LMFDB - Embedded newform 476.2.bl.a.465.12

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			465.12
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.51390 + 0.853353i) q^{3} +(0.0888586 - 1.35572i) q^{5} +(1.43000 + 2.22601i) q^{7} +(3.21140 + 2.46420i) q^{9} +O(q^{10})$	\(q+(2.51390 + 0.853353i) q^{3} +(0.0888586 - 1.35572i) q^{5} +(1.43000 + 2.22601i) q^{7} +(3.21140 + 2.46420i) q^{9} +(-1.32853 - 1.16509i) q^{11} +(1.91798 + 1.91798i) q^{13} +(1.38029 - 3.33231i) q^{15} +(-4.11902 + 0.183527i) q^{17} +(2.00973 - 0.264586i) q^{19} +(1.69530 + 6.81624i) q^{21} +(-0.196735 - 0.579563i) q^{23} +(3.12714 + 0.411696i) q^{25} +(1.54555 + 2.31308i) q^{27} +(-2.69119 - 1.79820i) q^{29} +(3.49639 - 10.3000i) q^{31} +(-2.34556 - 4.06262i) q^{33} +(3.14491 - 1.74088i) q^{35} +(0.329279 + 0.375471i) q^{37} +(3.18490 + 6.45833i) q^{39} +(-9.87781 + 6.60014i) q^{41} +(-7.74057 + 3.20625i) q^{43} +(3.62612 - 4.13480i) q^{45} +(-1.39224 + 5.19590i) q^{47} +(-2.91020 + 6.36637i) q^{49} +(-10.5114 - 3.05361i) q^{51} +(3.76118 - 2.88605i) q^{53} +(-1.69759 + 1.69759i) q^{55} +(5.27805 + 1.04987i) q^{57} +(0.939455 - 7.13587i) q^{59} +(3.38029 - 6.85455i) q^{61} +(-0.893010 + 10.6724i) q^{63} +(2.77068 - 2.42982i) q^{65} +(-1.03219 - 0.595934i) q^{67} -1.62485i q^{69} +(-1.90822 + 0.379568i) q^{71} +(-3.60559 + 1.77808i) q^{73} +(7.50999 + 3.70352i) q^{75} +(0.693699 - 4.62340i) q^{77} +(4.57637 - 1.55347i) q^{79} +(-1.23153 - 4.59614i) q^{81} +(-11.2223 - 4.64841i) q^{83} +(-0.117199 + 5.60055i) q^{85} +(-5.23088 - 6.81702i) q^{87} +(15.7381 + 4.21702i) q^{89} +(-1.52673 + 7.01216i) q^{91} +(17.5791 - 22.9095i) q^{93} +(-0.180123 - 2.74815i) q^{95} +(-4.66312 + 6.97885i) q^{97} +(-1.39544 - 7.01534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.51390	+	0.853353i	1.45140	+	0.492683i	0.932192	−	0.361965i	$-0.117894\pi$
$3$	2.51390	+	0.853353i	1.45140	+	0.492683i	0.519207	+	0.854648i	$0.326227\pi$
$4$		0			0
$5$	0.0888586	−	1.35572i	0.0397388	−	0.606297i	−0.930827	−	0.365460i	$-0.880912\pi$
$5$	0.0888586	−	1.35572i	0.0397388	−	0.606297i	0.970566	−	0.240836i	$-0.0774217\pi$
$6$		0			0
$7$	1.43000	+	2.22601i	0.540489	+	0.841351i
$7$	1.43000	+	2.22601i	0.540489	+	0.841351i
$8$		0			0
$9$	3.21140	+	2.46420i	1.07047	+	0.821399i
$10$		0			0
$11$	−1.32853	−	1.16509i	−0.400567	−	0.351288i	0.435237	−	0.900316i	$-0.356665\pi$
$11$	−1.32853	−	1.16509i	−0.400567	−	0.351288i	−0.835804	+	0.549028i	$0.814998\pi$
$12$		0			0
$13$	1.91798	+	1.91798i	0.531953	+	0.531953i	0.921153	−	0.389200i	$-0.127249\pi$
$13$	1.91798	+	1.91798i	0.531953	+	0.531953i	−0.389200	+	0.921153i	$0.627249\pi$
$14$		0			0
$15$	1.38029	−	3.33231i	0.356389	−	0.860399i
$16$		0			0
$17$	−4.11902	+	0.183527i	−0.999009	+	0.0445118i
$17$	−4.11902	+	0.183527i	−0.999009	+	0.0445118i
$18$		0			0
$19$	2.00973	−	0.264586i	0.461064	−	0.0607003i	0.103584	−	0.994621i	$-0.466969\pi$
$19$	2.00973	−	0.264586i	0.461064	−	0.0607003i	0.357481	+	0.933920i	$0.383636\pi$
$20$		0			0
$21$	1.69530	+	6.81624i	0.369945	+	1.48743i
$22$		0			0
$23$	−0.196735	−	0.579563i	−0.0410221	−	0.120847i	0.924489	−	0.381208i	$-0.124492\pi$
$23$	−0.196735	−	0.579563i	−0.0410221	−	0.120847i	−0.965511	+	0.260361i	$0.916159\pi$
$24$		0			0
$25$	3.12714	+	0.411696i	0.625429	+	0.0823392i
$26$		0			0
$27$	1.54555	+	2.31308i	0.297441	+	0.445152i
$28$		0			0
$29$	−2.69119	−	1.79820i	−0.499742	−	0.333917i	0.280019	−	0.959995i	$-0.409659\pi$
$29$	−2.69119	−	1.79820i	−0.499742	−	0.333917i	−0.779761	+	0.626078i	$0.784659\pi$
$30$		0			0
$31$	3.49639	−	10.3000i	0.627970	−	1.84994i	0.111233	−	0.993794i	$-0.464520\pi$
$31$	3.49639	−	10.3000i	0.627970	−	1.84994i	0.516737	−	0.856144i	$-0.327147\pi$
$32$		0			0
$33$	−2.34556	−	4.06262i	−0.408309	−	0.707212i
$34$		0			0
$35$	3.14491	−	1.74088i	0.531587	−	0.294262i
$36$		0			0
$37$	0.329279	+	0.375471i	0.0541332	+	0.0617271i	0.778273	−	0.627926i	$-0.216096\pi$
$37$	0.329279	+	0.375471i	0.0541332	+	0.0617271i	−0.724139	+	0.689654i	$0.757763\pi$
$38$		0			0
$39$	3.18490	+	6.45833i	0.509991	+	1.03416i
$40$		0			0
$41$	−9.87781	+	6.60014i	−1.54265	+	1.03077i	−0.563873	+	0.825861i	$0.690689\pi$
$41$	−9.87781	+	6.60014i	−1.54265	+	1.03077i	−0.978781	+	0.204908i	$0.934311\pi$
$42$		0			0
$43$	−7.74057	+	3.20625i	−1.18043	+	0.488948i	−0.884626	−	0.466301i	$-0.845586\pi$
$43$	−7.74057	+	3.20625i	−1.18043	+	0.488948i	−0.295800	+	0.955250i	$0.595586\pi$
$44$		0			0
$45$	3.62612	−	4.13480i	0.540550	−	0.616380i
$46$		0			0
$47$	−1.39224	+	5.19590i	−0.203079	+	0.757900i	0.786948	+	0.617019i	$0.211660\pi$
$47$	−1.39224	+	5.19590i	−0.203079	+	0.757900i	−0.990027	+	0.140881i	$0.955007\pi$
$48$		0			0
$49$	−2.91020	+	6.36637i	−0.415743	+	0.909482i
$50$		0			0
$51$	−10.5114	−	3.05361i	−1.47189	−	0.427591i
$52$		0			0
$53$	3.76118	−	2.88605i	0.516637	−	0.396430i	−0.317269	−	0.948336i	$-0.602766\pi$
$53$	3.76118	−	2.88605i	0.516637	−	0.396430i	0.833906	+	0.551906i	$0.186099\pi$
$54$		0			0
$55$	−1.69759	+	1.69759i	−0.228903	+	0.228903i
$56$		0			0
$57$	5.27805	+	1.04987i	0.699094	+	0.139058i
$58$		0			0
$59$	0.939455	−	7.13587i	0.122307	−	0.929011i	−0.814745	−	0.579820i	$-0.803123\pi$
$59$	0.939455	−	7.13587i	0.122307	−	0.929011i	0.937052	−	0.349191i	$-0.113544\pi$
$60$		0			0
$61$	3.38029	−	6.85455i	0.432802	−	0.877635i	−0.565788	−	0.824551i	$-0.691428\pi$
$61$	3.38029	−	6.85455i	0.432802	−	0.877635i	0.998590	−	0.0530845i	$-0.0169053\pi$
$62$		0			0
$63$	−0.893010	+	10.6724i	−0.112509	+	1.34460i
$64$		0			0
$65$	2.77068	−	2.42982i	0.343660	−	0.301382i
$66$		0			0
$67$	−1.03219	−	0.595934i	−0.126102	−	0.0728050i	0.435622	−	0.900130i	$-0.356528\pi$
$67$	−1.03219	−	0.595934i	−0.126102	−	0.0728050i	−0.561724	+	0.827325i	$0.689862\pi$
$68$		0			0
$69$		−	1.62485i		−	0.195609i
$70$		0			0
$71$	−1.90822	+	0.379568i	−0.226464	+	0.0450464i	−0.307018	−	0.951704i	$-0.599331\pi$
$71$	−1.90822	+	0.379568i	−0.226464	+	0.0450464i	0.0805540	+	0.996750i	$0.474331\pi$
$72$		0			0
$73$	−3.60559	+	1.77808i	−0.422002	+	0.208109i	−0.640876	−	0.767645i	$-0.721429\pi$
$73$	−3.60559	+	1.77808i	−0.422002	+	0.208109i	0.218873	+	0.975753i	$0.429762\pi$
$74$		0			0
$75$	7.50999	+	3.70352i	0.867179	+	0.427645i
$76$		0			0
$77$	0.693699	−	4.62340i	0.0790544	−	0.526885i
$78$		0			0
$79$	4.57637	−	1.55347i	0.514882	−	0.174779i	−0.0518911	−	0.998653i	$-0.516525\pi$
$79$	4.57637	−	1.55347i	0.514882	−	0.174779i	0.566773	+	0.823874i	$0.308192\pi$
$80$		0			0
$81$	−1.23153	−	4.59614i	−0.136837	−	0.510683i
$82$		0			0
$83$	−11.2223	−	4.64841i	−1.23180	−	0.510229i	−0.330659	−	0.943750i	$-0.607271\pi$
$83$	−11.2223	−	4.64841i	−1.23180	−	0.510229i	−0.901143	+	0.433521i	$0.857271\pi$
$84$		0			0
$85$	−0.117199	+	5.60055i	−0.0127121	+	0.607464i
$86$		0			0
$87$	−5.23088	−	6.81702i	−0.560810	−	0.730861i
$88$		0			0
$89$	15.7381	+	4.21702i	1.66824	+	0.447003i	0.964635	−	0.263589i	$-0.0849063\pi$
$89$	15.7381	+	4.21702i	1.66824	+	0.447003i	0.703604	+	0.710592i	$0.251573\pi$
$90$		0			0
$91$	−1.52673	+	7.01216i	−0.160044	+	0.735074i
$92$		0			0
$93$	17.5791	−	22.9095i	1.82287	−	2.37561i
$94$		0			0
$95$	−0.180123	−	2.74815i	−0.0184802	−	0.281954i
$96$		0			0
$97$	−4.66312	+	6.97885i	−0.473468	+	0.708595i	−0.988941	−	0.148311i	$-0.952616\pi$
$97$	−4.66312	+	6.97885i	−0.473468	+	0.708595i	0.515473	+	0.856906i	$0.327616\pi$
$98$		0			0
$99$	−1.39544	−	7.01534i	−0.140247	−	0.705068i
$100$		0			0
$101$	−1.03043	+	1.78476i	−0.102532	+	0.177590i	−0.912727	−	0.408570i	$-0.866028\pi$
$101$	−1.03043	+	1.78476i	−0.102532	+	0.177590i	0.810195	+	0.586160i	$0.199361\pi$
$102$		0			0
$103$	−10.2598	+	5.92350i	−1.01093	+	0.583659i	−0.911463	−	0.411382i	$-0.865046\pi$
$103$	−10.2598	+	5.92350i	−1.01093	+	0.583659i	−0.0994645	+	0.995041i	$0.531713\pi$
$104$		0			0
$105$	9.39156	−	1.69267i	0.916522	−	0.165188i
$106$		0			0
$107$	−16.8215	−	1.10254i	−1.62619	−	0.106586i	−0.775183	−	0.631737i	$-0.782342\pi$
$107$	−16.8215	−	1.10254i	−1.62619	−	0.106586i	−0.851010	+	0.525150i	$0.824009\pi$
$108$		0			0
$109$	7.62625	−	0.499851i	0.730462	−	0.0478770i	0.304366	−	0.952555i	$-0.401555\pi$
$109$	7.62625	−	0.499851i	0.730462	−	0.0478770i	0.426096	+	0.904678i	$0.359889\pi$
$110$		0			0
$111$	0.507365	+	1.22489i	0.0481570	+	0.116261i
$112$		0			0
$113$	0.0749986	−	0.377043i	0.00705527	−	0.0354693i	−0.977097	−	0.212793i	$-0.931744\pi$
$113$	0.0749986	−	0.377043i	0.00705527	−	0.0354693i	0.984153	+	0.177324i	$0.0567440\pi$
$114$		0			0
$115$	−0.803207	+	0.215219i	−0.0748995	+	0.0200693i
$116$		0			0
$117$	1.43313	+	10.8857i	0.132493	+	1.00638i
$118$		0			0
$119$	−6.29873	−	8.90652i	−0.577403	−	0.816459i
$120$		0			0
$121$	−1.02823	−	7.81017i	−0.0934754	−	0.710016i
$122$		0			0
$123$	−30.4640	+	8.16281i	−2.74685	+	0.736016i
$124$		0			0
$125$	2.16130	−	10.8656i	0.193312	−	0.971846i
$126$		0			0
$127$	−6.31104	−	15.2362i	−0.560014	−	1.35199i	−0.909755	−	0.415147i	$-0.863730\pi$
$127$	−6.31104	−	15.2362i	−0.560014	−	1.35199i	0.349741	−	0.936847i	$-0.386270\pi$
$128$		0			0
$129$	−22.1951	+	1.45474i	−1.95417	+	0.128083i
$130$		0			0
$131$	4.74891	+	0.311260i	0.414914	+	0.0271949i	0.271431	−	0.962458i	$-0.412503\pi$
$131$	4.74891	+	0.311260i	0.414914	+	0.0271949i	0.143483	+	0.989653i	$0.454170\pi$
$132$		0			0
$133$	3.46289	+	4.09532i	0.300270	+	0.355109i
$134$		0			0
$135$	3.27322	−	1.88979i	0.281714	−	0.162648i
$136$		0			0
$137$	−3.79924	+	6.58048i	−0.324591	+	0.562209i	−0.981430	−	0.191823i	$-0.938560\pi$
$137$	−3.79924	+	6.58048i	−0.324591	+	0.562209i	0.656838	+	0.754032i	$0.271893\pi$
$138$		0			0
$139$	1.82692	+	9.18452i	0.154957	+	0.779021i	0.977601	+	0.210465i	$0.0674978\pi$
$139$	1.82692	+	9.18452i	0.154957	+	0.779021i	−0.822644	+	0.568556i	$0.807502\pi$
$140$		0			0
$141$	−7.93388	+	11.8739i	−0.668153	+	0.999961i
$142$		0			0
$143$	−0.313476	−	4.78273i	−0.0262142	−	0.399952i
$144$		0			0
$145$	−2.67699	+	3.48872i	−0.222312	+	0.289722i
$146$		0			0
$147$	−12.7487	+	13.5210i	−1.05150	+	1.11519i
$148$		0			0
$149$	0.208854	+	0.0559623i	0.0171100	+	0.00458461i	0.267364	−	0.963596i	$-0.413847\pi$
$149$	0.208854	+	0.0559623i	0.0171100	+	0.00458461i	−0.250254	+	0.968180i	$0.580514\pi$
$150$		0			0
$151$	−1.57088	−	2.04721i	−0.127836	−	0.166599i	0.725050	−	0.688696i	$-0.241817\pi$
$151$	−1.57088	−	2.04721i	−0.127836	−	0.166599i	−0.852886	+	0.522097i	$0.825150\pi$
$152$		0			0
$153$	−13.6801	−	9.56069i	−1.10597	−	0.772936i
$154$		0			0
$155$	−13.6533	−	5.65537i	−1.09666	−	0.454250i
$156$		0			0
$157$	4.85959	+	18.1362i	0.387837	+	1.44743i	0.833645	+	0.552300i	$0.186250\pi$
$157$	4.85959	+	18.1362i	0.387837	+	1.44743i	−0.445808	+	0.895129i	$0.647084\pi$
$158$		0			0
$159$	11.9180	−	4.04563i	0.945161	−	0.320839i
$160$		0			0
$161$	1.00878	−	1.26671i	0.0795030	−	0.0998306i
$162$		0			0
$163$	−2.86145	−	1.41111i	−0.224126	−	0.110527i	0.326759	−	0.945108i	$-0.394043\pi$
$163$	−2.86145	−	1.41111i	−0.224126	−	0.110527i	−0.550886	+	0.834581i	$0.685710\pi$
$164$		0			0
$165$	−5.71620	+	2.81892i	−0.445006	+	0.219453i
$166$		0			0
$167$	11.8854	−	2.36416i	0.919722	−	0.182944i	0.287544	−	0.957767i	$-0.407161\pi$
$167$	11.8854	−	2.36416i	0.919722	−	0.182944i	0.632178	+	0.774823i	$0.282161\pi$
$168$		0			0
$169$		−	5.64268i		−	0.434052i
$170$		0			0
$171$	7.10606	+	4.10268i	0.543414	+	0.313740i
$172$		0			0
$173$	12.6273	−	11.0739i	0.960039	−	0.841931i	−0.0274497	−	0.999623i	$-0.508739\pi$
$173$	12.6273	−	11.0739i	0.960039	−	0.841931i	0.987488	+	0.157692i	$0.0504053\pi$
$174$		0			0
$175$	3.55537	+	7.54976i	0.268761	+	0.570708i
$176$		0			0
$177$	8.45110	−	17.1371i	0.635224	−	1.28811i
$178$		0			0
$179$	−0.531511	+	4.03722i	−0.0397270	+	0.301756i	0.960034	+	0.279884i	$0.0902960\pi$
$179$	−0.531511	+	4.03722i	−0.0397270	+	0.301756i	−0.999761	+	0.0218722i	$0.993037\pi$
$180$		0			0
$181$	7.20342	+	1.43285i	0.535426	+	0.106503i	0.455395	−	0.890290i	$-0.349498\pi$
$181$	7.20342	+	1.43285i	0.535426	+	0.106503i	0.0800310	+	0.996792i	$0.474498\pi$
$182$		0			0
$183$	14.3470	−	14.3470i	1.06056	−	1.06056i
$184$		0			0
$185$	0.538293	−	0.413047i	0.0395761	−	0.0303678i
$186$		0			0
$187$	5.68607	+	4.55521i	0.415807	+	0.333110i
$188$		0			0
$189$	−2.93879	+	6.74809i	−0.213765	+	0.490852i
$190$		0			0
$191$	0.635100	−	2.37023i	0.0459542	−	0.171503i	−0.939135	−	0.343549i	$-0.888371\pi$
$191$	0.635100	−	2.37023i	0.0459542	−	0.171503i	0.985089	+	0.172045i	$0.0550376\pi$
$192$		0			0
$193$	−13.0785	+	14.9132i	−0.941412	+	1.07347i	0.0557697	+	0.998444i	$0.482239\pi$
$193$	−13.0785	+	14.9132i	−0.941412	+	1.07347i	−0.997181	+	0.0750304i	$0.976095\pi$
$194$		0			0
$195$	9.03869	−	3.74395i	0.647274	−	0.268110i
$196$		0			0
$197$	0.955103	−	0.638179i	0.0680483	−	0.0454684i	−0.521081	−	0.853507i	$-0.674471\pi$
$197$	0.955103	−	0.638179i	0.0680483	−	0.0454684i	0.589129	+	0.808039i	$0.299471\pi$
$198$		0			0
$199$	2.31019	+	4.68460i	0.163765	+	0.332082i	0.963251	−	0.268602i	$-0.0865616\pi$
$199$	2.31019	+	4.68460i	0.163765	+	0.332082i	−0.799486	+	0.600684i	$0.794895\pi$
$200$		0			0
$201$	−2.08627	−	2.37894i	−0.147154	−	0.167797i
$202$		0			0
$203$	0.154393	−	8.56203i	0.0108363	−	0.600937i
$204$		0			0
$205$	8.07022	+	13.9780i	0.563648	+	0.976268i
$206$		0			0
$207$	0.796362	−	2.34601i	0.0553510	−	0.163059i
$208$		0			0
$209$	−2.97826	−	1.99001i	−0.206011	−	0.137652i
$210$		0			0
$211$	−9.59814	−	14.3646i	−0.660763	−	0.988902i	−0.998857	−	0.0477900i	$-0.984782\pi$
$211$	−9.59814	−	14.3646i	−0.660763	−	0.988902i	0.338094	−	0.941112i	$-0.390218\pi$
$212$		0			0
$213$	−5.12096	−	0.674188i	−0.350883	−	0.0461946i
$214$		0			0
$215$	3.65896	+	10.7790i	0.249539	+	0.735118i
$216$		0			0
$217$	27.9277	−	6.94605i	1.89586	−	0.471529i
$218$		0			0
$219$	−10.5814	+	1.39307i	−0.715025	+	0.0941349i
$220$		0			0
$221$	−8.25221	−	7.54821i	−0.555104	−	0.507748i
$222$		0			0
$223$	−2.21926	+	5.35776i	−0.148612	+	0.358782i	−0.980602	−	0.196009i	$-0.937202\pi$
$223$	−2.21926	+	5.35776i	−0.148612	+	0.358782i	0.831990	+	0.554791i	$0.187202\pi$
$224$		0			0
$225$	9.02802	+	9.02802i	0.601868	+	0.601868i
$226$		0			0
$227$	16.8790	+	14.8025i	1.12030	+	0.982473i	0.999947	−	0.0102586i	$-0.00326546\pi$
$227$	16.8790	+	14.8025i	1.12030	+	0.982473i	0.120349	+	0.992732i	$0.461599\pi$
$228$		0			0
$229$	10.5639	+	8.10595i	0.698081	+	0.535656i	0.895720	−	0.444619i	$-0.146661\pi$
$229$	10.5639	+	8.10595i	0.698081	+	0.535656i	−0.197639	+	0.980275i	$0.563327\pi$
$230$		0			0
$231$	5.68928	−	11.0308i	0.374327	−	0.725772i
$232$		0			0
$233$	−0.804195	+	12.2696i	−0.0526846	+	0.803811i	0.887000	+	0.461769i	$0.152785\pi$
$233$	−0.804195	+	12.2696i	−0.0526846	+	0.803811i	−0.939685	+	0.342042i	$0.888881\pi$
$234$		0			0
$235$	6.92047	+	2.34918i	0.451442	+	0.153244i
$236$		0			0
$237$	12.8302			0.833410
$238$		0			0
$239$	14.7733			0.955608			0.477804	−	0.878467i	$-0.341433\pi$
$239$	14.7733			0.955608			0.477804	+	0.878467i	$0.341433\pi$
$240$		0			0
$241$	28.0018	+	9.50533i	1.80375	+	0.612292i	0.999846	+	0.0175373i	$0.00558257\pi$
$241$	28.0018	+	9.50533i	1.80375	+	0.612292i	0.803907	+	0.594755i	$0.202751\pi$
$242$		0			0
$243$	1.37202	−	20.9330i	0.0880153	−	1.34285i
$244$		0			0
$245$	8.37243	+	4.51113i	0.534895	+	0.288205i
$246$		0			0
$247$	4.36211	+	3.34716i	0.277554	+	0.212975i
$248$		0			0
$249$	−24.2449	−	21.2622i	−1.53646	−	1.34743i
$250$		0			0
$251$	20.0481	+	20.0481i	1.26542	+	1.26542i	0.948427	+	0.316995i	$0.102674\pi$
$251$	20.0481	+	20.0481i	1.26542	+	1.26542i	0.316995	+	0.948427i	$0.397326\pi$
$252$		0			0
$253$	−0.413875	+	0.999182i	−0.0260201	+	0.0628181i
$254$		0			0
$255$	−5.07387	+	13.9792i	−0.317738	+	0.875410i
$256$		0			0
$257$	19.3162	−	2.54303i	1.20491	−	0.158630i	0.498792	−	0.866722i	$-0.333777\pi$
$257$	19.3162	−	2.54303i	1.20491	−	0.158630i	0.706120	+	0.708092i	$0.250444\pi$
$258$		0			0
$259$	−0.364932	+	1.26990i	−0.0226758	+	0.0789079i
$260$		0			0
$261$	−4.21139	−	12.4064i	−0.260679	−	0.767935i
$262$		0			0
$263$	−24.4433	−	3.21802i	−1.50724	−	0.198432i	−0.668805	−	0.743437i	$-0.733194\pi$
$263$	−24.4433	−	3.21802i	−1.50724	−	0.198432i	−0.838432	+	0.545006i	$0.816527\pi$
$264$		0			0
$265$	−3.57847	−	5.35555i	−0.219823	−	0.328989i
$266$		0			0
$267$	35.9654	+	24.0313i	2.20105	+	1.47069i
$268$		0			0
$269$	1.51141	−	4.45246i	0.0921521	−	0.271471i	−0.891075	−	0.453856i	$-0.850048\pi$
$269$	1.51141	−	4.45246i	0.0921521	−	0.271471i	0.983227	+	0.182384i	$0.0583815\pi$
$270$		0			0
$271$	15.8117	+	27.3867i	0.960494	+	1.66363i	0.721261	+	0.692663i	$0.243563\pi$
$271$	15.8117	+	27.3867i	0.960494	+	1.66363i	0.239233	+	0.970962i	$0.423104\pi$
$272$		0			0
$273$	−9.82188	+	16.3250i	−0.594447	+	0.988034i
$274$		0			0
$275$	−3.67484	−	4.19036i	−0.221601	−	0.252688i
$276$		0			0
$277$	5.22475	+	10.5947i	0.313925	+	0.636576i	0.995457	−	0.0952119i	$-0.0303529\pi$
$277$	5.22475	+	10.5947i	0.313925	+	0.636576i	−0.681533	+	0.731788i	$0.738686\pi$
$278$		0			0
$279$	36.6096	−	24.4617i	2.19176	−	1.46449i
$280$		0			0
$281$	−0.197559	+	0.0818317i	−0.0117854	+	0.00488167i	−0.388568	−	0.921420i	$-0.627030\pi$
$281$	−0.197559	+	0.0818317i	−0.0117854	+	0.00488167i	0.376783	+	0.926302i	$0.377030\pi$
$282$		0			0
$283$	−4.37771	+	4.99183i	−0.260228	+	0.296733i	−0.867169	−	0.498013i	$-0.834063\pi$
$283$	−4.37771	+	4.99183i	−0.260228	+	0.296733i	0.606941	+	0.794747i	$0.292396\pi$
$284$		0			0
$285$	1.89233	−	7.06226i	0.112092	−	0.418332i
$286$		0			0
$287$	−28.8172	−	12.5499i	−1.70103	−	0.740795i
$288$		0			0
$289$	16.9326	−	1.51190i	0.996037	−	0.0889353i
$290$		0			0
$291$	−17.6780	+	13.5648i	−1.03630	+	0.795184i
$292$		0			0
$293$	−16.2152	+	16.2152i	−0.947300	+	0.947300i	−0.998679	−	0.0513790i	$-0.983638\pi$
$293$	−16.2152	+	16.2152i	−0.947300	+	0.947300i	0.0513790	+	0.998679i	$0.483638\pi$
$294$		0			0
$295$	−9.59076	−	1.90772i	−0.558396	−	0.111072i
$296$		0			0
$297$	0.641634	−	4.87370i	0.0372314	−	0.282801i
$298$		0			0
$299$	0.734258	−	1.48893i	0.0424632	−	0.0861069i
$300$		0			0
$301$	−18.2061	−	12.6456i	−1.04938	−	0.728881i
$302$		0			0
$303$	−4.11343	+	3.60738i	−0.236311	+	0.207239i
$304$		0			0
$305$	−8.99248	−	5.19181i	−0.514908	−	0.297282i
$306$		0			0
$307$			1.79039i			0.102183i	0.998694	+	0.0510914i	$0.0162700\pi$
$307$			1.79039i			0.102183i	−0.998694	+	0.0510914i	$0.983730\pi$
$308$		0			0
$309$	−30.8469	+	6.13583i	−1.75482	+	0.349055i
$310$		0			0
$311$	11.6223	−	5.73147i	0.659039	−	0.325002i	−0.0818355	−	0.996646i	$-0.526078\pi$
$311$	11.6223	−	5.73147i	0.659039	−	0.325002i	0.740874	+	0.671644i	$0.234412\pi$
$312$		0			0
$313$	−18.8538	−	9.29766i	−1.06568	−	0.525535i	−0.177069	−	0.984198i	$-0.556662\pi$
$313$	−18.8538	−	9.29766i	−1.06568	−	0.525535i	−0.888610	+	0.458664i	$0.848328\pi$
$314$		0			0
$315$	14.3894	+	2.15901i	0.810753	+	0.121646i
$316$		0			0
$317$	25.5860	−	8.68527i	1.43705	−	0.487813i	0.509163	−	0.860670i	$-0.329955\pi$
$317$	25.5860	−	8.68527i	1.43705	−	0.487813i	0.927889	+	0.372857i	$0.121622\pi$
$318$		0			0
$319$	1.48027	+	5.52445i	0.0828793	+	0.309310i
$320$		0			0
$321$	−41.3466	−	17.1263i	−2.30774	−	0.955898i
$322$		0			0
$323$	−8.22957	+	1.45868i	−0.457905	+	0.0811629i
$324$		0			0
$325$	5.20818	+	6.78744i	0.288898	+	0.376499i
$326$		0			0
$327$	19.5981	+	5.25131i	1.08378	+	0.290398i
$328$		0			0
$329$	−13.5570	+	4.33101i	−0.747422	+	0.238776i
$330$		0			0
$331$	14.6779	−	19.1286i	0.806770	−	1.05140i	−0.190793	−	0.981630i	$-0.561106\pi$
$331$	14.6779	−	19.1286i	0.806770	−	1.05140i	0.997563	−	0.0697731i	$-0.0222275\pi$
$332$		0			0
$333$	0.132214	+	2.01720i	0.00724530	+	0.110542i
$334$		0			0
$335$	−0.899639	+	1.34641i	−0.0491525	+	0.0735620i
$336$		0			0
$337$	1.36755	+	6.87513i	0.0744952	+	0.374512i	0.999991	−	0.00424535i	$-0.00135134\pi$
$337$	1.36755	+	6.87513i	0.0744952	+	0.374512i	−0.925496	+	0.378758i	$0.876351\pi$
$338$		0			0
$339$	0.510290	−	0.883848i	0.0277151	−	0.0480040i
$340$		0			0
$341$	−16.6455	+	9.61030i	−0.901405	+	0.520427i
$342$		0			0
$343$	−18.3332	+	2.62579i	−0.989898	+	0.141779i
$344$		0			0
$345$	−2.20284	−	0.144382i	−0.118597	−	0.00777324i
$346$		0			0
$347$	25.6674	−	1.68233i	1.37790	−	0.0903122i	0.641636	−	0.767009i	$-0.278256\pi$
$347$	25.6674	−	1.68233i	1.37790	−	0.0903122i	0.736262	+	0.676697i	$0.236589\pi$
$348$		0			0
$349$	11.8103	+	28.5126i	0.632192	+	1.52625i	0.836862	+	0.547415i	$0.184388\pi$
$349$	11.8103	+	28.5126i	0.632192	+	1.52625i	−0.204670	+	0.978831i	$0.565612\pi$
$350$		0			0
$351$	−1.47211	+	7.40078i	−0.0785752	+	0.395024i
$352$		0			0
$353$	−28.8478	+	7.72974i	−1.53541	+	0.411413i	−0.924780	−	0.380502i	$-0.875751\pi$
$353$	−28.8478	+	7.72974i	−1.53541	+	0.411413i	−0.610632	+	0.791914i	$0.709085\pi$
$354$		0			0
$355$	0.345026	+	2.62074i	0.0183121	+	0.139094i
$356$		0			0
$357$	−8.23395	−	27.7651i	−0.435787	−	1.46948i
$358$		0			0
$359$	0.931848	+	7.07808i	0.0491810	+	0.373567i	0.998282	+	0.0585946i	$0.0186619\pi$
$359$	0.931848	+	7.07808i	0.0491810	+	0.373567i	−0.949101	+	0.314972i	$0.898005\pi$
$360$		0			0
$361$	−14.3836	+	3.85407i	−0.757030	+	0.202846i
$362$		0			0
$363$	4.07997	−	20.5114i	0.214143	−	1.07657i
$364$		0			0
$365$	2.09019	+	5.04617i	0.109406	+	0.264129i
$366$		0			0
$367$	−16.7366	+	1.09698i	−0.873644	+	0.0572616i	−0.495625	−	0.868536i	$-0.665061\pi$
$367$	−16.7366	+	1.09698i	−0.873644	+	0.0572616i	−0.378018	+	0.925798i	$0.623394\pi$
$368$		0			0
$369$	−47.9857	−	3.14515i	−2.49803	−	0.163730i
$370$		0			0
$371$	11.8028	+	4.24535i	0.612773	+	0.220407i
$372$		0			0
$373$	19.2562	−	11.1176i	0.997047	−	0.575645i	0.0896735	−	0.995971i	$-0.471418\pi$
$373$	19.2562	−	11.1176i	0.997047	−	0.575645i	0.907373	+	0.420326i	$0.138084\pi$
$374$		0			0
$375$	14.7054	−	25.4706i	0.759385	−	1.31529i
$376$		0			0
$377$	−1.71275	−	8.61058i	−0.0882112	−	0.443467i
$378$		0			0
$379$	6.76525	−	10.1249i	0.347508	−	0.520082i	−0.616006	−	0.787742i	$-0.711250\pi$
$379$	6.76525	−	10.1249i	0.347508	−	0.520082i	0.963514	+	0.267660i	$0.0862502\pi$
$380$		0			0
$381$	−2.86345	−	43.6877i	−0.146699	−	2.23819i
$382$		0			0
$383$	8.53039	−	11.1170i	0.435883	−	0.568053i	−0.522827	−	0.852439i	$-0.675123\pi$
$383$	8.53039	−	11.1170i	0.435883	−	0.568053i	0.958710	+	0.284385i	$0.0917894\pi$
$384$		0			0
$385$	−6.20639	−	1.35129i	−0.316307	−	0.0688682i
$386$		0			0
$387$	−32.7589	−	8.77773i	−1.66523	−	0.446197i
$388$		0			0
$389$	5.21774	+	6.79989i	0.264550	+	0.344768i	0.906674	−	0.421833i	$-0.138613\pi$
$389$	5.21774	+	6.79989i	0.264550	+	0.344768i	−0.642124	+	0.766601i	$0.721946\pi$
$390$		0			0
$391$	0.916721	+	2.35113i	0.0463606	+	0.118902i
$392$		0			0
$393$	11.6726	+	4.83497i	0.588807	+	0.243892i
$394$		0			0
$395$	−1.69942	−	6.34232i	−0.0855071	−	0.319117i
$396$		0			0
$397$	21.9442	−	7.44904i	1.10135	−	0.373857i	0.289175	−	0.957276i	$-0.406619\pi$
$397$	21.9442	−	7.44904i	1.10135	−	0.373857i	0.812171	+	0.583419i	$0.198286\pi$
$398$		0			0
$399$	5.21059	+	13.2503i	0.260856	+	0.663343i
$400$		0			0
$401$	−30.3879	−	14.9857i	−1.51750	−	0.748348i	−0.522926	−	0.852378i	$-0.675159\pi$
$401$	−30.3879	−	14.9857i	−1.51750	−	0.748348i	−0.994574	+	0.104030i	$0.966826\pi$
$402$		0			0
$403$	26.4613	−	13.0493i	1.31813	−	0.650030i
$404$		0			0
$405$	−6.34052	+	1.26121i	−0.315063	+	0.0626699i
$406$		0			0
$407$		−	0.882466i		−	0.0437422i
$408$		0			0
$409$	21.5558	+	12.4453i	1.06587	+	0.615378i	0.927049	−	0.374940i	$-0.122337\pi$
$409$	21.5558	+	12.4453i	1.06587	+	0.615378i	0.138817	+	0.990318i	$0.455670\pi$
$410$		0			0
$411$	−15.1664	+	13.3006i	−0.748102	+	0.656068i
$412$		0			0
$413$	17.2279	−	8.11305i	0.847730	−	0.399217i
$414$		0			0
$415$	−7.29914	+	14.8012i	−0.358301	+	0.726562i
$416$		0			0
$417$	−3.24496	+	24.6479i	−0.158907	+	1.20701i
$418$		0			0
$419$	0.862795	+	0.171621i	0.0421503	+	0.00838422i	0.216120	−	0.976367i	$-0.430660\pi$
$419$	0.862795	+	0.171621i	0.0421503	+	0.00838422i	−0.173970	+	0.984751i	$0.555660\pi$
$420$		0			0
$421$	−27.5840	+	27.5840i	−1.34436	+	1.34436i	−0.452701	+	0.891662i	$0.649540\pi$
$421$	−27.5840	+	27.5840i	−1.34436	+	1.34436i	−0.891662	+	0.452701i	$0.850460\pi$
$422$		0			0
$423$	−17.2748	+	13.2554i	−0.839927	+	0.644499i
$424$		0			0
$425$	−12.9563	−	1.12187i	−0.628474	−	0.0544187i
$426$		0			0
$427$	20.0921	−	2.27746i	0.972324	−	0.110214i
$428$		0			0
$429$	3.29331	−	12.2908i	0.159002	−	0.593405i
$430$		0			0
$431$	5.00243	−	5.70418i	0.240959	−	0.274761i	−0.618703	−	0.785625i	$-0.712341\pi$
$431$	5.00243	−	5.70418i	0.240959	−	0.274761i	0.859661	+	0.510865i	$0.170675\pi$
$432$		0			0
$433$	−15.9648	+	6.61284i	−0.767219	+	0.317793i	−0.731746	−	0.681578i	$-0.761294\pi$
$433$	−15.9648	+	6.61284i	−0.767219	+	0.317793i	−0.0354738	+	0.999371i	$0.511294\pi$
$434$		0			0
$435$	−9.70678	+	6.48586i	−0.465405	+	0.310973i
$436$		0			0
$437$	−0.548730	−	1.11271i	−0.0262493	−	0.0532283i
$438$		0			0
$439$	−18.9446	−	21.6022i	−0.904176	−	1.03101i	−0.999368	−	0.0355558i	$-0.988680\pi$
$439$	−18.9446	−	21.6022i	−0.904176	−	1.03101i	0.0951921	−	0.995459i	$-0.469653\pi$
$440$		0			0
$441$	−25.0338	+	13.2737i	−1.19209	+	0.632080i
$442$		0			0
$443$	12.9771	+	22.4769i	0.616559	+	1.06791i	0.990109	+	0.140301i	$0.0448071\pi$
$443$	12.9771	+	22.4769i	0.616559	+	1.06791i	−0.373550	+	0.927610i	$0.621860\pi$
$444$		0			0
$445$	7.11557	−	20.9618i	0.337310	−	0.993684i
$446$		0			0
$447$	0.477282	+	0.318910i	0.0225747	+	0.0150839i
$448$		0			0
$449$	3.23391	+	4.83989i	0.152618	+	0.228408i	0.899898	−	0.436100i	$-0.143641\pi$
$449$	3.23391	+	4.83989i	0.152618	+	0.228408i	−0.747280	+	0.664509i	$0.768641\pi$
$450$		0			0
$451$	20.8127	+	2.74005i	0.980034	+	0.129024i
$452$		0			0
$453$	−2.20203	−	6.48698i	−0.103461	−	0.304785i
$454$		0			0
$455$	9.37086	+	2.69291i	0.439313	+	0.126245i
$456$		0			0
$457$	−12.4447	+	1.63838i	−0.582139	+	0.0766400i	−0.415844	−	0.909436i	$-0.636514\pi$
$457$	−12.4447	+	1.63838i	−0.582139	+	0.0766400i	−0.166295	+	0.986076i	$0.553180\pi$
$458$		0			0
$459$	−6.79065	−	9.24395i	−0.316960	−	0.431471i
$460$		0			0
$461$	−6.60536	+	15.9467i	−0.307642	+	0.742714i	0.692138	+	0.721765i	$0.256669\pi$
$461$	−6.60536	+	15.9467i	−0.307642	+	0.742714i	−0.999781	+	0.0209492i	$0.993331\pi$
$462$		0			0
$463$	−15.5886	−	15.5886i	−0.724462	−	0.724462i	0.245049	−	0.969511i	$-0.421196\pi$
$463$	−15.5886	−	15.5886i	−0.724462	−	0.724462i	−0.969511	+	0.245049i	$0.921196\pi$
$464$		0			0
$465$	−29.4969	−	25.8681i	−1.36788	−	1.19960i
$466$		0			0
$467$	18.9337	+	14.5283i	0.876146	+	0.672290i	0.945613	−	0.325294i	$-0.105463\pi$
$467$	18.9337	+	14.5283i	0.876146	+	0.672290i	−0.0694673	+	0.997584i	$0.522130\pi$
$468$		0			0
$469$	−0.149476	−	3.14984i	−0.00690216	−	0.145446i
$470$		0			0
$471$	−3.26010	+	49.7396i	−0.150218	+	2.29188i
$472$		0			0
$473$	14.0192	+	4.75886i	0.644602	+	0.218813i
$474$		0			0
$475$	6.39365			0.293361
$476$		0			0
$477$	19.1905			0.878671
$478$		0			0
$479$	−36.3478	−	12.3384i	−1.66077	−	0.563757i	−0.675895	−	0.736998i	$-0.736243\pi$
$479$	−36.3478	−	12.3384i	−1.66077	−	0.563757i	−0.984880	+	0.173240i	$0.944576\pi$
$480$		0			0
$481$	−0.0885951	+	1.35170i	−0.00403959	+	0.0616322i
$482$		0			0
$483$	3.61692	−	2.32353i	0.164575	−	0.105724i
$484$		0			0
$485$	9.04701	+	6.94202i	0.410804	+	0.315221i
$486$		0			0
$487$	14.0987	+	12.3643i	0.638874	+	0.560278i	0.916312	−	0.400466i	$-0.131152\pi$
$487$	14.0987	+	12.3643i	0.638874	+	0.560278i	−0.277437	+	0.960744i	$0.589485\pi$
$488$		0			0
$489$	−5.98922	−	5.98922i	−0.270842	−	0.270842i
$490$		0			0
$491$	13.0416	−	31.4852i	0.588559	−	1.42091i	−0.296321	−	0.955088i	$-0.595760\pi$
$491$	13.0416	−	31.4852i	0.588559	−	1.42091i	0.884880	−	0.465818i	$-0.154240\pi$
$492$		0			0
$493$	11.4151	+	6.91291i	0.514110	+	0.311342i
$494$		0			0
$495$	−9.63483	+	1.26845i	−0.433054	+	0.0570126i
$496$		0			0
$497$	−3.57367	−	3.70492i	−0.160301	−	0.166188i
$498$		0			0
$499$	−12.4496	−	36.6755i	−0.557323	−	1.64182i	−0.750661	−	0.660687i	$-0.770265\pi$
$499$	−12.4496	−	36.6755i	−0.557323	−	1.64182i	0.193339	−	0.981132i	$-0.438068\pi$
$500$		0			0
$501$	31.8962	+	4.19921i	1.42502	+	0.187607i
$502$		0			0
$503$	−1.89771	−	2.84012i	−0.0846145	−	0.126635i	0.786748	−	0.617274i	$-0.211763\pi$
$503$	−1.89771	−	2.84012i	−0.0846145	−	0.126635i	−0.871363	+	0.490640i	$0.836763\pi$
$504$		0			0
$505$	2.32808	+	1.55557i	0.103598	+	0.0692220i
$506$		0			0
$507$	4.81519	−	14.1851i	0.213850	−	0.629983i
$508$		0			0
$509$	−18.8314	−	32.6169i	−0.834685	−	1.44572i	−0.894286	−	0.447495i	$-0.852316\pi$
$509$	−18.8314	−	32.6169i	−0.834685	−	1.44572i	0.0596010	−	0.998222i	$-0.481017\pi$
$510$		0			0
$511$	−9.11401	−	5.48341i	−0.403180	−	0.242572i
$512$		0			0
$513$	3.71815	+	4.23973i	0.164160	+	0.187189i
$514$		0			0
$515$	7.11893	+	14.4358i	0.313698	+	0.636116i
$516$		0			0
$517$	7.90333	−	5.28083i	0.347588	−	0.232251i
$518$		0			0
$519$	41.1937	−	17.0630i	1.80820	−	0.748983i
$520$		0			0
$521$	13.2042	−	15.0565i	0.578485	−	0.659636i	−0.386393	−	0.922334i	$-0.626279\pi$
$521$	13.2042	−	15.0565i	0.578485	−	0.659636i	0.964878	+	0.262699i	$0.0846125\pi$
$522$		0			0
$523$	7.09030	−	26.4614i	0.310037	−	1.15707i	−0.618485	−	0.785797i	$-0.712253\pi$
$523$	7.09030	−	26.4614i	0.310037	−	1.15707i	0.928522	−	0.371278i	$-0.121080\pi$
$524$		0			0
$525$	2.49523	+	22.0133i	0.108901	+	0.960740i
$526$		0			0
$527$	−12.5114	+	43.0677i	−0.545003	+	1.87606i
$528$		0			0
$529$	17.9499	−	13.7735i	0.780432	−	0.598847i
$530$		0			0
$531$	20.6011	−	20.6011i	0.894014	−	0.894014i
$532$		0			0
$533$	−31.6044	−	6.28651i	−1.36894	−	0.272299i
$534$		0			0
$535$	−2.98946	+	22.7072i	−0.129246	+	0.981719i
$536$		0			0
$537$	−4.78134	+	9.69560i	−0.206330	+	0.418396i
$538$		0			0
$539$	11.2837	−	5.06728i	0.486023	−	0.218263i
$540$		0			0
$541$	−26.3082	+	23.0716i	−1.13108	+	0.991928i	−0.131077	+	0.991372i	$0.541843\pi$
$541$	−26.3082	+	23.0716i	−1.13108	+	0.991928i	−1.00000		0.000555298i	$0.999823\pi$
$542$		0			0
$543$	16.8859	+	9.74909i	0.724644	+	0.418374i
$544$		0			0
$545$		−	10.3835i		−	0.444779i
$546$		0			0
$547$	−24.7351	+	4.92012i	−1.05760	+	0.210369i	−0.693104	−	0.720838i	$-0.743757\pi$
$547$	−24.7351	+	4.92012i	−1.05760	+	0.210369i	−0.364492	+	0.931206i	$0.618757\pi$
$548$		0			0
$549$	27.7464	−	13.6830i	1.18419	−	0.583977i
$550$		0			0
$551$	−5.88436	−	2.90184i	−0.250682	−	0.123623i
$552$		0			0
$553$	10.0022	+	7.96557i	0.425339	+	0.338731i
$554$		0			0
$555$	1.70569	−	0.579003i	0.0724024	−	0.0245773i
$556$		0			0
$557$	8.47343	+	31.6233i	0.359031	+	1.33992i	0.875335	+	0.483516i	$0.160641\pi$
$557$	8.47343	+	31.6233i	0.359031	+	1.33992i	−0.516304	+	0.856405i	$0.672693\pi$
$558$		0			0
$559$	−20.9958	−	8.69676i	−0.888029	−	0.367834i
$560$		0			0
$561$	10.4070	+	16.3036i	0.439384	+	0.688336i
$562$		0			0
$563$	−10.0886	−	13.1478i	−0.425186	−	0.554113i	0.530811	−	0.847490i	$-0.321887\pi$
$563$	−10.0886	−	13.1478i	−0.425186	−	0.554113i	−0.955997	+	0.293377i	$0.905221\pi$
$564$		0			0
$565$	−0.504501	−	0.135181i	−0.0212245	−	0.00568709i
$566$		0			0
$567$	8.46995	−	9.31388i	0.355704	−	0.391146i
$568$		0			0
$569$	−15.7021	+	20.4633i	−0.658265	+	0.857868i	−0.996534	−	0.0831815i	$-0.973492\pi$
$569$	−15.7021	+	20.4633i	−0.658265	+	0.857868i	0.338269	+	0.941049i	$0.390159\pi$
$570$		0			0
$571$	−1.90047	−	28.9955i	−0.0795320	−	1.21342i	−0.831993	−	0.554787i	$-0.812800\pi$
$571$	−1.90047	−	28.9955i	−0.0795320	−	1.21342i	0.752461	−	0.658637i	$-0.228867\pi$
$572$		0			0
$573$	3.61921	−	5.41654i	0.151195	−	0.226279i
$574$		0			0
$575$	−0.376615	−	1.89337i	−0.0157059	−	0.0789591i
$576$		0			0
$577$	−9.88554	+	17.1223i	−0.411540	+	0.712809i	−0.995058	−	0.0992914i	$-0.968342\pi$
$577$	−9.88554	+	17.1223i	−0.411540	+	0.712809i	0.583518	+	0.812100i	$0.301676\pi$
$578$		0			0
$579$	−45.6042	+	26.3296i	−1.89525	+	1.09422i
$580$		0			0
$581$	−5.70043	−	31.6280i	−0.236494	−	1.31215i
$582$		0			0
$583$	−8.35935	−	0.547901i	−0.346209	−	0.0226917i
$584$		0			0
$585$	14.8853	−	0.975636i	0.615432	−	0.0403376i
$586$		0			0
$587$	5.43341	+	13.1174i	0.224261	+	0.541414i	0.995460	−	0.0951801i	$-0.0303427\pi$
$587$	5.43341	+	13.1174i	0.224261	+	0.541414i	−0.771199	+	0.636594i	$0.780343\pi$
$588$		0			0
$589$	4.30156	−	21.6254i	0.177243	−	0.891059i
$590$		0			0
$591$	2.94562	−	0.789277i	0.121167	−	0.0324665i
$592$		0			0
$593$	4.25957	+	32.3546i	0.174919	+	1.32865i	0.823421	+	0.567431i	$0.192063\pi$
$593$	4.25957	+	32.3546i	0.174919	+	1.32865i	−0.648501	+	0.761214i	$0.724604\pi$
$594$		0			0
$595$	−12.6344	+	7.74789i	−0.517962	+	0.317633i
$596$		0			0
$597$	1.80996	+	13.7480i	0.0740767	+	0.562668i
$598$		0			0
$599$	−32.5449	+	8.72038i	−1.32975	+	0.356305i	−0.852621	−	0.522529i	$-0.824989\pi$
$599$	−32.5449	+	8.72038i	−1.32975	+	0.356305i	−0.477127	+	0.878834i	$0.658322\pi$
$600$		0			0
$601$	2.66886	−	13.4173i	0.108865	−	0.547302i	−0.887403	−	0.460994i	$-0.847493\pi$
$601$	2.66886	−	13.4173i	0.108865	−	0.547302i	0.996268	−	0.0863084i	$-0.0275070\pi$
$602$		0			0
$603$	−1.84627	−	4.45730i	−0.0751861	−	0.181515i
$604$		0			0
$605$	−10.6798	+	0.699990i	−0.434195	+	0.0284586i
$606$		0			0
$607$	−45.2027	−	2.96274i	−1.83472	−	0.120254i	−0.891625	−	0.452775i	$-0.850434\pi$
$607$	−45.2027	−	2.96274i	−1.83472	−	0.120254i	−0.943096	+	0.332521i	$0.892101\pi$
$608$		0			0
$609$	7.69456	−	21.3923i	0.311799	−	0.866860i
$610$		0			0
$611$	−12.6359	+	7.29536i	−0.511195	+	0.295139i
$612$		0			0
$613$	19.2229	−	33.2951i	0.776406	−	1.34477i	−0.157595	−	0.987504i	$-0.550374\pi$
$613$	19.2229	−	33.2951i	0.776406	−	1.34477i	0.934001	−	0.357271i	$-0.116293\pi$
$614$		0			0
$615$	8.35950	+	42.0260i	0.337088	+	1.69465i
$616$		0			0
$617$	12.7853	−	19.1346i	0.514717	−	0.770328i	−0.479520	−	0.877531i	$-0.659189\pi$
$617$	12.7853	−	19.1346i	0.514717	−	0.770328i	0.994237	+	0.107203i	$0.0341893\pi$
$618$		0			0
$619$	−0.326562	−	4.98237i	−0.0131256	−	0.200258i	−0.999385	−	0.0350562i	$-0.988839\pi$
$619$	−0.326562	−	4.98237i	−0.0131256	−	0.200258i	0.986260	−	0.165202i	$-0.0528277\pi$
$620$		0			0
$621$	1.03651	−	1.35081i	0.0415937	−	0.0542060i
$622$		0			0
$623$	13.1184	+	41.0635i	0.525578	+	1.64518i
$624$		0			0
$625$	0.694645	+	0.186130i	0.0277858	+	0.00744518i
$626$		0			0
$627$	−5.78886	−	7.54419i	−0.231185	−	0.301286i
$628$		0			0
$629$	−1.42522	−	1.48614i	−0.0568271	−	0.0592564i
$630$		0			0
$631$	−32.6721	−	13.5332i	−1.30066	−	0.538750i	−0.378513	−	0.925596i	$-0.623564\pi$
$631$	−32.6721	−	13.5332i	−1.30066	−	0.538750i	−0.922144	+	0.386846i	$0.873564\pi$
$632$		0			0
$633$	−11.8706	−	44.3018i	−0.471815	−	1.76084i
$634$		0			0
$635$	−21.2168	+	7.20213i	−0.841963	+	0.285808i
$636$		0			0
$637$	−17.7923	+	6.62888i	−0.704958	+	0.262646i
$638$		0			0
$639$	−7.06338	−	3.48328i	−0.279423	−	0.137796i
$640$		0			0
$641$	21.2200	−	10.4645i	0.838138	−	0.413324i	0.0280316	−	0.999607i	$-0.491076\pi$
$641$	21.2200	−	10.4645i	0.838138	−	0.413324i	0.810106	+	0.586283i	$0.199409\pi$
$642$		0			0
$643$	−16.8044	+	3.34260i	−0.662701	+	0.131819i	−0.514970	−	0.857208i	$-0.672197\pi$
$643$	−16.8044	+	3.34260i	−0.662701	+	0.131819i	−0.147731	+	0.989028i	$0.547197\pi$
$644$		0			0
$645$			30.2196i			1.18989i
$646$		0			0
$647$	16.5899	+	9.57821i	0.652218	+	0.376558i	0.789306	−	0.614001i	$-0.210441\pi$
$647$	16.5899	+	9.57821i	0.652218	+	0.376558i	−0.137087	+	0.990559i	$0.543774\pi$
$648$		0			0
$649$	−9.56203	+	8.38567i	−0.375342	+	0.329166i
$650$		0			0
$651$	76.1349	+	6.37056i	2.98396	+	0.249682i
$652$		0			0
$653$	16.4670	−	33.3917i	0.644402	−	1.30672i	−0.292212	−	0.956354i	$-0.594391\pi$
$653$	16.4670	−	33.3917i	0.644402	−	1.30672i	0.936614	−	0.350364i	$-0.113942\pi$
$654$		0			0
$655$	0.843962	−	6.41053i	0.0329763	−	0.250480i
$656$		0			0
$657$	−15.9605	−	3.17475i	−0.622680	−	0.123859i
$658$		0			0
$659$	−3.54899	+	3.54899i	−0.138249	+	0.138249i	−0.772844	−	0.634595i	$-0.781167\pi$
$659$	−3.54899	+	3.54899i	−0.138249	+	0.138249i	0.634595	+	0.772844i	$0.281167\pi$
$660$		0			0
$661$	−11.8175	+	9.06792i	−0.459649	+	0.352701i	−0.812483	−	0.582985i	$-0.801885\pi$
$661$	−11.8175	+	9.06792i	−0.459649	+	0.352701i	0.352834	+	0.935686i	$0.385218\pi$
$662$		0			0
$663$	−14.3039	−	26.0175i	−0.555518	−	1.01043i
$664$		0			0
$665$	5.85981	−	4.33080i	0.227234	−	0.167941i
$666$		0			0
$667$	−0.512717	+	1.91349i	−0.0198525	+	0.0740905i
$668$		0			0
$669$	−10.1510	+	11.5750i	−0.392462	+	0.447517i
$670$		0			0
$671$	−12.4770	+	5.16814i	−0.481669	+	0.199514i
$672$		0			0
$673$	8.07302	−	5.39422i	0.311192	−	0.207932i	−0.390160	−	0.920747i	$-0.627580\pi$
$673$	8.07302	−	5.39422i	0.311192	−	0.207932i	0.701352	+	0.712815i	$0.252580\pi$
$674$		0			0
$675$	3.88086	+	7.86961i	0.149374	+	0.302902i
$676$		0			0
$677$	20.1608	+	22.9890i	0.774843	+	0.883540i	0.995782	−	0.0917480i	$-0.0292454\pi$
$677$	20.1608	+	22.9890i	0.774843	+	0.883540i	−0.220939	+	0.975288i	$0.570912\pi$
$678$		0			0
$679$	−22.2032	−	0.400376i	−0.852082	−	0.0153650i
$680$		0			0
$681$	29.8002	+	51.6155i	1.14195	+	1.97791i
$682$		0			0
$683$	7.03013	−	20.7101i	0.269000	−	0.792450i	−0.725548	−	0.688172i	$-0.758414\pi$
$683$	7.03013	−	20.7101i	0.269000	−	0.792450i	0.994548	−	0.104278i	$-0.0332531\pi$
$684$		0			0
$685$	8.58370	+	5.73545i	0.327966	+	0.219140i
$686$		0			0
$687$	19.6393	+	29.3922i	0.749285	+	1.12138i
$688$		0			0
$689$	12.7493	+	1.67847i	0.485709	+	0.0639448i
$690$		0			0
$691$	5.11418	+	15.0659i	0.194552	+	0.573133i	0.999804	−	0.0198004i	$-0.00630309\pi$
$691$	5.11418	+	15.0659i	0.194552	+	0.573133i	−0.805252	+	0.592933i	$0.797970\pi$
$692$		0			0
$693$	13.6207	−	13.1382i	0.517408	−	0.499078i
$694$		0			0
$695$	12.6140	−	1.66066i	0.478476	−	0.0629925i
$696$		0			0
$697$	39.4756	−	28.9990i	1.49524	−	1.09841i
$698$		0			0
$699$	−12.4920	+	30.1584i	−0.472491	+	1.14069i
$700$		0			0
$701$	10.4440	+	10.4440i	0.394464	+	0.394464i	0.876275	−	0.481811i	$-0.160021\pi$
$701$	10.4440	+	10.4440i	0.394464	+	0.394464i	−0.481811	+	0.876275i	$0.660021\pi$
$702$		0			0
$703$	0.761108	+	0.667474i	0.0287057	+	0.0251743i
$704$		0			0
$705$	15.3927	+	11.8112i	0.579722	+	0.444836i
$706$		0			0
$707$	−5.44641	+	0.258460i	−0.204833	+	0.00972037i
$708$		0			0
$709$	−2.54500	+	38.8292i	−0.0955794	+	1.45826i	0.633453	+	0.773781i	$0.281637\pi$
$709$	−2.54500	+	38.8292i	−0.0955794	+	1.45826i	−0.729032	+	0.684479i	$0.760030\pi$
$710$		0			0
$711$	18.5246	+	6.28827i	0.694728	+	0.235828i
$712$		0			0
$713$	−6.65738			−0.249321
$714$		0			0
$715$	−6.51189			−0.243531
$716$		0			0
$717$	37.1386	+	12.6069i	1.38697	+	0.470812i
$718$		0			0
$719$	2.83602	−	43.2692i	0.105766	−	1.61367i	−0.534263	−	0.845319i	$-0.679411\pi$
$719$	2.83602	−	43.2692i	0.105766	−	1.61367i	0.640028	−	0.768352i	$-0.278923\pi$
$720$		0			0
$721$	−27.8572	−	14.3678i	−1.03746	−	0.535084i
$722$		0			0
$723$	62.2822	+	47.7908i	2.31630	+	1.77736i
$724$		0			0
$725$	−7.67543	−	6.73118i	−0.285058	−	0.249990i
$726$		0			0
$727$	−14.7502	−	14.7502i	−0.547055	−	0.547055i	0.378533	−	0.925588i	$-0.376429\pi$
$727$	−14.7502	−	14.7502i	−0.547055	−	0.547055i	−0.925588	+	0.378533i	$0.876429\pi$
$728$		0			0
$729$	15.8496	−	38.2644i	0.587024	−	1.41720i
$730$		0			0
$731$	31.2951	−	14.6272i	1.15749	−	0.541007i
$732$		0			0
$733$	37.5199	−	4.93958i	1.38583	−	0.182448i	0.599558	−	0.800331i	$-0.295343\pi$
$733$	37.5199	−	4.93958i	1.38583	−	0.182448i	0.786270	+	0.617883i	$0.212010\pi$
$734$		0			0
$735$	17.1978	+	18.4851i	0.634351	+	0.681835i
$736$		0			0
$737$	0.676977	+	1.99431i	0.0249368	+	0.0734614i
$738$		0			0
$739$	−2.23959	−	0.294848i	−0.0823848	−	0.0108462i	0.0892211	−	0.996012i	$-0.471562\pi$
$739$	−2.23959	−	0.294848i	−0.0823848	−	0.0108462i	−0.171606	+	0.985166i	$0.554896\pi$
$740$		0			0
$741$	8.10958	+	12.1368i	0.297913	+	0.445858i
$742$		0			0
$743$	11.9452	+	7.98154i	0.438228	+	0.292814i	0.755046	−	0.655672i	$-0.227615\pi$
$743$	11.9452	+	7.98154i	0.438228	+	0.292814i	−0.316818	+	0.948486i	$0.602615\pi$
$744$		0			0
$745$	0.0944277	−	0.278175i	0.00345956	−	0.0101915i
$746$		0			0
$747$	−24.5846	−	42.5818i	−0.899503	−	1.55799i
$748$		0			0
$749$	−21.6004	−	39.0213i	−0.789263	−	1.42581i
$750$		0			0
$751$	−25.8017	−	29.4212i	−0.941518	−	1.07360i	−0.997173	−	0.0751454i	$-0.976058\pi$
$751$	−25.8017	−	29.4212i	−0.941518	−	1.07360i	0.0556547	−	0.998450i	$-0.482275\pi$
$752$		0			0
$753$	33.2907	+	67.5068i	1.21318	+	2.46009i
$754$		0			0
$755$	−2.91503	+	1.94776i	−0.106089	+	0.0708862i
$756$		0			0
$757$	5.43628	−	2.25178i	0.197585	−	0.0818424i	−0.281697	−	0.959503i	$-0.590897\pi$
$757$	5.43628	−	2.25178i	0.197585	−	0.0818424i	0.479282	+	0.877661i	$0.340897\pi$
$758$		0			0
$759$	−1.89309	+	2.15866i	−0.0687149	+	0.0783544i
$760$		0			0
$761$	0.967600	−	3.61113i	0.0350755	−	0.130903i	−0.946168	−	0.323676i	$-0.895081\pi$
$761$	0.967600	−	3.61113i	0.0350755	−	0.130903i	0.981243	+	0.192772i	$0.0617479\pi$
$762$		0			0
$763$	12.0182	+	16.2613i	0.435088	+	0.588698i
$764$		0			0
$765$	−14.1772	+	17.6968i	−0.512578	+	0.639830i
$766$		0			0
$767$	15.4883	−	11.8846i	0.559251	−	0.429129i
$768$		0			0
$769$	−26.5027	+	26.5027i	−0.955711	+	0.955711i	−0.999060	−	0.0433491i	$-0.986197\pi$
$769$	−26.5027	+	26.5027i	−0.955711	+	0.955711i	0.0433491	+	0.999060i	$0.486197\pi$
$770$		0			0
$771$	50.7291	+	10.0906i	1.82696	+	0.363405i
$772$		0			0
$773$	2.46093	−	18.6926i	0.0885134	−	0.672326i	−0.888458	−	0.458957i	$-0.848223\pi$
$773$	2.46093	−	18.6926i	0.0885134	−	0.672326i	0.976972	−	0.213369i	$-0.0684436\pi$
$774$		0			0
$775$	15.1742	−	30.7702i	0.545073	−	1.10530i
$776$		0			0
$777$	−2.00107	+	2.88099i	−0.0717882	+	0.103355i
$778$		0			0
$779$	−18.1055	+	15.8781i	−0.648695	+	0.568890i
$780$		0			0
$781$	2.97736	+	1.71898i	0.106538	+	0.0615099i
$782$		0			0
$783$		−	9.00413i		−	0.321781i
$784$		0			0
$785$	25.0195	−	4.97668i	0.892983	−	0.177625i
$786$		0			0
$787$	−22.4820	+	11.0869i	−0.801398	+	0.395206i	−0.796391	−	0.604782i	$-0.793260\pi$
$787$	−22.4820	+	11.0869i	−0.801398	+	0.395206i	−0.00500688	+	0.999987i	$0.501594\pi$
$788$		0			0
$789$	−58.7018	−	28.9485i	−2.08984	−	1.03059i
$790$		0			0
$791$	0.946548	−	0.372225i	0.0336554	−	0.0132348i
$792$		0			0
$793$	19.6303	−	6.66357i	0.697091	−	0.236630i
$794$		0			0
$795$	−4.42572	−	16.5170i	−0.156964	−	0.585798i
$796$		0			0
$797$	5.74683	+	2.38041i	0.203563	+	0.0843186i	0.482136	−	0.876097i	$-0.339861\pi$
$797$	5.74683	+	2.38041i	0.203563	+	0.0843186i	−0.278572	+	0.960415i	$0.589861\pi$
$798$		0			0
$799$	4.78107	−	21.6575i	0.169142	−	0.766188i
$800$		0			0
$801$	40.1499	+	52.3244i	1.41863	+	1.84879i
$802$		0			0
$803$	6.86176	+	1.83860i	0.242146	+	0.0648829i
$804$		0			0
$805$	−1.62766	−	1.48018i	−0.0573676	−	0.0521695i
$806$		0			0
$807$	7.59904	−	9.90326i	0.267499	−	0.348611i
$808$		0			0
$809$	2.48384	+	37.8960i	0.0873271	+	1.33235i	0.786584	+	0.617483i	$0.211848\pi$
$809$	2.48384	+	37.8960i	0.0873271	+	1.33235i	−0.699257	+	0.714870i	$0.746486\pi$
$810$		0			0
$811$	30.4991	−	45.6451i	1.07097	−	1.60282i	0.313929	−	0.949446i	$-0.398355\pi$
$811$	30.4991	−	45.6451i	1.07097	−	1.60282i	0.757039	−	0.653370i	$-0.226645\pi$
$812$		0			0
$813$	16.3785	+	82.3404i	0.574420	+	2.88780i
$814$		0			0
$815$	−2.16734	+	3.75394i	−0.0759186	+	0.131495i
$816$		0			0
$817$	−14.7082	+	8.49175i	−0.514573	+	0.297089i
$818$		0			0
$819$	−22.1823	+	18.7567i	−0.775111	+	0.655413i
$820$		0			0
$821$	−25.8892	−	1.69687i	−0.903538	−	0.0592210i	−0.393453	−	0.919345i	$-0.628720\pi$
$821$	−25.8892	−	1.69687i	−0.903538	−	0.0592210i	−0.510086	+	0.860124i	$0.670386\pi$
$822$		0			0
$823$	8.00895	−	0.524934i	0.279174	−	0.0182981i	0.0748272	−	0.997197i	$-0.476159\pi$
$823$	8.00895	−	0.524934i	0.279174	−	0.0182981i	0.204347	+	0.978898i	$0.434493\pi$
$824$		0			0
$825$	−5.66232	−	13.6701i	−0.197137	−	0.475930i
$826$		0			0
$827$	−5.02039	+	25.2392i	−0.174576	+	0.877653i	0.789850	+	0.613300i	$0.210158\pi$
$827$	−5.02039	+	25.2392i	−0.174576	+	0.877653i	−0.964426	+	0.264353i	$0.914842\pi$
$828$		0			0
$829$	13.3355	−	3.57323i	0.463160	−	0.124103i	−0.0196906	−	0.999806i	$-0.506268\pi$
$829$	13.3355	−	3.57323i	0.463160	−	0.124103i	0.482851	+	0.875703i	$0.339601\pi$
$830$		0			0
$831$	4.09342	+	31.0926i	0.141999	+	1.07859i
$832$		0			0
$833$	10.8188	−	26.7573i	0.374848	−	0.927086i
$834$		0			0
$835$	−2.14901	−	16.3234i	−0.0743697	−	0.564894i
$836$		0			0
$837$	29.2286	−	7.83177i	1.01029	−	0.270706i
$838$		0			0
$839$	−5.16598	+	25.9711i	−0.178349	+	0.896623i	0.783153	+	0.621828i	$0.213610\pi$
$839$	−5.16598	+	25.9711i	−0.178349	+	0.896623i	−0.961503	+	0.274795i	$0.911390\pi$
$840$		0			0
$841$	−7.08881	−	17.1139i	−0.244442	−	0.590135i
$842$		0			0
$843$	−0.566475	+	0.0371287i	−0.0195104	+	0.00127878i
$844$		0			0
$845$	−7.64989	−	0.501400i	−0.263164	−	0.0172487i
$846$		0			0
$847$	15.9151	−	13.4574i	0.546850	−	0.462401i
$848$		0			0
$849$	−15.2649	+	8.81320i	−0.523890	+	0.302468i
$850$		0			0
$851$	0.152828	−	0.264707i	0.00523889	−	0.00907403i
$852$		0			0
$853$	−7.23864	−	36.3911i	−0.247846	−	1.24601i	−0.881423	−	0.472328i	$-0.843414\pi$
$853$	−7.23864	−	36.3911i	−0.247846	−	1.24601i	0.633577	−	0.773680i	$-0.281586\pi$
$854$		0			0
$855$	6.19353	−	9.26927i	0.211814	−	0.317002i
$856$		0			0
$857$	0.386957	+	5.90382i	0.0132182	+	0.201671i	0.999360	+	0.0357669i	$0.0113874\pi$
$857$	0.386957	+	5.90382i	0.0132182	+	0.201671i	−0.986142	+	0.165904i	$0.946946\pi$
$858$		0			0
$859$	−7.16357	+	9.33575i	−0.244418	+	0.318532i	−0.899412	−	0.437103i	$-0.856005\pi$
$859$	−7.16357	+	9.33575i	−0.244418	+	0.318532i	0.654994	+	0.755634i	$0.272671\pi$
$860$		0			0
$861$	−61.7340	−	56.1403i	−2.10389	−	1.91326i
$862$		0			0
$863$	23.0745	+	6.18280i	0.785466	+	0.210465i	0.629193	−	0.777249i	$-0.283385\pi$
$863$	23.0745	+	6.18280i	0.785466	+	0.210465i	0.156273	+	0.987714i	$0.450052\pi$
$864$		0			0
$865$	−13.8910	−	18.1031i	−0.472309	−	0.615525i
$866$		0			0
$867$	43.8571	+	10.6488i	1.48946	+	0.361651i
$868$		0			0
$869$	−7.88979	−	3.26806i	−0.267643	−	0.110861i
$870$		0			0
$871$	−0.836729	−	3.12271i	−0.0283515	−	0.105809i
$872$		0			0
$873$	−32.1724	+	10.9211i	−1.08887	+	0.369622i
$874$		0			0
$875$	27.2775	−	10.7267i	0.922147	−	0.362629i
$876$		0			0
$877$	−0.755702	−	0.372671i	−0.0255182	−	0.0125842i	0.429485	−	0.903074i	$-0.358695\pi$
$877$	−0.755702	−	0.372671i	−0.0255182	−	0.0125842i	−0.455003	+	0.890490i	$0.650362\pi$
$878$		0			0
$879$	−54.6005	+	26.9260i	−1.84163	+	0.908191i
$880$		0			0
$881$	−6.21471	+	1.23618i	−0.209379	+	0.0416481i	−0.298665	−	0.954358i	$-0.596541\pi$
$881$	−6.21471	+	1.23618i	−0.209379	+	0.0416481i	0.0892863	+	0.996006i	$0.471541\pi$
$882$		0			0
$883$			48.1456i			1.62023i	0.586272	+	0.810114i	$0.300595\pi$
$883$			48.1456i			1.62023i	−0.586272	+	0.810114i	$0.699405\pi$
$884$		0			0
$885$	−22.4822	−	12.9801i	−0.755731	−	0.436322i
$886$		0			0
$887$	37.8358	−	33.1811i	1.27040	−	1.11411i	0.282461	−	0.959279i	$-0.408849\pi$
$887$	37.8358	−	33.1811i	1.27040	−	1.11411i	0.987941	−	0.154834i	$-0.0494842\pi$
$888$		0			0
$889$	24.8911	−	35.8361i	0.834819	−	1.20191i
$890$		0			0
$891$	−3.71879	+	7.54097i	−0.124584	+	0.252632i
$892$		0			0
$893$	−1.42326	+	10.8107i	−0.0476276	+	0.361768i
$894$		0			0
$895$	5.42612	+	1.07932i	0.181375	+	0.0360777i
$896$		0			0
$897$	3.11643	−	3.11643i	0.104055	−	0.104055i
$898$		0			0
$899$	−27.9309	+	21.4322i	−0.931549	+	0.714803i
$900$		0			0
$901$	−14.9627	+	12.5780i	−0.498479	+	0.419033i
$902$		0			0
$903$	−34.9772	−	47.3260i	−1.16397	−	1.57491i
$904$		0			0
$905$	2.58263	−	9.63850i	0.0858495	−	0.320395i
$906$		0			0
$907$	22.1439	−	25.2503i	0.735278	−	0.838423i	−0.256480	−	0.966549i	$-0.582563\pi$
$907$	22.1439	−	25.2503i	0.735278	−	0.838423i	0.991758	+	0.128126i	$0.0408962\pi$
$908$		0			0
$909$	−7.70714	+	3.19240i	−0.255630	+	0.105885i
$910$		0			0
$911$	−28.7137	+	19.1859i	−0.951327	+	0.635657i	−0.931343	−	0.364144i	$-0.881362\pi$
$911$	−28.7137	+	19.1859i	−0.951327	+	0.635657i	−0.0199846	+	0.999800i	$0.506362\pi$
$912$		0			0
$913$	9.49330	+	19.2505i	0.314182	+	0.637099i
$914$		0			0
$915$	−18.1757	−	20.7254i	−0.600871	−	0.685162i
$916$		0			0
$917$	6.09807	+	11.0162i	0.201376	+	0.363787i
$918$		0			0
$919$	−3.48528	−	6.03669i	−0.114969	−	0.199132i	0.802798	−	0.596250i	$-0.203343\pi$
$919$	−3.48528	−	6.03669i	−0.114969	−	0.199132i	−0.917767	+	0.397119i	$0.870010\pi$
$920$		0			0
$921$	−1.52783	+	4.50084i	−0.0503437	+	0.148308i
$922$		0			0
$923$	−4.38793	−	2.93192i	−0.144431	−	0.0965055i
$924$		0			0
$925$	0.875124	+	1.30972i	0.0287739	+	0.0430632i
$926$		0			0
$927$	−47.5450	−	6.25942i	−1.56158	−	0.205586i
$928$		0			0
$929$	12.4550	+	36.6912i	0.408635	+	1.20380i	0.935339	+	0.353751i	$0.115094\pi$
$929$	12.4550	+	36.6912i	0.408635	+	1.20380i	−0.526704	+	0.850048i	$0.676573\pi$
$930$		0			0
$931$	−4.16427	+	13.5647i	−0.136479	+	0.444565i
$932$		0			0
$933$	34.1082	−	4.49042i	1.11665	−	0.147010i
$934$		0			0
$935$	6.68085	−	7.30395i	0.218487	−	0.238865i
$936$		0			0
$937$	6.71085	−	16.2014i	0.219234	−	0.529278i	−0.775550	−	0.631287i	$-0.782527\pi$
$937$	6.71085	−	16.2014i	0.219234	−	0.529278i	0.994783	+	0.102009i	$0.0325271\pi$
$938$		0			0
$939$	−39.4623	−	39.4623i	−1.28780	−	1.28780i
$940$		0			0
$941$	−1.35184	−	1.18553i	−0.0440687	−	0.0386473i	0.637028	−	0.770840i	$-0.280163\pi$
$941$	−1.35184	−	1.18553i	−0.0440687	−	0.0386473i	−0.681097	+	0.732193i	$0.738497\pi$
$942$		0			0
$943$	5.76851	+	4.42634i	0.187849	+	0.144141i
$944$		0			0
$945$	8.88739	+	4.58380i	0.289107	+	0.149111i
$946$		0			0
$947$	0.990565	−	15.1131i	0.0321891	−	0.491110i	−0.951079	−	0.308947i	$-0.900023\pi$
$947$	0.990565	−	15.1131i	0.0321891	−	0.491110i	0.983268	−	0.182163i	$-0.0583099\pi$
$948$		0			0
$949$	−10.3258	−	3.50513i	−0.335189	−	0.113781i
$950$		0			0
$951$	71.7321			2.32607
$952$		0			0
$953$	−6.75191			−0.218716			−0.109358	−	0.994002i	$-0.534879\pi$
$953$	−6.75191			−0.218716			−0.109358	+	0.994002i	$0.534879\pi$
$954$		0			0
$955$	−3.15693	−	1.07163i	−0.102156	−	0.0346772i
$956$		0			0
$957$	−0.993054	+	15.1511i	−0.0321009	+	0.489765i
$958$		0			0
$959$	−20.0811	+	0.952950i	−0.648453	+	0.0307724i
$960$		0			0
$961$	−69.2718	−	53.1541i	−2.23457	−	1.71465i
$962$		0			0
$963$	−51.3037	−	44.9921i	−1.65324	−	1.44985i
$964$		0			0
$965$	19.0560	+	19.0560i	0.613433	+	0.613433i
$966$		0			0
$967$	−0.384566	+	0.928425i	−0.0123668	+	0.0298561i	−0.929942	−	0.367705i	$-0.880143\pi$
$967$	−0.384566	+	0.928425i	−0.0123668	+	0.0298561i	0.917576	+	0.397562i	$0.130143\pi$
$968$		0			0
$969$	−21.9330	−	3.35577i	−0.704591	−	0.107803i
$970$		0			0
$971$	−33.3479	+	4.39033i	−1.07019	+	0.140893i	−0.644976	−	0.764203i	$-0.723133\pi$
$971$	−33.3479	+	4.39033i	−1.07019	+	0.140893i	−0.425209	+	0.905095i	$0.639799\pi$
$972$		0			0
$973$	−17.8323	+	17.2006i	−0.571678	+	0.551425i
$974$		0			0
$975$	7.30075	+	21.5073i	0.233811	+	0.688786i
$976$		0			0
$977$	−45.1439	−	5.94331i	−1.44428	−	0.190143i	−0.632706	−	0.774392i	$-0.718056\pi$
$977$	−45.1439	−	5.94331i	−1.44428	−	0.190143i	−0.811575	+	0.584249i	$0.801389\pi$
$978$		0			0
$979$	−15.9954	−	23.9388i	−0.511215	−	0.765087i
$980$		0			0
$981$	25.7227	+	17.1874i	0.821262	+	0.548750i
$982$		0			0
$983$	−12.1795	+	35.8796i	−0.388465	+	1.14438i	0.560271	+	0.828310i	$0.310697\pi$
$983$	−12.1795	+	35.8796i	−0.388465	+	1.14438i	−0.948736	+	0.316071i	$0.897636\pi$
$984$		0			0
$985$	−0.780324	−	1.35156i	−0.0248632	−	0.0430643i
$986$		0			0
$987$	−37.7768	−	0.681203i	−1.20245	−	0.0216829i
$988$		0			0
$989$	3.38107	+	3.85537i	0.107512	+	0.122594i
$990$		0			0
$991$	−2.73794	−	5.55200i	−0.0869736	−	0.176365i	0.849040	−	0.528328i	$-0.177181\pi$
$991$	−2.73794	−	5.55200i	−0.0869736	−	0.176365i	−0.936014	+	0.351963i	$0.885514\pi$
$992$		0			0
$993$	53.2222	−	35.5619i	1.68895	−	1.12852i
$994$		0			0
$995$	6.55628	−	2.71570i	0.207848	−	0.0860935i
$996$		0			0
$997$	2.70005	−	3.07881i	0.0855113	−	0.0975070i	−0.707502	−	0.706712i	$-0.750178\pi$
$997$	2.70005	−	3.07881i	0.0855113	−	0.0975070i	0.793013	+	0.609205i	$0.208511\pi$
$998$		0			0
$999$	−0.359576	+	1.34196i	−0.0113765	+	0.0424576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.12	yes	192
7.5	odd	6	inner	476.2.bl.a.397.12	yes	192
17.3	odd	16	inner	476.2.bl.a.241.12	yes	192
119.54	even	48	inner	476.2.bl.a.173.12	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.12	✓	192	119.54	even	48	inner
476.2.bl.a.241.12	yes	192	17.3	odd	16	inner
476.2.bl.a.397.12	yes	192	7.5	odd	6	inner
476.2.bl.a.465.12	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)

\(f(q)\)	\(=\)	\(q+(2.51390 + 0.853353i) q^{3} +(0.0888586 - 1.35572i) q^{5} +(1.43000 + 2.22601i) q^{7} +(3.21140 + 2.46420i) q^{9} +O(q^{10})\)	\(q+(2.51390 + 0.853353i) q^{3} +(0.0888586 - 1.35572i) q^{5} +(1.43000 + 2.22601i) q^{7} +(3.21140 + 2.46420i) q^{9} +(-1.32853 - 1.16509i) q^{11} +(1.91798 + 1.91798i) q^{13} +(1.38029 - 3.33231i) q^{15} +(-4.11902 + 0.183527i) q^{17} +(2.00973 - 0.264586i) q^{19} +(1.69530 + 6.81624i) q^{21} +(-0.196735 - 0.579563i) q^{23} +(3.12714 + 0.411696i) q^{25} +(1.54555 + 2.31308i) q^{27} +(-2.69119 - 1.79820i) q^{29} +(3.49639 - 10.3000i) q^{31} +(-2.34556 - 4.06262i) q^{33} +(3.14491 - 1.74088i) q^{35} +(0.329279 + 0.375471i) q^{37} +(3.18490 + 6.45833i) q^{39} +(-9.87781 + 6.60014i) q^{41} +(-7.74057 + 3.20625i) q^{43} +(3.62612 - 4.13480i) q^{45} +(-1.39224 + 5.19590i) q^{47} +(-2.91020 + 6.36637i) q^{49} +(-10.5114 - 3.05361i) q^{51} +(3.76118 - 2.88605i) q^{53} +(-1.69759 + 1.69759i) q^{55} +(5.27805 + 1.04987i) q^{57} +(0.939455 - 7.13587i) q^{59} +(3.38029 - 6.85455i) q^{61} +(-0.893010 + 10.6724i) q^{63} +(2.77068 - 2.42982i) q^{65} +(-1.03219 - 0.595934i) q^{67} -1.62485i q^{69} +(-1.90822 + 0.379568i) q^{71} +(-3.60559 + 1.77808i) q^{73} +(7.50999 + 3.70352i) q^{75} +(0.693699 - 4.62340i) q^{77} +(4.57637 - 1.55347i) q^{79} +(-1.23153 - 4.59614i) q^{81} +(-11.2223 - 4.64841i) q^{83} +(-0.117199 + 5.60055i) q^{85} +(-5.23088 - 6.81702i) q^{87} +(15.7381 + 4.21702i) q^{89} +(-1.52673 + 7.01216i) q^{91} +(17.5791 - 22.9095i) q^{93} +(-0.180123 - 2.74815i) q^{95} +(-4.66312 + 6.97885i) q^{97} +(-1.39544 - 7.01534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 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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