LMFDB - Embedded newform 54.21.b.a.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,21,Mod(53,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.53"); S:= CuspForms(chi, 21); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 21, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	54.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$136.897433155$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} - 40125045 x^{4} - 40221949036 x^{3} + 402545211574772 x^{2} + \cdots + 40\!\cdots\!12 $ x^6 - 2x^5 - 40125045x^4 - 40221949036x^3 + 402545211574772x^2 + 807759149696620656*x + 405259457235387315012
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{18}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.1
Root			$-1063.41 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	54.53
Dual form			54.21.b.a.53.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-724.077i q^{2} -524288. q^{4} -1.04203e7i q^{5} +3.13964e8 q^{7} +3.79625e8i q^{8} -7.54511e9 q^{10} -5.11515e9i q^{11} -8.38857e10 q^{13} -2.27334e11i q^{14} +2.74878e11 q^{16} -3.93049e11i q^{17} +2.35664e12 q^{19} +5.46324e12i q^{20} -3.70377e12 q^{22} +3.96304e13i q^{23} -1.32154e13 q^{25} +6.07397e13i q^{26} -1.64608e14 q^{28} +2.25420e14i q^{29} -7.57278e14 q^{31} -1.99033e14i q^{32} -2.84598e14 q^{34} -3.27161e15i q^{35} -7.93436e15 q^{37} -1.70639e15i q^{38} +3.95581e15 q^{40} -1.78659e16i q^{41} -1.01711e16 q^{43} +2.68181e15i q^{44} +2.86955e16 q^{46} +2.93759e16i q^{47} +1.87813e16 q^{49} +9.56897e15i q^{50} +4.39803e16 q^{52} -6.24962e15i q^{53} -5.33015e16 q^{55} +1.19189e17i q^{56} +1.63221e17 q^{58} -7.16002e17i q^{59} -1.56905e17 q^{61} +5.48328e17i q^{62} -1.44115e17 q^{64} +8.74115e17i q^{65} -7.08866e17 q^{67} +2.06071e17i q^{68} -2.36890e18 q^{70} -2.46105e18i q^{71} -7.33674e18 q^{73} +5.74509e18i q^{74} -1.23556e18 q^{76} -1.60598e18i q^{77} +5.21937e18 q^{79} -2.86431e18i q^{80} -1.29363e19 q^{82} +9.97723e18i q^{83} -4.09569e18 q^{85} +7.36463e18i q^{86} +1.94184e18 q^{88} -2.83384e19i q^{89} -2.63371e19 q^{91} -2.07777e19i q^{92} +2.12704e19 q^{94} -2.45569e19i q^{95} -6.43135e18 q^{97} -1.35991e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3145728 q^{4} - 218826006 q^{7} - 2440839168 q^{10} + 110239981338 q^{13} + 1649267441664 q^{16} + 6190167313578 q^{19} + 10915007348736 q^{22} + 100487054737446 q^{25} + 114727849033728 q^{28} - 16\!\cdots\!56 q^{31}+ \cdots - 95\!\cdots\!62 q^{97}+O(q^{100}) $ 6 * q - 3145728 * q^4 - 218826006 * q^7 - 2440839168 * q^10 + 110239981338 * q^13 + 1649267441664 * q^16 + 6190167313578 * q^19 + 10915007348736 * q^22 + 100487054737446 * q^25 + 114727849033728 * q^28 - 1637611802736756 * q^31 - 2210345032826880 * q^34 + 112704887438490 * q^37 + 1279702685712384 * q^40 + 7701958113650220 * q^43 - 28939400289239040 * q^46 + 110042316130515552 * q^49 - 57797499335737344 * q^52 - 689023188480948480 * q^55 - 218595762960629760 * q^58 - 1581758499272340678 * q^61 - 864691128455135232 * q^64 - 210023541682991286 * q^67 - 2960158445360234496 * q^70 - 18837667029635682630 * q^73 - 3245430440501182464 * q^76 - 50277794728287289110 * q^79 - 26254269238536142848 * q^82 - 79619923081461051648 * q^85 - 5722607372854099968 * q^88 - 103237866532007840010 * q^91 - 109916038192954687488 * q^94 - 95805416653628626662 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$-1$

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 $

$2$	− 724.077i	− 0.707107i
$2$	− 724.077i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−524288.	−0.500000
$5$	− 1.04203e7i	− 1.06704i	−0.845788	−	0.533520i	$-0.820869\pi$
$5$	− 1.04203e7i	− 1.06704i	0.845788	−	0.533520i	$-0.179131\pi$
$6$	0	0
$7$	3.13964e8	1.11148	0.555738	−	0.831358i	$-0.312436\pi$
$7$	3.13964e8	1.11148	0.555738	+	0.831358i	$0.312436\pi$
$8$	3.79625e8i	0.353553i
$9$	0	0
$10$	−7.54511e9	−0.754511
$11$	− 5.11515e9i	− 0.197211i	−0.995127	−	0.0986056i	$-0.968562\pi$
$11$	− 5.11515e9i	− 0.197211i	0.995127	−	0.0986056i	$-0.0314382\pi$
$12$	0	0
$13$	−8.38857e10	−0.608491	−0.304246	−	0.952594i	$-0.598404\pi$
$13$	−8.38857e10	−0.608491	−0.304246	+	0.952594i	$0.598404\pi$
$14$	− 2.27334e11i	− 0.785932i
$15$	0	0
$16$	2.74878e11	0.250000
$17$	− 3.93049e11i	− 0.194965i	−0.995237	−	0.0974826i	$-0.968921\pi$
$17$	− 3.93049e11i	− 0.194965i	0.995237	−	0.0974826i	$-0.0310790\pi$
$18$	0	0
$19$	2.35664e12	0.384377	0.192188	−	0.981358i	$-0.438442\pi$
$19$	2.35664e12	0.384377	0.192188	+	0.981358i	$0.438442\pi$
$20$	5.46324e12i	0.533520i
$21$	0	0
$22$	−3.70377e12	−0.139449
$23$	3.96304e13i	0.956643i	0.878185	+	0.478321i	$0.158755\pi$
$23$	3.96304e13i	0.956643i	−0.878185	+	0.478321i	$0.841245\pi$
$24$	0	0
$25$	−1.32154e13	−0.138574
$26$	6.07397e13i	0.430268i
$27$	0	0
$28$	−1.64608e14	−0.555738
$29$	2.25420e14i	0.535812i	0.963445	+	0.267906i	$0.0863316\pi$
$29$	2.25420e14i	0.535812i	−0.963445	+	0.267906i	$0.913668\pi$
$30$	0	0
$31$	−7.57278e14	−0.923928	−0.461964	−	0.886899i	$-0.652855\pi$
$31$	−7.57278e14	−0.923928	−0.461964	+	0.886899i	$0.652855\pi$
$32$	− 1.99033e14i	− 0.176777i
$33$	0	0
$34$	−2.84598e14	−0.137861
$35$	− 3.27161e15i	− 1.18599i
$36$	0	0
$37$	−7.93436e15	−1.65004	−0.825020	−	0.565103i	$-0.808836\pi$
$37$	−7.93436e15	−1.65004	−0.825020	+	0.565103i	$0.808836\pi$
$38$	− 1.70639e15i	− 0.271796i
$39$	0	0
$40$	3.95581e15	0.377255
$41$	− 1.78659e16i	− 1.33102i	−0.746387	−	0.665512i	$-0.768213\pi$
$41$	− 1.78659e16i	− 1.33102i	0.746387	−	0.665512i	$-0.231787\pi$
$42$	0	0
$43$	−1.01711e16	−0.470632	−0.235316	−	0.971919i	$-0.575613\pi$
$43$	−1.01711e16	−0.470632	−0.235316	+	0.971919i	$0.575613\pi$
$44$	2.68181e15i	0.0986056i
$45$	0	0
$46$	2.86955e16	0.676449
$47$	2.93759e16i	0.558485i	0.960221	+	0.279243i	$0.0900834\pi$
$47$	2.93759e16i	0.558485i	−0.960221	+	0.279243i	$0.909917\pi$
$48$	0	0
$49$	1.87813e16	0.235378
$50$	9.56897e15i	0.0979863i
$51$	0	0
$52$	4.39803e16	0.304246
$53$	− 6.24962e15i	− 0.0357351i	−0.999840	−	0.0178676i	$-0.994312\pi$
$53$	− 6.24962e15i	− 0.0357351i	0.999840	−	0.0178676i	$-0.00568772\pi$
$54$	0	0
$55$	−5.33015e16	−0.210432
$56$	1.19189e17i	0.392966i
$57$	0	0
$58$	1.63221e17	0.378876
$59$	− 7.16002e17i	− 1.40086i	−0.713722	−	0.700429i	$-0.752992\pi$
$59$	− 7.16002e17i	− 1.40086i	0.713722	−	0.700429i	$-0.247008\pi$
$60$	0	0
$61$	−1.56905e17	−0.219957	−0.109978	−	0.993934i	$-0.535078\pi$
$61$	−1.56905e17	−0.219957	−0.109978	+	0.993934i	$0.535078\pi$
$62$	5.48328e17i	0.653316i
$63$	0	0
$64$	−1.44115e17	−0.125000
$65$	8.74115e17i	0.649284i
$66$	0	0
$67$	−7.08866e17	−0.388880	−0.194440	−	0.980914i	$-0.562289\pi$
$67$	−7.08866e17	−0.388880	−0.194440	+	0.980914i	$0.562289\pi$
$68$	2.06071e17i	0.0974826i
$69$	0	0
$70$	−2.36890e18	−0.838620
$71$	− 2.46105e18i	− 0.756027i	−0.925800	−	0.378013i	$-0.876607\pi$
$71$	− 2.46105e18i	− 0.756027i	0.925800	−	0.378013i	$-0.123393\pi$
$72$	0	0
$73$	−7.33674e18	−1.70716	−0.853581	−	0.520961i	$-0.825574\pi$
$73$	−7.33674e18	−1.70716	−0.853581	+	0.520961i	$0.825574\pi$
$74$	5.74509e18i	1.16675i
$75$	0	0
$76$	−1.23556e18	−0.192188
$77$	− 1.60598e18i	− 0.219195i
$78$	0	0
$79$	5.21937e18	0.551248	0.275624	−	0.961266i	$-0.411116\pi$
$79$	5.21937e18	0.551248	0.275624	+	0.961266i	$0.411116\pi$
$80$	− 2.86431e18i	− 0.266760i
$81$	0	0
$82$	−1.29363e19	−0.941177
$83$	9.97723e18i	0.643027i	0.946905	+	0.321513i	$0.104192\pi$
$83$	9.97723e18i	0.643027i	−0.946905	+	0.321513i	$0.895808\pi$
$84$	0	0
$85$	−4.09569e18	−0.208036
$86$	7.36463e18i	0.332787i
$87$	0	0
$88$	1.94184e18	0.0697247
$89$	− 2.83384e19i	− 0.908815i	−0.890794	−	0.454408i	$-0.849851\pi$
$89$	− 2.83384e19i	− 0.908815i	0.890794	−	0.454408i	$-0.150149\pi$
$90$	0	0
$91$	−2.63371e19	−0.676323
$92$	− 2.07777e19i	− 0.478321i
$93$	0	0
$94$	2.12704e19	0.394909
$95$	− 2.45569e19i	− 0.410145i
$96$	0	0
$97$	−6.43135e18	−0.0872137	−0.0436069	−	0.999049i	$-0.513885\pi$
$97$	−6.43135e18	−0.0872137	−0.0436069	+	0.999049i	$0.513885\pi$
$98$	− 1.35991e19i	− 0.166437i
$99$	0	0
$100$	6.92868e18	0.0692868
$101$	5.23936e19i	0.474313i	0.971471	+	0.237156i	$0.0762154\pi$
$101$	5.23936e19i	0.474313i	−0.971471	+	0.237156i	$0.923785\pi$
$102$	0	0
$103$	−1.30791e20	−0.973205	−0.486602	−	0.873624i	$-0.661764\pi$
$103$	−1.30791e20	−0.973205	−0.486602	+	0.873624i	$0.661764\pi$
$104$	− 3.18451e19i	− 0.215134i
$105$	0	0
$106$	−4.52521e18	−0.0252685
$107$	3.10158e20i	1.57669i	0.615235	+	0.788344i	$0.289061\pi$
$107$	3.10158e20i	1.57669i	−0.615235	+	0.788344i	$0.710939\pi$
$108$	0	0
$109$	−4.47984e20	−1.89233	−0.946165	−	0.323683i	$-0.895079\pi$
$109$	−4.47984e20	−1.89233	−0.946165	+	0.323683i	$0.895079\pi$
$110$	3.85944e19i	0.148798i
$111$	0	0
$112$	8.63019e19	0.277869
$113$	5.49315e20i	1.61822i	0.587659	+	0.809109i	$0.300050\pi$
$113$	5.49315e20i	1.61822i	−0.587659	+	0.809109i	$0.699950\pi$
$114$	0	0
$115$	4.12961e20	1.02078
$116$	− 1.18185e20i	− 0.267906i
$117$	0	0
$118$	−5.18441e20	−0.990556
$119$	− 1.23403e20i	− 0.216699i
$120$	0	0
$121$	6.46585e20	0.961108
$122$	1.13611e20i	0.155533i
$123$	0	0
$124$	3.97032e20	0.461964
$125$	− 8.56050e20i	− 0.919176i
$126$	0	0
$127$	1.61262e21	1.47739	0.738695	−	0.674040i	$-0.235442\pi$
$127$	1.61262e21	1.47739	0.738695	+	0.674040i	$0.235442\pi$
$128$	1.04351e20i	0.0883883i
$129$	0	0
$130$	6.32927e20	0.459113
$131$	1.08517e21i	0.729099i	0.931184	+	0.364549i	$0.118777\pi$
$131$	1.08517e21i	0.729099i	−0.931184	+	0.364549i	$0.881223\pi$
$132$	0	0
$133$	7.39901e20	0.427226
$134$	5.13273e20i	0.274980i
$135$	0	0
$136$	1.49211e20	0.0689306
$137$	2.36341e21i	1.01469i	0.861743	+	0.507345i	$0.169373\pi$
$137$	2.36341e21i	1.01469i	−0.861743	+	0.507345i	$0.830627\pi$
$138$	0	0
$139$	−1.70853e20	−0.0634561	−0.0317281	−	0.999497i	$-0.510101\pi$
$139$	−1.70853e20	−0.0634561	−0.0317281	+	0.999497i	$0.510101\pi$
$140$	1.71526e21i	0.592994i
$141$	0	0
$142$	−1.78199e21	−0.534592
$143$	4.29088e20i	0.120001i
$144$	0	0
$145$	2.34894e21	0.571732
$146$	5.31237e21i	1.20715i
$147$	0	0
$148$	4.15989e21	0.825020
$149$	1.74220e21i	0.323025i	0.986871	+	0.161512i	$0.0516372\pi$
$149$	1.74220e21i	0.323025i	−0.986871	+	0.161512i	$0.948363\pi$
$150$	0	0
$151$	−3.42663e21	−0.556030	−0.278015	−	0.960577i	$-0.589676\pi$
$151$	−3.42663e21	−0.556030	−0.278015	+	0.960577i	$0.589676\pi$
$152$	8.94640e20i	0.135898i
$153$	0	0
$154$	−1.16285e21	−0.154995
$155$	7.89107e21i	0.985868i
$156$	0	0
$157$	−1.45330e22	−1.59720	−0.798600	−	0.601862i	$-0.794426\pi$
$157$	−1.45330e22	−1.59720	−0.798600	+	0.601862i	$0.794426\pi$
$158$	− 3.77922e21i	− 0.389791i
$159$	0	0
$160$	−2.07398e21	−0.188628
$161$	1.24425e22i	1.06329i
$162$	0	0
$163$	1.36234e22	1.02899	0.514495	−	0.857494i	$-0.327980\pi$
$163$	1.36234e22	1.02899	0.514495	+	0.857494i	$0.327980\pi$
$164$	9.36687e21i	0.665512i
$165$	0	0
$166$	7.22429e21	0.454689
$167$	2.08879e22i	1.23803i	0.785379	+	0.619015i	$0.212468\pi$
$167$	2.08879e22i	1.23803i	−0.785379	+	0.619015i	$0.787532\pi$
$168$	0	0
$169$	−1.19682e22	−0.629738
$170$	2.96559e21i	0.147103i
$171$	0	0
$172$	5.33256e21	0.235316
$173$	2.57673e22i	1.07302i	0.843894	+	0.536509i	$0.180257\pi$
$173$	2.57673e22i	1.07302i	−0.843894	+	0.536509i	$0.819743\pi$
$174$	0	0
$175$	−4.14917e21	−0.154021
$176$	− 1.40604e21i	− 0.0493028i
$177$	0	0
$178$	−2.05192e22	−0.642630
$179$	5.49391e22i	1.62686i	0.581660	+	0.813432i	$0.302403\pi$
$179$	5.49391e22i	1.62686i	−0.581660	+	0.813432i	$0.697597\pi$
$180$	0	0
$181$	1.07809e21	0.0285672	0.0142836	−	0.999898i	$-0.495453\pi$
$181$	1.07809e21	0.0285672	0.0142836	+	0.999898i	$0.495453\pi$
$182$	1.90701e22i	0.478233i
$183$	0	0
$184$	−1.50447e22	−0.338224
$185$	8.26785e22i	1.76066i
$186$	0	0
$187$	−2.01050e21	−0.0384493
$188$	− 1.54014e22i	− 0.279243i
$189$	0	0
$190$	−1.77811e22	−0.290017
$191$	− 8.79814e22i	− 1.36162i	−0.732458	−	0.680812i	$-0.761627\pi$
$191$	− 8.79814e22i	− 1.36162i	0.732458	−	0.680812i	$-0.238373\pi$
$192$	0	0
$193$	−5.87758e21	−0.0819644	−0.0409822	−	0.999160i	$-0.513049\pi$
$193$	−5.87758e21	−0.0819644	−0.0409822	+	0.999160i	$0.513049\pi$
$194$	4.65679e21i	0.0616694i
$195$	0	0
$196$	−9.84683e21	−0.117689
$197$	9.56068e22i	1.08599i	0.839735	+	0.542996i	$0.182710\pi$
$197$	9.56068e22i	1.08599i	−0.839735	+	0.542996i	$0.817290\pi$
$198$	0	0
$199$	−4.15798e22	−0.426925	−0.213463	−	0.976951i	$-0.568474\pi$
$199$	−4.15798e22	−0.426925	−0.213463	+	0.976951i	$0.568474\pi$
$200$	− 5.01690e21i	− 0.0489931i
$201$	0	0
$202$	3.79370e22	0.335390
$203$	7.07738e22i	0.595541i
$204$	0	0
$205$	−1.86168e23	−1.42026
$206$	9.47025e22i	0.688160i
$207$	0	0
$208$	−2.30583e22	−0.152123
$209$	− 1.20546e22i	− 0.0758035i
$210$	0	0
$211$	2.91736e23	1.66788	0.833940	−	0.551855i	$-0.186080\pi$
$211$	2.91736e23	1.66788	0.833940	+	0.551855i	$0.186080\pi$
$212$	3.27660e21i	0.0178676i
$213$	0	0
$214$	2.24579e23	1.11489
$215$	1.05986e23i	0.502183i
$216$	0	0
$217$	−2.37758e23	−1.02692
$218$	3.24375e23i	1.33808i
$219$	0	0
$220$	2.79453e22	0.105216
$221$	3.29711e22i	0.118635i
$222$	0	0
$223$	2.37184e23	0.779898	0.389949	−	0.920837i	$-0.372493\pi$
$223$	2.37184e23	0.779898	0.389949	+	0.920837i	$0.372493\pi$
$224$	− 6.24892e22i	− 0.196483i
$225$	0	0
$226$	3.97746e23	1.14425
$227$	− 1.26966e23i	− 0.349485i	−0.984614	−	0.174743i	$-0.944091\pi$
$227$	− 1.26966e23i	− 0.349485i	0.984614	−	0.174743i	$-0.0559093\pi$
$228$	0	0
$229$	4.25323e23	1.07242	0.536209	−	0.844085i	$-0.319856\pi$
$229$	4.25323e23	1.07242	0.536209	+	0.844085i	$0.319856\pi$
$230$	− 2.99016e23i	− 0.721798i
$231$	0	0
$232$	−8.55750e22	−0.189438
$233$	− 5.92521e22i	− 0.125645i	−0.998025	−	0.0628224i	$-0.979990\pi$
$233$	− 5.92521e22i	− 0.125645i	0.998025	−	0.0628224i	$-0.0200102\pi$
$234$	0	0
$235$	3.06105e23	0.595926
$236$	3.75391e23i	0.700429i
$237$	0	0
$238$	−8.93535e22	−0.153229
$239$	− 6.97869e23i	− 1.14761i	−0.818991	−	0.573806i	$-0.805466\pi$
$239$	− 6.97869e23i	− 1.14761i	0.818991	−	0.573806i	$-0.194534\pi$
$240$	0	0
$241$	−7.75276e23	−1.17297	−0.586484	−	0.809961i	$-0.699488\pi$
$241$	−7.75276e23	−1.17297	−0.586484	+	0.809961i	$0.699488\pi$
$242$	− 4.68178e23i	− 0.679606i
$243$	0	0
$244$	8.22633e22	0.109978
$245$	− 1.95707e23i	− 0.251158i
$246$	0	0
$247$	−1.97688e23	−0.233890
$248$	− 2.87482e23i	− 0.326658i
$249$	0	0
$250$	−6.19846e23	−0.649956
$251$	− 1.64731e24i	− 1.65973i	−0.557961	−	0.829867i	$-0.688416\pi$
$251$	− 1.64731e24i	− 1.65973i	0.557961	−	0.829867i	$-0.311584\pi$
$252$	0	0
$253$	2.02715e23	0.188661
$254$	− 1.16766e24i	− 1.04467i
$255$	0	0
$256$	7.55579e22	0.0625000
$257$	8.27802e23i	0.658560i	0.944232	+	0.329280i	$0.106806\pi$
$257$	8.27802e23i	0.658560i	−0.944232	+	0.329280i	$0.893194\pi$
$258$	0	0
$259$	−2.49111e24	−1.83398
$260$	− 4.58288e23i	− 0.324642i
$261$	0	0
$262$	7.85750e23	0.515551
$263$	− 1.55864e24i	− 0.984437i	−0.870472	−	0.492219i	$-0.836186\pi$
$263$	− 1.55864e24i	− 0.984437i	0.870472	−	0.492219i	$-0.163814\pi$
$264$	0	0
$265$	−6.51230e22	−0.0381308
$266$	− 5.35746e23i	− 0.302094i
$267$	0	0
$268$	3.71650e23	0.194440
$269$	2.45941e23i	0.123967i	0.998077	+	0.0619837i	$0.0197427\pi$
$269$	2.45941e23i	0.123967i	−0.998077	+	0.0619837i	$0.980257\pi$
$270$	0	0
$271$	−5.81935e23	−0.272384	−0.136192	−	0.990682i	$-0.543486\pi$
$271$	−5.81935e23	−0.272384	−0.136192	+	0.990682i	$0.543486\pi$
$272$	− 1.08040e23i	− 0.0487413i
$273$	0	0
$274$	1.71129e24	0.717494
$275$	6.75988e22i	0.0273283i
$276$	0	0
$277$	−3.03441e24	−1.14098	−0.570489	−	0.821305i	$-0.693246\pi$
$277$	−3.03441e24	−1.14098	−0.570489	+	0.821305i	$0.693246\pi$
$278$	1.23711e23i	0.0448703i
$279$	0	0
$280$	1.24198e24	0.419310
$281$	− 1.02520e24i	− 0.333999i	−0.985957	−	0.167000i	$-0.946592\pi$
$281$	− 1.02520e24i	− 0.333999i	0.985957	−	0.167000i	$-0.0534079\pi$
$282$	0	0
$283$	−1.03754e24	−0.314876	−0.157438	−	0.987529i	$-0.550323\pi$
$283$	−1.03754e24	−0.314876	−0.157438	+	0.987529i	$0.550323\pi$
$284$	1.29030e24i	0.378013i
$285$	0	0
$286$	3.10693e23	0.0848537
$287$	− 5.60925e24i	− 1.47940i
$288$	0	0
$289$	3.90974e24	0.961989
$290$	− 1.70082e24i	− 0.404276i
$291$	0	0
$292$	3.84656e24	0.853581
$293$	− 4.53179e24i	− 0.971837i	−0.874004	−	0.485919i	$-0.838485\pi$
$293$	− 4.53179e24i	− 0.971837i	0.874004	−	0.485919i	$-0.161515\pi$
$294$	0	0
$295$	−7.46096e24	−1.49477
$296$	− 3.01208e24i	− 0.583377i
$297$	0	0
$298$	1.26149e24	0.228413
$299$	− 3.32442e24i	− 0.582109i
$300$	0	0
$301$	−3.19335e24	−0.523096
$302$	2.48115e24i	0.393173i
$303$	0	0
$304$	6.47788e23	0.0960942
$305$	1.63500e24i	0.234703i
$306$	0	0
$307$	−8.33658e24	−1.12100	−0.560498	−	0.828156i	$-0.689390\pi$
$307$	−8.33658e24	−1.12100	−0.560498	+	0.828156i	$0.689390\pi$
$308$	8.41994e23i	0.109598i
$309$	0	0
$310$	5.71374e24	0.697114
$311$	− 5.51748e24i	− 0.651834i	−0.945398	−	0.325917i	$-0.894327\pi$
$311$	− 5.51748e24i	− 0.651834i	0.945398	−	0.325917i	$-0.105673\pi$
$312$	0	0
$313$	1.97116e24	0.218413	0.109207	−	0.994019i	$-0.465169\pi$
$313$	1.97116e24	0.218413	0.109207	+	0.994019i	$0.465169\pi$
$314$	1.05230e25i	1.12939i
$315$	0	0
$316$	−2.73645e24	−0.275624
$317$	1.43586e25i	1.40127i	0.713522	+	0.700633i	$0.247099\pi$
$317$	1.43586e25i	1.40127i	−0.713522	+	0.700633i	$0.752901\pi$
$318$	0	0
$319$	1.15306e24	0.105668
$320$	1.50172e24i	0.133380i
$321$	0	0
$322$	9.00935e24	0.751856
$323$	− 9.26274e23i	− 0.0749401i
$324$	0	0
$325$	1.10858e24	0.0843208
$326$	− 9.86443e24i	− 0.727605i
$327$	0	0
$328$	6.78234e24	0.470588
$329$	9.22297e24i	0.620743i
$330$	0	0
$331$	1.69933e25	1.07646	0.538231	−	0.842797i	$-0.319093\pi$
$331$	1.69933e25	1.07646	0.538231	+	0.842797i	$0.319093\pi$
$332$	− 5.23094e24i	− 0.321513i
$333$	0	0
$334$	1.51245e25	0.875419
$335$	7.38660e24i	0.414951i
$336$	0	0
$337$	−6.28038e23	−0.0332420	−0.0166210	−	0.999862i	$-0.505291\pi$
$337$	−6.28038e23	−0.0332420	−0.0166210	+	0.999862i	$0.505291\pi$
$338$	8.66587e24i	0.445292i
$339$	0	0
$340$	2.14732e24	0.104018
$341$	3.87359e24i	0.182209i
$342$	0	0
$343$	−1.91553e25	−0.849859
$344$	− 3.86119e24i	− 0.166394i
$345$	0	0
$346$	1.86575e25	0.758739
$347$	2.21916e25i	0.876785i	0.898784	+	0.438392i	$0.144452\pi$
$347$	2.21916e25i	0.876785i	−0.898784	+	0.438392i	$0.855548\pi$
$348$	0	0
$349$	−1.59168e25	−0.593749	−0.296874	−	0.954917i	$-0.595944\pi$
$349$	−1.59168e25	−0.593749	−0.296874	+	0.954917i	$0.595944\pi$
$350$	3.00432e24i	0.108909i
$351$	0	0
$352$	−1.01808e24	−0.0348624
$353$	2.70533e25i	0.900478i	0.892908	+	0.450239i	$0.148661\pi$
$353$	2.70533e25i	0.900478i	−0.892908	+	0.450239i	$0.851339\pi$
$354$	0	0
$355$	−2.56449e25	−0.806711
$356$	1.48575e25i	0.454408i
$357$	0	0
$358$	3.97801e25	1.15037
$359$	4.56320e25i	1.28329i	0.767002	+	0.641645i	$0.221748\pi$
$359$	4.56320e25i	1.28329i	−0.767002	+	0.641645i	$0.778252\pi$
$360$	0	0
$361$	−3.20362e25	−0.852254
$362$	− 7.80618e23i	− 0.0202001i
$363$	0	0
$364$	1.38082e25	0.338162
$365$	7.64511e25i	1.82161i
$366$	0	0
$367$	−5.41771e25	−1.22224	−0.611118	−	0.791539i	$-0.709280\pi$
$367$	−5.41771e25	−1.22224	−0.611118	+	0.791539i	$0.709280\pi$
$368$	1.08935e25i	0.239161i
$369$	0	0
$370$	5.98656e25	1.24497
$371$	− 1.96216e24i	− 0.0397187i
$372$	0	0
$373$	−7.75057e25	−1.48678	−0.743388	−	0.668861i	$-0.766782\pi$
$373$	−7.75057e25	−1.48678	−0.743388	+	0.668861i	$0.766782\pi$
$374$	1.45576e24i	0.0271878i
$375$	0	0
$376$	−1.11518e25	−0.197454
$377$	− 1.89095e25i	− 0.326037i
$378$	0	0
$379$	−4.48463e25	−0.733388	−0.366694	−	0.930342i	$-0.619510\pi$
$379$	−4.48463e25	−0.733388	−0.366694	+	0.930342i	$0.619510\pi$
$380$	1.28749e25i	0.205073i
$381$	0	0
$382$	−6.37054e25	−0.962814
$383$	3.82219e25i	0.562762i	0.959596	+	0.281381i	$0.0907924\pi$
$383$	3.82219e25i	0.562762i	−0.959596	+	0.281381i	$0.909208\pi$
$384$	0	0
$385$	−1.67348e25	−0.233890
$386$	4.25582e24i	0.0579576i
$387$	0	0
$388$	3.37188e24	0.0436069
$389$	− 1.22756e26i	− 1.54720i	−0.633671	−	0.773602i	$-0.718453\pi$
$389$	− 1.22756e26i	− 1.54720i	0.633671	−	0.773602i	$-0.281547\pi$
$390$	0	0
$391$	1.55767e25	0.186512
$392$	7.12986e24i	0.0832186i
$393$	0	0
$394$	6.92267e25	0.767912
$395$	− 5.43874e25i	− 0.588203i
$396$	0	0
$397$	−2.73686e25	−0.281415	−0.140707	−	0.990051i	$-0.544938\pi$
$397$	−2.73686e25	−0.281415	−0.140707	+	0.990051i	$0.544938\pi$
$398$	3.01070e25i	0.301882i
$399$	0	0
$400$	−3.63262e24	−0.0346434
$401$	− 2.05528e25i	− 0.191173i	−0.995421	−	0.0955865i	$-0.969527\pi$
$401$	− 2.05528e25i	− 0.191173i	0.995421	−	0.0955865i	$-0.0304727\pi$
$402$	0	0
$403$	6.35247e25	0.562202
$404$	− 2.74694e25i	− 0.237156i
$405$	0	0
$406$	5.12457e25	0.421111
$407$	4.05855e25i	0.325407i
$408$	0	0
$409$	−3.72462e25	−0.284347	−0.142174	−	0.989842i	$-0.545409\pi$
$409$	−3.72462e25	−0.284347	−0.142174	+	0.989842i	$0.545409\pi$
$410$	1.34800e26i	1.00427i
$411$	0	0
$412$	6.85719e25	0.486602
$413$	− 2.24799e26i	− 1.55702i
$414$	0	0
$415$	1.03966e26	0.686135
$416$	1.66960e25i	0.107567i
$417$	0	0
$418$	−8.72844e24	−0.0536011
$419$	2.48194e26i	1.48817i	0.668087	+	0.744083i	$0.267113\pi$
$419$	2.48194e26i	1.48817i	−0.668087	+	0.744083i	$0.732887\pi$
$420$	0	0
$421$	7.10062e25	0.405952	0.202976	−	0.979184i	$-0.434939\pi$
$421$	7.10062e25	0.405952	0.202976	+	0.979184i	$0.434939\pi$
$422$	− 2.11239e26i	− 1.17937i
$423$	0	0
$424$	2.37251e24	0.0126343
$425$	5.19430e24i	0.0270170i
$426$	0	0
$427$	−4.92625e25	−0.244477
$428$	− 1.62612e26i	− 0.788344i
$429$	0	0
$430$	7.67417e25	0.355097
$431$	− 1.39482e26i	− 0.630587i	−0.948994	−	0.315293i	$-0.897897\pi$
$431$	− 1.39482e26i	− 0.630587i	0.948994	−	0.315293i	$-0.102103\pi$
$432$	0	0
$433$	−1.83093e26	−0.790302	−0.395151	−	0.918616i	$-0.629308\pi$
$433$	−1.83093e26	−0.790302	−0.395151	+	0.918616i	$0.629308\pi$
$434$	1.72155e26i	0.726145i
$435$	0	0
$436$	2.34872e26	0.946165
$437$	9.33946e25i	0.367711i
$438$	0	0
$439$	6.46947e25	0.243345	0.121673	−	0.992570i	$-0.461174\pi$
$439$	6.46947e25	0.243345	0.121673	+	0.992570i	$0.461174\pi$
$440$	− 2.02346e25i	− 0.0743990i
$441$	0	0
$442$	2.38737e25	0.0838873
$443$	− 4.40844e26i	− 1.51443i	−0.653168	−	0.757213i	$-0.726561\pi$
$443$	− 4.40844e26i	− 1.51443i	0.653168	−	0.757213i	$-0.273439\pi$
$444$	0	0
$445$	−2.95295e26	−0.969742
$446$	− 1.71740e26i	− 0.551471i
$447$	0	0
$448$	−4.52470e25	−0.138934
$449$	− 4.19905e26i	− 1.26092i	−0.776222	−	0.630459i	$-0.782866\pi$
$449$	− 4.19905e26i	− 1.26092i	0.776222	−	0.630459i	$-0.217134\pi$
$450$	0	0
$451$	−9.13867e25	−0.262493
$452$	− 2.87999e26i	− 0.809109i
$453$	0	0
$454$	−9.19331e25	−0.247123
$455$	2.74441e26i	0.721663i
$456$	0	0
$457$	5.63254e26	1.41756	0.708781	−	0.705428i	$-0.249245\pi$
$457$	5.63254e26	1.41756	0.708781	+	0.705428i	$0.249245\pi$
$458$	− 3.07967e26i	− 0.758314i
$459$	0	0
$460$	−2.16510e26	−0.510388
$461$	− 5.58022e26i	− 1.28719i	−0.765367	−	0.643594i	$-0.777443\pi$
$461$	− 5.58022e26i	− 1.28719i	0.765367	−	0.643594i	$-0.222557\pi$
$462$	0	0
$463$	2.53609e26	0.560215	0.280108	−	0.959969i	$-0.409630\pi$
$463$	2.53609e26	0.560215	0.280108	+	0.959969i	$0.409630\pi$
$464$	6.19629e25i	0.133953i
$465$	0	0
$466$	−4.29031e25	−0.0888443
$467$	− 1.61173e26i	− 0.326680i	−0.986570	−	0.163340i	$-0.947773\pi$
$467$	− 1.61173e26i	− 0.326680i	0.986570	−	0.163340i	$-0.0522267\pi$
$468$	0	0
$469$	−2.22558e26	−0.432231
$470$	− 2.21644e26i	− 0.421383i
$471$	0	0
$472$	2.71812e26	0.495278
$473$	5.20265e25i	0.0928139i
$474$	0	0
$475$	−3.11440e25	−0.0532645
$476$	6.46988e25i	0.108350i
$477$	0	0
$478$	−5.05311e26	−0.811484
$479$	− 5.81055e26i	− 0.913823i	−0.889512	−	0.456911i	$-0.848956\pi$
$479$	− 5.81055e26i	− 0.913823i	0.889512	−	0.456911i	$-0.151044\pi$
$480$	0	0
$481$	6.65579e26	1.00404
$482$	5.61360e26i	0.829413i
$483$	0	0
$484$	−3.38997e26	−0.480554
$485$	6.70166e25i	0.0930605i
$486$	0	0
$487$	7.17255e26	0.955837	0.477919	−	0.878404i	$-0.341391\pi$
$487$	7.17255e26	0.955837	0.477919	+	0.878404i	$0.341391\pi$
$488$	− 5.95650e25i	− 0.0777665i
$489$	0	0
$490$	−1.41707e26	−0.177595
$491$	1.25920e27i	1.54624i	0.634257	+	0.773122i	$0.281306\pi$
$491$	1.25920e27i	1.54624i	−0.634257	+	0.773122i	$0.718694\pi$
$492$	0	0
$493$	8.86009e25	0.104465
$494$	1.43142e26i	0.165385i
$495$	0	0
$496$	−2.08159e26	−0.230982
$497$	− 7.72682e26i	− 0.840305i
$498$	0	0
$499$	−7.92090e26	−0.827502	−0.413751	−	0.910390i	$-0.635782\pi$
$499$	−7.92090e26	−0.827502	−0.413751	+	0.910390i	$0.635782\pi$
$500$	4.48816e26i	0.459588i
$501$	0	0
$502$	−1.19278e27	−1.17361
$503$	− 1.29072e27i	− 1.24496i	−0.782638	−	0.622478i	$-0.786126\pi$
$503$	− 1.29072e27i	− 1.24496i	0.782638	−	0.622478i	$-0.213874\pi$
$504$	0	0
$505$	5.45958e26	0.506110
$506$	− 1.46782e26i	− 0.133403i
$507$	0	0
$508$	−8.45478e26	−0.738695
$509$	1.99021e27i	1.70498i	0.522741	+	0.852492i	$0.324909\pi$
$509$	1.99021e27i	1.70498i	−0.522741	+	0.852492i	$0.675091\pi$
$510$	0	0
$511$	−2.30347e27	−1.89747
$512$	− 5.47097e25i	− 0.0441942i
$513$	0	0
$514$	5.99393e26	0.465672
$515$	1.36288e27i	1.03845i
$516$	0	0
$517$	1.50262e26	0.110140
$518$	1.80375e27i	1.29682i
$519$	0	0
$520$	−3.31836e26	−0.229557
$521$	− 1.13142e27i	− 0.767799i	−0.923375	−	0.383900i	$-0.874581\pi$
$521$	− 1.13142e27i	− 0.767799i	0.923375	−	0.383900i	$-0.125419\pi$
$522$	0	0
$523$	8.32412e26	0.543652	0.271826	−	0.962346i	$-0.412372\pi$
$523$	8.32412e26	0.543652	0.271826	+	0.962346i	$0.412372\pi$
$524$	− 5.68944e26i	− 0.364549i
$525$	0	0
$526$	−1.12858e27	−0.696102
$527$	2.97647e26i	0.180134i
$528$	0	0
$529$	1.45589e26	0.0848342
$530$	4.71541e25i	0.0269625i
$531$	0	0
$532$	−3.87921e26	−0.213613
$533$	1.49869e27i	0.809917i
$534$	0	0
$535$	3.23195e27	1.68239
$536$	− 2.69103e26i	− 0.137490i
$537$	0	0
$538$	1.78080e26	0.0876582
$539$	− 9.60694e25i	− 0.0464192i
$540$	0	0
$541$	2.48567e27	1.15736	0.578682	−	0.815553i	$-0.303567\pi$
$541$	2.48567e27	1.15736	0.578682	+	0.815553i	$0.303567\pi$
$542$	4.21366e26i	0.192605i
$543$	0	0
$544$	−7.82296e25	−0.0344653
$545$	4.66813e27i	2.01919i
$546$	0	0
$547$	−1.63365e27	−0.681218	−0.340609	−	0.940205i	$-0.610633\pi$
$547$	−1.63365e27	−0.681218	−0.340609	+	0.940205i	$0.610633\pi$
$548$	− 1.23911e27i	− 0.507345i
$549$	0	0
$550$	4.89468e25	0.0193240
$551$	5.31233e26i	0.205954i
$552$	0	0
$553$	1.63869e27	0.612698
$554$	2.19715e27i	0.806793i
$555$	0	0
$556$	8.95760e25	0.0317281
$557$	− 5.67978e26i	− 0.197597i	−0.995107	−	0.0987983i	$-0.968500\pi$
$557$	− 5.67978e26i	− 0.197597i	0.995107	−	0.0987983i	$-0.0314999\pi$
$558$	0	0
$559$	8.53206e26	0.286375
$560$	− 8.99292e26i	− 0.296497i
$561$	0	0
$562$	−7.42325e26	−0.236173
$563$	1.68438e27i	0.526449i	0.964735	+	0.263224i	$0.0847860\pi$
$563$	1.68438e27i	0.526449i	−0.964735	+	0.263224i	$0.915214\pi$
$564$	0	0
$565$	5.72403e27	1.72670
$566$	7.51258e26i	0.222651i
$567$	0	0
$568$	9.34277e26	0.267296
$569$	6.61314e27i	1.85902i	0.368792	+	0.929512i	$0.379771\pi$
$569$	6.61314e27i	1.85902i	−0.368792	+	0.929512i	$0.620229\pi$
$570$	0	0
$571$	6.15037e27	1.66932	0.834661	−	0.550764i	$-0.185664\pi$
$571$	6.15037e27	1.66932	0.834661	+	0.550764i	$0.185664\pi$
$572$	− 2.24966e26i	− 0.0600007i
$573$	0	0
$574$	−4.06153e27	−1.04609
$575$	− 5.23731e26i	− 0.132565i
$576$	0	0
$577$	−2.71752e27	−0.664376	−0.332188	−	0.943213i	$-0.607787\pi$
$577$	−2.71752e27	−0.664376	−0.332188	+	0.943213i	$0.607787\pi$
$578$	− 2.83096e27i	− 0.680229i
$579$	0	0
$580$	−1.23152e27	−0.285866
$581$	3.13249e27i	0.714709i
$582$	0	0
$583$	−3.19678e25	−0.00704736
$584$	− 2.78521e27i	− 0.603573i
$585$	0	0
$586$	−3.28137e27	−0.687193
$587$	− 8.01056e27i	− 1.64923i	−0.565693	−	0.824616i	$-0.691391\pi$
$587$	− 8.01056e27i	− 1.64923i	0.565693	−	0.824616i	$-0.308609\pi$
$588$	0	0
$589$	−1.78463e27	−0.355137
$590$	5.40231e27i	1.05696i
$591$	0	0
$592$	−2.18098e27	−0.412510
$593$	− 8.77137e27i	− 1.63125i	−0.578581	−	0.815625i	$-0.696393\pi$
$593$	− 8.77137e27i	− 1.63125i	0.578581	−	0.815625i	$-0.303607\pi$
$594$	0	0
$595$	−1.28590e27	−0.231226
$596$	− 9.13415e26i	− 0.161512i
$597$	0	0
$598$	−2.40714e27	−0.411613
$599$	9.92299e27i	1.66868i	0.551247	+	0.834342i	$0.314152\pi$
$599$	9.92299e27i	1.66868i	−0.551247	+	0.834342i	$0.685848\pi$
$600$	0	0
$601$	1.88593e27	0.306747	0.153373	−	0.988168i	$-0.450986\pi$
$601$	1.88593e27	0.306747	0.153373	+	0.988168i	$0.450986\pi$
$602$	2.31223e27i	0.369885i
$603$	0	0
$604$	1.79654e27	0.278015
$605$	− 6.73762e27i	− 1.02554i
$606$	0	0
$607$	1.98264e27	0.291982	0.145991	−	0.989286i	$-0.453363\pi$
$607$	1.98264e27	0.291982	0.145991	+	0.989286i	$0.453363\pi$
$608$	− 4.69049e26i	− 0.0679489i
$609$	0	0
$610$	1.18386e27	0.165960
$611$	− 2.46421e27i	− 0.339833i
$612$	0	0
$613$	−9.03545e27	−1.20599	−0.602997	−	0.797744i	$-0.706027\pi$
$613$	−9.03545e27	−1.20599	−0.602997	+	0.797744i	$0.706027\pi$
$614$	6.03633e27i	0.792664i
$615$	0	0
$616$	6.09668e26	0.0774973
$617$	9.50426e27i	1.18869i	0.804212	+	0.594343i	$0.202588\pi$
$617$	9.50426e27i	1.18869i	−0.804212	+	0.594343i	$0.797412\pi$
$618$	0	0
$619$	−1.11287e27	−0.134753	−0.0673766	−	0.997728i	$-0.521463\pi$
$619$	−1.11287e27	−0.134753	−0.0673766	+	0.997728i	$0.521463\pi$
$620$	− 4.13719e27i	− 0.492934i
$621$	0	0
$622$	−3.99508e27	−0.460916
$623$	− 8.89726e27i	− 1.01013i
$624$	0	0
$625$	−1.01806e28	−1.11937
$626$	− 1.42727e27i	− 0.154442i
$627$	0	0
$628$	7.61949e27	0.798600
$629$	3.11859e27i	0.321700i
$630$	0	0
$631$	6.99269e27	0.698797	0.349398	−	0.936974i	$-0.386386\pi$
$631$	6.99269e27	0.698797	0.349398	+	0.936974i	$0.386386\pi$
$632$	1.98140e27i	0.194896i
$633$	0	0
$634$	1.03968e28	0.990845
$635$	− 1.68040e28i	− 1.57643i
$636$	0	0
$637$	−1.57548e27	−0.143225
$638$	− 8.34902e26i	− 0.0747186i
$639$	0	0
$640$	1.08736e27	0.0943139
$641$	− 1.81506e28i	− 1.54992i	−0.632008	−	0.774962i	$-0.717769\pi$
$641$	− 1.81506e28i	− 1.54992i	0.632008	−	0.774962i	$-0.282231\pi$
$642$	0	0
$643$	−1.02830e28	−0.851157	−0.425578	−	0.904922i	$-0.639929\pi$
$643$	−1.02830e28	−0.851157	−0.425578	+	0.904922i	$0.639929\pi$
$644$	− 6.52347e27i	− 0.531643i
$645$	0	0
$646$	−6.70694e26	−0.0529907
$647$	− 1.41512e28i	− 1.10090i	−0.834867	−	0.550452i	$-0.814455\pi$
$647$	− 1.41512e28i	− 1.10090i	0.834867	−	0.550452i	$-0.185545\pi$
$648$	0	0
$649$	−3.66246e27	−0.276265
$650$	− 8.02700e26i	− 0.0596238i
$651$	0	0
$652$	−7.14261e27	−0.514495
$653$	− 1.42628e28i	− 1.01175i	−0.862606	−	0.505876i	$-0.831169\pi$
$653$	− 1.42628e28i	− 1.01175i	0.862606	−	0.505876i	$-0.168831\pi$
$654$	0	0
$655$	1.13078e28	0.777977
$656$	− 4.91094e27i	− 0.332756i
$657$	0	0
$658$	6.67814e27	0.438932
$659$	1.05281e27i	0.0681549i	0.999419	+	0.0340775i	$0.0108493\pi$
$659$	1.05281e27i	0.0681549i	−0.999419	+	0.0340775i	$0.989151\pi$
$660$	0	0
$661$	−1.58692e28	−0.996644	−0.498322	−	0.866992i	$-0.666050\pi$
$661$	−1.58692e28	−0.996644	−0.498322	+	0.866992i	$0.666050\pi$
$662$	− 1.23045e28i	− 0.761173i
$663$	0	0
$664$	−3.78761e27	−0.227344
$665$	− 7.71000e27i	− 0.455867i
$666$	0	0
$667$	−8.93347e27	−0.512580
$668$	− 1.09513e28i	− 0.619015i
$669$	0	0
$670$	5.34847e27	0.293414
$671$	8.02592e26i	0.0433780i
$672$	0	0
$673$	1.26992e28	0.666235	0.333117	−	0.942885i	$-0.391899\pi$
$673$	1.26992e28	0.666235	0.333117	+	0.942885i	$0.391899\pi$
$674$	4.54748e26i	0.0235056i
$675$	0	0
$676$	6.27476e27	0.314869
$677$	2.09069e28i	1.03372i	0.856070	+	0.516859i	$0.172899\pi$
$677$	2.09069e28i	1.03372i	−0.856070	+	0.516859i	$0.827101\pi$
$678$	0	0
$679$	−2.01921e27	−0.0969359
$680$	− 1.55483e27i	− 0.0735517i
$681$	0	0
$682$	2.80478e27	0.128841
$683$	3.83890e28i	1.73780i	0.494988	+	0.868900i	$0.335173\pi$
$683$	3.83890e28i	1.73780i	−0.494988	+	0.868900i	$0.664827\pi$
$684$	0	0
$685$	2.46275e28	1.08271
$686$	1.38699e28i	0.600941i
$687$	0	0
$688$	−2.79580e27	−0.117658
$689$	5.24254e26i	0.0217445i
$690$	0	0
$691$	−3.33633e28	−1.34428	−0.672138	−	0.740426i	$-0.734624\pi$
$691$	−3.33633e28	−1.34428	−0.672138	+	0.740426i	$0.734624\pi$
$692$	− 1.35095e28i	− 0.536509i
$693$	0	0
$694$	1.60684e28	0.619980
$695$	1.78034e27i	0.0677102i
$696$	0	0
$697$	−7.02216e27	−0.259503
$698$	1.15250e28i	0.419844i
$699$	0	0
$700$	2.17536e27	0.0770106
$701$	− 2.79732e28i	− 0.976251i	−0.872773	−	0.488126i	$-0.837681\pi$
$701$	− 2.79732e28i	− 0.976251i	0.872773	−	0.488126i	$-0.162319\pi$
$702$	0	0
$703$	−1.86984e28	−0.634237
$704$	7.37171e26i	0.0246514i
$705$	0	0
$706$	1.95887e28	0.636734
$707$	1.64497e28i	0.527187i
$708$	0	0
$709$	2.16291e28	0.673870	0.336935	−	0.941528i	$-0.390610\pi$
$709$	2.16291e28	0.673870	0.336935	+	0.941528i	$0.390610\pi$
$710$	1.85689e28i	0.570431i
$711$	0	0
$712$	1.07580e28	0.321315
$713$	− 3.00112e28i	− 0.883869i
$714$	0	0
$715$	4.47123e27	0.128046
$716$	− 2.88039e28i	− 0.813432i
$717$	0	0
$718$	3.30411e28	0.907423
$719$	4.82957e28i	1.30804i	0.756479	+	0.654018i	$0.226918\pi$
$719$	4.82957e28i	1.30804i	−0.756479	+	0.654018i	$0.773082\pi$
$720$	0	0
$721$	−4.10636e28	−1.08169
$722$	2.31967e28i	0.602635i
$723$	0	0
$724$	−5.65228e26	−0.0142836
$725$	− 2.97901e27i	− 0.0742493i
$726$	0	0
$727$	4.81585e28	1.16769	0.583846	−	0.811864i	$-0.301547\pi$
$727$	4.81585e28	1.16769	0.583846	+	0.811864i	$0.301547\pi$
$728$	− 9.99823e27i	− 0.239116i
$729$	0	0
$730$	5.53565e28	1.28807
$731$	3.99772e27i	0.0917569i
$732$	0	0
$733$	2.78638e28	0.622302	0.311151	−	0.950360i	$-0.399285\pi$
$733$	2.78638e28	0.622302	0.311151	+	0.950360i	$0.399285\pi$
$734$	3.92284e28i	0.864252i
$735$	0	0
$736$	7.88775e27	0.169112
$737$	3.62595e27i	0.0766916i
$738$	0	0
$739$	−8.06832e28	−1.66088	−0.830441	−	0.557107i	$-0.811911\pi$
$739$	−8.06832e28	−1.66088	−0.830441	+	0.557107i	$0.811911\pi$
$740$	− 4.33473e28i	− 0.880329i
$741$	0	0
$742$	−1.42075e27	−0.0280854
$743$	− 4.29709e28i	− 0.838081i	−0.907968	−	0.419040i	$-0.862367\pi$
$743$	− 4.29709e28i	− 0.838081i	0.907968	−	0.419040i	$-0.137633\pi$
$744$	0	0
$745$	1.81543e28	0.344680
$746$	5.61201e28i	1.05131i
$747$	0	0
$748$	1.05408e27	0.0192247
$749$	9.73787e28i	1.75245i
$750$	0	0
$751$	−1.78478e28	−0.312741	−0.156371	−	0.987698i	$-0.549979\pi$
$751$	−1.78478e28	−0.312741	−0.156371	+	0.987698i	$0.549979\pi$
$752$	8.07477e27i	0.139621i
$753$	0	0
$754$	−1.36919e28	−0.230543
$755$	3.57066e28i	0.593306i
$756$	0	0
$757$	−7.40875e28	−1.19891	−0.599455	−	0.800409i	$-0.704616\pi$
$757$	−7.40875e28	−1.19891	−0.599455	+	0.800409i	$0.704616\pi$
$758$	3.24722e28i	0.518584i
$759$	0	0
$760$	9.32242e27	0.145008
$761$	− 3.60560e28i	− 0.553517i	−0.960940	−	0.276759i	$-0.910740\pi$
$761$	− 3.60560e28i	− 0.553517i	0.960940	−	0.276759i	$-0.0892602\pi$
$762$	0	0
$763$	−1.40651e29	−2.10328
$764$	4.61276e28i	0.680812i
$765$	0	0
$766$	2.76756e28	0.397933
$767$	6.00623e28i	0.852410i
$768$	0	0
$769$	−2.66682e28	−0.368748	−0.184374	−	0.982856i	$-0.559026\pi$
$769$	−2.66682e28	−0.368748	−0.184374	+	0.982856i	$0.559026\pi$
$770$	1.21173e28i	0.165385i
$771$	0	0
$772$	3.08154e27	0.0409822
$773$	1.94813e28i	0.255754i	0.991790	+	0.127877i	$0.0408162\pi$
$773$	1.94813e28i	0.255754i	−0.991790	+	0.127877i	$0.959184\pi$
$774$	0	0
$775$	1.00077e28	0.128032
$776$	− 2.44150e27i	− 0.0308347i
$777$	0	0
$778$	−8.88851e28	−1.09404
$779$	− 4.21035e28i	− 0.511615i
$780$	0	0
$781$	−1.25887e28	−0.149097
$782$	− 1.12787e28i	− 0.131884i
$783$	0	0
$784$	5.16257e27	0.0588445
$785$	1.51439e29i	1.70428i
$786$	0	0
$787$	2.18659e28	0.239894	0.119947	−	0.992780i	$-0.461727\pi$
$787$	2.18659e28	0.239894	0.119947	+	0.992780i	$0.461727\pi$
$788$	− 5.01255e28i	− 0.542996i
$789$	0	0
$790$	−3.93807e28	−0.415923
$791$	1.72465e29i	1.79861i
$792$	0	0
$793$	1.31621e28	0.133842
$794$	1.98170e28i	0.198990i
$795$	0	0
$796$	2.17998e28	0.213463
$797$	− 1.43577e29i	− 1.38836i	−0.719800	−	0.694181i	$-0.755767\pi$
$797$	− 1.43577e29i	− 1.38836i	0.719800	−	0.694181i	$-0.244233\pi$
$798$	0	0
$799$	1.15461e28	0.108885
$800$	2.63030e27i	0.0244966i
$801$	0	0
$802$	−1.48818e28	−0.135180
$803$	3.75285e28i	0.336671i
$804$	0	0
$805$	1.29655e29	1.13457
$806$	− 4.59968e28i	− 0.397537i
$807$	0	0
$808$	−1.98899e28	−0.167695
$809$	− 5.61152e28i	− 0.467300i	−0.972321	−	0.233650i	$-0.924933\pi$
$809$	− 5.61152e28i	− 0.467300i	0.972321	−	0.233650i	$-0.0750669\pi$
$810$	0	0
$811$	2.07322e28	0.168437	0.0842184	−	0.996447i	$-0.473161\pi$
$811$	2.07322e28	0.168437	0.0842184	+	0.996447i	$0.473161\pi$
$812$	− 3.71058e28i	− 0.297771i
$813$	0	0
$814$	2.93870e28	0.230097
$815$	− 1.41961e29i	− 1.09797i
$816$	0	0
$817$	−2.39695e28	−0.180900
$818$	2.69691e28i	0.201064i
$819$	0	0
$820$	9.76057e28	0.710128
$821$	1.59535e29i	1.14663i	0.819334	+	0.573316i	$0.194343\pi$
$821$	1.59535e29i	1.14663i	−0.819334	+	0.573316i	$0.805657\pi$
$822$	0	0
$823$	1.02439e29	0.718564	0.359282	−	0.933229i	$-0.383022\pi$
$823$	1.02439e29	0.718564	0.359282	+	0.933229i	$0.383022\pi$
$824$	− 4.96514e28i	− 0.344080i
$825$	0	0
$826$	−1.62772e29	−1.10098
$827$	5.36629e28i	0.358607i	0.983794	+	0.179304i	$0.0573845\pi$
$827$	5.36629e28i	0.358607i	−0.983794	+	0.179304i	$0.942616\pi$
$828$	0	0
$829$	−3.08740e28	−0.201394	−0.100697	−	0.994917i	$-0.532107\pi$
$829$	−3.08740e28	−0.201394	−0.100697	+	0.994917i	$0.532107\pi$
$830$	− 7.52793e28i	− 0.485171i
$831$	0	0
$832$	1.20892e28	0.0760614
$833$	− 7.38198e27i	− 0.0458905i
$834$	0	0
$835$	2.17659e29	1.32103
$836$	6.32007e27i	0.0379017i
$837$	0	0
$838$	1.79712e29	1.05229
$839$	− 3.03733e29i	− 1.75740i	−0.477370	−	0.878702i	$-0.658410\pi$
$839$	− 3.03733e29i	− 1.75740i	0.477370	−	0.878702i	$-0.341590\pi$
$840$	0	0
$841$	1.26180e29	0.712906
$842$	− 5.14139e28i	− 0.287052i
$843$	0	0
$844$	−1.52953e29	−0.833940
$845$	1.24712e29i	0.671956i
$846$	0	0
$847$	2.03005e29	1.06825
$848$	− 1.71788e27i	− 0.00893378i
$849$	0	0
$850$	3.76107e27	0.0191039
$851$	− 3.14442e29i	− 1.57850i
$852$	0	0
$853$	−2.38478e29	−1.16939	−0.584694	−	0.811254i	$-0.698785\pi$
$853$	−2.38478e29	−1.16939	−0.584694	+	0.811254i	$0.698785\pi$
$854$	3.56699e28i	0.172871i
$855$	0	0
$856$	−1.17744e29	−0.557443
$857$	− 2.51470e29i	− 1.17674i	−0.808594	−	0.588368i	$-0.799771\pi$
$857$	− 2.51470e29i	− 1.17674i	0.808594	−	0.588368i	$-0.200229\pi$
$858$	0	0
$859$	−3.49300e29	−1.59686	−0.798430	−	0.602088i	$-0.794336\pi$
$859$	−3.49300e29	−1.59686	−0.798430	+	0.602088i	$0.794336\pi$
$860$	− 5.55670e28i	− 0.251092i
$861$	0	0
$862$	−1.00996e29	−0.445892
$863$	2.27258e29i	0.991772i	0.868388	+	0.495886i	$0.165157\pi$
$863$	2.27258e29i	0.991772i	−0.868388	+	0.495886i	$0.834843\pi$
$864$	0	0
$865$	2.68503e29	1.14495
$866$	1.32574e29i	0.558828i
$867$	0	0
$868$	1.24654e29	0.513462
$869$	− 2.66979e28i	− 0.108712i
$870$	0	0
$871$	5.94637e28	0.236630
$872$	− 1.70066e29i	− 0.669040i
$873$	0	0
$874$	6.76249e28	0.260011
$875$	− 2.68769e29i	− 1.02164i
$876$	0	0
$877$	6.12502e28	0.227568	0.113784	−	0.993506i	$-0.463703\pi$
$877$	6.12502e28	0.227568	0.113784	+	0.993506i	$0.463703\pi$
$878$	− 4.68439e28i	− 0.172071i
$879$	0	0
$880$	−1.46514e28	−0.0526081
$881$	− 3.69257e29i	− 1.31090i	−0.755238	−	0.655451i	$-0.772479\pi$
$881$	− 3.69257e29i	− 1.31090i	0.755238	−	0.655451i	$-0.227521\pi$
$882$	0	0
$883$	−3.95985e29	−1.37427	−0.687135	−	0.726530i	$-0.741132\pi$
$883$	−3.95985e29	−1.37427	−0.687135	+	0.726530i	$0.741132\pi$
$884$	− 1.72864e28i	− 0.0593173i
$885$	0	0
$886$	−3.19205e29	−1.07086
$887$	− 4.46924e29i	− 1.48251i	−0.671223	−	0.741255i	$-0.734231\pi$
$887$	− 4.46924e29i	− 1.48251i	0.671223	−	0.741255i	$-0.265769\pi$
$888$	0	0
$889$	5.06306e29	1.64208
$890$	2.13817e29i	0.685711i
$891$	0	0
$892$	−1.24353e29	−0.389949
$893$	6.92283e28i	0.214669i
$894$	0	0
$895$	5.72482e29	1.73593
$896$	3.27623e28i	0.0982415i
$897$	0	0
$898$	−3.04043e29	−0.891604
$899$	− 1.70705e29i	− 0.495051i
$900$	0	0
$901$	−2.45640e27	−0.00696710
$902$	6.61711e28i	0.185611i
$903$	0	0
$904$	−2.08534e29	−0.572126
$905$	− 1.12340e28i	− 0.0304823i
$906$	0	0
$907$	4.79047e29	1.27147	0.635734	−	0.771908i	$-0.280697\pi$
$907$	4.79047e29	1.27147	0.635734	+	0.771908i	$0.280697\pi$
$908$	6.65667e28i	0.174743i
$909$	0	0
$910$	1.98716e29	0.510293
$911$	− 6.43302e27i	− 0.0163392i	−0.999967	−	0.00816960i	$-0.997400\pi$
$911$	− 6.43302e27i	− 0.0163392i	0.999967	−	0.00816960i	$-0.00260049\pi$
$912$	0	0
$913$	5.10351e28	0.126812
$914$	− 4.07839e29i	− 1.00237i
$915$	0	0
$916$	−2.22992e29	−0.536209
$917$	3.40706e29i	0.810375i
$918$	0	0
$919$	−2.76775e29	−0.644127	−0.322064	−	0.946718i	$-0.604377\pi$
$919$	−2.76775e29	−0.644127	−0.322064	+	0.946718i	$0.604377\pi$
$920$	1.56770e29i	0.360899i
$921$	0	0
$922$	−4.04051e29	−0.910179
$923$	2.06447e29i	0.460036i
$924$	0	0
$925$	1.04856e29	0.228652
$926$	− 1.83633e29i	− 0.396132i
$927$	0	0
$928$	4.48660e28	0.0947190
$929$	3.21118e29i	0.670668i	0.942099	+	0.335334i	$0.108849\pi$
$929$	3.21118e29i	0.670668i	−0.942099	+	0.335334i	$0.891151\pi$
$930$	0	0
$931$	4.42608e28	0.0904738
$932$	3.10652e28i	0.0628224i
$933$	0	0
$934$	−1.16701e29	−0.230998
$935$	2.09501e28i	0.0410270i
$936$	0	0
$937$	−9.41950e29	−1.80564	−0.902822	−	0.430015i	$-0.858508\pi$
$937$	−9.41950e29	−1.80564	−0.902822	+	0.430015i	$0.858508\pi$
$938$	1.61150e29i	0.305633i
$939$	0	0
$940$	−1.60487e29	−0.297963
$941$	5.42308e29i	0.996208i	0.867117	+	0.498104i	$0.165970\pi$
$941$	5.42308e29i	0.996208i	−0.867117	+	0.498104i	$0.834030\pi$
$942$	0	0
$943$	7.08032e29	1.27332
$944$	− 1.96813e29i	− 0.350214i
$945$	0	0
$946$	3.76712e28	0.0656294
$947$	3.44395e28i	0.0593687i	0.999559	+	0.0296843i	$0.00945021\pi$
$947$	3.44395e28i	0.0593687i	−0.999559	+	0.0296843i	$0.990550\pi$
$948$	0	0
$949$	6.15447e29	1.03879
$950$	2.25506e28i	0.0376637i
$951$	0	0
$952$	4.68470e28	0.0766147
$953$	− 6.19623e29i	− 1.00276i	−0.865226	−	0.501381i	$-0.832825\pi$
$953$	− 6.19623e29i	− 1.00276i	0.865226	−	0.501381i	$-0.167175\pi$
$954$	0	0
$955$	−9.16794e29	−1.45291
$956$	3.65884e29i	0.573806i
$957$	0	0
$958$	−4.20729e29	−0.646170
$959$	7.42027e29i	1.12780i
$960$	0	0
$961$	−9.83212e28	−0.146357
$962$	− 4.81931e29i	− 0.709960i
$963$	0	0
$964$	4.06468e29	0.586484
$965$	6.12462e28i	0.0874593i
$966$	0	0
$967$	−1.15176e30	−1.61101	−0.805503	−	0.592592i	$-0.798105\pi$
$967$	−1.15176e30	−1.61101	−0.805503	+	0.592592i	$0.798105\pi$
$968$	2.45460e29i	0.339803i
$969$	0	0
$970$	4.85252e28	0.0658037
$971$	6.56350e29i	0.880933i	0.897769	+	0.440467i	$0.145187\pi$
$971$	6.56350e29i	0.880933i	−0.897769	+	0.440467i	$0.854813\pi$
$972$	0	0
$973$	−5.36416e28	−0.0705299
$974$	− 5.19348e29i	− 0.675879i
$975$	0	0
$976$	−4.31297e28	−0.0549892
$977$	− 1.88237e29i	− 0.237553i	−0.992921	−	0.118776i	$-0.962103\pi$
$977$	− 1.88237e29i	− 0.237553i	0.992921	−	0.118776i	$-0.0378971\pi$
$978$	0	0
$979$	−1.44955e29	−0.179229
$980$	1.02607e29i	0.125579i
$981$	0	0
$982$	9.11755e29	1.09336
$983$	6.00861e29i	0.713245i	0.934249	+	0.356623i	$0.116072\pi$
$983$	6.00861e29i	0.713245i	−0.934249	+	0.356623i	$0.883928\pi$
$984$	0	0
$985$	9.96252e29	1.15880
$986$	− 6.41539e28i	− 0.0738676i
$987$	0	0
$988$	1.03646e29	0.116945
$989$	− 4.03083e29i	− 0.450227i
$990$	0	0
$991$	−7.21036e29	−0.789260	−0.394630	−	0.918840i	$-0.629127\pi$
$991$	−7.21036e29	−0.789260	−0.394630	+	0.918840i	$0.629127\pi$
$992$	1.50723e29i	0.163329i
$993$	0	0
$994$	−5.59482e29	−0.594186
$995$	4.33275e29i	0.455546i
$996$	0	0
$997$	1.31126e30	1.35125	0.675627	−	0.737244i	$-0.263873\pi$
$997$	1.31126e30	1.35125	0.675627	+	0.737244i	$0.263873\pi$
$998$	5.73534e29i	0.585132i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.b.a.53.1	✓	6
3.2	odd	2	inner	54.21.b.a.53.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.21.b.a.53.1	✓	6	1.1	even	1	trivial
54.21.b.a.53.6	yes	6	3.2	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-724.077i q^{2} -524288. q^{4} -1.04203e7i q^{5} +3.13964e8 q^{7} +3.79625e8i q^{8} -7.54511e9 q^{10} -5.11515e9i q^{11} -8.38857e10 q^{13} -2.27334e11i q^{14} +2.74878e11 q^{16} -3.93049e11i q^{17} +2.35664e12 q^{19} +5.46324e12i q^{20} -3.70377e12 q^{22} +3.96304e13i q^{23} -1.32154e13 q^{25} +6.07397e13i q^{26} -1.64608e14 q^{28} +2.25420e14i q^{29} -7.57278e14 q^{31} -1.99033e14i q^{32} -2.84598e14 q^{34} -3.27161e15i q^{35} -7.93436e15 q^{37} -1.70639e15i q^{38} +3.95581e15 q^{40} -1.78659e16i q^{41} -1.01711e16 q^{43} +2.68181e15i q^{44} +2.86955e16 q^{46} +2.93759e16i q^{47} +1.87813e16 q^{49} +9.56897e15i q^{50} +4.39803e16 q^{52} -6.24962e15i q^{53} -5.33015e16 q^{55} +1.19189e17i q^{56} +1.63221e17 q^{58} -7.16002e17i q^{59} -1.56905e17 q^{61} +5.48328e17i q^{62} -1.44115e17 q^{64} +8.74115e17i q^{65} -7.08866e17 q^{67} +2.06071e17i q^{68} -2.36890e18 q^{70} -2.46105e18i q^{71} -7.33674e18 q^{73} +5.74509e18i q^{74} -1.23556e18 q^{76} -1.60598e18i q^{77} +5.21937e18 q^{79} -2.86431e18i q^{80} -1.29363e19 q^{82} +9.97723e18i q^{83} -4.09569e18 q^{85} +7.36463e18i q^{86} +1.94184e18 q^{88} -2.83384e19i q^{89} -2.63371e19 q^{91} -2.07777e19i q^{92} +2.12704e19 q^{94} -2.45569e19i q^{95} -6.43135e18 q^{97} -1.35991e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3145728 q^{4} - 218826006 q^{7} - 2440839168 q^{10} + 110239981338 q^{13} + 1649267441664 q^{16} + 6190167313578 q^{19} + 10915007348736 q^{22} + 100487054737446 q^{25} + 114727849033728 q^{28} - 16\!\cdots\!56 q^{31}+ \cdots - 95\!\cdots\!62 q^{97}+O(q^{100}) \) 6 * q - 3145728 * q^4 - 218826006 * q^7 - 2440839168 * q^10 + 110239981338 * q^13 + 1649267441664 * q^16 + 6190167313578 * q^19 + 10915007348736 * q^22 + 100487054737446 * q^25 + 114727849033728 * q^28 - 1637611802736756 * q^31 - 2210345032826880 * q^34 + 112704887438490 * q^37 + 1279702685712384 * q^40 + 7701958113650220 * q^43 - 28939400289239040 * q^46 + 110042316130515552 * q^49 - 57797499335737344 * q^52 - 689023188480948480 * q^55 - 218595762960629760 * q^58 - 1581758499272340678 * q^61 - 864691128455135232 * q^64 - 210023541682991286 * q^67 - 2960158445360234496 * q^70 - 18837667029635682630 * q^73 - 3245430440501182464 * q^76 - 50277794728287289110 * q^79 - 26254269238536142848 * q^82 - 79619923081461051648 * q^85 - 5722607372854099968 * q^88 - 103237866532007840010 * q^91 - 109916038192954687488 * q^94 - 95805416653628626662 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more