LMFDB - Embedded newform 888.2.br.a.785.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			785.8
Character	$\chi$	$=$	888.785
Dual form			888.2.br.a.569.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42713 - 0.981484i) q^{3} +(-0.212050 - 0.791381i) q^{5} +(-0.149206 + 0.258432i) q^{7} +(1.07338 + 2.80140i) q^{9} +1.40612 q^{11} +(2.07555 - 0.556143i) q^{13} +(-0.474106 + 1.33752i) q^{15} +(4.03302 + 1.08064i) q^{17} +(-4.30531 + 1.15360i) q^{19} +(0.466582 - 0.222372i) q^{21} +(3.40295 - 3.40295i) q^{23} +(3.74881 - 2.16438i) q^{25} +(1.21769 - 5.05146i) q^{27} +(-2.74173 - 2.74173i) q^{29} +(-0.659194 + 0.659194i) q^{31} +(-2.00671 - 1.38008i) q^{33} +(0.236157 + 0.0632781i) q^{35} +(-3.30552 + 5.10622i) q^{37} +(-3.50792 - 1.24344i) q^{39} +(5.90794 - 10.2328i) q^{41} +(-4.89804 - 4.89804i) q^{43} +(1.98937 - 1.44349i) q^{45} -10.9310i q^{47} +(3.45548 + 5.98506i) q^{49} +(-4.69499 - 5.50055i) q^{51} +(6.63976 - 3.83347i) q^{53} +(-0.298167 - 1.11277i) q^{55} +(7.27646 + 2.57925i) q^{57} +(-1.53365 - 0.410939i) q^{59} +(-0.777010 - 2.89984i) q^{61} +(-0.884126 - 0.140590i) q^{63} +(-0.880242 - 1.52462i) q^{65} +(-1.51826 - 0.876567i) q^{67} +(-8.19637 + 1.51650i) q^{69} +(-2.84275 - 1.64126i) q^{71} -0.542470i q^{73} +(-7.47432 - 0.590559i) q^{75} +(-0.209801 + 0.363386i) q^{77} +(4.66772 - 1.25071i) q^{79} +(-6.69572 + 6.01393i) q^{81} +(7.59339 - 4.38405i) q^{83} -3.42080i q^{85} +(1.22183 + 6.60376i) q^{87} +(1.75938 - 6.56608i) q^{89} +(-0.165959 + 0.619369i) q^{91} +(1.58774 - 0.293765i) q^{93} +(1.82588 + 3.16252i) q^{95} +(7.62300 + 7.62300i) q^{97} +(1.50930 + 3.93910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

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
$3$	−1.42713	−	0.981484i	−0.823952	−	0.566660i
$3$	−1.42713	−	0.981484i	−0.823952	−	0.566660i
$4$		0			0
$5$	−0.212050	−	0.791381i	−0.0948316	−	0.353916i	0.902162	−	0.431397i	$-0.141979\pi$
$5$	−0.212050	−	0.791381i	−0.0948316	−	0.353916i	−0.996994	+	0.0774806i	$0.975312\pi$
$6$		0			0
$7$	−0.149206	+	0.258432i	−0.0563945	+	0.0976781i	−0.892844	−	0.450365i	$-0.851294\pi$
$7$	−0.149206	+	0.258432i	−0.0563945	+	0.0976781i	0.836450	+	0.548043i	$0.184627\pi$
$8$		0			0
$9$	1.07338	+	2.80140i	0.357793	+	0.933801i
$10$		0			0
$11$	1.40612			0.423961			0.211980	−	0.977274i	$-0.432009\pi$
$11$	1.40612			0.423961			0.211980	+	0.977274i	$0.432009\pi$
$12$		0			0
$13$	2.07555	−	0.556143i	0.575655	−	0.154246i	0.0407662	−	0.999169i	$-0.487020\pi$
$13$	2.07555	−	0.556143i	0.575655	−	0.154246i	0.534889	+	0.844922i	$0.320353\pi$
$14$		0			0
$15$	−0.474106	+	1.33752i	−0.122414	+	0.345347i
$16$		0			0
$17$	4.03302	+	1.08064i	0.978150	+	0.262094i	0.712265	−	0.701910i	$-0.247669\pi$
$17$	4.03302	+	1.08064i	0.978150	+	0.262094i	0.265885	+	0.964005i	$0.414336\pi$
$18$		0			0
$19$	−4.30531	+	1.15360i	−0.987706	+	0.264655i	−0.716287	−	0.697806i	$-0.754160\pi$
$19$	−4.30531	+	1.15360i	−0.987706	+	0.264655i	−0.271419	+	0.962461i	$0.587493\pi$
$20$		0			0
$21$	0.466582	−	0.222372i	0.101817	−	0.0485255i
$22$		0			0
$23$	3.40295	−	3.40295i	0.709564	−	0.709564i	−0.256880	−	0.966443i	$-0.582694\pi$
$23$	3.40295	−	3.40295i	0.709564	−	0.709564i	0.966443	+	0.256880i	$0.0826944\pi$
$24$		0			0
$25$	3.74881	−	2.16438i	0.749762	−	0.432875i
$26$		0			0
$27$	1.21769	−	5.05146i	0.234344	−	0.972154i
$28$		0			0
$29$	−2.74173	−	2.74173i	−0.509126	−	0.509126i	0.405132	−	0.914258i	$-0.367226\pi$
$29$	−2.74173	−	2.74173i	−0.509126	−	0.509126i	−0.914258	+	0.405132i	$0.867226\pi$
$30$		0			0
$31$	−0.659194	+	0.659194i	−0.118395	+	0.118395i	−0.763822	−	0.645427i	$-0.776679\pi$
$31$	−0.659194	+	0.659194i	−0.118395	+	0.118395i	0.645427	+	0.763822i	$0.276679\pi$
$32$		0			0
$33$	−2.00671	−	1.38008i	−0.349323	−	0.240242i
$34$		0			0
$35$	0.236157	+	0.0632781i	0.0399178	+	0.0106959i
$36$		0			0
$37$	−3.30552	+	5.10622i	−0.543425	+	0.839458i
$37$	−3.30552	+	5.10622i	−0.543425	+	0.839458i
$38$		0			0
$39$	−3.50792	−	1.24344i	−0.561717	−	0.199109i
$40$		0			0
$41$	5.90794	−	10.2328i	0.922665	−	1.59810i	0.127390	−	0.991853i	$-0.459340\pi$
$41$	5.90794	−	10.2328i	0.922665	−	1.59810i	0.795275	−	0.606249i	$-0.207327\pi$
$42$		0			0
$43$	−4.89804	−	4.89804i	−0.746945	−	0.746945i	0.226960	−	0.973904i	$-0.427121\pi$
$43$	−4.89804	−	4.89804i	−0.746945	−	0.746945i	−0.973904	+	0.226960i	$0.927121\pi$
$44$		0			0
$45$	1.98937	−	1.44349i	0.296557	−	0.215182i
$46$		0			0
$47$		−	10.9310i		−	1.59444i	−0.603687	−	0.797222i	$-0.706302\pi$
$47$		−	10.9310i		−	1.59444i	0.603687	−	0.797222i	$-0.293698\pi$
$48$		0			0
$49$	3.45548	+	5.98506i	0.493639	+	0.855008i
$50$		0			0
$51$	−4.69499	−	5.50055i	−0.657430	−	0.770232i
$52$		0			0
$53$	6.63976	−	3.83347i	0.912041	−	0.526567i	0.0309539	−	0.999521i	$-0.490145\pi$
$53$	6.63976	−	3.83347i	0.912041	−	0.526567i	0.881087	+	0.472954i	$0.156812\pi$
$54$		0			0
$55$	−0.298167	−	1.11277i	−0.0402048	−	0.150047i
$56$		0			0
$57$	7.27646	+	2.57925i	0.963791	+	0.341631i
$58$		0			0
$59$	−1.53365	−	0.410939i	−0.199664	−	0.0534997i	0.157601	−	0.987503i	$-0.449624\pi$
$59$	−1.53365	−	0.410939i	−0.199664	−	0.0534997i	−0.357265	+	0.934003i	$0.616291\pi$
$60$		0			0
$61$	−0.777010	−	2.89984i	−0.0994859	−	0.371287i	0.898175	−	0.439637i	$-0.144893\pi$
$61$	−0.777010	−	2.89984i	−0.0994859	−	0.371287i	−0.997661	+	0.0683507i	$0.978226\pi$
$62$		0			0
$63$	−0.884126	−	0.140590i	−0.111389	−	0.0177127i
$64$		0			0
$65$	−0.880242	−	1.52462i	−0.109181	−	0.189106i
$66$		0			0
$67$	−1.51826	−	0.876567i	−0.185485	−	0.107090i	0.404382	−	0.914590i	$-0.367487\pi$
$67$	−1.51826	−	0.876567i	−0.185485	−	0.107090i	−0.589867	+	0.807500i	$0.700820\pi$
$68$		0			0
$69$	−8.19637	+	1.51650i	−0.986727	+	0.182565i
$70$		0			0
$71$	−2.84275	−	1.64126i	−0.337372	−	0.194782i	0.321737	−	0.946829i	$-0.395733\pi$
$71$	−2.84275	−	1.64126i	−0.337372	−	0.194782i	−0.659109	+	0.752047i	$0.729067\pi$
$72$		0			0
$73$		−	0.542470i		−	0.0634913i	−0.999496	−	0.0317457i	$-0.989893\pi$
$73$		−	0.542470i		−	0.0634913i	0.999496	−	0.0317457i	$-0.0101067\pi$
$74$		0			0
$75$	−7.47432	−	0.590559i	−0.863061	−	0.0681919i
$76$		0			0
$77$	−0.209801	+	0.363386i	−0.0239090	+	0.0414116i
$78$		0			0
$79$	4.66772	−	1.25071i	0.525159	−	0.140716i	0.0135071	−	0.999909i	$-0.495700\pi$
$79$	4.66772	−	1.25071i	0.525159	−	0.140716i	0.511652	+	0.859193i	$0.329034\pi$
$80$		0			0
$81$	−6.69572	+	6.01393i	−0.743969	+	0.668214i
$82$		0			0
$83$	7.59339	−	4.38405i	0.833483	−	0.481212i	−0.0215608	−	0.999768i	$-0.506864\pi$
$83$	7.59339	−	4.38405i	0.833483	−	0.481212i	0.855044	+	0.518556i	$0.173530\pi$
$84$		0			0
$85$		−	3.42080i		−	0.371038i
$86$		0			0
$87$	1.22183	+	6.60376i	0.130994	+	0.707997i
$88$		0			0
$89$	1.75938	−	6.56608i	0.186494	−	0.696004i	−0.807812	−	0.589440i	$-0.799349\pi$
$89$	1.75938	−	6.56608i	0.186494	−	0.696004i	0.994306	−	0.106564i	$-0.0339848\pi$
$90$		0			0
$91$	−0.165959	+	0.619369i	−0.0173973	+	0.0649275i
$92$		0			0
$93$	1.58774	−	0.293765i	0.164641	−	0.0304620i
$94$		0			0
$95$	1.82588	+	3.16252i	0.187331	+	0.324467i
$96$		0			0
$97$	7.62300	+	7.62300i	0.773998	+	0.773998i	0.978803	−	0.204805i	$-0.0656559\pi$
$97$	7.62300	+	7.62300i	0.773998	+	0.773998i	−0.204805	+	0.978803i	$0.565656\pi$
$98$		0			0
$99$	1.50930	+	3.93910i	0.151690	+	0.395895i
$100$		0			0
$101$	10.6782			1.06252			0.531261	−	0.847208i	$-0.321718\pi$
$101$	10.6782			1.06252			0.531261	+	0.847208i	$0.321718\pi$
$102$		0			0
$103$	−2.74833	+	2.74833i	−0.270801	+	0.270801i	−0.829423	−	0.558621i	$-0.811330\pi$
$103$	−2.74833	+	2.74833i	−0.270801	+	0.270801i	0.558621	+	0.829423i	$0.311330\pi$
$104$		0			0
$105$	−0.274919	−	0.322090i	−0.0268294	−	0.0314328i
$106$		0			0
$107$	5.37254	+	3.10184i	0.519383	+	0.299866i	0.736682	−	0.676239i	$-0.236391\pi$
$107$	5.37254	+	3.10184i	0.519383	+	0.299866i	−0.217299	+	0.976105i	$0.569725\pi$
$108$		0			0
$109$	3.46676	−	12.9381i	0.332055	−	1.23925i	−0.574971	−	0.818174i	$-0.694987\pi$
$109$	3.46676	−	12.9381i	0.332055	−	1.23925i	0.907026	−	0.421074i	$-0.138347\pi$
$110$		0			0
$111$	9.72907	−	4.04291i	0.923443	−	0.383736i
$112$		0			0
$113$	−1.51522	+	5.65487i	−0.142540	+	0.531965i	0.857313	+	0.514796i	$0.172132\pi$
$113$	−1.51522	+	5.65487i	−0.142540	+	0.531965i	−0.999853	+	0.0171696i	$0.994534\pi$
$114$		0			0
$115$	−3.41462	−	1.97143i	−0.318415	−	0.183837i
$116$		0			0
$117$	3.78584	+	5.21751i	0.350001	+	0.482359i
$118$		0			0
$119$	−0.881022	+	0.881022i	−0.0807631	+	0.0807631i
$120$		0			0
$121$	−9.02283			−0.820257
$122$		0			0
$123$	−18.4747	+	8.80502i	−1.66581	+	0.793922i
$124$		0			0
$125$	−5.40443	−	5.40443i	−0.483387	−	0.483387i
$126$		0			0
$127$	1.72200	+	2.98260i	0.152803	+	0.264663i	0.932257	−	0.361797i	$-0.117837\pi$
$127$	1.72200	+	2.98260i	0.152803	+	0.264663i	−0.779454	+	0.626460i	$0.784503\pi$
$128$		0			0
$129$	2.18277	+	11.7975i	0.192183	+	1.03871i
$130$		0			0
$131$	−0.105122	+	0.392319i	−0.00918451	+	0.0342771i	−0.970366	−	0.241640i	$-0.922315\pi$
$131$	−0.105122	+	0.392319i	−0.00918451	+	0.0342771i	0.961182	+	0.275917i	$0.0889814\pi$
$132$		0			0
$133$	0.344249	−	1.28475i	0.0298501	−	0.111402i
$134$		0			0
$135$	−4.25584	+	0.107507i	−0.366284	+	0.00925277i
$136$		0			0
$137$			13.8431i			1.18269i	0.806418	+	0.591346i	$0.201403\pi$
$137$			13.8431i			1.18269i	−0.806418	+	0.591346i	$0.798597\pi$
$138$		0			0
$139$	−4.02327	+	2.32284i	−0.341250	+	0.197021i	−0.660825	−	0.750540i	$-0.729793\pi$
$139$	−4.02327	+	2.32284i	−0.341250	+	0.197021i	0.319575	+	0.947561i	$0.396460\pi$
$140$		0			0
$141$	−10.7286	+	15.5998i	−0.903507	+	1.31374i
$142$		0			0
$143$	2.91847	−	0.782003i	0.244055	−	0.0653944i
$144$		0			0
$145$	−1.58837	+	2.75113i	−0.131907	+	0.228469i
$146$		0			0
$147$	0.942841	−	11.9329i	0.0777642	−	0.984211i
$148$		0			0
$149$			5.47982i			0.448925i	0.974483	+	0.224462i	$0.0720626\pi$
$149$			5.47982i			0.448925i	−0.974483	+	0.224462i	$0.927937\pi$
$150$		0			0
$151$	11.8910	+	6.86525i	0.967672	+	0.558686i	0.898526	−	0.438921i	$-0.144639\pi$
$151$	11.8910	+	6.86525i	0.967672	+	0.558686i	0.0691465	+	0.997607i	$0.477972\pi$
$152$		0			0
$153$	1.30163	+	12.4580i	0.105231	+	1.00717i
$154$		0			0
$155$	0.661456	+	0.381892i	0.0531294	+	0.0306743i
$156$		0			0
$157$	−8.21847	−	14.2348i	−0.655906	−	1.13606i	−0.981666	−	0.190609i	$-0.938954\pi$
$157$	−8.21847	−	14.2348i	−0.655906	−	1.13606i	0.325760	−	0.945452i	$-0.394380\pi$
$158$		0			0
$159$	−13.2383	−	1.04598i	−1.04986	−	0.0829514i
$160$		0			0
$161$	0.371691	+	1.38717i	0.0292933	+	0.109324i
$162$		0			0
$163$	9.11995	+	2.44368i	0.714329	+	0.191404i	0.597640	−	0.801764i	$-0.296105\pi$
$163$	9.11995	+	2.44368i	0.714329	+	0.191404i	0.116689	+	0.993168i	$0.462772\pi$
$164$		0			0
$165$	−0.666649	+	1.88072i	−0.0518985	+	0.146414i
$166$		0			0
$167$	5.71720	+	21.3369i	0.442410	+	1.65110i	0.722684	+	0.691178i	$0.242908\pi$
$167$	5.71720	+	21.3369i	0.442410	+	1.65110i	−0.280274	+	0.959920i	$0.590425\pi$
$168$		0			0
$169$	−7.25970	+	4.19139i	−0.558438	+	0.322415i
$170$		0			0
$171$	−7.85294	−	10.8227i	−0.600529	−	0.827629i
$172$		0			0
$173$	1.15167	+	1.99475i	0.0875600	+	0.151658i	0.906479	−	0.422250i	$-0.138760\pi$
$173$	1.15167	+	1.99475i	0.0875600	+	0.151658i	−0.818919	+	0.573909i	$0.805426\pi$
$174$		0			0
$175$			1.29175i			0.0976470i
$176$		0			0
$177$	1.78538	+	2.09171i	0.134197	+	0.157223i
$178$		0			0
$179$	−5.02745	−	5.02745i	−0.375769	−	0.375769i	0.493804	−	0.869573i	$-0.335606\pi$
$179$	−5.02745	−	5.02745i	−0.375769	−	0.375769i	−0.869573	+	0.493804i	$0.835606\pi$
$180$		0			0
$181$	1.16321	−	2.01475i	0.0864610	−	0.149755i	−0.819552	−	0.573005i	$-0.805778\pi$
$181$	1.16321	−	2.01475i	0.0864610	−	0.149755i	0.906013	+	0.423250i	$0.139111\pi$
$182$		0			0
$183$	−1.73726	+	4.90106i	−0.128422	+	0.362297i
$184$		0			0
$185$	4.74190	+	1.53315i	0.348632	+	0.112720i
$186$		0			0
$187$	5.67090	+	1.51951i	0.414697	+	0.111118i
$188$		0			0
$189$	1.12377	+	1.06840i	0.0817424	+	0.0777143i
$190$		0			0
$191$	0.422832	−	0.422832i	0.0305950	−	0.0305950i	−0.691644	−	0.722239i	$-0.743113\pi$
$191$	0.422832	−	0.422832i	0.0305950	−	0.0305950i	0.722239	+	0.691644i	$0.243113\pi$
$192$		0			0
$193$	4.99064	+	4.99064i	0.359234	+	0.359234i	0.863531	−	0.504297i	$-0.168248\pi$
$193$	4.99064	+	4.99064i	0.359234	+	0.359234i	−0.504297	+	0.863531i	$0.668248\pi$
$194$		0			0
$195$	−0.240178	+	3.03977i	−0.0171995	+	0.217683i
$196$		0			0
$197$	−18.9245	+	10.9261i	−1.34831	+	0.778450i	−0.988011	−	0.154386i	$-0.950660\pi$
$197$	−18.9245	+	10.9261i	−1.34831	+	0.778450i	−0.360303	+	0.932835i	$0.617327\pi$
$198$		0			0
$199$	−0.872803	+	0.872803i	−0.0618714	+	0.0618714i	−0.737365	−	0.675494i	$-0.763930\pi$
$199$	−0.872803	+	0.872803i	−0.0618714	+	0.0618714i	0.675494	+	0.737365i	$0.263930\pi$
$200$		0			0
$201$	1.30641	+	2.74112i	0.0921471	+	0.193344i
$202$		0			0
$203$	1.11763	−	0.299469i	0.0784424	−	0.0210186i
$204$		0			0
$205$	−9.35085	−	2.50555i	−0.653092	−	0.174995i
$206$		0			0
$207$	13.1857	+	5.88038i	0.916468	+	0.408715i
$208$		0			0
$209$	−6.05377	+	1.62210i	−0.418748	+	0.112203i
$210$		0			0
$211$	4.17439			0.287377			0.143688	−	0.989623i	$-0.454104\pi$
$211$	4.17439			0.287377			0.143688	+	0.989623i	$0.454104\pi$
$212$		0			0
$213$	2.44609	+	5.13240i	0.167603	+	0.351666i
$214$		0			0
$215$	−2.83759	+	4.91485i	−0.193522	+	0.335190i
$216$		0			0
$217$	−0.0720013	−	0.268712i	−0.00488776	−	0.0182414i
$218$		0			0
$219$	−0.532426	+	0.774173i	−0.0359780	+	0.0523138i
$220$		0			0
$221$	8.97174			0.603504
$222$		0			0
$223$	8.30690			0.556271			0.278136	−	0.960542i	$-0.410284\pi$
$223$	8.30690			0.556271			0.278136	+	0.960542i	$0.410284\pi$
$224$		0			0
$225$	10.0872	+	8.17873i	0.672479	+	0.545249i
$226$		0			0
$227$	5.82278	+	21.7309i	0.386472	+	1.44233i	0.835834	+	0.548983i	$0.184985\pi$
$227$	5.82278	+	21.7309i	0.386472	+	1.44233i	−0.449362	+	0.893350i	$0.648349\pi$
$228$		0			0
$229$	4.74287	−	8.21490i	0.313418	−	0.542856i	−0.665682	−	0.746236i	$-0.731859\pi$
$229$	4.74287	−	8.21490i	0.313418	−	0.542856i	0.979100	+	0.203380i	$0.0651926\pi$
$230$		0			0
$231$	0.656070	−	0.312681i	0.0431662	−	0.0205729i
$232$		0			0
$233$	−16.8897			−1.10648			−0.553242	−	0.833021i	$-0.686610\pi$
$233$	−16.8897			−1.10648			−0.553242	+	0.833021i	$0.686610\pi$
$234$		0			0
$235$	−8.65054	+	2.31791i	−0.564299	+	0.151204i
$236$		0			0
$237$	−7.88897	−	2.79637i	−0.512444	−	0.181644i
$238$		0			0
$239$	−10.0320	−	2.68805i	−0.648913	−	0.173876i	−0.0806757	−	0.996740i	$-0.525708\pi$
$239$	−10.0320	−	2.68805i	−0.648913	−	0.173876i	−0.568237	+	0.822865i	$0.692374\pi$
$240$		0			0
$241$	0.834899	−	0.223710i	0.0537806	−	0.0144105i	−0.231828	−	0.972757i	$-0.574471\pi$
$241$	0.834899	−	0.223710i	0.0537806	−	0.0144105i	0.285609	+	0.958346i	$0.407804\pi$
$242$		0			0
$243$	15.4582	−	2.01090i	0.991645	−	0.128999i
$244$		0			0
$245$	4.00373	−	4.00373i	0.255789	−	0.255789i
$246$		0			0
$247$	−8.29433	+	4.78874i	−0.527756	+	0.304700i
$248$		0			0
$249$	−15.1396	−	1.19620i	−0.959433	−	0.0758064i
$250$		0			0
$251$	−12.8319	−	12.8319i	−0.809941	−	0.809941i	0.174684	−	0.984625i	$-0.444110\pi$
$251$	−12.8319	−	12.8319i	−0.809941	−	0.809941i	−0.984625	+	0.174684i	$0.944110\pi$
$252$		0			0
$253$	4.78495	−	4.78495i	0.300827	−	0.300827i
$254$		0			0
$255$	−3.35746	+	4.88191i	−0.210252	+	0.305717i
$256$		0			0
$257$	19.1017	+	5.11828i	1.19153	+	0.319270i	0.799491	−	0.600679i	$-0.205103\pi$
$257$	19.1017	+	5.11828i	1.19153	+	0.319270i	0.392040	+	0.919948i	$0.371770\pi$
$258$		0			0
$259$	−0.826408	−	1.61613i	−0.0513505	−	0.100421i
$260$		0			0
$261$	4.73778	−	10.6236i	0.293261	−	0.657584i
$262$		0			0
$263$	4.10210	−	7.10505i	0.252946	−	0.438116i	−0.711389	−	0.702798i	$-0.751934\pi$
$263$	4.10210	−	7.10505i	0.252946	−	0.438116i	0.964336	+	0.264682i	$0.0852671\pi$
$264$		0			0
$265$	−4.44169	−	4.44169i	−0.272851	−	0.272851i
$266$		0			0
$267$	−8.95536	+	7.64383i	−0.548059	+	0.467795i
$268$		0			0
$269$		−	25.5860i		−	1.56001i	−0.625775	−	0.780004i	$-0.715217\pi$
$269$		−	25.5860i		−	1.56001i	0.625775	−	0.780004i	$-0.284783\pi$
$270$		0			0
$271$	−1.63277	−	2.82804i	−0.0991836	−	0.171791i	0.812163	−	0.583430i	$-0.198290\pi$
$271$	−1.63277	−	2.82804i	−0.0991836	−	0.171791i	−0.911347	+	0.411639i	$0.864956\pi$
$272$		0			0
$273$	0.844746	−	0.721031i	0.0511264	−	0.0436388i
$274$		0			0
$275$	5.27127	−	3.04337i	0.317869	−	0.183522i
$276$		0			0
$277$	−1.51976	−	5.67181i	−0.0913134	−	0.340786i	0.905121	−	0.425153i	$-0.139780\pi$
$277$	−1.51976	−	5.67181i	−0.0913134	−	0.340786i	−0.996435	+	0.0843671i	$0.973113\pi$
$278$		0			0
$279$	−2.55423	−	1.13910i	−0.152918	−	0.0681964i
$280$		0			0
$281$	−3.39223	−	0.908944i	−0.202363	−	0.0542231i	0.156214	−	0.987723i	$-0.450071\pi$
$281$	−3.39223	−	0.908944i	−0.202363	−	0.0542231i	−0.358577	+	0.933500i	$0.616738\pi$
$282$		0			0
$283$	6.29626	+	23.4980i	0.374274	+	1.39681i	0.854403	+	0.519611i	$0.173923\pi$
$283$	6.29626	+	23.4980i	0.374274	+	1.39681i	−0.480130	+	0.877198i	$0.659410\pi$
$284$		0			0
$285$	0.498199	−	6.30538i	0.0295108	−	0.373499i
$286$		0			0
$287$	1.76300	+	3.05360i	0.104066	+	0.180248i
$288$		0			0
$289$	0.374993	+	0.216503i	0.0220584	+	0.0127354i
$290$		0			0
$291$	−3.39713	−	18.3608i	−0.199143	−	1.07633i
$292$		0			0
$293$	−7.86659	−	4.54178i	−0.459571	−	0.265334i	0.252293	−	0.967651i	$-0.418815\pi$
$293$	−7.86659	−	4.54178i	−0.459571	−	0.265334i	−0.711864	+	0.702317i	$0.752149\pi$
$294$		0			0
$295$			1.30084i			0.0757376i
$296$		0			0
$297$	1.71221	−	7.10295i	0.0993526	−	0.412155i
$298$		0			0
$299$	5.17048	−	8.95553i	0.299016	−	0.517912i
$300$		0			0
$301$	1.99663	−	0.534994i	0.115084	−	0.0308366i
$302$		0			0
$303$	−15.2392	−	10.4805i	−0.875467	−	0.602089i
$304$		0			0
$305$	−2.13011	+	1.22982i	−0.121970	+	0.0704194i
$306$		0			0
$307$			26.7723i			1.52797i	0.645232	+	0.763987i	$0.276761\pi$
$307$			26.7723i			1.52797i	−0.645232	+	0.763987i	$0.723239\pi$
$308$		0			0
$309$	6.61967	−	1.22477i	0.376580	−	0.0696749i
$310$		0			0
$311$	7.60714	−	28.3902i	0.431361	−	1.60986i	−0.318265	−	0.948002i	$-0.603100\pi$
$311$	7.60714	−	28.3902i	0.431361	−	1.60986i	0.749627	−	0.661861i	$-0.230233\pi$
$312$		0			0
$313$	−1.97533	+	7.37201i	−0.111652	+	0.416691i	−0.999015	−	0.0443812i	$-0.985868\pi$
$313$	−1.97533	+	7.37201i	−0.111652	+	0.416691i	0.887363	+	0.461072i	$0.152535\pi$
$314$		0			0
$315$	0.0762184	+	0.729492i	0.00429442	+	0.0411022i
$316$		0			0
$317$	15.8478	+	27.4492i	0.890103	+	1.54170i	0.839751	+	0.542971i	$0.182701\pi$
$317$	15.8478	+	27.4492i	0.890103	+	1.54170i	0.0503515	+	0.998732i	$0.483966\pi$
$318$		0			0
$319$	−3.85520	−	3.85520i	−0.215850	−	0.215850i
$320$		0			0
$321$	−4.62289	−	9.69978i	−0.258025	−	0.541389i
$322$		0			0
$323$	−18.6100			−1.03549
$324$		0			0
$325$	6.57715	−	6.57715i	0.364835	−	0.364835i
$326$		0			0
$327$	−17.6461	+	15.0618i	−0.975829	+	0.832917i
$328$		0			0
$329$	2.82491	+	1.63096i	0.155742	+	0.0899178i
$330$		0			0
$331$	−2.66274	+	9.93749i	−0.146358	+	0.546214i	0.853334	+	0.521365i	$0.174577\pi$
$331$	−2.66274	+	9.93749i	−0.146358	+	0.546214i	−0.999691	+	0.0248487i	$0.992090\pi$
$332$		0			0
$333$	−17.8527	−	3.77919i	−0.978320	−	0.207098i
$334$		0			0
$335$	−0.371752	+	1.38740i	−0.0203110	+	0.0758016i
$336$		0			0
$337$	12.1148	+	6.99446i	0.659933	+	0.381013i	0.792251	−	0.610195i	$-0.208909\pi$
$337$	12.1148	+	6.99446i	0.659933	+	0.381013i	−0.132318	+	0.991207i	$0.542242\pi$
$338$		0			0
$339$	7.71257	−	6.58305i	0.418889	−	0.357542i
$340$		0			0
$341$	−0.926905	+	0.926905i	−0.0501947	+	0.0501947i
$342$		0			0
$343$	−4.15119			−0.224143
$344$		0			0
$345$	2.93817	+	6.16488i	0.158186	+	0.331906i
$346$		0			0
$347$	11.0258	+	11.0258i	0.591895	+	0.591895i	0.938143	−	0.346248i	$-0.112544\pi$
$347$	11.0258	+	11.0258i	0.591895	+	0.591895i	−0.346248	+	0.938143i	$0.612544\pi$
$348$		0			0
$349$	−17.1968	−	29.7857i	−0.920522	−	1.59439i	−0.798609	−	0.601850i	$-0.794431\pi$
$349$	−17.1968	−	29.7857i	−0.920522	−	1.59439i	−0.121913	−	0.992541i	$-0.538903\pi$
$350$		0			0
$351$	−0.281960	−	11.1618i	−0.0150499	−	0.595772i
$352$		0			0
$353$	4.29977	−	16.0470i	0.228854	−	0.854093i	−0.751970	−	0.659197i	$-0.770896\pi$
$353$	4.29977	−	16.0470i	0.228854	−	0.854093i	0.980824	−	0.194896i	$-0.0624370\pi$
$354$		0			0
$355$	−0.696059	+	2.59773i	−0.0369430	+	0.137873i
$356$		0			0
$357$	2.12204	−	0.392620i	0.112310	−	0.0207797i
$358$		0			0
$359$		−	11.4435i		−	0.603967i	−0.953313	−	0.301983i	$-0.902351\pi$
$359$		−	11.4435i		−	0.603967i	0.953313	−	0.301983i	$-0.0976487\pi$
$360$		0			0
$361$	0.750403	−	0.433245i	0.0394949	−	0.0228024i
$362$		0			0
$363$	12.8767	+	8.85577i	0.675852	+	0.464807i
$364$		0			0
$365$	−0.429300	+	0.115031i	−0.0224706	+	0.00602098i
$366$		0			0
$367$	15.7524	−	27.2839i	0.822267	−	1.42421i	−0.0817226	−	0.996655i	$-0.526042\pi$
$367$	15.7524	−	27.2839i	0.822267	−	1.42421i	0.903990	−	0.427554i	$-0.140625\pi$
$368$		0			0
$369$	35.0078	+	5.56680i	1.82243	+	0.289796i
$370$		0			0
$371$			2.28790i			0.118782i
$372$		0			0
$373$	−24.4872	−	14.1377i	−1.26790	−	0.732021i	−0.293308	−	0.956018i	$-0.594756\pi$
$373$	−24.4872	−	14.1377i	−1.26790	−	0.732021i	−0.974590	+	0.223997i	$0.928089\pi$
$374$		0			0
$375$	2.40844	+	13.0172i	0.124371	+	0.672204i
$376$		0			0
$377$	−7.21540	−	4.16581i	−0.371612	−	0.214550i
$378$		0			0
$379$	16.7954	+	29.0905i	0.862721	+	1.49428i	0.869293	+	0.494298i	$0.164575\pi$
$379$	16.7954	+	29.0905i	0.862721	+	1.49428i	−0.00657182	+	0.999978i	$0.502092\pi$
$380$		0			0
$381$	0.469856	−	5.94667i	0.0240714	−	0.304657i
$382$		0			0
$383$	5.84657	+	21.8197i	0.298746	+	1.11493i	0.938197	+	0.346103i	$0.112495\pi$
$383$	5.84657	+	21.8197i	0.298746	+	1.11493i	−0.639451	+	0.768832i	$0.720838\pi$
$384$		0			0
$385$	0.332065	+	0.0889765i	0.0169236	+	0.00453466i
$386$		0			0
$387$	8.46394	−	18.9788i	0.430246	−	0.964749i
$388$		0			0
$389$	2.21911	+	8.28182i	0.112513	+	0.419905i	0.999089	−	0.0426787i	$-0.0135892\pi$
$389$	2.21911	+	8.28182i	0.112513	+	0.419905i	−0.886576	+	0.462584i	$0.846923\pi$
$390$		0			0
$391$	17.4015	−	10.0468i	0.880032	−	0.508087i
$392$		0			0
$393$	0.535076	−	0.456713i	0.0269910	−	0.0230381i
$394$		0			0
$395$	−1.97958	−	3.42873i	−0.0996033	−	0.172518i
$396$		0			0
$397$		−	21.3332i		−	1.07068i	−0.844636	−	0.535342i	$-0.820183\pi$
$397$		−	21.3332i		−	1.07068i	0.844636	−	0.535342i	$-0.179817\pi$
$398$		0			0
$399$	−1.75225	+	1.49563i	−0.0877223	+	0.0748752i
$400$		0			0
$401$	−27.1195	−	27.1195i	−1.35428	−	1.35428i	−0.880804	−	0.473480i	$-0.842997\pi$
$401$	−27.1195	−	27.1195i	−1.35428	−	1.35428i	−0.473480	−	0.880804i	$-0.657003\pi$
$402$		0			0
$403$	−1.00159	+	1.73480i	−0.0498926	+	0.0864166i
$404$		0			0
$405$	6.17913	+	4.02361i	0.307044	+	0.199935i
$406$		0			0
$407$	−4.64796	+	7.17995i	−0.230391	+	0.355897i
$408$		0			0
$409$	9.39205	+	2.51659i	0.464407	+	0.124437i	0.483433	−	0.875382i	$-0.339390\pi$
$409$	9.39205	+	2.51659i	0.464407	+	0.124437i	−0.0190257	+	0.999819i	$0.506056\pi$
$410$		0			0
$411$	13.5867	−	19.7558i	0.670184	−	0.974481i
$412$		0			0
$413$	0.335028	−	0.335028i	0.0164857	−	0.0164857i
$414$		0			0
$415$	−5.07963	−	5.07963i	−0.249349	−	0.249349i
$416$		0			0
$417$	8.02155	+	0.633796i	0.392817	+	0.0310371i
$418$		0			0
$419$	−12.0661	+	6.96639i	−0.589469	+	0.340330i	−0.764888	−	0.644164i	$-0.777206\pi$
$419$	−12.0661	+	6.96639i	−0.589469	+	0.340330i	0.175418	+	0.984494i	$0.443872\pi$
$420$		0			0
$421$	−24.6291	+	24.6291i	−1.20035	+	1.20035i	−0.226291	+	0.974060i	$0.572660\pi$
$421$	−24.6291	+	24.6291i	−1.20035	+	1.20035i	−0.974060	+	0.226291i	$0.927340\pi$
$422$		0			0
$423$	30.6220	−	11.7330i	1.48889	−	0.570480i
$424$		0			0
$425$	17.4579	−	4.67784i	0.846834	−	0.226908i
$426$		0			0
$427$	0.865346	+	0.231869i	0.0418770	+	0.0112209i
$428$		0			0
$429$	−4.93255	−	1.74842i	−0.238146	−	0.0844145i
$430$		0			0
$431$	−28.8429	+	7.72842i	−1.38931	+	0.372265i	−0.874495	−	0.485035i	$-0.838807\pi$
$431$	−28.8429	+	7.72842i	−1.38931	+	0.372265i	−0.514817	+	0.857300i	$0.672140\pi$
$432$		0			0
$433$	−15.7590			−0.757329			−0.378665	−	0.925534i	$-0.623617\pi$
$433$	−15.7590			−0.757329			−0.378665	+	0.925534i	$0.623617\pi$
$434$		0			0
$435$	4.96700	−	2.36726i	0.238149	−	0.113501i
$436$		0			0
$437$	−10.7251	+	18.5764i	−0.513050	+	0.888630i
$438$		0			0
$439$	−0.284234	−	1.06078i	−0.0135658	−	0.0506281i	0.958811	−	0.284044i	$-0.0916762\pi$
$439$	−0.284234	−	1.06078i	−0.0135658	−	0.0506281i	−0.972377	+	0.233416i	$0.925010\pi$
$440$		0			0
$441$	−13.0575	+	16.1044i	−0.621787	+	0.766877i
$442$		0			0
$443$	27.6138			1.31197			0.655985	−	0.754774i	$-0.272253\pi$
$443$	27.6138			1.31197			0.655985	+	0.754774i	$0.272253\pi$
$444$		0			0
$445$	−5.56935			−0.264012
$446$		0			0
$447$	5.37836	−	7.82040i	0.254388	−	0.369892i
$448$		0			0
$449$	7.02491	+	26.2173i	0.331526	+	1.23727i	0.907587	+	0.419865i	$0.137922\pi$
$449$	7.02491	+	26.2173i	0.331526	+	1.23727i	−0.576061	+	0.817407i	$0.695411\pi$
$450$		0			0
$451$	8.30726	−	14.3886i	0.391173	−	0.677532i
$452$		0			0
$453$	−10.2318	−	21.4684i	−0.480730	−	1.00867i
$454$		0			0
$455$	0.525348			0.0246287
$456$		0			0
$457$	13.4969	−	3.61649i	0.631359	−	0.169172i	0.0710728	−	0.997471i	$-0.477358\pi$
$457$	13.4969	−	3.61649i	0.631359	−	0.169172i	0.560286	+	0.828299i	$0.310691\pi$
$458$		0			0
$459$	10.3698	−	19.0567i	0.484020	−	0.889492i
$460$		0			0
$461$	−7.45297	−	1.99702i	−0.347120	−	0.0930104i	0.0810469	−	0.996710i	$-0.474174\pi$
$461$	−7.45297	−	1.99702i	−0.347120	−	0.0930104i	−0.428166	+	0.903700i	$0.640840\pi$
$462$		0			0
$463$	3.20406	−	0.858525i	0.148905	−	0.0398990i	−0.183596	−	0.983002i	$-0.558774\pi$
$463$	3.20406	−	0.858525i	0.148905	−	0.0398990i	0.332502	+	0.943103i	$0.392107\pi$
$464$		0			0
$465$	−0.569160	−	1.19422i	−0.0263942	−	0.0553804i
$466$		0			0
$467$	6.52807	−	6.52807i	0.302083	−	0.302083i	−0.539745	−	0.841828i	$-0.681479\pi$
$467$	6.52807	−	6.52807i	0.302083	−	0.302083i	0.841828	+	0.539745i	$0.181479\pi$
$468$		0			0
$469$	0.453066	−	0.261578i	0.0209206	−	0.0120785i
$470$		0			0
$471$	−2.24244	+	28.3812i	−0.103326	+	1.30774i
$472$		0			0
$473$	−6.88723	−	6.88723i	−0.316675	−	0.316675i
$474$		0			0
$475$	−13.6429	+	13.6429i	−0.625981	+	0.625981i
$476$		0			0
$477$	17.8661	+	14.4859i	0.818031	+	0.663263i
$478$		0			0
$479$	15.0944	+	4.04453i	0.689680	+	0.184799i	0.586604	−	0.809874i	$-0.300465\pi$
$479$	15.0944	+	4.04453i	0.689680	+	0.184799i	0.103077	+	0.994673i	$0.467131\pi$
$480$		0			0
$481$	−4.02100	+	12.4366i	−0.183342	+	0.567060i
$482$		0			0
$483$	0.831035	−	2.34447i	0.0378134	−	0.106677i
$484$		0			0
$485$	4.41624	−	7.64915i	0.200531	−	0.347330i
$486$		0			0
$487$	8.22774	+	8.22774i	0.372834	+	0.372834i	0.868509	−	0.495674i	$-0.165079\pi$
$487$	8.22774	+	8.22774i	0.372834	+	0.372834i	−0.495674	+	0.868509i	$0.665079\pi$
$488$		0			0
$489$	−10.6169	−	12.4385i	−0.480112	−	0.562490i
$490$		0			0
$491$		−	14.8640i		−	0.670802i	−0.942076	−	0.335401i	$-0.891128\pi$
$491$		−	14.8640i		−	0.670802i	0.942076	−	0.335401i	$-0.108872\pi$
$492$		0			0
$493$	−8.09461	−	14.0203i	−0.364563	−	0.631441i
$494$		0			0
$495$	2.79728	−	2.02971i	0.125729	−	0.0912289i
$496$		0			0
$497$	0.848309	−	0.489771i	0.0380519	−	0.0219693i
$498$		0			0
$499$	6.32351	+	23.5997i	0.283079	+	1.05647i	0.950232	+	0.311545i	$0.100846\pi$
$499$	6.32351	+	23.5997i	0.283079	+	1.05647i	−0.667152	+	0.744921i	$0.732487\pi$
$500$		0			0
$501$	12.7826	−	36.0618i	0.571087	−	1.61112i
$502$		0			0
$503$	−37.5229	−	10.0542i	−1.67307	−	0.448297i	−0.707131	−	0.707083i	$-0.750011\pi$
$503$	−37.5229	−	10.0542i	−1.67307	−	0.448297i	−0.965935	+	0.258786i	$0.916677\pi$
$504$		0			0
$505$	−2.26431	−	8.45054i	−0.100761	−	0.376044i
$506$		0			0
$507$	14.4743	+	1.14364i	0.642826	+	0.0507907i
$508$		0			0
$509$	−7.49010	−	12.9732i	−0.331993	−	0.575029i	0.650910	−	0.759155i	$-0.274388\pi$
$509$	−7.49010	−	12.9732i	−0.331993	−	0.575029i	−0.982903	+	0.184127i	$0.941054\pi$
$510$		0			0
$511$	0.140192	+	0.0809396i	0.00620171	+	0.00358056i
$512$		0			0
$513$	0.584867	+	23.1528i	0.0258225	+	1.02222i
$514$		0			0
$515$	2.75776	+	1.59219i	0.121522	+	0.0701605i
$516$		0			0
$517$		−	15.3702i		−	0.675981i
$518$		0			0
$519$	0.314238	−	3.97711i	0.0137935	−	0.174576i
$520$		0			0
$521$	2.27386	−	3.93844i	0.0996197	−	0.172546i	−0.811908	−	0.583786i	$-0.801571\pi$
$521$	2.27386	−	3.93844i	0.0996197	−	0.172546i	0.911527	+	0.411240i	$0.134904\pi$
$522$		0			0
$523$	14.4021	−	3.85902i	0.629759	−	0.168743i	0.0701985	−	0.997533i	$-0.477637\pi$
$523$	14.4021	−	3.85902i	0.629759	−	0.168743i	0.559560	+	0.828790i	$0.310970\pi$
$524$		0			0
$525$	1.26783	−	1.84349i	0.0553327	−	0.0804564i
$526$		0			0
$527$	−3.37090	+	1.94619i	−0.146839	+	0.0847773i
$528$		0			0
$529$		−	0.160103i		−	0.00696099i
$530$		0			0
$531$	−0.494975	−	4.73745i	−0.0214801	−	0.205588i
$532$		0			0
$533$	6.57132	−	24.5245i	0.284635	−	1.06227i
$534$		0			0
$535$	1.31549	−	4.90947i	0.0568735	−	0.212255i
$536$		0			0
$537$	2.24044	+	12.1092i	0.0966823	+	0.522549i
$538$		0			0
$539$	4.85881	+	8.41570i	0.209284	+	0.362490i
$540$		0			0
$541$	−13.1303	−	13.1303i	−0.564516	−	0.564516i	0.366071	−	0.930587i	$-0.380703\pi$
$541$	−13.1303	−	13.1303i	−0.564516	−	0.564516i	−0.930587	+	0.366071i	$0.880703\pi$
$542$		0			0
$543$	−3.63749	+	1.73362i	−0.156100	+	0.0743968i
$544$		0			0
$545$	−10.9741			−0.470079
$546$		0			0
$547$	16.2813	−	16.2813i	0.696137	−	0.696137i	−0.267438	−	0.963575i	$-0.586177\pi$
$547$	16.2813	−	16.2813i	0.696137	−	0.696137i	0.963575	+	0.267438i	$0.0861771\pi$
$548$		0			0
$549$	7.28960	−	5.28934i	0.311112	−	0.225744i
$550$		0			0
$551$	14.9669	+	8.64112i	0.637610	+	0.368124i
$552$		0			0
$553$	−0.373226	+	1.39290i	−0.0158712	+	0.0592321i
$554$		0			0
$555$	−5.26253	−	6.84210i	−0.223382	−	0.290431i
$556$		0			0
$557$	−3.62511	+	13.5291i	−0.153601	+	0.573247i	0.845620	+	0.533785i	$0.179231\pi$
$557$	−3.62511	+	13.5291i	−0.153601	+	0.573247i	−0.999221	+	0.0394614i	$0.987436\pi$
$558$		0			0
$559$	−12.8902	−	7.44214i	−0.545196	−	0.314769i
$560$		0			0
$561$	−6.60171	−	7.73443i	−0.278724	−	0.326548i
$562$		0			0
$563$	20.4328	−	20.4328i	0.861139	−	0.861139i	−0.130331	−	0.991471i	$-0.541604\pi$
$563$	20.4328	−	20.4328i	0.861139	−	0.861139i	0.991471	+	0.130331i	$0.0416041\pi$
$564$		0			0
$565$	4.79645			0.201788
$566$		0			0
$567$	−0.555152	−	2.62770i	−0.0233142	−	0.110353i
$568$		0			0
$569$	8.73461	+	8.73461i	0.366174	+	0.366174i	0.866080	−	0.499906i	$-0.166632\pi$
$569$	8.73461	+	8.73461i	0.366174	+	0.366174i	−0.499906	+	0.866080i	$0.666632\pi$
$570$		0			0
$571$	19.8386	+	34.3615i	0.830220	+	1.43798i	0.897864	+	0.440274i	$0.145119\pi$
$571$	19.8386	+	34.3615i	0.830220	+	1.43798i	−0.0676438	+	0.997710i	$0.521548\pi$
$572$		0			0
$573$	−1.01844	+	0.188432i	−0.0425458	+	0.00787185i
$574$		0			0
$575$	5.39174	−	20.1223i	0.224851	−	0.839156i
$576$		0			0
$577$	−5.97998	+	22.3176i	−0.248950	+	0.929093i	0.722407	+	0.691468i	$0.243036\pi$
$577$	−5.97998	+	22.3176i	−0.248950	+	0.929093i	−0.971357	+	0.237625i	$0.923631\pi$
$578$		0			0
$579$	−2.22404	−	12.0205i	−0.0924279	−	0.499555i
$580$		0			0
$581$			2.61650i			0.108551i
$582$		0			0
$583$	9.33629	−	5.39031i	0.386670	−	0.223244i
$584$		0			0
$585$	3.32625	−	4.10241i	0.137524	−	0.169614i
$586$		0			0
$587$	−42.6232	+	11.4209i	−1.75925	+	0.471389i	−0.986560	−	0.163397i	$-0.947755\pi$
$587$	−42.6232	+	11.4209i	−1.75925	+	0.471389i	−0.772688	+	0.634786i	$0.781088\pi$
$588$		0			0
$589$	2.07759	−	3.59849i	0.0856055	−	0.148273i
$590$		0			0
$591$	37.7314	+	2.98122i	1.55206	+	0.122631i
$592$		0			0
$593$		−	21.8316i		−	0.896517i	−0.893904	−	0.448259i	$-0.852044\pi$
$593$		−	21.8316i		−	0.896517i	0.893904	−	0.448259i	$-0.147956\pi$
$594$		0			0
$595$	0.884044	+	0.510403i	0.0362423	+	0.0209245i
$596$		0			0
$597$	2.10224	−	0.388958i	0.0860391	−	0.0159190i
$598$		0			0
$599$	10.8724	+	6.27716i	0.444232	+	0.256478i	0.705391	−	0.708818i	$-0.250771\pi$
$599$	10.8724	+	6.27716i	0.444232	+	0.256478i	−0.261159	+	0.965296i	$0.584105\pi$
$600$		0			0
$601$	−8.80478	−	15.2503i	−0.359155	−	0.622074i	0.628665	−	0.777676i	$-0.283602\pi$
$601$	−8.80478	−	15.2503i	−0.359155	−	0.622074i	−0.987820	+	0.155602i	$0.950268\pi$
$602$		0			0
$603$	0.825952	−	5.19414i	0.0336354	−	0.211522i
$604$		0			0
$605$	1.91329	+	7.14049i	0.0777863	+	0.290302i
$606$		0			0
$607$	−38.0509	−	10.1957i	−1.54444	−	0.413831i	−0.616741	−	0.787166i	$-0.711547\pi$
$607$	−38.0509	−	10.1957i	−1.54444	−	0.413831i	−0.927696	+	0.373336i	$0.878214\pi$
$608$		0			0
$609$	−1.88893	−	0.669558i	−0.0765431	−	0.0271319i
$610$		0			0
$611$	−6.07917	−	22.6878i	−0.245937	−	0.917850i
$612$		0			0
$613$	−11.4577	+	6.61513i	−0.462774	+	0.267183i	−0.713210	−	0.700951i	$-0.752759\pi$
$613$	−11.4577	+	6.61513i	−0.462774	+	0.267183i	0.250436	+	0.968133i	$0.419426\pi$
$614$		0			0
$615$	10.8857	+	12.7535i	0.438953	+	0.514269i
$616$		0			0
$617$	14.4682	+	25.0597i	0.582468	+	1.00886i	0.995186	+	0.0980057i	$0.0312463\pi$
$617$	14.4682	+	25.0597i	0.582468	+	1.00886i	−0.412717	+	0.910859i	$0.635420\pi$
$618$		0			0
$619$			23.9466i			0.962496i	0.876585	+	0.481248i	$0.159816\pi$
$619$			23.9466i			0.962496i	−0.876585	+	0.481248i	$0.840184\pi$
$620$		0			0
$621$	−13.0461	−	21.3336i	−0.523523	−	0.856087i
$622$		0			0
$623$	1.43438	+	1.43438i	0.0574671	+	0.0574671i
$624$		0			0
$625$	7.69092	−	13.3211i	0.307637	−	0.532843i
$626$		0			0
$627$	10.2316	+	3.62674i	0.408609	+	0.144838i
$628$		0			0
$629$	−18.8492	+	17.0214i	−0.751568	+	0.678687i
$630$		0			0
$631$	−19.0966	−	5.11693i	−0.760225	−	0.203702i	−0.142176	−	0.989841i	$-0.545410\pi$
$631$	−19.0966	−	5.11693i	−0.760225	−	0.203702i	−0.618049	+	0.786140i	$0.712077\pi$
$632$		0			0
$633$	−5.95738	−	4.09710i	−0.236785	−	0.162845i
$634$		0			0
$635$	1.99522	−	1.99522i	0.0791779	−	0.0791779i
$636$		0			0
$637$	10.5006	+	10.5006i	0.416048	+	0.416048i
$638$		0			0
$639$	1.54649	−	9.72538i	0.0611783	−	0.384730i
$640$		0			0
$641$	−6.17813	+	3.56695i	−0.244022	+	0.140886i	−0.617024	−	0.786945i	$-0.711662\pi$
$641$	−6.17813	+	3.56695i	−0.244022	+	0.140886i	0.373002	+	0.927830i	$0.378328\pi$
$642$		0			0
$643$	16.5674	−	16.5674i	0.653354	−	0.653354i	−0.300445	−	0.953799i	$-0.597135\pi$
$643$	16.5674	−	16.5674i	0.653354	−	0.653354i	0.953799	+	0.300445i	$0.0971352\pi$
$644$		0			0
$645$	8.87344	−	4.22906i	0.349391	−	0.166519i
$646$		0			0
$647$	−13.6620	+	3.66072i	−0.537108	+	0.143918i	−0.517169	−	0.855883i	$-0.673014\pi$
$647$	−13.6620	+	3.66072i	−0.537108	+	0.143918i	−0.0199395	+	0.999801i	$0.506347\pi$
$648$		0			0
$649$	−2.15649	−	0.577829i	−0.0846495	−	0.0226818i
$650$		0			0
$651$	−0.160982	+	0.454155i	−0.00630938	+	0.0177997i
$652$		0			0
$653$	−26.2947	+	7.04565i	−1.02899	+	0.275717i	−0.733544	−	0.679642i	$-0.762135\pi$
$653$	−26.2947	+	7.04565i	−1.02899	+	0.275717i	−0.295447	+	0.955359i	$0.595469\pi$
$654$		0			0
$655$	0.332764			0.0130022
$656$		0			0
$657$	1.51968	−	0.582275i	0.0592883	−	0.0227167i
$658$		0			0
$659$	−24.4337	+	42.3204i	−0.951802	+	1.64857i	−0.210278	+	0.977642i	$0.567437\pi$
$659$	−24.4337	+	42.3204i	−0.951802	+	1.64857i	−0.741523	+	0.670927i	$0.765896\pi$
$660$		0			0
$661$	7.04581	+	26.2953i	0.274050	+	1.02277i	0.956475	+	0.291814i	$0.0942587\pi$
$661$	7.04581	+	26.2953i	0.274050	+	1.02277i	−0.682425	+	0.730956i	$0.739075\pi$
$662$		0			0
$663$	−12.8038	−	8.80561i	−0.497258	−	0.341982i
$664$		0			0
$665$	−1.08973			−0.0422578
$666$		0			0
$667$	−18.6599			−0.722515
$668$		0			0
$669$	−11.8550	−	8.15309i	−0.458340	−	0.315217i
$670$		0			0
$671$	−1.09257	−	4.07752i	−0.0421781	−	0.157411i
$672$		0			0
$673$	−19.3772	+	33.5623i	−0.746936	+	1.29373i	0.202349	+	0.979314i	$0.435143\pi$
$673$	−19.3772	+	33.5623i	−0.746936	+	1.29373i	−0.949285	+	0.314418i	$0.898191\pi$
$674$		0			0
$675$	−6.36838	−	21.5725i	−0.245119	−	0.830325i
$676$		0			0
$677$	20.2088			0.776688			0.388344	−	0.921515i	$-0.373047\pi$
$677$	20.2088			0.776688			0.388344	+	0.921515i	$0.373047\pi$
$678$		0			0
$679$	−3.10742	+	0.832631i	−0.119252	+	0.0319534i
$680$		0			0
$681$	13.0187	−	36.7277i	0.498878	−	1.40741i
$682$		0			0
$683$	−21.4254	−	5.74093i	−0.819821	−	0.219670i	−0.175553	−	0.984470i	$-0.556171\pi$
$683$	−21.4254	−	5.74093i	−0.819821	−	0.219670i	−0.644268	+	0.764799i	$0.722838\pi$
$684$		0			0
$685$	10.9551	−	2.93542i	0.418574	−	0.112157i
$686$		0			0
$687$	−14.8315	+	7.06864i	−0.565856	+	0.269686i
$688$		0			0
$689$	11.6492	−	11.6492i	0.443800	−	0.443800i
$690$		0			0
$691$	−9.14650	+	5.28074i	−0.347949	+	0.200889i	−0.663782	−	0.747926i	$-0.731050\pi$
$691$	−9.14650	+	5.28074i	−0.347949	+	0.200889i	0.315832	+	0.948815i	$0.397716\pi$
$692$		0			0
$693$	−1.24319	−	0.197686i	−0.0472247	−	0.00750949i
$694$		0			0
$695$	2.69138	+	2.69138i	0.102090	+	0.102090i
$696$		0			0
$697$	34.8849	−	34.8849i	1.32136	−	1.32136i
$698$		0			0
$699$	24.1038	+	16.5770i	0.911689	+	0.627000i
$700$		0			0
$701$	−31.0480	−	8.31929i	−1.17267	−	0.314215i	−0.380653	−	0.924718i	$-0.624301\pi$
$701$	−31.0480	−	8.31929i	−1.17267	−	0.314215i	−0.792014	+	0.610503i	$0.790968\pi$
$702$		0			0
$703$	8.34074	−	25.7971i	0.314577	−	0.972957i
$704$		0			0
$705$	14.6204	+	5.18243i	0.550636	+	0.195181i
$706$		0			0
$707$	−1.59325	+	2.75959i	−0.0599204	+	0.103785i
$708$		0			0
$709$	18.6822	+	18.6822i	0.701626	+	0.701626i	0.964760	−	0.263133i	$-0.0847558\pi$
$709$	18.6822	+	18.6822i	0.701626	+	0.701626i	−0.263133	+	0.964760i	$0.584756\pi$
$710$		0			0
$711$	8.51397	+	11.7337i	0.319299	+	0.440047i
$712$		0			0
$713$			4.48641i			0.168017i
$714$		0			0
$715$	−1.23772	−	2.14380i	−0.0462883	−	0.0801736i
$716$		0			0
$717$	11.6786	+	13.6824i	0.436145	+	0.510978i
$718$		0			0
$719$	−6.20481	+	3.58235i	−0.231400	+	0.133599i	−0.611218	−	0.791462i	$-0.709320\pi$
$719$	−6.20481	+	3.58235i	−0.231400	+	0.133599i	0.379818	+	0.925061i	$0.375987\pi$
$720$		0			0
$721$	−0.300190	−	1.12032i	−0.0111797	−	0.0417231i
$722$		0			0
$723$	−1.41107	−	0.500177i	−0.0524784	−	0.0186018i
$724$		0			0
$725$	−16.2124	−	4.34409i	−0.602112	−	0.161335i
$726$		0			0
$727$	−3.31953	−	12.3887i	−0.123115	−	0.459470i	0.876651	−	0.481127i	$-0.159772\pi$
$727$	−3.31953	−	12.3887i	−0.123115	−	0.459470i	−0.999765	+	0.0216571i	$0.993106\pi$
$728$		0			0
$729$	−24.0345	−	12.3022i	−0.890166	−	0.455637i
$730$		0			0
$731$	−14.4608	−	25.0469i	−0.534854	−	0.926394i
$732$		0			0
$733$	5.32634	+	3.07517i	0.196733	+	0.113584i	0.595131	−	0.803629i	$-0.297100\pi$
$733$	5.32634	+	3.07517i	0.196733	+	0.113584i	−0.398398	+	0.917213i	$0.630434\pi$
$734$		0			0
$735$	−9.64342	+	1.78423i	−0.355703	+	0.0658123i
$736$		0			0
$737$	−2.13485	−	1.23256i	−0.0786383	−	0.0454018i
$738$		0			0
$739$		−	21.5878i		−	0.794122i	−0.917792	−	0.397061i	$-0.870030\pi$
$739$		−	21.5878i		−	0.794122i	0.917792	−	0.397061i	$-0.129970\pi$
$740$		0			0
$741$	16.5371	+	1.30663i	0.607507	+	0.0480001i
$742$		0			0
$743$	−0.811485	+	1.40553i	−0.0297705	+	0.0515640i	−0.880527	−	0.473996i	$-0.842811\pi$
$743$	−0.811485	+	1.40553i	−0.0297705	+	0.0515640i	0.850756	+	0.525560i	$0.176144\pi$
$744$		0			0
$745$	4.33663	−	1.16200i	0.158882	−	0.0425722i
$746$		0			0
$747$	20.4321	+	16.5664i	0.747570	+	0.606133i
$748$		0			0
$749$	−1.60323	+	0.925624i	−0.0585807	+	0.0338216i
$750$		0			0
$751$		−	32.7253i		−	1.19416i	−0.802180	−	0.597082i	$-0.796327\pi$
$751$		−	32.7253i		−	1.19416i	0.802180	−	0.597082i	$-0.203673\pi$
$752$		0			0
$753$	5.71842	+	30.9070i	0.208391	+	1.12631i
$754$		0			0
$755$	2.91155	−	10.8660i	0.105962	−	0.395456i
$756$		0			0
$757$	−10.9136	+	40.7301i	−0.396662	+	1.48036i	0.422270	+	0.906470i	$0.361233\pi$
$757$	−10.9136	+	40.7301i	−0.396662	+	1.48036i	−0.818932	+	0.573891i	$0.805433\pi$
$758$		0			0
$759$	−11.5251	+	2.13237i	−0.418334	+	0.0774003i
$760$		0			0
$761$	21.3210	+	36.9291i	0.772887	+	1.33868i	0.935975	+	0.352068i	$0.114521\pi$
$761$	21.3210	+	36.9291i	0.772887	+	1.33868i	−0.163088	+	0.986612i	$0.552145\pi$
$762$		0			0
$763$	2.82636	+	2.82636i	0.102321	+	0.102321i
$764$		0			0
$765$	9.58304	−	3.67181i	0.346476	−	0.132755i
$766$		0			0
$767$	−3.41170			−0.123190
$768$		0			0
$769$	−21.7401	+	21.7401i	−0.783970	+	0.783970i	−0.980498	−	0.196529i	$-0.937033\pi$
$769$	−21.7401	+	21.7401i	−0.783970	+	0.783970i	0.196529	+	0.980498i	$0.437033\pi$
$770$		0			0
$771$	−22.2370	−	26.0524i	−0.800846	−	0.938255i
$772$		0			0
$773$	24.2155	+	13.9808i	0.870972	+	0.502856i	0.867671	−	0.497138i	$-0.165616\pi$
$773$	24.2155	+	13.9808i	0.870972	+	0.502856i	0.00330113	+	0.999995i	$0.498949\pi$
$774$		0			0
$775$	−1.04445	+	3.89794i	−0.0375177	+	0.140018i
$776$		0			0
$777$	−0.406817	+	3.11753i	−0.0145945	+	0.111841i
$778$		0			0
$779$	−13.6308	+	50.8710i	−0.488376	+	1.82264i
$780$		0			0
$781$	−3.99724	−	2.30781i	−0.143033	−	0.0825799i
$782$		0			0
$783$	−17.1883	+	10.5112i	−0.614260	+	0.375638i
$784$		0			0
$785$	−9.52243	+	9.52243i	−0.339870	+	0.339870i
$786$		0			0
$787$	−49.1038			−1.75036			−0.875180	−	0.483797i	$-0.839257\pi$
$787$	−49.1038			−1.75036			−0.875180	+	0.483797i	$0.839257\pi$
$788$		0			0
$789$	−12.8277	+	6.11365i	−0.456678	+	0.217652i
$790$		0			0
$791$	−1.23532	−	1.23532i	−0.0439229	−	0.0439229i
$792$		0			0
$793$	−3.22545	−	5.58665i	−0.114539	−	0.198388i
$794$		0			0
$795$	1.97941	+	10.6983i	0.0702023	+	0.379430i
$796$		0			0
$797$	2.53843	−	9.47356i	0.0899159	−	0.335571i	−0.906284	−	0.422670i	$-0.861093\pi$
$797$	2.53843	−	9.47356i	0.0899159	−	0.335571i	0.996200	+	0.0870990i	$0.0277597\pi$
$798$		0			0
$799$	11.8125	−	44.0847i	0.417895	−	1.55960i
$800$		0			0
$801$	20.2827	−	2.11917i	0.716655	−	0.0748771i
$802$		0			0
$803$		−	0.762777i		−	0.0269178i
$804$		0			0
$805$	1.01896	−	0.588298i	0.0359137	−	0.0207348i
$806$		0			0
$807$	−25.1123	+	36.5145i	−0.883994	+	1.28537i
$808$		0			0
$809$	−47.0890	+	12.6175i	−1.65556	+	0.443607i	−0.961163	−	0.275983i	$-0.910997\pi$
$809$	−47.0890	+	12.6175i	−1.65556	+	0.443607i	−0.694400	+	0.719589i	$0.744330\pi$
$810$		0			0
$811$	−11.9267	+	20.6576i	−0.418803	+	0.725387i	−0.995819	−	0.0913450i	$-0.970883\pi$
$811$	−11.9267	+	20.6576i	−0.418803	+	0.725387i	0.577017	+	0.816732i	$0.304217\pi$
$812$		0			0
$813$	−0.445507	+	5.63850i	−0.0156246	+	0.197751i
$814$		0			0
$815$		−	7.73553i		−	0.270964i
$816$		0			0
$817$	26.7380	+	15.4372i	0.935444	+	0.540079i
$818$		0			0
$819$	−1.91324	+	0.199898i	−0.0668540	+	0.00698500i
$820$		0			0
$821$	−9.44861	−	5.45516i	−0.329759	−	0.190386i	0.325975	−	0.945378i	$-0.394307\pi$
$821$	−9.44861	−	5.45516i	−0.329759	−	0.190386i	−0.655734	+	0.754992i	$0.727641\pi$
$822$		0			0
$823$	19.5227	+	33.8144i	0.680520	+	1.17869i	0.974822	+	0.222983i	$0.0715793\pi$
$823$	19.5227	+	33.8144i	0.680520	+	1.17869i	−0.294303	+	0.955712i	$0.595087\pi$
$824$		0			0
$825$	−10.5098	−	0.830395i	−0.365904	−	0.0289107i
$826$		0			0
$827$	13.4961	+	50.3680i	0.469304	+	1.75147i	0.642212	+	0.766527i	$0.278017\pi$
$827$	13.4961	+	50.3680i	0.469304	+	1.75147i	−0.172908	+	0.984938i	$0.555316\pi$
$828$		0			0
$829$	35.3785	+	9.47963i	1.22874	+	0.329241i	0.814091	−	0.580738i	$-0.197236\pi$
$829$	35.3785	+	9.47963i	1.22874	+	0.329241i	0.414654	+	0.909979i	$0.363903\pi$
$830$		0			0
$831$	−3.39791	+	9.58601i	−0.117872	+	0.332535i
$832$		0			0
$833$	7.46827	+	27.8720i	0.258760	+	0.965707i
$834$		0			0
$835$	15.6733	−	9.04897i	0.542396	−	0.313152i
$836$		0			0
$837$	2.52720	+	4.13259i	0.0873529	+	0.142843i
$838$		0			0
$839$	18.0726	+	31.3027i	0.623936	+	1.08069i	0.988745	+	0.149607i	$0.0478010\pi$
$839$	18.0726	+	31.3027i	0.623936	+	1.08069i	−0.364809	+	0.931082i	$0.618866\pi$
$840$		0			0
$841$		−	13.9658i		−	0.481581i
$842$		0			0
$843$	3.94902	+	4.62659i	0.136012	+	0.159348i
$844$		0			0
$845$	4.85640	+	4.85640i	0.167065	+	0.167065i
$846$		0			0
$847$	1.34626	−	2.33179i	0.0462580	−	0.0801212i
$848$		0			0
$849$	14.0773	−	39.7142i	0.483132	−	1.36299i
$850$		0			0
$851$	6.12769	+	28.6247i	0.210055	+	0.981243i
$852$		0			0
$853$	18.7517	+	5.02449i	0.642044	+	0.172035i	0.565129	−	0.825002i	$-0.308826\pi$
$853$	18.7517	+	5.02449i	0.642044	+	0.172035i	0.0769151	+	0.997038i	$0.475493\pi$
$854$		0			0
$855$	−6.89963	+	8.50960i	−0.235962	+	0.291022i
$856$		0			0
$857$	3.80945	−	3.80945i	0.130128	−	0.130128i	−0.639043	−	0.769171i	$-0.720669\pi$
$857$	3.80945	−	3.80945i	0.130128	−	0.130128i	0.769171	+	0.639043i	$0.220669\pi$
$858$		0			0
$859$	14.3197	+	14.3197i	0.488582	+	0.488582i	0.907859	−	0.419276i	$-0.137716\pi$
$859$	14.3197	+	14.3197i	0.488582	+	0.488582i	−0.419276	+	0.907859i	$0.637716\pi$
$860$		0			0
$861$	0.481041	−	6.08822i	0.0163938	−	0.207486i
$862$		0			0
$863$	−36.7084	+	21.1936i	−1.24957	+	0.721438i	−0.971023	−	0.238985i	$-0.923185\pi$
$863$	−36.7084	+	21.1936i	−1.24957	+	0.721438i	−0.278544	+	0.960423i	$0.589852\pi$
$864$		0			0
$865$	1.33440	−	1.33440i	0.0453709	−	0.0453709i
$866$		0			0
$867$	−0.322669	−	0.677026i	−0.0109584	−	0.0229930i
$868$		0			0
$869$	6.56336	−	1.75865i	0.222647	−	0.0596580i
$870$		0			0
$871$	−3.63873	−	0.974994i	−0.123294	−	0.0330364i
$872$		0			0
$873$	−13.1727	+	29.5375i	−0.445829	+	0.999691i
$874$		0			0
$875$	2.20305	−	0.590306i	0.0744767	−	0.0199560i
$876$		0			0
$877$	37.4443			1.26441			0.632203	−	0.774803i	$-0.282151\pi$
$877$	37.4443			1.26441			0.632203	+	0.774803i	$0.282151\pi$
$878$		0			0
$879$	6.76894	+	14.2026i	0.228311	+	0.479043i
$880$		0			0
$881$	−21.9509	+	38.0200i	−0.739543	+	1.28093i	0.213158	+	0.977018i	$0.431625\pi$
$881$	−21.9509	+	38.0200i	−0.739543	+	1.28093i	−0.952701	+	0.303909i	$0.901708\pi$
$882$		0			0
$883$	−10.2424	−	38.2251i	−0.344684	−	1.28638i	−0.892981	−	0.450094i	$-0.851390\pi$
$883$	−10.2424	−	38.2251i	−0.344684	−	1.28638i	0.548297	−	0.836284i	$-0.315276\pi$
$884$		0			0
$885$	1.27675	−	1.85646i	0.0429175	−	0.0624042i
$886$		0			0
$887$	44.5643			1.49632			0.748161	−	0.663517i	$-0.230937\pi$
$887$	44.5643			1.49632			0.748161	+	0.663517i	$0.230937\pi$
$888$		0			0
$889$	−1.02773			−0.0344690
$890$		0			0
$891$	−9.41497	+	8.45630i	−0.315413	+	0.283297i
$892$		0			0
$893$	12.6100	+	47.0611i	0.421977	+	1.57484i
$894$		0			0
$895$	−2.91256	+	5.04470i	−0.0973560	+	0.168626i
$896$		0			0
$897$	−16.1686	+	7.70593i	−0.539855	+	0.257293i
$898$		0			0
$899$	3.61467			0.120556
$900$		0			0
$901$	30.9209	−	8.28522i	1.03012	−	0.276021i
$902$		0			0
$903$	−3.37453	−	1.19615i	−0.112297	−	0.0398055i
$904$		0			0
$905$	−1.84109	−	0.493319i	−0.0611999	−	0.0163985i
$906$		0			0
$907$	−42.7218	+	11.4473i	−1.41855	+	0.380100i	−0.884971	−	0.465647i	$-0.845822\pi$
$907$	−42.7218	+	11.4473i	−1.41855	+	0.380100i	−0.533584	+	0.845747i	$0.679155\pi$
$908$		0			0
$909$	11.4618	+	29.9140i	0.380163	+	0.992185i
$910$		0			0
$911$	4.93313	−	4.93313i	0.163442	−	0.163442i	−0.620648	−	0.784090i	$-0.713130\pi$
$911$	4.93313	−	4.93313i	0.163442	−	0.163442i	0.784090	+	0.620648i	$0.213130\pi$
$912$		0			0
$913$	10.6772	−	6.16449i	0.353364	−	0.204015i
$914$		0			0
$915$	4.24699	+	0.335562i	0.140401	+	0.0110933i
$916$		0			0
$917$	−0.0857029	−	0.0857029i	−0.00283016	−	0.00283016i
$918$		0			0
$919$	−22.8842	+	22.8842i	−0.754881	+	0.754881i	−0.975386	−	0.220505i	$-0.929229\pi$
$919$	−22.8842	+	22.8842i	−0.754881	+	0.754881i	0.220505	+	0.975386i	$0.429229\pi$
$920$		0			0
$921$	26.2765	−	38.2074i	0.865841	−	1.25898i
$922$		0			0
$923$	−6.81306	−	1.82555i	−0.224255	−	0.0600888i
$924$		0			0
$925$	−1.33999	+	26.2966i	−0.0440585	+	0.864628i
$926$		0			0
$927$	−10.6492	−	4.74919i	−0.349765	−	0.155984i
$928$		0			0
$929$	3.39347	−	5.87766i	0.111336	−	0.192840i	−0.804973	−	0.593311i	$-0.797820\pi$
$929$	3.39347	−	5.87766i	0.111336	−	0.192840i	0.916309	+	0.400472i	$0.131154\pi$
$930$		0			0
$931$	−21.7813	−	21.7813i	−0.713853	−	0.713853i
$932$		0			0
$933$	−38.7209	+	33.0502i	−1.26767	+	1.08201i
$934$		0			0
$935$		−	4.81005i		−	0.157305i
$936$		0			0
$937$	21.5995	+	37.4115i	0.705626	+	1.22218i	0.966465	+	0.256798i	$0.0826676\pi$
$937$	21.5995	+	37.4115i	0.705626	+	1.22218i	−0.260839	+	0.965382i	$0.583999\pi$
$938$		0			0
$939$	10.0546	−	8.58204i	0.328118	−	0.280064i
$940$		0			0
$941$	35.3411	−	20.4042i	1.15209	−	0.665158i	0.202692	−	0.979242i	$-0.435031\pi$
$941$	35.3411	−	20.4042i	1.15209	−	0.665158i	0.949395	+	0.314085i	$0.101698\pi$
$942$		0			0
$943$	−14.7174	−	54.9262i	−0.479266	−	1.78864i
$944$		0			0
$945$	0.607212	−	1.11588i	0.0197526	−	0.0362997i
$946$		0			0
$947$	−22.8777	−	6.13006i	−0.743426	−	0.199200i	−0.132826	−	0.991139i	$-0.542405\pi$
$947$	−22.8777	−	6.13006i	−0.743426	−	0.199200i	−0.610600	+	0.791939i	$0.709072\pi$
$948$		0			0
$949$	−0.301691	−	1.12593i	−0.00979330	−	0.0365491i
$950$		0			0
$951$	4.32414	−	54.7279i	0.140220	−	1.77467i
$952$		0			0
$953$	−28.5262	−	49.4088i	−0.924054	−	1.60051i	−0.793075	−	0.609124i	$-0.791521\pi$
$953$	−28.5262	−	49.4088i	−0.924054	−	1.60051i	−0.130979	−	0.991385i	$-0.541812\pi$
$954$		0			0
$955$	−0.424282	−	0.244960i	−0.0137295	−	0.00792670i
$956$		0			0
$957$	1.71804	+	9.28566i	0.0555363	+	0.300163i
$958$		0			0
$959$	−3.57749	−	2.06546i	−0.115523	−	0.0666973i
$960$		0			0
$961$			30.1309i			0.971965i
$962$		0			0
$963$	−2.92273	+	18.3801i	−0.0941837	+	0.592291i
$964$		0			0
$965$	2.89123	−	5.00776i	0.0930720	−	0.161205i
$966$		0			0
$967$	−35.8321	+	9.60118i	−1.15228	+	0.308753i	−0.783880	−	0.620913i	$-0.786762\pi$
$967$	−35.8321	+	9.60118i	−1.15228	+	0.308753i	−0.368403	+	0.929666i	$0.620095\pi$
$968$		0			0
$969$	26.5588	+	18.2654i	0.853193	+	0.586770i
$970$		0			0
$971$	9.59093	−	5.53733i	0.307788	−	0.177701i	−0.338148	−	0.941093i	$-0.609801\pi$
$971$	9.59093	−	5.53733i	0.307788	−	0.177701i	0.645936	+	0.763392i	$0.276467\pi$
$972$		0			0
$973$		−	1.38632i		−	0.0444435i
$974$		0			0
$975$	−15.8418	+	2.93106i	−0.507344	+	0.0938689i
$976$		0			0
$977$	4.62017	−	17.2427i	0.147812	−	0.551643i	−0.851802	−	0.523864i	$-0.824490\pi$
$977$	4.62017	−	17.2427i	0.147812	−	0.551643i	0.999614	−	0.0277788i	$-0.00884339\pi$
$978$		0			0
$979$	2.47389	−	9.23269i	0.0790659	−	0.295078i
$980$		0			0
$981$	39.9660	−	4.17571i	1.27602	−	0.133320i
$982$		0			0
$983$	20.1423	+	34.8875i	0.642439	+	1.11274i	0.984887	+	0.173200i	$0.0554107\pi$
$983$	20.1423	+	34.8875i	0.642439	+	1.11274i	−0.342448	+	0.939537i	$0.611256\pi$
$984$		0			0
$985$	12.6596	+	12.6596i	0.403369	+	0.403369i
$986$		0			0
$987$	−2.43074	−	5.10019i	−0.0773712	−	0.162341i
$988$		0			0
$989$	−33.3356			−1.06001
$990$		0			0
$991$	−2.84174	+	2.84174i	−0.0902709	+	0.0902709i	−0.750800	−	0.660529i	$-0.770332\pi$
$991$	−2.84174	+	2.84174i	−0.0902709	+	0.0902709i	0.660529	+	0.750800i	$0.270332\pi$
$992$		0			0
$993$	13.5536	−	11.5686i	0.430109	−	0.367119i
$994$		0			0
$995$	0.875798	+	0.505642i	0.0277647	+	0.0160299i
$996$		0			0
$997$	−11.5050	+	42.9374i	−0.364368	+	1.35984i	0.503908	+	0.863758i	$0.331895\pi$
$997$	−11.5050	+	42.9374i	−0.364368	+	1.35984i	−0.868276	+	0.496082i	$0.834771\pi$
$998$		0			0
$999$	21.7688	+	22.9155i	0.688734	+	0.725014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.785.8	yes	152
3.2	odd	2	inner	888.2.br.a.785.6	yes	152
37.14	odd	12	inner	888.2.br.a.569.6	✓	152
111.14	even	12	inner	888.2.br.a.569.8	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.6	✓	152	37.14	odd	12	inner
888.2.br.a.569.8	yes	152	111.14	even	12	inner
888.2.br.a.785.6	yes	152	3.2	odd	2	inner
888.2.br.a.785.8	yes	152	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42713 - 0.981484i) q^{3} +(-0.212050 - 0.791381i) q^{5} +(-0.149206 + 0.258432i) q^{7} +(1.07338 + 2.80140i) q^{9} +1.40612 q^{11} +(2.07555 - 0.556143i) q^{13} +(-0.474106 + 1.33752i) q^{15} +(4.03302 + 1.08064i) q^{17} +(-4.30531 + 1.15360i) q^{19} +(0.466582 - 0.222372i) q^{21} +(3.40295 - 3.40295i) q^{23} +(3.74881 - 2.16438i) q^{25} +(1.21769 - 5.05146i) q^{27} +(-2.74173 - 2.74173i) q^{29} +(-0.659194 + 0.659194i) q^{31} +(-2.00671 - 1.38008i) q^{33} +(0.236157 + 0.0632781i) q^{35} +(-3.30552 + 5.10622i) q^{37} +(-3.50792 - 1.24344i) q^{39} +(5.90794 - 10.2328i) q^{41} +(-4.89804 - 4.89804i) q^{43} +(1.98937 - 1.44349i) q^{45} -10.9310i q^{47} +(3.45548 + 5.98506i) q^{49} +(-4.69499 - 5.50055i) q^{51} +(6.63976 - 3.83347i) q^{53} +(-0.298167 - 1.11277i) q^{55} +(7.27646 + 2.57925i) q^{57} +(-1.53365 - 0.410939i) q^{59} +(-0.777010 - 2.89984i) q^{61} +(-0.884126 - 0.140590i) q^{63} +(-0.880242 - 1.52462i) q^{65} +(-1.51826 - 0.876567i) q^{67} +(-8.19637 + 1.51650i) q^{69} +(-2.84275 - 1.64126i) q^{71} -0.542470i q^{73} +(-7.47432 - 0.590559i) q^{75} +(-0.209801 + 0.363386i) q^{77} +(4.66772 - 1.25071i) q^{79} +(-6.69572 + 6.01393i) q^{81} +(7.59339 - 4.38405i) q^{83} -3.42080i q^{85} +(1.22183 + 6.60376i) q^{87} +(1.75938 - 6.56608i) q^{89} +(-0.165959 + 0.619369i) q^{91} +(1.58774 - 0.293765i) q^{93} +(1.82588 + 3.16252i) q^{95} +(7.62300 + 7.62300i) q^{97} +(1.50930 + 3.93910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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