LMFDB - Embedded newform 495.2.ba.b.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(64,495)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("495.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.2
Character	$\chi$	$=$	495.64
Dual form			495.2.ba.b.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32725 - 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(0.00315652 + 2.23607i) q^{5} +(0.207582 - 0.285712i) q^{7} +(-2.85924 - 3.93540i) q^{8} +O(q^{10})$	\(q+(-2.32725 - 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(0.00315652 + 2.23607i) q^{5} +(0.207582 - 0.285712i) q^{7} +(-2.85924 - 3.93540i) q^{8} +(1.68350 - 5.20628i) q^{10} +(-0.393463 - 3.29320i) q^{11} +(3.50669 + 1.13939i) q^{13} +(-0.699143 + 0.507957i) q^{14} +(1.21368 + 3.73532i) q^{16} +(1.37802 - 0.447747i) q^{17} +(0.0752559 - 0.0546766i) q^{19} +(-5.23122 + 7.22157i) q^{20} +(-1.57453 + 7.96164i) q^{22} +4.86443i q^{23} +(-4.99998 + 0.0141164i) q^{25} +(-7.29937 - 5.30330i) q^{26} +(1.33944 - 0.435209i) q^{28} +(5.41495 + 3.93419i) q^{29} +(-1.21511 + 3.73973i) q^{31} +0.118080i q^{32} -3.54558 q^{34} +(0.639527 + 0.463265i) q^{35} +(-4.57856 + 6.30185i) q^{37} +(-0.216484 + 0.0703400i) q^{38} +(8.79080 - 6.40587i) q^{40} +(6.90591 - 5.01744i) q^{41} -8.13377i q^{43} +(6.44994 - 11.5471i) q^{44} +(3.67834 - 11.3208i) q^{46} +(4.54783 + 6.25956i) q^{47} +(2.12458 + 6.53878i) q^{49} +(11.6469 + 3.74798i) q^{50} +(8.64278 + 11.8958i) q^{52} +(12.6118 + 4.09781i) q^{53} +(7.36258 - 0.890205i) q^{55} -1.71792 q^{56} +(-9.62703 - 13.2505i) q^{58} +(-7.18751 - 5.22203i) q^{59} +(3.08181 + 9.48482i) q^{61} +(5.65574 - 7.78446i) q^{62} +(2.51664 - 7.74544i) q^{64} +(-2.53669 + 7.84478i) q^{65} +6.28888i q^{67} +(5.49541 + 1.78557i) q^{68} +(-1.13803 - 1.56173i) q^{70} +(0.313338 + 0.964354i) q^{71} +(6.18866 - 8.51796i) q^{73} +(15.4207 - 11.2038i) q^{74} +0.370960 q^{76} +(-1.02258 - 0.571193i) q^{77} +(-0.386590 + 1.18980i) q^{79} +(-8.34858 + 2.72565i) q^{80} +(-19.8658 + 6.45480i) q^{82} +(-11.4650 + 3.72521i) q^{83} +(1.00554 + 3.07993i) q^{85} +(-6.15052 + 18.9293i) q^{86} +(-11.8351 + 10.9645i) q^{88} -3.54180 q^{89} +(1.05346 - 0.765386i) q^{91} +(-11.4024 + 15.6940i) q^{92} +(-5.85067 - 18.0065i) q^{94} +(0.122498 + 0.168104i) q^{95} +(15.8990 + 5.16591i) q^{97} -16.8239i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4}+O(q^{10}) $ 48 * q + 12 * q^4	$ 48 q + 12 q^{4} - 12 q^{10} - 28 q^{16} + 22 q^{25} - 20 q^{31} + 40 q^{34} + 52 q^{40} - 52 q^{46} + 44 q^{49} + 60 q^{55} + 16 q^{61} - 64 q^{64} - 74 q^{70} + 152 q^{76} + 28 q^{79} - 38 q^{85} + 40 q^{91} - 64 q^{94}+O(q^{100}) $ 48 * q + 12 * q^4 - 12 * q^10 - 28 * q^16 + 22 * q^25 - 20 * q^31 + 40 * q^34 + 52 * q^40 - 52 * q^46 + 44 * q^49 + 60 * q^55 + 16 * q^61 - 64 * q^64 - 74 * q^70 + 152 * q^76 + 28 * q^79 - 38 * q^85 + 40 * q^91 - 64 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

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 $

$2$	−2.32725	−	0.756170i	−1.64562	−	0.534693i	−0.667833	−	0.744311i	$-0.732778\pi$
$2$	−2.32725	−	0.756170i	−1.64562	−	0.534693i	−0.977783	+	0.209618i	$0.932778\pi$
$3$		0			0
$3$		0			0
$4$	3.22628	+	2.34403i	1.61314	+	1.17201i
$5$	0.00315652	+	2.23607i	0.00141164	+	0.999999i
$5$	0.00315652	+	2.23607i	0.00141164	+	0.999999i
$6$		0			0
$7$	0.207582	−	0.285712i	0.0784586	−	0.107989i	−0.767984	−	0.640469i	$-0.778740\pi$
$7$	0.207582	−	0.285712i	0.0784586	−	0.107989i	0.846442	+	0.532480i	$0.178740\pi$
$8$	−2.85924	−	3.93540i	−1.01089	−	1.39138i
$9$		0			0
$10$	1.68350	−	5.20628i	0.532370	−	1.64637i
$11$	−0.393463	−	3.29320i	−0.118634	−	0.992938i
$11$	−0.393463	−	3.29320i	−0.118634	−	0.992938i
$12$		0			0
$13$	3.50669	+	1.13939i	0.972580	+	0.316010i	0.751857	−	0.659326i	$-0.229158\pi$
$13$	3.50669	+	1.13939i	0.972580	+	0.316010i	0.220723	+	0.975337i	$0.429158\pi$
$14$	−0.699143	+	0.507957i	−0.186854	+	0.135757i
$15$		0			0
$16$	1.21368	+	3.73532i	0.303420	+	0.933829i
$17$	1.37802	−	0.447747i	0.334219	−	0.108594i	−0.137100	−	0.990557i	$-0.543778\pi$
$17$	1.37802	−	0.447747i	0.334219	−	0.108594i	0.471319	+	0.881963i	$0.343778\pi$
$18$		0			0
$19$	0.0752559	−	0.0546766i	0.0172649	−	0.0125437i	−0.579119	−	0.815243i	$-0.696603\pi$
$19$	0.0752559	−	0.0546766i	0.0172649	−	0.0125437i	0.596384	+	0.802699i	$0.296603\pi$
$20$	−5.23122	+	7.22157i	−1.16974	+	1.61479i
$21$		0			0
$22$	−1.57453	+	7.96164i	−0.335692	+	1.69743i
$23$			4.86443i			1.01430i	0.861857	+	0.507152i	$0.169302\pi$
$23$			4.86443i			1.01430i	−0.861857	+	0.507152i	$0.830698\pi$
$24$		0			0
$25$	−4.99998	+	0.0141164i	−0.999996	+	0.00282327i
$26$	−7.29937	−	5.30330i	−1.43152	−	1.04006i
$27$		0			0
$28$	1.33944	−	0.435209i	0.253129	−	0.0822467i
$29$	5.41495	+	3.93419i	1.00553	+	0.730561i	0.963267	−	0.268546i	$-0.0865431\pi$
$29$	5.41495	+	3.93419i	1.00553	+	0.730561i	0.0422634	+	0.999107i	$0.486543\pi$
$30$		0			0
$31$	−1.21511	+	3.73973i	−0.218240	+	0.671674i	0.780667	+	0.624947i	$0.214879\pi$
$31$	−1.21511	+	3.73973i	−0.218240	+	0.671674i	−0.998908	+	0.0467277i	$0.985121\pi$
$32$			0.118080i			0.0208738i
$33$		0			0
$34$	−3.54558			−0.608062
$35$	0.639527	+	0.463265i	0.108100	+	0.0783061i
$36$		0			0
$37$	−4.57856	+	6.30185i	−0.752711	+	1.03602i	0.245075	+	0.969504i	$0.421187\pi$
$37$	−4.57856	+	6.30185i	−0.752711	+	1.03602i	−0.997786	+	0.0665132i	$0.978813\pi$
$38$	−0.216484	+	0.0703400i	−0.0351184	+	0.0114107i
$39$		0			0
$40$	8.79080	−	6.40587i	1.38995	−	1.01286i
$41$	6.90591	−	5.01744i	1.07852	−	0.783592i	0.101097	−	0.994877i	$-0.467765\pi$
$41$	6.90591	−	5.01744i	1.07852	−	0.783592i	0.977425	+	0.211284i	$0.0677647\pi$
$42$		0			0
$43$		−	8.13377i		−	1.24039i	−0.784448	−	0.620194i	$-0.787054\pi$
$43$		−	8.13377i		−	1.24039i	0.784448	−	0.620194i	$-0.212946\pi$
$44$	6.44994	−	11.5471i	0.972365	−	1.74079i
$45$		0			0
$46$	3.67834	−	11.3208i	0.542341	−	1.66915i
$47$	4.54783	+	6.25956i	0.663370	+	0.913050i	0.999587	−	0.0287344i	$-0.00914771\pi$
$47$	4.54783	+	6.25956i	0.663370	+	0.913050i	−0.336217	+	0.941784i	$0.609148\pi$
$48$		0			0
$49$	2.12458	+	6.53878i	0.303511	+	0.934111i
$50$	11.6469	+	3.74798i	1.64712	+	0.530045i
$51$		0			0
$52$	8.64278	+	11.8958i	1.19854	+	1.64965i
$53$	12.6118	+	4.09781i	1.73236	+	0.562878i	0.993787	−	0.111295i	$-0.0354999\pi$
$53$	12.6118	+	4.09781i	1.73236	+	0.562878i	0.738573	+	0.674173i	$0.235500\pi$
$54$		0			0
$55$	7.36258	−	0.890205i	0.992770	−	0.120035i
$56$	−1.71792			−0.229567
$57$		0			0
$58$	−9.62703	−	13.2505i	−1.26409	−	1.73987i
$59$	−7.18751	−	5.22203i	−0.935734	−	0.679850i	0.0116562	−	0.999932i	$-0.496290\pi$
$59$	−7.18751	−	5.22203i	−0.935734	−	0.679850i	−0.947390	+	0.320082i	$0.896290\pi$
$60$		0			0
$61$	3.08181	+	9.48482i	0.394585	+	1.21441i	0.929284	+	0.369365i	$0.120425\pi$
$61$	3.08181	+	9.48482i	0.394585	+	1.21441i	−0.534700	+	0.845042i	$0.679575\pi$
$62$	5.65574	−	7.78446i	0.718279	−	0.988627i
$63$		0			0
$64$	2.51664	−	7.74544i	0.314581	−	0.968180i
$65$	−2.53669	+	7.84478i	−0.314637	+	0.973025i
$66$		0			0
$67$			6.28888i			0.768309i	0.923269	+	0.384154i	$0.125507\pi$
$67$			6.28888i			0.768309i	−0.923269	+	0.384154i	$0.874493\pi$
$68$	5.49541	+	1.78557i	0.666417	+	0.216532i
$69$		0			0
$70$	−1.13803	−	1.56173i	−0.136021	−	0.186662i
$71$	0.313338	+	0.964354i	0.0371864	+	0.114448i	0.967927	−	0.251233i	$-0.0808361\pi$
$71$	0.313338	+	0.964354i	0.0371864	+	0.114448i	−0.930740	+	0.365681i	$0.880836\pi$
$72$		0			0
$73$	6.18866	−	8.51796i	0.724328	−	0.996952i	−0.275041	−	0.961432i	$-0.588692\pi$
$73$	6.18866	−	8.51796i	0.724328	−	0.996952i	0.999369	−	0.0355192i	$-0.0113085\pi$
$74$	15.4207	−	11.2038i	1.79262	−	1.30242i
$75$		0			0
$76$	0.370960			0.0425520
$77$	−1.02258	−	0.571193i	−0.116534	−	0.0650934i
$78$		0			0
$79$	−0.386590	+	1.18980i	−0.0434948	+	0.133863i	−0.970446	−	0.241319i	$-0.922420\pi$
$79$	−0.386590	+	1.18980i	−0.0434948	+	0.133863i	0.926951	+	0.375182i	$0.122420\pi$
$80$	−8.34858	+	2.72565i	−0.933400	+	0.304737i
$81$		0			0
$82$	−19.8658	+	6.45480i	−2.19381	+	0.712814i
$83$	−11.4650	+	3.72521i	−1.25845	+	0.408894i	−0.860941	−	0.508705i	$-0.830124\pi$
$83$	−11.4650	+	3.72521i	−1.25845	+	0.408894i	−0.397507	+	0.917599i	$0.630124\pi$
$84$		0			0
$85$	1.00554	+	3.07993i	0.109066	+	0.334066i
$86$	−6.15052	+	18.9293i	−0.663227	+	2.04120i
$87$		0			0
$88$	−11.8351	+	10.9645i	−1.26162	+	1.16882i
$89$	−3.54180			−0.375430			−0.187715	−	0.982224i	$-0.560108\pi$
$89$	−3.54180			−0.375430			−0.187715	+	0.982224i	$0.560108\pi$
$90$		0			0
$91$	1.05346	−	0.765386i	0.110433	−	0.0802342i
$92$	−11.4024	+	15.6940i	−1.18878	+	1.63621i
$93$		0			0
$94$	−5.85067	−	18.0065i	−0.603450	−	1.85723i
$95$	0.122498	+	0.168104i	0.0125680	+	0.0172472i
$96$		0			0
$97$	15.8990	+	5.16591i	1.61430	+	0.524519i	0.970588	−	0.240746i	$-0.0773921\pi$
$97$	15.8990	+	5.16591i	1.61430	+	0.524519i	0.643715	+	0.765265i	$0.277392\pi$
$98$		−	16.8239i		−	1.69947i
$99$		0			0
$100$	−16.1644	−	11.6746i	−1.61644	−	1.16746i
$101$	−2.65258	+	8.16380i	−0.263941	+	0.812328i	0.727994	+	0.685584i	$0.240453\pi$
$101$	−2.65258	+	8.16380i	−0.263941	+	0.812328i	−0.991935	+	0.126745i	$0.959547\pi$
$102$		0			0
$103$	6.12881	−	8.43558i	0.603890	−	0.831183i	−0.392168	−	0.919894i	$-0.628275\pi$
$103$	6.12881	−	8.43558i	0.603890	−	0.831183i	0.996057	+	0.0887109i	$0.0282747\pi$
$104$	−5.54249	−	17.0580i	−0.543486	−	1.67268i
$105$		0			0
$106$	−26.2521	−	19.0733i	−2.54983	−	1.85256i
$107$	1.73649	+	2.39007i	0.167873	+	0.231057i	0.884662	−	0.466233i	$-0.154389\pi$
$107$	1.73649	+	2.39007i	0.167873	+	0.231057i	−0.716789	+	0.697290i	$0.754389\pi$
$108$		0			0
$109$	−6.40314			−0.613310			−0.306655	−	0.951821i	$-0.599210\pi$
$109$	−6.40314			−0.613310			−0.306655	+	0.951821i	$0.599210\pi$
$110$	−17.8077	−	3.49563i	−1.69790	−	0.333295i
$111$		0			0
$112$	1.31916	+	0.428622i	0.124649	+	0.0405010i
$113$	−7.20636	−	9.91870i	−0.677917	−	0.933073i	0.321989	−	0.946743i	$-0.395649\pi$
$113$	−7.20636	−	9.91870i	−0.677917	−	0.933073i	−0.999907	+	0.0136701i	$0.995649\pi$
$114$		0			0
$115$	−10.8772	+	0.0153547i	−1.01430	+	0.00143183i
$116$	8.24827	+	25.3856i	0.765833	+	2.35699i
$117$		0			0
$118$	12.7784	+	17.5880i	1.17635	+	1.61910i
$119$	0.158126	−	0.486662i	0.0144954	−	0.0446122i
$120$		0			0
$121$	−10.6904	+	2.59151i	−0.971852	+	0.235592i
$122$		−	24.4040i		−	2.20943i
$123$		0			0
$124$	−12.6863	+	9.21714i	−1.13926	+	0.827724i
$125$	−0.0473476	−	11.1802i	−0.00423490	−	0.999991i
$126$		0			0
$127$	−13.6172	+	4.42450i	−1.20833	+	0.392610i	−0.842819	−	0.538196i	$-0.819106\pi$
$127$	−13.6172	+	4.42450i	−1.20833	+	0.392610i	−0.365511	+	0.930807i	$0.619106\pi$
$128$	−11.5749	+	15.9315i	−1.02309	+	1.40816i
$129$		0			0
$130$	11.8355	−	16.3386i	1.03804	−	1.43299i
$131$	6.51327			0.569067			0.284533	−	0.958666i	$-0.408161\pi$
$131$	6.51327			0.569067			0.284533	+	0.958666i	$0.408161\pi$
$132$		0			0
$133$		−	0.0328514i		−	0.00284858i
$134$	4.75546	−	14.6358i	0.410809	−	1.26434i
$135$		0			0
$136$	−5.70216	−	4.14286i	−0.488956	−	0.355247i
$137$	−4.79246	+	1.55716i	−0.409447	+	0.133038i	−0.506496	−	0.862242i	$-0.669060\pi$
$137$	−4.79246	+	1.55716i	−0.409447	+	0.133038i	0.0970490	+	0.995280i	$0.469060\pi$
$138$		0			0
$139$	8.56224	+	6.22083i	0.726240	+	0.527644i	0.888372	−	0.459125i	$-0.151837\pi$
$139$	8.56224	+	6.22083i	0.726240	+	0.527644i	−0.162132	+	0.986769i	$0.551837\pi$
$140$	0.977384	+	2.99369i	0.0826040	+	0.253013i
$141$		0			0
$142$		−	2.48123i		−	0.208220i
$143$	2.37250	−	11.9965i	0.198398	−	1.00320i
$144$		0			0
$145$	−8.78001	+	12.1206i	−0.729140	+	1.00656i
$146$	−20.8436	+	15.1438i	−1.72503	+	1.25331i
$147$		0			0
$148$	−29.5434	+	9.59924i	−2.42845	+	0.789053i
$149$	0.747429	+	2.30035i	0.0612318	+	0.188452i	0.976993	−	0.213271i	$-0.0684116\pi$
$149$	0.747429	+	2.30035i	0.0612318	+	0.188452i	−0.915761	+	0.401723i	$0.868412\pi$
$150$		0			0
$151$	9.52168	−	6.91790i	0.774863	−	0.562971i	−0.128570	−	0.991700i	$-0.541039\pi$
$151$	9.52168	−	6.91790i	0.774863	−	0.562971i	0.903433	+	0.428729i	$0.141039\pi$
$152$	−0.430349	−	0.139829i	−0.0349059	−	0.0113416i
$153$		0			0
$154$	1.94789	+	2.10256i	0.156966	+	0.169429i
$155$	−8.36611	−	2.70526i	−0.671982	−	0.217292i
$156$		0			0
$157$	−10.0244	−	13.7975i	−0.800037	−	1.10116i	−0.992785	−	0.119908i	$-0.961740\pi$
$157$	−10.0244	−	13.7975i	−0.800037	−	1.10116i	0.192748	−	0.981248i	$-0.438260\pi$
$158$	1.79939	−	2.47664i	0.143152	−	0.197031i
$159$		0			0
$160$	−0.264035		0.000372722i	−0.0208738		2.94663e-5i
$161$	1.38983	+	1.00977i	0.109534	+	0.0795809i
$162$		0			0
$163$	23.8832	+	7.76012i	1.87067	+	0.607819i	0.991288	+	0.131711i	$0.0420472\pi$
$163$	23.8832	+	7.76012i	1.87067	+	0.607819i	0.879387	+	0.476108i	$0.157953\pi$
$164$	34.0414			2.65819
$165$		0			0
$166$	29.4989			2.28956
$167$	−16.7906	−	5.45561i	−1.29930	−	0.422168i	−0.423962	−	0.905680i	$-0.639361\pi$
$167$	−16.7906	−	5.45561i	−1.29930	−	0.422168i	−0.875338	+	0.483512i	$0.839361\pi$
$168$		0			0
$169$	0.481418	+	0.349771i	0.0370322	+	0.0269055i
$170$	−0.0111917	−	7.92815i	−0.000858363	−	0.608061i
$171$		0			0
$172$	19.0658	−	26.2418i	1.45375	−	2.00092i
$173$	−1.39226	−	1.91628i	−0.105851	−	0.145692i	0.752805	−	0.658244i	$-0.228700\pi$
$173$	−1.39226	−	1.91628i	−0.105851	−	0.145692i	−0.858656	+	0.512552i	$0.828700\pi$
$174$		0			0
$175$	−1.03387	+	1.43149i	−0.0781535	+	0.108210i
$176$	11.8236	−	5.46660i	0.891239	−	0.412060i
$177$		0			0
$178$	8.24266	+	2.67820i	0.617813	+	0.200740i
$179$	1.57083	−	1.14127i	0.117409	−	0.0853028i	−0.527531	−	0.849536i	$-0.676882\pi$
$179$	1.57083	−	1.14127i	0.117409	−	0.0853028i	0.644940	+	0.764233i	$0.276882\pi$
$180$		0			0
$181$	4.72308	+	14.5362i	0.351064	+	1.08046i	0.958257	+	0.285909i	$0.0922956\pi$
$181$	4.72308	+	14.5362i	0.351064	+	1.08046i	−0.607193	+	0.794555i	$0.707704\pi$
$182$	−3.03044	+	0.984649i	−0.224631	+	0.0729870i
$183$		0			0
$184$	19.1435	−	13.9086i	1.41128	−	1.02535i
$185$	−14.1058	−	10.2181i	−1.03708	−	0.751247i
$186$		0			0
$187$	−2.01672	−	4.36193i	−0.147477	−	0.318976i
$188$			30.8553i			2.25036i
$189$		0			0
$190$	−0.157968	−	0.483851i	−0.0114602	−	0.0351022i
$191$	13.4231	+	9.75247i	0.971263	+	0.705664i	0.955739	−	0.294216i	$-0.0950585\pi$
$191$	13.4231	+	9.75247i	0.971263	+	0.705664i	0.0155237	+	0.999880i	$0.495058\pi$
$192$		0			0
$193$	−0.579932	+	0.188431i	−0.0417444	+	0.0135636i	−0.329815	−	0.944046i	$-0.606986\pi$
$193$	−0.579932	+	0.188431i	−0.0417444	+	0.0135636i	0.288070	+	0.957609i	$0.406986\pi$
$194$	−33.0948	−	24.0448i	−2.37607	−	1.72631i
$195$		0			0
$196$	−8.47260	+	26.0760i	−0.605186	+	1.86257i
$197$		−	8.15502i		−	0.581021i	−0.956872	−	0.290510i	$-0.906175\pi$
$197$		−	8.15502i		−	0.581021i	0.956872	−	0.290510i	$-0.0938251\pi$
$198$		0			0
$199$	−2.83277			−0.200809			−0.100405	−	0.994947i	$-0.532014\pi$
$199$	−2.83277			−0.200809			−0.100405	+	0.994947i	$0.532014\pi$
$200$	14.3517	+	19.6366i	1.01482	+	1.38852i
$201$		0			0
$202$	12.3464	−	16.9934i	0.868693	−	1.19565i
$203$	2.24809	−	0.730449i	0.157785	−	0.0512675i
$204$		0			0
$205$	11.2411	+	15.4262i	0.785114	+	1.07741i
$206$	−20.6420	+	14.9973i	−1.43820	+	1.04491i
$207$		0			0
$208$			14.4814i			1.00411i
$209$	−0.209672	−	0.226320i	−0.0145033	−	0.0156549i
$210$		0			0
$211$	7.75698	−	23.8735i	0.534013	−	1.64352i	−0.211760	−	0.977322i	$-0.567920\pi$
$211$	7.75698	−	23.8735i	0.534013	−	1.64352i	0.745773	−	0.666200i	$-0.232080\pi$
$212$	31.0837	+	42.7831i	2.13484	+	2.93835i
$213$		0			0
$214$	−2.23395	−	6.87538i	−0.152709	−	0.469991i
$215$	18.1876	−	0.0256744i	1.24039	−	0.00175098i
$216$		0			0
$217$	0.816250	+	1.12347i	0.0554107	+	0.0762662i
$218$	14.9017	+	4.84187i	1.00927	+	0.327933i
$219$		0			0
$220$	25.8404	+	14.3860i	1.74216	+	0.969907i
$221$	5.34245			0.359372
$222$		0			0
$223$	−8.61250	−	11.8541i	−0.576735	−	0.793808i	0.416597	−	0.909091i	$-0.363223\pi$
$223$	−8.61250	−	11.8541i	−0.576735	−	0.793808i	−0.993333	+	0.115283i	$0.963223\pi$
$224$	0.0337370	+	0.0245113i	0.00225415	+	0.00163773i
$225$		0			0
$226$	9.27079	+	28.5326i	0.616684	+	1.89796i
$227$	11.6950	−	16.0968i	0.776227	−	1.06839i	−0.219461	−	0.975621i	$-0.570430\pi$
$227$	11.6950	−	16.0968i	0.776227	−	1.06839i	0.995688	−	0.0927640i	$-0.0295702\pi$
$228$		0			0
$229$	1.41923	−	4.36794i	0.0937854	−	0.288642i	−0.893150	−	0.449759i	$-0.851510\pi$
$229$	1.41923	−	4.36794i	0.0937854	−	0.288642i	0.986935	+	0.161117i	$0.0515098\pi$
$230$	25.3256	+	8.18927i	1.66992	+	0.539984i
$231$		0			0
$232$		−	32.5588i		−	2.13759i
$233$	10.0602	+	3.26874i	0.659062	+	0.214142i	0.619406	−	0.785071i	$-0.287374\pi$
$233$	10.0602	+	3.26874i	0.659062	+	0.214142i	0.0396566	+	0.999213i	$0.487374\pi$
$234$		0			0
$235$	−13.9824	+	10.1890i	−0.912113	+	0.664658i
$236$	−10.9483	−	33.6954i	−0.712675	−	2.19339i
$237$		0			0
$238$	−0.735999	+	1.01302i	−0.0477077	+	0.0656640i
$239$	−15.7580	+	11.4488i	−1.01930	+	0.740563i	−0.966139	−	0.258023i	$-0.916929\pi$
$239$	−15.7580	+	11.4488i	−1.01930	+	0.740563i	−0.0531584	+	0.998586i	$0.516929\pi$
$240$		0			0
$241$	−16.4879			−1.06208			−0.531039	−	0.847347i	$-0.678198\pi$
$241$	−16.4879			−1.06208			−0.531039	+	0.847347i	$0.678198\pi$
$242$	26.8388	+	2.05265i	1.72526	+	0.131949i
$243$		0			0
$244$	−12.2899	+	37.8245i	−0.786782	+	2.42147i
$245$	−14.6144	+	4.77134i	−0.933682	+	0.304829i
$246$		0			0
$247$	0.326197	−	0.105988i	0.0207554	−	0.00674384i
$248$	18.1916	−	5.91082i	1.15517	−	0.375337i
$249$		0			0
$250$	−8.34398	+	26.0550i	−0.527719	+	1.64787i
$251$	7.27360	−	22.3858i	0.459106	−	1.41298i	−0.407141	−	0.913365i	$-0.633474\pi$
$251$	7.27360	−	22.3858i	0.459106	−	1.41298i	0.866247	−	0.499616i	$-0.166526\pi$
$252$		0			0
$253$	16.0195	−	1.91397i	1.00714	−	0.120330i
$254$	35.0363			2.19838
$255$		0			0
$256$	25.8074	−	18.7502i	1.61296	−	1.17189i
$257$	−1.62383	+	2.23501i	−0.101292	+	0.139416i	−0.856654	−	0.515891i	$-0.827461\pi$
$257$	−1.62383	+	2.23501i	−0.101292	+	0.139416i	0.755362	+	0.655307i	$0.227461\pi$
$258$		0			0
$259$	0.850088	+	2.61630i	0.0528219	+	0.162569i
$260$	−26.5724	+	19.3634i	−1.64795	+	1.20087i
$261$		0			0
$262$	−15.1580	−	4.92514i	−0.936466	−	0.304276i
$263$		−	7.70220i		−	0.474938i	−0.971395	−	0.237469i	$-0.923682\pi$
$263$		−	7.70220i		−	0.474938i	0.971395	−	0.237469i	$-0.0763178\pi$
$264$		0			0
$265$	−9.12317	+	28.2137i	−0.560432	+	1.73315i
$266$	−0.0248413	+	0.0764535i	−0.00152312	+	0.00468767i
$267$		0			0
$268$	−14.7413	+	20.2897i	−0.900469	+	1.23939i
$269$	−3.19820	−	9.84305i	−0.194998	−	0.600141i	−0.999977	−	0.00683787i	$-0.997823\pi$
$269$	−3.19820	−	9.84305i	−0.194998	−	0.600141i	0.804979	−	0.593303i	$-0.202177\pi$
$270$		0			0
$271$	−17.4594	−	12.6850i	−1.06058	−	0.770560i	−0.0863882	−	0.996262i	$-0.527533\pi$
$271$	−17.4594	−	12.6850i	−1.06058	−	0.770560i	−0.974196	+	0.225702i	$0.927533\pi$
$272$	3.34495	+	4.60393i	0.202817	+	0.279154i
$273$		0			0
$274$	12.3307			0.744928
$275$	2.01380	+	16.4604i	0.121436	+	0.992599i
$276$		0			0
$277$	7.67008	+	2.49216i	0.460851	+	0.149739i	0.530235	−	0.847851i	$-0.322104\pi$
$277$	7.67008	+	2.49216i	0.460851	+	0.149739i	−0.0693847	+	0.997590i	$0.522104\pi$
$278$	−15.2225	−	20.9520i	−0.912984	−	1.25662i
$279$		0			0
$280$	−0.00542264	−	3.84138i	−0.000324065	−	0.229566i
$281$	−8.81351	−	27.1252i	−0.525770	−	1.61815i	−0.762788	−	0.646649i	$-0.776170\pi$
$281$	−8.81351	−	27.1252i	−0.525770	−	1.61815i	0.237018	−	0.971505i	$-0.423830\pi$
$282$		0			0
$283$	−12.6223	−	17.3732i	−0.750320	−	1.03273i	−0.997958	−	0.0638743i	$-0.979654\pi$
$283$	−12.6223	−	17.3732i	−0.750320	−	1.03273i	0.247638	−	0.968853i	$-0.420346\pi$
$284$	−1.24956	+	3.84575i	−0.0741477	+	0.228203i
$285$		0			0
$286$	−14.5928	+	26.1250i	−0.862892	+	1.54480i
$287$		−	3.01463i		−	0.177948i
$288$		0			0
$289$	−12.0548	+	8.75834i	−0.709107	+	0.515196i
$290$	29.5985	−	21.5685i	1.73809	−	1.26655i
$291$		0			0
$292$	39.9327	−	12.9749i	2.33688	−	0.759299i
$293$	−8.97706	+	12.3559i	−0.524445	+	0.721837i	−0.986271	−	0.165134i	$-0.947194\pi$
$293$	−8.97706	+	12.3559i	−0.524445	+	0.721837i	0.461826	+	0.886971i	$0.347194\pi$
$294$		0			0
$295$	11.6541	−	16.0882i	0.678529	−	0.936693i
$296$	37.8915			2.20240
$297$		0			0
$298$		−	5.91868i		−	0.342860i
$299$	−5.54249	+	17.0580i	−0.320530	+	0.986491i
$300$		0			0
$301$	−2.32392	−	1.68843i	−0.133948	−	0.0973192i
$302$	−27.3905	+	8.89970i	−1.57614	+	0.512120i
$303$		0			0
$304$	0.295571	+	0.214745i	0.0169521	+	0.0123165i
$305$	−21.1990	+	6.92106i	−1.21385	+	0.396299i
$306$		0			0
$307$		−	27.5348i		−	1.57150i	−0.618547	−	0.785748i	$-0.712278\pi$
$307$		−	27.5348i		−	1.57150i	0.618547	−	0.785748i	$-0.287722\pi$
$308$	−1.96025	−	4.23979i	−0.111696	−	0.241585i
$309$		0			0
$310$	17.4244	+	12.6220i	0.989640	+	0.716883i
$311$	0.861489	−	0.625908i	0.0488506	−	0.0354920i	−0.563092	−	0.826394i	$-0.690388\pi$
$311$	0.861489	−	0.625908i	0.0488506	−	0.0354920i	0.611943	+	0.790902i	$0.290388\pi$
$312$		0			0
$313$	19.5956	−	6.36698i	1.10761	−	0.359883i	0.302581	−	0.953124i	$-0.402152\pi$
$313$	19.5956	−	6.36698i	1.10761	−	0.359883i	0.805025	+	0.593241i	$0.202152\pi$
$314$	12.8962	+	39.6903i	0.727773	+	2.23986i
$315$		0			0
$316$	−4.03618	+	2.93246i	−0.227053	+	0.164964i
$317$	−12.1992	−	3.96377i	−0.685177	−	0.222627i	−0.0543164	−	0.998524i	$-0.517298\pi$
$317$	−12.1992	−	3.96377i	−0.685177	−	0.222627i	−0.630860	+	0.775896i	$0.717298\pi$
$318$		0			0
$319$	10.8255	−	19.3805i	0.606112	−	1.08510i
$320$	17.3272	+	5.60293i	0.968623	+	0.313214i
$321$		0			0
$322$	−2.47092	−	3.40093i	−0.137699	−	0.189526i
$323$	0.0792230	−	0.109041i	0.00440809	−	0.00606721i
$324$		0			0
$325$	−17.5494	−	5.64743i	−0.973468	−	0.313263i
$326$	−49.7142	−	36.1195i	−2.75342	−	2.00047i
$327$		0			0
$328$	−39.4913	−	12.8315i	−2.18054	−	0.708501i
$329$	2.73248			0.150646
$330$		0			0
$331$	30.0181			1.64994			0.824972	−	0.565174i	$-0.191191\pi$
$331$	30.0181			1.64994			0.824972	+	0.565174i	$0.191191\pi$
$332$	−45.7213	−	14.8557i	−2.50928	−	0.815315i
$333$		0			0
$334$	34.9507	+	25.3932i	1.91242	+	1.38945i
$335$	−14.0623	+	0.0198510i	−0.768308	+	0.00108457i
$336$		0			0
$337$	−9.22285	+	12.6942i	−0.502400	+	0.691495i	−0.982615	−	0.185656i	$-0.940559\pi$
$337$	−9.22285	+	12.6942i	−0.502400	+	0.691495i	0.480214	+	0.877151i	$0.340559\pi$
$338$	−0.855896	−	1.17804i	−0.0465546	−	0.0640769i
$339$		0			0
$340$	−3.97530	+	12.2937i	−0.215591	+	0.666722i
$341$	12.7938	+	2.53016i	0.692822	+	0.137016i
$342$		0			0
$343$	4.66036	+	1.51424i	0.251636	+	0.0817614i
$344$	−32.0097	+	23.2564i	−1.72585	+	1.25390i
$345$		0			0
$346$	1.79110	+	5.51244i	0.0962902	+	0.296351i
$347$	−7.38011	+	2.39794i	−0.396185	+	0.128728i	−0.500332	−	0.865834i	$-0.666789\pi$
$347$	−7.38011	+	2.39794i	−0.396185	+	0.128728i	0.104147	+	0.994562i	$0.466789\pi$
$348$		0			0
$349$	2.83060	−	2.05655i	0.151518	−	0.110085i	−0.509443	−	0.860504i	$-0.670149\pi$
$349$	2.83060	−	2.05655i	0.151518	−	0.110085i	0.660962	+	0.750420i	$0.270149\pi$
$350$	3.48853	−	2.54965i	0.186470	−	0.136284i
$351$		0			0
$352$	0.388862	−	0.0464602i	0.0207264	−	0.00247634i
$353$		−	9.57594i		−	0.509676i	−0.966984	−	0.254838i	$-0.917978\pi$
$353$		−	9.57594i		−	0.509676i	0.966984	−	0.254838i	$-0.0820221\pi$
$354$		0			0
$355$	−2.15537	+	0.703688i	−0.114395	+	0.0373479i
$356$	−11.4268	−	8.30207i	−0.605621	−	0.440009i
$357$		0			0
$358$	−4.51871	+	1.46822i	−0.238821	+	0.0775978i
$359$	−1.57815	−	1.14659i	−0.0832917	−	0.0605149i	0.545360	−	0.838202i	$-0.316393\pi$
$359$	−1.57815	−	1.14659i	−0.0832917	−	0.0605149i	−0.628652	+	0.777687i	$0.716393\pi$
$360$		0			0
$361$	−5.86865	+	18.0618i	−0.308876	+	0.950623i
$362$		−	37.4008i		−	1.96574i
$363$		0			0
$364$	5.19285			0.272179
$365$	19.0663	+	13.8114i	0.997973	+	0.722920i
$366$		0			0
$367$	−6.32793	+	8.70965i	−0.330315	+	0.454640i	−0.941582	−	0.336785i	$-0.890660\pi$
$367$	−6.32793	+	8.70965i	−0.330315	+	0.454640i	0.611266	+	0.791425i	$0.290660\pi$
$368$	−18.1702	+	5.90385i	−0.947186	+	0.307759i
$369$		0			0
$370$	25.1012	+	34.4464i	1.30495	+	1.79078i
$371$	3.78877	−	2.75271i	0.196703	−	0.142913i
$372$		0			0
$373$		−	21.2460i		−	1.10007i	−0.835140	−	0.550037i	$-0.814614\pi$
$373$		−	21.2460i		−	1.10007i	0.835140	−	0.550037i	$-0.185386\pi$
$374$	1.39505	+	11.6763i	0.0721366	+	0.603768i
$375$		0			0
$376$	11.6305	−	35.7951i	0.599799	−	1.84599i
$377$	14.5059	+	19.9657i	0.747094	+	1.02829i
$378$		0			0
$379$	−9.70295	−	29.8626i	−0.498407	−	1.53394i	−0.811579	−	0.584243i	$-0.801391\pi$
$379$	−9.70295	−	29.8626i	−0.498407	−	1.53394i	0.313172	−	0.949697i	$-0.398609\pi$
$380$	0.00117094	+	0.829491i	6.00680e−5	+	0.0425520i
$381$		0			0
$382$	−23.8645	−	32.8466i	−1.22101	−	1.68058i
$383$	−19.2570	−	6.25699i	−0.983988	−	0.319717i	−0.227538	−	0.973769i	$-0.573068\pi$
$383$	−19.2570	−	6.25699i	−0.983988	−	0.319717i	−0.756449	+	0.654052i	$0.773068\pi$
$384$		0			0
$385$	1.27400	−	2.28837i	0.0649289	−	0.116626i
$386$	1.49213			0.0759476
$387$		0			0
$388$	39.1857	+	53.9345i	1.98935	+	2.73811i
$389$	21.3089	+	15.4818i	1.08040	+	0.784959i	0.977753	−	0.209758i	$-0.0672677\pi$
$389$	21.3089	+	15.4818i	1.08040	+	0.784959i	0.102650	+	0.994717i	$0.467268\pi$
$390$		0			0
$391$	2.17803	+	6.70329i	0.110148	+	0.339000i
$392$	19.6581	−	27.0570i	0.992882	−	1.36658i
$393$		0			0
$394$	−6.16658	+	18.9788i	−0.310668	+	0.956137i
$395$	−2.66170	−	0.860686i	−0.133925	−	0.0433058i
$396$		0			0
$397$			6.19375i			0.310855i	0.987847	+	0.155428i	$0.0496755\pi$
$397$			6.19375i			0.310855i	−0.987847	+	0.155428i	$0.950324\pi$
$398$	6.59256	+	2.14205i	0.330455	+	0.107371i
$399$		0			0
$400$	−6.12110	−	18.6594i	−0.306055	−	0.932969i
$401$	−3.95441	−	12.1704i	−0.197474	−	0.607763i	−0.999939	−	0.0110631i	$-0.996478\pi$
$401$	−3.95441	−	12.1704i	−0.197474	−	0.607763i	0.802465	−	0.596700i	$-0.203522\pi$
$402$		0			0
$403$	−8.52202	+	11.7296i	−0.424512	+	0.584291i
$404$	−27.6941	+	20.1210i	−1.37783	+	1.00106i
$405$		0			0
$406$	−5.78422			−0.287066
$407$	22.5548	+	12.5986i	1.11800	+	0.624489i
$408$		0			0
$409$	−3.78279	+	11.6422i	−0.187047	+	0.575672i	−0.999978	−	0.00668888i	$-0.997871\pi$
$409$	−3.78279	+	11.6422i	−0.187047	+	0.575672i	0.812931	+	0.582361i	$0.197871\pi$
$410$	−14.4961	−	44.4009i	−0.715910	−	2.19281i
$411$		0			0
$412$	39.5465	−	12.8494i	1.94832	−	0.633046i
$413$	−2.98400	+	0.969559i	−0.146833	+	0.0477089i
$414$		0			0
$415$	−8.36599	−	25.6247i	−0.410671	−	1.25787i
$416$	−0.134540	+	0.414071i	−0.00659635	+	0.0203015i
$417$		0			0
$418$	0.316823	+	0.685250i	0.0154963	+	0.0335167i
$419$	−26.2084			−1.28037			−0.640183	−	0.768223i	$-0.721141\pi$
$419$	−26.2084			−1.28037			−0.640183	+	0.768223i	$0.721141\pi$
$420$		0			0
$421$	13.1980	−	9.58889i	0.643230	−	0.467334i	−0.217729	−	0.976009i	$-0.569865\pi$
$421$	13.1980	−	9.58889i	0.643230	−	0.467334i	0.860958	+	0.508676i	$0.169865\pi$
$422$	−36.1049	+	49.6942i	−1.75756	+	2.41907i
$423$		0			0
$424$	−19.9335	−	61.3491i	−0.968057	−	2.97937i
$425$	−6.88376	+	2.25818i	−0.333912	+	0.109538i
$426$		0			0
$427$	3.34966	+	1.08837i	0.162101	+	0.0526699i
$428$			11.7814i			0.569476i
$429$		0			0
$430$	−42.3467	−	13.6932i	−2.04214	−	0.660345i
$431$	4.94269	−	15.2120i	0.238081	−	0.732738i	−0.758617	−	0.651537i	$-0.774124\pi$
$431$	4.94269	−	15.2120i	0.238081	−	0.732738i	0.996698	−	0.0812010i	$-0.0258756\pi$
$432$		0			0
$433$	−6.46373	+	8.89656i	−0.310627	+	0.427541i	−0.935577	−	0.353124i	$-0.885119\pi$
$433$	−6.46373	+	8.89656i	−0.310627	+	0.427541i	0.624950	+	0.780665i	$0.285119\pi$
$434$	−1.05008	−	3.23183i	−0.0504057	−	0.155133i
$435$		0			0
$436$	−20.6583	−	15.0091i	−0.989354	−	0.718808i
$437$	0.265970	+	0.366077i	0.0127231	+	0.0175118i
$438$		0			0
$439$	11.5564			0.551559			0.275779	−	0.961221i	$-0.411064\pi$
$439$	11.5564			0.551559			0.275779	+	0.961221i	$0.411064\pi$
$440$	−24.5547	−	26.4294i	−1.17060	−	1.25997i
$441$		0			0
$442$	−12.4332	−	4.03980i	−0.591389	−	0.192154i
$443$	7.55649	+	10.4006i	0.359020	+	0.494148i	0.949875	−	0.312629i	$-0.101210\pi$
$443$	7.55649	+	10.4006i	0.359020	+	0.494148i	−0.590856	+	0.806777i	$0.701210\pi$
$444$		0			0
$445$	−0.0111797	−	7.91969i	−0.000529971	−	0.375429i
$446$	11.0798	+	34.1000i	0.524641	+	1.61468i
$447$		0			0
$448$	−1.69056	−	2.32685i	−0.0798712	−	0.109933i
$449$	2.62163	−	8.06855i	0.123722	−	0.380778i	−0.869944	−	0.493151i	$-0.835845\pi$
$449$	2.62163	−	8.06855i	0.123722	−	0.380778i	0.993666	+	0.112373i	$0.0358450\pi$
$450$		0			0
$451$	−19.2407	−	20.7684i	−0.906007	−	0.977945i
$452$		−	48.8924i		−	2.29971i
$453$		0			0
$454$	−39.3893	+	28.6180i	−1.84863	+	1.34311i
$455$	1.71478	+	2.35320i	0.0803901	+	0.110320i
$456$		0			0
$457$	−34.8940	+	11.3378i	−1.63227	+	0.530358i	−0.974792	−	0.223114i	$-0.928378\pi$
$457$	−34.8940	+	11.3378i	−1.63227	+	0.530358i	−0.657481	+	0.753471i	$0.728378\pi$
$458$	−6.60582	+	9.09213i	−0.308670	+	0.424847i
$459$		0			0
$460$	−35.1288	−	25.4469i	−1.63789	−	1.18647i
$461$	18.4156			0.857698			0.428849	−	0.903376i	$-0.358919\pi$
$461$	18.4156			0.857698			0.428849	+	0.903376i	$0.358919\pi$
$462$		0			0
$463$			30.0776i			1.39782i	0.715208	+	0.698911i	$0.246332\pi$
$463$			30.0776i			1.39782i	−0.715208	+	0.698911i	$0.753668\pi$
$464$	−8.12344	+	25.0014i	−0.377121	+	1.16066i
$465$		0			0
$466$	−20.9408	−	15.2144i	−0.970063	−	0.704792i
$467$	8.78488	−	2.85438i	0.406516	−	0.132085i	−0.0986193	−	0.995125i	$-0.531443\pi$
$467$	8.78488	−	2.85438i	0.406516	−	0.132085i	0.505135	+	0.863040i	$0.331443\pi$
$468$		0			0
$469$	1.79681	+	1.30546i	0.0829689	+	0.0602805i
$470$	40.2453	−	13.1393i	1.85638	−	0.606071i
$471$		0			0
$472$			43.2168i			1.98921i
$473$	−26.7862	+	3.20034i	−1.23163	+	0.147152i
$474$		0			0
$475$	−0.375506	+	0.274444i	−0.0172294	+	0.0125924i
$476$	1.65091	−	1.19945i	0.0756692	−	0.0549769i
$477$		0			0
$478$	45.3300	−	14.7286i	2.07335	−	0.673671i
$479$	−6.58568	−	20.2686i	−0.300907	−	0.926098i	−0.981173	−	0.193132i	$-0.938135\pi$
$479$	−6.58568	−	20.2686i	−0.300907	−	0.926098i	0.680265	−	0.732966i	$-0.261865\pi$
$480$		0			0
$481$	−23.2358	+	16.8818i	−1.05946	+	0.769745i
$482$	38.3715	+	12.4677i	1.74777	+	0.567886i
$483$		0			0
$484$	−40.5647	−	16.6976i	−1.84385	−	0.758982i
$485$	−11.5011	+	35.5676i	−0.522240	+	1.61504i
$486$		0			0
$487$	5.90908	+	8.13315i	0.267766	+	0.368548i	0.921634	−	0.388060i	$-0.126855\pi$
$487$	5.90908	+	8.13315i	0.267766	+	0.368548i	−0.653868	+	0.756609i	$0.726855\pi$
$488$	28.5150	−	39.2475i	1.29081	−	1.77665i
$489$		0			0
$490$	37.6194	−	0.0531050i	1.69947	−	0.00239904i
$491$	32.8925	+	23.8978i	1.48442	+	1.07849i	0.976099	+	0.217324i	$0.0697329\pi$
$491$	32.8925	+	23.8978i	1.48442	+	1.07849i	0.508319	+	0.861169i	$0.330267\pi$
$492$		0			0
$493$	9.22344	+	2.99688i	0.415403	+	0.134972i
$494$	−0.839287			−0.0377613
$495$		0			0
$496$	−15.4438			−0.693448
$497$	0.340571	+	0.110658i	0.0152767	+	0.00496370i
$498$		0			0
$499$	−14.5253	−	10.5532i	−0.650241	−	0.472428i	0.213112	−	0.977028i	$-0.431640\pi$
$499$	−14.5253	−	10.5532i	−0.650241	−	0.472428i	−0.863353	+	0.504600i	$0.831640\pi$
$500$	26.0540	−	36.1816i	1.16517	−	1.61809i
$501$		0			0
$502$	−33.8550	+	46.5974i	−1.51102	+	2.07975i
$503$	23.2443	+	31.9931i	1.03641	+	1.42650i	0.900021	+	0.435846i	$0.143551\pi$
$503$	23.2443	+	31.9931i	1.03641	+	1.42650i	0.136393	+	0.990655i	$0.456449\pi$
$504$		0			0
$505$	−18.2632	−	5.90557i	−0.812700	−	0.262794i
$506$	−38.7288	−	7.65921i	−1.72171	−	0.340493i
$507$		0			0
$508$	−54.3040	−	17.6444i	−2.40935	−	0.782846i
$509$	−16.9885	+	12.3429i	−0.753002	+	0.547088i	−0.896756	−	0.442526i	$-0.854083\pi$
$509$	−16.9885	+	12.3429i	−0.753002	+	0.547088i	0.143754	+	0.989613i	$0.454083\pi$
$510$		0			0
$511$	−1.14903	−	3.53635i	−0.0508301	−	0.156439i
$512$	−36.7814	+	11.9510i	−1.62552	+	0.528165i
$513$		0			0
$514$	5.46911	−	3.97354i	0.241232	−	0.175265i
$515$	18.8819	+	13.6778i	0.832034	+	0.602716i
$516$		0			0
$517$	18.8246	−	17.4398i	0.827904	−	0.767003i
$518$		−	6.73161i		−	0.295770i
$519$		0			0
$520$	38.1254	−	12.4472i	1.67191	−	0.545846i
$521$	0.336879	+	0.244757i	0.0147589	+	0.0107230i	0.595140	−	0.803622i	$-0.297096\pi$
$521$	0.336879	+	0.244757i	0.0147589	+	0.0107230i	−0.580381	+	0.814345i	$0.697096\pi$
$522$		0			0
$523$	−9.33804	+	3.03411i	−0.408324	+	0.132672i	−0.505975	−	0.862548i	$-0.668867\pi$
$523$	−9.33804	+	3.03411i	−0.408324	+	0.132672i	0.0976509	+	0.995221i	$0.468867\pi$
$524$	21.0136	+	15.2673i	0.917984	+	0.666954i
$525$		0			0
$526$	−5.82418	+	17.9250i	−0.253946	+	0.781566i
$527$			5.69749i			0.248186i
$528$		0			0
$529$	−0.662654			−0.0288111
$530$	42.5663	−	58.7617i	1.84896	−	2.55245i
$531$		0			0
$532$	0.0770046	−	0.105988i	0.00333857	−	0.00459515i
$533$	29.9337	−	9.72605i	1.29657	−	0.421282i
$534$		0			0
$535$	−5.33887	+	3.89044i	−0.230820	+	0.168199i
$536$	24.7493	−	17.9814i	1.06901	−	0.776678i
$537$		0			0
$538$			25.3257i			1.09187i
$539$	20.6976	−	9.56943i	0.891508	−	0.412185i
$540$		0			0
$541$	7.90309	−	24.3232i	0.339780	−	1.04574i	−0.624539	−	0.780994i	$-0.714713\pi$
$541$	7.90309	−	24.3232i	0.339780	−	1.04574i	0.964319	−	0.264742i	$-0.0852869\pi$
$542$	31.0405	+	42.7235i	1.33330	+	1.83513i
$543$		0			0
$544$	0.0528700	+	0.162717i	0.00226678	+	0.00697644i
$545$	−0.0202116	−	14.3178i	−0.000865771	−	0.613309i
$546$		0			0
$547$	4.36898	+	6.01339i	0.186804	+	0.257114i	0.892140	−	0.451760i	$-0.149204\pi$
$547$	4.36898	+	6.01339i	0.186804	+	0.257114i	−0.705335	+	0.708874i	$0.749204\pi$
$548$	−19.1118	−	6.20981i	−0.816418	−	0.265270i
$549$		0			0
$550$	7.76025	−	39.8303i	0.330898	−	1.69837i
$551$	0.622615			0.0265243
$552$		0			0
$553$	0.259692	+	0.357435i	0.0110432	+	0.0151997i
$554$	−15.9657	−	11.5998i	−0.678319	−	0.492827i
$555$		0			0
$556$	13.0424	+	40.1403i	0.553120	+	1.70233i
$557$	15.7803	−	21.7197i	0.668631	−	0.920292i	−0.331097	−	0.943597i	$-0.607419\pi$
$557$	15.7803	−	21.7197i	0.668631	−	0.920292i	0.999728	+	0.0233046i	$0.00741876\pi$
$558$		0			0
$559$	9.26755	−	28.5226i	0.391976	−	1.20638i
$560$	−0.954263	+	2.95109i	−0.0403250	+	0.124706i
$561$		0			0
$562$			69.7917i			2.94399i
$563$	31.4429	+	10.2164i	1.32516	+	0.430571i	0.884264	−	0.466987i	$-0.154661\pi$
$563$	31.4429	+	10.2164i	1.32516	+	0.430571i	0.440896	+	0.897558i	$0.354661\pi$
$564$		0			0
$565$	22.1561	−	16.1452i	0.932115	−	0.679234i
$566$	16.2383	+	49.9764i	0.682547	+	2.10066i
$567$		0			0
$568$	2.89922	−	3.99043i	0.121648	−	0.167435i
$569$	24.2773	−	17.6385i	1.01776	−	0.739444i	0.0519357	−	0.998650i	$-0.483461\pi$
$569$	24.2773	−	17.6385i	1.01776	−	0.739444i	0.965822	+	0.259206i	$0.0834609\pi$
$570$		0			0
$571$	23.9194			1.00100			0.500499	−	0.865737i	$-0.333150\pi$
$571$	23.9194			1.00100			0.500499	+	0.865737i	$0.333150\pi$
$572$	35.7746	−	33.1430i	1.49581	−	1.38578i
$573$		0			0
$574$	−2.27958	+	7.01581i	−0.0951477	+	0.292834i
$575$	−0.0686680	−	24.3220i	−0.00286365	−	1.01430i
$576$		0			0
$577$	16.6186	−	5.39972i	0.691843	−	0.224793i	0.0580698	−	0.998313i	$-0.481505\pi$
$577$	16.6186	−	5.39972i	0.691843	−	0.224793i	0.633773	+	0.773519i	$0.281505\pi$
$578$	34.6774	−	11.2674i	1.44239	−	0.468661i
$579$		0			0
$580$	−56.7378	+	18.5238i	−2.35591	+	0.769160i
$581$	−1.31559	+	4.04898i	−0.0545800	+	0.167980i
$582$		0			0
$583$	8.53267	−	43.1455i	0.353387	−	1.78690i
$584$	−51.2165			−2.11935
$585$		0			0
$586$	30.2350	−	21.9670i	1.24900	−	0.907449i
$587$	−23.3598	+	32.1520i	−0.964163	+	1.32706i	−0.0192221	+	0.999815i	$0.506119\pi$
$587$	−23.3598	+	32.1520i	−0.964163	+	1.32706i	−0.944941	+	0.327241i	$0.893881\pi$
$588$		0			0
$589$	0.113031	+	0.347874i	0.00465737	+	0.0143339i
$590$	−39.2875	+	28.6289i	−1.61744	+	1.17863i
$591$		0			0
$592$	−29.0963	−	9.45396i	−1.19585	−	0.388555i
$593$			20.8206i			0.854999i	0.904016	+	0.427499i	$0.140605\pi$
$593$			20.8206i			0.854999i	−0.904016	+	0.427499i	$0.859395\pi$
$594$		0			0
$595$	1.08871	+	0.352044i	0.0446326	+	0.0144324i
$596$	−2.98067	+	9.17357i	−0.122093	+	0.375764i
$597$		0			0
$598$	25.7975	−	35.5073i	1.05494	−	1.45200i
$599$	1.69077	+	5.20367i	0.0690831	+	0.212616i	0.979638	−	0.200772i	$-0.0643452\pi$
$599$	1.69077	+	5.20367i	0.0690831	+	0.212616i	−0.910555	+	0.413388i	$0.864345\pi$
$600$		0			0
$601$	2.15734	+	1.56740i	0.0879999	+	0.0639356i	0.630915	−	0.775852i	$-0.282680\pi$
$601$	2.15734	+	1.56740i	0.0879999	+	0.0639356i	−0.542915	+	0.839787i	$0.682680\pi$
$602$	4.13161	+	5.68667i	0.168392	+	0.231771i
$603$		0			0
$604$	46.9353			1.90977
$605$	−5.82853	−	23.8962i	−0.236963	−	0.971519i
$606$		0			0
$607$	−13.6824	−	4.44568i	−0.555352	−	0.180445i	0.0178769	−	0.999840i	$-0.494309\pi$
$607$	−13.6824	−	4.44568i	−0.555352	−	0.180445i	−0.573229	+	0.819396i	$0.694309\pi$
$608$	0.00645623	+	0.00888623i	0.000261835	+	0.000360384i
$609$		0			0
$610$	54.5689	−	0.0770315i	2.20943	−	0.00311892i
$611$	8.81574	+	27.1321i	0.356647	+	1.09765i
$612$		0			0
$613$	−6.12249	−	8.42689i	−0.247285	−	0.340359i	0.667273	−	0.744813i	$-0.267461\pi$
$613$	−6.12249	−	8.42689i	−0.247285	−	0.340359i	−0.914558	+	0.404454i	$0.867461\pi$
$614$	−20.8210	+	64.0805i	−0.840268	+	2.58608i
$615$		0			0
$616$	0.675938	+	5.65746i	0.0272343	+	0.227946i
$617$			10.6235i			0.427685i	0.976868	+	0.213842i	$0.0685979\pi$
$617$			10.6235i			0.427685i	−0.976868	+	0.213842i	$0.931402\pi$
$618$		0			0
$619$	4.83119	−	3.51007i	0.194182	−	0.141082i	−0.486446	−	0.873711i	$-0.661707\pi$
$619$	4.83119	−	3.51007i	0.194182	−	0.141082i	0.680628	+	0.732629i	$0.261707\pi$
$620$	−20.6502	−	28.3383i	−0.829331	−	1.13809i
$621$		0			0
$622$	−2.47820	+	0.805215i	−0.0993666	+	0.0322862i
$623$	−0.735214	+	1.01193i	−0.0294557	+	0.0405423i
$624$		0			0
$625$	24.9996	−	0.141163i	0.999984	−	0.00564652i
$626$	−50.4183			−2.01512
$627$		0			0
$628$		−	68.0120i		−	2.71397i
$629$	−3.48773	+	10.7341i	−0.139065	+	0.427997i
$630$		0			0
$631$	3.86143	+	2.80550i	0.153721	+	0.111685i	0.661987	−	0.749515i	$-0.269713\pi$
$631$	3.86143	+	2.80550i	0.153721	+	0.111685i	−0.508266	+	0.861200i	$0.669713\pi$
$632$	5.78771	−	1.88054i	0.230223	−	0.0748039i
$633$		0			0
$634$	25.3934	+	18.4494i	1.00850	+	0.732719i
$635$	−9.93645	−	30.4350i	−0.394316	−	1.20778i
$636$		0			0
$637$			25.3502i			1.00441i
$638$	−39.8486	+	36.9173i	−1.57762	+	1.46157i
$639$		0			0
$640$	−35.6605	−	25.8320i	−1.40960	−	1.02110i
$641$	−0.0129404	+	0.00940174i	−0.000511115	+	0.000371346i	−0.588041	−	0.808831i	$-0.700101\pi$
$641$	−0.0129404	+	0.00940174i	−0.000511115	+	0.000371346i	0.587530	+	0.809203i	$0.300101\pi$
$642$		0			0
$643$	−14.9078	+	4.84385i	−0.587908	+	0.191023i	−0.587840	−	0.808977i	$-0.700022\pi$
$643$	−14.9078	+	4.84385i	−0.587908	+	0.191023i	−6.76766e−5		1.00000i	$0.500022\pi$
$644$	2.11704	+	6.51559i	0.0834231	+	0.256750i
$645$		0			0
$646$	−0.266826	+	0.193860i	−0.0104981	+	0.00762733i
$647$	0.996166	+	0.323674i	0.0391633	+	0.0127249i	0.328533	−	0.944492i	$-0.393446\pi$
$647$	0.996166	+	0.323674i	0.0391633	+	0.0127249i	−0.289370	+	0.957217i	$0.593446\pi$
$648$		0			0
$649$	−14.3692	+	25.7246i	−0.564040	+	1.00978i
$650$	36.5716	+	26.4134i	1.43446	+	1.03602i
$651$		0			0
$652$	58.8639	+	81.0192i	2.30529	+	3.17295i
$653$	−7.69760	+	10.5948i	−0.301230	+	0.414608i	−0.932621	−	0.360857i	$-0.882484\pi$
$653$	−7.69760	+	10.5948i	−0.301230	+	0.414608i	0.631391	+	0.775465i	$0.282484\pi$
$654$		0			0
$655$	0.0205592	+	14.5641i	0.000803316	+	0.569066i
$656$	27.1233	+	19.7062i	1.05899	+	0.769398i
$657$		0			0
$658$	−6.35917	−	2.06622i	−0.247906	−	0.0805496i
$659$	−35.8168			−1.39522			−0.697612	−	0.716476i	$-0.745754\pi$
$659$	−35.8168			−1.39522			−0.697612	+	0.716476i	$0.745754\pi$
$660$		0			0
$661$	−0.445990			−0.0173470			−0.00867351	−	0.999962i	$-0.502761\pi$
$661$	−0.445990			−0.0173470			−0.00867351	+	0.999962i	$0.502761\pi$
$662$	−69.8597	−	22.6988i	−2.71517	−	0.882214i
$663$		0			0
$664$	47.4414	+	34.4682i	1.84108	+	1.33762i
$665$	0.0734579		0.000103696i	0.00284858		4.02116e-6i
$666$		0			0
$667$	−19.1376	+	26.3406i	−0.741010	+	1.01991i
$668$	−41.3832	−	56.9591i	−1.60116	−	2.20381i
$669$		0			0
$670$	32.7416	+	10.5873i	1.26492	+	0.409024i
$671$	30.0229	−	13.8809i	1.15902	−	0.535868i
$672$		0			0
$673$	−16.9120	−	5.49505i	−0.651911	−	0.211819i	−0.0356542	−	0.999364i	$-0.511352\pi$
$673$	−16.9120	−	5.49505i	−0.651911	−	0.211819i	−0.616256	+	0.787546i	$0.711352\pi$
$674$	31.0628	−	22.5685i	1.19650	−	0.869305i
$675$		0			0
$676$	0.733317	+	2.25692i	0.0282045	+	0.0868045i
$677$	−11.9865	+	3.89464i	−0.460678	+	0.149683i	−0.530156	−	0.847900i	$-0.677867\pi$
$677$	−11.9865	+	3.89464i	−0.460678	+	0.149683i	0.0694780	+	0.997583i	$0.477867\pi$
$678$		0			0
$679$	4.77632	−	3.47020i	0.183298	−	0.133174i
$680$	9.24571	−	12.7635i	0.354557	−	0.489457i
$681$		0			0
$682$	−27.8611	−	15.5626i	−1.06686	−	0.595923i
$683$		−	39.7914i		−	1.52257i	−0.648415	−	0.761287i	$-0.724568\pi$
$683$		−	39.7914i		−	1.52257i	0.648415	−	0.761287i	$-0.275432\pi$
$684$		0			0
$685$	−3.49705	−	10.7113i	−0.133615	−	0.409259i
$686$	−9.70080	−	7.04805i	−0.370378	−	0.269096i
$687$		0			0
$688$	30.3822	−	9.87178i	1.15831	−	0.376358i
$689$	39.5565	+	28.7395i	1.50698	+	1.09489i
$690$		0			0
$691$	3.31613	−	10.2060i	0.126152	−	0.388255i	−0.867957	−	0.496639i	$-0.834567\pi$
$691$	3.31613	−	10.2060i	0.126152	−	0.388255i	0.994109	+	0.108384i	$0.0345675\pi$
$692$		−	9.44593i		−	0.359081i
$693$		0			0
$694$	18.9886			0.720799
$695$	−13.8832	+	19.1654i	−0.526618	+	0.726984i
$696$		0			0
$697$	7.26996	−	10.0062i	0.275369	−	0.379013i
$698$	−8.14262	+	2.64570i	−0.308203	+	0.100141i
$699$		0			0
$700$	−6.69101	+	2.19494i	−0.252896	+	0.0829611i
$701$	6.53445	−	4.74755i	0.246803	−	0.179313i	−0.457506	−	0.889207i	$-0.651257\pi$
$701$	6.53445	−	4.74755i	0.246803	−	0.179313i	0.704309	+	0.709894i	$0.251257\pi$
$702$		0			0
$703$			0.724591i			0.0273285i
$704$	−26.4975	−	5.24028i	−0.998662	−	0.197500i
$705$		0			0
$706$	−7.24104	+	22.2856i	−0.272520	+	0.838731i
$707$	1.78187	+	2.45253i	0.0670141	+	0.0922370i
$708$		0			0
$709$	3.70695	+	11.4088i	0.139217	+	0.428467i	0.996222	−	0.0868414i	$-0.0276773\pi$
$709$	3.70695	+	11.4088i	0.139217	+	0.428467i	−0.857005	+	0.515309i	$0.827677\pi$
$710$	5.54820	−	0.00783206i	0.208220	−	0.000293932i
$711$		0			0
$712$	10.1268	+	13.9384i	0.379520	+	0.522364i
$713$	−18.1916	−	5.91082i	−0.681282	−	0.221362i
$714$		0			0
$715$	26.8325	+	5.26719i	1.00348	+	0.196982i
$716$	7.74311			0.289374
$717$		0			0
$718$	2.80574	+	3.86177i	0.104709	+	0.144120i
$719$	−36.6833	−	26.6520i	−1.36806	−	0.993951i	−0.997886	−	0.0649865i	$-0.979300\pi$
$719$	−36.6833	−	26.6520i	−1.36806	−	0.993951i	−0.370170	−	0.928964i	$-0.620700\pi$
$720$		0			0
$721$	−1.13792	−	3.50215i	−0.0423783	−	0.130427i
$722$	27.3157	−	37.5968i	1.01658	−	1.39921i
$723$		0			0
$724$	−18.8352	+	57.9687i	−0.700004	+	2.15439i
$725$	−27.1302	−	19.5944i	−1.00759	−	0.727719i
$726$		0			0
$727$			6.88096i			0.255201i	0.991826	+	0.127600i	$0.0407275\pi$
$727$			6.88096i			0.255201i	−0.991826	+	0.127600i	$0.959273\pi$
$728$	−6.02421	−	1.95738i	−0.223272	−	0.0725455i
$729$		0			0
$730$	−33.9282	−	46.5599i	−1.25574	−	1.72326i
$731$	−3.64187	−	11.2085i	−0.134699	−	0.414562i
$732$		0			0
$733$	−12.1932	+	16.7826i	−0.450368	+	0.619878i	−0.972477	−	0.233001i	$-0.925145\pi$
$733$	−12.1932	+	16.7826i	−0.450368	+	0.619878i	0.522109	+	0.852879i	$0.325145\pi$
$734$	21.3127	−	15.4846i	0.786665	−	0.571545i
$735$		0			0
$736$	−0.574393			−0.0211724
$737$	20.7105	−	2.47444i	0.762883	−	0.0911472i
$738$		0			0
$739$	−3.95736	+	12.1795i	−0.145574	+	0.448030i	−0.997084	−	0.0763072i	$-0.975687\pi$
$739$	−3.95736	+	12.1795i	−0.145574	+	0.448030i	0.851510	+	0.524338i	$0.175687\pi$
$740$	−21.5578	−	66.0307i	−0.792480	−	2.42734i
$741$		0			0
$742$	−10.8990	+	3.54128i	−0.400113	+	0.130005i
$743$	3.87393	−	1.25872i	0.142121	−	0.0461779i	−0.237093	−	0.971487i	$-0.576195\pi$
$743$	3.87393	−	1.25872i	0.142121	−	0.0461779i	0.379214	+	0.925309i	$0.376195\pi$
$744$		0			0
$745$	−5.14137	+	1.67856i	−0.188365	+	0.0614977i
$746$	−16.0656	+	49.4447i	−0.588202	+	1.81030i
$747$		0			0
$748$	3.71800	−	18.8001i	0.135943	−	0.687399i
$749$	1.04334			0.0381227
$750$		0			0
$751$	−21.9864	+	15.9741i	−0.802296	+	0.582902i	−0.911587	−	0.411108i	$-0.865142\pi$
$751$	−21.9864	+	15.9741i	−0.802296	+	0.582902i	0.109291	+	0.994010i	$0.465142\pi$
$752$	−17.8618	+	24.5847i	−0.651353	+	0.896511i
$753$		0			0
$754$	−18.6615	−	57.4342i	−0.679612	−	2.09163i
$755$	15.4989	+	21.2693i	0.564064	+	0.774068i
$756$		0			0
$757$	8.75366	+	2.84424i	0.318157	+	0.103376i	0.463742	−	0.885970i	$-0.346506\pi$
$757$	8.75366	+	2.84424i	0.318157	+	0.103376i	−0.145585	+	0.989346i	$0.546506\pi$
$758$			76.8349i			2.79077i
$759$		0			0
$760$	0.311308	−	0.962730i	0.0112923	−	0.0349219i
$761$	−3.60607	+	11.0984i	−0.130720	+	0.402315i	−0.994900	−	0.100868i	$-0.967838\pi$
$761$	−3.60607	+	11.0984i	−0.130720	+	0.402315i	0.864180	+	0.503183i	$0.167838\pi$
$762$		0			0
$763$	−1.32918	+	1.82946i	−0.0481195	+	0.0662308i
$764$	20.4467	+	62.9283i	0.739734	+	2.27667i
$765$		0			0
$766$	40.0846	+	29.1232i	1.44832	+	1.05226i
$767$	−19.2544	−	26.5014i	−0.695236	−	0.956910i
$768$		0			0
$769$	−43.9597			−1.58523			−0.792614	−	0.609723i	$-0.791281\pi$
$769$	−43.9597			−1.58523			−0.792614	+	0.609723i	$0.791281\pi$
$770$	−4.69531	+	4.36225i	−0.169207	+	0.157205i
$771$		0			0
$772$	−2.31271	−	0.751445i	−0.0832362	−	0.0270451i
$773$	−2.38278	−	3.27962i	−0.0857028	−	0.117960i	0.764013	−	0.645201i	$-0.223226\pi$
$773$	−2.38278	−	3.27962i	−0.0857028	−	0.117960i	−0.849716	+	0.527241i	$0.823226\pi$
$774$		0			0
$775$	6.02274	−	18.7157i	0.216343	−	0.672288i
$776$	−25.1292	−	77.3398i	−0.902086	−	2.77634i
$777$		0			0
$778$	−37.8843	−	52.1433i	−1.35822	−	1.86943i
$779$	0.245374	−	0.755183i	0.00879143	−	0.0270572i
$780$		0			0
$781$	3.05253	−	1.41132i	0.109228	−	0.0505011i
$782$		−	17.2472i		−	0.616759i
$783$		0			0
$784$	−21.8459	+	15.8719i	−0.780209	+	0.566855i
$785$	30.8204	−	22.4589i	1.10003	−	0.801591i
$786$		0			0
$787$	14.7242	−	4.78417i	0.524860	−	0.170537i	−0.0345898	−	0.999402i	$-0.511012\pi$
$787$	14.7242	−	4.78417i	0.524860	−	0.170537i	0.559450	+	0.828864i	$0.311012\pi$
$788$	19.1156	−	26.3104i	0.680965	−	0.937267i
$789$		0			0
$790$	5.54362	+	4.01573i	0.197233	+	0.142873i
$791$	−4.32981			−0.153950
$792$		0			0
$793$			36.7717i			1.30580i
$794$	4.68353	−	14.4144i	0.166212	−	0.511549i
$795$		0			0
$796$	−9.13929	−	6.64008i	−0.323934	−	0.235352i
$797$	−35.1877	+	11.4332i	−1.24641	+	0.404984i	−0.856634	−	0.515925i	$-0.827448\pi$
$797$	−35.1877	+	11.4332i	−1.24641	+	0.404984i	−0.389778	+	0.920909i	$0.627448\pi$
$798$		0			0
$799$	9.06971	+	6.58953i	0.320863	+	0.233121i
$800$	−0.00166686	−	0.590399i	−5.89325e−5	−	0.0208738i
$801$		0			0
$802$			31.3139i			1.10573i
$803$	−30.4864	−	17.0290i	−1.07584	−	0.600941i
$804$		0			0
$805$	−2.25352	+	3.11093i	−0.0794262	+	0.109646i
$806$	28.7024	−	20.8535i	1.01100	−	0.734535i
$807$		0			0
$808$	39.7122	−	12.9033i	1.39707	−	0.453936i
$809$	−1.38117	−	4.25082i	−0.0485595	−	0.149451i	0.923837	−	0.382787i	$-0.125036\pi$
$809$	−1.38117	−	4.25082i	−0.0485595	−	0.149451i	−0.972396	+	0.233336i	$0.925036\pi$
$810$		0			0
$811$	−9.84293	+	7.15131i	−0.345632	+	0.251116i	−0.747034	−	0.664786i	$-0.768523\pi$
$811$	−9.84293	+	7.15131i	−0.345632	+	0.251116i	0.401402	+	0.915902i	$0.368523\pi$
$812$	8.96516	+	2.91296i	0.314616	+	0.102225i
$813$		0			0
$814$	−42.9640	−	46.3753i	−1.50589	−	1.62545i
$815$	−17.2767	+	53.4289i	−0.605178	+	1.87153i
$816$		0			0
$817$	−0.444727	−	0.612114i	−0.0155590	−	0.0214152i
$818$	17.6070	−	24.2340i	0.615616	−	0.847322i
$819$		0			0
$820$	0.107452	+	76.1188i	0.00375240	+	2.65818i
$821$	11.8701	+	8.62411i	0.414268	+	0.300984i	0.775328	−	0.631559i	$-0.217585\pi$
$821$	11.8701	+	8.62411i	0.414268	+	0.300984i	−0.361059	+	0.932543i	$0.617585\pi$
$822$		0			0
$823$	−9.27399	−	3.01330i	−0.323271	−	0.105037i	0.142886	−	0.989739i	$-0.454362\pi$
$823$	−9.27399	−	3.01330i	−0.323271	−	0.105037i	−0.466157	+	0.884702i	$0.654362\pi$
$824$	−50.7212			−1.76696
$825$		0			0
$826$	7.67766			0.267140
$827$	−16.0497	−	5.21486i	−0.558102	−	0.181338i	0.0163651	−	0.999866i	$-0.494791\pi$
$827$	−16.0497	−	5.21486i	−0.558102	−	0.181338i	−0.574467	+	0.818528i	$0.694791\pi$
$828$		0			0
$829$	32.1868	+	23.3851i	1.11789	+	0.812197i	0.983888	−	0.178783i	$-0.0572162\pi$
$829$	32.1868	+	23.3851i	1.11789	+	0.812197i	0.134005	+	0.990981i	$0.457216\pi$
$830$	0.0931137	+	65.9614i	0.00323202	+	2.28955i
$831$		0			0
$832$	17.6502	−	24.2934i	0.611910	−	0.842221i
$833$	5.85543	+	8.05931i	0.202879	+	0.279238i
$834$		0			0
$835$	12.1461	−	37.5622i	0.420333	−	1.29989i
$836$	−0.145959	−	1.22165i	−0.00504810	−	0.0422515i
$837$		0			0
$838$	60.9937	+	19.8180i	2.10699	+	0.684603i
$839$	−19.0738	+	13.8579i	−0.658501	+	0.478429i	−0.866156	−	0.499773i	$-0.833417\pi$
$839$	−19.0738	+	13.8579i	−0.658501	+	0.478429i	0.207655	+	0.978202i	$0.433417\pi$
$840$		0			0
$841$	4.88231	+	15.0262i	0.168356	+	0.518145i
$842$	−37.9658	+	12.3359i	−1.30839	+	0.425121i
$843$		0			0
$844$	80.9864	−	58.8401i	2.78767	−	2.02536i
$845$	−0.780591	+	1.07759i	−0.0268532	+	0.0370701i
$846$		0			0
$847$	−1.47870	+	3.59232i	−0.0508089	+	0.123434i
$848$			52.0824i			1.78852i
$849$		0			0
$850$	17.7278	−	0.0500507i	0.608059	−	0.00171672i
$851$	−30.6549	−	22.2721i	−1.05084	−	0.763477i
$852$		0			0
$853$	−35.6476	+	11.5826i	−1.22055	+	0.396580i	−0.847282	−	0.531143i	$-0.821763\pi$
$853$	−35.6476	+	11.5826i	−1.22055	+	0.396580i	−0.373267	+	0.927724i	$0.621763\pi$
$854$	−6.97251	−	5.06582i	−0.238594	−	0.173349i
$855$		0			0
$856$	4.44086	−	13.6676i	0.151785	−	0.467148i
$857$		−	40.5203i		−	1.38415i	−0.721827	−	0.692074i	$-0.756697\pi$
$857$		−	40.5203i		−	1.38415i	0.721827	−	0.692074i	$-0.243303\pi$
$858$		0			0
$859$	18.5806			0.633961			0.316981	−	0.948432i	$-0.397331\pi$
$859$	18.5806			0.633961			0.316981	+	0.948432i	$0.397331\pi$
$860$	58.7386	+	42.5495i	2.00297	+	1.45093i
$861$		0			0
$862$	−23.0058	+	31.6647i	−0.783580	+	1.07851i
$863$	−3.71672	+	1.20764i	−0.126519	+	0.0411084i	−0.371592	−	0.928396i	$-0.621188\pi$
$863$	−3.71672	+	1.20764i	−0.126519	+	0.0411084i	0.245073	+	0.969505i	$0.421188\pi$
$864$		0			0
$865$	4.28053	−	3.11923i	0.145542	−	0.106057i
$866$	21.7700	−	15.8169i	0.739776	−	0.537479i
$867$		0			0
$868$			5.53795i			0.187970i
$869$	4.07037	+	0.804977i	0.138078	+	0.0273070i
$870$		0			0
$871$	−7.16549	+	22.0531i	−0.242793	+	0.747242i
$872$	18.3081	+	25.1990i	0.619991	+	0.853344i
$873$		0			0
$874$	−0.342164	−	1.05307i	−0.0115739	−	0.0356207i
$875$	−3.20416	−	2.30729i	−0.108320	−	0.0780006i
$876$		0			0
$877$	−21.2356	−	29.2282i	−0.717074	−	0.986967i	−0.999616	−	0.0277125i	$-0.991178\pi$
$877$	−21.2356	−	29.2282i	−0.717074	−	0.986967i	0.282542	−	0.959255i	$-0.408822\pi$
$878$	−26.8948	−	8.73864i	−0.907654	−	0.294915i
$879$		0			0
$880$	12.2610	+	26.4211i	0.413318	+	0.890656i
$881$	−38.7801			−1.30654			−0.653268	−	0.757127i	$-0.726602\pi$
$881$	−38.7801			−1.30654			−0.653268	+	0.757127i	$0.726602\pi$
$882$		0			0
$883$	1.00263	+	1.38000i	0.0337412	+	0.0464407i	0.825554	−	0.564323i	$-0.190863\pi$
$883$	1.00263	+	1.38000i	0.0337412	+	0.0464407i	−0.791813	+	0.610763i	$0.790863\pi$
$884$	17.2362	+	12.5229i	0.579717	+	0.421189i
$885$		0			0
$886$	−9.72123	−	29.9189i	−0.326591	−	1.00514i
$887$	5.76014	−	7.92816i	0.193407	−	0.266201i	−0.701290	−	0.712877i	$-0.747392\pi$
$887$	5.76014	−	7.92816i	0.193407	−	0.266201i	0.894696	+	0.446675i	$0.147392\pi$
$888$		0			0
$889$	−1.56255	+	4.80905i	−0.0524064	+	0.161290i
$890$	−5.96262	+	18.4396i	−0.199867	+	0.618096i
$891$		0			0
$892$		−	58.4325i		−	1.95647i
$893$	0.684502	+	0.222408i	0.0229060	+	0.00744261i
$894$		0			0
$895$	2.55692	+	3.50887i	0.0854684	+	0.117289i
$896$	2.14908	+	6.61420i	0.0717958	+	0.220965i
$897$		0			0
$898$	−12.2024	+	16.7951i	−0.407199	+	0.560461i
$899$	−21.2925	+	15.4699i	−0.710146	+	0.515951i
$900$		0			0
$901$	19.2141			0.640114
$902$	29.0734	+	62.8825i	0.968040	+	2.09376i
$903$		0			0
$904$	−18.4294	+	56.7199i	−0.612953	+	1.88648i
$905$	−32.4889	+	10.6070i	−1.07997	+	0.352589i
$906$		0			0
$907$	25.8868	−	8.41114i	0.859558	−	0.279287i	0.154114	−	0.988053i	$-0.450748\pi$
$907$	25.8868	−	8.41114i	0.859558	−	0.279287i	0.705444	+	0.708766i	$0.250748\pi$
$908$	75.4629	−	24.5194i	2.50433	−	0.813705i
$909$		0			0
$910$	−2.21131	−	6.77315i	−0.0733041	−	0.224528i
$911$	13.5837	−	41.8062i	0.450046	−	1.38510i	−0.426807	−	0.904343i	$-0.640362\pi$
$911$	13.5837	−	41.8062i	0.450046	−	1.38510i	0.876853	−	0.480758i	$-0.159638\pi$
$912$		0			0
$913$	16.7789	+	36.2909i	0.555301	+	1.20105i
$914$	89.7805			2.96967
$915$		0			0
$916$	14.8174	−	10.7655i	0.489581	−	0.355702i
$917$	1.35204	−	1.86092i	0.0446482	−	0.0614530i
$918$		0			0
$919$	−0.146992	−	0.452394i	−0.00484881	−	0.0149231i	0.948603	−	0.316469i	$-0.102497\pi$
$919$	−0.146992	−	0.452394i	−0.00484881	−	0.0149231i	−0.953452	+	0.301546i	$0.902497\pi$
$920$	31.1609	+	42.7622i	1.02734	+	1.40983i
$921$		0			0
$922$	−42.8577	−	13.9253i	−1.41144	−	0.458605i
$923$			3.73870i			0.123061i
$924$		0			0
$925$	22.8038	−	31.5737i	0.749783	−	1.03814i
$926$	22.7438	−	69.9981i	0.747406	−	2.30028i
$927$		0			0
$928$	−0.464550	+	0.639398i	−0.0152496	+	0.0209893i
$929$	6.74237	+	20.7509i	0.221210	+	0.680814i	0.998654	+	0.0518624i	$0.0165157\pi$
$929$	6.74237	+	20.7509i	0.221210	+	0.680814i	−0.777444	+	0.628952i	$0.783484\pi$
$930$		0			0
$931$	0.517405	+	0.375917i	0.0169573	+	0.0123202i
$932$	24.7948	+	34.1272i	0.812182	+	1.11787i
$933$		0			0
$934$	−22.6030			−0.739594
$935$	9.74721	−	4.52329i	0.318768	−	0.147927i
$936$		0			0
$937$	29.4622	+	9.57286i	0.962490	+	0.312732i	0.747780	−	0.663946i	$-0.231120\pi$
$937$	29.4622	+	9.57286i	0.962490	+	0.312732i	0.214709	+	0.976678i	$0.431120\pi$
$938$	−3.19448	−	4.39682i	−0.104303	−	0.143561i
$939$		0			0
$940$	−68.9945	+	0.0973954i	−2.25035	+	0.00317669i
$941$	−10.1651	−	31.2848i	−0.331372	−	1.01986i	−0.968482	−	0.249084i	$-0.919870\pi$
$941$	−10.1651	−	31.2848i	−0.331372	−	1.01986i	0.637110	−	0.770773i	$-0.280130\pi$
$942$		0			0
$943$	24.4070	+	33.5933i	0.794800	+	1.09395i
$944$	10.7826	−	33.1855i	0.350944	−	1.08010i
$945$		0			0
$946$	64.7582	+	12.8069i	2.10547	+	0.416388i
$947$			13.1245i			0.426490i	0.976999	+	0.213245i	$0.0684033\pi$
$947$			13.1245i			0.426490i	−0.976999	+	0.213245i	$0.931597\pi$
$948$		0			0
$949$	31.4070	−	22.8185i	1.01951	−	0.740720i
$950$	1.08142	−	0.354755i	0.0350860	−	0.0115098i
$951$		0			0
$952$	−2.36733	+	0.769193i	−0.0767257	+	0.0249297i
$953$	17.5844	−	24.2028i	0.569614	−	0.784007i	−0.422895	−	0.906179i	$-0.638986\pi$
$953$	17.5844	−	24.2028i	0.569614	−	0.784007i	0.992509	+	0.122172i	$0.0389860\pi$
$954$		0			0
$955$	−21.7648	+	30.0458i	−0.704292	+	0.972258i
$956$	−77.6759			−2.51222
$957$		0			0
$958$			52.1502i			1.68489i
$959$	−0.549928	+	1.69250i	−0.0177581	+	0.0546538i
$960$		0			0
$961$	12.5705	+	9.13298i	0.405499	+	0.294612i
$962$	66.8412	−	21.7180i	2.15505	−	0.700218i
$963$		0			0
$964$	−53.1945	−	38.6481i	−1.71328	−	1.24477i
$965$	−0.423175	−	1.29617i	−0.0136225	−	0.0417252i
$966$		0			0
$967$		−	48.8957i		−	1.57238i	−0.617986	−	0.786189i	$-0.712051\pi$
$967$		−	48.8957i		−	1.57238i	0.617986	−	0.786189i	$-0.287949\pi$
$968$	40.7650	+	34.6612i	1.31024	+	1.11405i
$969$		0			0
$970$	53.6612	−	74.0780i	1.72296	−	2.37850i
$971$	24.0664	−	17.4853i	0.772329	−	0.561130i	−0.130338	−	0.991470i	$-0.541606\pi$
$971$	24.0664	−	17.4853i	0.772329	−	0.561130i	0.902667	+	0.430340i	$0.141606\pi$
$972$		0			0
$973$	3.55474	−	1.15500i	0.113960	−	0.0370277i
$974$	−7.60188	−	23.3962i	−0.243580	−	0.749662i
$975$		0			0
$976$	−31.6885	+	23.0230i	−1.01432	+	0.736950i
$977$	37.3087	+	12.1223i	1.19361	+	0.387828i	0.837407	−	0.546579i	$-0.184070\pi$
$977$	37.3087	+	12.1223i	1.19361	+	0.387828i	0.356205	+	0.934408i	$0.384070\pi$
$978$		0			0
$979$	1.39357	+	11.6639i	0.0445386	+	0.372779i
$980$	−58.3344	−	18.8630i	−1.86342	−	0.602556i
$981$		0			0
$982$	−58.4784	−	80.4886i	−1.86612	−	2.56849i
$983$	3.33715	−	4.59319i	0.106439	−	0.146500i	−0.752475	−	0.658621i	$-0.771140\pi$
$983$	3.33715	−	4.59319i	0.106439	−	0.146500i	0.858913	+	0.512121i	$0.171140\pi$
$984$		0			0
$985$	18.2352	−	0.0257415i	0.581020	−	0.000820191i
$986$	−19.1991	−	13.9490i	−0.611424	−	0.444226i
$987$		0			0
$988$	1.30084	+	0.422669i	0.0413852	+	0.0134469i
$989$	39.5661			1.25813
$990$		0			0
$991$	−52.6305			−1.67186			−0.835932	−	0.548833i	$-0.815072\pi$
$991$	−52.6305			−1.67186			−0.835932	+	0.548833i	$0.815072\pi$
$992$	−0.441588	−	0.143481i	−0.0140204	−	0.00455551i
$993$		0			0
$994$	−0.708919	−	0.515060i	−0.0224855	−	0.0163367i
$995$	−0.00894168	−	6.33425i	−0.000283470	−	0.200809i
$996$		0			0
$997$	16.8557	−	23.1999i	0.533826	−	0.734749i	−0.453881	−	0.891062i	$-0.649961\pi$
$997$	16.8557	−	23.1999i	0.533826	−	0.734749i	0.987708	+	0.156313i	$0.0499610\pi$
$998$	25.8240	+	35.5437i	0.817444	+	1.12511i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.ba.b.64.2	yes	48
3.2	odd	2	inner	495.2.ba.b.64.11	yes	48
5.4	even	2	inner	495.2.ba.b.64.12	yes	48
11.5	even	5	inner	495.2.ba.b.379.12	yes	48
15.14	odd	2	inner	495.2.ba.b.64.1	✓	48
33.5	odd	10	inner	495.2.ba.b.379.1	yes	48
55.49	even	10	inner	495.2.ba.b.379.2	yes	48
165.104	odd	10	inner	495.2.ba.b.379.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.ba.b.64.1	✓	48	15.14	odd	2	inner
495.2.ba.b.64.2	yes	48	1.1	even	1	trivial
495.2.ba.b.64.11	yes	48	3.2	odd	2	inner
495.2.ba.b.64.12	yes	48	5.4	even	2	inner
495.2.ba.b.379.1	yes	48	33.5	odd	10	inner
495.2.ba.b.379.2	yes	48	55.49	even	10	inner
495.2.ba.b.379.11	yes	48	165.104	odd	10	inner
495.2.ba.b.379.12	yes	48	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32725 - 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(0.00315652 + 2.23607i) q^{5} +(0.207582 - 0.285712i) q^{7} +(-2.85924 - 3.93540i) q^{8} +O(q^{10})\)	\(q+(-2.32725 - 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(0.00315652 + 2.23607i) q^{5} +(0.207582 - 0.285712i) q^{7} +(-2.85924 - 3.93540i) q^{8} +(1.68350 - 5.20628i) q^{10} +(-0.393463 - 3.29320i) q^{11} +(3.50669 + 1.13939i) q^{13} +(-0.699143 + 0.507957i) q^{14} +(1.21368 + 3.73532i) q^{16} +(1.37802 - 0.447747i) q^{17} +(0.0752559 - 0.0546766i) q^{19} +(-5.23122 + 7.22157i) q^{20} +(-1.57453 + 7.96164i) q^{22} +4.86443i q^{23} +(-4.99998 + 0.0141164i) q^{25} +(-7.29937 - 5.30330i) q^{26} +(1.33944 - 0.435209i) q^{28} +(5.41495 + 3.93419i) q^{29} +(-1.21511 + 3.73973i) q^{31} +0.118080i q^{32} -3.54558 q^{34} +(0.639527 + 0.463265i) q^{35} +(-4.57856 + 6.30185i) q^{37} +(-0.216484 + 0.0703400i) q^{38} +(8.79080 - 6.40587i) q^{40} +(6.90591 - 5.01744i) q^{41} -8.13377i q^{43} +(6.44994 - 11.5471i) q^{44} +(3.67834 - 11.3208i) q^{46} +(4.54783 + 6.25956i) q^{47} +(2.12458 + 6.53878i) q^{49} +(11.6469 + 3.74798i) q^{50} +(8.64278 + 11.8958i) q^{52} +(12.6118 + 4.09781i) q^{53} +(7.36258 - 0.890205i) q^{55} -1.71792 q^{56} +(-9.62703 - 13.2505i) q^{58} +(-7.18751 - 5.22203i) q^{59} +(3.08181 + 9.48482i) q^{61} +(5.65574 - 7.78446i) q^{62} +(2.51664 - 7.74544i) q^{64} +(-2.53669 + 7.84478i) q^{65} +6.28888i q^{67} +(5.49541 + 1.78557i) q^{68} +(-1.13803 - 1.56173i) q^{70} +(0.313338 + 0.964354i) q^{71} +(6.18866 - 8.51796i) q^{73} +(15.4207 - 11.2038i) q^{74} +0.370960 q^{76} +(-1.02258 - 0.571193i) q^{77} +(-0.386590 + 1.18980i) q^{79} +(-8.34858 + 2.72565i) q^{80} +(-19.8658 + 6.45480i) q^{82} +(-11.4650 + 3.72521i) q^{83} +(1.00554 + 3.07993i) q^{85} +(-6.15052 + 18.9293i) q^{86} +(-11.8351 + 10.9645i) q^{88} -3.54180 q^{89} +(1.05346 - 0.765386i) q^{91} +(-11.4024 + 15.6940i) q^{92} +(-5.85067 - 18.0065i) q^{94} +(0.122498 + 0.168104i) q^{95} +(15.8990 + 5.16591i) q^{97} -16.8239i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4}+O(q^{10}) \) 48 * q + 12 * q^4	\( 48 q + 12 q^{4} - 12 q^{10} - 28 q^{16} + 22 q^{25} - 20 q^{31} + 40 q^{34} + 52 q^{40} - 52 q^{46} + 44 q^{49} + 60 q^{55} + 16 q^{61} - 64 q^{64} - 74 q^{70} + 152 q^{76} + 28 q^{79} - 38 q^{85} + 40 q^{91} - 64 q^{94}+O(q^{100}) \) 48 * q + 12 * q^4 - 12 * q^10 - 28 * q^16 + 22 * q^25 - 20 * q^31 + 40 * q^34 + 52 * q^40 - 52 * q^46 + 44 * q^49 + 60 * q^55 + 16 * q^61 - 64 * q^64 - 74 * q^70 + 152 * q^76 + 28 * q^79 - 38 * q^85 + 40 * q^91 - 64 * q^94

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