LMFDB - Embedded newform 476.3.x.a.321.12

Error: no document with id 208683215 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [476,3,Mod(321,476)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("476.321"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(476, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 4, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			321.12
Character	$\chi$	$=$	476.321
Dual form			476.3.x.a.433.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0501663 + 0.0207796i) q^{3} +(0.962011 + 2.32250i) q^{5} +(4.78783 + 5.10654i) q^{7} +(-6.36188 + 6.36188i) q^{9} +(-1.18102 + 2.85123i) q^{11} -8.74049 q^{13} +(-0.0965212 - 0.0965212i) q^{15} +(-13.3103 - 10.5752i) q^{17} +(-7.21117 + 7.21117i) q^{19} +(-0.346299 - 0.156687i) q^{21} +(-0.658489 + 1.58973i) q^{23} +(13.2091 - 13.2091i) q^{25} +(0.373971 - 0.902846i) q^{27} +(-7.14167 + 2.95818i) q^{29} +(-37.2629 + 15.4348i) q^{31} -0.167577i q^{33} +(-7.25399 + 16.0323i) q^{35} +(13.4899 + 32.5675i) q^{37} +(0.438478 - 0.181624i) q^{39} +(-12.9801 + 31.3368i) q^{41} +(1.34176 - 1.34176i) q^{43} +(-20.8957 - 8.65526i) q^{45} -25.8144 q^{47} +(-3.15346 + 48.8984i) q^{49} +(0.887479 + 0.253938i) q^{51} +(36.4773 + 36.4773i) q^{53} -7.75813 q^{55} +(0.211913 - 0.511603i) q^{57} +(-52.4817 - 52.4817i) q^{59} +(-15.2031 + 36.7034i) q^{61} +(-62.9467 - 2.02761i) q^{63} +(-8.40845 - 20.2998i) q^{65} -22.8206 q^{67} -0.0934342i q^{69} +(34.7898 + 83.9900i) q^{71} +(29.5591 + 71.3619i) q^{73} +(-0.388174 + 0.937134i) q^{75} +(-20.2144 + 7.62027i) q^{77} +(3.74921 - 9.05140i) q^{79} -80.9204i q^{81} +(91.8612 - 91.8612i) q^{83} +(11.7563 - 41.0867i) q^{85} +(0.296802 - 0.296802i) q^{87} +62.5431 q^{89} +(-41.8479 - 44.6336i) q^{91} +(1.54861 - 1.54861i) q^{93} +(-23.6852 - 9.81072i) q^{95} +(32.9612 + 79.5755i) q^{97} +(-10.6257 - 25.6526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{11} - 16 q^{15} + 72 q^{23} + 72 q^{25} + 32 q^{35} - 256 q^{37} - 88 q^{39} - 32 q^{43} - 20 q^{49} - 120 q^{51} - 80 q^{53} + 492 q^{63} - 104 q^{65} - 144 q^{67} - 64 q^{71} + 84 q^{77}+ \cdots + 560 q^{99}+O(q^{100}) $ 96 * q - 40 * q^11 - 16 * q^15 + 72 * q^23 + 72 * q^25 + 32 * q^35 - 256 * q^37 - 88 * q^39 - 32 * q^43 - 20 * q^49 - 120 * q^51 - 80 * q^53 + 492 * q^63 - 104 * q^65 - 144 * q^67 - 64 * q^71 + 84 * q^77 - 256 * q^79 + 824 * q^85 - 368 * q^91 - 264 * q^93 + 104 * q^95 + 560 * q^99

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0501663	+	0.0207796i	−0.0167221	+	0.00692653i	−0.391029	−	0.920378i	$-0.627881\pi$
$3$	−0.0501663	+	0.0207796i	−0.0167221	+	0.00692653i	0.374307	+	0.927305i	$0.377881\pi$
$4$		0			0
$5$	0.962011	+	2.32250i	0.192402	+	0.464500i	0.990412	−	0.138144i	$-0.0441138\pi$
$5$	0.962011	+	2.32250i	0.192402	+	0.464500i	−0.798010	+	0.602644i	$0.794114\pi$
$6$		0			0
$7$	4.78783	+	5.10654i	0.683975	+	0.729505i
$7$	4.78783	+	5.10654i	0.683975	+	0.729505i
$8$		0			0
$9$	−6.36188	+	6.36188i	−0.706875	+	0.706875i
$10$		0			0
$11$	−1.18102	+	2.85123i	−0.107365	+	0.259203i	−0.968427	−	0.249298i	$-0.919800\pi$
$11$	−1.18102	+	2.85123i	−0.107365	+	0.259203i	0.861062	+	0.508501i	$0.169800\pi$
$12$		0			0
$13$	−8.74049			−0.672345			−0.336173	−	0.941800i	$-0.609133\pi$
$13$	−8.74049			−0.672345			−0.336173	+	0.941800i	$0.609133\pi$
$14$		0			0
$15$	−0.0965212	−	0.0965212i	−0.00643474	−	0.00643474i
$16$		0			0
$17$	−13.3103	−	10.5752i	−0.782960	−	0.622073i
$17$	−13.3103	−	10.5752i	−0.782960	−	0.622073i
$18$		0			0
$19$	−7.21117	+	7.21117i	−0.379535	+	0.379535i	−0.870934	−	0.491399i	$-0.836486\pi$
$19$	−7.21117	+	7.21117i	−0.379535	+	0.379535i	0.491399	+	0.870934i	$0.336486\pi$
$20$		0			0
$21$	−0.346299	−	0.156687i	−0.0164904	−	0.00746130i
$22$		0			0
$23$	−0.658489	+	1.58973i	−0.0286300	+	0.0691188i	−0.937548	−	0.347856i	$-0.886910\pi$
$23$	−0.658489	+	1.58973i	−0.0286300	+	0.0691188i	0.908918	+	0.416975i	$0.136910\pi$
$24$		0			0
$25$	13.2091	−	13.2091i	0.528365	−	0.528365i
$26$		0			0
$27$	0.373971	−	0.902846i	0.0138508	−	0.0334388i
$28$		0			0
$29$	−7.14167	+	2.95818i	−0.246264	+	0.102006i	−0.502402	−	0.864634i	$-0.667550\pi$
$29$	−7.14167	+	2.95818i	−0.246264	+	0.102006i	0.256137	+	0.966640i	$0.417550\pi$
$30$		0			0
$31$	−37.2629	+	15.4348i	−1.20203	+	0.497896i	−0.891654	−	0.452718i	$-0.850454\pi$
$31$	−37.2629	+	15.4348i	−1.20203	+	0.497896i	−0.310375	+	0.950614i	$0.600454\pi$
$32$		0			0
$33$		−	0.167577i		−	0.00507808i
$34$		0			0
$35$	−7.25399	+	16.0323i	−0.207257	+	0.458065i
$36$		0			0
$37$	13.4899	+	32.5675i	0.364592	+	0.880202i	0.994616	+	0.103627i	$0.0330447\pi$
$37$	13.4899	+	32.5675i	0.364592	+	0.880202i	−0.630025	+	0.776575i	$0.716955\pi$
$38$		0			0
$39$	0.438478	−	0.181624i	0.0112430	−	0.00465702i
$40$		0			0
$41$	−12.9801	+	31.3368i	−0.316589	+	0.764313i	0.682842	+	0.730567i	$0.260744\pi$
$41$	−12.9801	+	31.3368i	−0.316589	+	0.764313i	−0.999430	+	0.0337467i	$0.989256\pi$
$42$		0			0
$43$	1.34176	−	1.34176i	0.0312037	−	0.0312037i	−0.691333	−	0.722536i	$-0.742976\pi$
$43$	1.34176	−	1.34176i	0.0312037	−	0.0312037i	0.722536	+	0.691333i	$0.242976\pi$
$44$		0			0
$45$	−20.8957	−	8.65526i	−0.464348	−	0.192339i
$46$		0			0
$47$	−25.8144			−0.549243			−0.274622	−	0.961552i	$-0.588553\pi$
$47$	−25.8144			−0.549243			−0.274622	+	0.961552i	$0.588553\pi$
$48$		0			0
$49$	−3.15346	+	48.8984i	−0.0643563	+	0.997927i
$50$		0			0
$51$	0.887479	+	0.253938i	0.0174015	+	0.00497918i
$52$		0			0
$53$	36.4773	+	36.4773i	0.688251	+	0.688251i	0.961845	−	0.273594i	$-0.0882125\pi$
$53$	36.4773	+	36.4773i	0.688251	+	0.688251i	−0.273594	+	0.961845i	$0.588212\pi$
$54$		0			0
$55$	−7.75813			−0.141057
$56$		0			0
$57$	0.211913	−	0.511603i	0.00371777	−	0.00897550i
$58$		0			0
$59$	−52.4817	−	52.4817i	−0.889520	−	0.889520i	0.104957	−	0.994477i	$-0.466529\pi$
$59$	−52.4817	−	52.4817i	−0.889520	−	0.889520i	−0.994477	+	0.104957i	$0.966529\pi$
$60$		0			0
$61$	−15.2031	+	36.7034i	−0.249231	+	0.601696i	−0.998139	−	0.0609776i	$-0.980578\pi$
$61$	−15.2031	+	36.7034i	−0.249231	+	0.601696i	0.748909	+	0.662673i	$0.230578\pi$
$62$		0			0
$63$	−62.9467	−	2.02761i	−0.999154	−	0.0321843i
$64$		0			0
$65$	−8.40845	−	20.2998i	−0.129361	−	0.312304i
$66$		0			0
$67$	−22.8206			−0.340606			−0.170303	−	0.985392i	$-0.554475\pi$
$67$	−22.8206			−0.340606			−0.170303	+	0.985392i	$0.554475\pi$
$68$		0			0
$69$		−	0.0934342i		−	0.00135412i
$70$		0			0
$71$	34.7898	+	83.9900i	0.489997	+	1.18296i	0.954721	+	0.297502i	$0.0961536\pi$
$71$	34.7898	+	83.9900i	0.489997	+	1.18296i	−0.464724	+	0.885456i	$0.653846\pi$
$72$		0			0
$73$	29.5591	+	71.3619i	0.404919	+	0.977560i	0.986454	+	0.164039i	$0.0524522\pi$
$73$	29.5591	+	71.3619i	0.404919	+	0.977560i	−0.581535	+	0.813521i	$0.697548\pi$
$74$		0			0
$75$	−0.388174	+	0.937134i	−0.00517565	+	0.0124951i
$76$		0			0
$77$	−20.2144	+	7.62027i	−0.262525	+	0.0989646i
$78$		0			0
$79$	3.74921	−	9.05140i	0.0474584	−	0.114575i	−0.898373	−	0.439234i	$-0.855250\pi$
$79$	3.74921	−	9.05140i	0.0474584	−	0.114575i	0.945831	+	0.324660i	$0.105250\pi$
$80$		0			0
$81$		−	80.9204i		−	0.999017i
$82$		0			0
$83$	91.8612	−	91.8612i	1.10676	−	1.10676i	0.113188	−	0.993574i	$-0.463894\pi$
$83$	91.8612	−	91.8612i	1.10676	−	1.10676i	0.993574	−	0.113188i	$-0.0361062\pi$
$84$		0			0
$85$	11.7563	−	41.0867i	0.138310	−	0.483373i
$86$		0			0
$87$	0.296802	−	0.296802i	0.00341151	−	0.00341151i
$88$		0			0
$89$	62.5431			0.702732			0.351366	−	0.936238i	$-0.385717\pi$
$89$	62.5431			0.702732			0.351366	+	0.936238i	$0.385717\pi$
$90$		0			0
$91$	−41.8479	−	44.6336i	−0.459867	−	0.490480i
$92$		0			0
$93$	1.54861	−	1.54861i	0.0166518	−	0.0166518i
$94$		0			0
$95$	−23.6852	−	9.81072i	−0.249318	−	0.103271i
$96$		0			0
$97$	32.9612	+	79.5755i	0.339807	+	0.820366i	0.997734	+	0.0672843i	$0.0214334\pi$
$97$	32.9612	+	79.5755i	0.339807	+	0.820366i	−0.657927	+	0.753082i	$0.728567\pi$
$98$		0			0
$99$	−10.6257	−	25.6526i	−0.107330	−	0.259118i
$100$		0			0
$101$			50.4637i			0.499641i	0.968292	+	0.249820i	$0.0803715\pi$
$101$			50.4637i			0.499641i	−0.968292	+	0.249820i	$0.919628\pi$
$102$		0			0
$103$		−	32.4418i		−	0.314969i	−0.987521	−	0.157485i	$-0.949662\pi$
$103$		−	32.4418i		−	0.314969i	0.987521	−	0.157485i	$-0.0503385\pi$
$104$		0			0
$105$	0.0307625	−	0.955015i	0.000292976	−	0.00909538i
$106$		0			0
$107$	−54.7827	+	22.6918i	−0.511988	+	0.212072i	−0.623694	−	0.781669i	$-0.714369\pi$
$107$	−54.7827	+	22.6918i	−0.511988	+	0.212072i	0.111705	+	0.993741i	$0.464369\pi$
$108$		0			0
$109$	−10.8539	−	4.49584i	−0.0995773	−	0.0412463i	0.332339	−	0.943160i	$-0.392162\pi$
$109$	−10.8539	−	4.49584i	−0.0995773	−	0.0412463i	−0.431916	+	0.901914i	$0.642162\pi$
$110$		0			0
$111$	−1.35348	−	1.35348i	−0.0121935	−	0.0121935i
$112$		0			0
$113$	34.5323	−	83.3684i	0.305596	−	0.737773i	−0.694242	−	0.719742i	$-0.744260\pi$
$113$	34.5323	−	83.3684i	0.305596	−	0.737773i	0.999837	−	0.0180313i	$-0.00573984\pi$
$114$		0			0
$115$	−4.32563			−0.0376142
$116$		0			0
$117$	55.6059	−	55.6059i	0.475264	−	0.475264i
$118$		0			0
$119$	−9.72461	−	118.602i	−0.0817194	−	0.996655i
$120$		0			0
$121$	78.8252	+	78.8252i	0.651448	+	0.651448i
$122$		0			0
$123$		−	1.84178i		−	0.0149738i
$124$		0			0
$125$	101.448	+	42.0211i	0.811584	+	0.336169i
$126$		0			0
$127$	−19.4440	+	19.4440i	−0.153102	+	0.153102i	−0.779502	−	0.626400i	$-0.784528\pi$
$127$	−19.4440	+	19.4440i	−0.153102	+	0.153102i	0.626400	+	0.779502i	$0.284528\pi$
$128$		0			0
$129$	−0.0394299	+	0.0951923i	−0.000305658	+	0.000737925i
$130$		0			0
$131$	−0.136302	−	0.329063i	−0.00104048	−	0.00251193i	0.923358	−	0.383939i	$-0.125433\pi$
$131$	−0.136302	−	0.329063i	−0.00104048	−	0.00251193i	−0.924399	+	0.381427i	$0.875433\pi$
$132$		0			0
$133$	−71.3499	−	2.29829i	−0.536466	−	0.0172804i
$134$		0			0
$135$	2.45662			0.0181972
$136$		0			0
$137$	−37.6635			−0.274916			−0.137458	−	0.990508i	$-0.543893\pi$
$137$	−37.6635			−0.274916			−0.137458	+	0.990508i	$0.543893\pi$
$138$		0			0
$139$	165.030	−	68.3578i	1.18727	−	0.491783i	0.300404	−	0.953812i	$-0.402878\pi$
$139$	165.030	−	68.3578i	1.18727	−	0.491783i	0.886865	+	0.462029i	$0.152878\pi$
$140$		0			0
$141$	1.29502	−	0.536413i	0.00918451	−	0.00380435i
$142$		0			0
$143$	10.3227	−	24.9211i	0.0721865	−	0.174274i
$144$		0			0
$145$	−13.7407	−	13.7407i	−0.0947636	−	0.0947636i
$146$		0			0
$147$	−0.857891	−	2.51858i	−0.00583600	−	0.0171332i
$148$		0			0
$149$		−	108.097i		−	0.725485i	−0.931889	−	0.362743i	$-0.881840\pi$
$149$		−	108.097i		−	0.725485i	0.931889	−	0.362743i	$-0.118160\pi$
$150$		0			0
$151$	25.0577	+	25.0577i	0.165945	+	0.165945i	0.785194	−	0.619250i	$-0.212563\pi$
$151$	25.0577	+	25.0577i	0.165945	+	0.165945i	−0.619250	+	0.785194i	$0.712563\pi$
$152$		0			0
$153$	151.957	−	17.4002i	0.993182	−	0.113727i
$154$		0			0
$155$	−71.6946	−	71.6946i	−0.462546	−	0.462546i
$156$		0			0
$157$	34.9017			0.222304			0.111152	−	0.993803i	$-0.464546\pi$
$157$	34.9017			0.222304			0.111152	+	0.993803i	$0.464546\pi$
$158$		0			0
$159$	−2.58792	−	1.07195i	−0.0162762	−	0.00674182i
$160$		0			0
$161$	−11.2708	+	4.24877i	−0.0700048	+	0.0263899i
$162$		0			0
$163$	−156.384	−	64.7764i	−0.959412	−	0.397402i	−0.152652	−	0.988280i	$-0.548781\pi$
$163$	−156.384	−	64.7764i	−0.959412	−	0.397402i	−0.806761	+	0.590879i	$0.798781\pi$
$164$		0			0
$165$	0.389197	−	0.161211i	0.00235877	−	0.000977034i
$166$		0			0
$167$	154.053	−	63.8110i	0.922476	−	0.382102i	0.129657	−	0.991559i	$-0.458613\pi$
$167$	154.053	−	63.8110i	0.922476	−	0.382102i	0.792819	+	0.609457i	$0.208613\pi$
$168$		0			0
$169$	−92.6038			−0.547952
$170$		0			0
$171$		−	91.7532i		−	0.536568i
$172$		0			0
$173$	221.779	−	91.8638i	1.28196	−	0.531004i	0.365379	−	0.930859i	$-0.380939\pi$
$173$	221.779	−	91.8638i	1.28196	−	0.531004i	0.916579	+	0.399854i	$0.130939\pi$
$174$		0			0
$175$	130.696	+	4.20991i	0.746834	+	0.0240567i
$176$		0			0
$177$	3.72336	+	1.54227i	0.0210359	+	0.00871337i
$178$		0			0
$179$	4.48799	−	4.48799i	0.0250725	−	0.0250725i	−0.694459	−	0.719532i	$-0.744356\pi$
$179$	4.48799	−	4.48799i	0.0250725	−	0.0250725i	0.719532	+	0.694459i	$0.244356\pi$
$180$		0			0
$181$	264.382	+	109.511i	1.46068	+	0.605032i	0.964711	−	0.263311i	$-0.0848146\pi$
$181$	264.382	+	109.511i	1.46068	+	0.605032i	0.495964	+	0.868343i	$0.334815\pi$
$182$		0			0
$183$		−	2.15719i		−	0.0117879i
$184$		0			0
$185$	−62.6605	+	62.6605i	−0.338706	+	0.338706i
$186$		0			0
$187$	45.8721	−	25.4612i	0.245305	−	0.136156i
$188$		0			0
$189$	6.40093	−	2.41297i	0.0338673	−	0.0127670i
$190$		0			0
$191$		−	75.6760i		−	0.396209i	−0.980181	−	0.198105i	$-0.936521\pi$
$191$		−	75.6760i		−	0.396209i	0.980181	−	0.198105i	$-0.0634786\pi$
$192$		0			0
$193$	−17.2852	+	41.7303i	−0.0895608	+	0.216219i	−0.962313	−	0.271945i	$-0.912333\pi$
$193$	−17.2852	+	41.7303i	−0.0895608	+	0.216219i	0.872752	+	0.488164i	$0.162333\pi$
$194$		0			0
$195$	0.843642	+	0.843642i	0.00432637	+	0.00432637i
$196$		0			0
$197$	−14.2345	−	5.89613i	−0.0722565	−	0.0299296i	0.346262	−	0.938138i	$-0.387451\pi$
$197$	−14.2345	−	5.89613i	−0.0722565	−	0.0299296i	−0.418519	+	0.908208i	$0.637451\pi$
$198$		0			0
$199$	−42.6353	−	102.931i	−0.214248	−	0.517240i	0.779820	−	0.626004i	$-0.215311\pi$
$199$	−42.6353	−	102.931i	−0.214248	−	0.517240i	−0.994068	+	0.108764i	$0.965311\pi$
$200$		0			0
$201$	1.14482	−	0.474202i	0.00569564	−	0.00235921i
$202$		0			0
$203$	−49.2991	−	22.3060i	−0.242853	−	0.109882i
$204$		0			0
$205$	−85.2669			−0.415936
$206$		0			0
$207$	−5.92446	−	14.3029i	−0.0286206	−	0.0690962i
$208$		0			0
$209$	−12.0442	−	29.0772i	−0.0576276	−	0.139125i
$210$		0			0
$211$	214.007	+	88.6445i	1.01425	+	0.420116i	0.827003	−	0.562197i	$-0.190044\pi$
$211$	214.007	+	88.6445i	1.01425	+	0.420116i	0.187246	+	0.982313i	$0.440044\pi$
$212$		0			0
$213$	−3.49055	−	3.49055i	−0.0163876	−	0.0163876i
$214$		0			0
$215$	4.40702	+	1.82545i	0.0204978	+	0.00849045i
$216$		0			0
$217$	−257.226	−	116.385i	−1.18538	−	0.536337i
$218$		0			0
$219$	−2.96574	−	2.96574i	−0.0135422	−	0.0135422i
$220$		0			0
$221$	116.339	+	92.4327i	0.526419	+	0.418248i
$222$		0			0
$223$	−7.12076	+	7.12076i	−0.0319316	+	0.0319316i	−0.722892	−	0.690961i	$-0.757188\pi$
$223$	−7.12076	+	7.12076i	−0.0319316	+	0.0319316i	0.690961	+	0.722892i	$0.257188\pi$
$224$		0			0
$225$			168.070i			0.746976i
$226$		0			0
$227$	−306.416	−	126.922i	−1.34985	−	0.559127i	−0.413601	−	0.910458i	$-0.635729\pi$
$227$	−306.416	−	126.922i	−1.34985	−	0.559127i	−0.936251	+	0.351332i	$0.885729\pi$
$228$		0			0
$229$	157.377	+	157.377i	0.687235	+	0.687235i	0.961620	−	0.274385i	$-0.0884743\pi$
$229$	157.377	+	157.377i	0.687235	+	0.687235i	−0.274385	+	0.961620i	$0.588474\pi$
$230$		0			0
$231$	0.855737	−	0.802328i	0.00370449	−	0.00347328i
$232$		0			0
$233$	338.071	−	140.033i	1.45095	−	0.601002i	0.488522	−	0.872552i	$-0.337536\pi$
$233$	338.071	−	140.033i	1.45095	−	0.601002i	0.962424	+	0.271550i	$0.0875362\pi$
$234$		0			0
$235$	−24.8338	−	59.9540i	−0.105676	−	0.255123i
$236$		0			0
$237$			0.531983i			0.00224465i
$238$		0			0
$239$	−319.947			−1.33869			−0.669346	−	0.742951i	$-0.733425\pi$
$239$	−319.947			−1.33869			−0.669346	+	0.742951i	$0.733425\pi$
$240$		0			0
$241$	−391.205	+	162.042i	−1.62326	+	0.672375i	−0.994452	−	0.105189i	$-0.966455\pi$
$241$	−391.205	+	162.042i	−1.62326	+	0.672375i	−0.628804	+	0.777564i	$0.716455\pi$
$242$		0			0
$243$	5.04723	+	12.1851i	0.0207705	+	0.0501444i
$244$		0			0
$245$	−116.600	+	39.7169i	−0.475919	+	0.162110i
$246$		0			0
$247$	63.0292	−	63.0292i	0.255179	−	0.255179i
$248$		0			0
$249$	−2.69950	+	6.51718i	−0.0108414	+	0.0261734i
$250$		0			0
$251$	283.418			1.12916			0.564578	−	0.825380i	$-0.309039\pi$
$251$	283.418			1.12916			0.564578	+	0.825380i	$0.309039\pi$
$252$		0			0
$253$	−3.75501	−	3.75501i	−0.0148419	−	0.0148419i
$254$		0			0
$255$	0.263993	+	2.30546i	0.00103527	+	0.00904102i
$256$		0			0
$257$	−41.2861	+	41.2861i	−0.160646	+	0.160646i	−0.782853	−	0.622207i	$-0.786236\pi$
$257$	−41.2861	+	41.2861i	−0.160646	+	0.160646i	0.622207	+	0.782853i	$0.286236\pi$
$258$		0			0
$259$	−101.720	+	224.814i	−0.392740	+	0.868008i
$260$		0			0
$261$	26.6149	−	64.2539i	0.101973	−	0.246184i
$262$		0			0
$263$	−324.025	+	324.025i	−1.23204	+	1.23204i	−0.268855	+	0.963181i	$0.586645\pi$
$263$	−324.025	+	324.025i	−1.23204	+	1.23204i	−0.963181	+	0.268855i	$0.913355\pi$
$264$		0			0
$265$	−49.6270	+	119.810i	−0.187272	+	0.452114i
$266$		0			0
$267$	−3.13756	+	1.29962i	−0.0117512	+	0.00486749i
$268$		0			0
$269$	−16.1871	+	6.70491i	−0.0601751	+	0.0249253i	−0.412568	−	0.910927i	$-0.635368\pi$
$269$	−16.1871	+	6.70491i	−0.0601751	+	0.0249253i	0.352393	+	0.935852i	$0.385368\pi$
$270$		0			0
$271$			98.1739i			0.362265i	0.983459	+	0.181133i	$0.0579763\pi$
$271$			98.1739i			0.362265i	−0.983459	+	0.181133i	$0.942024\pi$
$272$		0			0
$273$	3.02683	+	1.36952i	0.0110873	+	0.00501657i
$274$		0			0
$275$	22.0620	+	53.2624i	0.0802256	+	0.193682i
$276$		0			0
$277$	294.882	−	122.144i	1.06456	−	0.440954i	0.219490	−	0.975615i	$-0.429561\pi$
$277$	294.882	−	122.144i	1.06456	−	0.440954i	0.845067	+	0.534661i	$0.179561\pi$
$278$		0			0
$279$	138.868	−	335.256i	0.497733	−	1.20163i
$280$		0			0
$281$	127.841	−	127.841i	0.454952	−	0.454952i	−0.442042	−	0.896994i	$-0.645746\pi$
$281$	127.841	−	127.841i	0.454952	−	0.454952i	0.896994	+	0.442042i	$0.145746\pi$
$282$		0			0
$283$	−428.042	−	177.301i	−1.51252	−	0.626505i	−0.536442	−	0.843937i	$-0.680232\pi$
$283$	−428.042	−	177.301i	−1.51252	−	0.626505i	−0.976075	+	0.217432i	$0.930232\pi$
$284$		0			0
$285$	1.39206			0.00488443
$286$		0			0
$287$	−222.169	+	83.7517i	−0.774110	+	0.291818i
$288$		0			0
$289$	65.3288	+	281.519i	0.226051	+	0.974115i
$290$		0			0
$291$	−3.30709	−	3.30709i	−0.0113646	−	0.0113646i
$292$		0			0
$293$	277.116			0.945789			0.472895	−	0.881119i	$-0.343209\pi$
$293$	277.116			0.945789			0.472895	+	0.881119i	$0.343209\pi$
$294$		0			0
$295$	71.4007	−	172.377i	0.242036	−	0.584327i
$296$		0			0
$297$	2.13255	+	2.13255i	0.00718032	+	0.00718032i
$298$		0			0
$299$	5.75552	−	13.8950i	0.0192492	−	0.0464717i
$300$		0			0
$301$	13.2758	+	0.427635i	0.0441058	+	0.00142071i
$302$		0			0
$303$	−1.04861	−	2.53158i	−0.00346077	−	0.00835505i
$304$		0			0
$305$	−99.8693			−0.327440
$306$		0			0
$307$			421.209i			1.37202i	0.727594	+	0.686008i	$0.240639\pi$
$307$			421.209i			1.37202i	−0.727594	+	0.686008i	$0.759361\pi$
$308$		0			0
$309$	0.674128	+	1.62749i	0.00218164	+	0.00526695i
$310$		0			0
$311$	−87.8427	−	212.071i	−0.282453	−	0.681901i	0.717439	−	0.696621i	$-0.245314\pi$
$311$	−87.8427	−	212.071i	−0.282453	−	0.681901i	−0.999892	+	0.0147205i	$0.995314\pi$
$312$		0			0
$313$	−97.3179	+	234.946i	−0.310920	+	0.750627i	0.688752	+	0.724997i	$0.258159\pi$
$313$	−97.3179	+	234.946i	−0.310920	+	0.750627i	−0.999672	+	0.0256294i	$0.991841\pi$
$314$		0			0
$315$	−55.8463	−	148.144i	−0.177290	−	0.470299i
$316$		0			0
$317$	−24.2521	+	58.5497i	−0.0765049	+	0.184699i	−0.957505	−	0.288417i	$-0.906871\pi$
$317$	−24.2521	+	58.5497i	−0.0765049	+	0.184699i	0.881000	+	0.473116i	$0.156871\pi$
$318$		0			0
$319$		−	23.8562i		−	0.0747842i
$320$		0			0
$321$	2.27672	−	2.27672i	0.00709260	−	0.00709260i
$322$		0			0
$323$	172.243	−	19.7231i	0.533259	−	0.0610623i
$324$		0			0
$325$	−115.454	+	115.454i	−0.355244	+	0.355244i
$326$		0			0
$327$	0.637923			0.00195084
$328$		0			0
$329$	−123.595	−	131.822i	−0.375669	−	0.400676i
$330$		0			0
$331$	−346.245	+	346.245i	−1.04606	+	1.04606i	−0.0471713	+	0.998887i	$0.515021\pi$
$331$	−346.245	+	346.245i	−1.04606	+	1.04606i	−0.998887	+	0.0471713i	$0.984979\pi$
$332$		0			0
$333$	−293.011	−	121.369i	−0.879913	−	0.364472i
$334$		0			0
$335$	−21.9536	−	53.0008i	−0.0655332	−	0.158211i
$336$		0			0
$337$	218.883	+	528.429i	0.649503	+	1.56804i	0.813491	+	0.581577i	$0.197564\pi$
$337$	218.883	+	528.429i	0.649503	+	1.56804i	−0.163988	+	0.986462i	$0.552436\pi$
$338$		0			0
$339$			4.89985i			0.0144538i
$340$		0			0
$341$		−	124.474i		−	0.365026i
$342$		0			0
$343$	−264.800	+	218.014i	−0.772011	+	0.635609i
$344$		0			0
$345$	0.217001	−	0.0898848i	0.000628989	−	0.000260536i
$346$		0			0
$347$	165.066	+	68.3727i	0.475696	+	0.197040i	0.607632	−	0.794219i	$-0.292120\pi$
$347$	165.066	+	68.3727i	0.475696	+	0.197040i	−0.131937	+	0.991258i	$0.542120\pi$
$348$		0			0
$349$	99.1742	+	99.1742i	0.284167	+	0.284167i	0.834768	−	0.550601i	$-0.185602\pi$
$349$	99.1742	+	99.1742i	0.284167	+	0.284167i	−0.550601	+	0.834768i	$0.685602\pi$
$350$		0			0
$351$	−3.26869	+	7.89132i	−0.00931251	+	0.0224824i
$352$		0			0
$353$	−469.425			−1.32982			−0.664908	−	0.746926i	$-0.731529\pi$
$353$	−469.425			−1.32982			−0.664908	+	0.746926i	$0.731529\pi$
$354$		0			0
$355$	−161.599	+	161.599i	−0.455207	+	0.455207i
$356$		0			0
$357$	2.95235	+	5.74775i	0.00826988	+	0.0161002i
$358$		0			0
$359$	−36.8627	−	36.8627i	−0.102682	−	0.102682i	0.653900	−	0.756581i	$-0.273132\pi$
$359$	−36.8627	−	36.8627i	−0.102682	−	0.102682i	−0.756581	+	0.653900i	$0.773132\pi$
$360$		0			0
$361$			256.998i			0.711906i
$362$		0			0
$363$	−5.59233	−	2.31642i	−0.0154059	−	0.00638132i
$364$		0			0
$365$	−137.302	+	137.302i	−0.376169	+	0.376169i
$366$		0			0
$367$	−211.909	+	511.594i	−0.577409	+	1.39399i	0.317722	+	0.948184i	$0.397082\pi$
$367$	−211.909	+	511.594i	−0.577409	+	1.39399i	−0.895131	+	0.445804i	$0.852918\pi$
$368$		0			0
$369$	−116.783	−	281.939i	−0.316485	−	0.764063i
$370$		0			0
$371$	−11.6258	+	360.920i	−0.0313363	+	0.972830i
$372$		0			0
$373$	264.454			0.708993			0.354496	−	0.935057i	$-0.384652\pi$
$373$	264.454			0.708993			0.354496	+	0.935057i	$0.384652\pi$
$374$		0			0
$375$	−5.96246			−0.0158999
$376$		0			0
$377$	62.4217	−	25.8559i	0.165575	−	0.0685833i
$378$		0			0
$379$	222.560	−	92.1873i	0.587229	−	0.243238i	−0.0692291	−	0.997601i	$-0.522054\pi$
$379$	222.560	−	92.1873i	0.587229	−	0.243238i	0.656458	+	0.754363i	$0.272054\pi$
$380$		0			0
$381$	0.571395	−	1.37947i	0.00149972	−	0.00362066i
$382$		0			0
$383$	−31.2145	−	31.2145i	−0.0815000	−	0.0815000i	0.665182	−	0.746682i	$-0.268354\pi$
$383$	−31.2145	−	31.2145i	−0.0815000	−	0.0815000i	−0.746682	+	0.665182i	$0.768354\pi$
$384$		0			0
$385$	−37.1446	−	39.6172i	−0.0964794	−	0.102902i
$386$		0			0
$387$			17.0722i			0.0441142i
$388$		0			0
$389$	−40.3894	−	40.3894i	−0.103829	−	0.103829i	0.653284	−	0.757113i	$-0.273391\pi$
$389$	−40.3894	−	40.3894i	−0.103829	−	0.103829i	−0.757113	+	0.653284i	$0.773391\pi$
$390$		0			0
$391$	25.5765	−	14.1962i	0.0654130	−	0.0363073i
$392$		0			0
$393$	0.0136756	+	0.0136756i	3.47979e−5	+	3.47979e-5i
$394$		0			0
$395$	24.6287			0.0623510
$396$		0			0
$397$	23.1247	+	9.57858i	0.0582487	+	0.0241274i	0.411618	−	0.911357i	$-0.364964\pi$
$397$	23.1247	+	9.57858i	0.0582487	+	0.0241274i	−0.353369	+	0.935484i	$0.614964\pi$
$398$		0			0
$399$	3.62712	−	1.36733i	0.00909054	−	0.00342688i
$400$		0			0
$401$	−557.027	−	230.728i	−1.38909	−	0.575382i	−0.442197	−	0.896918i	$-0.645801\pi$
$401$	−557.027	−	230.728i	−1.38909	−	0.575382i	−0.946897	+	0.321536i	$0.895801\pi$
$402$		0			0
$403$	325.696	−	134.908i	0.808178	−	0.334758i
$404$		0			0
$405$	187.938	−	77.8463i	0.464044	−	0.192213i
$406$		0			0
$407$	−108.789			−0.267295
$408$		0			0
$409$			434.053i			1.06125i	0.847605	+	0.530627i	$0.178044\pi$
$409$			434.053i			1.06125i	−0.847605	+	0.530627i	$0.821956\pi$
$410$		0			0
$411$	1.88944	−	0.782631i	0.00459717	−	0.00190421i
$412$		0			0
$413$	16.7266	−	519.273i	0.0405001	−	1.25732i
$414$		0			0
$415$	301.719	+	124.976i	0.727034	+	0.301147i
$416$		0			0
$417$	−6.85852	+	6.85852i	−0.0164473	+	0.0164473i
$418$		0			0
$419$	119.828	+	49.6343i	0.285985	+	0.118459i	0.521065	−	0.853517i	$-0.325535\pi$
$419$	119.828	+	49.6343i	0.285985	+	0.118459i	−0.235080	+	0.971976i	$0.575535\pi$
$420$		0			0
$421$		−	630.213i		−	1.49694i	−0.663168	−	0.748471i	$-0.730788\pi$
$421$		−	630.213i		−	1.49694i	0.663168	−	0.748471i	$-0.269212\pi$
$422$		0			0
$423$	164.228	−	164.228i	0.388246	−	0.388246i
$424$		0			0
$425$	−315.507	+	36.1280i	−0.742370	+	0.0850070i
$426$		0			0
$427$	−260.217	+	98.0946i	−0.609408	+	0.229730i
$428$		0			0
$429$			1.46470i			0.00341423i
$430$		0			0
$431$	190.866	−	460.791i	0.442844	−	1.06912i	−0.532102	−	0.846680i	$-0.678598\pi$
$431$	190.866	−	460.791i	0.442844	−	1.06912i	0.974946	−	0.222440i	$-0.0714022\pi$
$432$		0			0
$433$	274.013	+	274.013i	0.632824	+	0.632824i	0.948775	−	0.315952i	$-0.102324\pi$
$433$	274.013	+	274.013i	0.632824	+	0.632824i	−0.315952	+	0.948775i	$0.602324\pi$
$434$		0			0
$435$	0.974848	+	0.403795i	0.00224103	+	0.000928265i
$436$		0			0
$437$	−6.71536	−	16.2123i	−0.0153670	−	0.0370991i
$438$		0			0
$439$	408.138	−	169.056i	0.929699	−	0.385094i	0.134135	−	0.990963i	$-0.457174\pi$
$439$	408.138	−	169.056i	0.929699	−	0.385094i	0.795564	+	0.605869i	$0.207174\pi$
$440$		0			0
$441$	−291.024	−	331.148i	−0.659918	−	0.750902i
$442$		0			0
$443$	−246.023			−0.555357			−0.277678	−	0.960674i	$-0.589565\pi$
$443$	−246.023			−0.555357			−0.277678	+	0.960674i	$0.589565\pi$
$444$		0			0
$445$	60.1672	+	145.256i	0.135207	+	0.326419i
$446$		0			0
$447$	2.24622	+	5.42284i	0.00502509	+	0.0121316i
$448$		0			0
$449$	−258.791	−	107.195i	−0.576373	−	0.238742i	0.0754029	−	0.997153i	$-0.475976\pi$
$449$	−258.791	−	107.195i	−0.576373	−	0.238742i	−0.651776	+	0.758412i	$0.725976\pi$
$450$		0			0
$451$	−74.0187	−	74.0187i	−0.164121	−	0.164121i
$452$		0			0
$453$	−1.77774	−	0.736363i	−0.00392437	−	0.00162553i
$454$		0			0
$455$	63.4035	−	140.130i	0.139348	−	0.307978i
$456$		0			0
$457$	226.478	+	226.478i	0.495576	+	0.495576i	0.910058	−	0.414482i	$-0.136037\pi$
$457$	226.478	+	226.478i	0.495576	+	0.495576i	−0.414482	+	0.910058i	$0.636037\pi$
$458$		0			0
$459$	−14.5255	+	8.06233i	−0.0316459	+	0.0175650i
$460$		0			0
$461$	488.028	−	488.028i	1.05863	−	1.05863i	0.0604572	−	0.998171i	$-0.480744\pi$
$461$	488.028	−	488.028i	1.05863	−	1.05863i	0.998171	−	0.0604572i	$-0.0192559\pi$
$462$		0			0
$463$			402.340i			0.868985i	0.900676	+	0.434492i	$0.143072\pi$
$463$			402.340i			0.868985i	−0.900676	+	0.434492i	$0.856928\pi$
$464$		0			0
$465$	5.08644	+	2.10687i	0.0109386	+	0.00453091i
$466$		0			0
$467$	547.937	+	547.937i	1.17331	+	1.17331i	0.981415	+	0.191899i	$0.0614645\pi$
$467$	547.937	+	547.937i	1.17331	+	1.17331i	0.191899	+	0.981415i	$0.438535\pi$
$468$		0			0
$469$	−109.261	−	116.534i	−0.232966	−	0.248474i
$470$		0			0
$471$	−1.75089	+	0.725243i	−0.00371739	+	0.00153979i
$472$		0			0
$473$	2.24102	+	5.41030i	0.00473788	+	0.0114383i
$474$		0			0
$475$			190.507i			0.401066i
$476$		0			0
$477$	−464.128			−0.973015
$478$		0			0
$479$	506.556	−	209.822i	1.05753	−	0.438043i	0.214955	−	0.976624i	$-0.431040\pi$
$479$	506.556	−	209.822i	1.05753	−	0.438043i	0.842573	+	0.538581i	$0.181040\pi$
$480$		0			0
$481$	−117.908	−	284.656i	−0.245131	−	0.591800i
$482$		0			0
$483$	0.477126	−	0.447347i	0.000987838	−	0.000926184i
$484$		0			0
$485$	−153.105	+	153.105i	−0.315680	+	0.315680i
$486$		0			0
$487$	98.6577	−	238.181i	0.202582	−	0.489077i	−0.789638	−	0.613573i	$-0.789731\pi$
$487$	98.6577	−	238.181i	0.202582	−	0.489077i	0.992220	+	0.124496i	$0.0397314\pi$
$488$		0			0
$489$	9.19125			0.0187960
$490$		0			0
$491$	−288.400	−	288.400i	−0.587372	−	0.587372i	0.349547	−	0.936919i	$-0.386336\pi$
$491$	−288.400	−	288.400i	−0.587372	−	0.587372i	−0.936919	+	0.349547i	$0.886336\pi$
$492$		0			0
$493$	126.341	+	36.1506i	0.256270	+	0.0733277i
$494$		0			0
$495$	49.3563	−	49.3563i	0.0997096	−	0.0997096i
$496$		0			0
$497$	−262.331	+	579.785i	−0.527828	+	1.16657i
$498$		0			0
$499$	297.382	−	717.944i	0.595956	−	1.43877i	−0.281713	−	0.959499i	$-0.590903\pi$
$499$	297.382	−	717.944i	0.595956	−	1.43877i	0.877669	−	0.479267i	$-0.159097\pi$
$500$		0			0
$501$	−6.40233	+	6.40233i	−0.0127791	+	0.0127791i
$502$		0			0
$503$	26.4263	−	63.7988i	0.0525374	−	0.126837i	−0.895432	−	0.445199i	$-0.853133\pi$
$503$	26.4263	−	63.7988i	0.0525374	−	0.126837i	0.947969	+	0.318363i	$0.103133\pi$
$504$		0			0
$505$	−117.202	+	48.5466i	−0.232083	+	0.0961319i
$506$		0			0
$507$	4.64560	−	1.92427i	0.00916291	−	0.00379540i
$508$		0			0
$509$		−	583.954i		−	1.14726i	−0.819116	−	0.573628i	$-0.805535\pi$
$509$		−	583.954i		−	1.14726i	0.819116	−	0.573628i	$-0.194465\pi$
$510$		0			0
$511$	−222.889	+	492.613i	−0.436181	+	0.964017i
$512$		0			0
$513$	3.81381	+	9.20735i	0.00743433	+	0.0179480i
$514$		0			0
$515$	75.3462	−	31.2094i	0.146303	−	0.0606008i
$516$		0			0
$517$	30.4873	−	73.6028i	0.0589696	−	0.142365i
$518$		0			0
$519$	−9.21694	+	9.21694i	−0.0177590	+	0.0177590i
$520$		0			0
$521$	−32.4755	−	13.4518i	−0.0623331	−	0.0258192i	0.351299	−	0.936263i	$-0.385740\pi$
$521$	−32.4755	−	13.4518i	−0.0623331	−	0.0258192i	−0.413632	+	0.910444i	$0.635740\pi$
$522$		0			0
$523$	37.6372			0.0719640			0.0359820	−	0.999352i	$-0.488544\pi$
$523$	37.6372			0.0719640			0.0359820	+	0.999352i	$0.488544\pi$
$524$		0			0
$525$	−6.64402	+	2.50461i	−0.0126553	+	0.00477069i
$526$		0			0
$527$	659.207	+	188.622i	1.25087	+	0.357916i
$528$		0			0
$529$	371.966	+	371.966i	0.703149	+	0.703149i
$530$		0			0
$531$	667.764			1.25756
$532$		0			0
$533$	113.453	−	273.899i	0.212857	−	0.513882i
$534$		0			0
$535$	−105.403	−	105.403i	−0.197015	−	0.197015i
$536$		0			0
$537$	−0.131887	+	0.318404i	−0.000245600	+	0.000592932i
$538$		0			0
$539$	−135.696	−	66.7411i	−0.251756	−	0.123824i
$540$		0			0
$541$	−195.176	−	471.197i	−0.360769	−	0.870973i	−0.995188	−	0.0979841i	$-0.968761\pi$
$541$	−195.176	−	471.197i	−0.360769	−	0.870973i	0.634419	−	0.772989i	$-0.281239\pi$
$542$		0			0
$543$	−15.5387			−0.0286164
$544$		0			0
$545$		−	29.5333i		−	0.0541895i
$546$		0			0
$547$	343.800	+	830.006i	0.628519	+	1.51738i	0.841463	+	0.540314i	$0.181695\pi$
$547$	343.800	+	830.006i	0.628519	+	1.51738i	−0.212944	+	0.977064i	$0.568305\pi$
$548$		0			0
$549$	−136.783	−	330.223i	−0.249149	−	0.601499i
$550$		0			0
$551$	30.1679	−	72.8317i	0.0547511	−	0.132181i
$552$		0			0
$553$	64.1719	−	24.1910i	0.116043	−	0.0437451i
$554$		0			0
$555$	1.84139	−	4.44551i	0.00331782	−	0.00800993i
$556$		0			0
$557$		−	666.298i		−	1.19623i	−0.801412	−	0.598113i	$-0.795917\pi$
$557$		−	666.298i		−	1.19623i	0.801412	−	0.598113i	$-0.204083\pi$
$558$		0			0
$559$	−11.7276	+	11.7276i	−0.0209797	+	0.0209797i
$560$		0			0
$561$	−1.77216	+	2.23050i	−0.00315894	+	0.00397593i
$562$		0			0
$563$	259.433	−	259.433i	0.460804	−	0.460804i	−0.438115	−	0.898919i	$-0.644354\pi$
$563$	259.433	−	259.433i	0.460804	−	0.460804i	0.898919	+	0.438115i	$0.144354\pi$
$564$		0			0
$565$	226.843			0.401493
$566$		0			0
$567$	413.223	−	387.433i	0.728789	−	0.683303i
$568$		0			0
$569$	−590.604	+	590.604i	−1.03797	+	1.03797i	−0.0387181	+	0.999250i	$0.512327\pi$
$569$	−590.604	+	590.604i	−1.03797	+	1.03797i	−0.999250	+	0.0387181i	$0.987673\pi$
$570$		0			0
$571$	−711.789	−	294.833i	−1.24657	−	0.516345i	−0.340805	−	0.940134i	$-0.610700\pi$
$571$	−711.789	−	294.833i	−1.24657	−	0.516345i	−0.905761	+	0.423789i	$0.860700\pi$
$572$		0			0
$573$	1.57252	+	3.79639i	0.00274436	+	0.00662546i
$574$		0			0
$575$	12.3009	+	29.6971i	0.0213929	+	0.0516471i
$576$		0			0
$577$			560.703i			0.971755i	0.874027	+	0.485877i	$0.161500\pi$
$577$			560.703i			0.971755i	−0.874027	+	0.485877i	$0.838500\pi$
$578$		0			0
$579$		−	2.45263i		−	0.00423598i
$580$		0			0
$581$	908.908	+	29.2773i	1.56439	+	0.0503912i
$582$		0			0
$583$	−147.085	+	60.9248i	−0.252291	+	0.104502i
$584$		0			0
$585$	182.638	+	75.6512i	0.312202	+	0.129318i
$586$		0			0
$587$	445.016	+	445.016i	0.758119	+	0.758119i	0.975980	−	0.217861i	$-0.0699079\pi$
$587$	445.016	+	445.016i	0.758119	+	0.758119i	−0.217861	+	0.975980i	$0.569908\pi$
$588$		0			0
$589$	157.406	−	380.012i	0.267243	−	0.645182i
$590$		0			0
$591$	0.836613			0.00141559
$592$		0			0
$593$	308.677	−	308.677i	0.520535	−	0.520535i	−0.397198	−	0.917733i	$-0.630017\pi$
$593$	308.677	−	308.677i	0.520535	−	0.520535i	0.917733	+	0.397198i	$0.130017\pi$
$594$		0			0
$595$	266.098	−	136.682i	0.447223	−	0.229717i
$596$		0			0
$597$	4.27772	+	4.27772i	0.00716535	+	0.00716535i
$598$		0			0
$599$		−	166.616i		−	0.278158i	−0.990281	−	0.139079i	$-0.955586\pi$
$599$		−	166.616i		−	0.278158i	0.990281	−	0.139079i	$-0.0444141\pi$
$600$		0			0
$601$	−45.6274	−	18.8995i	−0.0759191	−	0.0314467i	0.344401	−	0.938823i	$-0.388082\pi$
$601$	−45.6274	−	18.8995i	−0.0759191	−	0.0314467i	−0.420320	+	0.907376i	$0.638082\pi$
$602$		0			0
$603$	145.182	−	145.182i	0.240766	−	0.240766i
$604$		0			0
$605$	−107.241	+	258.902i	−0.177258	+	0.427938i
$606$		0			0
$607$	222.191	+	536.416i	0.366048	+	0.883717i	0.994390	+	0.105780i	$0.0337339\pi$
$607$	222.191	+	536.416i	0.366048	+	0.883717i	−0.628342	+	0.777937i	$0.716266\pi$
$608$		0			0
$609$	2.93666	+	0.0945944i	0.00482211	+	0.000155327i
$610$		0			0
$611$	225.631			0.369281
$612$		0			0
$613$	−1111.13			−1.81261			−0.906303	−	0.422630i	$-0.861107\pi$
$613$	−1111.13			−1.81261			−0.906303	+	0.422630i	$0.861107\pi$
$614$		0			0
$615$	4.27753	−	1.77181i	0.00695533	−	0.00288099i
$616$		0			0
$617$	641.144	−	265.571i	1.03913	−	0.430422i	0.203131	−	0.979151i	$-0.434888\pi$
$617$	641.144	−	265.571i	1.03913	−	0.430422i	0.836000	+	0.548729i	$0.184888\pi$
$618$		0			0
$619$	358.572	−	865.669i	0.579276	−	1.39850i	−0.314188	−	0.949361i	$-0.601732\pi$
$619$	358.572	−	865.669i	0.579276	−	1.39850i	0.893464	−	0.449135i	$-0.148268\pi$
$620$		0			0
$621$	1.18903	+	1.18903i	0.00191470	+	0.00191470i
$622$		0			0
$623$	299.446	+	319.379i	0.480651	+	0.512647i
$624$		0			0
$625$		−	190.975i		−	0.305561i
$626$		0			0
$627$	1.20842	+	1.20842i	0.00192731	+	0.00192731i
$628$		0			0
$629$	164.854	−	576.142i	0.262089	−	0.915965i
$630$		0			0
$631$	38.3125	+	38.3125i	0.0607171	+	0.0607171i	0.736813	−	0.676096i	$-0.236330\pi$
$631$	38.3125	+	38.3125i	0.0607171	+	0.0607171i	−0.676096	+	0.736813i	$0.736330\pi$
$632$		0			0
$633$	−12.5779			−0.0198703
$634$		0			0
$635$	−63.8639	−	26.4533i	−0.100573	−	0.0416587i
$636$		0			0
$637$	27.5628	−	427.396i	0.0432696	−	0.670952i
$638$		0			0
$639$	−755.662	−	313.006i	−1.18257	−	0.489837i
$640$		0			0
$641$	36.0697	−	14.9405i	0.0562709	−	0.0233082i	−0.354370	−	0.935105i	$-0.615305\pi$
$641$	36.0697	−	14.9405i	0.0562709	−	0.0233082i	0.410641	+	0.911797i	$0.365305\pi$
$642$		0			0
$643$	−311.908	+	129.197i	−0.485082	+	0.200928i	−0.611802	−	0.791011i	$-0.709555\pi$
$643$	−311.908	+	129.197i	−0.485082	+	0.200928i	0.126720	+	0.991939i	$0.459555\pi$
$644$		0			0
$645$	−0.259016			−0.000401575
$646$		0			0
$647$			162.482i			0.251132i	0.992085	+	0.125566i	$0.0400747\pi$
$647$			162.482i			0.251132i	−0.992085	+	0.125566i	$0.959925\pi$
$648$		0			0
$649$	211.619	−	87.6554i	0.326069	−	0.135062i
$650$		0			0
$651$	15.3225	+	0.493563i	0.0235369	+	0.000758161i
$652$		0			0
$653$	−209.237	−	86.6689i	−0.320424	−	0.132724i	0.216673	−	0.976244i	$-0.430479\pi$
$653$	−209.237	−	86.6689i	−0.320424	−	0.132724i	−0.537098	+	0.843520i	$0.680479\pi$
$654$		0			0
$655$	0.633125	−	0.633125i	0.000966603	−	0.000966603i
$656$		0			0
$657$	−642.046	−	265.944i	−0.977240	−	0.404786i
$658$		0			0
$659$		−	1096.17i		−	1.66338i	−0.555240	−	0.831691i	$-0.687373\pi$
$659$		−	1096.17i		−	1.66338i	0.555240	−	0.831691i	$-0.312627\pi$
$660$		0			0
$661$	208.642	−	208.642i	0.315646	−	0.315646i	−0.531446	−	0.847092i	$-0.678351\pi$
$661$	208.642	−	208.642i	0.315646	−	0.315646i	0.847092	+	0.531446i	$0.178351\pi$
$662$		0			0
$663$	−7.75700	−	2.21954i	−0.0116998	−	0.00334773i
$664$		0			0
$665$	−63.3017	−	167.921i	−0.0951905	−	0.252513i
$666$		0			0
$667$		−	13.3013i		−	0.0199419i
$668$		0			0
$669$	0.209256	−	0.505189i	0.000312789	−	0.000755140i
$670$		0			0
$671$	−86.6948	−	86.6948i	−0.129202	−	0.129202i
$672$		0			0
$673$	−565.428	−	234.208i	−0.840161	−	0.348006i	−0.0792437	−	0.996855i	$-0.525251\pi$
$673$	−565.428	−	234.208i	−0.840161	−	0.348006i	−0.760917	+	0.648849i	$0.775251\pi$
$674$		0			0
$675$	−6.98598	−	16.8656i	−0.0103496	−	0.0249861i
$676$		0			0
$677$	−96.2272	+	39.8586i	−0.142138	+	0.0588754i	−0.452618	−	0.891704i	$-0.649510\pi$
$677$	−96.2272	+	39.8586i	−0.142138	+	0.0588754i	0.310481	+	0.950580i	$0.399510\pi$
$678$		0			0
$679$	−248.543	+	549.311i	−0.366042	+	0.809001i
$680$		0			0
$681$	18.0092			0.0264452
$682$		0			0
$683$	363.052	+	876.486i	0.531556	+	1.28329i	0.930493	+	0.366310i	$0.119379\pi$
$683$	363.052	+	876.486i	0.531556	+	1.28329i	−0.398937	+	0.916978i	$0.630621\pi$
$684$		0			0
$685$	−36.2327	−	87.4734i	−0.0528944	−	0.127698i
$686$		0			0
$687$	−11.1652	−	4.62479i	−0.0162522	−	0.00673187i
$688$		0			0
$689$	−318.830	−	318.830i	−0.462742	−	0.462742i
$690$		0			0
$691$	−322.534	−	133.598i	−0.466764	−	0.193340i	0.136890	−	0.990586i	$-0.456289\pi$
$691$	−322.534	−	133.598i	−0.466764	−	0.193340i	−0.603654	+	0.797246i	$0.706289\pi$
$692$		0			0
$693$	80.1223	−	177.081i	0.115617	−	0.255528i
$694$		0			0
$695$	317.522	+	317.522i	0.456866	+	0.456866i
$696$		0			0
$697$	504.164	−	279.835i	0.723335	−	0.401485i
$698$		0			0
$699$	−14.0499	+	14.0499i	−0.0201000	+	0.0201000i
$700$		0			0
$701$			1044.35i			1.48981i	0.667173	+	0.744903i	$0.267504\pi$
$701$			1044.35i			1.48981i	−0.667173	+	0.744903i	$0.732496\pi$
$702$		0			0
$703$	−332.127	−	137.572i	−0.472443	−	0.195692i
$704$		0			0
$705$	2.49164	+	2.49164i	0.00353424	+	0.00353424i
$706$		0			0
$707$	−257.695	+	241.611i	−0.364490	+	0.341742i
$708$		0			0
$709$	645.350	−	267.313i	0.910226	−	0.377028i	0.122083	−	0.992520i	$-0.461043\pi$
$709$	645.350	−	267.313i	0.910226	−	0.377028i	0.788143	+	0.615492i	$0.211043\pi$
$710$		0			0
$711$	33.7319	+	81.4359i	0.0474428	+	0.114537i
$712$		0			0
$713$		−	69.4017i		−	0.0973376i
$714$		0			0
$715$	67.8098			0.0948389
$716$		0			0
$717$	16.0506	−	6.64837i	0.0223857	−	0.00927248i
$718$		0			0
$719$	336.687	+	812.834i	0.468271	+	1.13051i	0.964918	+	0.262553i	$0.0845645\pi$
$719$	336.687	+	812.834i	0.468271	+	1.13051i	−0.496647	+	0.867953i	$0.665435\pi$
$720$		0			0
$721$	165.665	−	155.326i	0.229772	−	0.215431i
$722$		0			0
$723$	16.2581	−	16.2581i	0.0224871	−	0.0224871i
$724$		0			0
$725$	−55.2603	+	133.410i	−0.0762211	+	0.184014i
$726$		0			0
$727$	−1273.57			−1.75181			−0.875906	−	0.482483i	$-0.839735\pi$
$727$	−1273.57			−1.75181			−0.875906	+	0.482483i	$0.839735\pi$
$728$		0			0
$729$	514.468	+	514.468i	0.705717	+	0.705717i
$730$		0			0
$731$	−32.0486	+	3.66981i	−0.0438422	+	0.00502026i
$732$		0			0
$733$	774.634	−	774.634i	1.05680	−	1.05680i	0.0585134	−	0.998287i	$-0.481364\pi$
$733$	774.634	−	774.634i	1.05680	−	1.05680i	0.998287	−	0.0585134i	$-0.0186360\pi$
$734$		0			0
$735$	5.02411	−	4.41536i	0.00683552	−	0.00600729i
$736$		0			0
$737$	26.9515	−	65.0666i	0.0365692	−	0.0882858i
$738$		0			0
$739$	−565.268	+	565.268i	−0.764909	+	0.764909i	−0.977205	−	0.212297i	$-0.931906\pi$
$739$	−565.268	+	565.268i	−0.764909	+	0.764909i	0.212297	+	0.977205i	$0.431906\pi$
$740$		0			0
$741$	−1.85222	+	4.47166i	−0.00249963	+	0.00603463i
$742$		0			0
$743$	−342.440	+	141.843i	−0.460888	+	0.190906i	−0.601032	−	0.799225i	$-0.705244\pi$
$743$	−342.440	+	141.843i	−0.460888	+	0.190906i	0.140144	+	0.990131i	$0.455244\pi$
$744$		0			0
$745$	251.056	−	103.991i	0.336988	−	0.139585i
$746$		0			0
$747$			1168.82i			1.56468i
$748$		0			0
$749$	−378.166	−	171.106i	−0.504895	−	0.228446i
$750$		0			0
$751$	256.134	+	618.362i	0.341057	+	0.823385i	0.997609	+	0.0691043i	$0.0220141\pi$
$751$	256.134	+	618.362i	0.341057	+	0.823385i	−0.656552	+	0.754281i	$0.727986\pi$
$752$		0			0
$753$	−14.2180	+	5.88931i	−0.0188819	+	0.00782112i
$754$		0			0
$755$	−34.0907	+	82.3021i	−0.0451532	+	0.109009i
$756$		0			0
$757$	−253.706	+	253.706i	−0.335147	+	0.335147i	−0.854537	−	0.519390i	$-0.826159\pi$
$757$	−253.706	+	253.706i	−0.335147	+	0.335147i	0.519390	+	0.854537i	$0.326159\pi$
$758$		0			0
$759$	0.266402	+	0.110347i	0.000350991	+	0.000145385i
$760$		0			0
$761$	−1436.91			−1.88818			−0.944092	−	0.329683i	$-0.893058\pi$
$761$	−1436.91			−1.88818			−0.944092	+	0.329683i	$0.893058\pi$
$762$		0			0
$763$	−29.0085	−	76.9513i	−0.0380190	−	0.100854i
$764$		0			0
$765$	186.596	+	336.181i	0.243917	+	0.439452i
$766$		0			0
$767$	458.715	+	458.715i	0.598064	+	0.598064i
$768$		0			0
$769$	−513.474			−0.667717			−0.333858	−	0.942623i	$-0.608351\pi$
$769$	−513.474			−0.667717			−0.333858	+	0.942623i	$0.608351\pi$
$770$		0			0
$771$	1.21327	−	2.92908i	0.00157363	−	0.00379907i
$772$		0			0
$773$	541.648	+	541.648i	0.700709	+	0.700709i	0.964563	−	0.263854i	$-0.0849936\pi$
$773$	541.648	+	541.648i	0.700709	+	0.700709i	−0.263854	+	0.964563i	$0.584994\pi$
$774$		0			0
$775$	−288.330	+	696.090i	−0.372039	+	0.898181i
$776$		0			0
$777$	0.431370	−	13.3918i	0.000555174	−	0.0172352i
$778$		0			0
$779$	−132.373	−	319.577i	−0.169927	−	0.410241i
$780$		0			0
$781$	−280.562			−0.359234
$782$		0			0
$783$			7.55410i			0.00964764i
$784$		0			0
$785$	33.5758	+	81.0592i	0.0427717	+	0.103260i
$786$		0			0
$787$	127.617	+	308.094i	0.162156	+	0.391479i	0.983984	−	0.178256i	$-0.0570456\pi$
$787$	127.617	+	308.094i	0.162156	+	0.391479i	−0.821828	+	0.569736i	$0.807046\pi$
$788$		0			0
$789$	9.52206	−	22.9883i	0.0120685	−	0.0291360i
$790$		0			0
$791$	591.058	−	222.813i	0.747229	−	0.281685i
$792$		0			0
$793$	132.882	−	320.806i	0.167569	−	0.404547i
$794$		0			0
$795$		−	7.04166i		−	0.00885744i
$796$		0			0
$797$	−807.424	+	807.424i	−1.01308	+	1.01308i	−0.0131662	+	0.999913i	$0.504191\pi$
$797$	−807.424	+	807.424i	−1.01308	+	1.01308i	−0.999913	+	0.0131662i	$0.995809\pi$
$798$		0			0
$799$	343.598	+	272.994i	0.430035	+	0.341669i
$800$		0			0
$801$	−397.892	+	397.892i	−0.496744	+	0.496744i
$802$		0			0
$803$	−238.379			−0.296860
$804$		0			0
$805$	−20.7104	−	22.0890i	−0.0257272	−	0.0274397i
$806$		0			0
$807$	0.672722	−	0.672722i	0.000833609	−	0.000833609i
$808$		0			0
$809$	−295.305	−	122.320i	−0.365025	−	0.151198i	0.192629	−	0.981272i	$-0.438299\pi$
$809$	−295.305	−	122.320i	−0.365025	−	0.151198i	−0.557654	+	0.830073i	$0.688299\pi$
$810$		0			0
$811$	−106.752	−	257.722i	−0.131630	−	0.317783i	0.844299	−	0.535873i	$-0.180017\pi$
$811$	−106.752	−	257.722i	−0.131630	−	0.317783i	−0.975929	+	0.218090i	$0.930017\pi$
$812$		0			0
$813$	−2.04001	−	4.92503i	−0.00250924	−	0.00605784i
$814$		0			0
$815$		−	425.518i		−	0.522108i
$816$		0			0
$817$			19.3513i			0.0236858i
$818$		0			0
$819$	550.185	+	17.7223i	0.671777	+	0.0216389i
$820$		0			0
$821$	−311.690	+	129.106i	−0.379647	+	0.157255i	−0.564342	−	0.825541i	$-0.690870\pi$
$821$	−311.690	+	129.106i	−0.379647	+	0.157255i	0.184695	+	0.982796i	$0.440870\pi$
$822$		0			0
$823$	551.973	+	228.635i	0.670684	+	0.277806i	0.691926	−	0.721968i	$-0.256762\pi$
$823$	551.973	+	228.635i	0.670684	+	0.277806i	−0.0212428	+	0.999774i	$0.506762\pi$
$824$		0			0
$825$	−2.21354	−	2.21354i	−0.00268308	−	0.00268308i
$826$		0			0
$827$	166.845	−	402.800i	0.201747	−	0.487061i	−0.790331	−	0.612680i	$-0.790092\pi$
$827$	166.845	−	402.800i	0.201747	−	0.487061i	0.992079	+	0.125618i	$0.0400915\pi$
$828$		0			0
$829$	489.318			0.590250			0.295125	−	0.955459i	$-0.404639\pi$
$829$	489.318			0.590250			0.295125	+	0.955459i	$0.404639\pi$
$830$		0			0
$831$	−12.2551	+	12.2551i	−0.0147474	+	0.0147474i
$832$		0			0
$833$	559.086	−	617.505i	0.671171	−	0.741302i
$834$		0			0
$835$	296.402	+	296.402i	0.354973	+	0.354973i
$836$		0			0
$837$			39.4148i			0.0470906i
$838$		0			0
$839$	−620.176	−	256.885i	−0.739184	−	0.306180i	−0.0188642	−	0.999822i	$-0.506005\pi$
$839$	−620.176	−	256.885i	−0.739184	−	0.306180i	−0.720320	+	0.693642i	$0.756005\pi$
$840$		0			0
$841$	−552.424	+	552.424i	−0.656866	+	0.656866i
$842$		0			0
$843$	−3.75685	+	9.06983i	−0.00445652	+	0.0107590i
$844$		0			0
$845$	−89.0859	−	215.072i	−0.105427	−	0.254524i
$846$		0			0
$847$	−25.1226	+	779.925i	−0.0296607	+	0.920809i
$848$		0			0
$849$	25.1576			0.0296320
$850$		0			0
$851$	−60.6565			−0.0712768
$852$		0			0
$853$	−75.8387	+	31.4134i	−0.0889082	+	0.0368270i	−0.426694	−	0.904396i	$-0.640322\pi$
$853$	−75.8387	+	31.4134i	−0.0889082	+	0.0368270i	0.337786	+	0.941223i	$0.390322\pi$
$854$		0			0
$855$	213.097	−	88.2675i	0.249236	−	0.103237i
$856$		0			0
$857$	−418.831	+	1011.15i	−0.488717	+	1.17987i	0.466648	+	0.884443i	$0.345461\pi$
$857$	−418.831	+	1011.15i	−0.488717	+	1.17987i	−0.955366	+	0.295425i	$0.904539\pi$
$858$		0			0
$859$	−797.773	−	797.773i	−0.928722	−	0.928722i	0.0689011	−	0.997623i	$-0.478051\pi$
$859$	−797.773	−	797.773i	−0.928722	−	0.928722i	−0.997623	+	0.0689011i	$0.978051\pi$
$860$		0			0
$861$	9.40510	−	8.81811i	0.0109235	−	0.0102417i
$862$		0			0
$863$		−	1261.19i		−	1.46140i	−0.682696	−	0.730702i	$-0.739193\pi$
$863$		−	1261.19i		−	1.46140i	0.682696	−	0.730702i	$-0.260807\pi$
$864$		0			0
$865$	426.707	+	426.707i	0.493303	+	0.493303i
$866$		0			0
$867$	−9.12716	−	12.7653i	−0.0105273	−	0.0147235i
$868$		0			0
$869$	21.3797	+	21.3797i	0.0246027	+	0.0246027i
$870$		0			0
$871$	199.463			0.229005
$872$		0			0
$873$	−715.945	−	296.554i	−0.820097	−	0.339695i
$874$		0			0
$875$	271.133	+	719.238i	0.309866	+	0.821986i
$876$		0			0
$877$	−928.702	−	384.681i	−1.05895	−	0.438633i	−0.215874	−	0.976421i	$-0.569260\pi$
$877$	−928.702	−	384.681i	−1.05895	−	0.438633i	−0.843080	+	0.537788i	$0.819260\pi$
$878$		0			0
$879$	−13.9019	+	5.75836i	−0.0158156	+	0.00655103i
$880$		0			0
$881$	−1429.68	+	592.195i	−1.62280	+	0.672185i	−0.994397	−	0.105706i	$-0.966290\pi$
$881$	−1429.68	+	592.195i	−1.62280	+	0.672185i	−0.628400	+	0.777891i	$0.716290\pi$
$882$		0			0
$883$	−1336.76			−1.51389			−0.756943	−	0.653481i	$-0.773308\pi$
$883$	−1336.76			−1.51389			−0.756943	+	0.653481i	$0.773308\pi$
$884$		0			0
$885$			10.1312i			0.0114477i
$886$		0			0
$887$	−262.827	+	108.867i	−0.296310	+	0.122736i	−0.525886	−	0.850555i	$-0.676266\pi$
$887$	−262.827	+	108.867i	−0.296310	+	0.122736i	0.229576	+	0.973291i	$0.426266\pi$
$888$		0			0
$889$	−192.386	−	6.19703i	−0.216407	−	0.00697079i
$890$		0			0
$891$	230.723	+	95.5684i	0.258948	+	0.107260i
$892$		0			0
$893$	186.152	−	186.152i	0.208457	−	0.208457i
$894$		0			0
$895$	14.7408	+	6.10585i	0.0164702	+	0.00682218i
$896$		0			0
$897$			0.816661i			0.000910436i
$898$		0			0
$899$	220.460	−	220.460i	0.245228	−	0.245228i
$900$		0			0
$901$	−99.7683	−	871.280i	−0.110731	−	0.967015i
$902$		0			0
$903$	−0.674887	+	0.254414i	−0.000747383	+	0.000281743i
$904$		0			0
$905$			719.378i			0.794893i
$906$		0			0
$907$	−93.9464	+	226.807i	−0.103579	+	0.250062i	−0.967170	−	0.254132i	$-0.918210\pi$
$907$	−93.9464	+	226.807i	−0.103579	+	0.250062i	0.863590	+	0.504194i	$0.168210\pi$
$908$		0			0
$909$	−321.044	−	321.044i	−0.353183	−	0.353183i
$910$		0			0
$911$	104.765	+	43.3950i	0.115000	+	0.0476345i	0.439441	−	0.898271i	$-0.355176\pi$
$911$	104.765	+	43.3950i	0.115000	+	0.0476345i	−0.324442	+	0.945906i	$0.605176\pi$
$912$		0			0
$913$	153.428	+	370.407i	0.168048	+	0.405703i
$914$		0			0
$915$	5.01008	−	2.07524i	0.00547549	−	0.00226802i
$916$		0			0
$917$	1.02778	−	2.27153i	0.00112081	−	0.00247713i
$918$		0			0
$919$	−330.988			−0.360161			−0.180081	−	0.983652i	$-0.557636\pi$
$919$	−330.988			−0.360161			−0.180081	+	0.983652i	$0.557636\pi$
$920$		0			0
$921$	−8.75254	−	21.1305i	−0.00950331	−	0.0229430i
$922$		0			0
$923$	−304.080	−	734.114i	−0.329447	−	0.795356i
$924$		0			0
$925$	608.377	+	251.998i	0.657705	+	0.272430i
$926$		0			0
$927$	206.391	+	206.391i	0.222644	+	0.222644i
$928$		0			0
$929$	−549.576	−	227.642i	−0.591578	−	0.245039i	0.0667516	−	0.997770i	$-0.478736\pi$
$929$	−549.576	−	227.642i	−0.591578	−	0.245039i	−0.658329	+	0.752730i	$0.728736\pi$
$930$		0			0
$931$	−329.875	−	375.355i	−0.354323	−	0.403174i
$932$		0			0
$933$	8.81350	+	8.81350i	0.00944641	+	0.00944641i
$934$		0			0
$935$	103.263	+	82.0440i	0.110442	+	0.0877476i
$936$		0			0
$937$	−1227.11	+	1227.11i	−1.30962	+	1.30962i	−0.387927	+	0.921690i	$0.626809\pi$
$937$	−1227.11	+	1227.11i	−1.30962	+	1.30962i	−0.921690	+	0.387927i	$0.873191\pi$
$938$		0			0
$939$		−	13.8086i		−	0.0147057i
$940$		0			0
$941$	769.313	+	318.660i	0.817548	+	0.338640i	0.751961	−	0.659207i	$-0.229108\pi$
$941$	769.313	+	318.660i	0.817548	+	0.338640i	0.0655871	+	0.997847i	$0.479108\pi$
$942$		0			0
$943$	−41.2699	−	41.2699i	−0.0437645	−	0.0437645i
$944$		0			0
$945$	11.7619	+	12.5448i	0.0124464	+	0.0132750i
$946$		0			0
$947$	1075.24	−	445.381i	1.13542	−	0.470307i	0.265801	−	0.964028i	$-0.414364\pi$
$947$	1075.24	−	445.381i	1.13542	−	0.470307i	0.869620	+	0.493721i	$0.164364\pi$
$948$		0			0
$949$	−258.361	−	623.738i	−0.272245	−	0.657258i
$950$		0			0
$951$		−	3.44117i		−	0.00361848i
$952$		0			0
$953$	−650.038			−0.682097			−0.341048	−	0.940046i	$-0.610782\pi$
$953$	−650.038			−0.682097			−0.341048	+	0.940046i	$0.610782\pi$
$954$		0			0
$955$	175.758	−	72.8011i	0.184039	−	0.0762316i
$956$		0			0
$957$	0.495721	+	1.19678i	0.000517995	+	0.00125055i
$958$		0			0
$959$	−180.326	−	192.330i	−0.188035	−	0.200553i
$960$		0			0
$961$	470.760	−	470.760i	0.489865	−	0.489865i
$962$		0			0
$963$	204.159	−	492.883i	0.212003	−	0.511820i
$964$		0			0
$965$	−113.547			−0.117665
$966$		0			0
$967$	106.450	+	106.450i	0.110083	+	0.110083i	0.760003	−	0.649920i	$-0.225197\pi$
$967$	106.450	+	106.450i	0.110083	+	0.110083i	−0.649920	+	0.760003i	$0.725197\pi$
$968$		0			0
$969$	−8.23095	+	4.56857i	−0.00849427	+	0.00471473i
$970$		0			0
$971$	−826.660	+	826.660i	−0.851349	+	0.851349i	−0.990299	−	0.138950i	$-0.955627\pi$
$971$	−826.660	+	826.660i	−0.851349	+	0.851349i	0.138950	+	0.990299i	$0.455627\pi$
$972$		0			0
$973$	1139.21	+	515.449i	1.17082	+	0.529752i
$974$		0			0
$975$	3.39283	−	8.19101i	0.00347982	−	0.00840103i
$976$		0			0
$977$	−927.438	+	927.438i	−0.949271	+	0.949271i	−0.998774	−	0.0495026i	$-0.984236\pi$
$977$	−927.438	+	927.438i	−0.949271	+	0.949271i	0.0495026	+	0.998774i	$0.484236\pi$
$978$		0			0
$979$	−73.8645	+	178.325i	−0.0754490	+	0.182150i
$980$		0			0
$981$	97.6533	−	40.4493i	0.0995447	−	0.0412327i
$982$		0			0
$983$	582.485	−	241.273i	0.592559	−	0.245446i	−0.0661921	−	0.997807i	$-0.521085\pi$
$983$	582.485	−	241.273i	0.592559	−	0.245446i	0.658751	+	0.752361i	$0.271085\pi$
$984$		0			0
$985$		−	38.7318i		−	0.0393217i
$986$		0			0
$987$	8.93952	+	4.04479i	0.00905726	+	0.00409807i
$988$		0			0
$989$	1.24951	+	3.01657i	0.00126340	+	0.00305012i
$990$		0			0
$991$	1031.18	−	427.130i	1.04055	−	0.431009i	0.204039	−	0.978963i	$-0.434593\pi$
$991$	1031.18	−	427.130i	1.04055	−	0.431009i	0.836508	+	0.547954i	$0.184593\pi$
$992$		0			0
$993$	10.1750	−	24.5647i	0.0102468	−	0.0247379i
$994$		0			0
$995$	198.041	−	198.041i	0.199036	−	0.199036i
$996$		0			0
$997$	947.942	+	392.651i	0.950795	+	0.393832i	0.803529	−	0.595265i	$-0.202953\pi$
$997$	947.942	+	392.651i	0.950795	+	0.393832i	0.147265	+	0.989097i	$0.452953\pi$
$998$		0			0
$999$	34.4482			0.0344827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.x.a.321.12	✓	96
7.6	odd	2	inner	476.3.x.a.321.13	yes	96
17.8	even	8	inner	476.3.x.a.433.13	yes	96
119.76	odd	8	inner	476.3.x.a.433.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.x.a.321.12	✓	96	1.1	even	1	trivial
476.3.x.a.321.13	yes	96	7.6	odd	2	inner
476.3.x.a.433.12	yes	96	119.76	odd	8	inner
476.3.x.a.433.13	yes	96	17.8	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0501663 + 0.0207796i) q^{3} +(0.962011 + 2.32250i) q^{5} +(4.78783 + 5.10654i) q^{7} +(-6.36188 + 6.36188i) q^{9} +(-1.18102 + 2.85123i) q^{11} -8.74049 q^{13} +(-0.0965212 - 0.0965212i) q^{15} +(-13.3103 - 10.5752i) q^{17} +(-7.21117 + 7.21117i) q^{19} +(-0.346299 - 0.156687i) q^{21} +(-0.658489 + 1.58973i) q^{23} +(13.2091 - 13.2091i) q^{25} +(0.373971 - 0.902846i) q^{27} +(-7.14167 + 2.95818i) q^{29} +(-37.2629 + 15.4348i) q^{31} -0.167577i q^{33} +(-7.25399 + 16.0323i) q^{35} +(13.4899 + 32.5675i) q^{37} +(0.438478 - 0.181624i) q^{39} +(-12.9801 + 31.3368i) q^{41} +(1.34176 - 1.34176i) q^{43} +(-20.8957 - 8.65526i) q^{45} -25.8144 q^{47} +(-3.15346 + 48.8984i) q^{49} +(0.887479 + 0.253938i) q^{51} +(36.4773 + 36.4773i) q^{53} -7.75813 q^{55} +(0.211913 - 0.511603i) q^{57} +(-52.4817 - 52.4817i) q^{59} +(-15.2031 + 36.7034i) q^{61} +(-62.9467 - 2.02761i) q^{63} +(-8.40845 - 20.2998i) q^{65} -22.8206 q^{67} -0.0934342i q^{69} +(34.7898 + 83.9900i) q^{71} +(29.5591 + 71.3619i) q^{73} +(-0.388174 + 0.937134i) q^{75} +(-20.2144 + 7.62027i) q^{77} +(3.74921 - 9.05140i) q^{79} -80.9204i q^{81} +(91.8612 - 91.8612i) q^{83} +(11.7563 - 41.0867i) q^{85} +(0.296802 - 0.296802i) q^{87} +62.5431 q^{89} +(-41.8479 - 44.6336i) q^{91} +(1.54861 - 1.54861i) q^{93} +(-23.6852 - 9.81072i) q^{95} +(32.9612 + 79.5755i) q^{97} +(-10.6257 - 25.6526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{11} - 16 q^{15} + 72 q^{23} + 72 q^{25} + 32 q^{35} - 256 q^{37} - 88 q^{39} - 32 q^{43} - 20 q^{49} - 120 q^{51} - 80 q^{53} + 492 q^{63} - 104 q^{65} - 144 q^{67} - 64 q^{71} + 84 q^{77}+ \cdots + 560 q^{99}+O(q^{100}) \) 96 * q - 40 * q^11 - 16 * q^15 + 72 * q^23 + 72 * q^25 + 32 * q^35 - 256 * q^37 - 88 * q^39 - 32 * q^43 - 20 * q^49 - 120 * q^51 - 80 * q^53 + 492 * q^63 - 104 * q^65 - 144 * q^67 - 64 * q^71 + 84 * q^77 - 256 * q^79 + 824 * q^85 - 368 * q^91 - 264 * q^93 + 104 * q^95 + 560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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