LMFDB - Embedded newform 261.12.a.a.1.3

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			1.3
Root			$54.9918$ 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)

$f(q)$	$=$	$q-51.9918 q^{2} +655.142 q^{4} -3682.79 q^{5} -83752.5 q^{7} +72417.1 q^{8} +O(q^{10})$	\(q-51.9918 q^{2} +655.142 q^{4} -3682.79 q^{5} -83752.5 q^{7} +72417.1 q^{8} +191474. q^{10} -132980. q^{11} +193527. q^{13} +4.35444e6 q^{14} -5.10682e6 q^{16} -2.59769e6 q^{17} -4.52077e6 q^{19} -2.41275e6 q^{20} +6.91387e6 q^{22} -7.42631e6 q^{23} -3.52652e7 q^{25} -1.00618e7 q^{26} -5.48698e7 q^{28} -2.05111e7 q^{29} +4.28934e7 q^{31} +1.17202e8 q^{32} +1.35058e8 q^{34} +3.08443e8 q^{35} -8.25971e7 q^{37} +2.35043e8 q^{38} -2.66697e8 q^{40} +7.25750e8 q^{41} -1.14606e8 q^{43} -8.71209e7 q^{44} +3.86107e8 q^{46} +3.13358e8 q^{47} +5.03716e9 q^{49} +1.83350e9 q^{50} +1.26788e8 q^{52} +5.04903e8 q^{53} +4.89737e8 q^{55} -6.06512e9 q^{56} +1.06641e9 q^{58} -8.68166e9 q^{59} +4.85120e9 q^{61} -2.23010e9 q^{62} +4.36521e9 q^{64} -7.12717e8 q^{65} -1.44650e10 q^{67} -1.70186e9 q^{68} -1.60365e10 q^{70} +2.67681e10 q^{71} +2.46174e10 q^{73} +4.29437e9 q^{74} -2.96175e9 q^{76} +1.11374e10 q^{77} -3.86002e10 q^{79} +1.88073e10 q^{80} -3.77330e10 q^{82} -1.74415e9 q^{83} +9.56673e9 q^{85} +5.95859e9 q^{86} -9.63004e9 q^{88} +2.10441e10 q^{89} -1.62084e10 q^{91} -4.86529e9 q^{92} -1.62920e10 q^{94} +1.66490e10 q^{95} +1.02295e11 q^{97} -2.61891e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−51.9918	−1.14887	−0.574433	−	0.818552i	$-0.694777\pi$
$2$	−51.9918	−1.14887	−0.574433	+	0.818552i	$0.694777\pi$
$3$	0	0
$3$	0	0
$4$	655.142	0.319894
$5$	−3682.79	−0.527037	−0.263519	−	0.964654i	$-0.584883\pi$
$5$	−3682.79	−0.527037	−0.263519	+	0.964654i	$0.584883\pi$
$6$	0	0
$7$	−83752.5	−1.88347	−0.941735	−	0.336355i	$-0.890806\pi$
$7$	−83752.5	−1.88347	−0.941735	+	0.336355i	$0.890806\pi$
$8$	72417.1	0.781351
$9$	0	0
$10$	191474.	0.605495
$11$	−132980.	−0.248959	−0.124479	−	0.992222i	$-0.539726\pi$
$11$	−132980.	−0.248959	−0.124479	+	0.992222i	$0.539726\pi$
$12$	0	0
$13$	193527.	0.144561	0.0722807	−	0.997384i	$-0.476972\pi$
$13$	193527.	0.144561	0.0722807	+	0.997384i	$0.476972\pi$
$14$	4.35444e6	2.16386
$15$	0	0
$16$	−5.10682e6	−1.21756
$17$	−2.59769e6	−0.443729	−0.221865	−	0.975077i	$-0.571214\pi$
$17$	−2.59769e6	−0.443729	−0.221865	+	0.975077i	$0.571214\pi$
$18$	0	0
$19$	−4.52077e6	−0.418859	−0.209430	−	0.977824i	$-0.567161\pi$
$19$	−4.52077e6	−0.418859	−0.209430	+	0.977824i	$0.567161\pi$
$20$	−2.41275e6	−0.168596
$21$	0	0
$22$	6.91387e6	0.286020
$23$	−7.42631e6	−0.240586	−0.120293	−	0.992738i	$-0.538383\pi$
$23$	−7.42631e6	−0.240586	−0.120293	+	0.992738i	$0.538383\pi$
$24$	0	0
$25$	−3.52652e7	−0.722232
$26$	−1.00618e7	−0.166082
$27$	0	0
$28$	−5.48698e7	−0.602510
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	0	0
$31$	4.28934e7	0.269092	0.134546	−	0.990907i	$-0.457042\pi$
$31$	4.28934e7	0.269092	0.134546	+	0.990907i	$0.457042\pi$
$32$	1.17202e8	0.617464
$33$	0	0
$34$	1.35058e8	0.509786
$35$	3.08443e8	0.992659
$36$	0	0
$37$	−8.25971e7	−0.195819	−0.0979096	−	0.995195i	$-0.531216\pi$
$37$	−8.25971e7	−0.195819	−0.0979096	+	0.995195i	$0.531216\pi$
$38$	2.35043e8	0.481213
$39$	0	0
$40$	−2.66697e8	−0.411801
$41$	7.25750e8	0.978309	0.489154	−	0.872197i	$-0.337305\pi$
$41$	7.25750e8	0.978309	0.489154	+	0.872197i	$0.337305\pi$
$42$	0	0
$43$	−1.14606e8	−0.118887	−0.0594433	−	0.998232i	$-0.518933\pi$
$43$	−1.14606e8	−0.118887	−0.0594433	+	0.998232i	$0.518933\pi$
$44$	−8.71209e7	−0.0796403
$45$	0	0
$46$	3.86107e8	0.276401
$47$	3.13358e8	0.199298	0.0996490	−	0.995023i	$-0.468228\pi$
$47$	3.13358e8	0.199298	0.0996490	+	0.995023i	$0.468228\pi$
$48$	0	0
$49$	5.03716e9	2.54746
$50$	1.83350e9	0.829748
$51$	0	0
$52$	1.26788e8	0.0462443
$53$	5.04903e8	0.165840	0.0829202	−	0.996556i	$-0.473575\pi$
$53$	5.04903e8	0.165840	0.0829202	+	0.996556i	$0.473575\pi$
$54$	0	0
$55$	4.89737e8	0.131210
$56$	−6.06512e9	−1.47165
$57$	0	0
$58$	1.06641e9	0.213339
$59$	−8.68166e9	−1.58095	−0.790473	−	0.612497i	$-0.790165\pi$
$59$	−8.68166e9	−1.58095	−0.790473	+	0.612497i	$0.790165\pi$
$60$	0	0
$61$	4.85120e9	0.735420	0.367710	−	0.929941i	$-0.380142\pi$
$61$	4.85120e9	0.735420	0.367710	+	0.929941i	$0.380142\pi$
$62$	−2.23010e9	−0.309151
$63$	0	0
$64$	4.36521e9	0.508178
$65$	−7.12717e8	−0.0761893
$66$	0	0
$67$	−1.44650e10	−1.30890	−0.654452	−	0.756104i	$-0.727101\pi$
$67$	−1.44650e10	−1.30890	−0.654452	+	0.756104i	$0.727101\pi$
$68$	−1.70186e9	−0.141946
$69$	0	0
$70$	−1.60365e10	−1.14043
$71$	2.67681e10	1.76075	0.880374	−	0.474280i	$-0.157292\pi$
$71$	2.67681e10	1.76075	0.880374	+	0.474280i	$0.157292\pi$
$72$	0	0
$73$	2.46174e10	1.38985	0.694924	−	0.719084i	$-0.255438\pi$
$73$	2.46174e10	1.38985	0.694924	+	0.719084i	$0.255438\pi$
$74$	4.29437e9	0.224970
$75$	0	0
$76$	−2.96175e9	−0.133990
$77$	1.11374e10	0.468906
$78$	0	0
$79$	−3.86002e10	−1.41137	−0.705685	−	0.708526i	$-0.749360\pi$
$79$	−3.86002e10	−1.41137	−0.705685	+	0.708526i	$0.749360\pi$
$80$	1.88073e10	0.641700
$81$	0	0
$82$	−3.77330e10	−1.12395
$83$	−1.74415e9	−0.0486020	−0.0243010	−	0.999705i	$-0.507736\pi$
$83$	−1.74415e9	−0.0486020	−0.0243010	+	0.999705i	$0.507736\pi$
$84$	0	0
$85$	9.56673e9	0.233862
$86$	5.95859e9	0.136585
$87$	0	0
$88$	−9.63004e9	−0.194524
$89$	2.10441e10	0.399471	0.199735	−	0.979850i	$-0.435992\pi$
$89$	2.10441e10	0.399471	0.199735	+	0.979850i	$0.435992\pi$
$90$	0	0
$91$	−1.62084e10	−0.272277
$92$	−4.86529e9	−0.0769619
$93$	0	0
$94$	−1.62920e10	−0.228967
$95$	1.66490e10	0.220754
$96$	0	0
$97$	1.02295e11	1.20951	0.604757	−	0.796410i	$-0.293270\pi$
$97$	1.02295e11	1.20951	0.604757	+	0.796410i	$0.293270\pi$
$98$	−2.61891e11	−2.92669
$99$	0	0
$100$	−2.31037e10	−0.231037
$101$	−2.22830e10	−0.210963	−0.105481	−	0.994421i	$-0.533638\pi$
$101$	−2.22830e10	−0.210963	−0.105481	+	0.994421i	$0.533638\pi$
$102$	0	0
$103$	−1.18118e10	−0.100395	−0.0501976	−	0.998739i	$-0.515985\pi$
$103$	−1.18118e10	−0.100395	−0.0501976	+	0.998739i	$0.515985\pi$
$104$	1.40146e10	0.112953
$105$	0	0
$106$	−2.62508e10	−0.190528
$107$	2.30403e11	1.58810	0.794048	−	0.607855i	$-0.207970\pi$
$107$	2.30403e11	1.58810	0.794048	+	0.607855i	$0.207970\pi$
$108$	0	0
$109$	−7.31425e10	−0.455328	−0.227664	−	0.973740i	$-0.573109\pi$
$109$	−7.31425e10	−0.455328	−0.227664	+	0.973740i	$0.573109\pi$
$110$	−2.54623e10	−0.150743
$111$	0	0
$112$	4.27710e11	2.29324
$113$	2.78421e11	1.42158	0.710788	−	0.703407i	$-0.248339\pi$
$113$	2.78421e11	1.42158	0.710788	+	0.703407i	$0.248339\pi$
$114$	0	0
$115$	2.73495e10	0.126798
$116$	−1.34377e10	−0.0594028
$117$	0	0
$118$	4.51375e11	1.81629
$119$	2.17563e11	0.835751
$120$	0	0
$121$	−2.67628e11	−0.938020
$122$	−2.52223e11	−0.844899
$123$	0	0
$124$	2.81013e10	0.0860808
$125$	3.09698e11	0.907680
$126$	0	0
$127$	6.84159e11	1.83754	0.918769	−	0.394795i	$-0.129184\pi$
$127$	6.84159e11	1.83754	0.918769	+	0.394795i	$0.129184\pi$
$128$	−4.66986e11	−1.20129
$129$	0	0
$130$	3.70554e10	0.0875313
$131$	3.46467e11	0.784638	0.392319	−	0.919829i	$-0.371673\pi$
$131$	3.46467e11	0.784638	0.392319	+	0.919829i	$0.371673\pi$
$132$	0	0
$133$	3.78626e11	0.788909
$134$	7.52062e11	1.50376
$135$	0	0
$136$	−1.88117e11	−0.346708
$137$	2.96772e11	0.525364	0.262682	−	0.964883i	$-0.415393\pi$
$137$	2.96772e11	0.525364	0.262682	+	0.964883i	$0.415393\pi$
$138$	0	0
$139$	3.77869e11	0.617674	0.308837	−	0.951115i	$-0.400060\pi$
$139$	3.77869e11	0.617674	0.308837	+	0.951115i	$0.400060\pi$
$140$	2.02074e11	0.317545
$141$	0	0
$142$	−1.39172e12	−2.02286
$143$	−2.57352e10	−0.0359898
$144$	0	0
$145$	7.55382e10	0.0978684
$146$	−1.27990e12	−1.59675
$147$	0	0
$148$	−5.41128e10	−0.0626413
$149$	6.93233e11	0.773312	0.386656	−	0.922224i	$-0.373630\pi$
$149$	6.93233e11	0.773312	0.386656	+	0.922224i	$0.373630\pi$
$150$	0	0
$151$	−7.27671e11	−0.754331	−0.377165	−	0.926146i	$-0.623101\pi$
$151$	−7.27671e11	−0.754331	−0.377165	+	0.926146i	$0.623101\pi$
$152$	−3.27381e11	−0.327276
$153$	0	0
$154$	−5.79054e11	−0.538710
$155$	−1.57967e11	−0.141822
$156$	0	0
$157$	−1.94371e12	−1.62623	−0.813117	−	0.582101i	$-0.802231\pi$
$157$	−1.94371e12	−1.62623	−0.813117	+	0.582101i	$0.802231\pi$
$158$	2.00689e12	1.62147
$159$	0	0
$160$	−4.31631e11	−0.325427
$161$	6.21972e11	0.453136
$162$	0	0
$163$	1.07427e12	0.731277	0.365638	−	0.930757i	$-0.380851\pi$
$163$	1.07427e12	0.731277	0.365638	+	0.930757i	$0.380851\pi$
$164$	4.75469e11	0.312955
$165$	0	0
$166$	9.06813e10	0.0558371
$167$	2.05398e12	1.22365	0.611824	−	0.790994i	$-0.290436\pi$
$167$	2.05398e12	1.22365	0.611824	+	0.790994i	$0.290436\pi$
$168$	0	0
$169$	−1.75471e12	−0.979102
$170$	−4.97391e11	−0.268676
$171$	0	0
$172$	−7.50835e10	−0.0380310
$173$	−5.47972e10	−0.0268847	−0.0134423	−	0.999910i	$-0.504279\pi$
$173$	−5.47972e10	−0.0268847	−0.0134423	+	0.999910i	$0.504279\pi$
$174$	0	0
$175$	2.95355e12	1.36030
$176$	6.79106e11	0.303122
$177$	0	0
$178$	−1.09412e12	−0.458938
$179$	−1.01838e12	−0.414209	−0.207105	−	0.978319i	$-0.566404\pi$
$179$	−1.01838e12	−0.414209	−0.207105	+	0.978319i	$0.566404\pi$
$180$	0	0
$181$	4.66142e12	1.78355	0.891777	−	0.452476i	$-0.149459\pi$
$181$	4.66142e12	1.78355	0.891777	+	0.452476i	$0.149459\pi$
$182$	8.42701e11	0.312810
$183$	0	0
$184$	−5.37792e11	−0.187982
$185$	3.04187e11	0.103204
$186$	0	0
$187$	3.45441e11	0.110470
$188$	2.05294e11	0.0637541
$189$	0	0
$190$	−8.65612e11	−0.253617
$191$	3.44126e12	0.979567	0.489783	−	0.871844i	$-0.337076\pi$
$191$	3.44126e12	0.979567	0.489783	+	0.871844i	$0.337076\pi$
$192$	0	0
$193$	1.88765e12	0.507408	0.253704	−	0.967282i	$-0.418351\pi$
$193$	1.88765e12	0.507408	0.253704	+	0.967282i	$0.418351\pi$
$194$	−5.31851e12	−1.38957
$195$	0	0
$196$	3.30006e12	0.814917
$197$	−7.01609e12	−1.68473	−0.842366	−	0.538906i	$-0.818838\pi$
$197$	−7.01609e12	−1.68473	−0.842366	+	0.538906i	$0.818838\pi$
$198$	0	0
$199$	1.98650e12	0.451228	0.225614	−	0.974217i	$-0.427561\pi$
$199$	1.98650e12	0.451228	0.225614	+	0.974217i	$0.427561\pi$
$200$	−2.55381e12	−0.564317
$201$	0	0
$202$	1.15853e12	0.242368
$203$	1.71786e12	0.349752
$204$	0	0
$205$	−2.67278e12	−0.515605
$206$	6.14119e11	0.115341
$207$	0	0
$208$	−9.88307e11	−0.176012
$209$	6.01173e11	0.104279
$210$	0	0
$211$	−6.11632e12	−1.00678	−0.503392	−	0.864058i	$-0.667915\pi$
$211$	−6.11632e12	−1.00678	−0.503392	+	0.864058i	$0.667915\pi$
$212$	3.30783e11	0.0530513
$213$	0	0
$214$	−1.19790e13	−1.82451
$215$	4.22071e11	0.0626576
$216$	0	0
$217$	−3.59243e12	−0.506827
$218$	3.80281e12	0.523111
$219$	0	0
$220$	3.20848e11	0.0419734
$221$	−5.02722e11	−0.0641462
$222$	0	0
$223$	−1.23957e13	−1.50520	−0.752600	−	0.658478i	$-0.771201\pi$
$223$	−1.23957e13	−1.50520	−0.752600	+	0.658478i	$0.771201\pi$
$224$	−9.81600e12	−1.16298
$225$	0	0
$226$	−1.44756e13	−1.63320
$227$	−1.20542e13	−1.32739	−0.663694	−	0.748004i	$-0.731012\pi$
$227$	−1.20542e13	−1.32739	−0.663694	+	0.748004i	$0.731012\pi$
$228$	0	0
$229$	9.40324e12	0.986693	0.493347	−	0.869833i	$-0.335773\pi$
$229$	9.40324e12	0.986693	0.493347	+	0.869833i	$0.335773\pi$
$230$	−1.42195e12	−0.145674
$231$	0	0
$232$	−1.48536e12	−0.145093
$233$	1.26418e13	1.20601	0.603003	−	0.797739i	$-0.293971\pi$
$233$	1.26418e13	1.20601	0.603003	+	0.797739i	$0.293971\pi$
$234$	0	0
$235$	−1.15403e12	−0.105037
$236$	−5.68772e12	−0.505734
$237$	0	0
$238$	−1.13115e13	−0.960166
$239$	1.22673e13	1.01756	0.508781	−	0.860896i	$-0.330096\pi$
$239$	1.22673e13	1.01756	0.508781	+	0.860896i	$0.330096\pi$
$240$	0	0
$241$	−2.89078e12	−0.229046	−0.114523	−	0.993421i	$-0.536534\pi$
$241$	−2.89078e12	−0.229046	−0.114523	+	0.993421i	$0.536534\pi$
$242$	1.39144e13	1.07766
$243$	0	0
$244$	3.17823e12	0.235256
$245$	−1.85508e13	−1.34261
$246$	0	0
$247$	−8.74890e11	−0.0605509
$248$	3.10621e12	0.210255
$249$	0	0
$250$	−1.61017e13	−1.04280
$251$	−2.68736e13	−1.70263	−0.851314	−	0.524657i	$-0.824194\pi$
$251$	−2.68736e13	−1.70263	−0.851314	+	0.524657i	$0.824194\pi$
$252$	0	0
$253$	9.87552e11	0.0598959
$254$	−3.55706e13	−2.11109
$255$	0	0
$256$	1.53394e13	0.871947
$257$	1.28426e13	0.714533	0.357266	−	0.934003i	$-0.383709\pi$
$257$	1.28426e13	0.714533	0.357266	+	0.934003i	$0.383709\pi$
$258$	0	0
$259$	6.91771e12	0.368820
$260$	−4.66931e11	−0.0243725
$261$	0	0
$262$	−1.80134e13	−0.901444
$263$	−1.60237e13	−0.785248	−0.392624	−	0.919699i	$-0.628433\pi$
$263$	−1.60237e13	−0.785248	−0.392624	+	0.919699i	$0.628433\pi$
$264$	0	0
$265$	−1.85945e12	−0.0874041
$266$	−1.96854e13	−0.906350
$267$	0	0
$268$	−9.47665e12	−0.418710
$269$	−3.10713e13	−1.34500	−0.672500	−	0.740097i	$-0.734780\pi$
$269$	−3.10713e13	−1.34500	−0.672500	+	0.740097i	$0.734780\pi$
$270$	0	0
$271$	−1.82362e13	−0.757885	−0.378943	−	0.925420i	$-0.623712\pi$
$271$	−1.82362e13	−0.757885	−0.378943	+	0.925420i	$0.623712\pi$
$272$	1.32659e13	0.540268
$273$	0	0
$274$	−1.54297e13	−0.603573
$275$	4.68957e12	0.179806
$276$	0	0
$277$	−5.73318e12	−0.211230	−0.105615	−	0.994407i	$-0.533681\pi$
$277$	−5.73318e12	−0.211230	−0.105615	+	0.994407i	$0.533681\pi$
$278$	−1.96461e13	−0.709625
$279$	0	0
$280$	2.23365e13	0.775616
$281$	2.17147e13	0.739383	0.369692	−	0.929155i	$-0.379463\pi$
$281$	2.17147e13	0.739383	0.369692	+	0.929155i	$0.379463\pi$
$282$	0	0
$283$	−5.22739e13	−1.71182	−0.855912	−	0.517121i	$-0.827004\pi$
$283$	−5.22739e13	−1.71182	−0.855912	+	0.517121i	$0.827004\pi$
$284$	1.75369e13	0.563252
$285$	0	0
$286$	1.33802e12	0.0413475
$287$	−6.07834e13	−1.84262
$288$	0	0
$289$	−2.75239e13	−0.803104
$290$	−3.92736e12	−0.112438
$291$	0	0
$292$	1.61279e13	0.444603
$293$	−4.99463e13	−1.35124	−0.675619	−	0.737251i	$-0.736123\pi$
$293$	−4.99463e13	−1.35124	−0.675619	+	0.737251i	$0.736123\pi$
$294$	0	0
$295$	3.19727e13	0.833217
$296$	−5.98144e12	−0.153004
$297$	0	0
$298$	−3.60424e13	−0.888432
$299$	−1.43719e12	−0.0347794
$300$	0	0
$301$	9.59859e12	0.223919
$302$	3.78329e13	0.866625
$303$	0	0
$304$	2.30868e13	0.509987
$305$	−1.78659e13	−0.387594
$306$	0	0
$307$	−5.28549e13	−1.10618	−0.553088	−	0.833123i	$-0.686551\pi$
$307$	−5.28549e13	−1.10618	−0.553088	+	0.833123i	$0.686551\pi$
$308$	7.29660e12	0.150000
$309$	0	0
$310$	8.21298e12	0.162934
$311$	7.83474e13	1.52701	0.763506	−	0.645800i	$-0.223476\pi$
$311$	7.83474e13	1.52701	0.763506	+	0.645800i	$0.223476\pi$
$312$	0	0
$313$	8.71210e13	1.63919	0.819594	−	0.572944i	$-0.194199\pi$
$313$	8.71210e13	1.63919	0.819594	+	0.572944i	$0.194199\pi$
$314$	1.01057e14	1.86832
$315$	0	0
$316$	−2.52886e13	−0.451488
$317$	−7.95836e13	−1.39636	−0.698180	−	0.715922i	$-0.746007\pi$
$317$	−7.95836e13	−1.39636	−0.698180	+	0.715922i	$0.746007\pi$
$318$	0	0
$319$	2.72758e12	0.0462304
$320$	−1.60761e13	−0.267829
$321$	0	0
$322$	−3.23374e13	−0.520593
$323$	1.17436e13	0.185860
$324$	0	0
$325$	−6.82476e12	−0.104407
$326$	−5.58532e13	−0.840139
$327$	0	0
$328$	5.25567e13	0.764403
$329$	−2.62445e13	−0.375372
$330$	0	0
$331$	−5.59223e13	−0.773626	−0.386813	−	0.922158i	$-0.626424\pi$
$331$	−5.59223e13	−0.773626	−0.386813	+	0.922158i	$0.626424\pi$
$332$	−1.14266e12	−0.0155475
$333$	0	0
$334$	−1.06790e14	−1.40581
$335$	5.32716e13	0.689841
$336$	0	0
$337$	−8.02614e13	−1.00587	−0.502935	−	0.864324i	$-0.667747\pi$
$337$	−8.02614e13	−1.00587	−0.502935	+	0.864324i	$0.667747\pi$
$338$	9.12303e13	1.12486
$339$	0	0
$340$	6.26757e12	0.0748109
$341$	−5.70397e12	−0.0669928
$342$	0	0
$343$	−2.56269e14	−2.91460
$344$	−8.29947e12	−0.0928922
$345$	0	0
$346$	2.84900e12	0.0308869
$347$	−1.59883e13	−0.170605	−0.0853023	−	0.996355i	$-0.527186\pi$
$347$	−1.59883e13	−0.170605	−0.0853023	+	0.996355i	$0.527186\pi$
$348$	0	0
$349$	−2.67236e13	−0.276284	−0.138142	−	0.990412i	$-0.544113\pi$
$349$	−2.67236e13	−0.276284	−0.138142	+	0.990412i	$0.544113\pi$
$350$	−1.53560e14	−1.56281
$351$	0	0
$352$	−1.55856e13	−0.153723
$353$	9.23737e13	0.896989	0.448495	−	0.893786i	$-0.351960\pi$
$353$	9.23737e13	0.896989	0.448495	+	0.893786i	$0.351960\pi$
$354$	0	0
$355$	−9.85813e13	−0.927980
$356$	1.37869e13	0.127788
$357$	0	0
$358$	5.29475e13	0.475871
$359$	−5.10662e13	−0.451975	−0.225987	−	0.974130i	$-0.572561\pi$
$359$	−5.10662e13	−0.451975	−0.225987	+	0.974130i	$0.572561\pi$
$360$	0	0
$361$	−9.60529e13	−0.824557
$362$	−2.42355e14	−2.04906
$363$	0	0
$364$	−1.06188e13	−0.0870997
$365$	−9.06607e13	−0.732501
$366$	0	0
$367$	5.30370e13	0.415830	0.207915	−	0.978147i	$-0.433332\pi$
$367$	5.30370e13	0.415830	0.207915	+	0.978147i	$0.433332\pi$
$368$	3.79249e13	0.292928
$369$	0	0
$370$	−1.58152e13	−0.118568
$371$	−4.22869e13	−0.312356
$372$	0	0
$373$	2.07858e14	1.49062	0.745312	−	0.666716i	$-0.232301\pi$
$373$	2.07858e14	1.49062	0.745312	+	0.666716i	$0.232301\pi$
$374$	−1.79601e13	−0.126916
$375$	0	0
$376$	2.26925e13	0.155722
$377$	−3.96946e12	−0.0268444
$378$	0	0
$379$	1.89936e14	1.24765	0.623823	−	0.781566i	$-0.285579\pi$
$379$	1.89936e14	1.24765	0.623823	+	0.781566i	$0.285579\pi$
$380$	1.09075e13	0.0706179
$381$	0	0
$382$	−1.78917e14	−1.12539
$383$	2.53366e14	1.57092	0.785462	−	0.618910i	$-0.212426\pi$
$383$	2.53366e14	1.57092	0.785462	+	0.618910i	$0.212426\pi$
$384$	0	0
$385$	−4.10168e13	−0.247131
$386$	−9.81425e13	−0.582944
$387$	0	0
$388$	6.70179e13	0.386916
$389$	−2.50859e14	−1.42793	−0.713964	−	0.700182i	$-0.753102\pi$
$389$	−2.50859e14	−1.42793	−0.713964	+	0.700182i	$0.753102\pi$
$390$	0	0
$391$	1.92912e13	0.106755
$392$	3.64777e14	1.99046
$393$	0	0
$394$	3.64779e14	1.93553
$395$	1.42156e14	0.743844
$396$	0	0
$397$	−8.33694e13	−0.424286	−0.212143	−	0.977239i	$-0.568044\pi$
$397$	−8.33694e13	−0.424286	−0.212143	+	0.977239i	$0.568044\pi$
$398$	−1.03281e14	−0.518401
$399$	0	0
$400$	1.80093e14	0.879362
$401$	8.55764e13	0.412154	0.206077	−	0.978536i	$-0.433930\pi$
$401$	8.55764e13	0.412154	0.206077	+	0.978536i	$0.433930\pi$
$402$	0	0
$403$	8.30101e12	0.0389003
$404$	−1.45985e13	−0.0674857
$405$	0	0
$406$	−8.93146e13	−0.401818
$407$	1.09838e13	0.0487508
$408$	0	0
$409$	2.89966e14	1.25276	0.626382	−	0.779516i	$-0.284535\pi$
$409$	2.89966e14	1.25276	0.626382	+	0.779516i	$0.284535\pi$
$410$	1.38963e14	0.592361
$411$	0	0
$412$	−7.73844e12	−0.0321158
$413$	7.27111e14	2.97766
$414$	0	0
$415$	6.42332e12	0.0256150
$416$	2.26818e13	0.0892615
$417$	0	0
$418$	−3.12560e13	−0.119802
$419$	−1.15977e14	−0.438727	−0.219364	−	0.975643i	$-0.570398\pi$
$419$	−1.15977e14	−0.438727	−0.219364	+	0.975643i	$0.570398\pi$
$420$	0	0
$421$	−1.29586e14	−0.477535	−0.238767	−	0.971077i	$-0.576743\pi$
$421$	−1.29586e14	−0.477535	−0.238767	+	0.971077i	$0.576743\pi$
$422$	3.17998e14	1.15666
$423$	0	0
$424$	3.65636e13	0.129580
$425$	9.16081e13	0.320475
$426$	0	0
$427$	−4.06301e14	−1.38514
$428$	1.50947e14	0.508022
$429$	0	0
$430$	−2.19442e13	−0.0719853
$431$	−8.77012e13	−0.284041	−0.142020	−	0.989864i	$-0.545360\pi$
$431$	−8.77012e13	−0.284041	−0.142020	+	0.989864i	$0.545360\pi$
$432$	0	0
$433$	3.21721e14	1.01577	0.507886	−	0.861424i	$-0.330427\pi$
$433$	3.21721e14	1.01577	0.507886	+	0.861424i	$0.330427\pi$
$434$	1.86777e14	0.582276
$435$	0	0
$436$	−4.79188e13	−0.145656
$437$	3.35727e13	0.100772
$438$	0	0
$439$	4.76314e14	1.39424	0.697121	−	0.716954i	$-0.254464\pi$
$439$	4.76314e14	1.39424	0.697121	+	0.716954i	$0.254464\pi$
$440$	3.54654e13	0.102521
$441$	0	0
$442$	2.61374e13	0.0736954
$443$	−6.68817e13	−0.186246	−0.0931230	−	0.995655i	$-0.529685\pi$
$443$	−6.68817e13	−0.186246	−0.0931230	+	0.995655i	$0.529685\pi$
$444$	0	0
$445$	−7.75008e13	−0.210536
$446$	6.44474e14	1.72927
$447$	0	0
$448$	−3.65598e14	−0.957138
$449$	−3.99733e14	−1.03375	−0.516874	−	0.856062i	$-0.672904\pi$
$449$	−3.99733e14	−1.03375	−0.516874	+	0.856062i	$0.672904\pi$
$450$	0	0
$451$	−9.65104e13	−0.243558
$452$	1.82405e14	0.454753
$453$	0	0
$454$	6.26721e14	1.52499
$455$	5.96919e13	0.143500
$456$	0	0
$457$	4.42060e14	1.03739	0.518695	−	0.854959i	$-0.326418\pi$
$457$	4.42060e14	1.03739	0.518695	+	0.854959i	$0.326418\pi$
$458$	−4.88891e14	−1.13358
$459$	0	0
$460$	1.79178e13	0.0405618
$461$	−6.61295e14	−1.47925	−0.739623	−	0.673022i	$-0.764996\pi$
$461$	−6.61295e14	−1.47925	−0.739623	+	0.673022i	$0.764996\pi$
$462$	0	0
$463$	−1.41874e14	−0.309890	−0.154945	−	0.987923i	$-0.549520\pi$
$463$	−1.41874e14	−0.309890	−0.154945	+	0.987923i	$0.549520\pi$
$464$	1.04747e14	0.226096
$465$	0	0
$466$	−6.57267e14	−1.38554
$467$	−3.99126e14	−0.831509	−0.415755	−	0.909477i	$-0.636482\pi$
$467$	−3.99126e14	−0.831509	−0.415755	+	0.909477i	$0.636482\pi$
$468$	0	0
$469$	1.21148e15	2.46528
$470$	6.00001e13	0.120674
$471$	0	0
$472$	−6.28701e14	−1.23527
$473$	1.52404e13	0.0295978
$474$	0	0
$475$	1.59426e14	0.302513
$476$	1.42535e14	0.267351
$477$	0	0
$478$	−6.37799e14	−1.16904
$479$	−3.65975e14	−0.663141	−0.331570	−	0.943431i	$-0.607578\pi$
$479$	−3.65975e14	−0.663141	−0.331570	+	0.943431i	$0.607578\pi$
$480$	0	0
$481$	−1.59847e13	−0.0283079
$482$	1.50297e14	0.263143
$483$	0	0
$484$	−1.75334e14	−0.300066
$485$	−3.76731e14	−0.637459
$486$	0	0
$487$	5.80639e14	0.960499	0.480249	−	0.877132i	$-0.340546\pi$
$487$	5.80639e14	0.960499	0.480249	+	0.877132i	$0.340546\pi$
$488$	3.51310e14	0.574621
$489$	0	0
$490$	9.64488e14	1.54248
$491$	−6.75492e14	−1.06825	−0.534124	−	0.845406i	$-0.679358\pi$
$491$	−6.75492e14	−1.06825	−0.534124	+	0.845406i	$0.679358\pi$
$492$	0	0
$493$	5.32816e13	0.0823985
$494$	4.54871e13	0.0695648
$495$	0	0
$496$	−2.19049e14	−0.327636
$497$	−2.24190e15	−3.31632
$498$	0	0
$499$	−5.89501e14	−0.852965	−0.426483	−	0.904496i	$-0.640247\pi$
$499$	−5.89501e14	−0.852965	−0.426483	+	0.904496i	$0.640247\pi$
$500$	2.02896e14	0.290361
$501$	0	0
$502$	1.39720e15	1.95609
$503$	9.33902e14	1.29324	0.646618	−	0.762814i	$-0.276183\pi$
$503$	9.33902e14	1.29324	0.646618	+	0.762814i	$0.276183\pi$
$504$	0	0
$505$	8.20635e13	0.111185
$506$	−5.13446e13	−0.0688124
$507$	0	0
$508$	4.48221e14	0.587817
$509$	5.80951e14	0.753688	0.376844	−	0.926277i	$-0.377009\pi$
$509$	5.80951e14	0.753688	0.376844	+	0.926277i	$0.377009\pi$
$510$	0	0
$511$	−2.06177e15	−2.61774
$512$	1.58862e14	0.199543
$513$	0	0
$514$	−6.67711e14	−0.820902
$515$	4.35005e13	0.0529120
$516$	0	0
$517$	−4.16704e13	−0.0496169
$518$	−3.59664e14	−0.423724
$519$	0	0
$520$	−5.16129e13	−0.0595306
$521$	−6.16566e14	−0.703675	−0.351837	−	0.936061i	$-0.614443\pi$
$521$	−6.16566e14	−0.703675	−0.351837	+	0.936061i	$0.614443\pi$
$522$	0	0
$523$	−9.25923e14	−1.03470	−0.517351	−	0.855773i	$-0.673082\pi$
$523$	−9.25923e14	−1.03470	−0.517351	+	0.855773i	$0.673082\pi$
$524$	2.26985e14	0.251001
$525$	0	0
$526$	8.33101e14	0.902145
$527$	−1.11424e14	−0.119404
$528$	0	0
$529$	−8.97660e14	−0.942118
$530$	9.66760e13	0.100416
$531$	0	0
$532$	2.48054e14	0.252367
$533$	1.40452e14	0.141426
$534$	0	0
$535$	−8.48524e14	−0.836986
$536$	−1.04752e15	−1.02271
$537$	0	0
$538$	1.61545e15	1.54523
$539$	−6.69843e14	−0.634212
$540$	0	0
$541$	1.71163e15	1.58790	0.793952	−	0.607980i	$-0.208020\pi$
$541$	1.71163e15	1.58790	0.793952	+	0.607980i	$0.208020\pi$
$542$	9.48133e14	0.870709
$543$	0	0
$544$	−3.04456e14	−0.273987
$545$	2.69368e14	0.239975
$546$	0	0
$547$	3.09884e14	0.270563	0.135282	−	0.990807i	$-0.456806\pi$
$547$	3.09884e14	0.270563	0.135282	+	0.990807i	$0.456806\pi$
$548$	1.94428e14	0.168060
$549$	0	0
$550$	−2.43819e14	−0.206573
$551$	9.27262e13	0.0777802
$552$	0	0
$553$	3.23287e15	2.65827
$554$	2.98078e14	0.242676
$555$	0	0
$556$	2.47558e14	0.197590
$557$	1.41441e15	1.11782	0.558911	−	0.829227i	$-0.311219\pi$
$557$	1.41441e15	1.11782	0.558911	+	0.829227i	$0.311219\pi$
$558$	0	0
$559$	−2.21794e13	−0.0171864
$560$	−1.57516e15	−1.20862
$561$	0	0
$562$	−1.12899e15	−0.849452
$563$	−1.58073e14	−0.117778	−0.0588888	−	0.998265i	$-0.518756\pi$
$563$	−1.58073e14	−0.117778	−0.0588888	+	0.998265i	$0.518756\pi$
$564$	0	0
$565$	−1.02536e15	−0.749223
$566$	2.71781e15	1.96666
$567$	0	0
$568$	1.93847e15	1.37576
$569$	7.94297e14	0.558297	0.279149	−	0.960248i	$-0.409948\pi$
$569$	7.94297e14	0.558297	0.279149	+	0.960248i	$0.409948\pi$
$570$	0	0
$571$	−2.46506e15	−1.69953	−0.849764	−	0.527164i	$-0.823255\pi$
$571$	−2.46506e15	−1.69953	−0.849764	+	0.527164i	$0.823255\pi$
$572$	−1.68602e13	−0.0115129
$573$	0	0
$574$	3.16024e15	2.11692
$575$	2.61890e14	0.173759
$576$	0	0
$577$	−7.32129e14	−0.476563	−0.238282	−	0.971196i	$-0.576584\pi$
$577$	−7.32129e14	−0.476563	−0.238282	+	0.971196i	$0.576584\pi$
$578$	1.43102e15	0.922659
$579$	0	0
$580$	4.94882e13	0.0313075
$581$	1.46077e14	0.0915403
$582$	0	0
$583$	−6.71421e13	−0.0412874
$584$	1.78272e15	1.08596
$585$	0	0
$586$	2.59680e15	1.55239
$587$	1.85488e15	1.09851	0.549256	−	0.835654i	$-0.314911\pi$
$587$	1.85488e15	1.09851	0.549256	+	0.835654i	$0.314911\pi$
$588$	0	0
$589$	−1.93911e14	−0.112712
$590$	−1.66232e15	−0.957255
$591$	0	0
$592$	4.21809e14	0.238422
$593$	−2.47471e15	−1.38587	−0.692936	−	0.720999i	$-0.743683\pi$
$593$	−2.47471e15	−1.38587	−0.692936	+	0.720999i	$0.743683\pi$
$594$	0	0
$595$	−8.01238e14	−0.440472
$596$	4.54166e14	0.247377
$597$	0	0
$598$	7.47220e13	0.0399569
$599$	1.41526e15	0.749877	0.374938	−	0.927050i	$-0.377664\pi$
$599$	1.41526e15	0.749877	0.374938	+	0.927050i	$0.377664\pi$
$600$	0	0
$601$	−3.03423e15	−1.57848	−0.789240	−	0.614084i	$-0.789525\pi$
$601$	−3.03423e15	−1.57848	−0.789240	+	0.614084i	$0.789525\pi$
$602$	−4.99047e14	−0.257253
$603$	0	0
$604$	−4.76728e14	−0.241306
$605$	9.85616e14	0.494371
$606$	0	0
$607$	3.26634e14	0.160888	0.0804440	−	0.996759i	$-0.474366\pi$
$607$	3.26634e14	0.160888	0.0804440	+	0.996759i	$0.474366\pi$
$608$	−5.29846e14	−0.258630
$609$	0	0
$610$	9.28882e14	0.445293
$611$	6.06432e13	0.0288108
$612$	0	0
$613$	1.34079e15	0.625645	0.312822	−	0.949812i	$-0.398726\pi$
$613$	1.34079e15	0.625645	0.312822	+	0.949812i	$0.398726\pi$
$614$	2.74802e15	1.27085
$615$	0	0
$616$	8.06540e14	0.366380
$617$	−1.57502e15	−0.709117	−0.354558	−	0.935034i	$-0.615369\pi$
$617$	−1.57502e15	−0.709117	−0.354558	+	0.935034i	$0.615369\pi$
$618$	0	0
$619$	1.74802e15	0.773121	0.386561	−	0.922264i	$-0.373663\pi$
$619$	1.74802e15	0.773121	0.386561	+	0.922264i	$0.373663\pi$
$620$	−1.03491e14	−0.0453678
$621$	0	0
$622$	−4.07342e15	−1.75433
$623$	−1.76250e15	−0.752391
$624$	0	0
$625$	5.81384e14	0.243850
$626$	−4.52957e15	−1.88321
$627$	0	0
$628$	−1.27340e15	−0.520222
$629$	2.14561e14	0.0868907
$630$	0	0
$631$	−4.49331e15	−1.78815	−0.894077	−	0.447913i	$-0.852167\pi$
$631$	−4.49331e15	−1.78815	−0.894077	+	0.447913i	$0.852167\pi$
$632$	−2.79532e15	−1.10278
$633$	0	0
$634$	4.13769e15	1.60423
$635$	−2.51961e15	−0.968451
$636$	0	0
$637$	9.74826e14	0.368265
$638$	−1.41811e14	−0.0531126
$639$	0	0
$640$	1.71981e15	0.633126
$641$	1.93652e15	0.706809	0.353405	−	0.935471i	$-0.385024\pi$
$641$	1.93652e15	0.706809	0.353405	+	0.935471i	$0.385024\pi$
$642$	0	0
$643$	1.70043e15	0.610095	0.305048	−	0.952337i	$-0.401328\pi$
$643$	1.70043e15	0.610095	0.305048	+	0.952337i	$0.401328\pi$
$644$	4.07480e14	0.144955
$645$	0	0
$646$	−6.10568e14	−0.213528
$647$	−2.04196e14	−0.0708068	−0.0354034	−	0.999373i	$-0.511272\pi$
$647$	−2.04196e14	−0.0708068	−0.0354034	+	0.999373i	$0.511272\pi$
$648$	0	0
$649$	1.15449e15	0.393590
$650$	3.54831e14	0.119950
$651$	0	0
$652$	7.03800e14	0.233931
$653$	−2.57221e15	−0.847783	−0.423891	−	0.905713i	$-0.639336\pi$
$653$	−2.57221e15	−0.847783	−0.423891	+	0.905713i	$0.639336\pi$
$654$	0	0
$655$	−1.27596e15	−0.413533
$656$	−3.70628e15	−1.19115
$657$	0	0
$658$	1.36450e15	0.431252
$659$	1.82638e14	0.0572429	0.0286215	−	0.999590i	$-0.490888\pi$
$659$	1.82638e14	0.0572429	0.0286215	+	0.999590i	$0.490888\pi$
$660$	0	0
$661$	1.53812e15	0.474114	0.237057	−	0.971496i	$-0.423817\pi$
$661$	1.53812e15	0.474114	0.237057	+	0.971496i	$0.423817\pi$
$662$	2.90750e15	0.888793
$663$	0	0
$664$	−1.26306e14	−0.0379752
$665$	−1.39440e15	−0.415784
$666$	0	0
$667$	1.52322e14	0.0446757
$668$	1.34565e15	0.391437
$669$	0	0
$670$	−2.76968e15	−0.792535
$671$	−6.45114e14	−0.183089
$672$	0	0
$673$	5.36855e15	1.49890	0.749452	−	0.662058i	$-0.230317\pi$
$673$	5.36855e15	1.49890	0.749452	+	0.662058i	$0.230317\pi$
$674$	4.17293e15	1.15561
$675$	0	0
$676$	−1.14958e15	−0.313208
$677$	−1.47849e15	−0.399558	−0.199779	−	0.979841i	$-0.564022\pi$
$677$	−1.47849e15	−0.399558	−0.199779	+	0.979841i	$0.564022\pi$
$678$	0	0
$679$	−8.56749e15	−2.27808
$680$	6.92795e14	0.182728
$681$	0	0
$682$	2.96559e14	0.0769657
$683$	5.89943e15	1.51879	0.759393	−	0.650632i	$-0.225496\pi$
$683$	5.89943e15	1.51879	0.759393	+	0.650632i	$0.225496\pi$
$684$	0	0
$685$	−1.09295e15	−0.276886
$686$	1.33239e16	3.34848
$687$	0	0
$688$	5.85275e14	0.144752
$689$	9.77122e13	0.0239741
$690$	0	0
$691$	−2.68896e15	−0.649314	−0.324657	−	0.945832i	$-0.605249\pi$
$691$	−2.68896e15	−0.649314	−0.324657	+	0.945832i	$0.605249\pi$
$692$	−3.59000e13	−0.00860024
$693$	0	0
$694$	8.31260e14	0.196002
$695$	−1.39161e15	−0.325537
$696$	0	0
$697$	−1.88527e15	−0.434104
$698$	1.38941e15	0.317413
$699$	0	0
$700$	1.93500e15	0.435152
$701$	−1.81744e14	−0.0405520	−0.0202760	−	0.999794i	$-0.506454\pi$
$701$	−1.81744e14	−0.0405520	−0.0202760	+	0.999794i	$0.506454\pi$
$702$	0	0
$703$	3.73403e14	0.0820206
$704$	−5.80487e14	−0.126515
$705$	0	0
$706$	−4.80267e15	−1.03052
$707$	1.86626e15	0.397342
$708$	0	0
$709$	1.92897e15	0.404362	0.202181	−	0.979348i	$-0.435197\pi$
$709$	1.92897e15	0.404362	0.202181	+	0.979348i	$0.435197\pi$
$710$	5.12541e15	1.06612
$711$	0	0
$712$	1.52395e15	0.312127
$713$	−3.18539e14	−0.0647397
$714$	0	0
$715$	9.47773e13	0.0189680
$716$	−6.67186e14	−0.132503
$717$	0	0
$718$	2.65502e15	0.519258
$719$	5.16510e15	1.00247	0.501234	−	0.865312i	$-0.332880\pi$
$719$	5.16510e15	1.00247	0.501234	+	0.865312i	$0.332880\pi$
$720$	0	0
$721$	9.89272e14	0.189091
$722$	4.99396e15	0.947306
$723$	0	0
$724$	3.05389e15	0.570547
$725$	7.23330e14	0.134115
$726$	0	0
$727$	−1.46638e15	−0.267797	−0.133899	−	0.990995i	$-0.542750\pi$
$727$	−1.46638e15	−0.267797	−0.133899	+	0.990995i	$0.542750\pi$
$728$	−1.17376e15	−0.212744
$729$	0	0
$730$	4.71361e15	0.841546
$731$	2.97712e14	0.0527534
$732$	0	0
$733$	5.01638e15	0.875626	0.437813	−	0.899066i	$-0.355753\pi$
$733$	5.01638e15	0.875626	0.437813	+	0.899066i	$0.355753\pi$
$734$	−2.75749e15	−0.477733
$735$	0	0
$736$	−8.70382e14	−0.148553
$737$	1.92356e15	0.325863
$738$	0	0
$739$	−6.41227e15	−1.07021	−0.535103	−	0.844787i	$-0.679727\pi$
$739$	−6.41227e15	−1.07021	−0.535103	+	0.844787i	$0.679727\pi$
$740$	1.99286e14	0.0330143
$741$	0	0
$742$	2.19857e15	0.358855
$743$	−9.01527e15	−1.46063	−0.730315	−	0.683110i	$-0.760627\pi$
$743$	−9.01527e15	−1.46063	−0.730315	+	0.683110i	$0.760627\pi$
$744$	0	0
$745$	−2.55303e15	−0.407564
$746$	−1.08069e16	−1.71253
$747$	0	0
$748$	2.26313e14	0.0353387
$749$	−1.92968e16	−2.99113
$750$	0	0
$751$	−4.51349e15	−0.689434	−0.344717	−	0.938707i	$-0.612025\pi$
$751$	−4.51349e15	−0.689434	−0.344717	+	0.938707i	$0.612025\pi$
$752$	−1.60027e15	−0.242658
$753$	0	0
$754$	2.06379e14	0.0308406
$755$	2.67986e15	0.397560
$756$	0	0
$757$	−1.27132e15	−0.185878	−0.0929389	−	0.995672i	$-0.529626\pi$
$757$	−1.27132e15	−0.185878	−0.0929389	+	0.995672i	$0.529626\pi$
$758$	−9.87509e15	−1.43338
$759$	0	0
$760$	1.20568e15	0.172487
$761$	8.49793e15	1.20697	0.603486	−	0.797373i	$-0.293778\pi$
$761$	8.49793e15	1.20697	0.603486	+	0.797373i	$0.293778\pi$
$762$	0	0
$763$	6.12587e15	0.857597
$764$	2.25451e15	0.313357
$765$	0	0
$766$	−1.31729e16	−1.80478
$767$	−1.68013e15	−0.228544
$768$	0	0
$769$	−3.91757e15	−0.525317	−0.262659	−	0.964889i	$-0.584599\pi$
$769$	−3.91757e15	−0.525317	−0.262659	+	0.964889i	$0.584599\pi$
$770$	2.13253e15	0.283920
$771$	0	0
$772$	1.23668e15	0.162317
$773$	−1.11302e16	−1.45049	−0.725244	−	0.688492i	$-0.758273\pi$
$773$	−1.11302e16	−1.45049	−0.725244	+	0.688492i	$0.758273\pi$
$774$	0	0
$775$	−1.51264e15	−0.194347
$776$	7.40793e15	0.945055
$777$	0	0
$778$	1.30426e16	1.64050
$779$	−3.28095e15	−0.409773
$780$	0	0
$781$	−3.55963e15	−0.438353
$782$	−1.00299e15	−0.122647
$783$	0	0
$784$	−2.57239e16	−3.10169
$785$	7.15826e15	0.857086
$786$	0	0
$787$	−2.14922e15	−0.253758	−0.126879	−	0.991918i	$-0.540496\pi$
$787$	−2.14922e15	−0.253758	−0.126879	+	0.991918i	$0.540496\pi$
$788$	−4.59654e15	−0.538935
$789$	0	0
$790$	−7.39095e15	−0.854578
$791$	−2.33184e16	−2.67749
$792$	0	0
$793$	9.38838e14	0.106313
$794$	4.33452e15	0.487448
$795$	0	0
$796$	1.30144e15	0.144345
$797$	1.56355e16	1.72223	0.861116	−	0.508409i	$-0.169766\pi$
$797$	1.56355e16	1.72223	0.861116	+	0.508409i	$0.169766\pi$
$798$	0	0
$799$	−8.14007e14	−0.0884343
$800$	−4.13317e15	−0.445952
$801$	0	0
$802$	−4.44927e15	−0.473510
$803$	−3.27363e15	−0.346014
$804$	0	0
$805$	−2.29059e15	−0.238820
$806$	−4.31584e14	−0.0446913
$807$	0	0
$808$	−1.61367e15	−0.164836
$809$	1.58636e16	1.60948	0.804740	−	0.593628i	$-0.202305\pi$
$809$	1.58636e16	1.60948	0.804740	+	0.593628i	$0.202305\pi$
$810$	0	0
$811$	1.03213e16	1.03305	0.516524	−	0.856273i	$-0.327226\pi$
$811$	1.03213e16	1.03305	0.516524	+	0.856273i	$0.327226\pi$
$812$	1.12544e15	0.111883
$813$	0	0
$814$	−5.71065e14	−0.0560082
$815$	−3.95631e15	−0.385410
$816$	0	0
$817$	5.18110e14	0.0497967
$818$	−1.50759e16	−1.43926
$819$	0	0
$820$	−1.75105e15	−0.164939
$821$	−1.30461e16	−1.22065	−0.610327	−	0.792149i	$-0.708962\pi$
$821$	−1.30461e16	−1.22065	−0.610327	+	0.792149i	$0.708962\pi$
$822$	0	0
$823$	−9.40594e15	−0.868366	−0.434183	−	0.900825i	$-0.642963\pi$
$823$	−9.40594e15	−0.868366	−0.434183	+	0.900825i	$0.642963\pi$
$824$	−8.55380e14	−0.0784440
$825$	0	0
$826$	−3.78038e16	−3.42094
$827$	5.58618e15	0.502151	0.251076	−	0.967967i	$-0.419216\pi$
$827$	5.58618e15	0.502151	0.251076	+	0.967967i	$0.419216\pi$
$828$	0	0
$829$	1.46565e15	0.130011	0.0650054	−	0.997885i	$-0.479294\pi$
$829$	1.46565e15	0.130011	0.0650054	+	0.997885i	$0.479294\pi$
$830$	−3.33960e14	−0.0294283
$831$	0	0
$832$	8.44786e14	0.0734629
$833$	−1.30850e16	−1.13038
$834$	0	0
$835$	−7.56438e15	−0.644908
$836$	3.93854e14	0.0333580
$837$	0	0
$838$	6.02984e15	0.504039
$839$	2.31777e16	1.92477	0.962387	−	0.271684i	$-0.0875804\pi$
$839$	2.31777e16	1.92477	0.962387	+	0.271684i	$0.0875804\pi$
$840$	0	0
$841$	4.20707e14	0.0344828
$842$	6.73738e15	0.548623
$843$	0	0
$844$	−4.00706e15	−0.322064
$845$	6.46221e15	0.516023
$846$	0	0
$847$	2.24145e16	1.76673
$848$	−2.57845e15	−0.201921
$849$	0	0
$850$	−4.76286e15	−0.368183
$851$	6.13391e14	0.0471113
$852$	0	0
$853$	−1.62059e16	−1.22872	−0.614359	−	0.789027i	$-0.710585\pi$
$853$	−1.62059e16	−1.22872	−0.614359	+	0.789027i	$0.710585\pi$
$854$	2.11243e16	1.59134
$855$	0	0
$856$	1.66851e16	1.24086
$857$	1.76845e15	0.130677	0.0653383	−	0.997863i	$-0.479187\pi$
$857$	1.76845e15	0.130677	0.0653383	+	0.997863i	$0.479187\pi$
$858$	0	0
$859$	2.15096e16	1.56917	0.784586	−	0.620020i	$-0.212875\pi$
$859$	2.15096e16	1.56917	0.784586	+	0.620020i	$0.212875\pi$
$860$	2.76517e14	0.0200438
$861$	0	0
$862$	4.55974e15	0.326325
$863$	−2.05957e16	−1.46459	−0.732297	−	0.680986i	$-0.761552\pi$
$863$	−2.05957e16	−1.46459	−0.732297	+	0.680986i	$0.761552\pi$
$864$	0	0
$865$	2.01806e14	0.0141692
$866$	−1.67269e16	−1.16699
$867$	0	0
$868$	−2.35355e15	−0.162131
$869$	5.13306e15	0.351373
$870$	0	0
$871$	−2.79937e15	−0.189217
$872$	−5.29677e15	−0.355771
$873$	0	0
$874$	−1.74550e15	−0.115773
$875$	−2.59380e16	−1.70959
$876$	0	0
$877$	5.19470e15	0.338114	0.169057	−	0.985606i	$-0.445928\pi$
$877$	5.19470e15	0.338114	0.169057	+	0.985606i	$0.445928\pi$
$878$	−2.47644e16	−1.60180
$879$	0	0
$880$	−2.50100e15	−0.159757
$881$	1.55161e16	0.984952	0.492476	−	0.870326i	$-0.336092\pi$
$881$	1.55161e16	0.984952	0.492476	+	0.870326i	$0.336092\pi$
$882$	0	0
$883$	−1.33984e16	−0.839977	−0.419989	−	0.907529i	$-0.637966\pi$
$883$	−1.33984e16	−0.839977	−0.419989	+	0.907529i	$0.637966\pi$
$884$	−3.29355e14	−0.0205199
$885$	0	0
$886$	3.47730e15	0.213972
$887$	−4.71681e15	−0.288449	−0.144224	−	0.989545i	$-0.546069\pi$
$887$	−4.71681e15	−0.288449	−0.144224	+	0.989545i	$0.546069\pi$
$888$	0	0
$889$	−5.73000e16	−3.46095
$890$	4.02940e15	0.241878
$891$	0	0
$892$	−8.12095e15	−0.481504
$893$	−1.41662e15	−0.0834777
$894$	0	0
$895$	3.75049e15	0.218304
$896$	3.91112e16	2.26260
$897$	0	0
$898$	2.07828e16	1.18764
$899$	−8.79792e14	−0.0499691
$900$	0	0
$901$	−1.31158e15	−0.0735883
$902$	5.01774e15	0.279816
$903$	0	0
$904$	2.01624e16	1.11075
$905$	−1.71670e16	−0.939999
$906$	0	0
$907$	−4.70220e15	−0.254367	−0.127183	−	0.991879i	$-0.540594\pi$
$907$	−4.70220e15	−0.254367	−0.127183	+	0.991879i	$0.540594\pi$
$908$	−7.89724e15	−0.424623
$909$	0	0
$910$	−3.10349e15	−0.164863
$911$	−7.70359e15	−0.406763	−0.203382	−	0.979100i	$-0.565193\pi$
$911$	−7.70359e15	−0.406763	−0.203382	+	0.979100i	$0.565193\pi$
$912$	0	0
$913$	2.31937e14	0.0120999
$914$	−2.29835e16	−1.19182
$915$	0	0
$916$	6.16046e15	0.315637
$917$	−2.90175e16	−1.47784
$918$	0	0
$919$	2.83879e16	1.42856	0.714280	−	0.699860i	$-0.246754\pi$
$919$	2.83879e16	1.42856	0.714280	+	0.699860i	$0.246754\pi$
$920$	1.98057e15	0.0990735
$921$	0	0
$922$	3.43819e16	1.69945
$923$	5.18035e15	0.254536
$924$	0	0
$925$	2.91280e15	0.141427
$926$	7.37627e15	0.356022
$927$	0	0
$928$	−2.40396e15	−0.114660
$929$	2.43302e13	0.00115361	0.000576804	−	1.00000i	$-0.499816\pi$
$929$	2.43302e13	0.00115361	0.000576804		1.00000i	$0.499816\pi$
$930$	0	0
$931$	−2.27719e16	−1.06703
$932$	8.28214e15	0.385794
$933$	0	0
$934$	2.07512e16	0.955293
$935$	−1.27219e15	−0.0582219
$936$	0	0
$937$	−6.94518e15	−0.314135	−0.157067	−	0.987588i	$-0.550204\pi$
$937$	−6.94518e15	−0.314135	−0.157067	+	0.987588i	$0.550204\pi$
$938$	−6.29871e16	−2.83228
$939$	0	0
$940$	−7.56054e14	−0.0336008
$941$	3.11414e16	1.37593	0.687963	−	0.725745i	$-0.258505\pi$
$941$	3.11414e16	1.37593	0.687963	+	0.725745i	$0.258505\pi$
$942$	0	0
$943$	−5.38965e15	−0.235367
$944$	4.43357e16	1.92490
$945$	0	0
$946$	−7.92375e14	−0.0340039
$947$	3.66620e16	1.56420	0.782098	−	0.623155i	$-0.214149\pi$
$947$	3.66620e16	1.56420	0.782098	+	0.623155i	$0.214149\pi$
$948$	0	0
$949$	4.76413e15	0.200918
$950$	−8.28884e15	−0.347547
$951$	0	0
$952$	1.57553e16	0.653015
$953$	−1.01542e16	−0.418440	−0.209220	−	0.977869i	$-0.567092\pi$
$953$	−1.01542e16	−0.418440	−0.209220	+	0.977869i	$0.567092\pi$
$954$	0	0
$955$	−1.26734e16	−0.516268
$956$	8.03683e15	0.325512
$957$	0	0
$958$	1.90277e16	0.761860
$959$	−2.48554e16	−0.989507
$960$	0	0
$961$	−2.35686e16	−0.927589
$962$	8.31074e14	0.0325220
$963$	0	0
$964$	−1.89388e15	−0.0732702
$965$	−6.95183e15	−0.267423
$966$	0	0
$967$	−3.28531e16	−1.24949	−0.624743	−	0.780830i	$-0.714796\pi$
$967$	−3.28531e16	−1.24949	−0.624743	+	0.780830i	$0.714796\pi$
$968$	−1.93808e16	−0.732923
$969$	0	0
$970$	1.95869e16	0.732355
$971$	2.39850e16	0.891732	0.445866	−	0.895100i	$-0.352896\pi$
$971$	2.39850e16	0.891732	0.445866	+	0.895100i	$0.352896\pi$
$972$	0	0
$973$	−3.16475e16	−1.16337
$974$	−3.01884e16	−1.10348
$975$	0	0
$976$	−2.47742e16	−0.895419
$977$	1.64069e16	0.589667	0.294834	−	0.955549i	$-0.404736\pi$
$977$	1.64069e16	0.589667	0.294834	+	0.955549i	$0.404736\pi$
$978$	0	0
$979$	−2.79845e15	−0.0994517
$980$	−1.21534e16	−0.429491
$981$	0	0
$982$	3.51200e16	1.22727
$983$	4.35578e16	1.51364	0.756818	−	0.653626i	$-0.226753\pi$
$983$	4.35578e16	1.51364	0.756818	+	0.653626i	$0.226753\pi$
$984$	0	0
$985$	2.58387e16	0.887917
$986$	−2.77020e15	−0.0946648
$987$	0	0
$988$	−5.73178e14	−0.0193698
$989$	8.51103e14	0.0286024
$990$	0	0
$991$	−2.49086e16	−0.827835	−0.413918	−	0.910314i	$-0.635840\pi$
$991$	−2.49086e16	−0.827835	−0.413918	+	0.910314i	$0.635840\pi$
$992$	5.02721e15	0.166155
$993$	0	0
$994$	1.16560e17	3.81000
$995$	−7.31584e15	−0.237814
$996$	0	0
$997$	−2.41171e16	−0.775358	−0.387679	−	0.921795i	$-0.626723\pi$
$997$	−2.41171e16	−0.775358	−0.387679	+	0.921795i	$0.626723\pi$
$998$	3.06492e16	0.979943
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q-51.9918 q^{2} +655.142 q^{4} -3682.79 q^{5} -83752.5 q^{7} +72417.1 q^{8} +O(q^{10})\)	\(q-51.9918 q^{2} +655.142 q^{4} -3682.79 q^{5} -83752.5 q^{7} +72417.1 q^{8} +191474. q^{10} -132980. q^{11} +193527. q^{13} +4.35444e6 q^{14} -5.10682e6 q^{16} -2.59769e6 q^{17} -4.52077e6 q^{19} -2.41275e6 q^{20} +6.91387e6 q^{22} -7.42631e6 q^{23} -3.52652e7 q^{25} -1.00618e7 q^{26} -5.48698e7 q^{28} -2.05111e7 q^{29} +4.28934e7 q^{31} +1.17202e8 q^{32} +1.35058e8 q^{34} +3.08443e8 q^{35} -8.25971e7 q^{37} +2.35043e8 q^{38} -2.66697e8 q^{40} +7.25750e8 q^{41} -1.14606e8 q^{43} -8.71209e7 q^{44} +3.86107e8 q^{46} +3.13358e8 q^{47} +5.03716e9 q^{49} +1.83350e9 q^{50} +1.26788e8 q^{52} +5.04903e8 q^{53} +4.89737e8 q^{55} -6.06512e9 q^{56} +1.06641e9 q^{58} -8.68166e9 q^{59} +4.85120e9 q^{61} -2.23010e9 q^{62} +4.36521e9 q^{64} -7.12717e8 q^{65} -1.44650e10 q^{67} -1.70186e9 q^{68} -1.60365e10 q^{70} +2.67681e10 q^{71} +2.46174e10 q^{73} +4.29437e9 q^{74} -2.96175e9 q^{76} +1.11374e10 q^{77} -3.86002e10 q^{79} +1.88073e10 q^{80} -3.77330e10 q^{82} -1.74415e9 q^{83} +9.56673e9 q^{85} +5.95859e9 q^{86} -9.63004e9 q^{88} +2.10441e10 q^{89} -1.62084e10 q^{91} -4.86529e9 q^{92} -1.62920e10 q^{94} +1.66490e10 q^{95} +1.02295e11 q^{97} -2.61891e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) \) 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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