LMFDB - Embedded newform 117.10.a.c.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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.3567$ 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)

$f(q)$	$=$	$q-7.35673 q^{2} -457.879 q^{4} +1236.25 q^{5} +892.010 q^{7} +7135.13 q^{8} +O(q^{10})$	\(q-7.35673 q^{2} -457.879 q^{4} +1236.25 q^{5} +892.010 q^{7} +7135.13 q^{8} -9094.74 q^{10} +27149.8 q^{11} -28561.0 q^{13} -6562.27 q^{14} +181943. q^{16} +34643.4 q^{17} +428885. q^{19} -566052. q^{20} -199734. q^{22} -2.03704e6 q^{23} -424814. q^{25} +210115. q^{26} -408432. q^{28} +5.26400e6 q^{29} -4.15910e6 q^{31} -4.99169e6 q^{32} -254862. q^{34} +1.10275e6 q^{35} -7.58854e6 q^{37} -3.15519e6 q^{38} +8.82080e6 q^{40} +4.92536e6 q^{41} +1.71882e7 q^{43} -1.24313e7 q^{44} +1.49859e7 q^{46} +2.95568e7 q^{47} -3.95579e7 q^{49} +3.12524e6 q^{50} +1.30775e7 q^{52} +2.72331e7 q^{53} +3.35640e7 q^{55} +6.36461e6 q^{56} -3.87258e7 q^{58} +1.13602e8 q^{59} -3.76868e7 q^{61} +3.05973e7 q^{62} -5.64321e7 q^{64} -3.53085e7 q^{65} +1.90094e8 q^{67} -1.58625e7 q^{68} -8.11260e6 q^{70} -6.87130e7 q^{71} +3.61495e8 q^{73} +5.58268e7 q^{74} -1.96377e8 q^{76} +2.42179e7 q^{77} -1.42229e8 q^{79} +2.24926e8 q^{80} -3.62346e7 q^{82} +5.80240e7 q^{83} +4.28279e7 q^{85} -1.26449e8 q^{86} +1.93718e8 q^{88} +8.59928e8 q^{89} -2.54767e7 q^{91} +9.32716e8 q^{92} -2.17442e8 q^{94} +5.30208e8 q^{95} +1.46970e9 q^{97} +2.91017e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} + 1429 q^{4} - 471 q^{5} - 11241 q^{7} + 45543 q^{8}+O(q^{10}) $ 4 * q + 33 * q^2 + 1429 * q^4 - 471 * q^5 - 11241 * q^7 + 45543 * q^8	\( 4 q + 33 q^{2} + 1429 q^{4} - 471 q^{5} - 11241 q^{7} + 45543 q^{8} - 67831 q^{10} + 40140 q^{11} - 114244 q^{13} + 277653 q^{14} + 726609 q^{16} - 78717 q^{17} + 209664 q^{19} - 870843 q^{20} + 1364090 q^{22} + 4257444 q^{23} - 2900157 q^{25} - 942513 q^{26} + 4035181 q^{28} + 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 26257659 q^{34} + 13789797 q^{35} + 4636891 q^{37} - 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} - 33368081 q^{43} - 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 23294923 q^{49} + 4217748 q^{50} - 40813669 q^{52} + 171019326 q^{53} - 121160538 q^{55} + 281552967 q^{56} + 79964734 q^{58} + 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 768962465 q^{64} + 13452231 q^{65} - 41174072 q^{67} + 717615423 q^{68} + 409056389 q^{70} - 252460989 q^{71} + 594415068 q^{73} + 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} - 875148240 q^{82} + 79577862 q^{83} + 549463469 q^{85} + 589924887 q^{86} - 2327564370 q^{88} + 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} + 1859909503 q^{94} + 1273705170 q^{95} + 1049098084 q^{97} - 420532254 q^{98}+O(q^{100}) \) 4 * q + 33 * q^2 + 1429 * q^4 - 471 * q^5 - 11241 * q^7 + 45543 * q^8 - 67831 * q^10 + 40140 * q^11 - 114244 * q^13 + 277653 * q^14 + 726609 * q^16 - 78717 * q^17 + 209664 * q^19 - 870843 * q^20 + 1364090 * q^22 + 4257444 * q^23 - 2900157 * q^25 - 942513 * q^26 + 4035181 * q^28 + 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 26257659 * q^34 + 13789797 * q^35 + 4636891 * q^37 - 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 - 33368081 * q^43 - 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 23294923 * q^49 + 4217748 * q^50 - 40813669 * q^52 + 171019326 * q^53 - 121160538 * q^55 + 281552967 * q^56 + 79964734 * q^58 + 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 768962465 * q^64 + 13452231 * q^65 - 41174072 * q^67 + 717615423 * q^68 + 409056389 * q^70 - 252460989 * q^71 + 594415068 * q^73 + 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 - 875148240 * q^82 + 79577862 * q^83 + 549463469 * q^85 + 589924887 * q^86 - 2327564370 * q^88 + 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 + 1859909503 * q^94 + 1273705170 * q^95 + 1049098084 * q^97 - 420532254 * 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 $

$2$	−7.35673	−0.325124	−0.162562	−	0.986698i	$-0.551976\pi$
$2$	−7.35673	−0.325124	−0.162562	+	0.986698i	$0.551976\pi$
$3$	0	0
$3$	0	0
$4$	−457.879	−0.894294
$5$	1236.25	0.884588	0.442294	−	0.896870i	$-0.354165\pi$
$5$	1236.25	0.884588	0.442294	+	0.896870i	$0.354165\pi$
$6$	0	0
$7$	892.010	0.140420	0.0702099	−	0.997532i	$-0.477633\pi$
$7$	892.010	0.140420	0.0702099	+	0.997532i	$0.477633\pi$
$8$	7135.13	0.615881
$9$	0	0
$10$	−9094.74	−0.287601
$11$	27149.8	0.559114	0.279557	−	0.960129i	$-0.409812\pi$
$11$	27149.8	0.559114	0.279557	+	0.960129i	$0.409812\pi$
$12$	0	0
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−6562.27	−0.0456539
$15$	0	0
$16$	181943.	0.694056
$17$	34643.4	0.100601	0.0503003	−	0.998734i	$-0.483982\pi$
$17$	34643.4	0.100601	0.0503003	+	0.998734i	$0.483982\pi$
$18$	0	0
$19$	428885.	0.755004	0.377502	−	0.926009i	$-0.376783\pi$
$19$	428885.	0.755004	0.377502	+	0.926009i	$0.376783\pi$
$20$	−566052.	−0.791081
$21$	0	0
$22$	−199734.	−0.181782
$23$	−2.03704e6	−1.51783	−0.758916	−	0.651188i	$-0.774271\pi$
$23$	−2.03704e6	−1.51783	−0.758916	+	0.651188i	$0.774271\pi$
$24$	0	0
$25$	−424814.	−0.217505
$26$	210115.	0.0901733
$27$	0	0
$28$	−408432.	−0.125577
$29$	5.26400e6	1.38205	0.691026	−	0.722830i	$-0.257159\pi$
$29$	5.26400e6	1.38205	0.691026	+	0.722830i	$0.257159\pi$
$30$	0	0
$31$	−4.15910e6	−0.808856	−0.404428	−	0.914570i	$-0.632529\pi$
$31$	−4.15910e6	−0.808856	−0.404428	+	0.914570i	$0.632529\pi$
$32$	−4.99169e6	−0.841536
$33$	0	0
$34$	−254862.	−0.0327077
$35$	1.10275e6	0.124214
$36$	0	0
$37$	−7.58854e6	−0.665657	−0.332829	−	0.942987i	$-0.608003\pi$
$37$	−7.58854e6	−0.665657	−0.332829	+	0.942987i	$0.608003\pi$
$38$	−3.15519e6	−0.245470
$39$	0	0
$40$	8.82080e6	0.544801
$41$	4.92536e6	0.272214	0.136107	−	0.990694i	$-0.456541\pi$
$41$	4.92536e6	0.272214	0.136107	+	0.990694i	$0.456541\pi$
$42$	0	0
$43$	1.71882e7	0.766696	0.383348	−	0.923604i	$-0.374771\pi$
$43$	1.71882e7	0.766696	0.383348	+	0.923604i	$0.374771\pi$
$44$	−1.24313e7	−0.500012
$45$	0	0
$46$	1.49859e7	0.493484
$47$	2.95568e7	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$47$	2.95568e7	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$48$	0	0
$49$	−3.95579e7	−0.980282
$50$	3.12524e6	0.0707161
$51$	0	0
$52$	1.30775e7	0.248033
$53$	2.72331e7	0.474084	0.237042	−	0.971499i	$-0.423822\pi$
$53$	2.72331e7	0.474084	0.237042	+	0.971499i	$0.423822\pi$
$54$	0	0
$55$	3.35640e7	0.494585
$56$	6.36461e6	0.0864819
$57$	0	0
$58$	−3.87258e7	−0.449339
$59$	1.13602e8	1.22054	0.610272	−	0.792192i	$-0.291060\pi$
$59$	1.13602e8	1.22054	0.610272	+	0.792192i	$0.291060\pi$
$60$	0	0
$61$	−3.76868e7	−0.348502	−0.174251	−	0.984701i	$-0.555750\pi$
$61$	−3.76868e7	−0.348502	−0.174251	+	0.984701i	$0.555750\pi$
$62$	3.05973e7	0.262979
$63$	0	0
$64$	−5.64321e7	−0.420452
$65$	−3.53085e7	−0.245340
$66$	0	0
$67$	1.90094e8	1.15247	0.576237	−	0.817283i	$-0.304521\pi$
$67$	1.90094e8	1.15247	0.576237	+	0.817283i	$0.304521\pi$
$68$	−1.58625e7	−0.0899666
$69$	0	0
$70$	−8.11260e6	−0.0403849
$71$	−6.87130e7	−0.320905	−0.160453	−	0.987044i	$-0.551295\pi$
$71$	−6.87130e7	−0.320905	−0.160453	+	0.987044i	$0.551295\pi$
$72$	0	0
$73$	3.61495e8	1.48987	0.744937	−	0.667135i	$-0.232480\pi$
$73$	3.61495e8	1.48987	0.744937	+	0.667135i	$0.232480\pi$
$74$	5.58268e7	0.216421
$75$	0	0
$76$	−1.96377e8	−0.675196
$77$	2.42179e7	0.0785107
$78$	0	0
$79$	−1.42229e8	−0.410834	−0.205417	−	0.978675i	$-0.565855\pi$
$79$	−1.42229e8	−0.410834	−0.205417	+	0.978675i	$0.565855\pi$
$80$	2.24926e8	0.613953
$81$	0	0
$82$	−3.62346e7	−0.0885035
$83$	5.80240e7	0.134201	0.0671006	−	0.997746i	$-0.478625\pi$
$83$	5.80240e7	0.134201	0.0671006	+	0.997746i	$0.478625\pi$
$84$	0	0
$85$	4.28279e7	0.0889901
$86$	−1.26449e8	−0.249272
$87$	0	0
$88$	1.93718e8	0.344348
$89$	8.59928e8	1.45280	0.726402	−	0.687270i	$-0.241191\pi$
$89$	8.59928e8	1.45280	0.726402	+	0.687270i	$0.241191\pi$
$90$	0	0
$91$	−2.54767e7	−0.0389454
$92$	9.32716e8	1.35739
$93$	0	0
$94$	−2.17442e8	−0.287255
$95$	5.30208e8	0.667867
$96$	0	0
$97$	1.46970e9	1.68560	0.842802	−	0.538223i	$-0.180904\pi$
$97$	1.46970e9	1.68560	0.842802	+	0.538223i	$0.180904\pi$
$98$	2.91017e8	0.318714
$99$	0	0
$100$	1.94513e8	0.194513
$101$	4.15100e8	0.396923	0.198462	−	0.980109i	$-0.436405\pi$
$101$	4.15100e8	0.396923	0.198462	+	0.980109i	$0.436405\pi$
$102$	0	0
$103$	1.86377e9	1.63164	0.815821	−	0.578305i	$-0.196286\pi$
$103$	1.86377e9	1.63164	0.815821	+	0.578305i	$0.196286\pi$
$104$	−2.03786e8	−0.170815
$105$	0	0
$106$	−2.00346e8	−0.154136
$107$	7.50777e8	0.553712	0.276856	−	0.960911i	$-0.410707\pi$
$107$	7.50777e8	0.553712	0.276856	+	0.960911i	$0.410707\pi$
$108$	0	0
$109$	2.07010e9	1.40467	0.702333	−	0.711849i	$-0.252142\pi$
$109$	2.07010e9	1.40467	0.702333	+	0.711849i	$0.252142\pi$
$110$	−2.46921e8	−0.160802
$111$	0	0
$112$	1.62295e8	0.0974592
$113$	2.10155e9	1.21251	0.606257	−	0.795268i	$-0.292670\pi$
$113$	2.10155e9	1.21251	0.606257	+	0.795268i	$0.292670\pi$
$114$	0	0
$115$	−2.51829e9	−1.34266
$116$	−2.41027e9	−1.23596
$117$	0	0
$118$	−8.35741e8	−0.396828
$119$	3.09023e7	0.0141263
$120$	0	0
$121$	−1.62083e9	−0.687392
$122$	2.77251e8	0.113306
$123$	0	0
$124$	1.90436e9	0.723356
$125$	−2.93972e9	−1.07699
$126$	0	0
$127$	−4.77696e9	−1.62943	−0.814713	−	0.579865i	$-0.803105\pi$
$127$	−4.77696e9	−1.62943	−0.814713	+	0.579865i	$0.803105\pi$
$128$	2.97090e9	0.978235
$129$	0	0
$130$	2.59755e8	0.0797662
$131$	4.62884e9	1.37326	0.686628	−	0.727009i	$-0.259090\pi$
$131$	4.62884e9	1.37326	0.686628	+	0.727009i	$0.259090\pi$
$132$	0	0
$133$	3.82569e8	0.106018
$134$	−1.39847e9	−0.374697
$135$	0	0
$136$	2.47186e8	0.0619581
$137$	−3.85972e9	−0.936080	−0.468040	−	0.883707i	$-0.655040\pi$
$137$	−3.85972e9	−0.936080	−0.468040	+	0.883707i	$0.655040\pi$
$138$	0	0
$139$	−8.38068e9	−1.90420	−0.952100	−	0.305786i	$-0.901081\pi$
$139$	−8.38068e9	−1.90420	−0.952100	+	0.305786i	$0.901081\pi$
$140$	−5.04924e8	−0.111084
$141$	0	0
$142$	5.05503e8	0.104334
$143$	−7.75427e8	−0.155070
$144$	0	0
$145$	6.50761e9	1.22255
$146$	−2.65942e9	−0.484394
$147$	0	0
$148$	3.47463e9	0.595293
$149$	−3.96089e9	−0.658347	−0.329174	−	0.944269i	$-0.606770\pi$
$149$	−3.96089e9	−0.658347	−0.329174	+	0.944269i	$0.606770\pi$
$150$	0	0
$151$	1.11419e10	1.74407	0.872036	−	0.489442i	$-0.162799\pi$
$151$	1.11419e10	1.74407	0.872036	+	0.489442i	$0.162799\pi$
$152$	3.06015e9	0.464993
$153$	0	0
$154$	−1.78165e8	−0.0255257
$155$	−5.14168e9	−0.715504
$156$	0	0
$157$	−7.39104e9	−0.970861	−0.485430	−	0.874275i	$-0.661337\pi$
$157$	−7.39104e9	−0.970861	−0.485430	+	0.874275i	$0.661337\pi$
$158$	1.04634e9	0.133572
$159$	0	0
$160$	−6.17097e9	−0.744412
$161$	−1.81706e9	−0.213134
$162$	0	0
$163$	−7.32911e8	−0.0813218	−0.0406609	−	0.999173i	$-0.512946\pi$
$163$	−7.32911e8	−0.0813218	−0.0406609	+	0.999173i	$0.512946\pi$
$164$	−2.25522e9	−0.243440
$165$	0	0
$166$	−4.26867e8	−0.0436321
$167$	1.23516e10	1.22885	0.614427	−	0.788974i	$-0.289387\pi$
$167$	1.23516e10	1.22885	0.614427	+	0.788974i	$0.289387\pi$
$168$	0	0
$169$	8.15731e8	0.0769231
$170$	−3.15073e8	−0.0289329
$171$	0	0
$172$	−7.87012e9	−0.685651
$173$	−1.12727e10	−0.956794	−0.478397	−	0.878144i	$-0.658782\pi$
$173$	−1.12727e10	−0.956794	−0.478397	+	0.878144i	$0.658782\pi$
$174$	0	0
$175$	−3.78938e8	−0.0305420
$176$	4.93971e9	0.388056
$177$	0	0
$178$	−6.32626e9	−0.472342
$179$	3.32764e9	0.242269	0.121134	−	0.992636i	$-0.461347\pi$
$179$	3.32764e9	0.242269	0.121134	+	0.992636i	$0.461347\pi$
$180$	0	0
$181$	1.56098e10	1.08104	0.540521	−	0.841330i	$-0.318227\pi$
$181$	1.56098e10	1.08104	0.540521	+	0.841330i	$0.318227\pi$
$182$	1.87425e8	0.0126621
$183$	0	0
$184$	−1.45345e10	−0.934805
$185$	−9.38133e9	−0.588832
$186$	0	0
$187$	9.40564e8	0.0562472
$188$	−1.35334e10	−0.790129
$189$	0	0
$190$	−3.90060e9	−0.217140
$191$	−2.64757e10	−1.43945	−0.719725	−	0.694259i	$-0.755732\pi$
$191$	−2.64757e10	−1.43945	−0.719725	+	0.694259i	$0.755732\pi$
$192$	0	0
$193$	−2.67204e9	−0.138623	−0.0693114	−	0.997595i	$-0.522080\pi$
$193$	−2.67204e9	−0.138623	−0.0693114	+	0.997595i	$0.522080\pi$
$194$	−1.08122e10	−0.548031
$195$	0	0
$196$	1.81127e10	0.876661
$197$	−1.38233e10	−0.653903	−0.326951	−	0.945041i	$-0.606021\pi$
$197$	−1.38233e10	−0.653903	−0.326951	+	0.945041i	$0.606021\pi$
$198$	0	0
$199$	−1.21811e10	−0.550616	−0.275308	−	0.961356i	$-0.588780\pi$
$199$	−1.21811e10	−0.550616	−0.275308	+	0.961356i	$0.588780\pi$
$200$	−3.03110e9	−0.133957
$201$	0	0
$202$	−3.05378e9	−0.129049
$203$	4.69554e9	0.194068
$204$	0	0
$205$	6.08897e9	0.240797
$206$	−1.37112e10	−0.530486
$207$	0	0
$208$	−5.19646e9	−0.192497
$209$	1.16441e10	0.422133
$210$	0	0
$211$	−3.16880e9	−0.110058	−0.0550292	−	0.998485i	$-0.517525\pi$
$211$	−3.16880e9	−0.110058	−0.0550292	+	0.998485i	$0.517525\pi$
$212$	−1.24695e10	−0.423971
$213$	0	0
$214$	−5.52326e9	−0.180025
$215$	2.12489e10	0.678210
$216$	0	0
$217$	−3.70996e9	−0.113579
$218$	−1.52292e10	−0.456691
$219$	0	0
$220$	−1.53682e10	−0.442305
$221$	−9.89451e8	−0.0279016
$222$	0	0
$223$	−1.00184e10	−0.271285	−0.135642	−	0.990758i	$-0.543310\pi$
$223$	−1.00184e10	−0.271285	−0.135642	+	0.990758i	$0.543310\pi$
$224$	−4.45264e9	−0.118168
$225$	0	0
$226$	−1.54605e10	−0.394218
$227$	5.23965e10	1.30974	0.654871	−	0.755741i	$-0.272723\pi$
$227$	5.23965e10	1.30974	0.654871	+	0.755741i	$0.272723\pi$
$228$	0	0
$229$	−2.94853e10	−0.708510	−0.354255	−	0.935149i	$-0.615266\pi$
$229$	−2.94853e10	−0.708510	−0.354255	+	0.935149i	$0.615266\pi$
$230$	1.85263e10	0.436530
$231$	0	0
$232$	3.75593e10	0.851180
$233$	6.67468e10	1.48364	0.741820	−	0.670599i	$-0.233963\pi$
$233$	6.67468e10	1.48364	0.741820	+	0.670599i	$0.233963\pi$
$234$	0	0
$235$	3.65396e10	0.781553
$236$	−5.20161e10	−1.09152
$237$	0	0
$238$	−2.27340e8	−0.00459281
$239$	7.42940e10	1.47286	0.736432	−	0.676511i	$-0.236509\pi$
$239$	7.42940e10	1.47286	0.736432	+	0.676511i	$0.236509\pi$
$240$	0	0
$241$	9.01496e10	1.72142	0.860711	−	0.509095i	$-0.170020\pi$
$241$	9.01496e10	1.72142	0.860711	+	0.509095i	$0.170020\pi$
$242$	1.19240e10	0.223488
$243$	0	0
$244$	1.72560e10	0.311663
$245$	−4.89034e10	−0.867146
$246$	0	0
$247$	−1.22494e10	−0.209400
$248$	−2.96757e10	−0.498160
$249$	0	0
$250$	2.16267e10	0.350156
$251$	−3.62007e10	−0.575685	−0.287843	−	0.957678i	$-0.592938\pi$
$251$	−3.62007e10	−0.575685	−0.287843	+	0.957678i	$0.592938\pi$
$252$	0	0
$253$	−5.53053e10	−0.848641
$254$	3.51428e10	0.529766
$255$	0	0
$256$	7.03715e9	0.102404
$257$	1.97638e10	0.282600	0.141300	−	0.989967i	$-0.454872\pi$
$257$	1.97638e10	0.282600	0.141300	+	0.989967i	$0.454872\pi$
$258$	0	0
$259$	−6.76905e9	−0.0934714
$260$	1.61670e10	0.219407
$261$	0	0
$262$	−3.40531e10	−0.446479
$263$	1.70457e10	0.219692	0.109846	−	0.993949i	$-0.464964\pi$
$263$	1.70457e10	0.219692	0.109846	+	0.993949i	$0.464964\pi$
$264$	0	0
$265$	3.36669e10	0.419369
$266$	−2.81446e9	−0.0344689
$267$	0	0
$268$	−8.70398e10	−1.03065
$269$	−6.56819e10	−0.764822	−0.382411	−	0.923992i	$-0.624906\pi$
$269$	−6.56819e10	−0.764822	−0.382411	+	0.923992i	$0.624906\pi$
$270$	0	0
$271$	1.52442e11	1.71689	0.858447	−	0.512902i	$-0.171430\pi$
$271$	1.52442e11	1.71689	0.858447	+	0.512902i	$0.171430\pi$
$272$	6.30312e9	0.0698225
$273$	0	0
$274$	2.83949e10	0.304343
$275$	−1.15336e10	−0.121610
$276$	0	0
$277$	−1.21612e11	−1.24113	−0.620566	−	0.784154i	$-0.713097\pi$
$277$	−1.21612e11	−1.24113	−0.620566	+	0.784154i	$0.713097\pi$
$278$	6.16544e10	0.619102
$279$	0	0
$280$	7.86824e9	0.0765008
$281$	2.03083e11	1.94310	0.971548	−	0.236842i	$-0.0761124\pi$
$281$	2.03083e11	1.94310	0.971548	+	0.236842i	$0.0761124\pi$
$282$	0	0
$283$	3.09567e10	0.286891	0.143445	−	0.989658i	$-0.454182\pi$
$283$	3.09567e10	0.286891	0.143445	+	0.989658i	$0.454182\pi$
$284$	3.14622e10	0.286984
$285$	0	0
$286$	5.70460e9	0.0504171
$287$	4.39347e9	0.0382243
$288$	0	0
$289$	−1.17388e11	−0.989880
$290$	−4.78747e10	−0.397480
$291$	0	0
$292$	−1.65521e11	−1.33238
$293$	7.81733e10	0.619661	0.309831	−	0.950792i	$-0.399728\pi$
$293$	7.81733e10	0.619661	0.309831	+	0.950792i	$0.399728\pi$
$294$	0	0
$295$	1.40441e11	1.07968
$296$	−5.41452e10	−0.409966
$297$	0	0
$298$	2.91392e10	0.214045
$299$	5.81798e10	0.420971
$300$	0	0
$301$	1.53321e10	0.107659
$302$	−8.19682e10	−0.567040
$303$	0	0
$304$	7.80324e10	0.524015
$305$	−4.65902e10	−0.308280
$306$	0	0
$307$	1.19962e11	0.770766	0.385383	−	0.922757i	$-0.374069\pi$
$307$	1.19962e11	0.770766	0.385383	+	0.922757i	$0.374069\pi$
$308$	−1.10889e10	−0.0702116
$309$	0	0
$310$	3.78259e10	0.232628
$311$	−1.16227e11	−0.704504	−0.352252	−	0.935905i	$-0.614584\pi$
$311$	−1.16227e11	−0.704504	−0.352252	+	0.935905i	$0.614584\pi$
$312$	0	0
$313$	9.92344e10	0.584403	0.292202	−	0.956357i	$-0.405612\pi$
$313$	9.92344e10	0.584403	0.292202	+	0.956357i	$0.405612\pi$
$314$	5.43738e10	0.315651
$315$	0	0
$316$	6.51236e10	0.367406
$317$	2.98194e11	1.65856	0.829281	−	0.558832i	$-0.188750\pi$
$317$	2.98194e11	1.65856	0.829281	+	0.558832i	$0.188750\pi$
$318$	0	0
$319$	1.42917e11	0.772725
$320$	−6.97642e10	−0.371927
$321$	0	0
$322$	1.33676e10	0.0692950
$323$	1.48580e10	0.0759539
$324$	0	0
$325$	1.21331e10	0.0603250
$326$	5.39183e9	0.0264397
$327$	0	0
$328$	3.51431e10	0.167652
$329$	2.63650e10	0.124064
$330$	0	0
$331$	6.87707e10	0.314904	0.157452	−	0.987527i	$-0.449672\pi$
$331$	6.87707e10	0.314904	0.157452	+	0.987527i	$0.449672\pi$
$332$	−2.65680e10	−0.120015
$333$	0	0
$334$	−9.08675e10	−0.399530
$335$	2.35003e11	1.01946
$336$	0	0
$337$	−1.56091e11	−0.659239	−0.329619	−	0.944114i	$-0.606920\pi$
$337$	−1.56091e11	−0.659239	−0.329619	+	0.944114i	$0.606920\pi$
$338$	−6.00111e9	−0.0250096
$339$	0	0
$340$	−1.96100e10	−0.0795833
$341$	−1.12919e11	−0.452243
$342$	0	0
$343$	−7.12819e10	−0.278071
$344$	1.22640e11	0.472194
$345$	0	0
$346$	8.29298e10	0.311077
$347$	1.65467e11	0.612673	0.306337	−	0.951923i	$-0.400897\pi$
$347$	1.65467e11	0.612673	0.306337	+	0.951923i	$0.400897\pi$
$348$	0	0
$349$	−4.02009e11	−1.45051	−0.725257	−	0.688478i	$-0.758279\pi$
$349$	−4.02009e11	−1.45051	−0.725257	+	0.688478i	$0.758279\pi$
$350$	2.78775e9	0.00992995
$351$	0	0
$352$	−1.35524e11	−0.470514
$353$	−2.74001e11	−0.939217	−0.469609	−	0.882875i	$-0.655605\pi$
$353$	−2.74001e11	−0.939217	−0.469609	+	0.882875i	$0.655605\pi$
$354$	0	0
$355$	−8.49464e10	−0.283869
$356$	−3.93743e11	−1.29923
$357$	0	0
$358$	−2.44805e10	−0.0787675
$359$	−8.26405e10	−0.262584	−0.131292	−	0.991344i	$-0.541913\pi$
$359$	−8.26405e10	−0.262584	−0.131292	+	0.991344i	$0.541913\pi$
$360$	0	0
$361$	−1.38746e11	−0.429969
$362$	−1.14837e11	−0.351473
$363$	0	0
$364$	1.16652e10	0.0348287
$365$	4.46898e11	1.31792
$366$	0	0
$367$	4.83059e10	0.138996	0.0694980	−	0.997582i	$-0.477860\pi$
$367$	4.83059e10	0.138996	0.0694980	+	0.997582i	$0.477860\pi$
$368$	−3.70624e11	−1.05346
$369$	0	0
$370$	6.90158e10	0.191444
$371$	2.42922e10	0.0665708
$372$	0	0
$373$	8.53749e10	0.228371	0.114185	−	0.993459i	$-0.463574\pi$
$373$	8.53749e10	0.228371	0.114185	+	0.993459i	$0.463574\pi$
$374$	−6.91947e9	−0.0182873
$375$	0	0
$376$	2.10892e11	0.544145
$377$	−1.50345e11	−0.383312
$378$	0	0
$379$	−2.25085e11	−0.560365	−0.280182	−	0.959947i	$-0.590395\pi$
$379$	−2.25085e11	−0.560365	−0.280182	+	0.959947i	$0.590395\pi$
$380$	−2.42771e11	−0.597270
$381$	0	0
$382$	1.94774e11	0.468001
$383$	−6.84152e11	−1.62464	−0.812322	−	0.583210i	$-0.801797\pi$
$383$	−6.84152e11	−1.62464	−0.812322	+	0.583210i	$0.801797\pi$
$384$	0	0
$385$	2.99394e10	0.0694495
$386$	1.96574e10	0.0450696
$387$	0	0
$388$	−6.72944e11	−1.50743
$389$	−7.47317e11	−1.65475	−0.827374	−	0.561652i	$-0.810166\pi$
$389$	−7.47317e11	−1.65475	−0.827374	+	0.561652i	$0.810166\pi$
$390$	0	0
$391$	−7.05700e10	−0.152695
$392$	−2.82251e11	−0.603738
$393$	0	0
$394$	1.01694e11	0.212600
$395$	−1.75830e11	−0.363419
$396$	0	0
$397$	1.63235e11	0.329804	0.164902	−	0.986310i	$-0.447269\pi$
$397$	1.63235e11	0.329804	0.164902	+	0.986310i	$0.447269\pi$
$398$	8.96133e10	0.179019
$399$	0	0
$400$	−7.72918e10	−0.150961
$401$	7.33836e11	1.41726	0.708629	−	0.705581i	$-0.249314\pi$
$401$	7.33836e11	1.41726	0.708629	+	0.705581i	$0.249314\pi$
$402$	0	0
$403$	1.18788e11	0.224336
$404$	−1.90065e11	−0.354966
$405$	0	0
$406$	−3.45438e10	−0.0630961
$407$	−2.06028e11	−0.372178
$408$	0	0
$409$	7.45800e11	1.31785	0.658927	−	0.752207i	$-0.271010\pi$
$409$	7.45800e11	1.31785	0.658927	+	0.752207i	$0.271010\pi$
$410$	−4.47949e10	−0.0782891
$411$	0	0
$412$	−8.53380e11	−1.45917
$413$	1.01334e11	0.171388
$414$	0	0
$415$	7.17321e10	0.118713
$416$	1.42568e11	0.233400
$417$	0	0
$418$	−8.56628e10	−0.137246
$419$	5.46254e11	0.865828	0.432914	−	0.901435i	$-0.357485\pi$
$419$	5.46254e11	0.865828	0.432914	+	0.901435i	$0.357485\pi$
$420$	0	0
$421$	−2.95449e11	−0.458366	−0.229183	−	0.973383i	$-0.573606\pi$
$421$	−2.95449e11	−0.458366	−0.229183	+	0.973383i	$0.573606\pi$
$422$	2.33120e10	0.0357827
$423$	0	0
$424$	1.94312e11	0.291980
$425$	−1.47170e10	−0.0218811
$426$	0	0
$427$	−3.36170e10	−0.0489365
$428$	−3.43765e11	−0.495182
$429$	0	0
$430$	−1.56323e11	−0.220502
$431$	5.49479e11	0.767014	0.383507	−	0.923538i	$-0.374716\pi$
$431$	5.49479e11	0.767014	0.383507	+	0.923538i	$0.374716\pi$
$432$	0	0
$433$	−7.54093e11	−1.03093	−0.515465	−	0.856910i	$-0.672381\pi$
$433$	−7.54093e11	−1.03093	−0.515465	+	0.856910i	$0.672381\pi$
$434$	2.72931e10	0.0369275
$435$	0	0
$436$	−9.47856e11	−1.25618
$437$	−8.73654e11	−1.14597
$438$	0	0
$439$	9.98220e10	0.128273	0.0641366	−	0.997941i	$-0.479571\pi$
$439$	9.98220e10	0.128273	0.0641366	+	0.997941i	$0.479571\pi$
$440$	2.39483e11	0.304606
$441$	0	0
$442$	7.27912e9	0.00907149
$443$	1.08040e12	1.33281	0.666404	−	0.745591i	$-0.267832\pi$
$443$	1.08040e12	1.33281	0.666404	+	0.745591i	$0.267832\pi$
$444$	0	0
$445$	1.06309e12	1.28513
$446$	7.37024e10	0.0882013
$447$	0	0
$448$	−5.03380e10	−0.0590398
$449$	−1.02947e12	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$449$	−1.02947e12	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$450$	0	0
$451$	1.33723e11	0.152199
$452$	−9.62256e11	−1.08435
$453$	0	0
$454$	−3.85466e11	−0.425829
$455$	−3.14955e10	−0.0344507
$456$	0	0
$457$	1.06106e12	1.13793	0.568966	−	0.822361i	$-0.307343\pi$
$457$	1.06106e12	1.13793	0.568966	+	0.822361i	$0.307343\pi$
$458$	2.16915e11	0.230354
$459$	0	0
$460$	1.15307e12	1.20073
$461$	7.20760e11	0.743253	0.371626	−	0.928382i	$-0.378800\pi$
$461$	7.20760e11	0.743253	0.371626	+	0.928382i	$0.378800\pi$
$462$	0	0
$463$	1.41179e11	0.142776	0.0713880	−	0.997449i	$-0.477257\pi$
$463$	1.41179e11	0.142776	0.0713880	+	0.997449i	$0.477257\pi$
$464$	9.57745e11	0.959222
$465$	0	0
$466$	−4.91038e11	−0.482368
$467$	5.23104e11	0.508935	0.254467	−	0.967081i	$-0.418100\pi$
$467$	5.23104e11	0.508935	0.254467	+	0.967081i	$0.418100\pi$
$468$	0	0
$469$	1.69565e11	0.161830
$470$	−2.68812e11	−0.254102
$471$	0	0
$472$	8.10568e11	0.751710
$473$	4.66658e11	0.428670
$474$	0	0
$475$	−1.82196e11	−0.164217
$476$	−1.41495e10	−0.0126331
$477$	0	0
$478$	−5.46560e11	−0.478864
$479$	−1.22387e12	−1.06224	−0.531122	−	0.847295i	$-0.678230\pi$
$479$	−1.22387e12	−1.06224	−0.531122	+	0.847295i	$0.678230\pi$
$480$	0	0
$481$	2.16736e11	0.184620
$482$	−6.63206e11	−0.559676
$483$	0	0
$484$	7.42145e11	0.614730
$485$	1.81691e12	1.49107
$486$	0	0
$487$	−3.77344e11	−0.303988	−0.151994	−	0.988381i	$-0.548569\pi$
$487$	−3.77344e11	−0.303988	−0.151994	+	0.988381i	$0.548569\pi$
$488$	−2.68900e11	−0.214636
$489$	0	0
$490$	3.59769e11	0.281930
$491$	2.35736e12	1.83046	0.915229	−	0.402934i	$-0.132010\pi$
$491$	2.35736e12	1.83046	0.915229	+	0.402934i	$0.132010\pi$
$492$	0	0
$493$	1.82363e11	0.139035
$494$	9.01153e10	0.0680812
$495$	0	0
$496$	−7.56717e11	−0.561392
$497$	−6.12927e10	−0.0450614
$498$	0	0
$499$	−2.64345e12	−1.90862	−0.954309	−	0.298822i	$-0.903406\pi$
$499$	−2.64345e12	−1.90862	−0.954309	+	0.298822i	$0.903406\pi$
$500$	1.34604e12	0.963145
$501$	0	0
$502$	2.66319e11	0.187169
$503$	−1.53328e11	−0.106799	−0.0533994	−	0.998573i	$-0.517006\pi$
$503$	−1.53328e11	−0.106799	−0.0533994	+	0.998573i	$0.517006\pi$
$504$	0	0
$505$	5.13167e11	0.351113
$506$	4.06866e11	0.275914
$507$	0	0
$508$	2.18727e12	1.45719
$509$	6.36840e11	0.420533	0.210267	−	0.977644i	$-0.432567\pi$
$509$	6.36840e11	0.420533	0.210267	+	0.977644i	$0.432567\pi$
$510$	0	0
$511$	3.22457e11	0.209208
$512$	−1.57287e12	−1.01153
$513$	0	0
$514$	−1.45397e11	−0.0918801
$515$	2.30408e12	1.44333
$516$	0	0
$517$	8.02463e11	0.493989
$518$	4.97981e10	0.0303899
$519$	0	0
$520$	−2.51931e11	−0.151101
$521$	−1.84033e12	−1.09427	−0.547137	−	0.837043i	$-0.684282\pi$
$521$	−1.84033e12	−1.09427	−0.547137	+	0.837043i	$0.684282\pi$
$522$	0	0
$523$	−1.13176e10	−0.00661447	−0.00330724	−	0.999995i	$-0.501053\pi$
$523$	−1.13176e10	−0.00661447	−0.00330724	+	0.999995i	$0.501053\pi$
$524$	−2.11945e12	−1.22809
$525$	0	0
$526$	−1.25401e11	−0.0714272
$527$	−1.44085e11	−0.0813715
$528$	0	0
$529$	2.34837e12	1.30382
$530$	−2.47678e11	−0.136347
$531$	0	0
$532$	−1.75170e11	−0.0948108
$533$	−1.40673e11	−0.0754987
$534$	0	0
$535$	9.28148e11	0.489807
$536$	1.35634e12	0.709787
$537$	0	0
$538$	4.83203e11	0.248662
$539$	−1.07399e12	−0.548089
$540$	0	0
$541$	−2.25189e12	−1.13021	−0.565107	−	0.825018i	$-0.691165\pi$
$541$	−2.25189e12	−1.13021	−0.565107	+	0.825018i	$0.691165\pi$
$542$	−1.12148e12	−0.558204
$543$	0	0
$544$	−1.72929e11	−0.0846591
$545$	2.55916e12	1.24255
$546$	0	0
$547$	1.92777e11	0.0920686	0.0460343	−	0.998940i	$-0.485342\pi$
$547$	1.92777e11	0.0920686	0.0460343	+	0.998940i	$0.485342\pi$
$548$	1.76728e12	0.837131
$549$	0	0
$550$	8.48498e10	0.0395384
$551$	2.25765e12	1.04346
$552$	0	0
$553$	−1.26870e11	−0.0576892
$554$	8.94667e11	0.403522
$555$	0	0
$556$	3.83733e12	1.70292
$557$	−3.00574e12	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$557$	−3.00574e12	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$558$	0	0
$559$	−4.90913e11	−0.212643
$560$	2.00636e11	0.0862112
$561$	0	0
$562$	−1.49402e12	−0.631748
$563$	1.64962e11	0.0691984	0.0345992	−	0.999401i	$-0.488985\pi$
$563$	1.64962e11	0.0691984	0.0345992	+	0.999401i	$0.488985\pi$
$564$	0	0
$565$	2.59804e12	1.07258
$566$	−2.27740e11	−0.0932751
$567$	0	0
$568$	−4.90277e11	−0.197639
$569$	2.35127e11	0.0940368	0.0470184	−	0.998894i	$-0.485028\pi$
$569$	2.35127e11	0.0940368	0.0470184	+	0.998894i	$0.485028\pi$
$570$	0	0
$571$	−2.71697e12	−1.06960	−0.534801	−	0.844978i	$-0.679613\pi$
$571$	−2.71697e12	−1.06960	−0.534801	+	0.844978i	$0.679613\pi$
$572$	3.55051e11	0.138678
$573$	0	0
$574$	−3.23216e10	−0.0124276
$575$	8.65362e11	0.330136
$576$	0	0
$577$	−3.01507e12	−1.13242	−0.566209	−	0.824262i	$-0.691590\pi$
$577$	−3.01507e12	−1.13242	−0.566209	+	0.824262i	$0.691590\pi$
$578$	8.63589e11	0.321834
$579$	0	0
$580$	−2.97969e12	−1.09332
$581$	5.17580e10	0.0188445
$582$	0	0
$583$	7.39374e11	0.265067
$584$	2.57931e12	0.917585
$585$	0	0
$586$	−5.75100e11	−0.201467
$587$	9.84708e11	0.342323	0.171161	−	0.985243i	$-0.445248\pi$
$587$	9.84708e11	0.342323	0.171161	+	0.985243i	$0.445248\pi$
$588$	0	0
$589$	−1.78377e12	−0.610690
$590$	−1.03318e12	−0.351030
$591$	0	0
$592$	−1.38068e12	−0.462003
$593$	−1.01065e12	−0.335625	−0.167812	−	0.985819i	$-0.553670\pi$
$593$	−1.01065e12	−0.335625	−0.167812	+	0.985819i	$0.553670\pi$
$594$	0	0
$595$	3.82029e10	0.0124960
$596$	1.81361e12	0.588756
$597$	0	0
$598$	−4.28013e11	−0.136868
$599$	−5.47507e12	−1.73768	−0.868839	−	0.495095i	$-0.835133\pi$
$599$	−5.47507e12	−1.73768	−0.868839	+	0.495095i	$0.835133\pi$
$600$	0	0
$601$	9.94557e11	0.310953	0.155476	−	0.987840i	$-0.450309\pi$
$601$	9.94557e11	0.310953	0.155476	+	0.987840i	$0.450309\pi$
$602$	−1.12794e11	−0.0350027
$603$	0	0
$604$	−5.10165e12	−1.55971
$605$	−2.00375e12	−0.608058
$606$	0	0
$607$	4.57629e12	1.36825	0.684124	−	0.729366i	$-0.260185\pi$
$607$	4.57629e12	1.36825	0.684124	+	0.729366i	$0.260185\pi$
$608$	−2.14086e12	−0.635363
$609$	0	0
$610$	3.42752e11	0.100229
$611$	−8.44173e11	−0.245045
$612$	0	0
$613$	2.27107e12	0.649617	0.324809	−	0.945780i	$-0.394700\pi$
$613$	2.27107e12	0.649617	0.324809	+	0.945780i	$0.394700\pi$
$614$	−8.82531e11	−0.250595
$615$	0	0
$616$	1.72798e11	0.0483532
$617$	−3.53862e12	−0.982994	−0.491497	−	0.870879i	$-0.663550\pi$
$617$	−3.53862e12	−0.982994	−0.491497	+	0.870879i	$0.663550\pi$
$618$	0	0
$619$	1.97957e12	0.541956	0.270978	−	0.962586i	$-0.412653\pi$
$619$	1.97957e12	0.541956	0.270978	+	0.962586i	$0.412653\pi$
$620$	2.35426e12	0.639871
$621$	0	0
$622$	8.55047e11	0.229052
$623$	7.67065e11	0.204003
$624$	0	0
$625$	−2.80452e12	−0.735187
$626$	−7.30040e11	−0.190004
$627$	0	0
$628$	3.38420e12	0.868235
$629$	−2.62893e11	−0.0669656
$630$	0	0
$631$	3.71649e11	0.0933256	0.0466628	−	0.998911i	$-0.485141\pi$
$631$	3.71649e11	0.0933256	0.0466628	+	0.998911i	$0.485141\pi$
$632$	−1.01482e12	−0.253025
$633$	0	0
$634$	−2.19373e12	−0.539239
$635$	−5.90551e12	−1.44137
$636$	0	0
$637$	1.12981e12	0.271881
$638$	−1.05140e12	−0.251232
$639$	0	0
$640$	3.67277e12	0.865335
$641$	−1.07772e12	−0.252143	−0.126071	−	0.992021i	$-0.540237\pi$
$641$	−1.07772e12	−0.252143	−0.126071	+	0.992021i	$0.540237\pi$
$642$	0	0
$643$	−6.69209e12	−1.54388	−0.771938	−	0.635698i	$-0.780712\pi$
$643$	−6.69209e12	−1.54388	−0.771938	+	0.635698i	$0.780712\pi$
$644$	8.31992e11	0.190604
$645$	0	0
$646$	−1.09307e11	−0.0246945
$647$	−1.58975e12	−0.356664	−0.178332	−	0.983970i	$-0.557070\pi$
$647$	−1.58975e12	−0.356664	−0.178332	+	0.983970i	$0.557070\pi$
$648$	0	0
$649$	3.08429e12	0.682423
$650$	−8.92600e10	−0.0196131
$651$	0	0
$652$	3.35584e11	0.0727256
$653$	1.96565e12	0.423055	0.211527	−	0.977372i	$-0.432156\pi$
$653$	1.96565e12	0.423055	0.211527	+	0.977372i	$0.432156\pi$
$654$	0	0
$655$	5.72240e12	1.21476
$656$	8.96134e11	0.188932
$657$	0	0
$658$	−1.93960e11	−0.0403362
$659$	−1.09426e11	−0.0226014	−0.0113007	−	0.999936i	$-0.503597\pi$
$659$	−1.09426e11	−0.0226014	−0.0113007	+	0.999936i	$0.503597\pi$
$660$	0	0
$661$	−2.69590e12	−0.549285	−0.274643	−	0.961546i	$-0.588560\pi$
$661$	−2.69590e12	−0.549285	−0.274643	+	0.961546i	$0.588560\pi$
$662$	−5.05927e11	−0.102383
$663$	0	0
$664$	4.14009e11	0.0826520
$665$	4.72951e11	0.0937818
$666$	0	0
$667$	−1.07230e13	−2.09772
$668$	−5.65555e12	−1.09896
$669$	0	0
$670$	−1.72885e12	−0.331452
$671$	−1.02319e12	−0.194852
$672$	0	0
$673$	−6.37187e12	−1.19729	−0.598644	−	0.801015i	$-0.704294\pi$
$673$	−6.37187e12	−1.19729	−0.598644	+	0.801015i	$0.704294\pi$
$674$	1.14832e12	0.214335
$675$	0	0
$676$	−3.73506e11	−0.0687919
$677$	6.61270e12	1.20985	0.604923	−	0.796284i	$-0.293204\pi$
$677$	6.61270e12	1.20985	0.604923	+	0.796284i	$0.293204\pi$
$678$	0	0
$679$	1.31099e12	0.236692
$680$	3.05583e11	0.0548073
$681$	0	0
$682$	8.30713e11	0.147035
$683$	−3.52480e12	−0.619785	−0.309893	−	0.950772i	$-0.600293\pi$
$683$	−3.52480e12	−0.619785	−0.309893	+	0.950772i	$0.600293\pi$
$684$	0	0
$685$	−4.77157e12	−0.828045
$686$	5.24401e11	0.0904076
$687$	0	0
$688$	3.12727e12	0.532130
$689$	−7.77804e11	−0.131487
$690$	0	0
$691$	1.21020e12	0.201932	0.100966	−	0.994890i	$-0.467807\pi$
$691$	1.21020e12	0.201932	0.100966	+	0.994890i	$0.467807\pi$
$692$	5.16151e12	0.855656
$693$	0	0
$694$	−1.21730e12	−0.199195
$695$	−1.03606e13	−1.68443
$696$	0	0
$697$	1.70632e11	0.0273849
$698$	2.95747e12	0.471597
$699$	0	0
$700$	1.73508e11	0.0273135
$701$	−3.34752e12	−0.523591	−0.261796	−	0.965123i	$-0.584315\pi$
$701$	−3.34752e12	−0.523591	−0.261796	+	0.965123i	$0.584315\pi$
$702$	0	0
$703$	−3.25461e12	−0.502574
$704$	−1.53212e12	−0.235081
$705$	0	0
$706$	2.01575e12	0.305362
$707$	3.70273e11	0.0557359
$708$	0	0
$709$	1.09345e13	1.62514	0.812568	−	0.582866i	$-0.198069\pi$
$709$	1.09345e13	1.62514	0.812568	+	0.582866i	$0.198069\pi$
$710$	6.24928e11	0.0922926
$711$	0	0
$712$	6.13570e12	0.894755
$713$	8.47224e12	1.22771
$714$	0	0
$715$	−9.58620e11	−0.137173
$716$	−1.52365e12	−0.216660
$717$	0	0
$718$	6.07964e11	0.0853724
$719$	−4.73071e12	−0.660156	−0.330078	−	0.943954i	$-0.607075\pi$
$719$	−4.73071e12	−0.660156	−0.330078	+	0.943954i	$0.607075\pi$
$720$	0	0
$721$	1.66250e12	0.229115
$722$	1.02071e12	0.139793
$723$	0	0
$724$	−7.14738e12	−0.966770
$725$	−2.23622e12	−0.300603
$726$	0	0
$727$	1.40402e13	1.86410	0.932049	−	0.362333i	$-0.118020\pi$
$727$	1.40402e13	1.86410	0.932049	+	0.362333i	$0.118020\pi$
$728$	−1.81780e11	−0.0239858
$729$	0	0
$730$	−3.28770e12	−0.428489
$731$	5.95459e11	0.0771301
$732$	0	0
$733$	−1.78493e12	−0.228377	−0.114188	−	0.993459i	$-0.536427\pi$
$733$	−1.78493e12	−0.228377	−0.114188	+	0.993459i	$0.536427\pi$
$734$	−3.55373e11	−0.0451910
$735$	0	0
$736$	1.01683e13	1.27731
$737$	5.16101e12	0.644364
$738$	0	0
$739$	−1.24956e13	−1.54119	−0.770595	−	0.637325i	$-0.780041\pi$
$739$	−1.24956e13	−1.54119	−0.770595	+	0.637325i	$0.780041\pi$
$740$	4.29551e12	0.526589
$741$	0	0
$742$	−1.78711e11	−0.0216438
$743$	−4.21591e12	−0.507506	−0.253753	−	0.967269i	$-0.581665\pi$
$743$	−4.21591e12	−0.507506	−0.253753	+	0.967269i	$0.581665\pi$
$744$	0	0
$745$	−4.89665e12	−0.582366
$746$	−6.28080e11	−0.0742489
$747$	0	0
$748$	−4.30664e11	−0.0503016
$749$	6.69701e11	0.0777522
$750$	0	0
$751$	9.94988e12	1.14140	0.570701	−	0.821158i	$-0.306672\pi$
$751$	9.94988e12	1.14140	0.570701	+	0.821158i	$0.306672\pi$
$752$	5.37765e12	0.613214
$753$	0	0
$754$	1.10605e12	0.124624
$755$	1.37742e13	1.54278
$756$	0	0
$757$	−1.61992e13	−1.79293	−0.896465	−	0.443115i	$-0.853873\pi$
$757$	−1.61992e13	−1.79293	−0.896465	+	0.443115i	$0.853873\pi$
$758$	1.65589e12	0.182188
$759$	0	0
$760$	3.78310e12	0.411327
$761$	−4.79250e12	−0.518001	−0.259001	−	0.965877i	$-0.583393\pi$
$761$	−4.79250e12	−0.518001	−0.259001	+	0.965877i	$0.583393\pi$
$762$	0	0
$763$	1.84655e12	0.197243
$764$	1.21226e13	1.28729
$765$	0	0
$766$	5.03312e12	0.528211
$767$	−3.24460e12	−0.338518
$768$	0	0
$769$	−8.41625e11	−0.0867861	−0.0433930	−	0.999058i	$-0.513817\pi$
$769$	−8.41625e11	−0.0867861	−0.0433930	+	0.999058i	$0.513817\pi$
$770$	−2.20256e11	−0.0225797
$771$	0	0
$772$	1.22347e12	0.123970
$773$	−3.90333e12	−0.393213	−0.196607	−	0.980482i	$-0.562992\pi$
$773$	−3.90333e12	−0.393213	−0.196607	+	0.980482i	$0.562992\pi$
$774$	0	0
$775$	1.76684e12	0.175930
$776$	1.04865e13	1.03813
$777$	0	0
$778$	5.49781e12	0.537999
$779$	2.11241e12	0.205523
$780$	0	0
$781$	−1.86555e12	−0.179422
$782$	5.19164e11	0.0496449
$783$	0	0
$784$	−7.19727e12	−0.680371
$785$	−9.13716e12	−0.858812
$786$	0	0
$787$	−1.42677e13	−1.32577	−0.662884	−	0.748723i	$-0.730668\pi$
$787$	−1.42677e13	−1.32577	−0.662884	+	0.748723i	$0.730668\pi$
$788$	6.32939e12	0.584782
$789$	0	0
$790$	1.29354e12	0.118156
$791$	1.87460e12	0.170261
$792$	0	0
$793$	1.07637e12	0.0966570
$794$	−1.20087e12	−0.107227
$795$	0	0
$796$	5.57748e12	0.492413
$797$	−1.77300e13	−1.55649	−0.778245	−	0.627960i	$-0.783890\pi$
$797$	−1.77300e13	−1.55649	−0.778245	+	0.627960i	$0.783890\pi$
$798$	0	0
$799$	1.02395e12	0.0888829
$800$	2.12054e12	0.183038
$801$	0	0
$802$	−5.39863e12	−0.460785
$803$	9.81453e12	0.833009
$804$	0	0
$805$	−2.24634e12	−0.188535
$806$	−8.73891e11	−0.0729372
$807$	0	0
$808$	2.96179e12	0.244458
$809$	−6.57374e12	−0.539565	−0.269783	−	0.962921i	$-0.586952\pi$
$809$	−6.57374e12	−0.539565	−0.269783	+	0.962921i	$0.586952\pi$
$810$	0	0
$811$	1.30848e13	1.06212	0.531060	−	0.847334i	$-0.321794\pi$
$811$	1.30848e13	1.06212	0.531060	+	0.847334i	$0.321794\pi$
$812$	−2.14999e12	−0.173553
$813$	0	0
$814$	1.51569e12	0.121004
$815$	−9.06060e11	−0.0719363
$816$	0	0
$817$	7.37177e12	0.578858
$818$	−5.48665e12	−0.428467
$819$	0	0
$820$	−2.78801e12	−0.215344
$821$	−4.25638e12	−0.326961	−0.163480	−	0.986547i	$-0.552272\pi$
$821$	−4.25638e12	−0.326961	−0.163480	+	0.986547i	$0.552272\pi$
$822$	0	0
$823$	−4.41691e12	−0.335598	−0.167799	−	0.985821i	$-0.553666\pi$
$823$	−4.41691e12	−0.335598	−0.167799	+	0.985821i	$0.553666\pi$
$824$	1.32982e13	1.00490
$825$	0	0
$826$	−7.45489e11	−0.0557226
$827$	1.65971e13	1.23384	0.616919	−	0.787026i	$-0.288380\pi$
$827$	1.65971e13	1.23384	0.616919	+	0.787026i	$0.288380\pi$
$828$	0	0
$829$	−1.79742e13	−1.32176	−0.660882	−	0.750490i	$-0.729817\pi$
$829$	−1.79742e13	−1.32176	−0.660882	+	0.750490i	$0.729817\pi$
$830$	−5.27714e11	−0.0385964
$831$	0	0
$832$	1.61176e12	0.116612
$833$	−1.37042e12	−0.0986171
$834$	0	0
$835$	1.52697e13	1.08703
$836$	−5.33161e12	−0.377511
$837$	0	0
$838$	−4.01864e12	−0.281502
$839$	−3.10688e12	−0.216469	−0.108234	−	0.994125i	$-0.534520\pi$
$839$	−3.10688e12	−0.216469	−0.108234	+	0.994125i	$0.534520\pi$
$840$	0	0
$841$	1.32025e13	0.910070
$842$	2.17354e12	0.149026
$843$	0	0
$844$	1.45092e12	0.0984246
$845$	1.00845e12	0.0680452
$846$	0	0
$847$	−1.44580e12	−0.0965234
$848$	4.95486e12	0.329041
$849$	0	0
$850$	1.08269e11	0.00711409
$851$	1.54581e13	1.01036
$852$	0	0
$853$	1.20700e13	0.780613	0.390306	−	0.920685i	$-0.372369\pi$
$853$	1.20700e13	0.780613	0.390306	+	0.920685i	$0.372369\pi$
$854$	2.47311e11	0.0159105
$855$	0	0
$856$	5.35690e12	0.341021
$857$	6.31368e12	0.399824	0.199912	−	0.979814i	$-0.435934\pi$
$857$	6.31368e12	0.399824	0.199912	+	0.979814i	$0.435934\pi$
$858$	0	0
$859$	1.86663e13	1.16974	0.584870	−	0.811127i	$-0.301146\pi$
$859$	1.86663e13	1.16974	0.584870	+	0.811127i	$0.301146\pi$
$860$	−9.72943e12	−0.606519
$861$	0	0
$862$	−4.04237e12	−0.249375
$863$	1.78712e13	1.09675	0.548373	−	0.836234i	$-0.315247\pi$
$863$	1.78712e13	1.09675	0.548373	+	0.836234i	$0.315247\pi$
$864$	0	0
$865$	−1.39358e13	−0.846368
$866$	5.54766e12	0.335181
$867$	0	0
$868$	1.69871e12	0.101573
$869$	−3.86149e12	−0.229703
$870$	0	0
$871$	−5.42926e12	−0.319639
$872$	1.47705e13	0.865107
$873$	0	0
$874$	6.42723e12	0.372583
$875$	−2.62226e12	−0.151231
$876$	0	0
$877$	−3.76100e12	−0.214687	−0.107343	−	0.994222i	$-0.534234\pi$
$877$	−3.76100e12	−0.214687	−0.107343	+	0.994222i	$0.534234\pi$
$878$	−7.34363e11	−0.0417047
$879$	0	0
$880$	6.10671e12	0.343270
$881$	−2.05824e13	−1.15108	−0.575539	−	0.817775i	$-0.695208\pi$
$881$	−2.05824e13	−1.15108	−0.575539	+	0.817775i	$0.695208\pi$
$882$	0	0
$883$	−3.01536e13	−1.66923	−0.834616	−	0.550833i	$-0.814310\pi$
$883$	−3.01536e13	−1.66923	−0.834616	+	0.550833i	$0.814310\pi$
$884$	4.53049e11	0.0249522
$885$	0	0
$886$	−7.94821e12	−0.433329
$887$	3.34317e13	1.81343	0.906717	−	0.421739i	$-0.138580\pi$
$887$	3.34317e13	1.81343	0.906717	+	0.421739i	$0.138580\pi$
$888$	0	0
$889$	−4.26109e12	−0.228804
$890$	−7.82083e12	−0.417828
$891$	0	0
$892$	4.58720e12	0.242608
$893$	1.26765e13	0.667063
$894$	0	0
$895$	4.11379e12	0.214308
$896$	2.65007e12	0.137364
$897$	0	0
$898$	7.57351e12	0.388646
$899$	−2.18935e13	−1.11788
$900$	0	0
$901$	9.43448e11	0.0476932
$902$	−9.83762e11	−0.0494835
$903$	0	0
$904$	1.49948e13	0.746765
$905$	1.92976e13	0.956277
$906$	0	0
$907$	2.03004e13	0.996030	0.498015	−	0.867169i	$-0.334063\pi$
$907$	2.03004e13	0.996030	0.498015	+	0.867169i	$0.334063\pi$
$908$	−2.39912e13	−1.17129
$909$	0	0
$910$	2.31704e11	0.0112008
$911$	−1.74407e13	−0.838940	−0.419470	−	0.907769i	$-0.637784\pi$
$911$	−1.74407e13	−0.838940	−0.419470	+	0.907769i	$0.637784\pi$
$912$	0	0
$913$	1.57534e12	0.0750337
$914$	−7.80592e12	−0.369970
$915$	0	0
$916$	1.35007e13	0.633617
$917$	4.12897e12	0.192832
$918$	0	0
$919$	1.69619e13	0.784430	0.392215	−	0.919874i	$-0.371709\pi$
$919$	1.69619e13	0.784430	0.392215	+	0.919874i	$0.371709\pi$
$920$	−1.79683e13	−0.826917
$921$	0	0
$922$	−5.30243e12	−0.241650
$923$	1.96251e12	0.0890031
$924$	0	0
$925$	3.22372e12	0.144784
$926$	−1.03861e12	−0.0464200
$927$	0	0
$928$	−2.62762e13	−1.16305
$929$	−4.90922e12	−0.216243	−0.108121	−	0.994138i	$-0.534484\pi$
$929$	−4.90922e12	−0.216243	−0.108121	+	0.994138i	$0.534484\pi$
$930$	0	0
$931$	−1.69658e13	−0.740117
$932$	−3.05619e13	−1.32681
$933$	0	0
$934$	−3.84833e12	−0.165467
$935$	1.16277e12	0.0497556
$936$	0	0
$937$	1.13139e13	0.479497	0.239749	−	0.970835i	$-0.422935\pi$
$937$	1.13139e13	0.479497	0.239749	+	0.970835i	$0.422935\pi$
$938$	−1.24745e12	−0.0526149
$939$	0	0
$940$	−1.67307e13	−0.698938
$941$	−7.23052e11	−0.0300619	−0.0150310	−	0.999887i	$-0.504785\pi$
$941$	−7.23052e11	−0.0300619	−0.0150310	+	0.999887i	$0.504785\pi$
$942$	0	0
$943$	−1.00332e13	−0.413176
$944$	2.06691e13	0.847126
$945$	0	0
$946$	−3.43307e12	−0.139371
$947$	−4.04364e13	−1.63380	−0.816898	−	0.576782i	$-0.804308\pi$
$947$	−4.04364e13	−1.63380	−0.816898	+	0.576782i	$0.804308\pi$
$948$	0	0
$949$	−1.03247e13	−0.413216
$950$	1.34037e12	0.0533910
$951$	0	0
$952$	2.20492e11	0.00870014
$953$	−4.03093e13	−1.58302	−0.791511	−	0.611155i	$-0.790705\pi$
$953$	−4.03093e13	−1.58302	−0.791511	+	0.611155i	$0.790705\pi$
$954$	0	0
$955$	−3.27305e13	−1.27332
$956$	−3.40176e13	−1.31717
$957$	0	0
$958$	9.00366e12	0.345362
$959$	−3.44291e12	−0.131444
$960$	0	0
$961$	−9.14153e12	−0.345751
$962$	−1.59447e12	−0.0600245
$963$	0	0
$964$	−4.12776e13	−1.53946
$965$	−3.30330e12	−0.122624
$966$	0	0
$967$	1.74415e13	0.641451	0.320726	−	0.947172i	$-0.396073\pi$
$967$	1.74415e13	0.641451	0.320726	+	0.947172i	$0.396073\pi$
$968$	−1.15649e13	−0.423352
$969$	0	0
$970$	−1.33665e13	−0.484782
$971$	5.09597e13	1.83967	0.919836	−	0.392303i	$-0.128322\pi$
$971$	5.09597e13	1.83967	0.919836	+	0.392303i	$0.128322\pi$
$972$	0	0
$973$	−7.47565e12	−0.267388
$974$	2.77601e12	0.0988340
$975$	0	0
$976$	−6.85683e12	−0.241880
$977$	−3.19652e13	−1.12241	−0.561205	−	0.827677i	$-0.689662\pi$
$977$	−3.19652e13	−1.12241	−0.561205	+	0.827677i	$0.689662\pi$
$978$	0	0
$979$	2.33469e13	0.812283
$980$	2.23918e13	0.775483
$981$	0	0
$982$	−1.73425e13	−0.595127
$983$	5.12376e13	1.75024	0.875121	−	0.483904i	$-0.160782\pi$
$983$	5.12376e13	1.75024	0.875121	+	0.483904i	$0.160782\pi$
$984$	0	0
$985$	−1.70890e13	−0.578434
$986$	−1.34159e12	−0.0452038
$987$	0	0
$988$	5.60873e12	0.187266
$989$	−3.50131e13	−1.16372
$990$	0	0
$991$	−1.90444e13	−0.627243	−0.313622	−	0.949548i	$-0.601542\pi$
$991$	−1.90444e13	−0.627243	−0.313622	+	0.949548i	$0.601542\pi$
$992$	2.07609e13	0.680682
$993$	0	0
$994$	4.50914e11	0.0146506
$995$	−1.50589e13	−0.487068
$996$	0	0
$997$	4.27709e13	1.37095	0.685473	−	0.728098i	$-0.259595\pi$
$997$	4.27709e13	1.37095	0.685473	+	0.728098i	$0.259595\pi$
$998$	1.94471e13	0.620538
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.10.a.c.1.2		4
3.2	odd	2		13.10.a.a.1.3	✓	4
12.11	even	2		208.10.a.g.1.2		4
15.14	odd	2		325.10.a.a.1.2		4
39.38	odd	2		169.10.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.3	✓	4	3.2	odd	2
117.10.a.c.1.2		4	1.1	even	1	trivial
169.10.a.a.1.2		4	39.38	odd	2
208.10.a.g.1.2		4	12.11	even	2
325.10.a.a.1.2		4	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)

\(f(q)\)	\(=\)	\(q-7.35673 q^{2} -457.879 q^{4} +1236.25 q^{5} +892.010 q^{7} +7135.13 q^{8} +O(q^{10})\)	\(q-7.35673 q^{2} -457.879 q^{4} +1236.25 q^{5} +892.010 q^{7} +7135.13 q^{8} -9094.74 q^{10} +27149.8 q^{11} -28561.0 q^{13} -6562.27 q^{14} +181943. q^{16} +34643.4 q^{17} +428885. q^{19} -566052. q^{20} -199734. q^{22} -2.03704e6 q^{23} -424814. q^{25} +210115. q^{26} -408432. q^{28} +5.26400e6 q^{29} -4.15910e6 q^{31} -4.99169e6 q^{32} -254862. q^{34} +1.10275e6 q^{35} -7.58854e6 q^{37} -3.15519e6 q^{38} +8.82080e6 q^{40} +4.92536e6 q^{41} +1.71882e7 q^{43} -1.24313e7 q^{44} +1.49859e7 q^{46} +2.95568e7 q^{47} -3.95579e7 q^{49} +3.12524e6 q^{50} +1.30775e7 q^{52} +2.72331e7 q^{53} +3.35640e7 q^{55} +6.36461e6 q^{56} -3.87258e7 q^{58} +1.13602e8 q^{59} -3.76868e7 q^{61} +3.05973e7 q^{62} -5.64321e7 q^{64} -3.53085e7 q^{65} +1.90094e8 q^{67} -1.58625e7 q^{68} -8.11260e6 q^{70} -6.87130e7 q^{71} +3.61495e8 q^{73} +5.58268e7 q^{74} -1.96377e8 q^{76} +2.42179e7 q^{77} -1.42229e8 q^{79} +2.24926e8 q^{80} -3.62346e7 q^{82} +5.80240e7 q^{83} +4.28279e7 q^{85} -1.26449e8 q^{86} +1.93718e8 q^{88} +8.59928e8 q^{89} -2.54767e7 q^{91} +9.32716e8 q^{92} -2.17442e8 q^{94} +5.30208e8 q^{95} +1.46970e9 q^{97} +2.91017e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} + 1429 q^{4} - 471 q^{5} - 11241 q^{7} + 45543 q^{8}+O(q^{10}) \) 4 * q + 33 * q^2 + 1429 * q^4 - 471 * q^5 - 11241 * q^7 + 45543 * q^8	\( 4 q + 33 q^{2} + 1429 q^{4} - 471 q^{5} - 11241 q^{7} + 45543 q^{8} - 67831 q^{10} + 40140 q^{11} - 114244 q^{13} + 277653 q^{14} + 726609 q^{16} - 78717 q^{17} + 209664 q^{19} - 870843 q^{20} + 1364090 q^{22} + 4257444 q^{23} - 2900157 q^{25} - 942513 q^{26} + 4035181 q^{28} + 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 26257659 q^{34} + 13789797 q^{35} + 4636891 q^{37} - 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} - 33368081 q^{43} - 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 23294923 q^{49} + 4217748 q^{50} - 40813669 q^{52} + 171019326 q^{53} - 121160538 q^{55} + 281552967 q^{56} + 79964734 q^{58} + 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 768962465 q^{64} + 13452231 q^{65} - 41174072 q^{67} + 717615423 q^{68} + 409056389 q^{70} - 252460989 q^{71} + 594415068 q^{73} + 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} - 875148240 q^{82} + 79577862 q^{83} + 549463469 q^{85} + 589924887 q^{86} - 2327564370 q^{88} + 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} + 1859909503 q^{94} + 1273705170 q^{95} + 1049098084 q^{97} - 420532254 q^{98}+O(q^{100}) \) 4 * q + 33 * q^2 + 1429 * q^4 - 471 * q^5 - 11241 * q^7 + 45543 * q^8 - 67831 * q^10 + 40140 * q^11 - 114244 * q^13 + 277653 * q^14 + 726609 * q^16 - 78717 * q^17 + 209664 * q^19 - 870843 * q^20 + 1364090 * q^22 + 4257444 * q^23 - 2900157 * q^25 - 942513 * q^26 + 4035181 * q^28 + 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 26257659 * q^34 + 13789797 * q^35 + 4636891 * q^37 - 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 - 33368081 * q^43 - 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 23294923 * q^49 + 4217748 * q^50 - 40813669 * q^52 + 171019326 * q^53 - 121160538 * q^55 + 281552967 * q^56 + 79964734 * q^58 + 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 768962465 * q^64 + 13452231 * q^65 - 41174072 * q^67 + 717615423 * q^68 + 409056389 * q^70 - 252460989 * q^71 + 594415068 * q^73 + 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 - 875148240 * q^82 + 79577862 * q^83 + 549463469 * q^85 + 589924887 * q^86 - 2327564370 * q^88 + 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 + 1859909503 * q^94 + 1273705170 * q^95 + 1049098084 * q^97 - 420532254 * q^98

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