LMFDB - Embedded newform 75.14.a.g.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,14,Mod(1,75)] 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("75.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	75.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-52] 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:	$80.4231967139$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1651x^{2} + 4960x + 346125 $ x^4 - x^3 - 1651x^2 + 4960x + 346125
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-38.8667$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+143.467 q^{2} -729.000 q^{3} +12390.7 q^{4} -104587. q^{6} +115746. q^{7} +602380. q^{8} +531441. q^{9} -1.68912e6 q^{11} -9.03285e6 q^{12} -8.38266e6 q^{13} +1.66058e7 q^{14} -1.50834e7 q^{16} -1.18185e8 q^{17} +7.62442e7 q^{18} +2.93887e6 q^{19} -8.43791e7 q^{21} -2.42333e8 q^{22} +1.14328e9 q^{23} -4.39135e8 q^{24} -1.20263e9 q^{26} -3.87420e8 q^{27} +1.43418e9 q^{28} -2.58117e9 q^{29} -5.28510e9 q^{31} -7.09866e9 q^{32} +1.23137e9 q^{33} -1.69556e10 q^{34} +6.58495e9 q^{36} -2.25904e9 q^{37} +4.21631e8 q^{38} +6.11096e9 q^{39} +3.08318e10 q^{41} -1.21056e10 q^{42} -1.84280e10 q^{43} -2.09294e10 q^{44} +1.64023e11 q^{46} -8.91497e10 q^{47} +1.09958e10 q^{48} -8.34918e10 q^{49} +8.61570e10 q^{51} -1.03867e11 q^{52} -2.29652e11 q^{53} -5.55820e10 q^{54} +6.97232e10 q^{56} -2.14244e9 q^{57} -3.70312e11 q^{58} -1.48583e11 q^{59} -8.88553e10 q^{61} -7.58237e11 q^{62} +6.15124e10 q^{63} -8.94860e11 q^{64} +1.76661e11 q^{66} -1.15668e12 q^{67} -1.46440e12 q^{68} -8.33451e11 q^{69} -1.39371e12 q^{71} +3.20129e11 q^{72} +2.23868e12 q^{73} -3.24097e11 q^{74} +3.64148e10 q^{76} -1.95509e11 q^{77} +8.76720e11 q^{78} +4.29509e11 q^{79} +2.82430e11 q^{81} +4.42335e12 q^{82} -4.77368e12 q^{83} -1.04552e12 q^{84} -2.64380e12 q^{86} +1.88167e12 q^{87} -1.01749e12 q^{88} +4.52557e12 q^{89} -9.70262e11 q^{91} +1.41661e13 q^{92} +3.85284e12 q^{93} -1.27900e13 q^{94} +5.17493e12 q^{96} +1.54548e13 q^{97} -1.19783e13 q^{98} -8.97667e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 52 q^{2} - 2916 q^{3} + 20752 q^{4} + 37908 q^{6} + 298996 q^{7} - 423936 q^{8} + 2125764 q^{9} - 5874104 q^{11} - 15128208 q^{12} + 32044972 q^{13} - 64322292 q^{14} + 6196480 q^{16} - 67409368 q^{17}+ \cdots - 3121739703864 q^{99}+O(q^{100}) $ 4 * q - 52 * q^2 - 2916 * q^3 + 20752 * q^4 + 37908 * q^6 + 298996 * q^7 - 423936 * q^8 + 2125764 * q^9 - 5874104 * q^11 - 15128208 * q^12 + 32044972 * q^13 - 64322292 * q^14 + 6196480 * q^16 - 67409368 * q^17 - 27634932 * q^18 - 203930812 * q^19 - 217968084 * q^21 + 42656424 * q^22 + 577045608 * q^23 + 309049344 * q^24 - 3541675772 * q^26 - 1549681956 * q^27 + 11813256592 * q^28 - 8505376264 * q^29 - 2055088276 * q^31 - 1166925824 * q^32 + 4282221816 * q^33 - 5970330456 * q^34 + 11028463632 * q^36 + 15264235096 * q^37 + 50700107708 * q^38 - 23360784588 * q^39 + 33629458544 * q^41 + 46890950868 * q^42 - 12357161900 * q^43 - 7081880224 * q^44 + 135531435624 * q^46 + 94931088680 * q^47 - 4517233920 * q^48 + 15736414920 * q^49 + 49141429272 * q^51 + 265908970672 * q^52 - 334308021952 * q^53 + 20145865428 * q^54 - 609811407360 * q^56 + 148665561948 * q^57 - 47213104104 * q^58 + 361880587432 * q^59 - 360973874260 * q^61 - 236543379468 * q^62 + 158898733236 * q^63 - 875219197952 * q^64 - 31096533096 * q^66 - 66061390268 * q^67 - 3236755082144 * q^68 - 420666248232 * q^69 - 3883894237072 * q^71 - 225296971776 * q^72 - 825246053672 * q^73 - 2346427881112 * q^74 - 4343041077808 * q^76 + 897635955432 * q^77 + 2581881637788 * q^78 - 6040507323040 * q^79 + 1129718145924 * q^81 + 9720027045792 * q^82 - 7040089644456 * q^83 - 8611864055568 * q^84 + 3656045115916 * q^86 + 6200419296456 * q^87 - 4806631036416 * q^88 - 4255523514432 * q^89 + 15423506586364 * q^91 + 12929237479776 * q^92 + 1498159353204 * q^93 - 40012092718728 * q^94 + 850688925696 * q^96 + 17383619164252 * q^97 - 43175578697672 * q^98 - 3121739703864 * 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 $

$2$	143.467	1.58510	0.792550	−	0.609807i	$-0.208753\pi$
$2$	143.467	1.58510	0.792550	+	0.609807i	$0.208753\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	12390.7	1.51254
$5$	0	0
$5$	0	0
$6$	−104587.	−0.915158
$7$	115746.	0.371852	0.185926	−	0.982564i	$-0.440472\pi$
$7$	115746.	0.371852	0.185926	+	0.982564i	$0.440472\pi$
$8$	602380.	0.812429
$9$	531441.	0.333333
$10$	0	0
$11$	−1.68912e6	−0.287480	−0.143740	−	0.989615i	$-0.545913\pi$
$11$	−1.68912e6	−0.287480	−0.143740	+	0.989615i	$0.545913\pi$
$12$	−9.03285e6	−0.873266
$13$	−8.38266e6	−0.481670	−0.240835	−	0.970566i	$-0.577421\pi$
$13$	−8.38266e6	−0.481670	−0.240835	+	0.970566i	$0.577421\pi$
$14$	1.66058e7	0.589422
$15$	0	0
$16$	−1.50834e7	−0.224760
$17$	−1.18185e8	−1.18753	−0.593765	−	0.804638i	$-0.702359\pi$
$17$	−1.18185e8	−1.18753	−0.593765	+	0.804638i	$0.702359\pi$
$18$	7.62442e7	0.528367
$19$	2.93887e6	0.0143312	0.00716560	−	0.999974i	$-0.497719\pi$
$19$	2.93887e6	0.0143312	0.00716560	+	0.999974i	$0.497719\pi$
$20$	0	0
$21$	−8.43791e7	−0.214689
$22$	−2.42333e8	−0.455685
$23$	1.14328e9	1.61036	0.805178	−	0.593033i	$-0.202070\pi$
$23$	1.14328e9	1.61036	0.805178	+	0.593033i	$0.202070\pi$
$24$	−4.39135e8	−0.469056
$25$	0	0
$26$	−1.20263e9	−0.763496
$27$	−3.87420e8	−0.192450
$28$	1.43418e9	0.562441
$29$	−2.58117e9	−0.805804	−0.402902	−	0.915243i	$-0.631998\pi$
$29$	−2.58117e9	−0.805804	−0.402902	+	0.915243i	$0.631998\pi$
$30$	0	0
$31$	−5.28510e9	−1.06955	−0.534776	−	0.844994i	$-0.679604\pi$
$31$	−5.28510e9	−1.06955	−0.534776	+	0.844994i	$0.679604\pi$
$32$	−7.09866e9	−1.16870
$33$	1.23137e9	0.165977
$34$	−1.69556e10	−1.88235
$35$	0	0
$36$	6.58495e9	0.504180
$37$	−2.25904e9	−0.144748	−0.0723740	−	0.997378i	$-0.523058\pi$
$37$	−2.25904e9	−0.144748	−0.0723740	+	0.997378i	$0.523058\pi$
$38$	4.21631e8	0.0227164
$39$	6.11096e9	0.278093
$40$	0	0
$41$	3.08318e10	1.01369	0.506844	−	0.862038i	$-0.330812\pi$
$41$	3.08318e10	1.01369	0.506844	+	0.862038i	$0.330812\pi$
$42$	−1.21056e10	−0.340303
$43$	−1.84280e10	−0.444562	−0.222281	−	0.974983i	$-0.571350\pi$
$43$	−1.84280e10	−0.444562	−0.222281	+	0.974983i	$0.571350\pi$
$44$	−2.09294e10	−0.434826
$45$	0	0
$46$	1.64023e11	2.55257
$47$	−8.91497e10	−1.20638	−0.603190	−	0.797598i	$-0.706104\pi$
$47$	−8.91497e10	−1.20638	−0.603190	+	0.797598i	$0.706104\pi$
$48$	1.09958e10	0.129765
$49$	−8.34918e10	−0.861726
$50$	0	0
$51$	8.61570e10	0.685621
$52$	−1.03867e11	−0.728546
$53$	−2.29652e11	−1.42324	−0.711618	−	0.702567i	$-0.752037\pi$
$53$	−2.29652e11	−1.42324	−0.711618	+	0.702567i	$0.752037\pi$
$54$	−5.55820e10	−0.305053
$55$	0	0
$56$	6.97232e10	0.302103
$57$	−2.14244e9	−0.00827412
$58$	−3.70312e11	−1.27728
$59$	−1.48583e11	−0.458596	−0.229298	−	0.973356i	$-0.573643\pi$
$59$	−1.48583e11	−0.458596	−0.229298	+	0.973356i	$0.573643\pi$
$60$	0	0
$61$	−8.88553e10	−0.220821	−0.110410	−	0.993886i	$-0.535216\pi$
$61$	−8.88553e10	−0.220821	−0.110410	+	0.993886i	$0.535216\pi$
$62$	−7.58237e11	−1.69535
$63$	6.15124e10	0.123951
$64$	−8.94860e11	−1.62774
$65$	0	0
$66$	1.76661e11	0.263090
$67$	−1.15668e12	−1.56217	−0.781085	−	0.624425i	$-0.785333\pi$
$67$	−1.15668e12	−1.56217	−0.781085	+	0.624425i	$0.785333\pi$
$68$	−1.46440e12	−1.79619
$69$	−8.33451e11	−0.929739
$70$	0	0
$71$	−1.39371e12	−1.29120	−0.645601	−	0.763675i	$-0.723393\pi$
$71$	−1.39371e12	−1.29120	−0.645601	+	0.763675i	$0.723393\pi$
$72$	3.20129e11	0.270810
$73$	2.23868e12	1.73138	0.865691	−	0.500578i	$-0.166879\pi$
$73$	2.23868e12	1.73138	0.865691	+	0.500578i	$0.166879\pi$
$74$	−3.24097e11	−0.229440
$75$	0	0
$76$	3.64148e10	0.0216765
$77$	−1.95509e11	−0.106900
$78$	8.76720e11	0.440804
$79$	4.29509e11	0.198791	0.0993953	−	0.995048i	$-0.468309\pi$
$79$	4.29509e11	0.198791	0.0993953	+	0.995048i	$0.468309\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	4.42335e12	1.60680
$83$	−4.77368e12	−1.60267	−0.801337	−	0.598213i	$-0.795878\pi$
$83$	−4.77368e12	−1.60267	−0.801337	+	0.598213i	$0.795878\pi$
$84$	−1.04552e12	−0.324726
$85$	0	0
$86$	−2.64380e12	−0.704676
$87$	1.88167e12	0.465231
$88$	−1.01749e12	−0.233557
$89$	4.52557e12	0.965246	0.482623	−	0.875828i	$-0.339684\pi$
$89$	4.52557e12	0.965246	0.482623	+	0.875828i	$0.339684\pi$
$90$	0	0
$91$	−9.70262e11	−0.179110
$92$	1.41661e13	2.43573
$93$	3.85284e12	0.617507
$94$	−1.27900e13	−1.91223
$95$	0	0
$96$	5.17493e12	0.674747
$97$	1.54548e13	1.88385	0.941925	−	0.335822i	$-0.109014\pi$
$97$	1.54548e13	1.88385	0.941925	+	0.335822i	$0.109014\pi$
$98$	−1.19783e13	−1.36592
$99$	−8.97667e11	−0.0958267
$100$	0	0
$101$	−4.38671e12	−0.411197	−0.205599	−	0.978636i	$-0.565914\pi$
$101$	−4.38671e12	−0.411197	−0.205599	+	0.978636i	$0.565914\pi$
$102$	1.23607e13	1.08678
$103$	9.72298e12	0.802338	0.401169	−	0.916004i	$-0.368604\pi$
$103$	9.72298e12	0.802338	0.401169	+	0.916004i	$0.368604\pi$
$104$	−5.04954e12	−0.391323
$105$	0	0
$106$	−3.29474e13	−2.25597
$107$	7.70349e12	0.496241	0.248121	−	0.968729i	$-0.420187\pi$
$107$	7.70349e12	0.496241	0.248121	+	0.968729i	$0.420187\pi$
$108$	−4.80043e12	−0.291089
$109$	−1.04685e13	−0.597877	−0.298938	−	0.954272i	$-0.596633\pi$
$109$	−1.04685e13	−0.597877	−0.298938	+	0.954272i	$0.596633\pi$
$110$	0	0
$111$	1.64684e12	0.0835703
$112$	−1.74585e12	−0.0835776
$113$	5.48831e12	0.247987	0.123993	−	0.992283i	$-0.460430\pi$
$113$	5.48831e12	0.247987	0.123993	+	0.992283i	$0.460430\pi$
$114$	−3.07369e11	−0.0131153
$115$	0	0
$116$	−3.19826e13	−1.21881
$117$	−4.45489e12	−0.160557
$118$	−2.13167e13	−0.726920
$119$	−1.36795e13	−0.441586
$120$	0	0
$121$	−3.16696e13	−0.917355
$122$	−1.27478e13	−0.350023
$123$	−2.24764e13	−0.585253
$124$	−6.54863e13	−1.61774
$125$	0	0
$126$	8.82498e12	0.196474
$127$	−3.76054e13	−0.795291	−0.397645	−	0.917539i	$-0.630173\pi$
$127$	−3.76054e13	−0.795291	−0.397645	+	0.917539i	$0.630173\pi$
$128$	−7.02304e13	−1.41143
$129$	1.34340e13	0.256668
$130$	0	0
$131$	9.13894e13	1.57991	0.789955	−	0.613165i	$-0.210104\pi$
$131$	9.13894e13	1.57991	0.789955	+	0.613165i	$0.210104\pi$
$132$	1.52576e13	0.251047
$133$	3.40164e11	0.00532909
$134$	−1.65946e14	−2.47620
$135$	0	0
$136$	−7.11923e13	−0.964784
$137$	8.99178e13	1.16188	0.580941	−	0.813946i	$-0.302685\pi$
$137$	8.99178e13	1.16188	0.580941	+	0.813946i	$0.302685\pi$
$138$	−1.19573e14	−1.47373
$139$	−3.27383e13	−0.384999	−0.192499	−	0.981297i	$-0.561659\pi$
$139$	−3.27383e13	−0.384999	−0.192499	+	0.981297i	$0.561659\pi$
$140$	0	0
$141$	6.49901e13	0.696503
$142$	−1.99952e14	−2.04668
$143$	1.41593e13	0.138471
$144$	−8.01595e12	−0.0749201
$145$	0	0
$146$	3.21176e14	2.74441
$147$	6.08655e13	0.497518
$148$	−2.79912e13	−0.218937
$149$	−5.86656e13	−0.439211	−0.219605	−	0.975589i	$-0.570477\pi$
$149$	−5.86656e13	−0.439211	−0.219605	+	0.975589i	$0.570477\pi$
$150$	0	0
$151$	−9.17724e13	−0.630031	−0.315015	−	0.949087i	$-0.602010\pi$
$151$	−9.17724e13	−0.630031	−0.315015	+	0.949087i	$0.602010\pi$
$152$	1.77032e12	0.0116431
$153$	−6.28084e13	−0.395844
$154$	−2.80491e13	−0.169447
$155$	0	0
$156$	7.57193e13	0.420626
$157$	−9.62156e13	−0.512741	−0.256370	−	0.966579i	$-0.582527\pi$
$157$	−9.62156e13	−0.512741	−0.256370	+	0.966579i	$0.582527\pi$
$158$	6.16202e13	0.315103
$159$	1.67416e14	0.821705
$160$	0	0
$161$	1.32331e14	0.598814
$162$	4.05193e13	0.176122
$163$	3.61390e14	1.50923	0.754617	−	0.656166i	$-0.227823\pi$
$163$	3.61390e14	1.50923	0.754617	+	0.656166i	$0.227823\pi$
$164$	3.82029e14	1.53324
$165$	0	0
$166$	−6.84864e14	−2.54040
$167$	1.39666e14	0.498234	0.249117	−	0.968473i	$-0.419860\pi$
$167$	1.39666e14	0.498234	0.249117	+	0.968473i	$0.419860\pi$
$168$	−5.08282e13	−0.174419
$169$	−2.32606e14	−0.767994
$170$	0	0
$171$	1.56184e12	0.00477707
$172$	−2.28336e14	−0.672419
$173$	4.50349e14	1.27717	0.638586	−	0.769551i	$-0.279520\pi$
$173$	4.50349e14	1.27717	0.638586	+	0.769551i	$0.279520\pi$
$174$	2.69958e14	0.737438
$175$	0	0
$176$	2.54777e13	0.0646142
$177$	1.08317e14	0.264770
$178$	6.49269e14	1.53001
$179$	−4.63543e13	−0.105328	−0.0526642	−	0.998612i	$-0.516771\pi$
$179$	−4.63543e13	−0.105328	−0.0526642	+	0.998612i	$0.516771\pi$
$180$	0	0
$181$	−5.73683e14	−1.21272	−0.606361	−	0.795189i	$-0.707371\pi$
$181$	−5.73683e14	−1.21272	−0.606361	+	0.795189i	$0.707371\pi$
$182$	−1.39200e14	−0.283907
$183$	6.47755e13	0.127491
$184$	6.88689e14	1.30830
$185$	0	0
$186$	5.52755e14	0.978810
$187$	1.99629e14	0.341392
$188$	−1.10463e15	−1.82470
$189$	−4.48425e13	−0.0715629
$190$	0	0
$191$	−2.45056e14	−0.365214	−0.182607	−	0.983186i	$-0.558454\pi$
$191$	−2.45056e14	−0.365214	−0.182607	+	0.983186i	$0.558454\pi$
$192$	6.52353e14	0.939776
$193$	1.07891e15	1.50267	0.751335	−	0.659921i	$-0.229410\pi$
$193$	1.07891e15	1.50267	0.751335	+	0.659921i	$0.229410\pi$
$194$	2.21725e15	2.98609
$195$	0	0
$196$	−1.03452e15	−1.30340
$197$	5.37451e14	0.655101	0.327550	−	0.944834i	$-0.393777\pi$
$197$	5.37451e14	0.655101	0.327550	+	0.944834i	$0.393777\pi$
$198$	−1.28786e14	−0.151895
$199$	4.43570e14	0.506310	0.253155	−	0.967426i	$-0.418532\pi$
$199$	4.43570e14	0.506310	0.253155	+	0.967426i	$0.418532\pi$
$200$	0	0
$201$	8.43222e14	0.901919
$202$	−6.29348e14	−0.651789
$203$	−2.98761e14	−0.299640
$204$	1.06755e15	1.03703
$205$	0	0
$206$	1.39492e15	1.27179
$207$	6.07586e14	0.536785
$208$	1.26439e14	0.108260
$209$	−4.96411e12	−0.00411994
$210$	0	0
$211$	1.83905e15	1.43469	0.717345	−	0.696718i	$-0.245357\pi$
$211$	1.83905e15	1.43469	0.717345	+	0.696718i	$0.245357\pi$
$212$	−2.84555e15	−2.15270
$213$	1.01602e15	0.745475
$214$	1.10519e15	0.786592
$215$	0	0
$216$	−2.33374e14	−0.156352
$217$	−6.11731e14	−0.397715
$218$	−1.50188e15	−0.947695
$219$	−1.63200e15	−0.999614
$220$	0	0
$221$	9.90706e14	0.571999
$222$	2.36267e14	0.132467
$223$	2.71677e15	1.47935	0.739676	−	0.672963i	$-0.234979\pi$
$223$	2.71677e15	1.47935	0.739676	+	0.672963i	$0.234979\pi$
$224$	−8.21644e14	−0.434582
$225$	0	0
$226$	7.87390e14	0.393084
$227$	−1.47916e15	−0.717542	−0.358771	−	0.933426i	$-0.616804\pi$
$227$	−1.47916e15	−0.717542	−0.358771	+	0.933426i	$0.616804\pi$
$228$	−2.65464e13	−0.0125150
$229$	−3.13274e15	−1.43547	−0.717735	−	0.696316i	$-0.754821\pi$
$229$	−3.13274e15	−1.43547	−0.717735	+	0.696316i	$0.754821\pi$
$230$	0	0
$231$	1.42526e14	0.0617188
$232$	−1.55484e15	−0.654658
$233$	2.51709e14	0.103059	0.0515294	−	0.998671i	$-0.483590\pi$
$233$	2.51709e14	0.103059	0.0515294	+	0.998671i	$0.483590\pi$
$234$	−6.39129e14	−0.254499
$235$	0	0
$236$	−1.84105e15	−0.693645
$237$	−3.13112e14	−0.114772
$238$	−1.96255e15	−0.699957
$239$	−4.54846e15	−1.57862	−0.789311	−	0.613993i	$-0.789562\pi$
$239$	−4.54846e15	−1.57862	−0.789311	+	0.613993i	$0.789562\pi$
$240$	0	0
$241$	−9.11615e14	−0.299710	−0.149855	−	0.988708i	$-0.547881\pi$
$241$	−9.11615e14	−0.299710	−0.149855	+	0.988708i	$0.547881\pi$
$242$	−4.54354e15	−1.45410
$243$	−2.05891e14	−0.0641500
$244$	−1.10098e15	−0.334000
$245$	0	0
$246$	−3.22462e15	−0.927685
$247$	−2.46356e13	−0.00690292
$248$	−3.18364e15	−0.868936
$249$	3.48001e15	0.925305
$250$	0	0
$251$	5.57048e15	1.40609	0.703046	−	0.711145i	$-0.251823\pi$
$251$	5.57048e15	1.40609	0.703046	+	0.711145i	$0.251823\pi$
$252$	7.62183e14	0.187480
$253$	−1.93114e15	−0.462945
$254$	−5.39513e15	−1.26062
$255$	0	0
$256$	−2.74505e15	−0.609523
$257$	−4.51207e14	−0.0976811	−0.0488405	−	0.998807i	$-0.515553\pi$
$257$	−4.51207e14	−0.0976811	−0.0488405	+	0.998807i	$0.515553\pi$
$258$	1.92733e15	0.406845
$259$	−2.61475e14	−0.0538248
$260$	0	0
$261$	−1.37174e15	−0.268601
$262$	1.31113e16	2.50431
$263$	7.11310e15	1.32540	0.662700	−	0.748885i	$-0.269411\pi$
$263$	7.11310e15	1.32540	0.662700	+	0.748885i	$0.269411\pi$
$264$	7.41751e14	0.134844
$265$	0	0
$266$	4.88023e13	0.00844713
$267$	−3.29914e15	−0.557285
$268$	−1.43322e16	−2.36285
$269$	−1.34023e15	−0.215671	−0.107835	−	0.994169i	$-0.534392\pi$
$269$	−1.34023e15	−0.215671	−0.107835	+	0.994169i	$0.534392\pi$
$270$	0	0
$271$	6.00564e15	0.920998	0.460499	−	0.887660i	$-0.347670\pi$
$271$	6.00564e15	0.920998	0.460499	+	0.887660i	$0.347670\pi$
$272$	1.78264e15	0.266910
$273$	7.07321e14	0.103409
$274$	1.29002e16	1.84170
$275$	0	0
$276$	−1.03271e16	−1.40627
$277$	1.09407e16	1.45521	0.727607	−	0.685994i	$-0.240632\pi$
$277$	1.09407e16	1.45521	0.727607	+	0.685994i	$0.240632\pi$
$278$	−4.69686e15	−0.610262
$279$	−2.80872e15	−0.356518
$280$	0	0
$281$	−2.82786e15	−0.342662	−0.171331	−	0.985213i	$-0.554807\pi$
$281$	−2.82786e15	−0.342662	−0.171331	+	0.985213i	$0.554807\pi$
$282$	9.32393e15	1.10403
$283$	−5.47390e15	−0.633410	−0.316705	−	0.948524i	$-0.602576\pi$
$283$	−5.47390e15	−0.633410	−0.316705	+	0.948524i	$0.602576\pi$
$284$	−1.72691e16	−1.95300
$285$	0	0
$286$	2.03139e15	0.219490
$287$	3.56867e15	0.376942
$288$	−3.77252e15	−0.389566
$289$	4.06315e15	0.410229
$290$	0	0
$291$	−1.12665e16	−1.08764
$292$	2.77389e16	2.61879
$293$	1.00494e16	0.927897	0.463948	−	0.885862i	$-0.346432\pi$
$293$	1.00494e16	0.927897	0.463948	+	0.885862i	$0.346432\pi$
$294$	8.73218e15	0.788615
$295$	0	0
$296$	−1.36080e15	−0.117597
$297$	6.54400e14	0.0553256
$298$	−8.41657e15	−0.696193
$299$	−9.58373e15	−0.775661
$300$	0	0
$301$	−2.13297e15	−0.165311
$302$	−1.31663e16	−0.998662
$303$	3.19791e15	0.237405
$304$	−4.43283e13	−0.00322109
$305$	0	0
$306$	−9.01093e15	−0.627452
$307$	−4.72392e15	−0.322035	−0.161018	−	0.986952i	$-0.551478\pi$
$307$	−4.72392e15	−0.322035	−0.161018	+	0.986952i	$0.551478\pi$
$308$	−2.42251e15	−0.161691
$309$	−7.08805e15	−0.463230
$310$	0	0
$311$	−3.07381e16	−1.92635	−0.963174	−	0.268878i	$-0.913347\pi$
$311$	−3.07381e16	−1.92635	−0.963174	+	0.268878i	$0.913347\pi$
$312$	3.68112e15	0.225930
$313$	1.74281e16	1.04764	0.523819	−	0.851829i	$-0.324507\pi$
$313$	1.74281e16	1.04764	0.523819	+	0.851829i	$0.324507\pi$
$314$	−1.38038e16	−0.812745
$315$	0	0
$316$	5.32193e15	0.300679
$317$	−2.05312e16	−1.13639	−0.568197	−	0.822892i	$-0.692359\pi$
$317$	−2.05312e16	−1.13639	−0.568197	+	0.822892i	$0.692359\pi$
$318$	2.40187e16	1.30248
$319$	4.35990e15	0.231653
$320$	0	0
$321$	−5.61584e15	−0.286505
$322$	1.89850e16	0.949180
$323$	−3.47331e14	−0.0170187
$324$	3.49951e15	0.168060
$325$	0	0
$326$	5.18475e16	2.39229
$327$	7.63153e15	0.345184
$328$	1.85725e16	0.823549
$329$	−1.03188e16	−0.448594
$330$	0	0
$331$	1.08020e16	0.451463	0.225731	−	0.974190i	$-0.427523\pi$
$331$	1.08020e16	0.451463	0.225731	+	0.974190i	$0.427523\pi$
$332$	−5.91494e16	−2.42411
$333$	−1.20055e15	−0.0482493
$334$	2.00374e16	0.789750
$335$	0	0
$336$	1.27272e15	0.0482535
$337$	−2.49305e16	−0.927120	−0.463560	−	0.886065i	$-0.653428\pi$
$337$	−2.49305e16	−0.927120	−0.463560	+	0.886065i	$0.653428\pi$
$338$	−3.33713e16	−1.21735
$339$	−4.00098e15	−0.143175
$340$	0	0
$341$	8.92717e15	0.307475
$342$	2.24072e14	0.00757213
$343$	−2.08784e16	−0.692286
$344$	−1.11006e16	−0.361175
$345$	0	0
$346$	6.46101e16	2.02444
$347$	−4.84184e16	−1.48891	−0.744455	−	0.667672i	$-0.767291\pi$
$347$	−4.84184e16	−1.48891	−0.744455	+	0.667672i	$0.767291\pi$
$348$	2.33153e16	0.703681
$349$	3.58064e15	0.106071	0.0530353	−	0.998593i	$-0.483110\pi$
$349$	3.58064e15	0.106071	0.0530353	+	0.998593i	$0.483110\pi$
$350$	0	0
$351$	3.24761e15	0.0926975
$352$	1.19905e16	0.335977
$353$	−6.71086e16	−1.84605	−0.923023	−	0.384744i	$-0.874290\pi$
$353$	−6.71086e16	−1.84605	−0.923023	+	0.384744i	$0.874290\pi$
$354$	1.55399e16	0.419687
$355$	0	0
$356$	5.60751e16	1.45997
$357$	9.97235e15	0.254950
$358$	−6.65031e15	−0.166956
$359$	6.13471e16	1.51245	0.756224	−	0.654313i	$-0.227042\pi$
$359$	6.13471e16	1.51245	0.756224	+	0.654313i	$0.227042\pi$
$360$	0	0
$361$	−4.20443e16	−0.999795
$362$	−8.23045e16	−1.92229
$363$	2.30871e16	0.529635
$364$	−1.20223e16	−0.270911
$365$	0	0
$366$	9.29314e15	0.202086
$367$	1.34842e16	0.288067	0.144034	−	0.989573i	$-0.453993\pi$
$367$	1.34842e16	0.288067	0.144034	+	0.989573i	$0.453993\pi$
$368$	−1.72446e16	−0.361944
$369$	1.63853e16	0.337896
$370$	0	0
$371$	−2.65814e16	−0.529233
$372$	4.77395e16	0.934004
$373$	3.69623e16	0.710643	0.355322	−	0.934744i	$-0.384371\pi$
$373$	3.69623e16	0.710643	0.355322	+	0.934744i	$0.384371\pi$
$374$	2.86401e16	0.541140
$375$	0	0
$376$	−5.37020e16	−0.980097
$377$	2.16371e16	0.388132
$378$	−6.43341e15	−0.113434
$379$	−6.08164e14	−0.0105406	−0.00527031	−	0.999986i	$-0.501678\pi$
$379$	−6.08164e14	−0.0105406	−0.00527031	+	0.999986i	$0.501678\pi$
$380$	0	0
$381$	2.74143e16	0.459161
$382$	−3.51573e16	−0.578901
$383$	2.22248e16	0.359788	0.179894	−	0.983686i	$-0.442425\pi$
$383$	2.22248e16	0.359788	0.179894	+	0.983686i	$0.442425\pi$
$384$	5.11980e16	0.814892
$385$	0	0
$386$	1.54788e17	2.38188
$387$	−9.79338e15	−0.148187
$388$	1.91496e17	2.84940
$389$	−1.28354e15	−0.0187818	−0.00939088	−	0.999956i	$-0.502989\pi$
$389$	−1.28354e15	−0.0187818	−0.00939088	+	0.999956i	$0.502989\pi$
$390$	0	0
$391$	−1.35119e17	−1.91235
$392$	−5.02938e16	−0.700091
$393$	−6.66228e16	−0.912161
$394$	7.71064e16	1.03840
$395$	0	0
$396$	−1.11228e16	−0.144942
$397$	−9.82778e16	−1.25985	−0.629923	−	0.776658i	$-0.716913\pi$
$397$	−9.82778e16	−1.25985	−0.629923	+	0.776658i	$0.716913\pi$
$398$	6.36375e16	0.802552
$399$	−2.47980e14	−0.00307675
$400$	0	0
$401$	−1.22578e17	−1.47222	−0.736110	−	0.676862i	$-0.763339\pi$
$401$	−1.22578e17	−1.47222	−0.736110	+	0.676862i	$0.763339\pi$
$402$	1.20974e17	1.42963
$403$	4.43032e16	0.515172
$404$	−5.43546e16	−0.621953
$405$	0	0
$406$	−4.28623e16	−0.474959
$407$	3.81579e15	0.0416122
$408$	5.18992e16	0.557018
$409$	1.53819e17	1.62483	0.812417	−	0.583077i	$-0.198151\pi$
$409$	1.53819e17	1.62483	0.812417	+	0.583077i	$0.198151\pi$
$410$	0	0
$411$	−6.55501e16	−0.670813
$412$	1.20475e17	1.21357
$413$	−1.71979e16	−0.170530
$414$	8.71685e16	0.850858
$415$	0	0
$416$	5.95057e16	0.562927
$417$	2.38662e16	0.222279
$418$	−7.12185e14	−0.00653051
$419$	−6.70532e16	−0.605381	−0.302690	−	0.953089i	$-0.597885\pi$
$419$	−6.70532e16	−0.605381	−0.302690	+	0.953089i	$0.597885\pi$
$420$	0	0
$421$	−1.75428e17	−1.53555	−0.767776	−	0.640719i	$-0.778636\pi$
$421$	−1.75428e17	−1.53555	−0.767776	+	0.640719i	$0.778636\pi$
$422$	2.63843e17	2.27413
$423$	−4.73778e16	−0.402126
$424$	−1.38338e17	−1.15628
$425$	0	0
$426$	1.45765e17	1.18165
$427$	−1.02847e16	−0.0821125
$428$	9.54519e16	0.750585
$429$	−1.03221e16	−0.0799461
$430$	0	0
$431$	1.32859e17	0.998360	0.499180	−	0.866498i	$-0.333635\pi$
$431$	1.32859e17	0.998360	0.499180	+	0.866498i	$0.333635\pi$
$432$	5.84362e15	0.0432552
$433$	−7.83879e16	−0.571581	−0.285790	−	0.958292i	$-0.592256\pi$
$433$	−7.83879e16	−0.571581	−0.285790	+	0.958292i	$0.592256\pi$
$434$	−8.77631e16	−0.630418
$435$	0	0
$436$	−1.29712e17	−0.904314
$437$	3.35996e15	0.0230783
$438$	−2.34137e17	−1.58449
$439$	−5.39578e16	−0.359778	−0.179889	−	0.983687i	$-0.557574\pi$
$439$	−5.39578e16	−0.359778	−0.179889	+	0.983687i	$0.557574\pi$
$440$	0	0
$441$	−4.43710e16	−0.287242
$442$	1.42133e17	0.906675
$443$	3.24769e16	0.204150	0.102075	−	0.994777i	$-0.467452\pi$
$443$	3.24769e16	0.204150	0.102075	+	0.994777i	$0.467452\pi$
$444$	2.04056e16	0.126403
$445$	0	0
$446$	3.89767e17	2.34492
$447$	4.27672e16	0.253578
$448$	−1.03577e17	−0.605278
$449$	−1.12233e17	−0.646424	−0.323212	−	0.946327i	$-0.604763\pi$
$449$	−1.12233e17	−0.646424	−0.323212	+	0.946327i	$0.604763\pi$
$450$	0	0
$451$	−5.20787e16	−0.291415
$452$	6.80042e16	0.375090
$453$	6.69021e16	0.363748
$454$	−2.12211e17	−1.13738
$455$	0	0
$456$	−1.29056e15	−0.00672214
$457$	−2.41097e17	−1.23805	−0.619024	−	0.785372i	$-0.712471\pi$
$457$	−2.41097e17	−1.23805	−0.619024	+	0.785372i	$0.712471\pi$
$458$	−4.49445e17	−2.27536
$459$	4.57873e16	0.228540
$460$	0	0
$461$	−9.87829e16	−0.479320	−0.239660	−	0.970857i	$-0.577036\pi$
$461$	−9.87829e16	−0.479320	−0.239660	+	0.970857i	$0.577036\pi$
$462$	2.04478e16	0.0978304
$463$	2.02766e17	0.956576	0.478288	−	0.878203i	$-0.341258\pi$
$463$	2.02766e17	0.956576	0.478288	+	0.878203i	$0.341258\pi$
$464$	3.89328e16	0.181113
$465$	0	0
$466$	3.61119e16	0.163358
$467$	−1.35876e17	−0.606152	−0.303076	−	0.952966i	$-0.598014\pi$
$467$	−1.35876e17	−0.606152	−0.303076	+	0.952966i	$0.598014\pi$
$468$	−5.51994e16	−0.242849
$469$	−1.33882e17	−0.580896
$470$	0	0
$471$	7.01412e16	0.296031
$472$	−8.95032e16	−0.372576
$473$	3.11271e16	0.127803
$474$	−4.49212e16	−0.181925
$475$	0	0
$476$	−1.69499e17	−0.667916
$477$	−1.22046e17	−0.474412
$478$	−6.52554e17	−2.50227
$479$	−1.81495e17	−0.686568	−0.343284	−	0.939232i	$-0.611539\pi$
$479$	−1.81495e17	−0.686568	−0.343284	+	0.939232i	$0.611539\pi$
$480$	0	0
$481$	1.89368e16	0.0697208
$482$	−1.30787e17	−0.475070
$483$	−9.64689e16	−0.345725
$484$	−3.92410e17	−1.38754
$485$	0	0
$486$	−2.95386e16	−0.101684
$487$	−5.39647e17	−1.83304	−0.916518	−	0.399992i	$-0.869013\pi$
$487$	−5.39647e17	−1.83304	−0.916518	+	0.399992i	$0.869013\pi$
$488$	−5.35246e16	−0.179401
$489$	−2.63453e17	−0.871356
$490$	0	0
$491$	−3.53623e17	−1.13897	−0.569483	−	0.822003i	$-0.692857\pi$
$491$	−3.53623e17	−1.13897	−0.569483	+	0.822003i	$0.692857\pi$
$492$	−2.78499e17	−0.885219
$493$	3.05056e17	0.956917
$494$	−3.53439e15	−0.0109418
$495$	0	0
$496$	7.97174e16	0.240393
$497$	−1.61317e17	−0.480136
$498$	4.99266e17	1.46670
$499$	−1.25995e17	−0.365344	−0.182672	−	0.983174i	$-0.558475\pi$
$499$	−1.25995e17	−0.365344	−0.182672	+	0.983174i	$0.558475\pi$
$500$	0	0
$501$	−1.01816e17	−0.287655
$502$	7.99179e17	2.22879
$503$	1.25319e16	0.0345006	0.0172503	−	0.999851i	$-0.494509\pi$
$503$	1.25319e16	0.0345006	0.0172503	+	0.999851i	$0.494509\pi$
$504$	3.70538e16	0.100701
$505$	0	0
$506$	−2.77054e17	−0.733815
$507$	1.69570e17	0.443401
$508$	−4.65959e17	−1.20291
$509$	−3.72187e17	−0.948628	−0.474314	−	0.880356i	$-0.657304\pi$
$509$	−3.72187e17	−0.948628	−0.474314	+	0.880356i	$0.657304\pi$
$510$	0	0
$511$	2.59119e17	0.643818
$512$	1.81504e17	0.445279
$513$	−1.13858e15	−0.00275804
$514$	−6.47332e16	−0.154834
$515$	0	0
$516$	1.66457e17	0.388221
$517$	1.50585e17	0.346810
$518$	−3.75131e16	−0.0853177
$519$	−3.28304e17	−0.737375
$520$	0	0
$521$	−4.42287e17	−0.968855	−0.484428	−	0.874831i	$-0.660972\pi$
$521$	−4.42287e17	−0.968855	−0.484428	+	0.874831i	$0.660972\pi$
$522$	−1.96799e17	−0.425760
$523$	7.13084e17	1.52363	0.761816	−	0.647794i	$-0.224308\pi$
$523$	7.13084e17	1.52363	0.761816	+	0.647794i	$0.224308\pi$
$524$	1.13238e18	2.38968
$525$	0	0
$526$	1.02049e18	2.10089
$527$	6.24620e17	1.27013
$528$	−1.85732e16	−0.0373050
$529$	8.03054e17	1.59325
$530$	0	0
$531$	−7.89629e16	−0.152865
$532$	4.21488e15	0.00806046
$533$	−2.58453e17	−0.488264
$534$	−4.73317e17	−0.883352
$535$	0	0
$536$	−6.96762e17	−1.26915
$537$	3.37923e16	0.0608114
$538$	−1.92279e17	−0.341859
$539$	1.41028e17	0.247729
$540$	0	0
$541$	1.13125e18	1.93988	0.969941	−	0.243342i	$-0.0782437\pi$
$541$	1.13125e18	1.93988	0.969941	+	0.243342i	$0.0782437\pi$
$542$	8.61610e17	1.45987
$543$	4.18215e17	0.700166
$544$	8.38957e17	1.38786
$545$	0	0
$546$	1.01477e17	0.163914
$547$	7.05433e17	1.12600	0.563000	−	0.826457i	$-0.309647\pi$
$547$	7.05433e17	1.12600	0.563000	+	0.826457i	$0.309647\pi$
$548$	1.11415e18	1.75739
$549$	−4.72214e16	−0.0736069
$550$	0	0
$551$	−7.58573e15	−0.0115481
$552$	−5.02054e17	−0.755347
$553$	4.97140e16	0.0739206
$554$	1.56963e18	2.30666
$555$	0	0
$556$	−4.05651e17	−0.582327
$557$	−6.45619e17	−0.916047	−0.458023	−	0.888940i	$-0.651442\pi$
$557$	−6.45619e17	−0.916047	−0.458023	+	0.888940i	$0.651442\pi$
$558$	−4.02958e17	−0.565116
$559$	1.54475e17	0.214133
$560$	0	0
$561$	−1.45529e17	−0.197103
$562$	−4.05704e17	−0.543154
$563$	7.17316e17	0.949306	0.474653	−	0.880173i	$-0.342574\pi$
$563$	7.17316e17	0.949306	0.474653	+	0.880173i	$0.342574\pi$
$564$	8.05276e17	1.05349
$565$	0	0
$566$	−7.85323e17	−1.00402
$567$	3.26902e16	0.0413169
$568$	−8.39544e17	−1.04901
$569$	−1.04468e17	−0.129048	−0.0645241	−	0.997916i	$-0.520553\pi$
$569$	−1.04468e17	−0.129048	−0.0645241	+	0.997916i	$0.520553\pi$
$570$	0	0
$571$	5.56964e17	0.672500	0.336250	−	0.941773i	$-0.390841\pi$
$571$	5.56964e17	0.672500	0.336250	+	0.941773i	$0.390841\pi$
$572$	1.75444e17	0.209443
$573$	1.78645e17	0.210856
$574$	5.11986e17	0.597490
$575$	0	0
$576$	−4.75565e17	−0.542580
$577$	3.32481e17	0.375080	0.187540	−	0.982257i	$-0.439949\pi$
$577$	3.32481e17	0.375080	0.187540	+	0.982257i	$0.439949\pi$
$578$	5.82927e17	0.650254
$579$	−7.86527e17	−0.867566
$580$	0	0
$581$	−5.52536e17	−0.595958
$582$	−1.61637e18	−1.72402
$583$	3.87909e17	0.409152
$584$	1.34853e18	1.40663
$585$	0	0
$586$	1.44175e18	1.47081
$587$	8.00524e17	0.807657	0.403828	−	0.914835i	$-0.367679\pi$
$587$	8.00524e17	0.807657	0.403828	+	0.914835i	$0.367679\pi$
$588$	7.54169e17	0.752516
$589$	−1.55322e16	−0.0153280
$590$	0	0
$591$	−3.91802e17	−0.378223
$592$	3.40740e16	0.0325336
$593$	1.73961e18	1.64284	0.821421	−	0.570322i	$-0.193182\pi$
$593$	1.73961e18	1.64284	0.821421	+	0.570322i	$0.193182\pi$
$594$	9.38846e16	0.0876966
$595$	0	0
$596$	−7.26910e17	−0.664324
$597$	−3.23362e17	−0.292318
$598$	−1.37495e18	−1.22950
$599$	−1.43596e18	−1.27019	−0.635095	−	0.772434i	$-0.719039\pi$
$599$	−1.43596e18	−1.27019	−0.635095	+	0.772434i	$0.719039\pi$
$600$	0	0
$601$	−1.23937e18	−1.07279	−0.536396	−	0.843966i	$-0.680215\pi$
$601$	−1.23937e18	−1.07279	−0.536396	+	0.843966i	$0.680215\pi$
$602$	−3.06011e17	−0.262035
$603$	−6.14709e17	−0.520723
$604$	−1.13713e18	−0.952948
$605$	0	0
$606$	4.58795e17	0.376310
$607$	−2.40600e18	−1.95240	−0.976199	−	0.216875i	$-0.930414\pi$
$607$	−2.40600e18	−1.95240	−0.976199	+	0.216875i	$0.930414\pi$
$608$	−2.08621e16	−0.0167488
$609$	2.17797e17	0.172997
$610$	0	0
$611$	7.47312e17	0.581077
$612$	−7.78243e17	−0.598730
$613$	−7.71007e17	−0.586902	−0.293451	−	0.955974i	$-0.594804\pi$
$613$	−7.71007e17	−0.586902	−0.293451	+	0.955974i	$0.594804\pi$
$614$	−6.77726e17	−0.510458
$615$	0	0
$616$	−1.17771e17	−0.0868487
$617$	6.35119e17	0.463449	0.231724	−	0.972781i	$-0.425563\pi$
$617$	6.35119e17	0.463449	0.231724	+	0.972781i	$0.425563\pi$
$618$	−1.01690e18	−0.734266
$619$	1.75343e18	1.25285	0.626426	−	0.779481i	$-0.284517\pi$
$619$	1.75343e18	1.25285	0.626426	+	0.779481i	$0.284517\pi$
$620$	0	0
$621$	−4.42930e17	−0.309913
$622$	−4.40990e18	−3.05345
$623$	5.23818e17	0.358928
$624$	−9.21741e16	−0.0625042
$625$	0	0
$626$	2.50035e18	1.66061
$627$	3.61884e15	0.00237865
$628$	−1.19218e18	−0.775541
$629$	2.66985e17	0.171893
$630$	0	0
$631$	1.21896e18	0.768775	0.384387	−	0.923172i	$-0.374413\pi$
$631$	1.21896e18	0.768775	0.384387	+	0.923172i	$0.374413\pi$
$632$	2.58727e17	0.161503
$633$	−1.34067e18	−0.828318
$634$	−2.94555e18	−1.80130
$635$	0	0
$636$	2.07441e18	1.24286
$637$	6.99883e17	0.415068
$638$	6.25501e17	0.367193
$639$	−7.40676e17	−0.430400
$640$	0	0
$641$	1.09626e18	0.624216	0.312108	−	0.950047i	$-0.398965\pi$
$641$	1.09626e18	0.624216	0.312108	+	0.950047i	$0.398965\pi$
$642$	−8.05687e17	−0.454139
$643$	2.51721e18	1.40459	0.702293	−	0.711888i	$-0.252160\pi$
$643$	2.51721e18	1.40459	0.702293	+	0.711888i	$0.252160\pi$
$644$	1.63967e18	0.905731
$645$	0	0
$646$	−4.98305e16	−0.0269764
$647$	6.31684e17	0.338549	0.169275	−	0.985569i	$-0.445858\pi$
$647$	6.31684e17	0.338549	0.169275	+	0.985569i	$0.445858\pi$
$648$	1.70130e17	0.0902699
$649$	2.50974e17	0.131837
$650$	0	0
$651$	4.45952e17	0.229621
$652$	4.47789e18	2.28278
$653$	−2.66002e18	−1.34261	−0.671303	−	0.741183i	$-0.734265\pi$
$653$	−2.66002e18	−1.34261	−0.671303	+	0.741183i	$0.734265\pi$
$654$	1.09487e18	0.547152
$655$	0	0
$656$	−4.65049e17	−0.227837
$657$	1.18973e18	0.577128
$658$	−1.48040e18	−0.711067
$659$	−1.04314e18	−0.496121	−0.248061	−	0.968745i	$-0.579793\pi$
$659$	−1.04314e18	−0.496121	−0.248061	+	0.968745i	$0.579793\pi$
$660$	0	0
$661$	8.68858e17	0.405172	0.202586	−	0.979264i	$-0.435065\pi$
$661$	8.68858e17	0.405172	0.202586	+	0.979264i	$0.435065\pi$
$662$	1.54973e18	0.715613
$663$	−7.22224e17	−0.330243
$664$	−2.87557e18	−1.30206
$665$	0	0
$666$	−1.72239e17	−0.0764800
$667$	−2.95100e18	−1.29763
$668$	1.73056e18	0.753599
$669$	−1.98053e18	−0.854105
$670$	0	0
$671$	1.50087e17	0.0634815
$672$	5.98979e17	0.250906
$673$	2.71903e18	1.12802	0.564009	−	0.825769i	$-0.309258\pi$
$673$	2.71903e18	1.12802	0.564009	+	0.825769i	$0.309258\pi$
$674$	−3.57670e18	−1.46958
$675$	0	0
$676$	−2.88216e18	−1.16162
$677$	2.17548e18	0.868418	0.434209	−	0.900812i	$-0.357028\pi$
$677$	2.17548e18	0.868418	0.434209	+	0.900812i	$0.357028\pi$
$678$	−5.74007e17	−0.226947
$679$	1.78883e18	0.700514
$680$	0	0
$681$	1.07831e18	0.414273
$682$	1.28075e18	0.487379
$683$	−4.67971e18	−1.76394	−0.881970	−	0.471305i	$-0.843783\pi$
$683$	−4.67971e18	−1.76394	−0.881970	+	0.471305i	$0.843783\pi$
$684$	1.93523e16	0.00722551
$685$	0	0
$686$	−2.99536e18	−1.09734
$687$	2.28377e18	0.828769
$688$	2.77957e17	0.0999200
$689$	1.92509e18	0.685530
$690$	0	0
$691$	−3.58472e18	−1.25270	−0.626352	−	0.779541i	$-0.715453\pi$
$691$	−3.58472e18	−1.25270	−0.626352	+	0.779541i	$0.715453\pi$
$692$	5.58015e18	1.93177
$693$	−1.03902e17	−0.0356334
$694$	−6.94643e18	−2.36007
$695$	0	0
$696$	1.13348e18	0.377967
$697$	−3.64386e18	−1.20379
$698$	5.13703e17	0.168132
$699$	−1.83496e17	−0.0595010
$700$	0	0
$701$	−5.81898e18	−1.85217	−0.926083	−	0.377321i	$-0.876845\pi$
$701$	−5.81898e18	−1.85217	−0.926083	+	0.377321i	$0.876845\pi$
$702$	4.65925e17	0.146935
$703$	−6.63903e15	−0.00207441
$704$	1.51152e18	0.467943
$705$	0	0
$706$	−9.62786e18	−2.92617
$707$	−5.07746e17	−0.152905
$708$	1.34212e18	0.400476
$709$	6.35434e18	1.87876	0.939378	−	0.342884i	$-0.111404\pi$
$709$	6.35434e18	1.87876	0.939378	+	0.342884i	$0.111404\pi$
$710$	0	0
$711$	2.28258e17	0.0662635
$712$	2.72611e18	0.784193
$713$	−6.04235e18	−1.72236
$714$	1.43070e18	0.404120
$715$	0	0
$716$	−5.74364e17	−0.159313
$717$	3.31583e18	0.911418
$718$	8.80128e18	2.39738
$719$	2.59269e18	0.699863	0.349932	−	0.936775i	$-0.386205\pi$
$719$	2.59269e18	0.699863	0.349932	+	0.936775i	$0.386205\pi$
$720$	0	0
$721$	1.12540e18	0.298351
$722$	−6.03197e18	−1.58477
$723$	6.64568e17	0.173038
$724$	−7.10836e18	−1.83429
$725$	0	0
$726$	3.31224e18	0.839525
$727$	7.34447e18	1.84496	0.922479	−	0.386046i	$-0.126160\pi$
$727$	7.34447e18	1.84496	0.922479	+	0.386046i	$0.126160\pi$
$728$	−5.84466e17	−0.145514
$729$	1.50095e17	0.0370370
$730$	0	0
$731$	2.17791e18	0.527932
$732$	8.02617e17	0.192835
$733$	−4.76931e18	−1.13574	−0.567871	−	0.823118i	$-0.692233\pi$
$733$	−4.76931e18	−1.13574	−0.567871	+	0.823118i	$0.692233\pi$
$734$	1.93453e18	0.456616
$735$	0	0
$736$	−8.11576e18	−1.88202
$737$	1.95378e18	0.449093
$738$	2.35075e18	0.535599
$739$	−2.70323e18	−0.610513	−0.305256	−	0.952270i	$-0.598742\pi$
$739$	−2.70323e18	−0.610513	−0.305256	+	0.952270i	$0.598742\pi$
$740$	0	0
$741$	1.79593e16	0.00398540
$742$	−3.81354e18	−0.838887
$743$	−1.89279e18	−0.412738	−0.206369	−	0.978474i	$-0.566165\pi$
$743$	−1.89279e18	−0.412738	−0.206369	+	0.978474i	$0.566165\pi$
$744$	2.32087e18	0.501680
$745$	0	0
$746$	5.30287e18	1.12644
$747$	−2.53693e18	−0.534225
$748$	2.47355e18	0.516369
$749$	8.91650e17	0.184528
$750$	0	0
$751$	7.31039e18	1.48690	0.743448	−	0.668793i	$-0.233189\pi$
$751$	7.31039e18	1.48690	0.743448	+	0.668793i	$0.233189\pi$
$752$	1.34468e18	0.271146
$753$	−4.06088e18	−0.811807
$754$	3.10420e18	0.615228
$755$	0	0
$756$	−5.55632e17	−0.108242
$757$	−7.31767e18	−1.41335	−0.706675	−	0.707539i	$-0.749805\pi$
$757$	−7.31767e18	−1.41335	−0.706675	+	0.707539i	$0.749805\pi$
$758$	−8.72514e16	−0.0167079
$759$	1.40780e18	0.267282
$760$	0	0
$761$	4.77770e18	0.891700	0.445850	−	0.895108i	$-0.352901\pi$
$761$	4.77770e18	0.891700	0.445850	+	0.895108i	$0.352901\pi$
$762$	3.93305e18	0.727817
$763$	−1.21169e18	−0.222322
$764$	−3.03642e18	−0.552401
$765$	0	0
$766$	3.18852e18	0.570299
$767$	1.24552e18	0.220892
$768$	2.00114e18	0.351908
$769$	2.59264e18	0.452086	0.226043	−	0.974117i	$-0.427421\pi$
$769$	2.59264e18	0.452086	0.226043	+	0.974117i	$0.427421\pi$
$770$	0	0
$771$	3.28930e17	0.0563962
$772$	1.33685e19	2.27285
$773$	−5.76567e18	−0.972038	−0.486019	−	0.873948i	$-0.661551\pi$
$773$	−5.76567e18	−0.972038	−0.486019	+	0.873948i	$0.661551\pi$
$774$	−1.40503e18	−0.234892
$775$	0	0
$776$	9.30964e18	1.53049
$777$	1.90616e17	0.0310758
$778$	−1.84145e17	−0.0297710
$779$	9.06109e16	0.0145274
$780$	0	0
$781$	2.35415e18	0.371195
$782$	−1.93851e19	−3.03126
$783$	9.99998e17	0.155077
$784$	1.25934e18	0.193682
$785$	0	0
$786$	−9.55817e18	−1.44587
$787$	−1.72894e18	−0.259385	−0.129692	−	0.991554i	$-0.541399\pi$
$787$	−1.72894e18	−0.259385	−0.129692	+	0.991554i	$0.541399\pi$
$788$	6.65941e18	0.990867
$789$	−5.18545e18	−0.765220
$790$	0	0
$791$	6.35251e17	0.0922143
$792$	−5.40737e17	−0.0778524
$793$	7.44844e17	0.106363
$794$	−1.40996e19	−1.99698
$795$	0	0
$796$	5.49615e18	0.765815
$797$	−1.06264e19	−1.46861	−0.734305	−	0.678820i	$-0.762492\pi$
$797$	−1.06264e19	−1.46861	−0.734305	+	0.678820i	$0.762492\pi$
$798$	−3.55768e16	−0.00487695
$799$	1.05362e19	1.43261
$800$	0	0
$801$	2.40507e18	0.321749
$802$	−1.75858e19	−2.33361
$803$	−3.78139e18	−0.497738
$804$	1.04481e19	1.36419
$805$	0	0
$806$	6.35604e18	0.816599
$807$	9.77031e17	0.124517
$808$	−2.64247e18	−0.334069
$809$	−8.95164e18	−1.12263	−0.561316	−	0.827602i	$-0.689705\pi$
$809$	−8.95164e18	−1.12263	−0.561316	+	0.827602i	$0.689705\pi$
$810$	0	0
$811$	5.95858e18	0.735373	0.367686	−	0.929950i	$-0.380150\pi$
$811$	5.95858e18	0.735373	0.367686	+	0.929950i	$0.380150\pi$
$812$	−3.70187e18	−0.453217
$813$	−4.37811e18	−0.531739
$814$	5.47439e17	0.0659595
$815$	0	0
$816$	−1.29954e18	−0.154101
$817$	−5.41575e16	−0.00637111
$818$	2.20680e19	2.57552
$819$	−5.15637e17	−0.0597034
$820$	0	0
$821$	2.78763e18	0.317691	0.158846	−	0.987303i	$-0.449223\pi$
$821$	2.78763e18	0.317691	0.158846	+	0.987303i	$0.449223\pi$
$822$	−9.40426e18	−1.06331
$823$	3.20816e18	0.359880	0.179940	−	0.983678i	$-0.442410\pi$
$823$	3.20816e18	0.359880	0.179940	+	0.983678i	$0.442410\pi$
$824$	5.85692e18	0.651842
$825$	0	0
$826$	−2.46733e18	−0.270307
$827$	1.18081e18	0.128349	0.0641747	−	0.997939i	$-0.479559\pi$
$827$	1.18081e18	0.128349	0.0641747	+	0.997939i	$0.479559\pi$
$828$	7.52844e18	0.811910
$829$	3.64568e18	0.390099	0.195049	−	0.980793i	$-0.437513\pi$
$829$	3.64568e18	0.390099	0.195049	+	0.980793i	$0.437513\pi$
$830$	0	0
$831$	−7.97578e18	−0.840169
$832$	7.50130e18	0.784034
$833$	9.86749e18	1.02333
$834$	3.42401e18	0.352335
$835$	0	0
$836$	−6.15090e16	−0.00623157
$837$	2.04756e18	0.205836
$838$	−9.61992e18	−0.959589
$839$	−6.16574e18	−0.610285	−0.305142	−	0.952307i	$-0.598704\pi$
$839$	−6.16574e18	−0.610285	−0.305142	+	0.952307i	$0.598704\pi$
$840$	0	0
$841$	−3.59820e18	−0.350680
$842$	−2.51680e19	−2.43400
$843$	2.06151e18	0.197836
$844$	2.27872e19	2.17003
$845$	0	0
$846$	−6.79715e18	−0.637411
$847$	−3.66564e18	−0.341120
$848$	3.46393e18	0.319887
$849$	3.99047e18	0.365699
$850$	0	0
$851$	−2.58271e18	−0.233096
$852$	1.25892e19	1.12756
$853$	8.43377e18	0.749640	0.374820	−	0.927098i	$-0.377704\pi$
$853$	8.43377e18	0.749640	0.374820	+	0.927098i	$0.377704\pi$
$854$	−1.47551e18	−0.130157
$855$	0	0
$856$	4.64042e18	0.403161
$857$	9.57885e18	0.825920	0.412960	−	0.910749i	$-0.364495\pi$
$857$	9.57885e18	0.825920	0.412960	+	0.910749i	$0.364495\pi$
$858$	−1.48088e18	−0.126723
$859$	1.27645e19	1.08404	0.542022	−	0.840364i	$-0.317659\pi$
$859$	1.27645e19	1.08404	0.542022	+	0.840364i	$0.317659\pi$
$860$	0	0
$861$	−2.60156e18	−0.217627
$862$	1.90608e19	1.58250
$863$	−6.90133e18	−0.568673	−0.284337	−	0.958725i	$-0.591773\pi$
$863$	−6.90133e18	−0.568673	−0.284337	+	0.958725i	$0.591773\pi$
$864$	2.75017e18	0.224916
$865$	0	0
$866$	−1.12461e19	−0.906013
$867$	−2.96204e18	−0.236846
$868$	−7.57980e18	−0.601561
$869$	−7.25491e17	−0.0571483
$870$	0	0
$871$	9.69608e18	0.752451
$872$	−6.30601e18	−0.485733
$873$	8.21330e18	0.627950
$874$	4.82043e17	0.0365815
$875$	0	0
$876$	−2.02216e19	−1.51196
$877$	2.53540e19	1.88169	0.940846	−	0.338835i	$-0.110033\pi$
$877$	2.53540e19	1.88169	0.940846	+	0.338835i	$0.110033\pi$
$878$	−7.74115e18	−0.570284
$879$	−7.32600e18	−0.535721
$880$	0	0
$881$	2.27879e18	0.164195	0.0820976	−	0.996624i	$-0.473838\pi$
$881$	2.27879e18	0.164195	0.0820976	+	0.996624i	$0.473838\pi$
$882$	−6.36576e18	−0.455307
$883$	−1.55074e19	−1.10102	−0.550508	−	0.834830i	$-0.685566\pi$
$883$	−1.55074e19	−1.10102	−0.550508	+	0.834830i	$0.685566\pi$
$884$	1.22756e19	0.865171
$885$	0	0
$886$	4.65936e18	0.323599
$887$	5.37007e18	0.370234	0.185117	−	0.982716i	$-0.440734\pi$
$887$	5.37007e18	0.370234	0.185117	+	0.982716i	$0.440734\pi$
$888$	9.92022e17	0.0678949
$889$	−4.35269e18	−0.295730
$890$	0	0
$891$	−4.77057e17	−0.0319422
$892$	3.36628e19	2.23758
$893$	−2.62000e17	−0.0172889
$894$	6.13568e18	0.401947
$895$	0	0
$896$	−8.12892e18	−0.524844
$897$	6.98654e18	0.447828
$898$	−1.61016e19	−1.02465
$899$	1.36417e19	0.861850
$900$	0	0
$901$	2.71414e19	1.69014
$902$	−7.47156e18	−0.461922
$903$	1.55494e18	0.0954426
$904$	3.30604e18	0.201472
$905$	0	0
$906$	9.59823e18	0.576578
$907$	2.21370e19	1.32029	0.660147	−	0.751136i	$-0.270494\pi$
$907$	2.21370e19	1.32029	0.660147	+	0.751136i	$0.270494\pi$
$908$	−1.83279e19	−1.08531
$909$	−2.33128e18	−0.137066
$910$	0	0
$911$	−5.15063e18	−0.298532	−0.149266	−	0.988797i	$-0.547691\pi$
$911$	−5.15063e18	−0.298532	−0.149266	+	0.988797i	$0.547691\pi$
$912$	3.23153e16	0.00185970
$913$	8.06331e18	0.460737
$914$	−3.45895e19	−1.96243
$915$	0	0
$916$	−3.88170e19	−2.17121
$917$	1.05780e19	0.587492
$918$	6.56897e18	0.362259
$919$	−1.11627e19	−0.611247	−0.305624	−	0.952152i	$-0.598865\pi$
$919$	−1.11627e19	−0.611247	−0.305624	+	0.952152i	$0.598865\pi$
$920$	0	0
$921$	3.44374e18	0.185927
$922$	−1.41721e19	−0.759770
$923$	1.16830e19	0.621934
$924$	1.76601e18	0.0933522
$925$	0	0
$926$	2.90902e19	1.51627
$927$	5.16719e18	0.267446
$928$	1.83228e19	0.941740
$929$	4.48353e18	0.228833	0.114416	−	0.993433i	$-0.463500\pi$
$929$	4.48353e18	0.228833	0.114416	+	0.993433i	$0.463500\pi$
$930$	0	0
$931$	−2.45372e17	−0.0123496
$932$	3.11886e18	0.155881
$933$	2.24081e19	1.11218
$934$	−1.94936e19	−0.960812
$935$	0	0
$936$	−2.68353e18	−0.130441
$937$	−1.27997e19	−0.617864	−0.308932	−	0.951084i	$-0.599972\pi$
$937$	−1.27997e19	−0.617864	−0.308932	+	0.951084i	$0.599972\pi$
$938$	−1.92076e19	−0.920778
$939$	−1.27051e19	−0.604855
$940$	0	0
$941$	−2.16104e19	−1.01468	−0.507342	−	0.861745i	$-0.669372\pi$
$941$	−2.16104e19	−1.01468	−0.507342	+	0.861745i	$0.669372\pi$
$942$	1.00629e19	0.469239
$943$	3.52494e19	1.63240
$944$	2.24113e18	0.103074
$945$	0	0
$946$	4.46570e18	0.202580
$947$	−1.44301e19	−0.650120	−0.325060	−	0.945693i	$-0.605384\pi$
$947$	−1.44301e19	−0.650120	−0.325060	+	0.945693i	$0.605384\pi$
$948$	−3.87969e18	−0.173597
$949$	−1.87661e19	−0.833956
$950$	0	0
$951$	1.49672e19	0.656098
$952$	−8.24025e18	−0.358757
$953$	−2.49670e19	−1.07960	−0.539799	−	0.841794i	$-0.681500\pi$
$953$	−2.49670e19	−1.07960	−0.539799	+	0.841794i	$0.681500\pi$
$954$	−1.75096e19	−0.751990
$955$	0	0
$956$	−5.63588e19	−2.38773
$957$	−3.17837e18	−0.133745
$958$	−2.60385e19	−1.08828
$959$	1.04077e19	0.432048
$960$	0	0
$961$	3.51474e18	0.143943
$962$	2.71680e18	0.110514
$963$	4.09395e18	0.165414
$964$	−1.12956e19	−0.453323
$965$	0	0
$966$	−1.38401e19	−0.548009
$967$	−2.66065e19	−1.04644	−0.523222	−	0.852196i	$-0.675270\pi$
$967$	−2.66065e19	−1.04644	−0.523222	+	0.852196i	$0.675270\pi$
$968$	−1.90771e19	−0.745286
$969$	2.53205e17	0.00982578
$970$	0	0
$971$	1.94068e19	0.743069	0.371534	−	0.928419i	$-0.378832\pi$
$971$	1.94068e19	0.743069	0.371534	+	0.928419i	$0.378832\pi$
$972$	−2.55114e18	−0.0970296
$973$	−3.78934e18	−0.143163
$974$	−7.74214e19	−2.90555
$975$	0	0
$976$	1.34024e18	0.0496317
$977$	−3.01511e19	−1.10915	−0.554573	−	0.832135i	$-0.687118\pi$
$977$	−3.01511e19	−1.10915	−0.554573	+	0.832135i	$0.687118\pi$
$978$	−3.77968e19	−1.38119
$979$	−7.64422e18	−0.277489
$980$	0	0
$981$	−5.56339e18	−0.199292
$982$	−5.07332e19	−1.80538
$983$	−1.32822e19	−0.469540	−0.234770	−	0.972051i	$-0.575434\pi$
$983$	−1.32822e19	−0.469540	−0.234770	+	0.972051i	$0.575434\pi$
$984$	−1.35393e19	−0.475476
$985$	0	0
$986$	4.37654e19	1.51681
$987$	7.52237e18	0.258996
$988$	−3.05253e17	−0.0104409
$989$	−2.10683e19	−0.715904
$990$	0	0
$991$	−2.75507e19	−0.923960	−0.461980	−	0.886890i	$-0.652861\pi$
$991$	−2.75507e19	−0.923960	−0.461980	+	0.886890i	$0.652861\pi$
$992$	3.75172e19	1.24998
$993$	−7.87465e18	−0.260652
$994$	−2.31437e19	−0.761063
$995$	0	0
$996$	4.31199e19	1.39956
$997$	3.62751e19	1.16974	0.584870	−	0.811127i	$-0.301145\pi$
$997$	3.62751e19	1.16974	0.584870	+	0.811127i	$0.301145\pi$
$998$	−1.80762e19	−0.579106
$999$	8.75198e17	0.0278568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.14.a.g.1.4	✓	4
5.2	odd	4		75.14.b.g.49.7		8
5.3	odd	4		75.14.b.g.49.2		8
5.4	even	2		75.14.a.h.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.14.a.g.1.4	✓	4	1.1	even	1	trivial
75.14.a.h.1.1	yes	4	5.4	even	2
75.14.b.g.49.2		8	5.3	odd	4
75.14.b.g.49.7		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+143.467 q^{2} -729.000 q^{3} +12390.7 q^{4} -104587. q^{6} +115746. q^{7} +602380. q^{8} +531441. q^{9} -1.68912e6 q^{11} -9.03285e6 q^{12} -8.38266e6 q^{13} +1.66058e7 q^{14} -1.50834e7 q^{16} -1.18185e8 q^{17} +7.62442e7 q^{18} +2.93887e6 q^{19} -8.43791e7 q^{21} -2.42333e8 q^{22} +1.14328e9 q^{23} -4.39135e8 q^{24} -1.20263e9 q^{26} -3.87420e8 q^{27} +1.43418e9 q^{28} -2.58117e9 q^{29} -5.28510e9 q^{31} -7.09866e9 q^{32} +1.23137e9 q^{33} -1.69556e10 q^{34} +6.58495e9 q^{36} -2.25904e9 q^{37} +4.21631e8 q^{38} +6.11096e9 q^{39} +3.08318e10 q^{41} -1.21056e10 q^{42} -1.84280e10 q^{43} -2.09294e10 q^{44} +1.64023e11 q^{46} -8.91497e10 q^{47} +1.09958e10 q^{48} -8.34918e10 q^{49} +8.61570e10 q^{51} -1.03867e11 q^{52} -2.29652e11 q^{53} -5.55820e10 q^{54} +6.97232e10 q^{56} -2.14244e9 q^{57} -3.70312e11 q^{58} -1.48583e11 q^{59} -8.88553e10 q^{61} -7.58237e11 q^{62} +6.15124e10 q^{63} -8.94860e11 q^{64} +1.76661e11 q^{66} -1.15668e12 q^{67} -1.46440e12 q^{68} -8.33451e11 q^{69} -1.39371e12 q^{71} +3.20129e11 q^{72} +2.23868e12 q^{73} -3.24097e11 q^{74} +3.64148e10 q^{76} -1.95509e11 q^{77} +8.76720e11 q^{78} +4.29509e11 q^{79} +2.82430e11 q^{81} +4.42335e12 q^{82} -4.77368e12 q^{83} -1.04552e12 q^{84} -2.64380e12 q^{86} +1.88167e12 q^{87} -1.01749e12 q^{88} +4.52557e12 q^{89} -9.70262e11 q^{91} +1.41661e13 q^{92} +3.85284e12 q^{93} -1.27900e13 q^{94} +5.17493e12 q^{96} +1.54548e13 q^{97} -1.19783e13 q^{98} -8.97667e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 52 q^{2} - 2916 q^{3} + 20752 q^{4} + 37908 q^{6} + 298996 q^{7} - 423936 q^{8} + 2125764 q^{9} - 5874104 q^{11} - 15128208 q^{12} + 32044972 q^{13} - 64322292 q^{14} + 6196480 q^{16} - 67409368 q^{17}+ \cdots - 3121739703864 q^{99}+O(q^{100}) \) 4 * q - 52 * q^2 - 2916 * q^3 + 20752 * q^4 + 37908 * q^6 + 298996 * q^7 - 423936 * q^8 + 2125764 * q^9 - 5874104 * q^11 - 15128208 * q^12 + 32044972 * q^13 - 64322292 * q^14 + 6196480 * q^16 - 67409368 * q^17 - 27634932 * q^18 - 203930812 * q^19 - 217968084 * q^21 + 42656424 * q^22 + 577045608 * q^23 + 309049344 * q^24 - 3541675772 * q^26 - 1549681956 * q^27 + 11813256592 * q^28 - 8505376264 * q^29 - 2055088276 * q^31 - 1166925824 * q^32 + 4282221816 * q^33 - 5970330456 * q^34 + 11028463632 * q^36 + 15264235096 * q^37 + 50700107708 * q^38 - 23360784588 * q^39 + 33629458544 * q^41 + 46890950868 * q^42 - 12357161900 * q^43 - 7081880224 * q^44 + 135531435624 * q^46 + 94931088680 * q^47 - 4517233920 * q^48 + 15736414920 * q^49 + 49141429272 * q^51 + 265908970672 * q^52 - 334308021952 * q^53 + 20145865428 * q^54 - 609811407360 * q^56 + 148665561948 * q^57 - 47213104104 * q^58 + 361880587432 * q^59 - 360973874260 * q^61 - 236543379468 * q^62 + 158898733236 * q^63 - 875219197952 * q^64 - 31096533096 * q^66 - 66061390268 * q^67 - 3236755082144 * q^68 - 420666248232 * q^69 - 3883894237072 * q^71 - 225296971776 * q^72 - 825246053672 * q^73 - 2346427881112 * q^74 - 4343041077808 * q^76 + 897635955432 * q^77 + 2581881637788 * q^78 - 6040507323040 * q^79 + 1129718145924 * q^81 + 9720027045792 * q^82 - 7040089644456 * q^83 - 8611864055568 * q^84 + 3656045115916 * q^86 + 6200419296456 * q^87 - 4806631036416 * q^88 - 4255523514432 * q^89 + 15423506586364 * q^91 + 12929237479776 * q^92 + 1498159353204 * q^93 - 40012092718728 * q^94 + 850688925696 * q^96 + 17383619164252 * q^97 - 43175578697672 * q^98 - 3121739703864 * q^99

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