LMFDB - Embedded newform 810.2.s.a.17.12

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			17.12
Character	$\chi$	$=$	810.17
Dual form			810.2.s.a.143.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.04220 + 0.910725i) q^{5} +(-1.36563 - 0.119477i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.04220 + 0.910725i) q^{5} +(-1.36563 - 0.119477i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.46597 + 1.68847i) q^{10} +(-1.00994 + 0.178080i) q^{11} +(2.40245 - 5.15208i) q^{13} +(-1.28818 + 0.468858i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-1.81071 - 6.75766i) q^{17} +(3.88061 - 2.24047i) q^{19} +(-0.615044 + 2.14982i) q^{20} +(-0.840060 + 0.588216i) q^{22} +(-0.280375 - 3.20470i) q^{23} +(3.34116 - 3.71977i) q^{25} -5.68469i q^{26} +(-0.969337 + 0.969337i) q^{28} +(-7.70523 - 2.80447i) q^{29} +(1.58144 + 1.32699i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(-4.49697 - 5.35928i) q^{34} +(2.89771 - 0.999720i) q^{35} +(1.55405 - 0.416406i) q^{37} +(2.57016 - 3.67057i) q^{38} +(0.351133 + 2.20833i) q^{40} +(2.98153 + 8.19170i) q^{41} +(-5.02087 - 3.51565i) q^{43} +(-0.512762 + 0.888129i) q^{44} +(-1.60847 - 2.78595i) q^{46} +(-0.833651 + 9.52867i) q^{47} +(-5.04298 - 0.889213i) q^{49} +(1.45608 - 4.78329i) q^{50} +(-2.40245 - 5.15208i) q^{52} +(3.57469 + 3.57469i) q^{53} +(1.90032 - 1.28346i) q^{55} +(-0.468858 + 1.28818i) q^{56} +(-8.16853 + 0.714654i) q^{58} +(1.70697 - 9.68068i) q^{59} +(-7.76955 + 6.51943i) q^{61} +(1.99408 + 0.534312i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.214161 + 12.7095i) q^{65} +(8.44291 + 3.93699i) q^{67} +(-6.34057 - 2.95666i) q^{68} +(2.20371 - 2.13068i) q^{70} +(0.770875 + 0.445065i) q^{71} +(5.05755 + 1.35517i) q^{73} +(1.23246 - 1.03416i) q^{74} +(0.778107 - 4.41286i) q^{76} +(1.40049 - 0.122527i) q^{77} +(2.55545 - 7.02105i) q^{79} +(1.25151 + 1.85303i) q^{80} +(6.16415 + 6.16415i) q^{82} +(2.79708 + 5.99835i) q^{83} +(9.85221 + 12.1514i) q^{85} +(-6.03623 - 1.06435i) q^{86} +(-0.0893803 + 1.02162i) q^{88} +(-4.45891 - 7.72305i) q^{89} +(-3.89642 + 6.74881i) q^{91} +(-2.63516 - 1.84516i) q^{92} +(3.27145 + 8.98822i) q^{94} +(-5.88452 + 8.10966i) q^{95} +(0.255932 - 0.365508i) q^{97} +(-4.94629 + 1.32535i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$2$	0.906308	−	0.422618i	0.640856	−	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$	−2.04220	+	0.910725i	−0.913299	+	0.407289i
$5$	−2.04220	+	0.910725i	−0.913299	+	0.407289i
$6$		0			0
$7$	−1.36563	−	0.119477i	−0.516161	−	0.0451582i	−0.173900	−	0.984763i	$-0.555637\pi$
$7$	−1.36563	−	0.119477i	−0.516161	−	0.0451582i	−0.342261	+	0.939605i	$0.611193\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	−1.46597	+	1.68847i	−0.463581	+	0.533941i
$11$	−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
$13$	2.40245	−	5.15208i	0.666320	−	1.42893i	−0.224455	−	0.974484i	$-0.572060\pi$
$13$	2.40245	−	5.15208i	0.666320	−	1.42893i	0.890775	−	0.454444i	$-0.150162\pi$
$14$	−1.28818	+	0.468858i	−0.344280	+	0.125308i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−1.81071	−	6.75766i	−0.439162	−	1.63897i	−0.730906	−	0.682478i	$-0.760902\pi$
$17$	−1.81071	−	6.75766i	−0.439162	−	1.63897i	0.291745	−	0.956496i	$-0.405764\pi$
$18$		0			0
$19$	3.88061	−	2.24047i	0.890273	−	0.513999i	0.0162409	−	0.999868i	$-0.494830\pi$
$19$	3.88061	−	2.24047i	0.890273	−	0.513999i	0.874032	+	0.485869i	$0.161497\pi$
$20$	−0.615044	+	2.14982i	−0.137528	+	0.480714i
$21$		0			0
$22$	−0.840060	+	0.588216i	−0.179101	+	0.125408i
$23$	−0.280375	−	3.20470i	−0.0584621	−	0.668225i	−0.967726	−	0.252005i	$-0.918910\pi$
$23$	−0.280375	−	3.20470i	−0.0584621	−	0.668225i	0.909264	−	0.416220i	$-0.136645\pi$
$24$		0			0
$25$	3.34116	−	3.71977i	0.668232	−	0.743953i
$26$		−	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	$-0.664340\pi$
$29$	−7.70523	−	2.80447i	−1.43082	−	0.520778i	−0.937168	+	0.348879i	$0.886562\pi$
$30$		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	$0.662867\pi$
$32$	−0.573576	−	0.819152i	−0.101395	−	0.144807i
$33$		0			0
$34$	−4.49697	−	5.35928i	−0.771224	−	0.919110i
$35$	2.89771	−	0.999720i	0.489802	−	0.168984i
$36$		0			0
$37$	1.55405	−	0.416406i	0.255484	−	0.0684567i	−0.128804	−	0.991670i	$-0.541114\pi$
$37$	1.55405	−	0.416406i	0.255484	−	0.0684567i	0.384288	+	0.923213i	$0.374447\pi$
$38$	2.57016	−	3.67057i	0.416935	−	0.595445i
$39$		0			0
$40$	0.351133	+	2.20833i	0.0555190	+	0.349167i
$41$	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
$43$	−5.02087	−	3.51565i	−0.765675	−	0.536131i	0.124243	−	0.992252i	$-0.460350\pi$
$43$	−5.02087	−	3.51565i	−0.765675	−	0.536131i	−0.889918	+	0.456121i	$0.849239\pi$
$44$	−0.512762	+	0.888129i	−0.0773017	+	0.133891i
$45$		0			0
$46$	−1.60847	−	2.78595i	−0.237156	−	0.410766i
$47$	−0.833651	+	9.52867i	−0.121600	+	1.38990i	0.652957	+	0.757395i	$0.273528\pi$
$47$	−0.833651	+	9.52867i	−0.121600	+	1.38990i	−0.774557	+	0.632504i	$0.782027\pi$
$48$		0			0
$49$	−5.04298	−	0.889213i	−0.720425	−	0.127030i
$50$	1.45608	−	4.78329i	0.205920	−	0.676459i
$51$		0			0
$52$	−2.40245	−	5.15208i	−0.333160	−	0.714464i
$53$	3.57469	+	3.57469i	0.491021	+	0.491021i	0.908628	−	0.417607i	$-0.137131\pi$
$53$	3.57469	+	3.57469i	0.491021	+	0.491021i	−0.417607	+	0.908628i	$0.637131\pi$
$54$		0			0
$55$	1.90032	−	1.28346i	0.256240	−	0.173061i
$56$	−0.468858	+	1.28818i	−0.0626538	+	0.172140i
$57$		0			0
$58$	−8.16853	+	0.714654i	−1.07258	+	0.0938386i
$59$	1.70697	−	9.68068i	0.222228	−	1.26032i	−0.645686	−	0.763603i	$-0.723429\pi$
$59$	1.70697	−	9.68068i	0.222228	−	1.26032i	0.867914	−	0.496714i	$-0.165460\pi$
$60$		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	$0.502717\pi$
$62$	1.99408	+	0.534312i	0.253248	+	0.0678577i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−0.214161	+	12.7095i	−0.0265634	+	1.57642i
$66$		0			0
$67$	8.44291	+	3.93699i	1.03147	+	0.480980i	0.863254	−	0.504770i	$-0.168423\pi$
$67$	8.44291	+	3.93699i	1.03147	+	0.480980i	0.168212	+	0.985751i	$0.446201\pi$
$68$	−6.34057	−	2.95666i	−0.768907	−	0.358547i
$69$		0			0
$70$	2.20371	−	2.13068i	0.263394	−	0.254665i
$71$	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
$73$	5.05755	+	1.35517i	0.591942	+	0.158610i	0.542341	−	0.840159i	$-0.317538\pi$
$73$	5.05755	+	1.35517i	0.591942	+	0.158610i	0.0496014	+	0.998769i	$0.484205\pi$
$74$	1.23246	−	1.03416i	0.143271	−	0.120219i
$75$		0			0
$76$	0.778107	−	4.41286i	0.0892550	−	0.506190i
$77$	1.40049	−	0.122527i	0.159600	−	0.0139632i
$78$		0			0
$79$	2.55545	−	7.02105i	0.287511	−	0.789930i	−0.708902	−	0.705307i	$-0.750809\pi$
$79$	2.55545	−	7.02105i	0.287511	−	0.789930i	0.996413	−	0.0846230i	$-0.0269686\pi$
$80$	1.25151	+	1.85303i	0.139923	+	0.207175i
$81$		0			0
$82$	6.16415	+	6.16415i	0.680716	+	0.680716i
$83$	2.79708	+	5.99835i	0.307019	+	0.658405i	0.997914	−	0.0645500i	$-0.0205612\pi$
$83$	2.79708	+	5.99835i	0.307019	+	0.658405i	−0.690895	+	0.722955i	$0.742783\pi$
$84$		0			0
$85$	9.85221	+	12.1514i	1.06862	+	1.31801i
$86$	−6.03623	−	1.06435i	−0.650903	−	0.114772i
$87$		0			0
$88$	−0.0893803	+	1.02162i	−0.00952797	+	0.108905i
$89$	−4.45891	−	7.72305i	−0.472643	−	0.818642i	0.526867	−	0.849948i	$-0.323367\pi$
$89$	−4.45891	−	7.72305i	−0.472643	−	0.818642i	−0.999510	+	0.0313059i	$0.990033\pi$
$90$		0			0
$91$	−3.89642	+	6.74881i	−0.408456	+	0.707467i
$92$	−2.63516	−	1.84516i	−0.274734	−	0.192371i
$93$		0			0
$94$	3.27145	+	8.98822i	0.337424	+	0.927064i
$95$	−5.88452	+	8.10966i	−0.603739	+	0.832033i
$96$		0			0
$97$	0.255932	−	0.365508i	0.0259859	−	0.0371117i	−0.805949	−	0.591985i	$-0.798344\pi$
$97$	0.255932	−	0.365508i	0.0259859	−	0.0371117i	0.831935	+	0.554873i	$0.187233\pi$
$98$	−4.94629	+	1.32535i	−0.499650	+	0.133881i
$99$		0			0
$100$	−0.701851	−	4.95050i	−0.0701851	−	0.495050i
$101$	−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
$103$	−3.71220	−	5.30157i	−0.365774	−	0.522379i	0.593509	−	0.804828i	$-0.297742\pi$
$103$	−3.71220	−	5.30157i	−0.365774	−	0.522379i	−0.959283	+	0.282448i	$0.908853\pi$
$104$	−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	$-0.407936\pi$
$107$	12.8647	−	12.8647i	1.24368	−	1.24368i	0.958464	−	0.285213i	$-0.0920643\pi$
$108$		0			0
$109$			4.66649i			0.446969i	0.974708	+	0.223484i	$0.0717432\pi$
$109$			4.66649i			0.446969i	−0.974708	+	0.223484i	$0.928257\pi$
$110$	1.17987	−	1.96632i	0.112496	−	0.187481i
$111$		0			0
$112$	0.119477	+	1.36563i	0.0112896	+	0.129040i
$113$	1.51464	−	1.06056i	0.142485	−	0.0997691i	−0.500161	−	0.865933i	$-0.666726\pi$
$113$	1.51464	−	1.06056i	0.142485	−	0.0997691i	0.642646	+	0.766164i	$0.277837\pi$
$114$		0			0
$115$	3.49118	+	6.28928i	0.325554	+	0.586479i
$116$	−7.10118	+	4.09987i	−0.659328	+	0.380663i
$117$		0			0
$118$	−2.54420	−	9.49507i	−0.234212	−	0.874092i
$119$	1.66538	+	9.44483i	0.152665	+	0.865806i
$120$		0			0
$121$	−9.34835	+	3.40252i	−0.849850	+	0.309320i
$122$	−4.28638	+	9.19216i	−0.388070	+	0.832220i
$123$		0			0
$124$	2.03306	−	0.358483i	0.182574	−	0.0321928i
$125$	−3.43563	+	10.6394i	−0.307292	+	0.951615i
$126$		0			0
$127$	2.87299	−	10.7222i	0.254937	−	0.951437i	−0.713189	−	0.700972i	$-0.752750\pi$
$127$	2.87299	−	10.7222i	0.254937	−	0.951437i	0.968126	−	0.250465i	$-0.0805836\pi$
$128$	−0.996195	−	0.0871557i	−0.0880520	−	0.00770355i
$129$		0			0
$130$	5.17719	+	11.6093i	0.454069	+	1.01820i
$131$	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
$133$	−5.56717	+	2.59601i	−0.482735	+	0.225103i
$134$	9.31572			0.804756
$135$		0			0
$136$	−6.99605			−0.599906
$137$	2.07233	−	0.966343i	0.177051	−	0.0825603i	−0.332072	−	0.943254i	$-0.607748\pi$
$137$	2.07233	−	0.966343i	0.177051	−	0.0825603i	0.509123	+	0.860694i	$0.329970\pi$
$138$		0			0
$139$	−7.36374	+	8.77576i	−0.624584	+	0.744350i	−0.981851	−	0.189652i	$-0.939264\pi$
$139$	−7.36374	+	8.77576i	−0.624584	+	0.744350i	0.357268	+	0.934002i	$0.383708\pi$
$140$	1.09678	−	2.86238i	0.0926948	−	0.241915i
$141$		0			0
$142$	0.886742	+	0.0775799i	0.0744138	+	0.00651036i
$143$	−1.50886	+	5.63113i	−0.126177	+	0.470899i
$144$		0			0
$145$	18.2897	−	1.29005i	1.51888	−	0.107133i
$146$	5.15642	−	0.909216i	0.426748	−	0.0752472i
$147$		0			0
$148$	0.679937	−	1.45813i	0.0558905	−	0.119858i
$149$	12.5767	−	4.57756i	1.03033	−	0.375008i	0.229122	−	0.973398i	$-0.426415\pi$
$149$	12.5767	−	4.57756i	1.03033	−	0.375008i	0.801206	+	0.598389i	$0.204192\pi$
$150$		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	$0.917483\pi$
$152$	−1.15975	−	4.32826i	−0.0940684	−	0.351068i
$153$		0			0
$154$	1.21749	−	0.702919i	0.0981083	−	0.0566428i
$155$	−4.43814	−	1.26971i	−0.356480	−	0.101986i
$156$		0			0
$157$	1.74678	−	1.22311i	0.139408	−	0.0976147i	−0.501792	−	0.864988i	$-0.667326\pi$
$157$	1.74678	−	1.22311i	0.139408	−	0.0976147i	0.641200	+	0.767374i	$0.278437\pi$
$158$	−0.651197	−	7.44322i	−0.0518064	−	0.592150i
$159$		0			0
$160$	1.91738	+	1.15050i	0.151582	+	0.0909551i
$161$			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
$167$	−6.38770	−	9.12258i	−0.494295	−	0.705926i	0.492060	−	0.870561i	$-0.336244\pi$
$167$	−6.38770	−	9.12258i	−0.494295	−	0.705926i	−0.986355	+	0.164635i	$0.947355\pi$
$168$		0			0
$169$	−12.4159	−	14.7966i	−0.955066	−	1.13820i
$170$	14.0646	+	6.84922i	1.07870	+	0.525311i
$171$		0			0
$172$	−5.92049	+	1.58639i	−0.451433	+	0.120961i
$173$	2.29960	−	3.28417i	0.174835	−	0.249691i	−0.722165	−	0.691721i	$-0.756853\pi$
$173$	2.29960	−	3.28417i	0.174835	−	0.249691i	0.897000	+	0.442030i	$0.145742\pi$
$174$		0			0
$175$	−5.00722	+	4.68064i	−0.378511	+	0.353823i
$176$	0.350750	+	0.963677i	0.0264387	+	0.0726399i
$177$		0			0
$178$	−7.30505	−	5.11505i	−0.547536	−	0.383389i
$179$	5.37055	−	9.30206i	0.401414	−	0.695269i	−0.592483	−	0.805583i	$-0.701852\pi$
$179$	5.37055	−	9.30206i	0.401414	−	0.695269i	0.993897	+	0.110314i	$0.0351857\pi$
$180$		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	$0.544839\pi$
$182$	−0.679192	+	7.76319i	−0.0503450	+	0.575446i
$183$		0			0
$184$	−3.16806	−	0.558615i	−0.233553	−	0.0411817i
$185$	−2.79444	+	2.26569i	−0.205452	+	0.166577i
$186$		0			0
$187$	3.03212	+	6.50241i	0.221731	+	0.475503i
$188$	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
$193$	−19.5930	+	1.71416i	−1.41033	+	0.123388i	−0.766729	−	0.641971i	$-0.778117\pi$
$193$	−19.5930	+	1.71416i	−1.41033	+	0.123388i	−0.643603	+	0.765359i	$0.722561\pi$
$194$	0.0774823	−	0.439424i	0.00556291	−	0.0315488i
$195$		0			0
$196$	−3.92274	+	3.29157i	−0.280196	+	0.235112i
$197$	−3.54505	−	0.949894i	−0.252575	−	0.0676772i	0.130310	−	0.991473i	$-0.458403\pi$
$197$	−3.54505	−	0.949894i	−0.252575	−	0.0676772i	−0.382885	+	0.923796i	$0.625069\pi$
$198$		0			0
$199$	18.8661	+	10.8923i	1.33738	+	0.772138i	0.986419	−	0.164251i	$-0.0525208\pi$
$199$	18.8661	+	10.8923i	1.33738	+	0.772138i	0.350964	+	0.936389i	$0.385854\pi$
$200$	−2.72826	−	4.19006i	−0.192917	−	0.296282i
$201$		0			0
$202$	−1.30742	−	0.609659i	−0.0919896	−	0.0428955i
$203$	10.1874	+	4.75048i	0.715018	+	0.333419i
$204$		0			0
$205$	−13.5493	−	14.0137i	−0.946323	−	0.978761i
$206$	−5.60494	−	3.23601i	−0.390515	−	0.225464i
$207$		0			0
$208$	−5.49098	−	1.47130i	−0.380731	−	0.102017i
$209$	−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	$0.898740\pi$
$212$	5.03613	−	0.440604i	0.345883	−	0.0302608i
$213$		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
$218$	1.97214	+	4.22928i	0.133570	+	0.286443i
$219$		0			0
$220$	0.238320	−	2.28072i	0.0160675	−	0.153766i
$221$	−39.1661	−	6.90605i	−2.63460	−	0.464551i
$222$		0			0
$223$	−2.20968	+	25.2567i	−0.147971	+	1.69131i	0.452577	+	0.891725i	$0.350505\pi$
$223$	−2.20968	+	25.2567i	−0.147971	+	1.69131i	−0.600548	+	0.799589i	$0.705051\pi$
$224$	0.685425	+	1.18719i	0.0457969	+	0.0793225i
$225$		0			0
$226$	0.924515	−	1.60131i	0.0614979	−	0.106517i
$227$	17.3395	+	12.1412i	1.15086	+	0.805841i	0.983652	−	0.180080i	$-0.0576358\pi$
$227$	17.3395	+	12.1412i	1.15086	+	0.805841i	0.167209	+	0.985922i	$0.446525\pi$
$228$		0			0
$229$	−3.04795	−	8.37418i	−0.201414	−	0.553382i	0.797326	−	0.603548i	$-0.206247\pi$
$229$	−3.04795	−	8.37418i	−0.201414	−	0.553382i	−0.998741	+	0.0501667i	$0.984025\pi$
$230$	5.82205	+	4.22459i	0.383894	+	0.278561i
$231$		0			0
$232$	−4.70317	+	6.71683i	−0.308778	+	0.440981i
$233$	21.0206	−	5.63247i	1.37711	−	0.368995i	0.507038	−	0.861923i	$-0.330740\pi$
$233$	21.0206	−	5.63247i	1.37711	−	0.368995i	0.870070	+	0.492928i	$0.164074\pi$
$234$		0			0
$235$	−6.97552	−	20.2187i	−0.455033	−	1.31892i
$236$	−6.31862	−	7.53023i	−0.411307	−	0.490176i
$237$		0			0
$238$	5.50090	+	7.85610i	0.356570	+	0.509235i
$239$	22.4543	+	18.8414i	1.45245	+	1.21875i	0.930768	+	0.365609i	$0.119139\pi$
$239$	22.4543	+	18.8414i	1.45245	+	1.21875i	0.521681	+	0.853140i	$0.325305\pi$
$240$		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
$245$	11.1086	−	2.77682i	0.709702	−	0.177404i
$246$		0			0
$247$	−2.22010	−	25.3758i	−0.141261	−	1.61462i
$248$	1.69108	−	1.18410i	0.107383	−	0.0751907i
$249$		0			0
$250$	1.38266	+	11.0945i	0.0874472	+	0.701679i
$251$	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
$253$	0.853855	+	3.18663i	0.0536814	+	0.200342i
$254$	−1.92756	−	10.9318i	−0.120946	−	0.685919i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−7.39005	+	15.8480i	−0.460979	+	0.988573i	0.529165	+	0.848519i	$0.322505\pi$
$257$	−7.39005	+	15.8480i	−0.460979	+	0.988573i	−0.990144	+	0.140054i	$0.955273\pi$
$258$		0			0
$259$	−2.17201	+	0.382984i	−0.134962	+	0.0237975i
$260$	9.59841	+	8.33359i	0.595268	+	0.516827i
$261$		0			0
$262$	0.281259	−	1.04967i	0.0173763	−	0.0648491i
$263$	2.34098	+	0.204809i	0.144351	+	0.0126291i	0.159102	−	0.987262i	$-0.449140\pi$
$263$	2.34098	+	0.204809i	0.144351	+	0.0126291i	−0.0147511	+	0.999891i	$0.504696\pi$
$264$		0			0
$265$	−10.5558	−	4.04466i	−0.648436	−	0.248462i
$266$	−3.94845	+	4.70558i	−0.242095	+	0.288517i
$267$		0			0
$268$	8.44291	−	3.93699i	0.515733	−	0.240490i
$269$	−22.8011			−1.39021			−0.695103	−	0.718910i	$-0.744641\pi$
$269$	−22.8011			−1.39021			−0.695103	+	0.718910i	$0.744641\pi$
$270$		0			0
$271$	−24.2190			−1.47120			−0.735601	−	0.677415i	$-0.763100\pi$
$271$	−24.2190			−1.47120			−0.735601	+	0.677415i	$0.763100\pi$
$272$	−6.34057	+	2.95666i	−0.384454	+	0.179274i
$273$		0			0
$274$	1.46977	−	1.75161i	0.0887923	−	0.105819i
$275$	−2.71196	+	4.35175i	−0.163538	+	0.262420i
$276$		0			0
$277$	5.70183	+	0.498845i	0.342590	+	0.0299727i	0.257152	−	0.966371i	$-0.417216\pi$
$277$	5.70183	+	0.498845i	0.342590	+	0.0299727i	0.0854372	+	0.996344i	$0.472771\pi$
$278$	−2.96501	+	11.0656i	−0.177830	+	0.663670i
$279$		0			0
$280$	−0.215674	−	3.05772i	−0.0128890	−	0.182733i
$281$	−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
$283$	9.99414	−	21.4325i	0.594090	−	1.27403i	−0.347630	−	0.937632i	$-0.613013\pi$
$283$	9.99414	−	21.4325i	0.594090	−	1.27403i	0.941720	−	0.336398i	$-0.109209\pi$
$284$	0.836448	−	0.304442i	0.0496341	−	0.0180653i
$285$		0			0
$286$	1.01233	+	5.74121i	0.0598603	+	0.339485i
$287$	−3.09296	−	11.5431i	−0.182572	−	0.681367i
$288$		0			0
$289$	−27.6649	+	15.9723i	−1.62735	+	0.939550i
$290$	16.0309	−	8.89875i	0.941368	−	0.522553i
$291$		0			0
$292$	4.28905	−	3.00323i	0.250998	−	0.175751i
$293$	−2.25310	−	25.7530i	−0.131627	−	1.50451i	−0.718897	−	0.695117i	$-0.755353\pi$
$293$	−2.25310	−	25.7530i	−0.131627	−	1.50451i	0.587269	−	0.809392i	$-0.300203\pi$
$294$		0			0
$295$	5.33048	+	21.3245i	0.310352	+	1.24156i
$296$		−	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
$302$	1.19259	+	1.70319i	0.0686256	+	0.0980075i
$303$		0			0
$304$	−2.88029	−	3.43260i	−0.165196	−	0.196873i
$305$	9.92957	−	20.3899i	0.568565	−	1.16752i
$306$		0			0
$307$	25.2402	−	6.76310i	1.44054	−	0.385991i	0.547815	−	0.836600i	$-0.315460\pi$
$307$	25.2402	−	6.76310i	1.44054	−	0.385991i	0.892721	+	0.450609i	$0.148793\pi$
$308$	0.806356	−	1.15160i	0.0459464	−	0.0656182i
$309$		0			0
$310$	−4.55892	+	0.724887i	−0.258929	+	0.0411708i
$311$	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
$313$	8.61107	+	6.02953i	0.486726	+	0.340809i	0.791042	−	0.611762i	$-0.209539\pi$
$313$	8.61107	+	6.02953i	0.486726	+	0.340809i	−0.304316	+	0.952571i	$0.598428\pi$
$314$	1.06621	−	1.84673i	0.0601699	−	0.104217i
$315$		0			0
$316$	−3.73582	−	6.47064i	−0.210156	−	0.364002i
$317$	0.373396	−	4.26793i	0.0209720	−	0.239711i	−0.978472	−	0.206378i	$-0.933832\pi$
$317$	0.373396	−	4.26793i	0.0209720	−	0.239711i	0.999444	−	0.0333329i	$-0.0106121\pi$
$318$		0			0
$319$	8.28127	+	1.46021i	0.463662	+	0.0817561i
$320$	2.22396	+	0.232388i	0.124323	+	0.0129909i
$321$		0			0
$322$	1.86372	+	3.99676i	0.103861	+	0.222731i
$323$	−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
$328$	8.68425	−	0.759774i	0.479508	−	0.0419515i
$329$	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	$-0.0134674\pi$
$332$	6.39293	+	1.71298i	0.350858	+	0.0940121i
$333$		0			0
$334$	−9.64459	−	5.56830i	−0.527728	−	0.304684i
$335$	−20.8276	−	0.350954i	−1.13794	−	0.0191747i
$336$		0			0
$337$	0.246840	+	0.115103i	0.0134462	+	0.00627009i	0.429330	−	0.903148i	$-0.358750\pi$
$337$	0.246840	+	0.115103i	0.0134462	+	0.00627009i	−0.415884	+	0.909418i	$0.636528\pi$
$338$	−17.5059	−	8.16315i	−0.952197	−	0.444017i
$339$		0			0
$340$	15.6414	+	0.263564i	0.848275	+	0.0142938i
$341$	−1.83347	−	1.05856i	−0.0992882	−	0.0573241i
$342$		0			0
$343$	16.0496	+	4.30047i	0.866596	+	0.232204i
$344$	−4.69535	+	3.93987i	−0.253156	+	0.212423i
$345$		0			0
$346$	0.696196	−	3.94832i	0.0374277	−	0.212263i
$347$	36.3308	−	3.17854i	1.95034	−	0.170633i	0.957359	−	0.288899i	$-0.0932893\pi$
$347$	36.3308	−	3.17854i	1.95034	−	0.170633i	0.992982	+	0.118267i	$0.0377338\pi$
$348$		0			0
$349$	−8.59979	+	23.6277i	−0.460336	+	1.26476i	0.464898	+	0.885364i	$0.346091\pi$
$349$	−8.59979	+	23.6277i	−0.460336	+	1.26476i	−0.925234	+	0.379398i	$0.876131\pi$
$350$	−2.55996	+	6.35825i	−0.136836	+	0.339863i
$351$		0			0
$352$	0.725155	+	0.725155i	0.0386509	+	0.0386509i
$353$	−3.61855	−	7.76000i	−0.192596	−	0.413023i	0.786168	−	0.618012i	$-0.212062\pi$
$353$	−3.61855	−	7.76000i	−0.192596	−	0.413023i	−0.978764	+	0.204989i	$0.934284\pi$
$354$		0			0
$355$	−1.97961	−	0.206856i	−0.105067	−	0.0109788i
$356$	−8.78233	−	1.54856i	−0.465463	−	0.0820736i
$357$		0			0
$358$	0.936148	−	10.7002i	0.0494770	−	0.565524i
$359$	1.17311	+	2.03189i	0.0619144	+	0.107239i	0.895321	−	0.445421i	$-0.146946\pi$
$359$	1.17311	+	2.03189i	0.0619144	+	0.107239i	−0.833407	+	0.552660i	$0.813613\pi$
$360$		0			0
$361$	0.539412	−	0.934288i	0.0283901	−	0.0491731i
$362$	17.3518	+	12.1499i	0.911990	+	0.638583i
$363$		0			0
$364$	2.66531	+	7.32288i	0.139700	+	0.383823i
$365$	−11.5627	+	1.83852i	−0.605220	+	0.0962326i
$366$		0			0
$367$	−2.79412	+	3.99042i	−0.145852	+	0.208298i	−0.885430	−	0.464772i	$-0.846136\pi$
$367$	−2.79412	+	3.99042i	−0.145852	+	0.208298i	0.739578	+	0.673071i	$0.235025\pi$
$368$	−3.10732	+	0.832604i	−0.161980	+	0.0434025i
$369$		0			0
$370$	−1.57510	+	3.23440i	−0.0818857	+	0.168148i
$371$	−4.45461	−	5.30880i	−0.231272	−	0.275619i
$372$		0			0
$373$	−15.0493	−	21.4927i	−0.779226	−	1.11285i	−0.990780	−	0.135483i	$-0.956741\pi$
$373$	−15.0493	−	21.4927i	−0.779226	−	1.11285i	0.211554	−	0.977366i	$-0.432148\pi$
$374$	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	$-0.109955\pi$
$380$	2.42986	+	9.72059i	0.124649	+	0.498656i
$381$		0			0
$382$	0.0173416	+	0.198215i	0.000887273	+	0.0101416i
$383$	−10.6548	+	7.46056i	−0.544434	+	0.381217i	−0.813196	−	0.581990i	$-0.802274\pi$
$383$	−10.6548	+	7.46056i	−0.544434	+	0.381217i	0.268762	+	0.963207i	$0.413386\pi$
$384$		0			0
$385$	−2.74849	+	1.52568i	−0.140076	+	0.0777561i
$386$	−17.0328	+	9.83390i	−0.866947	+	0.500532i
$387$		0			0
$388$	−0.115486	−	0.430999i	−0.00586291	−	0.0218807i
$389$	−4.21015	−	23.8769i	−0.213463	−	1.21061i	−0.883554	−	0.468330i	$-0.844856\pi$
$389$	−4.21015	−	23.8769i	−0.213463	−	1.21061i	0.670091	−	0.742279i	$-0.266255\pi$
$390$		0			0
$391$	−21.1486	+	7.69745i	−1.06953	+	0.389277i
$392$	−2.16413	+	4.64100i	−0.109305	+	0.234406i
$393$		0			0
$394$	−3.61435	+	0.637308i	−0.182088	+	0.0321071i
$395$	1.17550	+	16.6657i	0.0591460	+	0.838543i
$396$		0			0
$397$	−9.15103	+	34.1521i	−0.459277	+	1.71404i	0.215923	+	0.976410i	$0.430724\pi$
$397$	−9.15103	+	34.1521i	−0.459277	+	1.71404i	−0.675200	+	0.737634i	$0.735943\pi$
$398$	21.7018	+	1.89866i	1.08781	+	0.0951713i
$399$		0			0
$400$	−4.24344	−	2.64447i	−0.212172	−	0.132223i
$401$	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
$403$	10.6361	−	4.95968i	0.529820	−	0.247059i
$404$	−1.44258			−0.0717708
$405$		0			0
$406$	11.2406			0.557862
$407$	−1.49535	+	0.697292i	−0.0741216	+	0.0345635i
$408$		0			0
$409$	9.13725	−	10.8893i	0.451808	−	0.538444i	−0.491274	−	0.871005i	$-0.663469\pi$
$409$	9.13725	−	10.8893i	0.451808	−	0.538444i	0.943082	+	0.332562i	$0.107913\pi$
$410$	−18.2023	−	6.97458i	−0.898946	−	0.344450i
$411$		0			0
$412$	−6.44740	−	0.564074i	−0.317640	−	0.0277899i
$413$	−3.48771	+	13.0163i	−0.171619	+	0.640491i
$414$		0			0
$415$	−11.1750	−	9.70247i	−0.548561	−	0.476275i
$416$	−5.59832	+	0.987135i	−0.274480	+	0.0483983i
$417$		0			0
$418$	−1.94206	+	4.16476i	−0.0949893	+	0.203705i
$419$	−11.2945	+	4.11085i	−0.551770	+	0.200828i	−0.602833	−	0.797868i	$-0.705961\pi$
$419$	−11.2945	+	4.11085i	−0.551770	+	0.200828i	0.0510626	+	0.998695i	$0.483739\pi$
$420$		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	$0.894630\pi$
$422$	3.55627	+	13.2722i	0.173117	+	0.646080i
$423$		0			0
$424$	4.37808	−	2.52768i	0.212618	−	0.122755i
$425$	−31.1868	−	15.8430i	−1.51278	−	0.768499i
$426$		0			0
$427$	11.3893	−	7.97486i	0.551166	−	0.385931i
$428$	−1.58566	−	18.1242i	−0.0766458	−	0.876066i
$429$		0			0
$430$	13.2965	−	3.32373i	0.641215	−	0.160285i
$431$		−	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	−0.657912	−	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
$437$	−8.26805	−	11.8080i	−0.395514	−	0.564853i
$438$		0			0
$439$	−9.97813	−	11.8915i	−0.476230	−	0.567549i	0.473430	−	0.880831i	$-0.343016\pi$
$439$	−9.97813	−	11.8915i	−0.476230	−	0.567549i	−0.949660	+	0.313283i	$0.898571\pi$
$440$	−0.747884	−	2.16775i	−0.0356540	−	0.103344i
$441$		0			0
$442$	−38.4152	+	10.2933i	−1.82722	+	0.489603i
$443$	12.5659	−	17.9460i	0.597025	−	0.852640i	−0.400959	−	0.916096i	$-0.631323\pi$
$443$	12.5659	−	17.9460i	0.597025	−	0.852640i	0.997985	+	0.0634554i	$0.0202120\pi$
$444$		0			0
$445$	16.1396	+	11.7112i	0.765088	+	0.555163i
$446$	8.67130	+	23.8242i	0.410598	+	1.12811i
$447$		0			0
$448$	1.12293	+	0.786287i	0.0530537	+	0.0371486i
$449$	−12.6539	+	21.9172i	−0.597175	+	1.03434i	0.396061	+	0.918224i	$0.370377\pi$
$449$	−12.6539	+	21.9172i	−0.597175	+	1.03434i	−0.993236	+	0.116113i	$0.962957\pi$
$450$		0			0
$451$	−4.46996	−	7.74220i	−0.210482	−	0.364566i
$452$	0.161154	−	1.84199i	0.00758003	−	0.0866401i
$453$		0			0
$454$	20.8460	+	3.67571i	0.978351	+	0.172510i
$455$	1.81097	−	17.3310i	0.0848995	−	0.812489i
$456$		0			0
$457$	−13.0314	−	27.9459i	−0.609582	−	1.30725i	−0.932618	−	0.360866i	$-0.882481\pi$
$457$	−13.0314	−	27.9459i	−0.609582	−	1.30725i	0.323036	−	0.946387i	$-0.395296\pi$
$458$	−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
$463$	26.2994	−	2.30090i	1.22224	−	0.106932i	0.542289	−	0.840192i	$-0.317558\pi$
$463$	26.2994	−	2.30090i	1.22224	−	0.106932i	0.679948	+	0.733260i	$0.262002\pi$
$464$	−1.42387	+	8.07516i	−0.0661014	+	0.374880i
$465$		0			0
$466$	16.6708	−	13.9885i	0.772260	−	0.648003i
$467$	−7.67904	−	2.05759i	−0.355343	−	0.0952140i	0.0767312	−	0.997052i	$-0.475552\pi$
$467$	−7.67904	−	2.05759i	−0.355343	−	0.0952140i	−0.432075	+	0.901838i	$0.642218\pi$
$468$		0			0
$469$	−11.0595	−	6.38523i	−0.510682	−	0.294842i
$470$	−14.8667	−	15.3764i	−0.685752	−	0.709258i
$471$		0			0
$472$	−8.90903	−	4.15435i	−0.410071	−	0.191219i
$473$	5.69686	+	2.65649i	0.261942	+	0.122145i
$474$		0			0
$475$	4.63170	−	21.9207i	0.212517	−	1.00579i
$476$	8.30564	+	4.79526i	0.380688	+	0.219791i
$477$		0			0
$478$	28.3133	+	7.58651i	1.29502	+	0.346999i
$479$	−9.93768	+	8.33870i	−0.454064	+	0.381005i	−0.840941	−	0.541126i	$-0.817998\pi$
$479$	−9.93768	+	8.33870i	−0.454064	+	0.381005i	0.386877	+	0.922131i	$0.373554\pi$
$480$		0			0
$481$	1.58817	−	9.00697i	0.0724144	−	0.410682i
$482$	0.325775	−	0.0285016i	0.0148386	−	0.00129821i
$483$		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	$0.802549\pi$
$488$	4.28638	+	9.19216i	0.194035	+	0.416110i
$489$		0			0
$490$	8.89427	−	7.21134i	0.401802	−	0.325775i
$491$	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
$493$	−4.99975	+	57.1474i	−0.225178	+	2.57379i
$494$	−12.7364	−	22.0600i	−0.573036	−	0.992528i
$495$		0			0
$496$	1.03221	−	1.78784i	0.0463477	−	0.0802765i
$497$	−0.999557	−	0.699897i	−0.0448363	−	0.0313947i
$498$		0			0
$499$	−12.2374	−	33.6221i	−0.547823	−	1.50513i	−0.836644	−	0.547747i	$-0.815485\pi$
$499$	−12.2374	−	33.6221i	−0.547823	−	1.50513i	0.288821	−	0.957383i	$-0.406737\pi$
$500$	5.94186	+	9.47071i	0.265728	+	0.423543i
$501$		0			0
$502$	3.98696	−	5.69398i	0.177947	−	0.254135i
$503$	−25.1757	+	6.74582i	−1.12253	+	0.300781i	−0.771907	−	0.635735i	$-0.780697\pi$
$503$	−25.1757	+	6.74582i	−1.12253	+	0.300781i	−0.350624	+	0.936516i	$0.614030\pi$
$504$		0			0
$505$	2.90009	+	1.41230i	0.129052	+	0.0628465i
$506$	2.12058	+	2.52721i	0.0942715	+	0.112348i
$507$		0			0
$508$	−6.36692	−	9.09291i	−0.282487	−	0.403433i
$509$	18.0808	+	15.1716i	0.801417	+	0.672469i	0.948543	−	0.316649i	$-0.102558\pi$
$509$	18.0808	+	15.1716i	0.801417	+	0.672469i	−0.147126	+	0.989118i	$0.547002\pi$
$510$		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
$515$	12.4093	+	7.44607i	0.546820	+	0.328113i
$516$		0			0
$517$	−0.854928	−	9.77187i	−0.0375997	−	0.429766i
$518$	−1.80665	+	1.26503i	−0.0793798	+	0.0555823i
$519$		0			0
$520$	12.2210	+	3.49633i	0.535928	+	0.153324i
$521$	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
$523$	−4.25218	−	15.8693i	−0.185935	−	0.693918i	−0.994429	−	0.105413i	$-0.966384\pi$
$523$	−4.25218	−	15.8693i	−0.185935	−	0.693918i	0.808494	−	0.588505i	$-0.200283\pi$
$524$	−0.188704	−	1.07019i	−0.00824357	−	0.0467516i
$525$		0			0
$526$	2.20821	−	0.803721i	0.0962823	−	0.0350439i
$527$	6.10379	−	13.0896i	0.265885	−	0.570193i
$528$		0			0
$529$	12.4591	−	2.19688i	0.541701	−	0.0955165i
$530$	−11.2761	+	0.795354i	−0.489804	+	0.0345480i
$531$		0			0
$532$	−1.58985	+	5.93339i	−0.0689286	+	0.257245i
$533$	49.3672	+	4.31907i	2.13833	+	0.187080i
$534$		0			0
$535$	−14.5561	+	37.9885i	−0.629314	+	1.64239i
$536$	5.98803	−	7.13626i	0.258644	−	0.308239i
$537$		0			0
$538$	−20.6648	+	9.63615i	−0.890922	+	0.415444i
$539$	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	$0.417885\pi$
$542$	−21.9499	+	10.2354i	−0.942829	+	0.439649i
$543$		0			0
$544$	−4.49697	+	5.35928i	−0.192806	+	0.229777i
$545$	−4.24989	−	9.52990i	−0.182045	−	0.408216i
$546$		0			0
$547$	31.7053	+	2.77386i	1.35562	+	0.118602i	0.741682	−	0.670751i	$-0.234028\pi$
$547$	31.7053	+	2.77386i	1.35562	+	0.118602i	0.613940	+	0.789353i	$0.289584\pi$
$548$	0.591806	−	2.20865i	0.0252807	−	0.0943488i
$549$		0			0
$550$	−0.618746	+	5.09015i	−0.0263834	+	0.217045i
$551$	−36.1843	+	6.38027i	−1.54150	+	0.271809i
$552$		0			0
$553$	−4.32867	+	9.28286i	−0.184074	+	0.394747i
$554$	5.37843	−	1.95759i	0.228508	−	0.0831700i
$555$		0			0
$556$	1.98930	+	11.2819i	0.0843652	+	0.478459i
$557$	−9.89332	−	36.9224i	−0.419193	−	1.56445i	−0.776285	−	0.630382i	$-0.782898\pi$
$557$	−9.89332	−	36.9224i	−0.419193	−	1.56445i	0.357092	−	0.934069i	$-0.383768\pi$
$558$		0			0
$559$	−30.1753	+	17.4217i	−1.27628	+	0.736859i
$560$	−1.48771	−	2.68008i	−0.0628674	−	0.113254i
$561$		0			0
$562$	−2.45468	+	1.71879i	−0.103544	+	0.0725026i
$563$	−2.26849	−	25.9290i	−0.0956055	−	1.09278i	−0.880788	−	0.473511i	$-0.842986\pi$
$563$	−2.26849	−	25.9290i	−0.0956055	−	1.09278i	0.785182	−	0.619265i	$-0.212569\pi$
$564$		0			0
$565$	−2.12731	+	3.54530i	−0.0894967	+	0.149152i
$566$		−	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	$-0.438719\pi$
$569$	−6.98942	−	2.54394i	−0.293012	−	0.106648i	−0.484344	+	0.874878i	$0.660942\pi$
$570$		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	$0.958228\pi$
$572$	3.34382	+	4.77547i	0.139812	+	0.199673i
$573$		0			0
$574$	−7.68149	−	9.15444i	−0.320619	−	0.382099i
$575$	−12.8575	−	9.66447i	−0.536195	−	0.403036i
$576$		0			0
$577$	−29.4311	+	7.88604i	−1.22523	+	0.328300i	−0.812722	−	0.582652i	$-0.802015\pi$
$577$	−29.4311	+	7.88604i	−1.22523	+	0.328300i	−0.412511	+	0.910952i	$0.635348\pi$
$578$	−18.3227	+	26.1676i	−0.762125	+	1.08843i
$579$		0			0
$580$	10.7682	−	14.8400i	0.447124	−	0.616196i
$581$	−3.10311	−	8.52574i	−0.128739	−	0.353707i
$582$		0			0
$583$	−4.24681	−	2.97365i	−0.175885	−	0.123156i
$584$	2.61798	−	4.53448i	0.108333	−	0.187638i
$585$		0			0
$586$	−12.9257	−	22.3880i	−0.533956	−	0.924839i
$587$	1.01547	−	11.6068i	0.0419128	−	0.479065i	−0.946012	−	0.324131i	$-0.894928\pi$
$587$	1.01547	−	11.6068i	0.0419128	−	0.479065i	0.987925	−	0.154934i	$-0.0495164\pi$
$588$		0			0
$589$	9.11002	+	1.60634i	0.375372	+	0.0661882i
$590$	13.8432	+	17.0738i	0.569914	+	0.702916i
$591$		0			0
$592$	−0.679937	−	1.45813i	−0.0279453	−	0.0599288i
$593$	18.3363	+	18.3363i	0.752980	+	0.752980i	0.975034	−	0.222055i	$-0.0712763\pi$
$593$	18.3363	+	18.3363i	0.752980	+	0.752980i	−0.222055	+	0.975034i	$0.571276\pi$
$594$		0			0
$595$	−12.0027	−	17.7715i	−0.492062	−	0.728561i
$596$	4.57756	−	12.5767i	0.187504	−	0.515164i
$597$		0			0
$598$	−18.2177	+	1.59384i	−0.744977	+	0.0651770i
$599$	−6.98391	+	39.6077i	−0.285355	+	1.61833i	0.418661	+	0.908142i	$0.362499\pi$
$599$	−6.98391	+	39.6077i	−0.285355	+	1.61833i	−0.704016	+	0.710184i	$0.748612\pi$
$600$		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	$0.0288468\pi$
$602$	8.11610	+	2.17470i	0.330788	+	0.0886343i
$603$		0			0
$604$	1.80065	+	1.03961i	0.0732674	+	0.0423009i
$605$	15.9924	−	15.4624i	0.650185	−	0.628636i
$606$		0			0
$607$	18.9990	+	8.85936i	0.771144	+	0.359590i	0.768038	−	0.640405i	$-0.221233\pi$
$607$	18.9990	+	8.85936i	0.771144	+	0.359590i	0.00310650	+	0.999995i	$0.499011\pi$
$608$	−4.06111	−	1.89373i	−0.164700	−	0.0768008i
$609$		0			0
$610$	0.382099	−	22.6759i	0.0154707	−	0.918122i
$611$	47.0896	+	27.1872i	1.90504	+	1.09988i
$612$		0			0
$613$	−6.95980	−	1.86487i	−0.281104	−	0.0753215i	0.115512	−	0.993306i	$-0.463149\pi$
$613$	−6.95980	−	1.86487i	−0.281104	−	0.0753215i	−0.396616	+	0.917984i	$0.629816\pi$
$614$	20.0172	−	16.7964i	0.807829	−	0.677849i
$615$		0			0
$616$	0.244121	−	1.38448i	0.00983593	−	0.0557823i
$617$	33.4274	−	2.92452i	1.34574	−	0.117737i	0.608597	−	0.793479i	$-0.291732\pi$
$617$	33.4274	−	2.92452i	1.34574	−	0.117737i	0.737138	+	0.675743i	$0.236177\pi$
$618$		0			0
$619$	3.68119	−	10.1140i	0.147960	−	0.406516i	−0.843467	−	0.537181i	$-0.819489\pi$
$619$	3.68119	−	10.1140i	0.147960	−	0.406516i	0.991427	+	0.130665i	$0.0417114\pi$
$620$	−3.82543	+	2.58365i	−0.153633	+	0.103762i
$621$		0			0
$622$	13.6739	+	13.6739i	0.548274	+	0.548274i
$623$	5.16650	+	11.0796i	0.206991	+	0.443895i
$624$		0			0
$625$	−2.67332	−	24.8567i	−0.106933	−	0.994266i
$626$	10.3525	+	1.82542i	0.413768	+	0.0729584i
$627$		0			0
$628$	0.185853	−	2.12431i	0.00741635	−	0.0847692i
$629$	−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	$0.257855\pi$
$632$	−6.12041	−	4.28556i	−0.243457	−	0.170470i
$633$		0			0
$634$	−1.46530	−	4.02586i	−0.0581943	−	0.159888i
$635$	3.89771	+	24.5133i	0.154676	+	0.972780i
$636$		0			0
$637$	−16.6968	+	23.8455i	−0.661551	+	0.944793i
$638$	8.12249	−	2.17641i	0.321572	−	0.0861650i
$639$		0			0
$640$	2.11380	−	0.729270i	0.0835554	−	0.0288269i
$641$	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
$643$	10.5460	+	15.0612i	0.415894	+	0.593958i	0.971369	−	0.237575i	$-0.0763526\pi$
$643$	10.5460	+	15.0612i	0.415894	+	0.593958i	−0.555476	+	0.831533i	$0.687464\pi$
$644$	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	$-0.706466\pi$
$647$	4.90447	−	4.90447i	0.192815	−	0.192815i	0.796911	+	0.604097i	$0.206466\pi$
$648$		0			0
$649$			10.0809i			0.395711i
$650$	−21.1457	−	18.9934i	−0.829403	−	0.744984i
$651$		0			0
$652$	−1.06599	−	12.1844i	−0.0417476	−	0.477177i
$653$	9.58730	−	6.71310i	0.375180	−	0.262704i	−0.370744	−	0.928735i	$-0.620897\pi$
$653$	9.58730	−	6.71310i	0.375180	−	0.262704i	0.745924	+	0.666031i	$0.232008\pi$
$654$		0			0
$655$	−0.668371	+	2.33621i	−0.0261154	+	0.0912835i
$656$	7.54951	−	4.35871i	0.294759	−	0.170179i
$657$		0			0
$658$	−3.39370	−	12.6655i	−0.132300	−	0.493752i
$659$	1.90453	+	10.8012i	0.0741901	+	0.420753i	0.999170	+	0.0407368i	$0.0129705\pi$
$659$	1.90453	+	10.8012i	0.0741901	+	0.420753i	−0.924980	+	0.380016i	$0.875918\pi$
$660$		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	$0.294106\pi$
$662$	12.1876	−	26.1363i	0.473683	−	1.01582i
$663$		0			0
$664$	6.51790	−	1.14928i	0.252944	−	0.0446008i
$665$	9.00502	−	10.3717i	0.349200	−	0.402199i
$666$		0			0
$667$	−6.82713	+	25.4792i	−0.264348	+	0.986559i
$668$	−11.0942	−	0.970619i	−0.429249	−	0.0375544i
$669$		0			0
$670$	−19.0246	+	8.48407i	−0.734983	+	0.327768i
$671$	6.68583	−	7.96786i	0.258103	−	0.307596i
$672$		0			0
$673$	−34.2048	+	15.9499i	−1.31850	+	0.614825i	−0.949255	−	0.314508i	$-0.898160\pi$
$673$	−34.2048	+	15.9499i	−1.31850	+	0.614825i	−0.369242	+	0.929333i	$0.620383\pi$
$674$	0.272358			0.0104908
$675$		0			0
$676$	−19.3157			−0.742910
$677$	15.8639	−	7.39747i	0.609700	−	0.284308i	−0.0931429	−	0.995653i	$-0.529691\pi$
$677$	15.8639	−	7.39747i	0.609700	−	0.284308i	0.702843	+	0.711345i	$0.251914\pi$
$678$		0			0
$679$	−0.393179	+	0.468572i	−0.0150888	+	0.0179821i
$680$	14.2873	−	6.37148i	0.547894	−	0.244335i
$681$		0			0
$682$	−2.10906	−	0.184519i	−0.0807600	−	0.00706559i
$683$	−11.5792	+	43.2142i	−0.443066	+	1.65355i	0.277926	+	0.960603i	$0.410353\pi$
$683$	−11.5792	+	43.2142i	−0.443066	+	1.65355i	−0.720992	+	0.692943i	$0.756314\pi$
$684$		0			0
$685$	−3.35204	+	3.86079i	−0.128075	+	0.147513i
$686$	16.3633	−	2.88530i	0.624755	−	0.110161i
$687$		0			0
$688$	−2.59037	+	5.55507i	−0.0987571	+	0.211785i
$689$	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	$0.953785\pi$
$692$	−1.03767	−	3.87262i	−0.0394461	−	0.147215i
$693$		0			0
$694$	31.5836	−	18.2348i	1.19890	−	0.692184i
$695$	7.04591	−	24.6282i	0.267267	−	0.934200i
$696$		0			0
$697$	49.9580	−	34.9810i	1.89230	−	1.32500i
$698$	2.19145	+	25.0484i	0.0829477	+	0.948096i
$699$		0			0
$700$	0.366998	+	6.84442i	0.0138712	+	0.258695i
$701$			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
$707$	1.13428	+	1.61992i	0.0426589	+	0.0609233i
$708$		0			0
$709$	−17.3164	−	20.6369i	−0.650332	−	0.775035i	0.335632	−	0.941993i	$-0.391050\pi$
$709$	−17.3164	−	20.6369i	−0.650332	−	0.775035i	−0.985964	+	0.166958i	$0.946606\pi$
$710$	−1.88156	+	0.649145i	−0.0706136	+	0.0243620i
$711$		0			0
$712$	−8.61395	+	2.30810i	−0.322821	+	0.0864997i
$713$	3.80919	−	5.44009i	0.142655	−	0.203733i
$714$		0			0
$715$	−2.04703	−	12.8741i	−0.0765545	−	0.481462i
$716$	−3.67367	−	10.0933i	−0.137292	−	0.377205i
$717$		0			0
$718$	1.92191	+	1.34574i	0.0717251	+	0.0502224i
$719$	−4.74675	+	8.22161i	−0.177024	+	0.306614i	−0.940860	−	0.338796i	$-0.889980\pi$
$719$	−4.74675	+	8.22161i	−0.177024	+	0.306614i	0.763836	+	0.645410i	$0.223314\pi$
$720$		0			0
$721$	4.43609	+	7.68353i	0.165208	+	0.286149i
$722$	0.0940257	−	1.07472i	0.00349927	−	0.0399969i
$723$		0			0
$724$	20.8608	+	3.67833i	0.775286	+	0.136704i
$725$	−36.1764	+	19.2915i	−1.34356	+	0.716467i
$726$		0			0
$727$	1.98498	+	4.25681i	0.0736189	+	0.157876i	0.939673	−	0.342074i	$-0.111129\pi$
$727$	1.98498	+	4.25681i	0.0736189	+	0.157876i	−0.866054	+	0.499950i	$0.833352\pi$
$728$	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
$733$	11.3003	−	0.988648i	0.417386	−	0.0365165i	0.123471	−	0.992348i	$-0.460597\pi$
$733$	11.3003	−	0.988648i	0.417386	−	0.0365165i	0.293915	+	0.955832i	$0.405042\pi$
$734$	−0.845910	+	4.79739i	−0.0312231	+	0.177075i
$735$		0			0
$736$	−2.46432	+	2.06781i	−0.0908359	+	0.0762204i
$737$	−9.22796	−	2.47263i	−0.339916	−	0.0910803i
$738$		0			0
$739$	11.8963	+	6.86835i	0.437614	+	0.252656i	0.702585	−	0.711600i	$-0.252029\pi$
$739$	11.8963	+	6.86835i	0.437614	+	0.252656i	−0.264971	+	0.964256i	$0.585362\pi$
$740$	−0.0606114	+	3.59703i	−0.00222812	+	0.132229i
$741$		0			0
$742$	−6.28085	−	2.92881i	−0.230577	−	0.107520i
$743$	8.32210	+	3.88066i	0.305308	+	0.142368i	0.569234	−	0.822175i	$-0.307240\pi$
$743$	8.32210	+	3.88066i	0.305308	+	0.142368i	−0.263926	+	0.964543i	$0.585018\pi$
$744$		0			0
$745$	−21.5153	+	20.8023i	−0.788261	+	0.762136i
$746$	−22.7225	−	13.1189i	−0.831932	−	0.480316i
$747$		0			0
$748$	6.93014	+	1.85693i	0.253391	+	0.0678959i
$749$	−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	$0.944982\pi$
$752$	9.52867	−	0.833651i	0.347475	−	0.0304001i
$753$		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	$0.588120\pi$
$758$	−5.57174	−	11.9486i	−0.202375	−	0.433994i
$759$		0			0
$760$	6.31030	+	7.78295i	0.228899	+	0.282317i
$761$	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
$763$	0.557540	−	6.37271i	0.0201843	−	0.230708i
$764$	0.0994862	+	0.172315i	0.00359929	+	0.00623414i
$765$		0			0
$766$	−6.50355	+	11.2645i	−0.234983	+	0.407002i
$767$	−45.7747	−	32.0518i	−1.65283	−	1.15732i
$768$		0			0
$769$	14.4008	+	39.5659i	0.519306	+	1.42678i	0.871287	+	0.490774i	$0.163286\pi$
$769$	14.4008	+	39.5659i	0.519306	+	1.42678i	−0.351981	+	0.936007i	$0.614492\pi$
$770$	−1.84619	+	2.54430i	−0.0665322	+	0.0916903i
$771$		0			0
$772$	−11.2810	+	16.1109i	−0.406012	+	0.579845i
$773$	−36.0013	+	9.64653i	−1.29488	+	0.346961i	−0.839511	−	0.543343i	$-0.817158\pi$
$773$	−36.0013	+	9.64653i	−1.29488	+	0.346961i	−0.455367	+	0.890304i	$0.650492\pi$
$774$		0			0
$775$	10.2199	−	1.44892i	0.367110	−	0.0520466i
$776$	−0.286814	−	0.341811i	−0.0102960	−	0.0122703i
$777$		0			0
$778$	−13.9065	−	19.8606i	−0.498573	−	0.712036i
$779$	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
$785$	−2.45336	+	4.08867i	−0.0875641	+	0.145931i
$786$		0			0
$787$	3.92459	+	44.8583i	0.139897	+	1.59902i	0.664241	+	0.747519i	$0.268755\pi$
$787$	3.92459	+	44.8583i	0.139897	+	1.59902i	−0.524344	+	0.851506i	$0.675690\pi$
$788$	−3.00638	+	2.10509i	−0.107098	+	0.0749907i
$789$		0			0
$790$	8.10860	+	14.6075i	0.288491	+	0.519710i
$791$	−2.19515	+	1.26737i	−0.0780506	+	0.0450625i
$792$		0			0
$793$	14.9226	+	55.6919i	0.529917	+	1.97768i
$794$	6.13965	+	34.8197i	0.217888	+	1.23571i
$795$		0			0
$796$	20.4709	−	7.45080i	0.725572	−	0.264087i
$797$	−8.10379	+	17.3786i	−0.287051	+	0.615583i	−0.995968	−	0.0897092i	$-0.971406\pi$
$797$	−8.10379	+	17.3786i	−0.287051	+	0.615583i	0.708917	+	0.705292i	$0.249184\pi$
$798$		0			0
$799$	65.9010	−	11.6201i	2.33141	−	0.411091i
$800$	−4.96346	−	0.603347i	−0.175485	−	0.0213315i
$801$		0			0
$802$	1.04526	−	3.90098i	0.0369096	−	0.137748i
$803$	−5.34917	−	0.467992i	−0.188768	−	0.0165151i
$804$		0			0
$805$	−4.01624	−	9.00597i	−0.141554	−	0.317419i
$806$	7.54350	−	8.98999i	0.265708	−	0.316659i
$807$		0			0
$808$	−1.30742	+	0.609659i	−0.0459948	+	0.0214477i
$809$	18.1480			0.638050			0.319025	−	0.947746i	$-0.396645\pi$
$809$	18.1480			0.638050			0.319025	+	0.947746i	$0.396645\pi$
$810$		0			0
$811$	−3.73964			−0.131317			−0.0656583	−	0.997842i	$-0.520915\pi$
$811$	−3.73964			−0.131317			−0.0656583	+	0.997842i	$0.520915\pi$
$812$	10.1874	−	4.75048i	0.357509	−	0.166709i
$813$		0			0
$814$	−1.06056	+	1.26392i	−0.0371725	+	0.0443004i
$815$	−9.78562	+	25.5386i	−0.342775	+	0.894576i
$816$		0			0
$817$	−27.3607	−	2.39375i	−0.957230	−	0.0837468i
$818$	3.67912	−	13.7307i	0.128637	−	0.480082i
$819$		0			0
$820$	−19.4444	+	1.37150i	−0.679029	+	0.0478948i
$821$	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
$823$	−2.02320	+	4.33877i	−0.0705244	+	0.151240i	−0.938410	−	0.345525i	$-0.887701\pi$
$823$	−2.02320	+	4.33877i	−0.0705244	+	0.151240i	0.867885	+	0.496765i	$0.165479\pi$
$824$	−6.08171	+	2.21356i	−0.211867	+	0.0771131i
$825$		0			0
$826$	2.33999	+	13.2708i	0.0814188	+	0.461749i
$827$	−7.29210	−	27.2145i	−0.253571	−	0.946340i	−0.968880	−	0.247532i	$-0.920381\pi$
$827$	−7.29210	−	27.2145i	−0.253571	−	0.946340i	0.715309	−	0.698808i	$-0.246286\pi$
$828$		0			0
$829$	6.06867	−	3.50375i	0.210774	−	0.121690i	−0.390897	−	0.920434i	$-0.627835\pi$
$829$	6.06867	−	3.50375i	0.210774	−	0.121690i	0.601671	+	0.798744i	$0.294502\pi$
$830$	−14.2285	−	4.07064i	−0.493877	−	0.141294i
$831$		0			0
$832$	−4.65662	+	3.26060i	−0.161439	+	0.113041i
$833$	3.12237	+	35.6888i	0.108184	+	1.23654i
$834$		0			0
$835$	21.3531	+	12.8127i	0.738955	+	0.443401i
$836$			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	$-0.264262\pi$
$839$	20.7733	+	7.56086i	0.717173	+	0.261030i	0.0424480	+	0.999099i	$0.486484\pi$
$840$		0			0
$841$	29.2902	+	24.5774i	1.01001	+	0.847496i
$842$	3.66852	+	5.23919i	0.126426	+	0.180555i
$843$		0			0
$844$	8.83214	+	10.5257i	0.304015	+	0.362311i
$845$	38.8314	+	18.9103i	1.33584	+	0.650533i
$846$		0			0
$847$	13.1729	−	3.52968i	0.452627	−	0.121281i
$848$	2.89964	−	4.14112i	0.0995741	−	0.142206i
$849$		0			0
$850$	−34.9604	−	1.17853i	−1.19913	−	0.0404232i
$851$	−1.77017	−	4.86350i	−0.0606806	−	0.166719i
$852$		0			0
$853$	29.2153	+	20.4568i	1.00031	+	0.700426i	0.954404	−	0.298519i	$-0.0964927\pi$
$853$	29.2153	+	20.4568i	1.00031	+	0.700426i	0.0459089	+	0.998946i	$0.485382\pi$
$854$	6.95187	−	12.0410i	0.237888	−	0.412034i
$855$		0			0
$856$	−9.09671	−	15.7560i	−0.310919	−	0.538528i
$857$	−2.38462	+	27.2563i	−0.0814570	+	0.931058i	0.840002	+	0.542583i	$0.182554\pi$
$857$	−2.38462	+	27.2563i	−0.0814570	+	0.931058i	−0.921459	+	0.388475i	$0.873002\pi$
$858$		0			0
$859$	18.2241	+	3.21341i	0.621800	+	0.109640i	0.475668	−	0.879625i	$-0.342206\pi$
$859$	18.2241	+	3.21341i	0.621800	+	0.109640i	0.146132	+	0.989265i	$0.453318\pi$
$860$	10.6461	−	8.63167i	0.363028	−	0.294338i
$861$		0			0
$862$	−7.77112	−	16.6652i	−0.264685	−	0.567620i
$863$	−15.7918	−	15.7918i	−0.537560	−	0.537560i	0.385252	−	0.922812i	$-0.374115\pi$
$863$	−15.7918	−	15.7918i	−0.537560	−	0.537560i	−0.922812	+	0.385252i	$0.874115\pi$
$864$		0			0
$865$	−1.70527	+	8.80124i	−0.0579808	+	0.299251i
$866$	0.958003	−	2.63209i	0.0325543	−	0.0894421i
$867$		0			0
$868$	−2.81924	+	0.246652i	−0.0956914	+	0.00837191i
$869$	−1.33055	+	7.54594i	−0.0451359	+	0.255978i
$870$		0			0
$871$	40.5674	−	34.0401i	1.37457	−	1.15340i
$872$	4.50748	+	1.20778i	0.152643	+	0.0409005i
$873$		0			0
$874$	−12.4837	−	7.20745i	−0.422266	−	0.243796i
$875$	5.96297	−	14.1190i	0.201585	−	0.477310i
$876$		0			0
$877$	−18.1351	−	8.45652i	−0.612378	−	0.285557i	0.0915805	−	0.995798i	$-0.470808\pi$
$877$	−18.1351	−	8.45652i	−0.612378	−	0.285557i	−0.703958	+	0.710241i	$0.748586\pi$
$878$	−14.0688	−	6.56039i	−0.474799	−	0.221402i
$879$		0			0
$880$	−1.59395	−	1.64858i	−0.0537319	−	0.0555737i
$881$	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
$883$	−34.6130	−	9.27453i	−1.16482	−	0.312113i	−0.375931	−	0.926648i	$-0.622677\pi$
$883$	−34.6130	−	9.27453i	−1.16482	−	0.312113i	−0.788890	+	0.614535i	$0.789344\pi$
$884$	−30.4658	+	25.5639i	−1.02468	+	0.859806i
$885$		0			0
$886$	3.80429	−	21.5752i	0.127808	−	0.724833i
$887$	−39.5685	+	3.46180i	−1.32858	+	0.116236i	−0.729240	−	0.684258i	$-0.760126\pi$
$887$	−39.5685	+	3.46180i	−1.32858	+	0.116236i	−0.599341	+	0.800494i	$0.704571\pi$
$888$		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
$893$	18.1136	+	38.8448i	0.606149	+	1.29989i
$894$		0			0
$895$	−2.49611	+	23.8878i	−0.0834357	+	0.798480i
$896$	1.35002	+	0.238046i	0.0451011	+	0.00795254i
$897$		0			0
$898$	−2.20572	+	25.2115i	−0.0736059	+	0.841319i
$899$	−8.46386	−	14.6598i	−0.282286	−	0.488933i
$900$		0			0
$901$	17.6838	−	30.6292i	0.589133	−	1.02041i
$902$	−7.32316	−	5.12773i	−0.243834	−	0.170735i
$903$		0			0
$904$	−0.632406	−	1.73752i	−0.0210335	−	0.0577891i
$905$	−38.3366	−	27.8178i	−1.27435	−	0.924694i
$906$		0			0
$907$	−20.4094	+	29.1476i	−0.677682	+	0.967830i	0.322095	+	0.946707i	$0.395613\pi$
$907$	−20.4094	+	29.1476i	−0.677682	+	0.967830i	−0.999777	+	0.0211225i	$0.993276\pi$
$908$	20.4463	−	5.47857i	0.678534	−	0.181813i
$909$		0			0
$910$	−5.68309	−	16.4726i	−0.188393	−	0.546060i
$911$	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
$913$	−3.89308	−	5.55989i	−0.128842	−	0.184006i
$914$	−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	$0.784800\pi$
$920$	6.97856	−	1.74443i	0.230076	−	0.0575122i
$921$		0			0
$922$	−1.25423	−	14.3359i	−0.0413058	−	0.472127i
$923$	4.14500	−	2.90236i	0.136434	−	0.0955323i
$924$		0			0
$925$	3.64339	−	7.17197i	0.119794	−	0.235813i
$926$	22.8630	−	13.1999i	0.751324	−	0.433777i
$927$		0			0
$928$	2.12225	+	7.92033i	0.0696662	+	0.259998i
$929$	3.45671	+	19.6040i	0.113411	+	0.643186i	0.987525	+	0.157464i	$0.0503319\pi$
$929$	3.45671	+	19.6040i	0.113411	+	0.643186i	−0.874114	+	0.485721i	$0.838557\pi$
$930$		0			0
$931$	−21.5621	+	7.84795i	−0.706668	+	0.257206i
$932$	9.19709	−	19.7232i	0.301261	−	0.646056i
$933$		0			0
$934$	−7.82915	+	1.38049i	−0.256178	+	0.0451710i
$935$	−12.1141	−	10.5178i	−0.396174	−	0.343968i
$936$		0			0
$937$	2.74853	−	10.2576i	0.0897905	−	0.335103i	−0.906388	−	0.422447i	$-0.861171\pi$
$937$	2.74853	−	10.2576i	0.0897905	−	0.335103i	0.996178	+	0.0873441i	$0.0278380\pi$
$938$	−12.7219	−	1.11302i	−0.415383	−	0.0363413i
$939$		0			0
$940$	−19.9722	−	7.65275i	−0.651421	−	0.249605i
$941$	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
$943$	25.4160	−	11.8517i	0.827657	−	0.385943i
$944$	−9.83002			−0.319940
$945$		0			0
$946$	6.28579			0.204369
$947$	−12.1720	+	5.67590i	−0.395537	+	0.184442i	−0.610202	−	0.792246i	$-0.708912\pi$
$947$	−12.1720	+	5.67590i	−0.395537	+	0.184442i	0.214665	+	0.976688i	$0.431134\pi$
$948$		0			0
$949$	19.1325	−	22.8012i	0.621066	−	0.740157i
$950$	−5.06635	−	21.8244i	−0.164374	−	0.708076i
$951$		0			0
$952$	9.55403	+	0.835870i	0.309648	+	0.0270907i
$953$	−6.20224	+	23.1471i	−0.200910	+	0.749807i	0.789747	+	0.613433i	$0.210212\pi$
$953$	−6.20224	+	23.1471i	−0.200910	+	0.749807i	−0.990657	+	0.136375i	$0.956455\pi$
$954$		0			0
$955$	−0.0313040	−	0.443813i	−0.00101298	−	0.0143615i
$956$	28.8667	−	5.08998i	0.933617	−	0.164622i
$957$		0			0
$958$	−5.48251	+	11.7573i	−0.177132	+	0.379860i
$959$	−2.94550	+	1.07207i	−0.0951151	+	0.0346191i
$960$		0			0
$961$	−4.64303	−	26.3319i	−0.149775	−	0.849418i
$962$	−2.36714	−	8.83427i	−0.0763195	−	0.284828i
$963$		0			0
$964$	0.283207	−	0.163510i	0.00912148	−	0.00526629i
$965$	38.4516	−	21.3445i	1.23780	−	0.687103i
$966$		0			0
$967$	−27.0335	+	18.9291i	−0.869339	+	0.608718i	−0.920834	−	0.389955i	$-0.872490\pi$
$967$	−27.0335	+	18.9291i	−0.869339	+	0.608718i	0.0514946	+	0.998673i	$0.483601\pi$
$968$	0.867052	+	9.91045i	0.0278681	+	0.318534i
$969$		0			0
$970$	0.241960	+	0.967957i	0.00776888	+	0.0310792i
$971$			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
$977$	−23.1250	−	33.0259i	−0.739834	−	1.05659i	−0.995947	−	0.0899460i	$-0.971331\pi$
$977$	−23.1250	−	33.0259i	−0.739834	−	1.05659i	0.256112	−	0.966647i	$-0.417558\pi$
$978$		0			0
$979$	5.87857	+	7.00580i	0.187880	+	0.223906i
$980$	5.01330	−	10.2946i	0.160144	−	0.328848i
$981$		0			0
$982$	33.1303	−	8.87723i	1.05723	−	0.283284i
$983$	13.2497	−	18.9226i	0.422601	−	0.603537i	−0.550241	−	0.835006i	$-0.685464\pi$
$983$	13.2497	−	18.9226i	0.422601	−	0.603537i	0.972842	+	0.231469i	$0.0743532\pi$
$984$		0			0
$985$	8.10480	−	1.28870i	0.258240	−	0.0410613i
$986$	19.6202	+	53.9061i	0.624835	+	1.71672i
$987$		0			0
$988$	−20.8660	−	14.6106i	−0.663837	−	0.464824i
$989$	−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	$0.799857\pi$
$992$	0.179926	−	2.05657i	0.00571267	−	0.0652961i
$993$		0			0
$994$	−1.20170	−	0.211891i	−0.0381155	−	0.00672079i
$995$	−48.4483	−	5.06251i	−1.53591	−	0.160492i
$996$		0			0
$997$	−26.3198	−	56.4430i	−0.833557	−	1.78757i	−0.566925	−	0.823769i	$-0.691867\pi$
$997$	−26.3198	−	56.4430i	−0.833557	−	1.78757i	−0.266631	−	0.963799i	$-0.585911\pi$
$998$	−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.17.12		216
3.2	odd	2		270.2.r.a.77.2	yes	216
5.3	odd	4	inner	810.2.s.a.503.3		216
15.8	even	4		270.2.r.a.23.12	✓	216
27.7	even	9		270.2.r.a.47.12	yes	216
27.20	odd	18	inner	810.2.s.a.467.3		216
135.88	odd	36		270.2.r.a.263.2	yes	216
135.128	even	36	inner	810.2.s.a.143.12		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.12	✓	216	15.8	even	4
270.2.r.a.47.12	yes	216	27.7	even	9
270.2.r.a.77.2	yes	216	3.2	odd	2
270.2.r.a.263.2	yes	216	135.88	odd	36
810.2.s.a.17.12		216	1.1	even	1	trivial
810.2.s.a.143.12		216	135.128	even	36	inner
810.2.s.a.467.3		216	27.20	odd	18	inner
810.2.s.a.503.3		216	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.04220 + 0.910725i) q^{5} +(-1.36563 - 0.119477i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.906308 - 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-2.04220 + 0.910725i) q^{5} +(-1.36563 - 0.119477i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.46597 + 1.68847i) q^{10} +(-1.00994 + 0.178080i) q^{11} +(2.40245 - 5.15208i) q^{13} +(-1.28818 + 0.468858i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-1.81071 - 6.75766i) q^{17} +(3.88061 - 2.24047i) q^{19} +(-0.615044 + 2.14982i) q^{20} +(-0.840060 + 0.588216i) q^{22} +(-0.280375 - 3.20470i) q^{23} +(3.34116 - 3.71977i) q^{25} -5.68469i q^{26} +(-0.969337 + 0.969337i) q^{28} +(-7.70523 - 2.80447i) q^{29} +(1.58144 + 1.32699i) q^{31} +(-0.573576 - 0.819152i) q^{32} +(-4.49697 - 5.35928i) q^{34} +(2.89771 - 0.999720i) q^{35} +(1.55405 - 0.416406i) q^{37} +(2.57016 - 3.67057i) q^{38} +(0.351133 + 2.20833i) q^{40} +(2.98153 + 8.19170i) q^{41} +(-5.02087 - 3.51565i) q^{43} +(-0.512762 + 0.888129i) q^{44} +(-1.60847 - 2.78595i) q^{46} +(-0.833651 + 9.52867i) q^{47} +(-5.04298 - 0.889213i) q^{49} +(1.45608 - 4.78329i) q^{50} +(-2.40245 - 5.15208i) q^{52} +(3.57469 + 3.57469i) q^{53} +(1.90032 - 1.28346i) q^{55} +(-0.468858 + 1.28818i) q^{56} +(-8.16853 + 0.714654i) q^{58} +(1.70697 - 9.68068i) q^{59} +(-7.76955 + 6.51943i) q^{61} +(1.99408 + 0.534312i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.214161 + 12.7095i) q^{65} +(8.44291 + 3.93699i) q^{67} +(-6.34057 - 2.95666i) q^{68} +(2.20371 - 2.13068i) q^{70} +(0.770875 + 0.445065i) q^{71} +(5.05755 + 1.35517i) q^{73} +(1.23246 - 1.03416i) q^{74} +(0.778107 - 4.41286i) q^{76} +(1.40049 - 0.122527i) q^{77} +(2.55545 - 7.02105i) q^{79} +(1.25151 + 1.85303i) q^{80} +(6.16415 + 6.16415i) q^{82} +(2.79708 + 5.99835i) q^{83} +(9.85221 + 12.1514i) q^{85} +(-6.03623 - 1.06435i) q^{86} +(-0.0893803 + 1.02162i) q^{88} +(-4.45891 - 7.72305i) q^{89} +(-3.89642 + 6.74881i) q^{91} +(-2.63516 - 1.84516i) q^{92} +(3.27145 + 8.98822i) q^{94} +(-5.88452 + 8.10966i) q^{95} +(0.255932 - 0.365508i) q^{97} +(-4.94629 + 1.32535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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

Varieties

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Representations

Groups

Database

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