LMFDB - Embedded newform 810.2.s.a.17.9

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			17.9
Character	$\chi$	$=$	810.17
Dual form			810.2.s.a.143.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.12538 + 0.694824i) q^{5} +(-3.31761 - 0.290253i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.12538 + 0.694824i) q^{5} +(-3.31761 - 0.290253i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.21989 + 0.268498i) q^{10} +(-5.15842 + 0.909569i) q^{11} +(1.34949 - 2.89399i) q^{13} +(3.12944 - 1.13902i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-1.15435 - 4.30809i) q^{17} +(4.29957 - 2.48236i) q^{19} +(1.89843 - 1.18151i) q^{20} +(4.29072 - 3.00439i) q^{22} +(-0.632975 - 7.23494i) q^{23} +(4.03444 + 2.95352i) q^{25} +3.19317i q^{26} +(-2.35487 + 2.35487i) q^{28} +(-3.90691 - 1.42200i) q^{29} +(-2.63399 - 2.21018i) q^{31} +(0.573576 + 0.819152i) q^{32} +(2.86687 + 3.41661i) q^{34} +(-6.84950 - 2.92205i) q^{35} +(0.781646 - 0.209441i) q^{37} +(-2.84764 + 4.06686i) q^{38} +(-1.22124 + 1.87312i) q^{40} +(3.96621 + 10.8971i) q^{41} +(-2.13984 - 1.49834i) q^{43} +(-2.61900 + 4.53624i) q^{44} +(3.63129 + 6.28957i) q^{46} +(0.898762 - 10.2729i) q^{47} +(4.02865 + 0.710360i) q^{49} +(-4.90466 - 0.971775i) q^{50} +(-1.34949 - 2.89399i) q^{52} +(-2.41770 - 2.41770i) q^{53} +(-11.5956 - 1.65102i) q^{55} +(1.13902 - 3.12944i) q^{56} +(4.14183 - 0.362363i) q^{58} +(0.499518 - 2.83291i) q^{59} +(6.40604 - 5.37530i) q^{61} +(3.32127 + 0.889931i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(4.87899 - 5.21316i) q^{65} +(-5.21653 - 2.43251i) q^{67} +(-4.04219 - 1.88490i) q^{68} +(7.44266 - 0.246441i) q^{70} +(1.88477 + 1.08817i) q^{71} +(1.77425 + 0.475408i) q^{73} +(-0.619898 + 0.520156i) q^{74} +(0.862114 - 4.88929i) q^{76} +(17.3776 - 1.52035i) q^{77} +(-3.14035 + 8.62803i) q^{79} +(0.315201 - 2.21374i) q^{80} +(-8.19991 - 8.19991i) q^{82} +(0.0541428 + 0.116110i) q^{83} +(0.539940 - 9.95838i) q^{85} +(2.57258 + 0.453616i) q^{86} +(0.456522 - 5.21807i) q^{88} +(-8.65625 - 14.9931i) q^{89} +(-5.31708 + 9.20945i) q^{91} +(-5.94915 - 4.16564i) q^{92} +(3.52696 + 9.69024i) q^{94} +(10.8630 - 2.28850i) q^{95} +(2.32602 - 3.32190i) q^{97} +(-3.95141 + 1.05878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.12538	+	0.694824i	0.950497	+	0.310735i
$5$	2.12538	+	0.694824i	0.950497	+	0.310735i
$6$		0			0
$7$	−3.31761	−	0.290253i	−1.25394	−	0.109705i	−0.559240	−	0.829006i	$-0.688907\pi$
$7$	−3.31761	−	0.290253i	−1.25394	−	0.109705i	−0.694699	+	0.719300i	$0.744463\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−2.21989	+	0.268498i	−0.701991	+	0.0849064i
$11$	−5.15842	+	0.909569i	−1.55532	+	0.274245i	−0.884203	−	0.467104i	$-0.845297\pi$
$11$	−5.15842	+	0.909569i	−1.55532	+	0.274245i	−0.671120	+	0.741349i	$0.734186\pi$
$12$		0			0
$13$	1.34949	−	2.89399i	0.374281	−	0.802649i	−0.625468	−	0.780250i	$-0.715092\pi$
$13$	1.34949	−	2.89399i	0.374281	−	0.802649i	0.999749	−	0.0223988i	$-0.00713034\pi$
$14$	3.12944	−	1.13902i	0.836379	−	0.304417i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−1.15435	−	4.30809i	−0.279971	−	1.04487i	−0.952437	−	0.304737i	$-0.901431\pi$
$17$	−1.15435	−	4.30809i	−0.279971	−	1.04487i	0.672466	−	0.740128i	$-0.265235\pi$
$18$		0			0
$19$	4.29957	−	2.48236i	0.986389	−	0.569492i	0.0821962	−	0.996616i	$-0.473807\pi$
$19$	4.29957	−	2.48236i	0.986389	−	0.569492i	0.904193	+	0.427124i	$0.140473\pi$
$20$	1.89843	−	1.18151i	0.424502	−	0.264193i
$21$		0			0
$22$	4.29072	−	3.00439i	0.914784	−	0.640538i
$23$	−0.632975	−	7.23494i	−0.131984	−	1.50859i	−0.716718	−	0.697363i	$-0.754356\pi$
$23$	−0.632975	−	7.23494i	−0.131984	−	1.50859i	0.584733	−	0.811226i	$-0.301199\pi$
$24$		0			0
$25$	4.03444	+	2.95352i	0.806888	+	0.590705i
$26$			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	$-0.515042\pi$
$29$	−3.90691	−	1.42200i	−0.725495	−	0.264059i	−0.678257	+	0.734825i	$0.737264\pi$
$30$		0			0
$31$	−2.63399	−	2.21018i	−0.473079	−	0.396960i	0.374837	−	0.927091i	$-0.377699\pi$
$31$	−2.63399	−	2.21018i	−0.473079	−	0.396960i	−0.847916	+	0.530130i	$0.822143\pi$
$32$	0.573576	+	0.819152i	0.101395	+	0.144807i
$33$		0			0
$34$	2.86687	+	3.41661i	0.491665	+	0.585943i
$35$	−6.84950	−	2.92205i	−1.15778	−	0.493917i
$36$		0			0
$37$	0.781646	−	0.209441i	0.128502	−	0.0344319i	−0.193995	−	0.981003i	$-0.562145\pi$
$37$	0.781646	−	0.209441i	0.128502	−	0.0344319i	0.322497	+	0.946571i	$0.395478\pi$
$38$	−2.84764	+	4.06686i	−0.461949	+	0.659731i
$39$		0			0
$40$	−1.22124	+	1.87312i	−0.193094	+	0.296166i
$41$	3.96621	+	10.8971i	0.619418	+	1.70184i	0.708407	+	0.705804i	$0.249414\pi$
$41$	3.96621	+	10.8971i	0.619418	+	1.70184i	−0.0889892	+	0.996033i	$0.528364\pi$
$42$		0			0
$43$	−2.13984	−	1.49834i	−0.326323	−	0.228494i	0.398922	−	0.916985i	$-0.369385\pi$
$43$	−2.13984	−	1.49834i	−0.326323	−	0.228494i	−0.725245	+	0.688491i	$0.758273\pi$
$44$	−2.61900	+	4.53624i	−0.394829	+	0.683864i
$45$		0			0
$46$	3.63129	+	6.28957i	0.535404	+	0.927347i
$47$	0.898762	−	10.2729i	0.131098	−	1.49846i	−0.591004	−	0.806669i	$-0.701268\pi$
$47$	0.898762	−	10.2729i	0.131098	−	1.49846i	0.722102	−	0.691787i	$-0.243176\pi$
$48$		0			0
$49$	4.02865	+	0.710360i	0.575521	+	0.101480i
$50$	−4.90466	−	0.971775i	−0.693623	−	0.137430i
$51$		0			0
$52$	−1.34949	−	2.89399i	−0.187141	−	0.401324i
$53$	−2.41770	−	2.41770i	−0.332096	−	0.332096i	0.521286	−	0.853382i	$-0.325453\pi$
$53$	−2.41770	−	2.41770i	−0.332096	−	0.332096i	−0.853382	+	0.521286i	$0.825453\pi$
$54$		0			0
$55$	−11.5956	−	1.65102i	−1.56355	−	0.222624i
$56$	1.13902	−	3.12944i	0.152209	−	0.418190i
$57$		0			0
$58$	4.14183	−	0.362363i	0.543848	−	0.0475806i
$59$	0.499518	−	2.83291i	0.0650317	−	0.368813i	−0.934873	−	0.354983i	$-0.884487\pi$
$59$	0.499518	−	2.83291i	0.0650317	−	0.368813i	0.999904	−	0.0138300i	$-0.00440235\pi$
$60$		0			0
$61$	6.40604	−	5.37530i	0.820209	−	0.688237i	−0.132812	−	0.991141i	$-0.542401\pi$
$61$	6.40604	−	5.37530i	0.820209	−	0.688237i	0.953021	+	0.302904i	$0.0979562\pi$
$62$	3.32127	+	0.889931i	0.421802	+	0.113021i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	4.87899	−	5.21316i	0.605164	−	0.646613i
$66$		0			0
$67$	−5.21653	−	2.43251i	−0.637301	−	0.297178i	0.0769849	−	0.997032i	$-0.475471\pi$
$67$	−5.21653	−	2.43251i	−0.637301	−	0.297178i	−0.714286	+	0.699854i	$0.753248\pi$
$68$	−4.04219	−	1.88490i	−0.490188	−	0.228578i
$69$		0			0
$70$	7.44266	−	0.246441i	0.889569	−	0.0294553i
$71$	1.88477	+	1.08817i	0.223681	+	0.129142i	0.607654	−	0.794202i	$-0.292111\pi$
$71$	1.88477	+	1.08817i	0.223681	+	0.129142i	−0.383973	+	0.923345i	$0.625444\pi$
$72$		0			0
$73$	1.77425	+	0.475408i	0.207660	+	0.0556423i	0.361149	−	0.932508i	$-0.382384\pi$
$73$	1.77425	+	0.475408i	0.207660	+	0.0556423i	−0.153490	+	0.988150i	$0.549051\pi$
$74$	−0.619898	+	0.520156i	−0.0720617	+	0.0604669i
$75$		0			0
$76$	0.862114	−	4.88929i	0.0988913	−	0.560840i
$77$	17.3776	−	1.52035i	1.98037	−	0.173260i
$78$		0			0
$79$	−3.14035	+	8.62803i	−0.353316	+	0.970729i	0.627981	+	0.778229i	$0.283882\pi$
$79$	−3.14035	+	8.62803i	−0.353316	+	0.970729i	−0.981297	+	0.192500i	$0.938340\pi$
$80$	0.315201	−	2.21374i	0.0352405	−	0.247504i
$81$		0			0
$82$	−8.19991	−	8.19991i	−0.905528	−	0.905528i
$83$	0.0541428	+	0.116110i	0.00594295	+	0.0127447i	0.909257	−	0.416235i	$-0.136651\pi$
$83$	0.0541428	+	0.116110i	0.00594295	+	0.0127447i	−0.903314	+	0.428980i	$0.858873\pi$
$84$		0			0
$85$	0.539940	−	9.95838i	0.0585647	−	1.08014i
$86$	2.57258	+	0.453616i	0.277409	+	0.0489146i
$87$		0			0
$88$	0.456522	−	5.21807i	0.0486654	−	0.556248i
$89$	−8.65625	−	14.9931i	−0.917560	−	1.58926i	−0.803109	−	0.595832i	$-0.796822\pi$
$89$	−8.65625	−	14.9931i	−0.917560	−	1.58926i	−0.114451	−	0.993429i	$-0.536511\pi$
$90$		0			0
$91$	−5.31708	+	9.20945i	−0.557381	+	0.965412i
$92$	−5.94915	−	4.16564i	−0.620242	−	0.434298i
$93$		0			0
$94$	3.52696	+	9.69024i	0.363778	+	0.999472i
$95$	10.8630	−	2.28850i	1.11452	−	0.234795i
$96$		0			0
$97$	2.32602	−	3.32190i	0.236171	−	0.337288i	−0.683519	−	0.729933i	$-0.739551\pi$
$97$	2.32602	−	3.32190i	0.236171	−	0.337288i	0.919690	+	0.392646i	$0.128440\pi$
$98$	−3.95141	+	1.05878i	−0.399152	+	0.106953i
$99$		0			0
$100$	4.85582	−	1.19207i	0.485582	−	0.119207i
$101$	−0.250288	−	0.298282i	−0.0249046	−	0.0296802i	0.753448	−	0.657507i	$-0.228389\pi$
$101$	−0.250288	−	0.298282i	−0.0249046	−	0.0296802i	−0.778353	+	0.627827i	$0.783945\pi$
$102$		0			0
$103$	−8.35436	−	11.9313i	−0.823180	−	1.17562i	−0.982105	−	0.188332i	$-0.939692\pi$
$103$	−8.35436	−	11.9313i	−0.823180	−	1.17562i	0.158926	−	0.987291i	$-0.449197\pi$
$104$	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	−0.762130	−	0.647424i	$-0.775846\pi$
$107$	−1.18652	+	1.18652i	−0.114705	+	0.114705i	0.647424	+	0.762130i	$0.275846\pi$
$108$		0			0
$109$			6.27716i			0.601243i	0.953744	+	0.300621i	$0.0971940\pi$
$109$			6.27716i			0.601243i	−0.953744	+	0.300621i	$0.902806\pi$
$110$	11.2069	−	3.40417i	1.06854	−	0.324574i
$111$		0			0
$112$	0.290253	+	3.31761i	0.0274264	+	0.313485i
$113$	−9.45592	+	6.62110i	−0.889538	+	0.622861i	−0.926434	−	0.376458i	$-0.877142\pi$
$113$	−9.45592	+	6.62110i	−0.889538	+	0.622861i	0.0368959	+	0.999319i	$0.488253\pi$
$114$		0			0
$115$	3.68170	−	15.8168i	0.343320	−	1.47492i
$116$	−3.60063	+	2.07882i	−0.334310	+	0.193014i
$117$		0			0
$118$	0.744522	+	2.77859i	0.0685388	+	0.255790i
$119$	2.57925	+	14.6276i	0.236439	+	1.34091i
$120$		0			0
$121$	15.4454	−	5.62165i	1.40412	−	0.511059i
$122$	−3.53414	+	7.57899i	−0.319966	+	0.686169i
$123$		0			0
$124$	−3.38619	+	0.597077i	−0.304089	+	0.0536191i
$125$	6.52252	+	9.08057i	0.583391	+	0.812191i
$126$		0			0
$127$	−3.35697	+	12.5284i	−0.297883	+	1.11171i	0.641018	+	0.767526i	$0.278512\pi$
$127$	−3.35697	+	12.5284i	−0.297883	+	1.11171i	−0.938901	+	0.344188i	$0.888154\pi$
$128$	0.996195	+	0.0871557i	0.0880520	+	0.00770355i
$129$		0			0
$130$	−2.21869	+	6.78667i	−0.194592	+	0.595231i
$131$	8.21463	−	9.78982i	0.717716	−	0.855340i	−0.276691	−	0.960959i	$-0.589238\pi$
$131$	8.21463	−	9.78982i	0.717716	−	0.855340i	0.994407	+	0.105619i	$0.0336823\pi$
$132$		0			0
$133$	−14.9848	+	6.98754i	−1.29935	+	0.605896i
$134$	5.75581			0.497226
$135$		0			0
$136$	4.46006			0.382447
$137$	−0.898383	+	0.418923i	−0.0767541	+	0.0357910i	−0.460616	−	0.887599i	$-0.652372\pi$
$137$	−0.898383	+	0.418923i	−0.0767541	+	0.0357910i	0.383862	+	0.923390i	$0.374594\pi$
$138$		0			0
$139$	−1.52525	+	1.81772i	−0.129370	+	0.154177i	−0.826841	−	0.562436i	$-0.809864\pi$
$139$	−1.52525	+	1.81772i	−0.129370	+	0.154177i	0.697471	+	0.716613i	$0.254309\pi$
$140$	−6.64119	+	3.36876i	−0.561283	+	0.284712i
$141$		0			0
$142$	−2.16806	−	0.189681i	−0.181940	−	0.0159177i
$143$	−4.32895	+	16.1559i	−0.362005	+	1.35102i
$144$		0			0
$145$	−7.31561	−	5.73690i	−0.607528	−	0.476423i
$146$	−1.80893	+	0.318963i	−0.149708	+	0.0263976i
$147$		0			0
$148$	0.341991	−	0.733402i	0.0281115	−	0.0602852i
$149$	−10.2800	+	3.74162i	−0.842172	+	0.306526i	−0.726845	−	0.686802i	$-0.759014\pi$
$149$	−10.2800	+	3.74162i	−0.842172	+	0.306526i	−0.115328	+	0.993328i	$0.536792\pi$
$150$		0			0
$151$	2.51598	+	14.2688i	0.204747	+	1.16118i	0.897837	+	0.440329i	$0.145138\pi$
$151$	2.51598	+	14.2688i	0.204747	+	1.16118i	−0.693089	+	0.720852i	$0.743751\pi$
$152$	1.28496	+	4.79555i	0.104224	+	0.388970i
$153$		0			0
$154$	−15.1070	+	8.72201i	−1.21735	+	0.702840i
$155$	−4.06253	−	6.52762i	−0.326310	−	0.524311i
$156$		0			0
$157$	5.34019	−	3.73924i	0.426194	−	0.298424i	−0.340731	−	0.940161i	$-0.610675\pi$
$157$	5.34019	−	3.73924i	0.426194	−	0.298424i	0.766925	+	0.641737i	$0.221786\pi$
$158$	−0.800243	−	9.14682i	−0.0636639	−	0.727682i
$159$		0			0
$160$	0.649898	+	2.13954i	0.0513790	+	0.169146i
$161$			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
$167$	11.4272	+	16.3198i	0.884266	+	1.26286i	0.963961	+	0.266044i	$0.0857165\pi$
$167$	11.4272	+	16.3198i	0.884266	+	1.26286i	−0.0796948	+	0.996819i	$0.525395\pi$
$168$		0			0
$169$	1.80218	+	2.14775i	0.138629	+	0.165212i
$170$	3.71924	+	9.25354i	0.285253	+	0.709714i
$171$		0			0
$172$	−2.52326	+	0.676105i	−0.192397	+	0.0515525i
$173$	6.57157	−	9.38517i	0.499627	−	0.713541i	−0.487563	−	0.873088i	$-0.662114\pi$
$173$	6.57157	−	9.38517i	0.499627	−	0.713541i	0.987190	+	0.159546i	$0.0510031\pi$
$174$		0			0
$175$	−12.5274	−	10.9697i	−0.946985	−	0.829228i
$176$	1.79150	+	4.92211i	0.135039	+	0.371018i
$177$		0			0
$178$	14.1816	+	9.93004i	1.06295	+	0.744288i
$179$	2.91563	−	5.05001i	0.217924	−	0.377456i	−0.736249	−	0.676711i	$-0.763405\pi$
$179$	2.91563	−	5.05001i	0.217924	−	0.377456i	0.954173	+	0.299255i	$0.0967381\pi$
$180$		0			0
$181$	−8.11707	−	14.0592i	−0.603337	−	1.04501i	−0.992312	−	0.123762i	$-0.960504\pi$
$181$	−8.11707	−	14.0592i	−0.603337	−	1.04501i	0.388975	−	0.921248i	$-0.372829\pi$
$182$	0.926827	−	10.5937i	0.0687010	−	0.785256i
$183$		0			0
$184$	7.15224	+	1.26113i	0.527270	+	0.0929719i
$185$	1.80682	+	0.0979650i	0.132840	+	0.00720253i
$186$		0			0
$187$	9.87312	+	21.1730i	0.721994	+	1.54832i
$188$	−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	−0.952213	−	0.305434i	$-0.901198\pi$
$191$	−0.365493	+	1.00418i	−0.0264461	+	0.0726601i	0.925767	+	0.378094i	$0.123421\pi$
$192$		0			0
$193$	−12.4014	+	1.08498i	−0.892669	+	0.0780984i	−0.524253	−	0.851563i	$-0.675655\pi$
$193$	−12.4014	+	1.08498i	−0.892669	+	0.0780984i	−0.368416	+	0.929661i	$0.620100\pi$
$194$	−0.704193	+	3.99368i	−0.0505581	+	0.286729i
$195$		0			0
$196$	3.13373	−	2.62951i	0.223838	−	0.187822i
$197$	−0.143182	−	0.0383654i	−0.0102013	−	0.00273342i	0.253715	−	0.967279i	$-0.418348\pi$
$197$	−0.143182	−	0.0383654i	−0.0102013	−	0.00273342i	−0.263916	+	0.964546i	$0.585014\pi$
$198$		0			0
$199$	−14.5760	−	8.41543i	−1.03326	−	0.596554i	−0.115344	−	0.993326i	$-0.536797\pi$
$199$	−14.5760	−	8.41543i	−1.03326	−	0.596554i	−0.917917	+	0.396772i	$0.870131\pi$
$200$	−3.89707	+	3.13254i	−0.275565	+	0.221504i
$201$		0			0
$202$	0.352898	+	0.164559i	0.0248298	+	0.0115783i
$203$	12.5489	+	5.85164i	0.880758	+	0.410704i
$204$		0			0
$205$	0.858134	+	25.9162i	0.0599347	+	1.81006i
$206$	12.6140	+	7.28269i	0.878858	+	0.507409i
$207$		0			0
$208$	−3.08436	−	0.826452i	−0.213862	−	0.0573041i
$209$	−19.9211	+	16.7158i	−1.37797	+	1.15626i
$210$		0			0
$211$	−3.79341	+	21.5135i	−0.261149	+	1.48105i	0.518631	+	0.854998i	$0.326442\pi$
$211$	−3.79341	+	21.5135i	−0.261149	+	1.48105i	−0.779780	+	0.626053i	$0.784669\pi$
$212$	−3.40613	+	0.297998i	−0.233934	+	0.0204666i
$213$		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
$218$	−2.65284	−	5.68904i	−0.179673	−	0.385310i
$219$		0			0
$220$	−8.71824	+	7.82146i	−0.587784	+	0.527323i
$221$	−14.0254	−	2.47305i	−0.943448	−	0.166355i
$222$		0			0
$223$	−0.620545	+	7.09286i	−0.0415548	+	0.474973i	0.946696	+	0.322130i	$0.104399\pi$
$223$	−0.620545	+	7.09286i	−0.0415548	+	0.474973i	−0.988250	+	0.152844i	$0.951157\pi$
$224$	−1.66514	−	2.88411i	−0.111257	−	0.192703i
$225$		0			0
$226$	5.77177	−	9.99700i	0.383933	−	0.664991i
$227$	−4.17213	−	2.92136i	−0.276914	−	0.193897i	0.426867	−	0.904315i	$-0.359617\pi$
$227$	−4.17213	−	2.92136i	−0.276914	−	0.193897i	−0.703781	+	0.710417i	$0.748506\pi$
$228$		0			0
$229$	0.607970	+	1.67038i	0.0401758	+	0.110382i	0.958158	−	0.286239i	$-0.0924050\pi$
$229$	0.607970	+	1.67038i	0.0401758	+	0.110382i	−0.917983	+	0.396621i	$0.870183\pi$
$230$	3.34770	+	15.8908i	0.220741	+	1.04781i
$231$		0			0
$232$	2.38473	−	3.40575i	0.156565	−	0.223598i
$233$	−13.4236	+	3.59685i	−0.879410	+	0.235637i	−0.670153	−	0.742223i	$-0.733771\pi$
$233$	−13.4236	+	3.59685i	−0.879410	+	0.235637i	−0.209258	+	0.977861i	$0.567105\pi$
$234$		0			0
$235$	9.04806	−	21.2093i	0.590230	−	1.38354i
$236$	−1.84905	−	2.20361i	−0.120363	−	0.143443i
$237$		0			0
$238$	−8.51949	−	12.1671i	−0.552237	−	0.788676i
$239$	0.330777	+	0.277555i	0.0213962	+	0.0179535i	0.653423	−	0.756993i	$-0.273332\pi$
$239$	0.330777	+	0.277555i	0.0213962	+	0.0179535i	−0.632027	+	0.774946i	$0.717777\pi$
$240$		0			0
$241$	10.5842	+	3.85234i	0.681790	+	0.248151i	0.659616	−	0.751603i	$-0.270719\pi$
$241$	10.5842	+	3.85234i	0.681790	+	0.248151i	0.0221741	+	0.999754i	$0.492941\pi$
$242$	−11.6224	+	11.6224i	−0.747119	+	0.747119i
$243$		0			0
$244$		−	8.36249i		−	0.535354i
$245$	8.06882	+	4.30898i	0.515498	+	0.275291i
$246$		0			0
$247$	−1.38169	−	15.7928i	−0.0879151	−	1.00487i
$248$	2.81660	−	1.97220i	0.178854	−	0.125235i
$249$		0			0
$250$	−9.74902	−	5.47326i	−0.616582	−	0.346159i
$251$	0.161890	−	0.0934671i	0.0102184	−	0.00589959i	−0.494882	−	0.868960i	$-0.664789\pi$
$251$	0.161890	−	0.0934671i	0.0102184	−	0.00589959i	0.505100	+	0.863061i	$0.331455\pi$
$252$		0			0
$253$	9.84582	+	36.7451i	0.619002	+	2.31015i
$254$	−2.25228	−	12.7733i	−0.141320	−	0.801467i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	7.65751	−	16.4216i	0.477662	−	1.02435i	−0.508879	−	0.860838i	$-0.669940\pi$
$257$	7.65751	−	16.4216i	0.477662	−	1.02435i	0.986541	−	0.163512i	$-0.0522823\pi$
$258$		0			0
$259$	−2.65399	+	0.467970i	−0.164911	+	0.0290782i
$260$	−0.857358	−	7.08847i	−0.0531711	−	0.439609i
$261$		0			0
$262$	−3.30763	+	12.3442i	−0.204346	+	0.762630i
$263$	−7.02700	−	0.614783i	−0.433304	−	0.0379092i	−0.131582	−	0.991305i	$-0.542006\pi$
$263$	−7.02700	−	0.614783i	−0.433304	−	0.0379092i	−0.301721	+	0.953396i	$0.597561\pi$
$264$		0			0
$265$	−3.45864	−	6.81839i	−0.212463	−	0.418850i
$266$	10.6278	−	12.6657i	0.651632	−	0.776585i
$267$		0			0
$268$	−5.21653	+	2.43251i	−0.318651	+	0.148589i
$269$	27.9259			1.70267			0.851337	−	0.524620i	$-0.175793\pi$
$269$	27.9259			1.70267			0.851337	+	0.524620i	$0.175793\pi$
$270$		0			0
$271$	25.6074			1.55554			0.777769	−	0.628550i	$-0.216351\pi$
$271$	25.6074			1.55554			0.777769	+	0.628550i	$0.216351\pi$
$272$	−4.04219	+	1.88490i	−0.245094	+	0.114289i
$273$		0			0
$274$	0.637167	−	0.759346i	0.0384927	−	0.0458738i
$275$	−23.4978	−	11.5659i	−1.41697	−	0.697451i
$276$		0			0
$277$	−6.95400	−	0.608396i	−0.417825	−	0.0365550i	−0.123695	−	0.992320i	$-0.539474\pi$
$277$	−6.95400	−	0.608396i	−0.417825	−	0.0365550i	−0.294130	+	0.955765i	$0.595030\pi$
$278$	0.614142	−	2.29201i	0.0368338	−	0.137466i
$279$		0			0
$280$	4.59527	−	5.85982i	0.274620	−	0.350191i
$281$	15.6364	−	2.75713i	0.932792	−	0.164476i	0.313456	−	0.949603i	$-0.398513\pi$
$281$	15.6364	−	2.75713i	0.932792	−	0.164476i	0.619336	+	0.785126i	$0.287402\pi$
$282$		0			0
$283$	−10.9847	+	23.5568i	−0.652974	+	1.40031i	0.248994	+	0.968505i	$0.419900\pi$
$283$	−10.9847	+	23.5568i	−0.652974	+	1.40031i	−0.901968	+	0.431802i	$0.857878\pi$
$284$	2.04509	−	0.744354i	0.121354	−	0.0441693i
$285$		0			0
$286$	−2.90440	−	16.4717i	−0.171741	−	0.973991i
$287$	−9.99543	−	37.3035i	−0.590012	−	2.20195i
$288$		0			0
$289$	−2.50469	+	1.44608i	−0.147335	+	0.0850636i
$290$	9.05471	+	2.10768i	0.531711	+	0.123767i
$291$		0			0
$292$	1.50465	−	1.05357i	0.0880528	−	0.0616552i
$293$	−1.45446	−	16.6246i	−0.0849706	−	0.971218i	−0.912306	−	0.409510i	$-0.865700\pi$
$293$	−1.45446	−	16.6246i	−0.0849706	−	0.971218i	0.827335	−	0.561708i	$-0.189856\pi$
$294$		0			0
$295$	3.03004	−	5.67392i	0.176416	−	0.330348i
$296$			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
$302$	−8.31052	−	11.8687i	−0.478217	−	0.682964i
$303$		0			0
$304$	−3.19126	−	3.80319i	−0.183031	−	0.218128i
$305$	17.3501	−	6.97347i	0.993465	−	0.399300i
$306$		0			0
$307$	20.3701	−	5.45815i	1.16258	−	0.311513i	0.374586	−	0.927192i	$-0.377785\pi$
$307$	20.3701	−	5.45815i	1.16258	−	0.311513i	0.787997	+	0.615679i	$0.211118\pi$
$308$	10.0055	−	14.2893i	0.570115	−	0.814209i
$309$		0			0
$310$	6.44060	+	4.19914i	0.365801	+	0.238495i
$311$	6.27658	+	17.2448i	0.355912	+	0.977861i	0.980433	+	0.196853i	$0.0630722\pi$
$311$	6.27658	+	17.2448i	0.355912	+	0.977861i	−0.624521	+	0.781008i	$0.714706\pi$
$312$		0			0
$313$	−8.33642	−	5.83723i	−0.471203	−	0.329940i	0.313739	−	0.949509i	$-0.398418\pi$
$313$	−8.33642	−	5.83723i	−0.471203	−	0.329940i	−0.784942	+	0.619570i	$0.787307\pi$
$314$	−3.25958	+	5.64577i	−0.183949	+	0.318609i
$315$		0			0
$316$	4.59088	+	7.95163i	0.258257	+	0.447314i
$317$	−2.01309	+	23.0097i	−0.113067	+	1.29236i	0.701661	+	0.712511i	$0.252442\pi$
$317$	−2.01309	+	23.0097i	−0.113067	+	1.29236i	−0.814727	+	0.579845i	$0.803113\pi$
$318$		0			0
$319$	21.4469	+	3.78167i	1.20080	+	0.211733i
$320$	−1.49322	−	1.66442i	−0.0834734	−	0.0930441i
$321$		0			0
$322$	−10.2216	−	21.9204i	−0.569629	−	1.22157i
$323$	−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
$328$	−11.5523	+	1.01069i	−0.637869	+	0.0558063i
$329$	−5.96349	+	33.8206i	−0.328778	+	1.86459i
$330$		0			0
$331$	−16.6856	+	14.0008i	−0.917121	+	0.769556i	−0.973460	−	0.228856i	$-0.926502\pi$
$331$	−16.6856	+	14.0008i	−0.917121	+	0.769556i	0.0563393	+	0.998412i	$0.482057\pi$
$332$	0.123748	+	0.0331580i	0.00679153	+	0.00181978i
$333$		0			0
$334$	−17.2536	−	9.96139i	−0.944077	−	0.545063i
$335$	−9.39693	−	8.79457i	−0.513409	−	0.480499i
$336$		0			0
$337$	2.78798	+	1.30005i	0.151871	+	0.0708185i	0.497068	−	0.867712i	$-0.334410\pi$
$337$	2.78798	+	1.30005i	0.151871	+	0.0708185i	−0.345197	+	0.938530i	$0.612188\pi$
$338$	−2.54101	−	1.18489i	−0.138213	−	0.0644496i
$339$		0			0
$340$	−7.28149	−	6.81474i	−0.394894	−	0.369581i
$341$	15.5975	+	9.00525i	0.844654	+	0.487661i
$342$		0			0
$343$	9.35835	+	2.50756i	0.505303	+	0.135396i
$344$	2.00111	−	1.67913i	0.107893	−	0.0905328i
$345$		0			0
$346$	−1.98952	+	11.2831i	−0.106957	+	0.606584i
$347$	15.0770	−	1.31907i	0.809377	−	0.0708113i	0.325048	−	0.945697i	$-0.394619\pi$
$347$	15.0770	−	1.31907i	0.809377	−	0.0708113i	0.484329	+	0.874886i	$0.339064\pi$
$348$		0			0
$349$	5.42372	−	14.9016i	0.290325	−	0.797662i	−0.705694	−	0.708517i	$-0.749364\pi$
$349$	5.42372	−	14.9016i	0.290325	−	0.797662i	0.996019	−	0.0891446i	$-0.0284133\pi$
$350$	15.9897	+	4.64756i	0.854685	+	0.248423i
$351$		0			0
$352$	−3.70382	−	3.70382i	−0.197414	−	0.197414i
$353$	10.4147	+	22.3345i	0.554320	+	1.18874i	0.961350	+	0.275329i	$0.0887866\pi$
$353$	10.4147	+	22.3345i	0.554320	+	1.18874i	−0.407030	+	0.913415i	$0.633436\pi$
$354$		0			0
$355$	3.24975	+	3.62236i	0.172479	+	0.192255i
$356$	−17.0495	−	3.00628i	−0.903620	−	0.159333i
$357$		0			0
$358$	−0.508227	+	5.80906i	−0.0268606	+	0.307019i
$359$	2.89852	+	5.02038i	0.152978	+	0.264965i	0.932321	−	0.361632i	$-0.117780\pi$
$359$	2.89852	+	5.02038i	0.152978	+	0.264965i	−0.779343	+	0.626598i	$0.784447\pi$
$360$		0			0
$361$	2.82421	−	4.89167i	0.148642	−	0.257456i
$362$	13.2982	+	9.31151i	0.698939	+	0.489402i
$363$		0			0
$364$	3.63709	+	9.99283i	0.190636	+	0.523767i
$365$	3.44061	+	2.24321i	0.180090	+	0.117415i
$366$		0			0
$367$	13.8366	−	19.7607i	0.722263	−	1.03150i	−0.275275	−	0.961366i	$-0.588769\pi$
$367$	13.8366	−	19.7607i	0.722263	−	1.03150i	0.997538	−	0.0701330i	$-0.0223424\pi$
$368$	−7.01511	+	1.87969i	−0.365688	+	0.0979857i
$369$		0			0
$370$	−1.67893	+	0.674807i	−0.0872835	+	0.0350815i
$371$	7.31924	+	8.72273i	0.379996	+	0.452862i
$372$		0			0
$373$	−4.71756	−	6.73737i	−0.244266	−	0.348848i	0.678233	−	0.734847i	$-0.262746\pi$
$373$	−4.71756	−	6.73737i	−0.244266	−	0.348848i	−0.922499	+	0.385999i	$0.873857\pi$
$374$	−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	$0.986104\pi$
$380$	5.22951	−	9.79256i	0.268268	−	0.502348i
$381$		0			0
$382$	−0.0931371	−	1.06456i	−0.00476531	−	0.0544678i
$383$	−2.92038	+	2.04487i	−0.149225	+	0.104488i	−0.645804	−	0.763503i	$-0.723478\pi$
$383$	−2.92038	+	2.04487i	−0.149225	+	0.104488i	0.496580	+	0.867991i	$0.334589\pi$
$384$		0			0
$385$	37.9904	+	8.84310i	1.93617	+	0.450686i
$386$	10.7809	−	6.22436i	0.548734	−	0.316812i
$387$		0			0
$388$	−1.04959	−	3.91711i	−0.0532847	−	0.198861i
$389$	1.27347	+	7.22223i	0.0645677	+	0.366182i	0.999922	+	0.0124700i	$0.00396943\pi$
$389$	1.27347	+	7.22223i	0.0645677	+	0.366182i	−0.935355	+	0.353712i	$0.884919\pi$
$390$		0			0
$391$	−30.4381	+	11.0786i	−1.53932	+	0.560267i
$392$	−1.72885	+	3.70752i	−0.0873199	+	0.187258i
$393$		0			0
$394$	0.145980	−	0.0257403i	0.00735439	−	0.00129678i
$395$	−12.6694	+	16.1558i	−0.637465	+	0.812887i
$396$		0			0
$397$	5.08887	−	18.9919i	0.255403	−	0.953177i	−0.712463	−	0.701710i	$-0.752420\pi$
$397$	5.08887	−	18.9919i	0.255403	−	0.953177i	0.967866	−	0.251467i	$-0.0809131\pi$
$398$	16.7668	+	1.46691i	0.840444	+	0.0735294i
$399$		0			0
$400$	2.20808	−	4.48602i	0.110404	−	0.224301i
$401$	−4.83413	+	5.76110i	−0.241405	+	0.287695i	−0.873120	−	0.487505i	$-0.837907\pi$
$401$	−4.83413	+	5.76110i	−0.241405	+	0.287695i	0.631715	+	0.775201i	$0.282351\pi$
$402$		0			0
$403$	−9.95079	+	4.64013i	−0.495684	+	0.231141i
$404$	−0.389380			−0.0193724
$405$		0			0
$406$	−13.8462			−0.687173
$407$	−3.84156	+	1.79135i	−0.190419	+	0.0887938i
$408$		0			0
$409$	13.3179	−	15.8717i	0.658529	−	0.784804i	−0.328645	−	0.944453i	$-0.606592\pi$
$409$	13.3179	−	15.8717i	0.658529	−	0.784804i	0.987174	+	0.159650i	$0.0510365\pi$
$410$	−11.7304	−	23.1254i	−0.579322	−	1.14208i
$411$		0			0
$412$	−14.5100	−	1.26946i	−0.714854	−	0.0625416i
$413$	−2.47947	+	9.25351i	−0.122007	+	0.455335i
$414$		0			0
$415$	0.0343980	+	0.284396i	0.00168853	+	0.0139605i
$416$	3.14465	−	0.554487i	0.154179	−	0.0271860i
$417$		0			0
$418$	10.9903	−	23.5687i	0.537551	−	1.15278i
$419$	17.4036	−	6.33438i	0.850220	−	0.309455i	0.120090	−	0.992763i	$-0.461682\pi$
$419$	17.4036	−	6.33438i	0.850220	−	0.309455i	0.730130	+	0.683308i	$0.239460\pi$
$420$		0			0
$421$	−4.31040	−	24.4455i	−0.210076	−	1.19140i	−0.889250	−	0.457422i	$-0.848773\pi$
$421$	−4.31040	−	24.4455i	−0.210076	−	1.19140i	0.679174	−	0.733978i	$-0.262338\pi$
$422$	−5.65400	−	21.1010i	−0.275233	−	1.02718i
$423$		0			0
$424$	2.96106	−	1.70957i	0.143802	−	0.0830241i
$425$	8.06690	−	20.7901i	0.391302	−	1.00847i
$426$		0			0
$427$	−22.8130	+	15.9738i	−1.10400	+	0.773026i
$428$	0.146247	+	1.67161i	0.00706911	+	0.0808002i
$429$		0			0
$430$	5.15252	+	2.75160i	0.248476	+	0.132694i
$431$		−	20.9323i		−	1.00827i	−0.863623	−	0.504137i	$-0.831811\pi$
$431$		−	20.9323i		−	1.00827i	0.863623	−	0.504137i	$-0.168189\pi$
$432$		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
$437$	−20.6812	−	29.5359i	−0.989317	−	1.41289i
$438$		0			0
$439$	−20.1404	−	24.0024i	−0.961250	−	1.14557i	−0.989290	−	0.145967i	$-0.953371\pi$
$439$	−20.1404	−	24.0024i	−0.961250	−	1.14557i	0.0280393	−	0.999607i	$-0.491074\pi$
$440$	4.59592	−	10.7731i	0.219102	−	0.513589i
$441$		0			0
$442$	13.7564	−	3.68603i	0.654327	−	0.175326i
$443$	−13.4266	+	19.1752i	−0.637918	+	0.911041i	−0.999775	−	0.0211922i	$-0.993254\pi$
$443$	−13.4266	+	19.1752i	−0.637918	+	0.911041i	0.361857	+	0.932233i	$0.382143\pi$
$444$		0			0
$445$	−7.98023	−	37.8804i	−0.378299	−	1.79571i
$446$	−2.43517	−	6.69057i	−0.115309	−	0.316808i
$447$		0			0
$448$	2.72801	+	1.91017i	0.128886	+	0.0902472i
$449$	14.8865	−	25.7843i	0.702540	−	1.21683i	−0.265032	−	0.964240i	$-0.585383\pi$
$449$	14.8865	−	25.7843i	0.702540	−	1.21683i	0.967572	−	0.252595i	$-0.0812840\pi$
$450$		0			0
$451$	−30.3710	−	52.6041i	−1.43012	−	2.47703i
$452$	−1.00609	+	11.4996i	−0.0473223	+	0.540896i
$453$		0			0
$454$	5.01586	+	0.884431i	0.235406	+	0.0415084i
$455$	−17.6997	+	15.8791i	−0.829776	+	0.744423i
$456$		0			0
$457$	−12.6471	−	27.1218i	−0.591608	−	1.26871i	−0.943098	−	0.332515i	$-0.892103\pi$
$457$	−12.6471	−	27.1218i	−0.591608	−	1.26871i	0.351490	−	0.936191i	$-0.385675\pi$
$458$	−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	−0.716976	−	0.697098i	$-0.754474\pi$
$461$	6.01927	−	16.5378i	0.280345	−	0.770243i	0.997321	−	0.0731448i	$-0.0233035\pi$
$462$		0			0
$463$	28.8143	−	2.52092i	1.33911	−	0.117157i	0.605022	−	0.796209i	$-0.293164\pi$
$463$	28.8143	−	2.52092i	1.33911	−	0.117157i	0.734091	+	0.679051i	$0.237609\pi$
$464$	−0.721968	+	4.09448i	−0.0335165	+	0.190082i
$465$		0			0
$466$	10.6458	−	8.93292i	0.493159	−	0.413809i
$467$	8.65083	+	2.31798i	0.400313	+	0.107263i	0.453358	−	0.891329i	$-0.350226\pi$
$467$	8.65083	+	2.31798i	0.400313	+	0.107263i	−0.0530450	+	0.998592i	$0.516893\pi$
$468$		0			0
$469$	16.6004	+	9.58424i	0.766535	+	0.442559i
$470$	0.763097	+	23.0460i	0.0351990	+	1.06303i
$471$		0			0
$472$	2.60709	+	1.21571i	0.120001	+	0.0559575i
$473$	12.4011	+	5.78271i	0.570201	+	0.265889i
$474$		0			0
$475$	24.6781	+	2.68396i	1.13231	+	0.123149i
$476$	12.8633	+	7.42664i	0.589589	+	0.340400i
$477$		0			0
$478$	−0.417085	−	0.111758i	−0.0190770	−	0.00511168i
$479$	8.50714	−	7.13834i	0.388701	−	0.326159i	−0.427406	−	0.904060i	$-0.640572\pi$
$479$	8.50714	−	7.13834i	0.388701	−	0.326159i	0.816107	+	0.577901i	$0.196128\pi$
$480$		0			0
$481$	0.448702	−	2.54471i	0.0204590	−	0.116029i
$482$	−11.2206	+	0.981679i	−0.511086	+	0.0447142i
$483$		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	$0.688601\pi$
$488$	3.53414	+	7.57899i	0.159983	+	0.343085i
$489$		0			0
$490$	−9.13389	−	0.495237i	−0.412627	−	0.0223725i
$491$	−24.2319	−	4.27274i	−1.09357	−	0.192826i	−0.402362	−	0.915481i	$-0.631811\pi$
$491$	−24.2319	−	4.27274i	−1.09357	−	0.192826i	−0.691209	+	0.722655i	$0.742922\pi$
$492$		0			0
$493$	−1.61616	+	18.4728i	−0.0727882	+	0.831973i
$494$	7.92658	+	13.7292i	0.356634	+	0.617708i
$495$		0			0
$496$	−1.71922	+	2.97777i	−0.0771950	+	0.133706i
$497$	−5.93709	−	4.15719i	−0.266315	−	0.186476i
$498$		0			0
$499$	9.81593	+	26.9690i	0.439421	+	1.20730i	0.939869	+	0.341534i	$0.110946\pi$
$499$	9.81593	+	26.9690i	0.439421	+	1.20730i	−0.500448	+	0.865767i	$0.666831\pi$
$500$	11.1487	+	0.840343i	0.498586	+	0.0375813i
$501$		0			0
$502$	−0.107221	+	0.153128i	−0.00478551	+	0.00683442i
$503$	26.7603	−	7.17039i	1.19318	−	0.319712i	0.393039	−	0.919522i	$-0.371424\pi$
$503$	26.7603	−	7.17039i	1.19318	−	0.319712i	0.800143	+	0.599810i	$0.204757\pi$
$504$		0			0
$505$	−0.324703	−	0.807868i	−0.0144491	−	0.0359497i
$506$	−24.4525	−	29.1414i	−1.08705	−	1.29549i
$507$		0			0
$508$	7.43948	+	10.6247i	0.330074	+	0.471394i
$509$	−18.9862	−	15.9313i	−0.841549	−	0.706144i	0.116363	−	0.993207i	$-0.462877\pi$
$509$	−18.9862	−	15.9313i	−0.841549	−	0.706144i	−0.957912	+	0.287063i	$0.907321\pi$
$510$		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
$515$	−9.46602	−	31.1632i	−0.417123	−	1.37322i
$516$		0			0
$517$	4.70771	+	53.8094i	0.207045	+	2.36653i
$518$	2.20756	−	1.54575i	0.0969945	−	0.0679163i
$519$		0			0
$520$	3.77275	+	6.06200i	0.165446	+	0.265836i
$521$	−27.3636	+	15.7984i	−1.19882	+	0.692141i	−0.960293	−	0.278994i	$-0.909999\pi$
$521$	−27.3636	+	15.7984i	−1.19882	+	0.692141i	−0.238530	+	0.971135i	$0.576666\pi$
$522$		0			0
$523$	3.72886	+	13.9163i	0.163052	+	0.608517i	0.998281	+	0.0586149i	$0.0186684\pi$
$523$	3.72886	+	13.9163i	0.163052	+	0.608517i	−0.835229	+	0.549902i	$0.814665\pi$
$524$	−2.21917	−	12.5855i	−0.0969450	−	0.549802i
$525$		0			0
$526$	6.62845	−	2.41256i	0.289014	−	0.105193i
$527$	−6.48111	+	13.8988i	−0.282322	+	0.605441i
$528$		0			0
$529$	−29.2931	+	5.16516i	−1.27361	+	0.224572i
$530$	6.01617	+	4.71788i	0.261326	+	0.204931i
$531$		0			0
$532$	−4.27929	+	15.9705i	−0.185531	+	0.692411i
$533$	36.8884	+	3.22732i	1.59781	+	0.139791i
$534$		0			0
$535$	−3.34622	+	1.69738i	−0.144670	+	0.0733841i
$536$	3.69976	−	4.40921i	0.159805	−	0.190449i
$537$		0			0
$538$	−25.3095	+	11.8020i	−1.09117	+	0.508820i
$539$	−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	$0.478940\pi$
$542$	−23.2082	+	10.8221i	−0.996876	+	0.464851i
$543$		0			0
$544$	2.86687	−	3.41661i	0.122916	−	0.146486i
$545$	−4.36152	+	13.3413i	−0.186827	+	0.571479i
$546$		0			0
$547$	−20.1663	−	1.76432i	−0.862247	−	0.0754368i	−0.352552	−	0.935792i	$-0.614686\pi$
$547$	−20.1663	−	1.76432i	−0.862247	−	0.0754368i	−0.509695	+	0.860355i	$0.670242\pi$
$548$	−0.256556	+	0.957480i	−0.0109595	+	0.0409015i
$549$		0			0
$550$	26.1842	+	0.551700i	1.11650	+	0.0235246i
$551$	−20.3280	+	3.58437i	−0.866000	+	0.152699i
$552$		0			0
$553$	12.9228	−	27.7130i	0.549532	−	1.17847i
$554$	6.55958	−	2.38749i	0.278690	−	0.101435i
$555$		0			0
$556$	0.412043	+	2.33681i	0.0174745	+	0.0991029i
$557$	9.17672	+	34.2480i	0.388830	+	1.45113i	0.832040	+	0.554716i	$0.187173\pi$
$557$	9.17672	+	34.2480i	0.388830	+	1.45113i	−0.443209	+	0.896418i	$0.646160\pi$
$558$		0			0
$559$	−7.22387	+	4.17070i	−0.305537	+	0.176402i
$560$	−1.68826	+	7.25285i	−0.0713420	+	0.306489i
$561$		0			0
$562$	−13.0062	+	9.10705i	−0.548634	+	0.384158i
$563$	−3.96350	−	45.3031i	−0.167042	−	1.90930i	−0.368215	−	0.929741i	$-0.620031\pi$
$563$	−3.96350	−	45.3031i	−0.167042	−	1.90930i	0.201174	−	0.979556i	$-0.435524\pi$
$564$		0			0
$565$	−24.6979	+	7.50213i	−1.03905	+	0.315617i
$566$		−	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	$-0.576223\pi$
$569$	−24.8870	−	9.05812i	−1.04332	−	0.379736i	−0.806137	+	0.591730i	$0.798445\pi$
$570$		0			0
$571$	8.21205	+	6.89073i	0.343664	+	0.288368i	0.798240	−	0.602340i	$-0.205765\pi$
$571$	8.21205	+	6.89073i	0.343664	+	0.288368i	−0.454576	+	0.890708i	$0.650209\pi$
$572$	9.59352	+	13.7010i	0.401125	+	0.572866i
$573$		0			0
$574$	24.8241	+	29.5842i	1.03614	+	1.23482i
$575$	18.8149	−	31.0584i	0.784634	−	1.29523i
$576$		0			0
$577$	−30.0633	+	8.05543i	−1.25155	+	0.335352i	−0.822935	−	0.568135i	$-0.807665\pi$
$577$	−30.0633	+	8.05543i	−1.25155	+	0.335352i	−0.428615	+	0.903487i	$0.640998\pi$
$578$	1.65888	−	2.36912i	0.0690002	−	0.0985425i
$579$		0			0
$580$	−9.09710	+	1.91648i	−0.377737	+	0.0795773i
$581$	−0.145924	−	0.400922i	−0.00605393	−	0.0166330i
$582$		0			0
$583$	14.6706	+	10.2724i	0.607593	+	0.425441i
$584$	−0.918417	+	1.59075i	−0.0380044	+	0.0658255i
$585$		0			0
$586$	8.34404	+	14.4523i	0.344689	+	0.597019i
$587$	−3.22648	+	36.8788i	−0.133171	+	1.52215i	0.576196	+	0.817312i	$0.304537\pi$
$587$	−3.22648	+	36.8788i	−0.133171	+	1.52215i	−0.709367	+	0.704840i	$0.751019\pi$
$588$		0			0
$589$	−16.8115	−	2.96432i	−0.692705	−	0.122143i
$590$	−0.348246	+	6.42286i	−0.0143371	+	0.264425i
$591$		0			0
$592$	−0.341991	−	0.733402i	−0.0140557	−	0.0301426i
$593$	7.77904	+	7.77904i	0.319447	+	0.319447i	0.848555	−	0.529108i	$-0.177473\pi$
$593$	7.77904	+	7.77904i	0.319447	+	0.319447i	−0.529108	+	0.848555i	$0.677473\pi$
$594$		0			0
$595$	−4.68177	+	32.8813i	−0.191934	+	1.34800i
$596$	−3.74162	+	10.2800i	−0.153263	+	0.421086i
$597$		0			0
$598$	23.1024	−	2.02119i	0.944726	−	0.0826528i
$599$	4.08580	−	23.1717i	0.166941	−	0.946771i	−0.780099	−	0.625656i	$-0.784831\pi$
$599$	4.08580	−	23.1717i	0.166941	−	0.946771i	0.947040	−	0.321115i	$-0.104058\pi$
$600$		0			0
$601$	−23.2731	+	19.5285i	−0.949331	+	0.796583i	−0.979185	−	0.202971i	$-0.934940\pi$
$601$	−23.2731	+	19.5285i	−0.949331	+	0.796583i	0.0298540	+	0.999554i	$0.490496\pi$
$602$	−8.40316	−	2.25162i	−0.342487	−	0.0917692i
$603$		0			0
$604$	12.5478	+	7.24447i	0.510563	+	0.294773i
$605$	36.7333	−	1.21631i	1.49342	−	0.0494499i
$606$		0			0
$607$	24.9308	+	11.6254i	1.01191	+	0.471861i	0.856587	−	0.516003i	$-0.172581\pi$
$607$	24.9308	+	11.6254i	1.01191	+	0.471861i	0.155322	+	0.987864i	$0.450359\pi$
$608$	4.49956	+	2.09818i	0.182481	+	0.0850924i
$609$		0			0
$610$	−12.7774	+	13.6526i	−0.517343	+	0.552777i
$611$	−28.5168	−	16.4642i	−1.15367	−	0.666069i
$612$		0			0
$613$	31.4834	+	8.43596i	1.27160	+	0.340725i	0.830645	−	0.556802i	$-0.187972\pi$
$613$	31.4834	+	8.43596i	1.27160	+	0.340725i	0.440959	+	0.897527i	$0.354638\pi$
$614$	−16.1549	+	13.5555i	−0.651958	+	0.547057i
$615$		0			0
$616$	−3.02912	+	17.1790i	−0.122047	+	0.692162i
$617$	38.6301	−	3.37969i	1.55519	−	0.136061i	0.723115	−	0.690728i	$-0.242710\pi$
$617$	38.6301	−	3.37969i	1.55519	−	0.136061i	0.832073	+	0.554666i	$0.187154\pi$
$618$		0			0
$619$	16.4915	−	45.3101i	0.662851	−	1.82117i	0.0993508	−	0.995052i	$-0.468323\pi$
$619$	16.4915	−	45.3101i	0.662851	−	1.82117i	0.563500	−	0.826116i	$-0.309454\pi$
$620$	−7.61179	−	1.08380i	−0.305697	−	0.0435263i
$621$		0			0
$622$	−12.9765	−	12.9765i	−0.520309	−	0.520309i
$623$	24.3663	+	52.2537i	0.976214	+	2.09350i
$624$		0			0
$625$	7.55339	+	23.8316i	0.302136	+	0.953265i
$626$	10.0223	+	1.76720i	0.400571	+	0.0706315i
$627$		0			0
$628$	0.568183	−	6.49436i	0.0226730	−	0.259153i
$629$	−1.80458	−	3.12563i	−0.0719535	−	0.124627i
$630$		0			0
$631$	16.3443	−	28.3092i	0.650656	−	1.12697i	−0.332308	−	0.943171i	$-0.607827\pi$
$631$	16.3443	−	28.3092i	0.650656	−	1.12697i	0.982964	−	0.183798i	$-0.0588394\pi$
$632$	−7.52125	−	5.26644i	−0.299179	−	0.209488i
$633$		0			0
$634$	−7.89986	−	21.7047i	−0.313743	−	0.862003i
$635$	−15.8398	+	24.2950i	−0.628585	+	0.964118i
$636$		0			0
$637$	7.49240	−	10.7003i	0.296860	−	0.423959i
$638$	−21.0357	+	5.63650i	−0.832811	+	0.223151i
$639$		0			0
$640$	2.05673	+	0.877419i	0.0812994	+	0.0346830i
$641$	14.7737	+	17.6066i	0.583526	+	0.695419i	0.974348	−	0.225047i	$-0.0722536\pi$
$641$	14.7737	+	17.6066i	0.583526	+	0.695419i	−0.390822	+	0.920466i	$0.627809\pi$
$642$		0			0
$643$	−6.62602	−	9.46294i	−0.261305	−	0.373182i	0.666965	−	0.745089i	$-0.267593\pi$
$643$	−6.62602	−	9.46294i	−0.261305	−	0.373182i	−0.928270	+	0.371907i	$0.878704\pi$
$644$	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	−0.281141	−	0.959666i	$-0.590713\pi$
$647$	17.2591	−	17.2591i	0.678525	−	0.678525i	0.959666	+	0.281141i	$0.0907130\pi$
$648$		0			0
$649$			15.0677i			0.591458i
$650$	−9.43109	+	12.8826i	−0.369918	+	0.505298i
$651$		0			0
$652$	−0.245619	−	2.80744i	−0.00961918	−	0.109948i
$653$	−0.356065	+	0.249319i	−0.0139339	+	0.00975662i	−0.580523	−	0.814244i	$-0.697152\pi$
$653$	−0.356065	+	0.249319i	−0.0139339	+	0.00975662i	0.566589	+	0.824001i	$0.308263\pi$
$654$		0			0
$655$	24.2614	−	15.0993i	0.947971	−	0.589979i
$656$	10.0428	−	5.79821i	0.392105	−	0.226382i
$657$		0			0
$658$	−8.88845	−	33.1722i	−0.346508	−	1.29319i
$659$	4.56670	+	25.8990i	0.177893	+	1.00888i	0.934751	+	0.355303i	$0.115622\pi$
$659$	4.56670	+	25.8990i	0.177893	+	1.00888i	−0.756858	+	0.653580i	$0.773266\pi$
$660$		0			0
$661$	8.09777	−	2.94735i	0.314967	−	0.114639i	−0.179699	−	0.983722i	$-0.557513\pi$
$661$	8.09777	−	2.94735i	0.314967	−	0.114639i	0.494666	+	0.869083i	$0.335290\pi$
$662$	9.20524	−	19.7407i	0.357772	−	0.767244i
$663$		0			0
$664$	−0.126167	+	0.0222466i	−0.00489621	+	0.000863334i
$665$	−36.7035	+	4.43932i	−1.42330	+	0.172149i
$666$		0			0
$667$	−7.81510	+	29.1663i	−0.302602	+	1.12933i
$668$	19.8470	+	1.73638i	0.767902	+	0.0671827i
$669$		0			0
$670$	12.2333	+	3.99928i	0.472612	+	0.154506i
$671$	−28.1558	+	33.5548i	−1.08694	+	1.29537i
$672$		0			0
$673$	−23.6958	+	11.0496i	−0.913408	+	0.425929i	−0.821741	−	0.569861i	$-0.806997\pi$
$673$	−23.6958	+	11.0496i	−0.913408	+	0.425929i	−0.0916665	+	0.995790i	$0.529219\pi$
$674$	−3.07619			−0.118490
$675$		0			0
$676$	2.80369			0.107834
$677$	−3.04384	+	1.41937i	−0.116984	+	0.0545507i	−0.480229	−	0.877143i	$-0.659447\pi$
$677$	−3.04384	+	1.41937i	−0.116984	+	0.0545507i	0.363245	+	0.931694i	$0.381669\pi$
$678$		0			0
$679$	−8.68102	+	10.3456i	−0.333147	+	0.397029i
$680$	9.47931	+	3.09896i	0.363515	+	0.118840i
$681$		0			0
$682$	−17.9420	−	1.56972i	−0.687033	−	0.0601076i
$683$	3.31641	−	12.3770i	0.126899	−	0.473593i	−0.873001	−	0.487718i	$-0.837830\pi$
$683$	3.31641	−	12.3770i	0.126899	−	0.473593i	0.999900	+	0.0141247i	$0.00449618\pi$
$684$		0			0
$685$	−2.20048	+	0.266150i	−0.0840760	+	0.0101691i
$686$	−9.54128	+	1.68239i	−0.364288	+	0.0642338i
$687$		0			0
$688$	−1.10399	+	2.36752i	−0.0420893	+	0.0902608i
$689$	−10.2595	+	3.73414i	−0.390854	+	0.142259i
$690$		0			0
$691$	−2.05589	−	11.6595i	−0.0782098	−	0.443550i	−0.998616	−	0.0525872i	$-0.983253\pi$
$691$	−2.05589	−	11.6595i	−0.0782098	−	0.443550i	0.920407	−	0.390963i	$-0.127858\pi$
$692$	−2.96534	−	11.0668i	−0.112725	−	0.420696i
$693$		0			0
$694$	−13.1070	+	7.56730i	−0.497533	+	0.287251i
$695$	−4.50471	+	2.80355i	−0.170874	+	0.106345i
$696$		0			0
$697$	42.3672	−	29.6658i	1.60477	−	1.12367i
$698$	1.38211	+	15.7976i	0.0523135	+	0.597946i
$699$		0			0
$700$	−16.4557	+	2.54541i	−0.621968	+	0.0962074i
$701$		−	48.4334i		−	1.82930i	−0.404243	−	0.914651i	$-0.632465\pi$
$701$		−	48.4334i		−	1.82930i	0.404243	−	0.914651i	$-0.367535\pi$
$702$		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
$707$	0.743783	+	1.06223i	0.0279728	+	0.0399493i
$708$		0			0
$709$	4.36975	+	5.20766i	0.164109	+	0.195578i	0.841832	−	0.539740i	$-0.181477\pi$
$709$	4.36975	+	5.20766i	0.164109	+	0.195578i	−0.677723	+	0.735318i	$0.737033\pi$
$710$	−4.47615	−	1.90957i	−0.167987	−	0.0716647i
$711$		0			0
$712$	16.7226	−	4.48080i	0.626705	−	0.167925i
$713$	−14.3233	+	20.4557i	−0.536411	+	0.766074i
$714$		0			0
$715$	−20.4261	+	31.3294i	−0.763894	+	1.17165i
$716$	−1.99441	−	5.47959i	−0.0745345	−	0.204782i
$717$		0			0
$718$	−4.74865	−	3.32504i	−0.177218	−	0.124089i
$719$	9.66731	−	16.7443i	0.360530	−	0.624456i	−0.627518	−	0.778602i	$-0.715929\pi$
$719$	9.66731	−	16.7443i	0.360530	−	0.624456i	0.988048	+	0.154146i	$0.0492626\pi$
$720$		0			0
$721$	24.2534	+	42.0082i	0.903245	+	1.56447i
$722$	−0.492292	+	5.62692i	−0.0183212	+	0.209412i
$723$		0			0
$724$	−15.9875	−	2.81903i	−0.594171	−	0.104768i
$725$	−11.5623	−	17.2761i	−0.429412	−	0.641619i
$726$		0			0
$727$	−1.23633	−	2.65131i	−0.0458528	−	0.0983317i	0.882047	−	0.471162i	$-0.156165\pi$
$727$	−1.23633	−	2.65131i	−0.0458528	−	0.0983317i	−0.927900	+	0.372830i	$0.878387\pi$
$728$	−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
$733$	−40.1260	+	3.51057i	−1.48209	+	0.129666i	−0.799292	−	0.600942i	$-0.794792\pi$
$733$	−40.1260	+	3.51057i	−1.48209	+	0.129666i	−0.682797	+	0.730608i	$0.739237\pi$
$734$	−4.18897	+	23.7568i	−0.154618	+	0.876881i
$735$		0			0
$736$	5.56345	−	4.66829i	0.205072	−	0.172076i
$737$	29.1216	+	7.80311i	1.07271	+	0.287431i
$738$		0			0
$739$	−35.1829	−	20.3128i	−1.29422	−	0.747220i	−0.314823	−	0.949150i	$-0.601945\pi$
$739$	−35.1829	−	20.3128i	−1.29422	−	0.747220i	−0.979400	+	0.201930i	$0.935279\pi$
$740$	1.23644	−	1.32113i	0.0454526	−	0.0485657i
$741$		0			0
$742$	−10.3199	−	4.81223i	−0.378854	−	0.176663i
$743$	9.41473	+	4.39016i	0.345393	+	0.161059i	0.587571	−	0.809172i	$-0.300084\pi$
$743$	9.41473	+	4.39016i	0.345393	+	0.161059i	−0.242179	+	0.970232i	$0.577862\pi$
$744$		0			0
$745$	−24.4487	+	0.809542i	−0.895730	+	0.0296593i
$746$	7.12290	+	4.11241i	0.260788	+	0.150566i
$747$		0			0
$748$	22.5658	+	6.04648i	0.825086	+	0.221081i
$749$	4.28081	−	3.59202i	0.156417	−	0.131250i
$750$		0			0
$751$	−4.24628	+	24.0819i	−0.154949	+	0.878760i	0.803883	+	0.594787i	$0.202764\pi$
$751$	−4.24628	+	24.0819i	−0.154949	+	0.878760i	−0.958832	+	0.283973i	$0.908347\pi$
$752$	−10.2729	+	0.898762i	−0.374614	+	0.0327745i
$753$		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	$0.440507\pi$
$758$	−0.718144	−	1.54006i	−0.0260842	−	0.0559377i
$759$		0			0
$760$	−0.601034	+	11.0852i	−0.0218018	+	0.402101i
$761$	−0.923556	−	0.162848i	−0.0334789	−	0.00590323i	0.156884	−	0.987617i	$-0.449855\pi$
$761$	−0.923556	−	0.162848i	−0.0334789	−	0.00590323i	−0.190363	+	0.981714i	$0.560966\pi$
$762$		0			0
$763$	1.82197	−	20.8252i	0.0659596	−	0.753922i
$764$	0.534314	+	0.925460i	0.0193308	+	0.0334820i
$765$		0			0
$766$	1.78256	−	3.08749i	0.0644067	−	0.111556i
$767$	−7.52432	−	5.26858i	−0.271687	−	0.190238i
$768$		0			0
$769$	3.60209	+	9.89666i	0.129895	+	0.356883i	0.987542	−	0.157356i	$-0.0502969\pi$
$769$	3.60209	+	9.89666i	0.129895	+	0.356883i	−0.857647	+	0.514238i	$0.828075\pi$
$770$	−38.1682	+	8.04086i	−1.37549	+	0.289772i
$771$		0			0
$772$	−7.14029	+	10.1974i	−0.256985	+	0.367012i
$773$	−30.8401	+	8.26359i	−1.10924	+	0.297221i	−0.766523	−	0.642217i	$-0.778015\pi$
$773$	−30.8401	+	8.26359i	−1.10924	+	0.297221i	−0.342720	+	0.939438i	$0.611348\pi$
$774$		0			0
$775$	−4.09885	−	16.6964i	−0.147235	−	0.599752i
$776$	2.60669	+	3.10653i	0.0935747	+	0.111518i
$777$		0			0
$778$	−4.20641	−	6.00737i	−0.150807	−	0.215375i
$779$	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
$785$	13.9480	−	4.23680i	0.497826	−	0.151218i
$786$		0			0
$787$	−2.34858	−	26.8444i	−0.0837180	−	0.956901i	−0.915638	−	0.402005i	$-0.868313\pi$
$787$	−2.34858	−	26.8444i	−0.0837180	−	0.956901i	0.831920	−	0.554896i	$-0.187242\pi$
$788$	−0.121425	+	0.0850226i	−0.00432558	+	0.00302881i
$789$		0			0
$790$	4.65461	−	19.9964i	0.165604	−	0.711441i
$791$	33.2929	−	19.2216i	1.18376	−	0.683443i
$792$		0			0
$793$	−6.91120	−	25.7929i	−0.245424	−	0.915934i
$794$	3.41425	+	19.3632i	0.121167	+	0.687174i
$795$		0			0
$796$	−15.8158	+	5.75649i	−0.560577	+	0.204033i
$797$	−4.58785	+	9.83868i	−0.162510	+	0.348504i	−0.970654	−	0.240482i	$-0.922695\pi$
$797$	−4.58785	+	9.83868i	−0.162510	+	0.348504i	0.808144	+	0.588985i	$0.200472\pi$
$798$		0			0
$799$	−45.2940	+	7.98656i	−1.60239	+	0.282544i
$800$	−0.105327	+	4.99889i	−0.00372385	+	0.176737i
$801$		0			0
$802$	1.94647	−	7.26432i	0.0687322	−	0.256512i
$803$	−9.58472	−	0.838555i	−0.338238	−	0.0295919i
$804$		0			0
$805$	−16.8053	+	51.4053i	−0.592310	+	1.81180i
$806$	7.05747	−	8.41077i	0.248589	−	0.296257i
$807$		0			0
$808$	0.352898	−	0.164559i	0.0124149	−	0.00578917i
$809$	31.3917			1.10367			0.551837	−	0.833952i	$-0.313927\pi$
$809$	31.3917			1.10367			0.551837	+	0.833952i	$0.313927\pi$
$810$		0			0
$811$	−32.1801			−1.12999			−0.564997	−	0.825093i	$-0.691123\pi$
$811$	−32.1801			−1.12999			−0.564997	+	0.825093i	$0.691123\pi$
$812$	12.5489	−	5.85164i	0.440379	−	0.205352i
$813$		0			0
$814$	2.72458	−	3.24702i	0.0954963	−	0.113808i
$815$	5.61992	−	2.85072i	0.196857	−	0.0998562i
$816$		0			0
$817$	−12.9198	−	1.13034i	−0.452007	−	0.0395455i
$818$	−5.36247	+	20.0130i	−0.187494	+	0.699739i
$819$		0			0
$820$	20.4045	+	16.0012i	0.712558	+	0.558787i
$821$	15.5403	−	2.74018i	0.542361	−	0.0956329i	0.104246	−	0.994552i	$-0.466757\pi$
$821$	15.5403	−	2.74018i	0.542361	−	0.0956329i	0.438115	+	0.898919i	$0.355646\pi$
$822$		0			0
$823$	18.5167	−	39.7093i	0.645453	−	1.38418i	−0.262428	−	0.964951i	$-0.584523\pi$
$823$	18.5167	−	39.7093i	0.645453	−	1.38418i	0.907881	−	0.419227i	$-0.137699\pi$
$824$	13.6870	−	4.98165i	0.476809	−	0.173544i
$825$		0			0
$826$	−1.66354	−	9.43439i	−0.0578819	−	0.328265i
$827$	4.99764	+	18.6514i	0.173785	+	0.648574i	0.996755	+	0.0804898i	$0.0256485\pi$
$827$	4.99764	+	18.6514i	0.173785	+	0.648574i	−0.822971	+	0.568084i	$0.807685\pi$
$828$		0			0
$829$	25.0901	−	14.4858i	0.871414	−	0.503111i	0.00359643	−	0.999994i	$-0.498855\pi$
$829$	25.0901	−	14.4858i	0.871414	−	0.503111i	0.867818	+	0.496882i	$0.165522\pi$
$830$	−0.151366	−	0.243213i	−0.00525400	−	0.00844206i
$831$		0			0
$832$	−2.61569	+	1.83152i	−0.0906827	+	0.0634967i
$833$	−1.59018	−	18.1758i	−0.0550963	−	0.629754i
$834$		0			0
$835$	12.9478	+	42.6256i	0.448077	+	1.47512i
$836$			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	$-0.249307\pi$
$839$	23.1135	+	8.41263i	0.797967	+	0.290436i	0.0893230	+	0.996003i	$0.471530\pi$
$840$		0			0
$841$	−8.97342	−	7.52959i	−0.309428	−	0.259641i
$842$	14.2377	+	20.3335i	0.490662	+	0.700738i
$843$		0			0
$844$	14.0419	+	16.7345i	0.483344	+	0.576027i
$845$	2.33800	+	5.81698i	0.0804295	+	0.200110i
$846$		0			0
$847$	−52.8734	+	14.1674i	−1.81675	+	0.486797i
$848$	−1.96114	+	2.80080i	−0.0673458	+	0.0961798i
$849$		0			0
$850$	1.47519	+	22.2515i	0.0505987	+	0.763219i
$851$	−2.01006	−	5.52259i	−0.0689039	−	0.189312i
$852$		0			0
$853$	−23.9084	−	16.7409i	−0.818609	−	0.573196i	0.0875369	−	0.996161i	$-0.472100\pi$
$853$	−23.9084	−	16.7409i	−0.818609	−	0.573196i	−0.906146	+	0.422965i	$0.860989\pi$
$854$	13.9247	−	24.1184i	0.476495	−	0.825313i
$855$		0			0
$856$	−0.838997	−	1.45319i	−0.0286763	−	0.0496688i
$857$	1.26962	−	14.5118i	0.0433695	−	0.495715i	−0.943183	−	0.332273i	$-0.892185\pi$
$857$	1.26962	−	14.5118i	0.0433695	−	0.495715i	0.986553	−	0.163443i	$-0.0522598\pi$
$858$		0			0
$859$	−34.2219	−	6.03425i	−1.16764	−	0.205886i	−0.443974	−	0.896039i	$-0.646432\pi$
$859$	−34.2219	−	6.03425i	−1.16764	−	0.205886i	−0.723663	+	0.690153i	$0.757543\pi$
$860$	−5.83264	−	0.316244i	−0.198891	−	0.0107838i
$861$		0			0
$862$	8.84638	+	18.9711i	0.301309	+	0.646159i
$863$	−3.52306	−	3.52306i	−0.119927	−	0.119927i	0.644596	−	0.764523i	$-0.277025\pi$
$863$	−3.52306	−	3.52306i	−0.119927	−	0.119927i	−0.764523	+	0.644596i	$0.777025\pi$
$864$		0			0
$865$	20.4881	−	15.3809i	0.696616	−	0.522967i
$866$	−4.15404	+	11.4131i	−0.141160	+	0.387834i
$867$		0			0
$868$	11.4074	−	0.998016i	0.387192	−	0.0338749i
$869$	8.35144	−	47.3634i	0.283303	−	1.60669i
$870$		0			0
$871$	−14.0793	+	11.8140i	−0.477060	+	0.400301i
$872$	−6.06327	−	1.62465i	−0.205328	−	0.0550175i
$873$		0			0
$874$	31.2260	+	18.0283i	1.05623	+	0.609817i
$875$	−19.0035	−	32.0190i	−0.642436	−	1.08244i
$876$		0			0
$877$	−0.708100	−	0.330192i	−0.0239108	−	0.0111498i	0.410626	−	0.911804i	$-0.365310\pi$
$877$	−0.708100	−	0.330192i	−0.0239108	−	0.0111498i	−0.434537	+	0.900654i	$0.643088\pi$
$878$	28.3973	+	13.2419i	0.958362	+	0.446892i
$879$		0			0
$880$	0.387611	+	11.7061i	0.0130664	+	0.394613i
$881$	27.0459	+	15.6150i	0.911199	+	0.526081i	0.880817	−	0.473457i	$-0.156994\pi$
$881$	27.0459	+	15.6150i	0.911199	+	0.526081i	0.0303824	+	0.999538i	$0.490327\pi$
$882$		0			0
$883$	−36.2231	−	9.70596i	−1.21901	−	0.326632i	−0.408716	−	0.912662i	$-0.634023\pi$
$883$	−36.2231	−	9.70596i	−1.21901	−	0.326632i	−0.810289	+	0.586030i	$0.800690\pi$
$884$	−10.9098	+	9.15440i	−0.366936	+	0.307896i
$885$		0			0
$886$	4.06486	−	23.0530i	0.136562	−	0.774480i
$887$	10.9678	−	0.959560i	0.368263	−	0.0322189i	0.0984777	−	0.995139i	$-0.468603\pi$
$887$	10.9678	−	0.959560i	0.368263	−	0.0322189i	0.269786	+	0.962920i	$0.413047\pi$
$888$		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
$893$	−21.6367	−	46.4001i	−0.724045	−	1.55272i
$894$		0			0
$895$	9.70567	−	8.70732i	0.324425	−	0.291054i
$896$	−3.27969	−	0.578298i	−0.109567	−	0.0193196i
$897$		0			0
$898$	−2.59490	+	29.6598i	−0.0865928	+	0.989760i
$899$	7.14789	+	12.3805i	0.238396	+	0.412913i
$900$		0			0
$901$	−7.62479	+	13.2065i	−0.254019	+	0.439973i
$902$	49.7570	+	34.8402i	1.65673	+	1.16005i
$903$		0			0
$904$	−3.94812	−	10.8474i	−0.131313	−	0.360779i
$905$	−7.48316	−	35.5209i	−0.248749	−	1.18076i
$906$		0			0
$907$	2.78099	−	3.97166i	0.0923411	−	0.131877i	−0.770323	−	0.637654i	$-0.779905\pi$
$907$	2.78099	−	3.97166i	0.0923411	−	0.131877i	0.862664	+	0.505777i	$0.168794\pi$
$908$	−4.91969	+	1.31823i	−0.163266	+	0.0437469i
$909$		0			0
$910$	9.33060	−	21.8716i	0.309307	−	0.725036i
$911$	−19.2529	−	22.9447i	−0.637878	−	0.760193i	0.346156	−	0.938177i	$-0.387487\pi$
$911$	−19.2529	−	22.9447i	−0.637878	−	0.760193i	−0.984033	+	0.177984i	$0.943042\pi$
$912$		0			0
$913$	−0.384901	−	0.549696i	−0.0127384	−	0.0181923i
$914$	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	$-0.153588\pi$
$920$	14.3249	+	7.64993i	0.472279	+	0.252211i
$921$		0			0
$922$	1.53387	+	17.5322i	0.0505153	+	0.577392i
$923$	5.69264	−	3.98603i	0.187375	−	0.131202i
$924$		0			0
$925$	3.77209	+	1.46363i	0.124026	+	0.0481239i
$926$	−25.0492	+	14.4622i	−0.823168	+	0.475256i
$927$		0			0
$928$	−1.07608	−	4.01598i	−0.0353240	−	0.131831i
$929$	−7.38000	−	41.8541i	−0.242130	−	1.37319i	−0.827065	−	0.562107i	$-0.809991\pi$
$929$	−7.38000	−	41.8541i	−0.242130	−	1.37319i	0.584935	−	0.811081i	$-0.301120\pi$
$930$		0			0
$931$	19.0848	−	6.94631i	0.625480	−	0.227656i
$932$	−5.87319	+	12.5951i	−0.192383	+	0.412566i
$933$		0			0
$934$	−8.81994	+	1.55519i	−0.288597	+	0.0508875i
$935$	6.27259	+	51.8606i	0.205136	+	1.69602i
$936$		0			0
$937$	0.674087	−	2.51573i	0.0220215	−	0.0821852i	−0.954041	−	0.299677i	$-0.903121\pi$
$937$	0.674087	−	2.51573i	0.0220215	−	0.0821852i	0.976062	+	0.217492i	$0.0697876\pi$
$938$	−19.0955	−	1.67064i	−0.623492	−	0.0545484i
$939$		0			0
$940$	−10.4313	−	20.5643i	−0.340230	−	0.670733i
$941$	−19.1836	+	22.8621i	−0.625366	+	0.745282i	−0.981983	−	0.188968i	$-0.939486\pi$
$941$	−19.1836	+	22.8621i	−0.625366	+	0.745282i	0.356617	+	0.934251i	$0.383930\pi$
$942$		0			0
$943$	76.3291	−	35.5929i	2.48562	−	1.15906i
$944$	−2.87661			−0.0936257
$945$		0			0
$946$	−13.6831			−0.444874
$947$	24.9214	−	11.6210i	0.809836	−	0.377633i	0.0268247	−	0.999640i	$-0.491460\pi$
$947$	24.9214	−	11.6210i	0.809836	−	0.377633i	0.783011	+	0.622007i	$0.213683\pi$
$948$		0			0
$949$	3.77015	−	4.49309i	0.122384	−	0.145852i
$950$	−23.5002	+	7.99690i	−0.762448	+	0.259454i
$951$		0			0
$952$	−14.7968	−	1.29455i	−0.479566	−	0.0419566i
$953$	−9.32527	+	34.8024i	−0.302075	+	1.12736i	0.633359	+	0.773858i	$0.281676\pi$
$953$	−9.32527	+	34.8024i	−0.302075	+	1.12736i	−0.935434	+	0.353502i	$0.884991\pi$
$954$		0			0
$955$	−1.47454	+	1.88031i	−0.0477150	+	0.0608455i
$956$	0.425238	−	0.0749810i	0.0137532	−	0.00242506i
$957$		0			0
$958$	−4.69330	+	10.0648i	−0.151634	+	0.325179i
$959$	3.10208	−	1.12907i	0.100171	−	0.0364594i
$960$		0			0
$961$	−3.33008	−	18.8858i	−0.107422	−	0.609221i
$962$	0.668781	+	2.49592i	0.0215624	+	0.0804718i
$963$		0			0
$964$	9.75448	−	5.63175i	0.314171	−	0.181386i
$965$	−27.1114	−	6.31078i	−0.872747	−	0.203151i
$966$		0			0
$967$	32.5433	−	22.7870i	1.04652	−	0.732782i	0.0819581	−	0.996636i	$-0.473883\pi$
$967$	32.5433	−	22.7870i	1.04652	−	0.732782i	0.964563	+	0.263854i	$0.0849937\pi$
$968$	1.43255	+	16.3741i	0.0460438	+	0.526283i
$969$		0			0
$970$	−4.27158	+	7.99878i	−0.137152	+	0.256825i
$971$		−	44.1783i		−	1.41775i	−0.705334	−	0.708875i	$-0.749203\pi$
$971$		−	44.1783i		−	1.41775i	0.705334	−	0.708875i	$-0.250797\pi$
$972$		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
$977$	5.37793	+	7.68048i	0.172055	+	0.245720i	0.895914	−	0.444228i	$-0.146522\pi$
$977$	5.37793	+	7.68048i	0.172055	+	0.245720i	−0.723858	+	0.689949i	$0.757633\pi$
$978$		0			0
$979$	58.2898	+	69.4670i	1.86295	+	2.22018i
$980$	8.48741	−	3.41131i	0.271120	−	0.108970i
$981$		0			0
$982$	23.7673	−	6.36843i	0.758445	−	0.203225i
$983$	19.8578	−	28.3599i	0.633366	−	0.904540i	−0.366297	−	0.930498i	$-0.619375\pi$
$983$	19.8578	−	28.3599i	0.633366	−	0.904540i	0.999663	+	0.0259580i	$0.00826361\pi$
$984$		0			0
$985$	−0.277657	−	0.181027i	−0.00884690	−	0.00576800i
$986$	−6.34221	−	17.4251i	−0.201977	−	0.554927i
$987$		0			0
$988$	−12.9862	−	9.09300i	−0.413145	−	0.289287i
$989$	−9.48589	+	16.4300i	−0.301634	+	0.522445i
$990$		0			0
$991$	−24.9663	−	43.2429i	−0.793081	−	1.37366i	−0.924051	−	0.382270i	$-0.875142\pi$
$991$	−24.9663	−	43.2429i	−0.793081	−	1.37366i	0.130970	−	0.991386i	$-0.458191\pi$
$992$	0.299679	−	3.42535i	0.00951482	−	0.108755i
$993$		0			0
$994$	7.13774	+	1.25858i	0.226395	+	0.0399196i
$995$	−25.1321	−	28.0137i	−0.796742	−	0.888093i
$996$		0			0
$997$	13.4179	+	28.7747i	0.424948	+	0.911305i	0.995912	+	0.0903293i	$0.0287919\pi$
$997$	13.4179	+	28.7747i	0.424948	+	0.911305i	−0.570964	+	0.820975i	$0.693430\pi$
$998$	−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.17.9		216
3.2	odd	2		270.2.r.a.77.14	yes	216
5.3	odd	4	inner	810.2.s.a.503.18		216
15.8	even	4		270.2.r.a.23.9	✓	216
27.7	even	9		270.2.r.a.47.9	yes	216
27.20	odd	18	inner	810.2.s.a.467.18		216
135.88	odd	36		270.2.r.a.263.14	yes	216
135.128	even	36	inner	810.2.s.a.143.9		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.9	✓	216	15.8	even	4
270.2.r.a.47.9	yes	216	27.7	even	9
270.2.r.a.77.14	yes	216	3.2	odd	2
270.2.r.a.263.14	yes	216	135.88	odd	36
810.2.s.a.17.9		216	1.1	even	1	trivial
810.2.s.a.143.9		216	135.128	even	36	inner
810.2.s.a.467.18		216	27.20	odd	18	inner
810.2.s.a.503.18		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)

\(f(q)\)	\(=\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.12538 + 0.694824i) q^{5} +(-3.31761 - 0.290253i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.12538 + 0.694824i) q^{5} +(-3.31761 - 0.290253i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.21989 + 0.268498i) q^{10} +(-5.15842 + 0.909569i) q^{11} +(1.34949 - 2.89399i) q^{13} +(3.12944 - 1.13902i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-1.15435 - 4.30809i) q^{17} +(4.29957 - 2.48236i) q^{19} +(1.89843 - 1.18151i) q^{20} +(4.29072 - 3.00439i) q^{22} +(-0.632975 - 7.23494i) q^{23} +(4.03444 + 2.95352i) q^{25} +3.19317i q^{26} +(-2.35487 + 2.35487i) q^{28} +(-3.90691 - 1.42200i) q^{29} +(-2.63399 - 2.21018i) q^{31} +(0.573576 + 0.819152i) q^{32} +(2.86687 + 3.41661i) q^{34} +(-6.84950 - 2.92205i) q^{35} +(0.781646 - 0.209441i) q^{37} +(-2.84764 + 4.06686i) q^{38} +(-1.22124 + 1.87312i) q^{40} +(3.96621 + 10.8971i) q^{41} +(-2.13984 - 1.49834i) q^{43} +(-2.61900 + 4.53624i) q^{44} +(3.63129 + 6.28957i) q^{46} +(0.898762 - 10.2729i) q^{47} +(4.02865 + 0.710360i) q^{49} +(-4.90466 - 0.971775i) q^{50} +(-1.34949 - 2.89399i) q^{52} +(-2.41770 - 2.41770i) q^{53} +(-11.5956 - 1.65102i) q^{55} +(1.13902 - 3.12944i) q^{56} +(4.14183 - 0.362363i) q^{58} +(0.499518 - 2.83291i) q^{59} +(6.40604 - 5.37530i) q^{61} +(3.32127 + 0.889931i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(4.87899 - 5.21316i) q^{65} +(-5.21653 - 2.43251i) q^{67} +(-4.04219 - 1.88490i) q^{68} +(7.44266 - 0.246441i) q^{70} +(1.88477 + 1.08817i) q^{71} +(1.77425 + 0.475408i) q^{73} +(-0.619898 + 0.520156i) q^{74} +(0.862114 - 4.88929i) q^{76} +(17.3776 - 1.52035i) q^{77} +(-3.14035 + 8.62803i) q^{79} +(0.315201 - 2.21374i) q^{80} +(-8.19991 - 8.19991i) q^{82} +(0.0541428 + 0.116110i) q^{83} +(0.539940 - 9.95838i) q^{85} +(2.57258 + 0.453616i) q^{86} +(0.456522 - 5.21807i) q^{88} +(-8.65625 - 14.9931i) q^{89} +(-5.31708 + 9.20945i) q^{91} +(-5.94915 - 4.16564i) q^{92} +(3.52696 + 9.69024i) q^{94} +(10.8630 - 2.28850i) q^{95} +(2.32602 - 3.32190i) q^{97} +(-3.95141 + 1.05878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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