LMFDB - Embedded newform 25.14.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,14,Mod(1,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-142] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$26.8077322380$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4466x - 18720 $ x^3 - x^2 - 4466*x - 18720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-64.1084$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-176.217 q^{2} +573.185 q^{3} +22860.4 q^{4} -101005. q^{6} +201493. q^{7} -2.58481e6 q^{8} -1.26578e6 q^{9} -3.34359e6 q^{11} +1.31032e7 q^{12} +7.80359e6 q^{13} -3.55065e7 q^{14} +2.68215e8 q^{16} +8.71750e7 q^{17} +2.23052e8 q^{18} -1.66766e7 q^{19} +1.15493e8 q^{21} +5.89196e8 q^{22} -1.13518e9 q^{23} -1.48158e9 q^{24} -1.37512e9 q^{26} -1.63937e9 q^{27} +4.60620e9 q^{28} +2.60673e9 q^{29} +8.33139e8 q^{31} -2.60892e10 q^{32} -1.91649e9 q^{33} -1.53617e10 q^{34} -2.89362e10 q^{36} +1.05494e10 q^{37} +2.93870e9 q^{38} +4.47290e9 q^{39} -4.33030e9 q^{41} -2.03518e10 q^{42} -1.93854e9 q^{43} -7.64356e10 q^{44} +2.00038e11 q^{46} -2.85468e10 q^{47} +1.53737e11 q^{48} -5.62896e10 q^{49} +4.99674e10 q^{51} +1.78393e11 q^{52} -1.23249e11 q^{53} +2.88884e11 q^{54} -5.20821e11 q^{56} -9.55879e9 q^{57} -4.59349e11 q^{58} -5.55404e11 q^{59} -4.10476e11 q^{61} -1.46813e11 q^{62} -2.55046e11 q^{63} +2.40014e12 q^{64} +3.37718e11 q^{66} -3.36861e11 q^{67} +1.99285e12 q^{68} -6.50671e11 q^{69} +1.57323e12 q^{71} +3.27181e12 q^{72} -2.05372e12 q^{73} -1.85898e12 q^{74} -3.81234e11 q^{76} -6.73709e11 q^{77} -7.88201e11 q^{78} -6.93000e11 q^{79} +1.07840e12 q^{81} +7.63071e11 q^{82} -2.01116e12 q^{83} +2.64021e12 q^{84} +3.41604e11 q^{86} +1.49414e12 q^{87} +8.64253e12 q^{88} -8.51832e12 q^{89} +1.57237e12 q^{91} -2.59507e13 q^{92} +4.77543e11 q^{93} +5.03042e12 q^{94} -1.49540e13 q^{96} +7.99814e12 q^{97} +9.91916e12 q^{98} +4.23225e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 142 q^{2} - 416 q^{3} + 17876 q^{4} + 120376 q^{6} - 448292 q^{7} - 2580360 q^{8} + 1286119 q^{9} - 6604004 q^{11} + 23722448 q^{12} + 33501974 q^{13} - 46562928 q^{14} + 199912208 q^{16} - 83129542 q^{17}+ \cdots + 126787366508 q^{99}+O(q^{100}) $ 3 * q - 142 * q^2 - 416 * q^3 + 17876 * q^4 + 120376 * q^6 - 448292 * q^7 - 2580360 * q^8 + 1286119 * q^9 - 6604004 * q^11 + 23722448 * q^12 + 33501974 * q^13 - 46562928 * q^14 + 199912208 * q^16 - 83129542 * q^17 + 30983914 * q^18 + 97491100 * q^19 + 438200736 * q^21 + 530907256 * q^22 - 316255836 * q^23 - 3890359200 * q^24 - 3746814044 * q^26 - 6518951360 * q^27 + 6227646976 * q^28 + 2236171850 * q^29 + 7482994376 * q^31 - 32169857312 * q^32 - 359182912 * q^33 - 30236073988 * q^34 - 43361833852 * q^36 - 31447174242 * q^37 + 42518132360 * q^38 - 70188571072 * q^39 - 10752884434 * q^41 - 92283853824 * q^42 - 16930554856 * q^43 - 68395825168 * q^44 + 246828204336 * q^46 - 31934201692 * q^47 + 80078828864 * q^48 - 38956926629 * q^49 - 129369882944 * q^51 + 18152597928 * q^52 + 221149123934 * q^53 + 246121937200 * q^54 - 522876451200 * q^56 + 763110695680 * q^57 - 854269976260 * q^58 - 55436423900 * q^59 + 496161392746 * q^61 + 598069940736 * q^62 - 1085454385236 * q^63 + 3297565494336 * q^64 - 22883875168 * q^66 - 459297824792 * q^67 + 2008021178776 * q^68 - 333379292832 * q^69 + 521997878336 * q^71 + 5658040941720 * q^72 - 2505025571086 * q^73 - 2418323586508 * q^74 + 621688050000 * q^76 + 385562457456 * q^77 + 2386950332528 * q^78 + 2990636883200 * q^79 + 320549052763 * q^81 - 5784848206924 * q^82 - 5137135467696 * q^83 - 814234130688 * q^84 + 2343313645096 * q^86 - 6885420178880 * q^87 + 8660607864480 * q^88 - 19423025958450 * q^89 - 6792522370184 * q^91 - 26870022340992 * q^92 + 11095902136128 * q^93 - 7003557875968 * q^94 - 2208331214464 * q^96 + 11088325396458 * q^97 + 10176508990306 * q^98 + 126787366508 * q^99

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 $

$2$	−176.217	−1.94694	−0.973469	−	0.228817i	$-0.926514\pi$
$2$	−176.217	−1.94694	−0.973469	+	0.228817i	$0.926514\pi$
$3$	573.185	0.453949	0.226974	−	0.973901i	$-0.427117\pi$
$3$	573.185	0.453949	0.226974	+	0.973901i	$0.427117\pi$
$4$	22860.4	2.79057
$5$	0	0
$5$	0	0
$6$	−101005.	−0.883810
$7$	201493.	0.647326	0.323663	−	0.946172i	$-0.395086\pi$
$7$	201493.	0.647326	0.323663	+	0.946172i	$0.395086\pi$
$8$	−2.58481e6	−3.48613
$9$	−1.26578e6	−0.793931
$10$	0	0
$11$	−3.34359e6	−0.569062	−0.284531	−	0.958667i	$-0.591838\pi$
$11$	−3.34359e6	−0.569062	−0.284531	+	0.958667i	$0.591838\pi$
$12$	1.31032e7	1.26678
$13$	7.80359e6	0.448397	0.224198	−	0.974544i	$-0.428024\pi$
$13$	7.80359e6	0.448397	0.224198	+	0.974544i	$0.428024\pi$
$14$	−3.55065e7	−1.26030
$15$	0	0
$16$	2.68215e8	3.99671
$17$	8.71750e7	0.875939	0.437969	−	0.898990i	$-0.355698\pi$
$17$	8.71750e7	0.875939	0.437969	+	0.898990i	$0.355698\pi$
$18$	2.23052e8	1.54573
$19$	−1.66766e7	−0.0813223	−0.0406612	−	0.999173i	$-0.512946\pi$
$19$	−1.66766e7	−0.0813223	−0.0406612	+	0.999173i	$0.512946\pi$
$20$	0	0
$21$	1.15493e8	0.293853
$22$	5.89196e8	1.10793
$23$	−1.13518e9	−1.59895	−0.799476	−	0.600698i	$-0.794889\pi$
$23$	−1.13518e9	−1.59895	−0.799476	+	0.600698i	$0.794889\pi$
$24$	−1.48158e9	−1.58253
$25$	0	0
$26$	−1.37512e9	−0.873002
$27$	−1.63937e9	−0.814352
$28$	4.60620e9	1.80641
$29$	2.60673e9	0.813783	0.406891	−	0.913477i	$-0.366613\pi$
$29$	2.60673e9	0.813783	0.406891	+	0.913477i	$0.366613\pi$
$30$	0	0
$31$	8.33139e8	0.168604	0.0843018	−	0.996440i	$-0.473134\pi$
$31$	8.33139e8	0.168604	0.0843018	+	0.996440i	$0.473134\pi$
$32$	−2.60892e10	−4.29523
$33$	−1.91649e9	−0.258325
$34$	−1.53617e10	−1.70540
$35$	0	0
$36$	−2.89362e10	−2.21552
$37$	1.05494e10	0.675953	0.337976	−	0.941155i	$-0.390258\pi$
$37$	1.05494e10	0.675953	0.337976	+	0.941155i	$0.390258\pi$
$38$	2.93870e9	0.158330
$39$	4.47290e9	0.203549
$40$	0	0
$41$	−4.33030e9	−0.142371	−0.0711857	−	0.997463i	$-0.522678\pi$
$41$	−4.33030e9	−0.142371	−0.0711857	+	0.997463i	$0.522678\pi$
$42$	−2.03518e10	−0.572113
$43$	−1.93854e9	−0.0467660	−0.0233830	−	0.999727i	$-0.507444\pi$
$43$	−1.93854e9	−0.0467660	−0.0233830	+	0.999727i	$0.507444\pi$
$44$	−7.64356e10	−1.58801
$45$	0	0
$46$	2.00038e11	3.11306
$47$	−2.85468e10	−0.386296	−0.193148	−	0.981170i	$-0.561870\pi$
$47$	−2.85468e10	−0.386296	−0.193148	+	0.981170i	$0.561870\pi$
$48$	1.53737e11	1.81430
$49$	−5.62896e10	−0.580969
$50$	0	0
$51$	4.99674e10	0.397631
$52$	1.78393e11	1.25128
$53$	−1.23249e11	−0.763819	−0.381910	−	0.924200i	$-0.624733\pi$
$53$	−1.23249e11	−0.763819	−0.381910	+	0.924200i	$0.624733\pi$
$54$	2.88884e11	1.58549
$55$	0	0
$56$	−5.20821e11	−2.25666
$57$	−9.55879e9	−0.0369162
$58$	−4.59349e11	−1.58439
$59$	−5.55404e11	−1.71424	−0.857118	−	0.515120i	$-0.827747\pi$
$59$	−5.55404e11	−1.71424	−0.857118	+	0.515120i	$0.827747\pi$
$60$	0	0
$61$	−4.10476e11	−1.02010	−0.510051	−	0.860144i	$-0.670373\pi$
$61$	−4.10476e11	−1.02010	−0.510051	+	0.860144i	$0.670373\pi$
$62$	−1.46813e11	−0.328261
$63$	−2.55046e11	−0.513932
$64$	2.40014e12	4.36583
$65$	0	0
$66$	3.37718e11	0.502943
$67$	−3.36861e11	−0.454951	−0.227475	−	0.973784i	$-0.573047\pi$
$67$	−3.36861e11	−0.454951	−0.227475	+	0.973784i	$0.573047\pi$
$68$	1.99285e12	2.44437
$69$	−6.50671e11	−0.725842
$70$	0	0
$71$	1.57323e12	1.45751	0.728757	−	0.684772i	$-0.240098\pi$
$71$	1.57323e12	1.45751	0.728757	+	0.684772i	$0.240098\pi$
$72$	3.27181e12	2.76775
$73$	−2.05372e12	−1.58834	−0.794170	−	0.607695i	$-0.792094\pi$
$73$	−2.05372e12	−1.58834	−0.794170	+	0.607695i	$0.792094\pi$
$74$	−1.85898e12	−1.31604
$75$	0	0
$76$	−3.81234e11	−0.226936
$77$	−6.73709e11	−0.368369
$78$	−7.88201e11	−0.396298
$79$	−6.93000e11	−0.320743	−0.160372	−	0.987057i	$-0.551269\pi$
$79$	−6.93000e11	−0.320743	−0.160372	+	0.987057i	$0.551269\pi$
$80$	0	0
$81$	1.07840e12	0.424256
$82$	7.63071e11	0.277188
$83$	−2.01116e12	−0.675212	−0.337606	−	0.941288i	$-0.609617\pi$
$83$	−2.01116e12	−0.675212	−0.337606	+	0.941288i	$0.609617\pi$
$84$	2.64021e12	0.820017
$85$	0	0
$86$	3.41604e11	0.0910505
$87$	1.49414e12	0.369416
$88$	8.64253e12	1.98383
$89$	−8.51832e12	−1.81685	−0.908424	−	0.418050i	$-0.862714\pi$
$89$	−8.51832e12	−1.81685	−0.908424	+	0.418050i	$0.862714\pi$
$90$	0	0
$91$	1.57237e12	0.290259
$92$	−2.59507e13	−4.46199
$93$	4.77543e11	0.0765374
$94$	5.03042e12	0.752096
$95$	0	0
$96$	−1.49540e13	−1.94981
$97$	7.99814e12	0.974929	0.487464	−	0.873143i	$-0.337922\pi$
$97$	7.99814e12	0.974929	0.487464	+	0.873143i	$0.337922\pi$
$98$	9.91916e12	1.13111
$99$	4.23225e12	0.451796
$100$	0	0
$101$	−1.60387e13	−1.50342	−0.751710	−	0.659494i	$-0.770771\pi$
$101$	−1.60387e13	−1.50342	−0.751710	+	0.659494i	$0.770771\pi$
$102$	−8.80509e12	−0.774164
$103$	−1.72566e13	−1.42401	−0.712004	−	0.702176i	$-0.752212\pi$
$103$	−1.72566e13	−1.42401	−0.712004	+	0.702176i	$0.752212\pi$
$104$	−2.01708e13	−1.56317
$105$	0	0
$106$	2.17186e13	1.48711
$107$	3.98196e11	0.0256509	0.0128254	−	0.999918i	$-0.495917\pi$
$107$	3.98196e11	0.0256509	0.0128254	+	0.999918i	$0.495917\pi$
$108$	−3.74766e13	−2.27251
$109$	1.09886e13	0.627582	0.313791	−	0.949492i	$-0.398401\pi$
$109$	1.09886e13	0.627582	0.313791	+	0.949492i	$0.398401\pi$
$110$	0	0
$111$	6.04676e12	0.306848
$112$	5.40435e13	2.58718
$113$	2.06154e13	0.931497	0.465748	−	0.884917i	$-0.345785\pi$
$113$	2.06154e13	0.931497	0.465748	+	0.884917i	$0.345785\pi$
$114$	1.68442e12	0.0718735
$115$	0	0
$116$	5.95907e13	2.27092
$117$	−9.87764e12	−0.355996
$118$	9.78714e13	3.33751
$119$	1.75651e13	0.567018
$120$	0	0
$121$	−2.33431e13	−0.676168
$122$	7.23327e13	1.98608
$123$	−2.48206e12	−0.0646293
$124$	1.90459e13	0.470500
$125$	0	0
$126$	4.49434e13	1.00059
$127$	−3.03181e13	−0.641177	−0.320588	−	0.947219i	$-0.603881\pi$
$127$	−3.03181e13	−0.641177	−0.320588	+	0.947219i	$0.603881\pi$
$128$	−2.09222e14	−4.20478
$129$	−1.11114e12	−0.0212294
$130$	0	0
$131$	−7.79100e13	−1.34688	−0.673441	−	0.739241i	$-0.735185\pi$
$131$	−7.79100e13	−1.34688	−0.673441	+	0.739241i	$0.735185\pi$
$132$	−4.38117e13	−0.720875
$133$	−3.36022e12	−0.0526420
$134$	5.93605e13	0.885761
$135$	0	0
$136$	−2.25331e14	−3.05364
$137$	1.01051e14	1.30574	0.652871	−	0.757469i	$-0.273564\pi$
$137$	1.01051e14	1.30574	0.652871	+	0.757469i	$0.273564\pi$
$138$	1.14659e14	1.41317
$139$	1.42505e14	1.67585	0.837924	−	0.545787i	$-0.183769\pi$
$139$	1.42505e14	1.67585	0.837924	+	0.545787i	$0.183769\pi$
$140$	0	0
$141$	−1.63626e13	−0.175359
$142$	−2.77230e14	−2.83769
$143$	−2.60920e13	−0.255166
$144$	−3.39502e14	−3.17311
$145$	0	0
$146$	3.61901e14	3.09240
$147$	−3.22643e13	−0.263730
$148$	2.41163e14	1.88629
$149$	−6.15555e13	−0.460846	−0.230423	−	0.973091i	$-0.574011\pi$
$149$	−6.15555e13	−0.460846	−0.230423	+	0.973091i	$0.574011\pi$
$150$	0	0
$151$	−4.43226e13	−0.304281	−0.152141	−	0.988359i	$-0.548617\pi$
$151$	−4.43226e13	−0.304281	−0.152141	+	0.988359i	$0.548617\pi$
$152$	4.31059e13	0.283500
$153$	−1.10344e14	−0.695435
$154$	1.18719e14	0.717191
$155$	0	0
$156$	1.02252e14	0.568019
$157$	1.81701e14	0.968301	0.484150	−	0.874985i	$-0.339129\pi$
$157$	1.81701e14	0.968301	0.484150	+	0.874985i	$0.339129\pi$
$158$	1.22118e14	0.624467
$159$	−7.06446e13	−0.346735
$160$	0	0
$161$	−2.28732e14	−1.03504
$162$	−1.90033e14	−0.826001
$163$	−9.09336e13	−0.379756	−0.189878	−	0.981808i	$-0.560809\pi$
$163$	−9.09336e13	−0.379756	−0.189878	+	0.981808i	$0.560809\pi$
$164$	−9.89921e13	−0.397297
$165$	0	0
$166$	3.54401e14	1.31460
$167$	2.40022e14	0.856237	0.428118	−	0.903723i	$-0.359177\pi$
$167$	2.40022e14	0.856237	0.428118	+	0.903723i	$0.359177\pi$
$168$	−2.98527e14	−1.02441
$169$	−2.41979e14	−0.798940
$170$	0	0
$171$	2.11090e13	0.0645643
$172$	−4.43158e13	−0.130504
$173$	−4.10274e14	−1.16352	−0.581760	−	0.813360i	$-0.697636\pi$
$173$	−4.10274e14	−1.16352	−0.581760	+	0.813360i	$0.697636\pi$
$174$	−2.63292e14	−0.719230
$175$	0	0
$176$	−8.96800e14	−2.27438
$177$	−3.18349e14	−0.778175
$178$	1.50107e15	3.53729
$179$	−2.37588e14	−0.539858	−0.269929	−	0.962880i	$-0.587000\pi$
$179$	−2.37588e14	−0.539858	−0.269929	+	0.962880i	$0.587000\pi$
$180$	0	0
$181$	5.41620e14	1.14494	0.572472	−	0.819924i	$-0.305985\pi$
$181$	5.41620e14	1.14494	0.572472	+	0.819924i	$0.305985\pi$
$182$	−2.77078e14	−0.565116
$183$	−2.35279e14	−0.463074
$184$	2.93424e15	5.57416
$185$	0	0
$186$	−8.41511e13	−0.149014
$187$	−2.91477e14	−0.498464
$188$	−6.52589e14	−1.07799
$189$	−3.30322e14	−0.527151
$190$	0	0
$191$	−2.56027e12	−0.00381565	−0.00190782	−	0.999998i	$-0.500607\pi$
$191$	−2.56027e12	−0.00381565	−0.00190782	+	0.999998i	$0.500607\pi$
$192$	1.37572e15	1.98186
$193$	−1.10496e15	−1.53895	−0.769475	−	0.638677i	$-0.779482\pi$
$193$	−1.10496e15	−1.53895	−0.769475	+	0.638677i	$0.779482\pi$
$194$	−1.40941e15	−1.89813
$195$	0	0
$196$	−1.28680e15	−1.62124
$197$	−7.90145e14	−0.963110	−0.481555	−	0.876416i	$-0.659928\pi$
$197$	−7.90145e14	−0.963110	−0.481555	+	0.876416i	$0.659928\pi$
$198$	−7.45793e14	−0.879619
$199$	−2.97088e14	−0.339109	−0.169555	−	0.985521i	$-0.554233\pi$
$199$	−2.97088e14	−0.339109	−0.169555	+	0.985521i	$0.554233\pi$
$200$	0	0
$201$	−1.93084e14	−0.206524
$202$	2.82629e15	2.92707
$203$	5.25237e14	0.526782
$204$	1.14227e15	1.10962
$205$	0	0
$206$	3.04090e15	2.77246
$207$	1.43689e15	1.26946
$208$	2.09304e15	1.79211
$209$	5.57597e13	0.0462775
$210$	0	0
$211$	−1.25602e15	−0.979851	−0.489926	−	0.871764i	$-0.662976\pi$
$211$	−1.25602e15	−0.979851	−0.489926	+	0.871764i	$0.662976\pi$
$212$	−2.81752e15	−2.13149
$213$	9.01752e14	0.661637
$214$	−7.01688e13	−0.0499407
$215$	0	0
$216$	4.23746e15	2.83894
$217$	1.67872e14	0.109141
$218$	−1.93638e15	−1.22186
$219$	−1.17716e15	−0.721025
$220$	0	0
$221$	6.80278e14	0.392768
$222$	−1.06554e15	−0.597414
$223$	1.17841e15	0.641676	0.320838	−	0.947134i	$-0.396036\pi$
$223$	1.17841e15	0.641676	0.320838	+	0.947134i	$0.396036\pi$
$224$	−5.25680e15	−2.78041
$225$	0	0
$226$	−3.63278e15	−1.81357
$227$	−4.91498e14	−0.238426	−0.119213	−	0.992869i	$-0.538037\pi$
$227$	−4.91498e14	−0.238426	−0.119213	+	0.992869i	$0.538037\pi$
$228$	−2.18517e14	−0.103017
$229$	3.17657e15	1.45555	0.727777	−	0.685814i	$-0.240554\pi$
$229$	3.17657e15	1.45555	0.727777	+	0.685814i	$0.240554\pi$
$230$	0	0
$231$	−3.86160e14	−0.167221
$232$	−6.73789e15	−2.83695
$233$	2.05201e14	0.0840168	0.0420084	−	0.999117i	$-0.486624\pi$
$233$	2.05201e14	0.0840168	0.0420084	+	0.999117i	$0.486624\pi$
$234$	1.74061e15	0.693103
$235$	0	0
$236$	−1.26967e16	−4.78370
$237$	−3.97218e14	−0.145601
$238$	−3.09527e15	−1.10395
$239$	4.78414e15	1.66042	0.830209	−	0.557453i	$-0.188221\pi$
$239$	4.78414e15	1.66042	0.830209	+	0.557453i	$0.188221\pi$
$240$	0	0
$241$	2.83675e15	0.932633	0.466316	−	0.884618i	$-0.345581\pi$
$241$	2.83675e15	0.932633	0.466316	+	0.884618i	$0.345581\pi$
$242$	4.11345e15	1.31646
$243$	3.23181e15	1.00694
$244$	−9.38362e15	−2.84667
$245$	0	0
$246$	4.37381e14	0.125829
$247$	−1.30138e14	−0.0364647
$248$	−2.15351e15	−0.587774
$249$	−1.15277e15	−0.306512
$250$	0	0
$251$	3.50075e15	0.883654	0.441827	−	0.897100i	$-0.354331\pi$
$251$	3.50075e15	0.883654	0.441827	+	0.897100i	$0.354331\pi$
$252$	−5.83045e15	−1.43416
$253$	3.79558e15	0.909903
$254$	5.34256e15	1.24833
$255$	0	0
$256$	1.72065e16	3.82061
$257$	7.14451e14	0.154670	0.0773352	−	0.997005i	$-0.475359\pi$
$257$	7.14451e14	0.154670	0.0773352	+	0.997005i	$0.475359\pi$
$258$	1.95802e14	0.0413323
$259$	2.12563e15	0.437562
$260$	0	0
$261$	−3.29955e15	−0.646087
$262$	1.37290e16	2.62230
$263$	6.41873e15	1.19601	0.598007	−	0.801491i	$-0.295959\pi$
$263$	6.41873e15	1.19601	0.598007	+	0.801491i	$0.295959\pi$
$264$	4.95377e15	0.900556
$265$	0	0
$266$	5.92128e14	0.102491
$267$	−4.88257e15	−0.824756
$268$	−7.70076e15	−1.26957
$269$	−1.09876e15	−0.176813	−0.0884063	−	0.996084i	$-0.528177\pi$
$269$	−1.09876e15	−0.176813	−0.0884063	+	0.996084i	$0.528177\pi$
$270$	0	0
$271$	1.60206e15	0.245684	0.122842	−	0.992426i	$-0.460799\pi$
$271$	1.60206e15	0.245684	0.122842	+	0.992426i	$0.460799\pi$
$272$	2.33816e16	3.50088
$273$	9.01259e14	0.131763
$274$	−1.78069e16	−2.54220
$275$	0	0
$276$	−1.48746e16	−2.02551
$277$	6.91414e14	0.0919644	0.0459822	−	0.998942i	$-0.485358\pi$
$277$	6.91414e14	0.0919644	0.0459822	+	0.998942i	$0.485358\pi$
$278$	−2.51118e16	−3.26277
$279$	−1.05457e15	−0.133860
$280$	0	0
$281$	2.20744e15	0.267484	0.133742	−	0.991016i	$-0.457301\pi$
$281$	2.20744e15	0.267484	0.133742	+	0.991016i	$0.457301\pi$
$282$	2.88336e15	0.341413
$283$	−8.67634e15	−1.00398	−0.501990	−	0.864873i	$-0.667399\pi$
$283$	−8.67634e15	−1.00398	−0.501990	+	0.864873i	$0.667399\pi$
$284$	3.59646e16	4.06730
$285$	0	0
$286$	4.59784e15	0.496792
$287$	−8.72525e14	−0.0921606
$288$	3.30233e16	3.41011
$289$	−2.30511e15	−0.232731
$290$	0	0
$291$	4.58442e15	0.442568
$292$	−4.69489e16	−4.43238
$293$	7.81345e15	0.721445	0.360723	−	0.932673i	$-0.382530\pi$
$293$	7.81345e15	0.721445	0.360723	+	0.932673i	$0.382530\pi$
$294$	5.68552e15	0.513467
$295$	0	0
$296$	−2.72682e16	−2.35646
$297$	5.48137e15	0.463417
$298$	1.08471e16	0.897239
$299$	−8.85851e15	−0.716965
$300$	0	0
$301$	−3.90603e14	−0.0302728
$302$	7.81039e15	0.592417
$303$	−9.19315e15	−0.682475
$304$	−4.47292e15	−0.325022
$305$	0	0
$306$	1.94445e16	1.35397
$307$	−1.73583e16	−1.18334	−0.591668	−	0.806182i	$-0.701530\pi$
$307$	−1.73583e16	−1.18334	−0.591668	+	0.806182i	$0.701530\pi$
$308$	−1.54012e16	−1.02796
$309$	−9.89120e15	−0.646426
$310$	0	0
$311$	−2.64097e15	−0.165509	−0.0827543	−	0.996570i	$-0.526372\pi$
$311$	−2.64097e15	−0.165509	−0.0827543	+	0.996570i	$0.526372\pi$
$312$	−1.15616e16	−0.709599
$313$	−1.04071e16	−0.625594	−0.312797	−	0.949820i	$-0.601266\pi$
$313$	−1.04071e16	−0.625594	−0.312797	+	0.949820i	$0.601266\pi$
$314$	−3.20188e16	−1.88522
$315$	0	0
$316$	−1.58422e16	−0.895057
$317$	1.64664e16	0.911410	0.455705	−	0.890131i	$-0.349387\pi$
$317$	1.64664e16	0.911410	0.455705	+	0.890131i	$0.349387\pi$
$318$	1.24488e16	0.675071
$319$	−8.71581e15	−0.463093
$320$	0	0
$321$	2.28240e14	0.0116442
$322$	4.03064e16	2.01516
$323$	−1.45378e15	−0.0712334
$324$	2.46527e16	1.18392
$325$	0	0
$326$	1.60240e16	0.739362
$327$	6.29851e15	0.284890
$328$	1.11930e16	0.496325
$329$	−5.75197e15	−0.250060
$330$	0	0
$331$	1.40904e16	0.588900	0.294450	−	0.955667i	$-0.404863\pi$
$331$	1.40904e16	0.588900	0.294450	+	0.955667i	$0.404863\pi$
$332$	−4.59759e16	−1.88423
$333$	−1.33532e16	−0.536660
$334$	−4.22959e16	−1.66704
$335$	0	0
$336$	3.09769e16	1.17445
$337$	−1.51673e16	−0.564044	−0.282022	−	0.959408i	$-0.591005\pi$
$337$	−1.51673e16	−0.564044	−0.282022	+	0.959408i	$0.591005\pi$
$338$	4.26408e16	1.55549
$339$	1.18164e16	0.422852
$340$	0	0
$341$	−2.78567e15	−0.0959460
$342$	−3.71975e15	−0.125703
$343$	−3.08644e16	−1.02340
$344$	5.01076e15	0.163032
$345$	0	0
$346$	7.22971e16	2.26530
$347$	−3.87222e15	−0.119074	−0.0595372	−	0.998226i	$-0.518962\pi$
$347$	−3.87222e15	−0.119074	−0.0595372	+	0.998226i	$0.518962\pi$
$348$	3.41565e16	1.03088
$349$	5.50673e16	1.63128	0.815640	−	0.578560i	$-0.196385\pi$
$349$	5.50673e16	1.63128	0.815640	+	0.578560i	$0.196385\pi$
$350$	0	0
$351$	−1.27930e16	−0.365153
$352$	8.72315e16	2.44425
$353$	4.84424e15	0.133257	0.0666285	−	0.997778i	$-0.478776\pi$
$353$	4.84424e15	0.133257	0.0666285	+	0.997778i	$0.478776\pi$
$354$	5.60985e16	1.51506
$355$	0	0
$356$	−1.94732e17	−5.07004
$357$	1.00681e16	0.257397
$358$	4.18670e16	1.05107
$359$	−5.71730e16	−1.40954	−0.704770	−	0.709436i	$-0.748950\pi$
$359$	−5.71730e16	−1.40954	−0.704770	+	0.709436i	$0.748950\pi$
$360$	0	0
$361$	−4.17749e16	−0.993387
$362$	−9.54426e16	−2.22914
$363$	−1.33799e16	−0.306946
$364$	3.59449e16	0.809988
$365$	0	0
$366$	4.14600e16	0.901576
$367$	3.48286e16	0.744057	0.372028	−	0.928221i	$-0.378662\pi$
$367$	3.48286e16	0.744057	0.372028	+	0.928221i	$0.378662\pi$
$368$	−3.04473e17	−6.39055
$369$	5.48121e15	0.113033
$370$	0	0
$371$	−2.48338e16	−0.494440
$372$	1.09168e16	0.213583
$373$	2.14588e16	0.412570	0.206285	−	0.978492i	$-0.433863\pi$
$373$	2.14588e16	0.412570	0.206285	+	0.978492i	$0.433863\pi$
$374$	5.13631e16	0.970479
$375$	0	0
$376$	7.37880e16	1.34668
$377$	2.03418e16	0.364898
$378$	5.82082e16	1.02633
$379$	−1.90361e16	−0.329930	−0.164965	−	0.986299i	$-0.552751\pi$
$379$	−1.90361e16	−0.329930	−0.164965	+	0.986299i	$0.552751\pi$
$380$	0	0
$381$	−1.73779e16	−0.291061
$382$	4.51162e14	0.00742884
$383$	1.03414e17	1.67412	0.837059	−	0.547112i	$-0.184273\pi$
$383$	1.03414e17	1.67412	0.837059	+	0.547112i	$0.184273\pi$
$384$	−1.19923e17	−1.90875
$385$	0	0
$386$	1.94713e17	2.99624
$387$	2.45377e15	0.0371290
$388$	1.82840e17	2.72061
$389$	9.11608e16	1.33394	0.666969	−	0.745085i	$-0.267591\pi$
$389$	9.11608e16	1.33394	0.666969	+	0.745085i	$0.267591\pi$
$390$	0	0
$391$	−9.89596e16	−1.40058
$392$	1.45498e17	2.02534
$393$	−4.46568e16	−0.611416
$394$	1.39237e17	1.87512
$395$	0	0
$396$	9.67507e16	1.26077
$397$	−7.19989e15	−0.0922970	−0.0461485	−	0.998935i	$-0.514695\pi$
$397$	−7.19989e15	−0.0922970	−0.0461485	+	0.998935i	$0.514695\pi$
$398$	5.23518e16	0.660225
$399$	−1.92603e15	−0.0238968
$400$	0	0
$401$	1.06602e17	1.28034	0.640172	−	0.768231i	$-0.278863\pi$
$401$	1.06602e17	1.28034	0.640172	+	0.768231i	$0.278863\pi$
$402$	3.40246e16	0.402090
$403$	6.50148e15	0.0756013
$404$	−3.66650e17	−4.19540
$405$	0	0
$406$	−9.25556e16	−1.02561
$407$	−3.52728e16	−0.384659
$408$	−1.29156e17	−1.38620
$409$	6.00154e16	0.633959	0.316980	−	0.948432i	$-0.397331\pi$
$409$	6.00154e16	0.633959	0.316980	+	0.948432i	$0.397331\pi$
$410$	0	0
$411$	5.79210e16	0.592740
$412$	−3.94491e17	−3.97379
$413$	−1.11910e17	−1.10967
$414$	−2.53205e17	−2.47155
$415$	0	0
$416$	−2.03590e17	−1.92597
$417$	8.16819e16	0.760749
$418$	−9.82580e15	−0.0900994
$419$	1.22532e17	1.10626	0.553130	−	0.833095i	$-0.313433\pi$
$419$	1.22532e17	1.10626	0.553130	+	0.833095i	$0.313433\pi$
$420$	0	0
$421$	−1.19508e17	−1.04607	−0.523037	−	0.852310i	$-0.675201\pi$
$421$	−1.19508e17	−1.04607	−0.523037	+	0.852310i	$0.675201\pi$
$422$	2.21332e17	1.90771
$423$	3.61340e16	0.306693
$424$	3.18576e17	2.66277
$425$	0	0
$426$	−1.58904e17	−1.28817
$427$	−8.27080e16	−0.660338
$428$	9.10290e15	0.0715806
$429$	−1.49555e16	−0.115832
$430$	0	0
$431$	−3.18425e16	−0.239279	−0.119640	−	0.992817i	$-0.538174\pi$
$431$	−3.18425e16	−0.239279	−0.119640	+	0.992817i	$0.538174\pi$
$432$	−4.39704e17	−3.25473
$433$	−1.24850e16	−0.0910366	−0.0455183	−	0.998964i	$-0.514494\pi$
$433$	−1.24850e16	−0.0910366	−0.0455183	+	0.998964i	$0.514494\pi$
$434$	−2.95818e16	−0.212492
$435$	0	0
$436$	2.51204e17	1.75131
$437$	1.89310e16	0.130030
$438$	2.07436e17	1.40379
$439$	−2.58876e17	−1.72613	−0.863063	−	0.505095i	$-0.831457\pi$
$439$	−2.58876e17	−1.72613	−0.863063	+	0.505095i	$0.831457\pi$
$440$	0	0
$441$	7.12503e16	0.461249
$442$	−1.19876e17	−0.764696
$443$	−1.53844e17	−0.967068	−0.483534	−	0.875326i	$-0.660647\pi$
$443$	−1.53844e17	−0.967068	−0.483534	+	0.875326i	$0.660647\pi$
$444$	1.38231e17	0.856281
$445$	0	0
$446$	−2.07656e17	−1.24930
$447$	−3.52827e16	−0.209201
$448$	4.83612e17	2.82611
$449$	−9.02887e16	−0.520034	−0.260017	−	0.965604i	$-0.583728\pi$
$449$	−9.02887e16	−0.520034	−0.260017	+	0.965604i	$0.583728\pi$
$450$	0	0
$451$	1.44787e16	0.0810182
$452$	4.71275e17	2.59941
$453$	−2.54051e16	−0.138128
$454$	8.66102e16	0.464201
$455$	0	0
$456$	2.47077e16	0.128695
$457$	9.78643e16	0.502538	0.251269	−	0.967917i	$-0.419152\pi$
$457$	9.78643e16	0.502538	0.251269	+	0.967917i	$0.419152\pi$
$458$	−5.59765e17	−2.83387
$459$	−1.42912e17	−0.713323
$460$	0	0
$461$	2.08140e17	1.00995	0.504976	−	0.863134i	$-0.331501\pi$
$461$	2.08140e17	1.00995	0.504976	+	0.863134i	$0.331501\pi$
$462$	6.80479e16	0.325568
$463$	2.44823e17	1.15498	0.577491	−	0.816397i	$-0.304032\pi$
$463$	2.44823e17	1.15498	0.577491	+	0.816397i	$0.304032\pi$
$464$	6.99163e17	3.25246
$465$	0	0
$466$	−3.61599e16	−0.163576
$467$	−3.54401e17	−1.58101	−0.790506	−	0.612454i	$-0.790182\pi$
$467$	−3.54401e17	−1.58101	−0.790506	+	0.612454i	$0.790182\pi$
$468$	−2.25806e17	−0.993432
$469$	−6.78751e16	−0.294501
$470$	0	0
$471$	1.04148e17	0.439559
$472$	1.43561e18	5.97605
$473$	6.48168e15	0.0266128
$474$	6.99964e16	0.283476
$475$	0	0
$476$	4.01546e17	1.58230
$477$	1.56006e17	0.606419
$478$	−8.43045e17	−3.23273
$479$	−1.54040e17	−0.582712	−0.291356	−	0.956615i	$-0.594106\pi$
$479$	−1.54040e17	−0.582712	−0.291356	+	0.956615i	$0.594106\pi$
$480$	0	0
$481$	8.23232e16	0.303095
$482$	−4.99883e17	−1.81578
$483$	−1.31106e17	−0.469856
$484$	−5.33633e17	−1.88689
$485$	0	0
$486$	−5.69499e17	−1.96046
$487$	−2.11302e17	−0.717736	−0.358868	−	0.933388i	$-0.616837\pi$
$487$	−2.11302e17	−0.717736	−0.358868	+	0.933388i	$0.616837\pi$
$488$	1.06100e18	3.55621
$489$	−5.21218e16	−0.172390
$490$	0	0
$491$	2.61474e17	0.842167	0.421083	−	0.907022i	$-0.361650\pi$
$491$	2.61474e17	0.842167	0.421083	+	0.907022i	$0.361650\pi$
$492$	−5.67408e16	−0.180353
$493$	2.27241e17	0.712824
$494$	2.29324e16	0.0709945
$495$	0	0
$496$	2.23460e17	0.673860
$497$	3.16995e17	0.943487
$498$	2.03137e17	0.596759
$499$	3.87524e17	1.12369	0.561843	−	0.827244i	$-0.310092\pi$
$499$	3.87524e17	1.12369	0.561843	+	0.827244i	$0.310092\pi$
$500$	0	0
$501$	1.37577e17	0.388688
$502$	−6.16891e17	−1.72042
$503$	4.12680e17	1.13611	0.568056	−	0.822990i	$-0.307696\pi$
$503$	4.12680e17	1.13611	0.568056	+	0.822990i	$0.307696\pi$
$504$	6.59246e17	1.79163
$505$	0	0
$506$	−6.68846e17	−1.77153
$507$	−1.38699e17	−0.362678
$508$	−6.93083e17	−1.78925
$509$	8.09532e16	0.206333	0.103166	−	0.994664i	$-0.467103\pi$
$509$	8.09532e16	0.206333	0.103166	+	0.994664i	$0.467103\pi$
$510$	0	0
$511$	−4.13811e17	−1.02817
$512$	−1.31813e18	−3.23372
$513$	2.73391e16	0.0662250
$514$	−1.25898e17	−0.301134
$515$	0	0
$516$	−2.54011e16	−0.0592420
$517$	9.54485e16	0.219827
$518$	−3.74572e17	−0.851906
$519$	−2.35163e17	−0.528178
$520$	0	0
$521$	−2.79201e17	−0.611607	−0.305803	−	0.952095i	$-0.598925\pi$
$521$	−2.79201e17	−0.611607	−0.305803	+	0.952095i	$0.598925\pi$
$522$	5.81436e17	1.25789
$523$	−9.97401e16	−0.213112	−0.106556	−	0.994307i	$-0.533982\pi$
$523$	−9.97401e16	−0.213112	−0.106556	+	0.994307i	$0.533982\pi$
$524$	−1.78105e18	−3.75857
$525$	0	0
$526$	−1.13109e18	−2.32857
$527$	7.26289e16	0.147686
$528$	−5.14032e17	−1.03245
$529$	7.84606e17	1.55665
$530$	0	0
$531$	7.03020e17	1.36098
$532$	−7.68159e16	−0.146901
$533$	−3.37919e16	−0.0638389
$534$	8.60391e17	1.60575
$535$	0	0
$536$	8.70721e17	1.58602
$537$	−1.36182e17	−0.245068
$538$	1.93620e17	0.344243
$539$	1.88209e17	0.330608
$540$	0	0
$541$	−2.15125e17	−0.368899	−0.184450	−	0.982842i	$-0.559050\pi$
$541$	−2.15125e17	−0.368899	−0.184450	+	0.982842i	$0.559050\pi$
$542$	−2.82309e17	−0.478332
$543$	3.10449e17	0.519746
$544$	−2.27433e18	−3.76236
$545$	0	0
$546$	−1.58817e17	−0.256534
$547$	−9.04541e17	−1.44381	−0.721906	−	0.691991i	$-0.756734\pi$
$547$	−9.04541e17	−1.44381	−0.721906	+	0.691991i	$0.756734\pi$
$548$	2.31007e18	3.64377
$549$	5.19573e17	0.809890
$550$	0	0
$551$	−4.34714e16	−0.0661787
$552$	1.68186e18	2.53038
$553$	−1.39635e17	−0.207625
$554$	−1.21839e17	−0.179049
$555$	0	0
$556$	3.25772e18	4.67657
$557$	9.25130e17	1.31263	0.656317	−	0.754485i	$-0.272113\pi$
$557$	9.25130e17	1.31263	0.656317	+	0.754485i	$0.272113\pi$
$558$	1.85833e17	0.260616
$559$	−1.51276e16	−0.0209697
$560$	0	0
$561$	−1.67070e17	−0.226277
$562$	−3.88987e17	−0.520774
$563$	7.77258e17	1.02863	0.514317	−	0.857600i	$-0.328046\pi$
$563$	7.77258e17	1.02863	0.514317	+	0.857600i	$0.328046\pi$
$564$	−3.74054e17	−0.489351
$565$	0	0
$566$	1.52892e18	1.95469
$567$	2.17291e17	0.274632
$568$	−4.06650e18	−5.08109
$569$	5.27222e17	0.651274	0.325637	−	0.945495i	$-0.394421\pi$
$569$	5.27222e17	0.651274	0.325637	+	0.945495i	$0.394421\pi$
$570$	0	0
$571$	−8.57655e17	−1.03557	−0.517783	−	0.855512i	$-0.673243\pi$
$571$	−8.57655e17	−1.03557	−0.517783	+	0.855512i	$0.673243\pi$
$572$	−5.96472e17	−0.712059
$573$	−1.46751e15	−0.00173211
$574$	1.53753e17	0.179431
$575$	0	0
$576$	−3.03805e18	−3.46617
$577$	6.01001e17	0.678004	0.339002	−	0.940786i	$-0.389911\pi$
$577$	6.01001e17	0.678004	0.339002	+	0.940786i	$0.389911\pi$
$578$	4.06198e17	0.453114
$579$	−6.33347e17	−0.698604
$580$	0	0
$581$	−4.05236e17	−0.437082
$582$	−8.07851e17	−0.861652
$583$	4.12094e17	0.434661
$584$	5.30849e18	5.53716
$585$	0	0
$586$	−1.37686e18	−1.40461
$587$	−2.25235e17	−0.227241	−0.113621	−	0.993524i	$-0.536245\pi$
$587$	−2.25235e17	−0.227241	−0.113621	+	0.993524i	$0.536245\pi$
$588$	−7.37574e17	−0.735958
$589$	−1.38940e16	−0.0137112
$590$	0	0
$591$	−4.52899e17	−0.437203
$592$	2.82951e18	2.70159
$593$	−8.69033e17	−0.820693	−0.410347	−	0.911930i	$-0.634592\pi$
$593$	−8.69033e17	−0.820693	−0.410347	+	0.911930i	$0.634592\pi$
$594$	−9.65910e17	−0.902245
$595$	0	0
$596$	−1.40718e18	−1.28602
$597$	−1.70286e17	−0.153938
$598$	1.56102e18	1.39589
$599$	−1.94567e18	−1.72105	−0.860527	−	0.509405i	$-0.829866\pi$
$599$	−1.94567e18	−1.72105	−0.860527	+	0.509405i	$0.829866\pi$
$600$	0	0
$601$	2.96725e17	0.256844	0.128422	−	0.991720i	$-0.459009\pi$
$601$	2.96725e17	0.256844	0.128422	+	0.991720i	$0.459009\pi$
$602$	6.88307e16	0.0589393
$603$	4.26392e17	0.361199
$604$	−1.01323e18	−0.849118
$605$	0	0
$606$	1.61999e18	1.32874
$607$	−2.06953e18	−1.67937	−0.839683	−	0.543076i	$-0.817259\pi$
$607$	−2.06953e18	−1.67937	−0.839683	+	0.543076i	$0.817259\pi$
$608$	4.35080e17	0.349298
$609$	3.01058e17	0.239132
$610$	0	0
$611$	−2.22767e17	−0.173214
$612$	−2.52251e18	−1.94066
$613$	−2.27988e18	−1.73548	−0.867738	−	0.497022i	$-0.834427\pi$
$613$	−2.27988e18	−1.73548	−0.867738	+	0.497022i	$0.834427\pi$
$614$	3.05883e18	2.30388
$615$	0	0
$616$	1.74141e18	1.28418
$617$	2.03478e18	1.48479	0.742394	−	0.669964i	$-0.233690\pi$
$617$	2.03478e18	1.48479	0.742394	+	0.669964i	$0.233690\pi$
$618$	1.74300e18	1.25855
$619$	−7.79671e17	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$619$	−7.79671e17	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$620$	0	0
$621$	1.86099e18	1.30211
$622$	4.65383e17	0.322235
$623$	−1.71638e18	−1.17609
$624$	1.19970e18	0.813528
$625$	0	0
$626$	1.83391e18	1.21799
$627$	3.19606e16	0.0210076
$628$	4.15376e18	2.70211
$629$	9.19643e17	0.592093
$630$	0	0
$631$	−1.75763e18	−1.10850	−0.554252	−	0.832349i	$-0.686995\pi$
$631$	−1.75763e18	−1.10850	−0.554252	+	0.832349i	$0.686995\pi$
$632$	1.79128e18	1.11815
$633$	−7.19931e17	−0.444802
$634$	−2.90166e18	−1.77446
$635$	0	0
$636$	−1.61496e18	−0.967588
$637$	−4.39261e17	−0.260505
$638$	1.53587e18	0.901614
$639$	−1.99137e18	−1.15717
$640$	0	0
$641$	2.32621e18	1.32456	0.662279	−	0.749257i	$-0.269589\pi$
$641$	2.32621e18	1.32456	0.662279	+	0.749257i	$0.269589\pi$
$642$	−4.02197e16	−0.0226705
$643$	−2.60316e18	−1.45254	−0.726272	−	0.687408i	$-0.758749\pi$
$643$	−2.60316e18	−1.45254	−0.726272	+	0.687408i	$0.758749\pi$
$644$	−5.22889e18	−2.88836
$645$	0	0
$646$	2.56181e17	0.138687
$647$	1.20524e18	0.645947	0.322974	−	0.946408i	$-0.395318\pi$
$647$	1.20524e18	0.645947	0.322974	+	0.946408i	$0.395318\pi$
$648$	−2.78747e18	−1.47901
$649$	1.85704e18	0.975507
$650$	0	0
$651$	9.62216e16	0.0495446
$652$	−2.07877e18	−1.05974
$653$	−1.72181e18	−0.869061	−0.434531	−	0.900657i	$-0.643086\pi$
$653$	−1.72181e18	−0.869061	−0.434531	+	0.900657i	$0.643086\pi$
$654$	−1.10990e18	−0.554664
$655$	0	0
$656$	−1.16145e18	−0.569018
$657$	2.59957e18	1.26103
$658$	1.01359e18	0.486851
$659$	−3.66491e18	−1.74304	−0.871521	−	0.490358i	$-0.836866\pi$
$659$	−3.66491e18	−1.74304	−0.871521	+	0.490358i	$0.836866\pi$
$660$	0	0
$661$	−3.66523e18	−1.70920	−0.854599	−	0.519289i	$-0.826197\pi$
$661$	−3.66523e18	−1.70920	−0.854599	+	0.519289i	$0.826197\pi$
$662$	−2.48297e18	−1.14655
$663$	3.89925e17	0.178297
$664$	5.19848e18	2.35388
$665$	0	0
$666$	2.35306e18	1.04484
$667$	−2.95911e18	−1.30120
$668$	5.48699e18	2.38939
$669$	6.75448e17	0.291288
$670$	0	0
$671$	1.37246e18	0.580502
$672$	−3.01312e18	−1.26216
$673$	3.60071e18	1.49379	0.746897	−	0.664940i	$-0.231543\pi$
$673$	3.60071e18	1.49379	0.746897	+	0.664940i	$0.231543\pi$
$674$	2.67273e18	1.09816
$675$	0	0
$676$	−5.53173e18	−2.22950
$677$	−1.46169e17	−0.0583484	−0.0291742	−	0.999574i	$-0.509288\pi$
$677$	−1.46169e17	−0.0583484	−0.0291742	+	0.999574i	$0.509288\pi$
$678$	−2.08225e18	−0.823267
$679$	1.61157e18	0.631097
$680$	0	0
$681$	−2.81720e17	−0.108233
$682$	4.90882e17	0.186801
$683$	2.32270e18	0.875505	0.437753	−	0.899095i	$-0.355775\pi$
$683$	2.32270e18	0.875505	0.437753	+	0.899095i	$0.355775\pi$
$684$	4.82558e17	0.180171
$685$	0	0
$686$	5.43883e18	1.99250
$687$	1.82076e18	0.660747
$688$	−5.19946e17	−0.186910
$689$	−9.61786e17	−0.342494
$690$	0	0
$691$	−6.92473e16	−0.0241989	−0.0120994	−	0.999927i	$-0.503851\pi$
$691$	−6.92473e16	−0.0241989	−0.0120994	+	0.999927i	$0.503851\pi$
$692$	−9.37900e18	−3.24688
$693$	8.52769e17	0.292459
$694$	6.82350e17	0.231831
$695$	0	0
$696$	−3.86206e18	−1.28783
$697$	−3.77493e17	−0.124709
$698$	−9.70378e18	−3.17600
$699$	1.17618e17	0.0381393
$700$	0	0
$701$	−6.22383e16	−0.0198103	−0.00990514	−	0.999951i	$-0.503153\pi$
$701$	−6.22383e16	−0.0198103	−0.00990514	+	0.999951i	$0.503153\pi$
$702$	2.25434e18	0.710931
$703$	−1.75928e17	−0.0549700
$704$	−8.02507e18	−2.48443
$705$	0	0
$706$	−8.53637e17	−0.259443
$707$	−3.23169e18	−0.973202
$708$	−7.27757e18	−2.17155
$709$	2.94114e18	0.869592	0.434796	−	0.900529i	$-0.356820\pi$
$709$	2.94114e18	0.869592	0.434796	+	0.900529i	$0.356820\pi$
$710$	0	0
$711$	8.77187e17	0.254648
$712$	2.20182e19	6.33377
$713$	−9.45766e17	−0.269589
$714$	−1.77417e18	−0.501136
$715$	0	0
$716$	−5.43134e18	−1.50651
$717$	2.74220e18	0.753744
$718$	1.00748e19	2.74429
$719$	4.39694e18	1.18690	0.593448	−	0.804872i	$-0.297766\pi$
$719$	4.39694e18	1.18690	0.593448	+	0.804872i	$0.297766\pi$
$720$	0	0
$721$	−3.47708e18	−0.921797
$722$	7.36143e18	1.93406
$723$	1.62598e18	0.423367
$724$	1.23816e19	3.19505
$725$	0	0
$726$	2.35777e18	0.597604
$727$	−6.21513e18	−1.56126	−0.780632	−	0.624991i	$-0.785103\pi$
$727$	−6.21513e18	−1.56126	−0.780632	+	0.624991i	$0.785103\pi$
$728$	−4.06428e18	−1.01188
$729$	1.33103e17	0.0328442
$730$	0	0
$731$	−1.68992e17	−0.0409641
$732$	−5.37855e18	−1.29224
$733$	1.54714e18	0.368429	0.184215	−	0.982886i	$-0.441026\pi$
$733$	1.54714e18	0.368429	0.184215	+	0.982886i	$0.441026\pi$
$734$	−6.13738e18	−1.44863
$735$	0	0
$736$	2.96161e19	6.86786
$737$	1.12632e18	0.258895
$738$	−9.65881e17	−0.220068
$739$	−1.96669e18	−0.444167	−0.222084	−	0.975028i	$-0.571286\pi$
$739$	−1.96669e18	−0.444167	−0.222084	+	0.975028i	$0.571286\pi$
$740$	0	0
$741$	−7.45929e16	−0.0165531
$742$	4.37614e18	0.962644
$743$	5.66492e18	1.23528	0.617641	−	0.786460i	$-0.288088\pi$
$743$	5.66492e18	1.23528	0.617641	+	0.786460i	$0.288088\pi$
$744$	−1.23436e18	−0.266819
$745$	0	0
$746$	−3.78140e18	−0.803249
$747$	2.54570e18	0.536071
$748$	−6.66327e18	−1.39100
$749$	8.02337e16	0.0166045
$750$	0	0
$751$	4.65838e18	0.947491	0.473745	−	0.880662i	$-0.342902\pi$
$751$	4.65838e18	0.947491	0.473745	+	0.880662i	$0.342902\pi$
$752$	−7.65667e18	−1.54392
$753$	2.00658e18	0.401133
$754$	−3.58457e18	−0.710434
$755$	0	0
$756$	−7.55127e18	−1.47105
$757$	3.51348e18	0.678602	0.339301	−	0.940678i	$-0.389810\pi$
$757$	3.51348e18	0.678602	0.339301	+	0.940678i	$0.389810\pi$
$758$	3.35447e18	0.642354
$759$	2.17557e18	0.413049
$760$	0	0
$761$	4.55489e18	0.850116	0.425058	−	0.905166i	$-0.360254\pi$
$761$	4.55489e18	0.850116	0.425058	+	0.905166i	$0.360254\pi$
$762$	3.06228e18	0.566679
$763$	2.21413e18	0.406250
$764$	−5.85286e16	−0.0106478
$765$	0	0
$766$	−1.82232e19	−3.25941
$767$	−4.33414e18	−0.768658
$768$	9.86252e18	1.73436
$769$	5.81779e18	1.01446	0.507232	−	0.861810i	$-0.330669\pi$
$769$	5.81779e18	1.01446	0.507232	+	0.861810i	$0.330669\pi$
$770$	0	0
$771$	4.09513e17	0.0702124
$772$	−2.52598e19	−4.29455
$773$	3.52257e18	0.593871	0.296936	−	0.954897i	$-0.404035\pi$
$773$	3.52257e18	0.593871	0.296936	+	0.954897i	$0.404035\pi$
$774$	−4.32396e17	−0.0722878
$775$	0	0
$776$	−2.06737e19	−3.39873
$777$	1.21838e18	0.198631
$778$	−1.60641e19	−2.59710
$779$	7.22147e16	0.0115780
$780$	0	0
$781$	−5.26023e18	−0.829417
$782$	1.74383e19	2.72685
$783$	−4.27339e18	−0.662706
$784$	−1.50977e19	−2.32197
$785$	0	0
$786$	7.86929e18	1.19039
$787$	−1.48350e18	−0.222562	−0.111281	−	0.993789i	$-0.535495\pi$
$787$	−1.48350e18	−0.222562	−0.111281	+	0.993789i	$0.535495\pi$
$788$	−1.80630e19	−2.68763
$789$	3.67912e18	0.542929
$790$	0	0
$791$	4.15386e18	0.602982
$792$	−1.09396e19	−1.57502
$793$	−3.20318e18	−0.457411
$794$	1.26874e18	0.179697
$795$	0	0
$796$	−6.79153e18	−0.946309
$797$	−3.72381e18	−0.514645	−0.257323	−	0.966326i	$-0.582840\pi$
$797$	−3.72381e18	−0.514645	−0.257323	+	0.966326i	$0.582840\pi$
$798$	3.39399e17	0.0465256
$799$	−2.48856e18	−0.338372
$800$	0	0
$801$	1.07823e19	1.44245
$802$	−1.87851e19	−2.49275
$803$	6.86680e18	0.903865
$804$	−4.41396e18	−0.576320
$805$	0	0
$806$	−1.14567e18	−0.147191
$807$	−6.29794e17	−0.0802639
$808$	4.14570e19	5.24112
$809$	−1.30799e19	−1.64036	−0.820181	−	0.572104i	$-0.806127\pi$
$809$	−1.30799e19	−1.64036	−0.820181	+	0.572104i	$0.806127\pi$
$810$	0	0
$811$	−4.17968e18	−0.515832	−0.257916	−	0.966167i	$-0.583036\pi$
$811$	−4.17968e18	−0.515832	−0.257916	+	0.966167i	$0.583036\pi$
$812$	1.20071e19	1.47002
$813$	9.18274e17	0.111528
$814$	6.21566e18	0.748908
$815$	0	0
$816$	1.34020e19	1.58922
$817$	3.23283e16	0.00380312
$818$	−1.05757e19	−1.23428
$819$	−1.99028e18	−0.230445
$820$	0	0
$821$	5.28864e18	0.602717	0.301358	−	0.953511i	$-0.402560\pi$
$821$	5.28864e18	0.602717	0.301358	+	0.953511i	$0.402560\pi$
$822$	−1.02067e19	−1.15403
$823$	−7.96616e18	−0.893614	−0.446807	−	0.894630i	$-0.647439\pi$
$823$	−7.96616e18	−0.893614	−0.446807	+	0.894630i	$0.647439\pi$
$824$	4.46049e19	4.96428
$825$	0	0
$826$	1.97204e19	2.16046
$827$	1.49178e19	1.62150	0.810752	−	0.585389i	$-0.199058\pi$
$827$	1.49178e19	1.62150	0.810752	+	0.585389i	$0.199058\pi$
$828$	3.28479e19	3.54251
$829$	−8.50781e18	−0.910360	−0.455180	−	0.890399i	$-0.650425\pi$
$829$	−8.50781e18	−0.910360	−0.455180	+	0.890399i	$0.650425\pi$
$830$	0	0
$831$	3.96308e17	0.0417471
$832$	1.87297e19	1.95763
$833$	−4.90704e18	−0.508894
$834$	−1.43937e19	−1.48113
$835$	0	0
$836$	1.27469e18	0.129141
$837$	−1.36582e18	−0.137303
$838$	−2.15921e19	−2.15382
$839$	−6.82788e18	−0.675823	−0.337912	−	0.941178i	$-0.609720\pi$
$839$	−6.82788e18	−0.675823	−0.337912	+	0.941178i	$0.609720\pi$
$840$	0	0
$841$	−3.46561e18	−0.337758
$842$	2.10593e19	2.03664
$843$	1.26527e18	0.121424
$844$	−2.87130e19	−2.73434
$845$	0	0
$846$	−6.36741e18	−0.597112
$847$	−4.70348e18	−0.437701
$848$	−3.30573e19	−3.05277
$849$	−4.97315e18	−0.455755
$850$	0	0
$851$	−1.19755e19	−1.08082
$852$	2.06144e19	1.84634
$853$	−6.17395e18	−0.548775	−0.274387	−	0.961619i	$-0.588475\pi$
$853$	−6.17395e18	−0.548775	−0.274387	+	0.961619i	$0.588475\pi$
$854$	1.45745e19	1.28564
$855$	0	0
$856$	−1.02926e18	−0.0894224
$857$	−1.69937e18	−0.146525	−0.0732625	−	0.997313i	$-0.523341\pi$
$857$	−1.69937e18	−0.146525	−0.0732625	+	0.997313i	$0.523341\pi$
$858$	2.63542e18	0.225518
$859$	3.92966e18	0.333734	0.166867	−	0.985979i	$-0.446635\pi$
$859$	3.92966e18	0.333734	0.166867	+	0.985979i	$0.446635\pi$
$860$	0	0
$861$	−5.00118e17	−0.0418362
$862$	5.61118e18	0.465862
$863$	−6.77611e18	−0.558354	−0.279177	−	0.960240i	$-0.590062\pi$
$863$	−6.77611e18	−0.558354	−0.279177	+	0.960240i	$0.590062\pi$
$864$	4.27699e19	3.49783
$865$	0	0
$866$	2.20006e18	0.177243
$867$	−1.32125e18	−0.105648
$868$	3.83761e18	0.304567
$869$	2.31711e18	0.182523
$870$	0	0
$871$	−2.62872e18	−0.203998
$872$	−2.84035e19	−2.18783
$873$	−1.01239e19	−0.774026
$874$	−3.33597e18	−0.253161
$875$	0	0
$876$	−2.69104e19	−2.01207
$877$	−1.66517e19	−1.23583	−0.617917	−	0.786243i	$-0.712023\pi$
$877$	−1.66517e19	−1.23583	−0.617917	+	0.786243i	$0.712023\pi$
$878$	4.56183e19	3.36066
$879$	4.47855e18	0.327499
$880$	0	0
$881$	1.72426e19	1.24239	0.621195	−	0.783656i	$-0.286647\pi$
$881$	1.72426e19	1.24239	0.621195	+	0.783656i	$0.286647\pi$
$882$	−1.25555e19	−0.898024
$883$	−3.03788e18	−0.215688	−0.107844	−	0.994168i	$-0.534395\pi$
$883$	−3.03788e18	−0.215688	−0.107844	+	0.994168i	$0.534395\pi$
$884$	1.55514e19	1.09605
$885$	0	0
$886$	2.71099e19	1.88282
$887$	−6.51405e18	−0.449105	−0.224552	−	0.974462i	$-0.572092\pi$
$887$	−6.51405e18	−0.449105	−0.224552	+	0.974462i	$0.572092\pi$
$888$	−1.56297e19	−1.06971
$889$	−6.10889e18	−0.415050
$890$	0	0
$891$	−3.60573e18	−0.241428
$892$	2.69389e19	1.79064
$893$	4.76063e17	0.0314145
$894$	6.21740e18	0.407301
$895$	0	0
$896$	−4.21568e19	−2.72186
$897$	−5.07757e18	−0.325465
$898$	1.59104e19	1.01248
$899$	2.17177e18	0.137207
$900$	0	0
$901$	−1.07442e19	−0.669059
$902$	−2.55139e18	−0.157737
$903$	−2.23888e17	−0.0137423
$904$	−5.32868e19	−3.24732
$905$	0	0
$906$	4.47680e18	0.268927
$907$	2.62324e19	1.56455	0.782277	−	0.622931i	$-0.214058\pi$
$907$	2.62324e19	1.56455	0.782277	+	0.622931i	$0.214058\pi$
$908$	−1.12358e19	−0.665345
$909$	2.03015e19	1.19361
$910$	0	0
$911$	−9.93847e18	−0.576037	−0.288018	−	0.957625i	$-0.592996\pi$
$911$	−9.93847e18	−0.576037	−0.288018	+	0.957625i	$0.592996\pi$
$912$	−2.56381e18	−0.147543
$913$	6.72450e18	0.384238
$914$	−1.72453e19	−0.978411
$915$	0	0
$916$	7.26176e19	4.06182
$917$	−1.56983e19	−0.871872
$918$	2.51835e19	1.38880
$919$	1.61779e19	0.885874	0.442937	−	0.896553i	$-0.353937\pi$
$919$	1.61779e19	0.885874	0.442937	+	0.896553i	$0.353937\pi$
$920$	0	0
$921$	−9.94953e18	−0.537174
$922$	−3.66778e19	−1.96631
$923$	1.22768e19	0.653545
$924$	−8.82776e18	−0.466641
$925$	0	0
$926$	−4.31419e19	−2.24868
$927$	2.18430e19	1.13056
$928$	−6.80074e19	−3.49538
$929$	2.14431e18	0.109442	0.0547211	−	0.998502i	$-0.482573\pi$
$929$	2.14431e18	0.109442	0.0547211	+	0.998502i	$0.482573\pi$
$930$	0	0
$931$	9.38720e17	0.0472458
$932$	4.69097e18	0.234455
$933$	−1.51376e18	−0.0751325
$934$	6.24514e19	3.07813
$935$	0	0
$936$	2.55318e19	1.24105
$937$	3.39502e19	1.63883	0.819417	−	0.573199i	$-0.194298\pi$
$937$	3.39502e19	1.63883	0.819417	+	0.573199i	$0.194298\pi$
$938$	1.19607e19	0.573376
$939$	−5.96521e18	−0.283988
$940$	0	0
$941$	−1.95970e19	−0.920149	−0.460074	−	0.887880i	$-0.652177\pi$
$941$	−1.95970e19	−0.920149	−0.460074	+	0.887880i	$0.652177\pi$
$942$	−1.83527e19	−0.855794
$943$	4.91568e18	0.227645
$944$	−1.48968e20	−6.85131
$945$	0	0
$946$	−1.14218e18	−0.0518134
$947$	1.67818e19	0.756072	0.378036	−	0.925791i	$-0.376600\pi$
$947$	1.67818e19	0.756072	0.378036	+	0.925791i	$0.376600\pi$
$948$	−9.08054e18	−0.406310
$949$	−1.60264e19	−0.712207
$950$	0	0
$951$	9.43831e18	0.413734
$952$	−4.54026e19	−1.97670
$953$	−9.68702e18	−0.418877	−0.209438	−	0.977822i	$-0.567164\pi$
$953$	−9.68702e18	−0.418877	−0.209438	+	0.977822i	$0.567164\pi$
$954$	−2.74910e19	−1.18066
$955$	0	0
$956$	1.09367e20	4.63351
$957$	−4.99577e18	−0.210221
$958$	2.71445e19	1.13450
$959$	2.03611e19	0.845241
$960$	0	0
$961$	−2.37234e19	−0.971573
$962$	−1.45067e19	−0.590108
$963$	−5.04029e17	−0.0203650
$964$	6.48492e19	2.60258
$965$	0	0
$966$	2.31030e19	0.914781
$967$	−2.34907e18	−0.0923899	−0.0461949	−	0.998932i	$-0.514710\pi$
$967$	−2.34907e18	−0.0923899	−0.0461949	+	0.998932i	$0.514710\pi$
$968$	6.03376e19	2.35721
$969$	−8.33287e17	−0.0323363
$970$	0	0
$971$	2.00271e19	0.766818	0.383409	−	0.923579i	$-0.374750\pi$
$971$	2.00271e19	0.766818	0.383409	+	0.923579i	$0.374750\pi$
$972$	7.38803e19	2.80995
$973$	2.87138e19	1.08482
$974$	3.72349e19	1.39739
$975$	0	0
$976$	−1.10096e20	−4.07706
$977$	−3.98189e19	−1.46479	−0.732394	−	0.680881i	$-0.761597\pi$
$977$	−3.98189e19	−1.46479	−0.732394	+	0.680881i	$0.761597\pi$
$978$	9.18473e18	0.335633
$979$	2.84817e19	1.03390
$980$	0	0
$981$	−1.39092e19	−0.498257
$982$	−4.60760e19	−1.63965
$983$	−2.29985e19	−0.813022	−0.406511	−	0.913646i	$-0.633255\pi$
$983$	−2.29985e19	−0.813022	−0.406511	+	0.913646i	$0.633255\pi$
$984$	6.41566e18	0.225306
$985$	0	0
$986$	−4.00437e19	−1.38782
$987$	−3.29695e18	−0.113514
$988$	−2.97499e18	−0.101757
$989$	2.20060e18	0.0747765
$990$	0	0
$991$	8.09114e18	0.271351	0.135675	−	0.990753i	$-0.456680\pi$
$991$	8.09114e18	0.271351	0.135675	+	0.990753i	$0.456680\pi$
$992$	−2.17360e19	−0.724191
$993$	8.07642e18	0.267331
$994$	−5.58598e19	−1.83691
$995$	0	0
$996$	−2.63527e19	−0.855342
$997$	2.26704e19	0.731039	0.365519	−	0.930804i	$-0.380891\pi$
$997$	2.26704e19	0.731039	0.365519	+	0.930804i	$0.380891\pi$
$998$	−6.82883e19	−2.18775
$999$	−1.72944e19	−0.550464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.a.b.1.1		3
5.2	odd	4		25.14.b.b.24.1		6
5.3	odd	4		25.14.b.b.24.6		6
5.4	even	2		5.14.a.b.1.3	✓	3
15.14	odd	2		45.14.a.e.1.1		3
20.19	odd	2		80.14.a.g.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.14.a.b.1.3	✓	3	5.4	even	2
25.14.a.b.1.1		3	1.1	even	1	trivial
25.14.b.b.24.1		6	5.2	odd	4
25.14.b.b.24.6		6	5.3	odd	4
45.14.a.e.1.1		3	15.14	odd	2
80.14.a.g.1.2		3	20.19	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-176.217 q^{2} +573.185 q^{3} +22860.4 q^{4} -101005. q^{6} +201493. q^{7} -2.58481e6 q^{8} -1.26578e6 q^{9} -3.34359e6 q^{11} +1.31032e7 q^{12} +7.80359e6 q^{13} -3.55065e7 q^{14} +2.68215e8 q^{16} +8.71750e7 q^{17} +2.23052e8 q^{18} -1.66766e7 q^{19} +1.15493e8 q^{21} +5.89196e8 q^{22} -1.13518e9 q^{23} -1.48158e9 q^{24} -1.37512e9 q^{26} -1.63937e9 q^{27} +4.60620e9 q^{28} +2.60673e9 q^{29} +8.33139e8 q^{31} -2.60892e10 q^{32} -1.91649e9 q^{33} -1.53617e10 q^{34} -2.89362e10 q^{36} +1.05494e10 q^{37} +2.93870e9 q^{38} +4.47290e9 q^{39} -4.33030e9 q^{41} -2.03518e10 q^{42} -1.93854e9 q^{43} -7.64356e10 q^{44} +2.00038e11 q^{46} -2.85468e10 q^{47} +1.53737e11 q^{48} -5.62896e10 q^{49} +4.99674e10 q^{51} +1.78393e11 q^{52} -1.23249e11 q^{53} +2.88884e11 q^{54} -5.20821e11 q^{56} -9.55879e9 q^{57} -4.59349e11 q^{58} -5.55404e11 q^{59} -4.10476e11 q^{61} -1.46813e11 q^{62} -2.55046e11 q^{63} +2.40014e12 q^{64} +3.37718e11 q^{66} -3.36861e11 q^{67} +1.99285e12 q^{68} -6.50671e11 q^{69} +1.57323e12 q^{71} +3.27181e12 q^{72} -2.05372e12 q^{73} -1.85898e12 q^{74} -3.81234e11 q^{76} -6.73709e11 q^{77} -7.88201e11 q^{78} -6.93000e11 q^{79} +1.07840e12 q^{81} +7.63071e11 q^{82} -2.01116e12 q^{83} +2.64021e12 q^{84} +3.41604e11 q^{86} +1.49414e12 q^{87} +8.64253e12 q^{88} -8.51832e12 q^{89} +1.57237e12 q^{91} -2.59507e13 q^{92} +4.77543e11 q^{93} +5.03042e12 q^{94} -1.49540e13 q^{96} +7.99814e12 q^{97} +9.91916e12 q^{98} +4.23225e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 142 q^{2} - 416 q^{3} + 17876 q^{4} + 120376 q^{6} - 448292 q^{7} - 2580360 q^{8} + 1286119 q^{9} - 6604004 q^{11} + 23722448 q^{12} + 33501974 q^{13} - 46562928 q^{14} + 199912208 q^{16} - 83129542 q^{17}+ \cdots + 126787366508 q^{99}+O(q^{100}) \) 3 * q - 142 * q^2 - 416 * q^3 + 17876 * q^4 + 120376 * q^6 - 448292 * q^7 - 2580360 * q^8 + 1286119 * q^9 - 6604004 * q^11 + 23722448 * q^12 + 33501974 * q^13 - 46562928 * q^14 + 199912208 * q^16 - 83129542 * q^17 + 30983914 * q^18 + 97491100 * q^19 + 438200736 * q^21 + 530907256 * q^22 - 316255836 * q^23 - 3890359200 * q^24 - 3746814044 * q^26 - 6518951360 * q^27 + 6227646976 * q^28 + 2236171850 * q^29 + 7482994376 * q^31 - 32169857312 * q^32 - 359182912 * q^33 - 30236073988 * q^34 - 43361833852 * q^36 - 31447174242 * q^37 + 42518132360 * q^38 - 70188571072 * q^39 - 10752884434 * q^41 - 92283853824 * q^42 - 16930554856 * q^43 - 68395825168 * q^44 + 246828204336 * q^46 - 31934201692 * q^47 + 80078828864 * q^48 - 38956926629 * q^49 - 129369882944 * q^51 + 18152597928 * q^52 + 221149123934 * q^53 + 246121937200 * q^54 - 522876451200 * q^56 + 763110695680 * q^57 - 854269976260 * q^58 - 55436423900 * q^59 + 496161392746 * q^61 + 598069940736 * q^62 - 1085454385236 * q^63 + 3297565494336 * q^64 - 22883875168 * q^66 - 459297824792 * q^67 + 2008021178776 * q^68 - 333379292832 * q^69 + 521997878336 * q^71 + 5658040941720 * q^72 - 2505025571086 * q^73 - 2418323586508 * q^74 + 621688050000 * q^76 + 385562457456 * q^77 + 2386950332528 * q^78 + 2990636883200 * q^79 + 320549052763 * q^81 - 5784848206924 * q^82 - 5137135467696 * q^83 - 814234130688 * q^84 + 2343313645096 * q^86 - 6885420178880 * q^87 + 8660607864480 * q^88 - 19423025958450 * q^89 - 6792522370184 * q^91 - 26870022340992 * q^92 + 11095902136128 * q^93 - 7003557875968 * q^94 - 2208331214464 * q^96 + 11088325396458 * q^97 + 10176508990306 * q^98 + 126787366508 * q^99

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