LMFDB - Embedded newform 315.2.ce.a.233.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(53,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.8
Character	$\chi$	$=$	315.233
Dual form			315.2.ce.a.242.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.135317 + 0.0362581i) q^{2} +(-1.71505 + 0.990187i) q^{4} +(-1.99289 - 1.01410i) q^{5} +(2.55076 - 0.702570i) q^{7} +(0.394292 - 0.394292i) q^{8} +(0.306441 + 0.0649676i) q^{10} +(4.85164 - 2.80110i) q^{11} +(2.57764 + 2.57764i) q^{13} +(-0.319688 + 0.187556i) q^{14} +(1.94132 - 3.36246i) q^{16} +(0.0721789 - 0.269375i) q^{17} +(4.44554 + 2.56664i) q^{19} +(4.42206 - 0.234084i) q^{20} +(-0.554948 + 0.554948i) q^{22} +(-1.19764 - 4.46964i) q^{23} +(2.94318 + 4.04199i) q^{25} +(-0.442260 - 0.255339i) q^{26} +(-3.67902 + 3.73068i) q^{28} -2.91358 q^{29} +(-1.09319 - 1.89346i) q^{31} +(-0.429419 + 1.60261i) q^{32} +0.0390682i q^{34} +(-5.79586 - 1.18660i) q^{35} +(-1.96975 - 7.35120i) q^{37} +(-0.694620 - 0.186123i) q^{38} +(-1.18563 + 0.385926i) q^{40} +8.73280i q^{41} +(-5.90533 - 5.90533i) q^{43} +(-5.54722 + 9.60806i) q^{44} +(0.324122 + 0.561396i) q^{46} +(10.8696 - 2.91250i) q^{47} +(6.01279 - 3.58418i) q^{49} +(-0.544818 - 0.440237i) q^{50} +(-6.97315 - 1.86845i) q^{52} +(-1.55853 - 0.417606i) q^{53} +(-12.5094 + 0.662190i) q^{55} +(0.728729 - 1.28276i) q^{56} +(0.394257 - 0.105641i) q^{58} +(1.62708 + 2.81818i) q^{59} +(-1.06088 + 1.83751i) q^{61} +(0.216580 + 0.216580i) q^{62} +7.53283i q^{64} +(-2.52295 - 7.75095i) q^{65} +(6.92780 + 1.85630i) q^{67} +(0.142941 + 0.533464i) q^{68} +(0.827304 - 0.0495794i) q^{70} +8.16308i q^{71} +(2.12220 - 7.92016i) q^{73} +(0.533082 + 0.923325i) q^{74} -10.1658 q^{76} +(10.4074 - 10.5535i) q^{77} +(0.500892 + 0.289190i) q^{79} +(-7.27871 + 4.73230i) q^{80} +(-0.316635 - 1.18170i) q^{82} +(-3.12616 + 3.12616i) q^{83} +(-0.417019 + 0.463637i) q^{85} +(1.01321 + 0.584977i) q^{86} +(0.808514 - 3.01741i) q^{88} +(-6.29155 + 10.8973i) q^{89} +(8.38594 + 4.76399i) q^{91} +(6.47980 + 6.47980i) q^{92} +(-1.36524 + 0.788224i) q^{94} +(-6.25662 - 9.62326i) q^{95} +(-8.25038 + 8.25038i) q^{97} +(-0.683679 + 0.703014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.135317	+	0.0362581i	−0.0956837	+	0.0256384i	−0.306343	−	0.951921i	$-0.599106\pi$
$2$	−0.135317	+	0.0362581i	−0.0956837	+	0.0256384i	0.210660	+	0.977559i	$0.432439\pi$
$3$		0			0
$3$		0			0
$4$	−1.71505	+	0.990187i	−0.857527	+	0.495094i
$5$	−1.99289	−	1.01410i	−0.891245	−	0.453522i
$5$	−1.99289	−	1.01410i	−0.891245	−	0.453522i
$6$		0			0
$7$	2.55076	−	0.702570i	0.964098	−	0.265546i
$7$	2.55076	−	0.702570i	0.964098	−	0.265546i
$8$	0.394292	−	0.394292i	0.139403	−	0.139403i
$9$		0			0
$10$	0.306441	+	0.0649676i	0.0969053	+	0.0205446i
$11$	4.85164	−	2.80110i	1.46282	−	0.844562i	0.463683	−	0.886001i	$-0.346528\pi$
$11$	4.85164	−	2.80110i	1.46282	−	0.844562i	0.999141	+	0.0414391i	$0.0131942\pi$
$12$		0			0
$13$	2.57764	+	2.57764i	0.714910	+	0.714910i	0.967558	−	0.252648i	$-0.0813016\pi$
$13$	2.57764	+	2.57764i	0.714910	+	0.714910i	−0.252648	+	0.967558i	$0.581302\pi$
$14$	−0.319688	+	0.187556i	−0.0854403	+	0.0501264i
$15$		0			0
$16$	1.94132	−	3.36246i	0.485329	−	0.840615i
$17$	0.0721789	−	0.269375i	0.0175059	−	0.0653331i	−0.956620	−	0.291338i	$-0.905900\pi$
$17$	0.0721789	−	0.269375i	0.0175059	−	0.0653331i	0.974126	+	0.226004i	$0.0725664\pi$
$18$		0			0
$19$	4.44554	+	2.56664i	1.01988	+	0.588827i	0.914069	−	0.405560i	$-0.132923\pi$
$19$	4.44554	+	2.56664i	1.01988	+	0.588827i	0.105809	+	0.994386i	$0.466257\pi$
$20$	4.42206	−	0.234084i	0.988803	−	0.0523428i
$21$		0			0
$22$	−0.554948	+	0.554948i	−0.118315	+	0.118315i
$23$	−1.19764	−	4.46964i	−0.249725	−	0.931985i	−0.970950	−	0.239284i	$-0.923087\pi$
$23$	−1.19764	−	4.46964i	−0.249725	−	0.931985i	0.721225	−	0.692701i	$-0.243579\pi$
$24$		0			0
$25$	2.94318	+	4.04199i	0.588636	+	0.808398i
$26$	−0.442260	−	0.255339i	−0.0867344	−	0.0500761i
$27$		0			0
$28$	−3.67902	+	3.73068i	−0.695270	+	0.705032i
$29$	−2.91358			−0.541038			−0.270519	−	0.962715i	$-0.587195\pi$
$29$	−2.91358			−0.541038			−0.270519	+	0.962715i	$0.587195\pi$
$30$		0			0
$31$	−1.09319	−	1.89346i	−0.196342	−	0.340075i	0.750998	−	0.660305i	$-0.229573\pi$
$31$	−1.09319	−	1.89346i	−0.196342	−	0.340075i	−0.947340	+	0.320230i	$0.896240\pi$
$32$	−0.429419	+	1.60261i	−0.0759113	+	0.283305i
$33$		0			0
$34$			0.0390682i			0.00670014i
$35$	−5.79586	−	1.18660i	−0.979679	−	0.200572i
$36$		0			0
$37$	−1.96975	−	7.35120i	−0.323825	−	1.20853i	−0.915488	−	0.402345i	$-0.868195\pi$
$37$	−1.96975	−	7.35120i	−0.323825	−	1.20853i	0.591664	−	0.806185i	$-0.298471\pi$
$38$	−0.694620	−	0.186123i	−0.112682	−	0.0301931i
$39$		0			0
$40$	−1.18563	+	0.385926i	−0.187465	+	0.0610202i
$41$			8.73280i			1.36383i	0.731429	+	0.681917i	$0.238854\pi$
$41$			8.73280i			1.36383i	−0.731429	+	0.681917i	$0.761146\pi$
$42$		0			0
$43$	−5.90533	−	5.90533i	−0.900554	−	0.900554i	0.0949298	−	0.995484i	$-0.469737\pi$
$43$	−5.90533	−	5.90533i	−0.900554	−	0.900554i	−0.995484	+	0.0949298i	$0.969737\pi$
$44$	−5.54722	+	9.60806i	−0.836275	+	1.44847i
$45$		0			0
$46$	0.324122	+	0.561396i	0.0477892	+	0.0827733i
$47$	10.8696	−	2.91250i	1.58549	−	0.424832i	0.644873	−	0.764289i	$-0.276910\pi$
$47$	10.8696	−	2.91250i	1.58549	−	0.424832i	0.940621	+	0.339457i	$0.110243\pi$
$48$		0			0
$49$	6.01279	−	3.58418i	0.858970	−	0.512025i
$50$	−0.544818	−	0.440237i	−0.0770490	−	0.0622589i
$51$		0			0
$52$	−6.97315	−	1.86845i	−0.967002	−	0.259107i
$53$	−1.55853	−	0.417606i	−0.214080	−	0.0573627i	0.150185	−	0.988658i	$-0.452013\pi$
$53$	−1.55853	−	0.417606i	−0.214080	−	0.0573627i	−0.364265	+	0.931295i	$0.618680\pi$
$54$		0			0
$55$	−12.5094	+	0.662190i	−1.68676	+	0.0892896i
$56$	0.728729	−	1.28276i	0.0973805	−	0.171417i
$57$		0			0
$58$	0.394257	−	0.105641i	0.0517685	−	0.0138713i
$59$	1.62708	+	2.81818i	0.211827	+	0.366896i	0.952286	−	0.305206i	$-0.0987252\pi$
$59$	1.62708	+	2.81818i	0.211827	+	0.366896i	−0.740459	+	0.672101i	$0.765392\pi$
$60$		0			0
$61$	−1.06088	+	1.83751i	−0.135832	+	0.235269i	−0.925915	−	0.377732i	$-0.876704\pi$
$61$	−1.06088	+	1.83751i	−0.135832	+	0.235269i	0.790083	+	0.613000i	$0.210038\pi$
$62$	0.216580	+	0.216580i	0.0275057	+	0.0275057i
$63$		0			0
$64$			7.53283i			0.941604i
$65$	−2.52295	−	7.75095i	−0.312933	−	0.961387i
$66$		0			0
$67$	6.92780	+	1.85630i	0.846366	+	0.226783i	0.655841	−	0.754899i	$-0.272314\pi$
$67$	6.92780	+	1.85630i	0.846366	+	0.226783i	0.190525	+	0.981682i	$0.438981\pi$
$68$	0.142941	+	0.533464i	0.0173342	+	0.0646920i
$69$		0			0
$70$	0.827304	−	0.0495794i	0.0988817	−	0.00592587i
$71$			8.16308i			0.968779i	0.874852	+	0.484390i	$0.160958\pi$
$71$			8.16308i			0.968779i	−0.874852	+	0.484390i	$0.839042\pi$
$72$		0			0
$73$	2.12220	−	7.92016i	0.248385	−	0.926985i	−0.723267	−	0.690569i	$-0.757360\pi$
$73$	2.12220	−	7.92016i	0.248385	−	0.926985i	0.971652	−	0.236416i	$-0.0759730\pi$
$74$	0.533082	+	0.923325i	0.0619695	+	0.107334i
$75$		0			0
$76$	−10.1658			−1.16610
$77$	10.4074	−	10.5535i	1.18604	−	1.20269i
$78$		0			0
$79$	0.500892	+	0.289190i	0.0563548	+	0.0325364i	0.527913	−	0.849299i	$-0.322975\pi$
$79$	0.500892	+	0.289190i	0.0563548	+	0.0325364i	−0.471558	+	0.881835i	$0.656308\pi$
$80$	−7.27871	+	4.73230i	−0.813784	+	0.529087i
$81$		0			0
$82$	−0.316635	−	1.18170i	−0.0349665	−	0.130497i
$83$	−3.12616	+	3.12616i	−0.343140	+	0.343140i	−0.857547	−	0.514406i	$-0.828012\pi$
$83$	−3.12616	+	3.12616i	−0.343140	+	0.343140i	0.514406	+	0.857547i	$0.328012\pi$
$84$		0			0
$85$	−0.417019	+	0.463637i	−0.0452321	+	0.0502885i
$86$	1.01321	+	0.584977i	0.109257	+	0.0630796i
$87$		0			0
$88$	0.808514	−	3.01741i	0.0861879	−	0.321657i
$89$	−6.29155	+	10.8973i	−0.666903	+	1.15511i	0.311863	+	0.950127i	$0.399047\pi$
$89$	−6.29155	+	10.8973i	−0.666903	+	1.15511i	−0.978766	+	0.204982i	$0.934286\pi$
$90$		0			0
$91$	8.38594	+	4.76399i	0.879085	+	0.499402i
$92$	6.47980	+	6.47980i	0.675566	+	0.675566i
$93$		0			0
$94$	−1.36524	+	0.788224i	−0.140814	+	0.0812991i
$95$	−6.25662	−	9.62326i	−0.641916	−	0.987326i
$96$		0			0
$97$	−8.25038	+	8.25038i	−0.837699	+	0.837699i	−0.988556	−	0.150857i	$-0.951797\pi$
$97$	−8.25038	+	8.25038i	−0.837699	+	0.837699i	0.150857	+	0.988556i	$0.451797\pi$
$98$	−0.683679	+	0.703014i	−0.0690620	+	0.0710151i
$99$		0			0
$100$	−9.05005	−	4.01793i	−0.905005	−	0.401793i
$101$	−4.26270	+	2.46107i	−0.424155	+	0.244886i	−0.696853	−	0.717214i	$-0.745417\pi$
$101$	−4.26270	+	2.46107i	−0.424155	+	0.244886i	0.272698	+	0.962100i	$0.412084\pi$
$102$		0			0
$103$	−15.1530	+	4.06023i	−1.49307	+	0.400066i	−0.910771	−	0.412911i	$-0.864512\pi$
$103$	−15.1530	+	4.06023i	−1.49307	+	0.400066i	−0.582295	+	0.812977i	$0.697845\pi$
$104$	2.03269			0.199322
$105$		0			0
$106$	0.226037			0.0219547
$107$	−18.3663	+	4.92124i	−1.77554	+	0.475755i	−0.989759	−	0.142749i	$-0.954406\pi$
$107$	−18.3663	+	4.92124i	−1.77554	+	0.475755i	−0.785782	+	0.618504i	$0.787739\pi$
$108$		0			0
$109$	9.50313	−	5.48663i	0.910234	−	0.525524i	0.0297279	−	0.999558i	$-0.490536\pi$
$109$	9.50313	−	5.48663i	0.910234	−	0.525524i	0.880507	+	0.474034i	$0.157203\pi$
$110$	1.66872	−	0.543172i	0.159107	−	0.0517894i
$111$		0			0
$112$	2.58948	−	9.94075i	0.244683	−	0.939312i
$113$	6.16850	−	6.16850i	0.580283	−	0.580283i	−0.354698	−	0.934981i	$-0.615416\pi$
$113$	6.16850	−	6.16850i	0.580283	−	0.580283i	0.934981	+	0.354698i	$0.115416\pi$
$114$		0			0
$115$	−2.14593	+	10.1220i	−0.200109	+	0.943883i
$116$	4.99695	−	2.88499i	0.463955	−	0.267864i
$117$		0			0
$118$	−0.322353	−	0.322353i	−0.0296750	−	0.0296750i
$119$	−0.00514358	−	0.737823i	−0.000471512	−	0.0676361i
$120$		0			0
$121$	10.1923	−	17.6535i	0.926570	−	1.60487i
$122$	0.0769314	−	0.287112i	0.00696504	−	0.0259939i
$123$		0			0
$124$	3.74975	+	2.16492i	0.336738	+	0.194416i
$125$	−1.76642	−	11.0399i	−0.157994	−	0.987440i
$126$		0			0
$127$	2.05336	−	2.05336i	0.182207	−	0.182207i	−0.610110	−	0.792317i	$-0.708875\pi$
$127$	2.05336	−	2.05336i	0.182207	−	0.182207i	0.792317	+	0.610110i	$0.208875\pi$
$128$	−1.13196	−	4.22455i	−0.100053	−	0.373401i
$129$		0			0
$130$	0.622433	+	0.957360i	0.0545910	+	0.0839660i
$131$	8.49260	+	4.90320i	0.742002	+	0.428395i	0.822797	−	0.568336i	$-0.192413\pi$
$131$	8.49260	+	4.90320i	0.742002	+	0.428395i	−0.0807949	+	0.996731i	$0.525746\pi$
$132$		0			0
$133$	13.1428	+	3.42358i	1.13962	+	0.296862i
$134$	−1.00476			−0.0867978
$135$		0			0
$136$	−0.0777530	−	0.134672i	−0.00666727	−	0.0115480i
$137$	0.448946	−	1.67549i	0.0383560	−	0.143147i	−0.944092	−	0.329681i	$-0.893059\pi$
$137$	0.448946	−	1.67549i	0.0383560	−	0.143147i	0.982448	+	0.186534i	$0.0597255\pi$
$138$		0			0
$139$			2.52988i			0.214581i	0.994228	+	0.107291i	$0.0342175\pi$
$139$			2.52988i			0.214581i	−0.994228	+	0.107291i	$0.965782\pi$
$140$	11.1152	−	3.70390i	0.939404	−	0.313037i
$141$		0			0
$142$	−0.295978	−	1.10461i	−0.0248379	−	0.0926964i
$143$	19.7260	+	5.28557i	1.64957	+	0.442002i
$144$		0			0
$145$	5.80643	+	2.95467i	0.482198	+	0.245372i
$146$			1.14868i			0.0950656i
$147$		0			0
$148$	10.6573	+	10.6573i	0.876024	+	0.876024i
$149$	−0.245378	+	0.425006i	−0.0201021	+	0.0348179i	−0.875901	−	0.482490i	$-0.839732\pi$
$149$	−0.245378	+	0.425006i	−0.0201021	+	0.0348179i	0.855799	+	0.517308i	$0.173066\pi$
$150$		0			0
$151$	2.23973	+	3.87932i	0.182266	+	0.315695i	0.942652	−	0.333777i	$-0.108323\pi$
$151$	2.23973	+	3.87932i	0.182266	+	0.315695i	−0.760386	+	0.649472i	$0.774990\pi$
$152$	2.76485	−	0.740839i	0.224259	−	0.0600900i
$153$		0			0
$154$	−1.02565	+	1.80543i	−0.0826494	+	0.145486i
$155$	0.258434	+	4.88205i	0.0207579	+	0.392135i
$156$		0			0
$157$	−4.84326	−	1.29775i	−0.386534	−	0.103572i	0.0603181	−	0.998179i	$-0.480788\pi$
$157$	−4.84326	−	1.29775i	−0.386534	−	0.103572i	−0.446853	+	0.894608i	$0.647455\pi$
$158$	−0.0782649	−	0.0209710i	−0.00622642	−	0.00166836i
$159$		0			0
$160$	2.48100	−	2.75835i	0.196140	−	0.218067i
$161$	−6.19512	−	10.5596i	−0.488244	−	0.832211i
$162$		0			0
$163$	−3.71540	+	0.995538i	−0.291013	+	0.0779766i	−0.401372	−	0.915915i	$-0.631466\pi$
$163$	−3.71540	+	0.995538i	−0.291013	+	0.0779766i	0.110359	+	0.993892i	$0.464800\pi$
$164$	−8.64711	−	14.9772i	−0.675226	−	1.16953i
$165$		0			0
$166$	0.309674	−	0.536372i	0.0240354	−	0.0416305i
$167$	6.52767	+	6.52767i	0.505126	+	0.505126i	0.913026	−	0.407900i	$-0.133739\pi$
$167$	6.52767	+	6.52767i	0.505126	+	0.505126i	−0.407900	+	0.913026i	$0.633739\pi$
$168$		0			0
$169$			0.288498i			0.0221921i
$170$	0.0396192	−	0.0778584i	0.00303866	−	0.00597147i
$171$		0			0
$172$	15.9753	+	4.28058i	1.21811	+	0.326391i
$173$	−5.72648	−	21.3715i	−0.435376	−	1.62485i	−0.740164	−	0.672426i	$-0.765252\pi$
$173$	−5.72648	−	21.3715i	−0.435376	−	1.62485i	0.304788	−	0.952420i	$-0.401414\pi$
$174$		0			0
$175$	10.3471	+	8.24237i	0.782170	+	0.623065i
$176$		−	21.7512i		−	1.63956i
$177$		0			0
$178$	0.456240	−	1.70271i	0.0341966	−	0.127624i
$179$	0.559683	+	0.969400i	0.0418327	+	0.0724564i	0.886184	−	0.463334i	$-0.153347\pi$
$179$	0.559683	+	0.969400i	0.0418327	+	0.0724564i	−0.844351	+	0.535790i	$0.820014\pi$
$180$		0			0
$181$	13.1037			0.973990			0.486995	−	0.873405i	$-0.338093\pi$
$181$	13.1037			0.973990			0.486995	+	0.873405i	$0.338093\pi$
$182$	−1.30750	−	0.340591i	−0.0969180	−	0.0252463i
$183$		0			0
$184$	−2.23457	−	1.29013i	−0.164734	−	0.0951094i
$185$	−3.52941	+	16.6476i	−0.259487	+	1.22396i
$186$		0			0
$187$	−0.404360	−	1.50909i	−0.0295697	−	0.110356i
$188$	−15.7580	+	15.7580i	−1.14927	+	1.14927i
$189$		0			0
$190$	1.19555	+	1.07534i	0.0867343	+	0.0780133i
$191$	4.65087	+	2.68518i	0.336525	+	0.194293i	0.658734	−	0.752375i	$-0.271092\pi$
$191$	4.65087	+	2.68518i	0.336525	+	0.194293i	−0.322209	+	0.946669i	$0.604425\pi$
$192$		0			0
$193$	−3.80447	+	14.1985i	−0.273852	+	1.02203i	0.682756	+	0.730647i	$0.260781\pi$
$193$	−3.80447	+	14.1985i	−0.273852	+	1.02203i	−0.956607	+	0.291381i	$0.905885\pi$
$194$	0.817275	−	1.41556i	0.0586769	−	0.101631i
$195$		0			0
$196$	−6.76326	+	12.1009i	−0.483090	+	0.864347i
$197$	−8.27206	−	8.27206i	−0.589360	−	0.589360i	0.348098	−	0.937458i	$-0.386828\pi$
$197$	−8.27206	−	8.27206i	−0.589360	−	0.589360i	−0.937458	+	0.348098i	$0.886828\pi$
$198$		0			0
$199$	−18.3771	+	10.6100i	−1.30272	+	0.752123i	−0.980869	−	0.194669i	$-0.937637\pi$
$199$	−18.3771	+	10.6100i	−1.30272	+	0.752123i	−0.321847	+	0.946792i	$0.604304\pi$
$200$	2.75420	+	0.433251i	0.194751	+	0.0306355i
$201$		0			0
$202$	0.487583	−	0.487583i	0.0343063	−	0.0343063i
$203$	−7.43185	+	2.04699i	−0.521614	+	0.143671i
$204$		0			0
$205$	8.85598	−	17.4035i	0.618528	−	1.21551i
$206$	1.90324	−	1.09884i	0.132605	−	0.0765596i
$207$		0			0
$208$	13.6712	−	3.66320i	0.947930	−	0.253997i
$209$	28.7576			1.98920
$210$		0			0
$211$	−6.90207			−0.475158			−0.237579	−	0.971368i	$-0.576354\pi$
$211$	−6.90207			−0.475158			−0.237579	+	0.971368i	$0.576354\pi$
$212$	3.08647	−	0.827017i	0.211980	−	0.0567998i
$213$		0			0
$214$	2.30685	−	1.33186i	0.157693	−	0.0910440i
$215$	5.78002	+	17.7573i	0.394194	+	1.21104i
$216$		0			0
$217$	−4.11875	−	4.06172i	−0.279599	−	0.275727i
$218$	−1.08700	+	1.08700i	−0.0736211	+	0.0736211i
$219$		0			0
$220$	20.7986	−	13.5223i	1.40224	−	0.911674i
$221$	0.880405	−	0.508302i	0.0592224	−	0.0341921i
$222$		0			0
$223$	1.35446	+	1.35446i	0.0907015	+	0.0907015i	0.751002	−	0.660300i	$-0.229571\pi$
$223$	1.35446	+	1.35446i	0.0907015	+	0.0907015i	−0.660300	+	0.751002i	$0.729571\pi$
$224$	0.0306011	+	4.38959i	0.00204462	+	0.293292i
$225$		0			0
$226$	−0.611046	+	1.05836i	−0.0406462	+	0.0704012i
$227$	2.10755	−	7.86549i	0.139883	−	0.522051i	−0.860047	−	0.510215i	$-0.829566\pi$
$227$	2.10755	−	7.86549i	0.139883	−	0.522051i	0.999930	−	0.0118356i	$-0.00376749\pi$
$228$		0			0
$229$	−11.4727	−	6.62377i	−0.758138	−	0.437711i	0.0704890	−	0.997513i	$-0.477544\pi$
$229$	−11.4727	−	6.62377i	−0.758138	−	0.437711i	−0.828627	+	0.559802i	$0.810877\pi$
$230$	−0.0766237	−	1.44749i	−0.00505242	−	0.0954447i
$231$		0			0
$232$	−1.14880	+	1.14880i	−0.0754225	+	0.0754225i
$233$	−2.10782	−	7.86648i	−0.138088	−	0.515350i	−0.999966	−	0.00823515i	$-0.997379\pi$
$233$	−2.10782	−	7.86648i	−0.138088	−	0.515350i	0.861878	−	0.507115i	$-0.169288\pi$
$234$		0			0
$235$	−24.6155	−	5.21864i	−1.60574	−	0.340426i
$236$	−5.58105	−	3.22222i	−0.363295	−	0.209749i
$237$		0			0
$238$	0.0274481	+	0.0996537i	0.00177920	+	0.00645959i
$239$	−8.41041			−0.544024			−0.272012	−	0.962294i	$-0.587689\pi$
$239$	−8.41041			−0.544024			−0.272012	+	0.962294i	$0.587689\pi$
$240$		0			0
$241$	0.122931	+	0.212922i	0.00791866	+	0.0137155i	0.869958	−	0.493127i	$-0.164146\pi$
$241$	0.122931	+	0.212922i	0.00791866	+	0.0137155i	−0.862039	+	0.506842i	$0.830813\pi$
$242$	−0.739106	+	2.75838i	−0.0475115	+	0.177315i
$243$		0			0
$244$		−	4.20190i		−	0.268999i
$245$	−15.6175	+	1.04525i	−0.997768	+	0.0667788i
$246$		0			0
$247$	4.84316	+	18.0749i	0.308163	+	1.15008i
$248$	−1.17761	−	0.315540i	−0.0747783	−	0.0200368i
$249$		0			0
$250$	0.639314	+	1.42984i	0.0404338	+	0.0904313i
$251$		−	0.458108i		−	0.0289155i	−0.999895	−	0.0144577i	$-0.995398\pi$
$251$		−	0.458108i		−	0.0289155i	0.999895	−	0.0144577i	$-0.00460220\pi$
$252$		0			0
$253$	−18.3304	−	18.3304i	−1.15242	−	1.15242i
$254$	−0.203404	+	0.352307i	−0.0127627	+	0.0221057i
$255$		0			0
$256$	−7.22649	−	12.5166i	−0.451655	−	0.782290i
$257$	−24.1439	+	6.46934i	−1.50605	+	0.403546i	−0.915123	−	0.403175i	$-0.867907\pi$
$257$	−24.1439	+	6.46934i	−1.50605	+	0.403546i	−0.590932	+	0.806721i	$0.701240\pi$
$258$		0			0
$259$	−10.1891	−	17.3673i	−0.633119	−	1.07915i
$260$	12.0019	+	10.7951i	0.744325	+	0.669485i
$261$		0			0
$262$	−1.32698	−	0.355562i	−0.0819809	−	0.0219667i
$263$	16.8221	+	4.50748i	1.03730	+	0.277943i	0.736993	−	0.675901i	$-0.236245\pi$
$263$	16.8221	+	4.50748i	1.03730	+	0.277943i	0.300304	+	0.953843i	$0.402912\pi$
$264$		0			0
$265$	2.68247	+	2.41275i	0.164783	+	0.148214i
$266$	−1.90258	+	0.0132634i	−0.116654	+	0.000813233i
$267$		0			0
$268$	−13.7196	+	3.67617i	−0.838061	+	0.224558i
$269$	−7.44692	−	12.8984i	−0.454047	−	0.786432i	0.544586	−	0.838705i	$-0.316687\pi$
$269$	−7.44692	−	12.8984i	−0.454047	−	0.786432i	−0.998633	+	0.0522730i	$0.983353\pi$
$270$		0			0
$271$	−7.64716	+	13.2453i	−0.464532	+	0.804593i	−0.999180	−	0.0404815i	$-0.987111\pi$
$271$	−7.64716	+	13.2453i	−0.464532	+	0.804593i	0.534648	+	0.845075i	$0.320444\pi$
$272$	−0.765641	−	0.765641i	−0.0464238	−	0.0464238i
$273$		0			0
$274$			0.243001i			0.0146802i
$275$	25.6013	+	11.3661i	1.54381	+	0.685404i
$276$		0			0
$277$	−9.97926	−	2.67393i	−0.599595	−	0.160661i	−0.0537606	−	0.998554i	$-0.517121\pi$
$277$	−9.97926	−	2.67393i	−0.599595	−	0.160661i	−0.545835	+	0.837893i	$0.683787\pi$
$278$	−0.0917287	−	0.342336i	−0.00550152	−	0.0205319i
$279$		0			0
$280$	−2.75313	+	1.81739i	−0.164531	+	0.108610i
$281$			23.6675i			1.41189i	0.708268	+	0.705943i	$0.249477\pi$
$281$			23.6675i			1.41189i	−0.708268	+	0.705943i	$0.750523\pi$
$282$		0			0
$283$	1.88659	−	7.04083i	0.112146	−	0.418534i	−0.886912	−	0.461939i	$-0.847154\pi$
$283$	1.88659	−	7.04083i	0.112146	−	0.418534i	0.999058	+	0.0434049i	$0.0138206\pi$
$284$	−8.08298	−	14.0001i	−0.479636	−	0.830755i
$285$		0			0
$286$	−2.86092			−0.169170
$287$	6.13540	+	22.2753i	0.362161	+	1.31487i
$288$		0			0
$289$	14.6551	+	8.46111i	0.862063	+	0.497713i
$290$	−0.892841	−	0.189288i	−0.0524294	−	0.0111154i
$291$		0			0
$292$	4.20275	+	15.6849i	0.245948	+	0.917889i
$293$	−10.0145	+	10.0145i	−0.585052	+	0.585052i	−0.936287	−	0.351235i	$-0.885762\pi$
$293$	−10.0145	+	10.0145i	−0.585052	+	0.585052i	0.351235	+	0.936287i	$0.385762\pi$
$294$		0			0
$295$	−0.384647	−	7.26633i	−0.0223950	−	0.423062i
$296$	−3.67518	−	2.12187i	−0.213615	−	0.123331i
$297$		0			0
$298$	0.0177939	−	0.0664076i	0.00103077	−	0.00384689i
$299$	8.43407	−	14.6082i	0.487755	−	0.844816i
$300$		0			0
$301$	−19.2120	−	10.9142i	−1.10736	−	0.629084i
$302$	−0.443731	−	0.443731i	−0.0255338	−	0.0255338i
$303$		0			0
$304$	17.2604	−	9.96531i	0.989953	−	0.571550i
$305$	3.97764	−	2.58609i	0.227759	−	0.148079i
$306$		0			0
$307$	−4.93300	+	4.93300i	−0.281541	+	0.281541i	−0.833723	−	0.552182i	$-0.813795\pi$
$307$	−4.93300	+	4.93300i	−0.281541	+	0.281541i	0.552182	+	0.833723i	$0.313795\pi$
$308$	−7.39931	+	28.4052i	−0.421615	+	1.61854i
$309$		0			0
$310$	−0.211984	−	0.651255i	−0.0120399	−	0.0369888i
$311$	−24.2000	+	13.9719i	−1.37226	+	0.792272i	−0.991212	−	0.132284i	$-0.957769\pi$
$311$	−24.2000	+	13.9719i	−1.37226	+	0.792272i	−0.381044	+	0.924557i	$0.624435\pi$
$312$		0			0
$313$	13.9090	−	3.72690i	0.786182	−	0.210657i	0.156674	−	0.987650i	$-0.449923\pi$
$313$	13.9090	−	3.72690i	0.786182	−	0.210657i	0.629509	+	0.776994i	$0.283256\pi$
$314$	0.702431			0.0396405
$315$		0			0
$316$	−1.14541			−0.0644343
$317$	−11.6964	+	3.13404i	−0.656935	+	0.176025i	−0.571863	−	0.820349i	$-0.693779\pi$
$317$	−11.6964	+	3.13404i	−0.656935	+	0.176025i	−0.0850728	+	0.996375i	$0.527112\pi$
$318$		0			0
$319$	−14.1356	+	8.16121i	−0.791444	+	0.456940i
$320$	7.63908	−	15.0121i	0.427038	−	0.839200i
$321$		0			0
$322$	1.22118	+	1.20427i	0.0680536	+	0.0671113i
$323$	1.01226	−	1.01226i	0.0563238	−	0.0563238i
$324$		0			0
$325$	−2.83233	+	18.0053i	−0.157110	+	0.998754i
$326$	0.466661	−	0.269427i	0.0258460	−	0.0149222i
$327$		0			0
$328$	3.44328	+	3.44328i	0.190123	+	0.190123i
$329$	25.6796	−	15.0658i	1.41576	−	0.830602i
$330$		0			0
$331$	−10.7503	+	18.6201i	−0.590892	+	1.02345i	0.403221	+	0.915103i	$0.367891\pi$
$331$	−10.7503	+	18.6201i	−0.590892	+	1.02345i	−0.994113	+	0.108352i	$0.965443\pi$
$332$	2.26605	−	8.45701i	0.124366	−	0.464139i
$333$		0			0
$334$	−1.11999	−	0.646625i	−0.0612830	−	0.0353817i
$335$	−11.9238	−	10.7249i	−0.651469	−	0.585964i
$336$		0			0
$337$	−8.10178	+	8.10178i	−0.441332	+	0.441332i	−0.892460	−	0.451127i	$-0.851022\pi$
$337$	−8.10178	+	8.10178i	−0.441332	+	0.441332i	0.451127	+	0.892460i	$0.351022\pi$
$338$	−0.0104604	−	0.0390387i	−0.000568970	−	0.00212343i
$339$		0			0
$340$	0.256123	−	1.20809i	0.0138902	−	0.0655178i
$341$	−10.6075	−	6.12424i	−0.574428	−	0.331646i
$342$		0			0
$343$	12.8191	−	13.3668i	0.692165	−	0.721739i
$344$	−4.65685			−0.251081
$345$		0			0
$346$	1.54978	+	2.68430i	0.0833169	+	0.144309i
$347$	−5.34680	+	19.9545i	−0.287031	+	1.07121i	0.660311	+	0.750992i	$0.270424\pi$
$347$	−5.34680	+	19.9545i	−0.287031	+	1.07121i	−0.947342	+	0.320222i	$0.896242\pi$
$348$		0			0
$349$		−	22.3959i		−	1.19882i	−0.800441	−	0.599411i	$-0.795401\pi$
$349$		−	22.3959i		−	1.19882i	0.800441	−	0.599411i	$-0.204599\pi$
$350$	−1.69900	−	0.740167i	−0.0908154	−	0.0395636i
$351$		0			0
$352$	2.40569	+	8.97815i	0.128224	+	0.478537i
$353$	32.6654	+	8.75267i	1.73860	+	0.465857i	0.982136	−	0.188173i	$-0.0602566\pi$
$353$	32.6654	+	8.75267i	1.73860	+	0.465857i	0.756468	+	0.654031i	$0.226923\pi$
$354$		0			0
$355$	8.27822	−	16.2681i	0.439362	−	0.863420i
$356$		−	24.9192i		−	1.32072i
$357$		0			0
$358$	−0.110883	−	0.110883i	−0.00586037	−	0.00586037i
$359$	5.51983	−	9.56063i	0.291326	−	0.504591i	−0.682798	−	0.730607i	$-0.739237\pi$
$359$	5.51983	−	9.56063i	0.291326	−	0.504591i	0.974123	+	0.226017i	$0.0725703\pi$
$360$		0			0
$361$	3.67525	+	6.36571i	0.193434	+	0.335038i
$362$	−1.77316	+	0.475116i	−0.0931950	+	0.0249715i
$363$		0			0
$364$	−19.0996	+	0.133149i	−1.00109	+	0.00697889i
$365$	−12.2612	+	13.6318i	−0.641780	+	0.713523i
$366$		0			0
$367$	3.72578	+	0.998319i	0.194484	+	0.0521118i	0.354746	−	0.934963i	$-0.384567\pi$
$367$	3.72578	+	0.998319i	0.194484	+	0.0521118i	−0.160262	+	0.987074i	$0.551234\pi$
$368$	−17.3540	−	4.64999i	−0.904639	−	0.242397i
$369$		0			0
$370$	−0.126023	−	2.38068i	−0.00655160	−	0.123766i
$371$	−4.26884	+	0.0297593i	−0.221627	+	0.00154503i
$372$		0			0
$373$	−10.0751	+	2.69962i	−0.521669	+	0.139781i	−0.510039	−	0.860151i	$-0.670369\pi$
$373$	−10.0751	+	2.69962i	−0.521669	+	0.139781i	−0.0116307	+	0.999932i	$0.503702\pi$
$374$	0.109434	+	0.189545i	0.00565868	+	0.00980112i
$375$		0			0
$376$	3.13743	−	5.43418i	0.161800	−	0.280246i
$377$	−7.51017	−	7.51017i	−0.386793	−	0.386793i
$378$		0			0
$379$		−	19.1988i		−	0.986177i	−0.869979	−	0.493089i	$-0.835868\pi$
$379$		−	19.1988i		−	0.986177i	0.869979	−	0.493089i	$-0.164132\pi$
$380$	20.2593	+	10.3092i	1.03928	+	0.528850i
$381$		0			0
$382$	−0.726703	−	0.194720i	−0.0371814	−	0.00996272i
$383$	9.12303	+	34.0476i	0.466165	+	1.73975i	0.652998	+	0.757359i	$0.273511\pi$
$383$	9.12303	+	34.0476i	0.466165	+	1.73975i	−0.186834	+	0.982392i	$0.559823\pi$
$384$		0			0
$385$	−31.4432	+	10.4778i	−1.60249	+	0.533998i
$386$		−	2.05924i		−	0.104813i
$387$		0			0
$388$	5.98043	−	22.3193i	0.303610	−	1.13309i
$389$	17.2123	+	29.8126i	0.872700	+	1.51156i	0.859192	+	0.511652i	$0.170966\pi$
$389$	17.2123	+	29.8126i	0.872700	+	1.51156i	0.0135078	+	0.999909i	$0.495700\pi$
$390$		0			0
$391$	−1.29046			−0.0652611
$392$	0.957584	−	3.78401i	0.0483653	−	0.191121i
$393$		0			0
$394$	1.41928	+	0.819423i	0.0715024	+	0.0412819i
$395$	−0.704951	−	1.08428i	−0.0354700	−	0.0545561i
$396$		0			0
$397$	−3.57770	−	13.3522i	−0.179560	−	0.670127i	−0.995730	−	0.0923147i	$-0.970573\pi$
$397$	−3.57770	−	13.3522i	−0.179560	−	0.670127i	0.816170	−	0.577812i	$-0.196093\pi$
$398$	2.10203	−	2.10203i	0.105365	−	0.105365i
$399$		0			0
$400$	19.3047	−	2.04955i	0.965233	−	0.102477i
$401$	10.4832	+	6.05249i	0.523507	+	0.302247i	0.738368	−	0.674398i	$-0.235597\pi$
$401$	10.4832	+	6.05249i	0.523507	+	0.302247i	−0.214862	+	0.976645i	$0.568930\pi$
$402$		0			0
$403$	2.06281	−	7.69850i	0.102756	−	0.383490i
$404$	4.87385	−	8.44175i	0.242483	−	0.419993i
$405$		0			0
$406$	0.931438	−	0.546459i	0.0462265	−	0.0271203i
$407$	−30.1479	−	30.1479i	−1.49438	−	1.49438i
$408$		0			0
$409$	−25.3797	+	14.6530i	−1.25495	+	0.724544i	−0.972088	−	0.234617i	$-0.924616\pi$
$409$	−25.3797	+	14.6530i	−1.25495	+	0.724544i	−0.282860	+	0.959161i	$0.591283\pi$
$410$	−0.567349	+	2.67609i	−0.0280194	+	0.132163i
$411$		0			0
$412$	21.9678	−	21.9678i	1.08228	−	1.08228i
$413$	6.13025	+	6.04537i	0.301650	+	0.297473i
$414$		0			0
$415$	9.40032	−	3.05982i	0.461444	−	0.150201i
$416$	−5.23786	+	3.02408i	−0.256807	+	0.148268i
$417$		0			0
$418$	−3.89140	+	1.04270i	−0.190334	+	0.0509999i
$419$	−4.45393			−0.217589			−0.108794	−	0.994064i	$-0.534699\pi$
$419$	−4.45393			−0.217589			−0.108794	+	0.994064i	$0.534699\pi$
$420$		0			0
$421$	27.1950			1.32540			0.662701	−	0.748884i	$-0.269410\pi$
$421$	27.1950			1.32540			0.662701	+	0.748884i	$0.269410\pi$
$422$	0.933969	−	0.250256i	0.0454649	−	0.0121823i
$423$		0			0
$424$	−0.779175	+	0.449857i	−0.0378401	+	0.0218470i
$425$	1.30125	−	0.501074i	0.0631198	−	0.0243057i
$426$		0			0
$427$	−1.41509	+	5.43239i	−0.0684810	+	0.262892i
$428$	26.6263	−	26.6263i	1.28703	−	1.28703i
$429$		0			0
$430$	−1.42598	−	2.19329i	−0.0687670	−	0.105770i
$431$	−22.2647	+	12.8545i	−1.07245	+	0.619180i	−0.928850	−	0.370456i	$-0.879201\pi$
$431$	−22.2647	+	12.8545i	−1.07245	+	0.619180i	−0.143601	+	0.989636i	$0.545868\pi$
$432$		0			0
$433$	23.5411	+	23.5411i	1.13131	+	1.13131i	0.989959	+	0.141353i	$0.0451452\pi$
$433$	23.5411	+	23.5411i	1.13131	+	1.13131i	0.141353	+	0.989959i	$0.454855\pi$
$434$	0.704608	+	0.400282i	0.0338223	+	0.0192142i
$435$		0			0
$436$	−10.8656	+	18.8198i	−0.520367	+	0.901303i
$437$	6.14780	−	22.9439i	0.294089	−	1.09756i
$438$		0			0
$439$	−8.62144	−	4.97759i	−0.411479	−	0.237567i	0.279946	−	0.960016i	$-0.409683\pi$
$439$	−8.62144	−	4.97759i	−0.411479	−	0.237567i	−0.691425	+	0.722448i	$0.743017\pi$
$440$	−4.67125	+	5.19344i	−0.222693	+	0.247588i
$441$		0			0
$442$	−0.100704	+	0.100704i	−0.00478999	+	0.00478999i
$443$	−7.68062	−	28.6645i	−0.364918	−	1.36189i	−0.867533	−	0.497380i	$-0.834295\pi$
$443$	−7.68062	−	28.6645i	−0.364918	−	1.36189i	0.502615	−	0.864510i	$-0.332371\pi$
$444$		0			0
$445$	23.5893	−	15.3367i	1.11824	−	0.727031i
$446$	−0.232393	−	0.134172i	−0.0110041	−	0.00635322i
$447$		0			0
$448$	5.29234	+	19.2145i	0.250040	+	0.907799i
$449$	26.4145			1.24658			0.623290	−	0.781991i	$-0.285796\pi$
$449$	26.4145			1.24658			0.623290	+	0.781991i	$0.285796\pi$
$450$		0			0
$451$	24.4614	+	42.3684i	1.15184	+	1.99505i
$452$	−4.47134	+	16.6873i	−0.210314	+	0.784903i
$453$		0			0
$454$			1.14075i			0.0535381i
$455$	−11.8810	−	17.9983i	−0.556991	−	0.843773i
$456$		0			0
$457$	8.97102	+	33.4803i	0.419646	+	1.56614i	0.775343	+	0.631540i	$0.217577\pi$
$457$	8.97102	+	33.4803i	0.419646	+	1.56614i	−0.355696	+	0.934602i	$0.615756\pi$
$458$	1.79262	+	0.480331i	0.0837637	+	0.0224444i
$459$		0			0
$460$	−6.34230	−	19.4847i	−0.295711	−	0.908478i
$461$		−	39.9716i		−	1.86166i	−0.365449	−	0.930831i	$-0.619085\pi$
$461$		−	39.9716i		−	1.86166i	0.365449	−	0.930831i	$-0.380915\pi$
$462$		0			0
$463$	6.57833	+	6.57833i	0.305721	+	0.305721i	0.843247	−	0.537526i	$-0.180641\pi$
$463$	6.57833	+	6.57833i	0.305721	+	0.305721i	−0.537526	+	0.843247i	$0.680641\pi$
$464$	−5.65618	+	9.79679i	−0.262581	+	0.454804i
$465$		0			0
$466$	0.570448	+	0.988045i	0.0264255	+	0.0457703i
$467$	13.5661	−	3.63502i	0.627763	−	0.168208i	0.0691084	−	0.997609i	$-0.477985\pi$
$467$	13.5661	−	3.63502i	0.627763	−	0.168208i	0.558654	+	0.829401i	$0.311318\pi$
$468$		0			0
$469$	18.9754	−	0.132283i	0.876201	−	0.00610826i
$470$	3.52011	−	0.186339i	0.162371	−	0.00859518i
$471$		0			0
$472$	1.75273	+	0.469643i	0.0806759	+	0.0216171i
$473$	−45.1919	−	12.1091i	−2.07793	−	0.556779i
$474$		0			0
$475$	2.70973	+	25.5229i	0.124331	+	1.17107i
$476$	0.739405	+	1.26031i	0.0338906	+	0.0577664i
$477$		0			0
$478$	1.13807	−	0.304946i	0.0520543	−	0.0139479i
$479$	−13.6012	−	23.5580i	−0.621454	−	1.07639i	−0.989215	−	0.146470i	$-0.953209\pi$
$479$	−13.6012	−	23.5580i	−0.621454	−	1.07639i	0.367761	−	0.929920i	$-0.380124\pi$
$480$		0			0
$481$	13.8715	−	24.0261i	0.632484	−	1.09550i
$482$	−0.0243548	−	0.0243548i	−0.00110933	−	0.00110933i
$483$		0			0
$484$			40.3690i			1.83496i
$485$	24.8088	−	8.07531i	1.12651	−	0.366681i
$486$		0			0
$487$	−14.7386	−	3.94920i	−0.667870	−	0.178955i	−0.0910748	−	0.995844i	$-0.529030\pi$
$487$	−14.7386	−	3.94920i	−0.667870	−	0.178955i	−0.576795	+	0.816889i	$0.695697\pi$
$488$	0.306216	+	1.14281i	0.0138617	+	0.0517327i
$489$		0			0
$490$	2.07542	−	0.707704i	0.0937581	−	0.0319708i
$491$		−	1.26640i		−	0.0571518i	−0.999592	−	0.0285759i	$-0.990903\pi$
$491$		−	1.26640i		−	0.0571518i	0.999592	−	0.0285759i	$-0.00909723\pi$
$492$		0			0
$493$	−0.210299	+	0.784846i	−0.00947138	+	0.0353477i
$494$	−1.31073	−	2.27024i	−0.0589723	−	0.102143i
$495$		0			0
$496$	−8.48889			−0.381162
$497$	5.73513	+	20.8221i	0.257256	+	0.933998i
$498$		0			0
$499$	12.5885	+	7.26798i	0.563539	+	0.325359i	0.754565	−	0.656226i	$-0.227848\pi$
$499$	12.5885	+	7.26798i	0.563539	+	0.325359i	−0.191026	+	0.981585i	$0.561181\pi$
$500$	13.9611	+	17.1850i	0.624359	+	0.768535i
$501$		0			0
$502$	0.0166101	+	0.0619899i	0.000741347	+	0.00276674i
$503$	16.6937	−	16.6937i	0.744336	−	0.744336i	−0.229073	−	0.973409i	$-0.573569\pi$
$503$	16.6937	−	16.6937i	0.744336	−	0.744336i	0.973409	+	0.229073i	$0.0735694\pi$
$504$		0			0
$505$	10.9909	−	0.581807i	0.489087	−	0.0258901i
$506$	3.14505	+	1.81579i	0.139814	+	0.0807218i
$507$		0			0
$508$	−1.48842	+	5.55485i	−0.0660378	+	0.246456i
$509$	−12.4710	+	21.6005i	−0.552769	+	0.957424i	0.445304	+	0.895379i	$0.353096\pi$
$509$	−12.4710	+	21.6005i	−0.552769	+	0.957424i	−0.998073	+	0.0620449i	$0.980238\pi$
$510$		0			0
$511$	−0.151232	−	21.6935i	−0.00669009	−	0.959662i
$512$	7.61687	+	7.61687i	0.336621	+	0.336621i
$513$		0			0
$514$	3.03252	−	1.75083i	0.133759	−	0.0772256i
$515$	34.3156	+	7.27514i	1.51213	+	0.320581i
$516$		0			0
$517$	44.5772	−	44.5772i	1.96050	−	1.96050i
$518$	2.00847	+	1.98066i	0.0882469	+	0.0870250i
$519$		0			0
$520$	−4.05092	−	2.06136i	−0.177645	−	0.0903967i
$521$	20.1930	−	11.6584i	0.884670	−	0.510765i	0.0124748	−	0.999922i	$-0.496029\pi$
$521$	20.1930	−	11.6584i	0.884670	−	0.510765i	0.872195	+	0.489158i	$0.162696\pi$
$522$		0			0
$523$	−28.0009	+	7.50283i	−1.22440	+	0.328076i	−0.812395	−	0.583108i	$-0.801836\pi$
$523$	−28.0009	+	7.50283i	−1.22440	+	0.328076i	−0.412001	+	0.911184i	$0.635170\pi$
$524$	−19.4204			−0.848382
$525$		0			0
$526$	−2.43976			−0.106378
$527$	−0.588955	+	0.157810i	−0.0256553	+	0.00687431i
$528$		0			0
$529$	1.37521	−	0.793979i	0.0597918	−	0.0345208i
$530$	−0.450467	−	0.229226i	−0.0195670	−	0.00995693i
$531$		0			0
$532$	−25.9306	+	7.14218i	−1.12423	+	0.309653i
$533$	−22.5101	+	22.5101i	−0.975019	+	0.975019i
$534$		0			0
$535$	41.5926	+	8.81792i	1.79821	+	0.381232i
$536$	3.46350	−	1.99965i	0.149601	−	0.0863719i
$537$		0			0
$538$	1.47537	+	1.47537i	0.0636077	+	0.0636077i
$539$	19.1323	−	34.2315i	0.824085	−	1.47446i
$540$		0			0
$541$	−1.50038	+	2.59873i	−0.0645063	+	0.111728i	−0.896475	−	0.443095i	$-0.853881\pi$
$541$	−1.50038	+	2.59873i	−0.0645063	+	0.111728i	0.831969	+	0.554823i	$0.187214\pi$
$542$	0.554544	−	2.06959i	0.0238197	−	0.0888964i
$543$		0			0
$544$	0.400709	+	0.231350i	0.0171803	+	0.00991904i
$545$	−24.5027	+	1.29706i	−1.04958	+	0.0555600i
$546$		0			0
$547$	−2.21247	+	2.21247i	−0.0945983	+	0.0945983i	−0.752822	−	0.658224i	$-0.771308\pi$
$547$	−2.21247	+	2.21247i	−0.0945983	+	0.0945983i	0.658224	+	0.752822i	$0.271308\pi$
$548$	0.889081	+	3.31810i	0.0379797	+	0.141742i
$549$		0			0
$550$	−3.87641	−	0.609781i	−0.165291	−	0.0260011i
$551$	−12.9524	−	7.47810i	−0.551793	−	0.318578i
$552$		0			0
$553$	1.48083	+	0.385744i	0.0629715	+	0.0164035i
$554$	1.44732			0.0614906
$555$		0			0
$556$	−2.50505	−	4.33888i	−0.106238	−	0.184009i
$557$	8.04984	−	30.0424i	0.341083	−	1.27294i	−0.556039	−	0.831156i	$-0.687680\pi$
$557$	8.04984	−	30.0424i	0.341083	−	1.27294i	0.897122	−	0.441782i	$-0.145654\pi$
$558$		0			0
$559$		−	30.4437i		−	1.28763i
$560$	−15.2415	+	17.1848i	−0.644071	+	0.726189i
$561$		0			0
$562$	−0.858141	−	3.20263i	−0.0361985	−	0.135095i
$563$	36.0117	+	9.64932i	1.51771	+	0.406670i	0.918989	−	0.394284i	$-0.129007\pi$
$563$	36.0117	+	9.64932i	1.51771	+	0.406670i	0.598726	+	0.800954i	$0.295674\pi$
$564$		0			0
$565$	−18.5486	+	6.03760i	−0.780346	+	0.254004i
$566$			1.02115i			0.0429222i
$567$		0			0
$568$	3.21864	+	3.21864i	0.135051	+	0.135051i
$569$	−8.69925	+	15.0675i	−0.364692	+	0.631664i	−0.988727	−	0.149732i	$-0.952159\pi$
$569$	−8.69925	+	15.0675i	−0.364692	+	0.631664i	0.624035	+	0.781396i	$0.285492\pi$
$570$		0			0
$571$	−17.3894	−	30.1193i	−0.727723	−	1.26045i	−0.957843	−	0.287292i	$-0.907245\pi$
$571$	−17.3894	−	30.1193i	−0.727723	−	1.26045i	0.230120	−	0.973162i	$-0.426088\pi$
$572$	−39.0649	+	10.4674i	−1.63339	+	0.437665i
$573$		0			0
$574$	−1.63789	−	2.79178i	−0.0683641	−	0.116527i
$575$	14.5414	−	17.9958i	0.606418	−	0.750477i
$576$		0			0
$577$	−23.1695	−	6.20825i	−0.964560	−	0.258453i	−0.258030	−	0.966137i	$-0.583074\pi$
$577$	−23.1695	−	6.20825i	−0.964560	−	0.258453i	−0.706529	+	0.707684i	$0.749740\pi$
$578$	−2.28987	−	0.613569i	−0.0952460	−	0.0255211i
$579$		0			0
$580$	−12.8840	+	0.682022i	−0.534980	+	0.0283194i
$581$	−5.77775	+	10.1704i	−0.239701	+	0.421941i
$582$		0			0
$583$	−8.73117	+	2.33951i	−0.361608	+	0.0968926i
$584$	−2.28609	−	3.95963i	−0.0945992	−	0.163851i
$585$		0			0
$586$	0.992026	−	1.71824i	0.0409802	−	0.0709798i
$587$	15.2114	+	15.2114i	0.627840	+	0.627840i	0.947524	−	0.319684i	$-0.103577\pi$
$587$	15.2114	+	15.2114i	0.627840	+	0.627840i	−0.319684	+	0.947524i	$0.603577\pi$
$588$		0			0
$589$		−	11.2233i		−	0.462446i
$590$	0.315513	+	0.969314i	0.0129895	+	0.0399060i
$591$		0			0
$592$	−28.5420	−	7.64781i	−1.17307	−	0.314323i
$593$	−5.29885	−	19.7756i	−0.217598	−	0.812085i	−0.985236	−	0.171202i	$-0.945235\pi$
$593$	−5.29885	−	19.7756i	−0.217598	−	0.812085i	0.767638	−	0.640883i	$-0.221432\pi$
$594$		0			0
$595$	−0.737980	+	1.47561i	−0.0302542	+	0.0604942i
$596$		−	0.971879i		−	0.0398097i
$597$		0			0
$598$	−0.611607	+	2.28255i	−0.0250105	+	0.0933404i
$599$	−2.45403	−	4.25050i	−0.100269	−	0.173671i	0.811527	−	0.584315i	$-0.198637\pi$
$599$	−2.45403	−	4.25050i	−0.100269	−	0.173671i	−0.911795	+	0.410645i	$0.865304\pi$
$600$		0			0
$601$	−10.2782			−0.419258			−0.209629	−	0.977781i	$-0.567226\pi$
$601$	−10.2782			−0.419258			−0.209629	+	0.977781i	$0.567226\pi$
$602$	2.99544	+	0.780287i	0.122085	+	0.0318021i
$603$		0			0
$604$	−7.68251	−	4.43550i	−0.312597	−	0.180478i
$605$	−38.2145	+	24.8454i	−1.55364	+	1.01011i
$606$		0			0
$607$	6.97762	+	26.0408i	0.283213	+	1.05696i	0.950135	+	0.311838i	$0.100945\pi$
$607$	6.97762	+	26.0408i	0.283213	+	1.05696i	−0.666922	+	0.745127i	$0.732389\pi$
$608$	−6.02233	+	6.02233i	−0.244238	+	0.244238i
$609$		0			0
$610$	−0.444477	+	0.494165i	−0.0179964	+	0.0200081i
$611$	35.5254	+	20.5106i	1.43720	+	0.829769i
$612$		0			0
$613$	2.56939	−	9.58910i	0.103777	−	0.387300i	−0.894427	−	0.447215i	$-0.852416\pi$
$613$	2.56939	−	9.58910i	0.103777	−	0.387300i	0.998204	+	0.0599142i	$0.0190827\pi$
$614$	0.488658	−	0.846381i	0.0197206	−	0.0341572i
$615$		0			0
$616$	−0.0576160	−	8.26475i	−0.00232142	−	0.332996i
$617$	13.2957	+	13.2957i	0.535264	+	0.535264i	0.922134	−	0.386870i	$-0.126444\pi$
$617$	13.2957	+	13.2957i	0.535264	+	0.535264i	−0.386870	+	0.922134i	$0.626444\pi$
$618$		0			0
$619$	−1.14004	+	0.658202i	−0.0458220	+	0.0264554i	−0.522736	−	0.852495i	$-0.675089\pi$
$619$	−1.14004	+	0.658202i	−0.0458220	+	0.0264554i	0.476914	+	0.878950i	$0.341755\pi$
$620$	−5.27737	−	8.11708i	−0.211944	−	0.325990i
$621$		0			0
$622$	2.76808	−	2.76808i	0.110990	−	0.110990i
$623$	−8.39215	+	32.2166i	−0.336225	+	1.29073i
$624$		0			0
$625$	−7.67536	+	23.7926i	−0.307014	+	0.951705i
$626$	−1.74699	+	1.00863i	−0.0698240	+	0.0403129i
$627$		0			0
$628$	9.59147	−	2.57003i	0.382741	−	0.102555i
$629$	−2.12241			−0.0846258
$630$		0			0
$631$	6.81277			0.271212			0.135606	−	0.990763i	$-0.456702\pi$
$631$	6.81277			0.271212			0.135606	+	0.990763i	$0.456702\pi$
$632$	0.311523	−	0.0834725i	0.0123917	−	0.00332036i
$633$		0			0
$634$	1.46909	−	0.848180i	0.0583450	−	0.0336855i
$635$	−6.17445	+	2.00979i	−0.245025	+	0.0797562i
$636$		0			0
$637$	24.7376	+	6.26010i	0.980138	+	0.248034i
$638$	1.61688	−	1.61688i	0.0640131	−	0.0640131i
$639$		0			0
$640$	−2.02826	+	9.56697i	−0.0801741	+	0.378168i
$641$	10.6830	−	6.16781i	0.421951	−	0.243614i	−0.273960	−	0.961741i	$-0.588334\pi$
$641$	10.6830	−	6.16781i	0.421951	−	0.243614i	0.695912	+	0.718127i	$0.255000\pi$
$642$		0			0
$643$	0.219128	+	0.219128i	0.00864157	+	0.00864157i	0.711414	−	0.702773i	$-0.248055\pi$
$643$	0.219128	+	0.219128i	0.00864157	+	0.00864157i	−0.702773	+	0.711414i	$0.748055\pi$
$644$	21.0809	+	11.9759i	0.830705	+	0.471917i
$645$		0			0
$646$	−0.100274	+	0.173679i	−0.00394522	+	0.00683332i
$647$	0.715393	−	2.66988i	0.0281250	−	0.104964i	−0.950437	−	0.310919i	$-0.899363\pi$
$647$	0.715393	−	2.66988i	0.0281250	−	0.104964i	0.978562	+	0.205955i	$0.0660300\pi$
$648$		0			0
$649$	15.7880	+	9.11519i	0.619732	+	0.357803i
$650$	−0.269575	−	2.53912i	−0.0105736	−	0.0995925i
$651$		0			0
$652$	5.38634	−	5.38634i	0.210946	−	0.210946i
$653$	−6.36119	−	23.7403i	−0.248933	−	0.929030i	−0.971366	−	0.237589i	$-0.923643\pi$
$653$	−6.36119	−	23.7403i	−0.248933	−	0.929030i	0.722433	−	0.691441i	$-0.243024\pi$
$654$		0			0
$655$	−11.9524	−	18.3839i	−0.467019	−	0.718319i
$656$	29.3637	+	16.9531i	1.14646	+	0.661909i
$657$		0			0
$658$	−2.92863	+	2.96975i	−0.114170	+	0.115773i
$659$	−47.4163			−1.84708			−0.923538	−	0.383506i	$-0.874716\pi$
$659$	−47.4163			−1.84708			−0.923538	+	0.383506i	$0.874716\pi$
$660$		0			0
$661$	−9.31689	−	16.1373i	−0.362385	−	0.627669i	0.625968	−	0.779849i	$-0.284704\pi$
$661$	−9.31689	−	16.1373i	−0.362385	−	0.627669i	−0.988353	+	0.152180i	$0.951371\pi$
$662$	0.779575	−	2.90941i	0.0302990	−	0.113078i
$663$		0			0
$664$			2.46524i			0.0956699i
$665$	−22.7202	−	20.1510i	−0.881051	−	0.781420i
$666$		0			0
$667$	3.48941	+	13.0227i	0.135111	+	0.504239i
$668$	−17.6589	−	4.73169i	−0.683244	−	0.183075i
$669$		0			0
$670$	2.00237	+	1.01893i	0.0773581	+	0.0393647i
$671$			11.8866i			0.458875i
$672$		0			0
$673$	−23.8659	−	23.8659i	−0.919962	−	0.919962i	0.0770643	−	0.997026i	$-0.475445\pi$
$673$	−23.8659	−	23.8659i	−0.919962	−	0.919962i	−0.997026	+	0.0770643i	$0.975445\pi$
$674$	0.802555	−	1.39007i	0.0309133	−	0.0535434i
$675$		0			0
$676$	−0.285667	−	0.494789i	−0.0109872	−	0.0190303i
$677$	−2.20069	+	0.589674i	−0.0845796	+	0.0226630i	−0.300861	−	0.953668i	$-0.597274\pi$
$677$	−2.20069	+	0.589674i	−0.0845796	+	0.0226630i	0.216281	+	0.976331i	$0.430607\pi$
$678$		0			0
$679$	−15.2483	+	26.8412i	−0.585176	+	1.03007i
$680$	0.0183811	+	0.347236i	0.000704883	+	0.0133159i
$681$		0			0
$682$	1.65743	+	0.444107i	0.0634663	+	0.0170057i
$683$	−28.2798	−	7.57756i	−1.08210	−	0.289947i	−0.326643	−	0.945148i	$-0.605917\pi$
$683$	−28.2798	−	7.57756i	−1.08210	−	0.289947i	−0.755455	+	0.655201i	$0.772584\pi$
$684$		0			0
$685$	−2.59382	+	2.88378i	−0.0991048	+	0.110184i
$686$	−1.24999	+	2.27355i	−0.0477247	+	0.0868047i
$687$		0			0
$688$	−31.3205	+	8.39231i	−1.19408	+	0.319954i
$689$	−2.94089	−	5.09377i	−0.112039	−	0.194057i
$690$		0			0
$691$	−7.90637	+	13.6942i	−0.300773	+	0.520953i	−0.976311	−	0.216371i	$-0.930578\pi$
$691$	−7.90637	+	13.6942i	−0.300773	+	0.520953i	0.675539	+	0.737325i	$0.263911\pi$
$692$	30.9830	+	30.9830i	1.17780	+	1.17780i
$693$		0			0
$694$		−	2.89405i		−	0.109857i
$695$	2.56556	−	5.04175i	0.0973173	−	0.191245i
$696$		0			0
$697$	2.35240	+	0.630324i	0.0891035	+	0.0238752i
$698$	0.812032	+	3.03055i	0.0307359	+	0.114708i
$699$		0			0
$700$	−25.9074	−	3.89051i	−0.979208	−	0.147047i
$701$			12.7450i			0.481372i	0.970603	+	0.240686i	$0.0773723\pi$
$701$			12.7450i			0.481372i	−0.970603	+	0.240686i	$0.922628\pi$
$702$		0			0
$703$	10.1113	−	37.7357i	0.381353	−	1.42323i
$704$	21.1002	+	36.5466i	0.795243	+	1.37740i
$705$		0			0
$706$	−4.73755			−0.178300
$707$	−9.14408	+	9.27246i	−0.343898	+	0.348727i
$708$		0			0
$709$	33.8769	+	19.5589i	1.27228	+	0.734549i	0.975416	−	0.220373i	$-0.0707273\pi$
$709$	33.8769	+	19.5589i	1.27228	+	0.734549i	0.296860	+	0.954921i	$0.404061\pi$
$710$	−0.530335	+	2.50150i	−0.0199031	+	0.0938798i
$711$		0			0
$712$	1.81601	+	6.77742i	0.0680577	+	0.253995i
$713$	−7.15383	+	7.15383i	−0.267913	+	0.267913i
$714$		0			0
$715$	−33.9516	−	30.5378i	−1.26972	−	1.14205i
$716$	−1.91978	−	1.10838i	−0.0717454	−	0.0414222i
$717$		0			0
$718$	−0.400278	+	1.49386i	−0.0149382	+	0.0557503i
$719$	−3.29942	+	5.71477i	−0.123048	+	0.213125i	−0.920968	−	0.389638i	$-0.872600\pi$
$719$	−3.29942	+	5.71477i	−0.123048	+	0.213125i	0.797920	+	0.602763i	$0.205933\pi$
$720$		0			0
$721$	−35.7991	+	21.0027i	−1.33323	+	0.782181i
$722$	−0.728133	−	0.728133i	−0.0270983	−	0.0270983i
$723$		0			0
$724$	−22.4735	+	12.9751i	−0.835223	+	0.482216i
$725$	−8.57519	−	11.7767i	−0.318475	−	0.437374i
$726$		0			0
$727$	6.51144	−	6.51144i	0.241496	−	0.241496i	−0.575973	−	0.817469i	$-0.695377\pi$
$727$	6.51144	−	6.51144i	0.241496	−	0.241496i	0.817469	+	0.575973i	$0.195377\pi$
$728$	5.18491	−	1.42811i	0.192166	−	0.0529292i
$729$		0			0
$730$	1.16488	−	2.28919i	0.0431143	−	0.0847268i
$731$	−2.01699	+	1.16451i	−0.0746010	+	0.0430709i
$732$		0			0
$733$	−9.73928	+	2.60963i	−0.359728	+	0.0963890i	−0.434157	−	0.900837i	$-0.642954\pi$
$733$	−9.73928	+	2.60963i	−0.359728	+	0.0963890i	0.0744281	+	0.997226i	$0.476287\pi$
$734$	−0.540359			−0.0199450
$735$		0			0
$736$	7.67740			0.282993
$737$	38.8109	−	10.3993i	1.42962	−	0.383065i
$738$		0			0
$739$	11.1510	−	6.43804i	0.410196	−	0.236827i	−0.280678	−	0.959802i	$-0.590559\pi$
$739$	11.1510	−	6.43804i	0.410196	−	0.236827i	0.690874	+	0.722975i	$0.257226\pi$
$740$	−10.4311	−	32.0464i	−0.383457	−	1.17805i
$741$		0			0
$742$	0.576568	−	0.158807i	0.0211665	−	0.00582999i
$743$	8.34588	−	8.34588i	0.306181	−	0.306181i	−0.537245	−	0.843426i	$-0.680535\pi$
$743$	8.34588	−	8.34588i	0.306181	−	0.306181i	0.843426	+	0.537245i	$0.180535\pi$
$744$		0			0
$745$	0.920010	−	0.598150i	0.0337066	−	0.0219145i
$746$	1.26545	−	0.730610i	0.0463315	−	0.0267495i
$747$		0			0
$748$	2.18778	+	2.18778i	0.0799932	+	0.0799932i
$749$	−43.3907	+	25.4566i	−1.58546	+	0.930162i
$750$		0			0
$751$	21.5986	−	37.4098i	0.788143	−	1.36510i	−0.138961	−	0.990298i	$-0.544376\pi$
$751$	21.5986	−	37.4098i	0.788143	−	1.36510i	0.927104	−	0.374805i	$-0.122290\pi$
$752$	11.3082	−	42.2027i	0.412367	−	1.53897i
$753$		0			0
$754$	1.28856	+	0.743951i	0.0469266	+	0.0270931i
$755$	−0.529480	−	10.0024i	−0.0192698	−	0.364023i
$756$		0			0
$757$	−19.7726	+	19.7726i	−0.718648	+	0.718648i	−0.968328	−	0.249680i	$-0.919674\pi$
$757$	−19.7726	+	19.7726i	−0.718648	+	0.718648i	0.249680	+	0.968328i	$0.419674\pi$
$758$	0.696114	+	2.59793i	0.0252840	+	0.0943611i
$759$		0			0
$760$	−6.26132	−	1.32744i	−0.227122	−	0.0481513i
$761$	39.3328	+	22.7088i	1.42581	+	0.823193i	0.996787	−	0.0801000i	$-0.0255240\pi$
$761$	39.3328	+	22.7088i	1.42581	+	0.823193i	0.429025	+	0.903293i	$0.358857\pi$
$762$		0			0
$763$	20.3855	−	20.6717i	0.738004	−	0.748366i
$764$	−10.6353			−0.384773
$765$		0			0
$766$	−2.46901	−	4.27644i	−0.0892088	−	0.154514i
$767$	−3.07024	+	11.4583i	−0.110860	+	0.413735i
$768$		0			0
$769$			23.0900i			0.832646i	0.909217	+	0.416323i	$0.136681\pi$
$769$			23.0900i			0.832646i	−0.909217	+	0.416323i	$0.863319\pi$
$770$	3.87490	−	2.55790i	0.139642	−	0.0921802i
$771$		0			0
$772$	−7.53427	−	28.1183i	−0.271164	−	1.01200i
$773$	20.2807	+	5.43421i	0.729448	+	0.195455i	0.604383	−	0.796694i	$-0.293420\pi$
$773$	20.2807	+	5.43421i	0.729448	+	0.195455i	0.125064	+	0.992149i	$0.460086\pi$
$774$		0			0
$775$	4.43588	−	9.99143i	0.159341	−	0.358903i
$776$			6.50612i			0.233556i
$777$		0			0
$778$	−3.41008	−	3.41008i	−0.122257	−	0.122257i
$779$	−22.4139	+	38.8221i	−0.803062	+	1.39094i
$780$		0			0
$781$	22.8656	+	39.6043i	0.818194	+	1.41715i
$782$	0.174621	−	0.0467895i	0.00624443	−	0.00167319i
$783$		0			0
$784$	−0.378919	−	27.1758i	−0.0135328	−	0.970564i
$785$	8.33601	+	7.49784i	0.297525	+	0.267609i
$786$		0			0
$787$	−8.93832	−	2.39502i	−0.318617	−	0.0853731i	0.0959663	−	0.995385i	$-0.469406\pi$
$787$	−8.93832	−	2.39502i	−0.318617	−	0.0853731i	−0.414583	+	0.910011i	$0.636073\pi$
$788$	22.3779	+	5.99614i	0.797180	+	0.213604i
$789$		0			0
$790$	0.134706	+	0.121162i	0.00479263	+	0.00431074i
$791$	11.4006	−	20.0682i	0.405358	−	0.713542i
$792$		0			0
$793$	−7.47102	+	2.00185i	−0.265304	+	0.0710879i
$794$	0.968250	+	1.67706i	0.0343619	+	0.0595166i
$795$		0			0
$796$	21.0118	−	36.3935i	0.744743	−	1.28993i
$797$	5.16770	+	5.16770i	0.183049	+	0.183049i	0.792683	−	0.609634i	$-0.208684\pi$
$797$	5.16770	+	5.16770i	0.183049	+	0.183049i	−0.609634	+	0.792683i	$0.708684\pi$
$798$		0			0
$799$		−	3.13822i		−	0.111022i
$800$	−7.74161	+	2.98108i	−0.273707	+	0.105397i
$801$		0			0
$802$	−1.63801	−	0.438904i	−0.0578402	−	0.0154982i
$803$	−11.8890	−	44.3703i	−0.419553	−	1.56579i
$804$		0			0
$805$	1.63765	+	27.3265i	0.0577196	+	0.963134i
$806$			1.11653i			0.0393282i
$807$		0			0
$808$	−0.710369	+	2.65113i	−0.0249907	+	0.0932666i
$809$	6.23501	+	10.7994i	0.219211	+	0.379685i	0.954567	−	0.297996i	$-0.0963183\pi$
$809$	6.23501	+	10.7994i	0.219211	+	0.379685i	−0.735356	+	0.677681i	$0.762985\pi$
$810$		0			0
$811$	21.2698			0.746883			0.373442	−	0.927654i	$-0.378178\pi$
$811$	21.2698			0.746883			0.373442	+	0.927654i	$0.378178\pi$
$812$	10.7191	−	10.8696i	0.376168	−	0.381449i
$813$		0			0
$814$	5.17264	+	2.98643i	0.181301	+	0.104674i
$815$	8.41394	+	1.78381i	0.294728	+	0.0624842i
$816$		0			0
$817$	−11.0956	−	41.4092i	−0.388185	−	1.44873i
$818$	2.90303	−	2.90303i	0.101502	−	0.101502i
$819$		0			0
$820$	2.04421	+	38.6170i	0.0713869	+	1.34856i
$821$	−17.0359	−	9.83568i	−0.594557	−	0.343268i	0.172340	−	0.985037i	$-0.444867\pi$
$821$	−17.0359	−	9.83568i	−0.594557	−	0.343268i	−0.766897	+	0.641770i	$0.778200\pi$
$822$		0			0
$823$	−13.8605	+	51.7281i	−0.483146	+	1.80313i	0.105120	+	0.994460i	$0.466477\pi$
$823$	−13.8605	+	51.7281i	−0.483146	+	1.80313i	−0.588266	+	0.808667i	$0.700189\pi$
$824$	−4.37378	+	7.57562i	−0.152368	+	0.263909i
$825$		0			0
$826$	−1.04872	−	0.595772i	−0.0364898	−	0.0207296i
$827$	−19.0500	−	19.0500i	−0.662432	−	0.662432i	0.293521	−	0.955953i	$-0.405173\pi$
$827$	−19.0500	−	19.0500i	−0.662432	−	0.662432i	−0.955953	+	0.293521i	$0.905173\pi$
$828$		0			0
$829$	35.0623	−	20.2433i	1.21777	−	0.703077i	0.253326	−	0.967381i	$-0.418475\pi$
$829$	35.0623	−	20.2433i	1.21777	−	0.703077i	0.964440	+	0.264304i	$0.0851421\pi$
$830$	−1.16108	+	0.754885i	−0.0403018	+	0.0262024i
$831$		0			0
$832$	−19.4170	+	19.4170i	−0.673162	+	0.673162i
$833$	−0.531492	−	1.87840i	−0.0184151	−	0.0650827i
$834$		0			0
$835$	−6.38915	−	19.6286i	−0.221106	−	0.679277i
$836$	−49.3208	+	28.4754i	−1.70580	+	0.984842i
$837$		0			0
$838$	0.602694	−	0.161491i	0.0208197	−	0.00557862i
$839$	27.5643			0.951626			0.475813	−	0.879546i	$-0.342154\pi$
$839$	27.5643			0.951626			0.475813	+	0.879546i	$0.342154\pi$
$840$		0			0
$841$	−20.5111			−0.707278
$842$	−3.67995	+	0.986040i	−0.126819	+	0.0339812i
$843$		0			0
$844$	11.8374	−	6.83434i	0.407461	−	0.235248i
$845$	0.292567	−	0.574942i	0.0100646	−	0.0197786i
$846$		0			0
$847$	13.5952	−	52.1908i	0.467138	−	1.79330i
$848$	−4.42978	+	4.42978i	−0.152119	+	0.152119i
$849$		0			0
$850$	−0.157913	+	0.114985i	−0.00541638	+	0.00394395i
$851$	−30.4982	+	17.6081i	−1.04546	+	0.603599i
$852$		0			0
$853$	−20.4305	−	20.4305i	−0.699527	−	0.699527i	0.264781	−	0.964308i	$-0.414700\pi$
$853$	−20.4305	−	20.4305i	−0.699527	−	0.699527i	−0.964308	+	0.264781i	$0.914700\pi$
$854$	−0.00548226	−	0.786404i	−0.000187599	−	0.0269102i
$855$		0			0
$856$	−5.30130	+	9.18211i	−0.181195	+	0.313838i
$857$	0.867998	−	3.23941i	0.0296503	−	0.110656i	−0.949515	−	0.313722i	$-0.898424\pi$
$857$	0.867998	−	3.23941i	0.0296503	−	0.110656i	0.979165	+	0.203066i	$0.0650906\pi$
$858$		0			0
$859$	32.2014	+	18.5915i	1.09870	+	0.634332i	0.935878	−	0.352324i	$-0.114608\pi$
$859$	32.2014	+	18.5915i	1.09870	+	0.634332i	0.162818	+	0.986656i	$0.447942\pi$
$860$	−27.4961	−	24.7314i	−0.937608	−	0.843333i
$861$		0			0
$862$	2.54671	−	2.54671i	0.0867413	−	0.0867413i
$863$	−9.95503	−	37.1527i	−0.338873	−	1.26469i	−0.899609	−	0.436697i	$-0.856148\pi$
$863$	−9.95503	−	37.1527i	−0.338873	−	1.26469i	0.560735	−	0.827995i	$-0.310518\pi$
$864$		0			0
$865$	−10.2607	+	48.3982i	−0.348876	+	1.64559i
$866$	−4.03907	−	2.33196i	−0.137253	−	0.0792432i
$867$		0			0
$868$	11.0857	+	2.88774i	0.376274	+	0.0980162i
$869$	3.24020			0.109916
$870$		0			0
$871$	13.0725	+	22.6423i	0.442946	+	0.767205i
$872$	1.58367	−	5.91035i	0.0536299	−	0.200150i
$873$		0			0
$874$			3.32761i			0.112558i
$875$	−12.2620	−	26.9192i	−0.414533	−	0.910035i
$876$		0			0
$877$	−6.32325	−	23.5987i	−0.213521	−	0.796871i	−0.986682	−	0.162661i	$-0.947992\pi$
$877$	−6.32325	−	23.5987i	−0.213521	−	0.796871i	0.773161	−	0.634210i	$-0.218674\pi$
$878$	1.34711	+	0.360956i	0.0454627	+	0.0121817i
$879$		0			0
$880$	−22.0580	+	43.3477i	−0.743577	+	1.46125i
$881$		−	13.5509i		−	0.456542i	−0.973598	−	0.228271i	$-0.926693\pi$
$881$		−	13.5509i		−	0.456542i	0.973598	−	0.228271i	$-0.0733073\pi$
$882$		0			0
$883$	32.5237	+	32.5237i	1.09451	+	1.09451i	0.995041	+	0.0994691i	$0.0317144\pi$
$883$	32.5237	+	32.5237i	1.09451	+	1.09451i	0.0994691	+	0.995041i	$0.468286\pi$
$884$	−1.00663	+	1.74353i	−0.0338566	+	0.0586413i
$885$		0			0
$886$	2.07864	+	3.60031i	0.0698334	+	0.120955i
$887$	36.4202	−	9.75876i	1.22287	−	0.327667i	0.411070	−	0.911604i	$-0.365155\pi$
$887$	36.4202	−	9.75876i	1.22287	−	0.327667i	0.811799	+	0.583937i	$0.198488\pi$
$888$		0			0
$889$	3.79502	−	6.68028i	0.127281	−	0.224049i
$890$	−2.63596	+	2.93063i	−0.0883576	+	0.0982350i
$891$		0			0
$892$	−3.66415	−	0.981806i	−0.122685	−	0.0328733i
$893$	55.7967	+	14.9507i	1.86716	+	0.500305i
$894$		0			0
$895$	−0.132311	−	2.49948i	−0.00442268	−	0.0835484i
$896$	−5.85542	−	9.98055i	−0.195616	−	0.333427i
$897$		0			0
$898$	−3.57434	+	0.957742i	−0.119277	+	0.0319603i
$899$	3.18509	+	5.51673i	0.106229	+	0.183993i
$900$		0			0
$901$	−0.224986	+	0.389687i	−0.00749536	+	0.0129823i
$902$	−4.84625	−	4.84625i	−0.161363	−	0.161363i
$903$		0			0
$904$		−	4.86438i		−	0.161787i
$905$	−26.1141	−	13.2885i	−0.868064	−	0.441725i
$906$		0			0
$907$	5.14802	+	1.37941i	0.170937	+	0.0458025i	0.343272	−	0.939236i	$-0.388465\pi$
$907$	5.14802	+	1.37941i	0.170937	+	0.0458025i	−0.172335	+	0.985038i	$0.555131\pi$
$908$	4.17374	+	15.5766i	0.138510	+	0.516928i
$909$		0			0
$910$	2.26029	+	2.00470i	0.0749280	+	0.0664550i
$911$			14.3597i			0.475757i	0.971295	+	0.237879i	$0.0764520\pi$
$911$			14.3597i			0.475757i	−0.971295	+	0.237879i	$0.923548\pi$
$912$		0			0
$913$	−6.41032	+	23.9237i	−0.212151	+	0.791757i
$914$	−2.42787	−	4.20519i	−0.0803067	−	0.139095i
$915$		0			0
$916$	26.2351			0.866832
$917$	25.1075	+	6.54027i	0.829121	+	0.215979i
$918$		0			0
$919$	−2.41391	−	1.39367i	−0.0796276	−	0.0459730i	0.459658	−	0.888096i	$-0.347972\pi$
$919$	−2.41391	−	1.39367i	−0.0796276	−	0.0459730i	−0.539285	+	0.842123i	$0.681305\pi$
$920$	3.14491	+	4.83716i	0.103685	+	0.159476i
$921$		0			0
$922$	1.44930	+	5.40885i	0.0477300	+	0.178131i
$923$	−21.0415	+	21.0415i	−0.692590	+	0.692590i
$924$		0			0
$925$	23.9161	−	29.5976i	0.786358	−	0.973164i
$926$	−1.12868	−	0.651644i	−0.0370907	−	0.0214143i
$927$		0			0
$928$	1.25115	−	4.66934i	0.0410709	−	0.153279i
$929$	−3.46522	+	6.00194i	−0.113690	+	0.196917i	−0.917255	−	0.398299i	$-0.869600\pi$
$929$	−3.46522	+	6.00194i	−0.113690	+	0.196917i	0.803565	+	0.595217i	$0.202934\pi$
$930$		0			0
$931$	35.9294	−	0.500974i	1.17754	−	0.0164187i
$932$	11.4043	+	11.4043i	0.373560	+	0.373560i
$933$		0			0
$934$	−1.70392	+	0.983761i	−0.0557541	+	0.0321896i
$935$	−0.724534	+	3.41751i	−0.0236948	+	0.111764i
$936$		0			0
$937$	−34.0816	+	34.0816i	−1.11340	+	1.11340i	−0.120710	+	0.992688i	$0.538517\pi$
$937$	−34.0816	+	34.0816i	−1.11340	+	1.11340i	−0.992688	+	0.120710i	$0.961483\pi$
$938$	−2.56290	+	0.705912i	−0.0836816	+	0.0230488i
$939$		0			0
$940$	47.3843	−	15.4237i	1.54551	−	0.503064i
$941$	34.7876	−	20.0846i	1.13404	−	0.654741i	0.189095	−	0.981959i	$-0.439445\pi$
$941$	34.7876	−	20.0846i	1.13404	−	0.654741i	0.944949	+	0.327218i	$0.106111\pi$
$942$		0			0
$943$	39.0325	−	10.4587i	1.27107	−	0.340583i
$944$	12.6347			0.411224
$945$		0			0
$946$	6.55430			0.213099
$947$	−6.91415	+	1.85264i	−0.224680	+	0.0602027i	−0.369402	−	0.929270i	$-0.620438\pi$
$947$	−6.91415	+	1.85264i	−0.224680	+	0.0602027i	0.144723	+	0.989472i	$0.453771\pi$
$948$		0			0
$949$	25.8856	−	14.9451i	0.840284	−	0.485138i
$950$	−1.29209	−	3.35544i	−0.0419209	−	0.108865i
$951$		0			0
$952$	−0.292946	−	0.288890i	−0.00949444	−	0.00936298i
$953$	22.1319	−	22.1319i	0.716922	−	0.716922i	−0.251052	−	0.967974i	$-0.580776\pi$
$953$	22.1319	−	22.1319i	0.716922	−	0.716922i	0.967974	+	0.251052i	$0.0807764\pi$
$954$		0			0
$955$	−6.54560	−	10.0677i	−0.211811	−	0.325784i
$956$	14.4243	−	8.32788i	0.466516	−	0.269343i
$957$		0			0
$958$	2.69464	+	2.69464i	0.0870600	+	0.0870600i
$959$	−0.0319926	−	4.58919i	−0.00103310	−	0.148193i
$960$		0			0
$961$	13.1099	−	22.7070i	0.422899	−	0.732483i
$962$	−1.00591	+	3.75410i	−0.0324318	+	0.121037i
$963$		0			0
$964$	−0.421666	−	0.243449i	−0.0135809	−	0.00784096i
$965$	21.9806	−	24.4378i	0.707581	−	0.786680i
$966$		0			0
$967$	29.9553	−	29.9553i	0.963297	−	0.963297i	−0.0360528	−	0.999350i	$-0.511478\pi$
$967$	29.9553	−	29.9553i	0.963297	−	0.963297i	0.999350	+	0.0360528i	$0.0114785\pi$
$968$	−2.94192	−	10.9794i	−0.0945568	−	0.352891i
$969$		0			0
$970$	−3.06426	+	1.99225i	−0.0983876	+	0.0639673i
$971$	−25.0340	−	14.4534i	−0.803378	−	0.463830i	0.0412730	−	0.999148i	$-0.486859\pi$
$971$	−25.0340	−	14.4534i	−0.803378	−	0.463830i	−0.844651	+	0.535317i	$0.820192\pi$
$972$		0			0
$973$	1.77741	+	6.45312i	0.0569813	+	0.206877i
$974$	2.13758			0.0684924
$975$		0			0
$976$	4.11902	+	7.13436i	0.131847	+	0.228365i
$977$	13.9144	−	51.9291i	0.445160	−	1.66136i	−0.270355	−	0.962761i	$-0.587141\pi$
$977$	13.9144	−	51.9291i	0.445160	−	1.66136i	0.715515	−	0.698598i	$-0.246192\pi$
$978$		0			0
$979$			70.4929i			2.25296i
$980$	25.7499	−	17.2570i	0.822551	−	0.551253i
$981$		0			0
$982$	0.0459173	+	0.171366i	0.00146528	+	0.00546850i
$983$	−20.9382	−	5.61039i	−0.667826	−	0.178944i	−0.0910508	−	0.995846i	$-0.529023\pi$
$983$	−20.9382	−	5.61039i	−0.667826	−	0.178944i	−0.576775	+	0.816903i	$0.695689\pi$
$984$		0			0
$985$	8.09653	+	24.8740i	0.257977	+	0.792551i
$986$		−	0.113828i		−	0.00362503i
$987$		0			0
$988$	−26.2038	−	26.2038i	−0.833655	−	0.833655i
$989$	−19.3223	+	33.4672i	−0.614412	+	1.06419i
$990$		0			0
$991$	−7.37279	−	12.7700i	−0.234204	−	0.405654i	0.724837	−	0.688921i	$-0.241915\pi$
$991$	−7.37279	−	12.7700i	−0.234204	−	0.405654i	−0.959041	+	0.283267i	$0.908582\pi$
$992$	3.50391	−	0.938871i	0.111249	−	0.0298092i
$993$		0			0
$994$	−1.53103	−	2.60964i	−0.0485614	−	0.0827728i
$995$	47.3830	−	2.50825i	1.50214	−	0.0795167i
$996$		0			0
$997$	−14.8255	−	3.97247i	−0.469527	−	0.125809i	0.0162947	−	0.999867i	$-0.494813\pi$
$997$	−14.8255	−	3.97247i	−0.469527	−	0.125809i	−0.485822	+	0.874058i	$0.661480\pi$
$998$	−1.96697	−	0.527047i	−0.0622632	−	0.0166834i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.233.8	yes	64
3.2	odd	2	inner	315.2.ce.a.233.9	yes	64
5.2	odd	4	inner	315.2.ce.a.107.8	yes	64
7.4	even	3	inner	315.2.ce.a.53.9	yes	64
15.2	even	4	inner	315.2.ce.a.107.9	yes	64
21.11	odd	6	inner	315.2.ce.a.53.8	✓	64
35.32	odd	12	inner	315.2.ce.a.242.9	yes	64
105.32	even	12	inner	315.2.ce.a.242.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.8	✓	64	21.11	odd	6	inner
315.2.ce.a.53.9	yes	64	7.4	even	3	inner
315.2.ce.a.107.8	yes	64	5.2	odd	4	inner
315.2.ce.a.107.9	yes	64	15.2	even	4	inner
315.2.ce.a.233.8	yes	64	1.1	even	1	trivial
315.2.ce.a.233.9	yes	64	3.2	odd	2	inner
315.2.ce.a.242.8	yes	64	105.32	even	12	inner
315.2.ce.a.242.9	yes	64	35.32	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.135317 + 0.0362581i) q^{2} +(-1.71505 + 0.990187i) q^{4} +(-1.99289 - 1.01410i) q^{5} +(2.55076 - 0.702570i) q^{7} +(0.394292 - 0.394292i) q^{8} +(0.306441 + 0.0649676i) q^{10} +(4.85164 - 2.80110i) q^{11} +(2.57764 + 2.57764i) q^{13} +(-0.319688 + 0.187556i) q^{14} +(1.94132 - 3.36246i) q^{16} +(0.0721789 - 0.269375i) q^{17} +(4.44554 + 2.56664i) q^{19} +(4.42206 - 0.234084i) q^{20} +(-0.554948 + 0.554948i) q^{22} +(-1.19764 - 4.46964i) q^{23} +(2.94318 + 4.04199i) q^{25} +(-0.442260 - 0.255339i) q^{26} +(-3.67902 + 3.73068i) q^{28} -2.91358 q^{29} +(-1.09319 - 1.89346i) q^{31} +(-0.429419 + 1.60261i) q^{32} +0.0390682i q^{34} +(-5.79586 - 1.18660i) q^{35} +(-1.96975 - 7.35120i) q^{37} +(-0.694620 - 0.186123i) q^{38} +(-1.18563 + 0.385926i) q^{40} +8.73280i q^{41} +(-5.90533 - 5.90533i) q^{43} +(-5.54722 + 9.60806i) q^{44} +(0.324122 + 0.561396i) q^{46} +(10.8696 - 2.91250i) q^{47} +(6.01279 - 3.58418i) q^{49} +(-0.544818 - 0.440237i) q^{50} +(-6.97315 - 1.86845i) q^{52} +(-1.55853 - 0.417606i) q^{53} +(-12.5094 + 0.662190i) q^{55} +(0.728729 - 1.28276i) q^{56} +(0.394257 - 0.105641i) q^{58} +(1.62708 + 2.81818i) q^{59} +(-1.06088 + 1.83751i) q^{61} +(0.216580 + 0.216580i) q^{62} +7.53283i q^{64} +(-2.52295 - 7.75095i) q^{65} +(6.92780 + 1.85630i) q^{67} +(0.142941 + 0.533464i) q^{68} +(0.827304 - 0.0495794i) q^{70} +8.16308i q^{71} +(2.12220 - 7.92016i) q^{73} +(0.533082 + 0.923325i) q^{74} -10.1658 q^{76} +(10.4074 - 10.5535i) q^{77} +(0.500892 + 0.289190i) q^{79} +(-7.27871 + 4.73230i) q^{80} +(-0.316635 - 1.18170i) q^{82} +(-3.12616 + 3.12616i) q^{83} +(-0.417019 + 0.463637i) q^{85} +(1.01321 + 0.584977i) q^{86} +(0.808514 - 3.01741i) q^{88} +(-6.29155 + 10.8973i) q^{89} +(8.38594 + 4.76399i) q^{91} +(6.47980 + 6.47980i) q^{92} +(-1.36524 + 0.788224i) q^{94} +(-6.25662 - 9.62326i) q^{95} +(-8.25038 + 8.25038i) q^{97} +(-0.683679 + 0.703014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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