LMFDB - Embedded newform 150.12.a.s.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,12,Mod(1,150)] 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("150.1"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	150.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,64,486,2048,0,15552,-24058] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$115.251477084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1092762 $ x^2 - x - 1092762
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1044.85$ of defining polynomial
Character	$\chi$	$=$	150.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +7776.00 q^{6} +50692.2 q^{7} +32768.0 q^{8} +59049.0 q^{9} -75916.1 q^{11} +248832. q^{12} +305005. q^{13} +1.62215e6 q^{14} +1.04858e6 q^{16} -1.08019e6 q^{17} +1.88957e6 q^{18} +7.09756e6 q^{19} +1.23182e7 q^{21} -2.42932e6 q^{22} +1.80419e7 q^{23} +7.96262e6 q^{24} +9.76015e6 q^{26} +1.43489e7 q^{27} +5.19088e7 q^{28} +7.29738e7 q^{29} +3.77162e7 q^{31} +3.35544e7 q^{32} -1.84476e7 q^{33} -3.45660e7 q^{34} +6.04662e7 q^{36} +1.48096e8 q^{37} +2.27122e8 q^{38} +7.41161e7 q^{39} -4.45125e8 q^{41} +3.94182e8 q^{42} -1.00624e9 q^{43} -7.77381e7 q^{44} +5.77340e8 q^{46} +8.45388e8 q^{47} +2.54804e8 q^{48} +5.92368e8 q^{49} -2.62486e8 q^{51} +3.12325e8 q^{52} -1.38443e9 q^{53} +4.59165e8 q^{54} +1.66108e9 q^{56} +1.72471e9 q^{57} +2.33516e9 q^{58} +9.47897e9 q^{59} +8.26835e9 q^{61} +1.20692e9 q^{62} +2.99332e9 q^{63} +1.07374e9 q^{64} -5.90324e8 q^{66} -2.06345e10 q^{67} -1.10611e9 q^{68} +4.38418e9 q^{69} +1.57969e10 q^{71} +1.93492e9 q^{72} +1.07362e10 q^{73} +4.73907e9 q^{74} +7.26790e9 q^{76} -3.84835e9 q^{77} +2.37172e9 q^{78} -2.29541e10 q^{79} +3.48678e9 q^{81} -1.42440e10 q^{82} +3.56526e10 q^{83} +1.26138e10 q^{84} -3.21998e10 q^{86} +1.77326e10 q^{87} -2.48762e9 q^{88} -7.98531e8 q^{89} +1.54613e10 q^{91} +1.84749e10 q^{92} +9.16503e9 q^{93} +2.70524e10 q^{94} +8.15373e9 q^{96} -4.48480e10 q^{97} +1.89558e10 q^{98} -4.48277e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 64 q^{2} + 486 q^{3} + 2048 q^{4} + 15552 q^{6} - 24058 q^{7} + 65536 q^{8} + 118098 q^{9} + 726264 q^{11} + 497664 q^{12} + 860894 q^{13} - 769856 q^{14} + 2097152 q^{16} + 6996912 q^{17} + 3779136 q^{18}+ \cdots + 42885162936 q^{99}+O(q^{100}) $ 2 * q + 64 * q^2 + 486 * q^3 + 2048 * q^4 + 15552 * q^6 - 24058 * q^7 + 65536 * q^8 + 118098 * q^9 + 726264 * q^11 + 497664 * q^12 + 860894 * q^13 - 769856 * q^14 + 2097152 * q^16 + 6996912 * q^17 + 3779136 * q^18 - 3241370 * q^19 - 5846094 * q^21 + 23240448 * q^22 - 4434096 * q^23 + 15925248 * q^24 + 27548608 * q^26 + 28697814 * q^27 - 24635392 * q^28 - 76210680 * q^29 - 12000926 * q^31 + 67108864 * q^32 + 176482152 * q^33 + 223901184 * q^34 + 120932352 * q^36 + 327050852 * q^37 - 103723840 * q^38 + 209197242 * q^39 + 352006044 * q^41 - 187075008 * q^42 + 907686614 * q^43 + 743694336 * q^44 - 141891072 * q^46 + 2292398292 * q^47 + 509607936 * q^48 + 4202628396 * q^49 + 1700249616 * q^51 + 881555456 * q^52 - 4539974436 * q^53 + 918330048 * q^54 - 788332544 * q^56 - 787652910 * q^57 - 2438741760 * q^58 + 6067482180 * q^59 + 13474911814 * q^61 - 384029632 * q^62 - 1420600842 * q^63 + 2147483648 * q^64 + 5647428864 * q^66 - 4794289018 * q^67 + 7164837888 * q^68 - 1077485328 * q^69 + 29632732284 * q^71 + 3869835264 * q^72 + 43334804804 * q^73 + 10465627264 * q^74 - 3319162880 * q^76 - 63811447056 * q^77 + 6694311744 * q^78 - 2876054480 * q^79 + 6973568802 * q^81 + 11264193408 * q^82 + 29784832284 * q^83 - 5986400256 * q^84 + 29045971648 * q^86 - 18519195240 * q^87 + 23798218752 * q^88 + 62927959920 * q^89 - 26091470326 * q^91 - 4540514304 * q^92 - 2916225018 * q^93 + 73356745344 * q^94 + 16307453952 * q^96 - 141777577858 * q^97 + 134484108672 * q^98 + 42885162936 * 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 $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	1024.00	0.500000
$5$	0	0
$5$	0	0
$6$	7776.00	0.408248
$7$	50692.2	1.13999	0.569996	−	0.821648i	$-0.306945\pi$
$7$	50692.2	1.13999	0.569996	+	0.821648i	$0.306945\pi$
$8$	32768.0	0.353553
$9$	59049.0	0.333333
$10$	0	0
$11$	−75916.1	−0.142126	−0.0710631	−	0.997472i	$-0.522639\pi$
$11$	−75916.1	−0.142126	−0.0710631	+	0.997472i	$0.522639\pi$
$12$	248832.	0.288675
$13$	305005.	0.227834	0.113917	−	0.993490i	$-0.463660\pi$
$13$	305005.	0.227834	0.113917	+	0.993490i	$0.463660\pi$
$14$	1.62215e6	0.806096
$15$	0	0
$16$	1.04858e6	0.250000
$17$	−1.08019e6	−0.184515	−0.0922573	−	0.995735i	$-0.529408\pi$
$17$	−1.08019e6	−0.184515	−0.0922573	+	0.995735i	$0.529408\pi$
$18$	1.88957e6	0.235702
$19$	7.09756e6	0.657603	0.328802	−	0.944399i	$-0.393355\pi$
$19$	7.09756e6	0.657603	0.328802	+	0.944399i	$0.393355\pi$
$20$	0	0
$21$	1.23182e7	0.658174
$22$	−2.42932e6	−0.100498
$23$	1.80419e7	0.584492	0.292246	−	0.956343i	$-0.405597\pi$
$23$	1.80419e7	0.584492	0.292246	+	0.956343i	$0.405597\pi$
$24$	7.96262e6	0.204124
$25$	0	0
$26$	9.76015e6	0.161103
$27$	1.43489e7	0.192450
$28$	5.19088e7	0.569996
$29$	7.29738e7	0.660660	0.330330	−	0.943865i	$-0.392840\pi$
$29$	7.29738e7	0.660660	0.330330	+	0.943865i	$0.392840\pi$
$30$	0	0
$31$	3.77162e7	0.236613	0.118306	−	0.992977i	$-0.462253\pi$
$31$	3.77162e7	0.236613	0.118306	+	0.992977i	$0.462253\pi$
$32$	3.35544e7	0.176777
$33$	−1.84476e7	−0.0820566
$34$	−3.45660e7	−0.130471
$35$	0	0
$36$	6.04662e7	0.166667
$37$	1.48096e8	0.351102	0.175551	−	0.984470i	$-0.443829\pi$
$37$	1.48096e8	0.351102	0.175551	+	0.984470i	$0.443829\pi$
$38$	2.27122e8	0.464996
$39$	7.41161e7	0.131540
$40$	0	0
$41$	−4.45125e8	−0.600026	−0.300013	−	0.953935i	$-0.596991\pi$
$41$	−4.45125e8	−0.600026	−0.300013	+	0.953935i	$0.596991\pi$
$42$	3.94182e8	0.465400
$43$	−1.00624e9	−1.04382	−0.521911	−	0.853000i	$-0.674781\pi$
$43$	−1.00624e9	−1.04382	−0.521911	+	0.853000i	$0.674781\pi$
$44$	−7.77381e7	−0.0710631
$45$	0	0
$46$	5.77340e8	0.413299
$47$	8.45388e8	0.537673	0.268836	−	0.963186i	$-0.413361\pi$
$47$	8.45388e8	0.537673	0.268836	+	0.963186i	$0.413361\pi$
$48$	2.54804e8	0.144338
$49$	5.92368e8	0.299580
$50$	0	0
$51$	−2.62486e8	−0.106530
$52$	3.12325e8	0.113917
$53$	−1.38443e9	−0.454729	−0.227365	−	0.973810i	$-0.573011\pi$
$53$	−1.38443e9	−0.454729	−0.227365	+	0.973810i	$0.573011\pi$
$54$	4.59165e8	0.136083
$55$	0	0
$56$	1.66108e9	0.403048
$57$	1.72471e9	0.379668
$58$	2.33516e9	0.467157
$59$	9.47897e9	1.72614	0.863068	−	0.505088i	$-0.168540\pi$
$59$	9.47897e9	1.72614	0.863068	+	0.505088i	$0.168540\pi$
$60$	0	0
$61$	8.26835e9	1.25344	0.626722	−	0.779243i	$-0.284396\pi$
$61$	8.26835e9	1.25344	0.626722	+	0.779243i	$0.284396\pi$
$62$	1.20692e9	0.167311
$63$	2.99332e9	0.379997
$64$	1.07374e9	0.125000
$65$	0	0
$66$	−5.90324e8	−0.0580228
$67$	−2.06345e10	−1.86717	−0.933583	−	0.358362i	$-0.883335\pi$
$67$	−2.06345e10	−1.86717	−0.933583	+	0.358362i	$0.883335\pi$
$68$	−1.10611e9	−0.0922573
$69$	4.38418e9	0.337457
$70$	0	0
$71$	1.57969e10	1.03908	0.519542	−	0.854445i	$-0.326103\pi$
$71$	1.57969e10	1.03908	0.519542	+	0.854445i	$0.326103\pi$
$72$	1.93492e9	0.117851
$73$	1.07362e10	0.606145	0.303072	−	0.952968i	$-0.401988\pi$
$73$	1.07362e10	0.606145	0.303072	+	0.952968i	$0.401988\pi$
$74$	4.73907e9	0.248267
$75$	0	0
$76$	7.26790e9	0.328802
$77$	−3.84835e9	−0.162023
$78$	2.37172e9	0.0930127
$79$	−2.29541e10	−0.839290	−0.419645	−	0.907688i	$-0.637845\pi$
$79$	−2.29541e10	−0.839290	−0.419645	+	0.907688i	$0.637845\pi$
$80$	0	0
$81$	3.48678e9	0.111111
$82$	−1.42440e10	−0.424283
$83$	3.56526e10	0.993486	0.496743	−	0.867898i	$-0.334529\pi$
$83$	3.56526e10	0.993486	0.496743	+	0.867898i	$0.334529\pi$
$84$	1.26138e10	0.329087
$85$	0	0
$86$	−3.21998e10	−0.738093
$87$	1.77326e10	0.381432
$88$	−2.48762e9	−0.0502492
$89$	−7.98531e8	−0.0151582	−0.00757909	−	0.999971i	$-0.502413\pi$
$89$	−7.98531e8	−0.0151582	−0.00757909	+	0.999971i	$0.502413\pi$
$90$	0	0
$91$	1.54613e10	0.259729
$92$	1.84749e10	0.292246
$93$	9.16503e9	0.136609
$94$	2.70524e10	0.380192
$95$	0	0
$96$	8.15373e9	0.102062
$97$	−4.48480e10	−0.530271	−0.265136	−	0.964211i	$-0.585417\pi$
$97$	−4.48480e10	−0.530271	−0.265136	+	0.964211i	$0.585417\pi$
$98$	1.89558e10	0.211835
$99$	−4.48277e9	−0.0473754
$100$	0	0
$101$	5.41836e10	0.512980	0.256490	−	0.966547i	$-0.417434\pi$
$101$	5.41836e10	0.512980	0.256490	+	0.966547i	$0.417434\pi$
$102$	−8.39955e9	−0.0753277
$103$	1.20789e11	1.02665	0.513324	−	0.858195i	$-0.328414\pi$
$103$	1.20789e11	1.02665	0.513324	+	0.858195i	$0.328414\pi$
$104$	9.99439e9	0.0805514
$105$	0	0
$106$	−4.43017e10	−0.321542
$107$	−1.41955e11	−0.978456	−0.489228	−	0.872156i	$-0.662721\pi$
$107$	−1.41955e11	−0.978456	−0.489228	+	0.872156i	$0.662721\pi$
$108$	1.46933e10	0.0962250
$109$	2.08333e10	0.129692	0.0648458	−	0.997895i	$-0.479344\pi$
$109$	2.08333e10	0.129692	0.0648458	+	0.997895i	$0.479344\pi$
$110$	0	0
$111$	3.59873e10	0.202709
$112$	5.31546e10	0.284998
$113$	2.32341e11	1.18630	0.593149	−	0.805093i	$-0.297884\pi$
$113$	2.32341e11	1.18630	0.593149	+	0.805093i	$0.297884\pi$
$114$	5.51906e10	0.268465
$115$	0	0
$116$	7.47252e10	0.330330
$117$	1.80102e10	0.0759446
$118$	3.03327e11	1.22056
$119$	−5.47571e10	−0.210345
$120$	0	0
$121$	−2.79548e11	−0.979800
$122$	2.64587e11	0.886319
$123$	−1.08165e11	−0.346425
$124$	3.86214e10	0.118306
$125$	0	0
$126$	9.57863e10	0.268699
$127$	2.90739e11	0.780876	0.390438	−	0.920629i	$-0.372323\pi$
$127$	2.90739e11	0.780876	0.390438	+	0.920629i	$0.372323\pi$
$128$	3.43597e10	0.0883883
$129$	−2.44517e11	−0.602651
$130$	0	0
$131$	7.23610e11	1.63875	0.819375	−	0.573258i	$-0.194321\pi$
$131$	7.23610e11	1.63875	0.819375	+	0.573258i	$0.194321\pi$
$132$	−1.88904e10	−0.0410283
$133$	3.59790e11	0.749662
$134$	−6.60304e11	−1.32029
$135$	0	0
$136$	−3.53956e10	−0.0652357
$137$	1.91230e11	0.338527	0.169264	−	0.985571i	$-0.445861\pi$
$137$	1.91230e11	0.338527	0.169264	+	0.985571i	$0.445861\pi$
$138$	1.40294e11	0.238618
$139$	−1.03256e12	−1.68785	−0.843927	−	0.536458i	$-0.819762\pi$
$139$	−1.03256e12	−1.68785	−0.843927	+	0.536458i	$0.819762\pi$
$140$	0	0
$141$	2.05429e11	0.310426
$142$	5.05500e11	0.734743
$143$	−2.31548e10	−0.0323812
$144$	6.19174e10	0.0833333
$145$	0	0
$146$	3.43559e11	0.428609
$147$	1.43946e11	0.172963
$148$	1.51650e11	0.175551
$149$	−8.15470e11	−0.909669	−0.454835	−	0.890576i	$-0.650302\pi$
$149$	−8.15470e11	−0.909669	−0.454835	+	0.890576i	$0.650302\pi$
$150$	0	0
$151$	6.11640e11	0.634049	0.317024	−	0.948417i	$-0.397316\pi$
$151$	6.11640e11	0.634049	0.317024	+	0.948417i	$0.397316\pi$
$152$	2.32573e11	0.232498
$153$	−6.37841e10	−0.0615048
$154$	−1.23147e11	−0.114567
$155$	0	0
$156$	7.58949e10	0.0657699
$157$	1.47006e12	1.22994	0.614972	−	0.788549i	$-0.289167\pi$
$157$	1.47006e12	1.22994	0.614972	+	0.788549i	$0.289167\pi$
$158$	−7.34533e11	−0.593468
$159$	−3.36416e11	−0.262538
$160$	0	0
$161$	9.14582e11	0.666316
$162$	1.11577e11	0.0785674
$163$	1.28912e12	0.877531	0.438765	−	0.898602i	$-0.355416\pi$
$163$	1.28912e12	0.877531	0.438765	+	0.898602i	$0.355416\pi$
$164$	−4.55808e11	−0.300013
$165$	0	0
$166$	1.14088e12	0.702501
$167$	−9.39303e11	−0.559584	−0.279792	−	0.960061i	$-0.590265\pi$
$167$	−9.39303e11	−0.559584	−0.279792	+	0.960061i	$0.590265\pi$
$168$	4.03643e11	0.232700
$169$	−1.69913e12	−0.948092
$170$	0	0
$171$	4.19104e11	0.219201
$172$	−1.03039e12	−0.521911
$173$	3.44324e12	1.68933	0.844664	−	0.535296i	$-0.179800\pi$
$173$	3.44324e12	1.68933	0.844664	+	0.535296i	$0.179800\pi$
$174$	5.67445e11	0.269713
$175$	0	0
$176$	−7.96038e10	−0.0355316
$177$	2.30339e12	0.996585
$178$	−2.55530e10	−0.0107184
$179$	−1.93673e12	−0.787728	−0.393864	−	0.919169i	$-0.628862\pi$
$179$	−1.93673e12	−0.787728	−0.393864	+	0.919169i	$0.628862\pi$
$180$	0	0
$181$	3.37063e11	0.128967	0.0644835	−	0.997919i	$-0.479460\pi$
$181$	3.37063e11	0.128967	0.0644835	+	0.997919i	$0.479460\pi$
$182$	4.94763e11	0.183656
$183$	2.00921e12	0.723676
$184$	5.91197e11	0.206649
$185$	0	0
$186$	2.93281e11	0.0965968
$187$	8.20038e10	0.0262244
$188$	8.65678e11	0.268836
$189$	7.27377e11	0.219391
$190$	0	0
$191$	9.42200e11	0.268200	0.134100	−	0.990968i	$-0.457186\pi$
$191$	9.42200e11	0.268200	0.134100	+	0.990968i	$0.457186\pi$
$192$	2.60919e11	0.0721688
$193$	5.10162e12	1.37133	0.685666	−	0.727916i	$-0.259511\pi$
$193$	5.10162e12	1.37133	0.685666	+	0.727916i	$0.259511\pi$
$194$	−1.43513e12	−0.374959
$195$	0	0
$196$	6.06585e11	0.149790
$197$	2.09359e12	0.502722	0.251361	−	0.967893i	$-0.419122\pi$
$197$	2.09359e12	0.502722	0.251361	+	0.967893i	$0.419122\pi$
$198$	−1.43449e11	−0.0334995
$199$	−3.42476e12	−0.777926	−0.388963	−	0.921253i	$-0.627167\pi$
$199$	−3.42476e12	−0.777926	−0.388963	+	0.921253i	$0.627167\pi$
$200$	0	0
$201$	−5.01419e12	−1.07801
$202$	1.73387e12	0.362731
$203$	3.69920e12	0.753147
$204$	−2.68786e11	−0.0532648
$205$	0	0
$206$	3.86524e12	0.725949
$207$	1.06536e12	0.194831
$208$	3.19821e11	0.0569584
$209$	−5.38819e11	−0.0934627
$210$	0	0
$211$	1.59301e11	0.0262219	0.0131109	−	0.999914i	$-0.495827\pi$
$211$	1.59301e11	0.0262219	0.0131109	+	0.999914i	$0.495827\pi$
$212$	−1.41765e12	−0.227365
$213$	3.83864e12	0.599915
$214$	−4.54257e12	−0.691873
$215$	0	0
$216$	4.70185e11	0.0680414
$217$	1.91192e12	0.269737
$218$	6.66664e11	0.0917057
$219$	2.60890e12	0.349958
$220$	0	0
$221$	−3.29463e11	−0.0420386
$222$	1.15159e12	0.143337
$223$	4.70223e11	0.0570988	0.0285494	−	0.999592i	$-0.490911\pi$
$223$	4.70223e11	0.0570988	0.0285494	+	0.999592i	$0.490911\pi$
$224$	1.70095e12	0.201524
$225$	0	0
$226$	7.43490e12	0.838839
$227$	−1.64771e13	−1.81443	−0.907214	−	0.420669i	$-0.861795\pi$
$227$	−1.64771e13	−1.81443	−0.907214	+	0.420669i	$0.861795\pi$
$228$	1.76610e12	0.189834
$229$	1.36753e13	1.43496	0.717482	−	0.696577i	$-0.245295\pi$
$229$	1.36753e13	1.43496	0.717482	+	0.696577i	$0.245295\pi$
$230$	0	0
$231$	−9.35150e11	−0.0935439
$232$	2.39121e12	0.233579
$233$	3.16743e12	0.302168	0.151084	−	0.988521i	$-0.451724\pi$
$233$	3.16743e12	0.302168	0.151084	+	0.988521i	$0.451724\pi$
$234$	5.76327e11	0.0537009
$235$	0	0
$236$	9.70646e12	0.863068
$237$	−5.57786e12	−0.484564
$238$	−1.75223e12	−0.148736
$239$	−4.28172e12	−0.355165	−0.177583	−	0.984106i	$-0.556828\pi$
$239$	−4.28172e12	−0.355165	−0.177583	+	0.984106i	$0.556828\pi$
$240$	0	0
$241$	−6.01989e12	−0.476974	−0.238487	−	0.971146i	$-0.576652\pi$
$241$	−6.01989e12	−0.476974	−0.238487	+	0.971146i	$0.576652\pi$
$242$	−8.94555e12	−0.692823
$243$	8.47289e11	0.0641500
$244$	8.46679e12	0.626722
$245$	0	0
$246$	−3.46129e12	−0.244960
$247$	2.16479e12	0.149824
$248$	1.23588e12	0.0836553
$249$	8.66359e12	0.573590
$250$	0	0
$251$	−1.03996e11	−0.00658888	−0.00329444	−	0.999995i	$-0.501049\pi$
$251$	−1.03996e11	−0.00658888	−0.00329444	+	0.999995i	$0.501049\pi$
$252$	3.06516e12	0.189999
$253$	−1.36967e12	−0.0830717
$254$	9.30364e12	0.552163
$255$	0	0
$256$	1.09951e12	0.0625000
$257$	−1.77317e13	−0.986549	−0.493275	−	0.869874i	$-0.664200\pi$
$257$	−1.77317e13	−0.986549	−0.493275	+	0.869874i	$0.664200\pi$
$258$	−7.82454e12	−0.426138
$259$	7.50731e12	0.400254
$260$	0	0
$261$	4.30903e12	0.220220
$262$	2.31555e13	1.15877
$263$	−1.97378e13	−0.967256	−0.483628	−	0.875274i	$-0.660681\pi$
$263$	−1.97378e13	−0.967256	−0.483628	+	0.875274i	$0.660681\pi$
$264$	−6.04492e11	−0.0290114
$265$	0	0
$266$	1.15133e13	0.530091
$267$	−1.94043e11	−0.00875157
$268$	−2.11297e13	−0.933583
$269$	−2.98190e13	−1.29079	−0.645396	−	0.763848i	$-0.723307\pi$
$269$	−2.98190e13	−1.29079	−0.645396	+	0.763848i	$0.723307\pi$
$270$	0	0
$271$	−2.89071e13	−1.20136	−0.600681	−	0.799489i	$-0.705104\pi$
$271$	−2.89071e13	−1.20136	−0.600681	+	0.799489i	$0.705104\pi$
$272$	−1.13266e12	−0.0461286
$273$	3.75711e12	0.149954
$274$	6.11937e12	0.239375
$275$	0	0
$276$	4.48940e12	0.168728
$277$	2.06140e13	0.759491	0.379745	−	0.925091i	$-0.376012\pi$
$277$	2.06140e13	0.759491	0.379745	+	0.925091i	$0.376012\pi$
$278$	−3.30420e13	−1.19349
$279$	2.22710e12	0.0788710
$280$	0	0
$281$	−6.03979e12	−0.205654	−0.102827	−	0.994699i	$-0.532789\pi$
$281$	−6.03979e12	−0.205654	−0.102827	+	0.994699i	$0.532789\pi$
$282$	6.57374e12	0.219504
$283$	−1.35178e13	−0.442670	−0.221335	−	0.975198i	$-0.571041\pi$
$283$	−1.35178e13	−0.442670	−0.221335	+	0.975198i	$0.571041\pi$
$284$	1.61760e13	0.519542
$285$	0	0
$286$	−7.40953e11	−0.0228969
$287$	−2.25643e13	−0.684025
$288$	1.98136e12	0.0589256
$289$	−3.31051e13	−0.965954
$290$	0	0
$291$	−1.08981e13	−0.306152
$292$	1.09939e13	0.303072
$293$	−3.76701e13	−1.01912	−0.509560	−	0.860435i	$-0.670192\pi$
$293$	−3.76701e13	−1.01912	−0.509560	+	0.860435i	$0.670192\pi$
$294$	4.60626e12	0.122303
$295$	0	0
$296$	4.85281e12	0.124133
$297$	−1.08931e12	−0.0273522
$298$	−2.60950e13	−0.643233
$299$	5.50286e12	0.133167
$300$	0	0
$301$	−5.10086e13	−1.18995
$302$	1.95725e13	0.448340
$303$	1.31666e13	0.296169
$304$	7.44233e12	0.164401
$305$	0	0
$306$	−2.04109e12	−0.0434905
$307$	−1.61401e13	−0.337789	−0.168894	−	0.985634i	$-0.554020\pi$
$307$	−1.61401e13	−0.337789	−0.168894	+	0.985634i	$0.554020\pi$
$308$	−3.94071e12	−0.0810114
$309$	2.93516e13	0.592735
$310$	0	0
$311$	−7.74446e13	−1.50942	−0.754708	−	0.656061i	$-0.772222\pi$
$311$	−7.74446e13	−1.50942	−0.754708	+	0.656061i	$0.772222\pi$
$312$	2.42864e12	0.0465064
$313$	−3.96245e13	−0.745539	−0.372769	−	0.927924i	$-0.621592\pi$
$313$	−3.96245e13	−0.745539	−0.372769	+	0.927924i	$0.621592\pi$
$314$	4.70418e13	0.869702
$315$	0	0
$316$	−2.35050e13	−0.419645
$317$	−6.63630e13	−1.16439	−0.582197	−	0.813048i	$-0.697807\pi$
$317$	−6.63630e13	−1.16439	−0.582197	+	0.813048i	$0.697807\pi$
$318$	−1.07653e13	−0.185642
$319$	−5.53989e12	−0.0938972
$320$	0	0
$321$	−3.44952e13	−0.564912
$322$	2.92666e13	0.471157
$323$	−7.66670e12	−0.121337
$324$	3.57047e12	0.0555556
$325$	0	0
$326$	4.12519e13	0.620508
$327$	5.06248e12	0.0748774
$328$	−1.45858e13	−0.212141
$329$	4.28546e13	0.612942
$330$	0	0
$331$	−1.35207e14	−1.87045	−0.935223	−	0.354059i	$-0.884801\pi$
$331$	−1.35207e14	−1.87045	−0.935223	+	0.354059i	$0.884801\pi$
$332$	3.65083e13	0.496743
$333$	8.74492e12	0.117034
$334$	−3.00577e13	−0.395686
$335$	0	0
$336$	1.29166e13	0.164544
$337$	−1.28718e14	−1.61314	−0.806572	−	0.591135i	$-0.798680\pi$
$337$	−1.28718e14	−1.61314	−0.806572	+	0.591135i	$0.798680\pi$
$338$	−5.43722e13	−0.670402
$339$	5.64588e13	0.684909
$340$	0	0
$341$	−2.86327e12	−0.0336289
$342$	1.34113e13	0.154999
$343$	−7.02065e13	−0.798472
$344$	−3.29726e13	−0.369047
$345$	0	0
$346$	1.10184e14	1.19454
$347$	−7.81048e13	−0.833423	−0.416711	−	0.909039i	$-0.636817\pi$
$347$	−7.81048e13	−0.833423	−0.416711	+	0.909039i	$0.636817\pi$
$348$	1.81582e13	0.190716
$349$	−1.80809e14	−1.86931	−0.934653	−	0.355562i	$-0.884290\pi$
$349$	−1.80809e14	−1.86931	−0.934653	+	0.355562i	$0.884290\pi$
$350$	0	0
$351$	4.37648e12	0.0438466
$352$	−2.54732e12	−0.0251246
$353$	2.93802e13	0.285295	0.142648	−	0.989774i	$-0.454438\pi$
$353$	2.93802e13	0.285295	0.142648	+	0.989774i	$0.454438\pi$
$354$	7.37085e13	0.704692
$355$	0	0
$356$	−8.17696e11	−0.00757909
$357$	−1.33060e13	−0.121443
$358$	−6.19752e13	−0.557008
$359$	5.78634e13	0.512135	0.256067	−	0.966659i	$-0.417573\pi$
$359$	5.78634e13	0.512135	0.256067	+	0.966659i	$0.417573\pi$
$360$	0	0
$361$	−6.61150e13	−0.567558
$362$	1.07860e13	0.0911934
$363$	−6.79303e13	−0.565688
$364$	1.58324e13	0.129864
$365$	0	0
$366$	6.42947e13	0.511716
$367$	6.30385e13	0.494246	0.247123	−	0.968984i	$-0.420515\pi$
$367$	6.30385e13	0.494246	0.247123	+	0.968984i	$0.420515\pi$
$368$	1.89183e13	0.146123
$369$	−2.62842e13	−0.200009
$370$	0	0
$371$	−7.01796e13	−0.518387
$372$	9.38499e12	0.0683043
$373$	2.26968e13	0.162767	0.0813834	−	0.996683i	$-0.474066\pi$
$373$	2.26968e13	0.162767	0.0813834	+	0.996683i	$0.474066\pi$
$374$	2.62412e12	0.0185434
$375$	0	0
$376$	2.77017e13	0.190096
$377$	2.22574e13	0.150521
$378$	2.32761e13	0.155133
$379$	−6.06246e13	−0.398229	−0.199115	−	0.979976i	$-0.563807\pi$
$379$	−6.06246e13	−0.398229	−0.199115	+	0.979976i	$0.563807\pi$
$380$	0	0
$381$	7.06495e13	0.450839
$382$	3.01504e13	0.189646
$383$	2.38540e14	1.47900	0.739500	−	0.673156i	$-0.235062\pi$
$383$	2.38540e14	1.47900	0.739500	+	0.673156i	$0.235062\pi$
$384$	8.34942e12	0.0510310
$385$	0	0
$386$	1.63252e14	0.969679
$387$	−5.94176e13	−0.347940
$388$	−4.59243e13	−0.265136
$389$	1.43501e14	0.816828	0.408414	−	0.912797i	$-0.366082\pi$
$389$	1.43501e14	0.816828	0.408414	+	0.912797i	$0.366082\pi$
$390$	0	0
$391$	−1.94886e13	−0.107847
$392$	1.94107e13	0.105918
$393$	1.75837e14	0.946132
$394$	6.69949e13	0.355478
$395$	0	0
$396$	−4.59036e12	−0.0236877
$397$	1.12723e14	0.573674	0.286837	−	0.957979i	$-0.407396\pi$
$397$	1.12723e14	0.573674	0.286837	+	0.957979i	$0.407396\pi$
$398$	−1.09592e14	−0.550077
$399$	8.74291e13	0.432818
$400$	0	0
$401$	1.94480e14	0.936655	0.468328	−	0.883555i	$-0.344857\pi$
$401$	1.94480e14	0.936655	0.468328	+	0.883555i	$0.344857\pi$
$402$	−1.60454e14	−0.762267
$403$	1.15036e13	0.0539084
$404$	5.54840e13	0.256490
$405$	0	0
$406$	1.18374e14	0.532555
$407$	−1.12429e13	−0.0499009
$408$	−8.60114e12	−0.0376639
$409$	−1.46521e14	−0.633027	−0.316513	−	0.948588i	$-0.602512\pi$
$409$	−1.46521e14	−0.633027	−0.316513	+	0.948588i	$0.602512\pi$
$410$	0	0
$411$	4.64690e13	0.195449
$412$	1.23688e14	0.513324
$413$	4.80509e14	1.96778
$414$	3.40914e13	0.137766
$415$	0	0
$416$	1.02343e13	0.0402757
$417$	−2.50913e14	−0.974483
$418$	−1.72422e13	−0.0660881
$419$	3.37095e14	1.27519	0.637595	−	0.770371i	$-0.279929\pi$
$419$	3.37095e14	1.27519	0.637595	+	0.770371i	$0.279929\pi$
$420$	0	0
$421$	−6.17552e13	−0.227574	−0.113787	−	0.993505i	$-0.536298\pi$
$421$	−6.17552e13	−0.227574	−0.113787	+	0.993505i	$0.536298\pi$
$422$	5.09762e12	0.0185417
$423$	4.99193e13	0.179224
$424$	−4.53649e13	−0.160771
$425$	0	0
$426$	1.22837e14	0.424204
$427$	4.19141e14	1.42892
$428$	−1.45362e14	−0.489228
$429$	−5.62661e12	−0.0186953
$430$	0	0
$431$	3.74885e13	0.121415	0.0607076	−	0.998156i	$-0.480664\pi$
$431$	3.74885e13	0.121415	0.0607076	+	0.998156i	$0.480664\pi$
$432$	1.50459e13	0.0481125
$433$	2.52848e14	0.798319	0.399160	−	0.916881i	$-0.369302\pi$
$433$	2.52848e14	0.798319	0.399160	+	0.916881i	$0.369302\pi$
$434$	6.11813e13	0.190733
$435$	0	0
$436$	2.13333e13	0.0648458
$437$	1.28053e14	0.384364
$438$	8.34849e13	0.247457
$439$	−4.21760e14	−1.23455	−0.617277	−	0.786746i	$-0.711764\pi$
$439$	−4.21760e14	−1.23455	−0.617277	+	0.786746i	$0.711764\pi$
$440$	0	0
$441$	3.49788e13	0.0998602
$442$	−1.05428e13	−0.0297258
$443$	3.38043e14	0.941349	0.470675	−	0.882307i	$-0.344011\pi$
$443$	3.38043e14	0.941349	0.470675	+	0.882307i	$0.344011\pi$
$444$	3.68510e13	0.101355
$445$	0	0
$446$	1.50471e13	0.0403750
$447$	−1.98159e14	−0.525198
$448$	5.44303e13	0.142499
$449$	−2.19965e14	−0.568851	−0.284426	−	0.958698i	$-0.591803\pi$
$449$	−2.19965e14	−0.568851	−0.284426	+	0.958698i	$0.591803\pi$
$450$	0	0
$451$	3.37921e13	0.0852795
$452$	2.37917e14	0.593149
$453$	1.48628e14	0.366068
$454$	−5.27269e14	−1.28299
$455$	0	0
$456$	5.65152e13	0.134233
$457$	5.24669e14	1.23125	0.615625	−	0.788040i	$-0.288904\pi$
$457$	5.24669e14	1.23125	0.615625	+	0.788040i	$0.288904\pi$
$458$	4.37609e14	1.01467
$459$	−1.54995e13	−0.0355098
$460$	0	0
$461$	−8.87822e13	−0.198596	−0.0992981	−	0.995058i	$-0.531660\pi$
$461$	−8.87822e13	−0.198596	−0.0992981	+	0.995058i	$0.531660\pi$
$462$	−2.99248e13	−0.0661455
$463$	−5.86281e14	−1.28059	−0.640296	−	0.768128i	$-0.721188\pi$
$463$	−5.86281e14	−1.28059	−0.640296	+	0.768128i	$0.721188\pi$
$464$	7.65186e13	0.165165
$465$	0	0
$466$	1.01358e14	0.213665
$467$	−2.07097e14	−0.431451	−0.215725	−	0.976454i	$-0.569212\pi$
$467$	−2.07097e14	−0.431451	−0.215725	+	0.976454i	$0.569212\pi$
$468$	1.84425e13	0.0379723
$469$	−1.04601e15	−2.12855
$470$	0	0
$471$	3.57224e14	0.710109
$472$	3.10607e14	0.610281
$473$	7.63900e13	0.148354
$474$	−1.78491e14	−0.342639
$475$	0	0
$476$	−5.60713e13	−0.105172
$477$	−8.17490e13	−0.151576
$478$	−1.37015e14	−0.251140
$479$	−3.65244e14	−0.661816	−0.330908	−	0.943663i	$-0.607355\pi$
$479$	−3.65244e14	−0.661816	−0.330908	+	0.943663i	$0.607355\pi$
$480$	0	0
$481$	4.51700e13	0.0799930
$482$	−1.92637e14	−0.337272
$483$	2.22243e14	0.384698
$484$	−2.86258e14	−0.489900
$485$	0	0
$486$	2.71132e13	0.0453609
$487$	−3.11560e14	−0.515386	−0.257693	−	0.966227i	$-0.582962\pi$
$487$	−3.11560e14	−0.515386	−0.257693	+	0.966227i	$0.582962\pi$
$488$	2.70937e14	0.443159
$489$	3.13257e14	0.506643
$490$	0	0
$491$	−7.38304e14	−1.16758	−0.583791	−	0.811904i	$-0.698431\pi$
$491$	−7.38304e14	−1.16758	−0.583791	+	0.811904i	$0.698431\pi$
$492$	−1.10761e14	−0.173213
$493$	−7.88255e13	−0.121901
$494$	6.92732e13	0.105942
$495$	0	0
$496$	3.95483e13	0.0591532
$497$	8.00778e14	1.18455
$498$	2.77235e14	0.405589
$499$	−9.26777e14	−1.34098	−0.670490	−	0.741918i	$-0.733916\pi$
$499$	−9.26777e14	−1.34098	−0.670490	+	0.741918i	$0.733916\pi$
$500$	0	0
$501$	−2.28251e14	−0.323076
$502$	−3.32787e12	−0.00465904
$503$	8.47541e14	1.17364	0.586822	−	0.809716i	$-0.300379\pi$
$503$	8.47541e14	1.17364	0.586822	+	0.809716i	$0.300379\pi$
$504$	9.80852e13	0.134349
$505$	0	0
$506$	−4.38294e13	−0.0587406
$507$	−4.12889e14	−0.547381
$508$	2.97716e14	0.390438
$509$	6.72162e14	0.872020	0.436010	−	0.899942i	$-0.356391\pi$
$509$	6.72162e14	0.872020	0.436010	+	0.899942i	$0.356391\pi$
$510$	0	0
$511$	5.44243e14	0.691000
$512$	3.51844e13	0.0441942
$513$	1.01842e14	0.126556
$514$	−5.67415e14	−0.697596
$515$	0	0
$516$	−2.50385e14	−0.301325
$517$	−6.41786e13	−0.0764174
$518$	2.40234e14	0.283022
$519$	8.36708e14	0.975334
$520$	0	0
$521$	1.29604e15	1.47914	0.739571	−	0.673079i	$-0.235028\pi$
$521$	1.29604e15	1.47914	0.739571	+	0.673079i	$0.235028\pi$
$522$	1.37889e14	0.155719
$523$	−1.60871e15	−1.79771	−0.898854	−	0.438248i	$-0.855599\pi$
$523$	−1.60871e15	−1.79771	−0.898854	+	0.438248i	$0.855599\pi$
$524$	7.40977e14	0.819375
$525$	0	0
$526$	−6.31609e14	−0.683954
$527$	−4.07406e13	−0.0436585
$528$	−1.93437e13	−0.0205142
$529$	−6.27300e14	−0.658369
$530$	0	0
$531$	5.59724e14	0.575379
$532$	3.68425e14	0.374831
$533$	−1.35765e14	−0.136706
$534$	−6.20938e12	−0.00618830
$535$	0	0
$536$	−6.76152e14	−0.660143
$537$	−4.70624e14	−0.454795
$538$	−9.54209e14	−0.912727
$539$	−4.49703e13	−0.0425782
$540$	0	0
$541$	−2.84573e14	−0.264003	−0.132002	−	0.991249i	$-0.542140\pi$
$541$	−2.84573e14	−0.264003	−0.132002	+	0.991249i	$0.542140\pi$
$542$	−9.25028e14	−0.849491
$543$	8.19062e13	0.0744591
$544$	−3.62451e13	−0.0326179
$545$	0	0
$546$	1.20227e14	0.106034
$547$	1.94391e14	0.169725	0.0848627	−	0.996393i	$-0.472955\pi$
$547$	1.94391e14	0.169725	0.0848627	+	0.996393i	$0.472955\pi$
$548$	1.95820e14	0.169264
$549$	4.88238e14	0.417815
$550$	0	0
$551$	5.17936e14	0.434452
$552$	1.43661e14	0.119309
$553$	−1.16360e15	−0.956784
$554$	6.59647e14	0.537041
$555$	0	0
$556$	−1.05734e15	−0.843927
$557$	1.83873e15	1.45316	0.726580	−	0.687082i	$-0.241109\pi$
$557$	1.83873e15	1.45316	0.726580	+	0.687082i	$0.241109\pi$
$558$	7.12673e13	0.0557702
$559$	−3.06909e14	−0.237818
$560$	0	0
$561$	1.99269e13	0.0151406
$562$	−1.93273e14	−0.145419
$563$	−1.91860e15	−1.42951	−0.714757	−	0.699373i	$-0.753463\pi$
$563$	−1.91860e15	−1.42951	−0.714757	+	0.699373i	$0.753463\pi$
$564$	2.10360e14	0.155213
$565$	0	0
$566$	−4.32569e14	−0.313015
$567$	1.76753e14	0.126666
$568$	5.17632e14	0.367372
$569$	1.48515e15	1.04388	0.521941	−	0.852981i	$-0.325208\pi$
$569$	1.48515e15	1.04388	0.521941	+	0.852981i	$0.325208\pi$
$570$	0	0
$571$	−6.49667e14	−0.447911	−0.223956	−	0.974599i	$-0.571897\pi$
$571$	−6.49667e14	−0.447911	−0.223956	+	0.974599i	$0.571897\pi$
$572$	−2.37105e13	−0.0161906
$573$	2.28954e14	0.154846
$574$	−7.22059e14	−0.483679
$575$	0	0
$576$	6.34034e13	0.0416667
$577$	1.60418e15	1.04420	0.522102	−	0.852883i	$-0.325148\pi$
$577$	1.60418e15	1.04420	0.522102	+	0.852883i	$0.325148\pi$
$578$	−1.05936e15	−0.683033
$579$	1.23969e15	0.791739
$580$	0	0
$581$	1.80731e15	1.13257
$582$	−3.48738e14	−0.216482
$583$	1.05100e14	0.0646290
$584$	3.51805e14	0.214304
$585$	0	0
$586$	−1.20544e15	−0.720626
$587$	−2.36229e15	−1.39902	−0.699509	−	0.714624i	$-0.746598\pi$
$587$	−2.36229e15	−1.39902	−0.699509	+	0.714624i	$0.746598\pi$
$588$	1.47400e14	0.0864814
$589$	2.67693e14	0.155597
$590$	0	0
$591$	5.08743e14	0.290247
$592$	1.55290e14	0.0877756
$593$	9.18852e14	0.514571	0.257285	−	0.966335i	$-0.417172\pi$
$593$	9.18852e14	0.514571	0.257285	+	0.966335i	$0.417172\pi$
$594$	−3.48580e13	−0.0193409
$595$	0	0
$596$	−8.35041e14	−0.454835
$597$	−8.32217e14	−0.449136
$598$	1.76092e14	0.0941634
$599$	2.23950e15	1.18660	0.593299	−	0.804982i	$-0.297825\pi$
$599$	2.23950e15	1.18660	0.593299	+	0.804982i	$0.297825\pi$
$600$	0	0
$601$	−1.82448e15	−0.949137	−0.474568	−	0.880219i	$-0.657396\pi$
$601$	−1.82448e15	−0.949137	−0.474568	+	0.880219i	$0.657396\pi$
$602$	−1.63228e15	−0.841420
$603$	−1.21845e15	−0.622389
$604$	6.26319e14	0.317024
$605$	0	0
$606$	4.21332e14	0.209423
$607$	1.78003e15	0.876778	0.438389	−	0.898785i	$-0.355549\pi$
$607$	1.78003e15	0.876778	0.438389	+	0.898785i	$0.355549\pi$
$608$	2.38154e14	0.116249
$609$	8.98906e14	0.434830
$610$	0	0
$611$	2.57847e14	0.122500
$612$	−6.53149e13	−0.0307524
$613$	−2.41155e15	−1.12529	−0.562645	−	0.826699i	$-0.690216\pi$
$613$	−2.41155e15	−1.12529	−0.562645	+	0.826699i	$0.690216\pi$
$614$	−5.16483e14	−0.238853
$615$	0	0
$616$	−1.26103e14	−0.0572837
$617$	−4.04949e15	−1.82319	−0.911595	−	0.411090i	$-0.865148\pi$
$617$	−4.04949e15	−1.82319	−0.911595	+	0.411090i	$0.865148\pi$
$618$	9.39252e14	0.419127
$619$	3.66980e15	1.62309	0.811547	−	0.584287i	$-0.198626\pi$
$619$	3.66980e15	1.62309	0.811547	+	0.584287i	$0.198626\pi$
$620$	0	0
$621$	2.58881e14	0.112486
$622$	−2.47823e15	−1.06732
$623$	−4.04793e13	−0.0172802
$624$	7.77164e13	0.0328850
$625$	0	0
$626$	−1.26798e15	−0.527175
$627$	−1.30933e14	−0.0539607
$628$	1.50534e15	0.614972
$629$	−1.59972e14	−0.0647835
$630$	0	0
$631$	−1.28463e14	−0.0511231	−0.0255616	−	0.999673i	$-0.508137\pi$
$631$	−1.28463e14	−0.0511231	−0.0255616	+	0.999673i	$0.508137\pi$
$632$	−7.52161e14	−0.296734
$633$	3.87100e13	0.0151392
$634$	−2.12361e15	−0.823351
$635$	0	0
$636$	−3.44490e14	−0.131269
$637$	1.80675e14	0.0682545
$638$	−1.77277e14	−0.0663953
$639$	9.32790e14	0.346361
$640$	0	0
$641$	1.55882e15	0.568954	0.284477	−	0.958683i	$-0.408180\pi$
$641$	1.55882e15	0.568954	0.284477	+	0.958683i	$0.408180\pi$
$642$	−1.10385e15	−0.399453
$643$	−3.23739e15	−1.16154	−0.580770	−	0.814068i	$-0.697248\pi$
$643$	−3.23739e15	−1.16154	−0.580770	+	0.814068i	$0.697248\pi$
$644$	9.36532e14	0.333158
$645$	0	0
$646$	−2.45334e14	−0.0857985
$647$	−1.01764e15	−0.352874	−0.176437	−	0.984312i	$-0.556457\pi$
$647$	−1.01764e15	−0.352874	−0.176437	+	0.984312i	$0.556457\pi$
$648$	1.14255e14	0.0392837
$649$	−7.19607e14	−0.245329
$650$	0	0
$651$	4.64595e14	0.155733
$652$	1.32006e15	0.438765
$653$	−5.06875e15	−1.67062	−0.835311	−	0.549778i	$-0.814712\pi$
$653$	−5.06875e15	−1.67062	−0.835311	+	0.549778i	$0.814712\pi$
$654$	1.61999e14	0.0529463
$655$	0	0
$656$	−4.66747e14	−0.150007
$657$	6.33964e14	0.202048
$658$	1.37135e15	0.433416
$659$	1.52920e15	0.479284	0.239642	−	0.970861i	$-0.422970\pi$
$659$	1.52920e15	0.479284	0.239642	+	0.970861i	$0.422970\pi$
$660$	0	0
$661$	−3.76754e15	−1.16131	−0.580657	−	0.814148i	$-0.697204\pi$
$661$	−3.76754e15	−1.16131	−0.580657	+	0.814148i	$0.697204\pi$
$662$	−4.32662e15	−1.32261
$663$	−8.00594e13	−0.0242710
$664$	1.16827e15	0.351250
$665$	0	0
$666$	2.79838e14	0.0827556
$667$	1.31659e15	0.386151
$668$	−9.61846e14	−0.279792
$669$	1.14264e14	0.0329660
$670$	0	0
$671$	−6.27701e14	−0.178147
$672$	4.13330e14	0.116350
$673$	−2.90026e15	−0.809757	−0.404878	−	0.914371i	$-0.632686\pi$
$673$	−2.90026e15	−0.809757	−0.404878	+	0.914371i	$0.632686\pi$
$674$	−4.11896e15	−1.14067
$675$	0	0
$676$	−1.73991e15	−0.474046
$677$	2.07034e15	0.559506	0.279753	−	0.960072i	$-0.409747\pi$
$677$	2.07034e15	0.559506	0.279753	+	0.960072i	$0.409747\pi$
$678$	1.80668e15	0.484304
$679$	−2.27344e15	−0.604505
$680$	0	0
$681$	−4.00395e15	−1.04756
$682$	−9.16245e13	−0.0237792
$683$	4.72888e15	1.21743	0.608716	−	0.793389i	$-0.291685\pi$
$683$	4.72888e15	1.21743	0.608716	+	0.793389i	$0.291685\pi$
$684$	4.29162e14	0.109601
$685$	0	0
$686$	−2.24661e15	−0.564605
$687$	3.32309e15	0.828477
$688$	−1.05512e15	−0.260955
$689$	−4.22257e14	−0.103603
$690$	0	0
$691$	−1.29144e15	−0.311849	−0.155925	−	0.987769i	$-0.549836\pi$
$691$	−1.29144e15	−0.311849	−0.155925	+	0.987769i	$0.549836\pi$
$692$	3.52588e15	0.844664
$693$	−2.27241e14	−0.0540076
$694$	−2.49935e15	−0.589319
$695$	0	0
$696$	5.81063e14	0.134857
$697$	4.80819e14	0.110714
$698$	−5.78589e15	−1.32180
$699$	7.69685e14	0.174457
$700$	0	0
$701$	6.26537e15	1.39797	0.698985	−	0.715136i	$-0.253635\pi$
$701$	6.26537e15	1.39797	0.698985	+	0.715136i	$0.253635\pi$
$702$	1.40047e14	0.0310042
$703$	1.05112e15	0.230886
$704$	−8.15143e13	−0.0177658
$705$	0	0
$706$	9.40168e14	0.201734
$707$	2.74668e15	0.584792
$708$	2.35867e15	0.498293
$709$	−2.87770e15	−0.603241	−0.301620	−	0.953428i	$-0.597528\pi$
$709$	−2.87770e15	−0.603241	−0.301620	+	0.953428i	$0.597528\pi$
$710$	0	0
$711$	−1.35542e15	−0.279763
$712$	−2.61663e13	−0.00535922
$713$	6.80471e14	0.138298
$714$	−4.25791e14	−0.0858730
$715$	0	0
$716$	−1.98321e15	−0.393864
$717$	−1.04046e15	−0.205055
$718$	1.85163e15	0.362134
$719$	−6.34976e15	−1.23239	−0.616195	−	0.787593i	$-0.711327\pi$
$719$	−6.34976e15	−1.23239	−0.616195	+	0.787593i	$0.711327\pi$
$720$	0	0
$721$	6.12304e15	1.17037
$722$	−2.11568e15	−0.401324
$723$	−1.46283e15	−0.275381
$724$	3.45152e14	0.0644835
$725$	0	0
$726$	−2.17377e15	−0.400002
$727$	4.58889e15	0.838047	0.419023	−	0.907975i	$-0.362373\pi$
$727$	4.58889e15	0.838047	0.419023	+	0.907975i	$0.362373\pi$
$728$	5.06637e14	0.0918279
$729$	2.05891e14	0.0370370
$730$	0	0
$731$	1.08693e15	0.192600
$732$	2.05743e15	0.361838
$733$	1.12999e15	0.197244	0.0986218	−	0.995125i	$-0.468557\pi$
$733$	1.12999e15	0.197244	0.0986218	+	0.995125i	$0.468557\pi$
$734$	2.01723e15	0.349484
$735$	0	0
$736$	6.05385e14	0.103325
$737$	1.56649e15	0.265373
$738$	−8.41093e14	−0.141428
$739$	3.41995e15	0.570788	0.285394	−	0.958410i	$-0.407875\pi$
$739$	3.41995e15	0.570788	0.285394	+	0.958410i	$0.407875\pi$
$740$	0	0
$741$	5.26043e14	0.0865011
$742$	−2.24575e15	−0.366555
$743$	1.08101e16	1.75142	0.875711	−	0.482835i	$-0.160393\pi$
$743$	1.08101e16	1.75142	0.875711	+	0.482835i	$0.160393\pi$
$744$	3.00320e14	0.0482984
$745$	0	0
$746$	7.26298e14	0.115094
$747$	2.10525e15	0.331162
$748$	8.39718e13	0.0131122
$749$	−7.19603e15	−1.11543
$750$	0	0
$751$	1.13998e16	1.74132	0.870661	−	0.491884i	$-0.163692\pi$
$751$	1.13998e16	1.74132	0.870661	+	0.491884i	$0.163692\pi$
$752$	8.86454e14	0.134418
$753$	−2.52710e13	−0.00380409
$754$	7.12236e14	0.106434
$755$	0	0
$756$	7.44834e14	0.109696
$757$	−3.86631e14	−0.0565287	−0.0282644	−	0.999600i	$-0.508998\pi$
$757$	−3.86631e14	−0.0565287	−0.0282644	+	0.999600i	$0.508998\pi$
$758$	−1.93999e15	−0.281591
$759$	−3.32830e14	−0.0479615
$760$	0	0
$761$	−9.19001e14	−0.130527	−0.0652635	−	0.997868i	$-0.520789\pi$
$761$	−9.19001e14	−0.130527	−0.0652635	+	0.997868i	$0.520789\pi$
$762$	2.26078e15	0.318791
$763$	1.05608e15	0.147847
$764$	9.64812e14	0.134100
$765$	0	0
$766$	7.63328e15	1.04581
$767$	2.89113e15	0.393272
$768$	2.67181e14	0.0360844
$769$	3.54298e15	0.475088	0.237544	−	0.971377i	$-0.423658\pi$
$769$	3.54298e15	0.475088	0.237544	+	0.971377i	$0.423658\pi$
$770$	0	0
$771$	−4.30881e15	−0.569584
$772$	5.22406e15	0.685666
$773$	4.60796e15	0.600512	0.300256	−	0.953859i	$-0.402928\pi$
$773$	4.60796e15	0.600512	0.300256	+	0.953859i	$0.402928\pi$
$774$	−1.90136e15	−0.246031
$775$	0	0
$776$	−1.46958e15	−0.187479
$777$	1.82428e15	0.231087
$778$	4.59202e15	0.577585
$779$	−3.15930e15	−0.394579
$780$	0	0
$781$	−1.19924e15	−0.147681
$782$	−6.23637e14	−0.0762596
$783$	1.04709e15	0.127144
$784$	6.21143e14	0.0748951
$785$	0	0
$786$	5.62679e15	0.669017
$787$	−6.46240e15	−0.763015	−0.381507	−	0.924366i	$-0.624595\pi$
$787$	−6.46240e15	−0.763015	−0.381507	+	0.924366i	$0.624595\pi$
$788$	2.14384e15	0.251361
$789$	−4.79628e15	−0.558446
$790$	0	0
$791$	1.17779e16	1.35237
$792$	−1.46891e14	−0.0167497
$793$	2.52189e15	0.285577
$794$	3.60714e15	0.405649
$795$	0	0
$796$	−3.50695e15	−0.388963
$797$	−1.71141e15	−0.188510	−0.0942548	−	0.995548i	$-0.530047\pi$
$797$	−1.71141e15	−0.188510	−0.0942548	+	0.995548i	$0.530047\pi$
$798$	2.79773e15	0.306048
$799$	−9.13179e14	−0.0992085
$800$	0	0
$801$	−4.71525e13	−0.00505272
$802$	6.22335e15	0.662315
$803$	−8.15053e14	−0.0861490
$804$	−5.13453e15	−0.539004
$805$	0	0
$806$	3.68116e14	0.0381190
$807$	−7.24602e15	−0.745239
$808$	1.77549e15	0.181366
$809$	−1.34056e16	−1.36009	−0.680046	−	0.733170i	$-0.738040\pi$
$809$	−1.34056e16	−1.36009	−0.680046	+	0.733170i	$0.738040\pi$
$810$	0	0
$811$	−3.70518e15	−0.370847	−0.185423	−	0.982659i	$-0.559366\pi$
$811$	−3.70518e15	−0.370847	−0.185423	+	0.982659i	$0.559366\pi$
$812$	3.78798e15	0.376574
$813$	−7.02443e15	−0.693607
$814$	−3.59772e14	−0.0352853
$815$	0	0
$816$	−2.75236e14	−0.0266324
$817$	−7.14186e15	−0.686421
$818$	−4.68868e15	−0.447617
$819$	9.12977e14	0.0865762
$820$	0	0
$821$	−8.02428e15	−0.750791	−0.375395	−	0.926865i	$-0.622493\pi$
$821$	−8.02428e15	−0.750791	−0.375395	+	0.926865i	$0.622493\pi$
$822$	1.48701e15	0.138203
$823$	1.93160e16	1.78328	0.891638	−	0.452750i	$-0.149557\pi$
$823$	1.93160e16	1.78328	0.891638	+	0.452750i	$0.149557\pi$
$824$	3.95800e15	0.362975
$825$	0	0
$826$	1.53763e16	1.39143
$827$	−1.98183e15	−0.178150	−0.0890751	−	0.996025i	$-0.528391\pi$
$827$	−1.98183e15	−0.178150	−0.0890751	+	0.996025i	$0.528391\pi$
$828$	1.09092e15	0.0974154
$829$	5.27226e15	0.467678	0.233839	−	0.972275i	$-0.424871\pi$
$829$	5.27226e15	0.467678	0.233839	+	0.972275i	$0.424871\pi$
$830$	0	0
$831$	5.00919e15	0.438492
$832$	3.27496e14	0.0284792
$833$	−6.39870e14	−0.0552770
$834$	−8.02920e15	−0.689063
$835$	0	0
$836$	−5.51751e14	−0.0467314
$837$	5.41186e14	0.0455362
$838$	1.07870e16	0.901696
$839$	−1.31150e16	−1.08912	−0.544562	−	0.838721i	$-0.683304\pi$
$839$	−1.31150e16	−1.08912	−0.544562	+	0.838721i	$0.683304\pi$
$840$	0	0
$841$	−6.87533e15	−0.563528
$842$	−1.97617e15	−0.160919
$843$	−1.46767e15	−0.118734
$844$	1.63124e14	0.0131109
$845$	0	0
$846$	1.59742e15	0.126731
$847$	−1.41709e16	−1.11696
$848$	−1.45168e15	−0.113682
$849$	−3.28482e15	−0.255575
$850$	0	0
$851$	2.67193e15	0.205217
$852$	3.93077e15	0.299958
$853$	1.31856e16	0.999721	0.499861	−	0.866106i	$-0.333385\pi$
$853$	1.31856e16	0.999721	0.499861	+	0.866106i	$0.333385\pi$
$854$	1.34125e16	1.01040
$855$	0	0
$856$	−4.65160e15	−0.345936
$857$	1.20555e16	0.890820	0.445410	−	0.895327i	$-0.353058\pi$
$857$	1.20555e16	0.890820	0.445410	+	0.895327i	$0.353058\pi$
$858$	−1.80052e14	−0.0132196
$859$	2.39322e16	1.74590	0.872951	−	0.487807i	$-0.162203\pi$
$859$	2.39322e16	1.74590	0.872951	+	0.487807i	$0.162203\pi$
$860$	0	0
$861$	−5.48313e15	−0.394922
$862$	1.19963e15	0.0858536
$863$	2.56601e16	1.82473	0.912366	−	0.409376i	$-0.134253\pi$
$863$	2.56601e16	1.82473	0.912366	+	0.409376i	$0.134253\pi$
$864$	4.81469e14	0.0340207
$865$	0	0
$866$	8.09115e15	0.564497
$867$	−8.04454e15	−0.557694
$868$	1.95780e15	0.134868
$869$	1.74259e15	0.119285
$870$	0	0
$871$	−6.29362e15	−0.425403
$872$	6.82664e14	0.0458529
$873$	−2.64823e15	−0.176757
$874$	4.09771e15	0.271787
$875$	0	0
$876$	2.67152e15	0.174979
$877$	−1.09298e16	−0.711402	−0.355701	−	0.934600i	$-0.615758\pi$
$877$	−1.09298e16	−0.711402	−0.355701	+	0.934600i	$0.615758\pi$
$878$	−1.34963e16	−0.872962
$879$	−9.15384e15	−0.588389
$880$	0	0
$881$	−1.22007e16	−0.774490	−0.387245	−	0.921977i	$-0.626573\pi$
$881$	−1.22007e16	−0.774490	−0.387245	+	0.921977i	$0.626573\pi$
$882$	1.11932e15	0.0706118
$883$	1.11717e16	0.700380	0.350190	−	0.936679i	$-0.386117\pi$
$883$	1.11717e16	0.700380	0.350190	+	0.936679i	$0.386117\pi$
$884$	−3.37370e14	−0.0210193
$885$	0	0
$886$	1.08174e16	0.665635
$887$	2.02845e15	0.124047	0.0620233	−	0.998075i	$-0.480245\pi$
$887$	2.02845e15	0.124047	0.0620233	+	0.998075i	$0.480245\pi$
$888$	1.17923e15	0.0716685
$889$	1.47382e16	0.890193
$890$	0	0
$891$	−2.64703e14	−0.0157918
$892$	4.81508e14	0.0285494
$893$	6.00019e15	0.353575
$894$	−6.34109e15	−0.371371
$895$	0	0
$896$	1.74177e15	0.100762
$897$	1.33719e15	0.0768841
$898$	−7.03888e15	−0.402238
$899$	2.75229e15	0.156321
$900$	0	0
$901$	1.49544e15	0.0839041
$902$	1.08135e15	0.0603017
$903$	−1.23951e16	−0.687016
$904$	7.61334e15	0.419420
$905$	0	0
$906$	4.75611e15	0.258849
$907$	−3.36811e16	−1.82199	−0.910996	−	0.412416i	$-0.864685\pi$
$907$	−3.36811e16	−1.82199	−0.910996	+	0.412416i	$0.864685\pi$
$908$	−1.68726e16	−0.907214
$909$	3.19949e15	0.170993
$910$	0	0
$911$	−8.09337e15	−0.427345	−0.213672	−	0.976905i	$-0.568542\pi$
$911$	−8.09337e15	−0.427345	−0.213672	+	0.976905i	$0.568542\pi$
$912$	1.80849e15	0.0949169
$913$	−2.70661e15	−0.141200
$914$	1.67894e16	0.870625
$915$	0	0
$916$	1.40035e16	0.717482
$917$	3.66814e16	1.86816
$918$	−4.95985e14	−0.0251092
$919$	9.80555e15	0.493442	0.246721	−	0.969087i	$-0.420647\pi$
$919$	9.80555e15	0.493442	0.246721	+	0.969087i	$0.420647\pi$
$920$	0	0
$921$	−3.92204e15	−0.195022
$922$	−2.84103e15	−0.140429
$923$	4.81812e15	0.236738
$924$	−9.57593e14	−0.0467719
$925$	0	0
$926$	−1.87610e16	−0.905515
$927$	7.13245e15	0.342216
$928$	2.44860e15	0.116789
$929$	−2.72736e16	−1.29317	−0.646586	−	0.762841i	$-0.723804\pi$
$929$	−2.72736e16	−1.29317	−0.646586	+	0.762841i	$0.723804\pi$
$930$	0	0
$931$	4.20437e15	0.197005
$932$	3.24344e15	0.151084
$933$	−1.88190e16	−0.871462
$934$	−6.62711e15	−0.305082
$935$	0	0
$936$	5.90159e14	0.0268505
$937$	4.79056e15	0.216680	0.108340	−	0.994114i	$-0.465446\pi$
$937$	4.79056e15	0.216680	0.108340	+	0.994114i	$0.465446\pi$
$938$	−3.34723e16	−1.50511
$939$	−9.62876e15	−0.430437
$940$	0	0
$941$	−2.71262e16	−1.19852	−0.599261	−	0.800553i	$-0.704539\pi$
$941$	−2.71262e16	−1.19852	−0.599261	+	0.800553i	$0.704539\pi$
$942$	1.14312e16	0.502123
$943$	−8.03089e15	−0.350711
$944$	9.93942e15	0.431534
$945$	0	0
$946$	2.44448e15	0.104902
$947$	1.71472e16	0.731593	0.365796	−	0.930695i	$-0.380797\pi$
$947$	1.71472e16	0.731593	0.365796	+	0.930695i	$0.380797\pi$
$948$	−5.71173e15	−0.242282
$949$	3.27460e15	0.138100
$950$	0	0
$951$	−1.61262e16	−0.672263
$952$	−1.79428e15	−0.0743682
$953$	−1.32342e16	−0.545363	−0.272681	−	0.962104i	$-0.587910\pi$
$953$	−1.32342e16	−0.545363	−0.272681	+	0.962104i	$0.587910\pi$
$954$	−2.61597e15	−0.107181
$955$	0	0
$956$	−4.38449e15	−0.177583
$957$	−1.34619e15	−0.0542116
$958$	−1.16878e16	−0.467975
$959$	9.69388e15	0.385918
$960$	0	0
$961$	−2.39860e16	−0.944014
$962$	1.44544e15	0.0565636
$963$	−8.38233e15	−0.326152
$964$	−6.16437e15	−0.238487
$965$	0	0
$966$	7.11179e15	0.272023
$967$	−2.85016e16	−1.08398	−0.541992	−	0.840383i	$-0.682330\pi$
$967$	−2.85016e16	−1.08398	−0.541992	+	0.840383i	$0.682330\pi$
$968$	−9.16024e15	−0.346412
$969$	−1.86301e15	−0.0700542
$970$	0	0
$971$	−1.14914e16	−0.427235	−0.213617	−	0.976917i	$-0.568525\pi$
$971$	−1.14914e16	−0.427235	−0.213617	+	0.976917i	$0.568525\pi$
$972$	8.67624e14	0.0320750
$973$	−5.23428e16	−1.92414
$974$	−9.96992e15	−0.364433
$975$	0	0
$976$	8.67000e15	0.313361
$977$	5.79239e15	0.208180	0.104090	−	0.994568i	$-0.466807\pi$
$977$	5.79239e15	0.208180	0.104090	+	0.994568i	$0.466807\pi$
$978$	1.00242e16	0.358251
$979$	6.06214e13	0.00215437
$980$	0	0
$981$	1.23018e15	0.0432305
$982$	−2.36257e16	−0.825605
$983$	−1.26558e16	−0.439791	−0.219895	−	0.975523i	$-0.570572\pi$
$983$	−1.26558e16	−0.439791	−0.219895	+	0.975523i	$0.570572\pi$
$984$	−3.54436e15	−0.122480
$985$	0	0
$986$	−2.52242e15	−0.0861973
$987$	1.04137e16	0.353882
$988$	2.21674e15	0.0749121
$989$	−1.81545e16	−0.610106
$990$	0	0
$991$	7.36077e14	0.0244635	0.0122317	−	0.999925i	$-0.496106\pi$
$991$	7.36077e14	0.0244635	0.0122317	+	0.999925i	$0.496106\pi$
$992$	1.26555e15	0.0418277
$993$	−3.28553e16	−1.07990
$994$	2.56249e16	0.837601
$995$	0	0
$996$	8.87151e15	0.286795
$997$	−3.93520e16	−1.26515	−0.632577	−	0.774498i	$-0.718003\pi$
$997$	−3.93520e16	−1.26515	−0.632577	+	0.774498i	$0.718003\pi$
$998$	−2.96569e16	−0.948216
$999$	2.12502e15	0.0675697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.12.a.s.1.2	yes	2
5.2	odd	4		150.12.c.m.49.4		4
5.3	odd	4		150.12.c.m.49.1		4
5.4	even	2		150.12.a.j.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.12.a.j.1.1	✓	2	5.4	even	2
150.12.a.s.1.2	yes	2	1.1	even	1	trivial
150.12.c.m.49.1		4	5.3	odd	4
150.12.c.m.49.4		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	150.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +7776.00 q^{6} +50692.2 q^{7} +32768.0 q^{8} +59049.0 q^{9} -75916.1 q^{11} +248832. q^{12} +305005. q^{13} +1.62215e6 q^{14} +1.04858e6 q^{16} -1.08019e6 q^{17} +1.88957e6 q^{18} +7.09756e6 q^{19} +1.23182e7 q^{21} -2.42932e6 q^{22} +1.80419e7 q^{23} +7.96262e6 q^{24} +9.76015e6 q^{26} +1.43489e7 q^{27} +5.19088e7 q^{28} +7.29738e7 q^{29} +3.77162e7 q^{31} +3.35544e7 q^{32} -1.84476e7 q^{33} -3.45660e7 q^{34} +6.04662e7 q^{36} +1.48096e8 q^{37} +2.27122e8 q^{38} +7.41161e7 q^{39} -4.45125e8 q^{41} +3.94182e8 q^{42} -1.00624e9 q^{43} -7.77381e7 q^{44} +5.77340e8 q^{46} +8.45388e8 q^{47} +2.54804e8 q^{48} +5.92368e8 q^{49} -2.62486e8 q^{51} +3.12325e8 q^{52} -1.38443e9 q^{53} +4.59165e8 q^{54} +1.66108e9 q^{56} +1.72471e9 q^{57} +2.33516e9 q^{58} +9.47897e9 q^{59} +8.26835e9 q^{61} +1.20692e9 q^{62} +2.99332e9 q^{63} +1.07374e9 q^{64} -5.90324e8 q^{66} -2.06345e10 q^{67} -1.10611e9 q^{68} +4.38418e9 q^{69} +1.57969e10 q^{71} +1.93492e9 q^{72} +1.07362e10 q^{73} +4.73907e9 q^{74} +7.26790e9 q^{76} -3.84835e9 q^{77} +2.37172e9 q^{78} -2.29541e10 q^{79} +3.48678e9 q^{81} -1.42440e10 q^{82} +3.56526e10 q^{83} +1.26138e10 q^{84} -3.21998e10 q^{86} +1.77326e10 q^{87} -2.48762e9 q^{88} -7.98531e8 q^{89} +1.54613e10 q^{91} +1.84749e10 q^{92} +9.16503e9 q^{93} +2.70524e10 q^{94} +8.15373e9 q^{96} -4.48480e10 q^{97} +1.89558e10 q^{98} -4.48277e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} + 486 q^{3} + 2048 q^{4} + 15552 q^{6} - 24058 q^{7} + 65536 q^{8} + 118098 q^{9} + 726264 q^{11} + 497664 q^{12} + 860894 q^{13} - 769856 q^{14} + 2097152 q^{16} + 6996912 q^{17} + 3779136 q^{18}+ \cdots + 42885162936 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 + 486 * q^3 + 2048 * q^4 + 15552 * q^6 - 24058 * q^7 + 65536 * q^8 + 118098 * q^9 + 726264 * q^11 + 497664 * q^12 + 860894 * q^13 - 769856 * q^14 + 2097152 * q^16 + 6996912 * q^17 + 3779136 * q^18 - 3241370 * q^19 - 5846094 * q^21 + 23240448 * q^22 - 4434096 * q^23 + 15925248 * q^24 + 27548608 * q^26 + 28697814 * q^27 - 24635392 * q^28 - 76210680 * q^29 - 12000926 * q^31 + 67108864 * q^32 + 176482152 * q^33 + 223901184 * q^34 + 120932352 * q^36 + 327050852 * q^37 - 103723840 * q^38 + 209197242 * q^39 + 352006044 * q^41 - 187075008 * q^42 + 907686614 * q^43 + 743694336 * q^44 - 141891072 * q^46 + 2292398292 * q^47 + 509607936 * q^48 + 4202628396 * q^49 + 1700249616 * q^51 + 881555456 * q^52 - 4539974436 * q^53 + 918330048 * q^54 - 788332544 * q^56 - 787652910 * q^57 - 2438741760 * q^58 + 6067482180 * q^59 + 13474911814 * q^61 - 384029632 * q^62 - 1420600842 * q^63 + 2147483648 * q^64 + 5647428864 * q^66 - 4794289018 * q^67 + 7164837888 * q^68 - 1077485328 * q^69 + 29632732284 * q^71 + 3869835264 * q^72 + 43334804804 * q^73 + 10465627264 * q^74 - 3319162880 * q^76 - 63811447056 * q^77 + 6694311744 * q^78 - 2876054480 * q^79 + 6973568802 * q^81 + 11264193408 * q^82 + 29784832284 * q^83 - 5986400256 * q^84 + 29045971648 * q^86 - 18519195240 * q^87 + 23798218752 * q^88 + 62927959920 * q^89 - 26091470326 * q^91 - 4540514304 * q^92 - 2916225018 * q^93 + 73356745344 * q^94 + 16307453952 * q^96 - 141777577858 * q^97 + 134484108672 * q^98 + 42885162936 * q^99

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