LMFDB - Embedded newform 117.10.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,10,Mod(1,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("117.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	117.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:	$60.2591928312$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 $ x^5 - 1438x^3 - 4164x^2 + 396957*x - 59580
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.150341$ of defining polynomial
Character	$\chi$	$=$	117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.15034 q^{2} -502.075 q^{4} -2554.62 q^{5} +9399.91 q^{7} +3194.68 q^{8} +O(q^{10})$	\(q-3.15034 q^{2} -502.075 q^{4} -2554.62 q^{5} +9399.91 q^{7} +3194.68 q^{8} +8047.92 q^{10} -44094.1 q^{11} +28561.0 q^{13} -29612.9 q^{14} +246998. q^{16} -28289.4 q^{17} +273836. q^{19} +1.28261e6 q^{20} +138911. q^{22} +1.12921e6 q^{23} +4.57295e6 q^{25} -89976.9 q^{26} -4.71947e6 q^{28} +1.63691e6 q^{29} +6.65402e6 q^{31} -2.41381e6 q^{32} +89121.2 q^{34} -2.40132e7 q^{35} -1.71193e7 q^{37} -862677. q^{38} -8.16119e6 q^{40} +5.15179e6 q^{41} -1.97275e7 q^{43} +2.21386e7 q^{44} -3.55739e6 q^{46} -4.82947e7 q^{47} +4.80048e7 q^{49} -1.44063e7 q^{50} -1.43398e7 q^{52} +3.06731e7 q^{53} +1.12644e8 q^{55} +3.00298e7 q^{56} -5.15683e6 q^{58} +1.15154e7 q^{59} -3.62567e7 q^{61} -2.09624e7 q^{62} -1.18859e8 q^{64} -7.29624e7 q^{65} -6.48390e7 q^{67} +1.42034e7 q^{68} +7.56497e7 q^{70} +1.47071e8 q^{71} -3.37321e8 q^{73} +5.39317e7 q^{74} -1.37486e8 q^{76} -4.14481e8 q^{77} -2.04060e8 q^{79} -6.30986e8 q^{80} -1.62299e7 q^{82} -7.61700e8 q^{83} +7.22685e7 q^{85} +6.21484e7 q^{86} -1.40867e8 q^{88} +8.29058e8 q^{89} +2.68471e8 q^{91} -5.66948e8 q^{92} +1.52145e8 q^{94} -6.99547e8 q^{95} +1.00647e9 q^{97} -1.51231e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8}+O(q^{10}) $ 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8} + 84505 q^{10} - 121746 q^{11} + 142805 q^{13} - 8475 q^{14} - 322463 q^{16} + 495669 q^{17} - 840738 q^{19} + 1595607 q^{20} - 2023594 q^{22} + 592152 q^{23} + 1670362 q^{25} - 428415 q^{26} + 2587955 q^{28} - 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 9934079 q^{34} - 8380731 q^{35} + 7171823 q^{37} + 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} + 12831975 q^{43} + 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 25249488 q^{49} + 16270770 q^{50} + 10310521 q^{52} - 93231780 q^{53} + 99448846 q^{55} - 199599225 q^{56} + 151020970 q^{58} - 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 91019105 q^{64} - 51495483 q^{65} - 369388534 q^{67} - 238172073 q^{68} - 144857425 q^{70} - 212150457 q^{71} - 252729806 q^{73} - 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} + 169559388 q^{82} - 1696894296 q^{83} - 775363765 q^{85} - 3291621459 q^{86} - 220227222 q^{88} + 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 272071215 q^{94} - 1442632962 q^{95} + 3824606 q^{97} - 1570614816 q^{98}+O(q^{100}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8 + 84505 * q^10 - 121746 * q^11 + 142805 * q^13 - 8475 * q^14 - 322463 * q^16 + 495669 * q^17 - 840738 * q^19 + 1595607 * q^20 - 2023594 * q^22 + 592152 * q^23 + 1670362 * q^25 - 428415 * q^26 + 2587955 * q^28 - 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 9934079 * q^34 - 8380731 * q^35 + 7171823 * q^37 + 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 + 12831975 * q^43 + 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 25249488 * q^49 + 16270770 * q^50 + 10310521 * q^52 - 93231780 * q^53 + 99448846 * q^55 - 199599225 * q^56 + 151020970 * q^58 - 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 91019105 * q^64 - 51495483 * q^65 - 369388534 * q^67 - 238172073 * q^68 - 144857425 * q^70 - 212150457 * q^71 - 252729806 * q^73 - 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 + 169559388 * q^82 - 1696894296 * q^83 - 775363765 * q^85 - 3291621459 * q^86 - 220227222 * q^88 + 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 272071215 * q^94 - 1442632962 * q^95 + 3824606 * q^97 - 1570614816 * 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 $

$2$	−3.15034	−0.139227	−0.0696134	−	0.997574i	$-0.522177\pi$
$2$	−3.15034	−0.139227	−0.0696134	+	0.997574i	$0.522177\pi$
$3$	0	0
$3$	0	0
$4$	−502.075	−0.980616
$5$	−2554.62	−1.82794	−0.913968	−	0.405787i	$-0.866998\pi$
$5$	−2554.62	−1.82794	−0.913968	+	0.405787i	$0.866998\pi$
$6$	0	0
$7$	9399.91	1.47973	0.739865	−	0.672755i	$-0.234889\pi$
$7$	9399.91	1.47973	0.739865	+	0.672755i	$0.234889\pi$
$8$	3194.68	0.275755
$9$	0	0
$10$	8047.92	0.254498
$11$	−44094.1	−0.908058	−0.454029	−	0.890987i	$-0.650014\pi$
$11$	−44094.1	−0.908058	−0.454029	+	0.890987i	$0.650014\pi$
$12$	0	0
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−29612.9	−0.206018
$15$	0	0
$16$	246998.	0.942223
$17$	−28289.4	−0.0821492	−0.0410746	−	0.999156i	$-0.513078\pi$
$17$	−28289.4	−0.0821492	−0.0410746	+	0.999156i	$0.513078\pi$
$18$	0	0
$19$	273836.	0.482058	0.241029	−	0.970518i	$-0.422515\pi$
$19$	273836.	0.482058	0.241029	+	0.970518i	$0.422515\pi$
$20$	1.28261e6	1.79250
$21$	0	0
$22$	138911.	0.126426
$23$	1.12921e6	0.841393	0.420697	−	0.907201i	$-0.361786\pi$
$23$	1.12921e6	0.841393	0.420697	+	0.907201i	$0.361786\pi$
$24$	0	0
$25$	4.57295e6	2.34135
$26$	−89976.9	−0.0386145
$27$	0	0
$28$	−4.71947e6	−1.45105
$29$	1.63691e6	0.429768	0.214884	−	0.976640i	$-0.431063\pi$
$29$	1.63691e6	0.429768	0.214884	+	0.976640i	$0.431063\pi$
$30$	0	0
$31$	6.65402e6	1.29407	0.647033	−	0.762462i	$-0.276009\pi$
$31$	6.65402e6	1.29407	0.647033	+	0.762462i	$0.276009\pi$
$32$	−2.41381e6	−0.406937
$33$	0	0
$34$	89121.2	0.0114374
$35$	−2.40132e7	−2.70485
$36$	0	0
$37$	−1.71193e7	−1.50169	−0.750843	−	0.660481i	$-0.770352\pi$
$37$	−1.71193e7	−1.50169	−0.750843	+	0.660481i	$0.770352\pi$
$38$	−862677.	−0.0671154
$39$	0	0
$40$	−8.16119e6	−0.504062
$41$	5.15179e6	0.284728	0.142364	−	0.989814i	$-0.454530\pi$
$41$	5.15179e6	0.284728	0.142364	+	0.989814i	$0.454530\pi$
$42$	0	0
$43$	−1.97275e7	−0.879962	−0.439981	−	0.898007i	$-0.645015\pi$
$43$	−1.97275e7	−0.879962	−0.439981	+	0.898007i	$0.645015\pi$
$44$	2.21386e7	0.890456
$45$	0	0
$46$	−3.55739e6	−0.117144
$47$	−4.82947e7	−1.44364	−0.721821	−	0.692080i	$-0.756695\pi$
$47$	−4.82947e7	−1.44364	−0.721821	+	0.692080i	$0.756695\pi$
$48$	0	0
$49$	4.80048e7	1.18960
$50$	−1.44063e7	−0.325978
$51$	0	0
$52$	−1.43398e7	−0.271974
$53$	3.06731e7	0.533970	0.266985	−	0.963701i	$-0.413973\pi$
$53$	3.06731e7	0.533970	0.266985	+	0.963701i	$0.413973\pi$
$54$	0	0
$55$	1.12644e8	1.65987
$56$	3.00298e7	0.408043
$57$	0	0
$58$	−5.15683e6	−0.0598352
$59$	1.15154e7	0.123722	0.0618609	−	0.998085i	$-0.480296\pi$
$59$	1.15154e7	0.123722	0.0618609	+	0.998085i	$0.480296\pi$
$60$	0	0
$61$	−3.62567e7	−0.335277	−0.167639	−	0.985849i	$-0.553614\pi$
$61$	−3.62567e7	−0.335277	−0.167639	+	0.985849i	$0.553614\pi$
$62$	−2.09624e7	−0.180169
$63$	0	0
$64$	−1.18859e8	−0.885567
$65$	−7.29624e7	−0.506978
$66$	0	0
$67$	−6.48390e7	−0.393097	−0.196548	−	0.980494i	$-0.562973\pi$
$67$	−6.48390e7	−0.393097	−0.196548	+	0.980494i	$0.562973\pi$
$68$	1.42034e7	0.0805568
$69$	0	0
$70$	7.56497e7	0.376588
$71$	1.47071e8	0.686853	0.343427	−	0.939180i	$-0.388412\pi$
$71$	1.47071e8	0.686853	0.343427	+	0.939180i	$0.388412\pi$
$72$	0	0
$73$	−3.37321e8	−1.39024	−0.695122	−	0.718892i	$-0.744650\pi$
$73$	−3.37321e8	−1.39024	−0.695122	+	0.718892i	$0.744650\pi$
$74$	5.39317e7	0.209075
$75$	0	0
$76$	−1.37486e8	−0.472714
$77$	−4.14481e8	−1.34368
$78$	0	0
$79$	−2.04060e8	−0.589436	−0.294718	−	0.955584i	$-0.595226\pi$
$79$	−2.04060e8	−0.589436	−0.294718	+	0.955584i	$0.595226\pi$
$80$	−6.30986e8	−1.72232
$81$	0	0
$82$	−1.62299e7	−0.0396418
$83$	−7.61700e8	−1.76170	−0.880851	−	0.473394i	$-0.843029\pi$
$83$	−7.61700e8	−1.76170	−0.880851	+	0.473394i	$0.843029\pi$
$84$	0	0
$85$	7.22685e7	0.150163
$86$	6.21484e7	0.122514
$87$	0	0
$88$	−1.40867e8	−0.250401
$89$	8.29058e8	1.40065	0.700326	−	0.713823i	$-0.253038\pi$
$89$	8.29058e8	1.40065	0.700326	+	0.713823i	$0.253038\pi$
$90$	0	0
$91$	2.68471e8	0.410403
$92$	−5.66948e8	−0.825084
$93$	0	0
$94$	1.52145e8	0.200994
$95$	−6.99547e8	−0.881172
$96$	0	0
$97$	1.00647e9	1.15432	0.577161	−	0.816631i	$-0.304161\pi$
$97$	1.00647e9	1.15432	0.577161	+	0.816631i	$0.304161\pi$
$98$	−1.51231e8	−0.165625
$99$	0	0
$100$	−2.29596e9	−2.29596
$101$	−1.59054e9	−1.52089	−0.760446	−	0.649401i	$-0.775020\pi$
$101$	−1.59054e9	−1.52089	−0.760446	+	0.649401i	$0.775020\pi$
$102$	0	0
$103$	1.13889e9	0.997040	0.498520	−	0.866878i	$-0.333877\pi$
$103$	1.13889e9	0.997040	0.498520	+	0.866878i	$0.333877\pi$
$104$	9.12434e7	0.0764806
$105$	0	0
$106$	−9.66309e7	−0.0743429
$107$	7.21432e8	0.532069	0.266035	−	0.963963i	$-0.414286\pi$
$107$	7.21432e8	0.532069	0.266035	+	0.963963i	$0.414286\pi$
$108$	0	0
$109$	−6.86462e8	−0.465798	−0.232899	−	0.972501i	$-0.574821\pi$
$109$	−6.86462e8	−0.465798	−0.232899	+	0.972501i	$0.574821\pi$
$110$	−3.54866e8	−0.231098
$111$	0	0
$112$	2.32176e9	1.39424
$113$	8.33795e8	0.481068	0.240534	−	0.970641i	$-0.422677\pi$
$113$	8.33795e8	0.481068	0.240534	+	0.970641i	$0.422677\pi$
$114$	0	0
$115$	−2.88470e9	−1.53801
$116$	−8.21852e8	−0.421437
$117$	0	0
$118$	−3.62775e7	−0.0172254
$119$	−2.65918e8	−0.121559
$120$	0	0
$121$	−4.13658e8	−0.175431
$122$	1.14221e8	0.0466796
$123$	0	0
$124$	−3.34082e9	−1.26898
$125$	−6.69264e9	−2.45190
$126$	0	0
$127$	−4.01307e8	−0.136886	−0.0684431	−	0.997655i	$-0.521803\pi$
$127$	−4.01307e8	−0.136886	−0.0684431	+	0.997655i	$0.521803\pi$
$128$	1.61031e9	0.530232
$129$	0	0
$130$	2.29857e8	0.0705849
$131$	3.78377e9	1.12255	0.561273	−	0.827631i	$-0.310312\pi$
$131$	3.78377e9	1.12255	0.561273	+	0.827631i	$0.310312\pi$
$132$	0	0
$133$	2.57404e9	0.713317
$134$	2.04265e8	0.0547296
$135$	0	0
$136$	−9.03756e7	−0.0226530
$137$	−1.45518e9	−0.352919	−0.176459	−	0.984308i	$-0.556464\pi$
$137$	−1.45518e9	−0.352919	−0.176459	+	0.984308i	$0.556464\pi$
$138$	0	0
$139$	1.50381e9	0.341685	0.170842	−	0.985298i	$-0.445351\pi$
$139$	1.50381e9	0.341685	0.170842	+	0.985298i	$0.445351\pi$
$140$	1.20564e10	2.65242
$141$	0	0
$142$	−4.63323e8	−0.0956283
$143$	−1.25937e9	−0.251850
$144$	0	0
$145$	−4.18168e9	−0.785588
$146$	1.06268e9	0.193559
$147$	0	0
$148$	8.59520e9	1.47258
$149$	4.28624e9	0.712423	0.356212	−	0.934405i	$-0.384068\pi$
$149$	4.28624e9	0.712423	0.356212	+	0.934405i	$0.384068\pi$
$150$	0	0
$151$	4.79918e8	0.0751226	0.0375613	−	0.999294i	$-0.488041\pi$
$151$	4.79918e8	0.0751226	0.0375613	+	0.999294i	$0.488041\pi$
$152$	8.74820e8	0.132930
$153$	0	0
$154$	1.30576e9	0.187076
$155$	−1.69985e10	−2.36547
$156$	0	0
$157$	−8.24624e9	−1.08320	−0.541598	−	0.840637i	$-0.682181\pi$
$157$	−8.24624e9	−1.08320	−0.541598	+	0.840637i	$0.682181\pi$
$158$	6.42860e8	0.0820652
$159$	0	0
$160$	6.16635e9	0.743855
$161$	1.06145e10	1.24504
$162$	0	0
$163$	−5.93537e9	−0.658573	−0.329286	−	0.944230i	$-0.606808\pi$
$163$	−5.93537e9	−0.658573	−0.329286	+	0.944230i	$0.606808\pi$
$164$	−2.58659e9	−0.279209
$165$	0	0
$166$	2.39961e9	0.245276
$167$	7.41172e9	0.737386	0.368693	−	0.929551i	$-0.379805\pi$
$167$	7.41172e9	0.737386	0.368693	+	0.929551i	$0.379805\pi$
$168$	0	0
$169$	8.15731e8	0.0769231
$170$	−2.27671e8	−0.0209068
$171$	0	0
$172$	9.90469e9	0.862905
$173$	−5.63923e9	−0.478643	−0.239322	−	0.970940i	$-0.576925\pi$
$173$	−5.63923e9	−0.478643	−0.239322	+	0.970940i	$0.576925\pi$
$174$	0	0
$175$	4.29853e10	3.46457
$176$	−1.08912e10	−0.855593
$177$	0	0
$178$	−2.61182e9	−0.195008
$179$	−1.23881e10	−0.901916	−0.450958	−	0.892545i	$-0.648918\pi$
$179$	−1.23881e10	−0.901916	−0.450958	+	0.892545i	$0.648918\pi$
$180$	0	0
$181$	−2.45852e10	−1.70263	−0.851314	−	0.524657i	$-0.824194\pi$
$181$	−2.45852e10	−1.70263	−0.851314	+	0.524657i	$0.824194\pi$
$182$	−8.45775e8	−0.0571391
$183$	0	0
$184$	3.60746e9	0.232018
$185$	4.37334e10	2.74499
$186$	0	0
$187$	1.24739e9	0.0745962
$188$	2.42476e10	1.41566
$189$	0	0
$190$	2.20381e9	0.122683
$191$	1.06604e10	0.579592	0.289796	−	0.957088i	$-0.406413\pi$
$191$	1.06604e10	0.579592	0.289796	+	0.957088i	$0.406413\pi$
$192$	0	0
$193$	−2.09640e10	−1.08759	−0.543797	−	0.839217i	$-0.683014\pi$
$193$	−2.09640e10	−1.08759	−0.543797	+	0.839217i	$0.683014\pi$
$194$	−3.17071e9	−0.160712
$195$	0	0
$196$	−2.41020e10	−1.16654
$197$	−1.27051e10	−0.601009	−0.300504	−	0.953780i	$-0.597155\pi$
$197$	−1.27051e10	−0.601009	−0.300504	+	0.953780i	$0.597155\pi$
$198$	0	0
$199$	2.57825e9	0.116543	0.0582715	−	0.998301i	$-0.481441\pi$
$199$	2.57825e9	0.116543	0.0582715	+	0.998301i	$0.481441\pi$
$200$	1.46091e10	0.645638
$201$	0	0
$202$	5.01075e9	0.211749
$203$	1.53868e10	0.635941
$204$	0	0
$205$	−1.31608e10	−0.520465
$206$	−3.58788e9	−0.138815
$207$	0	0
$208$	7.05452e9	0.261326
$209$	−1.20746e10	−0.437737
$210$	0	0
$211$	1.94301e10	0.674846	0.337423	−	0.941353i	$-0.390445\pi$
$211$	1.94301e10	0.674846	0.337423	+	0.941353i	$0.390445\pi$
$212$	−1.54002e10	−0.523620
$213$	0	0
$214$	−2.27276e9	−0.0740783
$215$	5.03962e10	1.60851
$216$	0	0
$217$	6.25472e10	1.91487
$218$	2.16259e9	0.0648515
$219$	0	0
$220$	−5.65556e10	−1.62770
$221$	−8.07973e8	−0.0227841
$222$	0	0
$223$	9.56077e9	0.258893	0.129447	−	0.991586i	$-0.458680\pi$
$223$	9.56077e9	0.258893	0.129447	+	0.991586i	$0.458680\pi$
$224$	−2.26896e10	−0.602158
$225$	0	0
$226$	−2.62674e9	−0.0669775
$227$	2.02032e10	0.505015	0.252507	−	0.967595i	$-0.418745\pi$
$227$	2.02032e10	0.505015	0.252507	+	0.967595i	$0.418745\pi$
$228$	0	0
$229$	−2.45816e10	−0.590678	−0.295339	−	0.955392i	$-0.595433\pi$
$229$	−2.45816e10	−0.590678	−0.295339	+	0.955392i	$0.595433\pi$
$230$	9.08778e9	0.214132
$231$	0	0
$232$	5.22941e9	0.118510
$233$	−7.93260e10	−1.76325	−0.881625	−	0.471951i	$-0.843550\pi$
$233$	−7.93260e10	−1.76325	−0.881625	+	0.471951i	$0.843550\pi$
$234$	0	0
$235$	1.23375e11	2.63888
$236$	−5.78161e9	−0.121324
$237$	0	0
$238$	8.37732e8	0.0169242
$239$	2.62515e10	0.520431	0.260215	−	0.965551i	$-0.416206\pi$
$239$	2.62515e10	0.520431	0.260215	+	0.965551i	$0.416206\pi$
$240$	0	0
$241$	−1.00766e11	−1.92415	−0.962074	−	0.272787i	$-0.912055\pi$
$241$	−1.00766e11	−1.92415	−0.962074	+	0.272787i	$0.912055\pi$
$242$	1.30316e9	0.0244247
$243$	0	0
$244$	1.82036e10	0.328778
$245$	−1.22634e11	−2.17452
$246$	0	0
$247$	7.82103e9	0.133699
$248$	2.12575e10	0.356845
$249$	0	0
$250$	2.10841e10	0.341370
$251$	8.72780e10	1.38795	0.693973	−	0.720001i	$-0.255858\pi$
$251$	8.72780e10	1.38795	0.693973	+	0.720001i	$0.255858\pi$
$252$	0	0
$253$	−4.97914e10	−0.764034
$254$	1.26425e9	0.0190582
$255$	0	0
$256$	5.57827e10	0.811744
$257$	−4.84205e10	−0.692358	−0.346179	−	0.938169i	$-0.612521\pi$
$257$	−4.84205e10	−0.692358	−0.346179	+	0.938169i	$0.612521\pi$
$258$	0	0
$259$	−1.60920e11	−2.22209
$260$	3.66326e10	0.497151
$261$	0	0
$262$	−1.19202e10	−0.156288
$263$	4.40656e9	0.0567935	0.0283968	−	0.999597i	$-0.490960\pi$
$263$	4.40656e9	0.0567935	0.0283968	+	0.999597i	$0.490960\pi$
$264$	0	0
$265$	−7.83582e10	−0.976063
$266$	−8.10909e9	−0.0993127
$267$	0	0
$268$	3.25540e10	0.385477
$269$	−1.41879e11	−1.65209	−0.826045	−	0.563604i	$-0.809414\pi$
$269$	−1.41879e11	−1.65209	−0.826045	+	0.563604i	$0.809414\pi$
$270$	0	0
$271$	−7.09707e10	−0.799313	−0.399657	−	0.916665i	$-0.630871\pi$
$271$	−7.09707e10	−0.799313	−0.399657	+	0.916665i	$0.630871\pi$
$272$	−6.98743e9	−0.0774029
$273$	0	0
$274$	4.58432e9	0.0491357
$275$	−2.01640e11	−2.12608
$276$	0	0
$277$	1.22293e11	1.24808	0.624039	−	0.781393i	$-0.285491\pi$
$277$	1.22293e11	1.24808	0.624039	+	0.781393i	$0.285491\pi$
$278$	−4.73751e9	−0.0475717
$279$	0	0
$280$	−7.67145e10	−0.745876
$281$	9.91936e10	0.949085	0.474543	−	0.880233i	$-0.342613\pi$
$281$	9.91936e10	0.949085	0.474543	+	0.880233i	$0.342613\pi$
$282$	0	0
$283$	1.89673e11	1.75779	0.878893	−	0.477019i	$-0.158283\pi$
$283$	1.89673e11	1.75779	0.878893	+	0.477019i	$0.158283\pi$
$284$	−7.38406e10	−0.673539
$285$	0	0
$286$	3.96745e9	0.0350642
$287$	4.84264e10	0.421321
$288$	0	0
$289$	−1.17788e11	−0.993252
$290$	1.31737e10	0.109375
$291$	0	0
$292$	1.69361e11	1.36329
$293$	−1.95772e11	−1.55183	−0.775917	−	0.630835i	$-0.782713\pi$
$293$	−1.95772e11	−1.55183	−0.775917	+	0.630835i	$0.782713\pi$
$294$	0	0
$295$	−2.94175e10	−0.226155
$296$	−5.46908e10	−0.414097
$297$	0	0
$298$	−1.35031e10	−0.0991884
$299$	3.22513e10	0.233360
$300$	0	0
$301$	−1.85437e11	−1.30211
$302$	−1.51190e9	−0.0104591
$303$	0	0
$304$	6.76370e10	0.454207
$305$	9.26220e10	0.612865
$306$	0	0
$307$	−7.17504e10	−0.461001	−0.230500	−	0.973072i	$-0.574036\pi$
$307$	−7.17504e10	−0.461001	−0.230500	+	0.973072i	$0.574036\pi$
$308$	2.08101e11	1.31763
$309$	0	0
$310$	5.35510e10	0.329337
$311$	−2.11023e10	−0.127911	−0.0639554	−	0.997953i	$-0.520372\pi$
$311$	−2.11023e10	−0.127911	−0.0639554	+	0.997953i	$0.520372\pi$
$312$	0	0
$313$	−1.44667e11	−0.851963	−0.425982	−	0.904732i	$-0.640071\pi$
$313$	−1.44667e11	−0.851963	−0.425982	+	0.904732i	$0.640071\pi$
$314$	2.59785e10	0.150810
$315$	0	0
$316$	1.02454e11	0.578010
$317$	−5.78709e10	−0.321880	−0.160940	−	0.986964i	$-0.551453\pi$
$317$	−5.78709e10	−0.321880	−0.160940	+	0.986964i	$0.551453\pi$
$318$	0	0
$319$	−7.21781e10	−0.390254
$320$	3.03639e11	1.61876
$321$	0	0
$322$	−3.34392e10	−0.173342
$323$	−7.74665e9	−0.0396007
$324$	0	0
$325$	1.30608e11	0.649373
$326$	1.86984e10	0.0916909
$327$	0	0
$328$	1.64583e10	0.0785151
$329$	−4.53966e11	−2.13620
$330$	0	0
$331$	−1.00283e11	−0.459199	−0.229600	−	0.973285i	$-0.573742\pi$
$331$	−1.00283e11	−0.459199	−0.229600	+	0.973285i	$0.573742\pi$
$332$	3.82431e11	1.72755
$333$	0	0
$334$	−2.33495e10	−0.102664
$335$	1.65639e11	0.718555
$336$	0	0
$337$	−5.73297e10	−0.242128	−0.121064	−	0.992645i	$-0.538631\pi$
$337$	−5.73297e10	−0.242128	−0.121064	+	0.992645i	$0.538631\pi$
$338$	−2.56983e9	−0.0107097
$339$	0	0
$340$	−3.62843e10	−0.147253
$341$	−2.93403e11	−1.17509
$342$	0	0
$343$	7.19204e10	0.280562
$344$	−6.30231e10	−0.242654
$345$	0	0
$346$	1.77655e10	0.0666399
$347$	2.34072e10	0.0866695	0.0433347	−	0.999061i	$-0.486202\pi$
$347$	2.34072e10	0.0866695	0.0433347	+	0.999061i	$0.486202\pi$
$348$	0	0
$349$	3.92804e11	1.41730	0.708649	−	0.705562i	$-0.249305\pi$
$349$	3.92804e11	1.41730	0.708649	+	0.705562i	$0.249305\pi$
$350$	−1.35418e11	−0.482360
$351$	0	0
$352$	1.06435e11	0.369523
$353$	−2.16422e11	−0.741849	−0.370925	−	0.928663i	$-0.620959\pi$
$353$	−2.16422e11	−0.741849	−0.370925	+	0.928663i	$0.620959\pi$
$354$	0	0
$355$	−3.75710e11	−1.25552
$356$	−4.16250e11	−1.37350
$357$	0	0
$358$	3.90267e10	0.125571
$359$	−3.49576e11	−1.11075	−0.555376	−	0.831600i	$-0.687426\pi$
$359$	−3.49576e11	−1.11075	−0.555376	+	0.831600i	$0.687426\pi$
$360$	0	0
$361$	−2.47701e11	−0.767620
$362$	7.74517e10	0.237051
$363$	0	0
$364$	−1.34793e11	−0.402448
$365$	8.61727e11	2.54128
$366$	0	0
$367$	−1.83237e9	−0.00527248	−0.00263624	−	0.999997i	$-0.500839\pi$
$367$	−1.83237e9	−0.00527248	−0.00263624	+	0.999997i	$0.500839\pi$
$368$	2.78913e11	0.792780
$369$	0	0
$370$	−1.37775e11	−0.382175
$371$	2.88325e11	0.790132
$372$	0	0
$373$	5.52030e10	0.147663	0.0738317	−	0.997271i	$-0.476477\pi$
$373$	5.52030e10	0.147663	0.0738317	+	0.997271i	$0.476477\pi$
$374$	−3.92972e9	−0.0103858
$375$	0	0
$376$	−1.54286e11	−0.398091
$377$	4.67518e10	0.119196
$378$	0	0
$379$	2.25258e11	0.560795	0.280397	−	0.959884i	$-0.409534\pi$
$379$	2.25258e11	0.560795	0.280397	+	0.959884i	$0.409534\pi$
$380$	3.51225e11	0.864091
$381$	0	0
$382$	−3.35838e10	−0.0806947
$383$	−4.64079e11	−1.10204	−0.551020	−	0.834492i	$-0.685761\pi$
$383$	−4.64079e11	−1.10204	−0.551020	+	0.834492i	$0.685761\pi$
$384$	0	0
$385$	1.05884e12	2.45616
$386$	6.60438e10	0.151422
$387$	0	0
$388$	−5.05322e11	−1.13195
$389$	2.63061e11	0.582482	0.291241	−	0.956650i	$-0.405932\pi$
$389$	2.63061e11	0.582482	0.291241	+	0.956650i	$0.405932\pi$
$390$	0	0
$391$	−3.19446e10	−0.0691198
$392$	1.53360e11	0.328039
$393$	0	0
$394$	4.00255e10	0.0836765
$395$	5.21296e11	1.07745
$396$	0	0
$397$	−1.80382e10	−0.0364449	−0.0182224	−	0.999834i	$-0.505801\pi$
$397$	−1.80382e10	−0.0364449	−0.0182224	+	0.999834i	$0.505801\pi$
$398$	−8.12236e9	−0.0162259
$399$	0	0
$400$	1.12951e12	2.20607
$401$	−7.18792e10	−0.138821	−0.0694103	−	0.997588i	$-0.522112\pi$
$401$	−7.18792e10	−0.138821	−0.0694103	+	0.997588i	$0.522112\pi$
$402$	0	0
$403$	1.90046e11	0.358910
$404$	7.98571e11	1.49141
$405$	0	0
$406$	−4.84737e10	−0.0885399
$407$	7.54862e11	1.36362
$408$	0	0
$409$	5.31862e11	0.939819	0.469910	−	0.882715i	$-0.344287\pi$
$409$	5.31862e11	0.939819	0.469910	+	0.882715i	$0.344287\pi$
$410$	4.14612e10	0.0724626
$411$	0	0
$412$	−5.71806e11	−0.977713
$413$	1.08244e11	0.183075
$414$	0	0
$415$	1.94585e12	3.22028
$416$	−6.89407e10	−0.112864
$417$	0	0
$418$	3.80390e10	0.0609446
$419$	−1.45942e11	−0.231322	−0.115661	−	0.993289i	$-0.536899\pi$
$419$	−1.45942e11	−0.231322	−0.115661	+	0.993289i	$0.536899\pi$
$420$	0	0
$421$	3.66247e11	0.568204	0.284102	−	0.958794i	$-0.408305\pi$
$421$	3.66247e11	0.568204	0.284102	+	0.958794i	$0.408305\pi$
$422$	−6.12115e10	−0.0939565
$423$	0	0
$424$	9.79910e10	0.147245
$425$	−1.29366e11	−0.192340
$426$	0	0
$427$	−3.40810e11	−0.496120
$428$	−3.62213e11	−0.521756
$429$	0	0
$430$	−1.58765e11	−0.223948
$431$	−7.66389e11	−1.06980	−0.534899	−	0.844916i	$-0.679650\pi$
$431$	−7.66389e11	−1.06980	−0.534899	+	0.844916i	$0.679650\pi$
$432$	0	0
$433$	−1.24176e12	−1.69763	−0.848813	−	0.528694i	$-0.822682\pi$
$433$	−1.24176e12	−1.69763	−0.848813	+	0.528694i	$0.822682\pi$
$434$	−1.97045e11	−0.266601
$435$	0	0
$436$	3.44656e11	0.456769
$437$	3.09218e11	0.405601
$438$	0	0
$439$	−1.48429e12	−1.90734	−0.953671	−	0.300852i	$-0.902729\pi$
$439$	−1.48429e12	−1.90734	−0.953671	+	0.300852i	$0.902729\pi$
$440$	3.59861e11	0.457717
$441$	0	0
$442$	2.54539e9	0.00317215
$443$	−1.03343e12	−1.27487	−0.637433	−	0.770506i	$-0.720004\pi$
$443$	−1.03343e12	−1.27487	−0.637433	+	0.770506i	$0.720004\pi$
$444$	0	0
$445$	−2.11793e12	−2.56030
$446$	−3.01197e10	−0.0360449
$447$	0	0
$448$	−1.11726e12	−1.31040
$449$	5.83072e11	0.677039	0.338519	−	0.940959i	$-0.390074\pi$
$449$	5.83072e11	0.677039	0.338519	+	0.940959i	$0.390074\pi$
$450$	0	0
$451$	−2.27163e11	−0.258550
$452$	−4.18628e11	−0.471743
$453$	0	0
$454$	−6.36470e10	−0.0703116
$455$	−6.85841e11	−0.750191
$456$	0	0
$457$	7.39681e11	0.793271	0.396635	−	0.917976i	$-0.370178\pi$
$457$	7.39681e11	0.793271	0.396635	+	0.917976i	$0.370178\pi$
$458$	7.74405e10	0.0822382
$459$	0	0
$460$	1.44834e12	1.50820
$461$	−1.45843e12	−1.50394	−0.751971	−	0.659197i	$-0.770896\pi$
$461$	−1.45843e12	−1.50394	−0.751971	+	0.659197i	$0.770896\pi$
$462$	0	0
$463$	−1.63194e12	−1.65040	−0.825200	−	0.564841i	$-0.808937\pi$
$463$	−1.63194e12	−1.65040	−0.825200	+	0.564841i	$0.808937\pi$
$464$	4.04314e11	0.404937
$465$	0	0
$466$	2.49904e11	0.245492
$467$	8.24440e11	0.802109	0.401054	−	0.916054i	$-0.368644\pi$
$467$	8.24440e11	0.802109	0.401054	+	0.916054i	$0.368644\pi$
$468$	0	0
$469$	−6.09481e11	−0.581677
$470$	−3.88672e11	−0.367403
$471$	0	0
$472$	3.67882e10	0.0341169
$473$	8.69866e11	0.799056
$474$	0	0
$475$	1.25224e12	1.12867
$476$	1.33511e11	0.119202
$477$	0	0
$478$	−8.27011e10	−0.0724579
$479$	1.80073e11	0.156293	0.0781463	−	0.996942i	$-0.475100\pi$
$479$	1.80073e11	0.156293	0.0781463	+	0.996942i	$0.475100\pi$
$480$	0	0
$481$	−4.88945e11	−0.416493
$482$	3.17448e11	0.267893
$483$	0	0
$484$	2.07688e11	0.172031
$485$	−2.57114e12	−2.11003
$486$	0	0
$487$	−7.22045e11	−0.581680	−0.290840	−	0.956772i	$-0.593935\pi$
$487$	−7.22045e11	−0.581680	−0.290840	+	0.956772i	$0.593935\pi$
$488$	−1.15829e11	−0.0924543
$489$	0	0
$490$	3.86339e11	0.302751
$491$	−1.98313e12	−1.53987	−0.769937	−	0.638119i	$-0.779713\pi$
$491$	−1.98313e12	−1.53987	−0.769937	+	0.638119i	$0.779713\pi$
$492$	0	0
$493$	−4.63072e10	−0.0353051
$494$	−2.46389e10	−0.0186145
$495$	0	0
$496$	1.64353e12	1.21930
$497$	1.38245e12	1.01636
$498$	0	0
$499$	−8.27327e11	−0.597344	−0.298672	−	0.954356i	$-0.596544\pi$
$499$	−8.27327e11	−0.597344	−0.298672	+	0.954356i	$0.596544\pi$
$500$	3.36021e12	2.40437
$501$	0	0
$502$	−2.74955e11	−0.193239
$503$	−4.94554e11	−0.344475	−0.172238	−	0.985055i	$-0.555100\pi$
$503$	−4.94554e11	−0.344475	−0.172238	+	0.985055i	$0.555100\pi$
$504$	0	0
$505$	4.06322e12	2.78009
$506$	1.56860e11	0.106374
$507$	0	0
$508$	2.01486e11	0.134233
$509$	2.31118e12	1.52617	0.763087	−	0.646296i	$-0.223683\pi$
$509$	2.31118e12	1.52617	0.763087	+	0.646296i	$0.223683\pi$
$510$	0	0
$511$	−3.17079e12	−2.05719
$512$	−1.00022e12	−0.643248
$513$	0	0
$514$	1.52541e11	0.0963947
$515$	−2.90942e12	−1.82252
$516$	0	0
$517$	2.12951e12	1.31091
$518$	5.06954e11	0.309374
$519$	0	0
$520$	−2.33092e11	−0.139802
$521$	−2.20997e12	−1.31406	−0.657031	−	0.753864i	$-0.728188\pi$
$521$	−2.20997e12	−1.31406	−0.657031	+	0.753864i	$0.728188\pi$
$522$	0	0
$523$	2.43867e12	1.42527	0.712633	−	0.701537i	$-0.247503\pi$
$523$	2.43867e12	1.42527	0.712633	+	0.701537i	$0.247503\pi$
$524$	−1.89974e12	−1.10079
$525$	0	0
$526$	−1.38822e10	−0.00790718
$527$	−1.88238e11	−0.106307
$528$	0	0
$529$	−5.26040e11	−0.292057
$530$	2.46855e11	0.135894
$531$	0	0
$532$	−1.29236e12	−0.699490
$533$	1.47140e11	0.0789694
$534$	0	0
$535$	−1.84298e12	−0.972588
$536$	−2.07140e11	−0.108398
$537$	0	0
$538$	4.46968e11	0.230015
$539$	−2.11673e12	−1.08023
$540$	0	0
$541$	−1.84418e12	−0.925585	−0.462792	−	0.886467i	$-0.653152\pi$
$541$	−1.84418e12	−0.925585	−0.462792	+	0.886467i	$0.653152\pi$
$542$	2.23582e11	0.111286
$543$	0	0
$544$	6.82851e10	0.0334296
$545$	1.75365e12	0.851448
$546$	0	0
$547$	−2.62022e12	−1.25140	−0.625698	−	0.780065i	$-0.715186\pi$
$547$	−2.62022e12	−1.25140	−0.625698	+	0.780065i	$0.715186\pi$
$548$	7.30611e11	0.346078
$549$	0	0
$550$	6.35235e11	0.296007
$551$	4.48245e11	0.207173
$552$	0	0
$553$	−1.91815e12	−0.872206
$554$	−3.85264e11	−0.173766
$555$	0	0
$556$	−7.55025e11	−0.335062
$557$	−2.45908e12	−1.08249	−0.541245	−	0.840865i	$-0.682047\pi$
$557$	−2.45908e12	−1.08249	−0.541245	+	0.840865i	$0.682047\pi$
$558$	0	0
$559$	−5.63437e11	−0.244058
$560$	−5.93122e12	−2.54858
$561$	0	0
$562$	−3.12494e11	−0.132138
$563$	1.30659e12	0.548091	0.274046	−	0.961717i	$-0.411638\pi$
$563$	1.30659e12	0.548091	0.274046	+	0.961717i	$0.411638\pi$
$564$	0	0
$565$	−2.13003e12	−0.879361
$566$	−5.97534e11	−0.244731
$567$	0	0
$568$	4.69845e11	0.189403
$569$	2.68810e12	1.07508	0.537539	−	0.843239i	$-0.319354\pi$
$569$	2.68810e12	1.07508	0.537539	+	0.843239i	$0.319354\pi$
$570$	0	0
$571$	2.99602e12	1.17946	0.589729	−	0.807601i	$-0.299235\pi$
$571$	2.99602e12	1.17946	0.589729	+	0.807601i	$0.299235\pi$
$572$	6.32299e11	0.246968
$573$	0	0
$574$	−1.52560e11	−0.0586592
$575$	5.16381e12	1.97000
$576$	0	0
$577$	6.04343e11	0.226982	0.113491	−	0.993539i	$-0.463797\pi$
$577$	6.04343e11	0.226982	0.113491	+	0.993539i	$0.463797\pi$
$578$	3.71071e11	0.138287
$579$	0	0
$580$	2.09952e12	0.770360
$581$	−7.15991e12	−2.60684
$582$	0	0
$583$	−1.35250e12	−0.484876
$584$	−1.07763e12	−0.383366
$585$	0	0
$586$	6.16747e11	0.216057
$587$	7.41276e11	0.257697	0.128848	−	0.991664i	$-0.458872\pi$
$587$	7.41276e11	0.257697	0.128848	+	0.991664i	$0.458872\pi$
$588$	0	0
$589$	1.82211e12	0.623816
$590$	9.26752e10	0.0314869
$591$	0	0
$592$	−4.22845e12	−1.41492
$593$	5.55536e12	1.84487	0.922435	−	0.386152i	$-0.126196\pi$
$593$	5.55536e12	1.84487	0.922435	+	0.386152i	$0.126196\pi$
$594$	0	0
$595$	6.79318e11	0.222201
$596$	−2.15201e12	−0.698614
$597$	0	0
$598$	−1.01603e11	−0.0324900
$599$	3.35363e12	1.06437	0.532187	−	0.846627i	$-0.321370\pi$
$599$	3.35363e12	1.06437	0.532187	+	0.846627i	$0.321370\pi$
$600$	0	0
$601$	1.88646e12	0.589809	0.294905	−	0.955527i	$-0.404712\pi$
$601$	1.88646e12	0.589809	0.294905	+	0.955527i	$0.404712\pi$
$602$	5.84189e11	0.181288
$603$	0	0
$604$	−2.40955e11	−0.0736664
$605$	1.05674e12	0.320677
$606$	0	0
$607$	1.01740e12	0.304188	0.152094	−	0.988366i	$-0.451398\pi$
$607$	1.01740e12	0.304188	0.152094	+	0.988366i	$0.451398\pi$
$608$	−6.60987e11	−0.196168
$609$	0	0
$610$	−2.91791e11	−0.0853272
$611$	−1.37935e12	−0.400394
$612$	0	0
$613$	−5.21446e11	−0.149155	−0.0745774	−	0.997215i	$-0.523761\pi$
$613$	−5.21446e11	−0.149155	−0.0745774	+	0.997215i	$0.523761\pi$
$614$	2.26038e11	0.0641836
$615$	0	0
$616$	−1.32413e12	−0.370526
$617$	−1.14541e12	−0.318183	−0.159092	−	0.987264i	$-0.550857\pi$
$617$	−1.14541e12	−0.318183	−0.159092	+	0.987264i	$0.550857\pi$
$618$	0	0
$619$	−1.10612e12	−0.302827	−0.151414	−	0.988470i	$-0.548383\pi$
$619$	−1.10612e12	−0.302827	−0.151414	+	0.988470i	$0.548383\pi$
$620$	8.53452e12	2.31962
$621$	0	0
$622$	6.64793e10	0.0178086
$623$	7.79308e12	2.07259
$624$	0	0
$625$	8.16561e12	2.14057
$626$	4.55751e11	0.118616
$627$	0	0
$628$	4.14023e12	1.06220
$629$	4.84295e11	0.123362
$630$	0	0
$631$	3.20443e12	0.804671	0.402336	−	0.915492i	$-0.368198\pi$
$631$	3.20443e12	0.804671	0.402336	+	0.915492i	$0.368198\pi$
$632$	−6.51908e11	−0.162540
$633$	0	0
$634$	1.82313e11	0.0448143
$635$	1.02518e12	0.250219
$636$	0	0
$637$	1.37106e12	0.329937
$638$	2.27386e11	0.0543338
$639$	0	0
$640$	−4.11374e12	−0.969230
$641$	4.90467e12	1.14749	0.573745	−	0.819034i	$-0.305490\pi$
$641$	4.90467e12	1.14749	0.573745	+	0.819034i	$0.305490\pi$
$642$	0	0
$643$	1.53529e12	0.354194	0.177097	−	0.984193i	$-0.443329\pi$
$643$	1.53529e12	0.354194	0.177097	+	0.984193i	$0.443329\pi$
$644$	−5.32926e12	−1.22090
$645$	0	0
$646$	2.44046e10	0.00551347
$647$	6.61326e11	0.148370	0.0741850	−	0.997244i	$-0.476364\pi$
$647$	6.61326e11	0.148370	0.0741850	+	0.997244i	$0.476364\pi$
$648$	0	0
$649$	−5.07763e11	−0.112347
$650$	−4.11460e11	−0.0904101
$651$	0	0
$652$	2.98000e12	0.645807
$653$	−4.61469e12	−0.993192	−0.496596	−	0.867982i	$-0.665417\pi$
$653$	−4.61469e12	−0.993192	−0.496596	+	0.867982i	$0.665417\pi$
$654$	0	0
$655$	−9.66610e12	−2.05194
$656$	1.27248e12	0.268278
$657$	0	0
$658$	1.43015e12	0.297416
$659$	9.04687e12	1.86859	0.934294	−	0.356502i	$-0.116031\pi$
$659$	9.04687e12	1.86859	0.934294	+	0.356502i	$0.116031\pi$
$660$	0	0
$661$	3.59295e12	0.732057	0.366028	−	0.930604i	$-0.380717\pi$
$661$	3.59295e12	0.732057	0.366028	+	0.930604i	$0.380717\pi$
$662$	3.15926e11	0.0639328
$663$	0	0
$664$	−2.43339e12	−0.485797
$665$	−6.57568e12	−1.30390
$666$	0	0
$667$	1.84841e12	0.361604
$668$	−3.72124e12	−0.723093
$669$	0	0
$670$	−5.21819e11	−0.100042
$671$	1.59871e12	0.304451
$672$	0	0
$673$	2.13714e12	0.401573	0.200786	−	0.979635i	$-0.435650\pi$
$673$	2.13714e12	0.401573	0.200786	+	0.979635i	$0.435650\pi$
$674$	1.80608e11	0.0337107
$675$	0	0
$676$	−4.09558e11	−0.0754320
$677$	2.55166e12	0.466847	0.233423	−	0.972375i	$-0.425007\pi$
$677$	2.55166e12	0.466847	0.233423	+	0.972375i	$0.425007\pi$
$678$	0	0
$679$	9.46070e12	1.70809
$680$	2.30875e11	0.0414083
$681$	0	0
$682$	9.24320e11	0.163604
$683$	−7.63188e12	−1.34196	−0.670978	−	0.741477i	$-0.734126\pi$
$683$	−7.63188e12	−1.34196	−0.670978	+	0.741477i	$0.734126\pi$
$684$	0	0
$685$	3.71743e12	0.645113
$686$	−2.26574e11	−0.0390617
$687$	0	0
$688$	−4.87266e12	−0.829121
$689$	8.76056e11	0.148097
$690$	0	0
$691$	−2.36970e12	−0.395405	−0.197703	−	0.980262i	$-0.563348\pi$
$691$	−2.36970e12	−0.395405	−0.197703	+	0.980262i	$0.563348\pi$
$692$	2.83132e12	0.469365
$693$	0	0
$694$	−7.37405e10	−0.0120667
$695$	−3.84165e12	−0.624578
$696$	0	0
$697$	−1.45741e11	−0.0233902
$698$	−1.23747e12	−0.197326
$699$	0	0
$700$	−2.15819e13	−3.39741
$701$	1.72803e12	0.270284	0.135142	−	0.990826i	$-0.456851\pi$
$701$	1.72803e12	0.270284	0.135142	+	0.990826i	$0.456851\pi$
$702$	0	0
$703$	−4.68789e12	−0.723900
$704$	5.24097e12	0.804146
$705$	0	0
$706$	6.81804e11	0.103285
$707$	−1.49509e13	−2.25051
$708$	0	0
$709$	−3.26440e12	−0.485172	−0.242586	−	0.970130i	$-0.577996\pi$
$709$	−3.26440e12	−0.485172	−0.242586	+	0.970130i	$0.577996\pi$
$710$	1.18361e12	0.174802
$711$	0	0
$712$	2.64858e12	0.386236
$713$	7.51378e12	1.08882
$714$	0	0
$715$	3.21721e12	0.460365
$716$	6.21976e12	0.884433
$717$	0	0
$718$	1.10128e12	0.154646
$719$	6.17850e11	0.0862191	0.0431095	−	0.999070i	$-0.486274\pi$
$719$	6.17850e11	0.0862191	0.0431095	+	0.999070i	$0.486274\pi$
$720$	0	0
$721$	1.07054e13	1.47535
$722$	7.80344e11	0.106873
$723$	0	0
$724$	1.23436e13	1.66962
$725$	7.48550e12	1.00624
$726$	0	0
$727$	5.84000e12	0.775368	0.387684	−	0.921792i	$-0.373275\pi$
$727$	5.84000e12	0.775368	0.387684	+	0.921792i	$0.373275\pi$
$728$	8.57680e11	0.113171
$729$	0	0
$730$	−2.71473e12	−0.353813
$731$	5.58079e11	0.0722882
$732$	0	0
$733$	−7.18908e10	−0.00919826	−0.00459913	−	0.999989i	$-0.501464\pi$
$733$	−7.18908e10	−0.00919826	−0.00459913	+	0.999989i	$0.501464\pi$
$734$	5.77258e9	0.000734070 0
$735$	0	0
$736$	−2.72569e12	−0.342394
$737$	2.85902e12	0.356954
$738$	0	0
$739$	−1.01033e13	−1.24613	−0.623067	−	0.782168i	$-0.714114\pi$
$739$	−1.01033e13	−1.24613	−0.623067	+	0.782168i	$0.714114\pi$
$740$	−2.19574e13	−2.69178
$741$	0	0
$742$	−9.08322e11	−0.110007
$743$	6.09193e12	0.733340	0.366670	−	0.930351i	$-0.380498\pi$
$743$	6.09193e12	0.733340	0.366670	+	0.930351i	$0.380498\pi$
$744$	0	0
$745$	−1.09497e13	−1.30226
$746$	−1.73908e11	−0.0205587
$747$	0	0
$748$	−6.26286e11	−0.0731502
$749$	6.78139e12	0.787319
$750$	0	0
$751$	−1.43572e13	−1.64698	−0.823491	−	0.567330i	$-0.807976\pi$
$751$	−1.43572e13	−1.64698	−0.823491	+	0.567330i	$0.807976\pi$
$752$	−1.19287e13	−1.36023
$753$	0	0
$754$	−1.47284e11	−0.0165953
$755$	−1.22601e12	−0.137319
$756$	0	0
$757$	1.33786e13	1.48074	0.740370	−	0.672200i	$-0.234651\pi$
$757$	1.33786e13	1.48074	0.740370	+	0.672200i	$0.234651\pi$
$758$	−7.09640e11	−0.0780776
$759$	0	0
$760$	−2.23483e12	−0.242987
$761$	−1.00649e13	−1.08788	−0.543938	−	0.839126i	$-0.683067\pi$
$761$	−1.00649e13	−1.08788	−0.543938	+	0.839126i	$0.683067\pi$
$762$	0	0
$763$	−6.45269e12	−0.689255
$764$	−5.35231e12	−0.568357
$765$	0	0
$766$	1.46201e12	0.153433
$767$	3.28892e11	0.0343142
$768$	0	0
$769$	4.34623e12	0.448172	0.224086	−	0.974569i	$-0.428060\pi$
$769$	4.34623e12	0.448172	0.224086	+	0.974569i	$0.428060\pi$
$770$	−3.33571e12	−0.341963
$771$	0	0
$772$	1.05255e13	1.06651
$773$	−2.50017e12	−0.251862	−0.125931	−	0.992039i	$-0.540192\pi$
$773$	−2.50017e12	−0.251862	−0.125931	+	0.992039i	$0.540192\pi$
$774$	0	0
$775$	3.04285e13	3.02986
$776$	3.21534e12	0.318310
$777$	0	0
$778$	−8.28731e11	−0.0810971
$779$	1.41075e12	0.137256
$780$	0	0
$781$	−6.48495e12	−0.623702
$782$	1.00636e11	0.00962332
$783$	0	0
$784$	1.18571e13	1.12087
$785$	2.10660e13	1.98001
$786$	0	0
$787$	−1.47010e13	−1.36603	−0.683013	−	0.730406i	$-0.739331\pi$
$787$	−1.47010e13	−1.36603	−0.683013	+	0.730406i	$0.739331\pi$
$788$	6.37893e12	0.589359
$789$	0	0
$790$	−1.64226e12	−0.150010
$791$	7.83761e12	0.711851
$792$	0	0
$793$	−1.03553e12	−0.0929892
$794$	5.68266e10	0.00507410
$795$	0	0
$796$	−1.29448e12	−0.114284
$797$	−8.96898e12	−0.787373	−0.393687	−	0.919245i	$-0.628801\pi$
$797$	−8.96898e12	−0.787373	−0.393687	+	0.919245i	$0.628801\pi$
$798$	0	0
$799$	1.36623e12	0.118594
$800$	−1.10382e13	−0.952782
$801$	0	0
$802$	2.26444e11	0.0193275
$803$	1.48739e13	1.26242
$804$	0	0
$805$	−2.71159e13	−2.27584
$806$	−5.98708e11	−0.0499698
$807$	0	0
$808$	−5.08127e12	−0.419393
$809$	−1.74450e13	−1.43187	−0.715934	−	0.698168i	$-0.753999\pi$
$809$	−1.74450e13	−1.43187	−0.715934	+	0.698168i	$0.753999\pi$
$810$	0	0
$811$	−8.34611e12	−0.677470	−0.338735	−	0.940882i	$-0.609999\pi$
$811$	−8.34611e12	−0.677470	−0.338735	+	0.940882i	$0.609999\pi$
$812$	−7.72534e12	−0.623614
$813$	0	0
$814$	−2.37807e12	−0.189852
$815$	1.51626e13	1.20383
$816$	0	0
$817$	−5.40210e12	−0.424193
$818$	−1.67555e12	−0.130848
$819$	0	0
$820$	6.60774e12	0.510376
$821$	−1.88288e13	−1.44637	−0.723183	−	0.690657i	$-0.757322\pi$
$821$	−1.88288e13	−1.44637	−0.723183	+	0.690657i	$0.757322\pi$
$822$	0	0
$823$	4.02178e12	0.305576	0.152788	−	0.988259i	$-0.451175\pi$
$823$	4.02178e12	0.305576	0.152788	+	0.988259i	$0.451175\pi$
$824$	3.63838e12	0.274938
$825$	0	0
$826$	−3.41006e11	−0.0254889
$827$	−3.84013e12	−0.285477	−0.142738	−	0.989760i	$-0.545591\pi$
$827$	−3.84013e12	−0.285477	−0.142738	+	0.989760i	$0.545591\pi$
$828$	0	0
$829$	1.81041e13	1.33132	0.665660	−	0.746255i	$-0.268150\pi$
$829$	1.81041e13	1.33132	0.665660	+	0.746255i	$0.268150\pi$
$830$	−6.13010e12	−0.448349
$831$	0	0
$832$	−3.39473e12	−0.245612
$833$	−1.35803e12	−0.0977249
$834$	0	0
$835$	−1.89341e13	−1.34789
$836$	6.06234e12	0.429252
$837$	0	0
$838$	4.59766e11	0.0322062
$839$	−1.83543e13	−1.27882	−0.639410	−	0.768866i	$-0.720821\pi$
$839$	−1.83543e13	−1.27882	−0.639410	+	0.768866i	$0.720821\pi$
$840$	0	0
$841$	−1.18277e13	−0.815300
$842$	−1.15380e12	−0.0791092
$843$	0	0
$844$	−9.75538e12	−0.661764
$845$	−2.08388e12	−0.140610
$846$	0	0
$847$	−3.88835e12	−0.259591
$848$	7.57621e12	0.503119
$849$	0	0
$850$	4.07546e11	0.0267789
$851$	−1.93313e13	−1.26351
$852$	0	0
$853$	−1.20116e13	−0.776835	−0.388418	−	0.921483i	$-0.626978\pi$
$853$	−1.20116e13	−0.776835	−0.388418	+	0.921483i	$0.626978\pi$
$854$	1.07367e12	0.0690732
$855$	0	0
$856$	2.30475e12	0.146721
$857$	6.17723e12	0.391183	0.195592	−	0.980685i	$-0.437337\pi$
$857$	6.17723e12	0.391183	0.195592	+	0.980685i	$0.437337\pi$
$858$	0	0
$859$	2.76160e13	1.73058	0.865291	−	0.501269i	$-0.167133\pi$
$859$	2.76160e13	1.73058	0.865291	+	0.501269i	$0.167133\pi$
$860$	−2.53027e13	−1.57733
$861$	0	0
$862$	2.41439e12	0.148944
$863$	−9.27582e12	−0.569251	−0.284626	−	0.958639i	$-0.591869\pi$
$863$	−9.27582e12	−0.569251	−0.284626	+	0.958639i	$0.591869\pi$
$864$	0	0
$865$	1.44061e13	0.874929
$866$	3.91197e12	0.236355
$867$	0	0
$868$	−3.14034e13	−1.87775
$869$	8.99785e12	0.535242
$870$	0	0
$871$	−1.85187e12	−0.109025
$872$	−2.19303e12	−0.128446
$873$	0	0
$874$	−9.74143e11	−0.0564704
$875$	−6.29103e13	−3.62815
$876$	0	0
$877$	−2.19078e13	−1.25055	−0.625274	−	0.780405i	$-0.715013\pi$
$877$	−2.19078e13	−1.25055	−0.625274	+	0.780405i	$0.715013\pi$
$878$	4.67602e12	0.265553
$879$	0	0
$880$	2.78228e13	1.56397
$881$	−2.92416e12	−0.163534	−0.0817672	−	0.996651i	$-0.526056\pi$
$881$	−2.92416e12	−0.163534	−0.0817672	+	0.996651i	$0.526056\pi$
$882$	0	0
$883$	3.35851e13	1.85919	0.929594	−	0.368585i	$-0.120158\pi$
$883$	3.35851e13	1.85919	0.929594	+	0.368585i	$0.120158\pi$
$884$	4.05663e11	0.0223424
$885$	0	0
$886$	3.25566e12	0.177495
$887$	3.31699e13	1.79924	0.899619	−	0.436676i	$-0.143844\pi$
$887$	3.31699e13	1.79924	0.899619	+	0.436676i	$0.143844\pi$
$888$	0	0
$889$	−3.77225e12	−0.202555
$890$	6.67219e12	0.356462
$891$	0	0
$892$	−4.80023e12	−0.253875
$893$	−1.32248e13	−0.695920
$894$	0	0
$895$	3.16469e13	1.64864
$896$	1.51368e13	0.784601
$897$	0	0
$898$	−1.83688e12	−0.0942619
$899$	1.08920e13	0.556148
$900$	0	0
$901$	−8.67724e11	−0.0438652
$902$	7.15642e11	0.0359970
$903$	0	0
$904$	2.66371e12	0.132657
$905$	6.28057e13	3.11229
$906$	0	0
$907$	2.27086e13	1.11418	0.557092	−	0.830451i	$-0.311917\pi$
$907$	2.27086e13	1.11418	0.557092	+	0.830451i	$0.311917\pi$
$908$	−1.01435e13	−0.495226
$909$	0	0
$910$	2.16063e12	0.104447
$911$	−4.92090e12	−0.236707	−0.118354	−	0.992972i	$-0.537762\pi$
$911$	−4.92090e12	−0.236707	−0.118354	+	0.992972i	$0.537762\pi$
$912$	0	0
$913$	3.35865e13	1.59973
$914$	−2.33025e12	−0.110444
$915$	0	0
$916$	1.23418e13	0.579229
$917$	3.55671e13	1.66107
$918$	0	0
$919$	−9.41621e12	−0.435468	−0.217734	−	0.976008i	$-0.569867\pi$
$919$	−9.41621e12	−0.435468	−0.217734	+	0.976008i	$0.569867\pi$
$920$	−9.21569e12	−0.424114
$921$	0	0
$922$	4.59455e12	0.209389
$923$	4.20049e12	0.190499
$924$	0	0
$925$	−7.82858e13	−3.51597
$926$	5.14116e12	0.229780
$927$	0	0
$928$	−3.95118e12	−0.174889
$929$	3.87518e13	1.70695	0.853476	−	0.521131i	$-0.174490\pi$
$929$	3.87518e13	1.70695	0.853476	+	0.521131i	$0.174490\pi$
$930$	0	0
$931$	1.31454e13	0.573458
$932$	3.98276e13	1.72907
$933$	0	0
$934$	−2.59727e12	−0.111675
$935$	−3.18662e12	−0.136357
$936$	0	0
$937$	1.41425e13	0.599373	0.299687	−	0.954038i	$-0.403118\pi$
$937$	1.41425e13	0.599373	0.299687	+	0.954038i	$0.403118\pi$
$938$	1.92007e12	0.0809850
$939$	0	0
$940$	−6.19433e13	−2.58773
$941$	2.29704e13	0.955027	0.477514	−	0.878624i	$-0.341538\pi$
$941$	2.29704e13	0.955027	0.477514	+	0.878624i	$0.341538\pi$
$942$	0	0
$943$	5.81744e12	0.239568
$944$	2.84429e12	0.116574
$945$	0	0
$946$	−2.74038e12	−0.111250
$947$	1.50510e12	0.0608120	0.0304060	−	0.999538i	$-0.490320\pi$
$947$	1.50510e12	0.0608120	0.0304060	+	0.999538i	$0.490320\pi$
$948$	0	0
$949$	−9.63423e12	−0.385584
$950$	−3.94498e12	−0.157141
$951$	0	0
$952$	−8.49523e11	−0.0335204
$953$	−2.42253e13	−0.951373	−0.475686	−	0.879615i	$-0.657800\pi$
$953$	−2.42253e13	−0.951373	−0.475686	+	0.879615i	$0.657800\pi$
$954$	0	0
$955$	−2.72332e13	−1.05946
$956$	−1.31802e13	−0.510343
$957$	0	0
$958$	−5.67291e11	−0.0217601
$959$	−1.36786e13	−0.522225
$960$	0	0
$961$	1.78364e13	0.674608
$962$	1.54034e12	0.0579869
$963$	0	0
$964$	5.05923e13	1.88685
$965$	5.35551e13	1.98805
$966$	0	0
$967$	2.41172e13	0.886967	0.443484	−	0.896282i	$-0.353742\pi$
$967$	2.41172e13	0.886967	0.443484	+	0.896282i	$0.353742\pi$
$968$	−1.32151e12	−0.0483760
$969$	0	0
$970$	8.09996e12	0.293772
$971$	−3.13584e13	−1.13206	−0.566028	−	0.824386i	$-0.691521\pi$
$971$	−3.13584e13	−1.13206	−0.566028	+	0.824386i	$0.691521\pi$
$972$	0	0
$973$	1.41357e13	0.505602
$974$	2.27469e12	0.0809854
$975$	0	0
$976$	−8.95534e12	−0.315906
$977$	−4.44366e13	−1.56033	−0.780163	−	0.625576i	$-0.784864\pi$
$977$	−4.44366e13	−1.56033	−0.780163	+	0.625576i	$0.784864\pi$
$978$	0	0
$979$	−3.65566e13	−1.27187
$980$	6.15714e13	2.13237
$981$	0	0
$982$	6.24755e12	0.214392
$983$	−1.53216e13	−0.523376	−0.261688	−	0.965153i	$-0.584279\pi$
$983$	−1.53216e13	−0.523376	−0.261688	+	0.965153i	$0.584279\pi$
$984$	0	0
$985$	3.24567e13	1.09861
$986$	1.45883e11	0.00491541
$987$	0	0
$988$	−3.92675e12	−0.131107
$989$	−2.22765e13	−0.740394
$990$	0	0
$991$	2.32887e13	0.767034	0.383517	−	0.923534i	$-0.374713\pi$
$991$	2.32887e13	0.767034	0.383517	+	0.923534i	$0.374713\pi$
$992$	−1.60615e13	−0.526604
$993$	0	0
$994$	−4.35520e12	−0.141504
$995$	−6.58644e12	−0.213033
$996$	0	0
$997$	−1.12247e13	−0.359788	−0.179894	−	0.983686i	$-0.557575\pi$
$997$	−1.12247e13	−0.359788	−0.179894	+	0.983686i	$0.557575\pi$
$998$	2.60636e12	0.0831663
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.10.a.e.1.3		5
3.2	odd	2		13.10.a.b.1.3	✓	5
12.11	even	2		208.10.a.h.1.4		5
15.14	odd	2		325.10.a.b.1.3		5
39.38	odd	2		169.10.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.3	✓	5	3.2	odd	2
117.10.a.e.1.3		5	1.1	even	1	trivial
169.10.a.b.1.3		5	39.38	odd	2
208.10.a.h.1.4		5	12.11	even	2
325.10.a.b.1.3		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	117.a (trivial)

\(f(q)\)	\(=\)	\(q-3.15034 q^{2} -502.075 q^{4} -2554.62 q^{5} +9399.91 q^{7} +3194.68 q^{8} +O(q^{10})\)	\(q-3.15034 q^{2} -502.075 q^{4} -2554.62 q^{5} +9399.91 q^{7} +3194.68 q^{8} +8047.92 q^{10} -44094.1 q^{11} +28561.0 q^{13} -29612.9 q^{14} +246998. q^{16} -28289.4 q^{17} +273836. q^{19} +1.28261e6 q^{20} +138911. q^{22} +1.12921e6 q^{23} +4.57295e6 q^{25} -89976.9 q^{26} -4.71947e6 q^{28} +1.63691e6 q^{29} +6.65402e6 q^{31} -2.41381e6 q^{32} +89121.2 q^{34} -2.40132e7 q^{35} -1.71193e7 q^{37} -862677. q^{38} -8.16119e6 q^{40} +5.15179e6 q^{41} -1.97275e7 q^{43} +2.21386e7 q^{44} -3.55739e6 q^{46} -4.82947e7 q^{47} +4.80048e7 q^{49} -1.44063e7 q^{50} -1.43398e7 q^{52} +3.06731e7 q^{53} +1.12644e8 q^{55} +3.00298e7 q^{56} -5.15683e6 q^{58} +1.15154e7 q^{59} -3.62567e7 q^{61} -2.09624e7 q^{62} -1.18859e8 q^{64} -7.29624e7 q^{65} -6.48390e7 q^{67} +1.42034e7 q^{68} +7.56497e7 q^{70} +1.47071e8 q^{71} -3.37321e8 q^{73} +5.39317e7 q^{74} -1.37486e8 q^{76} -4.14481e8 q^{77} -2.04060e8 q^{79} -6.30986e8 q^{80} -1.62299e7 q^{82} -7.61700e8 q^{83} +7.22685e7 q^{85} +6.21484e7 q^{86} -1.40867e8 q^{88} +8.29058e8 q^{89} +2.68471e8 q^{91} -5.66948e8 q^{92} +1.52145e8 q^{94} -6.99547e8 q^{95} +1.00647e9 q^{97} -1.51231e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8}+O(q^{10}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8} + 84505 q^{10} - 121746 q^{11} + 142805 q^{13} - 8475 q^{14} - 322463 q^{16} + 495669 q^{17} - 840738 q^{19} + 1595607 q^{20} - 2023594 q^{22} + 592152 q^{23} + 1670362 q^{25} - 428415 q^{26} + 2587955 q^{28} - 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 9934079 q^{34} - 8380731 q^{35} + 7171823 q^{37} + 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} + 12831975 q^{43} + 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 25249488 q^{49} + 16270770 q^{50} + 10310521 q^{52} - 93231780 q^{53} + 99448846 q^{55} - 199599225 q^{56} + 151020970 q^{58} - 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 91019105 q^{64} - 51495483 q^{65} - 369388534 q^{67} - 238172073 q^{68} - 144857425 q^{70} - 212150457 q^{71} - 252729806 q^{73} - 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} + 169559388 q^{82} - 1696894296 q^{83} - 775363765 q^{85} - 3291621459 q^{86} - 220227222 q^{88} + 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 272071215 q^{94} - 1442632962 q^{95} + 3824606 q^{97} - 1570614816 q^{98}+O(q^{100}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8 + 84505 * q^10 - 121746 * q^11 + 142805 * q^13 - 8475 * q^14 - 322463 * q^16 + 495669 * q^17 - 840738 * q^19 + 1595607 * q^20 - 2023594 * q^22 + 592152 * q^23 + 1670362 * q^25 - 428415 * q^26 + 2587955 * q^28 - 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 9934079 * q^34 - 8380731 * q^35 + 7171823 * q^37 + 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 + 12831975 * q^43 + 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 25249488 * q^49 + 16270770 * q^50 + 10310521 * q^52 - 93231780 * q^53 + 99448846 * q^55 - 199599225 * q^56 + 151020970 * q^58 - 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 91019105 * q^64 - 51495483 * q^65 - 369388534 * q^67 - 238172073 * q^68 - 144857425 * q^70 - 212150457 * q^71 - 252729806 * q^73 - 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 + 169559388 * q^82 - 1696894296 * q^83 - 775363765 * q^85 - 3291621459 * q^86 - 220227222 * q^88 + 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 272071215 * q^94 - 1442632962 * q^95 + 3824606 * q^97 - 1570614816 * q^98

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