	+	0.102795i
$366$		0			0
$367$	−1.37219	+	1.37219i	−0.0716276	+	0.0716276i	−0.742013	−	0.670385i	$-0.766129\pi$
$367$	−1.37219	+	1.37219i	−0.0716276	+	0.0716276i	0.670385	+	0.742013i	$0.266129\pi$
$368$		0			0
$369$		−	25.4624i		−	1.32552i
$370$		0			0
$371$	−1.71250	−	11.9107i	−0.0889085	−	0.618372i
$372$		0			0
$373$	12.9010	+	23.6264i	0.667987	+	1.22333i	0.963429	+	0.267965i	$0.0863513\pi$
$373$	12.9010	+	23.6264i	0.667987	+	1.22333i	−0.295442	+	0.955361i	$0.595467\pi$
$374$		0			0
$375$	−31.1991	−	5.03552i	−1.61111	−	0.260033i
$376$		0			0
$377$	−21.1128	−	11.5285i	−1.08736	−	0.593746i
$378$		0			0
$379$	12.7749	−	8.20994i	0.656203	−	0.421716i	−0.169725	−	0.985491i	$-0.554288\pi$
$379$	12.7749	−	8.20994i	0.656203	−	0.421716i	0.825928	+	0.563775i	$0.190652\pi$
$380$		0			0
$381$	4.18889	+	4.83424i	0.214603	+	0.247665i
$382$		0			0
$383$	−26.8453	+	20.0962i	−1.37173	+	1.02687i	−0.376802	+	0.926294i	$0.622976\pi$
$383$	−26.8453	+	20.0962i	−1.37173	+	1.02687i	−0.994930	+	0.100572i	$0.967933\pi$
$384$		0			0
$385$	14.0609	−	14.5781i	0.716608	−	0.742971i
$386$		0			0
$387$	57.0144	+	21.2653i	2.89821	+	1.08097i
$388$		0			0
$389$	−6.97210	−	4.48070i	−0.353499	−	0.227180i	0.351824	−	0.936066i	$-0.385562\pi$
$389$	−6.97210	−	4.48070i	−0.353499	−	0.227180i	−0.705323	+	0.708886i	$0.749198\pi$
$390$		0			0
$391$	−11.9224	+	12.1134i	−0.602941	+	0.612599i
$392$		0			0
$393$	−50.9215	+	11.0773i	−2.56865	+	0.558775i
$394$		0			0
$395$	−27.7386	−	23.1719i	−1.39568	−	1.16591i
$396$		0			0
$397$	0.590225	−	0.220142i	0.0296225	−	0.0110486i	−0.334609	−	0.942357i	$-0.608604\pi$
$397$	0.590225	−	0.220142i	0.0296225	−	0.0110486i	0.364232	+	0.931308i	$0.381332\pi$
$398$		0			0
$399$	39.9597	+	5.74534i	2.00049	+	0.287627i
$400$		0			0
$401$	−23.3200	+	20.2069i	−1.16454	+	1.00908i	−0.164802	+	0.986327i	$0.552699\pi$
$401$	−23.3200	+	20.2069i	−1.16454	+	1.00908i	−0.999741	+	0.0227560i	$0.992756\pi$
$402$		0			0
$403$	1.55638	−	7.15457i	0.0775289	−	0.356395i
$404$		0			0
$405$	−1.54592	+	1.38921i	−0.0768171	+	0.0690303i
$406$		0			0
$407$	−17.9504	+	1.28384i	−0.889767	+	0.0636374i
$408$		0			0
$409$	−6.21278	+	21.1588i	−0.307202	+	1.04623i	0.650746	+	0.759295i	$0.274456\pi$
$409$	−6.21278	+	21.1588i	−0.307202	+	1.04623i	−0.957949	+	0.286940i	$0.907362\pi$
$410$		0			0
$411$	8.33855	−	1.19890i	0.411310	−	0.0591375i
$412$		0			0
$413$	11.8014	+	11.8014i	0.580707	+	0.580707i
$414$		0			0
$415$	−12.8120	−	4.51680i	−0.628918	−	0.221721i
$416$		0			0
$417$	14.3812	−	19.2110i	0.704251	−	0.940769i
$418$		0			0
$419$	1.94068	+	0.569836i	0.0948085	+	0.0278383i	0.328793	−	0.944402i	$-0.393358\pi$
$419$	1.94068	+	0.569836i	0.0948085	+	0.0278383i	−0.233984	+	0.972240i	$0.575176\pi$
$420$		0			0
$421$	−11.6987	−	10.1370i	−0.570161	−	0.494048i	0.321403	−	0.946943i	$-0.395846\pi$
$421$	−11.6987	−	10.1370i	−0.570161	−	0.494048i	−0.891564	+	0.452895i	$0.850391\pi$
$422$		0			0
$423$	−28.8168	+	52.7740i	−1.40112	+	2.56596i
$424$		0			0
$425$	11.1245	+	13.7928i	0.539618	+	0.669050i
$426$		0			0
$427$	−1.01860	+	14.2418i	−0.0492933	+	0.689211i
$428$		0			0
$429$	−8.75603	+	60.8996i	−0.422745	+	2.94026i
$430$		0			0
$431$	7.88335	+	3.60020i	0.379728	+	0.173416i	0.596129	−	0.802889i	$-0.296705\pi$
$431$	7.88335	+	3.60020i	0.379728	+	0.173416i	−0.216401	+	0.976304i	$0.569432\pi$
$432$		0			0
$433$	0.848776	−	2.27566i	0.0407896	−	0.109361i	−0.914958	−	0.403549i	$-0.867776\pi$
$433$	0.848776	−	2.27566i	0.0407896	−	0.109361i	0.955748	+	0.294188i	$0.0950492\pi$
$434$		0			0
$435$	20.1276	+	25.8988i	0.965043	+	1.24175i
$436$		0			0
$437$	−23.0390	+	27.0193i	−1.10211	+	1.29251i
$438$		0			0
$439$	6.36171	−	9.89901i	0.303628	−	0.472454i	−0.655592	−	0.755115i	$-0.727581\pi$
$439$	6.36171	−	9.89901i	0.303628	−	0.472454i	0.959220	+	0.282661i	$0.0912172\pi$
$440$		0			0
$441$	6.79701	+	14.8834i	0.323667	+	0.708733i
$442$		0			0
$443$	−4.86129	−	13.0336i	−0.230967	−	0.619246i	0.768829	−	0.639455i	$-0.220840\pi$
$443$	−4.86129	−	13.0336i	−0.230967	−	0.619246i	−0.999796	+	0.0202083i	$0.993567\pi$
$444$		0			0
$445$	−4.11698	−	13.1386i	−0.195163	−	0.622828i
$446$		0			0
$447$	52.7775	+	3.77472i	2.49629	+	0.178538i
$448$		0			0
$449$	−7.46918	−	11.6223i	−0.352492	−	0.548489i	0.619051	−	0.785351i	$-0.287517\pi$
$449$	−7.46918	−	11.6223i	−0.352492	−	0.548489i	−0.971543	+	0.236862i	$0.923881\pi$
$450$		0			0
$451$	6.75060	+	22.9904i	0.317874	+	1.08258i
$452$		0			0
$453$	−0.269215	−	3.76412i	−0.0126488	−	0.176854i
$454$		0			0
$455$	3.20238	+	19.7359i	0.150130	+	0.925235i
$456$		0			0
$457$	−16.7972	−	12.5743i	−0.785741	−	0.588199i	0.129278	−	0.991608i	$-0.458734\pi$
$457$	−16.7972	−	12.5743i	−0.785741	−	0.588199i	−0.915019	+	0.403410i	$0.867825\pi$
$458$		0			0
$459$	19.9341			0.930446
$460$		0			0
$461$	11.5992			0.540228			0.270114	−	0.962828i	$-0.412939\pi$
$461$	11.5992			0.540228			0.270114	+	0.962828i	$0.412939\pi$
$462$		0			0
$463$	−4.35097	−	3.25710i	−0.202207	−	0.151370i	0.493376	−	0.869816i	$-0.335763\pi$
$463$	−4.35097	−	3.25710i	−0.202207	−	0.151370i	−0.695583	+	0.718446i	$0.744854\pi$
$464$		0			0
$465$	−5.83772	+	8.09914i	−0.270718	+	0.375589i
$466$		0			0
$467$	−1.42453	−	19.9175i	−0.0659192	−	0.921671i	−0.917573	−	0.397567i	$-0.869855\pi$
$467$	−1.42453	−	19.9175i	−0.0659192	−	0.921671i	0.851654	−	0.524104i	$-0.175600\pi$
$468$		0			0
$469$	4.02740	+	13.7161i	0.185968	+	0.633348i
$470$		0			0
$471$	−17.1061	−	26.6175i	−0.788205	−	1.22647i
$472$		0			0
$473$	−57.1172	−	4.08510i	−2.62625	−	0.187833i
$474$		0			0
$475$	25.2374	+	27.0841i	1.15797	+	1.24270i
$476$		0			0
$477$	−10.8779	−	29.1649i	−0.498067	−	1.33537i
$478$		0			0
$479$	8.59356	+	18.8173i	0.392650	+	0.859783i	0.997963	+	0.0637956i	$0.0203206\pi$
$479$	8.59356	+	18.8173i	0.392650	+	0.859783i	−0.605313	+	0.795987i	$0.706952\pi$
$480$		0			0
$481$	9.60455	−	14.9450i	0.437930	−	0.681432i
$482$		0			0
$483$	25.9121	+	3.51571i	1.17904	+	0.159970i
$484$		0			0
$485$	−6.41727	+	4.98725i	−0.291393	+	0.226459i
$486$		0			0
$487$	−9.70594	+	26.0226i	−0.439818	+	1.17920i	0.508272	+	0.861197i	$0.330284\pi$
$487$	−9.70594	+	26.0226i	−0.439818	+	1.17920i	−0.948090	+	0.318002i	$0.896988\pi$
$488$		0			0
$489$	11.9906	+	5.47595i	0.542236	+	0.247631i
$490$		0			0
$491$	3.51091	−	24.4189i	0.158445	−	1.10201i	−0.743055	−	0.669230i	$-0.766624\pi$
$491$	3.51091	−	24.4189i	0.158445	−	1.10201i	0.901500	−	0.432779i	$-0.142467\pi$
$492$		0			0
$493$	1.31203	−	18.3446i	0.0590909	−	0.826199i
$494$		0			0
$495$	27.5255	−	44.5806i	1.23718	−	2.00375i
$496$		0			0
$497$	6.53608	−	11.9699i	0.293183	−	0.536925i
$498$		0			0
$499$	−27.0754	−	23.4610i	−1.21206	−	1.05026i	−0.997288	−	0.0735924i	$-0.976554\pi$
$499$	−27.0754	−	23.4610i	−1.21206	−	1.05026i	−0.214772	−	0.976664i	$-0.568901\pi$
$500$		0			0
$501$	41.4324	+	12.1656i	1.85106	+	0.543521i
$502$		0			0
$503$	3.78329	−	5.05388i	0.168688	−	0.225341i	−0.708229	−	0.705983i	$-0.750505\pi$
$503$	3.78329	−	5.05388i	0.168688	−	0.225341i	0.876917	+	0.480642i	$0.159596\pi$
$504$		0			0
$505$	−3.70001	+	1.77118i	−0.164648	+	0.0788163i
$506$		0			0
$507$	−16.9631	−	16.9631i	−0.753356	−	0.753356i
$508$		0			0
$509$	11.2405	−	1.61614i	0.498227	−	0.0716342i	0.111379	−	0.993778i	$-0.464473\pi$
$509$	11.2405	−	1.61614i	0.498227	−	0.0716342i	0.386847	+	0.922144i	$0.373564\pi$
$510$		0			0
$511$	−2.44919	+	8.34116i	−0.108346	+	0.368991i
$512$		0			0
$513$	41.5396	−	2.97097i	1.83402	−	0.131172i
$514$		0			0
$515$	4.18316	+	0.223341i	0.184332	+	0.00984159i
$516$		0			0
$517$	12.0277	−	55.2905i	0.528978	−	2.43167i
$518$		0			0
$519$	22.8064	−	19.7618i	1.00109	−	0.867448i
$520$		0			0
$521$	−30.3195	−	4.35929i	−1.32832	−	0.190984i	−0.558640	−	0.829410i	$-0.688677\pi$
$521$	−30.3195	−	4.35929i	−1.32832	−	0.190984i	−0.769683	+	0.638426i	$0.779586\pi$
$522$		0			0
$523$	−34.7005	+	12.9426i	−1.51735	+	0.565941i	−0.963741	−	0.266839i	$-0.914021\pi$
$523$	−34.7005	+	12.9426i	−1.51735	+	0.565941i	−0.553605	+	0.832779i	$0.686748\pi$
$524$		0			0
$525$	6.73117	−	26.4188i	0.293772	−	1.15301i
$526$		0			0
$527$	5.47003	−	1.18993i	0.238278	−	0.0518342i
$528$		0			0
$529$	−14.7837	+	17.6194i	−0.642770	+	0.766059i
$530$		0			0
$531$	36.3193	+	23.3410i	1.57612	+	1.01291i
$532$		0			0
$533$	−22.1620	−	8.26600i	−0.959943	−	0.358040i
$534$		0			0
$535$	28.1742	+	27.1745i	1.21808	+	1.17486i
$536$		0			0
$537$	41.2328	−	30.8665i	1.77933	−	1.33199i
$538$		0			0
$539$	−10.0830	−	11.6365i	−0.434307	−	0.501217i
$540$		0			0
$541$	0.866413	−	0.556810i	0.0372500	−	0.0239391i	−0.521883	−	0.853017i	$-0.674770\pi$
$541$	0.866413	−	0.556810i	0.0372500	−	0.0239391i	0.559133	+	0.829078i	$0.311134\pi$
$542$		0			0
$543$	9.66339	+	5.27661i	0.414696	+	0.226441i
$544$		0			0
$545$	−1.88161	+	6.86442i	−0.0805994	+	0.294040i
$546$		0			0
$547$	−18.1666	−	33.2696i	−0.776748	−	1.42251i	−0.902610	−	0.430460i	$-0.858351\pi$
$547$	−18.1666	−	33.2696i	−0.776748	−	1.42251i	0.125862	−	0.992048i	$-0.459830\pi$
$548$		0			0
$549$	5.25640	+	36.5590i	0.224338	+	1.56030i
$550$		0			0
$551$		−	38.4228i		−	1.63687i
$552$		0			0
$553$	22.0476	−	22.0476i	0.937560	−	0.937560i
$554$		0			0
$555$	−20.1383	+	13.4621i	−0.854824	+	0.571435i
$556$		0			0
$557$	22.3222	−	12.1888i	0.945820	−	0.516457i	0.0691806	−	0.997604i	$-0.477962\pi$
$557$	22.3222	−	12.1888i	0.945820	−	0.516457i	0.876640	+	0.481147i	$0.159780\pi$
$558$		0			0
$559$	37.0178	−	42.7209i	1.56569	−	1.80690i
$560$		0			0
$561$	−45.1341	+	13.2526i	−1.90556	+	0.559524i
$562$		0			0
$563$	7.37852	+	1.60510i	0.310968	+	0.0676469i	0.365341	−	0.930874i	$-0.380952\pi$
$563$	7.37852	+	1.60510i	0.310968	+	0.0676469i	−0.0543732	+	0.998521i	$0.517316\pi$
$564$		0			0
$565$	6.42391	+	16.3170i	0.270256	+	0.686460i
$566$		0			0
$567$	−1.07449	−	1.43535i	−0.0451243	−	0.0602789i
$568$		0			0
$569$	4.91110	−	10.7538i	0.205884	−	0.450823i	−0.778318	−	0.627870i	$-0.783927\pi$
$569$	4.91110	−	10.7538i	0.205884	−	0.450823i	0.984202	+	0.177047i	$0.0566543\pi$
$570$		0			0
$571$	−19.3044	+	8.81604i	−0.807865	+	0.368940i	−0.776143	−	0.630557i	$-0.782827\pi$
$571$	−19.3044	+	8.81604i	−0.807865	+	0.368940i	−0.0317224	+	0.999497i	$0.510099\pi$
$572$		0			0
$573$	−15.8929	−	73.0584i	−0.663935	−	3.05206i
$574$		0			0
$575$	16.4861	+	17.4129i	0.687516	+	0.726169i
$576$		0			0
$577$	4.91072	+	22.5742i	0.204436	+	0.939776i	0.958968	+	0.283513i	$0.0915000\pi$
$577$	4.91072	+	22.5742i	0.204436	+	0.939776i	−0.754533	+	0.656263i	$0.772136\pi$
$578$		0			0
$579$	−34.1380	+	15.5903i	−1.41873	+	0.647911i
$580$		0			0
$581$	4.86836	−	10.6602i	0.201974	−	0.442261i
$582$		0			0
$583$	17.5541	+	23.4495i	0.727017	+	0.971181i
$584$		0			0
$585$	18.9467	+	48.1254i	0.783351	+	1.98974i
$586$		0			0
$587$	−15.0497	−	3.27386i	−0.621167	−	0.135127i	−0.109041	−	0.994037i	$-0.534778\pi$
$587$	−15.0497	−	3.27386i	−0.621167	−	0.135127i	−0.512125	+	0.858911i	$0.671142\pi$
$588$		0			0
$589$	11.2213	−	3.29488i	0.462367	−	0.135763i
$590$		0			0
$591$	2.78189	−	3.21048i	0.114432	−	0.132061i
$592$		0			0
$593$	18.2761	−	9.97949i	0.750508	−	0.409809i	−0.0579823	−	0.998318i	$-0.518467\pi$
$593$	18.2761	−	9.97949i	0.750508	−	0.409809i	0.808491	+	0.588509i	$0.200285\pi$
$594$		0			0
$595$	−12.7084	+	8.49537i	−0.520995	+	0.348276i
$596$		0			0
$597$	−11.2944	+	11.2944i	−0.462251	+	0.462251i
$598$		0			0
$599$		−	29.8012i		−	1.21764i	−0.793308	−	0.608821i	$-0.791643\pi$
$599$		−	29.8012i		−	1.21764i	0.793308	−	0.608821i	$-0.208357\pi$
$600$		0			0
$601$	−2.42944	−	16.8971i	−0.0990990	−	0.689249i	−0.977440	−	0.211214i	$-0.932258\pi$
$601$	−2.42944	−	16.8971i	−0.0990990	−	0.689249i	0.878341	−	0.478035i	$-0.158651\pi$
$602$		0			0
$603$	17.7220	+	32.4554i	0.721695	+	1.32169i
$604$		0			0
$605$	−6.53165	+	23.8285i	−0.265549	+	0.968766i
$606$		0			0
$607$	10.8601	+	5.93008i	0.440799	+	0.240694i	0.684292	−	0.729208i	$-0.260111\pi$
$607$	10.8601	+	5.93008i	0.440799	+	0.240694i	−0.243493	+	0.969903i	$0.578293\pi$
$608$		0			0
$609$	−23.8040	+	15.2979i	−0.964588	+	0.619903i
$610$		0			0
$611$	36.5786	+	42.2139i	1.47981	+	1.70779i
$612$		0			0
$613$	−10.7519	+	8.04879i	−0.434266	+	0.325087i	−0.793946	−	0.607988i	$-0.791977\pi$
$613$	−10.7519	+	8.04879i	−0.434266	+	0.325087i	0.359680	+	0.933076i	$0.382886\pi$
$614$		0			0
$615$	23.2140	+	22.3903i	0.936080	+	0.902865i
$616$		0			0
$617$	34.4191	+	12.8377i	1.38566	+	0.516824i	0.928092	−	0.372350i	$-0.121448\pi$
$617$	34.4191	+	12.8377i	1.38566	+	0.516824i	0.457568	+	0.889175i	$0.348721\pi$
$618$		0			0
$619$	9.84637	+	6.32788i	0.395759	+	0.254339i	0.723351	−	0.690480i	$-0.242601\pi$
$619$	9.84637	+	6.32788i	0.395759	+	0.254339i	−0.327592	+	0.944819i	$0.606237\pi$
$620$		0			0
$621$	26.8906	−	2.13811i	1.07908	−	0.0857996i
$622$		0			0
$623$	11.6062	−	2.52478i	0.464993	−	0.101153i
$624$		0			0
$625$	20.0009	−	14.9988i	0.800037	−	0.599950i
$626$		0			0
$627$	−92.0773	+	34.3431i	−3.67721	+	1.37153i
$628$		0			0
$629$	13.4441	+	1.93297i	0.536051	+	0.0770724i
$630$		0			0
$631$	−19.2728	+	16.6999i	−0.767237	+	0.664815i	−0.947842	−	0.318741i	$-0.896740\pi$
$631$	−19.2728	+	16.6999i	−0.767237	+	0.664815i	0.180605	+	0.983556i	$0.442194\pi$
$632$		0			0
$633$	10.4522	−	48.0481i	0.415439	−	1.90974i
$634$		0			0
$635$	−5.05296	−	0.269780i	−0.200521	−	0.0107059i
$636$		0			0
$637$	15.1608	−	1.08432i	0.600692	−	0.0429624i
$638$		0			0
$639$	9.93933	−	33.8502i	0.393194	−	1.33910i
$640$		0			0
$641$	9.81675	−	1.41144i	0.387738	−	0.0557484i	0.0543108	−	0.998524i	$-0.482704\pi$
$641$	9.81675	−	1.41144i	0.387738	−	0.0557484i	0.333428	+	0.942776i	$0.391795\pi$
$642$		0			0
$643$	−12.5540	−	12.5540i	−0.495083	−	0.495083i	0.414821	−	0.909903i	$-0.363844\pi$
$643$	−12.5540	−	12.5540i	−0.495083	−	0.495083i	−0.909903	+	0.414821i	$0.863844\pi$
$644$		0			0
$645$	−69.5231	+	33.2804i	−2.73747	+	1.31041i
$646$		0			0
$647$	−11.7291	+	15.6683i	−0.461119	+	0.615983i	−0.969483	−	0.245159i	$-0.921160\pi$
$647$	−11.7291	+	15.6683i	−0.461119	+	0.615983i	0.508364	+	0.861143i	$0.330251\pi$
$648$		0			0
$649$	−38.9816	−	11.4460i	−1.53016	−	0.449296i
$650$		0			0
$651$	−6.50901	−	5.64009i	−0.255108	−	0.221053i
$652$		0			0
$653$	−5.57611	+	10.2119i	−0.218210	+	0.399622i	−0.963737	−	0.266853i	$-0.914016\pi$
$653$	−5.57611	+	10.2119i	−0.218210	+	0.399622i	0.745527	+	0.666475i	$0.232198\pi$
$654$		0			0
$655$	21.6577	−	35.0771i	0.846237	−	1.37057i
$656$		0			0
$657$	−1.60427	+	22.4306i	−0.0625884	+	0.875101i
$658$		0			0
$659$	0.759985	−	5.28581i	0.0296048	−	0.205906i	−0.969650	−	0.244496i	$-0.921378\pi$
$659$	0.759985	−	5.28581i	0.0296048	−	0.205906i	0.999255	+	0.0385899i	$0.0122866\pi$
$660$		0			0
$661$	−36.0137	−	16.4469i	−1.40077	−	0.639710i	−0.435315	−	0.900278i	$-0.643363\pi$
$661$	−36.0137	−	16.4469i	−1.40077	−	0.639710i	−0.965456	+	0.260568i	$0.916090\pi$
$662$		0			0
$663$	16.2275	−	43.5077i	0.630226	−	1.68970i
$664$		0			0
$665$	−25.2163	+	19.5971i	−0.977844	+	0.759942i
$666$		0			0
$667$	−0.197728	−	24.8871i	−0.00765606	−	0.963631i
$668$		0			0
$669$	5.83856	−	9.08497i	0.225732	−	0.351245i
$670$		0			0
$671$	−14.4387	−	31.6162i	−0.557398	−	1.22053i
$672$		0			0
$673$	15.9234	+	42.6924i	0.613804	+	1.64567i	0.755027	+	0.655693i	$0.227624\pi$
$673$	15.9234	+	42.6924i	0.613804	+	1.64567i	−0.141224	+	0.989978i	$0.545104\pi$
$674$		0			0
$675$	0.992000	−	28.1064i	0.0381821	−	1.08181i
$676$		0			0
$677$	−16.6358	−	1.18982i	−0.639366	−	0.0457284i	−0.252107	−	0.967699i	$-0.581124\pi$
$677$	−16.6358	−	1.18982i	−0.639366	−	0.0457284i	−0.387259	+	0.921971i	$0.626578\pi$
$678$		0			0
$679$	−3.79055	−	5.89821i	−0.145468	−	0.226353i
$680$		0			0
$681$	5.83463	+	19.8709i	0.223583	+	0.761455i
$682$		0			0
$683$	0.725497	+	10.1438i	0.0277604	+	0.388141i	0.992270	+	0.124095i	$0.0396026\pi$
$683$	0.725497	+	10.1438i	0.0277604	+	0.388141i	−0.964510	+	0.264046i	$0.914943\pi$
$684$		0			0
$685$	−3.89671	+	5.40622i	−0.148886	+	0.206561i
$686$		0			0
$687$	3.25427	+	2.43612i	0.124158	+	0.0929437i
$688$		0			0
$689$	−28.9160			−1.10161
$690$		0			0
$691$	28.9562			1.10155			0.550773	−	0.834655i	$-0.314333\pi$
$691$	28.9562			1.10155			0.550773	+	0.834655i	$0.314333\pi$
$692$		0			0
$693$	36.1831	+	27.0863i	1.37448	+	1.02892i
$694$		0			0
$695$	3.04056	+	18.7386i	0.115335	+	0.710797i
$696$		0			0
$697$	−1.29011	−	18.0381i	−0.0488664	−	0.683242i
$698$		0			0
$699$	2.84433	+	9.68690i	0.107582	+	0.366392i
$700$		0			0
$701$	6.01224	+	9.35524i	0.227079	+	0.353342i	0.936033	−	0.351913i	$-0.114469\pi$
$701$	6.01224	+	9.35524i	0.227079	+	0.353342i	−0.708953	+	0.705255i	$0.750832\pi$
$702$		0			0
$703$	28.3035	+	2.02430i	1.06749	+	0.0763480i
$704$		0			0
$705$	−22.7740	−	72.6790i	−0.857717	−	2.73725i
$706$		0			0
$707$	−1.23666	−	3.31563i	−0.0465096	−	0.124697i
$708$		0			0
$709$	−16.9984	−	37.2214i	−0.638389	−	1.39788i	−0.901359	−	0.433073i	$-0.857429\pi$
$709$	−16.9984	−	37.2214i	−0.638389	−	1.39788i	0.262969	−	0.964804i	$-0.415298\pi$
$710$		0			0
$711$	43.6063	−	67.8527i	1.63536	−	2.54468i
$712$		0			0
$713$	7.25128	−	2.19189i	0.271563	−	0.0820871i
$714$		0			0
$715$	−29.8664	−	38.4301i	−1.11694	−	1.43721i
$716$		0			0
$717$	−5.15126	+	13.8111i	−0.192377	+	0.515783i
$718$		0			0
$719$	1.95295	+	0.891880i	0.0728326	+	0.0332615i	0.451498	−	0.892272i	$-0.350890\pi$
$719$	1.95295	+	0.891880i	0.0728326	+	0.0332615i	−0.378666	+	0.925534i	$0.623617\pi$
$720$		0			0
$721$	−0.514301	+	3.57704i	−0.0191536	+	0.133216i
$722$		0			0
$723$	−1.72396	+	24.1041i	−0.0641148	+	0.896442i
$724$		0			0
$725$	−25.7999	−	2.76281i	−0.958183	−	0.102608i
$726$		0			0
$727$	−9.36240	+	17.1460i	−0.347232	+	0.635908i	−0.991678	−	0.128741i	$-0.958906\pi$
$727$	−9.36240	+	17.1460i	−0.347232	+	0.635908i	0.644446	+	0.764650i	$0.277088\pi$
$728$		0			0
$729$	32.5423	+	28.1980i	1.20527	+	1.04437i
$730$		0			0
$731$	41.4677	+	12.1760i	1.53374	+	0.450346i
$732$		0			0
$733$	26.1578	−	34.9427i	0.966161	−	1.29064i	0.00934138	−	0.999956i	$-0.497027\pi$
$733$	26.1578	−	34.9427i	0.966161	−	1.29064i	0.956819	−	0.290683i	$-0.0938826\pi$
$734$		0			0
$735$	−19.5461	−	6.89086i	−0.720969	−	0.254173i
$736$		0			0
$737$	−24.6061	−	24.6061i	−0.906377	−	0.906377i
$738$		0			0
$739$	−43.5778	+	6.26554i	−1.60304	+	0.230482i	−0.885022	−	0.465548i	$-0.845857\pi$
$739$	−43.5778	+	6.26554i	−1.60304	+	0.230482i	−0.718013	+	0.696030i	$0.754948\pi$
$740$		0			0
$741$	27.3313	−	93.0819i	1.00404	−	3.41945i
$742$		0			0
$743$	−4.00128	+	0.286177i	−0.146793	+	0.0104988i	−0.144542	−	0.989499i	$-0.546171\pi$
$743$	−4.00128	+	0.286177i	−0.146793	+	0.0104988i	−0.00225064	+	0.999997i	$0.500716\pi$
$744$		0			0
$745$	−31.1334	+	27.9775i	−1.14064	+	1.02502i
$746$		0			0
$747$	6.44402	−	29.6227i	0.235774	−	1.08384i
$748$		0			0
$749$	−25.5203	+	22.1134i	−0.932490	+	0.808008i
$750$		0			0
$751$	−13.7162	−	1.97209i	−0.500512	−	0.0719628i	−0.112565	−	0.993644i	$-0.535907\pi$
$751$	−13.7162	−	1.97209i	−0.500512	−	0.0719628i	−0.387947	+	0.921682i	$0.626816\pi$
$752$		0			0
$753$	−4.17340	+	1.55660i	−0.152087	+	0.0567255i
$754$		0			0
$755$	2.29106	+	1.91388i	0.0833803	+	0.0696533i
$756$		0			0
$757$	−8.25264	+	1.79525i	−0.299947	+	0.0652496i	−0.360020	−	0.932944i	$-0.617230\pi$
$757$	−8.25264	+	1.79525i	−0.299947	+	0.0652496i	0.0600730	+	0.998194i	$0.480867\pi$
$758$		0			0
$759$	−59.4632	+	22.7184i	−2.15838	+	0.824625i
$760$		0			0
$761$	2.05531	+	1.32087i	0.0745049	+	0.0478814i	0.577363	−	0.816488i	$-0.304082\pi$
$761$	2.05531	+	1.32087i	0.0745049	+	0.0478814i	−0.502858	+	0.864369i	$0.667718\pi$
$762$		0			0
$763$	−5.75302	−	2.14577i	−0.208273	−	0.0776820i
$764$		0			0
$765$	−27.4517	+	28.4616i	−0.992517	+	1.02903i
$766$		0			0
$767$	32.1062	−	24.0344i	1.15929	−	0.867831i
$768$		0			0
$769$	−29.9941	−	34.6150i	−1.08161	−	1.24825i	−0.966983	−	0.254841i	$-0.917977\pi$
$769$	−29.9941	−	34.6150i	−1.08161	−	1.24825i	−0.114631	−	0.993408i	$-0.536568\pi$
$770$		0			0
$771$	−35.6127	+	22.8869i	−1.28256	+	0.824252i
$772$		0			0
$773$	43.4741	+	23.7387i	1.56365	+	0.853820i	0.999606	+	0.0280786i	$0.00893886\pi$
$773$	43.4741	+	23.7387i	1.56365	+	0.853820i	0.564049	+	0.825741i	$0.309243\pi$
$774$		0			0
$775$	−1.40555	−	7.77174i	−0.0504888	−	0.279169i
$776$		0			0
$777$	−10.0148	−	18.3408i	−0.359280	−	0.657971i
$778$		0			0
$779$	−5.37678	−	37.3963i	−0.192643	−	1.33986i
$780$		0			0
$781$			33.1991i			1.18796i
$782$		0			0
$783$	−20.6402	+	20.6402i	−0.737620	+	0.737620i
$784$		0			0
$785$	24.5497	+	4.87789i	0.876218	+	0.174099i
$786$		0			0
$787$	33.7868	−	18.4490i	1.20437	−	0.657635i	0.253531	−	0.967327i	$-0.418408\pi$
$787$	33.7868	−	18.4490i	1.20437	−	0.657635i	0.950837	+	0.309692i	$0.100226\pi$
$788$		0			0
$789$	−33.3070	+	38.4384i	−1.18576	+	1.36844i
$790$		0			0
$791$	−14.5150	+	4.26197i	−0.516092	+	0.151538i
$792$		0			0
$793$	33.5268	+	7.29330i	1.19057	+	0.258993i
$794$		0			0
$795$	36.1551	+	15.7287i	1.28229	+	0.557840i
$796$		0			0
$797$	0.516149	+	0.689494i	0.0182829	+	0.0244231i	0.809590	−	0.586996i	$-0.199690\pi$
$797$	0.516149	+	0.689494i	0.0182829	+	0.0244231i	−0.791307	+	0.611420i	$0.790599\pi$
$798$		0			0
$799$	−17.7405	+	38.8463i	−0.627614	+	1.37428i
$800$		0			0
$801$	27.9486	−	12.7637i	0.987516	−	0.450983i
$802$		0			0
$803$	−4.49829	−	20.6783i	−0.158741	−	0.729722i
$804$		0			0
$805$	−16.2321	+	12.8231i	−0.572107	+	0.451955i
$806$		0			0
$807$	15.7515	+	72.4083i	0.554478	+	2.54889i
$808$		0			0
$809$	33.0820	−	15.1080i	1.16310	−	0.531170i	0.262122	−	0.965035i	$-0.415578\pi$
$809$	33.0820	−	15.1080i	1.16310	−	0.531170i	0.900978	+	0.433865i	$0.142850\pi$
$810$		0			0
$811$	−6.28892	+	13.7708i	−0.220834	+	0.483558i	−0.987328	−	0.158693i	$-0.949272\pi$
$811$	−6.28892	+	13.7708i	−0.220834	+	0.483558i	0.766494	+	0.642251i	$0.221999\pi$
$812$		0			0
$813$	−14.5696	−	19.4627i	−0.510979	−	0.682588i
$814$		0			0
$815$	−9.70288	+	3.81998i	−0.339877	+	0.133808i
$816$		0			0
$817$	88.2269	+	19.1926i	3.08667	+	0.671464i
$818$		0			0
$819$	−42.8105	+	12.5703i	−1.49592	+	0.439242i
$820$		0			0
$821$	−28.9336	+	33.3912i	−1.00979	+	1.16536i	−0.0236047	+	0.999721i	$0.507514\pi$
$821$	−28.9336	+	33.3912i	−1.00979	+	1.16536i	−0.986186	+	0.165640i	$0.947031\pi$
$822$		0			0
$823$	−27.6013	+	15.0715i	−0.962121	+	0.525358i	−0.881909	−	0.471420i	$-0.843742\pi$
$823$	−27.6013	+	15.0715i	−0.962121	+	0.525358i	−0.0802121	+	0.996778i	$0.525560\pi$
$824$		0			0
$825$	16.4396	+	64.2968i	0.572352	+	2.23853i
$826$		0			0
$827$	33.8547	−	33.8547i	1.17724	−	1.17724i	0.196798	−	0.980444i	$-0.436946\pi$
$827$	33.8547	−	33.8547i	1.17724	−	1.17724i	0.980444	−	0.196798i	$-0.0630542\pi$
$828$		0			0
$829$		−	11.8644i		−	0.412068i	−0.978545	−	0.206034i	$-0.933944\pi$
$829$		−	11.8644i		−	0.412068i	0.978545	−	0.206034i	$-0.0660558\pi$
$830$		0			0
$831$	4.51028	+	31.3697i	0.156460	+	1.08820i
$832$		0			0
$833$	5.56925	+	10.1993i	0.192963	+	0.353386i
$834$		0			0
$835$	−29.6806	+	16.9097i	−1.02714	+	0.585184i
$836$		0			0
$837$	−7.79790	−	4.25798i	−0.269535	−	0.147177i
$838$		0			0
$839$	−23.7824	+	15.2840i	−0.821059	+	0.527662i	−0.882425	−	0.470453i	$-0.844091\pi$
$839$	−23.7824	+	15.2840i	−0.821059	+	0.527662i	0.0613665	+	0.998115i	$0.480454\pi$
$840$		0			0
$841$	−1.35512	−	1.56390i	−0.0467284	−	0.0539274i
$842$		0			0
$843$	44.7009	−	33.4627i	1.53958	−	1.15252i
$844$		0			0
$845$	18.9741	−	0.342710i	0.652731	−	0.0117896i
$846$		0			0
$847$	−19.9705	−	7.44861i	−0.686194	−	0.255937i
$848$		0			0
$849$	−10.5395	−	6.77333i	−0.361715	−	0.232460i
$850$		0			0
$851$	18.3430	+	1.16552i	0.628790	+	0.0399535i
$852$		0			0
$853$	19.4228	−	4.22516i	0.665022	−	0.144667i	0.132631	−	0.991165i	$-0.457657\pi$
$853$	19.4228	−	4.22516i	0.665022	−	0.144667i	0.532391	+	0.846499i	$0.321294\pi$
$854$		0			0
$855$	−52.9631	+	63.4009i	−1.81130	+	2.16826i
$856$		0			0
$857$	−40.3315	+	15.0429i	−1.37770	+	0.513854i	−0.925731	−	0.378182i	$-0.876549\pi$
$857$	−40.3315	+	15.0429i	−1.37770	+	0.513854i	−0.451965	+	0.892036i	$0.649277\pi$
$858$		0			0
$859$	−52.0022	−	7.47679i	−1.77429	−	0.255105i	−0.824028	−	0.566549i	$-0.808278\pi$
$859$	−52.0022	−	7.47679i	−1.77429	−	0.255105i	−0.950265	+	0.311444i	$0.899187\pi$
$860$		0			0
$861$	−21.0273	+	18.2203i	−0.716609	+	0.620946i
$862$		0			0
$863$	−5.76364	+	26.4950i	−0.196197	+	0.901902i	0.768769	+	0.639526i	$0.220869\pi$
$863$	−5.76364	+	26.4950i	−0.196197	+	0.901902i	−0.964966	+	0.262375i	$0.915494\pi$
$864$		0			0
$865$	−1.27274	+	23.8382i	−0.0432743	+	0.810525i
$866$		0			0
$867$	−12.5187	+	0.895355i	−0.425157	+	0.0304078i
$868$		0			0
$869$	−21.3838	+	72.8264i	−0.725394	+	2.47047i
$870$		0			0
$871$	34.0018	−	4.88872i	1.15211	−	0.165648i
$872$		0			0
$873$	−12.8246	−	12.8246i	−0.434046	−	0.434046i
$874$		0			0
$875$	11.3457	+	18.3412i	0.383555	+	0.620044i
$876$		0			0
$877$	−25.4010	+	33.9317i	−0.857730	+	1.14579i	0.130291	+	0.991476i	$0.458409\pi$
$877$	−25.4010	+	33.9317i	−0.857730	+	1.14579i	−0.988021	+	0.154317i	$0.950682\pi$
$878$		0			0
$879$	−32.8817	−	9.65492i	−1.10907	−	0.325653i
$880$		0			0
$881$	20.8771	+	18.0901i	0.703369	+	0.609473i	0.931321	−	0.364200i	$-0.118657\pi$
$881$	20.8771	+	18.0901i	0.703369	+	0.609473i	−0.227952	+	0.973672i	$0.573203\pi$
$882$		0			0
$883$	−3.76203	+	6.88964i	−0.126602	+	0.231855i	−0.933290	−	0.359123i	$-0.883076\pi$
$883$	−3.76203	+	6.88964i	−0.126602	+	0.231855i	0.806688	+	0.590977i	$0.201258\pi$
$884$		0			0
$885$	−53.2173	+	12.5874i	−1.78888	+	0.423121i
$886$		0			0
$887$	3.46185	−	48.4029i	0.116237	−	1.62521i	−0.520313	−	0.853976i	$-0.674185\pi$
$887$	3.46185	−	48.4029i	0.116237	−	1.62521i	0.636550	−	0.771235i	$-0.280361\pi$
$888$		0			0
$889$	0.621238	−	4.32081i	0.0208357	−	0.144915i
$890$		0			0
$891$	3.97017	+	1.81312i	0.133006	+	0.0607417i
$892$		0			0
$893$	−31.1788	+	83.5936i	−1.04336	+	2.79735i
$894$		0			0
$895$	−5.06933	+	40.4283i	−0.169449	+	1.35137i
$896$		0			0
$897$	17.2239	−	60.4313i	0.575090	−	2.01774i
$898$		0			0
$899$	−4.43169	+	6.89585i	−0.147805	+	0.229989i
$900$		0			0
$901$	−9.18387	−	20.1099i	−0.305959	−	0.669957i
$902$		0			0
$903$	−23.2369	−	62.3005i	−0.773276	−	2.07323i
$904$		0			0
$905$	−8.31131	+	2.60435i	−0.276277	+	0.0865715i
$906$		0			0
$907$	−45.3174	−	3.24116i	−1.50474	−	0.107621i	−0.705533	−	0.708677i	$-0.749292\pi$
$907$	−45.3174	−	3.24116i	−1.50474	−	0.107621i	−0.799207	+	0.601056i	$0.794747\pi$
$908$		0			0
$909$	−4.94905	−	7.70087i	−0.164150	−	0.255422i
$910$		0			0
$911$	−5.27073	−	17.9504i	−0.174627	−	0.594725i	−0.999565	−	0.0295012i	$-0.990608\pi$
$911$	−5.27073	−	17.9504i	−0.174627	−	0.594725i	0.824938	−	0.565223i	$-0.191210\pi$
$912$		0			0
$913$	2.03516	+	28.4553i	0.0673541	+	0.941733i
$914$		0			0
$915$	−37.9530	−	27.3559i	−1.25469	−	0.904358i
$916$		0			0
$917$	28.4697	+	21.3122i	0.940152	+	0.703789i
$918$		0			0
$919$	21.6210			0.713213			0.356606	−	0.934255i	$-0.383934\pi$
$919$	21.6210			0.713213			0.356606	+	0.934255i	$0.383934\pi$
$920$		0			0
$921$	50.0517			1.64926
$922$		0			0
$923$	−26.2360	−	19.6400i	−0.863568	−	0.646459i
$924$		0			0
$925$	3.39444	−	18.8594i	0.111608	−	0.620094i
$926$		0			0
$927$	0.666897	+	9.32444i	0.0219038	+	0.306255i
$928$		0			0
$929$	−5.21191	−	17.7501i	−0.170997	−	0.582363i	−0.999742	−	0.0227353i	$-0.992762\pi$
$929$	−5.21191	−	17.7501i	−0.170997	−	0.582363i	0.828744	−	0.559627i	$-0.189056\pi$
$930$		0			0
$931$	13.1256	+	20.4238i	0.430173	+	0.669362i
$932$		0			0
$933$	54.9504	+	3.93013i	1.79899	+	0.128667i
$934$		0			0
$935$	17.2409	−	32.9765i	0.563836	−	1.07845i
$936$		0			0
$937$	13.0310	+	34.9374i	0.425703	+	1.14135i	0.955955	+	0.293514i	$0.0948247\pi$
$937$	13.0310	+	34.9374i	0.425703	+	1.14135i	−0.530252	+	0.847840i	$0.677903\pi$
$938$		0			0
$939$	9.20913	+	20.1652i	0.300529	+	0.658066i
$940$		0			0
$941$	−0.470076	+	0.731452i	−0.0153240	+	0.0238447i	−0.848831	−	0.528664i	$-0.822693\pi$
$941$	−0.470076	+	0.731452i	−0.0153240	+	0.0238447i	0.833507	+	0.552509i	$0.186329\pi$
$942$		0			0
$943$	−3.67507	−	24.1945i	−0.119677	−	0.787882i
$944$		0			0
$945$	24.0731	+	3.01854i	0.783097	+	0.0981931i
$946$		0			0
$947$	−16.4137	+	44.0069i	−0.533374	+	1.43003i	0.338811	+	0.940854i	$0.389975\pi$
$947$	−16.4137	+	44.0069i	−0.533374	+	1.43003i	−0.872185	+	0.489176i	$0.837297\pi$
$948$		0			0
$949$	19.0024	+	8.67810i	0.616844	+	0.281703i
$950$		0			0
$951$	−9.53542	+	66.3203i	−0.309207	+	2.15058i
$952$		0			0
$953$	−0.460776	+	6.44249i	−0.0149260	+	0.208693i	0.984516	+	0.175294i	$0.0560876\pi$
$953$	−0.460776	+	6.44249i	−0.0149260	+	0.208693i	−0.999442	+	0.0333986i	$0.989367\pi$
$954$		0			0
$955$	50.3260	+	31.0729i	1.62851	+	1.00550i
$956$		0			0
$957$	33.0107	−	60.4547i	1.06709	−	1.95422i
$958$		0			0
$959$	−4.34480	−	3.76479i	−0.140301	−	0.121571i
$960$		0			0
$961$	27.3503	+	8.03078i	0.882269	+	0.259057i
$962$		0			0
$963$	−52.3479	+	69.9286i	−1.68689	+	2.25342i
$964$		0			0
$965$	9.87100	−	27.9993i	0.317759	−	0.901331i
$966$		0			0
$967$	−0.957238	−	0.957238i	−0.0307827	−	0.0307827i	0.691548	−	0.722331i	$-0.256929\pi$
$967$	−0.957238	−	0.957238i	−0.0307827	−	0.0307827i	−0.722331	+	0.691548i	$0.756929\pi$
$968$		0			0
$969$	73.4152	−	10.5555i	2.35844	−	0.339092i
$970$		0			0
$971$	8.63991	−	29.4248i	0.277268	−	0.944287i	−0.696655	−	0.717407i	$-0.745329\pi$
$971$	8.63991	−	29.4248i	0.277268	−	0.944287i	0.973923	−	0.226881i	$-0.0728528\pi$
$972$		0			0
$973$	−16.3349	+	1.16830i	−0.523674	+	0.0374539i
$974$		0			0
$975$	−60.5367	−	25.0453i	−1.93873	−	0.802092i
$976$		0			0
$977$	−0.178536	+	0.820717i	−0.00571188	+	0.0262571i	−0.979915	−	0.199418i	$-0.936095\pi$
$977$	−0.178536	+	0.820717i	−0.00571188	+	0.0262571i	0.974203	+	0.225675i	$0.0724586\pi$
$978$		0			0
$979$	−21.8514	+	18.9343i	−0.698374	+	0.605144i
$980$		0			0
$981$	−15.7217	−	2.26044i	−0.501957	−	0.0721705i
$982$		0			0
$983$	−35.3043	+	13.1678i	−1.12603	+	0.419988i	−0.842350	−	0.538930i	$-0.818829\pi$
$983$	−35.3043	+	13.1678i	−1.12603	+	0.419988i	−0.283682	+	0.958918i	$0.591556\pi$
$984$		0			0
$985$	0.300230	+	3.34708i	0.00956613	+	0.106647i
$986$		0			0
$987$	64.2024	−	13.9664i	2.04358	−	0.444554i
$988$		0			0
$989$	57.2447	+	11.9773i	1.82028	+	0.380856i
$990$		0			0
$991$	25.8500	+	16.6128i	0.821152	+	0.527723i	0.882455	−	0.470397i	$-0.155889\pi$
$991$	25.8500	+	16.6128i	0.821152	+	0.527723i	−0.0613028	+	0.998119i	$0.519526\pi$
$992$		0			0
$993$	7.06636	+	2.63561i	0.224244	+	0.0836387i
$994$		0			0
$995$	−0.228185	−	12.6335i	−0.00723396	−	0.400508i
$996$		0			0
$997$	−18.3298	+	13.7215i	−0.580511	+	0.434565i	−0.848755	−	0.528786i	$-0.822647\pi$
$997$	−18.3298	+	13.7215i	−0.580511	+	0.434565i	0.268244	+	0.963351i	$0.413557\pi$
$998$		0			0
$999$	−14.1168	−	16.2916i	−0.446635	−	0.515444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.297.5	yes	720
5.3	odd	4	inner	920.2.bv.a.113.32	yes	720
23.11	odd	22	inner	920.2.bv.a.57.32	✓	720
115.103	even	44	inner	920.2.bv.a.793.5	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.57.32	✓	720	23.11	odd	22	inner
920.2.bv.a.113.32	yes	720	5.3	odd	4	inner
920.2.bv.a.297.5	yes	720	1.1	even	1	trivial
920.2.bv.a.793.5	yes	720	115.103	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26284 - 1.69394i) q^{3} +(2.20720 - 0.358144i) q^{5} +(0.137612 + 1.92407i) q^{7} +(1.40582 + 4.78779i) q^{9} +O(q^{10})\)	\(q+(-2.26284 - 1.69394i) q^{3} +(2.20720 - 0.358144i) q^{5} +(0.137612 + 1.92407i) q^{7} +(1.40582 + 4.78779i) q^{9} +(-2.53868 - 3.95027i) q^{11} +(4.62358 + 0.330685i) q^{13} +(-5.60123 - 2.92845i) q^{15} +(1.23850 + 3.32054i) q^{17} +(3.07573 + 6.73491i) q^{19} +(2.94787 - 4.58698i) q^{21} +(2.02686 + 4.34648i) q^{23} +(4.74347 - 1.58099i) q^{25} +(1.96566 - 5.27013i) q^{27} +(-4.72051 - 2.15579i) q^{29} +(0.224795 - 1.56349i) q^{31} +(-0.946888 + 13.2392i) q^{33} +(0.992832 + 4.19753i) q^{35} +(1.83672 - 3.36370i) q^{37} +(-9.90229 - 8.58038i) q^{39} +(-4.89607 - 1.43762i) q^{41} +(7.30808 - 9.76246i) q^{43} +(4.81764 + 10.0641i) q^{45} +(8.52072 + 8.52072i) q^{47} +(3.24564 - 0.466652i) q^{49} +(2.82228 - 9.61181i) q^{51} +(-6.22219 + 0.445020i) q^{53} +(-7.01814 - 7.80982i) q^{55} +(4.44866 - 20.4502i) q^{57} +(6.53877 - 5.66587i) q^{59} +(7.32659 + 1.05340i) q^{61} +(-9.01858 + 3.36376i) q^{63} +(10.3236 - 0.926020i) q^{65} +(7.24133 - 1.57525i) q^{67} +(2.77623 - 13.2688i) q^{69} +(-5.94777 - 3.82240i) q^{71} +(4.22252 + 1.57492i) q^{73} +(-13.4118 - 4.45763i) q^{75} +(7.25124 - 5.42821i) q^{77} +(-10.5851 - 12.2159i) q^{79} +(-0.781936 + 0.502520i) q^{81} +(-5.33221 - 2.91161i) q^{83} +(3.92284 + 6.88554i) q^{85} +(7.03001 + 12.8745i) q^{87} +(-0.876298 - 6.09479i) q^{89} +8.94161i q^{91} +(-3.15714 + 3.15714i) q^{93} +(9.20081 + 13.7637i) q^{95} +(-3.19007 + 1.74191i) q^{97} +(15.3441 - 17.7080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * 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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