LMFDB - Embedded newform 117.10.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("117.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.5
Root			$-27.7188$ 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)

$f(q)$	$=$	$q+24.7188 q^{2} +99.0182 q^{4} +920.299 q^{5} +5359.02 q^{7} -10208.4 q^{8} +O(q^{10})$	\(q+24.7188 q^{2} +99.0182 q^{4} +920.299 q^{5} +5359.02 q^{7} -10208.4 q^{8} +22748.7 q^{10} -79284.0 q^{11} +28561.0 q^{13} +132468. q^{14} -303037. q^{16} -452068. q^{17} +212533. q^{19} +91126.3 q^{20} -1.95980e6 q^{22} +759566. q^{23} -1.10618e6 q^{25} +705993. q^{26} +530640. q^{28} +900101. q^{29} +2.27141e6 q^{31} -2.26400e6 q^{32} -1.11746e7 q^{34} +4.93189e6 q^{35} -4.70433e6 q^{37} +5.25355e6 q^{38} -9.39478e6 q^{40} -3.39775e7 q^{41} -2.33244e7 q^{43} -7.85057e6 q^{44} +1.87755e7 q^{46} +5.14121e7 q^{47} -1.16346e7 q^{49} -2.73433e7 q^{50} +2.82806e6 q^{52} -1.01005e8 q^{53} -7.29650e7 q^{55} -5.47070e7 q^{56} +2.22494e7 q^{58} -1.32234e8 q^{59} -1.23648e8 q^{61} +5.61465e7 q^{62} +9.91916e7 q^{64} +2.62846e7 q^{65} -2.15282e8 q^{67} -4.47630e7 q^{68} +1.21910e8 q^{70} +2.06198e8 q^{71} +3.44444e8 q^{73} -1.16285e8 q^{74} +2.10446e7 q^{76} -4.24884e8 q^{77} +5.03324e7 q^{79} -2.78884e8 q^{80} -8.39883e8 q^{82} -8.20266e7 q^{83} -4.16038e8 q^{85} -5.76552e8 q^{86} +8.09364e8 q^{88} +6.17891e8 q^{89} +1.53059e8 q^{91} +7.52109e7 q^{92} +1.27084e9 q^{94} +1.95594e8 q^{95} -9.91253e8 q^{97} -2.87592e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8}+O(q^{10}) $ 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8} + 84505 q^{10} - 121746 q^{11} + 142805 q^{13} - 8475 q^{14} - 322463 q^{16} + 495669 q^{17} - 840738 q^{19} + 1595607 q^{20} - 2023594 q^{22} + 592152 q^{23} + 1670362 q^{25} - 428415 q^{26} + 2587955 q^{28} - 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 9934079 q^{34} - 8380731 q^{35} + 7171823 q^{37} + 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} + 12831975 q^{43} + 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 25249488 q^{49} + 16270770 q^{50} + 10310521 q^{52} - 93231780 q^{53} + 99448846 q^{55} - 199599225 q^{56} + 151020970 q^{58} - 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 91019105 q^{64} - 51495483 q^{65} - 369388534 q^{67} - 238172073 q^{68} - 144857425 q^{70} - 212150457 q^{71} - 252729806 q^{73} - 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} + 169559388 q^{82} - 1696894296 q^{83} - 775363765 q^{85} - 3291621459 q^{86} - 220227222 q^{88} + 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 272071215 q^{94} - 1442632962 q^{95} + 3824606 q^{97} - 1570614816 q^{98}+O(q^{100}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8 + 84505 * q^10 - 121746 * q^11 + 142805 * q^13 - 8475 * q^14 - 322463 * q^16 + 495669 * q^17 - 840738 * q^19 + 1595607 * q^20 - 2023594 * q^22 + 592152 * q^23 + 1670362 * q^25 - 428415 * q^26 + 2587955 * q^28 - 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 9934079 * q^34 - 8380731 * q^35 + 7171823 * q^37 + 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 + 12831975 * q^43 + 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 25249488 * q^49 + 16270770 * q^50 + 10310521 * q^52 - 93231780 * q^53 + 99448846 * q^55 - 199599225 * q^56 + 151020970 * q^58 - 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 91019105 * q^64 - 51495483 * q^65 - 369388534 * q^67 - 238172073 * q^68 - 144857425 * q^70 - 212150457 * q^71 - 252729806 * q^73 - 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 + 169559388 * q^82 - 1696894296 * q^83 - 775363765 * q^85 - 3291621459 * q^86 - 220227222 * q^88 + 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 272071215 * q^94 - 1442632962 * q^95 + 3824606 * q^97 - 1570614816 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	24.7188	1.09243	0.546213	−	0.837646i	$-0.316069\pi$
$2$	24.7188	1.09243	0.546213	+	0.837646i	$0.316069\pi$
$3$	0	0
$3$	0	0
$4$	99.0182	0.193395
$5$	920.299	0.658512	0.329256	−	0.944241i	$-0.393202\pi$
$5$	920.299	0.658512	0.329256	+	0.944241i	$0.393202\pi$
$6$	0	0
$7$	5359.02	0.843614	0.421807	−	0.906686i	$-0.361396\pi$
$7$	5359.02	0.843614	0.421807	+	0.906686i	$0.361396\pi$
$8$	−10208.4	−0.881156
$9$	0	0
$10$	22748.7	0.719376
$11$	−79284.0	−1.63275	−0.816373	−	0.577525i	$-0.804019\pi$
$11$	−79284.0	−1.63275	−0.816373	+	0.577525i	$0.804019\pi$
$12$	0	0
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	132468.	0.921586
$15$	0	0
$16$	−303037.	−1.15599
$17$	−452068.	−1.31276	−0.656378	−	0.754432i	$-0.727912\pi$
$17$	−452068.	−1.31276	−0.656378	+	0.754432i	$0.727912\pi$
$18$	0	0
$19$	212533.	0.374141	0.187070	−	0.982347i	$-0.440101\pi$
$19$	212533.	0.374141	0.187070	+	0.982347i	$0.440101\pi$
$20$	91126.3	0.127353
$21$	0	0
$22$	−1.95980e6	−1.78365
$23$	759566.	0.565966	0.282983	−	0.959125i	$-0.408676\pi$
$23$	759566.	0.565966	0.282983	+	0.959125i	$0.408676\pi$
$24$	0	0
$25$	−1.10618e6	−0.566362
$26$	705993.	0.302985
$27$	0	0
$28$	530640.	0.163151
$29$	900101.	0.236320	0.118160	−	0.992995i	$-0.462300\pi$
$29$	900101.	0.236320	0.118160	+	0.992995i	$0.462300\pi$
$30$	0	0
$31$	2.27141e6	0.441742	0.220871	−	0.975303i	$-0.429110\pi$
$31$	2.27141e6	0.441742	0.220871	+	0.975303i	$0.429110\pi$
$32$	−2.26400e6	−0.381681
$33$	0	0
$34$	−1.11746e7	−1.43409
$35$	4.93189e6	0.555530
$36$	0	0
$37$	−4.70433e6	−0.412658	−0.206329	−	0.978483i	$-0.566152\pi$
$37$	−4.70433e6	−0.412658	−0.206329	+	0.978483i	$0.566152\pi$
$38$	5.25355e6	0.408721
$39$	0	0
$40$	−9.39478e6	−0.580252
$41$	−3.39775e7	−1.87786	−0.938932	−	0.344102i	$-0.888183\pi$
$41$	−3.39775e7	−1.87786	−0.938932	+	0.344102i	$0.888183\pi$
$42$	0	0
$43$	−2.33244e7	−1.04041	−0.520203	−	0.854042i	$-0.674144\pi$
$43$	−2.33244e7	−1.04041	−0.520203	+	0.854042i	$0.674144\pi$
$44$	−7.85057e6	−0.315765
$45$	0	0
$46$	1.87755e7	0.618276
$47$	5.14121e7	1.53683	0.768413	−	0.639954i	$-0.221046\pi$
$47$	5.14121e7	1.53683	0.768413	+	0.639954i	$0.221046\pi$
$48$	0	0
$49$	−1.16346e7	−0.288315
$50$	−2.73433e7	−0.618709
$51$	0	0
$52$	2.82806e6	0.0536381
$53$	−1.01005e8	−1.75834	−0.879170	−	0.476509i	$-0.841902\pi$
$53$	−1.01005e8	−1.75834	−0.879170	+	0.476509i	$0.841902\pi$
$54$	0	0
$55$	−7.29650e7	−1.07518
$56$	−5.47070e7	−0.743356
$57$	0	0
$58$	2.22494e7	0.258162
$59$	−1.32234e8	−1.42073	−0.710363	−	0.703836i	$-0.751469\pi$
$59$	−1.32234e8	−1.42073	−0.710363	+	0.703836i	$0.751469\pi$
$60$	0	0
$61$	−1.23648e8	−1.14341	−0.571706	−	0.820459i	$-0.693718\pi$
$61$	−1.23648e8	−1.14341	−0.571706	+	0.820459i	$0.693718\pi$
$62$	5.61465e7	0.482570
$63$	0	0
$64$	9.91916e7	0.739035
$65$	2.62846e7	0.182638
$66$	0	0
$67$	−2.15282e8	−1.30518	−0.652592	−	0.757710i	$-0.726318\pi$
$67$	−2.15282e8	−1.30518	−0.652592	+	0.757710i	$0.726318\pi$
$68$	−4.47630e7	−0.253880
$69$	0	0
$70$	1.21910e8	0.606876
$71$	2.06198e8	0.962992	0.481496	−	0.876448i	$-0.340094\pi$
$71$	2.06198e8	0.962992	0.481496	+	0.876448i	$0.340094\pi$
$72$	0	0
$73$	3.44444e8	1.41960	0.709800	−	0.704403i	$-0.248785\pi$
$73$	3.44444e8	1.41960	0.709800	+	0.704403i	$0.248785\pi$
$74$	−1.16285e8	−0.450799
$75$	0	0
$76$	2.10446e7	0.0723569
$77$	−4.24884e8	−1.37741
$78$	0	0
$79$	5.03324e7	0.145387	0.0726935	−	0.997354i	$-0.476841\pi$
$79$	5.03324e7	0.145387	0.0726935	+	0.997354i	$0.476841\pi$
$80$	−2.78884e8	−0.761236
$81$	0	0
$82$	−8.39883e8	−2.05143
$83$	−8.20266e7	−0.189716	−0.0948579	−	0.995491i	$-0.530240\pi$
$83$	−8.20266e7	−0.189716	−0.0948579	+	0.995491i	$0.530240\pi$
$84$	0	0
$85$	−4.16038e8	−0.864465
$86$	−5.76552e8	−1.13657
$87$	0	0
$88$	8.09364e8	1.43870
$89$	6.17891e8	1.04390	0.521948	−	0.852977i	$-0.325206\pi$
$89$	6.17891e8	1.04390	0.521948	+	0.852977i	$0.325206\pi$
$90$	0	0
$91$	1.53059e8	0.233976
$92$	7.52109e7	0.109455
$93$	0	0
$94$	1.27084e9	1.67887
$95$	1.95594e8	0.246376
$96$	0	0
$97$	−9.91253e8	−1.13687	−0.568436	−	0.822727i	$-0.692451\pi$
$97$	−9.91253e8	−1.13687	−0.568436	+	0.822727i	$0.692451\pi$
$98$	−2.87592e8	−0.314963
$99$	0	0
$100$	−1.09532e8	−0.109532
$101$	1.15157e9	1.10115	0.550573	−	0.834787i	$-0.314409\pi$
$101$	1.15157e9	1.10115	0.550573	+	0.834787i	$0.314409\pi$
$102$	0	0
$103$	1.28814e9	1.12770	0.563852	−	0.825876i	$-0.309319\pi$
$103$	1.28814e9	1.12770	0.563852	+	0.825876i	$0.309319\pi$
$104$	−2.91562e8	−0.244389
$105$	0	0
$106$	−2.49673e9	−1.92086
$107$	−7.90577e8	−0.583065	−0.291533	−	0.956561i	$-0.594165\pi$
$107$	−7.90577e8	−0.583065	−0.291533	+	0.956561i	$0.594165\pi$
$108$	0	0
$109$	−4.40070e8	−0.298609	−0.149304	−	0.988791i	$-0.547703\pi$
$109$	−4.40070e8	−0.298609	−0.149304	+	0.988791i	$0.547703\pi$
$110$	−1.80361e9	−1.17456
$111$	0	0
$112$	−1.62398e9	−0.975212
$113$	8.28687e8	0.478121	0.239060	−	0.971005i	$-0.423161\pi$
$113$	8.28687e8	0.478121	0.239060	+	0.971005i	$0.423161\pi$
$114$	0	0
$115$	6.99027e8	0.372695
$116$	8.91264e7	0.0457031
$117$	0	0
$118$	−3.26867e9	−1.55204
$119$	−2.42264e9	−1.10746
$120$	0	0
$121$	3.92801e9	1.66586
$122$	−3.05643e9	−1.24909
$123$	0	0
$124$	2.24911e8	0.0854306
$125$	−2.81547e9	−1.03147
$126$	0	0
$127$	−2.09036e9	−0.713025	−0.356513	−	0.934291i	$-0.616034\pi$
$127$	−2.09036e9	−0.713025	−0.356513	+	0.934291i	$0.616034\pi$
$128$	3.61106e9	1.18902
$129$	0	0
$130$	6.49724e8	0.199519
$131$	−1.23787e8	−0.0367243	−0.0183621	−	0.999831i	$-0.505845\pi$
$131$	−1.23787e8	−0.0367243	−0.0183621	+	0.999831i	$0.505845\pi$
$132$	0	0
$133$	1.13897e9	0.315630
$134$	−5.32152e9	−1.42582
$135$	0	0
$136$	4.61490e9	1.15674
$137$	1.31278e9	0.318383	0.159192	−	0.987248i	$-0.449111\pi$
$137$	1.31278e9	0.318383	0.159192	+	0.987248i	$0.449111\pi$
$138$	0	0
$139$	−4.82994e9	−1.09743	−0.548713	−	0.836011i	$-0.684882\pi$
$139$	−4.82994e9	−1.09743	−0.548713	+	0.836011i	$0.684882\pi$
$140$	4.88348e8	0.107437
$141$	0	0
$142$	5.09697e9	1.05200
$143$	−2.26443e9	−0.452842
$144$	0	0
$145$	8.28361e8	0.155619
$146$	8.51424e9	1.55081
$147$	0	0
$148$	−4.65815e8	−0.0798060
$149$	4.39244e9	0.730075	0.365037	−	0.930993i	$-0.381056\pi$
$149$	4.39244e9	0.730075	0.365037	+	0.930993i	$0.381056\pi$
$150$	0	0
$151$	−4.70301e9	−0.736172	−0.368086	−	0.929792i	$-0.619987\pi$
$151$	−4.70301e9	−0.736172	−0.368086	+	0.929792i	$0.619987\pi$
$152$	−2.16962e9	−0.329676
$153$	0	0
$154$	−1.05026e10	−1.50472
$155$	2.09038e9	0.290892
$156$	0	0
$157$	−5.28793e9	−0.694605	−0.347302	−	0.937753i	$-0.612902\pi$
$157$	−5.28793e9	−0.694605	−0.347302	+	0.937753i	$0.612902\pi$
$158$	1.24416e9	0.158825
$159$	0	0
$160$	−2.08355e9	−0.251342
$161$	4.07052e9	0.477457
$162$	0	0
$163$	6.72980e9	0.746721	0.373360	−	0.927686i	$-0.378206\pi$
$163$	6.72980e9	0.746721	0.373360	+	0.927686i	$0.378206\pi$
$164$	−3.36439e9	−0.363170
$165$	0	0
$166$	−2.02760e9	−0.207251
$167$	−5.87782e9	−0.584780	−0.292390	−	0.956299i	$-0.594450\pi$
$167$	−5.87782e9	−0.584780	−0.292390	+	0.956299i	$0.594450\pi$
$168$	0	0
$169$	8.15731e8	0.0769231
$170$	−1.02839e10	−0.944365
$171$	0	0
$172$	−2.30954e9	−0.201209
$173$	1.40328e10	1.19107	0.595534	−	0.803330i	$-0.296941\pi$
$173$	1.40328e10	1.19107	0.595534	+	0.803330i	$0.296941\pi$
$174$	0	0
$175$	−5.92801e9	−0.477791
$176$	2.40260e10	1.88744
$177$	0	0
$178$	1.52735e10	1.14038
$179$	2.48592e10	1.80987	0.904936	−	0.425548i	$-0.139919\pi$
$179$	2.48592e10	1.80987	0.904936	+	0.425548i	$0.139919\pi$
$180$	0	0
$181$	1.35989e10	0.941784	0.470892	−	0.882191i	$-0.343932\pi$
$181$	1.35989e10	0.941784	0.470892	+	0.882191i	$0.343932\pi$
$182$	3.78343e9	0.255602
$183$	0	0
$184$	−7.75396e9	−0.498704
$185$	−4.32939e9	−0.271740
$186$	0	0
$187$	3.58418e10	2.14340
$188$	5.09074e9	0.297215
$189$	0	0
$190$	4.83484e9	0.269148
$191$	1.65985e9	0.0902440	0.0451220	−	0.998981i	$-0.485632\pi$
$191$	1.65985e9	0.0902440	0.0451220	+	0.998981i	$0.485632\pi$
$192$	0	0
$193$	3.09499e10	1.60565	0.802827	−	0.596212i	$-0.203328\pi$
$193$	3.09499e10	1.60565	0.802827	+	0.596212i	$0.203328\pi$
$194$	−2.45026e10	−1.24195
$195$	0	0
$196$	−1.15203e9	−0.0557587
$197$	3.04341e10	1.43967	0.719835	−	0.694145i	$-0.244217\pi$
$197$	3.04341e10	1.43967	0.719835	+	0.694145i	$0.244217\pi$
$198$	0	0
$199$	4.44812e8	0.0201066	0.0100533	−	0.999949i	$-0.496800\pi$
$199$	4.44812e8	0.0201066	0.0100533	+	0.999949i	$0.496800\pi$
$200$	1.12923e10	0.499053
$201$	0	0
$202$	2.84655e10	1.20292
$203$	4.82365e9	0.199363
$204$	0	0
$205$	−3.12695e10	−1.23660
$206$	3.18412e10	1.23193
$207$	0	0
$208$	−8.65503e9	−0.320615
$209$	−1.68505e10	−0.610877
$210$	0	0
$211$	4.88078e9	0.169519	0.0847595	−	0.996401i	$-0.472988\pi$
$211$	4.88078e9	0.169519	0.0847595	+	0.996401i	$0.472988\pi$
$212$	−1.00014e10	−0.340054
$213$	0	0
$214$	−1.95421e10	−0.636956
$215$	−2.14654e10	−0.685120
$216$	0	0
$217$	1.21725e10	0.372660
$218$	−1.08780e10	−0.326208
$219$	0	0
$220$	−7.22486e9	−0.207935
$221$	−1.29115e10	−0.364093
$222$	0	0
$223$	2.47486e10	0.670162	0.335081	−	0.942189i	$-0.391236\pi$
$223$	2.47486e10	0.670162	0.335081	+	0.942189i	$0.391236\pi$
$224$	−1.21328e10	−0.321992
$225$	0	0
$226$	2.04841e10	0.522312
$227$	−2.62443e10	−0.656022	−0.328011	−	0.944674i	$-0.606378\pi$
$227$	−2.62443e10	−0.656022	−0.328011	+	0.944674i	$0.606378\pi$
$228$	0	0
$229$	−4.15262e10	−0.997844	−0.498922	−	0.866647i	$-0.666271\pi$
$229$	−4.15262e10	−0.997844	−0.498922	+	0.866647i	$0.666271\pi$
$230$	1.72791e10	0.407142
$231$	0	0
$232$	−9.18859e9	−0.208235
$233$	−3.67402e10	−0.816657	−0.408329	−	0.912835i	$-0.633888\pi$
$233$	−3.67402e10	−0.816657	−0.408329	+	0.912835i	$0.633888\pi$
$234$	0	0
$235$	4.73145e10	1.01202
$236$	−1.30936e10	−0.274761
$237$	0	0
$238$	−5.98847e10	−1.20982
$239$	4.35921e10	0.864206	0.432103	−	0.901824i	$-0.357772\pi$
$239$	4.35921e10	0.864206	0.432103	+	0.901824i	$0.357772\pi$
$240$	0	0
$241$	−1.04473e10	−0.199493	−0.0997464	−	0.995013i	$-0.531803\pi$
$241$	−1.04473e10	−0.199493	−0.0997464	+	0.995013i	$0.531803\pi$
$242$	9.70956e10	1.81983
$243$	0	0
$244$	−1.22434e10	−0.221130
$245$	−1.07073e10	−0.189859
$246$	0	0
$247$	6.07015e9	0.103768
$248$	−2.31875e10	−0.389243
$249$	0	0
$250$	−6.95950e10	−1.12680
$251$	−8.69402e10	−1.38258	−0.691288	−	0.722580i	$-0.742956\pi$
$251$	−8.69402e10	−1.38258	−0.691288	+	0.722580i	$0.742956\pi$
$252$	0	0
$253$	−6.02214e10	−0.924078
$254$	−5.16712e10	−0.778927
$255$	0	0
$256$	3.84749e10	0.559884
$257$	−4.05492e10	−0.579807	−0.289903	−	0.957056i	$-0.593623\pi$
$257$	−4.05492e10	−0.579807	−0.289903	+	0.957056i	$0.593623\pi$
$258$	0	0
$259$	−2.52106e10	−0.348124
$260$	2.60266e9	0.0353213
$261$	0	0
$262$	−3.05986e9	−0.0401185
$263$	−1.55920e10	−0.200956	−0.100478	−	0.994939i	$-0.532037\pi$
$263$	−1.55920e10	−0.200956	−0.100478	+	0.994939i	$0.532037\pi$
$264$	0	0
$265$	−9.29550e10	−1.15789
$266$	2.81539e10	0.344803
$267$	0	0
$268$	−2.13169e10	−0.252416
$269$	−1.34814e11	−1.56982	−0.784911	−	0.619608i	$-0.787292\pi$
$269$	−1.34814e11	−1.56982	−0.784911	+	0.619608i	$0.787292\pi$
$270$	0	0
$271$	1.08155e10	0.121810	0.0609052	−	0.998144i	$-0.480601\pi$
$271$	1.08155e10	0.121810	0.0609052	+	0.998144i	$0.480601\pi$
$272$	1.36993e11	1.51754
$273$	0	0
$274$	3.24504e10	0.347810
$275$	8.77021e10	0.924725
$276$	0	0
$277$	1.05265e11	1.07429	0.537147	−	0.843488i	$-0.319502\pi$
$277$	1.05265e11	1.07429	0.537147	+	0.843488i	$0.319502\pi$
$278$	−1.19390e11	−1.19886
$279$	0	0
$280$	−5.03468e10	−0.489509
$281$	−5.90656e10	−0.565140	−0.282570	−	0.959247i	$-0.591187\pi$
$281$	−5.90656e10	−0.565140	−0.282570	+	0.959247i	$0.591187\pi$
$282$	0	0
$283$	−1.45893e11	−1.35206	−0.676030	−	0.736875i	$-0.736301\pi$
$283$	−1.45893e11	−1.35206	−0.676030	+	0.736875i	$0.736301\pi$
$284$	2.04174e10	0.186238
$285$	0	0
$286$	−5.59740e10	−0.494697
$287$	−1.82086e11	−1.58419
$288$	0	0
$289$	8.57779e10	0.723328
$290$	2.04761e10	0.170003
$291$	0	0
$292$	3.41063e10	0.274544
$293$	7.69633e9	0.0610070	0.0305035	−	0.999535i	$-0.490289\pi$
$293$	7.69633e9	0.0610070	0.0305035	+	0.999535i	$0.490289\pi$
$294$	0	0
$295$	−1.21695e11	−0.935565
$296$	4.80238e10	0.363616
$297$	0	0
$298$	1.08576e11	0.797553
$299$	2.16940e10	0.156971
$300$	0	0
$301$	−1.24996e11	−0.877702
$302$	−1.16253e11	−0.804214
$303$	0	0
$304$	−6.44053e10	−0.432504
$305$	−1.13793e11	−0.752950
$306$	0	0
$307$	7.83929e10	0.503679	0.251839	−	0.967769i	$-0.418965\pi$
$307$	7.83929e10	0.503679	0.251839	+	0.967769i	$0.418965\pi$
$308$	−4.20713e10	−0.266384
$309$	0	0
$310$	5.16716e10	0.317778
$311$	2.02455e11	1.22717	0.613587	−	0.789627i	$-0.289726\pi$
$311$	2.02455e11	1.22717	0.613587	+	0.789627i	$0.289726\pi$
$312$	0	0
$313$	4.65893e10	0.274370	0.137185	−	0.990545i	$-0.456195\pi$
$313$	4.65893e10	0.274370	0.137185	+	0.990545i	$0.456195\pi$
$314$	−1.30711e11	−0.758804
$315$	0	0
$316$	4.98383e9	0.0281171
$317$	1.19232e10	0.0663170	0.0331585	−	0.999450i	$-0.489443\pi$
$317$	1.19232e10	0.0663170	0.0331585	+	0.999450i	$0.489443\pi$
$318$	0	0
$319$	−7.13636e10	−0.385850
$320$	9.12859e10	0.486663
$321$	0	0
$322$	1.00618e11	0.521586
$323$	−9.60794e10	−0.491155
$324$	0	0
$325$	−3.15935e10	−0.157081
$326$	1.66353e11	0.815737
$327$	0	0
$328$	3.46856e11	1.65469
$329$	2.75518e11	1.29649
$330$	0	0
$331$	1.99404e11	0.913076	0.456538	−	0.889704i	$-0.349089\pi$
$331$	1.99404e11	0.913076	0.456538	+	0.889704i	$0.349089\pi$
$332$	−8.12213e9	−0.0366901
$333$	0	0
$334$	−1.45293e11	−0.638829
$335$	−1.98124e11	−0.859479
$336$	0	0
$337$	3.29370e11	1.39107	0.695536	−	0.718491i	$-0.255167\pi$
$337$	3.29370e11	1.39107	0.695536	+	0.718491i	$0.255167\pi$
$338$	2.01639e10	0.0840328
$339$	0	0
$340$	−4.11953e10	−0.167183
$341$	−1.80087e11	−0.721252
$342$	0	0
$343$	−2.78605e11	−1.08684
$344$	2.38105e11	0.916761
$345$	0	0
$346$	3.46873e11	1.30115
$347$	2.16834e10	0.0802868	0.0401434	−	0.999194i	$-0.487219\pi$
$347$	2.16834e10	0.0802868	0.0401434	+	0.999194i	$0.487219\pi$
$348$	0	0
$349$	1.43336e11	0.517178	0.258589	−	0.965987i	$-0.416742\pi$
$349$	1.43336e11	0.517178	0.258589	+	0.965987i	$0.416742\pi$
$350$	−1.46533e11	−0.521951
$351$	0	0
$352$	1.79499e11	0.623188
$353$	8.38423e10	0.287393	0.143697	−	0.989622i	$-0.454101\pi$
$353$	8.38423e10	0.287393	0.143697	+	0.989622i	$0.454101\pi$
$354$	0	0
$355$	1.89764e11	0.634142
$356$	6.11825e10	0.201884
$357$	0	0
$358$	6.14488e11	1.97715
$359$	−1.26213e11	−0.401033	−0.200516	−	0.979690i	$-0.564262\pi$
$359$	−1.26213e11	−0.401033	−0.200516	+	0.979690i	$0.564262\pi$
$360$	0	0
$361$	−2.77517e11	−0.860019
$362$	3.36149e11	1.02883
$363$	0	0
$364$	1.51556e10	0.0452499
$365$	3.16992e11	0.934824
$366$	0	0
$367$	−6.56218e11	−1.88821	−0.944106	−	0.329642i	$-0.893072\pi$
$367$	−6.56218e11	−1.88821	−0.944106	+	0.329642i	$0.893072\pi$
$368$	−2.30176e11	−0.654253
$369$	0	0
$370$	−1.07017e11	−0.296856
$371$	−5.41289e11	−1.48336
$372$	0	0
$373$	−5.52730e11	−1.47851	−0.739253	−	0.673428i	$-0.764821\pi$
$373$	−5.52730e11	−1.47851	−0.739253	+	0.673428i	$0.764821\pi$
$374$	8.85966e11	2.34150
$375$	0	0
$376$	−5.24836e11	−1.35418
$377$	2.57078e10	0.0655433
$378$	0	0
$379$	−3.07664e11	−0.765950	−0.382975	−	0.923759i	$-0.625100\pi$
$379$	−3.07664e11	−0.765950	−0.382975	+	0.923759i	$0.625100\pi$
$380$	1.93673e10	0.0476479
$381$	0	0
$382$	4.10295e10	0.0985849
$383$	−1.31812e11	−0.313012	−0.156506	−	0.987677i	$-0.550023\pi$
$383$	−1.31812e11	−0.313012	−0.156506	+	0.987677i	$0.550023\pi$
$384$	0	0
$385$	−3.91021e11	−0.907040
$386$	7.65045e11	1.75406
$387$	0	0
$388$	−9.81521e10	−0.219865
$389$	−1.31742e11	−0.291709	−0.145855	−	0.989306i	$-0.546593\pi$
$389$	−1.31742e11	−0.291709	−0.145855	+	0.989306i	$0.546593\pi$
$390$	0	0
$391$	−3.43376e11	−0.742975
$392$	1.18770e11	0.254051
$393$	0	0
$394$	7.52295e11	1.57273
$395$	4.63208e10	0.0957391
$396$	0	0
$397$	4.44767e11	0.898619	0.449309	−	0.893376i	$-0.351670\pi$
$397$	4.44767e11	0.898619	0.449309	+	0.893376i	$0.351670\pi$
$398$	1.09952e10	0.0219649
$399$	0	0
$400$	3.35212e11	0.654711
$401$	8.36539e11	1.61561	0.807805	−	0.589450i	$-0.200655\pi$
$401$	8.36539e11	1.61561	0.807805	+	0.589450i	$0.200655\pi$
$402$	0	0
$403$	6.48738e10	0.122517
$404$	1.14027e11	0.212956
$405$	0	0
$406$	1.19235e11	0.217789
$407$	3.72979e11	0.673766
$408$	0	0
$409$	2.11826e11	0.374304	0.187152	−	0.982331i	$-0.440074\pi$
$409$	2.11826e11	0.374304	0.187152	+	0.982331i	$0.440074\pi$
$410$	−7.72943e11	−1.35089
$411$	0	0
$412$	1.27549e11	0.218092
$413$	−7.08646e11	−1.19854
$414$	0	0
$415$	−7.54890e10	−0.124930
$416$	−6.46620e10	−0.105859
$417$	0	0
$418$	−4.16523e11	−0.667338
$419$	−5.30153e11	−0.840308	−0.420154	−	0.907453i	$-0.638024\pi$
$419$	−5.30153e11	−0.840308	−0.420154	+	0.907453i	$0.638024\pi$
$420$	0	0
$421$	3.41563e10	0.0529909	0.0264955	−	0.999649i	$-0.491565\pi$
$421$	3.41563e10	0.0529909	0.0264955	+	0.999649i	$0.491565\pi$
$422$	1.20647e11	0.185187
$423$	0	0
$424$	1.03110e12	1.54937
$425$	5.00067e11	0.743495
$426$	0	0
$427$	−6.62631e11	−0.964598
$428$	−7.82815e10	−0.112762
$429$	0	0
$430$	−5.30600e11	−0.748443
$431$	−8.63019e11	−1.20468	−0.602342	−	0.798238i	$-0.705765\pi$
$431$	−8.63019e11	−1.20468	−0.602342	+	0.798238i	$0.705765\pi$
$432$	0	0
$433$	−3.23681e11	−0.442509	−0.221254	−	0.975216i	$-0.571015\pi$
$433$	−3.23681e11	−0.442509	−0.221254	+	0.975216i	$0.571015\pi$
$434$	3.00890e11	0.407103
$435$	0	0
$436$	−4.35749e10	−0.0577494
$437$	1.61433e11	0.211751
$438$	0	0
$439$	−1.45809e12	−1.87368	−0.936838	−	0.349763i	$-0.886262\pi$
$439$	−1.45809e12	−1.87368	−0.936838	+	0.349763i	$0.886262\pi$
$440$	7.44856e11	0.947404
$441$	0	0
$442$	−3.19157e11	−0.397745
$443$	−1.49027e12	−1.83844	−0.919219	−	0.393748i	$-0.871178\pi$
$443$	−1.49027e12	−1.83844	−0.919219	+	0.393748i	$0.871178\pi$
$444$	0	0
$445$	5.68645e11	0.687418
$446$	6.11756e11	0.732102
$447$	0	0
$448$	5.31569e11	0.623460
$449$	−3.04750e11	−0.353862	−0.176931	−	0.984223i	$-0.556617\pi$
$449$	−3.04750e11	−0.353862	−0.176931	+	0.984223i	$0.556617\pi$
$450$	0	0
$451$	2.69387e12	3.06608
$452$	8.20551e10	0.0924661
$453$	0	0
$454$	−6.48727e11	−0.716656
$455$	1.40860e11	0.154076
$456$	0	0
$457$	−1.23809e11	−0.132779	−0.0663896	−	0.997794i	$-0.521148\pi$
$457$	−1.23809e11	−0.132779	−0.0663896	+	0.997794i	$0.521148\pi$
$458$	−1.02648e12	−1.09007
$459$	0	0
$460$	6.92164e10	0.0720774
$461$	−3.16152e11	−0.326018	−0.163009	−	0.986625i	$-0.552120\pi$
$461$	−3.16152e11	−0.326018	−0.163009	+	0.986625i	$0.552120\pi$
$462$	0	0
$463$	1.73371e12	1.75332	0.876659	−	0.481112i	$-0.159767\pi$
$463$	1.73371e12	1.75332	0.876659	+	0.481112i	$0.159767\pi$
$464$	−2.72764e11	−0.273184
$465$	0	0
$466$	−9.08173e11	−0.892138
$467$	5.67889e11	0.552506	0.276253	−	0.961085i	$-0.410907\pi$
$467$	5.67889e11	0.552506	0.276253	+	0.961085i	$0.410907\pi$
$468$	0	0
$469$	−1.15370e12	−1.10107
$470$	1.16956e12	1.10556
$471$	0	0
$472$	1.34990e12	1.25188
$473$	1.84926e12	1.69872
$474$	0	0
$475$	−2.35099e11	−0.211899
$476$	−2.39886e11	−0.214177
$477$	0	0
$478$	1.07754e12	0.944081
$479$	−9.31010e11	−0.808062	−0.404031	−	0.914745i	$-0.632391\pi$
$479$	−9.31010e11	−0.808062	−0.404031	+	0.914745i	$0.632391\pi$
$480$	0	0
$481$	−1.34360e11	−0.114451
$482$	−2.58244e11	−0.217931
$483$	0	0
$484$	3.88945e11	0.322169
$485$	−9.12249e11	−0.748644
$486$	0	0
$487$	−4.49592e10	−0.0362192	−0.0181096	−	0.999836i	$-0.505765\pi$
$487$	−4.49592e10	−0.0362192	−0.0181096	+	0.999836i	$0.505765\pi$
$488$	1.26225e12	1.00752
$489$	0	0
$490$	−2.64671e11	−0.207407
$491$	−4.47956e11	−0.347831	−0.173916	−	0.984761i	$-0.555642\pi$
$491$	−4.47956e11	−0.347831	−0.173916	+	0.984761i	$0.555642\pi$
$492$	0	0
$493$	−4.06907e11	−0.310230
$494$	1.50047e11	0.113359
$495$	0	0
$496$	−6.88321e11	−0.510650
$497$	1.10502e12	0.812394
$498$	0	0
$499$	7.27774e11	0.525465	0.262733	−	0.964869i	$-0.415376\pi$
$499$	7.27774e11	0.525465	0.262733	+	0.964869i	$0.415376\pi$
$500$	−2.78783e11	−0.199481
$501$	0	0
$502$	−2.14906e12	−1.51036
$503$	−6.23613e11	−0.434369	−0.217185	−	0.976131i	$-0.569687\pi$
$503$	−6.23613e11	−0.434369	−0.217185	+	0.976131i	$0.569687\pi$
$504$	0	0
$505$	1.05979e12	0.725118
$506$	−1.48860e12	−1.00949
$507$	0	0
$508$	−2.06984e11	−0.137896
$509$	−1.18958e12	−0.785534	−0.392767	−	0.919638i	$-0.628482\pi$
$509$	−1.18958e12	−0.785534	−0.392767	+	0.919638i	$0.628482\pi$
$510$	0	0
$511$	1.84588e12	1.19760
$512$	−8.97810e11	−0.577390
$513$	0	0
$514$	−1.00233e12	−0.633396
$515$	1.18547e12	0.742607
$516$	0	0
$517$	−4.07616e12	−2.50925
$518$	−6.23175e11	−0.380300
$519$	0	0
$520$	−2.68324e11	−0.160933
$521$	−2.26245e12	−1.34527	−0.672635	−	0.739974i	$-0.734838\pi$
$521$	−2.26245e12	−1.34527	−0.672635	+	0.739974i	$0.734838\pi$
$522$	0	0
$523$	1.15246e12	0.673549	0.336775	−	0.941585i	$-0.390664\pi$
$523$	1.15246e12	0.673549	0.336775	+	0.941585i	$0.390664\pi$
$524$	−1.22571e10	−0.00710229
$525$	0	0
$526$	−3.85415e11	−0.219530
$527$	−1.02683e12	−0.579899
$528$	0	0
$529$	−1.22421e12	−0.679683
$530$	−2.29773e12	−1.26491
$531$	0	0
$532$	1.12778e11	0.0610413
$533$	−9.70432e11	−0.520826
$534$	0	0
$535$	−7.27567e11	−0.383955
$536$	2.19769e12	1.15007
$537$	0	0
$538$	−3.33244e12	−1.71492
$539$	9.22434e11	0.470745
$540$	0	0
$541$	1.31455e12	0.659766	0.329883	−	0.944022i	$-0.392991\pi$
$541$	1.31455e12	0.659766	0.329883	+	0.944022i	$0.392991\pi$
$542$	2.67346e11	0.133069
$543$	0	0
$544$	1.02348e12	0.501054
$545$	−4.04995e11	−0.196637
$546$	0	0
$547$	1.63148e12	0.779182	0.389591	−	0.920988i	$-0.372616\pi$
$547$	1.63148e12	0.779182	0.389591	+	0.920988i	$0.372616\pi$
$548$	1.29989e11	0.0615738
$549$	0	0
$550$	2.16789e12	1.01019
$551$	1.91301e11	0.0884168
$552$	0	0
$553$	2.69732e11	0.122651
$554$	2.60201e12	1.17359
$555$	0	0
$556$	−4.78252e11	−0.212237
$557$	2.20811e12	0.972013	0.486007	−	0.873955i	$-0.338453\pi$
$557$	2.20811e12	0.972013	0.486007	+	0.873955i	$0.338453\pi$
$558$	0	0
$559$	−6.66169e11	−0.288557
$560$	−1.49455e12	−0.642189
$561$	0	0
$562$	−1.46003e12	−0.617374
$563$	1.16602e12	0.489125	0.244563	−	0.969634i	$-0.421356\pi$
$563$	1.16602e12	0.489125	0.244563	+	0.969634i	$0.421356\pi$
$564$	0	0
$565$	7.62639e11	0.314848
$566$	−3.60630e12	−1.47702
$567$	0	0
$568$	−2.10496e12	−0.848547
$569$	2.63455e12	1.05366	0.526831	−	0.849970i	$-0.323380\pi$
$569$	2.63455e12	1.05366	0.526831	+	0.849970i	$0.323380\pi$
$570$	0	0
$571$	−1.65379e12	−0.651055	−0.325527	−	0.945533i	$-0.605542\pi$
$571$	−1.65379e12	−0.651055	−0.325527	+	0.945533i	$0.605542\pi$
$572$	−2.24220e11	−0.0875774
$573$	0	0
$574$	−4.50094e12	−1.73061
$575$	−8.40213e11	−0.320541
$576$	0	0
$577$	1.77685e12	0.667358	0.333679	−	0.942687i	$-0.391710\pi$
$577$	1.77685e12	0.667358	0.333679	+	0.942687i	$0.391710\pi$
$578$	2.12033e12	0.790182
$579$	0	0
$580$	8.20229e10	0.0300960
$581$	−4.39582e11	−0.160047
$582$	0	0
$583$	8.00811e12	2.87092
$584$	−3.51623e12	−1.25089
$585$	0	0
$586$	1.90244e11	0.0666456
$587$	−4.61417e12	−1.60406	−0.802032	−	0.597281i	$-0.796248\pi$
$587$	−4.61417e12	−1.60406	−0.802032	+	0.597281i	$0.796248\pi$
$588$	0	0
$589$	4.82750e11	0.165273
$590$	−3.00815e12	−1.02204
$591$	0	0
$592$	1.42559e12	0.477030
$593$	1.60396e12	0.532655	0.266328	−	0.963883i	$-0.414190\pi$
$593$	1.60396e12	0.532655	0.266328	+	0.963883i	$0.414190\pi$
$594$	0	0
$595$	−2.22955e12	−0.729275
$596$	4.34931e11	0.141193
$597$	0	0
$598$	5.36248e11	0.171479
$599$	3.56445e12	1.13128	0.565642	−	0.824651i	$-0.308628\pi$
$599$	3.56445e12	1.13128	0.565642	+	0.824651i	$0.308628\pi$
$600$	0	0
$601$	−4.23106e12	−1.32286	−0.661431	−	0.750006i	$-0.730051\pi$
$601$	−4.23106e12	−1.32286	−0.661431	+	0.750006i	$0.730051\pi$
$602$	−3.08975e12	−0.958824
$603$	0	0
$604$	−4.65683e11	−0.142372
$605$	3.61494e12	1.09699
$606$	0	0
$607$	2.69700e12	0.806366	0.403183	−	0.915119i	$-0.367904\pi$
$607$	2.69700e12	0.806366	0.403183	+	0.915119i	$0.367904\pi$
$608$	−4.81173e11	−0.142802
$609$	0	0
$610$	−2.81282e12	−0.822542
$611$	1.46838e12	0.426239
$612$	0	0
$613$	−4.29368e12	−1.22817	−0.614084	−	0.789240i	$-0.710475\pi$
$613$	−4.29368e12	−1.22817	−0.614084	+	0.789240i	$0.710475\pi$
$614$	1.93778e12	0.550232
$615$	0	0
$616$	4.33739e12	1.21371
$617$	−2.63888e12	−0.733054	−0.366527	−	0.930407i	$-0.619453\pi$
$617$	−2.63888e12	−0.733054	−0.366527	+	0.930407i	$0.619453\pi$
$618$	0	0
$619$	−2.36449e12	−0.647335	−0.323667	−	0.946171i	$-0.604916\pi$
$619$	−2.36449e12	−0.647335	−0.323667	+	0.946171i	$0.604916\pi$
$620$	2.06985e11	0.0562571
$621$	0	0
$622$	5.00444e12	1.34060
$623$	3.31129e12	0.880645
$624$	0	0
$625$	−4.30574e11	−0.112872
$626$	1.15163e12	0.299729
$627$	0	0
$628$	−5.23602e11	−0.134333
$629$	2.12668e12	0.541719
$630$	0	0
$631$	−4.08896e12	−1.02679	−0.513393	−	0.858153i	$-0.671612\pi$
$631$	−4.08896e12	−1.02679	−0.513393	+	0.858153i	$0.671612\pi$
$632$	−5.13814e11	−0.128109
$633$	0	0
$634$	2.94726e11	0.0724464
$635$	−1.92376e12	−0.469536
$636$	0	0
$637$	−3.32295e11	−0.0799642
$638$	−1.76402e12	−0.421513
$639$	0	0
$640$	3.32325e12	0.782985
$641$	3.55153e12	0.830911	0.415456	−	0.909613i	$-0.363622\pi$
$641$	3.55153e12	0.830911	0.415456	+	0.909613i	$0.363622\pi$
$642$	0	0
$643$	6.85000e12	1.58031	0.790153	−	0.612910i	$-0.210001\pi$
$643$	6.85000e12	1.58031	0.790153	+	0.612910i	$0.210001\pi$
$644$	4.03056e11	0.0923377
$645$	0	0
$646$	−2.37496e12	−0.536551
$647$	4.28931e12	0.962317	0.481159	−	0.876634i	$-0.340216\pi$
$647$	4.28931e12	0.962317	0.481159	+	0.876634i	$0.340216\pi$
$648$	0	0
$649$	1.04841e13	2.31968
$650$	−7.80952e11	−0.171599
$651$	0	0
$652$	6.66373e11	0.144412
$653$	−8.81913e12	−1.89809	−0.949045	−	0.315142i	$-0.897948\pi$
$653$	−8.81913e12	−1.89809	−0.949045	+	0.315142i	$0.897948\pi$
$654$	0	0
$655$	−1.13921e11	−0.0241834
$656$	1.02964e13	2.17080
$657$	0	0
$658$	6.81048e12	1.41632
$659$	−5.76538e12	−1.19081	−0.595406	−	0.803425i	$-0.703009\pi$
$659$	−5.76538e12	−1.19081	−0.595406	+	0.803425i	$0.703009\pi$
$660$	0	0
$661$	−4.77184e12	−0.972254	−0.486127	−	0.873888i	$-0.661591\pi$
$661$	−4.77184e12	−0.972254	−0.486127	+	0.873888i	$0.661591\pi$
$662$	4.92901e12	0.997468
$663$	0	0
$664$	8.37361e11	0.167169
$665$	1.04819e12	0.207846
$666$	0	0
$667$	6.83686e11	0.133749
$668$	−5.82012e11	−0.113093
$669$	0	0
$670$	−4.89738e12	−0.938918
$671$	9.80330e12	1.86690
$672$	0	0
$673$	1.38206e10	0.00259692	0.00129846	−	0.999999i	$-0.499587\pi$
$673$	1.38206e10	0.00259692	0.00129846	+	0.999999i	$0.499587\pi$
$674$	8.14163e12	1.51964
$675$	0	0
$676$	8.07722e10	0.0148765
$677$	2.70699e12	0.495265	0.247633	−	0.968854i	$-0.420347\pi$
$677$	2.70699e12	0.495265	0.247633	+	0.968854i	$0.420347\pi$
$678$	0	0
$679$	−5.31214e12	−0.959082
$680$	4.24708e12	0.761729
$681$	0	0
$682$	−4.45152e12	−0.787915
$683$	3.77305e12	0.663436	0.331718	−	0.943379i	$-0.392372\pi$
$683$	3.77305e12	0.663436	0.331718	+	0.943379i	$0.392372\pi$
$684$	0	0
$685$	1.20815e12	0.209659
$686$	−6.88679e12	−1.18729
$687$	0	0
$688$	7.06816e12	1.20270
$689$	−2.88481e12	−0.487676
$690$	0	0
$691$	−1.42326e12	−0.237484	−0.118742	−	0.992925i	$-0.537886\pi$
$691$	−1.42326e12	−0.237484	−0.118742	+	0.992925i	$0.537886\pi$
$692$	1.38950e12	0.230346
$693$	0	0
$694$	5.35986e11	0.0877074
$695$	−4.44499e12	−0.722668
$696$	0	0
$697$	1.53602e13	2.46518
$698$	3.54309e12	0.564979
$699$	0	0
$700$	−5.86981e11	−0.0924024
$701$	4.18953e12	0.655291	0.327645	−	0.944801i	$-0.393745\pi$
$701$	4.18953e12	0.655291	0.327645	+	0.944801i	$0.393745\pi$
$702$	0	0
$703$	−9.99825e11	−0.154392
$704$	−7.86431e12	−1.20666
$705$	0	0
$706$	2.07248e12	0.313956
$707$	6.17129e12	0.928942
$708$	0	0
$709$	−5.30584e12	−0.788580	−0.394290	−	0.918986i	$-0.629009\pi$
$709$	−5.30584e12	−0.788580	−0.394290	+	0.918986i	$0.629009\pi$
$710$	4.69074e12	0.692753
$711$	0	0
$712$	−6.30769e12	−0.919836
$713$	1.72529e12	0.250011
$714$	0	0
$715$	−2.08395e12	−0.298202
$716$	2.46151e12	0.350020
$717$	0	0
$718$	−3.11984e12	−0.438099
$719$	−2.67496e12	−0.373282	−0.186641	−	0.982428i	$-0.559760\pi$
$719$	−2.67496e12	−0.373282	−0.186641	+	0.982428i	$0.559760\pi$
$720$	0	0
$721$	6.90316e12	0.951347
$722$	−6.85989e12	−0.939507
$723$	0	0
$724$	1.34654e12	0.182136
$725$	−9.95669e11	−0.133843
$726$	0	0
$727$	−8.33355e12	−1.10643	−0.553217	−	0.833037i	$-0.686600\pi$
$727$	−8.33355e12	−1.10643	−0.553217	+	0.833037i	$0.686600\pi$
$728$	−1.56249e12	−0.206170
$729$	0	0
$730$	7.83565e12	1.02123
$731$	1.05442e13	1.36580
$732$	0	0
$733$	1.11038e11	0.0142071	0.00710355	−	0.999975i	$-0.497739\pi$
$733$	1.11038e11	0.0142071	0.00710355	+	0.999975i	$0.497739\pi$
$734$	−1.62209e13	−2.06273
$735$	0	0
$736$	−1.71965e12	−0.216018
$737$	1.70684e13	2.13103
$738$	0	0
$739$	1.02565e13	1.26502	0.632511	−	0.774551i	$-0.282024\pi$
$739$	1.02565e13	1.26502	0.632511	+	0.774551i	$0.282024\pi$
$740$	−4.28689e11	−0.0525532
$741$	0	0
$742$	−1.33800e13	−1.62046
$743$	−3.90792e12	−0.470431	−0.235215	−	0.971943i	$-0.575580\pi$
$743$	−3.90792e12	−0.470431	−0.235215	+	0.971943i	$0.575580\pi$
$744$	0	0
$745$	4.04235e12	0.480763
$746$	−1.36628e13	−1.61516
$747$	0	0
$748$	3.54899e12	0.414522
$749$	−4.23671e12	−0.491882
$750$	0	0
$751$	−2.63552e12	−0.302333	−0.151167	−	0.988508i	$-0.548303\pi$
$751$	−2.63552e12	−0.302333	−0.151167	+	0.988508i	$0.548303\pi$
$752$	−1.55798e13	−1.77656
$753$	0	0
$754$	6.35465e11	0.0716012
$755$	−4.32817e12	−0.484778
$756$	0	0
$757$	−1.02796e13	−1.13774	−0.568870	−	0.822428i	$-0.692619\pi$
$757$	−1.02796e13	−1.13774	−0.568870	+	0.822428i	$0.692619\pi$
$758$	−7.60508e12	−0.836744
$759$	0	0
$760$	−1.99670e12	−0.217096
$761$	−1.47695e12	−0.159638	−0.0798190	−	0.996809i	$-0.525434\pi$
$761$	−1.47695e12	−0.159638	−0.0798190	+	0.996809i	$0.525434\pi$
$762$	0	0
$763$	−2.35834e12	−0.251910
$764$	1.64355e11	0.0174527
$765$	0	0
$766$	−3.25823e12	−0.341942
$767$	−3.77674e12	−0.394038
$768$	0	0
$769$	−3.06990e12	−0.316560	−0.158280	−	0.987394i	$-0.550595\pi$
$769$	−3.06990e12	−0.316560	−0.158280	+	0.987394i	$0.550595\pi$
$770$	−9.66555e12	−0.990874
$771$	0	0
$772$	3.06461e12	0.310526
$773$	−1.22536e13	−1.23440	−0.617200	−	0.786807i	$-0.711733\pi$
$773$	−1.22536e13	−1.23440	−0.617200	+	0.786807i	$0.711733\pi$
$774$	0	0
$775$	−2.51258e12	−0.250186
$776$	1.01191e13	1.00176
$777$	0	0
$778$	−3.25650e12	−0.318671
$779$	−7.22134e12	−0.702585
$780$	0	0
$781$	−1.63482e13	−1.57232
$782$	−8.48783e12	−0.811645
$783$	0	0
$784$	3.52570e12	0.333290
$785$	−4.86648e12	−0.457405
$786$	0	0
$787$	1.16840e13	1.08569	0.542847	−	0.839832i	$-0.317347\pi$
$787$	1.16840e13	1.08569	0.542847	+	0.839832i	$0.317347\pi$
$788$	3.01353e12	0.278425
$789$	0	0
$790$	1.14499e12	0.104588
$791$	4.44095e12	0.403349
$792$	0	0
$793$	−3.53151e12	−0.317125
$794$	1.09941e13	0.981675
$795$	0	0
$796$	4.40445e10	0.00388851
$797$	1.05711e13	0.928024	0.464012	−	0.885829i	$-0.346410\pi$
$797$	1.05711e13	0.928024	0.464012	+	0.885829i	$0.346410\pi$
$798$	0	0
$799$	−2.32418e13	−2.01748
$800$	2.50438e12	0.216170
$801$	0	0
$802$	2.06782e13	1.76494
$803$	−2.73089e13	−2.31785
$804$	0	0
$805$	3.74610e12	0.314411
$806$	1.60360e12	0.133841
$807$	0	0
$808$	−1.17557e13	−0.970282
$809$	9.18043e12	0.753520	0.376760	−	0.926311i	$-0.377038\pi$
$809$	9.18043e12	0.753520	0.376760	+	0.926311i	$0.377038\pi$
$810$	0	0
$811$	−1.38738e12	−0.112616	−0.0563081	−	0.998413i	$-0.517933\pi$
$811$	−1.38738e12	−0.112616	−0.0563081	+	0.998413i	$0.517933\pi$
$812$	4.77630e11	0.0385558
$813$	0	0
$814$	9.21958e12	0.736040
$815$	6.19343e12	0.491725
$816$	0	0
$817$	−4.95721e12	−0.389258
$818$	5.23609e12	0.408900
$819$	0	0
$820$	−3.09625e12	−0.239152
$821$	−1.09862e12	−0.0843924	−0.0421962	−	0.999109i	$-0.513435\pi$
$821$	−1.09862e12	−0.0843924	−0.0421962	+	0.999109i	$0.513435\pi$
$822$	0	0
$823$	−1.94330e13	−1.47653	−0.738263	−	0.674513i	$-0.764354\pi$
$823$	−1.94330e13	−1.47653	−0.738263	+	0.674513i	$0.764354\pi$
$824$	−1.31498e13	−0.993684
$825$	0	0
$826$	−1.75169e13	−1.30932
$827$	2.56778e12	0.190890	0.0954448	−	0.995435i	$-0.469573\pi$
$827$	2.56778e12	0.190890	0.0954448	+	0.995435i	$0.469573\pi$
$828$	0	0
$829$	1.15684e13	0.850703	0.425352	−	0.905028i	$-0.360150\pi$
$829$	1.15684e13	0.850703	0.425352	+	0.905028i	$0.360150\pi$
$830$	−1.86600e12	−0.136477
$831$	0	0
$832$	2.83301e12	0.204971
$833$	5.25961e12	0.378487
$834$	0	0
$835$	−5.40935e12	−0.385085
$836$	−1.66850e12	−0.118140
$837$	0	0
$838$	−1.31047e13	−0.917974
$839$	1.07035e13	0.745754	0.372877	−	0.927881i	$-0.378371\pi$
$839$	1.07035e13	0.745754	0.372877	+	0.927881i	$0.378371\pi$
$840$	0	0
$841$	−1.36970e13	−0.944153
$842$	8.44302e11	0.0578887
$843$	0	0
$844$	4.83287e11	0.0327841
$845$	7.50716e11	0.0506548
$846$	0	0
$847$	2.10503e13	1.40534
$848$	3.06083e13	2.03263
$849$	0	0
$850$	1.23610e13	0.812213
$851$	−3.57325e12	−0.233550
$852$	0	0
$853$	1.85417e13	1.19917	0.599583	−	0.800313i	$-0.295333\pi$
$853$	1.85417e13	1.19917	0.599583	+	0.800313i	$0.295333\pi$
$854$	−1.63794e13	−1.05375
$855$	0	0
$856$	8.07053e12	0.513772
$857$	−8.38633e12	−0.531078	−0.265539	−	0.964100i	$-0.585550\pi$
$857$	−8.38633e12	−0.531078	−0.265539	+	0.964100i	$0.585550\pi$
$858$	0	0
$859$	2.49383e12	0.156278	0.0781390	−	0.996942i	$-0.475102\pi$
$859$	2.49383e12	0.156278	0.0781390	+	0.996942i	$0.475102\pi$
$860$	−2.12547e12	−0.132499
$861$	0	0
$862$	−2.13328e13	−1.31603
$863$	1.05758e12	0.0649029	0.0324515	−	0.999473i	$-0.489669\pi$
$863$	1.05758e12	0.0649029	0.0324515	+	0.999473i	$0.489669\pi$
$864$	0	0
$865$	1.29143e13	0.784332
$866$	−8.00101e12	−0.483408
$867$	0	0
$868$	1.20530e12	0.0720705
$869$	−3.99056e12	−0.237380
$870$	0	0
$871$	−6.14868e12	−0.361993
$872$	4.49241e12	0.263121
$873$	0	0
$874$	3.99042e12	0.231322
$875$	−1.50881e13	−0.870161
$876$	0	0
$877$	2.46623e13	1.40778	0.703891	−	0.710308i	$-0.251444\pi$
$877$	2.46623e13	1.40778	0.703891	+	0.710308i	$0.251444\pi$
$878$	−3.60423e13	−2.04685
$879$	0	0
$880$	2.21111e13	1.24290
$881$	7.21428e12	0.403461	0.201731	−	0.979441i	$-0.435343\pi$
$881$	7.21428e12	0.403461	0.201731	+	0.979441i	$0.435343\pi$
$882$	0	0
$883$	−5.65890e12	−0.313263	−0.156631	−	0.987657i	$-0.550063\pi$
$883$	−5.65890e12	−0.313263	−0.156631	+	0.987657i	$0.550063\pi$
$884$	−1.27848e12	−0.0704138
$885$	0	0
$886$	−3.68377e13	−2.00836
$887$	−1.70857e13	−0.926778	−0.463389	−	0.886155i	$-0.653367\pi$
$887$	−1.70857e13	−0.926778	−0.463389	+	0.886155i	$0.653367\pi$
$888$	0	0
$889$	−1.12023e13	−0.601518
$890$	1.40562e13	0.750953
$891$	0	0
$892$	2.45057e12	0.129606
$893$	1.09268e13	0.574989
$894$	0	0
$895$	2.28779e13	1.19182
$896$	1.93517e13	1.00308
$897$	0	0
$898$	−7.53304e12	−0.386569
$899$	2.04450e12	0.104392
$900$	0	0
$901$	4.56613e13	2.30827
$902$	6.65893e13	3.34946
$903$	0	0
$904$	−8.45957e12	−0.421299
$905$	1.25151e13	0.620176
$906$	0	0
$907$	4.31310e12	0.211620	0.105810	−	0.994386i	$-0.466256\pi$
$907$	4.31310e12	0.211620	0.105810	+	0.994386i	$0.466256\pi$
$908$	−2.59866e12	−0.126871
$909$	0	0
$910$	3.48188e12	0.168317
$911$	−3.59972e13	−1.73155	−0.865777	−	0.500430i	$-0.833175\pi$
$911$	−3.59972e13	−1.73155	−0.865777	+	0.500430i	$0.833175\pi$
$912$	0	0
$913$	6.50340e12	0.309758
$914$	−3.06041e12	−0.145051
$915$	0	0
$916$	−4.11185e12	−0.192978
$917$	−6.63375e11	−0.0309811
$918$	0	0
$919$	−1.78486e13	−0.825437	−0.412719	−	0.910859i	$-0.635421\pi$
$919$	−1.78486e13	−0.825437	−0.412719	+	0.910859i	$0.635421\pi$
$920$	−7.13595e12	−0.328403
$921$	0	0
$922$	−7.81490e12	−0.356151
$923$	5.88923e12	0.267086
$924$	0	0
$925$	5.20382e12	0.233714
$926$	4.28551e13	1.91537
$927$	0	0
$928$	−2.03782e12	−0.0901988
$929$	2.28123e13	1.00484	0.502422	−	0.864622i	$-0.332442\pi$
$929$	2.28123e13	1.00484	0.502422	+	0.864622i	$0.332442\pi$
$930$	0	0
$931$	−2.47272e12	−0.107870
$932$	−3.63795e12	−0.157937
$933$	0	0
$934$	1.40375e13	0.603572
$935$	3.29852e13	1.41145
$936$	0	0
$937$	9.14211e12	0.387452	0.193726	−	0.981056i	$-0.437943\pi$
$937$	9.14211e12	0.387452	0.193726	+	0.981056i	$0.437943\pi$
$938$	−2.85181e13	−1.20284
$939$	0	0
$940$	4.68500e12	0.195719
$941$	−2.42073e13	−1.00645	−0.503225	−	0.864155i	$-0.667853\pi$
$941$	−2.42073e13	−1.00645	−0.503225	+	0.864155i	$0.667853\pi$
$942$	0	0
$943$	−2.58082e13	−1.06281
$944$	4.00719e13	1.64235
$945$	0	0
$946$	4.57113e13	1.85573
$947$	−1.63239e13	−0.659550	−0.329775	−	0.944060i	$-0.606973\pi$
$947$	−1.63239e13	−0.659550	−0.329775	+	0.944060i	$0.606973\pi$
$948$	0	0
$949$	9.83767e12	0.393726
$950$	−5.81135e12	−0.231484
$951$	0	0
$952$	2.47313e13	0.975845
$953$	−2.42382e13	−0.951880	−0.475940	−	0.879478i	$-0.657892\pi$
$953$	−2.42382e13	−0.951880	−0.475940	+	0.879478i	$0.657892\pi$
$954$	0	0
$955$	1.52756e12	0.0594268
$956$	4.31641e12	0.167133
$957$	0	0
$958$	−2.30134e13	−0.882748
$959$	7.03523e12	0.268593
$960$	0	0
$961$	−2.12803e13	−0.804864
$962$	−3.32123e12	−0.125029
$963$	0	0
$964$	−1.03447e12	−0.0385809
$965$	2.84832e13	1.05734
$966$	0	0
$967$	−1.11387e13	−0.409654	−0.204827	−	0.978798i	$-0.565663\pi$
$967$	−1.11387e13	−0.409654	−0.204827	+	0.978798i	$0.565663\pi$
$968$	−4.00987e13	−1.46788
$969$	0	0
$970$	−2.25497e13	−0.817839
$971$	3.10112e13	1.11952	0.559760	−	0.828655i	$-0.310893\pi$
$971$	3.10112e13	1.11952	0.559760	+	0.828655i	$0.310893\pi$
$972$	0	0
$973$	−2.58837e13	−0.925804
$974$	−1.11134e12	−0.0395668
$975$	0	0
$976$	3.74699e13	1.32178
$977$	−1.16626e13	−0.409516	−0.204758	−	0.978813i	$-0.565641\pi$
$977$	−1.16626e13	−0.409516	−0.204758	+	0.978813i	$0.565641\pi$
$978$	0	0
$979$	−4.89889e13	−1.70442
$980$	−1.06021e12	−0.0367178
$981$	0	0
$982$	−1.10729e13	−0.379980
$983$	1.20376e13	0.411198	0.205599	−	0.978636i	$-0.434086\pi$
$983$	1.20376e13	0.411198	0.205599	+	0.978636i	$0.434086\pi$
$984$	0	0
$985$	2.80085e13	0.948040
$986$	−1.00582e13	−0.338904
$987$	0	0
$988$	6.01056e11	0.0200682
$989$	−1.77164e13	−0.588834
$990$	0	0
$991$	4.45908e13	1.46863	0.734317	−	0.678806i	$-0.237502\pi$
$991$	4.45908e13	1.46863	0.734317	+	0.678806i	$0.237502\pi$
$992$	−5.14247e12	−0.168604
$993$	0	0
$994$	2.73148e13	0.887480
$995$	4.09360e11	0.0132404
$996$	0	0
$997$	5.03829e13	1.61493	0.807467	−	0.589912i	$-0.200838\pi$
$997$	5.03829e13	1.61493	0.807467	+	0.589912i	$0.200838\pi$
$998$	1.79897e13	0.574032
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.10.a.e.1.5		5
3.2	odd	2		13.10.a.b.1.1	✓	5
12.11	even	2		208.10.a.h.1.2		5
15.14	odd	2		325.10.a.b.1.5		5
39.38	odd	2		169.10.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.1	✓	5	3.2	odd	2
117.10.a.e.1.5		5	1.1	even	1	trivial
169.10.a.b.1.5		5	39.38	odd	2
208.10.a.h.1.2		5	12.11	even	2
325.10.a.b.1.5		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+24.7188 q^{2} +99.0182 q^{4} +920.299 q^{5} +5359.02 q^{7} -10208.4 q^{8} +O(q^{10})\)	\(q+24.7188 q^{2} +99.0182 q^{4} +920.299 q^{5} +5359.02 q^{7} -10208.4 q^{8} +22748.7 q^{10} -79284.0 q^{11} +28561.0 q^{13} +132468. q^{14} -303037. q^{16} -452068. q^{17} +212533. q^{19} +91126.3 q^{20} -1.95980e6 q^{22} +759566. q^{23} -1.10618e6 q^{25} +705993. q^{26} +530640. q^{28} +900101. q^{29} +2.27141e6 q^{31} -2.26400e6 q^{32} -1.11746e7 q^{34} +4.93189e6 q^{35} -4.70433e6 q^{37} +5.25355e6 q^{38} -9.39478e6 q^{40} -3.39775e7 q^{41} -2.33244e7 q^{43} -7.85057e6 q^{44} +1.87755e7 q^{46} +5.14121e7 q^{47} -1.16346e7 q^{49} -2.73433e7 q^{50} +2.82806e6 q^{52} -1.01005e8 q^{53} -7.29650e7 q^{55} -5.47070e7 q^{56} +2.22494e7 q^{58} -1.32234e8 q^{59} -1.23648e8 q^{61} +5.61465e7 q^{62} +9.91916e7 q^{64} +2.62846e7 q^{65} -2.15282e8 q^{67} -4.47630e7 q^{68} +1.21910e8 q^{70} +2.06198e8 q^{71} +3.44444e8 q^{73} -1.16285e8 q^{74} +2.10446e7 q^{76} -4.24884e8 q^{77} +5.03324e7 q^{79} -2.78884e8 q^{80} -8.39883e8 q^{82} -8.20266e7 q^{83} -4.16038e8 q^{85} -5.76552e8 q^{86} +8.09364e8 q^{88} +6.17891e8 q^{89} +1.53059e8 q^{91} +7.52109e7 q^{92} +1.27084e9 q^{94} +1.95594e8 q^{95} -9.91253e8 q^{97} -2.87592e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8}+O(q^{10}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8	\( 5 q - 15 q^{2} + 361 q^{4} - 1803 q^{5} + 10099 q^{7} - 23151 q^{8} + 84505 q^{10} - 121746 q^{11} + 142805 q^{13} - 8475 q^{14} - 322463 q^{16} + 495669 q^{17} - 840738 q^{19} + 1595607 q^{20} - 2023594 q^{22} + 592152 q^{23} + 1670362 q^{25} - 428415 q^{26} + 2587955 q^{28} - 10678182 q^{29} + 12885296 q^{31} - 3282927 q^{32} - 9934079 q^{34} - 8380731 q^{35} + 7171823 q^{37} + 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} + 12831975 q^{43} + 41479074 q^{44} - 59319696 q^{46} - 43354215 q^{47} + 25249488 q^{49} + 16270770 q^{50} + 10310521 q^{52} - 93231780 q^{53} + 99448846 q^{55} - 199599225 q^{56} + 151020970 q^{58} - 246496182 q^{59} - 132232612 q^{61} - 158135724 q^{62} + 91019105 q^{64} - 51495483 q^{65} - 369388534 q^{67} - 238172073 q^{68} - 144857425 q^{70} - 212150457 q^{71} - 252729806 q^{73} - 192105957 q^{74} - 953775990 q^{76} - 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} + 169559388 q^{82} - 1696894296 q^{83} - 775363765 q^{85} - 3291621459 q^{86} - 220227222 q^{88} + 753854382 q^{89} + 288437539 q^{91} - 13876128 q^{92} + 272071215 q^{94} - 1442632962 q^{95} + 3824606 q^{97} - 1570614816 q^{98}+O(q^{100}) \) 5 * q - 15 * q^2 + 361 * q^4 - 1803 * q^5 + 10099 * q^7 - 23151 * q^8 + 84505 * q^10 - 121746 * q^11 + 142805 * q^13 - 8475 * q^14 - 322463 * q^16 + 495669 * q^17 - 840738 * q^19 + 1595607 * q^20 - 2023594 * q^22 + 592152 * q^23 + 1670362 * q^25 - 428415 * q^26 + 2587955 * q^28 - 10678182 * q^29 + 12885296 * q^31 - 3282927 * q^32 - 9934079 * q^34 - 8380731 * q^35 + 7171823 * q^37 + 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 + 12831975 * q^43 + 41479074 * q^44 - 59319696 * q^46 - 43354215 * q^47 + 25249488 * q^49 + 16270770 * q^50 + 10310521 * q^52 - 93231780 * q^53 + 99448846 * q^55 - 199599225 * q^56 + 151020970 * q^58 - 246496182 * q^59 - 132232612 * q^61 - 158135724 * q^62 + 91019105 * q^64 - 51495483 * q^65 - 369388534 * q^67 - 238172073 * q^68 - 144857425 * q^70 - 212150457 * q^71 - 252729806 * q^73 - 192105957 * q^74 - 953775990 * q^76 - 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 + 169559388 * q^82 - 1696894296 * q^83 - 775363765 * q^85 - 3291621459 * q^86 - 220227222 * q^88 + 753854382 * q^89 + 288437539 * q^91 - 13876128 * q^92 + 272071215 * q^94 - 1442632962 * q^95 + 3824606 * q^97 - 1570614816 * q^98

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