LMFDB - Embedded newform 864.2.bn.a.683.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not 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:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			683.9
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17233 + 0.790981i) q^{2} +(0.748697 - 1.85458i) q^{4} +(0.0883963 + 0.671437i) q^{5} +(-0.0557412 - 0.208029i) q^{7} +(0.589218 + 2.76637i) q^{8} +O(q^{10})$	\(q+(-1.17233 + 0.790981i) q^{2} +(0.748697 - 1.85458i) q^{4} +(0.0883963 + 0.671437i) q^{5} +(-0.0557412 - 0.208029i) q^{7} +(0.589218 + 2.76637i) q^{8} +(-0.634723 - 0.717223i) q^{10} +(4.50341 - 3.45559i) q^{11} +(-3.30781 + 4.31082i) q^{13} +(0.229894 + 0.199788i) q^{14} +(-2.87891 - 2.77703i) q^{16} +0.0148356 q^{17} +(3.86908 - 1.60262i) q^{19} +(1.31141 + 0.338765i) q^{20} +(-2.54616 + 7.61319i) q^{22} +(-0.419209 - 0.112327i) q^{23} +(4.38662 - 1.17539i) q^{25} +(0.468052 - 7.67011i) q^{26} +(-0.427539 - 0.0523744i) q^{28} +(-0.271469 - 0.0357395i) q^{29} +(-4.43423 + 2.56010i) q^{31} +(5.57160 + 0.978425i) q^{32} +(-0.0173922 + 0.0117347i) q^{34} +(0.134751 - 0.0558157i) q^{35} +(1.74098 - 4.20310i) q^{37} +(-3.26817 + 4.93916i) q^{38} +(-1.80536 + 0.640160i) q^{40} +(0.470501 - 1.75593i) q^{41} +(4.11098 + 5.35753i) q^{43} +(-3.03696 - 10.9391i) q^{44} +(0.580298 - 0.199903i) q^{46} +(10.1840 + 5.87973i) q^{47} +(6.02201 - 3.47681i) q^{49} +(-4.21283 + 4.84767i) q^{50} +(5.51820 + 9.36209i) q^{52} +(0.483863 - 1.16815i) q^{53} +(2.71829 + 2.71829i) q^{55} +(0.542642 - 0.276775i) q^{56} +(0.346519 - 0.172828i) q^{58} +(8.49106 - 1.11787i) q^{59} +(1.26680 - 9.62227i) q^{61} +(3.17337 - 6.50867i) q^{62} +(-7.30564 + 3.26000i) q^{64} +(-3.18684 - 1.83992i) q^{65} +(-8.50990 + 11.0903i) q^{67} +(0.0111074 - 0.0275138i) q^{68} +(-0.113823 + 0.172020i) q^{70} +(6.64660 + 6.64660i) q^{71} +(5.76433 - 5.76433i) q^{73} +(1.28358 + 6.30449i) q^{74} +(-0.0754224 - 8.37537i) q^{76} +(-0.969888 - 0.744221i) q^{77} +(-1.89962 + 3.29024i) q^{79} +(1.61012 - 2.17848i) q^{80} +(0.837330 + 2.43068i) q^{82} +(2.39015 + 0.314669i) q^{83} +(0.00131141 + 0.00996118i) q^{85} +(-9.05711 - 3.02907i) q^{86} +(12.2129 + 10.4220i) q^{88} +(-2.45783 + 2.45783i) q^{89} +(1.08116 + 0.447830i) q^{91} +(-0.522179 + 0.693356i) q^{92} +(-16.5897 + 1.16239i) q^{94} +(1.41807 + 2.45617i) q^{95} +(-4.10794 + 7.11516i) q^{97} +(-4.30967 + 8.83925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.17233	+	0.790981i	−0.828960	+	0.559308i
$2$	−1.17233	+	0.790981i	−0.828960	+	0.559308i
$3$		0			0
$3$		0			0
$4$	0.748697	−	1.85458i	0.374348	−	0.927288i
$5$	0.0883963	+	0.671437i	0.0395320	+	0.300276i	0.999777	+	0.0211169i	$0.00672223\pi$
$5$	0.0883963	+	0.671437i	0.0395320	+	0.300276i	−0.960245	+	0.279159i	$0.909944\pi$
$6$		0			0
$7$	−0.0557412	−	0.208029i	−0.0210682	−	0.0786276i	0.954591	−	0.297918i	$-0.0962923\pi$
$7$	−0.0557412	−	0.208029i	−0.0210682	−	0.0786276i	−0.975660	+	0.219291i	$0.929626\pi$
$8$	0.589218	+	2.76637i	0.208320	+	0.978061i
$9$		0			0
$10$	−0.634723	−	0.717223i	−0.200717	−	0.226806i
$11$	4.50341	−	3.45559i	1.35783	−	1.04190i	0.363950	−	0.931418i	$-0.381428\pi$
$11$	4.50341	−	3.45559i	1.35783	−	1.04190i	0.993878	−	0.110480i	$-0.0352389\pi$
$12$		0			0
$13$	−3.30781	+	4.31082i	−0.917422	+	1.19561i	0.0628641	+	0.998022i	$0.479977\pi$
$13$	−3.30781	+	4.31082i	−0.917422	+	1.19561i	−0.980286	+	0.197585i	$0.936690\pi$
$14$	0.229894	+	0.199788i	0.0614417	+	0.0533955i
$15$		0			0
$16$	−2.87891	−	2.77703i	−0.719726	−	0.694258i
$17$	0.0148356			0.00359817			0.00179908	−	0.999998i	$-0.499427\pi$
$17$	0.0148356			0.00359817			0.00179908	+	0.999998i	$0.499427\pi$
$18$		0			0
$19$	3.86908	−	1.60262i	0.887627	−	0.367667i	0.108177	−	0.994132i	$-0.465499\pi$
$19$	3.86908	−	1.60262i	0.887627	−	0.367667i	0.779450	+	0.626465i	$0.215499\pi$
$20$	1.31141	+	0.338765i	0.293241	+	0.0757501i
$21$		0			0
$22$	−2.54616	+	7.61319i	−0.542843	+	1.62314i
$23$	−0.419209	−	0.112327i	−0.0874111	−	0.0234217i	0.214848	−	0.976647i	$-0.431074\pi$
$23$	−0.419209	−	0.112327i	−0.0874111	−	0.0234217i	−0.302259	+	0.953226i	$0.597741\pi$
$24$		0			0
$25$	4.38662	−	1.17539i	0.877323	−	0.235078i
$26$	0.468052	−	7.67011i	0.0917926	−	1.50423i
$27$		0			0
$28$	−0.427539	−	0.0523744i	−0.0807973	−	0.00989783i
$29$	−0.271469	−	0.0357395i	−0.0504105	−	0.00663667i	0.105279	−	0.994443i	$-0.466427\pi$
$29$	−0.271469	−	0.0357395i	−0.0504105	−	0.00663667i	−0.155689	+	0.987806i	$0.549760\pi$
$30$		0			0
$31$	−4.43423	+	2.56010i	−0.796411	+	0.459808i	−0.842215	−	0.539142i	$-0.818749\pi$
$31$	−4.43423	+	2.56010i	−0.796411	+	0.459808i	0.0458035	+	0.998950i	$0.485415\pi$
$32$	5.57160	+	0.978425i	0.984928	+	0.172963i
$33$		0			0
$34$	−0.0173922	+	0.0117347i	−0.00298274	+	0.00201248i
$35$	0.134751	−	0.0558157i	0.0227771	−	0.00943457i
$36$		0			0
$37$	1.74098	−	4.20310i	0.286216	−	0.690985i	−0.713740	−	0.700411i	$-0.753000\pi$
$37$	1.74098	−	4.20310i	0.286216	−	0.690985i	0.999956	+	0.00942527i	$0.00300020\pi$
$38$	−3.26817	+	4.93916i	−0.530168	+	0.801238i
$39$		0			0
$40$	−1.80536	+	0.640160i	−0.285453	+	0.101218i
$41$	0.470501	−	1.75593i	0.0734799	−	0.274231i	−0.919404	−	0.393313i	$-0.871329\pi$
$41$	0.470501	−	1.75593i	0.0734799	−	0.274231i	0.992884	+	0.119083i	$0.0379954\pi$
$42$		0			0
$43$	4.11098	+	5.35753i	0.626918	+	0.817016i	0.993555	−	0.113348i	$-0.0361576\pi$
$43$	4.11098	+	5.35753i	0.626918	+	0.817016i	−0.366637	+	0.930364i	$0.619491\pi$
$44$	−3.03696	−	10.9391i	−0.457839	−	1.64913i
$45$		0			0
$46$	0.580298	−	0.199903i	0.0855602	−	0.0294741i
$47$	10.1840	+	5.87973i	1.48549	+	0.857647i	0.999864	−	0.0165209i	$-0.00525900\pi$
$47$	10.1840	+	5.87973i	1.48549	+	0.857647i	0.485624	+	0.874168i	$0.338592\pi$
$48$		0			0
$49$	6.02201	−	3.47681i	0.860287	−	0.496687i
$50$	−4.21283	+	4.84767i	−0.595784	+	0.685564i
$51$		0			0
$52$	5.51820	+	9.36209i	0.765237	+	1.29829i
$53$	0.483863	−	1.16815i	0.0664638	−	0.160458i	−0.887158	−	0.461467i	$-0.847323\pi$
$53$	0.483863	−	1.16815i	0.0664638	−	0.160458i	0.953621	+	0.301009i	$0.0973234\pi$
$54$		0			0
$55$	2.71829	+	2.71829i	0.366535	+	0.366535i
$56$	0.542642	−	0.276775i	0.0725136	−	0.0369857i
$57$		0			0
$58$	0.346519	−	0.172828i	0.0455002	−	0.0226935i
$59$	8.49106	−	1.11787i	1.10544	−	0.145534i	0.444360	−	0.895848i	$-0.353431\pi$
$59$	8.49106	−	1.11787i	1.10544	−	0.145534i	0.661081	+	0.750314i	$0.270098\pi$
$60$		0			0
$61$	1.26680	−	9.62227i	0.162197	−	1.23201i	−0.695757	−	0.718278i	$-0.744931\pi$
$61$	1.26680	−	9.62227i	0.162197	−	1.23201i	0.857953	−	0.513728i	$-0.171736\pi$
$62$	3.17337	−	6.50867i	0.403018	−	0.826602i
$63$		0			0
$64$	−7.30564	+	3.26000i	−0.913205	+	0.407499i
$65$	−3.18684	−	1.83992i	−0.395279	−	0.228215i
$66$		0			0
$67$	−8.50990	+	11.0903i	−1.03965	+	1.35490i	−0.106942	+	0.994265i	$0.534106\pi$
$67$	−8.50990	+	11.0903i	−1.03965	+	1.35490i	−0.932708	+	0.360633i	$0.882561\pi$
$68$	0.0111074	−	0.0275138i	0.00134697	−	0.00333654i
$69$		0			0
$70$	−0.113823	+	0.172020i	−0.0136044	+	0.0205603i
$71$	6.64660	+	6.64660i	0.788806	+	0.788806i	0.981298	−	0.192493i	$-0.0616571\pi$
$71$	6.64660	+	6.64660i	0.788806	+	0.788806i	−0.192493	+	0.981298i	$0.561657\pi$
$72$		0			0
$73$	5.76433	−	5.76433i	0.674664	−	0.674664i	−0.284123	−	0.958788i	$-0.591703\pi$
$73$	5.76433	−	5.76433i	0.674664	−	0.674664i	0.958788	+	0.284123i	$0.0917026\pi$
$74$	1.28358	+	6.30449i	0.149213	+	0.732882i
$75$		0			0
$76$	−0.0754224	−	8.37537i	−0.00865154	−	0.960721i
$77$	−0.969888	−	0.744221i	−0.110529	−	0.0848119i
$78$		0			0
$79$	−1.89962	+	3.29024i	−0.213724	+	0.370181i	−0.952877	−	0.303357i	$-0.901893\pi$
$79$	−1.89962	+	3.29024i	−0.213724	+	0.370181i	0.739153	+	0.673538i	$0.235226\pi$
$80$	1.61012	−	2.17848i	0.180016	−	0.243562i
$81$		0			0
$82$	0.837330	+	2.43068i	0.0924676	+	0.268424i
$83$	2.39015	+	0.314669i	0.262353	+	0.0345394i	0.260555	−	0.965459i	$-0.416094\pi$
$83$	2.39015	+	0.314669i	0.262353	+	0.0345394i	0.00179787	+	0.999998i	$0.499428\pi$
$84$		0			0
$85$	0.00131141	+	0.00996118i	0.000142243	+	0.00108044i
$86$	−9.05711	−	3.02907i	−0.976653	−	0.326633i
$87$		0			0
$88$	12.2129	+	10.4220i	1.30190	+	1.11099i
$89$	−2.45783	+	2.45783i	−0.260529	+	0.260529i	−0.825269	−	0.564740i	$-0.808977\pi$
$89$	−2.45783	+	2.45783i	−0.260529	+	0.260529i	0.564740	+	0.825269i	$0.308977\pi$
$90$		0			0
$91$	1.08116	+	0.447830i	0.113336	+	0.0469454i
$92$	−0.522179	+	0.693356i	−0.0544409	+	0.0722873i
$93$		0			0
$94$	−16.5897	+	1.16239i	−1.71110	+	0.119891i
$95$	1.41807	+	2.45617i	0.145491	+	0.251998i
$96$		0			0
$97$	−4.10794	+	7.11516i	−0.417098	+	0.722435i	−0.995646	−	0.0932134i	$-0.970286\pi$
$97$	−4.10794	+	7.11516i	−0.417098	+	0.722435i	0.578548	+	0.815648i	$0.303619\pi$
$98$	−4.30967	+	8.83925i	−0.435342	+	0.892899i
$99$		0			0
$100$	1.10440	−	9.01532i	0.110440	−	0.901532i
$101$	0.600080	−	0.460457i	0.0597102	−	0.0458172i	−0.578475	−	0.815700i	$-0.696352\pi$
$101$	0.600080	−	0.460457i	0.0597102	−	0.0458172i	0.638185	+	0.769883i	$0.279685\pi$
$102$		0			0
$103$	17.2779	+	4.62961i	1.70245	+	0.456169i	0.973554	−	0.228459i	$-0.0733685\pi$
$103$	17.2779	+	4.62961i	1.70245	+	0.456169i	0.728893	+	0.684628i	$0.240035\pi$
$104$	−13.8744	−	6.61062i	−1.36049	−	0.648225i
$105$		0			0
$106$	0.356739	+	1.75218i	0.0346495	+	0.170187i
$107$	−7.67127	−	3.17755i	−0.741610	−	0.307185i	−0.0202969	−	0.999794i	$-0.506461\pi$
$107$	−7.67127	−	3.17755i	−0.741610	−	0.307185i	−0.721313	+	0.692609i	$0.756461\pi$
$108$		0			0
$109$	3.88254	+	9.37329i	0.371880	+	0.897798i	0.993432	+	0.114425i	$0.0365025\pi$
$109$	3.88254	+	9.37329i	0.371880	+	0.897798i	−0.621552	+	0.783373i	$0.713497\pi$
$110$	−5.33684	−	1.03661i	−0.508848	−	0.0988366i
$111$		0			0
$112$	−0.417229	+	0.753691i	−0.0394245	+	0.0712171i
$113$	9.74325	+	16.8758i	0.916568	+	1.58754i	0.804589	+	0.593832i	$0.202385\pi$
$113$	9.74325	+	16.8758i	0.916568	+	1.58754i	0.111979	+	0.993711i	$0.464281\pi$
$114$		0			0
$115$	0.0383637	−	0.291401i	0.00357744	−	0.0271733i
$116$	−0.269530	+	0.476701i	−0.0250252	+	0.0442606i
$117$		0			0
$118$	−9.07007	+	8.02677i	−0.834968	+	0.738924i
$119$	−0.000826956	−	0.00308624i	−7.58069e−5	−	0.000282915i
$120$		0			0
$121$	5.49260	−	20.4986i	0.499327	−	1.86351i
$122$	6.12594	+	12.2825i	0.554616	+	1.11200i
$123$		0			0
$124$	1.42801	+	10.1404i	0.128239	+	0.910631i
$125$	2.47279	+	5.96983i	0.221173	+	0.533958i
$126$		0			0
$127$		−	14.8387i		−	1.31672i	−0.752704	−	0.658359i	$-0.771251\pi$
$127$		−	14.8387i		−	1.31672i	0.752704	−	0.658359i	$-0.228749\pi$
$128$	5.98600	−	9.60041i	0.529093	−	0.848564i
$129$		0			0
$130$	5.19137	−	0.363742i	0.455313	−	0.0319023i
$131$	4.18185	+	3.20885i	0.365370	+	0.280358i	0.775087	−	0.631854i	$-0.217706\pi$
$131$	4.18185	+	3.20885i	0.365370	+	0.280358i	−0.409717	+	0.912213i	$0.634373\pi$
$132$		0			0
$133$	−0.549059	−	0.715548i	−0.0476095	−	0.0620459i
$134$	1.20414	−	19.7326i	0.104022	−	1.70464i
$135$		0			0
$136$	0.00874142	+	0.0410409i	0.000749571	+	0.00351923i
$137$	−13.3449	+	3.57577i	−1.14014	+	0.305498i	−0.779005	−	0.627017i	$-0.784276\pi$
$137$	−13.3449	+	3.57577i	−1.14014	+	0.305498i	−0.361130	+	0.932516i	$0.617609\pi$
$138$		0			0
$139$	−1.29513	+	0.170507i	−0.109852	+	0.0144622i	−0.185252	−	0.982691i	$-0.559310\pi$
$139$	−1.29513	+	0.170507i	−0.109852	+	0.0144622i	0.0753999	+	0.997153i	$0.475977\pi$
$140$	−0.00262679	−	0.291695i	−0.000222004	−	0.0246527i
$141$		0			0
$142$	−13.0493	−	2.53464i	−1.09507	−	0.212703i
$143$			30.8438i			2.57929i
$144$		0			0
$145$		−	0.185433i		−	0.0153994i
$146$	−2.19820	+	11.3172i	−0.181924	+	0.936615i
$147$		0			0
$148$	−6.49150	−	6.37563i	−0.533598	−	0.524074i
$149$	−17.1826	+	2.26213i	−1.40765	+	0.185321i	−0.795756	−	0.605617i	$-0.792926\pi$
$149$	−17.1826	+	2.26213i	−1.40765	+	0.185321i	−0.611896	+	0.790938i	$0.709593\pi$
$150$		0			0
$151$	−0.547737	+	0.146766i	−0.0445742	+	0.0119436i	−0.281037	−	0.959697i	$-0.590678\pi$
$151$	−0.547737	+	0.146766i	−0.0445742	+	0.0119436i	0.236463	+	0.971640i	$0.424012\pi$
$152$	6.71318	+	9.75901i	0.544511	+	0.791560i
$153$		0			0
$154$	1.72569	+	0.105307i	0.139060	+	0.00848585i
$155$	−2.11092	−	2.75100i	−0.169553	−	0.220966i
$156$		0			0
$157$	−9.06471	−	6.95559i	−0.723442	−	0.555117i	0.180083	−	0.983651i	$-0.442363\pi$
$157$	−9.06471	−	6.95559i	−0.723442	−	0.555117i	−0.903525	+	0.428535i	$0.859030\pi$
$158$	−0.375543	−	5.35980i	−0.0298766	−	0.426403i
$159$		0			0
$160$	−0.164442	+	3.82746i	−0.0130003	+	0.302588i
$161$			0.0934688i			0.00736637i
$162$		0			0
$163$	−8.68977	−	20.9790i	−0.680635	−	1.64320i	−0.762843	−	0.646584i	$-0.776197\pi$
$163$	−8.68977	−	20.9790i	−0.680635	−	1.64320i	0.0822078	−	0.996615i	$-0.473803\pi$
$164$	−2.90425	−	2.18724i	−0.226784	−	0.170795i
$165$		0			0
$166$	−3.05093	+	1.52167i	−0.236798	+	0.118104i
$167$	3.77990	−	14.1068i	0.292498	−	1.09162i	−0.650687	−	0.759346i	$-0.725519\pi$
$167$	3.77990	−	14.1068i	0.292498	−	1.09162i	0.943184	−	0.332270i	$-0.107814\pi$
$168$		0			0
$169$	−4.27693	−	15.9617i	−0.328995	−	1.22783i
$170$	−0.00941652	−	0.0106405i	−0.000722214	−	0.000816085i
$171$		0			0
$172$	13.0138	−	3.61295i	0.992295	−	0.275485i
$173$	2.39785	−	18.2135i	0.182305	−	1.38475i	−0.618482	−	0.785799i	$-0.712252\pi$
$173$	2.39785	−	18.2135i	0.182305	−	1.38475i	0.800788	−	0.598948i	$-0.204415\pi$
$174$		0			0
$175$	−0.489030	−	0.847026i	−0.0369672	−	0.0640291i
$176$	−22.5612	−	2.55780i	−1.70061	−	0.192801i
$177$		0			0
$178$	0.937281	−	4.82548i	0.0702521	−	0.361685i
$179$	−5.10861	−	12.3333i	−0.381836	−	0.921833i	−0.991611	−	0.129258i	$-0.958740\pi$
$179$	−5.10861	−	12.3333i	−0.381836	−	0.921833i	0.609775	−	0.792574i	$-0.291260\pi$
$180$		0			0
$181$	0.783773	+	0.324649i	0.0582574	+	0.0241310i	0.411622	−	0.911355i	$-0.364962\pi$
$181$	0.783773	+	0.324649i	0.0582574	+	0.0241310i	−0.353364	+	0.935486i	$0.614962\pi$
$182$	−1.62169	+	0.330173i	−0.120208	+	0.0244740i
$183$		0			0
$184$	0.0637320	−	1.22587i	0.00469839	−	0.0903725i
$185$	2.97601	+	0.797420i	0.218801	+	0.0586275i
$186$		0			0
$187$	0.0668109	−	0.0512658i	0.00488569	−	0.00374892i
$188$	18.5291	−	14.4849i	1.35138	−	1.05642i
$189$		0			0
$190$	−3.60523	−	1.75777i	−0.261551	−	0.127522i
$191$	2.87740	−	4.98380i	0.208201	−	0.360615i	−0.742947	−	0.669350i	$-0.766572\pi$
$191$	2.87740	−	4.98380i	0.208201	−	0.360615i	0.951148	+	0.308736i	$0.0999058\pi$
$192$		0			0
$193$	−4.13279	−	7.15820i	−0.297485	−	0.515259i	0.678075	−	0.734993i	$-0.262814\pi$
$193$	−4.13279	−	7.15820i	−0.297485	−	0.515259i	−0.975560	+	0.219734i	$0.929481\pi$
$194$	−0.812114	−	11.5906i	−0.0583064	−	0.832156i
$195$		0			0
$196$	−1.93935	−	13.7714i	−0.138525	−	0.983668i
$197$	−24.2901	−	10.0613i	−1.73060	−	0.716838i	−0.999399	−	0.0346754i	$-0.988960\pi$
$197$	−24.2901	−	10.0613i	−1.73060	−	0.716838i	−0.731201	−	0.682162i	$-0.761040\pi$
$198$		0			0
$199$	0.714900	−	0.714900i	0.0506779	−	0.0506779i	−0.681314	−	0.731992i	$-0.738591\pi$
$199$	0.714900	−	0.714900i	0.0506779	−	0.0506779i	0.731992	+	0.681314i	$0.238591\pi$
$200$	5.83624	+	11.4425i	0.412685	+	0.809104i
$201$		0			0
$202$	−0.339276	+	1.01446i	−0.0238714	+	0.0713770i
$203$	0.00769713	+	0.0584655i	0.000540233	+	0.00410348i
$204$		0			0
$205$	1.22059	+	0.160694i	0.0852496	+	0.0112233i
$206$	−23.9173	+	8.23912i	−1.66640	+	0.574047i
$207$		0			0
$208$	21.4942	−	3.22456i	1.49035	−	0.223583i
$209$	11.8860	−	20.5872i	0.822173	−	1.42405i
$210$		0			0
$211$	0.458068	+	0.351488i	0.0315347	+	0.0241974i	0.624409	−	0.781098i	$-0.285340\pi$
$211$	0.458068	+	0.351488i	0.0315347	+	0.0241974i	−0.592874	+	0.805295i	$0.702007\pi$
$212$	−1.80416	−	1.77195i	−0.123910	−	0.121698i
$213$		0			0
$214$	11.5066	−	2.34271i	0.786576	−	0.160145i
$215$	−3.23385	+	3.23385i	−0.220547	+	0.220547i
$216$		0			0
$217$	0.779745	+	0.779745i	0.0529326	+	0.0529326i
$218$	−11.9657	−	7.91753i	−0.810419	−	0.536243i
$219$		0			0
$220$	7.07646	−	3.00610i	0.477095	−	0.202671i
$221$	−0.0490734	+	0.0639537i	−0.00330104	+	0.00430199i
$222$		0			0
$223$	13.9104	+	8.03118i	0.931510	+	0.537807i	0.887289	−	0.461214i	$-0.152586\pi$
$223$	13.9104	+	8.03118i	0.931510	+	0.537807i	0.0442211	+	0.999022i	$0.485919\pi$
$224$	−0.107027	−	1.21359i	−0.00715102	−	0.0810865i
$225$		0			0
$226$	−24.7707	−	12.0772i	−1.64772	−	0.803365i
$227$	−0.289351	+	2.19784i	−0.0192049	+	0.145876i	−0.998361	−	0.0572347i	$-0.981772\pi$
$227$	−0.289351	+	2.19784i	−0.0192049	+	0.145876i	0.979156	+	0.203110i	$0.0651050\pi$
$228$		0			0
$229$	−17.4568	+	2.29823i	−1.15358	+	0.151871i	−0.682953	−	0.730462i	$-0.739305\pi$
$229$	−17.4568	+	2.29823i	−1.15358	+	0.151871i	−0.470625	+	0.882334i	$0.655971\pi$
$230$	0.185518	+	0.371962i	0.0122327	+	0.0245265i
$231$		0			0
$232$	−0.0610854	−	0.772042i	−0.00401045	−	0.0506871i
$233$	0.891379	+	0.891379i	0.0583962	+	0.0583962i	0.735702	−	0.677306i	$-0.236853\pi$
$233$	0.891379	+	0.891379i	0.0583962	+	0.0583962i	−0.677306	+	0.735702i	$0.736853\pi$
$234$		0			0
$235$	−3.04764	+	7.35765i	−0.198806	+	0.479960i
$236$	4.28406	−	16.5843i	0.278868	−	1.07954i
$237$		0			0
$238$	0.00341062	+	0.00296397i	0.000221078	+	0.000192126i
$239$	−14.3675	+	8.29506i	−0.929354	+	0.536563i	−0.886607	−	0.462523i	$-0.846944\pi$
$239$	−14.3675	+	8.29506i	−0.929354	+	0.536563i	−0.0427467	+	0.999086i	$0.513611\pi$
$240$		0			0
$241$	6.98248	+	4.03134i	0.449781	+	0.259681i	0.707738	−	0.706475i	$-0.249716\pi$
$241$	6.98248	+	4.03134i	0.449781	+	0.259681i	−0.257957	+	0.966156i	$0.583049\pi$
$242$	9.77493	+	28.3756i	0.628357	+	1.82406i
$243$		0			0
$244$	−16.8968	−	9.55354i	−1.08171	−	0.611602i
$245$	2.86678	+	3.73606i	0.183152	+	0.238688i
$246$		0			0
$247$	−5.88954	+	21.9801i	−0.374743	+	1.39856i
$248$	−9.69493	−	10.7583i	−0.615629	−	0.683151i
$249$		0			0
$250$	−7.62094	−	5.04266i	−0.481990	−	0.318926i
$251$	−2.85834	+	6.90064i	−0.180417	+	0.435565i	−0.988053	−	0.154117i	$-0.950747\pi$
$251$	−2.85834	+	6.90064i	−0.180417	+	0.435565i	0.807636	+	0.589682i	$0.200747\pi$
$252$		0			0
$253$	−2.27602	+	0.942759i	−0.143092	+	0.0592708i
$254$	11.7371	+	17.3957i	0.736451	+	1.09151i
$255$		0			0
$256$	0.576196	+	15.9896i	0.0360123	+	0.999351i
$257$	6.91963	−	3.99505i	0.431635	−	0.249204i	−0.268408	−	0.963305i	$-0.586498\pi$
$257$	6.91963	−	3.99505i	0.431635	−	0.249204i	0.700043	+	0.714101i	$0.253164\pi$
$258$		0			0
$259$	−0.971411	−	0.127889i	−0.0603606	−	0.00794662i
$260$	−5.79826	+	4.53270i	−0.359593	+	0.281106i
$261$		0			0
$262$	−7.44064	−	0.454049i	−0.459684	−	0.0280513i
$263$	−25.6114	+	6.86256i	−1.57927	+	0.423164i	−0.938700	−	0.344736i	$-0.887968\pi$
$263$	−25.6114	+	6.86256i	−1.57927	+	0.423164i	−0.640569	+	0.767900i	$0.721302\pi$
$264$		0			0
$265$	0.827111	+	0.221624i	0.0508090	+	0.0136142i
$266$	1.20966	+	0.404560i	0.0741691	+	0.0248052i
$267$		0			0
$268$	14.1965	+	24.0855i	0.867189	+	1.47126i
$269$	15.4360	−	6.39378i	0.941147	−	0.389836i	0.141250	−	0.989974i	$-0.454888\pi$
$269$	15.4360	−	6.39378i	0.941147	−	0.389836i	0.799896	+	0.600138i	$0.204888\pi$
$270$		0			0
$271$	6.40082			0.388822			0.194411	−	0.980920i	$-0.437720\pi$
$271$	6.40082			0.388822			0.194411	+	0.980920i	$0.437720\pi$
$272$	−0.0427104	−	0.0411990i	−0.00258970	−	0.00249806i
$273$		0			0
$274$	12.8163	−	14.7476i	0.774258	−	0.890933i
$275$	15.6931	−	20.4516i	0.946327	−	1.23328i
$276$		0			0
$277$	−23.0844	+	17.7133i	−1.38701	+	1.06429i	−0.397844	+	0.917453i	$0.630242\pi$
$277$	−23.0844	+	17.7133i	−1.38701	+	1.06429i	−0.989161	+	0.146834i	$0.953092\pi$
$278$	1.38345	−	1.22431i	0.0829737	−	0.0734295i
$279$		0			0
$280$	0.233805	+	0.339884i	0.0139725	+	0.0203120i
$281$	−4.13455	−	15.4304i	−0.246647	−	0.920498i	−0.972549	−	0.232700i	$-0.925244\pi$
$281$	−4.13455	−	15.4304i	−0.246647	−	0.920498i	0.725902	−	0.687798i	$-0.241423\pi$
$282$		0			0
$283$	−1.03921	−	7.89357i	−0.0617745	−	0.469224i	−0.994173	−	0.107793i	$-0.965622\pi$
$283$	−1.03921	−	7.89357i	−0.0617745	−	0.469224i	0.932399	−	0.361431i	$-0.117712\pi$
$284$	17.3029	−	7.35033i	1.02674	−	0.436162i
$285$		0			0
$286$	−24.3969	−	36.1590i	−1.44262	−	2.13813i
$287$	−0.391511			−0.0231102
$288$		0			0
$289$	−16.9998			−0.999987
$290$	0.146674	+	0.217388i	0.00861301	+	0.0127655i
$291$		0			0
$292$	−6.37466	−	15.0061i	−0.373049	−	0.878168i
$293$	−3.42320	−	26.0018i	−0.199985	−	1.51904i	−0.737247	−	0.675624i	$-0.763874\pi$
$293$	−3.42320	−	26.0018i	−0.199985	−	1.51904i	0.537261	−	0.843416i	$-0.319459\pi$
$294$		0			0
$295$	1.50116	+	5.60239i	0.0874007	+	0.326184i
$296$	12.6532	+	2.33966i	0.735450	+	0.135990i
$297$		0			0
$298$	18.3543	−	16.2431i	1.06324	−	0.940936i
$299$	1.87088	−	1.43558i	0.108196	−	0.0830217i
$300$		0			0
$301$	0.885371	−	1.15384i	0.0510319	−	0.0665061i
$302$	0.526037	−	0.605307i	0.0302700	−	0.0348315i
$303$		0			0
$304$	−15.5892	−	6.13074i	−0.894104	−	0.351622i
$305$	6.57273			0.376353
$306$		0			0
$307$	−19.3223	+	8.00354i	−1.10278	+	0.456786i	−0.858445	−	0.512905i	$-0.828569\pi$
$307$	−19.3223	+	8.00354i	−1.10278	+	0.456786i	−0.244334	+	0.969691i	$0.578569\pi$
$308$	−2.10637	+	1.24153i	−0.120021	+	0.0707430i
$309$		0			0
$310$	4.65068	+	1.55537i	0.264141	+	0.0883393i
$311$	24.2485	+	6.49736i	1.37500	+	0.368431i	0.869304	−	0.494277i	$-0.164567\pi$
$311$	24.2485	+	6.49736i	1.37500	+	0.368431i	0.505701	+	0.862709i	$0.331234\pi$
$312$		0			0
$313$	11.2697	−	3.01970i	0.636999	−	0.170683i	0.0741554	−	0.997247i	$-0.476374\pi$
$313$	11.2697	−	3.01970i	0.636999	−	0.170683i	0.562844	+	0.826563i	$0.309707\pi$
$314$	16.1285	+	0.984210i	0.910186	+	0.0555422i
$315$		0			0
$316$	4.67976	+	5.98639i	0.263257	+	0.336761i
$317$	−15.6526	−	2.06070i	−0.879135	−	0.115740i	−0.322571	−	0.946545i	$-0.604547\pi$
$317$	−15.6526	−	2.06070i	−0.879135	−	0.115740i	−0.556564	+	0.830805i	$0.687881\pi$
$318$		0			0
$319$	−1.34604	+	0.777134i	−0.0753635	+	0.0435112i
$320$	−2.83467	−	4.61711i	−0.158463	−	0.258104i
$321$		0			0
$322$	−0.0739321	−	0.109576i	−0.00412007	−	0.00610643i
$323$	0.0574001	−	0.0237759i	0.00319383	−	0.00132293i
$324$		0			0
$325$	−9.44320	+	22.7979i	−0.523814	+	1.26460i
$326$	26.7812	+	17.7207i	1.48327	+	0.981461i
$327$		0			0
$328$	5.13479	+	0.266953i	0.283522	+	0.0147400i
$329$	0.655486	−	2.44631i	0.0361381	−	0.134869i
$330$		0			0
$331$	9.17055	+	11.9513i	0.504059	+	0.656903i	0.974199	−	0.225689i	$-0.0724633\pi$
$331$	9.17055	+	11.9513i	0.504059	+	0.656903i	−0.470140	+	0.882592i	$0.655797\pi$
$332$	2.37308	−	4.19712i	0.130240	−	0.230347i
$333$		0			0
$334$	6.72693	+	19.5276i	0.368081	+	1.06850i
$335$	−8.19869	−	4.73352i	−0.447942	−	0.258620i
$336$		0			0
$337$	8.56862	−	4.94710i	0.466763	−	0.269485i	−0.248121	−	0.968729i	$-0.579813\pi$
$337$	8.56862	−	4.94710i	0.466763	−	0.269485i	0.714883	+	0.699244i	$0.246480\pi$
$338$	17.6394	+	15.3294i	0.959457	+	0.833809i
$339$		0			0
$340$	0.0194556	+	0.00502579i	0.00105513	+	0.000272562i
$341$	−11.1225	+	26.8521i	−0.602316	+	1.45412i
$342$		0			0
$343$	−2.12497	−	2.12497i	−0.114737	−	0.114737i
$344$	−12.3987	+	14.5293i	−0.668491	+	0.783365i
$345$		0			0
$346$	11.5955	+	23.2488i	0.623377	+	1.24986i
$347$	−3.76455	+	0.495613i	−0.202092	+	0.0266059i	−0.230892	−	0.972979i	$-0.574165\pi$
$347$	−3.76455	+	0.495613i	−0.202092	+	0.0266059i	0.0288006	+	0.999585i	$0.490831\pi$
$348$		0			0
$349$	0.609483	−	4.62949i	0.0326249	−	0.247811i	−0.967359	−	0.253408i	$-0.918448\pi$
$349$	0.609483	−	4.62949i	0.0326249	−	0.247811i	0.999984	+	0.00559751i	$0.00178175\pi$
$350$	1.24328	+	0.606176i	0.0664564	+	0.0324015i
$351$		0			0
$352$	28.4722	−	14.8469i	1.51757	−	0.791342i
$353$	−10.8753	−	6.27887i	−0.578835	−	0.334191i	0.181835	−	0.983329i	$-0.441796\pi$
$353$	−10.8753	−	6.27887i	−0.578835	−	0.334191i	−0.760670	+	0.649138i	$0.775130\pi$
$354$		0			0
$355$	−3.87523	+	5.05030i	−0.205676	+	0.268042i
$356$	2.71806	+	6.39840i	0.144057	+	0.339115i
$357$		0			0
$358$	15.7444	+	10.4178i	0.832115	+	0.550598i
$359$	−9.17704	−	9.17704i	−0.484346	−	0.484346i	0.422171	−	0.906516i	$-0.361268\pi$
$359$	−9.17704	−	9.17704i	−0.484346	−	0.484346i	−0.906516	+	0.422171i	$0.861268\pi$
$360$		0			0
$361$	−1.03369	+	1.03369i	−0.0544046	+	0.0544046i
$362$	−1.17563	+	0.239355i	−0.0617897	+	0.0125802i
$363$		0			0
$364$	1.63999	−	1.66980i	0.0859591	−	0.0875213i
$365$	4.37993	+	3.36084i	0.229256	+	0.175914i
$366$		0			0
$367$	−13.9731	+	24.2020i	−0.729387	+	1.26334i	0.227755	+	0.973718i	$0.426861\pi$
$367$	−13.9731	+	24.2020i	−0.729387	+	1.26334i	−0.957142	+	0.289618i	$0.906472\pi$
$368$	0.894928	+	1.48753i	0.0466513	+	0.0775430i
$369$		0			0
$370$	−4.11960	+	1.41913i	−0.214168	+	0.0737773i
$371$	−0.269980	−	0.0355436i	−0.0140167	−	0.00184533i
$372$		0			0
$373$	0.404073	+	3.06924i	0.0209221	+	0.158919i	0.998717	−	0.0506467i	$-0.0161283\pi$
$373$	0.404073	+	3.06924i	0.0209221	+	0.158919i	−0.977795	+	0.209566i	$0.932795\pi$
$374$	−0.0377738	+	0.112946i	−0.00195324	+	0.00584032i
$375$		0			0
$376$	−10.2649	+	31.6372i	−0.529374	+	1.63156i
$377$	1.05203	−	1.05203i	0.0541825	−	0.0541825i
$378$		0			0
$379$	−1.15861	−	0.479912i	−0.0595138	−	0.0246514i	0.352728	−	0.935726i	$-0.385254\pi$
$379$	−1.15861	−	0.479912i	−0.0595138	−	0.0246514i	−0.412242	+	0.911074i	$0.635254\pi$
$380$	5.61687	−	0.790994i	0.288139	−	0.0405771i
$381$		0			0
$382$	0.568843	+	8.11860i	0.0291046	+	0.415384i
$383$	9.06305	+	15.6977i	0.463100	+	0.802113i	0.999114	−	0.0420964i	$-0.0134036\pi$
$383$	9.06305	+	15.6977i	0.463100	+	0.802113i	−0.536013	+	0.844210i	$0.680070\pi$
$384$		0			0
$385$	0.413963	−	0.717005i	0.0210975	−	0.0365419i
$386$	10.5070	+	5.12279i	0.534791	+	0.260743i
$387$		0			0
$388$	10.1200	+	12.9456i	0.513765	+	0.657212i
$389$	−21.8498	+	16.7660i	−1.10783	+	0.850068i	−0.989732	−	0.142934i	$-0.954346\pi$
$389$	−21.8498	+	16.7660i	−1.10783	+	0.850068i	−0.118098	+	0.993002i	$0.537680\pi$
$390$		0			0
$391$	−0.00621922	−	0.00166644i	−0.000314520	−	8.42753e-5i
$392$	13.1664	+	14.6105i	0.665005	+	0.737943i
$393$		0			0
$394$	36.4342	−	7.41791i	1.83553	−	0.373709i
$395$	−2.37711	−	0.984631i	−0.119605	−	0.0495421i
$396$		0			0
$397$	8.77052	+	21.1739i	0.440180	+	1.06269i	0.975885	+	0.218283i	$0.0700457\pi$
$397$	8.77052	+	21.1739i	0.440180	+	1.06269i	−0.535705	+	0.844405i	$0.679954\pi$
$398$	−0.272623	+	1.40357i	−0.0136654	+	0.0703545i
$399$		0			0
$400$	−15.8927	−	8.79793i	−0.794637	−	0.439897i
$401$	8.33898	+	14.4435i	0.416429	+	0.721275i	0.995577	−	0.0939465i	$-0.0299483\pi$
$401$	8.33898	+	14.4435i	0.416429	+	0.721275i	−0.579149	+	0.815222i	$0.696615\pi$
$402$		0			0
$403$	3.63144	−	27.5835i	0.180895	−	1.37403i
$404$	−0.404675	−	1.45764i	−0.0201334	−	0.0725201i
$405$		0			0
$406$	−0.0552687	−	0.0624524i	−0.00274294	−	0.00309946i
$407$	−6.68383	−	24.9444i	−0.331305	−	1.23645i
$408$		0			0
$409$	1.84560	−	6.88786i	0.0912589	−	0.340583i	−0.905167	−	0.425056i	$-0.860254\pi$
$409$	1.84560	−	6.88786i	0.0912589	−	0.340583i	0.996426	+	0.0844737i	$0.0269209\pi$
$410$	−1.55803	+	0.777078i	−0.0769458	+	0.0383771i
$411$		0			0
$412$	21.5219	−	28.5771i	1.06031	−	1.40789i
$413$	−0.705851	−	1.70407i	−0.0347327	−	0.0838520i
$414$		0			0
$415$			1.63265i			0.0801437i
$416$	−22.6476	+	20.7817i	−1.11039	+	1.01891i
$417$		0			0
$418$	2.34979	+	33.5365i	0.114932	+	1.64033i
$419$	−5.67603	−	4.35537i	−0.277292	−	0.212774i	0.460747	−	0.887531i	$-0.347581\pi$
$419$	−5.67603	−	4.35537i	−0.277292	−	0.212774i	−0.738039	+	0.674758i	$0.764248\pi$
$420$		0			0
$421$	−13.1087	−	17.0836i	−0.638878	−	0.832602i	0.355915	−	0.934518i	$-0.384169\pi$
$421$	−13.1087	−	17.0836i	−0.638878	−	0.832602i	−0.994793	+	0.101916i	$0.967503\pi$
$422$	−0.815026	−	0.0497353i	−0.0396748	−	0.00242107i
$423$		0			0
$424$	3.51664	+	0.650252i	0.170783	+	0.0315790i
$425$	0.0650782	−	0.0174376i	0.00315676	−	0.000845850i
$426$		0			0
$427$	−2.07232	+	0.272827i	−0.100287	+	0.0132030i
$428$	−11.6365	+	11.8479i	−0.562470	+	0.572692i
$429$		0			0
$430$	1.23321	−	6.34904i	0.0594707	−	0.306178i
$431$			16.5026i			0.794901i	0.917624	+	0.397451i	$0.130105\pi$
$431$			16.5026i			0.794901i	−0.917624	+	0.397451i	$0.869895\pi$
$432$		0			0
$433$			30.5881i			1.46997i	0.678084	+	0.734985i	$0.262811\pi$
$433$			30.5881i			1.46997i	−0.678084	+	0.734985i	$0.737189\pi$
$434$	−1.53088	−	0.297352i	−0.0734846	−	0.0142733i
$435$		0			0
$436$	20.2903	−	0.182720i	0.971730	−	0.00875068i
$437$	−1.80197	+	0.237233i	−0.0861998	+	0.0113484i
$438$		0			0
$439$	14.2147	−	3.80882i	0.678431	−	0.181785i	0.0968811	−	0.995296i	$-0.469113\pi$
$439$	14.2147	−	3.80882i	0.678431	−	0.181785i	0.581549	+	0.813511i	$0.302447\pi$
$440$	−5.91815	+	9.12148i	−0.282136	+	0.434850i
$441$		0			0
$442$	0.00694385	−	0.113791i	0.000330285	−	0.00541248i
$443$	5.95453	+	7.76010i	0.282908	+	0.368693i	0.913093	−	0.407752i	$-0.133687\pi$
$443$	5.95453	+	7.76010i	0.282908	+	0.368693i	−0.630184	+	0.776446i	$0.717021\pi$
$444$		0			0
$445$	−1.86754	−	1.43301i	−0.0885299	−	0.0679314i
$446$	−22.6600	+	1.58771i	−1.07298	+	0.0751804i
$447$		0			0
$448$	1.08540	+	1.33807i	0.0512803	+	0.0632179i
$449$			2.78748i			0.131549i	0.997835	+	0.0657747i	$0.0209519\pi$
$449$			2.78748i			0.131549i	−0.997835	+	0.0657747i	$0.979048\pi$
$450$		0			0
$451$	−3.94892	−	9.53354i	−0.185947	−	0.448917i
$452$	38.5922	−	5.43474i	1.81522	−	0.255629i
$453$		0			0
$454$	−1.39924	−	2.80545i	−0.0656694	−	0.131666i
$455$	−0.205119	+	0.765516i	−0.00961614	+	0.0358879i
$456$		0			0
$457$	1.60232	+	5.97994i	0.0749534	+	0.279730i	0.993223	−	0.116226i	$-0.0370798\pi$
$457$	1.60232	+	5.97994i	0.0749534	+	0.279730i	−0.918269	+	0.395956i	$0.870413\pi$
$458$	18.6472	−	16.5023i	0.871326	−	0.771101i
$459$		0			0
$460$	−0.511703	−	0.289320i	−0.0238583	−	0.0134896i
$461$	−4.18625	+	31.7978i	−0.194973	+	1.48097i	0.561790	+	0.827280i	$0.310113\pi$
$461$	−4.18625	+	31.7978i	−0.194973	+	1.48097i	−0.756763	+	0.653689i	$0.773220\pi$
$462$		0			0
$463$	11.9666	+	20.7268i	0.556137	+	0.963257i	0.997814	+	0.0660830i	$0.0210502\pi$
$463$	11.9666	+	20.7268i	0.556137	+	0.963257i	−0.441677	+	0.897174i	$0.645616\pi$
$464$	0.682283	+	0.856768i	0.0316742	+	0.0397745i
$465$		0			0
$466$	−1.75005	−	0.339923i	−0.0810696	−	0.0157466i
$467$	−11.5307	−	27.8376i	−0.533578	−	1.28817i	−0.929139	−	0.369731i	$-0.879450\pi$
$467$	−11.5307	−	27.8376i	−0.533578	−	1.28817i	0.395561	−	0.918440i	$-0.370550\pi$
$468$		0			0
$469$	2.78146	+	1.15212i	0.128436	+	0.0531999i
$470$	−2.24694	−	11.0362i	−0.103644	−	0.509062i
$471$		0			0
$472$	8.09553	+	22.8308i	0.372627	+	1.05087i
$473$	37.0268	+	9.92130i	1.70249	+	0.456182i
$474$		0			0
$475$	15.0884	−	11.5778i	0.692305	−	0.531224i
$476$	−0.00634281		0.000777006i	−0.000290722		3.56140e-5i
$477$		0			0
$478$	10.2821	−	21.0889i	0.470293	−	0.964584i
$479$	0.187642	−	0.325005i	0.00857356	−	0.0148498i	−0.861707	−	0.507407i	$-0.830604\pi$
$479$	0.187642	−	0.325005i	0.00857356	−	0.0148498i	0.870280	+	0.492557i	$0.163938\pi$
$480$		0			0
$481$	12.3600	+	21.4081i	0.563567	+	0.976126i
$482$	−11.3745	+	0.796970i	−0.518092	+	0.0363010i
$483$		0			0
$484$	−33.9040	−	25.5337i	−1.54109	−	1.16062i
$485$	−5.14051	−	2.12927i	−0.233418	−	0.0966850i
$486$		0			0
$487$	23.4958	−	23.4958i	1.06470	−	1.06470i	0.0669402	−	0.997757i	$-0.478676\pi$
$487$	23.4958	−	23.4958i	1.06470	−	1.06470i	0.997757	−	0.0669402i	$-0.0213237\pi$
$488$	27.3652	−	2.16519i	1.23877	−	0.0980134i
$489$		0			0
$490$	−6.31596	−	2.11231i	−0.285326	−	0.0954245i
$491$	3.56902	+	27.1094i	0.161068	+	1.22343i	0.860769	+	0.508996i	$0.169983\pi$
$491$	3.56902	+	27.1094i	0.161068	+	1.22343i	−0.699701	+	0.714436i	$0.746684\pi$
$492$		0			0
$493$	−0.00402741		0.000530218i	−0.000181385		2.38798e-5i
$494$	−10.4814	−	30.4263i	−0.471579	−	1.36895i
$495$		0			0
$496$	19.8752	+	4.94370i	0.892424	+	0.221979i
$497$	1.01220	−	1.75317i	0.0454032	−	0.0786406i
$498$		0			0
$499$	−23.1493	−	17.7631i	−1.03631	−	0.795185i	−0.0571640	−	0.998365i	$-0.518206\pi$
$499$	−23.1493	−	17.7631i	−1.03631	−	0.795185i	−0.979141	+	0.203180i	$0.934872\pi$
$500$	12.9229	−	0.116374i	0.577929	−	0.00520439i
$501$		0			0
$502$	−2.10737	−	10.3507i	−0.0940567	−	0.461974i
$503$	25.8068	−	25.8068i	1.15067	−	1.15067i	0.164251	−	0.986419i	$-0.447479\pi$
$503$	25.8068	−	25.8068i	1.15067	−	1.15067i	0.986419	−	0.164251i	$-0.0525207\pi$
$504$		0			0
$505$	0.362213	+	0.362213i	0.0161183	+	0.0161183i
$506$	1.92254	−	2.90551i	0.0854671	−	0.129166i
$507$		0			0
$508$	−27.5194	−	11.1097i	−1.22098	−	0.492911i
$509$	3.53290	−	4.60417i	0.156593	−	0.204076i	−0.708468	−	0.705743i	$-0.750613\pi$
$509$	3.53290	−	4.60417i	0.156593	−	0.204076i	0.865061	+	0.501667i	$0.167280\pi$
$510$		0			0
$511$	−1.52046	−	0.877838i	−0.0672612	−	0.0388333i
$512$	−13.3230	−	18.2893i	−0.588798	−	0.808280i
$513$		0			0
$514$	−4.95205	+	10.1568i	−0.218426	+	0.447997i
$515$	−1.58118	+	12.0103i	−0.0696753	+	0.529237i
$516$		0			0
$517$	66.1806	−	8.71284i	2.91062	−	0.383190i
$518$	1.23997	−	0.618441i	0.0544811	−	0.0271727i
$519$		0			0
$520$	3.21217	−	9.90012i	0.140863	−	0.434149i
$521$	−20.3324	−	20.3324i	−0.890777	−	0.890777i	0.103819	−	0.994596i	$-0.466894\pi$
$521$	−20.3324	−	20.3324i	−0.890777	−	0.890777i	−0.994596	+	0.103819i	$0.966894\pi$
$522$		0			0
$523$	−14.0229	+	33.8544i	−0.613181	+	1.48035i	0.246307	+	0.969192i	$0.420783\pi$
$523$	−14.0229	+	33.8544i	−0.613181	+	1.48035i	−0.859487	+	0.511157i	$0.829217\pi$
$524$	9.08200	−	5.35311i	0.396749	−	0.233852i
$525$		0			0
$526$	24.5968	−	28.3033i	1.07247	−	1.23408i
$527$	−0.0657846	+	0.0379807i	−0.00286562	+	0.00165447i
$528$		0			0
$529$	−19.7555	−	11.4058i	−0.858933	−	0.495905i
$530$	−1.14494	+	0.394414i	−0.0497332	+	0.0171322i
$531$		0			0
$532$	−1.73812	+	0.482544i	−0.0753569	+	0.0209209i
$533$	6.01319	+	7.83654i	0.260460	+	0.339438i
$534$		0			0
$535$	1.45541	−	5.43166i	0.0629228	−	0.234831i
$536$	−35.6941	−	17.0069i	−1.54175	−	0.734588i
$537$		0			0
$538$	−13.0386	+	19.7051i	−0.562134	+	0.849549i
$539$	15.1052	−	36.4671i	0.650625	−	1.57075i
$540$		0			0
$541$	27.4696	−	11.3783i	1.18101	−	0.489191i	0.296193	−	0.955128i	$-0.404283\pi$
$541$	27.4696	−	11.3783i	1.18101	−	0.489191i	0.884818	+	0.465937i	$0.154283\pi$
$542$	−7.50385	+	5.06293i	−0.322318	+	0.217472i
$543$		0			0
$544$	0.0826581	+	0.0145155i	0.00354394	+	0.000622349i
$545$	−5.95037	+	3.43545i	−0.254886	+	0.147158i
$546$		0			0
$547$	−13.0199	−	1.71410i	−0.556689	−	0.0732895i	−0.153068	−	0.988216i	$-0.548915\pi$
$547$	−13.0199	−	1.71410i	−0.556689	−	0.0732895i	−0.403621	+	0.914926i	$0.632249\pi$
$548$	−3.35979	+	27.4264i	−0.143523	+	1.17160i
$549$		0			0
$550$	−2.22055	+	36.3889i	−0.0946847	+	1.55163i
$551$	−1.10761	+	0.296783i	−0.0471858	+	0.0126434i
$552$		0			0
$553$	0.790353	+	0.211774i	0.0336092	+	0.00900556i
$554$	13.0516	−	39.0250i	0.554507	−	1.65801i
$555$		0			0
$556$	−0.653442	+	2.52958i	−0.0277121	+	0.107278i
$557$	7.13067	−	2.95362i	0.302136	−	0.125149i	−0.226465	−	0.974019i	$-0.572717\pi$
$557$	7.13067	−	2.95362i	0.302136	−	0.125149i	0.528601	+	0.848870i	$0.322717\pi$
$558$		0			0
$559$	−36.6937			−1.55198
$560$	−0.542937	−	0.213520i	−0.0229433	−	0.00902285i
$561$		0			0
$562$	17.0522	+	14.8191i	0.719303	+	0.625104i
$563$	−22.3260	+	29.0958i	−0.940929	+	1.22624i	0.0330156	+	0.999455i	$0.489489\pi$
$563$	−22.3260	+	29.0958i	−0.940929	+	1.22624i	−0.973944	+	0.226787i	$0.927178\pi$
$564$		0			0
$565$	−10.4698	+	8.03374i	−0.440467	+	0.337982i
$566$	7.46195	+	8.43184i	0.313649	+	0.354417i
$567$		0			0
$568$	−14.4707	+	22.3033i	−0.607176	+	0.935824i
$569$	0.708785	+	2.64522i	0.0297138	+	0.110893i	0.979190	−	0.202946i	$-0.0650514\pi$
$569$	0.708785	+	2.64522i	0.0297138	+	0.110893i	−0.949476	+	0.313839i	$0.898385\pi$
$570$		0			0
$571$	−4.98129	−	37.8367i	−0.208461	−	1.58342i	−0.701023	−	0.713139i	$-0.747273\pi$
$571$	−4.98129	−	37.8367i	−0.208461	−	1.58342i	0.492562	−	0.870277i	$-0.336060\pi$
$572$	57.2022	+	23.0927i	2.39174	+	0.965553i
$573$		0			0
$574$	0.458979	−	0.309678i	0.0191574	−	0.0129257i
$575$	−1.97094			−0.0821937
$576$		0			0
$577$	−33.6046			−1.39898			−0.699489	−	0.714643i	$-0.746589\pi$
$577$	−33.6046			−1.39898			−0.699489	+	0.714643i	$0.746589\pi$
$578$	19.9293	−	13.4465i	0.828949	−	0.559301i
$579$		0			0
$580$	−0.343900	−	0.138833i	−0.0142797	−	0.00576474i
$581$	−0.0677695	−	0.514761i	−0.00281155	−	0.0213559i
$582$		0			0
$583$	−1.85761	−	6.93269i	−0.0769343	−	0.287123i
$584$	19.3428	+	12.5498i	0.800409	+	0.519316i
$585$		0			0
$586$	24.5800	+	27.7749i	1.01539	+	1.14737i
$587$	31.6921	−	24.3182i	1.30807	−	1.00372i	0.309470	−	0.950909i	$-0.399848\pi$
$587$	31.6921	−	24.3182i	1.30807	−	1.00372i	0.998605	−	0.0528114i	$-0.0168182\pi$
$588$		0			0
$589$	−13.0535	+	17.0116i	−0.537860	+	0.700952i
$590$	−6.19123	−	5.38044i	−0.254889	−	0.221509i
$591$		0			0
$592$	−16.6843	+	7.26557i	−0.685719	+	0.298613i
$593$	33.6668			1.38253			0.691265	−	0.722601i	$-0.257054\pi$
$593$	33.6668			1.38253			0.691265	+	0.722601i	$0.257054\pi$
$594$		0			0
$595$	0.00199912		0.000828061i	8.19557e−5		3.39472e-5i
$596$	−8.66926	+	33.5601i	−0.355107	+	1.37467i
$597$		0			0
$598$	−1.05777	+	3.16280i	−0.0432554	+	0.129337i
$599$	−25.5424	−	6.84407i	−1.04363	−	0.279641i	−0.304016	−	0.952667i	$-0.598328\pi$
$599$	−25.5424	−	6.84407i	−1.04363	−	0.279641i	−0.739619	+	0.673026i	$0.764994\pi$
$600$		0			0
$601$	−43.5605	+	11.6720i	−1.77687	+	0.476111i	−0.990007	−	0.141018i	$-0.954962\pi$
$601$	−43.5605	+	11.6720i	−1.77687	+	0.476111i	−0.786862	+	0.617129i	$0.788296\pi$
$602$	−0.125279	+	2.05299i	−0.00510600	+	0.0836734i
$603$		0			0
$604$	−0.137901	+	1.12570i	−0.00561111	+	0.0458042i
$605$	14.2491	+	1.87593i	0.579307	+	0.0762672i
$606$		0			0
$607$	−22.1830	+	12.8074i	−0.900380	+	0.519835i	−0.877323	−	0.479899i	$-0.840673\pi$
$607$	−22.1830	+	12.8074i	−0.900380	+	0.519835i	−0.0230566	+	0.999734i	$0.507340\pi$
$608$	23.1250	−	5.14357i	0.937842	−	0.208599i
$609$		0			0
$610$	−7.70538	+	5.19890i	−0.311982	+	0.210497i
$611$	−59.0332	+	24.4523i	−2.38823	+	0.989236i
$612$		0			0
$613$	−0.393125	+	0.949089i	−0.0158782	+	0.0383333i	−0.931620	−	0.363434i	$-0.881604\pi$
$613$	−0.393125	+	0.949089i	−0.0158782	+	0.0383333i	0.915742	+	0.401768i	$0.131604\pi$
$614$	16.3213	−	24.6663i	0.658675	−	0.995451i
$615$		0			0
$616$	1.48732	−	3.12158i	0.0599257	−	0.125772i
$617$	1.95430	−	7.29355i	0.0786772	−	0.293627i	−0.915365	−	0.402626i	$-0.868098\pi$
$617$	1.95430	−	7.29355i	0.0786772	−	0.293627i	0.994042	+	0.108998i	$0.0347643\pi$
$618$		0			0
$619$	2.98955	+	3.89606i	0.120160	+	0.156596i	0.849560	−	0.527492i	$-0.176867\pi$
$619$	2.98955	+	3.89606i	0.120160	+	0.156596i	−0.729400	+	0.684087i	$0.760201\pi$
$620$	−6.68238	+	1.85519i	−0.268371	+	0.0745063i
$621$		0			0
$622$	−33.5664	+	11.5631i	−1.34589	+	0.463637i
$623$	0.648302	+	0.374298i	0.0259737	+	0.0149959i
$624$		0			0
$625$	15.8749	−	9.16537i	0.634995	−	0.366615i
$626$	−10.8232	+	12.4542i	−0.432582	+	0.497769i
$627$		0			0
$628$	−19.6864	+	11.6036i	−0.785573	+	0.463032i
$629$	0.0258285	−	0.0623556i	0.00102985	−	0.00248628i
$630$		0			0
$631$	23.6010	+	23.6010i	0.939541	+	0.939541i	0.998274	−	0.0587323i	$-0.0187058\pi$
$631$	23.6010	+	23.6010i	0.939541	+	0.939541i	−0.0587323	+	0.998274i	$0.518706\pi$
$632$	−10.2213	−	3.31639i	−0.406583	−	0.131919i
$633$		0			0
$634$	19.9799	−	9.96507i	0.793502	−	0.395763i
$635$	9.96322	−	1.31168i	0.395378	−	0.0520526i
$636$		0			0
$637$	−4.93176	+	37.4604i	−0.195403	+	1.48424i
$638$	0.963294	−	1.97574i	0.0381372	−	0.0782204i
$639$		0			0
$640$	6.97521	+	3.17058i	0.275719	+	0.125328i
$641$	28.2977	+	16.3377i	1.11769	+	0.645300i	0.940811	−	0.338932i	$-0.110066\pi$
$641$	28.2977	+	16.3377i	1.11769	+	0.645300i	0.176882	+	0.984232i	$0.443399\pi$
$642$		0			0
$643$	−8.11552	+	10.5764i	−0.320045	+	0.417091i	−0.925476	−	0.378807i	$-0.876334\pi$
$643$	−8.11552	+	10.5764i	−0.320045	+	0.417091i	0.605431	+	0.795898i	$0.293001\pi$
$644$	0.173345	+	0.0699798i	0.00683075	+	0.00275759i
$645$		0			0
$646$	−0.0484854	+	0.0732756i	−0.00190763	+	0.00288299i
$647$	11.4323	+	11.4323i	0.449448	+	0.449448i	0.895171	−	0.445723i	$-0.147053\pi$
$647$	11.4323	+	11.4323i	0.449448	+	0.449448i	−0.445723	+	0.895171i	$0.647053\pi$
$648$		0			0
$649$	34.3758	−	34.3758i	1.34937	−	1.34937i
$650$	−6.96220	−	34.1960i	−0.273080	−	1.34128i
$651$		0			0
$652$	−45.4131	+	0.408956i	−1.77851	+	0.0160160i
$653$	−32.7578	−	25.1359i	−1.28191	−	0.983645i	−0.999705	−	0.0242915i	$-0.992267\pi$
$653$	−32.7578	−	25.1359i	−1.28191	−	0.983645i	−0.282207	−	0.959354i	$-0.591066\pi$
$654$		0			0
$655$	−1.78488	+	3.09150i	−0.0697410	+	0.120795i
$656$	−6.23081	+	3.74857i	−0.243272	+	0.146357i
$657$		0			0
$658$	1.16654	+	3.38635i	0.0454765	+	0.132014i
$659$	0.227175	+	0.0299082i	0.00884949	+	0.00116506i	0.134950	−	0.990852i	$-0.456913\pi$
$659$	0.227175	+	0.0299082i	0.00884949	+	0.00116506i	−0.126100	+	0.992018i	$0.540246\pi$
$660$		0			0
$661$	−5.06243	−	38.4530i	−0.196906	−	1.49565i	−0.749392	−	0.662126i	$-0.769654\pi$
$661$	−5.06243	−	38.4530i	−0.196906	−	1.49565i	0.552486	−	0.833522i	$-0.313679\pi$
$662$	−20.2041	−	6.75708i	−0.785256	−	0.262621i
$663$		0			0
$664$	0.537827	+	6.79746i	0.0208718	+	0.263793i
$665$	0.431910	−	0.431910i	0.0167488	−	0.0167488i
$666$		0			0
$667$	0.109788	+	0.0454755i	0.00425099	+	0.00176082i
$668$	−23.3321	−	17.5718i	−0.902746	−	0.679874i
$669$		0			0
$670$	13.3557	−	0.935787i	0.515974	−	0.0361526i
$671$	−27.5457	−	47.7105i	−1.06339	−	1.84184i
$672$		0			0
$673$	−2.41000	+	4.17424i	−0.0928986	+	0.160905i	−0.908730	−	0.417385i	$-0.862947\pi$
$673$	−2.41000	+	4.17424i	−0.0928986	+	0.160905i	0.815831	+	0.578290i	$0.196280\pi$
$674$	−6.13216	+	12.5772i	−0.236202	+	0.484457i
$675$		0			0
$676$	−32.8044	−	4.01860i	−1.26171	−	0.154562i
$677$	7.79586	−	5.98197i	0.299619	−	0.229906i	−0.448000	−	0.894034i	$-0.647864\pi$
$677$	7.79586	−	5.98197i	0.299619	−	0.229906i	0.747619	+	0.664128i	$0.231197\pi$
$678$		0			0
$679$	1.70914	+	0.457963i	0.0655908	+	0.0175750i
$680$	−0.0267836	+	0.00949717i	−0.00102711	+	0.000364200i
$681$		0			0
$682$	−8.20030	−	40.2771i	−0.314006	−	1.54229i
$683$	22.2635	+	9.22185i	0.851890	+	0.352864i	0.765530	−	0.643400i	$-0.222477\pi$
$683$	22.2635	+	9.22185i	0.851890	+	0.352864i	0.0863595	+	0.996264i	$0.472477\pi$
$684$		0			0
$685$	−3.58054	−	8.64420i	−0.136806	−	0.330278i
$686$	4.17196	+	0.810344i	0.159286	+	0.0309391i
$687$		0			0
$688$	3.04291	−	26.8401i	0.116010	−	1.02327i
$689$	3.43516	+	5.94987i	0.130869	+	0.226672i
$690$		0			0
$691$	4.05827	−	30.8256i	0.154384	−	1.17266i	−0.722295	−	0.691585i	$-0.756913\pi$
$691$	4.05827	−	30.8256i	0.154384	−	1.17266i	0.876679	−	0.481076i	$-0.159754\pi$
$692$	−31.9831	−	18.0834i	−1.21581	−	0.687428i
$693$		0			0
$694$	4.02126	−	3.55871i	0.152645	−	0.135087i
$695$	−0.228970	−	0.854527i	−0.00868532	−	0.0324140i
$696$		0			0
$697$	0.00698017	−	0.0260504i	0.000264393	−	0.000986728i
$698$	2.94732	+	5.90936i	0.111558	+	0.223672i
$699$		0			0
$700$	−1.93701	+	0.272779i	−0.0732121	+	0.0103101i
$701$	−17.9882	−	43.4273i	−0.679404	−	1.64023i	−0.765104	−	0.643906i	$-0.777313\pi$
$701$	−17.9882	−	43.4273i	−0.679404	−	1.64023i	0.0856997	−	0.996321i	$-0.472687\pi$
$702$		0			0
$703$		−	19.0522i		−	0.718569i
$704$	−21.6351	+	39.9264i	−0.815403	+	1.50478i
$705$		0			0
$706$	17.7159	−	1.24129i	0.666747	−	0.0467167i
$707$	−0.129238	−	0.0991675i	−0.00486048	−	0.00372958i
$708$		0			0
$709$	−25.0771	−	32.6811i	−0.941791	−	1.22737i	−0.973691	−	0.227874i	$-0.926822\pi$
$709$	−25.0771	−	32.6811i	−0.941791	−	1.22737i	0.0319000	−	0.999491i	$-0.489844\pi$
$710$	0.548342	−	8.98584i	0.0205789	−	0.337233i
$711$		0			0
$712$	−8.24747	−	5.35108i	−0.309087	−	0.200540i
$713$	2.14644	−	0.575136i	0.0803847	−	0.0215390i
$714$		0			0
$715$	−20.7097	+	2.72648i	−0.774498	+	0.101965i
$716$	−26.6978	+	0.240421i	−0.997744	+	0.00898494i
$717$		0			0
$718$	18.0174	+	3.49962i	0.672402	+	0.130605i
$719$			17.9058i			0.667773i	0.942613	+	0.333886i	$0.108360\pi$
$719$			17.9058i			0.667773i	−0.942613	+	0.333886i	$0.891640\pi$
$720$		0			0
$721$		−	3.85237i		−	0.143470i
$722$	0.394191	−	2.02944i	0.0146703	−	0.0755281i
$723$		0			0
$724$	1.18890	−	1.21050i	0.0441850	−	0.0449880i
$725$	−1.23284	+	0.162306i	−0.0457864	+	0.00602790i
$726$		0			0
$727$	39.6198	−	10.6161i	1.46942	−	0.393729i	0.566686	−	0.823934i	$-0.308225\pi$
$727$	39.6198	−	10.6161i	1.46942	−	0.393729i	0.902732	+	0.430204i	$0.141558\pi$
$728$	−0.601828	+	3.25476i	−0.0223052	+	0.120629i
$729$		0			0
$730$	−7.79307	−	0.475556i	−0.288434	−	0.0176011i
$731$	0.0609889	+	0.0794823i	0.00225576	+	0.00293976i
$732$		0			0
$733$	18.3166	+	14.0548i	0.676539	+	0.519126i	0.888921	−	0.458060i	$-0.151456\pi$
$733$	18.3166	+	14.0548i	0.676539	+	0.519126i	−0.212383	+	0.977187i	$0.568122\pi$
$734$	−2.76239	−	39.4251i	−0.101962	−	1.45521i
$735$		0			0
$736$	−2.22576	−	1.03600i	−0.0820425	−	0.0381876i
$737$			79.3509i			2.92293i
$738$		0			0
$739$	−8.19677	−	19.7888i	−0.301523	−	0.727941i	−0.999925	−	0.0122357i	$-0.996105\pi$
$739$	−8.19677	−	19.7888i	−0.301523	−	0.727941i	0.698402	−	0.715706i	$-0.253895\pi$
$740$	3.70701	−	4.92222i	0.136272	−	0.180944i
$741$		0			0
$742$	0.344619	−	0.171881i	0.0126514	−	0.00630994i
$743$	−2.76434	+	10.3167i	−0.101414	+	0.378482i	−0.997914	−	0.0645625i	$-0.979435\pi$
$743$	−2.76434	+	10.3167i	−0.101414	+	0.378482i	0.896500	+	0.443044i	$0.146101\pi$
$744$		0			0
$745$	−3.03776	−	11.3371i	−0.111295	−	0.415358i
$746$	−2.90142	−	3.27853i	−0.106228	−	0.120036i
$747$		0			0
$748$	−0.0450552	−	0.162288i	−0.00164738	−	0.00593385i
$749$	−0.233416	+	1.77297i	−0.00852882	+	0.0647828i
$750$		0			0
$751$	−0.984092	−	1.70450i	−0.0359100	−	0.0621980i	0.847512	−	0.530777i	$-0.178100\pi$
$751$	−0.984092	−	1.70450i	−0.0359100	−	0.0621980i	−0.883422	+	0.468579i	$0.844766\pi$
$752$	−12.9906	−	45.2084i	−0.473717	−	1.64858i
$753$		0			0
$754$	−0.401188	+	2.06547i	−0.0146104	+	0.0752199i
$755$	−0.146962	−	0.354797i	−0.00534849	−	0.0129124i
$756$		0			0
$757$	−4.06977	−	1.68576i	−0.147918	−	0.0612698i	0.307496	−	0.951549i	$-0.400509\pi$
$757$	−4.06977	−	1.68576i	−0.147918	−	0.0612698i	−0.455414	+	0.890280i	$0.650509\pi$
$758$	1.73787	−	0.353825i	0.0631222	−	0.0128515i
$759$		0			0
$760$	−5.95914	+	5.37014i	−0.216161	+	0.194795i
$761$	4.44416	+	1.19081i	0.161101	+	0.0431668i	0.338468	−	0.940978i	$-0.390091\pi$
$761$	4.44416	+	1.19081i	0.161101	+	0.0431668i	−0.177367	+	0.984145i	$0.556758\pi$
$762$		0			0
$763$	1.73350	−	1.33016i	0.0627568	−	0.0481550i
$764$	−7.08853	−	9.06770i	−0.256454	−	0.328058i
$765$		0			0
$766$	−23.0414	−	11.2341i	−0.832520	−	0.405904i
$767$	−23.2679	+	40.3011i	−0.840154	+	1.45519i
$768$		0			0
$769$	8.62649	+	14.9415i	0.311079	+	0.538805i	0.978596	−	0.205789i	$-0.0659762\pi$
$769$	8.62649	+	14.9415i	0.311079	+	0.538805i	−0.667517	+	0.744595i	$0.732643\pi$
$770$	0.0818379	+	1.16800i	0.00294923	+	0.0420918i
$771$		0			0
$772$	−16.3696	+	2.30525i	−0.589156	+	0.0829678i
$773$	17.1447	+	7.10157i	0.616652	+	0.255426i	0.669070	−	0.743200i	$-0.266693\pi$
$773$	17.1447	+	7.10157i	0.616652	+	0.255426i	−0.0524178	+	0.998625i	$0.516693\pi$
$774$		0			0
$775$	−16.4421	+	16.4421i	−0.590619	+	0.590619i
$776$	−22.1037	−	7.17171i	−0.793475	−	0.257449i
$777$		0			0
$778$	12.3536	−	36.9380i	0.442897	−	1.32429i
$779$	−0.993696	−	7.54787i	−0.0356029	−	0.270431i
$780$		0			0
$781$	52.9002	+	6.96445i	1.89292	+	0.249207i
$782$	0.00860908	−	0.00296568i	0.000307860	−	0.000106053i
$783$		0			0
$784$	−26.9920	−	6.71390i	−0.964000	−	0.239782i
$785$	3.86895	−	6.70123i	0.138089	−	0.239177i
$786$		0			0
$787$	21.2521	+	16.3073i	0.757554	+	0.581292i	0.913675	−	0.406446i	$-0.133232\pi$
$787$	21.2521	+	16.3073i	0.757554	+	0.581292i	−0.156121	+	0.987738i	$0.549899\pi$
$788$	−36.8454	+	37.5150i	−1.31256	+	1.33642i
$789$		0			0
$790$	3.56557	−	0.725940i	0.126857	−	0.0258278i
$791$	2.96756	−	2.96756i	0.105514	−	0.105514i
$792$		0			0
$793$	37.2896	+	37.2896i	1.32419	+	1.32419i
$794$	−27.0301	−	17.8854i	−0.959262	−	0.634730i
$795$		0			0
$796$	−0.790593	−	1.86108i	−0.0280218	−	0.0659642i
$797$	−11.8786	+	15.4805i	−0.420762	+	0.548347i	−0.954853	−	0.297080i	$-0.903987\pi$
$797$	−11.8786	+	15.4805i	−0.420762	+	0.548347i	0.534091	+	0.845427i	$0.320654\pi$
$798$		0			0
$799$	0.151086	+	0.0872295i	0.00534503	+	0.00308596i
$800$	25.5905	−	2.25682i	0.904760	−	0.0797908i
$801$		0			0
$802$	−21.2006	−	10.3366i	−0.748618	−	0.364996i
$803$	6.03999	−	45.8783i	0.213147	−	1.61901i
$804$		0			0
$805$	−0.0627584	+	0.00826230i	−0.00221194	+	0.000291208i
$806$	17.5608	+	35.2093i	0.618554	+	1.24019i
$807$		0			0
$808$	1.62738	+	1.38873i	0.0572509	+	0.0488555i
$809$	0.0988201	+	0.0988201i	0.00347433	+	0.00347433i	0.708842	−	0.705367i	$-0.249218\pi$
$809$	0.0988201	+	0.0988201i	0.00347433	+	0.00347433i	−0.705367	+	0.708842i	$0.749218\pi$
$810$		0			0
$811$	9.29653	−	22.4438i	0.326445	−	0.788109i	−0.672405	−	0.740183i	$-0.734739\pi$
$811$	9.29653	−	22.4438i	0.326445	−	0.788109i	0.998851	−	0.0479260i	$-0.0152612\pi$
$812$	0.114192	+	0.0294981i	0.00400734	+	0.00103518i
$813$		0			0
$814$	27.5662	+	23.9562i	0.966194	+	0.839663i
$815$	13.3179	−	7.68909i	0.466506	−	0.269337i
$816$		0			0
$817$	24.4918	+	14.1403i	0.856859	+	0.494708i
$818$	3.28453	+	9.53465i	0.114841	+	0.333371i
$819$		0			0
$820$	1.21187	−	2.14336i	0.0423203	−	0.0748495i
$821$	32.0606	+	41.7822i	1.11892	+	1.45821i	0.872218	+	0.489117i	$0.162681\pi$
$821$	32.0606	+	41.7822i	1.11892	+	1.45821i	0.246704	+	0.969091i	$0.420652\pi$
$822$		0			0
$823$	7.43890	−	27.7624i	0.259304	−	0.967735i	−0.706341	−	0.707871i	$-0.749656\pi$
$823$	7.43890	−	27.7624i	0.259304	−	0.967735i	0.965645	−	0.259864i	$-0.0836777\pi$
$824$	−2.62675	+	50.5251i	−0.0915073	+	1.76013i
$825$		0			0
$826$	2.17538	+	1.43942i	0.0756911	+	0.0500837i
$827$	11.6589	−	28.1470i	0.405419	−	0.978767i	−0.580909	−	0.813969i	$-0.697303\pi$
$827$	11.6589	−	28.1470i	0.405419	−	0.978767i	0.986327	−	0.164798i	$-0.0526973\pi$
$828$		0			0
$829$	−22.6347	+	9.37559i	−0.786135	+	0.325628i	−0.739388	−	0.673279i	$-0.764885\pi$
$829$	−22.6347	+	9.37559i	−0.786135	+	0.325628i	−0.0467464	+	0.998907i	$0.514885\pi$
$830$	−1.29140	−	1.91400i	−0.0448250	−	0.0664359i
$831$		0			0
$832$	10.1124	−	42.2768i	0.350585	−	1.46568i
$833$	0.0893403	−	0.0515806i	0.00309546	−	0.00178716i
$834$		0			0
$835$	9.80594	+	1.29098i	0.339349	+	0.0446761i
$836$	−29.2815	−	37.4571i	−1.01272	−	1.29548i
$837$		0			0
$838$	10.0992	+	0.616281i	0.348870	+	0.0212891i
$839$	−7.24339	+	1.94086i	−0.250070	+	0.0670059i	−0.381676	−	0.924296i	$-0.624653\pi$
$839$	−7.24339	+	1.94086i	−0.250070	+	0.0670059i	0.131607	+	0.991302i	$0.457986\pi$
$840$		0			0
$841$	−27.9394	−	7.48635i	−0.963429	−	0.258150i
$842$	28.8804	+	9.65879i	0.995286	+	0.332864i
$843$		0			0
$844$	0.994816	−	0.586364i	0.0342430	−	0.0201835i
$845$	10.3392	−	4.28265i	0.355680	−	0.147328i
$846$		0			0
$847$	−4.57048			−0.157043
$848$	−4.63699	+	2.01929i	−0.159235	+	0.0693427i
$849$		0			0
$850$	−0.0625000	+	0.0719182i	−0.00214373	+	0.00246677i
$851$	−1.20195	+	1.56642i	−0.0412025	+	0.0536961i
$852$		0			0
$853$	−32.5584	+	24.9830i	−1.11478	+	0.855401i	−0.990591	−	0.136858i	$-0.956300\pi$
$853$	−32.5584	+	24.9830i	−1.11478	+	0.855401i	−0.124189	+	0.992259i	$0.539633\pi$
$854$	2.21364	−	1.95901i	0.0757492	−	0.0670360i
$855$		0			0
$856$	4.27022	−	23.0939i	0.145953	−	0.789332i
$857$	−7.74621	−	28.9093i	−0.264606	−	0.987522i	−0.962491	−	0.271313i	$-0.912542\pi$
$857$	−7.74621	−	28.9093i	−0.264606	−	0.987522i	0.697886	−	0.716209i	$-0.254124\pi$
$858$		0			0
$859$	2.74932	+	20.8832i	0.0938057	+	0.712525i	0.972127	+	0.234455i	$0.0753304\pi$
$859$	2.74932	+	20.8832i	0.0938057	+	0.712525i	−0.878321	+	0.478071i	$0.841336\pi$
$860$	3.57624	+	8.41859i	0.121949	+	0.287071i
$861$		0			0
$862$	−13.0532	−	19.3464i	−0.444595	−	0.658941i
$863$	33.8067			1.15079			0.575397	−	0.817874i	$-0.304848\pi$
$863$	33.8067			1.15079			0.575397	+	0.817874i	$0.304848\pi$
$864$		0			0
$865$	12.4412			0.423013
$866$	−24.1946	−	35.8592i	−0.822166	−	1.21855i
$867$		0			0
$868$	2.02989	−	0.862304i	0.0688990	−	0.0292685i
$869$	2.81494	+	21.3816i	0.0954904	+	0.725321i
$870$		0			0
$871$	−19.6593	−	73.3693i	−0.666129	−	2.48603i
$872$	−23.6423	+	16.2635i	−0.800631	+	0.550751i
$873$		0			0
$874$	1.92485	−	1.70344i	0.0651089	−	0.0576196i
$875$	1.10406	−	0.847177i	0.0373241	−	0.0286398i
$876$		0			0
$877$	−0.785283	+	1.02340i	−0.0265171	+	0.0345578i	−0.806424	−	0.591338i	$-0.798600\pi$
$877$	−0.785283	+	1.02340i	−0.0265171	+	0.0345578i	0.779907	+	0.625896i	$0.215267\pi$
$878$	−13.6516	+	15.7087i	−0.460718	+	0.530144i
$879$		0			0
$880$	−0.276925	−	15.3745i	−0.00933514	−	0.518274i
$881$	−29.1795			−0.983083			−0.491541	−	0.870854i	$-0.663566\pi$
$881$	−29.1795			−0.983083			−0.491541	+	0.870854i	$0.663566\pi$
$882$		0			0
$883$	31.0060	−	12.8431i	1.04344	−	0.432205i	0.205891	−	0.978575i	$-0.433991\pi$
$883$	31.0060	−	12.8431i	1.04344	−	0.432205i	0.837544	+	0.546370i	$0.183991\pi$
$884$	0.0818660	+	0.138892i	0.00275345	+	0.00467146i
$885$		0			0
$886$	−13.1188	−	4.38744i	−0.440733	−	0.147399i
$887$	−23.9620	−	6.42059i	−0.804564	−	0.215582i	−0.166977	−	0.985961i	$-0.553401\pi$
$887$	−23.9620	−	6.42059i	−0.804564	−	0.215582i	−0.637587	+	0.770378i	$0.720067\pi$
$888$		0			0
$889$	−3.08687	+	0.827125i	−0.103530	+	0.0277409i
$890$	3.32285	+	0.202770i	0.111382	+	0.00679687i
$891$		0			0
$892$	25.3091	−	19.7850i	0.847412	−	0.662451i
$893$	48.8256	+	6.42802i	1.63389	+	0.215105i
$894$		0			0
$895$	7.82943	−	4.52033i	0.261709	−	0.151098i
$896$	−2.33083	−	0.710124i	−0.0778676	−	0.0237236i
$897$		0			0
$898$	−2.20485	−	3.26784i	−0.0735767	−	0.109049i
$899$	1.29525	−	0.536511i	0.0431991	−	0.0178936i
$900$		0			0
$901$	0.00717842	−	0.0173302i	0.000239148	−	0.000577354i
$902$	12.1703	+	8.05289i	0.405226	+	0.268132i
$903$		0			0
$904$	−40.9439	+	36.8970i	−1.36177	+	1.22718i
$905$	−0.148699	+	0.554952i	−0.00494292	+	0.0184472i
$906$		0			0
$907$	15.0625	+	19.6298i	0.500141	+	0.651797i	0.973396	−	0.229129i	$-0.0735877\pi$
$907$	15.0625	+	19.6298i	0.500141	+	0.651797i	−0.473255	+	0.880926i	$0.656921\pi$
$908$	3.85942	+	2.18214i	0.128079	+	0.0724168i
$909$		0			0
$910$	−0.365042	−	1.05968i	−0.0121010	−	0.0351280i
$911$	−44.1489	−	25.4894i	−1.46272	−	0.844501i	−0.463582	−	0.886054i	$-0.653436\pi$
$911$	−44.1489	−	25.4894i	−1.46272	−	0.844501i	−0.999136	+	0.0415531i	$0.986769\pi$
$912$		0			0
$913$	11.8512	−	6.84229i	0.392217	−	0.226447i
$914$	−6.60847	−	5.74304i	−0.218589	−	0.189963i
$915$		0			0
$916$	−8.80761	+	34.0956i	−0.291012	+	1.12655i
$917$	0.434432	−	1.04881i	0.0143462	−	0.0346348i
$918$		0			0
$919$	−3.55656	−	3.55656i	−0.117320	−	0.117320i	0.646009	−	0.763330i	$-0.276437\pi$
$919$	−3.55656	−	3.55656i	−0.117320	−	0.117320i	−0.763330	+	0.646009i	$0.776437\pi$
$920$	0.828730	−	0.0655706i	0.0273224	−	0.00216180i
$921$		0			0
$922$	−20.2438	−	40.5886i	−0.666693	−	1.33671i
$923$	−50.6380	+	6.66662i	−1.66677	+	0.219434i
$924$		0			0
$925$	2.69673	−	20.4837i	0.0886680	−	0.673500i
$926$	−30.4233	−	14.8332i	−0.999772	−	0.487449i
$927$		0			0
$928$	−1.47755	−	0.464738i	−0.0485028	−	0.0152558i
$929$	21.8929	+	12.6399i	0.718284	+	0.414701i	0.814121	−	0.580696i	$-0.197219\pi$
$929$	21.8929	+	12.6399i	0.718284	+	0.414701i	−0.0958368	+	0.995397i	$0.530553\pi$
$930$		0			0
$931$	17.7276	−	23.1030i	0.580998	−	0.757172i
$932$	2.32050	−	0.985758i	0.0760106	−	0.0322896i
$933$		0			0
$934$	35.5368	+	23.5142i	1.16280	+	0.769407i
$935$	0.0403276	+	0.0403276i	0.00131885	+	0.00131885i
$936$		0			0
$937$	8.79433	−	8.79433i	0.287298	−	0.287298i	−0.548713	−	0.836011i	$-0.684882\pi$
$937$	8.79433	−	8.79433i	0.287298	−	0.287298i	0.836011	+	0.548713i	$0.184882\pi$
$938$	−4.17208	+	0.849424i	−0.136223	+	0.0277347i
$939$		0			0
$940$	11.3636	+	11.1607i	0.370639	+	0.364023i
$941$	−9.59558	−	7.36295i	−0.312807	−	0.240025i	0.440411	−	0.897796i	$-0.354833\pi$
$941$	−9.59558	−	7.36295i	−0.312807	−	0.240025i	−0.753218	+	0.657771i	$0.771499\pi$
$942$		0			0
$943$	−0.394476	+	0.683253i	−0.0128459	+	0.0222498i
$944$	−27.5493	−	20.3617i	−0.896654	−	0.662717i
$945$		0			0
$946$	−51.2551	+	17.6565i	−1.66645	+	0.574063i
$947$	2.26421	+	0.298089i	0.0735769	+	0.00968658i	0.167225	−	0.985919i	$-0.446519\pi$
$947$	2.26421	+	0.298089i	0.0735769	+	0.00968658i	−0.0936479	+	0.995605i	$0.529853\pi$
$948$		0			0
$949$	5.78170	+	43.9163i	0.187682	+	1.42559i
$950$	−8.53077	+	25.5076i	−0.276775	+	0.827576i
$951$		0			0
$952$	0.00805043	−	0.00410614i	0.000260916	−	0.000133081i
$953$	−18.6869	+	18.6869i	−0.605327	+	0.605327i	−0.941721	−	0.336394i	$-0.890793\pi$
$953$	−18.6869	+	18.6869i	−0.605327	+	0.605327i	0.336394	+	0.941721i	$0.390793\pi$
$954$		0			0
$955$	3.60065	+	1.49144i	0.116514	+	0.0482619i
$956$	4.62694	+	32.8560i	0.149646	+	1.06264i
$957$		0			0
$958$	0.0370956	+	0.529433i	0.00119850	+	0.0171052i
$959$	1.48773	+	2.57682i	0.0480412	+	0.0832098i
$960$		0			0
$961$	−2.39173	+	4.14260i	−0.0771527	+	0.133632i
$962$	−31.4234	−	15.3208i	−1.01313	−	0.493962i
$963$		0			0
$964$	12.7042	−	9.93129i	0.409174	−	0.319865i
$965$	4.44096	−	3.40767i	0.142959	−	0.109697i
$966$		0			0
$967$	−6.09250	−	1.63248i	−0.195922	−	0.0524971i	0.159524	−	0.987194i	$-0.449004\pi$
$967$	−6.09250	−	1.63248i	−0.195922	−	0.0524971i	−0.355445	+	0.934697i	$0.615671\pi$
$968$	59.9433	+	3.11640i	1.92665	+	0.100165i
$969$		0			0
$970$	7.71056	−	1.56985i	0.247571	−	0.0504048i
$971$	28.7852	+	11.9232i	0.923760	+	0.382634i	0.793308	−	0.608821i	$-0.208357\pi$
$971$	28.7852	+	11.9232i	0.923760	+	0.382634i	0.130452	+	0.991455i	$0.458357\pi$
$972$		0			0
$973$	0.107663	+	0.259921i	0.00345151	+	0.00833267i
$974$	−8.96001	+	46.1295i	−0.287097	+	1.47809i
$975$		0			0
$976$	−30.3683	+	24.1837i	−0.972067	+	0.774101i
$977$	−19.4991	−	33.7734i	−0.623831	−	1.08051i	−0.988766	−	0.149474i	$-0.952242\pi$
$977$	−19.4991	−	33.7734i	−0.623831	−	1.08051i	0.364935	−	0.931033i	$-0.381091\pi$
$978$		0			0
$979$	−2.57537	+	19.5619i	−0.0823091	+	0.625200i
$980$	9.07516	−	2.51949i	0.289895	−	0.0804820i
$981$		0			0
$982$	−25.6271	−	28.9581i	−0.817794	−	0.924089i
$983$	5.13194	+	19.1527i	0.163684	+	0.610875i	0.998204	+	0.0598990i	$0.0190779\pi$
$983$	5.13194	+	19.1527i	0.163684	+	0.610875i	−0.834521	+	0.550976i	$0.814255\pi$
$984$		0			0
$985$	4.60837	−	17.1987i	0.146835	−	0.547995i
$986$	0.00514083	−	0.00256402i	0.000163717	−	8.16549e-5i
$987$		0			0
$988$	36.3542	+	27.3790i	1.15658	+	0.871043i
$989$	−1.12156	−	2.70769i	−0.0356637	−	0.0860997i
$990$		0			0
$991$		−	18.4586i		−	0.586356i	−0.956058	−	0.293178i	$-0.905287\pi$
$991$		−	18.4586i		−	0.586356i	0.956058	−	0.293178i	$-0.0947129\pi$
$992$	−27.2106	+	9.92530i	−0.863938	+	0.315129i
$993$		0			0
$994$	0.200105	+	2.85592i	0.00634694	+	0.0905843i
$995$	0.543205	+	0.416816i	0.0172207	+	0.0132139i
$996$		0			0
$997$	−26.0134	−	33.9014i	−0.823854	−	1.07367i	−0.996067	−	0.0886072i	$-0.971758\pi$
$997$	−26.0134	−	33.9014i	−0.823854	−	1.07367i	0.172213	−	0.985060i	$-0.444908\pi$
$998$	41.1888	+	2.51346i	1.30381	+	0.0795622i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.9		368
3.2	odd	2		288.2.bf.a.11.38	✓	368
9.4	even	3		288.2.bf.a.203.23	yes	368
9.5	odd	6	inner	864.2.bn.a.395.24		368
32.3	odd	8	inner	864.2.bn.a.35.24		368
96.35	even	8		288.2.bf.a.227.23	yes	368
288.67	odd	24		288.2.bf.a.131.38	yes	368
288.131	even	24	inner	864.2.bn.a.611.9		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.38	✓	368	3.2	odd	2
288.2.bf.a.131.38	yes	368	288.67	odd	24
288.2.bf.a.203.23	yes	368	9.4	even	3
288.2.bf.a.227.23	yes	368	96.35	even	8
864.2.bn.a.35.24		368	32.3	odd	8	inner
864.2.bn.a.395.24		368	9.5	odd	6	inner
864.2.bn.a.611.9		368	288.131	even	24	inner
864.2.bn.a.683.9		368	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17233 + 0.790981i) q^{2} +(0.748697 - 1.85458i) q^{4} +(0.0883963 + 0.671437i) q^{5} +(-0.0557412 - 0.208029i) q^{7} +(0.589218 + 2.76637i) q^{8} +O(q^{10})\)	\(q+(-1.17233 + 0.790981i) q^{2} +(0.748697 - 1.85458i) q^{4} +(0.0883963 + 0.671437i) q^{5} +(-0.0557412 - 0.208029i) q^{7} +(0.589218 + 2.76637i) q^{8} +(-0.634723 - 0.717223i) q^{10} +(4.50341 - 3.45559i) q^{11} +(-3.30781 + 4.31082i) q^{13} +(0.229894 + 0.199788i) q^{14} +(-2.87891 - 2.77703i) q^{16} +0.0148356 q^{17} +(3.86908 - 1.60262i) q^{19} +(1.31141 + 0.338765i) q^{20} +(-2.54616 + 7.61319i) q^{22} +(-0.419209 - 0.112327i) q^{23} +(4.38662 - 1.17539i) q^{25} +(0.468052 - 7.67011i) q^{26} +(-0.427539 - 0.0523744i) q^{28} +(-0.271469 - 0.0357395i) q^{29} +(-4.43423 + 2.56010i) q^{31} +(5.57160 + 0.978425i) q^{32} +(-0.0173922 + 0.0117347i) q^{34} +(0.134751 - 0.0558157i) q^{35} +(1.74098 - 4.20310i) q^{37} +(-3.26817 + 4.93916i) q^{38} +(-1.80536 + 0.640160i) q^{40} +(0.470501 - 1.75593i) q^{41} +(4.11098 + 5.35753i) q^{43} +(-3.03696 - 10.9391i) q^{44} +(0.580298 - 0.199903i) q^{46} +(10.1840 + 5.87973i) q^{47} +(6.02201 - 3.47681i) q^{49} +(-4.21283 + 4.84767i) q^{50} +(5.51820 + 9.36209i) q^{52} +(0.483863 - 1.16815i) q^{53} +(2.71829 + 2.71829i) q^{55} +(0.542642 - 0.276775i) q^{56} +(0.346519 - 0.172828i) q^{58} +(8.49106 - 1.11787i) q^{59} +(1.26680 - 9.62227i) q^{61} +(3.17337 - 6.50867i) q^{62} +(-7.30564 + 3.26000i) q^{64} +(-3.18684 - 1.83992i) q^{65} +(-8.50990 + 11.0903i) q^{67} +(0.0111074 - 0.0275138i) q^{68} +(-0.113823 + 0.172020i) q^{70} +(6.64660 + 6.64660i) q^{71} +(5.76433 - 5.76433i) q^{73} +(1.28358 + 6.30449i) q^{74} +(-0.0754224 - 8.37537i) q^{76} +(-0.969888 - 0.744221i) q^{77} +(-1.89962 + 3.29024i) q^{79} +(1.61012 - 2.17848i) q^{80} +(0.837330 + 2.43068i) q^{82} +(2.39015 + 0.314669i) q^{83} +(0.00131141 + 0.00996118i) q^{85} +(-9.05711 - 3.02907i) q^{86} +(12.2129 + 10.4220i) q^{88} +(-2.45783 + 2.45783i) q^{89} +(1.08116 + 0.447830i) q^{91} +(-0.522179 + 0.693356i) q^{92} +(-16.5897 + 1.16239i) q^{94} +(1.41807 + 2.45617i) q^{95} +(-4.10794 + 7.11516i) q^{97} +(-4.30967 + 8.83925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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