LMFDB - Embedded newform 117.10.a.e.1.2

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			1.2
Root			$16.7176$ 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)

$f(q)$	$=$	$q-19.7176 q^{2} -123.217 q^{4} -1555.58 q^{5} -8329.39 q^{7} +12524.9 q^{8} +O(q^{10})$	\(q-19.7176 q^{2} -123.217 q^{4} -1555.58 q^{5} -8329.39 q^{7} +12524.9 q^{8} +30672.3 q^{10} -30751.5 q^{11} +28561.0 q^{13} +164236. q^{14} -183875. q^{16} +637455. q^{17} +105834. q^{19} +191674. q^{20} +606345. q^{22} +511169. q^{23} +466710. q^{25} -563154. q^{26} +1.02632e6 q^{28} -781868. q^{29} -2.83285e6 q^{31} -2.78721e6 q^{32} -1.25691e7 q^{34} +1.29571e7 q^{35} +1.22183e7 q^{37} -2.08680e6 q^{38} -1.94836e7 q^{40} +6.83367e6 q^{41} +3.84656e7 q^{43} +3.78910e6 q^{44} -1.00790e7 q^{46} +1.30402e7 q^{47} +2.90252e7 q^{49} -9.20238e6 q^{50} -3.51920e6 q^{52} +2.42871e7 q^{53} +4.78364e7 q^{55} -1.04325e8 q^{56} +1.54166e7 q^{58} -1.63738e8 q^{59} +1.90751e7 q^{61} +5.58569e7 q^{62} +1.49101e8 q^{64} -4.44290e7 q^{65} -7.22869e7 q^{67} -7.85452e7 q^{68} -2.55482e8 q^{70} -2.65461e7 q^{71} +2.42850e8 q^{73} -2.40916e8 q^{74} -1.30406e7 q^{76} +2.56141e8 q^{77} -4.64290e8 q^{79} +2.86032e8 q^{80} -1.34744e8 q^{82} -5.46643e8 q^{83} -9.91613e8 q^{85} -7.58449e8 q^{86} -3.85160e8 q^{88} -3.65672e8 q^{89} -2.37896e8 q^{91} -6.29847e7 q^{92} -2.57121e8 q^{94} -1.64634e8 q^{95} +9.98914e7 q^{97} -5.72307e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.7176	−0.871402	−0.435701	−	0.900091i	$-0.643500\pi$
$2$	−19.7176	−0.871402	−0.435701	+	0.900091i	$0.643500\pi$
$3$	0	0
$3$	0	0
$4$	−123.217	−0.240658
$5$	−1555.58	−1.11308	−0.556542	−	0.830820i	$-0.687872\pi$
$5$	−1555.58	−1.11308	−0.556542	+	0.830820i	$0.687872\pi$
$6$	0	0
$7$	−8329.39	−1.31121	−0.655605	−	0.755104i	$-0.727586\pi$
$7$	−8329.39	−1.31121	−0.655605	+	0.755104i	$0.727586\pi$
$8$	12524.9	1.08111
$9$	0	0
$10$	30672.3	0.969944
$11$	−30751.5	−0.633284	−0.316642	−	0.948545i	$-0.602555\pi$
$11$	−30751.5	−0.633284	−0.316642	+	0.948545i	$0.602555\pi$
$12$	0	0
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	164236.	1.14259
$15$	0	0
$16$	−183875.	−0.701426
$17$	637455.	1.85110	0.925549	−	0.378629i	$-0.123604\pi$
$17$	637455.	1.85110	0.925549	+	0.378629i	$0.123604\pi$
$18$	0	0
$19$	105834.	0.186310	0.0931548	−	0.995652i	$-0.470305\pi$
$19$	105834.	0.186310	0.0931548	+	0.995652i	$0.470305\pi$
$20$	191674.	0.267872
$21$	0	0
$22$	606345.	0.551845
$23$	511169.	0.380881	0.190441	−	0.981699i	$-0.439008\pi$
$23$	511169.	0.380881	0.190441	+	0.981699i	$0.439008\pi$
$24$	0	0
$25$	466710.	0.238955
$26$	−563154.	−0.241684
$27$	0	0
$28$	1.02632e6	0.315553
$29$	−781868.	−0.205278	−0.102639	−	0.994719i	$-0.532729\pi$
$29$	−781868.	−0.205278	−0.102639	+	0.994719i	$0.532729\pi$
$30$	0	0
$31$	−2.83285e6	−0.550929	−0.275464	−	0.961311i	$-0.588832\pi$
$31$	−2.83285e6	−0.550929	−0.275464	+	0.961311i	$0.588832\pi$
$32$	−2.78721e6	−0.469888
$33$	0	0
$34$	−1.25691e7	−1.61305
$35$	1.29571e7	1.45949
$36$	0	0
$37$	1.22183e7	1.07178	0.535889	−	0.844289i	$-0.319977\pi$
$37$	1.22183e7	1.07178	0.535889	+	0.844289i	$0.319977\pi$
$38$	−2.08680e6	−0.162351
$39$	0	0
$40$	−1.94836e7	−1.20337
$41$	6.83367e6	0.377682	0.188841	−	0.982008i	$-0.439527\pi$
$41$	6.83367e6	0.377682	0.188841	+	0.982008i	$0.439527\pi$
$42$	0	0
$43$	3.84656e7	1.71579	0.857896	−	0.513823i	$-0.171771\pi$
$43$	3.84656e7	1.71579	0.857896	+	0.513823i	$0.171771\pi$
$44$	3.78910e6	0.152405
$45$	0	0
$46$	−1.00790e7	−0.331901
$47$	1.30402e7	0.389802	0.194901	−	0.980823i	$-0.437561\pi$
$47$	1.30402e7	0.389802	0.194901	+	0.980823i	$0.437561\pi$
$48$	0	0
$49$	2.90252e7	0.719272
$50$	−9.20238e6	−0.208226
$51$	0	0
$52$	−3.51920e6	−0.0667465
$53$	2.42871e7	0.422800	0.211400	−	0.977400i	$-0.432198\pi$
$53$	2.42871e7	0.422800	0.211400	+	0.977400i	$0.432198\pi$
$54$	0	0
$55$	4.78364e7	0.704898
$56$	−1.04325e8	−1.41757
$57$	0	0
$58$	1.54166e7	0.178880
$59$	−1.63738e8	−1.75920	−0.879599	−	0.475716i	$-0.842189\pi$
$59$	−1.63738e8	−1.75920	−0.879599	+	0.475716i	$0.842189\pi$
$60$	0	0
$61$	1.90751e7	0.176394	0.0881968	−	0.996103i	$-0.471890\pi$
$61$	1.90751e7	0.176394	0.0881968	+	0.996103i	$0.471890\pi$
$62$	5.58569e7	0.480081
$63$	0	0
$64$	1.49101e8	1.11089
$65$	−4.44290e7	−0.308714
$66$	0	0
$67$	−7.22869e7	−0.438251	−0.219125	−	0.975697i	$-0.570320\pi$
$67$	−7.22869e7	−0.438251	−0.219125	+	0.975697i	$0.570320\pi$
$68$	−7.85452e7	−0.445481
$69$	0	0
$70$	−2.55482e8	−1.27180
$71$	−2.65461e7	−0.123976	−0.0619880	−	0.998077i	$-0.519744\pi$
$71$	−2.65461e7	−0.123976	−0.0619880	+	0.998077i	$0.519744\pi$
$72$	0	0
$73$	2.42850e8	1.00089	0.500445	−	0.865769i	$-0.333170\pi$
$73$	2.42850e8	1.00089	0.500445	+	0.865769i	$0.333170\pi$
$74$	−2.40916e8	−0.933950
$75$	0	0
$76$	−1.30406e7	−0.0448369
$77$	2.56141e8	0.830369
$78$	0	0
$79$	−4.64290e8	−1.34112	−0.670560	−	0.741855i	$-0.733946\pi$
$79$	−4.64290e8	−1.34112	−0.670560	+	0.741855i	$0.733946\pi$
$80$	2.86032e8	0.780746
$81$	0	0
$82$	−1.34744e8	−0.329113
$83$	−5.46643e8	−1.26431	−0.632153	−	0.774843i	$-0.717829\pi$
$83$	−5.46643e8	−1.26431	−0.632153	+	0.774843i	$0.717829\pi$
$84$	0	0
$85$	−9.91613e8	−2.06043
$86$	−7.58449e8	−1.49515
$87$	0	0
$88$	−3.85160e8	−0.684651
$89$	−3.65672e8	−0.617783	−0.308892	−	0.951097i	$-0.599958\pi$
$89$	−3.65672e8	−0.617783	−0.308892	+	0.951097i	$0.599958\pi$
$90$	0	0
$91$	−2.37896e8	−0.363664
$92$	−6.29847e7	−0.0916621
$93$	0	0
$94$	−2.57121e8	−0.339674
$95$	−1.64634e8	−0.207378
$96$	0	0
$97$	9.98914e7	0.114566	0.0572830	−	0.998358i	$-0.481756\pi$
$97$	9.98914e7	0.114566	0.0572830	+	0.998358i	$0.481756\pi$
$98$	−5.72307e8	−0.626775
$99$	0	0
$100$	−5.75065e7	−0.0575065
$101$	6.76155e8	0.646547	0.323273	−	0.946306i	$-0.395217\pi$
$101$	6.76155e8	0.646547	0.323273	+	0.946306i	$0.395217\pi$
$102$	0	0
$103$	−1.73267e8	−0.151687	−0.0758434	−	0.997120i	$-0.524165\pi$
$103$	−1.73267e8	−0.151687	−0.0758434	+	0.997120i	$0.524165\pi$
$104$	3.57725e8	0.299847
$105$	0	0
$106$	−4.78883e8	−0.368429
$107$	−1.23684e9	−0.912191	−0.456095	−	0.889931i	$-0.650752\pi$
$107$	−1.23684e9	−0.912191	−0.456095	+	0.889931i	$0.650752\pi$
$108$	0	0
$109$	−1.04481e9	−0.708956	−0.354478	−	0.935064i	$-0.615341\pi$
$109$	−1.04481e9	−0.708956	−0.354478	+	0.935064i	$0.615341\pi$
$110$	−9.43218e8	−0.614250
$111$	0	0
$112$	1.53156e9	0.919716
$113$	1.17492e9	0.677884	0.338942	−	0.940807i	$-0.389931\pi$
$113$	1.17492e9	0.677884	0.338942	+	0.940807i	$0.389931\pi$
$114$	0	0
$115$	−7.95166e8	−0.423953
$116$	9.63394e7	0.0494018
$117$	0	0
$118$	3.22851e9	1.53297
$119$	−5.30961e9	−2.42718
$120$	0	0
$121$	−1.41230e9	−0.598951
$122$	−3.76115e8	−0.153710
$123$	0	0
$124$	3.49055e8	0.132585
$125$	2.31224e9	0.847106
$126$	0	0
$127$	6.34961e8	0.216586	0.108293	−	0.994119i	$-0.465462\pi$
$127$	6.34961e8	0.216586	0.108293	+	0.994119i	$0.465462\pi$
$128$	−1.51286e9	−0.498142
$129$	0	0
$130$	8.76032e8	0.269014
$131$	5.68611e9	1.68692	0.843459	−	0.537193i	$-0.180515\pi$
$131$	5.68611e9	1.68692	0.843459	+	0.537193i	$0.180515\pi$
$132$	0	0
$133$	−8.81536e8	−0.244291
$134$	1.42532e9	0.381893
$135$	0	0
$136$	7.98408e9	2.00124
$137$	−4.47162e9	−1.08448	−0.542241	−	0.840223i	$-0.682424\pi$
$137$	−4.47162e9	−1.08448	−0.542241	+	0.840223i	$0.682424\pi$
$138$	0	0
$139$	−8.63285e9	−1.96150	−0.980748	−	0.195275i	$-0.937440\pi$
$139$	−8.63285e9	−1.96150	−0.980748	+	0.195275i	$0.937440\pi$
$140$	−1.59653e9	−0.351237
$141$	0	0
$142$	5.23424e8	0.108033
$143$	−8.78292e8	−0.175641
$144$	0	0
$145$	1.21626e9	0.228492
$146$	−4.78842e9	−0.872177
$147$	0	0
$148$	−1.50551e9	−0.257932
$149$	6.88630e9	1.14458	0.572292	−	0.820050i	$-0.306054\pi$
$149$	6.88630e9	1.14458	0.572292	+	0.820050i	$0.306054\pi$
$150$	0	0
$151$	4.01063e9	0.627792	0.313896	−	0.949457i	$-0.398366\pi$
$151$	4.01063e9	0.627792	0.313896	+	0.949457i	$0.398366\pi$
$152$	1.32557e9	0.201422
$153$	0	0
$154$	−5.05048e9	−0.723585
$155$	4.40672e9	0.613230
$156$	0	0
$157$	9.39913e9	1.23464	0.617318	−	0.786714i	$-0.288219\pi$
$157$	9.39913e9	1.23464	0.617318	+	0.786714i	$0.288219\pi$
$158$	9.15469e9	1.16866
$159$	0	0
$160$	4.33573e9	0.523025
$161$	−4.25773e9	−0.499415
$162$	0	0
$163$	3.72144e9	0.412920	0.206460	−	0.978455i	$-0.433806\pi$
$163$	3.72144e9	0.412920	0.206460	+	0.978455i	$0.433806\pi$
$164$	−8.42024e8	−0.0908923
$165$	0	0
$166$	1.07785e10	1.10172
$167$	4.48607e9	0.446315	0.223158	−	0.974782i	$-0.428364\pi$
$167$	4.48607e9	0.446315	0.223158	+	0.974782i	$0.428364\pi$
$168$	0	0
$169$	8.15731e8	0.0769231
$170$	1.95522e10	1.79546
$171$	0	0
$172$	−4.73962e9	−0.412919
$173$	1.69286e10	1.43686	0.718428	−	0.695602i	$-0.244862\pi$
$173$	1.69286e10	1.43686	0.718428	+	0.695602i	$0.244862\pi$
$174$	0	0
$175$	−3.88741e9	−0.313321
$176$	5.65441e9	0.444202
$177$	0	0
$178$	7.21016e9	0.538338
$179$	−1.23127e10	−0.896428	−0.448214	−	0.893926i	$-0.647940\pi$
$179$	−1.23127e10	−0.896428	−0.448214	+	0.893926i	$0.647940\pi$
$180$	0	0
$181$	−2.43748e10	−1.68806	−0.844030	−	0.536295i	$-0.819823\pi$
$181$	−2.43748e10	−1.68806	−0.844030	+	0.536295i	$0.819823\pi$
$182$	4.69073e9	0.316898
$183$	0	0
$184$	6.40237e9	0.411775
$185$	−1.90066e10	−1.19298
$186$	0	0
$187$	−1.96027e10	−1.17227
$188$	−1.60677e9	−0.0938089
$189$	0	0
$190$	3.24618e9	0.180710
$191$	8.67702e9	0.471759	0.235880	−	0.971782i	$-0.424203\pi$
$191$	8.67702e9	0.471759	0.235880	+	0.971782i	$0.424203\pi$
$192$	0	0
$193$	−2.33509e10	−1.21142	−0.605712	−	0.795684i	$-0.707112\pi$
$193$	−2.33509e10	−1.21142	−0.605712	+	0.795684i	$0.707112\pi$
$194$	−1.96962e9	−0.0998330
$195$	0	0
$196$	−3.57640e9	−0.173098
$197$	2.62332e9	0.124095	0.0620473	−	0.998073i	$-0.480237\pi$
$197$	2.62332e9	0.124095	0.0620473	+	0.998073i	$0.480237\pi$
$198$	0	0
$199$	8.36775e9	0.378242	0.189121	−	0.981954i	$-0.439436\pi$
$199$	8.36775e9	0.378242	0.189121	+	0.981954i	$0.439436\pi$
$200$	5.84551e9	0.258337
$201$	0	0
$202$	−1.33321e10	−0.563403
$203$	6.51249e9	0.269163
$204$	0	0
$205$	−1.06303e10	−0.420392
$206$	3.41640e9	0.132180
$207$	0	0
$208$	−5.25164e9	−0.194541
$209$	−3.25456e9	−0.117987
$210$	0	0
$211$	3.66318e10	1.27229	0.636147	−	0.771568i	$-0.280527\pi$
$211$	3.66318e10	1.27229	0.636147	+	0.771568i	$0.280527\pi$
$212$	−2.99258e9	−0.101750
$213$	0	0
$214$	2.43874e10	0.794885
$215$	−5.98364e10	−1.90982
$216$	0	0
$217$	2.35959e10	0.722383
$218$	2.06012e10	0.617786
$219$	0	0
$220$	−5.89425e9	−0.169639
$221$	1.82063e10	0.513402
$222$	0	0
$223$	6.22383e10	1.68533	0.842667	−	0.538435i	$-0.180984\pi$
$223$	6.22383e10	1.68533	0.842667	+	0.538435i	$0.180984\pi$
$224$	2.32158e10	0.616122
$225$	0	0
$226$	−2.31666e10	−0.590710
$227$	−4.00531e10	−1.00120	−0.500599	−	0.865679i	$-0.666887\pi$
$227$	−4.00531e10	−1.00120	−0.500599	+	0.865679i	$0.666887\pi$
$228$	0	0
$229$	4.61622e10	1.10924	0.554621	−	0.832103i	$-0.312863\pi$
$229$	4.61622e10	1.10924	0.554621	+	0.832103i	$0.312863\pi$
$230$	1.56787e10	0.369433
$231$	0	0
$232$	−9.79285e9	−0.221929
$233$	2.82042e10	0.626920	0.313460	−	0.949601i	$-0.398512\pi$
$233$	2.82042e10	0.626920	0.313460	+	0.949601i	$0.398512\pi$
$234$	0	0
$235$	−2.02851e10	−0.433882
$236$	2.01753e10	0.423365
$237$	0	0
$238$	1.04693e11	2.11505
$239$	−7.93923e9	−0.157394	−0.0786969	−	0.996899i	$-0.525076\pi$
$239$	−7.93923e9	−0.157394	−0.0786969	+	0.996899i	$0.525076\pi$
$240$	0	0
$241$	−4.33069e10	−0.826953	−0.413476	−	0.910515i	$-0.635686\pi$
$241$	−4.33069e10	−0.826953	−0.413476	+	0.910515i	$0.635686\pi$
$242$	2.78471e10	0.521927
$243$	0	0
$244$	−2.35037e9	−0.0424505
$245$	−4.51511e10	−0.800610
$246$	0	0
$247$	3.02273e9	0.0516730
$248$	−3.54812e10	−0.595616
$249$	0	0
$250$	−4.55918e10	−0.738171
$251$	−3.48447e10	−0.554121	−0.277061	−	0.960852i	$-0.589360\pi$
$251$	−3.48447e10	−0.554121	−0.277061	+	0.960852i	$0.589360\pi$
$252$	0	0
$253$	−1.57192e10	−0.241206
$254$	−1.25199e10	−0.188733
$255$	0	0
$256$	−4.65097e10	−0.676806
$257$	−6.17149e10	−0.882452	−0.441226	−	0.897396i	$-0.645456\pi$
$257$	−6.17149e10	−0.882452	−0.441226	+	0.897396i	$0.645456\pi$
$258$	0	0
$259$	−1.01771e11	−1.40533
$260$	5.47440e9	0.0742945
$261$	0	0
$262$	−1.12116e11	−1.46999
$263$	1.78558e10	0.230132	0.115066	−	0.993358i	$-0.463292\pi$
$263$	1.78558e10	0.230132	0.115066	+	0.993358i	$0.463292\pi$
$264$	0	0
$265$	−3.77806e10	−0.470611
$266$	1.73818e10	0.212876
$267$	0	0
$268$	8.90696e9	0.105469
$269$	5.24399e10	0.610628	0.305314	−	0.952252i	$-0.401239\pi$
$269$	5.24399e10	0.610628	0.305314	+	0.952252i	$0.401239\pi$
$270$	0	0
$271$	−5.03988e10	−0.567621	−0.283811	−	0.958880i	$-0.591599\pi$
$271$	−5.03988e10	−0.567621	−0.283811	+	0.958880i	$0.591599\pi$
$272$	−1.17212e11	−1.29841
$273$	0	0
$274$	8.81695e10	0.945020
$275$	−1.43520e10	−0.151327
$276$	0	0
$277$	−1.58677e11	−1.61941	−0.809703	−	0.586840i	$-0.800372\pi$
$277$	−1.58677e11	−1.61941	−0.809703	+	0.586840i	$0.800372\pi$
$278$	1.70219e11	1.70925
$279$	0	0
$280$	1.62286e11	1.57787
$281$	−3.04536e10	−0.291381	−0.145690	−	0.989330i	$-0.546540\pi$
$281$	−3.04536e10	−0.291381	−0.145690	+	0.989330i	$0.546540\pi$
$282$	0	0
$283$	4.21589e10	0.390706	0.195353	−	0.980733i	$-0.437415\pi$
$283$	4.21589e10	0.390706	0.195353	+	0.980733i	$0.437415\pi$
$284$	3.27092e9	0.0298358
$285$	0	0
$286$	1.73178e10	0.153054
$287$	−5.69204e10	−0.495221
$288$	0	0
$289$	2.87761e11	2.42656
$290$	−2.39817e10	−0.199108
$291$	0	0
$292$	−2.99233e10	−0.240872
$293$	−9.73493e10	−0.771665	−0.385832	−	0.922569i	$-0.626086\pi$
$293$	−9.73493e10	−0.771665	−0.385832	+	0.922569i	$0.626086\pi$
$294$	0	0
$295$	2.54707e11	1.95813
$296$	1.53034e11	1.15871
$297$	0	0
$298$	−1.35781e11	−0.997393
$299$	1.45995e10	0.105637
$300$	0	0
$301$	−3.20395e11	−2.24976
$302$	−7.90799e10	−0.547060
$303$	0	0
$304$	−1.94602e10	−0.130682
$305$	−2.96729e10	−0.196341
$306$	0	0
$307$	−1.62669e11	−1.04516	−0.522578	−	0.852591i	$-0.675030\pi$
$307$	−1.62669e11	−1.04516	−0.522578	+	0.852591i	$0.675030\pi$
$308$	−3.15609e10	−0.199835
$309$	0	0
$310$	−8.68900e10	−0.534370
$311$	−1.80301e11	−1.09289	−0.546445	−	0.837495i	$-0.684019\pi$
$311$	−1.80301e11	−1.09289	−0.546445	+	0.837495i	$0.684019\pi$
$312$	0	0
$313$	−6.08927e10	−0.358605	−0.179302	−	0.983794i	$-0.557384\pi$
$313$	−6.08927e10	−0.358605	−0.179302	+	0.983794i	$0.557384\pi$
$314$	−1.85328e11	−1.07586
$315$	0	0
$316$	5.72084e10	0.322751
$317$	−4.75152e10	−0.264281	−0.132140	−	0.991231i	$-0.542185\pi$
$317$	−4.75152e10	−0.264281	−0.132140	+	0.991231i	$0.542185\pi$
$318$	0	0
$319$	2.40436e10	0.129999
$320$	−2.31938e11	−1.23651
$321$	0	0
$322$	8.39522e10	0.435192
$323$	6.74646e10	0.344877
$324$	0	0
$325$	1.33297e10	0.0662743
$326$	−7.33777e10	−0.359820
$327$	0	0
$328$	8.55914e10	0.408317
$329$	−1.08617e11	−0.511112
$330$	0	0
$331$	−8.96236e10	−0.410390	−0.205195	−	0.978721i	$-0.565783\pi$
$331$	−8.96236e10	−0.410390	−0.205195	+	0.978721i	$0.565783\pi$
$332$	6.73557e10	0.304265
$333$	0	0
$334$	−8.84544e10	−0.388920
$335$	1.12448e11	0.487810
$336$	0	0
$337$	2.05747e11	0.868957	0.434478	−	0.900682i	$-0.356933\pi$
$337$	2.05747e11	0.868957	0.434478	+	0.900682i	$0.356933\pi$
$338$	−1.60842e10	−0.0670309
$339$	0	0
$340$	1.22183e11	0.495858
$341$	8.71142e10	0.348894
$342$	0	0
$343$	9.43587e10	0.368094
$344$	4.81780e11	1.85496
$345$	0	0
$346$	−3.33791e11	−1.25208
$347$	−3.41311e11	−1.26377	−0.631884	−	0.775063i	$-0.717718\pi$
$347$	−3.41311e11	−1.26377	−0.631884	+	0.775063i	$0.717718\pi$
$348$	0	0
$349$	−4.15352e11	−1.49866	−0.749328	−	0.662198i	$-0.769624\pi$
$349$	−4.15352e11	−1.49866	−0.749328	+	0.662198i	$0.769624\pi$
$350$	7.66503e10	0.273028
$351$	0	0
$352$	8.57107e10	0.297573
$353$	1.00300e11	0.343806	0.171903	−	0.985114i	$-0.445008\pi$
$353$	1.00300e11	0.343806	0.171903	+	0.985114i	$0.445008\pi$
$354$	0	0
$355$	4.12946e10	0.137996
$356$	4.50569e10	0.148675
$357$	0	0
$358$	2.42777e11	0.781149
$359$	3.35856e11	1.06716	0.533578	−	0.845751i	$-0.320847\pi$
$359$	3.35856e11	1.06716	0.533578	+	0.845751i	$0.320847\pi$
$360$	0	0
$361$	−3.11487e11	−0.965289
$362$	4.80613e11	1.47098
$363$	0	0
$364$	2.93128e10	0.0875187
$365$	−3.77774e11	−1.11407
$366$	0	0
$367$	3.43252e11	0.987679	0.493839	−	0.869553i	$-0.335593\pi$
$367$	3.43252e11	0.987679	0.493839	+	0.869553i	$0.335593\pi$
$368$	−9.39910e10	−0.267160
$369$	0	0
$370$	3.74765e11	1.03956
$371$	−2.02297e11	−0.554379
$372$	0	0
$373$	−3.20544e11	−0.857428	−0.428714	−	0.903440i	$-0.641033\pi$
$373$	−3.20544e11	−0.857428	−0.428714	+	0.903440i	$0.641033\pi$
$374$	3.86517e11	1.02152
$375$	0	0
$376$	1.63328e11	0.421420
$377$	−2.23309e10	−0.0569339
$378$	0	0
$379$	5.59129e11	1.39199	0.695994	−	0.718047i	$-0.254964\pi$
$379$	5.59129e11	1.39199	0.695994	+	0.718047i	$0.254964\pi$
$380$	2.02857e10	0.0499072
$381$	0	0
$382$	−1.71090e11	−0.411092
$383$	1.14158e11	0.271089	0.135544	−	0.990771i	$-0.456722\pi$
$383$	1.14158e11	0.271089	0.135544	+	0.990771i	$0.456722\pi$
$384$	0	0
$385$	−3.98448e11	−0.924270
$386$	4.60424e11	1.05564
$387$	0	0
$388$	−1.23083e10	−0.0275712
$389$	1.10883e11	0.245522	0.122761	−	0.992436i	$-0.460825\pi$
$389$	1.10883e11	0.245522	0.122761	+	0.992436i	$0.460825\pi$
$390$	0	0
$391$	3.25847e11	0.705048
$392$	3.63539e11	0.777613
$393$	0	0
$394$	−5.17255e10	−0.108136
$395$	7.22242e11	1.49278
$396$	0	0
$397$	2.31687e11	0.468107	0.234053	−	0.972224i	$-0.424801\pi$
$397$	2.31687e11	0.468107	0.234053	+	0.972224i	$0.424801\pi$
$398$	−1.64992e11	−0.329601
$399$	0	0
$400$	−8.58160e10	−0.167609
$401$	−5.44480e10	−0.105156	−0.0525778	−	0.998617i	$-0.516744\pi$
$401$	−5.44480e10	−0.105156	−0.0525778	+	0.998617i	$0.516744\pi$
$402$	0	0
$403$	−8.09089e10	−0.152800
$404$	−8.33137e10	−0.155597
$405$	0	0
$406$	−1.28411e11	−0.234549
$407$	−3.75732e11	−0.678740
$408$	0	0
$409$	2.35793e11	0.416654	0.208327	−	0.978059i	$-0.433198\pi$
$409$	2.35793e11	0.416654	0.208327	+	0.978059i	$0.433198\pi$
$410$	2.09605e11	0.366331
$411$	0	0
$412$	2.13494e10	0.0365046
$413$	1.36384e12	2.30668
$414$	0	0
$415$	8.50348e11	1.40728
$416$	−7.96055e10	−0.130324
$417$	0	0
$418$	6.41721e10	0.102814
$419$	−5.43639e11	−0.861682	−0.430841	−	0.902428i	$-0.641783\pi$
$419$	−5.43639e11	−0.861682	−0.430841	+	0.902428i	$0.641783\pi$
$420$	0	0
$421$	2.70622e11	0.419849	0.209925	−	0.977718i	$-0.432678\pi$
$421$	2.70622e11	0.419849	0.209925	+	0.977718i	$0.432678\pi$
$422$	−7.22291e11	−1.10868
$423$	0	0
$424$	3.04195e11	0.457094
$425$	2.97506e11	0.442329
$426$	0	0
$427$	−1.58884e11	−0.231289
$428$	1.52399e11	0.219526
$429$	0	0
$430$	1.17983e12	1.66422
$431$	1.07553e12	1.50132	0.750662	−	0.660687i	$-0.229735\pi$
$431$	1.07553e12	1.50132	0.750662	+	0.660687i	$0.229735\pi$
$432$	0	0
$433$	−2.63085e11	−0.359667	−0.179833	−	0.983697i	$-0.557556\pi$
$433$	−2.63085e11	−0.359667	−0.179833	+	0.983697i	$0.557556\pi$
$434$	−4.65254e11	−0.629486
$435$	0	0
$436$	1.28739e11	0.170616
$437$	5.40992e10	0.0709618
$438$	0	0
$439$	−8.20045e11	−1.05377	−0.526887	−	0.849935i	$-0.676641\pi$
$439$	−8.20045e11	−1.05377	−0.526887	+	0.849935i	$0.676641\pi$
$440$	5.99148e11	0.762074
$441$	0	0
$442$	−3.58985e11	−0.447380
$443$	1.77977e10	0.0219557	0.0109779	−	0.999940i	$-0.496506\pi$
$443$	1.77977e10	0.0219557	0.0109779	+	0.999940i	$0.496506\pi$
$444$	0	0
$445$	5.68832e11	0.687645
$446$	−1.22719e12	−1.46860
$447$	0	0
$448$	−1.24192e12	−1.45661
$449$	−1.15873e12	−1.34547	−0.672734	−	0.739885i	$-0.734880\pi$
$449$	−1.15873e12	−1.34547	−0.672734	+	0.739885i	$0.734880\pi$
$450$	0	0
$451$	−2.10145e11	−0.239180
$452$	−1.44770e11	−0.163138
$453$	0	0
$454$	7.89751e11	0.872446
$455$	3.70066e11	0.404789
$456$	0	0
$457$	−9.23583e11	−0.990497	−0.495249	−	0.868751i	$-0.664923\pi$
$457$	−9.23583e11	−0.990497	−0.495249	+	0.868751i	$0.664923\pi$
$458$	−9.10207e11	−0.966597
$459$	0	0
$460$	9.79778e10	0.102028
$461$	−6.32718e11	−0.652464	−0.326232	−	0.945290i	$-0.605779\pi$
$461$	−6.32718e11	−0.652464	−0.326232	+	0.945290i	$0.605779\pi$
$462$	0	0
$463$	2.14607e11	0.217035	0.108517	−	0.994095i	$-0.465390\pi$
$463$	2.14607e11	0.217035	0.108517	+	0.994095i	$0.465390\pi$
$464$	1.43766e11	0.143987
$465$	0	0
$466$	−5.56119e11	−0.546300
$467$	−5.49922e11	−0.535026	−0.267513	−	0.963554i	$-0.586202\pi$
$467$	−5.49922e11	−0.535026	−0.267513	+	0.963554i	$0.586202\pi$
$468$	0	0
$469$	6.02106e11	0.574639
$470$	3.99973e11	0.378086
$471$	0	0
$472$	−2.05081e12	−1.90189
$473$	−1.18287e12	−1.08658
$474$	0	0
$475$	4.93939e10	0.0445197
$476$	6.54234e11	0.584120
$477$	0	0
$478$	1.56542e11	0.137153
$479$	−1.60843e12	−1.39602	−0.698010	−	0.716088i	$-0.745931\pi$
$479$	−1.60843e12	−1.39602	−0.698010	+	0.716088i	$0.745931\pi$
$480$	0	0
$481$	3.48968e11	0.297258
$482$	8.53908e11	0.720609
$483$	0	0
$484$	1.74019e11	0.144142
$485$	−1.55389e11	−0.127521
$486$	0	0
$487$	−1.40030e12	−1.12808	−0.564040	−	0.825747i	$-0.690754\pi$
$487$	−1.40030e12	−1.12808	−0.564040	+	0.825747i	$0.690754\pi$
$488$	2.38915e11	0.190701
$489$	0	0
$490$	8.90270e11	0.697653
$491$	−1.31274e12	−1.01932	−0.509661	−	0.860376i	$-0.670229\pi$
$491$	−1.31274e12	−1.01932	−0.509661	+	0.860376i	$0.670229\pi$
$492$	0	0
$493$	−4.98406e11	−0.379990
$494$	−5.96010e10	−0.0450280
$495$	0	0
$496$	5.20888e11	0.386436
$497$	2.21113e11	0.162559
$498$	0	0
$499$	−3.50247e11	−0.252885	−0.126442	−	0.991974i	$-0.540356\pi$
$499$	−3.50247e11	−0.252885	−0.126442	+	0.991974i	$0.540356\pi$
$500$	−2.84907e11	−0.203863
$501$	0	0
$502$	6.87053e11	0.482863
$503$	−2.62962e12	−1.83163	−0.915815	−	0.401601i	$-0.868454\pi$
$503$	−2.62962e12	−1.83163	−0.915815	+	0.401601i	$0.868454\pi$
$504$	0	0
$505$	−1.05181e12	−0.719661
$506$	3.09945e11	0.210187
$507$	0	0
$508$	−7.82379e10	−0.0521231
$509$	−4.07673e11	−0.269204	−0.134602	−	0.990900i	$-0.542976\pi$
$509$	−4.07673e11	−0.269204	−0.134602	+	0.990900i	$0.542976\pi$
$510$	0	0
$511$	−2.02280e12	−1.31238
$512$	1.69164e12	1.08791
$513$	0	0
$514$	1.21687e12	0.768970
$515$	2.69531e11	0.168840
$516$	0	0
$517$	−4.01005e11	−0.246855
$518$	2.00669e12	1.22460
$519$	0	0
$520$	−5.56470e11	−0.333754
$521$	1.90638e12	1.13355	0.566773	−	0.823874i	$-0.308192\pi$
$521$	1.90638e12	1.13355	0.566773	+	0.823874i	$0.308192\pi$
$522$	0	0
$523$	−6.84980e11	−0.400332	−0.200166	−	0.979762i	$-0.564148\pi$
$523$	−6.84980e11	−0.400332	−0.200166	+	0.979762i	$0.564148\pi$
$524$	−7.00624e11	−0.405971
$525$	0	0
$526$	−3.52073e11	−0.200538
$527$	−1.80581e12	−1.01982
$528$	0	0
$529$	−1.53986e12	−0.854930
$530$	7.44942e11	0.410092
$531$	0	0
$532$	1.08620e11	0.0587906
$533$	1.95177e11	0.104750
$534$	0	0
$535$	1.92400e12	1.01534
$536$	−9.05389e11	−0.473798
$537$	0	0
$538$	−1.03399e12	−0.532103
$539$	−8.92568e11	−0.455503
$540$	0	0
$541$	−1.99962e12	−1.00360	−0.501798	−	0.864985i	$-0.667328\pi$
$541$	−1.99962e12	−1.00360	−0.501798	+	0.864985i	$0.667328\pi$
$542$	9.93743e11	0.494626
$543$	0	0
$544$	−1.77672e12	−0.869809
$545$	1.62529e12	0.789128
$546$	0	0
$547$	2.19967e12	1.05055	0.525273	−	0.850933i	$-0.323963\pi$
$547$	2.19967e12	1.05055	0.525273	+	0.850933i	$0.323963\pi$
$548$	5.50979e11	0.260989
$549$	0	0
$550$	2.82987e11	0.131866
$551$	−8.27485e10	−0.0382453
$552$	0	0
$553$	3.86726e12	1.75849
$554$	3.12873e12	1.41115
$555$	0	0
$556$	1.06371e12	0.472050
$557$	−2.10846e12	−0.928148	−0.464074	−	0.885797i	$-0.653613\pi$
$557$	−2.10846e12	−0.928148	−0.464074	+	0.885797i	$0.653613\pi$
$558$	0	0
$559$	1.09862e12	0.475875
$560$	−2.38247e12	−1.02372
$561$	0	0
$562$	6.00472e11	0.253910
$563$	−2.49136e12	−1.04508	−0.522540	−	0.852615i	$-0.675015\pi$
$563$	−2.49136e12	−1.04508	−0.522540	+	0.852615i	$0.675015\pi$
$564$	0	0
$565$	−1.82769e12	−0.754542
$566$	−8.31272e11	−0.340462
$567$	0	0
$568$	−3.32488e11	−0.134032
$569$	−6.91496e11	−0.276557	−0.138278	−	0.990393i	$-0.544157\pi$
$569$	−6.91496e11	−0.276557	−0.138278	+	0.990393i	$0.544157\pi$
$570$	0	0
$571$	−2.70238e11	−0.106386	−0.0531930	−	0.998584i	$-0.516940\pi$
$571$	−2.70238e11	−0.106386	−0.0531930	+	0.998584i	$0.516940\pi$
$572$	1.08220e11	0.0422695
$573$	0	0
$574$	1.12233e12	0.431537
$575$	2.38568e11	0.0910136
$576$	0	0
$577$	−3.66686e12	−1.37722	−0.688610	−	0.725132i	$-0.741779\pi$
$577$	−3.66686e12	−1.37722	−0.688610	+	0.725132i	$0.741779\pi$
$578$	−5.67395e12	−2.11451
$579$	0	0
$580$	−1.49864e11	−0.0549883
$581$	4.55321e12	1.65777
$582$	0	0
$583$	−7.46864e11	−0.267752
$584$	3.04169e12	1.08207
$585$	0	0
$586$	1.91949e12	0.672431
$587$	−1.16732e12	−0.405806	−0.202903	−	0.979199i	$-0.565038\pi$
$587$	−1.16732e12	−0.405806	−0.202903	+	0.979199i	$0.565038\pi$
$588$	0	0
$589$	−2.99812e11	−0.102643
$590$	−5.02221e12	−1.70632
$591$	0	0
$592$	−2.24664e12	−0.751773
$593$	−3.14463e12	−1.04430	−0.522148	−	0.852855i	$-0.674869\pi$
$593$	−3.14463e12	−1.04430	−0.522148	+	0.852855i	$0.674869\pi$
$594$	0	0
$595$	8.25954e12	2.70165
$596$	−8.48508e11	−0.275453
$597$	0	0
$598$	−2.87867e11	−0.0920527
$599$	−2.09251e12	−0.664120	−0.332060	−	0.943258i	$-0.607744\pi$
$599$	−2.09251e12	−0.664120	−0.332060	+	0.943258i	$0.607744\pi$
$600$	0	0
$601$	4.34608e12	1.35882	0.679410	−	0.733758i	$-0.262236\pi$
$601$	4.34608e12	1.35882	0.679410	+	0.733758i	$0.262236\pi$
$602$	6.31742e12	1.96045
$603$	0	0
$604$	−4.94177e11	−0.151083
$605$	2.19694e12	0.666683
$606$	0	0
$607$	1.73690e12	0.519310	0.259655	−	0.965701i	$-0.416391\pi$
$607$	1.73690e12	0.519310	0.259655	+	0.965701i	$0.416391\pi$
$608$	−2.94982e11	−0.0875447
$609$	0	0
$610$	5.85078e11	0.171092
$611$	3.72441e11	0.108112
$612$	0	0
$613$	4.02259e12	1.15062	0.575312	−	0.817934i	$-0.304881\pi$
$613$	4.02259e12	1.15062	0.575312	+	0.817934i	$0.304881\pi$
$614$	3.20744e12	0.910752
$615$	0	0
$616$	3.20815e12	0.897722
$617$	5.03083e12	1.39752	0.698758	−	0.715358i	$-0.253737\pi$
$617$	5.03083e12	1.39752	0.698758	+	0.715358i	$0.253737\pi$
$618$	0	0
$619$	−4.77626e12	−1.30761	−0.653807	−	0.756661i	$-0.726829\pi$
$619$	−4.77626e12	−1.30761	−0.653807	+	0.756661i	$0.726829\pi$
$620$	−5.42983e11	−0.147579
$621$	0	0
$622$	3.55510e12	0.952348
$623$	3.04582e12	0.810044
$624$	0	0
$625$	−4.50842e12	−1.18186
$626$	1.20066e12	0.312489
$627$	0	0
$628$	−1.15813e12	−0.297125
$629$	7.78864e12	1.98396
$630$	0	0
$631$	−3.04417e12	−0.764428	−0.382214	−	0.924074i	$-0.624838\pi$
$631$	−3.04417e12	−0.764428	−0.382214	+	0.924074i	$0.624838\pi$
$632$	−5.81521e12	−1.44990
$633$	0	0
$634$	9.36884e11	0.230295
$635$	−9.87734e11	−0.241078
$636$	0	0
$637$	8.28989e11	0.199490
$638$	−4.74081e11	−0.113282
$639$	0	0
$640$	2.35337e12	0.554473
$641$	1.53417e12	0.358932	0.179466	−	0.983764i	$-0.442563\pi$
$641$	1.53417e12	0.358932	0.179466	+	0.983764i	$0.442563\pi$
$642$	0	0
$643$	3.17074e12	0.731494	0.365747	−	0.930714i	$-0.380814\pi$
$643$	3.17074e12	0.731494	0.365747	+	0.930714i	$0.380814\pi$
$644$	5.24624e11	0.120188
$645$	0	0
$646$	−1.33024e12	−0.300527
$647$	6.75140e12	1.51469	0.757347	−	0.653013i	$-0.226495\pi$
$647$	6.75140e12	1.51469	0.757347	+	0.653013i	$0.226495\pi$
$648$	0	0
$649$	5.03517e12	1.11407
$650$	−2.62829e11	−0.0577516
$651$	0	0
$652$	−4.58544e11	−0.0993726
$653$	3.96591e12	0.853559	0.426780	−	0.904356i	$-0.359648\pi$
$653$	3.96591e12	0.853559	0.426780	+	0.904356i	$0.359648\pi$
$654$	0	0
$655$	−8.84520e12	−1.87768
$656$	−1.25654e12	−0.264916
$657$	0	0
$658$	2.14166e12	0.445384
$659$	1.08932e12	0.224993	0.112497	−	0.993652i	$-0.464115\pi$
$659$	1.08932e12	0.224993	0.112497	+	0.993652i	$0.464115\pi$
$660$	0	0
$661$	−9.01775e12	−1.83735	−0.918674	−	0.395017i	$-0.870739\pi$
$661$	−9.01775e12	−1.83735	−0.918674	+	0.395017i	$0.870739\pi$
$662$	1.76716e12	0.357615
$663$	0	0
$664$	−6.84667e12	−1.36686
$665$	1.37130e12	0.271916
$666$	0	0
$667$	−3.99667e11	−0.0781865
$668$	−5.52759e11	−0.107409
$669$	0	0
$670$	−2.21721e12	−0.425079
$671$	−5.86587e11	−0.111707
$672$	0	0
$673$	6.77812e12	1.27362	0.636812	−	0.771019i	$-0.280253\pi$
$673$	6.77812e12	1.27362	0.636812	+	0.771019i	$0.280253\pi$
$674$	−4.05683e12	−0.757211
$675$	0	0
$676$	−1.00512e11	−0.0185122
$677$	9.77011e12	1.78752	0.893759	−	0.448548i	$-0.148059\pi$
$677$	9.77011e12	1.78752	0.893759	+	0.448548i	$0.148059\pi$
$678$	0	0
$679$	−8.32035e11	−0.150220
$680$	−1.24199e13	−2.22755
$681$	0	0
$682$	−1.71768e12	−0.304027
$683$	−7.99180e12	−1.40524	−0.702621	−	0.711564i	$-0.747987\pi$
$683$	−7.99180e12	−1.40524	−0.702621	+	0.711564i	$0.747987\pi$
$684$	0	0
$685$	6.95597e12	1.20712
$686$	−1.86053e12	−0.320758
$687$	0	0
$688$	−7.07285e12	−1.20350
$689$	6.93664e11	0.117264
$690$	0	0
$691$	−7.13265e12	−1.19014	−0.595072	−	0.803672i	$-0.702877\pi$
$691$	−7.13265e12	−1.19014	−0.595072	+	0.803672i	$0.702877\pi$
$692$	−2.08589e12	−0.345791
$693$	0	0
$694$	6.72982e12	1.10125
$695$	1.34291e13	2.18331
$696$	0	0
$697$	4.35616e12	0.699127
$698$	8.18974e12	1.30593
$699$	0	0
$700$	4.78994e11	0.0754031
$701$	−1.19764e13	−1.87325	−0.936626	−	0.350330i	$-0.886069\pi$
$701$	−1.19764e13	−1.87325	−0.936626	+	0.350330i	$0.886069\pi$
$702$	0	0
$703$	1.29312e12	0.199683
$704$	−4.58507e12	−0.703507
$705$	0	0
$706$	−1.97767e12	−0.299594
$707$	−5.63196e12	−0.847759
$708$	0	0
$709$	−6.13692e12	−0.912099	−0.456050	−	0.889954i	$-0.650736\pi$
$709$	−6.13692e12	−0.912099	−0.456050	+	0.889954i	$0.650736\pi$
$710$	−8.14229e11	−0.120250
$711$	0	0
$712$	−4.58002e12	−0.667893
$713$	−1.44806e12	−0.209838
$714$	0	0
$715$	1.36626e12	0.195504
$716$	1.51713e12	0.215733
$717$	0	0
$718$	−6.62226e12	−0.929922
$719$	−4.74258e12	−0.661812	−0.330906	−	0.943664i	$-0.607354\pi$
$719$	−4.74258e12	−0.661812	−0.330906	+	0.943664i	$0.607354\pi$
$720$	0	0
$721$	1.44321e12	0.198893
$722$	6.14177e12	0.841155
$723$	0	0
$724$	3.00339e12	0.406245
$725$	−3.64905e11	−0.0490523
$726$	0	0
$727$	−9.67795e12	−1.28493	−0.642464	−	0.766316i	$-0.722088\pi$
$727$	−9.67795e12	−1.28493	−0.642464	+	0.766316i	$0.722088\pi$
$728$	−2.97963e12	−0.393162
$729$	0	0
$730$	7.44878e12	0.970806
$731$	2.45201e13	3.17610
$732$	0	0
$733$	1.50341e13	1.92357	0.961787	−	0.273798i	$-0.0882801\pi$
$733$	1.50341e13	1.92357	0.961787	+	0.273798i	$0.0882801\pi$
$734$	−6.76810e12	−0.860666
$735$	0	0
$736$	−1.42474e12	−0.178972
$737$	2.22293e12	0.277537
$738$	0	0
$739$	−2.14842e12	−0.264983	−0.132492	−	0.991184i	$-0.542298\pi$
$739$	−2.14842e12	−0.264983	−0.132492	+	0.991184i	$0.542298\pi$
$740$	2.34194e12	0.287100
$741$	0	0
$742$	3.98881e12	0.483087
$743$	−5.22310e12	−0.628751	−0.314376	−	0.949299i	$-0.601795\pi$
$743$	−5.22310e12	−0.628751	−0.314376	+	0.949299i	$0.601795\pi$
$744$	0	0
$745$	−1.07122e13	−1.27402
$746$	6.32035e12	0.747165
$747$	0	0
$748$	2.41538e12	0.282116
$749$	1.03021e13	1.19607
$750$	0	0
$751$	1.65523e13	1.89880	0.949399	−	0.314071i	$-0.101693\pi$
$751$	1.65523e13	1.89880	0.949399	+	0.314071i	$0.101693\pi$
$752$	−2.39776e12	−0.273417
$753$	0	0
$754$	4.40312e11	0.0496123
$755$	−6.23886e12	−0.698786
$756$	0	0
$757$	1.59809e13	1.76877	0.884384	−	0.466761i	$-0.154579\pi$
$757$	1.59809e13	1.76877	0.884384	+	0.466761i	$0.154579\pi$
$758$	−1.10247e13	−1.21298
$759$	0	0
$760$	−2.06203e12	−0.224199
$761$	−3.31655e12	−0.358473	−0.179236	−	0.983806i	$-0.557363\pi$
$761$	−3.31655e12	−0.358473	−0.179236	+	0.983806i	$0.557363\pi$
$762$	0	0
$763$	8.70266e12	0.929591
$764$	−1.06916e12	−0.113533
$765$	0	0
$766$	−2.25092e12	−0.236227
$767$	−4.67651e12	−0.487914
$768$	0	0
$769$	−2.26842e12	−0.233913	−0.116956	−	0.993137i	$-0.537314\pi$
$769$	−2.26842e12	−0.233913	−0.116956	+	0.993137i	$0.537314\pi$
$770$	7.85644e12	0.805411
$771$	0	0
$772$	2.87723e12	0.291539
$773$	−1.45998e13	−1.47075	−0.735375	−	0.677661i	$-0.762994\pi$
$773$	−1.45998e13	−1.47075	−0.735375	+	0.677661i	$0.762994\pi$
$774$	0	0
$775$	−1.32212e12	−0.131647
$776$	1.25113e12	0.123859
$777$	0	0
$778$	−2.18634e12	−0.213949
$779$	7.23237e11	0.0703659
$780$	0	0
$781$	8.16330e11	0.0785120
$782$	−6.42492e12	−0.614380
$783$	0	0
$784$	−5.33700e12	−0.504516
$785$	−1.46211e13	−1.37425
$786$	0	0
$787$	−1.26923e13	−1.17938	−0.589692	−	0.807628i	$-0.700751\pi$
$787$	−1.26923e13	−1.17938	−0.589692	+	0.807628i	$0.700751\pi$
$788$	−3.23237e11	−0.0298643
$789$	0	0
$790$	−1.42409e13	−1.30081
$791$	−9.78638e12	−0.888849
$792$	0	0
$793$	5.44804e11	0.0489228
$794$	−4.56831e12	−0.407909
$795$	0	0
$796$	−1.03105e12	−0.0910270
$797$	1.22392e13	1.07446	0.537230	−	0.843436i	$-0.319471\pi$
$797$	1.22392e13	1.07446	0.537230	+	0.843436i	$0.319471\pi$
$798$	0	0
$799$	8.31254e12	0.721561
$800$	−1.30082e12	−0.112282
$801$	0	0
$802$	1.07358e12	0.0916328
$803$	−7.46801e12	−0.633847
$804$	0	0
$805$	6.62325e12	0.555891
$806$	1.59533e12	0.133150
$807$	0	0
$808$	8.46880e12	0.698990
$809$	4.89425e12	0.401714	0.200857	−	0.979621i	$-0.435627\pi$
$809$	4.89425e12	0.401714	0.200857	+	0.979621i	$0.435627\pi$
$810$	0	0
$811$	−3.11178e12	−0.252590	−0.126295	−	0.991993i	$-0.540309\pi$
$811$	−3.11178e12	−0.252590	−0.126295	+	0.991993i	$0.540309\pi$
$812$	−8.02449e11	−0.0647761
$813$	0	0
$814$	7.40853e12	0.591456
$815$	−5.78900e12	−0.459615
$816$	0	0
$817$	4.07098e12	0.319669
$818$	−4.64926e12	−0.363073
$819$	0	0
$820$	1.30984e12	0.101171
$821$	−3.48502e12	−0.267708	−0.133854	−	0.991001i	$-0.542735\pi$
$821$	−3.48502e12	−0.267708	−0.133854	+	0.991001i	$0.542735\pi$
$822$	0	0
$823$	−4.38954e12	−0.333518	−0.166759	−	0.985998i	$-0.553330\pi$
$823$	−4.38954e12	−0.333518	−0.166759	+	0.985998i	$0.553330\pi$
$824$	−2.17016e12	−0.163990
$825$	0	0
$826$	−2.68916e13	−2.01004
$827$	1.21660e13	0.904424	0.452212	−	0.891910i	$-0.350635\pi$
$827$	1.21660e13	0.904424	0.452212	+	0.891910i	$0.350635\pi$
$828$	0	0
$829$	−1.35524e12	−0.0996600	−0.0498300	−	0.998758i	$-0.515868\pi$
$829$	−1.35524e12	−0.0996600	−0.0498300	+	0.998758i	$0.515868\pi$
$830$	−1.67668e13	−1.22631
$831$	0	0
$832$	4.25847e12	0.308105
$833$	1.85023e13	1.33144
$834$	0	0
$835$	−6.97845e12	−0.496786
$836$	4.01017e11	0.0283945
$837$	0	0
$838$	1.07192e13	0.750872
$839$	1.12215e13	0.781847	0.390924	−	0.920423i	$-0.372156\pi$
$839$	1.12215e13	0.781847	0.390924	+	0.920423i	$0.372156\pi$
$840$	0	0
$841$	−1.38958e13	−0.957861
$842$	−5.33601e12	−0.365858
$843$	0	0
$844$	−4.51366e12	−0.306188
$845$	−1.26894e12	−0.0856218
$846$	0	0
$847$	1.17636e13	0.785351
$848$	−4.46578e12	−0.296563
$849$	0	0
$850$	−5.86610e12	−0.385447
$851$	6.24564e12	0.408220
$852$	0	0
$853$	7.91778e11	0.0512074	0.0256037	−	0.999672i	$-0.491849\pi$
$853$	7.91778e11	0.0512074	0.0256037	+	0.999672i	$0.491849\pi$
$854$	3.13281e12	0.201546
$855$	0	0
$856$	−1.54913e13	−0.986180
$857$	−1.76782e13	−1.11950	−0.559751	−	0.828661i	$-0.689103\pi$
$857$	−1.76782e13	−1.11950	−0.559751	+	0.828661i	$0.689103\pi$
$858$	0	0
$859$	4.03561e12	0.252895	0.126448	−	0.991973i	$-0.459642\pi$
$859$	4.03561e12	0.252895	0.126448	+	0.991973i	$0.459642\pi$
$860$	7.37286e12	0.459614
$861$	0	0
$862$	−2.12068e13	−1.30826
$863$	7.74540e11	0.0475330	0.0237665	−	0.999718i	$-0.492434\pi$
$863$	7.74540e11	0.0475330	0.0237665	+	0.999718i	$0.492434\pi$
$864$	0	0
$865$	−2.63338e13	−1.59934
$866$	5.18739e12	0.313414
$867$	0	0
$868$	−2.90741e12	−0.173847
$869$	1.42776e13	0.849311
$870$	0	0
$871$	−2.06459e12	−0.121549
$872$	−1.30862e13	−0.766461
$873$	0	0
$874$	−1.06671e12	−0.0618363
$875$	−1.92596e13	−1.11073
$876$	0	0
$877$	−2.57530e13	−1.47004	−0.735020	−	0.678046i	$-0.762827\pi$
$877$	−2.57530e13	−1.47004	−0.735020	+	0.678046i	$0.762827\pi$
$878$	1.61693e13	0.918261
$879$	0	0
$880$	−8.79590e12	−0.494434
$881$	−1.93336e12	−0.108124	−0.0540620	−	0.998538i	$-0.517217\pi$
$881$	−1.93336e12	−0.108124	−0.0540620	+	0.998538i	$0.517217\pi$
$882$	0	0
$883$	2.94334e13	1.62936	0.814681	−	0.579910i	$-0.196912\pi$
$883$	2.94334e13	1.62936	0.814681	+	0.579910i	$0.196912\pi$
$884$	−2.24333e12	−0.123554
$885$	0	0
$886$	−3.50928e11	−0.0191323
$887$	−4.07138e12	−0.220844	−0.110422	−	0.993885i	$-0.535220\pi$
$887$	−4.07138e12	−0.220844	−0.110422	+	0.993885i	$0.535220\pi$
$888$	0	0
$889$	−5.28884e12	−0.283990
$890$	−1.12160e13	−0.599215
$891$	0	0
$892$	−7.66881e12	−0.405589
$893$	1.38010e12	0.0726238
$894$	0	0
$895$	1.91534e13	0.997799
$896$	1.26012e13	0.653168
$897$	0	0
$898$	2.28473e13	1.17244
$899$	2.21491e12	0.113094
$900$	0	0
$901$	1.54819e13	0.782643
$902$	4.14356e12	0.208422
$903$	0	0
$904$	1.47158e13	0.732869
$905$	3.79170e13	1.87895
$906$	0	0
$907$	−5.11710e12	−0.251068	−0.125534	−	0.992089i	$-0.540064\pi$
$907$	−5.11710e12	−0.251068	−0.125534	+	0.992089i	$0.540064\pi$
$908$	4.93522e12	0.240946
$909$	0	0
$910$	−7.29682e12	−0.352734
$911$	1.65675e13	0.796937	0.398468	−	0.917182i	$-0.369542\pi$
$911$	1.65675e13	0.796937	0.398468	+	0.917182i	$0.369542\pi$
$912$	0	0
$913$	1.68101e13	0.800665
$914$	1.82108e13	0.863121
$915$	0	0
$916$	−5.68796e12	−0.266948
$917$	−4.73618e13	−2.21191
$918$	0	0
$919$	2.46210e13	1.13864	0.569319	−	0.822117i	$-0.307207\pi$
$919$	2.46210e13	1.13864	0.569319	+	0.822117i	$0.307207\pi$
$920$	−9.95940e12	−0.458340
$921$	0	0
$922$	1.24757e13	0.568558
$923$	−7.58182e11	−0.0343848
$924$	0	0
$925$	5.70242e12	0.256107
$926$	−4.23153e12	−0.189125
$927$	0	0
$928$	2.17923e12	0.0964577
$929$	−2.10967e13	−0.929272	−0.464636	−	0.885502i	$-0.653815\pi$
$929$	−2.10967e13	−0.929272	−0.464636	+	0.885502i	$0.653815\pi$
$930$	0	0
$931$	3.07186e12	0.134007
$932$	−3.47524e12	−0.150873
$933$	0	0
$934$	1.08431e13	0.466223
$935$	3.04935e13	1.30484
$936$	0	0
$937$	−3.29230e13	−1.39531	−0.697656	−	0.716433i	$-0.745774\pi$
$937$	−3.29230e13	−1.39531	−0.697656	+	0.716433i	$0.745774\pi$
$938$	−1.18721e13	−0.500742
$939$	0	0
$940$	2.49947e12	0.104417
$941$	−3.85496e13	−1.60275	−0.801376	−	0.598161i	$-0.795898\pi$
$941$	−3.85496e13	−1.60275	−0.801376	+	0.598161i	$0.795898\pi$
$942$	0	0
$943$	3.49316e12	0.143852
$944$	3.01072e13	1.23395
$945$	0	0
$946$	2.33234e13	0.946852
$947$	−1.22394e13	−0.494521	−0.247261	−	0.968949i	$-0.579530\pi$
$947$	−1.22394e13	−0.494521	−0.247261	+	0.968949i	$0.579530\pi$
$948$	0	0
$949$	6.93605e12	0.277597
$950$	−9.73928e11	−0.0387945
$951$	0	0
$952$	−6.65026e13	−2.62405
$953$	−3.26425e13	−1.28194	−0.640968	−	0.767568i	$-0.721467\pi$
$953$	−3.26425e13	−1.28194	−0.640968	+	0.767568i	$0.721467\pi$
$954$	0	0
$955$	−1.34978e13	−0.525108
$956$	9.78247e11	0.0378781
$957$	0	0
$958$	3.17143e13	1.21649
$959$	3.72459e13	1.42198
$960$	0	0
$961$	−1.84146e13	−0.696478
$962$	−6.88081e12	−0.259031
$963$	0	0
$964$	5.33614e12	0.199013
$965$	3.63243e13	1.34842
$966$	0	0
$967$	−1.28552e13	−0.472780	−0.236390	−	0.971658i	$-0.575964\pi$
$967$	−1.28552e13	−0.472780	−0.236390	+	0.971658i	$0.575964\pi$
$968$	−1.76889e13	−0.647533
$969$	0	0
$970$	3.06390e12	0.111122
$971$	4.30846e13	1.55538	0.777689	−	0.628650i	$-0.216392\pi$
$971$	4.30846e13	1.55538	0.777689	+	0.628650i	$0.216392\pi$
$972$	0	0
$973$	7.19064e13	2.57193
$974$	2.76105e13	0.983012
$975$	0	0
$976$	−3.50743e12	−0.123727
$977$	−3.58870e13	−1.26012	−0.630059	−	0.776547i	$-0.716969\pi$
$977$	−3.58870e13	−1.26012	−0.630059	+	0.776547i	$0.716969\pi$
$978$	0	0
$979$	1.12449e13	0.391233
$980$	5.56338e12	0.192673
$981$	0	0
$982$	2.58840e13	0.888239
$983$	−4.49637e12	−0.153593	−0.0767964	−	0.997047i	$-0.524469\pi$
$983$	−4.49637e12	−0.153593	−0.0767964	+	0.997047i	$0.524469\pi$
$984$	0	0
$985$	−4.08078e12	−0.138128
$986$	9.82735e12	0.331124
$987$	0	0
$988$	−3.72452e11	−0.0124355
$989$	1.96624e13	0.653513
$990$	0	0
$991$	1.56221e13	0.514526	0.257263	−	0.966341i	$-0.417179\pi$
$991$	1.56221e13	0.514526	0.257263	+	0.966341i	$0.417179\pi$
$992$	7.89573e12	0.258875
$993$	0	0
$994$	−4.35981e12	−0.141654
$995$	−1.30167e13	−0.421015
$996$	0	0
$997$	−3.76783e13	−1.20771	−0.603856	−	0.797094i	$-0.706370\pi$
$997$	−3.76783e13	−1.20771	−0.603856	+	0.797094i	$0.706370\pi$
$998$	6.90603e12	0.220364
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.10.a.e.1.2		5
3.2	odd	2		13.10.a.b.1.4	✓	5
12.11	even	2		208.10.a.h.1.1		5
15.14	odd	2		325.10.a.b.1.2		5
39.38	odd	2		169.10.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.4	✓	5	3.2	odd	2
117.10.a.e.1.2		5	1.1	even	1	trivial
169.10.a.b.1.2		5	39.38	odd	2
208.10.a.h.1.1		5	12.11	even	2
325.10.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-19.7176 q^{2} -123.217 q^{4} -1555.58 q^{5} -8329.39 q^{7} +12524.9 q^{8} +O(q^{10})\)	\(q-19.7176 q^{2} -123.217 q^{4} -1555.58 q^{5} -8329.39 q^{7} +12524.9 q^{8} +30672.3 q^{10} -30751.5 q^{11} +28561.0 q^{13} +164236. q^{14} -183875. q^{16} +637455. q^{17} +105834. q^{19} +191674. q^{20} +606345. q^{22} +511169. q^{23} +466710. q^{25} -563154. q^{26} +1.02632e6 q^{28} -781868. q^{29} -2.83285e6 q^{31} -2.78721e6 q^{32} -1.25691e7 q^{34} +1.29571e7 q^{35} +1.22183e7 q^{37} -2.08680e6 q^{38} -1.94836e7 q^{40} +6.83367e6 q^{41} +3.84656e7 q^{43} +3.78910e6 q^{44} -1.00790e7 q^{46} +1.30402e7 q^{47} +2.90252e7 q^{49} -9.20238e6 q^{50} -3.51920e6 q^{52} +2.42871e7 q^{53} +4.78364e7 q^{55} -1.04325e8 q^{56} +1.54166e7 q^{58} -1.63738e8 q^{59} +1.90751e7 q^{61} +5.58569e7 q^{62} +1.49101e8 q^{64} -4.44290e7 q^{65} -7.22869e7 q^{67} -7.85452e7 q^{68} -2.55482e8 q^{70} -2.65461e7 q^{71} +2.42850e8 q^{73} -2.40916e8 q^{74} -1.30406e7 q^{76} +2.56141e8 q^{77} -4.64290e8 q^{79} +2.86032e8 q^{80} -1.34744e8 q^{82} -5.46643e8 q^{83} -9.91613e8 q^{85} -7.58449e8 q^{86} -3.85160e8 q^{88} -3.65672e8 q^{89} -2.37896e8 q^{91} -6.29847e7 q^{92} -2.57121e8 q^{94} -1.64634e8 q^{95} +9.98914e7 q^{97} -5.72307e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8}+O(q^{10}) \) 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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