LMFDB - Embedded newform 888.2.br.a.569.6

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)

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")

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);

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			569.6
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56355 + 0.745185i) q^{3} +(0.212050 - 0.791381i) q^{5} +(-0.149206 - 0.258432i) q^{7} +(1.88940 - 2.33027i) q^{9} -1.40612 q^{11} +(2.07555 + 0.556143i) q^{13} +(0.258174 + 1.39538i) q^{15} +(-4.03302 + 1.08064i) q^{17} +(-4.30531 - 1.15360i) q^{19} +(0.425871 + 0.292886i) q^{21} +(-3.40295 - 3.40295i) q^{23} +(3.74881 + 2.16438i) q^{25} +(-1.21769 + 5.05146i) q^{27} +(2.74173 - 2.74173i) q^{29} +(-0.659194 - 0.659194i) q^{31} +(2.19854 - 1.04782i) q^{33} +(-0.236157 + 0.0632781i) q^{35} +(-3.30552 - 5.10622i) q^{37} +(-3.65967 + 0.677114i) q^{39} +(-5.90794 - 10.2328i) q^{41} +(-4.89804 + 4.89804i) q^{43} +(-1.44349 - 1.98937i) q^{45} -10.9310i q^{47} +(3.45548 - 5.98506i) q^{49} +(5.50055 - 4.69499i) q^{51} +(-6.63976 - 3.83347i) q^{53} +(-0.298167 + 1.11277i) q^{55} +(7.59123 - 1.40453i) q^{57} +(1.53365 - 0.410939i) q^{59} +(-0.777010 + 2.89984i) q^{61} +(-0.884126 - 0.140590i) q^{63} +(0.880242 - 1.52462i) q^{65} +(-1.51826 + 0.876567i) q^{67} +(7.85652 + 2.78486i) q^{69} +(2.84275 - 1.64126i) q^{71} +0.542470i q^{73} +(-7.47432 - 0.590559i) q^{75} +(0.209801 + 0.363386i) q^{77} +(4.66772 + 1.25071i) q^{79} +(-1.86036 - 8.80563i) q^{81} +(-7.59339 - 4.38405i) q^{83} +3.42080i q^{85} +(-2.24374 + 6.32994i) q^{87} +(-1.75938 - 6.56608i) q^{89} +(-0.165959 - 0.619369i) q^{91} +(1.52191 + 0.539463i) q^{93} +(-1.82588 + 3.16252i) q^{95} +(7.62300 - 7.62300i) q^{97} +(-2.65672 + 3.27664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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
$3$	−1.56355	+	0.745185i	−0.902718	+	0.430233i
$3$	−1.56355	+	0.745185i	−0.902718	+	0.430233i
$4$		0			0
$5$	0.212050	−	0.791381i	0.0948316	−	0.353916i	−0.902162	−	0.431397i	$-0.858021\pi$
$5$	0.212050	−	0.791381i	0.0948316	−	0.353916i	0.996994	+	0.0774806i	$0.0246876\pi$
$6$		0			0
$7$	−0.149206	−	0.258432i	−0.0563945	−	0.0976781i	0.836450	−	0.548043i	$-0.184627\pi$
$7$	−0.149206	−	0.258432i	−0.0563945	−	0.0976781i	−0.892844	+	0.450365i	$0.851294\pi$
$8$		0			0
$9$	1.88940	−	2.33027i	0.629799	−	0.776758i
$10$		0			0
$11$	−1.40612			−0.423961			−0.211980	−	0.977274i	$-0.567991\pi$
$11$	−1.40612			−0.423961			−0.211980	+	0.977274i	$0.567991\pi$
$12$		0			0
$13$	2.07555	+	0.556143i	0.575655	+	0.154246i	0.534889	−	0.844922i	$-0.320353\pi$
$13$	2.07555	+	0.556143i	0.575655	+	0.154246i	0.0407662	+	0.999169i	$0.487020\pi$
$14$		0			0
$15$	0.258174	+	1.39538i	0.0666603	+	0.360286i
$16$		0			0
$17$	−4.03302	+	1.08064i	−0.978150	+	0.262094i	−0.712265	−	0.701910i	$-0.752331\pi$
$17$	−4.03302	+	1.08064i	−0.978150	+	0.262094i	−0.265885	+	0.964005i	$0.585664\pi$
$18$		0			0
$19$	−4.30531	−	1.15360i	−0.987706	−	0.264655i	−0.271419	−	0.962461i	$-0.587493\pi$
$19$	−4.30531	−	1.15360i	−0.987706	−	0.264655i	−0.716287	+	0.697806i	$0.754160\pi$
$20$		0			0
$21$	0.425871	+	0.292886i	0.0929326	+	0.0639130i
$22$		0			0
$23$	−3.40295	−	3.40295i	−0.709564	−	0.709564i	0.256880	−	0.966443i	$-0.417306\pi$
$23$	−3.40295	−	3.40295i	−0.709564	−	0.709564i	−0.966443	+	0.256880i	$0.917306\pi$
$24$		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	$-0.632774\pi$
$29$	2.74173	−	2.74173i	0.509126	−	0.509126i	0.914258	+	0.405132i	$0.132774\pi$
$30$		0			0
$31$	−0.659194	−	0.659194i	−0.118395	−	0.118395i	0.645427	−	0.763822i	$-0.276679\pi$
$31$	−0.659194	−	0.659194i	−0.118395	−	0.118395i	−0.763822	+	0.645427i	$0.776679\pi$
$32$		0			0
$33$	2.19854	−	1.04782i	0.382717	−	0.182402i
$34$		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
$39$	−3.65967	+	0.677114i	−0.586016	+	0.108425i
$40$		0			0
$41$	−5.90794	−	10.2328i	−0.922665	−	1.59810i	−0.795275	−	0.606249i	$-0.792673\pi$
$41$	−5.90794	−	10.2328i	−0.922665	−	1.59810i	−0.127390	−	0.991853i	$-0.540660\pi$
$42$		0			0
$43$	−4.89804	+	4.89804i	−0.746945	+	0.746945i	−0.973904	−	0.226960i	$-0.927121\pi$
$43$	−4.89804	+	4.89804i	−0.746945	+	0.746945i	0.226960	+	0.973904i	$0.427121\pi$
$44$		0			0
$45$	−1.44349	−	1.98937i	−0.215182	−	0.296557i
$46$		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
$51$	5.50055	−	4.69499i	0.770232	−	0.657430i
$52$		0			0
$53$	−6.63976	−	3.83347i	−0.912041	−	0.526567i	−0.0309539	−	0.999521i	$-0.509855\pi$
$53$	−6.63976	−	3.83347i	−0.912041	−	0.526567i	−0.881087	+	0.472954i	$0.843188\pi$
$54$		0			0
$55$	−0.298167	+	1.11277i	−0.0402048	+	0.150047i
$56$		0			0
$57$	7.59123	−	1.40453i	1.00548	−	0.186035i
$58$		0			0
$59$	1.53365	−	0.410939i	0.199664	−	0.0534997i	−0.157601	−	0.987503i	$-0.550376\pi$
$59$	1.53365	−	0.410939i	0.199664	−	0.0534997i	0.357265	+	0.934003i	$0.383709\pi$
$60$		0			0
$61$	−0.777010	+	2.89984i	−0.0994859	+	0.371287i	−0.997661	−	0.0683507i	$-0.978226\pi$
$61$	−0.777010	+	2.89984i	−0.0994859	+	0.371287i	0.898175	+	0.439637i	$0.144893\pi$
$62$		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	−0.589867	−	0.807500i	$-0.700820\pi$
$67$	−1.51826	+	0.876567i	−0.185485	+	0.107090i	0.404382	+	0.914590i	$0.367487\pi$
$68$		0			0
$69$	7.85652	+	2.78486i	0.945813	+	0.335258i
$70$		0			0
$71$	2.84275	−	1.64126i	0.337372	−	0.194782i	−0.321737	−	0.946829i	$-0.604267\pi$
$71$	2.84275	−	1.64126i	0.337372	−	0.194782i	0.659109	+	0.752047i	$0.270933\pi$
$72$		0			0
$73$			0.542470i			0.0634913i	0.999496	+	0.0317457i	$0.0101067\pi$
$73$			0.542470i			0.0634913i	−0.999496	+	0.0317457i	$0.989893\pi$
$74$		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	0.511652	−	0.859193i	$-0.329034\pi$
$79$	4.66772	+	1.25071i	0.525159	+	0.140716i	0.0135071	+	0.999909i	$0.495700\pi$
$80$		0			0
$81$	−1.86036	−	8.80563i	−0.206706	−	0.978403i
$82$		0			0
$83$	−7.59339	−	4.38405i	−0.833483	−	0.481212i	0.0215608	−	0.999768i	$-0.493136\pi$
$83$	−7.59339	−	4.38405i	−0.833483	−	0.481212i	−0.855044	+	0.518556i	$0.826470\pi$
$84$		0			0
$85$			3.42080i			0.371038i
$86$		0			0
$87$	−2.24374	+	6.32994i	−0.240554	+	0.678640i
$88$		0			0
$89$	−1.75938	−	6.56608i	−0.186494	−	0.696004i	−0.994306	−	0.106564i	$-0.966015\pi$
$89$	−1.75938	−	6.56608i	−0.186494	−	0.696004i	0.807812	−	0.589440i	$-0.200651\pi$
$90$		0			0
$91$	−0.165959	−	0.619369i	−0.0173973	−	0.0649275i
$92$		0			0
$93$	1.52191	+	0.539463i	0.157814	+	0.0559398i
$94$		0			0
$95$	−1.82588	+	3.16252i	−0.187331	+	0.324467i
$96$		0			0
$97$	7.62300	−	7.62300i	0.773998	−	0.773998i	−0.204805	−	0.978803i	$-0.565656\pi$
$97$	7.62300	−	7.62300i	0.773998	−	0.773998i	0.978803	+	0.204805i	$0.0656559\pi$
$98$		0			0
$99$	−2.65672	+	3.27664i	−0.267010	+	0.329315i
$100$		0			0
$101$	−10.6782			−1.06252			−0.531261	−	0.847208i	$-0.678282\pi$
$101$	−10.6782			−1.06252			−0.531261	+	0.847208i	$0.678282\pi$
$102$		0			0
$103$	−2.74833	−	2.74833i	−0.270801	−	0.270801i	0.558621	−	0.829423i	$-0.311330\pi$
$103$	−2.74833	−	2.74833i	−0.270801	−	0.270801i	−0.829423	+	0.558621i	$0.811330\pi$
$104$		0			0
$105$	0.322090	−	0.274919i	0.0314328	−	0.0268294i
$106$		0			0
$107$	−5.37254	+	3.10184i	−0.519383	+	0.299866i	−0.736682	−	0.676239i	$-0.763609\pi$
$107$	−5.37254	+	3.10184i	−0.519383	+	0.299866i	0.217299	+	0.976105i	$0.430275\pi$
$108$		0			0
$109$	3.46676	+	12.9381i	0.332055	+	1.23925i	0.907026	+	0.421074i	$0.138347\pi$
$109$	3.46676	+	12.9381i	0.332055	+	1.23925i	−0.574971	+	0.818174i	$0.694987\pi$
$110$		0			0
$111$	8.97344	+	5.52062i	0.851722	+	0.523995i
$112$		0			0
$113$	1.51522	+	5.65487i	0.142540	+	0.531965i	0.999853	+	0.0171696i	$0.00546551\pi$
$113$	1.51522	+	5.65487i	0.142540	+	0.531965i	−0.857313	+	0.514796i	$0.827868\pi$
$114$		0			0
$115$	−3.41462	+	1.97143i	−0.318415	+	0.183837i
$116$		0			0
$117$	5.21751	−	3.78584i	0.482359	−	0.350001i
$118$		0			0
$119$	0.881022	+	0.881022i	0.0807631	+	0.0807631i
$120$		0			0
$121$	−9.02283			−0.820257
$122$		0			0
$123$	16.8627	+	11.5971i	1.52046	+	1.04567i
$124$		0			0
$125$	5.40443	−	5.40443i	0.483387	−	0.483387i
$126$		0			0
$127$	1.72200	−	2.98260i	0.152803	−	0.264663i	−0.779454	−	0.626460i	$-0.784503\pi$
$127$	1.72200	−	2.98260i	0.152803	−	0.264663i	0.932257	+	0.361797i	$0.117837\pi$
$128$		0			0
$129$	4.00840	−	11.3083i	0.352920	−	0.995641i
$130$		0			0
$131$	0.105122	+	0.392319i	0.00918451	+	0.0342771i	0.970366	−	0.241640i	$-0.0776852\pi$
$131$	0.105122	+	0.392319i	0.00918451	+	0.0342771i	−0.961182	+	0.275917i	$0.911019\pi$
$132$		0			0
$133$	0.344249	+	1.28475i	0.0298501	+	0.111402i
$134$		0			0
$135$	3.73942	+	2.03481i	0.321838	+	0.175129i
$136$		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	0.319575	−	0.947561i	$-0.396460\pi$
$139$	−4.02327	−	2.32284i	−0.341250	−	0.197021i	−0.660825	+	0.750540i	$0.729793\pi$
$140$		0			0
$141$	8.14559	+	17.0911i	0.685982	+	1.43933i
$142$		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	0.0691465	−	0.997607i	$-0.477972\pi$
$151$	11.8910	−	6.86525i	0.967672	−	0.558686i	0.898526	+	0.438921i	$0.144639\pi$
$152$		0			0
$153$	−5.10177	+	11.4398i	−0.412454	+	0.924853i
$154$		0			0
$155$	−0.661456	+	0.381892i	−0.0531294	+	0.0306743i
$156$		0			0
$157$	−8.21847	+	14.2348i	−0.655906	+	1.13606i	0.325760	+	0.945452i	$0.394380\pi$
$157$	−8.21847	+	14.2348i	−0.655906	+	1.13606i	−0.981666	+	0.190609i	$0.938954\pi$
$158$		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	0.116689	−	0.993168i	$-0.462772\pi$
$163$	9.11995	−	2.44368i	0.714329	−	0.191404i	0.597640	+	0.801764i	$0.296105\pi$
$164$		0			0
$165$	−0.363023	−	1.96207i	−0.0282613	−	0.152747i
$166$		0			0
$167$	−5.71720	+	21.3369i	−0.442410	+	1.65110i	0.280274	+	0.959920i	$0.409575\pi$
$167$	−5.71720	+	21.3369i	−0.442410	+	1.65110i	−0.722684	+	0.691178i	$0.757092\pi$
$168$		0			0
$169$	−7.25970	−	4.19139i	−0.558438	−	0.322415i
$170$		0			0
$171$	−10.8227	+	7.85294i	−0.827629	+	0.600529i
$172$		0			0
$173$	−1.15167	+	1.99475i	−0.0875600	+	0.151658i	−0.906479	−	0.422250i	$-0.861240\pi$
$173$	−1.15167	+	1.99475i	−0.0875600	+	0.151658i	0.818919	+	0.573909i	$0.194574\pi$
$174$		0			0
$175$		−	1.29175i		−	0.0976470i
$176$		0			0
$177$	−2.09171	+	1.78538i	−0.157223	+	0.134197i
$178$		0			0
$179$	5.02745	−	5.02745i	0.375769	−	0.375769i	−0.493804	−	0.869573i	$-0.664394\pi$
$179$	5.02745	−	5.02745i	0.375769	−	0.375769i	0.869573	+	0.493804i	$0.164394\pi$
$180$		0			0
$181$	1.16321	+	2.01475i	0.0864610	+	0.149755i	0.906013	−	0.423250i	$-0.139111\pi$
$181$	1.16321	+	2.01475i	0.0864610	+	0.149755i	−0.819552	+	0.573005i	$0.805778\pi$
$182$		0			0
$183$	−0.946023	−	5.11307i	−0.0699320	−	0.377969i
$184$		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
$189$	1.48714	−	0.439018i	0.108174	−	0.0319338i
$190$		0			0
$191$	−0.422832	−	0.422832i	−0.0305950	−	0.0305950i	0.691644	−	0.722239i	$-0.256887\pi$
$191$	−0.422832	−	0.422832i	−0.0305950	−	0.0305950i	−0.722239	+	0.691644i	$0.756887\pi$
$192$		0			0
$193$	4.99064	−	4.99064i	0.359234	−	0.359234i	−0.504297	−	0.863531i	$-0.668248\pi$
$193$	4.99064	−	4.99064i	0.359234	−	0.359234i	0.863531	+	0.504297i	$0.168248\pi$
$194$		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	$-0.0493398\pi$
$197$	18.9245	+	10.9261i	1.34831	+	0.778450i	0.360303	+	0.932835i	$0.382673\pi$
$198$		0			0
$199$	−0.872803	−	0.872803i	−0.0618714	−	0.0618714i	0.675494	−	0.737365i	$-0.263930\pi$
$199$	−0.872803	−	0.872803i	−0.0618714	−	0.0618714i	−0.737365	+	0.675494i	$0.763930\pi$
$200$		0			0
$201$	1.72067	−	2.50194i	0.121367	−	0.176474i
$202$		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
$207$	−14.3593	+	1.50028i	−0.998042	+	0.104277i
$208$		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
$213$	−3.22175	+	4.68458i	−0.220750	+	0.320982i
$214$		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
$219$	−0.404241	−	0.848181i	−0.0273161	−	0.0573147i
$220$		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
$225$	12.1266	−	4.64639i	0.808439	−	0.309759i
$226$		0			0
$227$	−5.82278	+	21.7309i	−0.386472	+	1.44233i	0.449362	+	0.893350i	$0.351651\pi$
$227$	−5.82278	+	21.7309i	−0.386472	+	1.44233i	−0.835834	+	0.548983i	$0.815015\pi$
$228$		0			0
$229$	4.74287	+	8.21490i	0.313418	+	0.542856i	0.979100	−	0.203380i	$-0.0651926\pi$
$229$	4.74287	+	8.21490i	0.313418	+	0.542856i	−0.665682	+	0.746236i	$0.731859\pi$
$230$		0			0
$231$	−0.598825	−	0.411832i	−0.0393998	−	0.0270966i
$232$		0			0
$233$	16.8897			1.10648			0.553242	−	0.833021i	$-0.313390\pi$
$233$	16.8897			1.10648			0.553242	+	0.833021i	$0.313390\pi$
$234$		0			0
$235$	−8.65054	−	2.31791i	−0.564299	−	0.151204i
$236$		0			0
$237$	−8.23023	+	1.52276i	−0.534611	+	0.0989140i
$238$		0			0
$239$	10.0320	−	2.68805i	0.648913	−	0.173876i	0.0806757	−	0.996740i	$-0.474292\pi$
$239$	10.0320	−	2.68805i	0.648913	−	0.173876i	0.568237	+	0.822865i	$0.307626\pi$
$240$		0			0
$241$	0.834899	+	0.223710i	0.0537806	+	0.0144105i	0.285609	−	0.958346i	$-0.407804\pi$
$241$	0.834899	+	0.223710i	0.0537806	+	0.0144105i	−0.231828	+	0.972757i	$0.574471\pi$
$242$		0			0
$243$	9.47059	+	12.3818i	0.607539	+	0.794290i
$244$		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	$-0.555890\pi$
$251$	12.8319	−	12.8319i	0.809941	−	0.809941i	0.984625	+	0.174684i	$0.0558904\pi$
$252$		0			0
$253$	4.78495	+	4.78495i	0.300827	+	0.300827i
$254$		0			0
$255$	−2.54913	−	5.34860i	−0.159633	−	0.334943i
$256$		0			0
$257$	−19.1017	+	5.11828i	−1.19153	+	0.319270i	−0.799491	−	0.600679i	$-0.794897\pi$
$257$	−19.1017	+	5.11828i	−1.19153	+	0.319270i	−0.392040	+	0.919948i	$0.628230\pi$
$258$		0			0
$259$	−0.826408	+	1.61613i	−0.0513505	+	0.100421i
$260$		0			0
$261$	−1.20877	−	11.5692i	−0.0748207	−	0.716115i
$262$		0			0
$263$	−4.10210	−	7.10505i	−0.252946	−	0.438116i	0.711389	−	0.702798i	$-0.248066\pi$
$263$	−4.10210	−	7.10505i	−0.252946	−	0.438116i	−0.964336	+	0.264682i	$0.914733\pi$
$264$		0			0
$265$	−4.44169	+	4.44169i	−0.272851	+	0.272851i
$266$		0			0
$267$	7.64383	+	8.95536i	0.467795	+	0.548059i
$268$		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	−0.911347	−	0.411639i	$-0.864956\pi$
$271$	−1.63277	+	2.82804i	−0.0991836	+	0.171791i	0.812163	+	0.583430i	$0.198290\pi$
$272$		0			0
$273$	0.721031	+	0.844746i	0.0436388	+	0.0511264i
$274$		0			0
$275$	−5.27127	−	3.04337i	−0.317869	−	0.183522i
$276$		0			0
$277$	−1.51976	+	5.67181i	−0.0913134	+	0.340786i	−0.996435	−	0.0843671i	$-0.973113\pi$
$277$	−1.51976	+	5.67181i	−0.0913134	+	0.340786i	0.905121	+	0.425153i	$0.139780\pi$
$278$		0			0
$279$	−2.78158	+	0.290624i	−0.166529	+	0.0173992i
$280$		0			0
$281$	3.39223	−	0.908944i	0.202363	−	0.0542231i	−0.156214	−	0.987723i	$-0.549929\pi$
$281$	3.39223	−	0.908944i	0.202363	−	0.0542231i	0.358577	+	0.933500i	$0.383262\pi$
$282$		0			0
$283$	6.29626	−	23.4980i	0.374274	−	1.39681i	−0.480130	−	0.877198i	$-0.659410\pi$
$283$	6.29626	−	23.4980i	0.374274	−	1.39681i	0.854403	−	0.519611i	$-0.173923\pi$
$284$		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
$291$	−6.23842	+	17.5995i	−0.365702	+	1.03170i
$292$		0			0
$293$	7.86659	−	4.54178i	0.459571	−	0.265334i	−0.252293	−	0.967651i	$-0.581185\pi$
$293$	7.86659	−	4.54178i	0.459571	−	0.265334i	0.711864	+	0.702317i	$0.247851\pi$
$294$		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
$303$	16.6960	−	7.95725i	0.959158	−	0.457132i
$304$		0			0
$305$	2.13011	+	1.22982i	0.121970	+	0.0704194i
$306$		0			0
$307$		−	26.7723i		−	1.52797i	−0.645232	−	0.763987i	$-0.723239\pi$
$307$		−	26.7723i		−	1.52797i	0.645232	−	0.763987i	$-0.276761\pi$
$308$		0			0
$309$	6.34519	+	2.24915i	0.360965	+	0.127950i
$310$		0			0
$311$	−7.60714	−	28.3902i	−0.431361	−	1.60986i	−0.749627	−	0.661861i	$-0.769767\pi$
$311$	−7.60714	−	28.3902i	−0.431361	−	1.60986i	0.318265	−	0.948002i	$-0.396900\pi$
$312$		0			0
$313$	−1.97533	−	7.37201i	−0.111652	−	0.416691i	0.887363	−	0.461072i	$-0.152535\pi$
$313$	−1.97533	−	7.37201i	−0.111652	−	0.416691i	−0.999015	+	0.0443812i	$0.985868\pi$
$314$		0			0
$315$	−0.298739	+	0.669868i	−0.0168320	+	0.0377428i
$316$		0			0
$317$	−15.8478	+	27.4492i	−0.890103	+	1.54170i	−0.0503515	+	0.998732i	$0.516034\pi$
$317$	−15.8478	+	27.4492i	−0.890103	+	1.54170i	−0.839751	+	0.542971i	$0.817299\pi$
$318$		0			0
$319$	−3.85520	+	3.85520i	−0.215850	+	0.215850i
$320$		0			0
$321$	6.08881	−	8.85343i	0.339844	−	0.494150i
$322$		0			0
$323$	18.6100			1.03549
$324$		0			0
$325$	6.57715	+	6.57715i	0.364835	+	0.364835i
$326$		0			0
$327$	−15.0618	−	17.6461i	−0.832917	−	0.975829i
$328$		0			0
$329$	−2.82491	+	1.63096i	−0.155742	+	0.0899178i
$330$		0			0
$331$	−2.66274	−	9.93749i	−0.146358	−	0.546214i	−0.999691	−	0.0248487i	$-0.992090\pi$
$331$	−2.66274	−	9.93749i	−0.146358	−	0.546214i	0.853334	−	0.521365i	$-0.174577\pi$
$332$		0			0
$333$	−18.1443	−	1.94491i	−0.994304	−	0.106580i
$334$		0			0
$335$	0.371752	+	1.38740i	0.0203110	+	0.0758016i
$336$		0			0
$337$	12.1148	−	6.99446i	0.659933	−	0.381013i	−0.132318	−	0.991207i	$-0.542242\pi$
$337$	12.1148	−	6.99446i	0.659933	−	0.381013i	0.792251	+	0.610195i	$0.208909\pi$
$338$		0			0
$339$	−6.58305	−	7.71257i	−0.357542	−	0.418889i
$340$		0			0
$341$	0.926905	+	0.926905i	0.0501947	+	0.0501947i
$342$		0			0
$343$	−4.15119			−0.224143
$344$		0			0
$345$	3.86986	−	5.62697i	0.208346	−	0.302946i
$346$		0			0
$347$	−11.0258	+	11.0258i	−0.591895	+	0.591895i	−0.938143	−	0.346248i	$-0.887456\pi$
$347$	−11.0258	+	11.0258i	−0.591895	+	0.591895i	0.346248	+	0.938143i	$0.387456\pi$
$348$		0			0
$349$	−17.1968	+	29.7857i	−0.920522	+	1.59439i	−0.121913	+	0.992541i	$0.538903\pi$
$349$	−17.1968	+	29.7857i	−0.920522	+	1.59439i	−0.798609	+	0.601850i	$0.794431\pi$
$350$		0			0
$351$	−5.33671	+	9.80737i	−0.284852	+	0.523479i
$352$		0			0
$353$	−4.29977	−	16.0470i	−0.228854	−	0.854093i	−0.980824	−	0.194896i	$-0.937563\pi$
$353$	−4.29977	−	16.0470i	−0.228854	−	0.854093i	0.751970	−	0.659197i	$-0.229104\pi$
$354$		0			0
$355$	−0.696059	−	2.59773i	−0.0369430	−	0.137873i
$356$		0			0
$357$	−2.03405	−	0.721000i	−0.107653	−	0.0381593i
$358$		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
$363$	14.1077	−	6.72368i	0.740461	−	0.352902i
$364$		0			0
$365$	0.429300	+	0.115031i	0.0224706	+	0.00602098i
$366$		0			0
$367$	15.7524	+	27.2839i	0.822267	+	1.42421i	0.903990	+	0.427554i	$0.140625\pi$
$367$	15.7524	+	27.2839i	0.822267	+	1.42421i	−0.0817226	+	0.996655i	$0.526042\pi$
$368$		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	−0.974590	−	0.223997i	$-0.928089\pi$
$373$	−24.4872	+	14.1377i	−1.26790	+	0.732021i	−0.293308	+	0.956018i	$0.594756\pi$
$374$		0			0
$375$	−4.42281	+	12.4774i	−0.228393	+	0.644331i
$376$		0			0
$377$	7.21540	−	4.16581i	0.371612	−	0.214550i
$378$		0			0
$379$	16.7954	−	29.0905i	0.862721	−	1.49428i	−0.00657182	−	0.999978i	$-0.502092\pi$
$379$	16.7954	−	29.0905i	0.862721	−	1.49428i	0.869293	−	0.494298i	$-0.164575\pi$
$380$		0			0
$381$	−0.469856	+	5.94667i	−0.0240714	+	0.304657i
$382$		0			0
$383$	−5.84657	+	21.8197i	−0.298746	+	1.11493i	0.639451	+	0.768832i	$0.279162\pi$
$383$	−5.84657	+	21.8197i	−0.298746	+	1.11493i	−0.938197	+	0.346103i	$0.887505\pi$
$384$		0			0
$385$	0.332065	−	0.0889765i	0.0169236	−	0.00453466i
$386$		0			0
$387$	2.15944	+	20.6681i	0.109770	+	1.05062i
$388$		0			0
$389$	−2.21911	+	8.28182i	−0.112513	+	0.419905i	−0.999089	−	0.0426787i	$-0.986411\pi$
$389$	−2.21911	+	8.28182i	−0.112513	+	0.419905i	0.886576	+	0.462584i	$0.153077\pi$
$390$		0			0
$391$	17.4015	+	10.0468i	0.880032	+	0.508087i
$392$		0			0
$393$	−0.456713	−	0.535076i	−0.0230381	−	0.0269910i
$394$		0			0
$395$	1.97958	−	3.42873i	0.0996033	−	0.172518i
$396$		0			0
$397$			21.3332i			1.07068i	0.844636	+	0.535342i	$0.179817\pi$
$397$			21.3332i			1.07068i	−0.844636	+	0.535342i	$0.820183\pi$
$398$		0			0
$399$	−1.49563	−	1.75225i	−0.0748752	−	0.0877223i
$400$		0			0
$401$	27.1195	−	27.1195i	1.35428	−	1.35428i	0.473480	−	0.880804i	$-0.342997\pi$
$401$	27.1195	−	27.1195i	1.35428	−	1.35428i	0.880804	−	0.473480i	$-0.157003\pi$
$402$		0			0
$403$	−1.00159	−	1.73480i	−0.0498926	−	0.0864166i
$404$		0			0
$405$	−7.36309	−	0.394981i	−0.365875	−	0.0196268i
$406$		0			0
$407$	4.64796	+	7.17995i	0.230391	+	0.355897i
$408$		0			0
$409$	9.39205	−	2.51659i	0.464407	−	0.124437i	−0.0190257	−	0.999819i	$-0.506056\pi$
$409$	9.39205	−	2.51659i	0.464407	−	0.124437i	0.483433	+	0.875382i	$0.339390\pi$
$410$		0			0
$411$	−10.3156	−	21.6444i	−0.508833	−	1.06764i
$412$		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	$-0.222794\pi$
$419$	12.0661	+	6.96639i	0.589469	+	0.340330i	−0.175418	+	0.984494i	$0.556128\pi$
$420$		0			0
$421$	−24.6291	−	24.6291i	−1.20035	−	1.20035i	−0.974060	−	0.226291i	$-0.927340\pi$
$421$	−24.6291	−	24.6291i	−1.20035	−	1.20035i	−0.226291	−	0.974060i	$-0.572660\pi$
$422$		0			0
$423$	−25.4721	−	20.6529i	−1.23850	−	1.00418i
$424$		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
$429$	5.14593	−	0.952102i	0.248448	−	0.0459679i
$430$		0			0
$431$	28.8429	+	7.72842i	1.38931	+	0.372265i	0.874495	−	0.485035i	$-0.161193\pi$
$431$	28.8429	+	7.72842i	1.38931	+	0.372265i	0.514817	+	0.857300i	$0.327860\pi$
$432$		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
$435$	4.53360	+	3.11792i	0.217370	+	0.149493i
$436$		0			0
$437$	10.7251	+	18.5764i	0.513050	+	0.888630i
$438$		0			0
$439$	−0.284234	+	1.06078i	−0.0135658	+	0.0506281i	−0.972377	−	0.233416i	$-0.925010\pi$
$439$	−0.284234	+	1.06078i	−0.0135658	+	0.0506281i	0.958811	+	0.284044i	$0.0916762\pi$
$440$		0			0
$441$	−7.41806	−	19.3604i	−0.353241	−	0.921922i
$442$		0			0
$443$	−27.6138			−1.31197			−0.655985	−	0.754774i	$-0.727747\pi$
$443$	−27.6138			−1.31197			−0.655985	+	0.754774i	$0.727747\pi$
$444$		0			0
$445$	−5.56935			−0.264012
$446$		0			0
$447$	−4.08349	−	8.56800i	−0.193142	−	0.405252i
$448$		0			0
$449$	−7.02491	+	26.2173i	−0.331526	+	1.23727i	0.576061	+	0.817407i	$0.304589\pi$
$449$	−7.02491	+	26.2173i	−0.331526	+	1.23727i	−0.907587	+	0.419865i	$0.862078\pi$
$450$		0			0
$451$	8.30726	+	14.3886i	0.391173	+	0.677532i
$452$		0			0
$453$	−13.4763	+	19.5951i	−0.633170	+	0.920660i
$454$		0			0
$455$	−0.525348			−0.0246287
$456$		0			0
$457$	13.4969	+	3.61649i	0.631359	+	0.169172i	0.560286	−	0.828299i	$-0.310691\pi$
$457$	13.4969	+	3.61649i	0.631359	+	0.169172i	0.0710728	+	0.997471i	$0.477358\pi$
$458$		0			0
$459$	−0.547877	−	21.6885i	−0.0255727	−	1.01233i
$460$		0			0
$461$	7.45297	−	1.99702i	0.347120	−	0.0930104i	−0.0810469	−	0.996710i	$-0.525826\pi$
$461$	7.45297	−	1.99702i	0.347120	−	0.0930104i	0.428166	+	0.903700i	$0.359160\pi$
$462$		0			0
$463$	3.20406	+	0.858525i	0.148905	+	0.0398990i	0.332502	−	0.943103i	$-0.392107\pi$
$463$	3.20406	+	0.858525i	0.148905	+	0.0398990i	−0.183596	+	0.983002i	$0.558774\pi$
$464$		0			0
$465$	0.749641	−	1.09002i	0.0347638	−	0.0505482i
$466$		0			0
$467$	−6.52807	−	6.52807i	−0.302083	−	0.302083i	0.539745	−	0.841828i	$-0.318521\pi$
$467$	−6.52807	−	6.52807i	−0.302083	−	0.302083i	−0.841828	+	0.539745i	$0.818521\pi$
$468$		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
$477$	−21.4782	+	8.22952i	−0.983418	+	0.376804i
$478$		0			0
$479$	−15.0944	+	4.04453i	−0.689680	+	0.184799i	−0.586604	−	0.809874i	$-0.699535\pi$
$479$	−15.0944	+	4.04453i	−0.689680	+	0.184799i	−0.103077	+	0.994673i	$0.532869\pi$
$480$		0			0
$481$	−4.02100	−	12.4366i	−0.183342	−	0.567060i
$482$		0			0
$483$	−0.452540	−	2.44589i	−0.0205913	−	0.111292i
$484$		0			0
$485$	−4.41624	−	7.64915i	−0.200531	−	0.347330i
$486$		0			0
$487$	8.22774	−	8.22774i	0.372834	−	0.372834i	−0.495674	−	0.868509i	$-0.665079\pi$
$487$	8.22774	−	8.22774i	0.372834	−	0.372834i	0.868509	+	0.495674i	$0.165079\pi$
$488$		0			0
$489$	−12.4385	+	10.6169i	−0.562490	+	0.480112i
$490$		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
$495$	2.02971	+	2.79728i	0.0912289	+	0.125729i
$496$		0			0
$497$	−0.848309	−	0.489771i	−0.0380519	−	0.0219693i
$498$		0			0
$499$	6.32351	−	23.5997i	0.283079	−	1.05647i	−0.667152	−	0.744921i	$-0.732487\pi$
$499$	6.32351	−	23.5997i	0.283079	−	1.05647i	0.950232	−	0.311545i	$-0.100846\pi$
$500$		0			0
$501$	−6.96079	−	37.6217i	−0.310985	−	1.68082i
$502$		0			0
$503$	37.5229	−	10.0542i	1.67307	−	0.448297i	0.707131	−	0.707083i	$-0.249989\pi$
$503$	37.5229	−	10.0542i	1.67307	−	0.448297i	0.965935	+	0.258786i	$0.0833225\pi$
$504$		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	$-0.725612\pi$
$509$	7.49010	−	12.9732i	0.331993	−	0.575029i	0.982903	+	0.184127i	$0.0589456\pi$
$510$		0			0
$511$	0.140192	−	0.0809396i	0.00620171	−	0.00358056i
$512$		0			0
$513$	11.0699	−	20.3434i	0.488748	−	0.898182i
$514$		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	$-0.198429\pi$
$521$	−2.27386	−	3.93844i	−0.0996197	−	0.172546i	−0.911527	+	0.411240i	$0.865096\pi$
$522$		0			0
$523$	14.4021	+	3.85902i	0.629759	+	0.168743i	0.559560	−	0.828790i	$-0.310970\pi$
$523$	14.4021	+	3.85902i	0.629759	+	0.168743i	0.0701985	+	0.997533i	$0.477637\pi$
$524$		0			0
$525$	0.962593	+	2.01972i	0.0420110	+	0.0881477i
$526$		0			0
$527$	3.37090	+	1.94619i	0.146839	+	0.0847773i
$528$		0			0
$529$			0.160103i			0.00696099i
$530$		0			0
$531$	1.94006	−	4.35024i	0.0841916	−	0.188784i
$532$		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
$537$	−4.11430	+	11.6071i	−0.177545	+	0.500882i
$538$		0			0
$539$	−4.85881	+	8.41570i	−0.209284	+	0.362490i
$540$		0			0
$541$	−13.1303	+	13.1303i	−0.564516	+	0.564516i	−0.930587	−	0.366071i	$-0.880703\pi$
$541$	−13.1303	+	13.1303i	−0.564516	+	0.564516i	0.366071	+	0.930587i	$0.380703\pi$
$542$		0			0
$543$	−3.32011	−	2.28335i	−0.142479	−	0.0979880i
$544$		0			0
$545$	10.9741			0.470079
$546$		0			0
$547$	16.2813	+	16.2813i	0.696137	+	0.696137i	0.963575	−	0.267438i	$-0.0861771\pi$
$547$	16.2813	+	16.2813i	0.696137	+	0.696137i	−0.267438	+	0.963575i	$0.586177\pi$
$548$		0			0
$549$	5.28934	+	7.28960i	0.225744	+	0.311112i
$550$		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
$555$	6.27173	−	5.93076i	0.266220	−	0.251747i
$556$		0			0
$557$	3.62511	+	13.5291i	0.153601	+	0.573247i	0.999221	+	0.0394614i	$0.0125642\pi$
$557$	3.62511	+	13.5291i	0.153601	+	0.573247i	−0.845620	+	0.533785i	$0.820769\pi$
$558$		0			0
$559$	−12.8902	+	7.44214i	−0.545196	+	0.314769i
$560$		0			0
$561$	−7.73443	+	6.60171i	−0.326548	+	0.278724i
$562$		0			0
$563$	−20.4328	−	20.4328i	−0.861139	−	0.861139i	0.130331	−	0.991471i	$-0.458396\pi$
$563$	−20.4328	−	20.4328i	−0.861139	−	0.861139i	−0.991471	+	0.130331i	$0.958396\pi$
$564$		0			0
$565$	4.79645			0.201788
$566$		0			0
$567$	−1.99808	+	1.79463i	−0.0839114	+	0.0753672i
$568$		0			0
$569$	−8.73461	+	8.73461i	−0.366174	+	0.366174i	−0.866080	−	0.499906i	$-0.833368\pi$
$569$	−8.73461	+	8.73461i	−0.366174	+	0.366174i	0.499906	+	0.866080i	$0.333368\pi$
$570$		0			0
$571$	19.8386	−	34.3615i	0.830220	−	1.43798i	−0.0676438	−	0.997710i	$-0.521548\pi$
$571$	19.8386	−	34.3615i	0.830220	−	1.43798i	0.897864	−	0.440274i	$-0.145119\pi$
$572$		0			0
$573$	0.976208	+	0.346032i	0.0407817	+	0.0144557i
$574$		0			0
$575$	−5.39174	−	20.1223i	−0.224851	−	0.839156i
$576$		0			0
$577$	−5.97998	−	22.3176i	−0.248950	−	0.929093i	−0.971357	−	0.237625i	$-0.923631\pi$
$577$	−5.97998	−	22.3176i	−0.248950	−	0.929093i	0.722407	−	0.691468i	$-0.243036\pi$
$578$		0			0
$579$	−4.08418	+	11.5221i	−0.169733	+	0.478841i
$580$		0			0
$581$			2.61650i			0.108551i
$582$		0			0
$583$	9.33629	+	5.39031i	0.386670	+	0.223244i
$584$		0			0
$585$	−1.88966	−	4.93182i	−0.0781280	−	0.203906i
$586$		0			0
$587$	42.6232	+	11.4209i	1.75925	+	0.471389i	0.986560	−	0.163397i	$-0.0522452\pi$
$587$	42.6232	+	11.4209i	1.75925	+	0.471389i	0.772688	+	0.634786i	$0.218912\pi$
$588$		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
$597$	2.01508	+	0.714274i	0.0824715	+	0.0292333i
$598$		0			0
$599$	−10.8724	+	6.27716i	−0.444232	+	0.256478i	−0.705391	−	0.708818i	$-0.749229\pi$
$599$	−10.8724	+	6.27716i	−0.444232	+	0.256478i	0.261159	+	0.965296i	$0.415895\pi$
$600$		0			0
$601$	−8.80478	+	15.2503i	−0.359155	+	0.622074i	−0.987820	−	0.155602i	$-0.950268\pi$
$601$	−8.80478	+	15.2503i	−0.359155	+	0.622074i	0.628665	+	0.777676i	$0.283602\pi$
$602$		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	−0.927696	−	0.373336i	$-0.878214\pi$
$607$	−38.0509	+	10.1957i	−1.54444	+	0.413831i	−0.616741	+	0.787166i	$0.711547\pi$
$608$		0			0
$609$	1.97064	−	0.364608i	0.0798542	−	0.0147747i
$610$		0			0
$611$	6.07917	−	22.6878i	0.245937	−	0.917850i
$612$		0			0
$613$	−11.4577	−	6.61513i	−0.462774	−	0.267183i	0.250436	−	0.968133i	$-0.419426\pi$
$613$	−11.4577	−	6.61513i	−0.462774	−	0.267183i	−0.713210	+	0.700951i	$0.752759\pi$
$614$		0			0
$615$	12.7535	−	10.8857i	0.514269	−	0.438953i
$616$		0			0
$617$	−14.4682	+	25.0597i	−0.582468	+	1.00886i	0.412717	+	0.910859i	$0.364580\pi$
$617$	−14.4682	+	25.0597i	−0.582468	+	1.00886i	−0.995186	+	0.0980057i	$0.968754\pi$
$618$		0			0
$619$		−	23.9466i		−	0.962496i	−0.876585	−	0.481248i	$-0.840184\pi$
$619$		−	23.9466i		−	0.962496i	0.876585	−	0.481248i	$-0.159816\pi$
$620$		0			0
$621$	21.3336	−	13.0461i	0.856087	−	0.523523i
$622$		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
$627$	−10.6742	+	1.97494i	−0.426285	+	0.0788715i
$628$		0			0
$629$	18.8492	+	17.0214i	0.751568	+	0.678687i
$630$		0			0
$631$	−19.0966	+	5.11693i	−0.760225	+	0.203702i	−0.618049	−	0.786140i	$-0.712077\pi$
$631$	−19.0966	+	5.11693i	−0.760225	+	0.203702i	−0.142176	+	0.989841i	$0.545410\pi$
$632$		0			0
$633$	−6.52688	+	3.11070i	−0.259420	+	0.123639i
$634$		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	$-0.288338\pi$
$641$	6.17813	+	3.56695i	0.244022	+	0.140886i	−0.373002	+	0.927830i	$0.621672\pi$
$642$		0			0
$643$	16.5674	+	16.5674i	0.653354	+	0.653354i	0.953799	−	0.300445i	$-0.0971352\pi$
$643$	16.5674	+	16.5674i	0.653354	+	0.653354i	−0.300445	+	0.953799i	$0.597135\pi$
$644$		0			0
$645$	−8.09919	−	5.57009i	−0.318905	−	0.219322i
$646$		0			0
$647$	13.6620	+	3.66072i	0.537108	+	0.143918i	0.517169	−	0.855883i	$-0.326986\pi$
$647$	13.6620	+	3.66072i	0.537108	+	0.143918i	0.0199395	+	0.999801i	$0.493653\pi$
$648$		0			0
$649$	−2.15649	+	0.577829i	−0.0846495	+	0.0226818i
$650$		0			0
$651$	−0.0876628	−	0.473800i	−0.00343577	−	0.0185697i
$652$		0			0
$653$	26.2947	+	7.04565i	1.02899	+	0.275717i	0.733544	−	0.679642i	$-0.237865\pi$
$653$	26.2947	+	7.04565i	1.02899	+	0.275717i	0.295447	+	0.955359i	$0.404531\pi$
$654$		0			0
$655$	0.332764			0.0130022
$656$		0			0
$657$	1.26410	+	1.02494i	0.0493174	+	0.0399868i
$658$		0			0
$659$	24.4337	+	42.3204i	0.951802	+	1.64857i	0.741523	+	0.670927i	$0.234104\pi$
$659$	24.4337	+	42.3204i	0.951802	+	1.64857i	0.210278	+	0.977642i	$0.432563\pi$
$660$		0			0
$661$	7.04581	−	26.2953i	0.274050	−	1.02277i	−0.682425	−	0.730956i	$-0.739075\pi$
$661$	7.04581	−	26.2953i	0.274050	−	1.02277i	0.956475	−	0.291814i	$-0.0942587\pi$
$662$		0			0
$663$	14.0278	−	6.68561i	0.544794	−	0.259647i
$664$		0			0
$665$	1.08973			0.0422578
$666$		0			0
$667$	−18.6599			−0.722515
$668$		0			0
$669$	−12.9883	+	6.19018i	−0.502156	+	0.239326i
$670$		0			0
$671$	1.09257	−	4.07752i	0.0421781	−	0.157411i
$672$		0			0
$673$	−19.3772	−	33.5623i	−0.746936	−	1.29373i	−0.949285	−	0.314418i	$-0.898191\pi$
$673$	−19.3772	−	33.5623i	−0.746936	−	1.29373i	0.202349	−	0.979314i	$-0.435143\pi$
$674$		0			0
$675$	−15.4981	+	16.3014i	−0.596523	+	0.627442i
$676$		0			0
$677$	−20.2088			−0.776688			−0.388344	−	0.921515i	$-0.626953\pi$
$677$	−20.2088			−0.776688			−0.388344	+	0.921515i	$0.626953\pi$
$678$		0			0
$679$	−3.10742	−	0.832631i	−0.119252	−	0.0319534i
$680$		0			0
$681$	−7.08934	−	38.3165i	−0.271664	−	1.46829i
$682$		0			0
$683$	21.4254	−	5.74093i	0.819821	−	0.219670i	0.175553	−	0.984470i	$-0.443829\pi$
$683$	21.4254	−	5.74093i	0.819821	−	0.219670i	0.644268	+	0.764799i	$0.277162\pi$
$684$		0			0
$685$	10.9551	+	2.93542i	0.418574	+	0.112157i
$686$		0			0
$687$	−13.5374	−	9.31011i	−0.516482	−	0.355203i
$688$		0			0
$689$	−11.6492	−	11.6492i	−0.443800	−	0.443800i
$690$		0			0
$691$	−9.14650	−	5.28074i	−0.347949	−	0.200889i	0.315832	−	0.948815i	$-0.397716\pi$
$691$	−9.14650	−	5.28074i	−0.347949	−	0.200889i	−0.663782	+	0.747926i	$0.731050\pi$
$692$		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
$699$	−26.4080	+	12.5860i	−0.998843	+	0.476046i
$700$		0			0
$701$	31.0480	−	8.31929i	1.17267	−	0.314215i	0.380653	−	0.924718i	$-0.375699\pi$
$701$	31.0480	−	8.31929i	1.17267	−	0.314215i	0.792014	+	0.610503i	$0.209032\pi$
$702$		0			0
$703$	8.34074	+	25.7971i	0.314577	+	0.972957i
$704$		0			0
$705$	15.2529	−	2.82209i	0.574456	−	0.106286i
$706$		0			0
$707$	1.59325	+	2.75959i	0.0599204	+	0.103785i
$708$		0			0
$709$	18.6822	−	18.6822i	0.701626	−	0.701626i	−0.263133	−	0.964760i	$-0.584756\pi$
$709$	18.6822	−	18.6822i	0.701626	−	0.701626i	0.964760	+	0.263133i	$0.0847558\pi$
$710$		0			0
$711$	11.7337	−	8.51397i	0.440047	−	0.319299i
$712$		0			0
$713$			4.48641i			0.168017i
$714$		0			0
$715$	−1.23772	+	2.14380i	−0.0462883	+	0.0801736i
$716$		0			0
$717$	−13.6824	+	11.6786i	−0.510978	+	0.436145i
$718$		0			0
$719$	6.20481	+	3.58235i	0.231400	+	0.133599i	0.611218	−	0.791462i	$-0.290680\pi$
$719$	6.20481	+	3.58235i	0.231400	+	0.133599i	−0.379818	+	0.925061i	$0.624013\pi$
$720$		0			0
$721$	−0.300190	+	1.12032i	−0.0111797	+	0.0417231i
$722$		0			0
$723$	−1.47211	+	0.272371i	−0.0547485	+	0.0101296i
$724$		0			0
$725$	16.2124	−	4.34409i	0.602112	−	0.161335i
$726$		0			0
$727$	−3.31953	+	12.3887i	−0.123115	+	0.459470i	−0.999765	−	0.0216571i	$-0.993106\pi$
$727$	−3.31953	+	12.3887i	−0.123115	+	0.459470i	0.876651	+	0.481127i	$0.159772\pi$
$728$		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	−0.398398	−	0.917213i	$-0.630434\pi$
$733$	5.32634	−	3.07517i	0.196733	−	0.113584i	0.595131	+	0.803629i	$0.297100\pi$
$734$		0			0
$735$	9.24356	+	3.27652i	0.340954	+	0.120856i
$736$		0			0
$737$	2.13485	−	1.23256i	0.0786383	−	0.0454018i
$738$		0			0
$739$			21.5878i			0.794122i	0.917792	+	0.397061i	$0.129970\pi$
$739$			21.5878i			0.794122i	−0.917792	+	0.397061i	$0.870030\pi$
$740$		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	$-0.157189\pi$
$743$	0.811485	+	1.40553i	0.0297705	+	0.0515640i	−0.850756	+	0.525560i	$0.823856\pi$
$744$		0			0
$745$	4.33663	+	1.16200i	0.158882	+	0.0425722i
$746$		0			0
$747$	−24.5630	+	9.41148i	−0.898712	+	0.344348i
$748$		0			0
$749$	1.60323	+	0.925624i	0.0585807	+	0.0338216i
$750$		0			0
$751$			32.7253i			1.19416i	0.802180	+	0.597082i	$0.203673\pi$
$751$			32.7253i			1.19416i	−0.802180	+	0.597082i	$0.796327\pi$
$752$		0			0
$753$	−10.5012	+	29.6254i	−0.382685	+	1.07961i
$754$		0			0
$755$	−2.91155	−	10.8660i	−0.105962	−	0.395456i
$756$		0			0
$757$	−10.9136	−	40.7301i	−0.396662	−	1.48036i	−0.818932	−	0.573891i	$-0.805433\pi$
$757$	−10.9136	−	40.7301i	−0.396662	−	1.48036i	0.422270	−	0.906470i	$-0.361233\pi$
$758$		0			0
$759$	−11.0472	−	3.91585i	−0.400988	−	0.142136i
$760$		0			0
$761$	−21.3210	+	36.9291i	−0.772887	+	1.33868i	0.163088	+	0.986612i	$0.447855\pi$
$761$	−21.3210	+	36.9291i	−0.772887	+	1.33868i	−0.935975	+	0.352068i	$0.885479\pi$
$762$		0			0
$763$	2.82636	−	2.82636i	0.102321	−	0.102321i
$764$		0			0
$765$	7.97140	+	6.46325i	0.288207	+	0.233679i
$766$		0			0
$767$	3.41170			0.123190
$768$		0			0
$769$	−21.7401	−	21.7401i	−0.783970	−	0.783970i	0.196529	−	0.980498i	$-0.437033\pi$
$769$	−21.7401	−	21.7401i	−0.783970	−	0.783970i	−0.980498	+	0.196529i	$0.937033\pi$
$770$		0			0
$771$	26.0524	−	22.2370i	0.938255	−	0.800846i
$772$		0			0
$773$	−24.2155	+	13.9808i	−0.870972	+	0.502856i	−0.867671	−	0.497138i	$-0.834384\pi$
$773$	−24.2155	+	13.9808i	−0.870972	+	0.502856i	−0.00330113	+	0.999995i	$0.501051\pi$
$774$		0			0
$775$	−1.04445	−	3.89794i	−0.0375177	−	0.140018i
$776$		0			0
$777$	0.0878162	−	3.14273i	0.00315039	−	0.112745i
$778$		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
$783$	10.5112	+	17.1883i	0.375638	+	0.614260i
$784$		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
$789$	11.7084	+	8.05229i	0.416831	+	0.286669i
$790$		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
$795$	3.63494	−	10.2547i	0.128918	−	0.363697i
$796$		0			0
$797$	−2.53843	−	9.47356i	−0.0899159	−	0.335571i	0.906284	−	0.422670i	$-0.138907\pi$
$797$	−2.53843	−	9.47356i	−0.0899159	−	0.335571i	−0.996200	+	0.0870990i	$0.972240\pi$
$798$		0			0
$799$	11.8125	+	44.0847i	0.417895	+	1.55960i
$800$		0			0
$801$	−18.6249	−	8.30611i	−0.658080	−	0.293482i
$802$		0			0
$803$		−	0.762777i		−	0.0269178i
$804$		0			0
$805$	1.01896	+	0.588298i	0.0359137	+	0.0207348i
$806$		0			0
$807$	19.0663	+	40.0051i	0.671167	+	1.40825i
$808$		0			0
$809$	47.0890	+	12.6175i	1.65556	+	0.443607i	0.961163	−	0.275983i	$-0.0890032\pi$
$809$	47.0890	+	12.6175i	1.65556	+	0.443607i	0.694400	+	0.719589i	$0.255670\pi$
$810$		0			0
$811$	−11.9267	−	20.6576i	−0.418803	−	0.725387i	0.577017	−	0.816732i	$-0.304217\pi$
$811$	−11.9267	−	20.6576i	−0.418803	−	0.725387i	−0.995819	+	0.0913450i	$0.970883\pi$
$812$		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
$819$	−1.75686	−	0.783503i	−0.0613898	−	0.0273778i
$820$		0			0
$821$	9.44861	−	5.45516i	0.329759	−	0.190386i	−0.325975	−	0.945378i	$-0.605693\pi$
$821$	9.44861	−	5.45516i	0.329759	−	0.190386i	0.655734	+	0.754992i	$0.272359\pi$
$822$		0			0
$823$	19.5227	−	33.8144i	0.680520	−	1.17869i	−0.294303	−	0.955712i	$-0.595087\pi$
$823$	19.5227	−	33.8144i	0.680520	−	1.17869i	0.974822	−	0.222983i	$-0.0715793\pi$
$824$		0			0
$825$	10.5098	+	0.830395i	0.365904	+	0.0289107i
$826$		0			0
$827$	−13.4961	+	50.3680i	−0.469304	+	1.75147i	0.172908	+	0.984938i	$0.444684\pi$
$827$	−13.4961	+	50.3680i	−0.469304	+	1.75147i	−0.642212	+	0.766527i	$0.721983\pi$
$828$		0			0
$829$	35.3785	−	9.47963i	1.22874	−	0.329241i	0.414654	−	0.909979i	$-0.363903\pi$
$829$	35.3785	−	9.47963i	1.22874	−	0.329241i	0.814091	+	0.580738i	$0.197236\pi$
$830$		0			0
$831$	−1.85033	−	10.0007i	−0.0641873	−	0.346920i
$832$		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
$837$	4.13259	−	2.52720i	0.142843	−	0.0873529i
$838$		0			0
$839$	−18.0726	+	31.3027i	−0.623936	+	1.08069i	0.364809	+	0.931082i	$0.381134\pi$
$839$	−18.0726	+	31.3027i	−0.623936	+	1.08069i	−0.988745	+	0.149607i	$0.952199\pi$
$840$		0			0
$841$			13.9658i			0.481581i
$842$		0			0
$843$	−4.62659	+	3.94902i	−0.159348	+	0.136012i
$844$		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
$849$	7.66580	+	41.4322i	0.263090	+	1.42195i
$850$		0			0
$851$	−6.12769	+	28.6247i	−0.210055	+	0.981243i
$852$		0			0
$853$	18.7517	−	5.02449i	0.642044	−	0.172035i	0.0769151	−	0.997038i	$-0.475493\pi$
$853$	18.7517	−	5.02449i	0.642044	−	0.172035i	0.565129	+	0.825002i	$0.308826\pi$
$854$		0			0
$855$	3.91972	+	10.2301i	0.134052	+	0.349860i
$856$		0			0
$857$	−3.80945	−	3.80945i	−0.130128	−	0.130128i	0.639043	−	0.769171i	$-0.279331\pi$
$857$	−3.80945	−	3.80945i	−0.130128	−	0.130128i	−0.769171	+	0.639043i	$0.779331\pi$
$858$		0			0
$859$	14.3197	−	14.3197i	0.488582	−	0.488582i	−0.419276	−	0.907859i	$-0.637716\pi$
$859$	14.3197	−	14.3197i	0.488582	−	0.488582i	0.907859	+	0.419276i	$0.137716\pi$
$860$		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	$-0.0768147\pi$
$863$	36.7084	+	21.1936i	1.24957	+	0.721438i	0.278544	+	0.960423i	$0.410148\pi$
$864$		0			0
$865$	1.33440	+	1.33440i	0.0453709	+	0.0453709i
$866$		0			0
$867$	−0.424988	+	0.617953i	−0.0144333	+	0.0209868i
$868$		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
$873$	−3.36081	−	32.1666i	−0.113746	−	1.08867i
$874$		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
$879$	−8.91537	+	12.9634i	−0.300708	+	0.437244i
$880$		0			0
$881$	21.9509	+	38.0200i	0.739543	+	1.28093i	0.952701	+	0.303909i	$0.0982918\pi$
$881$	21.9509	+	38.0200i	0.739543	+	1.28093i	−0.213158	+	0.977018i	$0.568375\pi$
$882$		0			0
$883$	−10.2424	+	38.2251i	−0.344684	+	1.28638i	0.548297	+	0.836284i	$0.315276\pi$
$883$	−10.2424	+	38.2251i	−0.344684	+	1.28638i	−0.892981	+	0.450094i	$0.851390\pi$
$884$		0			0
$885$	0.969365	+	2.03393i	0.0325848	+	0.0683697i
$886$		0			0
$887$	−44.5643			−1.49632			−0.748161	−	0.663517i	$-0.769063\pi$
$887$	−44.5643			−1.49632			−0.748161	+	0.663517i	$0.769063\pi$
$888$		0			0
$889$	−1.02773			−0.0344690
$890$		0			0
$891$	2.61588	+	12.3818i	0.0876353	+	0.414804i
$892$		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
$897$	14.7578	+	10.1495i	0.492750	+	0.338881i
$898$		0			0
$899$	−3.61467			−0.120556
$900$		0			0
$901$	30.9209	+	8.28522i	1.03012	+	0.276021i
$902$		0			0
$903$	−3.52050	+	0.651365i	−0.117155	+	0.0216761i
$904$		0			0
$905$	1.84109	−	0.493319i	0.0611999	−	0.0163985i
$906$		0			0
$907$	−42.7218	−	11.4473i	−1.41855	−	0.380100i	−0.533584	−	0.845747i	$-0.679155\pi$
$907$	−42.7218	−	11.4473i	−1.41855	−	0.380100i	−0.884971	+	0.465647i	$0.845822\pi$
$908$		0			0
$909$	−20.1754	+	24.8832i	−0.669176	+	0.825323i
$910$		0			0
$911$	−4.93313	−	4.93313i	−0.163442	−	0.163442i	0.620648	−	0.784090i	$-0.286870\pi$
$911$	−4.93313	−	4.93313i	−0.163442	−	0.163442i	−0.784090	+	0.620648i	$0.786870\pi$
$912$		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	0.220505	−	0.975386i	$-0.429229\pi$
$919$	−22.8842	−	22.8842i	−0.754881	−	0.754881i	−0.975386	+	0.220505i	$0.929229\pi$
$920$		0			0
$921$	19.9503	+	41.8598i	0.657385	+	1.37933i
$922$		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
$927$	−11.5971	+	1.21168i	−0.380898	+	0.0397967i
$928$		0			0
$929$	−3.39347	−	5.87766i	−0.111336	−	0.192840i	0.804973	−	0.593311i	$-0.202180\pi$
$929$	−3.39347	−	5.87766i	−0.111336	−	0.192840i	−0.916309	+	0.400472i	$0.868846\pi$
$930$		0			0
$931$	−21.7813	+	21.7813i	−0.713853	+	0.713853i
$932$		0			0
$933$	33.0502	+	38.7209i	1.08201	+	1.26767i
$934$		0			0
$935$		−	4.81005i		−	0.157305i
$936$		0			0
$937$	21.5995	−	37.4115i	0.705626	−	1.22218i	−0.260839	−	0.965382i	$-0.583999\pi$
$937$	21.5995	−	37.4115i	0.705626	−	1.22218i	0.966465	−	0.256798i	$-0.0826676\pi$
$938$		0			0
$939$	8.58204	+	10.0546i	0.280064	+	0.328118i
$940$		0			0
$941$	−35.3411	−	20.4042i	−1.15209	−	0.665158i	−0.202692	−	0.979242i	$-0.564969\pi$
$941$	−35.3411	−	20.4042i	−1.15209	−	0.665158i	−0.949395	+	0.314085i	$0.898302\pi$
$942$		0			0
$943$	−14.7174	+	54.9262i	−0.479266	+	1.78864i
$944$		0			0
$945$	−0.0320815	−	1.26999i	−0.00104361	−	0.0413128i
$946$		0			0
$947$	22.8777	−	6.13006i	0.743426	−	0.199200i	0.132826	−	0.991139i	$-0.457595\pi$
$947$	22.8777	−	6.13006i	0.743426	−	0.199200i	0.610600	+	0.791939i	$0.290928\pi$
$948$		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	0.130979	−	0.991385i	$-0.458188\pi$
$953$	28.5262	−	49.4088i	0.924054	−	1.60051i	0.793075	−	0.609124i	$-0.208479\pi$
$954$		0			0
$955$	−0.424282	+	0.244960i	−0.0137295	+	0.00792670i
$956$		0			0
$957$	3.15497	−	8.90064i	0.101986	−	0.287717i
$958$		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	−0.368403	−	0.929666i	$-0.620095\pi$
$967$	−35.8321	−	9.60118i	−1.15228	−	0.308753i	−0.783880	+	0.620913i	$0.786762\pi$
$968$		0			0
$969$	−29.0977	+	13.8679i	−0.934754	+	0.445502i
$970$		0			0
$971$	−9.59093	−	5.53733i	−0.307788	−	0.177701i	0.338148	−	0.941093i	$-0.390199\pi$
$971$	−9.59093	−	5.53733i	−0.307788	−	0.177701i	−0.645936	+	0.763392i	$0.723533\pi$
$972$		0			0
$973$			1.38632i			0.0444435i
$974$		0			0
$975$	−15.1849	−	5.38253i	−0.486307	−	0.172379i
$976$		0			0
$977$	−4.62017	−	17.2427i	−0.147812	−	0.551643i	−0.999614	−	0.0277788i	$-0.991157\pi$
$977$	−4.62017	−	17.2427i	−0.147812	−	0.551643i	0.851802	−	0.523864i	$-0.175510\pi$
$978$		0			0
$979$	2.47389	+	9.23269i	0.0790659	+	0.295078i
$980$		0			0
$981$	36.6995	+	16.3667i	1.17172	+	0.522550i
$982$		0			0
$983$	−20.1423	+	34.8875i	−0.642439	+	1.11274i	0.342448	+	0.939537i	$0.388744\pi$
$983$	−20.1423	+	34.8875i	−0.642439	+	1.11274i	−0.984887	+	0.173200i	$0.944589\pi$
$984$		0			0
$985$	12.6596	−	12.6596i	0.403369	−	0.403369i
$986$		0			0
$987$	3.20152	−	4.65517i	0.101906	−	0.148176i
$988$		0			0
$989$	33.3356			1.06001
$990$		0			0
$991$	−2.84174	−	2.84174i	−0.0902709	−	0.0902709i	0.660529	−	0.750800i	$-0.270332\pi$
$991$	−2.84174	−	2.84174i	−0.0902709	−	0.0902709i	−0.750800	+	0.660529i	$0.770332\pi$
$992$		0			0
$993$	11.5686	+	13.5536i	0.367119	+	0.430109i
$994$		0			0
$995$	−0.875798	+	0.505642i	−0.0277647	+	0.0160299i
$996$		0			0
$997$	−11.5050	−	42.9374i	−0.364368	−	1.35984i	−0.868276	−	0.496082i	$-0.834771\pi$
$997$	−11.5050	−	42.9374i	−0.364368	−	1.35984i	0.503908	−	0.863758i	$-0.331895\pi$
$998$		0			0
$999$	29.8190	−	10.4799i	0.943430	−	0.331570i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.6	✓	152	1.1	even	1	trivial
888.2.br.a.569.8	yes	152	3.2	odd	2	inner
888.2.br.a.785.6	yes	152	111.8	even	12	inner
888.2.br.a.785.8	yes	152	37.8	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.56355 + 0.745185i) q^{3} +(0.212050 - 0.791381i) q^{5} +(-0.149206 - 0.258432i) q^{7} +(1.88940 - 2.33027i) q^{9} -1.40612 q^{11} +(2.07555 + 0.556143i) q^{13} +(0.258174 + 1.39538i) q^{15} +(-4.03302 + 1.08064i) q^{17} +(-4.30531 - 1.15360i) q^{19} +(0.425871 + 0.292886i) q^{21} +(-3.40295 - 3.40295i) q^{23} +(3.74881 + 2.16438i) q^{25} +(-1.21769 + 5.05146i) q^{27} +(2.74173 - 2.74173i) q^{29} +(-0.659194 - 0.659194i) q^{31} +(2.19854 - 1.04782i) q^{33} +(-0.236157 + 0.0632781i) q^{35} +(-3.30552 - 5.10622i) q^{37} +(-3.65967 + 0.677114i) q^{39} +(-5.90794 - 10.2328i) q^{41} +(-4.89804 + 4.89804i) q^{43} +(-1.44349 - 1.98937i) q^{45} -10.9310i q^{47} +(3.45548 - 5.98506i) q^{49} +(5.50055 - 4.69499i) q^{51} +(-6.63976 - 3.83347i) q^{53} +(-0.298167 + 1.11277i) q^{55} +(7.59123 - 1.40453i) q^{57} +(1.53365 - 0.410939i) q^{59} +(-0.777010 + 2.89984i) q^{61} +(-0.884126 - 0.140590i) q^{63} +(0.880242 - 1.52462i) q^{65} +(-1.51826 + 0.876567i) q^{67} +(7.85652 + 2.78486i) q^{69} +(2.84275 - 1.64126i) q^{71} +0.542470i q^{73} +(-7.47432 - 0.590559i) q^{75} +(0.209801 + 0.363386i) q^{77} +(4.66772 + 1.25071i) q^{79} +(-1.86036 - 8.80563i) q^{81} +(-7.59339 - 4.38405i) q^{83} +3.42080i q^{85} +(-2.24374 + 6.32994i) q^{87} +(-1.75938 - 6.56608i) q^{89} +(-0.165959 - 0.619369i) q^{91} +(1.52191 + 0.539463i) q^{93} +(-1.82588 + 3.16252i) q^{95} +(7.62300 - 7.62300i) q^{97} +(-2.65672 + 3.27664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 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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