LMFDB - Embedded newform 460.2.x.a.333.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			333.1
Character	$\chi$	$=$	460.333
Dual form			460.2.x.a.297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32883 + 1.74334i) q^{3} +(1.79098 + 1.33880i) q^{5} +(0.283864 - 3.96893i) q^{7} +(1.53902 - 5.24143i) q^{9} +O(q^{10})$	\(q+(-2.32883 + 1.74334i) q^{3} +(1.79098 + 1.33880i) q^{5} +(0.283864 - 3.96893i) q^{7} +(1.53902 - 5.24143i) q^{9} +(2.54334 - 3.95751i) q^{11} +(1.13767 - 0.0813681i) q^{13} +(-6.50488 + 0.00446730i) q^{15} +(-1.63886 + 4.39395i) q^{17} +(0.754595 - 1.65233i) q^{19} +(6.25814 + 9.73785i) q^{21} +(4.76999 + 0.497178i) q^{23} +(1.41525 + 4.79553i) q^{25} +(2.50363 + 6.71249i) q^{27} +(6.44518 - 2.94341i) q^{29} +(0.271688 + 1.88963i) q^{31} +(0.976289 + 13.6503i) q^{33} +(5.82199 - 6.72826i) q^{35} +(-2.54407 - 4.65912i) q^{37} +(-2.50760 + 2.17285i) q^{39} +(2.37912 - 0.698573i) q^{41} +(-3.45730 - 4.61841i) q^{43} +(9.77357 - 7.32688i) q^{45} +(-8.76251 + 8.76251i) q^{47} +(-8.74310 - 1.25707i) q^{49} +(-3.84353 - 13.0899i) q^{51} +(8.15266 + 0.583090i) q^{53} +(9.85338 - 3.68283i) q^{55} +(1.12326 + 5.16352i) q^{57} +(-1.06951 - 0.926737i) q^{59} +(5.40503 - 0.777126i) q^{61} +(-20.3660 - 7.59613i) q^{63} +(2.14649 + 1.37738i) q^{65} +(14.7374 + 3.20593i) q^{67} +(-11.9753 + 7.15788i) q^{69} +(8.58331 - 5.51616i) q^{71} +(-4.86635 + 1.81505i) q^{73} +(-11.6561 - 8.70071i) q^{75} +(-14.9851 - 11.2177i) q^{77} +(-3.92457 + 4.52920i) q^{79} +(-3.74614 - 2.40750i) q^{81} +(-9.26364 + 5.05833i) q^{83} +(-8.81777 + 5.67540i) q^{85} +(-9.87836 + 18.0909i) q^{87} +(1.39921 - 9.73170i) q^{89} -4.53845i q^{91} +(-3.92699 - 3.92699i) q^{93} +(3.56360 - 1.94905i) q^{95} +(-6.71138 - 3.66469i) q^{97} +(-16.8288 - 19.4214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.32883	+	1.74334i	−1.34455	+	1.00652i	−0.346910	+	0.937899i	$0.612769\pi$
$3$	−2.32883	+	1.74334i	−1.34455	+	1.00652i	−0.997643	+	0.0686207i	$0.978140\pi$
$4$		0			0
$5$	1.79098	+	1.33880i	0.800953	+	0.598728i
$5$	1.79098	+	1.33880i	0.800953	+	0.598728i
$6$		0			0
$7$	0.283864	−	3.96893i	0.107290	−	1.50012i	−0.603868	−	0.797084i	$-0.706375\pi$
$7$	0.283864	−	3.96893i	0.107290	−	1.50012i	0.711159	−	0.703031i	$-0.248171\pi$
$8$		0			0
$9$	1.53902	−	5.24143i	0.513007	−	1.74714i
$10$		0			0
$11$	2.54334	−	3.95751i	0.766846	−	1.19323i	−0.209667	−	0.977773i	$-0.567238\pi$
$11$	2.54334	−	3.95751i	0.766846	−	1.19323i	0.976512	−	0.215462i	$-0.0691258\pi$
$12$		0			0
$13$	1.13767	−	0.0813681i	0.315534	−	0.0225674i	0.0873259	−	0.996180i	$-0.472168\pi$
$13$	1.13767	−	0.0813681i	0.315534	−	0.0225674i	0.228208	+	0.973612i	$0.426713\pi$
$14$		0			0
$15$	−6.50488	+	0.00446730i	−1.67955	+	0.00115345i
$16$		0			0
$17$	−1.63886	+	4.39395i	−0.397482	+	1.06569i	0.571942	+	0.820294i	$0.306190\pi$
$17$	−1.63886	+	4.39395i	−0.397482	+	1.06569i	−0.969423	+	0.245395i	$0.921082\pi$
$18$		0			0
$19$	0.754595	−	1.65233i	0.173116	−	0.379071i	−0.803109	−	0.595833i	$-0.796822\pi$
$19$	0.754595	−	1.65233i	0.173116	−	0.379071i	0.976225	+	0.216762i	$0.0695495\pi$
$20$		0			0
$21$	6.25814	+	9.73785i	1.36564	+	2.12497i
$22$		0			0
$23$	4.76999	+	0.497178i	0.994612	+	0.103669i
$23$	4.76999	+	0.497178i	0.994612	+	0.103669i
$24$		0			0
$25$	1.41525	+	4.79553i	0.283050	+	0.959105i
$26$		0			0
$27$	2.50363	+	6.71249i	0.481824	+	1.29182i
$28$		0			0
$29$	6.44518	−	2.94341i	1.19684	−	0.546578i	0.285558	−	0.958362i	$-0.407821\pi$
$29$	6.44518	−	2.94341i	1.19684	−	0.546578i	0.911282	+	0.411783i	$0.135094\pi$
$30$		0			0
$31$	0.271688	+	1.88963i	0.0487966	+	0.339388i	0.999565	+	0.0294859i	$0.00938702\pi$
$31$	0.271688	+	1.88963i	0.0487966	+	0.339388i	−0.950769	+	0.309902i	$0.899704\pi$
$32$		0			0
$33$	0.976289	+	13.6503i	0.169950	+	2.37621i
$34$		0			0
$35$	5.82199	−	6.72826i	0.984095	−	1.13728i
$36$		0			0
$37$	−2.54407	−	4.65912i	−0.418243	−	0.765955i	0.580593	−	0.814194i	$-0.302821\pi$
$37$	−2.54407	−	4.65912i	−0.418243	−	0.765955i	−0.998836	+	0.0482392i	$0.984639\pi$
$38$		0			0
$39$	−2.50760	+	2.17285i	−0.401538	+	0.347934i
$40$		0			0
$41$	2.37912	−	0.698573i	0.371556	−	0.109099i	−0.0906231	−	0.995885i	$-0.528886\pi$
$41$	2.37912	−	0.698573i	0.371556	−	0.109099i	0.462179	+	0.886787i	$0.347068\pi$
$42$		0			0
$43$	−3.45730	−	4.61841i	−0.527233	−	0.704301i	0.455311	−	0.890333i	$-0.349528\pi$
$43$	−3.45730	−	4.61841i	−0.527233	−	0.704301i	−0.982544	+	0.186032i	$0.940437\pi$
$44$		0			0
$45$	9.77357	−	7.32688i	1.45696	−	1.09223i
$46$		0			0
$47$	−8.76251	+	8.76251i	−1.27814	+	1.27814i	−0.336437	+	0.941706i	$0.609222\pi$
$47$	−8.76251	+	8.76251i	−1.27814	+	1.27814i	−0.941706	+	0.336437i	$0.890778\pi$
$48$		0			0
$49$	−8.74310	−	1.25707i	−1.24901	−	0.179581i
$50$		0			0
$51$	−3.84353	−	13.0899i	−0.538202	−	1.83295i
$52$		0			0
$53$	8.15266	+	0.583090i	1.11985	+	0.0800936i	0.618966	−	0.785418i	$-0.287552\pi$
$53$	8.15266	+	0.583090i	1.11985	+	0.0800936i	0.500889	+	0.865512i	$0.333007\pi$
$54$		0			0
$55$	9.85338	−	3.68283i	1.32863	−	0.496593i
$56$		0			0
$57$	1.12326	+	5.16352i	0.148779	+	0.683925i
$58$		0			0
$59$	−1.06951	−	0.926737i	−0.139239	−	0.120651i	0.582457	−	0.812862i	$-0.302091\pi$
$59$	−1.06951	−	0.926737i	−0.139239	−	0.120651i	−0.721696	+	0.692211i	$0.756637\pi$
$60$		0			0
$61$	5.40503	−	0.777126i	0.692044	−	0.0995008i	0.212686	−	0.977121i	$-0.431779\pi$
$61$	5.40503	−	0.777126i	0.692044	−	0.0995008i	0.479357	+	0.877620i	$0.340870\pi$
$62$		0			0
$63$	−20.3660	−	7.59613i	−2.56588	−	0.957022i
$64$		0			0
$65$	2.14649	+	1.37738i	0.266240	+	0.170844i
$66$		0			0
$67$	14.7374	+	3.20593i	1.80046	+	0.391667i	0.982895	−	0.184165i	$-0.0589580\pi$
$67$	14.7374	+	3.20593i	1.80046	+	0.391667i	0.817568	+	0.575832i	$0.195322\pi$
$68$		0			0
$69$	−11.9753	+	7.15788i	−1.44165	+	0.861708i
$70$		0			0
$71$	8.58331	−	5.51616i	1.01865	−	0.654648i	0.0790332	−	0.996872i	$-0.474817\pi$
$71$	8.58331	−	5.51616i	1.01865	−	0.654648i	0.939618	+	0.342224i	$0.111180\pi$
$72$		0			0
$73$	−4.86635	+	1.81505i	−0.569563	+	0.212436i	−0.617712	−	0.786404i	$-0.711940\pi$
$73$	−4.86635	+	1.81505i	−0.569563	+	0.212436i	0.0481495	+	0.998840i	$0.484668\pi$
$74$		0			0
$75$	−11.6561	−	8.70071i	−1.34593	−	1.00467i
$76$		0			0
$77$	−14.9851	−	11.2177i	−1.70772	−	1.27838i
$78$		0			0
$79$	−3.92457	+	4.52920i	−0.441549	+	0.509575i	−0.932281	−	0.361736i	$-0.882184\pi$
$79$	−3.92457	+	4.52920i	−0.441549	+	0.509575i	0.490731	+	0.871311i	$0.336730\pi$
$80$		0			0
$81$	−3.74614	−	2.40750i	−0.416237	−	0.267500i
$82$		0			0
$83$	−9.26364	+	5.05833i	−1.01682	+	0.555224i	−0.899063	−	0.437819i	$-0.855751\pi$
$83$	−9.26364	+	5.05833i	−1.01682	+	0.555224i	−0.117754	+	0.993043i	$0.537569\pi$
$84$		0			0
$85$	−8.81777	+	5.67540i	−0.956422	+	0.615583i
$86$		0			0
$87$	−9.87836	+	18.0909i	−1.05907	+	1.93955i
$88$		0			0
$89$	1.39921	−	9.73170i	0.148316	−	1.03156i	−0.770661	−	0.637246i	$-0.780074\pi$
$89$	1.39921	−	9.73170i	0.148316	−	1.03156i	0.918976	−	0.394313i	$-0.129017\pi$
$90$		0			0
$91$		−	4.53845i		−	0.475759i
$92$		0			0
$93$	−3.92699	−	3.92699i	−0.407210	−	0.407210i
$94$		0			0
$95$	3.56360	−	1.94905i	0.365618	−	0.199969i
$96$		0			0
$97$	−6.71138	−	3.66469i	−0.681438	−	0.372093i	0.100944	−	0.994892i	$-0.467814\pi$
$97$	−6.71138	−	3.66469i	−0.681438	−	0.372093i	−0.782382	+	0.622799i	$0.785995\pi$
$98$		0			0
$99$	−16.8288	−	19.4214i	−1.69135	−	1.95193i
$100$		0			0
$101$	−4.18808	−	1.22973i	−0.416730	−	0.122363i	0.0666444	−	0.997777i	$-0.478771\pi$
$101$	−4.18808	−	1.22973i	−0.416730	−	0.122363i	−0.483374	+	0.875414i	$0.660589\pi$
$102$		0			0
$103$	−3.35756	+	0.730392i	−0.330830	+	0.0719677i	−0.374913	−	0.927060i	$-0.622327\pi$
$103$	−3.35756	+	0.730392i	−0.330830	+	0.0719677i	0.0440823	+	0.999028i	$0.485964\pi$
$104$		0			0
$105$	−1.82877	+	25.8187i	−0.178470	+	2.51965i
$106$		0			0
$107$	7.73088	−	10.3272i	0.747373	−	0.998373i	−0.252157	−	0.967686i	$-0.581140\pi$
$107$	7.73088	−	10.3272i	0.747373	−	0.998373i	0.999529	−	0.0306864i	$-0.00976930\pi$
$108$		0			0
$109$	4.33700	+	9.49671i	0.415409	+	0.909620i	0.995473	+	0.0950482i	$0.0303005\pi$
$109$	4.33700	+	9.49671i	0.415409	+	0.909620i	−0.580063	+	0.814571i	$0.696972\pi$
$110$		0			0
$111$	14.0472	+	6.41513i	1.33330	+	0.608897i
$112$		0			0
$113$	4.48226	−	20.6046i	0.421655	−	1.93832i	0.0861448	−	0.996283i	$-0.472545\pi$
$113$	4.48226	−	20.6046i	0.421655	−	1.93832i	0.335511	−	0.942036i	$-0.391091\pi$
$114$		0			0
$115$	7.87736	+	7.27648i	0.734568	+	0.678536i
$116$		0			0
$117$	1.32442	−	6.08827i	0.122443	−	0.562860i
$118$		0			0
$119$	16.9741	+	7.75180i	1.55601	+	0.710606i
$120$		0			0
$121$	−4.62377	−	10.1246i	−0.420343	−	0.920422i
$122$		0			0
$123$	−4.32272	+	5.77448i	−0.389767	+	0.520667i
$124$		0			0
$125$	−3.88554	+	10.4834i	−0.347533	+	0.937668i
$126$		0			0
$127$	−17.2607	+	3.75483i	−1.53164	+	0.333187i	−0.897844	−	0.440314i	$-0.854867\pi$
$127$	−17.2607	+	3.75483i	−1.53164	+	0.333187i	−0.633794	+	0.773502i	$0.718503\pi$
$128$		0			0
$129$	16.1029	+	4.72825i	1.41778	+	0.416299i
$130$		0			0
$131$	−6.39577	−	7.38111i	−0.558801	−	0.644891i	0.404110	−	0.914710i	$-0.367581\pi$
$131$	−6.39577	−	7.38111i	−0.558801	−	0.644891i	−0.962911	+	0.269820i	$0.913036\pi$
$132$		0			0
$133$	−6.34379	−	3.46397i	−0.550076	−	0.300364i
$134$		0			0
$135$	−4.50269	+	15.3738i	−0.387530	+	1.32317i
$136$		0			0
$137$	6.51039	+	6.51039i	0.556220	+	0.556220i	0.928229	−	0.372009i	$-0.121331\pi$
$137$	6.51039	+	6.51039i	0.556220	+	0.556220i	−0.372009	+	0.928229i	$0.621331\pi$
$138$		0			0
$139$			12.4069i			1.05234i	0.850380	+	0.526169i	$0.176372\pi$
$139$			12.4069i			1.05234i	−0.850380	+	0.526169i	$0.823628\pi$
$140$		0			0
$141$	5.13036	−	35.6825i	0.432055	−	3.00501i
$142$		0			0
$143$	2.57148	−	4.70931i	0.215038	−	0.393812i
$144$		0			0
$145$	15.4838	+	3.35717i	1.28586	+	0.278798i
$146$		0			0
$147$	22.5527	−	12.3147i	1.86012	−	1.01570i
$148$		0			0
$149$	−11.6203	−	7.46794i	−0.951976	−	0.611798i	−0.0302095	−	0.999544i	$-0.509617\pi$
$149$	−11.6203	−	7.46794i	−0.951976	−	0.611798i	−0.921766	+	0.387746i	$0.873254\pi$
$150$		0			0
$151$	−14.8029	+	17.0835i	−1.20465	+	1.39024i	−0.305728	+	0.952119i	$0.598900\pi$
$151$	−14.8029	+	17.0835i	−1.20465	+	1.39024i	−0.898918	+	0.438116i	$0.855646\pi$
$152$		0			0
$153$	20.5083	+	15.3523i	1.65800	+	1.24116i
$154$		0			0
$155$	−2.04324	+	3.74803i	−0.164117	+	0.301049i
$156$		0			0
$157$	16.5236	−	6.16299i	1.31873	−	0.491860i	0.411082	−	0.911598i	$-0.365151\pi$
$157$	16.5236	−	6.16299i	1.31873	−	0.491860i	0.907645	+	0.419739i	$0.137878\pi$
$158$		0			0
$159$	−20.0027	+	12.8550i	−1.58632	+	1.01946i
$160$		0			0
$161$	3.32729	−	18.7906i	0.262228	−	1.48091i
$162$		0			0
$163$	4.97211	+	1.08162i	0.389446	+	0.0847188i	0.403025	−	0.915189i	$-0.367959\pi$
$163$	4.97211	+	1.08162i	0.389446	+	0.0847188i	−0.0135789	+	0.999908i	$0.504322\pi$
$164$		0			0
$165$	−16.5264	+	25.7545i	−1.28658	+	2.00499i
$166$		0			0
$167$	9.59070	+	3.57715i	0.742151	+	0.276808i	0.691964	−	0.721932i	$-0.256746\pi$
$167$	9.59070	+	3.57715i	0.742151	+	0.276808i	0.0501867	+	0.998740i	$0.484018\pi$
$168$		0			0
$169$	−11.5800	+	1.66495i	−0.890769	+	0.128073i
$170$		0			0
$171$	−7.49924	−	6.49813i	−0.573481	−	0.496924i
$172$		0			0
$173$	0.0195239	+	0.0897499i	0.00148437	+	0.00682356i	0.977883	−	0.209152i	$-0.0670704\pi$
$173$	0.0195239	+	0.0897499i	0.00148437	+	0.00682356i	−0.976399	+	0.215976i	$0.930707\pi$
$174$		0			0
$175$	19.4349	−	4.25576i	1.46914	−	0.321705i
$176$		0			0
$177$	4.10634	+	0.293691i	0.308651	+	0.0220752i
$178$		0			0
$179$	−2.38229	−	8.11334i	−0.178061	−	0.606419i	−0.999355	−	0.0359143i	$-0.988566\pi$
$179$	−2.38229	−	8.11334i	−0.178061	−	0.606419i	0.821294	−	0.570505i	$-0.193253\pi$
$180$		0			0
$181$	12.2297	+	1.75836i	0.909023	+	0.130698i	0.580936	−	0.813949i	$-0.302687\pi$
$181$	12.2297	+	1.75836i	0.909023	+	0.130698i	0.328088	+	0.944647i	$0.393596\pi$
$182$		0			0
$183$	−11.2326	+	11.2326i	−0.830339	+	0.830339i
$184$		0			0
$185$	1.68122	−	11.7504i	0.123606	−	0.863907i
$186$		0			0
$187$	13.2209	+	17.6611i	0.966811	+	1.29151i
$188$		0			0
$189$	27.3521	−	8.03130i	1.98957	−	0.584191i
$190$		0			0
$191$	−10.7593	+	9.32301i	−0.778518	+	0.674589i	−0.950574	−	0.310498i	$-0.899504\pi$
$191$	−10.7593	+	9.32301i	−0.778518	+	0.674589i	0.172057	+	0.985087i	$0.444959\pi$
$192$		0			0
$193$	1.44417	+	2.64480i	0.103954	+	0.190377i	0.924479	−	0.381234i	$-0.124501\pi$
$193$	1.44417	+	2.64480i	0.103954	+	0.190377i	−0.820525	+	0.571610i	$0.806319\pi$
$194$		0			0
$195$	−7.40008	+	0.534372i	−0.529930	+	0.0382672i
$196$		0			0
$197$	0.168690	+	2.35860i	0.0120187	+	0.168043i	0.999916	+	0.0129359i	$0.00411775\pi$
$197$	0.168690	+	2.35860i	0.0120187	+	0.168043i	−0.987898	+	0.155107i	$0.950428\pi$
$198$		0			0
$199$	−0.768233	−	5.34318i	−0.0544586	−	0.378768i	−0.998764	−	0.0496983i	$-0.984174\pi$
$199$	−0.768233	−	5.34318i	−0.0544586	−	0.378768i	0.944306	−	0.329070i	$-0.106735\pi$
$200$		0			0
$201$	−39.9101	+	18.2263i	−2.81504	+	1.28558i
$202$		0			0
$203$	−9.85266	−	26.4160i	−0.691521	−	1.85404i
$204$		0			0
$205$	5.19621	+	1.93402i	0.362919	+	0.135078i
$206$		0			0
$207$	9.94705	−	24.2364i	0.691368	−	1.68455i
$208$		0			0
$209$	−4.61993	−	7.18876i	−0.319567	−	0.497257i
$210$		0			0
$211$	−6.74332	+	14.7658i	−0.464229	+	1.01652i	0.522274	+	0.852778i	$0.325084\pi$
$211$	−6.74332	+	14.7658i	−0.464229	+	1.01652i	−0.986503	+	0.163742i	$0.947643\pi$
$212$		0			0
$213$	−10.3725	+	27.8099i	−0.710715	+	1.90550i
$214$		0			0
$215$	−0.00885930	−	12.9001i	−0.000604199	−	0.879781i
$216$		0			0
$217$	7.57694	−	0.541913i	0.514356	−	0.0367875i
$218$		0			0
$219$	8.16865	−	12.7107i	0.551986	−	0.858907i
$220$		0			0
$221$	−1.50696	+	5.13223i	−0.101369	+	0.345231i
$222$		0			0
$223$	1.19593	−	16.7213i	0.0800856	−	1.11974i	−0.785460	−	0.618912i	$-0.787574\pi$
$223$	1.19593	−	16.7213i	0.0800856	−	1.11974i	0.865546	−	0.500830i	$-0.166972\pi$
$224$		0			0
$225$	27.3135	−	0.0375157i	1.82090	−	0.00250105i
$226$		0			0
$227$	−6.71158	+	5.02422i	−0.445463	+	0.333469i	−0.798347	−	0.602198i	$-0.794292\pi$
$227$	−6.71158	+	5.02422i	−0.445463	+	0.333469i	0.352884	+	0.935667i	$0.385201\pi$
$228$		0			0
$229$	−20.3994			−1.34803			−0.674014	−	0.738719i	$-0.735431\pi$
$229$	−20.3994			−1.34803			−0.674014	+	0.738719i	$0.735431\pi$
$230$		0			0
$231$	54.4542			3.58283
$232$		0			0
$233$	2.75053	−	2.05902i	0.180193	−	0.134891i	−0.505374	−	0.862901i	$-0.668645\pi$
$233$	2.75053	−	2.05902i	0.180193	−	0.134891i	0.685567	+	0.728010i	$0.259554\pi$
$234$		0			0
$235$	−27.4247	+	3.96231i	−1.78899	+	0.258472i
$236$		0			0
$237$	1.24373	−	17.3896i	0.0807890	−	1.12958i
$238$		0			0
$239$	−6.99416	+	23.8199i	−0.452415	+	1.54078i	0.345740	+	0.938331i	$0.387628\pi$
$239$	−6.99416	+	23.8199i	−0.452415	+	1.54078i	−0.798154	+	0.602453i	$0.794190\pi$
$240$		0			0
$241$	−7.16459	+	11.1483i	−0.461512	+	0.718127i	−0.991533	−	0.129858i	$-0.958548\pi$
$241$	−7.16459	+	11.1483i	−0.461512	+	0.718127i	0.530021	+	0.847985i	$0.322184\pi$
$242$		0			0
$243$	−8.51660	+	0.609119i	−0.546340	+	0.0390750i
$244$		0			0
$245$	−13.9758	−	13.9566i	−0.892881	−	0.891655i
$246$		0			0
$247$	0.724036	−	1.94122i	0.0460693	−	0.123517i
$248$		0			0
$249$	12.7551	−	27.9297i	0.808320	−	1.76997i
$250$		0			0
$251$	14.2931	+	22.2405i	0.902174	+	1.40381i	0.914808	+	0.403890i	$0.132342\pi$
$251$	14.2931	+	22.2405i	0.902174	+	1.40381i	−0.0126338	+	0.999920i	$0.504022\pi$
$252$		0			0
$253$	14.0993	−	17.6128i	0.886415	−	1.10731i
$254$		0			0
$255$	10.6410	−	28.5895i	0.666362	−	1.79034i
$256$		0			0
$257$	1.38363	+	3.70965i	0.0863082	+	0.231401i	0.972933	−	0.231089i	$-0.0742288\pi$
$257$	1.38363	+	3.70965i	0.0863082	+	0.231401i	−0.886624	+	0.462490i	$0.846956\pi$
$258$		0			0
$259$	−19.2139	+	8.77470i	−1.19389	+	0.545233i
$260$		0			0
$261$	−5.50842	−	38.3119i	−0.340963	−	2.37145i
$262$		0			0
$263$	−1.26808	−	17.7300i	−0.0781929	−	1.09328i	−0.873420	−	0.486968i	$-0.838103\pi$
$263$	−1.26808	−	17.7300i	−0.0781929	−	1.09328i	0.795227	−	0.606312i	$-0.207352\pi$
$264$		0			0
$265$	13.8207	+	11.9591i	0.848996	+	0.734639i
$266$		0			0
$267$	13.7072	+	25.1028i	0.838865	+	1.53627i
$268$		0			0
$269$	−3.47472	+	3.01086i	−0.211857	+	0.183575i	−0.754325	−	0.656501i	$-0.772036\pi$
$269$	−3.47472	+	3.01086i	−0.211857	+	0.183575i	0.542467	+	0.840077i	$0.317490\pi$
$270$		0			0
$271$	9.59787	−	2.81819i	0.583029	−	0.171193i	0.0230998	−	0.999733i	$-0.492646\pi$
$271$	9.59787	−	2.81819i	0.583029	−	0.171193i	0.559929	+	0.828540i	$0.310828\pi$
$272$		0			0
$273$	7.91207	+	10.5693i	0.478860	+	0.639683i
$274$		0			0
$275$	22.5778	+	6.59577i	1.36149	+	0.397740i
$276$		0			0
$277$	−19.8935	+	19.8935i	−1.19528	+	1.19528i	−0.219720	+	0.975563i	$0.570514\pi$
$277$	−19.8935	+	19.8935i	−1.19528	+	1.19528i	−0.975563	+	0.219720i	$0.929486\pi$
$278$		0			0
$279$	10.3225	+	1.48415i	0.617991	+	0.0888538i
$280$		0			0
$281$	3.33943	+	11.3731i	0.199214	+	0.678460i	0.997131	+	0.0756930i	$0.0241169\pi$
$281$	3.33943	+	11.3731i	0.199214	+	0.678460i	−0.797917	+	0.602767i	$0.794065\pi$
$282$		0			0
$283$	11.7555	+	0.840771i	0.698793	+	0.0499787i	0.416216	−	0.909266i	$-0.363356\pi$
$283$	11.7555	+	0.840771i	0.698793	+	0.0499787i	0.282577	+	0.959245i	$0.408811\pi$
$284$		0			0
$285$	−4.90117	+	10.7516i	−0.290320	+	0.636870i
$286$		0			0
$287$	−2.09724	−	9.64086i	−0.123796	−	0.569082i
$288$		0			0
$289$	−3.77319	−	3.26949i	−0.221953	−	0.192323i
$290$		0			0
$291$	22.0185	−	3.16578i	1.29075	−	0.185581i
$292$		0			0
$293$	1.51138	+	0.563715i	0.0882956	+	0.0329326i	0.393224	−	0.919443i	$-0.371360\pi$
$293$	1.51138	+	0.563715i	0.0882956	+	0.0329326i	−0.304928	+	0.952375i	$0.598632\pi$
$294$		0			0
$295$	−0.674767	−	3.09163i	−0.0392865	−	0.180002i
$296$		0			0
$297$	32.9323	+	7.16399i	1.91093	+	0.415697i
$298$		0			0
$299$	5.46715	+	0.177502i	0.316174	+	0.0102652i
$300$		0			0
$301$	−19.3116	+	12.4108i	−1.11310	+	0.715346i
$302$		0			0
$303$	11.8972	−	4.43742i	0.683475	−	0.254923i
$304$		0			0
$305$	10.7207	+	5.84442i	0.613868	+	0.334650i
$306$		0			0
$307$	−6.35278	−	4.75563i	−0.362572	−	0.271418i	0.402423	−	0.915454i	$-0.368168\pi$
$307$	−6.35278	−	4.75563i	−0.362572	−	0.271418i	−0.764996	+	0.644035i	$0.777259\pi$
$308$		0			0
$309$	6.54587	−	7.55434i	0.372382	−	0.429751i
$310$		0			0
$311$	−12.3519	−	7.93808i	−0.700411	−	0.450127i	0.141362	−	0.989958i	$-0.454852\pi$
$311$	−12.3519	−	7.93808i	−0.700411	−	0.450127i	−0.841773	+	0.539831i	$0.818488\pi$
$312$		0			0
$313$	−24.6161	+	13.4414i	−1.39138	+	0.759754i	−0.987879	−	0.155224i	$-0.950390\pi$
$313$	−24.6161	+	13.4414i	−1.39138	+	0.759754i	−0.403505	+	0.914977i	$0.632208\pi$
$314$		0			0
$315$	−26.3055	−	40.8705i	−1.48215	−	2.30279i
$316$		0			0
$317$	6.56052	−	12.0147i	0.368475	−	0.674812i	−0.625995	−	0.779827i	$-0.715307\pi$
$317$	6.56052	−	12.0147i	0.368475	−	0.674812i	0.994471	+	0.105014i	$0.0334889\pi$
$318$		0			0
$319$	4.74367	−	32.9930i	0.265595	−	1.84725i
$320$		0			0
$321$			37.5280i			2.09461i
$322$		0			0
$323$	6.02359	+	6.02359i	0.335161	+	0.335161i
$324$		0			0
$325$	2.00030	+	5.34059i	0.110957	+	0.296243i
$326$		0			0
$327$	−26.6562	−	14.5554i	−1.47409	−	0.804914i
$328$		0			0
$329$	32.2904	+	37.2652i	1.78023	+	2.05449i
$330$		0			0
$331$	−9.73181	−	2.85752i	−0.534909	−	0.157063i	0.00311166	−	0.999995i	$-0.499010\pi$
$331$	−9.73181	−	2.85752i	−0.534909	−	0.157063i	−0.538021	+	0.842932i	$0.680828\pi$
$332$		0			0
$333$	−28.3358	+	6.16408i	−1.55279	+	0.337790i
$334$		0			0
$335$	22.1024	+	25.4722i	1.20758	+	1.39169i
$336$		0			0
$337$	−13.8534	+	18.5060i	−0.754645	+	1.00809i	0.244615	+	0.969620i	$0.421338\pi$
$337$	−13.8534	+	18.5060i	−0.754645	+	1.00809i	−0.999260	+	0.0384674i	$0.987752\pi$
$338$		0			0
$339$	25.4825	+	55.7988i	1.38402	+	3.03058i
$340$		0			0
$341$	8.16923	+	3.73076i	0.442389	+	0.202032i
$342$		0			0
$343$	−1.55038	+	7.12696i	−0.0837124	+	0.384820i
$344$		0			0
$345$	−31.0305	−	3.21278i	−1.67062	−	0.172970i
$346$		0			0
$347$	−4.87763	+	22.4221i	−0.261845	+	1.20368i	0.638885	+	0.769302i	$0.279396\pi$
$347$	−4.87763	+	22.4221i	−0.261845	+	1.20368i	−0.900730	+	0.434380i	$0.856968\pi$
$348$		0			0
$349$	−13.0756	−	5.97145i	−0.699923	−	0.319644i	0.0334786	−	0.999439i	$-0.489341\pi$
$349$	−13.0756	−	5.97145i	−0.699923	−	0.319644i	−0.733402	+	0.679795i	$0.762069\pi$
$350$		0			0
$351$	3.39450	+	7.43291i	0.181185	+	0.396739i
$352$		0			0
$353$	4.13827	−	5.52809i	0.220258	−	0.294230i	−0.676778	−	0.736187i	$-0.736624\pi$
$353$	4.13827	−	5.52809i	0.220258	−	0.294230i	0.897037	+	0.441956i	$0.145715\pi$
$354$		0			0
$355$	22.7576	+	1.61195i	1.20785	+	0.0855532i
$356$		0			0
$357$	−53.0438	+	11.5390i	−2.80738	+	0.610708i
$358$		0			0
$359$	11.7941	+	3.46307i	0.622470	+	0.182774i	0.577734	−	0.816225i	$-0.303937\pi$
$359$	11.7941	+	3.46307i	0.622470	+	0.182774i	0.0447363	+	0.998999i	$0.485755\pi$
$360$		0			0
$361$	10.2816	+	11.8656i	0.541135	+	0.624503i
$362$		0			0
$363$	28.4187	+	15.5178i	1.49159	+	0.814472i
$364$		0			0
$365$	−11.1455	−	3.26431i	−0.583384	−	0.170862i
$366$		0			0
$367$	−8.82509	−	8.82509i	−0.460666	−	0.460666i	0.438208	−	0.898874i	$-0.355613\pi$
$367$	−8.82509	−	8.82509i	−0.460666	−	0.460666i	−0.898874	+	0.438208i	$0.855613\pi$
$368$		0			0
$369$		−	13.5451i		−	0.705130i
$370$		0			0
$371$	4.62849	−	32.1918i	0.240299	−	1.67132i
$372$		0			0
$373$	−1.41783	+	2.59656i	−0.0734123	+	0.134445i	−0.911807	−	0.410619i	$-0.865313\pi$
$373$	−1.41783	+	2.59656i	−0.0734123	+	0.134445i	0.838395	+	0.545064i	$0.183494\pi$
$374$		0			0
$375$	−9.22747	−	31.1880i	−0.476504	−	1.61054i
$376$		0			0
$377$	7.09302	−	3.87308i	0.365309	−	0.199474i
$378$		0			0
$379$	1.77111	+	1.13822i	0.0909759	+	0.0584666i	0.585338	−	0.810790i	$-0.300962\pi$
$379$	1.77111	+	1.13822i	0.0909759	+	0.0584666i	−0.494362	+	0.869256i	$0.664598\pi$
$380$		0			0
$381$	33.6513	−	38.8357i	1.72401	−	1.98961i
$382$		0			0
$383$	−17.3408	−	12.9812i	−0.886076	−	0.663308i	0.0561008	−	0.998425i	$-0.482133\pi$
$383$	−17.3408	−	12.9812i	−0.886076	−	0.663308i	−0.942176	+	0.335117i	$0.891224\pi$
$384$		0			0
$385$	−11.8199	−	40.1528i	−0.602398	−	2.04638i
$386$		0			0
$387$	−29.5279	+	11.0133i	−1.50099	+	0.559840i
$388$		0			0
$389$	5.53251	−	3.55553i	0.280509	−	0.180272i	−0.392819	−	0.919616i	$-0.628500\pi$
$389$	5.53251	−	3.55553i	0.280509	−	0.180272i	0.673329	+	0.739343i	$0.264864\pi$
$390$		0			0
$391$	−10.0019	+	20.1443i	−0.505819	+	1.01874i
$392$		0			0
$393$	27.7625	+	6.03936i	1.40043	+	0.304645i
$394$		0			0
$395$	−13.0925	+	2.85752i	−0.658757	+	0.143778i
$396$		0			0
$397$	−16.1484	−	6.02303i	−0.810463	−	0.302287i	−0.0901430	−	0.995929i	$-0.528732\pi$
$397$	−16.1484	−	6.02303i	−0.810463	−	0.302287i	−0.720320	+	0.693642i	$0.756005\pi$
$398$		0			0
$399$	20.8125	−	2.99239i	1.04193	−	0.149807i
$400$		0			0
$401$	−4.98341	−	4.31815i	−0.248860	−	0.215638i	0.521494	−	0.853255i	$-0.325375\pi$
$401$	−4.98341	−	4.31815i	−0.248860	−	0.215638i	−0.770354	+	0.637617i	$0.779920\pi$
$402$		0			0
$403$	0.462848	+	2.12768i	0.0230561	+	0.105987i
$404$		0			0
$405$	−3.48613	−	9.32710i	−0.173227	−	0.463467i
$406$		0			0
$407$	−24.9090	−	1.78152i	−1.23469	−	0.0883069i
$408$		0			0
$409$	2.16284	+	7.36594i	0.106945	+	0.364222i	0.995525	−	0.0945002i	$-0.0301253\pi$
$409$	2.16284	+	7.36594i	0.106945	+	0.364222i	−0.888579	+	0.458723i	$0.848307\pi$
$410$		0			0
$411$	−26.5114	−	3.81177i	−1.30771	−	0.188021i
$412$		0			0
$413$	−3.98175	+	3.98175i	−0.195929	+	0.195929i
$414$		0			0
$415$	−23.3631	−	3.34273i	−1.14685	−	0.164088i
$416$		0			0
$417$	−21.6295	−	28.8936i	−1.05920	−	1.41492i
$418$		0			0
$419$	−5.05743	+	1.48500i	−0.247072	+	0.0725468i	−0.402924	−	0.915234i	$-0.632006\pi$
$419$	−5.05743	+	1.48500i	−0.247072	+	0.0725468i	0.155852	+	0.987780i	$0.450188\pi$
$420$		0			0
$421$	6.08524	−	5.27289i	0.296576	−	0.256985i	−0.493843	−	0.869551i	$-0.664408\pi$
$421$	6.08524	−	5.27289i	0.296576	−	0.256985i	0.790419	+	0.612566i	$0.209863\pi$
$422$		0			0
$423$	32.4424	+	59.4137i	1.57740	+	2.88880i
$424$		0			0
$425$	−23.3907	−	1.64065i	−1.13462	−	0.0795830i
$426$		0			0
$427$	−1.55007	−	21.6728i	−0.0750131	−	1.04882i
$428$		0			0
$429$	2.22140	+	15.4502i	0.107250	+	0.745941i
$430$		0			0
$431$	−13.5698	+	6.19713i	−0.653635	+	0.298505i	−0.714494	−	0.699641i	$-0.753343\pi$
$431$	−13.5698	+	6.19713i	−0.653635	+	0.298505i	0.0608591	+	0.998146i	$0.480616\pi$
$432$		0			0
$433$	−6.36232	−	17.0580i	−0.305754	−	0.819757i	−0.995417	−	0.0956271i	$-0.969514\pi$
$433$	−6.36232	−	17.0580i	−0.305754	−	0.819757i	0.689664	−	0.724130i	$-0.257758\pi$
$434$		0			0
$435$	−41.9120	+	19.1754i	−2.00953	+	0.919388i
$436$		0			0
$437$	4.42091	−	7.50644i	0.211481	−	0.359082i
$438$		0			0
$439$	−10.4656	−	16.2847i	−0.499494	−	0.777228i	0.496368	−	0.868112i	$-0.334667\pi$
$439$	−10.4656	−	16.2847i	−0.499494	−	0.777228i	−0.995861	+	0.0908849i	$0.971030\pi$
$440$		0			0
$441$	−20.0446	+	43.8917i	−0.954507	+	2.09008i
$442$		0			0
$443$	9.43394	−	25.2934i	0.448220	−	1.20173i	−0.494805	−	0.869004i	$-0.664761\pi$
$443$	9.43394	−	25.2934i	0.448220	−	1.20173i	0.943025	−	0.332721i	$-0.107967\pi$
$444$		0			0
$445$	15.5347	−	15.5561i	0.736416	−	0.737429i
$446$		0			0
$447$	40.0810	−	2.86665i	1.89577	−	0.135588i
$448$		0			0
$449$	2.66358	−	4.14461i	0.125702	−	0.195596i	−0.772698	−	0.634773i	$-0.781094\pi$
$449$	2.66358	−	4.14461i	0.125702	−	0.195596i	0.898401	+	0.439177i	$0.144730\pi$
$450$		0			0
$451$	3.28630	−	11.1921i	0.154746	−	0.527016i
$452$		0			0
$453$	4.69118	−	65.5912i	0.220411	−	3.08174i
$454$		0			0
$455$	6.07606	−	8.12829i	0.284850	−	0.381060i
$456$		0			0
$457$	−31.0725	+	23.2606i	−1.45351	+	1.08808i	−0.475453	+	0.879741i	$0.657716\pi$
$457$	−31.0725	+	23.2606i	−1.45351	+	1.08808i	−0.978056	+	0.208342i	$0.933193\pi$
$458$		0			0
$459$	−33.5974			−1.56819
$460$		0			0
$461$	18.2937			0.852025			0.426012	−	0.904717i	$-0.359918\pi$
$461$	18.2937			0.852025			0.426012	+	0.904717i	$0.359918\pi$
$462$		0			0
$463$	14.5835	−	10.9171i	0.677752	−	0.507359i	−0.204061	−	0.978958i	$-0.565414\pi$
$463$	14.5835	−	10.9171i	0.677752	−	0.507359i	0.881813	+	0.471600i	$0.156323\pi$
$464$		0			0
$465$	−1.77574	−	12.2906i	−0.0823479	−	0.569963i
$466$		0			0
$467$	1.21100	−	16.9320i	0.0560383	−	0.783517i	−0.889279	−	0.457365i	$-0.848793\pi$
$467$	1.21100	−	16.9320i	0.0560383	−	0.783517i	0.945317	−	0.326152i	$-0.105752\pi$
$468$		0			0
$469$	16.9075	−	57.5818i	0.780718	−	2.65888i
$470$		0			0
$471$	−27.7365	+	43.1589i	−1.27803	+	1.98866i
$472$		0			0
$473$	−27.0705	+	1.93612i	−1.24470	+	0.0890229i
$474$		0			0
$475$	8.99174	+	1.28021i	0.412569	+	0.0587402i
$476$		0			0
$477$	15.6034	−	41.8342i	0.714428	−	1.91546i
$478$		0			0
$479$	−15.3017	+	33.5060i	−0.699152	+	1.53093i	0.141845	+	0.989889i	$0.454697\pi$
$479$	−15.3017	+	33.5060i	−0.699152	+	1.53093i	−0.840997	+	0.541040i	$0.818031\pi$
$480$		0			0
$481$	−3.27343	−	5.09356i	−0.149256	−	0.232246i
$482$		0			0
$483$	25.0098	+	49.5609i	1.13799	+	2.25510i
$484$		0			0
$485$	−7.11371	−	15.5486i	−0.323017	−	0.706024i
$486$		0			0
$487$	−2.37827	−	6.37638i	−0.107770	−	0.288941i	0.871860	−	0.489756i	$-0.162914\pi$
$487$	−2.37827	−	6.37638i	−0.107770	−	0.288941i	−0.979629	+	0.200814i	$0.935641\pi$
$488$		0			0
$489$	−13.4649	+	6.14919i	−0.608902	+	0.278076i
$490$		0			0
$491$	1.60863	+	11.1883i	0.0725965	+	0.504920i	0.993383	+	0.114852i	$0.0366394\pi$
$491$	1.60863	+	11.1883i	0.0725965	+	0.504920i	−0.920786	+	0.390068i	$0.872452\pi$
$492$		0			0
$493$	2.37048	+	33.1436i	0.106761	+	1.49271i
$494$		0			0
$495$	−4.13873	−	57.3138i	−0.186022	−	2.57606i
$496$		0			0
$497$	−19.4568	−	35.6324i	−0.872755	−	1.59833i
$498$		0			0
$499$	4.44661	−	3.85301i	0.199058	−	0.172484i	−0.549628	−	0.835409i	$-0.685231\pi$
$499$	4.44661	−	3.85301i	0.199058	−	0.172484i	0.748686	+	0.662925i	$0.230685\pi$
$500$		0			0
$501$	−28.5713	+	8.38930i	−1.27647	+	0.374806i
$502$		0			0
$503$	14.8219	+	19.7997i	0.660875	+	0.882826i	0.998286	−	0.0585316i	$-0.0186418\pi$
$503$	14.8219	+	19.7997i	0.660875	+	0.882826i	−0.337410	+	0.941358i	$0.609551\pi$
$504$		0			0
$505$	−5.85443	−	7.80942i	−0.260519	−	0.347514i
$506$		0			0
$507$	24.0653	−	24.0653i	1.06878	−	1.06878i
$508$		0			0
$509$	−20.2959	−	2.91812i	−0.899602	−	0.129343i	−0.323029	−	0.946389i	$-0.604701\pi$
$509$	−20.2959	−	2.91812i	−0.899602	−	0.129343i	−0.576573	+	0.817046i	$0.695610\pi$
$510$		0			0
$511$	5.82244	+	19.8294i	0.257570	+	0.877202i
$512$		0			0
$513$	12.9805	+	0.928382i	0.573102	+	0.0409891i
$514$		0			0
$515$	−6.99118	−	3.18697i	−0.308068	−	0.140435i
$516$		0			0
$517$	12.3917	+	56.9638i	0.544987	+	2.50526i
$518$		0			0
$519$	−0.201933	−	0.174976i	−0.00886386	−	0.00768058i
$520$		0			0
$521$	3.83874	−	0.551927i	0.168178	−	0.0241804i	−0.0577113	−	0.998333i	$-0.518380\pi$
$521$	3.83874	−	0.551927i	0.168178	−	0.0241804i	0.225889	+	0.974153i	$0.427471\pi$
$522$		0			0
$523$	40.3619	+	15.0542i	1.76490	+	0.658275i	0.999898	+	0.0142511i	$0.00453643\pi$
$523$	40.3619	+	15.0542i	1.76490	+	0.658275i	0.765005	+	0.644024i	$0.222736\pi$
$524$		0			0
$525$	−37.8413	+	43.7926i	−1.65153	+	1.91126i
$526$		0			0
$527$	−8.74820	−	1.90305i	−0.381077	−	0.0828983i
$528$		0			0
$529$	22.5056	+	4.74307i	0.978506	+	0.206221i
$530$		0			0
$531$	−6.50343	+	4.17950i	−0.282225	+	0.181375i
$532$		0			0
$533$	2.64982	−	0.988332i	0.114777	−	0.0428094i
$534$		0			0
$535$	27.6720	−	8.14587i	1.19636	−	0.352177i
$536$		0			0
$537$	19.6923	+	14.7415i	0.849785	+	0.636141i
$538$		0			0
$539$	−27.2115	+	31.4038i	−1.17208	+	1.35266i
$540$		0			0
$541$	−34.7193	−	22.3127i	−1.49270	−	0.959299i	−0.995806	−	0.0914859i	$-0.970838\pi$
$541$	−34.7193	−	22.3127i	−1.49270	−	0.959299i	−0.496891	−	0.867813i	$-0.665525\pi$
$542$		0			0
$543$	−31.5463	+	17.2256i	−1.35378	+	0.739219i
$544$		0			0
$545$	−4.94665	+	22.8148i	−0.211891	+	0.977279i
$546$		0			0
$547$	−4.70019	+	8.60776i	−0.200966	+	0.368041i	−0.958653	−	0.284576i	$-0.908147\pi$
$547$	−4.70019	+	8.60776i	−0.200966	+	0.368041i	0.757688	+	0.652617i	$0.226329\pi$
$548$		0			0
$549$	4.24521	−	29.5261i	0.181181	−	1.26014i
$550$		0			0
$551$		−	12.8707i		−	0.548308i
$552$		0			0
$553$	16.8620	+	16.8620i	0.717047	+	0.717047i
$554$		0			0
$555$	16.5697	+	30.2957i	0.703345	+	1.28598i
$556$		0			0
$557$	−2.19825	−	1.20033i	−0.0931427	−	0.0508598i	0.432002	−	0.901872i	$-0.357807\pi$
$557$	−2.19825	−	1.20033i	−0.0931427	−	0.0508598i	−0.525145	+	0.851013i	$0.675989\pi$
$558$		0			0
$559$	−4.30907	−	4.97293i	−0.182254	−	0.210333i
$560$		0			0
$561$	−61.5787	−	18.0811i	−2.59986	−	0.763386i
$562$		0			0
$563$	−24.7003	+	5.37323i	−1.04099	+	0.226455i	−0.700396	−	0.713754i	$-0.746993\pi$
$563$	−24.7003	+	5.37323i	−1.04099	+	0.226455i	−0.340599	+	0.940209i	$0.610630\pi$
$564$		0			0
$565$	35.6130	−	30.9017i	1.49825	−	1.30004i
$566$		0			0
$567$	−10.6186	+	14.1848i	−0.445939	+	0.595704i
$568$		0			0
$569$	5.88101	+	12.8776i	0.246545	+	0.539857i	0.991932	−	0.126775i	$-0.0404625\pi$
$569$	5.88101	+	12.8776i	0.246545	+	0.539857i	−0.745387	+	0.666632i	$0.767735\pi$
$570$		0			0
$571$	21.9309	+	10.0155i	0.917778	+	0.419135i	0.817569	−	0.575831i	$-0.195321\pi$
$571$	21.9309	+	10.0155i	0.917778	+	0.419135i	0.100210	+	0.994966i	$0.468049\pi$
$572$		0			0
$573$	8.80348	−	40.4689i	0.367770	−	1.69061i
$574$		0			0
$575$	4.36650	+	23.5782i	0.182096	+	0.983281i
$576$		0			0
$577$	−4.27433	+	19.6488i	−0.177943	+	0.817989i	0.798463	+	0.602044i	$0.205647\pi$
$577$	−4.27433	+	19.6488i	−0.177943	+	0.817989i	−0.976405	+	0.215945i	$0.930717\pi$
$578$		0			0
$579$	−7.97402	−	3.64161i	−0.331389	−	0.151340i
$580$		0			0
$581$	17.4466	+	38.2026i	0.723805	+	1.58491i
$582$		0			0
$583$	23.0426	−	30.7813i	0.954326	−	1.27483i
$584$		0			0
$585$	10.5230	−	9.13086i	0.435071	−	0.377515i
$586$		0			0
$587$	39.4885	−	8.59019i	1.62986	−	0.354555i	0.697643	−	0.716446i	$-0.254232\pi$
$587$	39.4885	−	8.59019i	1.62986	−	0.354555i	0.932221	+	0.361891i	$0.117869\pi$
$588$		0			0
$589$	3.32731	+	0.976986i	0.137099	+	0.0402560i
$590$		0			0
$591$	−4.50470	−	5.19870i	−0.185298	−	0.213846i
$592$		0			0
$593$	15.9594	+	8.71447i	0.655372	+	0.357860i	0.772280	−	0.635283i	$-0.219116\pi$
$593$	15.9594	+	8.71447i	0.655372	+	0.357860i	−0.116908	+	0.993143i	$0.537298\pi$
$594$		0			0
$595$	20.0222	+	36.6082i	0.820831	+	1.50079i
$596$		0			0
$597$	11.1041	+	11.1041i	0.454460	+	0.454460i
$598$		0			0
$599$		−	3.81961i		−	0.156065i	−0.996951	−	0.0780325i	$-0.975136\pi$
$599$		−	3.81961i		−	0.156065i	0.996951	−	0.0780325i	$-0.0248638\pi$
$600$		0			0
$601$	5.19296	−	36.1179i	0.211825	−	1.47328i	−0.555230	−	0.831697i	$-0.687370\pi$
$601$	5.19296	−	36.1179i	0.211825	−	1.47328i	0.767055	−	0.641581i	$-0.221721\pi$
$602$		0			0
$603$	39.4849	−	72.3112i	1.60795	−	2.94474i
$604$		0			0
$605$	5.27373	−	24.3234i	0.214408	−	0.988885i
$606$		0			0
$607$	16.2207	−	8.85717i	0.658377	−	0.359501i	−0.115074	−	0.993357i	$-0.536710\pi$
$607$	16.2207	−	8.85717i	0.658377	−	0.359501i	0.773451	+	0.633856i	$0.218529\pi$
$608$		0			0
$609$	68.9973	+	44.3419i	2.79591	+	1.79682i
$610$		0			0
$611$	−9.25589	+	10.6819i	−0.374453	+	0.432142i
$612$		0			0
$613$	−11.0135	−	8.24461i	−0.444831	−	0.332996i	0.353268	−	0.935522i	$-0.385070\pi$
$613$	−11.0135	−	8.24461i	−0.444831	−	0.332996i	−0.798100	+	0.602526i	$0.794161\pi$
$614$		0			0
$615$	−15.4728	+	4.55476i	−0.623922	+	0.183666i
$616$		0			0
$617$	−18.6754	+	6.96557i	−0.751844	+	0.280423i	−0.696025	−	0.718017i	$-0.745050\pi$
$617$	−18.6754	+	6.96557i	−0.751844	+	0.280423i	−0.0558193	+	0.998441i	$0.517777\pi$
$618$		0			0
$619$	6.65467	−	4.27669i	0.267474	−	0.171895i	−0.400029	−	0.916503i	$-0.631000\pi$
$619$	6.65467	−	4.27669i	0.267474	−	0.171895i	0.667502	+	0.744608i	$0.267363\pi$
$620$		0			0
$621$	8.60498	+	33.2633i	0.345306	+	1.33481i
$622$		0			0
$623$	−38.2273	−	8.31584i	−1.53154	−	0.333167i
$624$		0			0
$625$	−20.9941	+	13.5737i	−0.839765	+	0.542950i
$626$		0			0
$627$	23.2915	+	8.68729i	0.930174	+	0.346937i
$628$		0			0
$629$	24.6413	−	3.54289i	0.982514	−	0.141264i
$630$		0			0
$631$	33.9642	+	29.4301i	1.35209	+	1.17159i	0.968765	+	0.247981i	$0.0797671\pi$
$631$	33.9642	+	29.4301i	1.35209	+	1.17159i	0.383327	+	0.923613i	$0.374778\pi$
$632$		0			0
$633$	−10.0378	−	46.1430i	−0.398967	−	1.83402i
$634$		0			0
$635$	−35.9406	−	16.3837i	−1.42626	−	0.650167i
$636$		0			0
$637$	−10.0491	−	0.718724i	−0.398159	−	0.0284769i
$638$		0			0
$639$	−15.7026	−	53.4783i	−0.621187	−	2.11557i
$640$		0			0
$641$	46.8352	+	6.73389i	1.84988	+	0.265973i	0.975617	−	0.219479i	$-0.0704358\pi$
$641$	46.8352	+	6.73389i	1.84988	+	0.265973i	0.874263	+	0.485452i	$0.161345\pi$
$642$		0			0
$643$	12.4789	−	12.4789i	0.492120	−	0.492120i	−0.416854	−	0.908974i	$-0.636867\pi$
$643$	12.4789	−	12.4789i	0.492120	−	0.492120i	0.908974	+	0.416854i	$0.136867\pi$
$644$		0			0
$645$	22.5100	+	30.0268i	0.886329	+	1.18230i
$646$		0			0
$647$	11.9332	+	15.9409i	0.469141	+	0.626700i	0.971238	−	0.238112i	$-0.0765286\pi$
$647$	11.9332	+	15.9409i	0.469141	+	0.626700i	−0.502096	+	0.864812i	$0.667438\pi$
$648$		0			0
$649$	−6.38771	+	1.87560i	−0.250739	+	0.0736237i
$650$		0			0
$651$	−16.7007	+	14.4712i	−0.654551	+	0.567172i
$652$		0			0
$653$	11.3332	+	20.7553i	0.443504	+	0.812217i	0.999824	−	0.0187512i	$-0.00596905\pi$
$653$	11.3332	+	20.7553i	0.443504	+	0.812217i	−0.556320	+	0.830968i	$0.687787\pi$
$654$		0			0
$655$	−1.57292	−	21.7821i	−0.0614591	−	0.851097i
$656$		0			0
$657$	2.02406	+	28.3000i	0.0789660	+	1.10409i
$658$		0			0
$659$	1.74351	+	12.1264i	0.0679176	+	0.472377i	0.995188	+	0.0979848i	$0.0312397\pi$
$659$	1.74351	+	12.1264i	0.0679176	+	0.472377i	−0.927270	+	0.374393i	$0.877851\pi$
$660$		0			0
$661$	−3.24253	+	1.48081i	−0.126120	+	0.0575969i	−0.477475	−	0.878645i	$-0.658448\pi$
$661$	−3.24253	+	1.48081i	−0.126120	+	0.0575969i	0.351356	+	0.936242i	$0.385721\pi$
$662$		0			0
$663$	−5.43779	−	14.5793i	−0.211186	−	0.566212i
$664$		0			0
$665$	−6.72408	−	14.6970i	−0.260749	−	0.569924i
$666$		0			0
$667$	32.2068	−	10.8357i	1.24705	−	0.419558i
$668$		0			0
$669$	26.3659	+	41.0261i	1.01936	+	1.58616i
$670$		0			0
$671$	10.6713	−	23.3670i	0.411963	−	0.902072i
$672$		0			0
$673$	−6.78477	+	18.1907i	−0.261534	+	0.701199i	0.738115	+	0.674675i	$0.235716\pi$
$673$	−6.78477	+	18.1907i	−0.261534	+	0.701199i	−0.999648	+	0.0265234i	$0.991556\pi$
$674$		0			0
$675$	−28.6466	+	21.5061i	−1.10261	+	0.827769i
$676$		0			0
$677$	−4.07328	+	0.291326i	−0.156549	+	0.0111966i	−0.149394	−	0.988778i	$-0.547732\pi$
$677$	−4.07328	+	0.291326i	−0.156549	+	0.0111966i	−0.00715516	+	0.999974i	$0.502278\pi$
$678$		0			0
$679$	−16.4500	+	25.5967i	−0.631294	+	0.982313i
$680$		0			0
$681$	6.87120	−	23.4012i	0.263305	−	0.896734i
$682$		0			0
$683$	−0.189207	+	2.64546i	−0.00723981	+	0.101226i	−0.999787	−	0.0206344i	$-0.993431\pi$
$683$	−0.189207	+	2.64546i	−0.00723981	+	0.101226i	0.992547	+	0.121860i	$0.0388860\pi$
$684$		0			0
$685$	2.94392	+	20.3761i	0.112482	+	0.778530i
$686$		0			0
$687$	47.5067	−	35.5631i	1.81249	−	1.35682i
$688$		0			0
$689$	9.32252			0.355160
$690$		0			0
$691$	2.79340			0.106266			0.0531329	−	0.998587i	$-0.483079\pi$
$691$	2.79340			0.106266			0.0531329	+	0.998587i	$0.483079\pi$
$692$		0			0
$693$	−81.8594	+	61.2792i	−3.10958	+	2.32780i
$694$		0			0
$695$	−16.6103	+	22.2205i	−0.630064	+	0.842873i
$696$		0			0
$697$	−0.829548	+	11.5986i	−0.0314214	+	0.439328i
$698$		0			0
$699$	−2.81594	+	9.59022i	−0.106509	+	0.362736i
$700$		0			0
$701$	−7.43756	+	11.5731i	−0.280913	+	0.437109i	−0.952824	−	0.303523i	$-0.901837\pi$
$701$	−7.43756	+	11.5731i	−0.280913	+	0.437109i	0.671911	+	0.740632i	$0.265474\pi$
$702$		0			0
$703$	−9.61816	+	0.687904i	−0.362756	+	0.0259448i
$704$		0			0
$705$	56.9599	−	57.0382i	2.14524	−	2.14818i
$706$		0			0
$707$	−6.06956	+	16.2731i	−0.228269	+	0.612014i
$708$		0			0
$709$	−7.33381	+	16.0588i	−0.275427	+	0.603101i	−0.995908	−	0.0903737i	$-0.971194\pi$
$709$	−7.33381	+	16.0588i	−0.275427	+	0.603101i	0.720481	+	0.693475i	$0.243921\pi$
$710$		0			0
$711$	17.6995	+	27.5409i	0.663782	+	1.03287i
$712$		0			0
$713$	0.356465	+	9.14859i	0.0133497	+	0.342618i
$714$		0			0
$715$	10.9103	−	4.99161i	0.408021	−	0.186676i
$716$		0			0
$717$	−25.2381	−	67.6659i	−0.942533	−	2.52703i
$718$		0			0
$719$	28.3027	−	12.9254i	1.05551	−	0.482036i	0.189407	−	0.981899i	$-0.439344\pi$
$719$	28.3027	−	12.9254i	1.05551	−	0.482036i	0.866104	+	0.499863i	$0.166616\pi$
$720$		0			0
$721$	1.94579	+	13.5333i	0.0724650	+	0.504005i
$722$		0			0
$723$	−2.75021	−	38.4529i	−0.102281	−	1.43008i
$724$		0			0
$725$	23.2368	+	26.7423i	0.862992	+	0.993186i
$726$		0			0
$727$	−14.3161	−	26.2180i	−0.530955	−	0.972372i	−0.996192	−	0.0871856i	$-0.972213\pi$
$727$	−14.3161	−	26.2180i	−0.530955	−	0.972372i	0.465237	−	0.885186i	$-0.345969\pi$
$728$		0			0
$729$	28.8680	−	25.0143i	1.06918	−	0.926454i
$730$		0			0
$731$	25.9591	−	7.62227i	0.960131	−	0.281920i
$732$		0			0
$733$	−16.3575	−	21.8511i	−0.604179	−	0.807089i	0.389299	−	0.921111i	$-0.372717\pi$
$733$	−16.3575	−	21.8511i	−0.604179	−	0.807089i	−0.993478	+	0.114023i	$0.963626\pi$
$734$		0			0
$735$	56.8784	+	8.13802i	2.09799	+	0.300175i
$736$		0			0
$737$	50.1698	−	50.1698i	1.84803	−	1.84803i
$738$		0			0
$739$	−10.2747	−	1.47728i	−0.377962	−	0.0543428i	−0.0492842	−	0.998785i	$-0.515694\pi$
$739$	−10.2747	−	1.47728i	−0.377962	−	0.0543428i	−0.328678	+	0.944442i	$0.606603\pi$
$740$		0			0
$741$	1.69804	+	5.78301i	0.0623792	+	0.212444i
$742$		0			0
$743$	−6.94865	−	0.496977i	−0.254921	−	0.0182323i	−0.0567063	−	0.998391i	$-0.518060\pi$
$743$	−6.94865	−	0.496977i	−0.254921	−	0.0182323i	−0.198215	+	0.980159i	$0.563514\pi$
$744$		0			0
$745$	−10.8138	−	28.9322i	−0.396187	−	1.06000i
$746$		0			0
$747$	12.2559	+	56.3396i	0.448421	+	2.06136i
$748$		0			0
$749$	−38.7936	−	33.6149i	−1.41749	−	1.22826i
$750$		0			0
$751$	−50.4859	+	7.25878i	−1.84226	+	0.264877i	−0.973221	−	0.229872i	$-0.926169\pi$
$751$	−50.4859	+	7.25878i	−1.84226	+	0.264877i	−0.869036	+	0.494748i	$0.835260\pi$
$752$		0			0
$753$	−72.0592	−	26.8767i	−2.62598	−	0.979441i
$754$		0			0
$755$	−49.3831	+	10.7782i	−1.79724	+	0.392258i
$756$		0			0
$757$	−8.29674	−	1.80485i	−0.301550	−	0.0655982i	0.0592445	−	0.998244i	$-0.481131\pi$
$757$	−8.29674	−	1.80485i	−0.301550	−	0.0655982i	−0.360795	+	0.932645i	$0.617494\pi$
$758$		0			0
$759$	−2.12975	+	65.5972i	−0.0773049	+	2.38103i
$760$		0			0
$761$	2.90814	−	1.86895i	0.105420	−	0.0677494i	−0.486869	−	0.873475i	$-0.661861\pi$
$761$	2.90814	−	1.86895i	0.105420	−	0.0677494i	0.592289	+	0.805726i	$0.298225\pi$
$762$		0			0
$763$	38.9229	−	14.5175i	1.40910	−	0.525569i
$764$		0			0
$765$	16.1764	+	54.9523i	0.584861	+	1.98680i
$766$		0			0
$767$	−1.29216	−	0.967301i	−0.0466573	−	0.0349272i
$768$		0			0
$769$	−8.98988	+	10.3749i	−0.324183	+	0.374127i	−0.894324	−	0.447419i	$-0.852343\pi$
$769$	−8.98988	+	10.3749i	−0.324183	+	0.374127i	0.570141	+	0.821547i	$0.306889\pi$
$770$		0			0
$771$	−9.68942	−	6.22701i	−0.348956	−	0.224260i
$772$		0			0
$773$	23.1343	−	12.6323i	0.832081	−	0.454351i	−0.00594390	−	0.999982i	$-0.501892\pi$
$773$	23.1343	−	12.6323i	0.832081	−	0.454351i	0.838025	+	0.545632i	$0.183710\pi$
$774$		0			0
$775$	−8.67726	+	3.97719i	−0.311696	+	0.142865i
$776$		0			0
$777$	29.4487	−	53.9312i	1.05647	−	1.93477i
$778$		0			0
$779$	0.640997	−	4.45823i	0.0229661	−	0.159733i
$780$		0			0
$781$		−	47.9980i		−	1.71750i
$782$		0			0
$783$	35.8940	+	35.8940i	1.28275	+	1.28275i
$784$		0			0
$785$	37.8445	+	11.0839i	1.35073	+	0.395602i
$786$		0			0
$787$	29.1675	+	15.9267i	1.03971	+	0.567725i	0.905992	−	0.423295i	$-0.139126\pi$
$787$	29.1675	+	15.9267i	1.03971	+	0.567725i	0.133718	+	0.991019i	$0.457308\pi$
$788$		0			0
$789$	33.8626	+	39.0795i	1.20554	+	1.39127i
$790$		0			0
$791$	−80.5060	−	23.6387i	−2.86246	−	0.840495i
$792$		0			0
$793$	6.08594	−	1.32391i	0.216118	−	0.0470136i
$794$		0			0
$795$	−53.0347	−	3.75651i	−1.88095	−	0.133230i
$796$		0			0
$797$	9.95132	−	13.2934i	0.352494	−	0.470877i	−0.588890	−	0.808213i	$-0.700435\pi$
$797$	9.95132	−	13.2934i	0.352494	−	0.470877i	0.941384	+	0.337336i	$0.109526\pi$
$798$		0			0
$799$	−24.1415	−	52.8625i	−0.854065	−	1.87014i
$800$		0			0
$801$	−48.8546	−	22.3112i	−1.72619	−	0.788326i
$802$		0			0
$803$	−5.19367	+	23.8749i	−0.183281	+	0.842528i
$804$		0			0
$805$	31.1160	−	29.1992i	1.09669	−	1.02914i
$806$		0			0
$807$	2.84308	−	13.0694i	0.100081	−	0.460065i
$808$		0			0
$809$	6.53098	+	2.98260i	0.229617	+	0.104863i	0.526901	−	0.849926i	$-0.323354\pi$
$809$	6.53098	+	2.98260i	0.229617	+	0.104863i	−0.297284	+	0.954789i	$0.596081\pi$
$810$		0			0
$811$	1.09978	+	2.40818i	0.0386185	+	0.0845628i	0.927958	−	0.372685i	$-0.121563\pi$
$811$	1.09978	+	2.40818i	0.0386185	+	0.0845628i	−0.889340	+	0.457247i	$0.848835\pi$
$812$		0			0
$813$	−17.4388	+	23.2955i	−0.611604	+	0.817008i
$814$		0			0
$815$	7.45692	+	8.59381i	0.261204	+	0.301028i
$816$		0			0
$817$	−10.2400	+	2.22758i	−0.358252	+	0.0779330i
$818$		0			0
$819$	−23.7880	−	6.98478i	−0.831219	−	0.244068i
$820$		0			0
$821$	4.60681	+	5.31654i	0.160779	+	0.185549i	0.830423	−	0.557134i	$-0.188099\pi$
$821$	4.60681	+	5.31654i	0.160779	+	0.185549i	−0.669644	+	0.742682i	$0.733553\pi$
$822$		0			0
$823$	−17.9533	−	9.80325i	−0.625813	−	0.341720i	0.134850	−	0.990866i	$-0.456945\pi$
$823$	−17.9533	−	9.80325i	−0.625813	−	0.341720i	−0.760664	+	0.649146i	$0.775126\pi$
$824$		0			0
$825$	−64.0787	+	24.0004i	−2.23093	+	0.835587i
$826$		0			0
$827$	0.0259211	+	0.0259211i	0.000901366	+	0.000901366i	0.707557	−	0.706656i	$-0.249797\pi$
$827$	0.0259211	+	0.0259211i	0.000901366	+	0.000901366i	−0.706656	+	0.707557i	$0.749797\pi$
$828$		0			0
$829$		−	55.5470i		−	1.92923i	−0.263667	−	0.964614i	$-0.584932\pi$
$829$		−	55.5470i		−	1.92923i	0.263667	−	0.964614i	$-0.415068\pi$
$830$		0			0
$831$	11.6474	−	81.0097i	0.404045	−	2.81020i
$832$		0			0
$833$	19.8522	−	36.3566i	0.687837	−	1.25968i
$834$		0			0
$835$	12.3877	+	19.2466i	0.428695	+	0.666056i
$836$		0			0
$837$	−12.0039	+	6.55463i	−0.414916	+	0.226561i
$838$		0			0
$839$	−17.3578	−	11.1552i	−0.599258	−	0.385120i	0.205557	−	0.978645i	$-0.434099\pi$
$839$	−17.3578	−	11.1552i	−0.599258	−	0.385120i	−0.804815	+	0.593525i	$0.797736\pi$
$840$		0			0
$841$	13.8857	−	16.0249i	0.478816	−	0.552584i
$842$		0			0
$843$	−27.6041	−	20.6642i	−0.950736	−	0.711712i
$844$		0			0
$845$	−22.9686	−	12.5213i	−0.790145	−	0.430747i
$846$		0			0
$847$	−41.4965	+	15.4774i	−1.42584	+	0.531810i
$848$		0			0
$849$	−28.8424	+	18.5359i	−0.989869	+	0.636150i
$850$		0			0
$851$	−9.81879	−	23.4888i	−0.336584	−	0.805187i
$852$		0			0
$853$	16.4174	+	3.57138i	0.562120	+	0.122282i	0.484643	−	0.874712i	$-0.338950\pi$
$853$	16.4174	+	3.57138i	0.562120	+	0.122282i	0.0774778	+	0.996994i	$0.475313\pi$
$854$		0			0
$855$	−4.73135	−	21.6780i	−0.161809	−	0.741372i
$856$		0			0
$857$	15.6360	+	5.83194i	0.534117	+	0.199215i	0.602026	−	0.798476i	$-0.294360\pi$
$857$	15.6360	+	5.83194i	0.534117	+	0.199215i	−0.0679095	+	0.997691i	$0.521633\pi$
$858$		0			0
$859$	27.5937	−	3.96738i	0.941486	−	0.135365i	0.345553	−	0.938399i	$-0.387691\pi$
$859$	27.5937	−	3.96738i	0.941486	−	0.135365i	0.595933	+	0.803034i	$0.296782\pi$
$860$		0			0
$861$	21.6915	+	18.7958i	0.739243	+	0.640557i
$862$		0			0
$863$	9.97383	+	45.8489i	0.339513	+	1.56072i	0.757853	+	0.652426i	$0.226249\pi$
$863$	9.97383	+	45.8489i	0.339513	+	1.56072i	−0.418340	+	0.908291i	$0.637388\pi$
$864$		0			0
$865$	−0.0851898	+	0.186879i	−0.00289654	+	0.00635408i
$866$		0			0
$867$	14.4870	+	1.03613i	0.492004	+	0.0351888i
$868$		0			0
$869$	7.94285	+	27.0508i	0.269443	+	0.917637i
$870$		0			0
$871$	17.0273	+	2.44815i	0.576947	+	0.0829524i
$872$		0			0
$873$	−29.5372	+	29.5372i	−0.999682	+	0.999682i
$874$		0			0
$875$	40.5051	+	18.3973i	1.36932	+	0.621942i
$876$		0			0
$877$	17.3556	+	23.1844i	0.586058	+	0.782882i	0.991342	−	0.131309i	$-0.0419180\pi$
$877$	17.3556	+	23.1844i	0.586058	+	0.782882i	−0.405283	+	0.914191i	$0.632827\pi$
$878$		0			0
$879$	−4.50249	+	1.32205i	−0.151865	+	0.0445917i
$880$		0			0
$881$	9.35490	−	8.10607i	0.315175	−	0.273100i	−0.482879	−	0.875687i	$-0.660409\pi$
$881$	9.35490	−	8.10607i	0.315175	−	0.273100i	0.798053	+	0.602587i	$0.205863\pi$
$882$		0			0
$883$	−3.08923	−	5.65750i	−0.103961	−	0.190390i	0.820521	−	0.571617i	$-0.193684\pi$
$883$	−3.08923	−	5.65750i	−0.103961	−	0.190390i	−0.924482	+	0.381227i	$0.875502\pi$
$884$		0			0
$885$	6.96119	+	6.02354i	0.233998	+	0.202479i
$886$		0			0
$887$	−0.540983	−	7.56394i	−0.0181644	−	0.253972i	−0.998418	−	0.0562274i	$-0.982093\pi$
$887$	−0.540983	−	7.56394i	−0.0181644	−	0.253972i	0.980254	−	0.197745i	$-0.0633617\pi$
$888$		0			0
$889$	10.0030	+	69.5724i	0.335490	+	2.33338i
$890$		0			0
$891$	−19.0554	+	8.70231i	−0.638380	+	0.291538i
$892$		0			0
$893$	7.86643	+	21.0907i	0.263240	+	0.705774i
$894$		0			0
$895$	6.59546	−	17.7203i	0.220462	−	0.592323i
$896$		0			0
$897$	−13.0415	+	9.11774i	−0.435444	+	0.304433i
$898$		0			0
$899$	7.31304	+	11.3793i	0.243904	+	0.379521i
$900$		0			0
$901$	−15.9231	+	34.8668i	−0.530476	+	1.16158i
$902$		0			0
$903$	23.3371	−	62.5693i	0.776611	−	2.08218i
$904$		0			0
$905$	19.5490	+	19.5222i	0.649832	+	0.648940i
$906$		0			0
$907$	−8.86261	+	0.633866i	−0.294278	+	0.0210472i	−0.217698	−	0.976016i	$-0.569855\pi$
$907$	−8.86261	+	0.633866i	−0.294278	+	0.0210472i	−0.0765804	+	0.997063i	$0.524400\pi$
$908$		0			0
$909$	−12.8911	+	20.0589i	−0.427571	+	0.665313i
$910$		0			0
$911$	−8.27824	+	28.1931i	−0.274270	+	0.934079i	0.701018	+	0.713144i	$0.252729\pi$
$911$	−8.27824	+	28.1931i	−0.274270	+	0.934079i	−0.975288	+	0.220936i	$0.929089\pi$
$912$		0			0
$913$	−3.54217	+	49.5260i	−0.117229	+	1.63907i
$914$		0			0
$915$	−35.1556	+	5.07926i	−1.16221	+	0.167915i
$916$		0			0
$917$	−31.1107	+	23.2891i	−1.02736	+	0.769075i
$918$		0			0
$919$	−44.2708			−1.46036			−0.730180	−	0.683255i	$-0.760564\pi$
$919$	−44.2708			−1.46036			−0.730180	+	0.683255i	$0.760564\pi$
$920$		0			0
$921$	23.0853			0.760685
$922$		0			0
$923$	9.31617	−	6.97400i	0.306646	−	0.229552i
$924$		0			0
$925$	18.7424	−	18.7940i	0.616247	−	0.617943i
$926$		0			0
$927$	−1.33906	+	18.7225i	−0.0439805	+	0.614928i
$928$		0			0
$929$	−9.30150	+	31.6780i	−0.305172	+	1.03932i	0.653999	+	0.756495i	$0.273090\pi$
$929$	−9.30150	+	31.6780i	−0.305172	+	1.03932i	−0.959171	+	0.282826i	$0.908728\pi$
$930$		0			0
$931$	−8.67458	+	13.4979i	−0.284298	+	0.442376i
$932$		0			0
$933$	42.6043	−	3.04712i	1.39480	−	0.0997582i
$934$		0			0
$935$	0.0338785	+	49.3309i	0.00110795	+	1.61329i
$936$		0			0
$937$	−0.249579	+	0.669148i	−0.00815340	+	0.0218601i	−0.940963	−	0.338510i	$-0.890077\pi$
$937$	−0.249579	+	0.669148i	−0.00815340	+	0.0218601i	0.932809	+	0.360370i	$0.117350\pi$
$938$		0			0
$939$	33.8938	−	74.2171i	1.10608	−	2.42198i
$940$		0			0
$941$	−1.24166	−	1.93207i	−0.0404771	−	0.0629836i	0.820425	−	0.571754i	$-0.193737\pi$
$941$	−1.24166	−	1.93207i	−0.0404771	−	0.0629836i	−0.860902	+	0.508770i	$0.830100\pi$
$942$		0			0
$943$	11.6957	−	2.14934i	0.380864	−	0.0699921i
$944$		0			0
$945$	59.7395	+	22.2349i	1.94332	+	0.723303i
$946$		0			0
$947$	−2.62690	−	7.04300i	−0.0853628	−	0.228867i	0.887254	−	0.461281i	$-0.152610\pi$
$947$	−2.62690	−	7.04300i	−0.0853628	−	0.228867i	−0.972617	+	0.232415i	$0.925337\pi$
$948$		0			0
$949$	−5.38863	+	2.46090i	−0.174922	+	0.0798843i
$950$		0			0
$951$	5.66737	+	39.4174i	0.183777	+	1.27820i
$952$		0			0
$953$	4.04519	+	56.5591i	0.131037	+	1.83213i	0.460151	+	0.887841i	$0.347795\pi$
$953$	4.04519	+	56.5591i	0.131037	+	1.83213i	−0.329115	+	0.944290i	$0.606750\pi$
$954$		0			0
$955$	−31.7514	+	2.29282i	−1.02745	+	0.0741940i
$956$		0			0
$957$	46.4708	+	85.1050i	1.50219	+	2.75105i
$958$		0			0
$959$	27.6874	−	23.9912i	0.894071	−	0.774717i
$960$		0			0
$961$	26.2474	−	7.70693i	0.846690	−	0.248611i
$962$		0			0
$963$	−42.2315	−	56.4147i	−1.36089	−	1.81794i
$964$		0			0
$965$	−0.954361	+	6.67024i	−0.0307220	+	0.214723i
$966$		0			0
$967$	1.64299	−	1.64299i	0.0528351	−	0.0528351i	−0.680196	−	0.733031i	$-0.738105\pi$
$967$	1.64299	−	1.64299i	0.0528351	−	0.0528351i	0.733031	+	0.680196i	$0.238105\pi$
$968$		0			0
$969$	−24.5291	−	3.52675i	−0.787988	−	0.113296i
$970$		0			0
$971$	10.7909	+	36.7505i	0.346297	+	1.17938i	0.930045	+	0.367445i	$0.119767\pi$
$971$	10.7909	+	36.7505i	0.346297	+	1.17938i	−0.583748	+	0.811935i	$0.698415\pi$
$972$		0			0
$973$	49.2421	+	3.52186i	1.57863	+	0.112906i
$974$		0			0
$975$	−13.9688	−	8.95014i	−0.447361	−	0.286634i
$976$		0			0
$977$	−5.57687	−	25.6365i	−0.178420	−	0.820183i	−0.976138	−	0.217152i	$-0.930323\pi$
$977$	−5.57687	−	25.6365i	−0.178420	−	0.820183i	0.797718	−	0.603031i	$-0.206040\pi$
$978$		0			0
$979$	−34.9547	−	30.2884i	−1.11716	−	0.968021i
$980$		0			0
$981$	56.4510	−	8.11644i	1.80234	−	0.259138i
$982$		0			0
$983$	27.4549	+	10.2402i	0.875677	+	0.326611i	0.746799	−	0.665050i	$-0.231590\pi$
$983$	27.4549	+	10.2402i	0.875677	+	0.326611i	0.128878	+	0.991660i	$0.458862\pi$
$984$		0			0
$985$	−2.85556	+	4.45005i	−0.0909857	+	0.141790i
$986$		0			0
$987$	−140.165	−	30.4910i	−4.46150	−	0.970540i
$988$		0			0
$989$	−14.1951	−	23.7487i	−0.451378	−	0.755164i
$990$		0			0
$991$	−3.84312	+	2.46982i	−0.122081	+	0.0784565i	−0.600256	−	0.799808i	$-0.704935\pi$
$991$	−3.84312	+	2.46982i	−0.122081	+	0.0784565i	0.478175	+	0.878264i	$0.341298\pi$
$992$		0			0
$993$	27.6454	−	10.3112i	0.877300	−	0.327216i
$994$		0			0
$995$	5.77753	−	10.5981i	0.183160	−	0.335981i
$996$		0			0
$997$	22.5588	+	16.8873i	0.714445	+	0.534827i	0.893528	−	0.449007i	$-0.148222\pi$
$997$	22.5588	+	16.8873i	0.714445	+	0.534827i	−0.179083	+	0.983834i	$0.557313\pi$
$998$		0			0
$999$	24.9049	−	28.7418i	0.787956	−	0.909349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.333.1	yes	240
5.2	odd	4	inner	460.2.x.a.57.12	✓	240
23.21	odd	22	inner	460.2.x.a.113.12	yes	240
115.67	even	44	inner	460.2.x.a.297.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.57.12	✓	240	5.2	odd	4	inner
460.2.x.a.113.12	yes	240	23.21	odd	22	inner
460.2.x.a.297.1	yes	240	115.67	even	44	inner
460.2.x.a.333.1	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32883 + 1.74334i) q^{3} +(1.79098 + 1.33880i) q^{5} +(0.283864 - 3.96893i) q^{7} +(1.53902 - 5.24143i) q^{9} +O(q^{10})\)	\(q+(-2.32883 + 1.74334i) q^{3} +(1.79098 + 1.33880i) q^{5} +(0.283864 - 3.96893i) q^{7} +(1.53902 - 5.24143i) q^{9} +(2.54334 - 3.95751i) q^{11} +(1.13767 - 0.0813681i) q^{13} +(-6.50488 + 0.00446730i) q^{15} +(-1.63886 + 4.39395i) q^{17} +(0.754595 - 1.65233i) q^{19} +(6.25814 + 9.73785i) q^{21} +(4.76999 + 0.497178i) q^{23} +(1.41525 + 4.79553i) q^{25} +(2.50363 + 6.71249i) q^{27} +(6.44518 - 2.94341i) q^{29} +(0.271688 + 1.88963i) q^{31} +(0.976289 + 13.6503i) q^{33} +(5.82199 - 6.72826i) q^{35} +(-2.54407 - 4.65912i) q^{37} +(-2.50760 + 2.17285i) q^{39} +(2.37912 - 0.698573i) q^{41} +(-3.45730 - 4.61841i) q^{43} +(9.77357 - 7.32688i) q^{45} +(-8.76251 + 8.76251i) q^{47} +(-8.74310 - 1.25707i) q^{49} +(-3.84353 - 13.0899i) q^{51} +(8.15266 + 0.583090i) q^{53} +(9.85338 - 3.68283i) q^{55} +(1.12326 + 5.16352i) q^{57} +(-1.06951 - 0.926737i) q^{59} +(5.40503 - 0.777126i) q^{61} +(-20.3660 - 7.59613i) q^{63} +(2.14649 + 1.37738i) q^{65} +(14.7374 + 3.20593i) q^{67} +(-11.9753 + 7.15788i) q^{69} +(8.58331 - 5.51616i) q^{71} +(-4.86635 + 1.81505i) q^{73} +(-11.6561 - 8.70071i) q^{75} +(-14.9851 - 11.2177i) q^{77} +(-3.92457 + 4.52920i) q^{79} +(-3.74614 - 2.40750i) q^{81} +(-9.26364 + 5.05833i) q^{83} +(-8.81777 + 5.67540i) q^{85} +(-9.87836 + 18.0909i) q^{87} +(1.39921 - 9.73170i) q^{89} -4.53845i q^{91} +(-3.92699 - 3.92699i) q^{93} +(3.56360 - 1.94905i) q^{95} +(-6.71138 - 3.66469i) q^{97} +(-16.8288 - 19.4214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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