LMFDB - Embedded newform 75.14.a.c.1.1

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 = [2,-131] 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:	$2$
Coefficient field:	$\Q(\sqrt{3121}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 780 $ x^2 - x - 780
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$28.4330$ 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)

$f(q)$	$=$	\(q-149.299 q^{2} -729.000 q^{3} +14098.2 q^{4} +108839. q^{6} -384225. q^{7} -881782. q^{8} +531441. q^{9} +6.10216e6 q^{11} -1.02776e7 q^{12} -1.13332e6 q^{13} +5.73644e7 q^{14} +1.61570e7 q^{16} +2.69912e7 q^{17} -7.93435e7 q^{18} -3.29943e8 q^{19} +2.80100e8 q^{21} -9.11046e8 q^{22} -4.70204e8 q^{23} +6.42819e8 q^{24} +1.69203e8 q^{26} -3.87420e8 q^{27} -5.41687e9 q^{28} -4.24890e9 q^{29} +7.67054e9 q^{31} +4.81134e9 q^{32} -4.44848e9 q^{33} -4.02976e9 q^{34} +7.49234e9 q^{36} +2.83184e10 q^{37} +4.92601e10 q^{38} +8.26190e8 q^{39} -2.11336e10 q^{41} -4.18187e10 q^{42} +6.93928e10 q^{43} +8.60292e10 q^{44} +7.02010e10 q^{46} -1.01233e11 q^{47} -1.17784e10 q^{48} +5.07401e10 q^{49} -1.96766e10 q^{51} -1.59777e10 q^{52} +1.81846e11 q^{53} +5.78414e10 q^{54} +3.38803e11 q^{56} +2.40528e11 q^{57} +6.34357e11 q^{58} +3.10938e11 q^{59} +1.76596e11 q^{61} -1.14520e12 q^{62} -2.04193e11 q^{63} -8.50686e11 q^{64} +6.64152e11 q^{66} -6.25757e10 q^{67} +3.80526e11 q^{68} +3.42779e11 q^{69} +1.13419e12 q^{71} -4.68615e11 q^{72} +1.17191e11 q^{73} -4.22790e12 q^{74} -4.65158e12 q^{76} -2.34461e12 q^{77} -1.23349e11 q^{78} +3.99281e12 q^{79} +2.82430e11 q^{81} +3.15523e12 q^{82} -8.58275e11 q^{83} +3.94890e12 q^{84} -1.03603e13 q^{86} +3.09745e12 q^{87} -5.38077e12 q^{88} -9.67991e11 q^{89} +4.35450e11 q^{91} -6.62901e12 q^{92} -5.59183e12 q^{93} +1.51139e13 q^{94} -3.50747e12 q^{96} -2.50052e12 q^{97} -7.57544e12 q^{98} +3.24294e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 131 q^{2} - 1458 q^{3} + 6241 q^{4} + 95499 q^{6} - 496272 q^{7} - 1175463 q^{8} + 1062882 q^{9} + 6245888 q^{11} - 4549689 q^{12} - 1761164 q^{13} + 55314084 q^{14} + 75148705 q^{16} - 48151604 q^{17}+ \cdots + 3319320964608 q^{99}+O(q^{100}) $ 2 * q - 131 * q^2 - 1458 * q^3 + 6241 * q^4 + 95499 * q^6 - 496272 * q^7 - 1175463 * q^8 + 1062882 * q^9 + 6245888 * q^11 - 4549689 * q^12 - 1761164 * q^13 + 55314084 * q^14 + 75148705 * q^16 - 48151604 * q^17 - 69618771 * q^18 + 38475344 * q^19 + 361782288 * q^21 - 908415728 * q^22 - 734264616 * q^23 + 856912527 * q^24 + 157714454 * q^26 - 774840978 * q^27 - 4536499884 * q^28 + 1126474708 * q^29 + 6100104312 * q^31 + 8296660073 * q^32 - 4553252352 * q^33 - 5404788238 * q^34 + 3316723281 * q^36 + 46819674548 * q^37 + 56001723484 * q^38 + 1283888556 * q^39 - 29607909788 * q^41 - 40323967236 * q^42 + 63189768520 * q^43 + 84899911888 * q^44 + 65368954992 * q^46 - 105004415960 * q^47 - 54783405945 * q^48 - 33594444590 * q^49 + 35102519316 * q^51 - 11044638034 * q^52 - 48425833796 * q^53 + 50752084059 * q^54 + 371708899380 * q^56 - 28048525776 * q^57 + 732719858498 * q^58 + 722768180096 * q^59 - 229984402180 * q^61 - 1173940563384 * q^62 - 263739287952 * q^63 - 1270168541071 * q^64 + 662235065712 * q^66 - 359062188984 * q^67 + 970935017018 * q^68 + 535278905064 * q^69 + 736545668224 * q^71 - 624689232183 * q^72 + 1494470740204 * q^73 - 3889351112906 * q^74 - 7546301154644 * q^76 - 2360709208704 * q^77 - 114973836966 * q^78 + 3526348590120 * q^79 + 564859072962 * q^81 + 3000156702386 * q^82 - 5631050986968 * q^83 + 3307108415436 * q^84 - 10473766954252 * q^86 - 821200062132 * q^87 - 5422984137648 * q^88 + 5913121459764 * q^89 + 505797926592 * q^91 - 4554248300592 * q^92 - 4446976043448 * q^93 + 15044889696176 * q^94 - 6048265193217 * q^96 - 16383233322244 * q^97 - 9118668656251 * q^98 + 3319320964608 * 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 $

$2$	−149.299	−1.64954	−0.824768	−	0.565472i	$-0.808694\pi$
$2$	−149.299	−1.64954	−0.824768	+	0.565472i	$0.808694\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	14098.2	1.72097
$5$	0	0
$5$	0	0
$6$	108839.	0.952359
$7$	−384225.	−1.23438	−0.617190	−	0.786814i	$-0.711729\pi$
$7$	−384225.	−1.23438	−0.617190	+	0.786814i	$0.711729\pi$
$8$	−881782.	−1.18926
$9$	531441.	0.333333
$10$	0	0
$11$	6.10216e6	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$11$	6.10216e6	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$12$	−1.02776e7	−0.993600
$13$	−1.13332e6	−0.0651209	−0.0325605	−	0.999470i	$-0.510366\pi$
$13$	−1.13332e6	−0.0651209	−0.0325605	+	0.999470i	$0.510366\pi$
$14$	5.73644e7	2.03615
$15$	0	0
$16$	1.61570e7	0.240757
$17$	2.69912e7	0.271209	0.135605	−	0.990763i	$-0.456702\pi$
$17$	2.69912e7	0.271209	0.135605	+	0.990763i	$0.456702\pi$
$18$	−7.93435e7	−0.549845
$19$	−3.29943e8	−1.60894	−0.804471	−	0.593992i	$-0.797551\pi$
$19$	−3.29943e8	−1.60894	−0.804471	+	0.593992i	$0.797551\pi$
$20$	0	0
$21$	2.80100e8	0.712669
$22$	−9.11046e8	−1.71314
$23$	−4.70204e8	−0.662301	−0.331151	−	0.943578i	$-0.607437\pi$
$23$	−4.70204e8	−0.662301	−0.331151	+	0.943578i	$0.607437\pi$
$24$	6.42819e8	0.686619
$25$	0	0
$26$	1.69203e8	0.107419
$27$	−3.87420e8	−0.192450
$28$	−5.41687e9	−2.12433
$29$	−4.24890e9	−1.32645	−0.663224	−	0.748421i	$-0.730812\pi$
$29$	−4.24890e9	−1.32645	−0.663224	+	0.748421i	$0.730812\pi$
$30$	0	0
$31$	7.67054e9	1.55230	0.776149	−	0.630550i	$-0.217170\pi$
$31$	7.67054e9	1.55230	0.776149	+	0.630550i	$0.217170\pi$
$32$	4.81134e9	0.792121
$33$	−4.44848e9	−0.599612
$34$	−4.02976e9	−0.447369
$35$	0	0
$36$	7.49234e9	0.573655
$37$	2.83184e10	1.81450	0.907251	−	0.420590i	$-0.138177\pi$
$37$	2.83184e10	1.81450	0.907251	+	0.420590i	$0.138177\pi$
$38$	4.92601e10	2.65401
$39$	8.26190e8	0.0375976
$40$	0	0
$41$	−2.11336e10	−0.694831	−0.347415	−	0.937711i	$-0.612941\pi$
$41$	−2.11336e10	−0.694831	−0.347415	+	0.937711i	$0.612941\pi$
$42$	−4.18187e10	−1.17557
$43$	6.93928e10	1.67405	0.837026	−	0.547162i	$-0.184292\pi$
$43$	6.93928e10	1.67405	0.837026	+	0.547162i	$0.184292\pi$
$44$	8.60292e10	1.78732
$45$	0	0
$46$	7.02010e10	1.09249
$47$	−1.01233e11	−1.36989	−0.684943	−	0.728597i	$-0.740173\pi$
$47$	−1.01233e11	−1.36989	−0.684943	+	0.728597i	$0.740173\pi$
$48$	−1.17784e10	−0.139001
$49$	5.07401e10	0.523693
$50$	0	0
$51$	−1.96766e10	−0.156583
$52$	−1.59777e10	−0.112071
$53$	1.81846e11	1.12697	0.563484	−	0.826127i	$-0.309461\pi$
$53$	1.81846e11	1.12697	0.563484	+	0.826127i	$0.309461\pi$
$54$	5.78414e10	0.317453
$55$	0	0
$56$	3.38803e11	1.46800
$57$	2.40528e11	0.928923
$58$	6.34357e11	2.18802
$59$	3.10938e11	0.959701	0.479850	−	0.877350i	$-0.340691\pi$
$59$	3.10938e11	0.959701	0.479850	+	0.877350i	$0.340691\pi$
$60$	0	0
$61$	1.76596e11	0.438870	0.219435	−	0.975627i	$-0.429579\pi$
$61$	1.76596e11	0.438870	0.219435	+	0.975627i	$0.429579\pi$
$62$	−1.14520e12	−2.56057
$63$	−2.04193e11	−0.411460
$64$	−8.50686e11	−1.54739
$65$	0	0
$66$	6.64152e11	0.989082
$67$	−6.25757e10	−0.0845123	−0.0422561	−	0.999107i	$-0.513455\pi$
$67$	−6.25757e10	−0.0845123	−0.0422561	+	0.999107i	$0.513455\pi$
$68$	3.80526e11	0.466742
$69$	3.42779e11	0.382380
$70$	0	0
$71$	1.13419e12	1.05076	0.525382	−	0.850867i	$-0.323923\pi$
$71$	1.13419e12	1.05076	0.525382	+	0.850867i	$0.323923\pi$
$72$	−4.68615e11	−0.396419
$73$	1.17191e11	0.0906350	0.0453175	−	0.998973i	$-0.485570\pi$
$73$	1.17191e11	0.0906350	0.0453175	+	0.998973i	$0.485570\pi$
$74$	−4.22790e12	−2.99308
$75$	0	0
$76$	−4.65158e12	−2.76893
$77$	−2.34461e12	−1.28198
$78$	−1.23349e11	−0.0620185
$79$	3.99281e12	1.84800	0.924002	−	0.382387i	$-0.124898\pi$
$79$	3.99281e12	1.84800	0.924002	+	0.382387i	$0.124898\pi$
$80$	0	0
$81$	2.82430e11	0.111111
$82$	3.15523e12	1.14615
$83$	−8.58275e11	−0.288150	−0.144075	−	0.989567i	$-0.546021\pi$
$83$	−8.58275e11	−0.288150	−0.144075	+	0.989567i	$0.546021\pi$
$84$	3.94890e12	1.22648
$85$	0	0
$86$	−1.03603e13	−2.76141
$87$	3.09745e12	0.765825
$88$	−5.38077e12	−1.23512
$89$	−9.67991e11	−0.206460	−0.103230	−	0.994657i	$-0.532918\pi$
$89$	−9.67991e11	−0.206460	−0.103230	+	0.994657i	$0.532918\pi$
$90$	0	0
$91$	4.35450e11	0.0803839
$92$	−6.62901e12	−1.13980
$93$	−5.59183e12	−0.896220
$94$	1.51139e13	2.25967
$95$	0	0
$96$	−3.50747e12	−0.457331
$97$	−2.50052e12	−0.304799	−0.152400	−	0.988319i	$-0.548700\pi$
$97$	−2.50052e12	−0.304799	−0.152400	+	0.988319i	$0.548700\pi$
$98$	−7.57544e12	−0.863850
$99$	3.24294e12	0.346186
$100$	0	0
$101$	−3.51016e12	−0.329032	−0.164516	−	0.986374i	$-0.552606\pi$
$101$	−3.51016e12	−0.329032	−0.164516	+	0.986374i	$0.552606\pi$
$102$	2.93769e12	0.258289
$103$	1.08186e13	0.892747	0.446373	−	0.894847i	$-0.352715\pi$
$103$	1.08186e13	0.892747	0.446373	+	0.894847i	$0.352715\pi$
$104$	9.99340e11	0.0774456
$105$	0	0
$106$	−2.71495e13	−1.85897
$107$	−1.49010e13	−0.959892	−0.479946	−	0.877298i	$-0.659344\pi$
$107$	−1.49010e13	−0.959892	−0.479946	+	0.877298i	$0.659344\pi$
$108$	−5.46191e12	−0.331200
$109$	−2.01251e13	−1.14939	−0.574694	−	0.818369i	$-0.694879\pi$
$109$	−2.01251e13	−1.14939	−0.574694	+	0.818369i	$0.694879\pi$
$110$	0	0
$111$	−2.06441e13	−1.04760
$112$	−6.20791e12	−0.297186
$113$	−2.87905e13	−1.30088	−0.650442	−	0.759556i	$-0.725417\pi$
$113$	−2.87905e13	−1.30088	−0.650442	+	0.759556i	$0.725417\pi$
$114$	−3.59106e13	−1.53229
$115$	0	0
$116$	−5.99017e13	−2.28277
$117$	−6.02292e11	−0.0217070
$118$	−4.64227e13	−1.58306
$119$	−1.03707e13	−0.334775
$120$	0	0
$121$	2.71366e12	0.0786051
$122$	−2.63655e13	−0.723932
$123$	1.54064e13	0.401161
$124$	1.08140e14	2.67145
$125$	0	0
$126$	3.04858e13	0.678718
$127$	−7.01983e13	−1.48458	−0.742288	−	0.670081i	$-0.766259\pi$
$127$	−7.01983e13	−1.48458	−0.742288	+	0.670081i	$0.766259\pi$
$128$	8.75919e13	1.76035
$129$	−5.05873e13	−0.966515
$130$	0	0
$131$	9.26965e13	1.60251	0.801254	−	0.598325i	$-0.204167\pi$
$131$	9.26965e13	1.60251	0.801254	+	0.598325i	$0.204167\pi$
$132$	−6.27153e13	−1.03191
$133$	1.26772e14	1.98604
$134$	9.34249e12	0.139406
$135$	0	0
$136$	−2.38004e13	−0.322538
$137$	4.89202e13	0.632127	0.316064	−	0.948738i	$-0.397639\pi$
$137$	4.89202e13	0.632127	0.316064	+	0.948738i	$0.397639\pi$
$138$	−5.11765e13	−0.630749
$139$	4.48733e13	0.527706	0.263853	−	0.964563i	$-0.415007\pi$
$139$	4.48733e13	0.527706	0.263853	+	0.964563i	$0.415007\pi$
$140$	0	0
$141$	7.37986e13	0.790904
$142$	−1.69333e14	−1.73327
$143$	−6.91570e12	−0.0676319
$144$	8.58647e12	0.0802525
$145$	0	0
$146$	−1.74965e13	−0.149506
$147$	−3.69895e13	−0.302354
$148$	3.99237e14	3.12270
$149$	1.30203e14	0.974789	0.487395	−	0.873182i	$-0.337947\pi$
$149$	1.30203e14	0.974789	0.487395	+	0.873182i	$0.337947\pi$
$150$	0	0
$151$	−1.94653e14	−1.33632	−0.668160	−	0.744018i	$-0.732918\pi$
$151$	−1.94653e14	−1.33632	−0.668160	+	0.744018i	$0.732918\pi$
$152$	2.90938e14	1.91345
$153$	1.43442e13	0.0904031
$154$	3.50047e14	2.11466
$155$	0	0
$156$	1.16477e13	0.0647041
$157$	7.93587e13	0.422909	0.211454	−	0.977388i	$-0.432180\pi$
$157$	7.93587e13	0.422909	0.211454	+	0.977388i	$0.432180\pi$
$158$	−5.96123e14	−3.04835
$159$	−1.32566e14	−0.650655
$160$	0	0
$161$	1.80664e14	0.817531
$162$	−4.21664e13	−0.183282
$163$	1.62086e14	0.676904	0.338452	−	0.940984i	$-0.390097\pi$
$163$	1.62086e14	0.676904	0.338452	+	0.940984i	$0.390097\pi$
$164$	−2.97945e14	−1.19578
$165$	0	0
$166$	1.28139e14	0.475314
$167$	−2.62269e14	−0.935600	−0.467800	−	0.883834i	$-0.654953\pi$
$167$	−2.62269e14	−0.935600	−0.467800	+	0.883834i	$0.654953\pi$
$168$	−2.46987e14	−0.847548
$169$	−3.01591e14	−0.995759
$170$	0	0
$171$	−1.75345e14	−0.536314
$172$	9.78310e14	2.88099
$173$	−7.87595e13	−0.223359	−0.111679	−	0.993744i	$-0.535623\pi$
$173$	−7.87595e13	−0.223359	−0.111679	+	0.993744i	$0.535623\pi$
$174$	−4.62446e14	−1.26325
$175$	0	0
$176$	9.85923e13	0.250041
$177$	−2.26674e14	−0.554083
$178$	1.44520e14	0.340563
$179$	−7.53329e14	−1.71175	−0.855874	−	0.517184i	$-0.826980\pi$
$179$	−7.53329e14	−1.71175	−0.855874	+	0.517184i	$0.826980\pi$
$180$	0	0
$181$	−4.79674e14	−1.01399	−0.506997	−	0.861948i	$-0.669245\pi$
$181$	−4.79674e14	−1.01399	−0.506997	+	0.861948i	$0.669245\pi$
$182$	−6.50122e13	−0.132596
$183$	−1.28738e14	−0.253382
$184$	4.14618e14	0.787647
$185$	0	0
$186$	8.34853e14	1.47835
$187$	1.64705e14	0.281667
$188$	−1.42719e15	−2.35753
$189$	1.48857e14	0.237556
$190$	0	0
$191$	4.70960e14	0.701888	0.350944	−	0.936397i	$-0.385861\pi$
$191$	4.70960e14	0.701888	0.350944	+	0.936397i	$0.385861\pi$
$192$	6.20150e14	0.893385
$193$	1.24350e14	0.173191	0.0865954	−	0.996244i	$-0.472401\pi$
$193$	1.24350e14	0.173191	0.0865954	+	0.996244i	$0.472401\pi$
$194$	3.73324e14	0.502777
$195$	0	0
$196$	7.15342e14	0.901258
$197$	4.20205e12	0.00512190	0.00256095	−	0.999997i	$-0.499185\pi$
$197$	4.20205e12	0.00512190	0.00256095	+	0.999997i	$0.499185\pi$
$198$	−4.84167e14	−0.571047
$199$	1.09925e15	1.25474	0.627370	−	0.778722i	$-0.284132\pi$
$199$	1.09925e15	1.25474	0.627370	+	0.778722i	$0.284132\pi$
$200$	0	0
$201$	4.56177e13	0.0487932
$202$	5.24063e14	0.542749
$203$	1.63254e15	1.63734
$204$	−2.77404e14	−0.269474
$205$	0	0
$206$	−1.61520e15	−1.47262
$207$	−2.49886e14	−0.220767
$208$	−1.83110e13	−0.0156783
$209$	−2.01336e15	−1.67098
$210$	0	0
$211$	−4.43736e14	−0.346170	−0.173085	−	0.984907i	$-0.555373\pi$
$211$	−4.43736e14	−0.346170	−0.173085	+	0.984907i	$0.555373\pi$
$212$	2.56370e15	1.93947
$213$	−8.26822e14	−0.606659
$214$	2.22471e15	1.58337
$215$	0	0
$216$	3.41620e14	0.228873
$217$	−2.94722e15	−1.91613
$218$	3.00466e15	1.89595
$219$	−8.54323e13	−0.0523281
$220$	0	0
$221$	−3.05897e13	−0.0176614
$222$	3.08214e15	1.72806
$223$	2.15493e15	1.17342	0.586708	−	0.809799i	$-0.300424\pi$
$223$	2.15493e15	1.17342	0.586708	+	0.809799i	$0.300424\pi$
$224$	−1.84864e15	−0.977777
$225$	0	0
$226$	4.29838e15	2.14586
$227$	−3.86902e15	−1.87686	−0.938431	−	0.345466i	$-0.887721\pi$
$227$	−3.86902e15	−1.87686	−0.938431	+	0.345466i	$0.887721\pi$
$228$	3.39100e15	1.59864
$229$	−1.09844e15	−0.503324	−0.251662	−	0.967815i	$-0.580977\pi$
$229$	−1.09844e15	−0.503324	−0.251662	+	0.967815i	$0.580977\pi$
$230$	0	0
$231$	1.70922e15	0.740149
$232$	3.74661e15	1.57749
$233$	−4.34127e15	−1.77747	−0.888737	−	0.458417i	$-0.848417\pi$
$233$	−4.34127e15	−1.77747	−0.888737	+	0.458417i	$0.848417\pi$
$234$	8.99216e13	0.0358064
$235$	0	0
$236$	4.38365e15	1.65161
$237$	−2.91076e15	−1.06695
$238$	1.54834e15	0.552224
$239$	−1.70803e15	−0.592801	−0.296400	−	0.955064i	$-0.595786\pi$
$239$	−1.70803e15	−0.592801	−0.296400	+	0.955064i	$0.595786\pi$
$240$	0	0
$241$	2.87167e15	0.944114	0.472057	−	0.881568i	$-0.343512\pi$
$241$	2.87167e15	0.944114	0.472057	+	0.881568i	$0.343512\pi$
$242$	−4.05146e14	−0.129662
$243$	−2.05891e14	−0.0641500
$244$	2.48967e15	0.755281
$245$	0	0
$246$	−2.30016e15	−0.661729
$247$	3.73931e14	0.104776
$248$	−6.76374e15	−1.84608
$249$	6.25683e14	0.166364
$250$	0	0
$251$	−9.41402e14	−0.237627	−0.118813	−	0.992917i	$-0.537909\pi$
$251$	−9.41402e14	−0.237627	−0.118813	+	0.992917i	$0.537909\pi$
$252$	−2.87875e15	−0.708108
$253$	−2.86926e15	−0.687839
$254$	1.04805e16	2.44886
$255$	0	0
$256$	−6.10855e15	−1.35637
$257$	3.31316e15	0.717260	0.358630	−	0.933480i	$-0.383244\pi$
$257$	3.31316e15	0.717260	0.358630	+	0.933480i	$0.383244\pi$
$258$	7.55263e15	1.59430
$259$	−1.08806e16	−2.23978
$260$	0	0
$261$	−2.25804e15	−0.442149
$262$	−1.38395e16	−2.64339
$263$	3.12580e15	0.582437	0.291219	−	0.956657i	$-0.405939\pi$
$263$	3.12580e15	0.582437	0.291219	+	0.956657i	$0.405939\pi$
$264$	3.92258e15	0.713094
$265$	0	0
$266$	−1.89270e16	−3.27605
$267$	7.05666e14	0.119200
$268$	−8.82202e14	−0.145443
$269$	2.51897e15	0.405352	0.202676	−	0.979246i	$-0.435036\pi$
$269$	2.51897e15	0.405352	0.202676	+	0.979246i	$0.435036\pi$
$270$	0	0
$271$	−9.26522e14	−0.142087	−0.0710436	−	0.997473i	$-0.522633\pi$
$271$	−9.26522e14	−0.142087	−0.0710436	+	0.997473i	$0.522633\pi$
$272$	4.36096e14	0.0652957
$273$	−3.17443e14	−0.0464097
$274$	−7.30373e15	−1.04272
$275$	0	0
$276$	4.83255e15	0.658063
$277$	4.03418e14	0.0536583	0.0268292	−	0.999640i	$-0.491459\pi$
$277$	4.03418e14	0.0536583	0.0268292	+	0.999640i	$0.491459\pi$
$278$	−6.69953e15	−0.870469
$279$	4.07644e15	0.517433
$280$	0	0
$281$	−8.56272e15	−1.03758	−0.518789	−	0.854903i	$-0.673617\pi$
$281$	−8.56272e15	−1.03758	−0.518789	+	0.854903i	$0.673617\pi$
$282$	−1.10180e16	−1.30462
$283$	3.74874e15	0.433784	0.216892	−	0.976196i	$-0.430408\pi$
$283$	3.74874e15	0.433784	0.216892	+	0.976196i	$0.430408\pi$
$284$	1.59899e16	1.80833
$285$	0	0
$286$	1.03251e15	0.111561
$287$	8.12008e15	0.857685
$288$	2.55694e15	0.264040
$289$	−9.17605e15	−0.926445
$290$	0	0
$291$	1.82288e15	0.175976
$292$	1.65218e15	0.155980
$293$	−2.47408e15	−0.228441	−0.114221	−	0.993455i	$-0.536437\pi$
$293$	−2.47408e15	−0.228441	−0.114221	+	0.993455i	$0.536437\pi$
$294$	5.52250e15	0.498744
$295$	0	0
$296$	−2.49706e16	−2.15791
$297$	−2.36410e15	−0.199871
$298$	−1.94392e16	−1.60795
$299$	5.32892e14	0.0431297
$300$	0	0
$301$	−2.66625e16	−2.06642
$302$	2.90614e16	2.20431
$303$	2.55891e15	0.189967
$304$	−5.33087e15	−0.387365
$305$	0	0
$306$	−2.14158e15	−0.149123
$307$	−3.12228e15	−0.212849	−0.106425	−	0.994321i	$-0.533940\pi$
$307$	−3.12228e15	−0.212849	−0.106425	+	0.994321i	$0.533940\pi$
$308$	−3.30546e16	−2.20624
$309$	−7.88675e15	−0.515428
$310$	0	0
$311$	8.71900e15	0.546417	0.273209	−	0.961955i	$-0.411915\pi$
$311$	8.71900e15	0.546417	0.273209	+	0.961955i	$0.411915\pi$
$312$	−7.28519e14	−0.0447132
$313$	−1.94308e16	−1.16803	−0.584013	−	0.811744i	$-0.698518\pi$
$313$	−1.94308e16	−1.16803	−0.584013	+	0.811744i	$0.698518\pi$
$314$	−1.18482e16	−0.697603
$315$	0	0
$316$	5.62913e16	3.18035
$317$	−2.73728e16	−1.51508	−0.757538	−	0.652791i	$-0.773598\pi$
$317$	−2.73728e16	−1.51508	−0.757538	+	0.652791i	$0.773598\pi$
$318$	1.97920e16	1.07328
$319$	−2.59275e16	−1.37759
$320$	0	0
$321$	1.08629e16	0.554194
$322$	−2.69730e16	−1.34855
$323$	−8.90556e15	−0.436360
$324$	3.98173e15	0.191218
$325$	0	0
$326$	−2.41993e16	−1.11658
$327$	1.46712e16	0.663599
$328$	1.86352e16	0.826333
$329$	3.88961e16	1.69096
$330$	0	0
$331$	1.48805e16	0.621923	0.310961	−	0.950423i	$-0.399349\pi$
$331$	1.48805e16	0.621923	0.310961	+	0.950423i	$0.399349\pi$
$332$	−1.21001e16	−0.495897
$333$	1.50496e16	0.604834
$334$	3.91565e16	1.54330
$335$	0	0
$336$	4.52557e15	0.171580
$337$	9.51124e15	0.353706	0.176853	−	0.984237i	$-0.443408\pi$
$337$	9.51124e15	0.353706	0.176853	+	0.984237i	$0.443408\pi$
$338$	4.50271e16	1.64254
$339$	2.09883e16	0.751066
$340$	0	0
$341$	4.68069e16	1.61215
$342$	2.61788e16	0.884668
$343$	1.77316e16	0.587943
$344$	−6.11893e16	−1.99088
$345$	0	0
$346$	1.17587e16	0.368438
$347$	−2.02295e16	−0.622076	−0.311038	−	0.950398i	$-0.600677\pi$
$347$	−2.02295e16	−0.622076	−0.311038	+	0.950398i	$0.600677\pi$
$348$	4.36683e16	1.31796
$349$	8.80222e15	0.260751	0.130376	−	0.991465i	$-0.458382\pi$
$349$	8.80222e15	0.260751	0.130376	+	0.991465i	$0.458382\pi$
$350$	0	0
$351$	4.39071e14	0.0125325
$352$	2.93596e16	0.822664
$353$	−1.67276e16	−0.460148	−0.230074	−	0.973173i	$-0.573897\pi$
$353$	−1.67276e16	−0.460148	−0.230074	+	0.973173i	$0.573897\pi$
$354$	3.38421e16	0.913980
$355$	0	0
$356$	−1.36469e16	−0.355311
$357$	7.56025e15	0.193283
$358$	1.12471e17	2.82359
$359$	−7.94820e16	−1.95954	−0.979772	−	0.200119i	$-0.935867\pi$
$359$	−7.94820e16	−1.95954	−0.979772	+	0.200119i	$0.935867\pi$
$360$	0	0
$361$	6.68093e16	1.58869
$362$	7.16148e16	1.67262
$363$	−1.97826e15	−0.0453827
$364$	6.13904e15	0.138338
$365$	0	0
$366$	1.92205e16	0.417962
$367$	6.97003e16	1.48904	0.744518	−	0.667602i	$-0.232679\pi$
$367$	6.97003e16	1.48904	0.744518	+	0.667602i	$0.232679\pi$
$368$	−7.59707e15	−0.159454
$369$	−1.12313e16	−0.231610
$370$	0	0
$371$	−6.98700e16	−1.39111
$372$	−7.88344e16	−1.54236
$373$	−2.07893e16	−0.399698	−0.199849	−	0.979827i	$-0.564045\pi$
$373$	−2.07893e16	−0.399698	−0.199849	+	0.979827i	$0.564045\pi$
$374$	−2.45902e16	−0.464619
$375$	0	0
$376$	8.92650e16	1.62915
$377$	4.81537e15	0.0863795
$378$	−2.22241e16	−0.391858
$379$	7.77269e16	1.34715	0.673576	−	0.739118i	$-0.264757\pi$
$379$	7.77269e16	1.34715	0.673576	+	0.739118i	$0.264757\pi$
$380$	0	0
$381$	5.11746e16	0.857120
$382$	−7.03139e16	−1.15779
$383$	−6.62740e16	−1.07288	−0.536440	−	0.843938i	$-0.680231\pi$
$383$	−6.62740e16	−1.07288	−0.536440	+	0.843938i	$0.680231\pi$
$384$	−6.38545e16	−1.01634
$385$	0	0
$386$	−1.85654e16	−0.285684
$387$	3.68782e16	0.558018
$388$	−3.52527e16	−0.524549
$389$	−3.03230e15	−0.0443711	−0.0221855	−	0.999754i	$-0.507062\pi$
$389$	−3.03230e15	−0.0443711	−0.0221855	+	0.999754i	$0.507062\pi$
$390$	0	0
$391$	−1.26914e16	−0.179622
$392$	−4.47417e16	−0.622806
$393$	−6.75758e16	−0.925208
$394$	−6.27362e14	−0.00844876
$395$	0	0
$396$	4.57194e16	0.595775
$397$	−3.47691e16	−0.445712	−0.222856	−	0.974851i	$-0.571538\pi$
$397$	−3.47691e16	−0.445712	−0.222856	+	0.974851i	$0.571538\pi$
$398$	−1.64118e17	−2.06974
$399$	−9.24171e16	−1.14664
$400$	0	0
$401$	4.47291e16	0.537220	0.268610	−	0.963249i	$-0.413436\pi$
$401$	4.47291e16	0.537220	0.268610	+	0.963249i	$0.413436\pi$
$402$	−6.81067e15	−0.0804861
$403$	−8.69317e15	−0.101087
$404$	−4.94867e16	−0.566252
$405$	0	0
$406$	−2.43736e17	−2.70085
$407$	1.72803e17	1.88447
$408$	1.73505e16	0.186217
$409$	4.58740e16	0.484579	0.242290	−	0.970204i	$-0.422102\pi$
$409$	4.58740e16	0.484579	0.242290	+	0.970204i	$0.422102\pi$
$410$	0	0
$411$	−3.56628e16	−0.364959
$412$	1.52522e17	1.53639
$413$	−1.19470e17	−1.18463
$414$	3.73077e16	0.364163
$415$	0	0
$416$	−5.45279e15	−0.0515836
$417$	−3.27126e16	−0.304671
$418$	3.00593e17	2.75634
$419$	7.04588e16	0.636128	0.318064	−	0.948069i	$-0.396967\pi$
$419$	7.04588e16	0.636128	0.318064	+	0.948069i	$0.396967\pi$
$420$	0	0
$421$	−2.11625e16	−0.185239	−0.0926196	−	0.995702i	$-0.529524\pi$
$421$	−2.11625e16	−0.185239	−0.0926196	+	0.995702i	$0.529524\pi$
$422$	6.62493e16	0.571019
$423$	−5.37991e16	−0.456628
$424$	−1.60349e17	−1.34026
$425$	0	0
$426$	1.23444e17	1.00070
$427$	−6.78526e16	−0.541733
$428$	−2.10077e17	−1.65194
$429$	5.04154e15	0.0390473
$430$	0	0
$431$	4.09241e16	0.307523	0.153761	−	0.988108i	$-0.450861\pi$
$431$	4.09241e16	0.307523	0.153761	+	0.988108i	$0.450861\pi$
$432$	−6.25954e15	−0.0463338
$433$	−8.57212e16	−0.625053	−0.312527	−	0.949909i	$-0.601175\pi$
$433$	−8.57212e16	−0.625053	−0.312527	+	0.949909i	$0.601175\pi$
$434$	4.40016e17	3.16072
$435$	0	0
$436$	−2.83727e17	−1.97806
$437$	1.55141e17	1.06560
$438$	1.27549e16	0.0863171
$439$	3.70635e16	0.247131	0.123565	−	0.992336i	$-0.460567\pi$
$439$	3.70635e16	0.247131	0.123565	+	0.992336i	$0.460567\pi$
$440$	0	0
$441$	2.69654e16	0.174564
$442$	4.56700e15	0.0291331
$443$	1.55015e16	0.0974431	0.0487215	−	0.998812i	$-0.484485\pi$
$443$	1.55015e16	0.0974431	0.0487215	+	0.998812i	$0.484485\pi$
$444$	−2.91044e17	−1.80289
$445$	0	0
$446$	−3.21729e17	−1.93559
$447$	−9.49181e16	−0.562795
$448$	3.26855e17	1.91006
$449$	−2.75973e17	−1.58952	−0.794759	−	0.606925i	$-0.792403\pi$
$449$	−2.75973e17	−1.58952	−0.794759	+	0.606925i	$0.792403\pi$
$450$	0	0
$451$	−1.28961e17	−0.721623
$452$	−4.05892e17	−2.23878
$453$	1.41902e17	0.771524
$454$	5.77640e17	3.09595
$455$	0	0
$456$	−2.12093e17	−1.10473
$457$	−2.05141e17	−1.05341	−0.526703	−	0.850049i	$-0.676572\pi$
$457$	−2.05141e17	−1.05341	−0.526703	+	0.850049i	$0.676572\pi$
$458$	1.63997e17	0.830250
$459$	−1.04570e16	−0.0521943
$460$	0	0
$461$	2.29523e17	1.11370	0.556852	−	0.830612i	$-0.312009\pi$
$461$	2.29523e17	1.11370	0.556852	+	0.830612i	$0.312009\pi$
$462$	−2.55184e17	−1.22090
$463$	−1.90465e17	−0.898544	−0.449272	−	0.893395i	$-0.648317\pi$
$463$	−1.90465e17	−0.898544	−0.449272	+	0.893395i	$0.648317\pi$
$464$	−6.86493e16	−0.319352
$465$	0	0
$466$	6.48147e17	2.93201
$467$	1.67739e17	0.748297	0.374148	−	0.927369i	$-0.377935\pi$
$467$	1.67739e17	0.748297	0.374148	+	0.927369i	$0.377935\pi$
$468$	−8.49121e15	−0.0373570
$469$	2.40432e16	0.104320
$470$	0	0
$471$	−5.78525e16	−0.244166
$472$	−2.74179e17	−1.14133
$473$	4.23446e17	1.73860
$474$	4.34573e17	1.75996
$475$	0	0
$476$	−1.46208e17	−0.576137
$477$	9.66406e16	0.375656
$478$	2.55007e17	0.977845
$479$	−3.71727e17	−1.40619	−0.703095	−	0.711096i	$-0.748199\pi$
$479$	−3.71727e17	−1.40619	−0.703095	+	0.711096i	$0.748199\pi$
$480$	0	0
$481$	−3.20938e16	−0.118162
$482$	−4.28738e17	−1.55735
$483$	−1.31704e17	−0.472002
$484$	3.82576e16	0.135277
$485$	0	0
$486$	3.07393e16	0.105818
$487$	−4.87760e16	−0.165679	−0.0828397	−	0.996563i	$-0.526399\pi$
$487$	−4.87760e16	−0.165679	−0.0828397	+	0.996563i	$0.526399\pi$
$488$	−1.55719e17	−0.521930
$489$	−1.18161e17	−0.390810
$490$	0	0
$491$	−6.19444e16	−0.199513	−0.0997567	−	0.995012i	$-0.531806\pi$
$491$	−6.19444e16	−0.199513	−0.0997567	+	0.995012i	$0.531806\pi$
$492$	2.17202e17	0.690384
$493$	−1.14683e17	−0.359745
$494$	−5.58274e16	−0.172831
$495$	0	0
$496$	1.23933e17	0.373727
$497$	−4.35783e17	−1.29704
$498$	−9.34137e16	−0.274423
$499$	−2.79726e17	−0.811108	−0.405554	−	0.914071i	$-0.632921\pi$
$499$	−2.79726e17	−0.811108	−0.405554	+	0.914071i	$0.632921\pi$
$500$	0	0
$501$	1.91194e17	0.540169
$502$	1.40550e17	0.391974
$503$	−3.38759e17	−0.932609	−0.466304	−	0.884624i	$-0.654415\pi$
$503$	−3.38759e17	−0.932609	−0.466304	+	0.884624i	$0.654415\pi$
$504$	1.80054e17	0.489332
$505$	0	0
$506$	4.28378e17	1.13461
$507$	2.19860e17	0.574902
$508$	−9.89666e17	−2.55490
$509$	−3.81496e17	−0.972354	−0.486177	−	0.873860i	$-0.661609\pi$
$509$	−3.81496e17	−0.972354	−0.486177	+	0.873860i	$0.661609\pi$
$510$	0	0
$511$	−4.50278e16	−0.111878
$512$	1.94447e17	0.477032
$513$	1.27827e17	0.309641
$514$	−4.94651e17	−1.18315
$515$	0	0
$516$	−7.13188e17	−1.66334
$517$	−6.17738e17	−1.42271
$518$	1.62447e18	3.69460
$519$	5.74157e16	0.128956
$520$	0	0
$521$	−3.97604e17	−0.870975	−0.435487	−	0.900195i	$-0.643424\pi$
$521$	−3.97604e17	−0.870975	−0.435487	+	0.900195i	$0.643424\pi$
$522$	3.37123e17	0.729340
$523$	−6.78177e16	−0.144905	−0.0724523	−	0.997372i	$-0.523082\pi$
$523$	−6.78177e16	−0.144905	−0.0724523	+	0.997372i	$0.523082\pi$
$524$	1.30685e18	2.75786
$525$	0	0
$526$	−4.66679e17	−0.960750
$527$	2.07037e17	0.420998
$528$	−7.18738e16	−0.144361
$529$	−2.82944e17	−0.561357
$530$	0	0
$531$	1.65245e17	0.319900
$532$	1.78726e18	3.41792
$533$	2.39511e16	0.0452480
$534$	−1.05355e17	−0.196624
$535$	0	0
$536$	5.51781e16	0.100507
$537$	5.49177e17	0.988278
$538$	−3.76079e17	−0.668643
$539$	3.09624e17	0.543886
$540$	0	0
$541$	−9.53886e17	−1.63574	−0.817870	−	0.575403i	$-0.804845\pi$
$541$	−9.53886e17	−1.63574	−0.817870	+	0.575403i	$0.804845\pi$
$542$	1.38329e17	0.234378
$543$	3.49683e17	0.585430
$544$	1.29864e17	0.214830
$545$	0	0
$546$	4.73939e16	0.0765544
$547$	−5.54825e17	−0.885601	−0.442800	−	0.896620i	$-0.646015\pi$
$547$	−5.54825e17	−0.885601	−0.442800	+	0.896620i	$0.646015\pi$
$548$	6.89684e17	1.08787
$549$	9.38502e16	0.146290
$550$	0	0
$551$	1.40190e18	2.13418
$552$	−3.02256e17	−0.454748
$553$	−1.53414e18	−2.28114
$554$	−6.02299e16	−0.0885113
$555$	0	0
$556$	6.32630e17	0.908163
$557$	−8.83747e17	−1.25392	−0.626959	−	0.779052i	$-0.715701\pi$
$557$	−8.83747e17	−1.25392	−0.626959	+	0.779052i	$0.715701\pi$
$558$	−6.08608e17	−0.853523
$559$	−7.86442e16	−0.109016
$560$	0	0
$561$	−1.20070e17	−0.162620
$562$	1.27840e18	1.71152
$563$	−1.34034e18	−1.77383	−0.886913	−	0.461937i	$-0.847154\pi$
$563$	−1.34034e18	−1.77383	−0.886913	+	0.461937i	$0.847154\pi$
$564$	1.04042e18	1.36112
$565$	0	0
$566$	−5.59682e17	−0.715541
$567$	−1.08517e17	−0.137153
$568$	−1.00010e18	−1.24963
$569$	−2.62408e16	−0.0324151	−0.0162075	−	0.999869i	$-0.505159\pi$
$569$	−2.62408e16	−0.0324151	−0.0162075	+	0.999869i	$0.505159\pi$
$570$	0	0
$571$	6.67128e17	0.805517	0.402758	−	0.915306i	$-0.368051\pi$
$571$	6.67128e17	0.805517	0.402758	+	0.915306i	$0.368051\pi$
$572$	−9.74986e16	−0.116392
$573$	−3.43330e17	−0.405235
$574$	−1.21232e18	−1.41478
$575$	0	0
$576$	−4.52089e17	−0.515796
$577$	1.37034e17	0.154591	0.0772955	−	0.997008i	$-0.475372\pi$
$577$	1.37034e17	0.154591	0.0772955	+	0.997008i	$0.475372\pi$
$578$	1.36997e18	1.52820
$579$	−9.06515e16	−0.0999918
$580$	0	0
$581$	3.29771e17	0.355687
$582$	−2.72153e17	−0.290278
$583$	1.10966e18	1.17042
$584$	−1.03337e17	−0.107788
$585$	0	0
$586$	3.69378e17	0.376822
$587$	−1.19496e17	−0.120561	−0.0602805	−	0.998181i	$-0.519200\pi$
$587$	−1.19496e17	−0.120561	−0.0602805	+	0.998181i	$0.519200\pi$
$588$	−5.21484e17	−0.520342
$589$	−2.53084e18	−2.49756
$590$	0	0
$591$	−3.06330e15	−0.00295713
$592$	4.57539e17	0.436855
$593$	1.87526e18	1.77095	0.885475	−	0.464687i	$-0.153833\pi$
$593$	1.87526e18	1.77095	0.885475	+	0.464687i	$0.153833\pi$
$594$	3.52958e17	0.329694
$595$	0	0
$596$	1.83562e18	1.67758
$597$	−8.01357e17	−0.724424
$598$	−7.95601e16	−0.0711439
$599$	−5.19643e17	−0.459654	−0.229827	−	0.973231i	$-0.573816\pi$
$599$	−5.19643e17	−0.459654	−0.229827	+	0.973231i	$0.573816\pi$
$600$	0	0
$601$	5.26704e17	0.455913	0.227957	−	0.973671i	$-0.426796\pi$
$601$	5.26704e17	0.455913	0.227957	+	0.973671i	$0.426796\pi$
$602$	3.98067e18	3.40863
$603$	−3.32553e16	−0.0281708
$604$	−2.74424e18	−2.29976
$605$	0	0
$606$	−3.82042e17	−0.313356
$607$	−1.87571e18	−1.52209	−0.761043	−	0.648701i	$-0.775312\pi$
$607$	−1.87571e18	−1.52209	−0.761043	+	0.648701i	$0.775312\pi$
$608$	−1.58747e18	−1.27448
$609$	−1.19012e18	−0.945318
$610$	0	0
$611$	1.14729e17	0.0892082
$612$	2.02227e17	0.155581
$613$	4.47233e17	0.340440	0.170220	−	0.985406i	$-0.445552\pi$
$613$	4.47233e17	0.340440	0.170220	+	0.985406i	$0.445552\pi$
$614$	4.66152e17	0.351102
$615$	0	0
$616$	2.06743e18	1.52460
$617$	8.44420e17	0.616176	0.308088	−	0.951358i	$-0.400311\pi$
$617$	8.44420e17	0.616176	0.308088	+	0.951358i	$0.400311\pi$
$618$	1.17748e18	0.850216
$619$	2.36925e18	1.69286	0.846430	−	0.532500i	$-0.178747\pi$
$619$	2.36925e18	1.69286	0.846430	+	0.532500i	$0.178747\pi$
$620$	0	0
$621$	1.82167e17	0.127460
$622$	−1.30174e18	−0.901334
$623$	3.71927e17	0.254850
$624$	1.33487e16	0.00905190
$625$	0	0
$626$	2.90100e18	1.92670
$627$	1.46774e18	0.964741
$628$	1.11881e18	0.727811
$629$	7.64348e17	0.492110
$630$	0	0
$631$	−2.91193e18	−1.83649	−0.918247	−	0.396009i	$-0.870395\pi$
$631$	−2.91193e18	−1.83649	−0.918247	+	0.396009i	$0.870395\pi$
$632$	−3.52079e18	−2.19775
$633$	3.23484e17	0.199861
$634$	4.08673e18	2.49917
$635$	0	0
$636$	−1.86894e18	−1.11976
$637$	−5.75048e16	−0.0341034
$638$	3.87095e18	2.27239
$639$	6.02753e17	0.350255
$640$	0	0
$641$	−3.49512e17	−0.199014	−0.0995072	−	0.995037i	$-0.531727\pi$
$641$	−3.49512e17	−0.199014	−0.0995072	+	0.995037i	$0.531727\pi$
$642$	−1.62181e18	−0.914162
$643$	3.11686e18	1.73919	0.869593	−	0.493769i	$-0.164381\pi$
$643$	3.11686e18	1.73919	0.869593	+	0.493769i	$0.164381\pi$
$644$	2.54703e18	1.40694
$645$	0	0
$646$	1.32959e18	0.719791
$647$	−1.99766e18	−1.07064	−0.535321	−	0.844649i	$-0.679809\pi$
$647$	−1.99766e18	−1.07064	−0.535321	+	0.844649i	$0.679809\pi$
$648$	−2.49041e17	−0.132140
$649$	1.89739e18	0.996706
$650$	0	0
$651$	2.14852e18	1.10628
$652$	2.28512e18	1.16493
$653$	1.08626e18	0.548276	0.274138	−	0.961690i	$-0.411607\pi$
$653$	1.08626e18	0.548276	0.274138	+	0.961690i	$0.411607\pi$
$654$	−2.19040e18	−1.09463
$655$	0	0
$656$	−3.41455e17	−0.167286
$657$	6.22801e16	0.0302117
$658$	−5.80715e18	−2.78930
$659$	−1.64776e17	−0.0783678	−0.0391839	−	0.999232i	$-0.512476\pi$
$659$	−1.64776e17	−0.0783678	−0.0391839	+	0.999232i	$0.512476\pi$
$660$	0	0
$661$	−4.20993e18	−1.96320	−0.981601	−	0.190942i	$-0.938846\pi$
$661$	−4.20993e18	−1.96320	−0.981601	+	0.190942i	$0.938846\pi$
$662$	−2.22165e18	−1.02588
$663$	2.22999e16	0.0101968
$664$	7.56811e17	0.342685
$665$	0	0
$666$	−2.24688e18	−0.997695
$667$	1.99785e18	0.878508
$668$	−3.69751e18	−1.61013
$669$	−1.57094e18	−0.677472
$670$	0	0
$671$	1.07762e18	0.455793
$672$	1.34766e18	0.564520
$673$	2.30935e18	0.958057	0.479029	−	0.877799i	$-0.340989\pi$
$673$	2.30935e18	0.958057	0.479029	+	0.877799i	$0.340989\pi$
$674$	−1.42002e18	−0.583451
$675$	0	0
$676$	−4.25187e18	−1.71367
$677$	4.16216e18	1.66147	0.830736	−	0.556667i	$-0.187920\pi$
$677$	4.16216e18	1.66147	0.830736	+	0.556667i	$0.187920\pi$
$678$	−3.13352e18	−1.23891
$679$	9.60762e17	0.376238
$680$	0	0
$681$	2.82051e18	1.08361
$682$	−6.98822e18	−2.65930
$683$	5.67684e17	0.213979	0.106990	−	0.994260i	$-0.465879\pi$
$683$	5.67684e17	0.213979	0.106990	+	0.994260i	$0.465879\pi$
$684$	−2.47204e18	−0.922978
$685$	0	0
$686$	−2.64730e18	−0.969833
$687$	8.00766e17	0.290594
$688$	1.12118e18	0.403041
$689$	−2.06090e17	−0.0733892
$690$	0	0
$691$	1.60571e18	0.561126	0.280563	−	0.959836i	$-0.409479\pi$
$691$	1.60571e18	0.561126	0.280563	+	0.959836i	$0.409479\pi$
$692$	−1.11036e18	−0.384393
$693$	−1.24602e18	−0.427325
$694$	3.02024e18	1.02614
$695$	0	0
$696$	−2.73128e18	−0.910763
$697$	−5.70423e17	−0.188445
$698$	−1.31416e18	−0.430119
$699$	3.16479e18	1.02623
$700$	0	0
$701$	−2.88624e18	−0.918681	−0.459341	−	0.888260i	$-0.651914\pi$
$701$	−2.88624e18	−0.918681	−0.459341	+	0.888260i	$0.651914\pi$
$702$	−6.55528e16	−0.0206728
$703$	−9.34345e18	−2.91943
$704$	−5.19102e18	−1.60705
$705$	0	0
$706$	2.49741e18	0.759030
$707$	1.34869e18	0.406150
$708$	−3.19568e18	−0.953558
$709$	3.41704e18	1.01030	0.505150	−	0.863032i	$-0.331437\pi$
$709$	3.41704e18	1.01030	0.505150	+	0.863032i	$0.331437\pi$
$710$	0	0
$711$	2.12195e18	0.616002
$712$	8.53557e17	0.245535
$713$	−3.60672e18	−1.02809
$714$	−1.12874e18	−0.318826
$715$	0	0
$716$	−1.06205e19	−2.94586
$717$	1.24515e18	0.342254
$718$	1.18666e19	3.23234
$719$	−4.01107e18	−1.08274	−0.541368	−	0.840786i	$-0.682093\pi$
$719$	−4.01107e18	−1.08274	−0.541368	+	0.840786i	$0.682093\pi$
$720$	0	0
$721$	−4.15677e18	−1.10199
$722$	−9.97455e18	−2.62060
$723$	−2.09345e18	−0.545084
$724$	−6.76252e18	−1.74505
$725$	0	0
$726$	2.95352e17	0.0748603
$727$	2.32433e18	0.583881	0.291941	−	0.956436i	$-0.405699\pi$
$727$	2.32433e18	0.583881	0.291941	+	0.956436i	$0.405699\pi$
$728$	−3.83972e17	−0.0955973
$729$	1.50095e17	0.0370370
$730$	0	0
$731$	1.87300e18	0.454019
$732$	−1.81497e18	−0.436062
$733$	2.96621e17	0.0706359	0.0353180	−	0.999376i	$-0.488756\pi$
$733$	2.96621e17	0.0706359	0.0353180	+	0.999376i	$0.488756\pi$
$734$	−1.04062e19	−2.45622
$735$	0	0
$736$	−2.26231e18	−0.524622
$737$	−3.81847e17	−0.0877710
$738$	1.67682e18	0.382049
$739$	8.38574e18	1.89388	0.946940	−	0.321410i	$-0.104157\pi$
$739$	8.38574e18	1.89388	0.946940	+	0.321410i	$0.104157\pi$
$740$	0	0
$741$	−2.72595e17	−0.0604923
$742$	1.04315e19	2.29468
$743$	−1.06547e18	−0.232335	−0.116168	−	0.993230i	$-0.537061\pi$
$743$	−1.06547e18	−0.232335	−0.116168	+	0.993230i	$0.537061\pi$
$744$	4.93077e18	1.06584
$745$	0	0
$746$	3.10382e18	0.659316
$747$	−4.56123e17	−0.0960501
$748$	2.32203e18	0.484739
$749$	5.72536e18	1.18487
$750$	0	0
$751$	−9.57457e18	−1.94742	−0.973710	−	0.227792i	$-0.926849\pi$
$751$	−9.57457e18	−1.94742	−0.973710	+	0.227792i	$0.926849\pi$
$752$	−1.63561e18	−0.329810
$753$	6.86282e17	0.137194
$754$	−7.18929e17	−0.142486
$755$	0	0
$756$	2.09861e18	0.408827
$757$	−4.59607e18	−0.887695	−0.443847	−	0.896102i	$-0.646387\pi$
$757$	−4.59607e18	−0.887695	−0.443847	+	0.896102i	$0.646387\pi$
$758$	−1.16045e19	−2.22217
$759$	2.09169e18	0.397124
$760$	0	0
$761$	3.11769e18	0.581879	0.290940	−	0.956741i	$-0.406032\pi$
$761$	3.11769e18	0.581879	0.290940	+	0.956741i	$0.406032\pi$
$762$	−7.64030e18	−1.41385
$763$	7.73258e18	1.41878
$764$	6.63967e18	1.20792
$765$	0	0
$766$	9.89464e18	1.76975
$767$	−3.52392e17	−0.0624966
$768$	4.45313e18	0.783101
$769$	4.30427e18	0.750547	0.375274	−	0.926914i	$-0.377549\pi$
$769$	4.30427e18	0.750547	0.375274	+	0.926914i	$0.377549\pi$
$770$	0	0
$771$	−2.41529e18	−0.414110
$772$	1.75311e18	0.298056
$773$	6.51519e18	1.09840	0.549200	−	0.835691i	$-0.314933\pi$
$773$	6.51519e18	1.09840	0.549200	+	0.835691i	$0.314933\pi$
$774$	−5.50587e18	−0.920470
$775$	0	0
$776$	2.20491e18	0.362485
$777$	7.93199e18	1.29314
$778$	4.52719e17	0.0731916
$779$	6.97289e18	1.11794
$780$	0	0
$781$	6.92099e18	1.09128
$782$	1.89481e18	0.296293
$783$	1.64611e18	0.255275
$784$	8.19806e17	0.126083
$785$	0	0
$786$	1.00890e19	1.52616
$787$	7.49401e18	1.12429	0.562145	−	0.827039i	$-0.309976\pi$
$787$	7.49401e18	1.12429	0.562145	+	0.827039i	$0.309976\pi$
$788$	5.92412e16	0.00881462
$789$	−2.27871e18	−0.336270
$790$	0	0
$791$	1.10620e19	1.60579
$792$	−2.85956e18	−0.411705
$793$	−2.00139e17	−0.0285796
$794$	5.19098e18	0.735218
$795$	0	0
$796$	1.54975e19	2.15936
$797$	8.43590e18	1.16588	0.582938	−	0.812516i	$-0.301903\pi$
$797$	8.43590e18	1.16588	0.582938	+	0.812516i	$0.301903\pi$
$798$	1.37978e19	1.89143
$799$	−2.73239e18	−0.371526
$800$	0	0
$801$	−5.14430e17	−0.0688201
$802$	−6.67801e18	−0.886163
$803$	7.15119e17	0.0941298
$804$	6.43125e17	0.0839714
$805$	0	0
$806$	1.29788e18	0.166747
$807$	−1.83633e18	−0.234030
$808$	3.09519e18	0.391304
$809$	−2.98965e18	−0.374934	−0.187467	−	0.982271i	$-0.560028\pi$
$809$	−2.98965e18	−0.374934	−0.187467	+	0.982271i	$0.560028\pi$
$810$	0	0
$811$	−1.10858e19	−1.36814	−0.684072	−	0.729415i	$-0.739792\pi$
$811$	−1.10858e19	−1.36814	−0.684072	+	0.729415i	$0.739792\pi$
$812$	2.30157e19	2.81780
$813$	6.75434e17	0.0820341
$814$	−2.57993e19	−3.10849
$815$	0	0
$816$	−3.17914e17	−0.0376985
$817$	−2.28956e19	−2.69345
$818$	−6.84893e18	−0.799330
$819$	2.31416e17	0.0267946
$820$	0	0
$821$	1.97742e18	0.225356	0.112678	−	0.993632i	$-0.464057\pi$
$821$	1.97742e18	0.225356	0.112678	+	0.993632i	$0.464057\pi$
$822$	5.32442e18	0.602012
$823$	1.12620e19	1.26333	0.631665	−	0.775242i	$-0.282372\pi$
$823$	1.12620e19	1.26333	0.631665	+	0.775242i	$0.282372\pi$
$824$	−9.53963e18	−1.06171
$825$	0	0
$826$	1.78368e19	1.95410
$827$	1.16025e19	1.26115	0.630574	−	0.776129i	$-0.282819\pi$
$827$	1.16025e19	1.26115	0.630574	+	0.776129i	$0.282819\pi$
$828$	−3.52293e18	−0.379933
$829$	−4.67038e18	−0.499745	−0.249872	−	0.968279i	$-0.580389\pi$
$829$	−4.67038e18	−0.499745	−0.249872	+	0.968279i	$0.580389\pi$
$830$	0	0
$831$	−2.94092e17	−0.0309797
$832$	9.64098e17	0.100767
$833$	1.36954e18	0.142030
$834$	4.88396e18	0.502565
$835$	0	0
$836$	−2.83847e19	−2.87570
$837$	−2.97173e18	−0.298740
$838$	−1.05194e19	−1.04931
$839$	−8.73017e17	−0.0864112	−0.0432056	−	0.999066i	$-0.513757\pi$
$839$	−8.73017e17	−0.0864112	−0.0432056	+	0.999066i	$0.513757\pi$
$840$	0	0
$841$	7.79256e18	0.759462
$842$	3.15953e18	0.305559
$843$	6.24222e18	0.599046
$844$	−6.25586e18	−0.595746
$845$	0	0
$846$	8.03215e18	0.753225
$847$	−1.04266e18	−0.0970285
$848$	2.93808e18	0.271326
$849$	−2.73283e18	−0.250445
$850$	0	0
$851$	−1.33154e19	−1.20175
$852$	−1.16567e19	−1.04404
$853$	−1.24079e19	−1.10288	−0.551442	−	0.834213i	$-0.685922\pi$
$853$	−1.24079e19	−1.10288	−0.551442	+	0.834213i	$0.685922\pi$
$854$	1.01303e19	0.893607
$855$	0	0
$856$	1.31395e19	1.14156
$857$	−7.04934e18	−0.607817	−0.303909	−	0.952701i	$-0.598292\pi$
$857$	−7.04934e18	−0.607817	−0.303909	+	0.952701i	$0.598292\pi$
$858$	−7.52697e17	−0.0644099
$859$	−2.37855e17	−0.0202003	−0.0101001	−	0.999949i	$-0.503215\pi$
$859$	−2.37855e17	−0.0202003	−0.0101001	+	0.999949i	$0.503215\pi$
$860$	0	0
$861$	−5.91953e18	−0.495185
$862$	−6.10992e18	−0.507269
$863$	−1.21210e19	−0.998774	−0.499387	−	0.866379i	$-0.666441\pi$
$863$	−1.21210e19	−0.998774	−0.499387	+	0.866379i	$0.666441\pi$
$864$	−1.86401e18	−0.152444
$865$	0	0
$866$	1.27981e19	1.03105
$867$	6.68934e18	0.534884
$868$	−4.15503e19	−3.29759
$869$	2.43648e19	1.91926
$870$	0	0
$871$	7.09183e16	0.00550352
$872$	1.77460e19	1.36692
$873$	−1.32888e18	−0.101600
$874$	−2.31623e19	−1.75775
$875$	0	0
$876$	−1.20444e18	−0.0900549
$877$	3.74100e18	0.277645	0.138823	−	0.990317i	$-0.455668\pi$
$877$	3.74100e18	0.277645	0.138823	+	0.990317i	$0.455668\pi$
$878$	−5.53354e18	−0.407651
$879$	1.80361e18	0.131891
$880$	0	0
$881$	−1.36085e19	−0.980544	−0.490272	−	0.871570i	$-0.663102\pi$
$881$	−1.36085e19	−0.980544	−0.490272	+	0.871570i	$0.663102\pi$
$882$	−4.02590e18	−0.287950
$883$	−9.87005e18	−0.700769	−0.350384	−	0.936606i	$-0.613949\pi$
$883$	−9.87005e18	−0.700769	−0.350384	+	0.936606i	$0.613949\pi$
$884$	−4.31258e17	−0.0303947
$885$	0	0
$886$	−2.31436e18	−0.160736
$887$	−1.35100e19	−0.931432	−0.465716	−	0.884934i	$-0.654203\pi$
$887$	−1.35100e19	−0.931432	−0.465716	+	0.884934i	$0.654203\pi$
$888$	1.82036e19	1.24587
$889$	2.69720e19	1.83253
$890$	0	0
$891$	1.72343e18	0.115395
$892$	3.03805e19	2.01941
$893$	3.34010e19	2.20407
$894$	1.41712e19	0.928350
$895$	0	0
$896$	−3.36550e19	−2.17294
$897$	−3.88478e17	−0.0249009
$898$	4.12025e19	2.62197
$899$	−3.25914e19	−2.05904
$900$	0	0
$901$	4.90826e18	0.305644
$902$	1.92537e19	1.19034
$903$	1.94369e19	1.19305
$904$	2.53869e19	1.54709
$905$	0	0
$906$	−2.11858e19	−1.27266
$907$	7.78812e18	0.464500	0.232250	−	0.972656i	$-0.425391\pi$
$907$	7.78812e18	0.464500	0.232250	+	0.972656i	$0.425391\pi$
$908$	−5.45460e19	−3.23002
$909$	−1.86544e18	−0.109677
$910$	0	0
$911$	6.24185e17	0.0361779	0.0180890	−	0.999836i	$-0.494242\pi$
$911$	6.24185e17	0.0361779	0.0180890	+	0.999836i	$0.494242\pi$
$912$	3.88621e18	0.223645
$913$	−5.23733e18	−0.299261
$914$	3.06272e19	1.73763
$915$	0	0
$916$	−1.54860e19	−0.866203
$917$	−3.56164e19	−1.97810
$918$	1.56121e18	0.0860963
$919$	−3.08457e19	−1.68906	−0.844528	−	0.535511i	$-0.820119\pi$
$919$	−3.08457e19	−1.68906	−0.844528	+	0.535511i	$0.820119\pi$
$920$	0	0
$921$	2.27614e18	0.122888
$922$	−3.42675e19	−1.83709
$923$	−1.28539e18	−0.0684267
$924$	2.40968e19	1.27377
$925$	0	0
$926$	2.84363e19	1.48218
$927$	5.74944e18	0.297582
$928$	−2.04429e19	−1.05071
$929$	−2.60942e19	−1.33181	−0.665905	−	0.746037i	$-0.731954\pi$
$929$	−2.60942e19	−1.33181	−0.665905	+	0.746037i	$0.731954\pi$
$930$	0	0
$931$	−1.67413e19	−0.842592
$932$	−6.12039e19	−3.05897
$933$	−6.35615e18	−0.315474
$934$	−2.50432e19	−1.23434
$935$	0	0
$936$	5.31090e17	0.0258152
$937$	1.43219e19	0.691340	0.345670	−	0.938356i	$-0.387652\pi$
$937$	1.43219e19	0.691340	0.345670	+	0.938356i	$0.387652\pi$
$938$	−3.58962e18	−0.172080
$939$	1.41651e19	0.674361
$940$	0	0
$941$	−6.74040e18	−0.316485	−0.158242	−	0.987400i	$-0.550583\pi$
$941$	−6.74040e18	−0.316485	−0.158242	+	0.987400i	$0.550583\pi$
$942$	8.63731e18	0.402761
$943$	9.93712e18	0.460187
$944$	5.02381e18	0.231055
$945$	0	0
$946$	−6.32200e19	−2.86789
$947$	4.26475e18	0.192140	0.0960701	−	0.995375i	$-0.469373\pi$
$947$	4.26475e18	0.192140	0.0960701	+	0.995375i	$0.469373\pi$
$948$	−4.10364e19	−1.83618
$949$	−1.32815e17	−0.00590223
$950$	0	0
$951$	1.99548e19	0.874729
$952$	9.14471e18	0.398134
$953$	−2.39618e17	−0.0103613	−0.00518067	−	0.999987i	$-0.501649\pi$
$953$	−2.39618e17	−0.0103613	−0.00518067	+	0.999987i	$0.501649\pi$
$954$	−1.44283e19	−0.619658
$955$	0	0
$956$	−2.40800e19	−1.02019
$957$	1.89011e19	0.795354
$958$	5.54985e19	2.31956
$959$	−1.87964e19	−0.780285
$960$	0	0
$961$	3.44197e19	1.40963
$962$	4.79157e18	0.194912
$963$	−7.91903e18	−0.319964
$964$	4.04853e19	1.62479
$965$	0	0
$966$	1.96633e19	0.778584
$967$	−1.50588e19	−0.592268	−0.296134	−	0.955146i	$-0.595698\pi$
$967$	−1.50588e19	−0.592268	−0.296134	+	0.955146i	$0.595698\pi$
$968$	−2.39286e18	−0.0934817
$969$	6.49215e18	0.251933
$970$	0	0
$971$	1.51669e19	0.580728	0.290364	−	0.956916i	$-0.406224\pi$
$971$	1.51669e19	0.580728	0.290364	+	0.956916i	$0.406224\pi$
$972$	−2.90268e18	−0.110400
$973$	−1.72415e19	−0.651389
$974$	7.28221e18	0.273294
$975$	0	0
$976$	2.85325e18	0.105661
$977$	−5.43050e18	−0.199768	−0.0998838	−	0.994999i	$-0.531847\pi$
$977$	−5.43050e18	−0.199768	−0.0998838	+	0.994999i	$0.531847\pi$
$978$	1.76413e19	0.644656
$979$	−5.90684e18	−0.214421
$980$	0	0
$981$	−1.06953e19	−0.383129
$982$	9.24822e18	0.329104
$983$	4.45646e19	1.57540	0.787702	−	0.616057i	$-0.211271\pi$
$983$	4.45646e19	1.57540	0.787702	+	0.616057i	$0.211271\pi$
$984$	−1.35851e19	−0.477084
$985$	0	0
$986$	1.71221e19	0.593412
$987$	−2.83553e19	−0.976275
$988$	5.27173e18	0.180315
$989$	−3.26288e19	−1.10873
$990$	0	0
$991$	8.11044e18	0.271998	0.135999	−	0.990709i	$-0.456576\pi$
$991$	8.11044e18	0.271998	0.135999	+	0.990709i	$0.456576\pi$
$992$	3.69056e19	1.22961
$993$	−1.08479e19	−0.359067
$994$	6.50619e19	2.13951
$995$	0	0
$996$	8.82097e18	0.286306
$997$	−3.75569e19	−1.21107	−0.605537	−	0.795817i	$-0.707042\pi$
$997$	−3.75569e19	−1.21107	−0.605537	+	0.795817i	$0.707042\pi$
$998$	4.17627e19	1.33795
$999$	−1.09711e19	−0.349201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.14.a.c.1.1		2
5.2	odd	4		75.14.b.e.49.1		4
5.3	odd	4		75.14.b.e.49.4		4
5.4	even	2		15.14.a.c.1.2	✓	2
15.14	odd	2		45.14.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.14.a.c.1.2	✓	2	5.4	even	2
45.14.a.b.1.1		2	15.14	odd	2
75.14.a.c.1.1		2	1.1	even	1	trivial
75.14.b.e.49.1		4	5.2	odd	4
75.14.b.e.49.4		4	5.3	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)

\(f(q)\)	\(=\)	\(q-149.299 q^{2} -729.000 q^{3} +14098.2 q^{4} +108839. q^{6} -384225. q^{7} -881782. q^{8} +531441. q^{9} +6.10216e6 q^{11} -1.02776e7 q^{12} -1.13332e6 q^{13} +5.73644e7 q^{14} +1.61570e7 q^{16} +2.69912e7 q^{17} -7.93435e7 q^{18} -3.29943e8 q^{19} +2.80100e8 q^{21} -9.11046e8 q^{22} -4.70204e8 q^{23} +6.42819e8 q^{24} +1.69203e8 q^{26} -3.87420e8 q^{27} -5.41687e9 q^{28} -4.24890e9 q^{29} +7.67054e9 q^{31} +4.81134e9 q^{32} -4.44848e9 q^{33} -4.02976e9 q^{34} +7.49234e9 q^{36} +2.83184e10 q^{37} +4.92601e10 q^{38} +8.26190e8 q^{39} -2.11336e10 q^{41} -4.18187e10 q^{42} +6.93928e10 q^{43} +8.60292e10 q^{44} +7.02010e10 q^{46} -1.01233e11 q^{47} -1.17784e10 q^{48} +5.07401e10 q^{49} -1.96766e10 q^{51} -1.59777e10 q^{52} +1.81846e11 q^{53} +5.78414e10 q^{54} +3.38803e11 q^{56} +2.40528e11 q^{57} +6.34357e11 q^{58} +3.10938e11 q^{59} +1.76596e11 q^{61} -1.14520e12 q^{62} -2.04193e11 q^{63} -8.50686e11 q^{64} +6.64152e11 q^{66} -6.25757e10 q^{67} +3.80526e11 q^{68} +3.42779e11 q^{69} +1.13419e12 q^{71} -4.68615e11 q^{72} +1.17191e11 q^{73} -4.22790e12 q^{74} -4.65158e12 q^{76} -2.34461e12 q^{77} -1.23349e11 q^{78} +3.99281e12 q^{79} +2.82430e11 q^{81} +3.15523e12 q^{82} -8.58275e11 q^{83} +3.94890e12 q^{84} -1.03603e13 q^{86} +3.09745e12 q^{87} -5.38077e12 q^{88} -9.67991e11 q^{89} +4.35450e11 q^{91} -6.62901e12 q^{92} -5.59183e12 q^{93} +1.51139e13 q^{94} -3.50747e12 q^{96} -2.50052e12 q^{97} -7.57544e12 q^{98} +3.24294e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 131 q^{2} - 1458 q^{3} + 6241 q^{4} + 95499 q^{6} - 496272 q^{7} - 1175463 q^{8} + 1062882 q^{9} + 6245888 q^{11} - 4549689 q^{12} - 1761164 q^{13} + 55314084 q^{14} + 75148705 q^{16} - 48151604 q^{17}+ \cdots + 3319320964608 q^{99}+O(q^{100}) \) 2 * q - 131 * q^2 - 1458 * q^3 + 6241 * q^4 + 95499 * q^6 - 496272 * q^7 - 1175463 * q^8 + 1062882 * q^9 + 6245888 * q^11 - 4549689 * q^12 - 1761164 * q^13 + 55314084 * q^14 + 75148705 * q^16 - 48151604 * q^17 - 69618771 * q^18 + 38475344 * q^19 + 361782288 * q^21 - 908415728 * q^22 - 734264616 * q^23 + 856912527 * q^24 + 157714454 * q^26 - 774840978 * q^27 - 4536499884 * q^28 + 1126474708 * q^29 + 6100104312 * q^31 + 8296660073 * q^32 - 4553252352 * q^33 - 5404788238 * q^34 + 3316723281 * q^36 + 46819674548 * q^37 + 56001723484 * q^38 + 1283888556 * q^39 - 29607909788 * q^41 - 40323967236 * q^42 + 63189768520 * q^43 + 84899911888 * q^44 + 65368954992 * q^46 - 105004415960 * q^47 - 54783405945 * q^48 - 33594444590 * q^49 + 35102519316 * q^51 - 11044638034 * q^52 - 48425833796 * q^53 + 50752084059 * q^54 + 371708899380 * q^56 - 28048525776 * q^57 + 732719858498 * q^58 + 722768180096 * q^59 - 229984402180 * q^61 - 1173940563384 * q^62 - 263739287952 * q^63 - 1270168541071 * q^64 + 662235065712 * q^66 - 359062188984 * q^67 + 970935017018 * q^68 + 535278905064 * q^69 + 736545668224 * q^71 - 624689232183 * q^72 + 1494470740204 * q^73 - 3889351112906 * q^74 - 7546301154644 * q^76 - 2360709208704 * q^77 - 114973836966 * q^78 + 3526348590120 * q^79 + 564859072962 * q^81 + 3000156702386 * q^82 - 5631050986968 * q^83 + 3307108415436 * q^84 - 10473766954252 * q^86 - 821200062132 * q^87 - 5422984137648 * q^88 + 5913121459764 * q^89 + 505797926592 * q^91 - 4554248300592 * q^92 - 4446976043448 * q^93 + 15044889696176 * q^94 - 6048265193217 * q^96 - 16383233322244 * q^97 - 9118668656251 * q^98 + 3319320964608 * q^99

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