LMFDB - Embedded newform 162.7.b.b.161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(161,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.b (of order $2$, degree $1$, 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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 1382x^{6} - 288x^{5} + 716245x^{4} + 201312x^{3} - 164876604x^{2} - 33576768x + 14252103396 $ x^8 - 1382x^6 - 288x^5 + 716245x^4 + 201312x^3 - 164876604x^2 - 33576768x + 14252103396
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.2
Root			$20.5718 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.b.161.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} -136.059i q^{5} -187.053 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} -136.059i q^{5} -187.053 q^{7} +181.019i q^{8} -769.663 q^{10} -1841.13i q^{11} -581.527 q^{13} +1058.13i q^{14} +1024.00 q^{16} +1756.70i q^{17} -7719.53 q^{19} +4353.87i q^{20} -10415.0 q^{22} -14703.9i q^{23} -2886.92 q^{25} +3289.62i q^{26} +5985.70 q^{28} +31898.3i q^{29} +34026.8 q^{31} -5792.62i q^{32} +9937.41 q^{34} +25450.2i q^{35} -77087.6 q^{37} +43668.3i q^{38} +24629.2 q^{40} +11355.2i q^{41} -50297.7 q^{43} +58916.2i q^{44} -83177.8 q^{46} +25876.4i q^{47} -82660.2 q^{49} +16330.9i q^{50} +18608.9 q^{52} +195102. i q^{53} -250502. q^{55} -33860.2i q^{56} +180444. q^{58} +383191. i q^{59} +446436. q^{61} -192485. i q^{62} -32768.0 q^{64} +79121.8i q^{65} +464723. q^{67} -56214.5i q^{68} +143968. q^{70} +248916. i q^{71} -545587. q^{73} +436074. i q^{74} +247025. q^{76} +344389. i q^{77} +110263. q^{79} -139324. i q^{80} +64234.8 q^{82} -47388.1i q^{83} +239014. q^{85} +284527. i q^{86} +333280. q^{88} +37879.5i q^{89} +108776. q^{91} +470524. i q^{92} +146379. q^{94} +1.05031e6i q^{95} -897161. q^{97} +467596. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) $ 8 * q - 256 * q^4 + 964 * q^7	$ 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) $ 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$-1$

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 $

$2$	− 5.65685i	− 0.707107i
$2$	− 5.65685i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−32.0000	−0.500000
$5$	− 136.059i	− 1.08847i	−0.838933	−	0.544234i	$-0.816820\pi$
$5$	− 136.059i	− 1.08847i	0.838933	−	0.544234i	$-0.183180\pi$
$6$	0	0
$7$	−187.053	−0.545344	−0.272672	−	0.962107i	$-0.587907\pi$
$7$	−187.053	−0.545344	−0.272672	+	0.962107i	$0.587907\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	−769.663	−0.769663
$11$	− 1841.13i	− 1.38327i	−0.722248	−	0.691635i	$-0.756891\pi$
$11$	− 1841.13i	− 1.38327i	0.722248	−	0.691635i	$-0.243109\pi$
$12$	0	0
$13$	−581.527	−0.264692	−0.132346	−	0.991204i	$-0.542251\pi$
$13$	−581.527	−0.264692	−0.132346	+	0.991204i	$0.542251\pi$
$14$	1058.13i	0.385617i
$15$	0	0
$16$	1024.00	0.250000
$17$	1756.70i	0.357562i	0.983889	+	0.178781i	$0.0572154\pi$
$17$	1756.70i	0.357562i	−0.983889	+	0.178781i	$0.942785\pi$
$18$	0	0
$19$	−7719.53	−1.12546	−0.562730	−	0.826641i	$-0.690249\pi$
$19$	−7719.53	−1.12546	−0.562730	+	0.826641i	$0.690249\pi$
$20$	4353.87i	0.544234i
$21$	0	0
$22$	−10415.0	−0.978119
$23$	− 14703.9i	− 1.20851i	−0.796793	−	0.604253i	$-0.793472\pi$
$23$	− 14703.9i	− 1.20851i	0.796793	−	0.604253i	$-0.206528\pi$
$24$	0	0
$25$	−2886.92	−0.184763
$26$	3289.62i	0.187165i
$27$	0	0
$28$	5985.70	0.272672
$29$	31898.3i	1.30790i	0.756540	+	0.653948i	$0.226888\pi$
$29$	31898.3i	1.30790i	−0.756540	+	0.653948i	$0.773112\pi$
$30$	0	0
$31$	34026.8	1.14218	0.571092	−	0.820886i	$-0.306520\pi$
$31$	34026.8	1.14218	0.571092	+	0.820886i	$0.306520\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	9937.41	0.252835
$35$	25450.2i	0.593590i
$36$	0	0
$37$	−77087.6	−1.52188	−0.760939	−	0.648824i	$-0.775261\pi$
$37$	−77087.6	−1.52188	−0.760939	+	0.648824i	$0.775261\pi$
$38$	43668.3i	0.795821i
$39$	0	0
$40$	24629.2	0.384832
$41$	11355.2i	0.164757i	0.996601	+	0.0823785i	$0.0262516\pi$
$41$	11355.2i	0.164757i	−0.996601	+	0.0823785i	$0.973748\pi$
$42$	0	0
$43$	−50297.7	−0.632620	−0.316310	−	0.948656i	$-0.602444\pi$
$43$	−50297.7	−0.632620	−0.316310	+	0.948656i	$0.602444\pi$
$44$	58916.2i	0.691635i
$45$	0	0
$46$	−83177.8	−0.854543
$47$	25876.4i	0.249236i	0.992205	+	0.124618i	$0.0397706\pi$
$47$	25876.4i	0.249236i	−0.992205	+	0.124618i	$0.960229\pi$
$48$	0	0
$49$	−82660.2	−0.702600
$50$	16330.9i	0.130647i
$51$	0	0
$52$	18608.9	0.132346
$53$	195102.i	1.31049i	0.755416	+	0.655246i	$0.227435\pi$
$53$	195102.i	1.31049i	−0.755416	+	0.655246i	$0.772565\pi$
$54$	0	0
$55$	−250502.	−1.50564
$56$	− 33860.2i	− 0.192808i
$57$	0	0
$58$	180444.	0.924822
$59$	383191.i	1.86578i	0.360167	+	0.932888i	$0.382720\pi$
$59$	383191.i	1.86578i	−0.360167	+	0.932888i	$0.617280\pi$
$60$	0	0
$61$	446436.	1.96684	0.983421	−	0.181338i	$-0.0580427\pi$
$61$	446436.	1.96684	0.983421	+	0.181338i	$0.0580427\pi$
$62$	− 192485.i	− 0.807646i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	79121.8i	0.288108i
$66$	0	0
$67$	464723.	1.54515	0.772574	−	0.634925i	$-0.218969\pi$
$67$	464723.	1.54515	0.772574	+	0.634925i	$0.218969\pi$
$68$	− 56214.5i	− 0.178781i
$69$	0	0
$70$	143968.	0.419731
$71$	248916.i	0.695469i	0.937593	+	0.347734i	$0.113049\pi$
$71$	248916.i	0.695469i	−0.937593	+	0.347734i	$0.886951\pi$
$72$	0	0
$73$	−545587.	−1.40248	−0.701238	−	0.712928i	$-0.747369\pi$
$73$	−545587.	−1.40248	−0.701238	+	0.712928i	$0.747369\pi$
$74$	436074.i	1.07613i
$75$	0	0
$76$	247025.	0.562730
$77$	344389.i	0.754358i
$78$	0	0
$79$	110263.	0.223639	0.111820	−	0.993729i	$-0.464332\pi$
$79$	110263.	0.223639	0.111820	+	0.993729i	$0.464332\pi$
$80$	− 139324.i	− 0.272117i
$81$	0	0
$82$	64234.8	0.116501
$83$	− 47388.1i	− 0.0828772i	−0.999141	−	0.0414386i	$-0.986806\pi$
$83$	− 47388.1i	− 0.0828772i	0.999141	−	0.0414386i	$-0.0131941\pi$
$84$	0	0
$85$	239014.	0.389195
$86$	284527.i	0.447330i
$87$	0	0
$88$	333280.	0.489059
$89$	37879.5i	0.0537321i	0.999639	+	0.0268661i	$0.00855276\pi$
$89$	37879.5i	0.0537321i	−0.999639	+	0.0268661i	$0.991447\pi$
$90$	0	0
$91$	108776.	0.144348
$92$	470524.i	0.604253i
$93$	0	0
$94$	146379.	0.176237
$95$	1.05031e6i	1.22503i
$96$	0	0
$97$	−897161.	−0.983003	−0.491502	−	0.870877i	$-0.663552\pi$
$97$	−897161.	−0.983003	−0.491502	+	0.870877i	$0.663552\pi$
$98$	467596.i	0.496813i
$99$	0	0
$100$	92381.4	0.0923814
$101$	− 1.70877e6i	− 1.65852i	−0.558865	−	0.829259i	$-0.688763\pi$
$101$	− 1.70877e6i	− 1.65852i	0.558865	−	0.829259i	$-0.311237\pi$
$102$	0	0
$103$	−557376.	−0.510078	−0.255039	−	0.966931i	$-0.582088\pi$
$103$	−557376.	−0.510078	−0.255039	+	0.966931i	$0.582088\pi$
$104$	− 105268.i	− 0.0935826i
$105$	0	0
$106$	1.10366e6	0.926658
$107$	1.53518e6i	1.25316i	0.779356	+	0.626581i	$0.215546\pi$
$107$	1.53518e6i	1.25316i	−0.779356	+	0.626581i	$0.784454\pi$
$108$	0	0
$109$	−2.28491e6	−1.76437	−0.882186	−	0.470901i	$-0.843929\pi$
$109$	−2.28491e6	−1.76437	−0.882186	+	0.470901i	$0.843929\pi$
$110$	1.41705e6i	1.06465i
$111$	0	0
$112$	−191542.	−0.136336
$113$	− 1.70501e6i	− 1.18166i	−0.806796	−	0.590830i	$-0.798800\pi$
$113$	− 1.70501e6i	− 1.18166i	0.806796	−	0.590830i	$-0.201200\pi$
$114$	0	0
$115$	−2.00059e6	−1.31542
$116$	− 1.02074e6i	− 0.653948i
$117$	0	0
$118$	2.16766e6	1.31930
$119$	− 328597.i	− 0.194994i
$120$	0	0
$121$	−1.61820e6	−0.913433
$122$	− 2.52542e6i	− 1.39077i
$123$	0	0
$124$	−1.08886e6	−0.571092
$125$	− 1.73312e6i	− 0.887360i
$126$	0	0
$127$	1.75851e6	0.858489	0.429244	−	0.903188i	$-0.358780\pi$
$127$	1.75851e6	0.858489	0.429244	+	0.903188i	$0.358780\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	447580.	0.203723
$131$	− 1.41790e6i	− 0.630712i	−0.948973	−	0.315356i	$-0.897876\pi$
$131$	− 1.41790e6i	− 0.630712i	0.948973	−	0.315356i	$-0.102124\pi$
$132$	0	0
$133$	1.44396e6	0.613763
$134$	− 2.62887e6i	− 1.09258i
$135$	0	0
$136$	−317997.	−0.126417
$137$	− 1.47857e6i	− 0.575016i	−0.957778	−	0.287508i	$-0.907173\pi$
$137$	− 1.47857e6i	− 0.575016i	0.957778	−	0.287508i	$-0.0928268\pi$
$138$	0	0
$139$	−3.29115e6	−1.22547	−0.612735	−	0.790288i	$-0.709931\pi$
$139$	−3.29115e6	−1.22547	−0.612735	+	0.790288i	$0.709931\pi$
$140$	− 814405.i	− 0.296795i
$141$	0	0
$142$	1.40808e6	0.491771
$143$	1.07067e6i	0.366140i
$144$	0	0
$145$	4.34003e6	1.42360
$146$	3.08630e6i	0.991700i
$147$	0	0
$148$	2.46680e6	0.760939
$149$	− 161217.i	− 0.0487362i	−0.999703	−	0.0243681i	$-0.992243\pi$
$149$	− 161217.i	− 0.0487362i	0.999703	−	0.0243681i	$-0.00775737\pi$
$150$	0	0
$151$	−4.44111e6	−1.28991	−0.644957	−	0.764218i	$-0.723125\pi$
$151$	−4.44111e6	−1.28991	−0.644957	+	0.764218i	$0.723125\pi$
$152$	− 1.39738e6i	− 0.397910i
$153$	0	0
$154$	1.94816e6	0.533411
$155$	− 4.62964e6i	− 1.24323i
$156$	0	0
$157$	−5.98297e6	−1.54603	−0.773016	−	0.634387i	$-0.781253\pi$
$157$	−5.98297e6	−1.54603	−0.773016	+	0.634387i	$0.781253\pi$
$158$	− 623741.i	− 0.158137i
$159$	0	0
$160$	−788135.	−0.192416
$161$	2.75041e6i	0.659052i
$162$	0	0
$163$	1.87134e6	0.432105	0.216052	−	0.976382i	$-0.430682\pi$
$163$	1.87134e6	0.432105	0.216052	+	0.976382i	$0.430682\pi$
$164$	− 363367.i	− 0.0823785i
$165$	0	0
$166$	−268068.	−0.0586030
$167$	92219.5i	0.0198004i	0.999951	+	0.00990019i	$0.00315138\pi$
$167$	92219.5i	0.0198004i	−0.999951	+	0.00990019i	$0.996849\pi$
$168$	0	0
$169$	−4.48863e6	−0.929938
$170$	− 1.35207e6i	− 0.275202i
$171$	0	0
$172$	1.60953e6	0.316310
$173$	− 7.53470e6i	− 1.45522i	−0.685993	−	0.727609i	$-0.740632\pi$
$173$	− 7.53470e6i	− 1.45522i	0.685993	−	0.727609i	$-0.259368\pi$
$174$	0	0
$175$	540007.	0.100759
$176$	− 1.88532e6i	− 0.345817i
$177$	0	0
$178$	214279.	0.0379943
$179$	− 4.33502e6i	− 0.755844i	−0.925838	−	0.377922i	$-0.876639\pi$
$179$	− 4.33502e6i	− 0.755844i	0.925838	−	0.377922i	$-0.123361\pi$
$180$	0	0
$181$	3.65501e6	0.616387	0.308193	−	0.951324i	$-0.400276\pi$
$181$	3.65501e6	0.616387	0.308193	+	0.951324i	$0.400276\pi$
$182$	− 615333.i	− 0.102069i
$183$	0	0
$184$	2.66169e6	0.427271
$185$	1.04884e7i	1.65651i
$186$	0	0
$187$	3.23432e6	0.494605
$188$	− 828046.i	− 0.124618i
$189$	0	0
$190$	5.94144e6	0.866225
$191$	− 3.62164e6i	− 0.519763i	−0.965641	−	0.259881i	$-0.916317\pi$
$191$	− 3.62164e6i	− 0.519763i	0.965641	−	0.259881i	$-0.0836835\pi$
$192$	0	0
$193$	6.50942e6	0.905463	0.452731	−	0.891647i	$-0.350450\pi$
$193$	6.50942e6	0.905463	0.452731	+	0.891647i	$0.350450\pi$
$194$	5.07511e6i	0.695088i
$195$	0	0
$196$	2.64513e6	0.351300
$197$	− 6.32938e6i	− 0.827871i	−0.910306	−	0.413935i	$-0.864154\pi$
$197$	− 6.32938e6i	− 0.827871i	0.910306	−	0.413935i	$-0.135846\pi$
$198$	0	0
$199$	−8.27329e6	−1.04983	−0.524915	−	0.851155i	$-0.675903\pi$
$199$	−8.27329e6	−1.04983	−0.524915	+	0.851155i	$0.675903\pi$
$200$	− 522588.i	− 0.0653235i
$201$	0	0
$202$	−9.66627e6	−1.17275
$203$	− 5.96667e6i	− 0.713253i
$204$	0	0
$205$	1.54497e6	0.179333
$206$	3.15299e6i	0.360679i
$207$	0	0
$208$	−595484.	−0.0661729
$209$	1.42127e7i	1.55681i
$210$	0	0
$211$	8.76784e6	0.933352	0.466676	−	0.884428i	$-0.345451\pi$
$211$	8.76784e6	0.933352	0.466676	+	0.884428i	$0.345451\pi$
$212$	− 6.24327e6i	− 0.655246i
$213$	0	0
$214$	8.68428e6	0.886120
$215$	6.84343e6i	0.688587i
$216$	0	0
$217$	−6.36482e6	−0.622883
$218$	1.29254e7i	1.24760i
$219$	0	0
$220$	8.01605e6	0.752822
$221$	− 1.02157e6i	− 0.0946437i
$222$	0	0
$223$	1.22181e7	1.10177	0.550885	−	0.834581i	$-0.314290\pi$
$223$	1.22181e7	1.10177	0.550885	+	0.834581i	$0.314290\pi$
$224$	1.08353e6i	0.0964041i
$225$	0	0
$226$	−9.64502e6	−0.835560
$227$	− 2.24728e6i	− 0.192124i	−0.995375	−	0.0960618i	$-0.969375\pi$
$227$	− 2.24728e6i	− 0.192124i	0.995375	−	0.0960618i	$-0.0306246\pi$
$228$	0	0
$229$	−5.20660e6	−0.433559	−0.216779	−	0.976221i	$-0.569555\pi$
$229$	−5.20660e6	−0.433559	−0.216779	+	0.976221i	$0.569555\pi$
$230$	1.13170e7i	0.930142i
$231$	0	0
$232$	−5.77420e6	−0.462411
$233$	1.44501e6i	0.114236i	0.998367	+	0.0571179i	$0.0181911\pi$
$233$	1.44501e6i	0.114236i	−0.998367	+	0.0571179i	$0.981809\pi$
$234$	0	0
$235$	3.52071e6	0.271286
$236$	− 1.22621e7i	− 0.932888i
$237$	0	0
$238$	−1.85882e6	−0.137882
$239$	− 4.24422e6i	− 0.310888i	−0.987845	−	0.155444i	$-0.950319\pi$
$239$	− 4.24422e6i	− 0.310888i	0.987845	−	0.155444i	$-0.0496809\pi$
$240$	0	0
$241$	−8.63659e6	−0.617008	−0.308504	−	0.951223i	$-0.599828\pi$
$241$	−8.63659e6	−0.617008	−0.308504	+	0.951223i	$0.599828\pi$
$242$	9.15394e6i	0.645895i
$243$	0	0
$244$	−1.42859e7	−0.983421
$245$	1.12466e7i	0.764757i
$246$	0	0
$247$	4.48912e6	0.297900
$248$	6.15951e6i	0.403823i
$249$	0	0
$250$	−9.80403e6	−0.627458
$251$	1.25318e7i	0.792488i	0.918145	+	0.396244i	$0.129687\pi$
$251$	1.25318e7i	0.792488i	−0.918145	+	0.396244i	$0.870313\pi$
$252$	0	0
$253$	−2.70718e7	−1.67169
$254$	− 9.94766e6i	− 0.607043i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	9.78118e6i	0.576225i	0.957597	+	0.288112i	$0.0930277\pi$
$257$	9.78118e6i	0.576225i	−0.957597	+	0.288112i	$0.906972\pi$
$258$	0	0
$259$	1.44195e7	0.829947
$260$	− 2.53190e6i	− 0.144054i
$261$	0	0
$262$	−8.02084e6	−0.445981
$263$	2.88119e7i	1.58381i	0.610641	+	0.791907i	$0.290912\pi$
$263$	2.88119e7i	1.58381i	−0.610641	+	0.791907i	$0.709088\pi$
$264$	0	0
$265$	2.65453e7	1.42643
$266$	− 8.16828e6i	− 0.433996i
$267$	0	0
$268$	−1.48711e7	−0.772574
$269$	2.21154e7i	1.13616i	0.822974	+	0.568079i	$0.192313\pi$
$269$	2.21154e7i	1.13616i	−0.822974	+	0.568079i	$0.807687\pi$
$270$	0	0
$271$	−2.22233e7	−1.11661	−0.558303	−	0.829637i	$-0.688547\pi$
$271$	−2.22233e7	−1.11661	−0.558303	+	0.829637i	$0.688547\pi$
$272$	1.79886e6i	0.0893906i
$273$	0	0
$274$	−8.36405e6	−0.406598
$275$	5.31519e6i	0.255577i
$276$	0	0
$277$	−1.29282e7	−0.608271	−0.304136	−	0.952629i	$-0.598368\pi$
$277$	−1.29282e7	−0.608271	−0.304136	+	0.952629i	$0.598368\pi$
$278$	1.86175e7i	0.866538i
$279$	0	0
$280$	−4.60697e6	−0.209866
$281$	2.92462e7i	1.31811i	0.752097	+	0.659053i	$0.229043\pi$
$281$	2.92462e7i	1.31811i	−0.752097	+	0.659053i	$0.770957\pi$
$282$	0	0
$283$	−2.38615e7	−1.05278	−0.526392	−	0.850242i	$-0.676456\pi$
$283$	−2.38615e7	−1.05278	−0.526392	+	0.850242i	$0.676456\pi$
$284$	− 7.96531e6i	− 0.347734i
$285$	0	0
$286$	6.05661e6	0.258900
$287$	− 2.12403e6i	− 0.0898493i
$288$	0	0
$289$	2.10516e7	0.872149
$290$	− 2.45509e7i	− 1.00664i
$291$	0	0
$292$	1.74588e7	0.701238
$293$	− 1.54746e7i	− 0.615202i	−0.951515	−	0.307601i	$-0.900474\pi$
$293$	− 1.54746e7i	− 0.615202i	0.951515	−	0.307601i	$-0.0995261\pi$
$294$	0	0
$295$	5.21364e7	2.03084
$296$	− 1.39544e7i	− 0.538065i
$297$	0	0
$298$	−911980.	−0.0344617
$299$	8.55072e6i	0.319881i
$300$	0	0
$301$	9.40834e6	0.344996
$302$	2.51227e7i	0.912108i
$303$	0	0
$304$	−7.90480e6	−0.281365
$305$	− 6.07414e7i	− 2.14084i
$306$	0	0
$307$	4.16301e7	1.43877	0.719386	−	0.694610i	$-0.244423\pi$
$307$	4.16301e7	1.43877	0.719386	+	0.694610i	$0.244423\pi$
$308$	− 1.10205e7i	− 0.377179i
$309$	0	0
$310$	−2.61892e7	−0.879097
$311$	1.87156e6i	0.0622189i	0.999516	+	0.0311094i	$0.00990404\pi$
$311$	1.87156e6i	0.0622189i	−0.999516	+	0.0311094i	$0.990096\pi$
$312$	0	0
$313$	4.77886e6	0.155844	0.0779222	−	0.996959i	$-0.475171\pi$
$313$	4.77886e6	0.155844	0.0779222	+	0.996959i	$0.475171\pi$
$314$	3.38448e7i	1.09321i
$315$	0	0
$316$	−3.52841e6	−0.111820
$317$	1.18386e7i	0.371642i	0.982584	+	0.185821i	$0.0594944\pi$
$317$	1.18386e7i	0.371642i	−0.982584	+	0.185821i	$0.940506\pi$
$318$	0	0
$319$	5.87289e7	1.80917
$320$	4.45837e6i	0.136059i
$321$	0	0
$322$	1.55587e7	0.466020
$323$	− 1.35609e7i	− 0.402422i
$324$	0	0
$325$	1.67882e6	0.0489052
$326$	− 1.05859e7i	− 0.305544i
$327$	0	0
$328$	−2.05551e6	−0.0582504
$329$	− 4.84027e6i	− 0.135919i
$330$	0	0
$331$	−2.50710e7	−0.691334	−0.345667	−	0.938357i	$-0.612347\pi$
$331$	−2.50710e7	−0.691334	−0.345667	+	0.938357i	$0.612347\pi$
$332$	1.51642e6i	0.0414386i
$333$	0	0
$334$	521672.	0.0140010
$335$	− 6.32296e7i	− 1.68184i
$336$	0	0
$337$	−5.35176e7	−1.39832	−0.699160	−	0.714965i	$-0.746443\pi$
$337$	−5.35176e7	−1.39832	−0.699160	+	0.714965i	$0.746443\pi$
$338$	2.53916e7i	0.657566i
$339$	0	0
$340$	−7.64846e6	−0.194598
$341$	− 6.26478e7i	− 1.57995i
$342$	0	0
$343$	3.74684e7	0.928503
$344$	− 9.10486e6i	− 0.223665i
$345$	0	0
$346$	−4.26227e7	−1.02899
$347$	− 6.34294e7i	− 1.51811i	−0.651029	−	0.759053i	$-0.725662\pi$
$347$	− 6.34294e7i	− 1.51811i	0.651029	−	0.759053i	$-0.274338\pi$
$348$	0	0
$349$	−4.86064e6	−0.114345	−0.0571725	−	0.998364i	$-0.518209\pi$
$349$	−4.86064e6	−0.114345	−0.0571725	+	0.998364i	$0.518209\pi$
$350$	− 3.05474e6i	− 0.0712476i
$351$	0	0
$352$	−1.06650e7	−0.244530
$353$	− 9.78167e6i	− 0.222376i	−0.993799	−	0.111188i	$-0.964534\pi$
$353$	− 9.78167e6i	− 0.222376i	0.993799	−	0.111188i	$-0.0354656\pi$
$354$	0	0
$355$	3.38671e7	0.756996
$356$	− 1.21214e6i	− 0.0268661i
$357$	0	0
$358$	−2.45226e7	−0.534462
$359$	5.87733e7i	1.27027i	0.772400	+	0.635136i	$0.219056\pi$
$359$	5.87733e7i	1.27027i	−0.772400	+	0.635136i	$0.780944\pi$
$360$	0	0
$361$	1.25453e7	0.266661
$362$	− 2.06759e7i	− 0.435851i
$363$	0	0
$364$	−3.48085e6	−0.0721740
$365$	7.42317e7i	1.52655i
$366$	0	0
$367$	−5.50266e7	−1.11320	−0.556602	−	0.830779i	$-0.687895\pi$
$367$	−5.50266e7	−1.11320	−0.556602	+	0.830779i	$0.687895\pi$
$368$	− 1.50568e7i	− 0.302126i
$369$	0	0
$370$	5.93315e7	1.17133
$371$	− 3.64944e7i	− 0.714669i
$372$	0	0
$373$	−5.16072e7	−0.994453	−0.497226	−	0.867621i	$-0.665648\pi$
$373$	−5.16072e7	−0.994453	−0.497226	+	0.867621i	$0.665648\pi$
$374$	− 1.82961e7i	− 0.349738i
$375$	0	0
$376$	−4.68414e6	−0.0881183
$377$	− 1.85497e7i	− 0.346189i
$378$	0	0
$379$	9.95306e7	1.82826	0.914132	−	0.405416i	$-0.132873\pi$
$379$	9.95306e7	1.82826	0.914132	+	0.405416i	$0.132873\pi$
$380$	− 3.36099e7i	− 0.612514i
$381$	0	0
$382$	−2.04871e7	−0.367528
$383$	− 1.05697e7i	− 0.188133i	−0.995566	−	0.0940665i	$-0.970013\pi$
$383$	− 1.05697e7i	− 0.188133i	0.995566	−	0.0940665i	$-0.0299866\pi$
$384$	0	0
$385$	4.68571e7	0.821094
$386$	− 3.68229e7i	− 0.640259i
$387$	0	0
$388$	2.87091e7	0.491502
$389$	− 1.39422e7i	− 0.236855i	−0.992963	−	0.118428i	$-0.962215\pi$
$389$	− 1.39422e7i	− 0.236855i	0.992963	−	0.118428i	$-0.0377854\pi$
$390$	0	0
$391$	2.58304e7	0.432116
$392$	− 1.49631e7i	− 0.248407i
$393$	0	0
$394$	−3.58044e7	−0.585393
$395$	− 1.50022e7i	− 0.243424i
$396$	0	0
$397$	2.16064e7	0.345312	0.172656	−	0.984982i	$-0.444765\pi$
$397$	2.16064e7	0.345312	0.172656	+	0.984982i	$0.444765\pi$
$398$	4.68008e7i	0.742342i
$399$	0	0
$400$	−2.95620e6	−0.0461907
$401$	− 1.03802e8i	− 1.60980i	−0.593408	−	0.804902i	$-0.702218\pi$
$401$	− 1.03802e8i	− 1.60980i	0.593408	−	0.804902i	$-0.297782\pi$
$402$	0	0
$403$	−1.97875e7	−0.302326
$404$	5.46807e7i	0.829259i
$405$	0	0
$406$	−3.37526e7	−0.504346
$407$	1.41928e8i	2.10517i
$408$	0	0
$409$	−9.13731e7	−1.33551	−0.667757	−	0.744380i	$-0.732745\pi$
$409$	−9.13731e7	−1.33551	−0.667757	+	0.744380i	$0.732745\pi$
$410$	− 8.73970e6i	− 0.126807i
$411$	0	0
$412$	1.78360e7	0.255039
$413$	− 7.16771e7i	− 1.01749i
$414$	0	0
$415$	−6.44756e6	−0.0902092
$416$	3.36857e6i	0.0467913i
$417$	0	0
$418$	8.03990e7	1.10083
$419$	− 8.27671e7i	− 1.12516i	−0.826742	−	0.562582i	$-0.809808\pi$
$419$	− 8.27671e7i	− 1.12516i	0.826742	−	0.562582i	$-0.190192\pi$
$420$	0	0
$421$	−8.17479e7	−1.09554	−0.547772	−	0.836627i	$-0.684524\pi$
$421$	−8.17479e7	−1.09554	−0.547772	+	0.836627i	$0.684524\pi$
$422$	− 4.95984e7i	− 0.659979i
$423$	0	0
$424$	−3.53173e7	−0.463329
$425$	− 5.07146e6i	− 0.0660642i
$426$	0	0
$427$	−8.35072e7	−1.07261
$428$	− 4.91257e7i	− 0.626581i
$429$	0	0
$430$	3.87123e7	0.486904
$431$	1.53458e8i	1.91672i	0.285569	+	0.958358i	$0.407817\pi$
$431$	1.53458e8i	1.91672i	−0.285569	+	0.958358i	$0.592183\pi$
$432$	0	0
$433$	−1.15843e8	−1.42694	−0.713468	−	0.700688i	$-0.752876\pi$
$433$	−1.15843e8	−1.42694	−0.713468	+	0.700688i	$0.752876\pi$
$434$	3.60048e7i	0.440445i
$435$	0	0
$436$	7.31172e7	0.882186
$437$	1.13507e8i	1.36013i
$438$	0	0
$439$	4.22669e7	0.499582	0.249791	−	0.968300i	$-0.419638\pi$
$439$	4.22669e7	0.499582	0.249791	+	0.968300i	$0.419638\pi$
$440$	− 4.53456e7i	− 0.532326i
$441$	0	0
$442$	−5.77888e6	−0.0669232
$443$	− 1.67134e8i	− 1.92244i	−0.275775	−	0.961222i	$-0.588934\pi$
$443$	− 1.67134e8i	− 1.92244i	0.275775	−	0.961222i	$-0.411066\pi$
$444$	0	0
$445$	5.15382e6	0.0584857
$446$	− 6.91163e7i	− 0.779069i
$447$	0	0
$448$	6.12935e6	0.0681680
$449$	− 8.56152e7i	− 0.945827i	−0.881109	−	0.472914i	$-0.843202\pi$
$449$	− 8.56152e7i	− 0.945827i	0.881109	−	0.472914i	$-0.156798\pi$
$450$	0	0
$451$	2.09065e7	0.227903
$452$	5.45605e7i	0.590830i
$453$	0	0
$454$	−1.27126e7	−0.135852
$455$	− 1.48000e7i	− 0.157118i
$456$	0	0
$457$	−6.65392e6	−0.0697155	−0.0348577	−	0.999392i	$-0.511098\pi$
$457$	−6.65392e6	−0.0697155	−0.0348577	+	0.999392i	$0.511098\pi$
$458$	2.94530e7i	0.306572i
$459$	0	0
$460$	6.40189e7	0.657710
$461$	2.31770e7i	0.236567i	0.992980	+	0.118283i	$0.0377391\pi$
$461$	2.31770e7i	0.236567i	−0.992980	+	0.118283i	$0.962261\pi$
$462$	0	0
$463$	−3.76037e6	−0.0378868	−0.0189434	−	0.999821i	$-0.506030\pi$
$463$	−3.76037e6	−0.0378868	−0.0189434	+	0.999821i	$0.506030\pi$
$464$	3.26638e7i	0.326974i
$465$	0	0
$466$	8.17420e6	0.0807769
$467$	1.12748e8i	1.10703i	0.832839	+	0.553515i	$0.186714\pi$
$467$	1.12748e8i	1.10703i	−0.832839	+	0.553515i	$0.813286\pi$
$468$	0	0
$469$	−8.69279e7	−0.842637
$470$	− 1.99161e7i	− 0.191828i
$471$	0	0
$472$	−6.93650e7	−0.659651
$473$	9.26047e7i	0.875084i
$474$	0	0
$475$	2.22857e7	0.207943
$476$	1.05151e7i	0.0974972i
$477$	0	0
$478$	−2.40089e7	−0.219831
$479$	− 4.74220e7i	− 0.431493i	−0.976449	−	0.215746i	$-0.930782\pi$
$479$	− 4.74220e7i	− 0.431493i	0.976449	−	0.215746i	$-0.0692185\pi$
$480$	0	0
$481$	4.48286e7	0.402828
$482$	4.88559e7i	0.436291i
$483$	0	0
$484$	5.17825e7	0.456717
$485$	1.22066e8i	1.06997i
$486$	0	0
$487$	−2.03528e8	−1.76213	−0.881064	−	0.472997i	$-0.843172\pi$
$487$	−2.03528e8	−1.76213	−0.881064	+	0.472997i	$0.843172\pi$
$488$	8.08135e7i	0.695384i
$489$	0	0
$490$	6.36205e7	0.540765
$491$	1.44528e8i	1.22098i	0.792026	+	0.610488i	$0.209027\pi$
$491$	1.44528e8i	1.22098i	−0.792026	+	0.610488i	$0.790973\pi$
$492$	0	0
$493$	−5.60358e7	−0.467654
$494$	− 2.53943e7i	− 0.210647i
$495$	0	0
$496$	3.48434e7	0.285546
$497$	− 4.65605e7i	− 0.379270i
$498$	0	0
$499$	1.53434e8	1.23487	0.617433	−	0.786624i	$-0.288173\pi$
$499$	1.53434e8	1.23487	0.617433	+	0.786624i	$0.288173\pi$
$500$	5.54600e7i	0.443680i
$501$	0	0
$502$	7.08907e7	0.560374
$503$	1.94112e8i	1.52527i	0.646827	+	0.762637i	$0.276095\pi$
$503$	1.94112e8i	1.52527i	−0.646827	+	0.762637i	$0.723905\pi$
$504$	0	0
$505$	−2.32493e8	−1.80524
$506$	1.53141e8i	1.18206i
$507$	0	0
$508$	−5.62725e7	−0.429244
$509$	2.60821e7i	0.197783i	0.995098	+	0.0988915i	$0.0315297\pi$
$509$	2.60821e7i	0.197783i	−0.995098	+	0.0988915i	$0.968470\pi$
$510$	0	0
$511$	1.02054e8	0.764832
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	5.53307e7	0.407453
$515$	7.58357e7i	0.555203i
$516$	0	0
$517$	4.76419e7	0.344761
$518$	− 8.15689e7i	− 0.586861i
$519$	0	0
$520$	−1.43226e7	−0.101862
$521$	− 2.12883e8i	− 1.50532i	−0.658409	−	0.752660i	$-0.728770\pi$
$521$	− 2.12883e8i	− 1.50532i	0.658409	−	0.752660i	$-0.271230\pi$
$522$	0	0
$523$	1.36075e8	0.951204	0.475602	−	0.879661i	$-0.342230\pi$
$523$	1.36075e8	0.951204	0.475602	+	0.879661i	$0.342230\pi$
$524$	4.53728e7i	0.315356i
$525$	0	0
$526$	1.62985e8	1.11993
$527$	5.97750e7i	0.408402i
$528$	0	0
$529$	−6.81685e7	−0.460486
$530$	− 1.50163e8i	− 1.00864i
$531$	0	0
$532$	−4.62068e7	−0.306882
$533$	− 6.60337e6i	− 0.0436098i
$534$	0	0
$535$	2.08874e8	1.36403
$536$	8.41239e7i	0.546292i
$537$	0	0
$538$	1.25104e8	0.803385
$539$	1.52188e8i	0.971884i
$540$	0	0
$541$	2.00376e7	0.126547	0.0632737	−	0.997996i	$-0.479846\pi$
$541$	2.00376e7	0.126547	0.0632737	+	0.997996i	$0.479846\pi$
$542$	1.25714e8i	0.789560i
$543$	0	0
$544$	1.01759e7	0.0632087
$545$	3.10882e8i	1.92046i
$546$	0	0
$547$	1.32663e8	0.810566	0.405283	−	0.914191i	$-0.367173\pi$
$547$	1.32663e8	0.810566	0.405283	+	0.914191i	$0.367173\pi$
$548$	4.73142e7i	0.287508i
$549$	0	0
$550$	3.00673e7	0.180720
$551$	− 2.46240e8i	− 1.47198i
$552$	0	0
$553$	−2.06250e7	−0.121960
$554$	7.31327e7i	0.430113i
$555$	0	0
$556$	1.05317e8	0.612735
$557$	− 2.15296e8i	− 1.24586i	−0.782276	−	0.622932i	$-0.785941\pi$
$557$	− 2.15296e8i	− 1.24586i	0.782276	−	0.622932i	$-0.214059\pi$
$558$	0	0
$559$	2.92495e7	0.167449
$560$	2.60610e7i	0.148397i
$561$	0	0
$562$	1.65441e8	0.932041
$563$	− 2.69419e8i	− 1.50974i	−0.655873	−	0.754871i	$-0.727699\pi$
$563$	− 2.69419e8i	− 1.50974i	0.655873	−	0.754871i	$-0.272301\pi$
$564$	0	0
$565$	−2.31982e8	−1.28620
$566$	1.34981e8i	0.744431i
$567$	0	0
$568$	−4.50586e7	−0.245885
$569$	2.26063e8i	1.22714i	0.789642	+	0.613568i	$0.210267\pi$
$569$	2.26063e8i	1.22714i	−0.789642	+	0.613568i	$0.789733\pi$
$570$	0	0
$571$	−1.20184e8	−0.645560	−0.322780	−	0.946474i	$-0.604617\pi$
$571$	−1.20184e8	−0.645560	−0.322780	+	0.946474i	$0.604617\pi$
$572$	− 3.42614e7i	− 0.183070i
$573$	0	0
$574$	−1.20153e7	−0.0635330
$575$	4.24489e7i	0.223287i
$576$	0	0
$577$	−1.67233e8	−0.870549	−0.435275	−	0.900298i	$-0.643349\pi$
$577$	−1.67233e8	−0.870549	−0.435275	+	0.900298i	$0.643349\pi$
$578$	− 1.19086e8i	− 0.616703i
$579$	0	0
$580$	−1.38881e8	−0.711801
$581$	8.86409e6i	0.0451966i
$582$	0	0
$583$	3.59209e8	1.81276
$584$	− 9.87617e7i	− 0.495850i
$585$	0	0
$586$	−8.75377e7	−0.435013
$587$	− 2.55513e8i	− 1.26328i	−0.775263	−	0.631639i	$-0.782383\pi$
$587$	− 2.55513e8i	− 1.26328i	0.775263	−	0.631639i	$-0.217617\pi$
$588$	0	0
$589$	−2.62671e8	−1.28548
$590$	− 2.94928e8i	− 1.43602i
$591$	0	0
$592$	−7.89377e7	−0.380469
$593$	3.31215e8i	1.58835i	0.607689	+	0.794175i	$0.292097\pi$
$593$	3.31215e8i	1.58835i	−0.607689	+	0.794175i	$0.707903\pi$
$594$	0	0
$595$	−4.47084e7	−0.212245
$596$	5.15894e6i	0.0243681i
$597$	0	0
$598$	4.83702e7	0.226190
$599$	3.62266e7i	0.168557i	0.996442	+	0.0842786i	$0.0268586\pi$
$599$	3.62266e7i	0.168557i	−0.996442	+	0.0842786i	$0.973141\pi$
$600$	0	0
$601$	−1.12726e8	−0.519279	−0.259640	−	0.965706i	$-0.583604\pi$
$601$	−1.12726e8	−0.519279	−0.259640	+	0.965706i	$0.583604\pi$
$602$	− 5.32216e7i	− 0.243949i
$603$	0	0
$604$	1.42116e8	0.644957
$605$	2.20170e8i	0.994243i
$606$	0	0
$607$	−1.43166e8	−0.640138	−0.320069	−	0.947394i	$-0.603706\pi$
$607$	−1.43166e8	−0.640138	−0.320069	+	0.947394i	$0.603706\pi$
$608$	4.47163e7i	0.198955i
$609$	0	0
$610$	−3.43605e8	−1.51381
$611$	− 1.50479e7i	− 0.0659707i
$612$	0	0
$613$	1.40379e7	0.0609425	0.0304712	−	0.999536i	$-0.490299\pi$
$613$	1.40379e7	0.0609425	0.0304712	+	0.999536i	$0.490299\pi$
$614$	− 2.35495e8i	− 1.01737i
$615$	0	0
$616$	−6.23411e7	−0.266706
$617$	6.92633e7i	0.294882i	0.989071	+	0.147441i	$0.0471036\pi$
$617$	6.92633e7i	0.294882i	−0.989071	+	0.147441i	$0.952896\pi$
$618$	0	0
$619$	−2.14347e8	−0.903745	−0.451873	−	0.892083i	$-0.649244\pi$
$619$	−2.14347e8	−0.903745	−0.451873	+	0.892083i	$0.649244\pi$
$620$	1.48148e8i	0.621615i
$621$	0	0
$622$	1.05871e7	0.0439954
$623$	− 7.08547e6i	− 0.0293025i
$624$	0	0
$625$	−2.80914e8	−1.15063
$626$	− 2.70333e7i	− 0.110199i
$627$	0	0
$628$	1.91455e8	0.773016
$629$	− 1.35420e8i	− 0.544166i
$630$	0	0
$631$	−8.19880e7	−0.326334	−0.163167	−	0.986598i	$-0.552171\pi$
$631$	−8.19880e7	−0.326334	−0.163167	+	0.986598i	$0.552171\pi$
$632$	1.99597e7i	0.0790684i
$633$	0	0
$634$	6.69695e7	0.262790
$635$	− 2.39261e8i	− 0.934438i
$636$	0	0
$637$	4.80692e7	0.185972
$638$	− 3.32221e8i	− 1.27928i
$639$	0	0
$640$	2.52203e7	0.0962079
$641$	− 6.18900e7i	− 0.234988i	−0.993074	−	0.117494i	$-0.962514\pi$
$641$	− 6.18900e7i	− 0.234988i	0.993074	−	0.117494i	$-0.0374862\pi$
$642$	0	0
$643$	1.50284e8	0.565300	0.282650	−	0.959223i	$-0.408786\pi$
$643$	1.50284e8	0.565300	0.282650	+	0.959223i	$0.408786\pi$
$644$	− 8.80130e7i	− 0.329526i
$645$	0	0
$646$	−7.67122e7	−0.284555
$647$	− 1.70289e8i	− 0.628745i	−0.949300	−	0.314372i	$-0.898206\pi$
$647$	− 1.70289e8i	− 0.628745i	0.949300	−	0.314372i	$-0.101794\pi$
$648$	0	0
$649$	7.05505e8	2.58087
$650$	− 9.49685e6i	− 0.0345812i
$651$	0	0
$652$	−5.98828e7	−0.216052
$653$	− 1.64824e8i	− 0.591945i	−0.955196	−	0.295972i	$-0.904356\pi$
$653$	− 1.64824e8i	− 0.591945i	0.955196	−	0.295972i	$-0.0956437\pi$
$654$	0	0
$655$	−1.92917e8	−0.686510
$656$	1.16277e7i	0.0411893i
$657$	0	0
$658$	−2.73807e7	−0.0961096
$659$	− 1.67844e8i	− 0.586475i	−0.956040	−	0.293237i	$-0.905267\pi$
$659$	− 1.67844e8i	− 0.586475i	0.956040	−	0.293237i	$-0.0947327\pi$
$660$	0	0
$661$	−1.28227e7	−0.0443992	−0.0221996	−	0.999754i	$-0.507067\pi$
$661$	−1.28227e7	−0.0443992	−0.0221996	+	0.999754i	$0.507067\pi$
$662$	1.41823e8i	0.488847i
$663$	0	0
$664$	8.57816e6	0.0293015
$665$	− 1.96463e8i	− 0.668062i
$666$	0	0
$667$	4.69029e8	1.58060
$668$	− 2.95102e6i	− 0.00990019i
$669$	0	0
$670$	−3.57680e8	−1.18924
$671$	− 8.21947e8i	− 2.72067i
$672$	0	0
$673$	−5.21908e8	−1.71218	−0.856089	−	0.516829i	$-0.827112\pi$
$673$	−5.21908e8	−1.71218	−0.856089	+	0.516829i	$0.827112\pi$
$674$	3.02741e8i	0.988762i
$675$	0	0
$676$	1.43636e8	0.464969
$677$	3.98017e8i	1.28273i	0.767235	+	0.641366i	$0.221632\pi$
$677$	3.98017e8i	1.28273i	−0.767235	+	0.641366i	$0.778368\pi$
$678$	0	0
$679$	1.67817e8	0.536075
$680$	4.32662e7i	0.137601i
$681$	0	0
$682$	−3.54389e8	−1.11719
$683$	− 1.35724e8i	− 0.425986i	−0.977054	−	0.212993i	$-0.931679\pi$
$683$	− 1.35724e8i	− 0.425986i	0.977054	−	0.212993i	$-0.0683211\pi$
$684$	0	0
$685$	−2.01172e8	−0.625886
$686$	− 2.11953e8i	− 0.656551i
$687$	0	0
$688$	−5.15049e7	−0.158155
$689$	− 1.13457e8i	− 0.346876i
$690$	0	0
$691$	5.06358e8	1.53470	0.767350	−	0.641229i	$-0.221575\pi$
$691$	5.06358e8	1.53470	0.767350	+	0.641229i	$0.221575\pi$
$692$	2.41110e8i	0.727609i
$693$	0	0
$694$	−3.58811e8	−1.07346
$695$	4.47788e8i	1.33389i
$696$	0	0
$697$	−1.99478e7	−0.0589109
$698$	2.74960e7i	0.0808542i
$699$	0	0
$700$	−1.72802e7	−0.0503796
$701$	− 3.25042e8i	− 0.943595i	−0.881707	−	0.471798i	$-0.843605\pi$
$701$	− 3.25042e8i	− 0.943595i	0.881707	−	0.471798i	$-0.156395\pi$
$702$	0	0
$703$	5.95081e8	1.71281
$704$	6.03302e7i	0.172909i
$705$	0	0
$706$	−5.53335e7	−0.157244
$707$	3.19631e8i	0.904463i
$708$	0	0
$709$	3.33452e8	0.935609	0.467805	−	0.883832i	$-0.345045\pi$
$709$	3.33452e8	0.935609	0.467805	+	0.883832i	$0.345045\pi$
$710$	− 1.91581e8i	− 0.535277i
$711$	0	0
$712$	−6.85692e6	−0.0189972
$713$	− 5.00326e8i	− 1.38034i
$714$	0	0
$715$	1.45674e8	0.398531
$716$	1.38721e8i	0.377922i
$717$	0	0
$718$	3.32472e8	0.898218
$719$	2.30851e8i	0.621076i	0.950561	+	0.310538i	$0.100509\pi$
$719$	2.30851e8i	0.621076i	−0.950561	+	0.310538i	$0.899491\pi$
$720$	0	0
$721$	1.04259e8	0.278168
$722$	− 7.09670e7i	− 0.188558i
$723$	0	0
$724$	−1.16960e8	−0.308193
$725$	− 9.20877e7i	− 0.241650i
$726$	0	0
$727$	−3.57603e8	−0.930675	−0.465337	−	0.885133i	$-0.654067\pi$
$727$	−3.57603e8	−0.930675	−0.465337	+	0.885133i	$0.654067\pi$
$728$	1.96906e7i	0.0510347i
$729$	0	0
$730$	4.19918e8	1.07943
$731$	− 8.83582e7i	− 0.226201i
$732$	0	0
$733$	−4.04868e7	−0.102802	−0.0514010	−	0.998678i	$-0.516369\pi$
$733$	−4.04868e7	−0.102802	−0.0514010	+	0.998678i	$0.516369\pi$
$734$	3.11278e8i	0.787154i
$735$	0	0
$736$	−8.51740e7	−0.213636
$737$	− 8.55616e8i	− 2.13736i
$738$	0	0
$739$	2.40793e7	0.0596638	0.0298319	−	0.999555i	$-0.490503\pi$
$739$	2.40793e7	0.0596638	0.0298319	+	0.999555i	$0.490503\pi$
$740$	− 3.35630e8i	− 0.828257i
$741$	0	0
$742$	−2.06444e8	−0.505347
$743$	3.32030e8i	0.809489i	0.914430	+	0.404744i	$0.132639\pi$
$743$	3.32030e8i	0.809489i	−0.914430	+	0.404744i	$0.867361\pi$
$744$	0	0
$745$	−2.19349e7	−0.0530478
$746$	2.91935e8i	0.703184i
$747$	0	0
$748$	−1.03498e8	−0.247302
$749$	− 2.87160e8i	− 0.683405i
$750$	0	0
$751$	−8.65651e7	−0.204373	−0.102186	−	0.994765i	$-0.532584\pi$
$751$	−8.65651e7	−0.204373	−0.102186	+	0.994765i	$0.532584\pi$
$752$	2.64975e7i	0.0623090i
$753$	0	0
$754$	−1.04933e8	−0.244793
$755$	6.04251e8i	1.40403i
$756$	0	0
$757$	−4.37394e8	−1.00829	−0.504145	−	0.863619i	$-0.668192\pi$
$757$	−4.37394e8	−1.00829	−0.504145	+	0.863619i	$0.668192\pi$
$758$	− 5.63030e8i	− 1.29278i
$759$	0	0
$760$	−1.90126e8	−0.433113
$761$	3.43088e8i	0.778487i	0.921135	+	0.389244i	$0.127264\pi$
$761$	3.43088e8i	0.778487i	−0.921135	+	0.389244i	$0.872736\pi$
$762$	0	0
$763$	4.27400e8	0.962190
$764$	1.15893e8i	0.259881i
$765$	0	0
$766$	−5.97911e7	−0.133030
$767$	− 2.22836e8i	− 0.493855i
$768$	0	0
$769$	6.58946e8	1.44901	0.724504	−	0.689270i	$-0.242069\pi$
$769$	6.58946e8	1.44901	0.724504	+	0.689270i	$0.242069\pi$
$770$	− 2.65064e8i	− 0.580601i
$771$	0	0
$772$	−2.08302e8	−0.452731
$773$	− 7.79814e8i	− 1.68831i	−0.536098	−	0.844156i	$-0.680102\pi$
$773$	− 7.79814e8i	− 1.68831i	0.536098	−	0.844156i	$-0.319898\pi$
$774$	0	0
$775$	−9.82326e7	−0.211033
$776$	− 1.62403e8i	− 0.347544i
$777$	0	0
$778$	−7.88692e7	−0.167482
$779$	− 8.76570e7i	− 0.185428i
$780$	0	0
$781$	4.58287e8	0.962020
$782$	− 1.46119e8i	− 0.305552i
$783$	0	0
$784$	−8.46440e7	−0.175650
$785$	8.14035e8i	1.68281i
$786$	0	0
$787$	−1.42772e8	−0.292899	−0.146449	−	0.989218i	$-0.546785\pi$
$787$	−1.42772e8	−0.292899	−0.146449	+	0.989218i	$0.546785\pi$
$788$	2.02540e8i	0.413935i
$789$	0	0
$790$	−8.48653e7	−0.172127
$791$	3.18928e8i	0.644412i
$792$	0	0
$793$	−2.59615e8	−0.520607
$794$	− 1.22224e8i	− 0.244172i
$795$	0	0
$796$	2.64745e8	0.524915
$797$	1.91404e8i	0.378073i	0.981970	+	0.189037i	$0.0605365\pi$
$797$	1.91404e8i	0.378073i	−0.981970	+	0.189037i	$0.939464\pi$
$798$	0	0
$799$	−4.54572e7	−0.0891174
$800$	1.67228e7i	0.0326617i
$801$	0	0
$802$	−5.87193e8	−1.13830
$803$	1.00450e9i	1.94000i
$804$	0	0
$805$	3.74216e8	0.717357
$806$	1.11935e8i	0.213777i
$807$	0	0
$808$	3.09321e8	0.586374
$809$	9.44320e8i	1.78350i	0.452527	+	0.891751i	$0.350523\pi$
$809$	9.44320e8i	1.78350i	−0.452527	+	0.891751i	$0.649477\pi$
$810$	0	0
$811$	−2.09243e8	−0.392273	−0.196137	−	0.980577i	$-0.562840\pi$
$811$	−2.09243e8	−0.392273	−0.196137	+	0.980577i	$0.562840\pi$
$812$	1.90933e8i	0.356627i
$813$	0	0
$814$	8.02869e8	1.48858
$815$	− 2.54611e8i	− 0.470332i
$816$	0	0
$817$	3.88275e8	0.711989
$818$	5.16884e8i	0.944351i
$819$	0	0
$820$	−4.94392e7	−0.0896664
$821$	1.69674e7i	0.0306609i	0.999882	+	0.0153305i	$0.00488003\pi$
$821$	1.69674e7i	0.0306609i	−0.999882	+	0.0153305i	$0.995120\pi$
$822$	0	0
$823$	1.12486e8	0.201791	0.100895	−	0.994897i	$-0.467829\pi$
$823$	1.12486e8	0.201791	0.100895	+	0.994897i	$0.467829\pi$
$824$	− 1.00896e8i	− 0.180340i
$825$	0	0
$826$	−4.05467e8	−0.719474
$827$	− 6.84539e8i	− 1.21027i	−0.796123	−	0.605135i	$-0.793119\pi$
$827$	− 6.84539e8i	− 1.21027i	0.796123	−	0.605135i	$-0.206881\pi$
$828$	0	0
$829$	5.25177e8	0.921812	0.460906	−	0.887449i	$-0.347525\pi$
$829$	5.25177e8	0.921812	0.460906	+	0.887449i	$0.347525\pi$
$830$	3.64729e7i	0.0637875i
$831$	0	0
$832$	1.90555e7	0.0330865
$833$	− 1.45209e8i	− 0.251223i
$834$	0	0
$835$	1.25472e7	0.0215521
$836$	− 4.54806e8i	− 0.778407i
$837$	0	0
$838$	−4.68201e8	−0.795611
$839$	2.85269e8i	0.483025i	0.970398	+	0.241512i	$0.0776434\pi$
$839$	2.85269e8i	0.483025i	−0.970398	+	0.241512i	$0.922357\pi$
$840$	0	0
$841$	−4.22676e8	−0.710591
$842$	4.62436e8i	0.774667i
$843$	0	0
$844$	−2.80571e8	−0.466676
$845$	6.10717e8i	1.01221i
$846$	0	0
$847$	3.02690e8	0.498135
$848$	1.99785e8i	0.327623i
$849$	0	0
$850$	−2.86885e7	−0.0467144
$851$	1.13349e9i	1.83920i
$852$	0	0
$853$	5.96724e8	0.961449	0.480724	−	0.876872i	$-0.340374\pi$
$853$	5.96724e8	0.961449	0.480724	+	0.876872i	$0.340374\pi$
$854$	4.72388e8i	0.758447i
$855$	0	0
$856$	−2.77897e8	−0.443060
$857$	3.33233e8i	0.529427i	0.964327	+	0.264713i	$0.0852774\pi$
$857$	3.33233e8i	0.529427i	−0.964327	+	0.264713i	$0.914723\pi$
$858$	0	0
$859$	1.02803e9	1.62191	0.810957	−	0.585106i	$-0.198947\pi$
$859$	1.02803e9	1.62191	0.810957	+	0.585106i	$0.198947\pi$
$860$	− 2.18990e8i	− 0.344293i
$861$	0	0
$862$	8.68090e8	1.35532
$863$	7.49705e6i	0.0116643i	0.999983	+	0.00583214i	$0.00185644\pi$
$863$	7.49705e6i	0.0116643i	−0.999983	+	0.00583214i	$0.998144\pi$
$864$	0	0
$865$	−1.02516e9	−1.58396
$866$	6.55304e8i	1.00900i
$867$	0	0
$868$	2.03674e8	0.311442
$869$	− 2.03008e8i	− 0.309353i
$870$	0	0
$871$	−2.70249e8	−0.408988
$872$	− 4.13613e8i	− 0.623800i
$873$	0	0
$874$	6.42094e8	0.961754
$875$	3.24186e8i	0.483916i
$876$	0	0
$877$	−2.75252e8	−0.408067	−0.204033	−	0.978964i	$-0.565405\pi$
$877$	−2.75252e8	−0.408067	−0.204033	+	0.978964i	$0.565405\pi$
$878$	− 2.39098e8i	− 0.353258i
$879$	0	0
$880$	−2.56514e8	−0.376411
$881$	4.00012e8i	0.584986i	0.956268	+	0.292493i	$0.0944848\pi$
$881$	4.00012e8i	0.584986i	−0.956268	+	0.292493i	$0.905515\pi$
$882$	0	0
$883$	−1.04179e9	−1.51320	−0.756601	−	0.653877i	$-0.773141\pi$
$883$	−1.04179e9	−1.51320	−0.756601	+	0.653877i	$0.773141\pi$
$884$	3.26903e7i	0.0473219i
$885$	0	0
$886$	−9.45453e8	−1.35937
$887$	− 4.93260e8i	− 0.706814i	−0.935470	−	0.353407i	$-0.885023\pi$
$887$	− 4.93260e8i	− 0.706814i	0.935470	−	0.353407i	$-0.114977\pi$
$888$	0	0
$889$	−3.28935e8	−0.468172
$890$	− 2.91544e7i	− 0.0413556i
$891$	0	0
$892$	−3.90981e8	−0.550885
$893$	− 1.99754e8i	− 0.280505i
$894$	0	0
$895$	−5.89816e8	−0.822712
$896$	− 3.46729e7i	− 0.0482021i
$897$	0	0
$898$	−4.84313e8	−0.668801
$899$	1.08540e9i	1.49386i
$900$	0	0
$901$	−3.42737e8	−0.468582
$902$	− 1.18265e8i	− 0.161152i
$903$	0	0
$904$	3.08641e8	0.417780
$905$	− 4.97296e8i	− 0.670917i
$906$	0	0
$907$	−9.54492e8	−1.27924	−0.639618	−	0.768693i	$-0.720907\pi$
$907$	−9.54492e8	−1.27924	−0.639618	+	0.768693i	$0.720907\pi$
$908$	7.19131e7i	0.0960618i
$909$	0	0
$910$	−8.37213e7	−0.111099
$911$	1.01966e8i	0.134865i	0.997724	+	0.0674323i	$0.0214807\pi$
$911$	1.01966e8i	0.134865i	−0.997724	+	0.0674323i	$0.978519\pi$
$912$	0	0
$913$	−8.72477e7	−0.114641
$914$	3.76403e7i	0.0492963i
$915$	0	0
$916$	1.66611e8	0.216779
$917$	2.65222e8i	0.343955i
$918$	0	0
$919$	−7.10292e8	−0.915146	−0.457573	−	0.889172i	$-0.651281\pi$
$919$	−7.10292e8	−0.915146	−0.457573	+	0.889172i	$0.651281\pi$
$920$	− 3.62145e8i	− 0.465071i
$921$	0	0
$922$	1.31109e8	0.167278
$923$	− 1.44751e8i	− 0.184085i
$924$	0	0
$925$	2.22546e8	0.281186
$926$	2.12719e7i	0.0267900i
$927$	0	0
$928$	1.84774e8	0.231205
$929$	− 3.81949e8i	− 0.476386i	−0.971218	−	0.238193i	$-0.923445\pi$
$929$	− 3.81949e8i	− 0.476386i	0.971218	−	0.238193i	$-0.0765550\pi$
$930$	0	0
$931$	6.38098e8	0.790748
$932$	− 4.62402e7i	− 0.0571179i
$933$	0	0
$934$	6.37800e8	0.782788
$935$	− 4.40057e8i	− 0.538361i
$936$	0	0
$937$	−5.56713e8	−0.676726	−0.338363	−	0.941016i	$-0.609873\pi$
$937$	−5.56713e8	−0.676726	−0.338363	+	0.941016i	$0.609873\pi$
$938$	4.91738e8i	0.595835i
$939$	0	0
$940$	−1.12663e8	−0.135643
$941$	6.36438e8i	0.763813i	0.924201	+	0.381906i	$0.124732\pi$
$941$	6.36438e8i	0.763813i	−0.924201	+	0.381906i	$0.875268\pi$
$942$	0	0
$943$	1.66966e8	0.199110
$944$	3.92388e8i	0.466444i
$945$	0	0
$946$	5.23851e8	0.618778
$947$	− 1.18317e9i	− 1.39315i	−0.717482	−	0.696577i	$-0.754706\pi$
$947$	− 1.18317e9i	− 1.39315i	0.717482	−	0.696577i	$-0.245294\pi$
$948$	0	0
$949$	3.17274e8	0.371223
$950$	− 1.26067e8i	− 0.147038i
$951$	0	0
$952$	5.94824e7	0.0689410
$953$	− 1.06040e8i	− 0.122516i	−0.998122	−	0.0612579i	$-0.980489\pi$
$953$	− 1.06040e8i	− 0.122516i	0.998122	−	0.0612579i	$-0.0195112\pi$
$954$	0	0
$955$	−4.92755e8	−0.565745
$956$	1.35815e8i	0.155444i
$957$	0	0
$958$	−2.68259e8	−0.305112
$959$	2.76571e8i	0.313581i
$960$	0	0
$961$	2.70319e8	0.304584
$962$	− 2.53589e8i	− 0.284842i
$963$	0	0
$964$	2.76371e8	0.308504
$965$	− 8.85663e8i	− 0.985568i
$966$	0	0
$967$	−4.10331e8	−0.453789	−0.226895	−	0.973919i	$-0.572857\pi$
$967$	−4.10331e8	−0.453789	−0.226895	+	0.973919i	$0.572857\pi$
$968$	− 2.92926e8i	− 0.322947i
$969$	0	0
$970$	6.90512e8	0.756582
$971$	− 1.16518e9i	− 1.27273i	−0.771389	−	0.636364i	$-0.780438\pi$
$971$	− 1.16518e9i	− 1.27273i	0.771389	−	0.636364i	$-0.219562\pi$
$972$	0	0
$973$	6.15619e8	0.668303
$974$	1.15133e9i	1.24601i
$975$	0	0
$976$	4.57150e8	0.491710
$977$	− 2.95487e8i	− 0.316851i	−0.987371	−	0.158425i	$-0.949358\pi$
$977$	− 2.95487e8i	− 0.316851i	0.987371	−	0.158425i	$-0.0506417\pi$
$978$	0	0
$979$	6.97411e7	0.0743260
$980$	− 3.59892e8i	− 0.382379i
$981$	0	0
$982$	8.17573e8	0.863360
$983$	− 9.05870e8i	− 0.953685i	−0.878989	−	0.476843i	$-0.841781\pi$
$983$	− 9.05870e8i	− 0.953685i	0.878989	−	0.476843i	$-0.158219\pi$
$984$	0	0
$985$	−8.61166e8	−0.901111
$986$	3.16986e8i	0.330681i
$987$	0	0
$988$	−1.43652e8	−0.148950
$989$	7.39572e8i	0.764525i
$990$	0	0
$991$	1.78268e9	1.83169	0.915847	−	0.401529i	$-0.131521\pi$
$991$	1.78268e9	1.83169	0.915847	+	0.401529i	$0.131521\pi$
$992$	− 1.97104e8i	− 0.201911i
$993$	0	0
$994$	−2.63386e8	−0.268184
$995$	1.12565e9i	1.14271i
$996$	0	0
$997$	−1.81366e9	−1.83008	−0.915041	−	0.403360i	$-0.867842\pi$
$997$	−1.81366e9	−1.83008	−0.915041	+	0.403360i	$0.867842\pi$
$998$	− 8.67953e8i	− 0.873182i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.b.161.2	✓	8
3.2	odd	2	inner	162.7.b.b.161.7	yes	8
9.2	odd	6		162.7.d.g.53.6		16
9.4	even	3		162.7.d.g.107.6		16
9.5	odd	6		162.7.d.g.107.3		16
9.7	even	3		162.7.d.g.53.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.2	✓	8	1.1	even	1	trivial
162.7.b.b.161.7	yes	8	3.2	odd	2	inner
162.7.d.g.53.3		16	9.7	even	3
162.7.d.g.53.6		16	9.2	odd	6
162.7.d.g.107.3		16	9.5	odd	6
162.7.d.g.107.6		16	9.4	even	3

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} -136.059i q^{5} -187.053 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} -136.059i q^{5} -187.053 q^{7} +181.019i q^{8} -769.663 q^{10} -1841.13i q^{11} -581.527 q^{13} +1058.13i q^{14} +1024.00 q^{16} +1756.70i q^{17} -7719.53 q^{19} +4353.87i q^{20} -10415.0 q^{22} -14703.9i q^{23} -2886.92 q^{25} +3289.62i q^{26} +5985.70 q^{28} +31898.3i q^{29} +34026.8 q^{31} -5792.62i q^{32} +9937.41 q^{34} +25450.2i q^{35} -77087.6 q^{37} +43668.3i q^{38} +24629.2 q^{40} +11355.2i q^{41} -50297.7 q^{43} +58916.2i q^{44} -83177.8 q^{46} +25876.4i q^{47} -82660.2 q^{49} +16330.9i q^{50} +18608.9 q^{52} +195102. i q^{53} -250502. q^{55} -33860.2i q^{56} +180444. q^{58} +383191. i q^{59} +446436. q^{61} -192485. i q^{62} -32768.0 q^{64} +79121.8i q^{65} +464723. q^{67} -56214.5i q^{68} +143968. q^{70} +248916. i q^{71} -545587. q^{73} +436074. i q^{74} +247025. q^{76} +344389. i q^{77} +110263. q^{79} -139324. i q^{80} +64234.8 q^{82} -47388.1i q^{83} +239014. q^{85} +284527. i q^{86} +333280. q^{88} +37879.5i q^{89} +108776. q^{91} +470524. i q^{92} +146379. q^{94} +1.05031e6i q^{95} -897161. q^{97} +467596. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{4} + 964 q^{7}+O(q^{10}) \) 8 * q - 256 * q^4 + 964 * q^7	\( 8 q - 256 q^{4} + 964 q^{7} - 768 q^{10} + 4540 q^{13} + 8192 q^{16} - 23684 q^{19} + 27072 q^{22} - 32392 q^{25} - 30848 q^{28} + 77056 q^{31} - 52608 q^{34} - 11348 q^{37} + 24576 q^{40} - 226604 q^{43} - 162720 q^{46} + 1298088 q^{49} - 145280 q^{52} - 1460916 q^{55} + 867456 q^{58} - 327476 q^{61} - 262144 q^{64} + 1713292 q^{67} - 176352 q^{70} - 2189216 q^{73} + 757888 q^{76} - 1326884 q^{79} - 1158816 q^{82} + 3483180 q^{85} - 866304 q^{88} + 1130324 q^{91} - 26400 q^{94} - 2200064 q^{97}+O(q^{100}) \) 8 * q - 256 * q^4 + 964 * q^7 - 768 * q^10 + 4540 * q^13 + 8192 * q^16 - 23684 * q^19 + 27072 * q^22 - 32392 * q^25 - 30848 * q^28 + 77056 * q^31 - 52608 * q^34 - 11348 * q^37 + 24576 * q^40 - 226604 * q^43 - 162720 * q^46 + 1298088 * q^49 - 145280 * q^52 - 1460916 * q^55 + 867456 * q^58 - 327476 * q^61 - 262144 * q^64 + 1713292 * q^67 - 176352 * q^70 - 2189216 * q^73 + 757888 * q^76 - 1326884 * q^79 - 1158816 * q^82 + 3483180 * q^85 - 866304 * q^88 + 1130324 * q^91 - 26400 * q^94 - 2200064 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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