LMFDB - Embedded newform 9.30.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,30,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

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:	yes
Analytic conductor:	$47.9502381447$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{51349}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 12837 $ x^2 - x - 12837
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-112.802$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17433.9 q^{2} -2.32930e8 q^{4} +1.12623e10 q^{5} -2.98628e12 q^{7} -1.34206e13 q^{8} +O(q^{10})$	\(q+17433.9 q^{2} -2.32930e8 q^{4} +1.12623e10 q^{5} -2.98628e12 q^{7} -1.34206e13 q^{8} +1.96347e14 q^{10} +1.25811e15 q^{11} +6.09036e15 q^{13} -5.20625e16 q^{14} -1.08921e17 q^{16} -8.28952e16 q^{17} +3.72257e18 q^{19} -2.62334e18 q^{20} +2.19338e19 q^{22} +1.69513e19 q^{23} -5.94240e19 q^{25} +1.06179e20 q^{26} +6.95594e20 q^{28} +8.81402e20 q^{29} +3.71093e21 q^{31} +5.30623e21 q^{32} -1.44519e21 q^{34} -3.36325e22 q^{35} +1.97746e22 q^{37} +6.48990e22 q^{38} -1.51148e23 q^{40} +1.00635e23 q^{41} -1.61886e23 q^{43} -2.93051e23 q^{44} +2.95527e23 q^{46} +2.61745e24 q^{47} +5.69796e24 q^{49} -1.03599e24 q^{50} -1.41863e24 q^{52} +1.44856e25 q^{53} +1.41693e25 q^{55} +4.00778e25 q^{56} +1.53663e25 q^{58} -5.87125e24 q^{59} -6.18692e25 q^{61} +6.46960e25 q^{62} +1.50985e26 q^{64} +6.85917e25 q^{65} +1.29243e26 q^{67} +1.93088e25 q^{68} -5.86346e26 q^{70} +3.63672e26 q^{71} +1.45255e27 q^{73} +3.44748e26 q^{74} -8.67098e26 q^{76} -3.75707e27 q^{77} -3.93709e27 q^{79} -1.22670e27 q^{80} +1.75447e27 q^{82} -6.61171e27 q^{83} -9.33594e26 q^{85} -2.82231e27 q^{86} -1.68846e28 q^{88} -6.47986e27 q^{89} -1.81875e28 q^{91} -3.94847e27 q^{92} +4.56324e28 q^{94} +4.19249e28 q^{95} +9.52029e28 q^{97} +9.93377e28 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8640 q^{2} - 89952256 q^{4} + 17477788500 q^{5} - 3020312682800 q^{7} - 3150297169920 q^{8}+O(q^{10}) $ 2 * q - 8640 * q^2 - 89952256 * q^4 + 17477788500 * q^5 - 3020312682800 * q^7 - 3150297169920 * q^8	$ 2 q - 8640 q^{2} - 89952256 q^{4} + 17477788500 q^{5} - 3020312682800 q^{7} - 3150297169920 q^{8} + 34285866768000 q^{10} + 20\!\cdots\!16 q^{11}+ \cdots + 18\!\cdots\!20 q^{98}+O(q^{100}) $ 2 * q - 8640 * q^2 - 89952256 * q^4 + 17477788500 * q^5 - 3020312682800 * q^7 - 3150297169920 * q^8 + 34285866768000 * q^10 + 2055380519588616 * q^11 + 17139371179332220 * q^13 - 51175123348059648 * q^14 - 453469082063208448 * q^16 + 664795927907749980 * q^17 + 1232169445452155080 * q^19 - 1734668101813248000 * q^20 + 1145797484912974080 * q^22 + 18588430504374379920 * q^23 - 207056854502617281250 * q^25 - 181912132597777755264 * q^26 + 690727602371844997120 * q^28 - 996096417765761595420 * q^29 - 1087258664181924030656 * q^31 + 8776107971762202869760 * q^32 - 20940413403809031000192 * q^34 - 33844046536902649068000 * q^35 + 98878127759336138311660 * q^37 + 129833487351109249470720 * q^38 - 87313163228088238080000 * q^40 + 106699837259610025757676 * q^41 + 510640433114974031366200 * q^43 - 179059414424913371086848 * q^44 + 252841215606439776920064 * q^46 + 4521107671109825795039520 * q^47 + 2479210387392854586312114 * q^49 + 2813370491836752543000000 * q^50 + 161134672249303679180800 * q^52 + 16141544629666790250663540 * q^53 + 19124657798421120971058000 * q^55 + 39728224533177935352299520 * q^56 + 64319996083339084169992320 * q^58 + 83497291515660150276062760 * q^59 - 15876762943230179624113316 * q^61 + 189803556071494720042936320 * q^62 + 245489542813624183222697984 * q^64 + 137266226551726798673511000 * q^65 + 24468754434128844890782120 * q^67 + 126211850011481106095677440 * q^68 - 580830557953085152481664000 * q^70 + 188428428253360067209577136 * q^71 + 995872721297568533052080980 * q^73 - 1717790650063115374837542528 * q^74 - 1223170019527541658110935040 * q^76 - 3784200478484579386131729600 * q^77 - 7218460852587735797823642080 * q^79 - 3368223393577622373924864000 * q^80 + 1596346485209467674952913280 * q^82 - 2210846225248155523694669640 * q^83 + 3713635892367734904614943000 * q^85 - 20357697303796411232450244864 * q^86 - 8696387677835767416210063360 * q^88 - 5872964746600969363962031860 * q^89 - 18563550073842319069958420896 * q^91 - 3714393183413159199429918720 * q^92 - 4003342107705068447401638912 * q^94 + 26445947767121183571013410000 * q^95 + 109649982219471997093227005380 * q^97 + 183262972410594366168864121920 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	17433.9	0.752419	0.376209	−	0.926535i	$-0.377227\pi$
$2$	17433.9	0.752419	0.376209	+	0.926535i	$0.377227\pi$
$3$	0	0
$3$	0	0
$4$	−2.32930e8	−0.433866
$5$	1.12623e10	0.825209	0.412604	−	0.910910i	$-0.364619\pi$
$5$	1.12623e10	0.825209	0.412604	+	0.910910i	$0.364619\pi$
$6$	0	0
$7$	−2.98628e12	−1.66421	−0.832106	−	0.554616i	$-0.812865\pi$
$7$	−2.98628e12	−1.66421	−0.832106	+	0.554616i	$0.812865\pi$
$8$	−1.34206e13	−1.07887
$9$	0	0
$10$	1.96347e14	0.620903
$11$	1.25811e15	0.998906	0.499453	−	0.866341i	$-0.333534\pi$
$11$	1.25811e15	0.998906	0.499453	+	0.866341i	$0.333534\pi$
$12$	0	0
$13$	6.09036e15	0.429007	0.214503	−	0.976723i	$-0.431187\pi$
$13$	6.09036e15	0.429007	0.214503	+	0.976723i	$0.431187\pi$
$14$	−5.20625e16	−1.25219
$15$	0	0
$16$	−1.08921e17	−0.377895
$17$	−8.28952e16	−0.119404	−0.0597021	−	0.998216i	$-0.519015\pi$
$17$	−8.28952e16	−0.119404	−0.0597021	+	0.998216i	$0.519015\pi$
$18$	0	0
$19$	3.72257e18	1.06885	0.534424	−	0.845217i	$-0.320529\pi$
$19$	3.72257e18	1.06885	0.534424	+	0.845217i	$0.320529\pi$
$20$	−2.62334e18	−0.358030
$21$	0	0
$22$	2.19338e19	0.751596
$23$	1.69513e19	0.304894	0.152447	−	0.988312i	$-0.451285\pi$
$23$	1.69513e19	0.304894	0.152447	+	0.988312i	$0.451285\pi$
$24$	0	0
$25$	−5.94240e19	−0.319030
$26$	1.06179e20	0.322793
$27$	0	0
$28$	6.95594e20	0.722045
$29$	8.81402e20	0.550051	0.275026	−	0.961437i	$-0.411314\pi$
$29$	8.81402e20	0.550051	0.275026	+	0.961437i	$0.411314\pi$
$30$	0	0
$31$	3.71093e21	0.880518	0.440259	−	0.897871i	$-0.354887\pi$
$31$	3.71093e21	0.880518	0.440259	+	0.897871i	$0.354887\pi$
$32$	5.30623e21	0.794532
$33$	0	0
$34$	−1.44519e21	−0.0898420
$35$	−3.36325e22	−1.37332
$36$	0	0
$37$	1.97746e22	0.360730	0.180365	−	0.983600i	$-0.442272\pi$
$37$	1.97746e22	0.360730	0.180365	+	0.983600i	$0.442272\pi$
$38$	6.48990e22	0.804221
$39$	0	0
$40$	−1.51148e23	−0.890291
$41$	1.00635e23	0.414367	0.207183	−	0.978302i	$-0.433570\pi$
$41$	1.00635e23	0.414367	0.207183	+	0.978302i	$0.433570\pi$
$42$	0	0
$43$	−1.61886e23	−0.334131	−0.167066	−	0.985946i	$-0.553429\pi$
$43$	−1.61886e23	−0.334131	−0.167066	+	0.985946i	$0.553429\pi$
$44$	−2.93051e23	−0.433391
$45$	0	0
$46$	2.95527e23	0.229408
$47$	2.61745e24	1.48751	0.743755	−	0.668453i	$-0.233043\pi$
$47$	2.61745e24	1.48751	0.743755	+	0.668453i	$0.233043\pi$
$48$	0	0
$49$	5.69796e24	1.76960
$50$	−1.03599e24	−0.240045
$51$	0	0
$52$	−1.41863e24	−0.186131
$53$	1.44856e25	1.44190	0.720951	−	0.692986i	$-0.243705\pi$
$53$	1.44856e25	1.44190	0.720951	+	0.692986i	$0.243705\pi$
$54$	0	0
$55$	1.41693e25	0.824306
$56$	4.00778e25	1.79547
$57$	0	0
$58$	1.53663e25	0.413869
$59$	−5.87125e24	−0.123417	−0.0617087	−	0.998094i	$-0.519655\pi$
$59$	−5.87125e24	−0.123417	−0.0617087	+	0.998094i	$0.519655\pi$
$60$	0	0
$61$	−6.18692e25	−0.802032	−0.401016	−	0.916071i	$-0.631343\pi$
$61$	−6.18692e25	−0.802032	−0.401016	+	0.916071i	$0.631343\pi$
$62$	6.46960e25	0.662519
$63$	0	0
$64$	1.50985e26	0.975716
$65$	6.85917e25	0.354020
$66$	0	0
$67$	1.29243e26	0.429854	0.214927	−	0.976630i	$-0.431049\pi$
$67$	1.29243e26	0.429854	0.214927	+	0.976630i	$0.431049\pi$
$68$	1.93088e25	0.0518054
$69$	0	0
$70$	−5.86346e26	−1.03331
$71$	3.63672e26	0.521751	0.260876	−	0.965372i	$-0.415989\pi$
$71$	3.63672e26	0.521751	0.260876	+	0.965372i	$0.415989\pi$
$72$	0	0
$73$	1.45255e27	1.39299	0.696496	−	0.717561i	$-0.254741\pi$
$73$	1.45255e27	1.39299	0.696496	+	0.717561i	$0.254741\pi$
$74$	3.44748e26	0.271420
$75$	0	0
$76$	−8.67098e26	−0.463736
$77$	−3.75707e27	−1.66239
$78$	0	0
$79$	−3.93709e27	−1.20111	−0.600554	−	0.799584i	$-0.705053\pi$
$79$	−3.93709e27	−1.20111	−0.600554	+	0.799584i	$0.705053\pi$
$80$	−1.22670e27	−0.311842
$81$	0	0
$82$	1.75447e27	0.311778
$83$	−6.61171e27	−0.985556	−0.492778	−	0.870155i	$-0.664018\pi$
$83$	−6.61171e27	−0.985556	−0.492778	+	0.870155i	$0.664018\pi$
$84$	0	0
$85$	−9.33594e26	−0.0985335
$86$	−2.82231e27	−0.251407
$87$	0	0
$88$	−1.68846e28	−1.07769
$89$	−6.47986e27	−0.351084	−0.175542	−	0.984472i	$-0.556168\pi$
$89$	−6.47986e27	−0.351084	−0.175542	+	0.984472i	$0.556168\pi$
$90$	0	0
$91$	−1.81875e28	−0.713959
$92$	−3.94847e27	−0.132283
$93$	0	0
$94$	4.56324e28	1.11923
$95$	4.19249e28	0.882023
$96$	0	0
$97$	9.52029e28	1.48068	0.740338	−	0.672235i	$-0.234666\pi$
$97$	9.52029e28	1.48068	0.740338	+	0.672235i	$0.234666\pi$
$98$	9.93377e28	1.33148
$99$	0	0
$100$	1.38416e28	0.138416
$101$	−4.65862e28	−0.403271	−0.201635	−	0.979461i	$-0.564626\pi$
$101$	−4.65862e28	−0.403271	−0.201635	+	0.979461i	$0.564626\pi$
$102$	0	0
$103$	−1.34288e29	−0.874775	−0.437388	−	0.899273i	$-0.644096\pi$
$103$	−1.34288e29	−0.874775	−0.437388	+	0.899273i	$0.644096\pi$
$104$	−8.17365e28	−0.462842
$105$	0	0
$106$	2.52540e29	1.08491
$107$	4.69036e29	1.75850	0.879248	−	0.476364i	$-0.158045\pi$
$107$	4.69036e29	1.75850	0.879248	+	0.476364i	$0.158045\pi$
$108$	0	0
$109$	−5.33865e29	−1.53020	−0.765098	−	0.643913i	$-0.777310\pi$
$109$	−5.33865e29	−1.53020	−0.765098	+	0.643913i	$0.777310\pi$
$110$	2.47026e29	0.620223
$111$	0	0
$112$	3.25268e29	0.628897
$113$	−7.95436e29	−1.35197	−0.675987	−	0.736914i	$-0.736282\pi$
$113$	−7.95436e29	−1.35197	−0.675987	+	0.736914i	$0.736282\pi$
$114$	0	0
$115$	1.90911e29	0.251602
$116$	−2.05305e29	−0.238648
$117$	0	0
$118$	−1.02359e29	−0.0928615
$119$	2.47548e29	0.198714
$120$	0	0
$121$	−3.46951e27	−0.00218716
$122$	−1.07862e30	−0.603464
$123$	0	0
$124$	−8.64387e29	−0.382027
$125$	−2.76703e30	−1.08848
$126$	0	0
$127$	1.93923e29	0.0606003	0.0303002	−	0.999541i	$-0.490354\pi$
$127$	1.93923e29	0.0606003	0.0303002	+	0.999541i	$0.490354\pi$
$128$	−2.16508e29	−0.0603851
$129$	0	0
$130$	1.19582e30	0.266372
$131$	2.32229e30	0.462894	0.231447	−	0.972847i	$-0.425654\pi$
$131$	2.32229e30	0.462894	0.231447	+	0.972847i	$0.425654\pi$
$132$	0	0
$133$	−1.11166e31	−1.77879
$134$	2.25320e30	0.323430
$135$	0	0
$136$	1.11251e30	0.128821
$137$	−1.26990e31	−1.32228	−0.661139	−	0.750263i	$-0.729927\pi$
$137$	−1.26990e31	−1.32228	−0.661139	+	0.750263i	$0.729927\pi$
$138$	0	0
$139$	1.14547e31	0.966648	0.483324	−	0.875442i	$-0.339429\pi$
$139$	1.14547e31	0.966648	0.483324	+	0.875442i	$0.339429\pi$
$140$	7.83402e30	0.595838
$141$	0	0
$142$	6.34022e30	0.392575
$143$	7.66234e30	0.428538
$144$	0	0
$145$	9.92666e30	0.453907
$146$	2.53236e31	1.04811
$147$	0	0
$148$	−4.60609e30	−0.156508
$149$	5.74280e31	1.76979	0.884897	−	0.465787i	$-0.154229\pi$
$149$	5.74280e31	1.76979	0.884897	+	0.465787i	$0.154229\pi$
$150$	0	0
$151$	5.07974e31	1.29026	0.645128	−	0.764075i	$-0.276804\pi$
$151$	5.07974e31	1.29026	0.645128	+	0.764075i	$0.276804\pi$
$152$	−4.99593e31	−1.15315
$153$	0	0
$154$	−6.55003e31	−1.25082
$155$	4.17938e31	0.726611
$156$	0	0
$157$	−9.31373e30	−0.134455	−0.0672277	−	0.997738i	$-0.521415\pi$
$157$	−9.31373e30	−0.134455	−0.0672277	+	0.997738i	$0.521415\pi$
$158$	−6.86388e31	−0.903736
$159$	0	0
$160$	5.97606e31	0.655655
$161$	−5.06213e31	−0.507409
$162$	0	0
$163$	−4.45351e31	−0.373235	−0.186617	−	0.982433i	$-0.559752\pi$
$163$	−4.45351e31	−0.373235	−0.186617	+	0.982433i	$0.559752\pi$
$164$	−2.34410e31	−0.179780
$165$	0	0
$166$	−1.15268e32	−0.741551
$167$	−1.74608e32	−1.02962	−0.514808	−	0.857305i	$-0.672137\pi$
$167$	−1.74608e32	−1.02962	−0.514808	+	0.857305i	$0.672137\pi$
$168$	0	0
$169$	−1.64446e32	−0.815953
$170$	−1.62762e31	−0.0741384
$171$	0	0
$172$	3.77081e31	0.144968
$173$	−4.75360e31	−0.168017	−0.0840086	−	0.996465i	$-0.526772\pi$
$173$	−4.75360e31	−0.168017	−0.0840086	+	0.996465i	$0.526772\pi$
$174$	0	0
$175$	1.77457e32	0.530935
$176$	−1.37034e32	−0.377481
$177$	0	0
$178$	−1.12969e32	−0.264162
$179$	6.60198e32	1.42333	0.711664	−	0.702520i	$-0.247942\pi$
$179$	6.60198e32	1.42333	0.711664	+	0.702520i	$0.247942\pi$
$180$	0	0
$181$	5.34310e32	0.980515	0.490257	−	0.871578i	$-0.336903\pi$
$181$	5.34310e32	0.980515	0.490257	+	0.871578i	$0.336903\pi$
$182$	−3.17079e32	−0.537196
$183$	0	0
$184$	−2.27497e32	−0.328941
$185$	2.22708e32	0.297677
$186$	0	0
$187$	−1.04291e32	−0.119274
$188$	−6.09683e32	−0.645379
$189$	0	0
$190$	7.30915e32	0.663651
$191$	9.58754e32	0.806721	0.403360	−	0.915041i	$-0.367842\pi$
$191$	9.58754e32	0.806721	0.403360	+	0.915041i	$0.367842\pi$
$192$	0	0
$193$	7.81683e31	0.0565522	0.0282761	−	0.999600i	$-0.490998\pi$
$193$	7.81683e31	0.0565522	0.0282761	+	0.999600i	$0.490998\pi$
$194$	1.65976e33	1.11409
$195$	0	0
$196$	−1.32722e33	−0.767770
$197$	5.60393e32	0.301115	0.150557	−	0.988601i	$-0.451893\pi$
$197$	5.60393e32	0.301115	0.150557	+	0.988601i	$0.451893\pi$
$198$	0	0
$199$	8.91542e32	0.413783	0.206891	−	0.978364i	$-0.433665\pi$
$199$	8.91542e32	0.413783	0.206891	+	0.978364i	$0.433665\pi$
$200$	7.97508e32	0.344192
$201$	0	0
$202$	−8.12179e32	−0.303429
$203$	−2.63211e33	−0.915402
$204$	0	0
$205$	1.13339e33	0.341939
$206$	−2.34116e33	−0.658198
$207$	0	0
$208$	−6.63367e32	−0.162120
$209$	4.68340e33	1.06768
$210$	0	0
$211$	1.07645e33	0.213746	0.106873	−	0.994273i	$-0.465916\pi$
$211$	1.07645e33	0.213746	0.106873	+	0.994273i	$0.465916\pi$
$212$	−3.37412e33	−0.625592
$213$	0	0
$214$	8.17713e33	1.32313
$215$	−1.82322e33	−0.275728
$216$	0	0
$217$	−1.10819e34	−1.46537
$218$	−9.30735e33	−1.15135
$219$	0	0
$220$	−3.30045e33	−0.357638
$221$	−5.04861e32	−0.0512253
$222$	0	0
$223$	−3.94073e33	−0.350878	−0.175439	−	0.984490i	$-0.556134\pi$
$223$	−3.94073e33	−0.350878	−0.175439	+	0.984490i	$0.556134\pi$
$224$	−1.58459e34	−1.32227
$225$	0	0
$226$	−1.38676e34	−1.01725
$227$	2.60531e34	1.79260	0.896302	−	0.443445i	$-0.146244\pi$
$227$	2.60531e34	1.79260	0.896302	+	0.443445i	$0.146244\pi$
$228$	0	0
$229$	1.02479e34	0.620898	0.310449	−	0.950590i	$-0.399521\pi$
$229$	1.02479e34	0.620898	0.310449	+	0.950590i	$0.399521\pi$
$230$	3.32833e33	0.189310
$231$	0	0
$232$	−1.18290e34	−0.593432
$233$	−1.94574e34	−0.917113	−0.458557	−	0.888665i	$-0.651633\pi$
$233$	−1.94574e34	−0.917113	−0.458557	+	0.888665i	$0.651633\pi$
$234$	0	0
$235$	2.94786e34	1.22751
$236$	1.36759e33	0.0535465
$237$	0	0
$238$	4.31573e33	0.149516
$239$	4.56285e34	1.48753	0.743766	−	0.668440i	$-0.233037\pi$
$239$	4.56285e34	1.48753	0.743766	+	0.668440i	$0.233037\pi$
$240$	0	0
$241$	2.90791e34	0.840107	0.420053	−	0.907499i	$-0.362011\pi$
$241$	2.90791e34	0.840107	0.420053	+	0.907499i	$0.362011\pi$
$242$	−6.04870e31	−0.00164566
$243$	0	0
$244$	1.44112e34	0.347974
$245$	6.41724e34	1.46029
$246$	0	0
$247$	2.26718e34	0.458543
$248$	−4.98030e34	−0.949963
$249$	0	0
$250$	−4.82401e34	−0.818990
$251$	1.72418e34	0.276256	0.138128	−	0.990414i	$-0.455891\pi$
$251$	1.72418e34	0.276256	0.138128	+	0.990414i	$0.455891\pi$
$252$	0	0
$253$	2.13266e34	0.304561
$254$	3.38083e33	0.0455968
$255$	0	0
$256$	−8.48339e34	−1.02115
$257$	−4.22826e33	−0.0480985	−0.0240493	−	0.999711i	$-0.507656\pi$
$257$	−4.22826e33	−0.0480985	−0.0240493	+	0.999711i	$0.507656\pi$
$258$	0	0
$259$	−5.90524e34	−0.600331
$260$	−1.59771e34	−0.153597
$261$	0	0
$262$	4.04865e34	0.348290
$263$	3.28330e34	0.267271	0.133635	−	0.991031i	$-0.457335\pi$
$263$	3.28330e34	0.267271	0.133635	+	0.991031i	$0.457335\pi$
$264$	0	0
$265$	1.63142e35	1.18987
$266$	−1.93806e35	−1.33840
$267$	0	0
$268$	−3.01045e34	−0.186499
$269$	−2.79966e35	−1.64322	−0.821612	−	0.570048i	$-0.806925\pi$
$269$	−2.79966e35	−1.64322	−0.821612	+	0.570048i	$0.806925\pi$
$270$	0	0
$271$	−3.70768e35	−1.95455	−0.977277	−	0.211965i	$-0.932014\pi$
$271$	−3.70768e35	−1.95455	−0.977277	+	0.211965i	$0.932014\pi$
$272$	9.02901e33	0.0451223
$273$	0	0
$274$	−2.21394e35	−0.994907
$275$	−7.47620e34	−0.318681
$276$	0	0
$277$	3.33125e35	1.27835	0.639176	−	0.769060i	$-0.279275\pi$
$277$	3.33125e35	1.27835	0.639176	+	0.769060i	$0.279275\pi$
$278$	1.99700e35	0.727324
$279$	0	0
$280$	4.51370e35	1.48163
$281$	5.19345e35	1.61888	0.809440	−	0.587203i	$-0.199771\pi$
$281$	5.19345e35	1.61888	0.809440	+	0.587203i	$0.199771\pi$
$282$	0	0
$283$	−1.04587e34	−0.0294154	−0.0147077	−	0.999892i	$-0.504682\pi$
$283$	−1.04587e34	−0.0294154	−0.0147077	+	0.999892i	$0.504682\pi$
$284$	−8.47100e34	−0.226370
$285$	0	0
$286$	1.33585e35	0.322440
$287$	−3.00526e35	−0.689595
$288$	0	0
$289$	−4.75097e35	−0.985743
$290$	1.73060e35	0.341528
$291$	0	0
$292$	−3.38341e35	−0.604371
$293$	3.74269e35	0.636214	0.318107	−	0.948055i	$-0.396953\pi$
$293$	3.74269e35	0.636214	0.318107	+	0.948055i	$0.396953\pi$
$294$	0	0
$295$	−6.61240e34	−0.101845
$296$	−2.65387e35	−0.389180
$297$	0	0
$298$	1.00119e36	1.33163
$299$	1.03240e35	0.130802
$300$	0	0
$301$	4.83437e35	0.556065
$302$	8.85597e35	0.970813
$303$	0	0
$304$	−4.05465e35	−0.403912
$305$	−6.96792e35	−0.661844
$306$	0	0
$307$	−5.37563e35	−0.464433	−0.232217	−	0.972664i	$-0.574598\pi$
$307$	−5.37563e35	−0.464433	−0.232217	+	0.972664i	$0.574598\pi$
$308$	8.75133e35	0.721255
$309$	0	0
$310$	7.28629e35	0.546716
$311$	4.11459e35	0.294646	0.147323	−	0.989088i	$-0.452934\pi$
$311$	4.11459e35	0.294646	0.147323	+	0.989088i	$0.452934\pi$
$312$	0	0
$313$	−1.66582e36	−1.08702	−0.543508	−	0.839404i	$-0.682904\pi$
$313$	−1.66582e36	−1.08702	−0.543508	+	0.839404i	$0.682904\pi$
$314$	−1.62375e35	−0.101167
$315$	0	0
$316$	9.17065e35	0.521120
$317$	−2.49069e36	−1.35195	−0.675975	−	0.736925i	$-0.736277\pi$
$317$	−2.49069e36	−1.35195	−0.675975	+	0.736925i	$0.736277\pi$
$318$	0	0
$319$	1.10890e36	0.549449
$320$	1.70044e36	0.805170
$321$	0	0
$322$	−8.82527e35	−0.381784
$323$	−3.08583e35	−0.127625
$324$	0	0
$325$	−3.61914e35	−0.136866
$326$	−7.76421e35	−0.280829
$327$	0	0
$328$	−1.35059e36	−0.447047
$329$	−7.81644e36	−2.47553
$330$	0	0
$331$	1.70323e36	0.494046	0.247023	−	0.969010i	$-0.420548\pi$
$331$	1.70323e36	0.494046	0.247023	+	0.969010i	$0.420548\pi$
$332$	1.54006e36	0.427599
$333$	0	0
$334$	−3.04410e36	−0.774703
$335$	1.45557e36	0.354719
$336$	0	0
$337$	1.36026e36	0.304080	0.152040	−	0.988374i	$-0.451416\pi$
$337$	1.36026e36	0.304080	0.152040	+	0.988374i	$0.451416\pi$
$338$	−2.86693e36	−0.613939
$339$	0	0
$340$	2.17462e35	0.0427503
$341$	4.66876e36	0.879555
$342$	0	0
$343$	−7.40016e36	−1.28078
$344$	2.17261e36	0.360483
$345$	0	0
$346$	−8.28738e35	−0.126419
$347$	6.83587e36	1.00004	0.500019	−	0.866015i	$-0.333326\pi$
$347$	6.83587e36	1.00004	0.500019	+	0.866015i	$0.333326\pi$
$348$	0	0
$349$	4.60521e36	0.619842	0.309921	−	0.950762i	$-0.399697\pi$
$349$	4.60521e36	0.619842	0.309921	+	0.950762i	$0.399697\pi$
$350$	3.09377e36	0.399485
$351$	0	0
$352$	6.67582e36	0.793663
$353$	−1.14489e37	−1.30627	−0.653134	−	0.757243i	$-0.726546\pi$
$353$	−1.14489e37	−1.30627	−0.653134	+	0.757243i	$0.726546\pi$
$354$	0	0
$355$	4.09580e36	0.430554
$356$	1.50935e36	0.152323
$357$	0	0
$358$	1.15098e37	1.07094
$359$	1.33540e37	1.19328	0.596638	−	0.802510i	$-0.296503\pi$
$359$	1.33540e37	1.19328	0.596638	+	0.802510i	$0.296503\pi$
$360$	0	0
$361$	1.72772e36	0.142436
$362$	9.31511e36	0.737758
$363$	0	0
$364$	4.23642e36	0.309762
$365$	1.63591e37	1.14951
$366$	0	0
$367$	−1.51022e37	−0.980353	−0.490177	−	0.871623i	$-0.663068\pi$
$367$	−1.51022e37	−0.980353	−0.490177	+	0.871623i	$0.663068\pi$
$368$	−1.84635e36	−0.115218
$369$	0	0
$370$	3.88267e36	0.223978
$371$	−4.32580e37	−2.39963
$372$	0	0
$373$	−1.09297e36	−0.0560828	−0.0280414	−	0.999607i	$-0.508927\pi$
$373$	−1.09297e36	−0.0560828	−0.0280414	+	0.999607i	$0.508927\pi$
$374$	−1.81820e36	−0.0897437
$375$	0	0
$376$	−3.51279e37	−1.60483
$377$	5.36806e36	0.235976
$378$	0	0
$379$	1.45750e37	0.593392	0.296696	−	0.954972i	$-0.404115\pi$
$379$	1.45750e37	0.593392	0.296696	+	0.954972i	$0.404115\pi$
$380$	−9.76556e36	−0.382679
$381$	0	0
$382$	1.67148e37	0.606992
$383$	5.82118e36	0.203530	0.101765	−	0.994808i	$-0.467551\pi$
$383$	5.82118e36	0.203530	0.101765	+	0.994808i	$0.467551\pi$
$384$	0	0
$385$	−4.23134e37	−1.37182
$386$	1.36278e36	0.0425510
$387$	0	0
$388$	−2.21756e37	−0.642414
$389$	6.42121e36	0.179204	0.0896020	−	0.995978i	$-0.471440\pi$
$389$	6.42121e36	0.179204	0.0896020	+	0.995978i	$0.471440\pi$
$390$	0	0
$391$	−1.40518e36	−0.0364057
$392$	−7.64702e37	−1.90917
$393$	0	0
$394$	9.76983e36	0.226564
$395$	−4.43408e37	−0.991165
$396$	0	0
$397$	6.76912e37	1.40627	0.703137	−	0.711054i	$-0.251782\pi$
$397$	6.76912e37	1.40627	0.703137	+	0.711054i	$0.251782\pi$
$398$	1.55431e37	0.311338
$399$	0	0
$400$	6.47251e36	0.120560
$401$	8.28993e37	1.48922	0.744608	−	0.667502i	$-0.232636\pi$
$401$	8.28993e37	1.48922	0.744608	+	0.667502i	$0.232636\pi$
$402$	0	0
$403$	2.26009e37	0.377748
$404$	1.08513e37	0.174965
$405$	0	0
$406$	−4.58880e37	−0.688766
$407$	2.48786e37	0.360335
$408$	0	0
$409$	2.19435e37	0.296018	0.148009	−	0.988986i	$-0.452714\pi$
$409$	2.19435e37	0.296018	0.148009	+	0.988986i	$0.452714\pi$
$410$	1.97594e37	0.257282
$411$	0	0
$412$	3.12796e37	0.379535
$413$	1.75332e37	0.205393
$414$	0	0
$415$	−7.44633e37	−0.813289
$416$	3.23169e37	0.340860
$417$	0	0
$418$	8.16500e37	0.803341
$419$	1.94941e37	0.185268	0.0926338	−	0.995700i	$-0.470471\pi$
$419$	1.94941e37	0.185268	0.0926338	+	0.995700i	$0.470471\pi$
$420$	0	0
$421$	−3.14435e37	−0.278895	−0.139447	−	0.990229i	$-0.544533\pi$
$421$	−3.14435e37	−0.278895	−0.139447	+	0.990229i	$0.544533\pi$
$422$	1.87667e37	0.160827
$423$	0	0
$424$	−1.94406e38	−1.55562
$425$	4.92597e36	0.0380936
$426$	0	0
$427$	1.84759e38	1.33475
$428$	−1.09253e38	−0.762951
$429$	0	0
$430$	−3.17858e37	−0.207463
$431$	2.71956e38	1.71624	0.858120	−	0.513449i	$-0.171633\pi$
$431$	2.71956e38	1.71624	0.858120	+	0.513449i	$0.171633\pi$
$432$	0	0
$433$	1.20292e38	0.709842	0.354921	−	0.934896i	$-0.384508\pi$
$433$	1.20292e38	0.709842	0.354921	+	0.934896i	$0.384508\pi$
$434$	−1.93200e38	−1.10257
$435$	0	0
$436$	1.24353e38	0.663900
$437$	6.31025e37	0.325886
$438$	0	0
$439$	−6.48441e37	−0.313426	−0.156713	−	0.987644i	$-0.550090\pi$
$439$	−6.48441e37	−0.313426	−0.156713	+	0.987644i	$0.550090\pi$
$440$	−1.90161e38	−0.889317
$441$	0	0
$442$	−8.80171e36	−0.0385429
$443$	1.25901e38	0.533550	0.266775	−	0.963759i	$-0.414042\pi$
$443$	1.25901e38	0.533550	0.266775	+	0.963759i	$0.414042\pi$
$444$	0	0
$445$	−7.29785e37	−0.289717
$446$	−6.87022e37	−0.264007
$447$	0	0
$448$	−4.50883e38	−1.62380
$449$	−4.32701e38	−1.50874	−0.754372	−	0.656447i	$-0.772059\pi$
$449$	−4.32701e38	−1.50874	−0.754372	+	0.656447i	$0.772059\pi$
$450$	0	0
$451$	1.26610e38	0.413914
$452$	1.85281e38	0.586575
$453$	0	0
$454$	4.54207e38	1.34879
$455$	−2.04834e38	−0.589165
$456$	0	0
$457$	−5.34446e38	−1.44251	−0.721255	−	0.692670i	$-0.756434\pi$
$457$	−5.34446e38	−1.44251	−0.721255	+	0.692670i	$0.756434\pi$
$458$	1.78661e38	0.467176
$459$	0	0
$460$	−4.44690e37	−0.109161
$461$	2.70831e38	0.644220	0.322110	−	0.946702i	$-0.395608\pi$
$461$	2.70831e38	0.644220	0.322110	+	0.946702i	$0.395608\pi$
$462$	0	0
$463$	5.36275e38	1.19802	0.599009	−	0.800742i	$-0.295561\pi$
$463$	5.36275e38	1.19802	0.599009	+	0.800742i	$0.295561\pi$
$464$	−9.60030e37	−0.207862
$465$	0	0
$466$	−3.39218e38	−0.690054
$467$	−9.88390e38	−1.94910	−0.974549	−	0.224177i	$-0.928031\pi$
$467$	−9.88390e38	−1.94910	−0.974549	+	0.224177i	$0.928031\pi$
$468$	0	0
$469$	−3.85954e38	−0.715368
$470$	5.13928e38	0.923599
$471$	0	0
$472$	7.87958e37	0.133151
$473$	−2.03670e38	−0.333765
$474$	0	0
$475$	−2.21210e38	−0.340995
$476$	−5.76614e37	−0.0862152
$477$	0	0
$478$	7.95483e38	1.11925
$479$	1.66145e38	0.226789	0.113395	−	0.993550i	$-0.463828\pi$
$479$	1.66145e38	0.226789	0.113395	+	0.993550i	$0.463828\pi$
$480$	0	0
$481$	1.20434e38	0.154756
$482$	5.06963e38	0.632112
$483$	0	0
$484$	8.08152e35	0.000948932 0
$485$	1.07221e39	1.22187
$486$	0	0
$487$	−5.21209e38	−0.559554	−0.279777	−	0.960065i	$-0.590260\pi$
$487$	−5.21209e38	−0.559554	−0.279777	+	0.960065i	$0.590260\pi$
$488$	8.30323e38	0.865286
$489$	0	0
$490$	1.11878e39	1.09875
$491$	6.08070e38	0.579791	0.289896	−	0.957058i	$-0.406379\pi$
$491$	6.08070e38	0.579791	0.289896	+	0.957058i	$0.406379\pi$
$492$	0	0
$493$	−7.30640e37	−0.0656785
$494$	3.95258e38	0.345017
$495$	0	0
$496$	−4.04197e38	−0.332743
$497$	−1.08602e39	−0.868305
$498$	0	0
$499$	1.92541e39	1.45233	0.726165	−	0.687521i	$-0.241301\pi$
$499$	1.92541e39	1.45233	0.726165	+	0.687521i	$0.241301\pi$
$500$	6.44524e38	0.472252
$501$	0	0
$502$	3.00591e38	0.207861
$503$	−1.47205e39	−0.988981	−0.494490	−	0.869183i	$-0.664645\pi$
$503$	−1.47205e39	−0.988981	−0.494490	+	0.869183i	$0.664645\pi$
$504$	0	0
$505$	−5.24669e38	−0.332783
$506$	3.71806e38	0.229157
$507$	0	0
$508$	−4.51704e37	−0.0262924
$509$	−9.86933e37	−0.0558316	−0.0279158	−	0.999610i	$-0.508887\pi$
$509$	−9.86933e37	−0.0558316	−0.0279158	+	0.999610i	$0.508887\pi$
$510$	0	0
$511$	−4.33771e39	−2.31823
$512$	−1.36275e39	−0.707948
$513$	0	0
$514$	−7.37152e37	−0.0361903
$515$	−1.51239e39	−0.721872
$516$	0	0
$517$	3.29304e39	1.48588
$518$	−1.02951e39	−0.451701
$519$	0	0
$520$	−9.20545e38	−0.381941
$521$	−1.36208e39	−0.549613	−0.274806	−	0.961500i	$-0.588614\pi$
$521$	−1.36208e39	−0.549613	−0.274806	+	0.961500i	$0.588614\pi$
$522$	0	0
$523$	−3.92619e39	−1.49864	−0.749320	−	0.662208i	$-0.769619\pi$
$523$	−3.92619e39	−1.49864	−0.749320	+	0.662208i	$0.769619\pi$
$524$	−5.40930e38	−0.200834
$525$	0	0
$526$	5.72407e38	0.201100
$527$	−3.07618e38	−0.105138
$528$	0	0
$529$	−2.80371e39	−0.907039
$530$	2.84419e39	0.895281
$531$	0	0
$532$	2.58940e39	0.771756
$533$	6.12906e38	0.177766
$534$	0	0
$535$	5.28245e39	1.45113
$536$	−1.73452e39	−0.463756
$537$	0	0
$538$	−4.88089e39	−1.23639
$539$	7.16866e39	1.76767
$540$	0	0
$541$	3.64331e39	0.851405	0.425702	−	0.904863i	$-0.360027\pi$
$541$	3.64331e39	0.851405	0.425702	+	0.904863i	$0.360027\pi$
$542$	−6.46394e39	−1.47064
$543$	0	0
$544$	−4.39861e38	−0.0948706
$545$	−6.01257e39	−1.26273
$546$	0	0
$547$	−9.64716e38	−0.192125	−0.0960624	−	0.995375i	$-0.530625\pi$
$547$	−9.64716e38	−0.192125	−0.0960624	+	0.995375i	$0.530625\pi$
$548$	2.95799e39	0.573691
$549$	0	0
$550$	−1.30339e39	−0.239782
$551$	3.28108e39	0.587921
$552$	0	0
$553$	1.17572e40	1.99890
$554$	5.80767e39	0.961857
$555$	0	0
$556$	−2.66814e39	−0.419395
$557$	4.34857e39	0.665956	0.332978	−	0.942935i	$-0.391946\pi$
$557$	4.34857e39	0.665956	0.332978	+	0.942935i	$0.391946\pi$
$558$	0	0
$559$	−9.85944e38	−0.143345
$560$	3.66328e39	0.518972
$561$	0	0
$562$	9.05422e39	1.21808
$563$	5.22292e39	0.684765	0.342382	−	0.939561i	$-0.388766\pi$
$563$	5.22292e39	0.684765	0.342382	+	0.939561i	$0.388766\pi$
$564$	0	0
$565$	−8.95848e39	−1.11566
$566$	−1.82336e38	−0.0221327
$567$	0	0
$568$	−4.88070e39	−0.562900
$569$	−8.52031e39	−0.957916	−0.478958	−	0.877838i	$-0.658985\pi$
$569$	−8.52031e39	−0.957916	−0.478958	+	0.877838i	$0.658985\pi$
$570$	0	0
$571$	8.06636e38	0.0861894	0.0430947	−	0.999071i	$-0.486278\pi$
$571$	8.06636e38	0.0861894	0.0430947	+	0.999071i	$0.486278\pi$
$572$	−1.78479e39	−0.185928
$573$	0	0
$574$	−5.23933e39	−0.518864
$575$	−1.00732e39	−0.0972706
$576$	0	0
$577$	−1.60079e40	−1.46989	−0.734947	−	0.678125i	$-0.762793\pi$
$577$	−1.60079e40	−1.46989	−0.734947	+	0.678125i	$0.762793\pi$
$578$	−8.28280e39	−0.741691
$579$	0	0
$580$	−2.31221e39	−0.196935
$581$	1.97444e40	1.64017
$582$	0	0
$583$	1.82244e40	1.44032
$584$	−1.94941e40	−1.50285
$585$	0	0
$586$	6.52496e39	0.478699
$587$	7.25470e39	0.519239	0.259619	−	0.965711i	$-0.416403\pi$
$587$	7.25470e39	0.519239	0.259619	+	0.965711i	$0.416403\pi$
$588$	0	0
$589$	1.38142e40	0.941140
$590$	−1.15280e39	−0.0766302
$591$	0	0
$592$	−2.15386e39	−0.136318
$593$	−4.67095e39	−0.288478	−0.144239	−	0.989543i	$-0.546073\pi$
$593$	−4.67095e39	−0.288478	−0.144239	+	0.989543i	$0.546073\pi$
$594$	0	0
$595$	2.78797e39	0.163981
$596$	−1.33767e40	−0.767853
$597$	0	0
$598$	1.79987e39	0.0984178
$599$	−3.02320e40	−1.61353	−0.806766	−	0.590871i	$-0.798784\pi$
$599$	−3.02320e40	−1.61353	−0.806766	+	0.590871i	$0.798784\pi$
$600$	0	0
$601$	−1.75696e40	−0.893476	−0.446738	−	0.894665i	$-0.647414\pi$
$601$	−1.75696e40	−0.893476	−0.446738	+	0.894665i	$0.647414\pi$
$602$	8.42819e39	0.418394
$603$	0	0
$604$	−1.18322e40	−0.559798
$605$	−3.90748e37	−0.00180486
$606$	0	0
$607$	−2.78325e40	−1.22551	−0.612755	−	0.790273i	$-0.709939\pi$
$607$	−2.78325e40	−1.22551	−0.612755	+	0.790273i	$0.709939\pi$
$608$	1.97528e40	0.849234
$609$	0	0
$610$	−1.21478e40	−0.497984
$611$	1.59412e40	0.638152
$612$	0	0
$613$	2.63728e40	1.00688	0.503441	−	0.864030i	$-0.332067\pi$
$613$	2.63728e40	1.00688	0.503441	+	0.864030i	$0.332067\pi$
$614$	−9.37183e39	−0.349448
$615$	0	0
$616$	5.04222e40	1.79350
$617$	−9.21532e38	−0.0320166	−0.0160083	−	0.999872i	$-0.505096\pi$
$617$	−9.21532e38	−0.0320166	−0.0160083	+	0.999872i	$0.505096\pi$
$618$	0	0
$619$	−4.42763e40	−1.46777	−0.733883	−	0.679276i	$-0.762294\pi$
$619$	−4.42763e40	−1.46777	−0.733883	+	0.679276i	$0.762294\pi$
$620$	−9.73502e39	−0.315252
$621$	0	0
$622$	7.17333e39	0.221697
$623$	1.93507e40	0.584278
$624$	0	0
$625$	−2.00947e40	−0.579189
$626$	−2.90418e40	−0.817891
$627$	0	0
$628$	2.16945e39	0.0583356
$629$	−1.63922e39	−0.0430727
$630$	0	0
$631$	4.23643e40	1.06310	0.531551	−	0.847026i	$-0.321609\pi$
$631$	4.23643e40	1.06310	0.531551	+	0.847026i	$0.321609\pi$
$632$	5.28382e40	1.29584
$633$	0	0
$634$	−4.34225e40	−1.01723
$635$	2.18403e39	0.0500079
$636$	0	0
$637$	3.47026e40	0.759172
$638$	1.93325e40	0.413416
$639$	0	0
$640$	−2.43839e39	−0.0498303
$641$	4.13775e40	0.826652	0.413326	−	0.910583i	$-0.364367\pi$
$641$	4.13775e40	0.826652	0.413326	+	0.910583i	$0.364367\pi$
$642$	0	0
$643$	9.84722e40	1.88042	0.940209	−	0.340598i	$-0.110630\pi$
$643$	9.84722e40	1.88042	0.940209	+	0.340598i	$0.110630\pi$
$644$	1.17912e40	0.220147
$645$	0	0
$646$	−5.37981e39	−0.0960275
$647$	6.78001e39	0.118336	0.0591682	−	0.998248i	$-0.481155\pi$
$647$	6.78001e39	0.118336	0.0591682	+	0.998248i	$0.481155\pi$
$648$	0	0
$649$	−7.38667e39	−0.123282
$650$	−6.30957e39	−0.102981
$651$	0	0
$652$	1.03736e40	0.161934
$653$	−3.23913e40	−0.494524	−0.247262	−	0.968949i	$-0.579531\pi$
$653$	−3.23913e40	−0.494524	−0.247262	+	0.968949i	$0.579531\pi$
$654$	0	0
$655$	2.61544e40	0.381984
$656$	−1.09613e40	−0.156587
$657$	0	0
$658$	−1.36271e41	−1.86264
$659$	1.40926e40	0.188431	0.0942156	−	0.995552i	$-0.469966\pi$
$659$	1.40926e40	0.188431	0.0942156	+	0.995552i	$0.469966\pi$
$660$	0	0
$661$	−9.56737e40	−1.22425	−0.612127	−	0.790759i	$-0.709686\pi$
$661$	−9.56737e40	−1.22425	−0.612127	+	0.790759i	$0.709686\pi$
$662$	2.96940e40	0.371730
$663$	0	0
$664$	8.87333e40	1.06328
$665$	−1.25199e41	−1.46787
$666$	0	0
$667$	1.49409e40	0.167708
$668$	4.06714e40	0.446715
$669$	0	0
$670$	2.53764e40	0.266898
$671$	−7.78382e40	−0.801154
$672$	0	0
$673$	−1.43434e40	−0.141394	−0.0706972	−	0.997498i	$-0.522522\pi$
$673$	−1.43434e40	−0.141394	−0.0706972	+	0.997498i	$0.522522\pi$
$674$	2.37146e40	0.228796
$675$	0	0
$676$	3.83043e40	0.354014
$677$	−8.89678e40	−0.804817	−0.402408	−	0.915460i	$-0.631827\pi$
$677$	−8.89678e40	−0.804817	−0.402408	+	0.915460i	$0.631827\pi$
$678$	0	0
$679$	−2.84302e41	−2.46416
$680$	1.25294e40	0.106305
$681$	0	0
$682$	8.13947e40	0.661794
$683$	−1.49228e41	−1.18782	−0.593910	−	0.804531i	$-0.702417\pi$
$683$	−1.49228e41	−1.18782	−0.593910	+	0.804531i	$0.702417\pi$
$684$	0	0
$685$	−1.43021e41	−1.09116
$686$	−1.29014e41	−0.963687
$687$	0	0
$688$	1.76328e40	0.126266
$689$	8.82224e40	0.618586
$690$	0	0
$691$	2.54015e41	1.70776	0.853880	−	0.520469i	$-0.174243\pi$
$691$	2.54015e41	1.70776	0.853880	+	0.520469i	$0.174243\pi$
$692$	1.10725e40	0.0728969
$693$	0	0
$694$	1.19176e41	0.752447
$695$	1.29007e41	0.797686
$696$	0	0
$697$	−8.34219e39	−0.0494772
$698$	8.02868e40	0.466381
$699$	0	0
$700$	−4.13350e40	−0.230354
$701$	1.56415e40	0.0853824	0.0426912	−	0.999088i	$-0.486407\pi$
$701$	1.56415e40	0.0853824	0.0426912	+	0.999088i	$0.486407\pi$
$702$	0	0
$703$	7.36123e40	0.385565
$704$	1.89955e41	0.974649
$705$	0	0
$706$	−1.99600e41	−0.982860
$707$	1.39119e41	0.671129
$708$	0	0
$709$	−7.96882e40	−0.368998	−0.184499	−	0.982833i	$-0.559066\pi$
$709$	−7.96882e40	−0.368998	−0.184499	+	0.982833i	$0.559066\pi$
$710$	7.14057e40	0.323957
$711$	0	0
$712$	8.69638e40	0.378773
$713$	6.29051e40	0.268465
$714$	0	0
$715$	8.62959e40	0.353633
$716$	−1.53780e41	−0.617533
$717$	0	0
$718$	2.32812e41	0.897844
$719$	−6.70217e39	−0.0253306	−0.0126653	−	0.999920i	$-0.504032\pi$
$719$	−6.70217e39	−0.0253306	−0.0126653	+	0.999920i	$0.504032\pi$
$720$	0	0
$721$	4.01021e41	1.45581
$722$	3.01209e40	0.107171
$723$	0	0
$724$	−1.24457e41	−0.425412
$725$	−5.23765e40	−0.175483
$726$	0	0
$727$	−3.08325e41	−0.992565	−0.496283	−	0.868161i	$-0.665302\pi$
$727$	−3.08325e41	−0.992565	−0.496283	+	0.868161i	$0.665302\pi$
$728$	2.44088e41	0.770267
$729$	0	0
$730$	2.85203e41	0.864912
$731$	1.34196e40	0.0398967
$732$	0	0
$733$	−2.79480e41	−0.798626	−0.399313	−	0.916815i	$-0.630751\pi$
$733$	−2.79480e41	−0.798626	−0.399313	+	0.916815i	$0.630751\pi$
$734$	−2.63290e41	−0.737636
$735$	0	0
$736$	8.99476e40	0.242249
$737$	1.62601e41	0.429384
$738$	0	0
$739$	−4.36349e41	−1.10787	−0.553936	−	0.832560i	$-0.686875\pi$
$739$	−4.36349e41	−1.10787	−0.553936	+	0.832560i	$0.686875\pi$
$740$	−5.18754e40	−0.129152
$741$	0	0
$742$	−7.54155e41	−1.80553
$743$	1.06242e41	0.249437	0.124718	−	0.992192i	$-0.460197\pi$
$743$	1.06242e41	0.249437	0.124718	+	0.992192i	$0.460197\pi$
$744$	0	0
$745$	6.46774e41	1.46045
$746$	−1.90547e40	−0.0421977
$747$	0	0
$748$	2.42925e40	0.0517487
$749$	−1.40067e42	−2.92651
$750$	0	0
$751$	−1.53315e41	−0.308181	−0.154091	−	0.988057i	$-0.549245\pi$
$751$	−1.53315e41	−0.308181	−0.154091	+	0.988057i	$0.549245\pi$
$752$	−2.85095e41	−0.562122
$753$	0	0
$754$	9.35862e40	0.177553
$755$	5.72098e41	1.06473
$756$	0	0
$757$	−1.29063e41	−0.231160	−0.115580	−	0.993298i	$-0.536873\pi$
$757$	−1.29063e41	−0.231160	−0.115580	+	0.993298i	$0.536873\pi$
$758$	2.54100e41	0.446479
$759$	0	0
$760$	−5.62659e41	−0.951586
$761$	1.01002e42	1.67592	0.837962	−	0.545728i	$-0.183747\pi$
$761$	1.01002e42	1.67592	0.837962	+	0.545728i	$0.183747\pi$
$762$	0	0
$763$	1.59427e42	2.54657
$764$	−2.23322e41	−0.350008
$765$	0	0
$766$	1.01486e41	0.153140
$767$	−3.57580e40	−0.0529469
$768$	0	0
$769$	−8.10252e41	−1.15528	−0.577641	−	0.816291i	$-0.696027\pi$
$769$	−8.10252e41	−1.15528	−0.577641	+	0.816291i	$0.696027\pi$
$770$	−7.37688e41	−1.03218
$771$	0	0
$772$	−1.82077e40	−0.0245361
$773$	−3.13830e41	−0.415042	−0.207521	−	0.978231i	$-0.566539\pi$
$773$	−3.13830e41	−0.415042	−0.207521	+	0.978231i	$0.566539\pi$
$774$	0	0
$775$	−2.20519e41	−0.280912
$776$	−1.27768e42	−1.59745
$777$	0	0
$778$	1.11947e41	0.134836
$779$	3.74623e41	0.442895
$780$	0	0
$781$	4.57539e41	0.521180
$782$	−2.44978e40	−0.0273923
$783$	0	0
$784$	−6.20626e41	−0.668724
$785$	−1.04894e41	−0.110954
$786$	0	0
$787$	8.07245e41	0.822947	0.411473	−	0.911422i	$-0.365014\pi$
$787$	8.07245e41	0.822947	0.411473	+	0.911422i	$0.365014\pi$
$788$	−1.30532e41	−0.130643
$789$	0	0
$790$	−7.73034e41	−0.745771
$791$	2.37540e42	2.24997
$792$	0	0
$793$	−3.76805e41	−0.344077
$794$	1.18012e42	1.05811
$795$	0	0
$796$	−2.07667e41	−0.179526
$797$	−2.35976e41	−0.200319	−0.100160	−	0.994971i	$-0.531935\pi$
$797$	−2.35976e41	−0.200319	−0.100160	+	0.994971i	$0.531935\pi$
$798$	0	0
$799$	−2.16974e41	−0.177615
$800$	−3.15318e41	−0.253480
$801$	0	0
$802$	1.44526e42	1.12051
$803$	1.82746e42	1.39147
$804$	0	0
$805$	−5.70115e41	−0.418719
$806$	3.94022e41	0.284225
$807$	0	0
$808$	6.25216e41	0.435076
$809$	−2.25512e42	−1.54140	−0.770700	−	0.637198i	$-0.780093\pi$
$809$	−2.25512e42	−1.54140	−0.770700	+	0.637198i	$0.780093\pi$
$810$	0	0
$811$	8.17269e41	0.538967	0.269484	−	0.963005i	$-0.413147\pi$
$811$	8.17269e41	0.538967	0.269484	+	0.963005i	$0.413147\pi$
$812$	6.13098e41	0.397162
$813$	0	0
$814$	4.33731e41	0.271123
$815$	−5.01570e41	−0.307997
$816$	0	0
$817$	−6.02632e41	−0.357135
$818$	3.82560e41	0.222729
$819$	0	0
$820$	−2.64001e41	−0.148356
$821$	−8.86919e39	−0.00489675	−0.00244838	−	0.999997i	$-0.500779\pi$
$821$	−8.86919e39	−0.00489675	−0.00244838	+	0.999997i	$0.500779\pi$
$822$	0	0
$823$	4.50695e41	0.240207	0.120103	−	0.992761i	$-0.461677\pi$
$823$	4.50695e41	0.240207	0.120103	+	0.992761i	$0.461677\pi$
$824$	1.80223e42	0.943767
$825$	0	0
$826$	3.05672e41	0.154541
$827$	−1.64298e42	−0.816211	−0.408106	−	0.912935i	$-0.633810\pi$
$827$	−1.64298e42	−0.816211	−0.408106	+	0.912935i	$0.633810\pi$
$828$	0	0
$829$	9.28693e41	0.445483	0.222742	−	0.974878i	$-0.428499\pi$
$829$	9.28693e41	0.445483	0.222742	+	0.974878i	$0.428499\pi$
$830$	−1.29819e42	−0.611934
$831$	0	0
$832$	9.19552e41	0.418589
$833$	−4.72333e41	−0.211298
$834$	0	0
$835$	−1.96650e42	−0.849648
$836$	−1.09090e42	−0.463229
$837$	0	0
$838$	3.39858e41	0.139399
$839$	1.59653e42	0.643620	0.321810	−	0.946804i	$-0.395709\pi$
$839$	1.59653e42	0.643620	0.321810	+	0.946804i	$0.395709\pi$
$840$	0	0
$841$	−1.79082e42	−0.697444
$842$	−5.48183e41	−0.209846
$843$	0	0
$844$	−2.50737e41	−0.0927371
$845$	−1.85204e42	−0.673332
$846$	0	0
$847$	1.03609e40	0.00363989
$848$	−1.57778e42	−0.544887
$849$	0	0
$850$	8.58788e40	0.0286623
$851$	3.35205e41	0.109985
$852$	0	0
$853$	−2.50802e42	−0.795373	−0.397686	−	0.917521i	$-0.630187\pi$
$853$	−2.50802e42	−0.795373	−0.397686	+	0.917521i	$0.630187\pi$
$854$	3.22106e42	1.00429
$855$	0	0
$856$	−6.29476e42	−1.89719
$857$	−4.74569e42	−1.40630	−0.703149	−	0.711043i	$-0.748223\pi$
$857$	−4.74569e42	−1.40630	−0.703149	+	0.711043i	$0.748223\pi$
$858$	0	0
$859$	−1.19413e42	−0.342098	−0.171049	−	0.985263i	$-0.554716\pi$
$859$	−1.19413e42	−0.342098	−0.171049	+	0.985263i	$0.554716\pi$
$860$	4.24682e41	0.119629
$861$	0	0
$862$	4.74125e42	1.29133
$863$	−5.51388e42	−1.47673	−0.738364	−	0.674402i	$-0.764401\pi$
$863$	−5.51388e42	−1.47673	−0.738364	+	0.674402i	$0.764401\pi$
$864$	0	0
$865$	−5.35367e41	−0.138649
$866$	2.09716e42	0.534099
$867$	0	0
$868$	2.58130e42	0.635774
$869$	−4.95329e42	−1.19979
$870$	0	0
$871$	7.87134e41	0.184410
$872$	7.16481e42	1.65088
$873$	0	0
$874$	1.10012e42	0.245203
$875$	8.26312e42	1.81145
$876$	0	0
$877$	3.25016e42	0.689304	0.344652	−	0.938731i	$-0.387997\pi$
$877$	3.25016e42	0.689304	0.344652	+	0.938731i	$0.387997\pi$
$878$	−1.13049e42	−0.235828
$879$	0	0
$880$	−1.54333e42	−0.311501
$881$	−1.07364e42	−0.213162	−0.106581	−	0.994304i	$-0.533990\pi$
$881$	−1.07364e42	−0.213162	−0.106581	+	0.994304i	$0.533990\pi$
$882$	0	0
$883$	4.03526e42	0.775250	0.387625	−	0.921817i	$-0.373296\pi$
$883$	4.03526e42	0.775250	0.387625	+	0.921817i	$0.373296\pi$
$884$	1.17597e41	0.0222249
$885$	0	0
$886$	2.19495e42	0.401453
$887$	1.14783e42	0.206532	0.103266	−	0.994654i	$-0.467071\pi$
$887$	1.14783e42	0.206532	0.103266	+	0.994654i	$0.467071\pi$
$888$	0	0
$889$	−5.79108e41	−0.100852
$890$	−1.27230e42	−0.217989
$891$	0	0
$892$	9.17913e41	0.152234
$893$	9.74365e42	1.58992
$894$	0	0
$895$	7.43537e42	1.17454
$896$	6.46554e41	0.100494
$897$	0	0
$898$	−7.54366e42	−1.13521
$899$	3.27082e42	0.484330
$900$	0	0
$901$	−1.20078e42	−0.172169
$902$	2.20731e42	0.311436
$903$	0	0
$904$	1.06753e43	1.45860
$905$	6.01759e42	0.809129
$906$	0	0
$907$	−1.34894e43	−1.75666	−0.878328	−	0.478058i	$-0.841341\pi$
$907$	−1.34894e43	−1.75666	−0.878328	+	0.478058i	$0.841341\pi$
$908$	−6.06854e42	−0.777749
$909$	0	0
$910$	−3.57106e42	−0.443299
$911$	−3.01049e42	−0.367807	−0.183904	−	0.982944i	$-0.558873\pi$
$911$	−3.01049e42	−0.367807	−0.183904	+	0.982944i	$0.558873\pi$
$912$	0	0
$913$	−8.31825e42	−0.984477
$914$	−9.31747e42	−1.08537
$915$	0	0
$916$	−2.38704e42	−0.269386
$917$	−6.93499e42	−0.770355
$918$	0	0
$919$	6.28761e42	0.676723	0.338361	−	0.941016i	$-0.390127\pi$
$919$	6.28761e42	0.676723	0.338361	+	0.941016i	$0.390127\pi$
$920$	−2.56215e42	−0.271445
$921$	0	0
$922$	4.72163e42	0.484723
$923$	2.21489e42	0.223835
$924$	0	0
$925$	−1.17509e42	−0.115084
$926$	9.34937e42	0.901412
$927$	0	0
$928$	4.67692e42	0.437034
$929$	−1.66684e43	−1.53344	−0.766720	−	0.641982i	$-0.778112\pi$
$929$	−1.66684e43	−1.53344	−0.766720	+	0.641982i	$0.778112\pi$
$930$	0	0
$931$	2.12111e43	1.89144
$932$	4.53220e42	0.397904
$933$	0	0
$934$	−1.72315e43	−1.46654
$935$	−1.17456e42	−0.0984256
$936$	0	0
$937$	−1.87621e43	−1.52426	−0.762129	−	0.647425i	$-0.775846\pi$
$937$	−1.87621e43	−1.52426	−0.762129	+	0.647425i	$0.775846\pi$
$938$	−6.72869e42	−0.538257
$939$	0	0
$940$	−6.86646e42	−0.532573
$941$	−5.14783e42	−0.393165	−0.196582	−	0.980487i	$-0.562984\pi$
$941$	−5.14783e42	−0.393165	−0.196582	+	0.980487i	$0.562984\pi$
$942$	0	0
$943$	1.70590e42	0.126338
$944$	6.39501e41	0.0466388
$945$	0	0
$946$	−3.55077e42	−0.251131
$947$	2.96240e42	0.206333	0.103167	−	0.994664i	$-0.467103\pi$
$947$	2.96240e42	0.206333	0.103167	+	0.994664i	$0.467103\pi$
$948$	0	0
$949$	8.84653e42	0.597603
$950$	−3.85656e42	−0.256571
$951$	0	0
$952$	−3.32225e42	−0.214386
$953$	−1.30942e43	−0.832208	−0.416104	−	0.909317i	$-0.636605\pi$
$953$	−1.30942e43	−0.832208	−0.416104	+	0.909317i	$0.636605\pi$
$954$	0	0
$955$	1.07978e43	0.665713
$956$	−1.06282e43	−0.645390
$957$	0	0
$958$	2.89656e42	0.170640
$959$	3.79229e43	2.20055
$960$	0	0
$961$	−3.99088e42	−0.224688
$962$	2.09964e42	0.116441
$963$	0	0
$964$	−6.77340e42	−0.364493
$965$	8.80359e41	0.0466674
$966$	0	0
$967$	2.64169e43	1.35894	0.679468	−	0.733706i	$-0.262211\pi$
$967$	2.64169e43	1.35894	0.679468	+	0.733706i	$0.262211\pi$
$968$	4.65630e40	0.00235965
$969$	0	0
$970$	1.86928e43	0.919356
$971$	3.41602e43	1.65517	0.827583	−	0.561343i	$-0.189715\pi$
$971$	3.41602e43	1.65517	0.827583	+	0.561343i	$0.189715\pi$
$972$	0	0
$973$	−3.42069e43	−1.60871
$974$	−9.08670e42	−0.421019
$975$	0	0
$976$	6.73884e42	0.303084
$977$	−2.06179e43	−0.913636	−0.456818	−	0.889560i	$-0.651011\pi$
$977$	−2.06179e43	−0.913636	−0.456818	+	0.889560i	$0.651011\pi$
$978$	0	0
$979$	−8.15238e42	−0.350700
$980$	−1.49477e43	−0.633571
$981$	0	0
$982$	1.06010e43	0.436246
$983$	1.21841e43	0.494047	0.247023	−	0.969009i	$-0.420548\pi$
$983$	1.21841e43	0.494047	0.247023	+	0.969009i	$0.420548\pi$
$984$	0	0
$985$	6.31134e42	0.248483
$986$	−1.27379e42	−0.0494177
$987$	0	0
$988$	−5.28094e42	−0.198946
$989$	−2.74418e42	−0.101875
$990$	0	0
$991$	−1.94686e43	−0.701888	−0.350944	−	0.936397i	$-0.614139\pi$
$991$	−1.94686e43	−0.701888	−0.350944	+	0.936397i	$0.614139\pi$
$992$	1.96911e43	0.699600
$993$	0	0
$994$	−1.89337e43	−0.653329
$995$	1.00409e43	0.341457
$996$	0	0
$997$	2.12798e43	0.702891	0.351446	−	0.936208i	$-0.385690\pi$
$997$	2.12798e43	0.702891	0.351446	+	0.936208i	$0.385690\pi$
$998$	3.35674e43	1.09276
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.30.a.a.1.2		2
3.2	odd	2		1.30.a.a.1.1	✓	2
12.11	even	2		16.30.a.c.1.1		2
15.2	even	4		25.30.b.a.24.2		4
15.8	even	4		25.30.b.a.24.3		4
15.14	odd	2		25.30.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.30.a.a.1.1	✓	2	3.2	odd	2
9.30.a.a.1.2		2	1.1	even	1	trivial
16.30.a.c.1.1		2	12.11	even	2
25.30.a.a.1.2		2	15.14	odd	2
25.30.b.a.24.2		4	15.2	even	4
25.30.b.a.24.3		4	15.8	even	4

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+17433.9 q^{2} -2.32930e8 q^{4} +1.12623e10 q^{5} -2.98628e12 q^{7} -1.34206e13 q^{8} +O(q^{10})\)	\(q+17433.9 q^{2} -2.32930e8 q^{4} +1.12623e10 q^{5} -2.98628e12 q^{7} -1.34206e13 q^{8} +1.96347e14 q^{10} +1.25811e15 q^{11} +6.09036e15 q^{13} -5.20625e16 q^{14} -1.08921e17 q^{16} -8.28952e16 q^{17} +3.72257e18 q^{19} -2.62334e18 q^{20} +2.19338e19 q^{22} +1.69513e19 q^{23} -5.94240e19 q^{25} +1.06179e20 q^{26} +6.95594e20 q^{28} +8.81402e20 q^{29} +3.71093e21 q^{31} +5.30623e21 q^{32} -1.44519e21 q^{34} -3.36325e22 q^{35} +1.97746e22 q^{37} +6.48990e22 q^{38} -1.51148e23 q^{40} +1.00635e23 q^{41} -1.61886e23 q^{43} -2.93051e23 q^{44} +2.95527e23 q^{46} +2.61745e24 q^{47} +5.69796e24 q^{49} -1.03599e24 q^{50} -1.41863e24 q^{52} +1.44856e25 q^{53} +1.41693e25 q^{55} +4.00778e25 q^{56} +1.53663e25 q^{58} -5.87125e24 q^{59} -6.18692e25 q^{61} +6.46960e25 q^{62} +1.50985e26 q^{64} +6.85917e25 q^{65} +1.29243e26 q^{67} +1.93088e25 q^{68} -5.86346e26 q^{70} +3.63672e26 q^{71} +1.45255e27 q^{73} +3.44748e26 q^{74} -8.67098e26 q^{76} -3.75707e27 q^{77} -3.93709e27 q^{79} -1.22670e27 q^{80} +1.75447e27 q^{82} -6.61171e27 q^{83} -9.33594e26 q^{85} -2.82231e27 q^{86} -1.68846e28 q^{88} -6.47986e27 q^{89} -1.81875e28 q^{91} -3.94847e27 q^{92} +4.56324e28 q^{94} +4.19249e28 q^{95} +9.52029e28 q^{97} +9.93377e28 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8640 q^{2} - 89952256 q^{4} + 17477788500 q^{5} - 3020312682800 q^{7} - 3150297169920 q^{8}+O(q^{10}) \) 2 * q - 8640 * q^2 - 89952256 * q^4 + 17477788500 * q^5 - 3020312682800 * q^7 - 3150297169920 * q^8	\( 2 q - 8640 q^{2} - 89952256 q^{4} + 17477788500 q^{5} - 3020312682800 q^{7} - 3150297169920 q^{8} + 34285866768000 q^{10} + 20\!\cdots\!16 q^{11}+ \cdots + 18\!\cdots\!20 q^{98}+O(q^{100}) \) 2 * q - 8640 * q^2 - 89952256 * q^4 + 17477788500 * q^5 - 3020312682800 * q^7 - 3150297169920 * q^8 + 34285866768000 * q^10 + 2055380519588616 * q^11 + 17139371179332220 * q^13 - 51175123348059648 * q^14 - 453469082063208448 * q^16 + 664795927907749980 * q^17 + 1232169445452155080 * q^19 - 1734668101813248000 * q^20 + 1145797484912974080 * q^22 + 18588430504374379920 * q^23 - 207056854502617281250 * q^25 - 181912132597777755264 * q^26 + 690727602371844997120 * q^28 - 996096417765761595420 * q^29 - 1087258664181924030656 * q^31 + 8776107971762202869760 * q^32 - 20940413403809031000192 * q^34 - 33844046536902649068000 * q^35 + 98878127759336138311660 * q^37 + 129833487351109249470720 * q^38 - 87313163228088238080000 * q^40 + 106699837259610025757676 * q^41 + 510640433114974031366200 * q^43 - 179059414424913371086848 * q^44 + 252841215606439776920064 * q^46 + 4521107671109825795039520 * q^47 + 2479210387392854586312114 * q^49 + 2813370491836752543000000 * q^50 + 161134672249303679180800 * q^52 + 16141544629666790250663540 * q^53 + 19124657798421120971058000 * q^55 + 39728224533177935352299520 * q^56 + 64319996083339084169992320 * q^58 + 83497291515660150276062760 * q^59 - 15876762943230179624113316 * q^61 + 189803556071494720042936320 * q^62 + 245489542813624183222697984 * q^64 + 137266226551726798673511000 * q^65 + 24468754434128844890782120 * q^67 + 126211850011481106095677440 * q^68 - 580830557953085152481664000 * q^70 + 188428428253360067209577136 * q^71 + 995872721297568533052080980 * q^73 - 1717790650063115374837542528 * q^74 - 1223170019527541658110935040 * q^76 - 3784200478484579386131729600 * q^77 - 7218460852587735797823642080 * q^79 - 3368223393577622373924864000 * q^80 + 1596346485209467674952913280 * q^82 - 2210846225248155523694669640 * q^83 + 3713635892367734904614943000 * q^85 - 20357697303796411232450244864 * q^86 - 8696387677835767416210063360 * q^88 - 5872964746600969363962031860 * q^89 - 18563550073842319069958420896 * q^91 - 3714393183413159199429918720 * q^92 - 4003342107705068447401638912 * q^94 + 26445947767121183571013410000 * q^95 + 109649982219471997093227005380 * q^97 + 183262972410594366168864121920 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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