LMFDB - Embedded newform 261.12.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,12,Mod(1,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("261.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	261.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$200.537570126$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 $ x^11 - x^10 - 15790x^9 + 14666x^8 + 87206462x^7 - 14008334x^6 - 203974096304x^5 - 388180519304x^4 + 193065378004825x^3 + 1279291654973975x^2 - 65244901875230266*x - 758324542468966858
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-56.7551$ of defining polynomial
Character	$\chi$	$=$	261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+59.7551 q^{2} +1522.68 q^{4} +6379.08 q^{5} -23005.8 q^{7} -31390.8 q^{8} +O(q^{10})$	\(q+59.7551 q^{2} +1522.68 q^{4} +6379.08 q^{5} -23005.8 q^{7} -31390.8 q^{8} +381183. q^{10} -522514. q^{11} +1.47979e6 q^{13} -1.37472e6 q^{14} -4.99420e6 q^{16} -4.61480e6 q^{17} +1.36307e7 q^{19} +9.71327e6 q^{20} -3.12229e7 q^{22} +5.58468e7 q^{23} -8.13546e6 q^{25} +8.84253e7 q^{26} -3.50304e7 q^{28} -2.05111e7 q^{29} -1.47320e8 q^{31} -2.34141e8 q^{32} -2.75758e8 q^{34} -1.46756e8 q^{35} -1.64673e8 q^{37} +8.14503e8 q^{38} -2.00244e8 q^{40} -9.49494e6 q^{41} +7.59458e8 q^{43} -7.95619e8 q^{44} +3.33713e9 q^{46} -1.65847e9 q^{47} -1.44806e9 q^{49} -4.86136e8 q^{50} +2.25325e9 q^{52} -3.15983e9 q^{53} -3.33316e9 q^{55} +7.22171e8 q^{56} -1.22565e9 q^{58} -2.72696e9 q^{59} +2.15540e9 q^{61} -8.80314e9 q^{62} -3.76299e9 q^{64} +9.43973e9 q^{65} -1.36283e10 q^{67} -7.02685e9 q^{68} -8.76942e9 q^{70} -9.15005e9 q^{71} -2.13411e10 q^{73} -9.84006e9 q^{74} +2.07551e10 q^{76} +1.20209e10 q^{77} -3.95516e10 q^{79} -3.18584e10 q^{80} -5.67371e8 q^{82} -2.56121e10 q^{83} -2.94382e10 q^{85} +4.53815e10 q^{86} +1.64021e10 q^{88} +6.50080e10 q^{89} -3.40439e10 q^{91} +8.50365e10 q^{92} -9.91019e10 q^{94} +8.69512e10 q^{95} +1.86954e10 q^{97} -8.65290e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) $ 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8} - 685834 q^{10} + 612246 q^{11} + 1510364 q^{13} - 3955400 q^{14} + 3024818 q^{16} + 3291098 q^{17} - 44121388 q^{19} + 49472662 q^{20} - 43435618 q^{22} + 88684076 q^{23} - 44195521 q^{25} + 324999762 q^{26} - 391274848 q^{28} - 225622639 q^{29} - 292235934 q^{31} + 632542514 q^{32} - 1113307936 q^{34} + 1312820120 q^{35} - 1380429338 q^{37} + 1222857284 q^{38} - 2713154106 q^{40} + 1062067494 q^{41} + 74588594 q^{43} - 52891466 q^{44} - 87670324 q^{46} + 1821239394 q^{47} + 4692522003 q^{49} - 9494259926 q^{50} + 3266669866 q^{52} - 7818635688 q^{53} - 191002682 q^{55} - 11263587512 q^{56} - 656356768 q^{58} - 1230002712 q^{59} - 18602654230 q^{61} - 22075953162 q^{62} + 11813658086 q^{64} - 32245789334 q^{65} + 27481284652 q^{67} - 29588811820 q^{68} + 42862666712 q^{70} + 20347168516 q^{71} - 57740010478 q^{73} + 2640709564 q^{74} - 33350650772 q^{76} - 871959792 q^{77} - 120245016462 q^{79} + 84319695274 q^{80} - 111495532412 q^{82} + 142463983824 q^{83} - 181628566552 q^{85} - 47870165542 q^{86} - 180608014462 q^{88} + 96700717270 q^{89} - 355162031176 q^{91} + 22429477796 q^{92} + 172608565078 q^{94} + 195922150708 q^{95} - 303190852014 q^{97} + 123776497136 q^{98}+O(q^{100}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8 - 685834 * q^10 + 612246 * q^11 + 1510364 * q^13 - 3955400 * q^14 + 3024818 * q^16 + 3291098 * q^17 - 44121388 * q^19 + 49472662 * q^20 - 43435618 * q^22 + 88684076 * q^23 - 44195521 * q^25 + 324999762 * q^26 - 391274848 * q^28 - 225622639 * q^29 - 292235934 * q^31 + 632542514 * q^32 - 1113307936 * q^34 + 1312820120 * q^35 - 1380429338 * q^37 + 1222857284 * q^38 - 2713154106 * q^40 + 1062067494 * q^41 + 74588594 * q^43 - 52891466 * q^44 - 87670324 * q^46 + 1821239394 * q^47 + 4692522003 * q^49 - 9494259926 * q^50 + 3266669866 * q^52 - 7818635688 * q^53 - 191002682 * q^55 - 11263587512 * q^56 - 656356768 * q^58 - 1230002712 * q^59 - 18602654230 * q^61 - 22075953162 * q^62 + 11813658086 * q^64 - 32245789334 * q^65 + 27481284652 * q^67 - 29588811820 * q^68 + 42862666712 * q^70 + 20347168516 * q^71 - 57740010478 * q^73 + 2640709564 * q^74 - 33350650772 * q^76 - 871959792 * q^77 - 120245016462 * q^79 + 84319695274 * q^80 - 111495532412 * q^82 + 142463983824 * q^83 - 181628566552 * q^85 - 47870165542 * q^86 - 180608014462 * q^88 + 96700717270 * q^89 - 355162031176 * q^91 + 22429477796 * q^92 + 172608565078 * q^94 + 195922150708 * q^95 - 303190852014 * q^97 + 123776497136 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	59.7551	1.32041	0.660207	−	0.751084i	$-0.270468\pi$
$2$	59.7551	1.32041	0.660207	+	0.751084i	$0.270468\pi$
$3$	0	0
$3$	0	0
$4$	1522.68	0.743494
$5$	6379.08	0.912900	0.456450	−	0.889749i	$-0.349121\pi$
$5$	6379.08	0.912900	0.456450	+	0.889749i	$0.349121\pi$
$6$	0	0
$7$	−23005.8	−0.517367	−0.258683	−	0.965962i	$-0.583289\pi$
$7$	−23005.8	−0.517367	−0.258683	+	0.965962i	$0.583289\pi$
$8$	−31390.8	−0.338694
$9$	0	0
$10$	381183.	1.20541
$11$	−522514.	−0.978223	−0.489112	−	0.872221i	$-0.662679\pi$
$11$	−522514.	−0.978223	−0.489112	+	0.872221i	$0.662679\pi$
$12$	0	0
$13$	1.47979e6	1.10538	0.552692	−	0.833386i	$-0.313601\pi$
$13$	1.47979e6	1.10538	0.552692	+	0.833386i	$0.313601\pi$
$14$	−1.37472e6	−0.683138
$15$	0	0
$16$	−4.99420e6	−1.19071
$17$	−4.61480e6	−0.788286	−0.394143	−	0.919049i	$-0.628959\pi$
$17$	−4.61480e6	−0.788286	−0.394143	+	0.919049i	$0.628959\pi$
$18$	0	0
$19$	1.36307e7	1.26291	0.631456	−	0.775412i	$-0.282458\pi$
$19$	1.36307e7	1.26291	0.631456	+	0.775412i	$0.282458\pi$
$20$	9.71327e6	0.678736
$21$	0	0
$22$	−3.12229e7	−1.29166
$23$	5.58468e7	1.80923	0.904617	−	0.426225i	$-0.140157\pi$
$23$	5.58468e7	1.80923	0.904617	+	0.426225i	$0.140157\pi$
$24$	0	0
$25$	−8.13546e6	−0.166614
$26$	8.84253e7	1.45956
$27$	0	0
$28$	−3.50304e7	−0.384659
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	0	0
$31$	−1.47320e8	−0.924215	−0.462108	−	0.886824i	$-0.652907\pi$
$31$	−1.47320e8	−0.924215	−0.462108	+	0.886824i	$0.652907\pi$
$32$	−2.34141e8	−1.23354
$33$	0	0
$34$	−2.75758e8	−1.04086
$35$	−1.46756e8	−0.472304
$36$	0	0
$37$	−1.64673e8	−0.390403	−0.195201	−	0.980763i	$-0.562536\pi$
$37$	−1.64673e8	−0.390403	−0.195201	+	0.980763i	$0.562536\pi$
$38$	8.14503e8	1.66757
$39$	0	0
$40$	−2.00244e8	−0.309194
$41$	−9.49494e6	−0.0127991	−0.00639957	−	0.999980i	$-0.502037\pi$
$41$	−9.49494e6	−0.0127991	−0.00639957	+	0.999980i	$0.502037\pi$
$42$	0	0
$43$	7.59458e8	0.787820	0.393910	−	0.919149i	$-0.371122\pi$
$43$	7.59458e8	0.787820	0.393910	+	0.919149i	$0.371122\pi$
$44$	−7.95619e8	−0.727303
$45$	0	0
$46$	3.33713e9	2.38894
$47$	−1.65847e9	−1.05480	−0.527398	−	0.849618i	$-0.676832\pi$
$47$	−1.65847e9	−1.05480	−0.527398	+	0.849618i	$0.676832\pi$
$48$	0	0
$49$	−1.44806e9	−0.732332
$50$	−4.86136e8	−0.220000
$51$	0	0
$52$	2.25325e9	0.821846
$53$	−3.15983e9	−1.03788	−0.518940	−	0.854811i	$-0.673673\pi$
$53$	−3.15983e9	−1.03788	−0.518940	+	0.854811i	$0.673673\pi$
$54$	0	0
$55$	−3.33316e9	−0.893020
$56$	7.22171e8	0.175229
$57$	0	0
$58$	−1.22565e9	−0.245195
$59$	−2.72696e9	−0.496584	−0.248292	−	0.968685i	$-0.579869\pi$
$59$	−2.72696e9	−0.496584	−0.248292	+	0.968685i	$0.579869\pi$
$60$	0	0
$61$	2.15540e9	0.326748	0.163374	−	0.986564i	$-0.447762\pi$
$61$	2.15540e9	0.326748	0.163374	+	0.986564i	$0.447762\pi$
$62$	−8.80314e9	−1.22035
$63$	0	0
$64$	−3.76299e9	−0.438070
$65$	9.43973e9	1.00910
$66$	0	0
$67$	−1.36283e10	−1.23319	−0.616594	−	0.787281i	$-0.711488\pi$
$67$	−1.36283e10	−1.23319	−0.616594	+	0.787281i	$0.711488\pi$
$68$	−7.02685e9	−0.586086
$69$	0	0
$70$	−8.76942e9	−0.623637
$71$	−9.15005e9	−0.601870	−0.300935	−	0.953645i	$-0.597299\pi$
$71$	−9.15005e9	−0.601870	−0.300935	+	0.953645i	$0.597299\pi$
$72$	0	0
$73$	−2.13411e10	−1.20487	−0.602437	−	0.798166i	$-0.705804\pi$
$73$	−2.13411e10	−1.20487	−0.602437	+	0.798166i	$0.705804\pi$
$74$	−9.84006e9	−0.515493
$75$	0	0
$76$	2.07551e10	0.938967
$77$	1.20209e10	0.506100
$78$	0	0
$79$	−3.95516e10	−1.44616	−0.723078	−	0.690766i	$-0.757273\pi$
$79$	−3.95516e10	−1.44616	−0.723078	+	0.690766i	$0.757273\pi$
$80$	−3.18584e10	−1.08700
$81$	0	0
$82$	−5.67371e8	−0.0169002
$83$	−2.56121e10	−0.713699	−0.356850	−	0.934162i	$-0.616149\pi$
$83$	−2.56121e10	−0.713699	−0.356850	+	0.934162i	$0.616149\pi$
$84$	0	0
$85$	−2.94382e10	−0.719626
$86$	4.53815e10	1.04025
$87$	0	0
$88$	1.64021e10	0.331318
$89$	6.50080e10	1.23402	0.617009	−	0.786956i	$-0.288344\pi$
$89$	6.50080e10	1.23402	0.617009	+	0.786956i	$0.288344\pi$
$90$	0	0
$91$	−3.40439e10	−0.571889
$92$	8.50365e10	1.34516
$93$	0	0
$94$	−9.91019e10	−1.39277
$95$	8.69512e10	1.15291
$96$	0	0
$97$	1.86954e10	0.221050	0.110525	−	0.993873i	$-0.464747\pi$
$97$	1.86954e10	0.221050	0.110525	+	0.993873i	$0.464747\pi$
$98$	−8.65290e10	−0.966981
$99$	0	0
$100$	−1.23877e10	−0.123877
$101$	−6.62726e10	−0.627432	−0.313716	−	0.949517i	$-0.601574\pi$
$101$	−6.62726e10	−0.627432	−0.313716	+	0.949517i	$0.601574\pi$
$102$	0	0
$103$	5.60992e10	0.476817	0.238409	−	0.971165i	$-0.423374\pi$
$103$	5.60992e10	0.476817	0.238409	+	0.971165i	$0.423374\pi$
$104$	−4.64519e10	−0.374387
$105$	0	0
$106$	−1.88816e11	−1.37043
$107$	8.31258e10	0.572961	0.286481	−	0.958086i	$-0.407515\pi$
$107$	8.31258e10	0.572961	0.286481	+	0.958086i	$0.407515\pi$
$108$	0	0
$109$	−5.57921e9	−0.0347318	−0.0173659	−	0.999849i	$-0.505528\pi$
$109$	−5.57921e9	−0.0347318	−0.0173659	+	0.999849i	$0.505528\pi$
$110$	−1.99173e11	−1.17916
$111$	0	0
$112$	1.14896e11	0.616034
$113$	−1.83190e11	−0.935341	−0.467670	−	0.883903i	$-0.654907\pi$
$113$	−1.83190e11	−0.935341	−0.467670	+	0.883903i	$0.654907\pi$
$114$	0	0
$115$	3.56251e11	1.65165
$116$	−3.12318e10	−0.138063
$117$	0	0
$118$	−1.62950e11	−0.655696
$119$	1.06167e11	0.407833
$120$	0	0
$121$	−1.22910e10	−0.0430791
$122$	1.28796e11	0.431443
$123$	0	0
$124$	−2.24321e11	−0.687149
$125$	−3.63375e11	−1.06500
$126$	0	0
$127$	5.37204e11	1.44284	0.721421	−	0.692497i	$-0.243489\pi$
$127$	5.37204e11	1.44284	0.721421	+	0.692497i	$0.243489\pi$
$128$	2.54662e11	0.655103
$129$	0	0
$130$	5.64072e11	1.33244
$131$	1.80822e11	0.409506	0.204753	−	0.978814i	$-0.434361\pi$
$131$	1.80822e11	0.409506	0.204753	+	0.978814i	$0.434361\pi$
$132$	0	0
$133$	−3.13585e11	−0.653388
$134$	−8.14359e11	−1.62832
$135$	0	0
$136$	1.44862e11	0.266988
$137$	9.68864e10	0.171514	0.0857570	−	0.996316i	$-0.472669\pi$
$137$	9.68864e10	0.171514	0.0857570	+	0.996316i	$0.472669\pi$
$138$	0	0
$139$	−8.65857e11	−1.41535	−0.707677	−	0.706536i	$-0.750257\pi$
$139$	−8.65857e11	−1.41535	−0.707677	+	0.706536i	$0.750257\pi$
$140$	−2.23462e11	−0.351155
$141$	0	0
$142$	−5.46762e11	−0.794717
$143$	−7.73213e11	−1.08131
$144$	0	0
$145$	−1.30842e11	−0.169521
$146$	−1.27524e12	−1.59093
$147$	0	0
$148$	−2.50744e11	−0.290262
$149$	1.20498e12	1.34418	0.672089	−	0.740471i	$-0.265397\pi$
$149$	1.20498e12	1.34418	0.672089	+	0.740471i	$0.265397\pi$
$150$	0	0
$151$	−1.40735e12	−1.45891	−0.729457	−	0.684027i	$-0.760227\pi$
$151$	−1.40735e12	−1.45891	−0.729457	+	0.684027i	$0.760227\pi$
$152$	−4.27878e11	−0.427740
$153$	0	0
$154$	7.18308e11	0.668262
$155$	−9.39768e11	−0.843716
$156$	0	0
$157$	−9.92000e10	−0.0829973	−0.0414986	−	0.999139i	$-0.513213\pi$
$157$	−9.92000e10	−0.0829973	−0.0414986	+	0.999139i	$0.513213\pi$
$158$	−2.36341e12	−1.90953
$159$	0	0
$160$	−1.49360e12	−1.12610
$161$	−1.28480e12	−0.936038
$162$	0	0
$163$	−2.51668e12	−1.71315	−0.856577	−	0.516019i	$-0.827413\pi$
$163$	−2.51668e12	−1.71315	−0.856577	+	0.516019i	$0.827413\pi$
$164$	−1.44577e10	−0.00951609
$165$	0	0
$166$	−1.53045e12	−0.942379
$167$	3.10127e12	1.84756	0.923782	−	0.382919i	$-0.125081\pi$
$167$	3.10127e12	1.84756	0.923782	+	0.382919i	$0.125081\pi$
$168$	0	0
$169$	3.97632e11	0.221873
$170$	−1.75908e12	−0.950204
$171$	0	0
$172$	1.15641e12	0.585740
$173$	−3.96206e12	−1.94387	−0.971936	−	0.235244i	$-0.924411\pi$
$173$	−3.96206e12	−1.94387	−0.971936	+	0.235244i	$0.924411\pi$
$174$	0	0
$175$	1.87163e11	0.0862007
$176$	2.60954e12	1.16478
$177$	0	0
$178$	3.88456e12	1.62942
$179$	3.65706e12	1.48744	0.743721	−	0.668490i	$-0.233059\pi$
$179$	3.65706e12	1.48744	0.743721	+	0.668490i	$0.233059\pi$
$180$	0	0
$181$	−4.32276e11	−0.165397	−0.0826987	−	0.996575i	$-0.526354\pi$
$181$	−4.32276e11	−0.165397	−0.0826987	+	0.996575i	$0.526354\pi$
$182$	−2.03430e12	−0.755130
$183$	0	0
$184$	−1.75307e12	−0.612777
$185$	−1.05046e12	−0.356399
$186$	0	0
$187$	2.41130e12	0.771120
$188$	−2.52531e12	−0.784235
$189$	0	0
$190$	5.19578e12	1.52232
$191$	−1.14191e12	−0.325048	−0.162524	−	0.986705i	$-0.551963\pi$
$191$	−1.14191e12	−0.325048	−0.162524	+	0.986705i	$0.551963\pi$
$192$	0	0
$193$	−2.21005e12	−0.594068	−0.297034	−	0.954867i	$-0.595997\pi$
$193$	−2.21005e12	−0.594068	−0.297034	+	0.954867i	$0.595997\pi$
$194$	1.11715e12	0.291878
$195$	0	0
$196$	−2.20493e12	−0.544484
$197$	−4.19072e12	−1.00629	−0.503146	−	0.864201i	$-0.667824\pi$
$197$	−4.19072e12	−1.00629	−0.503146	+	0.864201i	$0.667824\pi$
$198$	0	0
$199$	−4.05306e12	−0.920643	−0.460322	−	0.887752i	$-0.652266\pi$
$199$	−4.05306e12	−0.920643	−0.460322	+	0.887752i	$0.652266\pi$
$200$	2.55379e11	0.0564313
$201$	0	0
$202$	−3.96013e12	−0.828470
$203$	4.71876e11	0.0960726
$204$	0	0
$205$	−6.05690e10	−0.0116843
$206$	3.35222e12	0.629596
$207$	0	0
$208$	−7.39039e12	−1.31619
$209$	−7.12222e12	−1.23541
$210$	0	0
$211$	−4.84297e12	−0.797184	−0.398592	−	0.917128i	$-0.630501\pi$
$211$	−4.84297e12	−0.797184	−0.398592	+	0.917128i	$0.630501\pi$
$212$	−4.81140e12	−0.771657
$213$	0	0
$214$	4.96720e12	0.756546
$215$	4.84464e12	0.719201
$216$	0	0
$217$	3.38922e12	0.478158
$218$	−3.33387e11	−0.0458604
$219$	0	0
$220$	−5.07532e12	−0.663955
$221$	−6.82896e12	−0.871358
$222$	0	0
$223$	−1.05727e11	−0.0128383	−0.00641915	−	0.999979i	$-0.502043\pi$
$223$	−1.05727e11	−0.0128383	−0.00641915	+	0.999979i	$0.502043\pi$
$224$	5.38660e12	0.638191
$225$	0	0
$226$	−1.09465e13	−1.23504
$227$	−7.03256e12	−0.774410	−0.387205	−	0.921994i	$-0.626559\pi$
$227$	−7.03256e12	−0.774410	−0.387205	+	0.921994i	$0.626559\pi$
$228$	0	0
$229$	1.66758e13	1.74981	0.874905	−	0.484294i	$-0.160923\pi$
$229$	1.66758e13	1.74981	0.874905	+	0.484294i	$0.160923\pi$
$230$	2.12878e13	2.18086
$231$	0	0
$232$	6.43861e11	0.0628939
$233$	3.37844e12	0.322298	0.161149	−	0.986930i	$-0.448480\pi$
$233$	3.37844e12	0.322298	0.161149	+	0.986930i	$0.448480\pi$
$234$	0	0
$235$	−1.05795e13	−0.962923
$236$	−4.15227e12	−0.369207
$237$	0	0
$238$	6.34404e12	0.538508
$239$	4.13774e12	0.343222	0.171611	−	0.985165i	$-0.445103\pi$
$239$	4.13774e12	0.343222	0.171611	+	0.985165i	$0.445103\pi$
$240$	0	0
$241$	−2.20806e13	−1.74952	−0.874758	−	0.484559i	$-0.838980\pi$
$241$	−2.20806e13	−1.74952	−0.874758	+	0.484559i	$0.838980\pi$
$242$	−7.34448e11	−0.0568822
$243$	0	0
$244$	3.28197e12	0.242936
$245$	−9.23728e12	−0.668545
$246$	0	0
$247$	2.01706e13	1.39600
$248$	4.62450e12	0.313026
$249$	0	0
$250$	−2.17135e13	−1.40624
$251$	9.99788e12	0.633435	0.316718	−	0.948520i	$-0.397419\pi$
$251$	9.99788e12	0.633435	0.316718	+	0.948520i	$0.397419\pi$
$252$	0	0
$253$	−2.91807e13	−1.76984
$254$	3.21007e13	1.90515
$255$	0	0
$256$	2.29240e13	1.30308
$257$	1.92790e13	1.07264	0.536319	−	0.844016i	$-0.319815\pi$
$257$	1.92790e13	1.07264	0.536319	+	0.844016i	$0.319815\pi$
$258$	0	0
$259$	3.78844e12	0.201981
$260$	1.43737e13	0.750263
$261$	0	0
$262$	1.08051e13	0.540717
$263$	−1.38093e13	−0.676729	−0.338364	−	0.941015i	$-0.609874\pi$
$263$	−1.38093e13	−0.676729	−0.338364	+	0.941015i	$0.609874\pi$
$264$	0	0
$265$	−2.01568e13	−0.947479
$266$	−1.87383e13	−0.862743
$267$	0	0
$268$	−2.07514e13	−0.916869
$269$	−2.07270e13	−0.897219	−0.448609	−	0.893728i	$-0.648081\pi$
$269$	−2.07270e13	−0.897219	−0.448609	+	0.893728i	$0.648081\pi$
$270$	0	0
$271$	1.20155e13	0.499356	0.249678	−	0.968329i	$-0.419675\pi$
$271$	1.20155e13	0.499356	0.249678	+	0.968329i	$0.419675\pi$
$272$	2.30472e13	0.938620
$273$	0	0
$274$	5.78946e12	0.226470
$275$	4.25089e12	0.162986
$276$	0	0
$277$	3.13772e13	1.15605	0.578024	−	0.816020i	$-0.303824\pi$
$277$	3.13772e13	1.15605	0.578024	+	0.816020i	$0.303824\pi$
$278$	−5.17394e13	−1.86885
$279$	0	0
$280$	4.60679e12	0.159966
$281$	−1.59297e13	−0.542404	−0.271202	−	0.962522i	$-0.587421\pi$
$281$	−1.59297e13	−0.542404	−0.271202	+	0.962522i	$0.587421\pi$
$282$	0	0
$283$	4.36081e13	1.42805	0.714023	−	0.700123i	$-0.246871\pi$
$283$	4.36081e13	1.42805	0.714023	+	0.700123i	$0.246871\pi$
$284$	−1.39326e13	−0.447487
$285$	0	0
$286$	−4.62035e13	−1.42778
$287$	2.18439e11	0.00662185
$288$	0	0
$289$	−1.29755e13	−0.378605
$290$	−7.81850e12	−0.223838
$291$	0	0
$292$	−3.24957e13	−0.895818
$293$	5.68721e13	1.53861	0.769303	−	0.638885i	$-0.220604\pi$
$293$	5.68721e13	1.53861	0.769303	+	0.638885i	$0.220604\pi$
$294$	0	0
$295$	−1.73955e13	−0.453331
$296$	5.16922e12	0.132227
$297$	0	0
$298$	7.20040e13	1.77487
$299$	8.26417e13	1.99990
$300$	0	0
$301$	−1.74720e13	−0.407592
$302$	−8.40965e13	−1.92637
$303$	0	0
$304$	−6.80744e13	−1.50376
$305$	1.37495e13	0.298288
$306$	0	0
$307$	−8.79181e13	−1.84000	−0.919998	−	0.391922i	$-0.871810\pi$
$307$	−8.79181e13	−1.84000	−0.919998	+	0.391922i	$0.871810\pi$
$308$	1.83039e13	0.376283
$309$	0	0
$310$	−5.61560e13	−1.11405
$311$	8.36586e12	0.163053	0.0815264	−	0.996671i	$-0.474020\pi$
$311$	8.36586e12	0.163053	0.0815264	+	0.996671i	$0.474020\pi$
$312$	0	0
$313$	8.42618e12	0.158539	0.0792697	−	0.996853i	$-0.474741\pi$
$313$	8.42618e12	0.158539	0.0792697	+	0.996853i	$0.474741\pi$
$314$	−5.92771e12	−0.109591
$315$	0	0
$316$	−6.02243e13	−1.07521
$317$	9.64046e13	1.69150	0.845750	−	0.533580i	$-0.179154\pi$
$317$	9.64046e13	1.69150	0.845750	+	0.533580i	$0.179154\pi$
$318$	0	0
$319$	1.07174e13	0.181652
$320$	−2.40044e13	−0.399914
$321$	0	0
$322$	−7.67734e13	−1.23596
$323$	−6.29029e13	−0.995535
$324$	0	0
$325$	−1.20388e13	−0.184173
$326$	−1.50385e14	−2.26207
$327$	0	0
$328$	2.98054e11	0.00433499
$329$	3.81544e13	0.545717
$330$	0	0
$331$	−2.88602e13	−0.399251	−0.199625	−	0.979872i	$-0.563973\pi$
$331$	−2.88602e13	−0.399251	−0.199625	+	0.979872i	$0.563973\pi$
$332$	−3.89989e13	−0.530631
$333$	0	0
$334$	1.85317e14	2.43955
$335$	−8.69359e13	−1.12578
$336$	0	0
$337$	4.06845e13	0.509876	0.254938	−	0.966957i	$-0.417945\pi$
$337$	4.06845e13	0.509876	0.254938	+	0.966957i	$0.417945\pi$
$338$	2.37606e13	0.292964
$339$	0	0
$340$	−4.48248e13	−0.535038
$341$	7.69769e13	0.904089
$342$	0	0
$343$	7.88038e13	0.896251
$344$	−2.38400e13	−0.266830
$345$	0	0
$346$	−2.36754e14	−2.56672
$347$	6.27388e12	0.0669460	0.0334730	−	0.999440i	$-0.489343\pi$
$347$	6.27388e12	0.0669460	0.0334730	+	0.999440i	$0.489343\pi$
$348$	0	0
$349$	1.09741e12	0.0113457	0.00567283	−	0.999984i	$-0.498194\pi$
$349$	1.09741e12	0.0113457	0.00567283	+	0.999984i	$0.498194\pi$
$350$	1.11840e13	0.113821
$351$	0	0
$352$	1.22342e14	1.20668
$353$	−5.86214e13	−0.569240	−0.284620	−	0.958640i	$-0.591867\pi$
$353$	−5.86214e13	−0.569240	−0.284620	+	0.958640i	$0.591867\pi$
$354$	0	0
$355$	−5.83689e13	−0.549447
$356$	9.89861e13	0.917486
$357$	0	0
$358$	2.18528e14	1.96404
$359$	−5.82298e13	−0.515378	−0.257689	−	0.966228i	$-0.582961\pi$
$359$	−5.82298e13	−0.515378	−0.257689	+	0.966228i	$0.582961\pi$
$360$	0	0
$361$	6.93053e13	0.594945
$362$	−2.58307e13	−0.218393
$363$	0	0
$364$	−5.18378e13	−0.425196
$365$	−1.36137e14	−1.09993
$366$	0	0
$367$	−2.00272e14	−1.57021	−0.785104	−	0.619364i	$-0.787390\pi$
$367$	−2.00272e14	−1.57021	−0.785104	+	0.619364i	$0.787390\pi$
$368$	−2.78910e14	−2.15427
$369$	0	0
$370$	−6.27705e13	−0.470594
$371$	7.26945e13	0.536964
$372$	0	0
$373$	1.06705e14	0.765219	0.382609	−	0.923910i	$-0.375026\pi$
$373$	1.06705e14	0.765219	0.382609	+	0.923910i	$0.375026\pi$
$374$	1.44087e14	1.01820
$375$	0	0
$376$	5.20606e13	0.357253
$377$	−3.03523e13	−0.205265
$378$	0	0
$379$	−2.74715e14	−1.80454	−0.902269	−	0.431173i	$-0.858100\pi$
$379$	−2.74715e14	−1.80454	−0.902269	+	0.431173i	$0.858100\pi$
$380$	1.32399e14	0.857183
$381$	0	0
$382$	−6.82348e13	−0.429198
$383$	−1.78808e14	−1.10865	−0.554323	−	0.832302i	$-0.687023\pi$
$383$	−1.78808e14	−1.10865	−0.554323	+	0.832302i	$0.687023\pi$
$384$	0	0
$385$	7.66820e13	0.462019
$386$	−1.32062e14	−0.784416
$387$	0	0
$388$	2.84671e13	0.164350
$389$	−3.37178e13	−0.191927	−0.0959635	−	0.995385i	$-0.530593\pi$
$389$	−3.37178e13	−0.191927	−0.0959635	+	0.995385i	$0.530593\pi$
$390$	0	0
$391$	−2.57722e14	−1.42619
$392$	4.54557e13	0.248036
$393$	0	0
$394$	−2.50417e14	−1.32872
$395$	−2.52303e14	−1.32020
$396$	0	0
$397$	6.71565e13	0.341775	0.170887	−	0.985291i	$-0.445337\pi$
$397$	6.71565e13	0.341775	0.170887	+	0.985291i	$0.445337\pi$
$398$	−2.42191e14	−1.21563
$399$	0	0
$400$	4.06302e13	0.198389
$401$	−3.26275e14	−1.57141	−0.785706	−	0.618600i	$-0.787700\pi$
$401$	−3.26275e14	−1.57141	−0.785706	+	0.618600i	$0.787700\pi$
$402$	0	0
$403$	−2.18004e14	−1.02161
$404$	−1.00912e14	−0.466492
$405$	0	0
$406$	2.81970e13	0.126856
$407$	8.60439e13	0.381901
$408$	0	0
$409$	2.71137e14	1.17142	0.585708	−	0.810522i	$-0.300817\pi$
$409$	2.71137e14	1.17142	0.585708	+	0.810522i	$0.300817\pi$
$410$	−3.61931e12	−0.0154282
$411$	0	0
$412$	8.54209e13	0.354511
$413$	6.27359e13	0.256916
$414$	0	0
$415$	−1.63381e14	−0.651536
$416$	−3.46480e14	−1.36353
$417$	0	0
$418$	−4.25589e14	−1.63125
$419$	4.36462e14	1.65109	0.825543	−	0.564339i	$-0.190869\pi$
$419$	4.36462e14	1.65109	0.825543	+	0.564339i	$0.190869\pi$
$420$	0	0
$421$	3.35884e14	1.23776	0.618881	−	0.785485i	$-0.287586\pi$
$421$	3.35884e14	1.23776	0.618881	+	0.785485i	$0.287586\pi$
$422$	−2.89392e14	−1.05261
$423$	0	0
$424$	9.91896e13	0.351523
$425$	3.75435e13	0.131340
$426$	0	0
$427$	−4.95867e13	−0.169049
$428$	1.26574e14	0.425993
$429$	0	0
$430$	2.89492e14	0.949643
$431$	3.93344e14	1.27394	0.636968	−	0.770890i	$-0.280188\pi$
$431$	3.93344e14	1.27394	0.636968	+	0.770890i	$0.280188\pi$
$432$	0	0
$433$	3.57057e14	1.12734	0.563668	−	0.826001i	$-0.309390\pi$
$433$	3.57057e14	1.12734	0.563668	+	0.826001i	$0.309390\pi$
$434$	2.02524e14	0.631367
$435$	0	0
$436$	−8.49534e12	−0.0258229
$437$	7.61229e14	2.28490
$438$	0	0
$439$	−3.37901e14	−0.989087	−0.494543	−	0.869153i	$-0.664665\pi$
$439$	−3.37901e14	−0.989087	−0.494543	+	0.869153i	$0.664665\pi$
$440$	1.04630e14	0.302460
$441$	0	0
$442$	−4.08065e14	−1.15055
$443$	−4.40752e14	−1.22737	−0.613683	−	0.789552i	$-0.710313\pi$
$443$	−4.40752e14	−1.22737	−0.613683	+	0.789552i	$0.710313\pi$
$444$	0	0
$445$	4.14691e14	1.12653
$446$	−6.31771e12	−0.0169519
$447$	0	0
$448$	8.65707e13	0.226643
$449$	4.87159e14	1.25984	0.629920	−	0.776660i	$-0.283087\pi$
$449$	4.87159e14	1.25984	0.629920	+	0.776660i	$0.283087\pi$
$450$	0	0
$451$	4.96124e12	0.0125204
$452$	−2.78939e14	−0.695421
$453$	0	0
$454$	−4.20231e14	−1.02254
$455$	−2.17169e14	−0.522077
$456$	0	0
$457$	−3.43377e14	−0.805809	−0.402905	−	0.915242i	$-0.631999\pi$
$457$	−3.43377e14	−0.805809	−0.402905	+	0.915242i	$0.631999\pi$
$458$	9.96464e14	2.31048
$459$	0	0
$460$	5.42455e14	1.22799
$461$	−1.17693e14	−0.263266	−0.131633	−	0.991299i	$-0.542022\pi$
$461$	−1.17693e14	−0.263266	−0.131633	+	0.991299i	$0.542022\pi$
$462$	0	0
$463$	6.04064e14	1.31943	0.659717	−	0.751514i	$-0.270676\pi$
$463$	6.04064e14	1.31943	0.659717	+	0.751514i	$0.270676\pi$
$464$	1.02437e14	0.221109
$465$	0	0
$466$	2.01879e14	0.425568
$467$	6.03902e14	1.25812	0.629062	−	0.777355i	$-0.283439\pi$
$467$	6.03902e14	1.25812	0.629062	+	0.777355i	$0.283439\pi$
$468$	0	0
$469$	3.13530e14	0.638011
$470$	−6.32179e14	−1.27146
$471$	0	0
$472$	8.56014e13	0.168190
$473$	−3.96827e14	−0.770664
$474$	0	0
$475$	−1.10892e14	−0.210419
$476$	1.61658e14	0.303221
$477$	0	0
$478$	2.47251e14	0.453195
$479$	6.97054e14	1.26305	0.631526	−	0.775355i	$-0.282429\pi$
$479$	6.97054e14	1.26305	0.631526	+	0.775355i	$0.282429\pi$
$480$	0	0
$481$	−2.43682e14	−0.431545
$482$	−1.31943e15	−2.31009
$483$	0	0
$484$	−1.87152e13	−0.0320290
$485$	1.19260e14	0.201797
$486$	0	0
$487$	−3.79054e14	−0.627035	−0.313517	−	0.949582i	$-0.601507\pi$
$487$	−3.79054e14	−0.627035	−0.313517	+	0.949582i	$0.601507\pi$
$488$	−6.76597e13	−0.110668
$489$	0	0
$490$	−5.51975e14	−0.882757
$491$	−2.28692e14	−0.361662	−0.180831	−	0.983514i	$-0.557879\pi$
$491$	−2.28692e14	−0.361662	−0.180831	+	0.983514i	$0.557879\pi$
$492$	0	0
$493$	9.46548e13	0.146381
$494$	1.20530e15	1.84330
$495$	0	0
$496$	7.35747e14	1.10047
$497$	2.10504e14	0.311387
$498$	0	0
$499$	4.01402e14	0.580800	0.290400	−	0.956905i	$-0.406212\pi$
$499$	4.01402e14	0.580800	0.290400	+	0.956905i	$0.406212\pi$
$500$	−5.53303e14	−0.791823
$501$	0	0
$502$	5.97424e14	0.836397
$503$	−3.05669e13	−0.0423280	−0.0211640	−	0.999776i	$-0.506737\pi$
$503$	−3.05669e13	−0.0423280	−0.0211640	+	0.999776i	$0.506737\pi$
$504$	0	0
$505$	−4.22758e14	−0.572782
$506$	−1.74370e15	−2.33692
$507$	0	0
$508$	8.17988e14	1.07274
$509$	9.50285e14	1.23284	0.616419	−	0.787418i	$-0.288583\pi$
$509$	9.50285e14	1.23284	0.616419	+	0.787418i	$0.288583\pi$
$510$	0	0
$511$	4.90971e14	0.623362
$512$	8.48278e14	1.06550
$513$	0	0
$514$	1.15202e15	1.41633
$515$	3.57861e14	0.435286
$516$	0	0
$517$	8.66572e14	1.03183
$518$	2.26379e14	0.266699
$519$	0	0
$520$	−2.96321e14	−0.341777
$521$	1.22076e15	1.39322	0.696612	−	0.717448i	$-0.254690\pi$
$521$	1.22076e15	1.39322	0.696612	+	0.717448i	$0.254690\pi$
$522$	0	0
$523$	−7.59341e14	−0.848550	−0.424275	−	0.905533i	$-0.639471\pi$
$523$	−7.59341e14	−0.848550	−0.424275	+	0.905533i	$0.639471\pi$
$524$	2.75334e14	0.304465
$525$	0	0
$526$	−8.25176e14	−0.893562
$527$	6.79854e14	0.728546
$528$	0	0
$529$	2.16605e15	2.27333
$530$	−1.20447e15	−1.25107
$531$	0	0
$532$	−4.77488e14	−0.485790
$533$	−1.40506e13	−0.0141480
$534$	0	0
$535$	5.30266e14	0.523056
$536$	4.27802e14	0.417673
$537$	0	0
$538$	−1.23854e15	−1.18470
$539$	7.56631e14	0.716384
$540$	0	0
$541$	1.08760e15	1.00898	0.504491	−	0.863417i	$-0.331680\pi$
$541$	1.08760e15	1.00898	0.504491	+	0.863417i	$0.331680\pi$
$542$	7.17987e14	0.659357
$543$	0	0
$544$	1.08051e15	0.972380
$545$	−3.55903e13	−0.0317066
$546$	0	0
$547$	−2.03385e15	−1.77578	−0.887888	−	0.460059i	$-0.847828\pi$
$547$	−2.03385e15	−1.77578	−0.887888	+	0.460059i	$0.847828\pi$
$548$	1.47527e14	0.127520
$549$	0	0
$550$	2.54013e14	0.215209
$551$	−2.79581e14	−0.234517
$552$	0	0
$553$	9.09918e14	0.748193
$554$	1.87495e15	1.52646
$555$	0	0
$556$	−1.31842e15	−1.05231
$557$	−1.33949e15	−1.05861	−0.529305	−	0.848432i	$-0.677547\pi$
$557$	−1.33949e15	−1.05861	−0.529305	+	0.848432i	$0.677547\pi$
$558$	0	0
$559$	1.12384e15	0.870844
$560$	7.32929e14	0.562377
$561$	0	0
$562$	−9.51882e14	−0.716198
$563$	2.15377e15	1.60474	0.802369	−	0.596829i	$-0.203573\pi$
$563$	2.15377e15	1.60474	0.802369	+	0.596829i	$0.203573\pi$
$564$	0	0
$565$	−1.16858e15	−0.853872
$566$	2.60581e15	1.88561
$567$	0	0
$568$	2.87227e14	0.203850
$569$	3.66146e14	0.257357	0.128679	−	0.991686i	$-0.458926\pi$
$569$	3.66146e14	0.257357	0.128679	+	0.991686i	$0.458926\pi$
$570$	0	0
$571$	1.16726e15	0.804767	0.402384	−	0.915471i	$-0.368182\pi$
$571$	1.16726e15	0.804767	0.402384	+	0.915471i	$0.368182\pi$
$572$	−1.17735e15	−0.803949
$573$	0	0
$574$	1.30528e13	0.00874359
$575$	−4.54339e14	−0.301444
$576$	0	0
$577$	1.33412e15	0.868419	0.434209	−	0.900812i	$-0.357028\pi$
$577$	1.33412e15	0.868419	0.434209	+	0.900812i	$0.357028\pi$
$578$	−7.75354e14	−0.499916
$579$	0	0
$580$	−1.99230e14	−0.126038
$581$	5.89227e14	0.369244
$582$	0	0
$583$	1.65106e15	1.01528
$584$	6.69915e14	0.408084
$585$	0	0
$586$	3.39840e15	2.03160
$587$	1.53095e15	0.906677	0.453339	−	0.891338i	$-0.350233\pi$
$587$	1.53095e15	0.906677	0.453339	+	0.891338i	$0.350233\pi$
$588$	0	0
$589$	−2.00808e15	−1.16720
$590$	−1.03947e15	−0.598585
$591$	0	0
$592$	8.22410e14	0.464857
$593$	−4.73205e14	−0.265002	−0.132501	−	0.991183i	$-0.542301\pi$
$593$	−4.73205e14	−0.265002	−0.132501	+	0.991183i	$0.542301\pi$
$594$	0	0
$595$	6.77249e14	0.372310
$596$	1.83480e15	0.999388
$597$	0	0
$598$	4.93827e15	2.64069
$599$	−1.14171e15	−0.604932	−0.302466	−	0.953160i	$-0.597810\pi$
$599$	−1.14171e15	−0.604932	−0.302466	+	0.953160i	$0.597810\pi$
$600$	0	0
$601$	1.00013e15	0.520290	0.260145	−	0.965570i	$-0.416230\pi$
$601$	1.00013e15	0.520290	0.260145	+	0.965570i	$0.416230\pi$
$602$	−1.04404e15	−0.538190
$603$	0	0
$604$	−2.14294e15	−1.08469
$605$	−7.84050e13	−0.0393269
$606$	0	0
$607$	−1.84033e15	−0.906480	−0.453240	−	0.891388i	$-0.649732\pi$
$607$	−1.84033e15	−0.906480	−0.453240	+	0.891388i	$0.649732\pi$
$608$	−3.19150e15	−1.55785
$609$	0	0
$610$	8.21601e14	0.393864
$611$	−2.45419e15	−1.16595
$612$	0	0
$613$	−3.47262e15	−1.62041	−0.810205	−	0.586146i	$-0.800644\pi$
$613$	−3.47262e15	−1.62041	−0.810205	+	0.586146i	$0.800644\pi$
$614$	−5.25356e15	−2.42956
$615$	0	0
$616$	−3.77344e14	−0.171413
$617$	−3.14997e15	−1.41820	−0.709101	−	0.705107i	$-0.750899\pi$
$617$	−3.14997e15	−1.41820	−0.709101	+	0.705107i	$0.750899\pi$
$618$	0	0
$619$	4.65762e14	0.205999	0.103000	−	0.994681i	$-0.467156\pi$
$619$	4.65762e14	0.205999	0.103000	+	0.994681i	$0.467156\pi$
$620$	−1.43096e15	−0.627298
$621$	0	0
$622$	4.99903e14	0.215297
$623$	−1.49556e15	−0.638440
$624$	0	0
$625$	−1.92076e15	−0.805625
$626$	5.03508e14	0.209338
$627$	0	0
$628$	−1.51050e14	−0.0617080
$629$	7.59933e14	0.307749
$630$	0	0
$631$	−3.09320e15	−1.23097	−0.615483	−	0.788150i	$-0.711039\pi$
$631$	−3.09320e15	−1.23097	−0.615483	+	0.788150i	$0.711039\pi$
$632$	1.24156e15	0.489805
$633$	0	0
$634$	5.76067e15	2.23348
$635$	3.42687e15	1.31717
$636$	0	0
$637$	−2.14283e15	−0.809507
$638$	6.40417e14	0.239855
$639$	0	0
$640$	1.62451e15	0.598044
$641$	2.63890e15	0.963170	0.481585	−	0.876399i	$-0.340061\pi$
$641$	2.63890e15	0.963170	0.481585	+	0.876399i	$0.340061\pi$
$642$	0	0
$643$	1.40968e15	0.505777	0.252889	−	0.967495i	$-0.418619\pi$
$643$	1.40968e15	0.505777	0.252889	+	0.967495i	$0.418619\pi$
$644$	−1.95633e15	−0.695939
$645$	0	0
$646$	−3.75877e15	−1.31452
$647$	5.04497e15	1.74938	0.874692	−	0.484679i	$-0.161064\pi$
$647$	5.04497e15	1.74938	0.874692	+	0.484679i	$0.161064\pi$
$648$	0	0
$649$	1.42487e15	0.485770
$650$	−7.19381e14	−0.243184
$651$	0	0
$652$	−3.83209e15	−1.27372
$653$	3.65428e15	1.20442	0.602212	−	0.798336i	$-0.294286\pi$
$653$	3.65428e15	1.20442	0.602212	+	0.798336i	$0.294286\pi$
$654$	0	0
$655$	1.15348e15	0.373838
$656$	4.74196e13	0.0152401
$657$	0	0
$658$	2.27992e15	0.720572
$659$	−1.48389e15	−0.465085	−0.232543	−	0.972586i	$-0.574704\pi$
$659$	−1.48389e15	−0.465085	−0.232543	+	0.972586i	$0.574704\pi$
$660$	0	0
$661$	3.44956e15	1.06330	0.531650	−	0.846964i	$-0.321572\pi$
$661$	3.44956e15	1.06330	0.531650	+	0.846964i	$0.321572\pi$
$662$	−1.72455e15	−0.527177
$663$	0	0
$664$	8.03983e14	0.241726
$665$	−2.00038e15	−0.596478
$666$	0	0
$667$	−1.14548e15	−0.335966
$668$	4.72223e15	1.37365
$669$	0	0
$670$	−5.19486e15	−1.48649
$671$	−1.12623e15	−0.319633
$672$	0	0
$673$	−2.06156e15	−0.575591	−0.287795	−	0.957692i	$-0.592922\pi$
$673$	−2.06156e15	−0.575591	−0.287795	+	0.957692i	$0.592922\pi$
$674$	2.43111e15	0.673247
$675$	0	0
$676$	6.05465e14	0.164961
$677$	−2.89101e15	−0.781290	−0.390645	−	0.920541i	$-0.627748\pi$
$677$	−2.89101e15	−0.781290	−0.390645	+	0.920541i	$0.627748\pi$
$678$	0	0
$679$	−4.30104e14	−0.114364
$680$	9.24088e14	0.243733
$681$	0	0
$682$	4.59976e15	1.19377
$683$	−4.53396e15	−1.16725	−0.583625	−	0.812023i	$-0.698366\pi$
$683$	−4.53396e15	−1.16725	−0.583625	+	0.812023i	$0.698366\pi$
$684$	0	0
$685$	6.18046e14	0.156575
$686$	4.70893e15	1.18342
$687$	0	0
$688$	−3.79289e15	−0.938066
$689$	−4.67590e15	−1.14725
$690$	0	0
$691$	3.83758e15	0.926677	0.463339	−	0.886181i	$-0.346651\pi$
$691$	3.83758e15	0.926677	0.463339	+	0.886181i	$0.346651\pi$
$692$	−6.03294e15	−1.44526
$693$	0	0
$694$	3.74897e14	0.0883964
$695$	−5.52337e15	−1.29208
$696$	0	0
$697$	4.38172e13	0.0100894
$698$	6.55759e13	0.0149810
$699$	0	0
$700$	2.84989e14	0.0640897
$701$	5.70841e15	1.27370	0.636848	−	0.770989i	$-0.280238\pi$
$701$	5.70841e15	1.27370	0.636848	+	0.770989i	$0.280238\pi$
$702$	0	0
$703$	−2.24461e15	−0.493044
$704$	1.96622e15	0.428530
$705$	0	0
$706$	−3.50293e15	−0.751633
$707$	1.52466e15	0.324612
$708$	0	0
$709$	−6.92299e15	−1.45124	−0.725620	−	0.688095i	$-0.758447\pi$
$709$	−6.92299e15	−1.45124	−0.725620	+	0.688095i	$0.758447\pi$
$710$	−3.48784e15	−0.725497
$711$	0	0
$712$	−2.04065e15	−0.417955
$713$	−8.22736e15	−1.67212
$714$	0	0
$715$	−4.93239e15	−0.987129
$716$	5.56852e15	1.10591
$717$	0	0
$718$	−3.47953e15	−0.680512
$719$	−4.05045e15	−0.786130	−0.393065	−	0.919511i	$-0.628585\pi$
$719$	−4.05045e15	−0.786130	−0.393065	+	0.919511i	$0.628585\pi$
$720$	0	0
$721$	−1.29061e15	−0.246689
$722$	4.14134e15	0.785573
$723$	0	0
$724$	−6.58216e14	−0.122972
$725$	1.66868e14	0.0309395
$726$	0	0
$727$	−2.30565e15	−0.421071	−0.210535	−	0.977586i	$-0.567521\pi$
$727$	−2.30565e15	−0.421071	−0.210535	+	0.977586i	$0.567521\pi$
$728$	1.06866e15	0.193695
$729$	0	0
$730$	−8.13488e15	−1.45236
$731$	−3.50475e15	−0.621028
$732$	0	0
$733$	−2.90432e15	−0.506959	−0.253479	−	0.967341i	$-0.581575\pi$
$733$	−2.90432e15	−0.506959	−0.253479	+	0.967341i	$0.581575\pi$
$734$	−1.19673e16	−2.07333
$735$	0	0
$736$	−1.30760e16	−2.23176
$737$	7.12096e15	1.20633
$738$	0	0
$739$	−1.98996e15	−0.332123	−0.166062	−	0.986115i	$-0.553105\pi$
$739$	−1.98996e15	−0.332123	−0.166062	+	0.986115i	$0.553105\pi$
$740$	−1.59951e15	−0.264980
$741$	0	0
$742$	4.34387e15	0.709015
$743$	7.35941e15	1.19235	0.596176	−	0.802854i	$-0.296686\pi$
$743$	7.35941e15	1.19235	0.596176	+	0.802854i	$0.296686\pi$
$744$	0	0
$745$	7.68669e15	1.22710
$746$	6.37616e15	1.01041
$747$	0	0
$748$	3.67162e15	0.573323
$749$	−1.91238e15	−0.296431
$750$	0	0
$751$	−1.82500e15	−0.278768	−0.139384	−	0.990238i	$-0.544512\pi$
$751$	−1.82500e15	−0.278768	−0.139384	+	0.990238i	$0.544512\pi$
$752$	8.28272e15	1.25596
$753$	0	0
$754$	−1.81371e15	−0.271034
$755$	−8.97761e15	−1.33184
$756$	0	0
$757$	7.72752e15	1.12983	0.564915	−	0.825149i	$-0.308909\pi$
$757$	7.72752e15	1.12983	0.564915	+	0.825149i	$0.308909\pi$
$758$	−1.64156e16	−2.38274
$759$	0	0
$760$	−2.72947e15	−0.390484
$761$	1.22550e16	1.74060	0.870298	−	0.492526i	$-0.163926\pi$
$761$	1.22550e16	1.74060	0.870298	+	0.492526i	$0.163926\pi$
$762$	0	0
$763$	1.28354e14	0.0179691
$764$	−1.73876e15	−0.241671
$765$	0	0
$766$	−1.06847e16	−1.46387
$767$	−4.03534e15	−0.548915
$768$	0	0
$769$	2.18975e15	0.293629	0.146815	−	0.989164i	$-0.453098\pi$
$769$	2.18975e15	0.293629	0.146815	+	0.989164i	$0.453098\pi$
$770$	4.58214e15	0.610056
$771$	0	0
$772$	−3.36519e15	−0.441686
$773$	−1.21172e16	−1.57912	−0.789559	−	0.613675i	$-0.789690\pi$
$773$	−1.21172e16	−1.57912	−0.789559	+	0.613675i	$0.789690\pi$
$774$	0	0
$775$	1.19852e15	0.153988
$776$	−5.86864e14	−0.0748683
$777$	0	0
$778$	−2.01481e15	−0.253423
$779$	−1.29422e14	−0.0161642
$780$	0	0
$781$	4.78103e15	0.588763
$782$	−1.54002e16	−1.88317
$783$	0	0
$784$	7.23190e15	0.871995
$785$	−6.32805e14	−0.0757682
$786$	0	0
$787$	1.10648e16	1.30642	0.653211	−	0.757176i	$-0.273422\pi$
$787$	1.10648e16	1.30642	0.653211	+	0.757176i	$0.273422\pi$
$788$	−6.38111e15	−0.748172
$789$	0	0
$790$	−1.50764e16	−1.74321
$791$	4.21443e15	0.483914
$792$	0	0
$793$	3.18955e15	0.361182
$794$	4.01295e15	0.451285
$795$	0	0
$796$	−6.17150e15	−0.684493
$797$	−2.33358e15	−0.257041	−0.128520	−	0.991707i	$-0.541023\pi$
$797$	−2.33358e15	−0.257041	−0.128520	+	0.991707i	$0.541023\pi$
$798$	0	0
$799$	7.65349e15	0.831481
$800$	1.90484e15	0.205525
$801$	0	0
$802$	−1.94966e16	−2.07491
$803$	1.11510e16	1.17864
$804$	0	0
$805$	−8.19584e15	−0.854508
$806$	−1.30268e16	−1.34895
$807$	0	0
$808$	2.08035e15	0.212507
$809$	−2.40076e15	−0.243575	−0.121787	−	0.992556i	$-0.538863\pi$
$809$	−2.40076e15	−0.243575	−0.121787	+	0.992556i	$0.538863\pi$
$810$	0	0
$811$	−2.60209e15	−0.260440	−0.130220	−	0.991485i	$-0.541568\pi$
$811$	−2.60209e15	−0.260440	−0.130220	+	0.991485i	$0.541568\pi$
$812$	7.18514e14	0.0714294
$813$	0	0
$814$	5.14157e15	0.504268
$815$	−1.60541e16	−1.56394
$816$	0	0
$817$	1.03519e16	0.994947
$818$	1.62018e16	1.54675
$819$	0	0
$820$	−9.22269e13	−0.00868723
$821$	−1.18775e16	−1.11132	−0.555659	−	0.831410i	$-0.687534\pi$
$821$	−1.18775e16	−1.11132	−0.555659	+	0.831410i	$0.687534\pi$
$822$	0	0
$823$	−1.52923e16	−1.41180	−0.705901	−	0.708311i	$-0.749457\pi$
$823$	−1.52923e16	−1.41180	−0.705901	+	0.708311i	$0.749457\pi$
$824$	−1.76100e15	−0.161495
$825$	0	0
$826$	3.74879e15	0.339235
$827$	1.82433e16	1.63992	0.819959	−	0.572422i	$-0.193996\pi$
$827$	1.82433e16	1.63992	0.819959	+	0.572422i	$0.193996\pi$
$828$	0	0
$829$	1.24346e16	1.10302	0.551508	−	0.834170i	$-0.314053\pi$
$829$	1.24346e16	1.10302	0.551508	+	0.834170i	$0.314053\pi$
$830$	−9.76288e15	−0.860297
$831$	0	0
$832$	−5.56846e15	−0.484236
$833$	6.68250e15	0.577287
$834$	0	0
$835$	1.97833e16	1.68664
$836$	−1.08448e16	−0.918520
$837$	0	0
$838$	2.60809e16	2.18012
$839$	1.21441e16	1.00850	0.504249	−	0.863558i	$-0.331769\pi$
$839$	1.21441e16	1.00850	0.504249	+	0.863558i	$0.331769\pi$
$840$	0	0
$841$	4.20707e14	0.0344828
$842$	2.00708e16	1.63436
$843$	0	0
$844$	−7.37428e15	−0.592702
$845$	2.53653e15	0.202548
$846$	0	0
$847$	2.82764e14	0.0222877
$848$	1.57808e16	1.23581
$849$	0	0
$850$	2.24342e15	0.173423
$851$	−9.19645e15	−0.706330
$852$	0	0
$853$	3.30637e15	0.250687	0.125343	−	0.992113i	$-0.459997\pi$
$853$	3.30637e15	0.250687	0.125343	+	0.992113i	$0.459997\pi$
$854$	−2.96306e15	−0.223214
$855$	0	0
$856$	−2.60939e15	−0.194058
$857$	1.61448e16	1.19299	0.596495	−	0.802617i	$-0.296559\pi$
$857$	1.61448e16	1.19299	0.596495	+	0.802617i	$0.296559\pi$
$858$	0	0
$859$	−2.41473e16	−1.76160	−0.880799	−	0.473491i	$-0.842994\pi$
$859$	−2.41473e16	−1.76160	−0.880799	+	0.473491i	$0.842994\pi$
$860$	7.37682e15	0.534722
$861$	0	0
$862$	2.35043e16	1.68212
$863$	4.67556e14	0.0332487	0.0166243	−	0.999862i	$-0.494708\pi$
$863$	4.67556e14	0.0332487	0.0166243	+	0.999862i	$0.494708\pi$
$864$	0	0
$865$	−2.52743e16	−1.77456
$866$	2.13360e16	1.48855
$867$	0	0
$868$	5.16069e15	0.355508
$869$	2.06663e16	1.41466
$870$	0	0
$871$	−2.01670e16	−1.36315
$872$	1.75136e14	0.0117634
$873$	0	0
$874$	4.54874e16	3.01702
$875$	8.35975e15	0.550996
$876$	0	0
$877$	−2.90591e16	−1.89140	−0.945701	−	0.325037i	$-0.894623\pi$
$877$	−2.90591e16	−1.89140	−0.945701	+	0.325037i	$0.894623\pi$
$878$	−2.01913e16	−1.30600
$879$	0	0
$880$	1.66465e16	1.06333
$881$	1.38771e16	0.880907	0.440453	−	0.897775i	$-0.354818\pi$
$881$	1.38771e16	0.880907	0.440453	+	0.897775i	$0.354818\pi$
$882$	0	0
$883$	−2.19395e16	−1.37544	−0.687721	−	0.725975i	$-0.741389\pi$
$883$	−2.19395e16	−1.37544	−0.687721	+	0.725975i	$0.741389\pi$
$884$	−1.03983e16	−0.647850
$885$	0	0
$886$	−2.63372e16	−1.62063
$887$	−8.16450e15	−0.499286	−0.249643	−	0.968338i	$-0.580313\pi$
$887$	−8.16450e15	−0.499286	−0.249643	+	0.968338i	$0.580313\pi$
$888$	0	0
$889$	−1.23588e16	−0.746478
$890$	2.47799e16	1.48749
$891$	0	0
$892$	−1.60987e14	−0.00954520
$893$	−2.26060e16	−1.33211
$894$	0	0
$895$	2.33287e16	1.35789
$896$	−5.85872e15	−0.338929
$897$	0	0
$898$	2.91102e16	1.66351
$899$	3.02171e15	0.171623
$900$	0	0
$901$	1.45820e16	0.818145
$902$	2.96459e14	0.0165321
$903$	0	0
$904$	5.75048e15	0.316794
$905$	−2.75752e15	−0.150991
$906$	0	0
$907$	3.62086e16	1.95872	0.979359	−	0.202129i	$-0.0647859\pi$
$907$	3.62086e16	1.95872	0.979359	+	0.202129i	$0.0647859\pi$
$908$	−1.07083e16	−0.575769
$909$	0	0
$910$	−1.29769e16	−0.689358
$911$	−3.03810e16	−1.60417	−0.802086	−	0.597209i	$-0.796276\pi$
$911$	−3.03810e16	−1.60417	−0.802086	+	0.597209i	$0.796276\pi$
$912$	0	0
$913$	1.33827e16	0.698157
$914$	−2.05185e16	−1.06400
$915$	0	0
$916$	2.53918e16	1.30097
$917$	−4.15997e15	−0.211865
$918$	0	0
$919$	−1.65057e16	−0.830613	−0.415306	−	0.909682i	$-0.636326\pi$
$919$	−1.65057e16	−0.830613	−0.415306	+	0.909682i	$0.636326\pi$
$920$	−1.11830e16	−0.559404
$921$	0	0
$922$	−7.03276e15	−0.347621
$923$	−1.35402e16	−0.665297
$924$	0	0
$925$	1.33969e15	0.0650467
$926$	3.60959e16	1.74220
$927$	0	0
$928$	4.80250e15	0.229062
$929$	3.43050e16	1.62656	0.813281	−	0.581872i	$-0.197679\pi$
$929$	3.43050e16	1.62656	0.813281	+	0.581872i	$0.197679\pi$
$930$	0	0
$931$	−1.97380e16	−0.924870
$932$	5.14427e15	0.239627
$933$	0	0
$934$	3.60863e16	1.66125
$935$	1.53819e16	0.703955
$936$	0	0
$937$	−1.98495e16	−0.897803	−0.448901	−	0.893581i	$-0.648185\pi$
$937$	−1.98495e16	−0.897803	−0.448901	+	0.893581i	$0.648185\pi$
$938$	1.87350e16	0.842438
$939$	0	0
$940$	−1.61091e16	−0.715928
$941$	3.49305e16	1.54334	0.771671	−	0.636022i	$-0.219421\pi$
$941$	3.49305e16	1.54334	0.771671	+	0.636022i	$0.219421\pi$
$942$	0	0
$943$	−5.30261e14	−0.0231566
$944$	1.36190e16	0.591287
$945$	0	0
$946$	−2.37125e16	−1.01760
$947$	−1.18034e16	−0.503595	−0.251797	−	0.967780i	$-0.581022\pi$
$947$	−1.18034e16	−0.503595	−0.251797	+	0.967780i	$0.581022\pi$
$948$	0	0
$949$	−3.15805e16	−1.33185
$950$	−6.62636e15	−0.277840
$951$	0	0
$952$	−3.33267e15	−0.138131
$953$	−3.85229e16	−1.58748	−0.793740	−	0.608257i	$-0.791869\pi$
$953$	−3.85229e16	−1.58748	−0.793740	+	0.608257i	$0.791869\pi$
$954$	0	0
$955$	−7.28432e15	−0.296736
$956$	6.30044e15	0.255183
$957$	0	0
$958$	4.16526e16	1.66775
$959$	−2.22895e15	−0.0887356
$960$	0	0
$961$	−3.70521e15	−0.145826
$962$	−1.45613e16	−0.569818
$963$	0	0
$964$	−3.36217e16	−1.30076
$965$	−1.40981e16	−0.542325
$966$	0	0
$967$	−1.53557e16	−0.584013	−0.292007	−	0.956416i	$-0.594323\pi$
$967$	−1.53557e16	−0.584013	−0.292007	+	0.956416i	$0.594323\pi$
$968$	3.85823e14	0.0145906
$969$	0	0
$970$	7.12637e15	0.266455
$971$	−2.11866e15	−0.0787689	−0.0393845	−	0.999224i	$-0.512540\pi$
$971$	−2.11866e15	−0.0787689	−0.0393845	+	0.999224i	$0.512540\pi$
$972$	0	0
$973$	1.99198e16	0.732257
$974$	−2.26504e16	−0.827946
$975$	0	0
$976$	−1.07645e16	−0.389063
$977$	2.31006e16	0.830239	0.415119	−	0.909767i	$-0.363740\pi$
$977$	2.31006e16	0.830239	0.415119	+	0.909767i	$0.363740\pi$
$978$	0	0
$979$	−3.39676e16	−1.20715
$980$	−1.40654e16	−0.497060
$981$	0	0
$982$	−1.36655e16	−0.477544
$983$	−3.15129e16	−1.09508	−0.547538	−	0.836781i	$-0.684435\pi$
$983$	−3.15129e16	−1.09508	−0.547538	+	0.836781i	$0.684435\pi$
$984$	0	0
$985$	−2.67329e16	−0.918644
$986$	5.65611e15	0.193284
$987$	0	0
$988$	3.07133e16	1.03792
$989$	4.24133e16	1.42535
$990$	0	0
$991$	9.24891e15	0.307387	0.153694	−	0.988119i	$-0.450883\pi$
$991$	9.24891e15	0.307387	0.153694	+	0.988119i	$0.450883\pi$
$992$	3.44937e16	1.14005
$993$	0	0
$994$	1.25787e16	0.411160
$995$	−2.58548e16	−0.840455
$996$	0	0
$997$	−7.77459e14	−0.0249950	−0.0124975	−	0.999922i	$-0.503978\pi$
$997$	−7.77459e14	−0.0249950	−0.0124975	+	0.999922i	$0.503978\pi$
$998$	2.39858e16	0.766897
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.12.a.a.1.9		11
3.2	odd	2		29.12.a.a.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.3	✓	11	3.2	odd	2
261.12.a.a.1.9		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	261.a (trivial)

\(f(q)\)	\(=\)	\(q+59.7551 q^{2} +1522.68 q^{4} +6379.08 q^{5} -23005.8 q^{7} -31390.8 q^{8} +O(q^{10})\)	\(q+59.7551 q^{2} +1522.68 q^{4} +6379.08 q^{5} -23005.8 q^{7} -31390.8 q^{8} +381183. q^{10} -522514. q^{11} +1.47979e6 q^{13} -1.37472e6 q^{14} -4.99420e6 q^{16} -4.61480e6 q^{17} +1.36307e7 q^{19} +9.71327e6 q^{20} -3.12229e7 q^{22} +5.58468e7 q^{23} -8.13546e6 q^{25} +8.84253e7 q^{26} -3.50304e7 q^{28} -2.05111e7 q^{29} -1.47320e8 q^{31} -2.34141e8 q^{32} -2.75758e8 q^{34} -1.46756e8 q^{35} -1.64673e8 q^{37} +8.14503e8 q^{38} -2.00244e8 q^{40} -9.49494e6 q^{41} +7.59458e8 q^{43} -7.95619e8 q^{44} +3.33713e9 q^{46} -1.65847e9 q^{47} -1.44806e9 q^{49} -4.86136e8 q^{50} +2.25325e9 q^{52} -3.15983e9 q^{53} -3.33316e9 q^{55} +7.22171e8 q^{56} -1.22565e9 q^{58} -2.72696e9 q^{59} +2.15540e9 q^{61} -8.80314e9 q^{62} -3.76299e9 q^{64} +9.43973e9 q^{65} -1.36283e10 q^{67} -7.02685e9 q^{68} -8.76942e9 q^{70} -9.15005e9 q^{71} -2.13411e10 q^{73} -9.84006e9 q^{74} +2.07551e10 q^{76} +1.20209e10 q^{77} -3.95516e10 q^{79} -3.18584e10 q^{80} -5.67371e8 q^{82} -2.56121e10 q^{83} -2.94382e10 q^{85} +4.53815e10 q^{86} +1.64021e10 q^{88} +6.50080e10 q^{89} -3.40439e10 q^{91} +8.50365e10 q^{92} -9.91019e10 q^{94} +8.69512e10 q^{95} +1.86954e10 q^{97} -8.65290e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8} - 685834 q^{10} + 612246 q^{11} + 1510364 q^{13} - 3955400 q^{14} + 3024818 q^{16} + 3291098 q^{17} - 44121388 q^{19} + 49472662 q^{20} - 43435618 q^{22} + 88684076 q^{23} - 44195521 q^{25} + 324999762 q^{26} - 391274848 q^{28} - 225622639 q^{29} - 292235934 q^{31} + 632542514 q^{32} - 1113307936 q^{34} + 1312820120 q^{35} - 1380429338 q^{37} + 1222857284 q^{38} - 2713154106 q^{40} + 1062067494 q^{41} + 74588594 q^{43} - 52891466 q^{44} - 87670324 q^{46} + 1821239394 q^{47} + 4692522003 q^{49} - 9494259926 q^{50} + 3266669866 q^{52} - 7818635688 q^{53} - 191002682 q^{55} - 11263587512 q^{56} - 656356768 q^{58} - 1230002712 q^{59} - 18602654230 q^{61} - 22075953162 q^{62} + 11813658086 q^{64} - 32245789334 q^{65} + 27481284652 q^{67} - 29588811820 q^{68} + 42862666712 q^{70} + 20347168516 q^{71} - 57740010478 q^{73} + 2640709564 q^{74} - 33350650772 q^{76} - 871959792 q^{77} - 120245016462 q^{79} + 84319695274 q^{80} - 111495532412 q^{82} + 142463983824 q^{83} - 181628566552 q^{85} - 47870165542 q^{86} - 180608014462 q^{88} + 96700717270 q^{89} - 355162031176 q^{91} + 22429477796 q^{92} + 172608565078 q^{94} + 195922150708 q^{95} - 303190852014 q^{97} + 123776497136 q^{98}+O(q^{100}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8 - 685834 * q^10 + 612246 * q^11 + 1510364 * q^13 - 3955400 * q^14 + 3024818 * q^16 + 3291098 * q^17 - 44121388 * q^19 + 49472662 * q^20 - 43435618 * q^22 + 88684076 * q^23 - 44195521 * q^25 + 324999762 * q^26 - 391274848 * q^28 - 225622639 * q^29 - 292235934 * q^31 + 632542514 * q^32 - 1113307936 * q^34 + 1312820120 * q^35 - 1380429338 * q^37 + 1222857284 * q^38 - 2713154106 * q^40 + 1062067494 * q^41 + 74588594 * q^43 - 52891466 * q^44 - 87670324 * q^46 + 1821239394 * q^47 + 4692522003 * q^49 - 9494259926 * q^50 + 3266669866 * q^52 - 7818635688 * q^53 - 191002682 * q^55 - 11263587512 * q^56 - 656356768 * q^58 - 1230002712 * q^59 - 18602654230 * q^61 - 22075953162 * q^62 + 11813658086 * q^64 - 32245789334 * q^65 + 27481284652 * q^67 - 29588811820 * q^68 + 42862666712 * q^70 + 20347168516 * q^71 - 57740010478 * q^73 + 2640709564 * q^74 - 33350650772 * q^76 - 871959792 * q^77 - 120245016462 * q^79 + 84319695274 * q^80 - 111495532412 * q^82 + 142463983824 * q^83 - 181628566552 * q^85 - 47870165542 * q^86 - 180608014462 * q^88 + 96700717270 * q^89 - 355162031176 * q^91 + 22429477796 * q^92 + 172608565078 * q^94 + 195922150708 * q^95 - 303190852014 * q^97 + 123776497136 * q^98

Introduction

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Database

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