LMFDB - Embedded newform 261.12.a.a.1.6

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			1.6
Root			$-18.9987$ 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)

$f(q)$	$=$	$q+21.9987 q^{2} -1564.06 q^{4} +886.321 q^{5} +44263.6 q^{7} -79460.6 q^{8} +O(q^{10})$	\(q+21.9987 q^{2} -1564.06 q^{4} +886.321 q^{5} +44263.6 q^{7} -79460.6 q^{8} +19497.9 q^{10} +480464. q^{11} +729102. q^{13} +973741. q^{14} +1.45516e6 q^{16} -6.80915e6 q^{17} -1.56192e7 q^{19} -1.38626e6 q^{20} +1.05696e7 q^{22} +3.18252e7 q^{23} -4.80426e7 q^{25} +1.60393e7 q^{26} -6.92307e7 q^{28} -2.05111e7 q^{29} -3.08016e8 q^{31} +1.94747e8 q^{32} -1.49793e8 q^{34} +3.92317e7 q^{35} +4.28251e8 q^{37} -3.43602e8 q^{38} -7.04276e7 q^{40} +1.00915e9 q^{41} +3.53819e8 q^{43} -7.51473e8 q^{44} +7.00114e8 q^{46} +2.87373e9 q^{47} -1.80646e7 q^{49} -1.05687e9 q^{50} -1.14036e9 q^{52} +1.08796e9 q^{53} +4.25846e8 q^{55} -3.51721e9 q^{56} -4.51219e8 q^{58} -9.69237e9 q^{59} +2.73036e9 q^{61} -6.77597e9 q^{62} +1.30402e9 q^{64} +6.46218e8 q^{65} +5.53037e9 q^{67} +1.06499e10 q^{68} +8.63048e8 q^{70} -1.51715e10 q^{71} +2.05445e10 q^{73} +9.42097e9 q^{74} +2.44293e10 q^{76} +2.12671e10 q^{77} -2.27864e10 q^{79} +1.28974e9 q^{80} +2.21999e10 q^{82} +6.37446e9 q^{83} -6.03510e9 q^{85} +7.78357e9 q^{86} -3.81780e10 q^{88} +2.92283e10 q^{89} +3.22726e10 q^{91} -4.97764e10 q^{92} +6.32185e10 q^{94} -1.38436e10 q^{95} -1.24338e11 q^{97} -3.97399e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.9987	0.486107	0.243054	−	0.970013i	$-0.421851\pi$
$2$	21.9987	0.486107	0.243054	+	0.970013i	$0.421851\pi$
$3$	0	0
$3$	0	0
$4$	−1564.06	−0.763700
$5$	886.321	0.126840	0.0634200	−	0.997987i	$-0.479799\pi$
$5$	886.321	0.126840	0.0634200	+	0.997987i	$0.479799\pi$
$6$	0	0
$7$	44263.6	0.995422	0.497711	−	0.867343i	$-0.334174\pi$
$7$	44263.6	0.995422	0.497711	+	0.867343i	$0.334174\pi$
$8$	−79460.6	−0.857348
$9$	0	0
$10$	19497.9	0.0616579
$11$	480464.	0.899500	0.449750	−	0.893154i	$-0.351513\pi$
$11$	480464.	0.899500	0.449750	+	0.893154i	$0.351513\pi$
$12$	0	0
$13$	729102.	0.544627	0.272314	−	0.962209i	$-0.412211\pi$
$13$	729102.	0.544627	0.272314	+	0.962209i	$0.412211\pi$
$14$	973741.	0.483882
$15$	0	0
$16$	1.45516e6	0.346936
$17$	−6.80915e6	−1.16312	−0.581559	−	0.813504i	$-0.697557\pi$
$17$	−6.80915e6	−1.16312	−0.581559	+	0.813504i	$0.697557\pi$
$18$	0	0
$19$	−1.56192e7	−1.44715	−0.723574	−	0.690246i	$-0.757502\pi$
$19$	−1.56192e7	−1.44715	−0.723574	+	0.690246i	$0.757502\pi$
$20$	−1.38626e6	−0.0968676
$21$	0	0
$22$	1.05696e7	0.437254
$23$	3.18252e7	1.03102	0.515511	−	0.856883i	$-0.327602\pi$
$23$	3.18252e7	1.03102	0.515511	+	0.856883i	$0.327602\pi$
$24$	0	0
$25$	−4.80426e7	−0.983912
$26$	1.60393e7	0.264748
$27$	0	0
$28$	−6.92307e7	−0.760203
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	0	0
$31$	−3.08016e8	−1.93234	−0.966172	−	0.257898i	$-0.916970\pi$
$31$	−3.08016e8	−1.93234	−0.966172	+	0.257898i	$0.916970\pi$
$32$	1.94747e8	1.02600
$33$	0	0
$34$	−1.49793e8	−0.565401
$35$	3.92317e7	0.126259
$36$	0	0
$37$	4.28251e8	1.01529	0.507643	−	0.861567i	$-0.330517\pi$
$37$	4.28251e8	1.01529	0.507643	+	0.861567i	$0.330517\pi$
$38$	−3.43602e8	−0.703470
$39$	0	0
$40$	−7.04276e7	−0.108746
$41$	1.00915e9	1.36033	0.680163	−	0.733061i	$-0.261909\pi$
$41$	1.00915e9	1.36033	0.680163	+	0.733061i	$0.261909\pi$
$42$	0	0
$43$	3.53819e8	0.367033	0.183516	−	0.983017i	$-0.441252\pi$
$43$	3.53819e8	0.367033	0.183516	+	0.983017i	$0.441252\pi$
$44$	−7.51473e8	−0.686948
$45$	0	0
$46$	7.00114e8	0.501188
$47$	2.87373e9	1.82772	0.913858	−	0.406035i	$-0.133089\pi$
$47$	2.87373e9	1.82772	0.913858	+	0.406035i	$0.133089\pi$
$48$	0	0
$49$	−1.80646e7	−0.00913589
$50$	−1.05687e9	−0.478287
$51$	0	0
$52$	−1.14036e9	−0.415932
$53$	1.08796e9	0.357353	0.178676	−	0.983908i	$-0.442818\pi$
$53$	1.08796e9	0.357353	0.178676	+	0.983908i	$0.442818\pi$
$54$	0	0
$55$	4.25846e8	0.114093
$56$	−3.51721e9	−0.853422
$57$	0	0
$58$	−4.51219e8	−0.0902679
$59$	−9.69237e9	−1.76500	−0.882499	−	0.470315i	$-0.844140\pi$
$59$	−9.69237e9	−1.76500	−0.882499	+	0.470315i	$0.844140\pi$
$60$	0	0
$61$	2.73036e9	0.413910	0.206955	−	0.978350i	$-0.433645\pi$
$61$	2.73036e9	0.413910	0.206955	+	0.978350i	$0.433645\pi$
$62$	−6.77597e9	−0.939327
$63$	0	0
$64$	1.30402e9	0.151808
$65$	6.46218e8	0.0690805
$66$	0	0
$67$	5.53037e9	0.500429	0.250215	−	0.968190i	$-0.419499\pi$
$67$	5.53037e9	0.500429	0.250215	+	0.968190i	$0.419499\pi$
$68$	1.06499e10	0.888273
$69$	0	0
$70$	8.63048e8	0.0613756
$71$	−1.51715e10	−0.997949	−0.498974	−	0.866617i	$-0.666290\pi$
$71$	−1.51715e10	−0.997949	−0.498974	+	0.866617i	$0.666290\pi$
$72$	0	0
$73$	2.05445e10	1.15990	0.579949	−	0.814653i	$-0.303072\pi$
$73$	2.05445e10	1.15990	0.579949	+	0.814653i	$0.303072\pi$
$74$	9.42097e9	0.493538
$75$	0	0
$76$	2.44293e10	1.10519
$77$	2.12671e10	0.895382
$78$	0	0
$79$	−2.27864e10	−0.833158	−0.416579	−	0.909100i	$-0.636771\pi$
$79$	−2.27864e10	−0.833158	−0.416579	+	0.909100i	$0.636771\pi$
$80$	1.28974e9	0.0440054
$81$	0	0
$82$	2.21999e10	0.661265
$83$	6.37446e9	0.177629	0.0888144	−	0.996048i	$-0.471692\pi$
$83$	6.37446e9	0.177629	0.0888144	+	0.996048i	$0.471692\pi$
$84$	0	0
$85$	−6.03510e9	−0.147530
$86$	7.78357e9	0.178417
$87$	0	0
$88$	−3.81780e10	−0.771184
$89$	2.92283e10	0.554828	0.277414	−	0.960751i	$-0.410523\pi$
$89$	2.92283e10	0.554828	0.277414	+	0.960751i	$0.410523\pi$
$90$	0	0
$91$	3.22726e10	0.542134
$92$	−4.97764e10	−0.787392
$93$	0	0
$94$	6.32185e10	0.888466
$95$	−1.38436e10	−0.183556
$96$	0	0
$97$	−1.24338e11	−1.47014	−0.735069	−	0.677992i	$-0.762850\pi$
$97$	−1.24338e11	−1.47014	−0.735069	+	0.677992i	$0.762850\pi$
$98$	−3.97399e8	−0.00444103
$99$	0	0
$100$	7.51413e10	0.751413
$101$	2.60286e10	0.246424	0.123212	−	0.992380i	$-0.460680\pi$
$101$	2.60286e10	0.246424	0.123212	+	0.992380i	$0.460680\pi$
$102$	0	0
$103$	−1.19818e11	−1.01840	−0.509200	−	0.860648i	$-0.670059\pi$
$103$	−1.19818e11	−1.01840	−0.509200	+	0.860648i	$0.670059\pi$
$104$	−5.79348e10	−0.466935
$105$	0	0
$106$	2.39338e10	0.173712
$107$	1.11393e11	0.767795	0.383897	−	0.923376i	$-0.374582\pi$
$107$	1.11393e11	0.767795	0.383897	+	0.923376i	$0.374582\pi$
$108$	0	0
$109$	1.17465e11	0.731247	0.365624	−	0.930763i	$-0.380856\pi$
$109$	1.17465e11	0.731247	0.365624	+	0.930763i	$0.380856\pi$
$110$	9.36806e9	0.0554613
$111$	0	0
$112$	6.44104e10	0.345348
$113$	−3.69905e11	−1.88868	−0.944340	−	0.328972i	$-0.893298\pi$
$113$	−3.69905e11	−1.88868	−0.944340	+	0.328972i	$0.893298\pi$
$114$	0	0
$115$	2.82074e10	0.130775
$116$	3.20806e10	0.141815
$117$	0	0
$118$	−2.13220e11	−0.857978
$119$	−3.01397e11	−1.15779
$120$	0	0
$121$	−5.44658e10	−0.190899
$122$	6.00645e10	0.201205
$123$	0	0
$124$	4.81755e11	1.47573
$125$	−8.58586e10	−0.251639
$126$	0	0
$127$	−5.07350e11	−1.36266	−0.681329	−	0.731977i	$-0.738598\pi$
$127$	−5.07350e11	−1.36266	−0.681329	+	0.731977i	$0.738598\pi$
$128$	−3.70155e11	−0.952201
$129$	0	0
$130$	1.42160e10	0.0335806
$131$	−3.44791e11	−0.780843	−0.390422	−	0.920636i	$-0.627671\pi$
$131$	−3.44791e11	−0.780843	−0.390422	+	0.920636i	$0.627671\pi$
$132$	0	0
$133$	−6.91360e11	−1.44052
$134$	1.21661e11	0.243262
$135$	0	0
$136$	5.41059e11	0.997197
$137$	−5.50954e11	−0.975332	−0.487666	−	0.873030i	$-0.662152\pi$
$137$	−5.50954e11	−0.975332	−0.487666	+	0.873030i	$0.662152\pi$
$138$	0	0
$139$	−9.76916e11	−1.59689	−0.798447	−	0.602065i	$-0.794345\pi$
$139$	−9.76916e11	−1.59689	−0.798447	+	0.602065i	$0.794345\pi$
$140$	−6.13606e10	−0.0964241
$141$	0	0
$142$	−3.33754e11	−0.485110
$143$	3.50307e11	0.489893
$144$	0	0
$145$	−1.81795e10	−0.0235536
$146$	4.51953e11	0.563835
$147$	0	0
$148$	−6.69808e11	−0.775374
$149$	5.22457e9	0.00582809	0.00291404	−	0.999996i	$-0.499072\pi$
$149$	5.22457e9	0.00582809	0.00291404	+	0.999996i	$0.499072\pi$
$150$	0	0
$151$	2.71454e11	0.281400	0.140700	−	0.990052i	$-0.455065\pi$
$151$	2.71454e11	0.281400	0.140700	+	0.990052i	$0.455065\pi$
$152$	1.24111e12	1.24071
$153$	0	0
$154$	4.67848e11	0.435252
$155$	−2.73002e11	−0.245099
$156$	0	0
$157$	−8.51389e11	−0.712328	−0.356164	−	0.934424i	$-0.615915\pi$
$157$	−8.51389e11	−0.712328	−0.356164	+	0.934424i	$0.615915\pi$
$158$	−5.01272e11	−0.405004
$159$	0	0
$160$	1.72608e11	0.130137
$161$	1.40870e12	1.02630
$162$	0	0
$163$	1.66971e12	1.13661	0.568304	−	0.822819i	$-0.307600\pi$
$163$	1.66971e12	1.13661	0.568304	+	0.822819i	$0.307600\pi$
$164$	−1.57836e12	−1.03888
$165$	0	0
$166$	1.40230e11	0.0863467
$167$	−1.10002e12	−0.655328	−0.327664	−	0.944794i	$-0.606261\pi$
$167$	−1.10002e12	−0.655328	−0.327664	+	0.944794i	$0.606261\pi$
$168$	0	0
$169$	−1.26057e12	−0.703381
$170$	−1.32764e11	−0.0717154
$171$	0	0
$172$	−5.53393e11	−0.280303
$173$	1.93882e12	0.951225	0.475612	−	0.879655i	$-0.342226\pi$
$173$	1.93882e12	0.951225	0.475612	+	0.879655i	$0.342226\pi$
$174$	0	0
$175$	−2.12653e12	−0.979407
$176$	6.99151e11	0.312069
$177$	0	0
$178$	6.42984e11	0.269706
$179$	−9.66841e11	−0.393245	−0.196623	−	0.980479i	$-0.562997\pi$
$179$	−9.66841e11	−0.393245	−0.196623	+	0.980479i	$0.562997\pi$
$180$	0	0
$181$	3.06155e12	1.17141	0.585705	−	0.810524i	$-0.300818\pi$
$181$	3.06155e12	1.17141	0.585705	+	0.810524i	$0.300818\pi$
$182$	7.09956e11	0.263535
$183$	0	0
$184$	−2.52885e12	−0.883945
$185$	3.79568e11	0.128779
$186$	0	0
$187$	−3.27155e12	−1.04623
$188$	−4.49468e12	−1.39583
$189$	0	0
$190$	−3.04542e11	−0.0892281
$191$	−1.59095e12	−0.452869	−0.226435	−	0.974026i	$-0.572707\pi$
$191$	−1.59095e12	−0.452869	−0.226435	+	0.974026i	$0.572707\pi$
$192$	0	0
$193$	−2.02014e12	−0.543021	−0.271511	−	0.962435i	$-0.587523\pi$
$193$	−2.02014e12	−0.543021	−0.271511	+	0.962435i	$0.587523\pi$
$194$	−2.73527e12	−0.714645
$195$	0	0
$196$	2.82541e10	0.00697708
$197$	1.30724e12	0.313901	0.156950	−	0.987607i	$-0.449834\pi$
$197$	1.30724e12	0.313901	0.156950	+	0.987607i	$0.449834\pi$
$198$	0	0
$199$	2.91409e12	0.661928	0.330964	−	0.943643i	$-0.392626\pi$
$199$	2.91409e12	0.661928	0.330964	+	0.943643i	$0.392626\pi$
$200$	3.81749e12	0.843554
$201$	0	0
$202$	5.72595e11	0.119789
$203$	−9.07896e11	−0.184845
$204$	0	0
$205$	8.94428e11	0.172544
$206$	−2.63585e12	−0.495052
$207$	0	0
$208$	1.06096e12	0.188951
$209$	−7.50445e12	−1.30171
$210$	0	0
$211$	7.99404e12	1.31587	0.657935	−	0.753075i	$-0.271430\pi$
$211$	7.99404e12	1.31587	0.657935	+	0.753075i	$0.271430\pi$
$212$	−1.70164e12	−0.272910
$213$	0	0
$214$	2.45049e12	0.373231
$215$	3.13597e11	0.0465544
$216$	0	0
$217$	−1.36339e13	−1.92350
$218$	2.58409e12	0.355465
$219$	0	0
$220$	−6.66047e11	−0.0871325
$221$	−4.96456e12	−0.633466
$222$	0	0
$223$	−8.85549e12	−1.07532	−0.537658	−	0.843163i	$-0.680691\pi$
$223$	−8.85549e12	−1.07532	−0.537658	+	0.843163i	$0.680691\pi$
$224$	8.62019e12	1.02130
$225$	0	0
$226$	−8.13743e12	−0.918101
$227$	9.57786e12	1.05469	0.527347	−	0.849650i	$-0.323187\pi$
$227$	9.57786e12	1.05469	0.527347	+	0.849650i	$0.323187\pi$
$228$	0	0
$229$	−1.53613e13	−1.61188	−0.805940	−	0.591998i	$-0.798339\pi$
$229$	−1.53613e13	−1.61188	−0.805940	+	0.591998i	$0.798339\pi$
$230$	6.20526e11	0.0635707
$231$	0	0
$232$	1.62983e12	0.159205
$233$	−1.29012e13	−1.23076	−0.615379	−	0.788231i	$-0.710997\pi$
$233$	−1.29012e13	−1.23076	−0.615379	+	0.788231i	$0.710997\pi$
$234$	0	0
$235$	2.54705e12	0.231827
$236$	1.51594e13	1.34793
$237$	0	0
$238$	−6.63035e12	−0.562812
$239$	6.63263e12	0.550170	0.275085	−	0.961420i	$-0.411294\pi$
$239$	6.63263e12	0.550170	0.275085	+	0.961420i	$0.411294\pi$
$240$	0	0
$241$	1.46207e13	1.15845	0.579223	−	0.815169i	$-0.303356\pi$
$241$	1.46207e13	1.15845	0.579223	+	0.815169i	$0.303356\pi$
$242$	−1.19818e12	−0.0927976
$243$	0	0
$244$	−4.27044e12	−0.316103
$245$	−1.60111e10	−0.00115880
$246$	0	0
$247$	−1.13880e13	−0.788157
$248$	2.44752e13	1.65669
$249$	0	0
$250$	−1.88878e12	−0.122324
$251$	−9.17406e12	−0.581241	−0.290620	−	0.956838i	$-0.593862\pi$
$251$	−9.17406e12	−0.581241	−0.290620	+	0.956838i	$0.593862\pi$
$252$	0	0
$253$	1.52909e13	0.927405
$254$	−1.11610e13	−0.662399
$255$	0	0
$256$	−1.08136e13	−0.614680
$257$	−1.33408e13	−0.742249	−0.371125	−	0.928583i	$-0.621028\pi$
$257$	−1.33408e13	−0.742249	−0.371125	+	0.928583i	$0.621028\pi$
$258$	0	0
$259$	1.89559e13	1.01064
$260$	−1.01072e12	−0.0527568
$261$	0	0
$262$	−7.58496e12	−0.379574
$263$	−1.17880e13	−0.577677	−0.288838	−	0.957378i	$-0.593269\pi$
$263$	−1.17880e13	−0.577677	−0.288838	+	0.957378i	$0.593269\pi$
$264$	0	0
$265$	9.64286e11	0.0453266
$266$	−1.52090e13	−0.700249
$267$	0	0
$268$	−8.64981e12	−0.382177
$269$	−4.69213e12	−0.203111	−0.101555	−	0.994830i	$-0.532382\pi$
$269$	−4.69213e12	−0.203111	−0.101555	+	0.994830i	$0.532382\pi$
$270$	0	0
$271$	2.00690e13	0.834056	0.417028	−	0.908894i	$-0.363072\pi$
$271$	2.00690e13	0.834056	0.417028	+	0.908894i	$0.363072\pi$
$272$	−9.90838e12	−0.403528
$273$	0	0
$274$	−1.21203e13	−0.474116
$275$	−2.30827e13	−0.885029
$276$	0	0
$277$	−3.83151e13	−1.41166	−0.705832	−	0.708379i	$-0.749427\pi$
$277$	−3.83151e13	−1.41166	−0.705832	+	0.708379i	$0.749427\pi$
$278$	−2.14909e13	−0.776262
$279$	0	0
$280$	−3.11738e12	−0.108248
$281$	−2.14260e13	−0.729552	−0.364776	−	0.931095i	$-0.618854\pi$
$281$	−2.14260e13	−0.729552	−0.364776	+	0.931095i	$0.618854\pi$
$282$	0	0
$283$	−1.96008e13	−0.641873	−0.320936	−	0.947101i	$-0.603998\pi$
$283$	−1.96008e13	−0.641873	−0.320936	+	0.947101i	$0.603998\pi$
$284$	2.37291e13	0.762133
$285$	0	0
$286$	7.70631e12	0.238140
$287$	4.46684e13	1.35410
$288$	0	0
$289$	1.20926e13	0.352844
$290$	−3.99925e11	−0.0114496
$291$	0	0
$292$	−3.21328e13	−0.885814
$293$	−5.83139e13	−1.57761	−0.788807	−	0.614642i	$-0.789301\pi$
$293$	−5.83139e13	−1.57761	−0.788807	+	0.614642i	$0.789301\pi$
$294$	0	0
$295$	−8.59056e12	−0.223872
$296$	−3.40291e13	−0.870453
$297$	0	0
$298$	1.14934e11	0.00283308
$299$	2.32038e13	0.561523
$300$	0	0
$301$	1.56613e13	0.365352
$302$	5.97165e12	0.136790
$303$	0	0
$304$	−2.27283e13	−0.502069
$305$	2.41998e12	0.0525004
$306$	0	0
$307$	−8.69471e13	−1.81968	−0.909838	−	0.414964i	$-0.863794\pi$
$307$	−8.69471e13	−1.81968	−0.909838	+	0.414964i	$0.863794\pi$
$308$	−3.32629e13	−0.683803
$309$	0	0
$310$	−6.00568e12	−0.119144
$311$	−2.77778e13	−0.541398	−0.270699	−	0.962664i	$-0.587255\pi$
$311$	−2.77778e13	−0.541398	−0.270699	+	0.962664i	$0.587255\pi$
$312$	0	0
$313$	−1.13541e13	−0.213629	−0.106814	−	0.994279i	$-0.534065\pi$
$313$	−1.13541e13	−0.213629	−0.106814	+	0.994279i	$0.534065\pi$
$314$	−1.87295e13	−0.346268
$315$	0	0
$316$	3.56393e13	0.636282
$317$	3.72872e13	0.654236	0.327118	−	0.944984i	$-0.393923\pi$
$317$	3.72872e13	0.654236	0.327118	+	0.944984i	$0.393923\pi$
$318$	0	0
$319$	−9.85487e12	−0.167033
$320$	1.15578e12	0.0192553
$321$	0	0
$322$	3.09895e13	0.498893
$323$	1.06353e14	1.68321
$324$	0	0
$325$	−3.50279e13	−0.535865
$326$	3.67316e13	0.552513
$327$	0	0
$328$	−8.01874e13	−1.16627
$329$	1.27202e14	1.81935
$330$	0	0
$331$	−1.28189e14	−1.77336	−0.886678	−	0.462388i	$-0.846993\pi$
$331$	−1.28189e14	−1.77336	−0.886678	+	0.462388i	$0.846993\pi$
$332$	−9.97001e12	−0.135655
$333$	0	0
$334$	−2.41989e13	−0.318560
$335$	4.90168e12	0.0634744
$336$	0	0
$337$	6.54934e13	0.820792	0.410396	−	0.911907i	$-0.365390\pi$
$337$	6.54934e13	0.820792	0.410396	+	0.911907i	$0.365390\pi$
$338$	−2.77309e13	−0.341919
$339$	0	0
$340$	9.43923e12	0.112669
$341$	−1.47991e14	−1.73814
$342$	0	0
$343$	−8.83231e13	−1.00452
$344$	−2.81147e13	−0.314675
$345$	0	0
$346$	4.26515e13	0.462398
$347$	−8.39610e13	−0.895912	−0.447956	−	0.894056i	$-0.647848\pi$
$347$	−8.39610e13	−0.895912	−0.447956	+	0.894056i	$0.647848\pi$
$348$	0	0
$349$	−1.07463e13	−0.111102	−0.0555509	−	0.998456i	$-0.517691\pi$
$349$	−1.07463e13	−0.111102	−0.0555509	+	0.998456i	$0.517691\pi$
$350$	−4.67810e13	−0.476097
$351$	0	0
$352$	9.35689e13	0.922884
$353$	1.25603e13	0.121966	0.0609832	−	0.998139i	$-0.480576\pi$
$353$	1.25603e13	0.121966	0.0609832	+	0.998139i	$0.480576\pi$
$354$	0	0
$355$	−1.34468e13	−0.126580
$356$	−4.57147e13	−0.423722
$357$	0	0
$358$	−2.12693e13	−0.191159
$359$	1.38150e14	1.22273	0.611365	−	0.791349i	$-0.290621\pi$
$359$	1.38150e14	1.22273	0.611365	+	0.791349i	$0.290621\pi$
$360$	0	0
$361$	1.27468e14	1.09424
$362$	6.73502e13	0.569432
$363$	0	0
$364$	−5.04762e13	−0.414027
$365$	1.82090e13	0.147121
$366$	0	0
$367$	2.02429e14	1.58712	0.793559	−	0.608494i	$-0.208226\pi$
$367$	2.02429e14	1.58712	0.793559	+	0.608494i	$0.208226\pi$
$368$	4.63107e13	0.357699
$369$	0	0
$370$	8.35000e12	0.0626004
$371$	4.81572e13	0.355717
$372$	0	0
$373$	2.52372e13	0.180985	0.0904927	−	0.995897i	$-0.471156\pi$
$373$	2.52372e13	0.180985	0.0904927	+	0.995897i	$0.471156\pi$
$374$	−7.19700e13	−0.508578
$375$	0	0
$376$	−2.28349e14	−1.56699
$377$	−1.49547e13	−0.101135
$378$	0	0
$379$	−5.31941e13	−0.349420	−0.174710	−	0.984620i	$-0.555899\pi$
$379$	−5.31941e13	−0.349420	−0.174710	+	0.984620i	$0.555899\pi$
$380$	2.16522e13	0.140182
$381$	0	0
$382$	−3.49988e13	−0.220143
$383$	−3.19109e14	−1.97854	−0.989272	−	0.146084i	$-0.953333\pi$
$383$	−3.19109e14	−1.97854	−0.989272	+	0.146084i	$0.953333\pi$
$384$	0	0
$385$	1.88494e13	0.113570
$386$	−4.44405e13	−0.263967
$387$	0	0
$388$	1.94471e14	1.12274
$389$	7.65689e13	0.435842	0.217921	−	0.975966i	$-0.430072\pi$
$389$	7.65689e13	0.435842	0.217921	+	0.975966i	$0.430072\pi$
$390$	0	0
$391$	−2.16703e14	−1.19920
$392$	1.43543e12	0.00783264
$393$	0	0
$394$	2.87577e13	0.152589
$395$	−2.01961e13	−0.105678
$396$	0	0
$397$	−3.97244e13	−0.202166	−0.101083	−	0.994878i	$-0.532231\pi$
$397$	−3.97244e13	−0.202166	−0.101083	+	0.994878i	$0.532231\pi$
$398$	6.41062e13	0.321768
$399$	0	0
$400$	−6.99095e13	−0.341355
$401$	−3.19615e14	−1.53934	−0.769668	−	0.638444i	$-0.779578\pi$
$401$	−3.19615e14	−1.53934	−0.769668	+	0.638444i	$0.779578\pi$
$402$	0	0
$403$	−2.24575e14	−1.05241
$404$	−4.07102e13	−0.188194
$405$	0	0
$406$	−1.99726e13	−0.0898546
$407$	2.05759e14	0.913250
$408$	0	0
$409$	−1.92549e14	−0.831885	−0.415942	−	0.909391i	$-0.636548\pi$
$409$	−1.92549e14	−0.831885	−0.415942	+	0.909391i	$0.636548\pi$
$410$	1.96763e13	0.0838748
$411$	0	0
$412$	1.87403e14	0.777752
$413$	−4.29019e14	−1.75692
$414$	0	0
$415$	5.64982e12	0.0225304
$416$	1.41990e14	0.558786
$417$	0	0
$418$	−1.65088e14	−0.632771
$419$	4.17916e13	0.158093	0.0790464	−	0.996871i	$-0.474812\pi$
$419$	4.17916e13	0.158093	0.0790464	+	0.996871i	$0.474812\pi$
$420$	0	0
$421$	2.60522e14	0.960048	0.480024	−	0.877255i	$-0.340628\pi$
$421$	2.60522e14	0.960048	0.480024	+	0.877255i	$0.340628\pi$
$422$	1.75859e14	0.639654
$423$	0	0
$424$	−8.64503e13	−0.306376
$425$	3.27129e14	1.14441
$426$	0	0
$427$	1.20856e14	0.412015
$428$	−1.74224e14	−0.586365
$429$	0	0
$430$	6.89874e12	0.0226305
$431$	1.31690e14	0.426508	0.213254	−	0.976997i	$-0.431594\pi$
$431$	1.31690e14	0.426508	0.213254	+	0.976997i	$0.431594\pi$
$432$	0	0
$433$	−1.19097e13	−0.0376026	−0.0188013	−	0.999823i	$-0.505985\pi$
$433$	−1.19097e13	−0.0376026	−0.0188013	+	0.999823i	$0.505985\pi$
$434$	−2.99928e14	−0.935027
$435$	0	0
$436$	−1.83723e14	−0.558453
$437$	−4.97084e14	−1.49204
$438$	0	0
$439$	−5.65097e14	−1.65413	−0.827063	−	0.562110i	$-0.809990\pi$
$439$	−5.65097e14	−1.65413	−0.827063	+	0.562110i	$0.809990\pi$
$440$	−3.38380e13	−0.0978170
$441$	0	0
$442$	−1.09214e14	−0.307933
$443$	1.77548e14	0.494419	0.247210	−	0.968962i	$-0.420486\pi$
$443$	1.77548e14	0.494419	0.247210	+	0.968962i	$0.420486\pi$
$444$	0	0
$445$	2.59056e13	0.0703743
$446$	−1.94809e14	−0.522719
$447$	0	0
$448$	5.77206e13	0.151113
$449$	7.83747e13	0.202685	0.101342	−	0.994852i	$-0.467686\pi$
$449$	7.83747e13	0.202685	0.101342	+	0.994852i	$0.467686\pi$
$450$	0	0
$451$	4.84859e14	1.22361
$452$	5.78552e14	1.44238
$453$	0	0
$454$	2.10701e14	0.512694
$455$	2.86039e13	0.0687643
$456$	0	0
$457$	−4.40497e14	−1.03372	−0.516861	−	0.856069i	$-0.672900\pi$
$457$	−4.40497e14	−1.03372	−0.516861	+	0.856069i	$0.672900\pi$
$458$	−3.37929e14	−0.783547
$459$	0	0
$460$	−4.41179e13	−0.0998727
$461$	−2.97082e14	−0.664541	−0.332270	−	0.943184i	$-0.607815\pi$
$461$	−2.97082e14	−0.664541	−0.332270	+	0.943184i	$0.607815\pi$
$462$	0	0
$463$	1.07028e14	0.233776	0.116888	−	0.993145i	$-0.462708\pi$
$463$	1.07028e14	0.233776	0.116888	+	0.993145i	$0.462708\pi$
$464$	−2.98469e13	−0.0644245
$465$	0	0
$466$	−2.83810e14	−0.598281
$467$	2.59277e14	0.540158	0.270079	−	0.962838i	$-0.412950\pi$
$467$	2.59277e14	0.540158	0.270079	+	0.962838i	$0.412950\pi$
$468$	0	0
$469$	2.44794e14	0.498138
$470$	5.60319e13	0.112693
$471$	0	0
$472$	7.70162e14	1.51322
$473$	1.69997e14	0.330146
$474$	0	0
$475$	7.50385e14	1.42387
$476$	4.71402e14	0.884206
$477$	0	0
$478$	1.45909e14	0.267442
$479$	9.69340e13	0.175643	0.0878215	−	0.996136i	$-0.472009\pi$
$479$	9.69340e13	0.175643	0.0878215	+	0.996136i	$0.472009\pi$
$480$	0	0
$481$	3.12238e14	0.552953
$482$	3.21637e14	0.563129
$483$	0	0
$484$	8.51876e13	0.145790
$485$	−1.10203e14	−0.186472
$486$	0	0
$487$	4.95544e14	0.819735	0.409867	−	0.912145i	$-0.365575\pi$
$487$	4.95544e14	0.819735	0.409867	+	0.912145i	$0.365575\pi$
$488$	−2.16956e14	−0.354865
$489$	0	0
$490$	−3.52223e11	−0.000563300 0
$491$	9.75658e14	1.54294	0.771471	−	0.636264i	$-0.219521\pi$
$491$	9.75658e14	1.54294	0.771471	+	0.636264i	$0.219521\pi$
$492$	0	0
$493$	1.39664e14	0.215986
$494$	−2.50521e14	−0.383129
$495$	0	0
$496$	−4.48212e14	−0.670401
$497$	−6.71545e14	−0.993380
$498$	0	0
$499$	1.26831e15	1.83516	0.917579	−	0.397554i	$-0.130141\pi$
$499$	1.26831e15	1.83516	0.917579	+	0.397554i	$0.130141\pi$
$500$	1.34288e14	0.192177
$501$	0	0
$502$	−2.01817e14	−0.282545
$503$	−7.13091e14	−0.987463	−0.493732	−	0.869614i	$-0.664368\pi$
$503$	−7.13091e14	−0.987463	−0.493732	+	0.869614i	$0.664368\pi$
$504$	0	0
$505$	2.30697e13	0.0312564
$506$	3.36380e14	0.450819
$507$	0	0
$508$	7.93524e14	1.04066
$509$	1.47779e14	0.191719	0.0958597	−	0.995395i	$-0.469440\pi$
$509$	1.47779e14	0.191719	0.0958597	+	0.995395i	$0.469440\pi$
$510$	0	0
$511$	9.09373e14	1.15459
$512$	5.20193e14	0.653400
$513$	0	0
$514$	−2.93480e14	−0.360813
$515$	−1.06198e14	−0.129174
$516$	0	0
$517$	1.38073e15	1.64403
$518$	4.17005e14	0.491279
$519$	0	0
$520$	−5.13489e13	−0.0592260
$521$	−2.60928e14	−0.297792	−0.148896	−	0.988853i	$-0.547572\pi$
$521$	−2.60928e14	−0.297792	−0.148896	+	0.988853i	$0.547572\pi$
$522$	0	0
$523$	7.01208e14	0.783587	0.391794	−	0.920053i	$-0.371855\pi$
$523$	7.01208e14	0.783587	0.391794	+	0.920053i	$0.371855\pi$
$524$	5.39273e14	0.596330
$525$	0	0
$526$	−2.59322e14	−0.280813
$527$	2.09733e15	2.24755
$528$	0	0
$529$	6.00349e13	0.0630082
$530$	2.12130e13	0.0220336
$531$	0	0
$532$	1.08133e15	1.10013
$533$	7.35770e14	0.740871
$534$	0	0
$535$	9.87296e13	0.0973871
$536$	−4.39446e14	−0.429042
$537$	0	0
$538$	−1.03221e14	−0.0987336
$539$	−8.67942e12	−0.00821774
$540$	0	0
$541$	−1.43669e15	−1.33284	−0.666419	−	0.745578i	$-0.732174\pi$
$541$	−1.43669e15	−1.33284	−0.666419	+	0.745578i	$0.732174\pi$
$542$	4.41493e14	0.405441
$543$	0	0
$544$	−1.32606e15	−1.19335
$545$	1.04112e14	0.0927514
$546$	0	0
$547$	−9.61440e14	−0.839444	−0.419722	−	0.907653i	$-0.637872\pi$
$547$	−9.61440e14	−0.839444	−0.419722	+	0.907653i	$0.637872\pi$
$548$	8.61724e14	0.744861
$549$	0	0
$550$	−5.07790e14	−0.430219
$551$	3.20367e14	0.268729
$552$	0	0
$553$	−1.00861e15	−0.829343
$554$	−8.42884e14	−0.686221
$555$	0	0
$556$	1.52795e15	1.21955
$557$	2.91552e14	0.230416	0.115208	−	0.993341i	$-0.463247\pi$
$557$	2.91552e14	0.230416	0.115208	+	0.993341i	$0.463247\pi$
$558$	0	0
$559$	2.57970e14	0.199896
$560$	5.70883e13	0.0438039
$561$	0	0
$562$	−4.71344e14	−0.354641
$563$	6.42960e14	0.479057	0.239529	−	0.970889i	$-0.423007\pi$
$563$	6.42960e14	0.479057	0.239529	+	0.970889i	$0.423007\pi$
$564$	0	0
$565$	−3.27854e14	−0.239560
$566$	−4.31193e14	−0.312019
$567$	0	0
$568$	1.20554e15	0.855589
$569$	−4.54572e14	−0.319511	−0.159755	−	0.987157i	$-0.551071\pi$
$569$	−4.54572e14	−0.319511	−0.159755	+	0.987157i	$0.551071\pi$
$570$	0	0
$571$	−1.61565e15	−1.11391	−0.556955	−	0.830543i	$-0.688030\pi$
$571$	−1.61565e15	−1.11391	−0.556955	+	0.830543i	$0.688030\pi$
$572$	−5.47900e14	−0.374131
$573$	0	0
$574$	9.82647e14	0.658237
$575$	−1.52897e15	−1.01444
$576$	0	0
$577$	−3.96128e14	−0.257851	−0.128926	−	0.991654i	$-0.541153\pi$
$577$	−3.96128e14	−0.257851	−0.128926	+	0.991654i	$0.541153\pi$
$578$	2.66022e14	0.171520
$579$	0	0
$580$	2.84337e13	0.0179879
$581$	2.82156e14	0.176816
$582$	0	0
$583$	5.22728e14	0.321439
$584$	−1.63248e15	−0.994436
$585$	0	0
$586$	−1.28283e15	−0.766890
$587$	6.16212e14	0.364939	0.182470	−	0.983211i	$-0.441591\pi$
$587$	6.16212e14	0.364939	0.182470	+	0.983211i	$0.441591\pi$
$588$	0	0
$589$	4.81096e15	2.79639
$590$	−1.88981e14	−0.108826
$591$	0	0
$592$	6.23172e14	0.352240
$593$	1.04704e15	0.586360	0.293180	−	0.956057i	$-0.405286\pi$
$593$	1.04704e15	0.586360	0.293180	+	0.956057i	$0.405286\pi$
$594$	0	0
$595$	−2.67135e14	−0.146854
$596$	−8.17152e12	−0.00445091
$597$	0	0
$598$	5.10454e14	0.272961
$599$	3.29250e15	1.74453	0.872265	−	0.489033i	$-0.162650\pi$
$599$	3.29250e15	1.74453	0.872265	+	0.489033i	$0.162650\pi$
$600$	0	0
$601$	−2.47950e14	−0.128990	−0.0644949	−	0.997918i	$-0.520544\pi$
$601$	−2.47950e14	−0.128990	−0.0644949	+	0.997918i	$0.520544\pi$
$602$	3.44528e14	0.177600
$603$	0	0
$604$	−4.24570e14	−0.214905
$605$	−4.82742e13	−0.0242137
$606$	0	0
$607$	−2.44547e15	−1.20455	−0.602274	−	0.798290i	$-0.705738\pi$
$607$	−2.44547e15	−1.20455	−0.602274	+	0.798290i	$0.705738\pi$
$608$	−3.04179e15	−1.48477
$609$	0	0
$610$	5.32364e13	0.0255208
$611$	2.09524e15	0.995424
$612$	0	0
$613$	2.10077e15	0.980270	0.490135	−	0.871646i	$-0.336947\pi$
$613$	2.10077e15	0.980270	0.490135	+	0.871646i	$0.336947\pi$
$614$	−1.91272e15	−0.884558
$615$	0	0
$616$	−1.68989e15	−0.767653
$617$	2.30636e14	0.103839	0.0519194	−	0.998651i	$-0.483466\pi$
$617$	2.30636e14	0.103839	0.0519194	+	0.998651i	$0.483466\pi$
$618$	0	0
$619$	−1.04593e15	−0.462599	−0.231300	−	0.972883i	$-0.574298\pi$
$619$	−1.04593e15	−0.462599	−0.231300	+	0.972883i	$0.574298\pi$
$620$	4.26990e14	0.187182
$621$	0	0
$622$	−6.11077e14	−0.263177
$623$	1.29375e15	0.552287
$624$	0	0
$625$	2.26973e15	0.951994
$626$	−2.49776e14	−0.103846
$627$	0	0
$628$	1.33162e15	0.544004
$629$	−2.91602e15	−1.18090
$630$	0	0
$631$	8.37986e14	0.333484	0.166742	−	0.986001i	$-0.446675\pi$
$631$	8.37986e14	0.333484	0.166742	+	0.986001i	$0.446675\pi$
$632$	1.81062e15	0.714306
$633$	0	0
$634$	8.20271e14	0.318029
$635$	−4.49675e14	−0.172840
$636$	0	0
$637$	−1.31710e13	−0.00497566
$638$	−2.16795e14	−0.0811960
$639$	0	0
$640$	−3.28076e14	−0.120777
$641$	4.90090e15	1.78878	0.894390	−	0.447288i	$-0.147610\pi$
$641$	4.90090e15	1.78878	0.894390	+	0.447288i	$0.147610\pi$
$642$	0	0
$643$	1.71965e15	0.616991	0.308496	−	0.951226i	$-0.400174\pi$
$643$	1.71965e15	0.616991	0.308496	+	0.951226i	$0.400174\pi$
$644$	−2.20328e15	−0.783787
$645$	0	0
$646$	2.33964e15	0.818219
$647$	−8.99014e14	−0.311740	−0.155870	−	0.987778i	$-0.549818\pi$
$647$	−8.99014e14	−0.311740	−0.155870	+	0.987778i	$0.549818\pi$
$648$	0	0
$649$	−4.65684e15	−1.58762
$650$	−7.70569e14	−0.260488
$651$	0	0
$652$	−2.61153e15	−0.868026
$653$	−1.85055e15	−0.609927	−0.304964	−	0.952364i	$-0.598644\pi$
$653$	−1.85055e15	−0.609927	−0.304964	+	0.952364i	$0.598644\pi$
$654$	0	0
$655$	−3.05596e14	−0.0990421
$656$	1.46847e15	0.471947
$657$	0	0
$658$	2.79827e15	0.884398
$659$	8.51169e14	0.266776	0.133388	−	0.991064i	$-0.457414\pi$
$659$	8.51169e14	0.266776	0.133388	+	0.991064i	$0.457414\pi$
$660$	0	0
$661$	5.25610e15	1.62015	0.810075	−	0.586326i	$-0.199426\pi$
$661$	5.25610e15	1.62015	0.810075	+	0.586326i	$0.199426\pi$
$662$	−2.81999e15	−0.862042
$663$	0	0
$664$	−5.06518e14	−0.152290
$665$	−6.12767e14	−0.182716
$666$	0	0
$667$	−6.52772e14	−0.191456
$668$	1.72049e15	0.500473
$669$	0	0
$670$	1.07831e14	0.0308554
$671$	1.31184e15	0.372313
$672$	0	0
$673$	6.49345e14	0.181298	0.0906490	−	0.995883i	$-0.471106\pi$
$673$	6.49345e14	0.181298	0.0906490	+	0.995883i	$0.471106\pi$
$674$	1.44077e15	0.398993
$675$	0	0
$676$	1.97160e15	0.537172
$677$	−4.60763e15	−1.24520	−0.622601	−	0.782540i	$-0.713924\pi$
$677$	−4.60763e15	−1.24520	−0.622601	+	0.782540i	$0.713924\pi$
$678$	0	0
$679$	−5.50363e15	−1.46341
$680$	4.79552e14	0.126484
$681$	0	0
$682$	−3.25561e15	−0.844925
$683$	1.97762e15	0.509131	0.254566	−	0.967056i	$-0.418068\pi$
$683$	1.97762e15	0.509131	0.254566	+	0.967056i	$0.418068\pi$
$684$	0	0
$685$	−4.88323e14	−0.123711
$686$	−1.94299e15	−0.488303
$687$	0	0
$688$	5.14862e14	0.127337
$689$	7.93236e14	0.194624
$690$	0	0
$691$	−5.65502e15	−1.36554	−0.682770	−	0.730633i	$-0.739225\pi$
$691$	−5.65502e15	−1.36554	−0.682770	+	0.730633i	$0.739225\pi$
$692$	−3.03242e15	−0.726450
$693$	0	0
$694$	−1.84703e15	−0.435510
$695$	−8.65862e14	−0.202550
$696$	0	0
$697$	−6.87143e15	−1.58222
$698$	−2.36406e14	−0.0540074
$699$	0	0
$700$	3.32602e15	0.747973
$701$	−6.37840e15	−1.42319	−0.711595	−	0.702590i	$-0.752027\pi$
$701$	−6.37840e15	−1.42319	−0.711595	+	0.702590i	$0.752027\pi$
$702$	0	0
$703$	−6.68892e15	−1.46927
$704$	6.26535e14	0.136551
$705$	0	0
$706$	2.76311e14	0.0592887
$707$	1.15212e15	0.245296
$708$	0	0
$709$	−1.82210e15	−0.381961	−0.190980	−	0.981594i	$-0.561167\pi$
$709$	−1.82210e15	−0.381961	−0.190980	+	0.981594i	$0.561167\pi$
$710$	−2.95813e14	−0.0615314
$711$	0	0
$712$	−2.32250e15	−0.475680
$713$	−9.80269e15	−1.99229
$714$	0	0
$715$	3.10485e14	0.0621380
$716$	1.51219e15	0.300321
$717$	0	0
$718$	3.03912e15	0.594378
$719$	−4.72441e15	−0.916935	−0.458467	−	0.888711i	$-0.651601\pi$
$719$	−4.72441e15	−0.916935	−0.458467	+	0.888711i	$0.651601\pi$
$720$	0	0
$721$	−5.30358e15	−1.01374
$722$	2.80414e15	0.531918
$723$	0	0
$724$	−4.78844e15	−0.894606
$725$	9.85408e14	0.182708
$726$	0	0
$727$	9.76903e15	1.78407	0.892035	−	0.451966i	$-0.149277\pi$
$727$	9.76903e15	1.78407	0.892035	+	0.451966i	$0.149277\pi$
$728$	−2.56440e15	−0.464797
$729$	0	0
$730$	4.00575e14	0.0715169
$731$	−2.40921e15	−0.426902
$732$	0	0
$733$	−2.30118e15	−0.401678	−0.200839	−	0.979624i	$-0.564367\pi$
$733$	−2.30118e15	−0.401678	−0.200839	+	0.979624i	$0.564367\pi$
$734$	4.45317e15	0.771510
$735$	0	0
$736$	6.19786e15	1.05783
$737$	2.65714e15	0.450136
$738$	0	0
$739$	7.78978e15	1.30011	0.650056	−	0.759886i	$-0.274745\pi$
$739$	7.78978e15	1.30011	0.650056	+	0.759886i	$0.274745\pi$
$740$	−5.93665e14	−0.0983484
$741$	0	0
$742$	1.05940e15	0.172917
$743$	7.50411e14	0.121580	0.0607898	−	0.998151i	$-0.480638\pi$
$743$	7.50411e14	0.121580	0.0607898	+	0.998151i	$0.480638\pi$
$744$	0	0
$745$	4.63065e12	0.000739234 0
$746$	5.55187e14	0.0879783
$747$	0	0
$748$	5.11689e15	0.799002
$749$	4.93063e15	0.764280
$750$	0	0
$751$	−8.59656e15	−1.31312	−0.656561	−	0.754273i	$-0.727989\pi$
$751$	−8.59656e15	−1.31312	−0.656561	+	0.754273i	$0.727989\pi$
$752$	4.18174e15	0.634101
$753$	0	0
$754$	−3.28984e14	−0.0491624
$755$	2.40596e14	0.0356927
$756$	0	0
$757$	−5.23719e15	−0.765722	−0.382861	−	0.923806i	$-0.625061\pi$
$757$	−5.23719e15	−0.765722	−0.382861	+	0.923806i	$0.625061\pi$
$758$	−1.17020e15	−0.169856
$759$	0	0
$760$	1.10002e15	0.157372
$761$	5.40274e15	0.767358	0.383679	−	0.923466i	$-0.374657\pi$
$761$	5.40274e15	0.767358	0.383679	+	0.923466i	$0.374657\pi$
$762$	0	0
$763$	5.19944e15	0.727899
$764$	2.48834e15	0.345856
$765$	0	0
$766$	−7.01999e15	−0.961785
$767$	−7.06672e15	−0.961266
$768$	0	0
$769$	1.68378e15	0.225783	0.112891	−	0.993607i	$-0.463989\pi$
$769$	1.68378e15	0.225783	0.112891	+	0.993607i	$0.463989\pi$
$770$	4.14663e14	0.0552073
$771$	0	0
$772$	3.15962e15	0.414705
$773$	6.91163e14	0.0900727	0.0450363	−	0.998985i	$-0.485660\pi$
$773$	6.91163e14	0.0900727	0.0450363	+	0.998985i	$0.485660\pi$
$774$	0	0
$775$	1.47979e16	1.90126
$776$	9.87995e15	1.26042
$777$	0	0
$778$	1.68442e15	0.211866
$779$	−1.57620e16	−1.96859
$780$	0	0
$781$	−7.28937e15	−0.897655
$782$	−4.76718e15	−0.582941
$783$	0	0
$784$	−2.62869e13	−0.00316957
$785$	−7.54604e14	−0.0903516
$786$	0	0
$787$	−8.76844e15	−1.03529	−0.517644	−	0.855596i	$-0.673191\pi$
$787$	−8.76844e15	−1.03529	−0.517644	+	0.855596i	$0.673191\pi$
$788$	−2.04460e15	−0.239726
$789$	0	0
$790$	−4.44288e14	−0.0513707
$791$	−1.63733e16	−1.88003
$792$	0	0
$793$	1.99071e15	0.225427
$794$	−8.73885e14	−0.0982746
$795$	0	0
$796$	−4.55780e15	−0.505514
$797$	9.97692e15	1.09894	0.549472	−	0.835512i	$-0.314829\pi$
$797$	9.97692e15	1.09894	0.549472	+	0.835512i	$0.314829\pi$
$798$	0	0
$799$	−1.95677e16	−2.12585
$800$	−9.35614e15	−1.00949
$801$	0	0
$802$	−7.03113e15	−0.748283
$803$	9.87090e15	1.04333
$804$	0	0
$805$	1.24856e15	0.130176
$806$	−4.94037e15	−0.511583
$807$	0	0
$808$	−2.06825e15	−0.211271
$809$	−1.81464e16	−1.84108	−0.920540	−	0.390648i	$-0.872251\pi$
$809$	−1.81464e16	−1.84108	−0.920540	+	0.390648i	$0.872251\pi$
$810$	0	0
$811$	1.48265e16	1.48397	0.741984	−	0.670418i	$-0.233885\pi$
$811$	1.48265e16	1.48397	0.741984	+	0.670418i	$0.233885\pi$
$812$	1.42000e15	0.141166
$813$	0	0
$814$	4.52644e15	0.443938
$815$	1.47990e15	0.144167
$816$	0	0
$817$	−5.52636e15	−0.531151
$818$	−4.23583e15	−0.404385
$819$	0	0
$820$	−1.39894e15	−0.131772
$821$	1.98325e16	1.85562	0.927812	−	0.373048i	$-0.121687\pi$
$821$	1.98325e16	1.85562	0.927812	+	0.373048i	$0.121687\pi$
$822$	0	0
$823$	−4.07918e15	−0.376594	−0.188297	−	0.982112i	$-0.560297\pi$
$823$	−4.07918e15	−0.376594	−0.188297	+	0.982112i	$0.560297\pi$
$824$	9.52083e15	0.873123
$825$	0	0
$826$	−9.43786e15	−0.854050
$827$	1.50273e16	1.35083	0.675417	−	0.737436i	$-0.263964\pi$
$827$	1.50273e16	1.35083	0.675417	+	0.737436i	$0.263964\pi$
$828$	0	0
$829$	1.78355e15	0.158211	0.0791054	−	0.996866i	$-0.474794\pi$
$829$	1.78355e15	0.158211	0.0791054	+	0.996866i	$0.474794\pi$
$830$	1.24289e14	0.0109522
$831$	0	0
$832$	9.50763e14	0.0826787
$833$	1.23005e14	0.0106261
$834$	0	0
$835$	−9.74968e14	−0.0831217
$836$	1.17374e16	0.994116
$837$	0	0
$838$	9.19362e14	0.0768501
$839$	−2.08273e16	−1.72959	−0.864794	−	0.502126i	$-0.832551\pi$
$839$	−2.08273e16	−1.72959	−0.864794	+	0.502126i	$0.832551\pi$
$840$	0	0
$841$	4.20707e14	0.0344828
$842$	5.73115e15	0.466686
$843$	0	0
$844$	−1.25031e16	−1.00493
$845$	−1.11727e15	−0.0892168
$846$	0	0
$847$	−2.41085e15	−0.190025
$848$	1.58316e15	0.123979
$849$	0	0
$850$	7.19642e15	0.556304
$851$	1.36292e16	1.04678
$852$	0	0
$853$	−2.58806e16	−1.96225	−0.981126	−	0.193370i	$-0.938058\pi$
$853$	−2.58806e16	−1.96225	−0.981126	+	0.193370i	$0.938058\pi$
$854$	2.65867e15	0.200284
$855$	0	0
$856$	−8.85132e15	−0.658267
$857$	1.86002e16	1.37443	0.687215	−	0.726454i	$-0.258833\pi$
$857$	1.86002e16	1.37443	0.687215	+	0.726454i	$0.258833\pi$
$858$	0	0
$859$	−1.99564e16	−1.45586	−0.727931	−	0.685650i	$-0.759518\pi$
$859$	−1.99564e16	−1.45586	−0.727931	+	0.685650i	$0.759518\pi$
$860$	−4.90484e14	−0.0355536
$861$	0	0
$862$	2.89701e15	0.207329
$863$	−5.86095e14	−0.0416782	−0.0208391	−	0.999783i	$-0.506634\pi$
$863$	−5.86095e14	−0.0416782	−0.0208391	+	0.999783i	$0.506634\pi$
$864$	0	0
$865$	1.71841e15	0.120653
$866$	−2.61998e14	−0.0182789
$867$	0	0
$868$	2.13242e16	1.46897
$869$	−1.09481e16	−0.749425
$870$	0	0
$871$	4.03220e15	0.272547
$872$	−9.33387e15	−0.626933
$873$	0	0
$874$	−1.09352e16	−0.725294
$875$	−3.80040e15	−0.250487
$876$	0	0
$877$	−2.50479e16	−1.63032	−0.815162	−	0.579232i	$-0.803352\pi$
$877$	−2.50479e16	−1.63032	−0.815162	+	0.579232i	$0.803352\pi$
$878$	−1.24314e16	−0.804083
$879$	0	0
$880$	6.19672e14	0.0395829
$881$	2.71552e16	1.72379	0.861896	−	0.507085i	$-0.169277\pi$
$881$	2.71552e16	1.72379	0.861896	+	0.507085i	$0.169277\pi$
$882$	0	0
$883$	−6.82561e14	−0.0427915	−0.0213958	−	0.999771i	$-0.506811\pi$
$883$	−6.82561e14	−0.0427915	−0.0213958	+	0.999771i	$0.506811\pi$
$884$	7.76486e15	0.483778
$885$	0	0
$886$	3.90583e15	0.240341
$887$	−1.46682e16	−0.897008	−0.448504	−	0.893781i	$-0.648043\pi$
$887$	−1.46682e16	−0.897008	−0.448504	+	0.893781i	$0.648043\pi$
$888$	0	0
$889$	−2.24571e16	−1.35642
$890$	5.69891e14	0.0342095
$891$	0	0
$892$	1.38505e16	0.821218
$893$	−4.48854e16	−2.64498
$894$	0	0
$895$	−8.56932e14	−0.0498792
$896$	−1.63844e16	−0.947841
$897$	0	0
$898$	1.72414e15	0.0985266
$899$	6.31777e15	0.358827
$900$	0	0
$901$	−7.40811e15	−0.415644
$902$	1.06663e16	0.594808
$903$	0	0
$904$	2.93928e16	1.61925
$905$	2.71352e15	0.148582
$906$	0	0
$907$	1.65196e16	0.893634	0.446817	−	0.894625i	$-0.352558\pi$
$907$	1.65196e16	0.893634	0.446817	+	0.894625i	$0.352558\pi$
$908$	−1.49803e16	−0.805469
$909$	0	0
$910$	6.29249e14	0.0334268
$911$	2.65587e16	1.40235	0.701173	−	0.712991i	$-0.252660\pi$
$911$	2.65587e16	1.40235	0.701173	+	0.712991i	$0.252660\pi$
$912$	0	0
$913$	3.06270e15	0.159777
$914$	−9.69037e15	−0.502500
$915$	0	0
$916$	2.40259e16	1.23099
$917$	−1.52617e16	−0.777268
$918$	0	0
$919$	1.23677e16	0.622378	0.311189	−	0.950348i	$-0.399273\pi$
$919$	1.23677e16	0.622378	0.311189	+	0.950348i	$0.399273\pi$
$920$	−2.24137e15	−0.112120
$921$	0	0
$922$	−6.53543e15	−0.323038
$923$	−1.10616e16	−0.543510
$924$	0	0
$925$	−2.05743e16	−0.998952
$926$	2.35447e15	0.113640
$927$	0	0
$928$	−3.99448e15	−0.190523
$929$	2.12065e16	1.00550	0.502751	−	0.864432i	$-0.332321\pi$
$929$	2.12065e16	1.00550	0.502751	+	0.864432i	$0.332321\pi$
$930$	0	0
$931$	2.82155e14	0.0132210
$932$	2.01782e16	0.939929
$933$	0	0
$934$	5.70376e15	0.262575
$935$	−2.89965e15	−0.132703
$936$	0	0
$937$	4.75067e15	0.214876	0.107438	−	0.994212i	$-0.465735\pi$
$937$	4.75067e15	0.214876	0.107438	+	0.994212i	$0.465735\pi$
$938$	5.38515e15	0.242149
$939$	0	0
$940$	−3.98373e15	−0.177046
$941$	−1.38698e16	−0.612813	−0.306406	−	0.951901i	$-0.599127\pi$
$941$	−1.38698e16	−0.612813	−0.306406	+	0.951901i	$0.599127\pi$
$942$	0	0
$943$	3.21163e16	1.40253
$944$	−1.41039e16	−0.612342
$945$	0	0
$946$	3.73972e15	0.160486
$947$	5.40709e15	0.230695	0.115348	−	0.993325i	$-0.463202\pi$
$947$	5.40709e15	0.230695	0.115348	+	0.993325i	$0.463202\pi$
$948$	0	0
$949$	1.49790e16	0.631713
$950$	1.65075e16	0.692152
$951$	0	0
$952$	2.39492e16	0.992631
$953$	2.32910e16	0.959793	0.479896	−	0.877325i	$-0.340674\pi$
$953$	2.32910e16	0.959793	0.479896	+	0.877325i	$0.340674\pi$
$954$	0	0
$955$	−1.41009e15	−0.0574419
$956$	−1.03738e16	−0.420165
$957$	0	0
$958$	2.13242e15	0.0853814
$959$	−2.43872e16	−0.970867
$960$	0	0
$961$	6.94656e16	2.73396
$962$	6.86884e15	0.268795
$963$	0	0
$964$	−2.28677e16	−0.884704
$965$	−1.79050e15	−0.0688768
$966$	0	0
$967$	−4.20715e16	−1.60008	−0.800042	−	0.599944i	$-0.795189\pi$
$967$	−4.20715e16	−1.60008	−0.800042	+	0.599944i	$0.795189\pi$
$968$	4.32789e15	0.163667
$969$	0	0
$970$	−2.42433e15	−0.0906456
$971$	4.86896e16	1.81022	0.905108	−	0.425181i	$-0.139790\pi$
$971$	4.86896e16	1.81022	0.905108	+	0.425181i	$0.139790\pi$
$972$	0	0
$973$	−4.32418e16	−1.58958
$974$	1.09013e16	0.398479
$975$	0	0
$976$	3.97311e15	0.143601
$977$	3.15141e15	0.113262	0.0566311	−	0.998395i	$-0.481964\pi$
$977$	3.15141e15	0.113262	0.0566311	+	0.998395i	$0.481964\pi$
$978$	0	0
$979$	1.40431e16	0.499068
$980$	2.50422e13	0.000884972 0
$981$	0	0
$982$	2.14632e16	0.750036
$983$	−1.18477e16	−0.411709	−0.205855	−	0.978583i	$-0.565997\pi$
$983$	−1.18477e16	−0.411709	−0.205855	+	0.978583i	$0.565997\pi$
$984$	0	0
$985$	1.15864e15	0.0398151
$986$	3.07242e15	0.104992
$987$	0	0
$988$	1.78114e16	0.601915
$989$	1.12604e16	0.378419
$990$	0	0
$991$	3.30955e16	1.09993	0.549963	−	0.835189i	$-0.314642\pi$
$991$	3.30955e16	1.09993	0.549963	+	0.835189i	$0.314642\pi$
$992$	−5.99852e16	−1.98258
$993$	0	0
$994$	−1.47731e16	−0.482889
$995$	2.58282e15	0.0839589
$996$	0	0
$997$	1.17372e15	0.0377346	0.0188673	−	0.999822i	$-0.493994\pi$
$997$	1.17372e15	0.0377346	0.0188673	+	0.999822i	$0.493994\pi$
$998$	2.79013e16	0.892084
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.12.a.a.1.6		11
3.2	odd	2		29.12.a.a.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.6	✓	11	3.2	odd	2
261.12.a.a.1.6		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)

\(f(q)\)	\(=\)	\(q+21.9987 q^{2} -1564.06 q^{4} +886.321 q^{5} +44263.6 q^{7} -79460.6 q^{8} +O(q^{10})\)	\(q+21.9987 q^{2} -1564.06 q^{4} +886.321 q^{5} +44263.6 q^{7} -79460.6 q^{8} +19497.9 q^{10} +480464. q^{11} +729102. q^{13} +973741. q^{14} +1.45516e6 q^{16} -6.80915e6 q^{17} -1.56192e7 q^{19} -1.38626e6 q^{20} +1.05696e7 q^{22} +3.18252e7 q^{23} -4.80426e7 q^{25} +1.60393e7 q^{26} -6.92307e7 q^{28} -2.05111e7 q^{29} -3.08016e8 q^{31} +1.94747e8 q^{32} -1.49793e8 q^{34} +3.92317e7 q^{35} +4.28251e8 q^{37} -3.43602e8 q^{38} -7.04276e7 q^{40} +1.00915e9 q^{41} +3.53819e8 q^{43} -7.51473e8 q^{44} +7.00114e8 q^{46} +2.87373e9 q^{47} -1.80646e7 q^{49} -1.05687e9 q^{50} -1.14036e9 q^{52} +1.08796e9 q^{53} +4.25846e8 q^{55} -3.51721e9 q^{56} -4.51219e8 q^{58} -9.69237e9 q^{59} +2.73036e9 q^{61} -6.77597e9 q^{62} +1.30402e9 q^{64} +6.46218e8 q^{65} +5.53037e9 q^{67} +1.06499e10 q^{68} +8.63048e8 q^{70} -1.51715e10 q^{71} +2.05445e10 q^{73} +9.42097e9 q^{74} +2.44293e10 q^{76} +2.12671e10 q^{77} -2.27864e10 q^{79} +1.28974e9 q^{80} +2.21999e10 q^{82} +6.37446e9 q^{83} -6.03510e9 q^{85} +7.78357e9 q^{86} -3.81780e10 q^{88} +2.92283e10 q^{89} +3.22726e10 q^{91} -4.97764e10 q^{92} +6.32185e10 q^{94} -1.38436e10 q^{95} -1.24338e11 q^{97} -3.97399e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) \) 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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