LMFDB - Embedded newform 864.2.v.a.109.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.17
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0434074 - 1.41355i) q^{2} +(-1.99623 - 0.122717i) q^{4} +(-2.68483 + 1.11209i) q^{5} +(1.54691 - 1.54691i) q^{7} +(-0.260117 + 2.81644i) q^{8} +O(q^{10})$	\(q+(0.0434074 - 1.41355i) q^{2} +(-1.99623 - 0.122717i) q^{4} +(-2.68483 + 1.11209i) q^{5} +(1.54691 - 1.54691i) q^{7} +(-0.260117 + 2.81644i) q^{8} +(1.45545 + 3.84340i) q^{10} +(-0.284805 - 0.687579i) q^{11} +(-2.08570 - 0.863924i) q^{13} +(-2.11949 - 2.25378i) q^{14} +(3.96988 + 0.489942i) q^{16} +6.20670i q^{17} +(-0.566840 - 0.234793i) q^{19} +(5.49601 - 1.89052i) q^{20} +(-0.984289 + 0.372739i) q^{22} +(4.42017 + 4.42017i) q^{23} +(2.43601 - 2.43601i) q^{25} +(-1.31173 + 2.91073i) q^{26} +(-3.27783 + 2.89816i) q^{28} +(-1.81939 + 4.39239i) q^{29} +7.34680 q^{31} +(0.864879 - 5.59035i) q^{32} +(8.77346 + 0.269417i) q^{34} +(-2.43288 + 5.87350i) q^{35} +(5.10608 - 2.11501i) q^{37} +(-0.356496 + 0.791064i) q^{38} +(-2.43377 - 7.85093i) q^{40} +(4.87073 + 4.87073i) q^{41} +(2.38680 + 5.76224i) q^{43} +(0.484159 + 1.40752i) q^{44} +(6.43999 - 6.05625i) q^{46} -7.05366i q^{47} +2.21413i q^{49} +(-3.33768 - 3.54916i) q^{50} +(4.05752 + 1.98054i) q^{52} +(-1.34706 - 3.25209i) q^{53} +(1.52930 + 1.52930i) q^{55} +(3.95441 + 4.75917i) q^{56} +(6.12987 + 2.76245i) q^{58} +(6.36373 - 2.63594i) q^{59} +(3.05830 - 7.38339i) q^{61} +(0.318905 - 10.3850i) q^{62} +(-7.86468 - 1.46521i) q^{64} +6.56050 q^{65} +(-3.58513 + 8.65526i) q^{67} +(0.761666 - 12.3900i) q^{68} +(8.19686 + 3.69395i) q^{70} +(-4.40258 + 4.40258i) q^{71} +(7.67341 + 7.67341i) q^{73} +(-2.76802 - 7.30949i) q^{74} +(1.10273 + 0.538262i) q^{76} +(-1.50419 - 0.623057i) q^{77} +10.9657i q^{79} +(-11.2033 + 3.09946i) q^{80} +(7.09643 - 6.67358i) q^{82} +(-12.4669 - 5.16396i) q^{83} +(-6.90242 - 16.6639i) q^{85} +(8.24880 - 3.12373i) q^{86} +(2.01061 - 0.623284i) q^{88} +(-9.45976 + 9.45976i) q^{89} +(-4.56281 + 1.88998i) q^{91} +(-8.28126 - 9.36611i) q^{92} +(-9.97069 - 0.306181i) q^{94} +1.78298 q^{95} -13.6291 q^{97} +(3.12977 + 0.0961094i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	0.0434074	−	1.41355i	0.0306937	−	0.999529i
$2$	0.0434074	−	1.41355i	0.0306937	−	0.999529i
$3$		0			0
$3$		0			0
$4$	−1.99623	−	0.122717i	−0.998116	−	0.0613584i
$5$	−2.68483	+	1.11209i	−1.20069	+	0.497342i	−0.891222	−	0.453567i	$-0.850151\pi$
$5$	−2.68483	+	1.11209i	−1.20069	+	0.497342i	−0.309469	+	0.950910i	$0.600151\pi$
$6$		0			0
$7$	1.54691	−	1.54691i	0.584678	−	0.584678i	−0.351507	−	0.936185i	$-0.614331\pi$
$7$	1.54691	−	1.54691i	0.584678	−	0.584678i	0.936185	+	0.351507i	$0.114331\pi$
$8$	−0.260117	+	2.81644i	−0.0919653	+	0.995762i
$9$		0			0
$10$	1.45545	+	3.84340i	0.460255	+	1.21539i
$11$	−0.284805	−	0.687579i	−0.0858719	−	0.207313i	0.875110	−	0.483924i	$-0.160789\pi$
$11$	−0.284805	−	0.687579i	−0.0858719	−	0.207313i	−0.960982	+	0.276611i	$0.910789\pi$
$12$		0			0
$13$	−2.08570	−	0.863924i	−0.578468	−	0.239609i	0.0742124	−	0.997242i	$-0.476356\pi$
$13$	−2.08570	−	0.863924i	−0.578468	−	0.239609i	−0.652681	+	0.757633i	$0.726356\pi$
$14$	−2.11949	−	2.25378i	−0.566456	−	0.602348i
$15$		0			0
$16$	3.96988	+	0.489942i	0.992470	+	0.122486i
$17$			6.20670i			1.50535i	0.658395	+	0.752673i	$0.271236\pi$
$17$			6.20670i			1.50535i	−0.658395	+	0.752673i	$0.728764\pi$
$18$		0			0
$19$	−0.566840	−	0.234793i	−0.130042	−	0.0538652i	0.316713	−	0.948521i	$-0.397421\pi$
$19$	−0.566840	−	0.234793i	−0.130042	−	0.0538652i	−0.446756	+	0.894656i	$0.647421\pi$
$20$	5.49601	−	1.89052i	1.22894	−	0.422733i
$21$		0			0
$22$	−0.984289	+	0.372739i	−0.209851	+	0.0794682i
$23$	4.42017	+	4.42017i	0.921669	+	0.921669i	0.997147	−	0.0754781i	$-0.0240483\pi$
$23$	4.42017	+	4.42017i	0.921669	+	0.921669i	−0.0754781	+	0.997147i	$0.524048\pi$
$24$		0			0
$25$	2.43601	−	2.43601i	0.487203	−	0.487203i
$26$	−1.31173	+	2.91073i	−0.257252	+	0.570841i
$27$		0			0
$28$	−3.27783	+	2.89816i	−0.619451	+	0.547701i
$29$	−1.81939	+	4.39239i	−0.337852	+	0.815646i	0.660070	+	0.751204i	$0.270527\pi$
$29$	−1.81939	+	4.39239i	−0.337852	+	0.815646i	−0.997921	+	0.0644418i	$0.979473\pi$
$30$		0			0
$31$	7.34680			1.31952			0.659762	−	0.751475i	$-0.270657\pi$
$31$	7.34680			1.31952			0.659762	+	0.751475i	$0.270657\pi$
$32$	0.864879	−	5.59035i	0.152890	−	0.988243i
$33$		0			0
$34$	8.77346	+	0.269417i	1.50464	+	0.0462046i
$35$	−2.43288	+	5.87350i	−0.411232	+	0.992803i
$36$		0			0
$37$	5.10608	−	2.11501i	0.839434	−	0.347705i	0.0788036	−	0.996890i	$-0.474890\pi$
$37$	5.10608	−	2.11501i	0.839434	−	0.347705i	0.760630	+	0.649185i	$0.224890\pi$
$38$	−0.356496	+	0.791064i	−0.0578313	+	0.128327i
$39$		0			0
$40$	−2.43377	−	7.85093i	−0.384813	−	1.24134i
$41$	4.87073	+	4.87073i	0.760680	+	0.760680i	0.976445	−	0.215765i	$-0.0692245\pi$
$41$	4.87073	+	4.87073i	0.760680	+	0.760680i	−0.215765	+	0.976445i	$0.569225\pi$
$42$		0			0
$43$	2.38680	+	5.76224i	0.363983	+	0.878733i	0.994710	+	0.102728i	$0.0327570\pi$
$43$	2.38680	+	5.76224i	0.363983	+	0.878733i	−0.630726	+	0.776005i	$0.717243\pi$
$44$	0.484159	+	1.40752i	0.0729897	+	0.212191i
$45$		0			0
$46$	6.43999	−	6.05625i	0.949525	−	0.892946i
$47$		−	7.05366i		−	1.02888i	−0.857526	−	0.514441i	$-0.827999\pi$
$47$		−	7.05366i		−	1.02888i	0.857526	−	0.514441i	$-0.172001\pi$
$48$		0			0
$49$			2.21413i			0.316304i
$50$	−3.33768	−	3.54916i	−0.472019	−	0.501927i
$51$		0			0
$52$	4.05752	+	1.98054i	0.562676	+	0.274652i
$53$	−1.34706	−	3.25209i	−0.185033	−	0.446709i	0.803958	−	0.594686i	$-0.202724\pi$
$53$	−1.34706	−	3.25209i	−0.185033	−	0.446709i	−0.988991	+	0.147977i	$0.952724\pi$
$54$		0			0
$55$	1.52930	+	1.52930i	0.206211	+	0.206211i
$56$	3.95441	+	4.75917i	0.528430	+	0.635970i
$57$		0			0
$58$	6.12987	+	2.76245i	0.804892	+	0.362728i
$59$	6.36373	−	2.63594i	0.828487	−	0.343171i	0.0721835	−	0.997391i	$-0.477003\pi$
$59$	6.36373	−	2.63594i	0.828487	−	0.343171i	0.756304	+	0.654221i	$0.227003\pi$
$60$		0			0
$61$	3.05830	−	7.38339i	0.391575	−	0.945347i	−0.598022	−	0.801480i	$-0.704046\pi$
$61$	3.05830	−	7.38339i	0.391575	−	0.945347i	0.989597	−	0.143867i	$-0.0459537\pi$
$62$	0.318905	−	10.3850i	0.0405010	−	1.31890i
$63$		0			0
$64$	−7.86468	−	1.46521i	−0.983085	−	0.183151i
$65$	6.56050			0.813730
$66$		0			0
$67$	−3.58513	+	8.65526i	−0.437993	+	1.05741i	0.538648	+	0.842531i	$0.318935\pi$
$67$	−3.58513	+	8.65526i	−0.437993	+	1.05741i	−0.976641	+	0.214878i	$0.931065\pi$
$68$	0.761666	−	12.3900i	0.0923656	−	1.50251i
$69$		0			0
$70$	8.19686	+	3.69395i	0.979713	+	0.441511i
$71$	−4.40258	+	4.40258i	−0.522490	+	0.522490i	−0.918323	−	0.395833i	$-0.870456\pi$
$71$	−4.40258	+	4.40258i	−0.522490	+	0.522490i	0.395833	+	0.918323i	$0.370456\pi$
$72$		0			0
$73$	7.67341	+	7.67341i	0.898105	+	0.898105i	0.995268	−	0.0971633i	$-0.0309769\pi$
$73$	7.67341	+	7.67341i	0.898105	+	0.898105i	−0.0971633	+	0.995268i	$0.530977\pi$
$74$	−2.76802	−	7.30949i	−0.321776	−	0.849711i
$75$		0			0
$76$	1.10273	+	0.538262i	0.126492	+	0.0617429i
$77$	−1.50419	−	0.623057i	−0.171419	−	0.0710039i
$78$		0			0
$79$			10.9657i			1.23374i	0.787066	+	0.616869i	$0.211599\pi$
$79$			10.9657i			1.23374i	−0.787066	+	0.616869i	$0.788401\pi$
$80$	−11.2033	+	3.09946i	−1.25257	+	0.346530i
$81$		0			0
$82$	7.09643	−	6.67358i	0.783670	−	0.736974i
$83$	−12.4669	−	5.16396i	−1.36842	−	0.566818i	−0.427060	−	0.904223i	$-0.640451\pi$
$83$	−12.4669	−	5.16396i	−1.36842	−	0.566818i	−0.941360	+	0.337405i	$0.890451\pi$
$84$		0			0
$85$	−6.90242	−	16.6639i	−0.748672	−	1.80745i
$86$	8.24880	−	3.12373i	0.889491	−	0.336840i
$87$		0			0
$88$	2.01061	−	0.623284i	0.214332	−	0.0664423i
$89$	−9.45976	+	9.45976i	−1.00273	+	1.00273i	−0.00273639	+	0.999996i	$0.500871\pi$
$89$	−9.45976	+	9.45976i	−1.00273	+	1.00273i	−0.999996	+	0.00273639i	$0.999129\pi$
$90$		0			0
$91$	−4.56281	+	1.88998i	−0.478312	+	0.198123i
$92$	−8.28126	−	9.36611i	−0.863381	−	0.976485i
$93$		0			0
$94$	−9.97069	−	0.306181i	−1.02840	−	0.0315802i
$95$	1.78298			0.182930
$96$		0			0
$97$	−13.6291			−1.38383			−0.691913	−	0.721981i	$-0.743232\pi$
$97$	−13.6291			−1.38383			−0.691913	+	0.721981i	$0.743232\pi$
$98$	3.12977	+	0.0961094i	0.316155	+	0.00970852i
$99$		0			0
$100$	−5.16179	+	4.56391i	−0.516179	+	0.456391i
$101$	−5.64384	+	2.33775i	−0.561583	+	0.232615i	−0.645372	−	0.763868i	$-0.723298\pi$
$101$	−5.64384	+	2.33775i	−0.561583	+	0.232615i	0.0837893	+	0.996483i	$0.473298\pi$
$102$		0			0
$103$	−11.5772	+	11.5772i	−1.14074	+	1.14074i	−0.152421	+	0.988316i	$0.548707\pi$
$103$	−11.5772	+	11.5772i	−1.14074	+	1.14074i	−0.988316	+	0.152421i	$0.951293\pi$
$104$	2.97572	−	5.64952i	0.291793	−	0.553981i
$105$		0			0
$106$	−4.65546	+	1.76297i	−0.452178	+	0.171235i
$107$	4.65403	+	11.2358i	0.449922	+	1.08621i	0.972351	+	0.233525i	$0.0750259\pi$
$107$	4.65403	+	11.2358i	0.449922	+	1.08621i	−0.522429	+	0.852683i	$0.674974\pi$
$108$		0			0
$109$	1.58025	+	0.654563i	0.151361	+	0.0626958i	0.457078	−	0.889427i	$-0.348896\pi$
$109$	1.58025	+	0.654563i	0.151361	+	0.0626958i	−0.305717	+	0.952122i	$0.598896\pi$
$110$	2.22812	−	2.09536i	0.212443	−	0.199785i
$111$		0			0
$112$	6.89896	−	5.38316i	0.651890	−	0.508661i
$113$		−	11.4422i		−	1.07639i	−0.842821	−	0.538194i	$-0.819107\pi$
$113$		−	11.4422i		−	1.07639i	0.842821	−	0.538194i	$-0.180893\pi$
$114$		0			0
$115$	−16.7830	−	6.95176i	−1.56503	−	0.648255i
$116$	4.17094	−	8.54496i	0.387262	−	0.793379i
$117$		0			0
$118$	−3.44980	−	9.10985i	−0.317580	−	0.838630i
$119$	9.60122	+	9.60122i	0.880142	+	0.880142i
$120$		0			0
$121$	7.38652	−	7.38652i	0.671502	−	0.671502i
$122$	−10.3040	−	4.64355i	−0.932882	−	0.420407i
$123$		0			0
$124$	−14.6659	−	0.901575i	−1.31704	−	0.0809639i
$125$	1.72926	−	4.17479i	0.154669	−	0.373405i
$126$		0			0
$127$	13.2006			1.17136			0.585680	−	0.810542i	$-0.300828\pi$
$127$	13.2006			1.17136			0.585680	+	0.810542i	$0.300828\pi$
$128$	−2.41253	+	11.0535i	−0.213239	+	0.977000i
$129$		0			0
$130$	0.284774	−	9.27358i	0.0249764	−	0.813346i
$131$	−5.20614	+	12.5687i	−0.454863	+	1.09814i	0.515588	+	0.856837i	$0.327574\pi$
$131$	−5.20614	+	12.5687i	−0.454863	+	1.09814i	−0.970451	+	0.241299i	$0.922426\pi$
$132$		0			0
$133$	−1.24006	+	0.513648i	−0.107526	+	0.0445389i
$134$	12.0790	+	5.44345i	1.04347	+	0.470242i
$135$		0			0
$136$	−17.4808	−	1.61447i	−1.49897	−	0.138440i
$137$	7.48430	+	7.48430i	0.639427	+	0.639427i	0.950414	−	0.310987i	$-0.100660\pi$
$137$	7.48430	+	7.48430i	0.639427	+	0.639427i	−0.310987	+	0.950414i	$0.600660\pi$
$138$		0			0
$139$	3.29371	+	7.95171i	0.279369	+	0.674456i	0.999819	−	0.0190515i	$-0.00606464\pi$
$139$	3.29371	+	7.95171i	0.279369	+	0.674456i	−0.720450	+	0.693507i	$0.756065\pi$
$140$	5.57738	−	11.4263i	0.471374	−	0.965699i
$141$		0			0
$142$	6.03214	+	6.41435i	0.506206	+	0.538281i
$143$			1.68013i			0.140500i
$144$		0			0
$145$		−	13.8161i		−	1.14737i
$146$	11.1798	−	10.5137i	0.925248	−	0.870116i
$147$		0			0
$148$	−10.4525	+	3.59544i	−0.859187	+	0.295543i
$149$	−8.60348	−	20.7706i	−0.704825	−	1.70160i	−0.712544	−	0.701627i	$-0.752457\pi$
$149$	−8.60348	−	20.7706i	−0.704825	−	1.70160i	0.00771944	−	0.999970i	$-0.497543\pi$
$150$		0			0
$151$	−3.82668	−	3.82668i	−0.311410	−	0.311410i	0.534045	−	0.845456i	$-0.320671\pi$
$151$	−3.82668	−	3.82668i	−0.311410	−	0.311410i	−0.845456	+	0.534045i	$0.820671\pi$
$152$	0.808725	−	1.53540i	0.0655963	−	0.124537i
$153$		0			0
$154$	−0.946014	+	2.09920i	−0.0762320	+	0.169159i
$155$	−19.7249	+	8.17031i	−1.58434	+	0.656255i
$156$		0			0
$157$	6.05233	−	14.6116i	0.483028	−	1.16613i	−0.475136	−	0.879913i	$-0.657601\pi$
$157$	6.05233	−	14.6116i	0.483028	−	1.16613i	0.958164	−	0.286221i	$-0.0923990\pi$
$158$	15.5005	+	0.475993i	1.23316	+	0.0378680i
$159$		0			0
$160$	3.89493	+	15.9709i	0.307921	+	1.26261i
$161$	13.6752			1.07776
$162$		0			0
$163$	−1.51310	+	3.65294i	−0.118515	+	0.286121i	−0.971994	−	0.235007i	$-0.924489\pi$
$163$	−1.51310	+	3.65294i	−0.118515	+	0.286121i	0.853479	+	0.521128i	$0.174489\pi$
$164$	−9.12538	−	10.3208i	−0.712573	−	0.805921i
$165$		0			0
$166$	−7.84065	+	17.3984i	−0.608553	+	1.35038i
$167$	9.15910	−	9.15910i	0.708752	−	0.708752i	−0.257521	−	0.966273i	$-0.582906\pi$
$167$	9.15910	−	9.15910i	0.708752	−	0.708752i	0.966273	+	0.257521i	$0.0829055\pi$
$168$		0			0
$169$	−5.58862	−	5.58862i	−0.429894	−	0.429894i
$170$	−23.8548	+	9.03355i	−1.82958	+	0.692842i
$171$		0			0
$172$	−4.05748	−	11.7957i	−0.309380	−	0.899411i
$173$	17.6996	+	7.33141i	1.34567	+	0.557397i	0.935085	−	0.354423i	$-0.115323\pi$
$173$	17.6996	+	7.33141i	1.34567	+	0.557397i	0.410590	+	0.911820i	$0.365323\pi$
$174$		0			0
$175$		−	7.53660i		−	0.569713i
$176$	−0.793767	−	2.86915i	−0.0598324	−	0.216270i
$177$		0			0
$178$	12.9612	+	13.7824i	0.971483	+	1.03304i
$179$	−1.23311	−	0.510772i	−0.0921672	−	0.0381769i	0.336123	−	0.941818i	$-0.390884\pi$
$179$	−1.23311	−	0.510772i	−0.0921672	−	0.0381769i	−0.428291	+	0.903641i	$0.640884\pi$
$180$		0			0
$181$	8.76496	+	21.1605i	0.651494	+	1.57285i	0.810610	+	0.585586i	$0.199136\pi$
$181$	8.76496	+	21.1605i	0.651494	+	1.57285i	−0.159116	+	0.987260i	$0.550864\pi$
$182$	2.47351	+	6.53178i	0.183349	+	0.484168i
$183$		0			0
$184$	−13.5989	+	11.2994i	−1.00253	+	0.833002i
$185$	−11.3569	+	11.3569i	−0.834972	+	0.834972i
$186$		0			0
$187$	4.26760	−	1.76770i	0.312078	−	0.129267i
$188$	−0.865603	+	14.0807i	−0.0631306	+	1.02694i
$189$		0			0
$190$	0.0773945	−	2.52032i	0.00561478	−	0.182844i
$191$	6.67271			0.482820			0.241410	−	0.970423i	$-0.422390\pi$
$191$	6.67271			0.482820			0.241410	+	0.970423i	$0.422390\pi$
$192$		0			0
$193$	−4.61893			−0.332478			−0.166239	−	0.986086i	$-0.553162\pi$
$193$	−4.61893			−0.332478			−0.166239	+	0.986086i	$0.553162\pi$
$194$	−0.591604	+	19.2654i	−0.0424747	+	1.38317i
$195$		0			0
$196$	0.271710	−	4.41991i	0.0194079	−	0.315708i
$197$	−2.02402	+	0.838378i	−0.144206	+	0.0597320i	−0.453619	−	0.891196i	$-0.649867\pi$
$197$	−2.02402	+	0.838378i	−0.144206	+	0.0597320i	0.309413	+	0.950928i	$0.399867\pi$
$198$		0			0
$199$	−7.33083	+	7.33083i	−0.519669	+	0.519669i	−0.917471	−	0.397803i	$-0.869773\pi$
$199$	−7.33083	+	7.33083i	−0.519669	+	0.519669i	0.397803	+	0.917471i	$0.369773\pi$
$200$	6.22724	+	7.49453i	0.440332	+	0.529944i
$201$		0			0
$202$	3.05954	+	8.07931i	0.215269	+	0.568458i
$203$	3.98021	+	9.60907i	0.279356	+	0.674425i
$204$		0			0
$205$	−18.4938	−	7.66037i	−1.29166	−	0.535023i
$206$	15.8624	+	16.8675i	1.10519	+	1.17521i
$207$		0			0
$208$	−7.85670	−	4.45155i	−0.544764	−	0.308659i
$209$			0.456618i			0.0315849i
$210$		0			0
$211$	14.2270	+	5.89300i	0.979424	+	0.405691i	0.814212	−	0.580567i	$-0.197169\pi$
$211$	14.2270	+	5.89300i	0.979424	+	0.405691i	0.165212	+	0.986258i	$0.447169\pi$
$212$	2.28996	+	6.65723i	0.157275	+	0.457221i
$213$		0			0
$214$	16.0844	−	6.09097i	1.09951	−	0.416370i
$215$	−12.8163	−	12.8163i	−0.874063	−	0.874063i
$216$		0			0
$217$	11.3648	−	11.3648i	0.771496	−	0.771496i
$218$	0.993851	−	2.20535i	0.0673120	−	0.149365i
$219$		0			0
$220$	−2.86517	−	3.24051i	−0.193170	−	0.218475i
$221$	5.36212	−	12.9453i	0.360695	−	0.870795i
$222$		0			0
$223$	−24.5345			−1.64295			−0.821475	−	0.570245i	$-0.806848\pi$
$223$	−24.5345			−1.64295			−0.821475	+	0.570245i	$0.806848\pi$
$224$	−7.30988	−	9.98567i	−0.488412	−	0.667196i
$225$		0			0
$226$	−16.1740	−	0.496674i	−1.07588	−	0.0330383i
$227$	−5.42289	+	13.0920i	−0.359930	+	0.868947i	0.635379	+	0.772200i	$0.280844\pi$
$227$	−5.42289	+	13.0920i	−0.359930	+	0.868947i	−0.995309	+	0.0967468i	$0.969156\pi$
$228$		0			0
$229$	−16.3687	+	6.78014i	−1.08168	+	0.448045i	−0.851097	−	0.525009i	$-0.824062\pi$
$229$	−16.3687	+	6.78014i	−1.08168	+	0.448045i	−0.230579	+	0.973054i	$0.574062\pi$
$230$	−10.5551	+	23.4218i	−0.695986	+	1.54439i
$231$		0			0
$232$	−11.8976	−	6.26673i	−0.781119	−	0.411431i
$233$	10.7205	+	10.7205i	0.702321	+	0.702321i	0.964908	−	0.262588i	$-0.0845759\pi$
$233$	10.7205	+	10.7205i	0.702321	+	0.702321i	−0.262588	+	0.964908i	$0.584576\pi$
$234$		0			0
$235$	7.84432	+	18.9379i	0.511707	+	1.23537i
$236$	−13.0270	+	4.48102i	−0.847983	+	0.291689i
$237$		0			0
$238$	13.9885	−	13.1550i	0.906742	−	0.852712i
$239$		−	16.8887i		−	1.09244i	−0.837642	−	0.546219i	$-0.816067\pi$
$239$		−	16.8887i		−	1.09244i	0.837642	−	0.546219i	$-0.183933\pi$
$240$		0			0
$241$		−	30.4276i		−	1.96002i	−0.198960	−	0.980008i	$-0.563756\pi$
$241$		−	30.4276i		−	1.96002i	0.198960	−	0.980008i	$-0.436244\pi$
$242$	−10.1206	−	10.7618i	−0.650575	−	0.691797i
$243$		0			0
$244$	−7.01115	+	14.3637i	−0.448843	+	0.919539i
$245$	−2.46231	−	5.94454i	−0.157311	−	0.379783i
$246$		0			0
$247$	0.979414	+	0.979414i	0.0623186	+	0.0623186i
$248$	−1.91103	+	20.6918i	−0.121350	+	1.31393i
$249$		0			0
$250$	−5.82620	−	2.62560i	−0.368481	−	0.166058i
$251$	−5.16495	+	2.13939i	−0.326009	+	0.135037i	−0.539684	−	0.841867i	$-0.681456\pi$
$251$	−5.16495	+	2.13939i	−0.326009	+	0.135037i	0.213676	+	0.976905i	$0.431456\pi$
$252$		0			0
$253$	1.78033	−	4.29810i	0.111929	−	0.270220i
$254$	0.573002	−	18.6596i	0.0359533	−	1.17081i
$255$		0			0
$256$	15.5199	+	3.89003i	0.969995	+	0.243127i
$257$	−4.42196			−0.275834			−0.137917	−	0.990444i	$-0.544041\pi$
$257$	−4.42196			−0.275834			−0.137917	+	0.990444i	$0.544041\pi$
$258$		0			0
$259$	4.62692	−	11.1704i	0.287503	−	0.694094i
$260$	−13.0963	−	0.805084i	−0.812197	−	0.0499292i
$261$		0			0
$262$	17.5405	+	7.90471i	1.08366	+	0.488354i
$263$	12.8365	−	12.8365i	0.791530	−	0.791530i	−0.190213	−	0.981743i	$-0.560918\pi$
$263$	12.8365	−	12.8365i	0.791530	−	0.791530i	0.981743	+	0.190213i	$0.0609178\pi$
$264$		0			0
$265$	7.23325	+	7.23325i	0.444335	+	0.444335i
$266$	0.672238	+	1.77517i	0.0412176	+	0.108843i
$267$		0			0
$268$	8.21889	−	16.8379i	0.502048	−	1.02854i
$269$	−20.3936	−	8.44729i	−1.24342	−	0.515041i	−0.338637	−	0.940917i	$-0.609966\pi$
$269$	−20.3936	−	8.44729i	−1.24342	−	0.515041i	−0.904781	+	0.425877i	$0.859966\pi$
$270$		0			0
$271$		−	0.594609i		−	0.0361199i	−0.999837	−	0.0180600i	$-0.994251\pi$
$271$		−	0.594609i		−	0.0361199i	0.999837	−	0.0180600i	$-0.00574898\pi$
$272$	−3.04092	+	24.6398i	−0.184383	+	1.49401i
$273$		0			0
$274$	10.9043	−	10.2545i	0.658752	−	0.619499i
$275$	−2.36874	−	0.981164i	−0.142840	−	0.0591664i
$276$		0			0
$277$	0.534800	+	1.29112i	0.0321330	+	0.0775759i	0.939131	−	0.343558i	$-0.111632\pi$
$277$	0.534800	+	1.29112i	0.0321330	+	0.0775759i	−0.906998	+	0.421134i	$0.861632\pi$
$278$	11.3831	−	4.31065i	0.682713	−	0.258535i
$279$		0			0
$280$	−15.9095	−	8.37987i	−0.950776	−	0.500793i
$281$	12.9326	−	12.9326i	0.771493	−	0.771493i	−0.206875	−	0.978367i	$-0.566329\pi$
$281$	12.9326	−	12.9326i	0.771493	−	0.771493i	0.978367	+	0.206875i	$0.0663292\pi$
$282$		0			0
$283$	10.0071	−	4.14508i	0.594861	−	0.246399i	−0.0648795	−	0.997893i	$-0.520666\pi$
$283$	10.0071	−	4.14508i	0.594861	−	0.246399i	0.659740	+	0.751494i	$0.270666\pi$
$284$	9.32883	−	8.24829i	0.553564	−	0.489446i
$285$		0			0
$286$	2.37495	+	0.0729302i	0.140434	+	0.00431245i
$287$	15.0692			0.889506
$288$		0			0
$289$	−21.5231			−1.26606
$290$	−19.5297	−	0.599722i	−1.14683	−	0.0352169i
$291$		0			0
$292$	−14.3763	−	16.2596i	−0.841307	−	0.951519i
$293$	−9.37955	+	3.88514i	−0.547959	+	0.226972i	−0.639449	−	0.768834i	$-0.720837\pi$
$293$	−9.37955	+	3.88514i	−0.547959	+	0.226972i	0.0914893	+	0.995806i	$0.470837\pi$
$294$		0			0
$295$	−14.1541	+	14.1541i	−0.824084	+	0.824084i
$296$	4.62861	+	14.9311i	0.269033	+	0.867853i
$297$		0			0
$298$	−29.7337	+	11.2598i	−1.72243	+	0.652264i
$299$	−5.40045	−	13.0378i	−0.312316	−	0.753997i
$300$		0			0
$301$	12.6058	+	5.22151i	0.726589	+	0.300963i
$302$	−5.57529	+	5.24308i	−0.320822	+	0.301705i
$303$		0			0
$304$	−2.13525	−	1.20982i	−0.122465	−	0.0693879i
$305$			23.2242i			1.32982i
$306$		0			0
$307$	−13.7186	−	5.68242i	−0.782961	−	0.324313i	−0.0448512	−	0.998994i	$-0.514281\pi$
$307$	−13.7186	−	5.68242i	−0.782961	−	0.324313i	−0.738110	+	0.674681i	$0.764281\pi$
$308$	2.92626	+	1.42836i	0.166739	+	0.0813881i
$309$		0			0
$310$	10.6929	+	28.2367i	0.607317	+	1.60374i
$311$	4.16715	+	4.16715i	0.236297	+	0.236297i	0.815315	−	0.579018i	$-0.196564\pi$
$311$	4.16715	+	4.16715i	0.236297	+	0.236297i	−0.579018	+	0.815315i	$0.696564\pi$
$312$		0			0
$313$	−11.6442	+	11.6442i	−0.658172	+	0.658172i	−0.954947	−	0.296776i	$-0.904089\pi$
$313$	−11.6442	+	11.6442i	−0.658172	+	0.658172i	0.296776	+	0.954947i	$0.404089\pi$
$314$	−20.3915	−	9.18950i	−1.15076	−	0.518593i
$315$		0			0
$316$	1.34568	−	21.8901i	0.0757002	−	1.23141i
$317$	0.906521	−	2.18853i	0.0509153	−	0.122920i	−0.896375	−	0.443296i	$-0.853809\pi$
$317$	0.906521	−	2.18853i	0.0509153	−	0.122920i	0.947291	+	0.320376i	$0.103809\pi$
$318$		0			0
$319$	3.53829			0.198106
$320$	22.7447	−	4.81241i	1.27147	−	0.269022i
$321$		0			0
$322$	0.593606	−	19.3306i	0.0330804	−	1.07725i
$323$	1.45729	−	3.51821i	0.0810857	−	0.195758i
$324$		0			0
$325$	−7.18532	+	2.97626i	−0.398570	+	0.165093i
$326$	5.09793	+	2.29740i	0.282348	+	0.127241i
$327$		0			0
$328$	−14.9851	+	12.4512i	−0.827413	+	0.687500i
$329$	−10.9114	−	10.9114i	−0.601565	−	0.601565i
$330$		0			0
$331$	7.68076	+	18.5430i	0.422173	+	1.01922i	0.981705	+	0.190407i	$0.0609807\pi$
$331$	7.68076	+	18.5430i	0.422173	+	1.01922i	−0.559533	+	0.828808i	$0.689019\pi$
$332$	24.2531	+	11.8384i	1.33106	+	0.649714i
$333$		0			0
$334$	−12.5492	−	13.3444i	−0.686664	−	0.730172i
$335$		−	27.2249i		−	1.48745i
$336$		0			0
$337$			31.4978i			1.71580i	0.513820	+	0.857898i	$0.328230\pi$
$337$			31.4978i			1.71580i	−0.513820	+	0.857898i	$0.671770\pi$
$338$	−8.14236	+	7.65719i	−0.442886	+	0.416496i
$339$		0			0
$340$	11.7339	+	34.1121i	0.636359	+	1.84999i
$341$	−2.09240	−	5.05151i	−0.113310	−	0.273554i
$342$		0			0
$343$	14.2534	+	14.2534i	0.769614	+	0.769614i
$344$	−16.8499	+	5.22342i	−0.908483	+	0.281628i
$345$		0			0
$346$	11.1316	−	24.7010i	0.598438	−	1.32793i
$347$	11.6297	−	4.81720i	0.624317	−	0.258601i	−0.0480193	−	0.998846i	$-0.515291\pi$
$347$	11.6297	−	4.81720i	0.624317	−	0.258601i	0.672336	+	0.740246i	$0.265291\pi$
$348$		0			0
$349$	3.03378	−	7.32419i	0.162395	−	0.392055i	−0.821646	−	0.569998i	$-0.806944\pi$
$349$	3.03378	−	7.32419i	0.162395	−	0.392055i	0.984041	+	0.177943i	$0.0569441\pi$
$350$	−10.6533	−	0.327144i	−0.569445	−	0.0174866i
$351$		0			0
$352$	−4.09013	+	0.997484i	−0.218005	+	0.0531661i
$353$	0.844854			0.0449670			0.0224835	−	0.999747i	$-0.492843\pi$
$353$	0.844854			0.0449670			0.0224835	+	0.999747i	$0.492843\pi$
$354$		0			0
$355$	6.92409	−	16.7162i	0.367492	−	0.887205i
$356$	20.0447	−	17.7230i	1.06237	−	0.939317i
$357$		0			0
$358$	−0.775527	+	1.72089i	−0.0409879	+	0.0909520i
$359$	9.29970	−	9.29970i	0.490819	−	0.490819i	−0.417745	−	0.908564i	$-0.637179\pi$
$359$	9.29970	−	9.29970i	0.490819	−	0.490819i	0.908564	+	0.417745i	$0.137179\pi$
$360$		0			0
$361$	−13.1688	−	13.1688i	−0.693097	−	0.693097i
$362$	30.2918	−	11.4712i	1.59210	−	0.602911i
$363$		0			0
$364$	9.34035	−	3.21290i	0.489567	−	0.168402i
$365$	−29.1353	−	12.0682i	−1.52501	−	0.631681i
$366$		0			0
$367$		−	18.5025i		−	0.965823i	−0.875669	−	0.482912i	$-0.839579\pi$
$367$		−	18.5025i		−	0.965823i	0.875669	−	0.482912i	$-0.160421\pi$
$368$	15.3819	+	19.7132i	0.801838	+	1.02762i
$369$		0			0
$370$	15.5605	+	16.5464i	0.808951	+	0.860207i
$371$	−7.11448	−	2.94692i	−0.369366	−	0.152996i
$372$		0			0
$373$	14.3153	+	34.5603i	0.741220	+	1.78946i	0.600845	+	0.799365i	$0.294831\pi$
$373$	14.3153	+	34.5603i	0.741220	+	1.78946i	0.140375	+	0.990098i	$0.455169\pi$
$374$	−2.31348	−	6.10918i	−0.119627	−	0.315898i
$375$		0			0
$376$	19.8662	+	1.83478i	1.02452	+	0.0946215i
$377$	7.58938	−	7.58938i	0.390873	−	0.390873i
$378$		0			0
$379$	2.63258	−	1.09045i	0.135226	−	0.0560126i	−0.314044	−	0.949408i	$-0.601684\pi$
$379$	2.63258	−	1.09045i	0.135226	−	0.0560126i	0.449270	+	0.893396i	$0.351684\pi$
$380$	−3.55924	−	0.218801i	−0.182585	−	0.0112243i
$381$		0			0
$382$	0.289645	−	9.43219i	0.0148195	−	0.482593i
$383$	31.3865			1.60378			0.801888	−	0.597474i	$-0.203829\pi$
$383$	31.3865			1.60378			0.801888	+	0.597474i	$0.203829\pi$
$384$		0			0
$385$	4.73139			0.241134
$386$	−0.200496	+	6.52908i	−0.0102050	+	0.332321i
$387$		0			0
$388$	27.2069	+	1.67252i	1.38122	+	0.0849094i
$389$	5.95656	−	2.46729i	0.302009	−	0.125096i	−0.226533	−	0.974004i	$-0.572739\pi$
$389$	5.95656	−	2.46729i	0.302009	−	0.125096i	0.528542	+	0.848907i	$0.322739\pi$
$390$		0			0
$391$	−27.4347	+	27.4347i	−1.38743	+	1.38743i
$392$	−6.23595	−	0.575932i	−0.314963	−	0.0290890i
$393$		0			0
$394$	1.09723	+	2.89745i	0.0552776	+	0.145971i
$395$	−12.1949	−	29.4410i	−0.613591	−	1.48134i
$396$		0			0
$397$	22.5721	+	9.34967i	1.13286	+	0.469246i	0.868752	−	0.495247i	$-0.164922\pi$
$397$	22.5721	+	9.34967i	1.13286	+	0.469246i	0.264109	+	0.964493i	$0.414922\pi$
$398$	10.0443	+	10.6807i	0.503473	+	0.535374i
$399$		0			0
$400$	10.8642	−	8.47717i	0.543209	−	0.423859i
$401$			13.5924i			0.678770i	0.940648	+	0.339385i	$0.110219\pi$
$401$			13.5924i			0.678770i	−0.940648	+	0.339385i	$0.889781\pi$
$402$		0			0
$403$	−15.3232	−	6.34708i	−0.763303	−	0.316170i
$404$	11.5533	−	3.97411i	0.574798	−	0.197719i
$405$		0			0
$406$	13.7556	−	5.20911i	0.682681	−	0.258524i
$407$	−2.90847	−	2.90847i	−0.144167	−	0.144167i
$408$		0			0
$409$	19.8362	−	19.8362i	0.980835	−	0.980835i	−0.0189849	−	0.999820i	$-0.506043\pi$
$409$	19.8362	−	19.8362i	0.980835	−	0.980835i	0.999820	+	0.0189849i	$0.00604344\pi$
$410$	−11.6311	+	25.8093i	−0.574417	+	1.27463i
$411$		0			0
$412$	24.5315	−	21.6901i	1.20858	−	1.06859i
$413$	5.76656	−	13.9217i	0.283754	−	0.685042i
$414$		0			0
$415$	39.2143			1.92495
$416$	−6.63351	+	10.9126i	−0.325235	+	0.535034i
$417$		0			0
$418$	0.645451	+	0.0198206i	0.0315700	+	0.000969457i
$419$	−3.11401	+	7.51789i	−0.152129	+	0.367273i	−0.981510	−	0.191411i	$-0.938694\pi$
$419$	−3.11401	+	7.51789i	−0.152129	+	0.367273i	0.829381	+	0.558684i	$0.188694\pi$
$420$		0			0
$421$	4.27411	−	1.77039i	0.208307	−	0.0862837i	−0.276090	−	0.961132i	$-0.589039\pi$
$421$	4.27411	−	1.77039i	0.208307	−	0.0862837i	0.484398	+	0.874848i	$0.339039\pi$
$422$	8.94759	−	19.8547i	0.435562	−	0.966511i
$423$		0			0
$424$	9.50971	−	2.94799i	0.461833	−	0.143167i
$425$	15.1196	+	15.1196i	0.733408	+	0.733408i
$426$		0			0
$427$	−6.69054	−	16.1524i	−0.323778	−	0.781669i
$428$	−7.91169	−	23.0004i	−0.382426	−	1.11177i
$429$		0			0
$430$	−18.6727	+	17.5601i	−0.900479	+	0.846823i
$431$		−	16.2399i		−	0.782250i	−0.920338	−	0.391125i	$-0.872086\pi$
$431$		−	16.2399i		−	0.782250i	0.920338	−	0.391125i	$-0.127914\pi$
$432$		0			0
$433$		−	26.9220i		−	1.29379i	−0.762580	−	0.646893i	$-0.776068\pi$
$433$		−	26.9220i		−	1.29379i	0.762580	−	0.646893i	$-0.223932\pi$
$434$	−15.5714	−	16.5581i	−0.747453	−	0.794813i
$435$		0			0
$436$	−3.07423	−	1.50058i	−0.147229	−	0.0718649i
$437$	−1.46771	−	3.54336i	−0.0702099	−	0.169502i
$438$		0			0
$439$	−4.24243	−	4.24243i	−0.202480	−	0.202480i	0.598582	−	0.801062i	$-0.295731\pi$
$439$	−4.24243	−	4.24243i	−0.202480	−	0.202480i	−0.801062	+	0.598582i	$0.795731\pi$
$440$	−4.70499	+	3.90939i	−0.224302	+	0.186373i
$441$		0			0
$442$	−18.0660	−	8.14153i	−0.859313	−	0.387253i
$443$	−18.9940	+	7.86757i	−0.902432	+	0.373800i	−0.785155	−	0.619299i	$-0.787417\pi$
$443$	−18.9940	+	7.86757i	−0.902432	+	0.373800i	−0.117278	+	0.993099i	$0.537417\pi$
$444$		0			0
$445$	14.8777	−	35.9179i	0.705271	−	1.70267i
$446$	−1.06498	+	34.6806i	−0.0504281	+	1.64218i
$447$		0			0
$448$	−14.4325	+	9.89942i	−0.681872	+	0.467703i
$449$	17.6500			0.832955			0.416478	−	0.909146i	$-0.363264\pi$
$449$	17.6500			0.832955			0.416478	+	0.909146i	$0.363264\pi$
$450$		0			0
$451$	1.96181	−	4.73622i	0.0923779	−	0.223020i
$452$	−1.40414	+	22.8412i	−0.0660454	+	1.07436i
$453$		0			0
$454$	18.2708	+	8.23379i	0.857490	+	0.386431i
$455$	10.1485	−	10.1485i	0.475770	−	0.475770i
$456$		0			0
$457$	26.8486	+	26.8486i	1.25593	+	1.25593i	0.953021	+	0.302904i	$0.0979561\pi$
$457$	26.8486	+	26.8486i	1.25593	+	1.25593i	0.302904	+	0.953021i	$0.402044\pi$
$458$	8.87353	+	23.4323i	0.414633	+	1.09492i
$459$		0			0
$460$	32.6497	+	15.9369i	1.52230	+	0.743061i
$461$	−16.8536	−	6.98098i	−0.784949	−	0.325137i	−0.0460383	−	0.998940i	$-0.514660\pi$
$461$	−16.8536	−	6.98098i	−0.784949	−	0.325137i	−0.738911	+	0.673803i	$0.764660\pi$
$462$		0			0
$463$		−	10.6733i		−	0.496032i	−0.968756	−	0.248016i	$-0.920221\pi$
$463$		−	10.6733i		−	0.496032i	0.968756	−	0.248016i	$-0.0797786\pi$
$464$	−9.37477	+	16.5459i	−0.435213	+	0.768123i
$465$		0			0
$466$	15.6192	−	14.6885i	0.723546	−	0.680433i
$467$	−9.60844	−	3.97995i	−0.444626	−	0.184170i	0.149126	−	0.988818i	$-0.452354\pi$
$467$	−9.60844	−	3.97995i	−0.444626	−	0.184170i	−0.593752	+	0.804648i	$0.702354\pi$
$468$		0			0
$469$	7.84305	+	18.9348i	0.362158	+	0.874328i
$470$	27.1101	−	10.2663i	1.25049	−	0.473548i
$471$		0			0
$472$	5.76866	+	18.6087i	0.265524	+	0.856536i
$473$	3.28223	−	3.28223i	0.150917	−	0.150917i
$474$		0			0
$475$	−1.95279	+	0.808871i	−0.0896001	+	0.0371136i
$476$	−17.9880	−	20.3445i	−0.824479	−	0.932488i
$477$		0			0
$478$	−23.8730	−	0.733094i	−1.09192	−	0.0335309i
$479$	−40.8303			−1.86559			−0.932793	−	0.360414i	$-0.882636\pi$
$479$	−40.8303			−1.86559			−0.932793	+	0.360414i	$0.882636\pi$
$480$		0			0
$481$	−12.4769			−0.568899
$482$	−43.0109	−	1.32078i	−1.95909	−	0.0601600i
$483$		0			0
$484$	−15.6517	+	13.8388i	−0.711439	+	0.629035i
$485$	36.5918	−	15.1568i	1.66155	−	0.688236i
$486$		0			0
$487$	19.7323	−	19.7323i	0.894154	−	0.894154i	−0.100757	−	0.994911i	$-0.532127\pi$
$487$	19.7323	−	19.7323i	0.894154	−	0.894154i	0.994911	+	0.100757i	$0.0321265\pi$
$488$	19.9994	+	10.5341i	0.905329	+	0.476855i
$489$		0			0
$490$	−8.50977	+	3.22255i	−0.384432	+	0.145580i
$491$	1.14776	+	2.77093i	0.0517976	+	0.125050i	0.947660	−	0.319281i	$-0.103441\pi$
$491$	1.14776	+	2.77093i	0.0517976	+	0.125050i	−0.895863	+	0.444331i	$0.853441\pi$
$492$		0			0
$493$	−27.2622	−	11.2924i	−1.22783	−	0.508583i
$494$	1.42696	−	1.34193i	0.0642020	−	0.0603765i
$495$		0			0
$496$	29.1659	+	3.59951i	1.30959	+	0.161623i
$497$			13.6208i			0.610976i
$498$		0			0
$499$	16.5637	+	6.86089i	0.741491	+	0.307136i	0.721264	−	0.692660i	$-0.243561\pi$
$499$	16.5637	+	6.86089i	0.741491	+	0.307136i	0.0202265	+	0.999795i	$0.493561\pi$
$500$	−3.96431	+	8.12164i	−0.177289	+	0.363211i
$501$		0			0
$502$	2.79993	+	7.39376i	0.124967	+	0.330000i
$503$	−14.5527	−	14.5527i	−0.648872	−	0.648872i	0.303849	−	0.952720i	$-0.401728\pi$
$503$	−14.5527	−	14.5527i	−0.648872	−	0.648872i	−0.952720	+	0.303849i	$0.901728\pi$
$504$		0			0
$505$	12.5529	−	12.5529i	0.558598	−	0.558598i
$506$	−5.99829	−	2.70315i	−0.266657	−	0.120170i
$507$		0			0
$508$	−26.3514	−	1.61993i	−1.16915	−	0.0718728i
$509$	2.69930	−	6.51668i	0.119644	−	0.288847i	−0.852699	−	0.522402i	$-0.825036\pi$
$509$	2.69930	−	6.51668i	0.119644	−	0.288847i	0.972343	+	0.233555i	$0.0750360\pi$
$510$		0			0
$511$	23.7402			1.05020
$512$	6.17241	−	21.7693i	0.272785	−	0.962075i
$513$		0			0
$514$	−0.191946	+	6.25065i	−0.00846637	+	0.275704i
$515$	18.2079	−	43.9577i	0.802335	−	1.93701i
$516$		0			0
$517$	−4.84995	+	2.00892i	−0.213301	+	0.0883521i
$518$	−15.5890	−	7.02525i	−0.684942	−	0.308672i
$519$		0			0
$520$	−1.70650	+	18.4773i	−0.0748349	+	0.810281i
$521$	−19.8528	−	19.8528i	−0.869769	−	0.869769i	0.122678	−	0.992447i	$-0.460852\pi$
$521$	−19.8528	−	19.8528i	−0.869769	−	0.869769i	−0.992447	+	0.122678i	$0.960852\pi$
$522$		0			0
$523$	13.5479	+	32.7076i	0.592410	+	1.43021i	0.881168	+	0.472803i	$0.156758\pi$
$523$	13.5479	+	32.7076i	0.592410	+	1.43021i	−0.288758	+	0.957402i	$0.593242\pi$
$524$	11.9351	−	24.4512i	0.521386	−	1.06816i
$525$		0			0
$526$	−17.5877	−	18.7021i	−0.766862	−	0.815452i
$527$			45.5993i			1.98634i
$528$		0			0
$529$			16.0758i			0.698949i
$530$	10.5385	−	9.91056i	0.457764	−	0.430487i
$531$		0			0
$532$	2.53847	−	0.873185i	0.110057	−	0.0378574i
$533$	−5.95093	−	14.3668i	−0.257763	−	0.622296i
$534$		0			0
$535$	−24.9905	−	24.9905i	−1.08043	−	1.08043i
$536$	−23.4445	−	12.3487i	−1.01265	−	0.533382i
$537$		0			0
$538$	−12.8259	+	28.4606i	−0.552963	+	1.22702i
$539$	1.52239	−	0.630593i	0.0655739	−	0.0271616i
$540$		0			0
$541$	2.60015	−	6.27731i	0.111789	−	0.269883i	−0.858077	−	0.513521i	$-0.828341\pi$
$541$	2.60015	−	6.27731i	0.111789	−	0.269883i	0.969866	+	0.243638i	$0.0783409\pi$
$542$	−0.840508	−	0.0258104i	−0.0361029	−	0.00110865i
$543$		0			0
$544$	34.6976	+	5.36804i	1.48765	+	0.230153i
$545$	−4.97064			−0.212919
$546$		0			0
$547$	15.2999	−	36.9371i	0.654175	−	1.57932i	−0.152487	−	0.988305i	$-0.548728\pi$
$547$	15.2999	−	36.9371i	0.654175	−	1.57932i	0.806662	−	0.591013i	$-0.201272\pi$
$548$	−14.0220	−	15.8589i	−0.598988	−	0.677456i
$549$		0			0
$550$	−1.48974	+	3.30574i	−0.0635229	+	0.140957i
$551$	2.06260	−	2.06260i	0.0878699	−	0.0878699i
$552$		0			0
$553$	16.9630	+	16.9630i	0.721340	+	0.721340i
$554$	1.84827	−	0.699920i	0.0785256	−	0.0297368i
$555$		0			0
$556$	−5.59919	−	16.2777i	−0.237459	−	0.690326i
$557$	−20.6271	−	8.54402i	−0.873998	−	0.362022i	−0.0998320	−	0.995004i	$-0.531831\pi$
$557$	−20.6271	−	8.54402i	−0.873998	−	0.362022i	−0.774166	+	0.632982i	$0.781831\pi$
$558$		0			0
$559$		−	14.0803i		−	0.595533i
$560$	−12.5359	+	22.1251i	−0.529740	+	0.934957i
$561$		0			0
$562$	−17.7194	−	18.8422i	−0.747450	−	0.794809i
$563$	27.4646	+	11.3762i	1.15749	+	0.479450i	0.877040	−	0.480418i	$-0.159515\pi$
$563$	27.4646	+	11.3762i	1.15749	+	0.479450i	0.280454	+	0.959867i	$0.409515\pi$
$564$		0			0
$565$	12.7247	+	30.7202i	0.535333	+	1.29241i
$566$	−5.42488	−	14.3254i	−0.228025	−	0.602143i
$567$		0			0
$568$	−11.2544	−	13.5448i	−0.472224	−	0.568326i
$569$	22.5116	−	22.5116i	0.943737	−	0.943737i	−0.0547629	−	0.998499i	$-0.517440\pi$
$569$	22.5116	−	22.5116i	0.943737	−	0.943737i	0.998499	+	0.0547629i	$0.0174403\pi$
$570$		0			0
$571$	3.49351	−	1.44706i	0.146199	−	0.0605576i	−0.308384	−	0.951262i	$-0.599788\pi$
$571$	3.49351	−	1.44706i	0.146199	−	0.0605576i	0.454583	+	0.890704i	$0.349788\pi$
$572$	0.206181	−	3.35393i	0.00862084	−	0.140235i
$573$		0			0
$574$	0.654114	−	21.3010i	0.0273022	−	0.889087i
$575$	21.5352			0.898079
$576$		0			0
$577$	12.1286			0.504919			0.252460	−	0.967607i	$-0.418761\pi$
$577$	12.1286			0.504919			0.252460	+	0.967607i	$0.418761\pi$
$578$	−0.934261	+	30.4239i	−0.0388601	+	1.26547i
$579$		0			0
$580$	−1.69547	+	27.5802i	−0.0704006	+	1.14521i
$581$	−27.2734	+	11.2970i	−1.13149	+	0.468679i
$582$		0			0
$583$	−1.85242	+	1.85242i	−0.0767195	+	0.0767195i
$584$	−23.6077	+	19.6157i	−0.976894	+	0.811705i
$585$		0			0
$586$	5.08468	+	13.4271i	0.210046	+	0.554668i
$587$	13.2562	+	32.0032i	0.547140	+	1.32091i	0.919597	+	0.392864i	$0.128516\pi$
$587$	13.2562	+	32.0032i	0.547140	+	1.32091i	−0.372456	+	0.928050i	$0.621484\pi$
$588$		0			0
$589$	−4.16446	−	1.72498i	−0.171594	−	0.0710764i
$590$	19.3931	+	20.6219i	0.798401	+	0.848990i
$591$		0			0
$592$	21.3068	−	5.89464i	0.875702	−	0.242268i
$593$		−	17.1199i		−	0.703031i	−0.936182	−	0.351516i	$-0.885666\pi$
$593$		−	17.1199i		−	0.703031i	0.936182	−	0.351516i	$-0.114334\pi$
$594$		0			0
$595$	−36.4550	−	15.1002i	−1.49451	−	0.619047i
$596$	14.6256	+	42.5188i	0.599089	+	1.74164i
$597$		0			0
$598$	−18.6640	+	7.06785i	−0.763228	+	0.289026i
$599$	22.3994	+	22.3994i	0.915215	+	0.915215i	0.996676	−	0.0814616i	$-0.0259588\pi$
$599$	22.3994	+	22.3994i	0.915215	+	0.915215i	−0.0814616	+	0.996676i	$0.525959\pi$
$600$		0			0
$601$	−5.12504	+	5.12504i	−0.209055	+	0.209055i	−0.803866	−	0.594811i	$-0.797227\pi$
$601$	−5.12504	+	5.12504i	−0.209055	+	0.209055i	0.594811	+	0.803866i	$0.297227\pi$
$602$	7.92804	−	17.5923i	0.323123	−	0.717009i
$603$		0			0
$604$	7.16933	+	8.10853i	0.291716	+	0.329931i
$605$	−11.6170	+	28.0460i	−0.472300	+	1.14023i
$606$		0			0
$607$	1.69963			0.0689858			0.0344929	−	0.999405i	$-0.489018\pi$
$607$	1.69963			0.0689858			0.0344929	+	0.999405i	$0.489018\pi$
$608$	−1.80282	+	2.96577i	−0.0731141	+	0.120278i
$609$		0			0
$610$	32.8286	+	1.00810i	1.32919	+	0.0408169i
$611$	−6.09383	+	14.7118i	−0.246530	+	0.595176i
$612$		0			0
$613$	−33.4008	+	13.8351i	−1.34905	+	0.558793i	−0.936027	−	0.351929i	$-0.885526\pi$
$613$	−33.4008	+	13.8351i	−1.34905	+	0.558793i	−0.413019	+	0.910722i	$0.635526\pi$
$614$	−8.62786	+	19.1452i	−0.348192	+	0.772638i
$615$		0			0
$616$	2.14607	−	4.07440i	0.0864676	−	0.164162i
$617$	14.3469	+	14.3469i	0.577585	+	0.577585i	0.934237	−	0.356652i	$-0.116082\pi$
$617$	14.3469	+	14.3469i	0.577585	+	0.577585i	−0.356652	+	0.934237i	$0.616082\pi$
$618$		0			0
$619$	10.5891	+	25.5644i	0.425613	+	1.02752i	0.980663	+	0.195704i	$0.0626993\pi$
$619$	10.5891	+	25.5644i	0.425613	+	1.02752i	−0.555049	+	0.831817i	$0.687301\pi$
$620$	40.3781	−	13.8893i	1.62162	−	0.557806i
$621$		0			0
$622$	6.07134	−	5.70957i	0.243439	−	0.228933i
$623$			29.2668i			1.17255i
$624$		0			0
$625$			30.3569i			1.21428i
$626$	15.9542	+	16.9651i	0.637660	+	0.678063i
$627$		0			0
$628$	−13.8749	+	28.4254i	−0.553670	+	1.13430i
$629$	13.1272	+	31.6919i	0.523416	+	1.26364i
$630$		0			0
$631$	2.22063	+	2.22063i	0.0884019	+	0.0884019i	0.749925	−	0.661523i	$-0.230090\pi$
$631$	2.22063	+	2.22063i	0.0884019	+	0.0884019i	−0.661523	+	0.749925i	$0.730090\pi$
$632$	−30.8843	−	2.85237i	−1.22851	−	0.113461i
$633$		0			0
$634$	−3.05425	−	1.37641i	−0.121300	−	0.0546642i
$635$	−35.4412	+	14.6802i	−1.40644	+	0.582567i
$636$		0			0
$637$	1.91284	−	4.61800i	0.0757894	−	0.182972i
$638$	0.153588	−	5.00153i	0.00608060	−	0.198013i
$639$		0			0
$640$	−5.81528	−	32.3597i	−0.229869	−	1.27913i
$641$	−20.8946			−0.825288			−0.412644	−	0.910892i	$-0.635395\pi$
$641$	−20.8946			−0.825288			−0.412644	+	0.910892i	$0.635395\pi$
$642$		0			0
$643$	13.0644	−	31.5403i	0.515210	−	1.24383i	−0.425606	−	0.904908i	$-0.639939\pi$
$643$	13.0644	−	31.5403i	0.515210	−	1.24383i	0.940816	−	0.338918i	$-0.110061\pi$
$644$	−27.2989	−	1.67818i	−1.07573	−	0.0661296i
$645$		0			0
$646$	−4.90989	−	2.21266i	−0.193177	−	0.0870560i
$647$	12.1360	−	12.1360i	0.477115	−	0.477115i	−0.427093	−	0.904208i	$-0.640462\pi$
$647$	12.1360	−	12.1360i	0.477115	−	0.477115i	0.904208	+	0.427093i	$0.140462\pi$
$648$		0			0
$649$	−3.62484	−	3.62484i	−0.142287	−	0.142287i
$650$	3.89518	+	10.2860i	0.152782	+	0.403449i
$651$		0			0
$652$	3.46877	−	7.10644i	0.135848	−	0.278310i
$653$	−11.0172	−	4.56347i	−0.431136	−	0.178582i	0.156553	−	0.987670i	$-0.449962\pi$
$653$	−11.0172	−	4.56347i	−0.431136	−	0.178582i	−0.587688	+	0.809087i	$0.699962\pi$
$654$		0			0
$655$		−	39.5346i		−	1.54474i
$656$	16.9498	+	21.7226i	0.661780	+	0.848125i
$657$		0			0
$658$	−15.8974	+	14.9501i	−0.619746	+	0.582817i
$659$	−11.9865	−	4.96498i	−0.466929	−	0.193408i	0.136799	−	0.990599i	$-0.456319\pi$
$659$	−11.9865	−	4.96498i	−0.466929	−	0.193408i	−0.603728	+	0.797191i	$0.706319\pi$
$660$		0			0
$661$	−14.8437	−	35.8357i	−0.577351	−	1.39385i	−0.895182	−	0.445701i	$-0.852954\pi$
$661$	−14.8437	−	35.8357i	−0.577351	−	1.39385i	0.317830	−	0.948148i	$-0.397046\pi$
$662$	26.5448	−	10.0522i	1.03169	−	0.390690i
$663$		0			0
$664$	17.7868	−	33.7690i	0.690263	−	1.31049i
$665$	2.75811	−	2.75811i	0.106955	−	0.106955i
$666$		0			0
$667$	−27.4571	+	11.3731i	−1.06314	+	0.440369i
$668$	−19.4077	+	17.1597i	−0.750905	+	0.663929i
$669$		0			0
$670$	−38.4836	−	1.18176i	−1.48675	−	0.0456554i
$671$	−5.94769			−0.229608
$672$		0			0
$673$	−31.4578			−1.21261			−0.606305	−	0.795232i	$-0.707349\pi$
$673$	−31.4578			−1.21261			−0.606305	+	0.795232i	$0.707349\pi$
$674$	44.5237	+	1.36724i	1.71499	+	0.0526641i
$675$		0			0
$676$	10.4704	+	11.8420i	0.402706	+	0.455461i
$677$	32.9576	−	13.6515i	1.26666	−	0.524669i	0.354714	−	0.934975i	$-0.384578\pi$
$677$	32.9576	−	13.6515i	1.26666	−	0.524669i	0.911948	+	0.410306i	$0.134578\pi$
$678$		0			0
$679$	−21.0830	+	21.0830i	−0.809093	+	0.809093i
$680$	48.7283	−	15.1057i	1.86865	−	0.579276i
$681$		0			0
$682$	−7.23137	+	2.73844i	−0.276903	+	0.104860i
$683$	4.23976	+	10.2357i	0.162230	+	0.391657i	0.984002	−	0.178159i	$-0.0570142\pi$
$683$	4.23976	+	10.2357i	0.162230	+	0.391657i	−0.821772	+	0.569817i	$0.807014\pi$
$684$		0			0
$685$	−28.4173	−	11.7708i	−1.08577	−	0.449740i
$686$	20.7666	−	19.5292i	0.792873	−	0.745629i
$687$		0			0
$688$	6.65214	+	24.0448i	0.253610	+	0.916699i
$689$			7.94664i			0.302743i
$690$		0			0
$691$	−8.64837	−	3.58227i	−0.328999	−	0.136276i	0.212069	−	0.977255i	$-0.431980\pi$
$691$	−8.64837	−	3.58227i	−0.328999	−	0.136276i	−0.541068	+	0.840979i	$0.681980\pi$
$692$	−34.4328	−	16.8072i	−1.30894	−	0.638915i
$693$		0			0
$694$	−6.30452	−	16.6483i	−0.239316	−	0.631960i
$695$	−17.6861	−	17.6861i	−0.670871	−	0.670871i
$696$		0			0
$697$	−30.2311	+	30.2311i	−1.14509	+	1.14509i
$698$	−10.2214	−	4.60632i	−0.386886	−	0.174352i
$699$		0			0
$700$	−0.924867	+	15.0448i	−0.0349567	+	0.568640i
$701$	11.8422	−	28.5895i	0.447273	−	1.07981i	−0.526067	−	0.850443i	$-0.676334\pi$
$701$	11.8422	−	28.5895i	0.447273	−	1.07981i	0.973340	−	0.229369i	$-0.0736661\pi$
$702$		0			0
$703$	−3.39092			−0.127891
$704$	1.23245	+	5.82489i	0.0464497	+	0.219534i
$705$		0			0
$706$	0.0366729	−	1.19424i	0.00138020	−	0.0449459i
$707$	−5.11422	+	12.3468i	−0.192340	+	0.464350i
$708$		0			0
$709$	9.23855	−	3.82673i	0.346961	−	0.143716i	−0.202396	−	0.979304i	$-0.564873\pi$
$709$	9.23855	−	3.82673i	0.346961	−	0.143716i	0.549357	+	0.835588i	$0.314873\pi$
$710$	−23.3286	−	10.5131i	−0.875507	−	0.394551i
$711$		0			0
$712$	−24.1822	−	29.1035i	−0.906267	−	1.09070i
$713$	32.4741	+	32.4741i	1.21616	+	1.21616i
$714$		0			0
$715$	−1.86846	−	4.51086i	−0.0698765	−	0.168697i
$716$	2.39890	+	1.17094i	0.0896511	+	0.0437602i
$717$		0			0
$718$	−12.7419	−	13.5492i	−0.475523	−	0.505653i
$719$			45.6659i			1.70305i	0.524313	+	0.851526i	$0.324322\pi$
$719$			45.6659i			1.70305i	−0.524313	+	0.851526i	$0.675678\pi$
$720$		0			0
$721$			35.8179i			1.33393i
$722$	−19.1864	+	18.0432i	−0.714044	+	0.671497i
$723$		0			0
$724$	−14.9001	−	43.3168i	−0.553759	−	1.60986i
$725$	6.26786	+	15.1320i	0.232783	+	0.561987i
$726$		0			0
$727$	10.2015	+	10.2015i	0.378353	+	0.378353i	0.870508	−	0.492154i	$-0.163790\pi$
$727$	10.2015	+	10.2015i	0.378353	+	0.378353i	−0.492154	+	0.870508i	$0.663790\pi$
$728$	−4.13614	−	13.3425i	−0.153296	−	0.494506i
$729$		0			0
$730$	−18.3237	+	40.6603i	−0.678192	+	1.50491i
$731$	−35.7645	+	14.8141i	−1.32280	+	0.547920i
$732$		0			0
$733$	0.687226	−	1.65911i	0.0253833	−	0.0612806i	−0.910680	−	0.413113i	$-0.864441\pi$
$733$	0.687226	−	1.65911i	0.0253833	−	0.0612806i	0.936063	+	0.351833i	$0.114441\pi$
$734$	−26.1542	−	0.803146i	−0.965368	−	0.0296447i
$735$		0			0
$736$	28.5332	−	20.8874i	1.05175	−	0.769919i
$737$	6.97224			0.256826
$738$		0			0
$739$	−3.04573	+	7.35305i	−0.112039	+	0.270486i	−0.969947	−	0.243318i	$-0.921764\pi$
$739$	−3.04573	+	7.35305i	−0.112039	+	0.270486i	0.857908	+	0.513804i	$0.171764\pi$
$740$	24.0646	−	21.2772i	0.884632	−	0.782166i
$741$		0			0
$742$	−4.47442	+	9.92874i	−0.164261	+	0.364495i
$743$	−15.7888	+	15.7888i	−0.579237	+	0.579237i	−0.934693	−	0.355456i	$-0.884325\pi$
$743$	−15.7888	+	15.7888i	−0.579237	+	0.579237i	0.355456	+	0.934693i	$0.384325\pi$
$744$		0			0
$745$	46.1977	+	46.1977i	1.69255	+	1.69255i
$746$	49.4740	−	18.7352i	1.81137	−	0.685946i
$747$		0			0
$748$	−8.73604	+	3.00503i	−0.319421	+	0.109875i
$749$	24.5802	+	10.1814i	0.898141	+	0.372022i
$750$		0			0
$751$		−	21.2937i		−	0.777017i	−0.921445	−	0.388509i	$-0.872990\pi$
$751$		−	21.2937i		−	0.777017i	0.921445	−	0.388509i	$-0.127010\pi$
$752$	3.45589	−	28.0022i	0.126023	−	1.02114i
$753$		0			0
$754$	−10.3985	−	11.0574i	−0.378692	−	0.402686i
$755$	14.5296	+	6.01835i	0.528785	+	0.219030i
$756$		0			0
$757$	18.2134	+	43.9710i	0.661977	+	1.59815i	0.794701	+	0.607001i	$0.207628\pi$
$757$	18.2134	+	43.9710i	0.661977	+	1.59815i	−0.132724	+	0.991153i	$0.542372\pi$
$758$	−1.42713	−	3.76861i	−0.0518356	−	0.136882i
$759$		0			0
$760$	−0.463784	+	5.02165i	−0.0168232	+	0.182155i
$761$	6.20086	−	6.20086i	0.224781	−	0.224781i	−0.585727	−	0.810508i	$-0.699191\pi$
$761$	6.20086	−	6.20086i	0.224781	−	0.224781i	0.810508	+	0.585727i	$0.199191\pi$
$762$		0			0
$763$	3.45707	−	1.43196i	0.125154	−	0.0518406i
$764$	−13.3203	−	0.818854i	−0.481911	−	0.0296251i
$765$		0			0
$766$	1.36241	−	44.3663i	0.0492258	−	1.60302i
$767$	−15.5501			−0.561481
$768$		0			0
$769$	−28.5485			−1.02949			−0.514743	−	0.857344i	$-0.672113\pi$
$769$	−28.5485			−1.02949			−0.514743	+	0.857344i	$0.672113\pi$
$770$	0.205377	−	6.68805i	0.00740129	−	0.241021i
$771$		0			0
$772$	9.22045	+	0.566820i	0.331851	+	0.0204003i
$773$	−40.3910	+	16.7305i	−1.45276	+	0.601754i	−0.962855	−	0.270019i	$-0.912970\pi$
$773$	−40.3910	+	16.7305i	−1.45276	+	0.601754i	−0.489909	+	0.871774i	$0.662970\pi$
$774$		0			0
$775$	17.8969	−	17.8969i	0.642875	−	0.642875i
$776$	3.54517	−	38.3856i	0.127264	−	1.37796i
$777$		0			0
$778$	−3.22907	−	8.52697i	−0.115768	−	0.305707i
$779$	−1.61731	−	3.90454i	−0.0579462	−	0.139895i
$780$		0			0
$781$	4.28099	+	1.77325i	0.153186	+	0.0634517i
$782$	37.5893	+	39.9711i	1.34419	+	1.42936i
$783$		0			0
$784$	−1.08479	+	8.78981i	−0.0387426	+	0.313922i
$785$			45.9604i			1.64040i
$786$		0			0
$787$	−44.0309	−	18.2382i	−1.56953	−	0.650122i	−0.582820	−	0.812601i	$-0.698051\pi$
$787$	−44.0309	−	18.2382i	−1.56953	−	0.650122i	−0.986712	+	0.162480i	$0.948051\pi$
$788$	4.14330	−	1.42522i	0.147599	−	0.0507712i
$789$		0			0
$790$	−42.1456	+	15.9601i	−1.49947	+	0.567834i
$791$	−17.7000	−	17.7000i	−0.629340	−	0.629340i
$792$		0			0
$793$	−12.7574	+	12.7574i	−0.453028	+	0.453028i
$794$	14.1960	−	31.5009i	0.503797	−	1.11792i
$795$		0			0
$796$	15.5336	−	13.7344i	0.550575	−	0.486803i
$797$	0.560093	−	1.35218i	0.0198395	−	0.0478968i	−0.913649	−	0.406503i	$-0.866748\pi$
$797$	0.560093	−	1.35218i	0.0198395	−	0.0478968i	0.933489	+	0.358606i	$0.116748\pi$
$798$		0			0
$799$	43.7800			1.54882
$800$	−11.5113	−	15.7250i	−0.406986	−	0.555963i
$801$		0			0
$802$	19.2134	+	0.590009i	0.678450	+	0.0208339i
$803$	3.09066	−	7.46151i	0.109067	−	0.263311i
$804$		0			0
$805$	−36.7156	+	15.2081i	−1.29406	+	0.536016i
$806$	−9.63703	+	21.3846i	−0.339450	+	0.753239i
$807$		0			0
$808$	−5.11609	−	16.5036i	−0.179983	−	0.580596i
$809$	−7.68002	−	7.68002i	−0.270015	−	0.270015i	0.559091	−	0.829106i	$-0.311150\pi$
$809$	−7.68002	−	7.68002i	−0.270015	−	0.270015i	−0.829106	+	0.559091i	$0.811150\pi$
$810$		0			0
$811$	−14.0967	−	34.0323i	−0.495000	−	1.19504i	−0.952146	−	0.305645i	$-0.901128\pi$
$811$	−14.0967	−	34.0323i	−0.495000	−	1.19504i	0.457145	−	0.889392i	$-0.348872\pi$
$812$	−6.76622	−	19.6704i	−0.237448	−	0.690295i
$813$		0			0
$814$	−4.23751	+	3.98501i	−0.148525	+	0.139675i
$815$		−	11.4902i		−	0.402485i
$816$		0			0
$817$		−	3.82667i		−	0.133878i
$818$	−27.1783	−	28.9004i	−0.950267	−	1.01048i
$819$		0			0
$820$	35.9778	+	17.5614i	1.25640	+	0.613269i
$821$	−6.14697	−	14.8401i	−0.214531	−	0.517923i	0.779579	−	0.626304i	$-0.215433\pi$
$821$	−6.14697	−	14.8401i	−0.214531	−	0.517923i	−0.994109	+	0.108381i	$0.965433\pi$
$822$		0			0
$823$	−6.06767	−	6.06767i	−0.211506	−	0.211506i	0.593401	−	0.804907i	$-0.297785\pi$
$823$	−6.06767	−	6.06767i	−0.211506	−	0.211506i	−0.804907	+	0.593401i	$0.797785\pi$
$824$	−29.5951	−	35.6180i	−1.03099	−	1.24081i
$825$		0			0
$826$	−19.4287	−	8.75561i	−0.676010	−	0.304647i
$827$	−6.97158	+	2.88772i	−0.242426	+	0.100416i	−0.500588	−	0.865686i	$-0.666883\pi$
$827$	−6.97158	+	2.88772i	−0.242426	+	0.100416i	0.258163	+	0.966101i	$0.416883\pi$
$828$		0			0
$829$	−11.1779	+	26.9857i	−0.388223	+	0.937253i	0.602094	+	0.798425i	$0.294333\pi$
$829$	−11.1779	+	26.9857i	−0.388223	+	0.937253i	−0.990317	+	0.138827i	$0.955667\pi$
$830$	1.70219	−	55.4312i	0.0590838	−	1.92405i
$831$		0			0
$832$	15.1375	+	9.85047i	0.524799	+	0.341504i
$833$	−13.7424			−0.476146
$834$		0			0
$835$	−14.4048	+	34.7763i	−0.498500	+	1.20349i
$836$	0.0560347	−	0.911515i	0.00193800	−	0.0315254i
$837$		0			0
$838$	10.4917	+	4.72813i	0.362430	+	0.163331i
$839$	−7.81100	+	7.81100i	−0.269666	+	0.269666i	−0.828966	−	0.559300i	$-0.811070\pi$
$839$	−7.81100	+	7.81100i	−0.269666	+	0.269666i	0.559300	+	0.828966i	$0.311070\pi$
$840$		0			0
$841$	4.52319	+	4.52319i	0.155972	+	0.155972i
$842$	−2.31701	−	6.11850i	−0.0798494	−	0.210858i
$843$		0			0
$844$	−27.6771	−	13.5097i	−0.952686	−	0.465022i
$845$	21.2195	+	8.78942i	0.729974	+	0.302365i
$846$		0			0
$847$		−	22.8526i		−	0.785225i
$848$	−3.75433	−	13.5704i	−0.128924	−	0.466009i
$849$		0			0
$850$	22.0286	−	20.7160i	0.755573	−	0.710551i
$851$	31.9184	+	13.2210i	1.09415	+	0.453212i
$852$		0			0
$853$	3.44282	+	8.31171i	0.117880	+	0.284587i	0.971796	−	0.235824i	$-0.0757787\pi$
$853$	3.44282	+	8.31171i	0.117880	+	0.284587i	−0.853916	+	0.520411i	$0.825779\pi$
$854$	−23.1226	+	8.75626i	−0.791238	+	0.299633i
$855$		0			0
$856$	−32.8556	+	10.1852i	−1.12298	+	0.348122i
$857$	−26.7099	+	26.7099i	−0.912394	+	0.912394i	−0.996460	−	0.0840657i	$-0.973209\pi$
$857$	−26.7099	+	26.7099i	−0.912394	+	0.912394i	0.0840657	+	0.996460i	$0.473209\pi$
$858$		0			0
$859$	47.3381	−	19.6081i	1.61516	−	0.669020i	0.621702	−	0.783254i	$-0.286441\pi$
$859$	47.3381	−	19.6081i	1.61516	−	0.669020i	0.993454	+	0.114234i	$0.0364414\pi$
$860$	24.0115	+	27.1570i	0.818785	+	0.926047i
$861$		0			0
$862$	−22.9559	−	0.704933i	−0.781881	−	0.0240101i
$863$	37.2458			1.26786			0.633931	−	0.773390i	$-0.281440\pi$
$863$	37.2458			1.26786			0.633931	+	0.773390i	$0.281440\pi$
$864$		0			0
$865$	−55.6735			−1.89296
$866$	−38.0555	−	1.16861i	−1.29318	−	0.0397111i
$867$		0			0
$868$	−24.0815	+	21.2922i	−0.817380	+	0.722705i
$869$	7.53980	−	3.12309i	0.255770	−	0.105943i
$870$		0			0
$871$	14.9550	−	14.9550i	0.506730	−	0.506730i
$872$	−2.25459	+	4.28043i	−0.0763500	+	0.144954i
$873$		0			0
$874$	−5.07241	+	1.92086i	−0.171577	+	0.0649742i
$875$	−3.78303	−	9.13304i	−0.127890	−	0.308753i
$876$		0			0
$877$	3.39328	+	1.40554i	0.114583	+	0.0474618i	0.439238	−	0.898371i	$-0.355248\pi$
$877$	3.39328	+	1.40554i	0.114583	+	0.0474618i	−0.324655	+	0.945832i	$0.605248\pi$
$878$	−6.18102	+	5.81272i	−0.208599	+	0.196170i
$879$		0			0
$880$	5.32188	+	6.82042i	0.179401	+	0.229916i
$881$		−	25.8068i		−	0.869454i	−0.900562	−	0.434727i	$-0.856845\pi$
$881$		−	25.8068i		−	0.869454i	0.900562	−	0.434727i	$-0.143155\pi$
$882$		0			0
$883$	−45.1787	−	18.7136i	−1.52039	−	0.629764i	−0.542716	−	0.839916i	$-0.682604\pi$
$883$	−45.1787	−	18.7136i	−1.52039	−	0.629764i	−0.977669	+	0.210152i	$0.932604\pi$
$884$	−12.2926	+	25.1838i	−0.413446	+	0.847022i
$885$		0			0
$886$	10.2967	+	27.1904i	0.345925	+	0.913481i
$887$	−19.4975	−	19.4975i	−0.654662	−	0.654662i	0.299450	−	0.954112i	$-0.403197\pi$
$887$	−19.4975	−	19.4975i	−0.654662	−	0.654662i	−0.954112	+	0.299450i	$0.903197\pi$
$888$		0			0
$889$	20.4201	−	20.4201i	0.684868	−	0.684868i
$890$	−50.1259	−	22.5894i	−1.68022	−	0.757199i
$891$		0			0
$892$	48.9765	+	3.01079i	1.63985	+	0.100809i
$893$	−1.65615	+	3.99830i	−0.0554210	+	0.133798i
$894$		0			0
$895$	3.87872			0.129651
$896$	13.3668	+	20.8308i	0.446554	+	0.695907i
$897$		0			0
$898$	0.766141	−	24.9491i	0.0255665	−	0.832563i
$899$	−13.3667	+	32.2700i	−0.445803	+	1.07626i
$900$		0			0
$901$	20.1847	−	8.36079i	0.672451	−	0.278538i
$902$	−6.60971	−	2.97869i	−0.220079	−	0.0991796i
$903$		0			0
$904$	32.2262	+	2.97630i	1.07183	+	0.0989903i
$905$	−47.0648	−	47.0648i	−1.56449	−	1.56449i
$906$		0			0
$907$	−10.4059	−	25.1221i	−0.345522	−	0.834164i	−0.997137	−	0.0756143i	$-0.975908\pi$
$907$	−10.4059	−	25.1221i	−0.345522	−	0.834164i	0.651615	−	0.758550i	$-0.274092\pi$
$908$	12.4319	−	25.4692i	0.412569	−	0.845225i
$909$		0			0
$910$	−13.9049	−	14.7859i	−0.460943	−	0.490149i
$911$		−	41.3838i		−	1.37111i	−0.728023	−	0.685553i	$-0.759561\pi$
$911$		−	41.3838i		−	1.37111i	0.728023	−	0.685553i	$-0.240439\pi$
$912$		0			0
$913$			10.0427i			0.332365i
$914$	39.1172	−	36.7864i	1.29388	−	1.21678i
$915$		0			0
$916$	33.5078	−	11.5260i	1.10713	−	0.380830i
$917$	11.3893	+	27.4962i	0.376108	+	0.908004i
$918$		0			0
$919$	−12.6775	−	12.6775i	−0.418191	−	0.418191i	0.466389	−	0.884580i	$-0.345555\pi$
$919$	−12.6775	−	12.6775i	−0.418191	−	0.418191i	−0.884580	+	0.466389i	$0.845555\pi$
$920$	23.9448	−	45.4601i	0.789436	−	1.49878i
$921$		0			0
$922$	−10.5995	+	23.5203i	−0.349076	+	0.774600i
$923$	12.9859	−	5.37895i	0.427437	−	0.177050i
$924$		0			0
$925$	7.28629	−	17.5907i	0.239572	−	0.578377i
$926$	−15.0873	−	0.463302i	−0.495798	−	0.0152250i
$927$		0			0
$928$	22.9814	+	13.9699i	0.754402	+	0.458584i
$929$	−26.0458			−0.854536			−0.427268	−	0.904125i	$-0.640524\pi$
$929$	−26.0458			−0.854536			−0.427268	+	0.904125i	$0.640524\pi$
$930$		0			0
$931$	0.519861	−	1.25506i	0.0170378	−	0.0411328i
$932$	−20.0849	−	22.7161i	−0.657904	−	0.744091i
$933$		0			0
$934$	−6.04292	+	13.4092i	−0.197730	+	0.438763i
$935$	−9.49192	+	9.49192i	−0.310419	+	0.310419i
$936$		0			0
$937$	8.86842	+	8.86842i	0.289719	+	0.289719i	0.836969	−	0.547250i	$-0.184325\pi$
$937$	8.86842	+	8.86842i	0.289719	+	0.289719i	−0.547250	+	0.836969i	$0.684325\pi$
$938$	27.1057	−	10.2646i	0.885032	−	0.335152i
$939$		0			0
$940$	−13.3351	−	38.7670i	−0.434943	−	1.26444i
$941$	2.59847	+	1.07632i	0.0847079	+	0.0350871i	0.424635	−	0.905365i	$-0.360402\pi$
$941$	2.59847	+	1.07632i	0.0847079	+	0.0350871i	−0.339927	+	0.940452i	$0.610402\pi$
$942$		0			0
$943$			43.0589i			1.40219i
$944$	26.5547	−	7.34652i	0.864282	−	0.239109i
$945$		0			0
$946$	−4.49711	−	4.78205i	−0.146214	−	0.155478i
$947$	54.1420	+	22.4264i	1.75938	+	0.728759i	0.996627	+	0.0820687i	$0.0261527\pi$
$947$	54.1420	+	22.4264i	1.75938	+	0.728759i	0.762753	+	0.646690i	$0.223847\pi$
$948$		0			0
$949$	−9.37517	−	22.6337i	−0.304331	−	0.734720i
$950$	1.05861	+	2.79547i	0.0343459	+	0.0906970i
$951$		0			0
$952$	−29.5387	+	24.5438i	−0.957355	+	0.795470i
$953$	−16.3332	+	16.3332i	−0.529084	+	0.529084i	−0.920299	−	0.391215i	$-0.872055\pi$
$953$	−16.3332	+	16.3332i	−0.529084	+	0.529084i	0.391215	+	0.920299i	$0.372055\pi$
$954$		0			0
$955$	−17.9151	+	7.42067i	−0.579718	+	0.240127i
$956$	−2.07253	+	33.7137i	−0.0670303	+	1.09038i
$957$		0			0
$958$	−1.77234	+	57.7156i	−0.0572616	+	1.86471i
$959$	23.1551			0.747718
$960$		0			0
$961$	22.9754			0.741143
$962$	−0.541591	+	17.6367i	−0.0174616	+	0.568631i
$963$		0			0
$964$	−3.73398	+	60.7406i	−0.120263	+	1.95632i
$965$	12.4010	−	5.13667i	0.399203	−	0.165355i
$966$		0			0
$967$	−22.3067	+	22.3067i	−0.717336	+	0.717336i	−0.968059	−	0.250723i	$-0.919332\pi$
$967$	−22.3067	+	22.3067i	−0.717336	+	0.717336i	0.250723	+	0.968059i	$0.419332\pi$
$968$	18.8823	+	22.7251i	0.606901	+	0.730411i
$969$		0			0
$970$	−19.8365	−	52.3822i	−0.636912	−	1.68189i
$971$	−6.14798	−	14.8425i	−0.197298	−	0.476320i	0.794006	−	0.607910i	$-0.207992\pi$
$971$	−6.14798	−	14.8425i	−0.197298	−	0.476320i	−0.991304	+	0.131590i	$0.957992\pi$
$972$		0			0
$973$	17.3957	+	7.20553i	0.557680	+	0.230999i
$974$	−27.0359	−	28.7490i	−0.866288	−	0.921177i
$975$		0			0
$976$	15.7585	−	27.8128i	0.504418	−	0.890266i
$977$		−	24.8029i		−	0.793515i	−0.917923	−	0.396758i	$-0.870135\pi$
$977$		−	24.8029i		−	0.793515i	0.917923	−	0.396758i	$-0.129865\pi$
$978$		0			0
$979$	9.19852	+	3.81015i	0.293986	+	0.121773i
$980$	4.18585	+	12.1689i	0.133712	+	0.388720i
$981$		0			0
$982$	3.96666	−	1.50213i	0.126581	−	0.0479349i
$983$	28.9376	+	28.9376i	0.922966	+	0.922966i	0.997238	−	0.0742719i	$-0.0236633\pi$
$983$	28.9376	+	28.9376i	0.922966	+	0.922966i	−0.0742719	+	0.997238i	$0.523663\pi$
$984$		0			0
$985$	4.50180	−	4.50180i	0.143439	−	0.143439i
$986$	−17.1457	+	38.0463i	−0.546030	+	1.21164i
$987$		0			0
$988$	−1.83495	−	2.07533i	−0.0583774	−	0.0660250i
$989$	−14.9200	+	36.0201i	−0.474429	+	1.14537i
$990$		0			0
$991$	33.5852			1.06687			0.533434	−	0.845841i	$-0.320901\pi$
$991$	33.5852			1.06687			0.533434	+	0.845841i	$0.320901\pi$
$992$	6.35409	−	41.0711i	0.201743	−	1.30401i
$993$		0			0
$994$	19.2536	+	0.591243i	0.610688	+	0.0187531i
$995$	11.5294	−	27.8346i	0.365508	−	0.882415i
$996$		0			0
$997$	−35.7689	+	14.8159i	−1.13281	+	0.469226i	−0.868735	−	0.495276i	$-0.835067\pi$
$997$	−35.7689	+	14.8159i	−1.13281	+	0.469226i	−0.264075	+	0.964502i	$0.585067\pi$
$998$	10.4172	−	23.1157i	0.329750	−	0.731714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.17	yes	128
3.2	odd	2	inner	864.2.v.a.109.16	✓	128
32.5	even	8	inner	864.2.v.a.325.17	yes	128
96.5	odd	8	inner	864.2.v.a.325.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.16	✓	128	3.2	odd	2	inner
864.2.v.a.109.17	yes	128	1.1	even	1	trivial
864.2.v.a.325.16	yes	128	96.5	odd	8	inner
864.2.v.a.325.17	yes	128	32.5	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0434074 - 1.41355i) q^{2} +(-1.99623 - 0.122717i) q^{4} +(-2.68483 + 1.11209i) q^{5} +(1.54691 - 1.54691i) q^{7} +(-0.260117 + 2.81644i) q^{8} +O(q^{10})\)	\(q+(0.0434074 - 1.41355i) q^{2} +(-1.99623 - 0.122717i) q^{4} +(-2.68483 + 1.11209i) q^{5} +(1.54691 - 1.54691i) q^{7} +(-0.260117 + 2.81644i) q^{8} +(1.45545 + 3.84340i) q^{10} +(-0.284805 - 0.687579i) q^{11} +(-2.08570 - 0.863924i) q^{13} +(-2.11949 - 2.25378i) q^{14} +(3.96988 + 0.489942i) q^{16} +6.20670i q^{17} +(-0.566840 - 0.234793i) q^{19} +(5.49601 - 1.89052i) q^{20} +(-0.984289 + 0.372739i) q^{22} +(4.42017 + 4.42017i) q^{23} +(2.43601 - 2.43601i) q^{25} +(-1.31173 + 2.91073i) q^{26} +(-3.27783 + 2.89816i) q^{28} +(-1.81939 + 4.39239i) q^{29} +7.34680 q^{31} +(0.864879 - 5.59035i) q^{32} +(8.77346 + 0.269417i) q^{34} +(-2.43288 + 5.87350i) q^{35} +(5.10608 - 2.11501i) q^{37} +(-0.356496 + 0.791064i) q^{38} +(-2.43377 - 7.85093i) q^{40} +(4.87073 + 4.87073i) q^{41} +(2.38680 + 5.76224i) q^{43} +(0.484159 + 1.40752i) q^{44} +(6.43999 - 6.05625i) q^{46} -7.05366i q^{47} +2.21413i q^{49} +(-3.33768 - 3.54916i) q^{50} +(4.05752 + 1.98054i) q^{52} +(-1.34706 - 3.25209i) q^{53} +(1.52930 + 1.52930i) q^{55} +(3.95441 + 4.75917i) q^{56} +(6.12987 + 2.76245i) q^{58} +(6.36373 - 2.63594i) q^{59} +(3.05830 - 7.38339i) q^{61} +(0.318905 - 10.3850i) q^{62} +(-7.86468 - 1.46521i) q^{64} +6.56050 q^{65} +(-3.58513 + 8.65526i) q^{67} +(0.761666 - 12.3900i) q^{68} +(8.19686 + 3.69395i) q^{70} +(-4.40258 + 4.40258i) q^{71} +(7.67341 + 7.67341i) q^{73} +(-2.76802 - 7.30949i) q^{74} +(1.10273 + 0.538262i) q^{76} +(-1.50419 - 0.623057i) q^{77} +10.9657i q^{79} +(-11.2033 + 3.09946i) q^{80} +(7.09643 - 6.67358i) q^{82} +(-12.4669 - 5.16396i) q^{83} +(-6.90242 - 16.6639i) q^{85} +(8.24880 - 3.12373i) q^{86} +(2.01061 - 0.623284i) q^{88} +(-9.45976 + 9.45976i) q^{89} +(-4.56281 + 1.88998i) q^{91} +(-8.28126 - 9.36611i) q^{92} +(-9.97069 - 0.306181i) q^{94} +1.78298 q^{95} -13.6291 q^{97} +(3.12977 + 0.0961094i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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