LMFDB - Embedded newform 810.2.s.a.467.3

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			467.3
Character	$\chi$	$=$	810.467
Dual form			810.2.s.a.503.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(-1.60755 + 1.55428i) q^{5} +(-0.119477 - 1.36563i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(-1.60755 + 1.55428i) q^{5} +(-0.119477 - 1.36563i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.729270 - 2.11380i) q^{10} +(-1.00994 - 0.178080i) q^{11} +(5.15208 - 2.40245i) q^{13} +(1.28818 + 0.468858i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-6.75766 - 1.81071i) q^{17} +(-3.88061 - 2.24047i) q^{19} +(2.22396 + 0.232388i) q^{20} +(0.588216 - 0.840060i) q^{22} +(3.20470 + 0.280375i) q^{23} +(0.168456 - 4.99716i) q^{25} +5.68469i q^{26} +(-0.969337 + 0.969337i) q^{28} +(7.70523 - 2.80447i) q^{29} +(1.58144 - 1.32699i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(4.49697 - 5.35928i) q^{34} +(2.31464 + 2.00963i) q^{35} +(-0.416406 + 1.55405i) q^{37} +(3.67057 - 2.57016i) q^{38} +(-1.15050 + 1.91738i) q^{40} +(2.98153 - 8.19170i) q^{41} +(3.51565 + 5.02087i) q^{43} +(0.512762 + 0.888129i) q^{44} +(-1.60847 + 2.78595i) q^{46} +(9.52867 - 0.833651i) q^{47} +(5.04298 - 0.889213i) q^{49} +(4.45777 + 2.26456i) q^{50} +(-5.15208 - 2.40245i) q^{52} +(-3.57469 - 3.57469i) q^{53} +(1.90032 - 1.28346i) q^{55} +(-0.468858 - 1.28818i) q^{56} +(-0.714654 + 8.16853i) q^{58} +(-1.70697 - 9.68068i) q^{59} +(-7.76955 - 6.51943i) q^{61} +(0.534312 + 1.99408i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-4.54816 + 11.8698i) q^{65} +(3.93699 + 8.44291i) q^{67} +(2.95666 + 6.34057i) q^{68} +(-2.79955 + 1.24847i) q^{70} +(0.770875 - 0.445065i) q^{71} +(-1.35517 - 5.05755i) q^{73} +(-1.23246 - 1.03416i) q^{74} +(0.778107 + 4.41286i) q^{76} +(-0.122527 + 1.40049i) q^{77} +(-2.55545 - 7.02105i) q^{79} +(-1.25151 - 1.85303i) q^{80} +(6.16415 + 6.16415i) q^{82} +(-5.99835 - 2.79708i) q^{83} +(13.6776 - 7.59246i) q^{85} +(-6.03623 + 1.06435i) q^{86} +(-1.02162 + 0.0893803i) q^{88} +(4.45891 - 7.72305i) q^{89} +(-3.89642 - 6.74881i) q^{91} +(-1.84516 - 2.63516i) q^{92} +(-3.27145 + 8.98822i) q^{94} +(9.72059 - 2.42986i) q^{95} +(-0.365508 + 0.255932i) q^{97} +(-1.32535 + 4.94629i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * 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} + 48 q^{92} + 60 q^{95} - 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$3$		0			0
$3$		0			0
$4$	−0.642788	−	0.766044i	−0.321394	−	0.383022i
$5$	−1.60755	+	1.55428i	−0.718920	+	0.695093i
$5$	−1.60755	+	1.55428i	−0.718920	+	0.695093i
$6$		0			0
$7$	−0.119477	−	1.36563i	−0.0451582	−	0.516161i	−0.984763	−	0.173900i	$-0.944363\pi$
$7$	−0.119477	−	1.36563i	−0.0451582	−	0.516161i	0.939605	−	0.342261i	$-0.111193\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$		0			0
$10$	−0.729270	−	2.11380i	−0.230616	−	0.668443i
$11$	−1.00994	−	0.178080i	−0.304509	−	0.0536932i	0.0193056	−	0.999814i	$-0.493854\pi$
$11$	−1.00994	−	0.178080i	−0.304509	−	0.0536932i	−0.323815	+	0.946120i	$0.604966\pi$
$12$		0			0
$13$	5.15208	−	2.40245i	1.42893	−	0.666320i	0.454444	−	0.890775i	$-0.349838\pi$
$13$	5.15208	−	2.40245i	1.42893	−	0.666320i	0.974484	+	0.224455i	$0.0720602\pi$
$14$	1.28818	+	0.468858i	0.344280	+	0.125308i
$15$		0			0
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	−6.75766	−	1.81071i	−1.63897	−	0.439162i	−0.682478	−	0.730906i	$-0.739098\pi$
$17$	−6.75766	−	1.81071i	−1.63897	−	0.439162i	−0.956496	+	0.291745i	$0.905764\pi$
$18$		0			0
$19$	−3.88061	−	2.24047i	−0.890273	−	0.513999i	−0.0162409	−	0.999868i	$-0.505170\pi$
$19$	−3.88061	−	2.24047i	−0.890273	−	0.513999i	−0.874032	+	0.485869i	$0.838503\pi$
$20$	2.22396	+	0.232388i	0.497292	+	0.0519636i
$21$		0			0
$22$	0.588216	−	0.840060i	0.125408	−	0.179101i
$23$	3.20470	+	0.280375i	0.668225	+	0.0584621i	0.416220	−	0.909264i	$-0.363355\pi$
$23$	3.20470	+	0.280375i	0.668225	+	0.0584621i	0.252005	+	0.967726i	$0.418910\pi$
$24$		0			0
$25$	0.168456	−	4.99716i	0.0336913	−	0.999432i
$26$			5.68469i			1.11486i
$27$		0			0
$28$	−0.969337	+	0.969337i	−0.183187	+	0.183187i
$29$	7.70523	−	2.80447i	1.43082	−	0.520778i	0.493657	−	0.869657i	$-0.335660\pi$
$29$	7.70523	−	2.80447i	1.43082	−	0.520778i	0.937168	+	0.348879i	$0.113438\pi$
$30$		0			0
$31$	1.58144	−	1.32699i	0.284035	−	0.238334i	−0.489627	−	0.871932i	$-0.662867\pi$
$31$	1.58144	−	1.32699i	0.284035	−	0.238334i	0.773662	+	0.633598i	$0.218423\pi$
$32$	−0.819152	−	0.573576i	−0.144807	−	0.101395i
$33$		0			0
$34$	4.49697	−	5.35928i	0.771224	−	0.919110i
$35$	2.31464	+	2.00963i	0.391245	+	0.339689i
$36$		0			0
$37$	−0.416406	+	1.55405i	−0.0684567	+	0.255484i	−0.991670	−	0.128804i	$-0.958886\pi$
$37$	−0.416406	+	1.55405i	−0.0684567	+	0.255484i	0.923213	+	0.384288i	$0.125553\pi$
$38$	3.67057	−	2.57016i	0.595445	−	0.416935i
$39$		0			0
$40$	−1.15050	+	1.91738i	−0.181910	+	0.303164i
$41$	2.98153	−	8.19170i	0.465637	−	1.27933i	−0.455550	−	0.890210i	$-0.650557\pi$
$41$	2.98153	−	8.19170i	0.465637	−	1.27933i	0.921188	−	0.389118i	$-0.127220\pi$
$42$		0			0
$43$	3.51565	+	5.02087i	0.536131	+	0.765675i	0.992252	−	0.124243i	$-0.0396503\pi$
$43$	3.51565	+	5.02087i	0.536131	+	0.765675i	−0.456121	+	0.889918i	$0.650761\pi$
$44$	0.512762	+	0.888129i	0.0773017	+	0.133891i
$45$		0			0
$46$	−1.60847	+	2.78595i	−0.237156	+	0.410766i
$47$	9.52867	−	0.833651i	1.38990	−	0.121600i	0.632504	−	0.774557i	$-0.282027\pi$
$47$	9.52867	−	0.833651i	1.38990	−	0.121600i	0.757395	+	0.652957i	$0.226472\pi$
$48$		0			0
$49$	5.04298	−	0.889213i	0.720425	−	0.127030i
$50$	4.45777	+	2.26456i	0.630424	+	0.320258i
$51$		0			0
$52$	−5.15208	−	2.40245i	−0.714464	−	0.333160i
$53$	−3.57469	−	3.57469i	−0.491021	−	0.491021i	0.417607	−	0.908628i	$-0.362869\pi$
$53$	−3.57469	−	3.57469i	−0.491021	−	0.491021i	−0.908628	+	0.417607i	$0.862869\pi$
$54$		0			0
$55$	1.90032	−	1.28346i	0.256240	−	0.173061i
$56$	−0.468858	−	1.28818i	−0.0626538	−	0.172140i
$57$		0			0
$58$	−0.714654	+	8.16853i	−0.0938386	+	1.07258i
$59$	−1.70697	−	9.68068i	−0.222228	−	1.26032i	−0.867914	−	0.496714i	$-0.834540\pi$
$59$	−1.70697	−	9.68068i	−0.222228	−	1.26032i	0.645686	−	0.763603i	$-0.276571\pi$
$60$		0			0
$61$	−7.76955	−	6.51943i	−0.994789	−	0.834727i	−0.00853536	−	0.999964i	$-0.502717\pi$
$61$	−7.76955	−	6.51943i	−0.994789	−	0.834727i	−0.986254	+	0.165236i	$0.947161\pi$
$62$	0.534312	+	1.99408i	0.0678577	+	0.253248i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−4.54816	+	11.8698i	−0.564130	+	1.47227i
$66$		0			0
$67$	3.93699	+	8.44291i	0.480980	+	1.03147i	0.985751	+	0.168212i	$0.0537994\pi$
$67$	3.93699	+	8.44291i	0.480980	+	1.03147i	−0.504770	+	0.863254i	$0.668423\pi$
$68$	2.95666	+	6.34057i	0.358547	+	0.768907i
$69$		0			0
$70$	−2.79955	+	1.24847i	−0.334610	+	0.149220i
$71$	0.770875	−	0.445065i	0.0914860	−	0.0528195i	−0.453559	−	0.891226i	$-0.649846\pi$
$71$	0.770875	−	0.445065i	0.0914860	−	0.0528195i	0.545045	+	0.838407i	$0.316513\pi$
$72$		0			0
$73$	−1.35517	−	5.05755i	−0.158610	−	0.591942i	−0.998769	−	0.0496014i	$-0.984205\pi$
$73$	−1.35517	−	5.05755i	−0.158610	−	0.591942i	0.840159	−	0.542341i	$-0.182462\pi$
$74$	−1.23246	−	1.03416i	−0.143271	−	0.120219i
$75$		0			0
$76$	0.778107	+	4.41286i	0.0892550	+	0.506190i
$77$	−0.122527	+	1.40049i	−0.0139632	+	0.159600i
$78$		0			0
$79$	−2.55545	−	7.02105i	−0.287511	−	0.789930i	−0.996413	−	0.0846230i	$-0.973031\pi$
$79$	−2.55545	−	7.02105i	−0.287511	−	0.789930i	0.708902	−	0.705307i	$-0.249191\pi$
$80$	−1.25151	−	1.85303i	−0.139923	−	0.207175i
$81$		0			0
$82$	6.16415	+	6.16415i	0.680716	+	0.680716i
$83$	−5.99835	−	2.79708i	−0.658405	−	0.307019i	0.0645500	−	0.997914i	$-0.479439\pi$
$83$	−5.99835	−	2.79708i	−0.658405	−	0.307019i	−0.722955	+	0.690895i	$0.757217\pi$
$84$		0			0
$85$	13.6776	−	7.59246i	1.48355	−	0.823517i
$86$	−6.03623	+	1.06435i	−0.650903	+	0.114772i
$87$		0			0
$88$	−1.02162	+	0.0893803i	−0.108905	+	0.00952797i
$89$	4.45891	−	7.72305i	0.472643	−	0.818642i	−0.526867	−	0.849948i	$-0.676633\pi$
$89$	4.45891	−	7.72305i	0.472643	−	0.818642i	0.999510	+	0.0313059i	$0.00996662\pi$
$90$		0			0
$91$	−3.89642	−	6.74881i	−0.408456	−	0.707467i
$92$	−1.84516	−	2.63516i	−0.192371	−	0.274734i
$93$		0			0
$94$	−3.27145	+	8.98822i	−0.337424	+	0.927064i
$95$	9.72059	−	2.42986i	0.997312	−	0.249298i
$96$		0			0
$97$	−0.365508	+	0.255932i	−0.0371117	+	0.0259859i	−0.591985	−	0.805949i	$-0.701656\pi$
$97$	−0.365508	+	0.255932i	−0.0371117	+	0.0259859i	0.554873	+	0.831935i	$0.312767\pi$
$98$	−1.32535	+	4.94629i	−0.133881	+	0.499650i
$99$		0			0
$100$	−3.93633	+	3.08307i	−0.393633	+	0.308307i
$101$	−0.927270	+	1.10508i	−0.0922668	+	0.109959i	−0.810202	−	0.586150i	$-0.800643\pi$
$101$	−0.927270	+	1.10508i	−0.0922668	+	0.109959i	0.717936	+	0.696110i	$0.245087\pi$
$102$		0			0
$103$	5.30157	+	3.71220i	0.522379	+	0.365774i	0.804828	−	0.593509i	$-0.202258\pi$
$103$	5.30157	+	3.71220i	0.522379	+	0.365774i	−0.282448	+	0.959283i	$0.591147\pi$
$104$	4.35472	−	3.65405i	0.427016	−	0.358309i
$105$		0			0
$106$	4.75049	−	1.72904i	0.461409	−	0.167939i
$107$	−12.8647	+	12.8647i	−1.24368	+	1.24368i	−0.285213	+	0.958464i	$0.592064\pi$
$107$	−12.8647	+	12.8647i	−1.24368	+	1.24368i	−0.958464	+	0.285213i	$0.907936\pi$
$108$		0			0
$109$			4.66649i			0.446969i	0.974708	+	0.223484i	$0.0717432\pi$
$109$			4.66649i			0.446969i	−0.974708	+	0.223484i	$0.928257\pi$
$110$	0.360095	+	2.26469i	0.0343337	+	0.215930i
$111$		0			0
$112$	1.36563	+	0.119477i	0.129040	+	0.0112896i
$113$	1.06056	−	1.51464i	0.0997691	−	0.142485i	−0.766164	−	0.642646i	$-0.777837\pi$
$113$	1.06056	−	1.51464i	0.0997691	−	0.142485i	0.865933	+	0.500161i	$0.166726\pi$
$114$		0			0
$115$	−5.58750	+	4.53026i	−0.521037	+	0.422449i
$116$	−7.10118	−	4.09987i	−0.659328	−	0.380663i
$117$		0			0
$118$	9.49507	+	2.54420i	0.874092	+	0.234212i
$119$	−1.66538	+	9.44483i	−0.152665	+	0.865806i
$120$		0			0
$121$	−9.34835	−	3.40252i	−0.849850	−	0.309320i
$122$	9.19216	−	4.28638i	0.832220	−	0.388070i
$123$		0			0
$124$	−2.03306	−	0.358483i	−0.182574	−	0.0321928i
$125$	7.49616	+	8.29503i	0.670477	+	0.741930i
$126$		0			0
$127$	−10.7222	+	2.87299i	−0.951437	+	0.254937i	−0.700972	−	0.713189i	$-0.747250\pi$
$127$	−10.7222	+	2.87299i	−0.951437	+	0.254937i	−0.250465	+	0.968126i	$0.580584\pi$
$128$	0.0871557	+	0.996195i	0.00770355	+	0.0880520i
$129$		0			0
$130$	−8.83557	−	9.13844i	−0.774930	−	0.801494i
$131$	0.698519	+	0.832463i	0.0610299	+	0.0727326i	0.795696	−	0.605697i	$-0.207105\pi$
$131$	0.698519	+	0.832463i	0.0610299	+	0.0727326i	−0.734666	+	0.678429i	$0.762661\pi$
$132$		0			0
$133$	−2.59601	+	5.56717i	−0.225103	+	0.482735i
$134$	−9.31572			−0.804756
$135$		0			0
$136$	−6.99605			−0.599906
$137$	−0.966343	+	2.07233i	−0.0825603	+	0.177051i	−0.943254	−	0.332072i	$-0.892252\pi$
$137$	−0.966343	+	2.07233i	−0.0825603	+	0.177051i	0.860694	+	0.509123i	$0.170030\pi$
$138$		0			0
$139$	7.36374	+	8.77576i	0.624584	+	0.744350i	0.981851	−	0.189652i	$-0.0607360\pi$
$139$	7.36374	+	8.77576i	0.624584	+	0.744350i	−0.357268	+	0.934002i	$0.616292\pi$
$140$	0.0516445	−	3.06488i	0.00436475	−	0.259029i
$141$		0			0
$142$	0.0775799	+	0.886742i	0.00651036	+	0.0744138i
$143$	−5.63113	+	1.50886i	−0.470899	+	0.126177i
$144$		0			0
$145$	−8.02764	+	16.4844i	−0.666659	+	1.36895i
$146$	5.15642	+	0.909216i	0.426748	+	0.0752472i
$147$		0			0
$148$	1.45813	−	0.679937i	0.119858	−	0.0558905i
$149$	−12.5767	−	4.57756i	−1.03033	−	0.375008i	−0.229122	−	0.973398i	$-0.573585\pi$
$149$	−12.5767	−	4.57756i	−1.03033	−	0.375008i	−0.801206	+	0.598389i	$0.795808\pi$
$150$		0			0
$151$	0.361051	−	2.04762i	0.0293819	−	0.166633i	−0.966586	−	0.256342i	$-0.917483\pi$
$151$	0.361051	−	2.04762i	0.0293819	−	0.166633i	0.995968	+	0.0897090i	$0.0285937\pi$
$152$	−4.32826	−	1.15975i	−0.351068	−	0.0940684i
$153$		0			0
$154$	−1.21749	−	0.702919i	−0.0981083	−	0.0566428i
$155$	−0.479748	+	4.59119i	−0.0385343	+	0.368774i
$156$		0			0
$157$	−1.22311	+	1.74678i	−0.0976147	+	0.139408i	−0.864988	−	0.501792i	$-0.832674\pi$
$157$	−1.22311	+	1.74678i	−0.0976147	+	0.139408i	0.767374	+	0.641200i	$0.221563\pi$
$158$	7.44322	+	0.651197i	0.592150	+	0.0518064i
$159$		0			0
$160$	2.20833	−	0.351133i	0.174584	−	0.0277595i
$161$		−	4.40994i		−	0.347552i
$162$		0			0
$163$	8.64856	−	8.64856i	0.677408	−	0.677408i	−0.282005	−	0.959413i	$-0.591000\pi$
$163$	8.64856	−	8.64856i	0.677408	−	0.677408i	0.959413	+	0.282005i	$0.0909996\pi$
$164$	−8.19170	+	2.98153i	−0.639664	+	0.232819i
$165$		0			0
$166$	5.07003	−	4.25426i	0.393510	−	0.330195i
$167$	−9.12258	−	6.38770i	−0.705926	−	0.494295i	0.164635	−	0.986355i	$-0.447355\pi$
$167$	−9.12258	−	6.38770i	−0.705926	−	0.494295i	−0.870561	+	0.492060i	$0.836244\pi$
$168$		0			0
$169$	12.4159	−	14.7966i	0.955066	−	1.13820i
$170$	1.10068	+	15.6049i	0.0844181	+	1.19684i
$171$		0			0
$172$	1.58639	−	5.92049i	0.120961	−	0.451433i
$173$	3.28417	−	2.29960i	0.249691	−	0.174835i	−0.442030	−	0.897000i	$-0.645742\pi$
$173$	3.28417	−	2.29960i	0.249691	−	0.174835i	0.691721	+	0.722165i	$0.256853\pi$
$174$		0			0
$175$	−6.84442	+	0.366998i	−0.517389	+	0.0277425i
$176$	0.350750	−	0.963677i	0.0264387	−	0.0726399i
$177$		0			0
$178$	5.11505	+	7.30505i	0.383389	+	0.547536i
$179$	−5.37055	−	9.30206i	−0.401414	−	0.695269i	0.592483	−	0.805583i	$-0.298148\pi$
$179$	−5.37055	−	9.30206i	−0.401414	−	0.695269i	−0.993897	+	0.110314i	$0.964814\pi$
$180$		0			0
$181$	10.5913	−	18.3447i	0.787246	−	1.36355i	−0.140401	−	0.990095i	$-0.544839\pi$
$181$	10.5913	−	18.3447i	0.787246	−	1.36355i	0.927648	−	0.373456i	$-0.121827\pi$
$182$	7.76319	−	0.679192i	0.575446	−	0.0503450i
$183$		0			0
$184$	3.16806	−	0.558615i	0.233553	−	0.0411817i
$185$	−1.74602	−	3.14542i	−0.128370	−	0.231256i
$186$		0			0
$187$	6.50241	+	3.03212i	0.475503	+	0.221731i
$188$	−6.76352	−	6.76352i	−0.493281	−	0.493281i
$189$		0			0
$190$	−1.90590	+	9.83675i	−0.138269	+	0.713633i
$191$	−0.0680526	−	0.186973i	−0.00492411	−	0.0135289i	0.937206	−	0.348776i	$-0.113403\pi$
$191$	−0.0680526	−	0.186973i	−0.00492411	−	0.0135289i	−0.942130	+	0.335247i	$0.891180\pi$
$192$		0			0
$193$	−1.71416	+	19.5930i	−0.123388	+	1.41033i	0.641971	+	0.766729i	$0.278117\pi$
$193$	−1.71416	+	19.5930i	−0.123388	+	1.41033i	−0.765359	+	0.643603i	$0.777439\pi$
$194$	−0.0774823	−	0.439424i	−0.00556291	−	0.0315488i
$195$		0			0
$196$	−3.92274	−	3.29157i	−0.280196	−	0.235112i
$197$	−0.949894	−	3.54505i	−0.0676772	−	0.252575i	0.923796	−	0.382885i	$-0.125069\pi$
$197$	−0.949894	−	3.54505i	−0.0676772	−	0.252575i	−0.991473	+	0.130310i	$0.958403\pi$
$198$		0			0
$199$	−18.8661	+	10.8923i	−1.33738	+	0.772138i	−0.986419	−	0.164251i	$-0.947479\pi$
$199$	−18.8661	+	10.8923i	−1.33738	+	0.772138i	−0.350964	+	0.936389i	$0.614146\pi$
$200$	−1.13064	−	4.87049i	−0.0799486	−	0.344395i
$201$		0			0
$202$	−0.609659	−	1.30742i	−0.0428955	−	0.0919896i
$203$	−4.75048	−	10.1874i	−0.333419	−	0.715018i
$204$		0			0
$205$	7.93918	+	17.8027i	0.554496	+	1.24340i
$206$	−5.60494	+	3.23601i	−0.390515	+	0.225464i
$207$		0			0
$208$	1.47130	+	5.49098i	0.102017	+	0.380731i
$209$	3.52021	+	2.95381i	0.243498	+	0.204319i
$210$		0			0
$211$	−2.38599	−	13.5316i	−0.164258	−	0.931556i	−0.949826	−	0.312780i	$-0.898740\pi$
$211$	−2.38599	−	13.5316i	−0.164258	−	0.931556i	0.785567	−	0.618776i	$-0.212371\pi$
$212$	−0.440604	+	5.03613i	−0.0302608	+	0.345883i
$213$		0			0
$214$	−6.22252	−	17.0962i	−0.425363	−	1.16867i
$215$	−13.4554	−	2.60703i	−0.917651	−	0.177798i
$216$		0			0
$217$	−2.00112	−	2.00112i	−0.135845	−	0.135845i
$218$	−4.22928	−	1.97214i	−0.286443	−	0.133570i
$219$		0			0
$220$	−2.20469	−	0.630742i	−0.148640	−	0.0425246i
$221$	−39.1661	+	6.90605i	−2.63460	+	0.464551i
$222$		0			0
$223$	−25.2567	+	2.20968i	−1.69131	+	0.147971i	−0.891725	−	0.452577i	$-0.850505\pi$
$223$	−25.2567	+	2.20968i	−1.69131	+	0.147971i	−0.799589	+	0.600548i	$0.794949\pi$
$224$	−0.685425	+	1.18719i	−0.0457969	+	0.0793225i
$225$		0			0
$226$	0.924515	+	1.60131i	0.0614979	+	0.106517i
$227$	12.1412	+	17.3395i	0.805841	+	1.15086i	0.985922	+	0.167209i	$0.0534753\pi$
$227$	12.1412	+	17.3395i	0.805841	+	1.15086i	−0.180080	+	0.983652i	$0.557636\pi$
$228$		0			0
$229$	3.04795	−	8.37418i	0.201414	−	0.553382i	−0.797326	−	0.603548i	$-0.793753\pi$
$229$	3.04795	−	8.37418i	0.201414	−	0.553382i	0.998741	+	0.0501667i	$0.0159753\pi$
$230$	−1.74443	−	6.97856i	−0.115024	−	0.460153i
$231$		0			0
$232$	6.71683	−	4.70317i	0.440981	−	0.308778i
$233$	5.63247	−	21.0206i	0.368995	−	1.37711i	−0.492928	−	0.870070i	$-0.664074\pi$
$233$	5.63247	−	21.0206i	0.368995	−	1.37711i	0.861923	−	0.507038i	$-0.169260\pi$
$234$		0			0
$235$	−14.0221	+	16.1503i	−0.914702	+	1.05353i
$236$	−6.31862	+	7.53023i	−0.411307	+	0.490176i
$237$		0			0
$238$	−7.85610	−	5.50090i	−0.509235	−	0.356570i
$239$	−22.4543	+	18.8414i	−1.45245	+	1.21875i	−0.521681	+	0.853140i	$0.674695\pi$
$239$	−22.4543	+	18.8414i	−1.45245	+	1.21875i	−0.930768	+	0.365609i	$0.880861\pi$
$240$		0			0
$241$	0.307297	−	0.111847i	0.0197948	−	0.00720471i	−0.332104	−	0.943243i	$-0.607758\pi$
$241$	0.307297	−	0.111847i	0.0197948	−	0.00720471i	0.351899	+	0.936038i	$0.385536\pi$
$242$	7.03451	−	7.03451i	0.452196	−	0.452196i
$243$		0			0
$244$			10.1424i			0.649303i
$245$	−6.72477	+	9.26763i	−0.429630	+	0.592087i
$246$		0			0
$247$	−25.3758	−	2.22010i	−1.61462	−	0.141261i
$248$	1.18410	−	1.69108i	0.0751907	−	0.107383i
$249$		0			0
$250$	−10.6859	+	3.28820i	−0.675834	+	0.207964i
$251$	6.01980	+	3.47553i	0.379966	+	0.219374i	0.677804	−	0.735243i	$-0.262932\pi$
$251$	6.01980	+	3.47553i	0.379966	+	0.219374i	−0.297837	+	0.954617i	$0.596265\pi$
$252$		0			0
$253$	−3.18663	−	0.853855i	−0.200342	−	0.0536814i
$254$	1.92756	−	10.9318i	0.120946	−	0.685919i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	15.8480	−	7.39005i	0.988573	−	0.460979i	0.140054	−	0.990144i	$-0.455273\pi$
$257$	15.8480	−	7.39005i	0.988573	−	0.460979i	0.848519	+	0.529165i	$0.177495\pi$
$258$		0			0
$259$	2.17201	+	0.382984i	0.134962	+	0.0237975i
$260$	12.0163	−	4.14567i	0.745220	−	0.257104i
$261$		0			0
$262$	−1.04967	+	0.281259i	−0.0648491	+	0.0173763i
$263$	−0.204809	−	2.34098i	−0.0126291	−	0.144351i	0.987262	−	0.159102i	$-0.0508599\pi$
$263$	−0.204809	−	2.34098i	−0.0126291	−	0.144351i	−0.999891	+	0.0147511i	$0.995304\pi$
$264$		0			0
$265$	11.3025	+	0.190453i	0.694310	+	0.0116994i
$266$	−3.94845	−	4.70558i	−0.242095	−	0.288517i
$267$		0			0
$268$	3.93699	−	8.44291i	0.240490	−	0.515733i
$269$	22.8011			1.39021			0.695103	−	0.718910i	$-0.255359\pi$
$269$	22.8011			1.39021			0.695103	+	0.718910i	$0.255359\pi$
$270$		0			0
$271$	−24.2190			−1.47120			−0.735601	−	0.677415i	$-0.763100\pi$
$271$	−24.2190			−1.47120			−0.735601	+	0.677415i	$0.763100\pi$
$272$	2.95666	−	6.34057i	0.179274	−	0.384454i
$273$		0			0
$274$	−1.46977	−	1.75161i	−0.0887923	−	0.105819i
$275$	−1.06003	+	5.01685i	−0.0639220	+	0.302528i
$276$		0			0
$277$	0.498845	+	5.70183i	0.0299727	+	0.342590i	0.996344	+	0.0854372i	$0.0272287\pi$
$277$	0.498845	+	5.70183i	0.0299727	+	0.342590i	−0.966371	+	0.257152i	$0.917216\pi$
$278$	−11.0656	+	2.96501i	−0.663670	+	0.177830i
$279$		0			0
$280$	2.75590	+	1.34208i	0.164696	+	0.0802046i
$281$	−2.95109	−	0.520356i	−0.176047	−	0.0310418i	0.0849296	−	0.996387i	$-0.472933\pi$
$281$	−2.95109	−	0.520356i	−0.176047	−	0.0310418i	−0.260977	+	0.965345i	$0.584045\pi$
$282$		0			0
$283$	21.4325	−	9.99414i	1.27403	−	0.594090i	0.336398	−	0.941720i	$-0.390791\pi$
$283$	21.4325	−	9.99414i	1.27403	−	0.594090i	0.937632	+	0.347630i	$0.113013\pi$
$284$	−0.836448	−	0.304442i	−0.0496341	−	0.0180653i
$285$		0			0
$286$	1.01233	−	5.74121i	0.0598603	−	0.339485i
$287$	−11.5431	−	3.09296i	−0.681367	−	0.182572i
$288$		0			0
$289$	27.6649	+	15.9723i	1.62735	+	0.939550i
$290$	−11.5473	−	14.2421i	−0.678081	−	0.836326i
$291$		0			0
$292$	−3.00323	+	4.28905i	−0.175751	+	0.250998i
$293$	25.7530	+	2.25310i	1.50451	+	0.131627i	0.809392	−	0.587269i	$-0.199797\pi$
$293$	25.7530	+	2.25310i	1.50451	+	0.131627i	0.695117	+	0.718897i	$0.255353\pi$
$294$		0			0
$295$	17.7905	+	12.9091i	1.03580	+	0.751598i
$296$			1.60887i			0.0935136i
$297$		0			0
$298$	9.46384	−	9.46384i	0.548226	−	0.548226i
$299$	17.1844	−	6.25462i	0.993800	−	0.361714i
$300$		0			0
$301$	6.43662	−	5.40096i	0.371001	−	0.311306i
$302$	1.70319	+	1.19259i	0.0980075	+	0.0686256i
$303$		0			0
$304$	2.88029	−	3.43260i	0.165196	−	0.196873i
$305$	22.6230	−	1.59569i	1.29539	−	0.0913692i
$306$		0			0
$307$	−6.76310	+	25.2402i	−0.385991	+	1.44054i	0.450609	+	0.892721i	$0.351207\pi$
$307$	−6.76310	+	25.2402i	−0.385991	+	1.44054i	−0.836600	+	0.547815i	$0.815460\pi$
$308$	1.15160	−	0.806356i	0.0656182	−	0.0459464i
$309$		0			0
$310$	−3.95828	−	2.37512i	−0.224815	−	0.134898i
$311$	6.61393	−	18.1716i	0.375042	−	1.03042i	−0.598343	−	0.801240i	$-0.704174\pi$
$311$	6.61393	−	18.1716i	0.375042	−	1.03042i	0.973384	−	0.229179i	$-0.0736040\pi$
$312$		0			0
$313$	−6.02953	−	8.61107i	−0.340809	−	0.486726i	0.611762	−	0.791042i	$-0.290461\pi$
$313$	−6.02953	−	8.61107i	−0.340809	−	0.486726i	−0.952571	+	0.304316i	$0.901572\pi$
$314$	−1.06621	−	1.84673i	−0.0601699	−	0.104217i
$315$		0			0
$316$	−3.73582	+	6.47064i	−0.210156	+	0.364002i
$317$	−4.26793	+	0.373396i	−0.239711	+	0.0209720i	−0.206378	−	0.978472i	$-0.566168\pi$
$317$	−4.26793	+	0.373396i	−0.239711	+	0.0209720i	−0.0333329	+	0.999444i	$0.510612\pi$
$318$		0			0
$319$	−8.28127	+	1.46021i	−0.463662	+	0.0817561i
$320$	−0.615044	+	2.14982i	−0.0343820	+	0.120179i
$321$		0			0
$322$	3.99676	+	1.86372i	0.222731	+	0.103861i
$323$	22.1670	+	22.1670i	1.23340	+	1.23340i
$324$		0			0
$325$	−11.1375	−	26.1505i	−0.617800	−	1.45057i
$326$	4.18322	+	11.4933i	0.231687	+	0.636555i
$327$		0			0
$328$	0.759774	−	8.68425i	0.0419515	−	0.479508i
$329$	−2.27692	−	12.9131i	−0.125531	−	0.711920i
$330$		0			0
$331$	22.0914	+	18.5369i	1.21425	+	1.01888i	0.999105	+	0.0422965i	$0.0134674\pi$
$331$	22.0914	+	18.5369i	1.21425	+	1.01888i	0.215147	+	0.976582i	$0.430977\pi$
$332$	1.71298	+	6.39293i	0.0940121	+	0.350858i
$333$		0			0
$334$	9.64459	−	5.56830i	0.527728	−	0.304684i
$335$	−19.4515	−	7.45326i	−1.06275	−	0.407215i
$336$		0			0
$337$	0.115103	+	0.246840i	0.00627009	+	0.0134462i	0.909418	−	0.415884i	$-0.136528\pi$
$337$	0.115103	+	0.246840i	0.00627009	+	0.0134462i	−0.903148	+	0.429330i	$0.858750\pi$
$338$	8.16315	+	17.5059i	0.444017	+	0.952197i
$339$		0			0
$340$	−14.6080	−	5.59735i	−0.792229	−	0.303559i
$341$	−1.83347	+	1.05856i	−0.0992882	+	0.0573241i
$342$		0			0
$343$	−4.30047	−	16.0496i	−0.232204	−	0.866596i
$344$	4.69535	+	3.93987i	0.253156	+	0.212423i
$345$		0			0
$346$	0.696196	+	3.94832i	0.0374277	+	0.212263i
$347$	−3.17854	+	36.3308i	−0.170633	+	1.95034i	0.118267	+	0.992982i	$0.462266\pi$
$347$	−3.17854	+	36.3308i	−0.170633	+	1.95034i	−0.288899	+	0.957359i	$0.593289\pi$
$348$		0			0
$349$	8.59979	+	23.6277i	0.460336	+	1.26476i	0.925234	+	0.379398i	$0.123869\pi$
$349$	8.59979	+	23.6277i	0.460336	+	1.26476i	−0.464898	+	0.885364i	$0.653909\pi$
$350$	2.55996	−	6.35825i	0.136836	−	0.339863i
$351$		0			0
$352$	0.725155	+	0.725155i	0.0386509	+	0.0386509i
$353$	7.76000	+	3.61855i	0.413023	+	0.192596i	0.618012	−	0.786168i	$-0.287938\pi$
$353$	7.76000	+	3.61855i	0.413023	+	0.192596i	−0.204989	+	0.978764i	$0.565716\pi$
$354$		0			0
$355$	−0.547469	+	1.91362i	−0.0290567	+	0.101564i
$356$	−8.78233	+	1.54856i	−0.465463	+	0.0820736i
$357$		0			0
$358$	10.7002	−	0.936148i	0.565524	−	0.0494770i
$359$	−1.17311	+	2.03189i	−0.0619144	+	0.107239i	−0.895321	−	0.445421i	$-0.853054\pi$
$359$	−1.17311	+	2.03189i	−0.0619144	+	0.107239i	0.833407	+	0.552660i	$0.186387\pi$
$360$		0			0
$361$	0.539412	+	0.934288i	0.0283901	+	0.0491731i
$362$	12.1499	+	17.3518i	0.638583	+	0.911990i
$363$		0			0
$364$	−2.66531	+	7.32288i	−0.139700	+	0.383823i
$365$	10.0393	+	6.02399i	0.525483	+	0.315310i
$366$		0			0
$367$	3.99042	−	2.79412i	0.208298	−	0.145852i	−0.464772	−	0.885430i	$-0.653864\pi$
$367$	3.99042	−	2.79412i	0.208298	−	0.145852i	0.673071	+	0.739578i	$0.264975\pi$
$368$	−0.832604	+	3.10732i	−0.0434025	+	0.161980i
$369$		0			0
$370$	3.58862	−	0.253121i	0.186564	−	0.0131591i
$371$	−4.45461	+	5.30880i	−0.231272	+	0.275619i
$372$		0			0
$373$	21.4927	+	15.0493i	1.11285	+	0.779226i	0.977366	−	0.211554i	$-0.0678524\pi$
$373$	21.4927	+	15.0493i	1.11285	+	0.779226i	0.135483	+	0.990780i	$0.456741\pi$
$374$	−5.49607	+	4.61175i	−0.284195	+	0.238468i
$375$		0			0
$376$	8.98822	−	3.27145i	0.463532	−	0.168712i
$377$	32.9603	−	32.9603i	1.69754	−	1.69754i
$378$		0			0
$379$		−	13.1839i		−	0.677209i	−0.940929	−	0.338604i	$-0.890045\pi$
$379$		−	13.1839i		−	0.677209i	0.940929	−	0.338604i	$-0.109955\pi$
$380$	−8.10966	−	5.88452i	−0.416017	−	0.301870i
$381$		0			0
$382$	0.198215	+	0.0173416i	0.0101416	+	0.000887273i
$383$	−7.46056	+	10.6548i	−0.381217	+	0.544434i	−0.963207	−	0.268762i	$-0.913386\pi$
$383$	−7.46056	+	10.6548i	−0.381217	+	0.544434i	0.581990	+	0.813196i	$0.302274\pi$
$384$		0			0
$385$	−1.97978	−	2.44180i	−0.100899	−	0.124446i
$386$	−17.0328	−	9.83390i	−0.866947	−	0.500532i
$387$		0			0
$388$	0.430999	+	0.115486i	0.0218807	+	0.00586291i
$389$	4.21015	−	23.8769i	0.213463	−	1.21061i	−0.670091	−	0.742279i	$-0.733745\pi$
$389$	4.21015	−	23.8769i	0.213463	−	1.21061i	0.883554	−	0.468330i	$-0.155144\pi$
$390$		0			0
$391$	−21.1486	−	7.69745i	−1.06953	−	0.389277i
$392$	4.64100	−	2.16413i	0.234406	−	0.109305i
$393$		0			0
$394$	3.61435	+	0.637308i	0.182088	+	0.0321071i
$395$	15.0207	+	7.31484i	0.755772	+	0.368049i
$396$		0			0
$397$	34.1521	−	9.15103i	1.71404	−	0.459277i	0.737634	−	0.675200i	$-0.235943\pi$
$397$	34.1521	−	9.15103i	1.71404	−	0.459277i	0.976410	+	0.215923i	$0.0692762\pi$
$398$	−1.89866	−	21.7018i	−0.0951713	−	1.08781i
$399$		0			0
$400$	4.89199	+	1.03365i	0.244600	+	0.0516823i
$401$	2.59596	+	3.09374i	0.129636	+	0.154494i	0.826958	−	0.562264i	$-0.190070\pi$
$401$	2.59596	+	3.09374i	0.129636	+	0.154494i	−0.697322	+	0.716758i	$0.745625\pi$
$402$		0			0
$403$	4.95968	−	10.6361i	0.247059	−	0.529820i
$404$	1.44258			0.0717708
$405$		0			0
$406$	11.2406			0.557862
$407$	0.697292	−	1.49535i	0.0345635	−	0.0741216i
$408$		0			0
$409$	−9.13725	−	10.8893i	−0.451808	−	0.538444i	0.491274	−	0.871005i	$-0.336531\pi$
$409$	−9.13725	−	10.8893i	−0.451808	−	0.538444i	−0.943082	+	0.332562i	$0.892087\pi$
$410$	−19.4900	−	0.328414i	−0.962542	−	0.0162192i
$411$		0			0
$412$	−0.564074	−	6.44740i	−0.0277899	−	0.317640i
$413$	−13.0163	+	3.48771i	−0.640491	+	0.171619i
$414$		0			0
$415$	13.9901	−	4.82664i	0.686747	−	0.236930i
$416$	−5.59832	−	0.987135i	−0.274480	−	0.0483983i
$417$		0			0
$418$	−4.16476	+	1.94206i	−0.203705	+	0.0949893i
$419$	11.2945	+	4.11085i	0.551770	+	0.200828i	0.602833	−	0.797868i	$-0.294039\pi$
$419$	11.2945	+	4.11085i	0.551770	+	0.200828i	−0.0510626	+	0.998695i	$0.516261\pi$
$420$		0			0
$421$	1.11063	−	6.29871i	0.0541289	−	0.306980i	−0.945708	−	0.325016i	$-0.894630\pi$
$421$	1.11063	−	6.29871i	0.0541289	−	0.306980i	0.999837	+	0.0180360i	$0.00574134\pi$
$422$	13.2722	+	3.55627i	0.646080	+	0.173117i
$423$		0			0
$424$	−4.37808	−	2.52768i	−0.212618	−	0.122755i
$425$	−10.1868	+	33.4641i	−0.494132	+	1.62325i
$426$		0			0
$427$	−7.97486	+	11.3893i	−0.385931	+	0.551166i
$428$	18.1242	+	1.58566i	0.876066	+	0.0766458i
$429$		0			0
$430$	8.04926	−	11.0930i	0.388170	−	0.534950i
$431$			18.3880i			0.885721i	0.896591	+	0.442860i	$0.146036\pi$
$431$			18.3880i			0.885721i	−0.896591	+	0.442860i	$0.853964\pi$
$432$		0			0
$433$	1.98062	−	1.98062i	0.0951823	−	0.0951823i	−0.657912	−	0.753095i	$-0.728560\pi$
$433$	1.98062	−	1.98062i	0.0951823	−	0.0951823i	0.753095	+	0.657912i	$0.228560\pi$
$434$	2.65934	−	0.967922i	0.127653	−	0.0464617i
$435$		0			0
$436$	3.57474	−	2.99956i	0.171199	−	0.143653i
$437$	−11.8080	−	8.26805i	−0.564853	−	0.395514i
$438$		0			0
$439$	9.97813	−	11.8915i	0.476230	−	0.567549i	−0.473430	−	0.880831i	$-0.656984\pi$
$439$	9.97813	−	11.8915i	0.476230	−	0.567549i	0.949660	+	0.313283i	$0.101429\pi$
$440$	1.50339	−	1.73156i	0.0716712	−	0.0825491i
$441$		0			0
$442$	10.2933	−	38.4152i	0.489603	−	1.82722i
$443$	17.9460	−	12.5659i	0.852640	−	0.597025i	−0.0634554	−	0.997985i	$-0.520212\pi$
$443$	17.9460	−	12.5659i	0.852640	−	0.597025i	0.916096	+	0.400959i	$0.131323\pi$
$444$		0			0
$445$	4.83582	+	19.3456i	0.229240	+	0.917069i
$446$	8.67130	−	23.8242i	0.410598	−	1.12811i
$447$		0			0
$448$	−0.786287	−	1.12293i	−0.0371486	−	0.0530537i
$449$	12.6539	+	21.9172i	0.597175	+	1.03434i	0.993236	+	0.116113i	$0.0370434\pi$
$449$	12.6539	+	21.9172i	0.597175	+	1.03434i	−0.396061	+	0.918224i	$0.629623\pi$
$450$		0			0
$451$	−4.46996	+	7.74220i	−0.210482	+	0.364566i
$452$	−1.84199	+	0.161154i	−0.0866401	+	0.00758003i
$453$		0			0
$454$	−20.8460	+	3.67571i	−0.978351	+	0.172510i
$455$	16.7532	+	4.79295i	0.785403	+	0.224697i
$456$		0			0
$457$	−27.9459	−	13.0314i	−1.30725	−	0.609582i	−0.360866	−	0.932618i	$-0.617519\pi$
$457$	−27.9459	−	13.0314i	−1.30725	−	0.609582i	−0.946387	+	0.323036i	$0.895296\pi$
$458$	6.30147	+	6.30147i	0.294448	+	0.294448i
$459$		0			0
$460$	7.06196	+	1.36828i	0.329265	+	0.0637962i
$461$	4.92189	+	13.5228i	0.229235	+	0.629819i	0.999973	−	0.00733363i	$-0.00233439\pi$
$461$	4.92189	+	13.5228i	0.229235	+	0.629819i	−0.770738	+	0.637152i	$0.780112\pi$
$462$		0			0
$463$	2.30090	−	26.2994i	0.106932	−	1.22224i	−0.733260	−	0.679948i	$-0.762002\pi$
$463$	2.30090	−	26.2994i	0.106932	−	1.22224i	0.840192	−	0.542289i	$-0.182442\pi$
$464$	1.42387	+	8.07516i	0.0661014	+	0.374880i
$465$		0			0
$466$	16.6708	+	13.9885i	0.772260	+	0.648003i
$467$	−2.05759	−	7.67904i	−0.0952140	−	0.355343i	0.901838	−	0.432075i	$-0.142218\pi$
$467$	−2.05759	−	7.67904i	−0.0952140	−	0.355343i	−0.997052	+	0.0767312i	$0.975552\pi$
$468$		0			0
$469$	11.0595	−	6.38523i	0.510682	−	0.294842i
$470$	−8.71115	−	19.5338i	−0.401815	−	0.901026i
$471$		0			0
$472$	−4.15435	−	8.90903i	−0.191219	−	0.410071i
$473$	−2.65649	−	5.69686i	−0.122145	−	0.261942i
$474$		0			0
$475$	−11.8497	+	19.0146i	−0.543702	+	0.872450i
$476$	8.30564	−	4.79526i	0.380688	−	0.219791i
$477$		0			0
$478$	−7.58651	−	28.3133i	−0.346999	−	1.29502i
$479$	9.93768	+	8.33870i	0.454064	+	0.381005i	0.840941	−	0.541126i	$-0.182002\pi$
$479$	9.93768	+	8.33870i	0.454064	+	0.381005i	−0.386877	+	0.922131i	$0.626446\pi$
$480$		0			0
$481$	1.58817	+	9.00697i	0.0724144	+	0.410682i
$482$	−0.0285016	+	0.325775i	−0.00129821	+	0.0148386i
$483$		0			0
$484$	3.40252	+	9.34835i	0.154660	+	0.424925i
$485$	0.189786	−	0.979524i	0.00861773	−	0.0444779i
$486$		0			0
$487$	−5.12880	−	5.12880i	−0.232408	−	0.232408i	0.581289	−	0.813697i	$-0.302549\pi$
$487$	−5.12880	−	5.12880i	−0.232408	−	0.232408i	−0.813697	+	0.581289i	$0.802549\pi$
$488$	−9.19216	−	4.28638i	−0.416110	−	0.194035i
$489$		0			0
$490$	−5.55731	−	10.0114i	−0.251054	−	0.452268i
$491$	33.7779	−	5.95595i	1.52437	−	0.268788i	0.652224	−	0.758026i	$-0.273836\pi$
$491$	33.7779	−	5.95595i	1.52437	−	0.268788i	0.872151	+	0.489238i	$0.162725\pi$
$492$		0			0
$493$	−57.1474	+	4.99975i	−2.57379	+	0.225178i
$494$	12.7364	−	22.0600i	0.573036	−	0.992528i
$495$		0			0
$496$	1.03221	+	1.78784i	0.0463477	+	0.0802765i
$497$	−0.699897	−	0.999557i	−0.0313947	−	0.0448363i
$498$		0			0
$499$	12.2374	−	33.6221i	0.547823	−	1.50513i	−0.288821	−	0.957383i	$-0.593263\pi$
$499$	12.2374	−	33.6221i	0.547823	−	1.50513i	0.836644	−	0.547747i	$-0.184515\pi$
$500$	1.53592	−	11.0743i	0.0686886	−	0.495259i
$501$		0			0
$502$	−5.69398	+	3.98696i	−0.254135	+	0.177947i
$503$	−6.74582	+	25.1757i	−0.300781	+	1.12253i	0.635735	+	0.771907i	$0.280697\pi$
$503$	−6.74582	+	25.1757i	−0.300781	+	1.12253i	−0.936516	+	0.350624i	$0.885970\pi$
$504$		0			0
$505$	−0.226958	−	3.21770i	−0.0100995	−	0.143186i
$506$	2.12058	−	2.52721i	0.0942715	−	0.112348i
$507$		0			0
$508$	9.09291	+	6.36692i	0.403433	+	0.282487i
$509$	−18.0808	+	15.1716i	−0.801417	+	0.672469i	−0.948543	−	0.316649i	$-0.897442\pi$
$509$	−18.0808	+	15.1716i	−0.801417	+	0.672469i	0.147126	+	0.989118i	$0.452998\pi$
$510$		0			0
$511$	−6.74485	+	2.45493i	−0.298375	+	0.108599i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			17.4864i			0.771290i
$515$	−14.2923	+	2.27254i	−0.629796	+	0.100140i
$516$		0			0
$517$	−9.77187	−	0.854928i	−0.429766	−	0.0375997i
$518$	−1.26503	+	1.80665i	−0.0555823	+	0.0793798i
$519$		0			0
$520$	−1.32106	+	12.6425i	−0.0579321	+	0.554411i
$521$	5.61731	+	3.24316i	0.246099	+	0.142085i	0.617977	−	0.786196i	$-0.287953\pi$
$521$	5.61731	+	3.24316i	0.246099	+	0.142085i	−0.371878	+	0.928282i	$0.621286\pi$
$522$		0			0
$523$	15.8693	+	4.25218i	0.693918	+	0.185935i	0.588505	−	0.808494i	$-0.299717\pi$
$523$	15.8693	+	4.25218i	0.693918	+	0.185935i	0.105413	+	0.994429i	$0.466384\pi$
$524$	0.188704	−	1.07019i	0.00824357	−	0.0467516i
$525$		0			0
$526$	2.20821	+	0.803721i	0.0962823	+	0.0350439i
$527$	−13.0896	+	6.10379i	−0.570193	+	0.265885i
$528$		0			0
$529$	−12.4591	−	2.19688i	−0.541701	−	0.0955165i
$530$	−4.94927	+	10.1631i	−0.214983	+	0.441457i
$531$		0			0
$532$	5.93339	−	1.58985i	0.257245	−	0.0689286i
$533$	−4.31907	−	49.3672i	−0.187080	−	2.13833i
$534$		0			0
$535$	0.685407	−	40.6760i	0.0296327	−	1.75858i
$536$	5.98803	+	7.13626i	0.258644	+	0.308239i
$537$		0			0
$538$	−9.63615	+	20.6648i	−0.415444	+	0.890922i
$539$	−5.25147			−0.226197
$540$		0			0
$541$	11.8678			0.510238			0.255119	−	0.966910i	$-0.417885\pi$
$541$	11.8678			0.510238			0.255119	+	0.966910i	$0.417885\pi$
$542$	10.2354	−	21.9499i	0.439649	−	0.942829i
$543$		0			0
$544$	4.49697	+	5.35928i	0.192806	+	0.229777i
$545$	−7.25301	−	7.50163i	−0.310685	−	0.321335i
$546$		0			0
$547$	2.77386	+	31.7053i	0.118602	+	1.35562i	0.789353	+	0.613940i	$0.210416\pi$
$547$	2.77386	+	31.7053i	0.118602	+	1.35562i	−0.670751	+	0.741682i	$0.734028\pi$
$548$	2.20865	−	0.591806i	0.0943488	−	0.0252807i
$549$		0			0
$550$	−4.09882	−	3.08092i	−0.174774	−	0.131371i
$551$	−36.1843	−	6.38027i	−1.54150	−	0.271809i
$552$		0			0
$553$	−9.28286	+	4.32867i	−0.394747	+	0.184074i
$554$	−5.37843	−	1.95759i	−0.228508	−	0.0831700i
$555$		0			0
$556$	1.98930	−	11.2819i	0.0843652	−	0.478459i
$557$	−36.9224	−	9.89332i	−1.56445	−	0.419193i	−0.630382	−	0.776285i	$-0.717102\pi$
$557$	−36.9224	−	9.89332i	−1.56445	−	0.419193i	−0.934069	+	0.357092i	$0.883768\pi$
$558$		0			0
$559$	30.1753	+	17.4217i	1.27628	+	0.736859i
$560$	−2.38103	+	1.93050i	−0.100617	+	0.0815787i
$561$		0			0
$562$	1.71879	−	2.45468i	0.0725026	−	0.103544i
$563$	25.9290	+	2.26849i	1.09278	+	0.0956055i	0.619265	−	0.785182i	$-0.287431\pi$
$563$	25.9290	+	2.26849i	1.09278	+	0.0956055i	0.473511	+	0.880788i	$0.342986\pi$
$564$		0			0
$565$	0.649256	+	4.08326i	0.0273144	+	0.171784i
$566$			23.6482i			0.994006i
$567$		0			0
$568$	0.629417	−	0.629417i	0.0264097	−	0.0264097i
$569$	6.98942	−	2.54394i	0.293012	−	0.106648i	−0.191332	−	0.981525i	$-0.561281\pi$
$569$	6.98942	−	2.54394i	0.293012	−	0.106648i	0.484344	+	0.874878i	$0.339058\pi$
$570$		0			0
$571$	−24.7246	+	20.7464i	−1.03469	+	0.868209i	−0.991402	−	0.130853i	$-0.958228\pi$
$571$	−24.7246	+	20.7464i	−1.03469	+	0.868209i	−0.0432898	+	0.999063i	$0.513784\pi$
$572$	4.77547	+	3.34382i	0.199673	+	0.139812i
$573$		0			0
$574$	7.68149	−	9.15444i	0.320619	−	0.382099i
$575$	1.94093	−	15.9671i	0.0809423	−	0.665876i
$576$		0			0
$577$	7.88604	−	29.4311i	0.328300	−	1.22523i	−0.582652	−	0.812722i	$-0.697985\pi$
$577$	7.88604	−	29.4311i	0.328300	−	1.22523i	0.910952	−	0.412511i	$-0.135348\pi$
$578$	−26.1676	+	18.3227i	−1.08843	+	0.762125i
$579$		0			0
$580$	17.7878	−	4.44643i	0.738600	−	0.184628i
$581$	−3.10311	+	8.52574i	−0.128739	+	0.353707i
$582$		0			0
$583$	2.97365	+	4.24681i	0.123156	+	0.175885i
$584$	−2.61798	−	4.53448i	−0.108333	−	0.187638i
$585$		0			0
$586$	−12.9257	+	22.3880i	−0.533956	+	0.924839i
$587$	−11.6068	+	1.01547i	−0.479065	+	0.0419128i	−0.324131	−	0.946012i	$-0.605072\pi$
$587$	−11.6068	+	1.01547i	−0.479065	+	0.0419128i	−0.154934	+	0.987925i	$0.549516\pi$
$588$		0			0
$589$	−9.11002	+	1.60634i	−0.375372	+	0.0661882i
$590$	−19.2182	+	10.6680i	−0.791202	+	0.439196i
$591$		0			0
$592$	−1.45813	−	0.679937i	−0.0599288	−	0.0279453i
$593$	−18.3363	−	18.3363i	−0.752980	−	0.752980i	0.222055	−	0.975034i	$-0.428724\pi$
$593$	−18.3363	−	18.3363i	−0.752980	−	0.752980i	−0.975034	+	0.222055i	$0.928724\pi$
$594$		0			0
$595$	−12.0027	−	17.7715i	−0.492062	−	0.728561i
$596$	4.57756	+	12.5767i	0.187504	+	0.515164i
$597$		0			0
$598$	−1.59384	+	18.2177i	−0.0651770	+	0.744977i
$599$	6.98391	+	39.6077i	0.285355	+	1.61833i	0.704016	+	0.710184i	$0.251388\pi$
$599$	6.98391	+	39.6077i	0.285355	+	1.61833i	−0.418661	+	0.908142i	$0.637501\pi$
$600$		0			0
$601$	26.4693	+	22.2104i	1.07971	+	0.905981i	0.995896	−	0.0905010i	$-0.0288468\pi$
$601$	26.4693	+	22.2104i	1.07971	+	0.905981i	0.0838095	+	0.996482i	$0.473291\pi$
$602$	2.17470	+	8.11610i	0.0886343	+	0.330788i
$603$		0			0
$604$	−1.80065	+	1.03961i	−0.0732674	+	0.0423009i
$605$	20.3164	−	9.06017i	0.825980	−	0.368348i
$606$		0			0
$607$	8.85936	+	18.9990i	0.359590	+	0.771144i	0.999995	+	0.00310650i	$0.000988831\pi$
$607$	8.85936	+	18.9990i	0.359590	+	0.771144i	−0.640405	+	0.768038i	$0.721233\pi$
$608$	1.89373	+	4.06111i	0.0768008	+	0.164700i
$609$		0			0
$610$	−8.11469	+	21.1777i	−0.328554	+	0.857461i
$611$	47.0896	−	27.1872i	1.90504	−	1.09988i
$612$		0			0
$613$	1.86487	+	6.95980i	0.0753215	+	0.281104i	0.993306	−	0.115512i	$-0.0368510\pi$
$613$	1.86487	+	6.95980i	0.0753215	+	0.281104i	−0.917984	+	0.396616i	$0.870184\pi$
$614$	−20.0172	−	16.7964i	−0.807829	−	0.677849i
$615$		0			0
$616$	0.244121	+	1.38448i	0.00983593	+	0.0557823i
$617$	−2.92452	+	33.4274i	−0.117737	+	1.34574i	0.675743	+	0.737138i	$0.263823\pi$
$617$	−2.92452	+	33.4274i	−0.117737	+	1.34574i	−0.793479	+	0.608597i	$0.791732\pi$
$618$		0			0
$619$	−3.68119	−	10.1140i	−0.147960	−	0.406516i	0.843467	−	0.537181i	$-0.180511\pi$
$619$	−3.68119	−	10.1140i	−0.147960	−	0.406516i	−0.991427	+	0.130665i	$0.958289\pi$
$620$	3.82543	−	2.58365i	0.153633	−	0.103762i
$621$		0			0
$622$	13.6739	+	13.6739i	0.548274	+	0.548274i
$623$	−11.0796	−	5.16650i	−0.443895	−	0.206991i
$624$		0			0
$625$	−24.9432	−	1.68361i	−0.997730	−	0.0673443i
$626$	10.3525	−	1.82542i	0.413768	−	0.0729584i
$627$		0			0
$628$	2.12431	−	0.185853i	0.0847692	−	0.00741635i
$629$	5.62786	−	9.74774i	0.224398	−	0.388668i
$630$		0			0
$631$	−7.09822	−	12.2945i	−0.282576	−	0.489435i	0.689443	−	0.724340i	$-0.257855\pi$
$631$	−7.09822	−	12.2945i	−0.282576	−	0.489435i	−0.972018	+	0.234905i	$0.924522\pi$
$632$	−4.28556	−	6.12041i	−0.170470	−	0.243457i
$633$		0			0
$634$	1.46530	−	4.02586i	0.0581943	−	0.159888i
$635$	12.7710	−	21.2837i	0.506802	−	0.844617i
$636$		0			0
$637$	23.8455	−	16.6968i	0.944793	−	0.661551i
$638$	2.17641	−	8.12249i	0.0861650	−	0.321572i
$639$		0			0
$640$	−1.68847	−	1.46597i	−0.0667426	−	0.0579476i
$641$	4.59449	−	5.47551i	0.181472	−	0.216269i	−0.667638	−	0.744486i	$-0.732695\pi$
$641$	4.59449	−	5.47551i	0.181472	−	0.216269i	0.849110	+	0.528217i	$0.177139\pi$
$642$		0			0
$643$	−15.0612	−	10.5460i	−0.593958	−	0.415894i	0.237575	−	0.971369i	$-0.423647\pi$
$643$	−15.0612	−	10.5460i	−0.593958	−	0.415894i	−0.831533	+	0.555476i	$0.812536\pi$
$644$	−3.37821	+	2.83465i	−0.133120	+	0.111701i
$645$		0			0
$646$	−29.4583	+	10.7219i	−1.15902	+	0.421849i
$647$	−4.90447	+	4.90447i	−0.192815	+	0.192815i	−0.796911	−	0.604097i	$-0.793534\pi$
$647$	−4.90447	+	4.90447i	−0.192815	+	0.192815i	0.604097	+	0.796911i	$0.293534\pi$
$648$		0			0
$649$			10.0809i			0.395711i
$650$	28.4073	+	0.957621i	1.11423	+	0.0375610i
$651$		0			0
$652$	−12.1844	−	1.06599i	−0.477177	−	0.0417476i
$653$	6.71310	−	9.58730i	0.262704	−	0.375180i	−0.666031	−	0.745924i	$-0.732008\pi$
$653$	6.71310	−	9.58730i	0.262704	−	0.375180i	0.928735	+	0.370744i	$0.120897\pi$
$654$		0			0
$655$	−2.41678	−	0.252537i	−0.0944315	−	0.00986745i
$656$	7.54951	+	4.35871i	0.294759	+	0.170179i
$657$		0			0
$658$	12.6655	+	3.39370i	0.493752	+	0.132300i
$659$	−1.90453	+	10.8012i	−0.0741901	+	0.420753i	0.924980	+	0.380016i	$0.124082\pi$
$659$	−1.90453	+	10.8012i	−0.0741901	+	0.420753i	−0.999170	+	0.0407368i	$0.987029\pi$
$660$		0			0
$661$	14.1762	+	5.15971i	0.551390	+	0.200689i	0.602664	−	0.797995i	$-0.294106\pi$
$661$	14.1762	+	5.15971i	0.551390	+	0.200689i	−0.0512741	+	0.998685i	$0.516328\pi$
$662$	−26.1363	+	12.1876i	−1.01582	+	0.473683i
$663$		0			0
$664$	−6.51790	−	1.14928i	−0.252944	−	0.0446008i
$665$	−4.47969	−	12.9844i	−0.173715	−	0.503515i
$666$		0			0
$667$	25.4792	−	6.82713i	0.986559	−	0.264348i
$668$	0.970619	+	11.0942i	0.0375544	+	0.429249i
$669$		0			0
$670$	14.9755	−	14.4792i	0.578555	−	0.559380i
$671$	6.68583	+	7.96786i	0.258103	+	0.307596i
$672$		0			0
$673$	−15.9499	+	34.2048i	−0.614825	+	1.31850i	0.314508	+	0.949255i	$0.398160\pi$
$673$	−15.9499	+	34.2048i	−0.614825	+	1.31850i	−0.929333	+	0.369242i	$0.879617\pi$
$674$	−0.272358			−0.0104908
$675$		0			0
$676$	−19.3157			−0.742910
$677$	−7.39747	+	15.8639i	−0.284308	+	0.609700i	−0.995653	−	0.0931429i	$-0.970309\pi$
$677$	−7.39747	+	15.8639i	−0.284308	+	0.609700i	0.711345	+	0.702843i	$0.248086\pi$
$678$		0			0
$679$	0.393179	+	0.468572i	0.0150888	+	0.0179821i
$680$	11.2465	−	10.8738i	0.431284	−	0.416991i
$681$		0			0
$682$	−0.184519	−	2.10906i	−0.00706559	−	0.0807600i
$683$	−43.2142	+	11.5792i	−1.65355	+	0.443066i	−0.960603	−	0.277926i	$-0.910353\pi$
$683$	−43.2142	+	11.5792i	−1.65355	+	0.443066i	−0.692943	+	0.720992i	$0.743686\pi$
$684$		0			0
$685$	−1.66752	−	4.83334i	−0.0637128	−	0.184673i
$686$	16.3633	+	2.88530i	0.624755	+	0.110161i
$687$		0			0
$688$	−5.55507	+	2.59037i	−0.211785	+	0.0987571i
$689$	−27.0051	−	9.82904i	−1.02881	−	0.374456i
$690$		0			0
$691$	−0.267841	+	1.51900i	−0.0101891	+	0.0577855i	−0.989478	−	0.144681i	$-0.953785\pi$
$691$	−0.267841	+	1.51900i	−0.0101891	+	0.0577855i	0.979289	+	0.202466i	$0.0648956\pi$
$692$	−3.87262	−	1.03767i	−0.147215	−	0.0394461i
$693$		0			0
$694$	−31.5836	−	18.2348i	−1.19890	−	0.692184i
$695$	−25.4775	−	2.66223i	−0.966418	−	0.100984i
$696$		0			0
$697$	−34.9810	+	49.9580i	−1.32500	+	1.89230i
$698$	−25.0484	−	2.19145i	−0.948096	−	0.0829477i
$699$		0			0
$700$	4.68064	+	5.00722i	0.176912	+	0.189255i
$701$		−	16.8030i		−	0.634642i	−0.948318	−	0.317321i	$-0.897217\pi$
$701$		−	16.8030i		−	0.634642i	0.948318	−	0.317321i	$-0.102783\pi$
$702$		0			0
$703$	5.09771	−	5.09771i	0.192264	−	0.192264i
$704$	−0.963677	+	0.350750i	−0.0363199	+	0.0132194i
$705$		0			0
$706$	−6.55904	+	5.50369i	−0.246853	+	0.207134i
$707$	1.61992	+	1.13428i	0.0609233	+	0.0426589i
$708$		0			0
$709$	17.3164	−	20.6369i	0.650332	−	0.775035i	−0.335632	−	0.941993i	$-0.608950\pi$
$709$	17.3164	−	20.6369i	0.650332	−	0.775035i	0.985964	+	0.166958i	$0.0533944\pi$
$710$	−1.50296	−	1.30491i	−0.0564049	−	0.0489722i
$711$		0			0
$712$	2.30810	−	8.61395i	0.0864997	−	0.322821i
$713$	5.44009	−	3.80919i	0.203733	−	0.142655i
$714$		0			0
$715$	6.70717	−	11.1779i	0.250834	−	0.418030i
$716$	−3.67367	+	10.0933i	−0.137292	+	0.377205i
$717$		0			0
$718$	−1.34574	−	1.92191i	−0.0502224	−	0.0717251i
$719$	4.74675	+	8.22161i	0.177024	+	0.306614i	0.940860	−	0.338796i	$-0.110020\pi$
$719$	4.74675	+	8.22161i	0.177024	+	0.306614i	−0.763836	+	0.645410i	$0.776686\pi$
$720$		0			0
$721$	4.43609	−	7.68353i	0.165208	−	0.286149i
$722$	−1.07472	+	0.0940257i	−0.0399969	+	0.00349927i
$723$		0			0
$724$	−20.8608	+	3.67833i	−0.775286	+	0.136704i
$725$	−12.7164	−	38.9767i	−0.472276	−	1.44756i
$726$		0			0
$727$	4.25681	+	1.98498i	0.157876	+	0.0736189i	0.499950	−	0.866054i	$-0.333352\pi$
$727$	4.25681	+	1.98498i	0.157876	+	0.0736189i	−0.342074	+	0.939673i	$0.611129\pi$
$728$	−5.51038	−	5.51038i	−0.204228	−	0.204228i
$729$		0			0
$730$	−9.70239	+	6.55288i	−0.359102	+	0.242533i
$731$	−14.6662	−	40.2951i	−0.542450	−	1.49037i
$732$		0			0
$733$	0.988648	−	11.3003i	0.0365165	−	0.417386i	−0.955832	−	0.293915i	$-0.905042\pi$
$733$	0.988648	−	11.3003i	0.0365165	−	0.417386i	0.992348	−	0.123471i	$-0.0394026\pi$
$734$	0.845910	+	4.79739i	0.0312231	+	0.177075i
$735$		0			0
$736$	−2.46432	−	2.06781i	−0.0908359	−	0.0762204i
$737$	−2.47263	−	9.22796i	−0.0910803	−	0.339916i
$738$		0			0
$739$	−11.8963	+	6.86835i	−0.437614	+	0.252656i	−0.702585	−	0.711600i	$-0.747971\pi$
$739$	−11.8963	+	6.86835i	−0.437614	+	0.252656i	0.264971	+	0.964256i	$0.414638\pi$
$740$	−1.28721	+	3.35937i	−0.0473189	+	0.123493i
$741$		0			0
$742$	−2.92881	−	6.28085i	−0.107520	−	0.230577i
$743$	−3.88066	−	8.32210i	−0.142368	−	0.305308i	0.822175	−	0.569234i	$-0.192760\pi$
$743$	−3.88066	−	8.32210i	−0.142368	−	0.305308i	−0.964543	+	0.263926i	$0.914982\pi$
$744$		0			0
$745$	27.3326	−	12.1891i	1.00139	−	0.446572i
$746$	−22.7225	+	13.1189i	−0.831932	+	0.480316i
$747$		0			0
$748$	−1.85693	−	6.93014i	−0.0678959	−	0.253391i
$749$	19.1055	+	16.0314i	0.698099	+	0.585775i
$750$		0			0
$751$	−3.24004	−	18.3752i	−0.118231	−	0.670520i	−0.985100	−	0.171984i	$-0.944982\pi$
$751$	−3.24004	−	18.3752i	−0.118231	−	0.670520i	0.866869	−	0.498536i	$-0.166129\pi$
$752$	−0.833651	+	9.52867i	−0.0304001	+	0.347475i
$753$		0			0
$754$	15.9426	+	43.8018i	0.580593	+	1.59517i
$755$	2.60216	+	3.85284i	0.0947023	+	0.140219i
$756$		0			0
$757$	18.9461	+	18.9461i	0.688609	+	0.688609i	0.961924	−	0.273316i	$-0.0881204\pi$
$757$	18.9461	+	18.9461i	0.688609	+	0.688609i	−0.273316	+	0.961924i	$0.588120\pi$
$758$	11.9486	+	5.57174i	0.433994	+	0.202375i
$759$		0			0
$760$	8.76048	−	4.86294i	0.317776	−	0.176397i
$761$	5.07157	−	0.894255i	0.183844	−	0.0324167i	−0.0809679	−	0.996717i	$-0.525801\pi$
$761$	5.07157	−	0.894255i	0.183844	−	0.0324167i	0.264812	+	0.964300i	$0.414690\pi$
$762$		0			0
$763$	6.37271	−	0.557540i	0.230708	−	0.0201843i
$764$	−0.0994862	+	0.172315i	−0.00359929	+	0.00623414i
$765$		0			0
$766$	−6.50355	−	11.2645i	−0.234983	−	0.407002i
$767$	−32.0518	−	45.7747i	−1.15732	−	1.65283i
$768$		0			0
$769$	−14.4008	+	39.5659i	−0.519306	+	1.42678i	0.351981	+	0.936007i	$0.385508\pi$
$769$	−14.4008	+	39.5659i	−0.519306	+	1.42678i	−0.871287	+	0.490774i	$0.836714\pi$
$770$	3.04971	−	0.762337i	0.109904	−	0.0274727i
$771$		0			0
$772$	16.1109	−	11.2810i	0.579845	−	0.406012i
$773$	−9.64653	+	36.0013i	−0.346961	+	1.29488i	0.543343	+	0.839511i	$0.317158\pi$
$773$	−9.64653	+	36.0013i	−0.346961	+	1.29488i	−0.890304	+	0.455367i	$0.849508\pi$
$774$		0			0
$775$	−6.36476	−	8.12625i	−0.228629	−	0.291904i
$776$	−0.286814	+	0.341811i	−0.0102960	+	0.0122703i
$777$		0			0
$778$	19.8606	+	13.9065i	0.712036	+	0.498573i
$779$	−29.9234	+	25.1087i	−1.07212	+	0.899614i
$780$		0			0
$781$	−0.857797	+	0.312213i	−0.0306944	+	0.0111718i
$782$	15.9140	−	15.9140i	0.569085	−	0.569085i
$783$		0			0
$784$			5.12077i			0.182885i
$785$	−0.748765	−	4.70909i	−0.0267246	−	0.168075i
$786$		0			0
$787$	44.8583	+	3.92459i	1.59902	+	0.139897i	0.851506	−	0.524344i	$-0.175690\pi$
$787$	44.8583	+	3.92459i	1.59902	+	0.139897i	0.747519	+	0.664241i	$0.231245\pi$
$788$	−2.10509	+	3.00638i	−0.0749907	+	0.107098i
$789$		0			0
$790$	−12.9775	+	10.5220i	−0.461719	+	0.374355i
$791$	−2.19515	−	1.26737i	−0.0780506	−	0.0450625i
$792$		0			0
$793$	−55.6919	−	14.9226i	−1.97768	−	0.529917i
$794$	−6.13965	+	34.8197i	−0.217888	+	1.23571i
$795$		0			0
$796$	20.4709	+	7.45080i	0.725572	+	0.264087i
$797$	17.3786	−	8.10379i	0.615583	−	0.287051i	−0.0897092	−	0.995968i	$-0.528594\pi$
$797$	17.3786	−	8.10379i	0.615583	−	0.287051i	0.705292	+	0.708917i	$0.250816\pi$
$798$		0			0
$799$	−65.9010	−	11.6201i	−2.33141	−	0.411091i
$800$	−3.00425	+	3.99681i	−0.106216	+	0.141309i
$801$		0			0
$802$	−3.90098	+	1.04526i	−0.137748	+	0.0369096i
$803$	0.467992	+	5.34917i	0.0165151	+	0.188768i
$804$		0			0
$805$	6.85425	+	7.08921i	0.241581	+	0.249862i
$806$	7.54350	+	8.98999i	0.265708	+	0.316659i
$807$		0			0
$808$	−0.609659	+	1.30742i	−0.0214477	+	0.0459948i
$809$	−18.1480			−0.638050			−0.319025	−	0.947746i	$-0.603355\pi$
$809$	−18.1480			−0.638050			−0.319025	+	0.947746i	$0.603355\pi$
$810$		0			0
$811$	−3.73964			−0.131317			−0.0656583	−	0.997842i	$-0.520915\pi$
$811$	−3.73964			−0.131317			−0.0656583	+	0.997842i	$0.520915\pi$
$812$	−4.75048	+	10.1874i	−0.166709	+	0.357509i
$813$		0			0
$814$	1.06056	+	1.26392i	0.0371725	+	0.0443004i
$815$	−0.460779	+	27.3453i	−0.0161404	+	0.957863i
$816$		0			0
$817$	−2.39375	−	27.3607i	−0.0837468	−	0.957230i
$818$	13.7307	−	3.67912i	0.480082	−	0.128637i
$819$		0			0
$820$	8.53447	−	17.5251i	0.298037	−	0.612004i
$821$	5.91344	+	1.04270i	0.206380	+	0.0363904i	0.275882	−	0.961191i	$-0.411030\pi$
$821$	5.91344	+	1.04270i	0.206380	+	0.0363904i	−0.0695021	+	0.997582i	$0.522141\pi$
$822$		0			0
$823$	−4.33877	+	2.02320i	−0.151240	+	0.0705244i	−0.496765	−	0.867885i	$-0.665479\pi$
$823$	−4.33877	+	2.02320i	−0.151240	+	0.0705244i	0.345525	+	0.938410i	$0.387701\pi$
$824$	6.08171	+	2.21356i	0.211867	+	0.0771131i
$825$		0			0
$826$	2.33999	−	13.2708i	0.0814188	−	0.461749i
$827$	−27.2145	−	7.29210i	−0.946340	−	0.253571i	−0.247532	−	0.968880i	$-0.579619\pi$
$827$	−27.2145	−	7.29210i	−0.946340	−	0.253571i	−0.698808	+	0.715309i	$0.746286\pi$
$828$		0			0
$829$	−6.06867	−	3.50375i	−0.210774	−	0.121690i	0.390897	−	0.920434i	$-0.372165\pi$
$829$	−6.06867	−	3.50375i	−0.210774	−	0.121690i	−0.601671	+	0.798744i	$0.705498\pi$
$830$	−1.53805	+	14.7192i	−0.0533866	+	0.510910i
$831$		0			0
$832$	3.26060	−	4.65662i	0.113041	−	0.161439i
$833$	−35.6888	−	3.12237i	−1.23654	−	0.108184i
$834$		0			0
$835$	24.5933	−	3.91043i	0.851085	−	0.135326i
$836$		−	4.59531i		−	0.158932i
$837$		0			0
$838$	−8.49893	+	8.49893i	−0.293591	+	0.293591i
$839$	−20.7733	+	7.56086i	−0.717173	+	0.261030i	−0.674725	−	0.738069i	$-0.735738\pi$
$839$	−20.7733	+	7.56086i	−0.717173	+	0.261030i	−0.0424480	+	0.999099i	$0.513516\pi$
$840$		0			0
$841$	29.2902	−	24.5774i	1.01001	−	0.847496i
$842$	5.23919	+	3.66852i	0.180555	+	0.126426i
$843$		0			0
$844$	−8.83214	+	10.5257i	−0.304015	+	0.362311i
$845$	3.03890	+	43.0841i	0.104541	+	1.48214i
$846$		0			0
$847$	−3.52968	+	13.1729i	−0.121281	+	0.452627i
$848$	4.14112	−	2.89964i	0.142206	−	0.0995741i
$849$		0			0
$850$	−26.0237	−	23.3749i	−0.892604	−	0.801753i
$851$	−1.77017	+	4.86350i	−0.0606806	+	0.166719i
$852$		0			0
$853$	−20.4568	−	29.2153i	−0.700426	−	1.00031i	−0.998946	−	0.0459089i	$-0.985382\pi$
$853$	−20.4568	−	29.2153i	−0.700426	−	1.00031i	0.298519	−	0.954404i	$-0.403507\pi$
$854$	−6.95187	−	12.0410i	−0.237888	−	0.412034i
$855$		0			0
$856$	−9.09671	+	15.7560i	−0.310919	+	0.538528i
$857$	27.2563	−	2.38462i	0.931058	−	0.0814570i	0.388475	−	0.921459i	$-0.373002\pi$
$857$	27.2563	−	2.38462i	0.931058	−	0.0814570i	0.542583	+	0.840002i	$0.317446\pi$
$858$		0			0
$859$	−18.2241	+	3.21341i	−0.621800	+	0.109640i	−0.475668	−	0.879625i	$-0.657794\pi$
$859$	−18.2241	+	3.21341i	−0.621800	+	0.109640i	−0.146132	+	0.989265i	$0.546682\pi$
$860$	6.65187	+	11.9832i	0.226827	+	0.408624i
$861$		0			0
$862$	−16.6652	−	7.77112i	−0.567620	−	0.264685i
$863$	15.7918	+	15.7918i	0.537560	+	0.537560i	0.922812	−	0.385252i	$-0.125885\pi$
$863$	15.7918	+	15.7918i	0.537560	+	0.537560i	−0.385252	+	0.922812i	$0.625885\pi$
$864$		0			0
$865$	−1.70527	+	8.80124i	−0.0579808	+	0.299251i
$866$	0.958003	+	2.63209i	0.0325543	+	0.0894421i
$867$		0			0
$868$	−0.246652	+	2.81924i	−0.00837191	+	0.0956914i
$869$	1.33055	+	7.54594i	0.0451359	+	0.255978i
$870$		0			0
$871$	40.5674	+	34.0401i	1.37457	+	1.15340i
$872$	1.20778	+	4.50748i	0.0409005	+	0.152643i
$873$		0			0
$874$	12.4837	−	7.20745i	0.422266	−	0.243796i
$875$	10.4323	−	11.2281i	0.352678	−	0.379578i
$876$		0			0
$877$	−8.45652	−	18.1351i	−0.285557	−	0.612378i	0.710241	−	0.703958i	$-0.248586\pi$
$877$	−8.45652	−	18.1351i	−0.285557	−	0.612378i	−0.995798	+	0.0915805i	$0.970808\pi$
$878$	6.56039	+	14.0688i	0.221402	+	0.474799i
$879$		0			0
$880$	0.933970	+	2.09432i	0.0314841	+	0.0705996i
$881$	34.8537	−	20.1228i	1.17425	−	0.677953i	0.219572	−	0.975596i	$-0.429534\pi$
$881$	34.8537	−	20.1228i	1.17425	−	0.677953i	0.954677	+	0.297643i	$0.0962004\pi$
$882$		0			0
$883$	9.27453	+	34.6130i	0.312113	+	1.16482i	0.926648	+	0.375931i	$0.122677\pi$
$883$	9.27453	+	34.6130i	0.312113	+	1.16482i	−0.614535	+	0.788890i	$0.710656\pi$
$884$	30.4658	+	25.5639i	1.02468	+	0.859806i
$885$		0			0
$886$	3.80429	+	21.5752i	0.127808	+	0.724833i
$887$	3.46180	−	39.5685i	0.116236	−	1.32858i	−0.684258	−	0.729240i	$-0.739874\pi$
$887$	3.46180	−	39.5685i	0.116236	−	1.32858i	0.800494	−	0.599341i	$-0.204571\pi$
$888$		0			0
$889$	5.20451	+	14.2993i	0.174554	+	0.479582i
$890$	−19.5768	−	3.79306i	−0.656215	−	0.127144i
$891$		0			0
$892$	17.9274	+	17.9274i	0.600254	+	0.600254i
$893$	−38.8448	−	18.1136i	−1.29989	−	0.606149i
$894$		0			0
$895$	23.0914	+	6.60625i	0.771861	+	0.220823i
$896$	1.35002	−	0.238046i	0.0451011	−	0.00795254i
$897$		0			0
$898$	−25.2115	+	2.20572i	−0.841319	+	0.0736059i
$899$	8.46386	−	14.6598i	0.282286	−	0.488933i
$900$		0			0
$901$	17.6838	+	30.6292i	0.589133	+	1.02041i
$902$	−5.12773	−	7.32316i	−0.170735	−	0.243834i
$903$		0			0
$904$	0.632406	−	1.73752i	0.0210335	−	0.0577891i
$905$	11.4866	+	45.9519i	0.381828	+	1.52749i
$906$		0			0
$907$	29.1476	−	20.4094i	0.967830	−	0.677682i	0.0211225	−	0.999777i	$-0.493276\pi$
$907$	29.1476	−	20.4094i	0.967830	−	0.677682i	0.946707	+	0.322095i	$0.104387\pi$
$908$	5.47857	−	20.4463i	0.181813	−	0.678534i
$909$		0			0
$910$	−11.4241	+	13.1580i	−0.378705	+	0.436183i
$911$	19.8514	−	23.6579i	0.657705	−	0.783822i	−0.329349	−	0.944208i	$-0.606829\pi$
$911$	19.8514	−	23.6579i	0.657705	−	0.783822i	0.987054	+	0.160386i	$0.0512739\pi$
$912$		0			0
$913$	5.55989	+	3.89308i	0.184006	+	0.128842i
$914$	23.6209	−	19.8203i	0.781309	−	0.655596i
$915$		0			0
$916$	−8.37418	+	3.04795i	−0.276691	+	0.100707i
$917$	1.05338	−	1.05338i	0.0347857	−	0.0347857i
$918$		0			0
$919$			37.9382i			1.25147i	0.780037	+	0.625734i	$0.215200\pi$
$919$			37.9382i			1.25147i	−0.780037	+	0.625734i	$0.784800\pi$
$920$	−4.22459	+	5.82205i	−0.139281	+	0.191947i
$921$		0			0
$922$	−14.3359	−	1.25423i	−0.472127	−	0.0413058i
$923$	2.90236	−	4.14500i	0.0955323	−	0.136434i
$924$		0			0
$925$	7.69568	+	2.34264i	0.253032	+	0.0770254i
$926$	22.8630	+	13.1999i	0.751324	+	0.433777i
$927$		0			0
$928$	−7.92033	−	2.12225i	−0.259998	−	0.0696662i
$929$	−3.45671	+	19.6040i	−0.113411	+	0.643186i	0.874114	+	0.485721i	$0.161443\pi$
$929$	−3.45671	+	19.6040i	−0.113411	+	0.643186i	−0.987525	+	0.157464i	$0.949668\pi$
$930$		0			0
$931$	−21.5621	−	7.84795i	−0.706668	−	0.257206i
$932$	−19.7232	+	9.19709i	−0.646056	+	0.301261i
$933$		0			0
$934$	7.82915	+	1.38049i	0.256178	+	0.0451710i
$935$	−15.1657	+	5.23223i	−0.495972	+	0.171112i
$936$		0			0
$937$	−10.2576	+	2.74853i	−0.335103	+	0.0897905i	−0.422447	−	0.906388i	$-0.638829\pi$
$937$	−10.2576	+	2.74853i	−0.335103	+	0.0897905i	0.0873441	+	0.996178i	$0.472162\pi$
$938$	1.11302	+	12.7219i	0.0363413	+	0.415383i
$939$		0			0
$940$	21.3851	+	0.360348i	0.697505	+	0.0117533i
$941$	0.798523	+	0.951643i	0.0260311	+	0.0310227i	0.778903	−	0.627144i	$-0.215776\pi$
$941$	0.798523	+	0.951643i	0.0260311	+	0.0310227i	−0.752872	+	0.658167i	$0.771332\pi$
$942$		0			0
$943$	11.8517	−	25.4160i	0.385943	−	0.827657i
$944$	9.83002			0.319940
$945$		0			0
$946$	6.28579			0.204369
$947$	5.67590	−	12.1720i	0.184442	−	0.395537i	−0.792246	−	0.610202i	$-0.791088\pi$
$947$	5.67590	−	12.1720i	0.184442	−	0.395537i	0.976688	+	0.214665i	$0.0688660\pi$
$948$		0			0
$949$	−19.1325	−	22.8012i	−0.621066	−	0.740157i
$950$	−12.2252	−	18.7754i	−0.396637	−	0.609154i
$951$		0			0
$952$	0.835870	+	9.55403i	0.0270907	+	0.309648i
$953$	−23.1471	+	6.20224i	−0.749807	+	0.200910i	−0.613433	−	0.789747i	$-0.710212\pi$
$953$	−23.1471	+	6.20224i	−0.749807	+	0.200910i	−0.136375	+	0.990657i	$0.543545\pi$
$954$		0			0
$955$	0.400006	+	0.194797i	0.0129439	+	0.00630347i
$956$	28.8667	+	5.08998i	0.933617	+	0.164622i
$957$		0			0
$958$	−11.7573	+	5.48251i	−0.379860	+	0.177132i
$959$	2.94550	+	1.07207i	0.0951151	+	0.0346191i
$960$		0			0
$961$	−4.64303	+	26.3319i	−0.149775	+	0.849418i
$962$	−8.83427	−	2.36714i	−0.284828	−	0.0763195i
$963$		0			0
$964$	−0.283207	−	0.163510i	−0.00912148	−	0.00526629i
$965$	−27.6972	−	34.1610i	−0.891606	−	1.09968i
$966$		0			0
$967$	18.9291	−	27.0335i	0.608718	−	0.869339i	−0.389955	−	0.920834i	$-0.627510\pi$
$967$	18.9291	−	27.0335i	0.608718	−	0.869339i	0.998673	+	0.0514946i	$0.0163985\pi$
$968$	−9.91045	−	0.867052i	−0.318534	−	0.0278681i
$969$		0			0
$970$	0.807543	+	0.585969i	0.0259286	+	0.0188143i
$971$		−	1.33222i		−	0.0427529i	−0.999771	−	0.0213765i	$-0.993195\pi$
$971$		−	1.33222i		−	0.0427529i	0.999771	−	0.0213765i	$-0.00680486\pi$
$972$		0			0
$973$	11.1047	−	11.1047i	0.355999	−	0.355999i
$974$	6.81580	−	2.48075i	0.218392	−	0.0794883i
$975$		0			0
$976$	7.76955	−	6.51943i	0.248697	−	0.208682i
$977$	−33.0259	−	23.1250i	−1.05659	−	0.739834i	−0.0899460	−	0.995947i	$-0.528669\pi$
$977$	−33.0259	−	23.1250i	−1.05659	−	0.739834i	−0.966647	+	0.256112i	$0.917558\pi$
$978$		0			0
$979$	−5.87857	+	7.00580i	−0.187880	+	0.223906i
$980$	11.4220	−	0.805644i	0.364863	−	0.0257353i
$981$		0			0
$982$	−8.87723	+	33.1303i	−0.283284	+	1.05723i
$983$	18.9226	−	13.2497i	0.603537	−	0.422601i	−0.231469	−	0.972842i	$-0.574353\pi$
$983$	18.9226	−	13.2497i	0.603537	−	0.422601i	0.835006	+	0.550241i	$0.185464\pi$
$984$		0			0
$985$	7.03700	+	4.22247i	0.224217	+	0.134539i
$986$	19.6202	−	53.9061i	0.624835	−	1.71672i
$987$		0			0
$988$	14.6106	+	20.8660i	0.464824	+	0.663837i
$989$	9.85886	+	17.0760i	0.313493	+	0.542987i
$990$		0			0
$991$	3.30469	−	5.72388i	0.104977	−	0.181825i	−0.808752	−	0.588150i	$-0.799857\pi$
$991$	3.30469	−	5.72388i	0.104977	−	0.181825i	0.913729	+	0.406325i	$0.133190\pi$
$992$	−2.05657	+	0.179926i	−0.0652961	+	0.00571267i
$993$		0			0
$994$	1.20170	−	0.211891i	0.0381155	−	0.00672079i
$995$	13.3986	−	46.8331i	0.424763	−	1.48471i
$996$		0			0
$997$	−56.4430	−	26.3198i	−1.78757	−	0.833557i	−0.963799	−	0.266631i	$-0.914089\pi$
$997$	−56.4430	−	26.3198i	−1.78757	−	0.833557i	−0.823769	−	0.566925i	$-0.808133\pi$
$998$	25.3002	+	25.3002i	0.800863	+	0.800863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.467.3		216
3.2	odd	2		270.2.r.a.47.12	yes	216
5.3	odd	4	inner	810.2.s.a.143.12		216
15.8	even	4		270.2.r.a.263.2	yes	216
27.4	even	9		270.2.r.a.77.2	yes	216
27.23	odd	18	inner	810.2.s.a.17.12		216
135.23	even	36	inner	810.2.s.a.503.3		216
135.58	odd	36		270.2.r.a.23.12	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.12	✓	216	135.58	odd	36
270.2.r.a.47.12	yes	216	3.2	odd	2
270.2.r.a.77.2	yes	216	27.4	even	9
270.2.r.a.263.2	yes	216	15.8	even	4
810.2.s.a.17.12		216	27.23	odd	18	inner
810.2.s.a.143.12		216	5.3	odd	4	inner
810.2.s.a.467.3		216	1.1	even	1	trivial
810.2.s.a.503.3		216	135.23	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(-1.60755 + 1.55428i) q^{5} +(-0.119477 - 1.36563i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(-1.60755 + 1.55428i) q^{5} +(-0.119477 - 1.36563i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.729270 - 2.11380i) q^{10} +(-1.00994 - 0.178080i) q^{11} +(5.15208 - 2.40245i) q^{13} +(1.28818 + 0.468858i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-6.75766 - 1.81071i) q^{17} +(-3.88061 - 2.24047i) q^{19} +(2.22396 + 0.232388i) q^{20} +(0.588216 - 0.840060i) q^{22} +(3.20470 + 0.280375i) q^{23} +(0.168456 - 4.99716i) q^{25} +5.68469i q^{26} +(-0.969337 + 0.969337i) q^{28} +(7.70523 - 2.80447i) q^{29} +(1.58144 - 1.32699i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(4.49697 - 5.35928i) q^{34} +(2.31464 + 2.00963i) q^{35} +(-0.416406 + 1.55405i) q^{37} +(3.67057 - 2.57016i) q^{38} +(-1.15050 + 1.91738i) q^{40} +(2.98153 - 8.19170i) q^{41} +(3.51565 + 5.02087i) q^{43} +(0.512762 + 0.888129i) q^{44} +(-1.60847 + 2.78595i) q^{46} +(9.52867 - 0.833651i) q^{47} +(5.04298 - 0.889213i) q^{49} +(4.45777 + 2.26456i) q^{50} +(-5.15208 - 2.40245i) q^{52} +(-3.57469 - 3.57469i) q^{53} +(1.90032 - 1.28346i) q^{55} +(-0.468858 - 1.28818i) q^{56} +(-0.714654 + 8.16853i) q^{58} +(-1.70697 - 9.68068i) q^{59} +(-7.76955 - 6.51943i) q^{61} +(0.534312 + 1.99408i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-4.54816 + 11.8698i) q^{65} +(3.93699 + 8.44291i) q^{67} +(2.95666 + 6.34057i) q^{68} +(-2.79955 + 1.24847i) q^{70} +(0.770875 - 0.445065i) q^{71} +(-1.35517 - 5.05755i) q^{73} +(-1.23246 - 1.03416i) q^{74} +(0.778107 + 4.41286i) q^{76} +(-0.122527 + 1.40049i) q^{77} +(-2.55545 - 7.02105i) q^{79} +(-1.25151 - 1.85303i) q^{80} +(6.16415 + 6.16415i) q^{82} +(-5.99835 - 2.79708i) q^{83} +(13.6776 - 7.59246i) q^{85} +(-6.03623 + 1.06435i) q^{86} +(-1.02162 + 0.0893803i) q^{88} +(4.45891 - 7.72305i) q^{89} +(-3.89642 - 6.74881i) q^{91} +(-1.84516 - 2.63516i) q^{92} +(-3.27145 + 8.98822i) q^{94} +(9.72059 - 2.42986i) q^{95} +(-0.365508 + 0.255932i) q^{97} +(-1.32535 + 4.94629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 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

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Database

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