LMFDB - Embedded newform 117.10.a.c.1.1

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			1.1
Root			$-36.8028$ 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)

$f(q)$	$=$	$q-28.8028 q^{2} +317.603 q^{4} +258.914 q^{5} -8862.28 q^{7} +5599.18 q^{8} +O(q^{10})$	\(q-28.8028 q^{2} +317.603 q^{4} +258.914 q^{5} -8862.28 q^{7} +5599.18 q^{8} -7457.46 q^{10} -36087.9 q^{11} -28561.0 q^{13} +255259. q^{14} -323885. q^{16} -327405. q^{17} +265525. q^{19} +82231.9 q^{20} +1.03943e6 q^{22} +2.42458e6 q^{23} -1.88609e6 q^{25} +822638. q^{26} -2.81469e6 q^{28} -3.99178e6 q^{29} -6.45220e6 q^{31} +6.46202e6 q^{32} +9.43018e6 q^{34} -2.29457e6 q^{35} -8.15498e6 q^{37} -7.64787e6 q^{38} +1.44971e6 q^{40} +720241. q^{41} -4.13245e7 q^{43} -1.14616e7 q^{44} -6.98348e7 q^{46} -3.67369e7 q^{47} +3.81864e7 q^{49} +5.43247e7 q^{50} -9.07106e6 q^{52} -1.67334e7 q^{53} -9.34367e6 q^{55} -4.96215e7 q^{56} +1.14975e8 q^{58} +5.89865e7 q^{59} +1.28785e8 q^{61} +1.85842e8 q^{62} -2.02955e7 q^{64} -7.39484e6 q^{65} -1.91470e8 q^{67} -1.03985e8 q^{68} +6.60901e7 q^{70} -3.40865e8 q^{71} +3.19890e8 q^{73} +2.34887e8 q^{74} +8.43316e7 q^{76} +3.19821e8 q^{77} +2.44328e8 q^{79} -8.38584e7 q^{80} -2.07450e7 q^{82} +4.38630e8 q^{83} -8.47697e7 q^{85} +1.19026e9 q^{86} -2.02063e8 q^{88} +7.90342e8 q^{89} +2.53116e8 q^{91} +7.70054e8 q^{92} +1.05813e9 q^{94} +6.87481e7 q^{95} -1.65696e8 q^{97} -1.09988e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−28.8028	−1.27292	−0.636459	−	0.771311i	$-0.719601\pi$
$2$	−28.8028	−1.27292	−0.636459	+	0.771311i	$0.719601\pi$
$3$	0	0
$3$	0	0
$4$	317.603	0.620318
$5$	258.914	0.185264	0.0926319	−	0.995700i	$-0.470472\pi$
$5$	258.914	0.185264	0.0926319	+	0.995700i	$0.470472\pi$
$6$	0	0
$7$	−8862.28	−1.39510	−0.697548	−	0.716538i	$-0.745726\pi$
$7$	−8862.28	−1.39510	−0.697548	+	0.716538i	$0.745726\pi$
$8$	5599.18	0.483303
$9$	0	0
$10$	−7457.46	−0.235825
$11$	−36087.9	−0.743181	−0.371591	−	0.928397i	$-0.621188\pi$
$11$	−36087.9	−0.743181	−0.371591	+	0.928397i	$0.621188\pi$
$12$	0	0
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	255259.	1.77584
$15$	0	0
$16$	−323885.	−1.23552
$17$	−327405.	−0.950747	−0.475373	−	0.879784i	$-0.657687\pi$
$17$	−327405.	−0.950747	−0.475373	+	0.879784i	$0.657687\pi$
$18$	0	0
$19$	265525.	0.467428	0.233714	−	0.972305i	$-0.424912\pi$
$19$	265525.	0.467428	0.233714	+	0.972305i	$0.424912\pi$
$20$	82231.9	0.114923
$21$	0	0
$22$	1.03943e6	0.946008
$23$	2.42458e6	1.80660	0.903299	−	0.429012i	$-0.141138\pi$
$23$	2.42458e6	1.80660	0.903299	+	0.429012i	$0.141138\pi$
$24$	0	0
$25$	−1.88609e6	−0.965677
$26$	822638.	0.353044
$27$	0	0
$28$	−2.81469e6	−0.865404
$29$	−3.99178e6	−1.04803	−0.524017	−	0.851708i	$-0.675567\pi$
$29$	−3.99178e6	−1.04803	−0.524017	+	0.851708i	$0.675567\pi$
$30$	0	0
$31$	−6.45220e6	−1.25482	−0.627408	−	0.778691i	$-0.715884\pi$
$31$	−6.45220e6	−1.25482	−0.627408	+	0.778691i	$0.715884\pi$
$32$	6.46202e6	1.08942
$33$	0	0
$34$	9.43018e6	1.21022
$35$	−2.29457e6	−0.258461
$36$	0	0
$37$	−8.15498e6	−0.715344	−0.357672	−	0.933847i	$-0.616429\pi$
$37$	−8.15498e6	−0.715344	−0.357672	+	0.933847i	$0.616429\pi$
$38$	−7.64787e6	−0.594997
$39$	0	0
$40$	1.44971e6	0.0895386
$41$	720241.	0.0398062	0.0199031	−	0.999802i	$-0.493664\pi$
$41$	720241.	0.0398062	0.0199031	+	0.999802i	$0.493664\pi$
$42$	0	0
$43$	−4.13245e7	−1.84332	−0.921658	−	0.388004i	$-0.873165\pi$
$43$	−4.13245e7	−1.84332	−0.921658	+	0.388004i	$0.873165\pi$
$44$	−1.14616e7	−0.461009
$45$	0	0
$46$	−6.98348e7	−2.29965
$47$	−3.67369e7	−1.09815	−0.549076	−	0.835772i	$-0.685020\pi$
$47$	−3.67369e7	−1.09815	−0.549076	+	0.835772i	$0.685020\pi$
$48$	0	0
$49$	3.81864e7	0.946295
$50$	5.43247e7	1.22923
$51$	0	0
$52$	−9.07106e6	−0.172045
$53$	−1.67334e7	−0.291302	−0.145651	−	0.989336i	$-0.546528\pi$
$53$	−1.67334e7	−0.291302	−0.145651	+	0.989336i	$0.546528\pi$
$54$	0	0
$55$	−9.34367e6	−0.137685
$56$	−4.96215e7	−0.674255
$57$	0	0
$58$	1.14975e8	1.33406
$59$	5.89865e7	0.633751	0.316875	−	0.948467i	$-0.397366\pi$
$59$	5.89865e7	0.633751	0.316875	+	0.948467i	$0.397366\pi$
$60$	0	0
$61$	1.28785e8	1.19091	0.595456	−	0.803388i	$-0.296971\pi$
$61$	1.28785e8	1.19091	0.595456	+	0.803388i	$0.296971\pi$
$62$	1.85842e8	1.59728
$63$	0	0
$64$	−2.02955e7	−0.151213
$65$	−7.39484e6	−0.0513829
$66$	0	0
$67$	−1.91470e8	−1.16082	−0.580410	−	0.814324i	$-0.697108\pi$
$67$	−1.91470e8	−1.16082	−0.580410	+	0.814324i	$0.697108\pi$
$68$	−1.03985e8	−0.589766
$69$	0	0
$70$	6.60901e7	0.328999
$71$	−3.40865e8	−1.59192	−0.795958	−	0.605351i	$-0.793033\pi$
$71$	−3.40865e8	−1.59192	−0.795958	+	0.605351i	$0.793033\pi$
$72$	0	0
$73$	3.19890e8	1.31840	0.659200	−	0.751968i	$-0.270895\pi$
$73$	3.19890e8	1.31840	0.659200	+	0.751968i	$0.270895\pi$
$74$	2.34887e8	0.910574
$75$	0	0
$76$	8.43316e7	0.289954
$77$	3.19821e8	1.03681
$78$	0	0
$79$	2.44328e8	0.705751	0.352876	−	0.935670i	$-0.385204\pi$
$79$	2.44328e8	0.705751	0.352876	+	0.935670i	$0.385204\pi$
$80$	−8.38584e7	−0.228898
$81$	0	0
$82$	−2.07450e7	−0.0506700
$83$	4.38630e8	1.01449	0.507244	−	0.861802i	$-0.330664\pi$
$83$	4.38630e8	1.01449	0.507244	+	0.861802i	$0.330664\pi$
$84$	0	0
$85$	−8.47697e7	−0.176139
$86$	1.19026e9	2.34639
$87$	0	0
$88$	−2.02063e8	−0.359182
$89$	7.90342e8	1.33524	0.667621	−	0.744501i	$-0.267312\pi$
$89$	7.90342e8	1.33524	0.667621	+	0.744501i	$0.267312\pi$
$90$	0	0
$91$	2.53116e8	0.386930
$92$	7.70054e8	1.12067
$93$	0	0
$94$	1.05813e9	1.39786
$95$	6.87481e7	0.0865974
$96$	0	0
$97$	−1.65696e8	−0.190037	−0.0950185	−	0.995476i	$-0.530291\pi$
$97$	−1.65696e8	−0.190037	−0.0950185	+	0.995476i	$0.530291\pi$
$98$	−1.09988e9	−1.20456
$99$	0	0
$100$	−5.99027e8	−0.599027
$101$	7.41636e8	0.709161	0.354580	−	0.935026i	$-0.384624\pi$
$101$	7.41636e8	0.709161	0.354580	+	0.935026i	$0.384624\pi$
$102$	0	0
$103$	1.42175e9	1.24467	0.622336	−	0.782750i	$-0.286184\pi$
$103$	1.42175e9	1.24467	0.622336	+	0.782750i	$0.286184\pi$
$104$	−1.59918e8	−0.134044
$105$	0	0
$106$	4.81970e8	0.370803
$107$	1.44196e9	1.06347	0.531736	−	0.846910i	$-0.321540\pi$
$107$	1.44196e9	1.06347	0.531736	+	0.846910i	$0.321540\pi$
$108$	0	0
$109$	−8.42758e7	−0.0571852	−0.0285926	−	0.999591i	$-0.509103\pi$
$109$	−8.42758e7	−0.0571852	−0.0285926	+	0.999591i	$0.509103\pi$
$110$	2.69124e8	0.175261
$111$	0	0
$112$	2.87036e9	1.72367
$113$	−8.60241e8	−0.496326	−0.248163	−	0.968718i	$-0.579827\pi$
$113$	−8.60241e8	−0.496326	−0.248163	+	0.968718i	$0.579827\pi$
$114$	0	0
$115$	6.27758e8	0.334697
$116$	−1.26780e9	−0.650115
$117$	0	0
$118$	−1.69898e9	−0.806712
$119$	2.90155e9	1.32638
$120$	0	0
$121$	−1.05561e9	−0.447681
$122$	−3.70936e9	−1.51593
$123$	0	0
$124$	−2.04924e9	−0.778386
$125$	−9.94026e8	−0.364169
$126$	0	0
$127$	−1.44120e9	−0.491596	−0.245798	−	0.969321i	$-0.579050\pi$
$127$	−1.44120e9	−0.491596	−0.245798	+	0.969321i	$0.579050\pi$
$128$	−2.72399e9	−0.896934
$129$	0	0
$130$	2.12992e8	0.0654062
$131$	4.54928e9	1.34965	0.674827	−	0.737976i	$-0.264218\pi$
$131$	4.54928e9	1.34965	0.674827	+	0.737976i	$0.264218\pi$
$132$	0	0
$133$	−2.35316e9	−0.652107
$134$	5.51489e9	1.47763
$135$	0	0
$136$	−1.83320e9	−0.459499
$137$	1.99742e9	0.484426	0.242213	−	0.970223i	$-0.422127\pi$
$137$	1.99742e9	0.484426	0.242213	+	0.970223i	$0.422127\pi$
$138$	0	0
$139$	3.55325e8	0.0807345	0.0403672	−	0.999185i	$-0.487147\pi$
$139$	3.55325e8	0.0807345	0.0403672	+	0.999185i	$0.487147\pi$
$140$	−7.28762e8	−0.160328
$141$	0	0
$142$	9.81789e9	2.02638
$143$	1.03071e9	0.206121
$144$	0	0
$145$	−1.03353e9	−0.194163
$146$	−9.21372e9	−1.67821
$147$	0	0
$148$	−2.59005e9	−0.443741
$149$	−5.92546e9	−0.984881	−0.492440	−	0.870346i	$-0.663895\pi$
$149$	−5.92546e9	−0.984881	−0.492440	+	0.870346i	$0.663895\pi$
$150$	0	0
$151$	−1.07568e10	−1.68378	−0.841891	−	0.539647i	$-0.818558\pi$
$151$	−1.07568e10	−1.68378	−0.841891	+	0.539647i	$0.818558\pi$
$152$	1.48672e9	0.225909
$153$	0	0
$154$	−9.21176e9	−1.31977
$155$	−1.67056e9	−0.232472
$156$	0	0
$157$	8.87634e9	1.16597	0.582983	−	0.812485i	$-0.301886\pi$
$157$	8.87634e9	1.16597	0.582983	+	0.812485i	$0.301886\pi$
$158$	−7.03734e9	−0.898363
$159$	0	0
$160$	1.67311e9	0.201829
$161$	−2.14873e10	−2.52038
$162$	0	0
$163$	2.75052e9	0.305190	0.152595	−	0.988289i	$-0.451237\pi$
$163$	2.75052e9	0.305190	0.152595	+	0.988289i	$0.451237\pi$
$164$	2.28751e8	0.0246925
$165$	0	0
$166$	−1.26338e10	−1.29136
$167$	9.17849e9	0.913160	0.456580	−	0.889682i	$-0.349074\pi$
$167$	9.17849e9	0.913160	0.456580	+	0.889682i	$0.349074\pi$
$168$	0	0
$169$	8.15731e8	0.0769231
$170$	2.44161e9	0.224210
$171$	0	0
$172$	−1.31248e10	−1.14344
$173$	−9.75049e8	−0.0827598	−0.0413799	−	0.999143i	$-0.513175\pi$
$173$	−9.75049e8	−0.0827598	−0.0413799	+	0.999143i	$0.513175\pi$
$174$	0	0
$175$	1.67150e10	1.34721
$176$	1.16883e10	0.918218
$177$	0	0
$178$	−2.27641e10	−1.69965
$179$	8.88356e9	0.646768	0.323384	−	0.946268i	$-0.395180\pi$
$179$	8.88356e9	0.646768	0.323384	+	0.946268i	$0.395180\pi$
$180$	0	0
$181$	−5.22791e9	−0.362055	−0.181028	−	0.983478i	$-0.557942\pi$
$181$	−5.22791e9	−0.362055	−0.181028	+	0.983478i	$0.557942\pi$
$182$	−7.29045e9	−0.492530
$183$	0	0
$184$	1.35757e10	0.873134
$185$	−2.11144e9	−0.132527
$186$	0	0
$187$	1.18154e10	0.706577
$188$	−1.16678e10	−0.681204
$189$	0	0
$190$	−1.98014e9	−0.110231
$191$	−9.23471e9	−0.502080	−0.251040	−	0.967977i	$-0.580773\pi$
$191$	−9.23471e9	−0.502080	−0.251040	+	0.967977i	$0.580773\pi$
$192$	0	0
$193$	1.07065e10	0.555441	0.277720	−	0.960662i	$-0.410421\pi$
$193$	1.07065e10	0.555441	0.277720	+	0.960662i	$0.410421\pi$
$194$	4.77250e9	0.241901
$195$	0	0
$196$	1.21281e10	0.587004
$197$	2.77001e10	1.31034	0.655169	−	0.755482i	$-0.272597\pi$
$197$	2.77001e10	1.31034	0.655169	+	0.755482i	$0.272597\pi$
$198$	0	0
$199$	3.32299e10	1.50207	0.751035	−	0.660262i	$-0.229555\pi$
$199$	3.32299e10	1.50207	0.751035	+	0.660262i	$0.229555\pi$
$200$	−1.05606e10	−0.466715
$201$	0	0
$202$	−2.13612e10	−0.902703
$203$	3.53763e10	1.46211
$204$	0	0
$205$	1.86481e8	0.00737465
$206$	−4.09503e10	−1.58436
$207$	0	0
$208$	9.25048e9	0.342673
$209$	−9.58225e9	−0.347383
$210$	0	0
$211$	−1.49261e10	−0.518411	−0.259205	−	0.965822i	$-0.583461\pi$
$211$	−1.49261e10	−0.518411	−0.259205	+	0.965822i	$0.583461\pi$
$212$	−5.31458e9	−0.180700
$213$	0	0
$214$	−4.15325e10	−1.35371
$215$	−1.06995e10	−0.341500
$216$	0	0
$217$	5.71812e10	1.75059
$218$	2.42738e9	0.0727920
$219$	0	0
$220$	−2.96758e9	−0.0854083
$221$	9.35101e9	0.263690
$222$	0	0
$223$	2.23373e10	0.604865	0.302433	−	0.953171i	$-0.402201\pi$
$223$	2.23373e10	0.604865	0.302433	+	0.953171i	$0.402201\pi$
$224$	−5.72683e10	−1.51984
$225$	0	0
$226$	2.47774e10	0.631782
$227$	−5.20726e9	−0.130165	−0.0650824	−	0.997880i	$-0.520731\pi$
$227$	−5.20726e9	−0.130165	−0.0650824	+	0.997880i	$0.520731\pi$
$228$	0	0
$229$	1.35573e10	0.325773	0.162887	−	0.986645i	$-0.447920\pi$
$229$	1.35573e10	0.325773	0.162887	+	0.986645i	$0.447920\pi$
$230$	−1.80812e10	−0.426042
$231$	0	0
$232$	−2.23507e10	−0.506518
$233$	−2.06224e8	−0.00458393	−0.00229196	−	0.999997i	$-0.500730\pi$
$233$	−2.06224e8	−0.00458393	−0.00229196	+	0.999997i	$0.500730\pi$
$234$	0	0
$235$	−9.51170e9	−0.203448
$236$	1.87343e10	0.393127
$237$	0	0
$238$	−8.35729e10	−1.68838
$239$	−1.89887e10	−0.376448	−0.188224	−	0.982126i	$-0.560273\pi$
$239$	−1.89887e10	−0.376448	−0.188224	+	0.982126i	$0.560273\pi$
$240$	0	0
$241$	−6.11533e10	−1.16773	−0.583866	−	0.811850i	$-0.698461\pi$
$241$	−6.11533e10	−1.16773	−0.583866	+	0.811850i	$0.698461\pi$
$242$	3.04045e10	0.569861
$243$	0	0
$244$	4.09024e10	0.738745
$245$	9.88700e9	0.175314
$246$	0	0
$247$	−7.58366e9	−0.129641
$248$	−3.61270e10	−0.606457
$249$	0	0
$250$	2.86308e10	0.463557
$251$	3.20685e9	0.0509973	0.0254986	−	0.999675i	$-0.491883\pi$
$251$	3.20685e9	0.0509973	0.0254986	+	0.999675i	$0.491883\pi$
$252$	0	0
$253$	−8.74981e10	−1.34263
$254$	4.15107e10	0.625761
$255$	0	0
$256$	8.88499e10	1.29294
$257$	2.80963e10	0.401744	0.200872	−	0.979617i	$-0.435622\pi$
$257$	2.80963e10	0.401744	0.200872	+	0.979617i	$0.435622\pi$
$258$	0	0
$259$	7.22717e10	0.997975
$260$	−2.34862e9	−0.0318738
$261$	0	0
$262$	−1.31032e11	−1.71800
$263$	1.25524e11	1.61780	0.808902	−	0.587944i	$-0.200062\pi$
$263$	1.25524e11	1.61780	0.808902	+	0.587944i	$0.200062\pi$
$264$	0	0
$265$	−4.33252e9	−0.0539677
$266$	6.77776e10	0.830078
$267$	0	0
$268$	−6.08116e10	−0.720078
$269$	1.78558e10	0.207918	0.103959	−	0.994582i	$-0.466849\pi$
$269$	1.78558e10	0.207918	0.103959	+	0.994582i	$0.466849\pi$
$270$	0	0
$271$	1.25204e11	1.41013	0.705063	−	0.709144i	$-0.250919\pi$
$271$	1.25204e11	1.41013	0.705063	+	0.709144i	$0.250919\pi$
$272$	1.06041e11	1.17467
$273$	0	0
$274$	−5.75314e10	−0.616634
$275$	6.80650e10	0.717673
$276$	0	0
$277$	−5.55594e10	−0.567020	−0.283510	−	0.958969i	$-0.591499\pi$
$277$	−5.55594e10	−0.567020	−0.283510	+	0.958969i	$0.591499\pi$
$278$	−1.02344e10	−0.102768
$279$	0	0
$280$	−1.28477e10	−0.124915
$281$	−1.01237e11	−0.968635	−0.484317	−	0.874892i	$-0.660932\pi$
$281$	−1.01237e11	−0.968635	−0.484317	+	0.874892i	$0.660932\pi$
$282$	0	0
$283$	−1.08041e11	−1.00127	−0.500635	−	0.865658i	$-0.666900\pi$
$283$	−1.08041e11	−1.00127	−0.500635	+	0.865658i	$0.666900\pi$
$284$	−1.08260e11	−0.987495
$285$	0	0
$286$	−2.96873e10	−0.262376
$287$	−6.38298e9	−0.0555335
$288$	0	0
$289$	−1.13940e10	−0.0960810
$290$	2.97685e10	0.247153
$291$	0	0
$292$	1.01598e11	0.817828
$293$	−3.53224e9	−0.0279992	−0.0139996	−	0.999902i	$-0.504456\pi$
$293$	−3.53224e9	−0.0279992	−0.0139996	+	0.999902i	$0.504456\pi$
$294$	0	0
$295$	1.52724e10	0.117411
$296$	−4.56612e10	−0.345728
$297$	0	0
$298$	1.70670e11	1.25367
$299$	−6.92485e10	−0.501060
$300$	0	0
$301$	3.66229e11	2.57160
$302$	3.09826e11	2.14332
$303$	0	0
$304$	−8.59996e10	−0.577518
$305$	3.33441e10	0.220633
$306$	0	0
$307$	−1.82031e11	−1.16956	−0.584781	−	0.811191i	$-0.698820\pi$
$307$	−1.82031e11	−1.16956	−0.584781	+	0.811191i	$0.698820\pi$
$308$	1.01576e11	0.643152
$309$	0	0
$310$	4.81170e10	0.295918
$311$	1.51907e11	0.920781	0.460390	−	0.887717i	$-0.347709\pi$
$311$	1.51907e11	0.920781	0.460390	+	0.887717i	$0.347709\pi$
$312$	0	0
$313$	6.10194e10	0.359351	0.179675	−	0.983726i	$-0.442495\pi$
$313$	6.10194e10	0.359351	0.179675	+	0.983726i	$0.442495\pi$
$314$	−2.55664e11	−1.48418
$315$	0	0
$316$	7.75994e10	0.437790
$317$	−6.89227e10	−0.383350	−0.191675	−	0.981458i	$-0.561392\pi$
$317$	−6.89227e10	−0.383350	−0.191675	+	0.981458i	$0.561392\pi$
$318$	0	0
$319$	1.44055e11	0.778880
$320$	−5.25478e9	−0.0280143
$321$	0	0
$322$	6.18896e11	3.20823
$323$	−8.69341e10	−0.444405
$324$	0	0
$325$	5.38686e10	0.267831
$326$	−7.92227e10	−0.388481
$327$	0	0
$328$	4.03276e9	0.0192385
$329$	3.25573e11	1.53203
$330$	0	0
$331$	4.70422e10	0.215408	0.107704	−	0.994183i	$-0.465650\pi$
$331$	4.70422e10	0.215408	0.107704	+	0.994183i	$0.465650\pi$
$332$	1.39310e11	0.629306
$333$	0	0
$334$	−2.64366e11	−1.16238
$335$	−4.95744e10	−0.215058
$336$	0	0
$337$	−3.76711e11	−1.59101	−0.795507	−	0.605944i	$-0.792795\pi$
$337$	−3.76711e11	−1.59101	−0.795507	+	0.605944i	$0.792795\pi$
$338$	−2.34954e10	−0.0979167
$339$	0	0
$340$	−2.69231e10	−0.109262
$341$	2.32846e11	0.932556
$342$	0	0
$343$	1.92062e10	0.0749235
$344$	−2.31383e11	−0.890880
$345$	0	0
$346$	2.80842e10	0.105346
$347$	−1.68331e11	−0.623278	−0.311639	−	0.950201i	$-0.600878\pi$
$347$	−1.68331e11	−0.623278	−0.311639	+	0.950201i	$0.600878\pi$
$348$	0	0
$349$	−9.36126e10	−0.337769	−0.168884	−	0.985636i	$-0.554016\pi$
$349$	−9.36126e10	−0.337769	−0.168884	+	0.985636i	$0.554016\pi$
$350$	−4.81441e11	−1.71489
$351$	0	0
$352$	−2.33201e11	−0.809634
$353$	3.49043e11	1.19644	0.598222	−	0.801330i	$-0.295874\pi$
$353$	3.49043e11	1.19644	0.598222	+	0.801330i	$0.295874\pi$
$354$	0	0
$355$	−8.82548e10	−0.294924
$356$	2.51015e11	0.828276
$357$	0	0
$358$	−2.55872e11	−0.823282
$359$	−5.83173e11	−1.85299	−0.926493	−	0.376312i	$-0.877192\pi$
$359$	−5.83173e11	−1.85299	−0.926493	+	0.376312i	$0.877192\pi$
$360$	0	0
$361$	−2.52184e11	−0.781512
$362$	1.50579e11	0.460866
$363$	0	0
$364$	8.03903e10	0.240020
$365$	8.28239e10	0.244252
$366$	0	0
$367$	5.28604e11	1.52101	0.760507	−	0.649329i	$-0.224950\pi$
$367$	5.28604e11	1.52101	0.760507	+	0.649329i	$0.224950\pi$
$368$	−7.85286e11	−2.23209
$369$	0	0
$370$	6.08154e10	0.168696
$371$	1.48296e11	0.406394
$372$	0	0
$373$	−4.19405e11	−1.12187	−0.560937	−	0.827858i	$-0.689559\pi$
$373$	−4.19405e11	−1.12187	−0.560937	+	0.827858i	$0.689559\pi$
$374$	−3.40316e11	−0.899414
$375$	0	0
$376$	−2.05697e11	−0.530740
$377$	1.14009e11	0.290672
$378$	0	0
$379$	4.24128e11	1.05590	0.527948	−	0.849277i	$-0.322962\pi$
$379$	4.24128e11	1.05590	0.527948	+	0.849277i	$0.322962\pi$
$380$	2.18346e10	0.0537180
$381$	0	0
$382$	2.65986e11	0.639107
$383$	−6.52696e10	−0.154995	−0.0774973	−	0.996993i	$-0.524693\pi$
$383$	−6.52696e10	−0.154995	−0.0774973	+	0.996993i	$0.524693\pi$
$384$	0	0
$385$	8.28062e10	0.192083
$386$	−3.08376e11	−0.707030
$387$	0	0
$388$	−5.26254e10	−0.117883
$389$	5.91803e11	1.31040	0.655200	−	0.755455i	$-0.272584\pi$
$389$	5.91803e11	1.31040	0.655200	+	0.755455i	$0.272584\pi$
$390$	0	0
$391$	−7.93819e11	−1.71762
$392$	2.13813e11	0.457347
$393$	0	0
$394$	−7.97842e11	−1.66795
$395$	6.32600e10	0.130750
$396$	0	0
$397$	−3.05131e11	−0.616495	−0.308248	−	0.951306i	$-0.599743\pi$
$397$	−3.05131e11	−0.616495	−0.308248	+	0.951306i	$0.599743\pi$
$398$	−9.57115e11	−1.91201
$399$	0	0
$400$	6.10876e11	1.19312
$401$	−2.56722e11	−0.495808	−0.247904	−	0.968785i	$-0.579742\pi$
$401$	−2.56722e11	−0.495808	−0.247904	+	0.968785i	$0.579742\pi$
$402$	0	0
$403$	1.84281e11	0.348023
$404$	2.35546e11	0.439906
$405$	0	0
$406$	−1.01894e12	−1.86114
$407$	2.94296e11	0.531631
$408$	0	0
$409$	−4.57003e11	−0.807540	−0.403770	−	0.914860i	$-0.632300\pi$
$409$	−4.57003e11	−0.807540	−0.403770	+	0.914860i	$0.632300\pi$
$410$	−5.37117e9	−0.00938732
$411$	0	0
$412$	4.51551e11	0.772093
$413$	−5.22755e11	−0.884144
$414$	0	0
$415$	1.13567e11	0.187948
$416$	−1.84562e11	−0.302150
$417$	0	0
$418$	2.75996e11	0.442190
$419$	1.65068e11	0.261637	0.130818	−	0.991406i	$-0.458240\pi$
$419$	1.65068e11	0.261637	0.130818	+	0.991406i	$0.458240\pi$
$420$	0	0
$421$	−9.10255e10	−0.141219	−0.0706096	−	0.997504i	$-0.522494\pi$
$421$	−9.10255e10	−0.141219	−0.0706096	+	0.997504i	$0.522494\pi$
$422$	4.29913e11	0.659894
$423$	0	0
$424$	−9.36935e10	−0.140787
$425$	6.17514e11	0.918114
$426$	0	0
$427$	−1.14133e12	−1.66144
$428$	4.57971e11	0.659691
$429$	0	0
$430$	3.08176e11	0.434701
$431$	−7.94605e11	−1.10918	−0.554592	−	0.832122i	$-0.687126\pi$
$431$	−7.94605e11	−1.10918	−0.554592	+	0.832122i	$0.687126\pi$
$432$	0	0
$433$	−8.26325e11	−1.12968	−0.564840	−	0.825200i	$-0.691062\pi$
$433$	−8.26325e11	−1.12968	−0.564840	+	0.825200i	$0.691062\pi$
$434$	−1.64698e12	−2.22836
$435$	0	0
$436$	−2.67662e10	−0.0354730
$437$	6.43787e11	0.844453
$438$	0	0
$439$	1.21562e12	1.56210	0.781050	−	0.624469i	$-0.214684\pi$
$439$	1.21562e12	1.56210	0.781050	+	0.624469i	$0.214684\pi$
$440$	−5.23169e10	−0.0665434
$441$	0	0
$442$	−2.69335e11	−0.335655
$443$	8.73136e11	1.07712	0.538561	−	0.842586i	$-0.318968\pi$
$443$	8.73136e11	1.07712	0.538561	+	0.842586i	$0.318968\pi$
$444$	0	0
$445$	2.04631e11	0.247372
$446$	−6.43377e11	−0.769943
$447$	0	0
$448$	1.79864e11	0.210957
$449$	−1.22107e12	−1.41785	−0.708927	−	0.705282i	$-0.750821\pi$
$449$	−1.22107e12	−1.41785	−0.708927	+	0.705282i	$0.750821\pi$
$450$	0	0
$451$	−2.59920e10	−0.0295832
$452$	−2.73215e11	−0.307880
$453$	0	0
$454$	1.49984e11	0.165689
$455$	6.55352e10	0.0716842
$456$	0	0
$457$	6.32643e11	0.678478	0.339239	−	0.940700i	$-0.389830\pi$
$457$	6.32643e11	0.678478	0.339239	+	0.940700i	$0.389830\pi$
$458$	−3.90490e11	−0.414682
$459$	0	0
$460$	1.99378e11	0.207619
$461$	−8.09117e11	−0.834367	−0.417184	−	0.908822i	$-0.636983\pi$
$461$	−8.09117e11	−0.834367	−0.417184	+	0.908822i	$0.636983\pi$
$462$	0	0
$463$	7.69685e11	0.778393	0.389196	−	0.921155i	$-0.372753\pi$
$463$	7.69685e11	0.778393	0.389196	+	0.921155i	$0.372753\pi$
$464$	1.29288e12	1.29487
$465$	0	0
$466$	5.93984e9	0.00583496
$467$	−1.59708e12	−1.55382	−0.776909	−	0.629613i	$-0.783213\pi$
$467$	−1.59708e12	−1.55382	−0.776909	+	0.629613i	$0.783213\pi$
$468$	0	0
$469$	1.69686e12	1.61946
$470$	2.73964e11	0.258972
$471$	0	0
$472$	3.30276e11	0.306294
$473$	1.49132e12	1.36992
$474$	0	0
$475$	−5.00804e11	−0.451384
$476$	9.21542e11	0.822780
$477$	0	0
$478$	5.46929e11	0.479187
$479$	−1.61308e12	−1.40006	−0.700028	−	0.714115i	$-0.746829\pi$
$479$	−1.61308e12	−1.40006	−0.700028	+	0.714115i	$0.746829\pi$
$480$	0	0
$481$	2.32914e11	0.198401
$482$	1.76139e12	1.48643
$483$	0	0
$484$	−3.35265e11	−0.277705
$485$	−4.29009e10	−0.0352070
$486$	0	0
$487$	9.29058e11	0.748449	0.374225	−	0.927338i	$-0.377909\pi$
$487$	9.29058e11	0.748449	0.374225	+	0.927338i	$0.377909\pi$
$488$	7.21089e11	0.575572
$489$	0	0
$490$	−2.84774e11	−0.223160
$491$	2.30662e12	1.79106	0.895528	−	0.445005i	$-0.146798\pi$
$491$	2.30662e12	1.79106	0.895528	+	0.445005i	$0.146798\pi$
$492$	0	0
$493$	1.30693e12	0.996415
$494$	2.18431e11	0.165022
$495$	0	0
$496$	2.08977e12	1.55036
$497$	3.02084e12	2.22088
$498$	0	0
$499$	−1.31410e11	−0.0948800	−0.0474400	−	0.998874i	$-0.515106\pi$
$499$	−1.31410e11	−0.0948800	−0.0474400	+	0.998874i	$0.515106\pi$
$500$	−3.15706e11	−0.225901
$501$	0	0
$502$	−9.23664e10	−0.0649153
$503$	1.88419e12	1.31241	0.656203	−	0.754584i	$-0.272162\pi$
$503$	1.88419e12	1.31241	0.656203	+	0.754584i	$0.272162\pi$
$504$	0	0
$505$	1.92020e11	0.131382
$506$	2.52019e12	1.70906
$507$	0	0
$508$	−4.57730e11	−0.304946
$509$	1.00390e11	0.0662919	0.0331459	−	0.999451i	$-0.489447\pi$
$509$	1.00390e11	0.0662919	0.0331459	+	0.999451i	$0.489447\pi$
$510$	0	0
$511$	−2.83495e12	−1.83930
$512$	−1.16445e12	−0.748866
$513$	0	0
$514$	−8.09252e11	−0.511387
$515$	3.68110e11	0.230593
$516$	0	0
$517$	1.32576e12	0.816126
$518$	−2.08163e12	−1.27034
$519$	0	0
$520$	−4.14051e10	−0.0248335
$521$	1.04516e11	0.0621462	0.0310731	−	0.999517i	$-0.490108\pi$
$521$	1.04516e11	0.0621462	0.0310731	+	0.999517i	$0.490108\pi$
$522$	0	0
$523$	1.17694e12	0.687855	0.343927	−	0.938996i	$-0.388243\pi$
$523$	1.17694e12	0.687855	0.343927	+	0.938996i	$0.388243\pi$
$524$	1.44487e12	0.837215
$525$	0	0
$526$	−3.61544e12	−2.05933
$527$	2.11248e12	1.19301
$528$	0	0
$529$	4.07744e12	2.26379
$530$	1.24789e11	0.0686964
$531$	0	0
$532$	−7.47370e11	−0.404514
$533$	−2.05708e10	−0.0110403
$534$	0	0
$535$	3.73343e11	0.197023
$536$	−1.07208e12	−0.561028
$537$	0	0
$538$	−5.14296e11	−0.264663
$539$	−1.37807e12	−0.703269
$540$	0	0
$541$	−2.98502e12	−1.49817	−0.749083	−	0.662476i	$-0.769506\pi$
$541$	−2.98502e12	−1.49817	−0.749083	+	0.662476i	$0.769506\pi$
$542$	−3.60624e12	−1.79497
$543$	0	0
$544$	−2.11570e12	−1.03576
$545$	−2.18202e10	−0.0105943
$546$	0	0
$547$	3.78628e12	1.80830	0.904148	−	0.427219i	$-0.140507\pi$
$547$	3.78628e12	1.80830	0.904148	+	0.427219i	$0.140507\pi$
$548$	6.34387e11	0.300498
$549$	0	0
$550$	−1.96047e12	−0.913539
$551$	−1.05992e12	−0.489880
$552$	0	0
$553$	−2.16530e12	−0.984591
$554$	1.60027e12	0.721770
$555$	0	0
$556$	1.12852e11	0.0500811
$557$	−1.00551e12	−0.442627	−0.221313	−	0.975203i	$-0.571034\pi$
$557$	−1.00551e12	−0.442627	−0.221313	+	0.975203i	$0.571034\pi$
$558$	0	0
$559$	1.18027e12	0.511244
$560$	7.43177e11	0.319335
$561$	0	0
$562$	2.91591e12	1.23299
$563$	−2.76515e11	−0.115993	−0.0579964	−	0.998317i	$-0.518471\pi$
$563$	−2.76515e11	−0.115993	−0.0579964	+	0.998317i	$0.518471\pi$
$564$	0	0
$565$	−2.22728e11	−0.0919512
$566$	3.11190e12	1.27453
$567$	0	0
$568$	−1.90857e12	−0.769378
$569$	−8.39220e11	−0.335638	−0.167819	−	0.985818i	$-0.553672\pi$
$569$	−8.39220e11	−0.335638	−0.167819	+	0.985818i	$0.553672\pi$
$570$	0	0
$571$	−1.02285e11	−0.0402672	−0.0201336	−	0.999797i	$-0.506409\pi$
$571$	−1.02285e11	−0.0402672	−0.0201336	+	0.999797i	$0.506409\pi$
$572$	3.27356e11	0.127861
$573$	0	0
$574$	1.83848e11	0.0706896
$575$	−4.57297e12	−1.74459
$576$	0	0
$577$	−1.44021e12	−0.540921	−0.270461	−	0.962731i	$-0.587176\pi$
$577$	−1.44021e12	−0.540921	−0.270461	+	0.962731i	$0.587176\pi$
$578$	3.28181e11	0.122303
$579$	0	0
$580$	−3.28251e11	−0.120443
$581$	−3.88726e12	−1.41531
$582$	0	0
$583$	6.03874e11	0.216490
$584$	1.79112e12	0.637187
$585$	0	0
$586$	1.01738e11	0.0356407
$587$	2.13185e11	0.0741116	0.0370558	−	0.999313i	$-0.488202\pi$
$587$	2.13185e11	0.0741116	0.0370558	+	0.999313i	$0.488202\pi$
$588$	0	0
$589$	−1.71322e12	−0.586536
$590$	−4.39889e11	−0.149455
$591$	0	0
$592$	2.64128e12	0.883825
$593$	1.76049e12	0.584640	0.292320	−	0.956321i	$-0.405573\pi$
$593$	1.76049e12	0.584640	0.292320	+	0.956321i	$0.405573\pi$
$594$	0	0
$595$	7.51253e11	0.245731
$596$	−1.88194e12	−0.610940
$597$	0	0
$598$	1.99455e12	0.637808
$599$	2.06753e12	0.656191	0.328096	−	0.944644i	$-0.393593\pi$
$599$	2.06753e12	0.656191	0.328096	+	0.944644i	$0.393593\pi$
$600$	0	0
$601$	−1.24403e12	−0.388951	−0.194476	−	0.980907i	$-0.562301\pi$
$601$	−1.24403e12	−0.388951	−0.194476	+	0.980907i	$0.562301\pi$
$602$	−1.05484e13	−3.27344
$603$	0	0
$604$	−3.41639e12	−1.04448
$605$	−2.73312e11	−0.0829391
$606$	0	0
$607$	−1.31511e12	−0.393200	−0.196600	−	0.980484i	$-0.562990\pi$
$607$	−1.31511e12	−0.393200	−0.196600	+	0.980484i	$0.562990\pi$
$608$	1.71583e12	0.509223
$609$	0	0
$610$	−9.60406e11	−0.280847
$611$	1.04924e12	0.304573
$612$	0	0
$613$	−3.08252e12	−0.881726	−0.440863	−	0.897574i	$-0.645328\pi$
$613$	−3.08252e12	−0.881726	−0.440863	+	0.897574i	$0.645328\pi$
$614$	5.24301e12	1.48876
$615$	0	0
$616$	1.79074e12	0.501094
$617$	2.29075e10	0.00636348	0.00318174	−	0.999995i	$-0.498987\pi$
$617$	2.29075e10	0.00636348	0.00318174	+	0.999995i	$0.498987\pi$
$618$	0	0
$619$	−4.45350e12	−1.21925	−0.609626	−	0.792689i	$-0.708680\pi$
$619$	−4.45350e12	−1.21925	−0.609626	+	0.792689i	$0.708680\pi$
$620$	−5.30576e11	−0.144207
$621$	0	0
$622$	−4.37535e12	−1.17208
$623$	−7.00424e12	−1.86279
$624$	0	0
$625$	3.42640e12	0.898210
$626$	−1.75753e12	−0.457423
$627$	0	0
$628$	2.81915e12	0.723270
$629$	2.66998e12	0.680111
$630$	0	0
$631$	3.83831e12	0.963847	0.481923	−	0.876213i	$-0.339938\pi$
$631$	3.83831e12	0.963847	0.481923	+	0.876213i	$0.339938\pi$
$632$	1.36804e12	0.341092
$633$	0	0
$634$	1.98517e12	0.487973
$635$	−3.73148e11	−0.0910749
$636$	0	0
$637$	−1.09064e12	−0.262455
$638$	−4.14919e12	−0.991449
$639$	0	0
$640$	−7.05279e11	−0.166169
$641$	−9.09238e11	−0.212724	−0.106362	−	0.994327i	$-0.533920\pi$
$641$	−9.09238e11	−0.212724	−0.106362	+	0.994327i	$0.533920\pi$
$642$	0	0
$643$	8.23839e12	1.90061	0.950305	−	0.311321i	$-0.100771\pi$
$643$	8.23839e12	1.90061	0.950305	+	0.311321i	$0.100771\pi$
$644$	−6.82444e12	−1.56344
$645$	0	0
$646$	2.50395e12	0.565691
$647$	8.73559e12	1.95985	0.979925	−	0.199365i	$-0.0638880\pi$
$647$	8.73559e12	1.95985	0.979925	+	0.199365i	$0.0638880\pi$
$648$	0	0
$649$	−2.12870e12	−0.470992
$650$	−1.55157e12	−0.340926
$651$	0	0
$652$	8.73573e11	0.189315
$653$	6.13232e11	0.131982	0.0659911	−	0.997820i	$-0.478979\pi$
$653$	6.13232e11	0.131982	0.0659911	+	0.997820i	$0.478979\pi$
$654$	0	0
$655$	1.17787e12	0.250042
$656$	−2.33275e11	−0.0491815
$657$	0	0
$658$	−9.37742e12	−1.95015
$659$	8.83233e12	1.82428	0.912139	−	0.409882i	$-0.134430\pi$
$659$	8.83233e12	1.82428	0.912139	+	0.409882i	$0.134430\pi$
$660$	0	0
$661$	−5.61801e12	−1.14466	−0.572329	−	0.820024i	$-0.693960\pi$
$661$	−5.61801e12	−1.14466	−0.572329	+	0.820024i	$0.693960\pi$
$662$	−1.35495e12	−0.274196
$663$	0	0
$664$	2.45597e12	0.490306
$665$	−6.09265e11	−0.120812
$666$	0	0
$667$	−9.67839e12	−1.89338
$668$	2.91511e12	0.566450
$669$	0	0
$670$	1.42788e12	0.273751
$671$	−4.64757e12	−0.885064
$672$	0	0
$673$	4.50151e12	0.845844	0.422922	−	0.906166i	$-0.361004\pi$
$673$	4.50151e12	0.845844	0.422922	+	0.906166i	$0.361004\pi$
$674$	1.08503e13	2.02523
$675$	0	0
$676$	2.59079e11	0.0477168
$677$	−4.33098e12	−0.792387	−0.396193	−	0.918167i	$-0.629669\pi$
$677$	−4.33098e12	−0.792387	−0.396193	+	0.918167i	$0.629669\pi$
$678$	0	0
$679$	1.46844e12	0.265120
$680$	−4.74641e11	−0.0851285
$681$	0	0
$682$	−6.70664e12	−1.18707
$683$	−6.25107e12	−1.09916	−0.549580	−	0.835441i	$-0.685212\pi$
$683$	−6.25107e12	−1.09916	−0.549580	+	0.835441i	$0.685212\pi$
$684$	0	0
$685$	5.17161e11	0.0897466
$686$	−5.53193e11	−0.0953715
$687$	0	0
$688$	1.33844e13	2.27746
$689$	4.77923e11	0.0807926
$690$	0	0
$691$	7.34082e12	1.22488	0.612440	−	0.790517i	$-0.290188\pi$
$691$	7.34082e12	1.22488	0.612440	+	0.790517i	$0.290188\pi$
$692$	−3.09679e11	−0.0513374
$693$	0	0
$694$	4.84841e12	0.793381
$695$	9.19986e10	0.0149572
$696$	0	0
$697$	−2.35810e11	−0.0378456
$698$	2.69631e12	0.429952
$699$	0	0
$700$	5.30875e12	0.835701
$701$	1.71509e11	0.0268259	0.0134130	−	0.999910i	$-0.495730\pi$
$701$	1.71509e11	0.0268259	0.0134130	+	0.999910i	$0.495730\pi$
$702$	0	0
$703$	−2.16535e12	−0.334372
$704$	7.32421e11	0.112379
$705$	0	0
$706$	−1.00534e13	−1.52297
$707$	−6.57259e12	−0.989348
$708$	0	0
$709$	−1.00896e13	−1.49956	−0.749780	−	0.661687i	$-0.769841\pi$
$709$	−1.00896e13	−1.49956	−0.749780	+	0.661687i	$0.769841\pi$
$710$	2.54199e12	0.375414
$711$	0	0
$712$	4.42527e12	0.645327
$713$	−1.56439e13	−2.26695
$714$	0	0
$715$	2.66865e11	0.0381868
$716$	2.82145e12	0.401202
$717$	0	0
$718$	1.67970e13	2.35870
$719$	−8.18068e12	−1.14159	−0.570794	−	0.821093i	$-0.693365\pi$
$719$	−8.18068e12	−1.14159	−0.570794	+	0.821093i	$0.693365\pi$
$720$	0	0
$721$	−1.25999e13	−1.73644
$722$	7.26362e12	0.994800
$723$	0	0
$724$	−1.66040e12	−0.224589
$725$	7.52885e12	1.01206
$726$	0	0
$727$	−9.98421e11	−0.132559	−0.0662795	−	0.997801i	$-0.521113\pi$
$727$	−9.98421e11	−0.132559	−0.0662795	+	0.997801i	$0.521113\pi$
$728$	1.41724e12	0.187005
$729$	0	0
$730$	−2.38556e12	−0.310912
$731$	1.35298e13	1.75253
$732$	0	0
$733$	−2.10457e12	−0.269274	−0.134637	−	0.990895i	$-0.542987\pi$
$733$	−2.10457e12	−0.269274	−0.134637	+	0.990895i	$0.542987\pi$
$734$	−1.52253e13	−1.93613
$735$	0	0
$736$	1.56677e13	1.96814
$737$	6.90977e12	0.862700
$738$	0	0
$739$	−1.28931e13	−1.59023	−0.795113	−	0.606461i	$-0.792588\pi$
$739$	−1.28931e13	−1.59023	−0.795113	+	0.606461i	$0.792588\pi$
$740$	−6.70599e11	−0.0822092
$741$	0	0
$742$	−4.27135e12	−0.517306
$743$	−2.72357e11	−0.0327861	−0.0163930	−	0.999866i	$-0.505218\pi$
$743$	−2.72357e11	−0.0327861	−0.0163930	+	0.999866i	$0.505218\pi$
$744$	0	0
$745$	−1.53418e12	−0.182463
$746$	1.20801e13	1.42805
$747$	0	0
$748$	3.75259e12	0.438303
$749$	−1.27790e13	−1.48365
$750$	0	0
$751$	−1.40530e13	−1.61209	−0.806045	−	0.591855i	$-0.798396\pi$
$751$	−1.40530e13	−1.61209	−0.806045	+	0.591855i	$0.798396\pi$
$752$	1.18985e13	1.35679
$753$	0	0
$754$	−3.28379e12	−0.370002
$755$	−2.78508e12	−0.311944
$756$	0	0
$757$	8.53220e12	0.944342	0.472171	−	0.881507i	$-0.343470\pi$
$757$	8.53220e12	0.944342	0.472171	+	0.881507i	$0.343470\pi$
$758$	−1.22161e13	−1.34407
$759$	0	0
$760$	3.84933e11	0.0418528
$761$	−1.13835e13	−1.23039	−0.615197	−	0.788373i	$-0.710924\pi$
$761$	−1.13835e13	−1.23039	−0.615197	+	0.788373i	$0.710924\pi$
$762$	0	0
$763$	7.46876e11	0.0797789
$764$	−2.93297e12	−0.311450
$765$	0	0
$766$	1.87995e12	0.197295
$767$	−1.68471e12	−0.175771
$768$	0	0
$769$	1.94858e12	0.200933	0.100466	−	0.994940i	$-0.467967\pi$
$769$	1.94858e12	0.200933	0.100466	+	0.994940i	$0.467967\pi$
$770$	−2.38505e12	−0.244506
$771$	0	0
$772$	3.40040e12	0.344550
$773$	1.09355e13	1.10161	0.550807	−	0.834633i	$-0.314320\pi$
$773$	1.09355e13	1.10161	0.550807	+	0.834633i	$0.314320\pi$
$774$	0	0
$775$	1.21694e13	1.21175
$776$	−9.27760e11	−0.0918455
$777$	0	0
$778$	−1.70456e13	−1.66803
$779$	1.91242e11	0.0186065
$780$	0	0
$781$	1.23011e13	1.18308
$782$	2.28642e13	2.18638
$783$	0	0
$784$	−1.23680e13	−1.16917
$785$	2.29821e12	0.216011
$786$	0	0
$787$	7.50366e12	0.697247	0.348623	−	0.937263i	$-0.386649\pi$
$787$	7.50366e12	0.697247	0.348623	+	0.937263i	$0.386649\pi$
$788$	8.79764e12	0.812827
$789$	0	0
$790$	−1.82207e12	−0.166434
$791$	7.62369e12	0.692423
$792$	0	0
$793$	−3.67822e12	−0.330300
$794$	8.78865e12	0.784747
$795$	0	0
$796$	1.05539e13	0.931762
$797$	−1.65844e12	−0.145592	−0.0727962	−	0.997347i	$-0.523192\pi$
$797$	−1.65844e12	−0.145592	−0.0727962	+	0.997347i	$0.523192\pi$
$798$	0	0
$799$	1.20278e13	1.04406
$800$	−1.21880e13	−1.05202
$801$	0	0
$802$	7.39433e12	0.631123
$803$	−1.15441e13	−0.979810
$804$	0	0
$805$	−5.56337e12	−0.466935
$806$	−5.30782e12	−0.443005
$807$	0	0
$808$	4.15256e12	0.342740
$809$	7.07921e12	0.581054	0.290527	−	0.956867i	$-0.406169\pi$
$809$	7.07921e12	0.581054	0.290527	+	0.956867i	$0.406169\pi$
$810$	0	0
$811$	−1.84596e13	−1.49840	−0.749201	−	0.662343i	$-0.769562\pi$
$811$	−1.84596e13	−1.49840	−0.749201	+	0.662343i	$0.769562\pi$
$812$	1.12356e13	0.906973
$813$	0	0
$814$	−8.47657e12	−0.676722
$815$	7.12147e11	0.0565406
$816$	0	0
$817$	−1.09727e13	−0.861616
$818$	1.31630e13	1.02793
$819$	0	0
$820$	5.92268e10	0.00457463
$821$	−2.40377e13	−1.84650	−0.923250	−	0.384200i	$-0.874477\pi$
$821$	−2.40377e13	−1.84650	−0.923250	+	0.384200i	$0.874477\pi$
$822$	0	0
$823$	−1.26494e12	−0.0961104	−0.0480552	−	0.998845i	$-0.515302\pi$
$823$	−1.26494e12	−0.0961104	−0.0480552	+	0.998845i	$0.515302\pi$
$824$	7.96062e12	0.601554
$825$	0	0
$826$	1.50568e13	1.12544
$827$	9.81229e12	0.729450	0.364725	−	0.931115i	$-0.381163\pi$
$827$	9.81229e12	0.729450	0.364725	+	0.931115i	$0.381163\pi$
$828$	0	0
$829$	1.26128e13	0.927504	0.463752	−	0.885965i	$-0.346503\pi$
$829$	1.26128e13	0.927504	0.463752	+	0.885965i	$0.346503\pi$
$830$	−3.27107e12	−0.239242
$831$	0	0
$832$	5.79658e11	0.0419389
$833$	−1.25024e13	−0.899687
$834$	0	0
$835$	2.37644e12	0.169175
$836$	−3.04335e12	−0.215488
$837$	0	0
$838$	−4.75441e12	−0.333042
$839$	8.53632e12	0.594760	0.297380	−	0.954759i	$-0.403887\pi$
$839$	8.53632e12	0.594760	0.297380	+	0.954759i	$0.403887\pi$
$840$	0	0
$841$	1.42715e12	0.0983759
$842$	2.62179e12	0.179760
$843$	0	0
$844$	−4.74056e12	−0.321580
$845$	2.11204e11	0.0142511
$846$	0	0
$847$	9.35511e12	0.624559
$848$	5.41970e12	0.359910
$849$	0	0
$850$	−1.77862e13	−1.16868
$851$	−1.97724e13	−1.29234
$852$	0	0
$853$	−1.12025e13	−0.724507	−0.362254	−	0.932080i	$-0.617993\pi$
$853$	−1.12025e13	−0.724507	−0.362254	+	0.932080i	$0.617993\pi$
$854$	3.28734e13	2.11487
$855$	0	0
$856$	8.07379e12	0.513979
$857$	2.23241e13	1.41371	0.706856	−	0.707357i	$-0.250113\pi$
$857$	2.23241e13	1.41371	0.706856	+	0.707357i	$0.250113\pi$
$858$	0	0
$859$	−2.11323e13	−1.32428	−0.662138	−	0.749382i	$-0.730351\pi$
$859$	−2.11323e13	−1.32428	−0.662138	+	0.749382i	$0.730351\pi$
$860$	−3.39819e12	−0.211838
$861$	0	0
$862$	2.28869e13	1.41190
$863$	−1.17061e13	−0.718395	−0.359197	−	0.933262i	$-0.616950\pi$
$863$	−1.17061e13	−0.718395	−0.359197	+	0.933262i	$0.616950\pi$
$864$	0	0
$865$	−2.52454e11	−0.0153324
$866$	2.38005e13	1.43799
$867$	0	0
$868$	1.81609e13	1.08592
$869$	−8.81730e12	−0.524501
$870$	0	0
$871$	5.46859e12	0.321954
$872$	−4.71876e11	−0.0276378
$873$	0	0
$874$	−1.85429e13	−1.07492
$875$	8.80934e12	0.508051
$876$	0	0
$877$	1.17836e13	0.672638	0.336319	−	0.941748i	$-0.390818\pi$
$877$	1.17836e13	0.672638	0.336319	+	0.941748i	$0.390818\pi$
$878$	−3.50134e13	−1.98842
$879$	0	0
$880$	3.02627e12	0.170113
$881$	1.93741e13	1.08350	0.541751	−	0.840539i	$-0.317762\pi$
$881$	1.93741e13	1.08350	0.541751	+	0.840539i	$0.317762\pi$
$882$	0	0
$883$	−1.50199e13	−0.831466	−0.415733	−	0.909487i	$-0.636475\pi$
$883$	−1.50199e13	−0.831466	−0.415733	+	0.909487i	$0.636475\pi$
$884$	2.96991e12	0.163572
$885$	0	0
$886$	−2.51488e13	−1.37109
$887$	−1.23661e13	−0.670776	−0.335388	−	0.942080i	$-0.608867\pi$
$887$	−1.23661e13	−0.670776	−0.335388	+	0.942080i	$0.608867\pi$
$888$	0	0
$889$	1.27723e13	0.685824
$890$	−5.89394e12	−0.314884
$891$	0	0
$892$	7.09439e12	0.375209
$893$	−9.75457e12	−0.513306
$894$	0	0
$895$	2.30008e12	0.119823
$896$	2.41408e13	1.25131
$897$	0	0
$898$	3.51702e13	1.80481
$899$	2.57558e13	1.31509
$900$	0	0
$901$	5.47860e12	0.276954
$902$	7.48644e11	0.0376570
$903$	0	0
$904$	−4.81664e12	−0.239876
$905$	−1.35358e12	−0.0670757
$906$	0	0
$907$	9.76708e12	0.479217	0.239608	−	0.970870i	$-0.422981\pi$
$907$	9.76708e12	0.479217	0.239608	+	0.970870i	$0.422981\pi$
$908$	−1.65384e12	−0.0807436
$909$	0	0
$910$	−1.88760e12	−0.0912480
$911$	1.91556e13	0.921430	0.460715	−	0.887548i	$-0.347593\pi$
$911$	1.91556e13	0.921430	0.460715	+	0.887548i	$0.347593\pi$
$912$	0	0
$913$	−1.58293e13	−0.753949
$914$	−1.82219e13	−0.863647
$915$	0	0
$916$	4.30586e12	0.202083
$917$	−4.03170e13	−1.88290
$918$	0	0
$919$	−2.82464e13	−1.30630	−0.653150	−	0.757229i	$-0.726553\pi$
$919$	−2.82464e13	−1.30630	−0.653150	+	0.757229i	$0.726553\pi$
$920$	3.51493e12	0.161760
$921$	0	0
$922$	2.33049e13	1.06208
$923$	9.73546e12	0.441518
$924$	0	0
$925$	1.53810e13	0.690792
$926$	−2.21691e13	−0.990830
$927$	0	0
$928$	−2.57950e13	−1.14175
$929$	−1.81017e13	−0.797348	−0.398674	−	0.917093i	$-0.630529\pi$
$929$	−1.81017e13	−0.797348	−0.398674	+	0.917093i	$0.630529\pi$
$930$	0	0
$931$	1.01395e13	0.442324
$932$	−6.54974e10	−0.00284350
$933$	0	0
$934$	4.60004e13	1.97788
$935$	3.05916e12	0.130903
$936$	0	0
$937$	2.51202e13	1.06462	0.532310	−	0.846550i	$-0.321324\pi$
$937$	2.51202e13	1.06462	0.532310	+	0.846550i	$0.321324\pi$
$938$	−4.88745e13	−2.06143
$939$	0	0
$940$	−3.02095e12	−0.126202
$941$	−8.09156e11	−0.0336418	−0.0168209	−	0.999859i	$-0.505355\pi$
$941$	−8.09156e11	−0.0336418	−0.0168209	+	0.999859i	$0.505355\pi$
$942$	0	0
$943$	1.74628e12	0.0719138
$944$	−1.91048e13	−0.783014
$945$	0	0
$946$	−4.29541e13	−1.74379
$947$	1.25569e13	0.507349	0.253675	−	0.967290i	$-0.418361\pi$
$947$	1.25569e13	0.507349	0.253675	+	0.967290i	$0.418361\pi$
$948$	0	0
$949$	−9.13636e12	−0.365658
$950$	1.44246e13	0.574575
$951$	0	0
$952$	1.62463e13	0.641045
$953$	3.64201e13	1.43029	0.715144	−	0.698977i	$-0.246361\pi$
$953$	3.64201e13	1.43029	0.715144	+	0.698977i	$0.246361\pi$
$954$	0	0
$955$	−2.39100e12	−0.0930173
$956$	−6.03087e12	−0.233518
$957$	0	0
$958$	4.64612e13	1.78216
$959$	−1.77017e13	−0.675821
$960$	0	0
$961$	1.51913e13	0.574564
$962$	−6.70859e12	−0.252548
$963$	0	0
$964$	−1.94225e13	−0.724366
$965$	2.77205e12	0.102903
$966$	0	0
$967$	2.96691e13	1.09115	0.545575	−	0.838062i	$-0.316311\pi$
$967$	2.96691e13	1.09115	0.545575	+	0.838062i	$0.316311\pi$
$968$	−5.91055e12	−0.216366
$969$	0	0
$970$	1.23567e12	0.0448156
$971$	1.05417e13	0.380563	0.190281	−	0.981730i	$-0.439060\pi$
$971$	1.05417e13	0.380563	0.190281	+	0.981730i	$0.439060\pi$
$972$	0	0
$973$	−3.14899e12	−0.112632
$974$	−2.67595e13	−0.952714
$975$	0	0
$976$	−4.17114e13	−1.47140
$977$	2.40729e13	0.845285	0.422643	−	0.906296i	$-0.361103\pi$
$977$	2.40729e13	0.845285	0.422643	+	0.906296i	$0.361103\pi$
$978$	0	0
$979$	−2.85218e13	−0.992328
$980$	3.14014e12	0.108751
$981$	0	0
$982$	−6.64372e13	−2.27987
$983$	3.57135e13	1.21995	0.609974	−	0.792421i	$-0.291180\pi$
$983$	3.57135e13	1.21995	0.609974	+	0.792421i	$0.291180\pi$
$984$	0	0
$985$	7.17195e12	0.242758
$986$	−3.76432e13	−1.26835
$987$	0	0
$988$	−2.40859e12	−0.0804187
$989$	−1.00195e14	−3.33013
$990$	0	0
$991$	2.48780e13	0.819376	0.409688	−	0.912226i	$-0.365638\pi$
$991$	2.48780e13	0.819376	0.409688	+	0.912226i	$0.365638\pi$
$992$	−4.16943e13	−1.36702
$993$	0	0
$994$	−8.70089e13	−2.82699
$995$	8.60369e12	0.278279
$996$	0	0
$997$	−3.31717e13	−1.06326	−0.531630	−	0.846977i	$-0.678420\pi$
$997$	−3.31717e13	−1.06326	−0.531630	+	0.846977i	$0.678420\pi$
$998$	3.78497e12	0.120774
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.10.a.c.1.1		4
3.2	odd	2		13.10.a.a.1.4	✓	4
12.11	even	2		208.10.a.g.1.4		4
15.14	odd	2		325.10.a.a.1.1		4
39.38	odd	2		169.10.a.a.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.4	✓	4	3.2	odd	2
117.10.a.c.1.1		4	1.1	even	1	trivial
169.10.a.a.1.1		4	39.38	odd	2
208.10.a.g.1.4		4	12.11	even	2
325.10.a.a.1.1		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)

\(f(q)\)	\(=\)	\(q-28.8028 q^{2} +317.603 q^{4} +258.914 q^{5} -8862.28 q^{7} +5599.18 q^{8} +O(q^{10})\)	\(q-28.8028 q^{2} +317.603 q^{4} +258.914 q^{5} -8862.28 q^{7} +5599.18 q^{8} -7457.46 q^{10} -36087.9 q^{11} -28561.0 q^{13} +255259. q^{14} -323885. q^{16} -327405. q^{17} +265525. q^{19} +82231.9 q^{20} +1.03943e6 q^{22} +2.42458e6 q^{23} -1.88609e6 q^{25} +822638. q^{26} -2.81469e6 q^{28} -3.99178e6 q^{29} -6.45220e6 q^{31} +6.46202e6 q^{32} +9.43018e6 q^{34} -2.29457e6 q^{35} -8.15498e6 q^{37} -7.64787e6 q^{38} +1.44971e6 q^{40} +720241. q^{41} -4.13245e7 q^{43} -1.14616e7 q^{44} -6.98348e7 q^{46} -3.67369e7 q^{47} +3.81864e7 q^{49} +5.43247e7 q^{50} -9.07106e6 q^{52} -1.67334e7 q^{53} -9.34367e6 q^{55} -4.96215e7 q^{56} +1.14975e8 q^{58} +5.89865e7 q^{59} +1.28785e8 q^{61} +1.85842e8 q^{62} -2.02955e7 q^{64} -7.39484e6 q^{65} -1.91470e8 q^{67} -1.03985e8 q^{68} +6.60901e7 q^{70} -3.40865e8 q^{71} +3.19890e8 q^{73} +2.34887e8 q^{74} +8.43316e7 q^{76} +3.19821e8 q^{77} +2.44328e8 q^{79} -8.38584e7 q^{80} -2.07450e7 q^{82} +4.38630e8 q^{83} -8.47697e7 q^{85} +1.19026e9 q^{86} -2.02063e8 q^{88} +7.90342e8 q^{89} +2.53116e8 q^{91} +7.70054e8 q^{92} +1.05813e9 q^{94} +6.87481e7 q^{95} -1.65696e8 q^{97} -1.09988e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} + 1429 q^{4} - 471 q^{5} - 11241 q^{7} + 45543 q^{8}+O(q^{10}) \) 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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