LMFDB - Embedded newform 325.10.a.k.1.19

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)

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")

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);

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			1.19
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)

$f(q)$	$=$	\(q+18.1415 q^{2} +10.3900 q^{3} -182.888 q^{4} +188.489 q^{6} +11293.6 q^{7} -12606.3 q^{8} -19575.0 q^{9} +60195.2 q^{11} -1900.20 q^{12} +28561.0 q^{13} +204883. q^{14} -135058. q^{16} -224981. q^{17} -355120. q^{18} -556885. q^{19} +117340. q^{21} +1.09203e6 q^{22} -1.16710e6 q^{23} -130979. q^{24} +518138. q^{26} -407890. q^{27} -2.06546e6 q^{28} -2.07628e6 q^{29} -2.19865e6 q^{31} +4.00427e6 q^{32} +625427. q^{33} -4.08148e6 q^{34} +3.58003e6 q^{36} +2.23731e7 q^{37} -1.01027e7 q^{38} +296748. q^{39} -1.66587e7 q^{41} +2.12873e6 q^{42} +4.07487e7 q^{43} -1.10090e7 q^{44} -2.11728e7 q^{46} -3.75678e7 q^{47} -1.40325e6 q^{48} +8.71922e7 q^{49} -2.33754e6 q^{51} -5.22345e6 q^{52} +1.84297e7 q^{53} -7.39972e6 q^{54} -1.42370e8 q^{56} -5.78602e6 q^{57} -3.76667e7 q^{58} -1.18597e8 q^{59} +3.63845e7 q^{61} -3.98868e7 q^{62} -2.21073e8 q^{63} +1.41793e8 q^{64} +1.13462e7 q^{66} -7.71724e7 q^{67} +4.11462e7 q^{68} -1.21261e7 q^{69} -3.52032e8 q^{71} +2.46768e8 q^{72} +8.03083e7 q^{73} +4.05880e8 q^{74} +1.01847e8 q^{76} +6.79822e8 q^{77} +5.38344e6 q^{78} -2.09520e8 q^{79} +3.81058e8 q^{81} -3.02213e8 q^{82} +3.40426e8 q^{83} -2.14601e7 q^{84} +7.39242e8 q^{86} -2.15725e7 q^{87} -7.58837e8 q^{88} -4.09952e8 q^{89} +3.22557e8 q^{91} +2.13448e8 q^{92} -2.28440e7 q^{93} -6.81534e8 q^{94} +4.16043e7 q^{96} -4.17219e8 q^{97} +1.58179e9 q^{98} -1.17832e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.1415	0.801747	0.400873	−	0.916134i	$-0.368707\pi$
$2$	18.1415	0.801747	0.400873	+	0.916134i	$0.368707\pi$
$3$	10.3900	0.0740575	0.0370287	−	0.999314i	$-0.488211\pi$
$3$	10.3900	0.0740575	0.0370287	+	0.999314i	$0.488211\pi$
$4$	−182.888	−0.357202
$5$	0	0
$5$	0	0
$6$	188.489	0.0593753
$7$	11293.6	1.77784	0.888918	−	0.458065i	$-0.151457\pi$
$7$	11293.6	1.77784	0.888918	+	0.458065i	$0.151457\pi$
$8$	−12606.3	−1.08813
$9$	−19575.0	−0.994515
$10$	0	0
$11$	60195.2	1.23964	0.619819	−	0.784745i	$-0.287206\pi$
$11$	60195.2	1.23964	0.619819	+	0.784745i	$0.287206\pi$
$12$	−1900.20	−0.0264535
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	204883.	1.42537
$15$	0	0
$16$	−135058.	−0.515204
$17$	−224981.	−0.653319	−0.326659	−	0.945142i	$-0.605923\pi$
$17$	−224981.	−0.653319	−0.326659	+	0.945142i	$0.605923\pi$
$18$	−355120.	−0.797349
$19$	−556885.	−0.980335	−0.490167	−	0.871628i	$-0.663064\pi$
$19$	−556885.	−0.980335	−0.490167	+	0.871628i	$0.663064\pi$
$20$	0	0
$21$	117340.	0.131662
$22$	1.09203e6	0.993875
$23$	−1.16710e6	−0.869625	−0.434812	−	0.900521i	$-0.643185\pi$
$23$	−1.16710e6	−0.869625	−0.434812	+	0.900521i	$0.643185\pi$
$24$	−130979.	−0.0805843
$25$	0	0
$26$	518138.	0.222364
$27$	−407890.	−0.147709
$28$	−2.06546e6	−0.635048
$29$	−2.07628e6	−0.545123	−0.272562	−	0.962138i	$-0.587871\pi$
$29$	−2.07628e6	−0.545123	−0.272562	+	0.962138i	$0.587871\pi$
$30$	0	0
$31$	−2.19865e6	−0.427592	−0.213796	−	0.976878i	$-0.568583\pi$
$31$	−2.19865e6	−0.427592	−0.213796	+	0.976878i	$0.568583\pi$
$32$	4.00427e6	0.675069
$33$	625427.	0.0918044
$34$	−4.08148e6	−0.523796
$35$	0	0
$36$	3.58003e6	0.355243
$37$	2.23731e7	1.96254	0.981268	−	0.192646i	$-0.0617068\pi$
$37$	2.23731e7	1.96254	0.981268	+	0.192646i	$0.0617068\pi$
$38$	−1.01027e7	−0.785980
$39$	296748.	0.0205398
$40$	0	0
$41$	−1.66587e7	−0.920691	−0.460346	−	0.887740i	$-0.652274\pi$
$41$	−1.66587e7	−0.920691	−0.460346	+	0.887740i	$0.652274\pi$
$42$	2.12873e6	0.105560
$43$	4.07487e7	1.81763	0.908817	−	0.417196i	$-0.136987\pi$
$43$	4.07487e7	1.81763	0.908817	+	0.417196i	$0.136987\pi$
$44$	−1.10090e7	−0.442802
$45$	0	0
$46$	−2.11728e7	−0.697219
$47$	−3.75678e7	−1.12299	−0.561494	−	0.827481i	$-0.689773\pi$
$47$	−3.75678e7	−1.12299	−0.561494	+	0.827481i	$0.689773\pi$
$48$	−1.40325e6	−0.0381547
$49$	8.71922e7	2.16070
$50$	0	0
$51$	−2.33754e6	−0.0483831
$52$	−5.22345e6	−0.0990701
$53$	1.84297e7	0.320832	0.160416	−	0.987050i	$-0.448716\pi$
$53$	1.84297e7	0.320832	0.160416	+	0.987050i	$0.448716\pi$
$54$	−7.39972e6	−0.118425
$55$	0	0
$56$	−1.42370e8	−1.93452
$57$	−5.78602e6	−0.0726011
$58$	−3.76667e7	−0.437051
$59$	−1.18597e8	−1.27420	−0.637101	−	0.770780i	$-0.719867\pi$
$59$	−1.18597e8	−1.27420	−0.637101	+	0.770780i	$0.719867\pi$
$60$	0	0
$61$	3.63845e7	0.336459	0.168229	−	0.985748i	$-0.446195\pi$
$61$	3.63845e7	0.336459	0.168229	+	0.985748i	$0.446195\pi$
$62$	−3.98868e7	−0.342820
$63$	−2.21073e8	−1.76809
$64$	1.41793e8	1.05644
$65$	0	0
$66$	1.13462e7	0.0736039
$67$	−7.71724e7	−0.467870	−0.233935	−	0.972252i	$-0.575160\pi$
$67$	−7.71724e7	−0.467870	−0.233935	+	0.972252i	$0.575160\pi$
$68$	4.11462e7	0.233367
$69$	−1.21261e7	−0.0644022
$70$	0	0
$71$	−3.52032e8	−1.64407	−0.822034	−	0.569439i	$-0.807161\pi$
$71$	−3.52032e8	−1.64407	−0.822034	+	0.569439i	$0.807161\pi$
$72$	2.46768e8	1.08216
$73$	8.03083e7	0.330984	0.165492	−	0.986211i	$-0.447079\pi$
$73$	8.03083e7	0.330984	0.165492	+	0.986211i	$0.447079\pi$
$74$	4.05880e8	1.57346
$75$	0	0
$76$	1.01847e8	0.350178
$77$	6.79822e8	2.20387
$78$	5.38344e6	0.0164678
$79$	−2.09520e8	−0.605208	−0.302604	−	0.953116i	$-0.597856\pi$
$79$	−2.09520e8	−0.605208	−0.302604	+	0.953116i	$0.597856\pi$
$80$	0	0
$81$	3.81058e8	0.983577
$82$	−3.02213e8	−0.738161
$83$	3.40426e8	0.787355	0.393678	−	0.919249i	$-0.371203\pi$
$83$	3.40426e8	0.787355	0.393678	+	0.919249i	$0.371203\pi$
$84$	−2.14601e7	−0.0470300
$85$	0	0
$86$	7.39242e8	1.45728
$87$	−2.15725e7	−0.0403705
$88$	−7.58837e8	−1.34889
$89$	−4.09952e8	−0.692593	−0.346297	−	0.938125i	$-0.612561\pi$
$89$	−4.09952e8	−0.692593	−0.346297	+	0.938125i	$0.612561\pi$
$90$	0	0
$91$	3.22557e8	0.493083
$92$	2.13448e8	0.310632
$93$	−2.28440e7	−0.0316664
$94$	−6.81534e8	−0.900352
$95$	0	0
$96$	4.16043e7	0.0499939
$97$	−4.17219e8	−0.478510	−0.239255	−	0.970957i	$-0.576903\pi$
$97$	−4.17219e8	−0.478510	−0.239255	+	0.970957i	$0.576903\pi$
$98$	1.58179e9	1.73234
$99$	−1.17832e9	−1.23284
$100$	0	0
$101$	−1.66183e9	−1.58906	−0.794529	−	0.607227i	$-0.792282\pi$
$101$	−1.66183e9	−1.58906	−0.794529	+	0.607227i	$0.792282\pi$
$102$	−4.24064e7	−0.0387910
$103$	6.57408e8	0.575529	0.287765	−	0.957701i	$-0.407088\pi$
$103$	6.57408e8	0.575529	0.287765	+	0.957701i	$0.407088\pi$
$104$	−3.60048e8	−0.301794
$105$	0	0
$106$	3.34342e8	0.257226
$107$	−2.26707e9	−1.67200	−0.836002	−	0.548726i	$-0.815113\pi$
$107$	−2.26707e9	−1.67200	−0.836002	+	0.548726i	$0.815113\pi$
$108$	7.45981e7	0.0527619
$109$	−2.58265e9	−1.75246	−0.876228	−	0.481897i	$-0.839948\pi$
$109$	−2.58265e9	−1.75246	−0.876228	+	0.481897i	$0.839948\pi$
$110$	0	0
$111$	2.32456e8	0.145341
$112$	−1.52529e9	−0.915949
$113$	−1.04027e9	−0.600197	−0.300099	−	0.953908i	$-0.597020\pi$
$113$	−1.04027e9	−0.600197	−0.300099	+	0.953908i	$0.597020\pi$
$114$	−1.04967e8	−0.0582077
$115$	0	0
$116$	3.79726e8	0.194719
$117$	−5.59083e8	−0.275829
$118$	−2.15152e9	−1.02159
$119$	−2.54085e9	−1.16149
$120$	0	0
$121$	1.26552e9	0.536702
$122$	6.60067e8	0.269755
$123$	−1.73084e8	−0.0681841
$124$	4.02107e8	0.152737
$125$	0	0
$126$	−4.01059e9	−1.41756
$127$	4.10884e9	1.40153	0.700766	−	0.713391i	$-0.252842\pi$
$127$	4.10884e9	1.40153	0.700766	+	0.713391i	$0.252842\pi$
$128$	5.22141e8	0.171927
$129$	4.23378e8	0.134609
$130$	0	0
$131$	−3.20548e9	−0.950982	−0.475491	−	0.879721i	$-0.657730\pi$
$131$	−3.20548e9	−0.950982	−0.475491	+	0.879721i	$0.657730\pi$
$132$	−1.14383e8	−0.0327928
$133$	−6.28925e9	−1.74288
$134$	−1.40002e9	−0.375114
$135$	0	0
$136$	2.83617e9	0.710897
$137$	−1.55645e9	−0.377479	−0.188740	−	0.982027i	$-0.560440\pi$
$137$	−1.55645e9	−0.377479	−0.188740	+	0.982027i	$0.560440\pi$
$138$	−2.19985e8	−0.0516342
$139$	−1.87975e9	−0.427103	−0.213551	−	0.976932i	$-0.568503\pi$
$139$	−1.87975e9	−0.427103	−0.213551	+	0.976932i	$0.568503\pi$
$140$	0	0
$141$	−3.90328e8	−0.0831656
$142$	−6.38637e9	−1.31813
$143$	1.71924e9	0.343814
$144$	2.64376e9	0.512378
$145$	0	0
$146$	1.45691e9	0.265366
$147$	9.05925e8	0.160016
$148$	−4.09176e9	−0.701023
$149$	−2.06267e9	−0.342840	−0.171420	−	0.985198i	$-0.554835\pi$
$149$	−2.06267e9	−0.342840	−0.171420	+	0.985198i	$0.554835\pi$
$150$	0	0
$151$	−8.25715e9	−1.29251	−0.646255	−	0.763121i	$-0.723666\pi$
$151$	−8.25715e9	−1.29251	−0.646255	+	0.763121i	$0.723666\pi$
$152$	7.02025e9	1.06673
$153$	4.40401e9	0.649736
$154$	1.23330e10	1.76695
$155$	0	0
$156$	−5.42716e7	−0.00733688
$157$	−2.86960e8	−0.0376941	−0.0188470	−	0.999822i	$-0.506000\pi$
$157$	−2.86960e8	−0.0376941	−0.0188470	+	0.999822i	$0.506000\pi$
$158$	−3.80101e9	−0.485223
$159$	1.91484e8	0.0237600
$160$	0	0
$161$	−1.31808e10	−1.54605
$162$	6.91294e9	0.788579
$163$	−1.28538e10	−1.42623	−0.713114	−	0.701048i	$-0.752716\pi$
$163$	−1.28538e10	−1.42623	−0.713114	+	0.701048i	$0.752716\pi$
$164$	3.04667e9	0.328873
$165$	0	0
$166$	6.17582e9	0.631260
$167$	−1.28563e9	−0.127906	−0.0639530	−	0.997953i	$-0.520371\pi$
$167$	−1.28563e9	−0.127906	−0.0639530	+	0.997953i	$0.520371\pi$
$168$	−1.47923e9	−0.143266
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	1.09011e10	0.974958
$172$	−7.45244e9	−0.649263
$173$	1.48032e10	1.25646	0.628231	−	0.778027i	$-0.283779\pi$
$173$	1.48032e10	1.25646	0.628231	+	0.778027i	$0.283779\pi$
$174$	−3.91356e8	−0.0323669
$175$	0	0
$176$	−8.12982e9	−0.638666
$177$	−1.23222e9	−0.0943642
$178$	−7.43713e9	−0.555284
$179$	−8.22798e9	−0.599038	−0.299519	−	0.954090i	$-0.596826\pi$
$179$	−8.22798e9	−0.599038	−0.299519	+	0.954090i	$0.596826\pi$
$180$	0	0
$181$	2.76654e10	1.91594	0.957972	−	0.286861i	$-0.0926119\pi$
$181$	2.76654e10	1.91594	0.957972	+	0.286861i	$0.0926119\pi$
$182$	5.85165e9	0.395328
$183$	3.78034e8	0.0249173
$184$	1.47127e10	0.946267
$185$	0	0
$186$	−4.14423e8	−0.0253884
$187$	−1.35428e10	−0.809879
$188$	6.87068e9	0.401134
$189$	−4.60656e9	−0.262602
$190$	0	0
$191$	−8.08599e9	−0.439625	−0.219813	−	0.975542i	$-0.570545\pi$
$191$	−8.08599e9	−0.439625	−0.219813	+	0.975542i	$0.570545\pi$
$192$	1.47322e9	0.0782372
$193$	−9.37272e9	−0.486248	−0.243124	−	0.969995i	$-0.578172\pi$
$193$	−9.37272e9	−0.486248	−0.243124	+	0.969995i	$0.578172\pi$
$194$	−7.56895e9	−0.383644
$195$	0	0
$196$	−1.59464e10	−0.771809
$197$	−7.19857e9	−0.340524	−0.170262	−	0.985399i	$-0.554461\pi$
$197$	−7.19857e9	−0.340524	−0.170262	+	0.985399i	$0.554461\pi$
$198$	−2.13765e10	−0.988425
$199$	−2.27057e10	−1.02635	−0.513175	−	0.858284i	$-0.671531\pi$
$199$	−2.27057e10	−1.02635	−0.513175	+	0.858284i	$0.671531\pi$
$200$	0	0
$201$	−8.01820e8	−0.0346493
$202$	−3.01480e10	−1.27402
$203$	−2.34487e10	−0.969141
$204$	4.27508e8	0.0172826
$205$	0	0
$206$	1.19263e10	0.461429
$207$	2.28460e10	0.864855
$208$	−3.85738e9	−0.142892
$209$	−3.35218e10	−1.21526
$210$	0	0
$211$	1.39078e10	0.483043	0.241522	−	0.970395i	$-0.422354\pi$
$211$	1.39078e10	0.483043	0.241522	+	0.970395i	$0.422354\pi$
$212$	−3.37057e9	−0.114602
$213$	−3.65760e9	−0.121755
$214$	−4.11279e10	−1.34052
$215$	0	0
$216$	5.14197e9	0.160727
$217$	−2.48308e10	−0.760188
$218$	−4.68531e10	−1.40503
$219$	8.34401e8	0.0245119
$220$	0	0
$221$	−6.42567e9	−0.181198
$222$	4.21708e9	0.116526
$223$	−1.53075e10	−0.414506	−0.207253	−	0.978287i	$-0.566452\pi$
$223$	−1.53075e10	−0.414506	−0.207253	+	0.978287i	$0.566452\pi$
$224$	4.52227e10	1.20016
$225$	0	0
$226$	−1.88721e10	−0.481206
$227$	−3.16606e10	−0.791412	−0.395706	−	0.918377i	$-0.629500\pi$
$227$	−3.16606e10	−0.791412	−0.395706	+	0.918377i	$0.629500\pi$
$228$	1.05819e9	0.0259333
$229$	2.89545e10	0.695755	0.347878	−	0.937540i	$-0.386902\pi$
$229$	2.89545e10	0.695755	0.347878	+	0.937540i	$0.386902\pi$
$230$	0	0
$231$	7.06333e9	0.163213
$232$	2.61741e10	0.593166
$233$	−4.54048e9	−0.100925	−0.0504627	−	0.998726i	$-0.516070\pi$
$233$	−4.54048e9	−0.100925	−0.0504627	+	0.998726i	$0.516070\pi$
$234$	−1.01426e10	−0.221145
$235$	0	0
$236$	2.16899e10	0.455148
$237$	−2.17691e9	−0.0448202
$238$	−4.60946e10	−0.931224
$239$	−1.35092e10	−0.267818	−0.133909	−	0.990994i	$-0.542753\pi$
$239$	−1.35092e10	−0.267818	−0.133909	+	0.990994i	$0.542753\pi$
$240$	0	0
$241$	2.53954e10	0.484928	0.242464	−	0.970160i	$-0.422044\pi$
$241$	2.53954e10	0.484928	0.242464	+	0.970160i	$0.422044\pi$
$242$	2.29583e10	0.430299
$243$	1.19877e10	0.220550
$244$	−6.65427e9	−0.120184
$245$	0	0
$246$	−3.13999e9	−0.0546663
$247$	−1.59052e10	−0.271896
$248$	2.77168e10	0.465276
$249$	3.53701e9	0.0583095
$250$	0	0
$251$	8.82045e10	1.40268	0.701340	−	0.712827i	$-0.252585\pi$
$251$	8.82045e10	1.40268	0.701340	+	0.712827i	$0.252585\pi$
$252$	4.04315e10	0.631565
$253$	−7.02537e10	−1.07802
$254$	7.45404e10	1.12367
$255$	0	0
$256$	−6.31255e10	−0.918597
$257$	−7.90254e10	−1.12997	−0.564986	−	0.825100i	$-0.691119\pi$
$257$	−7.90254e10	−1.12997	−0.564986	+	0.825100i	$0.691119\pi$
$258$	7.68070e9	0.107923
$259$	2.52673e11	3.48907
$260$	0	0
$261$	4.06433e10	0.542134
$262$	−5.81521e10	−0.762446
$263$	−3.69673e10	−0.476449	−0.238225	−	0.971210i	$-0.576565\pi$
$263$	−3.69673e10	−0.476449	−0.238225	+	0.971210i	$0.576565\pi$
$264$	−7.88430e9	−0.0998954
$265$	0	0
$266$	−1.14096e11	−1.39734
$267$	−4.25939e9	−0.0512917
$268$	1.41139e10	0.167124
$269$	5.36192e10	0.624361	0.312180	−	0.950023i	$-0.398941\pi$
$269$	5.36192e10	0.624361	0.312180	+	0.950023i	$0.398941\pi$
$270$	0	0
$271$	1.30113e11	1.46541	0.732705	−	0.680547i	$-0.238258\pi$
$271$	1.30113e11	1.46541	0.732705	+	0.680547i	$0.238258\pi$
$272$	3.03854e10	0.336592
$273$	3.35136e9	0.0365165
$274$	−2.82363e10	−0.302643
$275$	0	0
$276$	2.21772e9	0.0230046
$277$	4.80139e10	0.490014	0.245007	−	0.969521i	$-0.421210\pi$
$277$	4.80139e10	0.490014	0.245007	+	0.969521i	$0.421210\pi$
$278$	−3.41013e10	−0.342428
$279$	4.30388e10	0.425247
$280$	0	0
$281$	−1.87376e11	−1.79282	−0.896408	−	0.443229i	$-0.853833\pi$
$281$	−1.87376e11	−1.79282	−0.896408	+	0.443229i	$0.853833\pi$
$282$	−7.08112e9	−0.0666778
$283$	−1.50406e11	−1.39388	−0.696941	−	0.717129i	$-0.745456\pi$
$283$	−1.50406e11	−1.39388	−0.696941	+	0.717129i	$0.745456\pi$
$284$	6.43823e10	0.587265
$285$	0	0
$286$	3.11894e10	0.275651
$287$	−1.88137e11	−1.63684
$288$	−7.83838e10	−0.671367
$289$	−6.79716e10	−0.573175
$290$	0	0
$291$	−4.33489e9	−0.0354372
$292$	−1.46874e10	−0.118228
$293$	−1.47660e11	−1.17047	−0.585234	−	0.810865i	$-0.698997\pi$
$293$	−1.47660e11	−1.17047	−0.585234	+	0.810865i	$0.698997\pi$
$294$	1.64348e10	0.128292
$295$	0	0
$296$	−2.82041e11	−2.13550
$297$	−2.45530e10	−0.183105
$298$	−3.74198e10	−0.274871
$299$	−3.33335e10	−0.241191
$300$	0	0
$301$	4.60201e11	3.23146
$302$	−1.49797e11	−1.03627
$303$	−1.72663e10	−0.117682
$304$	7.52116e10	0.505072
$305$	0	0
$306$	7.98951e10	0.520923
$307$	2.66838e11	1.71445	0.857226	−	0.514941i	$-0.172186\pi$
$307$	2.66838e11	1.71445	0.857226	+	0.514941i	$0.172186\pi$
$308$	−1.24331e11	−0.787229
$309$	6.83045e9	0.0426222
$310$	0	0
$311$	−1.74684e11	−1.05885	−0.529423	−	0.848358i	$-0.677591\pi$
$311$	−1.74684e11	−1.05885	−0.529423	+	0.848358i	$0.677591\pi$
$312$	−3.74089e9	−0.0223501
$313$	−2.00516e11	−1.18086	−0.590431	−	0.807088i	$-0.701042\pi$
$313$	−2.00516e11	−1.18086	−0.590431	+	0.807088i	$0.701042\pi$
$314$	−5.20587e9	−0.0302211
$315$	0	0
$316$	3.83187e10	0.216182
$317$	−6.12644e9	−0.0340754	−0.0170377	−	0.999855i	$-0.505424\pi$
$317$	−6.12644e9	−0.0340754	−0.0170377	+	0.999855i	$0.505424\pi$
$318$	3.47381e9	0.0190495
$319$	−1.24982e11	−0.675756
$320$	0	0
$321$	−2.35548e10	−0.123824
$322$	−2.39118e11	−1.23954
$323$	1.25288e11	0.640471
$324$	−6.96908e10	−0.351336
$325$	0	0
$326$	−2.33187e11	−1.14347
$327$	−2.68337e10	−0.129782
$328$	2.10004e11	1.00183
$329$	−4.24276e11	−1.99649
$330$	0	0
$331$	−1.52746e11	−0.699428	−0.349714	−	0.936857i	$-0.613721\pi$
$331$	−1.52746e11	−0.699428	−0.349714	+	0.936857i	$0.613721\pi$
$332$	−6.22596e10	−0.281245
$333$	−4.37954e11	−1.95177
$334$	−2.33231e10	−0.102548
$335$	0	0
$336$	−1.58477e10	−0.0678328
$337$	−1.29233e11	−0.545808	−0.272904	−	0.962041i	$-0.587984\pi$
$337$	−1.29233e11	−0.545808	−0.272904	+	0.962041i	$0.587984\pi$
$338$	1.47985e10	0.0616728
$339$	−1.08084e10	−0.0444491
$340$	0	0
$341$	−1.32348e11	−0.530059
$342$	1.97761e11	0.781669
$343$	5.28977e11	2.06354
$344$	−5.13690e11	−1.97783
$345$	0	0
$346$	2.68552e11	1.00736
$347$	3.18336e11	1.17870	0.589350	−	0.807878i	$-0.299384\pi$
$347$	3.18336e11	1.17870	0.589350	+	0.807878i	$0.299384\pi$
$348$	3.94534e9	0.0144204
$349$	1.13814e10	0.0410658	0.0205329	−	0.999789i	$-0.493464\pi$
$349$	1.13814e10	0.0410658	0.0205329	+	0.999789i	$0.493464\pi$
$350$	0	0
$351$	−1.16498e10	−0.0409670
$352$	2.41038e11	0.836842
$353$	−5.50331e10	−0.188642	−0.0943209	−	0.995542i	$-0.530068\pi$
$353$	−5.50331e10	−0.188642	−0.0943209	+	0.995542i	$0.530068\pi$
$354$	−2.23542e10	−0.0756562
$355$	0	0
$356$	7.49752e10	0.247396
$357$	−2.63993e10	−0.0860173
$358$	−1.49267e11	−0.480277
$359$	3.66360e11	1.16408	0.582040	−	0.813160i	$-0.302255\pi$
$359$	3.66360e11	1.16408	0.582040	+	0.813160i	$0.302255\pi$
$360$	0	0
$361$	−1.25666e10	−0.0389436
$362$	5.01890e11	1.53610
$363$	1.31487e10	0.0397468
$364$	−5.89917e10	−0.176131
$365$	0	0
$366$	6.85808e9	0.0199773
$367$	−6.91629e10	−0.199010	−0.0995052	−	0.995037i	$-0.531726\pi$
$367$	−6.91629e10	−0.199010	−0.0995052	+	0.995037i	$0.531726\pi$
$368$	1.57625e11	0.448034
$369$	3.26095e11	0.915642
$370$	0	0
$371$	2.08138e11	0.570387
$372$	4.17788e9	0.0113113
$373$	3.83893e11	1.02688	0.513441	−	0.858125i	$-0.328370\pi$
$373$	3.83893e11	1.02688	0.513441	+	0.858125i	$0.328370\pi$
$374$	−2.45685e11	−0.649317
$375$	0	0
$376$	4.73589e11	1.22196
$377$	−5.93006e10	−0.151190
$378$	−8.35696e10	−0.210540
$379$	1.84827e10	0.0460140	0.0230070	−	0.999735i	$-0.492676\pi$
$379$	1.84827e10	0.0460140	0.0230070	+	0.999735i	$0.492676\pi$
$380$	0	0
$381$	4.26908e10	0.103794
$382$	−1.46692e11	−0.352468
$383$	3.17940e11	0.755007	0.377503	−	0.926008i	$-0.376783\pi$
$383$	3.17940e11	0.755007	0.377503	+	0.926008i	$0.376783\pi$
$384$	5.42503e9	0.0127324
$385$	0	0
$386$	−1.70035e11	−0.389847
$387$	−7.97659e11	−1.80766
$388$	7.63041e10	0.170925
$389$	−1.98361e11	−0.439221	−0.219611	−	0.975588i	$-0.570479\pi$
$389$	−1.98361e11	−0.439221	−0.219611	+	0.975588i	$0.570479\pi$
$390$	0	0
$391$	2.62574e11	0.568142
$392$	−1.09917e12	−2.35113
$393$	−3.33049e10	−0.0704273
$394$	−1.30593e11	−0.273014
$395$	0	0
$396$	2.15501e11	0.440373
$397$	−3.13360e11	−0.633121	−0.316560	−	0.948572i	$-0.602528\pi$
$397$	−3.13360e11	−0.633121	−0.316560	+	0.948572i	$0.602528\pi$
$398$	−4.11914e11	−0.822872
$399$	−6.53451e10	−0.129073
$400$	0	0
$401$	−1.39874e11	−0.270138	−0.135069	−	0.990836i	$-0.543126\pi$
$401$	−1.39874e11	−0.270138	−0.135069	+	0.990836i	$0.543126\pi$
$402$	−1.45462e10	−0.0277800
$403$	−6.27958e10	−0.118593
$404$	3.03928e11	0.567615
$405$	0	0
$406$	−4.25394e11	−0.777005
$407$	1.34675e12	2.43284
$408$	2.94677e10	0.0526472
$409$	−5.75115e11	−1.01625	−0.508124	−	0.861284i	$-0.669661\pi$
$409$	−5.75115e11	−1.01625	−0.508124	+	0.861284i	$0.669661\pi$
$410$	0	0
$411$	−1.61715e10	−0.0279552
$412$	−1.20232e11	−0.205580
$413$	−1.33939e12	−2.26532
$414$	4.14459e11	0.693395
$415$	0	0
$416$	1.14366e11	0.187231
$417$	−1.95305e10	−0.0316301
$418$	−6.08135e11	−0.974331
$419$	8.76921e11	1.38994	0.694972	−	0.719036i	$-0.255417\pi$
$419$	8.76921e11	1.38994	0.694972	+	0.719036i	$0.255417\pi$
$420$	0	0
$421$	4.75911e11	0.738340	0.369170	−	0.929362i	$-0.379642\pi$
$421$	4.75911e11	0.738340	0.369170	+	0.929362i	$0.379642\pi$
$422$	2.52307e11	0.387278
$423$	7.35391e11	1.11683
$424$	−2.32330e11	−0.349108
$425$	0	0
$426$	−6.63543e10	−0.0976170
$427$	4.10912e11	0.598169
$428$	4.14619e11	0.597244
$429$	1.78628e10	0.0254620
$430$	0	0
$431$	−6.24144e11	−0.871239	−0.435620	−	0.900131i	$-0.643471\pi$
$431$	−6.24144e11	−0.871239	−0.435620	+	0.900131i	$0.643471\pi$
$432$	5.50887e10	0.0761001
$433$	7.79305e11	1.06540	0.532699	−	0.846305i	$-0.321178\pi$
$433$	7.79305e11	1.06540	0.532699	+	0.846305i	$0.321178\pi$
$434$	−4.50466e11	−0.609478
$435$	0	0
$436$	4.72336e11	0.625982
$437$	6.49939e11	0.852523
$438$	1.51373e10	0.0196523
$439$	−4.84490e11	−0.622579	−0.311289	−	0.950315i	$-0.600761\pi$
$439$	−4.84490e11	−0.622579	−0.311289	+	0.950315i	$0.600761\pi$
$440$	0	0
$441$	−1.70679e12	−2.14885
$442$	−1.16571e11	−0.145275
$443$	1.77743e11	0.219268	0.109634	−	0.993972i	$-0.465032\pi$
$443$	1.77743e11	0.219268	0.109634	+	0.993972i	$0.465032\pi$
$444$	−4.25133e10	−0.0519160
$445$	0	0
$446$	−2.77699e11	−0.332329
$447$	−2.14311e10	−0.0253898
$448$	1.60135e12	1.87818
$449$	3.05737e11	0.355009	0.177504	−	0.984120i	$-0.443198\pi$
$449$	3.05737e11	0.355009	0.177504	+	0.984120i	$0.443198\pi$
$450$	0	0
$451$	−1.00277e12	−1.14132
$452$	1.90253e11	0.214392
$453$	−8.57916e10	−0.0957200
$454$	−5.74369e11	−0.634512
$455$	0	0
$456$	7.29402e10	0.0789996
$457$	−6.59511e11	−0.707293	−0.353646	−	0.935379i	$-0.615058\pi$
$457$	−6.59511e11	−0.707293	−0.353646	+	0.935379i	$0.615058\pi$
$458$	5.25277e11	0.557819
$459$	9.17674e10	0.0965009
$460$	0	0
$461$	−9.46343e11	−0.975876	−0.487938	−	0.872878i	$-0.662251\pi$
$461$	−9.46343e11	−0.975876	−0.487938	+	0.872878i	$0.662251\pi$
$462$	1.28139e11	0.130856
$463$	−4.26878e11	−0.431707	−0.215854	−	0.976426i	$-0.569253\pi$
$463$	−4.26878e11	−0.431707	−0.215854	+	0.976426i	$0.569253\pi$
$464$	2.80417e11	0.280850
$465$	0	0
$466$	−8.23710e10	−0.0809166
$467$	1.49321e12	1.45277	0.726384	−	0.687289i	$-0.241200\pi$
$467$	1.49321e12	1.45277	0.726384	+	0.687289i	$0.241200\pi$
$468$	1.02249e11	0.0985268
$469$	−8.71556e11	−0.831797
$470$	0	0
$471$	−2.98151e9	−0.00279153
$472$	1.49506e12	1.38650
$473$	2.45288e12	2.25321
$474$	−3.94924e10	−0.0359344
$475$	0	0
$476$	4.64689e11	0.414889
$477$	−3.60763e11	−0.319072
$478$	−2.45076e11	−0.214722
$479$	−1.16369e11	−0.101001	−0.0505006	−	0.998724i	$-0.516082\pi$
$479$	−1.16369e11	−0.101001	−0.0505006	+	0.998724i	$0.516082\pi$
$480$	0	0
$481$	6.38997e11	0.544310
$482$	4.60709e11	0.388790
$483$	−1.36948e11	−0.114497
$484$	−2.31447e11	−0.191711
$485$	0	0
$486$	2.17474e11	0.176825
$487$	3.00620e11	0.242179	0.121090	−	0.992642i	$-0.461361\pi$
$487$	3.00620e11	0.242179	0.121090	+	0.992642i	$0.461361\pi$
$488$	−4.58673e11	−0.366112
$489$	−1.33551e11	−0.105623
$490$	0	0
$491$	1.72579e11	0.134005	0.0670024	−	0.997753i	$-0.478656\pi$
$491$	1.72579e11	0.134005	0.0670024	+	0.997753i	$0.478656\pi$
$492$	3.16548e10	0.0243555
$493$	4.67123e11	0.356139
$494$	−2.88543e11	−0.217992
$495$	0	0
$496$	2.96945e11	0.220297
$497$	−3.97572e12	−2.92288
$498$	6.41666e10	0.0467495
$499$	1.95665e12	1.41274	0.706368	−	0.707845i	$-0.250332\pi$
$499$	1.95665e12	1.41274	0.706368	+	0.707845i	$0.250332\pi$
$500$	0	0
$501$	−1.33576e10	−0.00947239
$502$	1.60016e12	1.12459
$503$	−1.26777e12	−0.883051	−0.441526	−	0.897249i	$-0.645563\pi$
$503$	−1.26777e12	−0.883051	−0.441526	+	0.897249i	$0.645563\pi$
$504$	2.78691e12	1.92391
$505$	0	0
$506$	−1.27450e12	−0.864299
$507$	8.47542e9	0.00569673
$508$	−7.51457e11	−0.500631
$509$	9.72804e10	0.0642385	0.0321192	−	0.999484i	$-0.489774\pi$
$509$	9.72804e10	0.0642385	0.0321192	+	0.999484i	$0.489774\pi$
$510$	0	0
$511$	9.06971e11	0.588436
$512$	−1.41252e12	−0.908409
$513$	2.27148e11	0.144804
$514$	−1.43364e12	−0.905951
$515$	0	0
$516$	−7.74307e10	−0.0480828
$517$	−2.26140e12	−1.39210
$518$	4.58385e12	2.79735
$519$	1.53805e11	0.0930503
$520$	0	0
$521$	2.76982e12	1.64696	0.823479	−	0.567347i	$-0.192030\pi$
$521$	2.76982e12	1.64696	0.823479	+	0.567347i	$0.192030\pi$
$522$	7.37328e11	0.434654
$523$	1.17979e12	0.689518	0.344759	−	0.938691i	$-0.387961\pi$
$523$	1.17979e12	0.689518	0.344759	+	0.938691i	$0.387961\pi$
$524$	5.86243e11	0.339693
$525$	0	0
$526$	−6.70640e11	−0.381992
$527$	4.94655e11	0.279354
$528$	−8.44686e10	−0.0472980
$529$	−4.39036e11	−0.243753
$530$	0	0
$531$	2.32153e12	1.26721
$532$	1.15023e12	0.622559
$533$	−4.75789e11	−0.255354
$534$	−7.72716e10	−0.0411229
$535$	0	0
$536$	9.72857e11	0.509105
$537$	−8.54885e10	−0.0443632
$538$	9.72731e11	0.500579
$539$	5.24855e12	2.67849
$540$	0	0
$541$	2.03947e12	1.02360	0.511799	−	0.859105i	$-0.328979\pi$
$541$	2.03947e12	1.02360	0.511799	+	0.859105i	$0.328979\pi$
$542$	2.36044e12	1.17489
$543$	2.87442e11	0.141890
$544$	−9.00883e11	−0.441035
$545$	0	0
$546$	6.07985e10	0.0292770
$547$	−3.88695e10	−0.0185638	−0.00928189	−	0.999957i	$-0.502955\pi$
$547$	−3.88695e10	−0.0185638	−0.00928189	+	0.999957i	$0.502955\pi$
$548$	2.84656e11	0.134837
$549$	−7.12228e11	−0.334613
$550$	0	0
$551$	1.15625e12	0.534403
$552$	1.52865e11	0.0700781
$553$	−2.36624e12	−1.07596
$554$	8.71043e11	0.392867
$555$	0	0
$556$	3.43782e11	0.152562
$557$	3.92981e12	1.72991	0.864955	−	0.501850i	$-0.167347\pi$
$557$	3.92981e12	1.72991	0.864955	+	0.501850i	$0.167347\pi$
$558$	7.80786e11	0.340940
$559$	1.16382e12	0.504121
$560$	0	0
$561$	−1.40709e11	−0.0599776
$562$	−3.39928e12	−1.43738
$563$	7.21665e11	0.302725	0.151362	−	0.988478i	$-0.451634\pi$
$563$	7.21665e11	0.302725	0.151362	+	0.988478i	$0.451634\pi$
$564$	7.13862e10	0.0297070
$565$	0	0
$566$	−2.72858e12	−1.11754
$567$	4.30352e12	1.74864
$568$	4.43781e12	1.78896
$569$	−2.75023e12	−1.09993	−0.549964	−	0.835188i	$-0.685359\pi$
$569$	−2.75023e12	−1.09993	−0.549964	+	0.835188i	$0.685359\pi$
$570$	0	0
$571$	3.90328e12	1.53662	0.768311	−	0.640076i	$-0.221097\pi$
$571$	3.90328e12	1.53662	0.768311	+	0.640076i	$0.221097\pi$
$572$	−3.14427e11	−0.122811
$573$	−8.40132e10	−0.0325575
$574$	−3.41308e12	−1.31233
$575$	0	0
$576$	−2.77560e12	−1.05064
$577$	1.25866e12	0.472735	0.236367	−	0.971664i	$-0.424043\pi$
$577$	1.25866e12	0.472735	0.236367	+	0.971664i	$0.424043\pi$
$578$	−1.23310e12	−0.459541
$579$	−9.73823e10	−0.0360103
$580$	0	0
$581$	3.84464e12	1.39979
$582$	−7.86412e10	−0.0284117
$583$	1.10938e12	0.397715
$584$	−1.01239e12	−0.360155
$585$	0	0
$586$	−2.67877e12	−0.938419
$587$	−2.64664e12	−0.920074	−0.460037	−	0.887900i	$-0.652164\pi$
$587$	−2.64664e12	−0.920074	−0.460037	+	0.887900i	$0.652164\pi$
$588$	−1.65682e11	−0.0571582
$589$	1.22440e12	0.419183
$590$	0	0
$591$	−7.47930e10	−0.0252184
$592$	−3.02165e12	−1.01111
$593$	2.75964e12	0.916444	0.458222	−	0.888838i	$-0.348486\pi$
$593$	2.75964e12	0.916444	0.458222	+	0.888838i	$0.348486\pi$
$594$	−4.45428e11	−0.146804
$595$	0	0
$596$	3.77237e11	0.122463
$597$	−2.35911e11	−0.0760088
$598$	−6.04718e11	−0.193374
$599$	1.40559e12	0.446106	0.223053	−	0.974806i	$-0.428398\pi$
$599$	1.40559e12	0.446106	0.223053	+	0.974806i	$0.428398\pi$
$600$	0	0
$601$	8.92614e11	0.279080	0.139540	−	0.990216i	$-0.455438\pi$
$601$	8.92614e11	0.279080	0.139540	+	0.990216i	$0.455438\pi$
$602$	8.34871e12	2.59081
$603$	1.51065e12	0.465304
$604$	1.51013e12	0.461688
$605$	0	0
$606$	−3.13237e11	−0.0943508
$607$	−2.63701e12	−0.788430	−0.394215	−	0.919018i	$-0.628983\pi$
$607$	−2.63701e12	−0.788430	−0.394215	+	0.919018i	$0.628983\pi$
$608$	−2.22992e12	−0.661794
$609$	−2.43631e11	−0.0717721
$610$	0	0
$611$	−1.07297e12	−0.311461
$612$	−8.05439e11	−0.232087
$613$	−1.47284e12	−0.421291	−0.210645	−	0.977563i	$-0.567557\pi$
$613$	−1.47284e12	−0.421291	−0.210645	+	0.977563i	$0.567557\pi$
$614$	4.84083e12	1.37456
$615$	0	0
$616$	−8.57002e12	−2.39811
$617$	−2.88683e12	−0.801933	−0.400966	−	0.916093i	$-0.631326\pi$
$617$	−2.88683e12	−0.801933	−0.400966	+	0.916093i	$0.631326\pi$
$618$	1.23914e11	0.0341722
$619$	−3.40763e12	−0.932921	−0.466461	−	0.884542i	$-0.654471\pi$
$619$	−3.40763e12	−0.932921	−0.466461	+	0.884542i	$0.654471\pi$
$620$	0	0
$621$	4.76048e11	0.128451
$622$	−3.16903e12	−0.848926
$623$	−4.62984e12	−1.23132
$624$	−4.00781e10	−0.0105822
$625$	0	0
$626$	−3.63765e12	−0.946752
$627$	−3.48291e11	−0.0899991
$628$	5.24815e10	0.0134644
$629$	−5.03351e12	−1.28216
$630$	0	0
$631$	−5.62075e12	−1.41144	−0.705719	−	0.708492i	$-0.749376\pi$
$631$	−5.62075e12	−1.41144	−0.705719	+	0.708492i	$0.749376\pi$
$632$	2.64127e12	0.658546
$633$	1.44501e11	0.0357730
$634$	−1.11143e11	−0.0273199
$635$	0	0
$636$	−3.50201e10	−0.00848713
$637$	2.49030e12	0.599271
$638$	−2.26736e12	−0.541785
$639$	6.89105e12	1.63505
$640$	0	0
$641$	3.27017e12	0.765083	0.382542	−	0.923938i	$-0.375049\pi$
$641$	3.27017e12	0.765083	0.382542	+	0.923938i	$0.375049\pi$
$642$	−4.27318e11	−0.0992758
$643$	5.51761e12	1.27292	0.636461	−	0.771309i	$-0.280398\pi$
$643$	5.51761e12	1.27292	0.636461	+	0.771309i	$0.280398\pi$
$644$	2.41060e12	0.552253
$645$	0	0
$646$	2.27291e12	0.513495
$647$	−4.89879e12	−1.09906	−0.549528	−	0.835475i	$-0.685192\pi$
$647$	−4.89879e12	−1.09906	−0.549528	+	0.835475i	$0.685192\pi$
$648$	−4.80372e12	−1.07026
$649$	−7.13895e12	−1.57955
$650$	0	0
$651$	−2.57991e11	−0.0562976
$652$	2.35081e12	0.509452
$653$	8.27175e12	1.78028	0.890139	−	0.455689i	$-0.150607\pi$
$653$	8.27175e12	1.78028	0.890139	+	0.455689i	$0.150607\pi$
$654$	−4.86803e11	−0.104053
$655$	0	0
$656$	2.24989e12	0.474344
$657$	−1.57204e12	−0.329169
$658$	−7.69698e12	−1.60068
$659$	3.49908e12	0.722719	0.361359	−	0.932427i	$-0.382313\pi$
$659$	3.49908e12	0.722719	0.361359	+	0.932427i	$0.382313\pi$
$660$	0	0
$661$	−7.95593e12	−1.62100	−0.810502	−	0.585735i	$-0.800806\pi$
$661$	−7.95593e12	−1.62100	−0.810502	+	0.585735i	$0.800806\pi$
$662$	−2.77103e12	−0.560764
$663$	−6.67626e10	−0.0134191
$664$	−4.29150e12	−0.856747
$665$	0	0
$666$	−7.94512e12	−1.56483
$667$	2.42322e12	0.474053
$668$	2.35125e11	0.0456883
$669$	−1.59044e11	−0.0306973
$670$	0	0
$671$	2.19017e12	0.417087
$672$	4.69863e11	0.0888811
$673$	1.21071e12	0.227495	0.113748	−	0.993510i	$-0.463714\pi$
$673$	1.21071e12	0.227495	0.113748	+	0.993510i	$0.463714\pi$
$674$	−2.34448e12	−0.437600
$675$	0	0
$676$	−1.49187e11	−0.0274771
$677$	7.92478e12	1.44990	0.724950	−	0.688802i	$-0.241863\pi$
$677$	7.92478e12	1.44990	0.724950	+	0.688802i	$0.241863\pi$
$678$	−1.96080e11	−0.0356369
$679$	−4.71191e12	−0.850713
$680$	0	0
$681$	−3.28953e11	−0.0586100
$682$	−2.40099e12	−0.424973
$683$	3.03429e12	0.533536	0.266768	−	0.963761i	$-0.414044\pi$
$683$	3.03429e12	0.533536	0.266768	+	0.963761i	$0.414044\pi$
$684$	−1.99367e12	−0.348257
$685$	0	0
$686$	9.59642e12	1.65444
$687$	3.00837e11	0.0515259
$688$	−5.50343e12	−0.936452
$689$	5.26371e11	0.0889828
$690$	0	0
$691$	5.11513e12	0.853503	0.426752	−	0.904369i	$-0.359658\pi$
$691$	5.11513e12	0.853503	0.426752	+	0.904369i	$0.359658\pi$
$692$	−2.70733e12	−0.448811
$693$	−1.33075e13	−2.19179
$694$	5.77508e12	0.945019
$695$	0	0
$696$	2.71949e11	0.0439284
$697$	3.74789e12	0.601505
$698$	2.06475e11	0.0329244
$699$	−4.71755e10	−0.00747428
$700$	0	0
$701$	6.81685e12	1.06624	0.533118	−	0.846041i	$-0.321020\pi$
$701$	6.81685e12	1.06624	0.533118	+	0.846041i	$0.321020\pi$
$702$	−2.11343e11	−0.0328452
$703$	−1.24592e13	−1.92394
$704$	8.53525e12	1.30960
$705$	0	0
$706$	−9.98381e11	−0.151243
$707$	−1.87680e13	−2.82509
$708$	2.25357e11	0.0337071
$709$	8.86632e11	0.131776	0.0658878	−	0.997827i	$-0.479012\pi$
$709$	8.86632e11	0.131776	0.0658878	+	0.997827i	$0.479012\pi$
$710$	0	0
$711$	4.10137e12	0.601889
$712$	5.16797e12	0.753633
$713$	2.56604e12	0.371844
$714$	−4.78922e11	−0.0689641
$715$	0	0
$716$	1.50480e12	0.213978
$717$	−1.40360e11	−0.0198339
$718$	6.64630e12	0.933298
$719$	8.70793e12	1.21516	0.607582	−	0.794257i	$-0.292139\pi$
$719$	8.70793e12	1.21516	0.607582	+	0.794257i	$0.292139\pi$
$720$	0	0
$721$	7.42451e12	1.02320
$722$	−2.27977e11	−0.0312229
$723$	2.63857e11	0.0359126
$724$	−5.05965e12	−0.684380
$725$	0	0
$726$	2.38536e11	0.0318669
$727$	−2.20524e12	−0.292786	−0.146393	−	0.989227i	$-0.546766\pi$
$727$	−2.20524e12	−0.292786	−0.146393	+	0.989227i	$0.546766\pi$
$728$	−4.06624e12	−0.536540
$729$	−7.37581e12	−0.967243
$730$	0	0
$731$	−9.16768e12	−1.18749
$732$	−6.91377e10	−0.00890051
$733$	7.14820e12	0.914595	0.457297	−	0.889314i	$-0.348817\pi$
$733$	7.14820e12	0.914595	0.457297	+	0.889314i	$0.348817\pi$
$734$	−1.25472e12	−0.159556
$735$	0	0
$736$	−4.67337e12	−0.587057
$737$	−4.64541e12	−0.579990
$738$	5.91584e12	0.734112
$739$	8.77288e12	1.08204	0.541019	−	0.841011i	$-0.318039\pi$
$739$	8.77288e12	1.08204	0.541019	+	0.841011i	$0.318039\pi$
$740$	0	0
$741$	−1.65255e11	−0.0201359
$742$	3.77593e12	0.457306
$743$	−8.90048e12	−1.07143	−0.535715	−	0.844399i	$-0.679958\pi$
$743$	−8.90048e12	−1.07143	−0.535715	+	0.844399i	$0.679958\pi$
$744$	2.87977e11	0.0344572
$745$	0	0
$746$	6.96438e12	0.823300
$747$	−6.66385e12	−0.783037
$748$	2.47680e12	0.289291
$749$	−2.56034e13	−2.97255
$750$	0	0
$751$	−3.55908e12	−0.408280	−0.204140	−	0.978942i	$-0.565440\pi$
$751$	−3.55908e12	−0.408280	−0.204140	+	0.978942i	$0.565440\pi$
$752$	5.07381e12	0.578568
$753$	9.16442e11	0.103879
$754$	−1.07580e12	−0.121216
$755$	0	0
$756$	8.42482e11	0.0938021
$757$	−1.36105e13	−1.50641	−0.753205	−	0.657786i	$-0.771493\pi$
$757$	−1.36105e13	−1.50641	−0.753205	+	0.657786i	$0.771493\pi$
$758$	3.35304e11	0.0368915
$759$	−7.29934e11	−0.0798354
$760$	0	0
$761$	5.95073e11	0.0643190	0.0321595	−	0.999483i	$-0.489762\pi$
$761$	5.95073e11	0.0643190	0.0321595	+	0.999483i	$0.489762\pi$
$762$	7.74473e11	0.0832164
$763$	−2.91675e13	−3.11558
$764$	1.47883e12	0.157035
$765$	0	0
$766$	5.76789e12	0.605324
$767$	−3.38724e12	−0.353400
$768$	−6.55872e11	−0.0680290
$769$	−1.44263e13	−1.48760	−0.743799	−	0.668404i	$-0.766978\pi$
$769$	−1.44263e13	−1.48760	−0.743799	+	0.668404i	$0.766978\pi$
$770$	0	0
$771$	−8.21072e11	−0.0836829
$772$	1.71415e12	0.173689
$773$	−1.59316e11	−0.0160491	−0.00802455	−	0.999968i	$-0.502554\pi$
$773$	−1.59316e11	−0.0160491	−0.00802455	+	0.999968i	$0.502554\pi$
$774$	−1.44707e13	−1.44929
$775$	0	0
$776$	5.25957e12	0.520682
$777$	2.62527e12	0.258392
$778$	−3.59856e12	−0.352144
$779$	9.27699e12	0.902586
$780$	0	0
$781$	−2.11906e13	−2.03805
$782$	4.76348e12	0.455506
$783$	8.46894e11	0.0805195
$784$	−1.17760e13	−1.11320
$785$	0	0
$786$	−6.04199e11	−0.0564649
$787$	1.43791e13	1.33612	0.668062	−	0.744106i	$-0.267124\pi$
$787$	1.43791e13	1.33612	0.668062	+	0.744106i	$0.267124\pi$
$788$	1.31653e12	0.121636
$789$	−3.84089e11	−0.0352846
$790$	0	0
$791$	−1.17484e13	−1.06705
$792$	1.48543e13	1.34149
$793$	1.03918e12	0.0933169
$794$	−5.68481e12	−0.507603
$795$	0	0
$796$	4.15258e12	0.366615
$797$	−1.59429e13	−1.39960	−0.699801	−	0.714338i	$-0.746728\pi$
$797$	−1.59429e13	−1.39960	−0.699801	+	0.714338i	$0.746728\pi$
$798$	−1.18546e12	−0.103484
$799$	8.45202e12	0.733669
$800$	0	0
$801$	8.02483e12	0.688795
$802$	−2.53751e12	−0.216582
$803$	4.83418e12	0.410301
$804$	1.46643e11	0.0123768
$805$	0	0
$806$	−1.13921e12	−0.0950812
$807$	5.57103e11	0.0462386
$808$	2.09494e13	1.72910
$809$	−8.36659e12	−0.686720	−0.343360	−	0.939204i	$-0.611565\pi$
$809$	−8.36659e12	−0.686720	−0.343360	+	0.939204i	$0.611565\pi$
$810$	0	0
$811$	−3.93687e12	−0.319564	−0.159782	−	0.987152i	$-0.551079\pi$
$811$	−3.93687e12	−0.319564	−0.159782	+	0.987152i	$0.551079\pi$
$812$	4.28848e12	0.346179
$813$	1.35187e12	0.108525
$814$	2.44320e13	1.95052
$815$	0	0
$816$	3.15703e11	0.0249272
$817$	−2.26924e13	−1.78189
$818$	−1.04334e13	−0.814774
$819$	−6.31407e12	−0.490379
$820$	0	0
$821$	4.48730e12	0.344700	0.172350	−	0.985036i	$-0.444864\pi$
$821$	4.48730e12	0.344700	0.172350	+	0.985036i	$0.444864\pi$
$822$	−2.93375e11	−0.0224130
$823$	−1.71862e13	−1.30581	−0.652907	−	0.757438i	$-0.726451\pi$
$823$	−1.71862e13	−1.30581	−0.652907	+	0.757438i	$0.726451\pi$
$824$	−8.28746e12	−0.626252
$825$	0	0
$826$	−2.42984e13	−1.81622
$827$	−1.26065e13	−0.937172	−0.468586	−	0.883418i	$-0.655236\pi$
$827$	−1.26065e13	−0.937172	−0.468586	+	0.883418i	$0.655236\pi$
$828$	−4.17825e12	−0.308928
$829$	1.39995e13	1.02948	0.514739	−	0.857347i	$-0.327889\pi$
$829$	1.39995e13	1.02948	0.514739	+	0.857347i	$0.327889\pi$
$830$	0	0
$831$	4.98864e11	0.0362892
$832$	4.04974e12	0.293003
$833$	−1.96166e13	−1.41163
$834$	−3.54312e11	−0.0253594
$835$	0	0
$836$	6.13073e12	0.434094
$837$	8.96809e11	0.0631591
$838$	1.59086e13	1.11438
$839$	1.42265e13	0.991217	0.495608	−	0.868546i	$-0.334945\pi$
$839$	1.42265e13	0.991217	0.495608	+	0.868546i	$0.334945\pi$
$840$	0	0
$841$	−1.01962e13	−0.702840
$842$	8.63372e12	0.591962
$843$	−1.94683e12	−0.132771
$844$	−2.54356e12	−0.172544
$845$	0	0
$846$	1.33411e13	0.895414
$847$	1.42923e13	0.954169
$848$	−2.48908e12	−0.165294
$849$	−1.56271e12	−0.103227
$850$	0	0
$851$	−2.61116e13	−1.70667
$852$	6.68931e11	0.0434914
$853$	−2.21914e13	−1.43521	−0.717603	−	0.696452i	$-0.754761\pi$
$853$	−2.21914e13	−1.43521	−0.717603	+	0.696452i	$0.754761\pi$
$854$	7.45455e12	0.479580
$855$	0	0
$856$	2.85793e13	1.81936
$857$	9.68268e12	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$857$	9.68268e12	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$858$	3.24057e11	0.0204140
$859$	2.58740e13	1.62142	0.810708	−	0.585450i	$-0.199082\pi$
$859$	2.58740e13	1.62142	0.810708	+	0.585450i	$0.199082\pi$
$860$	0	0
$861$	−1.95474e12	−0.121220
$862$	−1.13229e13	−0.698513
$863$	−4.92056e12	−0.301972	−0.150986	−	0.988536i	$-0.548245\pi$
$863$	−4.92056e12	−0.301972	−0.150986	+	0.988536i	$0.548245\pi$
$864$	−1.63330e12	−0.0997137
$865$	0	0
$866$	1.41377e13	0.854179
$867$	−7.06223e11	−0.0424479
$868$	4.54124e12	0.271541
$869$	−1.26121e13	−0.750239
$870$	0	0
$871$	−2.20412e12	−0.129764
$872$	3.25576e13	1.90690
$873$	8.16708e12	0.475885
$874$	1.17908e13	0.683508
$875$	0	0
$876$	−1.52602e11	−0.00875570
$877$	−2.87925e12	−0.164354	−0.0821772	−	0.996618i	$-0.526187\pi$
$877$	−2.87925e12	−0.164354	−0.0821772	+	0.996618i	$0.526187\pi$
$878$	−8.78935e12	−0.499150
$879$	−1.53419e12	−0.0866819
$880$	0	0
$881$	−6.65889e12	−0.372401	−0.186200	−	0.982512i	$-0.559617\pi$
$881$	−6.65889e12	−0.372401	−0.186200	+	0.982512i	$0.559617\pi$
$882$	−3.09637e13	−1.72284
$883$	−3.08529e13	−1.70794	−0.853971	−	0.520321i	$-0.825812\pi$
$883$	−3.08529e13	−1.70794	−0.853971	+	0.520321i	$0.825812\pi$
$884$	1.17518e12	0.0647244
$885$	0	0
$886$	3.22452e12	0.175798
$887$	1.18791e10	0.000644358 0	0.000322179	−	1.00000i	$-0.499897\pi$
$887$	1.18791e10	0.000644358 0	0.000322179		1.00000i	$0.499897\pi$
$888$	−2.93040e12	−0.158150
$889$	4.64037e13	2.49169
$890$	0	0
$891$	2.29379e13	1.21928
$892$	2.79954e12	0.148063
$893$	2.09209e13	1.10090
$894$	−3.88791e11	−0.0203562
$895$	0	0
$896$	5.89686e12	0.305657
$897$	−3.46334e11	−0.0178620
$898$	5.54651e12	0.284627
$899$	4.56502e12	0.233090
$900$	0	0
$901$	−4.14633e12	−0.209605
$902$	−1.81918e13	−0.915052
$903$	4.78147e12	0.239313
$904$	1.31140e13	0.653094
$905$	0	0
$906$	−1.55638e12	−0.0767432
$907$	3.04467e13	1.49385	0.746925	−	0.664908i	$-0.231529\pi$
$907$	3.04467e13	1.49385	0.746925	+	0.664908i	$0.231529\pi$
$908$	5.79033e12	0.282694
$909$	3.25303e13	1.58034
$910$	0	0
$911$	2.66394e13	1.28142	0.640709	−	0.767784i	$-0.278640\pi$
$911$	2.66394e13	1.28142	0.640709	+	0.767784i	$0.278640\pi$
$912$	7.81446e11	0.0374044
$913$	2.04920e13	0.976036
$914$	−1.19645e13	−0.567070
$915$	0	0
$916$	−5.29542e12	−0.248525
$917$	−3.62015e13	−1.69069
$918$	1.66479e12	0.0773693
$919$	−1.74445e13	−0.806749	−0.403374	−	0.915035i	$-0.632163\pi$
$919$	−1.74445e13	−0.806749	−0.403374	+	0.915035i	$0.632163\pi$
$920$	0	0
$921$	2.77244e12	0.126968
$922$	−1.71680e13	−0.782405
$923$	−1.00544e13	−0.455982
$924$	−1.29180e12	−0.0583002
$925$	0	0
$926$	−7.74419e12	−0.346120
$927$	−1.28688e13	−0.572373
$928$	−8.31398e12	−0.367996
$929$	9.41088e11	0.0414533	0.0207267	−	0.999785i	$-0.493402\pi$
$929$	9.41088e11	0.0414533	0.0207267	+	0.999785i	$0.493402\pi$
$930$	0	0
$931$	−4.85560e13	−2.11821
$932$	8.30398e11	0.0360508
$933$	−1.81497e12	−0.0784154
$934$	2.70891e13	1.16475
$935$	0	0
$936$	7.04795e12	0.300138
$937$	2.62108e13	1.11084	0.555421	−	0.831569i	$-0.312557\pi$
$937$	2.62108e13	1.11084	0.555421	+	0.831569i	$0.312557\pi$
$938$	−1.58113e13	−0.666891
$939$	−2.08335e12	−0.0874516
$940$	0	0
$941$	1.51403e13	0.629478	0.314739	−	0.949178i	$-0.398083\pi$
$941$	1.51403e13	0.629478	0.314739	+	0.949178i	$0.398083\pi$
$942$	−5.40889e10	−0.00223810
$943$	1.94423e13	0.800656
$944$	1.60174e13	0.656474
$945$	0	0
$946$	4.44988e13	1.80650
$947$	−2.72173e13	−1.09969	−0.549844	−	0.835267i	$-0.685313\pi$
$947$	−2.72173e13	−1.09969	−0.549844	+	0.835267i	$0.685313\pi$
$948$	3.98130e11	0.0160099
$949$	2.29369e12	0.0917986
$950$	0	0
$951$	−6.36535e10	−0.00252354
$952$	3.20306e13	1.26386
$953$	1.23445e13	0.484791	0.242395	−	0.970178i	$-0.422067\pi$
$953$	1.23445e13	0.484791	0.242395	+	0.970178i	$0.422067\pi$
$954$	−6.54476e12	−0.255815
$955$	0	0
$956$	2.47067e12	0.0956651
$957$	−1.29856e12	−0.0500448
$958$	−2.11110e12	−0.0809774
$959$	−1.75780e13	−0.671097
$960$	0	0
$961$	−2.16055e13	−0.817165
$962$	1.15923e13	0.436398
$963$	4.43780e13	1.66283
$964$	−4.64450e12	−0.173218
$965$	0	0
$966$	−2.48443e12	−0.0917973
$967$	−6.76105e12	−0.248654	−0.124327	−	0.992241i	$-0.539677\pi$
$967$	−6.76105e12	−0.248654	−0.124327	+	0.992241i	$0.539677\pi$
$968$	−1.59534e13	−0.584003
$969$	1.30174e12	0.0474317
$970$	0	0
$971$	−1.26803e13	−0.457764	−0.228882	−	0.973454i	$-0.573507\pi$
$971$	−1.26803e13	−0.457764	−0.228882	+	0.973454i	$0.573507\pi$
$972$	−2.19240e12	−0.0787810
$973$	−2.12291e13	−0.759319
$974$	5.45368e12	0.194166
$975$	0	0
$976$	−4.91400e12	−0.173345
$977$	3.66498e13	1.28690	0.643452	−	0.765487i	$-0.277502\pi$
$977$	3.66498e13	1.28690	0.643452	+	0.765487i	$0.277502\pi$
$978$	−2.42281e12	−0.0846827
$979$	−2.46772e13	−0.858565
$980$	0	0
$981$	5.05556e13	1.74284
$982$	3.13083e12	0.107438
$983$	1.15392e13	0.394172	0.197086	−	0.980386i	$-0.436852\pi$
$983$	1.15392e13	0.394172	0.197086	+	0.980386i	$0.436852\pi$
$984$	2.18194e12	0.0741933
$985$	0	0
$986$	8.47429e12	0.285533
$987$	−4.40822e12	−0.147855
$988$	2.90886e12	0.0971219
$989$	−4.75578e13	−1.58066
$990$	0	0
$991$	−4.69768e13	−1.54722	−0.773610	−	0.633663i	$-0.781551\pi$
$991$	−4.69768e13	−1.54722	−0.773610	+	0.633663i	$0.781551\pi$
$992$	−8.80401e12	−0.288654
$993$	−1.58702e12	−0.0517979
$994$	−7.21253e13	−2.34341
$995$	0	0
$996$	−6.46876e11	−0.0208283
$997$	−1.57384e13	−0.504467	−0.252233	−	0.967666i	$-0.581165\pi$
$997$	−1.57384e13	−0.504467	−0.252233	+	0.967666i	$0.581165\pi$
$998$	3.54965e13	1.13266
$999$	−9.12575e12	−0.289884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.k.1.19		27
5.2	odd	4		65.10.b.a.14.37	yes	54
5.3	odd	4		65.10.b.a.14.18	✓	54
5.4	even	2		325.10.a.l.1.9		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.b.a.14.18	✓	54	5.3	odd	4
65.10.b.a.14.37	yes	54	5.2	odd	4
325.10.a.k.1.19		27	1.1	even	1	trivial
325.10.a.l.1.9		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)

\(f(q)\)	\(=\)	\(q+18.1415 q^{2} +10.3900 q^{3} -182.888 q^{4} +188.489 q^{6} +11293.6 q^{7} -12606.3 q^{8} -19575.0 q^{9} +60195.2 q^{11} -1900.20 q^{12} +28561.0 q^{13} +204883. q^{14} -135058. q^{16} -224981. q^{17} -355120. q^{18} -556885. q^{19} +117340. q^{21} +1.09203e6 q^{22} -1.16710e6 q^{23} -130979. q^{24} +518138. q^{26} -407890. q^{27} -2.06546e6 q^{28} -2.07628e6 q^{29} -2.19865e6 q^{31} +4.00427e6 q^{32} +625427. q^{33} -4.08148e6 q^{34} +3.58003e6 q^{36} +2.23731e7 q^{37} -1.01027e7 q^{38} +296748. q^{39} -1.66587e7 q^{41} +2.12873e6 q^{42} +4.07487e7 q^{43} -1.10090e7 q^{44} -2.11728e7 q^{46} -3.75678e7 q^{47} -1.40325e6 q^{48} +8.71922e7 q^{49} -2.33754e6 q^{51} -5.22345e6 q^{52} +1.84297e7 q^{53} -7.39972e6 q^{54} -1.42370e8 q^{56} -5.78602e6 q^{57} -3.76667e7 q^{58} -1.18597e8 q^{59} +3.63845e7 q^{61} -3.98868e7 q^{62} -2.21073e8 q^{63} +1.41793e8 q^{64} +1.13462e7 q^{66} -7.71724e7 q^{67} +4.11462e7 q^{68} -1.21261e7 q^{69} -3.52032e8 q^{71} +2.46768e8 q^{72} +8.03083e7 q^{73} +4.05880e8 q^{74} +1.01847e8 q^{76} +6.79822e8 q^{77} +5.38344e6 q^{78} -2.09520e8 q^{79} +3.81058e8 q^{81} -3.02213e8 q^{82} +3.40426e8 q^{83} -2.14601e7 q^{84} +7.39242e8 q^{86} -2.15725e7 q^{87} -7.58837e8 q^{88} -4.09952e8 q^{89} +3.22557e8 q^{91} +2.13448e8 q^{92} -2.28440e7 q^{93} -6.81534e8 q^{94} +4.16043e7 q^{96} -4.17219e8 q^{97} +1.58179e9 q^{98} -1.17832e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) \) 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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