LMFDB - Embedded newform 920.2.bv.a.697.12

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			697.12
Character	$\chi$	$=$	920.697
Dual form			920.2.bv.a.33.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.252761 + 1.16193i) q^{3} +(-1.19598 + 1.88935i) q^{5} +(1.80796 - 3.31103i) q^{7} +(1.44271 + 0.658865i) q^{9} +O(q^{10})$	\(q+(-0.252761 + 1.16193i) q^{3} +(-1.19598 + 1.88935i) q^{5} +(1.80796 - 3.31103i) q^{7} +(1.44271 + 0.658865i) q^{9} +(2.85252 - 2.47173i) q^{11} +(1.15893 - 0.632824i) q^{13} +(-1.89299 - 1.86719i) q^{15} +(-2.34194 - 3.12846i) q^{17} +(0.174948 + 1.21679i) q^{19} +(3.39019 + 2.93762i) q^{21} +(3.65685 - 3.10282i) q^{23} +(-2.13928 - 4.51924i) q^{25} +(-3.26802 + 4.36556i) q^{27} +(1.68187 + 0.241816i) q^{29} +(2.63296 + 1.69210i) q^{31} +(2.15095 + 3.93918i) q^{33} +(4.09342 + 7.37579i) q^{35} +(-2.27434 - 6.09775i) q^{37} +(0.442361 + 1.50654i) q^{39} +(0.616498 + 1.34994i) q^{41} +(9.30770 + 2.02477i) q^{43} +(-2.97028 + 1.93780i) q^{45} +(5.17350 + 5.17350i) q^{47} +(-3.90974 - 6.08367i) q^{49} +(4.22699 - 1.93040i) q^{51} +(12.1122 + 6.61374i) q^{53} +(1.25840 + 8.34554i) q^{55} +(-1.45804 - 0.104281i) q^{57} +(-2.63780 + 8.98353i) q^{59} +(-0.888176 + 1.38203i) q^{61} +(4.78990 - 3.58567i) q^{63} +(-0.190429 + 2.94647i) q^{65} +(0.258650 + 3.61640i) q^{67} +(2.68093 + 5.03325i) q^{69} +(-1.30292 + 1.50365i) q^{71} +(-9.83644 - 7.36347i) q^{73} +(5.79174 - 1.34339i) q^{75} +(-3.02672 - 13.9136i) q^{77} +(3.37219 + 0.990164i) q^{79} +(-1.13052 - 1.30469i) q^{81} +(-4.05317 + 1.51175i) q^{83} +(8.71166 - 0.683168i) q^{85} +(-0.706085 + 1.89309i) q^{87} +(-12.2904 + 7.89859i) q^{89} -4.98138i q^{91} +(-2.63160 + 2.63160i) q^{93} +(-2.50817 - 1.12471i) q^{95} +(-10.2534 - 3.82433i) q^{97} +(5.74391 - 1.68656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{19}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.252761	+	1.16193i	−0.145932	+	0.670838i	0.844809	+	0.535069i	$0.179714\pi$
$3$	−0.252761	+	1.16193i	−0.145932	+	0.670838i	−0.990740	+	0.135769i	$0.956649\pi$
$4$		0			0
$5$	−1.19598	+	1.88935i	−0.534857	+	0.844942i
$5$	−1.19598	+	1.88935i	−0.534857	+	0.844942i
$6$		0			0
$7$	1.80796	−	3.31103i	0.683345	−	1.25145i	−0.273784	−	0.961791i	$-0.588275\pi$
$7$	1.80796	−	3.31103i	0.683345	−	1.25145i	0.957129	−	0.289662i	$-0.0935430\pi$
$8$		0			0
$9$	1.44271	+	0.658865i	0.480905	+	0.219622i
$10$		0			0
$11$	2.85252	−	2.47173i	0.860068	−	0.745254i	−0.108475	−	0.994099i	$-0.534597\pi$
$11$	2.85252	−	2.47173i	0.860068	−	0.745254i	0.968543	+	0.248846i	$0.0800512\pi$
$12$		0			0
$13$	1.15893	−	0.632824i	0.321429	−	0.175514i	−0.310431	−	0.950596i	$-0.600473\pi$
$13$	1.15893	−	0.632824i	0.321429	−	0.175514i	0.631860	+	0.775082i	$0.282292\pi$
$14$		0			0
$15$	−1.89299	−	1.86719i	−0.488767	−	0.482106i
$16$		0			0
$17$	−2.34194	−	3.12846i	−0.568003	−	0.758763i	0.420935	−	0.907091i	$-0.361702\pi$
$17$	−2.34194	−	3.12846i	−0.568003	−	0.758763i	−0.988938	+	0.148327i	$0.952611\pi$
$18$		0			0
$19$	0.174948	+	1.21679i	0.0401358	+	0.279151i	0.999999	−	0.00131754i	$-0.000419386\pi$
$19$	0.174948	+	1.21679i	0.0401358	+	0.279151i	−0.959863	+	0.280468i	$0.909510\pi$
$20$		0			0
$21$	3.39019	+	2.93762i	0.739801	+	0.641041i
$22$		0			0
$23$	3.65685	−	3.10282i	0.762505	−	0.646982i
$23$	3.65685	−	3.10282i	0.762505	−	0.646982i
$24$		0			0
$25$	−2.13928	−	4.51924i	−0.427856	−	0.903847i
$26$		0			0
$27$	−3.26802	+	4.36556i	−0.628930	+	0.840153i
$28$		0			0
$29$	1.68187	+	0.241816i	0.312316	+	0.0449042i	0.296690	−	0.954974i	$-0.404117\pi$
$29$	1.68187	+	0.241816i	0.312316	+	0.0449042i	0.0156251	+	0.999878i	$0.495026\pi$
$30$		0			0
$31$	2.63296	+	1.69210i	0.472893	+	0.303910i	0.755294	−	0.655387i	$-0.227494\pi$
$31$	2.63296	+	1.69210i	0.472893	+	0.303910i	−0.282400	+	0.959297i	$0.591131\pi$
$32$		0			0
$33$	2.15095	+	3.93918i	0.374433	+	0.685723i
$34$		0			0
$35$	4.09342	+	7.37579i	0.691914	+	1.24674i
$36$		0			0
$37$	−2.27434	−	6.09775i	−0.373899	−	1.00246i	−0.978557	−	0.205977i	$-0.933963\pi$
$37$	−2.27434	−	6.09775i	−0.373899	−	1.00246i	0.604657	−	0.796486i	$-0.293310\pi$
$38$		0			0
$39$	0.442361	+	1.50654i	0.0708345	+	0.241240i
$40$		0			0
$41$	0.616498	+	1.34994i	0.0962808	+	0.210826i	0.951644	−	0.307203i	$-0.0993932\pi$
$41$	0.616498	+	1.34994i	0.0962808	+	0.210826i	−0.855363	+	0.518029i	$0.826666\pi$
$42$		0			0
$43$	9.30770	+	2.02477i	1.41941	+	0.308774i	0.855817	−	0.517278i	$-0.173055\pi$
$43$	9.30770	+	2.02477i	1.41941	+	0.308774i	0.563594	+	0.826052i	$0.309418\pi$
$44$		0			0
$45$	−2.97028	+	1.93780i	−0.442783	+	0.288870i
$46$		0			0
$47$	5.17350	+	5.17350i	0.754632	+	0.754632i	0.975340	−	0.220708i	$-0.0708367\pi$
$47$	5.17350	+	5.17350i	0.754632	+	0.754632i	−0.220708	+	0.975340i	$0.570837\pi$
$48$		0			0
$49$	−3.90974	−	6.08367i	−0.558534	−	0.869096i
$50$		0			0
$51$	4.22699	−	1.93040i	0.591897	−	0.270310i
$52$		0			0
$53$	12.1122	+	6.61374i	1.66373	+	0.908467i	0.984678	+	0.174380i	$0.0557922\pi$
$53$	12.1122	+	6.61374i	1.66373	+	0.908467i	0.679055	+	0.734087i	$0.262390\pi$
$54$		0			0
$55$	1.25840	+	8.34554i	0.169683	+	1.12531i
$56$		0			0
$57$	−1.45804	−	0.104281i	−0.193122	−	0.0138123i
$58$		0			0
$59$	−2.63780	+	8.98353i	−0.343413	+	1.16956i	0.588992	+	0.808139i	$0.299525\pi$
$59$	−2.63780	+	8.98353i	−0.343413	+	1.16956i	−0.932404	+	0.361417i	$0.882293\pi$
$60$		0			0
$61$	−0.888176	+	1.38203i	−0.113719	+	0.176951i	−0.893448	−	0.449167i	$-0.851721\pi$
$61$	−0.888176	+	1.38203i	−0.113719	+	0.176951i	0.779728	+	0.626118i	$0.215357\pi$
$62$		0			0
$63$	4.78990	−	3.58567i	0.603470	−	0.451752i
$64$		0			0
$65$	−0.190429	+	2.94647i	−0.0236198	+	0.365464i
$66$		0			0
$67$	0.258650	+	3.61640i	0.0315991	+	0.441814i	0.988482	+	0.151339i	$0.0483586\pi$
$67$	0.258650	+	3.61640i	0.0315991	+	0.441814i	−0.956883	+	0.290475i	$0.906187\pi$
$68$		0			0
$69$	2.68093	+	5.03325i	0.322747	+	0.605933i
$70$		0			0
$71$	−1.30292	+	1.50365i	−0.154628	+	0.178450i	−0.827778	−	0.561056i	$-0.810395\pi$
$71$	−1.30292	+	1.50365i	−0.154628	+	0.178450i	0.673150	+	0.739506i	$0.264941\pi$
$72$		0			0
$73$	−9.83644	−	7.36347i	−1.15127	−	0.861829i	−0.159165	−	0.987252i	$-0.550880\pi$
$73$	−9.83644	−	7.36347i	−1.15127	−	0.861829i	−0.992103	+	0.125423i	$0.959971\pi$
$74$		0			0
$75$	5.79174	−	1.34339i	0.668773	−	0.155122i
$76$		0			0
$77$	−3.02672	−	13.9136i	−0.344926	−	1.58560i
$78$		0			0
$79$	3.37219	+	0.990164i	0.379401	+	0.111402i	0.465872	−	0.884852i	$-0.345741\pi$
$79$	3.37219	+	0.990164i	0.379401	+	0.111402i	−0.0864708	+	0.996254i	$0.527559\pi$
$80$		0			0
$81$	−1.13052	−	1.30469i	−0.125613	−	0.144965i
$82$		0			0
$83$	−4.05317	+	1.51175i	−0.444893	+	0.165936i	−0.561919	−	0.827192i	$-0.689937\pi$
$83$	−4.05317	+	1.51175i	−0.444893	+	0.165936i	0.117026	+	0.993129i	$0.462664\pi$
$84$		0			0
$85$	8.71166	−	0.683168i	0.944912	−	0.0740999i
$86$		0			0
$87$	−0.706085	+	1.89309i	−0.0757002	+	0.202960i
$88$		0			0
$89$	−12.2904	+	7.89859i	−1.30278	+	0.837249i	−0.993512	−	0.113724i	$-0.963722\pi$
$89$	−12.2904	+	7.89859i	−1.30278	+	0.837249i	−0.309273	+	0.950973i	$0.600086\pi$
$90$		0			0
$91$		−	4.98138i		−	0.522190i
$92$		0			0
$93$	−2.63160	+	2.63160i	−0.272884	+	0.272884i
$94$		0			0
$95$	−2.50817	−	1.12471i	−0.257333	−	0.115393i
$96$		0			0
$97$	−10.2534	−	3.82433i	−1.04108	−	0.388302i	−0.229969	−	0.973198i	$-0.573862\pi$
$97$	−10.2534	−	3.82433i	−1.04108	−	0.388302i	−0.811108	+	0.584896i	$0.801135\pi$
$98$		0			0
$99$	5.74391	−	1.68656i	0.577285	−	0.169506i
$100$		0			0
$101$	−5.41166	+	11.8499i	−0.538480	+	1.17911i	0.423477	+	0.905907i	$0.360809\pi$
$101$	−5.41166	+	11.8499i	−0.538480	+	1.17911i	−0.961957	+	0.273200i	$0.911918\pi$
$102$		0			0
$103$	1.39787	−	19.5448i	0.137737	−	1.92581i	−0.191375	−	0.981517i	$-0.561295\pi$
$103$	1.39787	−	19.5448i	0.137737	−	1.92581i	0.329111	−	0.944291i	$-0.393251\pi$
$104$		0			0
$105$	−9.60478	+	2.89193i	−0.937330	+	0.282224i
$106$		0			0
$107$	−2.90031	+	0.630925i	−0.280384	+	0.0609938i	−0.350558	−	0.936541i	$-0.614008\pi$
$107$	−2.90031	+	0.630925i	−0.280384	+	0.0609938i	0.0701742	+	0.997535i	$0.477644\pi$
$108$		0			0
$109$	2.33465	−	16.2379i	0.223619	−	1.55531i	−0.500564	−	0.865699i	$-0.666874\pi$
$109$	2.33465	−	16.2379i	0.223619	−	1.55531i	0.724184	−	0.689607i	$-0.242217\pi$
$110$		0			0
$111$	7.65999	−	1.10134i	0.727054	−	0.104535i
$112$		0			0
$113$	6.62285	−	0.473676i	0.623026	−	0.0445597i	0.243742	−	0.969840i	$-0.421625\pi$
$113$	6.62285	−	0.473676i	0.623026	−	0.0445597i	0.379284	+	0.925280i	$0.376170\pi$
$114$		0			0
$115$	1.48880	+	10.6200i	0.138832	+	0.990316i
$116$		0			0
$117$	2.08895	−	0.149405i	0.193124	−	0.0138125i
$118$		0			0
$119$	−14.5926	+	2.09810i	−1.33770	+	0.192332i
$120$		0			0
$121$	0.462000	−	3.21328i	0.0420000	−	0.292117i
$122$		0			0
$123$	−1.72436	+	0.375111i	−0.155480	+	0.0338226i
$124$		0			0
$125$	11.0969	+	1.36306i	0.992540	+	0.121916i
$126$		0			0
$127$	0.829428	−	11.5969i	0.0735998	−	1.02906i	−0.817700	−	0.575645i	$-0.804751\pi$
$127$	0.829428	−	11.5969i	0.0735998	−	1.02906i	0.891299	−	0.453415i	$-0.149794\pi$
$128$		0			0
$129$	−4.70525	+	10.3031i	−0.414275	+	0.907135i
$130$		0			0
$131$	11.6286	−	3.41446i	1.01599	−	0.298323i	0.268991	−	0.963143i	$-0.413310\pi$
$131$	11.6286	−	3.41446i	1.01599	−	0.298323i	0.747004	+	0.664820i	$0.231492\pi$
$132$		0			0
$133$	4.34513	+	1.62065i	0.376771	+	0.140528i
$134$		0			0
$135$	−4.33959	−	11.3955i	−0.373493	−	0.980772i
$136$		0			0
$137$	2.84104	−	2.84104i	0.242726	−	0.242726i	−0.575251	−	0.817977i	$-0.695096\pi$
$137$	2.84104	−	2.84104i	0.242726	−	0.242726i	0.817977	+	0.575251i	$0.195096\pi$
$138$		0			0
$139$		−	20.7804i		−	1.76257i	−0.472587	−	0.881284i	$-0.656680\pi$
$139$		−	20.7804i		−	1.76257i	0.472587	−	0.881284i	$-0.343320\pi$
$140$		0			0
$141$	−7.31888	+	4.70356i	−0.616361	+	0.396111i
$142$		0			0
$143$	1.74171	−	4.66970i	0.145649	−	0.390500i
$144$		0			0
$145$	−2.46835	+	2.88843i	−0.204986	+	0.239871i
$146$		0			0
$147$	8.05701	−	3.00511i	0.664531	−	0.247857i
$148$		0			0
$149$	7.59137	+	8.76091i	0.621909	+	0.717722i	0.976068	−	0.217464i	$-0.0697784\pi$
$149$	7.59137	+	8.76091i	0.621909	+	0.717722i	−0.354159	+	0.935185i	$0.615233\pi$
$150$		0			0
$151$	−5.59174	−	1.64188i	−0.455049	−	0.133614i	0.0461725	−	0.998933i	$-0.485298\pi$
$151$	−5.59174	−	1.64188i	−0.455049	−	0.133614i	−0.501221	+	0.865319i	$0.667116\pi$
$152$		0			0
$153$	−1.31751	−	6.05649i	−0.106514	−	0.489639i
$154$		0			0
$155$	−6.34592	+	2.95086i	−0.509717	+	0.237019i
$156$		0			0
$157$	−10.7860	−	8.07433i	−0.860820	−	0.644401i	0.0748826	−	0.997192i	$-0.476142\pi$
$157$	−10.7860	−	8.07433i	−0.860820	−	0.644401i	−0.935702	+	0.352791i	$0.885233\pi$
$158$		0			0
$159$	−10.7462	+	12.4017i	−0.852226	+	0.983521i
$160$		0			0
$161$	−3.66210	−	17.7177i	−0.288614	−	1.39635i
$162$		0			0
$163$	1.26052	+	17.6243i	0.0987312	+	1.38044i	0.769439	+	0.638721i	$0.220536\pi$
$163$	1.26052	+	17.6243i	0.0987312	+	1.38044i	−0.670707	+	0.741722i	$0.734009\pi$
$164$		0			0
$165$	−10.0150	−	0.647264i	−0.779664	−	0.0503894i
$166$		0			0
$167$	13.6353	−	10.2072i	1.05513	−	0.789860i	0.0768271	−	0.997044i	$-0.475521\pi$
$167$	13.6353	−	10.2072i	1.05513	−	0.789860i	0.978302	+	0.207185i	$0.0664301\pi$
$168$		0			0
$169$	−6.08568	+	9.46950i	−0.468129	+	0.728423i
$170$		0			0
$171$	−0.549301	+	1.87075i	−0.0420061	+	0.143060i
$172$		0			0
$173$	−19.1909	−	1.37256i	−1.45906	−	0.104354i	−0.680878	−	0.732397i	$-0.738402\pi$
$173$	−19.1909	−	1.37256i	−1.45906	−	0.104354i	−0.778179	+	0.628043i	$0.783856\pi$
$174$		0			0
$175$	−18.8311	−	1.08738i	−1.42350	−	0.0821983i
$176$		0			0
$177$	−9.77146	−	5.33562i	−0.734468	−	0.401050i
$178$		0			0
$179$	−4.65367	+	2.12526i	−0.347831	+	0.158849i	−0.581667	−	0.813427i	$-0.697599\pi$
$179$	−4.65367	+	2.12526i	−0.347831	+	0.158849i	0.233836	+	0.972276i	$0.424872\pi$
$180$		0			0
$181$	8.82877	+	13.7378i	0.656237	+	1.02113i	0.996724	+	0.0808759i	$0.0257718\pi$
$181$	8.82877	+	13.7378i	0.656237	+	1.02113i	−0.340487	+	0.940249i	$0.610592\pi$
$182$		0			0
$183$	−1.38132	−	1.38132i	−0.102110	−	0.102110i
$184$		0			0
$185$	14.2408	+	2.99574i	1.04701	+	0.220251i
$186$		0			0
$187$	−14.4131	−	3.13538i	−1.05399	−	0.229282i
$188$		0			0
$189$	8.54607	+	18.7133i	0.621635	+	1.36119i
$190$		0			0
$191$	1.58046	+	5.38254i	0.114358	+	0.389467i	0.996703	−	0.0811356i	$-0.0258547\pi$
$191$	1.58046	+	5.38254i	0.114358	+	0.389467i	−0.882345	+	0.470603i	$0.844037\pi$
$192$		0			0
$193$	−0.0870802	−	0.233471i	−0.00626817	−	0.0168056i	0.933778	−	0.357853i	$-0.116491\pi$
$193$	−0.0870802	−	0.233471i	−0.00626817	−	0.0168056i	−0.940046	+	0.341047i	$0.889218\pi$
$194$		0			0
$195$	−3.37544	−	0.966017i	−0.241720	−	0.0691779i
$196$		0			0
$197$	0.367745	+	0.673476i	0.0262008	+	0.0479831i	0.890451	−	0.455078i	$-0.150389\pi$
$197$	0.367745	+	0.673476i	0.0262008	+	0.0479831i	−0.864251	+	0.503061i	$0.832207\pi$
$198$		0			0
$199$	−4.15998	−	2.67346i	−0.294893	−	0.189517i	0.384825	−	0.922989i	$-0.374262\pi$
$199$	−4.15998	−	2.67346i	−0.294893	−	0.189517i	−0.679719	+	0.733473i	$0.737898\pi$
$200$		0			0
$201$	−4.26737	−	0.613555i	−0.300997	−	0.0432768i
$202$		0			0
$203$	3.84142	−	5.13154i	0.269615	−	0.360163i
$204$		0			0
$205$	−3.28783	−	0.449720i	−0.229632	−	0.0314098i
$206$		0			0
$207$	7.32012	−	2.06711i	0.508784	−	0.143674i
$208$		0			0
$209$	3.50661	+	3.03850i	0.242558	+	0.210177i
$210$		0			0
$211$	1.54764	+	10.7641i	0.106544	+	0.741031i	0.971131	+	0.238547i	$0.0766712\pi$
$211$	1.54764	+	10.7641i	0.106544	+	0.741031i	−0.864587	+	0.502484i	$0.832420\pi$
$212$		0			0
$213$	−1.41780	−	1.89395i	−0.0971458	−	0.129772i
$214$		0			0
$215$	−14.9573	+	15.1639i	−1.02008	+	1.03417i
$216$		0			0
$217$	10.3629	−	5.65856i	0.703478	−	0.384128i
$218$		0			0
$219$	11.0421	−	9.56801i	0.746154	−	0.646546i
$220$		0			0
$221$	−4.69390	−	2.14363i	−0.315746	−	0.144196i
$222$		0			0
$223$	−1.22440	+	2.24231i	−0.0819916	+	0.150156i	−0.915458	−	0.402414i	$-0.868171\pi$
$223$	−1.22440	+	2.24231i	−0.0819916	+	0.150156i	0.833466	+	0.552571i	$0.186353\pi$
$224$		0			0
$225$	−0.108798	−	7.92946i	−0.00725321	−	0.528631i
$226$		0			0
$227$	4.01281	−	18.4466i	0.266340	−	1.22434i	−0.628448	−	0.777852i	$-0.716310\pi$
$227$	4.01281	−	18.4466i	0.266340	−	1.22434i	0.894788	−	0.446492i	$-0.147327\pi$
$228$		0			0
$229$	−1.04003			−0.0687269			−0.0343634	−	0.999409i	$-0.510940\pi$
$229$	−1.04003			−0.0687269			−0.0343634	+	0.999409i	$0.510940\pi$
$230$		0			0
$231$	16.9316			1.11402
$232$		0			0
$233$	2.40119	−	11.0381i	0.157307	−	0.723130i	−0.829138	−	0.559043i	$-0.811169\pi$
$233$	2.40119	−	11.0381i	0.157307	−	0.723130i	0.986446	−	0.164087i	$-0.0524678\pi$
$234$		0			0
$235$	−15.9619	+	3.58716i	−1.04124	+	0.234000i
$236$		0			0
$237$	−2.00286	+	3.66796i	−0.130100	+	0.238259i
$238$		0			0
$239$	−0.0301011	−	0.0137467i	−0.00194708	−	0.000889202i	0.414441	−	0.910076i	$-0.363977\pi$
$239$	−0.0301011	−	0.0137467i	−0.00194708	−	0.000889202i	−0.416388	+	0.909187i	$0.636704\pi$
$240$		0			0
$241$	−8.96172	+	7.76538i	−0.577275	+	0.500212i	−0.893856	−	0.448354i	$-0.852011\pi$
$241$	−8.96172	+	7.76538i	−0.577275	+	0.500212i	0.316581	+	0.948566i	$0.397465\pi$
$242$		0			0
$243$	−12.5569	+	6.85661i	−0.805528	+	0.439852i
$244$		0			0
$245$	16.1701	−	0.110928i	1.03307	−	0.00708693i
$246$		0			0
$247$	0.972765	+	1.29946i	0.0618956	+	0.0826828i
$248$		0			0
$249$	−0.732060	−	5.09159i	−0.0463924	−	0.322666i
$250$		0			0
$251$	−16.2645	−	14.0932i	−1.02660	−	0.889557i	−0.0326622	−	0.999466i	$-0.510399\pi$
$251$	−16.2645	−	14.0932i	−1.02660	−	0.889557i	−0.993942	+	0.109909i	$0.964944\pi$
$252$		0			0
$253$	2.76192	−	17.8896i	0.173640	−	1.12471i
$254$		0			0
$255$	−1.40818	+	10.2950i	−0.0881837	+	0.644696i
$256$		0			0
$257$	−5.50198	+	7.34979i	−0.343204	+	0.458467i	−0.938621	−	0.344950i	$-0.887896\pi$
$257$	−5.50198	+	7.34979i	−0.343204	+	0.458467i	0.595417	+	0.803417i	$0.296987\pi$
$258$		0			0
$259$	−24.3018	−	3.49407i	−1.51004	−	0.217111i
$260$		0			0
$261$	2.26713	+	1.45700i	0.140332	+	0.0901859i
$262$		0			0
$263$	9.44173	+	17.2912i	0.582202	+	1.06622i	0.988319	+	0.152402i	$0.0487007\pi$
$263$	9.44173	+	17.2912i	0.582202	+	1.06622i	−0.406117	+	0.913821i	$0.633117\pi$
$264$		0			0
$265$	−26.9815	+	14.9742i	−1.65746	+	0.919859i
$266$		0			0
$267$	−6.07102	−	16.2770i	−0.371541	−	0.996139i
$268$		0			0
$269$	−0.297750	−	1.01404i	−0.0181541	−	0.0618273i	0.949918	−	0.312500i	$-0.101166\pi$
$269$	−0.297750	−	1.01404i	−0.0181541	−	0.0618273i	−0.968072	+	0.250673i	$0.919348\pi$
$270$		0			0
$271$	5.43112	+	11.8925i	0.329917	+	0.722418i	0.999799	−	0.0200501i	$-0.00638257\pi$
$271$	5.43112	+	11.8925i	0.329917	+	0.722418i	−0.669882	+	0.742468i	$0.733655\pi$
$272$		0			0
$273$	5.78799	+	1.25910i	0.350305	+	0.0762042i
$274$		0			0
$275$	−17.2727	−	7.60352i	−1.04158	−	0.458509i
$276$		0			0
$277$	−20.8264	−	20.8264i	−1.25133	−	1.25133i	−0.955122	−	0.296213i	$-0.904276\pi$
$277$	−20.8264	−	20.8264i	−1.25133	−	1.25133i	−0.296213	−	0.955122i	$-0.595724\pi$
$278$		0			0
$279$	2.68374	+	4.17598i	0.160671	+	0.250009i
$280$		0			0
$281$	−2.68048	+	1.22413i	−0.159904	+	0.0730257i	−0.493759	−	0.869599i	$-0.664378\pi$
$281$	−2.68048	+	1.22413i	−0.159904	+	0.0730257i	0.333855	+	0.942624i	$0.391650\pi$
$282$		0			0
$283$	5.27573	+	2.88077i	0.313610	+	0.171244i	0.628343	−	0.777936i	$-0.283733\pi$
$283$	5.27573	+	2.88077i	0.313610	+	0.171244i	−0.314734	+	0.949180i	$0.601915\pi$
$284$		0			0
$285$	1.94080	−	2.63003i	0.114963	−	0.155789i
$286$		0			0
$287$	5.58431	+	0.399398i	0.329631	+	0.0235757i
$288$		0			0
$289$	0.486853	−	1.65807i	0.0286384	−	0.0975334i
$290$		0			0
$291$	7.03525	−	10.9471i	0.412414	−	0.641728i
$292$		0			0
$293$	19.0746	−	14.2791i	1.11435	−	0.834192i	0.126867	−	0.991920i	$-0.459508\pi$
$293$	19.0746	−	14.2791i	1.11435	−	0.834192i	0.987483	+	0.157728i	$0.0504168\pi$
$294$		0			0
$295$	−13.8183	−	15.7278i	−0.804531	−	0.915710i
$296$		0			0
$297$	1.46837	+	20.5305i	0.0852035	+	1.19130i
$298$		0			0
$299$	2.27449	−	5.91009i	0.131537	−	0.341789i
$300$		0			0
$301$	23.5320	−	27.1574i	1.35636	−	1.56533i
$302$		0			0
$303$	−12.4008	−	9.28314i	−0.712408	−	0.533302i
$304$		0			0
$305$	−1.54890	−	3.33095i	−0.0886895	−	0.190730i
$306$		0			0
$307$	4.06839	+	18.7021i	0.232195	+	1.06738i	0.934626	+	0.355632i	$0.115734\pi$
$307$	4.06839	+	18.7021i	0.232195	+	1.06738i	−0.702431	+	0.711752i	$0.747902\pi$
$308$		0			0
$309$	22.3563	+	6.56440i	1.27180	+	0.373436i
$310$		0			0
$311$	8.70169	+	10.0423i	0.493428	+	0.569446i	0.946778	−	0.321886i	$-0.104317\pi$
$311$	8.70169	+	10.0423i	0.493428	+	0.569446i	−0.453351	+	0.891332i	$0.649771\pi$
$312$		0			0
$313$	−12.5882	+	4.69516i	−0.711528	+	0.265386i	−0.679056	−	0.734086i	$-0.737611\pi$
$313$	−12.5882	+	4.69516i	−0.711528	+	0.265386i	−0.0324721	+	0.999473i	$0.510338\pi$
$314$		0			0
$315$	1.04598	+	13.3382i	0.0589342	+	0.751521i
$316$		0			0
$317$	−0.523552	+	1.40370i	−0.0294056	+	0.0788395i	−0.950823	−	0.309735i	$-0.899760\pi$
$317$	−0.523552	+	1.40370i	−0.0294056	+	0.0788395i	0.921417	+	0.388574i	$0.127032\pi$
$318$		0			0
$319$	5.39528	−	3.46734i	0.302078	−	0.194134i
$320$		0			0
$321$		−	3.52942i		−	0.196993i
$322$		0			0
$323$	3.39696	−	3.39696i	0.189012	−	0.189012i
$324$		0			0
$325$	−5.33915	−	3.88369i	−0.296163	−	0.215428i
$326$		0			0
$327$	18.2771	+	6.81700i	1.01073	+	0.376981i
$328$		0			0
$329$	26.4831	−	7.77615i	1.46006	−	0.428713i
$330$		0			0
$331$	−9.47026	+	20.7370i	−0.520532	+	1.13981i	0.448705	+	0.893680i	$0.351885\pi$
$331$	−9.47026	+	20.7370i	−0.520532	+	1.13981i	−0.969238	+	0.246127i	$0.920842\pi$
$332$		0			0
$333$	0.736369	−	10.2958i	0.0403528	−	0.564206i
$334$		0			0
$335$	−7.14198	−	3.83645i	−0.390208	−	0.209608i
$336$		0			0
$337$	−33.3935	+	7.26431i	−1.81906	+	0.395712i	−0.987228	−	0.159315i	$-0.949072\pi$
$337$	−33.3935	+	7.26431i	−1.81906	+	0.395712i	−0.831832	+	0.555027i	$0.812708\pi$
$338$		0			0
$339$	−1.12363	+	7.81499i	−0.0610270	+	0.424452i
$340$		0			0
$341$	11.6930	−	1.68120i	0.633210	−	0.0910419i
$342$		0			0
$343$	−0.871772	+	0.0623504i	−0.0470713	+	0.00336660i
$344$		0			0
$345$	−12.7159	−	0.954436i	−0.684601	−	0.0513851i
$346$		0			0
$347$	−31.0254	+	2.21898i	−1.66553	+	0.119121i	−0.872031	−	0.489450i	$-0.837198\pi$
$347$	−31.0254	+	2.21898i	−1.66553	+	0.119121i	−0.793500	+	0.608571i	$0.791743\pi$
$348$		0			0
$349$	17.9994	−	2.58792i	0.963485	−	0.138528i	0.357421	−	0.933944i	$-0.383656\pi$
$349$	17.9994	−	2.58792i	0.963485	−	0.138528i	0.606065	+	0.795415i	$0.292747\pi$
$350$		0			0
$351$	−1.02477	+	7.12746i	−0.0546984	+	0.380436i
$352$		0			0
$353$	−14.0800	+	3.06291i	−0.749401	+	0.163022i	−0.571016	−	0.820939i	$-0.693451\pi$
$353$	−14.0800	+	3.06291i	−0.749401	+	0.163022i	−0.178384	+	0.983961i	$0.557087\pi$
$354$		0			0
$355$	−1.28265	−	4.25999i	−0.0680761	−	0.226097i
$356$		0			0
$357$	1.25061	−	17.4858i	0.0661892	−	0.925447i
$358$		0			0
$359$	0.569950	−	1.24802i	0.0300808	−	0.0658678i	−0.893995	−	0.448077i	$-0.852109\pi$
$359$	0.569950	−	1.24802i	0.0300808	−	0.0658678i	0.924076	+	0.382209i	$0.124836\pi$
$360$		0			0
$361$	16.7804	−	4.92717i	0.883179	−	0.259325i
$362$		0			0
$363$	3.61682	+	1.34900i	0.189834	+	0.0708043i
$364$		0			0
$365$	25.6763	−	9.77793i	1.34396	−	0.511800i
$366$		0			0
$367$	0.453329	−	0.453329i	0.0236636	−	0.0236636i	−0.695176	−	0.718840i	$-0.744674\pi$
$367$	0.453329	−	0.453329i	0.0236636	−	0.0236636i	0.718840	+	0.695176i	$0.244674\pi$
$368$		0			0
$369$			2.35377i			0.122532i
$370$		0			0
$371$	43.7967	−	28.1464i	2.27381	−	1.46129i
$372$		0			0
$373$	−7.56022	+	20.2697i	−0.391454	+	1.04953i	0.580480	+	0.814274i	$0.302865\pi$
$373$	−7.56022	+	20.2697i	−0.391454	+	1.04953i	−0.971934	+	0.235253i	$0.924408\pi$
$374$		0			0
$375$	−4.38865	+	12.5493i	−0.226629	+	0.648042i
$376$		0			0
$377$	2.10220	−	0.784079i	0.108269	−	0.0403821i
$378$		0			0
$379$	4.18679	+	4.83182i	0.215061	+	0.248194i	0.853022	−	0.521875i	$-0.174767\pi$
$379$	4.18679	+	4.83182i	0.215061	+	0.248194i	−0.637961	+	0.770069i	$0.720222\pi$
$380$		0			0
$381$	13.2651	+	3.89499i	0.679592	+	0.199546i
$382$		0			0
$383$	8.28855	+	38.1019i	0.423525	+	1.94691i	0.296602	+	0.955001i	$0.404147\pi$
$383$	8.28855	+	38.1019i	0.423525	+	1.94691i	0.126923	+	0.991913i	$0.459490\pi$
$384$		0			0
$385$	29.9075	+	10.9218i	1.52423	+	0.556627i
$386$		0			0
$387$	12.0943	+	9.05368i	0.614788	+	0.460224i
$388$		0			0
$389$	−21.7293	+	25.0770i	−1.10172	+	1.27145i	−0.142191	+	0.989839i	$0.545415\pi$
$389$	−21.7293	+	25.0770i	−1.10172	+	1.27145i	−0.959528	+	0.281613i	$0.909131\pi$
$390$		0			0
$391$	−18.2711	−	4.17369i	−0.924012	−	0.211073i
$392$		0			0
$393$	1.02809	+	14.3746i	0.0518604	+	0.725103i
$394$		0			0
$395$	−5.90383	+	5.18703i	−0.297054	+	0.260988i
$396$		0			0
$397$	−15.5379	+	11.6315i	−0.779823	+	0.583768i	−0.913302	−	0.407284i	$-0.866476\pi$
$397$	−15.5379	+	11.6315i	−0.779823	+	0.583768i	0.133479	+	0.991052i	$0.457385\pi$
$398$		0			0
$399$	−2.98136	+	4.63908i	−0.149254	+	0.232244i
$400$		0			0
$401$	−5.56926	+	18.9672i	−0.278115	+	0.947174i	0.695413	+	0.718610i	$0.255221\pi$
$401$	−5.56926	+	18.9672i	−0.278115	+	0.947174i	−0.973529	+	0.228564i	$0.926597\pi$
$402$		0			0
$403$	4.12221	+	0.294827i	0.205342	+	0.0146864i
$404$		0			0
$405$	3.81708	−	0.575567i	0.189672	−	0.0286001i
$406$		0			0
$407$	−21.5596	−	11.7724i	−1.06867	−	0.583537i
$408$		0			0
$409$	9.81565	−	4.48266i	0.485353	−	0.221653i	−0.157682	−	0.987490i	$-0.550402\pi$
$409$	9.81565	−	4.48266i	0.485353	−	0.221653i	0.643035	+	0.765837i	$0.277675\pi$
$410$		0			0
$411$	2.58297	+	4.01918i	0.127408	+	0.198251i
$412$		0			0
$413$	24.9757	+	24.9757i	1.22898	+	1.22898i
$414$		0			0
$415$	1.99126	−	9.46586i	0.0977473	−	0.464661i
$416$		0			0
$417$	24.1452	+	5.25248i	1.18240	+	0.257215i
$418$		0			0
$419$	−4.64754	−	10.1767i	−0.227047	−	0.497164i	0.761484	−	0.648184i	$-0.224471\pi$
$419$	−4.64754	−	10.1767i	−0.227047	−	0.497164i	−0.988531	+	0.151020i	$0.951744\pi$
$420$		0			0
$421$	7.70294	+	26.2338i	0.375419	+	1.27856i	0.903215	+	0.429188i	$0.141200\pi$
$421$	7.70294	+	26.2338i	0.375419	+	1.27856i	−0.527797	+	0.849371i	$0.676982\pi$
$422$		0			0
$423$	4.05524	+	10.8725i	0.197172	+	0.528640i
$424$		0			0
$425$	−9.12820	+	17.2764i	−0.442783	+	0.838029i
$426$		0			0
$427$	2.97016	+	5.43944i	0.143736	+	0.263233i
$428$		0			0
$429$	4.98561	+	3.20406i	0.240707	+	0.154693i
$430$		0			0
$431$	−6.20819	−	0.892603i	−0.299038	−	0.0429952i	−0.00883714	−	0.999961i	$-0.502813\pi$
$431$	−6.20819	−	0.892603i	−0.299038	−	0.0429952i	−0.290201	+	0.956966i	$0.593722\pi$
$432$		0			0
$433$	15.2440	−	20.3637i	0.732582	−	0.978615i	−0.267306	−	0.963612i	$-0.586133\pi$
$433$	15.2440	−	20.3637i	0.732582	−	0.978615i	0.999887	−	0.0150030i	$-0.00477578\pi$
$434$		0			0
$435$	−2.73224	−	3.59813i	−0.131001	−	0.172517i
$436$		0			0
$437$	4.41523	+	3.90678i	0.211209	+	0.186887i
$438$		0			0
$439$	8.59930	+	7.45134i	0.410422	+	0.355633i	0.835468	−	0.549539i	$-0.185197\pi$
$439$	8.59930	+	7.45134i	0.410422	+	0.355633i	−0.425046	+	0.905172i	$0.639742\pi$
$440$		0			0
$441$	−1.63231	−	11.3530i	−0.0777292	−	0.540619i
$442$		0			0
$443$	−20.0229	−	26.7475i	−0.951319	−	1.27081i	−0.962614	−	0.270877i	$-0.912686\pi$
$443$	−20.0229	−	26.7475i	−0.951319	−	1.27081i	0.0112953	−	0.999936i	$-0.496405\pi$
$444$		0			0
$445$	−0.224101	−	32.6675i	−0.0106234	−	1.54859i
$446$		0			0
$447$	−12.0983	+	6.60619i	−0.572231	+	0.312462i
$448$		0			0
$449$	−8.21019	+	7.11417i	−0.387463	+	0.335739i	−0.826711	−	0.562628i	$-0.809791\pi$
$449$	−8.21019	+	7.11417i	−0.387463	+	0.335739i	0.439248	+	0.898366i	$0.355245\pi$
$450$		0			0
$451$	5.09526	+	2.32693i	0.239927	+	0.109571i
$452$		0			0
$453$	3.32112	−	6.08217i	0.156040	−	0.285766i
$454$		0			0
$455$	9.41156	+	5.95761i	0.441221	+	0.279297i
$456$		0			0
$457$	−3.97189	+	18.2585i	−0.185797	+	0.854096i	0.785990	+	0.618239i	$0.212153\pi$
$457$	−3.97189	+	18.2585i	−0.185797	+	0.854096i	−0.971788	+	0.235857i	$0.924210\pi$
$458$		0			0
$459$	21.3110			0.994711
$460$		0			0
$461$	−1.13990			−0.0530906			−0.0265453	−	0.999648i	$-0.508451\pi$
$461$	−1.13990			−0.0530906			−0.0265453	+	0.999648i	$0.508451\pi$
$462$		0			0
$463$	6.62810	−	30.4689i	0.308034	−	1.41601i	−0.519441	−	0.854506i	$-0.673860\pi$
$463$	6.62810	−	30.4689i	0.308034	−	1.41601i	0.827475	−	0.561503i	$-0.189777\pi$
$464$		0			0
$465$	−1.82468	−	8.11935i	−0.0846175	−	0.376526i
$466$		0			0
$467$	9.98531	−	18.2867i	0.462065	−	0.846209i	−0.537930	−	0.842990i	$-0.680793\pi$
$467$	9.98531	−	18.2867i	0.462065	−	0.846209i	0.999995	−	0.00321954i	$-0.00102481\pi$
$468$		0			0
$469$	12.4417	+	5.68192i	0.574503	+	0.262367i
$470$		0			0
$471$	12.1081	−	10.4917i	0.557910	−	0.483432i
$472$		0			0
$473$	31.5551	−	17.2304i	1.45091	−	0.792254i
$474$		0			0
$475$	5.12470	−	3.39368i	0.235137	−	0.155713i
$476$		0			0
$477$	13.1168	+	17.5220i	0.600578	+	0.802278i
$478$		0			0
$479$	−4.87406	−	33.8998i	−0.222702	−	1.54892i	−0.727756	−	0.685836i	$-0.759437\pi$
$479$	−4.87406	−	33.8998i	−0.222702	−	1.54892i	0.505055	−	0.863087i	$-0.331472\pi$
$480$		0			0
$481$	−6.49460	−	5.62760i	−0.296128	−	0.256597i
$482$		0			0
$483$	21.5123	+	0.223264i	0.978844	+	0.0101588i
$484$		0			0
$485$	19.4883	−	14.7985i	0.884920	−	0.671964i
$486$		0			0
$487$	7.58814	−	10.1366i	0.343851	−	0.459332i	−0.594964	−	0.803752i	$-0.702834\pi$
$487$	7.58814	−	10.1366i	0.343851	−	0.459332i	0.938815	+	0.344421i	$0.111925\pi$
$488$		0			0
$489$	−20.7967	−	2.99012i	−0.940461	−	0.135218i
$490$		0			0
$491$	−15.7370	−	10.1135i	−0.710200	−	0.456418i	0.135015	−	0.990844i	$-0.456892\pi$
$491$	−15.7370	−	10.1135i	−0.710200	−	0.456418i	−0.845216	+	0.534426i	$0.820528\pi$
$492$		0			0
$493$	−3.18232	−	5.82798i	−0.143325	−	0.262479i
$494$		0			0
$495$	−3.68308	+	12.8693i	−0.165542	+	0.578434i
$496$		0			0
$497$	2.62300	+	7.03253i	0.117658	+	0.315452i
$498$		0			0
$499$	−3.76998	−	12.8394i	−0.168768	−	0.574770i	−0.999827	−	0.0185865i	$-0.994083\pi$
$499$	−3.76998	−	12.8394i	−0.168768	−	0.574770i	0.831060	−	0.556183i	$-0.187735\pi$
$500$		0			0
$501$	8.41358	+	18.4232i	0.375891	+	0.823086i
$502$		0			0
$503$	−1.34944	−	0.293552i	−0.0601684	−	0.0130888i	0.182380	−	0.983228i	$-0.441620\pi$
$503$	−1.34944	−	0.293552i	−0.0601684	−	0.0130888i	−0.242549	+	0.970139i	$0.577983\pi$
$504$		0			0
$505$	−15.9163	−	24.3967i	−0.708268	−	1.08564i
$506$		0			0
$507$	−9.46463	−	9.46463i	−0.420339	−	0.420339i
$508$		0			0
$509$	−10.5456	−	16.4093i	−0.467425	−	0.727328i	0.524876	−	0.851179i	$-0.324112\pi$
$509$	−10.5456	−	16.4093i	−0.467425	−	0.727328i	−0.992301	+	0.123851i	$0.960475\pi$
$510$		0			0
$511$	−42.1646	+	19.2559i	−1.86525	+	0.851832i
$512$		0			0
$513$	−5.88370	−	3.21274i	−0.259772	−	0.141846i
$514$		0			0
$515$	35.2552	+	26.0162i	1.55353	+	1.14641i
$516$		0			0
$517$	27.5450	+	1.97006i	1.21143	+	0.0866430i
$518$		0			0
$519$	6.44553	−	21.9515i	0.282927	−	0.963562i
$520$		0			0
$521$	7.68099	−	11.9519i	0.336510	−	0.523620i	−0.631222	−	0.775603i	$-0.717446\pi$
$521$	7.68099	−	11.9519i	0.336510	−	0.523620i	0.967732	+	0.251982i	$0.0810825\pi$
$522$		0			0
$523$	−24.3809	+	18.2513i	−1.06610	+	0.798074i	−0.980156	−	0.198226i	$-0.936482\pi$
$523$	−24.3809	+	18.2513i	−1.06610	+	0.798074i	−0.0859455	+	0.996300i	$0.527391\pi$
$524$		0			0
$525$	6.02323	−	21.6055i	0.262875	−	0.942940i
$526$		0			0
$527$	−0.872553	−	12.1999i	−0.0380090	−	0.531436i
$528$		0			0
$529$	3.74503	−	22.6931i	0.162828	−	0.986655i
$530$		0			0
$531$	−9.72453	+	11.2227i	−0.422009	+	0.487024i
$532$		0			0
$533$	1.56875	+	1.17435i	0.0679502	+	0.0508669i
$534$		0			0
$535$	2.27667	−	6.23428i	0.0984291	−	0.269531i
$536$		0			0
$537$	−1.29312	−	5.94440i	−0.0558024	−	0.256520i
$538$		0			0
$539$	−26.1898	−	7.69002i	−1.12807	−	0.331233i
$540$		0			0
$541$	3.00657	+	3.46977i	0.129263	+	0.149177i	0.816691	−	0.577075i	$-0.195806\pi$
$541$	3.00657	+	3.46977i	0.129263	+	0.149177i	−0.687428	+	0.726252i	$0.741261\pi$
$542$		0			0
$543$	−18.1939	+	6.78598i	−0.780775	+	0.291214i
$544$		0			0
$545$	27.8868	+	23.8311i	1.19454	+	1.02081i
$546$		0			0
$547$	−0.705193	+	1.89070i	−0.0301519	+	0.0808403i	−0.951153	−	0.308719i	$-0.900100\pi$
$547$	−0.705193	+	1.89070i	−0.0301519	+	0.0808403i	0.921002	+	0.389559i	$0.127373\pi$
$548$		0			0
$549$	−2.19195	+	1.40868i	−0.0935503	+	0.0601212i
$550$		0			0
$551$			2.08879i			0.0889853i
$552$		0			0
$553$	9.37526	−	9.37526i	0.398677	−	0.398677i
$554$		0			0
$555$	−7.08036	+	15.7896i	−0.300544	+	0.670230i
$556$		0			0
$557$	40.7637	+	15.2041i	1.72722	+	0.644218i	0.999147	−	0.0412870i	$-0.0131458\pi$
$557$	40.7637	+	15.2041i	1.72722	+	0.644218i	0.728068	+	0.685505i	$0.240419\pi$
$558$		0			0
$559$	12.0683	−	3.54357i	0.510435	−	0.149877i
$560$		0			0
$561$	7.28616	−	15.9545i	0.307622	−	0.673598i
$562$		0			0
$563$	0.341553	−	4.77553i	0.0143947	−	0.201265i	−0.985165	−	0.171608i	$-0.945104\pi$
$563$	0.341553	−	4.77553i	0.0143947	−	0.201265i	0.999560	−	0.0296571i	$-0.00944155\pi$
$564$		0			0
$565$	−7.02584	+	13.0794i	−0.295579	+	0.550254i
$566$		0			0
$567$	−6.36380	+	1.38436i	−0.267254	+	0.0581376i
$568$		0			0
$569$	−5.15335	+	35.8423i	−0.216040	+	1.50259i	0.536421	+	0.843951i	$0.319776\pi$
$569$	−5.15335	+	35.8423i	−0.216040	+	1.50259i	−0.752460	+	0.658637i	$0.771133\pi$
$570$		0			0
$571$	25.3984	−	3.65174i	1.06289	−	0.152821i	0.411383	−	0.911463i	$-0.365046\pi$
$571$	25.3984	−	3.65174i	1.06289	−	0.152821i	0.651508	+	0.758642i	$0.274137\pi$
$572$		0			0
$573$	−6.65359	+	0.475874i	−0.277958	+	0.0198799i
$574$		0			0
$575$	−21.8454	−	9.88835i	−0.911015	−	0.412373i
$576$		0			0
$577$	−3.10478	+	0.222058i	−0.129254	+	0.00924441i	−0.135816	−	0.990734i	$-0.543366\pi$
$577$	−3.10478	+	0.222058i	−0.129254	+	0.00924441i	0.00656242	+	0.999978i	$0.497911\pi$
$578$		0			0
$579$	0.293287	−	0.0421682i	0.0121886	−	0.00175245i
$580$		0			0
$581$	−2.32250	+	16.1534i	−0.0963536	+	0.670154i
$582$		0			0
$583$	50.8976	−	11.0721i	2.10796	−	0.458559i
$584$		0			0
$585$	−2.21606	+	4.12544i	−0.0916228	+	0.170566i
$586$		0			0
$587$	−2.22457	+	31.1035i	−0.0918177	+	1.28378i	0.717562	+	0.696494i	$0.245258\pi$
$587$	−2.22457	+	31.1035i	−0.0918177	+	1.28378i	−0.809380	+	0.587285i	$0.800197\pi$
$588$		0			0
$589$	−1.59830	+	3.49978i	−0.0658567	+	0.144206i
$590$		0			0
$591$	−0.875480	+	0.257064i	−0.0360124	+	0.0105742i
$592$		0			0
$593$	−18.6308	−	6.94893i	−0.765075	−	0.285358i	−0.0635268	−	0.997980i	$-0.520235\pi$
$593$	−18.6308	−	6.94893i	−0.765075	−	0.285358i	−0.701548	+	0.712622i	$0.747508\pi$
$594$		0			0
$595$	13.4883	−	30.0797i	0.552968	−	1.23315i
$596$		0			0
$597$	4.15784	−	4.15784i	0.170169	−	0.170169i
$598$		0			0
$599$		−	42.2696i		−	1.72709i	−0.504272	−	0.863545i	$-0.668239\pi$
$599$		−	42.2696i		−	1.72709i	0.504272	−	0.863545i	$-0.331761\pi$
$600$		0			0
$601$	−35.2127	+	22.6298i	−1.43636	+	0.923090i	−0.436631	+	0.899641i	$0.643828\pi$
$601$	−35.2127	+	22.6298i	−1.43636	+	0.923090i	−0.999725	+	0.0234488i	$0.992535\pi$
$602$		0			0
$603$	−2.00956	+	5.38785i	−0.0818358	+	0.219410i
$604$		0			0
$605$	5.51847	+	4.71589i	0.224358	+	0.191728i
$606$		0			0
$607$	10.5321	−	3.92826i	0.427483	−	0.159443i	−0.126508	−	0.991966i	$-0.540377\pi$
$607$	10.5321	−	3.92826i	0.427483	−	0.159443i	0.553991	+	0.832523i	$0.313104\pi$
$608$		0			0
$609$	4.99150	+	5.76050i	0.202266	+	0.233427i
$610$		0			0
$611$	9.26963	+	2.72181i	0.375009	+	0.110113i
$612$		0			0
$613$	−6.75964	−	31.0736i	−0.273019	−	1.25505i	−0.885528	−	0.464586i	$-0.846203\pi$
$613$	−6.75964	−	31.0736i	−0.273019	−	1.25505i	0.612509	−	0.790464i	$-0.290160\pi$
$614$		0			0
$615$	1.35358	−	3.70654i	0.0545815	−	0.149462i
$616$		0			0
$617$	−17.8799	−	13.3847i	−0.719817	−	0.538848i	0.175390	−	0.984499i	$-0.443881\pi$
$617$	−17.8799	−	13.3847i	−0.719817	−	0.538848i	−0.895207	+	0.445651i	$0.852972\pi$
$618$		0			0
$619$	5.08627	−	5.86987i	0.204435	−	0.235930i	−0.644269	−	0.764799i	$-0.722838\pi$
$619$	5.08627	−	5.86987i	0.204435	−	0.235930i	0.848703	+	0.528869i	$0.177384\pi$
$620$		0			0
$621$	1.59491	+	26.1042i	0.0640015	+	1.04753i
$622$		0			0
$623$	3.93185	+	54.9744i	0.157526	+	2.20250i
$624$		0			0
$625$	−15.8470	+	19.3358i	−0.633879	+	0.773432i
$626$		0			0
$627$	−4.41684	+	3.30641i	−0.176392	+	0.132045i
$628$		0			0
$629$	−13.7502	+	21.3957i	−0.548256	+	0.853103i
$630$		0			0
$631$	9.07907	−	30.9205i	0.361432	−	1.23092i	−0.555377	−	0.831599i	$-0.687426\pi$
$631$	9.07907	−	30.9205i	0.361432	−	1.23092i	0.916809	−	0.399326i	$-0.130756\pi$
$632$		0			0
$633$	−12.8983	−	0.922502i	−0.512660	−	0.0366661i
$634$		0			0
$635$	20.9187	+	15.4367i	0.830131	+	0.612588i
$636$		0			0
$637$	−8.38101	−	4.57638i	−0.332068	−	0.181323i
$638$		0			0
$639$	−2.87043	+	1.31088i	−0.113553	+	0.0518578i
$640$		0			0
$641$	16.5398	+	25.7364i	0.653283	+	1.01653i	0.996996	+	0.0774538i	$0.0246790\pi$
$641$	16.5398	+	25.7364i	0.653283	+	1.01653i	−0.343713	+	0.939075i	$0.611685\pi$
$642$		0			0
$643$	−0.289569	−	0.289569i	−0.0114195	−	0.0114195i	0.701374	−	0.712793i	$-0.252570\pi$
$643$	−0.289569	−	0.289569i	−0.0114195	−	0.0114195i	−0.712793	+	0.701374i	$0.752570\pi$
$644$		0			0
$645$	−13.8387	−	21.2121i	−0.544899	−	0.835226i
$646$		0			0
$647$	−2.44369	−	0.531593i	−0.0960715	−	0.0208991i	0.164273	−	0.986415i	$-0.447472\pi$
$647$	−2.44369	−	0.531593i	−0.0960715	−	0.0208991i	−0.260344	+	0.965516i	$0.583836\pi$
$648$		0			0
$649$	14.6804	+	32.1457i	0.576258	+	1.26183i
$650$		0			0
$651$	3.95549	+	13.4712i	0.155028	+	0.527976i
$652$		0			0
$653$	12.4702	+	33.4339i	0.487997	+	1.30837i	0.914757	+	0.404006i	$0.132382\pi$
$653$	12.4702	+	33.4339i	0.487997	+	1.30837i	−0.426759	+	0.904365i	$0.640345\pi$
$654$		0			0
$655$	−7.45642	+	26.0541i	−0.291346	+	1.01802i
$656$		0			0
$657$	−9.33964	−	17.1043i	−0.364374	−	0.667301i
$658$		0			0
$659$	−15.0131	−	9.64834i	−0.584828	−	0.375846i	0.214516	−	0.976721i	$-0.431183\pi$
$659$	−15.0131	−	9.64834i	−0.584828	−	0.375846i	−0.799343	+	0.600875i	$0.794819\pi$
$660$		0			0
$661$	−38.5455	−	5.54201i	−1.49925	−	0.215559i	−0.656688	−	0.754163i	$-0.728043\pi$
$661$	−38.5455	−	5.54201i	−1.49925	−	0.215559i	−0.842559	+	0.538604i	$0.818952\pi$
$662$		0			0
$663$	3.67718	−	4.91214i	0.142810	−	0.190772i
$664$		0			0
$665$	−8.25865	+	6.27121i	−0.320257	+	0.243187i
$666$		0			0
$667$	6.90065	−	4.33425i	0.267194	−	0.167823i
$668$		0			0
$669$	−2.29592	−	1.98943i	−0.0887654	−	0.0769156i
$670$		0			0
$671$	0.882453	+	6.13760i	0.0340667	+	0.236939i
$672$		0			0
$673$	−9.11271	−	12.1732i	−0.351269	−	0.469241i	0.589754	−	0.807583i	$-0.299225\pi$
$673$	−9.11271	−	12.1732i	−0.351269	−	0.469241i	−0.941023	+	0.338342i	$0.890134\pi$
$674$		0			0
$675$	26.7202	+	5.42979i	1.02846	+	0.208993i
$676$		0			0
$677$	−5.62551	+	3.07176i	−0.216206	+	0.118057i	−0.583703	−	0.811967i	$-0.698397\pi$
$677$	−5.62551	+	3.07176i	−0.216206	+	0.118057i	0.367497	+	0.930025i	$0.380215\pi$
$678$		0			0
$679$	−31.2003	+	27.0352i	−1.19736	+	1.03752i
$680$		0			0
$681$	20.4193	+	9.32517i	0.782469	+	0.357341i
$682$		0			0
$683$	−15.6412	+	28.6447i	−0.598493	+	1.09606i	0.386308	+	0.922370i	$0.373750\pi$
$683$	−15.6412	+	28.6447i	−0.598493	+	1.09606i	−0.984801	+	0.173688i	$0.944432\pi$
$684$		0			0
$685$	1.96989	+	8.76552i	0.0752658	+	0.334913i
$686$		0			0
$687$	0.262878	−	1.20843i	0.0100294	−	0.0461046i
$688$		0			0
$689$	18.2225			0.694221
$690$		0			0
$691$	−14.2831			−0.543356			−0.271678	−	0.962388i	$-0.587579\pi$
$691$	−14.2831			−0.543356			−0.271678	+	0.962388i	$0.587579\pi$
$692$		0			0
$693$	4.80050	−	22.0675i	0.182356	−	0.838276i
$694$		0			0
$695$	39.2614	+	24.8529i	1.48927	+	0.942722i
$696$		0			0
$697$	2.77944	−	5.09017i	0.105279	−	0.192804i
$698$		0			0
$699$	12.2185	+	5.58001i	0.462147	+	0.211055i
$700$		0			0
$701$	−24.7101	+	21.4114i	−0.933288	+	0.808699i	−0.981760	−	0.190126i	$-0.939110\pi$
$701$	−24.7101	+	21.4114i	−0.933288	+	0.808699i	0.0484715	+	0.998825i	$0.484565\pi$
$702$		0			0
$703$	7.02178	−	3.83418i	0.264831	−	0.144609i
$704$		0			0
$705$	−0.133450	−	19.4533i	−0.00502603	−	0.732652i
$706$		0			0
$707$	29.4513	+	39.3423i	1.10763	+	1.47962i
$708$		0			0
$709$	2.04637	+	14.2328i	0.0768529	+	0.534524i	0.991483	+	0.130233i	$0.0415725\pi$
$709$	2.04637	+	14.2328i	0.0768529	+	0.534524i	−0.914631	+	0.404291i	$0.867518\pi$
$710$		0			0
$711$	4.21272	+	3.65034i	0.157989	+	0.136899i
$712$		0			0
$713$	14.8786	−	1.98185i	0.557208	−	0.0742207i
$714$		0			0
$715$	6.73965	+	8.87555i	0.252049	+	0.331927i
$716$		0			0
$717$	0.0235811	−	0.0315006i	0.000880652	−	0.00117641i
$718$		0			0
$719$	−47.8812	−	6.88427i	−1.78567	−	0.256740i	−0.831395	−	0.555682i	$-0.812457\pi$
$719$	−47.8812	−	6.88427i	−1.78567	−	0.256740i	−0.954271	+	0.298942i	$0.903366\pi$
$720$		0			0
$721$	−62.1863	−	39.9647i	−2.31594	−	1.48836i
$722$		0			0
$723$	−6.75761	−	12.3756i	−0.251318	−	0.460255i
$724$		0			0
$725$	−2.50516	−	8.11808i	−0.0930394	−	0.301498i
$726$		0			0
$727$	7.70990	+	20.6710i	0.285944	+	0.766646i	0.997921	+	0.0644436i	$0.0205273\pi$
$727$	7.70990	+	20.6710i	0.285944	+	0.766646i	−0.711977	+	0.702203i	$0.752200\pi$
$728$		0			0
$729$	−6.25206	−	21.2926i	−0.231558	−	0.788614i
$730$		0			0
$731$	−15.4636	−	33.8607i	−0.571943	−	1.25238i
$732$		0			0
$733$	37.2339	+	8.09974i	1.37527	+	0.299171i	0.838657	−	0.544660i	$-0.183341\pi$
$733$	37.2339	+	8.09974i	1.37527	+	0.299171i	0.536609	+	0.843831i	$0.319705\pi$
$734$		0			0
$735$	−3.95830	+	18.8165i	−0.146004	+	0.694058i
$736$		0			0
$737$	9.67656	+	9.67656i	0.356441	+	0.356441i
$738$		0			0
$739$	−1.69841	−	2.64277i	−0.0624769	−	0.0972160i	0.808610	−	0.588346i	$-0.200221\pi$
$739$	−1.69841	−	2.64277i	−0.0624769	−	0.0972160i	−0.871087	+	0.491130i	$0.836584\pi$
$740$		0			0
$741$	−1.75576	+	0.801827i	−0.0644993	+	0.0294558i
$742$		0			0
$743$	−10.6887	−	5.83648i	−0.392131	−	0.214120i	0.271073	−	0.962559i	$-0.412622\pi$
$743$	−10.6887	−	5.83648i	−0.392131	−	0.214120i	−0.663203	+	0.748439i	$0.730804\pi$
$744$		0			0
$745$	−25.6315	+	3.86490i	−0.939066	+	0.141599i
$746$		0			0
$747$	−6.84360	−	0.489464i	−0.250394	−	0.0179085i
$748$		0			0
$749$	−3.15464	+	10.7437i	−0.115268	+	0.392567i
$750$		0			0
$751$	5.50683	−	8.56880i	0.200947	−	0.312680i	−0.726125	−	0.687563i	$-0.758681\pi$
$751$	5.50683	−	8.56880i	0.200947	−	0.312680i	0.927072	+	0.374883i	$0.122317\pi$
$752$		0			0
$753$	20.4863	−	15.3359i	0.746563	−	0.558870i
$754$		0			0
$755$	9.78967	−	8.60109i	0.356283	−	0.313026i
$756$		0			0
$757$	−3.31242	−	46.3136i	−0.120392	−	1.68330i	−0.595488	−	0.803364i	$-0.703041\pi$
$757$	−3.31242	−	46.3136i	−0.120392	−	1.68330i	0.475096	−	0.879934i	$-0.342413\pi$
$758$		0			0
$759$	20.0883	+	7.73094i	0.729157	+	0.280615i
$760$		0			0
$761$	10.8085	−	12.4737i	0.391810	−	0.452172i	−0.525235	−	0.850957i	$-0.676023\pi$
$761$	10.8085	−	12.4737i	0.391810	−	0.452172i	0.917044	+	0.398785i	$0.130568\pi$
$762$		0			0
$763$	−49.5432	−	37.0876i	−1.79358	−	1.34266i
$764$		0			0
$765$	13.0185	+	4.75419i	0.470686	+	0.171888i
$766$		0			0
$767$	2.62796	+	12.0806i	0.0948902	+	0.436203i
$768$		0			0
$769$	−4.63318	−	1.36043i	−0.167077	−	0.0490582i	0.197124	−	0.980379i	$-0.436840\pi$
$769$	−4.63318	−	1.36043i	−0.167077	−	0.0490582i	−0.364201	+	0.931320i	$0.618658\pi$
$770$		0			0
$771$	−7.14922	−	8.25064i	−0.257473	−	0.297139i
$772$		0			0
$773$	−33.2992	+	12.4199i	−1.19769	+	0.446715i	−0.867613	−	0.497240i	$-0.834347\pi$
$773$	−33.2992	+	12.4199i	−1.19769	+	0.446715i	−0.330075	+	0.943955i	$0.607074\pi$
$774$		0			0
$775$	2.01437	−	15.5188i	0.0723582	−	0.557453i
$776$		0			0
$777$	10.2024	−	27.3537i	0.366009	−	0.981308i
$778$		0			0
$779$	−1.53474	+	0.986318i	−0.0549878	+	0.0353385i
$780$		0			0
$781$			7.50964i			0.268716i
$782$		0			0
$783$	−6.55205	+	6.55205i	−0.234151	+	0.234151i
$784$		0			0
$785$	28.1551	−	10.7219i	1.00490	−	0.382680i
$786$		0			0
$787$	24.5088	+	9.14130i	0.873643	+	0.325852i	0.745982	−	0.665966i	$-0.231980\pi$
$787$	24.5088	+	9.14130i	0.873643	+	0.325852i	0.127661	+	0.991818i	$0.459253\pi$
$788$		0			0
$789$	−22.4776	+	6.60002i	−0.800224	+	0.234967i
$790$		0			0
$791$	10.4055	−	22.7849i	0.369977	−	0.810137i
$792$		0			0
$793$	−0.154753	+	2.16373i	−0.00549545	+	0.0768364i
$794$		0			0
$795$	−10.5790	−	35.1354i	−0.375200	−	1.24613i
$796$		0			0
$797$	−25.7174	+	5.59447i	−0.910956	+	0.198166i	−0.643538	−	0.765414i	$-0.722534\pi$
$797$	−25.7174	+	5.59447i	−0.910956	+	0.198166i	−0.267418	+	0.963581i	$0.586170\pi$
$798$		0			0
$799$	4.06908	−	28.3011i	0.143954	−	1.00122i
$800$		0			0
$801$	−22.9357	+	3.29766i	−0.810393	+	0.116517i
$802$		0			0
$803$	−46.2592	+	3.30852i	−1.63245	+	0.116755i
$804$		0			0
$805$	37.8547	+	14.2710i	1.33420	+	0.502986i
$806$		0			0
$807$	1.25350	−	0.0896522i	0.0441253	−	0.00315591i
$808$		0			0
$809$	3.17032	−	0.455823i	0.111463	−	0.0160259i	−0.0863578	−	0.996264i	$-0.527523\pi$
$809$	3.17032	−	0.455823i	0.111463	−	0.0160259i	0.197820	+	0.980238i	$0.436614\pi$
$810$		0			0
$811$	−3.07589	+	21.3933i	−0.108009	+	0.751219i	0.861781	+	0.507280i	$0.169349\pi$
$811$	−3.07589	+	21.3933i	−0.108009	+	0.751219i	−0.969790	+	0.243940i	$0.921560\pi$
$812$		0			0
$813$	−15.1910	+	3.30459i	−0.532770	+	0.115897i
$814$		0			0
$815$	−34.8060	−	18.6967i	−1.21920	−	0.654918i
$816$		0			0
$817$	−0.835352	+	11.6797i	−0.0292252	+	0.408622i
$818$		0			0
$819$	3.28206	−	7.18670i	0.114684	−	0.251124i
$820$		0			0
$821$	−10.4366	+	3.06447i	−0.364241	+	0.106951i	−0.458731	−	0.888575i	$-0.651696\pi$
$821$	−10.4366	+	3.06447i	−0.364241	+	0.106951i	0.0944904	+	0.995526i	$0.469878\pi$
$822$		0			0
$823$	−44.7949	−	16.7076i	−1.56145	−	0.582392i	−0.587517	−	0.809212i	$-0.699894\pi$
$823$	−44.7949	−	16.7076i	−1.56145	−	0.582392i	−0.973937	+	0.226820i	$0.927167\pi$
$824$		0			0
$825$	13.2006	−	18.1477i	0.459585	−	0.631820i
$826$		0			0
$827$	8.48374	−	8.48374i	0.295009	−	0.295009i	−0.544046	−	0.839055i	$-0.683108\pi$
$827$	8.48374	−	8.48374i	0.295009	−	0.295009i	0.839055	+	0.544046i	$0.183108\pi$
$828$		0			0
$829$		−	24.9559i		−	0.866753i	−0.901213	−	0.433376i	$-0.857322\pi$
$829$		−	24.9559i		−	0.866753i	0.901213	−	0.433376i	$-0.142678\pi$
$830$		0			0
$831$	29.4628	−	18.9346i	1.02205	−	0.656833i
$832$		0			0
$833$	−9.87617	+	26.4790i	−0.342189	+	0.917445i
$834$		0			0
$835$	2.97756	+	37.9694i	0.103043	+	1.31399i
$836$		0			0
$837$	−15.9915	+	5.96453i	−0.552747	+	0.206164i
$838$		0			0
$839$	37.1610	+	42.8861i	1.28294	+	1.48059i	0.793517	+	0.608548i	$0.208248\pi$
$839$	37.1610	+	42.8861i	1.28294	+	1.48059i	0.489425	+	0.872046i	$0.337207\pi$
$840$		0			0
$841$	−25.0551	−	7.35684i	−0.863968	−	0.253684i
$842$		0			0
$843$	−0.744831	−	3.42393i	−0.0256533	−	0.117926i
$844$		0			0
$845$	−10.6129	−	22.8233i	−0.365093	−	0.785144i
$846$		0			0
$847$	−9.80401	−	7.33919i	−0.336870	−	0.252178i
$848$		0			0
$849$	−4.68074	+	5.40186i	−0.160643	+	0.185391i
$850$		0			0
$851$	−27.2371	−	15.2416i	−0.933676	−	0.522477i
$852$		0			0
$853$	1.41871	+	19.8361i	0.0485756	+	0.679176i	0.962153	+	0.272511i	$0.0878540\pi$
$853$	1.41871	+	19.8361i	0.0485756	+	0.679176i	−0.913577	+	0.406666i	$0.866691\pi$
$854$		0			0
$855$	−2.87754	−	3.27519i	−0.0984098	−	0.112009i
$856$		0			0
$857$	−11.8014	+	8.83441i	−0.403128	+	0.301778i	−0.781535	−	0.623862i	$-0.785563\pi$
$857$	−11.8014	+	8.83441i	−0.403128	+	0.301778i	0.378407	+	0.925639i	$0.376472\pi$
$858$		0			0
$859$	5.35696	−	8.33559i	0.182777	−	0.284407i	−0.737759	−	0.675064i	$-0.764116\pi$
$859$	5.35696	−	8.33559i	0.182777	−	0.284407i	0.920536	+	0.390657i	$0.127752\pi$
$860$		0			0
$861$	−1.87557	+	6.38760i	−0.0639192	+	0.217689i
$862$		0			0
$863$	−37.4135	−	2.67587i	−1.27357	−	0.0910876i	−0.581876	−	0.813278i	$-0.697681\pi$
$863$	−37.4135	−	2.67587i	−1.27357	−	0.0910876i	−0.691695	+	0.722190i	$0.743136\pi$
$864$		0			0
$865$	25.5451	−	34.6167i	0.868560	−	1.17700i
$866$		0			0
$867$	1.80349	+	0.984782i	0.0612499	+	0.0334450i
$868$		0			0
$869$	12.0667	−	5.51066i	0.409334	−	0.186936i
$870$		0			0
$871$	2.58830	+	4.02748i	0.0877013	+	0.136466i
$872$		0			0
$873$	−12.2730	−	12.2730i	−0.415379	−	0.415379i
$874$		0			0
$875$	24.5760	−	34.2780i	0.830820	−	1.15881i
$876$		0			0
$877$	−12.4456	−	2.70737i	−0.420258	−	0.0914214i	−0.00253657	−	0.999997i	$-0.500807\pi$
$877$	−12.4456	−	2.70737i	−0.420258	−	0.0914214i	−0.417721	+	0.908575i	$0.637171\pi$
$878$		0			0
$879$	11.7699	+	25.7725i	0.396988	+	0.869283i
$880$		0			0
$881$	−14.6664	−	49.9492i	−0.494124	−	1.68283i	−0.708198	−	0.706014i	$-0.750492\pi$
$881$	−14.6664	−	49.9492i	−0.494124	−	1.68283i	0.214074	−	0.976817i	$-0.431327\pi$
$882$		0			0
$883$	0.540634	+	1.44950i	0.0181938	+	0.0487794i	0.945729	−	0.324956i	$-0.105350\pi$
$883$	0.540634	+	1.44950i	0.0181938	+	0.0487794i	−0.927535	+	0.373735i	$0.878077\pi$
$884$		0			0
$885$	21.7673	−	12.0804i	0.731699	−	0.406079i
$886$		0			0
$887$	14.2836	+	26.1584i	0.479595	+	0.878313i	0.999707	+	0.0242150i	$0.00770861\pi$
$887$	14.2836	+	26.1584i	0.479595	+	0.878313i	−0.520111	+	0.854098i	$0.674110\pi$
$888$		0			0
$889$	−36.8982	−	23.7131i	−1.23753	−	0.795310i
$890$		0			0
$891$	−6.44966	−	0.927321i	−0.216072	−	0.0310664i
$892$		0			0
$893$	−5.38996	+	7.20015i	−0.180368	+	0.240944i
$894$		0			0
$895$	1.55032	−	11.3342i	0.0518216	−	0.378859i
$896$		0			0
$897$	6.29218	+	4.13663i	0.210090	+	0.138118i
$898$		0			0
$899$	4.01912	+	3.48258i	0.134045	+	0.116151i
$900$		0			0
$901$	−7.67509	−	53.3814i	−0.255694	−	1.77839i
$902$		0			0
$903$	25.6069	+	34.2068i	0.852144	+	1.13833i
$904$		0			0
$905$	−36.5146	+	0.250492i	−1.21379	+	0.00832663i
$906$		0			0
$907$	37.1693	−	20.2960i	1.23419	−	0.673917i	0.276303	−	0.961071i	$-0.410891\pi$
$907$	37.1693	−	20.2960i	1.23419	−	0.673917i	0.957885	+	0.287153i	$0.0927089\pi$
$908$		0			0
$909$	−15.6150	+	13.5304i	−0.517915	+	0.448776i
$910$		0			0
$911$	−13.9089	−	6.35200i	−0.460824	−	0.210451i	0.171455	−	0.985192i	$-0.445153\pi$
$911$	−13.9089	−	6.35200i	−0.460824	−	0.210451i	−0.632279	+	0.774741i	$0.717880\pi$
$912$		0			0
$913$	−7.82511	+	14.3306i	−0.258973	+	0.474274i
$914$		0			0
$915$	4.26181	−	0.957767i	0.140891	−	0.0316628i
$916$		0			0
$917$	9.71864	−	44.6759i	0.320938	−	1.47533i
$918$		0			0
$919$	−20.9135			−0.689872			−0.344936	−	0.938626i	$-0.612099\pi$
$919$	−20.9135			−0.689872			−0.344936	+	0.938626i	$0.612099\pi$
$920$		0			0
$921$	−22.7588			−0.749927
$922$		0			0
$923$	−0.558446	+	2.56714i	−0.0183815	+	0.0844983i
$924$		0			0
$925$	−22.6917	+	23.3231i	−0.746098	+	0.766857i
$926$		0			0
$927$	14.8941	−	27.2766i	0.489188	−	0.895880i
$928$		0			0
$929$	33.6702	+	15.3767i	1.10468	+	0.504492i	0.882405	−	0.470491i	$-0.155923\pi$
$929$	33.6702	+	15.3767i	1.10468	+	0.504492i	0.222279	+	0.974983i	$0.428650\pi$
$930$		0			0
$931$	6.71855	−	5.82166i	0.220192	−	0.190797i
$932$		0			0
$933$	−13.8678	+	7.57241i	−0.454013	+	0.247910i
$934$		0			0
$935$	23.1616	−	23.4816i	0.757466	−	0.767930i
$936$		0			0
$937$	33.2962	+	44.4785i	1.08774	+	1.45305i	0.880066	+	0.474850i	$0.157498\pi$
$937$	33.2962	+	44.4785i	1.08774	+	1.45305i	0.207672	+	0.978198i	$0.433411\pi$
$938$		0			0
$939$	−2.27361	−	15.8133i	−0.0741966	−	0.516048i
$940$		0			0
$941$	−31.2335	−	27.0640i	−1.01818	−	0.882261i	−0.0251013	−	0.999685i	$-0.507991\pi$
$941$	−31.2335	−	27.0640i	−1.01818	−	0.882261i	−0.993082	+	0.117424i	$0.962536\pi$
$942$		0			0
$943$	6.44306	+	3.02365i	0.209815	+	0.0984635i
$944$		0			0
$945$	−45.5768	−	6.23415i	−1.48261	−	0.202797i
$946$		0			0
$947$	−25.5845	+	34.1768i	−0.831383	+	1.11060i	0.160945	+	0.986963i	$0.448546\pi$
$947$	−25.5845	+	34.1768i	−0.831383	+	1.11060i	−0.992328	+	0.123634i	$0.960545\pi$
$948$		0			0
$949$	−16.0595	−	2.30901i	−0.521314	−	0.0749537i
$950$		0			0
$951$	−1.49866	−	0.963129i	−0.0485973	−	0.0312316i
$952$		0			0
$953$	23.0071	+	42.1344i	0.745275	+	1.36487i	0.924547	+	0.381069i	$0.124444\pi$
$953$	23.0071	+	42.1344i	0.745275	+	1.36487i	−0.179272	+	0.983800i	$0.557374\pi$
$954$		0			0
$955$	−12.0597	−	3.45136i	−0.390242	−	0.111683i
$956$		0			0
$957$	2.66507	+	7.14532i	0.0861494	+	0.230975i
$958$		0			0
$959$	−4.27028	−	14.5433i	−0.137895	−	0.469626i
$960$		0			0
$961$	−8.80860	−	19.2881i	−0.284148	−	0.622198i
$962$		0			0
$963$	−4.60002	−	1.00067i	−0.148233	−	0.0322462i
$964$		0			0
$965$	0.545254	+	0.114701i	0.0175524	+	0.00369236i
$966$		0			0
$967$	29.3650	+	29.3650i	0.944314	+	0.944314i	0.998529	−	0.0542150i	$-0.0172656\pi$
$967$	29.3650	+	29.3650i	0.944314	+	0.944314i	−0.0542150	+	0.998529i	$0.517266\pi$
$968$		0			0
$969$	3.08839	+	4.80563i	0.0992135	+	0.154379i
$970$		0			0
$971$	1.93645	−	0.884345i	0.0621435	−	0.0283800i	−0.384101	−	0.923291i	$-0.625489\pi$
$971$	1.93645	−	0.884345i	0.0621435	−	0.0283800i	0.446244	+	0.894911i	$0.352761\pi$
$972$		0			0
$973$	−68.8045	−	37.5701i	−2.20577	−	1.20444i
$974$		0			0
$975$	5.86209	−	5.22205i	0.187737	−	0.167239i
$976$		0			0
$977$	−38.1837	−	2.73095i	−1.22160	−	0.0873708i	−0.554403	−	0.832248i	$-0.687053\pi$
$977$	−38.1837	−	2.73095i	−1.22160	−	0.0873708i	−0.667201	+	0.744878i	$0.732508\pi$
$978$		0			0
$979$	−15.5356	+	52.9095i	−0.496521	+	1.69100i
$980$		0			0
$981$	14.0668	−	21.8884i	0.449119	−	0.698843i
$982$		0			0
$983$	−19.3208	+	14.4634i	−0.616237	+	0.461309i	−0.861230	−	0.508216i	$-0.830305\pi$
$983$	−19.3208	+	14.4634i	−0.616237	+	0.461309i	0.244993	+	0.969525i	$0.421214\pi$
$984$		0			0
$985$	−1.71225	−	0.110662i	−0.0545567	−	0.00352598i
$986$		0			0
$987$	2.34139	+	32.7369i	0.0745273	+	1.04203i
$988$		0			0
$989$	40.3193	−	21.4759i	1.28208	−	0.682892i
$990$		0			0
$991$	−9.76340	+	11.2676i	−0.310145	+	0.357926i	−0.889327	−	0.457272i	$-0.848827\pi$
$991$	−9.76340	+	11.2676i	−0.310145	+	0.357926i	0.579182	+	0.815198i	$0.303372\pi$
$992$		0			0
$993$	−21.7011	−	16.2452i	−0.688663	−	0.515527i
$994$		0			0
$995$	10.0263	−	4.66226i	0.317856	−	0.147804i
$996$		0			0
$997$	−0.624774	−	2.87204i	−0.0197868	−	0.0909584i	0.966195	−	0.257814i	$-0.0830022\pi$
$997$	−0.624774	−	2.87204i	−0.0197868	−	0.0909584i	−0.985981	+	0.166856i	$0.946639\pi$
$998$		0			0
$999$	34.0527	+	9.99876i	1.07738	+	0.316347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.697.12	yes	720
5.3	odd	4	inner	920.2.bv.a.513.12	yes	720
23.10	odd	22	inner	920.2.bv.a.217.12	yes	720
115.33	even	44	inner	920.2.bv.a.33.12	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.12	✓	720	115.33	even	44	inner
920.2.bv.a.217.12	yes	720	23.10	odd	22	inner
920.2.bv.a.513.12	yes	720	5.3	odd	4	inner
920.2.bv.a.697.12	yes	720	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.252761 + 1.16193i) q^{3} +(-1.19598 + 1.88935i) q^{5} +(1.80796 - 3.31103i) q^{7} +(1.44271 + 0.658865i) q^{9} +O(q^{10})\)	\(q+(-0.252761 + 1.16193i) q^{3} +(-1.19598 + 1.88935i) q^{5} +(1.80796 - 3.31103i) q^{7} +(1.44271 + 0.658865i) q^{9} +(2.85252 - 2.47173i) q^{11} +(1.15893 - 0.632824i) q^{13} +(-1.89299 - 1.86719i) q^{15} +(-2.34194 - 3.12846i) q^{17} +(0.174948 + 1.21679i) q^{19} +(3.39019 + 2.93762i) q^{21} +(3.65685 - 3.10282i) q^{23} +(-2.13928 - 4.51924i) q^{25} +(-3.26802 + 4.36556i) q^{27} +(1.68187 + 0.241816i) q^{29} +(2.63296 + 1.69210i) q^{31} +(2.15095 + 3.93918i) q^{33} +(4.09342 + 7.37579i) q^{35} +(-2.27434 - 6.09775i) q^{37} +(0.442361 + 1.50654i) q^{39} +(0.616498 + 1.34994i) q^{41} +(9.30770 + 2.02477i) q^{43} +(-2.97028 + 1.93780i) q^{45} +(5.17350 + 5.17350i) q^{47} +(-3.90974 - 6.08367i) q^{49} +(4.22699 - 1.93040i) q^{51} +(12.1122 + 6.61374i) q^{53} +(1.25840 + 8.34554i) q^{55} +(-1.45804 - 0.104281i) q^{57} +(-2.63780 + 8.98353i) q^{59} +(-0.888176 + 1.38203i) q^{61} +(4.78990 - 3.58567i) q^{63} +(-0.190429 + 2.94647i) q^{65} +(0.258650 + 3.61640i) q^{67} +(2.68093 + 5.03325i) q^{69} +(-1.30292 + 1.50365i) q^{71} +(-9.83644 - 7.36347i) q^{73} +(5.79174 - 1.34339i) q^{75} +(-3.02672 - 13.9136i) q^{77} +(3.37219 + 0.990164i) q^{79} +(-1.13052 - 1.30469i) q^{81} +(-4.05317 + 1.51175i) q^{83} +(8.71166 - 0.683168i) q^{85} +(-0.706085 + 1.89309i) q^{87} +(-12.2904 + 7.89859i) q^{89} -4.98138i q^{91} +(-2.63160 + 2.63160i) q^{93} +(-2.50817 - 1.12471i) q^{95} +(-10.2534 - 3.82433i) q^{97} +(5.74391 - 1.68656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 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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