LMFDB - Embedded newform 325.10.a.k.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,10,Mod(1,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

Newform invariants

comment:select newform

sage:traces = [27,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$167.386646753$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	325.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.3195 q^{2} -195.494 q^{3} -245.673 q^{4} +3190.36 q^{6} +4181.36 q^{7} +12364.9 q^{8} +18534.7 q^{9} +74976.3 q^{11} +48027.5 q^{12} +28561.0 q^{13} -68237.8 q^{14} -76003.9 q^{16} -35861.7 q^{17} -302478. q^{18} -521133. q^{19} -817429. q^{21} -1.22358e6 q^{22} -2.36188e6 q^{23} -2.41725e6 q^{24} -466102. q^{26} +224480. q^{27} -1.02725e6 q^{28} +5.19987e6 q^{29} -8.86231e6 q^{31} -5.09046e6 q^{32} -1.46574e7 q^{33} +585246. q^{34} -4.55349e6 q^{36} +1.81091e7 q^{37} +8.50463e6 q^{38} -5.58349e6 q^{39} +2.69439e7 q^{41} +1.33400e7 q^{42} -2.29368e7 q^{43} -1.84197e7 q^{44} +3.85447e7 q^{46} +3.00540e6 q^{47} +1.48583e7 q^{48} -2.28698e7 q^{49} +7.01074e6 q^{51} -7.01668e6 q^{52} -1.08125e7 q^{53} -3.66340e6 q^{54} +5.17019e7 q^{56} +1.01878e8 q^{57} -8.48594e7 q^{58} -5.90734e7 q^{59} +8.27948e7 q^{61} +1.44629e8 q^{62} +7.75003e7 q^{63} +1.21988e8 q^{64} +2.39201e8 q^{66} -1.38456e8 q^{67} +8.81027e6 q^{68} +4.61732e8 q^{69} +1.21792e8 q^{71} +2.29179e8 q^{72} -4.39909e8 q^{73} -2.95533e8 q^{74} +1.28028e8 q^{76} +3.13503e8 q^{77} +9.11199e7 q^{78} +6.33272e8 q^{79} -4.08703e8 q^{81} -4.39711e8 q^{82} -2.04969e8 q^{83} +2.00820e8 q^{84} +3.74317e8 q^{86} -1.01654e9 q^{87} +9.27071e8 q^{88} -1.00666e8 q^{89} +1.19424e8 q^{91} +5.80250e8 q^{92} +1.73252e9 q^{93} -4.90467e7 q^{94} +9.95153e8 q^{96} -3.40802e8 q^{97} +3.73225e8 q^{98} +1.38966e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) $ 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * q^99

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 $

$2$	−16.3195	−0.721228	−0.360614	−	0.932715i	$-0.617433\pi$
$2$	−16.3195	−0.721228	−0.360614	+	0.932715i	$0.617433\pi$
$3$	−195.494	−1.39344	−0.696718	−	0.717345i	$-0.745357\pi$
$3$	−195.494	−1.39344	−0.696718	+	0.717345i	$0.745357\pi$
$4$	−245.673	−0.479831
$5$	0	0
$5$	0	0
$6$	3190.36	1.00498
$7$	4181.36	0.658228	0.329114	−	0.944290i	$-0.393250\pi$
$7$	4181.36	0.658228	0.329114	+	0.944290i	$0.393250\pi$
$8$	12364.9	1.06729
$9$	18534.7	0.941662
$10$	0	0
$11$	74976.3	1.54403	0.772017	−	0.635602i	$-0.219248\pi$
$11$	74976.3	1.54403	0.772017	+	0.635602i	$0.219248\pi$
$12$	48027.5	0.668613
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−68237.8	−0.474732
$15$	0	0
$16$	−76003.9	−0.289932
$17$	−35861.7	−0.104138	−0.0520692	−	0.998643i	$-0.516582\pi$
$17$	−35861.7	−0.104138	−0.0520692	+	0.998643i	$0.516582\pi$
$18$	−302478.	−0.679152
$19$	−521133.	−0.917396	−0.458698	−	0.888592i	$-0.651684\pi$
$19$	−521133.	−0.917396	−0.458698	+	0.888592i	$0.651684\pi$
$20$	0	0
$21$	−817429.	−0.917198
$22$	−1.22358e6	−1.11360
$23$	−2.36188e6	−1.75988	−0.879938	−	0.475089i	$-0.842416\pi$
$23$	−2.36188e6	−1.75988	−0.879938	+	0.475089i	$0.842416\pi$
$24$	−2.41725e6	−1.48721
$25$	0	0
$26$	−466102.	−0.200033
$27$	224480.	0.0812906
$28$	−1.02725e6	−0.315838
$29$	5.19987e6	1.36522	0.682608	−	0.730784i	$-0.260845\pi$
$29$	5.19987e6	1.36522	0.682608	+	0.730784i	$0.260845\pi$
$30$	0	0
$31$	−8.86231e6	−1.72353	−0.861766	−	0.507306i	$-0.830641\pi$
$31$	−8.86231e6	−1.72353	−0.861766	+	0.507306i	$0.830641\pi$
$32$	−5.09046e6	−0.858188
$33$	−1.46574e7	−2.15151
$34$	585246.	0.0751075
$35$	0	0
$36$	−4.55349e6	−0.451838
$37$	1.81091e7	1.58851	0.794256	−	0.607584i	$-0.207861\pi$
$37$	1.81091e7	1.58851	0.794256	+	0.607584i	$0.207861\pi$
$38$	8.50463e6	0.661652
$39$	−5.58349e6	−0.386469
$40$	0	0
$41$	2.69439e7	1.48913	0.744565	−	0.667550i	$-0.232657\pi$
$41$	2.69439e7	1.48913	0.744565	+	0.667550i	$0.232657\pi$
$42$	1.33400e7	0.661508
$43$	−2.29368e7	−1.02312	−0.511558	−	0.859249i	$-0.670931\pi$
$43$	−2.29368e7	−1.02312	−0.511558	+	0.859249i	$0.670931\pi$
$44$	−1.84197e7	−0.740875
$45$	0	0
$46$	3.85447e7	1.26927
$47$	3.00540e6	0.0898385	0.0449192	−	0.998991i	$-0.485697\pi$
$47$	3.00540e6	0.0898385	0.0449192	+	0.998991i	$0.485697\pi$
$48$	1.48583e7	0.404001
$49$	−2.28698e7	−0.566736
$50$	0	0
$51$	7.01074e6	0.145110
$52$	−7.01668e6	−0.133081
$53$	−1.08125e7	−0.188227	−0.0941137	−	0.995561i	$-0.530002\pi$
$53$	−1.08125e7	−0.188227	−0.0941137	+	0.995561i	$0.530002\pi$
$54$	−3.66340e6	−0.0586290
$55$	0	0
$56$	5.17019e7	0.702523
$57$	1.01878e8	1.27833
$58$	−8.48594e7	−0.984632
$59$	−5.90734e7	−0.634685	−0.317342	−	0.948311i	$-0.602790\pi$
$59$	−5.90734e7	−0.634685	−0.317342	+	0.948311i	$0.602790\pi$
$60$	0	0
$61$	8.27948e7	0.765630	0.382815	−	0.923825i	$-0.374955\pi$
$61$	8.27948e7	0.765630	0.382815	+	0.923825i	$0.374955\pi$
$62$	1.44629e8	1.24306
$63$	7.75003e7	0.619828
$64$	1.21988e8	0.908881
$65$	0	0
$66$	2.39201e8	1.55173
$67$	−1.38456e8	−0.839415	−0.419707	−	0.907659i	$-0.637867\pi$
$67$	−1.38456e8	−0.839415	−0.419707	+	0.907659i	$0.637867\pi$
$68$	8.81027e6	0.0499688
$69$	4.61732e8	2.45227
$70$	0	0
$71$	1.21792e8	0.568798	0.284399	−	0.958706i	$-0.408206\pi$
$71$	1.21792e8	0.568798	0.284399	+	0.958706i	$0.408206\pi$
$72$	2.29179e8	1.00503
$73$	−4.39909e8	−1.81305	−0.906525	−	0.422152i	$-0.861275\pi$
$73$	−4.39909e8	−1.81305	−0.906525	+	0.422152i	$0.861275\pi$
$74$	−2.95533e8	−1.14568
$75$	0	0
$76$	1.28028e8	0.440195
$77$	3.13503e8	1.01633
$78$	9.11199e7	0.278732
$79$	6.33272e8	1.82923	0.914616	−	0.404324i	$-0.132493\pi$
$79$	6.33272e8	1.82923	0.914616	+	0.404324i	$0.132493\pi$
$80$	0	0
$81$	−4.08703e8	−1.05493
$82$	−4.39711e8	−1.07400
$83$	−2.04969e8	−0.474063	−0.237032	−	0.971502i	$-0.576174\pi$
$83$	−2.04969e8	−0.474063	−0.237032	+	0.971502i	$0.576174\pi$
$84$	2.00820e8	0.440100
$85$	0	0
$86$	3.74317e8	0.737899
$87$	−1.01654e9	−1.90234
$88$	9.27071e8	1.64794
$89$	−1.00666e8	−0.170070	−0.0850350	−	0.996378i	$-0.527100\pi$
$89$	−1.00666e8	−0.170070	−0.0850350	+	0.996378i	$0.527100\pi$
$90$	0	0
$91$	1.19424e8	0.182560
$92$	5.80250e8	0.844442
$93$	1.73252e9	2.40163
$94$	−4.90467e7	−0.0647940
$95$	0	0
$96$	9.95153e8	1.19583
$97$	−3.40802e8	−0.390868	−0.195434	−	0.980717i	$-0.562612\pi$
$97$	−3.40802e8	−0.390868	−0.195434	+	0.980717i	$0.562612\pi$
$98$	3.73225e8	0.408746
$99$	1.38966e9	1.45396
$100$	0	0
$101$	2.01832e9	1.92994	0.964972	−	0.262354i	$-0.0844988\pi$
$101$	2.01832e9	1.92994	0.964972	+	0.262354i	$0.0844988\pi$
$102$	−1.14412e8	−0.104657
$103$	−7.03308e8	−0.615713	−0.307856	−	0.951433i	$-0.599612\pi$
$103$	−7.03308e8	−0.615713	−0.307856	+	0.951433i	$0.599612\pi$
$104$	3.53153e8	0.296014
$105$	0	0
$106$	1.76454e8	0.135755
$107$	−4.26374e8	−0.314459	−0.157229	−	0.987562i	$-0.550256\pi$
$107$	−4.26374e8	−0.314459	−0.157229	+	0.987562i	$0.550256\pi$
$108$	−5.51487e7	−0.0390057
$109$	−4.82003e8	−0.327062	−0.163531	−	0.986538i	$-0.552288\pi$
$109$	−4.82003e8	−0.327062	−0.163531	+	0.986538i	$0.552288\pi$
$110$	0	0
$111$	−3.54022e9	−2.21349
$112$	−3.17800e8	−0.190841
$113$	−5.99380e8	−0.345819	−0.172910	−	0.984938i	$-0.555317\pi$
$113$	−5.99380e8	−0.345819	−0.172910	+	0.984938i	$0.555317\pi$
$114$	−1.66260e9	−0.921969
$115$	0	0
$116$	−1.27747e9	−0.655073
$117$	5.29370e8	0.261170
$118$	9.64050e8	0.457752
$119$	−1.49951e8	−0.0685468
$120$	0	0
$121$	3.26349e9	1.38404
$122$	−1.35117e9	−0.552193
$123$	−5.26735e9	−2.07501
$124$	2.17723e9	0.827004
$125$	0	0
$126$	−1.26477e9	−0.447037
$127$	−3.94945e9	−1.34716	−0.673581	−	0.739113i	$-0.735245\pi$
$127$	−3.94945e9	−1.34716	−0.673581	+	0.739113i	$0.735245\pi$
$128$	6.15533e8	0.202678
$129$	4.48399e9	1.42565
$130$	0	0
$131$	4.51582e9	1.33973	0.669863	−	0.742485i	$-0.266353\pi$
$131$	4.51582e9	1.33973	0.669863	+	0.742485i	$0.266353\pi$
$132$	3.60093e9	1.03236
$133$	−2.17904e9	−0.603856
$134$	2.25954e9	0.605409
$135$	0	0
$136$	−4.43425e8	−0.111146
$137$	9.24727e7	0.0224270	0.0112135	−	0.999937i	$-0.496431\pi$
$137$	9.24727e7	0.0224270	0.0112135	+	0.999937i	$0.496431\pi$
$138$	−7.53524e9	−1.76865
$139$	4.80677e9	1.09216	0.546080	−	0.837733i	$-0.316119\pi$
$139$	4.80677e9	1.09216	0.546080	+	0.837733i	$0.316119\pi$
$140$	0	0
$141$	−5.87537e8	−0.125184
$142$	−1.98759e9	−0.410233
$143$	2.14140e9	0.428238
$144$	−1.40871e9	−0.273018
$145$	0	0
$146$	7.17910e9	1.30762
$147$	4.47091e9	0.789710
$148$	−4.44893e9	−0.762216
$149$	−3.69674e9	−0.614442	−0.307221	−	0.951638i	$-0.599399\pi$
$149$	−3.69674e9	−0.614442	−0.307221	+	0.951638i	$0.599399\pi$
$150$	0	0
$151$	−7.58747e9	−1.18768	−0.593842	−	0.804582i	$-0.702389\pi$
$151$	−7.58747e9	−1.18768	−0.593842	+	0.804582i	$0.702389\pi$
$152$	−6.44373e9	−0.979132
$153$	−6.64687e8	−0.0980632
$154$	−5.11621e9	−0.733002
$155$	0	0
$156$	1.37171e9	0.185440
$157$	−1.35722e9	−0.178279	−0.0891396	−	0.996019i	$-0.528412\pi$
$157$	−1.35722e9	−0.178279	−0.0891396	+	0.996019i	$0.528412\pi$
$158$	−1.03347e10	−1.31929
$159$	2.11376e9	0.262283
$160$	0	0
$161$	−9.87585e9	−1.15840
$162$	6.66984e9	0.760848
$163$	1.27247e10	1.41190	0.705950	−	0.708262i	$-0.250520\pi$
$163$	1.27247e10	1.41190	0.705950	+	0.708262i	$0.250520\pi$
$164$	−6.61939e9	−0.714530
$165$	0	0
$166$	3.34499e9	0.341907
$167$	1.26284e9	0.125639	0.0628197	−	0.998025i	$-0.479991\pi$
$167$	1.26284e9	0.125639	0.0628197	+	0.998025i	$0.479991\pi$
$168$	−1.01074e10	−0.978920
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−9.65905e9	−0.863877
$172$	5.63496e9	0.490922
$173$	1.39337e10	1.18266	0.591328	−	0.806431i	$-0.298604\pi$
$173$	1.39337e10	1.18266	0.591328	+	0.806431i	$0.298604\pi$
$174$	1.65895e10	1.37202
$175$	0	0
$176$	−5.69849e9	−0.447665
$177$	1.15485e10	0.884392
$178$	1.64282e9	0.122659
$179$	1.05518e9	0.0768222	0.0384111	−	0.999262i	$-0.487770\pi$
$179$	1.05518e9	0.0768222	0.0384111	+	0.999262i	$0.487770\pi$
$180$	0	0
$181$	−2.35110e9	−0.162823	−0.0814117	−	0.996681i	$-0.525943\pi$
$181$	−2.35110e9	−0.162823	−0.0814117	+	0.996681i	$0.525943\pi$
$182$	−1.94894e9	−0.131667
$183$	−1.61858e10	−1.06686
$184$	−2.92043e10	−1.87831
$185$	0	0
$186$	−2.82740e10	−1.73212
$187$	−2.68878e9	−0.160793
$188$	−7.38347e8	−0.0431073
$189$	9.38630e8	0.0535077
$190$	0	0
$191$	−6.57693e9	−0.357580	−0.178790	−	0.983887i	$-0.557218\pi$
$191$	−6.57693e9	−0.357580	−0.178790	+	0.983887i	$0.557218\pi$
$192$	−2.38478e10	−1.26647
$193$	−4.90525e9	−0.254480	−0.127240	−	0.991872i	$-0.540612\pi$
$193$	−4.90525e9	−0.254480	−0.127240	+	0.991872i	$0.540612\pi$
$194$	5.56173e9	0.281905
$195$	0	0
$196$	5.61851e9	0.271937
$197$	3.33003e10	1.57525	0.787626	−	0.616154i	$-0.211310\pi$
$197$	3.33003e10	1.57525	0.787626	+	0.616154i	$0.211310\pi$
$198$	−2.26787e10	−1.04863
$199$	−1.41182e10	−0.638176	−0.319088	−	0.947725i	$-0.603377\pi$
$199$	−1.41182e10	−0.638176	−0.319088	+	0.947725i	$0.603377\pi$
$200$	0	0
$201$	2.70673e10	1.16967
$202$	−3.29381e10	−1.39193
$203$	2.17425e10	0.898624
$204$	−1.72235e9	−0.0696283
$205$	0	0
$206$	1.14777e10	0.444069
$207$	−4.37767e10	−1.65721
$208$	−2.17075e9	−0.0804126
$209$	−3.90726e10	−1.41649
$210$	0	0
$211$	−2.36131e10	−0.820128	−0.410064	−	0.912057i	$-0.634494\pi$
$211$	−2.36131e10	−0.820128	−0.410064	+	0.912057i	$0.634494\pi$
$212$	2.65633e9	0.0903173
$213$	−2.38096e10	−0.792583
$214$	6.95821e9	0.226796
$215$	0	0
$216$	2.77566e9	0.0867610
$217$	−3.70565e10	−1.13448
$218$	7.86606e9	0.235886
$219$	8.59993e10	2.52637
$220$	0	0
$221$	−1.02425e9	−0.0288828
$222$	5.77747e10	1.59643
$223$	−3.82739e10	−1.03641	−0.518203	−	0.855257i	$-0.673399\pi$
$223$	−3.82739e10	−1.03641	−0.518203	+	0.855257i	$0.673399\pi$
$224$	−2.12851e10	−0.564883
$225$	0	0
$226$	9.78159e9	0.249414
$227$	7.86598e9	0.196624	0.0983120	−	0.995156i	$-0.468656\pi$
$227$	7.86598e9	0.196624	0.0983120	+	0.995156i	$0.468656\pi$
$228$	−2.50287e10	−0.613383
$229$	−2.70282e9	−0.0649469	−0.0324734	−	0.999473i	$-0.510338\pi$
$229$	−2.70282e9	−0.0649469	−0.0324734	+	0.999473i	$0.510338\pi$
$230$	0	0
$231$	−6.12878e10	−1.41618
$232$	6.42957e10	1.45709
$233$	−6.47198e9	−0.143858	−0.0719292	−	0.997410i	$-0.522916\pi$
$233$	−6.47198e9	−0.143858	−0.0719292	+	0.997410i	$0.522916\pi$
$234$	−8.63907e9	−0.188363
$235$	0	0
$236$	1.45128e10	0.304541
$237$	−1.23801e11	−2.54892
$238$	2.44712e9	0.0494379
$239$	−8.94464e9	−0.177326	−0.0886630	−	0.996062i	$-0.528259\pi$
$239$	−8.94464e9	−0.177326	−0.0886630	+	0.996062i	$0.528259\pi$
$240$	0	0
$241$	9.58346e10	1.82998	0.914988	−	0.403480i	$-0.132200\pi$
$241$	9.58346e10	1.82998	0.914988	+	0.403480i	$0.132200\pi$
$242$	−5.32587e10	−0.998208
$243$	7.54804e10	1.38869
$244$	−2.03405e10	−0.367373
$245$	0	0
$246$	8.59606e10	1.49655
$247$	−1.48841e10	−0.254440
$248$	−1.09581e11	−1.83952
$249$	4.00701e10	0.660576
$250$	0	0
$251$	−1.46628e10	−0.233177	−0.116588	−	0.993180i	$-0.537196\pi$
$251$	−1.46628e10	−0.233177	−0.116588	+	0.993180i	$0.537196\pi$
$252$	−1.90398e10	−0.297412
$253$	−1.77085e11	−2.71731
$254$	6.44532e10	0.971611
$255$	0	0
$256$	−7.25030e10	−1.05506
$257$	2.49501e10	0.356758	0.178379	−	0.983962i	$-0.442915\pi$
$257$	2.49501e10	0.356758	0.178379	+	0.983962i	$0.442915\pi$
$258$	−7.31766e10	−1.02821
$259$	7.57208e10	1.04560
$260$	0	0
$261$	9.63782e10	1.28557
$262$	−7.36960e10	−0.966247
$263$	1.44606e10	0.186374	0.0931872	−	0.995649i	$-0.470295\pi$
$263$	1.44606e10	0.186374	0.0931872	+	0.995649i	$0.470295\pi$
$264$	−1.81236e11	−2.29630
$265$	0	0
$266$	3.55609e10	0.435517
$267$	1.96796e10	0.236982
$268$	3.40151e10	0.402777
$269$	2.72584e10	0.317406	0.158703	−	0.987326i	$-0.449269\pi$
$269$	2.72584e10	0.317406	0.158703	+	0.987326i	$0.449269\pi$
$270$	0	0
$271$	−2.09550e10	−0.236007	−0.118004	−	0.993013i	$-0.537649\pi$
$271$	−2.09550e10	−0.236007	−0.118004	+	0.993013i	$0.537649\pi$
$272$	2.72563e9	0.0301931
$273$	−2.33466e10	−0.254385
$274$	−1.50911e9	−0.0161750
$275$	0	0
$276$	−1.13435e11	−1.17668
$277$	−8.78317e10	−0.896381	−0.448190	−	0.893938i	$-0.647931\pi$
$277$	−8.78317e10	−0.896381	−0.448190	+	0.893938i	$0.647931\pi$
$278$	−7.84441e10	−0.787696
$279$	−1.64261e11	−1.62298
$280$	0	0
$281$	5.56211e10	0.532183	0.266092	−	0.963948i	$-0.414268\pi$
$281$	5.56211e10	0.532183	0.266092	+	0.963948i	$0.414268\pi$
$282$	9.58832e9	0.0902862
$283$	7.28077e10	0.674743	0.337371	−	0.941372i	$-0.390462\pi$
$283$	7.28077e10	0.674743	0.337371	+	0.941372i	$0.390462\pi$
$284$	−2.99212e10	−0.272927
$285$	0	0
$286$	−3.49466e10	−0.308857
$287$	1.12662e11	0.980186
$288$	−9.43504e10	−0.808123
$289$	−1.17302e11	−0.989155
$290$	0	0
$291$	6.66247e10	0.544649
$292$	1.08074e11	0.869957
$293$	−4.53763e10	−0.359687	−0.179844	−	0.983695i	$-0.557559\pi$
$293$	−4.53763e10	−0.359687	−0.179844	+	0.983695i	$0.557559\pi$
$294$	−7.29631e10	−0.569561
$295$	0	0
$296$	2.23917e11	1.69541
$297$	1.68307e10	0.125515
$298$	6.03290e10	0.443152
$299$	−6.74575e10	−0.488102
$300$	0	0
$301$	−9.59069e10	−0.673443
$302$	1.23824e11	0.856590
$303$	−3.94569e11	−2.68925
$304$	3.96081e10	0.265982
$305$	0	0
$306$	1.08474e10	0.0707259
$307$	−9.23710e10	−0.593489	−0.296745	−	0.954957i	$-0.595901\pi$
$307$	−9.23710e10	−0.593489	−0.296745	+	0.954957i	$0.595901\pi$
$308$	−7.70192e10	−0.487664
$309$	1.37492e11	0.857956
$310$	0	0
$311$	7.80707e10	0.473223	0.236612	−	0.971604i	$-0.423963\pi$
$311$	7.80707e10	0.473223	0.236612	+	0.971604i	$0.423963\pi$
$312$	−6.90391e10	−0.412477
$313$	−4.52121e10	−0.266259	−0.133130	−	0.991099i	$-0.542503\pi$
$313$	−4.52121e10	−0.266259	−0.133130	+	0.991099i	$0.542503\pi$
$314$	2.21491e10	0.128580
$315$	0	0
$316$	−1.55578e11	−0.877721
$317$	−1.84668e11	−1.02713	−0.513564	−	0.858051i	$-0.671675\pi$
$317$	−1.84668e11	−1.02713	−0.513564	+	0.858051i	$0.671675\pi$
$318$	−3.44956e10	−0.189165
$319$	3.89867e11	2.10794
$320$	0	0
$321$	8.33533e10	0.438178
$322$	1.61169e11	0.835469
$323$	1.86887e10	0.0955362
$324$	1.00408e11	0.506190
$325$	0	0
$326$	−2.07661e11	−1.01830
$327$	9.42285e10	0.455740
$328$	3.33157e11	1.58934
$329$	1.25667e10	0.0591342
$330$	0	0
$331$	−3.61831e9	−0.0165684	−0.00828419	−	0.999966i	$-0.502637\pi$
$331$	−3.61831e9	−0.0165684	−0.00828419	+	0.999966i	$0.502637\pi$
$332$	5.03553e10	0.227470
$333$	3.35648e11	1.49584
$334$	−2.06090e10	−0.0906146
$335$	0	0
$336$	6.21278e10	0.265925
$337$	−1.29191e11	−0.545630	−0.272815	−	0.962067i	$-0.587955\pi$
$337$	−1.29191e11	−0.545630	−0.272815	+	0.962067i	$0.587955\pi$
$338$	−1.33123e10	−0.0554791
$339$	1.17175e11	0.481877
$340$	0	0
$341$	−6.64463e11	−2.66119
$342$	1.57631e11	0.623052
$343$	−2.64360e11	−1.03127
$344$	−2.83610e11	−1.09197
$345$	0	0
$346$	−2.27391e11	−0.852965
$347$	−2.15064e11	−0.796314	−0.398157	−	0.917317i	$-0.630350\pi$
$347$	−2.15064e11	−0.796314	−0.398157	+	0.917317i	$0.630350\pi$
$348$	2.49737e11	0.912802
$349$	−4.00566e11	−1.44531	−0.722654	−	0.691210i	$-0.757078\pi$
$349$	−4.00566e11	−1.44531	−0.722654	+	0.691210i	$0.757078\pi$
$350$	0	0
$351$	6.41137e9	0.0225460
$352$	−3.81664e11	−1.32507
$353$	−1.78250e11	−0.611005	−0.305502	−	0.952191i	$-0.598824\pi$
$353$	−1.78250e11	−0.611005	−0.305502	+	0.952191i	$0.598824\pi$
$354$	−1.88466e11	−0.637848
$355$	0	0
$356$	2.47309e10	0.0816048
$357$	2.93144e10	0.0955156
$358$	−1.72200e10	−0.0554063
$359$	3.02613e11	0.961531	0.480765	−	0.876849i	$-0.340359\pi$
$359$	3.02613e11	0.961531	0.480765	+	0.876849i	$0.340359\pi$
$360$	0	0
$361$	−5.11086e10	−0.158384
$362$	3.83688e10	0.117433
$363$	−6.37992e11	−1.92857
$364$	−2.93392e10	−0.0875977
$365$	0	0
$366$	2.64145e11	0.769446
$367$	−1.61166e11	−0.463743	−0.231871	−	0.972746i	$-0.574485\pi$
$367$	−1.61166e11	−0.463743	−0.231871	+	0.972746i	$0.574485\pi$
$368$	1.79512e11	0.510244
$369$	4.99397e11	1.40226
$370$	0	0
$371$	−4.52107e10	−0.123896
$372$	−4.25635e11	−1.15238
$373$	3.29190e11	0.880557	0.440278	−	0.897861i	$-0.354880\pi$
$373$	3.29190e11	0.880557	0.440278	+	0.897861i	$0.354880\pi$
$374$	4.38796e10	0.115969
$375$	0	0
$376$	3.71614e10	0.0958842
$377$	1.48514e11	0.378643
$378$	−1.53180e10	−0.0385913
$379$	−1.32343e10	−0.0329478	−0.0164739	−	0.999864i	$-0.505244\pi$
$379$	−1.32343e10	−0.0329478	−0.0164739	+	0.999864i	$0.505244\pi$
$380$	0	0
$381$	7.72092e11	1.87718
$382$	1.07332e11	0.257896
$383$	5.90539e11	1.40234	0.701171	−	0.712993i	$-0.252661\pi$
$383$	5.90539e11	1.40234	0.701171	+	0.712993i	$0.252661\pi$
$384$	−1.20333e11	−0.282419
$385$	0	0
$386$	8.00513e10	0.183538
$387$	−4.25127e11	−0.963429
$388$	8.37261e10	0.187550
$389$	1.22822e11	0.271959	0.135980	−	0.990712i	$-0.456582\pi$
$389$	1.22822e11	0.271959	0.135980	+	0.990712i	$0.456582\pi$
$390$	0	0
$391$	8.47010e10	0.183271
$392$	−2.82783e11	−0.604875
$393$	−8.82814e11	−1.86682
$394$	−5.43445e11	−1.13611
$395$	0	0
$396$	−3.41404e11	−0.697653
$397$	6.75533e11	1.36486	0.682432	−	0.730949i	$-0.260922\pi$
$397$	6.75533e11	1.36486	0.682432	+	0.730949i	$0.260922\pi$
$398$	2.30402e11	0.460271
$399$	4.25989e11	0.841434
$400$	0	0
$401$	−7.61393e11	−1.47048	−0.735240	−	0.677807i	$-0.762931\pi$
$401$	−7.61393e11	−1.47048	−0.735240	+	0.677807i	$0.762931\pi$
$402$	−4.41726e11	−0.843598
$403$	−2.53116e11	−0.478022
$404$	−4.95848e11	−0.926046
$405$	0	0
$406$	−3.54828e11	−0.648112
$407$	1.35776e12	2.45271
$408$	8.66868e10	0.154875
$409$	9.73874e11	1.72087	0.860435	−	0.509561i	$-0.170192\pi$
$409$	9.73874e11	1.72087	0.860435	+	0.509561i	$0.170192\pi$
$410$	0	0
$411$	−1.80778e10	−0.0312506
$412$	1.72784e11	0.295438
$413$	−2.47007e11	−0.417767
$414$	7.14415e11	1.19522
$415$	0	0
$416$	−1.45389e11	−0.238019
$417$	−9.39692e11	−1.52185
$418$	6.37646e11	1.02161
$419$	5.89320e11	0.934089	0.467044	−	0.884234i	$-0.345319\pi$
$419$	5.89320e11	0.934089	0.467044	+	0.884234i	$0.345319\pi$
$420$	0	0
$421$	−1.88724e11	−0.292791	−0.146395	−	0.989226i	$-0.546767\pi$
$421$	−1.88724e11	−0.292791	−0.146395	+	0.989226i	$0.546767\pi$
$422$	3.85354e11	0.591499
$423$	5.57043e10	0.0845975
$424$	−1.33694e11	−0.200894
$425$	0	0
$426$	3.88562e11	0.571633
$427$	3.46195e11	0.503959
$428$	1.04749e11	0.150887
$429$	−4.18629e11	−0.596722
$430$	0	0
$431$	−5.30948e11	−0.741146	−0.370573	−	0.928803i	$-0.620839\pi$
$431$	−5.30948e11	−0.741146	−0.370573	+	0.928803i	$0.620839\pi$
$432$	−1.70613e10	−0.0235687
$433$	7.56173e11	1.03377	0.516887	−	0.856054i	$-0.327091\pi$
$433$	7.56173e11	1.03377	0.516887	+	0.856054i	$0.327091\pi$
$434$	6.04744e11	0.818216
$435$	0	0
$436$	1.18415e11	0.156935
$437$	1.23085e12	1.61450
$438$	−1.40347e12	−1.82209
$439$	−1.13771e12	−1.46198	−0.730990	−	0.682388i	$-0.760942\pi$
$439$	−1.13771e12	−1.46198	−0.730990	+	0.682388i	$0.760942\pi$
$440$	0	0
$441$	−4.23886e11	−0.533674
$442$	1.67152e10	0.0208311
$443$	3.84463e11	0.474284	0.237142	−	0.971475i	$-0.423789\pi$
$443$	3.84463e11	0.474284	0.237142	+	0.971475i	$0.423789\pi$
$444$	8.69738e11	1.06210
$445$	0	0
$446$	6.24611e11	0.747485
$447$	7.22689e11	0.856185
$448$	5.10075e11	0.598251
$449$	−1.00488e12	−1.16683	−0.583414	−	0.812175i	$-0.698283\pi$
$449$	−1.00488e12	−1.16683	−0.583414	+	0.812175i	$0.698283\pi$
$450$	0	0
$451$	2.02015e12	2.29927
$452$	1.47252e11	0.165935
$453$	1.48330e12	1.65496
$454$	−1.28369e11	−0.141811
$455$	0	0
$456$	1.25971e12	1.36436
$457$	2.63249e11	0.282322	0.141161	−	0.989987i	$-0.454917\pi$
$457$	2.63249e11	0.282322	0.141161	+	0.989987i	$0.454917\pi$
$458$	4.41088e10	0.0468415
$459$	−8.05023e9	−0.00846548
$460$	0	0
$461$	1.15282e12	1.18880	0.594398	−	0.804171i	$-0.297390\pi$
$461$	1.15282e12	1.18880	0.594398	+	0.804171i	$0.297390\pi$
$462$	1.00019e12	1.02139
$463$	1.51155e12	1.52865	0.764325	−	0.644831i	$-0.223072\pi$
$463$	1.51155e12	1.52865	0.764325	+	0.644831i	$0.223072\pi$
$464$	−3.95211e11	−0.395820
$465$	0	0
$466$	1.05620e11	0.103755
$467$	−5.02573e11	−0.488960	−0.244480	−	0.969654i	$-0.578617\pi$
$467$	−5.02573e11	−0.488960	−0.244480	+	0.969654i	$0.578617\pi$
$468$	−1.30052e11	−0.125317
$469$	−5.78936e11	−0.552526
$470$	0	0
$471$	2.65327e11	0.248421
$472$	−7.30435e11	−0.677396
$473$	−1.71972e12	−1.57972
$474$	2.02037e12	1.83835
$475$	0	0
$476$	3.68389e10	0.0328909
$477$	−2.00406e11	−0.177246
$478$	1.45972e11	0.127892
$479$	−1.01303e12	−0.879252	−0.439626	−	0.898181i	$-0.644889\pi$
$479$	−1.01303e12	−0.879252	−0.439626	+	0.898181i	$0.644889\pi$
$480$	0	0
$481$	5.17215e11	0.440574
$482$	−1.56397e12	−1.31983
$483$	1.93067e12	1.61415
$484$	−8.01754e11	−0.664105
$485$	0	0
$486$	−1.23180e12	−1.00156
$487$	−2.08642e12	−1.68082	−0.840412	−	0.541948i	$-0.817687\pi$
$487$	−2.08642e12	−1.68082	−0.840412	+	0.541948i	$0.817687\pi$
$488$	1.02375e12	0.817153
$489$	−2.48760e12	−1.96739
$490$	0	0
$491$	9.71272e11	0.754178	0.377089	−	0.926177i	$-0.376925\pi$
$491$	9.71272e11	0.754178	0.377089	+	0.926177i	$0.376925\pi$
$492$	1.29405e12	0.995651
$493$	−1.86476e11	−0.142172
$494$	2.42901e11	0.183509
$495$	0	0
$496$	6.73570e11	0.499707
$497$	5.09258e11	0.374398
$498$	−6.53924e11	−0.476426
$499$	2.28883e12	1.65257	0.826286	−	0.563250i	$-0.190449\pi$
$499$	2.28883e12	1.65257	0.826286	+	0.563250i	$0.190449\pi$
$500$	0	0
$501$	−2.46878e11	−0.175070
$502$	2.39290e11	0.168174
$503$	3.05827e10	0.0213020	0.0106510	−	0.999943i	$-0.496610\pi$
$503$	3.05827e10	0.0213020	0.0106510	+	0.999943i	$0.496610\pi$
$504$	9.58281e11	0.661539
$505$	0	0
$506$	2.88994e12	1.95980
$507$	−1.59470e11	−0.107187
$508$	9.70275e11	0.646410
$509$	1.25203e12	0.826768	0.413384	−	0.910557i	$-0.364347\pi$
$509$	1.25203e12	0.826768	0.413384	+	0.910557i	$0.364347\pi$
$510$	0	0
$511$	−1.83942e12	−1.19340
$512$	8.68061e11	0.558259
$513$	−1.16984e11	−0.0745757
$514$	−4.07174e11	−0.257304
$515$	0	0
$516$	−1.10160e12	−0.684068
$517$	2.25334e11	0.138714
$518$	−1.23573e12	−0.754117
$519$	−2.72395e12	−1.64796
$520$	0	0
$521$	−1.79829e12	−1.06928	−0.534640	−	0.845080i	$-0.679553\pi$
$521$	−1.79829e12	−1.06928	−0.534640	+	0.845080i	$0.679553\pi$
$522$	−1.57285e12	−0.927190
$523$	6.61177e11	0.386420	0.193210	−	0.981157i	$-0.438110\pi$
$523$	6.61177e11	0.386420	0.193210	+	0.981157i	$0.438110\pi$
$524$	−1.10942e12	−0.642842
$525$	0	0
$526$	−2.35990e11	−0.134418
$527$	3.17818e11	0.179486
$528$	1.11402e12	0.623792
$529$	3.77731e12	2.09716
$530$	0	0
$531$	−1.09491e12	−0.597658
$532$	5.35332e11	0.289748
$533$	7.69544e11	0.413010
$534$	−3.21161e11	−0.170918
$535$	0	0
$536$	−1.71200e12	−0.895903
$537$	−2.06280e11	−0.107047
$538$	−4.44844e11	−0.228922
$539$	−1.71470e12	−0.875060
$540$	0	0
$541$	8.36642e10	0.0419906	0.0209953	−	0.999780i	$-0.493317\pi$
$541$	8.36642e10	0.0419906	0.0209953	+	0.999780i	$0.493317\pi$
$542$	3.41975e11	0.170215
$543$	4.59624e11	0.226884
$544$	1.82553e11	0.0893704
$545$	0	0
$546$	3.81005e11	0.183469
$547$	1.69522e11	0.0809624	0.0404812	−	0.999180i	$-0.487111\pi$
$547$	1.69522e11	0.0809624	0.0404812	+	0.999180i	$0.487111\pi$
$548$	−2.27181e10	−0.0107612
$549$	1.53458e12	0.720964
$550$	0	0
$551$	−2.70982e12	−1.25244
$552$	5.70925e12	2.61730
$553$	2.64794e12	1.20405
$554$	1.43337e12	0.646495
$555$	0	0
$556$	−1.18089e12	−0.524052
$557$	4.05791e11	0.178630	0.0893149	−	0.996003i	$-0.471532\pi$
$557$	4.05791e11	0.178630	0.0893149	+	0.996003i	$0.471532\pi$
$558$	2.68065e12	1.17054
$559$	−6.55098e11	−0.283761
$560$	0	0
$561$	5.25639e11	0.224055
$562$	−9.07710e11	−0.383825
$563$	−5.64194e11	−0.236669	−0.118334	−	0.992974i	$-0.537755\pi$
$563$	−5.64194e11	−0.236669	−0.118334	+	0.992974i	$0.537755\pi$
$564$	1.44342e11	0.0600672
$565$	0	0
$566$	−1.18819e12	−0.486643
$567$	−1.70894e12	−0.694387
$568$	1.50595e12	0.607075
$569$	−3.52259e12	−1.40882	−0.704412	−	0.709791i	$-0.748789\pi$
$569$	−3.52259e12	−1.40882	−0.704412	+	0.709791i	$0.748789\pi$
$570$	0	0
$571$	−2.34039e11	−0.0921351	−0.0460676	−	0.998938i	$-0.514669\pi$
$571$	−2.34039e11	−0.0921351	−0.0460676	+	0.998938i	$0.514669\pi$
$572$	−5.26084e11	−0.205482
$573$	1.28575e12	0.498264
$574$	−1.83859e12	−0.706938
$575$	0	0
$576$	2.26101e12	0.855858
$577$	−2.36947e12	−0.889938	−0.444969	−	0.895546i	$-0.646785\pi$
$577$	−2.36947e12	−0.889938	−0.444969	+	0.895546i	$0.646785\pi$
$578$	1.91431e12	0.713406
$579$	9.58945e11	0.354601
$580$	0	0
$581$	−8.57048e11	−0.312041
$582$	−1.08728e12	−0.392816
$583$	−8.10677e11	−0.290629
$584$	−5.43941e12	−1.93506
$585$	0	0
$586$	7.40520e11	0.259417
$587$	4.42240e11	0.153740	0.0768699	−	0.997041i	$-0.475507\pi$
$587$	4.42240e11	0.153740	0.0768699	+	0.997041i	$0.475507\pi$
$588$	−1.09838e12	−0.378927
$589$	4.61844e12	1.58116
$590$	0	0
$591$	−6.50999e12	−2.19501
$592$	−1.37637e12	−0.460560
$593$	3.51413e12	1.16700	0.583501	−	0.812112i	$-0.301682\pi$
$593$	3.51413e12	1.16700	0.583501	+	0.812112i	$0.301682\pi$
$594$	−2.74668e11	−0.0905252
$595$	0	0
$596$	9.08191e11	0.294828
$597$	2.76002e12	0.889258
$598$	1.10087e12	0.352032
$599$	−3.89728e12	−1.23692	−0.618459	−	0.785817i	$-0.712243\pi$
$599$	−3.89728e12	−1.23692	−0.618459	+	0.785817i	$0.712243\pi$
$600$	0	0
$601$	−6.31022e12	−1.97292	−0.986460	−	0.164000i	$-0.947560\pi$
$601$	−6.31022e12	−1.97292	−0.986460	+	0.164000i	$0.947560\pi$
$602$	1.56516e12	0.485706
$603$	−2.56625e12	−0.790445
$604$	1.86404e12	0.569887
$605$	0	0
$606$	6.43918e12	1.93956
$607$	1.30553e12	0.390336	0.195168	−	0.980770i	$-0.437475\pi$
$607$	1.30553e12	0.390336	0.195168	+	0.980770i	$0.437475\pi$
$608$	2.65281e12	0.787298
$609$	−4.25052e12	−1.25217
$610$	0	0
$611$	8.58373e10	0.0249167
$612$	1.63296e11	0.0470537
$613$	−2.66230e12	−0.761526	−0.380763	−	0.924673i	$-0.624339\pi$
$613$	−2.66230e12	−0.761526	−0.380763	+	0.924673i	$0.624339\pi$
$614$	1.50745e12	0.428041
$615$	0	0
$616$	3.87642e12	1.08472
$617$	−2.54811e12	−0.707840	−0.353920	−	0.935276i	$-0.615152\pi$
$617$	−2.54811e12	−0.707840	−0.353920	+	0.935276i	$0.615152\pi$
$618$	−2.24381e12	−0.618782
$619$	−4.97728e12	−1.36265	−0.681325	−	0.731981i	$-0.738596\pi$
$619$	−4.97728e12	−1.36265	−0.681325	+	0.731981i	$0.738596\pi$
$620$	0	0
$621$	−5.30193e11	−0.143061
$622$	−1.27408e12	−0.341302
$623$	−4.20921e11	−0.111945
$624$	4.24367e11	0.112050
$625$	0	0
$626$	7.37839e11	0.192034
$627$	7.63844e12	1.97379
$628$	3.33432e11	0.0855438
$629$	−6.49425e11	−0.165425
$630$	0	0
$631$	−2.63483e12	−0.661638	−0.330819	−	0.943694i	$-0.607325\pi$
$631$	−2.63483e12	−0.661638	−0.330819	+	0.943694i	$0.607325\pi$
$632$	7.83033e12	1.95233
$633$	4.61621e12	1.14280
$634$	3.01369e12	0.740793
$635$	0	0
$636$	−5.19295e11	−0.125851
$637$	−6.53186e11	−0.157184
$638$	−6.36244e12	−1.52031
$639$	2.25739e12	0.535615
$640$	0	0
$641$	1.76148e12	0.412114	0.206057	−	0.978540i	$-0.433937\pi$
$641$	1.76148e12	0.412114	0.206057	+	0.978540i	$0.433937\pi$
$642$	−1.36029e12	−0.316026
$643$	−3.25395e12	−0.750691	−0.375346	−	0.926885i	$-0.622476\pi$
$643$	−3.25395e12	−0.750691	−0.375346	+	0.926885i	$0.622476\pi$
$644$	2.42623e12	0.555835
$645$	0	0
$646$	−3.04991e11	−0.0689034
$647$	−9.68172e11	−0.217212	−0.108606	−	0.994085i	$-0.534639\pi$
$647$	−9.68172e11	−0.217212	−0.108606	+	0.994085i	$0.534639\pi$
$648$	−5.05356e12	−1.12593
$649$	−4.42911e12	−0.979975
$650$	0	0
$651$	7.24431e12	1.58082
$652$	−3.12612e12	−0.677473
$653$	−7.28208e12	−1.56728	−0.783639	−	0.621216i	$-0.786639\pi$
$653$	−7.28208e12	−1.56728	−0.783639	+	0.621216i	$0.786639\pi$
$654$	−1.53776e12	−0.328692
$655$	0	0
$656$	−2.04784e12	−0.431746
$657$	−8.15359e12	−1.70728
$658$	−2.05082e11	−0.0426492
$659$	4.28818e12	0.885704	0.442852	−	0.896595i	$-0.353967\pi$
$659$	4.28818e12	0.885704	0.442852	+	0.896595i	$0.353967\pi$
$660$	0	0
$661$	−5.28587e12	−1.07698	−0.538492	−	0.842630i	$-0.681006\pi$
$661$	−5.28587e12	−1.07698	−0.538492	+	0.842630i	$0.681006\pi$
$662$	5.90491e10	0.0119496
$663$	2.00234e11	0.0402463
$664$	−2.53441e12	−0.505965
$665$	0	0
$666$	−5.47762e12	−1.07884
$667$	−1.22815e13	−2.40261
$668$	−3.10247e11	−0.0602856
$669$	7.48229e12	1.44417
$670$	0	0
$671$	6.20765e12	1.18216
$672$	4.16109e12	0.787128
$673$	−4.57588e12	−0.859818	−0.429909	−	0.902872i	$-0.641454\pi$
$673$	−4.57588e12	−0.859818	−0.429909	+	0.902872i	$0.641454\pi$
$674$	2.10834e12	0.393523
$675$	0	0
$676$	−2.00403e11	−0.0369101
$677$	−2.34137e12	−0.428372	−0.214186	−	0.976793i	$-0.568710\pi$
$677$	−2.34137e12	−0.428372	−0.214186	+	0.976793i	$0.568710\pi$
$678$	−1.91224e12	−0.347543
$679$	−1.42502e12	−0.257280
$680$	0	0
$681$	−1.53775e12	−0.273983
$682$	1.08437e13	1.91933
$683$	5.58769e12	0.982516	0.491258	−	0.871014i	$-0.336537\pi$
$683$	5.58769e12	0.982516	0.491258	+	0.871014i	$0.336537\pi$
$684$	2.37297e12	0.414515
$685$	0	0
$686$	4.31423e12	0.743780
$687$	5.28385e11	0.0904993
$688$	1.74329e12	0.296634
$689$	−3.08814e11	−0.0522049
$690$	0	0
$691$	1.07059e13	1.78637	0.893186	−	0.449688i	$-0.148465\pi$
$691$	1.07059e13	1.78637	0.893186	+	0.449688i	$0.148465\pi$
$692$	−3.42313e12	−0.567475
$693$	5.81069e12	0.957035
$694$	3.50973e12	0.574323
$695$	0	0
$696$	−1.25694e13	−2.03036
$697$	−9.66253e11	−0.155076
$698$	6.53705e12	1.04240
$699$	1.26523e12	0.200457
$700$	0	0
$701$	−7.07932e12	−1.10729	−0.553644	−	0.832753i	$-0.686763\pi$
$701$	−7.07932e12	−1.10729	−0.553644	+	0.832753i	$0.686763\pi$
$702$	−1.04630e11	−0.0162608
$703$	−9.43727e12	−1.45729
$704$	9.14620e12	1.40334
$705$	0	0
$706$	2.90896e12	0.440673
$707$	8.43933e12	1.27034
$708$	−2.83715e12	−0.424358
$709$	−2.17524e12	−0.323295	−0.161647	−	0.986849i	$-0.551681\pi$
$709$	−2.17524e12	−0.323295	−0.161647	+	0.986849i	$0.551681\pi$
$710$	0	0
$711$	1.17375e13	1.72252
$712$	−1.24472e12	−0.181515
$713$	2.09317e13	3.03320
$714$	−4.78397e11	−0.0688885
$715$	0	0
$716$	−2.59229e11	−0.0368617
$717$	1.74862e12	0.247092
$718$	−4.93851e12	−0.693483
$719$	−9.42350e12	−1.31502	−0.657510	−	0.753446i	$-0.728390\pi$
$719$	−9.42350e12	−1.31502	−0.657510	+	0.753446i	$0.728390\pi$
$720$	0	0
$721$	−2.94078e12	−0.405279
$722$	8.34068e11	0.114231
$723$	−1.87350e13	−2.54995
$724$	5.77601e11	0.0781276
$725$	0	0
$726$	1.04117e13	1.39094
$727$	−1.32240e13	−1.75574	−0.877868	−	0.478903i	$-0.841035\pi$
$727$	−1.32240e13	−1.75574	−0.877868	+	0.478903i	$0.841035\pi$
$728$	1.47666e12	0.194845
$729$	−6.71143e12	−0.880119
$730$	0	0
$731$	8.22553e11	0.106546
$732$	3.97643e12	0.511910
$733$	−1.26122e13	−1.61370	−0.806849	−	0.590758i	$-0.798829\pi$
$733$	−1.26122e13	−1.61370	−0.806849	+	0.590758i	$0.798829\pi$
$734$	2.63016e12	0.334464
$735$	0	0
$736$	1.20230e13	1.51030
$737$	−1.03809e13	−1.29608
$738$	−8.14992e12	−1.01135
$739$	−1.82154e11	−0.0224666	−0.0112333	−	0.999937i	$-0.503576\pi$
$739$	−1.82154e11	−0.0224666	−0.0112333	+	0.999937i	$0.503576\pi$
$740$	0	0
$741$	2.90974e12	0.354546
$742$	7.37817e11	0.0893576
$743$	−1.20049e13	−1.44514	−0.722569	−	0.691299i	$-0.757039\pi$
$743$	−1.20049e13	−1.44514	−0.722569	+	0.691299i	$0.757039\pi$
$744$	2.14224e13	2.56325
$745$	0	0
$746$	−5.37223e12	−0.635082
$747$	−3.79904e12	−0.446407
$748$	6.60561e11	0.0771535
$749$	−1.78282e12	−0.206985
$750$	0	0
$751$	−1.27467e13	−1.46224	−0.731121	−	0.682248i	$-0.761003\pi$
$751$	−1.27467e13	−1.46224	−0.731121	+	0.682248i	$0.761003\pi$
$752$	−2.28422e11	−0.0260470
$753$	2.86648e12	0.324917
$754$	−2.42367e12	−0.273088
$755$	0	0
$756$	−2.30596e11	−0.0256746
$757$	6.25355e11	0.0692142	0.0346071	−	0.999401i	$-0.488982\pi$
$757$	6.25355e11	0.0692142	0.0346071	+	0.999401i	$0.488982\pi$
$758$	2.15978e11	0.0237628
$759$	3.46189e13	3.78639
$760$	0	0
$761$	1.42335e13	1.53844	0.769219	−	0.638985i	$-0.220645\pi$
$761$	1.42335e13	1.53844	0.769219	+	0.638985i	$0.220645\pi$
$762$	−1.26002e13	−1.35388
$763$	−2.01543e12	−0.215281
$764$	1.61578e12	0.171578
$765$	0	0
$766$	−9.63732e12	−1.01141
$767$	−1.68720e12	−0.176030
$768$	1.41739e13	1.47015
$769$	1.51992e12	0.156730	0.0783648	−	0.996925i	$-0.475030\pi$
$769$	1.51992e12	0.156730	0.0783648	+	0.996925i	$0.475030\pi$
$770$	0	0
$771$	−4.87759e12	−0.497120
$772$	1.20509e12	0.122107
$773$	1.29024e13	1.29976	0.649878	−	0.760038i	$-0.274820\pi$
$773$	1.29024e13	1.29976	0.649878	+	0.760038i	$0.274820\pi$
$774$	6.93787e12	0.694851
$775$	0	0
$776$	−4.21398e12	−0.417171
$777$	−1.48029e13	−1.45698
$778$	−2.00440e12	−0.196145
$779$	−1.40413e13	−1.36612
$780$	0	0
$781$	9.13155e12	0.878243
$782$	−1.38228e12	−0.132180
$783$	1.16727e12	0.110979
$784$	1.73820e12	0.164315
$785$	0	0
$786$	1.44071e13	1.34640
$787$	1.11094e13	1.03230	0.516149	−	0.856499i	$-0.327365\pi$
$787$	1.11094e13	1.03230	0.516149	+	0.856499i	$0.327365\pi$
$788$	−8.18099e12	−0.755854
$789$	−2.82696e12	−0.259701
$790$	0	0
$791$	−2.50622e12	−0.227628
$792$	1.71830e13	1.55180
$793$	2.36470e12	0.212347
$794$	−1.10244e13	−0.984377
$795$	0	0
$796$	3.46847e12	0.306217
$797$	−1.81065e13	−1.58954	−0.794771	−	0.606910i	$-0.792409\pi$
$797$	−1.81065e13	−1.58954	−0.794771	+	0.606910i	$0.792409\pi$
$798$	−6.95193e12	−0.606865
$799$	−1.07779e11	−0.00935564
$800$	0	0
$801$	−1.86582e12	−0.160148
$802$	1.24256e13	1.06055
$803$	−3.29827e13	−2.79941
$804$	−6.64972e12	−0.561244
$805$	0	0
$806$	4.13074e12	0.344763
$807$	−5.32884e12	−0.442285
$808$	2.49563e13	2.05982
$809$	−6.50769e12	−0.534144	−0.267072	−	0.963677i	$-0.586056\pi$
$809$	−6.50769e12	−0.534144	−0.267072	+	0.963677i	$0.586056\pi$
$810$	0	0
$811$	1.60778e12	0.130506	0.0652532	−	0.997869i	$-0.479214\pi$
$811$	1.60778e12	0.130506	0.0652532	+	0.997869i	$0.479214\pi$
$812$	−5.34156e12	−0.431187
$813$	4.09656e12	0.328861
$814$	−2.21579e13	−1.76897
$815$	0	0
$816$	−5.32843e11	−0.0420721
$817$	1.19531e13	0.938602
$818$	−1.58932e13	−1.24114
$819$	2.21349e12	0.171909
$820$	0	0
$821$	−4.16062e11	−0.0319605	−0.0159803	−	0.999872i	$-0.505087\pi$
$821$	−4.16062e11	−0.0319605	−0.0159803	+	0.999872i	$0.505087\pi$
$822$	2.95021e11	0.0225388
$823$	−1.39121e13	−1.05705	−0.528524	−	0.848918i	$-0.677254\pi$
$823$	−1.39121e13	−1.05705	−0.528524	+	0.848918i	$0.677254\pi$
$824$	−8.69631e12	−0.657147
$825$	0	0
$826$	4.03104e12	0.301305
$827$	−1.82572e13	−1.35725	−0.678624	−	0.734486i	$-0.737423\pi$
$827$	−1.82572e13	−1.35725	−0.678624	+	0.734486i	$0.737423\pi$
$828$	1.07548e13	0.795179
$829$	−7.88052e12	−0.579508	−0.289754	−	0.957101i	$-0.593573\pi$
$829$	−7.88052e12	−0.579508	−0.289754	+	0.957101i	$0.593573\pi$
$830$	0	0
$831$	1.71705e13	1.24905
$832$	3.48410e12	0.252078
$833$	8.20152e11	0.0590190
$834$	1.53353e13	1.09760
$835$	0	0
$836$	9.59909e12	0.679676
$837$	−1.98941e12	−0.140107
$838$	−9.61742e12	−0.673691
$839$	−4.27424e12	−0.297804	−0.148902	−	0.988852i	$-0.547574\pi$
$839$	−4.27424e12	−0.297804	−0.148902	+	0.988852i	$0.547574\pi$
$840$	0	0
$841$	1.25315e13	0.863817
$842$	3.07988e12	0.211169
$843$	−1.08736e13	−0.741563
$844$	5.80111e12	0.393523
$845$	0	0
$846$	−9.09068e11	−0.0610140
$847$	1.36458e13	0.911014
$848$	8.21788e11	0.0545731
$849$	−1.42334e13	−0.940211
$850$	0	0
$851$	−4.27716e13	−2.79558
$852$	5.84939e12	0.380306
$853$	−3.57321e12	−0.231094	−0.115547	−	0.993302i	$-0.536862\pi$
$853$	−3.57321e12	−0.231094	−0.115547	+	0.993302i	$0.536862\pi$
$854$	−5.64973e12	−0.363469
$855$	0	0
$856$	−5.27205e12	−0.335620
$857$	−4.73369e12	−0.299768	−0.149884	−	0.988704i	$-0.547890\pi$
$857$	−4.73369e12	−0.299768	−0.149884	+	0.988704i	$0.547890\pi$
$858$	6.83183e12	0.430372
$859$	−1.03474e13	−0.648430	−0.324215	−	0.945983i	$-0.605100\pi$
$859$	−1.03474e13	−0.648430	−0.324215	+	0.945983i	$0.605100\pi$
$860$	0	0
$861$	−2.20247e13	−1.36583
$862$	8.66481e12	0.534535
$863$	−5.98909e12	−0.367546	−0.183773	−	0.982969i	$-0.558831\pi$
$863$	−5.98909e12	−0.367546	−0.183773	+	0.982969i	$0.558831\pi$
$864$	−1.14271e12	−0.0697626
$865$	0	0
$866$	−1.23404e13	−0.745586
$867$	2.29317e13	1.37832
$868$	9.10379e12	0.544357
$869$	4.74804e13	2.82440
$870$	0	0
$871$	−3.95445e12	−0.232812
$872$	−5.95990e12	−0.349072
$873$	−6.31668e12	−0.368065
$874$	−2.00869e13	−1.16442
$875$	0	0
$876$	−2.11277e13	−1.21223
$877$	−1.39807e13	−0.798053	−0.399027	−	0.916939i	$-0.630652\pi$
$877$	−1.39807e13	−0.798053	−0.399027	+	0.916939i	$0.630652\pi$
$878$	1.85669e13	1.05442
$879$	8.87078e12	0.501201
$880$	0	0
$881$	9.73989e12	0.544707	0.272353	−	0.962197i	$-0.412198\pi$
$881$	9.73989e12	0.544707	0.272353	+	0.962197i	$0.412198\pi$
$882$	6.91762e12	0.384900
$883$	1.68629e13	0.933490	0.466745	−	0.884392i	$-0.345427\pi$
$883$	1.68629e13	0.933490	0.466745	+	0.884392i	$0.345427\pi$
$884$	2.51630e11	0.0138589
$885$	0	0
$886$	−6.27426e12	−0.342066
$887$	2.63796e13	1.43091	0.715455	−	0.698659i	$-0.246219\pi$
$887$	2.63796e13	1.43091	0.715455	+	0.698659i	$0.246219\pi$
$888$	−4.37744e13	−2.36244
$889$	−1.65141e13	−0.886740
$890$	0	0
$891$	−3.06431e13	−1.62886
$892$	9.40286e12	0.497300
$893$	−1.56621e12	−0.0824175
$894$	−1.17939e13	−0.617504
$895$	0	0
$896$	2.57376e12	0.133408
$897$	1.31875e13	0.680138
$898$	1.63992e13	0.841548
$899$	−4.60829e13	−2.35300
$900$	0	0
$901$	3.87753e11	0.0196017
$902$	−3.29679e13	−1.65829
$903$	1.87492e13	0.938399
$904$	−7.41125e12	−0.369091
$905$	0	0
$906$	−2.42068e13	−1.19360
$907$	3.67807e13	1.80463	0.902313	−	0.431081i	$-0.141868\pi$
$907$	3.67807e13	1.80463	0.902313	+	0.431081i	$0.141868\pi$
$908$	−1.93246e12	−0.0943462
$909$	3.74091e13	1.81735
$910$	0	0
$911$	−3.52262e13	−1.69447	−0.847233	−	0.531221i	$-0.821733\pi$
$911$	−3.52262e13	−1.69447	−0.847233	+	0.531221i	$0.821733\pi$
$912$	−7.74313e12	−0.370629
$913$	−1.53678e13	−0.731969
$914$	−4.29610e12	−0.203618
$915$	0	0
$916$	6.64012e11	0.0311635
$917$	1.88823e13	0.881845
$918$	1.31376e11	0.00610554
$919$	−5.40716e12	−0.250063	−0.125031	−	0.992153i	$-0.539903\pi$
$919$	−5.40716e12	−0.250063	−0.125031	+	0.992153i	$0.539903\pi$
$920$	0	0
$921$	1.80579e13	0.826989
$922$	−1.88135e13	−0.857393
$923$	3.47851e12	0.157756
$924$	1.50568e13	0.679529
$925$	0	0
$926$	−2.46678e13	−1.10250
$927$	−1.30356e13	−0.579793
$928$	−2.64698e13	−1.17161
$929$	−3.35013e13	−1.47568	−0.737838	−	0.674978i	$-0.764153\pi$
$929$	−3.35013e13	−1.47568	−0.737838	+	0.674978i	$0.764153\pi$
$930$	0	0
$931$	1.19182e13	0.519922
$932$	1.58999e12	0.0690277
$933$	−1.52623e13	−0.659406
$934$	8.20175e12	0.352651
$935$	0	0
$936$	6.54559e12	0.278745
$937$	−1.55385e13	−0.658538	−0.329269	−	0.944236i	$-0.606802\pi$
$937$	−1.55385e13	−0.658538	−0.329269	+	0.944236i	$0.606802\pi$
$938$	9.44796e12	0.398497
$939$	8.83867e12	0.371015
$940$	0	0
$941$	3.17799e13	1.32130	0.660648	−	0.750696i	$-0.270282\pi$
$941$	3.17799e13	1.32130	0.660648	+	0.750696i	$0.270282\pi$
$942$	−4.33001e12	−0.179168
$943$	−6.36381e13	−2.62068
$944$	4.48981e12	0.184015
$945$	0	0
$946$	2.80649e13	1.13934
$947$	−2.39555e13	−0.967900	−0.483950	−	0.875096i	$-0.660798\pi$
$947$	−2.39555e13	−0.967900	−0.483950	+	0.875096i	$0.660798\pi$
$948$	3.04145e13	1.22305
$949$	−1.25642e13	−0.502850
$950$	0	0
$951$	3.61014e13	1.43124
$952$	−1.85412e12	−0.0731597
$953$	−3.51324e13	−1.37971	−0.689857	−	0.723945i	$-0.742327\pi$
$953$	−3.51324e13	−1.37971	−0.689857	+	0.723945i	$0.742327\pi$
$954$	3.27053e12	0.127835
$955$	0	0
$956$	2.19746e12	0.0850864
$957$	−7.62165e13	−2.93728
$958$	1.65322e13	0.634141
$959$	3.86661e11	0.0147621
$960$	0	0
$961$	5.21009e13	1.97056
$962$	−8.44071e12	−0.317754
$963$	−7.90272e12	−0.296114
$964$	−2.35440e13	−0.878079
$965$	0	0
$966$	−3.15075e13	−1.16417
$967$	−1.51033e13	−0.555459	−0.277729	−	0.960659i	$-0.589582\pi$
$967$	−1.51033e13	−0.555459	−0.277729	+	0.960659i	$0.589582\pi$
$968$	4.03527e13	1.47718
$969$	−3.65352e12	−0.133124
$970$	0	0
$971$	−2.72070e13	−0.982186	−0.491093	−	0.871107i	$-0.663403\pi$
$971$	−2.72070e13	−0.982186	−0.491093	+	0.871107i	$0.663403\pi$
$972$	−1.85435e13	−0.666337
$973$	2.00988e13	0.718890
$974$	3.40494e13	1.21226
$975$	0	0
$976$	−6.29273e12	−0.221980
$977$	−3.80106e13	−1.33469	−0.667343	−	0.744751i	$-0.732568\pi$
$977$	−3.80106e13	−1.33469	−0.667343	+	0.744751i	$0.732568\pi$
$978$	4.05964e13	1.41894
$979$	−7.54756e12	−0.262594
$980$	0	0
$981$	−8.93379e12	−0.307982
$982$	−1.58507e13	−0.543934
$983$	5.13119e13	1.75278	0.876389	−	0.481604i	$-0.159945\pi$
$983$	5.13119e13	1.75278	0.876389	+	0.481604i	$0.159945\pi$
$984$	−6.51301e13	−2.21464
$985$	0	0
$986$	3.04321e12	0.102538
$987$	−2.45670e12	−0.0823997
$988$	3.65662e12	0.122088
$989$	5.41739e13	1.80056
$990$	0	0
$991$	−2.44860e13	−0.806465	−0.403233	−	0.915098i	$-0.632113\pi$
$991$	−2.44860e13	−0.806465	−0.403233	+	0.915098i	$0.632113\pi$
$992$	4.51133e13	1.47911
$993$	7.07356e11	0.0230870
$994$	−8.31084e12	−0.270027
$995$	0	0
$996$	−9.84414e12	−0.316965
$997$	2.51672e13	0.806689	0.403345	−	0.915048i	$-0.367848\pi$
$997$	2.51672e13	0.806689	0.403345	+	0.915048i	$0.367848\pi$
$998$	−3.73526e13	−1.19188
$999$	4.06514e12	0.129131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.k.1.11		27
5.2	odd	4		65.10.b.a.14.20	✓	54
5.3	odd	4		65.10.b.a.14.35	yes	54
5.4	even	2		325.10.a.l.1.17		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.b.a.14.20	✓	54	5.2	odd	4
65.10.b.a.14.35	yes	54	5.3	odd	4
325.10.a.k.1.11		27	1.1	even	1	trivial
325.10.a.l.1.17		27	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-16.3195 q^{2} -195.494 q^{3} -245.673 q^{4} +3190.36 q^{6} +4181.36 q^{7} +12364.9 q^{8} +18534.7 q^{9} +74976.3 q^{11} +48027.5 q^{12} +28561.0 q^{13} -68237.8 q^{14} -76003.9 q^{16} -35861.7 q^{17} -302478. q^{18} -521133. q^{19} -817429. q^{21} -1.22358e6 q^{22} -2.36188e6 q^{23} -2.41725e6 q^{24} -466102. q^{26} +224480. q^{27} -1.02725e6 q^{28} +5.19987e6 q^{29} -8.86231e6 q^{31} -5.09046e6 q^{32} -1.46574e7 q^{33} +585246. q^{34} -4.55349e6 q^{36} +1.81091e7 q^{37} +8.50463e6 q^{38} -5.58349e6 q^{39} +2.69439e7 q^{41} +1.33400e7 q^{42} -2.29368e7 q^{43} -1.84197e7 q^{44} +3.85447e7 q^{46} +3.00540e6 q^{47} +1.48583e7 q^{48} -2.28698e7 q^{49} +7.01074e6 q^{51} -7.01668e6 q^{52} -1.08125e7 q^{53} -3.66340e6 q^{54} +5.17019e7 q^{56} +1.01878e8 q^{57} -8.48594e7 q^{58} -5.90734e7 q^{59} +8.27948e7 q^{61} +1.44629e8 q^{62} +7.75003e7 q^{63} +1.21988e8 q^{64} +2.39201e8 q^{66} -1.38456e8 q^{67} +8.81027e6 q^{68} +4.61732e8 q^{69} +1.21792e8 q^{71} +2.29179e8 q^{72} -4.39909e8 q^{73} -2.95533e8 q^{74} +1.28028e8 q^{76} +3.13503e8 q^{77} +9.11199e7 q^{78} +6.33272e8 q^{79} -4.08703e8 q^{81} -4.39711e8 q^{82} -2.04969e8 q^{83} +2.00820e8 q^{84} +3.74317e8 q^{86} -1.01654e9 q^{87} +9.27071e8 q^{88} -1.00666e8 q^{89} +1.19424e8 q^{91} +5.80250e8 q^{92} +1.73252e9 q^{93} -4.90467e7 q^{94} +9.95153e8 q^{96} -3.40802e8 q^{97} +3.73225e8 q^{98} +1.38966e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) \) 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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