LMFDB - Embedded newform 315.2.ce.a.107.9

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			107.9
Character	$\chi$	$=$	315.107
Dual form			315.2.ce.a.53.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0362581 + 0.135317i) q^{2} +(1.71505 - 0.990187i) q^{4} +(1.87468 + 1.21884i) q^{5} +(0.702570 + 2.55076i) q^{7} +(0.394292 + 0.394292i) q^{8} +(-0.0969571 + 0.297870i) q^{10} +(-4.85164 + 2.80110i) q^{11} +(2.57764 - 2.57764i) q^{13} +(-0.319688 + 0.187556i) q^{14} +(1.94132 - 3.36246i) q^{16} +(-0.269375 - 0.0721789i) q^{17} +(-4.44554 - 2.56664i) q^{19} +(4.42206 + 0.234084i) q^{20} +(-0.554948 - 0.554948i) q^{22} +(4.46964 - 1.19764i) q^{23} +(2.02887 + 4.56987i) q^{25} +(0.442260 + 0.255339i) q^{26} +(3.73068 + 3.67902i) q^{28} -2.91358 q^{29} +(-1.09319 - 1.89346i) q^{31} +(1.60261 + 0.429419i) q^{32} -0.0390682i q^{34} +(-1.79187 + 5.63819i) q^{35} +(7.35120 - 1.96975i) q^{37} +(0.186123 - 0.694620i) q^{38} +(0.258595 + 1.21975i) q^{40} -8.73280i q^{41} +(-5.90533 + 5.90533i) q^{43} +(-5.54722 + 9.60806i) q^{44} +(0.324122 + 0.561396i) q^{46} +(-2.91250 - 10.8696i) q^{47} +(-6.01279 + 3.58418i) q^{49} +(-0.544818 + 0.440237i) q^{50} +(1.86845 - 6.97315i) q^{52} +(0.417606 - 1.55853i) q^{53} +(-12.5094 - 0.662190i) q^{55} +(-0.728729 + 1.28276i) q^{56} +(-0.105641 - 0.394257i) q^{58} +(1.62708 + 2.81818i) q^{59} +(-1.06088 + 1.83751i) q^{61} +(0.216580 - 0.216580i) q^{62} -7.53283i q^{64} +(7.97399 - 1.69054i) q^{65} +(-1.85630 + 6.92780i) q^{67} +(-0.533464 + 0.142941i) q^{68} +(-0.827914 - 0.0380404i) q^{70} -8.16308i q^{71} +(-7.92016 - 2.12220i) q^{73} +(0.533082 + 0.923325i) q^{74} -10.1658 q^{76} +(-10.5535 - 10.4074i) q^{77} +(-0.500892 - 0.289190i) q^{79} +(7.73764 - 3.93740i) q^{80} +(1.18170 - 0.316635i) q^{82} +(-3.12616 - 3.12616i) q^{83} +(-0.417019 - 0.463637i) q^{85} +(-1.01321 - 0.584977i) q^{86} +(-3.01741 - 0.808514i) q^{88} +(-6.29155 + 10.8973i) q^{89} +(8.38594 + 4.76399i) q^{91} +(6.47980 - 6.47980i) q^{92} +(1.36524 - 0.788224i) q^{94} +(-5.20568 - 10.2300i) q^{95} +(-8.25038 - 8.25038i) q^{97} +(-0.703014 - 0.683679i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0362581	+	0.135317i	0.0256384	+	0.0956837i	0.977559	−	0.210660i	$-0.0675611\pi$
$2$	0.0362581	+	0.135317i	0.0256384	+	0.0956837i	−0.951921	+	0.306343i	$0.900894\pi$
$3$		0			0
$3$		0			0
$4$	1.71505	−	0.990187i	0.857527	−	0.495094i
$5$	1.87468	+	1.21884i	0.838384	+	0.545080i
$5$	1.87468	+	1.21884i	0.838384	+	0.545080i
$6$		0			0
$7$	0.702570	+	2.55076i	0.265546	+	0.964098i
$7$	0.702570	+	2.55076i	0.265546	+	0.964098i
$8$	0.394292	+	0.394292i	0.139403	+	0.139403i
$9$		0			0
$10$	−0.0969571	+	0.297870i	−0.0306605	+	0.0941947i
$11$	−4.85164	+	2.80110i	−1.46282	+	0.844562i	−0.999141	−	0.0414391i	$-0.986806\pi$
$11$	−4.85164	+	2.80110i	−1.46282	+	0.844562i	−0.463683	+	0.886001i	$0.653472\pi$
$12$		0			0
$13$	2.57764	−	2.57764i	0.714910	−	0.714910i	−0.252648	−	0.967558i	$-0.581302\pi$
$13$	2.57764	−	2.57764i	0.714910	−	0.714910i	0.967558	+	0.252648i	$0.0813016\pi$
$14$	−0.319688	+	0.187556i	−0.0854403	+	0.0501264i
$15$		0			0
$16$	1.94132	−	3.36246i	0.485329	−	0.840615i
$17$	−0.269375	−	0.0721789i	−0.0653331	−	0.0175059i	0.226004	−	0.974126i	$-0.427434\pi$
$17$	−0.269375	−	0.0721789i	−0.0653331	−	0.0175059i	−0.291338	+	0.956620i	$0.594100\pi$
$18$		0			0
$19$	−4.44554	−	2.56664i	−1.01988	−	0.588827i	−0.105809	−	0.994386i	$-0.533743\pi$
$19$	−4.44554	−	2.56664i	−1.01988	−	0.588827i	−0.914069	+	0.405560i	$0.867077\pi$
$20$	4.42206	+	0.234084i	0.988803	+	0.0523428i
$21$		0			0
$22$	−0.554948	−	0.554948i	−0.118315	−	0.118315i
$23$	4.46964	−	1.19764i	0.931985	−	0.249725i	0.239284	−	0.970950i	$-0.423087\pi$
$23$	4.46964	−	1.19764i	0.931985	−	0.249725i	0.692701	+	0.721225i	$0.256421\pi$
$24$		0			0
$25$	2.02887	+	4.56987i	0.405775	+	0.913973i
$26$	0.442260	+	0.255339i	0.0867344	+	0.0500761i
$27$		0			0
$28$	3.73068	+	3.67902i	0.705032	+	0.695270i
$29$	−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	$0.896240\pi$
$32$	1.60261	+	0.429419i	0.283305	+	0.0759113i
$33$		0			0
$34$		−	0.0390682i		−	0.00670014i
$35$	−1.79187	+	5.63819i	−0.302881	+	0.953028i
$36$		0			0
$37$	7.35120	−	1.96975i	1.20853	−	0.323825i	0.402345	−	0.915488i	$-0.368195\pi$
$37$	7.35120	−	1.96975i	1.20853	−	0.323825i	0.806185	+	0.591664i	$0.201529\pi$
$38$	0.186123	−	0.694620i	0.0301931	−	0.112682i
$39$		0			0
$40$	0.258595	+	1.21975i	0.0408875	+	0.192860i
$41$		−	8.73280i		−	1.36383i	−0.731429	−	0.681917i	$-0.761146\pi$
$41$		−	8.73280i		−	1.36383i	0.731429	−	0.681917i	$-0.238854\pi$
$42$		0			0
$43$	−5.90533	+	5.90533i	−0.900554	+	0.900554i	−0.995484	−	0.0949298i	$-0.969737\pi$
$43$	−5.90533	+	5.90533i	−0.900554	+	0.900554i	0.0949298	+	0.995484i	$0.469737\pi$
$44$	−5.54722	+	9.60806i	−0.836275	+	1.44847i
$45$		0			0
$46$	0.324122	+	0.561396i	0.0477892	+	0.0827733i
$47$	−2.91250	−	10.8696i	−0.424832	−	1.58549i	−0.764289	−	0.644873i	$-0.776910\pi$
$47$	−2.91250	−	10.8696i	−0.424832	−	1.58549i	0.339457	−	0.940621i	$-0.389757\pi$
$48$		0			0
$49$	−6.01279	+	3.58418i	−0.858970	+	0.512025i
$50$	−0.544818	+	0.440237i	−0.0770490	+	0.0622589i
$51$		0			0
$52$	1.86845	−	6.97315i	0.259107	−	0.967002i
$53$	0.417606	−	1.55853i	0.0573627	−	0.214080i	−0.931295	−	0.364265i	$-0.881320\pi$
$53$	0.417606	−	1.55853i	0.0573627	−	0.214080i	0.988658	+	0.150185i	$0.0479869\pi$
$54$		0			0
$55$	−12.5094	−	0.662190i	−1.68676	−	0.0892896i
$56$	−0.728729	+	1.28276i	−0.0973805	+	0.171417i
$57$		0			0
$58$	−0.105641	−	0.394257i	−0.0138713	−	0.0517685i
$59$	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
$65$	7.97399	−	1.69054i	0.989052	−	0.209686i
$66$		0			0
$67$	−1.85630	+	6.92780i	−0.226783	+	0.846366i	0.754899	+	0.655841i	$0.227686\pi$
$67$	−1.85630	+	6.92780i	−0.226783	+	0.846366i	−0.981682	+	0.190525i	$0.938981\pi$
$68$	−0.533464	+	0.142941i	−0.0646920	+	0.0173342i
$69$		0			0
$70$	−0.827914	−	0.0380404i	−0.0989547	−	0.00454670i
$71$		−	8.16308i		−	0.968779i	−0.874852	−	0.484390i	$-0.839042\pi$
$71$		−	8.16308i		−	0.968779i	0.874852	−	0.484390i	$-0.160958\pi$
$72$		0			0
$73$	−7.92016	−	2.12220i	−0.926985	−	0.248385i	−0.236416	−	0.971652i	$-0.575973\pi$
$73$	−7.92016	−	2.12220i	−0.926985	−	0.248385i	−0.690569	+	0.723267i	$0.742640\pi$
$74$	0.533082	+	0.923325i	0.0619695	+	0.107334i
$75$		0			0
$76$	−10.1658			−1.16610
$77$	−10.5535	−	10.4074i	−1.20269	−	1.18604i
$78$		0			0
$79$	−0.500892	−	0.289190i	−0.0563548	−	0.0325364i	0.471558	−	0.881835i	$-0.343692\pi$
$79$	−0.500892	−	0.289190i	−0.0563548	−	0.0325364i	−0.527913	+	0.849299i	$0.677025\pi$
$80$	7.73764	−	3.93740i	0.865095	−	0.440214i
$81$		0			0
$82$	1.18170	−	0.316635i	0.130497	−	0.0349665i
$83$	−3.12616	−	3.12616i	−0.343140	−	0.343140i	0.514406	−	0.857547i	$-0.328012\pi$
$83$	−3.12616	−	3.12616i	−0.343140	−	0.343140i	−0.857547	+	0.514406i	$0.828012\pi$
$84$		0			0
$85$	−0.417019	−	0.463637i	−0.0452321	−	0.0502885i
$86$	−1.01321	−	0.584977i	−0.109257	−	0.0630796i
$87$		0			0
$88$	−3.01741	−	0.808514i	−0.321657	−	0.0861879i
$89$	−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
$95$	−5.20568	−	10.2300i	−0.534091	−	1.04958i
$96$		0			0
$97$	−8.25038	−	8.25038i	−0.837699	−	0.837699i	0.150857	−	0.988556i	$-0.451797\pi$
$97$	−8.25038	−	8.25038i	−0.837699	−	0.837699i	−0.988556	+	0.150857i	$0.951797\pi$
$98$	−0.703014	−	0.683679i	−0.0710151	−	0.0690620i
$99$		0			0
$100$	8.00465	+	5.82860i	0.800465	+	0.582860i
$101$	4.26270	−	2.46107i	0.424155	−	0.244886i	−0.272698	−	0.962100i	$-0.587916\pi$
$101$	4.26270	−	2.46107i	0.424155	−	0.244886i	0.696853	+	0.717214i	$0.254583\pi$
$102$		0			0
$103$	4.06023	+	15.1530i	0.400066	+	1.49307i	0.812977	+	0.582295i	$0.197845\pi$
$103$	4.06023	+	15.1530i	0.400066	+	1.49307i	−0.412911	+	0.910771i	$0.635488\pi$
$104$	2.03269			0.199322
$105$		0			0
$106$	0.226037			0.0219547
$107$	4.92124	+	18.3663i	0.475755	+	1.77554i	0.618504	+	0.785782i	$0.287739\pi$
$107$	4.92124	+	18.3663i	0.475755	+	1.77554i	−0.142749	+	0.989759i	$0.545594\pi$
$108$		0			0
$109$	−9.50313	+	5.48663i	−0.910234	+	0.525524i	−0.880507	−	0.474034i	$-0.842797\pi$
$109$	−9.50313	+	5.48663i	−0.910234	+	0.525524i	−0.0297279	+	0.999558i	$0.509464\pi$
$110$	−0.363961	−	1.71674i	−0.0347023	−	0.163685i
$111$		0			0
$112$	9.94075	+	2.58948i	0.939312	+	0.244683i
$113$	6.16850	+	6.16850i	0.580283	+	0.580283i	0.934981	−	0.354698i	$-0.115416\pi$
$113$	6.16850	+	6.16850i	0.580283	+	0.580283i	−0.354698	+	0.934981i	$0.615416\pi$
$114$		0			0
$115$	9.83889	+	3.20257i	0.917481	+	0.298642i
$116$	−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
$122$	−0.287112	−	0.0769314i	−0.0259939	−	0.00696504i
$123$		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	0.792317	−	0.610110i	$-0.208875\pi$
$127$	2.05336	+	2.05336i	0.182207	+	0.182207i	−0.610110	+	0.792317i	$0.708875\pi$
$128$	4.22455	−	1.13196i	0.373401	−	0.100053i
$129$		0			0
$130$	0.517881	+	1.01772i	0.0454212	+	0.0892602i
$131$	−8.49260	−	4.90320i	−0.742002	−	0.428395i	0.0807949	−	0.996731i	$-0.474254\pi$
$131$	−8.49260	−	4.90320i	−0.742002	−	0.428395i	−0.822797	+	0.568336i	$0.807587\pi$
$132$		0			0
$133$	3.42358	−	13.1428i	0.296862	−	1.13962i
$134$	−1.00476			−0.0867978
$135$		0			0
$136$	−0.0777530	−	0.134672i	−0.00666727	−	0.0115480i
$137$	−1.67549	−	0.448946i	−0.143147	−	0.0383560i	0.186534	−	0.982448i	$-0.440274\pi$
$137$	−1.67549	−	0.448946i	−0.143147	−	0.0383560i	−0.329681	+	0.944092i	$0.606941\pi$
$138$		0			0
$139$		−	2.52988i		−	0.214581i	−0.994228	−	0.107291i	$-0.965782\pi$
$139$		−	2.52988i		−	0.214581i	0.994228	−	0.107291i	$-0.0342175\pi$
$140$	2.50971	+	11.4441i	0.212109	+	0.967202i
$141$		0			0
$142$	1.10461	−	0.295978i	0.0926964	−	0.0248379i
$143$	−5.28557	+	19.7260i	−0.442002	+	1.64957i
$144$		0			0
$145$	−5.46204	−	3.55118i	−0.453598	−	0.294909i
$146$		−	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	$0.774990\pi$
$152$	−0.740839	−	2.76485i	−0.0600900	−	0.224259i
$153$		0			0
$154$	1.02565	−	1.80543i	0.0826494	−	0.145486i
$155$	0.258434	−	4.88205i	0.0207579	−	0.392135i
$156$		0			0
$157$	1.29775	−	4.84326i	0.103572	−	0.386534i	−0.894608	−	0.446853i	$-0.852545\pi$
$157$	1.29775	−	4.84326i	0.103572	−	0.386534i	0.998179	+	0.0603181i	$0.0192115\pi$
$158$	0.0209710	−	0.0782649i	0.00166836	−	0.00622642i
$159$		0			0
$160$	2.48100	+	2.75835i	0.196140	+	0.218067i
$161$	6.19512	+	10.5596i	0.488244	+	0.832211i
$162$		0			0
$163$	0.995538	+	3.71540i	0.0779766	+	0.291013i	0.993892	−	0.110359i	$-0.0352002\pi$
$163$	0.995538	+	3.71540i	0.0779766	+	0.291013i	−0.915915	+	0.401372i	$0.868534\pi$
$164$	−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	−0.407900	−	0.913026i	$-0.633739\pi$
$167$	6.52767	−	6.52767i	0.505126	−	0.505126i	0.913026	+	0.407900i	$0.133739\pi$
$168$		0			0
$169$		−	0.288498i		−	0.0221921i
$170$	0.0476177	−	0.0732405i	0.00365211	−	0.00561729i
$171$		0			0
$172$	−4.28058	+	15.9753i	−0.326391	+	1.21811i
$173$	21.3715	−	5.72648i	1.62485	−	0.435376i	0.672426	−	0.740164i	$-0.265252\pi$
$173$	21.3715	−	5.72648i	1.62485	−	0.435376i	0.952420	+	0.304788i	$0.0985855\pi$
$174$		0			0
$175$	−10.2312	+	8.38583i	−0.773408	+	0.633909i
$176$			21.7512i			1.63956i
$177$		0			0
$178$	−1.70271	−	0.456240i	−0.127624	−	0.0341966i
$179$	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	$0.338093\pi$
$182$	−0.340591	+	1.30750i	−0.0252463	+	0.0969180i
$183$		0			0
$184$	2.23457	+	1.29013i	0.164734	+	0.0951094i
$185$	16.1820	+	5.26726i	1.18972	+	0.387257i
$186$		0			0
$187$	1.50909	−	0.404360i	0.110356	−	0.0295697i
$188$	−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	0.322209	−	0.946669i	$-0.395575\pi$
$191$	−4.65087	−	2.68518i	−0.336525	−	0.194293i	−0.658734	+	0.752375i	$0.728908\pi$
$192$		0			0
$193$	14.1985	+	3.80447i	1.02203	+	0.273852i	0.730647	−	0.682756i	$-0.239219\pi$
$193$	14.1985	+	3.80447i	1.02203	+	0.273852i	0.291381	+	0.956607i	$0.405885\pi$
$194$	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	−0.937458	−	0.348098i	$-0.886828\pi$
$197$	−8.27206	+	8.27206i	−0.589360	+	0.589360i	0.348098	+	0.937458i	$0.386828\pi$
$198$		0			0
$199$	18.3771	−	10.6100i	1.30272	−	0.752123i	0.321847	−	0.946792i	$-0.395696\pi$
$199$	18.3771	−	10.6100i	1.30272	−	0.752123i	0.980869	+	0.194669i	$0.0623632\pi$
$200$	−1.00189	+	2.60183i	−0.0708446	+	0.183977i
$201$		0			0
$202$	0.487583	+	0.487583i	0.0343063	+	0.0343063i
$203$	−2.04699	−	7.43185i	−0.143671	−	0.521614i
$204$		0			0
$205$	10.6439	−	16.3712i	0.743399	−	1.14342i
$206$	−1.90324	+	1.09884i	−0.132605	+	0.0765596i
$207$		0			0
$208$	−3.66320	−	13.6712i	−0.253997	−	0.947930i
$209$	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	$0.576354\pi$
$212$	−0.827017	−	3.08647i	−0.0567998	−	0.211980i
$213$		0			0
$214$	−2.30685	+	1.33186i	−0.157693	+	0.0910440i
$215$	−18.2683	+	3.87299i	−1.24588	+	0.264136i
$216$		0			0
$217$	4.06172	−	4.11875i	0.275727	−	0.279599i
$218$	−1.08700	−	1.08700i	−0.0736211	−	0.0736211i
$219$		0			0
$220$	−22.1099	+	11.2509i	−1.49065	+	0.758537i
$221$	−0.880405	+	0.508302i	−0.0592224	+	0.0341921i
$222$		0			0
$223$	1.35446	−	1.35446i	0.0907015	−	0.0907015i	−0.660300	−	0.751002i	$-0.729571\pi$
$223$	1.35446	−	1.35446i	0.0907015	−	0.0907015i	0.751002	+	0.660300i	$0.229571\pi$
$224$	0.0306011	+	4.38959i	0.00204462	+	0.293292i
$225$		0			0
$226$	−0.611046	+	1.05836i	−0.0406462	+	0.0704012i
$227$	−7.86549	−	2.10755i	−0.522051	−	0.139883i	−0.0118356	−	0.999930i	$-0.503767\pi$
$227$	−7.86549	−	2.10755i	−0.522051	−	0.139883i	−0.510215	+	0.860047i	$0.670434\pi$
$228$		0			0
$229$	11.4727	+	6.62377i	0.758138	+	0.437711i	0.828627	−	0.559802i	$-0.189123\pi$
$229$	11.4727	+	6.62377i	0.758138	+	0.437711i	−0.0704890	+	0.997513i	$0.522456\pi$
$230$	−0.0766237	+	1.44749i	−0.00505242	+	0.0954447i
$231$		0			0
$232$	−1.14880	−	1.14880i	−0.0754225	−	0.0754225i
$233$	7.86648	−	2.10782i	0.515350	−	0.138088i	0.00823515	−	0.999966i	$-0.497379\pi$
$233$	7.86648	−	2.10782i	0.515350	−	0.138088i	0.507115	+	0.861878i	$0.330712\pi$
$234$		0			0
$235$	7.78826	−	23.9269i	0.508050	−	1.56082i
$236$	5.58105	+	3.22222i	0.363295	+	0.209749i
$237$		0			0
$238$	0.0996537	−	0.0274481i	0.00645959	−	0.00177920i
$239$	−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	$0.830813\pi$
$242$	2.75838	+	0.739106i	0.177315	+	0.0475115i
$243$		0			0
$244$			4.20190i			0.268999i
$245$	−15.6406	−	0.609413i	−0.999242	−	0.0389339i
$246$		0			0
$247$	−18.0749	+	4.84316i	−1.15008	+	0.308163i
$248$	0.315540	−	1.17761i	0.0200368	−	0.0747783i
$249$		0			0
$250$	−1.55794	+	0.161259i	−0.0985327	+	0.0101989i
$251$			0.458108i			0.0289155i	0.999895	+	0.0144577i	$0.00460220\pi$
$251$			0.458108i			0.0289155i	−0.999895	+	0.0144577i	$0.995398\pi$
$252$		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
$257$	6.46934	+	24.1439i	0.403546	+	1.50605i	0.806721	+	0.590932i	$0.201240\pi$
$257$	6.46934	+	24.1439i	0.403546	+	1.50605i	−0.403175	+	0.915123i	$0.632093\pi$
$258$		0			0
$259$	10.1891	+	17.3673i	0.633119	+	1.07915i
$260$	12.0019	−	10.7951i	0.744325	−	0.669485i
$261$		0			0
$262$	0.355562	−	1.32698i	0.0219667	−	0.0819809i
$263$	−4.50748	+	16.8221i	−0.277943	+	1.03730i	0.675901	+	0.736993i	$0.263755\pi$
$263$	−4.50748	+	16.8221i	−0.277943	+	1.03730i	−0.953843	+	0.300304i	$0.902912\pi$
$264$		0			0
$265$	2.68247	−	2.41275i	0.164783	−	0.148214i
$266$	1.90258	−	0.0132634i	0.116654	−	0.000813233i
$267$		0			0
$268$	3.67617	+	13.7196i	0.224558	+	0.838061i
$269$	−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
$275$	−22.6440	−	16.4883i	−1.36548	−	0.994280i
$276$		0			0
$277$	2.67393	−	9.97926i	0.160661	−	0.599595i	−0.837893	−	0.545835i	$-0.816213\pi$
$277$	2.67393	−	9.97926i	0.160661	−	0.599595i	0.998554	−	0.0537606i	$-0.0171208\pi$
$278$	0.342336	−	0.0917287i	0.0205319	−	0.00550152i
$279$		0			0
$280$	−2.92962	+	1.51658i	−0.175078	+	0.0906327i
$281$		−	23.6675i		−	1.41189i	−0.708268	−	0.705943i	$-0.750523\pi$
$281$		−	23.6675i		−	1.41189i	0.708268	−	0.705943i	$-0.249477\pi$
$282$		0			0
$283$	−7.04083	−	1.88659i	−0.418534	−	0.112146i	0.0434049	−	0.999058i	$-0.486179\pi$
$283$	−7.04083	−	1.88659i	−0.418534	−	0.112146i	−0.461939	+	0.886912i	$0.652846\pi$
$284$	−8.08298	−	14.0001i	−0.479636	−	0.830755i
$285$		0			0
$286$	−2.86092			−0.169170
$287$	22.2753	−	6.13540i	1.31487	−	0.362161i
$288$		0			0
$289$	−14.6551	−	8.46111i	−0.862063	−	0.497713i
$290$	0.282492	−	0.867867i	0.0165885	−	0.0509629i
$291$		0			0
$292$	−15.6849	+	4.20275i	−0.917889	+	0.245948i
$293$	−10.0145	−	10.0145i	−0.585052	−	0.585052i	0.351235	−	0.936287i	$-0.385762\pi$
$293$	−10.0145	−	10.0145i	−0.585052	−	0.585052i	−0.936287	+	0.351235i	$0.885762\pi$
$294$		0			0
$295$	−0.384647	+	7.26633i	−0.0223950	+	0.423062i
$296$	3.67518	+	2.12187i	0.213615	+	0.123331i
$297$		0			0
$298$	−0.0664076	−	0.0177939i	−0.00384689	−	0.00103077i
$299$	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
$305$	−4.22844	+	2.15170i	−0.242120	+	0.123206i
$306$		0			0
$307$	−4.93300	−	4.93300i	−0.281541	−	0.281541i	0.552182	−	0.833723i	$-0.313795\pi$
$307$	−4.93300	−	4.93300i	−0.281541	−	0.281541i	−0.833723	+	0.552182i	$0.813795\pi$
$308$	−28.4052	−	7.39931i	−1.61854	−	0.421615i
$309$		0			0
$310$	0.669995	−	0.142043i	0.0380532	−	0.00806752i
$311$	24.2000	−	13.9719i	1.37226	−	0.792272i	0.381044	−	0.924557i	$-0.375565\pi$
$311$	24.2000	−	13.9719i	1.37226	−	0.792272i	0.991212	+	0.132284i	$0.0422312\pi$
$312$		0			0
$313$	−3.72690	−	13.9090i	−0.210657	−	0.786182i	−0.987650	−	0.156674i	$-0.949923\pi$
$313$	−3.72690	−	13.9090i	−0.210657	−	0.786182i	0.776994	−	0.629509i	$-0.216744\pi$
$314$	0.702431			0.0396405
$315$		0			0
$316$	−1.14541			−0.0644343
$317$	3.13404	+	11.6964i	0.176025	+	0.656935i	0.996375	+	0.0850728i	$0.0271123\pi$
$317$	3.13404	+	11.6964i	0.176025	+	0.656935i	−0.820349	+	0.571863i	$0.806221\pi$
$318$		0			0
$319$	14.1356	−	8.16121i	0.791444	−	0.456940i
$320$	9.18129	−	14.1217i	0.513250	−	0.789426i
$321$		0			0
$322$	−1.20427	+	1.22118i	−0.0671113	+	0.0680536i
$323$	1.01226	+	1.01226i	0.0563238	+	0.0563238i
$324$		0			0
$325$	17.0092	+	6.54977i	0.943501	+	0.363316i
$326$	−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	$0.965443\pi$
$332$	−8.45701	−	2.26605i	−0.464139	−	0.124366i
$333$		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	0.451127	−	0.892460i	$-0.351022\pi$
$337$	−8.10178	−	8.10178i	−0.441332	−	0.441332i	−0.892460	+	0.451127i	$0.851022\pi$
$338$	0.0390387	−	0.0104604i	0.00212343	−	0.000568970i
$339$		0			0
$340$	−1.17430	−	0.382236i	−0.0636852	−	0.0207296i
$341$	10.6075	+	6.12424i	0.574428	+	0.331646i
$342$		0			0
$343$	−13.3668	−	12.8191i	−0.721739	−	0.692165i
$344$	−4.65685			−0.251081
$345$		0			0
$346$	1.54978	+	2.68430i	0.0833169	+	0.144309i
$347$	19.9545	+	5.34680i	1.07121	+	0.287031i	0.750992	−	0.660311i	$-0.229576\pi$
$347$	19.9545	+	5.34680i	1.07121	+	0.287031i	0.320222	+	0.947342i	$0.396242\pi$
$348$		0			0
$349$			22.3959i			1.19882i	0.800441	+	0.599411i	$0.204599\pi$
$349$			22.3959i			1.19882i	−0.800441	+	0.599411i	$0.795401\pi$
$350$	−1.50571	−	1.08041i	−0.0804837	−	0.0577501i
$351$		0			0
$352$	−8.97815	+	2.40569i	−0.478537	+	0.128224i
$353$	−8.75267	+	32.6654i	−0.465857	+	1.73860i	0.188173	+	0.982136i	$0.439743\pi$
$353$	−8.75267	+	32.6654i	−0.465857	+	1.73860i	−0.654031	+	0.756468i	$0.726923\pi$
$354$		0			0
$355$	9.94946	−	15.3032i	0.528063	−	0.812209i
$356$			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
$362$	0.475116	+	1.77316i	0.0249715	+	0.0931950i
$363$		0			0
$364$	19.0996	−	0.133149i	1.00109	−	0.00697889i
$365$	−12.2612	−	13.6318i	−0.641780	−	0.713523i
$366$		0			0
$367$	−0.998319	+	3.72578i	−0.0521118	+	0.194484i	−0.987074	−	0.160262i	$-0.948766\pi$
$367$	−0.998319	+	3.72578i	−0.0521118	+	0.194484i	0.934963	+	0.354746i	$0.115433\pi$
$368$	4.64999	−	17.3540i	0.242397	−	0.904639i
$369$		0			0
$370$	−0.126023	+	2.38068i	−0.00655160	+	0.123766i
$371$	4.26884	−	0.0297593i	0.221627	−	0.00154503i
$372$		0			0
$373$	2.69962	+	10.0751i	0.139781	+	0.521669i	0.999932	+	0.0116307i	$0.00370227\pi$
$373$	2.69962	+	10.0751i	0.139781	+	0.521669i	−0.860151	+	0.510039i	$0.829631\pi$
$374$	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	$0.164132\pi$
$379$			19.1988i			0.986177i	−0.869979	+	0.493089i	$0.835868\pi$
$380$	−19.0577	−	12.3905i	−0.977637	−	0.635617i
$381$		0			0
$382$	0.194720	−	0.726703i	0.00996272	−	0.0371814i
$383$	−34.0476	+	9.12303i	−1.73975	+	0.466165i	−0.982392	−	0.186834i	$-0.940177\pi$
$383$	−34.0476	+	9.12303i	−1.73975	+	0.466165i	−0.757359	+	0.652998i	$0.773511\pi$
$384$		0			0
$385$	−7.09961	−	32.3737i	−0.361830	−	1.64991i
$386$			2.05924i			0.104813i
$387$		0			0
$388$	−22.3193	−	5.98043i	−1.13309	−	0.303610i
$389$	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
$392$	−3.78401	−	0.957584i	−0.191121	−	0.0483653i
$393$		0			0
$394$	−1.41928	−	0.819423i	−0.0715024	−	0.0412819i
$395$	−0.586539	−	1.15265i	−0.0295120	−	0.0579959i
$396$		0			0
$397$	13.3522	−	3.57770i	0.670127	−	0.179560i	0.0923147	−	0.995730i	$-0.470573\pi$
$397$	13.3522	−	3.57770i	0.670127	−	0.179560i	0.577812	+	0.816170i	$0.303907\pi$
$398$	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	0.214862	−	0.976645i	$-0.431070\pi$
$401$	−10.4832	−	6.05249i	−0.523507	−	0.302247i	−0.738368	+	0.674398i	$0.764403\pi$
$402$		0			0
$403$	−7.69850	−	2.06281i	−0.383490	−	0.102756i
$404$	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	0.282860	−	0.959161i	$-0.408717\pi$
$409$	25.3797	−	14.6530i	1.25495	−	0.724544i	0.972088	+	0.234617i	$0.0753836\pi$
$410$	2.60124	+	0.846707i	0.128466	+	0.0418159i
$411$		0			0
$412$	21.9678	+	21.9678i	1.08228	+	1.08228i
$413$	−6.04537	+	6.13025i	−0.297473	+	0.301650i
$414$		0			0
$415$	−2.05028	−	9.67083i	−0.100644	−	0.474722i
$416$	5.23786	−	3.02408i	0.256807	−	0.148268i
$417$		0			0
$418$	1.04270	+	3.89140i	0.0509999	+	0.190334i
$419$	−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	$0.269410\pi$
$422$	−0.250256	−	0.933969i	−0.0121823	−	0.0454649i
$423$		0			0
$424$	0.779175	−	0.449857i	0.0378401	−	0.0218470i
$425$	−0.216681	−	1.37745i	−0.0105106	−	0.0668161i
$426$		0			0
$427$	−5.43239	−	1.41509i	−0.262892	−	0.0684810i
$428$	26.6263	+	26.6263i	1.28703	+	1.28703i
$429$		0			0
$430$	−1.18646	−	2.33158i	−0.0572160	−	0.112439i
$431$	22.2647	−	12.8545i	1.07245	−	0.619180i	0.143601	−	0.989636i	$-0.454132\pi$
$431$	22.2647	−	12.8545i	1.07245	−	0.619180i	0.928850	+	0.370456i	$0.120799\pi$
$432$		0			0
$433$	23.5411	−	23.5411i	1.13131	−	1.13131i	0.141353	−	0.989959i	$-0.454855\pi$
$433$	23.5411	−	23.5411i	1.13131	−	1.13131i	0.989959	−	0.141353i	$-0.0451452\pi$
$434$	0.704608	+	0.400282i	0.0338223	+	0.0192142i
$435$		0			0
$436$	−10.8656	+	18.8198i	−0.520367	+	0.901303i
$437$	−22.9439	−	6.14780i	−1.09756	−	0.294089i
$438$		0			0
$439$	8.62144	+	4.97759i	0.411479	+	0.237567i	0.691425	−	0.722448i	$-0.256983\pi$
$439$	8.62144	+	4.97759i	0.411479	+	0.237567i	−0.279946	+	0.960016i	$0.590317\pi$
$440$	−4.67125	−	5.19344i	−0.222693	−	0.247588i
$441$		0			0
$442$	−0.100704	−	0.100704i	−0.00478999	−	0.00478999i
$443$	28.6645	−	7.68062i	1.36189	−	0.364918i	0.497380	−	0.867533i	$-0.334295\pi$
$443$	28.6645	−	7.68062i	1.36189	−	0.364918i	0.864510	+	0.502615i	$0.167629\pi$
$444$		0			0
$445$	−25.0767	+	12.7606i	−1.18875	+	0.604909i
$446$	0.232393	+	0.134172i	0.0110041	+	0.00635322i
$447$		0			0
$448$	19.2145	−	5.29234i	0.907799	−	0.250040i
$449$	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
$452$	16.6873	+	4.47134i	0.784903	+	0.210314i
$453$		0			0
$454$		−	1.14075i		−	0.0535381i
$455$	9.91445	+	19.1521i	0.464797	+	0.897862i
$456$		0			0
$457$	−33.4803	+	8.97102i	−1.56614	+	0.419646i	−0.934602	−	0.355696i	$-0.884244\pi$
$457$	−33.4803	+	8.97102i	−1.56614	+	0.419646i	−0.631540	+	0.775343i	$0.717577\pi$
$458$	−0.480331	+	1.79262i	−0.0224444	+	0.0837637i
$459$		0			0
$460$	20.0454	−	4.24975i	0.934621	−	0.198146i
$461$			39.9716i			1.86166i	0.365449	+	0.930831i	$0.380915\pi$
$461$			39.9716i			1.86166i	−0.365449	+	0.930831i	$0.619085\pi$
$462$		0			0
$463$	6.57833	−	6.57833i	0.305721	−	0.305721i	−0.537526	−	0.843247i	$-0.680641\pi$
$463$	6.57833	−	6.57833i	0.305721	−	0.305721i	0.843247	+	0.537526i	$0.180641\pi$
$464$	−5.65618	+	9.79679i	−0.262581	+	0.454804i
$465$		0			0
$466$	0.570448	+	0.988045i	0.0264255	+	0.0457703i
$467$	−3.63502	−	13.5661i	−0.168208	−	0.627763i	−0.997609	−	0.0691084i	$-0.977985\pi$
$467$	−3.63502	−	13.5661i	−0.168208	−	0.627763i	0.829401	−	0.558654i	$-0.188682\pi$
$468$		0			0
$469$	−18.9754	+	0.132283i	−0.876201	+	0.00610826i
$470$	3.52011	+	0.186339i	0.162371	+	0.00859518i
$471$		0			0
$472$	−0.469643	+	1.75273i	−0.0216171	+	0.0806759i
$473$	12.1091	−	45.1919i	0.556779	−	2.07793i
$474$		0			0
$475$	2.70973	−	25.5229i	0.124331	−	1.17107i
$476$	−0.739405	−	1.26031i	−0.0338906	−	0.0577664i
$477$		0			0
$478$	−0.304946	−	1.13807i	−0.0139479	−	0.0520543i
$479$	−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
$485$	−5.41098	−	25.5227i	−0.245700	−	1.15893i
$486$		0			0
$487$	3.94920	−	14.7386i	0.178955	−	0.667870i	−0.816889	−	0.576795i	$-0.804303\pi$
$487$	3.94920	−	14.7386i	0.178955	−	0.667870i	0.995844	−	0.0910748i	$-0.0290302\pi$
$488$	−1.14281	+	0.306216i	−0.0517327	+	0.0138617i
$489$		0			0
$490$	−0.484635	−	2.13854i	−0.0218936	−	0.0966094i
$491$			1.26640i			0.0571518i	0.999592	+	0.0285759i	$0.00909723\pi$
$491$			1.26640i			0.0571518i	−0.999592	+	0.0285759i	$0.990903\pi$
$492$		0			0
$493$	0.784846	+	0.210299i	0.0353477	+	0.00947138i
$494$	−1.31073	−	2.27024i	−0.0589723	−	0.102143i
$495$		0			0
$496$	−8.48889			−0.381162
$497$	20.8221	−	5.73513i	0.933998	−	0.257256i
$498$		0			0
$499$	−12.5885	−	7.26798i	−0.563539	−	0.325359i	0.191026	−	0.981585i	$-0.438819\pi$
$499$	−12.5885	−	7.26798i	−0.563539	−	0.325359i	−0.754565	+	0.656226i	$0.772152\pi$
$500$	7.90207	+	20.6831i	0.353391	+	0.924979i
$501$		0			0
$502$	−0.0619899	+	0.0166101i	−0.00276674	+	0.000741347i
$503$	16.6937	+	16.6937i	0.744336	+	0.744336i	0.973409	−	0.229073i	$-0.0735694\pi$
$503$	16.6937	+	16.6937i	0.744336	+	0.744336i	−0.229073	+	0.973409i	$0.573569\pi$
$504$		0			0
$505$	10.9909	+	0.581807i	0.489087	+	0.0258901i
$506$	−3.14505	−	1.81579i	−0.139814	−	0.0807218i
$507$		0			0
$508$	5.55485	+	1.48842i	0.246456	+	0.0660378i
$509$	−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
$515$	−10.8574	+	33.3558i	−0.478432	+	1.46983i
$516$		0			0
$517$	44.5772	+	44.5772i	1.96050	+	1.96050i
$518$	−1.98066	+	2.00847i	−0.0870250	+	0.0882469i
$519$		0			0
$520$	3.81065	+	2.47752i	0.167108	+	0.108646i
$521$	−20.1930	+	11.6584i	−0.884670	+	0.510765i	−0.872195	−	0.489158i	$-0.837304\pi$
$521$	−20.1930	+	11.6584i	−0.884670	+	0.510765i	−0.0124748	+	0.999922i	$0.503971\pi$
$522$		0			0
$523$	7.50283	+	28.0009i	0.328076	+	1.22440i	0.911184	+	0.412001i	$0.135170\pi$
$523$	7.50283	+	28.0009i	0.328076	+	1.22440i	−0.583108	+	0.812395i	$0.698164\pi$
$524$	−19.4204			−0.848382
$525$		0			0
$526$	−2.43976			−0.106378
$527$	0.157810	+	0.588955i	0.00687431	+	0.0256553i
$528$		0			0
$529$	−1.37521	+	0.793979i	−0.0597918	+	0.0345208i
$530$	0.423749	+	0.275503i	0.0184065	+	0.0119671i
$531$		0			0
$532$	−7.14218	−	25.9306i	−0.309653	−	1.12423i
$533$	−22.5101	−	22.5101i	−0.975019	−	0.975019i
$534$		0			0
$535$	−13.1598	+	40.4292i	−0.568947	+	1.74791i
$536$	−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	$0.187214\pi$
$542$	−2.06959	−	0.554544i	−0.0888964	−	0.0238197i
$543$		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	0.658224	−	0.752822i	$-0.271308\pi$
$547$	−2.21247	−	2.21247i	−0.0945983	−	0.0945983i	−0.752822	+	0.658224i	$0.771308\pi$
$548$	−3.31810	+	0.889081i	−0.141742	+	0.0379797i
$549$		0			0
$550$	1.41012	−	3.66196i	0.0601276	−	0.156146i
$551$	12.9524	+	7.47810i	0.551793	+	0.318578i
$552$		0			0
$553$	0.385744	−	1.48083i	0.0164035	−	0.0629715i
$554$	1.44732			0.0614906
$555$		0			0
$556$	−2.50505	−	4.33888i	−0.106238	−	0.184009i
$557$	−30.0424	−	8.04984i	−1.27294	−	0.341083i	−0.441782	−	0.897122i	$-0.645654\pi$
$557$	−30.0424	−	8.04984i	−1.27294	−	0.341083i	−0.831156	+	0.556039i	$0.812320\pi$
$558$		0			0
$559$			30.4437i			1.28763i
$560$	15.4796	+	16.9706i	0.654133	+	0.717139i
$561$		0			0
$562$	3.20263	−	0.858141i	0.135095	−	0.0361985i
$563$	−9.64932	+	36.0117i	−0.406670	+	1.51771i	0.394284	+	0.918989i	$0.370993\pi$
$563$	−9.64932	+	36.0117i	−0.406670	+	1.51771i	−0.800954	+	0.598726i	$0.795674\pi$
$564$		0			0
$565$	4.04559	+	19.0824i	0.170199	+	0.802801i
$566$		−	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	$-0.426088\pi$
$572$	10.4674	+	39.0649i	0.437665	+	1.63339i
$573$		0			0
$574$	1.63789	+	2.79178i	0.0683641	+	0.116527i
$575$	14.5414	+	17.9958i	0.606418	+	0.750477i
$576$		0			0
$577$	6.20825	−	23.1695i	0.258453	−	0.964560i	−0.707684	−	0.706529i	$-0.750260\pi$
$577$	6.20825	−	23.1695i	0.258453	−	0.964560i	0.966137	−	0.258030i	$-0.0830735\pi$
$578$	0.613569	−	2.28987i	0.0255211	−	0.0952460i
$579$		0			0
$580$	−12.8840	−	0.682022i	−0.534980	−	0.0283194i
$581$	5.77775	−	10.1704i	0.239701	−	0.421941i
$582$		0			0
$583$	2.33951	+	8.73117i	0.0968926	+	0.361608i
$584$	−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	−0.319684	−	0.947524i	$-0.603577\pi$
$587$	15.2114	−	15.2114i	0.627840	−	0.627840i	0.947524	+	0.319684i	$0.103577\pi$
$588$		0			0
$589$			11.2233i			0.462446i
$590$	−0.997207	+	0.211414i	−0.0410544	+	0.00870379i
$591$		0			0
$592$	7.64781	−	28.5420i	0.314323	−	1.17307i
$593$	19.7756	−	5.29885i	0.812085	−	0.217598i	0.171202	−	0.985236i	$-0.445235\pi$
$593$	19.7756	−	5.29885i	0.812085	−	0.217598i	0.640883	+	0.767638i	$0.278568\pi$
$594$		0			0
$595$	0.889643	−	1.38945i	0.0364718	−	0.0569621i
$596$			0.971879i			0.0398097i
$597$		0			0
$598$	2.28255	+	0.611607i	0.0933404	+	0.0250105i
$599$	−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	$0.567226\pi$
$602$	0.780287	−	2.99544i	0.0318021	−	0.122085i
$603$		0			0
$604$	7.68251	+	4.43550i	0.312597	+	0.180478i
$605$	40.6240	−	20.6721i	1.65160	−	0.840439i
$606$		0			0
$607$	−26.0408	+	6.97762i	−1.05696	+	0.283213i	−0.745127	−	0.666922i	$-0.767611\pi$
$607$	−26.0408	+	6.97762i	−1.05696	+	0.283213i	−0.311838	+	0.950135i	$0.600945\pi$
$608$	−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
$613$	−9.58910	−	2.56939i	−0.387300	−	0.103777i	0.0599142	−	0.998204i	$-0.480917\pi$
$613$	−9.58910	−	2.56939i	−0.387300	−	0.103777i	−0.447215	+	0.894427i	$0.647584\pi$
$614$	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	−0.386870	−	0.922134i	$-0.626444\pi$
$617$	13.2957	−	13.2957i	0.535264	−	0.535264i	0.922134	+	0.386870i	$0.126444\pi$
$618$		0			0
$619$	1.14004	−	0.658202i	0.0458220	−	0.0264554i	−0.476914	−	0.878950i	$-0.658245\pi$
$619$	1.14004	−	0.658202i	0.0458220	−	0.0264554i	0.522736	+	0.852495i	$0.324911\pi$
$620$	−4.39091	−	8.62887i	−0.176343	−	0.346544i
$621$		0			0
$622$	2.76808	+	2.76808i	0.110990	+	0.110990i
$623$	−32.2166	−	8.39215i	−1.29073	−	0.336225i
$624$		0			0
$625$	−16.7673	+	18.5434i	−0.670694	+	0.741735i
$626$	1.74699	−	1.00863i	0.0698240	−	0.0403129i
$627$		0			0
$628$	−2.57003	−	9.59147i	−0.102555	−	0.382741i
$629$	−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	$0.456702\pi$
$632$	−0.0834725	−	0.311523i	−0.00332036	−	0.0123917i
$633$		0			0
$634$	−1.46909	+	0.848180i	−0.0583450	+	0.0336855i
$635$	1.34669	+	6.35212i	0.0534418	+	0.252076i
$636$		0			0
$637$	−6.26010	+	24.7376i	−0.248034	+	0.980138i
$638$	1.61688	+	1.61688i	0.0640131	+	0.0640131i
$639$		0			0
$640$	9.29937	+	3.02696i	0.367590	+	0.119651i
$641$	−10.6830	+	6.16781i	−0.421951	+	0.243614i	−0.695912	−	0.718127i	$-0.745000\pi$
$641$	−10.6830	+	6.16781i	−0.421951	+	0.243614i	0.273960	+	0.961741i	$0.411666\pi$
$642$		0			0
$643$	0.219128	−	0.219128i	0.00864157	−	0.00864157i	−0.702773	−	0.711414i	$-0.748055\pi$
$643$	0.219128	−	0.219128i	0.00864157	−	0.00864157i	0.711414	+	0.702773i	$0.248055\pi$
$644$	21.0809	+	11.9759i	0.830705	+	0.471917i
$645$		0			0
$646$	−0.100274	+	0.173679i	−0.00394522	+	0.00683332i
$647$	−2.66988	−	0.715393i	−0.104964	−	0.0281250i	0.205955	−	0.978562i	$-0.433970\pi$
$647$	−2.66988	−	0.715393i	−0.104964	−	0.0281250i	−0.310919	+	0.950437i	$0.600637\pi$
$648$		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
$653$	23.7403	−	6.36119i	0.929030	−	0.248933i	0.237589	−	0.971366i	$-0.423643\pi$
$653$	23.7403	−	6.36119i	0.929030	−	0.248933i	0.691441	+	0.722433i	$0.256976\pi$
$654$		0			0
$655$	−9.94473	−	19.5430i	−0.388573	−	0.763610i
$656$	−29.3637	−	16.9531i	−1.14646	−	0.661909i
$657$		0			0
$658$	2.96975	+	2.92863i	0.115773	+	0.114170i
$659$	−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	$0.951371\pi$
$662$	−2.90941	−	0.779575i	−0.113078	−	0.0302990i
$663$		0			0
$664$		−	2.46524i		−	0.0956699i
$665$	22.4370	−	20.4658i	0.870070	−	0.793628i
$666$		0			0
$667$	−13.0227	+	3.48941i	−0.504239	+	0.135111i
$668$	4.73169	−	17.6589i	0.183075	−	0.683244i
$669$		0			0
$670$	−1.88360	−	1.22463i	−0.0727699	−	0.0473118i
$671$		−	11.8866i		−	0.458875i
$672$		0			0
$673$	−23.8659	+	23.8659i	−0.919962	+	0.919962i	−0.997026	−	0.0770643i	$-0.975445\pi$
$673$	−23.8659	+	23.8659i	−0.919962	+	0.919962i	0.0770643	+	0.997026i	$0.475445\pi$
$674$	0.802555	−	1.39007i	0.0309133	−	0.0535434i
$675$		0			0
$676$	−0.285667	−	0.494789i	−0.0109872	−	0.0190303i
$677$	0.589674	+	2.20069i	0.0226630	+	0.0845796i	0.976331	−	0.216281i	$-0.0693928\pi$
$677$	0.589674	+	2.20069i	0.0226630	+	0.0845796i	−0.953668	+	0.300861i	$0.902726\pi$
$678$		0			0
$679$	15.2483	−	26.8412i	0.585176	−	1.03007i
$680$	0.0183811	−	0.347236i	0.000704883	−	0.0133159i
$681$		0			0
$682$	−0.444107	+	1.65743i	−0.0170057	+	0.0634663i
$683$	7.57756	−	28.2798i	0.289947	−	1.08210i	−0.655201	−	0.755455i	$-0.727416\pi$
$683$	7.57756	−	28.2798i	0.289947	−	1.08210i	0.945148	−	0.326643i	$-0.105917\pi$
$684$		0			0
$685$	−2.59382	−	2.88378i	−0.0991048	−	0.110184i
$686$	1.24999	−	2.27355i	0.0477247	−	0.0868047i
$687$		0			0
$688$	8.39231	+	31.3205i	0.319954	+	1.19408i
$689$	−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
$695$	3.08351	−	4.74272i	0.116964	−	0.179902i
$696$		0			0
$697$	−0.630324	+	2.35240i	−0.0238752	+	0.0891035i
$698$	−3.03055	+	0.812032i	−0.114708	+	0.0307359i
$699$		0			0
$700$	−9.24356	+	24.5130i	−0.349374	+	0.926504i
$701$		−	12.7450i		−	0.481372i	−0.970603	−	0.240686i	$-0.922628\pi$
$701$		−	12.7450i		−	0.481372i	0.970603	−	0.240686i	$-0.0773723\pi$
$702$		0			0
$703$	−37.7357	−	10.1113i	−1.42323	−	0.381353i
$704$	21.1002	+	36.5466i	0.795243	+	1.37740i
$705$		0			0
$706$	−4.73755			−0.178300
$707$	9.27246	+	9.14408i	0.348727	+	0.343898i
$708$		0			0
$709$	−33.8769	−	19.5589i	−1.27228	−	0.734549i	−0.296860	−	0.954921i	$-0.595939\pi$
$709$	−33.8769	−	19.5589i	−1.27228	−	0.734549i	−0.975416	+	0.220373i	$0.929273\pi$
$710$	2.43153	+	0.791468i	0.0912539	+	0.0297033i
$711$		0			0
$712$	−6.77742	+	1.81601i	−0.253995	+	0.0680577i
$713$	−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
$718$	1.49386	+	0.400278i	0.0557503	+	0.0149382i
$719$	−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
$725$	−5.91129	−	13.3147i	−0.219540	−	0.494494i
$726$		0			0
$727$	6.51144	+	6.51144i	0.241496	+	0.241496i	0.817469	−	0.575973i	$-0.195377\pi$
$727$	6.51144	+	6.51144i	0.241496	+	0.241496i	−0.575973	+	0.817469i	$0.695377\pi$
$728$	1.42811	+	5.18491i	0.0529292	+	0.192166i
$729$		0			0
$730$	1.40006	−	2.15341i	0.0518184	−	0.0797015i
$731$	2.01699	−	1.16451i	0.0746010	−	0.0430709i
$732$		0			0
$733$	2.60963	+	9.73928i	0.0963890	+	0.359728i	0.997226	−	0.0744281i	$-0.0237131\pi$
$733$	2.60963	+	9.73928i	0.0963890	+	0.359728i	−0.900837	+	0.434157i	$0.857046\pi$
$734$	−0.540359			−0.0199450
$735$		0			0
$736$	7.67740			0.282993
$737$	−10.3993	−	38.8109i	−0.383065	−	1.42962i
$738$		0			0
$739$	−11.1510	+	6.43804i	−0.410196	+	0.236827i	−0.690874	−	0.722975i	$-0.742774\pi$
$739$	−11.1510	+	6.43804i	−0.410196	+	0.236827i	0.280678	+	0.959802i	$0.409441\pi$
$740$	32.9685	−	6.98955i	1.21195	−	0.256941i
$741$		0			0
$742$	0.158807	+	0.576568i	0.00582999	+	0.0211665i
$743$	8.34588	+	8.34588i	0.306181	+	0.306181i	0.843426	−	0.537245i	$-0.180535\pi$
$743$	8.34588	+	8.34588i	0.306181	+	0.306181i	−0.537245	+	0.843426i	$0.680535\pi$
$744$		0			0
$745$	−0.978018	+	0.497677i	−0.0358318	+	0.0182335i
$746$	−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	$-0.122290\pi$
$752$	−42.2027	−	11.3082i	−1.53897	−	0.412367i
$753$		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	0.249680	−	0.968328i	$-0.419674\pi$
$757$	−19.7726	−	19.7726i	−0.718648	−	0.718648i	−0.968328	+	0.249680i	$0.919674\pi$
$758$	−2.59793	+	0.696114i	−0.0943611	+	0.0252840i
$759$		0			0
$760$	1.98106	−	6.08618i	0.0718606	−	0.220769i
$761$	−39.3328	−	22.7088i	−1.42581	−	0.823193i	−0.429025	−	0.903293i	$-0.641143\pi$
$761$	−39.3328	−	22.7088i	−1.42581	−	0.823193i	−0.996787	+	0.0801000i	$0.974476\pi$
$762$		0			0
$763$	−20.6717	−	20.3855i	−0.748366	−	0.738004i
$764$	−10.6353			−0.384773
$765$		0			0
$766$	−2.46901	−	4.27644i	−0.0892088	−	0.154514i
$767$	11.4583	+	3.07024i	0.413735	+	0.110860i
$768$		0			0
$769$		−	23.0900i		−	0.832646i	−0.909217	−	0.416323i	$-0.863319\pi$
$769$		−	23.0900i		−	0.832646i	0.909217	−	0.416323i	$-0.136681\pi$
$770$	4.12330	−	2.13451i	0.148593	−	0.0769224i
$771$		0			0
$772$	28.1183	−	7.53427i	1.01200	−	0.271164i
$773$	−5.43421	+	20.2807i	−0.195455	+	0.729448i	0.796694	+	0.604383i	$0.206580\pi$
$773$	−5.43421	+	20.2807i	−0.195455	+	0.729448i	−0.992149	+	0.125064i	$0.960086\pi$
$774$		0			0
$775$	6.43490	−	8.83730i	0.231148	−	0.317445i
$776$		−	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
$782$	−0.0467895	−	0.174621i	−0.00167319	−	0.00624443i
$783$		0			0
$784$	0.378919	+	27.1758i	0.0135328	+	0.970564i
$785$	8.33601	−	7.49784i	0.297525	−	0.267609i
$786$		0			0
$787$	2.39502	−	8.93832i	0.0853731	−	0.318617i	−0.910011	−	0.414583i	$-0.863927\pi$
$787$	2.39502	−	8.93832i	0.0853731	−	0.318617i	0.995385	+	0.0959663i	$0.0305941\pi$
$788$	−5.99614	+	22.3779i	−0.213604	+	0.797180i
$789$		0			0
$790$	0.134706	−	0.121162i	0.00479263	−	0.00431074i
$791$	−11.4006	+	20.0682i	−0.405358	+	0.713542i
$792$		0			0
$793$	2.00185	+	7.47102i	0.0710879	+	0.265304i
$794$	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	−0.609634	−	0.792683i	$-0.708684\pi$
$797$	5.16770	−	5.16770i	0.183049	−	0.183049i	0.792683	+	0.609634i	$0.208684\pi$
$798$		0			0
$799$			3.13822i			0.111022i
$800$	1.28911	+	8.19497i	0.0455771	+	0.289736i
$801$		0			0
$802$	0.438904	−	1.63801i	0.0154982	−	0.0578402i
$803$	44.3703	−	11.8890i	1.56579	−	0.419553i
$804$		0			0
$805$	−1.25651	+	27.3467i	−0.0442860	+	0.963845i
$806$		−	1.11653i		−	0.0393282i
$807$		0			0
$808$	2.65113	+	0.710369i	0.0932666	+	0.0249907i
$809$	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	$0.378178\pi$
$812$	−10.8696	−	10.7191i	−0.381449	−	0.376168i
$813$		0			0
$814$	−5.17264	−	2.98643i	−0.181301	−	0.104674i
$815$	−2.66215	+	8.17860i	−0.0932509	+	0.286484i
$816$		0			0
$817$	41.4092	−	11.0956i	1.44873	−	0.388185i
$818$	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	0.766897	−	0.641770i	$-0.221800\pi$
$821$	17.0359	+	9.83568i	0.594557	+	0.343268i	−0.172340	+	0.985037i	$0.555133\pi$
$822$		0			0
$823$	51.7281	+	13.8605i	1.80313	+	0.483146i	0.994460	−	0.105120i	$-0.0335226\pi$
$823$	51.7281	+	13.8605i	1.80313	+	0.483146i	0.808667	+	0.588266i	$0.200189\pi$
$824$	−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	−0.955953	−	0.293521i	$-0.905173\pi$
$827$	−19.0500	+	19.0500i	−0.662432	+	0.662432i	0.293521	+	0.955953i	$0.405173\pi$
$828$		0			0
$829$	−35.0623	+	20.2433i	−1.21777	+	0.703077i	−0.964440	−	0.264304i	$-0.914858\pi$
$829$	−35.0623	+	20.2433i	−1.21777	+	0.703077i	−0.253326	+	0.967381i	$0.581525\pi$
$830$	1.23429	−	0.628085i	0.0428429	−	0.0218011i
$831$		0			0
$832$	−19.4170	−	19.4170i	−0.673162	−	0.673162i
$833$	1.87840	−	0.531492i	0.0650827	−	0.0184151i
$834$		0			0
$835$	20.1935	−	4.28115i	0.698824	−	0.148155i
$836$	49.3208	−	28.4754i	1.70580	−	0.984842i
$837$		0			0
$838$	−0.161491	−	0.602694i	−0.00557862	−	0.0208197i
$839$	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
$842$	0.986040	+	3.67995i	0.0339812	+	0.126819i
$843$		0			0
$844$	−11.8374	+	6.83434i	−0.407461	+	0.235248i
$845$	0.351631	−	0.540842i	0.0120965	−	0.0186055i
$846$		0			0
$847$	52.1908	+	13.5952i	1.79330	+	0.467138i
$848$	−4.42978	−	4.42978i	−0.152119	−	0.152119i
$849$		0			0
$850$	0.178536	−	0.0792644i	0.00612375	−	0.00271875i
$851$	30.4982	−	17.6081i	1.04546	−	0.603599i
$852$		0			0
$853$	−20.4305	+	20.4305i	−0.699527	+	0.699527i	−0.964308	−	0.264781i	$-0.914700\pi$
$853$	−20.4305	+	20.4305i	−0.699527	+	0.699527i	0.264781	+	0.964308i	$0.414700\pi$
$854$	−0.00548226	−	0.786404i	−0.000187599	−	0.0269102i
$855$		0			0
$856$	−5.30130	+	9.18211i	−0.181195	+	0.313838i
$857$	−3.23941	−	0.867998i	−0.110656	−	0.0296503i	0.203066	−	0.979165i	$-0.434909\pi$
$857$	−3.23941	−	0.867998i	−0.110656	−	0.0296503i	−0.313722	+	0.949515i	$0.601576\pi$
$858$		0			0
$859$	−32.2014	−	18.5915i	−1.09870	−	0.634332i	−0.162818	−	0.986656i	$-0.552058\pi$
$859$	−32.2014	−	18.5915i	−1.09870	−	0.634332i	−0.935878	+	0.352324i	$0.885392\pi$
$860$	−27.4961	+	24.7314i	−0.937608	+	0.843333i
$861$		0			0
$862$	2.54671	+	2.54671i	0.0867413	+	0.0867413i
$863$	37.1527	−	9.95503i	1.26469	−	0.338873i	0.436697	−	0.899609i	$-0.356148\pi$
$863$	37.1527	−	9.95503i	1.26469	−	0.338873i	0.827995	+	0.560735i	$0.189482\pi$
$864$		0			0
$865$	47.0445	+	15.3131i	1.59956	+	0.520659i
$866$	4.03907	+	2.33196i	0.137253	+	0.0792432i
$867$		0			0
$868$	2.88774	−	11.0857i	0.0980162	−	0.376274i
$869$	3.24020			0.109916
$870$		0			0
$871$	13.0725	+	22.6423i	0.442946	+	0.767205i
$872$	−5.91035	−	1.58367i	−0.200150	−	0.0536299i
$873$		0			0
$874$		−	3.32761i		−	0.112558i
$875$	−29.4013	+	3.25058i	−0.993944	+	0.109890i
$876$		0			0
$877$	23.5987	−	6.32325i	0.796871	−	0.213521i	0.162661	−	0.986682i	$-0.447992\pi$
$877$	23.5987	−	6.32325i	0.796871	−	0.213521i	0.634210	+	0.773161i	$0.281326\pi$
$878$	−0.360956	+	1.34711i	−0.0121817	+	0.0454627i
$879$		0			0
$880$	−26.5112	+	40.7767i	−0.893693	+	1.37458i
$881$			13.5509i			0.456542i	0.973598	+	0.228271i	$0.0733073\pi$
$881$			13.5509i			0.456542i	−0.973598	+	0.228271i	$0.926693\pi$
$882$		0			0
$883$	32.5237	−	32.5237i	1.09451	−	1.09451i	0.0994691	−	0.995041i	$-0.468286\pi$
$883$	32.5237	−	32.5237i	1.09451	−	1.09451i	0.995041	−	0.0994691i	$-0.0317144\pi$
$884$	−1.00663	+	1.74353i	−0.0338566	+	0.0586413i
$885$		0			0
$886$	2.07864	+	3.60031i	0.0698334	+	0.120955i
$887$	−9.75876	−	36.4202i	−0.327667	−	1.22287i	−0.911604	−	0.411070i	$-0.865155\pi$
$887$	−9.75876	−	36.4202i	−0.327667	−	1.22287i	0.583937	−	0.811799i	$-0.301512\pi$
$888$		0			0
$889$	−3.79502	+	6.68028i	−0.127281	+	0.224049i
$890$	−2.63596	−	2.93063i	−0.0883576	−	0.0982350i
$891$		0			0
$892$	0.981806	−	3.66415i	0.0328733	−	0.122685i
$893$	−14.9507	+	55.7967i	−0.500305	+	1.86716i
$894$		0			0
$895$	−0.132311	+	2.49948i	−0.00442268	+	0.0835484i
$896$	5.85542	+	9.98055i	0.195616	+	0.333427i
$897$		0			0
$898$	0.957742	+	3.57434i	0.0319603	+	0.119277i
$899$	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
$905$	24.5653	+	15.9713i	0.816577	+	0.530903i
$906$		0			0
$907$	−1.37941	+	5.14802i	−0.0458025	+	0.170937i	−0.985038	−	0.172335i	$-0.944869\pi$
$907$	−1.37941	+	5.14802i	−0.0458025	+	0.170937i	0.939236	+	0.343272i	$0.111535\pi$
$908$	−15.5766	+	4.17374i	−0.516928	+	0.138510i
$909$		0			0
$910$	−2.23212	+	2.03601i	−0.0739942	+	0.0674932i
$911$		−	14.3597i		−	0.475757i	−0.971295	−	0.237879i	$-0.923548\pi$
$911$		−	14.3597i		−	0.475757i	0.971295	−	0.237879i	$-0.0764520\pi$
$912$		0			0
$913$	23.9237	+	6.41032i	0.791757	+	0.212151i
$914$	−2.42787	−	4.20519i	−0.0803067	−	0.139095i
$915$		0			0
$916$	26.2351			0.866832
$917$	6.54027	−	25.1075i	0.215979	−	0.829121i
$918$		0			0
$919$	2.41391	+	1.39367i	0.0796276	+	0.0459730i	0.539285	−	0.842123i	$-0.318695\pi$
$919$	2.41391	+	1.39367i	0.0796276	+	0.0459730i	−0.459658	+	0.888096i	$0.652028\pi$
$920$	2.61665	+	5.14215i	0.0862683	+	0.169532i
$921$		0			0
$922$	−5.40885	+	1.44930i	−0.178131	+	0.0477300i
$923$	−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
$928$	−4.66934	−	1.25115i	−0.153279	−	0.0410709i
$929$	−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
$935$	3.32192	+	1.08129i	0.108638	+	0.0353619i
$936$		0			0
$937$	−34.0816	−	34.0816i	−1.11340	−	1.11340i	−0.992688	−	0.120710i	$-0.961483\pi$
$937$	−34.0816	−	34.0816i	−1.11340	−	1.11340i	−0.120710	−	0.992688i	$-0.538517\pi$
$938$	−0.705912	−	2.56290i	−0.0230488	−	0.0836816i
$939$		0			0
$940$	−10.3349	−	48.7478i	−0.337086	−	1.58998i
$941$	−34.7876	+	20.0846i	−1.13404	+	0.654741i	−0.944949	−	0.327218i	$-0.893889\pi$
$941$	−34.7876	+	20.0846i	−1.13404	+	0.654741i	−0.189095	+	0.981959i	$0.560555\pi$
$942$		0			0
$943$	−10.4587	−	39.0325i	−0.340583	−	1.27107i
$944$	12.6347			0.411224
$945$		0			0
$946$	6.55430			0.213099
$947$	1.85264	+	6.91415i	0.0602027	+	0.224680i	0.989472	−	0.144723i	$-0.0462291\pi$
$947$	1.85264	+	6.91415i	0.0602027	+	0.224680i	−0.929270	+	0.369402i	$0.879562\pi$
$948$		0			0
$949$	−25.8856	+	14.9451i	−0.840284	+	0.485138i
$950$	3.55194	−	0.558741i	0.115240	−	0.0181279i
$951$		0			0
$952$	0.288890	−	0.292946i	0.00936298	−	0.00949444i
$953$	22.1319	+	22.1319i	0.716922	+	0.716922i	0.967974	−	0.251052i	$-0.0807764\pi$
$953$	22.1319	+	22.1319i	0.716922	+	0.716922i	−0.251052	+	0.967974i	$0.580776\pi$
$954$		0			0
$955$	−5.44612	−	10.7025i	−0.176232	−	0.346326i
$956$	−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
$962$	3.75410	+	1.00591i	0.121037	+	0.0324318i
$963$		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	0.999350	−	0.0360528i	$-0.0114785\pi$
$967$	29.9553	+	29.9553i	0.963297	+	0.963297i	−0.0360528	+	0.999350i	$0.511478\pi$
$968$	10.9794	−	2.94192i	0.352891	−	0.0945568i
$969$		0			0
$970$	3.25747	−	1.65761i	0.104591	−	0.0532225i
$971$	25.0340	+	14.4534i	0.803378	+	0.463830i	0.844651	−	0.535317i	$-0.179808\pi$
$971$	25.0340	+	14.4534i	0.803378	+	0.463830i	−0.0412730	+	0.999148i	$0.513141\pi$
$972$		0			0
$973$	6.45312	−	1.77741i	0.206877	−	0.0569813i
$974$	2.13758			0.0684924
$975$		0			0
$976$	4.11902	+	7.13436i	0.131847	+	0.228365i
$977$	−51.9291	−	13.9144i	−1.66136	−	0.445160i	−0.698598	−	0.715515i	$-0.746192\pi$
$977$	−51.9291	−	13.9144i	−1.66136	−	0.445160i	−0.962761	+	0.270355i	$0.912859\pi$
$978$		0			0
$979$		−	70.4929i		−	2.25296i
$980$	−27.4279	+	14.4420i	−0.876153	+	0.461331i
$981$		0			0
$982$	−0.171366	+	0.0459173i	−0.00546850	+	0.00146528i
$983$	5.61039	−	20.9382i	0.178944	−	0.667826i	−0.816903	−	0.576775i	$-0.804311\pi$
$983$	5.61039	−	20.9382i	0.178944	−	0.667826i	0.995846	−	0.0910508i	$-0.0290226\pi$
$984$		0			0
$985$	−25.5898	+	5.42520i	−0.815358	+	0.172861i
$986$			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	$0.908582\pi$
$992$	−0.938871	−	3.50391i	−0.0298092	−	0.111249i
$993$		0			0
$994$	1.53103	+	2.60964i	0.0485614	+	0.0827728i
$995$	47.3830	+	2.50825i	1.50214	+	0.0795167i
$996$		0			0
$997$	3.97247	−	14.8255i	0.125809	−	0.469527i	−0.874058	−	0.485822i	$-0.838520\pi$
$997$	3.97247	−	14.8255i	0.125809	−	0.469527i	0.999867	+	0.0162947i	$0.00518699\pi$
$998$	0.527047	−	1.96697i	0.0166834	−	0.0622632i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.8	✓	64	35.18	odd	12	inner
315.2.ce.a.53.9	yes	64	105.53	even	12	inner
315.2.ce.a.107.8	yes	64	3.2	odd	2	inner
315.2.ce.a.107.9	yes	64	1.1	even	1	trivial
315.2.ce.a.233.8	yes	64	15.8	even	4	inner
315.2.ce.a.233.9	yes	64	5.3	odd	4	inner
315.2.ce.a.242.8	yes	64	7.4	even	3	inner
315.2.ce.a.242.9	yes	64	21.11	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.0362581 + 0.135317i) q^{2} +(1.71505 - 0.990187i) q^{4} +(1.87468 + 1.21884i) q^{5} +(0.702570 + 2.55076i) q^{7} +(0.394292 + 0.394292i) q^{8} +(-0.0969571 + 0.297870i) q^{10} +(-4.85164 + 2.80110i) q^{11} +(2.57764 - 2.57764i) q^{13} +(-0.319688 + 0.187556i) q^{14} +(1.94132 - 3.36246i) q^{16} +(-0.269375 - 0.0721789i) q^{17} +(-4.44554 - 2.56664i) q^{19} +(4.42206 + 0.234084i) q^{20} +(-0.554948 - 0.554948i) q^{22} +(4.46964 - 1.19764i) q^{23} +(2.02887 + 4.56987i) q^{25} +(0.442260 + 0.255339i) q^{26} +(3.73068 + 3.67902i) q^{28} -2.91358 q^{29} +(-1.09319 - 1.89346i) q^{31} +(1.60261 + 0.429419i) q^{32} -0.0390682i q^{34} +(-1.79187 + 5.63819i) q^{35} +(7.35120 - 1.96975i) q^{37} +(0.186123 - 0.694620i) q^{38} +(0.258595 + 1.21975i) q^{40} -8.73280i q^{41} +(-5.90533 + 5.90533i) q^{43} +(-5.54722 + 9.60806i) q^{44} +(0.324122 + 0.561396i) q^{46} +(-2.91250 - 10.8696i) q^{47} +(-6.01279 + 3.58418i) q^{49} +(-0.544818 + 0.440237i) q^{50} +(1.86845 - 6.97315i) q^{52} +(0.417606 - 1.55853i) q^{53} +(-12.5094 - 0.662190i) q^{55} +(-0.728729 + 1.28276i) q^{56} +(-0.105641 - 0.394257i) q^{58} +(1.62708 + 2.81818i) q^{59} +(-1.06088 + 1.83751i) q^{61} +(0.216580 - 0.216580i) q^{62} -7.53283i q^{64} +(7.97399 - 1.69054i) q^{65} +(-1.85630 + 6.92780i) q^{67} +(-0.533464 + 0.142941i) q^{68} +(-0.827914 - 0.0380404i) q^{70} -8.16308i q^{71} +(-7.92016 - 2.12220i) q^{73} +(0.533082 + 0.923325i) q^{74} -10.1658 q^{76} +(-10.5535 - 10.4074i) q^{77} +(-0.500892 - 0.289190i) q^{79} +(7.73764 - 3.93740i) q^{80} +(1.18170 - 0.316635i) q^{82} +(-3.12616 - 3.12616i) q^{83} +(-0.417019 - 0.463637i) q^{85} +(-1.01321 - 0.584977i) q^{86} +(-3.01741 - 0.808514i) q^{88} +(-6.29155 + 10.8973i) q^{89} +(8.38594 + 4.76399i) q^{91} +(6.47980 - 6.47980i) q^{92} +(1.36524 - 0.788224i) q^{94} +(-5.20568 - 10.2300i) q^{95} +(-8.25038 - 8.25038i) q^{97} +(-0.703014 - 0.683679i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 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

Related objects

Downloads

Learn more