LMFDB - Embedded newform 50.18.a.g.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,18,Mod(1,50)] 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("50.1"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,512,6308] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{36061}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 9015 $ x^2 - x - 9015
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$95.4487$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000 q^{2} -12037.8 q^{3} +65536.0 q^{4} -3.08167e6 q^{6} +9.53475e6 q^{7} +1.67772e7 q^{8} +1.57682e7 q^{9} +4.01191e8 q^{11} -7.88908e8 q^{12} -8.56166e8 q^{13} +2.44090e9 q^{14} +4.29497e9 q^{16} +3.89127e10 q^{17} +4.03665e9 q^{18} -1.13839e11 q^{19} -1.14777e11 q^{21} +1.02705e11 q^{22} -1.64834e10 q^{23} -2.01961e11 q^{24} -2.19179e11 q^{26} +1.36475e12 q^{27} +6.24870e11 q^{28} -2.27472e12 q^{29} -1.63788e12 q^{31} +1.09951e12 q^{32} -4.82946e12 q^{33} +9.96164e12 q^{34} +1.03338e12 q^{36} +1.75967e13 q^{37} -2.91428e13 q^{38} +1.03064e13 q^{39} -2.95532e13 q^{41} -2.93830e13 q^{42} -1.37690e14 q^{43} +2.62925e13 q^{44} -4.21974e12 q^{46} +1.65452e14 q^{47} -5.17019e13 q^{48} -1.41719e14 q^{49} -4.68422e14 q^{51} -5.61097e13 q^{52} +7.25259e14 q^{53} +3.49376e14 q^{54} +1.59967e14 q^{56} +1.37037e15 q^{57} -5.82328e14 q^{58} +1.62177e15 q^{59} +2.46915e15 q^{61} -4.19296e14 q^{62} +1.50346e14 q^{63} +2.81475e14 q^{64} -1.23634e15 q^{66} +2.03244e14 q^{67} +2.55018e15 q^{68} +1.98423e14 q^{69} +9.39117e15 q^{71} +2.64546e14 q^{72} -1.54865e15 q^{73} +4.50475e15 q^{74} -7.46056e15 q^{76} +3.82526e15 q^{77} +2.63843e15 q^{78} +8.30977e15 q^{79} -1.84648e16 q^{81} -7.56562e15 q^{82} +6.14697e15 q^{83} -7.52205e15 q^{84} -3.52485e16 q^{86} +2.73826e16 q^{87} +6.73087e15 q^{88} +4.67428e15 q^{89} -8.16334e15 q^{91} -1.08025e15 q^{92} +1.97164e16 q^{93} +4.23558e16 q^{94} -1.32357e16 q^{96} -1.01799e17 q^{97} -3.62801e16 q^{98} +6.32605e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 512 q^{2} + 6308 q^{3} + 131072 q^{4} + 1614848 q^{6} - 6543844 q^{7} + 33554432 q^{8} + 223195906 q^{9} + 1189408704 q^{11} + 413401088 q^{12} + 2017919228 q^{13} - 1675224064 q^{14} + 8589934592 q^{16}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 512 * q^2 + 6308 * q^3 + 131072 * q^4 + 1614848 * q^6 - 6543844 * q^7 + 33554432 * q^8 + 223195906 * q^9 + 1189408704 * q^11 + 413401088 * q^12 + 2017919228 * q^13 - 1675224064 * q^14 + 8589934592 * q^16 + 18755639436 * q^17 + 57138151936 * q^18 - 136704830600 * q^19 - 409751898376 * q^21 + 304488628224 * q^22 + 649234170708 * q^23 + 105830678528 * q^24 + 516587322368 * q^26 + 2800995425720 * q^27 - 428857360384 * q^28 - 4696543420020 * q^29 + 7120867378744 * q^31 + 2199023255552 * q^32 + 9631011282816 * q^33 + 4801443695616 * q^34 + 14627366895616 * q^36 - 9933114637444 * q^37 - 34996436633600 * q^38 + 63033715222712 * q^39 + 9622711880844 * q^41 - 104896485984256 * q^42 - 7708436011852 * q^43 + 77949088825344 * q^44 + 166203947701248 * q^46 + 466072575837996 * q^47 + 27092653703168 * q^48 - 115828146887046 * q^49 - 838218717084456 * q^51 + 132246354526208 * q^52 + 623333120284428 * q^53 + 717054828984320 * q^54 - 109787484258304 * q^56 + 950883425062000 * q^57 - 1202315115525120 * q^58 + 654616071995160 * q^59 + 1329040385162884 * q^61 + 1822942048958464 * q^62 - 3184801966786532 * q^63 + 562949953421312 * q^64 + 2465538888400896 * q^66 + 4249016411877596 * q^67 + 1229169586077696 * q^68 + 12411535659353832 * q^69 + 2035131949347624 * q^71 + 3744605925277696 * q^72 - 2248593461347972 * q^73 - 2542877347185664 * q^74 - 8959087778201600 * q^76 - 8848168987836288 * q^77 + 16136631097014272 * q^78 + 19188427678495120 * q^79 - 18903014015714198 * q^81 + 2463414241496064 * q^82 + 18474649086611988 * q^83 - 26853500411969536 * q^84 - 1973359619034112 * q^86 - 17047661699498280 * q^87 + 19954966739288064 * q^88 - 17458912916395020 * q^89 - 54374608211433016 * q^91 + 42548210611519488 * q^92 + 180402465813627376 * q^93 + 119314579414526976 * q^94 + 6935719348011008 * q^96 - 195934325822490244 * q^97 - 29652005603083776 * q^98 + 169824195828146112 * 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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	−12037.8	−1.05929	−0.529646	−	0.848219i	$-0.677675\pi$
$3$	−12037.8	−1.05929	−0.529646	+	0.848219i	$0.677675\pi$
$4$	65536.0	0.500000
$5$	0	0
$5$	0	0
$6$	−3.08167e6	−0.749033
$7$	9.53475e6	0.625138	0.312569	−	0.949895i	$-0.398810\pi$
$7$	9.53475e6	0.625138	0.312569	+	0.949895i	$0.398810\pi$
$8$	1.67772e7	0.353553
$9$	1.57682e7	0.122101
$10$	0	0
$11$	4.01191e8	0.564305	0.282152	−	0.959370i	$-0.408952\pi$
$11$	4.01191e8	0.564305	0.282152	+	0.959370i	$0.408952\pi$
$12$	−7.88908e8	−0.529646
$13$	−8.56166e8	−0.291098	−0.145549	−	0.989351i	$-0.546495\pi$
$13$	−8.56166e8	−0.291098	−0.145549	+	0.989351i	$0.546495\pi$
$14$	2.44090e9	0.442040
$15$	0	0
$16$	4.29497e9	0.250000
$17$	3.89127e10	1.35293	0.676465	−	0.736475i	$-0.263511\pi$
$17$	3.89127e10	1.35293	0.676465	+	0.736475i	$0.263511\pi$
$18$	4.03665e9	0.0863385
$19$	−1.13839e11	−1.53775	−0.768876	−	0.639398i	$-0.779184\pi$
$19$	−1.13839e11	−1.53775	−0.768876	+	0.639398i	$0.779184\pi$
$20$	0	0
$21$	−1.14777e11	−0.662205
$22$	1.02705e11	0.399024
$23$	−1.64834e10	−0.0438894	−0.0219447	−	0.999759i	$-0.506986\pi$
$23$	−1.64834e10	−0.0438894	−0.0219447	+	0.999759i	$0.506986\pi$
$24$	−2.01961e11	−0.374517
$25$	0	0
$26$	−2.19179e11	−0.205838
$27$	1.36475e12	0.929952
$28$	6.24870e11	0.312569
$29$	−2.27472e12	−0.844394	−0.422197	−	0.906504i	$-0.638741\pi$
$29$	−2.27472e12	−0.844394	−0.422197	+	0.906504i	$0.638741\pi$
$30$	0	0
$31$	−1.63788e12	−0.344911	−0.172455	−	0.985017i	$-0.555170\pi$
$31$	−1.63788e12	−0.344911	−0.172455	+	0.985017i	$0.555170\pi$
$32$	1.09951e12	0.176777
$33$	−4.82946e12	−0.597764
$34$	9.96164e12	0.956665
$35$	0	0
$36$	1.03338e12	0.0610506
$37$	1.75967e13	0.823599	0.411799	−	0.911275i	$-0.364900\pi$
$37$	1.75967e13	0.823599	0.411799	+	0.911275i	$0.364900\pi$
$38$	−2.91428e13	−1.08735
$39$	1.03064e13	0.308358
$40$	0	0
$41$	−2.95532e13	−0.578018	−0.289009	−	0.957326i	$-0.593326\pi$
$41$	−2.95532e13	−0.578018	−0.289009	+	0.957326i	$0.593326\pi$
$42$	−2.93830e13	−0.468249
$43$	−1.37690e14	−1.79647	−0.898233	−	0.439519i	$-0.855149\pi$
$43$	−1.37690e14	−1.79647	−0.898233	+	0.439519i	$0.855149\pi$
$44$	2.62925e13	0.282152
$45$	0	0
$46$	−4.21974e12	−0.0310345
$47$	1.65452e14	1.01354	0.506770	−	0.862081i	$-0.330839\pi$
$47$	1.65452e14	1.01354	0.506770	+	0.862081i	$0.330839\pi$
$48$	−5.17019e13	−0.264823
$49$	−1.41719e14	−0.609202
$50$	0	0
$51$	−4.68422e14	−1.43315
$52$	−5.61097e13	−0.145549
$53$	7.25259e14	1.60010	0.800052	−	0.599931i	$-0.204805\pi$
$53$	7.25259e14	1.60010	0.800052	+	0.599931i	$0.204805\pi$
$54$	3.49376e14	0.657575
$55$	0	0
$56$	1.59967e14	0.221020
$57$	1.37037e15	1.62893
$58$	−5.82328e14	−0.597076
$59$	1.62177e15	1.43796	0.718981	−	0.695030i	$-0.244609\pi$
$59$	1.62177e15	1.43796	0.718981	+	0.695030i	$0.244609\pi$
$60$	0	0
$61$	2.46915e15	1.64909	0.824545	−	0.565796i	$-0.191431\pi$
$61$	2.46915e15	1.64909	0.824545	+	0.565796i	$0.191431\pi$
$62$	−4.19296e14	−0.243889
$63$	1.50346e14	0.0763301
$64$	2.81475e14	0.125000
$65$	0	0
$66$	−1.23634e15	−0.422683
$67$	2.03244e14	0.0611479	0.0305739	−	0.999533i	$-0.490266\pi$
$67$	2.03244e14	0.0611479	0.0305739	+	0.999533i	$0.490266\pi$
$68$	2.55018e15	0.676465
$69$	1.98423e14	0.0464917
$70$	0	0
$71$	9.39117e15	1.72593	0.862966	−	0.505262i	$-0.168604\pi$
$71$	9.39117e15	1.72593	0.862966	+	0.505262i	$0.168604\pi$
$72$	2.64546e14	0.0431693
$73$	−1.54865e15	−0.224754	−0.112377	−	0.993666i	$-0.535847\pi$
$73$	−1.54865e15	−0.224754	−0.112377	+	0.993666i	$0.535847\pi$
$74$	4.50475e15	0.582372
$75$	0	0
$76$	−7.46056e15	−0.768876
$77$	3.82526e15	0.352769
$78$	2.63843e15	0.218042
$79$	8.30977e15	0.616252	0.308126	−	0.951345i	$-0.400298\pi$
$79$	8.30977e15	0.616252	0.308126	+	0.951345i	$0.400298\pi$
$80$	0	0
$81$	−1.84648e16	−1.10719
$82$	−7.56562e15	−0.408721
$83$	6.14697e15	0.299569	0.149785	−	0.988719i	$-0.452142\pi$
$83$	6.14697e15	0.299569	0.149785	+	0.988719i	$0.452142\pi$
$84$	−7.52205e15	−0.331102
$85$	0	0
$86$	−3.52485e16	−1.27029
$87$	2.73826e16	0.894460
$88$	6.73087e15	0.199512
$89$	4.67428e15	0.125863	0.0629317	−	0.998018i	$-0.479955\pi$
$89$	4.67428e15	0.125863	0.0629317	+	0.998018i	$0.479955\pi$
$90$	0	0
$91$	−8.16334e15	−0.181977
$92$	−1.08025e15	−0.0219447
$93$	1.97164e16	0.365362
$94$	4.23558e16	0.716681
$95$	0	0
$96$	−1.32357e16	−0.187258
$97$	−1.01799e17	−1.31881	−0.659407	−	0.751786i	$-0.729192\pi$
$97$	−1.01799e17	−1.31881	−0.659407	+	0.751786i	$0.729192\pi$
$98$	−3.62801e16	−0.430771
$99$	6.32605e15	0.0689023
$100$	0	0
$101$	3.11898e16	0.286603	0.143302	−	0.989679i	$-0.454228\pi$
$101$	3.11898e16	0.286603	0.143302	+	0.989679i	$0.454228\pi$
$102$	−1.19916e17	−1.01339
$103$	1.71633e17	1.33501	0.667505	−	0.744606i	$-0.267362\pi$
$103$	1.71633e17	1.33501	0.667505	+	0.744606i	$0.267362\pi$
$104$	−1.43641e16	−0.102919
$105$	0	0
$106$	1.85666e17	1.13144
$107$	1.64074e17	0.923159	0.461579	−	0.887099i	$-0.347283\pi$
$107$	1.64074e17	0.923159	0.461579	+	0.887099i	$0.347283\pi$
$108$	8.94401e16	0.464976
$109$	2.80332e17	1.34756	0.673779	−	0.738933i	$-0.264670\pi$
$109$	2.80332e17	1.34756	0.673779	+	0.738933i	$0.264670\pi$
$110$	0	0
$111$	−2.11825e17	−0.872432
$112$	4.09515e16	0.156285
$113$	5.30659e17	1.87780	0.938899	−	0.344193i	$-0.111847\pi$
$113$	5.30659e17	1.87780	0.938899	+	0.344193i	$0.111847\pi$
$114$	3.50815e17	1.15183
$115$	0	0
$116$	−1.49076e17	−0.422197
$117$	−1.35002e16	−0.0355434
$118$	4.15173e17	1.01679
$119$	3.71023e17	0.845768
$120$	0	0
$121$	−3.44493e17	−0.681560
$122$	6.32103e17	1.16608
$123$	3.55755e17	0.612291
$124$	−1.07340e17	−0.172455
$125$	0	0
$126$	3.84885e16	0.0539735
$127$	−3.45518e17	−0.453043	−0.226522	−	0.974006i	$-0.572735\pi$
$127$	−3.45518e17	−0.453043	−0.226522	+	0.974006i	$0.572735\pi$
$128$	7.20576e16	0.0883883
$129$	1.65748e18	1.90298
$130$	0	0
$131$	−5.92983e17	−0.597360	−0.298680	−	0.954353i	$-0.596546\pi$
$131$	−5.92983e17	−0.597360	−0.298680	+	0.954353i	$0.596546\pi$
$132$	−3.16503e17	−0.298882
$133$	−1.08543e18	−0.961307
$134$	5.20304e16	0.0432381
$135$	0	0
$136$	6.52846e17	0.478333
$137$	5.64525e17	0.388650	0.194325	−	0.980937i	$-0.437748\pi$
$137$	5.64525e17	0.388650	0.194325	+	0.980937i	$0.437748\pi$
$138$	5.07964e16	0.0328746
$139$	2.13511e18	1.29956	0.649778	−	0.760124i	$-0.274862\pi$
$139$	2.13511e18	1.29956	0.649778	+	0.760124i	$0.274862\pi$
$140$	0	0
$141$	−1.99168e18	−1.07364
$142$	2.40414e18	1.22042
$143$	−3.43487e17	−0.164268
$144$	6.77237e16	0.0305253
$145$	0	0
$146$	−3.96454e17	−0.158925
$147$	1.70598e18	0.645323
$148$	1.15321e18	0.411799
$149$	2.11167e18	0.712103	0.356051	−	0.934466i	$-0.384123\pi$
$149$	2.11167e18	0.712103	0.356051	+	0.934466i	$0.384123\pi$
$150$	0	0
$151$	1.09446e18	0.329532	0.164766	−	0.986333i	$-0.447313\pi$
$151$	1.09446e18	0.329532	0.164766	+	0.986333i	$0.447313\pi$
$152$	−1.90990e18	−0.543677
$153$	6.13581e17	0.165194
$154$	9.79267e17	0.249445
$155$	0	0
$156$	6.75437e17	0.154179
$157$	−2.67975e18	−0.579359	−0.289680	−	0.957124i	$-0.593549\pi$
$157$	−2.67975e18	−0.579359	−0.289680	+	0.957124i	$0.593549\pi$
$158$	2.12730e18	0.435756
$159$	−8.73051e18	−1.69498
$160$	0	0
$161$	−1.57165e17	−0.0274369
$162$	−4.72700e18	−0.782903
$163$	9.47539e18	1.48937	0.744685	−	0.667416i	$-0.232600\pi$
$163$	9.47539e18	1.48937	0.744685	+	0.667416i	$0.232600\pi$
$164$	−1.93680e18	−0.289009
$165$	0	0
$166$	1.57362e18	0.211827
$167$	6.70665e18	0.857859	0.428929	−	0.903338i	$-0.358891\pi$
$167$	6.70665e18	0.857859	0.428929	+	0.903338i	$0.358891\pi$
$168$	−1.92564e18	−0.234125
$169$	−7.91739e18	−0.915262
$170$	0	0
$171$	−1.79503e18	−0.187761
$172$	−9.02362e18	−0.898233
$173$	−1.05695e19	−1.00152	−0.500762	−	0.865585i	$-0.666947\pi$
$173$	−1.05695e19	−1.00152	−0.500762	+	0.865585i	$0.666947\pi$
$174$	7.00994e18	0.632479
$175$	0	0
$176$	1.72310e18	0.141076
$177$	−1.95225e19	−1.52322
$178$	1.19662e18	0.0889989
$179$	−1.98718e19	−1.40924	−0.704621	−	0.709583i	$-0.748883\pi$
$179$	−1.98718e19	−1.40924	−0.704621	+	0.709583i	$0.748883\pi$
$180$	0	0
$181$	2.50176e19	1.61428	0.807138	−	0.590363i	$-0.201015\pi$
$181$	2.50176e19	1.61428	0.807138	+	0.590363i	$0.201015\pi$
$182$	−2.08981e18	−0.128677
$183$	−2.97231e19	−1.74687
$184$	−2.76545e17	−0.0155172
$185$	0	0
$186$	5.04740e18	0.258350
$187$	1.56114e19	0.763464
$188$	1.08431e19	0.506770
$189$	1.30125e19	0.581349
$190$	0	0
$191$	−2.63385e19	−1.07599	−0.537995	−	0.842948i	$-0.680818\pi$
$191$	−2.63385e19	−1.07599	−0.537995	+	0.842948i	$0.680818\pi$
$192$	−3.38834e18	−0.132412
$193$	−3.68856e19	−1.37918	−0.689589	−	0.724201i	$-0.742209\pi$
$193$	−3.68856e19	−1.37918	−0.689589	+	0.724201i	$0.742209\pi$
$194$	−2.60605e19	−0.932542
$195$	0	0
$196$	−9.28769e18	−0.304601
$197$	4.04920e19	1.27176	0.635882	−	0.771786i	$-0.280636\pi$
$197$	4.04920e19	1.27176	0.635882	+	0.771786i	$0.280636\pi$
$198$	1.61947e18	0.0487212
$199$	−3.32772e19	−0.959171	−0.479586	−	0.877495i	$-0.659213\pi$
$199$	−3.32772e19	−0.959171	−0.479586	+	0.877495i	$0.659213\pi$
$200$	0	0
$201$	−2.44660e18	−0.0647735
$202$	7.98459e18	0.202659
$203$	−2.16889e19	−0.527863
$204$	−3.06985e19	−0.716574
$205$	0	0
$206$	4.39380e19	0.943994
$207$	−2.59912e17	−0.00535894
$208$	−3.67721e18	−0.0727746
$209$	−4.56713e19	−0.867761
$210$	0	0
$211$	−2.42162e19	−0.424331	−0.212166	−	0.977234i	$-0.568052\pi$
$211$	−2.42162e19	−0.424331	−0.212166	+	0.977234i	$0.568052\pi$
$212$	4.75306e19	0.800052
$213$	−1.13049e20	−1.82827
$214$	4.20028e19	0.652772
$215$	0	0
$216$	2.28967e19	0.328788
$217$	−1.56168e19	−0.215617
$218$	7.17650e19	0.952867
$219$	1.86423e19	0.238081
$220$	0	0
$221$	−3.33157e19	−0.393835
$222$	−5.42272e19	−0.616903
$223$	−7.42273e19	−0.812779	−0.406390	−	0.913700i	$-0.633212\pi$
$223$	−7.42273e19	−0.812779	−0.406390	+	0.913700i	$0.633212\pi$
$224$	1.04836e19	0.110510
$225$	0	0
$226$	1.35849e20	1.32780
$227$	−9.57531e18	−0.0901432	−0.0450716	−	0.998984i	$-0.514352\pi$
$227$	−9.57531e18	−0.0901432	−0.0450716	+	0.998984i	$0.514352\pi$
$228$	8.98087e19	0.814464
$229$	1.97753e20	1.72791	0.863955	−	0.503569i	$-0.167980\pi$
$229$	1.97753e20	1.72791	0.863955	+	0.503569i	$0.167980\pi$
$230$	0	0
$231$	−4.60477e19	−0.373685
$232$	−3.81635e19	−0.298538
$233$	1.79778e20	1.35585	0.677925	−	0.735131i	$-0.262880\pi$
$233$	1.79778e20	1.35585	0.677925	+	0.735131i	$0.262880\pi$
$234$	−3.45604e18	−0.0251330
$235$	0	0
$236$	1.06284e20	0.718981
$237$	−1.00031e20	−0.652792
$238$	9.49818e19	0.598048
$239$	−2.00207e20	−1.21646	−0.608229	−	0.793761i	$-0.708120\pi$
$239$	−2.00207e20	−1.21646	−0.608229	+	0.793761i	$0.708120\pi$
$240$	0	0
$241$	−1.81616e20	−1.02804	−0.514018	−	0.857779i	$-0.671844\pi$
$241$	−1.81616e20	−1.02804	−0.514018	+	0.857779i	$0.671844\pi$
$242$	−8.81901e19	−0.481936
$243$	4.60321e19	0.242889
$244$	1.61818e20	0.824545
$245$	0	0
$246$	9.10733e19	0.432955
$247$	9.74653e19	0.447637
$248$	−2.74790e19	−0.121944
$249$	−7.39959e19	−0.317332
$250$	0	0
$251$	−3.20192e20	−1.28288	−0.641438	−	0.767175i	$-0.721662\pi$
$251$	−3.20192e20	−1.28288	−0.641438	+	0.767175i	$0.721662\pi$
$252$	9.85304e18	0.0381651
$253$	−6.61299e18	−0.0247670
$254$	−8.84527e19	−0.320350
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	3.34539e20	1.09652	0.548259	−	0.836309i	$-0.315291\pi$
$257$	3.34539e20	1.09652	0.548259	+	0.836309i	$0.315291\pi$
$258$	4.24314e20	1.34561
$259$	1.67780e20	0.514863
$260$	0	0
$261$	−3.58681e19	−0.103101
$262$	−1.51804e20	−0.422397
$263$	−2.95034e20	−0.794782	−0.397391	−	0.917649i	$-0.630084\pi$
$263$	−2.95034e20	−0.794782	−0.397391	+	0.917649i	$0.630084\pi$
$264$	−8.10248e19	−0.211341
$265$	0	0
$266$	−2.77870e20	−0.679747
$267$	−5.62680e19	−0.133326
$268$	1.33198e19	0.0305739
$269$	7.56967e20	1.68338	0.841690	−	0.539960i	$-0.181561\pi$
$269$	7.56967e20	1.68338	0.841690	+	0.539960i	$0.181561\pi$
$270$	0	0
$271$	−1.18908e20	−0.248298	−0.124149	−	0.992264i	$-0.539620\pi$
$271$	−1.18908e20	−0.248298	−0.124149	+	0.992264i	$0.539620\pi$
$272$	1.67129e20	0.338232
$273$	9.82685e19	0.192767
$274$	1.44518e20	0.274817
$275$	0	0
$276$	1.30039e19	0.0232458
$277$	1.96379e20	0.340421	0.170211	−	0.985408i	$-0.445555\pi$
$277$	1.96379e20	0.340421	0.170211	+	0.985408i	$0.445555\pi$
$278$	5.46589e20	0.918925
$279$	−2.58263e19	−0.0421140
$280$	0	0
$281$	−3.39035e20	−0.520284	−0.260142	−	0.965570i	$-0.583769\pi$
$281$	−3.39035e20	−0.520284	−0.260142	+	0.965570i	$0.583769\pi$
$282$	−5.09870e20	−0.759175
$283$	−4.03445e20	−0.582908	−0.291454	−	0.956585i	$-0.594139\pi$
$283$	−4.03445e20	−0.582908	−0.291454	+	0.956585i	$0.594139\pi$
$284$	6.15460e20	0.862966
$285$	0	0
$286$	−8.79326e19	−0.116155
$287$	−2.81782e20	−0.361341
$288$	1.73373e19	0.0215846
$289$	6.86955e20	0.830418
$290$	0	0
$291$	1.22543e21	1.39701
$292$	−1.01492e20	−0.112377
$293$	1.05777e20	0.113767	0.0568836	−	0.998381i	$-0.481884\pi$
$293$	1.05777e20	0.113767	0.0568836	+	0.998381i	$0.481884\pi$
$294$	4.36732e20	0.456312
$295$	0	0
$296$	2.95223e20	0.291186
$297$	5.47525e20	0.524776
$298$	5.40587e20	0.503533
$299$	1.41125e19	0.0127761
$300$	0	0
$301$	−1.31284e21	−1.12304
$302$	2.80183e20	0.233014
$303$	−3.75456e20	−0.303597
$304$	−4.88936e20	−0.384438
$305$	0	0
$306$	1.57077e20	0.116810
$307$	1.82911e21	1.32301	0.661504	−	0.749941i	$-0.269918\pi$
$307$	1.82911e21	1.32301	0.661504	+	0.749941i	$0.269918\pi$
$308$	2.50692e20	0.176384
$309$	−2.06608e21	−1.41417
$310$	0	0
$311$	2.00748e21	1.30073	0.650366	−	0.759621i	$-0.274616\pi$
$311$	2.00748e21	1.30073	0.650366	+	0.759621i	$0.274616\pi$
$312$	1.72912e20	0.109021
$313$	2.84834e21	1.74769	0.873846	−	0.486203i	$-0.161619\pi$
$313$	2.84834e21	1.74769	0.873846	+	0.486203i	$0.161619\pi$
$314$	−6.86017e20	−0.409669
$315$	0	0
$316$	5.44589e20	0.308126
$317$	−2.74347e20	−0.151111	−0.0755554	−	0.997142i	$-0.524073\pi$
$317$	−2.74347e20	−0.151111	−0.0755554	+	0.997142i	$0.524073\pi$
$318$	−2.23501e21	−1.19853
$319$	−9.12598e20	−0.476495
$320$	0	0
$321$	−1.97508e21	−0.977895
$322$	−4.02342e19	−0.0194008
$323$	−4.42979e21	−2.08047
$324$	−1.21011e21	−0.553596
$325$	0	0
$326$	2.42570e21	1.05314
$327$	−3.37458e21	−1.42746
$328$	−4.95820e20	−0.204360
$329$	1.57755e21	0.633603
$330$	0	0
$331$	1.83521e20	0.0700082	0.0350041	−	0.999387i	$-0.488856\pi$
$331$	1.83521e20	0.0700082	0.0350041	+	0.999387i	$0.488856\pi$
$332$	4.02848e20	0.149785
$333$	2.77467e20	0.100562
$334$	1.71690e21	0.606598
$335$	0	0
$336$	−4.92965e20	−0.165551
$337$	6.21202e20	0.203413	0.101706	−	0.994814i	$-0.467570\pi$
$337$	6.21202e20	0.203413	0.101706	+	0.994814i	$0.467570\pi$
$338$	−2.02685e21	−0.647188
$339$	−6.38796e21	−1.98914
$340$	0	0
$341$	−6.57102e20	−0.194635
$342$	−4.59529e20	−0.132767
$343$	−3.56933e21	−1.00597
$344$	−2.31005e21	−0.635147
$345$	0	0
$346$	−2.70579e21	−0.708185
$347$	−5.08978e21	−1.29987	−0.649933	−	0.759992i	$-0.725203\pi$
$347$	−5.08978e21	−1.29987	−0.649933	+	0.759992i	$0.725203\pi$
$348$	1.79455e21	0.447230
$349$	−3.81066e20	−0.0926796	−0.0463398	−	0.998926i	$-0.514756\pi$
$349$	−3.81066e20	−0.0926796	−0.0463398	+	0.998926i	$0.514756\pi$
$350$	0	0
$351$	−1.16845e21	−0.270707
$352$	4.41115e20	0.0997559
$353$	−2.34699e21	−0.518115	−0.259058	−	0.965862i	$-0.583412\pi$
$353$	−2.34699e21	−0.518115	−0.259058	+	0.965862i	$0.583412\pi$
$354$	−4.99777e21	−1.07708
$355$	0	0
$356$	3.06334e20	0.0629317
$357$	−4.46629e21	−0.895916
$358$	−5.08717e21	−0.996485
$359$	−6.19792e19	−0.0118561	−0.00592807	−	0.999982i	$-0.501887\pi$
$359$	−6.19792e19	−0.0118561	−0.00592807	+	0.999982i	$0.501887\pi$
$360$	0	0
$361$	7.47897e21	1.36468
$362$	6.40451e21	1.14147
$363$	4.14693e21	0.721972
$364$	−5.34992e20	−0.0909884
$365$	0	0
$366$	−7.60912e21	−1.23522
$367$	3.40565e21	0.540180	0.270090	−	0.962835i	$-0.412946\pi$
$367$	3.40565e21	0.540180	0.270090	+	0.962835i	$0.412946\pi$
$368$	−7.07955e19	−0.0109723
$369$	−4.65999e20	−0.0705767
$370$	0	0
$371$	6.91517e21	1.00029
$372$	1.29213e21	0.182681
$373$	6.44986e21	0.891302	0.445651	−	0.895207i	$-0.352972\pi$
$373$	6.44986e21	0.891302	0.445651	+	0.895207i	$0.352972\pi$
$374$	3.99652e21	0.539851
$375$	0	0
$376$	2.77583e21	0.358340
$377$	1.94754e21	0.245802
$378$	3.33121e21	0.411076
$379$	−5.68235e21	−0.685638	−0.342819	−	0.939401i	$-0.611382\pi$
$379$	−5.68235e21	−0.685638	−0.342819	+	0.939401i	$0.611382\pi$
$380$	0	0
$381$	4.15928e21	0.479905
$382$	−6.74266e21	−0.760839
$383$	1.28548e22	1.41865	0.709327	−	0.704879i	$-0.248999\pi$
$383$	1.28548e22	1.41865	0.709327	+	0.704879i	$0.248999\pi$
$384$	−8.67414e20	−0.0936291
$385$	0	0
$386$	−9.44272e21	−0.975226
$387$	−2.17111e21	−0.219351
$388$	−6.67149e21	−0.659407
$389$	1.70189e22	1.64573	0.822867	−	0.568234i	$-0.192373\pi$
$389$	1.70189e22	1.64573	0.822867	+	0.568234i	$0.192373\pi$
$390$	0	0
$391$	−6.41412e20	−0.0593792
$392$	−2.37765e21	−0.215385
$393$	7.13820e21	0.632779
$394$	1.03660e22	0.899273
$395$	0	0
$396$	4.14584e20	0.0344511
$397$	1.81182e22	1.47365	0.736827	−	0.676081i	$-0.236323\pi$
$397$	1.81182e22	1.47365	0.736827	+	0.676081i	$0.236323\pi$
$398$	−8.51897e21	−0.678236
$399$	1.30662e22	1.01831
$400$	0	0
$401$	1.75008e22	1.30717	0.653585	−	0.756853i	$-0.273264\pi$
$401$	1.75008e22	1.30717	0.653585	+	0.756853i	$0.273264\pi$
$402$	−6.26331e20	−0.0458018
$403$	1.40230e21	0.100403
$404$	2.04406e21	0.143302
$405$	0	0
$406$	−5.55236e21	−0.373255
$407$	7.05963e21	0.464761
$408$	−7.85882e21	−0.506694
$409$	9.06225e21	0.572253	0.286127	−	0.958192i	$-0.407632\pi$
$409$	9.06225e21	0.572253	0.286127	+	0.958192i	$0.407632\pi$
$410$	0	0
$411$	−6.79563e21	−0.411694
$412$	1.12481e22	0.667505
$413$	1.54632e22	0.898925
$414$	−6.65376e19	−0.00378934
$415$	0	0
$416$	−9.41365e20	−0.0514594
$417$	−2.57020e22	−1.37661
$418$	−1.16919e22	−0.613599
$419$	7.49706e21	0.385542	0.192771	−	0.981244i	$-0.438253\pi$
$419$	7.49706e21	0.385542	0.192771	+	0.981244i	$0.438253\pi$
$420$	0	0
$421$	−2.95580e22	−1.45975	−0.729873	−	0.683583i	$-0.760421\pi$
$421$	−2.95580e22	−1.45975	−0.729873	+	0.683583i	$0.760421\pi$
$422$	−6.19935e21	−0.300048
$423$	2.60888e21	0.123754
$424$	1.21678e22	0.565722
$425$	0	0
$426$	−2.89405e22	−1.29278
$427$	2.35428e22	1.03091
$428$	1.07527e22	0.461579
$429$	4.13482e21	0.174008
$430$	0	0
$431$	−7.37016e21	−0.298140	−0.149070	−	0.988827i	$-0.547628\pi$
$431$	−7.37016e21	−0.298140	−0.149070	+	0.988827i	$0.547628\pi$
$432$	5.86155e21	0.232488
$433$	−1.77584e21	−0.0690650	−0.0345325	−	0.999404i	$-0.510994\pi$
$433$	−1.77584e21	−0.0690650	−0.0345325	+	0.999404i	$0.510994\pi$
$434$	−3.99789e21	−0.152464
$435$	0	0
$436$	1.83718e22	0.673779
$437$	1.87645e21	0.0674909
$438$	4.77243e21	0.168349
$439$	−2.92011e22	−1.01030	−0.505151	−	0.863031i	$-0.668563\pi$
$439$	−2.92011e22	−1.01030	−0.505151	+	0.863031i	$0.668563\pi$
$440$	0	0
$441$	−2.23465e21	−0.0743842
$442$	−8.52882e21	−0.278484
$443$	4.06554e22	1.30223	0.651113	−	0.758980i	$-0.274302\pi$
$443$	4.06554e22	1.30223	0.651113	+	0.758980i	$0.274302\pi$
$444$	−1.38822e22	−0.436216
$445$	0	0
$446$	−1.90022e22	−0.574722
$447$	−2.54198e22	−0.754325
$448$	2.68379e21	0.0781423
$449$	4.62783e21	0.132216	0.0661079	−	0.997812i	$-0.478942\pi$
$449$	4.62783e21	0.132216	0.0661079	+	0.997812i	$0.478942\pi$
$450$	0	0
$451$	−1.18565e22	−0.326179
$452$	3.47773e22	0.938899
$453$	−1.31749e22	−0.349071
$454$	−2.45128e21	−0.0637409
$455$	0	0
$456$	2.29910e22	0.575913
$457$	−6.30841e22	−1.55107	−0.775536	−	0.631303i	$-0.782520\pi$
$457$	−6.30841e22	−1.55107	−0.775536	+	0.631303i	$0.782520\pi$
$458$	5.06247e22	1.22182
$459$	5.31060e22	1.25816
$460$	0	0
$461$	5.62982e22	1.28539	0.642697	−	0.766120i	$-0.277815\pi$
$461$	5.62982e22	1.28539	0.642697	+	0.766120i	$0.277815\pi$
$462$	−1.17882e22	−0.264235
$463$	−5.90180e21	−0.129881	−0.0649405	−	0.997889i	$-0.520686\pi$
$463$	−5.90180e21	−0.129881	−0.0649405	+	0.997889i	$0.520686\pi$
$464$	−9.76985e21	−0.211098
$465$	0	0
$466$	4.60232e22	0.958730
$467$	−2.51115e22	−0.513663	−0.256832	−	0.966456i	$-0.582679\pi$
$467$	−2.51115e22	−0.513663	−0.256832	+	0.966456i	$0.582679\pi$
$468$	−8.84747e20	−0.0177717
$469$	1.93788e21	0.0382259
$470$	0	0
$471$	3.22583e22	0.613711
$472$	2.72088e22	0.508396
$473$	−5.52399e22	−1.01375
$474$	−2.56080e22	−0.461594
$475$	0	0
$476$	2.43153e22	0.422884
$477$	1.14360e22	0.195375
$478$	−5.12530e22	−0.860166
$479$	−3.54309e22	−0.584158	−0.292079	−	0.956394i	$-0.594347\pi$
$479$	−3.54309e22	−0.584158	−0.292079	+	0.956394i	$0.594347\pi$
$480$	0	0
$481$	−1.50657e22	−0.239748
$482$	−4.64936e22	−0.726931
$483$	1.89192e21	0.0290637
$484$	−2.25767e22	−0.340780
$485$	0	0
$486$	1.17842e22	0.171748
$487$	1.51696e22	0.217259	0.108629	−	0.994082i	$-0.465354\pi$
$487$	1.51696e22	0.217259	0.108629	+	0.994082i	$0.465354\pi$
$488$	4.14255e22	0.583041
$489$	−1.14063e23	−1.57768
$490$	0	0
$491$	−6.96906e22	−0.931068	−0.465534	−	0.885030i	$-0.654138\pi$
$491$	−6.96906e22	−0.931068	−0.465534	+	0.885030i	$0.654138\pi$
$492$	2.33148e22	0.306145
$493$	−8.85154e22	−1.14240
$494$	2.49511e22	0.316527
$495$	0	0
$496$	−7.03463e21	−0.0862277
$497$	8.95425e22	1.07895
$498$	−1.89430e22	−0.224387
$499$	−5.10974e22	−0.595037	−0.297518	−	0.954716i	$-0.596159\pi$
$499$	−5.10974e22	−0.595037	−0.297518	+	0.954716i	$0.596159\pi$
$500$	0	0
$501$	−8.07332e22	−0.908723
$502$	−8.19693e22	−0.907130
$503$	−6.26474e21	−0.0681671	−0.0340836	−	0.999419i	$-0.510851\pi$
$503$	−6.26474e21	−0.0681671	−0.0340836	+	0.999419i	$0.510851\pi$
$504$	2.52238e21	0.0269868
$505$	0	0
$506$	−1.69292e21	−0.0175129
$507$	9.53079e22	0.969530
$508$	−2.26439e22	−0.226522
$509$	−7.41555e22	−0.729528	−0.364764	−	0.931100i	$-0.618850\pi$
$509$	−7.41555e22	−0.729528	−0.364764	+	0.931100i	$0.618850\pi$
$510$	0	0
$511$	−1.47660e22	−0.140503
$512$	4.72237e21	0.0441942
$513$	−1.55362e23	−1.43003
$514$	8.56421e22	0.775355
$515$	0	0
$516$	1.08624e23	0.951492
$517$	6.63780e22	0.571945
$518$	4.29516e22	0.364063
$519$	1.27233e23	1.06091
$520$	0	0
$521$	9.53386e21	0.0769393	0.0384696	−	0.999260i	$-0.487752\pi$
$521$	9.53386e21	0.0769393	0.0384696	+	0.999260i	$0.487752\pi$
$522$	−9.18225e21	−0.0729037
$523$	−1.49123e23	−1.16487	−0.582437	−	0.812876i	$-0.697901\pi$
$523$	−1.49123e23	−1.16487	−0.582437	+	0.812876i	$0.697901\pi$
$524$	−3.88617e22	−0.298680
$525$	0	0
$526$	−7.55287e22	−0.561996
$527$	−6.37341e22	−0.466640
$528$	−2.07424e22	−0.149441
$529$	−1.40778e23	−0.998074
$530$	0	0
$531$	2.55723e22	0.175577
$532$	−7.11347e22	−0.480654
$533$	2.53025e22	0.168260
$534$	−1.44046e22	−0.0942759
$535$	0	0
$536$	3.40986e21	0.0216190
$537$	2.39212e23	1.49280
$538$	1.93783e23	1.19033
$539$	−5.68564e22	−0.343776
$540$	0	0
$541$	8.46775e22	0.496125	0.248063	−	0.968744i	$-0.420206\pi$
$541$	8.46775e22	0.496125	0.248063	+	0.968744i	$0.420206\pi$
$542$	−3.04405e22	−0.175573
$543$	−3.01157e23	−1.70999
$544$	4.27849e22	0.239166
$545$	0	0
$546$	2.51567e22	0.136307
$547$	−4.72359e22	−0.251988	−0.125994	−	0.992031i	$-0.540212\pi$
$547$	−4.72359e22	−0.251988	−0.125994	+	0.992031i	$0.540212\pi$
$548$	3.69967e22	0.194325
$549$	3.89340e22	0.201356
$550$	0	0
$551$	2.58952e23	1.29847
$552$	3.32899e21	0.0164373
$553$	7.92316e22	0.385243
$554$	5.02730e22	0.240714
$555$	0	0
$556$	1.39927e23	0.649778
$557$	−3.77820e23	−1.72789	−0.863945	−	0.503587i	$-0.832013\pi$
$557$	−3.77820e23	−1.72789	−0.863945	+	0.503587i	$0.832013\pi$
$558$	−6.61153e21	−0.0297791
$559$	1.17885e23	0.522949
$560$	0	0
$561$	−1.87927e23	−0.808732
$562$	−8.67929e22	−0.367896
$563$	4.35959e23	1.82022	0.910112	−	0.414363i	$-0.135995\pi$
$563$	4.35959e23	1.82022	0.910112	+	0.414363i	$0.135995\pi$
$564$	−1.30527e23	−0.536818
$565$	0	0
$566$	−1.03282e23	−0.412178
$567$	−1.76058e23	−0.692149
$568$	1.57558e23	0.610209
$569$	−1.25095e23	−0.477293	−0.238647	−	0.971106i	$-0.576704\pi$
$569$	−1.25095e23	−0.477293	−0.238647	+	0.971106i	$0.576704\pi$
$570$	0	0
$571$	−3.10316e23	−1.14920	−0.574602	−	0.818433i	$-0.694843\pi$
$571$	−3.10316e23	−1.14920	−0.574602	+	0.818433i	$0.694843\pi$
$572$	−2.25107e22	−0.0821341
$573$	3.17058e23	1.13979
$574$	−7.21363e22	−0.255507
$575$	0	0
$576$	4.43834e21	0.0152626
$577$	2.11578e23	0.716928	0.358464	−	0.933544i	$-0.383301\pi$
$577$	2.11578e23	0.716928	0.358464	+	0.933544i	$0.383301\pi$
$578$	1.75860e23	0.587194
$579$	4.44021e23	1.46095
$580$	0	0
$581$	5.86099e22	0.187272
$582$	3.13711e23	0.987835
$583$	2.90968e23	0.902947
$584$	−2.59820e22	−0.0794627
$585$	0	0
$586$	2.70790e22	0.0804456
$587$	−2.15996e23	−0.632443	−0.316222	−	0.948685i	$-0.602414\pi$
$587$	−2.15996e23	−0.632443	−0.316222	+	0.948685i	$0.602414\pi$
$588$	1.11803e23	0.322662
$589$	1.86455e23	0.530387
$590$	0	0
$591$	−4.87434e23	−1.34717
$592$	7.55771e22	0.205900
$593$	−3.56471e23	−0.957326	−0.478663	−	0.877999i	$-0.658878\pi$
$593$	−3.56471e23	−0.957326	−0.478663	+	0.877999i	$0.658878\pi$
$594$	1.40166e23	0.371073
$595$	0	0
$596$	1.38390e23	0.356051
$597$	4.00584e23	1.01604
$598$	3.61280e21	0.00903408
$599$	3.17118e23	0.781796	0.390898	−	0.920434i	$-0.372165\pi$
$599$	3.17118e23	0.781796	0.390898	+	0.920434i	$0.372165\pi$
$600$	0	0
$601$	−2.47473e23	−0.593055	−0.296528	−	0.955024i	$-0.595829\pi$
$601$	−2.47473e23	−0.593055	−0.296528	+	0.955024i	$0.595829\pi$
$602$	−3.36086e23	−0.794109
$603$	3.20478e21	0.00746622
$604$	7.17268e22	0.164766
$605$	0	0
$606$	−9.61168e22	−0.214675
$607$	−1.27464e23	−0.280726	−0.140363	−	0.990100i	$-0.544827\pi$
$607$	−1.27464e23	−0.280726	−0.140363	+	0.990100i	$0.544827\pi$
$608$	−1.25168e23	−0.271839
$609$	2.61086e23	0.559161
$610$	0	0
$611$	−1.41655e23	−0.295040
$612$	4.02116e22	0.0825971
$613$	−2.08992e23	−0.423366	−0.211683	−	0.977338i	$-0.567895\pi$
$613$	−2.08992e23	−0.423366	−0.211683	+	0.977338i	$0.567895\pi$
$614$	4.68251e23	0.935508
$615$	0	0
$616$	6.41772e22	0.124723
$617$	−2.52173e23	−0.483364	−0.241682	−	0.970356i	$-0.577699\pi$
$617$	−2.52173e23	−0.483364	−0.241682	+	0.970356i	$0.577699\pi$
$618$	−5.28917e23	−0.999966
$619$	−8.32171e23	−1.55182	−0.775911	−	0.630842i	$-0.782709\pi$
$619$	−8.32171e23	−1.55182	−0.775911	+	0.630842i	$0.782709\pi$
$620$	0	0
$621$	−2.24956e22	−0.0408150
$622$	5.13915e23	0.919756
$623$	4.45681e22	0.0786821
$624$	4.42654e22	0.0770896
$625$	0	0
$626$	7.29175e23	1.23580
$627$	5.49781e23	0.919212
$628$	−1.75620e23	−0.289680
$629$	6.84733e23	1.11427
$630$	0	0
$631$	2.44878e23	0.387883	0.193942	−	0.981013i	$-0.437873\pi$
$631$	2.44878e23	0.387883	0.193942	+	0.981013i	$0.437873\pi$
$632$	1.39415e23	0.217878
$633$	2.91510e23	0.449491
$634$	−7.02327e22	−0.106852
$635$	0	0
$636$	−5.72163e23	−0.847489
$637$	1.21335e23	0.177338
$638$	−2.33625e23	−0.336933
$639$	1.48081e23	0.210738
$640$	0	0
$641$	8.76132e23	1.21416	0.607081	−	0.794640i	$-0.292340\pi$
$641$	8.76132e23	1.21416	0.607081	+	0.794640i	$0.292340\pi$
$642$	−5.05621e23	−0.691477
$643$	3.14015e23	0.423796	0.211898	−	0.977292i	$-0.432036\pi$
$643$	3.14015e23	0.423796	0.211898	+	0.977292i	$0.432036\pi$
$644$	−1.03000e22	−0.0137185
$645$	0	0
$646$	−1.13403e24	−1.47111
$647$	7.19139e22	0.0920718	0.0460359	−	0.998940i	$-0.485341\pi$
$647$	7.19139e22	0.0920718	0.0460359	+	0.998940i	$0.485341\pi$
$648$	−3.09789e23	−0.391452
$649$	6.50640e23	0.811448
$650$	0	0
$651$	1.87991e23	0.228402
$652$	6.20979e23	0.744685
$653$	7.53337e23	0.891717	0.445858	−	0.895103i	$-0.352898\pi$
$653$	7.53337e23	0.891717	0.445858	+	0.895103i	$0.352898\pi$
$654$	−8.63892e23	−1.00937
$655$	0	0
$656$	−1.26930e23	−0.144505
$657$	−2.44193e22	−0.0274428
$658$	4.03852e23	0.448025
$659$	−1.78954e24	−1.95981	−0.979906	−	0.199459i	$-0.936081\pi$
$659$	−1.78954e24	−1.95981	−0.979906	+	0.199459i	$0.936081\pi$
$660$	0	0
$661$	3.55263e23	0.379173	0.189586	−	0.981864i	$-0.439285\pi$
$661$	3.55263e23	0.379173	0.189586	+	0.981864i	$0.439285\pi$
$662$	4.69815e22	0.0495033
$663$	4.01047e23	0.417187
$664$	1.03129e23	0.105914
$665$	0	0
$666$	7.10315e22	0.0711083
$667$	3.74951e22	0.0370599
$668$	4.39527e23	0.428929
$669$	8.93533e23	0.860971
$670$	0	0
$671$	9.90603e23	0.930589
$672$	−1.26199e23	−0.117062
$673$	−5.15130e23	−0.471833	−0.235917	−	0.971773i	$-0.575809\pi$
$673$	−5.15130e23	−0.471833	−0.235917	+	0.971773i	$0.575809\pi$
$674$	1.59028e23	0.143835
$675$	0	0
$676$	−5.18874e23	−0.457631
$677$	−1.69205e23	−0.147370	−0.0736851	−	0.997282i	$-0.523476\pi$
$677$	−1.69205e23	−0.147370	−0.0736851	+	0.997282i	$0.523476\pi$
$678$	−1.63532e24	−1.40653
$679$	−9.70628e23	−0.824441
$680$	0	0
$681$	1.15265e23	0.0954880
$682$	−1.68218e23	−0.137628
$683$	−1.97763e23	−0.159797	−0.0798987	−	0.996803i	$-0.525460\pi$
$683$	−1.97763e23	−0.159797	−0.0798987	+	0.996803i	$0.525460\pi$
$684$	−1.17639e23	−0.0938806
$685$	0	0
$686$	−9.13749e23	−0.711331
$687$	−2.38051e24	−1.83036
$688$	−5.91372e23	−0.449117
$689$	−6.20943e23	−0.465788
$690$	0	0
$691$	2.62293e24	1.91966	0.959828	−	0.280589i	$-0.0905298\pi$
$691$	2.62293e24	1.91966	0.959828	+	0.280589i	$0.0905298\pi$
$692$	−6.92681e23	−0.500762
$693$	6.03173e22	0.0430734
$694$	−1.30298e24	−0.919144
$695$	0	0
$696$	4.59404e23	0.316239
$697$	−1.14999e24	−0.782018
$698$	−9.75529e22	−0.0655344
$699$	−2.16413e24	−1.43624
$700$	0	0
$701$	−4.05441e22	−0.0262618	−0.0131309	−	0.999914i	$-0.504180\pi$
$701$	−4.05441e22	−0.0262618	−0.0131309	+	0.999914i	$0.504180\pi$
$702$	−2.99124e23	−0.191419
$703$	−2.00319e24	−1.26649
$704$	1.12925e23	0.0705381
$705$	0	0
$706$	−6.00830e23	−0.366363
$707$	2.97387e23	0.179167
$708$	−1.27943e24	−0.761611
$709$	−7.92278e23	−0.465999	−0.232999	−	0.972477i	$-0.574854\pi$
$709$	−7.92278e23	−0.465999	−0.232999	+	0.972477i	$0.574854\pi$
$710$	0	0
$711$	1.31030e23	0.0752451
$712$	7.84214e22	0.0444995
$713$	2.69977e22	0.0151379
$714$	−1.14337e24	−0.633508
$715$	0	0
$716$	−1.30232e24	−0.704621
$717$	2.41005e24	1.28859
$718$	−1.58667e22	−0.00838355
$719$	−7.47670e23	−0.390404	−0.195202	−	0.980763i	$-0.562536\pi$
$719$	−7.47670e23	−0.390404	−0.195202	+	0.980763i	$0.562536\pi$
$720$	0	0
$721$	1.63648e24	0.834566
$722$	1.91462e24	0.964974
$723$	2.18625e24	1.08899
$724$	1.63955e24	0.807138
$725$	0	0
$726$	1.06161e24	0.510511
$727$	−5.40980e23	−0.257122	−0.128561	−	0.991702i	$-0.541036\pi$
$727$	−5.40980e23	−0.257122	−0.128561	+	0.991702i	$0.541036\pi$
$728$	−1.36958e23	−0.0643385
$729$	1.83043e24	0.849902
$730$	0	0
$731$	−5.35787e24	−2.43049
$732$	−1.94794e24	−0.873435
$733$	−2.02014e24	−0.895361	−0.447680	−	0.894194i	$-0.647750\pi$
$733$	−2.02014e24	−0.895361	−0.447680	+	0.894194i	$0.647750\pi$
$734$	8.71847e23	0.381965
$735$	0	0
$736$	−1.81237e22	−0.00775862
$737$	8.15396e22	0.0345060
$738$	−1.19296e23	−0.0499053
$739$	−2.11021e24	−0.872666	−0.436333	−	0.899785i	$-0.643723\pi$
$739$	−2.11021e24	−0.872666	−0.436333	+	0.899785i	$0.643723\pi$
$740$	0	0
$741$	−1.17327e24	−0.474179
$742$	1.77028e24	0.707309
$743$	−1.34376e24	−0.530784	−0.265392	−	0.964141i	$-0.585501\pi$
$743$	−1.34376e24	−0.530784	−0.265392	+	0.964141i	$0.585501\pi$
$744$	3.30786e23	0.129175
$745$	0	0
$746$	1.65116e24	0.630246
$747$	9.69264e22	0.0365777
$748$	1.02311e24	0.381732
$749$	1.56440e24	0.577102
$750$	0	0
$751$	2.72368e24	0.982236	0.491118	−	0.871093i	$-0.336588\pi$
$751$	2.72368e24	0.982236	0.491118	+	0.871093i	$0.336588\pi$
$752$	7.10612e23	0.253385
$753$	3.85441e24	1.35894
$754$	4.98570e23	0.173808
$755$	0	0
$756$	8.52790e23	0.290674
$757$	3.29400e24	1.11022	0.555109	−	0.831777i	$-0.312676\pi$
$757$	3.29400e24	1.11022	0.555109	+	0.831777i	$0.312676\pi$
$758$	−1.45468e24	−0.484819
$759$	7.96057e22	0.0262355
$760$	0	0
$761$	−4.29576e24	−1.38443	−0.692215	−	0.721692i	$-0.743365\pi$
$761$	−4.29576e24	−1.38443	−0.692215	+	0.721692i	$0.743365\pi$
$762$	1.06477e24	0.339344
$763$	2.67290e24	0.842410
$764$	−1.72612e24	−0.537995
$765$	0	0
$766$	3.29083e24	1.00314
$767$	−1.38851e24	−0.418588
$768$	−2.22058e23	−0.0662058
$769$	5.93781e24	1.75086	0.875432	−	0.483341i	$-0.160577\pi$
$769$	5.93781e24	1.75086	0.875432	+	0.483341i	$0.160577\pi$
$770$	0	0
$771$	−4.02711e24	−1.16153
$772$	−2.41734e24	−0.689589
$773$	1.98352e24	0.559642	0.279821	−	0.960052i	$-0.409725\pi$
$773$	1.98352e24	0.559642	0.279821	+	0.960052i	$0.409725\pi$
$774$	−5.55804e23	−0.155104
$775$	0	0
$776$	−1.70790e24	−0.466271
$777$	−2.01970e24	−0.545391
$778$	4.35684e24	1.16371
$779$	3.36431e24	0.888849
$780$	0	0
$781$	3.76766e24	0.973952
$782$	−1.64201e23	−0.0419874
$783$	−3.10442e24	−0.785246
$784$	−6.08678e23	−0.152300
$785$	0	0
$786$	1.82738e24	0.447442
$787$	−3.61371e24	−0.875322	−0.437661	−	0.899140i	$-0.644193\pi$
$787$	−3.61371e24	−0.875322	−0.437661	+	0.899140i	$0.644193\pi$
$788$	2.65369e24	0.635882
$789$	3.55156e24	0.841907
$790$	0	0
$791$	5.05970e24	1.17388
$792$	1.06133e23	0.0243606
$793$	−2.11401e24	−0.480047
$794$	4.63826e24	1.04203
$795$	0	0
$796$	−2.18086e24	−0.479586
$797$	4.63064e24	1.00750	0.503751	−	0.863849i	$-0.331953\pi$
$797$	4.63064e24	1.00750	0.503751	+	0.863849i	$0.331953\pi$
$798$	3.34494e24	0.720051
$799$	6.43819e24	1.37125
$800$	0	0
$801$	7.37048e22	0.0153681
$802$	4.48022e24	0.924308
$803$	−6.21304e23	−0.126830
$804$	−1.60341e23	−0.0323867
$805$	0	0
$806$	3.58988e23	0.0709956
$807$	−9.11220e24	−1.78319
$808$	5.23278e23	0.101330
$809$	−1.22642e24	−0.235005	−0.117502	−	0.993073i	$-0.537489\pi$
$809$	−1.22642e24	−0.235005	−0.117502	+	0.993073i	$0.537489\pi$
$810$	0	0
$811$	−2.42686e24	−0.455373	−0.227686	−	0.973735i	$-0.573116\pi$
$811$	−2.42686e24	−0.455373	−0.227686	+	0.973735i	$0.573116\pi$
$812$	−1.42140e24	−0.263931
$813$	1.43139e24	0.263020
$814$	1.80726e24	0.328635
$815$	0	0
$816$	−2.01186e24	−0.358287
$817$	1.56745e25	2.76252
$818$	2.31994e24	0.404644
$819$	−1.28721e23	−0.0222196
$820$	0	0
$821$	−9.87401e24	−1.66946	−0.834731	−	0.550658i	$-0.814377\pi$
$821$	−9.87401e24	−1.66946	−0.834731	+	0.550658i	$0.814377\pi$
$822$	−1.73968e24	−0.291111
$823$	3.09810e24	0.513094	0.256547	−	0.966532i	$-0.417415\pi$
$823$	3.09810e24	0.513094	0.256547	+	0.966532i	$0.417415\pi$
$824$	2.87952e24	0.471997
$825$	0	0
$826$	3.95857e24	0.635636
$827$	3.89248e24	0.618628	0.309314	−	0.950960i	$-0.399901\pi$
$827$	3.89248e24	0.618628	0.309314	+	0.950960i	$0.399901\pi$
$828$	−1.70336e22	−0.00267947
$829$	−1.04208e25	−1.62251	−0.811256	−	0.584691i	$-0.801216\pi$
$829$	−1.04208e25	−1.62251	−0.811256	+	0.584691i	$0.801216\pi$
$830$	0	0
$831$	−2.36397e24	−0.360606
$832$	−2.40989e23	−0.0363873
$833$	−5.51466e24	−0.824207
$834$	−6.57972e24	−0.973410
$835$	0	0
$836$	−2.99311e24	−0.433880
$837$	−2.23529e24	−0.320750
$838$	1.91925e24	0.272619
$839$	−6.67595e24	−0.938721	−0.469360	−	0.883007i	$-0.655515\pi$
$839$	−6.67595e24	−0.938721	−0.469360	+	0.883007i	$0.655515\pi$
$840$	0	0
$841$	−2.08280e24	−0.286999
$842$	−7.56685e24	−1.03220
$843$	4.08123e24	0.551133
$844$	−1.58703e24	−0.212166
$845$	0	0
$846$	6.67873e23	0.0875075
$847$	−3.28465e24	−0.426069
$848$	3.11496e24	0.400026
$849$	4.85659e24	0.617470
$850$	0	0
$851$	−2.90052e23	−0.0361472
$852$	−7.40877e24	−0.914134
$853$	−9.79573e24	−1.19666	−0.598329	−	0.801250i	$-0.704169\pi$
$853$	−9.79573e24	−1.19666	−0.598329	+	0.801250i	$0.704169\pi$
$854$	6.02695e24	0.728963
$855$	0	0
$856$	2.75270e24	0.326386
$857$	4.38126e24	0.514354	0.257177	−	0.966364i	$-0.417208\pi$
$857$	4.38126e24	0.514354	0.257177	+	0.966364i	$0.417208\pi$
$858$	1.05851e24	0.123042
$859$	−1.50626e25	−1.73364	−0.866821	−	0.498620i	$-0.833841\pi$
$859$	−1.50626e25	−1.73364	−0.866821	+	0.498620i	$0.833841\pi$
$860$	0	0
$861$	3.39204e24	0.382766
$862$	−1.88676e24	−0.210817
$863$	−1.37694e25	−1.52344	−0.761718	−	0.647909i	$-0.775644\pi$
$863$	−1.37694e25	−1.52344	−0.761718	+	0.647909i	$0.775644\pi$
$864$	1.50056e24	0.164394
$865$	0	0
$866$	−4.54616e23	−0.0488363
$867$	−8.26942e24	−0.879655
$868$	−1.02346e24	−0.107808
$869$	3.33381e24	0.347754
$870$	0	0
$871$	−1.74010e23	−0.0178000
$872$	4.70319e24	0.476434
$873$	−1.60518e24	−0.161029
$874$	4.80372e23	0.0477233
$875$	0	0
$876$	1.22174e24	0.119040
$877$	7.56082e24	0.729579	0.364790	−	0.931090i	$-0.381141\pi$
$877$	7.56082e24	0.729579	0.364790	+	0.931090i	$0.381141\pi$
$878$	−7.47549e24	−0.714391
$879$	−1.27332e24	−0.120513
$880$	0	0
$881$	5.11196e24	0.474561	0.237281	−	0.971441i	$-0.423744\pi$
$881$	5.11196e24	0.474561	0.237281	+	0.971441i	$0.423744\pi$
$882$	−5.72070e23	−0.0525976
$883$	1.37334e25	1.25058	0.625289	−	0.780393i	$-0.284981\pi$
$883$	1.37334e25	1.25058	0.625289	+	0.780393i	$0.284981\pi$
$884$	−2.18338e24	−0.196918
$885$	0	0
$886$	1.04078e25	0.920813
$887$	−1.15450e25	−1.01168	−0.505838	−	0.862628i	$-0.668817\pi$
$887$	−1.15450e25	−1.01168	−0.505838	+	0.862628i	$0.668817\pi$
$888$	−3.55383e24	−0.308451
$889$	−3.29443e24	−0.283215
$890$	0	0
$891$	−7.40794e24	−0.624794
$892$	−4.86456e24	−0.406390
$893$	−1.88349e25	−1.55857
$894$	−6.50748e24	−0.533389
$895$	0	0
$896$	6.87051e23	0.0552550
$897$	−1.69883e23	−0.0135337
$898$	1.18472e24	0.0934907
$899$	3.72571e24	0.291240
$900$	0	0
$901$	2.82218e25	2.16483
$902$	−3.03526e24	−0.230643
$903$	1.58036e25	1.18963
$904$	8.90298e24	0.663902
$905$	0	0
$906$	−3.37278e24	−0.246830
$907$	1.74990e25	1.26868	0.634338	−	0.773056i	$-0.281273\pi$
$907$	1.74990e25	1.26868	0.634338	+	0.773056i	$0.281273\pi$
$908$	−6.27527e23	−0.0450716
$909$	4.91806e23	0.0349946
$910$	0	0
$911$	−1.12560e25	−0.786102	−0.393051	−	0.919517i	$-0.628580\pi$
$911$	−1.12560e25	−0.786102	−0.393051	+	0.919517i	$0.628580\pi$
$912$	5.88570e24	0.407232
$913$	2.46611e24	0.169048
$914$	−1.61495e25	−1.09677
$915$	0	0
$916$	1.29599e25	0.863955
$917$	−5.65395e24	−0.373433
$918$	1.35951e25	0.889653
$919$	−2.33947e24	−0.151682	−0.0758412	−	0.997120i	$-0.524164\pi$
$919$	−2.33947e24	−0.151682	−0.0758412	+	0.997120i	$0.524164\pi$
$920$	0	0
$921$	−2.20184e25	−1.40145
$922$	1.44123e25	0.908911
$923$	−8.04040e24	−0.502416
$924$	−3.01778e24	−0.186843
$925$	0	0
$926$	−1.51086e24	−0.0918398
$927$	2.70634e24	0.163006
$928$	−2.50108e24	−0.149269
$929$	3.62091e24	0.214133	0.107067	−	0.994252i	$-0.465854\pi$
$929$	3.62091e24	0.214133	0.107067	+	0.994252i	$0.465854\pi$
$930$	0	0
$931$	1.61332e25	0.936801
$932$	1.17819e25	0.677925
$933$	−2.41656e25	−1.37786
$934$	−6.42853e24	−0.363215
$935$	0	0
$936$	−2.26495e23	−0.0125665
$937$	−4.50917e24	−0.247919	−0.123960	−	0.992287i	$-0.539559\pi$
$937$	−4.50917e24	−0.247919	−0.123960	+	0.992287i	$0.539559\pi$
$938$	4.96097e23	0.0270298
$939$	−3.42877e25	−1.85132
$940$	0	0
$941$	2.46547e25	1.30734	0.653669	−	0.756780i	$-0.273229\pi$
$941$	2.46547e25	1.30734	0.653669	+	0.756780i	$0.273229\pi$
$942$	8.25812e24	0.433959
$943$	4.87136e23	0.0253689
$944$	6.96545e24	0.359490
$945$	0	0
$946$	−1.41414e25	−0.716833
$947$	−2.52153e25	−1.26675	−0.633373	−	0.773847i	$-0.718330\pi$
$947$	−2.52153e25	−1.26675	−0.633373	+	0.773847i	$0.718330\pi$
$948$	−6.55565e24	−0.326396
$949$	1.32590e24	0.0654257
$950$	0	0
$951$	3.30253e24	0.160071
$952$	6.22473e24	0.299024
$953$	−2.22635e25	−1.05999	−0.529996	−	0.848000i	$-0.677807\pi$
$953$	−2.22635e25	−1.05999	−0.529996	+	0.848000i	$0.677807\pi$
$954$	2.92762e24	0.138151
$955$	0	0
$956$	−1.31208e25	−0.608229
$957$	1.09857e25	0.504748
$958$	−9.07031e24	−0.413062
$959$	5.38261e24	0.242960
$960$	0	0
$961$	−1.98675e25	−0.881037
$962$	−3.85681e24	−0.169528
$963$	2.58714e24	0.112719
$964$	−1.19024e25	−0.514018
$965$	0	0
$966$	4.84331e23	0.0205512
$967$	4.73776e24	0.199273	0.0996363	−	0.995024i	$-0.468232\pi$
$967$	4.73776e24	0.199273	0.0996363	+	0.995024i	$0.468232\pi$
$968$	−5.77963e24	−0.240968
$969$	5.33248e25	2.20383
$970$	0	0
$971$	−3.41703e25	−1.38767	−0.693833	−	0.720136i	$-0.744079\pi$
$971$	−3.41703e25	−1.38767	−0.693833	+	0.720136i	$0.744079\pi$
$972$	3.01676e24	0.121445
$973$	2.03578e25	0.812402
$974$	3.88341e24	0.153625
$975$	0	0
$976$	1.06049e25	0.412273
$977$	−6.32382e24	−0.243711	−0.121856	−	0.992548i	$-0.538884\pi$
$977$	−6.32382e24	−0.243711	−0.121856	+	0.992548i	$0.538884\pi$
$978$	−2.92001e25	−1.11559
$979$	1.87528e24	0.0710254
$980$	0	0
$981$	4.42032e24	0.164538
$982$	−1.78408e25	−0.658365
$983$	5.13743e25	1.87949	0.939747	−	0.341870i	$-0.111060\pi$
$983$	5.13743e25	1.87949	0.939747	+	0.341870i	$0.111060\pi$
$984$	5.96858e24	0.216477
$985$	0	0
$986$	−2.26599e25	−0.807802
$987$	−1.89902e25	−0.671171
$988$	6.38749e24	0.223818
$989$	2.26959e24	0.0788458
$990$	0	0
$991$	3.11936e25	1.06522	0.532610	−	0.846361i	$-0.321211\pi$
$991$	3.11936e25	1.06522	0.532610	+	0.846361i	$0.321211\pi$
$992$	−1.80086e24	−0.0609722
$993$	−2.20919e24	−0.0741592
$994$	2.29229e25	0.762930
$995$	0	0
$996$	−4.84940e24	−0.158666
$997$	4.66217e25	1.51244	0.756222	−	0.654315i	$-0.227043\pi$
$997$	4.66217e25	1.51244	0.756222	+	0.654315i	$0.227043\pi$
$998$	−1.30809e25	−0.420755
$999$	2.40150e25	0.765907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.a.g.1.1		2
5.2	odd	4		50.18.b.e.49.4		4
5.3	odd	4		50.18.b.e.49.1		4
5.4	even	2		10.18.a.b.1.2	✓	2
15.14	odd	2		90.18.a.n.1.1		2
20.19	odd	2		80.18.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.b.1.2	✓	2	5.4	even	2
50.18.a.g.1.1		2	1.1	even	1	trivial
50.18.b.e.49.1		4	5.3	odd	4
50.18.b.e.49.4		4	5.2	odd	4
80.18.a.e.1.1		2	20.19	odd	2
90.18.a.n.1.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q+256.000 q^{2} -12037.8 q^{3} +65536.0 q^{4} -3.08167e6 q^{6} +9.53475e6 q^{7} +1.67772e7 q^{8} +1.57682e7 q^{9} +4.01191e8 q^{11} -7.88908e8 q^{12} -8.56166e8 q^{13} +2.44090e9 q^{14} +4.29497e9 q^{16} +3.89127e10 q^{17} +4.03665e9 q^{18} -1.13839e11 q^{19} -1.14777e11 q^{21} +1.02705e11 q^{22} -1.64834e10 q^{23} -2.01961e11 q^{24} -2.19179e11 q^{26} +1.36475e12 q^{27} +6.24870e11 q^{28} -2.27472e12 q^{29} -1.63788e12 q^{31} +1.09951e12 q^{32} -4.82946e12 q^{33} +9.96164e12 q^{34} +1.03338e12 q^{36} +1.75967e13 q^{37} -2.91428e13 q^{38} +1.03064e13 q^{39} -2.95532e13 q^{41} -2.93830e13 q^{42} -1.37690e14 q^{43} +2.62925e13 q^{44} -4.21974e12 q^{46} +1.65452e14 q^{47} -5.17019e13 q^{48} -1.41719e14 q^{49} -4.68422e14 q^{51} -5.61097e13 q^{52} +7.25259e14 q^{53} +3.49376e14 q^{54} +1.59967e14 q^{56} +1.37037e15 q^{57} -5.82328e14 q^{58} +1.62177e15 q^{59} +2.46915e15 q^{61} -4.19296e14 q^{62} +1.50346e14 q^{63} +2.81475e14 q^{64} -1.23634e15 q^{66} +2.03244e14 q^{67} +2.55018e15 q^{68} +1.98423e14 q^{69} +9.39117e15 q^{71} +2.64546e14 q^{72} -1.54865e15 q^{73} +4.50475e15 q^{74} -7.46056e15 q^{76} +3.82526e15 q^{77} +2.63843e15 q^{78} +8.30977e15 q^{79} -1.84648e16 q^{81} -7.56562e15 q^{82} +6.14697e15 q^{83} -7.52205e15 q^{84} -3.52485e16 q^{86} +2.73826e16 q^{87} +6.73087e15 q^{88} +4.67428e15 q^{89} -8.16334e15 q^{91} -1.08025e15 q^{92} +1.97164e16 q^{93} +4.23558e16 q^{94} -1.32357e16 q^{96} -1.01799e17 q^{97} -3.62801e16 q^{98} +6.32605e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 512 q^{2} + 6308 q^{3} + 131072 q^{4} + 1614848 q^{6} - 6543844 q^{7} + 33554432 q^{8} + 223195906 q^{9} + 1189408704 q^{11} + 413401088 q^{12} + 2017919228 q^{13} - 1675224064 q^{14} + 8589934592 q^{16}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 512 * q^2 + 6308 * q^3 + 131072 * q^4 + 1614848 * q^6 - 6543844 * q^7 + 33554432 * q^8 + 223195906 * q^9 + 1189408704 * q^11 + 413401088 * q^12 + 2017919228 * q^13 - 1675224064 * q^14 + 8589934592 * q^16 + 18755639436 * q^17 + 57138151936 * q^18 - 136704830600 * q^19 - 409751898376 * q^21 + 304488628224 * q^22 + 649234170708 * q^23 + 105830678528 * q^24 + 516587322368 * q^26 + 2800995425720 * q^27 - 428857360384 * q^28 - 4696543420020 * q^29 + 7120867378744 * q^31 + 2199023255552 * q^32 + 9631011282816 * q^33 + 4801443695616 * q^34 + 14627366895616 * q^36 - 9933114637444 * q^37 - 34996436633600 * q^38 + 63033715222712 * q^39 + 9622711880844 * q^41 - 104896485984256 * q^42 - 7708436011852 * q^43 + 77949088825344 * q^44 + 166203947701248 * q^46 + 466072575837996 * q^47 + 27092653703168 * q^48 - 115828146887046 * q^49 - 838218717084456 * q^51 + 132246354526208 * q^52 + 623333120284428 * q^53 + 717054828984320 * q^54 - 109787484258304 * q^56 + 950883425062000 * q^57 - 1202315115525120 * q^58 + 654616071995160 * q^59 + 1329040385162884 * q^61 + 1822942048958464 * q^62 - 3184801966786532 * q^63 + 562949953421312 * q^64 + 2465538888400896 * q^66 + 4249016411877596 * q^67 + 1229169586077696 * q^68 + 12411535659353832 * q^69 + 2035131949347624 * q^71 + 3744605925277696 * q^72 - 2248593461347972 * q^73 - 2542877347185664 * q^74 - 8959087778201600 * q^76 - 8848168987836288 * q^77 + 16136631097014272 * q^78 + 19188427678495120 * q^79 - 18903014015714198 * q^81 + 2463414241496064 * q^82 + 18474649086611988 * q^83 - 26853500411969536 * q^84 - 1973359619034112 * q^86 - 17047661699498280 * q^87 + 19954966739288064 * q^88 - 17458912916395020 * q^89 - 54374608211433016 * q^91 + 42548210611519488 * q^92 + 180402465813627376 * q^93 + 119314579414526976 * q^94 + 6935719348011008 * q^96 - 195934325822490244 * q^97 - 29652005603083776 * q^98 + 169824195828146112 * q^99

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