LMFDB - Embedded newform 150.12.a.t.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)

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")

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);

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 = [3,-96,729,3072,0,-23328,-67384] 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:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 175039x - 13178910 $ x^3 - 175039*x - 13178910
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 5^{3} $
Twist minimal:	no (minimal twist has level 30)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$451.888$ 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)

$f(q)$	$=$	\(q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} -7776.00 q^{6} -41527.6 q^{7} -32768.0 q^{8} +59049.0 q^{9} +839520. q^{11} +248832. q^{12} +1.66178e6 q^{13} +1.32888e6 q^{14} +1.04858e6 q^{16} -3.23669e6 q^{17} -1.88957e6 q^{18} +5.44307e6 q^{19} -1.00912e7 q^{21} -2.68646e7 q^{22} -2.97481e7 q^{23} -7.96262e6 q^{24} -5.31769e7 q^{26} +1.43489e7 q^{27} -4.25243e7 q^{28} +1.55089e8 q^{29} -2.76977e8 q^{31} -3.35544e7 q^{32} +2.04003e8 q^{33} +1.03574e8 q^{34} +6.04662e7 q^{36} +4.58098e8 q^{37} -1.74178e8 q^{38} +4.03812e8 q^{39} +1.42131e8 q^{41} +3.22919e8 q^{42} +1.09829e9 q^{43} +8.59668e8 q^{44} +9.51939e8 q^{46} -1.89330e9 q^{47} +2.54804e8 q^{48} -2.52786e8 q^{49} -7.86516e8 q^{51} +1.70166e9 q^{52} -1.28322e9 q^{53} -4.59165e8 q^{54} +1.36078e9 q^{56} +1.32267e9 q^{57} -4.96286e9 q^{58} -5.01298e9 q^{59} +7.45699e9 q^{61} +8.86325e9 q^{62} -2.45216e9 q^{63} +1.07374e9 q^{64} -6.52811e9 q^{66} -1.14069e9 q^{67} -3.31437e9 q^{68} -7.22879e9 q^{69} +8.23753e9 q^{71} -1.93492e9 q^{72} -1.90626e10 q^{73} -1.46591e10 q^{74} +5.57371e9 q^{76} -3.48632e10 q^{77} -1.29220e10 q^{78} +2.39605e10 q^{79} +3.48678e9 q^{81} -4.54818e9 q^{82} +6.55948e10 q^{83} -1.03334e10 q^{84} -3.51452e10 q^{86} +3.76867e10 q^{87} -2.75094e10 q^{88} +3.18476e10 q^{89} -6.90096e10 q^{91} -3.04621e10 q^{92} -6.73053e10 q^{93} +6.05855e10 q^{94} -8.15373e9 q^{96} -4.42047e10 q^{97} +8.08914e9 q^{98} +4.95728e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 96 q^{2} + 729 q^{3} + 3072 q^{4} - 23328 q^{6} - 67384 q^{7} - 98304 q^{8} + 177147 q^{9} + 876700 q^{11} + 746496 q^{12} - 315192 q^{13} + 2156288 q^{14} + 3145728 q^{16} - 2874324 q^{17} - 5668704 q^{18}+ \cdots + 51768258300 q^{99}+O(q^{100}) $ 3 * q - 96 * q^2 + 729 * q^3 + 3072 * q^4 - 23328 * q^6 - 67384 * q^7 - 98304 * q^8 + 177147 * q^9 + 876700 * q^11 + 746496 * q^12 - 315192 * q^13 + 2156288 * q^14 + 3145728 * q^16 - 2874324 * q^17 - 5668704 * q^18 + 2034912 * q^19 - 16374312 * q^21 - 28054400 * q^22 - 49866300 * q^23 - 23887872 * q^24 + 10086144 * q^26 + 43046721 * q^27 - 69001216 * q^28 - 35857782 * q^29 - 61121676 * q^31 - 100663296 * q^32 + 213038100 * q^33 + 91978368 * q^34 + 181398528 * q^36 + 935590592 * q^37 - 65117184 * q^38 - 76591656 * q^39 + 1003384282 * q^41 + 523977984 * q^42 + 980338484 * q^43 + 897740800 * q^44 + 1595721600 * q^46 + 2190634500 * q^47 + 764411904 * q^48 + 4795452723 * q^49 - 698460732 * q^51 - 322756608 * q^52 - 6993816924 * q^53 - 1377495072 * q^54 + 2208038912 * q^56 + 494483616 * q^57 + 1147449024 * q^58 + 2034730100 * q^59 - 6193233330 * q^61 + 1955893632 * q^62 - 3978957816 * q^63 + 3221225472 * q^64 - 6817219200 * q^66 - 5079955484 * q^67 - 2943307776 * q^68 - 12117510900 * q^69 + 6851752800 * q^71 - 5804752896 * q^72 - 54889949992 * q^73 - 29938898944 * q^74 + 2083749888 * q^76 + 32141607600 * q^77 + 2450932992 * q^78 + 6719163876 * q^79 + 10460353203 * q^81 - 32108297024 * q^82 - 57462212652 * q^83 - 16767295488 * q^84 - 31370831488 * q^86 - 8713441026 * q^87 - 28727705600 * q^88 + 63718294546 * q^89 + 135921691776 * q^91 - 51063091200 * q^92 - 14852567268 * q^93 - 70100304000 * q^94 - 24461180928 * q^96 - 315259594808 * q^97 - 153454487136 * q^98 + 51768258300 * 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
$7$	−41527.6	−0.933894	−0.466947	−	0.884285i	$-0.654646\pi$
$7$	−41527.6	−0.933894	−0.466947	+	0.884285i	$0.654646\pi$
$8$	−32768.0	−0.353553
$9$	59049.0	0.333333
$10$	0	0
$11$	839520.	1.57171	0.785853	−	0.618414i	$-0.212224\pi$
$11$	839520.	1.57171	0.785853	+	0.618414i	$0.212224\pi$
$12$	248832.	0.288675
$13$	1.66178e6	1.24132	0.620661	−	0.784079i	$-0.286864\pi$
$13$	1.66178e6	1.24132	0.620661	+	0.784079i	$0.286864\pi$
$14$	1.32888e6	0.660363
$15$	0	0
$16$	1.04858e6	0.250000
$17$	−3.23669e6	−0.552882	−0.276441	−	0.961031i	$-0.589155\pi$
$17$	−3.23669e6	−0.552882	−0.276441	+	0.961031i	$0.589155\pi$
$18$	−1.88957e6	−0.235702
$19$	5.44307e6	0.504312	0.252156	−	0.967687i	$-0.418860\pi$
$19$	5.44307e6	0.504312	0.252156	+	0.967687i	$0.418860\pi$
$20$	0	0
$21$	−1.00912e7	−0.539184
$22$	−2.68646e7	−1.11136
$23$	−2.97481e7	−0.963732	−0.481866	−	0.876245i	$-0.660041\pi$
$23$	−2.97481e7	−0.963732	−0.481866	+	0.876245i	$0.660041\pi$
$24$	−7.96262e6	−0.204124
$25$	0	0
$26$	−5.31769e7	−0.877747
$27$	1.43489e7	0.192450
$28$	−4.25243e7	−0.466947
$29$	1.55089e8	1.40408	0.702042	−	0.712136i	$-0.252272\pi$
$29$	1.55089e8	1.40408	0.702042	+	0.712136i	$0.252272\pi$
$30$	0	0
$31$	−2.76977e8	−1.73762	−0.868808	−	0.495150i	$-0.835113\pi$
$31$	−2.76977e8	−1.73762	−0.868808	+	0.495150i	$0.835113\pi$
$32$	−3.35544e7	−0.176777
$33$	2.04003e8	0.907425
$34$	1.03574e8	0.390946
$35$	0	0
$36$	6.04662e7	0.166667
$37$	4.58098e8	1.08605	0.543023	−	0.839718i	$-0.317280\pi$
$37$	4.58098e8	1.08605	0.543023	+	0.839718i	$0.317280\pi$
$38$	−1.74178e8	−0.356602
$39$	4.03812e8	0.716678
$40$	0	0
$41$	1.42131e8	0.191592	0.0957958	−	0.995401i	$-0.469460\pi$
$41$	1.42131e8	0.191592	0.0957958	+	0.995401i	$0.469460\pi$
$42$	3.22919e8	0.381261
$43$	1.09829e9	1.13930	0.569652	−	0.821886i	$-0.307078\pi$
$43$	1.09829e9	1.13930	0.569652	+	0.821886i	$0.307078\pi$
$44$	8.59668e8	0.785853
$45$	0	0
$46$	9.51939e8	0.681461
$47$	−1.89330e9	−1.20415	−0.602075	−	0.798440i	$-0.705659\pi$
$47$	−1.89330e9	−1.20415	−0.602075	+	0.798440i	$0.705659\pi$
$48$	2.54804e8	0.144338
$49$	−2.52786e8	−0.127842
$50$	0	0
$51$	−7.86516e8	−0.319206
$52$	1.70166e9	0.620661
$53$	−1.28322e9	−0.421487	−0.210743	−	0.977541i	$-0.567588\pi$
$53$	−1.28322e9	−0.421487	−0.210743	+	0.977541i	$0.567588\pi$
$54$	−4.59165e8	−0.136083
$55$	0	0
$56$	1.36078e9	0.330181
$57$	1.32267e9	0.291165
$58$	−4.96286e9	−0.992837
$59$	−5.01298e9	−0.912872	−0.456436	−	0.889756i	$-0.650874\pi$
$59$	−5.01298e9	−0.912872	−0.456436	+	0.889756i	$0.650874\pi$
$60$	0	0
$61$	7.45699e9	1.13045	0.565223	−	0.824938i	$-0.308790\pi$
$61$	7.45699e9	1.13045	0.565223	+	0.824938i	$0.308790\pi$
$62$	8.86325e9	1.22868
$63$	−2.45216e9	−0.311298
$64$	1.07374e9	0.125000
$65$	0	0
$66$	−6.52811e9	−0.641646
$67$	−1.14069e9	−0.103219	−0.0516093	−	0.998667i	$-0.516435\pi$
$67$	−1.14069e9	−0.103219	−0.0516093	+	0.998667i	$0.516435\pi$
$68$	−3.31437e9	−0.276441
$69$	−7.22879e9	−0.556411
$70$	0	0
$71$	8.23753e9	0.541847	0.270923	−	0.962601i	$-0.412671\pi$
$71$	8.23753e9	0.541847	0.270923	+	0.962601i	$0.412671\pi$
$72$	−1.93492e9	−0.117851
$73$	−1.90626e10	−1.07623	−0.538116	−	0.842871i	$-0.680864\pi$
$73$	−1.90626e10	−1.07623	−0.538116	+	0.842871i	$0.680864\pi$
$74$	−1.46591e10	−0.767951
$75$	0	0
$76$	5.57371e9	0.252156
$77$	−3.48632e10	−1.46781
$78$	−1.29220e10	−0.506768
$79$	2.39605e10	0.876085	0.438042	−	0.898954i	$-0.355672\pi$
$79$	2.39605e10	0.876085	0.438042	+	0.898954i	$0.355672\pi$
$80$	0	0
$81$	3.48678e9	0.111111
$82$	−4.54818e9	−0.135476
$83$	6.55948e10	1.82785	0.913924	−	0.405885i	$-0.133037\pi$
$83$	6.55948e10	1.82785	0.913924	+	0.405885i	$0.133037\pi$
$84$	−1.03334e10	−0.269592
$85$	0	0
$86$	−3.51452e10	−0.805610
$87$	3.76867e10	0.810648
$88$	−2.75094e10	−0.555682
$89$	3.18476e10	0.604549	0.302274	−	0.953221i	$-0.402254\pi$
$89$	3.18476e10	0.604549	0.302274	+	0.953221i	$0.402254\pi$
$90$	0	0
$91$	−6.90096e10	−1.15926
$92$	−3.04621e10	−0.481866
$93$	−6.73053e10	−1.00321
$94$	6.05855e10	0.851462
$95$	0	0
$96$	−8.15373e9	−0.102062
$97$	−4.42047e10	−0.522665	−0.261333	−	0.965249i	$-0.584162\pi$
$97$	−4.42047e10	−0.522665	−0.261333	+	0.965249i	$0.584162\pi$
$98$	8.08914e9	0.0903980
$99$	4.95728e10	0.523902
$100$	0	0
$101$	1.88396e11	1.78362	0.891812	−	0.452407i	$-0.149435\pi$
$101$	1.88396e11	1.78362	0.891812	+	0.452407i	$0.149435\pi$
$102$	2.51685e10	0.225713
$103$	−1.74933e11	−1.48685	−0.743424	−	0.668820i	$-0.766800\pi$
$103$	−1.74933e11	−1.48685	−0.743424	+	0.668820i	$0.766800\pi$
$104$	−5.44531e10	−0.438874
$105$	0	0
$106$	4.10630e10	0.298036
$107$	−1.75156e11	−1.20730	−0.603650	−	0.797249i	$-0.706288\pi$
$107$	−1.75156e11	−1.20730	−0.603650	+	0.797249i	$0.706288\pi$
$108$	1.46933e10	0.0962250
$109$	5.67974e10	0.353576	0.176788	−	0.984249i	$-0.443429\pi$
$109$	5.67974e10	0.353576	0.176788	+	0.984249i	$0.443429\pi$
$110$	0	0
$111$	1.11318e11	0.627029
$112$	−4.35448e10	−0.233473
$113$	−7.76853e10	−0.396650	−0.198325	−	0.980136i	$-0.563550\pi$
$113$	−7.76853e10	−0.396650	−0.198325	+	0.980136i	$0.563550\pi$
$114$	−4.23253e10	−0.205884
$115$	0	0
$116$	1.58811e11	0.702042
$117$	9.81263e10	0.413774
$118$	1.60415e11	0.645498
$119$	1.34412e11	0.516333
$120$	0	0
$121$	4.19482e11	1.47026
$122$	−2.38624e11	−0.799346
$123$	3.45377e10	0.110615
$124$	−2.83624e11	−0.868808
$125$	0	0
$126$	7.84692e10	0.220121
$127$	2.44393e11	0.656401	0.328200	−	0.944608i	$-0.393558\pi$
$127$	2.44393e11	0.656401	0.328200	+	0.944608i	$0.393558\pi$
$128$	−3.43597e10	−0.0883883
$129$	2.66884e11	0.657778
$130$	0	0
$131$	3.21349e10	0.0727755	0.0363877	−	0.999338i	$-0.488415\pi$
$131$	3.21349e10	0.0727755	0.0363877	+	0.999338i	$0.488415\pi$
$132$	2.08899e11	0.453712
$133$	−2.26038e11	−0.470974
$134$	3.65022e10	0.0729866
$135$	0	0
$136$	1.06060e11	0.195473
$137$	1.03419e12	1.83079	0.915395	−	0.402557i	$-0.131878\pi$
$137$	1.03419e12	1.83079	0.915395	+	0.402557i	$0.131878\pi$
$138$	2.31321e11	0.393442
$139$	−6.51000e11	−1.06414	−0.532071	−	0.846700i	$-0.678586\pi$
$139$	−6.51000e11	−1.06414	−0.532071	+	0.846700i	$0.678586\pi$
$140$	0	0
$141$	−4.60071e11	−0.695216
$142$	−2.63601e11	−0.383143
$143$	1.39510e12	1.95099
$144$	6.19174e10	0.0833333
$145$	0	0
$146$	6.10002e11	0.761011
$147$	−6.14269e10	−0.0738097
$148$	4.69092e11	0.543023
$149$	1.48776e12	1.65962	0.829808	−	0.558049i	$-0.188450\pi$
$149$	1.48776e12	1.65962	0.829808	+	0.558049i	$0.188450\pi$
$150$	0	0
$151$	1.69992e12	1.76220	0.881100	−	0.472929i	$-0.156803\pi$
$151$	1.69992e12	1.76220	0.881100	+	0.472929i	$0.156803\pi$
$152$	−1.78359e11	−0.178301
$153$	−1.91123e11	−0.184294
$154$	1.11562e12	1.03790
$155$	0	0
$156$	4.13503e11	0.358339
$157$	−3.75740e11	−0.314369	−0.157184	−	0.987569i	$-0.550242\pi$
$157$	−3.75740e11	−0.314369	−0.157184	+	0.987569i	$0.550242\pi$
$158$	−7.66735e11	−0.619485
$159$	−3.11822e11	−0.243345
$160$	0	0
$161$	1.23537e12	0.900023
$162$	−1.11577e11	−0.0785674
$163$	1.19182e12	0.811296	0.405648	−	0.914029i	$-0.367046\pi$
$163$	1.19182e12	0.811296	0.405648	+	0.914029i	$0.367046\pi$
$164$	1.45542e11	0.0957958
$165$	0	0
$166$	−2.09903e12	−1.29248
$167$	7.86209e11	0.468379	0.234190	−	0.972191i	$-0.424756\pi$
$167$	7.86209e11	0.468379	0.234190	+	0.972191i	$0.424756\pi$
$168$	3.30669e11	0.190630
$169$	9.69345e11	0.540880
$170$	0	0
$171$	3.21408e11	0.168104
$172$	1.12465e12	0.569652
$173$	2.61407e11	0.128252	0.0641258	−	0.997942i	$-0.479574\pi$
$173$	2.61407e11	0.128252	0.0641258	+	0.997942i	$0.479574\pi$
$174$	−1.20597e12	−0.573215
$175$	0	0
$176$	8.80300e11	0.392926
$177$	−1.21815e12	−0.527047
$178$	−1.01912e12	−0.427481
$179$	1.08084e12	0.439614	0.219807	−	0.975543i	$-0.429457\pi$
$179$	1.08084e12	0.439614	0.219807	+	0.975543i	$0.429457\pi$
$180$	0	0
$181$	3.87701e12	1.48342	0.741711	−	0.670720i	$-0.234015\pi$
$181$	3.87701e12	1.48342	0.741711	+	0.670720i	$0.234015\pi$
$182$	2.20831e12	0.819723
$183$	1.81205e12	0.652663
$184$	9.74786e11	0.340731
$185$	0	0
$186$	2.15377e12	0.709378
$187$	−2.71727e12	−0.868967
$188$	−1.93874e12	−0.602075
$189$	−5.95876e11	−0.179728
$190$	0	0
$191$	4.34227e12	1.23604	0.618021	−	0.786161i	$-0.287935\pi$
$191$	4.34227e12	1.23604	0.618021	+	0.786161i	$0.287935\pi$
$192$	2.60919e11	0.0721688
$193$	4.45221e11	0.119677	0.0598384	−	0.998208i	$-0.480941\pi$
$193$	4.45221e11	0.119677	0.0598384	+	0.998208i	$0.480941\pi$
$194$	1.41455e12	0.369580
$195$	0	0
$196$	−2.58852e11	−0.0639210
$197$	1.92250e12	0.461640	0.230820	−	0.972997i	$-0.425859\pi$
$197$	1.92250e12	0.461640	0.230820	+	0.972997i	$0.425859\pi$
$198$	−1.58633e12	−0.370455
$199$	−2.52317e12	−0.573131	−0.286566	−	0.958061i	$-0.592514\pi$
$199$	−2.52317e12	−0.573131	−0.286566	+	0.958061i	$0.592514\pi$
$200$	0	0
$201$	−2.77189e11	−0.0595933
$202$	−6.02866e12	−1.26121
$203$	−6.44048e12	−1.31126
$204$	−8.05392e11	−0.159603
$205$	0	0
$206$	5.59785e12	1.05136
$207$	−1.75660e12	−0.321244
$208$	1.74250e12	0.310331
$209$	4.56957e12	0.792630
$210$	0	0
$211$	7.60254e12	1.25143	0.625713	−	0.780053i	$-0.284808\pi$
$211$	7.60254e12	1.25143	0.625713	+	0.780053i	$0.284808\pi$
$212$	−1.31402e12	−0.210743
$213$	2.00172e12	0.312835
$214$	5.60501e12	0.853690
$215$	0	0
$216$	−4.70185e11	−0.0680414
$217$	1.15022e13	1.62275
$218$	−1.81752e12	−0.250016
$219$	−4.63221e12	−0.621363
$220$	0	0
$221$	−5.37866e12	−0.686304
$222$	−3.56217e12	−0.443377
$223$	−2.46671e12	−0.299531	−0.149765	−	0.988722i	$-0.547852\pi$
$223$	−2.46671e12	−0.299531	−0.149765	+	0.988722i	$0.547852\pi$
$224$	1.39343e12	0.165091
$225$	0	0
$226$	2.48593e12	0.280474
$227$	−1.11438e13	−1.22713	−0.613567	−	0.789642i	$-0.710266\pi$
$227$	−1.11438e13	−1.22713	−0.613567	+	0.789642i	$0.710266\pi$
$228$	1.35441e12	0.145582
$229$	−1.12840e13	−1.18404	−0.592021	−	0.805923i	$-0.701670\pi$
$229$	−1.12840e13	−1.18404	−0.592021	+	0.805923i	$0.701670\pi$
$230$	0	0
$231$	−8.47177e12	−0.847438
$232$	−5.08197e12	−0.496418
$233$	−3.66685e12	−0.349813	−0.174906	−	0.984585i	$-0.555962\pi$
$233$	−3.66685e12	−0.349813	−0.174906	+	0.984585i	$0.555962\pi$
$234$	−3.14004e12	−0.292582
$235$	0	0
$236$	−5.13329e12	−0.456436
$237$	5.82239e12	0.505808
$238$	−4.30118e12	−0.365102
$239$	1.40189e13	1.16285	0.581427	−	0.813598i	$-0.302494\pi$
$239$	1.40189e13	1.16285	0.581427	+	0.813598i	$0.302494\pi$
$240$	0	0
$241$	−1.19865e13	−0.949723	−0.474862	−	0.880060i	$-0.657502\pi$
$241$	−1.19865e13	−0.949723	−0.474862	+	0.880060i	$0.657502\pi$
$242$	−1.34234e13	−1.03963
$243$	8.47289e11	0.0641500
$244$	7.63596e12	0.565223
$245$	0	0
$246$	−1.10521e12	−0.0782169
$247$	9.04517e12	0.626014
$248$	9.07597e12	0.614340
$249$	1.59395e13	1.05531
$250$	0	0
$251$	−4.71793e12	−0.298914	−0.149457	−	0.988768i	$-0.547753\pi$
$251$	−4.71793e12	−0.298914	−0.149457	+	0.988768i	$0.547753\pi$
$252$	−2.51101e12	−0.155649
$253$	−2.49741e13	−1.51470
$254$	−7.82059e12	−0.464146
$255$	0	0
$256$	1.09951e12	0.0625000
$257$	2.26178e13	1.25840	0.629199	−	0.777244i	$-0.283383\pi$
$257$	2.26178e13	1.25840	0.629199	+	0.777244i	$0.283383\pi$
$258$	−8.54029e12	−0.465119
$259$	−1.90237e13	−1.01425
$260$	0	0
$261$	9.15787e12	0.468028
$262$	−1.02832e12	−0.0514600
$263$	2.63896e13	1.29323	0.646617	−	0.762815i	$-0.276183\pi$
$263$	2.63896e13	1.29323	0.646617	+	0.762815i	$0.276183\pi$
$264$	−6.68478e12	−0.320823
$265$	0	0
$266$	7.23321e12	0.333029
$267$	7.73896e12	0.349036
$268$	−1.16807e12	−0.0516093
$269$	1.82859e13	0.791550	0.395775	−	0.918347i	$-0.370476\pi$
$269$	1.82859e13	0.791550	0.395775	+	0.918347i	$0.370476\pi$
$270$	0	0
$271$	−2.37685e13	−0.987803	−0.493902	−	0.869518i	$-0.664430\pi$
$271$	−2.37685e13	−0.987803	−0.493902	+	0.869518i	$0.664430\pi$
$272$	−3.39392e12	−0.138220
$273$	−1.67693e13	−0.669301
$274$	−3.30942e13	−1.29456
$275$	0	0
$276$	−7.40228e12	−0.278205
$277$	2.00012e13	0.736914	0.368457	−	0.929645i	$-0.379886\pi$
$277$	2.00012e13	0.736914	0.368457	+	0.929645i	$0.379886\pi$
$278$	2.08320e13	0.752462
$279$	−1.63552e13	−0.579205
$280$	0	0
$281$	2.16062e13	0.735689	0.367845	−	0.929887i	$-0.380096\pi$
$281$	2.16062e13	0.735689	0.367845	+	0.929887i	$0.380096\pi$
$282$	1.47223e13	0.491592
$283$	4.22652e13	1.38407	0.692034	−	0.721865i	$-0.256715\pi$
$283$	4.22652e13	1.38407	0.692034	+	0.721865i	$0.256715\pi$
$284$	8.43523e12	0.270923
$285$	0	0
$286$	−4.46431e13	−1.37956
$287$	−5.90234e12	−0.178926
$288$	−1.98136e12	−0.0589256
$289$	−2.37957e13	−0.694322
$290$	0	0
$291$	−1.07417e13	−0.301761
$292$	−1.95201e13	−0.538116
$293$	5.66640e13	1.53298	0.766488	−	0.642259i	$-0.222003\pi$
$293$	5.66640e13	1.53298	0.766488	+	0.642259i	$0.222003\pi$
$294$	1.96566e12	0.0521913
$295$	0	0
$296$	−1.50109e13	−0.383975
$297$	1.20462e13	0.302475
$298$	−4.76082e13	−1.17353
$299$	−4.94347e13	−1.19630
$300$	0	0
$301$	−4.56093e13	−1.06399
$302$	−5.43975e13	−1.24606
$303$	4.57801e13	1.02978
$304$	5.70747e12	0.126078
$305$	0	0
$306$	6.11595e12	0.130315
$307$	1.99364e13	0.417239	0.208619	−	0.977997i	$-0.433103\pi$
$307$	1.99364e13	0.417239	0.208619	+	0.977997i	$0.433103\pi$
$308$	−3.57000e13	−0.733903
$309$	−4.25087e13	−0.858433
$310$	0	0
$311$	1.05339e13	0.205309	0.102655	−	0.994717i	$-0.467266\pi$
$311$	1.05339e13	0.205309	0.102655	+	0.994717i	$0.467266\pi$
$312$	−1.32321e13	−0.253384
$313$	−5.27355e13	−0.992224	−0.496112	−	0.868259i	$-0.665239\pi$
$313$	−5.27355e13	−0.992224	−0.496112	+	0.868259i	$0.665239\pi$
$314$	1.20237e13	0.222292
$315$	0	0
$316$	2.45355e13	0.438042
$317$	6.68311e13	1.17261	0.586304	−	0.810091i	$-0.300583\pi$
$317$	6.68311e13	1.17261	0.586304	+	0.810091i	$0.300583\pi$
$318$	9.97832e12	0.172071
$319$	1.30201e14	2.20681
$320$	0	0
$321$	−4.25630e13	−0.697035
$322$	−3.95317e13	−0.636412
$323$	−1.76175e13	−0.278825
$324$	3.57047e12	0.0555556
$325$	0	0
$326$	−3.81383e13	−0.573673
$327$	1.38018e13	0.204137
$328$	−4.65734e12	−0.0677379
$329$	7.86241e13	1.12455
$330$	0	0
$331$	2.79590e13	0.386783	0.193392	−	0.981122i	$-0.438051\pi$
$331$	2.79590e13	0.386783	0.193392	+	0.981122i	$0.438051\pi$
$332$	6.71691e13	0.913924
$333$	2.70502e13	0.362016
$334$	−2.51587e13	−0.331194
$335$	0	0
$336$	−1.05814e13	−0.134796
$337$	−1.16982e14	−1.46606	−0.733032	−	0.680194i	$-0.761896\pi$
$337$	−1.16982e14	−1.46606	−0.733032	+	0.680194i	$0.761896\pi$
$338$	−3.10190e13	−0.382460
$339$	−1.88775e13	−0.229006
$340$	0	0
$341$	−2.32527e14	−2.73102
$342$	−1.02851e13	−0.118867
$343$	9.26112e13	1.05328
$344$	−3.59887e13	−0.402805
$345$	0	0
$346$	−8.36501e12	−0.0906876
$347$	1.62553e12	0.0173453	0.00867265	−	0.999962i	$-0.497239\pi$
$347$	1.62553e12	0.0173453	0.00867265	+	0.999962i	$0.497239\pi$
$348$	3.85912e13	0.405324
$349$	−1.40028e14	−1.44769	−0.723843	−	0.689965i	$-0.757626\pi$
$349$	−1.40028e14	−1.44769	−0.723843	+	0.689965i	$0.757626\pi$
$350$	0	0
$351$	2.38447e13	0.238893
$352$	−2.81696e13	−0.277841
$353$	1.07894e13	0.104770	0.0523850	−	0.998627i	$-0.483318\pi$
$353$	1.07894e13	0.104770	0.0523850	+	0.998627i	$0.483318\pi$
$354$	3.89809e13	0.372678
$355$	0	0
$356$	3.26119e13	0.302274
$357$	3.26621e13	0.298105
$358$	−3.45870e13	−0.310854
$359$	−8.36216e13	−0.740114	−0.370057	−	0.929009i	$-0.620662\pi$
$359$	−8.36216e13	−0.740114	−0.370057	+	0.929009i	$0.620662\pi$
$360$	0	0
$361$	−8.68632e13	−0.745669
$362$	−1.24064e14	−1.04894
$363$	1.01934e14	0.848854
$364$	−7.06659e13	−0.579632
$365$	0	0
$366$	−5.79856e13	−0.461502
$367$	−1.00049e13	−0.0784420	−0.0392210	−	0.999231i	$-0.512488\pi$
$367$	−1.00049e13	−0.0784420	−0.0392210	+	0.999231i	$0.512488\pi$
$368$	−3.11931e13	−0.240933
$369$	8.39267e12	0.0638639
$370$	0	0
$371$	5.32890e13	0.393624
$372$	−6.89206e13	−0.501606
$373$	−2.32365e14	−1.66637	−0.833186	−	0.552993i	$-0.813486\pi$
$373$	−2.32365e14	−1.66637	−0.833186	+	0.552993i	$0.813486\pi$
$374$	8.69525e13	0.614453
$375$	0	0
$376$	6.20395e13	0.425731
$377$	2.57724e14	1.74292
$378$	1.90680e13	0.127087
$379$	1.60902e14	1.05693	0.528465	−	0.848955i	$-0.322768\pi$
$379$	1.60902e14	1.05693	0.528465	+	0.848955i	$0.322768\pi$
$380$	0	0
$381$	5.93876e13	0.378973
$382$	−1.38953e14	−0.874014
$383$	3.41226e12	0.0211568	0.0105784	−	0.999944i	$-0.496633\pi$
$383$	3.41226e12	0.0211568	0.0105784	+	0.999944i	$0.496633\pi$
$384$	−8.34942e12	−0.0510310
$385$	0	0
$386$	−1.42471e13	−0.0846243
$387$	6.48528e13	0.379768
$388$	−4.52656e13	−0.261333
$389$	−2.49915e14	−1.42255	−0.711277	−	0.702912i	$-0.751883\pi$
$389$	−2.49915e14	−1.42255	−0.711277	+	0.702912i	$0.751883\pi$
$390$	0	0
$391$	9.62854e13	0.532830
$392$	8.28328e12	0.0451990
$393$	7.80879e12	0.0420169
$394$	−6.15201e13	−0.326428
$395$	0	0
$396$	5.07626e13	0.261951
$397$	2.50976e14	1.27727	0.638637	−	0.769508i	$-0.279498\pi$
$397$	2.50976e14	1.27727	0.638637	+	0.769508i	$0.279498\pi$
$398$	8.07414e13	0.405265
$399$	−5.49272e13	−0.271917
$400$	0	0
$401$	3.56396e14	1.71648	0.858240	−	0.513248i	$-0.171558\pi$
$401$	3.56396e14	1.71648	0.858240	+	0.513248i	$0.171558\pi$
$402$	8.87004e12	0.0421388
$403$	−4.60273e14	−2.15694
$404$	1.92917e14	0.891812
$405$	0	0
$406$	2.06096e14	0.927204
$407$	3.84582e14	1.70695
$408$	2.57726e13	0.112857
$409$	−4.76849e13	−0.206017	−0.103008	−	0.994680i	$-0.532847\pi$
$409$	−4.76849e13	−0.206017	−0.103008	+	0.994680i	$0.532847\pi$
$410$	0	0
$411$	2.51309e14	1.05701
$412$	−1.79131e14	−0.743424
$413$	2.08177e14	0.852525
$414$	5.62111e13	0.227154
$415$	0	0
$416$	−5.57600e13	−0.219437
$417$	−1.58193e14	−0.614382
$418$	−1.46226e14	−0.560474
$419$	2.26851e14	0.858150	0.429075	−	0.903269i	$-0.358840\pi$
$419$	2.26851e14	0.858150	0.429075	+	0.903269i	$0.358840\pi$
$420$	0	0
$421$	−1.36580e14	−0.503309	−0.251654	−	0.967817i	$-0.580975\pi$
$421$	−1.36580e14	−0.503309	−0.251654	+	0.967817i	$0.580975\pi$
$422$	−2.43281e14	−0.884892
$423$	−1.11797e14	−0.401383
$424$	4.20485e13	0.149018
$425$	0	0
$426$	−6.40551e13	−0.221208
$427$	−3.09671e14	−1.05572
$428$	−1.79360e14	−0.603650
$429$	3.39008e14	1.12641
$430$	0	0
$431$	1.21003e13	0.0391896	0.0195948	−	0.999808i	$-0.493762\pi$
$431$	1.21003e13	0.0391896	0.0195948	+	0.999808i	$0.493762\pi$
$432$	1.50459e13	0.0481125
$433$	3.05977e14	0.966064	0.483032	−	0.875603i	$-0.339536\pi$
$433$	3.05977e14	0.966064	0.483032	+	0.875603i	$0.339536\pi$
$434$	−3.68069e14	−1.14746
$435$	0	0
$436$	5.81606e13	0.176788
$437$	−1.61921e14	−0.486021
$438$	1.48231e14	0.439370
$439$	3.68147e14	1.07762	0.538811	−	0.842427i	$-0.318874\pi$
$439$	3.68147e14	1.07762	0.538811	+	0.842427i	$0.318874\pi$
$440$	0	0
$441$	−1.49267e13	−0.0426140
$442$	1.72117e14	0.485290
$443$	1.38978e13	0.0387012	0.0193506	−	0.999813i	$-0.493840\pi$
$443$	1.38978e13	0.0387012	0.0193506	+	0.999813i	$0.493840\pi$
$444$	1.13989e14	0.313515
$445$	0	0
$446$	7.89347e13	0.211800
$447$	3.61525e14	0.958179
$448$	−4.45899e13	−0.116737
$449$	3.92376e13	0.101472	0.0507362	−	0.998712i	$-0.483843\pi$
$449$	3.92376e13	0.101472	0.0507362	+	0.998712i	$0.483843\pi$
$450$	0	0
$451$	1.19321e14	0.301126
$452$	−7.95497e13	−0.198325
$453$	4.13081e14	1.01741
$454$	3.56602e14	0.867715
$455$	0	0
$456$	−4.33411e13	−0.102942
$457$	−1.37201e14	−0.321973	−0.160986	−	0.986957i	$-0.551468\pi$
$457$	−1.37201e14	−0.321973	−0.160986	+	0.986957i	$0.551468\pi$
$458$	3.61087e14	0.837244
$459$	−4.64430e13	−0.106402
$460$	0	0
$461$	2.48659e14	0.556223	0.278111	−	0.960549i	$-0.410292\pi$
$461$	2.48659e14	0.556223	0.278111	+	0.960549i	$0.410292\pi$
$462$	2.71097e14	0.599229
$463$	−6.31268e14	−1.37885	−0.689427	−	0.724355i	$-0.742138\pi$
$463$	−6.31268e14	−1.37885	−0.689427	+	0.724355i	$0.742138\pi$
$464$	1.62623e14	0.351021
$465$	0	0
$466$	1.17339e14	0.247355
$467$	−8.60246e14	−1.79217	−0.896086	−	0.443880i	$-0.853602\pi$
$467$	−8.60246e14	−1.79217	−0.896086	+	0.443880i	$0.853602\pi$
$468$	1.00481e14	0.206887
$469$	4.73703e13	0.0963952
$470$	0	0
$471$	−9.13048e13	−0.181501
$472$	1.64265e14	0.322749
$473$	9.22035e14	1.79065
$474$	−1.86317e14	−0.357660
$475$	0	0
$476$	1.37638e14	0.258166
$477$	−7.57728e13	−0.140496
$478$	−4.48605e14	−0.822263
$479$	−5.71890e14	−1.03626	−0.518129	−	0.855303i	$-0.673371\pi$
$479$	−5.71890e14	−1.03626	−0.518129	+	0.855303i	$0.673371\pi$
$480$	0	0
$481$	7.61256e14	1.34813
$482$	3.83567e14	0.671556
$483$	3.00194e14	0.519629
$484$	4.29550e14	0.735129
$485$	0	0
$486$	−2.71132e13	−0.0453609
$487$	7.95200e14	1.31543	0.657714	−	0.753268i	$-0.271524\pi$
$487$	7.95200e14	1.31543	0.657714	+	0.753268i	$0.271524\pi$
$488$	−2.44351e14	−0.399673
$489$	2.89612e14	0.468402
$490$	0	0
$491$	−5.04124e13	−0.0797240	−0.0398620	−	0.999205i	$-0.512692\pi$
$491$	−5.04124e13	−0.0797240	−0.0398620	+	0.999205i	$0.512692\pi$
$492$	3.53666e13	0.0553077
$493$	−5.01976e14	−0.776292
$494$	−2.89446e14	−0.442658
$495$	0	0
$496$	−2.90431e14	−0.434404
$497$	−3.42085e14	−0.506027
$498$	−5.10065e14	−0.746216
$499$	−2.91835e14	−0.422264	−0.211132	−	0.977458i	$-0.567715\pi$
$499$	−2.91835e14	−0.422264	−0.211132	+	0.977458i	$0.567715\pi$
$500$	0	0
$501$	1.91049e14	0.270419
$502$	1.50974e14	0.211364
$503$	7.29427e14	1.01008	0.505042	−	0.863095i	$-0.331477\pi$
$503$	7.29427e14	1.01008	0.505042	+	0.863095i	$0.331477\pi$
$504$	8.03525e13	0.110060
$505$	0	0
$506$	7.99172e14	1.07106
$507$	2.35551e14	0.312277
$508$	2.50259e14	0.328200
$509$	−3.75076e14	−0.486600	−0.243300	−	0.969951i	$-0.578230\pi$
$509$	−3.75076e14	−0.486600	−0.243300	+	0.969951i	$0.578230\pi$
$510$	0	0
$511$	7.91623e14	1.00509
$512$	−3.51844e13	−0.0441942
$513$	7.81021e13	0.0970549
$514$	−7.23769e14	−0.889822
$515$	0	0
$516$	2.73289e14	0.328889
$517$	−1.58946e15	−1.89257
$518$	6.08758e14	0.717185
$519$	6.35218e13	0.0740461
$520$	0	0
$521$	−1.27745e15	−1.45793	−0.728967	−	0.684549i	$-0.759999\pi$
$521$	−1.27745e15	−1.45793	−0.728967	+	0.684549i	$0.759999\pi$
$522$	−2.93052e14	−0.330946
$523$	−1.16147e15	−1.29792	−0.648959	−	0.760824i	$-0.724795\pi$
$523$	−1.16147e15	−1.29792	−0.648959	+	0.760824i	$0.724795\pi$
$524$	3.29062e13	0.0363877
$525$	0	0
$526$	−8.44469e14	−0.914454
$527$	8.96487e14	0.960696
$528$	2.13913e14	0.226856
$529$	−6.78604e13	−0.0712213
$530$	0	0
$531$	−2.96011e14	−0.304291
$532$	−2.31463e14	−0.235487
$533$	2.36190e14	0.237827
$534$	−2.47647e14	−0.246806
$535$	0	0
$536$	3.73783e13	0.0364933
$537$	2.62645e14	0.253811
$538$	−5.85149e14	−0.559711
$539$	−2.12219e14	−0.200930
$540$	0	0
$541$	1.14931e15	1.06623	0.533115	−	0.846043i	$-0.321021\pi$
$541$	1.14931e15	1.06623	0.533115	+	0.846043i	$0.321021\pi$
$542$	7.60592e14	0.698482
$543$	9.42113e14	0.856454
$544$	1.08605e14	0.0977366
$545$	0	0
$546$	5.36619e14	0.473267
$547$	5.91724e13	0.0516641	0.0258321	−	0.999666i	$-0.491776\pi$
$547$	5.91724e13	0.0516641	0.0258321	+	0.999666i	$0.491776\pi$
$548$	1.05901e15	0.915395
$549$	4.40328e14	0.376815
$550$	0	0
$551$	8.44162e14	0.708096
$552$	2.36873e14	0.196721
$553$	−9.95020e14	−0.818170
$554$	−6.40037e14	−0.521077
$555$	0	0
$556$	−6.66624e14	−0.532071
$557$	8.98701e14	0.710251	0.355125	−	0.934819i	$-0.384438\pi$
$557$	8.98701e14	0.710251	0.355125	+	0.934819i	$0.384438\pi$
$558$	5.23366e14	0.409560
$559$	1.82511e15	1.41424
$560$	0	0
$561$	−6.60296e14	−0.501699
$562$	−6.91400e14	−0.520211
$563$	−1.00499e15	−0.748799	−0.374399	−	0.927268i	$-0.622151\pi$
$563$	−1.00499e15	−0.748799	−0.374399	+	0.927268i	$0.622151\pi$
$564$	−4.71113e14	−0.347608
$565$	0	0
$566$	−1.35249e15	−0.978684
$567$	−1.44798e14	−0.103766
$568$	−2.69928e14	−0.191572
$569$	2.14457e15	1.50738	0.753691	−	0.657228i	$-0.228271\pi$
$569$	2.14457e15	1.50738	0.753691	+	0.657228i	$0.228271\pi$
$570$	0	0
$571$	−1.36068e15	−0.938119	−0.469060	−	0.883167i	$-0.655407\pi$
$571$	−1.36068e15	−0.938119	−0.469060	+	0.883167i	$0.655407\pi$
$572$	1.42858e15	0.975496
$573$	1.05517e15	0.713629
$574$	1.88875e14	0.126520
$575$	0	0
$576$	6.34034e13	0.0416667
$577$	−9.41505e14	−0.612852	−0.306426	−	0.951894i	$-0.599133\pi$
$577$	−9.41505e14	−0.612852	−0.306426	+	0.951894i	$0.599133\pi$
$578$	7.61463e14	0.490960
$579$	1.08189e14	0.0690955
$580$	0	0
$581$	−2.72400e15	−1.70702
$582$	3.43736e14	0.213377
$583$	−1.07729e15	−0.662453
$584$	6.24642e14	0.380505
$585$	0	0
$586$	−1.81325e15	−1.08398
$587$	−7.11947e14	−0.421636	−0.210818	−	0.977525i	$-0.567613\pi$
$587$	−7.11947e14	−0.421636	−0.210818	+	0.977525i	$0.567613\pi$
$588$	−6.29011e13	−0.0369048
$589$	−1.50760e15	−0.876300
$590$	0	0
$591$	4.67169e14	0.266528
$592$	4.80350e14	0.271512
$593$	−2.44357e15	−1.36844	−0.684218	−	0.729278i	$-0.739856\pi$
$593$	−2.44357e15	−1.36844	−0.684218	+	0.729278i	$0.739856\pi$
$594$	−3.85478e14	−0.213882
$595$	0	0
$596$	1.52346e15	0.829808
$597$	−6.13130e14	−0.330898
$598$	1.58191e15	0.845913
$599$	−6.81013e14	−0.360835	−0.180417	−	0.983590i	$-0.557745\pi$
$599$	−6.81013e14	−0.360835	−0.180417	+	0.983590i	$0.557745\pi$
$600$	0	0
$601$	−1.35124e15	−0.702947	−0.351474	−	0.936198i	$-0.614319\pi$
$601$	−1.35124e15	−0.702947	−0.351474	+	0.936198i	$0.614319\pi$
$602$	1.45950e15	0.752354
$603$	−6.73569e13	−0.0344062
$604$	1.74072e15	0.881100
$605$	0	0
$606$	−1.46496e15	−0.728161
$607$	−2.98246e15	−1.46905	−0.734524	−	0.678582i	$-0.762595\pi$
$607$	−2.98246e15	−1.46905	−0.734524	+	0.678582i	$0.762595\pi$
$608$	−1.82639e14	−0.0891506
$609$	−1.56504e15	−0.757059
$610$	0	0
$611$	−3.14624e15	−1.49474
$612$	−1.95710e14	−0.0921470
$613$	−2.62361e15	−1.22424	−0.612119	−	0.790766i	$-0.709683\pi$
$613$	−2.62361e15	−1.22424	−0.612119	+	0.790766i	$0.709683\pi$
$614$	−6.37964e14	−0.295032
$615$	0	0
$616$	1.14240e15	0.518948
$617$	−1.36222e15	−0.613310	−0.306655	−	0.951821i	$-0.599210\pi$
$617$	−1.36222e15	−0.613310	−0.306655	+	0.951821i	$0.599210\pi$
$618$	1.36028e15	0.607003
$619$	−4.10602e15	−1.81603	−0.908013	−	0.418942i	$-0.862401\pi$
$619$	−4.10602e15	−1.81603	−0.908013	+	0.418942i	$0.862401\pi$
$620$	0	0
$621$	−4.26853e14	−0.185470
$622$	−3.37086e14	−0.145176
$623$	−1.32255e15	−0.564585
$624$	4.23428e14	0.179169
$625$	0	0
$626$	1.68754e15	0.701608
$627$	1.11040e15	0.457625
$628$	−3.84757e14	−0.157184
$629$	−1.48272e15	−0.600455
$630$	0	0
$631$	−3.07651e15	−1.22433	−0.612163	−	0.790731i	$-0.709700\pi$
$631$	−3.07651e15	−1.22433	−0.612163	+	0.790731i	$0.709700\pi$
$632$	−7.85136e14	−0.309743
$633$	1.84742e15	0.722511
$634$	−2.13859e15	−0.829159
$635$	0	0
$636$	−3.19306e14	−0.121673
$637$	−4.20073e14	−0.158693
$638$	−4.16642e15	−1.56045
$639$	4.86418e14	0.180616
$640$	0	0
$641$	−2.43456e14	−0.0888590	−0.0444295	−	0.999013i	$-0.514147\pi$
$641$	−2.43456e14	−0.0888590	−0.0444295	+	0.999013i	$0.514147\pi$
$642$	1.36202e15	0.492878
$643$	6.07705e14	0.218038	0.109019	−	0.994040i	$-0.465229\pi$
$643$	6.07705e14	0.218038	0.109019	+	0.994040i	$0.465229\pi$
$644$	1.26502e15	0.450012
$645$	0	0
$646$	5.63761e14	0.197159
$647$	−3.75432e14	−0.130184	−0.0650919	−	0.997879i	$-0.520734\pi$
$647$	−3.75432e14	−0.130184	−0.0650919	+	0.997879i	$0.520734\pi$
$648$	−1.14255e14	−0.0392837
$649$	−4.20849e15	−1.43477
$650$	0	0
$651$	2.79503e15	0.936894
$652$	1.22042e15	0.405648
$653$	2.76536e15	0.911442	0.455721	−	0.890123i	$-0.349382\pi$
$653$	2.76536e15	0.911442	0.455721	+	0.890123i	$0.349382\pi$
$654$	−4.41657e14	−0.144347
$655$	0	0
$656$	1.49035e14	0.0478979
$657$	−1.12563e15	−0.358744
$658$	−2.51597e15	−0.795176
$659$	3.26634e15	1.02374	0.511872	−	0.859062i	$-0.328952\pi$
$659$	3.26634e15	1.02374	0.511872	+	0.859062i	$0.328952\pi$
$660$	0	0
$661$	1.72112e15	0.530521	0.265260	−	0.964177i	$-0.414542\pi$
$661$	1.72112e15	0.530521	0.265260	+	0.964177i	$0.414542\pi$
$662$	−8.94688e14	−0.273497
$663$	−1.30701e15	−0.396238
$664$	−2.14941e15	−0.646242
$665$	0	0
$666$	−8.65606e14	−0.255984
$667$	−4.61361e15	−1.35316
$668$	8.05078e14	0.234190
$669$	−5.99410e14	−0.172934
$670$	0	0
$671$	6.26029e15	1.77673
$672$	3.38605e14	0.0953152
$673$	−4.18650e15	−1.16888	−0.584438	−	0.811438i	$-0.698685\pi$
$673$	−4.18650e15	−1.16888	−0.584438	+	0.811438i	$0.698685\pi$
$674$	3.74341e15	1.03666
$675$	0	0
$676$	9.92609e14	0.270440
$677$	4.21054e15	1.13789	0.568945	−	0.822376i	$-0.307352\pi$
$677$	4.21054e15	1.13789	0.568945	+	0.822376i	$0.307352\pi$
$678$	6.04081e14	0.161932
$679$	1.83571e15	0.488114
$680$	0	0
$681$	−2.70795e15	−0.708486
$682$	7.44087e15	1.93112
$683$	6.85825e15	1.76563	0.882814	−	0.469722i	$-0.155646\pi$
$683$	6.85825e15	1.76563	0.882814	+	0.469722i	$0.155646\pi$
$684$	3.29122e14	0.0840520
$685$	0	0
$686$	−2.96356e15	−0.744785
$687$	−2.74201e15	−0.683607
$688$	1.15164e15	0.284826
$689$	−2.13243e15	−0.523201
$690$	0	0
$691$	−7.01392e15	−1.69368	−0.846841	−	0.531847i	$-0.821498\pi$
$691$	−7.01392e15	−1.69368	−0.846841	+	0.531847i	$0.821498\pi$
$692$	2.67680e14	0.0641258
$693$	−2.05864e15	−0.489269
$694$	−5.20168e13	−0.0122650
$695$	0	0
$696$	−1.23492e15	−0.286607
$697$	−4.60033e14	−0.105927
$698$	4.48089e15	1.02367
$699$	−8.91045e14	−0.201965
$700$	0	0
$701$	−3.59916e15	−0.803067	−0.401533	−	0.915844i	$-0.631523\pi$
$701$	−3.59916e15	−0.803067	−0.401533	+	0.915844i	$0.631523\pi$
$702$	−7.63030e14	−0.168923
$703$	2.49346e15	0.547706
$704$	9.01428e14	0.196463
$705$	0	0
$706$	−3.45261e14	−0.0740836
$707$	−7.82361e15	−1.66571
$708$	−1.24739e15	−0.263523
$709$	9.13743e15	1.91544	0.957722	−	0.287695i	$-0.0928888\pi$
$709$	9.13743e15	1.91544	0.957722	+	0.287695i	$0.0928888\pi$
$710$	0	0
$711$	1.41484e15	0.292028
$712$	−1.04358e15	−0.213740
$713$	8.23952e15	1.67459
$714$	−1.04519e15	−0.210792
$715$	0	0
$716$	1.10678e15	0.219807
$717$	3.40659e15	0.671375
$718$	2.67589e15	0.523340
$719$	−4.61453e15	−0.895609	−0.447805	−	0.894131i	$-0.647794\pi$
$719$	−4.61453e15	−0.895609	−0.447805	+	0.894131i	$0.647794\pi$
$720$	0	0
$721$	7.26454e15	1.38856
$722$	2.77962e15	0.527268
$723$	−2.91271e15	−0.548323
$724$	3.97006e15	0.741711
$725$	0	0
$726$	−3.26189e15	−0.600231
$727$	4.47421e15	0.817104	0.408552	−	0.912735i	$-0.366034\pi$
$727$	4.47421e15	0.817104	0.408552	+	0.912735i	$0.366034\pi$
$728$	2.26131e15	0.409861
$729$	2.05891e14	0.0370370
$730$	0	0
$731$	−3.55482e15	−0.629901
$732$	1.85554e15	0.326332
$733$	4.68168e15	0.817203	0.408601	−	0.912713i	$-0.366017\pi$
$733$	4.68168e15	0.817203	0.408601	+	0.912713i	$0.366017\pi$
$734$	3.20156e14	0.0554669
$735$	0	0
$736$	9.98181e14	0.170365
$737$	−9.57636e14	−0.162229
$738$	−2.68565e14	−0.0451586
$739$	5.58278e15	0.931764	0.465882	−	0.884847i	$-0.345737\pi$
$739$	5.58278e15	0.931764	0.465882	+	0.884847i	$0.345737\pi$
$740$	0	0
$741$	2.19798e15	0.361429
$742$	−1.70525e15	−0.278334
$743$	−5.84984e15	−0.947776	−0.473888	−	0.880585i	$-0.657150\pi$
$743$	−5.84984e15	−0.947776	−0.473888	+	0.880585i	$0.657150\pi$
$744$	2.20546e15	0.354689
$745$	0	0
$746$	7.43568e15	1.17830
$747$	3.87331e15	0.609283
$748$	−2.78248e15	−0.434484
$749$	7.27383e15	1.12749
$750$	0	0
$751$	6.23385e15	0.952218	0.476109	−	0.879386i	$-0.342047\pi$
$751$	6.23385e15	0.952218	0.476109	+	0.879386i	$0.342047\pi$
$752$	−1.98527e15	−0.301037
$753$	−1.14646e15	−0.172578
$754$	−8.24716e15	−1.23243
$755$	0	0
$756$	−6.10177e14	−0.0898640
$757$	1.20579e16	1.76297	0.881486	−	0.472210i	$-0.156543\pi$
$757$	1.20579e16	1.76297	0.881486	+	0.472210i	$0.156543\pi$
$758$	−5.14887e15	−0.747362
$759$	−6.06871e15	−0.874514
$760$	0	0
$761$	5.06900e15	0.719957	0.359979	−	0.932961i	$-0.382784\pi$
$761$	5.06900e15	0.719957	0.359979	+	0.932961i	$0.382784\pi$
$762$	−1.90040e15	−0.267975
$763$	−2.35866e15	−0.330203
$764$	4.44649e15	0.618021
$765$	0	0
$766$	−1.09192e14	−0.0149601
$767$	−8.33045e15	−1.13317
$768$	2.67181e14	0.0360844
$769$	1.35439e15	0.181614	0.0908072	−	0.995868i	$-0.471055\pi$
$769$	1.35439e15	0.181614	0.0908072	+	0.995868i	$0.471055\pi$
$770$	0	0
$771$	5.49612e15	0.726537
$772$	4.55906e14	0.0598384
$773$	−8.61815e15	−1.12312	−0.561561	−	0.827435i	$-0.689799\pi$
$773$	−8.61815e15	−1.12312	−0.561561	+	0.827435i	$0.689799\pi$
$774$	−2.07529e15	−0.268537
$775$	0	0
$776$	1.44850e15	0.184790
$777$	−4.62276e15	−0.585579
$778$	7.99727e15	1.00590
$779$	7.73627e14	0.0966219
$780$	0	0
$781$	6.91557e15	0.851623
$782$	−3.08113e15	−0.376767
$783$	2.22536e15	0.270216
$784$	−2.65065e14	−0.0319605
$785$	0	0
$786$	−2.49881e14	−0.0297105
$787$	4.95922e15	0.585534	0.292767	−	0.956184i	$-0.405424\pi$
$787$	4.95922e15	0.585534	0.292767	+	0.956184i	$0.405424\pi$
$788$	1.96864e15	0.230820
$789$	6.41268e15	0.746649
$790$	0	0
$791$	3.22608e15	0.370429
$792$	−1.62440e15	−0.185227
$793$	1.23919e16	1.40325
$794$	−8.03123e15	−0.903170
$795$	0	0
$796$	−2.58372e15	−0.286566
$797$	1.48779e16	1.63878	0.819391	−	0.573235i	$-0.194312\pi$
$797$	1.48779e16	1.63878	0.819391	+	0.573235i	$0.194312\pi$
$798$	1.75767e15	0.192274
$799$	6.12802e15	0.665752
$800$	0	0
$801$	1.88057e15	0.201516
$802$	−1.14047e16	−1.21374
$803$	−1.60034e16	−1.69152
$804$	−2.83841e14	−0.0297966
$805$	0	0
$806$	1.47287e16	1.52519
$807$	4.44347e15	0.457002
$808$	−6.17335e15	−0.630606
$809$	−1.18817e16	−1.20549	−0.602744	−	0.797935i	$-0.705926\pi$
$809$	−1.18817e16	−1.20549	−0.602744	+	0.797935i	$0.705926\pi$
$810$	0	0
$811$	−7.07941e14	−0.0708569	−0.0354284	−	0.999372i	$-0.511280\pi$
$811$	−7.07941e14	−0.0708569	−0.0354284	+	0.999372i	$0.511280\pi$
$812$	−6.59506e15	−0.655632
$813$	−5.77574e15	−0.570309
$814$	−1.23066e16	−1.20699
$815$	0	0
$816$	−8.24722e14	−0.0798016
$817$	5.97806e15	0.574565
$818$	1.52592e15	0.145676
$819$	−4.07495e15	−0.386421
$820$	0	0
$821$	4.20085e15	0.393052	0.196526	−	0.980499i	$-0.437034\pi$
$821$	4.20085e15	0.393052	0.196526	+	0.980499i	$0.437034\pi$
$822$	−8.04189e15	−0.747417
$823$	1.76608e16	1.63046	0.815232	−	0.579135i	$-0.196609\pi$
$823$	1.76608e16	1.63046	0.815232	+	0.579135i	$0.196609\pi$
$824$	5.73220e15	0.525680
$825$	0	0
$826$	−6.66166e15	−0.602826
$827$	7.42500e15	0.667446	0.333723	−	0.942671i	$-0.391695\pi$
$827$	7.42500e15	0.667446	0.333723	+	0.942671i	$0.391695\pi$
$828$	−1.79875e15	−0.160622
$829$	−1.02610e16	−0.910208	−0.455104	−	0.890438i	$-0.650398\pi$
$829$	−1.02610e16	−0.910208	−0.455104	+	0.890438i	$0.650398\pi$
$830$	0	0
$831$	4.86028e15	0.425457
$832$	1.78432e15	0.155165
$833$	8.18189e14	0.0706816
$834$	5.06217e15	0.434434
$835$	0	0
$836$	4.67924e15	0.396315
$837$	−3.97431e15	−0.334404
$838$	−7.25923e15	−0.606804
$839$	5.46116e15	0.453518	0.226759	−	0.973951i	$-0.427187\pi$
$839$	5.46116e15	0.453518	0.226759	+	0.973951i	$0.427187\pi$
$840$	0	0
$841$	1.18522e16	0.971449
$842$	4.37055e15	0.355893
$843$	5.25032e15	0.424750
$844$	7.78500e15	0.625713
$845$	0	0
$846$	3.57751e15	0.283821
$847$	−1.74201e16	−1.37307
$848$	−1.34555e15	−0.105372
$849$	1.02704e16	0.799092
$850$	0	0
$851$	−1.36275e16	−1.04666
$852$	2.04976e15	0.156418
$853$	−1.38989e16	−1.05380	−0.526902	−	0.849926i	$-0.676647\pi$
$853$	−1.38989e16	−1.05380	−0.526902	+	0.849926i	$0.676647\pi$
$854$	9.90947e15	0.746504
$855$	0	0
$856$	5.73953e15	0.426845
$857$	−1.35605e16	−1.00203	−0.501017	−	0.865437i	$-0.667041\pi$
$857$	−1.35605e16	−1.00203	−0.501017	+	0.865437i	$0.667041\pi$
$858$	−1.08483e16	−0.796490
$859$	4.45328e15	0.324876	0.162438	−	0.986719i	$-0.448064\pi$
$859$	4.45328e15	0.324876	0.162438	+	0.986719i	$0.448064\pi$
$860$	0	0
$861$	−1.43427e15	−0.103303
$862$	−3.87209e14	−0.0277112
$863$	−1.15395e16	−0.820593	−0.410297	−	0.911952i	$-0.634575\pi$
$863$	−1.15395e16	−0.820593	−0.410297	+	0.911952i	$0.634575\pi$
$864$	−4.81469e14	−0.0340207
$865$	0	0
$866$	−9.79127e15	−0.683110
$867$	−5.78236e15	−0.400867
$868$	1.17782e16	0.811374
$869$	2.01153e16	1.37695
$870$	0	0
$871$	−1.89558e15	−0.128128
$872$	−1.86114e15	−0.125008
$873$	−2.61024e15	−0.174222
$874$	5.18147e15	0.343669
$875$	0	0
$876$	−4.74338e15	−0.310681
$877$	−1.61714e16	−1.05257	−0.526285	−	0.850308i	$-0.676416\pi$
$877$	−1.61714e16	−1.05257	−0.526285	+	0.850308i	$0.676416\pi$
$878$	−1.17807e16	−0.761994
$879$	1.37693e16	0.885064
$880$	0	0
$881$	−2.06661e16	−1.31187	−0.655936	−	0.754817i	$-0.727726\pi$
$881$	−2.06661e16	−1.31187	−0.655936	+	0.754817i	$0.727726\pi$
$882$	4.77656e14	0.0301327
$883$	2.69113e15	0.168714	0.0843569	−	0.996436i	$-0.473116\pi$
$883$	2.69113e15	0.168714	0.0843569	+	0.996436i	$0.473116\pi$
$884$	−5.50775e15	−0.343152
$885$	0	0
$886$	−4.44728e14	−0.0273659
$887$	2.20727e16	1.34982	0.674911	−	0.737900i	$-0.264182\pi$
$887$	2.20727e16	1.34982	0.674911	+	0.737900i	$0.264182\pi$
$888$	−3.64766e15	−0.221688
$889$	−1.01491e16	−0.613009
$890$	0	0
$891$	2.92722e15	0.174634
$892$	−2.52591e15	−0.149765
$893$	−1.03053e16	−0.607267
$894$	−1.15688e16	−0.677535
$895$	0	0
$896$	1.42688e15	0.0825453
$897$	−1.20126e16	−0.690685
$898$	−1.25560e15	−0.0717518
$899$	−4.29561e16	−2.43976
$900$	0	0
$901$	4.15339e15	0.233032
$902$	−3.81829e15	−0.212928
$903$	−1.10831e16	−0.614295
$904$	2.54559e15	0.140237
$905$	0	0
$906$	−1.32186e16	−0.719416
$907$	2.50362e16	1.35434	0.677170	−	0.735827i	$-0.263206\pi$
$907$	2.50362e16	1.35434	0.677170	+	0.735827i	$0.263206\pi$
$908$	−1.14113e16	−0.613567
$909$	1.11246e16	0.594541
$910$	0	0
$911$	−1.34918e16	−0.712393	−0.356196	−	0.934411i	$-0.615927\pi$
$911$	−1.34918e16	−0.712393	−0.356196	+	0.934411i	$0.615927\pi$
$912$	1.38692e15	0.0727912
$913$	5.50682e16	2.87284
$914$	4.39044e15	0.227669
$915$	0	0
$916$	−1.15548e16	−0.592021
$917$	−1.33449e15	−0.0679646
$918$	1.48618e15	0.0752377
$919$	1.86406e16	0.938048	0.469024	−	0.883185i	$-0.344606\pi$
$919$	1.86406e16	0.938048	0.469024	+	0.883185i	$0.344606\pi$
$920$	0	0
$921$	4.84454e15	0.240893
$922$	−7.95708e15	−0.393309
$923$	1.36889e16	0.672606
$924$	−8.67509e15	−0.423719
$925$	0	0
$926$	2.02006e16	0.974997
$927$	−1.03296e16	−0.495616
$928$	−5.20393e15	−0.248209
$929$	1.26618e16	0.600358	0.300179	−	0.953883i	$-0.402954\pi$
$929$	1.26618e16	0.600358	0.300179	+	0.953883i	$0.402954\pi$
$930$	0	0
$931$	−1.37593e15	−0.0644723
$932$	−3.75486e15	−0.174906
$933$	2.55975e15	0.118535
$934$	2.75279e16	1.26726
$935$	0	0
$936$	−3.21540e15	−0.146291
$937$	3.98788e16	1.80374	0.901871	−	0.432006i	$-0.142194\pi$
$937$	3.98788e16	1.80374	0.901871	+	0.432006i	$0.142194\pi$
$938$	−1.51585e15	−0.0681617
$939$	−1.28147e16	−0.572861
$940$	0	0
$941$	−2.35800e16	−1.04184	−0.520920	−	0.853606i	$-0.674411\pi$
$941$	−2.35800e16	−1.04184	−0.520920	+	0.853606i	$0.674411\pi$
$942$	2.92175e15	0.128340
$943$	−4.22812e15	−0.184643
$944$	−5.25649e15	−0.228218
$945$	0	0
$946$	−2.95051e16	−1.26618
$947$	2.50128e16	1.06718	0.533591	−	0.845743i	$-0.320842\pi$
$947$	2.50128e16	1.06718	0.533591	+	0.845743i	$0.320842\pi$
$948$	5.96213e15	0.252904
$949$	−3.16778e16	−1.33595
$950$	0	0
$951$	1.62400e16	0.677005
$952$	−4.40441e15	−0.182551
$953$	3.78726e16	1.56068	0.780340	−	0.625355i	$-0.215046\pi$
$953$	3.78726e16	1.56068	0.780340	+	0.625355i	$0.215046\pi$
$954$	2.42473e15	0.0993453
$955$	0	0
$956$	1.43554e16	0.581427
$957$	3.16387e16	1.27410
$958$	1.83005e16	0.732744
$959$	−4.29476e16	−1.70976
$960$	0	0
$961$	5.13075e16	2.01931
$962$	−2.43602e16	−0.953274
$963$	−1.03428e16	−0.402433
$964$	−1.22741e16	−0.474862
$965$	0	0
$966$	−9.60621e15	−0.367433
$967$	−1.01035e16	−0.384262	−0.192131	−	0.981369i	$-0.561540\pi$
$967$	−1.01035e16	−0.384262	−0.192131	+	0.981369i	$0.561540\pi$
$968$	−1.37456e16	−0.519815
$969$	−4.28106e15	−0.160980
$970$	0	0
$971$	−1.09869e16	−0.408478	−0.204239	−	0.978921i	$-0.565472\pi$
$971$	−1.09869e16	−0.408478	−0.204239	+	0.978921i	$0.565472\pi$
$972$	8.67624e14	0.0320750
$973$	2.70344e16	0.993795
$974$	−2.54464e16	−0.930148
$975$	0	0
$976$	7.81922e15	0.282611
$977$	−2.52822e16	−0.908644	−0.454322	−	0.890837i	$-0.650119\pi$
$977$	−2.52822e16	−0.908644	−0.454322	+	0.890837i	$0.650119\pi$
$978$	−9.26760e15	−0.331210
$979$	2.67367e16	0.950173
$980$	0	0
$981$	3.35383e15	0.117859
$982$	1.61320e15	0.0563734
$983$	−4.29168e16	−1.49136	−0.745680	−	0.666304i	$-0.767875\pi$
$983$	−4.29168e16	−1.49136	−0.745680	+	0.666304i	$0.767875\pi$
$984$	−1.13173e15	−0.0391085
$985$	0	0
$986$	1.60632e16	0.548921
$987$	1.91056e16	0.649258
$988$	9.26226e15	0.313007
$989$	−3.26720e16	−1.09798
$990$	0	0
$991$	−5.20325e16	−1.72930	−0.864648	−	0.502377i	$-0.832459\pi$
$991$	−5.20325e16	−1.72930	−0.864648	+	0.502377i	$0.832459\pi$
$992$	9.29379e15	0.307170
$993$	6.79404e15	0.223309
$994$	1.09467e16	0.357815
$995$	0	0
$996$	1.63221e16	0.527654
$997$	5.42887e16	1.74537	0.872683	−	0.488288i	$-0.162378\pi$
$997$	5.42887e16	1.74537	0.872683	+	0.488288i	$0.162378\pi$
$998$	9.33872e15	0.298586
$999$	6.57320e15	0.209010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.12.a.t.1.2		3
5.2	odd	4		30.12.c.b.19.3	✓	6
5.3	odd	4		30.12.c.b.19.6	yes	6
5.4	even	2		150.12.a.u.1.2		3
15.2	even	4		90.12.c.c.19.4		6
15.8	even	4		90.12.c.c.19.1		6
20.3	even	4		240.12.f.b.49.3		6
20.7	even	4		240.12.f.b.49.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.c.b.19.3	✓	6	5.2	odd	4
30.12.c.b.19.6	yes	6	5.3	odd	4
90.12.c.c.19.1		6	15.8	even	4
90.12.c.c.19.4		6	15.2	even	4
150.12.a.t.1.2		3	1.1	even	1	trivial
150.12.a.u.1.2		3	5.4	even	2
240.12.f.b.49.3		6	20.3	even	4
240.12.f.b.49.6		6	20.7	even	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)

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} -7776.00 q^{6} -41527.6 q^{7} -32768.0 q^{8} +59049.0 q^{9} +839520. q^{11} +248832. q^{12} +1.66178e6 q^{13} +1.32888e6 q^{14} +1.04858e6 q^{16} -3.23669e6 q^{17} -1.88957e6 q^{18} +5.44307e6 q^{19} -1.00912e7 q^{21} -2.68646e7 q^{22} -2.97481e7 q^{23} -7.96262e6 q^{24} -5.31769e7 q^{26} +1.43489e7 q^{27} -4.25243e7 q^{28} +1.55089e8 q^{29} -2.76977e8 q^{31} -3.35544e7 q^{32} +2.04003e8 q^{33} +1.03574e8 q^{34} +6.04662e7 q^{36} +4.58098e8 q^{37} -1.74178e8 q^{38} +4.03812e8 q^{39} +1.42131e8 q^{41} +3.22919e8 q^{42} +1.09829e9 q^{43} +8.59668e8 q^{44} +9.51939e8 q^{46} -1.89330e9 q^{47} +2.54804e8 q^{48} -2.52786e8 q^{49} -7.86516e8 q^{51} +1.70166e9 q^{52} -1.28322e9 q^{53} -4.59165e8 q^{54} +1.36078e9 q^{56} +1.32267e9 q^{57} -4.96286e9 q^{58} -5.01298e9 q^{59} +7.45699e9 q^{61} +8.86325e9 q^{62} -2.45216e9 q^{63} +1.07374e9 q^{64} -6.52811e9 q^{66} -1.14069e9 q^{67} -3.31437e9 q^{68} -7.22879e9 q^{69} +8.23753e9 q^{71} -1.93492e9 q^{72} -1.90626e10 q^{73} -1.46591e10 q^{74} +5.57371e9 q^{76} -3.48632e10 q^{77} -1.29220e10 q^{78} +2.39605e10 q^{79} +3.48678e9 q^{81} -4.54818e9 q^{82} +6.55948e10 q^{83} -1.03334e10 q^{84} -3.51452e10 q^{86} +3.76867e10 q^{87} -2.75094e10 q^{88} +3.18476e10 q^{89} -6.90096e10 q^{91} -3.04621e10 q^{92} -6.73053e10 q^{93} +6.05855e10 q^{94} -8.15373e9 q^{96} -4.42047e10 q^{97} +8.08914e9 q^{98} +4.95728e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 96 q^{2} + 729 q^{3} + 3072 q^{4} - 23328 q^{6} - 67384 q^{7} - 98304 q^{8} + 177147 q^{9} + 876700 q^{11} + 746496 q^{12} - 315192 q^{13} + 2156288 q^{14} + 3145728 q^{16} - 2874324 q^{17} - 5668704 q^{18}+ \cdots + 51768258300 q^{99}+O(q^{100}) \) 3 * q - 96 * q^2 + 729 * q^3 + 3072 * q^4 - 23328 * q^6 - 67384 * q^7 - 98304 * q^8 + 177147 * q^9 + 876700 * q^11 + 746496 * q^12 - 315192 * q^13 + 2156288 * q^14 + 3145728 * q^16 - 2874324 * q^17 - 5668704 * q^18 + 2034912 * q^19 - 16374312 * q^21 - 28054400 * q^22 - 49866300 * q^23 - 23887872 * q^24 + 10086144 * q^26 + 43046721 * q^27 - 69001216 * q^28 - 35857782 * q^29 - 61121676 * q^31 - 100663296 * q^32 + 213038100 * q^33 + 91978368 * q^34 + 181398528 * q^36 + 935590592 * q^37 - 65117184 * q^38 - 76591656 * q^39 + 1003384282 * q^41 + 523977984 * q^42 + 980338484 * q^43 + 897740800 * q^44 + 1595721600 * q^46 + 2190634500 * q^47 + 764411904 * q^48 + 4795452723 * q^49 - 698460732 * q^51 - 322756608 * q^52 - 6993816924 * q^53 - 1377495072 * q^54 + 2208038912 * q^56 + 494483616 * q^57 + 1147449024 * q^58 + 2034730100 * q^59 - 6193233330 * q^61 + 1955893632 * q^62 - 3978957816 * q^63 + 3221225472 * q^64 - 6817219200 * q^66 - 5079955484 * q^67 - 2943307776 * q^68 - 12117510900 * q^69 + 6851752800 * q^71 - 5804752896 * q^72 - 54889949992 * q^73 - 29938898944 * q^74 + 2083749888 * q^76 + 32141607600 * q^77 + 2450932992 * q^78 + 6719163876 * q^79 + 10460353203 * q^81 - 32108297024 * q^82 - 57462212652 * q^83 - 16767295488 * q^84 - 31370831488 * q^86 - 8713441026 * q^87 - 28727705600 * q^88 + 63718294546 * q^89 + 135921691776 * q^91 - 51063091200 * q^92 - 14852567268 * q^93 - 70100304000 * q^94 - 24461180928 * q^96 - 315259594808 * q^97 - 153454487136 * q^98 + 51768258300 * q^99

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