LMFDB - Embedded newform 261.12.a.a.1.10

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			1.10
Root			$-65.3340$ 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)

$f(q)$	$=$	$q+68.3340 q^{2} +2621.54 q^{4} -8265.40 q^{5} -68659.4 q^{7} +39192.0 q^{8} +O(q^{10})$	\(q+68.3340 q^{2} +2621.54 q^{4} -8265.40 q^{5} -68659.4 q^{7} +39192.0 q^{8} -564808. q^{10} +970140. q^{11} +1.54127e6 q^{13} -4.69177e6 q^{14} -2.69076e6 q^{16} +3.34371e6 q^{17} +5.46951e6 q^{19} -2.16680e7 q^{20} +6.62936e7 q^{22} +3.32547e7 q^{23} +1.94887e7 q^{25} +1.05321e8 q^{26} -1.79993e8 q^{28} -2.05111e7 q^{29} -8.71995e7 q^{31} -2.64136e8 q^{32} +2.28489e8 q^{34} +5.67498e8 q^{35} -1.97918e8 q^{37} +3.73754e8 q^{38} -3.23938e8 q^{40} -1.10998e9 q^{41} -9.82013e8 q^{43} +2.54326e9 q^{44} +2.27243e9 q^{46} +2.38472e9 q^{47} +2.73679e9 q^{49} +1.33174e9 q^{50} +4.04048e9 q^{52} -2.86882e9 q^{53} -8.01859e9 q^{55} -2.69090e9 q^{56} -1.40161e9 q^{58} +7.54410e9 q^{59} -1.25957e10 q^{61} -5.95869e9 q^{62} -1.25388e10 q^{64} -1.27392e10 q^{65} -2.53077e8 q^{67} +8.76565e9 q^{68} +3.87794e10 q^{70} +7.66739e9 q^{71} -1.59232e10 q^{73} -1.35245e10 q^{74} +1.43385e10 q^{76} -6.66093e10 q^{77} +1.03493e10 q^{79} +2.22402e10 q^{80} -7.58492e10 q^{82} -2.23246e10 q^{83} -2.76371e10 q^{85} -6.71049e10 q^{86} +3.80218e10 q^{88} -7.10371e10 q^{89} -1.05822e11 q^{91} +8.71784e10 q^{92} +1.62957e11 q^{94} -4.52077e10 q^{95} -5.61657e9 q^{97} +1.87016e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	68.3340	1.50998	0.754991	−	0.655735i	$-0.227641\pi$
$2$	68.3340	1.50998	0.754991	+	0.655735i	$0.227641\pi$
$3$	0	0
$3$	0	0
$4$	2621.54	1.28005
$5$	−8265.40	−1.18285	−0.591424	−	0.806361i	$-0.701434\pi$
$5$	−8265.40	−1.18285	−0.591424	+	0.806361i	$0.701434\pi$
$6$	0	0
$7$	−68659.4	−1.54405	−0.772024	−	0.635593i	$-0.780756\pi$
$7$	−68659.4	−1.54405	−0.772024	+	0.635593i	$0.780756\pi$
$8$	39192.0	0.422866
$9$	0	0
$10$	−564808.	−1.78608
$11$	970140.	1.81625	0.908123	−	0.418703i	$-0.137515\pi$
$11$	970140.	1.81625	0.908123	+	0.418703i	$0.137515\pi$
$12$	0	0
$13$	1.54127e6	1.15130	0.575651	−	0.817696i	$-0.304749\pi$
$13$	1.54127e6	1.15130	0.575651	+	0.817696i	$0.304749\pi$
$14$	−4.69177e6	−2.33149
$15$	0	0
$16$	−2.69076e6	−0.641527
$17$	3.34371e6	0.571162	0.285581	−	0.958355i	$-0.407813\pi$
$17$	3.34371e6	0.571162	0.285581	+	0.958355i	$0.407813\pi$
$18$	0	0
$19$	5.46951e6	0.506762	0.253381	−	0.967367i	$-0.418457\pi$
$19$	5.46951e6	0.506762	0.253381	+	0.967367i	$0.418457\pi$
$20$	−2.16680e7	−1.51410
$21$	0	0
$22$	6.62936e7	2.74250
$23$	3.32547e7	1.07733	0.538667	−	0.842519i	$-0.318928\pi$
$23$	3.32547e7	1.07733	0.538667	+	0.842519i	$0.318928\pi$
$24$	0	0
$25$	1.94887e7	0.399128
$26$	1.05321e8	1.73845
$27$	0	0
$28$	−1.79993e8	−1.97646
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	0	0
$31$	−8.71995e7	−0.547047	−0.273523	−	0.961865i	$-0.588189\pi$
$31$	−8.71995e7	−0.547047	−0.273523	+	0.961865i	$0.588189\pi$
$32$	−2.64136e8	−1.39156
$33$	0	0
$34$	2.28489e8	0.862445
$35$	5.67498e8	1.82637
$36$	0	0
$37$	−1.97918e8	−0.469220	−0.234610	−	0.972090i	$-0.575381\pi$
$37$	−1.97918e8	−0.469220	−0.234610	+	0.972090i	$0.575381\pi$
$38$	3.73754e8	0.765201
$39$	0	0
$40$	−3.23938e8	−0.500186
$41$	−1.10998e9	−1.49625	−0.748123	−	0.663560i	$-0.769045\pi$
$41$	−1.10998e9	−1.49625	−0.748123	+	0.663560i	$0.769045\pi$
$42$	0	0
$43$	−9.82013e8	−1.01869	−0.509344	−	0.860563i	$-0.670112\pi$
$43$	−9.82013e8	−1.01869	−0.509344	+	0.860563i	$0.670112\pi$
$44$	2.54326e9	2.32488
$45$	0	0
$46$	2.27243e9	1.62675
$47$	2.38472e9	1.51670	0.758348	−	0.651850i	$-0.226007\pi$
$47$	2.38472e9	1.51670	0.758348	+	0.651850i	$0.226007\pi$
$48$	0	0
$49$	2.73679e9	1.38409
$50$	1.33174e9	0.602676
$51$	0	0
$52$	4.04048e9	1.47372
$53$	−2.86882e9	−0.942293	−0.471147	−	0.882055i	$-0.656160\pi$
$53$	−2.86882e9	−0.942293	−0.471147	+	0.882055i	$0.656160\pi$
$54$	0	0
$55$	−8.01859e9	−2.14834
$56$	−2.69090e9	−0.652926
$57$	0	0
$58$	−1.40161e9	−0.280397
$59$	7.54410e9	1.37379	0.686896	−	0.726755i	$-0.258973\pi$
$59$	7.54410e9	1.37379	0.686896	+	0.726755i	$0.258973\pi$
$60$	0	0
$61$	−1.25957e10	−1.90945	−0.954723	−	0.297496i	$-0.903849\pi$
$61$	−1.25957e10	−1.90945	−0.954723	+	0.297496i	$0.903849\pi$
$62$	−5.95869e9	−0.826031
$63$	0	0
$64$	−1.25388e10	−1.45970
$65$	−1.27392e10	−1.36181
$66$	0	0
$67$	−2.53077e8	−0.0229003	−0.0114502	−	0.999934i	$-0.503645\pi$
$67$	−2.53077e8	−0.0229003	−0.0114502	+	0.999934i	$0.503645\pi$
$68$	8.76565e9	0.731114
$69$	0	0
$70$	3.87794e10	2.75779
$71$	7.66739e9	0.504344	0.252172	−	0.967682i	$-0.418855\pi$
$71$	7.66739e9	0.504344	0.252172	+	0.967682i	$0.418855\pi$
$72$	0	0
$73$	−1.59232e10	−0.898991	−0.449495	−	0.893283i	$-0.648396\pi$
$73$	−1.59232e10	−0.898991	−0.449495	+	0.893283i	$0.648396\pi$
$74$	−1.35245e10	−0.708513
$75$	0	0
$76$	1.43385e10	0.648679
$77$	−6.66093e10	−2.80437
$78$	0	0
$79$	1.03493e10	0.378411	0.189205	−	0.981938i	$-0.439409\pi$
$79$	1.03493e10	0.378411	0.189205	+	0.981938i	$0.439409\pi$
$80$	2.22402e10	0.758828
$81$	0	0
$82$	−7.58492e10	−2.25930
$83$	−2.23246e10	−0.622091	−0.311046	−	0.950395i	$-0.600679\pi$
$83$	−2.23246e10	−0.622091	−0.311046	+	0.950395i	$0.600679\pi$
$84$	0	0
$85$	−2.76371e10	−0.675598
$86$	−6.71049e10	−1.53820
$87$	0	0
$88$	3.80218e10	0.768029
$89$	−7.10371e10	−1.34847	−0.674233	−	0.738518i	$-0.735526\pi$
$89$	−7.10371e10	−1.34847	−0.674233	+	0.738518i	$0.735526\pi$
$90$	0	0
$91$	−1.05822e11	−1.77767
$92$	8.71784e10	1.37904
$93$	0	0
$94$	1.62957e11	2.29018
$95$	−4.52077e10	−0.599422
$96$	0	0
$97$	−5.61657e9	−0.0664090	−0.0332045	−	0.999449i	$-0.510571\pi$
$97$	−5.61657e9	−0.0664090	−0.0332045	+	0.999449i	$0.510571\pi$
$98$	1.87016e11	2.08995
$99$	0	0
$100$	5.10903e10	0.510903
$101$	−1.50942e11	−1.42904	−0.714518	−	0.699617i	$-0.753354\pi$
$101$	−1.50942e11	−1.42904	−0.714518	+	0.699617i	$0.753354\pi$
$102$	0	0
$103$	−4.18049e10	−0.355322	−0.177661	−	0.984092i	$-0.556853\pi$
$103$	−4.18049e10	−0.355322	−0.177661	+	0.984092i	$0.556853\pi$
$104$	6.04054e10	0.486847
$105$	0	0
$106$	−1.96038e11	−1.42285
$107$	−3.91482e10	−0.269837	−0.134918	−	0.990857i	$-0.543077\pi$
$107$	−3.91482e10	−0.269837	−0.134918	+	0.990857i	$0.543077\pi$
$108$	0	0
$109$	−1.25846e11	−0.783421	−0.391710	−	0.920089i	$-0.628116\pi$
$109$	−1.25846e11	−0.783421	−0.391710	+	0.920089i	$0.628116\pi$
$110$	−5.47943e11	−3.24396
$111$	0	0
$112$	1.84746e11	0.990548
$113$	−8.94509e10	−0.456724	−0.228362	−	0.973576i	$-0.573337\pi$
$113$	−8.94509e10	−0.456724	−0.228362	+	0.973576i	$0.573337\pi$
$114$	0	0
$115$	−2.74863e11	−1.27432
$116$	−5.37707e10	−0.237699
$117$	0	0
$118$	5.15518e11	2.07440
$119$	−2.29577e11	−0.881902
$120$	0	0
$121$	6.55860e11	2.29875
$122$	−8.60713e11	−2.88323
$123$	0	0
$124$	−2.28597e11	−0.700246
$125$	2.42502e11	0.710740
$126$	0	0
$127$	1.50285e11	0.403642	0.201821	−	0.979422i	$-0.435314\pi$
$127$	1.50285e11	0.403642	0.201821	+	0.979422i	$0.435314\pi$
$128$	−3.15875e11	−0.812569
$129$	0	0
$130$	−8.70519e11	−2.05632
$131$	2.82004e11	0.638651	0.319326	−	0.947645i	$-0.396544\pi$
$131$	2.82004e11	0.638651	0.319326	+	0.947645i	$0.396544\pi$
$132$	0	0
$133$	−3.75534e11	−0.782465
$134$	−1.72938e10	−0.0345791
$135$	0	0
$136$	1.31047e11	0.241525
$137$	−3.90301e11	−0.690933	−0.345467	−	0.938431i	$-0.612279\pi$
$137$	−3.90301e11	−0.690933	−0.345467	+	0.938431i	$0.612279\pi$
$138$	0	0
$139$	−4.80262e10	−0.0785049	−0.0392524	−	0.999229i	$-0.512498\pi$
$139$	−4.80262e10	−0.0785049	−0.0392524	+	0.999229i	$0.512498\pi$
$140$	1.48772e12	2.33785
$141$	0	0
$142$	5.23943e11	0.761550
$143$	1.49524e12	2.09105
$144$	0	0
$145$	1.69533e11	0.219649
$146$	−1.08810e12	−1.35746
$147$	0	0
$148$	−5.18850e11	−0.600623
$149$	7.91388e11	0.882805	0.441402	−	0.897309i	$-0.354481\pi$
$149$	7.91388e11	0.882805	0.441402	+	0.897309i	$0.354481\pi$
$150$	0	0
$151$	1.31177e12	1.35983	0.679915	−	0.733291i	$-0.262016\pi$
$151$	1.31177e12	1.35983	0.679915	+	0.733291i	$0.262016\pi$
$152$	2.14361e11	0.214292
$153$	0	0
$154$	−4.55168e12	−4.23455
$155$	7.20738e11	0.647073
$156$	0	0
$157$	−6.76641e11	−0.566122	−0.283061	−	0.959102i	$-0.591350\pi$
$157$	−6.76641e11	−0.566122	−0.283061	+	0.959102i	$0.591350\pi$
$158$	7.07211e11	0.571394
$159$	0	0
$160$	2.18319e12	1.64600
$161$	−2.28325e12	−1.66346
$162$	0	0
$163$	8.90844e11	0.606415	0.303207	−	0.952925i	$-0.401943\pi$
$163$	8.90844e11	0.606415	0.303207	+	0.952925i	$0.401943\pi$
$164$	−2.90985e12	−1.91527
$165$	0	0
$166$	−1.52553e12	−0.939347
$167$	−7.38410e11	−0.439903	−0.219952	−	0.975511i	$-0.570590\pi$
$167$	−7.38410e11	−0.439903	−0.219952	+	0.975511i	$0.570590\pi$
$168$	0	0
$169$	5.83339e11	0.325495
$170$	−1.88855e12	−1.02014
$171$	0	0
$172$	−2.57438e12	−1.30397
$173$	1.13157e12	0.555170	0.277585	−	0.960701i	$-0.410466\pi$
$173$	1.13157e12	0.555170	0.277585	+	0.960701i	$0.410466\pi$
$174$	0	0
$175$	−1.33808e12	−0.616273
$176$	−2.61041e12	−1.16517
$177$	0	0
$178$	−4.85425e12	−2.03616
$179$	−4.03407e12	−1.64079	−0.820393	−	0.571799i	$-0.806246\pi$
$179$	−4.03407e12	−1.64079	−0.820393	+	0.571799i	$0.806246\pi$
$180$	0	0
$181$	−3.88701e12	−1.48725	−0.743625	−	0.668597i	$-0.766895\pi$
$181$	−3.88701e12	−1.48725	−0.743625	+	0.668597i	$0.766895\pi$
$182$	−7.23127e12	−2.68424
$183$	0	0
$184$	1.30332e12	0.455568
$185$	1.63587e12	0.555015
$186$	0	0
$187$	3.24387e12	1.03737
$188$	6.25162e12	1.94144
$189$	0	0
$190$	−3.08922e12	−0.905117
$191$	2.12510e12	0.604916	0.302458	−	0.953163i	$-0.402193\pi$
$191$	2.12510e12	0.604916	0.302458	+	0.953163i	$0.402193\pi$
$192$	0	0
$193$	1.38130e12	0.371298	0.185649	−	0.982616i	$-0.440561\pi$
$193$	1.38130e12	0.371298	0.185649	+	0.982616i	$0.440561\pi$
$194$	−3.83803e11	−0.100276
$195$	0	0
$196$	7.17460e12	1.77170
$197$	−4.09906e12	−0.984283	−0.492142	−	0.870515i	$-0.663786\pi$
$197$	−4.09906e12	−0.984283	−0.492142	+	0.870515i	$0.663786\pi$
$198$	0	0
$199$	2.67780e12	0.608255	0.304127	−	0.952631i	$-0.401635\pi$
$199$	2.67780e12	0.608255	0.304127	+	0.952631i	$0.401635\pi$
$200$	7.63801e11	0.168778
$201$	0	0
$202$	−1.03145e13	−2.15782
$203$	1.40828e12	0.286723
$204$	0	0
$205$	9.17440e12	1.76983
$206$	−2.85669e12	−0.536530
$207$	0	0
$208$	−4.14717e12	−0.738590
$209$	5.30619e12	0.920404
$210$	0	0
$211$	−4.90054e12	−0.806660	−0.403330	−	0.915055i	$-0.632147\pi$
$211$	−4.90054e12	−0.806660	−0.403330	+	0.915055i	$0.632147\pi$
$212$	−7.52072e12	−1.20618
$213$	0	0
$214$	−2.67515e12	−0.407449
$215$	8.11673e12	1.20495
$216$	0	0
$217$	5.98707e12	0.844667
$218$	−8.59959e12	−1.18295
$219$	0	0
$220$	−2.10210e13	−2.74998
$221$	5.15354e12	0.657580
$222$	0	0
$223$	1.59341e13	1.93487	0.967435	−	0.253120i	$-0.0814566\pi$
$223$	1.59341e13	1.93487	0.967435	+	0.253120i	$0.0814566\pi$
$224$	1.81354e13	2.14864
$225$	0	0
$226$	−6.11254e12	−0.689645
$227$	−1.88453e12	−0.207520	−0.103760	−	0.994602i	$-0.533087\pi$
$227$	−1.88453e12	−0.207520	−0.103760	+	0.994602i	$0.533087\pi$
$228$	0	0
$229$	−4.25535e12	−0.446519	−0.223259	−	0.974759i	$-0.571670\pi$
$229$	−4.25535e12	−0.446519	−0.223259	+	0.974759i	$0.571670\pi$
$230$	−1.87825e13	−1.92420
$231$	0	0
$232$	−8.03874e11	−0.0785243
$233$	−6.22697e12	−0.594045	−0.297022	−	0.954871i	$-0.595994\pi$
$233$	−6.22697e12	−0.594045	−0.297022	+	0.954871i	$0.595994\pi$
$234$	0	0
$235$	−1.97106e13	−1.79402
$236$	1.97771e13	1.75852
$237$	0	0
$238$	−1.56879e13	−1.33166
$239$	−1.79781e13	−1.49127	−0.745633	−	0.666357i	$-0.767853\pi$
$239$	−1.79781e13	−1.49127	−0.745633	+	0.666357i	$0.767853\pi$
$240$	0	0
$241$	−1.00728e13	−0.798097	−0.399048	−	0.916930i	$-0.630659\pi$
$241$	−1.00728e13	−0.798097	−0.399048	+	0.916930i	$0.630659\pi$
$242$	4.48176e13	3.47107
$243$	0	0
$244$	−3.30200e13	−2.44418
$245$	−2.26207e13	−1.63716
$246$	0	0
$247$	8.42997e12	0.583436
$248$	−3.41753e12	−0.231328
$249$	0	0
$250$	1.65711e13	1.07320
$251$	−1.15166e13	−0.729654	−0.364827	−	0.931075i	$-0.618872\pi$
$251$	−1.15166e13	−0.729654	−0.364827	+	0.931075i	$0.618872\pi$
$252$	0	0
$253$	3.22617e13	1.95670
$254$	1.02696e13	0.609493
$255$	0	0
$256$	4.09441e12	0.232740
$257$	3.13280e13	1.74301	0.871506	−	0.490384i	$-0.163143\pi$
$257$	3.13280e13	1.74301	0.871506	+	0.490384i	$0.163143\pi$
$258$	0	0
$259$	1.35890e13	0.724498
$260$	−3.33962e13	−1.74319
$261$	0	0
$262$	1.92705e13	0.964352
$263$	−9.17362e12	−0.449556	−0.224778	−	0.974410i	$-0.572166\pi$
$263$	−9.17362e12	−0.449556	−0.224778	+	0.974410i	$0.572166\pi$
$264$	0	0
$265$	2.37119e13	1.11459
$266$	−2.56617e13	−1.18151
$267$	0	0
$268$	−6.63450e11	−0.0293135
$269$	2.94832e13	1.27625	0.638127	−	0.769931i	$-0.279709\pi$
$269$	2.94832e13	1.27625	0.638127	+	0.769931i	$0.279709\pi$
$270$	0	0
$271$	−8.20600e12	−0.341036	−0.170518	−	0.985355i	$-0.554544\pi$
$271$	−8.20600e12	−0.341036	−0.170518	+	0.985355i	$0.554544\pi$
$272$	−8.99711e12	−0.366416
$273$	0	0
$274$	−2.66708e13	−1.04330
$275$	1.89067e13	0.724915
$276$	0	0
$277$	2.31768e13	0.853915	0.426958	−	0.904272i	$-0.359585\pi$
$277$	2.31768e13	0.853915	0.426958	+	0.904272i	$0.359585\pi$
$278$	−3.28182e12	−0.118541
$279$	0	0
$280$	2.22414e13	0.772312
$281$	−4.19264e13	−1.42759	−0.713793	−	0.700357i	$-0.753024\pi$
$281$	−4.19264e13	−1.42759	−0.713793	+	0.700357i	$0.753024\pi$
$282$	0	0
$283$	−1.71390e13	−0.561254	−0.280627	−	0.959817i	$-0.590542\pi$
$283$	−1.71390e13	−0.561254	−0.280627	+	0.959817i	$0.590542\pi$
$284$	2.01003e13	0.645584
$285$	0	0
$286$	1.02176e14	3.15744
$287$	7.62104e13	2.31028
$288$	0	0
$289$	−2.30915e13	−0.673774
$290$	1.15849e13	0.331667
$291$	0	0
$292$	−4.17433e13	−1.15075
$293$	−6.88609e13	−1.86295	−0.931474	−	0.363807i	$-0.881477\pi$
$293$	−6.88609e13	−1.86295	−0.931474	+	0.363807i	$0.881477\pi$
$294$	0	0
$295$	−6.23550e13	−1.62499
$296$	−7.75682e12	−0.198417
$297$	0	0
$298$	5.40787e13	1.33302
$299$	5.12543e13	1.24034
$300$	0	0
$301$	6.74245e13	1.57290
$302$	8.96386e13	2.05332
$303$	0	0
$304$	−1.47171e13	−0.325101
$305$	1.04108e14	2.25858
$306$	0	0
$307$	−3.43334e13	−0.718547	−0.359273	−	0.933232i	$-0.616975\pi$
$307$	−3.43334e13	−0.718547	−0.359273	+	0.933232i	$0.616975\pi$
$308$	−1.74619e14	−3.58973
$309$	0	0
$310$	4.92509e13	0.977069
$311$	7.11998e13	1.38770	0.693852	−	0.720118i	$-0.255912\pi$
$311$	7.11998e13	1.38770	0.693852	+	0.720118i	$0.255912\pi$
$312$	0	0
$313$	−8.48846e13	−1.59711	−0.798555	−	0.601922i	$-0.794402\pi$
$313$	−8.48846e13	−1.59711	−0.798555	+	0.601922i	$0.794402\pi$
$314$	−4.62376e13	−0.854834
$315$	0	0
$316$	2.71312e13	0.484384
$317$	−6.68644e13	−1.17319	−0.586595	−	0.809880i	$-0.699532\pi$
$317$	−6.68644e13	−1.17319	−0.586595	+	0.809880i	$0.699532\pi$
$318$	0	0
$319$	−1.98987e13	−0.337268
$320$	1.03638e14	1.72661
$321$	0	0
$322$	−1.56024e14	−2.51179
$323$	1.82885e13	0.289443
$324$	0	0
$325$	3.00372e13	0.459517
$326$	6.08749e13	0.915675
$327$	0	0
$328$	−4.35023e13	−0.632712
$329$	−1.63733e14	−2.34185
$330$	0	0
$331$	−1.01165e13	−0.139951	−0.0699755	−	0.997549i	$-0.522292\pi$
$331$	−1.01165e13	−0.139951	−0.0699755	+	0.997549i	$0.522292\pi$
$332$	−5.85247e13	−0.796306
$333$	0	0
$334$	−5.04585e13	−0.664246
$335$	2.09178e12	0.0270876
$336$	0	0
$337$	−1.36391e14	−1.70931	−0.854653	−	0.519199i	$-0.826230\pi$
$337$	−1.36391e14	−1.70931	−0.854653	+	0.519199i	$0.826230\pi$
$338$	3.98619e13	0.491492
$339$	0	0
$340$	−7.24516e13	−0.864797
$341$	−8.45957e13	−0.993572
$342$	0	0
$343$	−5.21445e13	−0.593049
$344$	−3.84871e13	−0.430768
$345$	0	0
$346$	7.73244e13	0.838297
$347$	−1.51964e14	−1.62154	−0.810769	−	0.585366i	$-0.800951\pi$
$347$	−1.51964e14	−1.62154	−0.810769	+	0.585366i	$0.800951\pi$
$348$	0	0
$349$	−3.81552e13	−0.394470	−0.197235	−	0.980356i	$-0.563196\pi$
$349$	−3.81552e13	−0.394470	−0.197235	+	0.980356i	$0.563196\pi$
$350$	−9.14365e13	−0.930562
$351$	0	0
$352$	−2.56248e14	−2.52742
$353$	−5.20789e13	−0.505710	−0.252855	−	0.967504i	$-0.581369\pi$
$353$	−5.20789e13	−0.505710	−0.252855	+	0.967504i	$0.581369\pi$
$354$	0	0
$355$	−6.33740e13	−0.596562
$356$	−1.86226e14	−1.72610
$357$	0	0
$358$	−2.75664e14	−2.47756
$359$	1.56134e14	1.38190	0.690950	−	0.722902i	$-0.257192\pi$
$359$	1.56134e14	1.38190	0.690950	+	0.722902i	$0.257192\pi$
$360$	0	0
$361$	−8.65747e13	−0.743192
$362$	−2.65615e14	−2.24572
$363$	0	0
$364$	−2.77417e14	−2.27550
$365$	1.31612e14	1.06337
$366$	0	0
$367$	−1.58571e14	−1.24326	−0.621629	−	0.783312i	$-0.713529\pi$
$367$	−1.58571e14	−1.24326	−0.621629	+	0.783312i	$0.713529\pi$
$368$	−8.94803e13	−0.691138
$369$	0	0
$370$	1.11786e14	0.838063
$371$	1.96972e14	1.45495
$372$	0	0
$373$	1.84813e14	1.32536	0.662682	−	0.748901i	$-0.269418\pi$
$373$	1.84813e14	1.32536	0.662682	+	0.748901i	$0.269418\pi$
$374$	2.21666e14	1.56641
$375$	0	0
$376$	9.34619e13	0.641360
$377$	−3.16131e13	−0.213791
$378$	0	0
$379$	−5.17503e13	−0.339936	−0.169968	−	0.985450i	$-0.554366\pi$
$379$	−5.17503e13	−0.339936	−0.169968	+	0.985450i	$0.554366\pi$
$380$	−1.18514e14	−0.767288
$381$	0	0
$382$	1.45216e14	0.913413
$383$	−1.91406e14	−1.18676	−0.593379	−	0.804923i	$-0.702207\pi$
$383$	−1.91406e14	−1.18676	−0.593379	+	0.804923i	$0.702207\pi$
$384$	0	0
$385$	5.50552e14	3.31715
$386$	9.43897e13	0.560653
$387$	0	0
$388$	−1.47240e13	−0.0850066
$389$	−7.30496e12	−0.0415810	−0.0207905	−	0.999784i	$-0.506618\pi$
$389$	−7.30496e12	−0.0415810	−0.0207905	+	0.999784i	$0.506618\pi$
$390$	0	0
$391$	1.11194e14	0.615332
$392$	1.07260e14	0.585284
$393$	0	0
$394$	−2.80105e14	−1.48625
$395$	−8.55414e13	−0.447602
$396$	0	0
$397$	2.82104e13	0.143569	0.0717846	−	0.997420i	$-0.477131\pi$
$397$	2.82104e13	0.143569	0.0717846	+	0.997420i	$0.477131\pi$
$398$	1.82985e14	0.918454
$399$	0	0
$400$	−5.24393e13	−0.256051
$401$	1.73909e14	0.837585	0.418793	−	0.908082i	$-0.362453\pi$
$401$	1.73909e14	0.837585	0.418793	+	0.908082i	$0.362453\pi$
$402$	0	0
$403$	−1.34398e14	−0.629816
$404$	−3.95700e14	−1.82923
$405$	0	0
$406$	9.62337e13	0.432946
$407$	−1.92008e14	−0.852218
$408$	0	0
$409$	−1.51365e14	−0.653953	−0.326977	−	0.945032i	$-0.606030\pi$
$409$	−1.51365e14	−0.653953	−0.326977	+	0.945032i	$0.606030\pi$
$410$	6.26924e14	2.67241
$411$	0	0
$412$	−1.09593e14	−0.454829
$413$	−5.17974e14	−2.12120
$414$	0	0
$415$	1.84522e14	0.735839
$416$	−4.07103e14	−1.60211
$417$	0	0
$418$	3.62594e14	1.38979
$419$	−1.96755e14	−0.744303	−0.372151	−	0.928172i	$-0.621380\pi$
$419$	−1.96755e14	−0.744303	−0.372151	+	0.928172i	$0.621380\pi$
$420$	0	0
$421$	1.30439e14	0.480681	0.240340	−	0.970689i	$-0.422741\pi$
$421$	1.30439e14	0.480681	0.240340	+	0.970689i	$0.422741\pi$
$422$	−3.34874e14	−1.21804
$423$	0	0
$424$	−1.12435e14	−0.398464
$425$	6.51645e13	0.227967
$426$	0	0
$427$	8.64812e14	2.94828
$428$	−1.02628e14	−0.345404
$429$	0	0
$430$	5.54649e14	1.81946
$431$	3.01242e14	0.975642	0.487821	−	0.872944i	$-0.337792\pi$
$431$	3.01242e14	0.975642	0.487821	+	0.872944i	$0.337792\pi$
$432$	0	0
$433$	−4.01236e14	−1.26682	−0.633412	−	0.773815i	$-0.718346\pi$
$433$	−4.01236e14	−1.26682	−0.633412	+	0.773815i	$0.718346\pi$
$434$	4.09120e14	1.27543
$435$	0	0
$436$	−3.29911e14	−1.00282
$437$	1.81887e14	0.545951
$438$	0	0
$439$	1.67628e14	0.490673	0.245337	−	0.969438i	$-0.421102\pi$
$439$	1.67628e14	0.490673	0.245337	+	0.969438i	$0.421102\pi$
$440$	−3.14265e14	−0.908461
$441$	0	0
$442$	3.52162e14	0.992934
$443$	−2.50447e14	−0.697421	−0.348710	−	0.937231i	$-0.613380\pi$
$443$	−2.50447e14	−0.697421	−0.348710	+	0.937231i	$0.613380\pi$
$444$	0	0
$445$	5.87150e14	1.59503
$446$	1.08884e15	2.92162
$447$	0	0
$448$	8.60905e14	2.25386
$449$	5.39495e14	1.39519	0.697593	−	0.716494i	$-0.254254\pi$
$449$	5.39495e14	1.39519	0.697593	+	0.716494i	$0.254254\pi$
$450$	0	0
$451$	−1.07683e15	−2.71755
$452$	−2.34499e14	−0.584628
$453$	0	0
$454$	−1.28777e14	−0.313352
$455$	8.74665e14	2.10271
$456$	0	0
$457$	1.34613e14	0.315899	0.157949	−	0.987447i	$-0.449512\pi$
$457$	1.34613e14	0.315899	0.157949	+	0.987447i	$0.449512\pi$
$458$	−2.90785e14	−0.674236
$459$	0	0
$460$	−7.20564e14	−1.63119
$461$	7.83557e14	1.75273	0.876367	−	0.481645i	$-0.159960\pi$
$461$	7.83557e14	1.75273	0.876367	+	0.481645i	$0.159960\pi$
$462$	0	0
$463$	−1.86516e14	−0.407401	−0.203700	−	0.979033i	$-0.565297\pi$
$463$	−1.86516e14	−0.407401	−0.203700	+	0.979033i	$0.565297\pi$
$464$	5.51905e13	0.119128
$465$	0	0
$466$	−4.25514e14	−0.896997
$467$	6.06343e14	1.26321	0.631605	−	0.775290i	$-0.282396\pi$
$467$	6.06343e14	1.26321	0.631605	+	0.775290i	$0.282396\pi$
$468$	0	0
$469$	1.73761e13	0.0353592
$470$	−1.34691e15	−2.70894
$471$	0	0
$472$	2.95669e14	0.580931
$473$	−9.52690e14	−1.85019
$474$	0	0
$475$	1.06594e14	0.202263
$476$	−6.01845e14	−1.12888
$477$	0	0
$478$	−1.22851e15	−2.25179
$479$	−6.70378e14	−1.21471	−0.607357	−	0.794429i	$-0.707770\pi$
$479$	−6.70378e14	−1.21471	−0.607357	+	0.794429i	$0.707770\pi$
$480$	0	0
$481$	−3.05044e14	−0.540213
$482$	−6.88313e14	−1.20511
$483$	0	0
$484$	1.71936e15	2.94251
$485$	4.64232e13	0.0785517
$486$	0	0
$487$	3.36789e14	0.557120	0.278560	−	0.960419i	$-0.410143\pi$
$487$	3.36789e14	0.557120	0.278560	+	0.960419i	$0.410143\pi$
$488$	−4.93650e14	−0.807440
$489$	0	0
$490$	−1.54576e15	−2.47209
$491$	−3.28879e14	−0.520102	−0.260051	−	0.965595i	$-0.583739\pi$
$491$	−3.28879e14	−0.520102	−0.260051	+	0.965595i	$0.583739\pi$
$492$	0	0
$493$	−6.85833e13	−0.106062
$494$	5.76054e14	0.880978
$495$	0	0
$496$	2.34633e14	0.350945
$497$	−5.26439e14	−0.778731
$498$	0	0
$499$	−1.89240e14	−0.273817	−0.136908	−	0.990584i	$-0.543717\pi$
$499$	−1.89240e14	−0.273817	−0.136908	+	0.990584i	$0.543717\pi$
$500$	6.35728e14	0.909780
$501$	0	0
$502$	−7.86972e14	−1.10176
$503$	−1.64969e14	−0.228444	−0.114222	−	0.993455i	$-0.536437\pi$
$503$	−1.64969e14	−0.228444	−0.114222	+	0.993455i	$0.536437\pi$
$504$	0	0
$505$	1.24760e15	1.69033
$506$	2.20457e15	2.95459
$507$	0	0
$508$	3.93979e14	0.516681
$509$	−7.09880e14	−0.920952	−0.460476	−	0.887672i	$-0.652321\pi$
$509$	−7.09880e14	−0.920952	−0.460476	+	0.887672i	$0.652321\pi$
$510$	0	0
$511$	1.09328e15	1.38809
$512$	9.26699e14	1.16400
$513$	0	0
$514$	2.14077e15	2.63192
$515$	3.45534e14	0.420292
$516$	0	0
$517$	2.31351e15	2.75469
$518$	9.28587e14	1.09398
$519$	0	0
$520$	−4.99274e14	−0.575865
$521$	2.38844e14	0.272588	0.136294	−	0.990668i	$-0.456481\pi$
$521$	2.38844e14	0.272588	0.136294	+	0.990668i	$0.456481\pi$
$522$	0	0
$523$	−5.08191e13	−0.0567895	−0.0283948	−	0.999597i	$-0.509040\pi$
$523$	−5.08191e13	−0.0567895	−0.0283948	+	0.999597i	$0.509040\pi$
$524$	7.39285e14	0.817504
$525$	0	0
$526$	−6.26870e14	−0.678822
$527$	−2.91570e14	−0.312452
$528$	0	0
$529$	1.53066e14	0.160647
$530$	1.62033e15	1.68301
$531$	0	0
$532$	−9.84475e14	−1.00159
$533$	−1.71077e15	−1.72263
$534$	0	0
$535$	3.23575e14	0.319176
$536$	−9.91860e12	−0.00968376
$537$	0	0
$538$	2.01471e15	1.92712
$539$	2.65507e15	2.51384
$540$	0	0
$541$	−1.83247e15	−1.70001	−0.850007	−	0.526771i	$-0.823402\pi$
$541$	−1.83247e15	−1.70001	−0.850007	+	0.526771i	$0.823402\pi$
$542$	−5.60749e14	−0.514959
$543$	0	0
$544$	−8.83192e14	−0.794806
$545$	1.04017e15	0.926667
$546$	0	0
$547$	3.76524e14	0.328747	0.164374	−	0.986398i	$-0.447440\pi$
$547$	3.76524e14	0.328747	0.164374	+	0.986398i	$0.447440\pi$
$548$	−1.02319e15	−0.884427
$549$	0	0
$550$	1.29197e15	1.09461
$551$	−1.12186e14	−0.0941033
$552$	0	0
$553$	−7.10580e14	−0.584285
$554$	1.58376e15	1.28940
$555$	0	0
$556$	−1.25902e14	−0.100490
$557$	7.28798e14	0.575975	0.287987	−	0.957634i	$-0.407014\pi$
$557$	7.28798e14	0.575975	0.287987	+	0.957634i	$0.407014\pi$
$558$	0	0
$559$	−1.51354e15	−1.17282
$560$	−1.52700e15	−1.17167
$561$	0	0
$562$	−2.86500e15	−2.15563
$563$	2.20017e15	1.63930	0.819652	−	0.572862i	$-0.194167\pi$
$563$	2.20017e15	1.63930	0.819652	+	0.572862i	$0.194167\pi$
$564$	0	0
$565$	7.39348e14	0.540234
$566$	−1.17117e15	−0.847483
$567$	0	0
$568$	3.00501e14	0.213270
$569$	1.15616e15	0.812643	0.406321	−	0.913730i	$-0.366811\pi$
$569$	1.15616e15	0.812643	0.406321	+	0.913730i	$0.366811\pi$
$570$	0	0
$571$	1.61701e15	1.11485	0.557423	−	0.830229i	$-0.311790\pi$
$571$	1.61701e15	1.11485	0.557423	+	0.830229i	$0.311790\pi$
$572$	3.91984e15	2.67664
$573$	0	0
$574$	5.20776e15	3.48848
$575$	6.48090e14	0.429994
$576$	0	0
$577$	1.33066e15	0.866163	0.433081	−	0.901355i	$-0.357426\pi$
$577$	1.33066e15	0.866163	0.433081	+	0.901355i	$0.357426\pi$
$578$	−1.57794e15	−1.01739
$579$	0	0
$580$	4.44436e14	0.281161
$581$	1.53279e15	0.960539
$582$	0	0
$583$	−2.78316e15	−1.71144
$584$	−6.24064e14	−0.380153
$585$	0	0
$586$	−4.70554e15	−2.81302
$587$	−2.02127e15	−1.19706	−0.598530	−	0.801101i	$-0.704248\pi$
$587$	−2.02127e15	−1.19706	−0.598530	+	0.801101i	$0.704248\pi$
$588$	0	0
$589$	−4.76939e14	−0.277222
$590$	−4.26097e15	−2.45370
$591$	0	0
$592$	5.32550e14	0.301017
$593$	−1.76241e15	−0.986973	−0.493486	−	0.869754i	$-0.664278\pi$
$593$	−1.76241e15	−0.986973	−0.493486	+	0.869754i	$0.664278\pi$
$594$	0	0
$595$	1.89755e15	1.04316
$596$	2.07465e15	1.13003
$597$	0	0
$598$	3.50241e15	1.87288
$599$	3.33607e15	1.76761	0.883807	−	0.467851i	$-0.154972\pi$
$599$	3.33607e15	1.76761	0.883807	+	0.467851i	$0.154972\pi$
$600$	0	0
$601$	−9.06258e14	−0.471457	−0.235729	−	0.971819i	$-0.575748\pi$
$601$	−9.06258e14	−0.471457	−0.235729	+	0.971819i	$0.575748\pi$
$602$	4.60738e15	2.37506
$603$	0	0
$604$	3.43886e15	1.74065
$605$	−5.42095e15	−2.71907
$606$	0	0
$607$	1.31379e15	0.647125	0.323562	−	0.946207i	$-0.395119\pi$
$607$	1.31379e15	0.647125	0.323562	+	0.946207i	$0.395119\pi$
$608$	−1.44469e15	−0.705189
$609$	0	0
$610$	7.11414e15	3.41042
$611$	3.67548e15	1.74617
$612$	0	0
$613$	−1.67634e15	−0.782219	−0.391110	−	0.920344i	$-0.627909\pi$
$613$	−1.67634e15	−0.782219	−0.391110	+	0.920344i	$0.627909\pi$
$614$	−2.34614e15	−1.08499
$615$	0	0
$616$	−2.61055e15	−1.18587
$617$	1.29504e15	0.583063	0.291532	−	0.956561i	$-0.405835\pi$
$617$	1.29504e15	0.583063	0.291532	+	0.956561i	$0.405835\pi$
$618$	0	0
$619$	−2.90800e15	−1.28616	−0.643082	−	0.765797i	$-0.722345\pi$
$619$	−2.90800e15	−1.28616	−0.643082	+	0.765797i	$0.722345\pi$
$620$	1.88944e15	0.828284
$621$	0	0
$622$	4.86537e15	2.09541
$623$	4.87737e15	2.08210
$624$	0	0
$625$	−2.95597e15	−1.23982
$626$	−5.80050e15	−2.41161
$627$	0	0
$628$	−1.77384e15	−0.724663
$629$	−6.61781e14	−0.268000
$630$	0	0
$631$	−7.31735e14	−0.291201	−0.145600	−	0.989343i	$-0.546511\pi$
$631$	−7.31735e14	−0.291201	−0.145600	+	0.989343i	$0.546511\pi$
$632$	4.05612e14	0.160017
$633$	0	0
$634$	−4.56911e15	−1.77150
$635$	−1.24217e15	−0.477447
$636$	0	0
$637$	4.21812e15	1.59350
$638$	−1.35976e15	−0.509269
$639$	0	0
$640$	2.61083e15	0.961145
$641$	4.90606e15	1.79066	0.895331	−	0.445401i	$-0.146939\pi$
$641$	4.90606e15	1.79066	0.895331	+	0.445401i	$0.146939\pi$
$642$	0	0
$643$	−1.88025e15	−0.674612	−0.337306	−	0.941395i	$-0.609516\pi$
$643$	−1.88025e15	−0.674612	−0.337306	+	0.941395i	$0.609516\pi$
$644$	−5.98562e15	−2.12930
$645$	0	0
$646$	1.24972e15	0.437054
$647$	1.81526e15	0.629457	0.314728	−	0.949182i	$-0.398087\pi$
$647$	1.81526e15	0.629457	0.314728	+	0.949182i	$0.398087\pi$
$648$	0	0
$649$	7.31883e15	2.49515
$650$	2.05256e15	0.693862
$651$	0	0
$652$	2.33538e15	0.776239
$653$	−1.09915e15	−0.362271	−0.181135	−	0.983458i	$-0.557977\pi$
$653$	−1.09915e15	−0.362271	−0.181135	+	0.983458i	$0.557977\pi$
$654$	0	0
$655$	−2.33088e15	−0.755427
$656$	2.98668e15	0.959881
$657$	0	0
$658$	−1.11886e16	−3.53616
$659$	−4.07550e14	−0.127735	−0.0638677	−	0.997958i	$-0.520344\pi$
$659$	−4.07550e14	−0.127735	−0.0638677	+	0.997958i	$0.520344\pi$
$660$	0	0
$661$	−1.78308e15	−0.549620	−0.274810	−	0.961499i	$-0.588615\pi$
$661$	−1.78308e15	−0.549620	−0.274810	+	0.961499i	$0.588615\pi$
$662$	−6.91300e14	−0.211324
$663$	0	0
$664$	−8.74946e14	−0.263061
$665$	3.10394e15	0.925537
$666$	0	0
$667$	−6.82092e14	−0.200056
$668$	−1.93577e15	−0.563097
$669$	0	0
$670$	1.42940e14	0.0409017
$671$	−1.22196e16	−3.46802
$672$	0	0
$673$	−2.92949e15	−0.817917	−0.408958	−	0.912553i	$-0.634108\pi$
$673$	−2.92949e15	−0.817917	−0.408958	+	0.912553i	$0.634108\pi$
$674$	−9.32012e15	−2.58102
$675$	0	0
$676$	1.52925e15	0.416649
$677$	5.65022e15	1.52696	0.763480	−	0.645831i	$-0.223489\pi$
$677$	5.65022e15	1.52696	0.763480	+	0.645831i	$0.223489\pi$
$678$	0	0
$679$	3.85631e14	0.102539
$680$	−1.08315e15	−0.285687
$681$	0	0
$682$	−5.78076e15	−1.50028
$683$	1.87327e15	0.482266	0.241133	−	0.970492i	$-0.422481\pi$
$683$	1.87327e15	0.482266	0.241133	+	0.970492i	$0.422481\pi$
$684$	0	0
$685$	3.22599e15	0.817268
$686$	−3.56324e15	−0.895494
$687$	0	0
$688$	2.64236e15	0.653515
$689$	−4.42161e15	−1.08486
$690$	0	0
$691$	−4.71553e15	−1.13868	−0.569339	−	0.822103i	$-0.692801\pi$
$691$	−4.71553e15	−1.13868	−0.569339	+	0.822103i	$0.692801\pi$
$692$	2.96644e15	0.710644
$693$	0	0
$694$	−1.03843e16	−2.44849
$695$	3.96956e14	0.0928593
$696$	0	0
$697$	−3.71144e15	−0.854599
$698$	−2.60730e15	−0.595643
$699$	0	0
$700$	−3.50783e15	−0.788859
$701$	2.35508e15	0.525480	0.262740	−	0.964867i	$-0.415374\pi$
$701$	2.35508e15	0.525480	0.262740	+	0.964867i	$0.415374\pi$
$702$	0	0
$703$	−1.08252e15	−0.237783
$704$	−1.21644e16	−2.65118
$705$	0	0
$706$	−3.55876e15	−0.763613
$707$	1.03636e16	2.20650
$708$	0	0
$709$	7.95473e15	1.66752	0.833760	−	0.552126i	$-0.186183\pi$
$709$	7.95473e15	1.66752	0.833760	+	0.552126i	$0.186183\pi$
$710$	−4.33060e15	−0.900797
$711$	0	0
$712$	−2.78409e15	−0.570221
$713$	−2.89979e15	−0.589352
$714$	0	0
$715$	−1.23588e16	−2.47339
$716$	−1.05755e16	−2.10028
$717$	0	0
$718$	1.06692e16	2.08665
$719$	1.98037e15	0.384360	0.192180	−	0.981360i	$-0.438444\pi$
$719$	1.98037e15	0.384360	0.192180	+	0.981360i	$0.438444\pi$
$720$	0	0
$721$	2.87030e15	0.548635
$722$	−5.91600e15	−1.12221
$723$	0	0
$724$	−1.01899e16	−1.90375
$725$	−3.99735e14	−0.0741162
$726$	0	0
$727$	3.46705e15	0.633171	0.316585	−	0.948564i	$-0.397464\pi$
$727$	3.46705e15	0.633171	0.316585	+	0.948564i	$0.397464\pi$
$728$	−4.14740e15	−0.751715
$729$	0	0
$730$	8.99356e15	1.60567
$731$	−3.28357e15	−0.581835
$732$	0	0
$733$	4.26101e15	0.743774	0.371887	−	0.928278i	$-0.378711\pi$
$733$	4.26101e15	0.743774	0.371887	+	0.928278i	$0.378711\pi$
$734$	−1.08358e16	−1.87730
$735$	0	0
$736$	−8.78375e15	−1.49917
$737$	−2.45520e14	−0.0415926
$738$	0	0
$739$	4.74592e15	0.792093	0.396046	−	0.918230i	$-0.370382\pi$
$739$	4.74592e15	0.792093	0.396046	+	0.918230i	$0.370382\pi$
$740$	4.28850e15	0.710446
$741$	0	0
$742$	1.34599e16	2.19694
$743$	−4.32897e15	−0.701369	−0.350685	−	0.936494i	$-0.614051\pi$
$743$	−4.32897e15	−0.701369	−0.350685	+	0.936494i	$0.614051\pi$
$744$	0	0
$745$	−6.54113e15	−1.04422
$746$	1.26290e16	2.00128
$747$	0	0
$748$	8.50391e15	1.32788
$749$	2.68789e15	0.416641
$750$	0	0
$751$	1.89924e15	0.290108	0.145054	−	0.989424i	$-0.453664\pi$
$751$	1.89924e15	0.290108	0.145054	+	0.989424i	$0.453664\pi$
$752$	−6.41669e15	−0.973001
$753$	0	0
$754$	−2.16025e15	−0.322821
$755$	−1.08423e16	−1.60847
$756$	0	0
$757$	−6.04958e15	−0.884500	−0.442250	−	0.896892i	$-0.645820\pi$
$757$	−6.04958e15	−0.884500	−0.442250	+	0.896892i	$0.645820\pi$
$758$	−3.53631e15	−0.513298
$759$	0	0
$760$	−1.77178e15	−0.253475
$761$	9.10355e15	1.29299	0.646495	−	0.762918i	$-0.276234\pi$
$761$	9.10355e15	1.29299	0.646495	+	0.762918i	$0.276234\pi$
$762$	0	0
$763$	8.64054e15	1.20964
$764$	5.57102e15	0.774321
$765$	0	0
$766$	−1.30795e16	−1.79198
$767$	1.16275e16	1.58165
$768$	0	0
$769$	−5.47973e15	−0.734792	−0.367396	−	0.930065i	$-0.619751\pi$
$769$	−5.47973e15	−0.734792	−0.367396	+	0.930065i	$0.619751\pi$
$770$	3.76214e16	5.00883
$771$	0	0
$772$	3.62113e15	0.475279
$773$	−7.09370e15	−0.924455	−0.462228	−	0.886761i	$-0.652950\pi$
$773$	−7.09370e15	−0.924455	−0.462228	+	0.886761i	$0.652950\pi$
$774$	0	0
$775$	−1.69940e15	−0.218342
$776$	−2.20125e14	−0.0280821
$777$	0	0
$778$	−4.99177e14	−0.0627866
$779$	−6.07104e15	−0.758240
$780$	0	0
$781$	7.43844e15	0.916012
$782$	7.59834e15	0.929140
$783$	0	0
$784$	−7.36404e15	−0.887928
$785$	5.59271e15	0.669636
$786$	0	0
$787$	−2.33437e15	−0.275619	−0.137810	−	0.990459i	$-0.544006\pi$
$787$	−2.33437e15	−0.275619	−0.137810	+	0.990459i	$0.544006\pi$
$788$	−1.07458e16	−1.25993
$789$	0	0
$790$	−5.84538e15	−0.675871
$791$	6.14165e15	0.705204
$792$	0	0
$793$	−1.94133e16	−2.19835
$794$	1.92773e15	0.216787
$795$	0	0
$796$	7.01994e15	0.778595
$797$	5.40712e13	0.00595587	0.00297793	−	0.999996i	$-0.499052\pi$
$797$	5.40712e13	0.00595587	0.00297793	+	0.999996i	$0.499052\pi$
$798$	0	0
$799$	7.97380e15	0.866279
$800$	−5.14765e15	−0.555411
$801$	0	0
$802$	1.18839e16	1.26474
$803$	−1.54478e16	−1.63279
$804$	0	0
$805$	1.88720e16	1.96761
$806$	−9.18392e15	−0.951011
$807$	0	0
$808$	−5.91573e15	−0.604291
$809$	−4.45684e15	−0.452179	−0.226090	−	0.974107i	$-0.572594\pi$
$809$	−4.45684e15	−0.452179	−0.226090	+	0.974107i	$0.572594\pi$
$810$	0	0
$811$	−5.02280e15	−0.502726	−0.251363	−	0.967893i	$-0.580879\pi$
$811$	−5.02280e15	−0.502726	−0.251363	+	0.967893i	$0.580879\pi$
$812$	3.69187e15	0.367019
$813$	0	0
$814$	−1.31207e16	−1.28683
$815$	−7.36318e15	−0.717296
$816$	0	0
$817$	−5.37113e15	−0.516232
$818$	−1.03434e16	−0.987458
$819$	0	0
$820$	2.40510e16	2.26547
$821$	−1.69234e15	−0.158343	−0.0791716	−	0.996861i	$-0.525228\pi$
$821$	−1.69234e15	−0.158343	−0.0791716	+	0.996861i	$0.525228\pi$
$822$	0	0
$823$	−9.20529e15	−0.849842	−0.424921	−	0.905230i	$-0.639698\pi$
$823$	−9.20529e15	−0.849842	−0.424921	+	0.905230i	$0.639698\pi$
$824$	−1.63842e15	−0.150254
$825$	0	0
$826$	−3.53952e16	−3.20298
$827$	−2.50113e15	−0.224831	−0.112415	−	0.993661i	$-0.535859\pi$
$827$	−2.50113e15	−0.224831	−0.112415	+	0.993661i	$0.535859\pi$
$828$	0	0
$829$	4.39695e15	0.390033	0.195017	−	0.980800i	$-0.437524\pi$
$829$	4.39695e15	0.390033	0.195017	+	0.980800i	$0.437524\pi$
$830$	1.26091e16	1.11110
$831$	0	0
$832$	−1.93256e16	−1.68056
$833$	9.15104e15	0.790538
$834$	0	0
$835$	6.10326e15	0.520339
$836$	1.39104e16	1.17816
$837$	0	0
$838$	−1.34451e16	−1.12388
$839$	−9.17137e15	−0.761629	−0.380814	−	0.924652i	$-0.624356\pi$
$839$	−9.17137e15	−0.761629	−0.380814	+	0.924652i	$0.624356\pi$
$840$	0	0
$841$	4.20707e14	0.0344828
$842$	8.91344e15	0.725820
$843$	0	0
$844$	−1.28469e16	−1.03256
$845$	−4.82153e15	−0.385011
$846$	0	0
$847$	−4.50310e16	−3.54938
$848$	7.71930e15	0.604506
$849$	0	0
$850$	4.45295e15	0.344226
$851$	−6.58171e15	−0.505506
$852$	0	0
$853$	7.56207e15	0.573352	0.286676	−	0.958028i	$-0.407450\pi$
$853$	7.56207e15	0.573352	0.286676	+	0.958028i	$0.407450\pi$
$854$	5.90961e16	4.45185
$855$	0	0
$856$	−1.53430e15	−0.114105
$857$	9.34890e15	0.690821	0.345411	−	0.938452i	$-0.387740\pi$
$857$	9.34890e15	0.690821	0.345411	+	0.938452i	$0.387740\pi$
$858$	0	0
$859$	−1.20867e16	−0.881749	−0.440875	−	0.897569i	$-0.645332\pi$
$859$	−1.20867e16	−0.881749	−0.440875	+	0.897569i	$0.645332\pi$
$860$	2.12783e16	1.54239
$861$	0	0
$862$	2.05851e16	1.47320
$863$	5.66080e15	0.402549	0.201275	−	0.979535i	$-0.435492\pi$
$863$	5.66080e15	0.402549	0.201275	+	0.979535i	$0.435492\pi$
$864$	0	0
$865$	−9.35284e15	−0.656681
$866$	−2.74181e16	−1.91288
$867$	0	0
$868$	1.56953e16	1.08121
$869$	1.00403e16	0.687287
$870$	0	0
$871$	−3.90059e14	−0.0263651
$872$	−4.93218e15	−0.331282
$873$	0	0
$874$	1.24291e16	0.824377
$875$	−1.66501e16	−1.09742
$876$	0	0
$877$	−8.61237e15	−0.560564	−0.280282	−	0.959918i	$-0.590428\pi$
$877$	−8.61237e15	−0.560564	−0.280282	+	0.959918i	$0.590428\pi$
$878$	1.14547e16	0.740908
$879$	0	0
$880$	2.15761e16	1.37822
$881$	−7.82338e15	−0.496623	−0.248312	−	0.968680i	$-0.579876\pi$
$881$	−7.82338e15	−0.496623	−0.248312	+	0.968680i	$0.579876\pi$
$882$	0	0
$883$	2.57988e16	1.61739	0.808696	−	0.588226i	$-0.200174\pi$
$883$	2.57988e16	1.61739	0.808696	+	0.588226i	$0.200174\pi$
$884$	1.35102e16	0.841733
$885$	0	0
$886$	−1.71140e16	−1.05309
$887$	−1.53064e16	−0.936035	−0.468017	−	0.883719i	$-0.655032\pi$
$887$	−1.53064e16	−0.936035	−0.468017	+	0.883719i	$0.655032\pi$
$888$	0	0
$889$	−1.03185e16	−0.623243
$890$	4.01223e16	2.40847
$891$	0	0
$892$	4.17719e16	2.47672
$893$	1.30432e16	0.768604
$894$	0	0
$895$	3.33432e16	1.94080
$896$	2.16878e16	1.25465
$897$	0	0
$898$	3.68658e16	2.10671
$899$	1.78856e15	0.101584
$900$	0	0
$901$	−9.59250e15	−0.538202
$902$	−7.35844e16	−4.10345
$903$	0	0
$904$	−3.50577e15	−0.193133
$905$	3.21277e16	1.75919
$906$	0	0
$907$	3.15987e15	0.170934	0.0854672	−	0.996341i	$-0.472762\pi$
$907$	3.15987e15	0.170934	0.0854672	+	0.996341i	$0.472762\pi$
$908$	−4.94036e15	−0.265635
$909$	0	0
$910$	5.97693e16	3.17505
$911$	2.95195e16	1.55868	0.779342	−	0.626599i	$-0.215554\pi$
$911$	2.95195e16	1.55868	0.779342	+	0.626599i	$0.215554\pi$
$912$	0	0
$913$	−2.16580e16	−1.12987
$914$	9.19864e15	0.477001
$915$	0	0
$916$	−1.11555e16	−0.571565
$917$	−1.93623e16	−0.986109
$918$	0	0
$919$	2.89215e16	1.45541	0.727704	−	0.685891i	$-0.240587\pi$
$919$	2.89215e16	1.45541	0.727704	+	0.685891i	$0.240587\pi$
$920$	−1.07725e16	−0.538867
$921$	0	0
$922$	5.35436e16	2.64660
$923$	1.18175e16	0.580652
$924$	0	0
$925$	−3.85716e15	−0.187279
$926$	−1.27454e16	−0.615168
$927$	0	0
$928$	5.41772e15	0.258406
$929$	−1.99050e16	−0.943792	−0.471896	−	0.881654i	$-0.656430\pi$
$929$	−1.99050e16	−0.943792	−0.471896	+	0.881654i	$0.656430\pi$
$930$	0	0
$931$	1.49689e16	0.701402
$932$	−1.63242e16	−0.760405
$933$	0	0
$934$	4.14339e16	1.90743
$935$	−2.68118e16	−1.22705
$936$	0	0
$937$	2.81833e16	1.27475	0.637373	−	0.770556i	$-0.280021\pi$
$937$	2.81833e16	1.27475	0.637373	+	0.770556i	$0.280021\pi$
$938$	1.18738e15	0.0533917
$939$	0	0
$940$	−5.16722e16	−2.29643
$941$	−1.92625e16	−0.851079	−0.425540	−	0.904940i	$-0.639916\pi$
$941$	−1.92625e16	−0.851079	−0.425540	+	0.904940i	$0.639916\pi$
$942$	0	0
$943$	−3.69120e16	−1.61196
$944$	−2.02993e16	−0.881325
$945$	0	0
$946$	−6.51012e16	−2.79375
$947$	1.32271e16	0.564339	0.282170	−	0.959365i	$-0.408946\pi$
$947$	1.32271e16	0.564339	0.282170	+	0.959365i	$0.408946\pi$
$948$	0	0
$949$	−2.45419e16	−1.03501
$950$	7.28397e15	0.305413
$951$	0	0
$952$	−8.99760e15	−0.372927
$953$	7.28946e15	0.300389	0.150195	−	0.988656i	$-0.452010\pi$
$953$	7.28946e15	0.300389	0.150195	+	0.988656i	$0.452010\pi$
$954$	0	0
$955$	−1.75648e16	−0.715523
$956$	−4.71302e16	−1.90889
$957$	0	0
$958$	−4.58096e16	−1.83420
$959$	2.67978e16	1.06683
$960$	0	0
$961$	−1.78047e16	−0.700740
$962$	−2.08449e16	−0.815713
$963$	0	0
$964$	−2.64062e16	−1.02160
$965$	−1.14170e16	−0.439189
$966$	0	0
$967$	−1.90917e16	−0.726104	−0.363052	−	0.931769i	$-0.618265\pi$
$967$	−1.90917e16	−0.726104	−0.363052	+	0.931769i	$0.618265\pi$
$968$	2.57045e16	0.972064
$969$	0	0
$970$	3.17228e15	0.118612
$971$	−1.19393e16	−0.443888	−0.221944	−	0.975059i	$-0.571240\pi$
$971$	−1.19393e16	−0.443888	−0.221944	+	0.975059i	$0.571240\pi$
$972$	0	0
$973$	3.29745e15	0.121215
$974$	2.30141e16	0.841241
$975$	0	0
$976$	3.38919e16	1.22496
$977$	−4.01267e16	−1.44216	−0.721080	−	0.692852i	$-0.756354\pi$
$977$	−4.01267e16	−1.44216	−0.721080	+	0.692852i	$0.756354\pi$
$978$	0	0
$979$	−6.89160e16	−2.44915
$980$	−5.93009e16	−2.09565
$981$	0	0
$982$	−2.24736e16	−0.785344
$983$	3.80717e16	1.32299	0.661497	−	0.749948i	$-0.269922\pi$
$983$	3.80717e16	1.32299	0.661497	+	0.749948i	$0.269922\pi$
$984$	0	0
$985$	3.38804e16	1.16426
$986$	−4.68657e15	−0.160152
$987$	0	0
$988$	2.20995e16	0.746825
$989$	−3.26566e16	−1.09747
$990$	0	0
$991$	−2.32664e16	−0.773257	−0.386629	−	0.922236i	$-0.626360\pi$
$991$	−2.32664e16	−0.773257	−0.386629	+	0.922236i	$0.626360\pi$
$992$	2.30325e16	0.761249
$993$	0	0
$994$	−3.59737e16	−1.17587
$995$	−2.21331e16	−0.719473
$996$	0	0
$997$	6.76473e14	0.0217484	0.0108742	−	0.999941i	$-0.496539\pi$
$997$	6.76473e14	0.0217484	0.0108742	+	0.999941i	$0.496539\pi$
$998$	−1.29315e16	−0.413459
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.12.a.a.1.10		11
3.2	odd	2		29.12.a.a.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.2	✓	11	3.2	odd	2
261.12.a.a.1.10		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)

\(f(q)\)	\(=\)	\(q+68.3340 q^{2} +2621.54 q^{4} -8265.40 q^{5} -68659.4 q^{7} +39192.0 q^{8} +O(q^{10})\)	\(q+68.3340 q^{2} +2621.54 q^{4} -8265.40 q^{5} -68659.4 q^{7} +39192.0 q^{8} -564808. q^{10} +970140. q^{11} +1.54127e6 q^{13} -4.69177e6 q^{14} -2.69076e6 q^{16} +3.34371e6 q^{17} +5.46951e6 q^{19} -2.16680e7 q^{20} +6.62936e7 q^{22} +3.32547e7 q^{23} +1.94887e7 q^{25} +1.05321e8 q^{26} -1.79993e8 q^{28} -2.05111e7 q^{29} -8.71995e7 q^{31} -2.64136e8 q^{32} +2.28489e8 q^{34} +5.67498e8 q^{35} -1.97918e8 q^{37} +3.73754e8 q^{38} -3.23938e8 q^{40} -1.10998e9 q^{41} -9.82013e8 q^{43} +2.54326e9 q^{44} +2.27243e9 q^{46} +2.38472e9 q^{47} +2.73679e9 q^{49} +1.33174e9 q^{50} +4.04048e9 q^{52} -2.86882e9 q^{53} -8.01859e9 q^{55} -2.69090e9 q^{56} -1.40161e9 q^{58} +7.54410e9 q^{59} -1.25957e10 q^{61} -5.95869e9 q^{62} -1.25388e10 q^{64} -1.27392e10 q^{65} -2.53077e8 q^{67} +8.76565e9 q^{68} +3.87794e10 q^{70} +7.66739e9 q^{71} -1.59232e10 q^{73} -1.35245e10 q^{74} +1.43385e10 q^{76} -6.66093e10 q^{77} +1.03493e10 q^{79} +2.22402e10 q^{80} -7.58492e10 q^{82} -2.23246e10 q^{83} -2.76371e10 q^{85} -6.71049e10 q^{86} +3.80218e10 q^{88} -7.10371e10 q^{89} -1.05822e11 q^{91} +8.71784e10 q^{92} +1.62957e11 q^{94} -4.52077e10 q^{95} -5.61657e9 q^{97} +1.87016e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) \) 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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