LMFDB - Embedded newform 460.2.s.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	460.29
Dual form			460.2.s.a.349.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.277288 - 0.944356i) q^{3} +(0.855101 + 2.06611i) q^{5} +(1.03968 + 0.149483i) q^{7} +(1.70884 + 1.09821i) q^{9} +O(q^{10})$	\(q+(0.277288 - 0.944356i) q^{3} +(0.855101 + 2.06611i) q^{5} +(1.03968 + 0.149483i) q^{7} +(1.70884 + 1.09821i) q^{9} +(0.934389 + 2.04603i) q^{11} +(-3.11707 + 0.448167i) q^{13} +(2.18825 - 0.234613i) q^{15} +(-4.37493 - 3.79090i) q^{17} +(4.89879 + 5.65351i) q^{19} +(0.429455 - 0.940375i) q^{21} +(3.59053 + 3.17932i) q^{23} +(-3.53760 + 3.53346i) q^{25} +(3.74242 - 3.24282i) q^{27} +(5.86067 - 6.76357i) q^{29} +(0.288195 - 0.0846216i) q^{31} +(2.19127 - 0.315057i) q^{33} +(0.580181 + 2.27591i) q^{35} +(1.53371 - 2.38649i) q^{37} +(-0.441097 + 3.06790i) q^{39} +(-0.261686 + 0.168175i) q^{41} +(0.410368 - 1.39758i) q^{43} +(-0.807779 + 4.46973i) q^{45} -6.52909i q^{47} +(-5.65787 - 1.66130i) q^{49} +(-4.79307 + 3.08032i) q^{51} +(0.490601 + 0.0705378i) q^{53} +(-3.42831 + 3.68011i) q^{55} +(6.69730 - 3.05855i) q^{57} +(-1.35162 - 9.40069i) q^{59} +(5.66056 - 1.66209i) q^{61} +(1.61248 + 1.39722i) q^{63} +(-3.59137 - 6.05698i) q^{65} +(-6.74385 - 3.07982i) q^{67} +(3.99802 - 2.50915i) q^{69} +(-1.71713 + 3.75999i) q^{71} +(-12.1150 + 10.4977i) q^{73} +(2.35591 + 4.32054i) q^{75} +(0.665617 + 2.26688i) q^{77} +(1.69613 + 11.7968i) q^{79} +(0.506850 + 1.10985i) q^{81} +(-6.06101 + 9.43112i) q^{83} +(4.09140 - 12.2807i) q^{85} +(-4.76213 - 7.41001i) q^{87} +(-16.2853 - 4.78181i) q^{89} -3.30774 q^{91} -0.295623i q^{93} +(-7.49179 + 14.9557i) q^{95} +(-0.636547 - 0.990486i) q^{97} +(-0.650235 + 4.52249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{11}\right)$

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
$3$	0.277288	−	0.944356i	0.160092	−	0.545224i	−0.839905	−	0.542734i	$-0.817389\pi$
$3$	0.277288	−	0.944356i	0.160092	−	0.545224i	0.999997	−	0.00249012i	$-0.000792631\pi$
$4$		0			0
$5$	0.855101	+	2.06611i	0.382413	+	0.923992i
$5$	0.855101	+	2.06611i	0.382413	+	0.923992i
$6$		0			0
$7$	1.03968	+	0.149483i	0.392961	+	0.0564993i	0.335963	−	0.941875i	$-0.390938\pi$
$7$	1.03968	+	0.149483i	0.392961	+	0.0564993i	0.0569976	+	0.998374i	$0.481847\pi$
$8$		0			0
$9$	1.70884	+	1.09821i	0.569614	+	0.366069i
$10$		0			0
$11$	0.934389	+	2.04603i	0.281729	+	0.616900i	0.996603	−	0.0823527i	$-0.0262434\pi$
$11$	0.934389	+	2.04603i	0.281729	+	0.616900i	−0.714874	+	0.699253i	$0.753516\pi$
$12$		0			0
$13$	−3.11707	+	0.448167i	−0.864520	+	0.124299i	−0.560287	−	0.828298i	$-0.689309\pi$
$13$	−3.11707	+	0.448167i	−0.864520	+	0.124299i	−0.304233	+	0.952598i	$0.598400\pi$
$14$		0			0
$15$	2.18825	−	0.234613i	0.565004	−	0.0605768i
$16$		0			0
$17$	−4.37493	−	3.79090i	−1.06108	−	0.919428i	−0.0641637	−	0.997939i	$-0.520438\pi$
$17$	−4.37493	−	3.79090i	−1.06108	−	0.919428i	−0.996913	+	0.0785110i	$0.974983\pi$
$18$		0			0
$19$	4.89879	+	5.65351i	1.12386	+	1.29700i	0.950006	+	0.312231i	$0.101076\pi$
$19$	4.89879	+	5.65351i	1.12386	+	1.29700i	0.173853	+	0.984772i	$0.444378\pi$
$20$		0			0
$21$	0.429455	−	0.940375i	0.0937148	−	0.205207i
$22$		0			0
$23$	3.59053	+	3.17932i	0.748678	+	0.662934i
$23$	3.59053	+	3.17932i	0.748678	+	0.662934i
$24$		0			0
$25$	−3.53760	+	3.53346i	−0.707521	+	0.706692i
$26$		0			0
$27$	3.74242	−	3.24282i	0.720229	−	0.624082i
$28$		0			0
$29$	5.86067	−	6.76357i	1.08830	−	1.25596i	0.123678	−	0.992322i	$-0.460531\pi$
$29$	5.86067	−	6.76357i	1.08830	−	1.25596i	0.964621	−	0.263641i	$-0.0849236\pi$
$30$		0			0
$31$	0.288195	−	0.0846216i	0.0517613	−	0.0151985i	−0.255749	−	0.966743i	$-0.582322\pi$
$31$	0.288195	−	0.0846216i	0.0517613	−	0.0151985i	0.307511	+	0.951545i	$0.400504\pi$
$32$		0			0
$33$	2.19127	−	0.315057i	0.381451	−	0.0548444i
$34$		0			0
$35$	0.580181	+	2.27591i	0.0980685	+	0.384699i
$36$		0			0
$37$	1.53371	−	2.38649i	0.252140	−	0.392337i	−0.691992	−	0.721905i	$-0.743267\pi$
$37$	1.53371	−	2.38649i	0.252140	−	0.392337i	0.944132	+	0.329568i	$0.106903\pi$
$38$		0			0
$39$	−0.441097	+	3.06790i	−0.0706321	+	0.491257i
$40$		0			0
$41$	−0.261686	+	0.168175i	−0.0408684	+	0.0262645i	−0.560916	−	0.827873i	$-0.689551\pi$
$41$	−0.261686	+	0.168175i	−0.0408684	+	0.0262645i	0.520047	+	0.854138i	$0.325914\pi$
$42$		0			0
$43$	0.410368	−	1.39758i	0.0625805	−	0.213129i	−0.922267	−	0.386554i	$-0.873665\pi$
$43$	0.410368	−	1.39758i	0.0625805	−	0.213129i	0.984847	+	0.173425i	$0.0554834\pi$
$44$		0			0
$45$	−0.807779	+	4.46973i	−0.120417	+	0.666308i
$46$		0			0
$47$		−	6.52909i		−	0.952366i	−0.879346	−	0.476183i	$-0.842020\pi$
$47$		−	6.52909i		−	0.952366i	0.879346	−	0.476183i	$-0.157980\pi$
$48$		0			0
$49$	−5.65787	−	1.66130i	−0.808267	−	0.237329i
$50$		0			0
$51$	−4.79307	+	3.08032i	−0.671165	+	0.431331i
$52$		0			0
$53$	0.490601	+	0.0705378i	0.0673893	+	0.00968911i	0.175927	−	0.984403i	$-0.443708\pi$
$53$	0.490601	+	0.0705378i	0.0673893	+	0.00968911i	−0.108538	+	0.994092i	$0.534617\pi$
$54$		0			0
$55$	−3.42831	+	3.68011i	−0.462274	+	0.496226i
$56$		0			0
$57$	6.69730	−	3.05855i	0.887078	−	0.405115i
$58$		0			0
$59$	−1.35162	−	9.40069i	−0.175965	−	1.22387i	−0.865983	−	0.500073i	$-0.833306\pi$
$59$	−1.35162	−	9.40069i	−0.175965	−	1.22387i	0.690018	−	0.723793i	$-0.257603\pi$
$60$		0			0
$61$	5.66056	−	1.66209i	0.724760	−	0.212809i	0.101513	−	0.994834i	$-0.467632\pi$
$61$	5.66056	−	1.66209i	0.724760	−	0.212809i	0.623247	+	0.782025i	$0.285813\pi$
$62$		0			0
$63$	1.61248	+	1.39722i	0.203153	+	0.176033i
$64$		0			0
$65$	−3.59137	−	6.05698i	−0.445455	−	0.751276i
$66$		0			0
$67$	−6.74385	−	3.07982i	−0.823893	−	0.376259i	−0.0415725	−	0.999135i	$-0.513237\pi$
$67$	−6.74385	−	3.07982i	−0.823893	−	0.376259i	−0.782320	+	0.622876i	$0.785964\pi$
$68$		0			0
$69$	3.99802	−	2.50915i	0.481305	−	0.302067i
$70$		0			0
$71$	−1.71713	+	3.75999i	−0.203786	+	0.446229i	−0.983738	−	0.179610i	$-0.942516\pi$
$71$	−1.71713	+	3.75999i	−0.203786	+	0.446229i	0.779952	+	0.625840i	$0.215244\pi$
$72$		0			0
$73$	−12.1150	+	10.4977i	−1.41795	+	1.22866i	−0.482177	+	0.876074i	$0.660154\pi$
$73$	−12.1150	+	10.4977i	−1.41795	+	1.22866i	−0.935778	+	0.352591i	$0.885301\pi$
$74$		0			0
$75$	2.35591	+	4.32054i	0.272037	+	0.498893i
$76$		0			0
$77$	0.665617	+	2.26688i	0.0758541	+	0.258335i
$78$		0			0
$79$	1.69613	+	11.7968i	0.190829	+	1.32725i	0.829819	+	0.558033i	$0.188444\pi$
$79$	1.69613	+	11.7968i	0.190829	+	1.32725i	−0.638989	+	0.769216i	$0.720647\pi$
$80$		0			0
$81$	0.506850	+	1.10985i	0.0563166	+	0.123316i
$82$		0			0
$83$	−6.06101	+	9.43112i	−0.665282	+	1.03520i	0.330531	+	0.943795i	$0.392772\pi$
$83$	−6.06101	+	9.43112i	−0.665282	+	1.03520i	−0.995814	+	0.0914047i	$0.970864\pi$
$84$		0			0
$85$	4.09140	−	12.2807i	0.443775	−	1.33203i
$86$		0			0
$87$	−4.76213	−	7.41001i	−0.510554	−	0.794437i
$88$		0			0
$89$	−16.2853	−	4.78181i	−1.72624	−	0.506871i	−0.740062	−	0.672539i	$-0.765204\pi$
$89$	−16.2853	−	4.78181i	−1.72624	−	0.506871i	−0.986182	+	0.165668i	$0.947022\pi$
$90$		0			0
$91$	−3.30774			−0.346746
$92$		0			0
$93$		−	0.295623i		−	0.0306547i
$94$		0			0
$95$	−7.49179	+	14.9557i	−0.768642	+	1.53443i
$96$		0			0
$97$	−0.636547	−	0.990486i	−0.0646315	−	0.100569i	0.807434	−	0.589958i	$-0.200856\pi$
$97$	−0.636547	−	0.990486i	−0.0646315	−	0.100569i	−0.872065	+	0.489390i	$0.837220\pi$
$98$		0			0
$99$	−0.650235	+	4.52249i	−0.0653511	+	0.454527i
$100$		0			0
$101$	−13.7626	−	8.84468i	−1.36943	−	0.880079i	−0.370616	−	0.928786i	$-0.620853\pi$
$101$	−13.7626	−	8.84468i	−1.36943	−	0.880079i	−0.998813	+	0.0487077i	$0.984490\pi$
$102$		0			0
$103$	12.9041	−	5.89310i	1.27148	−	0.580664i	0.338625	−	0.940922i	$-0.390038\pi$
$103$	12.9041	−	5.89310i	1.27148	−	0.580664i	0.932853	+	0.360257i	$0.117311\pi$
$104$		0			0
$105$	2.31014	+	0.0831845i	0.225447	+	0.00811798i
$106$		0			0
$107$	−2.83210	−	9.64525i	−0.273789	−	0.932441i	−0.975504	−	0.219983i	$-0.929400\pi$
$107$	−2.83210	−	9.64525i	−0.273789	−	0.932441i	0.701714	−	0.712458i	$-0.252418\pi$
$108$		0			0
$109$	1.88122	−	2.17104i	0.180188	−	0.207948i	−0.658469	−	0.752608i	$-0.728796\pi$
$109$	1.88122	−	2.17104i	0.180188	−	0.207948i	0.838657	+	0.544659i	$0.183341\pi$
$110$		0			0
$111$	−1.82842	−	2.11011i	−0.173546	−	0.200283i
$112$		0			0
$113$	8.12065	+	3.70858i	0.763926	+	0.348874i	0.758980	−	0.651114i	$-0.225698\pi$
$113$	8.12065	+	3.70858i	0.763926	+	0.348874i	0.00494674	+	0.999988i	$0.498425\pi$
$114$		0			0
$115$	−3.49855	+	10.1371i	−0.326242	+	0.945286i
$116$		0			0
$117$	−5.81876	−	2.65734i	−0.537945	−	0.245671i
$118$		0			0
$119$	−3.98184	−	4.59529i	−0.365015	−	0.421250i
$120$		0			0
$121$	3.89033	−	4.48968i	0.353666	−	0.408152i
$122$		0			0
$123$	0.0862549	+	0.293757i	0.00777734	+	0.0264872i
$124$		0			0
$125$	−10.3255	−	4.28761i	−0.923543	−	0.383495i
$126$		0			0
$127$	4.16636	−	1.90271i	0.369705	−	0.168839i	−0.221894	−	0.975071i	$-0.571224\pi$
$127$	4.16636	−	1.90271i	0.369705	−	0.168839i	0.591599	+	0.806232i	$0.298497\pi$
$128$		0			0
$129$	−1.20603	−	0.775066i	−0.106185	−	0.0682408i
$130$		0			0
$131$	2.32895	−	16.1982i	0.203481	−	1.41524i	−0.590371	−	0.807132i	$-0.701019\pi$
$131$	2.32895	−	16.1982i	0.203481	−	1.41524i	0.793852	−	0.608111i	$-0.208072\pi$
$132$		0			0
$133$	4.24806	+	6.61011i	0.368353	+	0.573169i
$134$		0			0
$135$	9.90017	+	4.95930i	0.852071	+	0.426828i
$136$		0			0
$137$		−	14.7810i		−	1.26282i	−0.775448	−	0.631411i	$-0.782476\pi$
$137$		−	14.7810i		−	1.26282i	0.775448	−	0.631411i	$-0.217524\pi$
$138$		0			0
$139$	−13.2936			−1.12755			−0.563775	−	0.825929i	$-0.690651\pi$
$139$	−13.2936			−1.12755			−0.563775	+	0.825929i	$0.690651\pi$
$140$		0			0
$141$	−6.16578	−	1.81044i	−0.519253	−	0.152466i
$142$		0			0
$143$	−3.82952	−	5.95885i	−0.320241	−	0.498304i
$144$		0			0
$145$	18.9857	+	6.32524i	1.57668	+	0.525282i
$146$		0			0
$147$	−3.13772	+	4.88238i	−0.258794	+	0.402692i
$148$		0			0
$149$	0.310236	+	0.679323i	0.0254155	+	0.0556523i	0.921914	−	0.387394i	$-0.126625\pi$
$149$	0.310236	+	0.679323i	0.0254155	+	0.0556523i	−0.896499	+	0.443047i	$0.853898\pi$
$150$		0			0
$151$	1.02963	+	7.16126i	0.0837904	+	0.582775i	0.987855	+	0.155379i	$0.0496599\pi$
$151$	1.02963	+	7.16126i	0.0837904	+	0.582775i	−0.904065	+	0.427396i	$0.859431\pi$
$152$		0			0
$153$	−3.31288	−	11.2826i	−0.267830	−	0.912146i
$154$		0			0
$155$	0.421273	+	0.523081i	0.0338375	+	0.0420149i
$156$		0			0
$157$	15.0115	−	13.0076i	1.19805	−	1.03812i	0.199750	−	0.979847i	$-0.435987\pi$
$157$	15.0115	−	13.0076i	1.19805	−	1.03812i	0.998301	−	0.0582696i	$-0.0185583\pi$
$158$		0			0
$159$	0.202651	−	0.443743i	0.0160712	−	0.0351911i
$160$		0			0
$161$	3.25774	+	3.84219i	0.256746	+	0.302807i
$162$		0			0
$163$	−6.34580	−	2.89803i	−0.497041	−	0.226991i	0.151090	−	0.988520i	$-0.451722\pi$
$163$	−6.34580	−	2.89803i	−0.497041	−	0.226991i	−0.648131	+	0.761529i	$0.724449\pi$
$164$		0			0
$165$	2.52470	+	4.25800i	0.196548	+	0.331485i
$166$		0			0
$167$	12.6188	+	10.9342i	0.976471	+	0.846117i	0.988100	−	0.153815i	$-0.0491561\pi$
$167$	12.6188	+	10.9342i	0.976471	+	0.846117i	−0.0116284	+	0.999932i	$0.503702\pi$
$168$		0			0
$169$	−2.95812	+	0.868582i	−0.227548	+	0.0668140i
$170$		0			0
$171$	2.16254	+	15.0408i	0.165374	+	1.15020i
$172$		0			0
$173$	−12.5743	+	5.74250i	−0.956008	+	0.436594i	−0.831439	−	0.555617i	$-0.812482\pi$
$173$	−12.5743	+	5.74250i	−0.956008	+	0.436594i	−0.124570	+	0.992211i	$0.539755\pi$
$174$		0			0
$175$	−4.20616	+	3.14485i	−0.317956	+	0.237728i
$176$		0			0
$177$	−9.25238	−	1.33029i	−0.695452	−	0.0999909i
$178$		0			0
$179$	8.49631	−	5.46025i	0.635044	−	0.408118i	−0.183130	−	0.983089i	$-0.558623\pi$
$179$	8.49631	−	5.46025i	0.635044	−	0.408118i	0.818174	+	0.574971i	$0.194987\pi$
$180$		0			0
$181$	10.5008	+	3.08332i	0.780520	+	0.229181i	0.647636	−	0.761950i	$-0.275758\pi$
$181$	10.5008	+	3.08332i	0.780520	+	0.229181i	0.132884	+	0.991132i	$0.457576\pi$
$182$		0			0
$183$		−	5.80646i		−	0.429226i
$184$		0			0
$185$	6.24223	+	1.12811i	0.458938	+	0.0829403i
$186$		0			0
$187$	3.66839	−	12.4934i	0.268260	−	0.913608i
$188$		0			0
$189$	4.37565	−	2.81206i	0.318282	−	0.204547i
$190$		0			0
$191$	1.99464	−	13.8730i	0.144327	−	1.00382i	−0.780968	−	0.624571i	$-0.785274\pi$
$191$	1.99464	−	13.8730i	0.144327	−	1.00382i	0.925295	−	0.379247i	$-0.123817\pi$
$192$		0			0
$193$	−13.0733	+	20.3425i	−0.941038	+	1.46428i	−0.0561806	+	0.998421i	$0.517892\pi$
$193$	−13.0733	+	20.3425i	−0.941038	+	1.46428i	−0.884857	+	0.465863i	$0.845744\pi$
$194$		0			0
$195$	−6.71579	+	1.71201i	−0.480928	+	0.122599i
$196$		0			0
$197$	−8.07741	+	1.16136i	−0.575491	+	0.0827432i	−0.423914	−	0.905702i	$-0.639344\pi$
$197$	−8.07741	+	1.16136i	−0.575491	+	0.0827432i	−0.151577	+	0.988445i	$0.548435\pi$
$198$		0			0
$199$	1.23170	−	0.361660i	0.0873130	−	0.0256374i	−0.237784	−	0.971318i	$-0.576421\pi$
$199$	1.23170	−	0.361660i	0.0873130	−	0.0256374i	0.325097	+	0.945681i	$0.394603\pi$
$200$		0			0
$201$	−4.77843	+	5.51460i	−0.337044	+	0.388970i
$202$		0			0
$203$	7.10424	−	6.15586i	0.498620	−	0.432057i
$204$		0			0
$205$	−0.571236	−	0.396864i	−0.0398968	−	0.0277182i
$206$		0			0
$207$	2.64410	+	9.37610i	0.183778	+	0.651684i
$208$		0			0
$209$	−6.98985	+	15.3056i	−0.483498	+	1.05871i
$210$		0			0
$211$	8.65943	+	9.99352i	0.596140	+	0.687982i	0.970995	−	0.239101i	$-0.0768528\pi$
$211$	8.65943	+	9.99352i	0.596140	+	0.687982i	−0.374855	+	0.927084i	$0.622307\pi$
$212$		0			0
$213$	3.07463	+	2.66418i	0.210670	+	0.182547i
$214$		0			0
$215$	3.23846	−	0.347211i	0.220861	−	0.0236796i
$216$		0			0
$217$	0.312279	−	0.0448989i	0.0211989	−	0.00304794i
$218$		0			0
$219$	6.55423	+	14.3518i	0.442894	+	0.969803i
$220$		0			0
$221$	15.3359	+	9.85581i	1.03161	+	0.662974i
$222$		0			0
$223$	10.3881	+	1.49358i	0.695636	+	0.100017i	0.481057	−	0.876689i	$-0.340253\pi$
$223$	10.3881	+	1.49358i	0.695636	+	0.100017i	0.214579	+	0.976707i	$0.431162\pi$
$224$		0			0
$225$	−9.92567	+	2.15311i	−0.661711	+	0.143541i
$226$		0			0
$227$	−5.31658	+	18.1066i	−0.352874	+	1.20178i	0.571600	+	0.820532i	$0.306323\pi$
$227$	−5.31658	+	18.1066i	−0.352874	+	1.20178i	−0.924474	+	0.381245i	$0.875495\pi$
$228$		0			0
$229$	9.62964			0.636345			0.318172	−	0.948033i	$-0.396931\pi$
$229$	9.62964			0.636345			0.318172	+	0.948033i	$0.396931\pi$
$230$		0			0
$231$	2.32531			0.152994
$232$		0			0
$233$	1.03648	−	3.52992i	0.0679019	−	0.231252i	−0.918550	−	0.395306i	$-0.870639\pi$
$233$	1.03648	−	3.52992i	0.0679019	−	0.231252i	0.986451	+	0.164053i	$0.0524569\pi$
$234$		0			0
$235$	13.4898	−	5.58303i	0.879978	−	0.364197i
$236$		0			0
$237$	11.6107	+	1.66937i	0.754198	+	0.108437i
$238$		0			0
$239$	2.85728	+	1.83626i	0.184822	+	0.118778i	0.629780	−	0.776774i	$-0.283145\pi$
$239$	2.85728	+	1.83626i	0.184822	+	0.118778i	−0.444958	+	0.895551i	$0.646781\pi$
$240$		0			0
$241$	0.974062	+	2.13290i	0.0627449	+	0.137392i	0.938407	−	0.345533i	$-0.112302\pi$
$241$	0.974062	+	2.13290i	0.0627449	+	0.137392i	−0.875662	+	0.482925i	$0.839574\pi$
$242$		0			0
$243$	15.8932	−	2.28510i	1.01955	−	0.146589i
$244$		0			0
$245$	−1.40562	−	13.1103i	−0.0898020	−	0.837589i
$246$		0			0
$247$	−17.8036	−	15.4269i	−1.13282	−	0.981591i
$248$		0			0
$249$	7.22569	+	8.33889i	0.457909	+	0.528455i
$250$		0			0
$251$	5.86391	−	12.8402i	0.370127	−	0.810464i	−0.629318	−	0.777148i	$-0.716666\pi$
$251$	5.86391	−	12.8402i	0.370127	−	0.810464i	0.999445	−	0.0333167i	$-0.0106070\pi$
$252$		0			0
$253$	−3.15002	+	10.3170i	−0.198040	+	0.648627i
$254$		0			0
$255$	−10.4628	−	7.26902i	−0.655208	−	0.455204i
$256$		0			0
$257$	5.65207	−	4.89755i	0.352566	−	0.305501i	−0.460513	−	0.887653i	$-0.652335\pi$
$257$	5.65207	−	4.89755i	0.352566	−	0.305501i	0.813080	+	0.582152i	$0.197789\pi$
$258$		0			0
$259$	1.95130	−	2.25192i	0.121248	−	0.139928i
$260$		0			0
$261$	17.4427	−	5.12165i	1.07968	−	0.317022i
$262$		0			0
$263$	12.1764	−	1.75070i	0.750827	−	0.107953i	0.243732	−	0.969843i	$-0.421628\pi$
$263$	12.1764	−	1.75070i	0.750827	−	0.107953i	0.507095	+	0.861890i	$0.330719\pi$
$264$		0			0
$265$	0.273775	+	1.07395i	0.0168179	+	0.0659724i
$266$		0			0
$267$	−9.03146	+	14.0532i	−0.552716	+	0.860043i
$268$		0			0
$269$	0.0907808	−	0.631395i	0.00553501	−	0.0384968i	−0.986867	−	0.161536i	$-0.948355\pi$
$269$	0.0907808	−	0.631395i	0.00553501	−	0.0384968i	0.992402	+	0.123040i	$0.0392642\pi$
$270$		0			0
$271$	−14.8673	+	9.55463i	−0.903124	+	0.580403i	−0.907715	−	0.419587i	$-0.862175\pi$
$271$	−14.8673	+	9.55463i	−0.903124	+	0.580403i	0.00459112	+	0.999989i	$0.498539\pi$
$272$		0			0
$273$	−0.917197	+	3.12369i	−0.0555113	+	0.189054i
$274$		0			0
$275$	−10.5351	−	3.93640i	−0.635288	−	0.237374i
$276$		0			0
$277$		−	30.5816i		−	1.83747i	−0.394871	−	0.918736i	$-0.629211\pi$
$277$		−	30.5816i		−	1.83747i	0.394871	−	0.918736i	$-0.370789\pi$
$278$		0			0
$279$	0.585411	+	0.171892i	0.0350476	+	0.0102909i
$280$		0			0
$281$	−7.61936	+	4.89666i	−0.454533	+	0.292110i	−0.747805	−	0.663919i	$-0.768892\pi$
$281$	−7.61936	+	4.89666i	−0.454533	+	0.292110i	0.293272	+	0.956029i	$0.405256\pi$
$282$		0			0
$283$	15.9526	+	2.29363i	0.948281	+	0.136342i	0.599065	−	0.800700i	$-0.295539\pi$
$283$	15.9526	+	2.29363i	0.948281	+	0.136342i	0.349216	+	0.937042i	$0.386448\pi$
$284$		0			0
$285$	12.0462	+	11.2220i	0.713553	+	0.664732i
$286$		0			0
$287$	−0.297208	+	0.135730i	−0.0175436	+	0.00801190i
$288$		0			0
$289$	2.34975	+	16.3429i	0.138221	+	0.961347i
$290$		0			0
$291$	−1.11188	+	0.326477i	−0.0651794	+	0.0191384i
$292$		0			0
$293$	−9.15223	−	7.93045i	−0.534679	−	0.463302i	0.345180	−	0.938536i	$-0.387818\pi$
$293$	−9.15223	−	7.93045i	−0.534679	−	0.463302i	−0.879859	+	0.475235i	$0.842363\pi$
$294$		0			0
$295$	18.2671	−	10.8311i	1.06355	−	0.630612i
$296$		0			0
$297$	10.1318	+	4.62703i	0.587905	+	0.268487i
$298$		0			0
$299$	−12.6168	−	8.30101i	−0.729649	−	0.480060i
$300$		0			0
$301$	0.635565	−	1.39169i	0.0366333	−	0.0802158i
$302$		0			0
$303$	−12.1687	+	10.5443i	−0.699075	+	0.605752i
$304$		0			0
$305$	8.27440	+	10.2741i	0.473791	+	0.588291i
$306$		0			0
$307$	6.90614	+	23.5201i	0.394154	+	1.34237i	0.882745	+	0.469853i	$0.155693\pi$
$307$	6.90614	+	23.5201i	0.394154	+	1.34237i	−0.488591	+	0.872513i	$0.662489\pi$
$308$		0			0
$309$	−1.98704	−	13.8201i	−0.113039	−	0.786200i
$310$		0			0
$311$	−9.75624	−	21.3632i	−0.553225	−	1.21139i	−0.955259	−	0.295770i	$-0.904424\pi$
$311$	−9.75624	−	21.3632i	−0.553225	−	1.21139i	0.402034	−	0.915625i	$-0.368303\pi$
$312$		0			0
$313$	−8.45986	+	13.1638i	−0.478179	+	0.744062i	−0.993610	−	0.112870i	$-0.963996\pi$
$313$	−8.45986	+	13.1638i	−0.478179	+	0.744062i	0.515430	+	0.856931i	$0.327632\pi$
$314$		0			0
$315$	−1.50798	+	4.52632i	−0.0849649	+	0.255029i
$316$		0			0
$317$	4.03299	+	6.27546i	0.226515	+	0.352465i	0.935845	−	0.352412i	$-0.114638\pi$
$317$	4.03299	+	6.27546i	0.226515	+	0.352465i	−0.709329	+	0.704877i	$0.751002\pi$
$318$		0			0
$319$	19.3146	+	5.67128i	1.08141	+	0.317530i
$320$		0			0
$321$	−9.89385			−0.552221
$322$		0			0
$323$		−	43.3045i		−	2.40953i
$324$		0			0
$325$	9.44339	−	12.5995i	0.523825	−	0.698894i
$326$		0			0
$327$	−1.52860	−	2.37855i	−0.0845317	−	0.131534i
$328$		0			0
$329$	0.975988	−	6.78815i	0.0538080	−	0.374243i
$330$		0			0
$331$	9.80803	+	6.30324i	0.539098	+	0.346457i	0.781686	−	0.623672i	$-0.214360\pi$
$331$	9.80803	+	6.30324i	0.539098	+	0.346457i	−0.242588	+	0.970129i	$0.577996\pi$
$332$		0			0
$333$	5.24172	−	2.39382i	0.287245	−	0.131180i
$334$		0			0
$335$	0.596554	−	16.5671i	0.0325932	−	0.905157i
$336$		0			0
$337$	4.35456	+	14.8303i	0.237208	+	0.807856i	0.988931	+	0.148377i	$0.0474049\pi$
$337$	4.35456	+	14.8303i	0.237208	+	0.807856i	−0.751723	+	0.659479i	$0.770777\pi$
$338$		0			0
$339$	5.75397	−	6.64044i	0.312513	−	0.360659i
$340$		0			0
$341$	0.442424	+	0.510584i	0.0239586	+	0.0276497i
$342$		0			0
$343$	−12.3222	−	5.62734i	−0.665334	−	0.303848i
$344$		0			0
$345$	8.60289	+	6.11476i	0.463164	+	0.329208i
$346$		0			0
$347$	−18.0798	−	8.25677i	−0.970575	−	0.443247i	−0.133929	−	0.990991i	$-0.542759\pi$
$347$	−18.0798	−	8.25677i	−0.970575	−	0.443247i	−0.836646	+	0.547744i	$0.815487\pi$
$348$		0			0
$349$	−5.63371	−	6.50165i	−0.301565	−	0.348025i	0.584661	−	0.811278i	$-0.301228\pi$
$349$	−5.63371	−	6.50165i	−0.301565	−	0.348025i	−0.886226	+	0.463253i	$0.846682\pi$
$350$		0			0
$351$	−10.2121	+	11.7853i	−0.545080	+	0.629055i
$352$		0			0
$353$	2.36875	+	8.06722i	0.126076	+	0.429375i	0.998204	−	0.0599023i	$-0.0190789\pi$
$353$	2.36875	+	8.06722i	0.126076	+	0.429375i	−0.872128	+	0.489277i	$0.837261\pi$
$354$		0			0
$355$	−9.23688	−	0.332605i	−0.490243	−	0.0176528i
$356$		0			0
$357$	−5.44371	+	2.48606i	−0.288111	+	0.131576i
$358$		0			0
$359$	3.33592	+	2.14387i	0.176063	+	0.113149i	0.625704	−	0.780060i	$-0.284812\pi$
$359$	3.33592	+	2.14387i	0.176063	+	0.113149i	−0.449641	+	0.893209i	$0.648448\pi$
$360$		0			0
$361$	−5.25999	+	36.5841i	−0.276842	+	1.92548i
$362$		0			0
$363$	−3.16111	−	4.91879i	−0.165915	−	0.258169i
$364$		0			0
$365$	−32.0490	−	16.0543i	−1.67752	−	0.840321i
$366$		0			0
$367$			14.7372i			0.769276i	0.923068	+	0.384638i	$0.125674\pi$
$367$			14.7372i			0.769276i	−0.923068	+	0.384638i	$0.874326\pi$
$368$		0			0
$369$	−0.631870			−0.0328938
$370$		0			0
$371$	0.499523	+	0.146673i	0.0259339	+	0.00761489i
$372$		0			0
$373$	−6.77266	−	10.5385i	−0.350675	−	0.545661i	0.620446	−	0.784249i	$-0.286952\pi$
$373$	−6.77266	−	10.5385i	−0.350675	−	0.545661i	−0.971121	+	0.238588i	$0.923315\pi$
$374$		0			0
$375$	−6.91217	+	8.56207i	−0.356943	+	0.442143i
$376$		0			0
$377$	−15.2369	+	23.7091i	−0.784741	+	1.22108i
$378$		0			0
$379$	−14.6378	−	32.0524i	−0.751895	−	1.64642i	−0.762930	−	0.646482i	$-0.776240\pi$
$379$	−14.6378	−	32.0524i	−0.751895	−	1.64642i	0.0110345	−	0.999939i	$-0.496488\pi$
$380$		0			0
$381$	−0.641557	−	4.46213i	−0.0328680	−	0.228602i
$382$		0			0
$383$	−3.87122	−	13.1842i	−0.197810	−	0.673680i	−0.997329	−	0.0730390i	$-0.976730\pi$
$383$	−3.87122	−	13.1842i	−0.197810	−	0.673680i	0.799519	−	0.600641i	$-0.205088\pi$
$384$		0			0
$385$	−4.11445	+	3.31365i	−0.209692	+	0.168879i
$386$		0			0
$387$	2.23609	−	1.93758i	0.113667	−	0.0984928i
$388$		0			0
$389$	−5.46929	+	11.9761i	−0.277304	+	0.607211i	−0.996122	−	0.0879875i	$-0.971956\pi$
$389$	−5.46929	+	11.9761i	−0.277304	+	0.607211i	0.718817	+	0.695199i	$0.244684\pi$
$390$		0			0
$391$	−3.65585	−	27.5207i	−0.184884	−	1.39178i
$392$		0			0
$393$	−14.6511	−	6.69092i	−0.739049	−	0.337512i
$394$		0			0
$395$	−22.9232	+	13.5919i	−1.15339	+	0.683882i
$396$		0			0
$397$	16.2840	+	14.1101i	0.817269	+	0.708168i	0.959513	−	0.281664i	$-0.0908863\pi$
$397$	16.2840	+	14.1101i	0.817269	+	0.708168i	−0.142244	+	0.989832i	$0.545432\pi$
$398$		0			0
$399$	7.42023	−	2.17878i	0.371476	−	0.109075i
$400$		0			0
$401$	0.975924	+	6.78770i	0.0487353	+	0.338962i	0.999572	+	0.0292676i	$0.00931751\pi$
$401$	0.975924	+	6.78770i	0.0487353	+	0.338962i	−0.950836	+	0.309694i	$0.899773\pi$
$402$		0			0
$403$	−0.860399	+	0.392931i	−0.0428595	+	0.0195733i
$404$		0			0
$405$	−1.85965	+	1.99624i	−0.0924070	+	0.0991938i
$406$		0			0
$407$	6.31591	+	0.908091i	0.313068	+	0.0450124i
$408$		0			0
$409$	2.14856	−	1.38080i	0.106240	−	0.0682760i	−0.486442	−	0.873713i	$-0.661706\pi$
$409$	2.14856	−	1.38080i	0.106240	−	0.0682760i	0.592682	+	0.805437i	$0.298069\pi$
$410$		0			0
$411$	−13.9585	−	4.09858i	−0.688521	−	0.202168i
$412$		0			0
$413$		−	9.97573i		−	0.490874i
$414$		0			0
$415$	−24.6685	−	4.45815i	−1.21093	−	0.218842i
$416$		0			0
$417$	−3.68616	+	12.5539i	−0.180512	+	0.614767i
$418$		0			0
$419$	14.7617	−	9.48677i	0.721157	−	0.463459i	−0.127882	−	0.991789i	$-0.540818\pi$
$419$	14.7617	−	9.48677i	0.721157	−	0.463459i	0.849039	+	0.528330i	$0.177182\pi$
$420$		0			0
$421$	3.11834	−	21.6886i	0.151979	−	1.05704i	−0.760919	−	0.648847i	$-0.775251\pi$
$421$	3.11834	−	21.6886i	0.151979	−	1.05704i	0.912898	−	0.408189i	$-0.133839\pi$
$422$		0			0
$423$	7.17028	−	11.1572i	0.348631	−	0.542481i
$424$		0			0
$425$	28.8718	−	2.04795i	1.40049	−	0.0993403i
$426$		0			0
$427$	6.13361	−	0.881879i	0.296826	−	0.0426771i
$428$		0			0
$429$	−6.68916	+	1.96411i	−0.322955	+	0.0948283i
$430$		0			0
$431$	−0.546445	+	0.630632i	−0.0263214	+	0.0303765i	−0.768758	−	0.639540i	$-0.779125\pi$
$431$	−0.546445	+	0.630632i	−0.0263214	+	0.0303765i	0.742436	+	0.669917i	$0.233670\pi$
$432$		0			0
$433$	5.94710	−	5.15320i	0.285800	−	0.247647i	−0.500148	−	0.865940i	$-0.666721\pi$
$433$	5.94710	−	5.15320i	0.285800	−	0.247647i	0.785948	+	0.618293i	$0.212176\pi$
$434$		0			0
$435$	11.2378	−	16.1754i	0.538811	−	0.775550i
$436$		0			0
$437$	−0.385041	+	35.8739i	−0.0184190	+	1.71608i
$438$		0			0
$439$	0.703278	−	1.53996i	0.0335656	−	0.0734984i	−0.892107	−	0.451825i	$-0.850773\pi$
$439$	0.703278	−	1.53996i	0.0335656	−	0.0734984i	0.925672	+	0.378327i	$0.123500\pi$
$440$		0			0
$441$	−7.84395	−	9.05240i	−0.373521	−	0.431067i
$442$		0			0
$443$	27.6207	+	23.9335i	1.31230	+	1.13712i	0.981089	+	0.193559i	$0.0620031\pi$
$443$	27.6207	+	23.9335i	1.31230	+	1.13712i	0.331212	+	0.943556i	$0.392542\pi$
$444$		0			0
$445$	−4.04588	−	37.7362i	−0.191793	−	1.78887i
$446$		0			0
$447$	0.727547	−	0.104605i	0.0344118	−	0.00494767i
$448$		0			0
$449$	3.52226	+	7.71268i	0.166226	+	0.363984i	0.974353	−	0.225024i	$-0.0722460\pi$
$449$	3.52226	+	7.71268i	0.166226	+	0.363984i	−0.808127	+	0.589008i	$0.799519\pi$
$450$		0			0
$451$	−0.588607	−	0.378275i	−0.0277164	−	0.0178123i
$452$		0			0
$453$	7.04828	+	1.01339i	0.331157	+	0.0476132i
$454$		0			0
$455$	−2.82845	−	6.83415i	−0.132600	−	0.320390i
$456$		0			0
$457$	−2.50962	+	8.54697i	−0.117395	+	0.399810i	−0.997135	−	0.0756450i	$-0.975898\pi$
$457$	−2.50962	+	8.54697i	−0.117395	+	0.399810i	0.879740	+	0.475455i	$0.157717\pi$
$458$		0			0
$459$	−28.6660			−1.33802
$460$		0			0
$461$	1.24286			0.0578855			0.0289428	−	0.999581i	$-0.490786\pi$
$461$	1.24286			0.0578855			0.0289428	+	0.999581i	$0.490786\pi$
$462$		0			0
$463$	−8.17017	+	27.8250i	−0.379700	+	1.29314i	0.519075	+	0.854729i	$0.326277\pi$
$463$	−8.17017	+	27.8250i	−0.379700	+	1.29314i	−0.898775	+	0.438411i	$0.855542\pi$
$464$		0			0
$465$	0.610789	−	0.252787i	0.0283247	−	0.0117227i
$466$		0			0
$467$	18.3159	+	2.63342i	0.847557	+	0.121860i	0.552391	−	0.833585i	$-0.313716\pi$
$467$	18.3159	+	2.63342i	0.847557	+	0.121860i	0.295167	+	0.955446i	$0.404625\pi$
$468$		0			0
$469$	−6.55105	−	4.21011i	−0.302499	−	0.194405i
$470$		0			0
$471$	−8.12125	−	17.7831i	−0.374208	−	0.819400i
$472$		0			0
$473$	3.24294	−	0.466264i	0.149110	−	0.0214388i
$474$		0			0
$475$	−37.3064	−	2.69018i	−1.71174	−	0.123434i
$476$		0			0
$477$	0.760895	+	0.659319i	0.0348390	+	0.0301881i
$478$		0			0
$479$	−25.0341	−	28.8909i	−1.14384	−	1.32006i	−0.940048	−	0.341043i	$-0.889220\pi$
$479$	−25.0341	−	28.8909i	−1.14384	−	1.32006i	−0.203789	−	0.979015i	$-0.565326\pi$
$480$		0			0
$481$	−3.71113	+	8.12624i	−0.169213	+	0.370524i
$482$		0			0
$483$	4.53173	−	2.01107i	0.206201	−	0.0915070i
$484$		0			0
$485$	1.50214	−	2.16214i	0.0682086	−	0.0981777i
$486$		0			0
$487$	−23.8426	+	20.6597i	−1.08041	+	0.936182i	−0.998172	−	0.0604306i	$-0.980753\pi$
$487$	−23.8426	+	20.6597i	−1.08041	+	0.936182i	−0.0822392	+	0.996613i	$0.526207\pi$
$488$		0			0
$489$	−4.49638	+	5.18910i	−0.203333	+	0.234659i
$490$		0			0
$491$	−13.2130	+	3.87968i	−0.596294	+	0.175088i	−0.565933	−	0.824451i	$-0.691484\pi$
$491$	−13.2130	+	3.87968i	−0.596294	+	0.175088i	−0.0303608	+	0.999539i	$0.509666\pi$
$492$		0			0
$493$	−51.2801	+	7.37296i	−2.30954	+	0.332061i
$494$		0			0
$495$	−9.89996	+	2.52373i	−0.444970	+	0.113433i
$496$		0			0
$497$	−2.34732	+	3.65250i	−0.105292	+	0.163837i
$498$		0			0
$499$	1.09448	−	7.61225i	0.0489955	−	0.340771i	−0.950549	−	0.310576i	$-0.899478\pi$
$499$	1.09448	−	7.61225i	0.0489955	−	0.340771i	0.999544	−	0.0301950i	$-0.00961283\pi$
$500$		0			0
$501$	13.8249	−	8.88469i	0.617649	−	0.396939i
$502$		0			0
$503$	0.985617	−	3.35670i	0.0439465	−	0.149668i	−0.934597	−	0.355708i	$-0.884240\pi$
$503$	0.985617	−	3.35670i	0.0439465	−	0.149668i	0.978543	+	0.206040i	$0.0660578\pi$
$504$		0			0
$505$	6.50566	−	35.9981i	0.289498	−	1.60189i
$506$		0			0
$507$			3.03436i			0.134761i
$508$		0			0
$509$	33.0115	+	9.69304i	1.46321	+	0.429637i	0.913885	−	0.405974i	$-0.133067\pi$
$509$	33.0115	+	9.69304i	1.46321	+	0.429637i	0.549323	+	0.835610i	$0.314886\pi$
$510$		0			0
$511$	−14.1649	+	9.10325i	−0.626620	+	0.402704i
$512$		0			0
$513$	36.6666	+	5.27187i	1.61887	+	0.232759i
$514$		0			0
$515$	23.2101	+	21.6220i	1.02276	+	0.952781i
$516$		0			0
$517$	13.3587	−	6.10071i	0.587515	−	0.268309i
$518$		0			0
$519$	1.93626	+	13.4670i	0.0849922	+	0.591134i
$520$		0			0
$521$	−36.4970	+	10.7165i	−1.59896	+	0.469497i	−0.955257	−	0.295778i	$-0.904421\pi$
$521$	−36.4970	+	10.7165i	−1.59896	+	0.469497i	−0.643704	+	0.765275i	$0.722603\pi$
$522$		0			0
$523$	−10.4277	−	9.03566i	−0.455972	−	0.395102i	0.396367	−	0.918092i	$-0.370271\pi$
$523$	−10.4277	−	9.03566i	−0.455972	−	0.395102i	−0.852338	+	0.522991i	$0.824816\pi$
$524$		0			0
$525$	1.80354	+	4.84414i	0.0787129	+	0.211416i
$526$		0			0
$527$	−1.58162	−	0.722304i	−0.0688966	−	0.0314640i
$528$		0			0
$529$	2.78384	+	22.8309i	0.121037	+	0.992648i
$530$		0			0
$531$	8.01420	−	17.5486i	0.347787	−	0.761546i
$532$		0			0
$533$	0.740322	−	0.641493i	0.0320669	−	0.0277861i
$534$		0			0
$535$	17.5064	−	14.0991i	0.756867	−	0.609556i
$536$		0			0
$537$	−2.80049	−	9.53760i	−0.120850	−	0.411578i
$538$		0			0
$539$	−1.88759	−	13.1284i	−0.0813041	−	0.565482i
$540$		0			0
$541$	−9.76825	−	21.3895i	−0.419970	−	0.919606i	−0.994849	−	0.101368i	$-0.967678\pi$
$541$	−9.76825	−	21.3895i	−0.419970	−	0.919606i	0.574879	−	0.818238i	$-0.305049\pi$
$542$		0			0
$543$	5.82350	−	9.06154i	0.249910	−	0.388868i
$544$		0			0
$545$	6.09425	+	2.03034i	0.261049	+	0.0869703i
$546$		0			0
$547$	7.69934	+	11.9804i	0.329200	+	0.512245i	0.965917	−	0.258853i	$-0.0833444\pi$
$547$	7.69934	+	11.9804i	0.329200	+	0.512245i	−0.636717	+	0.771098i	$0.719708\pi$
$548$		0			0
$549$	11.4983	+	3.37621i	0.490736	+	0.144093i
$550$		0			0
$551$	66.9481			2.85208
$552$		0			0
$553$			12.5184i			0.532339i
$554$		0			0
$555$	2.79623	−	5.58208i	0.118693	−	0.236946i
$556$		0			0
$557$	16.5067	+	25.6849i	0.699410	+	1.08830i	0.991271	+	0.131842i	$0.0420891\pi$
$557$	16.5067	+	25.6849i	0.699410	+	1.08830i	−0.291861	+	0.956461i	$0.594274\pi$
$558$		0			0
$559$	−0.652794	+	4.54028i	−0.0276103	+	0.192034i
$560$		0			0
$561$	−10.7810	−	6.92854i	−0.455175	−	0.292523i
$562$		0			0
$563$	30.3173	−	13.8454i	1.27772	−	0.583516i	0.343146	−	0.939282i	$-0.388507\pi$
$563$	30.3173	−	13.8454i	1.27772	−	0.583516i	0.934575	+	0.355766i	$0.115780\pi$
$564$		0			0
$565$	−0.718343	+	19.9493i	−0.0302209	+	0.839275i
$566$		0			0
$567$	0.361057	+	1.22965i	0.0151630	+	0.0516403i
$568$		0			0
$569$	−12.2659	+	14.1556i	−0.514212	+	0.593432i	−0.952172	−	0.305562i	$-0.901156\pi$
$569$	−12.2659	+	14.1556i	−0.514212	+	0.593432i	0.437960	+	0.898994i	$0.355701\pi$
$570$		0			0
$571$	0.464018	+	0.535506i	0.0194186	+	0.0224102i	0.765376	−	0.643584i	$-0.222553\pi$
$571$	0.464018	+	0.535506i	0.0194186	+	0.0224102i	−0.745957	+	0.665994i	$0.768008\pi$
$572$		0			0
$573$	−12.5480	−	5.73048i	−0.524200	−	0.239394i
$574$		0			0
$575$	−23.9359	+	1.43983i	−0.998196	+	0.0600451i
$576$		0			0
$577$	−33.4701	−	15.2853i	−1.39338	−	0.636334i	−0.429594	−	0.903022i	$-0.641343\pi$
$577$	−33.4701	−	15.2853i	−1.39338	−	0.636334i	−0.963783	+	0.266688i	$0.914071\pi$
$578$		0			0
$579$	15.5855	+	17.9866i	0.647710	+	0.747497i
$580$		0			0
$581$	−7.71129	+	8.89930i	−0.319918	+	0.369205i
$582$		0			0
$583$	0.314090	+	1.06969i	0.0130083	+	0.0443022i
$584$		0			0
$585$	0.514721	−	14.2945i	0.0212811	−	0.591004i
$586$		0			0
$587$	−33.7263	+	15.4023i	−1.39203	+	0.635720i	−0.963476	−	0.267794i	$-0.913705\pi$
$587$	−33.7263	+	15.4023i	−1.39203	+	0.635720i	−0.428557	+	0.903515i	$0.640978\pi$
$588$		0			0
$589$	1.89021	+	1.21477i	0.0778849	+	0.0500536i
$590$		0			0
$591$	−1.14303	+	7.94998i	−0.0470181	+	0.327018i
$592$		0			0
$593$	−20.2948	−	31.5793i	−0.833407	−	1.29681i	−0.952689	−	0.303946i	$-0.901696\pi$
$593$	−20.2948	−	31.5793i	−0.833407	−	1.29681i	0.119283	−	0.992860i	$-0.461941\pi$
$594$		0			0
$595$	6.08949	−	12.1564i	0.249645	−	0.498362i
$596$		0			0
$597$		−	1.26345i		−	0.0517095i
$598$		0			0
$599$	4.02582			0.164490			0.0822452	−	0.996612i	$-0.473791\pi$
$599$	4.02582			0.164490			0.0822452	+	0.996612i	$0.473791\pi$
$600$		0			0
$601$	−17.8551	−	5.24274i	−0.728326	−	0.213856i	−0.103511	−	0.994628i	$-0.533008\pi$
$601$	−17.8551	−	5.24274i	−0.728326	−	0.213856i	−0.624815	+	0.780772i	$0.714826\pi$
$602$		0			0
$603$	−8.14191	−	12.6691i	−0.331564	−	0.515924i
$604$		0			0
$605$	12.6028	+	4.19871i	0.512376	+	0.170702i
$606$		0			0
$607$	−15.4786	+	24.0851i	−0.628255	+	0.977584i	0.370555	+	0.928811i	$0.379168\pi$
$607$	−15.4786	+	24.0851i	−0.628255	+	0.977584i	−0.998810	+	0.0487735i	$0.984469\pi$
$608$		0			0
$609$	−3.84340	−	8.41588i	−0.155743	−	0.341029i
$610$		0			0
$611$	2.92613	+	20.3516i	0.118378	+	0.823340i
$612$		0			0
$613$	−4.43720	−	15.1117i	−0.179217	−	0.610357i	−0.999275	−	0.0380763i	$-0.987877\pi$
$613$	−4.43720	−	15.1117i	−0.179217	−	0.610357i	0.820058	−	0.572281i	$-0.193941\pi$
$614$		0			0
$615$	−0.533177	+	0.429404i	−0.0214998	+	0.0173152i
$616$		0			0
$617$	14.0155	−	12.1445i	0.564244	−	0.488920i	−0.325399	−	0.945577i	$-0.605499\pi$
$617$	14.0155	−	12.1445i	0.564244	−	0.488920i	0.889643	+	0.456657i	$0.150953\pi$
$618$		0			0
$619$	−5.00050	+	10.9496i	−0.200987	+	0.440100i	−0.983108	−	0.183027i	$-0.941411\pi$
$619$	−5.00050	+	10.9496i	−0.200987	+	0.440100i	0.782121	+	0.623127i	$0.214138\pi$
$620$		0			0
$621$	23.7472	+	0.254883i	0.952944	+	0.0102281i
$622$		0			0
$623$	−16.2167	−	7.40592i	−0.649709	−	0.296712i
$624$		0			0
$625$	0.0292899	−	25.0000i	0.00117159	−	0.999999i
$626$		0			0
$627$	12.5158	+	10.8450i	0.499831	+	0.433106i
$628$		0			0
$629$	−15.7568	+	4.62662i	−0.628266	+	0.184476i
$630$		0			0
$631$	2.92964	+	20.3761i	0.116627	+	0.811160i	0.961226	+	0.275761i	$0.0889298\pi$
$631$	2.92964	+	20.3761i	0.116627	+	0.811160i	−0.844599	+	0.535399i	$0.820161\pi$
$632$		0			0
$633$	11.8386	−	5.40651i	0.470542	−	0.214889i
$634$		0			0
$635$	7.49387	+	6.98114i	0.297385	+	0.277038i
$636$		0			0
$637$	18.3805	+	2.64272i	0.728263	+	0.104708i
$638$		0			0
$639$	−7.06355	+	4.53947i	−0.279430	+	0.179579i
$640$		0			0
$641$	31.6611	+	9.29655i	1.25054	+	0.367192i	0.838966	−	0.544184i	$-0.183161\pi$
$641$	31.6611	+	9.29655i	1.25054	+	0.367192i	0.411574	+	0.911376i	$0.364979\pi$
$642$		0			0
$643$			10.2560i			0.404459i	0.979338	+	0.202230i	$0.0648187\pi$
$643$			10.2560i			0.404459i	−0.979338	+	0.202230i	$0.935181\pi$
$644$		0			0
$645$	0.570096	−	3.15454i	0.0224475	−	0.124210i
$646$		0			0
$647$	5.34938	−	18.2183i	0.210306	−	0.716236i	−0.785003	−	0.619492i	$-0.787339\pi$
$647$	5.34938	−	18.2183i	0.210306	−	0.716236i	0.995309	−	0.0967447i	$-0.0308430\pi$
$648$		0			0
$649$	17.9711	−	11.5493i	0.705429	−	0.453351i
$650$		0			0
$651$	0.0441906	−	0.307352i	0.00173197	−	0.0120461i
$652$		0			0
$653$	−5.18071	+	8.06134i	−0.202737	+	0.315465i	−0.927703	−	0.373320i	$-0.878219\pi$
$653$	−5.18071	+	8.06134i	−0.202737	+	0.315465i	0.724966	+	0.688785i	$0.241856\pi$
$654$		0			0
$655$	35.4587	−	9.03923i	1.38549	−	0.353192i
$656$		0			0
$657$	−32.2313	+	4.63416i	−1.25746	+	0.180796i
$658$		0			0
$659$	11.2276	−	3.29671i	0.437364	−	0.128422i	−0.0556356	−	0.998451i	$-0.517719\pi$
$659$	11.2276	−	3.29671i	0.437364	−	0.128422i	0.493000	+	0.870029i	$0.335900\pi$
$660$		0			0
$661$	9.56510	−	11.0387i	0.372039	−	0.429356i	−0.538598	−	0.842563i	$-0.681046\pi$
$661$	9.56510	−	11.0387i	0.372039	−	0.429356i	0.910637	+	0.413207i	$0.135591\pi$
$662$		0			0
$663$	13.5599	−	11.7497i	0.526621	−	0.456320i
$664$		0			0
$665$	−10.0247	+	14.4293i	−0.388740	+	0.559542i
$666$		0			0
$667$	42.5465	−	5.65188i	1.64741	−	0.218842i
$668$		0			0
$669$	4.29095	−	9.39587i	0.165898	−	0.363265i
$670$		0			0
$671$	8.68984	+	10.0286i	0.335468	+	0.387150i
$672$		0			0
$673$	24.0238	+	20.8167i	0.926048	+	0.802425i	0.980587	−	0.196087i	$-0.0628234\pi$
$673$	24.0238	+	20.8167i	0.926048	+	0.802425i	−0.0545386	+	0.998512i	$0.517369\pi$
$674$		0			0
$675$	−1.78080	+	24.6955i	−0.0685430	+	0.950531i
$676$		0			0
$677$	14.0924	−	2.02618i	0.541616	−	0.0778726i	0.133923	−	0.990992i	$-0.457243\pi$
$677$	14.0924	−	2.02618i	0.541616	−	0.0778726i	0.407693	+	0.913119i	$0.366333\pi$
$678$		0			0
$679$	−0.513742	−	1.12494i	−0.0197156	−	0.0431712i
$680$		0			0
$681$	15.6249	+	10.0415i	0.598746	+	0.384791i
$682$		0			0
$683$	11.2316	+	1.61486i	0.429766	+	0.0617910i	0.353804	−	0.935320i	$-0.384888\pi$
$683$	11.2316	+	1.61486i	0.429766	+	0.0617910i	0.0759620	+	0.997111i	$0.475797\pi$
$684$		0			0
$685$	30.5391	−	12.6392i	1.16684	−	0.482919i
$686$		0			0
$687$	2.67018	−	9.09381i	0.101874	−	0.346950i
$688$		0			0
$689$	−1.56085			−0.0594638
$690$		0			0
$691$	32.7427			1.24559			0.622795	−	0.782385i	$-0.285997\pi$
$691$	32.7427			1.24559			0.622795	+	0.782385i	$0.285997\pi$
$692$		0			0
$693$	−1.35207	+	4.60473i	−0.0513609	+	0.174919i
$694$		0			0
$695$	−11.3674	−	27.4660i	−0.431189	−	1.04185i
$696$		0			0
$697$	1.78239	+	0.256269i	0.0675129	+	0.00970689i
$698$		0			0
$699$	−3.04609	−	1.95761i	−0.115214	−	0.0740435i
$700$		0			0
$701$	6.21998	+	13.6199i	0.234925	+	0.514415i	0.989973	−	0.141255i	$-0.0451136\pi$
$701$	6.21998	+	13.6199i	0.234925	+	0.514415i	−0.755048	+	0.655670i	$0.772386\pi$
$702$		0			0
$703$	21.0054	−	3.02012i	0.792233	−	0.113906i
$704$		0			0
$705$	−1.53181	−	14.2873i	−0.0576913	−	0.538090i
$706$		0			0
$707$	−12.9865	−	11.2529i	−0.488408	−	0.423208i
$708$		0			0
$709$	−3.32844	−	3.84123i	−0.125002	−	0.144260i	0.689798	−	0.724001i	$-0.257699\pi$
$709$	−3.32844	−	3.84123i	−0.125002	−	0.144260i	−0.814801	+	0.579741i	$0.803154\pi$
$710$		0			0
$711$	−10.0569	+	22.0216i	−0.377165	+	0.825876i
$712$		0			0
$713$	1.30381	+	0.612427i	0.0488281	+	0.0229356i
$714$		0			0
$715$	9.03700	−	13.0076i	0.337965	−	0.486458i
$716$		0			0
$717$	2.52637	−	2.18912i	0.0943492	−	0.0817540i
$718$		0			0
$719$	−18.0078	+	20.7821i	−0.671579	+	0.775043i	−0.984622	−	0.174696i	$-0.944106\pi$
$719$	−18.0078	+	20.7821i	−0.671579	+	0.775043i	0.313044	+	0.949739i	$0.398651\pi$
$720$		0			0
$721$	14.2970	−	4.19798i	0.532448	−	0.156341i
$722$		0			0
$723$	2.28431	−	0.328434i	0.0849545	−	0.0122146i
$724$		0			0
$725$	3.16610	+	44.6353i	0.117586	+	1.65771i
$726$		0			0
$727$	−21.4522	+	33.3803i	−0.795618	+	1.23801i	0.171878	+	0.985118i	$0.445017\pi$
$727$	−21.4522	+	33.3803i	−0.795618	+	1.23801i	−0.967496	+	0.252887i	$0.918620\pi$
$728$		0			0
$729$	1.72813	−	12.0194i	0.0640049	−	0.445164i
$730$		0			0
$731$	−7.09343	+	4.55867i	−0.262360	+	0.168609i
$732$		0			0
$733$	−11.2020	+	38.1505i	−0.413755	+	1.40912i	0.444445	+	0.895806i	$0.353401\pi$
$733$	−11.2020	+	38.1505i	−0.413755	+	1.40912i	−0.858200	+	0.513315i	$0.828417\pi$
$734$		0			0
$735$	−12.7706	−	2.30793i	−0.471050	−	0.0851293i
$736$		0			0
$737$		−	16.6758i		−	0.614263i
$738$		0			0
$739$	26.5830	+	7.80548i	0.977872	+	0.287129i	0.731346	−	0.682007i	$-0.238893\pi$
$739$	26.5830	+	7.80548i	0.977872	+	0.287129i	0.246526	+	0.969136i	$0.420711\pi$
$740$		0			0
$741$	−19.5052	+	12.5352i	−0.716542	+	0.460494i
$742$		0			0
$743$	−16.0301	−	2.30479i	−0.588089	−	0.0845544i	−0.158154	−	0.987414i	$-0.550554\pi$
$743$	−16.0301	−	2.30479i	−0.588089	−	0.0845544i	−0.429935	+	0.902860i	$0.641463\pi$
$744$		0			0
$745$	−1.13827	+	1.22187i	−0.0417030	+	0.0447659i
$746$		0			0
$747$	−20.7146	+	9.46005i	−0.757908	+	0.346125i
$748$		0			0
$749$	−1.50267	−	10.4513i	−0.0549063	−	0.381882i
$750$		0			0
$751$	31.3909	−	9.21721i	1.14547	−	0.336341i	0.346700	−	0.937976i	$-0.387302\pi$
$751$	31.3909	−	9.21721i	1.14547	−	0.336341i	0.798771	+	0.601635i	$0.205484\pi$
$752$		0			0
$753$	−10.4997	−	9.09804i	−0.382630	−	0.331551i
$754$		0			0
$755$	−13.9155	+	8.25093i	−0.506437	+	0.300282i
$756$		0			0
$757$	37.7787	+	17.2529i	1.37309	+	0.627069i	0.959062	−	0.283196i	$-0.0913946\pi$
$757$	37.7787	+	17.2529i	1.37309	+	0.627069i	0.414027	+	0.910265i	$0.364122\pi$
$758$		0			0
$759$	8.86950	+	5.83553i	0.321942	+	0.211816i
$760$		0			0
$761$	−11.8787	+	26.0106i	−0.430601	+	0.942884i	0.562628	+	0.826710i	$0.309790\pi$
$761$	−11.8787	+	26.0106i	−0.430601	+	0.942884i	−0.993229	+	0.116174i	$0.962937\pi$
$762$		0			0
$763$	2.28040	−	1.97597i	0.0825559	−	0.0715351i
$764$		0			0
$765$	20.4783	−	16.4925i	0.740393	−	0.596289i
$766$		0			0
$767$	8.42617	+	28.6969i	0.304251	+	1.03618i
$768$		0			0
$769$	−5.96259	−	41.4707i	−0.215016	−	1.49547i	−0.756074	−	0.654486i	$-0.772885\pi$
$769$	−5.96259	−	41.4707i	−0.215016	−	1.49547i	0.541058	−	0.840985i	$-0.318024\pi$
$770$		0			0
$771$	−3.05778	−	6.69560i	−0.110123	−	0.241136i
$772$		0			0
$773$	0.898728	−	1.39845i	0.0323250	−	0.0502987i	−0.824715	−	0.565549i	$-0.808665\pi$
$773$	0.898728	−	1.39845i	0.0323250	−	0.0502987i	0.857040	+	0.515250i	$0.172301\pi$
$774$		0			0
$775$	−0.720512	+	1.31768i	−0.0258815	+	0.0473326i
$776$		0			0
$777$	−1.58554	−	2.46715i	−0.0568810	−	0.0885086i
$778$		0			0
$779$	−2.23272	−	0.655586i	−0.0799956	−	0.0234888i
$780$		0			0
$781$	−9.29752			−0.332691
$782$		0			0
$783$		−	44.3172i		−	1.58377i
$784$		0			0
$785$	39.7114	+	19.8927i	1.41736	+	0.709999i
$786$		0			0
$787$	−27.7602	−	43.1958i	−0.989546	−	1.53976i	−0.833875	−	0.551954i	$-0.813882\pi$
$787$	−27.7602	−	43.1958i	−0.989546	−	1.53976i	−0.155671	−	0.987809i	$-0.549754\pi$
$788$		0			0
$789$	1.72308	−	11.9843i	0.0613432	−	0.426651i
$790$		0			0
$791$	7.88849	+	5.06962i	0.280482	+	0.180255i
$792$		0			0
$793$	−16.8995	+	7.71773i	−0.600118	+	0.274065i
$794$		0			0
$795$	1.09011	+	0.0392530i	0.0386621	+	0.00139216i
$796$		0			0
$797$	2.64033	+	8.99214i	0.0935253	+	0.318518i	0.992946	−	0.118566i	$-0.0378296\pi$
$797$	2.64033	+	8.99214i	0.0935253	+	0.318518i	−0.899421	+	0.437084i	$0.856011\pi$
$798$		0			0
$799$	−24.7511	+	28.5643i	−0.875632	+	1.01053i
$800$		0			0
$801$	−22.5777	−	26.0560i	−0.797742	−	0.920644i
$802$		0			0
$803$	−32.7987	−	14.9787i	−1.15744	−	0.528586i
$804$		0			0
$805$	−5.15268	+	10.0163i	−0.181608	+	0.353028i
$806$		0			0
$807$	−0.571089	−	0.260808i	−0.0201033	−	0.00918086i
$808$		0			0
$809$	34.4661	+	39.7760i	1.21176	+	1.39845i	0.892661	+	0.450728i	$0.148836\pi$
$809$	34.4661	+	39.7760i	1.21176	+	1.39845i	0.319102	+	0.947720i	$0.396619\pi$
$810$		0			0
$811$	−1.49074	+	1.72040i	−0.0523468	+	0.0604115i	−0.781319	−	0.624132i	$-0.785453\pi$
$811$	−1.49074	+	1.72040i	−0.0523468	+	0.0604115i	0.728972	+	0.684543i	$0.239998\pi$
$812$		0			0
$813$	4.90045	+	16.6894i	0.171866	+	0.585323i
$814$		0			0
$815$	0.561342	−	15.5892i	0.0196630	−	0.546066i
$816$		0			0
$817$	9.91155	−	4.52645i	0.346761	−	0.158361i
$818$		0			0
$819$	−5.65241	−	3.63258i	−0.197511	−	0.126933i
$820$		0			0
$821$	−2.88070	+	20.0357i	−0.100537	+	0.699251i	0.875749	+	0.482766i	$0.160368\pi$
$821$	−2.88070	+	20.0357i	−0.100537	+	0.699251i	−0.976286	+	0.216484i	$0.930541\pi$
$822$		0			0
$823$	0.415056	+	0.645839i	0.0144679	+	0.0225125i	0.848412	−	0.529336i	$-0.177559\pi$
$823$	0.415056	+	0.645839i	0.0144679	+	0.0225125i	−0.833944	+	0.551849i	$0.813923\pi$
$824$		0			0
$825$	−6.63861	+	8.85732i	−0.231127	+	0.308372i
$826$		0			0
$827$			16.2044i			0.563483i	0.959490	+	0.281741i	$0.0909120\pi$
$827$			16.2044i			0.563483i	−0.959490	+	0.281741i	$0.909088\pi$
$828$		0			0
$829$	−26.3656			−0.915717			−0.457858	−	0.889025i	$-0.651383\pi$
$829$	−26.3656			−0.915717			−0.457858	+	0.889025i	$0.651383\pi$
$830$		0			0
$831$	−28.8800	−	8.47992i	−1.00183	−	0.294165i
$832$		0			0
$833$	18.4550	+	28.7165i	0.639427	+	0.994967i
$834$		0			0
$835$	−11.8010	+	35.4217i	−0.408390	+	1.22582i
$836$		0			0
$837$	0.804132	−	1.25125i	0.0277949	−	0.0432497i
$838$		0			0
$839$	23.3573	+	51.1453i	0.806383	+	1.76573i	0.622231	+	0.782833i	$0.286226\pi$
$839$	23.3573	+	51.1453i	0.806383	+	1.76573i	0.184151	+	0.982898i	$0.441046\pi$
$840$		0			0
$841$	−7.27134	−	50.5733i	−0.250736	−	1.74391i
$842$		0			0
$843$	2.51144	+	8.55317i	0.0864985	+	0.294587i
$844$		0			0
$845$	−4.32407	−	5.36907i	−0.148753	−	0.184702i
$846$		0			0
$847$	4.71581	−	4.08628i	0.162037	−	0.140406i
$848$		0			0
$849$	6.58945	−	14.4289i	0.226149	−	0.495198i
$850$		0			0
$851$	13.0943	−	3.69264i	0.448865	−	0.126582i
$852$		0			0
$853$	−16.4134	−	7.49577i	−0.561985	−	0.256650i	0.114105	−	0.993469i	$-0.463600\pi$
$853$	−16.4134	−	7.49577i	−0.561985	−	0.256650i	−0.676091	+	0.736819i	$0.736327\pi$
$854$		0			0
$855$	−29.2268	+	17.3295i	−0.999534	+	0.592655i
$856$		0			0
$857$	−24.9904	−	21.6543i	−0.853655	−	0.739697i	0.113593	−	0.993527i	$-0.463764\pi$
$857$	−24.9904	−	21.6543i	−0.853655	−	0.739697i	−0.967249	+	0.253831i	$0.918309\pi$
$858$		0			0
$859$	−33.2577	+	9.76533i	−1.13474	+	0.333189i	−0.794568	−	0.607176i	$-0.792302\pi$
$859$	−33.2577	+	9.76533i	−1.13474	+	0.333189i	−0.340169	+	0.940364i	$0.610484\pi$
$860$		0			0
$861$	0.0457655	+	0.318306i	0.00155969	+	0.0108479i
$862$		0			0
$863$	21.2743	−	9.71563i	0.724184	−	0.330724i	−0.0189921	−	0.999820i	$-0.506046\pi$
$863$	21.2743	−	9.71563i	0.724184	−	0.330724i	0.743176	+	0.669096i	$0.233318\pi$
$864$		0			0
$865$	−22.6169	−	21.0695i	−0.768999	−	0.716384i
$866$		0			0
$867$	16.0851	+	2.31268i	0.546278	+	0.0785429i
$868$		0			0
$869$	−22.5518	+	14.4932i	−0.765018	+	0.491647i
$870$		0			0
$871$	22.4014	+	6.57763i	0.759041	+	0.222875i
$872$		0			0
$873$		−	2.39164i		−	0.0809448i
$874$		0			0
$875$	−10.0943	−	6.00122i	−0.341249	−	0.202878i
$876$		0			0
$877$	2.75779	−	9.39216i	0.0931238	−	0.317151i	−0.899736	−	0.436434i	$-0.856241\pi$
$877$	2.75779	−	9.39216i	0.0931238	−	0.317151i	0.992860	+	0.119283i	$0.0380596\pi$
$878$		0			0
$879$	−10.0270	+	6.44394i	−0.338201	+	0.217349i
$880$		0			0
$881$	6.39281	−	44.4629i	0.215379	−	1.49799i	−0.539419	−	0.842037i	$-0.681356\pi$
$881$	6.39281	−	44.4629i	0.215379	−	1.49799i	0.754798	−	0.655957i	$-0.227735\pi$
$882$		0			0
$883$	−20.0931	+	31.2655i	−0.676186	+	1.05217i	0.318370	+	0.947967i	$0.396865\pi$
$883$	−20.0931	+	31.2655i	−0.676186	+	1.05217i	−0.994556	+	0.104200i	$0.966772\pi$
$884$		0			0
$885$	−5.16320	−	20.2540i	−0.173559	−	0.680829i
$886$		0			0
$887$	1.76411	−	0.253641i	0.0592332	−	0.00851644i	−0.112635	−	0.993636i	$-0.535929\pi$
$887$	1.76411	−	0.253641i	0.0592332	−	0.00851644i	0.171868	+	0.985120i	$0.445020\pi$
$888$		0			0
$889$	4.61610	−	1.35541i	0.154819	−	0.0454589i
$890$		0			0
$891$	−1.79718	+	2.07406i	−0.0602078	+	0.0694835i
$892$		0			0
$893$	36.9122	−	31.9846i	1.23522	−	1.07033i
$894$		0			0
$895$	18.5467	+	12.8852i	0.619946	+	0.430706i
$896$		0			0
$897$	−11.3376	+	9.61300i	−0.378552	+	0.320969i
$898$		0			0
$899$	1.11667	−	2.44516i	0.0372430	−	0.0815508i
$900$		0			0
$901$	−1.87895	−	2.16842i	−0.0625967	−	0.0722405i
$902$		0			0
$903$	−1.13802	−	0.986099i	−0.0378709	−	0.0328153i
$904$		0			0
$905$	2.60879	+	24.3324i	0.0867192	+	0.808836i
$906$		0			0
$907$	35.5549	−	5.11203i	1.18058	−	0.169742i	0.476053	−	0.879417i	$-0.342067\pi$
$907$	35.5549	−	5.11203i	1.18058	−	0.169742i	0.704530	+	0.709675i	$0.251158\pi$
$908$		0			0
$909$	−13.8048	−	30.2283i	−0.457877	−	1.00261i
$910$		0			0
$911$	−22.5248	−	14.4758i	−0.746280	−	0.479605i	0.111408	−	0.993775i	$-0.464464\pi$
$911$	−22.5248	−	14.4758i	−0.746280	−	0.479605i	−0.857689	+	0.514169i	$0.828100\pi$
$912$		0			0
$913$	−24.9597	−	3.58866i	−0.826044	−	0.118767i
$914$		0			0
$915$	11.9968	−	4.96511i	0.396601	−	0.164141i
$916$		0			0
$917$	4.84271	−	16.4928i	0.159920	−	0.544639i
$918$		0			0
$919$	−6.66218			−0.219765			−0.109883	−	0.993945i	$-0.535047\pi$
$919$	−6.66218			−0.219765			−0.109883	+	0.993945i	$0.535047\pi$
$920$		0			0
$921$	24.1264			0.794991
$922$		0			0
$923$	3.66732	−	12.4897i	0.120711	−	0.411105i
$924$		0			0
$925$	3.00694	+	13.8618i	0.0988676	+	0.455772i
$926$		0			0
$927$	28.5229	+	4.10097i	0.936814	+	0.134694i
$928$		0			0
$929$	22.0734	+	14.1857i	0.724206	+	0.465419i	0.850098	−	0.526625i	$-0.176543\pi$
$929$	22.0734	+	14.1857i	0.724206	+	0.465419i	−0.125892	+	0.992044i	$0.540179\pi$
$930$		0			0
$931$	−18.3245	−	40.1251i	−0.600562	−	1.31505i
$932$		0			0
$933$	−22.8797	+	3.28961i	−0.749049	+	0.107697i
$934$		0			0
$935$	28.9496	−	3.10382i	0.946752	−	0.101506i
$936$		0			0
$937$	−33.9687	−	29.4340i	−1.10971	−	0.961568i	−0.110232	−	0.993906i	$-0.535159\pi$
$937$	−33.9687	−	29.4340i	−1.10971	−	0.961568i	−0.999477	+	0.0323380i	$0.989705\pi$
$938$		0			0
$939$	10.0855	+	11.6393i	0.329127	+	0.379833i
$940$		0			0
$941$	1.55638	−	3.40799i	0.0507365	−	0.111097i	−0.882566	−	0.470188i	$-0.844186\pi$
$941$	1.55638	−	3.40799i	0.0507365	−	0.111097i	0.933303	+	0.359091i	$0.116913\pi$
$942$		0			0
$943$	−1.47427	−	0.228144i	−0.0480089	−	0.00742940i
$944$		0			0
$945$	9.55165	+	6.63598i	0.310715	+	0.215868i
$946$		0			0
$947$	13.7584	−	11.9217i	0.447087	−	0.387403i	−0.402014	−	0.915633i	$-0.631690\pi$
$947$	13.7584	−	11.9217i	0.447087	−	0.387403i	0.849101	+	0.528231i	$0.177144\pi$
$948$		0			0
$949$	33.0586	−	38.1517i	1.07313	−	1.23846i
$950$		0			0
$951$	7.04457	−	2.06847i	0.228436	−	0.0670748i
$952$		0			0
$953$	−4.07277	+	0.585577i	−0.131930	+	0.0189687i	−0.207964	−	0.978137i	$-0.566684\pi$
$953$	−4.07277	+	0.585577i	−0.131930	+	0.0189687i	0.0760334	+	0.997105i	$0.475774\pi$
$954$		0			0
$955$	30.3688	−	7.74171i	0.982712	−	0.250516i
$956$		0			0
$957$	10.7114	−	16.6673i	0.346251	−	0.538776i
$958$		0			0
$959$	2.20950	−	15.3674i	0.0713485	−	0.496240i
$960$		0			0
$961$	−26.0030	+	16.7111i	−0.838805	+	0.539067i
$962$		0			0
$963$	5.75285	−	19.5924i	0.185383	−	0.631357i
$964$		0			0
$965$	−53.2087	−	9.61601i	−1.71285	−	0.309550i
$966$		0			0
$967$		−	49.3283i		−	1.58629i	−0.609032	−	0.793146i	$-0.708442\pi$
$967$		−	49.3283i		−	1.58629i	0.609032	−	0.793146i	$-0.291558\pi$
$968$		0			0
$969$	−40.8949	−	12.0078i	−1.31373	−	0.385747i
$970$		0			0
$971$	−42.8229	+	27.5206i	−1.37425	+	0.883178i	−0.999042	−	0.0437614i	$-0.986066\pi$
$971$	−42.8229	+	27.5206i	−1.37425	+	0.883178i	−0.375210	+	0.926940i	$0.622429\pi$
$972$		0			0
$973$	−13.8211	−	1.98717i	−0.443083	−	0.0637057i
$974$		0			0
$975$	−9.27987	−	12.4116i	−0.297194	−	0.397490i
$976$		0			0
$977$	−21.2617	+	9.70990i	−0.680223	+	0.310647i	−0.725396	−	0.688332i	$-0.758343\pi$
$977$	−21.2617	+	9.70990i	−0.680223	+	0.310647i	0.0451732	+	0.998979i	$0.485616\pi$
$978$		0			0
$979$	−5.43314	−	37.7883i	−0.173644	−	1.20772i
$980$		0			0
$981$	5.59896	−	1.64400i	0.178761	−	0.0524890i
$982$		0			0
$983$	45.2097	+	39.1744i	1.44197	+	1.24947i	0.917321	+	0.398149i	$0.130347\pi$
$983$	45.2097	+	39.1744i	1.44197	+	1.24947i	0.524645	+	0.851321i	$0.324198\pi$
$984$		0			0
$985$	−9.30649	−	15.6957i	−0.296529	−	0.500107i
$986$		0			0
$987$	−6.13980	−	2.80395i	−0.195432	−	0.0892507i
$988$		0			0
$989$	5.91680	−	3.71338i	0.188143	−	0.118079i
$990$		0			0
$991$	−15.7116	+	34.4036i	−0.499095	+	1.09287i	0.477667	+	0.878541i	$0.341483\pi$
$991$	−15.7116	+	34.4036i	−0.499095	+	1.09287i	−0.976762	+	0.214326i	$0.931245\pi$
$992$		0			0
$993$	8.67215	−	7.51446i	0.275202	−	0.238464i
$994$		0			0
$995$	1.80046	+	2.23557i	0.0570783	+	0.0708724i
$996$		0			0
$997$	−8.27363	−	28.1774i	−0.262029	−	0.892388i	−0.980448	−	0.196778i	$-0.936952\pi$
$997$	−8.27363	−	28.1774i	−0.262029	−	0.892388i	0.718420	−	0.695610i	$-0.244866\pi$
$998$		0			0
$999$	−1.99921	−	13.9048i	−0.0632522	−	0.439929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.29.8	yes	120
5.4	even	2	inner	460.2.s.a.29.5	✓	120
23.4	even	11	inner	460.2.s.a.349.5	yes	120
115.4	even	22	inner	460.2.s.a.349.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.29.5	✓	120	5.4	even	2	inner
460.2.s.a.29.8	yes	120	1.1	even	1	trivial
460.2.s.a.349.5	yes	120	23.4	even	11	inner
460.2.s.a.349.8	yes	120	115.4	even	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277288 - 0.944356i) q^{3} +(0.855101 + 2.06611i) q^{5} +(1.03968 + 0.149483i) q^{7} +(1.70884 + 1.09821i) q^{9} +O(q^{10})\)	\(q+(0.277288 - 0.944356i) q^{3} +(0.855101 + 2.06611i) q^{5} +(1.03968 + 0.149483i) q^{7} +(1.70884 + 1.09821i) q^{9} +(0.934389 + 2.04603i) q^{11} +(-3.11707 + 0.448167i) q^{13} +(2.18825 - 0.234613i) q^{15} +(-4.37493 - 3.79090i) q^{17} +(4.89879 + 5.65351i) q^{19} +(0.429455 - 0.940375i) q^{21} +(3.59053 + 3.17932i) q^{23} +(-3.53760 + 3.53346i) q^{25} +(3.74242 - 3.24282i) q^{27} +(5.86067 - 6.76357i) q^{29} +(0.288195 - 0.0846216i) q^{31} +(2.19127 - 0.315057i) q^{33} +(0.580181 + 2.27591i) q^{35} +(1.53371 - 2.38649i) q^{37} +(-0.441097 + 3.06790i) q^{39} +(-0.261686 + 0.168175i) q^{41} +(0.410368 - 1.39758i) q^{43} +(-0.807779 + 4.46973i) q^{45} -6.52909i q^{47} +(-5.65787 - 1.66130i) q^{49} +(-4.79307 + 3.08032i) q^{51} +(0.490601 + 0.0705378i) q^{53} +(-3.42831 + 3.68011i) q^{55} +(6.69730 - 3.05855i) q^{57} +(-1.35162 - 9.40069i) q^{59} +(5.66056 - 1.66209i) q^{61} +(1.61248 + 1.39722i) q^{63} +(-3.59137 - 6.05698i) q^{65} +(-6.74385 - 3.07982i) q^{67} +(3.99802 - 2.50915i) q^{69} +(-1.71713 + 3.75999i) q^{71} +(-12.1150 + 10.4977i) q^{73} +(2.35591 + 4.32054i) q^{75} +(0.665617 + 2.26688i) q^{77} +(1.69613 + 11.7968i) q^{79} +(0.506850 + 1.10985i) q^{81} +(-6.06101 + 9.43112i) q^{83} +(4.09140 - 12.2807i) q^{85} +(-4.76213 - 7.41001i) q^{87} +(-16.2853 - 4.78181i) q^{89} -3.30774 q^{91} -0.295623i q^{93} +(-7.49179 + 14.9557i) q^{95} +(-0.636547 - 0.990486i) q^{97} +(-0.650235 + 4.52249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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