LMFDB - Embedded newform 810.2.s.a.503.3

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			503.3
Character	$\chi$	$=$	810.503
Dual form			810.2.s.a.467.3

$q$-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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

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	0.939605	+	0.342261i	$0.111193\pi$
$7$	−0.119477	+	1.36563i	−0.0451582	+	0.516161i	−0.984763	+	0.173900i	$0.944363\pi$
$8$	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	−0.323815	−	0.946120i	$-0.604966\pi$
$11$	−1.00994	+	0.178080i	−0.304509	+	0.0536932i	0.0193056	+	0.999814i	$0.493854\pi$
$12$		0			0
$13$	5.15208	+	2.40245i	1.42893	+	0.666320i	0.974484	−	0.224455i	$-0.0720602\pi$
$13$	5.15208	+	2.40245i	1.42893	+	0.666320i	0.454444	+	0.890775i	$0.349838\pi$
$14$	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	−0.956496	−	0.291745i	$-0.905764\pi$
$17$	−6.75766	+	1.81071i	−1.63897	+	0.439162i	−0.682478	+	0.730906i	$0.739098\pi$
$18$		0			0
$19$	−3.88061	+	2.24047i	−0.890273	+	0.513999i	−0.874032	−	0.485869i	$-0.838503\pi$
$19$	−3.88061	+	2.24047i	−0.890273	+	0.513999i	−0.0162409	+	0.999868i	$0.505170\pi$
$20$	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	0.252005	−	0.967726i	$-0.418910\pi$
$23$	3.20470	−	0.280375i	0.668225	−	0.0584621i	0.416220	+	0.909264i	$0.363355\pi$
$24$		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	0.937168	−	0.348879i	$-0.113438\pi$
$29$	7.70523	+	2.80447i	1.43082	+	0.520778i	0.493657	+	0.869657i	$0.335660\pi$
$30$		0			0
$31$	1.58144	+	1.32699i	0.284035	+	0.238334i	0.773662	−	0.633598i	$-0.218423\pi$
$31$	1.58144	+	1.32699i	0.284035	+	0.238334i	−0.489627	+	0.871932i	$0.662867\pi$
$32$	−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	0.923213	−	0.384288i	$-0.125553\pi$
$37$	−0.416406	−	1.55405i	−0.0684567	−	0.255484i	−0.991670	+	0.128804i	$0.958886\pi$
$38$	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	0.921188	+	0.389118i	$0.127220\pi$
$41$	2.98153	+	8.19170i	0.465637	+	1.27933i	−0.455550	+	0.890210i	$0.650557\pi$
$42$		0			0
$43$	3.51565	−	5.02087i	0.536131	−	0.765675i	−0.456121	−	0.889918i	$-0.650761\pi$
$43$	3.51565	−	5.02087i	0.536131	−	0.765675i	0.992252	+	0.124243i	$0.0396503\pi$
$44$	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	0.757395	−	0.652957i	$-0.226472\pi$
$47$	9.52867	+	0.833651i	1.38990	+	0.121600i	0.632504	+	0.774557i	$0.282027\pi$
$48$		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	−0.908628	−	0.417607i	$-0.862869\pi$
$53$	−3.57469	+	3.57469i	−0.491021	+	0.491021i	0.417607	+	0.908628i	$0.362869\pi$
$54$		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	0.645686	+	0.763603i	$0.276571\pi$
$59$	−1.70697	+	9.68068i	−0.222228	+	1.26032i	−0.867914	+	0.496714i	$0.834540\pi$
$60$		0			0
$61$	−7.76955	+	6.51943i	−0.994789	+	0.834727i	−0.986254	−	0.165236i	$-0.947161\pi$
$61$	−7.76955	+	6.51943i	−0.994789	+	0.834727i	−0.00853536	+	0.999964i	$0.502717\pi$
$62$	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	−0.504770	−	0.863254i	$-0.668423\pi$
$67$	3.93699	−	8.44291i	0.480980	−	1.03147i	0.985751	−	0.168212i	$-0.0537994\pi$
$68$	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	0.545045	−	0.838407i	$-0.316513\pi$
$71$	0.770875	+	0.445065i	0.0914860	+	0.0528195i	−0.453559	+	0.891226i	$0.649846\pi$
$72$		0			0
$73$	−1.35517	+	5.05755i	−0.158610	+	0.591942i	0.840159	+	0.542341i	$0.182462\pi$
$73$	−1.35517	+	5.05755i	−0.158610	+	0.591942i	−0.998769	+	0.0496014i	$0.984205\pi$
$74$	−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	0.708902	+	0.705307i	$0.249191\pi$
$79$	−2.55545	+	7.02105i	−0.287511	+	0.789930i	−0.996413	+	0.0846230i	$0.973031\pi$
$80$	−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	−0.722955	−	0.690895i	$-0.757217\pi$
$83$	−5.99835	+	2.79708i	−0.658405	+	0.307019i	0.0645500	+	0.997914i	$0.479439\pi$
$84$		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	0.999510	−	0.0313059i	$-0.00996662\pi$
$89$	4.45891	+	7.72305i	0.472643	+	0.818642i	−0.526867	+	0.849948i	$0.676633\pi$
$90$		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	0.554873	−	0.831935i	$-0.312767\pi$
$97$	−0.365508	−	0.255932i	−0.0371117	−	0.0259859i	−0.591985	+	0.805949i	$0.701656\pi$
$98$	−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	0.717936	−	0.696110i	$-0.245087\pi$
$101$	−0.927270	−	1.10508i	−0.0922668	−	0.109959i	−0.810202	+	0.586150i	$0.800643\pi$
$102$		0			0
$103$	5.30157	−	3.71220i	0.522379	−	0.365774i	−0.282448	−	0.959283i	$-0.591147\pi$
$103$	5.30157	−	3.71220i	0.522379	−	0.365774i	0.804828	+	0.593509i	$0.202258\pi$
$104$	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	−0.958464	−	0.285213i	$-0.907936\pi$
$107$	−12.8647	−	12.8647i	−1.24368	−	1.24368i	−0.285213	−	0.958464i	$-0.592064\pi$
$108$		0			0
$109$		−	4.66649i		−	0.446969i	−0.974708	−	0.223484i	$-0.928257\pi$
$109$		−	4.66649i		−	0.446969i	0.974708	−	0.223484i	$-0.0717432\pi$
$110$	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	0.865933	−	0.500161i	$-0.166726\pi$
$113$	1.06056	+	1.51464i	0.0997691	+	0.142485i	−0.766164	+	0.642646i	$0.777837\pi$
$114$		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	−0.250465	−	0.968126i	$-0.580584\pi$
$127$	−10.7222	−	2.87299i	−0.951437	−	0.254937i	−0.700972	+	0.713189i	$0.747250\pi$
$128$	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	−0.734666	−	0.678429i	$-0.762661\pi$
$131$	0.698519	−	0.832463i	0.0610299	−	0.0727326i	0.795696	+	0.605697i	$0.207105\pi$
$132$		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	0.860694	−	0.509123i	$-0.170030\pi$
$137$	−0.966343	−	2.07233i	−0.0825603	−	0.177051i	−0.943254	+	0.332072i	$0.892252\pi$
$138$		0			0
$139$	7.36374	−	8.77576i	0.624584	−	0.744350i	−0.357268	−	0.934002i	$-0.616292\pi$
$139$	7.36374	−	8.77576i	0.624584	−	0.744350i	0.981851	+	0.189652i	$0.0607360\pi$
$140$	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	−0.801206	−	0.598389i	$-0.795808\pi$
$149$	−12.5767	+	4.57756i	−1.03033	+	0.375008i	−0.229122	+	0.973398i	$0.573585\pi$
$150$		0			0
$151$	0.361051	+	2.04762i	0.0293819	+	0.166633i	0.995968	−	0.0897090i	$-0.0285937\pi$
$151$	0.361051	+	2.04762i	0.0293819	+	0.166633i	−0.966586	+	0.256342i	$0.917483\pi$
$152$	−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	0.767374	−	0.641200i	$-0.221563\pi$
$157$	−1.22311	−	1.74678i	−0.0976147	−	0.139408i	−0.864988	+	0.501792i	$0.832674\pi$
$158$	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	0.959413	−	0.282005i	$-0.0909996\pi$
$163$	8.64856	+	8.64856i	0.677408	+	0.677408i	−0.282005	+	0.959413i	$0.591000\pi$
$164$	−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	−0.870561	−	0.492060i	$-0.836244\pi$
$167$	−9.12258	+	6.38770i	−0.705926	+	0.494295i	0.164635	+	0.986355i	$0.447355\pi$
$168$		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	0.691721	−	0.722165i	$-0.256853\pi$
$173$	3.28417	+	2.29960i	0.249691	+	0.174835i	−0.442030	+	0.897000i	$0.645742\pi$
$174$		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	−0.993897	−	0.110314i	$-0.964814\pi$
$179$	−5.37055	+	9.30206i	−0.401414	+	0.695269i	0.592483	+	0.805583i	$0.298148\pi$
$180$		0			0
$181$	10.5913	+	18.3447i	0.787246	+	1.36355i	0.927648	+	0.373456i	$0.121827\pi$
$181$	10.5913	+	18.3447i	0.787246	+	1.36355i	−0.140401	+	0.990095i	$0.544839\pi$
$182$	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	−0.942130	−	0.335247i	$-0.891180\pi$
$191$	−0.0680526	+	0.186973i	−0.00492411	+	0.0135289i	0.937206	+	0.348776i	$0.113403\pi$
$192$		0			0
$193$	−1.71416	−	19.5930i	−0.123388	−	1.41033i	−0.765359	−	0.643603i	$-0.777439\pi$
$193$	−1.71416	−	19.5930i	−0.123388	−	1.41033i	0.641971	−	0.766729i	$-0.278117\pi$
$194$	−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	−0.991473	−	0.130310i	$-0.958403\pi$
$197$	−0.949894	+	3.54505i	−0.0676772	+	0.252575i	0.923796	+	0.382885i	$0.125069\pi$
$198$		0			0
$199$	−18.8661	−	10.8923i	−1.33738	−	0.772138i	−0.350964	−	0.936389i	$-0.614146\pi$
$199$	−18.8661	−	10.8923i	−1.33738	−	0.772138i	−0.986419	+	0.164251i	$0.947479\pi$
$200$	−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	0.785567	+	0.618776i	$0.212371\pi$
$211$	−2.38599	+	13.5316i	−0.164258	+	0.931556i	−0.949826	+	0.312780i	$0.898740\pi$
$212$	−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	−0.799589	−	0.600548i	$-0.794949\pi$
$223$	−25.2567	−	2.20968i	−1.69131	−	0.147971i	−0.891725	+	0.452577i	$0.850505\pi$
$224$	−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	−0.180080	−	0.983652i	$-0.557636\pi$
$227$	12.1412	−	17.3395i	0.805841	−	1.15086i	0.985922	−	0.167209i	$-0.0534753\pi$
$228$		0			0
$229$	3.04795	+	8.37418i	0.201414	+	0.553382i	0.998741	−	0.0501667i	$-0.0159753\pi$
$229$	3.04795	+	8.37418i	0.201414	+	0.553382i	−0.797326	+	0.603548i	$0.793753\pi$
$230$	−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	0.861923	+	0.507038i	$0.169260\pi$
$233$	5.63247	+	21.0206i	0.368995	+	1.37711i	−0.492928	+	0.870070i	$0.664074\pi$
$234$		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	−0.930768	−	0.365609i	$-0.880861\pi$
$239$	−22.4543	−	18.8414i	−1.45245	−	1.21875i	−0.521681	−	0.853140i	$-0.674695\pi$
$240$		0			0
$241$	0.307297	+	0.111847i	0.0197948	+	0.00720471i	0.351899	−	0.936038i	$-0.385536\pi$
$241$	0.307297	+	0.111847i	0.0197948	+	0.00720471i	−0.332104	+	0.943243i	$0.607758\pi$
$242$	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	−0.297837	−	0.954617i	$-0.596265\pi$
$251$	6.01980	−	3.47553i	0.379966	−	0.219374i	0.677804	+	0.735243i	$0.262932\pi$
$252$		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	0.848519	−	0.529165i	$-0.177495\pi$
$257$	15.8480	+	7.39005i	0.988573	+	0.460979i	0.140054	+	0.990144i	$0.455273\pi$
$258$		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	−0.999891	−	0.0147511i	$-0.995304\pi$
$263$	−0.204809	+	2.34098i	−0.0126291	+	0.144351i	0.987262	+	0.159102i	$0.0508599\pi$
$264$		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	−0.966371	−	0.257152i	$-0.917216\pi$
$277$	0.498845	−	5.70183i	0.0299727	−	0.342590i	0.996344	−	0.0854372i	$-0.0272287\pi$
$278$	−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	−0.260977	−	0.965345i	$-0.584045\pi$
$281$	−2.95109	+	0.520356i	−0.176047	+	0.0310418i	0.0849296	+	0.996387i	$0.472933\pi$
$282$		0			0
$283$	21.4325	+	9.99414i	1.27403	+	0.594090i	0.937632	−	0.347630i	$-0.113013\pi$
$283$	21.4325	+	9.99414i	1.27403	+	0.594090i	0.336398	+	0.941720i	$0.390791\pi$
$284$	−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	0.695117	−	0.718897i	$-0.255353\pi$
$293$	25.7530	−	2.25310i	1.50451	−	0.131627i	0.809392	+	0.587269i	$0.199797\pi$
$294$		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	−0.836600	−	0.547815i	$-0.815460\pi$
$307$	−6.76310	−	25.2402i	−0.385991	−	1.44054i	0.450609	−	0.892721i	$-0.351207\pi$
$308$	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	0.973384	+	0.229179i	$0.0736040\pi$
$311$	6.61393	+	18.1716i	0.375042	+	1.03042i	−0.598343	+	0.801240i	$0.704174\pi$
$312$		0			0
$313$	−6.02953	+	8.61107i	−0.340809	+	0.486726i	−0.952571	−	0.304316i	$-0.901572\pi$
$313$	−6.02953	+	8.61107i	−0.340809	+	0.486726i	0.611762	+	0.791042i	$0.290461\pi$
$314$	−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	−0.0333329	−	0.999444i	$-0.510612\pi$
$317$	−4.26793	−	0.373396i	−0.239711	−	0.0209720i	−0.206378	+	0.978472i	$0.566168\pi$
$318$		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	0.215147	−	0.976582i	$-0.430977\pi$
$331$	22.0914	−	18.5369i	1.21425	−	1.01888i	0.999105	−	0.0422965i	$-0.0134674\pi$
$332$	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	−0.903148	−	0.429330i	$-0.858750\pi$
$337$	0.115103	−	0.246840i	0.00627009	−	0.0134462i	0.909418	+	0.415884i	$0.136528\pi$
$338$	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	−0.288899	−	0.957359i	$-0.593289\pi$
$347$	−3.17854	−	36.3308i	−0.170633	−	1.95034i	0.118267	−	0.992982i	$-0.462266\pi$
$348$		0			0
$349$	8.59979	−	23.6277i	0.460336	−	1.26476i	−0.464898	−	0.885364i	$-0.653909\pi$
$349$	8.59979	−	23.6277i	0.460336	−	1.26476i	0.925234	−	0.379398i	$-0.123869\pi$
$350$	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	−0.204989	−	0.978764i	$-0.565716\pi$
$353$	7.76000	−	3.61855i	0.413023	−	0.192596i	0.618012	+	0.786168i	$0.287938\pi$
$354$		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	0.833407	−	0.552660i	$-0.186387\pi$
$359$	−1.17311	−	2.03189i	−0.0619144	−	0.107239i	−0.895321	+	0.445421i	$0.853054\pi$
$360$		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	0.673071	−	0.739578i	$-0.264975\pi$
$367$	3.99042	+	2.79412i	0.208298	+	0.145852i	−0.464772	+	0.885430i	$0.653864\pi$
$368$	−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	0.135483	−	0.990780i	$-0.456741\pi$
$373$	21.4927	−	15.0493i	1.11285	−	0.779226i	0.977366	+	0.211554i	$0.0678524\pi$
$374$	−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	$0.109955\pi$
$379$			13.1839i			0.677209i	−0.940929	+	0.338604i	$0.890045\pi$
$380$	−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	0.581990	−	0.813196i	$-0.302274\pi$
$383$	−7.46056	−	10.6548i	−0.381217	−	0.544434i	−0.963207	+	0.268762i	$0.913386\pi$
$384$		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	0.883554	+	0.468330i	$0.155144\pi$
$389$	4.21015	+	23.8769i	0.213463	+	1.21061i	−0.670091	+	0.742279i	$0.733745\pi$
$390$		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	0.976410	−	0.215923i	$-0.0692762\pi$
$397$	34.1521	+	9.15103i	1.71404	+	0.459277i	0.737634	+	0.675200i	$0.235943\pi$
$398$	−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	−0.697322	−	0.716758i	$-0.745625\pi$
$401$	2.59596	−	3.09374i	0.129636	−	0.154494i	0.826958	+	0.562264i	$0.190070\pi$
$402$		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	−0.943082	−	0.332562i	$-0.892087\pi$
$409$	−9.13725	+	10.8893i	−0.451808	+	0.538444i	0.491274	+	0.871005i	$0.336531\pi$
$410$	−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	−0.0510626	−	0.998695i	$-0.516261\pi$
$419$	11.2945	−	4.11085i	0.551770	−	0.200828i	0.602833	+	0.797868i	$0.294039\pi$
$420$		0			0
$421$	1.11063	+	6.29871i	0.0541289	+	0.306980i	0.999837	−	0.0180360i	$-0.00574134\pi$
$421$	1.11063	+	6.29871i	0.0541289	+	0.306980i	−0.945708	+	0.325016i	$0.894630\pi$
$422$	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	$-0.853964\pi$
$431$		−	18.3880i		−	0.885721i	0.896591	−	0.442860i	$-0.146036\pi$
$432$		0			0
$433$	1.98062	+	1.98062i	0.0951823	+	0.0951823i	0.753095	−	0.657912i	$-0.228560\pi$
$433$	1.98062	+	1.98062i	0.0951823	+	0.0951823i	−0.657912	+	0.753095i	$0.728560\pi$
$434$	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	0.949660	−	0.313283i	$-0.101429\pi$
$439$	9.97813	+	11.8915i	0.476230	+	0.567549i	−0.473430	+	0.880831i	$0.656984\pi$
$440$	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	0.916096	−	0.400959i	$-0.131323\pi$
$443$	17.9460	+	12.5659i	0.852640	+	0.597025i	−0.0634554	+	0.997985i	$0.520212\pi$
$444$		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	−0.396061	−	0.918224i	$-0.629623\pi$
$449$	12.6539	−	21.9172i	0.597175	−	1.03434i	0.993236	−	0.116113i	$-0.0370434\pi$
$450$		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	−0.946387	−	0.323036i	$-0.895296\pi$
$457$	−27.9459	+	13.0314i	−1.30725	+	0.609582i	−0.360866	+	0.932618i	$0.617519\pi$
$458$	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	−0.770738	−	0.637152i	$-0.780112\pi$
$461$	4.92189	−	13.5228i	0.229235	−	0.629819i	0.999973	+	0.00733363i	$0.00233439\pi$
$462$		0			0
$463$	2.30090	+	26.2994i	0.106932	+	1.22224i	0.840192	+	0.542289i	$0.182442\pi$
$463$	2.30090	+	26.2994i	0.106932	+	1.22224i	−0.733260	+	0.679948i	$0.762002\pi$
$464$	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	−0.997052	−	0.0767312i	$-0.975552\pi$
$467$	−2.05759	+	7.67904i	−0.0952140	+	0.355343i	0.901838	+	0.432075i	$0.142218\pi$
$468$		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	−0.386877	−	0.922131i	$-0.626446\pi$
$479$	9.93768	−	8.33870i	0.454064	−	0.381005i	0.840941	+	0.541126i	$0.182002\pi$
$480$		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	−0.813697	−	0.581289i	$-0.802549\pi$
$487$	−5.12880	+	5.12880i	−0.232408	+	0.232408i	0.581289	+	0.813697i	$0.302549\pi$
$488$	−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	0.872151	−	0.489238i	$-0.162725\pi$
$491$	33.7779	+	5.95595i	1.52437	+	0.268788i	0.652224	+	0.758026i	$0.273836\pi$
$492$		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	0.836644	+	0.547747i	$0.184515\pi$
$499$	12.2374	+	33.6221i	0.547823	+	1.50513i	−0.288821	+	0.957383i	$0.593263\pi$
$500$	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	−0.936516	−	0.350624i	$-0.885970\pi$
$503$	−6.74582	−	25.1757i	−0.300781	−	1.12253i	0.635735	−	0.771907i	$-0.280697\pi$
$504$		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	0.147126	−	0.989118i	$-0.452998\pi$
$509$	−18.0808	−	15.1716i	−0.801417	−	0.672469i	−0.948543	+	0.316649i	$0.897442\pi$
$510$		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	−0.371878	−	0.928282i	$-0.621286\pi$
$521$	5.61731	−	3.24316i	0.246099	−	0.142085i	0.617977	+	0.786196i	$0.287953\pi$
$522$		0			0
$523$	15.8693	−	4.25218i	0.693918	−	0.185935i	0.105413	−	0.994429i	$-0.466384\pi$
$523$	15.8693	−	4.25218i	0.693918	−	0.185935i	0.588505	+	0.808494i	$0.299717\pi$
$524$	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	−0.670751	−	0.741682i	$-0.734028\pi$
$547$	2.77386	−	31.7053i	0.118602	−	1.35562i	0.789353	−	0.613940i	$-0.210416\pi$
$548$	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	−0.934069	−	0.357092i	$-0.883768\pi$
$557$	−36.9224	+	9.89332i	−1.56445	+	0.419193i	−0.630382	+	0.776285i	$0.717102\pi$
$558$		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	0.473511	−	0.880788i	$-0.342986\pi$
$563$	25.9290	−	2.26849i	1.09278	−	0.0956055i	0.619265	+	0.785182i	$0.287431\pi$
$564$		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	0.484344	−	0.874878i	$-0.339058\pi$
$569$	6.98942	+	2.54394i	0.293012	+	0.106648i	−0.191332	+	0.981525i	$0.561281\pi$
$570$		0			0
$571$	−24.7246	−	20.7464i	−1.03469	−	0.868209i	−0.0432898	−	0.999063i	$-0.513784\pi$
$571$	−24.7246	−	20.7464i	−1.03469	−	0.868209i	−0.991402	+	0.130853i	$0.958228\pi$
$572$	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	0.910952	+	0.412511i	$0.135348\pi$
$577$	7.88604	+	29.4311i	0.328300	+	1.22523i	−0.582652	+	0.812722i	$0.697985\pi$
$578$	−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	−0.154934	−	0.987925i	$-0.549516\pi$
$587$	−11.6068	−	1.01547i	−0.479065	−	0.0419128i	−0.324131	+	0.946012i	$0.605072\pi$
$588$		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	−0.975034	−	0.222055i	$-0.928724\pi$
$593$	−18.3363	+	18.3363i	−0.752980	+	0.752980i	0.222055	+	0.975034i	$0.428724\pi$
$594$		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	−0.418661	−	0.908142i	$-0.637501\pi$
$599$	6.98391	−	39.6077i	0.285355	−	1.61833i	0.704016	−	0.710184i	$-0.251388\pi$
$600$		0			0
$601$	26.4693	−	22.2104i	1.07971	−	0.905981i	0.0838095	−	0.996482i	$-0.473291\pi$
$601$	26.4693	−	22.2104i	1.07971	−	0.905981i	0.995896	+	0.0905010i	$0.0288468\pi$
$602$	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	−0.640405	−	0.768038i	$-0.721233\pi$
$607$	8.85936	−	18.9990i	0.359590	−	0.771144i	0.999995	−	0.00310650i	$-0.000988831\pi$
$608$	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	−0.917984	−	0.396616i	$-0.870184\pi$
$613$	1.86487	−	6.95980i	0.0753215	−	0.281104i	0.993306	+	0.115512i	$0.0368510\pi$
$614$	−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	−0.793479	−	0.608597i	$-0.791732\pi$
$617$	−2.92452	−	33.4274i	−0.117737	−	1.34574i	0.675743	−	0.737138i	$-0.263823\pi$
$618$		0			0
$619$	−3.68119	+	10.1140i	−0.147960	+	0.406516i	−0.991427	−	0.130665i	$-0.958289\pi$
$619$	−3.68119	+	10.1140i	−0.147960	+	0.406516i	0.843467	+	0.537181i	$0.180511\pi$
$620$	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	−0.972018	−	0.234905i	$-0.924522\pi$
$631$	−7.09822	+	12.2945i	−0.282576	+	0.489435i	0.689443	+	0.724340i	$0.257855\pi$
$632$	−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	0.849110	−	0.528217i	$-0.177139\pi$
$641$	4.59449	+	5.47551i	0.181472	+	0.216269i	−0.667638	+	0.744486i	$0.732695\pi$
$642$		0			0
$643$	−15.0612	+	10.5460i	−0.593958	+	0.415894i	−0.831533	−	0.555476i	$-0.812536\pi$
$643$	−15.0612	+	10.5460i	−0.593958	+	0.415894i	0.237575	+	0.971369i	$0.423647\pi$
$644$	−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	0.604097	−	0.796911i	$-0.293534\pi$
$647$	−4.90447	−	4.90447i	−0.192815	−	0.192815i	−0.796911	+	0.604097i	$0.793534\pi$
$648$		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	0.928735	−	0.370744i	$-0.120897\pi$
$653$	6.71310	+	9.58730i	0.262704	+	0.375180i	−0.666031	+	0.745924i	$0.732008\pi$
$654$		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	−0.999170	−	0.0407368i	$-0.987029\pi$
$659$	−1.90453	−	10.8012i	−0.0741901	−	0.420753i	0.924980	−	0.380016i	$-0.124082\pi$
$660$		0			0
$661$	14.1762	−	5.15971i	0.551390	−	0.200689i	−0.0512741	−	0.998685i	$-0.516328\pi$
$661$	14.1762	−	5.15971i	0.551390	−	0.200689i	0.602664	+	0.797995i	$0.294106\pi$
$662$	−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	−0.929333	−	0.369242i	$-0.879617\pi$
$673$	−15.9499	−	34.2048i	−0.614825	−	1.31850i	0.314508	−	0.949255i	$-0.398160\pi$
$674$	−0.272358			−0.0104908
$675$		0			0
$676$	−19.3157			−0.742910
$677$	−7.39747	−	15.8639i	−0.284308	−	0.609700i	0.711345	−	0.702843i	$-0.248086\pi$
$677$	−7.39747	−	15.8639i	−0.284308	−	0.609700i	−0.995653	+	0.0931429i	$0.970309\pi$
$678$		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	−0.692943	−	0.720992i	$-0.743686\pi$
$683$	−43.2142	−	11.5792i	−1.65355	−	0.443066i	−0.960603	+	0.277926i	$0.910353\pi$
$684$		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	0.979289	−	0.202466i	$-0.0648956\pi$
$691$	−0.267841	−	1.51900i	−0.0101891	−	0.0577855i	−0.989478	+	0.144681i	$0.953785\pi$
$692$	−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	$0.102783\pi$
$701$			16.8030i			0.634642i	−0.948318	+	0.317321i	$0.897217\pi$
$702$		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	0.985964	−	0.166958i	$-0.0533944\pi$
$709$	17.3164	+	20.6369i	0.650332	+	0.775035i	−0.335632	+	0.941993i	$0.608950\pi$
$710$	−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	−0.763836	−	0.645410i	$-0.776686\pi$
$719$	4.74675	−	8.22161i	0.177024	−	0.306614i	0.940860	+	0.338796i	$0.110020\pi$
$720$		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	−0.342074	−	0.939673i	$-0.611129\pi$
$727$	4.25681	−	1.98498i	0.157876	−	0.0736189i	0.499950	+	0.866054i	$0.333352\pi$
$728$	−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	0.992348	+	0.123471i	$0.0394026\pi$
$733$	0.988648	+	11.3003i	0.0365165	+	0.417386i	−0.955832	+	0.293915i	$0.905042\pi$
$734$	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	0.264971	−	0.964256i	$-0.414638\pi$
$739$	−11.8963	−	6.86835i	−0.437614	−	0.252656i	−0.702585	+	0.711600i	$0.747971\pi$
$740$	−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	−0.964543	−	0.263926i	$-0.914982\pi$
$743$	−3.88066	+	8.32210i	−0.142368	+	0.305308i	0.822175	+	0.569234i	$0.192760\pi$
$744$		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	0.866869	+	0.498536i	$0.166129\pi$
$751$	−3.24004	+	18.3752i	−0.118231	+	0.670520i	−0.985100	+	0.171984i	$0.944982\pi$
$752$	−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	−0.273316	−	0.961924i	$-0.588120\pi$
$757$	18.9461	−	18.9461i	0.688609	−	0.688609i	0.961924	+	0.273316i	$0.0881204\pi$
$758$	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	0.264812	−	0.964300i	$-0.414690\pi$
$761$	5.07157	+	0.894255i	0.183844	+	0.0324167i	−0.0809679	+	0.996717i	$0.525801\pi$
$762$		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	−0.871287	−	0.490774i	$-0.836714\pi$
$769$	−14.4008	−	39.5659i	−0.519306	−	1.42678i	0.351981	−	0.936007i	$-0.385508\pi$
$770$	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	−0.890304	−	0.455367i	$-0.849508\pi$
$773$	−9.64653	−	36.0013i	−0.346961	−	1.29488i	0.543343	−	0.839511i	$-0.317158\pi$
$774$		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	0.747519	−	0.664241i	$-0.231245\pi$
$787$	44.8583	−	3.92459i	1.59902	−	0.139897i	0.851506	+	0.524344i	$0.175690\pi$
$788$	−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	0.705292	−	0.708917i	$-0.250816\pi$
$797$	17.3786	+	8.10379i	0.615583	+	0.287051i	−0.0897092	+	0.995968i	$0.528594\pi$
$798$		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	−0.0695021	−	0.997582i	$-0.522141\pi$
$821$	5.91344	−	1.04270i	0.206380	−	0.0363904i	0.275882	+	0.961191i	$0.411030\pi$
$822$		0			0
$823$	−4.33877	−	2.02320i	−0.151240	−	0.0705244i	0.345525	−	0.938410i	$-0.387701\pi$
$823$	−4.33877	−	2.02320i	−0.151240	−	0.0705244i	−0.496765	+	0.867885i	$0.665479\pi$
$824$	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	−0.698808	−	0.715309i	$-0.746286\pi$
$827$	−27.2145	+	7.29210i	−0.946340	+	0.253571i	−0.247532	+	0.968880i	$0.579619\pi$
$828$		0			0
$829$	−6.06867	+	3.50375i	−0.210774	+	0.121690i	−0.601671	−	0.798744i	$-0.705498\pi$
$829$	−6.06867	+	3.50375i	−0.210774	+	0.121690i	0.390897	+	0.920434i	$0.372165\pi$
$830$	−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	−0.0424480	−	0.999099i	$-0.513516\pi$
$839$	−20.7733	−	7.56086i	−0.717173	−	0.261030i	−0.674725	+	0.738069i	$0.735738\pi$
$840$		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	0.298519	+	0.954404i	$0.403507\pi$
$853$	−20.4568	+	29.2153i	−0.700426	+	1.00031i	−0.998946	+	0.0459089i	$0.985382\pi$
$854$	−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	0.542583	−	0.840002i	$-0.317446\pi$
$857$	27.2563	+	2.38462i	0.931058	+	0.0814570i	0.388475	+	0.921459i	$0.373002\pi$
$858$		0			0
$859$	−18.2241	−	3.21341i	−0.621800	−	0.109640i	−0.146132	−	0.989265i	$-0.546682\pi$
$859$	−18.2241	−	3.21341i	−0.621800	−	0.109640i	−0.475668	+	0.879625i	$0.657794\pi$
$860$	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	−0.385252	−	0.922812i	$-0.625885\pi$
$863$	15.7918	−	15.7918i	0.537560	−	0.537560i	0.922812	+	0.385252i	$0.125885\pi$
$864$		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	−0.995798	−	0.0915805i	$-0.970808\pi$
$877$	−8.45652	+	18.1351i	−0.285557	+	0.612378i	0.710241	+	0.703958i	$0.248586\pi$
$878$	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	0.954677	−	0.297643i	$-0.0962004\pi$
$881$	34.8537	+	20.1228i	1.17425	+	0.677953i	0.219572	+	0.975596i	$0.429534\pi$
$882$		0			0
$883$	9.27453	−	34.6130i	0.312113	−	1.16482i	−0.614535	−	0.788890i	$-0.710656\pi$
$883$	9.27453	−	34.6130i	0.312113	−	1.16482i	0.926648	−	0.375931i	$-0.122677\pi$
$884$	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	0.800494	+	0.599341i	$0.204571\pi$
$887$	3.46180	+	39.5685i	0.116236	+	1.32858i	−0.684258	+	0.729240i	$0.739874\pi$
$888$		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	0.946707	−	0.322095i	$-0.104387\pi$
$907$	29.1476	+	20.4094i	0.967830	+	0.677682i	0.0211225	+	0.999777i	$0.493276\pi$
$908$	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	0.987054	−	0.160386i	$-0.0512739\pi$
$911$	19.8514	+	23.6579i	0.657705	+	0.783822i	−0.329349	+	0.944208i	$0.606829\pi$
$912$		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	$-0.784800\pi$
$919$		−	37.9382i		−	1.25147i	0.780037	−	0.625734i	$-0.215200\pi$
$920$	−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	−0.987525	−	0.157464i	$-0.949668\pi$
$929$	−3.45671	−	19.6040i	−0.113411	−	0.643186i	0.874114	−	0.485721i	$-0.161443\pi$
$930$		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	0.0873441	−	0.996178i	$-0.472162\pi$
$937$	−10.2576	−	2.74853i	−0.335103	−	0.0897905i	−0.422447	+	0.906388i	$0.638829\pi$
$938$	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	−0.752872	−	0.658167i	$-0.771332\pi$
$941$	0.798523	−	0.951643i	0.0260311	−	0.0310227i	0.778903	+	0.627144i	$0.215776\pi$
$942$		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	0.976688	−	0.214665i	$-0.0688660\pi$
$947$	5.67590	+	12.1720i	0.184442	+	0.395537i	−0.792246	+	0.610202i	$0.791088\pi$
$948$		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	−0.136375	−	0.990657i	$-0.543545\pi$
$953$	−23.1471	−	6.20224i	−0.749807	−	0.200910i	−0.613433	+	0.789747i	$0.710212\pi$
$954$		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	0.998673	−	0.0514946i	$-0.0163985\pi$
$967$	18.9291	+	27.0335i	0.608718	+	0.869339i	−0.389955	+	0.920834i	$0.627510\pi$
$968$	−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	$0.00680486\pi$
$971$			1.33222i			0.0427529i	−0.999771	+	0.0213765i	$0.993195\pi$
$972$		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	−0.966647	−	0.256112i	$-0.917558\pi$
$977$	−33.0259	+	23.1250i	−1.05659	+	0.739834i	−0.0899460	+	0.995947i	$0.528669\pi$
$978$		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	0.835006	−	0.550241i	$-0.185464\pi$
$983$	18.9226	+	13.2497i	0.603537	+	0.422601i	−0.231469	+	0.972842i	$0.574353\pi$
$984$		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	0.913729	−	0.406325i	$-0.133190\pi$
$991$	3.30469	+	5.72388i	0.104977	+	0.181825i	−0.808752	+	0.588150i	$0.799857\pi$
$992$	−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	−0.823769	+	0.566925i	$0.808133\pi$
$997$	−56.4430	+	26.3198i	−1.78757	+	0.833557i	−0.963799	+	0.266631i	$0.914089\pi$
$998$	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.503.3		216
3.2	odd	2		270.2.r.a.23.12	✓	216
5.2	odd	4	inner	810.2.s.a.17.12		216
15.2	even	4		270.2.r.a.77.2	yes	216
27.7	even	9		270.2.r.a.263.2	yes	216
27.20	odd	18	inner	810.2.s.a.143.12		216
135.7	odd	36		270.2.r.a.47.12	yes	216
135.47	even	36	inner	810.2.s.a.467.3		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.12	✓	216	3.2	odd	2
270.2.r.a.47.12	yes	216	135.7	odd	36
270.2.r.a.77.2	yes	216	15.2	even	4
270.2.r.a.263.2	yes	216	27.7	even	9
810.2.s.a.17.12		216	5.2	odd	4	inner
810.2.s.a.143.12		216	27.20	odd	18	inner
810.2.s.a.467.3		216	135.47	even	36	inner
810.2.s.a.503.3		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)

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