LMFDB - Embedded newform 476.2.bl.a.465.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			465.2
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30404 - 0.782116i) q^{3} +(-0.269222 + 4.10753i) q^{5} +(2.27945 - 1.34318i) q^{7} +(2.31684 + 1.77777i) q^{9} +O(q^{10})$	\(q+(-2.30404 - 0.782116i) q^{3} +(-0.269222 + 4.10753i) q^{5} +(2.27945 - 1.34318i) q^{7} +(2.31684 + 1.77777i) q^{9} +(-2.16596 - 1.89950i) q^{11} +(-0.342758 - 0.342758i) q^{13} +(3.83286 - 9.25335i) q^{15} +(-2.59802 + 3.20161i) q^{17} +(-7.13106 + 0.938822i) q^{19} +(-6.30246 + 1.31194i) q^{21} +(0.477587 + 1.40692i) q^{23} +(-11.8421 - 1.55904i) q^{25} +(0.107727 + 0.161225i) q^{27} +(2.08008 + 1.38987i) q^{29} +(-0.0864844 + 0.254775i) q^{31} +(3.50483 + 6.07055i) q^{33} +(4.90346 + 9.72450i) q^{35} +(-5.47373 - 6.24159i) q^{37} +(0.521651 + 1.05780i) q^{39} +(-3.76913 + 2.51845i) q^{41} +(-11.7045 + 4.84817i) q^{43} +(-7.92599 + 9.03785i) q^{45} +(0.422381 - 1.57635i) q^{47} +(3.39175 - 6.12340i) q^{49} +(8.48997 - 5.34469i) q^{51} +(-4.76901 + 3.65939i) q^{53} +(8.38536 - 8.38536i) q^{55} +(17.1645 + 3.41424i) q^{57} +(0.415355 - 3.15494i) q^{59} +(-2.31768 + 4.69979i) q^{61} +(7.66897 + 0.940410i) q^{63} +(1.50016 - 1.31561i) q^{65} +(-2.68341 - 1.54927i) q^{67} -3.61514i q^{69} +(-1.77968 + 0.354000i) q^{71} +(7.65200 - 3.77355i) q^{73} +(26.0653 + 12.8540i) q^{75} +(-7.48855 - 1.42053i) q^{77} +(13.3024 - 4.51554i) q^{79} +(-2.38960 - 8.91813i) q^{81} +(-3.39816 - 1.40756i) q^{83} +(-12.4513 - 11.5334i) q^{85} +(-3.70556 - 4.82918i) q^{87} +(6.97709 + 1.86950i) q^{89} +(-1.24168 - 0.320913i) q^{91} +(0.398527 - 0.519371i) q^{93} +(-1.93640 - 29.5438i) q^{95} +(-4.24434 + 6.35210i) q^{97} +(-1.64131 - 8.25141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−2.30404	−	0.782116i	−1.33024	−	0.451555i	−0.436323	−	0.899790i	$-0.643719\pi$
$3$	−2.30404	−	0.782116i	−1.33024	−	0.451555i	−0.893916	+	0.448235i	$0.852053\pi$
$4$		0			0
$5$	−0.269222	+	4.10753i	−0.120400	+	1.83694i	0.329843	+	0.944036i	$0.393004\pi$
$5$	−0.269222	+	4.10753i	−0.120400	+	1.83694i	−0.450243	+	0.892906i	$0.648662\pi$
$6$		0			0
$7$	2.27945	−	1.34318i	0.861550	−	0.507673i
$7$	2.27945	−	1.34318i	0.861550	−	0.507673i
$8$		0			0
$9$	2.31684	+	1.77777i	0.772279	+	0.592590i
$10$		0			0
$11$	−2.16596	−	1.89950i	−0.653062	−	0.572720i	0.267384	−	0.963590i	$-0.413841\pi$
$11$	−2.16596	−	1.89950i	−0.653062	−	0.572720i	−0.920446	+	0.390870i	$0.872174\pi$
$12$		0			0
$13$	−0.342758	−	0.342758i	−0.0950638	−	0.0950638i	0.657975	−	0.753039i	$-0.271413\pi$
$13$	−0.342758	−	0.342758i	−0.0950638	−	0.0950638i	−0.753039	+	0.657975i	$0.771413\pi$
$14$		0			0
$15$	3.83286	−	9.25335i	0.989641	−	2.38920i
$16$		0			0
$17$	−2.59802	+	3.20161i	−0.630112	+	0.776505i
$17$	−2.59802	+	3.20161i	−0.630112	+	0.776505i
$18$		0			0
$19$	−7.13106	+	0.938822i	−1.63598	+	0.215381i	−0.891745	−	0.452539i	$-0.850518\pi$
$19$	−7.13106	+	0.938822i	−1.63598	+	0.215381i	−0.744234	+	0.667919i	$0.767185\pi$
$20$		0			0
$21$	−6.30246	+	1.31194i	−1.37531	+	0.286290i
$22$		0			0
$23$	0.477587	+	1.40692i	0.0995837	+	0.293364i	0.985292	−	0.170878i	$-0.0546603\pi$
$23$	0.477587	+	1.40692i	0.0995837	+	0.293364i	−0.885709	+	0.464242i	$0.846327\pi$
$24$		0			0
$25$	−11.8421	−	1.55904i	−2.36842	−	0.311808i
$26$		0			0
$27$	0.107727	+	0.161225i	0.0207320	+	0.0310277i
$28$		0			0
$29$	2.08008	+	1.38987i	0.386262	+	0.258092i	0.733506	−	0.679683i	$-0.237883\pi$
$29$	2.08008	+	1.38987i	0.386262	+	0.258092i	−0.347244	+	0.937775i	$0.612883\pi$
$30$		0			0
$31$	−0.0864844	+	0.254775i	−0.0155331	+	0.0457589i	−0.954420	−	0.298466i	$-0.903525\pi$
$31$	−0.0864844	+	0.254775i	−0.0155331	+	0.0457589i	0.938887	+	0.344225i	$0.111858\pi$
$32$		0			0
$33$	3.50483	+	6.07055i	0.610113	+	1.05675i
$34$		0			0
$35$	4.90346	+	9.72450i	0.828837	+	1.64374i
$36$		0			0
$37$	−5.47373	−	6.24159i	−0.899876	−	1.02611i	−0.999517	−	0.0310881i	$-0.990103\pi$
$37$	−5.47373	−	6.24159i	−0.899876	−	1.02611i	0.0996410	−	0.995023i	$-0.468231\pi$
$38$		0			0
$39$	0.521651	+	1.05780i	0.0835310	+	0.169384i
$40$		0			0
$41$	−3.76913	+	2.51845i	−0.588639	+	0.393316i	−0.813919	−	0.580978i	$-0.802670\pi$
$41$	−3.76913	+	2.51845i	−0.588639	+	0.393316i	0.225280	+	0.974294i	$0.427670\pi$
$42$		0			0
$43$	−11.7045	+	4.84817i	−1.78492	+	0.739339i	−0.793510	+	0.608557i	$0.791749\pi$
$43$	−11.7045	+	4.84817i	−1.78492	+	0.739339i	−0.991411	+	0.130782i	$0.958251\pi$
$44$		0			0
$45$	−7.92599	+	9.03785i	−1.18154	+	1.34728i
$46$		0			0
$47$	0.422381	−	1.57635i	0.0616107	−	0.229934i	−0.928254	−	0.371946i	$-0.878691\pi$
$47$	0.422381	−	1.57635i	0.0616107	−	0.229934i	0.989865	+	0.142012i	$0.0453572\pi$
$48$		0			0
$49$	3.39175	−	6.12340i	0.484535	−	0.874772i
$50$		0			0
$51$	8.48997	−	5.34469i	1.18883	−	0.748406i
$52$		0			0
$53$	−4.76901	+	3.65939i	−0.655074	+	0.502656i	−0.881996	−	0.471257i	$-0.843800\pi$
$53$	−4.76901	+	3.65939i	−0.655074	+	0.502656i	0.226922	+	0.973913i	$0.427134\pi$
$54$		0			0
$55$	8.38536	−	8.38536i	1.13068	−	1.13068i
$56$		0			0
$57$	17.1645	+	3.41424i	2.27350	+	0.452227i
$58$		0			0
$59$	0.415355	−	3.15494i	0.0540747	−	0.410738i	−0.942904	−	0.333064i	$-0.891917\pi$
$59$	0.415355	−	3.15494i	0.0540747	−	0.410738i	0.996979	−	0.0776737i	$-0.0247492\pi$
$60$		0			0
$61$	−2.31768	+	4.69979i	−0.296748	+	0.601746i	−0.993274	−	0.115786i	$-0.963061\pi$
$61$	−2.31768	+	4.69979i	−0.296748	+	0.601746i	0.696526	+	0.717532i	$0.254728\pi$
$62$		0			0
$63$	7.66897	+	0.940410i	0.966199	+	0.118481i
$64$		0			0
$65$	1.50016	−	1.31561i	0.186072	−	0.163181i
$66$		0			0
$67$	−2.68341	−	1.54927i	−0.327831	−	0.189273i	0.327047	−	0.945008i	$-0.393947\pi$
$67$	−2.68341	−	1.54927i	−0.327831	−	0.189273i	−0.654878	+	0.755735i	$0.727280\pi$
$68$		0			0
$69$		−	3.61514i		−	0.435212i
$70$		0			0
$71$	−1.77968	+	0.354000i	−0.211209	+	0.0420121i	−0.299561	−	0.954077i	$-0.596840\pi$
$71$	−1.77968	+	0.354000i	−0.211209	+	0.0420121i	0.0883516	+	0.996089i	$0.471840\pi$
$72$		0			0
$73$	7.65200	−	3.77355i	0.895598	−	0.441660i	0.0645846	−	0.997912i	$-0.479428\pi$
$73$	7.65200	−	3.77355i	0.895598	−	0.441660i	0.831014	+	0.556252i	$0.187761\pi$
$74$		0			0
$75$	26.0653	+	12.8540i	3.00976	+	1.48425i
$76$		0			0
$77$	−7.48855	−	1.42053i	−0.853400	−	0.161884i
$78$		0			0
$79$	13.3024	−	4.51554i	1.49663	−	0.508038i	0.551345	−	0.834278i	$-0.314115\pi$
$79$	13.3024	−	4.51554i	1.49663	−	0.508038i	0.945287	+	0.326240i	$0.105782\pi$
$80$		0			0
$81$	−2.38960	−	8.91813i	−0.265512	−	0.990903i
$82$		0			0
$83$	−3.39816	−	1.40756i	−0.372996	−	0.154500i	0.188307	−	0.982110i	$-0.439700\pi$
$83$	−3.39816	−	1.40756i	−0.372996	−	0.154500i	−0.561303	+	0.827610i	$0.689700\pi$
$84$		0			0
$85$	−12.4513	−	11.5334i	−1.35053	−	1.25097i
$86$		0			0
$87$	−3.70556	−	4.82918i	−0.397278	−	0.517743i
$88$		0			0
$89$	6.97709	+	1.86950i	0.739570	+	0.198167i	0.608887	−	0.793257i	$-0.291616\pi$
$89$	6.97709	+	1.86950i	0.739570	+	0.198167i	0.130683	+	0.991424i	$0.458283\pi$
$90$		0			0
$91$	−1.24168	−	0.320913i	−0.130164	−	0.0336408i
$92$		0			0
$93$	0.398527	−	0.519371i	0.0413254	−	0.0538563i
$94$		0			0
$95$	−1.93640	−	29.5438i	−0.198671	−	3.03113i
$96$		0			0
$97$	−4.24434	+	6.35210i	−0.430947	+	0.644958i	−0.981861	−	0.189604i	$-0.939280\pi$
$97$	−4.24434	+	6.35210i	−0.430947	+	0.644958i	0.550913	+	0.834563i	$0.314280\pi$
$98$		0			0
$99$	−1.64131	−	8.25141i	−0.164958	−	0.829297i
$100$		0			0
$101$	−3.78135	+	6.54949i	−0.376259	+	0.651699i	−0.990515	−	0.137408i	$-0.956123\pi$
$101$	−3.78135	+	6.54949i	−0.376259	+	0.651699i	0.614256	+	0.789107i	$0.289456\pi$
$102$		0			0
$103$	−10.0167	+	5.78314i	−0.986973	+	0.569829i	−0.904368	−	0.426753i	$-0.859657\pi$
$103$	−10.0167	+	5.78314i	−0.986973	+	0.569829i	−0.0826050	+	0.996582i	$0.526324\pi$
$104$		0			0
$105$	−3.69209	−	26.2407i	−0.360311	−	2.56083i
$106$		0			0
$107$	16.5036	+	1.08170i	1.59546	+	0.104572i	0.837021	−	0.547170i	$-0.184295\pi$
$107$	16.5036	+	1.08170i	1.59546	+	0.104572i	0.758440	+	0.651742i	$0.225962\pi$
$108$		0			0
$109$	18.3904	−	1.20537i	1.76148	−	0.115453i	0.849994	−	0.526792i	$-0.176605\pi$
$109$	18.3904	−	1.20537i	1.76148	−	0.115453i	0.911482	+	0.411339i	$0.134939\pi$
$110$		0			0
$111$	7.73004	+	18.6620i	0.733703	+	1.77132i
$112$		0			0
$113$	−3.20388	+	16.1070i	−0.301396	+	1.51522i	0.472173	+	0.881506i	$0.343470\pi$
$113$	−3.20388	+	16.1070i	−0.301396	+	1.51522i	−0.773569	+	0.633712i	$0.781530\pi$
$114$		0			0
$115$	−5.90756	+	1.58293i	−0.550883	+	0.147609i
$116$		0			0
$117$	−0.184769	−	1.40346i	−0.0170819	−	0.129750i
$118$		0			0
$119$	−1.62171	+	10.7875i	−0.148662	+	0.988888i
$120$		0			0
$121$	−0.352489	−	2.67742i	−0.0320445	−	0.243402i
$122$		0			0
$123$	10.6539	−	2.85472i	0.960634	−	0.257401i
$124$		0			0
$125$	5.57665	−	28.0357i	0.498790	−	2.50759i
$126$		0			0
$127$	3.43064	+	8.28231i	0.304420	+	0.734936i	0.999866	+	0.0163574i	$0.00520695\pi$
$127$	3.43064	+	8.28231i	0.304420	+	0.734936i	−0.695446	+	0.718579i	$0.744793\pi$
$128$		0			0
$129$	30.7595	−	2.01608i	2.70822	−	0.177506i
$130$		0			0
$131$	1.43977	+	0.0943677i	0.125794	+	0.00824494i	0.128170	−	0.991752i	$-0.459090\pi$
$131$	1.43977	+	0.0943677i	0.125794	+	0.00824494i	−0.00237631	+	0.999997i	$0.500756\pi$
$132$		0			0
$133$	−14.9939	+	11.7183i	−1.30013	+	1.01610i
$134$		0			0
$135$	−0.691237	+	0.399086i	−0.0594922	+	0.0343478i
$136$		0			0
$137$	−7.10480	+	12.3059i	−0.607004	+	1.05136i	0.384728	+	0.923030i	$0.374295\pi$
$137$	−7.10480	+	12.3059i	−0.607004	+	1.05136i	−0.991731	+	0.128331i	$0.959038\pi$
$138$		0			0
$139$	3.51646	+	17.6785i	0.298263	+	1.49947i	0.781460	+	0.623956i	$0.214476\pi$
$139$	3.51646	+	17.6785i	0.298263	+	1.49947i	−0.483197	+	0.875512i	$0.660524\pi$
$140$		0			0
$141$	−2.20607	+	3.30162i	−0.185785	+	0.278047i
$142$		0			0
$143$	0.0913326	+	1.39347i	0.00763762	+	0.116527i
$144$		0			0
$145$	−6.26893	+	8.16982i	−0.520606	+	0.678467i
$146$		0			0
$147$	−12.6039	+	11.4558i	−1.03956	+	0.944860i
$148$		0			0
$149$	20.1653	+	5.40328i	1.65201	+	0.442654i	0.960174	−	0.279404i	$-0.0901368\pi$
$149$	20.1653	+	5.40328i	1.65201	+	0.442654i	0.691833	+	0.722058i	$0.256803\pi$
$150$		0			0
$151$	−8.17107	−	10.6487i	−0.664952	−	0.866583i	0.332105	−	0.943242i	$-0.392241\pi$
$151$	−8.17107	−	10.6487i	−0.664952	−	0.866583i	−0.997057	+	0.0766598i	$0.975574\pi$
$152$		0			0
$153$	−11.7109	+	2.79893i	−0.946771	+	0.226280i
$154$		0			0
$155$	−1.02321	−	0.423828i	−0.0821863	−	0.0340427i
$156$		0			0
$157$	2.70554	+	10.0972i	0.215926	+	0.805846i	0.985839	+	0.167697i	$0.0536330\pi$
$157$	2.70554	+	10.0972i	0.215926	+	0.805846i	−0.769913	+	0.638149i	$0.779700\pi$
$158$		0			0
$159$	13.8501	−	4.70146i	1.09838	−	0.372850i
$160$		0			0
$161$	2.97838	+	2.56553i	0.234729	+	0.202192i
$162$		0			0
$163$	−8.17419	−	4.03107i	−0.640252	−	0.315737i	0.0930285	−	0.995663i	$-0.470345\pi$
$163$	−8.17419	−	4.03107i	−0.640252	−	0.315737i	−0.733281	+	0.679926i	$0.762012\pi$
$164$		0			0
$165$	−25.8785	+	12.7619i	−2.01464	+	0.993511i
$166$		0			0
$167$	−14.4296	+	2.87024i	−1.11660	+	0.222105i	−0.718698	−	0.695323i	$-0.755262\pi$
$167$	−14.4296	+	2.87024i	−1.11660	+	0.222105i	−0.397902	+	0.917428i	$0.630262\pi$
$168$		0			0
$169$		−	12.7650i		−	0.981926i
$170$		0			0
$171$	−18.1905	−	10.5023i	−1.39106	−	0.803131i
$172$		0			0
$173$	8.25446	−	7.23896i	0.627575	−	0.550368i	−0.285388	−	0.958412i	$-0.592122\pi$
$173$	8.25446	−	7.23896i	0.627575	−	0.550368i	0.912962	+	0.408044i	$0.133789\pi$
$174$		0			0
$175$	−29.0874	+	12.3523i	−2.19880	+	0.933744i
$176$		0			0
$177$	−3.42452	+	6.94425i	−0.257403	+	0.521962i
$178$		0			0
$179$	−0.963969	+	7.32207i	−0.0720504	+	0.547277i	0.916910	+	0.399095i	$0.130676\pi$
$179$	−0.963969	+	7.32207i	−0.0720504	+	0.547277i	−0.988960	+	0.148182i	$0.952658\pi$
$180$		0			0
$181$	17.1764	+	3.41660i	1.27671	+	0.253954i	0.786467	−	0.617632i	$-0.211908\pi$
$181$	17.1764	+	3.41660i	1.27671	+	0.253954i	0.490244	+	0.871585i	$0.336908\pi$
$182$		0			0
$183$	9.01580	−	9.01580i	0.666467	−	0.666467i
$184$		0			0
$185$	27.1112	−	20.8031i	1.99325	−	1.52948i
$186$		0			0
$187$	11.7087	−	1.99964i	0.856221	−	0.146228i
$188$		0			0
$189$	0.462111	+	0.222806i	0.0336136	+	0.0162068i
$190$		0			0
$191$	0.628568	−	2.34585i	0.0454816	−	0.169739i	−0.939449	−	0.342688i	$-0.888663\pi$
$191$	0.628568	−	2.34585i	0.0454816	−	0.169739i	0.984931	+	0.172948i	$0.0553294\pi$
$192$		0			0
$193$	−9.88959	+	11.2769i	−0.711868	+	0.811730i	−0.988814	−	0.149155i	$-0.952345\pi$
$193$	−9.88959	+	11.2769i	−0.711868	+	0.811730i	0.276945	+	0.960886i	$0.410678\pi$
$194$		0			0
$195$	−4.48540	+	1.85791i	−0.321206	+	0.133048i
$196$		0			0
$197$	−7.60955	+	5.08454i	−0.542158	+	0.362258i	−0.796294	−	0.604910i	$-0.793209\pi$
$197$	−7.60955	+	5.08454i	−0.542158	+	0.362258i	0.254136	+	0.967169i	$0.418209\pi$
$198$		0			0
$199$	−10.6094	−	21.5137i	−0.752080	−	1.52507i	−0.848187	−	0.529696i	$-0.822306\pi$
$199$	−10.6094	−	21.5137i	−0.752080	−	1.52507i	0.0961074	−	0.995371i	$-0.469361\pi$
$200$		0			0
$201$	4.97098	+	5.66832i	0.350626	+	0.399812i
$202$		0			0
$203$	6.60828	+	0.374206i	0.463810	+	0.0262641i
$204$		0			0
$205$	−9.32987	−	16.1598i	−0.651627	−	1.12865i
$206$		0			0
$207$	−1.39470	+	4.10865i	−0.0969384	+	0.285571i
$208$		0			0
$209$	17.2289	+	11.5120i	1.19175	+	0.796300i
$210$		0			0
$211$	0.510181	+	0.763540i	0.0351223	+	0.0525643i	0.848615	−	0.529010i	$-0.177437\pi$
$211$	0.510181	+	0.763540i	0.0351223	+	0.0525643i	−0.813493	+	0.581575i	$0.802437\pi$
$212$		0			0
$213$	4.37732	+	0.576285i	0.299929	+	0.0394864i
$214$		0			0
$215$	−16.7629	−	49.3818i	−1.14322	−	3.36781i
$216$		0			0
$217$	0.145071	+	0.696910i	0.00984809	+	0.0473093i
$218$		0			0
$219$	−20.5819	+	2.70965i	−1.39079	+	0.183101i
$220$		0			0
$221$	1.98787	−	0.206886i	0.133718	−	0.0139167i
$222$		0			0
$223$	−4.17674	+	10.0835i	−0.279695	+	0.675244i	−0.999827	−	0.0185932i	$-0.994081\pi$
$223$	−4.17674	+	10.0835i	−0.279695	+	0.675244i	0.720132	+	0.693837i	$0.244081\pi$
$224$		0			0
$225$	−24.6645	−	24.6645i	−1.64430	−	1.64430i
$226$		0			0
$227$	−12.4461	−	10.9149i	−0.826075	−	0.724449i	0.137898	−	0.990446i	$-0.455965\pi$
$227$	−12.4461	−	10.9149i	−0.826075	−	0.724449i	−0.963974	+	0.265998i	$0.914299\pi$
$228$		0			0
$229$	−8.59270	−	6.59341i	−0.567821	−	0.435705i	0.284535	−	0.958666i	$-0.408161\pi$
$229$	−8.59270	−	6.59341i	−0.567821	−	0.435705i	−0.852357	+	0.522961i	$0.824827\pi$
$230$		0			0
$231$	16.1429	+	9.12988i	1.06213	+	0.600702i
$232$		0			0
$233$	1.01604	−	15.5018i	0.0665632	−	1.01556i	−0.825719	−	0.564081i	$-0.809231\pi$
$233$	1.01604	−	15.5018i	0.0665632	−	1.01556i	0.892283	−	0.451477i	$-0.149103\pi$
$234$		0			0
$235$	6.36118	+	2.15933i	0.414958	+	0.140859i
$236$		0			0
$237$	−34.1808			−2.22028
$238$		0			0
$239$	16.5800			1.07247			0.536234	−	0.844069i	$-0.319846\pi$
$239$	16.5800			1.07247			0.536234	+	0.844069i	$0.319846\pi$
$240$		0			0
$241$	4.82492	+	1.63784i	0.310801	+	0.105503i	0.472482	−	0.881340i	$-0.343358\pi$
$241$	4.82492	+	1.63784i	0.310801	+	0.105503i	−0.161681	+	0.986843i	$0.551692\pi$
$242$		0			0
$243$	−1.43122	+	21.8362i	−0.0918129	+	1.40079i
$244$		0			0
$245$	24.2389	+	15.5802i	1.54857	+	0.995386i
$246$		0			0
$247$	2.76601	+	2.12244i	0.175997	+	0.135047i
$248$		0			0
$249$	6.72861	+	5.90083i	0.426408	+	0.373950i
$250$		0			0
$251$	−11.0399	−	11.0399i	−0.696832	−	0.696832i	0.266894	−	0.963726i	$-0.414003\pi$
$251$	−11.0399	−	11.0399i	−0.696832	−	0.696832i	−0.963726	+	0.266894i	$0.914003\pi$
$252$		0			0
$253$	1.63802	−	3.95452i	0.102981	−	0.248618i
$254$		0			0
$255$	19.6678	+	36.3117i	1.23164	+	2.27393i
$256$		0			0
$257$	7.39096	−	0.973038i	0.461035	−	0.0606965i	0.103569	−	0.994622i	$-0.466974\pi$
$257$	7.39096	−	0.973038i	0.461035	−	0.0606965i	0.357467	+	0.933926i	$0.383641\pi$
$258$		0			0
$259$	−20.8606	−	6.87518i	−1.29622	−	0.427203i
$260$		0			0
$261$	2.34835	+	6.91801i	0.145359	+	0.428214i
$262$		0			0
$263$	16.6072	+	2.18638i	1.02404	+	0.134818i	0.623794	−	0.781589i	$-0.285590\pi$
$263$	16.6072	+	2.18638i	1.02404	+	0.134818i	0.400249	+	0.916407i	$0.368924\pi$
$264$		0			0
$265$	−13.7471	−	20.5740i	−0.844479	−	1.26385i
$266$		0			0
$267$	−14.6133	−	9.76431i	−0.894321	−	0.597566i
$268$		0			0
$269$	1.67736	−	4.94134i	0.102270	−	0.301279i	−0.883736	−	0.467985i	$-0.844980\pi$
$269$	1.67736	−	4.94134i	0.102270	−	0.301279i	0.986007	+	0.166707i	$0.0533133\pi$
$270$		0			0
$271$	8.05615	+	13.9537i	0.489377	+	0.847625i	0.999925	−	0.0122238i	$-0.00389105\pi$
$271$	8.05615	+	13.9537i	0.489377	+	0.847625i	−0.510549	+	0.859849i	$0.670558\pi$
$272$		0			0
$273$	2.60989	+	1.71054i	0.157958	+	0.103526i
$274$		0			0
$275$	22.6881	+	25.8708i	1.36814	+	1.56007i
$276$		0			0
$277$	8.69316	+	17.6280i	0.522321	+	1.05916i	0.984987	+	0.172630i	$0.0552264\pi$
$277$	8.69316	+	17.6280i	0.522321	+	1.05916i	−0.462666	+	0.886533i	$0.653107\pi$
$278$		0			0
$279$	−0.653302	+	0.436522i	−0.0391122	+	0.0261339i
$280$		0			0
$281$	−18.8970	+	7.82741i	−1.12730	+	0.466944i	−0.866863	−	0.498546i	$-0.833868\pi$
$281$	−18.8970	+	7.82741i	−1.12730	+	0.466944i	−0.260440	+	0.965490i	$0.583868\pi$
$282$		0			0
$283$	14.7858	−	16.8599i	0.878922	−	1.00222i	−0.121032	−	0.992649i	$-0.538620\pi$
$283$	14.7858	−	16.8599i	0.878922	−	1.00222i	0.999954	−	0.00957014i	$-0.00304632\pi$
$284$		0			0
$285$	−18.6451	+	69.5846i	−1.10444	+	4.12184i
$286$		0			0
$287$	−5.20880	+	10.8033i	−0.307466	+	0.637697i
$288$		0			0
$289$	−3.50061	−	16.6357i	−0.205919	−	0.978569i
$290$		0			0
$291$	14.7472	−	11.3159i	0.864497	−	0.663352i
$292$		0			0
$293$	−8.03843	+	8.03843i	−0.469610	+	0.469610i	−0.901788	−	0.432178i	$-0.857745\pi$
$293$	−8.03843	+	8.03843i	−0.469610	+	0.469610i	0.432178	+	0.901788i	$0.357745\pi$
$294$		0			0
$295$	12.8472	+	2.55546i	0.747991	+	0.148785i
$296$		0			0
$297$	0.0729135	−	0.553833i	0.00423087	−	0.0321366i
$298$		0			0
$299$	0.318538	−	0.645930i	0.0184215	−	0.0373551i
$300$		0			0
$301$	−20.1679	+	26.7724i	−1.16246	+	1.54313i
$302$		0			0
$303$	13.8349	−	12.1328i	0.794792	−	0.697014i
$304$		0			0
$305$	−18.6805	−	10.7852i	−1.06964	−	0.617559i
$306$		0			0
$307$		−	13.3723i		−	0.763200i	−0.924328	−	0.381600i	$-0.875373\pi$
$307$		−	13.3723i		−	0.763200i	0.924328	−	0.381600i	$-0.124627\pi$
$308$		0			0
$309$	27.6019	−	5.49037i	1.57022	−	0.312336i
$310$		0			0
$311$	−21.4555	+	10.5807i	−1.21663	+	0.599975i	−0.933317	−	0.359053i	$-0.883100\pi$
$311$	−21.4555	+	10.5807i	−1.21663	+	0.599975i	−0.283312	+	0.959028i	$0.591433\pi$
$312$		0			0
$313$	−3.39098	−	1.67225i	−0.191670	−	0.0945209i	0.343922	−	0.938998i	$-0.388245\pi$
$313$	−3.39098	−	1.67225i	−0.191670	−	0.0945209i	−0.535591	+	0.844477i	$0.679911\pi$
$314$		0			0
$315$	−5.92741	+	31.2473i	−0.333972	+	1.76059i
$316$		0			0
$317$	−2.90680	+	0.986726i	−0.163262	+	0.0554201i	−0.401874	−	0.915695i	$-0.631641\pi$
$317$	−2.90680	+	0.986726i	−0.163262	+	0.0554201i	0.238612	+	0.971115i	$0.423308\pi$
$318$		0			0
$319$	−1.86533	−	6.96151i	−0.104439	−	0.389770i
$320$		0			0
$321$	−37.1789	−	15.4000i	−2.07512	−	0.859545i
$322$		0			0
$323$	15.5209	−	25.2700i	0.863605	−	1.40606i
$324$		0			0
$325$	3.52459	+	4.59333i	0.195509	+	0.254792i
$326$		0			0
$327$	−43.3149	−	11.6062i	−2.39532	−	0.641823i
$328$		0			0
$329$	−1.15452	−	4.16054i	−0.0636508	−	0.229378i
$330$		0			0
$331$	−14.0260	+	18.2791i	−0.770940	+	1.00471i	0.228574	+	0.973527i	$0.426594\pi$
$331$	−14.0260	+	18.2791i	−0.770940	+	1.00471i	−0.999514	+	0.0311816i	$0.990073\pi$
$332$		0			0
$333$	−1.58561	−	24.1918i	−0.0868911	−	1.32570i
$334$		0			0
$335$	7.08609	−	10.6051i	0.387155	−	0.579418i
$336$		0			0
$337$	0.948432	+	4.76809i	0.0516644	+	0.259734i	0.997981	−	0.0635053i	$-0.0202280\pi$
$337$	0.948432	+	4.76809i	0.0516644	+	0.259734i	−0.946317	+	0.323240i	$0.895228\pi$
$338$		0			0
$339$	19.9794	−	34.6054i	1.08513	−	1.87950i
$340$		0			0
$341$	0.671266	−	0.387556i	0.0363511	−	0.0209873i
$342$		0			0
$343$	−0.493511	−	18.5137i	−0.0266471	−	0.999645i
$344$		0			0
$345$	14.8493	+	0.973274i	0.799459	+	0.0523993i
$346$		0			0
$347$	−14.7902	+	0.969399i	−0.793978	+	0.0520401i	−0.456994	−	0.889470i	$-0.651074\pi$
$347$	−14.7902	+	0.969399i	−0.793978	+	0.0520401i	−0.336985	+	0.941510i	$0.609407\pi$
$348$		0			0
$349$	−2.03026	−	4.90149i	−0.108677	−	0.262371i	0.860180	−	0.509991i	$-0.170351\pi$
$349$	−2.03026	−	4.90149i	−0.108677	−	0.262371i	−0.968857	+	0.247621i	$0.920351\pi$
$350$		0			0
$351$	0.0183368	−	0.0921851i	0.000978744	−	0.00492048i
$352$		0			0
$353$	−12.8973	+	3.45582i	−0.686455	+	0.183935i	−0.585156	−	0.810921i	$-0.698967\pi$
$353$	−12.8973	+	3.45582i	−0.686455	+	0.183935i	−0.101299	+	0.994856i	$0.532300\pi$
$354$		0			0
$355$	−0.974938	−	7.40539i	−0.0517443	−	0.393037i
$356$		0			0
$357$	12.1736	−	23.5865i	0.644293	−	1.24833i
$358$		0			0
$359$	2.17869	+	16.5488i	0.114987	+	0.873411i	0.947578	+	0.319524i	$0.103523\pi$
$359$	2.17869	+	16.5488i	0.114987	+	0.873411i	−0.832592	+	0.553887i	$0.813144\pi$
$360$		0			0
$361$	31.6181	−	8.47205i	1.66411	−	0.445897i
$362$		0			0
$363$	−1.28191	+	6.44458i	−0.0672826	+	0.338253i
$364$		0			0
$365$	13.4399	+	32.4467i	0.703475	+	1.69834i
$366$		0			0
$367$	−21.6488	+	1.41893i	−1.13006	+	0.0740678i	−0.618936	−	0.785442i	$-0.712436\pi$
$367$	−21.6488	+	1.41893i	−1.13006	+	0.0740678i	−0.511120	+	0.859509i	$0.670769\pi$
$368$		0			0
$369$	−13.2097	−	0.865808i	−0.687669	−	0.0450722i
$370$		0			0
$371$	−5.95549	+	14.7470i	−0.309194	+	0.765627i
$372$		0			0
$373$	−5.59293	+	3.22908i	−0.289591	+	0.167195i	−0.637757	−	0.770237i	$-0.720138\pi$
$373$	−5.59293	+	3.22908i	−0.289591	+	0.167195i	0.348166	+	0.937433i	$0.386804\pi$
$374$		0			0
$375$	−34.7760	+	60.2338i	−1.79582	+	3.11046i
$376$		0			0
$377$	−0.236577	−	1.18935i	−0.0121843	−	0.0612548i
$378$		0			0
$379$	10.7002	−	16.0139i	0.549630	−	0.822579i	−0.447807	−	0.894130i	$-0.647795\pi$
$379$	10.7002	−	16.0139i	0.549630	−	0.822579i	0.997437	+	0.0715509i	$0.0227948\pi$
$380$		0			0
$381$	−1.42661	−	21.7659i	−0.0730877	−	1.11510i
$382$		0			0
$383$	−13.0232	+	16.9721i	−0.665452	+	0.867235i	−0.997095	−	0.0761707i	$-0.975731\pi$
$383$	−13.0232	+	16.9721i	−0.665452	+	0.867235i	0.331642	+	0.943405i	$0.392397\pi$
$384$		0			0
$385$	7.85094	−	30.3770i	0.400121	−	1.54816i
$386$		0			0
$387$	−35.7364	−	9.57553i	−1.81658	−	0.486752i
$388$		0			0
$389$	9.35248	+	12.1884i	0.474189	+	0.617976i	0.967804	−	0.251705i	$-0.0809913\pi$
$389$	9.35248	+	12.1884i	0.474189	+	0.617976i	−0.493615	+	0.869681i	$0.664325\pi$
$390$		0			0
$391$	−5.74520	−	2.12617i	−0.290547	−	0.107525i
$392$		0			0
$393$	−3.24349	−	1.34350i	−0.163612	−	0.0677704i
$394$		0			0
$395$	14.9664	+	55.8555i	0.753043	+	2.81039i
$396$		0			0
$397$	4.59576	−	1.56005i	0.230655	−	0.0782968i	−0.203719	−	0.979029i	$-0.565303\pi$
$397$	4.59576	−	1.56005i	0.230655	−	0.0782968i	0.434374	+	0.900733i	$0.356970\pi$
$398$		0			0
$399$	43.7115	−	15.2724i	2.18831	−	0.764579i
$400$		0			0
$401$	34.1299	+	16.8310i	1.70437	+	0.840501i	0.990056	+	0.140674i	$0.0449270\pi$
$401$	34.1299	+	16.8310i	1.70437	+	0.840501i	0.714312	+	0.699827i	$0.246740\pi$
$402$		0			0
$403$	0.116969	−	0.0576828i	0.00582665	−	0.00287339i
$404$		0			0
$405$	37.2748	−	7.41442i	1.85220	−	0.368425i
$406$		0			0
$407$			23.9164i			1.18549i
$408$		0			0
$409$	−19.8484	−	11.4595i	−0.981442	−	0.566636i	−0.0787365	−	0.996895i	$-0.525089\pi$
$409$	−19.8484	−	11.4595i	−0.981442	−	0.566636i	−0.902705	+	0.430260i	$0.858422\pi$
$410$		0			0
$411$	25.9944	−	22.7964i	1.28221	−	1.12447i
$412$		0			0
$413$	−3.29086	−	7.74941i	−0.161933	−	0.381323i
$414$		0			0
$415$	6.69646	−	13.5791i	0.328716	−	0.666570i
$416$		0			0
$417$	5.72454	−	43.4822i	0.280332	−	2.12933i
$418$		0			0
$419$	0.428481	+	0.0852302i	0.0209327	+	0.00416377i	0.205546	−	0.978648i	$-0.434103\pi$
$419$	0.428481	+	0.0852302i	0.0209327	+	0.00416377i	−0.184613	+	0.982811i	$0.559103\pi$
$420$		0			0
$421$	3.03092	−	3.03092i	0.147718	−	0.147718i	−0.629380	−	0.777098i	$-0.716691\pi$
$421$	3.03092	−	3.03092i	0.147718	−	0.147718i	0.777098	+	0.629380i	$0.216691\pi$
$422$		0			0
$423$	3.78098	−	2.90124i	0.183837	−	0.141063i
$424$		0			0
$425$	35.7574	−	33.8633i	1.73449	−	1.64261i
$426$		0			0
$427$	1.02963	+	13.8260i	0.0498271	+	0.669085i
$428$		0			0
$429$	0.879419	−	3.28204i	0.0424587	−	0.158458i
$430$		0			0
$431$	−3.63808	+	4.14843i	−0.175240	+	0.199823i	−0.832792	−	0.553586i	$-0.813259\pi$
$431$	−3.63808	+	4.14843i	−0.175240	+	0.199823i	0.657552	+	0.753410i	$0.271592\pi$
$432$		0			0
$433$	14.6361	−	6.06247i	0.703365	−	0.291343i	−0.00219067	−	0.999998i	$-0.500697\pi$
$433$	14.6361	−	6.06247i	0.703365	−	0.291343i	0.705556	+	0.708654i	$0.250697\pi$
$434$		0			0
$435$	20.8336	−	13.9206i	0.998895	−	0.667440i
$436$		0			0
$437$	−4.72655	−	9.58450i	−0.226102	−	0.458489i
$438$		0			0
$439$	4.59363	+	5.23803i	0.219242	+	0.249997i	0.850997	−	0.525171i	$-0.175999\pi$
$439$	4.59363	+	5.23803i	0.219242	+	0.249997i	−0.631755	+	0.775168i	$0.717665\pi$
$440$		0			0
$441$	18.7441	−	8.15717i	0.892578	−	0.388437i
$442$		0			0
$443$	−15.0751	−	26.1108i	−0.716239	−	1.24056i	−0.962480	−	0.271354i	$-0.912529\pi$
$443$	−15.0751	−	26.1108i	−0.716239	−	1.24056i	0.246240	−	0.969209i	$-0.420805\pi$
$444$		0			0
$445$	−9.55742	+	28.1553i	−0.453065	+	1.33469i
$446$		0			0
$447$	−42.2357	−	28.2210i	−1.99768	−	1.33481i
$448$		0			0
$449$	18.9590	+	28.3742i	0.894732	+	1.33906i	0.940388	+	0.340104i	$0.110462\pi$
$449$	18.9590	+	28.3742i	0.894732	+	1.33906i	−0.0456562	+	0.998957i	$0.514538\pi$
$450$		0			0
$451$	12.9476	+	1.70458i	0.609677	+	0.0802655i
$452$		0			0
$453$	10.4979	+	30.9259i	0.493235	+	1.45302i
$454$		0			0
$455$	1.65245	−	5.01384i	0.0774679	−	0.235053i
$456$		0			0
$457$	−15.5234	+	2.04370i	−0.726155	+	0.0956001i	−0.484536	−	0.874771i	$-0.661012\pi$
$457$	−15.5234	+	2.04370i	−0.726155	+	0.0956001i	−0.241619	+	0.970371i	$0.577678\pi$
$458$		0			0
$459$	−0.796054	−	0.0739649i	−0.0371566	−	0.00345239i
$460$		0			0
$461$	8.90172	−	21.4907i	0.414594	−	1.00092i	−0.569294	−	0.822134i	$-0.692783\pi$
$461$	8.90172	−	21.4907i	0.414594	−	1.00092i	0.983888	−	0.178785i	$-0.0572167\pi$
$462$		0			0
$463$	8.13650	+	8.13650i	0.378135	+	0.378135i	0.870429	−	0.492294i	$-0.163841\pi$
$463$	8.13650	+	8.13650i	0.378135	+	0.378135i	−0.492294	+	0.870429i	$0.663841\pi$
$464$		0			0
$465$	2.02604	+	1.77679i	0.0939553	+	0.0823966i
$466$		0			0
$467$	18.3779	+	14.1018i	0.850427	+	0.652556i	0.939153	−	0.343500i	$-0.111613\pi$
$467$	18.3779	+	14.1018i	0.850427	+	0.652556i	−0.0887253	+	0.996056i	$0.528279\pi$
$468$		0			0
$469$	−8.19763	+	0.0728249i	−0.378531	+	0.00336274i
$470$		0			0
$471$	1.66352	−	25.3804i	0.0766511	−	1.16947i
$472$		0			0
$473$	34.5606	+	11.7317i	1.58910	+	0.539426i
$474$		0			0
$475$	85.9103			3.94183
$476$		0			0
$477$	−17.5546			−0.803769
$478$		0			0
$479$	−35.0439	−	11.8958i	−1.60120	−	0.543533i	−0.628940	−	0.777454i	$-0.716511\pi$
$479$	−35.0439	−	11.8958i	−1.60120	−	0.543533i	−0.972256	+	0.233921i	$0.924844\pi$
$480$		0			0
$481$	−0.263191	+	4.01552i	−0.0120005	+	0.183092i
$482$		0			0
$483$	−4.85578	−	8.24052i	−0.220945	−	0.374956i
$484$		0			0
$485$	−24.9488	−	19.1439i	−1.13287	−	0.869278i
$486$		0			0
$487$	28.7213	+	25.1879i	1.30149	+	1.14137i	0.980976	+	0.194131i	$0.0621885\pi$
$487$	28.7213	+	25.1879i	1.30149	+	1.14137i	0.320513	+	0.947244i	$0.396145\pi$
$488$		0			0
$489$	15.6809	+	15.6809i	0.709115	+	0.709115i
$490$		0			0
$491$	−5.76131	+	13.9090i	−0.260004	+	0.627706i	−0.998938	−	0.0460721i	$-0.985330\pi$
$491$	−5.76131	+	13.9090i	−0.260004	+	0.627706i	0.738934	+	0.673778i	$0.235330\pi$
$492$		0			0
$493$	−9.85391	+	3.04872i	−0.443798	+	0.137307i
$494$		0			0
$495$	34.3347	−	4.52026i	1.54323	−	0.203170i
$496$		0			0
$497$	−3.58120	+	3.19735i	−0.160639	+	0.143421i
$498$		0			0
$499$	6.37513	+	18.7805i	0.285390	+	0.840731i	0.991205	+	0.132335i	$0.0422476\pi$
$499$	6.37513	+	18.7805i	0.285390	+	0.840731i	−0.705815	+	0.708396i	$0.749419\pi$
$500$		0			0
$501$	35.4914	+	4.67252i	1.58564	+	0.208753i
$502$		0			0
$503$	11.9025	+	17.8134i	0.530706	+	0.794258i	0.995853	−	0.0909754i	$-0.0289985\pi$
$503$	11.9025	+	17.8134i	0.530706	+	0.794258i	−0.465147	+	0.885234i	$0.653998\pi$
$504$		0			0
$505$	−25.8842	−	17.2953i	−1.15183	−	0.769630i
$506$		0			0
$507$	−9.98374	+	29.4112i	−0.443394	+	1.30620i
$508$		0			0
$509$	−15.2838	−	26.4723i	−0.677441	−	1.17336i	−0.975749	−	0.218893i	$-0.929755\pi$
$509$	−15.2838	−	26.4723i	−0.677441	−	1.17336i	0.298308	−	0.954470i	$-0.403578\pi$
$510$		0			0
$511$	12.3738	−	18.8796i	0.547383	−	0.835184i
$512$		0			0
$513$	−0.919568	−	1.04857i	−0.0405999	−	0.0462953i
$514$		0			0
$515$	−21.0577	−	42.7007i	−0.927912	−	1.88162i
$516$		0			0
$517$	−3.90913	+	2.61200i	−0.171923	+	0.114876i
$518$		0			0
$519$	−24.6803	+	10.2229i	−1.08335	+	0.448736i
$520$		0			0
$521$	−5.62138	+	6.40996i	−0.246277	+	0.280825i	−0.861750	−	0.507332i	$-0.830632\pi$
$521$	−5.62138	+	6.40996i	−0.246277	+	0.280825i	0.615473	+	0.788158i	$0.288965\pi$
$522$		0			0
$523$	3.40395	−	12.7037i	0.148844	−	0.555494i	−0.850710	−	0.525636i	$-0.823828\pi$
$523$	3.40395	−	12.7037i	0.148844	−	0.555494i	0.999554	−	0.0298588i	$-0.00950577\pi$
$524$		0			0
$525$	76.6795	−	5.71036i	3.34657	−	0.249221i
$526$		0			0
$527$	−0.591002	−	0.938799i	−0.0257445	−	0.0408947i
$528$		0			0
$529$	16.4958	−	12.6577i	0.717208	−	0.550333i
$530$		0			0
$531$	6.57107	−	6.57107i	0.285160	−	0.285160i
$532$		0			0
$533$	2.15511	+	0.428679i	0.0933484	+	0.0185681i
$534$		0			0
$535$	−8.88624	+	67.4977i	−0.384186	+	2.91818i
$536$		0			0
$537$	7.94774	−	16.1164i	0.342970	−	0.695475i
$538$		0			0
$539$	−18.9778	+	6.82043i	−0.817431	+	0.293777i
$540$		0			0
$541$	5.00566	−	4.38985i	0.215210	−	0.188734i	−0.544953	−	0.838467i	$-0.683452\pi$
$541$	5.00566	−	4.38985i	0.215210	−	0.188734i	0.760163	+	0.649733i	$0.225119\pi$
$542$		0			0
$543$	−36.9029	−	21.3059i	−1.58366	−	0.914324i
$544$		0			0
$545$			75.8634i			3.24963i
$546$		0			0
$547$	−4.25690	+	0.846750i	−0.182012	+	0.0362044i	−0.285255	−	0.958452i	$-0.592078\pi$
$547$	−4.25690	+	0.846750i	−0.182012	+	0.0362044i	0.103243	+	0.994656i	$0.467078\pi$
$548$		0			0
$549$	−13.7248	+	6.76833i	−0.585761	+	0.288865i
$550$		0			0
$551$	−16.1381	−	7.95841i	−0.687504	−	0.339040i
$552$		0			0
$553$	24.2568	−	28.1604i	1.03151	−	1.19750i
$554$		0			0
$555$	−78.7357	+	26.7272i	−3.34214	+	1.13450i
$556$		0			0
$557$	−6.53806	−	24.4004i	−0.277026	−	1.03388i	−0.954471	−	0.298303i	$-0.903579\pi$
$557$	−6.53806	−	24.4004i	−0.277026	−	1.03388i	0.677445	−	0.735574i	$-0.263087\pi$
$558$		0			0
$559$	5.67356	+	2.35006i	0.239966	+	0.0993971i
$560$		0			0
$561$	−28.5412	−	4.55028i	−1.20501	−	0.192113i
$562$		0			0
$563$	−1.58803	−	2.06956i	−0.0669276	−	0.0872217i	0.758690	−	0.651452i	$-0.225840\pi$
$563$	−1.58803	−	2.06956i	−0.0669276	−	0.0872217i	−0.825618	+	0.564230i	$0.809173\pi$
$564$		0			0
$565$	−65.2973	−	17.4964i	−2.74708	−	0.736078i
$566$		0			0
$567$	−17.4256	−	17.1187i	−0.731807	−	0.718919i
$568$		0			0
$569$	5.22809	−	6.81338i	0.219173	−	0.285632i	−0.670807	−	0.741632i	$-0.734052\pi$
$569$	5.22809	−	6.81338i	0.219173	−	0.285632i	0.889979	+	0.456001i	$0.150719\pi$
$570$		0			0
$571$	−1.85916	−	28.3653i	−0.0778033	−	1.18705i	−0.841056	−	0.540949i	$-0.818065\pi$
$571$	−1.85916	−	28.3653i	−0.0778033	−	1.18705i	0.763252	−	0.646101i	$-0.223601\pi$
$572$		0			0
$573$	−3.28297	+	4.91331i	−0.137148	+	0.205257i
$574$		0			0
$575$	−3.46217	−	17.4055i	−0.144382	−	0.725859i
$576$		0			0
$577$	12.3270	−	21.3509i	0.513178	−	0.888851i	−0.486705	−	0.873566i	$-0.661801\pi$
$577$	12.3270	−	21.3509i	0.513178	−	0.888851i	0.999883	−	0.0152844i	$-0.00486535\pi$
$578$		0			0
$579$	31.6059	−	18.2477i	1.31350	−	0.758347i
$580$		0			0
$581$	−9.63652	+	1.35586i	−0.399790	+	0.0562507i
$582$		0			0
$583$	17.2805	+	1.13262i	0.715685	+	0.0469085i
$584$		0			0
$585$	5.81448	−	0.381101i	0.240399	−	0.0157566i
$586$		0			0
$587$	1.25952	+	3.04075i	0.0519860	+	0.125505i	0.947739	−	0.319047i	$-0.103363\pi$
$587$	1.25952	+	3.04075i	0.0519860	+	0.125505i	−0.895753	+	0.444552i	$0.853363\pi$
$588$		0			0
$589$	0.377538	−	1.89801i	0.0155562	−	0.0782061i
$590$		0			0
$591$	21.5094	−	5.76343i	0.884779	−	0.237076i
$592$		0			0
$593$	−2.54909	−	19.3623i	−0.104679	−	0.795113i	−0.960586	−	0.277984i	$-0.910334\pi$
$593$	−2.54909	−	19.3623i	−0.104679	−	0.795113i	0.855907	−	0.517130i	$-0.172999\pi$
$594$		0			0
$595$	−43.8733	−	9.56544i	−1.79863	−	0.392145i
$596$		0			0
$597$	7.61824	+	57.8663i	0.311794	+	2.36831i
$598$		0			0
$599$	−14.2294	+	3.81276i	−0.581398	+	0.155785i	−0.537519	−	0.843252i	$-0.680638\pi$
$599$	−14.2294	+	3.81276i	−0.581398	+	0.155785i	−0.0438789	+	0.999037i	$0.513972\pi$
$600$		0			0
$601$	−2.07299	+	10.4216i	−0.0845591	+	0.425107i	0.915197	+	0.403008i	$0.132035\pi$
$601$	−2.07299	+	10.4216i	−0.0845591	+	0.425107i	−0.999756	+	0.0220998i	$0.992965\pi$
$602$		0			0
$603$	−3.46278	−	8.35989i	−0.141015	−	0.340441i
$604$		0			0
$605$	11.0925	−	0.727040i	0.450974	−	0.0295584i
$606$		0			0
$607$	−1.06586	−	0.0698603i	−0.0432620	−	0.00283554i	0.0437568	−	0.999042i	$-0.486067\pi$
$607$	−1.06586	−	0.0698603i	−0.0432620	−	0.00283554i	−0.0870188	+	0.996207i	$0.527734\pi$
$608$		0			0
$609$	−14.9331	−	6.03063i	−0.605119	−	0.244373i
$610$		0			0
$611$	−0.685080	+	0.395531i	−0.0277154	+	0.0160015i
$612$		0			0
$613$	−16.0574	+	27.8122i	−0.648552	+	1.12332i	0.334917	+	0.942247i	$0.391292\pi$
$613$	−16.0574	+	27.8122i	−0.648552	+	1.12332i	−0.983469	+	0.181077i	$0.942042\pi$
$614$		0			0
$615$	8.85755	+	44.5299i	0.357171	+	1.79562i
$616$		0			0
$617$	22.3043	−	33.3807i	0.897937	−	1.34386i	−0.0407792	−	0.999168i	$-0.512984\pi$
$617$	22.3043	−	33.3807i	0.897937	−	1.34386i	0.938717	−	0.344690i	$-0.112016\pi$
$618$		0			0
$619$	1.00262	+	15.2970i	0.0402987	+	0.614839i	0.969473	+	0.245198i	$0.0788528\pi$
$619$	1.00262	+	15.2970i	0.0402987	+	0.614839i	−0.929174	+	0.369642i	$0.879481\pi$
$620$		0			0
$621$	−0.175382	+	0.228562i	−0.00703784	+	0.00917189i
$622$		0			0
$623$	18.4150	−	5.11003i	0.737780	−	0.204729i
$624$		0			0
$625$	55.9697	+	14.9970i	2.23879	+	0.599881i
$626$		0			0
$627$	−30.6924	−	39.9991i	−1.22574	−	1.59741i
$628$		0			0
$629$	34.2040	−	1.30898i	1.36380	−	0.0521926i
$630$		0			0
$631$	−11.3222	−	4.68980i	−0.450729	−	0.186698i	0.145759	−	0.989320i	$-0.453438\pi$
$631$	−11.3222	−	4.68980i	−0.450729	−	0.186698i	−0.596488	+	0.802622i	$0.703438\pi$
$632$		0			0
$633$	−0.578301	−	2.15825i	−0.0229854	−	0.0857827i
$634$		0			0
$635$	−34.9434	+	11.8617i	−1.38669	+	0.470717i
$636$		0			0
$637$	−3.26139	+	0.936295i	−0.129221	+	0.0370974i
$638$		0			0
$639$	−4.75256	−	2.34370i	−0.188008	−	0.0927154i
$640$		0			0
$641$	−31.4757	+	15.5221i	−1.24321	+	0.613085i	−0.940434	−	0.339975i	$-0.889581\pi$
$641$	−31.4757	+	15.5221i	−1.24321	+	0.613085i	−0.302779	+	0.953061i	$0.597915\pi$
$642$		0			0
$643$	6.13749	−	1.22082i	0.242039	−	0.0481445i	−0.0725800	−	0.997363i	$-0.523123\pi$
$643$	6.13749	−	1.22082i	0.242039	−	0.0481445i	0.314619	+	0.949218i	$0.398123\pi$
$644$		0			0
$645$			126.888i			4.99622i
$646$		0			0
$647$	−18.6242	−	10.7527i	−0.732193	−	0.422732i	0.0870311	−	0.996206i	$-0.472262\pi$
$647$	−18.6242	−	10.7527i	−0.732193	−	0.422732i	−0.819224	+	0.573474i	$0.805595\pi$
$648$		0			0
$649$	−6.89244	+	6.04451i	−0.270552	+	0.237268i
$650$		0			0
$651$	0.210814	−	1.71917i	0.00826245	−	0.0673796i
$652$		0			0
$653$	0.716480	−	1.45288i	0.0280380	−	0.0568555i	−0.882403	−	0.470494i	$-0.844076\pi$
$653$	0.716480	−	1.45288i	0.0280380	−	0.0568555i	0.910441	+	0.413639i	$0.135742\pi$
$654$		0			0
$655$	−0.775236	+	5.88850i	−0.0302910	+	0.230083i
$656$		0			0
$657$	24.4369	+	4.86081i	0.953375	+	0.189638i
$658$		0			0
$659$	−14.2102	+	14.2102i	−0.553551	+	0.553551i	−0.927464	−	0.373913i	$-0.878016\pi$
$659$	−14.2102	+	14.2102i	−0.553551	+	0.553551i	0.373913	+	0.927464i	$0.378016\pi$
$660$		0			0
$661$	7.58143	−	5.81743i	0.294883	−	0.226272i	−0.450714	−	0.892668i	$-0.648831\pi$
$661$	7.58143	−	5.81743i	0.294883	−	0.226272i	0.745598	+	0.666396i	$0.232164\pi$
$662$		0			0
$663$	−4.74193	−	1.07807i	−0.184161	−	0.0418687i
$664$		0			0
$665$	−44.0965	−	64.7425i	−1.70999	−	2.51061i
$666$		0			0
$667$	−0.962019	+	3.59031i	−0.0372495	+	0.139017i
$668$		0			0
$669$	17.5099	−	19.9662i	0.676971	−	0.771938i
$670$		0			0
$671$	13.9472	−	5.77713i	0.538427	−	0.223024i
$672$		0			0
$673$	−34.8769	+	23.3040i	−1.34440	+	0.898303i	−0.999191	−	0.0402213i	$-0.987194\pi$
$673$	−34.8769	+	23.3040i	−1.34440	+	0.898303i	−0.345214	+	0.938524i	$0.612194\pi$
$674$		0			0
$675$	−1.02435	−	2.07718i	−0.0394274	−	0.0799508i
$676$		0			0
$677$	−6.89454	−	7.86172i	−0.264979	−	0.302150i	0.604016	−	0.796973i	$-0.293566\pi$
$677$	−6.89454	−	7.86172i	−0.264979	−	0.302150i	−0.868994	+	0.494822i	$0.835233\pi$
$678$		0			0
$679$	−1.14274	+	20.1802i	−0.0438543	+	0.774444i
$680$		0			0
$681$	20.1395	+	34.8827i	0.771749	+	1.33671i
$682$		0			0
$683$	−6.53916	+	19.2637i	−0.250214	+	0.737106i	0.747157	+	0.664647i	$0.231418\pi$
$683$	−6.53916	+	19.2637i	−0.250214	+	0.737106i	−0.997371	+	0.0724593i	$0.976915\pi$
$684$		0			0
$685$	−48.6339	−	32.4962i	−1.85821	−	1.24161i
$686$		0			0
$687$	14.6411	+	21.9120i	0.558593	+	0.835994i
$688$		0			0
$689$	2.88890	+	0.380331i	0.110058	+	0.0144894i
$690$		0			0
$691$	−9.89034	−	29.1360i	−0.376246	−	1.10839i	−0.955943	−	0.293553i	$-0.905162\pi$
$691$	−9.89034	−	29.1360i	−0.376246	−	1.10839i	0.579696	−	0.814833i	$-0.303171\pi$
$692$		0			0
$693$	−14.8244	−	16.6041i	−0.563131	−	0.630736i
$694$		0			0
$695$	−73.5615	+	9.68455i	−2.79035	+	0.367356i
$696$		0			0
$697$	1.72916	−	18.6103i	0.0654967	−	0.704914i
$698$		0			0
$699$	−14.4652	+	34.9222i	−0.547125	+	1.32088i
$700$		0			0
$701$	−14.1798	−	14.1798i	−0.535562	−	0.535562i	0.386660	−	0.922222i	$-0.373629\pi$
$701$	−14.1798	−	14.1798i	−0.535562	−	0.535562i	−0.922222	+	0.386660i	$0.873629\pi$
$702$		0			0
$703$	44.8933	+	39.3703i	1.69318	+	1.48488i
$704$		0			0
$705$	−12.9676	−	9.95037i	−0.488387	−	0.374753i
$706$		0			0
$707$	0.177746	+	20.0082i	0.00668483	+	0.752488i
$708$		0			0
$709$	−1.41432	+	21.5784i	−0.0531160	+	0.810393i	0.885329	+	0.464965i	$0.153933\pi$
$709$	−1.41432	+	21.5784i	−0.0531160	+	0.810393i	−0.938445	+	0.345428i	$0.887734\pi$
$710$		0			0
$711$	38.8470	+	13.1868i	1.45688	+	0.494543i
$712$		0			0
$713$	−0.399753			−0.0149709
$714$		0			0
$715$	−5.74829			−0.214974
$716$		0			0
$717$	−38.2009	−	12.9675i	−1.42664	−	0.484278i
$718$		0			0
$719$	−2.68920	+	41.0292i	−0.100290	+	1.53013i	0.590477	+	0.807054i	$0.298939\pi$
$719$	−2.68920	+	41.0292i	−0.100290	+	1.53013i	−0.690768	+	0.723077i	$0.742727\pi$
$720$		0			0
$721$	−15.0647	+	26.6365i	−0.561039	+	0.991996i
$722$		0			0
$723$	−9.83584	−	7.54730i	−0.365799	−	0.280687i
$724$		0			0
$725$	−22.4657	−	19.7019i	−0.834354	−	0.731709i
$726$		0			0
$727$	26.3704	+	26.3704i	0.978026	+	0.978026i	0.999764	−	0.0217380i	$-0.00691997\pi$
$727$	26.3704	+	26.3704i	0.978026	+	0.978026i	−0.0217380	+	0.999764i	$0.506920\pi$
$728$		0			0
$729$	9.77642	−	23.6024i	0.362089	−	0.874161i
$730$		0			0
$731$	14.8866	−	50.0689i	0.550600	−	1.85187i
$732$		0			0
$733$	−19.4305	+	2.55807i	−0.717680	+	0.0944844i	−0.480517	−	0.876985i	$-0.659551\pi$
$733$	−19.4305	+	2.55807i	−0.717680	+	0.0944844i	−0.237163	+	0.971470i	$0.576218\pi$
$734$		0			0
$735$	−43.6619	−	54.8552i	−1.61049	−	2.02336i
$736$		0			0
$737$	2.86933	+	8.45278i	0.105693	+	0.311362i
$738$		0			0
$739$	27.0646	+	3.56312i	0.995587	+	0.131071i	0.610674	−	0.791882i	$-0.290898\pi$
$739$	27.0646	+	3.56312i	0.995587	+	0.131071i	0.384912	+	0.922953i	$0.374232\pi$
$740$		0			0
$741$	−4.71302	−	7.05353i	−0.173137	−	0.259118i
$742$		0			0
$743$	31.8164	+	21.2590i	1.16723	+	0.779919i	0.979330	−	0.202269i	$-0.0648316\pi$
$743$	31.8164	+	21.2590i	1.16723	+	0.779919i	0.187901	+	0.982188i	$0.439832\pi$
$744$		0			0
$745$	−27.6231	+	81.3749i	−1.01203	+	2.98135i
$746$		0			0
$747$	−5.37065	−	9.30223i	−0.196502	−	0.340351i
$748$		0			0
$749$	39.0719	−	19.7016i	1.42766	−	0.719879i
$750$		0			0
$751$	9.12375	+	10.4036i	0.332930	+	0.379634i	0.893949	−	0.448169i	$-0.147924\pi$
$751$	9.12375	+	10.4036i	0.332930	+	0.379634i	−0.561019	+	0.827803i	$0.689590\pi$
$752$		0			0
$753$	16.8019	+	34.0708i	0.612294	+	1.24161i
$754$		0			0
$755$	45.9398	−	30.6960i	1.67192	−	1.11714i
$756$		0			0
$757$	6.73795	−	2.79095i	0.244895	−	0.101439i	−0.256860	−	0.966449i	$-0.582688\pi$
$757$	6.73795	−	2.79095i	0.244895	−	0.101439i	0.501755	+	0.865010i	$0.332688\pi$
$758$		0			0
$759$	−6.86695	+	7.83025i	−0.249254	+	0.284220i
$760$		0			0
$761$	2.39862	−	8.95178i	0.0869500	−	0.324502i	−0.908726	−	0.417392i	$-0.862944\pi$
$761$	2.39862	−	8.95178i	0.0869500	−	0.324502i	0.995676	+	0.0928907i	$0.0296107\pi$
$762$		0			0
$763$	40.3008	−	27.4491i	1.45899	−	0.993724i
$764$		0			0
$765$	−8.34384	−	48.8564i	−0.301672	−	1.76641i
$766$		0			0
$767$	−1.22374	+	0.939013i	−0.0441869	+	0.0339058i
$768$		0			0
$769$	−2.39510	+	2.39510i	−0.0863697	+	0.0863697i	−0.748972	−	0.662602i	$-0.769452\pi$
$769$	−2.39510	+	2.39510i	−0.0863697	+	0.0863697i	0.662602	+	0.748972i	$0.269452\pi$
$770$		0			0
$771$	−17.7901	−	3.53867i	−0.640695	−	0.127442i
$772$		0			0
$773$	5.55635	−	42.2047i	0.199848	−	1.51800i	−0.537951	−	0.842976i	$-0.680802\pi$
$773$	5.55635	−	42.2047i	0.199848	−	1.51800i	0.737799	−	0.675020i	$-0.235865\pi$
$774$		0			0
$775$	1.42136	−	2.88223i	0.0510567	−	0.103533i
$776$		0			0
$777$	42.6866	+	32.1561i	1.53137	+	1.15360i
$778$		0			0
$779$	24.5135	−	21.4978i	0.878288	−	0.770238i
$780$		0			0
$781$	4.52714	+	2.61374i	0.161994	+	0.0935271i
$782$		0			0
$783$			0.485087i			0.0173356i
$784$		0			0
$785$	−42.2030	+	8.39470i	−1.50629	+	0.299620i
$786$		0			0
$787$	−12.7886	+	6.30662i	−0.455863	+	0.224807i	−0.655699	−	0.755023i	$-0.727626\pi$
$787$	−12.7886	+	6.30662i	−0.455863	+	0.224807i	0.199836	+	0.979829i	$0.435959\pi$
$788$		0			0
$789$	−36.5536	−	18.0262i	−1.30134	−	0.641751i
$790$		0			0
$791$	14.3315	+	41.0184i	0.509569	+	1.45845i
$792$		0			0
$793$	2.40529	−	0.816486i	0.0854143	−	0.0289943i
$794$		0			0
$795$	15.5826	+	58.1552i	0.552660	+	2.06255i
$796$		0			0
$797$	−10.6834	−	4.42522i	−0.378427	−	0.156749i	0.185358	−	0.982671i	$-0.440655\pi$
$797$	−10.6834	−	4.42522i	−0.378427	−	0.156749i	−0.563785	+	0.825922i	$0.690655\pi$
$798$		0			0
$799$	3.94950	+	5.44768i	0.139723	+	0.192725i
$800$		0			0
$801$	12.8412	+	16.7350i	0.453722	+	0.591302i
$802$		0			0
$803$	−23.7418	−	6.36159i	−0.837829	−	0.224495i
$804$		0			0
$805$	−11.3398	+	11.5431i	−0.399676	+	0.406841i
$806$		0			0
$807$	−7.72941	+	10.0732i	−0.272088	+	0.354592i
$808$		0			0
$809$	0.810108	+	12.3599i	0.0284819	+	0.434549i	0.988158	+	0.153441i	$0.0490354\pi$
$809$	0.810108	+	12.3599i	0.0284819	+	0.434549i	−0.959676	+	0.281109i	$0.909298\pi$
$810$		0			0
$811$	5.16015	−	7.72271i	0.181197	−	0.271181i	−0.729741	−	0.683724i	$-0.760359\pi$
$811$	5.16015	−	7.72271i	0.181197	−	0.271181i	0.910938	+	0.412543i	$0.135359\pi$
$812$		0			0
$813$	−7.64831	−	38.4507i	−0.268238	−	1.34852i
$814$		0			0
$815$	18.7584	−	32.4905i	0.657077	−	1.13809i
$816$		0			0
$817$	78.9141	−	45.5611i	2.76085	−	1.59398i
$818$		0			0
$819$	−2.30626	−	2.95093i	−0.0805874	−	0.103114i
$820$		0			0
$821$	−14.4011	−	0.943898i	−0.502602	−	0.0329423i	−0.188006	−	0.982168i	$-0.560202\pi$
$821$	−14.4011	−	0.943898i	−0.502602	−	0.0329423i	−0.314596	+	0.949226i	$0.601869\pi$
$822$		0			0
$823$	−5.61896	+	0.368286i	−0.195864	+	0.0128376i	−0.163020	−	0.986623i	$-0.552123\pi$
$823$	−5.61896	+	0.368286i	−0.195864	+	0.0128376i	−0.0328449	+	0.999460i	$0.510457\pi$
$824$		0			0
$825$	−32.0403	−	77.3521i	−1.11550	−	2.69305i
$826$		0			0
$827$	−7.68712	+	38.6458i	−0.267307	+	1.34385i	0.580811	+	0.814039i	$0.302736\pi$
$827$	−7.68712	+	38.6458i	−0.267307	+	1.34385i	−0.848118	+	0.529807i	$0.822264\pi$
$828$		0			0
$829$	2.56654	−	0.687702i	0.0891396	−	0.0238849i	−0.213974	−	0.976839i	$-0.568641\pi$
$829$	2.56654	−	0.687702i	0.0891396	−	0.0238849i	0.303113	+	0.952955i	$0.401974\pi$
$830$		0			0
$831$	−6.24226	−	47.4146i	−0.216541	−	1.64480i
$832$		0			0
$833$	10.7929	+	26.7678i	0.373953	+	0.927448i
$834$		0			0
$835$	−7.90480	−	60.0429i	−0.273557	−	2.07787i
$836$		0			0
$837$	−0.0503927	+	0.0135027i	−0.00174183	+	0.000466721i
$838$		0			0
$839$	−4.12899	+	20.7578i	−0.142549	+	0.716640i	0.841713	+	0.539925i	$0.181547\pi$
$839$	−4.12899	+	20.7578i	−0.142549	+	0.716640i	−0.984262	+	0.176716i	$0.943453\pi$
$840$		0			0
$841$	−8.70280	−	21.0104i	−0.300097	−	0.724497i
$842$		0			0
$843$	49.6615	−	3.25499i	1.71043	−	0.112108i
$844$		0			0
$845$	52.4327	+	3.43662i	1.80374	+	0.118223i
$846$		0			0
$847$	−4.39973	−	5.62958i	−0.151177	−	0.193435i
$848$		0			0
$849$	−47.2534	+	27.2818i	−1.62173	+	0.936308i
$850$		0			0
$851$	6.16727	−	10.6820i	0.211411	−	0.366175i
$852$		0			0
$853$	−2.28941	−	11.5097i	−0.0783880	−	0.394083i	−0.999982	−	0.00592890i	$-0.998113\pi$
$853$	−2.28941	−	11.5097i	−0.0783880	−	0.394083i	0.921594	−	0.388154i	$-0.126887\pi$
$854$		0			0
$855$	48.0358	−	71.8906i	1.64279	−	2.45861i
$856$		0			0
$857$	0.188572	+	2.87705i	0.00644150	+	0.0982783i	0.999869	−	0.0161846i	$-0.00515196\pi$
$857$	0.188572	+	2.87705i	0.00644150	+	0.0982783i	−0.993428	+	0.114463i	$0.963485\pi$
$858$		0			0
$859$	0.736450	−	0.959760i	0.0251273	−	0.0327466i	−0.780621	−	0.625005i	$-0.785097\pi$
$859$	0.736450	−	0.959760i	0.0251273	−	0.0327466i	0.805748	+	0.592258i	$0.201764\pi$
$860$		0			0
$861$	20.4507	−	20.8173i	0.696958	−	0.709452i
$862$		0			0
$863$	−17.3365	−	4.64531i	−0.590142	−	0.158128i	−0.0486238	−	0.998817i	$-0.515484\pi$
$863$	−17.3365	−	4.64531i	−0.590142	−	0.158128i	−0.541518	+	0.840689i	$0.682150\pi$
$864$		0			0
$865$	27.5120	+	35.8543i	0.935435	+	1.21908i
$866$		0			0
$867$	−4.94548	+	41.0672i	−0.167957	+	1.39471i
$868$		0			0
$869$	−37.3896	−	15.4873i	−1.26836	−	0.525370i
$870$		0			0
$871$	0.388736	+	1.45078i	0.0131718	+	0.0491579i
$872$		0			0
$873$	−21.1260	+	7.17132i	−0.715008	+	0.242712i
$874$		0			0
$875$	−24.9453	−	71.3963i	−0.843303	−	2.41363i
$876$		0			0
$877$	−14.8755	−	7.33576i	−0.502308	−	0.247711i	0.173439	−	0.984845i	$-0.444512\pi$
$877$	−14.8755	−	7.33576i	−0.502308	−	0.247711i	−0.675747	+	0.737134i	$0.736179\pi$
$878$		0			0
$879$	24.8078	−	12.2339i	0.836748	−	0.412638i
$880$		0			0
$881$	−54.3004	+	10.8010i	−1.82943	+	0.363895i	−0.985106	−	0.171945i	$-0.944995\pi$
$881$	−54.3004	+	10.8010i	−1.82943	+	0.363895i	−0.844319	+	0.535841i	$0.819995\pi$
$882$		0			0
$883$			4.02541i			0.135466i	0.997703	+	0.0677329i	$0.0215766\pi$
$883$			4.02541i			0.135466i	−0.997703	+	0.0677329i	$0.978423\pi$
$884$		0			0
$885$	−27.6017	−	15.9359i	−0.927822	−	0.535678i
$886$		0			0
$887$	−25.0943	+	22.0071i	−0.842584	+	0.738926i	−0.967400	−	0.253254i	$-0.918499\pi$
$887$	−25.0943	+	22.0071i	−0.842584	+	0.738926i	0.124816	+	0.992180i	$0.460166\pi$
$888$		0			0
$889$	18.9446	+	14.2711i	0.635381	+	0.478638i
$890$		0			0
$891$	−11.7642	+	23.8554i	−0.394114	+	0.799185i
$892$		0			0
$893$	−1.53212	+	11.6376i	−0.0512704	+	0.389437i
$894$		0			0
$895$	−29.8161	−	5.93079i	−0.996642	−	0.198244i
$896$		0			0
$897$	−1.23912	+	1.23912i	−0.0413729	+	0.0413729i
$898$		0			0
$899$	−0.533999	+	0.409752i	−0.0178098	+	0.0136660i
$900$		0			0
$901$	0.674029	−	24.7757i	0.0224552	−	0.825397i
$902$		0			0
$903$	67.4067	−	45.9110i	2.24315	−	1.52782i
$904$		0			0
$905$	−18.6580	+	69.6327i	−0.620214	+	2.31467i
$906$		0			0
$907$	−1.16689	+	1.33058i	−0.0387458	+	0.0441811i	−0.770888	−	0.636971i	$-0.780187\pi$
$907$	−1.16689	+	1.33058i	−0.0387458	+	0.0441811i	0.732142	+	0.681152i	$0.238521\pi$
$908$		0			0
$909$	−20.4043	+	8.45173i	−0.676767	+	0.280326i
$910$		0			0
$911$	13.8714	−	9.26860i	0.459581	−	0.307082i	−0.304141	−	0.952627i	$-0.598370\pi$
$911$	13.8714	−	9.26860i	0.459581	−	0.307082i	0.763723	+	0.645544i	$0.223370\pi$
$912$		0			0
$913$	4.68661	+	9.50351i	0.155104	+	0.314520i
$914$		0			0
$915$	34.6054	+	39.4599i	1.14402	+	1.30450i
$916$		0			0
$917$	3.40864	−	1.71876i	0.112563	−	0.0567586i
$918$		0			0
$919$	−28.1897	−	48.8260i	−0.929893	−	1.61062i	−0.783496	−	0.621397i	$-0.786565\pi$
$919$	−28.1897	−	48.8260i	−0.929893	−	1.61062i	−0.146398	−	0.989226i	$-0.546768\pi$
$920$		0			0
$921$	−10.4587	+	30.8104i	−0.344627	+	1.01524i
$922$		0			0
$923$	0.731335	+	0.488662i	0.0240722	+	0.0160845i
$924$		0			0
$925$	55.0894	+	82.4472i	1.81133	+	2.71085i
$926$		0			0
$927$	−33.4881	−	4.40879i	−1.09989	−	0.144804i
$928$		0			0
$929$	−3.69081	−	10.8728i	−0.121091	−	0.356724i	0.869435	−	0.494048i	$-0.164483\pi$
$929$	−3.69081	−	10.8728i	−0.121091	−	0.356724i	−0.990526	+	0.137324i	$0.956150\pi$
$930$		0			0
$931$	−18.4380	+	46.8506i	−0.604281	+	1.53547i
$932$		0			0
$933$	57.7096	−	7.59762i	1.88933	−	0.248735i
$934$		0			0
$935$	5.06134	+	48.6319i	0.165524	+	1.59043i
$936$		0			0
$937$	−13.0862	+	31.5928i	−0.427507	+	1.03209i	0.552569	+	0.833467i	$0.313648\pi$
$937$	−13.0862	+	31.5928i	−0.427507	+	1.03209i	−0.980075	+	0.198625i	$0.936352\pi$
$938$		0			0
$939$	6.50506	+	6.50506i	0.212285	+	0.212285i
$940$		0			0
$941$	−38.8454	−	34.0665i	−1.26632	−	1.11054i	−0.988710	−	0.149844i	$-0.952123\pi$
$941$	−38.8454	−	34.0665i	−1.26632	−	1.11054i	−0.277615	−	0.960693i	$-0.589544\pi$
$942$		0			0
$943$	−5.34336	−	4.10010i	−0.174004	−	0.133518i
$944$		0			0
$945$	−1.03959	+	1.83815i	−0.0338180	+	0.0597950i
$946$		0			0
$947$	0.420513	−	6.41579i	0.0136648	−	0.208485i	−0.985567	−	0.169288i	$-0.945853\pi$
$947$	0.420513	−	6.41579i	0.0136648	−	0.208485i	0.999231	−	0.0391973i	$-0.0124801\pi$
$948$		0			0
$949$	−3.91619	−	1.32937i	−0.127125	−	0.0431531i
$950$		0			0
$951$	7.46912			0.242203
$952$		0			0
$953$	−27.9715			−0.906085			−0.453042	−	0.891489i	$-0.649661\pi$
$953$	−27.9715			−0.906085			−0.453042	+	0.891489i	$0.649661\pi$
$954$		0			0
$955$	9.46640	+	3.21341i	0.306326	+	0.103984i
$956$		0			0
$957$	−1.14691	+	17.4985i	−0.0370744	+	0.565647i
$958$		0			0
$959$	0.333968	+	37.5936i	0.0107844	+	1.21396i
$960$		0			0
$961$	24.5365	+	18.8275i	0.791501	+	0.607340i
$962$		0			0
$963$	36.3131	+	31.8457i	1.17017	+	1.02621i
$964$		0			0
$965$	−43.6578	−	43.6578i	−1.40539	−	1.40539i
$966$		0			0
$967$	5.55575	−	13.4128i	0.178661	−	0.431326i	−0.809025	−	0.587774i	$-0.800004\pi$
$967$	5.55575	−	13.4128i	0.178661	−	0.431326i	0.987686	+	0.156448i	$0.0500044\pi$
$968$		0			0
$969$	−55.5248	+	46.0839i	−1.78371	+	1.48043i
$970$		0			0
$971$	−7.41250	+	0.975874i	−0.237878	+	0.0313173i	−0.248523	−	0.968626i	$-0.579945\pi$
$971$	−7.41250	+	0.975874i	−0.237878	+	0.0313173i	0.0106444	+	0.999943i	$0.496612\pi$
$972$		0			0
$973$	31.7609	+	35.5739i	1.01821	+	1.14045i
$974$		0			0
$975$	−4.52827	−	13.3399i	−0.145021	−	0.427218i
$976$		0			0
$977$	58.5636	+	7.71004i	1.87361	+	0.246666i	0.979539	−	0.201252i	$-0.0645011\pi$
$977$	58.5636	+	7.71004i	1.87361	+	0.246666i	0.894075	+	0.447918i	$0.147834\pi$
$978$		0			0
$979$	−11.5610	−	17.3022i	−0.369490	−	0.552982i
$980$		0			0
$981$	44.7503	+	29.9012i	1.42877	+	0.954672i
$982$		0			0
$983$	14.8277	−	43.6811i	0.472931	−	1.39321i	−0.404953	−	0.914337i	$-0.632712\pi$
$983$	14.8277	−	43.6811i	0.472931	−	1.39321i	0.877884	−	0.478873i	$-0.158954\pi$
$984$		0			0
$985$	−18.8362	−	32.6253i	−0.600172	−	1.03953i
$986$		0			0
$987$	−0.593960	+	10.4890i	−0.0189059	+	0.333869i
$988$		0			0
$989$	−12.4109	−	14.1519i	−0.394644	−	0.450006i
$990$		0			0
$991$	−11.1140	−	22.5370i	−0.353049	−	0.715912i	0.645819	−	0.763491i	$-0.276516\pi$
$991$	−11.1140	−	22.5370i	−0.353049	−	0.715912i	−0.998867	+	0.0475788i	$0.984849\pi$
$992$		0			0
$993$	46.6129	−	31.1457i	1.47921	−	0.988380i
$994$		0			0
$995$	91.2245	−	37.7864i	2.89201	−	1.19791i
$996$		0			0
$997$	−6.75404	+	7.70150i	−0.213902	+	0.243909i	−0.848834	−	0.528659i	$-0.822695\pi$
$997$	−6.75404	+	7.70150i	−0.213902	+	0.243909i	0.634932	+	0.772568i	$0.281028\pi$
$998$		0			0
$999$	0.416631	−	1.55489i	0.0131816	−	0.0491944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.2	yes	192
7.5	odd	6	inner	476.2.bl.a.397.2	yes	192
17.3	odd	16	inner	476.2.bl.a.241.2	yes	192
119.54	even	48	inner	476.2.bl.a.173.2	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.2	✓	192	119.54	even	48	inner
476.2.bl.a.241.2	yes	192	17.3	odd	16	inner
476.2.bl.a.397.2	yes	192	7.5	odd	6	inner
476.2.bl.a.465.2	yes	192	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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30404 - 0.782116i) q^{3} +(-0.269222 + 4.10753i) q^{5} +(2.27945 - 1.34318i) q^{7} +(2.31684 + 1.77777i) q^{9} +O(q^{10})\)	\(q+(-2.30404 - 0.782116i) q^{3} +(-0.269222 + 4.10753i) q^{5} +(2.27945 - 1.34318i) q^{7} +(2.31684 + 1.77777i) q^{9} +(-2.16596 - 1.89950i) q^{11} +(-0.342758 - 0.342758i) q^{13} +(3.83286 - 9.25335i) q^{15} +(-2.59802 + 3.20161i) q^{17} +(-7.13106 + 0.938822i) q^{19} +(-6.30246 + 1.31194i) q^{21} +(0.477587 + 1.40692i) q^{23} +(-11.8421 - 1.55904i) q^{25} +(0.107727 + 0.161225i) q^{27} +(2.08008 + 1.38987i) q^{29} +(-0.0864844 + 0.254775i) q^{31} +(3.50483 + 6.07055i) q^{33} +(4.90346 + 9.72450i) q^{35} +(-5.47373 - 6.24159i) q^{37} +(0.521651 + 1.05780i) q^{39} +(-3.76913 + 2.51845i) q^{41} +(-11.7045 + 4.84817i) q^{43} +(-7.92599 + 9.03785i) q^{45} +(0.422381 - 1.57635i) q^{47} +(3.39175 - 6.12340i) q^{49} +(8.48997 - 5.34469i) q^{51} +(-4.76901 + 3.65939i) q^{53} +(8.38536 - 8.38536i) q^{55} +(17.1645 + 3.41424i) q^{57} +(0.415355 - 3.15494i) q^{59} +(-2.31768 + 4.69979i) q^{61} +(7.66897 + 0.940410i) q^{63} +(1.50016 - 1.31561i) q^{65} +(-2.68341 - 1.54927i) q^{67} -3.61514i q^{69} +(-1.77968 + 0.354000i) q^{71} +(7.65200 - 3.77355i) q^{73} +(26.0653 + 12.8540i) q^{75} +(-7.48855 - 1.42053i) q^{77} +(13.3024 - 4.51554i) q^{79} +(-2.38960 - 8.91813i) q^{81} +(-3.39816 - 1.40756i) q^{83} +(-12.4513 - 11.5334i) q^{85} +(-3.70556 - 4.82918i) q^{87} +(6.97709 + 1.86950i) q^{89} +(-1.24168 - 0.320913i) q^{91} +(0.398527 - 0.519371i) q^{93} +(-1.93640 - 29.5438i) q^{95} +(-4.24434 + 6.35210i) q^{97} +(-1.64131 - 8.25141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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