LMFDB - Embedded newform 810.2.s.a.557.1

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			557.1
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.18527 + 0.473911i) q^{5} +(-0.171895 - 0.368630i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.18527 + 0.473911i) q^{5} +(-0.171895 - 0.368630i) q^{7} +(0.258819 - 0.965926i) q^{8} +(2.06189 + 0.865214i) q^{10} +(3.16016 + 3.76614i) q^{11} +(-2.75679 - 3.93710i) q^{13} +(-0.0706294 + 0.400559i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.352969 - 1.31730i) q^{17} +(-0.763415 + 0.440758i) q^{19} +(-1.19274 - 1.89140i) q^{20} +(-0.428487 - 4.89763i) q^{22} +(-0.893489 - 0.416641i) q^{23} +(4.55082 - 2.07125i) q^{25} +4.80631i q^{26} +(0.287607 - 0.287607i) q^{28} +(-1.09136 - 6.18939i) q^{29} +(-7.20395 + 2.62202i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.466436 + 1.28152i) q^{34} +(0.550335 + 0.724094i) q^{35} +(-8.35530 + 2.23880i) q^{37} +(0.878161 + 0.0768291i) q^{38} +(-0.107827 + 2.23347i) q^{40} +(-10.9197 - 1.92544i) q^{41} +(1.07657 - 12.3052i) q^{43} +(-2.45817 + 4.25768i) q^{44} +(0.492928 + 0.853777i) q^{46} +(-3.46784 + 1.61708i) q^{47} +(4.39317 - 5.23558i) q^{49} +(-4.91583 - 0.913573i) q^{50} +(2.75679 - 3.93710i) q^{52} +(-0.890669 - 0.890669i) q^{53} +(-8.69063 - 6.73239i) q^{55} +(-0.400559 + 0.0706294i) q^{56} +(-2.65610 + 5.69603i) q^{58} +(-0.0286877 - 0.0240719i) q^{59} +(3.45774 + 1.25852i) q^{61} +(7.40506 + 1.98418i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(7.89016 + 7.29716i) q^{65} +(-2.00593 + 1.40457i) q^{67} +(1.11713 - 0.782224i) q^{68} +(-0.0354851 - 0.908802i) q^{70} +(-4.92728 - 2.84477i) q^{71} +(-0.355086 - 0.0951449i) q^{73} +(8.12838 + 2.95849i) q^{74} +(-0.675280 - 0.566627i) q^{76} +(0.845095 - 1.81231i) q^{77} +(-1.82023 + 0.320955i) q^{79} +(1.36939 - 1.76770i) q^{80} +(7.84051 + 7.84051i) q^{82} +(0.186315 - 0.266085i) q^{83} +(1.39561 + 2.71137i) q^{85} +(-7.93987 + 9.46237i) q^{86} +(4.45572 - 2.07774i) q^{88} +(-6.26296 - 10.8478i) q^{89} +(-0.977456 + 1.69300i) q^{91} +(0.0859230 - 0.982105i) q^{92} +(3.76820 + 0.664436i) q^{94} +(1.45939 - 1.32497i) q^{95} +(-0.287260 - 0.0251320i) q^{97} +(-6.60168 + 1.76892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.18527	+	0.473911i	−0.977283	+	0.211940i
$5$	−2.18527	+	0.473911i	−0.977283	+	0.211940i
$6$		0			0
$7$	−0.171895	−	0.368630i	−0.0649702	−	0.139329i	0.871141	−	0.491032i	$-0.163380\pi$
$7$	−0.171895	−	0.368630i	−0.0649702	−	0.139329i	−0.936111	+	0.351703i	$0.885603\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	2.06189	+	0.865214i	0.652028	+	0.273605i
$11$	3.16016	+	3.76614i	0.952825	+	1.13553i	0.990675	+	0.136249i	$0.0435048\pi$
$11$	3.16016	+	3.76614i	0.952825	+	1.13553i	−0.0378496	+	0.999283i	$0.512051\pi$
$12$		0			0
$13$	−2.75679	−	3.93710i	−0.764595	−	1.09196i	−0.992968	−	0.118382i	$-0.962229\pi$
$13$	−2.75679	−	3.93710i	−0.764595	−	1.09196i	0.228373	−	0.973574i	$-0.426659\pi$
$14$	−0.0706294	+	0.400559i	−0.0188765	+	0.107054i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.352969	−	1.31730i	−0.0856075	−	0.319491i	0.909821	−	0.415001i	$-0.136219\pi$
$17$	−0.352969	−	1.31730i	−0.0856075	−	0.319491i	−0.995429	+	0.0955093i	$0.969552\pi$
$18$		0			0
$19$	−0.763415	+	0.440758i	−0.175139	+	0.101117i	−0.585007	−	0.811028i	$-0.698908\pi$
$19$	−0.763415	+	0.440758i	−0.175139	+	0.101117i	0.409868	+	0.912145i	$0.365575\pi$
$20$	−1.19274	−	1.89140i	−0.266704	−	0.422929i
$21$		0			0
$22$	−0.428487	−	4.89763i	−0.0913538	−	1.04418i
$23$	−0.893489	−	0.416641i	−0.186305	−	0.0868756i	0.327227	−	0.944946i	$-0.393886\pi$
$23$	−0.893489	−	0.416641i	−0.186305	−	0.0868756i	−0.513533	+	0.858070i	$0.671663\pi$
$24$		0			0
$25$	4.55082	−	2.07125i	0.910163	−	0.414250i
$26$			4.80631i			0.942596i
$27$		0			0
$28$	0.287607	−	0.287607i	0.0543527	−	0.0543527i
$29$	−1.09136	−	6.18939i	−0.202660	−	1.14934i	−0.901080	−	0.433653i	$-0.857224\pi$
$29$	−1.09136	−	6.18939i	−0.202660	−	1.14934i	0.698420	−	0.715688i	$-0.253887\pi$
$30$		0			0
$31$	−7.20395	+	2.62202i	−1.29387	+	0.470929i	−0.894995	−	0.446077i	$-0.852821\pi$
$31$	−7.20395	+	2.62202i	−1.29387	+	0.470929i	−0.398873	+	0.917006i	$0.630599\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	−0.466436	+	1.28152i	−0.0799930	+	0.219779i
$35$	0.550335	+	0.724094i	0.0930236	+	0.122394i
$36$		0			0
$37$	−8.35530	+	2.23880i	−1.37360	+	0.368056i	−0.868793	−	0.495175i	$-0.835104\pi$
$37$	−8.35530	+	2.23880i	−1.37360	+	0.368056i	−0.504810	+	0.863231i	$0.668437\pi$
$38$	0.878161	+	0.0768291i	0.142456	+	0.0124633i
$39$		0			0
$40$	−0.107827	+	2.23347i	−0.0170489	+	0.353142i
$41$	−10.9197	−	1.92544i	−1.70537	−	0.300703i	−0.765806	−	0.643072i	$-0.777660\pi$
$41$	−10.9197	−	1.92544i	−1.70537	−	0.300703i	−0.939566	+	0.342369i	$0.888771\pi$
$42$		0			0
$43$	1.07657	−	12.3052i	0.164175	−	1.87653i	−0.252666	−	0.967553i	$-0.581307\pi$
$43$	1.07657	−	12.3052i	0.164175	−	1.87653i	0.416842	−	0.908979i	$-0.363137\pi$
$44$	−2.45817	+	4.25768i	−0.370583	+	0.641869i
$45$		0			0
$46$	0.492928	+	0.853777i	0.0726783	+	0.125882i
$47$	−3.46784	+	1.61708i	−0.505836	+	0.235875i	−0.658747	−	0.752365i	$-0.728913\pi$
$47$	−3.46784	+	1.61708i	−0.505836	+	0.235875i	0.152911	+	0.988240i	$0.451135\pi$
$48$		0			0
$49$	4.39317	−	5.23558i	0.627596	−	0.747940i
$50$	−4.91583	−	0.913573i	−0.695203	−	0.129199i
$51$		0			0
$52$	2.75679	−	3.93710i	0.382298	−	0.545978i
$53$	−0.890669	−	0.890669i	−0.122343	−	0.122343i	0.643284	−	0.765627i	$-0.277571\pi$
$53$	−0.890669	−	0.890669i	−0.122343	−	0.122343i	−0.765627	+	0.643284i	$0.777571\pi$
$54$		0			0
$55$	−8.69063	−	6.73239i	−1.17184	−	0.907795i
$56$	−0.400559	+	0.0706294i	−0.0535269	+	0.00943825i
$57$		0			0
$58$	−2.65610	+	5.69603i	−0.348763	+	0.747925i
$59$	−0.0286877	−	0.0240719i	−0.00373482	−	0.00313389i	0.640918	−	0.767609i	$-0.278554\pi$
$59$	−0.0286877	−	0.0240719i	−0.00373482	−	0.00313389i	−0.644653	+	0.764475i	$0.722998\pi$
$60$		0			0
$61$	3.45774	+	1.25852i	0.442719	+	0.161136i	0.553754	−	0.832680i	$-0.313195\pi$
$61$	3.45774	+	1.25852i	0.442719	+	0.161136i	−0.111036	+	0.993816i	$0.535417\pi$
$62$	7.40506	+	1.98418i	0.940444	+	0.251991i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	7.89016	+	7.29716i	0.978654	+	0.905101i
$66$		0			0
$67$	−2.00593	+	1.40457i	−0.245063	+	0.171595i	−0.689655	−	0.724138i	$-0.742238\pi$
$67$	−2.00593	+	1.40457i	−0.245063	+	0.171595i	0.444592	+	0.895733i	$0.353349\pi$
$68$	1.11713	−	0.782224i	0.135472	−	0.0948586i
$69$		0			0
$70$	−0.0354851	−	0.908802i	−0.00424129	−	0.108623i
$71$	−4.92728	−	2.84477i	−0.584761	−	0.337612i	0.178262	−	0.983983i	$-0.442952\pi$
$71$	−4.92728	−	2.84477i	−0.584761	−	0.337612i	−0.763023	+	0.646371i	$0.776286\pi$
$72$		0			0
$73$	−0.355086	−	0.0951449i	−0.0415596	−	0.0111359i	0.237979	−	0.971270i	$-0.423515\pi$
$73$	−0.355086	−	0.0951449i	−0.0415596	−	0.0111359i	−0.279539	+	0.960134i	$0.590182\pi$
$74$	8.12838	+	2.95849i	0.944905	+	0.343917i
$75$		0			0
$76$	−0.675280	−	0.566627i	−0.0774599	−	0.0649966i
$77$	0.845095	−	1.81231i	0.0963075	−	0.206532i
$78$		0			0
$79$	−1.82023	+	0.320955i	−0.204792	+	0.0361103i	−0.275103	−	0.961415i	$-0.588712\pi$
$79$	−1.82023	+	0.320955i	−0.204792	+	0.0361103i	0.0703111	+	0.997525i	$0.477601\pi$
$80$	1.36939	−	1.76770i	0.153102	−	0.197635i
$81$		0			0
$82$	7.84051	+	7.84051i	0.865840	+	0.865840i
$83$	0.186315	−	0.266085i	0.0204507	−	0.0292067i	−0.808797	−	0.588089i	$-0.799881\pi$
$83$	0.186315	−	0.266085i	0.0204507	−	0.0292067i	0.829247	+	0.558882i	$0.188770\pi$
$84$		0			0
$85$	1.39561	+	2.71137i	0.151376	+	0.294090i
$86$	−7.93987	+	9.46237i	−0.856179	+	1.02035i
$87$		0			0
$88$	4.45572	−	2.07774i	0.474981	−	0.221487i
$89$	−6.26296	−	10.8478i	−0.663873	−	1.14986i	−0.979590	−	0.201008i	$-0.935578\pi$
$89$	−6.26296	−	10.8478i	−0.663873	−	1.14986i	0.315717	−	0.948853i	$-0.397755\pi$
$90$		0			0
$91$	−0.977456	+	1.69300i	−0.102465	+	0.177475i
$92$	0.0859230	−	0.982105i	0.00895810	−	0.102392i
$93$		0			0
$94$	3.76820	+	0.664436i	0.388660	+	0.0685313i
$95$	1.45939	−	1.32497i	0.149730	−	0.135939i
$96$		0			0
$97$	−0.287260	−	0.0251320i	−0.0291668	−	0.00255177i	0.0725630	−	0.997364i	$-0.476882\pi$
$97$	−0.287260	−	0.0251320i	−0.0291668	−	0.00255177i	−0.101730	+	0.994812i	$0.532438\pi$
$98$	−6.60168	+	1.76892i	−0.666871	+	0.178687i
$99$		0			0
$100$	3.50281	+	3.56796i	0.350281	+	0.356796i
$101$	−5.92352	+	16.2747i	−0.589412	+	1.61940i	0.182171	+	0.983267i	$0.441688\pi$
$101$	−5.92352	+	16.2747i	−0.589412	+	1.61940i	−0.771583	+	0.636129i	$0.780535\pi$
$102$		0			0
$103$	−16.2287	+	1.41983i	−1.59906	+	0.139900i	−0.851524	−	0.524316i	$-0.824321\pi$
$103$	−16.2287	+	1.41983i	−1.59906	+	0.139900i	−0.747540	+	0.664216i	$0.768765\pi$
$104$	−4.51646	+	1.64386i	−0.442875	+	0.161193i
$105$		0			0
$106$	0.218726	+	1.24046i	0.0212446	+	0.120484i
$107$	13.5507	−	13.5507i	1.30999	−	1.30999i	0.388577	−	0.921416i	$-0.372967\pi$
$107$	13.5507	−	13.5507i	1.30999	−	1.30999i	0.921416	−	0.388577i	$-0.127033\pi$
$108$		0			0
$109$			6.41957i			0.614883i	0.951567	+	0.307441i	$0.0994728\pi$
$109$			6.41957i			0.614883i	−0.951567	+	0.307441i	$0.900527\pi$
$110$	3.25740	+	10.4996i	0.310581	+	1.00110i
$111$		0			0
$112$	0.368630	+	0.171895i	0.0348323	+	0.0162426i
$113$	−0.743569	−	8.49903i	−0.0699491	−	0.799522i	−0.947441	−	0.319930i	$-0.896340\pi$
$113$	−0.743569	−	8.49903i	−0.0699491	−	0.799522i	0.877492	−	0.479591i	$-0.159215\pi$
$114$		0			0
$115$	2.14997	+	0.487039i	0.200485	+	0.0454166i
$116$	5.44286	−	3.14244i	0.505357	−	0.291768i
$117$		0			0
$118$	0.00969256	+	0.0361731i	0.000892272	+	0.00333001i
$119$	−0.424922	+	0.356552i	−0.0389525	+	0.0326850i
$120$		0			0
$121$	−2.28702	+	12.9703i	−0.207911	+	1.17912i
$122$	−2.11056	−	3.01420i	−0.191081	−	0.272892i
$123$		0			0
$124$	−4.92779	−	5.87272i	−0.442529	−	0.527385i
$125$	−8.96318	+	6.68292i	−0.801691	+	0.597739i
$126$		0			0
$127$	−0.951785	+	3.55211i	−0.0844573	+	0.315199i	−0.995211	−	0.0977513i	$-0.968835\pi$
$127$	−0.951785	+	3.55211i	−0.0844573	+	0.315199i	0.910754	+	0.412950i	$0.135502\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	−2.27777	−	10.5031i	−0.199773	−	0.921182i
$131$	−1.51123	−	4.15206i	−0.132036	−	0.362767i	0.856003	−	0.516972i	$-0.172941\pi$
$131$	−1.51123	−	4.15206i	−0.132036	−	0.362767i	−0.988039	+	0.154205i	$0.950718\pi$
$132$		0			0
$133$	0.293704	+	0.205654i	0.0254673	+	0.0178324i
$134$	2.44879			0.211543
$135$		0			0
$136$	−1.36377			−0.116942
$137$	1.91667	+	1.34206i	0.163752	+	0.114660i	0.652580	−	0.757720i	$-0.273687\pi$
$137$	1.91667	+	1.34206i	0.163752	+	0.114660i	−0.488828	+	0.872380i	$0.662575\pi$
$138$		0			0
$139$	6.31446	+	17.3488i	0.535585	+	1.47151i	0.852333	+	0.522999i	$0.175187\pi$
$139$	6.31446	+	17.3488i	0.535585	+	1.47151i	−0.316748	+	0.948510i	$0.602591\pi$
$140$	−0.492200	+	0.764800i	−0.0415985	+	0.0646374i
$141$		0			0
$142$	2.40450	+	5.15647i	0.201781	+	0.432721i
$143$	6.11576	−	22.8243i	0.511425	−	1.90867i
$144$		0			0
$145$	5.31813	+	13.0083i	0.441647	+	1.08028i
$146$	0.236296	+	0.281607i	0.0195560	+	0.0233059i
$147$		0			0
$148$	−4.96146	−	7.08570i	−0.407830	−	0.582441i
$149$	−1.59126	+	9.02448i	−0.130361	+	0.739314i	0.847617	+	0.530608i	$0.178036\pi$
$149$	−1.59126	+	9.02448i	−0.130361	+	0.739314i	−0.977978	+	0.208706i	$0.933075\pi$
$150$		0			0
$151$	15.0933	−	12.6648i	1.22828	−	1.03065i	0.229928	−	0.973208i	$-0.426151\pi$
$151$	15.0933	−	12.6648i	1.22828	−	1.03065i	0.998349	−	0.0574393i	$-0.0182936\pi$
$152$	0.228153	+	0.851478i	0.0185056	+	0.0690640i
$153$		0			0
$154$	−1.73176	+	0.999832i	−0.139549	+	0.0805688i
$155$	14.5000	−	9.14387i	1.16467	−	0.734453i
$156$		0			0
$157$	−0.108016	−	1.23463i	−0.00862059	−	0.0985339i	0.990665	−	0.136316i	$-0.0435263\pi$
$157$	−0.108016	−	1.23463i	−0.00862059	−	0.0985339i	−0.999286	+	0.0377822i	$0.987971\pi$
$158$	1.67514	+	0.781129i	0.133267	+	0.0621433i
$159$		0			0
$160$	−2.13565	+	0.662567i	−0.168838	+	0.0523805i
$161$			0.400986i			0.0316021i
$162$		0			0
$163$	8.84311	−	8.84311i	0.692645	−	0.692645i	−0.270168	−	0.962813i	$-0.587079\pi$
$163$	8.84311	−	8.84311i	0.692645	−	0.692645i	0.962813	+	0.270168i	$0.0870792\pi$
$164$	−1.92544	−	10.9197i	−0.150352	−	0.852686i
$165$		0			0
$166$	−0.305241	+	0.111098i	−0.0236913	+	0.00862292i
$167$	10.7410	−	0.939719i	0.831167	−	0.0727177i	0.336374	−	0.941729i	$-0.390799\pi$
$167$	10.7410	−	0.939719i	0.831167	−	0.0727177i	0.494793	+	0.869011i	$0.335244\pi$
$168$		0			0
$169$	−3.45462	+	9.49150i	−0.265740	+	0.730115i
$170$	0.411961	−	3.02152i	0.0315959	−	0.231740i
$171$		0			0
$172$	11.9314	−	3.19700i	0.909758	−	0.243769i
$173$	−0.412759	−	0.0361117i	−0.0313815	−	0.00274552i	0.0714542	−	0.997444i	$-0.477236\pi$
$173$	−0.412759	−	0.0361117i	−0.0313815	−	0.00274552i	−0.102836	+	0.994698i	$0.532792\pi$
$174$		0			0
$175$	−1.54579	−	1.32153i	−0.116851	−	0.0998983i
$176$	−4.84165	−	0.853714i	−0.364953	−	0.0643511i
$177$		0			0
$178$	−1.09171	+	12.4783i	−0.0818268	+	0.935285i
$179$	4.06125	−	7.03429i	0.303552	−	0.525768i	−0.673386	−	0.739291i	$-0.735161\pi$
$179$	4.06125	−	7.03429i	0.303552	−	0.525768i	0.976938	+	0.213523i	$0.0684940\pi$
$180$		0			0
$181$	8.72101	+	15.1052i	0.648228	+	1.12276i	0.983546	+	0.180658i	$0.0578229\pi$
$181$	8.72101	+	15.1052i	0.648228	+	1.12276i	−0.335318	+	0.942105i	$0.608844\pi$
$182$	1.77175	−	0.826181i	0.131331	−	0.0612406i
$183$		0			0
$184$	−0.633696	+	0.755210i	−0.0467167	+	0.0556748i
$185$	17.1976	−	8.85205i	1.26439	−	0.650816i
$186$		0			0
$187$	3.84568	−	5.49220i	0.281224	−	0.401630i
$188$	−2.70563	−	2.70563i	−0.197328	−	0.197328i
$189$		0			0
$190$	−1.95543	+	0.248278i	−0.141862	+	0.0180120i
$191$	14.7058	−	2.59304i	1.06408	−	0.187625i	0.385912	−	0.922535i	$-0.373887\pi$
$191$	14.7058	−	2.59304i	1.06408	−	0.187625i	0.678165	+	0.734910i	$0.262776\pi$
$192$		0			0
$193$	5.58975	−	11.9873i	0.402359	−	0.862861i	−0.595853	−	0.803093i	$-0.703186\pi$
$193$	5.58975	−	11.9873i	0.402359	−	0.862861i	0.998212	−	0.0597682i	$-0.0190361\pi$
$194$	0.220894	+	0.185352i	0.0158593	+	0.0133075i
$195$		0			0
$196$	6.42239	+	2.33756i	0.458742	+	0.166968i
$197$	5.88450	+	1.57675i	0.419253	+	0.112339i	0.462277	−	0.886735i	$-0.347032\pi$
$197$	5.88450	+	1.57675i	0.419253	+	0.112339i	−0.0430238	+	0.999074i	$0.513699\pi$
$198$		0			0
$199$	−10.5371	−	6.08357i	−0.746952	−	0.431253i	0.0776393	−	0.996982i	$-0.475262\pi$
$199$	−10.5371	−	6.08357i	−0.746952	−	0.431253i	−0.824592	+	0.565728i	$0.808595\pi$
$200$	−0.822835	−	4.93183i	−0.0581832	−	0.348733i
$201$		0			0
$202$	14.1871	−	9.93389i	0.998198	−	0.698946i
$203$	−2.09400	+	1.46623i	−0.146970	+	0.102909i
$204$		0			0
$205$	24.7750	−	0.967366i	1.73036	−	0.0675638i
$206$	14.1082	+	8.14536i	0.982963	+	0.567514i
$207$		0			0
$208$	4.64254	+	1.24397i	0.321902	+	0.0862535i
$209$	−4.07247	−	1.48226i	−0.281698	−	0.102530i
$210$		0			0
$211$	11.3070	+	9.48769i	0.778405	+	0.653159i	0.942846	−	0.333228i	$-0.108138\pi$
$211$	11.3070	+	9.48769i	0.778405	+	0.653159i	−0.164442	+	0.986387i	$0.552582\pi$
$212$	0.532328	−	1.14158i	0.0365604	−	0.0784041i
$213$		0			0
$214$	−18.8724	+	3.32772i	−1.29009	+	0.227478i
$215$	3.47900	+	27.4005i	0.237266	+	1.86870i
$216$		0			0
$217$	2.20488	+	2.20488i	0.149677	+	0.149677i
$218$	3.68211	−	5.25860i	0.249384	−	0.356157i
$219$		0			0
$220$	3.35401	−	10.4691i	0.226127	−	0.705829i
$221$	−4.21327	+	5.02118i	−0.283415	+	0.337761i
$222$		0			0
$223$	−6.92078	+	3.22721i	−0.463449	+	0.216110i	−0.640296	−	0.768128i	$-0.721188\pi$
$223$	−6.92078	+	3.22721i	−0.463449	+	0.216110i	0.176846	+	0.984238i	$0.443410\pi$
$224$	−0.203369	−	0.352246i	−0.0135882	−	0.0235354i
$225$		0			0
$226$	−4.26575	+	7.38850i	−0.283753	+	0.491475i
$227$	−2.32997	+	26.6317i	−0.154646	+	1.76761i	0.382343	+	0.924021i	$0.375117\pi$
$227$	−2.32997	+	26.6317i	−0.154646	+	1.76761i	−0.536989	+	0.843590i	$0.680438\pi$
$228$		0			0
$229$	−22.6821	−	3.99947i	−1.49888	−	0.264292i	−0.636783	−	0.771043i	$-0.719735\pi$
$229$	−22.6821	−	3.99947i	−1.49888	−	0.264292i	−0.862093	+	0.506751i	$0.830846\pi$
$230$	−1.48180	−	1.63213i	−0.0977067	−	0.107619i
$231$		0			0
$232$	−6.26096	−	0.547763i	−0.411052	−	0.0359624i
$233$	−21.1162	+	5.65807i	−1.38337	+	0.370672i	−0.872343	−	0.488894i	$-0.837400\pi$
$233$	−21.1162	+	5.65807i	−1.38337	+	0.370672i	−0.511024	+	0.859566i	$0.670734\pi$
$234$		0			0
$235$	6.81181	−	5.17720i	0.444353	−	0.337723i
$236$	0.0128084	−	0.0351907i	0.000833754	−	0.00229072i
$237$		0			0
$238$	0.552585	−	0.0483449i	0.0358188	−	0.00313374i
$239$	−12.8682	+	4.68365i	−0.832376	+	0.302960i	−0.722834	−	0.691022i	$-0.757161\pi$
$239$	−12.8682	+	4.68365i	−0.832376	+	0.302960i	−0.109542	+	0.993982i	$0.534938\pi$
$240$		0			0
$241$	−0.643351	−	3.64862i	−0.0414419	−	0.235028i	0.957050	−	0.289922i	$-0.0936293\pi$
$241$	−0.643351	−	3.64862i	−0.0414419	−	0.235028i	−0.998492	+	0.0548932i	$0.982518\pi$
$242$	9.31289	−	9.31289i	0.598655	−	0.598655i
$243$		0			0
$244$			3.67965i			0.235566i
$245$	−7.11907	+	13.5231i	−0.454821	+	0.863961i
$246$		0			0
$247$	3.83988	+	1.79057i	0.244326	+	0.113931i
$248$	0.668161	+	7.63711i	0.0424283	+	0.484957i
$249$		0			0
$250$	11.1754	−	0.333262i	0.706793	−	0.0210773i
$251$	12.3698	−	7.14169i	0.780773	−	0.450780i	−0.0559309	−	0.998435i	$-0.517813\pi$
$251$	12.3698	−	7.14169i	0.780773	−	0.450780i	0.836704	+	0.547655i	$0.184479\pi$
$252$		0			0
$253$	−1.25445	−	4.68165i	−0.0788663	−	0.294333i
$254$	2.81706	−	2.36380i	0.176758	−	0.148318i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	7.26247	+	10.3719i	0.453020	+	0.646980i	0.979082	−	0.203466i	$-0.0652207\pi$
$257$	7.26247	+	10.3719i	0.453020	+	0.646980i	−0.526062	+	0.850447i	$0.676332\pi$
$258$		0			0
$259$	2.26152	+	2.69518i	0.140524	+	0.167470i
$260$	−4.15849	+	9.91010i	−0.257899	+	0.614599i
$261$		0			0
$262$	−1.14360	+	4.26797i	−0.0706518	+	0.263676i
$263$	−4.29041	−	9.20082i	−0.264558	−	0.567347i	0.728490	−	0.685057i	$-0.240223\pi$
$263$	−4.29041	−	9.20082i	−0.264558	−	0.567347i	−0.993048	+	0.117710i	$0.962445\pi$
$264$		0			0
$265$	2.36845	+	1.52425i	0.145493	+	0.0936342i
$266$	−0.122630	−	0.336923i	−0.00751892	−	0.0206581i
$267$		0			0
$268$	−2.00593	−	1.40457i	−0.122532	−	0.0857975i
$269$	27.3971			1.67043			0.835215	−	0.549924i	$-0.185343\pi$
$269$	27.3971			1.67043			0.835215	+	0.549924i	$0.185343\pi$
$270$		0			0
$271$	3.81676			0.231852			0.115926	−	0.993258i	$-0.463016\pi$
$271$	3.81676			0.231852			0.115926	+	0.993258i	$0.463016\pi$
$272$	1.11713	+	0.782224i	0.0677361	+	0.0474293i
$273$		0			0
$274$	−0.800265	−	2.19871i	−0.0483458	−	0.132829i
$275$	22.1819	+	10.5935i	1.33762	+	0.638813i
$276$		0			0
$277$	−10.8334	−	23.2323i	−0.650917	−	1.39590i	−0.903613	−	0.428350i	$-0.859095\pi$
$277$	−10.8334	−	23.2323i	−0.650917	−	1.39590i	0.252696	−	0.967546i	$-0.418683\pi$
$278$	4.77838	−	17.8332i	0.286588	−	1.06956i
$279$		0			0
$280$	0.841858	−	0.344174i	0.0503106	−	0.0205683i
$281$	−13.2554	−	15.7972i	−0.790752	−	0.942381i	0.208614	−	0.977998i	$-0.433105\pi$
$281$	−13.2554	−	15.7972i	−0.790752	−	0.942381i	−0.999366	+	0.0356167i	$0.988660\pi$
$282$		0			0
$283$	−8.83022	−	12.6109i	−0.524902	−	0.749638i	0.465918	−	0.884828i	$-0.345724\pi$
$283$	−8.83022	−	12.6109i	−0.524902	−	0.749638i	−0.990820	+	0.135190i	$0.956835\pi$
$284$	0.987977	−	5.60310i	0.0586257	−	0.332483i
$285$		0			0
$286$	−18.1012	+	15.1887i	−1.07035	+	0.898129i
$287$	1.16727	+	4.35631i	0.0689017	+	0.257145i
$288$		0			0
$289$	13.1117	−	7.57007i	0.771279	−	0.445298i
$290$	3.10489	−	13.7061i	0.182325	−	0.804851i
$291$		0			0
$292$	−0.0320395	−	0.366213i	−0.00187497	−	0.0214310i
$293$	19.4637	+	9.07610i	1.13708	+	0.530231i	0.897662	−	0.440684i	$-0.145264\pi$
$293$	19.4637	+	9.07610i	1.13708	+	0.530231i	0.239422	+	0.970916i	$0.423042\pi$
$294$		0			0
$295$	0.0740984	+	0.0390081i	0.00431417	+	0.00227114i
$296$			8.65005i			0.502774i
$297$		0			0
$298$	6.47971	−	6.47971i	0.375360	−	0.375360i
$299$	0.822803	+	4.66635i	0.0475839	+	0.269862i
$300$		0			0
$301$	−4.72114	+	1.71835i	−0.272122	+	0.0990443i
$302$	−19.6280	+	1.71722i	−1.12946	+	0.0988151i
$303$		0			0
$304$	0.301496	−	0.828353i	0.0172920	−	0.0475093i
$305$	−8.15253	−	1.11153i	−0.466812	−	0.0636462i
$306$		0			0
$307$	20.7061	−	5.54817i	1.18176	−	0.316651i	0.386134	−	0.922443i	$-0.373810\pi$
$307$	20.7061	−	5.54817i	1.18176	−	0.316651i	0.795623	+	0.605792i	$0.207144\pi$
$308$	1.99205	+	0.174282i	0.113508	+	0.00993065i
$309$		0			0
$310$	−17.1224	−	0.826629i	−0.972487	−	0.0469494i
$311$	−4.66943	−	0.823346i	−0.264779	−	0.0466877i	0.0396824	−	0.999212i	$-0.487365\pi$
$311$	−4.66943	−	0.823346i	−0.264779	−	0.0466877i	−0.304461	+	0.952525i	$0.598476\pi$
$312$		0			0
$313$	−3.03344	+	34.6724i	−0.171460	+	1.95980i	0.0937170	+	0.995599i	$0.470125\pi$
$313$	−3.03344	+	34.6724i	−0.171460	+	1.95980i	−0.265177	+	0.964200i	$0.585430\pi$
$314$	−0.619671	+	1.07330i	−0.0349700	+	0.0605699i
$315$		0			0
$316$	−0.924154	−	1.60068i	−0.0519877	−	0.0900454i
$317$	−19.8896	+	9.27469i	−1.11711	+	0.520919i	−0.891374	−	0.453269i	$-0.850258\pi$
$317$	−19.8896	+	9.27469i	−1.11711	+	0.520919i	−0.225740	+	0.974188i	$0.572480\pi$
$318$		0			0
$319$	19.8612	−	23.6697i	1.11201	−	1.32525i
$320$	2.12946	+	0.682216i	0.119040	+	0.0381370i
$321$		0			0
$322$	0.229996	−	0.328468i	0.0128172	−	0.0183048i
$323$	0.850070	+	0.850070i	0.0472992	+	0.0472992i
$324$		0			0
$325$	−20.7004	−	12.2070i	−1.14825	−	0.677124i
$326$	−12.3160	+	2.17165i	−0.682123	+	0.120277i
$327$		0			0
$328$	−4.68606	+	10.0493i	−0.258744	+	0.554879i
$329$	1.19221	+	1.00038i	0.0657285	+	0.0551528i
$330$		0			0
$331$	−17.1882	−	6.25599i	−0.944748	−	0.343860i	−0.176709	−	0.984263i	$-0.556545\pi$
$331$	−17.1882	−	6.25599i	−0.944748	−	0.343860i	−0.768039	+	0.640403i	$0.778767\pi$
$332$	0.313762	+	0.0840723i	0.0172199	+	0.00461406i
$333$		0			0
$334$	−9.33755	−	5.39104i	−0.510928	−	0.294984i
$335$	3.71785	−	4.01999i	0.203128	−	0.219635i
$336$		0			0
$337$	−2.20082	+	1.54103i	−0.119886	+	0.0839454i	−0.631982	−	0.774983i	$-0.717758\pi$
$337$	−2.20082	+	1.54103i	−0.119886	+	0.0839454i	0.512095	+	0.858929i	$0.328869\pi$
$338$	8.27396	−	5.79349i	0.450044	−	0.315124i
$339$		0			0
$340$	−2.07053	+	2.23879i	−0.112290	+	0.121416i
$341$	−32.6406	−	18.8450i	−1.76759	−	1.02052i
$342$		0			0
$343$	−5.43531	−	1.45639i	−0.293479	−	0.0786375i
$344$	−11.6073	−	4.22472i	−0.625825	−	0.227782i
$345$		0			0
$346$	0.317399	+	0.266330i	0.0170635	+	0.0143180i
$347$	−4.94512	+	10.6048i	−0.265468	+	0.569298i	−0.993181	−	0.116584i	$-0.962806\pi$
$347$	−4.94512	+	10.6048i	−0.265468	+	0.569298i	0.727713	+	0.685882i	$0.240583\pi$
$348$		0			0
$349$	−15.6692	+	2.76290i	−0.838753	+	0.147895i	−0.576492	−	0.817103i	$-0.695579\pi$
$349$	−15.6692	+	2.76290i	−0.838753	+	0.147895i	−0.262260	+	0.964997i	$0.584468\pi$
$350$	0.508236	+	1.96916i	0.0271664	+	0.105256i
$351$		0			0
$352$	3.47638	+	3.47638i	0.185292	+	0.185292i
$353$	−17.8114	+	25.4374i	−0.948007	+	1.35389i	−0.0127527	+	0.999919i	$0.504059\pi$
$353$	−17.8114	+	25.4374i	−0.948007	+	1.35389i	−0.935255	+	0.353976i	$0.884829\pi$
$354$		0			0
$355$	12.1156	+	3.88149i	0.643030	+	0.206008i
$356$	8.05151	−	9.59541i	0.426729	−	0.508556i
$357$		0			0
$358$	−7.36149	+	3.43272i	−0.389067	+	0.181425i
$359$	−12.1305	−	21.0107i	−0.640224	−	1.10890i	−0.985383	−	0.170356i	$-0.945508\pi$
$359$	−12.1305	−	21.0107i	−0.640224	−	1.10890i	0.345159	−	0.938544i	$-0.387825\pi$
$360$		0			0
$361$	−9.11147	+	15.7815i	−0.479551	+	0.830606i
$362$	1.52017	−	17.3757i	0.0798985	−	0.913244i
$363$		0			0
$364$	−1.92521	−	0.339467i	−0.100909	−	0.0177929i
$365$	0.821048	+	0.0396383i	0.0429756	+	0.00207476i
$366$		0			0
$367$	0.594855	+	0.0520431i	0.0310512	+	0.00271663i	0.102671	−	0.994715i	$-0.467261\pi$
$367$	0.594855	+	0.0520431i	0.0310512	+	0.00271663i	−0.0716196	+	0.997432i	$0.522817\pi$
$368$	0.952264	−	0.255158i	0.0496402	−	0.0133011i
$369$		0			0
$370$	−19.1648	−	2.61297i	−0.996329	−	0.135842i
$371$	−0.175226	+	0.481429i	−0.00909727	+	0.0249945i
$372$		0			0
$373$	−7.18255	+	0.628392i	−0.371898	+	0.0325369i	−0.271573	−	0.962418i	$-0.587544\pi$
$373$	−7.18255	+	0.628392i	−0.371898	+	0.0325369i	−0.100325	+	0.994955i	$0.531988\pi$
$374$	−6.30039	+	2.29316i	−0.325786	+	0.118576i
$375$		0			0
$376$	0.664436	+	3.76820i	0.0342657	+	0.194330i
$377$	−21.3596	+	21.3596i	−1.10008	+	1.10008i
$378$		0			0
$379$			10.2590i			0.526967i	0.964664	+	0.263484i	$0.0848715\pi$
$379$			10.2590i			0.526967i	−0.964664	+	0.263484i	$0.915128\pi$
$380$	1.74420	+	0.918211i	0.0894756	+	0.0471032i
$381$		0			0
$382$	−13.5336	−	6.31083i	−0.692440	−	0.322890i
$383$	−1.27613	−	14.5862i	−0.0652072	−	0.745322i	−0.956469	−	0.291833i	$-0.905735\pi$
$383$	−1.27613	−	14.5862i	−0.0652072	−	0.745322i	0.891262	−	0.453489i	$-0.149821\pi$
$384$		0			0
$385$	−0.987886	+	4.36089i	−0.0503473	+	0.222252i
$386$	−11.4545	+	6.61324i	−0.583017	+	0.336605i
$387$		0			0
$388$	−0.0746323	−	0.278532i	−0.00378888	−	0.0141403i
$389$	10.5654	−	8.86544i	0.535688	−	0.449496i	−0.334372	−	0.942441i	$-0.608524\pi$
$389$	10.5654	−	8.86544i	0.535688	−	0.449496i	0.870060	+	0.492945i	$0.164080\pi$
$390$		0			0
$391$	−0.233466	+	1.32405i	−0.0118069	+	0.0669602i
$392$	−3.92014	−	5.59855i	−0.197997	−	0.282769i
$393$		0			0
$394$	−3.91592	−	4.66681i	−0.197281	−	0.235110i
$395$	3.82559	−	1.56400i	0.192486	−	0.0786935i
$396$		0			0
$397$	−1.44774	+	5.40305i	−0.0726601	+	0.271171i	−0.992693	−	0.120671i	$-0.961495\pi$
$397$	−1.44774	+	5.40305i	−0.0726601	+	0.271171i	0.920032	+	0.391842i	$0.128162\pi$
$398$	5.14206	+	11.0272i	0.257748	+	0.552743i
$399$		0			0
$400$	−2.15475	+	4.51188i	−0.107738	+	0.225594i
$401$	−5.50338	−	15.1204i	−0.274826	−	0.755077i	−0.997928	−	0.0643367i	$-0.979507\pi$
$401$	−5.50338	−	15.1204i	−0.274826	−	0.755077i	0.723103	−	0.690741i	$-0.242715\pi$
$402$		0			0
$403$	30.1829	+	21.1343i	1.50352	+	1.05278i
$404$	−17.3192			−0.861663
$405$		0			0
$406$	2.55630			0.126867
$407$	−34.8357	−	24.3922i	−1.72674	−	1.20908i
$408$		0			0
$409$	3.41626	+	9.38610i	0.168923	+	0.464113i	0.995050	−	0.0993708i	$-0.0316830\pi$
$409$	3.41626	+	9.38610i	0.168923	+	0.464113i	−0.826127	+	0.563484i	$0.809461\pi$
$410$	−20.8494	−	13.4179i	−1.02968	−	0.662665i
$411$		0			0
$412$	−6.88475	−	14.7644i	−0.339188	−	0.727390i
$413$	−0.00394233	+	0.0147130i	−0.000193990	+	0.000723979i
$414$		0			0
$415$	−0.281048	+	0.669765i	−0.0137961	+	0.0328775i
$416$	−3.08944	−	3.68185i	−0.151472	−	0.180518i
$417$		0			0
$418$	2.48578	+	3.55007i	0.121584	+	0.173639i
$419$	−2.10945	+	11.9633i	−0.103053	+	0.584443i	0.888927	+	0.458049i	$0.151452\pi$
$419$	−2.10945	+	11.9633i	−0.103053	+	0.584443i	−0.991980	+	0.126394i	$0.959660\pi$
$420$		0			0
$421$	7.50747	−	6.29951i	0.365892	−	0.307019i	−0.441242	−	0.897388i	$-0.645462\pi$
$421$	7.50747	−	6.29951i	0.365892	−	0.307019i	0.807134	+	0.590369i	$0.201018\pi$
$422$	−3.82023	−	14.2573i	−0.185966	−	0.694033i
$423$		0			0
$424$	−1.09084	+	0.629798i	−0.0529760	+	0.0305857i
$425$	−4.33475	−	5.26369i	−0.210266	−	0.255327i
$426$		0			0
$427$	−0.130442	−	1.49096i	−0.00631254	−	0.0721526i
$428$	17.3681	+	8.09887i	0.839518	+	0.391473i
$429$		0			0
$430$	12.8664	−	24.4406i	0.620475	−	1.17863i
$431$			29.6576i			1.42856i	0.699861	+	0.714279i	$0.253245\pi$
$431$			29.6576i			1.42856i	−0.699861	+	0.714279i	$0.746755\pi$
$432$		0			0
$433$	−13.5685	+	13.5685i	−0.652059	+	0.652059i	−0.953488	−	0.301429i	$-0.902536\pi$
$433$	−13.5685	+	13.5685i	−0.652059	+	0.652059i	0.301429	+	0.953488i	$0.402536\pi$
$434$	−0.541465	−	3.07080i	−0.0259911	−	0.147403i
$435$		0			0
$436$	−6.03242	+	2.19562i	−0.288900	+	0.105151i
$437$	0.865740	−	0.0757425i	0.0414140	−	0.00362325i
$438$		0			0
$439$	7.02958	−	19.3136i	0.335503	−	0.921788i	−0.651149	−	0.758950i	$-0.725713\pi$
$439$	7.02958	−	19.3136i	0.335503	−	0.921788i	0.986653	−	0.162838i	$-0.0520649\pi$
$440$	−8.75229	+	6.65203i	−0.417249	+	0.317123i
$441$		0			0
$442$	6.33134	−	1.69648i	0.301151	−	0.0806932i
$443$	−37.3595	−	3.26853i	−1.77500	−	0.155293i	−0.847915	−	0.530133i	$-0.822142\pi$
$443$	−37.3595	−	3.26853i	−1.77500	−	0.155293i	−0.927090	+	0.374840i	$0.877698\pi$
$444$		0			0
$445$	18.8271	+	20.7372i	0.892492	+	0.983038i
$446$	7.52022	+	1.32602i	0.356093	+	0.0627888i
$447$		0			0
$448$	−0.0354496	+	0.405191i	−0.00167484	+	0.0191435i
$449$	−12.6239	+	21.8652i	−0.595759	+	1.03188i	0.397680	+	0.917524i	$0.369815\pi$
$449$	−12.6239	+	21.8652i	−0.595759	+	1.03188i	−0.993439	+	0.114361i	$0.963518\pi$
$450$		0			0
$451$	−27.2566	−	47.2098i	−1.28346	−	2.22302i
$452$	7.73216	−	3.60557i	0.363690	−	0.169592i
$453$		0			0
$454$	17.1839	−	20.4790i	0.806482	−	0.961128i
$455$	1.33367	−	4.16290i	0.0625235	−	0.195160i
$456$		0			0
$457$	−15.8663	+	22.6594i	−0.742194	+	1.05996i	0.253507	+	0.967334i	$0.418416\pi$
$457$	−15.8663	+	22.6594i	−0.742194	+	1.05996i	−0.995701	+	0.0926292i	$0.970473\pi$
$458$	16.2861	+	16.2861i	0.760999	+	0.760999i
$459$		0			0
$460$	0.277665	+	2.18688i	0.0129462	+	0.101964i
$461$	39.0635	−	6.88795i	1.81937	−	0.320804i	0.843164	−	0.537656i	$-0.180690\pi$
$461$	39.0635	−	6.88795i	1.81937	−	0.320804i	0.976204	+	0.216852i	$0.0695791\pi$
$462$		0			0
$463$	5.77067	−	12.3752i	0.268186	−	0.575126i	−0.725385	−	0.688344i	$-0.758338\pi$
$463$	5.77067	−	12.3752i	0.268186	−	0.575126i	0.993570	+	0.113218i	$0.0361158\pi$
$464$	4.81449	+	4.03984i	0.223507	+	0.187545i
$465$		0			0
$466$	20.5427	+	7.47693i	0.951622	+	0.346362i
$467$	−5.95485	−	1.59560i	−0.275557	−	0.0738354i	0.118394	−	0.992967i	$-0.462225\pi$
$467$	−5.95485	−	1.59560i	−0.275557	−	0.0738354i	−0.393951	+	0.919131i	$0.628892\pi$
$468$		0			0
$469$	0.862574	+	0.498007i	0.0398300	+	0.0229958i
$470$	−8.54943	+	0.333822i	−0.394356	+	0.0153980i
$471$		0			0
$472$	−0.0306766	+	0.0214800i	−0.00141200	+	0.000988695i
$473$	49.7454	−	34.8321i	2.28729	−	1.60158i
$474$		0			0
$475$	−2.56124	+	3.58703i	−0.117518	+	0.164584i
$476$	−0.480381	−	0.277348i	−0.0220182	−	0.0127122i
$477$		0			0
$478$	13.2275	+	3.54429i	0.605010	+	0.162112i
$479$	−10.9658	−	3.99121i	−0.501038	−	0.182363i	0.0791226	−	0.996865i	$-0.474788\pi$
$479$	−10.9658	−	3.99121i	−0.501038	−	0.182363i	−0.580161	+	0.814502i	$0.697010\pi$
$480$		0			0
$481$	31.8482	+	26.7238i	1.45215	+	1.21850i
$482$	−1.56576	+	3.35779i	−0.0713185	+	0.152943i
$483$		0			0
$484$	−12.9703	+	2.28702i	−0.589560	+	0.103955i
$485$	0.639651	−	0.0812155i	0.0290451	−	0.00368781i
$486$		0			0
$487$	−17.2353	−	17.2353i	−0.781004	−	0.781004i	0.198996	−	0.980000i	$-0.436232\pi$
$487$	−17.2353	−	17.2353i	−0.781004	−	0.781004i	−0.980000	+	0.198996i	$0.936232\pi$
$488$	2.11056	−	3.01420i	0.0955407	−	0.136446i
$489$		0			0
$490$	13.5882	−	6.99417i	0.613850	−	0.315964i
$491$	−11.9155	+	14.2003i	−0.537737	+	0.640850i	−0.964679	−	0.263429i	$-0.915147\pi$
$491$	−11.9155	+	14.2003i	−0.537737	+	0.640850i	0.426942	+	0.904279i	$0.359591\pi$
$492$		0			0
$493$	−7.76805	+	3.62230i	−0.349855	+	0.163140i
$494$	−2.11842	−	3.66921i	−0.0953122	−	0.165086i
$495$		0			0
$496$	3.83314	−	6.63920i	0.172113	−	0.298109i
$497$	−0.201692	+	2.30535i	−0.00904710	+	0.103409i
$498$		0			0
$499$	34.0517	+	6.00424i	1.52436	+	0.268787i	0.872146	−	0.489245i	$-0.162728\pi$
$499$	34.0517	+	6.00424i	1.52436	+	0.268787i	0.652218	+	0.758032i	$0.273839\pi$
$500$	−9.34548	−	6.13694i	−0.417943	−	0.274452i
$501$		0			0
$502$	−14.2290	−	1.24488i	−0.635073	−	0.0555617i
$503$	−16.5983	+	4.44751i	−0.740082	+	0.198304i	−0.609115	−	0.793082i	$-0.708475\pi$
$503$	−16.5983	+	4.44751i	−0.740082	+	0.198304i	−0.130968	+	0.991387i	$0.541808\pi$
$504$		0			0
$505$	5.23171	−	38.3719i	0.232808	−	1.70753i
$506$	−1.65771	+	4.55451i	−0.0736940	+	0.202473i
$507$		0			0
$508$	−3.66342	+	0.320508i	−0.162538	+	0.0142202i
$509$	−13.0323	+	4.74338i	−0.577648	+	0.210247i	−0.614288	−	0.789082i	$-0.710557\pi$
$509$	−13.0323	+	4.74338i	−0.577648	+	0.210247i	0.0366399	+	0.999329i	$0.488335\pi$
$510$		0			0
$511$	0.0259642	+	0.147250i	0.00114859	+	0.00651396i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	12.6617i		−	0.558485i
$515$	34.7913	−	10.7937i	1.53309	−	0.475627i
$516$		0			0
$517$	−17.0491	−	7.95011i	−0.749817	−	0.349645i
$518$	−0.306640	−	3.50492i	−0.0134730	−	0.153997i
$519$		0			0
$520$	9.09064	−	5.73267i	0.398651	−	0.251394i
$521$	−10.0874	+	5.82399i	−0.441939	+	0.255153i	−0.704420	−	0.709784i	$-0.748793\pi$
$521$	−10.0874	+	5.82399i	−0.441939	+	0.255153i	0.262481	+	0.964937i	$0.415459\pi$
$522$		0			0
$523$	−5.73230	−	21.3932i	−0.250656	−	0.935460i	−0.970456	−	0.241279i	$-0.922433\pi$
$523$	−5.73230	−	21.3932i	−0.250656	−	0.935460i	0.719800	−	0.694181i	$-0.244233\pi$
$524$	3.38479	−	2.84017i	0.147865	−	0.124074i
$525$		0			0
$526$	−1.76287	+	9.99775i	−0.0768649	+	0.435923i
$527$	5.99676	+	8.56425i	0.261223	+	0.373065i
$528$		0			0
$529$	−14.1594	−	16.8745i	−0.615625	−	0.733674i
$530$	−1.06584	−	2.60708i	−0.0462973	−	0.113244i
$531$		0			0
$532$	−0.0927985	+	0.346329i	−0.00402333	+	0.0150153i
$533$	22.5227	+	48.3000i	0.975565	+	2.09211i
$534$		0			0
$535$	−23.1901	+	36.0337i	−1.00259	+	1.55787i
$536$	0.837534	+	2.30111i	0.0361760	+	0.0993926i
$537$		0			0
$538$	−22.4424	−	15.7143i	−0.967559	−	0.677492i
$539$	33.6010			1.44730
$540$		0			0
$541$	18.8963			0.812414			0.406207	−	0.913781i	$-0.366851\pi$
$541$	18.8963			0.812414			0.406207	+	0.913781i	$0.366851\pi$
$542$	−3.12651	−	2.18921i	−0.134295	−	0.0940344i
$543$		0			0
$544$	−0.466436	−	1.28152i	−0.0199983	−	0.0549448i
$545$	−3.04230	−	14.0285i	−0.130318	−	0.600914i
$546$		0			0
$547$	1.46114	+	3.13344i	0.0624740	+	0.133976i	0.935066	−	0.354474i	$-0.115340\pi$
$547$	1.46114	+	3.13344i	0.0624740	+	0.133976i	−0.872592	+	0.488450i	$0.837562\pi$
$548$	−0.605590	+	2.26009i	−0.0258695	+	0.0965463i
$549$		0			0
$550$	−12.0942	−	21.4007i	−0.515698	−	0.912530i
$551$	3.56118	+	4.24405i	0.151711	+	0.180802i
$552$		0			0
$553$	0.431202	+	0.615820i	0.0183366	+	0.0261873i
$554$	−4.45131	+	25.2446i	−0.189118	+	1.07254i
$555$		0			0
$556$	−14.1429	+	11.8673i	−0.599792	+	0.503286i
$557$	2.66431	+	9.94333i	0.112890	+	0.421312i	0.999120	−	0.0419330i	$-0.0133516\pi$
$557$	2.66431	+	9.94333i	0.112890	+	0.421312i	−0.886230	+	0.463245i	$0.846685\pi$
$558$		0			0
$559$	−51.4149	+	29.6844i	−2.17462	+	1.25552i
$560$	−0.887019	−	0.200939i	−0.0374834	−	0.00849123i
$561$		0			0
$562$	1.79731	+	20.5433i	0.0758148	+	0.866567i
$563$	−12.2464	−	5.71060i	−0.516125	−	0.240673i	0.147061	−	0.989127i	$-0.453019\pi$
$563$	−12.2464	−	5.71060i	−0.516125	−	0.240673i	−0.663186	+	0.748454i	$0.730796\pi$
$564$		0			0
$565$	5.65269	+	18.2203i	0.237810	+	0.766534i
$566$			15.3950i			0.647101i
$567$		0			0
$568$	−4.02311	+	4.02311i	−0.168806	+	0.168806i
$569$	2.57078	+	14.5796i	0.107773	+	0.611209i	0.990077	+	0.140529i	$0.0448803\pi$
$569$	2.57078	+	14.5796i	0.107773	+	0.611209i	−0.882304	+	0.470680i	$0.844009\pi$
$570$		0			0
$571$	−3.87639	+	1.41089i	−0.162222	+	0.0590440i	−0.421855	−	0.906663i	$-0.638621\pi$
$571$	−3.87639	+	1.41089i	−0.162222	+	0.0590440i	0.259633	+	0.965707i	$0.416399\pi$
$572$	23.5396	−	2.05944i	0.984238	−	0.0861097i
$573$		0			0
$574$	1.54250	−	4.23799i	0.0643829	−	0.176890i
$575$	−4.92907	−	0.0454176i	−0.205557	−	0.00189405i
$576$		0			0
$577$	−5.16492	+	1.38393i	−0.215018	+	0.0576140i	−0.364720	−	0.931117i	$-0.618835\pi$
$577$	−5.16492	+	1.38393i	−0.215018	+	0.0576140i	0.149702	+	0.988731i	$0.452169\pi$
$578$	−15.0825	−	1.31955i	−0.627350	−	0.0548861i
$579$		0			0
$580$	−10.4049	+	9.44651i	−0.432039	+	0.392245i
$581$	−0.130114	−	0.0229426i	−0.00539803	−	0.000951818i
$582$		0			0
$583$	0.539721	−	6.16904i	0.0223530	−	0.255495i
$584$	−0.183806	+	0.318361i	−0.00760594	+	0.0131739i
$585$		0			0
$586$	−10.7379	−	18.5986i	−0.443580	−	0.768303i
$587$	19.5533	−	9.11787i	0.807053	−	0.376335i	0.0251097	−	0.999685i	$-0.492006\pi$
$587$	19.5533	−	9.11787i	0.807053	−	0.376335i	0.781943	+	0.623350i	$0.214229\pi$
$588$		0			0
$589$	4.34393	−	5.17689i	0.178988	−	0.213310i
$590$	−0.0383237	−	0.0744546i	−0.00157776	−	0.00306525i
$591$		0			0
$592$	4.96146	−	7.08570i	0.203915	−	0.291221i
$593$	−0.406766	−	0.406766i	−0.0167039	−	0.0167039i	0.698706	−	0.715409i	$-0.253760\pi$
$593$	−0.406766	−	0.406766i	−0.0167039	−	0.0167039i	−0.715409	+	0.698706i	$0.753760\pi$
$594$		0			0
$595$	0.759595	−	0.980537i	0.0311404	−	0.0401981i
$596$	−9.02448	+	1.59126i	−0.369657	+	0.0651805i
$597$		0			0
$598$	2.00251	−	4.29439i	0.0818886	−	0.175611i
$599$	−0.414424	−	0.347743i	−0.0169329	−	0.0142084i	0.634282	−	0.773102i	$-0.281296\pi$
$599$	−0.414424	−	0.347743i	−0.0169329	−	0.0142084i	−0.651215	+	0.758893i	$0.725740\pi$
$600$		0			0
$601$	−36.6533	−	13.3407i	−1.49512	−	0.544180i	−0.540329	−	0.841454i	$-0.681700\pi$
$601$	−36.6533	−	13.3407i	−1.49512	−	0.544180i	−0.954792	+	0.297274i	$0.903922\pi$
$602$	4.85294	+	1.30034i	0.197791	+	0.0529980i
$603$		0			0
$604$	17.0632	+	9.85147i	0.694293	+	0.400850i
$605$	−1.14903	−	29.4275i	−0.0467146	−	1.19640i
$606$		0			0
$607$	18.1799	−	12.7297i	0.737899	−	0.516682i	−0.143154	−	0.989700i	$-0.545724\pi$
$607$	18.1799	−	12.7297i	0.737899	−	0.516682i	0.881053	+	0.473018i	$0.156835\pi$
$608$	−0.722095	+	0.505616i	−0.0292848	+	0.0205055i
$609$		0			0
$610$	6.04061	+	5.58661i	0.244577	+	0.226195i
$611$	15.9267	+	9.19528i	0.644325	+	0.372001i
$612$		0			0
$613$	36.4009	+	9.75358i	1.47022	+	0.393943i	0.903006	−	0.429629i	$-0.141356\pi$
$613$	36.4009	+	9.75358i	1.47022	+	0.393943i	0.567211	+	0.823572i	$0.308022\pi$
$614$	−20.1437	−	7.33171i	−0.812934	−	0.295884i
$615$		0			0
$616$	−1.53183	−	1.28536i	−0.0617193	−	0.0517886i
$617$	−11.3662	+	24.3749i	−0.457585	+	0.981295i	0.533217	+	0.845979i	$0.320983\pi$
$617$	−11.3662	+	24.3749i	−0.457585	+	0.981295i	−0.990802	+	0.135317i	$0.956795\pi$
$618$		0			0
$619$	30.9485	−	5.45705i	1.24392	−	0.219337i	0.487328	−	0.873219i	$-0.337972\pi$
$619$	30.9485	−	5.45705i	1.24392	−	0.219337i	0.756597	+	0.653882i	$0.226861\pi$
$620$	13.5517	+	10.4981i	0.544250	+	0.421615i
$621$		0			0
$622$	3.35272	+	3.35272i	0.134432	+	0.134432i
$623$	−2.92224	+	4.17339i	−0.117077	+	0.167203i
$624$		0			0
$625$	16.4199	−	18.8517i	0.656794	−	0.754070i
$626$	22.3721	−	26.6620i	0.894169	−	1.06563i
$627$		0			0
$628$	1.12323	−	0.523768i	0.0448216	−	0.0209006i
$629$	5.89832	+	10.2162i	0.235181	+	0.407346i
$630$		0			0
$631$	19.8577	−	34.3945i	0.790522	−	1.36922i	−0.135123	−	0.990829i	$-0.543143\pi$
$631$	19.8577	−	34.3945i	0.790522	−	1.36922i	0.925644	−	0.378395i	$-0.123524\pi$
$632$	−0.161091	+	1.84128i	−0.00640784	+	0.0732420i
$633$		0			0
$634$	21.6124	+	3.81085i	0.858338	+	0.151348i
$635$	0.396523	−	8.21339i	0.0157355	−	0.325938i
$636$		0			0
$637$	−32.7241	−	2.86298i	−1.29657	−	0.113436i
$638$	−29.8457	+	7.99714i	−1.18160	+	0.316610i
$639$		0			0
$640$	−1.35304	−	1.78024i	−0.0534838	−	0.0703703i
$641$	12.9130	−	35.4783i	0.510034	−	1.40131i	−0.371167	−	0.928566i	$-0.621042\pi$
$641$	12.9130	−	35.4783i	0.510034	−	1.40131i	0.881201	−	0.472742i	$-0.156736\pi$
$642$		0			0
$643$	−30.4822	+	2.66684i	−1.20210	+	0.105170i	−0.670555	−	0.741860i	$-0.733944\pi$
$643$	−30.4822	+	2.66684i	−1.20210	+	0.105170i	−0.531545	+	0.847030i	$0.678388\pi$
$644$	−0.376803	+	0.137145i	−0.0148481	+	0.00540427i
$645$		0			0
$646$	−0.208756	−	1.18392i	−0.00821341	−	0.0465806i
$647$	22.2916	−	22.2916i	0.876373	−	0.876373i	−0.116784	−	0.993157i	$-0.537259\pi$
$647$	22.2916	−	22.2916i	0.876373	−	0.876373i	0.993157	+	0.116784i	$0.0372586\pi$
$648$		0			0
$649$		−	0.184113i		−	0.00722706i
$650$	9.95507	+	21.8726i	0.390470	+	0.857916i
$651$		0			0
$652$	11.3343	+	5.28528i	0.443886	+	0.206988i
$653$	−0.550847	−	6.29621i	−0.0215563	−	0.246390i	−0.999326	−	0.0367082i	$-0.988313\pi$
$653$	−0.550847	−	6.29621i	−0.0215563	−	0.246390i	0.977770	−	0.209682i	$-0.0672428\pi$
$654$		0			0
$655$	5.27014	+	8.35718i	0.205921	+	0.326542i
$656$	9.60263	−	5.54408i	0.374920	−	0.216460i
$657$		0			0
$658$	−0.402804	−	1.50329i	−0.0157029	−	0.0586042i
$659$	17.6333	−	14.7961i	0.686895	−	0.576374i	−0.231117	−	0.972926i	$-0.574238\pi$
$659$	17.6333	−	14.7961i	0.686895	−	0.576374i	0.918012	+	0.396552i	$0.129793\pi$
$660$		0			0
$661$	6.82216	−	38.6904i	0.265351	−	1.50488i	−0.502682	−	0.864471i	$-0.667653\pi$
$661$	6.82216	−	38.6904i	0.265351	−	1.50488i	0.768033	−	0.640410i	$-0.221235\pi$
$662$	10.4915	+	14.9833i	0.407762	+	0.582344i
$663$		0			0
$664$	−0.208797	−	0.248834i	−0.00810289	−	0.00965665i
$665$	−0.739284	−	0.310219i	−0.0286682	−	0.0120298i
$666$		0			0
$667$	−1.60364	+	5.98486i	−0.0620931	+	0.231735i
$668$	4.55670	+	9.77187i	0.176304	+	0.378085i
$669$		0			0
$670$	−5.35126	+	1.16051i	−0.206737	+	0.0448343i
$671$	6.18729	+	16.9994i	0.238858	+	0.656256i
$672$		0			0
$673$	26.3078	+	18.4209i	1.01409	+	0.710074i	0.957533	−	0.288325i	$-0.0930984\pi$
$673$	26.3078	+	18.4209i	1.01409	+	0.710074i	0.0565583	+	0.998399i	$0.481987\pi$
$674$	2.68671			0.103488
$675$		0			0
$676$	−10.1006			−0.388486
$677$	−17.2253	−	12.0613i	−0.662023	−	0.463554i	0.193650	−	0.981071i	$-0.437967\pi$
$677$	−17.2253	−	12.0613i	−0.662023	−	0.463554i	−0.855673	+	0.517517i	$0.826856\pi$
$678$		0			0
$679$	0.0401141	+	0.110213i	0.00153944	+	0.00422958i
$680$	2.98020	−	0.646304i	0.114285	−	0.0247846i
$681$		0			0
$682$	15.9285	+	34.1588i	0.609934	+	1.30801i
$683$	−6.69087	+	24.9707i	−0.256019	+	0.955476i	0.711502	+	0.702684i	$0.248015\pi$
$683$	−6.69087	+	24.9707i	−0.256019	+	0.955476i	−0.967521	+	0.252791i	$0.918651\pi$
$684$		0			0
$685$	−4.82446	−	2.02445i	−0.184333	−	0.0773501i
$686$	3.61700	+	4.31057i	0.138098	+	0.164578i
$687$		0			0
$688$	7.08496	+	10.1184i	0.270112	+	0.385759i
$689$	−1.05127	+	5.96204i	−0.0400501	+	0.227136i
$690$		0			0
$691$	22.5848	−	18.9509i	0.859165	−	0.720925i	−0.102623	−	0.994720i	$-0.532724\pi$
$691$	22.5848	−	18.9509i	0.859165	−	0.720925i	0.961788	+	0.273796i	$0.0882792\pi$
$692$	−0.107238	−	0.400217i	−0.00407657	−	0.0152140i
$693$		0			0
$694$	10.1335	−	5.85057i	0.384662	−	0.222085i
$695$	−22.0206	−	34.9194i	−0.835289	−	1.32457i
$696$		0			0
$697$	1.31794	+	15.0641i	0.0499205	+	0.570594i
$698$	14.4202	+	6.72424i	0.545812	+	0.254516i
$699$		0			0
$700$	0.713142	−	1.90455i	0.0269542	−	0.0719854i
$701$		−	16.1011i		−	0.608129i	−0.952651	−	0.304064i	$-0.901656\pi$
$701$		−	16.1011i		−	0.608129i	0.952651	−	0.304064i	$-0.0983438\pi$
$702$		0			0
$703$	5.39179	−	5.39179i	0.203355	−	0.203355i
$704$	−0.853714	−	4.84165i	−0.0321755	−	0.182477i
$705$		0			0
$706$	29.1806	−	10.6209i	1.09822	−	0.399721i
$707$	7.01758	−	0.613958i	0.263923	−	0.0230903i
$708$		0			0
$709$	−10.1660	+	27.9308i	−0.381792	+	1.04896i	0.588810	+	0.808272i	$0.299597\pi$
$709$	−10.1660	+	27.9308i	−0.381792	+	1.04896i	−0.970601	+	0.240692i	$0.922625\pi$
$710$	−7.69819	−	10.1288i	−0.288908	−	0.380126i
$711$		0			0
$712$	−12.0991	+	3.24195i	−0.453433	+	0.121497i
$713$	7.52910	+	0.658711i	0.281967	+	0.0246689i
$714$		0			0
$715$	−2.54789	+	52.7756i	−0.0952855	+	1.97370i
$716$	7.99910	+	1.41046i	0.298941	+	0.0527113i
$717$		0			0
$718$	−2.11449	+	24.1687i	−0.0789120	+	0.901968i
$719$	11.6590	−	20.1939i	0.434806	−	0.753106i	−0.562474	−	0.826815i	$-0.690150\pi$
$719$	11.6590	−	20.1939i	0.434806	−	0.753106i	0.997280	+	0.0737091i	$0.0234836\pi$
$720$		0			0
$721$	3.31303	+	5.73833i	0.123384	+	0.213707i
$722$	16.5156	−	7.70134i	0.614646	−	0.286614i
$723$		0			0
$724$	−11.2115	+	13.3614i	−0.416673	+	0.496571i
$725$	−17.7863	−	25.9063i	−0.660568	−	0.962136i
$726$		0			0
$727$	−21.1206	+	30.1634i	−0.783321	+	1.11870i	0.206786	+	0.978386i	$0.433699\pi$
$727$	−21.1206	+	30.1634i	−0.783321	+	1.11870i	−0.990107	+	0.140312i	$0.955189\pi$
$728$	1.38233	+	1.38233i	0.0512326	+	0.0512326i
$729$		0			0
$730$	−0.649828	−	0.503404i	−0.0240512	−	0.0186318i
$731$	−16.5897	+	2.92520i	−0.613591	+	0.108193i
$732$		0			0
$733$	15.9282	−	34.1581i	0.588321	−	1.26166i	−0.356568	−	0.934269i	$-0.616053\pi$
$733$	15.9282	−	34.1581i	0.588321	−	1.26166i	0.944889	−	0.327390i	$-0.106169\pi$
$734$	−0.457426	−	0.383826i	−0.0168839	−	0.0141673i
$735$		0			0
$736$	−0.926402	−	0.337183i	−0.0341476	−	0.0124287i
$737$	−11.6288	−	3.11594i	−0.428354	−	0.114777i
$738$		0			0
$739$	22.4008	+	12.9331i	0.824028	+	0.475753i	0.851803	−	0.523862i	$-0.175509\pi$
$739$	22.4008	+	12.9331i	0.824028	+	0.475753i	−0.0277758	+	0.999614i	$0.508842\pi$
$740$	14.2001	+	13.1329i	0.522007	+	0.482774i
$741$		0			0
$742$	0.419673	−	0.293858i	0.0154067	−	0.0107879i
$743$	−4.47147	+	3.13096i	−0.164042	+	0.114864i	−0.652715	−	0.757603i	$-0.726370\pi$
$743$	−4.47147	+	3.13096i	−0.164042	+	0.114864i	0.488673	+	0.872467i	$0.337481\pi$
$744$		0			0
$745$	−0.799470	−	20.4750i	−0.0292903	−	0.750148i
$746$	6.24403	+	3.60499i	0.228610	+	0.131988i
$747$		0			0
$748$	6.47628	+	1.73531i	0.236796	+	0.0634494i
$749$	−7.32448	−	2.66589i	−0.267631	−	0.0974096i
$750$		0			0
$751$	3.28059	+	2.75274i	0.119710	+	0.100449i	0.700678	−	0.713478i	$-0.252881\pi$
$751$	3.28059	+	2.75274i	0.119710	+	0.100449i	−0.580967	+	0.813927i	$0.697326\pi$
$752$	1.61708	−	3.46784i	0.0589688	−	0.126459i
$753$		0			0
$754$	29.7481	−	5.24540i	1.08336	−	0.191026i
$755$	−26.9810	+	34.8289i	−0.981939	+	1.26755i
$756$		0			0
$757$	29.8405	+	29.8405i	1.08457	+	1.08457i	0.996077	+	0.0884958i	$0.0282060\pi$
$757$	29.8405	+	29.8405i	1.08457	+	1.08457i	0.0884958	+	0.996077i	$0.471794\pi$
$758$	5.88430	−	8.40365i	0.213727	−	0.305234i
$759$		0			0
$760$	−0.902101	−	1.75259i	−0.0327226	−	0.0635730i
$761$	14.1582	−	16.8731i	0.513234	−	0.611649i	−0.445733	−	0.895166i	$-0.647057\pi$
$761$	14.1582	−	16.8731i	0.513234	−	0.611649i	0.958967	+	0.283517i	$0.0915013\pi$
$762$		0			0
$763$	2.36645	−	1.10349i	0.0856711	−	0.0399491i
$764$	7.46635	+	12.9321i	0.270123	+	0.467867i
$765$		0			0
$766$	−7.32097	+	12.6803i	−0.264518	+	0.458158i
$767$	−0.0156874	+	0.179307i	−0.000566438	+	0.00647442i
$768$		0			0
$769$	−20.9077	−	3.68659i	−0.753951	−	0.132942i	−0.216553	−	0.976271i	$-0.569481\pi$
$769$	−20.9077	−	3.68659i	−0.753951	−	0.132942i	−0.537398	+	0.843329i	$0.680593\pi$
$770$	3.31053	−	3.00560i	0.119303	−	0.108314i
$771$		0			0
$772$	13.1761	+	1.15276i	0.474220	+	0.0414888i
$773$	34.0772	−	9.13096i	1.22567	−	0.328418i	0.412779	−	0.910831i	$-0.364558\pi$
$773$	34.0772	−	9.13096i	1.22567	−	0.328418i	0.812893	+	0.582413i	$0.197892\pi$
$774$		0			0
$775$	−27.3530	+	26.8535i	−0.982549	+	0.964607i
$776$	−0.0986240	+	0.270967i	−0.00354039	+	0.00972715i
$777$		0			0
$778$	−13.7397	+	1.20207i	−0.492592	+	0.0430962i
$779$	9.18491	−	3.34304i	0.329084	−	0.119777i
$780$		0			0
$781$	−4.85723	−	27.5467i	−0.173805	−	0.985700i
$782$	0.950689	−	0.950689i	0.0339966	−	0.0339966i
$783$		0			0
$784$			6.83456i			0.244092i
$785$	0.821147	+	2.64680i	0.0293080	+	0.0944684i
$786$		0			0
$787$	−29.6309	−	13.8171i	−1.05623	−	0.492527i	−0.184660	−	0.982803i	$-0.559118\pi$
$787$	−29.6309	−	13.8171i	−1.05623	−	0.492527i	−0.871567	+	0.490276i	$0.836896\pi$
$788$	0.530960	+	6.06890i	0.0189147	+	0.216196i
$789$		0			0
$790$	−4.03081	−	0.913112i	−0.143410	−	0.0324871i
$791$	−3.00518	+	1.73504i	−0.106852	+	0.0616911i
$792$		0			0
$793$	−4.57736	−	17.0829i	−0.162547	−	0.606633i
$794$	4.28498	−	3.59553i	0.152068	−	0.127600i
$795$		0			0
$796$	2.11280	−	11.9823i	0.0748863	−	0.424701i
$797$	−0.786283	−	1.12293i	−0.0278516	−	0.0397762i	0.804985	−	0.593295i	$-0.202173\pi$
$797$	−0.786283	−	1.12293i	−0.0278516	−	0.0397762i	−0.832836	+	0.553519i	$0.813285\pi$
$798$		0			0
$799$	3.35421	+	3.99739i	0.118663	+	0.141418i
$800$	4.35298	−	2.46000i	0.153901	−	0.0869740i
$801$		0			0
$802$	−4.16461	+	15.5425i	−0.147057	+	0.548826i
$803$	−0.763800	−	1.63797i	−0.0269539	−	0.0578028i
$804$		0			0
$805$	−0.190032	−	0.876262i	−0.00669773	−	0.0308842i
$806$	−12.6023	−	34.6245i	−0.443896	−	1.21959i
$807$		0			0
$808$	14.1871	+	9.93389i	0.499099	+	0.349473i
$809$	18.6415			0.655400			0.327700	−	0.944782i	$-0.393726\pi$
$809$	18.6415			0.655400			0.327700	+	0.944782i	$0.393726\pi$
$810$		0			0
$811$	3.32667			0.116815			0.0584075	−	0.998293i	$-0.481398\pi$
$811$	3.32667			0.116815			0.0584075	+	0.998293i	$0.481398\pi$
$812$	−2.09400	−	1.46623i	−0.0734849	−	0.0514547i
$813$		0			0
$814$	14.5449	+	39.9619i	0.509800	+	1.40066i
$815$	−15.1337	+	23.5154i	−0.530112	+	0.823709i
$816$		0			0
$817$	4.60176	+	9.86851i	0.160995	+	0.345255i
$818$	2.58521	−	9.64813i	0.0903897	−	0.337339i
$819$		0			0
$820$	9.38258	+	22.9500i	0.327654	+	0.801450i
$821$	6.20284	+	7.39226i	0.216481	+	0.257991i	0.863346	−	0.504613i	$-0.168365\pi$
$821$	6.20284	+	7.39226i	0.216481	+	0.257991i	−0.646865	+	0.762604i	$0.723920\pi$
$822$		0			0
$823$	4.79156	+	6.84305i	0.167023	+	0.238534i	0.893935	−	0.448197i	$-0.147934\pi$
$823$	4.79156	+	6.84305i	0.167023	+	0.238534i	−0.726911	+	0.686731i	$0.759045\pi$
$824$	−2.82885	+	16.0432i	−0.0985478	+	0.558892i
$825$		0			0
$826$	0.0116684	−	0.00979095i	0.000405995	−	0.000340671i
$827$	6.62114	+	24.7104i	0.230240	+	0.859266i	0.980237	+	0.197825i	$0.0633879\pi$
$827$	6.62114	+	24.7104i	0.230240	+	0.859266i	−0.749998	+	0.661440i	$0.769945\pi$
$828$		0			0
$829$	13.9167	−	8.03481i	0.483347	−	0.279060i	−0.238463	−	0.971151i	$-0.576644\pi$
$829$	13.9167	−	8.03481i	0.483347	−	0.279060i	0.721810	+	0.692091i	$0.243310\pi$
$830$	0.614383	−	0.387437i	0.0213255	−	0.0134481i
$831$		0			0
$832$	0.418898	+	4.78802i	0.0145227	+	0.165995i
$833$	−8.44747	−	3.93912i	−0.292687	−	0.136482i
$834$		0			0
$835$	−23.0267	+	7.14384i	−0.796873	+	0.247223i
$836$		−	4.33383i		−	0.149889i
$837$		0			0
$838$	8.58980	−	8.58980i	0.296730	−	0.296730i
$839$	−2.77516	−	15.7387i	−0.0958091	−	0.543361i	−0.994496	−	0.104771i	$-0.966589\pi$
$839$	−2.77516	−	15.7387i	−0.0958091	−	0.543361i	0.898687	−	0.438590i	$-0.144522\pi$
$840$		0			0
$841$	−9.86641	+	3.59108i	−0.340221	+	0.123830i
$842$	−9.76301	+	0.854153i	−0.336456	+	0.0294360i
$843$		0			0
$844$	−5.04829	+	13.8701i	−0.173769	+	0.477427i
$845$	3.05116	−	22.3787i	0.104963	−	0.769850i
$846$		0			0
$847$	5.17438	−	1.38647i	0.177794	−	0.0476397i
$848$	1.25480	+	0.109781i	0.0430901	+	0.00376989i
$849$		0			0
$850$	0.531687	+	6.79807i	0.0182367	+	0.233172i
$851$	8.39815	+	1.48082i	0.287885	+	0.0507619i
$852$		0			0
$853$	−0.838734	+	9.58678i	−0.0287177	+	0.328245i	0.968223	+	0.250087i	$0.0804593\pi$
$853$	−0.838734	+	9.58678i	−0.0287177	+	0.328245i	−0.996941	+	0.0781577i	$0.975096\pi$
$854$	−0.748328	+	1.29614i	−0.0256073	+	0.0443531i
$855$		0			0
$856$	−9.58177	−	16.5961i	−0.327498	−	0.567244i
$857$	44.8825	−	20.9291i	1.53316	−	0.714923i	0.541129	−	0.840940i	$-0.317997\pi$
$857$	44.8825	−	20.9291i	1.53316	−	0.714923i	0.992028	+	0.126017i	$0.0402194\pi$
$858$		0			0
$859$	19.0279	−	22.6765i	0.649223	−	0.773714i	−0.336574	−	0.941657i	$-0.609268\pi$
$859$	19.0279	−	22.6765i	0.649223	−	0.773714i	0.985797	+	0.167943i	$0.0537126\pi$
$860$	−24.5582	+	12.6407i	−0.837426	+	0.431045i
$861$		0			0
$862$	17.0109	−	24.2941i	0.579394	−	0.827461i
$863$	−4.80772	−	4.80772i	−0.163657	−	0.163657i	0.620528	−	0.784184i	$-0.286918\pi$
$863$	−4.80772	−	4.80772i	−0.163657	−	0.163657i	−0.784184	+	0.620528i	$0.786918\pi$
$864$		0			0
$865$	0.919103	−	0.116697i	0.0312505	−	0.00396782i
$866$	18.8972	−	3.33209i	0.642153	−	0.113229i
$867$		0			0
$868$	−1.31780	+	2.82602i	−0.0447289	+	0.0959215i
$869$	−6.96098	−	5.84096i	−0.236135	−	0.198141i
$870$		0			0
$871$	11.0598	+	4.02545i	0.374748	+	0.136397i
$872$	6.20082	+	1.66151i	0.209986	+	0.0562657i
$873$		0			0
$874$	−0.752617	−	0.434524i	−0.0254577	−	0.0146980i
$875$	4.00425	+	2.15534i	0.135368	+	0.0728636i
$876$		0			0
$877$	33.8017	−	23.6682i	1.14140	−	0.799219i	0.159238	−	0.987240i	$-0.449096\pi$
$877$	33.8017	−	23.6682i	1.14140	−	0.799219i	0.982165	+	0.188022i	$0.0602075\pi$
$878$	−16.8361	+	11.7888i	−0.568191	+	0.397852i
$879$		0			0
$880$	10.9849	−	0.428917i	0.370301	−	0.0144588i
$881$	−0.747853	−	0.431773i	−0.0251958	−	0.0145468i	0.487349	−	0.873207i	$-0.337964\pi$
$881$	−0.747853	−	0.431773i	−0.0251958	−	0.0145468i	−0.512545	+	0.858660i	$0.671297\pi$
$882$		0			0
$883$	−2.27249	−	0.608912i	−0.0764754	−	0.0204915i	0.220378	−	0.975414i	$-0.429271\pi$
$883$	−2.27249	−	0.608912i	−0.0764754	−	0.0204915i	−0.296854	+	0.954923i	$0.595937\pi$
$884$	−6.15939	−	2.24184i	−0.207163	−	0.0754011i
$885$		0			0
$886$	28.7284	+	24.1060i	0.965149	+	0.809856i
$887$	18.0297	−	38.6648i	0.605377	−	1.29824i	−0.329798	−	0.944051i	$-0.606981\pi$
$887$	18.0297	−	38.6648i	0.605377	−	1.29824i	0.935176	−	0.354184i	$-0.115241\pi$
$888$		0			0
$889$	1.47302	−	0.259734i	0.0494036	−	0.00871118i
$890$	−3.52791	−	27.7857i	−0.118256	−	0.931380i
$891$		0			0
$892$	−5.39963	−	5.39963i	−0.180793	−	0.180793i
$893$	1.93466	−	2.76298i	0.0647408	−	0.0924595i
$894$		0			0
$895$	−5.54130	+	17.2965i	−0.185225	+	0.578159i
$896$	0.261446	−	0.311580i	0.00873431	−	0.0104091i
$897$		0			0
$898$	22.8823	−	10.6702i	0.763592	−	0.356069i
$899$	24.0908	+	41.7265i	0.803474	+	1.39166i
$900$		0			0
$901$	−0.858897	+	1.48765i	−0.0286140	+	0.0495609i
$902$	−4.75114	+	54.3057i	−0.158196	+	1.80818i
$903$		0			0
$904$	−8.40189	−	1.48148i	−0.279443	−	0.0492733i
$905$	−26.2163	−	28.8760i	−0.871460	−	0.959872i
$906$		0			0
$907$	−33.8221	−	2.95905i	−1.12304	−	0.0982537i	−0.489532	−	0.871986i	$-0.662832\pi$
$907$	−33.8221	−	2.95905i	−1.12304	−	0.0982537i	−0.633513	+	0.773732i	$0.718388\pi$
$908$	−25.8225	+	6.91913i	−0.856951	+	0.229619i
$909$		0			0
$910$	−3.48022	+	2.64508i	−0.115368	+	0.0876836i
$911$	6.69421	−	18.3922i	0.221789	−	0.609361i	−0.778033	−	0.628223i	$-0.783782\pi$
$911$	6.69421	−	18.3922i	0.221789	−	0.609361i	0.999822	+	0.0188629i	$0.00600460\pi$
$912$		0			0
$913$	1.59090	−	0.139186i	0.0526511	−	0.00460637i
$914$	25.9938	−	9.46097i	0.859799	−	0.312941i
$915$		0			0
$916$	−3.99947	−	22.6821i	−0.132146	−	0.749438i
$917$	−1.27080	+	1.27080i	−0.0419655	+	0.0419655i
$918$		0			0
$919$			20.5760i			0.678741i	0.940653	+	0.339370i	$0.110214\pi$
$919$			20.5760i			0.678741i	−0.940653	+	0.339370i	$0.889786\pi$
$920$	1.02690	−	1.95065i	0.0338557	−	0.0643111i
$921$		0			0
$922$	−35.9497	−	16.7636i	−1.18394	−	0.552081i
$923$	2.38333	+	27.2416i	0.0784484	+	0.896669i
$924$		0			0
$925$	−33.3863	+	27.4943i	−1.09774	+	0.904006i
$926$	−11.8252	+	6.82728i	−0.388600	+	0.224358i
$927$		0			0
$928$	−1.62664	−	6.07072i	−0.0533972	−	0.199281i
$929$	−1.59987	+	1.34245i	−0.0524900	+	0.0440443i	−0.668655	−	0.743573i	$-0.733130\pi$
$929$	−1.59987	+	1.34245i	−0.0524900	+	0.0440443i	0.616165	+	0.787617i	$0.288685\pi$
$930$		0			0
$931$	−1.04619	+	5.93324i	−0.0342875	+	0.194454i
$932$	−12.5390	−	17.9076i	−0.410729	−	0.586581i
$933$		0			0
$934$	3.96273	+	4.72260i	0.129664	+	0.154528i
$935$	−5.80104	+	13.8245i	−0.189714	+	0.452108i
$936$		0			0
$937$	1.67198	−	6.23993i	0.0546213	−	0.203850i	−0.933223	−	0.359299i	$-0.883016\pi$
$937$	1.67198	−	6.23993i	0.0546213	−	0.203850i	0.987844	+	0.155449i	$0.0496825\pi$
$938$	−0.420934	−	0.902696i	−0.0137440	−	0.0294741i
$939$		0			0
$940$	7.19475	+	4.63030i	0.234667	+	0.151024i
$941$	5.62938	+	15.4666i	0.183513	+	0.504197i	0.997001	−	0.0773838i	$-0.0246567\pi$
$941$	5.62938	+	15.4666i	0.183513	+	0.504197i	−0.813489	+	0.581581i	$0.802434\pi$
$942$		0			0
$943$	8.95442	+	6.26995i	0.291596	+	0.204178i
$944$	0.0374492			0.00121887
$945$		0			0
$946$	−60.7279			−1.97443
$947$	−25.9103	−	18.1426i	−0.841971	−	0.589554i	0.0710476	−	0.997473i	$-0.477366\pi$
$947$	−25.9103	−	18.1426i	−0.841971	−	0.589554i	−0.913018	+	0.407919i	$0.866255\pi$
$948$		0			0
$949$	0.604301	+	1.66030i	0.0196164	+	0.0538957i
$950$	4.15548	−	1.46925i	0.134822	−	0.0476689i
$951$		0			0
$952$	0.234425	+	0.502725i	0.00759775	+	0.0162934i
$953$	−0.570406	+	2.12878i	−0.0184773	+	0.0689581i	−0.974549	−	0.224175i	$-0.928031\pi$
$953$	−0.570406	+	2.12878i	−0.0184773	+	0.0689581i	0.956072	+	0.293133i	$0.0946979\pi$
$954$		0			0
$955$	−30.9074	+	12.6357i	−1.00014	+	0.408883i
$956$	−8.80238	−	10.4903i	−0.284689	−	0.339280i
$957$		0			0
$958$	6.69336	+	9.55911i	0.216253	+	0.308841i
$959$	0.165260	−	0.937236i	0.00533652	−	0.0302649i
$960$		0			0
$961$	21.2745	−	17.8515i	0.686276	−	0.575854i
$962$	−10.7604	−	40.1582i	−0.346928	−	1.29475i
$963$		0			0
$964$	3.20854	−	1.85245i	0.103340	−	0.0596635i
$965$	−6.53422	+	28.8444i	−0.210344	+	0.928535i
$966$		0			0
$967$	3.39853	+	38.8454i	0.109289	+	1.24918i	0.830717	+	0.556694i	$0.187931\pi$
$967$	3.39853	+	38.8454i	0.109289	+	1.24918i	−0.721428	+	0.692489i	$0.756514\pi$
$968$	11.9364	+	5.56606i	0.383652	+	0.178900i
$969$		0			0
$970$	−0.570555	−	0.300361i	−0.0183194	−	0.00964401i
$971$		−	35.9512i		−	1.15373i	−0.816840	−	0.576864i	$-0.804276\pi$
$971$		−	35.9512i		−	1.15373i	0.816840	−	0.576864i	$-0.195724\pi$
$972$		0			0
$973$	5.30988	−	5.30988i	0.170227	−	0.170227i
$974$	4.23256	+	24.0040i	0.135620	+	0.769139i
$975$		0			0
$976$	−3.45774	+	1.25852i	−0.110680	+	0.0402841i
$977$	−22.9839	+	2.01083i	−0.735322	+	0.0643323i	−0.448664	−	0.893701i	$-0.648100\pi$
$977$	−22.9839	+	2.01083i	−0.735322	+	0.0643323i	−0.286658	+	0.958033i	$0.592544\pi$
$978$		0			0
$979$	21.0622	−	57.8679i	0.673150	−	1.84947i
$980$	−15.1425	−	2.06456i	−0.483708	−	0.0659498i
$981$		0			0
$982$	17.9055	−	4.79777i	0.571388	−	0.153103i
$983$	−30.8067	−	2.69524i	−0.982583	−	0.0859648i	−0.415472	−	0.909606i	$-0.636383\pi$
$983$	−30.8067	−	2.69524i	−0.982583	−	0.0859648i	−0.567111	+	0.823641i	$0.691939\pi$
$984$		0			0
$985$	−13.6065	−	0.656889i	−0.433538	−	0.0209302i
$986$	8.44088	+	1.48836i	0.268812	+	0.0473989i
$987$		0			0
$988$	−0.369265	+	4.22072i	−0.0117479	+	0.134279i
$989$	−6.08877	+	10.5461i	−0.193612	+	0.335345i
$990$		0			0
$991$	20.7932	+	36.0148i	0.660517	+	1.14405i	0.980480	+	0.196619i	$0.0629962\pi$
$991$	20.7932	+	36.0148i	0.660517	+	1.14405i	−0.319963	+	0.947430i	$0.603670\pi$
$992$	−6.94802	+	3.23991i	−0.220600	+	0.102867i
$993$		0			0
$994$	1.48751	−	1.77274i	0.0471809	−	0.0562280i
$995$	25.9094	+	8.30063i	0.821383	+	0.263148i
$996$		0			0
$997$	−17.8180	+	25.4468i	−0.564303	+	0.805908i	−0.995340	−	0.0964258i	$-0.969259\pi$
$997$	−17.8180	+	25.4468i	−0.564303	+	0.805908i	0.431037	+	0.902334i	$0.358148\pi$
$998$	−24.4496	−	24.4496i	−0.773940	−	0.773940i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.1		216
3.2	odd	2		270.2.r.a.257.16	yes	216
5.3	odd	4	inner	810.2.s.a.233.5		216
15.8	even	4		270.2.r.a.203.12	yes	216
27.2	odd	18	inner	810.2.s.a.737.5		216
27.25	even	9		270.2.r.a.137.12	yes	216
135.83	even	36	inner	810.2.s.a.413.1		216
135.133	odd	36		270.2.r.a.83.16	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.16	✓	216	135.133	odd	36
270.2.r.a.137.12	yes	216	27.25	even	9
270.2.r.a.203.12	yes	216	15.8	even	4
270.2.r.a.257.16	yes	216	3.2	odd	2
810.2.s.a.233.5		216	5.3	odd	4	inner
810.2.s.a.413.1		216	135.83	even	36	inner
810.2.s.a.557.1		216	1.1	even	1	trivial
810.2.s.a.737.5		216	27.2	odd	18	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)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.18527 + 0.473911i) q^{5} +(-0.171895 - 0.368630i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.18527 + 0.473911i) q^{5} +(-0.171895 - 0.368630i) q^{7} +(0.258819 - 0.965926i) q^{8} +(2.06189 + 0.865214i) q^{10} +(3.16016 + 3.76614i) q^{11} +(-2.75679 - 3.93710i) q^{13} +(-0.0706294 + 0.400559i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.352969 - 1.31730i) q^{17} +(-0.763415 + 0.440758i) q^{19} +(-1.19274 - 1.89140i) q^{20} +(-0.428487 - 4.89763i) q^{22} +(-0.893489 - 0.416641i) q^{23} +(4.55082 - 2.07125i) q^{25} +4.80631i q^{26} +(0.287607 - 0.287607i) q^{28} +(-1.09136 - 6.18939i) q^{29} +(-7.20395 + 2.62202i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.466436 + 1.28152i) q^{34} +(0.550335 + 0.724094i) q^{35} +(-8.35530 + 2.23880i) q^{37} +(0.878161 + 0.0768291i) q^{38} +(-0.107827 + 2.23347i) q^{40} +(-10.9197 - 1.92544i) q^{41} +(1.07657 - 12.3052i) q^{43} +(-2.45817 + 4.25768i) q^{44} +(0.492928 + 0.853777i) q^{46} +(-3.46784 + 1.61708i) q^{47} +(4.39317 - 5.23558i) q^{49} +(-4.91583 - 0.913573i) q^{50} +(2.75679 - 3.93710i) q^{52} +(-0.890669 - 0.890669i) q^{53} +(-8.69063 - 6.73239i) q^{55} +(-0.400559 + 0.0706294i) q^{56} +(-2.65610 + 5.69603i) q^{58} +(-0.0286877 - 0.0240719i) q^{59} +(3.45774 + 1.25852i) q^{61} +(7.40506 + 1.98418i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(7.89016 + 7.29716i) q^{65} +(-2.00593 + 1.40457i) q^{67} +(1.11713 - 0.782224i) q^{68} +(-0.0354851 - 0.908802i) q^{70} +(-4.92728 - 2.84477i) q^{71} +(-0.355086 - 0.0951449i) q^{73} +(8.12838 + 2.95849i) q^{74} +(-0.675280 - 0.566627i) q^{76} +(0.845095 - 1.81231i) q^{77} +(-1.82023 + 0.320955i) q^{79} +(1.36939 - 1.76770i) q^{80} +(7.84051 + 7.84051i) q^{82} +(0.186315 - 0.266085i) q^{83} +(1.39561 + 2.71137i) q^{85} +(-7.93987 + 9.46237i) q^{86} +(4.45572 - 2.07774i) q^{88} +(-6.26296 - 10.8478i) q^{89} +(-0.977456 + 1.69300i) q^{91} +(0.0859230 - 0.982105i) q^{92} +(3.76820 + 0.664436i) q^{94} +(1.45939 - 1.32497i) q^{95} +(-0.287260 - 0.0251320i) q^{97} +(-6.60168 + 1.76892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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