LMFDB - Embedded newform 810.2.s.a.467.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			467.18
Character	$\chi$	$=$	810.467
Dual form			810.2.s.a.503.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.422618 - 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(2.23484 - 0.0739999i) q^{5} +(-0.290253 - 3.31761i) q^{7} +(-0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.422618 - 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(2.23484 - 0.0739999i) q^{5} +(-0.290253 - 3.31761i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.877419 - 2.05673i) q^{10} +(-5.15842 - 0.909569i) q^{11} +(2.89399 - 1.34949i) q^{13} +(-3.12944 - 1.13902i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-4.30809 - 1.15435i) q^{17} +(-4.29957 - 2.48236i) q^{19} +(-1.49322 - 1.66442i) q^{20} +(-3.00439 + 4.29072i) q^{22} +(7.23494 + 0.632975i) q^{23} +(4.98905 - 0.330756i) q^{25} -3.19317i q^{26} +(-2.35487 + 2.35487i) q^{28} +(3.90691 - 1.42200i) q^{29} +(-2.63399 + 2.21018i) q^{31} +(0.819152 + 0.573576i) q^{32} +(-2.86687 + 3.41661i) q^{34} +(-0.894174 - 7.39286i) q^{35} +(-0.209441 + 0.781646i) q^{37} +(-4.06686 + 2.84764i) q^{38} +(-2.13954 + 0.649898i) q^{40} +(3.96621 - 10.8971i) q^{41} +(1.49834 + 2.13984i) q^{43} +(2.61900 + 4.53624i) q^{44} +(3.63129 - 6.28957i) q^{46} +(-10.2729 + 0.898762i) q^{47} +(-4.02865 + 0.710360i) q^{49} +(1.80870 - 4.66140i) q^{50} +(-2.89399 - 1.34949i) q^{52} +(2.41770 + 2.41770i) q^{53} +(-11.5956 - 1.65102i) q^{55} +(1.13902 + 3.12944i) q^{56} +(0.362363 - 4.14183i) q^{58} +(-0.499518 - 2.83291i) q^{59} +(6.40604 + 5.37530i) q^{61} +(0.889931 + 3.32127i) q^{62} +(0.866025 - 0.500000i) q^{64} +(6.36775 - 3.23005i) q^{65} +(-2.43251 - 5.21653i) q^{67} +(1.88490 + 4.04219i) q^{68} +(-7.07810 - 2.31396i) q^{70} +(1.88477 - 1.08817i) q^{71} +(-0.475408 - 1.77425i) q^{73} +(0.619898 + 0.520156i) q^{74} +(0.862114 + 4.88929i) q^{76} +(-1.52035 + 17.3776i) q^{77} +(3.14035 + 8.62803i) q^{79} +(-0.315201 + 2.21374i) q^{80} +(-8.19991 - 8.19991i) q^{82} +(-0.116110 - 0.0541428i) q^{83} +(-9.71333 - 2.26099i) q^{85} +(2.57258 - 0.453616i) q^{86} +(5.21807 - 0.456522i) q^{88} +(8.65625 - 14.9931i) q^{89} +(-5.31708 - 9.20945i) q^{91} +(-4.16564 - 5.94915i) q^{92} +(-3.52696 + 9.69024i) q^{94} +(-9.79256 - 5.22951i) q^{95} +(-3.32190 + 2.32602i) q^{97} +(-1.05878 + 3.95141i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.422618	−	0.906308i	0.298836	−	0.640856i
$2$	0.422618	−	0.906308i	0.298836	−	0.640856i
$3$		0			0
$3$		0			0
$4$	−0.642788	−	0.766044i	−0.321394	−	0.383022i
$5$	2.23484	−	0.0739999i	0.999452	−	0.0330938i
$5$	2.23484	−	0.0739999i	0.999452	−	0.0330938i
$6$		0			0
$7$	−0.290253	−	3.31761i	−0.109705	−	1.25394i	−0.829006	−	0.559240i	$-0.811093\pi$
$7$	−0.290253	−	3.31761i	−0.109705	−	1.25394i	0.719300	−	0.694699i	$-0.244463\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$		0			0
$10$	0.877419	−	2.05673i	0.277464	−	0.650395i
$11$	−5.15842	−	0.909569i	−1.55532	−	0.274245i	−0.671120	−	0.741349i	$-0.734186\pi$
$11$	−5.15842	−	0.909569i	−1.55532	−	0.274245i	−0.884203	+	0.467104i	$0.845297\pi$
$12$		0			0
$13$	2.89399	−	1.34949i	0.802649	−	0.374281i	0.0223988	−	0.999749i	$-0.492870\pi$
$13$	2.89399	−	1.34949i	0.802649	−	0.374281i	0.780250	+	0.625468i	$0.215092\pi$
$14$	−3.12944	−	1.13902i	−0.836379	−	0.304417i
$15$		0			0
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	−4.30809	−	1.15435i	−1.04487	−	0.279971i	−0.304737	−	0.952437i	$-0.598569\pi$
$17$	−4.30809	−	1.15435i	−1.04487	−	0.279971i	−0.740128	+	0.672466i	$0.765235\pi$
$18$		0			0
$19$	−4.29957	−	2.48236i	−0.986389	−	0.569492i	−0.0821962	−	0.996616i	$-0.526193\pi$
$19$	−4.29957	−	2.48236i	−0.986389	−	0.569492i	−0.904193	+	0.427124i	$0.859527\pi$
$20$	−1.49322	−	1.66442i	−0.333893	−	0.372176i
$21$		0			0
$22$	−3.00439	+	4.29072i	−0.640538	+	0.914784i
$23$	7.23494	+	0.632975i	1.50859	+	0.131984i	0.811226	−	0.584733i	$-0.198801\pi$
$23$	7.23494	+	0.632975i	1.50859	+	0.131984i	0.697363	+	0.716718i	$0.254356\pi$
$24$		0			0
$25$	4.98905	−	0.330756i	0.997810	−	0.0661513i
$26$		−	3.19317i		−	0.626231i
$27$		0			0
$28$	−2.35487	+	2.35487i	−0.445028	+	0.445028i
$29$	3.90691	−	1.42200i	0.725495	−	0.264059i	0.0472384	−	0.998884i	$-0.484958\pi$
$29$	3.90691	−	1.42200i	0.725495	−	0.264059i	0.678257	+	0.734825i	$0.262736\pi$
$30$		0			0
$31$	−2.63399	+	2.21018i	−0.473079	+	0.396960i	−0.847916	−	0.530130i	$-0.822143\pi$
$31$	−2.63399	+	2.21018i	−0.473079	+	0.396960i	0.374837	+	0.927091i	$0.377699\pi$
$32$	0.819152	+	0.573576i	0.144807	+	0.101395i
$33$		0			0
$34$	−2.86687	+	3.41661i	−0.491665	+	0.585943i
$35$	−0.894174	−	7.39286i	−0.151143	−	1.24962i
$36$		0			0
$37$	−0.209441	+	0.781646i	−0.0344319	+	0.128502i	−0.981003	−	0.193995i	$-0.937855\pi$
$37$	−0.209441	+	0.781646i	−0.0344319	+	0.128502i	0.946571	+	0.322497i	$0.104522\pi$
$38$	−4.06686	+	2.84764i	−0.659731	+	0.461949i
$39$		0			0
$40$	−2.13954	+	0.649898i	−0.338291	+	0.102758i
$41$	3.96621	−	10.8971i	0.619418	−	1.70184i	−0.0889892	−	0.996033i	$-0.528364\pi$
$41$	3.96621	−	10.8971i	0.619418	−	1.70184i	0.708407	−	0.705804i	$-0.249414\pi$
$42$		0			0
$43$	1.49834	+	2.13984i	0.228494	+	0.326323i	0.916985	−	0.398922i	$-0.130615\pi$
$43$	1.49834	+	2.13984i	0.228494	+	0.326323i	−0.688491	+	0.725245i	$0.741727\pi$
$44$	2.61900	+	4.53624i	0.394829	+	0.683864i
$45$		0			0
$46$	3.63129	−	6.28957i	0.535404	−	0.927347i
$47$	−10.2729	+	0.898762i	−1.49846	+	0.131098i	−0.806669	−	0.591004i	$-0.798732\pi$
$47$	−10.2729	+	0.898762i	−1.49846	+	0.131098i	−0.691787	+	0.722102i	$0.743176\pi$
$48$		0			0
$49$	−4.02865	+	0.710360i	−0.575521	+	0.101480i
$50$	1.80870	−	4.66140i	0.255788	−	0.659221i
$51$		0			0
$52$	−2.89399	−	1.34949i	−0.401324	−	0.187141i
$53$	2.41770	+	2.41770i	0.332096	+	0.332096i	0.853382	−	0.521286i	$-0.174547\pi$
$53$	2.41770	+	2.41770i	0.332096	+	0.332096i	−0.521286	+	0.853382i	$0.674547\pi$
$54$		0			0
$55$	−11.5956	−	1.65102i	−1.56355	−	0.222624i
$56$	1.13902	+	3.12944i	0.152209	+	0.418190i
$57$		0			0
$58$	0.362363	−	4.14183i	0.0475806	−	0.543848i
$59$	−0.499518	−	2.83291i	−0.0650317	−	0.368813i	−0.999904	−	0.0138300i	$-0.995598\pi$
$59$	−0.499518	−	2.83291i	−0.0650317	−	0.368813i	0.934873	−	0.354983i	$-0.115513\pi$
$60$		0			0
$61$	6.40604	+	5.37530i	0.820209	+	0.688237i	0.953021	−	0.302904i	$-0.0979562\pi$
$61$	6.40604	+	5.37530i	0.820209	+	0.688237i	−0.132812	+	0.991141i	$0.542401\pi$
$62$	0.889931	+	3.32127i	0.113021	+	0.421802i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	6.36775	−	3.23005i	0.789823	−	0.400639i
$66$		0			0
$67$	−2.43251	−	5.21653i	−0.297178	−	0.637301i	0.699854	−	0.714286i	$-0.253248\pi$
$67$	−2.43251	−	5.21653i	−0.297178	−	0.637301i	−0.997032	+	0.0769849i	$0.975471\pi$
$68$	1.88490	+	4.04219i	0.228578	+	0.490188i
$69$		0			0
$70$	−7.07810	−	2.31396i	−0.845995	−	0.276571i
$71$	1.88477	−	1.08817i	0.223681	−	0.129142i	−0.383973	−	0.923345i	$-0.625444\pi$
$71$	1.88477	−	1.08817i	0.223681	−	0.129142i	0.607654	+	0.794202i	$0.292111\pi$
$72$		0			0
$73$	−0.475408	−	1.77425i	−0.0556423	−	0.207660i	0.932508	−	0.361149i	$-0.117616\pi$
$73$	−0.475408	−	1.77425i	−0.0556423	−	0.207660i	−0.988150	+	0.153490i	$0.950949\pi$
$74$	0.619898	+	0.520156i	0.0720617	+	0.0604669i
$75$		0			0
$76$	0.862114	+	4.88929i	0.0988913	+	0.560840i
$77$	−1.52035	+	17.3776i	−0.173260	+	1.98037i
$78$		0			0
$79$	3.14035	+	8.62803i	0.353316	+	0.970729i	0.981297	+	0.192500i	$0.0616595\pi$
$79$	3.14035	+	8.62803i	0.353316	+	0.970729i	−0.627981	+	0.778229i	$0.716118\pi$
$80$	−0.315201	+	2.21374i	−0.0352405	+	0.247504i
$81$		0			0
$82$	−8.19991	−	8.19991i	−0.905528	−	0.905528i
$83$	−0.116110	−	0.0541428i	−0.0127447	−	0.00594295i	0.416235	−	0.909257i	$-0.363349\pi$
$83$	−0.116110	−	0.0541428i	−0.0127447	−	0.00594295i	−0.428980	+	0.903314i	$0.641127\pi$
$84$		0			0
$85$	−9.71333	−	2.26099i	−1.05356	−	0.245239i
$86$	2.57258	−	0.453616i	0.277409	−	0.0489146i
$87$		0			0
$88$	5.21807	−	0.456522i	0.556248	−	0.0486654i
$89$	8.65625	−	14.9931i	0.917560	−	1.58926i	0.114451	−	0.993429i	$-0.463489\pi$
$89$	8.65625	−	14.9931i	0.917560	−	1.58926i	0.803109	−	0.595832i	$-0.203178\pi$
$90$		0			0
$91$	−5.31708	−	9.20945i	−0.557381	−	0.965412i
$92$	−4.16564	−	5.94915i	−0.434298	−	0.620242i
$93$		0			0
$94$	−3.52696	+	9.69024i	−0.363778	+	0.999472i
$95$	−9.79256	−	5.22951i	−1.00470	−	0.536537i
$96$		0			0
$97$	−3.32190	+	2.32602i	−0.337288	+	0.236171i	−0.729933	−	0.683519i	$-0.760449\pi$
$97$	−3.32190	+	2.32602i	−0.337288	+	0.236171i	0.392646	+	0.919690i	$0.371560\pi$
$98$	−1.05878	+	3.95141i	−0.106953	+	0.399152i
$99$		0			0
$100$	−3.46027	−	3.60923i	−0.346027	−	0.360923i
$101$	−0.250288	+	0.298282i	−0.0249046	+	0.0296802i	−0.778353	−	0.627827i	$-0.783945\pi$
$101$	−0.250288	+	0.298282i	−0.0249046	+	0.0296802i	0.753448	+	0.657507i	$0.228389\pi$
$102$		0			0
$103$	11.9313	+	8.35436i	1.17562	+	0.823180i	0.987291	−	0.158926i	$-0.0508031\pi$
$103$	11.9313	+	8.35436i	1.17562	+	0.823180i	0.188332	+	0.982105i	$0.439692\pi$
$104$	−2.44611	+	2.05253i	−0.239861	+	0.201267i
$105$		0			0
$106$	3.21294	−	1.16942i	0.312069	−	0.113584i
$107$	1.18652	−	1.18652i	0.114705	−	0.114705i	−0.647424	−	0.762130i	$-0.724154\pi$
$107$	1.18652	−	1.18652i	0.114705	−	0.114705i	0.762130	+	0.647424i	$0.224154\pi$
$108$		0			0
$109$			6.27716i			0.601243i	0.953744	+	0.300621i	$0.0971940\pi$
$109$			6.27716i			0.601243i	−0.953744	+	0.300621i	$0.902806\pi$
$110$	−6.39683	+	9.81140i	−0.609914	+	0.935481i
$111$		0			0
$112$	3.31761	+	0.290253i	0.313485	+	0.0274264i
$113$	−6.62110	+	9.45592i	−0.622861	+	0.889538i	−0.999319	−	0.0368959i	$-0.988253\pi$
$113$	−6.62110	+	9.45592i	−0.622861	+	0.889538i	0.376458	+	0.926434i	$0.377142\pi$
$114$		0			0
$115$	16.2158	+	0.879215i	1.51213	+	0.0819873i
$116$	−3.60063	−	2.07882i	−0.334310	−	0.193014i
$117$		0			0
$118$	−2.77859	−	0.744522i	−0.255790	−	0.0685388i
$119$	−2.57925	+	14.6276i	−0.236439	+	1.34091i
$120$		0			0
$121$	15.4454	+	5.62165i	1.40412	+	0.511059i
$122$	7.57899	−	3.53414i	0.686169	−	0.319966i
$123$		0			0
$124$	3.38619	+	0.597077i	0.304089	+	0.0536191i
$125$	11.1253	−	1.10838i	0.995074	−	0.0991363i
$126$		0			0
$127$	12.5284	−	3.35697i	1.11171	−	0.297883i	0.344188	−	0.938901i	$-0.388154\pi$
$127$	12.5284	−	3.35697i	1.11171	−	0.297883i	0.767526	+	0.641018i	$0.221488\pi$
$128$	−0.0871557	−	0.996195i	−0.00770355	−	0.0880520i
$129$		0			0
$130$	−0.236294	−	7.13622i	−0.0207243	−	0.625888i
$131$	8.21463	+	9.78982i	0.717716	+	0.855340i	0.994407	−	0.105619i	$-0.0336823\pi$
$131$	8.21463	+	9.78982i	0.717716	+	0.855340i	−0.276691	+	0.960959i	$0.589238\pi$
$132$		0			0
$133$	−6.98754	+	14.9848i	−0.605896	+	1.29935i
$134$	−5.75581			−0.497226
$135$		0			0
$136$	4.46006			0.382447
$137$	0.418923	−	0.898383i	0.0357910	−	0.0767541i	−0.887599	−	0.460616i	$-0.847628\pi$
$137$	0.418923	−	0.898383i	0.0357910	−	0.0767541i	0.923390	+	0.383862i	$0.125406\pi$
$138$		0			0
$139$	1.52525	+	1.81772i	0.129370	+	0.154177i	0.826841	−	0.562436i	$-0.190136\pi$
$139$	1.52525	+	1.81772i	0.129370	+	0.154177i	−0.697471	+	0.716613i	$0.745691\pi$
$140$	−5.08850	+	5.43702i	−0.430057	+	0.459512i
$141$		0			0
$142$	−0.189681	−	2.16806i	−0.0159177	−	0.181940i
$143$	−16.1559	+	4.32895i	−1.35102	+	0.362005i
$144$		0			0
$145$	8.62610	−	3.46706i	0.716359	−	0.287923i
$146$	−1.80893	−	0.318963i	−0.149708	−	0.0263976i
$147$		0			0
$148$	0.733402	−	0.341991i	0.0602852	−	0.0281115i
$149$	10.2800	+	3.74162i	0.842172	+	0.306526i	0.726845	−	0.686802i	$-0.240986\pi$
$149$	10.2800	+	3.74162i	0.842172	+	0.306526i	0.115328	+	0.993328i	$0.463208\pi$
$150$		0			0
$151$	2.51598	−	14.2688i	0.204747	−	1.16118i	−0.693089	−	0.720852i	$-0.743751\pi$
$151$	2.51598	−	14.2688i	0.204747	−	1.16118i	0.897837	−	0.440329i	$-0.145138\pi$
$152$	4.79555	+	1.28496i	0.388970	+	0.104224i
$153$		0			0
$154$	15.1070	+	8.72201i	1.21735	+	0.702840i
$155$	−5.72300	+	5.13432i	−0.459683	+	0.412399i
$156$		0			0
$157$	−3.73924	+	5.34019i	−0.298424	+	0.426194i	−0.940161	−	0.340731i	$-0.889325\pi$
$157$	−3.73924	+	5.34019i	−0.298424	+	0.426194i	0.641737	+	0.766925i	$0.278214\pi$
$158$	9.14682	+	0.800243i	0.727682	+	0.0636639i
$159$		0			0
$160$	1.87312	+	1.22124i	0.148083	+	0.0965472i
$161$		−	24.1864i		−	1.90616i
$162$		0			0
$163$	1.99274	−	1.99274i	0.156083	−	0.156083i	−0.624745	−	0.780829i	$-0.714797\pi$
$163$	1.99274	−	1.99274i	0.156083	−	0.156083i	0.780829	+	0.624745i	$0.214797\pi$
$164$	−10.8971	+	3.96621i	−0.850918	+	0.309709i
$165$		0			0
$166$	−0.0981401	+	0.0823493i	−0.00761715	+	0.00639155i
$167$	16.3198	+	11.4272i	1.26286	+	0.884266i	0.996819	−	0.0796948i	$-0.0253946\pi$
$167$	16.3198	+	11.4272i	1.26286	+	0.884266i	0.266044	+	0.963961i	$0.414283\pi$
$168$		0			0
$169$	−1.80218	+	2.14775i	−0.138629	+	0.165212i
$170$	−6.15418	+	7.84773i	−0.472004	+	0.601893i
$171$		0			0
$172$	0.676105	−	2.52326i	0.0515525	−	0.192397i
$173$	9.38517	−	6.57157i	0.713541	−	0.499627i	−0.159546	−	0.987190i	$-0.551003\pi$
$173$	9.38517	−	6.57157i	0.713541	−	0.499627i	0.873088	+	0.487563i	$0.162114\pi$
$174$		0			0
$175$	−2.54541	−	16.4557i	−0.192415	−	1.24394i
$176$	1.79150	−	4.92211i	0.135039	−	0.371018i
$177$		0			0
$178$	−9.93004	−	14.1816i	−0.744288	−	1.06295i
$179$	−2.91563	−	5.05001i	−0.217924	−	0.377456i	0.736249	−	0.676711i	$-0.236595\pi$
$179$	−2.91563	−	5.05001i	−0.217924	−	0.377456i	−0.954173	+	0.299255i	$0.903262\pi$
$180$		0			0
$181$	−8.11707	+	14.0592i	−0.603337	+	1.04501i	0.388975	+	0.921248i	$0.372829\pi$
$181$	−8.11707	+	14.0592i	−0.603337	+	1.04501i	−0.992312	+	0.123762i	$0.960504\pi$
$182$	−10.5937	+	0.926827i	−0.785256	+	0.0687010i
$183$		0			0
$184$	−7.15224	+	1.26113i	−0.527270	+	0.0929719i
$185$	−0.410227	+	1.76235i	−0.0301605	+	0.129571i
$186$		0			0
$187$	21.1730	+	9.87312i	1.54832	+	0.721994i
$188$	7.29178	+	7.29178i	0.531808	+	0.531808i
$189$		0			0
$190$	−8.87806	+	6.66499i	−0.644082	+	0.483529i
$191$	−0.365493	−	1.00418i	−0.0264461	−	0.0726601i	0.925767	−	0.378094i	$-0.123421\pi$
$191$	−0.365493	−	1.00418i	−0.0264461	−	0.0726601i	−0.952213	+	0.305434i	$0.901198\pi$
$192$		0			0
$193$	−1.08498	+	12.4014i	−0.0780984	+	0.892669i	0.851563	+	0.524253i	$0.175655\pi$
$193$	−1.08498	+	12.4014i	−0.0780984	+	0.892669i	−0.929661	+	0.368416i	$0.879900\pi$
$194$	0.704193	+	3.99368i	0.0505581	+	0.286729i
$195$		0			0
$196$	3.13373	+	2.62951i	0.223838	+	0.187822i
$197$	−0.0383654	−	0.143182i	−0.00273342	−	0.0102013i	0.964546	−	0.263916i	$-0.0850142\pi$
$197$	−0.0383654	−	0.143182i	−0.00273342	−	0.0102013i	−0.967279	+	0.253715i	$0.918348\pi$
$198$		0			0
$199$	14.5760	−	8.41543i	1.03326	−	0.596554i	0.115344	−	0.993326i	$-0.463203\pi$
$199$	14.5760	−	8.41543i	1.03326	−	0.596554i	0.917917	+	0.396772i	$0.129869\pi$
$200$	−4.73344	+	1.61075i	−0.334705	+	0.113897i
$201$		0			0
$202$	0.164559	+	0.352898i	0.0115783	+	0.0248298i
$203$	−5.85164	−	12.5489i	−0.410704	−	0.880758i
$204$		0			0
$205$	8.05747	−	24.6467i	0.562758	−	1.72140i
$206$	12.6140	−	7.28269i	0.878858	−	0.507409i
$207$		0			0
$208$	0.826452	+	3.08436i	0.0573041	+	0.213862i
$209$	19.9211	+	16.7158i	1.37797	+	1.15626i
$210$		0			0
$211$	−3.79341	−	21.5135i	−0.261149	−	1.48105i	−0.779780	−	0.626053i	$-0.784669\pi$
$211$	−3.79341	−	21.5135i	−0.261149	−	1.48105i	0.518631	−	0.854998i	$-0.326442\pi$
$212$	0.297998	−	3.40613i	0.0204666	−	0.233934i
$213$		0			0
$214$	−0.573908	−	1.57680i	−0.0392315	−	0.107788i
$215$	3.50689	+	4.67134i	0.239168	+	0.318583i
$216$		0			0
$217$	8.09705	+	8.09705i	0.549663	+	0.549663i
$218$	5.68904	+	2.65284i	0.385310	+	0.179673i
$219$		0			0
$220$	6.18873	+	9.94398i	0.417244	+	0.670423i
$221$	−14.0254	+	2.47305i	−0.943448	+	0.166355i
$222$		0			0
$223$	−7.09286	+	0.620545i	−0.474973	+	0.0415548i	−0.322130	−	0.946696i	$-0.604399\pi$
$223$	−7.09286	+	0.620545i	−0.474973	+	0.0415548i	−0.152844	+	0.988250i	$0.548843\pi$
$224$	1.66514	−	2.88411i	0.111257	−	0.192703i
$225$		0			0
$226$	5.77177	+	9.99700i	0.383933	+	0.664991i
$227$	−2.92136	−	4.17213i	−0.193897	−	0.276914i	0.710417	−	0.703781i	$-0.248506\pi$
$227$	−2.92136	−	4.17213i	−0.193897	−	0.276914i	−0.904315	+	0.426867i	$0.859617\pi$
$228$		0			0
$229$	−0.607970	+	1.67038i	−0.0401758	+	0.110382i	−0.958158	−	0.286239i	$-0.907595\pi$
$229$	−0.607970	+	1.67038i	−0.0401758	+	0.110382i	0.917983	+	0.396621i	$0.129817\pi$
$230$	7.64993	−	14.3249i	0.504421	−	0.944558i
$231$		0			0
$232$	−3.40575	+	2.38473i	−0.223598	+	0.156565i
$233$	−3.59685	+	13.4236i	−0.235637	+	0.879410i	0.742223	+	0.670153i	$0.233771\pi$
$233$	−3.59685	+	13.4236i	−0.235637	+	0.879410i	−0.977861	+	0.209258i	$0.932895\pi$
$234$		0			0
$235$	−22.8918	+	2.76878i	−1.49330	+	0.180616i
$236$	−1.84905	+	2.20361i	−0.120363	+	0.143443i
$237$		0			0
$238$	12.1671	+	8.51949i	0.788676	+	0.552237i
$239$	−0.330777	+	0.277555i	−0.0213962	+	0.0179535i	−0.653423	−	0.756993i	$-0.726668\pi$
$239$	−0.330777	+	0.277555i	−0.0213962	+	0.0179535i	0.632027	+	0.774946i	$0.282223\pi$
$240$		0			0
$241$	10.5842	−	3.85234i	0.681790	−	0.248151i	0.0221741	−	0.999754i	$-0.492941\pi$
$241$	10.5842	−	3.85234i	0.681790	−	0.248151i	0.659616	+	0.751603i	$0.270719\pi$
$242$	11.6224	−	11.6224i	0.747119	−	0.747119i
$243$		0			0
$244$		−	8.36249i		−	0.535354i
$245$	−8.95083	+	1.88566i	−0.571848	+	0.120471i
$246$		0			0
$247$	−15.7928	−	1.38169i	−1.00487	−	0.0879151i
$248$	1.97220	−	2.81660i	0.125235	−	0.178854i
$249$		0			0
$250$	3.69721	−	10.5513i	0.233832	−	0.667325i
$251$	0.161890	+	0.0934671i	0.0102184	+	0.00589959i	0.505100	−	0.863061i	$-0.331455\pi$
$251$	0.161890	+	0.0934671i	0.0102184	+	0.00589959i	−0.494882	+	0.868960i	$0.664789\pi$
$252$		0			0
$253$	−36.7451	−	9.84582i	−2.31015	−	0.619002i
$254$	2.25228	−	12.7733i	0.141320	−	0.801467i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−16.4216	+	7.65751i	−1.02435	+	0.477662i	−0.860838	−	0.508879i	$-0.830060\pi$
$257$	−16.4216	+	7.65751i	−1.02435	+	0.477662i	−0.163512	+	0.986541i	$0.552282\pi$
$258$		0			0
$259$	2.65399	+	0.467970i	0.164911	+	0.0290782i
$260$	−6.56748	−	2.80174i	−0.407298	−	0.173757i
$261$		0			0
$262$	12.3442	−	3.30763i	0.762630	−	0.204346i
$263$	0.614783	+	7.02700i	0.0379092	+	0.433304i	0.991305	+	0.131582i	$0.0420057\pi$
$263$	0.614783	+	7.02700i	0.0379092	+	0.433304i	−0.953396	+	0.301721i	$0.902439\pi$
$264$		0			0
$265$	5.58209	+	5.22427i	0.342905	+	0.320924i
$266$	10.6278	+	12.6657i	0.651632	+	0.776585i
$267$		0			0
$268$	−2.43251	+	5.21653i	−0.148589	+	0.318651i
$269$	−27.9259			−1.70267			−0.851337	−	0.524620i	$-0.824207\pi$
$269$	−27.9259			−1.70267			−0.851337	+	0.524620i	$0.824207\pi$
$270$		0			0
$271$	25.6074			1.55554			0.777769	−	0.628550i	$-0.216351\pi$
$271$	25.6074			1.55554			0.777769	+	0.628550i	$0.216351\pi$
$272$	1.88490	−	4.04219i	0.114289	−	0.245094i
$273$		0			0
$274$	−0.637167	−	0.759346i	−0.0384927	−	0.0458738i
$275$	−26.0365	−	2.83170i	−1.57006	−	0.170758i
$276$		0			0
$277$	−0.608396	−	6.95400i	−0.0365550	−	0.417825i	−0.992320	−	0.123695i	$-0.960526\pi$
$277$	−0.608396	−	6.95400i	−0.0365550	−	0.417825i	0.955765	−	0.294130i	$-0.0950300\pi$
$278$	2.29201	−	0.614142i	0.137466	−	0.0368338i
$279$		0			0
$280$	2.77712	+	6.90953i	0.165965	+	0.412923i
$281$	15.6364	+	2.75713i	0.932792	+	0.164476i	0.619336	−	0.785126i	$-0.287402\pi$
$281$	15.6364	+	2.75713i	0.932792	+	0.164476i	0.313456	+	0.949603i	$0.398513\pi$
$282$		0			0
$283$	−23.5568	+	10.9847i	−1.40031	+	0.652974i	−0.968505	−	0.248994i	$-0.919900\pi$
$283$	−23.5568	+	10.9847i	−1.40031	+	0.652974i	−0.431802	+	0.901968i	$0.642122\pi$
$284$	−2.04509	−	0.744354i	−0.121354	−	0.0441693i
$285$		0			0
$286$	−2.90440	+	16.4717i	−0.171741	+	0.973991i
$287$	−37.3035	−	9.99543i	−2.20195	−	0.590012i
$288$		0			0
$289$	2.50469	+	1.44608i	0.147335	+	0.0850636i
$290$	0.503329	−	9.28315i	0.0295565	−	0.545125i
$291$		0			0
$292$	−1.05357	+	1.50465i	−0.0616552	+	0.0880528i
$293$	16.6246	+	1.45446i	0.971218	+	0.0849706i	0.561708	−	0.827335i	$-0.310144\pi$
$293$	16.6246	+	1.45446i	0.971218	+	0.0849706i	0.409510	+	0.912306i	$0.365700\pi$
$294$		0			0
$295$	−1.32598	−	6.29414i	−0.0772015	−	0.366459i
$296$		−	0.809219i		−	0.0470349i
$297$		0			0
$298$	7.73559	−	7.73559i	0.448111	−	0.448111i
$299$	21.7920	−	7.93165i	1.26027	−	0.458699i
$300$		0			0
$301$	6.66428	−	5.59199i	0.384123	−	0.322317i
$302$	−11.8687	−	8.31052i	−0.682964	−	0.478217i
$303$		0			0
$304$	3.19126	−	3.80319i	0.183031	−	0.218128i
$305$	14.7143	+	11.5389i	0.842536	+	0.660716i
$306$		0			0
$307$	−5.45815	+	20.3701i	−0.311513	+	1.16258i	0.615679	+	0.787997i	$0.288882\pi$
$307$	−5.45815	+	20.3701i	−0.311513	+	1.16258i	−0.927192	+	0.374586i	$0.877785\pi$
$308$	14.2893	−	10.0055i	0.814209	−	0.570115i
$309$		0			0
$310$	2.23463	+	7.35666i	0.126918	+	0.417830i
$311$	6.27658	−	17.2448i	0.355912	−	0.977861i	−0.624521	−	0.781008i	$-0.714706\pi$
$311$	6.27658	−	17.2448i	0.355912	−	0.977861i	0.980433	−	0.196853i	$-0.0630722\pi$
$312$		0			0
$313$	5.83723	+	8.33642i	0.329940	+	0.471203i	0.949509	−	0.313739i	$-0.101582\pi$
$313$	5.83723	+	8.33642i	0.329940	+	0.471203i	−0.619570	+	0.784942i	$0.712693\pi$
$314$	3.25958	+	5.64577i	0.183949	+	0.318609i
$315$		0			0
$316$	4.59088	−	7.95163i	0.258257	−	0.447314i
$317$	23.0097	−	2.01309i	1.29236	−	0.113067i	0.579845	−	0.814727i	$-0.303113\pi$
$317$	23.0097	−	2.01309i	1.29236	−	0.113067i	0.712511	+	0.701661i	$0.247558\pi$
$318$		0			0
$319$	−21.4469	+	3.78167i	−1.20080	+	0.211733i
$320$	1.89843	−	1.18151i	0.106126	−	0.0660483i
$321$		0			0
$322$	−21.9204	−	10.2216i	−1.22157	−	0.569629i
$323$	15.6574	+	15.6574i	0.871203	+	0.871203i
$324$		0			0
$325$	13.9919	−	7.68988i	0.776131	−	0.426558i
$326$	−0.963868	−	2.64820i	−0.0533837	−	0.146670i
$327$		0			0
$328$	−1.01069	+	11.5523i	−0.0558063	+	0.637869i
$329$	5.96349	+	33.8206i	0.328778	+	1.86459i
$330$		0			0
$331$	−16.6856	−	14.0008i	−0.917121	−	0.769556i	0.0563393	−	0.998412i	$-0.482057\pi$
$331$	−16.6856	−	14.0008i	−0.917121	−	0.769556i	−0.973460	+	0.228856i	$0.926502\pi$
$332$	0.0331580	+	0.123748i	0.00181978	+	0.00679153i
$333$		0			0
$334$	17.2536	−	9.96139i	0.944077	−	0.545063i
$335$	−5.82230	−	11.4781i	−0.318106	−	0.627117i
$336$		0			0
$337$	1.30005	+	2.78798i	0.0708185	+	0.151871i	0.938530	−	0.345197i	$-0.112188\pi$
$337$	1.30005	+	2.78798i	0.0708185	+	0.151871i	−0.867712	+	0.497068i	$0.834410\pi$
$338$	1.18489	+	2.54101i	0.0644496	+	0.138213i
$339$		0			0
$340$	4.51159	+	8.89418i	0.244675	+	0.482355i
$341$	15.5975	−	9.00525i	0.844654	−	0.487661i
$342$		0			0
$343$	−2.50756	−	9.35835i	−0.135396	−	0.505303i
$344$	−2.00111	−	1.67913i	−0.107893	−	0.0905328i
$345$		0			0
$346$	−1.98952	−	11.2831i	−0.106957	−	0.606584i
$347$	−1.31907	+	15.0770i	−0.0708113	+	0.809377i	0.874886	+	0.484329i	$0.160936\pi$
$347$	−1.31907	+	15.0770i	−0.0708113	+	0.809377i	−0.945697	+	0.325048i	$0.894619\pi$
$348$		0			0
$349$	−5.42372	−	14.9016i	−0.290325	−	0.797662i	−0.996019	−	0.0891446i	$-0.971587\pi$
$349$	−5.42372	−	14.9016i	−0.290325	−	0.797662i	0.705694	−	0.708517i	$-0.250636\pi$
$350$	−15.9897	−	4.64756i	−0.854685	−	0.248423i
$351$		0			0
$352$	−3.70382	−	3.70382i	−0.197414	−	0.197414i
$353$	−22.3345	−	10.4147i	−1.18874	−	0.554320i	−0.275329	−	0.961350i	$-0.588787\pi$
$353$	−22.3345	−	10.4147i	−1.18874	−	0.554320i	−0.913415	+	0.407030i	$0.866564\pi$
$354$		0			0
$355$	4.13164	−	2.57137i	0.219285	−	0.136474i
$356$	−17.0495	+	3.00628i	−0.903620	+	0.159333i
$357$		0			0
$358$	−5.80906	+	0.508227i	−0.307019	+	0.0268606i
$359$	−2.89852	+	5.02038i	−0.152978	+	0.264965i	−0.932321	−	0.361632i	$-0.882220\pi$
$359$	−2.89852	+	5.02038i	−0.152978	+	0.264965i	0.779343	+	0.626598i	$0.215553\pi$
$360$		0			0
$361$	2.82421	+	4.89167i	0.148642	+	0.257456i
$362$	9.31151	+	13.2982i	0.489402	+	0.698939i
$363$		0			0
$364$	−3.63709	+	9.99283i	−0.190636	+	0.523767i
$365$	−1.19376	−	3.92998i	−0.0624840	−	0.205705i
$366$		0			0
$367$	−19.7607	+	13.8366i	−1.03150	+	0.722263i	−0.961366	−	0.275275i	$-0.911231\pi$
$367$	−19.7607	+	13.8366i	−1.03150	+	0.722263i	−0.0701330	+	0.997538i	$0.522342\pi$
$368$	−1.87969	+	7.01511i	−0.0979857	+	0.365688i
$369$		0			0
$370$	1.42387	+	1.11659i	0.0740233	+	0.0580490i
$371$	7.31924	−	8.72273i	0.379996	−	0.452862i
$372$		0			0
$373$	6.73737	+	4.71756i	0.348848	+	0.244266i	0.734847	−	0.678233i	$-0.237254\pi$
$373$	6.73737	+	4.71756i	0.348848	+	0.244266i	−0.385999	+	0.922499i	$0.626143\pi$
$374$	17.8962	−	15.0167i	0.925389	−	0.776494i
$375$		0			0
$376$	9.69024	−	3.52696i	0.499736	−	0.181889i
$377$	9.38759	−	9.38759i	0.483485	−	0.483485i
$378$		0			0
$379$			1.69927i			0.0872858i	0.999047	+	0.0436429i	$0.0138964\pi$
$379$			1.69927i			0.0872858i	−0.999047	+	0.0436429i	$0.986104\pi$
$380$	2.28850	+	10.8630i	0.117397	+	0.557260i
$381$		0			0
$382$	−1.06456	−	0.0931371i	−0.0544678	−	0.00476531i
$383$	−2.04487	+	2.92038i	−0.104488	+	0.149225i	−0.867991	−	0.496580i	$-0.834589\pi$
$383$	−2.04487	+	2.92038i	−0.104488	+	0.149225i	0.763503	+	0.645804i	$0.223478\pi$
$384$		0			0
$385$	−2.11179	+	38.9488i	−0.107627	+	1.98502i
$386$	10.7809	+	6.22436i	0.548734	+	0.316812i
$387$		0			0
$388$	3.91711	+	1.04959i	0.198861	+	0.0532847i
$389$	−1.27347	+	7.22223i	−0.0645677	+	0.366182i	0.935355	+	0.353712i	$0.115081\pi$
$389$	−1.27347	+	7.22223i	−0.0645677	+	0.366182i	−0.999922	+	0.0124700i	$0.996031\pi$
$390$		0			0
$391$	−30.4381	−	11.0786i	−1.53932	−	0.560267i
$392$	3.70752	−	1.72885i	0.187258	−	0.0873199i
$393$		0			0
$394$	−0.145980	−	0.0257403i	−0.00735439	−	0.00129678i
$395$	7.65665	+	19.0499i	0.385248	+	0.958505i
$396$		0			0
$397$	−18.9919	+	5.08887i	−0.953177	+	0.255403i	−0.701710	−	0.712463i	$-0.747580\pi$
$397$	−18.9919	+	5.08887i	−0.953177	+	0.255403i	−0.251467	+	0.967866i	$0.580913\pi$
$398$	−1.46691	−	16.7668i	−0.0735294	−	0.840444i
$399$		0			0
$400$	−0.540608	+	4.97069i	−0.0270304	+	0.248534i
$401$	−4.83413	−	5.76110i	−0.241405	−	0.287695i	0.631715	−	0.775201i	$-0.282351\pi$
$401$	−4.83413	−	5.76110i	−0.241405	−	0.287695i	−0.873120	+	0.487505i	$0.837907\pi$
$402$		0			0
$403$	−4.64013	+	9.95079i	−0.231141	+	0.495684i
$404$	0.389380			0.0193724
$405$		0			0
$406$	−13.8462			−0.687173
$407$	1.79135	−	3.84156i	0.0887938	−	0.190419i
$408$		0			0
$409$	−13.3179	−	15.8717i	−0.658529	−	0.784804i	0.328645	−	0.944453i	$-0.393408\pi$
$409$	−13.3179	−	15.8717i	−0.658529	−	0.784804i	−0.987174	+	0.159650i	$0.948964\pi$
$410$	−18.9323	−	17.7187i	−0.935000	−	0.875065i
$411$		0			0
$412$	−1.26946	−	14.5100i	−0.0625416	−	0.714854i
$413$	−9.25351	+	2.47947i	−0.455335	+	0.122007i
$414$		0			0
$415$	−0.263493	−	0.112409i	−0.0129344	−	0.00551792i
$416$	3.14465	+	0.554487i	0.154179	+	0.0271860i
$417$		0			0
$418$	23.5687	−	10.9903i	1.15278	−	0.537551i
$419$	−17.4036	−	6.33438i	−0.850220	−	0.309455i	−0.120090	−	0.992763i	$-0.538318\pi$
$419$	−17.4036	−	6.33438i	−0.850220	−	0.309455i	−0.730130	+	0.683308i	$0.760540\pi$
$420$		0			0
$421$	−4.31040	+	24.4455i	−0.210076	+	1.19140i	0.679174	+	0.733978i	$0.262338\pi$
$421$	−4.31040	+	24.4455i	−0.210076	+	1.19140i	−0.889250	+	0.457422i	$0.848773\pi$
$422$	−21.1010	−	5.65400i	−1.02718	−	0.275233i
$423$		0			0
$424$	−2.96106	−	1.70957i	−0.143802	−	0.0830241i
$425$	−21.8751	−	4.33418i	−1.06110	−	0.210238i
$426$		0			0
$427$	15.9738	−	22.8130i	0.773026	−	1.10400i
$428$	−1.67161	−	0.146247i	−0.0808002	−	0.00706911i
$429$		0			0
$430$	5.71575	−	1.20413i	0.275638	−	0.0580683i
$431$			20.9323i			1.00827i	0.863623	+	0.504137i	$0.168189\pi$
$431$			20.9323i			1.00827i	−0.863623	+	0.504137i	$0.831811\pi$
$432$		0			0
$433$	8.58824	−	8.58824i	0.412725	−	0.412725i	−0.469962	−	0.882687i	$-0.655732\pi$
$433$	8.58824	−	8.58824i	0.412725	−	0.412725i	0.882687	+	0.469962i	$0.155732\pi$
$434$	10.7604	−	3.91646i	0.516515	−	0.187996i
$435$		0			0
$436$	4.80858	−	4.03488i	0.230289	−	0.193236i
$437$	−29.5359	−	20.6812i	−1.41289	−	0.989317i
$438$		0			0
$439$	20.1404	−	24.0024i	0.961250	−	1.14557i	−0.0280393	−	0.999607i	$-0.508926\pi$
$439$	20.1404	−	24.0024i	0.961250	−	1.14557i	0.989290	−	0.145967i	$-0.0466292\pi$
$440$	11.6278	−	1.40639i	0.554332	−	0.0670470i
$441$		0			0
$442$	−3.68603	+	13.7564i	−0.175326	+	0.654327i
$443$	−19.1752	+	13.4266i	−0.911041	+	0.637918i	−0.932233	−	0.361857i	$-0.882143\pi$
$443$	−19.1752	+	13.4266i	−0.911041	+	0.637918i	0.0211922	+	0.999775i	$0.493254\pi$
$444$		0			0
$445$	18.2359	−	34.1477i	0.864463	−	1.61876i
$446$	−2.43517	+	6.69057i	−0.115309	+	0.316808i
$447$		0			0
$448$	−1.91017	−	2.72801i	−0.0902472	−	0.128886i
$449$	−14.8865	−	25.7843i	−0.702540	−	1.21683i	−0.967572	−	0.252595i	$-0.918716\pi$
$449$	−14.8865	−	25.7843i	−0.702540	−	1.21683i	0.265032	−	0.964240i	$-0.414617\pi$
$450$		0			0
$451$	−30.3710	+	52.6041i	−1.43012	+	2.47703i
$452$	11.4996	−	1.00609i	0.540896	−	0.0473223i
$453$		0			0
$454$	−5.01586	+	0.884431i	−0.235406	+	0.0415084i
$455$	−12.5643	−	20.1882i	−0.589025	−	0.946438i
$456$		0			0
$457$	−27.1218	−	12.6471i	−1.26871	−	0.591608i	−0.332515	−	0.943098i	$-0.607897\pi$
$457$	−27.1218	−	12.6471i	−1.26871	−	0.591608i	−0.936191	+	0.351490i	$0.885675\pi$
$458$	1.25694	+	1.25694i	0.0587330	+	0.0587330i
$459$		0			0
$460$	−9.74979	−	12.9872i	−0.454586	−	0.605530i
$461$	6.01927	+	16.5378i	0.280345	+	0.770243i	0.997321	+	0.0731448i	$0.0233035\pi$
$461$	6.01927	+	16.5378i	0.280345	+	0.770243i	−0.716976	+	0.697098i	$0.754474\pi$
$462$		0			0
$463$	2.52092	−	28.8143i	0.117157	−	1.33911i	−0.679051	−	0.734091i	$-0.737609\pi$
$463$	2.52092	−	28.8143i	0.117157	−	1.33911i	0.796209	−	0.605022i	$-0.206836\pi$
$464$	0.721968	+	4.09448i	0.0335165	+	0.190082i
$465$		0			0
$466$	10.6458	+	8.93292i	0.493159	+	0.413809i
$467$	2.31798	+	8.65083i	0.107263	+	0.400313i	0.998592	−	0.0530450i	$-0.0168927\pi$
$467$	2.31798	+	8.65083i	0.107263	+	0.400313i	−0.891329	+	0.453358i	$0.850226\pi$
$468$		0			0
$469$	−16.6004	+	9.58424i	−0.766535	+	0.442559i
$470$	−7.16512	+	21.9172i	−0.330502	+	1.01096i
$471$		0			0
$472$	1.21571	+	2.60709i	0.0559575	+	0.120001i
$473$	−5.78271	−	12.4011i	−0.265889	−	0.570201i
$474$		0			0
$475$	−22.2718	−	10.9625i	−1.02190	−	0.502994i
$476$	12.8633	−	7.42664i	0.589589	−	0.340400i
$477$		0			0
$478$	0.111758	+	0.417085i	0.00511168	+	0.0190770i
$479$	−8.50714	−	7.13834i	−0.388701	−	0.326159i	0.427406	−	0.904060i	$-0.359428\pi$
$479$	−8.50714	−	7.13834i	−0.388701	−	0.326159i	−0.816107	+	0.577901i	$0.803872\pi$
$480$		0			0
$481$	0.448702	+	2.54471i	0.0204590	+	0.116029i
$482$	0.981679	−	11.2206i	0.0447142	−	0.511086i
$483$		0			0
$484$	−5.62165	−	15.4454i	−0.255530	−	0.702062i
$485$	−7.25180	+	5.44411i	−0.329287	+	0.247204i
$486$		0			0
$487$	5.98263	+	5.98263i	0.271099	+	0.271099i	0.829542	−	0.558444i	$-0.188601\pi$
$487$	5.98263	+	5.98263i	0.271099	+	0.271099i	−0.558444	+	0.829542i	$0.688601\pi$
$488$	−7.57899	−	3.53414i	−0.343085	−	0.159983i
$489$		0			0
$490$	−2.07380	+	8.90912i	−0.0936845	+	0.402473i
$491$	−24.2319	+	4.27274i	−1.09357	+	0.192826i	−0.691209	−	0.722655i	$-0.742922\pi$
$491$	−24.2319	+	4.27274i	−1.09357	+	0.192826i	−0.402362	+	0.915481i	$0.631811\pi$
$492$		0			0
$493$	−18.4728	+	1.61616i	−0.831973	+	0.0727882i
$494$	−7.92658	+	13.7292i	−0.356634	+	0.617708i
$495$		0			0
$496$	−1.71922	−	2.97777i	−0.0771950	−	0.133706i
$497$	−4.15719	−	5.93709i	−0.186476	−	0.266315i
$498$		0			0
$499$	−9.81593	+	26.9690i	−0.439421	+	1.20730i	0.500448	+	0.865767i	$0.333169\pi$
$499$	−9.81593	+	26.9690i	−0.439421	+	1.20730i	−0.939869	+	0.341534i	$0.889054\pi$
$500$	−8.00025	−	7.81000i	−0.357782	−	0.349274i
$501$		0			0
$502$	0.153128	−	0.107221i	0.00683442	−	0.00478551i
$503$	7.17039	−	26.7603i	0.319712	−	1.19318i	−0.599810	−	0.800143i	$-0.704757\pi$
$503$	7.17039	−	26.7603i	0.319712	−	1.19318i	0.919522	−	0.393039i	$-0.128576\pi$
$504$		0			0
$505$	−0.537283	+	0.685135i	−0.0239088	+	0.0304881i
$506$	−24.4525	+	29.1414i	−1.08705	+	1.29549i
$507$		0			0
$508$	−10.6247	−	7.43948i	−0.471394	−	0.330074i
$509$	18.9862	−	15.9313i	0.841549	−	0.706144i	−0.116363	−	0.993207i	$-0.537123\pi$
$509$	18.9862	−	15.9313i	0.841549	−	0.706144i	0.957912	+	0.287063i	$0.0926790\pi$
$510$		0			0
$511$	−5.74827	+	2.09220i	−0.254289	+	0.0925535i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			18.1192i			0.799204i
$515$	27.2827	+	17.7878i	1.20222	+	0.783823i
$516$		0			0
$517$	53.8094	+	4.70771i	2.36653	+	0.207045i
$518$	1.54575	−	2.20756i	0.0679163	−	0.0969945i
$519$		0			0
$520$	−5.31478	+	4.76809i	−0.233068	+	0.209095i
$521$	−27.3636	−	15.7984i	−1.19882	−	0.692141i	−0.238530	−	0.971135i	$-0.576666\pi$
$521$	−27.3636	−	15.7984i	−1.19882	−	0.692141i	−0.960293	+	0.278994i	$0.909999\pi$
$522$		0			0
$523$	−13.9163	−	3.72886i	−0.608517	−	0.163052i	−0.0586149	−	0.998281i	$-0.518668\pi$
$523$	−13.9163	−	3.72886i	−0.608517	−	0.163052i	−0.549902	+	0.835229i	$0.685335\pi$
$524$	2.21917	−	12.5855i	0.0969450	−	0.549802i
$525$		0			0
$526$	6.62845	+	2.41256i	0.289014	+	0.105193i
$527$	13.8988	−	6.48111i	0.605441	−	0.282322i
$528$		0			0
$529$	29.2931	+	5.16516i	1.27361	+	0.224572i
$530$	7.09388	−	2.85122i	0.308139	−	0.123849i
$531$		0			0
$532$	15.9705	−	4.27929i	0.692411	−	0.185531i
$533$	−3.22732	−	36.8884i	−0.139791	−	1.59781i
$534$		0			0
$535$	2.56389	−	2.73949i	0.110846	−	0.118438i
$536$	3.69976	+	4.40921i	0.159805	+	0.190449i
$537$		0			0
$538$	−11.8020	+	25.3095i	−0.508820	+	1.09117i
$539$	21.4276			0.922951
$540$		0			0
$541$	3.07552			0.132227			0.0661135	−	0.997812i	$-0.478940\pi$
$541$	3.07552			0.132227			0.0661135	+	0.997812i	$0.478940\pi$
$542$	10.8221	−	23.2082i	0.464851	−	0.996876i
$543$		0			0
$544$	−2.86687	−	3.41661i	−0.122916	−	0.146486i
$545$	0.464509	+	14.0285i	0.0198974	+	0.600913i
$546$		0			0
$547$	−1.76432	−	20.1663i	−0.0754368	−	0.862247i	−0.935792	−	0.352552i	$-0.885314\pi$
$547$	−1.76432	−	20.1663i	−0.0754368	−	0.862247i	0.860355	−	0.509695i	$-0.170242\pi$
$548$	−0.957480	+	0.256556i	−0.0409015	+	0.0109595i
$549$		0			0
$550$	−13.5699	+	22.4003i	−0.578621	+	0.955152i
$551$	−20.3280	−	3.58437i	−0.866000	−	0.152699i
$552$		0			0
$553$	27.7130	−	12.9228i	1.17847	−	0.549532i
$554$	−6.55958	−	2.38749i	−0.278690	−	0.101435i
$555$		0			0
$556$	0.412043	−	2.33681i	0.0174745	−	0.0991029i
$557$	34.2480	+	9.17672i	1.45113	+	0.388830i	0.896418	−	0.443209i	$-0.146160\pi$
$557$	34.2480	+	9.17672i	1.45113	+	0.388830i	0.554716	+	0.832040i	$0.312827\pi$
$558$		0			0
$559$	7.22387	+	4.17070i	0.305537	+	0.176402i
$560$	7.43582	+	0.403168i	0.314221	+	0.0170370i
$561$		0			0
$562$	9.10705	−	13.0062i	0.384158	−	0.548634i
$563$	45.3031	+	3.96350i	1.90930	+	0.167042i	0.979556	−	0.201174i	$-0.0644755\pi$
$563$	45.3031	+	3.96350i	1.90930	+	0.167042i	0.929741	+	0.368215i	$0.120031\pi$
$564$		0			0
$565$	−14.0974	+	21.6225i	−0.593082	+	0.909663i
$566$			25.9921i			1.09253i
$567$		0			0
$568$	−1.53891	+	1.53891i	−0.0645711	+	0.0645711i
$569$	24.8870	−	9.05812i	1.04332	−	0.379736i	0.237180	−	0.971466i	$-0.423777\pi$
$569$	24.8870	−	9.05812i	1.04332	−	0.379736i	0.806137	+	0.591730i	$0.201555\pi$
$570$		0			0
$571$	8.21205	−	6.89073i	0.343664	−	0.288368i	−0.454576	−	0.890708i	$-0.650209\pi$
$571$	8.21205	−	6.89073i	0.343664	−	0.288368i	0.798240	+	0.602340i	$0.205765\pi$
$572$	13.7010	+	9.59352i	0.572866	+	0.401125i
$573$		0			0
$574$	−24.8241	+	29.5842i	−1.03614	+	1.23482i
$575$	36.3048	+	0.764942i	1.51402	+	0.0319003i
$576$		0			0
$577$	8.05543	−	30.0633i	0.335352	−	1.25155i	−0.568135	−	0.822935i	$-0.692335\pi$
$577$	8.05543	−	30.0633i	0.335352	−	1.25155i	0.903487	−	0.428615i	$-0.140998\pi$
$578$	2.36912	−	1.65888i	0.0985425	−	0.0690002i
$579$		0			0
$580$	−8.20067	−	4.37940i	−0.340514	−	0.181845i
$581$	−0.145924	+	0.400922i	−0.00605393	+	0.0166330i
$582$		0			0
$583$	−10.2724	−	14.6706i	−0.425441	−	0.607593i
$584$	0.918417	+	1.59075i	0.0380044	+	0.0658255i
$585$		0			0
$586$	8.34404	−	14.4523i	0.344689	−	0.597019i
$587$	36.8788	−	3.22648i	1.52215	−	0.133171i	0.704840	−	0.709367i	$-0.251019\pi$
$587$	36.8788	−	3.22648i	1.52215	−	0.133171i	0.817312	+	0.576196i	$0.195463\pi$
$588$		0			0
$589$	16.8115	−	2.96432i	0.692705	−	0.122143i
$590$	−6.26481	−	1.45827i	−0.257918	−	0.0600362i
$591$		0			0
$592$	−0.733402	−	0.341991i	−0.0301426	−	0.0140557i
$593$	−7.77904	−	7.77904i	−0.319447	−	0.319447i	0.529108	−	0.848555i	$-0.322527\pi$
$593$	−7.77904	−	7.77904i	−0.319447	−	0.319447i	−0.848555	+	0.529108i	$0.822527\pi$
$594$		0			0
$595$	−4.68177	+	32.8813i	−0.191934	+	1.34800i
$596$	−3.74162	−	10.2800i	−0.153263	−	0.421086i
$597$		0			0
$598$	2.02119	−	23.1024i	0.0826528	−	0.944726i
$599$	−4.08580	−	23.1717i	−0.166941	−	0.946771i	−0.947040	−	0.321115i	$-0.895942\pi$
$599$	−4.08580	−	23.1717i	−0.166941	−	0.946771i	0.780099	−	0.625656i	$-0.215169\pi$
$600$		0			0
$601$	−23.2731	−	19.5285i	−0.949331	−	0.796583i	0.0298540	−	0.999554i	$-0.490496\pi$
$601$	−23.2731	−	19.5285i	−0.949331	−	0.796583i	−0.979185	+	0.202971i	$0.934940\pi$
$602$	−2.25162	−	8.40316i	−0.0917692	−	0.342487i
$603$		0			0
$604$	−12.5478	+	7.24447i	−0.510563	+	0.294773i
$605$	34.9340	+	11.4206i	1.42027	+	0.464312i
$606$		0			0
$607$	11.6254	+	24.9308i	0.471861	+	1.01191i	0.987864	+	0.155322i	$0.0496414\pi$
$607$	11.6254	+	24.9308i	0.471861	+	1.01191i	−0.516003	+	0.856587i	$0.672581\pi$
$608$	−2.09818	−	4.49956i	−0.0850924	−	0.182481i
$609$		0			0
$610$	16.6763	−	8.45909i	0.675205	−	0.342499i
$611$	−28.5168	+	16.4642i	−1.15367	+	0.666069i
$612$		0			0
$613$	−8.43596	−	31.4834i	−0.340725	−	1.27160i	−0.897527	−	0.440959i	$-0.854638\pi$
$613$	−8.43596	−	31.4834i	−0.340725	−	1.27160i	0.556802	−	0.830645i	$-0.312028\pi$
$614$	16.1549	+	13.5555i	0.651958	+	0.547057i
$615$		0			0
$616$	−3.02912	−	17.1790i	−0.122047	−	0.692162i
$617$	−3.37969	+	38.6301i	−0.136061	+	1.55519i	0.554666	+	0.832073i	$0.312846\pi$
$617$	−3.37969	+	38.6301i	−0.136061	+	1.55519i	−0.690728	+	0.723115i	$0.742710\pi$
$618$		0			0
$619$	−16.4915	−	45.3101i	−0.662851	−	1.82117i	−0.563500	−	0.826116i	$-0.690546\pi$
$619$	−16.4915	−	45.3101i	−0.662851	−	1.82117i	−0.0993508	−	0.995052i	$-0.531677\pi$
$620$	7.61179	+	1.08380i	0.305697	+	0.0435263i
$621$		0			0
$622$	−12.9765	−	12.9765i	−0.520309	−	0.520309i
$623$	−52.2537	−	24.3663i	−2.09350	−	0.976214i
$624$		0			0
$625$	24.7812	−	3.30032i	0.991248	−	0.132013i
$626$	10.0223	−	1.76720i	0.400571	−	0.0706315i
$627$		0			0
$628$	6.49436	−	0.568183i	0.259153	−	0.0226730i
$629$	1.80458	−	3.12563i	0.0719535	−	0.124627i
$630$		0			0
$631$	16.3443	+	28.3092i	0.650656	+	1.12697i	0.982964	+	0.183798i	$0.0588394\pi$
$631$	16.3443	+	28.3092i	0.650656	+	1.12697i	−0.332308	+	0.943171i	$0.607827\pi$
$632$	−5.26644	−	7.52125i	−0.209488	−	0.299179i
$633$		0			0
$634$	7.89986	−	21.7047i	0.313743	−	0.862003i
$635$	27.7506	−	8.42940i	1.10125	−	0.334511i
$636$		0			0
$637$	−10.7003	+	7.49240i	−0.423959	+	0.296860i
$638$	−5.63650	+	21.0357i	−0.223151	+	0.832811i
$639$		0			0
$640$	−0.268498	−	2.21989i	−0.0106133	−	0.0877488i
$641$	14.7737	−	17.6066i	0.583526	−	0.695419i	−0.390822	−	0.920466i	$-0.627809\pi$
$641$	14.7737	−	17.6066i	0.583526	−	0.695419i	0.974348	+	0.225047i	$0.0722536\pi$
$642$		0			0
$643$	9.46294	+	6.62602i	0.373182	+	0.261305i	0.745089	−	0.666965i	$-0.232407\pi$
$643$	9.46294	+	6.62602i	0.373182	+	0.261305i	−0.371907	+	0.928270i	$0.621296\pi$
$644$	−18.5279	+	15.5467i	−0.730101	+	0.612628i
$645$		0			0
$646$	20.8076	−	7.57334i	0.818663	−	0.297969i
$647$	−17.2591	+	17.2591i	−0.678525	+	0.678525i	−0.959666	−	0.281141i	$-0.909287\pi$
$647$	−17.2591	+	17.2591i	−0.678525	+	0.678525i	0.281141	+	0.959666i	$0.409287\pi$
$648$		0			0
$649$			15.0677i			0.591458i
$650$	−1.05616	−	15.9309i	−0.0414260	−	0.624860i
$651$		0			0
$652$	−2.80744	−	0.245619i	−0.109948	−	0.00961918i
$653$	−0.249319	+	0.356065i	−0.00975662	+	0.0139339i	−0.824001	−	0.566589i	$-0.808263\pi$
$653$	−0.249319	+	0.356065i	−0.00975662	+	0.0139339i	0.814244	+	0.580523i	$0.197152\pi$
$654$		0			0
$655$	19.0829	+	21.2708i	0.745629	+	0.831120i
$656$	10.0428	+	5.79821i	0.392105	+	0.226382i
$657$		0			0
$658$	33.1722	+	8.88845i	1.29319	+	0.346508i
$659$	−4.56670	+	25.8990i	−0.177893	+	1.00888i	0.756858	+	0.653580i	$0.226734\pi$
$659$	−4.56670	+	25.8990i	−0.177893	+	1.00888i	−0.934751	+	0.355303i	$0.884378\pi$
$660$		0			0
$661$	8.09777	+	2.94735i	0.314967	+	0.114639i	0.494666	−	0.869083i	$-0.335290\pi$
$661$	8.09777	+	2.94735i	0.314967	+	0.114639i	−0.179699	+	0.983722i	$0.557513\pi$
$662$	−19.7407	+	9.20524i	−0.767244	+	0.357772i
$663$		0			0
$664$	0.126167	+	0.0222466i	0.00489621	+	0.000863334i
$665$	−14.5072	+	34.0058i	−0.562564	+	1.31869i
$666$		0			0
$667$	29.1663	−	7.81510i	1.12933	−	0.302602i
$668$	−1.73638	−	19.8470i	−0.0671827	−	0.767902i
$669$		0			0
$670$	−12.8633	+	0.425929i	−0.496954	+	0.0164551i
$671$	−28.1558	−	33.5548i	−1.08694	−	1.29537i
$672$		0			0
$673$	−11.0496	+	23.6958i	−0.425929	+	0.913408i	0.569861	+	0.821741i	$0.306997\pi$
$673$	−11.0496	+	23.6958i	−0.425929	+	0.913408i	−0.995790	+	0.0916665i	$0.970781\pi$
$674$	3.07619			0.118490
$675$		0			0
$676$	2.80369			0.107834
$677$	1.41937	−	3.04384i	0.0545507	−	0.116984i	−0.877143	−	0.480229i	$-0.840553\pi$
$677$	1.41937	−	3.04384i	0.0545507	−	0.116984i	0.931694	+	0.363245i	$0.118331\pi$
$678$		0			0
$679$	8.68102	+	10.3456i	0.333147	+	0.397029i
$680$	9.96754	−	0.330044i	0.382238	−	0.0126566i
$681$		0			0
$682$	−1.56972	−	17.9420i	−0.0601076	−	0.687033i
$683$	12.3770	−	3.31641i	0.473593	−	0.126899i	−0.0141247	−	0.999900i	$-0.504496\pi$
$683$	12.3770	−	3.31641i	0.473593	−	0.126899i	0.487718	+	0.873001i	$0.337830\pi$
$684$		0			0
$685$	0.869747	−	2.03875i	0.0332313	−	0.0778965i
$686$	−9.54128	−	1.68239i	−0.364288	−	0.0642338i
$687$		0			0
$688$	−2.36752	+	1.10399i	−0.0902608	+	0.0420893i
$689$	10.2595	+	3.73414i	0.390854	+	0.142259i
$690$		0			0
$691$	−2.05589	+	11.6595i	−0.0782098	+	0.443550i	0.920407	+	0.390963i	$0.127858\pi$
$691$	−2.05589	+	11.6595i	−0.0782098	+	0.443550i	−0.998616	+	0.0525872i	$0.983253\pi$
$692$	−11.0668	−	2.96534i	−0.420696	−	0.112725i
$693$		0			0
$694$	13.1070	+	7.56730i	0.497533	+	0.287251i
$695$	3.54320	+	3.94945i	0.134401	+	0.149811i
$696$		0			0
$697$	−29.6658	+	42.3672i	−1.12367	+	1.60477i
$698$	−15.7976	−	1.38211i	−0.597946	−	0.0523135i
$699$		0			0
$700$	−10.9697	+	12.5274i	−0.414614	+	0.473492i
$701$			48.4334i			1.82930i	0.404243	+	0.914651i	$0.367535\pi$
$701$			48.4334i			1.82930i	−0.404243	+	0.914651i	$0.632465\pi$
$702$		0			0
$703$	2.84083	−	2.84083i	0.107144	−	0.107144i
$704$	−4.92211	+	1.79150i	−0.185509	+	0.0675197i
$705$		0			0
$706$	−18.8779	+	15.8404i	−0.710479	+	0.596163i
$707$	1.06223	+	0.743783i	0.0399493	+	0.0279728i
$708$		0			0
$709$	−4.36975	+	5.20766i	−0.164109	+	0.195578i	−0.841832	−	0.539740i	$-0.818523\pi$
$709$	−4.36975	+	5.20766i	−0.164109	+	0.195578i	0.677723	+	0.735318i	$0.262967\pi$
$710$	−0.584343	−	4.83124i	−0.0219300	−	0.181313i
$711$		0			0
$712$	−4.48080	+	16.7226i	−0.167925	+	0.626705i
$713$	−20.4557	+	14.3233i	−0.766074	+	0.536411i
$714$		0			0
$715$	−35.7855	+	10.8701i	−1.33830	+	0.406517i
$716$	−1.99441	+	5.47959i	−0.0745345	+	0.204782i
$717$		0			0
$718$	3.32504	+	4.74865i	0.124089	+	0.177218i
$719$	−9.66731	−	16.7443i	−0.360530	−	0.624456i	0.627518	−	0.778602i	$-0.284071\pi$
$719$	−9.66731	−	16.7443i	−0.360530	−	0.624456i	−0.988048	+	0.154146i	$0.950737\pi$
$720$		0			0
$721$	24.2534	−	42.0082i	0.903245	−	1.56447i
$722$	5.62692	−	0.492292i	0.209412	−	0.0183212i
$723$		0			0
$724$	15.9875	−	2.81903i	0.594171	−	0.104768i
$725$	19.0214	−	8.38666i	0.706438	−	0.311473i
$726$		0			0
$727$	−2.65131	−	1.23633i	−0.0983317	−	0.0458528i	0.372830	−	0.927900i	$-0.378387\pi$
$727$	−2.65131	−	1.23633i	−0.0983317	−	0.0458528i	−0.471162	+	0.882047i	$0.656165\pi$
$728$	7.51948	+	7.51948i	0.278690	+	0.278690i
$729$		0			0
$730$	−4.06628	−	0.578972i	−0.150500	−	0.0214287i
$731$	−3.98484	−	10.9482i	−0.147384	−	0.404935i
$732$		0			0
$733$	−3.51057	+	40.1260i	−0.129666	+	1.48209i	0.600942	+	0.799292i	$0.294792\pi$
$733$	−3.51057	+	40.1260i	−0.129666	+	1.48209i	−0.730608	+	0.682797i	$0.760763\pi$
$734$	4.18897	+	23.7568i	0.154618	+	0.876881i
$735$		0			0
$736$	5.56345	+	4.66829i	0.205072	+	0.172076i
$737$	7.80311	+	29.1216i	0.287431	+	1.07271i
$738$		0			0
$739$	35.1829	−	20.3128i	1.29422	−	0.747220i	0.314823	−	0.949150i	$-0.398055\pi$
$739$	35.1829	−	20.3128i	1.29422	−	0.747220i	0.979400	+	0.201930i	$0.0647214\pi$
$740$	1.61373	−	0.818567i	0.0593219	−	0.0300911i
$741$		0			0
$742$	−4.81223	−	10.3199i	−0.176663	−	0.378854i
$743$	−4.39016	−	9.41473i	−0.161059	−	0.345393i	0.809172	−	0.587571i	$-0.199916\pi$
$743$	−4.39016	−	9.41473i	−0.161059	−	0.345393i	−0.970232	+	0.242179i	$0.922138\pi$
$744$		0			0
$745$	23.2511	+	7.60122i	0.851855	+	0.278487i
$746$	7.12290	−	4.11241i	0.260788	−	0.150566i
$747$		0			0
$748$	−6.04648	−	22.5658i	−0.221081	−	0.825086i
$749$	−4.28081	−	3.59202i	−0.156417	−	0.131250i
$750$		0			0
$751$	−4.24628	−	24.0819i	−0.154949	−	0.878760i	−0.958832	−	0.283973i	$-0.908347\pi$
$751$	−4.24628	−	24.0819i	−0.154949	−	0.878760i	0.803883	−	0.594787i	$-0.202764\pi$
$752$	0.898762	−	10.2729i	0.0327745	−	0.374614i
$753$		0			0
$754$	−4.54068	−	12.4754i	−0.165362	−	0.454328i
$755$	4.56693	−	32.0748i	0.166208	−	1.16732i
$756$		0			0
$757$	32.1470	+	32.1470i	1.16840	+	1.16840i	0.982584	+	0.185818i	$0.0594935\pi$
$757$	32.1470	+	32.1470i	1.16840	+	1.16840i	0.185818	+	0.982584i	$0.440507\pi$
$758$	1.54006	+	0.718144i	0.0559377	+	0.0260842i
$759$		0			0
$760$	10.8124	+	2.51682i	0.392206	+	0.0912947i
$761$	−0.923556	+	0.162848i	−0.0334789	+	0.00590323i	−0.190363	−	0.981714i	$-0.560966\pi$
$761$	−0.923556	+	0.162848i	−0.0334789	+	0.00590323i	0.156884	+	0.987617i	$0.449855\pi$
$762$		0			0
$763$	20.8252	−	1.82197i	0.753922	−	0.0659596i
$764$	−0.534314	+	0.925460i	−0.0193308	+	0.0334820i
$765$		0			0
$766$	1.78256	+	3.08749i	0.0644067	+	0.111556i
$767$	−5.26858	−	7.52432i	−0.190238	−	0.271687i
$768$		0			0
$769$	−3.60209	+	9.89666i	−0.129895	+	0.356883i	−0.987542	−	0.157356i	$-0.949703\pi$
$769$	−3.60209	+	9.89666i	−0.129895	+	0.356883i	0.857647	+	0.514238i	$0.171925\pi$
$770$	34.4071	+	18.3744i	1.23995	+	0.662168i
$771$		0			0
$772$	10.1974	−	7.14029i	0.367012	−	0.256985i
$773$	−8.26359	+	30.8401i	−0.297221	+	1.10924i	0.642217	+	0.766523i	$0.278015\pi$
$773$	−8.26359	+	30.8401i	−0.297221	+	1.10924i	−0.939438	+	0.342720i	$0.888652\pi$
$774$		0			0
$775$	−12.4101	+	11.8979i	−0.445783	+	0.427385i
$776$	2.60669	−	3.10653i	0.0935747	−	0.111518i
$777$		0			0
$778$	6.00737	+	4.20641i	0.215375	+	0.150807i
$779$	−44.1034	+	37.0072i	−1.58017	+	1.32592i
$780$		0			0
$781$	−10.7122	+	3.89892i	−0.383313	+	0.139514i
$782$	−22.9043	+	22.9043i	−0.819055	+	0.819055i
$783$		0			0
$784$		−	4.09080i		−	0.146100i
$785$	−7.96144	+	12.2112i	−0.284156	+	0.435836i
$786$		0			0
$787$	−26.8444	−	2.34858i	−0.956901	−	0.0837180i	−0.402005	−	0.915638i	$-0.631687\pi$
$787$	−26.8444	−	2.34858i	−0.956901	−	0.0837180i	−0.554896	+	0.831920i	$0.687242\pi$
$788$	−0.0850226	+	0.121425i	−0.00302881	+	0.00432558i
$789$		0			0
$790$	20.5009	+	1.11155i	0.729390	+	0.0395473i
$791$	33.2929	+	19.2216i	1.18376	+	0.683443i
$792$		0			0
$793$	25.7929	+	6.91120i	0.915934	+	0.245424i
$794$	−3.41425	+	19.3632i	−0.121167	+	0.687174i
$795$		0			0
$796$	−15.8158	−	5.75649i	−0.560577	−	0.204033i
$797$	9.83868	−	4.58785i	0.348504	−	0.162510i	−0.240482	−	0.970654i	$-0.577305\pi$
$797$	9.83868	−	4.58785i	0.348504	−	0.162510i	0.588985	+	0.808144i	$0.299528\pi$
$798$		0			0
$799$	45.2940	+	7.98656i	1.60239	+	0.282544i
$800$	4.27650	+	2.59066i	0.151197	+	0.0915937i
$801$		0			0
$802$	−7.26432	+	1.94647i	−0.256512	+	0.0687322i
$803$	0.838555	+	9.58472i	0.0295919	+	0.338238i
$804$		0			0
$805$	−1.78979	−	54.0529i	−0.0630819	−	1.90511i
$806$	7.05747	+	8.41077i	0.248589	+	0.296257i
$807$		0			0
$808$	0.164559	−	0.352898i	0.00578917	−	0.0124149i
$809$	−31.3917			−1.10367			−0.551837	−	0.833952i	$-0.686073\pi$
$809$	−31.3917			−1.10367			−0.551837	+	0.833952i	$0.686073\pi$
$810$		0			0
$811$	−32.1801			−1.12999			−0.564997	−	0.825093i	$-0.691123\pi$
$811$	−32.1801			−1.12999			−0.564997	+	0.825093i	$0.691123\pi$
$812$	−5.85164	+	12.5489i	−0.205352	+	0.440379i
$813$		0			0
$814$	−2.72458	−	3.24702i	−0.0954963	−	0.113808i
$815$	4.30600	−	4.60092i	0.150833	−	0.161163i
$816$		0			0
$817$	−1.13034	−	12.9198i	−0.0395455	−	0.452007i
$818$	−20.0130	+	5.36247i	−0.699739	+	0.187494i
$819$		0			0
$820$	−24.0597	+	9.67024i	−0.840203	+	0.337699i
$821$	15.5403	+	2.74018i	0.542361	+	0.0956329i	0.438115	−	0.898919i	$-0.355646\pi$
$821$	15.5403	+	2.74018i	0.542361	+	0.0956329i	0.104246	+	0.994552i	$0.466757\pi$
$822$		0			0
$823$	39.7093	−	18.5167i	1.38418	−	0.645453i	0.419227	−	0.907881i	$-0.362301\pi$
$823$	39.7093	−	18.5167i	1.38418	−	0.645453i	0.964951	+	0.262428i	$0.0845234\pi$
$824$	−13.6870	−	4.98165i	−0.476809	−	0.173544i
$825$		0			0
$826$	−1.66354	+	9.43439i	−0.0578819	+	0.328265i
$827$	18.6514	+	4.99764i	0.648574	+	0.173785i	0.568084	−	0.822971i	$-0.307685\pi$
$827$	18.6514	+	4.99764i	0.648574	+	0.173785i	0.0804898	+	0.996755i	$0.474352\pi$
$828$		0			0
$829$	−25.0901	−	14.4858i	−0.871414	−	0.503111i	−0.00359643	−	0.999994i	$-0.501145\pi$
$829$	−25.0901	−	14.4858i	−0.871414	−	0.503111i	−0.867818	+	0.496882i	$0.834478\pi$
$830$	−0.213234	+	0.191300i	−0.00740146	+	0.00664013i
$831$		0			0
$832$	1.83152	−	2.61569i	0.0634967	−	0.0906827i
$833$	18.1758	+	1.59018i	0.629754	+	0.0550963i
$834$		0			0
$835$	37.3178	+	24.3304i	1.29143	+	0.841989i
$836$		−	26.0052i		−	0.899408i
$837$		0			0
$838$	−13.0960	+	13.0960i	−0.452392	+	0.452392i
$839$	−23.1135	+	8.41263i	−0.797967	+	0.290436i	−0.708644	−	0.705567i	$-0.750693\pi$
$839$	−23.1135	+	8.41263i	−0.797967	+	0.290436i	−0.0893230	+	0.996003i	$0.528470\pi$
$840$		0			0
$841$	−8.97342	+	7.52959i	−0.309428	+	0.259641i
$842$	20.3335	+	14.2377i	0.700738	+	0.490662i
$843$		0			0
$844$	−14.0419	+	16.7345i	−0.483344	+	0.576027i
$845$	−3.86865	+	4.93325i	−0.133086	+	0.169709i
$846$		0			0
$847$	14.1674	−	52.8734i	0.486797	−	1.81675i
$848$	−2.80080	+	1.96114i	−0.0961798	+	0.0673458i
$849$		0			0
$850$	−13.1729	+	17.9939i	−0.451827	+	0.617184i
$851$	−2.01006	+	5.52259i	−0.0689039	+	0.189312i
$852$		0			0
$853$	16.7409	+	23.9084i	0.573196	+	0.818609i	0.996161	−	0.0875369i	$-0.0278996\pi$
$853$	16.7409	+	23.9084i	0.573196	+	0.818609i	−0.422965	+	0.906146i	$0.639011\pi$
$854$	−13.9247	−	24.1184i	−0.476495	−	0.825313i
$855$		0			0
$856$	−0.838997	+	1.45319i	−0.0286763	+	0.0496688i
$857$	−14.5118	+	1.26962i	−0.495715	+	0.0433695i	−0.332273	−	0.943183i	$-0.607815\pi$
$857$	−14.5118	+	1.26962i	−0.495715	+	0.0433695i	−0.163443	+	0.986553i	$0.552260\pi$
$858$		0			0
$859$	34.2219	−	6.03425i	1.16764	−	0.205886i	0.443974	−	0.896039i	$-0.353568\pi$
$859$	34.2219	−	6.03425i	1.16764	−	0.205886i	0.723663	+	0.690153i	$0.242457\pi$
$860$	1.32427	−	5.68911i	0.0451571	−	0.193997i
$861$		0			0
$862$	18.9711	+	8.84638i	0.646159	+	0.301309i
$863$	3.52306	+	3.52306i	0.119927	+	0.119927i	0.764523	−	0.644596i	$-0.222975\pi$
$863$	3.52306	+	3.52306i	0.119927	+	0.119927i	−0.644596	+	0.764523i	$0.722975\pi$
$864$		0			0
$865$	20.4881	−	15.3809i	0.696616	−	0.522967i
$866$	−4.15404	−	11.4131i	−0.141160	−	0.387834i
$867$		0			0
$868$	0.998016	−	11.4074i	0.0338749	−	0.387192i
$869$	−8.35144	−	47.3634i	−0.283303	−	1.60669i
$870$		0			0
$871$	−14.0793	−	11.8140i	−0.477060	−	0.400301i
$872$	−1.62465	−	6.06327i	−0.0550175	−	0.205328i
$873$		0			0
$874$	−31.2260	+	18.0283i	−1.05623	+	0.609817i
$875$	−6.90631	−	36.5876i	−0.233476	−	1.23689i
$876$		0			0
$877$	−0.330192	−	0.708100i	−0.0111498	−	0.0239108i	0.900654	−	0.434537i	$-0.143088\pi$
$877$	−0.330192	−	0.708100i	−0.0111498	−	0.0239108i	−0.911804	+	0.410626i	$0.865310\pi$
$878$	−13.2419	−	28.3973i	−0.446892	−	0.958362i
$879$		0			0
$880$	3.63949	−	11.1327i	0.122687	−	0.375284i
$881$	27.0459	−	15.6150i	0.911199	−	0.526081i	0.0303824	−	0.999538i	$-0.490327\pi$
$881$	27.0459	−	15.6150i	0.911199	−	0.526081i	0.880817	+	0.473457i	$0.156994\pi$
$882$		0			0
$883$	9.70596	+	36.2231i	0.326632	+	1.21901i	0.912662	+	0.408716i	$0.134023\pi$
$883$	9.70596	+	36.2231i	0.326632	+	1.21901i	−0.586030	+	0.810289i	$0.699310\pi$
$884$	10.9098	+	9.15440i	0.366936	+	0.307896i
$885$		0			0
$886$	4.06486	+	23.0530i	0.136562	+	0.774480i
$887$	−0.959560	+	10.9678i	−0.0322189	+	0.368263i	0.962920	+	0.269786i	$0.0869529\pi$
$887$	−0.959560	+	10.9678i	−0.0322189	+	0.368263i	−0.995139	+	0.0984777i	$0.968603\pi$
$888$		0			0
$889$	−14.7735	−	40.5899i	−0.495488	−	1.36134i
$890$	−23.2415	−	30.9587i	−0.779057	−	1.03774i
$891$		0			0
$892$	5.03457	+	5.03457i	0.168570	+	0.168570i
$893$	46.4001	+	21.6367i	1.55272	+	0.724045i
$894$		0			0
$895$	−6.88967	−	11.0702i	−0.230296	−	0.370037i
$896$	−3.27969	+	0.578298i	−0.109567	+	0.0193196i
$897$		0			0
$898$	−29.6598	+	2.59490i	−0.989760	+	0.0865928i
$899$	−7.14789	+	12.3805i	−0.238396	+	0.412913i
$900$		0			0
$901$	−7.62479	−	13.2065i	−0.254019	−	0.439973i
$902$	34.8402	+	49.7570i	1.16005	+	1.65673i
$903$		0			0
$904$	3.94812	−	10.8474i	0.131313	−	0.360779i
$905$	−17.1000	+	32.0207i	−0.568423	+	1.06440i
$906$		0			0
$907$	−3.97166	+	2.78099i	−0.131877	+	0.0923411i	−0.637654	−	0.770323i	$-0.720095\pi$
$907$	−3.97166	+	2.78099i	−0.131877	+	0.0923411i	0.505777	+	0.862664i	$0.331206\pi$
$908$	−1.31823	+	4.91969i	−0.0437469	+	0.163266i
$909$		0			0
$910$	−23.6066	+	2.85525i	−0.782552	+	0.0946505i
$911$	−19.2529	+	22.9447i	−0.637878	+	0.760193i	−0.984033	−	0.177984i	$-0.943042\pi$
$911$	−19.2529	+	22.9447i	−0.637878	+	0.760193i	0.346156	+	0.938177i	$0.387487\pi$
$912$		0			0
$913$	0.549696	+	0.384901i	0.0181923	+	0.0127384i
$914$	−22.9244	+	19.2358i	−0.758271	+	0.636265i
$915$		0			0
$916$	1.67038	−	0.607970i	0.0551910	−	0.0200879i
$917$	30.0945	−	30.0945i	0.993808	−	0.993808i
$918$		0			0
$919$		−	28.1326i		−	0.928008i	−0.885833	−	0.464004i	$-0.846412\pi$
$919$		−	28.1326i		−	0.928008i	0.885833	−	0.464004i	$-0.153588\pi$
$920$	−15.8908	+	3.34770i	−0.523904	+	0.110370i
$921$		0			0
$922$	17.5322	+	1.53387i	0.577392	+	0.0505153i
$923$	3.98603	−	5.69264i	0.131202	−	0.187375i
$924$		0			0
$925$	−0.786379	+	3.96894i	−0.0258560	+	0.130498i
$926$	−25.0492	−	14.4622i	−0.823168	−	0.475256i
$927$		0			0
$928$	4.01598	+	1.07608i	0.131831	+	0.0353240i
$929$	7.38000	−	41.8541i	0.242130	−	1.37319i	−0.584935	−	0.811081i	$-0.698880\pi$
$929$	7.38000	−	41.8541i	0.242130	−	1.37319i	0.827065	−	0.562107i	$-0.190009\pi$
$930$		0			0
$931$	19.0848	+	6.94631i	0.625480	+	0.227656i
$932$	12.5951	−	5.87319i	0.412566	−	0.192383i
$933$		0			0
$934$	8.81994	+	1.55519i	0.288597	+	0.0508875i
$935$	48.0489	+	20.4981i	1.57137	+	0.670359i
$936$		0			0
$937$	−2.51573	+	0.674087i	−0.0821852	+	0.0220215i	−0.299677	−	0.954041i	$-0.596879\pi$
$937$	−2.51573	+	0.674087i	−0.0821852	+	0.0220215i	0.217492	+	0.976062i	$0.430212\pi$
$938$	1.67064	+	19.0955i	0.0545484	+	0.623492i
$939$		0			0
$940$	16.8356	+	15.7564i	0.549116	+	0.513917i
$941$	−19.1836	−	22.8621i	−0.625366	−	0.745282i	0.356617	−	0.934251i	$-0.383930\pi$
$941$	−19.1836	−	22.8621i	−0.625366	−	0.745282i	−0.981983	+	0.188968i	$0.939486\pi$
$942$		0			0
$943$	35.5929	−	76.3291i	1.15906	−	2.48562i
$944$	2.87661			0.0936257
$945$		0			0
$946$	−13.6831			−0.444874
$947$	−11.6210	+	24.9214i	−0.377633	+	0.809836i	0.622007	+	0.783011i	$0.286317\pi$
$947$	−11.6210	+	24.9214i	−0.377633	+	0.809836i	−0.999640	+	0.0268247i	$0.991460\pi$
$948$		0			0
$949$	−3.77015	−	4.49309i	−0.122384	−	0.145852i
$950$	−19.3479	+	15.5522i	−0.627728	+	0.504579i
$951$		0			0
$952$	−1.29455	−	14.7968i	−0.0419566	−	0.479566i
$953$	−34.8024	+	9.32527i	−1.12736	+	0.302075i	−0.773858	−	0.633359i	$-0.781676\pi$
$953$	−34.8024	+	9.32527i	−1.12736	+	0.302075i	−0.353502	+	0.935434i	$0.615009\pi$
$954$		0			0
$955$	−0.891128	−	2.21714i	−0.0288362	−	0.0717451i
$956$	0.425238	+	0.0749810i	0.0137532	+	0.00242506i
$957$		0			0
$958$	−10.0648	+	4.69330i	−0.325179	+	0.151634i
$959$	−3.10208	−	1.12907i	−0.100171	−	0.0364594i
$960$		0			0
$961$	−3.33008	+	18.8858i	−0.107422	+	0.609221i
$962$	2.49592	+	0.668781i	0.0804718	+	0.0215624i
$963$		0			0
$964$	−9.75448	−	5.63175i	−0.314171	−	0.181386i
$965$	−1.50706	+	27.7954i	−0.0485139	+	0.894764i
$966$		0			0
$967$	−22.7870	+	32.5433i	−0.732782	+	1.04652i	0.263854	+	0.964563i	$0.415006\pi$
$967$	−22.7870	+	32.5433i	−0.732782	+	1.04652i	−0.996636	+	0.0819581i	$0.973883\pi$
$968$	−16.3741	−	1.43255i	−0.526283	−	0.0460438i
$969$		0			0
$970$	1.86929	+	8.87314i	0.0600194	+	0.284899i
$971$			44.1783i			1.41775i	0.705334	+	0.708875i	$0.250797\pi$
$971$			44.1783i			1.41775i	−0.705334	+	0.708875i	$0.749203\pi$
$972$		0			0
$973$	5.58777	−	5.58777i	0.179136	−	0.179136i
$974$	7.95047	−	2.89373i	0.254749	−	0.0927212i
$975$		0			0
$976$	−6.40604	+	5.37530i	−0.205052	+	0.172059i
$977$	7.68048	+	5.37793i	0.245720	+	0.172055i	0.689949	−	0.723858i	$-0.257633\pi$
$977$	7.68048	+	5.37793i	0.245720	+	0.172055i	−0.444228	+	0.895914i	$0.646522\pi$
$978$		0			0
$979$	−58.2898	+	69.4670i	−1.86295	+	2.22018i
$980$	7.19798	+	5.64466i	0.229931	+	0.180312i
$981$		0			0
$982$	−6.36843	+	23.7673i	−0.203225	+	0.758445i
$983$	28.3599	−	19.8578i	0.904540	−	0.633366i	−0.0259580	−	0.999663i	$-0.508264\pi$
$983$	28.3599	−	19.8578i	0.904540	−	0.633366i	0.930498	+	0.366297i	$0.119375\pi$
$984$		0			0
$985$	−0.0963360	−	0.317149i	−0.00306952	−	0.0101052i
$986$	−6.34221	+	17.4251i	−0.201977	+	0.554927i
$987$		0			0
$988$	9.09300	+	12.9862i	0.289287	+	0.413145i
$989$	9.48589	+	16.4300i	0.301634	+	0.522445i
$990$		0			0
$991$	−24.9663	+	43.2429i	−0.793081	+	1.37366i	0.130970	+	0.991386i	$0.458191\pi$
$991$	−24.9663	+	43.2429i	−0.793081	+	1.37366i	−0.924051	+	0.382270i	$0.875142\pi$
$992$	−3.42535	+	0.299679i	−0.108755	+	0.00951482i
$993$		0			0
$994$	−7.13774	+	1.25858i	−0.226395	+	0.0399196i
$995$	31.9522	−	19.8858i	1.01295	−	0.630422i
$996$		0			0
$997$	28.7747	+	13.4179i	0.911305	+	0.424948i	0.820975	−	0.570964i	$-0.193430\pi$
$997$	28.7747	+	13.4179i	0.911305	+	0.424948i	0.0903293	+	0.995912i	$0.471208\pi$
$998$	20.2939	+	20.2939i	0.642391	+	0.642391i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.467.18		216
3.2	odd	2		270.2.r.a.47.9	yes	216
5.3	odd	4	inner	810.2.s.a.143.9		216
15.8	even	4		270.2.r.a.263.14	yes	216
27.4	even	9		270.2.r.a.77.14	yes	216
27.23	odd	18	inner	810.2.s.a.17.9		216
135.23	even	36	inner	810.2.s.a.503.18		216
135.58	odd	36		270.2.r.a.23.9	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.9	✓	216	135.58	odd	36
270.2.r.a.47.9	yes	216	3.2	odd	2
270.2.r.a.77.14	yes	216	27.4	even	9
270.2.r.a.263.14	yes	216	15.8	even	4
810.2.s.a.17.9		216	27.23	odd	18	inner
810.2.s.a.143.9		216	5.3	odd	4	inner
810.2.s.a.467.18		216	1.1	even	1	trivial
810.2.s.a.503.18		216	135.23	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.422618 - 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(2.23484 - 0.0739999i) q^{5} +(-0.290253 - 3.31761i) q^{7} +(-0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.422618 - 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(2.23484 - 0.0739999i) q^{5} +(-0.290253 - 3.31761i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.877419 - 2.05673i) q^{10} +(-5.15842 - 0.909569i) q^{11} +(2.89399 - 1.34949i) q^{13} +(-3.12944 - 1.13902i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-4.30809 - 1.15435i) q^{17} +(-4.29957 - 2.48236i) q^{19} +(-1.49322 - 1.66442i) q^{20} +(-3.00439 + 4.29072i) q^{22} +(7.23494 + 0.632975i) q^{23} +(4.98905 - 0.330756i) q^{25} -3.19317i q^{26} +(-2.35487 + 2.35487i) q^{28} +(3.90691 - 1.42200i) q^{29} +(-2.63399 + 2.21018i) q^{31} +(0.819152 + 0.573576i) q^{32} +(-2.86687 + 3.41661i) q^{34} +(-0.894174 - 7.39286i) q^{35} +(-0.209441 + 0.781646i) q^{37} +(-4.06686 + 2.84764i) q^{38} +(-2.13954 + 0.649898i) q^{40} +(3.96621 - 10.8971i) q^{41} +(1.49834 + 2.13984i) q^{43} +(2.61900 + 4.53624i) q^{44} +(3.63129 - 6.28957i) q^{46} +(-10.2729 + 0.898762i) q^{47} +(-4.02865 + 0.710360i) q^{49} +(1.80870 - 4.66140i) q^{50} +(-2.89399 - 1.34949i) q^{52} +(2.41770 + 2.41770i) q^{53} +(-11.5956 - 1.65102i) q^{55} +(1.13902 + 3.12944i) q^{56} +(0.362363 - 4.14183i) q^{58} +(-0.499518 - 2.83291i) q^{59} +(6.40604 + 5.37530i) q^{61} +(0.889931 + 3.32127i) q^{62} +(0.866025 - 0.500000i) q^{64} +(6.36775 - 3.23005i) q^{65} +(-2.43251 - 5.21653i) q^{67} +(1.88490 + 4.04219i) q^{68} +(-7.07810 - 2.31396i) q^{70} +(1.88477 - 1.08817i) q^{71} +(-0.475408 - 1.77425i) q^{73} +(0.619898 + 0.520156i) q^{74} +(0.862114 + 4.88929i) q^{76} +(-1.52035 + 17.3776i) q^{77} +(3.14035 + 8.62803i) q^{79} +(-0.315201 + 2.21374i) q^{80} +(-8.19991 - 8.19991i) q^{82} +(-0.116110 - 0.0541428i) q^{83} +(-9.71333 - 2.26099i) q^{85} +(2.57258 - 0.453616i) q^{86} +(5.21807 - 0.456522i) q^{88} +(8.65625 - 14.9931i) q^{89} +(-5.31708 - 9.20945i) q^{91} +(-4.16564 - 5.94915i) q^{92} +(-3.52696 + 9.69024i) q^{94} +(-9.79256 - 5.22951i) q^{95} +(-3.32190 + 2.32602i) q^{97} +(-1.05878 + 3.95141i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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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