LMFDB - Embedded newform 9.20.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,20,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, 20, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 20 $
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:	$20.5935026901$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{87481}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 21870 $ x^2 - x - 21870
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-147.386$ 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)

$f(q)$	$=$	$q+536.316 q^{2} -236654. q^{4} +683163. q^{5} +1.13677e8 q^{7} -4.08105e8 q^{8} +O(q^{10})$	\(q+536.316 q^{2} -236654. q^{4} +683163. q^{5} +1.13677e8 q^{7} -4.08105e8 q^{8} +3.66391e8 q^{10} -6.43152e9 q^{11} -5.75132e10 q^{13} +6.09670e10 q^{14} -9.47984e10 q^{16} -6.85083e11 q^{17} +1.22275e12 q^{19} -1.61673e11 q^{20} -3.44932e12 q^{22} -5.02230e12 q^{23} -1.86068e13 q^{25} -3.08453e13 q^{26} -2.69022e13 q^{28} -1.53748e14 q^{29} +3.92872e13 q^{31} +1.63123e14 q^{32} -3.67421e14 q^{34} +7.76602e13 q^{35} +1.35709e15 q^{37} +6.55779e14 q^{38} -2.78802e14 q^{40} +5.75410e14 q^{41} +3.36667e14 q^{43} +1.52204e15 q^{44} -2.69354e15 q^{46} +6.99998e15 q^{47} +1.52367e15 q^{49} -9.97910e15 q^{50} +1.36107e16 q^{52} -1.69895e16 q^{53} -4.39377e15 q^{55} -4.63923e16 q^{56} -8.24573e16 q^{58} +2.70689e16 q^{59} -5.11533e16 q^{61} +2.10704e16 q^{62} +1.37187e17 q^{64} -3.92909e16 q^{65} +2.07437e17 q^{67} +1.62127e17 q^{68} +4.16504e16 q^{70} +2.35123e17 q^{71} +7.43858e16 q^{73} +7.27828e17 q^{74} -2.89368e17 q^{76} -7.31118e17 q^{77} -6.98697e17 q^{79} -6.47627e16 q^{80} +3.08601e17 q^{82} -3.25532e18 q^{83} -4.68023e17 q^{85} +1.80560e17 q^{86} +2.62473e18 q^{88} +1.43575e18 q^{89} -6.53796e18 q^{91} +1.18855e18 q^{92} +3.75420e18 q^{94} +8.35337e17 q^{95} +1.66911e18 q^{97} +8.17166e17 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 702 q^{2} + 772484 q^{4} - 6016140 q^{5} + 113892064 q^{7} - 1008501624 q^{8}+O(q^{10}) $ 2 * q - 702 * q^2 + 772484 * q^4 - 6016140 * q^5 + 113892064 * q^7 - 1008501624 * q^8	$ 2 q - 702 q^{2} + 772484 q^{4} - 6016140 q^{5} + 113892064 q^{7} - 1008501624 q^{8} + 8662242420 q^{10} + 6650071272 q^{11} - 44072356148 q^{13} + 60701219424 q^{14} + 119603620880 q^{16} - 336281471748 q^{17} + 602118925096 q^{19} - 6922191196440 q^{20} - 19648459326744 q^{22} - 2368252165968 q^{23} + 7200399078350 q^{25} - 47489309789364 q^{26} - 26685589805888 q^{28} - 280977251970492 q^{29} + 41610149253712 q^{31} + 212406109003296 q^{32} - 799347349171332 q^{34} + 76222408017600 q^{35} + 637994163989884 q^{37} + 14\!\cdots\!32 q^{38}+ \cdots + 14\!\cdots\!02 q^{98}+O(q^{100}) $ 2 * q - 702 * q^2 + 772484 * q^4 - 6016140 * q^5 + 113892064 * q^7 - 1008501624 * q^8 + 8662242420 * q^10 + 6650071272 * q^11 - 44072356148 * q^13 + 60701219424 * q^14 + 119603620880 * q^16 - 336281471748 * q^17 + 602118925096 * q^19 - 6922191196440 * q^20 - 19648459326744 * q^22 - 2368252165968 * q^23 + 7200399078350 * q^25 - 47489309789364 * q^26 - 26685589805888 * q^28 - 280977251970492 * q^29 + 41610149253712 * q^31 + 212406109003296 * q^32 - 799347349171332 * q^34 + 76222408017600 * q^35 + 637994163989884 * q^37 + 1424314643816232 * q^38 + 3743437831857360 * q^40 - 1150038430280532 * q^41 + 2820518953538200 * q^43 + 14723164414050768 * q^44 - 5980094010800208 * q^46 + 5603091319500480 * q^47 - 9875183230193070 * q^49 - 41936530073800050 * q^50 + 27174417188397208 * q^52 - 27537868857647628 * q^53 - 92031302621896560 * q^55 - 46521172561587840 * q^56 + 75092921304821316 * q^58 + 55153474421835816 * q^59 - 87192569066205620 * q^61 + 18193883108252112 * q^62 - 36250046218631104 * q^64 - 129335487918703560 * q^65 + 499299710877878248 * q^67 + 514116238109034744 * q^68 + 43430850442699200 * q^70 - 84915048436970544 * q^71 - 241433711161728332 * q^73 + 1618295867440077564 * q^74 - 915668569473570224 * q^76 - 728310910203957888 * q^77 + 1131591466033523440 * q^79 - 1501106673028491360 * q^80 + 2445251486788059948 * q^82 - 1607743276003583784 * q^83 - 2804751519619294440 * q^85 - 2895233411994836328 * q^86 - 5229410429487705696 * q^88 - 4322797626369576276 * q^89 - 6535073681312344768 * q^91 + 3866849612692780896 * q^92 + 5483985680095257024 * q^94 + 4993123012930175760 * q^95 + 7902201235299458308 * q^97 + 14932538668319232402 * 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 $

$2$	536.316	0.740688	0.370344	−	0.928895i	$-0.379240\pi$
$2$	536.316	0.740688	0.370344	+	0.928895i	$0.379240\pi$
$3$	0	0
$3$	0	0
$4$	−236654.	−0.451381
$5$	683163.	0.156426	0.0782131	−	0.996937i	$-0.475079\pi$
$5$	683163.	0.156426	0.0782131	+	0.996937i	$0.475079\pi$
$6$	0	0
$7$	1.13677e8	1.06474	0.532369	−	0.846512i	$-0.321302\pi$
$7$	1.13677e8	1.06474	0.532369	+	0.846512i	$0.321302\pi$
$8$	−4.08105e8	−1.07502
$9$	0	0
$10$	3.66391e8	0.115863
$11$	−6.43152e9	−0.822400	−0.411200	−	0.911545i	$-0.634890\pi$
$11$	−6.43152e9	−0.822400	−0.411200	+	0.911545i	$0.634890\pi$
$12$	0	0
$13$	−5.75132e10	−1.50420	−0.752101	−	0.659048i	$-0.770959\pi$
$13$	−5.75132e10	−1.50420	−0.752101	+	0.659048i	$0.770959\pi$
$14$	6.09670e10	0.788639
$15$	0	0
$16$	−9.47984e10	−0.344874
$17$	−6.85083e11	−1.40113	−0.700565	−	0.713588i	$-0.747069\pi$
$17$	−6.85083e11	−1.40113	−0.700565	+	0.713588i	$0.747069\pi$
$18$	0	0
$19$	1.22275e12	0.869317	0.434658	−	0.900595i	$-0.356869\pi$
$19$	1.22275e12	0.869317	0.434658	+	0.900595i	$0.356869\pi$
$20$	−1.61673e11	−0.0706078
$21$	0	0
$22$	−3.44932e12	−0.609142
$23$	−5.02230e12	−0.581418	−0.290709	−	0.956811i	$-0.593891\pi$
$23$	−5.02230e12	−0.581418	−0.290709	+	0.956811i	$0.593891\pi$
$24$	0	0
$25$	−1.86068e13	−0.975531
$26$	−3.08453e13	−1.11414
$27$	0	0
$28$	−2.69022e13	−0.480603
$29$	−1.53748e14	−1.96801	−0.984006	−	0.178134i	$-0.942994\pi$
$29$	−1.53748e14	−1.96801	−0.984006	+	0.178134i	$0.942994\pi$
$30$	0	0
$31$	3.92872e13	0.266880	0.133440	−	0.991057i	$-0.457398\pi$
$31$	3.92872e13	0.266880	0.133440	+	0.991057i	$0.457398\pi$
$32$	1.63123e14	0.819576
$33$	0	0
$34$	−3.67421e14	−1.03780
$35$	7.76602e13	0.166553
$36$	0	0
$37$	1.35709e15	1.71669	0.858346	−	0.513072i	$-0.171493\pi$
$37$	1.35709e15	1.71669	0.858346	+	0.513072i	$0.171493\pi$
$38$	6.55779e14	0.643893
$39$	0	0
$40$	−2.78802e14	−0.168161
$41$	5.75410e14	0.274493	0.137246	−	0.990537i	$-0.456175\pi$
$41$	5.75410e14	0.274493	0.137246	+	0.990537i	$0.456175\pi$
$42$	0	0
$43$	3.36667e14	0.102153	0.0510763	−	0.998695i	$-0.483735\pi$
$43$	3.36667e14	0.102153	0.0510763	+	0.998695i	$0.483735\pi$
$44$	1.52204e15	0.371215
$45$	0	0
$46$	−2.69354e15	−0.430650
$47$	6.99998e15	0.912362	0.456181	−	0.889887i	$-0.349217\pi$
$47$	6.99998e15	0.912362	0.456181	+	0.889887i	$0.349217\pi$
$48$	0	0
$49$	1.52367e15	0.133668
$50$	−9.97910e15	−0.722564
$51$	0	0
$52$	1.36107e16	0.678968
$53$	−1.69895e16	−0.707231	−0.353615	−	0.935391i	$-0.615048\pi$
$53$	−1.69895e16	−0.707231	−0.353615	+	0.935391i	$0.615048\pi$
$54$	0	0
$55$	−4.39377e15	−0.128645
$56$	−4.63923e16	−1.14462
$57$	0	0
$58$	−8.24573e16	−1.45768
$59$	2.70689e16	0.406796	0.203398	−	0.979096i	$-0.434802\pi$
$59$	2.70689e16	0.406796	0.203398	+	0.979096i	$0.434802\pi$
$60$	0	0
$61$	−5.11533e16	−0.560068	−0.280034	−	0.959990i	$-0.590346\pi$
$61$	−5.11533e16	−0.560068	−0.280034	+	0.959990i	$0.590346\pi$
$62$	2.10704e16	0.197675
$63$	0	0
$64$	1.37187e17	0.951925
$65$	−3.92909e16	−0.235296
$66$	0	0
$67$	2.07437e17	0.931487	0.465743	−	0.884920i	$-0.345787\pi$
$67$	2.07437e17	0.931487	0.465743	+	0.884920i	$0.345787\pi$
$68$	1.62127e17	0.632443
$69$	0	0
$70$	4.16504e16	0.123364
$71$	2.35123e17	0.608613	0.304306	−	0.952574i	$-0.401575\pi$
$71$	2.35123e17	0.608613	0.304306	+	0.952574i	$0.401575\pi$
$72$	0	0
$73$	7.43858e16	0.147885	0.0739423	−	0.997263i	$-0.476442\pi$
$73$	7.43858e16	0.147885	0.0739423	+	0.997263i	$0.476442\pi$
$74$	7.27828e17	1.27153
$75$	0	0
$76$	−2.89368e17	−0.392393
$77$	−7.31118e17	−0.875641
$78$	0	0
$79$	−6.98697e17	−0.655890	−0.327945	−	0.944697i	$-0.606356\pi$
$79$	−6.98697e17	−0.655890	−0.327945	+	0.944697i	$0.606356\pi$
$80$	−6.47627e16	−0.0539474
$81$	0	0
$82$	3.08601e17	0.203314
$83$	−3.25532e18	−1.91140	−0.955701	−	0.294338i	$-0.904901\pi$
$83$	−3.25532e18	−1.91140	−0.955701	+	0.294338i	$0.904901\pi$
$84$	0	0
$85$	−4.68023e17	−0.219173
$86$	1.80560e17	0.0756633
$87$	0	0
$88$	2.62473e18	0.884097
$89$	1.43575e18	0.434385	0.217193	−	0.976129i	$-0.430310\pi$
$89$	1.43575e18	0.434385	0.217193	+	0.976129i	$0.430310\pi$
$90$	0	0
$91$	−6.53796e18	−1.60158
$92$	1.18855e18	0.262441
$93$	0	0
$94$	3.75420e18	0.675776
$95$	8.35337e17	0.135984
$96$	0	0
$97$	1.66911e18	0.222922	0.111461	−	0.993769i	$-0.464447\pi$
$97$	1.66911e18	0.222922	0.111461	+	0.993769i	$0.464447\pi$
$98$	8.17166e17	0.0990062
$99$	0	0
$100$	4.40336e18	0.440336
$101$	−9.99068e18	−0.908955	−0.454477	−	0.890758i	$-0.650174\pi$
$101$	−9.99068e18	−0.908955	−0.454477	+	0.890758i	$0.650174\pi$
$102$	0	0
$103$	1.17501e18	0.0887333	0.0443666	−	0.999015i	$-0.485873\pi$
$103$	1.17501e18	0.0887333	0.0443666	+	0.999015i	$0.485873\pi$
$104$	2.34714e19	1.61705
$105$	0	0
$106$	−9.11176e18	−0.523837
$107$	1.73164e19	0.910568	0.455284	−	0.890346i	$-0.349538\pi$
$107$	1.73164e19	0.910568	0.455284	+	0.890346i	$0.349538\pi$
$108$	0	0
$109$	1.57748e19	0.695685	0.347842	−	0.937553i	$-0.386914\pi$
$109$	1.57748e19	0.695685	0.347842	+	0.937553i	$0.386914\pi$
$110$	−2.35645e18	−0.0952857
$111$	0	0
$112$	−1.07764e19	−0.367201
$113$	−4.78817e19	−1.49942	−0.749712	−	0.661764i	$-0.769808\pi$
$113$	−4.78817e19	−1.49942	−0.749712	+	0.661764i	$0.769808\pi$
$114$	0	0
$115$	−3.43105e18	−0.0909490
$116$	3.63850e19	0.888323
$117$	0	0
$118$	1.45175e19	0.301309
$119$	−7.78785e19	−1.49184
$120$	0	0
$121$	−1.97947e19	−0.323659
$122$	−2.74343e19	−0.414836
$123$	0	0
$124$	−9.29747e18	−0.120464
$125$	−2.57418e19	−0.309025
$126$	0	0
$127$	−1.25232e20	−1.29294	−0.646472	−	0.762938i	$-0.723756\pi$
$127$	−1.25232e20	−1.29294	−0.646472	+	0.762938i	$0.723756\pi$
$128$	−1.19478e19	−0.114497
$129$	0	0
$130$	−2.10723e19	−0.174281
$131$	2.09329e20	1.60972	0.804862	−	0.593462i	$-0.202239\pi$
$131$	2.09329e20	1.60972	0.804862	+	0.593462i	$0.202239\pi$
$132$	0	0
$133$	1.38999e20	0.925595
$134$	1.11252e20	0.689941
$135$	0	0
$136$	2.79586e20	1.50624
$137$	−1.53205e20	−0.769888	−0.384944	−	0.922940i	$-0.625779\pi$
$137$	−1.53205e20	−0.769888	−0.384944	+	0.922940i	$0.625779\pi$
$138$	0	0
$139$	−2.54374e19	−0.111386	−0.0556932	−	0.998448i	$-0.517737\pi$
$139$	−2.54374e19	−0.111386	−0.0556932	+	0.998448i	$0.517737\pi$
$140$	−1.83786e19	−0.0751788
$141$	0	0
$142$	1.26100e20	0.450792
$143$	3.69897e20	1.23705
$144$	0	0
$145$	−1.05035e20	−0.307849
$146$	3.98942e19	0.109536
$147$	0	0
$148$	−3.21160e20	−0.774882
$149$	−1.67659e20	−0.379453	−0.189727	−	0.981837i	$-0.560760\pi$
$149$	−1.67659e20	−0.379453	−0.189727	+	0.981837i	$0.560760\pi$
$150$	0	0
$151$	−4.29868e20	−0.857144	−0.428572	−	0.903508i	$-0.640983\pi$
$151$	−4.29868e20	−0.857144	−0.428572	+	0.903508i	$0.640983\pi$
$152$	−4.99010e20	−0.934533
$153$	0	0
$154$	−3.92110e20	−0.648577
$155$	2.68396e19	0.0417470
$156$	0	0
$157$	9.16306e20	1.26181	0.630905	−	0.775860i	$-0.282684\pi$
$157$	9.16306e20	1.26181	0.630905	+	0.775860i	$0.282684\pi$
$158$	−3.74722e20	−0.485810
$159$	0	0
$160$	1.11439e20	0.128203
$161$	−5.70923e20	−0.619058
$162$	0	0
$163$	4.50070e20	0.434008	0.217004	−	0.976171i	$-0.430372\pi$
$163$	4.50070e20	0.434008	0.217004	+	0.976171i	$0.430372\pi$
$164$	−1.36173e20	−0.123901
$165$	0	0
$166$	−1.74588e21	−1.41575
$167$	1.62414e20	0.124399	0.0621993	−	0.998064i	$-0.480189\pi$
$167$	1.62414e20	0.124399	0.0621993	+	0.998064i	$0.480189\pi$
$168$	0	0
$169$	1.84585e21	1.26262
$170$	−2.51008e20	−0.162339
$171$	0	0
$172$	−7.96734e19	−0.0461098
$173$	3.29538e21	1.80496	0.902481	−	0.430731i	$-0.141744\pi$
$173$	3.29538e21	1.80496	0.902481	+	0.430731i	$0.141744\pi$
$174$	0	0
$175$	−2.11517e21	−1.03869
$176$	6.09697e20	0.283625
$177$	0	0
$178$	7.70017e20	0.321744
$179$	9.81720e20	0.388941	0.194471	−	0.980908i	$-0.437701\pi$
$179$	9.81720e20	0.388941	0.194471	+	0.980908i	$0.437701\pi$
$180$	0	0
$181$	1.51701e20	0.0540807	0.0270403	−	0.999634i	$-0.491392\pi$
$181$	1.51701e20	0.0540807	0.0270403	+	0.999634i	$0.491392\pi$
$182$	−3.50641e21	−1.18627
$183$	0	0
$184$	2.04963e21	0.625037
$185$	9.27114e20	0.268535
$186$	0	0
$187$	4.40612e21	1.15229
$188$	−1.65657e21	−0.411823
$189$	0	0
$190$	4.48004e20	0.100722
$191$	5.13044e21	1.09733	0.548666	−	0.836042i	$-0.315136\pi$
$191$	5.13044e21	1.09733	0.548666	+	0.836042i	$0.315136\pi$
$192$	0	0
$193$	−9.72873e21	−1.88478	−0.942392	−	0.334510i	$-0.891429\pi$
$193$	−9.72873e21	−1.88478	−0.942392	+	0.334510i	$0.891429\pi$
$194$	8.95169e20	0.165116
$195$	0	0
$196$	−3.60581e20	−0.0603351
$197$	−7.68506e21	−1.22523	−0.612616	−	0.790381i	$-0.709883\pi$
$197$	−7.68506e21	−1.22523	−0.612616	+	0.790381i	$0.709883\pi$
$198$	0	0
$199$	4.55786e21	0.660172	0.330086	−	0.943951i	$-0.392922\pi$
$199$	4.55786e21	0.660172	0.330086	+	0.943951i	$0.392922\pi$
$200$	7.59351e21	1.04872
$201$	0	0
$202$	−5.35816e21	−0.673252
$203$	−1.74777e22	−2.09542
$204$	0	0
$205$	3.93099e20	0.0429378
$206$	6.30174e20	0.0657237
$207$	0	0
$208$	5.45216e21	0.518761
$209$	−7.86413e21	−0.714926
$210$	0	0
$211$	−1.71334e22	−1.42285	−0.711426	−	0.702761i	$-0.751950\pi$
$211$	−1.71334e22	−1.42285	−0.711426	+	0.702761i	$0.751950\pi$
$212$	4.02064e21	0.319230
$213$	0	0
$214$	9.28707e21	0.674447
$215$	2.29998e20	0.0159794
$216$	0	0
$217$	4.46607e21	0.284157
$218$	8.46028e21	0.515286
$219$	0	0
$220$	1.03980e21	0.0580678
$221$	3.94014e22	2.10758
$222$	0	0
$223$	3.17895e22	1.56095	0.780473	−	0.625189i	$-0.214978\pi$
$223$	3.17895e22	1.56095	0.780473	+	0.625189i	$0.214978\pi$
$224$	1.85434e22	0.872634
$225$	0	0
$226$	−2.56797e22	−1.11061
$227$	−2.55774e22	−1.06074	−0.530372	−	0.847765i	$-0.677948\pi$
$227$	−2.55774e22	−1.06074	−0.530372	+	0.847765i	$0.677948\pi$
$228$	0	0
$229$	−2.23445e22	−0.852576	−0.426288	−	0.904588i	$-0.640179\pi$
$229$	−2.23445e22	−0.852576	−0.426288	+	0.904588i	$0.640179\pi$
$230$	−1.84013e21	−0.0673648
$231$	0	0
$232$	6.27452e22	2.11565
$233$	2.52369e21	0.0816874	0.0408437	−	0.999166i	$-0.486995\pi$
$233$	2.52369e21	0.0816874	0.0408437	+	0.999166i	$0.486995\pi$
$234$	0	0
$235$	4.78213e21	0.142717
$236$	−6.40595e21	−0.183620
$237$	0	0
$238$	−4.17675e22	−1.10499
$239$	−3.93020e22	−0.999158	−0.499579	−	0.866268i	$-0.666512\pi$
$239$	−3.93020e22	−0.999158	−0.499579	+	0.866268i	$0.666512\pi$
$240$	0	0
$241$	−1.99943e22	−0.469618	−0.234809	−	0.972042i	$-0.575447\pi$
$241$	−1.99943e22	−0.469618	−0.234809	+	0.972042i	$0.575447\pi$
$242$	−1.06162e22	−0.239730
$243$	0	0
$244$	1.21056e22	0.252804
$245$	1.04091e21	0.0209091
$246$	0	0
$247$	−7.03242e22	−1.30763
$248$	−1.60333e22	−0.286901
$249$	0	0
$250$	−1.38057e22	−0.228891
$251$	4.94152e22	0.788788	0.394394	−	0.918942i	$-0.370955\pi$
$251$	4.94152e22	0.788788	0.394394	+	0.918942i	$0.370955\pi$
$252$	0	0
$253$	3.23010e22	0.478158
$254$	−6.71638e22	−0.957668
$255$	0	0
$256$	−7.83332e22	−1.03673
$257$	−1.79354e22	−0.228742	−0.114371	−	0.993438i	$-0.536485\pi$
$257$	−1.79354e22	−0.228742	−0.114371	+	0.993438i	$0.536485\pi$
$258$	0	0
$259$	1.54271e23	1.82783
$260$	9.29834e21	0.106208
$261$	0	0
$262$	1.12266e23	1.19230
$263$	−2.64384e22	−0.270804	−0.135402	−	0.990791i	$-0.543233\pi$
$263$	−2.64384e22	−0.270804	−0.135402	+	0.990791i	$0.543233\pi$
$264$	0	0
$265$	−1.16066e22	−0.110629
$266$	7.45473e22	0.685577
$267$	0	0
$268$	−4.90908e22	−0.420455
$269$	6.26512e22	0.517944	0.258972	−	0.965885i	$-0.416616\pi$
$269$	6.26512e22	0.517944	0.258972	+	0.965885i	$0.416616\pi$
$270$	0	0
$271$	−8.23488e22	−0.634525	−0.317263	−	0.948338i	$-0.602764\pi$
$271$	−8.23488e22	−0.634525	−0.317263	+	0.948338i	$0.602764\pi$
$272$	6.49448e22	0.483214
$273$	0	0
$274$	−8.21662e22	−0.570247
$275$	1.19670e23	0.802276
$276$	0	0
$277$	1.42704e23	0.893057	0.446528	−	0.894769i	$-0.352660\pi$
$277$	1.42704e23	0.893057	0.446528	+	0.894769i	$0.352660\pi$
$278$	−1.36425e22	−0.0825026
$279$	0	0
$280$	−3.16935e22	−0.179048
$281$	−4.36986e22	−0.238648	−0.119324	−	0.992855i	$-0.538073\pi$
$281$	−4.36986e22	−0.238648	−0.119324	+	0.992855i	$0.538073\pi$
$282$	0	0
$283$	−2.42461e23	−1.23786	−0.618929	−	0.785447i	$-0.712433\pi$
$283$	−2.42461e23	−1.23786	−0.618929	+	0.785447i	$0.712433\pi$
$284$	−5.56427e22	−0.274716
$285$	0	0
$286$	1.98382e23	0.916272
$287$	6.54112e22	0.292263
$288$	0	0
$289$	2.30266e23	0.963166
$290$	−5.63318e22	−0.228020
$291$	0	0
$292$	−1.76037e22	−0.0667522
$293$	−1.65262e22	−0.0606638	−0.0303319	−	0.999540i	$-0.509656\pi$
$293$	−1.65262e22	−0.0606638	−0.0303319	+	0.999540i	$0.509656\pi$
$294$	0	0
$295$	1.84925e22	0.0636335
$296$	−5.53835e23	−1.84548
$297$	0	0
$298$	−8.99184e22	−0.281057
$299$	2.88849e23	0.874570
$300$	0	0
$301$	3.82714e22	0.108766
$302$	−2.30545e23	−0.634876
$303$	0	0
$304$	−1.15915e23	−0.299805
$305$	−3.49461e22	−0.0876092
$306$	0	0
$307$	−7.14354e23	−1.68306	−0.841528	−	0.540213i	$-0.818344\pi$
$307$	−7.14354e23	−1.68306	−0.841528	+	0.540213i	$0.818344\pi$
$308$	1.73022e23	0.395247
$309$	0	0
$310$	1.43945e22	0.0309215
$311$	−3.74882e23	−0.781037	−0.390518	−	0.920595i	$-0.627704\pi$
$311$	−3.74882e23	−0.781037	−0.390518	+	0.920595i	$0.627704\pi$
$312$	0	0
$313$	−2.04132e23	−0.400166	−0.200083	−	0.979779i	$-0.564121\pi$
$313$	−2.04132e23	−0.400166	−0.200083	+	0.979779i	$0.564121\pi$
$314$	4.91429e23	0.934607
$315$	0	0
$316$	1.65349e23	0.296056
$317$	2.74437e23	0.476848	0.238424	−	0.971161i	$-0.423369\pi$
$317$	2.74437e23	0.476848	0.238424	+	0.971161i	$0.423369\pi$
$318$	0	0
$319$	9.88832e23	1.61849
$320$	9.37210e22	0.148906
$321$	0	0
$322$	−3.06195e23	−0.458529
$323$	−8.37684e23	−1.21803
$324$	0	0
$325$	1.07014e24	1.46739
$326$	2.41379e23	0.321464
$327$	0	0
$328$	−2.34828e23	−0.295085
$329$	7.95740e23	0.971427
$330$	0	0
$331$	−2.31592e23	−0.266906	−0.133453	−	0.991055i	$-0.542607\pi$
$331$	−2.31592e23	−0.266906	−0.133453	+	0.991055i	$0.542607\pi$
$332$	7.70384e23	0.862771
$333$	0	0
$334$	8.71049e22	0.0921406
$335$	1.41714e23	0.145709
$336$	0	0
$337$	−1.11237e23	−0.108085	−0.0540425	−	0.998539i	$-0.517211\pi$
$337$	−1.11237e23	−0.108085	−0.0540425	+	0.998539i	$0.517211\pi$
$338$	9.89960e23	0.935209
$339$	0	0
$340$	1.10759e23	0.0989307
$341$	−2.52677e23	−0.219482
$342$	0	0
$343$	−1.12259e24	−0.922417
$344$	−1.37395e23	−0.109816
$345$	0	0
$346$	1.76737e24	1.33691
$347$	−2.05609e24	−1.51326	−0.756629	−	0.653844i	$-0.773155\pi$
$347$	−2.05609e24	−1.51326	−0.756629	+	0.653844i	$0.773155\pi$
$348$	0	0
$349$	−1.75492e24	−1.22297	−0.611487	−	0.791255i	$-0.709428\pi$
$349$	−1.75492e24	−1.22297	−0.611487	+	0.791255i	$0.709428\pi$
$350$	−1.13440e24	−0.769342
$351$	0	0
$352$	−1.04913e24	−0.674019
$353$	−8.21430e23	−0.513702	−0.256851	−	0.966451i	$-0.582685\pi$
$353$	−8.21430e23	−0.513702	−0.256851	+	0.966451i	$0.582685\pi$
$354$	0	0
$355$	1.60627e23	0.0952029
$356$	−3.39776e23	−0.196073
$357$	0	0
$358$	5.26512e23	0.288084
$359$	−5.29683e23	−0.282240	−0.141120	−	0.989992i	$-0.545070\pi$
$359$	−5.29683e23	−0.282240	−0.141120	+	0.989992i	$0.545070\pi$
$360$	0	0
$361$	−4.83305e23	−0.244289
$362$	8.13596e22	0.0400569
$363$	0	0
$364$	1.54723e24	0.722923
$365$	5.08176e22	0.0231330
$366$	0	0
$367$	−2.30180e24	−0.994809	−0.497404	−	0.867519i	$-0.665713\pi$
$367$	−2.30180e24	−0.994809	−0.497404	+	0.867519i	$0.665713\pi$
$368$	4.76106e23	0.200516
$369$	0	0
$370$	4.97225e23	0.198901
$371$	−1.93133e24	−0.753016
$372$	0	0
$373$	1.64953e24	0.611120	0.305560	−	0.952173i	$-0.401156\pi$
$373$	1.64953e24	0.611120	0.305560	+	0.952173i	$0.401156\pi$
$374$	2.36307e24	0.853487
$375$	0	0
$376$	−2.85673e24	−0.980808
$377$	8.84253e24	2.96029
$378$	0	0
$379$	3.36454e24	1.07116	0.535579	−	0.844485i	$-0.320094\pi$
$379$	3.36454e24	1.07116	0.535579	+	0.844485i	$0.320094\pi$
$380$	−1.97685e23	−0.0613805
$381$	0	0
$382$	2.75154e24	0.812780
$383$	−1.55219e24	−0.447257	−0.223628	−	0.974674i	$-0.571790\pi$
$383$	−1.55219e24	−0.447257	−0.223628	+	0.974674i	$0.571790\pi$
$384$	0	0
$385$	−4.99473e23	−0.136973
$386$	−5.21767e24	−1.39604
$387$	0	0
$388$	−3.95000e23	−0.100623
$389$	1.19996e23	0.0298295	0.0149148	−	0.999889i	$-0.495252\pi$
$389$	1.19996e23	0.0298295	0.0149148	+	0.999889i	$0.495252\pi$
$390$	0	0
$391$	3.44070e24	0.814643
$392$	−6.21815e23	−0.143696
$393$	0	0
$394$	−4.12162e24	−0.907515
$395$	−4.77324e23	−0.102598
$396$	0	0
$397$	−1.23812e24	−0.253661	−0.126831	−	0.991924i	$-0.540480\pi$
$397$	−1.23812e24	−0.253661	−0.126831	+	0.991924i	$0.540480\pi$
$398$	2.44445e24	0.488981
$399$	0	0
$400$	1.76389e24	0.336436
$401$	6.55287e24	1.22056	0.610281	−	0.792185i	$-0.291057\pi$
$401$	6.55287e24	1.22056	0.610281	+	0.792185i	$0.291057\pi$
$402$	0	0
$403$	−2.25954e24	−0.401441
$404$	2.36433e24	0.410285
$405$	0	0
$406$	−9.37354e24	−1.55205
$407$	−8.72815e24	−1.41181
$408$	0	0
$409$	8.56848e24	1.32292	0.661458	−	0.749982i	$-0.269938\pi$
$409$	8.56848e24	1.32292	0.661458	+	0.749982i	$0.269938\pi$
$410$	2.10825e23	0.0318036
$411$	0	0
$412$	−2.78069e23	−0.0400525
$413$	3.07712e24	0.433131
$414$	0	0
$415$	−2.22392e24	−0.298993
$416$	−9.38171e24	−1.23281
$417$	0	0
$418$	−4.21766e24	−0.529537
$419$	−8.09987e24	−0.994134	−0.497067	−	0.867712i	$-0.665590\pi$
$419$	−8.09987e24	−0.994134	−0.497067	+	0.867712i	$0.665590\pi$
$420$	0	0
$421$	9.99748e24	1.17276	0.586382	−	0.810035i	$-0.300552\pi$
$421$	9.99748e24	1.17276	0.586382	+	0.810035i	$0.300552\pi$
$422$	−9.18890e24	−1.05389
$423$	0	0
$424$	6.93352e24	0.760288
$425$	1.27472e25	1.36685
$426$	0	0
$427$	−5.81498e24	−0.596326
$428$	−4.09799e24	−0.411013
$429$	0	0
$430$	1.23352e23	0.0118357
$431$	4.59733e24	0.431491	0.215745	−	0.976450i	$-0.430782\pi$
$431$	4.59733e24	0.431491	0.215745	+	0.976450i	$0.430782\pi$
$432$	0	0
$433$	−7.51468e24	−0.674956	−0.337478	−	0.941333i	$-0.609574\pi$
$433$	−7.51468e24	−0.674956	−0.337478	+	0.941333i	$0.609574\pi$
$434$	2.39523e24	0.210472
$435$	0	0
$436$	−3.73317e24	−0.314019
$437$	−6.14102e24	−0.505436
$438$	0	0
$439$	−2.04197e25	−1.60930	−0.804649	−	0.593751i	$-0.797647\pi$
$439$	−2.04197e25	−1.60930	−0.804649	+	0.593751i	$0.797647\pi$
$440$	1.79312e24	0.138296
$441$	0	0
$442$	2.11316e25	1.56106
$443$	1.84340e25	1.33286	0.666428	−	0.745569i	$-0.267822\pi$
$443$	1.84340e25	1.33286	0.666428	+	0.745569i	$0.267822\pi$
$444$	0	0
$445$	9.80854e23	0.0679492
$446$	1.70492e25	1.15617
$447$	0	0
$448$	1.55951e25	1.01355
$449$	−7.82616e24	−0.497976	−0.248988	−	0.968507i	$-0.580098\pi$
$449$	−7.82616e24	−0.497976	−0.248988	+	0.968507i	$0.580098\pi$
$450$	0	0
$451$	−3.70076e24	−0.225743
$452$	1.13314e25	0.676811
$453$	0	0
$454$	−1.37176e25	−0.785681
$455$	−4.46649e24	−0.250529
$456$	0	0
$457$	2.15612e25	1.16003	0.580015	−	0.814606i	$-0.303047\pi$
$457$	2.15612e25	1.16003	0.580015	+	0.814606i	$0.303047\pi$
$458$	−1.19837e25	−0.631493
$459$	0	0
$460$	8.11971e23	0.0410526
$461$	−4.52754e24	−0.224235	−0.112118	−	0.993695i	$-0.535763\pi$
$461$	−4.52754e24	−0.224235	−0.112118	+	0.993695i	$0.535763\pi$
$462$	0	0
$463$	1.12552e25	0.534974	0.267487	−	0.963562i	$-0.413807\pi$
$463$	1.12552e25	0.534974	0.267487	+	0.963562i	$0.413807\pi$
$464$	1.45750e25	0.678717
$465$	0	0
$466$	1.35350e24	0.0605049
$467$	−1.73792e25	−0.761237	−0.380618	−	0.924732i	$-0.624289\pi$
$467$	−1.73792e25	−0.761237	−0.380618	+	0.924732i	$0.624289\pi$
$468$	0	0
$469$	2.35810e25	0.991790
$470$	2.56473e24	0.105709
$471$	0	0
$472$	−1.10469e25	−0.437314
$473$	−2.16528e24	−0.0840104
$474$	0	0
$475$	−2.27514e25	−0.848045
$476$	1.84302e25	0.673387
$477$	0	0
$478$	−2.10783e25	−0.740065
$479$	−4.26798e25	−1.46904	−0.734522	−	0.678585i	$-0.762593\pi$
$479$	−4.26798e25	−1.46904	−0.734522	+	0.678585i	$0.762593\pi$
$480$	0	0
$481$	−7.80506e25	−2.58225
$482$	−1.07233e25	−0.347841
$483$	0	0
$484$	4.68448e24	0.146093
$485$	1.14027e24	0.0348708
$486$	0	0
$487$	−6.57071e24	−0.193236	−0.0966178	−	0.995322i	$-0.530802\pi$
$487$	−6.57071e24	−0.193236	−0.0966178	+	0.995322i	$0.530802\pi$
$488$	2.08759e25	0.602085
$489$	0	0
$490$	5.58257e23	0.0154872
$491$	−5.24168e25	−1.42625	−0.713126	−	0.701035i	$-0.752721\pi$
$491$	−5.24168e25	−1.42625	−0.713126	+	0.701035i	$0.752721\pi$
$492$	0	0
$493$	1.05330e26	2.75744
$494$	−3.77160e25	−0.968544
$495$	0	0
$496$	−3.72437e24	−0.0920400
$497$	2.67282e25	0.648013
$498$	0	0
$499$	−2.55146e25	−0.595434	−0.297717	−	0.954654i	$-0.596225\pi$
$499$	−2.55146e25	−0.595434	−0.297717	+	0.954654i	$0.596225\pi$
$500$	6.09188e24	0.139488
$501$	0	0
$502$	2.65021e25	0.584246
$503$	5.69466e25	1.23189	0.615945	−	0.787789i	$-0.288775\pi$
$503$	5.69466e25	1.23189	0.615945	+	0.787789i	$0.288775\pi$
$504$	0	0
$505$	−6.82527e24	−0.142184
$506$	1.73236e25	0.354166
$507$	0	0
$508$	2.96366e25	0.583610
$509$	3.26878e25	0.631781	0.315891	−	0.948796i	$-0.397697\pi$
$509$	3.26878e25	0.631781	0.315891	+	0.948796i	$0.397697\pi$
$510$	0	0
$511$	8.45598e24	0.157458
$512$	−3.57472e25	−0.653398
$513$	0	0
$514$	−9.61903e24	−0.169427
$515$	8.02721e23	0.0138802
$516$	0	0
$517$	−4.50205e25	−0.750326
$518$	8.27377e25	1.35385
$519$	0	0
$520$	1.60348e25	0.252949
$521$	9.30404e25	1.44116	0.720581	−	0.693370i	$-0.243875\pi$
$521$	9.30404e25	1.44116	0.720581	+	0.693370i	$0.243875\pi$
$522$	0	0
$523$	4.88002e25	0.728879	0.364440	−	0.931227i	$-0.381261\pi$
$523$	4.88002e25	0.728879	0.364440	+	0.931227i	$0.381261\pi$
$524$	−4.95384e25	−0.726599
$525$	0	0
$526$	−1.41793e25	−0.200582
$527$	−2.69150e25	−0.373933
$528$	0	0
$529$	−4.93919e25	−0.661953
$530$	−6.22482e24	−0.0819419
$531$	0	0
$532$	−3.28946e25	−0.417796
$533$	−3.30937e25	−0.412892
$534$	0	0
$535$	1.18299e25	0.142437
$536$	−8.46562e25	−1.00137
$537$	0	0
$538$	3.36008e25	0.383635
$539$	−9.79948e24	−0.109928
$540$	0	0
$541$	8.45858e25	0.916059	0.458030	−	0.888937i	$-0.348555\pi$
$541$	8.45858e25	0.916059	0.458030	+	0.888937i	$0.348555\pi$
$542$	−4.41649e25	−0.469985
$543$	0	0
$544$	−1.11753e26	−1.14833
$545$	1.07768e25	0.108823
$546$	0	0
$547$	−2.08591e25	−0.203430	−0.101715	−	0.994814i	$-0.532433\pi$
$547$	−2.08591e25	−0.203430	−0.101715	+	0.994814i	$0.532433\pi$
$548$	3.62565e25	0.347513
$549$	0	0
$550$	6.41808e25	0.594237
$551$	−1.87995e26	−1.71083
$552$	0	0
$553$	−7.94260e25	−0.698352
$554$	7.65345e25	0.661477
$555$	0	0
$556$	6.01985e24	0.0502777
$557$	1.19573e25	0.0981768	0.0490884	−	0.998794i	$-0.484368\pi$
$557$	1.19573e25	0.0981768	0.0490884	+	0.998794i	$0.484368\pi$
$558$	0	0
$559$	−1.93628e25	−0.153658
$560$	−7.36206e24	−0.0574398
$561$	0	0
$562$	−2.34362e25	−0.176764
$563$	1.51109e26	1.12063	0.560313	−	0.828281i	$-0.310681\pi$
$563$	1.51109e26	1.12063	0.560313	+	0.828281i	$0.310681\pi$
$564$	0	0
$565$	−3.27110e25	−0.234549
$566$	−1.30036e26	−0.916866
$567$	0	0
$568$	−9.59549e25	−0.654271
$569$	1.31930e26	0.884661	0.442331	−	0.896852i	$-0.354152\pi$
$569$	1.31930e26	0.884661	0.442331	+	0.896852i	$0.354152\pi$
$570$	0	0
$571$	2.65239e26	1.72026	0.860130	−	0.510076i	$-0.170383\pi$
$571$	2.65239e26	1.72026	0.860130	+	0.510076i	$0.170383\pi$
$572$	−8.75375e25	−0.558383
$573$	0	0
$574$	3.50810e25	0.216476
$575$	9.34489e25	0.567191
$576$	0	0
$577$	−9.99355e25	−0.586880	−0.293440	−	0.955977i	$-0.594800\pi$
$577$	−9.99355e25	−0.586880	−0.293440	+	0.955977i	$0.594800\pi$
$578$	1.23496e26	0.713406
$579$	0	0
$580$	2.48569e25	0.138957
$581$	−3.70057e26	−2.03514
$582$	0	0
$583$	1.09269e26	0.581626
$584$	−3.03572e25	−0.158979
$585$	0	0
$586$	−8.86324e24	−0.0449330
$587$	1.90494e26	0.950209	0.475104	−	0.879930i	$-0.342410\pi$
$587$	1.90494e26	0.950209	0.475104	+	0.879930i	$0.342410\pi$
$588$	0	0
$589$	4.80384e25	0.232003
$590$	9.91779e24	0.0471326
$591$	0	0
$592$	−1.28650e26	−0.592043
$593$	2.37669e26	1.07635	0.538173	−	0.842834i	$-0.319115\pi$
$593$	2.37669e26	1.07635	0.538173	+	0.842834i	$0.319115\pi$
$594$	0	0
$595$	−5.32037e25	−0.233362
$596$	3.96772e25	0.171278
$597$	0	0
$598$	1.54914e26	0.647784
$599$	3.08975e26	1.27165	0.635826	−	0.771832i	$-0.280659\pi$
$599$	3.08975e26	1.27165	0.635826	+	0.771832i	$0.280659\pi$
$600$	0	0
$601$	−2.61533e26	−1.04284	−0.521421	−	0.853299i	$-0.674598\pi$
$601$	−2.61533e26	−1.04284	−0.521421	+	0.853299i	$0.674598\pi$
$602$	2.05256e25	0.0805616
$603$	0	0
$604$	1.01730e26	0.386898
$605$	−1.35230e25	−0.0506287
$606$	0	0
$607$	5.37620e25	0.195067	0.0975334	−	0.995232i	$-0.468905\pi$
$607$	5.37620e25	0.195067	0.0975334	+	0.995232i	$0.468905\pi$
$608$	1.99458e26	0.712471
$609$	0	0
$610$	−1.87421e25	−0.0648911
$611$	−4.02591e26	−1.37238
$612$	0	0
$613$	3.16087e26	1.04456	0.522278	−	0.852775i	$-0.325082\pi$
$613$	3.16087e26	1.04456	0.522278	+	0.852775i	$0.325082\pi$
$614$	−3.83119e26	−1.24662
$615$	0	0
$616$	2.98373e26	0.941332
$617$	−1.98562e26	−0.616862	−0.308431	−	0.951247i	$-0.599804\pi$
$617$	−1.98562e26	−0.616862	−0.308431	+	0.951247i	$0.599804\pi$
$618$	0	0
$619$	−4.82992e26	−1.45505	−0.727527	−	0.686080i	$-0.759330\pi$
$619$	−4.82992e26	−1.45505	−0.727527	+	0.686080i	$0.759330\pi$
$620$	−6.35169e24	−0.0188438
$621$	0	0
$622$	−2.01055e26	−0.578505
$623$	1.63213e26	0.462507
$624$	0	0
$625$	3.37310e26	0.927191
$626$	−1.09479e26	−0.296398
$627$	0	0
$628$	−2.16847e26	−0.569556
$629$	−9.29719e26	−2.40531
$630$	0	0
$631$	−6.27693e26	−1.57568	−0.787841	−	0.615879i	$-0.788801\pi$
$631$	−6.27693e26	−1.57568	−0.787841	+	0.615879i	$0.788801\pi$
$632$	2.85141e26	0.705096
$633$	0	0
$634$	1.47185e26	0.353196
$635$	−8.55538e25	−0.202250
$636$	0	0
$637$	−8.76310e25	−0.201063
$638$	5.30326e26	1.19880
$639$	0	0
$640$	−8.16228e24	−0.0179103
$641$	−2.15915e26	−0.466800	−0.233400	−	0.972381i	$-0.574985\pi$
$641$	−2.15915e26	−0.466800	−0.233400	+	0.972381i	$0.574985\pi$
$642$	0	0
$643$	4.68779e26	0.983929	0.491964	−	0.870615i	$-0.336279\pi$
$643$	4.68779e26	0.983929	0.491964	+	0.870615i	$0.336279\pi$
$644$	1.35111e26	0.279431
$645$	0	0
$646$	−4.49263e26	−0.902177
$647$	2.10829e26	0.417196	0.208598	−	0.978001i	$-0.433110\pi$
$647$	2.10829e26	0.417196	0.208598	+	0.978001i	$0.433110\pi$
$648$	0	0
$649$	−1.74094e26	−0.334549
$650$	5.73931e26	1.08688
$651$	0	0
$652$	−1.06511e26	−0.195903
$653$	−2.88194e26	−0.522408	−0.261204	−	0.965284i	$-0.584120\pi$
$653$	−2.88194e26	−0.522408	−0.261204	+	0.965284i	$0.584120\pi$
$654$	0	0
$655$	1.43006e26	0.251803
$656$	−5.45480e25	−0.0946656
$657$	0	0
$658$	4.26768e26	0.719524
$659$	7.36091e26	1.22326	0.611632	−	0.791143i	$-0.290514\pi$
$659$	7.36091e26	1.22326	0.611632	+	0.791143i	$0.290514\pi$
$660$	0	0
$661$	3.05440e25	0.0493187	0.0246594	−	0.999696i	$-0.492150\pi$
$661$	3.05440e25	0.0493187	0.0246594	+	0.999696i	$0.492150\pi$
$662$	−1.24207e26	−0.197694
$663$	0	0
$664$	1.32851e27	2.05480
$665$	9.49589e25	0.144787
$666$	0	0
$667$	7.72168e26	1.14424
$668$	−3.84357e25	−0.0561512
$669$	0	0
$670$	7.60032e25	0.107925
$671$	3.28994e26	0.460600
$672$	0	0
$673$	−9.62645e26	−1.31016	−0.655078	−	0.755561i	$-0.727364\pi$
$673$	−9.62645e26	−1.31016	−0.655078	+	0.755561i	$0.727364\pi$
$674$	−5.96582e25	−0.0800573
$675$	0	0
$676$	−4.36828e26	−0.569923
$677$	−1.18974e27	−1.53059	−0.765295	−	0.643680i	$-0.777407\pi$
$677$	−1.18974e27	−1.53059	−0.765295	+	0.643680i	$0.777407\pi$
$678$	0	0
$679$	1.89740e26	0.237354
$680$	1.91003e26	0.235616
$681$	0	0
$682$	−1.35514e26	−0.162568
$683$	1.51240e27	1.78925	0.894624	−	0.446819i	$-0.147443\pi$
$683$	1.51240e27	1.78925	0.894624	+	0.446819i	$0.147443\pi$
$684$	0	0
$685$	−1.04664e26	−0.120431
$686$	−6.02063e26	−0.683224
$687$	0	0
$688$	−3.19155e25	−0.0352299
$689$	9.77124e26	1.06382
$690$	0	0
$691$	−1.40247e27	−1.48543	−0.742716	−	0.669606i	$-0.766463\pi$
$691$	−1.40247e27	−1.48543	−0.742716	+	0.669606i	$0.766463\pi$
$692$	−7.79864e26	−0.814725
$693$	0	0
$694$	−1.10272e27	−1.12085
$695$	−1.73779e25	−0.0174238
$696$	0	0
$697$	−3.94204e26	−0.384600
$698$	−9.41194e26	−0.905842
$699$	0	0
$700$	5.00563e26	0.468843
$701$	−6.64167e26	−0.613700	−0.306850	−	0.951758i	$-0.599275\pi$
$701$	−6.64167e26	−0.613700	−0.306850	+	0.951758i	$0.599275\pi$
$702$	0	0
$703$	1.65938e27	1.49235
$704$	−8.82320e26	−0.782863
$705$	0	0
$706$	−4.40546e26	−0.380493
$707$	−1.13572e27	−0.967799
$708$	0	0
$709$	1.03445e27	0.858163	0.429081	−	0.903266i	$-0.358837\pi$
$709$	1.03445e27	0.858163	0.429081	+	0.903266i	$0.358837\pi$
$710$	8.61470e25	0.0705157
$711$	0	0
$712$	−5.85938e26	−0.466973
$713$	−1.97313e26	−0.155169
$714$	0	0
$715$	2.52700e26	0.193508
$716$	−2.32328e26	−0.175561
$717$	0	0
$718$	−2.84077e26	−0.209052
$719$	1.59383e26	0.115749	0.0578744	−	0.998324i	$-0.481568\pi$
$719$	1.59383e26	0.115749	0.0578744	+	0.998324i	$0.481568\pi$
$720$	0	0
$721$	1.33572e26	0.0944777
$722$	−2.59204e26	−0.180942
$723$	0	0
$724$	−3.59006e25	−0.0244110
$725$	2.86075e27	1.91986
$726$	0	0
$727$	1.66059e27	1.08564	0.542819	−	0.839850i	$-0.317357\pi$
$727$	1.66059e27	1.08564	0.542819	+	0.839850i	$0.317357\pi$
$728$	2.66817e27	1.72173
$729$	0	0
$730$	2.72543e25	0.0171343
$731$	−2.30645e26	−0.143129
$732$	0	0
$733$	−1.36074e27	−0.822786	−0.411393	−	0.911458i	$-0.634958\pi$
$733$	−1.36074e27	−0.822786	−0.411393	+	0.911458i	$0.634958\pi$
$734$	−1.23449e27	−0.736843
$735$	0	0
$736$	−8.19251e26	−0.476517
$737$	−1.33414e27	−0.766054
$738$	0	0
$739$	9.59784e26	0.537095	0.268548	−	0.963266i	$-0.413456\pi$
$739$	9.59784e26	0.537095	0.268548	+	0.963266i	$0.413456\pi$
$740$	−2.19405e26	−0.121212
$741$	0	0
$742$	−1.03580e27	−0.557750
$743$	1.18287e27	0.628846	0.314423	−	0.949283i	$-0.398189\pi$
$743$	1.18287e27	0.628846	0.314423	+	0.949283i	$0.398189\pi$
$744$	0	0
$745$	−1.14539e26	−0.0593564
$746$	8.84670e26	0.452650
$747$	0	0
$748$	−1.04273e27	−0.520121
$749$	1.96849e27	0.969516
$750$	0	0
$751$	−1.02382e27	−0.491637	−0.245819	−	0.969316i	$-0.579057\pi$
$751$	−1.02382e27	−0.491637	−0.245819	+	0.969316i	$0.579057\pi$
$752$	−6.63587e26	−0.314650
$753$	0	0
$754$	4.74239e27	2.19265
$755$	−2.93670e26	−0.134080
$756$	0	0
$757$	2.74415e25	0.0122179	0.00610897	−	0.999981i	$-0.498055\pi$
$757$	2.74415e25	0.0122179	0.00610897	+	0.999981i	$0.498055\pi$
$758$	1.80446e27	0.793394
$759$	0	0
$760$	−3.40905e26	−0.146185
$761$	−1.89240e27	−0.801416	−0.400708	−	0.916206i	$-0.631236\pi$
$761$	−1.89240e27	−0.801416	−0.400708	+	0.916206i	$0.631236\pi$
$762$	0	0
$763$	1.79324e27	0.740722
$764$	−1.21414e27	−0.495314
$765$	0	0
$766$	−8.32465e26	−0.331278
$767$	−1.55682e27	−0.611902
$768$	0	0
$769$	−1.93865e27	−0.743359	−0.371679	−	0.928361i	$-0.621218\pi$
$769$	−1.93865e27	−0.743359	−0.371679	+	0.928361i	$0.621218\pi$
$770$	−2.67875e26	−0.101454
$771$	0	0
$772$	2.30234e27	0.850756
$773$	7.63732e24	0.00278764	0.00139382	−	0.999999i	$-0.499556\pi$
$773$	7.63732e24	0.00278764	0.00139382	+	0.999999i	$0.499556\pi$
$774$	0	0
$775$	−7.31009e26	−0.260349
$776$	−6.81171e26	−0.239646
$777$	0	0
$778$	6.43559e25	0.0220944
$779$	7.03582e26	0.238621
$780$	0	0
$781$	−1.51220e27	−0.500523
$782$	1.84530e27	0.603396
$783$	0	0
$784$	−1.44441e26	−0.0460986
$785$	6.25986e26	0.197380
$786$	0	0
$787$	−4.61341e27	−1.41991	−0.709956	−	0.704246i	$-0.751285\pi$
$787$	−4.61341e27	−1.41991	−0.709956	+	0.704246i	$0.751285\pi$
$788$	1.81870e27	0.553046
$789$	0	0
$790$	−2.55996e26	−0.0759934
$791$	−5.44307e27	−1.59649
$792$	0	0
$793$	2.94199e27	0.842455
$794$	−6.64025e26	−0.187884
$795$	0	0
$796$	−1.07863e27	−0.297989
$797$	−1.01219e27	−0.276316	−0.138158	−	0.990410i	$-0.544118\pi$
$797$	−1.01219e27	−0.276316	−0.138158	+	0.990410i	$0.544118\pi$
$798$	0	0
$799$	−4.79557e27	−1.27834
$800$	−3.03519e27	−0.799522
$801$	0	0
$802$	3.51440e27	0.904056
$803$	−4.78413e26	−0.121620
$804$	0	0
$805$	−3.90033e26	−0.0968369
$806$	−1.21183e27	−0.297343
$807$	0	0
$808$	4.07725e27	0.977145
$809$	−3.00853e27	−0.712597	−0.356298	−	0.934372i	$-0.615961\pi$
$809$	−3.00853e27	−0.712597	−0.356298	+	0.934372i	$0.615961\pi$
$810$	0	0
$811$	3.54753e27	0.820782	0.410391	−	0.911910i	$-0.365392\pi$
$811$	3.54753e27	0.820782	0.410391	+	0.911910i	$0.365392\pi$
$812$	4.13615e27	0.945832
$813$	0	0
$814$	−4.68104e27	−1.04571
$815$	3.07471e26	0.0678901
$816$	0	0
$817$	4.11659e26	0.0888030
$818$	4.59541e27	0.979869
$819$	0	0
$820$	−9.30283e25	−0.0193813
$821$	4.28797e27	0.883063	0.441532	−	0.897246i	$-0.354435\pi$
$821$	4.28797e27	0.883063	0.441532	+	0.897246i	$0.354435\pi$
$822$	0	0
$823$	3.20459e27	0.644874	0.322437	−	0.946591i	$-0.395498\pi$
$823$	3.20459e27	0.644874	0.322437	+	0.946591i	$0.395498\pi$
$824$	−4.79526e26	−0.0953901
$825$	0	0
$826$	1.65031e27	0.320815
$827$	4.02192e27	0.772914	0.386457	−	0.922308i	$-0.373699\pi$
$827$	4.02192e27	0.772914	0.386457	+	0.922308i	$0.373699\pi$
$828$	0	0
$829$	−1.58908e27	−0.298455	−0.149227	−	0.988803i	$-0.547679\pi$
$829$	−1.58908e27	−0.298455	−0.149227	+	0.988803i	$0.547679\pi$
$830$	−1.19272e27	−0.221461
$831$	0	0
$832$	−7.89006e27	−1.43189
$833$	−1.04384e27	−0.187286
$834$	0	0
$835$	1.10955e26	0.0194592
$836$	1.86107e27	0.322704
$837$	0	0
$838$	−4.34409e27	−0.736343
$839$	5.31813e27	0.891293	0.445646	−	0.895209i	$-0.352974\pi$
$839$	5.31813e27	0.891293	0.445646	+	0.895209i	$0.352974\pi$
$840$	0	0
$841$	1.75351e28	2.87307
$842$	5.36180e27	0.868652
$843$	0	0
$844$	4.05467e27	0.642248
$845$	1.26102e27	0.197507
$846$	0	0
$847$	−2.25021e27	−0.344612
$848$	1.61058e27	0.243906
$849$	0	0
$850$	6.83652e27	1.01241
$851$	−6.81572e27	−0.998115
$852$	0	0
$853$	−1.60722e27	−0.230176	−0.115088	−	0.993355i	$-0.536715\pi$
$853$	−1.60722e27	−0.230176	−0.115088	+	0.993355i	$0.536715\pi$
$854$	−3.11867e27	−0.441691
$855$	0	0
$856$	−7.06692e27	−0.978879
$857$	−8.25782e27	−1.13122	−0.565611	−	0.824672i	$-0.691359\pi$
$857$	−8.25782e27	−1.13122	−0.565611	+	0.824672i	$0.691359\pi$
$858$	0	0
$859$	−9.31408e27	−1.24797	−0.623986	−	0.781436i	$-0.714488\pi$
$859$	−9.31408e27	−1.24797	−0.623986	+	0.781436i	$0.714488\pi$
$860$	−5.44299e25	−0.00721277
$861$	0	0
$862$	2.46562e27	0.319600
$863$	−6.65457e27	−0.853134	−0.426567	−	0.904456i	$-0.640277\pi$
$863$	−6.65457e27	−0.853134	−0.426567	+	0.904456i	$0.640277\pi$
$864$	0	0
$865$	2.25128e27	0.282343
$866$	−4.03024e27	−0.499932
$867$	0	0
$868$	−1.05691e27	−0.128263
$869$	4.49368e27	0.539404
$870$	0	0
$871$	−1.19304e28	−1.40114
$872$	−6.43778e27	−0.747876
$873$	0	0
$874$	−3.29352e27	−0.374371
$875$	−2.92626e27	−0.329030
$876$	0	0
$877$	−1.08073e27	−0.118911	−0.0594554	−	0.998231i	$-0.518936\pi$
$877$	−1.08073e27	−0.118911	−0.0594554	+	0.998231i	$0.518936\pi$
$878$	−1.09514e28	−1.19199
$879$	0	0
$880$	4.16523e26	0.0443663
$881$	1.38540e28	1.45983	0.729916	−	0.683536i	$-0.239559\pi$
$881$	1.38540e28	1.45983	0.729916	+	0.683536i	$0.239559\pi$
$882$	0	0
$883$	6.76336e27	0.697487	0.348743	−	0.937218i	$-0.386608\pi$
$883$	6.76336e27	0.697487	0.348743	+	0.937218i	$0.386608\pi$
$884$	−9.32447e27	−0.951322
$885$	0	0
$886$	9.88642e27	0.987231
$887$	1.60903e28	1.58960	0.794802	−	0.606869i	$-0.207575\pi$
$887$	1.60903e28	1.58960	0.794802	+	0.606869i	$0.207575\pi$
$888$	0	0
$889$	−1.42360e28	−1.37665
$890$	5.26047e26	0.0503292
$891$	0	0
$892$	−7.52311e27	−0.704581
$893$	8.55921e27	0.793131
$894$	0	0
$895$	6.70675e26	0.0608406
$896$	−1.35819e27	−0.121909
$897$	0	0
$898$	−4.19729e27	−0.368845
$899$	−6.04033e27	−0.525223
$900$	0	0
$901$	1.16393e28	0.990922
$902$	−1.98478e27	−0.167205
$903$	0	0
$904$	1.95408e28	1.61191
$905$	1.03636e26	0.00845963
$906$	0	0
$907$	−4.87731e26	−0.0389862	−0.0194931	−	0.999810i	$-0.506205\pi$
$907$	−4.87731e26	−0.0389862	−0.0194931	+	0.999810i	$0.506205\pi$
$908$	6.05299e27	0.478800
$909$	0	0
$910$	−2.39545e27	−0.185564
$911$	−2.04975e28	−1.57136	−0.785680	−	0.618634i	$-0.787687\pi$
$911$	−2.04975e28	−1.57136	−0.785680	+	0.618634i	$0.787687\pi$
$912$	0	0
$913$	2.09367e28	1.57194
$914$	1.15636e28	0.859221
$915$	0	0
$916$	5.28790e27	0.384836
$917$	2.37960e28	1.71394
$918$	0	0
$919$	7.36209e27	0.519402	0.259701	−	0.965689i	$-0.416376\pi$
$919$	7.36209e27	0.519402	0.259701	+	0.965689i	$0.416376\pi$
$920$	1.40023e27	0.0977720
$921$	0	0
$922$	−2.42819e27	−0.166088
$923$	−1.35227e28	−0.915476
$924$	0	0
$925$	−2.52511e28	−1.67469
$926$	6.03632e27	0.396249
$927$	0	0
$928$	−2.50797e28	−1.61294
$929$	9.18844e27	0.584915	0.292457	−	0.956279i	$-0.405527\pi$
$929$	9.18844e27	0.584915	0.292457	+	0.956279i	$0.405527\pi$
$930$	0	0
$931$	1.86306e27	0.116200
$932$	−5.97241e26	−0.0368721
$933$	0	0
$934$	−9.32074e27	−0.563839
$935$	3.01010e27	0.180248
$936$	0	0
$937$	1.55615e28	0.913113	0.456557	−	0.889694i	$-0.349083\pi$
$937$	1.55615e28	0.913113	0.456557	+	0.889694i	$0.349083\pi$
$938$	1.26468e28	0.734607
$939$	0	0
$940$	−1.13171e27	−0.0644198
$941$	4.21264e27	0.237385	0.118693	−	0.992931i	$-0.462130\pi$
$941$	4.21264e27	0.237385	0.118693	+	0.992931i	$0.462130\pi$
$942$	0	0
$943$	−2.88989e27	−0.159595
$944$	−2.56609e27	−0.140293
$945$	0	0
$946$	−1.16127e27	−0.0622255
$947$	−1.60906e27	−0.0853584	−0.0426792	−	0.999089i	$-0.513589\pi$
$947$	−1.60906e27	−0.0853584	−0.0426792	+	0.999089i	$0.513589\pi$
$948$	0	0
$949$	−4.27817e27	−0.222448
$950$	−1.22019e28	−0.628137
$951$	0	0
$952$	3.17826e28	1.60376
$953$	−2.00721e28	−1.00279	−0.501396	−	0.865218i	$-0.667180\pi$
$953$	−2.00721e28	−1.00279	−0.501396	+	0.865218i	$0.667180\pi$
$954$	0	0
$955$	3.50493e27	0.171651
$956$	9.30095e27	0.451001
$957$	0	0
$958$	−2.28898e28	−1.08810
$959$	−1.74160e28	−0.819729
$960$	0	0
$961$	−2.01272e28	−0.928775
$962$	−4.18598e28	−1.91264
$963$	0	0
$964$	4.73173e27	0.211977
$965$	−6.64631e27	−0.294830
$966$	0	0
$967$	3.69606e28	1.60764	0.803818	−	0.594876i	$-0.202799\pi$
$967$	3.69606e28	1.60764	0.803818	+	0.594876i	$0.202799\pi$
$968$	8.07830e27	0.347940
$969$	0	0
$970$	6.11546e26	0.0258284
$971$	2.54073e28	1.06261	0.531306	−	0.847180i	$-0.321701\pi$
$971$	2.54073e28	1.06261	0.531306	+	0.847180i	$0.321701\pi$
$972$	0	0
$973$	−2.89166e27	−0.118597
$974$	−3.52397e27	−0.143127
$975$	0	0
$976$	4.84925e27	0.193153
$977$	−8.52403e27	−0.336238	−0.168119	−	0.985767i	$-0.553769\pi$
$977$	−8.52403e27	−0.336238	−0.168119	+	0.985767i	$0.553769\pi$
$978$	0	0
$979$	−9.23408e27	−0.357238
$980$	−2.46336e26	−0.00943799
$981$	0	0
$982$	−2.81120e28	−1.05641
$983$	−3.09592e28	−1.15221	−0.576105	−	0.817376i	$-0.695428\pi$
$983$	−3.09592e28	−1.15221	−0.576105	+	0.817376i	$0.695428\pi$
$984$	0	0
$985$	−5.25015e27	−0.191658
$986$	5.64901e28	2.04240
$987$	0	0
$988$	1.66425e28	0.590238
$989$	−1.69084e27	−0.0593934
$990$	0	0
$991$	−2.94856e28	−1.01604	−0.508020	−	0.861345i	$-0.669622\pi$
$991$	−2.94856e28	−1.01604	−0.508020	+	0.861345i	$0.669622\pi$
$992$	6.40864e27	0.218728
$993$	0	0
$994$	1.43347e28	0.479976
$995$	3.11376e27	0.103268
$996$	0	0
$997$	−3.29038e28	−1.07064	−0.535318	−	0.844650i	$-0.679808\pi$
$997$	−3.29038e28	−1.07064	−0.535318	+	0.844650i	$0.679808\pi$
$998$	−1.36839e28	−0.441031
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.20.a.c.1.2		2
3.2	odd	2		3.20.a.b.1.1	✓	2
12.11	even	2		48.20.a.j.1.1		2
15.2	even	4		75.20.b.b.49.2		4
15.8	even	4		75.20.b.b.49.3		4
15.14	odd	2		75.20.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.b.1.1	✓	2	3.2	odd	2
9.20.a.c.1.2		2	1.1	even	1	trivial
48.20.a.j.1.1		2	12.11	even	2
75.20.a.b.1.2		2	15.14	odd	2
75.20.b.b.49.2		4	15.2	even	4
75.20.b.b.49.3		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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+536.316 q^{2} -236654. q^{4} +683163. q^{5} +1.13677e8 q^{7} -4.08105e8 q^{8} +O(q^{10})\)	\(q+536.316 q^{2} -236654. q^{4} +683163. q^{5} +1.13677e8 q^{7} -4.08105e8 q^{8} +3.66391e8 q^{10} -6.43152e9 q^{11} -5.75132e10 q^{13} +6.09670e10 q^{14} -9.47984e10 q^{16} -6.85083e11 q^{17} +1.22275e12 q^{19} -1.61673e11 q^{20} -3.44932e12 q^{22} -5.02230e12 q^{23} -1.86068e13 q^{25} -3.08453e13 q^{26} -2.69022e13 q^{28} -1.53748e14 q^{29} +3.92872e13 q^{31} +1.63123e14 q^{32} -3.67421e14 q^{34} +7.76602e13 q^{35} +1.35709e15 q^{37} +6.55779e14 q^{38} -2.78802e14 q^{40} +5.75410e14 q^{41} +3.36667e14 q^{43} +1.52204e15 q^{44} -2.69354e15 q^{46} +6.99998e15 q^{47} +1.52367e15 q^{49} -9.97910e15 q^{50} +1.36107e16 q^{52} -1.69895e16 q^{53} -4.39377e15 q^{55} -4.63923e16 q^{56} -8.24573e16 q^{58} +2.70689e16 q^{59} -5.11533e16 q^{61} +2.10704e16 q^{62} +1.37187e17 q^{64} -3.92909e16 q^{65} +2.07437e17 q^{67} +1.62127e17 q^{68} +4.16504e16 q^{70} +2.35123e17 q^{71} +7.43858e16 q^{73} +7.27828e17 q^{74} -2.89368e17 q^{76} -7.31118e17 q^{77} -6.98697e17 q^{79} -6.47627e16 q^{80} +3.08601e17 q^{82} -3.25532e18 q^{83} -4.68023e17 q^{85} +1.80560e17 q^{86} +2.62473e18 q^{88} +1.43575e18 q^{89} -6.53796e18 q^{91} +1.18855e18 q^{92} +3.75420e18 q^{94} +8.35337e17 q^{95} +1.66911e18 q^{97} +8.17166e17 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 702 q^{2} + 772484 q^{4} - 6016140 q^{5} + 113892064 q^{7} - 1008501624 q^{8}+O(q^{10}) \) 2 * q - 702 * q^2 + 772484 * q^4 - 6016140 * q^5 + 113892064 * q^7 - 1008501624 * q^8	\( 2 q - 702 q^{2} + 772484 q^{4} - 6016140 q^{5} + 113892064 q^{7} - 1008501624 q^{8} + 8662242420 q^{10} + 6650071272 q^{11} - 44072356148 q^{13} + 60701219424 q^{14} + 119603620880 q^{16} - 336281471748 q^{17} + 602118925096 q^{19} - 6922191196440 q^{20} - 19648459326744 q^{22} - 2368252165968 q^{23} + 7200399078350 q^{25} - 47489309789364 q^{26} - 26685589805888 q^{28} - 280977251970492 q^{29} + 41610149253712 q^{31} + 212406109003296 q^{32} - 799347349171332 q^{34} + 76222408017600 q^{35} + 637994163989884 q^{37} + 14\!\cdots\!32 q^{38}+ \cdots + 14\!\cdots\!02 q^{98}+O(q^{100}) \) 2 * q - 702 * q^2 + 772484 * q^4 - 6016140 * q^5 + 113892064 * q^7 - 1008501624 * q^8 + 8662242420 * q^10 + 6650071272 * q^11 - 44072356148 * q^13 + 60701219424 * q^14 + 119603620880 * q^16 - 336281471748 * q^17 + 602118925096 * q^19 - 6922191196440 * q^20 - 19648459326744 * q^22 - 2368252165968 * q^23 + 7200399078350 * q^25 - 47489309789364 * q^26 - 26685589805888 * q^28 - 280977251970492 * q^29 + 41610149253712 * q^31 + 212406109003296 * q^32 - 799347349171332 * q^34 + 76222408017600 * q^35 + 637994163989884 * q^37 + 1424314643816232 * q^38 + 3743437831857360 * q^40 - 1150038430280532 * q^41 + 2820518953538200 * q^43 + 14723164414050768 * q^44 - 5980094010800208 * q^46 + 5603091319500480 * q^47 - 9875183230193070 * q^49 - 41936530073800050 * q^50 + 27174417188397208 * q^52 - 27537868857647628 * q^53 - 92031302621896560 * q^55 - 46521172561587840 * q^56 + 75092921304821316 * q^58 + 55153474421835816 * q^59 - 87192569066205620 * q^61 + 18193883108252112 * q^62 - 36250046218631104 * q^64 - 129335487918703560 * q^65 + 499299710877878248 * q^67 + 514116238109034744 * q^68 + 43430850442699200 * q^70 - 84915048436970544 * q^71 - 241433711161728332 * q^73 + 1618295867440077564 * q^74 - 915668569473570224 * q^76 - 728310910203957888 * q^77 + 1131591466033523440 * q^79 - 1501106673028491360 * q^80 + 2445251486788059948 * q^82 - 1607743276003583784 * q^83 - 2804751519619294440 * q^85 - 2895233411994836328 * q^86 - 5229410429487705696 * q^88 - 4322797626369576276 * q^89 - 6535073681312344768 * q^91 + 3866849612692780896 * q^92 + 5483985680095257024 * q^94 + 4993123012930175760 * q^95 + 7902201235299458308 * q^97 + 14932538668319232402 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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