LMFDB - Embedded newform 169.14.a.f.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,14,Mod(1,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.1"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	169.a (trivial)

Newform invariants

comment:select newform

sage:traces = [30,0] 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:	$181.220269929$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-131.328 q^{2} -395.120 q^{3} +9055.01 q^{4} +34433.6 q^{5} +51890.3 q^{6} +374853. q^{7} -113337. q^{8} -1.43820e6 q^{9} -4.52209e6 q^{10} +6.52193e6 q^{11} -3.57782e6 q^{12} -4.92287e7 q^{14} -1.36054e7 q^{15} -5.92943e7 q^{16} -1.13330e8 q^{17} +1.88876e8 q^{18} -7.26088e7 q^{19} +3.11796e8 q^{20} -1.48112e8 q^{21} -8.56511e8 q^{22} -2.61354e8 q^{23} +4.47816e7 q^{24} -3.50307e7 q^{25} +1.19821e9 q^{27} +3.39430e9 q^{28} -4.36764e9 q^{29} +1.78677e9 q^{30} -2.46004e9 q^{31} +8.71545e9 q^{32} -2.57695e9 q^{33} +1.48834e10 q^{34} +1.29076e10 q^{35} -1.30229e10 q^{36} +1.21767e10 q^{37} +9.53555e9 q^{38} -3.90259e9 q^{40} -3.26081e10 q^{41} +1.94512e10 q^{42} +1.89264e10 q^{43} +5.90561e10 q^{44} -4.95225e10 q^{45} +3.43231e10 q^{46} +1.30245e11 q^{47} +2.34284e10 q^{48} +4.36261e10 q^{49} +4.60051e9 q^{50} +4.47791e10 q^{51} +9.35113e10 q^{53} -1.57359e11 q^{54} +2.24574e11 q^{55} -4.24847e10 q^{56} +2.86892e10 q^{57} +5.73593e11 q^{58} +3.85302e11 q^{59} -1.23197e11 q^{60} +1.30762e11 q^{61} +3.23072e11 q^{62} -5.39115e11 q^{63} -6.58843e11 q^{64} +3.38425e11 q^{66} -1.00086e12 q^{67} -1.02621e12 q^{68} +1.03266e11 q^{69} -1.69512e12 q^{70} -1.79269e12 q^{71} +1.63001e11 q^{72} +1.44196e12 q^{73} -1.59913e12 q^{74} +1.38413e10 q^{75} -6.57473e11 q^{76} +2.44477e12 q^{77} -1.00167e12 q^{79} -2.04172e12 q^{80} +1.81952e12 q^{81} +4.28235e12 q^{82} +4.32147e12 q^{83} -1.34116e12 q^{84} -3.90237e12 q^{85} -2.48557e12 q^{86} +1.72574e12 q^{87} -7.39175e11 q^{88} +9.30942e11 q^{89} +6.50368e12 q^{90} -2.36656e12 q^{92} +9.72012e11 q^{93} -1.71048e13 q^{94} -2.50018e12 q^{95} -3.44365e12 q^{96} +9.20926e12 q^{97} -5.72932e12 q^{98} -9.37986e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 1460 q^{3} + 131070 q^{4} + 18234142 q^{9} + 7786950 q^{10} - 27694876 q^{12} + 61125588 q^{14} + 700365042 q^{16} - 47049798 q^{17} + 256370724 q^{22} + 834173772 q^{23} + 11926991364 q^{25} + 5605403288 q^{27}+ \cdots + 22616629029900 q^{95}+O(q^{100}) $ 30 * q + 1460 * q^3 + 131070 * q^4 + 18234142 * q^9 + 7786950 * q^10 - 27694876 * q^12 + 61125588 * q^14 + 700365042 * q^16 - 47049798 * q^17 + 256370724 * q^22 + 834173772 * q^23 + 11926991364 * q^25 + 5605403288 * q^27 + 17620379154 * q^29 - 19873358484 * q^30 - 2118481440 * q^35 + 111801927430 * q^36 + 45168847944 * q^38 + 137282090274 * q^40 + 68249929572 * q^42 + 276653280960 * q^43 - 1261191382396 * q^48 + 228555270606 * q^49 + 178343342508 * q^51 + 938994404670 * q^53 + 281220246240 * q^55 + 1865948401440 * q^56 - 568996466874 * q^61 + 5148167694060 * q^62 + 4989806279958 * q^64 + 12037245084948 * q^66 + 6248093284554 * q^68 + 2413972855992 * q^69 - 3446868460146 * q^74 + 3819696303368 * q^75 + 8153714196816 * q^77 + 10732970056200 * q^79 - 53747712890 * q^81 - 1848896034654 * q^82 + 12885932252268 * q^87 - 22189213625376 * q^88 - 53932182551466 * q^90 - 48706576133844 * q^92 - 7058933840292 * q^94 + 22616629029900 * q^95

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 $

$2$	−131.328	−1.45098	−0.725491	−	0.688232i	$-0.758387\pi$
$2$	−131.328	−1.45098	−0.725491	+	0.688232i	$0.758387\pi$
$3$	−395.120	−0.312926	−0.156463	−	0.987684i	$-0.550009\pi$
$3$	−395.120	−0.312926	−0.156463	+	0.987684i	$0.550009\pi$
$4$	9055.01	1.10535
$5$	34433.6	0.985547	0.492773	−	0.870158i	$-0.335983\pi$
$5$	34433.6	0.985547	0.492773	+	0.870158i	$0.335983\pi$
$6$	51890.3	0.454049
$7$	374853.	1.20427	0.602136	−	0.798394i	$-0.294317\pi$
$7$	374853.	1.20427	0.602136	+	0.798394i	$0.294317\pi$
$8$	−113337.	−0.152857
$9$	−1.43820e6	−0.902078
$10$	−4.52209e6	−1.43001
$11$	6.52193e6	1.11000	0.555001	−	0.831850i	$-0.312718\pi$
$11$	6.52193e6	1.11000	0.555001	+	0.831850i	$0.312718\pi$
$12$	−3.57782e6	−0.345891
$13$	0	0
$13$	0	0
$14$	−4.92287e7	−1.74738
$15$	−1.36054e7	−0.308403
$16$	−5.92943e7	−0.883554
$17$	−1.13330e8	−1.13875	−0.569375	−	0.822078i	$-0.692815\pi$
$17$	−1.13330e8	−1.13875	−0.569375	+	0.822078i	$0.692815\pi$
$18$	1.88876e8	1.30890
$19$	−7.26088e7	−0.354071	−0.177036	−	0.984204i	$-0.556651\pi$
$19$	−7.26088e7	−0.354071	−0.177036	+	0.984204i	$0.556651\pi$
$20$	3.11796e8	1.08937
$21$	−1.48112e8	−0.376847
$22$	−8.56511e8	−1.61059
$23$	−2.61354e8	−0.368128	−0.184064	−	0.982914i	$-0.558925\pi$
$23$	−2.61354e8	−0.368128	−0.184064	+	0.982914i	$0.558925\pi$
$24$	4.47816e7	0.0478329
$25$	−3.50307e7	−0.0286972
$26$	0	0
$27$	1.19821e9	0.595209
$28$	3.39430e9	1.33114
$29$	−4.36764e9	−1.36352	−0.681758	−	0.731578i	$-0.738784\pi$
$29$	−4.36764e9	−1.36352	−0.681758	+	0.731578i	$0.738784\pi$
$30$	1.78677e9	0.447487
$31$	−2.46004e9	−0.497842	−0.248921	−	0.968524i	$-0.580076\pi$
$31$	−2.46004e9	−0.497842	−0.248921	+	0.968524i	$0.580076\pi$
$32$	8.71545e9	1.43488
$33$	−2.57695e9	−0.347348
$34$	1.48834e10	1.65230
$35$	1.29076e10	1.18687
$36$	−1.30229e10	−0.997109
$37$	1.21767e10	0.780219	0.390110	−	0.920768i	$-0.372437\pi$
$37$	1.21767e10	0.780219	0.390110	+	0.920768i	$0.372437\pi$
$38$	9.53555e9	0.513751
$39$	0	0
$40$	−3.90259e9	−0.150648
$41$	−3.26081e10	−1.07209	−0.536044	−	0.844190i	$-0.680082\pi$
$41$	−3.26081e10	−1.07209	−0.536044	+	0.844190i	$0.680082\pi$
$42$	1.94512e10	0.546798
$43$	1.89264e10	0.456587	0.228294	−	0.973592i	$-0.426685\pi$
$43$	1.89264e10	0.456587	0.228294	+	0.973592i	$0.426685\pi$
$44$	5.90561e10	1.22694
$45$	−4.95225e10	−0.889040
$46$	3.43231e10	0.534146
$47$	1.30245e11	1.76248	0.881242	−	0.472665i	$-0.156708\pi$
$47$	1.30245e11	1.76248	0.881242	+	0.472665i	$0.156708\pi$
$48$	2.34284e10	0.276487
$49$	4.36261e10	0.450269
$50$	4.60051e9	0.0416391
$51$	4.47791e10	0.356344
$52$	0	0
$53$	9.35113e10	0.579524	0.289762	−	0.957099i	$-0.406424\pi$
$53$	9.35113e10	0.579524	0.289762	+	0.957099i	$0.406424\pi$
$54$	−1.57359e11	−0.863637
$55$	2.24574e11	1.09396
$56$	−4.24847e10	−0.184082
$57$	2.86892e10	0.110798
$58$	5.73593e11	1.97844
$59$	3.85302e11	1.18922	0.594612	−	0.804013i	$-0.297306\pi$
$59$	3.85302e11	1.18922	0.594612	+	0.804013i	$0.297306\pi$
$60$	−1.23197e11	−0.340892
$61$	1.30762e11	0.324966	0.162483	−	0.986711i	$-0.448050\pi$
$61$	1.30762e11	0.324966	0.162483	+	0.986711i	$0.448050\pi$
$62$	3.23072e11	0.722359
$63$	−5.39115e11	−1.08635
$64$	−6.58843e11	−1.19843
$65$	0	0
$66$	3.38425e11	0.503995
$67$	−1.00086e12	−1.35172	−0.675858	−	0.737032i	$-0.736227\pi$
$67$	−1.00086e12	−1.35172	−0.675858	+	0.737032i	$0.736227\pi$
$68$	−1.02621e12	−1.25871
$69$	1.03266e11	0.115197
$70$	−1.69512e12	−1.72212
$71$	−1.79269e12	−1.66083	−0.830416	−	0.557145i	$-0.811897\pi$
$71$	−1.79269e12	−1.66083	−0.830416	+	0.557145i	$0.811897\pi$
$72$	1.63001e11	0.137889
$73$	1.44196e12	1.11521	0.557604	−	0.830107i	$-0.311721\pi$
$73$	1.44196e12	1.11521	0.557604	+	0.830107i	$0.311721\pi$
$74$	−1.59913e12	−1.13208
$75$	1.38413e10	0.00898008
$76$	−6.57473e11	−0.391372
$77$	2.44477e12	1.33674
$78$	0	0
$79$	−1.00167e12	−0.463606	−0.231803	−	0.972763i	$-0.574462\pi$
$79$	−1.00167e12	−0.463606	−0.231803	+	0.972763i	$0.574462\pi$
$80$	−2.04172e12	−0.870784
$81$	1.81952e12	0.715822
$82$	4.28235e12	1.55558
$83$	4.32147e12	1.45086	0.725428	−	0.688299i	$-0.241642\pi$
$83$	4.32147e12	1.45086	0.725428	+	0.688299i	$0.241642\pi$
$84$	−1.34116e12	−0.416547
$85$	−3.90237e12	−1.12229
$86$	−2.48557e12	−0.662500
$87$	1.72574e12	0.426679
$88$	−7.39175e11	−0.169672
$89$	9.30942e11	0.198558	0.0992791	−	0.995060i	$-0.468346\pi$
$89$	9.30942e11	0.198558	0.0992791	+	0.995060i	$0.468346\pi$
$90$	6.50368e12	1.28998
$91$	0	0
$92$	−2.36656e12	−0.406909
$93$	9.72012e11	0.155787
$94$	−1.71048e13	−2.55733
$95$	−2.50018e12	−0.348954
$96$	−3.44365e12	−0.449010
$97$	9.20926e12	1.12256	0.561279	−	0.827627i	$-0.310310\pi$
$97$	9.20926e12	1.12256	0.561279	+	0.827627i	$0.310310\pi$
$98$	−5.72932e12	−0.653332
$99$	−9.37986e12	−1.00131
$100$	−3.17204e11	−0.0317204
$101$	−1.23879e12	−0.116121	−0.0580603	−	0.998313i	$-0.518492\pi$
$101$	−1.23879e12	−0.116121	−0.0580603	+	0.998313i	$0.518492\pi$
$102$	−5.88074e12	−0.517048
$103$	−1.09950e12	−0.0907304	−0.0453652	−	0.998970i	$-0.514445\pi$
$103$	−1.09950e12	−0.0907304	−0.0453652	+	0.998970i	$0.514445\pi$
$104$	0	0
$105$	−5.10003e12	−0.371401
$106$	−1.22806e13	−0.840878
$107$	−2.80481e13	−1.80680	−0.903398	−	0.428804i	$-0.858935\pi$
$107$	−2.80481e13	−1.80680	−0.903398	+	0.428804i	$0.858935\pi$
$108$	1.08498e13	0.657912
$109$	2.96951e13	1.69595	0.847974	−	0.530038i	$-0.177822\pi$
$109$	2.96951e13	1.69595	0.847974	+	0.530038i	$0.177822\pi$
$110$	−2.94928e13	−1.58731
$111$	−4.81124e12	−0.244151
$112$	−2.22267e13	−1.06404
$113$	3.71605e13	1.67908	0.839541	−	0.543297i	$-0.182824\pi$
$113$	3.71605e13	1.67908	0.839541	+	0.543297i	$0.182824\pi$
$114$	−3.76769e12	−0.160766
$115$	−8.99936e12	−0.362807
$116$	−3.95490e13	−1.50716
$117$	0	0
$118$	−5.06009e13	−1.72554
$119$	−4.24823e13	−1.37136
$120$	1.54199e12	0.0471416
$121$	8.01287e12	0.232104
$122$	−1.71727e13	−0.471519
$123$	1.28841e13	0.335484
$124$	−2.22757e13	−0.550288
$125$	−4.32394e13	−1.01383
$126$	7.08009e13	1.57627
$127$	−1.51445e13	−0.320281	−0.160141	−	0.987094i	$-0.551195\pi$
$127$	−1.51445e13	−0.320281	−0.160141	+	0.987094i	$0.551195\pi$
$128$	1.51274e13	0.304018
$129$	−7.47822e12	−0.142878
$130$	0	0
$131$	−3.82953e13	−0.662037	−0.331018	−	0.943624i	$-0.607392\pi$
$131$	−3.82953e13	−0.662037	−0.331018	+	0.943624i	$0.607392\pi$
$132$	−2.33343e13	−0.383940
$133$	−2.72176e13	−0.426398
$134$	1.31440e14	1.96132
$135$	4.12587e13	0.586606
$136$	1.28445e13	0.174066
$137$	−1.18739e14	−1.53430	−0.767152	−	0.641466i	$-0.778327\pi$
$137$	−1.18739e14	−1.53430	−0.767152	+	0.641466i	$0.778327\pi$
$138$	−1.35617e13	−0.167148
$139$	1.01210e13	0.119022	0.0595111	−	0.998228i	$-0.481046\pi$
$139$	1.01210e13	0.119022	0.0595111	+	0.998228i	$0.481046\pi$
$140$	1.16878e14	1.31190
$141$	−5.14625e13	−0.551526
$142$	2.35430e14	2.40984
$143$	0	0
$144$	8.52773e13	0.797035
$145$	−1.50394e14	−1.34381
$146$	−1.89370e14	−1.61814
$147$	−1.72375e13	−0.140901
$148$	1.10260e14	0.862414
$149$	7.43757e13	0.556827	0.278413	−	0.960461i	$-0.410191\pi$
$149$	7.43757e13	0.556827	0.278413	+	0.960461i	$0.410191\pi$
$150$	−1.81775e12	−0.0130299
$151$	1.57208e14	1.07926	0.539628	−	0.841904i	$-0.318565\pi$
$151$	1.57208e14	1.07926	0.539628	+	0.841904i	$0.318565\pi$
$152$	8.22924e12	0.0541223
$153$	1.62992e14	1.02724
$154$	−3.21066e14	−1.93959
$155$	−8.47081e13	−0.490647
$156$	0	0
$157$	−2.26348e13	−0.120622	−0.0603112	−	0.998180i	$-0.519209\pi$
$157$	−2.26348e13	−0.120622	−0.0603112	+	0.998180i	$0.519209\pi$
$158$	1.31547e14	0.672684
$159$	−3.69482e13	−0.181348
$160$	3.00104e14	1.41414
$161$	−9.79695e13	−0.443326
$162$	−2.38954e14	−1.03864
$163$	1.24004e14	0.517863	0.258932	−	0.965896i	$-0.416630\pi$
$163$	1.24004e14	0.517863	0.258932	+	0.965896i	$0.416630\pi$
$164$	−2.95267e14	−1.18503
$165$	−8.87335e13	−0.342328
$166$	−5.67530e14	−2.10516
$167$	2.37469e14	0.847128	0.423564	−	0.905866i	$-0.360779\pi$
$167$	2.37469e14	0.847128	0.423564	+	0.905866i	$0.360779\pi$
$168$	1.67866e13	0.0576038
$169$	0	0
$170$	5.12490e14	1.62842
$171$	1.04426e14	0.319400
$172$	1.71379e14	0.504688
$173$	3.85044e14	1.09197	0.545984	−	0.837795i	$-0.316156\pi$
$173$	3.85044e14	1.09197	0.545984	+	0.837795i	$0.316156\pi$
$174$	−2.26638e14	−0.619103
$175$	−1.31314e13	−0.0345592
$176$	−3.86714e14	−0.980747
$177$	−1.52241e14	−0.372138
$178$	−1.22259e14	−0.288104
$179$	2.34906e14	0.533763	0.266882	−	0.963729i	$-0.414007\pi$
$179$	2.34906e14	0.533763	0.266882	+	0.963729i	$0.414007\pi$
$180$	−4.48427e14	−0.982698
$181$	5.06681e14	1.07108	0.535542	−	0.844509i	$-0.320107\pi$
$181$	5.06681e14	1.07108	0.535542	+	0.844509i	$0.320107\pi$
$182$	0	0
$183$	−5.16667e13	−0.101690
$184$	2.96210e13	0.0562710
$185$	4.19286e14	0.768943
$186$	−1.27652e14	−0.226045
$187$	−7.39133e14	−1.26401
$188$	1.17937e15	1.94816
$189$	4.49154e14	0.716793
$190$	3.28343e14	0.506326
$191$	5.63941e14	0.840460	0.420230	−	0.907418i	$-0.361949\pi$
$191$	5.63941e14	0.840460	0.420230	+	0.907418i	$0.361949\pi$
$192$	2.60322e14	0.375019
$193$	1.26967e15	1.76835	0.884176	−	0.467154i	$-0.154720\pi$
$193$	1.26967e15	1.76835	0.884176	+	0.467154i	$0.154720\pi$
$194$	−1.20943e15	−1.62881
$195$	0	0
$196$	3.95035e14	0.497703
$197$	1.13691e15	1.38578	0.692891	−	0.721042i	$-0.256337\pi$
$197$	1.13691e15	1.38578	0.692891	+	0.721042i	$0.256337\pi$
$198$	1.23184e15	1.45288
$199$	−1.27254e15	−1.45254	−0.726269	−	0.687411i	$-0.758747\pi$
$199$	−1.27254e15	−1.45254	−0.726269	+	0.687411i	$0.758747\pi$
$200$	3.97027e12	0.00438657
$201$	3.95459e14	0.422987
$202$	1.62688e14	0.168489
$203$	−1.63723e15	−1.64204
$204$	4.05475e14	0.393884
$205$	−1.12281e15	−1.05659
$206$	1.44395e14	0.131648
$207$	3.75880e14	0.332080
$208$	0	0
$209$	−4.73549e14	−0.393020
$210$	6.69776e14	0.538895
$211$	4.45383e14	0.347454	0.173727	−	0.984794i	$-0.444419\pi$
$211$	4.45383e14	0.347454	0.173727	+	0.984794i	$0.444419\pi$
$212$	8.46746e14	0.640575
$213$	7.08327e14	0.519716
$214$	3.68350e15	2.62163
$215$	6.51705e14	0.449988
$216$	−1.35801e14	−0.0909819
$217$	−9.22155e14	−0.599537
$218$	−3.89979e15	−2.46079
$219$	−5.69749e14	−0.348977
$220$	2.03351e15	1.20920
$221$	0	0
$222$	6.31850e14	0.354258
$223$	3.06892e15	1.67110	0.835552	−	0.549411i	$-0.185148\pi$
$223$	3.06892e15	1.67110	0.835552	+	0.549411i	$0.185148\pi$
$224$	3.26702e15	1.72798
$225$	5.03813e13	0.0258871
$226$	−4.88021e15	−2.43632
$227$	3.41750e15	1.65783	0.828917	−	0.559372i	$-0.188958\pi$
$227$	3.41750e15	1.65783	0.828917	+	0.559372i	$0.188958\pi$
$228$	2.59781e14	0.122470
$229$	1.32062e15	0.605127	0.302564	−	0.953129i	$-0.402158\pi$
$229$	1.32062e15	0.605127	0.302564	+	0.953129i	$0.402158\pi$
$230$	1.18187e15	0.526426
$231$	−9.65977e14	−0.418301
$232$	4.95014e14	0.208423
$233$	−4.74976e14	−0.194473	−0.0972363	−	0.995261i	$-0.531000\pi$
$233$	−4.74976e14	−0.194473	−0.0972363	+	0.995261i	$0.531000\pi$
$234$	0	0
$235$	4.48481e15	1.73701
$236$	3.48891e15	1.31450
$237$	3.95780e14	0.145074
$238$	5.57911e15	1.98982
$239$	−7.23199e14	−0.250999	−0.125499	−	0.992094i	$-0.540053\pi$
$239$	−7.23199e14	−0.250999	−0.125499	+	0.992094i	$0.540053\pi$
$240$	8.06724e14	0.272491
$241$	−1.64374e15	−0.540407	−0.270204	−	0.962803i	$-0.587091\pi$
$241$	−1.64374e15	−0.540407	−0.270204	+	0.962803i	$0.587091\pi$
$242$	−1.05231e15	−0.336779
$243$	−2.62927e15	−0.819208
$244$	1.18405e15	0.359200
$245$	1.50220e15	0.443761
$246$	−1.69204e15	−0.486781
$247$	0	0
$248$	2.78813e14	0.0760987
$249$	−1.70750e15	−0.454010
$250$	5.67854e15	1.47105
$251$	−1.46017e15	−0.368574	−0.184287	−	0.982872i	$-0.558998\pi$
$251$	−1.46017e15	−0.368574	−0.184287	+	0.982872i	$0.558998\pi$
$252$	−4.88169e15	−1.20079
$253$	−1.70453e15	−0.408622
$254$	1.98890e15	0.464722
$255$	1.54191e15	0.351194
$256$	3.41059e15	0.757303
$257$	5.99785e15	1.29846	0.649232	−	0.760590i	$-0.275090\pi$
$257$	5.99785e15	1.29846	0.649232	+	0.760590i	$0.275090\pi$
$258$	9.82098e14	0.207313
$259$	4.56446e15	0.939596
$260$	0	0
$261$	6.28156e15	1.23000
$262$	5.02924e15	0.960603
$263$	−1.37873e15	−0.256902	−0.128451	−	0.991716i	$-0.541001\pi$
$263$	−1.37873e15	−0.256902	−0.128451	+	0.991716i	$0.541001\pi$
$264$	2.92063e14	0.0530946
$265$	3.21993e15	0.571148
$266$	3.57444e15	0.618695
$267$	−3.67834e14	−0.0621339
$268$	−9.06276e15	−1.49412
$269$	−5.03972e15	−0.810993	−0.405496	−	0.914097i	$-0.632901\pi$
$269$	−5.03972e15	−0.810993	−0.405496	+	0.914097i	$0.632901\pi$
$270$	−5.41842e15	−0.851155
$271$	−9.37288e15	−1.43738	−0.718692	−	0.695329i	$-0.755259\pi$
$271$	−9.37288e15	−1.43738	−0.718692	+	0.695329i	$0.755259\pi$
$272$	6.71985e15	1.00615
$273$	0	0
$274$	1.55938e16	2.22625
$275$	−2.28468e14	−0.0318539
$276$	9.35077e14	0.127332
$277$	1.25003e16	1.66266	0.831329	−	0.555780i	$-0.187580\pi$
$277$	1.25003e16	1.66266	0.831329	+	0.555780i	$0.187580\pi$
$278$	−1.32917e15	−0.172699
$279$	3.53804e15	0.449092
$280$	−1.46290e15	−0.181421
$281$	−9.83881e15	−1.19221	−0.596103	−	0.802908i	$-0.703285\pi$
$281$	−9.83881e15	−1.19221	−0.596103	+	0.802908i	$0.703285\pi$
$282$	6.75845e15	0.800255
$283$	−5.84477e15	−0.676326	−0.338163	−	0.941088i	$-0.609805\pi$
$283$	−5.84477e15	−0.676326	−0.338163	+	0.941088i	$0.609805\pi$
$284$	−1.62328e16	−1.83580
$285$	9.87872e14	0.109197
$286$	0	0
$287$	−1.22233e16	−1.29108
$288$	−1.25346e16	−1.29437
$289$	2.93919e15	0.296750
$290$	1.97509e16	1.94984
$291$	−3.63876e15	−0.351277
$292$	1.30570e16	1.23269
$293$	−4.86348e15	−0.449064	−0.224532	−	0.974467i	$-0.572085\pi$
$293$	−4.86348e15	−0.449064	−0.224532	+	0.974467i	$0.572085\pi$
$294$	2.26377e15	0.204444
$295$	1.32673e16	1.17204
$296$	−1.38006e15	−0.119262
$297$	7.81466e15	0.660683
$298$	−9.76760e15	−0.807945
$299$	0	0
$300$	1.25333e14	0.00992611
$301$	7.09464e15	0.549855
$302$	−2.06458e16	−1.56598
$303$	4.89471e14	0.0363371
$304$	4.30529e15	0.312841
$305$	4.50260e15	0.320269
$306$	−2.14054e16	−1.49051
$307$	7.25301e15	0.494446	0.247223	−	0.968959i	$-0.420482\pi$
$307$	7.25301e15	0.494446	0.247223	+	0.968959i	$0.420482\pi$
$308$	2.21374e16	1.47757
$309$	4.34434e14	0.0283919
$310$	1.11245e16	0.711919
$311$	1.02335e16	0.641328	0.320664	−	0.947193i	$-0.396094\pi$
$311$	1.02335e16	0.641328	0.320664	+	0.947193i	$0.396094\pi$
$312$	0	0
$313$	−3.13076e16	−1.88197	−0.940983	−	0.338454i	$-0.890096\pi$
$313$	−3.13076e16	−1.88197	−0.940983	+	0.338454i	$0.890096\pi$
$314$	2.97258e15	0.175021
$315$	−1.85637e16	−1.07064
$316$	−9.07014e15	−0.512446
$317$	8.32828e15	0.460967	0.230484	−	0.973076i	$-0.425969\pi$
$317$	8.32828e15	0.460967	0.230484	+	0.973076i	$0.425969\pi$
$318$	4.85233e15	0.263132
$319$	−2.84855e16	−1.51350
$320$	−2.26863e16	−1.18111
$321$	1.10824e16	0.565392
$322$	1.28661e16	0.643257
$323$	8.22878e15	0.403198
$324$	1.64758e16	0.791232
$325$	0	0
$326$	−1.62851e16	−0.751410
$327$	−1.17331e16	−0.530705
$328$	3.69570e15	0.163876
$329$	4.88228e16	2.12251
$330$	1.16532e16	0.496711
$331$	−9.65066e15	−0.403344	−0.201672	−	0.979453i	$-0.564637\pi$
$331$	−9.65066e15	−0.403344	−0.201672	+	0.979453i	$0.564637\pi$
$332$	3.91310e16	1.60370
$333$	−1.75125e16	−0.703819
$334$	−3.11862e16	−1.22917
$335$	−3.44631e16	−1.33218
$336$	8.78221e15	0.332965
$337$	−2.02797e16	−0.754167	−0.377084	−	0.926179i	$-0.623073\pi$
$337$	−2.02797e16	−0.754167	−0.377084	+	0.926179i	$0.623073\pi$
$338$	0	0
$339$	−1.46829e16	−0.525427
$340$	−3.53360e16	−1.24052
$341$	−1.60442e16	−0.552605
$342$	−1.37141e16	−0.463443
$343$	−1.99658e16	−0.662025
$344$	−2.14506e15	−0.0697927
$345$	3.55583e15	0.113532
$346$	−5.05669e16	−1.58443
$347$	4.02927e16	1.23904	0.619520	−	0.784981i	$-0.287327\pi$
$347$	4.02927e16	1.23904	0.619520	+	0.784981i	$0.287327\pi$
$348$	1.56266e16	0.471628
$349$	−3.14751e16	−0.932399	−0.466200	−	0.884679i	$-0.654377\pi$
$349$	−3.14751e16	−0.932399	−0.466200	+	0.884679i	$0.654377\pi$
$350$	1.72452e15	0.0501447
$351$	0	0
$352$	5.68416e16	1.59272
$353$	7.78706e15	0.214209	0.107105	−	0.994248i	$-0.465842\pi$
$353$	7.78706e15	0.214209	0.107105	+	0.994248i	$0.465842\pi$
$354$	1.99934e16	0.539966
$355$	−6.17287e16	−1.63683
$356$	8.42969e15	0.219476
$357$	1.67856e16	0.429134
$358$	−3.08497e16	−0.774481
$359$	4.57955e16	1.12904	0.564519	−	0.825420i	$-0.309062\pi$
$359$	4.57955e16	1.12904	0.564519	+	0.825420i	$0.309062\pi$
$360$	5.61272e15	0.135896
$361$	−3.67810e16	−0.874634
$362$	−6.65413e16	−1.55412
$363$	−3.16605e15	−0.0726313
$364$	0	0
$365$	4.96520e16	1.09909
$366$	6.78527e15	0.147550
$367$	−2.08270e16	−0.444935	−0.222468	−	0.974940i	$-0.571411\pi$
$367$	−2.08270e16	−0.444935	−0.222468	+	0.974940i	$0.571411\pi$
$368$	1.54968e16	0.325261
$369$	4.68971e16	0.967107
$370$	−5.50639e16	−1.11572
$371$	3.50530e16	0.697903
$372$	8.80157e15	0.172199
$373$	−5.08603e16	−0.977849	−0.488925	−	0.872326i	$-0.662611\pi$
$373$	−5.08603e16	−0.977849	−0.488925	+	0.872326i	$0.662611\pi$
$374$	9.70687e16	1.83406
$375$	1.70848e16	0.317253
$376$	−1.47616e16	−0.269408
$377$	0	0
$378$	−5.89864e16	−1.04005
$379$	1.37467e15	0.0238256	0.0119128	−	0.999929i	$-0.496208\pi$
$379$	1.37467e15	0.0238256	0.0119128	+	0.999929i	$0.496208\pi$
$380$	−2.26392e16	−0.385715
$381$	5.98391e15	0.100224
$382$	−7.40612e16	−1.21949
$383$	−5.21022e16	−0.843459	−0.421730	−	0.906722i	$-0.638577\pi$
$383$	−5.21022e16	−0.843459	−0.421730	+	0.906722i	$0.638577\pi$
$384$	−5.97714e15	−0.0951350
$385$	8.41822e16	1.31742
$386$	−1.66743e17	−2.56585
$387$	−2.72201e16	−0.411877
$388$	8.33899e16	1.24082
$389$	3.60091e16	0.526914	0.263457	−	0.964671i	$-0.415137\pi$
$389$	3.60091e16	0.526914	0.263457	+	0.964671i	$0.415137\pi$
$390$	0	0
$391$	2.96194e16	0.419205
$392$	−4.94444e15	−0.0688268
$393$	1.51312e16	0.207168
$394$	−1.49308e17	−2.01075
$395$	−3.44911e16	−0.456906
$396$	−8.49347e16	−1.10679
$397$	8.48776e16	1.08807	0.544033	−	0.839064i	$-0.316897\pi$
$397$	8.48776e16	1.08807	0.544033	+	0.839064i	$0.316897\pi$
$398$	1.67120e17	2.10761
$399$	1.07542e16	0.133431
$400$	2.07712e15	0.0253555
$401$	1.13816e17	1.36699	0.683497	−	0.729953i	$-0.260458\pi$
$401$	1.13816e17	1.36699	0.683497	+	0.729953i	$0.260458\pi$
$402$	−5.19347e16	−0.613746
$403$	0	0
$404$	−1.12173e16	−0.128354
$405$	6.26527e16	0.705476
$406$	2.15013e17	2.38257
$407$	7.94153e16	0.866045
$408$	−5.07512e15	−0.0544697
$409$	1.27900e17	1.35104	0.675520	−	0.737342i	$-0.263919\pi$
$409$	1.27900e17	1.35104	0.675520	+	0.737342i	$0.263919\pi$
$410$	1.47457e17	1.53310
$411$	4.69163e16	0.480123
$412$	−9.95597e15	−0.100289
$413$	1.44432e17	1.43215
$414$	−4.93636e16	−0.481842
$415$	1.48804e17	1.42989
$416$	0	0
$417$	−3.99902e15	−0.0372451
$418$	6.21902e16	0.570264
$419$	5.71614e16	0.516074	0.258037	−	0.966135i	$-0.416924\pi$
$419$	5.71614e16	0.516074	0.258037	+	0.966135i	$0.416924\pi$
$420$	−4.61808e16	−0.410527
$421$	1.01036e17	0.884391	0.442196	−	0.896919i	$-0.354200\pi$
$421$	1.01036e17	0.884391	0.442196	+	0.896919i	$0.354200\pi$
$422$	−5.84911e16	−0.504149
$423$	−1.87319e17	−1.58990
$424$	−1.05983e16	−0.0885844
$425$	3.97004e15	0.0326789
$426$	−9.30231e16	−0.754099
$427$	4.90165e16	0.391347
$428$	−2.53976e17	−1.99714
$429$	0	0
$430$	−8.55871e16	−0.652925
$431$	−4.57527e16	−0.343807	−0.171904	−	0.985114i	$-0.554992\pi$
$431$	−4.57527e16	−0.343807	−0.171904	+	0.985114i	$0.554992\pi$
$432$	−7.10472e16	−0.525899
$433$	−1.90037e17	−1.38569	−0.692847	−	0.721085i	$-0.743644\pi$
$433$	−1.90037e17	−1.38569	−0.692847	+	0.721085i	$0.743644\pi$
$434$	1.21105e17	0.869917
$435$	5.94235e16	0.420512
$436$	2.68889e17	1.87461
$437$	1.89766e16	0.130343
$438$	7.48239e16	0.506359
$439$	−1.84977e17	−1.23338	−0.616692	−	0.787205i	$-0.711527\pi$
$439$	−1.84977e17	−1.23338	−0.616692	+	0.787205i	$0.711527\pi$
$440$	−2.54524e16	−0.167220
$441$	−6.27432e16	−0.406177
$442$	0	0
$443$	3.66792e16	0.230566	0.115283	−	0.993333i	$-0.463222\pi$
$443$	3.66792e16	0.230566	0.115283	+	0.993333i	$0.463222\pi$
$444$	−4.35658e16	−0.269871
$445$	3.20557e16	0.195688
$446$	−4.03034e17	−2.42474
$447$	−2.93873e16	−0.174245
$448$	−2.46969e17	−1.44323
$449$	−2.02229e17	−1.16478	−0.582389	−	0.812910i	$-0.697882\pi$
$449$	−2.02229e17	−1.16478	−0.582389	+	0.812910i	$0.697882\pi$
$450$	−6.61647e15	−0.0375617
$451$	−2.12668e17	−1.19002
$452$	3.36489e17	1.85597
$453$	−6.21160e16	−0.337727
$454$	−4.48813e17	−2.40549
$455$	0	0
$456$	−3.25154e15	−0.0169363
$457$	3.18023e17	1.63307	0.816533	−	0.577299i	$-0.195893\pi$
$457$	3.18023e17	1.63307	0.816533	+	0.577299i	$0.195893\pi$
$458$	−1.73434e17	−0.878028
$459$	−1.35794e17	−0.677794
$460$	−8.14893e16	−0.401028
$461$	−1.82782e17	−0.886906	−0.443453	−	0.896298i	$-0.646247\pi$
$461$	−1.82782e17	−0.886906	−0.443453	+	0.896298i	$0.646247\pi$
$462$	1.26860e17	0.606947
$463$	1.90228e17	0.897424	0.448712	−	0.893677i	$-0.351883\pi$
$463$	1.90228e17	0.897424	0.448712	+	0.893677i	$0.351883\pi$
$464$	2.58976e17	1.20474
$465$	3.34699e16	0.153536
$466$	6.23776e16	0.282176
$467$	2.67874e17	1.19501	0.597504	−	0.801866i	$-0.296159\pi$
$467$	2.67874e17	1.19501	0.597504	+	0.801866i	$0.296159\pi$
$468$	0	0
$469$	−3.75174e17	−1.62783
$470$	−5.88980e17	−2.52037
$471$	8.94345e15	0.0377459
$472$	−4.36689e16	−0.181781
$473$	1.23437e17	0.506813
$474$	−5.19770e16	−0.210500
$475$	2.54354e15	0.0101608
$476$	−3.84677e17	−1.51583
$477$	−1.34488e17	−0.522775
$478$	9.49761e16	0.364194
$479$	2.90930e17	1.10054	0.550272	−	0.834985i	$-0.314524\pi$
$479$	2.90930e17	1.10054	0.550272	+	0.834985i	$0.314524\pi$
$480$	−1.18577e17	−0.442521
$481$	0	0
$482$	2.15868e17	0.784121
$483$	3.87097e16	0.138728
$484$	7.25566e16	0.256556
$485$	3.17108e17	1.10633
$486$	3.45296e17	1.18865
$487$	−1.50117e17	−0.509909	−0.254954	−	0.966953i	$-0.582060\pi$
$487$	−1.50117e17	−0.509909	−0.254954	+	0.966953i	$0.582060\pi$
$488$	−1.48201e16	−0.0496733
$489$	−4.89964e16	−0.162053
$490$	−1.97281e17	−0.643889
$491$	−4.04108e17	−1.30157	−0.650785	−	0.759262i	$-0.725560\pi$
$491$	−4.04108e17	−1.30157	−0.650785	+	0.759262i	$0.725560\pi$
$492$	1.16666e17	0.370826
$493$	4.94986e17	1.55270
$494$	0	0
$495$	−3.22982e17	−0.986836
$496$	1.45867e17	0.439870
$497$	−6.71995e17	−2.00009
$498$	2.24242e17	0.658760
$499$	1.63567e17	0.474288	0.237144	−	0.971475i	$-0.423789\pi$
$499$	1.63567e17	0.474288	0.237144	+	0.971475i	$0.423789\pi$
$500$	−3.91533e17	−1.12063
$501$	−9.38286e16	−0.265088
$502$	1.91761e17	0.534794
$503$	9.71299e16	0.267400	0.133700	−	0.991022i	$-0.457314\pi$
$503$	9.71299e16	0.267400	0.133700	+	0.991022i	$0.457314\pi$
$504$	6.11016e16	0.166056
$505$	−4.26560e16	−0.114442
$506$	2.23853e17	0.592904
$507$	0	0
$508$	−1.37134e17	−0.354022
$509$	2.40330e17	0.612550	0.306275	−	0.951943i	$-0.400917\pi$
$509$	2.40330e17	0.612550	0.306275	+	0.951943i	$0.400917\pi$
$510$	−2.02495e17	−0.509575
$511$	5.40525e17	1.34301
$512$	−5.71829e17	−1.40285
$513$	−8.70007e16	−0.210746
$514$	−7.87684e17	−1.88405
$515$	−3.78597e16	−0.0894191
$516$	−6.77153e16	−0.157930
$517$	8.49449e17	1.95636
$518$	−5.99441e17	−1.36334
$519$	−1.52138e17	−0.341705
$520$	0	0
$521$	−1.01539e17	−0.222428	−0.111214	−	0.993796i	$-0.535474\pi$
$521$	−1.01539e17	−0.222428	−0.111214	+	0.993796i	$0.535474\pi$
$522$	−8.24943e17	−1.78470
$523$	−7.50671e17	−1.60394	−0.801971	−	0.597363i	$-0.796215\pi$
$523$	−7.50671e17	−1.60394	−0.801971	+	0.597363i	$0.796215\pi$
$524$	−3.46764e17	−0.731781
$525$	5.18848e15	0.0108144
$526$	1.81066e17	0.372760
$527$	2.78797e17	0.566917
$528$	1.52798e17	0.306901
$529$	−4.35730e17	−0.864482
$530$	−4.22867e17	−0.828725
$531$	−5.54143e17	−1.07277
$532$	−2.46456e17	−0.471318
$533$	0	0
$534$	4.83069e16	0.0901552
$535$	−9.65797e17	−1.78068
$536$	1.13434e17	0.206620
$537$	−9.28159e16	−0.167028
$538$	6.61856e17	1.17674
$539$	2.84526e17	0.499799
$540$	3.73598e17	0.648404
$541$	1.02532e18	1.75824	0.879120	−	0.476601i	$-0.158131\pi$
$541$	1.02532e18	1.75824	0.879120	+	0.476601i	$0.158131\pi$
$542$	1.23092e18	2.08562
$543$	−2.00200e17	−0.335170
$544$	−9.87725e17	−1.63397
$545$	1.02251e18	1.67144
$546$	0	0
$547$	9.61246e17	1.53432	0.767162	−	0.641454i	$-0.221668\pi$
$547$	9.61246e17	1.53432	0.767162	+	0.641454i	$0.221668\pi$
$548$	−1.07519e18	−1.69594
$549$	−1.88062e17	−0.293144
$550$	3.00042e16	0.0462195
$551$	3.17129e17	0.482782
$552$	−1.17039e16	−0.0176086
$553$	−3.75480e17	−0.558307
$554$	−1.64164e18	−2.41249
$555$	−1.65668e17	−0.240622
$556$	9.16459e16	0.131561
$557$	1.09446e18	1.55289	0.776443	−	0.630188i	$-0.217022\pi$
$557$	1.09446e18	1.55289	0.776443	+	0.630188i	$0.217022\pi$
$558$	−4.64643e17	−0.651624
$559$	0	0
$560$	−7.65345e17	−1.04866
$561$	2.92046e17	0.395542
$562$	1.29211e18	1.72987
$563$	1.00277e18	1.32708	0.663542	−	0.748139i	$-0.269052\pi$
$563$	1.00277e18	1.32708	0.663542	+	0.748139i	$0.269052\pi$
$564$	−4.65993e17	−0.609628
$565$	1.27957e18	1.65481
$566$	7.67582e17	0.981336
$567$	6.82054e17	0.862043
$568$	2.03177e17	0.253870
$569$	2.47556e17	0.305804	0.152902	−	0.988241i	$-0.451138\pi$
$569$	2.47556e17	0.305804	0.152902	+	0.988241i	$0.451138\pi$
$570$	−1.29735e17	−0.158442
$571$	−4.36442e17	−0.526977	−0.263489	−	0.964662i	$-0.584873\pi$
$571$	−4.36442e17	−0.526977	−0.263489	+	0.964662i	$0.584873\pi$
$572$	0	0
$573$	−2.22825e17	−0.263001
$574$	1.60525e18	1.87334
$575$	9.15543e15	0.0105642
$576$	9.47549e17	1.08107
$577$	−2.14944e17	−0.242483	−0.121242	−	0.992623i	$-0.538688\pi$
$577$	−2.14944e17	−0.242483	−0.121242	+	0.992623i	$0.538688\pi$
$578$	−3.85997e17	−0.430579
$579$	−5.01673e17	−0.553363
$580$	−1.36182e18	−1.48538
$581$	1.61992e18	1.74722
$582$	4.77871e17	0.509696
$583$	6.09874e17	0.643272
$584$	−1.63427e17	−0.170467
$585$	0	0
$586$	6.38711e17	0.651583
$587$	7.60913e17	0.767693	0.383846	−	0.923397i	$-0.374599\pi$
$587$	7.60913e17	0.767693	0.383846	+	0.923397i	$0.374599\pi$
$588$	−1.56086e17	−0.155744
$589$	1.78621e17	0.176271
$590$	−1.74237e18	−1.70060
$591$	−4.49216e17	−0.433647
$592$	−7.22007e17	−0.689366
$593$	−1.17587e18	−1.11046	−0.555230	−	0.831697i	$-0.687370\pi$
$593$	−1.17587e18	−1.11046	−0.555230	+	0.831697i	$0.687370\pi$
$594$	−1.02628e18	−0.958638
$595$	−1.46282e18	−1.35154
$596$	6.73472e17	0.615487
$597$	5.02807e17	0.454536
$598$	0	0
$599$	8.19079e15	0.00724522	0.00362261	−	0.999993i	$-0.498847\pi$
$599$	8.19079e15	0.00724522	0.00362261	+	0.999993i	$0.498847\pi$
$600$	−1.56873e15	−0.00137267
$601$	1.82135e18	1.57655	0.788277	−	0.615320i	$-0.210973\pi$
$601$	1.82135e18	1.57655	0.788277	+	0.615320i	$0.210973\pi$
$602$	−9.31724e17	−0.797829
$603$	1.43943e18	1.21935
$604$	1.42352e18	1.19295
$605$	2.75912e17	0.228750
$606$	−6.42812e16	−0.0527244
$607$	5.44050e17	0.441481	0.220741	−	0.975333i	$-0.429153\pi$
$607$	5.44050e17	0.441481	0.220741	+	0.975333i	$0.429153\pi$
$608$	−6.32818e17	−0.508049
$609$	6.46901e17	0.513837
$610$	−5.91317e17	−0.464704
$611$	0	0
$612$	1.47589e18	1.13546
$613$	−3.56930e16	−0.0271700	−0.0135850	−	0.999908i	$-0.504324\pi$
$613$	−3.56930e16	−0.0271700	−0.0135850	+	0.999908i	$0.504324\pi$
$614$	−9.52522e17	−0.717432
$615$	4.43647e17	0.330635
$616$	−2.77082e17	−0.204331
$617$	5.92640e17	0.432451	0.216226	−	0.976343i	$-0.430625\pi$
$617$	5.92640e17	0.432451	0.216226	+	0.976343i	$0.430625\pi$
$618$	−5.70533e16	−0.0411961
$619$	1.92570e18	1.37594	0.687969	−	0.725740i	$-0.258502\pi$
$619$	1.92570e18	1.37594	0.687969	+	0.725740i	$0.258502\pi$
$620$	−7.67032e17	−0.542335
$621$	−3.13158e17	−0.219113
$622$	−1.34394e18	−0.930554
$623$	3.48967e17	0.239118
$624$	0	0
$625$	−1.44613e18	−0.970479
$626$	4.11156e18	2.73070
$627$	1.87109e17	0.122986
$628$	−2.04958e17	−0.133330
$629$	−1.37998e18	−0.888475
$630$	2.43793e18	1.55349
$631$	1.45499e17	0.0917632	0.0458816	−	0.998947i	$-0.485390\pi$
$631$	1.45499e17	0.0917632	0.0458816	+	0.998947i	$0.485390\pi$
$632$	1.13526e17	0.0708655
$633$	−1.75980e17	−0.108727
$634$	−1.09373e18	−0.668855
$635$	−5.21480e17	−0.315652
$636$	−3.34566e17	−0.200452
$637$	0	0
$638$	3.74093e18	2.19607
$639$	2.57825e18	1.49820
$640$	5.20891e17	0.299624
$641$	−2.86100e17	−0.162907	−0.0814536	−	0.996677i	$-0.525956\pi$
$641$	−2.86100e17	−0.162907	−0.0814536	+	0.996677i	$0.525956\pi$
$642$	−1.45542e18	−0.820374
$643$	6.03216e17	0.336590	0.168295	−	0.985737i	$-0.446174\pi$
$643$	6.03216e17	0.336590	0.168295	+	0.985737i	$0.446174\pi$
$644$	−8.87115e17	−0.490029
$645$	−2.57502e17	−0.140813
$646$	−1.08067e18	−0.585033
$647$	−1.64825e18	−0.883375	−0.441688	−	0.897169i	$-0.645620\pi$
$647$	−1.64825e18	−0.883375	−0.441688	+	0.897169i	$0.645620\pi$
$648$	−2.06219e17	−0.109418
$649$	2.51291e18	1.32004
$650$	0	0
$651$	3.64362e17	0.187610
$652$	1.12285e18	0.572419
$653$	2.14977e18	1.08506	0.542532	−	0.840035i	$-0.317466\pi$
$653$	2.14977e18	1.08506	0.542532	+	0.840035i	$0.317466\pi$
$654$	1.54089e18	0.770044
$655$	−1.31864e18	−0.652468
$656$	1.93348e18	0.947248
$657$	−2.07384e18	−1.00600
$658$	−6.41180e18	−3.07972
$659$	1.20457e18	0.572899	0.286449	−	0.958095i	$-0.407525\pi$
$659$	1.20457e18	0.572899	0.286449	+	0.958095i	$0.407525\pi$
$660$	−8.03483e17	−0.378391
$661$	−1.01556e17	−0.0473583	−0.0236791	−	0.999720i	$-0.507538\pi$
$661$	−1.01556e17	−0.0473583	−0.0236791	+	0.999720i	$0.507538\pi$
$662$	1.26740e18	0.585244
$663$	0	0
$664$	−4.89782e17	−0.221774
$665$	−9.37201e17	−0.420235
$666$	2.29988e18	1.02123
$667$	1.14150e18	0.501948
$668$	2.15028e18	0.936371
$669$	−1.21259e18	−0.522931
$670$	4.52596e18	1.93297
$671$	8.52820e17	0.360712
$672$	−1.29086e18	−0.540730
$673$	1.43921e18	0.597073	0.298537	−	0.954398i	$-0.403501\pi$
$673$	1.43921e18	0.597073	0.298537	+	0.954398i	$0.403501\pi$
$674$	2.66329e18	1.09428
$675$	−4.19742e16	−0.0170808
$676$	0	0
$677$	2.58231e18	1.03082	0.515410	−	0.856944i	$-0.327640\pi$
$677$	2.58231e18	1.03082	0.515410	+	0.856944i	$0.327640\pi$
$678$	1.92827e18	0.762385
$679$	3.45212e18	1.35186
$680$	4.42282e17	0.171550
$681$	−1.35032e18	−0.518778
$682$	2.10705e18	0.801820
$683$	1.41325e18	0.532703	0.266351	−	0.963876i	$-0.414182\pi$
$683$	1.41325e18	0.532703	0.266351	+	0.963876i	$0.414182\pi$
$684$	9.45579e17	0.353048
$685$	−4.08862e18	−1.51213
$686$	2.62206e18	0.960587
$687$	−5.21803e17	−0.189360
$688$	−1.12223e18	−0.403420
$689$	0	0
$690$	−4.66979e17	−0.164732
$691$	−2.24990e18	−0.786240	−0.393120	−	0.919487i	$-0.628604\pi$
$691$	−2.24990e18	−0.786240	−0.393120	+	0.919487i	$0.628604\pi$
$692$	3.48657e18	1.20700
$693$	−3.51607e18	−1.20585
$694$	−5.29156e18	−1.79782
$695$	3.48503e17	0.117302
$696$	−1.95590e17	−0.0652209
$697$	3.69549e18	1.22084
$698$	4.13356e18	1.35289
$699$	1.87673e17	0.0608555
$700$	−1.18905e17	−0.0381999
$701$	−1.45384e18	−0.462754	−0.231377	−	0.972864i	$-0.574323\pi$
$701$	−1.45384e18	−0.462754	−0.231377	+	0.972864i	$0.574323\pi$
$702$	0	0
$703$	−8.84132e17	−0.276253
$704$	−4.29693e18	−1.33026
$705$	−1.77204e18	−0.543555
$706$	−1.02266e18	−0.310813
$707$	−4.64365e17	−0.139841
$708$	−1.37854e18	−0.411342
$709$	−1.03106e18	−0.304848	−0.152424	−	0.988315i	$-0.548708\pi$
$709$	−1.03106e18	−0.304848	−0.152424	+	0.988315i	$0.548708\pi$
$710$	8.10670e18	2.37501
$711$	1.44061e18	0.418209
$712$	−1.05510e17	−0.0303510
$713$	6.42942e17	0.183269
$714$	−2.20442e18	−0.622666
$715$	0	0
$716$	2.12707e18	0.589994
$717$	2.85750e17	0.0785438
$718$	−6.01422e18	−1.63821
$719$	4.01205e18	1.08300	0.541500	−	0.840701i	$-0.317856\pi$
$719$	4.01205e18	1.08300	0.541500	+	0.840701i	$0.317856\pi$
$720$	2.93640e18	0.785515
$721$	−4.12151e17	−0.109264
$722$	4.83036e18	1.26908
$723$	6.49473e17	0.169107
$724$	4.58800e18	1.18392
$725$	1.53002e17	0.0391290
$726$	4.15790e17	0.105387
$727$	−3.16021e18	−0.793856	−0.396928	−	0.917850i	$-0.629924\pi$
$727$	−3.16021e18	−0.793856	−0.396928	+	0.917850i	$0.629924\pi$
$728$	0	0
$729$	−1.86203e18	−0.459471
$730$	−6.52069e18	−1.59476
$731$	−2.14494e18	−0.519939
$732$	−4.67842e17	−0.112403
$733$	1.64864e16	0.00392601	0.00196300	−	0.999998i	$-0.499375\pi$
$733$	1.64864e16	0.00392601	0.00196300	+	0.999998i	$0.499375\pi$
$734$	2.73516e18	0.645593
$735$	−5.93551e17	−0.138864
$736$	−2.27782e18	−0.528218
$737$	−6.52752e18	−1.50041
$738$	−6.15889e18	−1.40325
$739$	−3.68743e18	−0.832789	−0.416395	−	0.909184i	$-0.636707\pi$
$739$	−3.68743e18	−0.832789	−0.416395	+	0.909184i	$0.636707\pi$
$740$	3.79664e18	0.849949
$741$	0	0
$742$	−4.60344e18	−1.01264
$743$	2.64028e18	0.575736	0.287868	−	0.957670i	$-0.407054\pi$
$743$	2.64028e18	0.575736	0.287868	+	0.957670i	$0.407054\pi$
$744$	−1.10165e17	−0.0238132
$745$	2.56102e18	0.548779
$746$	6.67938e18	1.41884
$747$	−6.21515e18	−1.30878
$748$	−6.69285e18	−1.39717
$749$	−1.05139e19	−2.17587
$750$	−2.24371e18	−0.460328
$751$	8.20198e17	0.166824	0.0834121	−	0.996515i	$-0.473418\pi$
$751$	8.20198e17	0.166824	0.0834121	+	0.996515i	$0.473418\pi$
$752$	−7.72280e18	−1.55725
$753$	5.76943e17	0.115336
$754$	0	0
$755$	5.41324e18	1.06366
$756$	4.06709e18	0.792305
$757$	−5.41071e17	−0.104503	−0.0522517	−	0.998634i	$-0.516640\pi$
$757$	−5.41071e17	−0.104503	−0.0522517	+	0.998634i	$0.516640\pi$
$758$	−1.80532e17	−0.0345705
$759$	6.73496e17	0.127868
$760$	2.83362e17	0.0533401
$761$	−9.55846e17	−0.178397	−0.0891985	−	0.996014i	$-0.528431\pi$
$761$	−9.55846e17	−0.178397	−0.0891985	+	0.996014i	$0.528431\pi$
$762$	−7.85854e17	−0.145423
$763$	1.11313e19	2.04238
$764$	5.10649e18	0.929000
$765$	5.61240e18	1.01239
$766$	6.84247e18	1.22384
$767$	0	0
$768$	−1.34759e18	−0.236979
$769$	−8.62926e18	−1.50471	−0.752354	−	0.658759i	$-0.771082\pi$
$769$	−8.62926e18	−1.50471	−0.752354	+	0.658759i	$0.771082\pi$
$770$	−1.10555e19	−1.91156
$771$	−2.36987e18	−0.406323
$772$	1.14969e19	1.95464
$773$	−8.01344e17	−0.135099	−0.0675495	−	0.997716i	$-0.521518\pi$
$773$	−8.01344e17	−0.135099	−0.0675495	+	0.997716i	$0.521518\pi$
$774$	3.57475e18	0.597626
$775$	8.61771e16	0.0142867
$776$	−1.04375e18	−0.171591
$777$	−1.80351e18	−0.294023
$778$	−4.72899e18	−0.764542
$779$	2.36763e18	0.379596
$780$	0	0
$781$	−1.16918e19	−1.84353
$782$	−3.88985e18	−0.608259
$783$	−5.23336e18	−0.811576
$784$	−2.58678e18	−0.397837
$785$	−7.79396e17	−0.118879
$786$	−1.98715e18	−0.300597
$787$	−1.06991e19	−1.60514	−0.802569	−	0.596559i	$-0.796534\pi$
$787$	−1.06991e19	−1.60514	−0.802569	+	0.596559i	$0.796534\pi$
$788$	1.02947e19	1.53177
$789$	5.44765e17	0.0803912
$790$	4.52965e18	0.662962
$791$	1.39297e19	2.02207
$792$	1.06308e18	0.153057
$793$	0	0
$794$	−1.11468e19	−1.57876
$795$	−1.27226e18	−0.178727
$796$	−1.15229e19	−1.60556
$797$	6.30434e18	0.871286	0.435643	−	0.900120i	$-0.356521\pi$
$797$	6.30434e18	0.871286	0.435643	+	0.900120i	$0.356521\pi$
$798$	−1.41233e18	−0.193606
$799$	−1.47607e19	−2.00703
$800$	−3.05309e17	−0.0411770
$801$	−1.33888e18	−0.179115
$802$	−1.49473e19	−1.98348
$803$	9.40438e18	1.23788
$804$	3.58088e18	0.467547
$805$	−3.37344e18	−0.436918
$806$	0	0
$807$	1.99130e18	0.253780
$808$	1.40401e17	0.0177499
$809$	4.55086e18	0.570727	0.285364	−	0.958419i	$-0.407886\pi$
$809$	4.55086e18	0.570727	0.285364	+	0.958419i	$0.407886\pi$
$810$	−8.22804e18	−1.02363
$811$	7.25312e17	0.0895137	0.0447568	−	0.998998i	$-0.485749\pi$
$811$	7.25312e17	0.0895137	0.0447568	+	0.998998i	$0.485749\pi$
$812$	−1.48251e19	−1.81503
$813$	3.70341e18	0.449794
$814$	−1.04294e19	−1.25662
$815$	4.26989e18	0.510379
$816$	−2.65515e18	−0.314849
$817$	−1.37423e18	−0.161664
$818$	−1.67968e19	−1.96033
$819$	0	0
$820$	−1.01671e19	−1.16790
$821$	−7.12450e18	−0.811940	−0.405970	−	0.913886i	$-0.633066\pi$
$821$	−7.12450e18	−0.811940	−0.405970	+	0.913886i	$0.633066\pi$
$822$	−6.16142e18	−0.696649
$823$	−8.32183e18	−0.933512	−0.466756	−	0.884386i	$-0.654577\pi$
$823$	−8.32183e18	−0.933512	−0.466756	+	0.884386i	$0.654577\pi$
$824$	1.24614e17	0.0138688
$825$	9.02723e16	0.00996791
$826$	−1.89679e19	−2.07802
$827$	−2.03770e18	−0.221491	−0.110745	−	0.993849i	$-0.535324\pi$
$827$	−2.03770e18	−0.221491	−0.110745	+	0.993849i	$0.535324\pi$
$828$	3.40360e18	0.367064
$829$	1.72064e19	1.84113	0.920567	−	0.390585i	$-0.127727\pi$
$829$	1.72064e19	1.84113	0.920567	+	0.390585i	$0.127727\pi$
$830$	−1.95421e19	−2.07474
$831$	−4.93913e18	−0.520288
$832$	0	0
$833$	−4.94416e18	−0.512743
$834$	5.25182e17	0.0540419
$835$	8.17690e18	0.834884
$836$	−4.28799e18	−0.434423
$837$	−2.94765e18	−0.296320
$838$	−7.50689e18	−0.748814
$839$	6.83173e18	0.676205	0.338102	−	0.941109i	$-0.390215\pi$
$839$	6.83173e18	0.676205	0.338102	+	0.941109i	$0.390215\pi$
$840$	5.78021e17	0.0567713
$841$	8.81567e18	0.859175
$842$	−1.32689e19	−1.28324
$843$	3.88751e18	0.373072
$844$	4.03294e18	0.384057
$845$	0	0
$846$	2.46002e19	2.30691
$847$	3.00365e18	0.279516
$848$	−5.54469e18	−0.512041
$849$	2.30939e18	0.211640
$850$	−5.21377e17	−0.0474165
$851$	−3.18242e18	−0.287220
$852$	6.41391e18	0.574467
$853$	−5.24391e18	−0.466108	−0.233054	−	0.972464i	$-0.574872\pi$
$853$	−5.24391e18	−0.466108	−0.233054	+	0.972464i	$0.574872\pi$
$854$	−6.43724e18	−0.567837
$855$	3.59577e18	0.314783
$856$	3.17888e18	0.276182
$857$	−7.70440e18	−0.664299	−0.332149	−	0.943227i	$-0.607774\pi$
$857$	−7.70440e18	−0.664299	−0.332149	+	0.943227i	$0.607774\pi$
$858$	0	0
$859$	−1.00646e19	−0.854755	−0.427378	−	0.904073i	$-0.640563\pi$
$859$	−1.00646e19	−0.854755	−0.427378	+	0.904073i	$0.640563\pi$
$860$	5.90119e18	0.497393
$861$	4.82966e18	0.404013
$862$	6.00861e18	0.498858
$863$	1.70633e19	1.40602	0.703011	−	0.711179i	$-0.251839\pi$
$863$	1.70633e19	1.40602	0.703011	+	0.711179i	$0.251839\pi$
$864$	1.04430e19	0.854052
$865$	1.32584e19	1.07619
$866$	2.49572e19	2.01062
$867$	−1.16133e18	−0.0928608
$868$	−8.35012e18	−0.662696
$869$	−6.53283e18	−0.514604
$870$	−7.80397e18	−0.610155
$871$	0	0
$872$	−3.36555e18	−0.259238
$873$	−1.32448e19	−1.01263
$874$	−2.49216e18	−0.189126
$875$	−1.62084e19	−1.22093
$876$	−5.15908e18	−0.385741
$877$	7.32897e18	0.543933	0.271966	−	0.962307i	$-0.412326\pi$
$877$	7.32897e18	0.543933	0.271966	+	0.962307i	$0.412326\pi$
$878$	2.42926e19	1.78962
$879$	1.92166e18	0.140523
$880$	−1.33159e19	−0.966572
$881$	−4.06767e18	−0.293091	−0.146546	−	0.989204i	$-0.546815\pi$
$881$	−4.06767e18	−0.293091	−0.146546	+	0.989204i	$0.546815\pi$
$882$	8.23993e18	0.589356
$883$	1.19014e19	0.844993	0.422497	−	0.906365i	$-0.361154\pi$
$883$	1.19014e19	0.844993	0.422497	+	0.906365i	$0.361154\pi$
$884$	0	0
$885$	−5.24219e18	−0.366760
$886$	−4.81700e18	−0.334547
$887$	2.29331e19	1.58110	0.790550	−	0.612397i	$-0.209795\pi$
$887$	2.29331e19	1.58110	0.790550	+	0.612397i	$0.209795\pi$
$888$	5.45291e17	0.0373202
$889$	−5.67698e18	−0.385705
$890$	−4.20981e18	−0.283940
$891$	1.18668e19	0.794563
$892$	2.77891e19	1.84715
$893$	−9.45693e18	−0.624045
$894$	3.85937e18	0.252827
$895$	8.08864e18	0.526049
$896$	5.67056e18	0.366120
$897$	0	0
$898$	2.65583e19	1.69007
$899$	1.07446e19	0.678815
$900$	4.56203e17	0.0286142
$901$	−1.05977e19	−0.659932
$902$	2.79292e19	1.72670
$903$	−2.80323e18	−0.172064
$904$	−4.21165e18	−0.256660
$905$	1.74468e19	1.05560
$906$	8.15757e18	0.490035
$907$	2.56355e19	1.52895	0.764476	−	0.644652i	$-0.222998\pi$
$907$	2.56355e19	1.52895	0.764476	+	0.644652i	$0.222998\pi$
$908$	3.09455e19	1.83248
$909$	1.78163e18	0.104750
$910$	0	0
$911$	1.54584e19	0.895972	0.447986	−	0.894040i	$-0.352141\pi$
$911$	1.54584e19	0.895972	0.447986	+	0.894040i	$0.352141\pi$
$912$	−1.70111e18	−0.0978960
$913$	2.81843e19	1.61045
$914$	−4.17653e19	−2.36955
$915$	−1.77907e18	−0.100220
$916$	1.19582e19	0.668876
$917$	−1.43551e19	−0.797272
$918$	1.78335e19	0.983466
$919$	−1.30782e19	−0.716139	−0.358070	−	0.933695i	$-0.616565\pi$
$919$	−1.30782e19	−0.716139	−0.358070	+	0.933695i	$0.616565\pi$
$920$	1.01996e18	0.0554577
$921$	−2.86581e18	−0.154725
$922$	2.40044e19	1.28688
$923$	0	0
$924$	−8.74693e18	−0.462368
$925$	−4.26557e17	−0.0223901
$926$	−2.49822e19	−1.30215
$927$	1.58130e18	0.0818459
$928$	−3.80660e19	−1.95648
$929$	−2.64343e18	−0.134917	−0.0674584	−	0.997722i	$-0.521489\pi$
$929$	−2.64343e18	−0.134917	−0.0674584	+	0.997722i	$0.521489\pi$
$930$	−4.39553e18	−0.222778
$931$	−3.16764e18	−0.159427
$932$	−4.30091e18	−0.214960
$933$	−4.04345e18	−0.200688
$934$	−3.51793e19	−1.73394
$935$	−2.54510e19	−1.24575
$936$	0	0
$937$	−1.80007e19	−0.868926	−0.434463	−	0.900690i	$-0.643062\pi$
$937$	−1.80007e19	−0.868926	−0.434463	+	0.900690i	$0.643062\pi$
$938$	4.92709e19	2.36196
$939$	1.23703e19	0.588915
$940$	4.06099e19	1.92000
$941$	−2.55731e19	−1.20075	−0.600374	−	0.799720i	$-0.704981\pi$
$941$	−2.55731e19	−1.20075	−0.600374	+	0.799720i	$0.704981\pi$
$942$	−1.17452e18	−0.0547685
$943$	8.52226e18	0.394665
$944$	−2.28462e19	−1.05074
$945$	1.54660e19	0.706433
$946$	−1.62107e19	−0.735376
$947$	3.17471e19	1.43031	0.715154	−	0.698967i	$-0.246356\pi$
$947$	3.17471e19	1.43031	0.715154	+	0.698967i	$0.246356\pi$
$948$	3.58379e18	0.160357
$949$	0	0
$950$	−3.34037e17	−0.0147432
$951$	−3.29067e18	−0.144248
$952$	4.81480e18	0.209623
$953$	1.42575e19	0.616508	0.308254	−	0.951304i	$-0.400255\pi$
$953$	1.42575e19	0.616508	0.308254	+	0.951304i	$0.400255\pi$
$954$	1.76621e19	0.758537
$955$	1.94185e19	0.828313
$956$	−6.54857e18	−0.277441
$957$	1.12552e19	0.473614
$958$	−3.82072e19	−1.59687
$959$	−4.45099e19	−1.84772
$960$	8.96382e18	0.369598
$961$	−1.83657e19	−0.752153
$962$	0	0
$963$	4.03389e19	1.62987
$964$	−1.48840e19	−0.597338
$965$	4.37193e19	1.74279
$966$	−5.08367e18	−0.201292
$967$	−4.77797e19	−1.87919	−0.939596	−	0.342284i	$-0.888799\pi$
$967$	−4.77797e19	−1.87919	−0.939596	+	0.342284i	$0.888799\pi$
$968$	−9.08153e17	−0.0354788
$969$	−3.25135e18	−0.126171
$970$	−4.16451e19	−1.60527
$971$	1.16863e18	0.0447457	0.0223728	−	0.999750i	$-0.492878\pi$
$971$	1.16863e18	0.0447457	0.0223728	+	0.999750i	$0.492878\pi$
$972$	−2.38080e19	−0.905509
$973$	3.79390e18	0.143335
$974$	1.97146e19	0.739868
$975$	0	0
$976$	−7.75344e18	−0.287125
$977$	1.43892e19	0.529324	0.264662	−	0.964341i	$-0.414740\pi$
$977$	1.43892e19	0.529324	0.264662	+	0.964341i	$0.414740\pi$
$978$	6.43459e18	0.235135
$979$	6.07154e18	0.220400
$980$	1.36025e19	0.490510
$981$	−4.27076e19	−1.52988
$982$	5.30706e19	1.88855
$983$	−3.13740e19	−1.10910	−0.554551	−	0.832150i	$-0.687110\pi$
$983$	−3.13740e19	−1.10910	−0.554551	+	0.832150i	$0.687110\pi$
$984$	−1.46024e18	−0.0512811
$985$	3.91479e19	1.36575
$986$	−6.50055e19	−2.25294
$987$	−1.92909e19	−0.664187
$988$	0	0
$989$	−4.94650e18	−0.168082
$990$	4.24166e19	1.43188
$991$	−2.67695e19	−0.897762	−0.448881	−	0.893592i	$-0.648177\pi$
$991$	−2.67695e19	−0.897762	−0.448881	+	0.893592i	$0.648177\pi$
$992$	−2.14404e19	−0.714343
$993$	3.81317e18	0.126217
$994$	8.82517e19	2.90209
$995$	−4.38182e19	−1.43154
$996$	−1.54614e19	−0.501838
$997$	2.26280e19	0.729672	0.364836	−	0.931072i	$-0.381125\pi$
$997$	2.26280e19	0.729672	0.364836	+	0.931072i	$0.381125\pi$
$998$	−2.14809e19	−0.688183
$999$	1.45902e19	0.464393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.14.a.f.1.5		30
13.6	odd	12		13.14.e.a.10.13	yes	30
13.11	odd	12		13.14.e.a.4.13	✓	30
13.12	even	2	inner	169.14.a.f.1.26		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.e.a.4.13	✓	30	13.11	odd	12
13.14.e.a.10.13	yes	30	13.6	odd	12
169.14.a.f.1.5		30	1.1	even	1	trivial
169.14.a.f.1.26		30	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q-131.328 q^{2} -395.120 q^{3} +9055.01 q^{4} +34433.6 q^{5} +51890.3 q^{6} +374853. q^{7} -113337. q^{8} -1.43820e6 q^{9} -4.52209e6 q^{10} +6.52193e6 q^{11} -3.57782e6 q^{12} -4.92287e7 q^{14} -1.36054e7 q^{15} -5.92943e7 q^{16} -1.13330e8 q^{17} +1.88876e8 q^{18} -7.26088e7 q^{19} +3.11796e8 q^{20} -1.48112e8 q^{21} -8.56511e8 q^{22} -2.61354e8 q^{23} +4.47816e7 q^{24} -3.50307e7 q^{25} +1.19821e9 q^{27} +3.39430e9 q^{28} -4.36764e9 q^{29} +1.78677e9 q^{30} -2.46004e9 q^{31} +8.71545e9 q^{32} -2.57695e9 q^{33} +1.48834e10 q^{34} +1.29076e10 q^{35} -1.30229e10 q^{36} +1.21767e10 q^{37} +9.53555e9 q^{38} -3.90259e9 q^{40} -3.26081e10 q^{41} +1.94512e10 q^{42} +1.89264e10 q^{43} +5.90561e10 q^{44} -4.95225e10 q^{45} +3.43231e10 q^{46} +1.30245e11 q^{47} +2.34284e10 q^{48} +4.36261e10 q^{49} +4.60051e9 q^{50} +4.47791e10 q^{51} +9.35113e10 q^{53} -1.57359e11 q^{54} +2.24574e11 q^{55} -4.24847e10 q^{56} +2.86892e10 q^{57} +5.73593e11 q^{58} +3.85302e11 q^{59} -1.23197e11 q^{60} +1.30762e11 q^{61} +3.23072e11 q^{62} -5.39115e11 q^{63} -6.58843e11 q^{64} +3.38425e11 q^{66} -1.00086e12 q^{67} -1.02621e12 q^{68} +1.03266e11 q^{69} -1.69512e12 q^{70} -1.79269e12 q^{71} +1.63001e11 q^{72} +1.44196e12 q^{73} -1.59913e12 q^{74} +1.38413e10 q^{75} -6.57473e11 q^{76} +2.44477e12 q^{77} -1.00167e12 q^{79} -2.04172e12 q^{80} +1.81952e12 q^{81} +4.28235e12 q^{82} +4.32147e12 q^{83} -1.34116e12 q^{84} -3.90237e12 q^{85} -2.48557e12 q^{86} +1.72574e12 q^{87} -7.39175e11 q^{88} +9.30942e11 q^{89} +6.50368e12 q^{90} -2.36656e12 q^{92} +9.72012e11 q^{93} -1.71048e13 q^{94} -2.50018e12 q^{95} -3.44365e12 q^{96} +9.20926e12 q^{97} -5.72932e12 q^{98} -9.37986e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 1460 q^{3} + 131070 q^{4} + 18234142 q^{9} + 7786950 q^{10} - 27694876 q^{12} + 61125588 q^{14} + 700365042 q^{16} - 47049798 q^{17} + 256370724 q^{22} + 834173772 q^{23} + 11926991364 q^{25} + 5605403288 q^{27}+ \cdots + 22616629029900 q^{95}+O(q^{100}) \) 30 * q + 1460 * q^3 + 131070 * q^4 + 18234142 * q^9 + 7786950 * q^10 - 27694876 * q^12 + 61125588 * q^14 + 700365042 * q^16 - 47049798 * q^17 + 256370724 * q^22 + 834173772 * q^23 + 11926991364 * q^25 + 5605403288 * q^27 + 17620379154 * q^29 - 19873358484 * q^30 - 2118481440 * q^35 + 111801927430 * q^36 + 45168847944 * q^38 + 137282090274 * q^40 + 68249929572 * q^42 + 276653280960 * q^43 - 1261191382396 * q^48 + 228555270606 * q^49 + 178343342508 * q^51 + 938994404670 * q^53 + 281220246240 * q^55 + 1865948401440 * q^56 - 568996466874 * q^61 + 5148167694060 * q^62 + 4989806279958 * q^64 + 12037245084948 * q^66 + 6248093284554 * q^68 + 2413972855992 * q^69 - 3446868460146 * q^74 + 3819696303368 * q^75 + 8153714196816 * q^77 + 10732970056200 * q^79 - 53747712890 * q^81 - 1848896034654 * q^82 + 12885932252268 * q^87 - 22189213625376 * q^88 - 53932182551466 * q^90 - 48706576133844 * q^92 - 7058933840292 * q^94 + 22616629029900 * q^95

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