LMFDB - Embedded newform 810.2.s.a.773.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.1
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.19457 + 0.428806i) q^{5} +(0.926438 + 0.648699i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.22359 - 0.235905i) q^{10} +(1.09129 - 2.99831i) q^{11} +(-0.104097 - 1.18984i) q^{13} +(-0.866375 - 0.726975i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.07725 + 0.824548i) q^{17} +(-4.45771 + 2.57366i) q^{19} +(-2.23569 + 0.0412092i) q^{20} +(-1.34846 + 2.89179i) q^{22} +(0.618138 + 0.882792i) q^{23} +(4.63225 - 1.88209i) q^{25} +1.19438i q^{26} +(0.799718 + 0.799718i) q^{28} +(4.18252 - 3.50955i) q^{29} +(1.18252 - 6.70642i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.13741 - 0.553210i) q^{34} +(-2.31130 - 1.02635i) q^{35} +(-2.00428 - 7.48009i) q^{37} +(4.66505 - 2.17535i) q^{38} +(2.23077 + 0.153801i) q^{40} +(3.43229 - 4.09044i) q^{41} +(-2.90752 - 6.23520i) q^{43} +(1.59537 - 2.76326i) q^{44} +(-0.538845 - 0.933307i) q^{46} +(-2.77457 + 3.96249i) q^{47} +(-1.95666 - 5.37589i) q^{49} +(-4.77866 + 1.47120i) q^{50} +(0.104097 - 1.18984i) q^{52} +(-3.59451 + 3.59451i) q^{53} +(-1.10923 + 7.04794i) q^{55} +(-0.726975 - 0.866375i) q^{56} +(-4.47248 + 3.13167i) q^{58} +(5.86932 - 2.13626i) q^{59} +(-2.36034 - 13.3861i) q^{61} +(-1.76253 + 6.57784i) q^{62} +(0.866025 + 0.500000i) q^{64} +(0.738658 + 2.56654i) q^{65} +(4.47588 - 0.391589i) q^{67} +(-3.17368 + 0.277661i) q^{68} +(2.21305 + 1.22389i) q^{70} +(-5.95249 - 3.43667i) q^{71} +(-2.81344 + 10.4999i) q^{73} +(1.34472 + 7.62631i) q^{74} +(-4.83689 + 1.76049i) q^{76} +(2.95602 - 2.06982i) q^{77} +(1.98062 + 2.36041i) q^{79} +(-2.20888 - 0.347640i) q^{80} +(-3.77573 + 3.77573i) q^{82} +(1.48805 - 17.0085i) q^{83} +(6.39967 - 3.12907i) q^{85} +(2.35302 + 6.46488i) q^{86} +(-1.83013 + 2.61369i) q^{88} +(-7.57232 - 13.1156i) q^{89} +(0.675406 - 1.16984i) q^{91} +(0.455452 + 0.976719i) q^{92} +(3.10936 - 3.70559i) q^{94} +(8.67914 - 7.55956i) q^{95} +(-0.363881 + 0.169680i) q^{97} +(1.48068 + 5.52597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−2.19457	+	0.428806i	−0.981440	+	0.191768i
$5$	−2.19457	+	0.428806i	−0.981440	+	0.191768i
$6$		0			0
$7$	0.926438	+	0.648699i	0.350161	+	0.245185i	0.735403	−	0.677631i	$-0.236993\pi$
$7$	0.926438	+	0.648699i	0.350161	+	0.245185i	−0.385242	+	0.922816i	$0.625882\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	2.22359	−	0.235905i	0.703161	−	0.0745998i
$11$	1.09129	−	2.99831i	0.329038	−	0.904024i	−0.659318	−	0.751864i	$-0.729155\pi$
$11$	1.09129	−	2.99831i	0.329038	−	0.904024i	0.988356	−	0.152160i	$-0.0486228\pi$
$12$		0			0
$13$	−0.104097	−	1.18984i	−0.0288714	−	0.330001i	−0.996871	−	0.0790487i	$-0.974812\pi$
$13$	−0.104097	−	1.18984i	−0.0288714	−	0.330001i	0.967999	−	0.250953i	$-0.0807438\pi$
$14$	−0.866375	−	0.726975i	−0.231548	−	0.194292i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−3.07725	+	0.824548i	−0.746344	+	0.199982i	−0.611896	−	0.790938i	$-0.709593\pi$
$17$	−3.07725	+	0.824548i	−0.746344	+	0.199982i	−0.134448	+	0.990921i	$0.542926\pi$
$18$		0			0
$19$	−4.45771	+	2.57366i	−1.02267	+	0.590438i	−0.914876	−	0.403736i	$-0.867712\pi$
$19$	−4.45771	+	2.57366i	−1.02267	+	0.590438i	−0.107792	+	0.994173i	$0.534378\pi$
$20$	−2.23569	+	0.0412092i	−0.499915	+	0.00921465i
$21$		0			0
$22$	−1.34846	+	2.89179i	−0.287493	+	0.616531i
$23$	0.618138	+	0.882792i	0.128891	+	0.184075i	0.878410	−	0.477907i	$-0.158604\pi$
$23$	0.618138	+	0.882792i	0.128891	+	0.184075i	−0.749520	+	0.661982i	$0.769716\pi$
$24$		0			0
$25$	4.63225	−	1.88209i	0.926450	−	0.376418i
$26$			1.19438i			0.234237i
$27$		0			0
$28$	0.799718	+	0.799718i	0.151132	+	0.151132i
$29$	4.18252	−	3.50955i	0.776675	−	0.651708i	−0.165734	−	0.986170i	$-0.552999\pi$
$29$	4.18252	−	3.50955i	0.776675	−	0.651708i	0.942409	+	0.334463i	$0.108555\pi$
$30$		0			0
$31$	1.18252	−	6.70642i	0.212387	−	1.20451i	−0.672996	−	0.739646i	$-0.734993\pi$
$31$	1.18252	−	6.70642i	0.212387	−	1.20451i	0.885383	−	0.464862i	$-0.153896\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	3.13741	−	0.553210i	0.538061	−	0.0948747i
$35$	−2.31130	−	1.02635i	−0.390680	−	0.173485i
$36$		0			0
$37$	−2.00428	−	7.48009i	−0.329502	−	1.22972i	−0.909708	−	0.415249i	$-0.863695\pi$
$37$	−2.00428	−	7.48009i	−0.329502	−	1.22972i	0.580206	−	0.814470i	$-0.302972\pi$
$38$	4.66505	−	2.17535i	0.756771	−	0.352888i
$39$		0			0
$40$	2.23077	+	0.153801i	0.352716	+	0.0243180i
$41$	3.43229	−	4.09044i	0.536033	−	0.638820i	−0.428260	−	0.903655i	$-0.640873\pi$
$41$	3.43229	−	4.09044i	0.536033	−	0.638820i	0.964294	+	0.264836i	$0.0853178\pi$
$42$		0			0
$43$	−2.90752	−	6.23520i	−0.443393	−	0.950859i	−0.993293	−	0.115628i	$-0.963112\pi$
$43$	−2.90752	−	6.23520i	−0.443393	−	0.950859i	0.549900	−	0.835231i	$-0.314666\pi$
$44$	1.59537	−	2.76326i	0.240510	−	0.416576i
$45$		0			0
$46$	−0.538845	−	0.933307i	−0.0794484	−	0.137609i
$47$	−2.77457	+	3.96249i	−0.404712	+	0.577989i	−0.968836	−	0.247701i	$-0.920325\pi$
$47$	−2.77457	+	3.96249i	−0.404712	+	0.577989i	0.564125	+	0.825690i	$0.309214\pi$
$48$		0			0
$49$	−1.95666	−	5.37589i	−0.279523	−	0.767984i
$50$	−4.77866	+	1.47120i	−0.675804	+	0.208059i
$51$		0			0
$52$	0.104097	−	1.18984i	0.0144357	−	0.165001i
$53$	−3.59451	+	3.59451i	−0.493743	+	0.493743i	−0.909483	−	0.415740i	$-0.863523\pi$
$53$	−3.59451	+	3.59451i	−0.493743	+	0.493743i	0.415740	+	0.909483i	$0.363523\pi$
$54$		0			0
$55$	−1.10923	+	7.04794i	−0.149568	+	0.950344i
$56$	−0.726975	−	0.866375i	−0.0971461	−	0.115774i
$57$		0			0
$58$	−4.47248	+	3.13167i	−0.587266	+	0.411208i
$59$	5.86932	−	2.13626i	0.764120	−	0.278117i	0.0695853	−	0.997576i	$-0.477832\pi$
$59$	5.86932	−	2.13626i	0.764120	−	0.278117i	0.694535	+	0.719459i	$0.255610\pi$
$60$		0			0
$61$	−2.36034	−	13.3861i	−0.302210	−	1.71392i	−0.636354	−	0.771397i	$-0.719558\pi$
$61$	−2.36034	−	13.3861i	−0.302210	−	1.71392i	0.334144	−	0.942522i	$-0.391553\pi$
$62$	−1.76253	+	6.57784i	−0.223841	+	0.835386i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	0.738658	+	2.56654i	0.0916192	+	0.318340i
$66$		0			0
$67$	4.47588	−	0.391589i	0.546816	−	0.0478402i	0.189599	−	0.981862i	$-0.439281\pi$
$67$	4.47588	−	0.391589i	0.546816	−	0.0478402i	0.357217	+	0.934021i	$0.383726\pi$
$68$	−3.17368	+	0.277661i	−0.384866	+	0.0336714i
$69$		0			0
$70$	2.21305	+	1.22389i	0.264510	+	0.146283i
$71$	−5.95249	−	3.43667i	−0.706431	−	0.407858i	0.103307	−	0.994649i	$-0.467057\pi$
$71$	−5.95249	−	3.43667i	−0.706431	−	0.407858i	−0.809738	+	0.586792i	$0.800391\pi$
$72$		0			0
$73$	−2.81344	+	10.4999i	−0.329289	+	1.22892i	0.580641	+	0.814160i	$0.302802\pi$
$73$	−2.81344	+	10.4999i	−0.329289	+	1.22892i	−0.909930	+	0.414763i	$0.863865\pi$
$74$	1.34472	+	7.62631i	0.156321	+	0.886540i
$75$		0			0
$76$	−4.83689	+	1.76049i	−0.554830	+	0.201942i
$77$	2.95602	−	2.06982i	0.336869	−	0.235878i
$78$		0			0
$79$	1.98062	+	2.36041i	0.222837	+	0.265567i	0.865867	−	0.500274i	$-0.166767\pi$
$79$	1.98062	+	2.36041i	0.222837	+	0.265567i	−0.643030	+	0.765841i	$0.722323\pi$
$80$	−2.20888	−	0.347640i	−0.246960	−	0.0388673i
$81$		0			0
$82$	−3.77573	+	3.77573i	−0.416960	+	0.416960i
$83$	1.48805	−	17.0085i	0.163334	−	1.86692i	−0.266264	−	0.963900i	$-0.585789\pi$
$83$	1.48805	−	17.0085i	0.163334	−	1.86692i	0.429599	−	0.903020i	$-0.358655\pi$
$84$		0			0
$85$	6.39967	−	3.12907i	0.694142	−	0.339395i
$86$	2.35302	+	6.46488i	0.253733	+	0.697126i
$87$		0			0
$88$	−1.83013	+	2.61369i	−0.195092	+	0.278621i
$89$	−7.57232	−	13.1156i	−0.802664	−	1.39025i	−0.917857	−	0.396912i	$-0.870082\pi$
$89$	−7.57232	−	13.1156i	−0.802664	−	1.39025i	0.115193	−	0.993343i	$-0.463251\pi$
$90$		0			0
$91$	0.675406	−	1.16984i	0.0708018	−	0.122632i
$92$	0.455452	+	0.976719i	0.0474841	+	0.101830i
$93$		0			0
$94$	3.10936	−	3.70559i	0.320706	−	0.382203i
$95$	8.67914	−	7.55956i	0.890461	−	0.775594i
$96$		0			0
$97$	−0.363881	+	0.169680i	−0.0369465	+	0.0172284i	−0.441004	−	0.897505i	$-0.645377\pi$
$97$	−0.363881	+	0.169680i	−0.0369465	+	0.0172284i	0.404057	+	0.914734i	$0.367600\pi$
$98$	1.48068	+	5.52597i	0.149571	+	0.558207i
$99$		0			0
$100$	4.88870	−	1.04911i	0.488870	−	0.104911i
$101$	9.54126	−	1.68238i	0.949391	−	0.167403i	0.322552	−	0.946552i	$-0.395459\pi$
$101$	9.54126	−	1.68238i	0.949391	−	0.167403i	0.626839	+	0.779149i	$0.284348\pi$
$102$		0			0
$103$	−15.4682	−	7.21293i	−1.52412	−	0.710711i	−0.533308	−	0.845921i	$-0.679051\pi$
$103$	−15.4682	−	7.21293i	−1.52412	−	0.710711i	−0.990817	+	0.135210i	$0.956829\pi$
$104$	−0.207402	+	1.17624i	−0.0203375	+	0.115339i
$105$		0			0
$106$	3.89411	−	3.26755i	0.378229	−	0.317372i
$107$	−3.95538	−	3.95538i	−0.382381	−	0.382381i	0.489578	−	0.871959i	$-0.337151\pi$
$107$	−3.95538	−	3.95538i	−0.382381	−	0.382381i	−0.871959	+	0.489578i	$0.837151\pi$
$108$		0			0
$109$			11.2281i			1.07546i	0.843118	+	0.537729i	$0.180718\pi$
$109$			11.2281i			1.07546i	−0.843118	+	0.537729i	$0.819282\pi$
$110$	1.71927	−	6.92445i	0.163926	−	0.660220i
$111$		0			0
$112$	0.648699	+	0.926438i	0.0612963	+	0.0875401i
$113$	−7.70168	+	16.5163i	−0.724513	+	1.55372i	0.104519	+	0.994523i	$0.466670\pi$
$113$	−7.70168	+	16.5163i	−0.724513	+	1.55372i	−0.829032	+	0.559201i	$0.811108\pi$
$114$		0			0
$115$	−1.73509	−	1.67229i	−0.161798	−	0.155941i
$116$	4.72841	−	2.72995i	0.439022	−	0.253469i
$117$		0			0
$118$	−6.03317	+	1.61658i	−0.555398	+	0.148819i
$119$	−3.38577	−	1.23232i	−0.310373	−	0.112966i
$120$		0			0
$121$	0.627564	+	0.526589i	0.0570513	+	0.0478717i
$122$	1.18468	+	13.5409i	0.107256	+	1.22594i
$123$		0			0
$124$	2.32912	−	6.39919i	0.209161	−	0.574664i
$125$	−9.35873	+	6.11671i	−0.837071	+	0.547095i
$126$		0			0
$127$	18.7938	+	5.03579i	1.66768	+	0.446854i	0.964485	−	0.264139i	$-0.0850877\pi$
$127$	18.7938	+	5.03579i	1.66768	+	0.446854i	0.703199	+	0.710993i	$0.251754\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	−0.512158	−	2.62115i	−0.0449193	−	0.229890i
$131$	10.8691	+	1.91651i	0.949635	+	0.167446i	0.626949	−	0.779060i	$-0.284303\pi$
$131$	10.8691	+	1.91651i	0.949635	+	0.167446i	0.322686	+	0.946506i	$0.395414\pi$
$132$		0			0
$133$	−5.79932	−	0.507374i	−0.502865	−	0.0439949i
$134$	−4.49298			−0.388134
$135$		0			0
$136$	3.18581			0.273181
$137$	16.4149	+	1.43611i	1.40242	+	0.122695i	0.763116	−	0.646262i	$-0.223669\pi$
$137$	16.4149	+	1.43611i	1.40242	+	0.122695i	0.639300	+	0.768957i	$0.279224\pi$
$138$		0			0
$139$	−11.5017	−	2.02806i	−0.975562	−	0.172018i	−0.336930	−	0.941530i	$-0.609388\pi$
$139$	−11.5017	−	2.02806i	−0.975562	−	0.172018i	−0.638632	+	0.769512i	$0.720500\pi$
$140$	−2.09796	−	1.41211i	−0.177310	−	0.119345i
$141$		0			0
$142$	5.63031	+	3.94239i	0.472485	+	0.330838i
$143$	−3.68110	−	0.986347i	−0.307829	−	0.0824825i
$144$		0			0
$145$	−7.67391	+	9.49544i	−0.637283	+	0.788554i
$146$	3.71787	−	10.2148i	0.307693	−	0.845379i
$147$		0			0
$148$	−0.674930	−	7.71449i	−0.0554789	−	0.634127i
$149$	−3.89911	−	3.27174i	−0.319427	−	0.268031i	0.468948	−	0.883226i	$-0.344633\pi$
$149$	−3.89911	−	3.27174i	−0.319427	−	0.268031i	−0.788375	+	0.615194i	$0.789078\pi$
$150$		0			0
$151$	−4.47413	−	1.62845i	−0.364100	−	0.132521i	0.153491	−	0.988150i	$-0.450949\pi$
$151$	−4.47413	−	1.62845i	−0.364100	−	0.132521i	−0.517590	+	0.855629i	$0.673171\pi$
$152$	4.97193	−	1.33222i	0.403276	−	0.108058i
$153$		0			0
$154$	−3.12516	+	1.80431i	−0.251833	+	0.145396i
$155$	0.280629	+	15.2248i	0.0225407	+	1.22288i
$156$		0			0
$157$	−6.14078	+	13.1689i	−0.490088	+	1.05100i	0.493364	+	0.869823i	$0.335767\pi$
$157$	−6.14078	+	13.1689i	−0.490088	+	1.05100i	−0.983451	+	0.181173i	$0.942011\pi$
$158$	−1.76736	−	2.52405i	−0.140604	−	0.200803i
$159$		0			0
$160$	2.17017	+	0.538834i	0.171567	+	0.0425985i
$161$			1.21884i			0.0960578i
$162$		0			0
$163$	2.10388	+	2.10388i	0.164789	+	0.164789i	0.784684	−	0.619896i	$-0.212825\pi$
$163$	2.10388	+	2.10388i	0.164789	+	0.164789i	−0.619896	+	0.784684i	$0.712825\pi$
$164$	4.09044	−	3.43229i	0.319410	−	0.268017i
$165$		0			0
$166$	−2.96477	+	16.8140i	−0.230111	+	1.30502i
$167$	−1.12763	−	0.525822i	−0.0872586	−	0.0406893i	0.378499	−	0.925602i	$-0.376440\pi$
$167$	−1.12763	−	0.525822i	−0.0872586	−	0.0406893i	−0.465758	+	0.884912i	$0.654218\pi$
$168$		0			0
$169$	11.3976	−	2.00971i	0.876740	−	0.154593i
$170$	−6.64803	+	2.55940i	−0.509881	+	0.196297i
$171$		0			0
$172$	−1.78062	−	6.64536i	−0.135771	−	0.506704i
$173$	−16.2164	+	7.56183i	−1.23291	+	0.574916i	−0.926252	−	0.376904i	$-0.876989\pi$
$173$	−16.2164	+	7.56183i	−1.23291	+	0.574916i	−0.306658	+	0.951820i	$0.599211\pi$
$174$		0			0
$175$	5.51240	+	1.26130i	0.416698	+	0.0953451i
$176$	2.05096	−	2.44424i	0.154597	−	0.184242i
$177$		0			0
$178$	6.40040	+	13.7257i	0.479730	+	1.02878i
$179$	11.5793	−	20.0559i	0.865478	−	1.49905i	−0.00109448	−	0.999999i	$-0.500348\pi$
$179$	11.5793	−	20.0559i	0.865478	−	1.49905i	0.866572	−	0.499052i	$-0.166318\pi$
$180$		0			0
$181$	9.43545	+	16.3427i	0.701332	+	1.21474i	0.967999	+	0.250953i	$0.0807441\pi$
$181$	9.43545	+	16.3427i	0.701332	+	1.21474i	−0.266668	+	0.963789i	$0.585923\pi$
$182$	−0.774794	+	1.10652i	−0.0574315	+	0.0820207i
$183$		0			0
$184$	−0.368592	−	1.01270i	−0.0271729	−	0.0746570i
$185$	7.60604	+	15.5561i	0.559207	+	1.14371i
$186$		0			0
$187$	−0.885943	+	10.1264i	−0.0647866	+	0.740514i
$188$	−3.42049	+	3.42049i	−0.249465	+	0.249465i
$189$		0			0
$190$	−9.30497	+	6.77436i	−0.675053	+	0.491463i
$191$	8.36847	+	9.97316i	0.605522	+	0.721632i	0.978509	−	0.206204i	$-0.0661110\pi$
$191$	8.36847	+	9.97316i	0.605522	+	0.721632i	−0.372988	+	0.927836i	$0.621667\pi$
$192$		0			0
$193$	1.45804	−	1.02093i	0.104952	−	0.0734881i	−0.519922	−	0.854214i	$-0.674039\pi$
$193$	1.45804	−	1.02093i	0.104952	−	0.0734881i	0.624874	+	0.780725i	$0.285150\pi$
$194$	0.377285	−	0.137320i	0.0270875	−	0.00985904i
$195$		0			0
$196$	−0.993424	−	5.63399i	−0.0709589	−	0.402428i
$197$	0.190238	−	0.709978i	0.0135539	−	0.0505838i	−0.958818	−	0.284022i	$-0.908331\pi$
$197$	0.190238	−	0.709978i	0.0135539	−	0.0505838i	0.972372	+	0.233438i	$0.0749977\pi$
$198$		0			0
$199$	−6.40248	−	3.69647i	−0.453860	−	0.262036i	0.255599	−	0.966783i	$-0.417727\pi$
$199$	−6.40248	−	3.69647i	−0.453860	−	0.262036i	−0.709459	+	0.704747i	$0.751061\pi$
$200$	−4.96153	+	0.619043i	−0.350833	+	0.0437730i
$201$		0			0
$202$	−9.65158	+	0.844404i	−0.679083	+	0.0594121i
$203$	6.15149	−	0.538186i	0.431750	−	0.0377732i
$204$		0			0
$205$	−5.77838	+	10.4485i	−0.403580	+	0.729757i
$206$	14.7807	+	8.53362i	1.02982	+	0.594566i
$207$		0			0
$208$	0.309129	−	1.15368i	0.0214342	−	0.0799936i
$209$	2.85195	+	16.1742i	0.197273	+	1.11879i
$210$		0			0
$211$	15.1336	−	5.50818i	1.04184	−	0.379199i	0.236263	−	0.971689i	$-0.424077\pi$
$211$	15.1336	−	5.50818i	1.04184	−	0.379199i	0.805578	+	0.592490i	$0.201855\pi$
$212$	−4.16408	+	2.91572i	−0.285990	+	0.200252i
$213$		0			0
$214$	3.59559	+	4.28506i	0.245790	+	0.292921i
$215$	9.05444	+	12.4368i	0.617508	+	0.848183i
$216$		0			0
$217$	5.44598	−	5.44598i	0.369697	−	0.369697i
$218$	0.978595	−	11.1854i	0.0662788	−	0.757570i
$219$		0			0
$220$	−2.31624	+	6.74825i	−0.156161	+	0.454967i
$221$	1.30141	+	3.57560i	0.0875423	+	0.240521i
$222$		0			0
$223$	−7.79176	+	11.1278i	−0.521775	+	0.745171i	−0.990401	−	0.138225i	$-0.955860\pi$
$223$	−7.79176	+	11.1278i	−0.521775	+	0.745171i	0.468626	+	0.883397i	$0.344749\pi$
$224$	−0.565486	−	0.979450i	−0.0377831	−	0.0654423i
$225$		0			0
$226$	9.11187	−	15.7822i	0.606112	−	1.04982i
$227$	−8.68406	−	18.6230i	−0.576381	−	1.23605i	−0.951091	−	0.308911i	$-0.900035\pi$
$227$	−8.68406	−	18.6230i	−0.576381	−	1.23605i	0.374710	−	0.927142i	$-0.377742\pi$
$228$		0			0
$229$	−18.4551	+	21.9940i	−1.21955	+	1.45340i	−0.367432	+	0.930050i	$0.619763\pi$
$229$	−18.4551	+	21.9940i	−1.21955	+	1.45340i	−0.852117	+	0.523352i	$0.824681\pi$
$230$	1.58274	+	1.81714i	0.104363	+	0.119819i
$231$		0			0
$232$	−4.94835	+	2.30745i	−0.324875	+	0.151492i
$233$	1.33220	+	4.97183i	0.0872751	+	0.325715i	0.995735	−	0.0922563i	$-0.0294079\pi$
$233$	1.33220	+	4.97183i	0.0872751	+	0.325715i	−0.908460	+	0.417971i	$0.862741\pi$
$234$		0			0
$235$	4.38983	−	9.88570i	0.286361	−	0.644872i
$236$	6.15111	−	1.08461i	0.400403	−	0.0706019i
$237$		0			0
$238$	3.26548	+	1.52272i	0.211670	+	0.0987032i
$239$	−4.26039	+	24.1619i	−0.275582	+	1.56290i	0.461526	+	0.887127i	$0.347302\pi$
$239$	−4.26039	+	24.1619i	−0.275582	+	1.56290i	−0.737108	+	0.675775i	$0.763809\pi$
$240$		0			0
$241$	4.85421	−	4.07316i	0.312687	−	0.262376i	−0.472915	−	0.881108i	$-0.656798\pi$
$241$	4.85421	−	4.07316i	0.312687	−	0.262376i	0.785602	+	0.618733i	$0.212354\pi$
$242$	−0.579281	−	0.579281i	−0.0372376	−	0.0372376i
$243$		0			0
$244$		−	13.5926i		−	0.870179i
$245$	6.59925	+	10.9587i	0.421610	+	0.700127i
$246$		0			0
$247$	3.52627	+	5.03603i	0.224371	+	0.320435i
$248$	−2.87798	+	6.17184i	−0.182752	+	0.391913i
$249$		0			0
$250$	9.85623	−	5.27776i	0.623363	−	0.333795i
$251$	−10.1466	+	5.85814i	−0.640448	+	0.369763i	−0.784787	−	0.619766i	$-0.787228\pi$
$251$	−10.1466	+	5.85814i	−0.640448	+	0.369763i	0.144339	+	0.989528i	$0.453894\pi$
$252$		0			0
$253$	3.32145	−	0.889981i	0.208818	−	0.0559526i
$254$	−18.2834	−	6.65462i	−1.14720	−	0.417548i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.13762	+	13.0030i	0.0709625	+	0.811105i	0.945388	+	0.325946i	$0.105683\pi$
$257$	1.13762	+	13.0030i	0.0709625	+	0.811105i	−0.874426	+	0.485159i	$0.838762\pi$
$258$		0			0
$259$	2.99548	−	8.23001i	0.186130	−	0.511388i
$260$	0.281761	+	2.65581i	0.0174741	+	0.164707i
$261$		0			0
$262$	−10.6607	−	2.85652i	−0.658619	−	0.176476i
$263$	−7.22524	−	5.05916i	−0.445527	−	0.311961i	0.329197	−	0.944261i	$-0.393222\pi$
$263$	−7.22524	−	5.05916i	−0.445527	−	0.311961i	−0.774724	+	0.632300i	$0.782111\pi$
$264$		0			0
$265$	6.34704	−	9.42973i	0.389895	−	0.579264i
$266$	5.73303	+	1.01089i	0.351514	+	0.0619815i
$267$		0			0
$268$	4.47588	+	0.391589i	0.273408	+	0.0239201i
$269$	7.62387			0.464836			0.232418	−	0.972616i	$-0.425336\pi$
$269$	7.62387			0.464836			0.232418	+	0.972616i	$0.425336\pi$
$270$		0			0
$271$	−11.6917			−0.710220			−0.355110	−	0.934824i	$-0.615557\pi$
$271$	−11.6917			−0.710220			−0.355110	+	0.934824i	$0.615557\pi$
$272$	−3.17368	−	0.277661i	−0.192433	−	0.0168357i
$273$		0			0
$274$	−16.2272	−	2.86130i	−0.980322	−	0.172857i
$275$	−0.587930	−	15.9428i	−0.0354535	−	0.961389i
$276$		0			0
$277$	17.0953	+	11.9702i	1.02716	+	0.719223i	0.960422	−	0.278548i	$-0.0898532\pi$
$277$	17.0953	+	11.9702i	1.02716	+	0.719223i	0.0667341	+	0.997771i	$0.478742\pi$
$278$	11.2812	+	3.02278i	0.676600	+	0.181294i
$279$		0			0
$280$	1.96690	+	1.58959i	0.117545	+	0.0949959i
$281$	−1.91060	+	5.24932i	−0.113977	+	0.313148i	−0.983545	−	0.180665i	$-0.942175\pi$
$281$	−1.91060	+	5.24932i	−0.113977	+	0.313148i	0.869568	+	0.493813i	$0.164397\pi$
$282$		0			0
$283$	−0.910123	−	10.4028i	−0.0541012	−	0.618379i	−0.974049	−	0.226338i	$-0.927325\pi$
$283$	−0.910123	−	10.4028i	−0.0541012	−	0.618379i	0.919948	−	0.392041i	$-0.128231\pi$
$284$	−5.26529	−	4.41810i	−0.312437	−	0.262166i
$285$		0			0
$286$	3.58112	+	1.30342i	0.211756	+	0.0770730i
$287$	5.83327	−	1.56302i	0.344327	−	0.0922621i
$288$		0			0
$289$	−5.93282	+	3.42531i	−0.348989	+	0.201489i
$290$	8.47229	−	8.79048i	0.497510	−	0.516195i
$291$		0			0
$292$	−4.59399	+	9.85185i	−0.268843	+	0.576536i
$293$	−13.0655	−	18.6594i	−0.763292	−	1.09009i	−0.993147	−	0.116869i	$-0.962714\pi$
$293$	−13.0655	−	18.6594i	−0.763292	−	1.09009i	0.229855	−	0.973225i	$-0.426175\pi$
$294$		0			0
$295$	−11.9646	+	7.20496i	−0.696604	+	0.419489i
$296$			7.74396i			0.450108i
$297$		0			0
$298$	3.59912	+	3.59912i	0.208491	+	0.208491i
$299$	0.986032	−	0.827379i	0.0570237	−	0.0478486i
$300$		0			0
$301$	1.35113	−	7.66263i	0.0778777	−	0.441667i
$302$	4.31518	+	2.01220i	0.248310	+	0.115789i
$303$		0			0
$304$	−5.06912	+	0.893822i	−0.290734	+	0.0512642i
$305$	10.9200	+	28.3646i	0.625276	+	1.62415i
$306$		0			0
$307$	−1.78961	−	6.67890i	−0.102138	−	0.381185i	0.895867	−	0.444323i	$-0.146556\pi$
$307$	−1.78961	−	6.67890i	−0.102138	−	0.381185i	−0.998005	+	0.0631383i	$0.979889\pi$
$308$	3.27053	−	1.52507i	0.186356	−	0.0868990i
$309$		0			0
$310$	1.04736	−	15.1913i	0.0594863	−	0.862807i
$311$	−8.21971	+	9.79586i	−0.466097	+	0.555472i	−0.946972	−	0.321317i	$-0.895875\pi$
$311$	−8.21971	+	9.79586i	−0.466097	+	0.555472i	0.480875	+	0.876789i	$0.340319\pi$
$312$		0			0
$313$	−3.48857	−	7.48125i	−0.197185	−	0.422865i	0.782708	−	0.622390i	$-0.213838\pi$
$313$	−3.48857	−	7.48125i	−0.197185	−	0.422865i	−0.979893	+	0.199524i	$0.936060\pi$
$314$	7.26516	−	12.5836i	0.409997	−	0.710135i
$315$		0			0
$316$	1.54065	+	2.66848i	0.0866682	+	0.150114i
$317$	−6.75880	+	9.65257i	−0.379612	+	0.542142i	−0.962807	−	0.270190i	$-0.912913\pi$
$317$	−6.75880	+	9.65257i	−0.379612	+	0.542142i	0.583195	+	0.812332i	$0.301802\pi$
$318$		0			0
$319$	−5.95836	−	16.3704i	−0.333604	−	0.916569i
$320$	−2.11495	−	0.725926i	−0.118230	−	0.0405805i
$321$		0			0
$322$	0.106229	−	1.21420i	0.00591989	−	0.0676647i
$323$	11.5954	−	11.5954i	0.645185	−	0.645185i
$324$		0			0
$325$	−2.72158	−	5.31570i	−0.150966	−	0.294862i
$326$	−1.91251	−	2.27924i	−0.105924	−	0.126236i
$327$		0			0
$328$	−4.37402	+	3.06272i	−0.241515	+	0.169111i
$329$	−5.14092	+	1.87114i	−0.283428	+	0.103159i
$330$		0			0
$331$	−3.66404	−	20.7798i	−0.201394	−	1.14216i	−0.903014	−	0.429611i	$-0.858651\pi$
$331$	−3.66404	−	20.7798i	−0.201394	−	1.14216i	0.701620	−	0.712551i	$-0.252461\pi$
$332$	4.41893	−	16.4917i	0.242520	−	0.905097i
$333$		0			0
$334$	1.07751	+	0.622100i	0.0589587	+	0.0340398i
$335$	−9.65471	+	2.77865i	−0.527493	+	0.151814i
$336$		0			0
$337$	−9.24896	+	0.809179i	−0.503823	+	0.0440788i	−0.336235	−	0.941778i	$-0.609153\pi$
$337$	−9.24896	+	0.809179i	−0.503823	+	0.0440788i	−0.167588	+	0.985857i	$0.553598\pi$
$338$	−11.5294	+	1.00869i	−0.627117	+	0.0548657i
$339$		0			0
$340$	6.84580	−	1.97024i	0.371266	−	0.106851i
$341$	−18.8174	−	10.8642i	−1.01902	−	0.588332i
$342$		0			0
$343$	3.72362	−	13.8968i	0.201057	−	0.750354i
$344$	1.19466	+	6.77526i	0.0644118	+	0.365298i
$345$		0			0
$346$	16.8138	−	6.11971i	0.903913	−	0.328997i
$347$	18.4345	−	12.9080i	0.989618	−	0.692938i	0.0376997	−	0.999289i	$-0.487997\pi$
$347$	18.4345	−	12.9080i	0.989618	−	0.692938i	0.951919	+	0.306351i	$0.0991081\pi$
$348$		0			0
$349$	4.63398	+	5.52256i	0.248051	+	0.295616i	0.875675	−	0.482901i	$-0.160417\pi$
$349$	4.63398	+	5.52256i	0.248051	+	0.295616i	−0.627624	+	0.778517i	$0.715972\pi$
$350$	−5.38149	−	1.73693i	−0.287653	−	0.0928431i
$351$		0			0
$352$	−2.25619	+	2.25619i	−0.120255	+	0.120255i
$353$	2.52835	−	28.8992i	0.134571	−	1.53815i	−0.565904	−	0.824471i	$-0.691473\pi$
$353$	2.52835	−	28.8992i	0.134571	−	1.53815i	0.700474	−	0.713678i	$-0.252972\pi$
$354$		0			0
$355$	14.5368	+	4.98954i	0.771534	+	0.264817i
$356$	−5.17977	−	14.2313i	−0.274527	−	0.754257i
$357$		0			0
$358$	−13.2832	+	18.9704i	−0.702040	+	1.00262i
$359$	−2.11334	−	3.66042i	−0.111538	−	0.193190i	0.804853	−	0.593475i	$-0.202244\pi$
$359$	−2.11334	−	3.66042i	−0.111538	−	0.193190i	−0.916391	+	0.400285i	$0.868911\pi$
$360$		0			0
$361$	3.74743	−	6.49074i	0.197233	−	0.341618i
$362$	−7.97519	−	17.1028i	−0.419167	−	0.898906i
$363$		0			0
$364$	0.868285	−	1.03478i	0.0455105	−	0.0542373i
$365$	1.67186	−	24.2492i	0.0875093	−	1.26926i
$366$		0			0
$367$	−3.07831	+	1.43544i	−0.160686	+	0.0749293i	−0.501298	−	0.865275i	$-0.667144\pi$
$367$	−3.07831	+	1.43544i	−0.160686	+	0.0749293i	0.340611	+	0.940204i	$0.389366\pi$
$368$	0.278927	+	1.04097i	0.0145401	+	0.0542642i
$369$		0			0
$370$	−6.22130	−	16.1598i	−0.323430	−	0.840109i
$371$	−5.66184	+	0.998334i	−0.293948	+	0.0518309i
$372$		0			0
$373$	16.5381	+	7.71185i	0.856312	+	0.399305i	0.800641	−	0.599145i	$-0.204493\pi$
$373$	16.5381	+	7.71185i	0.856312	+	0.399305i	0.0556707	+	0.998449i	$0.482270\pi$
$374$	1.76514	−	10.0106i	0.0912734	−	0.517637i
$375$		0			0
$376$	3.70559	−	3.10936i	0.191101	−	0.160353i
$377$	−4.61118	−	4.61118i	−0.237488	−	0.237488i
$378$		0			0
$379$		−	28.6213i		−	1.47018i	−0.677971	−	0.735089i	$-0.737140\pi$
$379$		−	28.6213i		−	1.47018i	0.677971	−	0.735089i	$-0.262860\pi$
$380$	9.85998	−	5.93760i	0.505806	−	0.304592i
$381$		0			0
$382$	−7.46741	−	10.6646i	−0.382066	−	0.545647i
$383$	11.5430	−	24.7541i	0.589822	−	1.26488i	−0.354254	−	0.935149i	$-0.615265\pi$
$383$	11.5430	−	24.7541i	0.589822	−	1.26488i	0.944076	−	0.329728i	$-0.106957\pi$
$384$		0			0
$385$	−5.59962	+	5.80993i	−0.285383	+	0.296101i
$386$	−1.54147	+	0.889967i	−0.0784587	+	0.0452981i
$387$		0			0
$388$	−0.387817	+	0.103915i	−0.0196884	+	0.00527550i
$389$	−15.0288	−	5.47002i	−0.761988	−	0.277341i	−0.0683468	−	0.997662i	$-0.521772\pi$
$389$	−15.0288	−	5.47002i	−0.761988	−	0.277341i	−0.693641	+	0.720321i	$0.743995\pi$
$390$		0			0
$391$	−2.63007	−	2.20689i	−0.133008	−	0.111607i
$392$	0.498610	+	5.69913i	0.0251836	+	0.287850i
$393$		0			0
$394$	−0.251393	+	0.690696i	−0.0126650	+	0.0347968i
$395$	−5.35876	−	4.33078i	−0.269628	−	0.217905i
$396$		0			0
$397$	16.6411	+	4.45898i	0.835195	+	0.223790i	0.650979	−	0.759096i	$-0.274359\pi$
$397$	16.6411	+	4.45898i	0.835195	+	0.223790i	0.184216	+	0.982886i	$0.441025\pi$
$398$	6.05595	+	4.24042i	0.303557	+	0.212553i
$399$		0			0
$400$	4.99660	−	0.184262i	0.249830	−	0.00921308i
$401$	−20.1195	−	3.54761i	−1.00472	−	0.177159i	−0.353003	−	0.935622i	$-0.614839\pi$
$401$	−20.1195	−	3.54761i	−1.00472	−	0.177159i	−0.651716	+	0.758463i	$0.725951\pi$
$402$		0			0
$403$	−8.10264	−	0.708889i	−0.403621	−	0.0353123i
$404$	9.68845			0.482018
$405$		0			0
$406$	−6.17499			−0.306459
$407$	−24.6149	−	2.15352i	−1.22011	−	0.106746i
$408$		0			0
$409$	6.05191	+	1.06712i	0.299248	+	0.0527655i	0.321256	−	0.946992i	$-0.395895\pi$
$409$	6.05191	+	1.06712i	0.299248	+	0.0527655i	−0.0220083	+	0.999758i	$0.507006\pi$
$410$	6.66704	−	9.90516i	0.329262	−	0.489181i
$411$		0			0
$412$	−13.9807	−	9.78937i	−0.688778	−	0.482288i
$413$	6.82335	+	1.82831i	0.335755	+	0.0899653i
$414$		0			0
$415$	4.02771	+	37.9643i	0.197713	+	1.86359i
$416$	−0.408503	+	1.12235i	−0.0200285	+	0.0550278i
$417$		0			0
$418$	−1.43142	−	16.3612i	−0.0700131	−	0.800253i
$419$	15.8913	+	13.3344i	0.776342	+	0.651428i	0.942325	−	0.334701i	$-0.108635\pi$
$419$	15.8913	+	13.3344i	0.776342	+	0.651428i	−0.165983	+	0.986129i	$0.553080\pi$
$420$		0			0
$421$	1.41099	+	0.513559i	0.0687675	+	0.0250293i	0.376175	−	0.926549i	$-0.377239\pi$
$421$	1.41099	+	0.513559i	0.0687675	+	0.0250293i	−0.307407	+	0.951578i	$0.599461\pi$
$422$	−15.5561	+	4.16824i	−0.757259	+	0.202907i
$423$		0			0
$424$	4.40235	−	2.54170i	0.213797	−	0.123436i
$425$	−12.7027	+	9.61118i	−0.616173	+	0.466210i
$426$		0			0
$427$	6.49686	−	13.9326i	0.314405	−	0.674244i
$428$	−3.20844	−	4.58213i	−0.155086	−	0.221486i
$429$		0			0
$430$	−7.93605	−	13.1786i	−0.382710	−	0.635530i
$431$		−	28.5354i		−	1.37450i	−0.726420	−	0.687251i	$-0.758817\pi$
$431$		−	28.5354i		−	1.37450i	0.726420	−	0.687251i	$-0.241183\pi$
$432$		0			0
$433$	14.0624	+	14.0624i	0.675794	+	0.675794i	0.959046	−	0.283252i	$-0.0914132\pi$
$433$	14.0624	+	14.0624i	0.675794	+	0.675794i	−0.283252	+	0.959046i	$0.591413\pi$
$434$	−5.89990	+	4.95061i	−0.283204	+	0.237637i
$435$		0			0
$436$	−1.94974	+	11.0575i	−0.0933757	+	0.529560i
$437$	−5.02748	−	2.34435i	−0.240497	−	0.112146i
$438$		0			0
$439$	2.83318	−	0.499565i	0.135220	−	0.0238430i	−0.105628	−	0.994406i	$-0.533685\pi$
$439$	2.83318	−	0.499565i	0.135220	−	0.0238430i	0.240849	+	0.970563i	$0.422574\pi$
$440$	2.89557	−	6.52070i	0.138041	−	0.310862i
$441$		0			0
$442$	−0.984824	−	3.67542i	−0.0468433	−	0.174822i
$443$	−8.27956	+	3.86082i	−0.393374	+	0.183433i	−0.609233	−	0.792991i	$-0.708523\pi$
$443$	−8.27956	+	3.86082i	−0.393374	+	0.183433i	0.215859	+	0.976425i	$0.430745\pi$
$444$		0			0
$445$	22.2420	+	25.5361i	1.05437	+	1.21053i
$446$	8.73196	−	10.4063i	0.413470	−	0.492755i
$447$		0			0
$448$	0.477969	+	1.02501i	0.0225819	+	0.0484271i
$449$	−13.5910	+	23.5404i	−0.641401	+	1.11094i	0.343719	+	0.939073i	$0.388313\pi$
$449$	−13.5910	+	23.5404i	−0.641401	+	1.11094i	−0.985120	+	0.171867i	$0.945020\pi$
$450$		0			0
$451$	−8.51877	−	14.7549i	−0.401133	−	0.694783i
$452$	−10.4527	+	14.9280i	−0.491654	+	0.702154i
$453$		0			0
$454$	7.02791	+	19.3090i	0.329836	+	0.906217i
$455$	−0.980590	+	2.85690i	−0.0459708	+	0.133934i
$456$		0			0
$457$	−0.145454	+	1.66254i	−0.00680403	+	0.0777705i	−0.998838	−	0.0482041i	$-0.984650\pi$
$457$	−0.145454	+	1.66254i	−0.00680403	+	0.0777705i	0.992033	+	0.125975i	$0.0402058\pi$
$458$	20.3018	−	20.3018i	0.948641	−	0.948641i
$459$		0			0
$460$	−1.41834	−	1.94817i	−0.0661305	−	0.0908341i
$461$	14.0670	+	16.7644i	0.655165	+	0.780795i	0.986683	−	0.162654i	$-0.0520053\pi$
$461$	14.0670	+	16.7644i	0.655165	+	0.780795i	−0.331518	+	0.943449i	$0.607561\pi$
$462$		0			0
$463$	29.0934	−	20.3714i	1.35208	−	0.946739i	0.352142	−	0.935947i	$-0.385454\pi$
$463$	29.0934	−	20.3714i	1.35208	−	0.946739i	0.999942	−	0.0107924i	$-0.00343538\pi$
$464$	5.13062	−	1.86739i	0.238183	−	0.0866916i
$465$		0			0
$466$	−0.893804	−	5.06901i	−0.0414047	−	0.234818i
$467$	2.67194	−	9.97182i	0.123643	−	0.461441i	−0.876145	−	0.482048i	$-0.839893\pi$
$467$	2.67194	−	9.97182i	0.123643	−	0.461441i	0.999788	+	0.0206070i	$0.00655988\pi$
$468$		0			0
$469$	4.40065	+	2.54072i	0.203203	+	0.117319i
$470$	−5.23472	+	9.46548i	−0.241460	+	0.436610i
$471$		0			0
$472$	−6.22223	+	0.544375i	−0.286401	+	0.0250569i
$473$	−21.8680	+	1.91320i	−1.00549	+	0.0879692i
$474$		0			0
$475$	−15.8054	+	20.3116i	−0.725200	+	0.931961i
$476$	−3.12034	−	1.80153i	−0.143021	−	0.0825730i
$477$		0			0
$478$	6.35003	−	23.6986i	0.290443	−	1.08395i
$479$	4.95279	+	28.0887i	0.226299	+	1.28340i	0.860187	+	0.509979i	$0.170347\pi$
$479$	4.95279	+	28.0887i	0.226299	+	1.28340i	−0.633888	+	0.773425i	$0.718542\pi$
$480$		0			0
$481$	−8.69144	+	3.16343i	−0.396296	+	0.144240i
$482$	−5.19074	+	3.63459i	−0.236432	+	0.165551i
$483$		0			0
$484$	0.526589	+	0.627564i	0.0239359	+	0.0285257i
$485$	0.725801	−	0.528410i	0.0329569	−	0.0239938i
$486$		0			0
$487$	−1.18335	+	1.18335i	−0.0536226	+	0.0536226i	−0.733410	−	0.679787i	$-0.762072\pi$
$487$	−1.18335	+	1.18335i	−0.0536226	+	0.0536226i	0.679787	+	0.733410i	$0.262072\pi$
$488$	−1.18468	+	13.5409i	−0.0536278	+	0.612968i
$489$		0			0
$490$	−5.61902	−	11.4922i	−0.253841	−	0.519164i
$491$	1.79507	+	4.93192i	0.0810105	+	0.222575i	0.973585	−	0.228326i	$-0.0733252\pi$
$491$	1.79507	+	4.93192i	0.0810105	+	0.222575i	−0.892574	+	0.450900i	$0.851103\pi$
$492$		0			0
$493$	−9.97689	+	14.2485i	−0.449337	+	0.641719i
$494$	−3.07393	−	5.32420i	−0.138303	−	0.239547i
$495$		0			0
$496$	3.40494	−	5.89753i	0.152886	−	0.264807i
$497$	−3.28525	−	7.04524i	−0.147363	−	0.316022i
$498$		0			0
$499$	−6.72332	+	8.01254i	−0.300977	+	0.358690i	−0.895243	−	0.445578i	$-0.852998\pi$
$499$	−6.72332	+	8.01254i	−0.300977	+	0.358690i	0.594266	+	0.804269i	$0.297443\pi$
$500$	−10.2787	+	4.39865i	−0.459678	+	0.196714i
$501$		0			0
$502$	10.6186	−	4.95152i	0.473930	−	0.220997i
$503$	2.81738	+	10.5146i	0.125621	+	0.468823i	0.999861	−	0.0166705i	$-0.00530664\pi$
$503$	2.81738	+	10.5146i	0.125621	+	0.468823i	−0.874240	+	0.485493i	$0.838640\pi$
$504$		0			0
$505$	−20.2175	+	7.78345i	−0.899668	+	0.346359i
$506$	−3.38638	+	0.597110i	−0.150543	+	0.0265448i
$507$		0			0
$508$	17.6339	+	8.22281i	0.782376	+	0.364828i
$509$	5.87930	−	33.3432i	0.260595	−	1.47791i	−0.520696	−	0.853742i	$-0.674327\pi$
$509$	5.87930	−	33.3432i	0.260595	−	1.47791i	0.781291	−	0.624167i	$-0.214562\pi$
$510$		0			0
$511$	−9.41776	+	7.90244i	−0.416617	+	0.349583i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	13.0527i		−	0.575729i
$515$	37.0389	+	9.19641i	1.63213	+	0.405242i
$516$		0			0
$517$	8.85290	+	12.6432i	0.389350	+	0.556049i
$518$	−3.70137	+	7.93762i	−0.162629	+	0.348759i
$519$		0			0
$520$	−0.0492195	−	2.67026i	−0.00215842	−	0.117099i
$521$	6.63301	−	3.82957i	0.290597	−	0.167777i	−0.347614	−	0.937638i	$-0.613008\pi$
$521$	6.63301	−	3.82957i	0.290597	−	0.167777i	0.638211	+	0.769861i	$0.279675\pi$
$522$		0			0
$523$	30.9441	−	8.29145i	1.35309	−	0.362560i	0.491817	−	0.870699i	$-0.336333\pi$
$523$	30.9441	−	8.29145i	1.35309	−	0.362560i	0.861275	+	0.508139i	$0.169666\pi$
$524$	10.3711	+	3.77479i	0.453066	+	0.164902i
$525$		0			0
$526$	6.75681	+	5.66963i	0.294611	+	0.247208i
$527$	1.89084	+	21.6124i	0.0823663	+	0.941451i
$528$		0			0
$529$	7.46924	−	20.5216i	0.324749	−	0.892242i
$530$	−7.14474	+	8.84067i	−0.310348	+	0.384014i
$531$		0			0
$532$	−5.62311	−	1.50671i	−0.243793	−	0.0653240i
$533$	−5.22425	−	3.65806i	−0.226287	−	0.158448i
$534$		0			0
$535$	10.3764	+	6.98425i	0.448613	+	0.301956i
$536$	−4.42472	−	0.780198i	−0.191119	−	0.0336994i
$537$		0			0
$538$	−7.59486	−	0.664464i	−0.327438	−	0.0286471i
$539$	−18.2539			−0.786250
$540$		0			0
$541$	−34.2148			−1.47101			−0.735505	−	0.677519i	$-0.763055\pi$
$541$	−34.2148			−1.47101			−0.735505	+	0.677519i	$0.763055\pi$
$542$	11.6472	+	1.01900i	0.500291	+	0.0437697i
$543$		0			0
$544$	3.13741	+	0.553210i	0.134515	+	0.0237187i
$545$	−4.81469	−	24.6409i	−0.206239	−	1.05550i
$546$		0			0
$547$	−26.2646	−	18.3907i	−1.12299	−	0.786329i	−0.143871	−	0.989596i	$-0.545955\pi$
$547$	−26.2646	−	18.3907i	−1.12299	−	0.786329i	−0.979123	+	0.203268i	$0.934844\pi$
$548$	15.9161	+	4.26471i	0.679902	+	0.182179i
$549$		0			0
$550$	−0.803816	+	15.9334i	−0.0342748	+	0.679402i
$551$	−9.61207	+	26.4089i	−0.409488	+	1.12506i
$552$		0			0
$553$	0.303725	+	3.47160i	0.0129157	+	0.147627i
$554$	−15.9870	−	13.4147i	−0.679221	−	0.569934i
$555$		0			0
$556$	−10.9748	−	3.99450i	−0.465435	−	0.169405i
$557$	10.1237	−	2.71264i	0.428956	−	0.114938i	−0.0378802	−	0.999282i	$-0.512061\pi$
$557$	10.1237	−	2.71264i	0.428956	−	0.114938i	0.466836	+	0.884344i	$0.345394\pi$
$558$		0			0
$559$	−7.11620	+	4.10854i	−0.300983	+	0.173773i
$560$	−1.82088	−	1.75496i	−0.0769460	−	0.0741608i
$561$		0			0
$562$	2.36084	−	5.06283i	0.0995858	−	0.213563i
$563$	1.61046	+	2.29998i	0.0678728	+	0.0969324i	0.851653	−	0.524105i	$-0.175600\pi$
$563$	1.61046	+	2.29998i	0.0678728	+	0.0969324i	−0.783781	+	0.621038i	$0.786711\pi$
$564$		0			0
$565$	9.81956	−	39.5487i	0.413112	−	1.66383i
$566$			10.4425i			0.438931i
$567$		0			0
$568$	4.86019	+	4.86019i	0.203929	+	0.203929i
$569$	−6.84132	+	5.74055i	−0.286803	+	0.240656i	−0.774826	−	0.632174i	$-0.782163\pi$
$569$	−6.84132	+	5.74055i	−0.286803	+	0.240656i	0.488023	+	0.872831i	$0.337718\pi$
$570$		0			0
$571$	2.54909	−	14.4566i	0.106676	−	0.604991i	−0.883861	−	0.467749i	$-0.845065\pi$
$571$	2.54909	−	14.4566i	0.106676	−	0.604991i	0.990538	−	0.137242i	$-0.0438238\pi$
$572$	−3.45390	−	1.61058i	−0.144415	−	0.0673416i
$573$		0			0
$574$	−5.94729	+	1.04867i	−0.248235	+	0.0437706i
$575$	4.52486	+	2.92592i	0.188700	+	0.122019i
$576$		0			0
$577$	−10.8748	−	40.5851i	−0.452722	−	1.68958i	−0.694700	−	0.719299i	$-0.744463\pi$
$577$	−10.8748	−	40.5851i	−0.452722	−	1.68958i	0.241978	−	0.970282i	$-0.422204\pi$
$578$	6.20878	−	2.89520i	0.258251	−	0.120424i
$579$		0			0
$580$	−9.20619	+	8.01862i	−0.382266	+	0.332955i
$581$	12.4119	−	14.7920i	0.514934	−	0.613675i
$582$		0			0
$583$	6.85477	+	14.7001i	0.283895	+	0.608816i
$584$	5.43516	−	9.41397i	0.224908	−	0.389553i
$585$		0			0
$586$	11.3895	+	19.7271i	0.470494	+	0.814920i
$587$	5.61394	−	8.01754i	0.231712	−	0.330919i	−0.686411	−	0.727213i	$-0.740815\pi$
$587$	5.61394	−	8.01754i	0.231712	−	0.330919i	0.918124	+	0.396294i	$0.129704\pi$
$588$		0			0
$589$	11.9887	+	32.9387i	0.493985	+	1.35721i
$590$	12.5470	−	6.13476i	0.516552	−	0.252564i
$591$		0			0
$592$	0.674930	−	7.71449i	0.0277395	−	0.317063i
$593$	−18.8143	+	18.8143i	−0.772610	+	0.772610i	−0.978562	−	0.205952i	$-0.933971\pi$
$593$	−18.8143	+	18.8143i	−0.772610	+	0.772610i	0.205952	+	0.978562i	$0.433971\pi$
$594$		0			0
$595$	7.95872	+	1.25257i	0.326276	+	0.0513503i
$596$	−3.27174	−	3.89911i	−0.134016	−	0.159714i
$597$		0			0
$598$	−1.05439	+	0.738292i	−0.0431172	+	0.0301910i
$599$	24.3696	−	8.86980i	0.995714	−	0.362410i	0.207784	−	0.978175i	$-0.433375\pi$
$599$	24.3696	−	8.86980i	0.995714	−	0.362410i	0.787930	+	0.615765i	$0.211153\pi$
$600$		0			0
$601$	7.10108	+	40.2723i	0.289659	+	1.64274i	0.688151	+	0.725568i	$0.258423\pi$
$601$	7.10108	+	40.2723i	0.289659	+	1.64274i	−0.398492	+	0.917172i	$0.630466\pi$
$602$	−2.01383	+	7.51571i	−0.0820775	+	0.306318i
$603$		0			0
$604$	−4.12338	−	2.38063i	−0.167778	−	0.0968667i
$605$	−1.60304	−	0.886532i	−0.0651727	−	0.0360426i
$606$		0			0
$607$	8.87017	−	0.776039i	0.360029	−	0.0314984i	0.0942935	−	0.995544i	$-0.469941\pi$
$607$	8.87017	−	0.776039i	0.360029	−	0.0314984i	0.265735	+	0.964046i	$0.414385\pi$
$608$	5.12773	−	0.448618i	0.207957	−	0.0181939i
$609$		0			0
$610$	−8.40628	−	29.2084i	−0.340360	−	1.18262i
$611$	5.00354	+	2.88879i	0.202422	+	0.116868i
$612$		0			0
$613$	8.12000	−	30.3043i	0.327964	−	1.22398i	−0.583335	−	0.812232i	$-0.698252\pi$
$613$	8.12000	−	30.3043i	0.327964	−	1.22398i	0.911299	−	0.411746i	$-0.135081\pi$
$614$	1.20069	+	6.80946i	0.0484559	+	0.274807i
$615$		0			0
$616$	−3.39100	+	1.23422i	−0.136627	+	0.0497283i
$617$	4.68604	−	3.28120i	0.188653	−	0.132096i	−0.475435	−	0.879751i	$-0.657709\pi$
$617$	4.68604	−	3.28120i	0.188653	−	0.132096i	0.664087	+	0.747655i	$0.268820\pi$
$618$		0			0
$619$	−7.21421	−	8.59756i	−0.289963	−	0.345565i	0.601323	−	0.799006i	$-0.294641\pi$
$619$	−7.21421	−	8.59756i	−0.289963	−	0.345565i	−0.891286	+	0.453441i	$0.850196\pi$
$620$	−2.36739	+	15.0422i	−0.0950765	+	0.604109i
$621$		0			0
$622$	9.04219	−	9.04219i	0.362559	−	0.362559i
$623$	1.49282	−	17.0630i	0.0598085	−	0.683614i
$624$		0			0
$625$	17.9155	−	17.4366i	0.716619	−	0.697464i
$626$	2.82326	+	7.75683i	0.112840	+	0.310025i
$627$		0			0
$628$	−8.33425	+	11.9025i	−0.332573	+	0.474963i
$629$	12.3354	+	21.3655i	0.491844	+	0.851898i
$630$		0			0
$631$	−15.1396	+	26.2225i	−0.602696	+	1.04390i	0.389715	+	0.920936i	$0.372574\pi$
$631$	−15.1396	+	26.2225i	−0.602696	+	1.04390i	−0.992411	+	0.122965i	$0.960760\pi$
$632$	−1.30221	−	2.79260i	−0.0517992	−	0.111084i
$633$		0			0
$634$	7.57436	−	9.02677i	0.300816	−	0.358499i
$635$	−43.4037	−	2.99247i	−1.72242	−	0.118753i
$636$		0			0
$637$	−6.19275	+	2.88773i	−0.245366	+	0.114416i
$638$	4.50890	+	16.8275i	0.178509	+	0.666205i
$639$		0			0
$640$	2.04364	+	0.907494i	0.0807819	+	0.0358719i
$641$	20.2410	−	3.56904i	0.799473	−	0.140969i	0.241036	−	0.970516i	$-0.422513\pi$
$641$	20.2410	−	3.56904i	0.799473	−	0.140969i	0.558436	+	0.829547i	$0.311402\pi$
$642$		0			0
$643$	−40.1555	−	18.7248i	−1.58358	−	0.738435i	−0.586157	−	0.810197i	$-0.699360\pi$
$643$	−40.1555	−	18.7248i	−1.58358	−	0.738435i	−0.997422	+	0.0717624i	$0.977138\pi$
$644$	−0.211649	+	1.20032i	−0.00834013	+	0.0472992i
$645$		0			0
$646$	−12.5619	+	10.5407i	−0.494240	+	0.414717i
$647$	7.18701	+	7.18701i	0.282551	+	0.282551i	0.834125	−	0.551575i	$-0.185973\pi$
$647$	7.18701	+	7.18701i	0.282551	+	0.282551i	−0.551575	+	0.834125i	$0.685973\pi$
$648$		0			0
$649$		−	19.9293i		−	0.782294i
$650$	2.24793	+	5.53267i	0.0881711	+	0.217009i
$651$		0			0
$652$	1.70659	+	2.43726i	0.0668350	+	0.0954503i
$653$	−14.9249	+	32.0065i	−0.584056	+	1.25251i	0.363104	+	0.931749i	$0.381717\pi$
$653$	−14.9249	+	32.0065i	−0.584056	+	1.25251i	−0.947160	+	0.320763i	$0.896061\pi$
$654$		0			0
$655$	−24.6747	+	0.454815i	−0.964121	+	0.0177711i
$656$	4.62431	−	2.66985i	0.180549	−	0.104240i
$657$		0			0
$658$	5.28444	−	1.41596i	0.206009	−	0.0551999i
$659$	−29.9973	−	10.9181i	−1.16853	−	0.425309i	−0.316391	−	0.948629i	$-0.602471\pi$
$659$	−29.9973	−	10.9181i	−1.16853	−	0.425309i	−0.852137	+	0.523319i	$0.824693\pi$
$660$		0			0
$661$	16.9251	+	14.2018i	0.658309	+	0.552387i	0.909579	−	0.415530i	$-0.136404\pi$
$661$	16.9251	+	14.2018i	0.658309	+	0.552387i	−0.251271	+	0.967917i	$0.580848\pi$
$662$	1.83902	+	21.0201i	0.0714756	+	0.816969i
$663$		0			0
$664$	−5.83945	+	16.0438i	−0.226615	+	0.622619i
$665$	12.9446	−	1.37332i	0.501968	−	0.0532549i
$666$		0			0
$667$	5.68358	+	1.52291i	0.220069	+	0.0589673i
$668$	−1.01919	−	0.713644i	−0.0394336	−	0.0276117i
$669$		0			0
$670$	9.86014	−	1.92662i	0.380931	−	0.0744317i
$671$	−42.7116	−	7.53120i	−1.64886	−	0.290739i
$672$		0			0
$673$	−20.9435	−	1.83232i	−0.807311	−	0.0706306i	−0.323975	−	0.946066i	$-0.605019\pi$
$673$	−20.9435	−	1.83232i	−0.807311	−	0.0706306i	−0.483336	+	0.875435i	$0.660575\pi$
$674$	9.28429			0.357617
$675$		0			0
$676$	11.5735			0.445133
$677$	2.59238	+	0.226804i	0.0996333	+	0.00871679i	0.136863	−	0.990590i	$-0.456298\pi$
$677$	2.59238	+	0.226804i	0.0996333	+	0.00871679i	−0.0372300	+	0.999307i	$0.511853\pi$
$678$		0			0
$679$	−0.447185	−	0.0788507i	−0.0171614	−	0.00302601i
$680$	−6.99147	+	1.36609i	−0.268111	+	0.0523873i
$681$		0			0
$682$	17.7989	+	12.4630i	0.681557	+	0.477231i
$683$	37.2905	+	9.99195i	1.42688	+	0.382331i	0.887919	−	0.460000i	$-0.152151\pi$
$683$	37.2905	+	9.99195i	1.42688	+	0.382331i	0.538960	+	0.842331i	$0.318817\pi$
$684$		0			0
$685$	−36.6393	+	3.88714i	−1.39992	+	0.148520i
$686$	−4.92064	+	13.5193i	−0.187871	+	0.516171i
$687$		0			0
$688$	−0.599612	−	6.85360i	−0.0228600	−	0.261291i
$689$	4.65105	+	3.90270i	0.177191	+	0.148681i
$690$		0			0
$691$	31.6695	+	11.5267i	1.20476	+	0.438498i	0.864884	−	0.501971i	$-0.167392\pi$
$691$	31.6695	+	11.5267i	1.20476	+	0.438498i	0.339879	+	0.940469i	$0.389614\pi$
$692$	−17.2831	+	4.63100i	−0.657006	+	0.176044i
$693$		0			0
$694$	−19.4894	+	11.2522i	−0.739808	+	0.427128i
$695$	26.1109	−	0.481288i	0.990443	−	0.0182563i
$696$		0			0
$697$	−7.18926	+	15.4174i	−0.272313	+	0.583976i
$698$	−4.13502	−	5.90542i	−0.156513	−	0.223524i
$699$		0			0
$700$	5.20963	+	2.19935i	0.196906	+	0.0831277i
$701$		−	18.1902i		−	0.687035i	−0.939146	−	0.343517i	$-0.888382\pi$
$701$		−	18.1902i		−	0.687035i	0.939146	−	0.343517i	$-0.111618\pi$
$702$		0			0
$703$	28.1857	+	28.1857i	1.06304	+	1.06304i
$704$	2.44424	−	2.05096i	0.0921209	−	0.0772986i
$705$		0			0
$706$	−5.03746	+	28.5689i	−0.189587	+	1.07520i
$707$	9.93075	+	4.63078i	0.373484	+	0.174159i
$708$		0			0
$709$	32.0348	−	5.64859i	1.20309	−	0.212137i	0.464056	−	0.885806i	$-0.346393\pi$
$709$	32.0348	−	5.64859i	1.20309	−	0.212137i	0.739034	+	0.673668i	$0.235282\pi$
$710$	−14.0466	−	6.23752i	−0.527160	−	0.234090i
$711$		0			0
$712$	3.91972	+	14.6286i	0.146898	+	0.548230i
$713$	6.65134	−	3.10157i	0.249094	−	0.116155i
$714$		0			0
$715$	8.50137	+	0.586127i	0.317933	+	0.0219199i
$716$	14.8861	−	17.7405i	0.556318	−	0.662994i
$717$		0			0
$718$	1.78628	+	3.83068i	0.0666632	+	0.142960i
$719$	0.584768	−	1.01285i	0.0218082	−	0.0377729i	−0.854915	−	0.518768i	$-0.826391\pi$
$719$	0.584768	−	1.01285i	0.0218082	−	0.0377729i	0.876724	+	0.480995i	$0.159724\pi$
$720$		0			0
$721$	−9.65129	−	16.7165i	−0.359433	−	0.622556i
$722$	−4.29888	+	6.13943i	−0.159988	+	0.228486i
$723$		0			0
$724$	6.45423	+	17.7328i	0.239870	+	0.659036i
$725$	12.7692	−	24.1290i	0.474236	−	0.896129i
$726$		0			0
$727$	0.455700	−	5.20867i	0.0169010	−	0.193179i	−0.983051	−	0.183335i	$-0.941311\pi$
$727$	0.455700	−	5.20867i	0.0169010	−	0.193179i	0.999952	−	0.00984440i	$-0.00313362\pi$
$728$	−0.955168	+	0.955168i	−0.0354009	+	0.0354009i
$729$		0			0
$730$	−3.77896	+	24.0112i	−0.139865	+	0.888695i
$731$	14.0884	+	16.7899i	0.521078	+	0.620997i
$732$		0			0
$733$	9.50733	−	6.65711i	0.351161	−	0.245886i	−0.384665	−	0.923056i	$-0.625683\pi$
$733$	9.50733	−	6.65711i	0.351161	−	0.245886i	0.735826	+	0.677171i	$0.236794\pi$
$734$	3.19170	−	1.16168i	0.117808	−	0.0428785i
$735$		0			0
$736$	−0.187139	−	1.06132i	−0.00689803	−	0.0391207i
$737$	3.71040	−	13.8474i	0.136674	−	0.510076i
$738$		0			0
$739$	36.2743	+	20.9430i	1.33437	+	0.770399i	0.985966	−	0.166945i	$-0.0533904\pi$
$739$	36.2743	+	20.9430i	1.33437	+	0.770399i	0.348404	+	0.937344i	$0.386724\pi$
$740$	4.78920	+	16.6405i	0.176055	+	0.611719i
$741$		0			0
$742$	5.72730	−	0.501074i	0.210256	−	0.0183950i
$743$	3.03978	−	0.265946i	0.111519	−	0.00975663i	−0.0312597	−	0.999511i	$-0.509952\pi$
$743$	3.03978	−	0.265946i	0.111519	−	0.00975663i	0.142779	+	0.989755i	$0.454396\pi$
$744$		0			0
$745$	9.95979	+	5.50809i	0.364899	+	0.201801i
$746$	−15.8031	−	9.12390i	−0.578591	−	0.334050i
$747$		0			0
$748$	−2.63091	+	9.81869i	−0.0961956	+	0.359007i
$749$	−1.09856	−	6.23026i	−0.0401406	−	0.227649i
$750$		0			0
$751$	−42.1399	+	15.3377i	−1.53771	+	0.559680i	−0.965494	−	0.260425i	$-0.916137\pi$
$751$	−42.1399	+	15.3377i	−1.53771	+	0.559680i	−0.572213	+	0.820105i	$0.693915\pi$
$752$	−3.96249	+	2.77457i	−0.144497	+	0.101178i
$753$		0			0
$754$	4.19175	+	4.99553i	0.152654	+	0.181926i
$755$	10.5171	+	1.65521i	0.382755	+	0.0602392i
$756$		0			0
$757$	6.92783	−	6.92783i	0.251796	−	0.251796i	−0.569911	−	0.821707i	$-0.693022\pi$
$757$	6.92783	−	6.92783i	0.251796	−	0.251796i	0.821707	+	0.569911i	$0.193022\pi$
$758$	−2.49451	+	28.5124i	−0.0906047	+	1.03562i
$759$		0			0
$760$	−10.3400	+	5.05565i	−0.375070	+	0.183388i
$761$	4.27445	+	11.7440i	0.154949	+	0.425718i	0.992741	−	0.120271i	$-0.0383762\pi$
$761$	4.27445	+	11.7440i	0.154949	+	0.425718i	−0.837792	+	0.545989i	$0.816154\pi$
$762$		0			0
$763$	−7.28366	+	10.4022i	−0.263686	+	0.376583i
$764$	6.50952	+	11.2748i	0.235506	+	0.407908i
$765$		0			0
$766$	−13.6566	+	23.6539i	−0.493432	+	0.854650i
$767$	−3.15278	−	6.76115i	−0.113840	−	0.244131i
$768$		0			0
$769$	−17.6496	+	21.0339i	−0.636460	+	0.758503i	−0.983807	−	0.179233i	$-0.942638\pi$
$769$	−17.6496	+	21.0339i	−0.636460	+	0.758503i	0.347347	+	0.937737i	$0.387083\pi$
$770$	6.08468	−	5.29978i	0.219277	−	0.190991i
$771$		0			0
$772$	1.61317	−	0.752233i	0.0580592	−	0.0270735i
$773$	9.79849	+	36.5685i	0.352427	+	1.31528i	0.883691	+	0.468070i	$0.155051\pi$
$773$	9.79849	+	36.5685i	0.352427	+	1.31528i	−0.531264	+	0.847206i	$0.678283\pi$
$774$		0			0
$775$	−7.14433	−	33.2914i	−0.256632	−	1.19586i
$776$	0.395399	−	0.0697194i	0.0141940	−	0.00250278i
$777$		0			0
$778$	14.4948	+	6.75905i	0.519664	+	0.242324i
$779$	−4.77274	+	27.0675i	−0.171001	+	0.969795i
$780$		0			0
$781$	−16.8001	+	14.0970i	−0.601156	+	0.504429i
$782$	2.42772	+	2.42772i	0.0868151	+	0.0868151i
$783$		0			0
$784$		−	5.72090i		−	0.204318i
$785$	7.82943	−	31.5333i	0.279444	−	1.12547i
$786$		0			0
$787$	−18.3450	−	26.1994i	−0.653930	−	0.933909i	0.346060	−	0.938212i	$-0.387519\pi$
$787$	−18.3450	−	26.1994i	−0.653930	−	0.933909i	−0.999991	+	0.00430285i	$0.998630\pi$
$788$	0.310634	−	0.666157i	0.0110659	−	0.0237309i
$789$		0			0
$790$	4.96092	+	4.78134i	0.176501	+	0.170113i
$791$	−17.8492	+	10.3053i	−0.634646	+	0.366413i
$792$		0			0
$793$	−15.6816	+	4.20187i	−0.556870	+	0.149213i
$794$	−16.1892	−	5.89238i	−0.574533	−	0.209113i
$795$		0			0
$796$	−5.66333	−	4.75210i	−0.200731	−	0.168434i
$797$	−1.03571	−	11.8382i	−0.0366866	−	0.419330i	−0.992224	−	0.124462i	$-0.960280\pi$
$797$	−1.03571	−	11.8382i	−0.0366866	−	0.419330i	0.955538	−	0.294869i	$-0.0952759\pi$
$798$		0			0
$799$	5.27078	−	14.4813i	0.186467	−	0.512313i
$800$	−4.99365	−	0.251922i	−0.176552	−	0.00890679i
$801$		0			0
$802$	19.7337	+	5.28764i	0.696822	+	0.186713i
$803$	28.4117	+	19.8941i	1.00263	+	0.702047i
$804$		0			0
$805$	−0.522645	−	2.67482i	−0.0184208	−	0.0942750i
$806$	8.01002	+	1.41238i	0.282141	+	0.0497491i
$807$		0			0
$808$	−9.65158	−	0.844404i	−0.339542	−	0.0297060i
$809$	−4.00985			−0.140979			−0.0704895	−	0.997513i	$-0.522456\pi$
$809$	−4.00985			−0.140979			−0.0704895	+	0.997513i	$0.522456\pi$
$810$		0			0
$811$	−33.3615			−1.17148			−0.585741	−	0.810498i	$-0.699196\pi$
$811$	−33.3615			−1.17148			−0.585741	+	0.810498i	$0.699196\pi$
$812$	6.15149	+	0.538186i	0.215875	+	0.0188866i
$813$		0			0
$814$	24.3335	+	4.29065i	0.852889	+	0.150387i
$815$	−5.51927	−	3.71495i	−0.193332	−	0.130129i
$816$		0			0
$817$	29.0081	+	20.3117i	1.01487	+	0.710617i
$818$	−5.93588	−	1.59051i	−0.207543	−	0.0556110i
$819$		0			0
$820$	−7.50496	+	9.28639i	−0.262085	+	0.324295i
$821$	7.77808	−	21.3701i	0.271457	−	0.745821i	−0.726803	−	0.686846i	$-0.758995\pi$
$821$	7.77808	−	21.3701i	0.271457	−	0.745821i	0.998259	−	0.0589750i	$-0.0187832\pi$
$822$		0			0
$823$	1.60564	+	18.3526i	0.0559692	+	0.639731i	0.971430	+	0.237325i	$0.0762706\pi$
$823$	1.60564	+	18.3526i	0.0559692	+	0.639731i	−0.915461	+	0.402406i	$0.868174\pi$
$824$	13.0743	+	10.9706i	0.455464	+	0.382179i
$825$		0			0
$826$	−6.63803	−	2.41605i	−0.230967	−	0.0840650i
$827$	42.9106	−	11.4979i	1.49215	−	0.399820i	0.581687	−	0.813413i	$-0.302393\pi$
$827$	42.9106	−	11.4979i	1.49215	−	0.399820i	0.910462	+	0.413593i	$0.135726\pi$
$828$		0			0
$829$	−38.2777	+	22.0997i	−1.32944	+	0.767553i	−0.985213	−	0.171334i	$-0.945192\pi$
$829$	−38.2777	+	22.0997i	−1.32944	+	0.767553i	−0.344227	+	0.938886i	$0.611859\pi$
$830$	−0.703581	−	38.1708i	−0.0244217	−	1.32493i
$831$		0			0
$832$	0.504767	−	1.08248i	0.0174997	−	0.0375281i
$833$	10.4538	+	14.9296i	0.362204	+	0.517281i
$834$		0			0
$835$	2.70013	+	0.670417i	0.0934420	+	0.0232008i
$836$			16.4237i			0.568026i
$837$		0			0
$838$	−14.6687	−	14.6687i	−0.506721	−	0.506721i
$839$	−28.9780	+	24.3154i	−1.00043	+	0.839461i	−0.987044	−	0.160449i	$-0.948706\pi$
$839$	−28.9780	+	24.3154i	−1.00043	+	0.839461i	−0.0133867	+	0.999910i	$0.504261\pi$
$840$		0			0
$841$	0.140735	−	0.798146i	0.00485292	−	0.0275223i
$842$	−1.36086	−	0.634581i	−0.0468984	−	0.0218691i
$843$		0			0
$844$	15.8602	−	2.79658i	0.545930	−	0.0962622i
$845$	−24.1511	+	9.29782i	−0.830822	+	0.319855i
$846$		0			0
$847$	0.239802	+	0.894952i	0.00823968	+	0.0307509i
$848$	−4.60712	+	2.14834i	−0.158209	+	0.0737742i
$849$		0			0
$850$	13.4921	−	8.46749i	0.462774	−	0.290432i
$851$	5.36444	−	6.39309i	0.183891	−	0.219152i
$852$		0			0
$853$	−8.28192	−	17.7606i	−0.283567	−	0.608112i	0.711998	−	0.702181i	$-0.247790\pi$
$853$	−8.28192	−	17.7606i	−0.283567	−	0.608112i	−0.995566	+	0.0940690i	$0.970013\pi$
$854$	−7.68644	+	13.3133i	−0.263025	+	0.455572i
$855$		0			0
$856$	2.79688	+	4.84433i	0.0955952	+	0.165576i
$857$	−0.752075	+	1.07407i	−0.0256904	+	0.0366897i	−0.831792	−	0.555088i	$-0.812685\pi$
$857$	−0.752075	+	1.07407i	−0.0256904	+	0.0366897i	0.806101	+	0.591777i	$0.201574\pi$
$858$		0			0
$859$	−3.67262	−	10.0904i	−0.125308	−	0.344282i	0.861137	−	0.508373i	$-0.169753\pi$
$859$	−3.67262	−	10.0904i	−0.125308	−	0.344282i	−0.986445	+	0.164092i	$0.947531\pi$
$860$	6.75726	+	13.8201i	0.230421	+	0.471263i
$861$		0			0
$862$	−2.48702	+	28.4268i	−0.0847083	+	0.968221i
$863$	9.45993	−	9.45993i	0.322020	−	0.322020i	−0.527522	−	0.849541i	$-0.676879\pi$
$863$	9.45993	−	9.45993i	0.322020	−	0.322020i	0.849541	+	0.527522i	$0.176879\pi$
$864$		0			0
$865$	32.3454	−	23.5487i	1.09978	−	0.800678i
$866$	−12.7832	−	15.2345i	−0.434392	−	0.517688i
$867$		0			0
$868$	6.30893	−	4.41756i	0.214139	−	0.149942i
$869$	9.23867	−	3.36260i	0.313401	−	0.114068i
$870$		0			0
$871$	−0.931853	−	5.28480i	−0.0315747	−	0.179069i
$872$	2.90605	−	10.8455i	0.0984113	−	0.367276i
$873$		0			0
$874$	4.80403	+	2.77361i	0.162499	+	0.0938186i
$875$	−12.6382	−	0.404249i	−0.427249	−	0.0136661i
$876$		0			0
$877$	−6.06416	+	0.530545i	−0.204772	+	0.0179152i	−0.189080	−	0.981962i	$-0.560551\pi$
$877$	−6.06416	+	0.530545i	−0.204772	+	0.0179152i	−0.0156919	+	0.999877i	$0.504995\pi$
$878$	−2.86593	+	0.250737i	−0.0967206	+	0.00846196i
$879$		0			0
$880$	−3.45287	+	6.24352i	−0.116396	+	0.210469i
$881$	10.7118	+	6.18446i	0.360890	+	0.208360i	0.669471	−	0.742838i	$-0.266521\pi$
$881$	10.7118	+	6.18446i	0.360890	+	0.208360i	−0.308581	+	0.951198i	$0.599854\pi$
$882$		0			0
$883$	−2.23942	+	8.35762i	−0.0753624	+	0.281256i	−0.993315	−	0.115433i	$-0.963174\pi$
$883$	−2.23942	+	8.35762i	−0.0753624	+	0.281256i	0.917953	+	0.396689i	$0.129841\pi$
$884$	0.660743	+	3.74726i	0.0222232	+	0.126034i
$885$		0			0
$886$	8.58455	−	3.12452i	0.288403	−	0.104970i
$887$	14.2651	−	9.98850i	0.478974	−	0.335381i	−0.309029	−	0.951053i	$-0.600004\pi$
$887$	14.2651	−	9.98850i	0.478974	−	0.335381i	0.788003	+	0.615672i	$0.211115\pi$
$888$		0			0
$889$	14.1446	+	16.8569i	0.474395	+	0.565362i
$890$	−19.9318	−	27.3774i	−0.668115	−	0.917694i
$891$		0			0
$892$	−9.60570	+	9.60570i	−0.321623	+	0.321623i
$893$	2.17010	−	24.8044i	0.0726198	−	0.830048i
$894$		0			0
$895$	−16.8114	+	48.9794i	−0.561945	+	1.63720i
$896$	−0.386815	−	1.06277i	−0.0129226	−	0.0355045i
$897$		0			0
$898$	15.5910	−	22.2663i	0.520279	−	0.743035i
$899$	−18.5906	−	32.1999i	−0.620032	−	1.07393i
$900$		0			0
$901$	8.09736	−	14.0250i	0.269762	−	0.467242i
$902$	7.20037	+	15.4412i	0.239746	+	0.514137i
$903$		0			0
$904$	11.7140	−	13.9602i	0.389601	−	0.464309i
$905$	−27.7146	−	31.8191i	−0.921264	−	1.05770i
$906$		0			0
$907$	15.5493	−	7.25077i	0.516307	−	0.240758i	−0.146958	−	0.989143i	$-0.546948\pi$
$907$	15.5493	−	7.25077i	0.516307	−	0.240758i	0.663265	+	0.748385i	$0.269170\pi$
$908$	−5.31827	−	19.8481i	−0.176493	−	0.658681i
$909$		0			0
$910$	1.22585	−	2.76057i	0.0406367	−	0.0915120i
$911$	−17.3243	+	3.05474i	−0.573979	+	0.101208i	−0.453101	−	0.891459i	$-0.649682\pi$
$911$	−17.3243	+	3.05474i	−0.573979	+	0.101208i	−0.120878	+	0.992667i	$0.538571\pi$
$912$		0			0
$913$	−49.3727	−	23.0229i	−1.63400	−	0.761945i
$914$	0.289800	−	1.64354i	0.00958574	−	0.0543634i
$915$		0			0
$916$	−21.9940	+	18.4551i	−0.726701	+	0.609775i
$917$	8.82628	+	8.82628i	0.291469	+	0.291469i
$918$		0			0
$919$		−	28.3470i		−	0.935080i	−0.883972	−	0.467540i	$-0.845140\pi$
$919$		−	28.3470i		−	0.935080i	0.883972	−	0.467540i	$-0.154860\pi$
$920$	1.24315	+	2.06438i	0.0409855	+	0.0680605i
$921$		0			0
$922$	−12.5523	−	17.9266i	−0.413390	−	0.590381i
$923$	−3.46944	+	7.44024i	−0.114198	+	0.244898i
$924$		0			0
$925$	−23.3625	−	30.8774i	−0.768155	−	1.01524i
$926$	−30.7581	+	17.7582i	−1.01078	+	0.583571i
$927$		0			0
$928$	−5.27385	+	1.41312i	−0.173123	+	0.0463881i
$929$	49.9623	+	18.1848i	1.63921	+	0.596623i	0.986901	−	0.161330i	$-0.0515783\pi$
$929$	49.9623	+	18.1848i	1.63921	+	0.596623i	0.652309	+	0.757953i	$0.273801\pi$
$930$		0			0
$931$	22.5579	+	18.9284i	0.739307	+	0.620352i
$932$	0.448609	+	5.12763i	0.0146947	+	0.167961i
$933$		0			0
$934$	−3.53087	+	9.70100i	−0.115534	+	0.317426i
$935$	−2.39799	−	22.6029i	−0.0784227	−	0.739194i
$936$		0			0
$937$	−29.5474	−	7.91721i	−0.965273	−	0.258644i	−0.258442	−	0.966027i	$-0.583209\pi$
$937$	−29.5474	−	7.91721i	−0.965273	−	0.258644i	−0.706831	+	0.707383i	$0.749876\pi$
$938$	−4.16247	−	2.91459i	−0.135909	−	0.0951647i
$939$		0			0
$940$	6.03977	−	8.97323i	0.196996	−	0.292674i
$941$	−15.0014	−	2.64515i	−0.489032	−	0.0862295i	−0.0763054	−	0.997084i	$-0.524312\pi$
$941$	−15.0014	−	2.64515i	−0.489032	−	0.0862295i	−0.412727	+	0.910855i	$0.635423\pi$
$942$		0			0
$943$	5.73264	+	0.501541i	0.186680	+	0.0163324i
$944$	6.24600			0.203290
$945$		0			0
$946$	21.9515			0.713706
$947$	−45.5039	−	3.98107i	−1.47868	−	0.129368i	−0.680925	−	0.732353i	$-0.738422\pi$
$947$	−45.5039	−	3.98107i	−1.47868	−	0.129368i	−0.797752	+	0.602985i	$0.793978\pi$
$948$		0			0
$949$	12.7861	+	2.25453i	0.415053	+	0.0731850i
$950$	17.5155	−	18.8568i	0.568278	−	0.611796i
$951$		0			0
$952$	2.95145	+	2.06663i	0.0956571	+	0.0669798i
$953$	28.6561	+	7.67838i	0.928262	+	0.248727i	0.691113	−	0.722746i	$-0.257120\pi$
$953$	28.6561	+	7.67838i	0.928262	+	0.248727i	0.237149	+	0.971473i	$0.423787\pi$
$954$		0			0
$955$	−22.6417	−	18.2983i	−0.732669	−	0.592120i
$956$	−8.39133	+	23.0550i	−0.271395	+	0.745652i
$957$		0			0
$958$	−2.48585	−	28.4134i	−0.0803143	−	0.917997i
$959$	14.2757	+	11.9788i	0.460988	+	0.386814i
$960$		0			0
$961$	−14.4472	−	5.25836i	−0.466040	−	0.169625i
$962$	8.93408	−	2.39388i	0.288046	−	0.0771817i
$963$		0			0
$964$	5.48776	−	3.16836i	0.176749	−	0.102046i
$965$	−2.76198	+	2.86571i	−0.0889113	+	0.0922505i
$966$		0			0
$967$	2.36319	−	5.06787i	0.0759950	−	0.162972i	−0.864640	−	0.502393i	$-0.832453\pi$
$967$	2.36319	−	5.06787i	0.0759950	−	0.162972i	0.940635	+	0.339421i	$0.110231\pi$
$968$	−0.469889	−	0.671072i	−0.0151028	−	0.0215691i
$969$		0			0
$970$	−0.769093	+	0.463141i	−0.0246941	+	0.0148706i
$971$			42.4292i			1.36162i	0.732461	+	0.680809i	$0.238372\pi$
$971$			42.4292i			1.36162i	−0.732461	+	0.680809i	$0.761628\pi$
$972$		0			0
$973$	−9.34001	−	9.34001i	−0.299427	−	0.299427i
$974$	1.28198	−	1.07571i	0.0410773	−	0.0344679i
$975$		0			0
$976$	2.36034	−	13.3861i	0.0755525	−	0.428480i
$977$	2.71564	+	1.26633i	0.0868811	+	0.0405133i	0.465573	−	0.885009i	$-0.345848\pi$
$977$	2.71564	+	1.26633i	0.0868811	+	0.0405133i	−0.378692	+	0.925523i	$0.623626\pi$
$978$		0			0
$979$	−47.5884	+	8.39111i	−1.52093	+	0.268181i
$980$	4.59603	+	11.9382i	0.146815	+	0.381351i
$981$		0			0
$982$	−1.35840	−	5.06961i	−0.0433482	−	0.161778i
$983$	20.0843	−	9.36548i	0.640591	−	0.298712i	−0.0750511	−	0.997180i	$-0.523912\pi$
$983$	20.0843	−	9.36548i	0.640591	−	0.298712i	0.715642	+	0.698467i	$0.246134\pi$
$984$		0			0
$985$	−0.113047	+	1.63967i	−0.00360198	+	0.0522442i
$986$	11.1808	−	13.3247i	0.356068	−	0.424345i
$987$		0			0
$988$	2.59820	+	5.57185i	0.0826597	+	0.177264i
$989$	3.70714	−	6.42095i	0.117880	−	0.204174i
$990$		0			0
$991$	16.2954	+	28.2245i	0.517640	+	0.896580i	0.999790	+	0.0204906i	$0.00652283\pi$
$991$	16.2954	+	28.2245i	0.517640	+	0.896580i	−0.482150	+	0.876089i	$0.660144\pi$
$992$	−3.90599	+	5.57832i	−0.124015	+	0.177112i
$993$		0			0
$994$	2.65871	+	7.30476i	0.0843293	+	0.231693i
$995$	15.6357	+	5.36674i	0.495687	+	0.170137i
$996$		0			0
$997$	2.38272	−	27.2346i	0.0754615	−	0.862529i	−0.860275	−	0.509830i	$-0.829708\pi$
$997$	2.38272	−	27.2346i	0.0754615	−	0.862529i	0.935737	−	0.352699i	$-0.114736\pi$
$998$	7.39607	−	7.39607i	0.234119	−	0.234119i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.1		216
3.2	odd	2		270.2.r.a.113.13	✓	216
5.2	odd	4	inner	810.2.s.a.287.17		216
15.2	even	4		270.2.r.a.167.8	yes	216
27.11	odd	18	inner	810.2.s.a.683.17		216
27.16	even	9		270.2.r.a.173.8	yes	216
135.92	even	36	inner	810.2.s.a.197.1		216
135.97	odd	36		270.2.r.a.227.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.13	✓	216	3.2	odd	2
270.2.r.a.167.8	yes	216	15.2	even	4
270.2.r.a.173.8	yes	216	27.16	even	9
270.2.r.a.227.13	yes	216	135.97	odd	36
810.2.s.a.197.1		216	135.92	even	36	inner
810.2.s.a.287.17		216	5.2	odd	4	inner
810.2.s.a.683.17		216	27.11	odd	18	inner
810.2.s.a.773.1		216	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.19457 + 0.428806i) q^{5} +(0.926438 + 0.648699i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.22359 - 0.235905i) q^{10} +(1.09129 - 2.99831i) q^{11} +(-0.104097 - 1.18984i) q^{13} +(-0.866375 - 0.726975i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.07725 + 0.824548i) q^{17} +(-4.45771 + 2.57366i) q^{19} +(-2.23569 + 0.0412092i) q^{20} +(-1.34846 + 2.89179i) q^{22} +(0.618138 + 0.882792i) q^{23} +(4.63225 - 1.88209i) q^{25} +1.19438i q^{26} +(0.799718 + 0.799718i) q^{28} +(4.18252 - 3.50955i) q^{29} +(1.18252 - 6.70642i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.13741 - 0.553210i) q^{34} +(-2.31130 - 1.02635i) q^{35} +(-2.00428 - 7.48009i) q^{37} +(4.66505 - 2.17535i) q^{38} +(2.23077 + 0.153801i) q^{40} +(3.43229 - 4.09044i) q^{41} +(-2.90752 - 6.23520i) q^{43} +(1.59537 - 2.76326i) q^{44} +(-0.538845 - 0.933307i) q^{46} +(-2.77457 + 3.96249i) q^{47} +(-1.95666 - 5.37589i) q^{49} +(-4.77866 + 1.47120i) q^{50} +(0.104097 - 1.18984i) q^{52} +(-3.59451 + 3.59451i) q^{53} +(-1.10923 + 7.04794i) q^{55} +(-0.726975 - 0.866375i) q^{56} +(-4.47248 + 3.13167i) q^{58} +(5.86932 - 2.13626i) q^{59} +(-2.36034 - 13.3861i) q^{61} +(-1.76253 + 6.57784i) q^{62} +(0.866025 + 0.500000i) q^{64} +(0.738658 + 2.56654i) q^{65} +(4.47588 - 0.391589i) q^{67} +(-3.17368 + 0.277661i) q^{68} +(2.21305 + 1.22389i) q^{70} +(-5.95249 - 3.43667i) q^{71} +(-2.81344 + 10.4999i) q^{73} +(1.34472 + 7.62631i) q^{74} +(-4.83689 + 1.76049i) q^{76} +(2.95602 - 2.06982i) q^{77} +(1.98062 + 2.36041i) q^{79} +(-2.20888 - 0.347640i) q^{80} +(-3.77573 + 3.77573i) q^{82} +(1.48805 - 17.0085i) q^{83} +(6.39967 - 3.12907i) q^{85} +(2.35302 + 6.46488i) q^{86} +(-1.83013 + 2.61369i) q^{88} +(-7.57232 - 13.1156i) q^{89} +(0.675406 - 1.16984i) q^{91} +(0.455452 + 0.976719i) q^{92} +(3.10936 - 3.70559i) q^{94} +(8.67914 - 7.55956i) q^{95} +(-0.363881 + 0.169680i) q^{97} +(1.48068 + 5.52597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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