LMFDB - Embedded newform 552.2.u.a.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))

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

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

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908372 + 1.47474i) q^{3} +(-1.46204 + 0.939594i) q^{5} +(-4.39604 - 0.632056i) q^{7} +(-1.34972 + 2.67923i) q^{9} +O(q^{10})$	\(q+(0.908372 + 1.47474i) q^{3} +(-1.46204 + 0.939594i) q^{5} +(-4.39604 - 0.632056i) q^{7} +(-1.34972 + 2.67923i) q^{9} +(-0.745816 - 1.63311i) q^{11} +(-0.680183 - 4.73078i) q^{13} +(-2.71373 - 1.30262i) q^{15} +(-4.28776 + 4.94834i) q^{17} +(2.94151 - 2.54883i) q^{19} +(-3.06112 - 7.05717i) q^{21} +(-3.18468 - 3.58578i) q^{23} +(-0.822360 + 1.80072i) q^{25} +(-5.17721 + 0.443246i) q^{27} +(2.86320 + 2.48097i) q^{29} +(1.79339 - 0.526588i) q^{31} +(1.73093 - 2.58335i) q^{33} +(7.02106 - 3.20641i) q^{35} +(-3.48043 + 5.41566i) q^{37} +(6.35881 - 5.30040i) q^{39} +(-0.243417 - 0.378764i) q^{41} +(-3.56373 + 12.1370i) q^{43} +(-0.544044 - 5.18532i) q^{45} -7.01626i q^{47} +(12.2093 + 3.58496i) q^{49} +(-11.1924 - 1.82840i) q^{51} +(-0.558964 + 3.88768i) q^{53} +(2.62487 + 1.68690i) q^{55} +(6.43085 + 2.02268i) q^{57} +(-6.04549 + 0.869211i) q^{59} +(1.23808 + 4.21650i) q^{61} +(7.62685 - 10.9249i) q^{63} +(5.43946 + 6.27748i) q^{65} +(-12.1243 - 5.53697i) q^{67} +(2.39523 - 7.95380i) q^{69} +(-2.04642 - 0.934571i) q^{71} +(2.20646 + 2.54639i) q^{73} +(-3.40260 + 0.422953i) q^{75} +(2.24642 + 7.65061i) q^{77} +(-4.58105 + 0.658656i) q^{79} +(-5.35651 - 7.23241i) q^{81} +(-1.85653 - 1.19312i) q^{83} +(1.61943 - 11.2634i) q^{85} +(-1.05795 + 6.47612i) q^{87} +(-7.62241 - 2.23814i) q^{89} +21.2266i q^{91} +(2.40565 + 2.16645i) q^{93} +(-1.90573 + 6.49031i) q^{95} +(7.32145 + 11.3924i) q^{97} +(5.38211 + 0.206031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

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
$3$	0.908372	+	1.47474i	0.524449	+	0.851442i
$3$	0.908372	+	1.47474i	0.524449	+	0.851442i
$4$		0			0
$5$	−1.46204	+	0.939594i	−0.653843	+	0.420199i	−0.825069	−	0.565032i	$-0.808864\pi$
$5$	−1.46204	+	0.939594i	−0.653843	+	0.420199i	0.171226	+	0.985232i	$0.445227\pi$
$6$		0			0
$7$	−4.39604	−	0.632056i	−1.66155	−	0.238895i	−0.753406	−	0.657556i	$-0.771590\pi$
$7$	−4.39604	−	0.632056i	−1.66155	−	0.238895i	−0.908143	+	0.418661i	$0.862500\pi$
$8$		0			0
$9$	−1.34972	+	2.67923i	−0.449907	+	0.893075i
$10$		0			0
$11$	−0.745816	−	1.63311i	−0.224872	−	0.492401i	0.763244	−	0.646110i	$-0.223605\pi$
$11$	−0.745816	−	1.63311i	−0.224872	−	0.492401i	−0.988116	+	0.153709i	$0.950878\pi$
$12$		0			0
$13$	−0.680183	−	4.73078i	−0.188649	−	1.31208i	−0.835511	−	0.549474i	$-0.814828\pi$
$13$	−0.680183	−	4.73078i	−0.188649	−	1.31208i	0.646862	−	0.762607i	$-0.276081\pi$
$14$		0			0
$15$	−2.71373	−	1.30262i	−0.700683	−	0.336336i
$16$		0			0
$17$	−4.28776	+	4.94834i	−1.03993	+	1.20015i	−0.0605445	+	0.998165i	$0.519284\pi$
$17$	−4.28776	+	4.94834i	−1.03993	+	1.20015i	−0.979389	+	0.201982i	$0.935262\pi$
$18$		0			0
$19$	2.94151	−	2.54883i	0.674828	−	0.584742i	−0.248557	−	0.968617i	$-0.579956\pi$
$19$	2.94151	−	2.54883i	0.674828	−	0.584742i	0.923385	+	0.383875i	$0.125411\pi$
$20$		0			0
$21$	−3.06112	−	7.05717i	−0.667992	−	1.54000i
$22$		0			0
$23$	−3.18468	−	3.58578i	−0.664051	−	0.747687i
$23$	−3.18468	−	3.58578i	−0.664051	−	0.747687i
$24$		0			0
$25$	−0.822360	+	1.80072i	−0.164472	+	0.360143i
$26$		0			0
$27$	−5.17721	+	0.443246i	−0.996355	+	0.0853027i
$28$		0			0
$29$	2.86320	+	2.48097i	0.531682	+	0.460705i	0.878850	−	0.477098i	$-0.158311\pi$
$29$	2.86320	+	2.48097i	0.531682	+	0.460705i	−0.347168	+	0.937803i	$0.612857\pi$
$30$		0			0
$31$	1.79339	−	0.526588i	0.322103	−	0.0945780i	−0.116684	−	0.993169i	$-0.537226\pi$
$31$	1.79339	−	0.526588i	0.322103	−	0.0945780i	0.438787	+	0.898591i	$0.355408\pi$
$32$		0			0
$33$	1.73093	−	2.58335i	0.301317	−	0.449704i
$34$		0			0
$35$	7.02106	−	3.20641i	1.18678	−	0.541982i
$36$		0			0
$37$	−3.48043	+	5.41566i	−0.572179	+	0.890328i	−0.999908	−	0.0135789i	$-0.995678\pi$
$37$	−3.48043	+	5.41566i	−0.572179	+	0.890328i	0.427728	+	0.903907i	$0.359314\pi$
$38$		0			0
$39$	6.35881	−	5.30040i	1.01822	−	0.848743i
$40$		0			0
$41$	−0.243417	−	0.378764i	−0.0380153	−	0.0591530i	0.821726	−	0.569883i	$-0.193012\pi$
$41$	−0.243417	−	0.378764i	−0.0380153	−	0.0591530i	−0.859741	+	0.510730i	$0.829375\pi$
$42$		0			0
$43$	−3.56373	+	12.1370i	−0.543464	+	1.85087i	−0.0183600	+	0.999831i	$0.505845\pi$
$43$	−3.56373	+	12.1370i	−0.543464	+	1.85087i	−0.525104	+	0.851038i	$0.675974\pi$
$44$		0			0
$45$	−0.544044	−	5.18532i	−0.0811013	−	0.772982i
$46$		0			0
$47$		−	7.01626i		−	1.02343i	−0.859156	−	0.511713i	$-0.829011\pi$
$47$		−	7.01626i		−	1.02343i	0.859156	−	0.511713i	$-0.170989\pi$
$48$		0			0
$49$	12.2093	+	3.58496i	1.74418	+	0.512137i
$50$		0			0
$51$	−11.1924	−	1.82840i	−1.56725	−	0.256027i
$52$		0			0
$53$	−0.558964	+	3.88768i	−0.0767796	+	0.534014i	0.914739	+	0.404046i	$0.132397\pi$
$53$	−0.558964	+	3.88768i	−0.0767796	+	0.534014i	−0.991518	+	0.129968i	$0.958513\pi$
$54$		0			0
$55$	2.62487	+	1.68690i	0.353937	+	0.227462i
$56$		0			0
$57$	6.43085	+	2.02268i	0.851787	+	0.267910i
$58$		0			0
$59$	−6.04549	+	0.869211i	−0.787056	+	0.113162i	−0.524112	−	0.851649i	$-0.675603\pi$
$59$	−6.04549	+	0.869211i	−0.787056	+	0.113162i	−0.262944	+	0.964811i	$0.584694\pi$
$60$		0			0
$61$	1.23808	+	4.21650i	0.158519	+	0.539867i	1.00000		0.000420219i	$-0.000133760\pi$
$61$	1.23808	+	4.21650i	0.158519	+	0.539867i	−0.841481	+	0.540287i	$0.818316\pi$
$62$		0			0
$63$	7.62685	−	10.9249i	0.960893	−	1.37641i
$64$		0			0
$65$	5.43946	+	6.27748i	0.674682	+	0.778625i
$66$		0			0
$67$	−12.1243	−	5.53697i	−1.48121	−	0.676448i	−0.499414	−	0.866363i	$-0.666451\pi$
$67$	−12.1243	−	5.53697i	−1.48121	−	0.676448i	−0.981800	+	0.189915i	$0.939179\pi$
$68$		0			0
$69$	2.39523	−	7.95380i	0.288351	−	0.957525i
$70$		0			0
$71$	−2.04642	−	0.934571i	−0.242866	−	0.110913i	0.290264	−	0.956947i	$-0.406257\pi$
$71$	−2.04642	−	0.934571i	−0.242866	−	0.110913i	−0.533130	+	0.846034i	$0.678984\pi$
$72$		0			0
$73$	2.20646	+	2.54639i	0.258246	+	0.298032i	0.870036	−	0.492989i	$-0.164096\pi$
$73$	2.20646	+	2.54639i	0.258246	+	0.298032i	−0.611790	+	0.791021i	$0.709550\pi$
$74$		0			0
$75$	−3.40260	+	0.422953i	−0.392898	+	0.0488384i
$76$		0			0
$77$	2.24642	+	7.65061i	0.256004	+	0.871868i
$78$		0			0
$79$	−4.58105	+	0.658656i	−0.515409	+	0.0741046i	−0.395111	−	0.918633i	$-0.629294\pi$
$79$	−4.58105	+	0.658656i	−0.515409	+	0.0741046i	−0.120298	+	0.992738i	$0.538385\pi$
$80$		0			0
$81$	−5.35651	−	7.23241i	−0.595168	−	0.803602i
$82$		0			0
$83$	−1.85653	−	1.19312i	−0.203780	−	0.130962i	0.434771	−	0.900541i	$-0.356829\pi$
$83$	−1.85653	−	1.19312i	−0.203780	−	0.130962i	−0.638551	+	0.769580i	$0.720466\pi$
$84$		0			0
$85$	1.61943	−	11.2634i	0.175652	−	1.22169i
$86$		0			0
$87$	−1.05795	+	6.47612i	−0.113424	+	0.694313i
$88$		0			0
$89$	−7.62241	−	2.23814i	−0.807973	−	0.237242i	−0.148444	−	0.988921i	$-0.547426\pi$
$89$	−7.62241	−	2.23814i	−0.807973	−	0.237242i	−0.659530	+	0.751678i	$0.729245\pi$
$90$		0			0
$91$			21.2266i			2.22515i
$92$		0			0
$93$	2.40565	+	2.16645i	0.249454	+	0.224651i
$94$		0			0
$95$	−1.90573	+	6.49031i	−0.195524	+	0.665892i
$96$		0			0
$97$	7.32145	+	11.3924i	0.743381	+	1.15672i	0.982596	+	0.185757i	$0.0594737\pi$
$97$	7.32145	+	11.3924i	0.743381	+	1.15672i	−0.239215	+	0.970967i	$0.576890\pi$
$98$		0			0
$99$	5.38211	+	0.206031i	0.540922	+	0.0207069i
$100$		0			0
$101$	−9.74644	+	15.1658i	−0.969807	+	1.50905i	−0.112883	+	0.993608i	$0.536008\pi$
$101$	−9.74644	+	15.1658i	−0.969807	+	1.50905i	−0.856925	+	0.515441i	$0.827628\pi$
$102$		0			0
$103$	−0.828252	+	0.378250i	−0.0816101	+	0.0372701i	−0.455802	−	0.890081i	$-0.650647\pi$
$103$	−0.828252	+	0.378250i	−0.0816101	+	0.0372701i	0.374192	+	0.927351i	$0.377920\pi$
$104$		0			0
$105$	11.1064	+	7.44163i	1.08387	+	0.726228i
$106$		0			0
$107$	0.114220	−	0.0335379i	0.0110420	−	0.00324223i	−0.276207	−	0.961098i	$-0.589077\pi$
$107$	0.114220	−	0.0335379i	0.0110420	−	0.00324223i	0.287249	+	0.957856i	$0.407259\pi$
$108$		0			0
$109$	5.98064	+	5.18225i	0.572841	+	0.496370i	0.892430	−	0.451187i	$-0.148999\pi$
$109$	5.98064	+	5.18225i	0.572841	+	0.496370i	−0.319588	+	0.947557i	$0.603545\pi$
$110$		0			0
$111$	−11.1482	−	0.213303i	−1.05814	−	0.0202458i
$112$		0			0
$113$	7.42147	−	16.2508i	0.698153	−	1.52874i	−0.144043	−	0.989571i	$-0.546010\pi$
$113$	7.42147	−	16.2508i	0.698153	−	1.52874i	0.842196	−	0.539171i	$-0.181262\pi$
$114$		0			0
$115$	8.02530	+	2.25024i	0.748363	+	0.209836i
$116$		0			0
$117$	13.5929	+	4.56286i	1.25666	+	0.421837i
$118$		0			0
$119$	21.9768	−	19.0430i	2.01461	−	1.74567i
$120$		0			0
$121$	5.09267	−	5.87725i	0.462970	−	0.534295i
$122$		0			0
$123$	0.337466	−	0.703035i	0.0304283	−	0.0633906i
$124$		0			0
$125$	−1.72629	−	12.0066i	−0.154404	−	1.07390i
$126$		0			0
$127$	−5.26343	−	11.5253i	−0.467054	−	1.02271i	−0.985823	−	0.167791i	$-0.946337\pi$
$127$	−5.26343	−	11.5253i	−0.467054	−	1.02271i	0.518769	−	0.854915i	$-0.326391\pi$
$128$		0			0
$129$	−21.1361	+	5.76929i	−1.86093	+	0.507958i
$130$		0			0
$131$	12.8526	+	1.84793i	1.12294	+	0.161454i	0.678673	−	0.734441i	$-0.262555\pi$
$131$	12.8526	+	1.84793i	1.12294	+	0.161454i	0.444266	+	0.895895i	$0.353465\pi$
$132$		0			0
$133$	−14.5420	+	9.34558i	−1.26095	+	0.810364i
$134$		0			0
$135$	7.15281	−	5.51252i	0.615616	−	0.474442i
$136$		0			0
$137$	14.6698			1.25332			0.626661	−	0.779292i	$-0.284421\pi$
$137$	14.6698			1.25332			0.626661	+	0.779292i	$0.284421\pi$
$138$		0			0
$139$	20.4626			1.73562			0.867808	−	0.496900i	$-0.165529\pi$
$139$	20.4626			1.73562			0.867808	+	0.496900i	$0.165529\pi$
$140$		0			0
$141$	10.3472	−	6.37338i	0.871389	−	0.536735i
$142$		0			0
$143$	−7.21858	+	4.63910i	−0.603648	+	0.387941i
$144$		0			0
$145$	−6.51721	−	0.937033i	−0.541225	−	0.0778164i
$146$		0			0
$147$	5.80366	+	21.2620i	0.478678	+	1.75366i
$148$		0			0
$149$	−7.85147	−	17.1923i	−0.643218	−	1.40845i	−0.897367	−	0.441285i	$-0.854523\pi$
$149$	−7.85147	−	17.1923i	−0.643218	−	1.40845i	0.254149	−	0.967165i	$-0.418205\pi$
$150$		0			0
$151$	1.83891	+	12.7899i	0.149648	+	1.04083i	0.916796	+	0.399356i	$0.130766\pi$
$151$	1.83891	+	12.7899i	0.149648	+	1.04083i	−0.767148	+	0.641471i	$0.778325\pi$
$152$		0			0
$153$	−7.47044	−	18.1667i	−0.603949	−	1.46869i
$154$		0			0
$155$	−2.12723	+	2.45496i	−0.170863	+	0.197187i
$156$		0			0
$157$	−10.4831	+	9.08364i	−0.836641	+	0.724954i	−0.963713	−	0.266940i	$-0.913987\pi$
$157$	−10.4831	+	9.08364i	−0.836641	+	0.724954i	0.127072	+	0.991893i	$0.459442\pi$
$158$		0			0
$159$	−6.24107	+	2.70713i	−0.494949	+	0.214690i
$160$		0			0
$161$	11.7336	+	17.7761i	0.924735	+	1.40096i
$162$		0			0
$163$	4.39102	−	9.61500i	0.343931	−	0.753105i	−0.656067	−	0.754702i	$-0.727781\pi$
$163$	4.39102	−	9.61500i	0.343931	−	0.753105i	0.999999	+	0.00159767i	$0.000508555\pi$
$164$		0			0
$165$	−0.103384	+	5.40334i	−0.00804844	+	0.420649i
$166$		0			0
$167$	18.2790	+	15.8389i	1.41447	+	1.22565i	0.938081	+	0.346415i	$0.112601\pi$
$167$	18.2790	+	15.8389i	1.41447	+	1.22565i	0.476392	+	0.879233i	$0.341944\pi$
$168$		0			0
$169$	−9.44419	+	2.77306i	−0.726476	+	0.213313i
$170$		0			0
$171$	2.85868	+	11.3212i	0.218609	+	0.865752i
$172$		0			0
$173$	−2.19063	+	1.00043i	−0.166550	+	0.0760611i	−0.496946	−	0.867782i	$-0.665545\pi$
$173$	−2.19063	+	1.00043i	−0.166550	+	0.0760611i	0.330395	+	0.943843i	$0.392818\pi$
$174$		0			0
$175$	4.75328	−	7.39625i	0.359314	−	0.559104i
$176$		0			0
$177$	−6.77342	−	8.12597i	−0.509121	−	0.610785i
$178$		0			0
$179$	−4.78761	−	7.44967i	−0.357843	−	0.556815i	0.614928	−	0.788583i	$-0.289185\pi$
$179$	−4.78761	−	7.44967i	−0.357843	−	0.556815i	−0.972771	+	0.231769i	$0.925549\pi$
$180$		0			0
$181$	1.51988	−	5.17623i	0.112972	−	0.384746i	−0.883524	−	0.468385i	$-0.844836\pi$
$181$	1.51988	−	5.17623i	0.112972	−	0.384746i	0.996496	+	0.0836387i	$0.0266542\pi$
$182$		0			0
$183$	−5.09361	+	5.65599i	−0.376530	+	0.418103i
$184$		0			0
$185$		−	11.1881i		−	0.822564i
$186$		0			0
$187$	11.2790	+	3.31183i	0.824805	+	0.242185i
$188$		0			0
$189$	23.0394	+	1.32376i	1.67587	+	0.0962892i
$190$		0			0
$191$	0.281265	−	1.95624i	0.0203516	−	0.141549i	−0.977112	−	0.212725i	$-0.931766\pi$
$191$	0.281265	−	1.95624i	0.0203516	−	0.141549i	0.997464	+	0.0711763i	$0.0226753\pi$
$192$		0			0
$193$	−0.631451	−	0.405809i	−0.0454528	−	0.0292108i	0.517717	−	0.855552i	$-0.326782\pi$
$193$	−0.631451	−	0.405809i	−0.0454528	−	0.0292108i	−0.563170	+	0.826341i	$0.690418\pi$
$194$		0			0
$195$	−4.31659	+	13.7241i	−0.309118	+	0.982802i
$196$		0			0
$197$	−15.7314	+	2.26184i	−1.12082	+	0.161149i	−0.677717	−	0.735323i	$-0.737030\pi$
$197$	−15.7314	+	2.26184i	−1.12082	+	0.161149i	−0.443100	+	0.896472i	$0.646121\pi$
$198$		0			0
$199$	−1.49791	−	5.10142i	−0.106184	−	0.361630i	0.889210	−	0.457500i	$-0.151255\pi$
$199$	−1.49791	−	5.10142i	−0.106184	−	0.361630i	−0.995394	+	0.0958698i	$0.969437\pi$
$200$		0			0
$201$	−2.84775	−	22.9098i	−0.200865	−	1.61593i
$202$		0			0
$203$	−11.0186	−	12.7162i	−0.773356	−	0.892500i
$204$		0			0
$205$	0.711769	+	0.325054i	0.0497121	+	0.0227028i
$206$		0			0
$207$	13.9055	−	3.69267i	0.966502	−	0.256658i
$208$		0			0
$209$	−6.35634	−	2.90284i	−0.439677	−	0.200794i
$210$		0			0
$211$	−2.54751	−	2.93999i	−0.175378	−	0.202397i	0.661254	−	0.750162i	$-0.270024\pi$
$211$	−2.54751	−	2.93999i	−0.175378	−	0.202397i	−0.836632	+	0.547765i	$0.815479\pi$
$212$		0			0
$213$	−0.480665	−	3.86688i	−0.0329346	−	0.264954i
$214$		0			0
$215$	−6.19351	−	21.0932i	−0.422394	−	1.43854i
$216$		0			0
$217$	−8.21668	+	1.18138i	−0.557784	+	0.0801973i
$218$		0			0
$219$	−1.75098	+	5.56702i	−0.118320	+	0.376184i
$220$		0			0
$221$	26.3259	+	16.9186i	1.77087	+	1.13807i
$222$		0			0
$223$	0.157688	−	1.09675i	0.0105596	−	0.0734436i	−0.983860	−	0.178939i	$-0.942734\pi$
$223$	0.157688	−	1.09675i	0.0105596	−	0.0734436i	0.994420	+	0.105495i	$0.0336427\pi$
$224$		0			0
$225$	−3.71457	−	4.63375i	−0.247638	−	0.308917i
$226$		0			0
$227$	−8.13014	−	2.38722i	−0.539616	−	0.158446i	0.000556357	−	1.00000i	$-0.499823\pi$
$227$	−8.13014	−	2.38722i	−0.539616	−	0.158446i	−0.540173	+	0.841554i	$0.681641\pi$
$228$		0			0
$229$		−	2.36073i		−	0.156001i	−0.996953	−	0.0780006i	$-0.975146\pi$
$229$		−	2.36073i		−	0.156001i	0.996953	−	0.0780006i	$-0.0248536\pi$
$230$		0			0
$231$	−9.24209	+	10.2625i	−0.608085	+	0.675223i
$232$		0			0
$233$	−4.15413	+	14.1477i	−0.272146	+	0.926844i	0.704086	+	0.710115i	$0.251357\pi$
$233$	−4.15413	+	14.1477i	−0.272146	+	0.926844i	−0.976232	+	0.216729i	$0.930461\pi$
$234$		0			0
$235$	6.59244	+	10.2580i	0.430043	+	0.669161i
$236$		0			0
$237$	−5.13265	−	6.15756i	−0.333401	−	0.399977i
$238$		0			0
$239$	3.38061	−	5.26033i	0.218674	−	0.340263i	−0.714534	−	0.699601i	$-0.753361\pi$
$239$	3.38061	−	5.26033i	0.218674	−	0.340263i	0.933207	+	0.359338i	$0.116998\pi$
$240$		0			0
$241$	−8.93920	+	4.08239i	−0.575824	+	0.262970i	−0.681970	−	0.731381i	$-0.738876\pi$
$241$	−8.93920	+	4.08239i	−0.575824	+	0.262970i	0.106145	+	0.994351i	$0.466149\pi$
$242$		0			0
$243$	5.80024	−	14.4692i	0.372085	−	0.928199i
$244$		0			0
$245$	−21.2188	+	6.23040i	−1.35562	+	0.398046i
$246$		0			0
$247$	−14.0587	−	12.1819i	−0.894535	−	0.775119i
$248$		0			0
$249$	0.0731219	−	3.82169i	0.00463391	−	0.242190i
$250$		0			0
$251$	−10.3047	+	22.5642i	−0.650430	+	1.42424i	0.240748	+	0.970588i	$0.422607\pi$
$251$	−10.3047	+	22.5642i	−0.650430	+	1.42424i	−0.891178	+	0.453655i	$0.850120\pi$
$252$		0			0
$253$	−3.48079	+	7.87526i	−0.218835	+	0.495113i
$254$		0			0
$255$	18.0816	−	7.84312i	1.13232	−	0.491155i
$256$		0			0
$257$	2.62352	−	2.27330i	0.163651	−	0.141804i	−0.569186	−	0.822209i	$-0.692741\pi$
$257$	2.62352	−	2.27330i	0.163651	−	0.141804i	0.732837	+	0.680405i	$0.238196\pi$
$258$		0			0
$259$	18.7231	−	21.6076i	1.16340	−	1.34263i
$260$		0			0
$261$	−10.5116	+	4.32253i	−0.650652	+	0.267558i
$262$		0			0
$263$	−0.465178	−	3.23539i	−0.0286841	−	0.199502i	0.970440	−	0.241342i	$-0.0775874\pi$
$263$	−0.465178	−	3.23539i	−0.0286841	−	0.199502i	−0.999124	+	0.0418391i	$0.986678\pi$
$264$		0			0
$265$	−2.83562	−	6.20913i	−0.174191	−	0.381424i
$266$		0			0
$267$	−3.62330	−	13.2741i	−0.221743	−	0.812364i
$268$		0			0
$269$	3.92226	+	0.563935i	0.239144	+	0.0343837i	0.260845	−	0.965381i	$-0.415999\pi$
$269$	3.92226	+	0.563935i	0.239144	+	0.0343837i	−0.0217005	+	0.999765i	$0.506908\pi$
$270$		0			0
$271$	−12.4093	+	7.97495i	−0.753810	+	0.484444i	−0.860248	−	0.509875i	$-0.829692\pi$
$271$	−12.4093	+	7.97495i	−0.753810	+	0.484444i	0.106439	+	0.994319i	$0.466055\pi$
$272$		0			0
$273$	−31.3038	+	19.2817i	−1.89459	+	1.16698i
$274$		0			0
$275$	3.55409			0.214320
$276$		0			0
$277$	−13.1133			−0.787899			−0.393950	−	0.919132i	$-0.628892\pi$
$277$	−13.1133			−0.787899			−0.393950	+	0.919132i	$0.628892\pi$
$278$		0			0
$279$	−1.00973	+	5.51566i	−0.0604511	+	0.330214i
$280$		0			0
$281$	−2.04779	+	1.31604i	−0.122161	+	0.0785082i	−0.600294	−	0.799779i	$-0.704950\pi$
$281$	−2.04779	+	1.31604i	−0.122161	+	0.0785082i	0.478133	+	0.878287i	$0.341314\pi$
$282$		0			0
$283$	4.07194	+	0.585457i	0.242052	+	0.0348018i	0.262273	−	0.964994i	$-0.415528\pi$
$283$	4.07194	+	0.585457i	0.242052	+	0.0348018i	−0.0202211	+	0.999796i	$0.506437\pi$
$284$		0			0
$285$	−11.3026	+	3.08516i	−0.669510	+	0.182749i
$286$		0			0
$287$	0.830671	+	1.81892i	0.0490330	+	0.107367i
$288$		0			0
$289$	−3.68181	−	25.6075i	−0.216577	−	1.50633i
$290$		0			0
$291$	−10.1502	+	21.1458i	−0.595018	+	1.23959i
$292$		0			0
$293$	−6.81334	+	7.86301i	−0.398039	+	0.459362i	−0.919022	−	0.394205i	$-0.871020\pi$
$293$	−6.81334	+	7.86301i	−0.398039	+	0.459362i	0.520983	+	0.853567i	$0.325565\pi$
$294$		0			0
$295$	8.02203	−	6.95113i	0.467061	−	0.404710i
$296$		0			0
$297$	4.58512	+	8.12437i	0.266055	+	0.471424i
$298$		0			0
$299$	−14.7974	+	17.5050i	−0.855754	+	1.01234i
$300$		0			0
$301$	23.3376	−	51.1021i	1.34515	−	2.94548i
$302$		0			0
$303$	−31.2190	−	0.597324i	−1.79348	−	0.0343154i
$304$		0			0
$305$	−5.77191	−	5.00139i	−0.330498	−	0.286379i
$306$		0			0
$307$	−23.3388	+	6.85288i	−1.33201	+	0.391114i	−0.868813	−	0.495140i	$-0.835117\pi$
$307$	−23.3388	+	6.85288i	−1.33201	+	0.391114i	−0.463200	+	0.886254i	$0.653299\pi$
$308$		0			0
$309$	−1.31018	−	0.877865i	−0.0745336	−	0.0499400i
$310$		0			0
$311$	−28.1068	+	12.8359i	−1.59379	+	0.727859i	−0.997207	−	0.0746921i	$-0.976203\pi$
$311$	−28.1068	+	12.8359i	−1.59379	+	0.727859i	−0.596583	+	0.802551i	$0.703475\pi$
$312$		0			0
$313$	13.4288	−	20.8955i	0.759038	−	1.18109i	−0.219619	−	0.975586i	$-0.570481\pi$
$313$	13.4288	−	20.8955i	0.759038	−	1.18109i	0.978657	−	0.205500i	$-0.0658822\pi$
$314$		0			0
$315$	−0.885770	+	23.1388i	−0.0499075	+	1.30372i
$316$		0			0
$317$	−14.5793	−	22.6859i	−0.818857	−	1.27417i	−0.958821	−	0.284010i	$-0.908335\pi$
$317$	−14.5793	−	22.6859i	−0.818857	−	1.27417i	0.139965	−	0.990157i	$-0.455301\pi$
$318$		0			0
$319$	1.91628	−	6.52626i	0.107291	−	0.365400i
$320$		0			0
$321$	0.153214	+	0.137980i	0.00855155	+	0.00770127i
$322$		0			0
$323$			25.4843i			1.41799i
$324$		0			0
$325$	9.07814	+	2.66558i	0.503565	+	0.147860i
$326$		0			0
$327$	−2.20984	+	13.5273i	−0.122204	+	0.748062i
$328$		0			0
$329$	−4.43467	+	30.8438i	−0.244491	+	1.70047i
$330$		0			0
$331$	−9.39325	−	6.03667i	−0.516300	−	0.331806i	0.256407	−	0.966569i	$-0.417461\pi$
$331$	−9.39325	−	6.03667i	−0.516300	−	0.331806i	−0.772707	+	0.634763i	$0.781098\pi$
$332$		0			0
$333$	−9.81216	−	16.6345i	−0.537703	−	0.911564i
$334$		0			0
$335$	22.9286	−	3.29664i	1.25272	−	0.180115i
$336$		0			0
$337$	−1.74989	−	5.95958i	−0.0953227	−	0.324639i	0.898002	−	0.439991i	$-0.145019\pi$
$337$	−1.74989	−	5.95958i	−0.0953227	−	0.324639i	−0.993325	+	0.115352i	$0.963200\pi$
$338$		0			0
$339$	30.7071	−	3.81698i	1.66778	−	0.207310i
$340$		0			0
$341$	−2.19752	−	2.53607i	−0.119002	−	0.137336i
$342$		0			0
$343$	−23.1272	−	10.5618i	−1.24875	−	0.570286i
$344$		0			0
$345$	3.97143	+	13.8793i	0.213815	+	0.747236i
$346$		0			0
$347$	−1.81409	−	0.828466i	−0.0973853	−	0.0444744i	0.366127	−	0.930565i	$-0.380684\pi$
$347$	−1.81409	−	0.828466i	−0.0973853	−	0.0444744i	−0.463512	+	0.886091i	$0.653411\pi$
$348$		0			0
$349$	−5.28457	−	6.09872i	−0.282876	−	0.326457i	0.596474	−	0.802633i	$-0.296568\pi$
$349$	−5.28457	−	6.09872i	−0.282876	−	0.326457i	−0.879350	+	0.476176i	$0.842023\pi$
$350$		0			0
$351$	5.61835	+	24.1907i	0.299885	+	1.29121i
$352$		0			0
$353$	−2.43797	−	8.30297i	−0.129760	−	0.441923i	0.868824	−	0.495121i	$-0.164876\pi$
$353$	−2.43797	−	8.30297i	−0.129760	−	0.441923i	−0.998584	+	0.0531989i	$0.983058\pi$
$354$		0			0
$355$	3.87007	−	0.556431i	0.205402	−	0.0295323i
$356$		0			0
$357$	48.0466	+	15.1119i	2.54290	+	0.799809i
$358$		0			0
$359$	15.4531	+	9.93108i	0.815582	+	0.524143i	0.880666	−	0.473737i	$-0.157095\pi$
$359$	15.4531	+	9.93108i	0.815582	+	0.524143i	−0.0650845	+	0.997880i	$0.520732\pi$
$360$		0			0
$361$	−0.548052	+	3.81179i	−0.0288449	+	0.200620i
$362$		0			0
$363$	13.2935	+	2.17163i	0.697725	+	0.113981i
$364$		0			0
$365$	−5.61849	−	1.64974i	−0.294085	−	0.0863512i
$366$		0			0
$367$		−	17.8779i		−	0.933221i	−0.884463	−	0.466610i	$-0.845475\pi$
$367$		−	17.8779i		−	0.933221i	0.884463	−	0.466610i	$-0.154525\pi$
$368$		0			0
$369$	1.34334	−	0.140943i	0.0699315	−	0.00733721i
$370$		0			0
$371$	4.91446	−	16.7371i	0.255146	−	0.868948i
$372$		0			0
$373$	−0.299176	−	0.465527i	−0.0154907	−	0.0241041i	0.833422	−	0.552637i	$-0.186379\pi$
$373$	−0.299176	−	0.465527i	−0.0154907	−	0.0241041i	−0.848913	+	0.528533i	$0.822742\pi$
$374$		0			0
$375$	16.1385	−	13.4523i	0.833388	−	0.694672i
$376$		0			0
$377$	9.78944	−	15.2327i	0.504182	−	0.784522i
$378$		0			0
$379$	−20.8014	+	9.49969i	−1.06850	+	0.487966i	−0.870465	−	0.492230i	$-0.836182\pi$
$379$	−20.8014	+	9.49969i	−1.06850	+	0.487966i	−0.198031	+	0.980196i	$0.563455\pi$
$380$		0			0
$381$	12.2157	−	18.2315i	0.625829	−	0.934026i
$382$		0			0
$383$	13.3804	−	3.92885i	0.683709	−	0.200755i	0.0786101	−	0.996905i	$-0.474952\pi$
$383$	13.3804	−	3.92885i	0.683709	−	0.200755i	0.605099	+	0.796150i	$0.293134\pi$
$384$		0			0
$385$	−10.4728	−	9.07476i	−0.533745	−	0.462492i
$386$		0			0
$387$	−27.7076	−	25.9296i	−1.40846	−	1.31807i
$388$		0			0
$389$	2.29457	−	5.02440i	0.116339	−	0.254747i	−0.842500	−	0.538696i	$-0.818917\pi$
$389$	2.29457	−	5.02440i	0.116339	−	0.254747i	0.958839	+	0.283949i	$0.0916445\pi$
$390$		0			0
$391$	31.3988	−	0.383890i	1.58790	−	0.0194141i
$392$		0			0
$393$	8.94974	+	20.6329i	0.451455	+	1.04079i
$394$		0			0
$395$	6.07880	−	5.26731i	0.305858	−	0.265027i
$396$		0			0
$397$	−6.57793	+	7.59134i	−0.330137	+	0.380999i	−0.896415	−	0.443216i	$-0.853837\pi$
$397$	−6.57793	+	7.59134i	−0.330137	+	0.380999i	0.566278	+	0.824214i	$0.308383\pi$
$398$		0			0
$399$	−26.9919	−	12.9564i	−1.35128	−	0.648633i
$400$		0			0
$401$	−2.79724	−	19.4552i	−0.139687	−	0.971547i	−0.932265	−	0.361776i	$-0.882170\pi$
$401$	−2.79724	−	19.4552i	−0.139687	−	0.971547i	0.792578	−	0.609771i	$-0.208739\pi$
$402$		0			0
$403$	−3.71101	−	8.12597i	−0.184858	−	0.404784i
$404$		0			0
$405$	14.6269	+	5.54112i	0.726819	+	0.275340i
$406$		0			0
$407$	11.4401	+	1.64484i	0.567065	+	0.0815317i
$408$		0			0
$409$	−11.3919	+	7.32114i	−0.563294	+	0.362007i	−0.791088	−	0.611702i	$-0.790485\pi$
$409$	−11.3919	+	7.32114i	−0.563294	+	0.362007i	0.227794	+	0.973709i	$0.426849\pi$
$410$		0			0
$411$	13.3256	+	21.6341i	0.657303	+	1.06713i
$412$		0			0
$413$	27.1256			1.33477
$414$		0			0
$415$	3.83536			0.188270
$416$		0			0
$417$	18.5877	+	30.1770i	0.910241	+	1.47778i
$418$		0			0
$419$	−17.2081	+	11.0590i	−0.840670	+	0.540266i	−0.888652	−	0.458583i	$-0.848357\pi$
$419$	−17.2081	+	11.0590i	−0.840670	+	0.540266i	0.0479821	+	0.998848i	$0.484721\pi$
$420$		0			0
$421$	21.8240	+	3.13782i	1.06364	+	0.152928i	0.651847	−	0.758350i	$-0.273994\pi$
$421$	21.8240	+	3.13782i	1.06364	+	0.152928i	0.411791	+	0.911278i	$0.364903\pi$
$422$		0			0
$423$	18.7982	+	9.46999i	0.913998	+	0.460447i
$424$		0			0
$425$	−5.38447	−	11.7903i	−0.261185	−	0.571916i
$426$		0			0
$427$	−2.77757	−	19.3184i	−0.134416	−	0.934885i
$428$		0			0
$429$	−13.3986	−	6.43151i	−0.646892	−	0.310516i
$430$		0			0
$431$	14.8581	−	17.1472i	0.715690	−	0.825951i	−0.275091	−	0.961418i	$-0.588708\pi$
$431$	14.8581	−	17.1472i	0.715690	−	0.825951i	0.990782	+	0.135467i	$0.0432536\pi$
$432$		0			0
$433$	−29.4803	+	25.5448i	−1.41673	+	1.22761i	−0.480137	+	0.877194i	$0.659413\pi$
$433$	−29.4803	+	25.5448i	−1.41673	+	1.22761i	−0.936596	+	0.350412i	$0.886042\pi$
$434$		0			0
$435$	−4.53817	−	10.4624i	−0.217589	−	0.501632i
$436$		0			0
$437$	−18.5073	−	2.43040i	−0.885325	−	0.116262i
$438$		0			0
$439$	−10.7048	+	23.4403i	−0.510913	+	1.11874i	0.461853	+	0.886956i	$0.347185\pi$
$439$	−10.7048	+	23.4403i	−0.510913	+	1.11874i	−0.972766	+	0.231788i	$0.925543\pi$
$440$		0			0
$441$	−26.0840	+	27.8727i	−1.24210	+	1.32727i
$442$		0			0
$443$	5.97940	+	5.18118i	0.284090	+	0.246165i	0.785235	−	0.619198i	$-0.212542\pi$
$443$	5.97940	+	5.18118i	0.284090	+	0.246165i	−0.501145	+	0.865363i	$0.667088\pi$
$444$		0			0
$445$	13.2472	−	3.88972i	0.627977	−	0.184391i
$446$		0			0
$447$	18.2222	−	27.1959i	0.861879	−	1.28632i
$448$		0			0
$449$	37.6326	−	17.1862i	1.77599	−	0.811067i	0.797928	−	0.602752i	$-0.205929\pi$
$449$	37.6326	−	17.1862i	1.77599	−	0.811067i	0.978062	−	0.208315i	$-0.0667980\pi$
$450$		0			0
$451$	−0.437019	+	0.680014i	−0.0205784	+	0.0320206i
$452$		0			0
$453$	−17.1914	+	14.3299i	−0.807721	+	0.673277i
$454$		0			0
$455$	−19.9444	−	31.0341i	−0.935008	−	1.45490i
$456$		0			0
$457$	7.16420	−	24.3990i	0.335127	−	1.14134i	−0.603775	−	0.797154i	$-0.706338\pi$
$457$	7.16420	−	24.3990i	0.335127	−	1.14134i	0.938902	−	0.344183i	$-0.111844\pi$
$458$		0			0
$459$	20.0053	−	27.5191i	0.933767	−	1.28448i
$460$		0			0
$461$			37.4061i			1.74218i	0.491127	+	0.871088i	$0.336585\pi$
$461$			37.4061i			1.74218i	−0.491127	+	0.871088i	$0.663415\pi$
$462$		0			0
$463$	−14.0462	−	4.12434i	−0.652783	−	0.191674i	−0.0614604	−	0.998110i	$-0.519576\pi$
$463$	−14.0462	−	4.12434i	−0.652783	−	0.191674i	−0.591322	+	0.806435i	$0.701394\pi$
$464$		0			0
$465$	−5.55274	−	0.907101i	−0.257502	−	0.0420658i
$466$		0			0
$467$	−1.81474	+	12.6218i	−0.0839762	+	0.584068i	0.903772	+	0.428014i	$0.140786\pi$
$467$	−1.81474	+	12.6218i	−0.0839762	+	0.584068i	−0.987749	+	0.156054i	$0.950123\pi$
$468$		0			0
$469$	49.7991	+	32.0040i	2.29951	+	1.47781i
$470$		0			0
$471$	−22.9186	−	7.20850i	−1.05603	−	0.332150i
$472$		0			0
$473$	22.4789	−	3.23197i	1.03358	−	0.148606i
$474$		0			0
$475$	2.17074	+	7.39288i	0.0996006	+	0.339209i
$476$		0			0
$477$	−9.66153	−	6.74488i	−0.442371	−	0.308827i
$478$		0			0
$479$	8.38932	+	9.68179i	0.383318	+	0.442372i	0.914317	−	0.405000i	$-0.132729\pi$
$479$	8.38932	+	9.68179i	0.383318	+	0.442372i	−0.530999	+	0.847373i	$0.678183\pi$
$480$		0			0
$481$	27.9876	+	12.7815i	1.27612	+	0.582786i
$482$		0			0
$483$	−15.5568	+	33.4513i	−0.707857	+	1.52209i
$484$		0			0
$485$	−21.4085	−	9.77692i	−0.972109	−	0.443947i
$486$		0			0
$487$	19.8007	+	22.8512i	0.897254	+	1.03549i	0.999172	+	0.0406939i	$0.0129568\pi$
$487$	19.8007	+	22.8512i	0.897254	+	1.03549i	−0.101917	+	0.994793i	$0.532498\pi$
$488$		0			0
$489$	18.1683	−	2.25837i	0.821599	−	0.102127i
$490$		0			0
$491$	−3.03518	−	10.3369i	−0.136976	−	0.466497i	0.862223	−	0.506530i	$-0.169072\pi$
$491$	−3.03518	−	10.3369i	−0.136976	−	0.466497i	−0.999198	+	0.0400328i	$0.987254\pi$
$492$		0			0
$493$	−24.5534	+	3.53024i	−1.10583	+	0.158994i
$494$		0			0
$495$	−8.06243	+	4.75577i	−0.362379	+	0.213756i
$496$		0			0
$497$	8.40547	+	5.40187i	0.377037	+	0.242307i
$498$		0			0
$499$	−0.454123	+	3.15849i	−0.0203293	+	0.141394i	−0.997458	−	0.0712546i	$-0.977300\pi$
$499$	−0.454123	+	3.15849i	−0.0203293	+	0.141394i	0.977129	+	0.212648i	$0.0682088\pi$
$500$		0			0
$501$	−6.75407	+	41.3444i	−0.301749	+	1.84713i
$502$		0			0
$503$	−37.8059	−	11.1008i	−1.68568	−	0.494961i	−0.708205	−	0.706007i	$-0.750495\pi$
$503$	−37.8059	−	11.1008i	−1.68568	−	0.494961i	−0.977476	+	0.211046i	$0.932313\pi$
$504$		0			0
$505$		−	31.3306i		−	1.39419i
$506$		0			0
$507$	−12.6684	−	11.4088i	−0.562623	−	0.506681i
$508$		0			0
$509$	−3.97081	+	13.5233i	−0.176003	+	0.599412i	0.823482	+	0.567342i	$0.192028\pi$
$509$	−3.97081	+	13.5233i	−0.176003	+	0.599412i	−0.999486	+	0.0320701i	$0.989790\pi$
$510$		0			0
$511$	−8.09022	−	12.5886i	−0.357890	−	0.556888i
$512$		0			0
$513$	−14.0991	+	14.4997i	−0.622489	+	0.640175i
$514$		0			0
$515$	0.855533	−	1.33124i	0.0376993	−	0.0586613i
$516$		0			0
$517$	−11.4583	+	5.23284i	−0.503936	+	0.230140i
$518$		0			0
$519$	−3.46528	−	2.32185i	−0.152109	−	0.101918i
$520$		0			0
$521$	39.1767	−	11.5033i	1.71636	−	0.503969i	0.732177	−	0.681115i	$-0.238505\pi$
$521$	39.1767	−	11.5033i	1.71636	−	0.503969i	0.984185	+	0.177146i	$0.0566864\pi$
$522$		0			0
$523$	−9.46618	−	8.20249i	−0.413927	−	0.358670i	0.422863	−	0.906194i	$-0.361025\pi$
$523$	−9.46618	−	8.20249i	−0.413927	−	0.358670i	−0.836790	+	0.547524i	$0.815571\pi$
$524$		0			0
$525$	15.2253	+	0.291312i	0.664487	+	0.0127139i
$526$		0			0
$527$	−5.08391	+	11.1322i	−0.221458	+	0.484926i
$528$		0			0
$529$	−2.71566	+	22.8391i	−0.118072	+	0.993005i
$530$		0			0
$531$	5.83091	−	17.3704i	0.253040	−	0.753813i
$532$		0			0
$533$	−1.62628	+	1.40918i	−0.0704420	+	0.0610383i
$534$		0			0
$535$	−0.135481	+	0.156354i	−0.00585737	+	0.00675977i
$536$		0			0
$537$	6.63740	−	13.8276i	0.286425	−	0.596704i
$538$		0			0
$539$	−3.25122	−	22.6128i	−0.140040	−	0.974001i
$540$		0			0
$541$	2.67466	+	5.85669i	0.114993	+	0.251799i	0.958374	−	0.285517i	$-0.0921654\pi$
$541$	2.67466	+	5.85669i	0.114993	+	0.251799i	−0.843381	+	0.537316i	$0.819438\pi$
$542$		0			0
$543$	9.01422	−	2.46052i	0.386837	−	0.105591i
$544$		0			0
$545$	−13.6131	−	1.95727i	−0.583123	−	0.0838404i
$546$		0			0
$547$	13.0217	−	8.36852i	0.556766	−	0.357812i	−0.231798	−	0.972764i	$-0.574461\pi$
$547$	13.0217	−	8.36852i	0.556766	−	0.357812i	0.788565	+	0.614952i	$0.210825\pi$
$548$		0			0
$549$	−12.9680	−	2.37401i	−0.553461	−	0.101320i
$550$		0			0
$551$	14.7457			0.628188
$552$		0			0
$553$	20.5548			0.874080
$554$		0			0
$555$	16.4995	−	10.1629i	0.700366	−	0.431393i
$556$		0			0
$557$	9.51274	−	6.11347i	0.403068	−	0.259036i	−0.323364	−	0.946275i	$-0.604814\pi$
$557$	9.51274	−	6.11347i	0.403068	−	0.259036i	0.726432	+	0.687239i	$0.241177\pi$
$558$		0			0
$559$	59.8412	+	8.60387i	2.53101	+	0.363905i
$560$		0			0
$561$	5.36148	+	19.6420i	0.226362	+	0.829287i
$562$		0			0
$563$	19.3344	+	42.3364i	0.814848	+	1.78427i	0.584982	+	0.811046i	$0.301101\pi$
$563$	19.3344	+	42.3364i	0.814848	+	1.78427i	0.229866	+	0.973222i	$0.426171\pi$
$564$		0			0
$565$	4.41865	+	30.7324i	0.185894	+	1.29292i
$566$		0			0
$567$	18.9762	+	35.1796i	0.796924	+	1.47741i
$568$		0			0
$569$	0.936382	−	1.08064i	0.0392552	−	0.0453029i	−0.735782	−	0.677218i	$-0.763185\pi$
$569$	0.936382	−	1.08064i	0.0392552	−	0.0453029i	0.775038	+	0.631915i	$0.217731\pi$
$570$		0			0
$571$	−11.6425	+	10.0883i	−0.487225	+	0.422183i	−0.863518	−	0.504318i	$-0.831744\pi$
$571$	−11.6425	+	10.0883i	−0.487225	+	0.422183i	0.376293	+	0.926501i	$0.377199\pi$
$572$		0			0
$573$	3.14044	−	1.36220i	0.131194	−	0.0569068i
$574$		0			0
$575$	9.07593	−	2.78590i	0.378492	−	0.116180i
$576$		0			0
$577$	−11.0224	+	24.1356i	−0.458867	+	1.00478i	0.528877	+	0.848698i	$0.322613\pi$
$577$	−11.0224	+	24.1356i	−0.458867	+	1.00478i	−0.987744	+	0.156081i	$0.950114\pi$
$578$		0			0
$579$	0.0248706	−	1.29985i	0.00103359	−	0.0540200i
$580$		0			0
$581$	7.40726	+	6.41843i	0.307305	+	0.266281i
$582$		0			0
$583$	6.76589	−	1.98664i	0.280215	−	0.0822784i
$584$		0			0
$585$	−24.1605	+	6.10072i	−0.998915	+	0.252234i
$586$		0			0
$587$	−2.68778	+	1.22747i	−0.110937	+	0.0506630i	−0.470110	−	0.882608i	$-0.655786\pi$
$587$	−2.68778	+	1.22747i	−0.110937	+	0.0506630i	0.359174	+	0.933271i	$0.383059\pi$
$588$		0			0
$589$	3.93310	−	6.12002i	0.162061	−	0.252171i
$590$		0			0
$591$	−17.6256	−	21.1452i	−0.725020	−	0.869796i
$592$		0			0
$593$	10.6283	+	16.5379i	0.436450	+	0.679130i	0.987902	−	0.155076i	$-0.0495624\pi$
$593$	10.6283	+	16.5379i	0.436450	+	0.679130i	−0.551452	+	0.834207i	$0.685926\pi$
$594$		0			0
$595$	−14.2382	+	48.4908i	−0.583709	+	1.98793i
$596$		0			0
$597$	6.16261	−	6.84302i	0.252219	−	0.280066i
$598$		0			0
$599$		−	41.5768i		−	1.69878i	−0.527763	−	0.849391i	$-0.676969\pi$
$599$		−	41.5768i		−	1.69878i	0.527763	−	0.849391i	$-0.323031\pi$
$600$		0			0
$601$	−41.5702	−	12.2061i	−1.69568	−	0.497898i	−0.715942	−	0.698160i	$-0.754003\pi$
$601$	−41.5702	−	12.2061i	−1.69568	−	0.497898i	−0.979742	+	0.200262i	$0.935821\pi$
$602$		0			0
$603$	31.1992	−	25.0103i	1.27053	−	1.01850i
$604$		0			0
$605$	−1.92344	+	13.3778i	−0.0781988	+	0.543885i
$606$		0			0
$607$	−9.13674	−	5.87183i	−0.370849	−	0.238330i	0.341920	−	0.939729i	$-0.388923\pi$
$607$	−9.13674	−	5.87183i	−0.370849	−	0.238330i	−0.712769	+	0.701399i	$0.752559\pi$
$608$		0			0
$609$	8.74405	−	27.8006i	0.354327	−	1.12654i
$610$		0			0
$611$	−33.1924	+	4.77234i	−1.34282	+	0.193068i
$612$		0			0
$613$	9.19951	+	31.3306i	0.371565	+	1.26543i	0.907098	+	0.420919i	$0.138292\pi$
$613$	9.19951	+	31.3306i	0.371565	+	1.26543i	−0.535534	+	0.844514i	$0.679889\pi$
$614$		0			0
$615$	0.167181	+	1.34494i	0.00674137	+	0.0542334i
$616$		0			0
$617$	−9.89036	−	11.4141i	−0.398171	−	0.459514i	0.520893	−	0.853622i	$-0.325599\pi$
$617$	−9.89036	−	11.4141i	−0.398171	−	0.459514i	−0.919064	+	0.394108i	$0.871054\pi$
$618$		0			0
$619$	33.8358	+	15.4523i	1.35998	+	0.621080i	0.955913	−	0.293650i	$-0.0948702\pi$
$619$	33.8358	+	15.4523i	1.35998	+	0.621080i	0.404064	+	0.914731i	$0.367597\pi$
$620$		0			0
$621$	18.0771	+	17.1528i	0.725410	+	0.688317i
$622$		0			0
$623$	32.0938	+	14.6567i	1.28581	+	0.587210i
$624$		0			0
$625$	7.32337	+	8.45162i	0.292935	+	0.338065i
$626$		0			0
$627$	−1.49298	−	12.0108i	−0.0596239	−	0.479666i
$628$		0			0
$629$	−11.8752	−	40.4434i	−0.473497	−	1.61258i
$630$		0			0
$631$	−33.7046	+	4.84599i	−1.34176	+	0.192916i	−0.775519	−	0.631324i	$-0.782512\pi$
$631$	−33.7046	+	4.84599i	−1.34176	+	0.192916i	−0.566240	+	0.824240i	$0.691603\pi$
$632$		0			0
$633$	2.02163	−	6.42752i	0.0803525	−	0.255471i
$634$		0			0
$635$	18.5244	+	11.9049i	0.735120	+	0.472433i
$636$		0			0
$637$	8.65512	−	60.1977i	0.342928	−	2.38512i
$638$		0			0
$639$	5.26603	−	4.22142i	0.208321	−	0.166997i
$640$		0			0
$641$	−26.4641	−	7.77057i	−1.04527	−	0.306919i	−0.286365	−	0.958121i	$-0.592447\pi$
$641$	−26.4641	−	7.77057i	−1.04527	−	0.306919i	−0.758905	+	0.651202i	$0.774265\pi$
$642$		0			0
$643$		−	9.11358i		−	0.359405i	−0.983721	−	0.179702i	$-0.942487\pi$
$643$		−	9.11358i		−	0.359405i	0.983721	−	0.179702i	$-0.0575135\pi$
$644$		0			0
$645$	25.4809	−	28.2943i	1.00331	−	1.11409i
$646$		0			0
$647$	−13.0019	+	44.2803i	−0.511157	+	1.74084i	0.148150	+	0.988965i	$0.452668\pi$
$647$	−13.0019	+	44.2803i	−0.511157	+	1.74084i	−0.659306	+	0.751874i	$0.729150\pi$
$648$		0			0
$649$	5.92834	+	9.22467i	0.232708	+	0.362100i
$650$		0			0
$651$	−9.20603	−	11.0443i	−0.360813	−	0.432862i
$652$		0			0
$653$	−19.8498	+	30.8869i	−0.776784	+	1.20870i	0.196816	+	0.980440i	$0.436940\pi$
$653$	−19.8498	+	30.8869i	−0.776784	+	1.20870i	−0.973600	+	0.228259i	$0.926697\pi$
$654$		0			0
$655$	−20.5273	+	9.37451i	−0.802068	+	0.366292i
$656$		0			0
$657$	−9.80045	+	2.47469i	−0.382352	+	0.0965467i
$658$		0			0
$659$	−18.5574	+	5.44895i	−0.722895	+	0.212261i	−0.622425	−	0.782679i	$-0.713853\pi$
$659$	−18.5574	+	5.44895i	−0.722895	+	0.212261i	−0.100469	+	0.994940i	$0.532034\pi$
$660$		0			0
$661$	−22.7377	−	19.7024i	−0.884396	−	0.766333i	0.0888633	−	0.996044i	$-0.471677\pi$
$661$	−22.7377	−	19.7024i	−0.884396	−	0.766333i	−0.973259	+	0.229711i	$0.926222\pi$
$662$		0			0
$663$	−1.03688	+	54.1923i	−0.0402692	+	2.10466i
$664$		0			0
$665$	12.4799	−	27.3272i	0.483950	−	1.05970i
$666$		0			0
$667$	−0.222126	−	18.1679i	−0.00860074	−	0.703464i
$668$		0			0
$669$	1.76066	−	0.763704i	0.0680709	−	0.0295265i
$670$		0			0
$671$	5.96262	−	5.16664i	0.230184	−	0.199456i
$672$		0			0
$673$	10.0015	−	11.5424i	0.385531	−	0.444926i	−0.529500	−	0.848310i	$-0.677620\pi$
$673$	10.0015	−	11.5424i	0.385531	−	0.444926i	0.915031	+	0.403383i	$0.132166\pi$
$674$		0			0
$675$	3.45937	−	9.68720i	0.133151	−	0.372860i
$676$		0			0
$677$	2.90013	+	20.1708i	0.111461	+	0.775228i	0.966500	+	0.256665i	$0.0826238\pi$
$677$	2.90013	+	20.1708i	0.111461	+	0.775228i	−0.855039	+	0.518563i	$0.826467\pi$
$678$		0			0
$679$	−24.9848	−	54.7091i	−0.958829	−	2.09954i
$680$		0			0
$681$	−3.86465	−	14.1583i	−0.148094	−	0.542549i
$682$		0			0
$683$	40.2436	+	5.78616i	1.53988	+	0.221401i	0.859377	−	0.511343i	$-0.170852\pi$
$683$	40.2436	+	5.78616i	1.53988	+	0.221401i	0.680504	+	0.732745i	$0.261761\pi$
$684$		0			0
$685$	−21.4477	+	13.7836i	−0.819476	+	0.526645i
$686$		0			0
$687$	3.48146	−	2.14442i	0.132826	−	0.0818146i
$688$		0			0
$689$	18.7719			0.715154
$690$		0			0
$691$	−22.1095			−0.841085			−0.420542	−	0.907273i	$-0.638160\pi$
$691$	−22.1095			−0.841085			−0.420542	+	0.907273i	$0.638160\pi$
$692$		0			0
$693$	−23.5298	−	4.30752i	−0.893822	−	0.163629i
$694$		0			0
$695$	−29.9171	+	19.2265i	−1.13482	+	0.729304i
$696$		0			0
$697$	2.91796	+	0.419540i	0.110526	+	0.0158912i
$698$		0			0
$699$	−24.6376	+	6.72508i	−0.931881	+	0.254366i
$700$		0			0
$701$	4.89430	+	10.7170i	0.184855	+	0.404776i	0.979259	−	0.202614i	$-0.0649437\pi$
$701$	4.89430	+	10.7170i	0.184855	+	0.404776i	−0.794404	+	0.607390i	$0.792216\pi$
$702$		0			0
$703$	3.56588	+	24.8012i	0.134490	+	0.935396i
$704$		0			0
$705$	−9.13956	+	19.0403i	−0.344216	+	0.717097i
$706$		0			0
$707$	52.4314	−	60.5091i	1.97189	−	2.27568i
$708$		0			0
$709$	16.9940	−	14.7254i	0.638222	−	0.553022i	−0.274509	−	0.961585i	$-0.588515\pi$
$709$	16.9940	−	14.7254i	0.638222	−	0.553022i	0.912730	+	0.408562i	$0.133970\pi$
$710$		0			0
$711$	4.41845	−	13.1627i	0.165705	−	0.493639i
$712$		0			0
$713$	−7.59961	−	4.75371i	−0.284608	−	0.178028i
$714$		0			0
$715$	6.19496	−	13.5651i	0.231678	−	0.507305i
$716$		0			0
$717$	10.8285	+	0.207185i	0.404397	+	0.00773748i
$718$		0			0
$719$	−20.1249	−	17.4383i	−0.750532	−	0.650340i	0.193159	−	0.981167i	$-0.438127\pi$
$719$	−20.1249	−	17.4383i	−0.750532	−	0.650340i	−0.943691	+	0.330828i	$0.892672\pi$
$720$		0			0
$721$	3.88011	−	1.13930i	0.144503	−	0.0424298i
$722$		0			0
$723$	−14.1406	−	9.47466i	−0.525894	−	0.352367i
$724$		0			0
$725$	−6.82211	+	3.11555i	−0.253367	+	0.115709i
$726$		0			0
$727$	−3.88461	+	6.04458i	−0.144072	+	0.224181i	−0.905789	−	0.423730i	$-0.860721\pi$
$727$	−3.88461	+	6.04458i	−0.144072	+	0.224181i	0.761716	+	0.647911i	$0.224357\pi$
$728$		0			0
$729$	26.6071	−	4.58956i	0.985447	−	0.169984i
$730$		0			0
$731$	−44.7773	−	69.6749i	−1.65615	−	2.57702i
$732$		0			0
$733$	−1.34662	+	4.58616i	−0.0497385	+	0.169394i	−0.980617	−	0.195936i	$-0.937226\pi$
$733$	−1.34662	+	4.58616i	−0.0497385	+	0.169394i	0.930878	+	0.365330i	$0.119044\pi$
$734$		0			0
$735$	−28.4628	−	25.6327i	−1.04987	−	0.945477i
$736$		0			0
$737$			23.9298i			0.881465i
$738$		0			0
$739$	3.94026	+	1.15696i	0.144945	+	0.0425596i	0.353400	−	0.935472i	$-0.385025\pi$
$739$	3.94026	+	1.15696i	0.144945	+	0.0425596i	−0.208455	+	0.978032i	$0.566844\pi$
$740$		0			0
$741$	5.19467	−	31.7987i	0.190831	−	1.16815i
$742$		0			0
$743$	−0.814398	+	5.66426i	−0.0298774	+	0.207802i	−0.999292	−	0.0376278i	$-0.988020\pi$
$743$	−0.814398	+	5.66426i	−0.0298774	+	0.207802i	0.969414	+	0.245429i	$0.0789290\pi$
$744$		0			0
$745$	27.6330	+	17.7586i	1.01239	+	0.650626i
$746$		0			0
$747$	5.70243	−	3.36368i	0.208641	−	0.123071i
$748$		0			0
$749$	−0.523313	+	0.0752410i	−0.0191214	+	0.00274925i
$750$		0			0
$751$	2.79553	+	9.52069i	0.102010	+	0.347415i	0.994643	−	0.103370i	$-0.0329625\pi$
$751$	2.79553	+	9.52069i	0.102010	+	0.347415i	−0.892633	+	0.450785i	$0.851144\pi$
$752$		0			0
$753$	−42.6369	+	5.29990i	−1.55378	+	0.193139i
$754$		0			0
$755$	−14.7059	−	16.9715i	−0.535201	−	0.617655i
$756$		0			0
$757$	−25.6415	−	11.7101i	−0.931956	−	0.425610i	−0.109210	−	0.994019i	$-0.534832\pi$
$757$	−25.6415	−	11.7101i	−0.931956	−	0.425610i	−0.822746	+	0.568409i	$0.807559\pi$
$758$		0			0
$759$	−14.7758	+	2.02040i	−0.536328	+	0.0733359i
$760$		0			0
$761$	−2.83257	−	1.29359i	−0.102681	−	0.0468927i	0.363413	−	0.931628i	$-0.381612\pi$
$761$	−2.83257	−	1.29359i	−0.102681	−	0.0468927i	−0.466093	+	0.884736i	$0.654339\pi$
$762$		0			0
$763$	−23.0157	−	26.5615i	−0.833224	−	0.961591i
$764$		0			0
$765$	27.9914	+	19.5413i	1.01203	+	0.706516i
$766$		0			0
$767$	8.22408	+	28.0086i	0.296954	+	1.01133i
$768$		0			0
$769$	6.49723	−	0.934161i	0.234296	−	0.0336867i	−0.0241665	−	0.999708i	$-0.507693\pi$
$769$	6.49723	−	0.934161i	0.234296	−	0.0336867i	0.258463	+	0.966021i	$0.416784\pi$
$770$		0			0
$771$	5.73566	+	1.80402i	0.206565	+	0.0649702i
$772$		0			0
$773$	6.25498	+	4.01983i	0.224976	+	0.144583i	0.648274	−	0.761407i	$-0.275491\pi$
$773$	6.25498	+	4.01983i	0.224976	+	0.144583i	−0.423298	+	0.905991i	$0.639128\pi$
$774$		0			0
$775$	−0.526579	+	3.66244i	−0.0189153	+	0.131559i
$776$		0			0
$777$	48.8732	+	7.98398i	1.75332	+	0.286424i
$778$		0			0
$779$	−1.68142	−	0.493709i	−0.0602431	−	0.0176890i
$780$		0			0
$781$			4.03905i			0.144529i
$782$		0			0
$783$	−15.9231	−	11.5754i	−0.569044	−	0.413672i
$784$		0			0
$785$	6.79172	−	23.1305i	0.242407	−	0.825562i
$786$		0			0
$787$	9.93931	+	15.4659i	0.354298	+	0.551299i	0.971960	−	0.235145i	$-0.0755565\pi$
$787$	9.93931	+	15.4659i	0.354298	+	0.551299i	−0.617662	+	0.786443i	$0.711920\pi$
$788$		0			0
$789$	4.34880	−	3.62495i	0.154821	−	0.129052i
$790$		0			0
$791$	−42.8965	+	66.7482i	−1.52522	+	2.37329i
$792$		0			0
$793$	19.1052	−	8.72505i	0.678445	−	0.309835i
$794$		0			0
$795$	6.58107	−	9.82200i	0.233406	−	0.348351i
$796$		0			0
$797$	−4.33460	+	1.27275i	−0.153540	+	0.0450833i	−0.357599	−	0.933875i	$-0.616405\pi$
$797$	−4.33460	+	1.27275i	−0.153540	+	0.0450833i	0.204060	+	0.978958i	$0.434586\pi$
$798$		0			0
$799$	34.7188	+	30.0840i	1.22826	+	1.06430i
$800$		0			0
$801$	16.2846	−	17.4013i	0.575388	−	0.614844i
$802$		0			0
$803$	2.51292	−	5.50252i	0.0886789	−	0.194180i
$804$		0			0
$805$	−33.8573	−	14.9646i	−1.19331	−	0.527433i
$806$		0			0
$807$	2.73121	+	6.29657i	0.0961431	+	0.221650i
$808$		0			0
$809$	25.9166	−	22.4568i	0.911178	−	0.789540i	−0.0669044	−	0.997759i	$-0.521312\pi$
$809$	25.9166	−	22.4568i	0.911178	−	0.789540i	0.978082	+	0.208219i	$0.0667668\pi$
$810$		0			0
$811$	25.1637	−	29.0404i	0.883615	−	1.01975i	−0.116033	−	0.993245i	$-0.537018\pi$
$811$	25.1637	−	29.0404i	0.883615	−	1.01975i	0.999649	−	0.0265013i	$-0.00843661\pi$
$812$		0			0
$813$	−23.0332	−	11.0562i	−0.807810	−	0.387759i
$814$		0			0
$815$	2.61436	+	18.1833i	0.0915770	+	0.636932i
$816$		0			0
$817$	20.4523	+	44.7843i	0.715536	+	1.56681i
$818$		0			0
$819$	−56.8709	−	28.6500i	−1.98723	−	1.00111i
$820$		0			0
$821$	−30.7343	−	4.41893i	−1.07264	−	0.154222i	−0.416704	−	0.909042i	$-0.636815\pi$
$821$	−30.7343	−	4.41893i	−1.07264	−	0.154222i	−0.655932	+	0.754820i	$0.727724\pi$
$822$		0			0
$823$	45.4201	−	29.1898i	1.58325	−	1.01749i	0.608674	−	0.793421i	$-0.291702\pi$
$823$	45.4201	−	29.1898i	1.58325	−	1.01749i	0.974573	−	0.224070i	$-0.0719345\pi$
$824$		0			0
$825$	3.22844	+	5.24137i	0.112400	+	0.182481i
$826$		0			0
$827$	11.3900			0.396070			0.198035	−	0.980195i	$-0.436544\pi$
$827$	11.3900			0.396070			0.198035	+	0.980195i	$0.436544\pi$
$828$		0			0
$829$	34.3222			1.19206			0.596030	−	0.802962i	$-0.296744\pi$
$829$	34.3222			1.19206			0.596030	+	0.802962i	$0.296744\pi$
$830$		0			0
$831$	−11.9117	−	19.3387i	−0.413213	−	0.670850i
$832$		0			0
$833$	−70.0899	+	45.0441i	−2.42847	+	1.56068i
$834$		0			0
$835$	−41.6067	−	5.98214i	−1.43986	−	0.207021i
$836$		0			0
$837$	−9.05138	+	3.52117i	−0.312861	+	0.121710i
$838$		0			0
$839$	9.86699	+	21.6057i	0.340646	+	0.745911i	0.999982	−	0.00593703i	$-0.00188983\pi$
$839$	9.86699	+	21.6057i	0.340646	+	0.745911i	−0.659336	+	0.751848i	$0.729163\pi$
$840$		0			0
$841$	−2.08447	−	14.4978i	−0.0718782	−	0.499924i
$842$		0			0
$843$	−3.80097	−	1.82451i	−0.130912	−	0.0628396i
$844$		0			0
$845$	11.2022	−	12.9280i	0.385367	−	0.444738i
$846$		0			0
$847$	−26.1023	+	22.6178i	−0.896887	+	0.777157i
$848$		0			0
$849$	2.83544	+	6.53687i	0.0973121	+	0.224345i
$850$		0			0
$851$	30.5034	−	4.76705i	1.04564	−	0.163412i
$852$		0			0
$853$	−11.4062	+	24.9760i	−0.390539	+	0.855162i	0.607603	+	0.794241i	$0.292131\pi$
$853$	−11.4062	+	24.9760i	−0.390539	+	0.855162i	−0.998143	+	0.0609209i	$0.980596\pi$
$854$		0			0
$855$	−14.8168	−	13.8660i	−0.506724	−	0.474207i
$856$		0			0
$857$	37.1626	+	32.2016i	1.26945	+	1.09999i	0.990184	+	0.139772i	$0.0446368\pi$
$857$	37.1626	+	32.2016i	1.26945	+	1.09999i	0.279267	+	0.960214i	$0.409909\pi$
$858$		0			0
$859$	−18.6917	+	5.48837i	−0.637751	+	0.187261i	−0.584595	−	0.811326i	$-0.698746\pi$
$859$	−18.6917	+	5.48837i	−0.637751	+	0.187261i	−0.0531566	+	0.998586i	$0.516928\pi$
$860$		0			0
$861$	−1.92787	+	2.87728i	−0.0657017	+	0.0980574i
$862$		0			0
$863$	−42.0729	+	19.2140i	−1.43218	+	0.654053i	−0.972259	−	0.233908i	$-0.924849\pi$
$863$	−42.0729	+	19.2140i	−1.43218	+	0.654053i	−0.459918	+	0.887961i	$0.652121\pi$
$864$		0			0
$865$	2.26279	−	3.52096i	0.0769370	−	0.119716i
$866$		0			0
$867$	34.4200	−	28.6909i	1.16897	−	0.974394i
$868$		0			0
$869$	4.49228	+	6.99012i	0.152390	+	0.237124i
$870$		0			0
$871$	−17.9474	+	61.1233i	−0.608125	+	2.07109i
$872$		0			0
$873$	−40.4048	+	4.23927i	−1.36749	+	0.143477i
$874$		0			0
$875$			53.8726i			1.82123i
$876$		0			0
$877$	12.0445	+	3.53659i	0.406715	+	0.119422i	0.478690	−	0.877984i	$-0.341112\pi$
$877$	12.0445	+	3.53659i	0.406715	+	0.119422i	−0.0719748	+	0.997406i	$0.522930\pi$
$878$		0			0
$879$	−17.7849	−	2.90537i	−0.599871	−	0.0979956i
$880$		0			0
$881$	1.87262	−	13.0244i	0.0630903	−	0.438803i	−0.933654	−	0.358176i	$-0.883399\pi$
$881$	1.87262	−	13.0244i	0.0630903	−	0.438803i	0.996744	−	0.0806266i	$-0.0256921\pi$
$882$		0			0
$883$	5.50238	+	3.53616i	0.185170	+	0.119001i	0.629942	−	0.776643i	$-0.283079\pi$
$883$	5.50238	+	3.53616i	0.185170	+	0.119001i	−0.444772	+	0.895644i	$0.646715\pi$
$884$		0			0
$885$	17.5381	+	5.51620i	0.589537	+	0.185425i
$886$		0			0
$887$	−18.8795	+	2.71446i	−0.633910	+	0.0911426i	−0.451776	−	0.892131i	$-0.649210\pi$
$887$	−18.8795	+	2.71446i	−0.633910	+	0.0911426i	−0.182134	+	0.983274i	$0.558300\pi$
$888$		0			0
$889$	15.8536	+	53.9925i	0.531714	+	1.81085i
$890$		0			0
$891$	−7.81635	+	14.1418i	−0.261858	+	0.473768i
$892$		0			0
$893$	−17.8833	−	20.6384i	−0.598441	−	0.690638i
$894$		0			0
$895$	13.9993	+	6.39329i	0.467946	+	0.213704i
$896$		0			0
$897$	−39.2568	−	5.92125i	−1.31075	−	0.197705i
$898$		0			0
$899$	6.44129	+	2.94164i	0.214829	+	0.0981092i
$900$		0			0
$901$	−16.8408	−	19.4354i	−0.561050	−	0.647486i
$902$		0			0
$903$	96.5616	−	12.0029i	3.21337	−	0.399431i
$904$		0			0
$905$	2.64144	+	8.99592i	0.0878044	+	0.299034i
$906$		0			0
$907$	−38.8745	+	5.58931i	−1.29081	+	0.185590i	−0.753304	−	0.657672i	$-0.771541\pi$
$907$	−38.8745	+	5.58931i	−1.29081	+	0.185590i	−0.537503	+	0.843262i	$0.680632\pi$
$908$		0			0
$909$	−27.4775	−	46.5825i	−0.911372	−	1.54504i
$910$		0			0
$911$	3.55037	+	2.28168i	0.117629	+	0.0755955i	0.598132	−	0.801397i	$-0.295910\pi$
$911$	3.55037	+	2.28168i	0.117629	+	0.0755955i	−0.480504	+	0.876993i	$0.659546\pi$
$912$		0			0
$913$	−0.563864	+	3.92176i	−0.0186612	+	0.129791i
$914$		0			0
$915$	2.13271	−	13.0552i	0.0705052	−	0.431591i
$916$		0			0
$917$	−55.3327	−	16.2471i	−1.82725	−	0.536528i
$918$		0			0
$919$		−	9.62069i		−	0.317357i	−0.987330	−	0.158679i	$-0.949277\pi$
$919$		−	9.62069i		−	0.317357i	0.987330	−	0.158679i	$-0.0507234\pi$
$920$		0			0
$921$	−31.3065	−	28.1937i	−1.03158	−	0.929012i
$922$		0			0
$923$	−3.02930	+	10.3169i	−0.0997107	+	0.339583i
$924$		0			0
$925$	−6.88989	−	10.7209i	−0.226538	−	0.352501i
$926$		0			0
$927$	0.104491	−	2.72961i	0.00343195	−	0.0896520i
$928$		0			0
$929$	9.14128	−	14.2241i	0.299916	−	0.466678i	−0.658287	−	0.752767i	$-0.728719\pi$
$929$	9.14128	−	14.2241i	0.299916	−	0.466678i	0.958203	+	0.286089i	$0.0923552\pi$
$930$		0			0
$931$	45.0511	−	20.5741i	1.47649	−	0.674291i
$932$		0			0
$933$	−44.4611	−	29.7904i	−1.45559	−	0.975294i
$934$		0			0
$935$	−19.6022	+	5.75571i	−0.641059	+	0.188232i
$936$		0			0
$937$	−23.8957	−	20.7058i	−0.780640	−	0.676428i	0.170442	−	0.985368i	$-0.445480\pi$
$937$	−23.8957	−	20.7058i	−0.780640	−	0.676428i	−0.951082	+	0.308940i	$0.900026\pi$
$938$		0			0
$939$	43.0138	+	0.823000i	1.40370	+	0.0268576i
$940$		0			0
$941$	23.1883	−	50.7754i	0.755918	−	1.65523i	0.000488648	−	1.00000i	$-0.499844\pi$
$941$	23.1883	−	50.7754i	0.755918	−	1.65523i	0.755429	−	0.655230i	$-0.227428\pi$
$942$		0			0
$943$	−0.582961	+	2.07908i	−0.0189838	+	0.0677042i
$944$		0			0
$945$	−34.9283	+	19.7123i	−1.13622	+	0.641242i
$946$		0			0
$947$	−17.7989	+	15.4228i	−0.578386	+	0.501175i	−0.894213	−	0.447642i	$-0.852264\pi$
$947$	−17.7989	+	15.4228i	−0.578386	+	0.501175i	0.315826	+	0.948817i	$0.397718\pi$
$948$		0			0
$949$	10.5456	−	12.1703i	0.342324	−	0.395063i
$950$		0			0
$951$	20.2123	−	42.1080i	0.655430	−	1.36544i
$952$		0			0
$953$	−2.21924	−	15.4351i	−0.0718882	−	0.499993i	−0.993675	−	0.112296i	$-0.964180\pi$
$953$	−2.21924	−	15.4351i	−0.0718882	−	0.499993i	0.921787	−	0.387698i	$-0.126730\pi$
$954$		0			0
$955$	1.42685	+	3.12437i	0.0461719	+	0.101102i
$956$		0			0
$957$	11.3652	−	3.10225i	0.367386	−	0.100282i
$958$		0			0
$959$	−64.4889	−	9.27211i	−2.08246	−	0.299412i
$960$		0			0
$961$	−23.1399	+	14.8711i	−0.746448	+	0.479713i
$962$		0			0
$963$	−0.0643090	+	0.351287i	−0.00207233	+	0.0113201i
$964$		0			0
$965$	1.30450			0.0419933
$966$		0			0
$967$	−26.9221			−0.865756			−0.432878	−	0.901453i	$-0.642502\pi$
$967$	−26.9221			−0.865756			−0.432878	+	0.901453i	$0.642502\pi$
$968$		0			0
$969$	−37.5828	+	23.1493i	−1.20733	+	0.743661i
$970$		0			0
$971$	19.1302	−	12.2942i	0.613917	−	0.394540i	−0.196407	−	0.980522i	$-0.562927\pi$
$971$	19.1302	−	12.2942i	0.613917	−	0.394540i	0.810324	+	0.585982i	$0.199291\pi$
$972$		0			0
$973$	−89.9545	−	12.9335i	−2.88381	−	0.414629i
$974$		0			0
$975$	4.31529	+	15.8092i	0.138200	+	0.506301i
$976$		0			0
$977$	−3.28101	−	7.18440i	−0.104969	−	0.229849i	0.849859	−	0.527011i	$-0.176687\pi$
$977$	−3.28101	−	7.18440i	−0.104969	−	0.229849i	−0.954827	+	0.297161i	$0.903960\pi$
$978$		0			0
$979$	2.02978	+	14.1175i	0.0648722	+	0.451196i
$980$		0			0
$981$	−21.9566	+	9.02889i	−0.701021	+	0.288270i
$982$		0			0
$983$	10.0841	−	11.6376i	0.321632	−	0.371183i	−0.571791	−	0.820399i	$-0.693751\pi$
$983$	10.0841	−	11.6376i	0.321632	−	0.371183i	0.893423	+	0.449216i	$0.148297\pi$
$984$		0			0
$985$	20.8747	−	18.0880i	0.665123	−	0.576333i
$986$		0			0
$987$	−49.5149	+	21.4777i	−1.57608	+	0.683641i
$988$		0			0
$989$	54.8698	−	25.8735i	1.74476	−	0.822731i
$990$		0			0
$991$	−10.3878	+	22.7460i	−0.329978	+	0.722551i	−0.999801	−	0.0199700i	$-0.993643\pi$
$991$	−10.3878	+	22.7460i	−0.329978	+	0.722551i	0.669822	+	0.742521i	$0.266370\pi$
$992$		0			0
$993$	0.369966	−	19.3362i	0.0117405	−	0.613614i
$994$		0			0
$995$	6.98327	+	6.05104i	0.221384	+	0.191831i
$996$		0			0
$997$	−34.5395	+	10.1417i	−1.09388	+	0.321191i	−0.778416	−	0.627748i	$-0.783977\pi$
$997$	−34.5395	+	10.1417i	−1.09388	+	0.321191i	−0.315459	+	0.948939i	$0.602159\pi$
$998$		0			0
$999$	15.6185	−	29.5807i	0.494146	−	0.935892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.16	✓	240
3.2	odd	2	inner	552.2.u.a.17.22	yes	240
23.19	odd	22	inner	552.2.u.a.65.22	yes	240
69.65	even	22	inner	552.2.u.a.65.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.16	✓	240	1.1	even	1	trivial
552.2.u.a.17.22	yes	240	3.2	odd	2	inner
552.2.u.a.65.16	yes	240	69.65	even	22	inner
552.2.u.a.65.22	yes	240	23.19	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.908372 + 1.47474i) q^{3} +(-1.46204 + 0.939594i) q^{5} +(-4.39604 - 0.632056i) q^{7} +(-1.34972 + 2.67923i) q^{9} +O(q^{10})\)	\(q+(0.908372 + 1.47474i) q^{3} +(-1.46204 + 0.939594i) q^{5} +(-4.39604 - 0.632056i) q^{7} +(-1.34972 + 2.67923i) q^{9} +(-0.745816 - 1.63311i) q^{11} +(-0.680183 - 4.73078i) q^{13} +(-2.71373 - 1.30262i) q^{15} +(-4.28776 + 4.94834i) q^{17} +(2.94151 - 2.54883i) q^{19} +(-3.06112 - 7.05717i) q^{21} +(-3.18468 - 3.58578i) q^{23} +(-0.822360 + 1.80072i) q^{25} +(-5.17721 + 0.443246i) q^{27} +(2.86320 + 2.48097i) q^{29} +(1.79339 - 0.526588i) q^{31} +(1.73093 - 2.58335i) q^{33} +(7.02106 - 3.20641i) q^{35} +(-3.48043 + 5.41566i) q^{37} +(6.35881 - 5.30040i) q^{39} +(-0.243417 - 0.378764i) q^{41} +(-3.56373 + 12.1370i) q^{43} +(-0.544044 - 5.18532i) q^{45} -7.01626i q^{47} +(12.2093 + 3.58496i) q^{49} +(-11.1924 - 1.82840i) q^{51} +(-0.558964 + 3.88768i) q^{53} +(2.62487 + 1.68690i) q^{55} +(6.43085 + 2.02268i) q^{57} +(-6.04549 + 0.869211i) q^{59} +(1.23808 + 4.21650i) q^{61} +(7.62685 - 10.9249i) q^{63} +(5.43946 + 6.27748i) q^{65} +(-12.1243 - 5.53697i) q^{67} +(2.39523 - 7.95380i) q^{69} +(-2.04642 - 0.934571i) q^{71} +(2.20646 + 2.54639i) q^{73} +(-3.40260 + 0.422953i) q^{75} +(2.24642 + 7.65061i) q^{77} +(-4.58105 + 0.658656i) q^{79} +(-5.35651 - 7.23241i) q^{81} +(-1.85653 - 1.19312i) q^{83} +(1.61943 - 11.2634i) q^{85} +(-1.05795 + 6.47612i) q^{87} +(-7.62241 - 2.23814i) q^{89} +21.2266i q^{91} +(2.40565 + 2.16645i) q^{93} +(-1.90573 + 6.49031i) q^{95} +(7.32145 + 11.3924i) q^{97} +(5.38211 + 0.206031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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