LMFDB - Embedded newform 495.2.ba.b.64.12

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			64.12
Character	$\chi$	$=$	495.64
Dual form			495.2.ba.b.379.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.32725 + 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(1.31177 + 1.81087i) q^{5} +(-0.207582 + 0.285712i) q^{7} +(2.85924 + 3.93540i) q^{8} +O(q^{10})$	\(q+(2.32725 + 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(1.31177 + 1.81087i) q^{5} +(-0.207582 + 0.285712i) q^{7} +(2.85924 + 3.93540i) q^{8} +(1.68350 + 5.20628i) q^{10} +(-0.393463 - 3.29320i) q^{11} +(-3.50669 - 1.13939i) q^{13} +(-0.699143 + 0.507957i) q^{14} +(1.21368 + 3.73532i) q^{16} +(-1.37802 + 0.447747i) q^{17} +(0.0752559 - 0.0546766i) q^{19} +(-0.0125879 + 8.91721i) q^{20} +(1.57453 - 7.96164i) q^{22} -4.86443i q^{23} +(-1.55850 + 4.75090i) q^{25} +(-7.29937 - 5.30330i) q^{26} +(-1.33944 + 0.435209i) q^{28} +(5.41495 + 3.93419i) q^{29} +(-1.21511 + 3.73973i) q^{31} -0.118080i q^{32} -3.54558 q^{34} +(-0.789688 - 0.00111475i) q^{35} +(4.57856 - 6.30185i) q^{37} +(0.216484 - 0.0703400i) q^{38} +(-3.37584 + 10.3401i) q^{40} +(6.90591 - 5.01744i) q^{41} +8.13377i q^{43} +(6.44994 - 11.5471i) q^{44} +(3.67834 - 11.3208i) q^{46} +(-4.54783 - 6.25956i) q^{47} +(2.12458 + 6.53878i) q^{49} +(-7.21952 + 9.87805i) q^{50} +(-8.64278 - 11.8958i) q^{52} +(-12.6118 - 4.09781i) q^{53} +(5.44743 - 5.03245i) q^{55} -1.71792 q^{56} +(9.62703 + 13.2505i) q^{58} +(-7.18751 - 5.22203i) q^{59} +(3.08181 + 9.48482i) q^{61} +(-5.65574 + 7.78446i) q^{62} +(2.51664 - 7.74544i) q^{64} +(-2.53669 - 7.84478i) q^{65} -6.28888i q^{67} +(-5.49541 - 1.78557i) q^{68} +(-1.83696 - 0.599733i) q^{70} +(0.313338 + 0.964354i) q^{71} +(-6.18866 + 8.51796i) q^{73} +(15.4207 - 11.2038i) q^{74} +0.370960 q^{76} +(1.02258 + 0.571193i) q^{77} +(-0.386590 + 1.18980i) q^{79} +(-5.17211 + 7.09770i) q^{80} +(19.8658 - 6.45480i) q^{82} +(11.4650 - 3.72521i) q^{83} +(-2.61846 - 1.90808i) q^{85} +(-6.15052 + 18.9293i) q^{86} +(11.8351 - 10.9645i) q^{88} -3.54180 q^{89} +(1.05346 - 0.765386i) q^{91} +(11.4024 - 15.6940i) q^{92} +(-5.85067 - 18.0065i) q^{94} +(0.197731 + 0.0645554i) q^{95} +(-15.8990 - 5.16591i) q^{97} +16.8239i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.977783	−	0.209618i	$-0.0672220\pi$
$2$	2.32725	+	0.756170i	1.64562	+	0.534693i	0.667833	+	0.744311i	$0.267222\pi$
$3$		0			0
$3$		0			0
$4$	3.22628	+	2.34403i	1.61314	+	1.17201i
$5$	1.31177	+	1.81087i	0.586643	+	0.809846i
$5$	1.31177	+	1.81087i	0.586643	+	0.809846i
$6$		0			0
$7$	−0.207582	+	0.285712i	−0.0784586	+	0.107989i	−0.846442	−	0.532480i	$-0.821260\pi$
$7$	−0.207582	+	0.285712i	−0.0784586	+	0.107989i	0.767984	+	0.640469i	$0.221260\pi$
$8$	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	−0.220723	−	0.975337i	$-0.570842\pi$
$13$	−3.50669	−	1.13939i	−0.972580	−	0.316010i	−0.751857	+	0.659326i	$0.770842\pi$
$14$	−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	−0.471319	−	0.881963i	$-0.656222\pi$
$17$	−1.37802	+	0.447747i	−0.334219	+	0.108594i	0.137100	+	0.990557i	$0.456222\pi$
$18$		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	$0.296603\pi$
$20$	−0.0125879	+	8.91721i	−0.00281473	+	1.99395i
$21$		0			0
$22$	1.57453	−	7.96164i	0.335692	−	1.69743i
$23$		−	4.86443i		−	1.01430i	−0.861857	−	0.507152i	$-0.830698\pi$
$23$		−	4.86443i		−	1.01430i	0.861857	−	0.507152i	$-0.169302\pi$
$24$		0			0
$25$	−1.55850	+	4.75090i	−0.311701	+	0.950180i
$26$	−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
$35$	−0.789688	−	0.00111475i	−0.133482	−	0.000188428i
$36$		0			0
$37$	4.57856	−	6.30185i	0.752711	−	1.03602i	−0.245075	−	0.969504i	$-0.578813\pi$
$37$	4.57856	−	6.30185i	0.752711	−	1.03602i	0.997786	−	0.0665132i	$-0.0211875\pi$
$38$	0.216484	−	0.0703400i	0.0351184	−	0.0114107i
$39$		0			0
$40$	−3.37584	+	10.3401i	−0.533767	+	1.63491i
$41$	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	$0.212946\pi$
$43$			8.13377i			1.24039i	−0.784448	+	0.620194i	$0.787054\pi$
$44$	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	0.336217	−	0.941784i	$-0.390852\pi$
$47$	−4.54783	−	6.25956i	−0.663370	−	0.913050i	−0.999587	+	0.0287344i	$0.990852\pi$
$48$		0			0
$49$	2.12458	+	6.53878i	0.303511	+	0.934111i
$50$	−7.21952	+	9.87805i	−1.02099	+	1.39697i
$51$		0			0
$52$	−8.64278	−	11.8958i	−1.19854	−	1.64965i
$53$	−12.6118	−	4.09781i	−1.73236	−	0.562878i	−0.738573	−	0.674173i	$-0.764500\pi$
$53$	−12.6118	−	4.09781i	−1.73236	−	0.562878i	−0.993787	+	0.111295i	$0.964500\pi$
$54$		0			0
$55$	5.44743	−	5.03245i	0.734531	−	0.678575i
$56$	−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	$-0.874493\pi$
$67$		−	6.28888i		−	0.768309i	0.923269	−	0.384154i	$-0.125507\pi$
$68$	−5.49541	−	1.78557i	−0.666417	−	0.216532i
$69$		0			0
$70$	−1.83696	−	0.599733i	−0.219559	−	0.0716818i
$71$	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	$0.411308\pi$
$73$	−6.18866	+	8.51796i	−0.724328	+	0.996952i	−0.999369	+	0.0355192i	$0.988692\pi$
$74$	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	$0.122420\pi$
$80$	−5.17211	+	7.09770i	−0.578259	+	0.793547i
$81$		0			0
$82$	19.8658	−	6.45480i	2.19381	−	0.712814i
$83$	11.4650	−	3.72521i	1.25845	−	0.408894i	0.397507	−	0.917599i	$-0.369876\pi$
$83$	11.4650	−	3.72521i	1.25845	−	0.408894i	0.860941	+	0.508705i	$0.169876\pi$
$84$		0			0
$85$	−2.61846	−	1.90808i	−0.284012	−	0.206960i
$86$	−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
$95$	0.197731	+	0.0645554i	0.0202868	+	0.00662324i
$96$		0			0
$97$	−15.8990	−	5.16591i	−1.61430	−	0.524519i	−0.643715	−	0.765265i	$-0.722608\pi$
$97$	−15.8990	−	5.16591i	−1.61430	−	0.524519i	−0.970588	+	0.240746i	$0.922608\pi$
$98$			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	−0.996057	−	0.0887109i	$-0.971725\pi$
$103$	−6.12881	+	8.43558i	−0.603890	+	0.831183i	0.392168	+	0.919894i	$0.371725\pi$
$104$	−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	0.716789	−	0.697290i	$-0.245611\pi$
$107$	−1.73649	−	2.39007i	−0.167873	−	0.231057i	−0.884662	+	0.466233i	$0.845611\pi$
$108$		0			0
$109$	−6.40314			−0.613310			−0.306655	−	0.951821i	$-0.599210\pi$
$109$	−6.40314			−0.613310			−0.306655	+	0.951821i	$0.599210\pi$
$110$	16.4829	−	7.59259i	1.57159	−	0.723925i
$111$		0			0
$112$	−1.31916	−	0.428622i	−0.124649	−	0.0405010i
$113$	7.20636	+	9.91870i	0.677917	+	0.933073i	0.999907	−	0.0136701i	$-0.00435146\pi$
$113$	7.20636	+	9.91870i	0.677917	+	0.933073i	−0.321989	+	0.946743i	$0.604351\pi$
$114$		0			0
$115$	8.80885	−	6.38102i	0.821429	−	0.595034i
$116$	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
$125$	−10.6477	+	3.40985i	−0.952357	+	0.304987i
$126$		0			0
$127$	13.6172	−	4.42450i	1.20833	−	0.392610i	0.365511	−	0.930807i	$-0.380894\pi$
$127$	13.6172	−	4.42450i	1.20833	−	0.392610i	0.842819	+	0.538196i	$0.180894\pi$
$128$	11.5749	−	15.9315i	1.02309	−	1.40816i
$129$		0			0
$130$	0.0284797	−	20.1750i	0.00249784	−	1.76946i
$131$	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	−0.0970490	−	0.995280i	$-0.530940\pi$
$137$	4.79246	−	1.55716i	0.409447	−	0.133038i	0.506496	+	0.862242i	$0.330940\pi$
$138$		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	$0.551837\pi$
$140$	−2.54514	−	1.85465i	−0.215104	−	0.156746i
$141$		0			0
$142$			2.48123i			0.208220i
$143$	−2.37250	+	11.9965i	−0.198398	+	1.00320i
$144$		0			0
$145$	−0.0211273	+	14.9665i	−0.00175453	+	1.24290i
$146$	−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	$0.0382601\pi$
$157$	10.0244	+	13.7975i	0.800037	+	1.10116i	−0.192748	+	0.981248i	$0.561740\pi$
$158$	−1.79939	+	2.47664i	−0.143152	+	0.197031i
$159$		0			0
$160$	0.213828	−	0.154894i	0.0169046	−	0.0122455i
$161$	1.38983	+	1.00977i	0.109534	+	0.0795809i
$162$		0			0
$163$	−23.8832	−	7.76012i	−1.87067	−	0.607819i	−0.991288	−	0.131711i	$-0.957953\pi$
$163$	−23.8832	−	7.76012i	−1.87067	−	0.607819i	−0.879387	−	0.476108i	$-0.842047\pi$
$164$	34.0414			2.65819
$165$		0			0
$166$	29.4989			2.28956
$167$	16.7906	+	5.45561i	1.29930	+	0.422168i	0.875338	−	0.483512i	$-0.160639\pi$
$167$	16.7906	+	5.45561i	1.29930	+	0.422168i	0.423962	+	0.905680i	$0.360639\pi$
$168$		0			0
$169$	0.481418	+	0.349771i	0.0370322	+	0.0269055i
$170$	−4.65099	−	6.42058i	−0.356715	−	0.492436i
$171$		0			0
$172$	−19.0658	+	26.2418i	−1.45375	+	2.00092i
$173$	1.39226	+	1.91628i	0.105851	+	0.145692i	0.858656	−	0.512552i	$-0.171300\pi$
$173$	1.39226	+	1.91628i	0.105851	+	0.145692i	−0.752805	+	0.658244i	$0.771300\pi$
$174$		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
$185$	17.4179	+	0.0245877i	1.28059	+	0.00180773i
$186$		0			0
$187$	2.01672	+	4.36193i	0.147477	+	0.318976i
$188$		−	30.8553i		−	2.25036i
$189$		0			0
$190$	0.411355	+	0.299755i	0.0298428	+	0.0217465i
$191$	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	−0.288070	−	0.957609i	$-0.593014\pi$
$193$	0.579932	−	0.188431i	0.0417444	−	0.0135636i	0.329815	+	0.944046i	$0.393014\pi$
$194$	−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	$0.0938251\pi$
$197$			8.15502i			0.581021i	−0.956872	+	0.290510i	$0.906175\pi$
$198$		0			0
$199$	−2.83277			−0.200809			−0.100405	−	0.994947i	$-0.532014\pi$
$199$	−2.83277			−0.200809			−0.100405	+	0.994947i	$0.532014\pi$
$200$	−23.1529	+	7.45062i	−1.63715	+	0.526838i
$201$		0			0
$202$	−12.3464	+	16.9934i	−0.868693	+	1.19565i
$203$	−2.24809	+	0.730449i	−0.157785	+	0.0512675i
$204$		0			0
$205$	18.1449	+	5.92397i	1.26730	+	0.413748i
$206$	−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
$215$	−14.7292	+	10.6697i	−1.00452	+	0.727665i
$216$		0			0
$217$	−0.816250	−	1.12347i	−0.0554107	−	0.0762662i
$218$	−14.9017	−	4.84187i	−1.00927	−	0.327933i
$219$		0			0
$220$	29.3711	−	3.46714i	1.98020	−	0.233754i
$221$	5.34245			0.359372
$222$		0			0
$223$	8.61250	+	11.8541i	0.576735	+	0.793808i	0.993333	−	0.115283i	$-0.0367775\pi$
$223$	8.61250	+	11.8541i	0.576735	+	0.793808i	−0.416597	+	0.909091i	$0.636777\pi$
$224$	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	$0.429570\pi$
$227$	−11.6950	+	16.0968i	−0.776227	+	1.06839i	−0.995688	+	0.0927640i	$0.970430\pi$
$228$		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	−0.0396566	−	0.999213i	$-0.512626\pi$
$233$	−10.0602	−	3.26874i	−0.659062	−	0.214142i	−0.619406	+	0.785071i	$0.712626\pi$
$234$		0			0
$235$	5.36952	−	16.4467i	0.350269	−	1.07286i
$236$	−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
$245$	−9.05392	+	12.4247i	−0.578434	+	0.793787i
$246$		0			0
$247$	−0.326197	+	0.105988i	−0.0207554	+	0.00674384i
$248$	−18.1916	+	5.91082i	−1.15517	+	0.375337i
$249$		0			0
$250$	−27.3583	−	0.115861i	−1.73029	−	0.00732766i
$251$	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	−0.755362	−	0.655307i	$-0.772539\pi$
$257$	1.62383	−	2.23501i	0.101292	−	0.139416i	0.856654	+	0.515891i	$0.172539\pi$
$258$		0			0
$259$	0.850088	+	2.61630i	0.0528219	+	0.162569i
$260$	10.2043	−	31.2555i	0.632846	−	1.93838i
$261$		0			0
$262$	15.1580	+	4.92514i	0.936466	+	0.304276i
$263$			7.70220i			0.474938i	0.971395	+	0.237469i	$0.0763178\pi$
$263$			7.70220i			0.474938i	−0.971395	+	0.237469i	$0.923682\pi$
$264$		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
$275$	16.2589	+	3.26317i	0.980448	+	0.196776i
$276$		0			0
$277$	−7.67008	−	2.49216i	−0.460851	−	0.149739i	0.0693847	−	0.997590i	$-0.477896\pi$
$277$	−7.67008	−	2.49216i	−0.460851	−	0.149739i	−0.530235	+	0.847851i	$0.677896\pi$
$278$	15.2225	+	20.9520i	0.912984	+	1.25662i
$279$		0			0
$280$	−2.25352	−	3.11093i	−0.134674	−	0.185914i
$281$	−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	$0.0203457\pi$
$283$	12.6223	+	17.3732i	0.750320	+	1.03273i	−0.247638	+	0.968853i	$0.579654\pi$
$284$	−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
$290$	−11.3664	+	34.8149i	−0.667459	+	2.04440i
$291$		0			0
$292$	−39.9327	+	12.9749i	−2.33688	+	0.759299i
$293$	8.97706	−	12.3559i	0.524445	−	0.721837i	−0.461826	−	0.886971i	$-0.652806\pi$
$293$	8.97706	−	12.3559i	0.524445	−	0.721837i	0.986271	+	0.165134i	$0.0528055\pi$
$294$		0			0
$295$	0.0280433	−	19.8658i	0.00163274	−	1.15663i
$296$	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
$305$	−13.1332	+	18.0227i	−0.752003	+	1.03198i
$306$		0			0
$307$			27.5348i			1.57150i	0.618547	+	0.785748i	$0.287722\pi$
$307$			27.5348i			1.57150i	−0.618547	+	0.785748i	$0.712278\pi$
$308$	1.96025	+	4.23979i	0.111696	+	0.241585i
$309$		0			0
$310$	−21.5157	−	0.0303724i	−1.22201	−	0.00172504i
$311$	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	−0.805025	−	0.593241i	$-0.797848\pi$
$313$	−19.5956	+	6.36698i	−1.10761	+	0.359883i	−0.302581	+	0.953124i	$0.597848\pi$
$314$	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	0.630860	−	0.775896i	$-0.282702\pi$
$317$	12.1992	+	3.96377i	0.685177	+	0.222627i	0.0543164	+	0.998524i	$0.482702\pi$
$318$		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
$325$	10.8783	−	14.8842i	0.603421	−	0.825626i
$326$	−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
$335$	11.3883	−	8.24958i	0.622212	−	0.450723i
$336$		0			0
$337$	9.22285	−	12.6942i	0.502400	−	0.691495i	−0.480214	−	0.877151i	$-0.659441\pi$
$337$	9.22285	−	12.6942i	0.502400	−	0.691495i	0.982615	+	0.185656i	$0.0594411\pi$
$338$	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	−0.104147	−	0.994562i	$-0.533211\pi$
$347$	7.38011	−	2.39794i	0.396185	−	0.128728i	0.500332	+	0.865834i	$0.333211\pi$
$348$		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	$0.270149\pi$
$350$	−1.32364	−	4.11321i	−0.0707514	−	0.219860i
$351$		0			0
$352$	−0.388862	+	0.0464602i	−0.0207264	+	0.00247634i
$353$			9.57594i			0.509676i	0.966984	+	0.254838i	$0.0820221\pi$
$353$			9.57594i			0.509676i	−0.966984	+	0.254838i	$0.917978\pi$
$354$		0			0
$355$	−1.33529	+	1.83243i	−0.0708700	+	0.0972552i
$356$	−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
$365$	−23.5430	−	0.0332343i	−1.23230	−	0.00173956i
$366$		0			0
$367$	6.32793	−	8.70965i	0.330315	−	0.454640i	−0.611266	−	0.791425i	$-0.709340\pi$
$367$	6.32793	−	8.70965i	0.330315	−	0.454640i	0.941582	+	0.336785i	$0.109340\pi$
$368$	18.1702	−	5.90385i	0.947186	−	0.307759i
$369$		0			0
$370$	40.5172	+	13.2281i	2.10639	+	0.687696i
$371$	3.78877	−	2.75271i	0.196703	−	0.142913i
$372$		0			0
$373$			21.2460i			1.10007i	0.835140	+	0.550037i	$0.185386\pi$
$373$			21.2460i			1.10007i	−0.835140	+	0.550037i	$0.814614\pi$
$374$	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	$-0.398609\pi$
$380$	0.486615	+	0.671760i	0.0249628	+	0.0344606i
$381$		0			0
$382$	23.8645	+	32.8466i	1.22101	+	1.68058i
$383$	19.2570	+	6.25699i	0.983988	+	0.319717i	0.756449	−	0.654052i	$-0.226932\pi$
$383$	19.2570	+	6.25699i	0.983988	+	0.319717i	0.227538	+	0.973769i	$0.426932\pi$
$384$		0			0
$385$	0.307042	+	2.60104i	0.0156483	+	0.132561i
$386$	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	$-0.950324\pi$
$397$		−	6.19375i		−	0.310855i	0.987847	−	0.155428i	$-0.0496755\pi$
$398$	−6.59256	−	2.14205i	−0.330455	−	0.107371i
$399$		0			0
$400$	−19.6376	−	0.0554426i	−0.981882	−	0.00277213i
$401$	−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	$0.197871\pi$
$410$	37.7483	+	27.5072i	1.86425	+	1.35848i
$411$		0			0
$412$	−39.5465	+	12.8494i	−1.94832	+	0.633046i
$413$	2.98400	−	0.969559i	0.146833	−	0.0477089i
$414$		0			0
$415$	21.7853	+	15.8750i	1.06940	+	0.779274i
$416$	−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
$425$	0.0204537	−	7.24466i	0.000992152	−	0.351418i
$426$		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	−0.624950	−	0.780665i	$-0.714881\pi$
$433$	6.46373	−	8.89656i	0.310627	−	0.427541i	0.935577	+	0.353124i	$0.114881\pi$
$434$	−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	$0.411064\pi$
$440$	35.3802	+	7.04888i	1.68669	+	0.336042i
$441$		0			0
$442$	12.4332	+	4.03980i	0.591389	+	0.192154i
$443$	−7.55649	−	10.4006i	−0.359020	−	0.494148i	0.590856	−	0.806777i	$-0.298790\pi$
$443$	−7.55649	−	10.4006i	−0.359020	−	0.494148i	−0.949875	+	0.312629i	$0.898790\pi$
$444$		0			0
$445$	−4.64603	−	6.41374i	−0.220243	−	0.304040i
$446$	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
$455$	2.76792	+	0.903673i	0.129762	+	0.0423649i
$456$		0			0
$457$	34.8940	−	11.3378i	1.63227	−	0.530358i	0.657481	−	0.753471i	$-0.271622\pi$
$457$	34.8940	−	11.3378i	1.63227	−	0.530358i	0.974792	+	0.223114i	$0.0716221\pi$
$458$	6.60582	−	9.09213i	0.308670	−	0.424847i
$459$		0			0
$460$	43.3771	+	0.0612328i	2.02247	+	0.00285499i
$461$	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	$-0.753668\pi$
$463$		−	30.0776i		−	1.39782i	0.715208	−	0.698911i	$-0.246332\pi$
$464$	−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	−0.505135	−	0.863040i	$-0.668557\pi$
$467$	−8.78488	+	2.85438i	−0.406516	+	0.132085i	0.0986193	+	0.995125i	$0.468557\pi$
$468$		0			0
$469$	1.79681	+	1.30546i	0.0829689	+	0.0602805i
$470$	24.9327	−	34.2152i	1.15006	−	1.57823i
$471$		0			0
$472$		−	43.2168i		−	1.98921i
$473$	26.7862	−	3.20034i	1.23163	−	0.147152i
$474$		0			0
$475$	0.142477	+	0.442747i	0.00653727	+	0.0203146i
$476$	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	0.653868	−	0.756609i	$-0.273145\pi$
$487$	−5.90908	−	8.13315i	−0.267766	−	0.368548i	−0.921634	+	0.388060i	$0.873145\pi$
$488$	−28.5150	+	39.2475i	−1.29081	+	1.77665i
$489$		0			0
$490$	−30.4660	+	22.0692i	−1.37631	+	0.996984i
$491$	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	$0.831640\pi$
$500$	−42.3451	−	13.9573i	−1.89373	−	0.624190i
$501$		0			0
$502$	33.8550	−	46.5974i	1.51102	−	2.07975i
$503$	−23.2443	−	31.9931i	−1.03641	−	1.42650i	−0.900021	−	0.435846i	$-0.856449\pi$
$503$	−23.2443	−	31.9931i	−1.03641	−	1.42650i	−0.136393	−	0.990655i	$-0.543551\pi$
$504$		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
$515$	−23.3154	−	0.0329129i	−1.02740	−	0.00145031i
$516$		0			0
$517$	−18.8246	+	17.4398i	−0.827904	+	0.767003i
$518$			6.73161i			0.295770i
$519$		0			0
$520$	23.6194	−	32.4130i	1.03578	−	1.42140i
$521$	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	−0.0976509	−	0.995221i	$-0.531133\pi$
$523$	9.33804	−	3.03411i	0.408324	−	0.132672i	0.505975	+	0.862548i	$0.331133\pi$
$524$	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
$530$	0.102427	−	72.5591i	0.00444915	−	3.15177i
$531$		0			0
$532$	−0.0770046	+	0.105988i	−0.00333857	+	0.00459515i
$533$	−29.9337	+	9.72605i	−1.29657	+	0.421282i
$534$		0			0
$535$	2.05023	−	6.27978i	0.0886392	−	0.271499i
$536$	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
$545$	−8.39947	−	11.5953i	−0.359794	−	0.496686i
$546$		0			0
$547$	−4.36898	−	6.01339i	−0.186804	−	0.257114i	0.705335	−	0.708874i	$-0.250796\pi$
$547$	−4.36898	−	6.01339i	−0.186804	−	0.257114i	−0.892140	+	0.451760i	$0.850796\pi$
$548$	19.1118	+	6.20981i	0.816418	+	0.265270i
$549$		0			0
$550$	35.3711	+	19.8887i	1.50823	+	0.848057i
$551$	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	−0.999728	−	0.0233046i	$-0.992581\pi$
$557$	−15.7803	+	21.7197i	−0.668631	+	0.920292i	0.331097	+	0.943597i	$0.392581\pi$
$558$		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	−0.440896	−	0.897558i	$-0.645339\pi$
$563$	−31.4429	−	10.2164i	−1.32516	−	0.430571i	−0.884264	+	0.466987i	$0.845339\pi$
$564$		0			0
$565$	−8.50838	+	26.0609i	−0.357950	+	1.09639i
$566$	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
$575$	23.1104	+	7.58123i	0.963771	+	0.316159i
$576$		0			0
$577$	−16.6186	+	5.39972i	−0.691843	+	0.224793i	−0.633773	−	0.773519i	$-0.718495\pi$
$577$	−16.6186	+	5.39972i	−0.691843	+	0.224793i	−0.0580698	+	0.998313i	$0.518495\pi$
$578$	−34.6774	+	11.2674i	−1.44239	+	0.468661i
$579$		0			0
$580$	−35.1501	+	48.2367i	−1.45953	+	2.00292i
$581$	−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	$-0.493881\pi$
$587$	23.3598	−	32.1520i	0.964163	−	1.32706i	0.944941	−	0.327241i	$-0.106119\pi$
$588$		0			0
$589$	0.113031	+	0.347874i	0.00465737	+	0.0143339i
$590$	15.0872	−	46.2114i	0.621129	−	1.90250i
$591$		0			0
$592$	29.0963	+	9.45396i	1.19585	+	0.388555i
$593$		−	20.8206i		−	0.854999i	−0.904016	−	0.427499i	$-0.859395\pi$
$593$		−	20.8206i		−	0.854999i	0.904016	−	0.427499i	$-0.140605\pi$
$594$		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
$605$	−18.7162	−	15.9594i	−0.760923	−	0.648842i
$606$		0			0
$607$	13.6824	+	4.44568i	0.555352	+	0.180445i	0.573229	−	0.819396i	$-0.305691\pi$
$607$	13.6824	+	4.44568i	0.555352	+	0.180445i	−0.0178769	+	0.999840i	$0.505691\pi$
$608$	−0.00645623	−	0.00888623i	−0.000261835	−	0.000360384i
$609$		0			0
$610$	−44.1924	+	32.0124i	−1.78930	+	1.29615i
$611$	8.81574	+	27.1321i	0.356647	+	1.09765i
$612$		0			0
$613$	6.12249	+	8.42689i	0.247285	+	0.340359i	0.914558	−	0.404454i	$-0.132539\pi$
$613$	6.12249	+	8.42689i	0.247285	+	0.340359i	−0.667273	+	0.744813i	$0.732539\pi$
$614$	−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	$-0.931402\pi$
$617$		−	10.6235i		−	0.427685i	0.976868	−	0.213842i	$-0.0685979\pi$
$618$		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	$0.261707\pi$
$620$	−33.3326	−	10.8825i	−1.33867	−	0.437050i
$621$		0			0
$622$	2.47820	−	0.805215i	0.0993666	−	0.0322862i
$623$	0.735214	−	1.01193i	0.0294557	−	0.0405423i
$624$		0			0
$625$	−20.1421	−	14.8086i	−0.805685	−	0.592344i
$626$	−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
$635$	25.8749	+	18.8550i	1.02681	+	0.748240i
$636$		0			0
$637$		−	25.3502i		−	1.00441i
$638$	39.8486	−	36.9173i	1.57762	−	1.46157i
$639$		0			0
$640$	44.0336	+	0.0621595i	1.74058	+	0.00245707i
$641$	−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	6.76766e−5	−	1.00000i	$-0.499978\pi$
$643$	14.9078	−	4.84385i	0.587908	−	0.191023i	0.587840	+	0.808977i	$0.299978\pi$
$644$	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	0.289370	−	0.957217i	$-0.406554\pi$
$647$	−0.996166	−	0.323674i	−0.0391633	−	0.0127249i	−0.328533	+	0.944492i	$0.606554\pi$
$648$		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	−0.631391	−	0.775465i	$-0.717516\pi$
$653$	7.69760	−	10.5948i	0.301230	−	0.414608i	0.932621	+	0.360857i	$0.117516\pi$
$654$		0			0
$655$	8.54393	+	11.7947i	0.333839	+	0.460856i
$656$	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
$665$	−0.0594896	+	0.0430936i	−0.00230691	+	0.00167110i
$666$		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	0.616256	−	0.787546i	$-0.288648\pi$
$673$	16.9120	+	5.49505i	0.651911	+	0.211819i	0.0356542	+	0.999364i	$0.488648\pi$
$674$	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	−0.0694780	−	0.997583i	$-0.522133\pi$
$677$	11.9865	−	3.89464i	0.460678	−	0.149683i	0.530156	+	0.847900i	$0.322133\pi$
$678$		0			0
$679$	4.77632	−	3.47020i	0.183298	−	0.133174i
$680$	0.0222479	−	15.7604i	0.000853170	−	0.604382i
$681$		0			0
$682$	27.8611	+	15.5626i	1.06686	+	0.595923i
$683$			39.7914i			1.52257i	0.648415	+	0.761287i	$0.275432\pi$
$683$			39.7914i			1.52257i	−0.648415	+	0.761287i	$0.724568\pi$
$684$		0			0
$685$	9.10644	+	6.63588i	0.347939	+	0.253544i
$686$	−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
$695$	−0.0334070	+	23.6654i	−0.00126720	+	0.897681i
$696$		0			0
$697$	−7.26996	+	10.0062i	−0.275369	+	0.379013i
$698$	8.14262	−	2.64570i	0.308203	−	0.100141i
$699$		0			0
$700$	0.0198810	−	7.04180i	0.000751431	−	0.266155i
$701$	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	$0.827677\pi$
$710$	−4.49319	+	3.25481i	−0.168627	+	0.122151i
$711$		0			0
$712$	−10.1268	−	13.9384i	−0.379520	−	0.522364i
$713$	18.1916	+	5.91082i	0.681282	+	0.221362i
$714$		0			0
$715$	−24.8364	+	11.4405i	−0.928827	+	0.427849i
$716$	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	$-0.959273\pi$
$727$		−	6.88096i		−	0.255201i	0.991826	−	0.127600i	$-0.0407275\pi$
$728$	6.02421	+	1.95738i	0.223272	+	0.0725455i
$729$		0			0
$730$	−54.7655	−	17.8799i	−2.02696	−	0.661764i
$731$	−3.64187	−	11.2085i	−0.134699	−	0.414562i
$732$		0			0
$733$	12.1932	−	16.7826i	0.450368	−	0.619878i	−0.522109	−	0.852879i	$-0.674855\pi$
$733$	12.1932	−	16.7826i	0.450368	−	0.619878i	0.972477	+	0.233001i	$0.0748545\pi$
$734$	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	$0.175687\pi$
$740$	56.1372	+	40.9073i	2.06365	+	1.50378i
$741$		0			0
$742$	10.8990	−	3.54128i	0.400113	−	0.130005i
$743$	−3.87393	+	1.25872i	−0.142121	+	0.0461779i	−0.379214	−	0.925309i	$-0.623805\pi$
$743$	−3.87393	+	1.25872i	−0.142121	+	0.0461779i	0.237093	+	0.971487i	$0.423805\pi$
$744$		0			0
$745$	−3.18518	+	4.37103i	−0.116696	+	0.160142i
$746$	−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
$755$	25.0177	+	8.16781i	0.910487	+	0.297257i
$756$		0			0
$757$	−8.75366	−	2.84424i	−0.318157	−	0.103376i	0.145585	−	0.989346i	$-0.453494\pi$
$757$	−8.75366	−	2.84424i	−0.318157	−	0.103376i	−0.463742	+	0.885970i	$0.653494\pi$
$758$		−	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	$0.791281\pi$
$770$	−1.25227	+	6.28546i	−0.0451285	+	0.226512i
$771$		0			0
$772$	2.31271	+	0.751445i	0.0832362	+	0.0270451i
$773$	2.38278	+	3.27962i	0.0857028	+	0.117960i	0.849716	−	0.527241i	$-0.176774\pi$
$773$	2.38278	+	3.27962i	0.0857028	+	0.117960i	−0.764013	+	0.645201i	$0.776774\pi$
$774$		0			0
$775$	−15.8733	−	11.6012i	−0.570186	−	0.416729i
$776$	−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
$785$	−11.8356	+	36.2521i	−0.422431	+	1.29389i
$786$		0			0
$787$	−14.7242	+	4.78417i	−0.524860	+	0.170537i	−0.559450	−	0.828864i	$-0.688988\pi$
$787$	−14.7242	+	4.78417i	−0.524860	+	0.170537i	0.0345898	+	0.999402i	$0.488988\pi$
$788$	−19.1156	+	26.3104i	−0.680965	+	0.937267i
$789$		0			0
$790$	−6.84527	−	0.00966305i	−0.243544	−	0.000343796i
$791$	−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	0.389778	−	0.920909i	$-0.372552\pi$
$797$	35.1877	−	11.4332i	1.24641	−	0.404984i	0.856634	+	0.515925i	$0.172552\pi$
$798$		0			0
$799$	9.06971	+	6.58953i	0.320863	+	0.233121i
$800$	0.560988	+	0.184029i	0.0198339	+	0.00650639i
$801$		0			0
$802$		−	31.3139i		−	1.10573i
$803$	30.4864	+	17.0290i	1.07584	+	0.600941i
$804$		0			0
$805$	−0.00542264	+	3.84138i	−0.000191123	+	0.135391i
$806$	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
$820$	44.6546	+	61.6446i	1.55941	+	2.15272i
$821$	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	0.466157	−	0.884702i	$-0.345638\pi$
$823$	9.27399	+	3.01330i	0.323271	+	0.105037i	−0.142886	+	0.989739i	$0.545638\pi$
$824$	−50.7212			−1.76696
$825$		0			0
$826$	7.67766			0.267140
$827$	16.0497	+	5.21486i	0.558102	+	0.181338i	0.574467	−	0.818528i	$-0.305209\pi$
$827$	16.0497	+	5.21486i	0.558102	+	0.181338i	−0.0163651	+	0.999866i	$0.505209\pi$
$828$		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	$0.457216\pi$
$830$	38.6958	+	53.4186i	1.34315	+	1.85419i
$831$		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
$845$	−0.00187834	+	1.33061i	−6.46167e−5	+	0.0457743i
$846$		0			0
$847$	1.47870	−	3.59232i	0.0508089	−	0.123434i
$848$		−	52.0824i		−	1.78852i
$849$		0			0
$850$	5.52580	−	16.8447i	0.189533	−	0.577768i
$851$	−30.6549	−	22.2721i	−1.05084	−	0.763477i
$852$		0			0
$853$	35.6476	−	11.5826i	1.22055	−	0.396580i	0.373267	−	0.927724i	$-0.378237\pi$
$853$	35.6476	−	11.5826i	1.22055	−	0.396580i	0.847282	+	0.531143i	$0.178237\pi$
$854$	−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	$0.243303\pi$
$857$			40.5203i			1.38415i	−0.721827	+	0.692074i	$0.756697\pi$
$858$		0			0
$859$	18.5806			0.633961			0.316981	−	0.948432i	$-0.397331\pi$
$859$	18.5806			0.633961			0.316981	+	0.948432i	$0.397331\pi$
$860$	−72.5305	−	0.102387i	−2.47327	−	0.00349136i
$861$		0			0
$862$	23.0058	−	31.6647i	0.783580	−	1.07851i
$863$	3.71672	−	1.20764i	0.126519	−	0.0411084i	−0.245073	−	0.969505i	$-0.578812\pi$
$863$	3.71672	−	1.20764i	0.126519	−	0.0411084i	0.371592	+	0.928396i	$0.378812\pi$
$864$		0			0
$865$	−1.64381	+	5.03492i	−0.0558911	+	0.171192i
$866$	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
$875$	1.23603	−	3.74999i	0.0417854	−	0.126773i
$876$		0			0
$877$	21.2356	+	29.2282i	0.717074	+	0.986967i	0.999616	+	0.0277125i	$0.00882230\pi$
$877$	21.2356	+	29.2282i	0.717074	+	0.986967i	−0.282542	+	0.959255i	$0.591178\pi$
$878$	26.8948	+	8.73864i	0.907654	+	0.294915i
$879$		0			0
$880$	25.4092	+	14.2401i	0.856544	+	0.480034i
$881$	−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	0.791813	−	0.610763i	$-0.209137\pi$
$883$	−1.00263	−	1.38000i	−0.0337412	−	0.0464407i	−0.825554	+	0.564323i	$0.809137\pi$
$884$	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	−0.894696	−	0.446675i	$-0.852608\pi$
$887$	−5.76014	+	7.92816i	−0.193407	+	0.266201i	0.701290	+	0.712877i	$0.252608\pi$
$888$		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
$895$	4.12727	+	1.34747i	0.137959	+	0.0450411i
$896$	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
$905$	−20.1275	+	27.6210i	−0.669060	+	0.918154i
$906$		0			0
$907$	−25.8868	+	8.41114i	−0.859558	+	0.279287i	−0.705444	−	0.708766i	$-0.749252\pi$
$907$	−25.8868	+	8.41114i	−0.859558	+	0.279287i	−0.154114	+	0.988053i	$0.549252\pi$
$908$	−75.4629	+	24.5194i	−2.50433	+	0.813705i
$909$		0			0
$910$	5.75832	+	4.19610i	0.190886	+	0.139099i
$911$	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	$0.902497\pi$
$920$	50.2985	+	16.4215i	1.65829	+	0.541401i
$921$		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
$935$	−5.25342	+	9.37389i	−0.171805	+	0.306559i
$936$		0			0
$937$	−29.4622	−	9.57286i	−0.962490	−	0.312732i	−0.214709	−	0.976678i	$-0.568880\pi$
$937$	−29.4622	−	9.57286i	−0.962490	−	0.312732i	−0.747780	+	0.663946i	$0.768880\pi$
$938$	3.19448	+	4.39682i	0.104303	+	0.143561i
$939$		0			0
$940$	55.8750	−	40.4752i	1.82244	−	1.32015i
$941$	−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	$-0.931597\pi$
$947$		−	13.1245i		−	0.426490i	0.976999	−	0.213245i	$-0.0684033\pi$
$948$		0			0
$949$	31.4070	−	22.8185i	1.01951	−	0.740720i
$950$	−0.00321324	+	1.13812i	−0.000104251	+	0.0369255i
$951$		0			0
$952$	2.36733	−	0.769193i	0.0767257	−	0.0249297i
$953$	−17.5844	+	24.2028i	−0.569614	+	0.784007i	−0.992509	−	0.122172i	$-0.961014\pi$
$953$	−17.5844	+	24.2028i	−0.569614	+	0.784007i	0.422895	+	0.906179i	$0.361014\pi$
$954$		0			0
$955$	−0.0523726	+	37.1005i	−0.00169474	+	1.20055i
$956$	−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
$965$	1.10196	+	0.803002i	0.0354735	+	0.0258496i
$966$		0			0
$967$			48.8957i			1.57238i	0.617986	+	0.786189i	$0.287949\pi$
$967$			48.8957i			1.57238i	−0.617986	+	0.786189i	$0.712051\pi$
$968$	−40.7650	−	34.6612i	−1.31024	−	1.11405i
$969$		0			0
$970$	0.129125	−	91.4717i	0.00414595	−	2.93698i
$971$	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	−0.356205	−	0.934408i	$-0.615930\pi$
$977$	−37.3087	−	12.1223i	−1.19361	−	0.387828i	−0.837407	+	0.546579i	$0.815930\pi$
$978$		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	−0.858913	−	0.512121i	$-0.828860\pi$
$983$	−3.33715	+	4.59319i	−0.106439	+	0.146500i	0.752475	+	0.658621i	$0.228860\pi$
$984$		0			0
$985$	−14.7677	+	10.6975i	−0.470537	+	0.340852i
$986$	−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
$995$	−3.71595	−	5.12977i	−0.117803	−	0.162625i
$996$		0			0
$997$	−16.8557	+	23.1999i	−0.533826	+	0.734749i	−0.987708	−	0.156313i	$-0.950039\pi$
$997$	−16.8557	+	23.1999i	−0.533826	+	0.734749i	0.453881	+	0.891062i	$0.350039\pi$
$998$	−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.64.12	yes	48
3.2	odd	2	inner	495.2.ba.b.64.1	✓	48
5.4	even	2	inner	495.2.ba.b.64.2	yes	48
11.5	even	5	inner	495.2.ba.b.379.2	yes	48
15.14	odd	2	inner	495.2.ba.b.64.11	yes	48
33.5	odd	10	inner	495.2.ba.b.379.11	yes	48
55.49	even	10	inner	495.2.ba.b.379.12	yes	48
165.104	odd	10	inner	495.2.ba.b.379.1	yes	48

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

\(f(q)\)	\(=\)	\(q+(2.32725 + 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(1.31177 + 1.81087i) q^{5} +(-0.207582 + 0.285712i) q^{7} +(2.85924 + 3.93540i) q^{8} +O(q^{10})\)	\(q+(2.32725 + 0.756170i) q^{2} +(3.22628 + 2.34403i) q^{4} +(1.31177 + 1.81087i) q^{5} +(-0.207582 + 0.285712i) q^{7} +(2.85924 + 3.93540i) q^{8} +(1.68350 + 5.20628i) q^{10} +(-0.393463 - 3.29320i) q^{11} +(-3.50669 - 1.13939i) q^{13} +(-0.699143 + 0.507957i) q^{14} +(1.21368 + 3.73532i) q^{16} +(-1.37802 + 0.447747i) q^{17} +(0.0752559 - 0.0546766i) q^{19} +(-0.0125879 + 8.91721i) q^{20} +(1.57453 - 7.96164i) q^{22} -4.86443i q^{23} +(-1.55850 + 4.75090i) q^{25} +(-7.29937 - 5.30330i) q^{26} +(-1.33944 + 0.435209i) q^{28} +(5.41495 + 3.93419i) q^{29} +(-1.21511 + 3.73973i) q^{31} -0.118080i q^{32} -3.54558 q^{34} +(-0.789688 - 0.00111475i) q^{35} +(4.57856 - 6.30185i) q^{37} +(0.216484 - 0.0703400i) q^{38} +(-3.37584 + 10.3401i) q^{40} +(6.90591 - 5.01744i) q^{41} +8.13377i q^{43} +(6.44994 - 11.5471i) q^{44} +(3.67834 - 11.3208i) q^{46} +(-4.54783 - 6.25956i) q^{47} +(2.12458 + 6.53878i) q^{49} +(-7.21952 + 9.87805i) q^{50} +(-8.64278 - 11.8958i) q^{52} +(-12.6118 - 4.09781i) q^{53} +(5.44743 - 5.03245i) q^{55} -1.71792 q^{56} +(9.62703 + 13.2505i) q^{58} +(-7.18751 - 5.22203i) q^{59} +(3.08181 + 9.48482i) q^{61} +(-5.65574 + 7.78446i) q^{62} +(2.51664 - 7.74544i) q^{64} +(-2.53669 - 7.84478i) q^{65} -6.28888i q^{67} +(-5.49541 - 1.78557i) q^{68} +(-1.83696 - 0.599733i) q^{70} +(0.313338 + 0.964354i) q^{71} +(-6.18866 + 8.51796i) q^{73} +(15.4207 - 11.2038i) q^{74} +0.370960 q^{76} +(1.02258 + 0.571193i) q^{77} +(-0.386590 + 1.18980i) q^{79} +(-5.17211 + 7.09770i) q^{80} +(19.8658 - 6.45480i) q^{82} +(11.4650 - 3.72521i) q^{83} +(-2.61846 - 1.90808i) q^{85} +(-6.15052 + 18.9293i) q^{86} +(11.8351 - 10.9645i) q^{88} -3.54180 q^{89} +(1.05346 - 0.765386i) q^{91} +(11.4024 - 15.6940i) q^{92} +(-5.85067 - 18.0065i) q^{94} +(0.197731 + 0.0645554i) q^{95} +(-15.8990 - 5.16591i) q^{97} +16.8239i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4}+O(q^{10}) \) 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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