LMFDB - Embedded newform 150.12.a.j.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:	$1$
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)

$f(q)$	$=$	\(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +7776.00 q^{6} +74750.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} +802180. q^{11} -248832. q^{12} -555889. q^{13} -2.39201e6 q^{14} +1.04858e6 q^{16} -8.07710e6 q^{17} -1.88957e6 q^{18} -1.03389e7 q^{19} -1.81643e7 q^{21} -2.56698e7 q^{22} +2.24760e7 q^{23} +7.96262e6 q^{24} +1.77885e7 q^{26} -1.43489e7 q^{27} +7.65442e7 q^{28} -1.49185e8 q^{29} -4.97171e7 q^{31} -3.35544e7 q^{32} -1.94930e8 q^{33} +2.58467e8 q^{34} +6.04662e7 q^{36} -1.78955e8 q^{37} +3.30846e8 q^{38} +1.35081e8 q^{39} +7.97131e8 q^{41} +5.81257e8 q^{42} -1.91393e9 q^{43} +8.21432e8 q^{44} -7.19231e8 q^{46} -1.44701e9 q^{47} -2.54804e8 q^{48} +3.61026e9 q^{49} +1.96274e9 q^{51} -5.69231e8 q^{52} +3.15555e9 q^{53} +4.59165e8 q^{54} -2.44941e9 q^{56} +2.51236e9 q^{57} +4.77390e9 q^{58} -3.41149e9 q^{59} +5.20656e9 q^{61} +1.59095e9 q^{62} +4.41392e9 q^{63} +1.07374e9 q^{64} +6.23775e9 q^{66} -1.58402e10 q^{67} -8.27095e9 q^{68} -5.46166e9 q^{69} +1.38358e10 q^{71} -1.93492e9 q^{72} -3.25986e10 q^{73} +5.72655e9 q^{74} -1.05871e10 q^{76} +5.99631e10 q^{77} -4.32260e9 q^{78} +2.00781e10 q^{79} +3.48678e9 q^{81} -2.55082e10 q^{82} +5.86779e9 q^{83} -1.86002e10 q^{84} +6.12457e10 q^{86} +3.62518e10 q^{87} -2.62858e10 q^{88} +6.37265e10 q^{89} -4.15528e10 q^{91} +2.30154e10 q^{92} +1.20813e10 q^{93} +4.63043e10 q^{94} +8.15373e9 q^{96} +9.69296e10 q^{97} -1.15528e11 q^{98} +4.73679e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	74750.2	1.68102	0.840510	−	0.541796i	$-0.182255\pi$
$7$	74750.2	1.68102	0.840510	+	0.541796i	$0.182255\pi$
$8$	−32768.0	−0.353553
$9$	59049.0	0.333333
$10$	0	0
$11$	802180.	1.50180	0.750900	−	0.660416i	$-0.229620\pi$
$11$	802180.	1.50180	0.750900	+	0.660416i	$0.229620\pi$
$12$	−248832.	−0.288675
$13$	−555889.	−0.415241	−0.207620	−	0.978209i	$-0.566572\pi$
$13$	−555889.	−0.415241	−0.207620	+	0.978209i	$0.566572\pi$
$14$	−2.39201e6	−1.18866
$15$	0	0
$16$	1.04858e6	0.250000
$17$	−8.07710e6	−1.37971	−0.689853	−	0.723950i	$-0.742325\pi$
$17$	−8.07710e6	−1.37971	−0.689853	+	0.723950i	$0.742325\pi$
$18$	−1.88957e6	−0.235702
$19$	−1.03389e7	−0.957923	−0.478962	−	0.877836i	$-0.658987\pi$
$19$	−1.03389e7	−0.957923	−0.478962	+	0.877836i	$0.658987\pi$
$20$	0	0
$21$	−1.81643e7	−0.970537
$22$	−2.56698e7	−1.06193
$23$	2.24760e7	0.728141	0.364071	−	0.931371i	$-0.381387\pi$
$23$	2.24760e7	0.728141	0.364071	+	0.931371i	$0.381387\pi$
$24$	7.96262e6	0.204124
$25$	0	0
$26$	1.77885e7	0.293620
$27$	−1.43489e7	−0.192450
$28$	7.65442e7	0.840510
$29$	−1.49185e8	−1.35062	−0.675312	−	0.737532i	$-0.735991\pi$
$29$	−1.49185e8	−1.35062	−0.675312	+	0.737532i	$0.735991\pi$
$30$	0	0
$31$	−4.97171e7	−0.311901	−0.155950	−	0.987765i	$-0.549844\pi$
$31$	−4.97171e7	−0.311901	−0.155950	+	0.987765i	$0.549844\pi$
$32$	−3.35544e7	−0.176777
$33$	−1.94930e8	−0.867065
$34$	2.58467e8	0.975599
$35$	0	0
$36$	6.04662e7	0.166667
$37$	−1.78955e8	−0.424262	−0.212131	−	0.977241i	$-0.568040\pi$
$37$	−1.78955e8	−0.424262	−0.212131	+	0.977241i	$0.568040\pi$
$38$	3.30846e8	0.677354
$39$	1.35081e8	0.239739
$40$	0	0
$41$	7.97131e8	1.07453	0.537265	−	0.843414i	$-0.319458\pi$
$41$	7.97131e8	1.07453	0.537265	+	0.843414i	$0.319458\pi$
$42$	5.81257e8	0.686274
$43$	−1.91393e9	−1.98541	−0.992703	−	0.120584i	$-0.961523\pi$
$43$	−1.91393e9	−1.98541	−0.992703	+	0.120584i	$0.961523\pi$
$44$	8.21432e8	0.750900
$45$	0	0
$46$	−7.19231e8	−0.514874
$47$	−1.44701e9	−0.920308	−0.460154	−	0.887839i	$-0.652206\pi$
$47$	−1.44701e9	−0.920308	−0.460154	+	0.887839i	$0.652206\pi$
$48$	−2.54804e8	−0.144338
$49$	3.61026e9	1.82583
$50$	0	0
$51$	1.96274e9	0.796573
$52$	−5.69231e8	−0.207620
$53$	3.15555e9	1.03647	0.518236	−	0.855238i	$-0.326589\pi$
$53$	3.15555e9	1.03647	0.518236	+	0.855238i	$0.326589\pi$
$54$	4.59165e8	0.136083
$55$	0	0
$56$	−2.44941e9	−0.594330
$57$	2.51236e9	0.553057
$58$	4.77390e9	0.955036
$59$	−3.41149e9	−0.621237	−0.310619	−	0.950535i	$-0.600536\pi$
$59$	−3.41149e9	−0.621237	−0.310619	+	0.950535i	$0.600536\pi$
$60$	0	0
$61$	5.20656e9	0.789290	0.394645	−	0.918834i	$-0.370868\pi$
$61$	5.20656e9	0.789290	0.394645	+	0.918834i	$0.370868\pi$
$62$	1.59095e9	0.220547
$63$	4.41392e9	0.560340
$64$	1.07374e9	0.125000
$65$	0	0
$66$	6.23775e9	0.613107
$67$	−1.58402e10	−1.43334	−0.716671	−	0.697411i	$-0.754335\pi$
$67$	−1.58402e10	−1.43334	−0.716671	+	0.697411i	$0.754335\pi$
$68$	−8.27095e9	−0.689853
$69$	−5.46166e9	−0.420393
$70$	0	0
$71$	1.38358e10	0.910091	0.455045	−	0.890468i	$-0.349623\pi$
$71$	1.38358e10	0.910091	0.455045	+	0.890468i	$0.349623\pi$
$72$	−1.93492e9	−0.117851
$73$	−3.25986e10	−1.84045	−0.920223	−	0.391396i	$-0.871992\pi$
$73$	−3.25986e10	−1.84045	−0.920223	+	0.391396i	$0.871992\pi$
$74$	5.72655e9	0.299998
$75$	0	0
$76$	−1.05871e10	−0.478962
$77$	5.99631e10	2.52456
$78$	−4.32260e9	−0.169521
$79$	2.00781e10	0.734131	0.367065	−	0.930195i	$-0.380363\pi$
$79$	2.00781e10	0.734131	0.367065	+	0.930195i	$0.380363\pi$
$80$	0	0
$81$	3.48678e9	0.111111
$82$	−2.55082e10	−0.759807
$83$	5.86779e9	0.163510	0.0817551	−	0.996652i	$-0.473947\pi$
$83$	5.86779e9	0.163510	0.0817551	+	0.996652i	$0.473947\pi$
$84$	−1.86002e10	−0.485269
$85$	0	0
$86$	6.12457e10	1.40389
$87$	3.62518e10	0.779784
$88$	−2.62858e10	−0.530967
$89$	6.37265e10	1.20969	0.604846	−	0.796342i	$-0.293235\pi$
$89$	6.37265e10	1.20969	0.604846	+	0.796342i	$0.293235\pi$
$90$	0	0
$91$	−4.15528e10	−0.698028
$92$	2.30154e10	0.364071
$93$	1.20813e10	0.180076
$94$	4.63043e10	0.650756
$95$	0	0
$96$	8.15373e9	0.102062
$97$	9.69296e10	1.14607	0.573036	−	0.819530i	$-0.305765\pi$
$97$	9.69296e10	1.14607	0.573036	+	0.819530i	$0.305765\pi$
$98$	−1.15528e11	−1.29106
$99$	4.73679e10	0.500600
$100$	0	0
$101$	3.62863e10	0.343539	0.171769	−	0.985137i	$-0.445052\pi$
$101$	3.62863e10	0.343539	0.171769	+	0.985137i	$0.445052\pi$
$102$	−6.28075e10	−0.563262
$103$	−1.23377e11	−1.04865	−0.524324	−	0.851519i	$-0.675682\pi$
$103$	−1.23377e11	−1.04865	−0.524324	+	0.851519i	$0.675682\pi$
$104$	1.82154e10	0.146810
$105$	0	0
$106$	−1.00978e11	−0.732896
$107$	−2.47752e11	−1.70768	−0.853838	−	0.520538i	$-0.825731\pi$
$107$	−2.47752e11	−1.70768	−0.853838	+	0.520538i	$0.825731\pi$
$108$	−1.46933e10	−0.0962250
$109$	−2.20320e11	−1.37154	−0.685768	−	0.727820i	$-0.740534\pi$
$109$	−2.20320e11	−1.37154	−0.685768	+	0.727820i	$0.740534\pi$
$110$	0	0
$111$	4.34860e10	0.244948
$112$	7.83812e10	0.420255
$113$	−7.45232e10	−0.380505	−0.190252	−	0.981735i	$-0.560931\pi$
$113$	−7.45232e10	−0.380505	−0.190252	+	0.981735i	$0.560931\pi$
$114$	−8.03955e10	−0.391070
$115$	0	0
$116$	−1.52765e11	−0.675312
$117$	−3.28247e10	−0.138414
$118$	1.09168e11	0.439281
$119$	−6.03765e11	−2.31931
$120$	0	0
$121$	3.58181e11	1.25540
$122$	−1.66610e11	−0.558112
$123$	−1.93703e11	−0.620380
$124$	−5.09103e10	−0.155950
$125$	0	0
$126$	−1.41246e11	−0.396220
$127$	1.37238e11	0.368598	0.184299	−	0.982870i	$-0.440999\pi$
$127$	1.37238e11	0.368598	0.184299	+	0.982870i	$0.440999\pi$
$128$	−3.43597e10	−0.0883883
$129$	4.65085e11	1.14627
$130$	0	0
$131$	7.96588e10	0.180402	0.0902011	−	0.995924i	$-0.471249\pi$
$131$	7.96588e10	0.180402	0.0902011	+	0.995924i	$0.471249\pi$
$132$	−1.99608e11	−0.433532
$133$	−7.72836e11	−1.61029
$134$	5.06887e11	1.01353
$135$	0	0
$136$	2.64670e11	0.487800
$137$	−6.88285e10	−0.121844	−0.0609222	−	0.998143i	$-0.519404\pi$
$137$	−6.88285e10	−0.121844	−0.0609222	+	0.998143i	$0.519404\pi$
$138$	1.74773e11	0.297262
$139$	−3.34458e11	−0.546714	−0.273357	−	0.961913i	$-0.588134\pi$
$139$	−3.34458e11	−0.546714	−0.273357	+	0.961913i	$0.588134\pi$
$140$	0	0
$141$	3.51623e11	0.531340
$142$	−4.42747e11	−0.643532
$143$	−4.45923e11	−0.623609
$144$	6.19174e10	0.0833333
$145$	0	0
$146$	1.04315e12	1.30139
$147$	−8.77293e11	−1.05414
$148$	−1.83250e11	−0.212131
$149$	−1.73770e12	−1.93843	−0.969213	−	0.246223i	$-0.920810\pi$
$149$	−1.73770e12	−1.93843	−0.969213	+	0.246223i	$0.920810\pi$
$150$	0	0
$151$	5.01763e11	0.520146	0.260073	−	0.965589i	$-0.416253\pi$
$151$	5.01763e11	0.520146	0.260073	+	0.965589i	$0.416253\pi$
$152$	3.38786e11	0.338677
$153$	−4.76945e11	−0.459902
$154$	−1.91882e12	−1.78513
$155$	0	0
$156$	1.38323e11	0.119870
$157$	4.03146e11	0.337298	0.168649	−	0.985676i	$-0.446060\pi$
$157$	4.03146e11	0.337298	0.168649	+	0.985676i	$0.446060\pi$
$158$	−6.42499e11	−0.519109
$159$	−7.66798e11	−0.598407
$160$	0	0
$161$	1.68008e12	1.22402
$162$	−1.11577e11	−0.0785674
$163$	3.16791e11	0.215646	0.107823	−	0.994170i	$-0.465612\pi$
$163$	3.16791e11	0.215646	0.107823	+	0.994170i	$0.465612\pi$
$164$	8.16262e11	0.537265
$165$	0	0
$166$	−1.87769e11	−0.115619
$167$	−2.11724e12	−1.26133	−0.630667	−	0.776053i	$-0.717219\pi$
$167$	−2.11724e12	−1.26133	−0.630667	+	0.776053i	$0.717219\pi$
$168$	5.95207e11	0.343137
$169$	−1.48315e12	−0.827575
$170$	0	0
$171$	−6.10503e11	−0.319308
$172$	−1.95986e12	−0.992703
$173$	9.66212e11	0.474044	0.237022	−	0.971504i	$-0.423829\pi$
$173$	9.66212e11	0.474044	0.237022	+	0.971504i	$0.423829\pi$
$174$	−1.16006e12	−0.551390
$175$	0	0
$176$	8.41147e11	0.375450
$177$	8.28991e11	0.358671
$178$	−2.03925e12	−0.855382
$179$	−1.30643e12	−0.531366	−0.265683	−	0.964060i	$-0.585597\pi$
$179$	−1.30643e12	−0.531366	−0.265683	+	0.964060i	$0.585597\pi$
$180$	0	0
$181$	−2.52558e12	−0.966337	−0.483169	−	0.875527i	$-0.660514\pi$
$181$	−2.52558e12	−0.966337	−0.483169	+	0.875527i	$0.660514\pi$
$182$	1.32969e12	0.493580
$183$	−1.26519e12	−0.455697
$184$	−7.36493e11	−0.257437
$185$	0	0
$186$	−3.86600e11	−0.127333
$187$	−6.47929e12	−2.07204
$188$	−1.48174e12	−0.460154
$189$	−1.07258e12	−0.323512
$190$	0	0
$191$	−3.52503e11	−0.100341	−0.0501706	−	0.998741i	$-0.515977\pi$
$191$	−3.52503e11	−0.100341	−0.0501706	+	0.998741i	$0.515977\pi$
$192$	−2.60919e11	−0.0721688
$193$	−6.60892e12	−1.77650	−0.888250	−	0.459360i	$-0.848079\pi$
$193$	−6.60892e12	−1.77650	−0.888250	+	0.459360i	$0.848079\pi$
$194$	−3.10175e12	−0.810395
$195$	0	0
$196$	3.69691e12	0.912914
$197$	6.69180e12	1.60686	0.803431	−	0.595397i	$-0.203005\pi$
$197$	6.69180e12	1.60686	0.803431	+	0.595397i	$0.203005\pi$
$198$	−1.51577e12	−0.353978
$199$	7.47387e12	1.69767	0.848835	−	0.528657i	$-0.177304\pi$
$199$	7.47387e12	1.69767	0.848835	+	0.528657i	$0.177304\pi$
$200$	0	0
$201$	3.84917e12	0.827541
$202$	−1.16116e12	−0.242919
$203$	−1.11516e13	−2.27043
$204$	2.00984e12	0.398287
$205$	0	0
$206$	3.94806e12	0.741506
$207$	1.32718e12	0.242714
$208$	−5.82892e11	−0.103810
$209$	−8.29368e12	−1.43861
$210$	0	0
$211$	−1.88751e12	−0.310696	−0.155348	−	0.987860i	$-0.549650\pi$
$211$	−1.88751e12	−0.310696	−0.155348	+	0.987860i	$0.549650\pi$
$212$	3.23128e12	0.518236
$213$	−3.36211e12	−0.525441
$214$	7.92805e12	1.20751
$215$	0	0
$216$	4.70185e11	0.0680414
$217$	−3.71636e12	−0.524312
$218$	7.05023e12	0.969823
$219$	7.92145e12	1.06258
$220$	0	0
$221$	4.48997e12	0.572910
$222$	−1.39155e12	−0.173204
$223$	−1.03301e13	−1.25437	−0.627187	−	0.778869i	$-0.715794\pi$
$223$	−1.03301e13	−1.25437	−0.627187	+	0.778869i	$0.715794\pi$
$224$	−2.50820e12	−0.297165
$225$	0	0
$226$	2.38474e12	0.269057
$227$	7.81273e12	0.860322	0.430161	−	0.902752i	$-0.358457\pi$
$227$	7.81273e12	0.860322	0.430161	+	0.902752i	$0.358457\pi$
$228$	2.57266e12	0.276529
$229$	−1.39300e13	−1.46170	−0.730848	−	0.682541i	$-0.760875\pi$
$229$	−1.39300e13	−1.46170	−0.730848	+	0.682541i	$0.760875\pi$
$230$	0	0
$231$	−1.45710e13	−1.45755
$232$	4.88848e12	0.477518
$233$	1.85940e12	0.177384	0.0886921	−	0.996059i	$-0.471731\pi$
$233$	1.85940e12	0.177384	0.0886921	+	0.996059i	$0.471731\pi$
$234$	1.05039e12	0.0978732
$235$	0	0
$236$	−3.49336e12	−0.310619
$237$	−4.87898e12	−0.423851
$238$	1.93205e13	1.64000
$239$	1.16641e13	0.967530	0.483765	−	0.875198i	$-0.339269\pi$
$239$	1.16641e13	0.967530	0.483765	+	0.875198i	$0.339269\pi$
$240$	0	0
$241$	3.44941e12	0.273307	0.136654	−	0.990619i	$-0.456365\pi$
$241$	3.44941e12	0.273307	0.136654	+	0.990619i	$0.456365\pi$
$242$	−1.14618e13	−0.887704
$243$	−8.47289e11	−0.0641500
$244$	5.33152e12	0.394645
$245$	0	0
$246$	6.19849e12	0.438675
$247$	5.74730e12	0.397769
$248$	1.62913e12	0.110274
$249$	−1.42587e12	−0.0944026
$250$	0	0
$251$	−1.59703e11	−0.0101183	−0.00505916	−	0.999987i	$-0.501610\pi$
$251$	−1.59703e11	−0.0101183	−0.00505916	+	0.999987i	$0.501610\pi$
$252$	4.51986e12	0.280170
$253$	1.80298e13	1.09352
$254$	−4.39161e12	−0.260638
$255$	0	0
$256$	1.09951e12	0.0625000
$257$	2.36770e13	1.31733	0.658664	−	0.752437i	$-0.271122\pi$
$257$	2.36770e13	1.31733	0.658664	+	0.752437i	$0.271122\pi$
$258$	−1.48827e13	−0.810539
$259$	−1.33769e13	−0.713193
$260$	0	0
$261$	−8.80920e12	−0.450208
$262$	−2.54908e12	−0.127564
$263$	3.42374e12	0.167782	0.0838909	−	0.996475i	$-0.473265\pi$
$263$	3.42374e12	0.167782	0.0838909	+	0.996475i	$0.473265\pi$
$264$	6.38746e12	0.306554
$265$	0	0
$266$	2.47308e13	1.13865
$267$	−1.54855e13	−0.698416
$268$	−1.62204e13	−0.716671
$269$	2.86821e13	1.24158	0.620788	−	0.783978i	$-0.286813\pi$
$269$	2.86821e13	1.24158	0.620788	+	0.783978i	$0.286813\pi$
$270$	0	0
$271$	5.59038e12	0.232332	0.116166	−	0.993230i	$-0.462939\pi$
$271$	5.59038e12	0.232332	0.116166	+	0.993230i	$0.462939\pi$
$272$	−8.46945e12	−0.344926
$273$	1.00973e13	0.403007
$274$	2.20251e12	0.0861570
$275$	0	0
$276$	−5.59274e12	−0.210196
$277$	4.28065e11	0.0157714	0.00788571	−	0.999969i	$-0.497490\pi$
$277$	4.28065e11	0.0157714	0.00788571	+	0.999969i	$0.497490\pi$
$278$	1.07027e13	0.386585
$279$	−2.93575e12	−0.103967
$280$	0	0
$281$	−1.08985e13	−0.371093	−0.185546	−	0.982636i	$-0.559406\pi$
$281$	−1.08985e13	−0.371093	−0.185546	+	0.982636i	$0.559406\pi$
$282$	−1.12519e13	−0.375714
$283$	5.65412e13	1.85157	0.925783	−	0.378055i	$-0.123407\pi$
$283$	5.65412e13	1.85157	0.925783	+	0.378055i	$0.123407\pi$
$284$	1.41679e13	0.455045
$285$	0	0
$286$	1.42695e13	0.440958
$287$	5.95856e13	1.80631
$288$	−1.98136e12	−0.0589256
$289$	3.09677e13	0.903588
$290$	0	0
$291$	−2.35539e13	−0.661685
$292$	−3.33809e13	−0.920223
$293$	1.18315e13	0.320086	0.160043	−	0.987110i	$-0.448837\pi$
$293$	1.18315e13	0.320086	0.160043	+	0.987110i	$0.448837\pi$
$294$	2.80734e13	0.745391
$295$	0	0
$296$	5.86399e12	0.149999
$297$	−1.15104e13	−0.289022
$298$	5.56063e13	1.37067
$299$	−1.24942e13	−0.302354
$300$	0	0
$301$	−1.43067e14	−3.33751
$302$	−1.60564e13	−0.367799
$303$	−8.81758e12	−0.198342
$304$	−1.08412e13	−0.239481
$305$	0	0
$306$	1.52622e13	0.325200
$307$	2.35820e13	0.493537	0.246768	−	0.969074i	$-0.420631\pi$
$307$	2.35820e13	0.493537	0.246768	+	0.969074i	$0.420631\pi$
$308$	6.14022e13	1.26228
$309$	2.99806e13	0.605437
$310$	0	0
$311$	−7.08127e13	−1.38016	−0.690079	−	0.723734i	$-0.742424\pi$
$311$	−7.08127e13	−1.38016	−0.690079	+	0.723734i	$0.742424\pi$
$312$	−4.42634e12	−0.0847606
$313$	−4.57873e13	−0.861492	−0.430746	−	0.902473i	$-0.641749\pi$
$313$	−4.57873e13	−0.861492	−0.430746	+	0.902473i	$0.641749\pi$
$314$	−1.29007e13	−0.238506
$315$	0	0
$316$	2.05600e13	0.367065
$317$	3.48800e13	0.611999	0.305999	−	0.952032i	$-0.401009\pi$
$317$	3.48800e13	0.611999	0.305999	+	0.952032i	$0.401009\pi$
$318$	2.45375e13	0.423138
$319$	−1.19673e14	−2.02837
$320$	0	0
$321$	6.02036e13	0.985928
$322$	−5.37627e13	−0.865513
$323$	8.35086e13	1.32165
$324$	3.57047e12	0.0555556
$325$	0	0
$326$	−1.01373e13	−0.152485
$327$	5.35377e13	0.791857
$328$	−2.61204e13	−0.379904
$329$	−1.08164e14	−1.54706
$330$	0	0
$331$	−1.24374e14	−1.72058	−0.860291	−	0.509804i	$-0.829718\pi$
$331$	−1.24374e14	−1.72058	−0.860291	+	0.509804i	$0.829718\pi$
$332$	6.00861e12	0.0817551
$333$	−1.05671e13	−0.141421
$334$	6.77518e13	0.891898
$335$	0	0
$336$	−1.90466e13	−0.242634
$337$	−9.29365e13	−1.16472	−0.582360	−	0.812931i	$-0.697871\pi$
$337$	−9.29365e13	−1.16472	−0.582360	+	0.812931i	$0.697871\pi$
$338$	4.74607e13	0.585184
$339$	1.81091e13	0.219684
$340$	0	0
$341$	−3.98821e13	−0.468413
$342$	1.95361e13	0.225785
$343$	1.22062e14	1.38823
$344$	6.27156e13	0.701947
$345$	0	0
$346$	−3.09188e13	−0.335200
$347$	1.70524e13	0.181959	0.0909793	−	0.995853i	$-0.471000\pi$
$347$	1.70524e13	0.181959	0.0909793	+	0.995853i	$0.471000\pi$
$348$	3.71219e13	0.389892
$349$	9.74613e13	1.00761	0.503805	−	0.863817i	$-0.331933\pi$
$349$	9.74613e13	1.00761	0.503805	+	0.863817i	$0.331933\pi$
$350$	0	0
$351$	7.97640e12	0.0799131
$352$	−2.69167e13	−0.265483
$353$	−1.26376e14	−1.22717	−0.613584	−	0.789630i	$-0.710273\pi$
$353$	−1.26376e14	−1.22717	−0.613584	+	0.789630i	$0.710273\pi$
$354$	−2.65277e13	−0.253619
$355$	0	0
$356$	6.52559e13	0.604846
$357$	1.46715e14	1.33906
$358$	4.18057e13	0.375732
$359$	1.40779e14	1.24600	0.623002	−	0.782221i	$-0.285913\pi$
$359$	1.40779e14	1.24600	0.623002	+	0.782221i	$0.285913\pi$
$360$	0	0
$361$	−9.59686e12	−0.0823834
$362$	8.08185e13	0.683304
$363$	−8.70381e13	−0.724808
$364$	−4.25501e13	−0.349014
$365$	0	0
$366$	4.04862e13	0.322226
$367$	2.05934e14	1.61460	0.807300	−	0.590141i	$-0.200928\pi$
$367$	2.05934e14	1.61460	0.807300	+	0.590141i	$0.200928\pi$
$368$	2.35678e13	0.182035
$369$	4.70698e13	0.358176
$370$	0	0
$371$	2.35878e14	1.74233
$372$	1.23712e13	0.0900380
$373$	−1.16370e14	−0.834533	−0.417267	−	0.908784i	$-0.637012\pi$
$373$	−1.16370e14	−0.834533	−0.417267	+	0.908784i	$0.637012\pi$
$374$	2.07337e14	1.46515
$375$	0	0
$376$	4.74156e13	0.325378
$377$	8.29301e13	0.560834
$378$	3.43227e13	0.228758
$379$	−1.53683e14	−1.00951	−0.504756	−	0.863262i	$-0.668418\pi$
$379$	−1.53683e14	−1.00951	−0.504756	+	0.863262i	$0.668418\pi$
$380$	0	0
$381$	−3.33488e13	−0.212810
$382$	1.12801e13	0.0709520
$383$	−1.08265e14	−0.671266	−0.335633	−	0.941993i	$-0.608950\pi$
$383$	−1.08265e14	−0.671266	−0.335633	+	0.941993i	$0.608950\pi$
$384$	8.34942e12	0.0510310
$385$	0	0
$386$	2.11485e14	1.25618
$387$	−1.13016e14	−0.661802
$388$	9.92559e13	0.573036
$389$	−2.05175e13	−0.116789	−0.0583944	−	0.998294i	$-0.518598\pi$
$389$	−2.05175e13	−0.116789	−0.0583944	+	0.998294i	$0.518598\pi$
$390$	0	0
$391$	−1.81541e14	−1.00462
$392$	−1.18301e14	−0.645528
$393$	−1.93571e13	−0.104155
$394$	−2.14138e14	−1.13622
$395$	0	0
$396$	4.85048e13	0.250300
$397$	−3.54572e14	−1.80450	−0.902248	−	0.431217i	$-0.858084\pi$
$397$	−3.54572e14	−1.80450	−0.902248	+	0.431217i	$0.858084\pi$
$398$	−2.39164e14	−1.20043
$399$	1.87799e14	0.929700
$400$	0	0
$401$	−2.67932e14	−1.29042	−0.645208	−	0.764007i	$-0.723229\pi$
$401$	−2.67932e14	−1.29042	−0.645208	+	0.764007i	$0.723229\pi$
$402$	−1.23174e14	−0.585160
$403$	2.76372e13	0.129514
$404$	3.71572e13	0.171769
$405$	0	0
$406$	3.56850e14	1.60543
$407$	−1.43554e14	−0.637156
$408$	−6.43149e13	−0.281631
$409$	−3.26525e14	−1.41071	−0.705357	−	0.708853i	$-0.749213\pi$
$409$	−3.26525e14	−1.41071	−0.705357	+	0.708853i	$0.749213\pi$
$410$	0	0
$411$	1.67253e13	0.0703469
$412$	−1.26338e14	−0.524324
$413$	−2.55009e14	−1.04431
$414$	−4.24699e13	−0.171625
$415$	0	0
$416$	1.86526e13	0.0734049
$417$	8.12733e13	0.315646
$418$	2.65398e14	1.01725
$419$	2.71180e14	1.02584	0.512921	−	0.858436i	$-0.328563\pi$
$419$	2.71180e14	1.02584	0.512921	+	0.858436i	$0.328563\pi$
$420$	0	0
$421$	2.40923e14	0.887824	0.443912	−	0.896071i	$-0.353590\pi$
$421$	2.40923e14	0.887824	0.443912	+	0.896071i	$0.353590\pi$
$422$	6.04003e13	0.219695
$423$	−8.54445e13	−0.306769
$424$	−1.03401e14	−0.366448
$425$	0	0
$426$	1.07588e14	0.371543
$427$	3.89191e14	1.32681
$428$	−2.53698e14	−0.853838
$429$	1.08359e14	0.360041
$430$	0	0
$431$	−4.57546e14	−1.48187	−0.740934	−	0.671578i	$-0.765617\pi$
$431$	−4.57546e14	−1.48187	−0.740934	+	0.671578i	$0.765617\pi$
$432$	−1.50459e13	−0.0481125
$433$	1.44657e14	0.456727	0.228363	−	0.973576i	$-0.426663\pi$
$433$	1.44657e14	0.456727	0.228363	+	0.973576i	$0.426663\pi$
$434$	1.18924e14	0.370744
$435$	0	0
$436$	−2.25607e14	−0.685768
$437$	−2.32378e14	−0.697503
$438$	−2.53486e14	−0.751359
$439$	−3.09661e14	−0.906425	−0.453213	−	0.891402i	$-0.649722\pi$
$439$	−3.09661e14	−0.906425	−0.453213	+	0.891402i	$0.649722\pi$
$440$	0	0
$441$	2.13182e14	0.608610
$442$	−1.43679e14	−0.405108
$443$	−1.15594e14	−0.321895	−0.160947	−	0.986963i	$-0.551455\pi$
$443$	−1.15594e14	−0.321895	−0.160947	+	0.986963i	$0.551455\pi$
$444$	4.45297e13	0.122474
$445$	0	0
$446$	3.30563e14	0.886977
$447$	4.22260e14	1.11915
$448$	8.02624e13	0.210128
$449$	3.41151e13	0.0882251	0.0441126	−	0.999027i	$-0.485954\pi$
$449$	3.41151e13	0.0882251	0.0441126	+	0.999027i	$0.485954\pi$
$450$	0	0
$451$	6.39442e14	1.61373
$452$	−7.63117e13	−0.190252
$453$	−1.21928e14	−0.300307
$454$	−2.50007e14	−0.608339
$455$	0	0
$456$	−8.23250e13	−0.195535
$457$	−4.07927e14	−0.957290	−0.478645	−	0.878008i	$-0.658872\pi$
$457$	−4.07927e14	−0.957290	−0.478645	+	0.878008i	$0.658872\pi$
$458$	4.45761e14	1.03357
$459$	1.15898e14	0.265524
$460$	0	0
$461$	1.19457e14	0.267211	0.133606	−	0.991035i	$-0.457344\pi$
$461$	1.19457e14	0.267211	0.133606	+	0.991035i	$0.457344\pi$
$462$	4.66273e14	1.03065
$463$	−7.00809e14	−1.53075	−0.765375	−	0.643585i	$-0.777446\pi$
$463$	−7.00809e14	−1.53075	−0.765375	+	0.643585i	$0.777446\pi$
$464$	−1.56431e14	−0.337656
$465$	0	0
$466$	−5.95008e13	−0.125430
$467$	−7.08354e14	−1.47573	−0.737866	−	0.674947i	$-0.764166\pi$
$467$	−7.08354e14	−1.47573	−0.737866	+	0.674947i	$0.764166\pi$
$468$	−3.36125e13	−0.0692068
$469$	−1.18406e15	−2.40948
$470$	0	0
$471$	−9.79644e13	−0.194739
$472$	1.11788e14	0.219641
$473$	−1.53532e15	−2.98168
$474$	1.56127e14	0.299708
$475$	0	0
$476$	−6.18255e14	−1.15966
$477$	1.86332e14	0.345491
$478$	−3.73253e14	−0.684147
$479$	9.47376e13	0.171663	0.0858316	−	0.996310i	$-0.472645\pi$
$479$	9.47376e13	0.171663	0.0858316	+	0.996310i	$0.472645\pi$
$480$	0	0
$481$	9.94791e13	0.176171
$482$	−1.10381e14	−0.193257
$483$	−4.08260e14	−0.706688
$484$	3.66778e14	0.627702
$485$	0	0
$486$	2.71132e13	0.0453609
$487$	−8.16124e14	−1.35004	−0.675020	−	0.737799i	$-0.735865\pi$
$487$	−8.16124e14	−1.35004	−0.675020	+	0.737799i	$0.735865\pi$
$488$	−1.70608e14	−0.279056
$489$	−7.69802e13	−0.124503
$490$	0	0
$491$	1.18590e15	1.87542	0.937712	−	0.347414i	$-0.112940\pi$
$491$	1.18590e15	1.87542	0.937712	+	0.347414i	$0.112940\pi$
$492$	−1.98352e14	−0.310190
$493$	1.20498e15	1.86346
$494$	−1.83914e14	−0.281265
$495$	0	0
$496$	−5.21322e13	−0.0779752
$497$	1.03423e15	1.52988
$498$	4.56279e13	0.0667528
$499$	−1.22260e15	−1.76901	−0.884506	−	0.466530i	$-0.845504\pi$
$499$	−1.22260e15	−1.76901	−0.884506	+	0.466530i	$0.845504\pi$
$500$	0	0
$501$	5.14490e14	0.728232
$502$	5.11050e12	0.00715473
$503$	6.35941e14	0.880629	0.440314	−	0.897844i	$-0.354867\pi$
$503$	6.35941e14	0.880629	0.440314	+	0.897844i	$0.354867\pi$
$504$	−1.44635e14	−0.198110
$505$	0	0
$506$	−5.76953e14	−0.773237
$507$	3.60405e14	0.477801
$508$	1.40531e14	0.184299
$509$	−9.13225e14	−1.18476	−0.592379	−	0.805659i	$-0.701811\pi$
$509$	−9.13225e14	−1.18476	−0.592379	+	0.805659i	$0.701811\pi$
$510$	0	0
$511$	−2.43675e15	−3.09383
$512$	−3.51844e13	−0.0441942
$513$	1.48352e14	0.184352
$514$	−7.57663e14	−0.931492
$515$	0	0
$516$	4.76247e14	0.573137
$517$	−1.16076e15	−1.38212
$518$	4.28061e14	0.504303
$519$	−2.34790e14	−0.273690
$520$	0	0
$521$	−3.94860e13	−0.0450646	−0.0225323	−	0.999746i	$-0.507173\pi$
$521$	−3.94860e13	−0.0450646	−0.0225323	+	0.999746i	$0.507173\pi$
$522$	2.81894e14	0.318345
$523$	1.53528e15	1.71565	0.857826	−	0.513940i	$-0.171814\pi$
$523$	1.53528e15	1.71565	0.857826	+	0.513940i	$0.171814\pi$
$524$	8.15706e13	0.0902011
$525$	0	0
$526$	−1.09560e14	−0.118640
$527$	4.01570e14	0.430331
$528$	−2.04399e14	−0.216766
$529$	−4.47640e14	−0.469810
$530$	0	0
$531$	−2.01445e14	−0.207079
$532$	−7.91384e14	−0.805144
$533$	−4.43116e14	−0.446188
$534$	4.95537e14	0.493855
$535$	0	0
$536$	5.19052e14	0.506763
$537$	3.17462e14	0.306784
$538$	−9.17827e14	−0.877927
$539$	2.89608e15	2.74203
$540$	0	0
$541$	5.01924e14	0.465643	0.232821	−	0.972520i	$-0.425204\pi$
$541$	5.01924e14	0.465643	0.232821	+	0.972520i	$0.425204\pi$
$542$	−1.78892e14	−0.164284
$543$	6.13715e14	0.557915
$544$	2.71023e14	0.243900
$545$	0	0
$546$	−3.23115e14	−0.284969
$547$	−1.76289e15	−1.53920	−0.769601	−	0.638525i	$-0.779545\pi$
$547$	−1.76289e15	−1.53920	−0.769601	+	0.638525i	$0.779545\pi$
$548$	−7.04804e13	−0.0609222
$549$	3.07442e14	0.263097
$550$	0	0
$551$	1.54241e15	1.29379
$552$	1.78968e14	0.148631
$553$	1.50084e15	1.23409
$554$	−1.36981e13	−0.0111521
$555$	0	0
$556$	−3.42485e14	−0.273357
$557$	1.58933e15	1.25606	0.628030	−	0.778189i	$-0.283862\pi$
$557$	1.58933e15	1.25606	0.628030	+	0.778189i	$0.283862\pi$
$558$	9.39439e13	0.0735157
$559$	1.06393e15	0.824421
$560$	0	0
$561$	1.57447e15	1.19629
$562$	3.48752e14	0.262402
$563$	−1.88077e15	−1.40132	−0.700662	−	0.713493i	$-0.747112\pi$
$563$	−1.88077e15	−1.40132	−0.700662	+	0.713493i	$0.747112\pi$
$564$	3.60062e14	0.265670
$565$	0	0
$566$	−1.80932e15	−1.30926
$567$	2.60638e14	0.186780
$568$	−4.53373e14	−0.321766
$569$	2.32892e15	1.63696	0.818479	−	0.574536i	$-0.194818\pi$
$569$	2.32892e15	1.63696	0.818479	+	0.574536i	$0.194818\pi$
$570$	0	0
$571$	1.33508e14	0.0920468	0.0460234	−	0.998940i	$-0.485345\pi$
$571$	1.33508e14	0.0920468	0.0460234	+	0.998940i	$0.485345\pi$
$572$	−4.56626e14	−0.311804
$573$	8.56583e13	0.0579320
$574$	−1.90674e15	−1.27725
$575$	0	0
$576$	6.34034e13	0.0416667
$577$	2.30907e15	1.50304	0.751521	−	0.659710i	$-0.229321\pi$
$577$	2.30907e15	1.50304	0.751521	+	0.659710i	$0.229321\pi$
$578$	−9.90965e14	−0.638933
$579$	1.60597e15	1.02566
$580$	0	0
$581$	4.38618e14	0.274864
$582$	7.53725e14	0.467882
$583$	2.53132e15	1.55657
$584$	1.06819e15	0.650696
$585$	0	0
$586$	−3.78607e14	−0.226335
$587$	−2.59880e15	−1.53909	−0.769543	−	0.638595i	$-0.779516\pi$
$587$	−2.59880e15	−1.53909	−0.769543	+	0.638595i	$0.779516\pi$
$588$	−8.98348e14	−0.527071
$589$	5.14022e14	0.298777
$590$	0	0
$591$	−1.62611e15	−0.927723
$592$	−1.87648e14	−0.106065
$593$	3.42653e15	1.91891	0.959453	−	0.281867i	$-0.0909537\pi$
$593$	3.42653e15	1.91891	0.959453	+	0.281867i	$0.0909537\pi$
$594$	3.68333e14	0.204369
$595$	0	0
$596$	−1.77940e15	−0.969213
$597$	−1.81615e15	−0.980151
$598$	3.99813e14	0.213796
$599$	−5.85067e14	−0.309997	−0.154999	−	0.987915i	$-0.549537\pi$
$599$	−5.85067e14	−0.309997	−0.154999	+	0.987915i	$0.549537\pi$
$600$	0	0
$601$	8.31015e14	0.432314	0.216157	−	0.976359i	$-0.430648\pi$
$601$	8.31015e14	0.432314	0.216157	+	0.976359i	$0.430648\pi$
$602$	4.57813e15	2.35997
$603$	−9.35349e14	−0.477781
$604$	5.13805e14	0.260073
$605$	0	0
$606$	2.82163e14	0.140249
$607$	2.43525e15	1.19952	0.599758	−	0.800182i	$-0.295264\pi$
$607$	2.43525e15	1.19952	0.599758	+	0.800182i	$0.295264\pi$
$608$	3.46917e14	0.169338
$609$	2.70983e15	1.31083
$610$	0	0
$611$	8.04377e14	0.382149
$612$	−4.88391e14	−0.229951
$613$	−3.67501e14	−0.171485	−0.0857425	−	0.996317i	$-0.527326\pi$
$613$	−3.67501e14	−0.171485	−0.0857425	+	0.996317i	$0.527326\pi$
$614$	−7.54624e14	−0.348983
$615$	0	0
$616$	−1.96487e15	−0.892565
$617$	−1.63543e15	−0.736316	−0.368158	−	0.929763i	$-0.620011\pi$
$617$	−1.63543e15	−0.736316	−0.368158	+	0.929763i	$0.620011\pi$
$618$	−9.59380e14	−0.428108
$619$	−1.39239e15	−0.615831	−0.307916	−	0.951414i	$-0.599631\pi$
$619$	−1.39239e15	−0.615831	−0.307916	+	0.951414i	$0.599631\pi$
$620$	0	0
$621$	−3.22506e14	−0.140131
$622$	2.26601e15	0.975919
$623$	4.76357e15	2.03352
$624$	1.41643e14	0.0599348
$625$	0	0
$626$	1.46519e15	0.609167
$627$	2.01536e15	0.830581
$628$	4.12821e14	0.168649
$629$	1.44544e15	0.585356
$630$	0	0
$631$	−2.72790e15	−1.08559	−0.542796	−	0.839865i	$-0.682634\pi$
$631$	−2.72790e15	−1.08559	−0.542796	+	0.839865i	$0.682634\pi$
$632$	−6.57919e14	−0.259554
$633$	4.58665e14	0.179380
$634$	−1.11616e15	−0.432748
$635$	0	0
$636$	−7.85201e14	−0.299204
$637$	−2.00690e15	−0.758158
$638$	3.82953e15	1.43427
$639$	8.16993e14	0.303364
$640$	0	0
$641$	−1.08741e15	−0.396894	−0.198447	−	0.980112i	$-0.563590\pi$
$641$	−1.08741e15	−0.396894	−0.198447	+	0.980112i	$0.563590\pi$
$642$	−1.92652e15	−0.697156
$643$	−3.77029e14	−0.135274	−0.0676371	−	0.997710i	$-0.521546\pi$
$643$	−3.77029e14	−0.135274	−0.0676371	+	0.997710i	$0.521546\pi$
$644$	1.72041e15	0.612010
$645$	0	0
$646$	−2.67227e15	−0.934549
$647$	3.69951e15	1.28284	0.641418	−	0.767192i	$-0.278347\pi$
$647$	3.69951e15	1.28284	0.641418	+	0.767192i	$0.278347\pi$
$648$	−1.14255e14	−0.0392837
$649$	−2.73663e15	−0.932974
$650$	0	0
$651$	9.03076e14	0.302711
$652$	3.24394e14	0.107823
$653$	−5.26986e15	−1.73691	−0.868453	−	0.495771i	$-0.834886\pi$
$653$	−5.26986e15	−1.73691	−0.868453	+	0.495771i	$0.834886\pi$
$654$	−1.71320e15	−0.559927
$655$	0	0
$656$	8.35852e14	0.268632
$657$	−1.92491e15	−0.613482
$658$	3.46126e15	1.09393
$659$	−4.27769e15	−1.34072	−0.670362	−	0.742034i	$-0.733861\pi$
$659$	−4.27769e15	−1.34072	−0.670362	+	0.742034i	$0.733861\pi$
$660$	0	0
$661$	7.65436e14	0.235939	0.117970	−	0.993017i	$-0.462361\pi$
$661$	7.65436e14	0.235939	0.117970	+	0.993017i	$0.462361\pi$
$662$	3.97996e15	1.21663
$663$	−1.09106e15	−0.330770
$664$	−1.92276e14	−0.0578096
$665$	0	0
$666$	3.38147e14	0.0999995
$667$	−3.35307e15	−0.983446
$668$	−2.16806e15	−0.630667
$669$	2.51021e15	0.724213
$670$	0	0
$671$	4.17660e15	1.18536
$672$	6.09492e14	0.171568
$673$	2.28621e15	0.638313	0.319157	−	0.947702i	$-0.396600\pi$
$673$	2.28621e15	0.638313	0.319157	+	0.947702i	$0.396600\pi$
$674$	2.97397e15	0.823582
$675$	0	0
$676$	−1.51874e15	−0.413788
$677$	2.47195e15	0.668039	0.334020	−	0.942566i	$-0.391595\pi$
$677$	2.47195e15	0.668039	0.334020	+	0.942566i	$0.391595\pi$
$678$	−5.79492e14	−0.155340
$679$	7.24550e15	1.92657
$680$	0	0
$681$	−1.89849e15	−0.496707
$682$	1.27623e15	0.331218
$683$	1.51816e15	0.390844	0.195422	−	0.980719i	$-0.437392\pi$
$683$	1.51816e15	0.390844	0.195422	+	0.980719i	$0.437392\pi$
$684$	−6.25155e14	−0.159654
$685$	0	0
$686$	−3.90598e15	−0.981630
$687$	3.38500e15	0.843910
$688$	−2.00690e15	−0.496352
$689$	−1.75414e15	−0.430385
$690$	0	0
$691$	3.61124e15	0.872022	0.436011	−	0.899941i	$-0.356391\pi$
$691$	3.61124e15	0.872022	0.436011	+	0.899941i	$0.356391\pi$
$692$	9.89401e14	0.237022
$693$	3.54076e15	0.841519
$694$	−5.45676e14	−0.128664
$695$	0	0
$696$	−1.18790e15	−0.275695
$697$	−6.43850e15	−1.48253
$698$	−3.11876e15	−0.712488
$699$	−4.51834e14	−0.102413
$700$	0	0
$701$	−7.61693e15	−1.69954	−0.849769	−	0.527155i	$-0.823259\pi$
$701$	−7.61693e15	−1.69954	−0.849769	+	0.527155i	$0.823259\pi$
$702$	−2.55245e14	−0.0565071
$703$	1.85020e15	0.406410
$704$	8.61334e14	0.187725
$705$	0	0
$706$	4.04403e15	0.867738
$707$	2.71241e15	0.577495
$708$	8.48887e14	0.179336
$709$	1.17640e15	0.246603	0.123302	−	0.992369i	$-0.460652\pi$
$709$	1.17640e15	0.246603	0.123302	+	0.992369i	$0.460652\pi$
$710$	0	0
$711$	1.18559e15	0.244710
$712$	−2.08819e15	−0.427691
$713$	−1.11744e15	−0.227108
$714$	−4.69487e15	−0.946856
$715$	0	0
$716$	−1.33778e15	−0.265683
$717$	−2.83439e15	−0.558604
$718$	−4.50494e15	−0.881057
$719$	2.86879e15	0.556789	0.278394	−	0.960467i	$-0.410198\pi$
$719$	2.86879e15	0.556789	0.278394	+	0.960467i	$0.410198\pi$
$720$	0	0
$721$	−9.22245e15	−1.76280
$722$	3.07099e14	0.0582538
$723$	−8.38206e14	−0.157794
$724$	−2.58619e15	−0.483169
$725$	0	0
$726$	2.78522e15	0.512516
$727$	−5.56955e15	−1.01714	−0.508570	−	0.861020i	$-0.669826\pi$
$727$	−5.56955e15	−1.01714	−0.508570	+	0.861020i	$0.669826\pi$
$728$	1.36160e15	0.246790
$729$	2.05891e14	0.0370370
$730$	0	0
$731$	1.54590e16	2.73928
$732$	−1.29556e15	−0.227848
$733$	6.43548e15	1.12334	0.561668	−	0.827363i	$-0.310160\pi$
$733$	6.43548e15	1.12334	0.561668	+	0.827363i	$0.310160\pi$
$734$	−6.58989e15	−1.14169
$735$	0	0
$736$	−7.54169e14	−0.128718
$737$	−1.27067e16	−2.15259
$738$	−1.50623e15	−0.253269
$739$	−4.26005e15	−0.711001	−0.355500	−	0.934676i	$-0.615689\pi$
$739$	−4.26005e15	−0.711001	−0.355500	+	0.934676i	$0.615689\pi$
$740$	0	0
$741$	−1.39659e15	−0.229652
$742$	−7.54809e15	−1.23201
$743$	−1.05025e15	−0.170158	−0.0850792	−	0.996374i	$-0.527114\pi$
$743$	−1.05025e15	−0.170158	−0.0850792	+	0.996374i	$0.527114\pi$
$744$	−3.95879e14	−0.0636665
$745$	0	0
$746$	3.72385e15	0.590104
$747$	3.46487e14	0.0545034
$748$	−6.63479e15	−1.03602
$749$	−1.85195e16	−2.87064
$750$	0	0
$751$	3.21524e15	0.491127	0.245564	−	0.969380i	$-0.421027\pi$
$751$	3.21524e15	0.491127	0.245564	+	0.969380i	$0.421027\pi$
$752$	−1.51730e15	−0.230077
$753$	3.88079e13	0.00584181
$754$	−2.65376e15	−0.396570
$755$	0	0
$756$	−1.09833e15	−0.161756
$757$	3.23511e15	0.473000	0.236500	−	0.971631i	$-0.424000\pi$
$757$	3.23511e15	0.473000	0.236500	+	0.971631i	$0.424000\pi$
$758$	4.91787e15	0.713833
$759$	−4.38124e15	−0.631346
$760$	0	0
$761$	7.22075e15	1.02557	0.512787	−	0.858516i	$-0.328613\pi$
$761$	7.22075e15	1.02557	0.512787	+	0.858516i	$0.328613\pi$
$762$	1.06716e15	0.150479
$763$	−1.64689e16	−2.30558
$764$	−3.60963e14	−0.0501706
$765$	0	0
$766$	3.46448e15	0.474657
$767$	1.89641e15	0.257963
$768$	−2.67181e14	−0.0360844
$769$	6.56763e15	0.880672	0.440336	−	0.897833i	$-0.354859\pi$
$769$	6.56763e15	0.880672	0.440336	+	0.897833i	$0.354859\pi$
$770$	0	0
$771$	−5.75351e15	−0.760560
$772$	−6.76753e15	−0.888250
$773$	5.15062e15	0.671232	0.335616	−	0.941999i	$-0.391056\pi$
$773$	5.15062e15	0.671232	0.335616	+	0.941999i	$0.391056\pi$
$774$	3.61650e15	0.467965
$775$	0	0
$776$	−3.17619e15	−0.405198
$777$	3.25059e15	0.411762
$778$	6.56560e14	0.0825822
$779$	−8.24148e15	−1.02932
$780$	0	0
$781$	1.10988e16	1.36677
$782$	5.80931e15	0.710374
$783$	2.14063e15	0.259928
$784$	3.78563e15	0.456457
$785$	0	0
$786$	6.19427e14	0.0736489
$787$	7.05175e15	0.832599	0.416299	−	0.909228i	$-0.363327\pi$
$787$	7.05175e15	0.832599	0.416299	+	0.909228i	$0.363327\pi$
$788$	6.85241e15	0.803431
$789$	−8.31970e14	−0.0968688
$790$	0	0
$791$	−5.57062e15	−0.639636
$792$	−1.55215e15	−0.176989
$793$	−2.89427e15	−0.327745
$794$	1.13463e16	1.27597
$795$	0	0
$796$	7.65324e15	0.848835
$797$	1.94619e15	0.214370	0.107185	−	0.994239i	$-0.465816\pi$
$797$	1.94619e15	0.214370	0.107185	+	0.994239i	$0.465816\pi$
$798$	−6.00958e15	−0.657397
$799$	1.16876e16	1.26975
$800$	0	0
$801$	3.76299e15	0.403231
$802$	8.57381e15	0.912462
$803$	−2.61499e16	−2.76398
$804$	3.94155e15	0.413770
$805$	0	0
$806$	−8.84391e14	−0.0915802
$807$	−6.96975e15	−0.716824
$808$	−1.18903e15	−0.121459
$809$	−3.86583e15	−0.392217	−0.196108	−	0.980582i	$-0.562830\pi$
$809$	−3.86583e15	−0.392217	−0.196108	+	0.980582i	$0.562830\pi$
$810$	0	0
$811$	−3.90743e15	−0.391090	−0.195545	−	0.980695i	$-0.562648\pi$
$811$	−3.90743e15	−0.391090	−0.195545	+	0.980695i	$0.562648\pi$
$812$	−1.14192e16	−1.13521
$813$	−1.35846e15	−0.134137
$814$	4.59373e15	0.450538
$815$	0	0
$816$	2.05808e15	0.199143
$817$	1.97880e16	1.90187
$818$	1.04488e16	0.997525
$819$	−2.45365e15	−0.232676
$820$	0	0
$821$	1.70915e15	0.159916	0.0799580	−	0.996798i	$-0.474521\pi$
$821$	1.70915e15	0.159916	0.0799580	+	0.996798i	$0.474521\pi$
$822$	−5.35211e14	−0.0497427
$823$	−2.02375e15	−0.186835	−0.0934173	−	0.995627i	$-0.529779\pi$
$823$	−2.02375e15	−0.186835	−0.0934173	+	0.995627i	$0.529779\pi$
$824$	4.04282e15	0.370753
$825$	0	0
$826$	8.16029e15	0.738440
$827$	−1.00880e16	−0.906826	−0.453413	−	0.891300i	$-0.649794\pi$
$827$	−1.00880e16	−0.906826	−0.453413	+	0.891300i	$0.649794\pi$
$828$	1.35904e15	0.121357
$829$	−3.31015e15	−0.293628	−0.146814	−	0.989164i	$-0.546902\pi$
$829$	−3.31015e15	−0.293628	−0.146814	+	0.989164i	$0.546902\pi$
$830$	0	0
$831$	−1.04020e14	−0.00910564
$832$	−5.96882e14	−0.0519051
$833$	−2.91604e16	−2.51911
$834$	−2.60075e15	−0.223195
$835$	0	0
$836$	−8.49273e15	−0.719304
$837$	7.13386e14	0.0600253
$838$	−8.67776e15	−0.725380
$839$	4.00589e15	0.332666	0.166333	−	0.986070i	$-0.446807\pi$
$839$	4.00589e15	0.332666	0.166333	+	0.986070i	$0.446807\pi$
$840$	0	0
$841$	1.00555e16	0.824188
$842$	−7.70953e15	−0.627786
$843$	2.64834e15	0.214251
$844$	−1.93281e15	−0.155348
$845$	0	0
$846$	2.73422e15	0.216919
$847$	2.67741e16	2.11036
$848$	3.30883e15	0.259118
$849$	−1.37395e16	−1.06900
$850$	0	0
$851$	−4.02219e15	−0.308923
$852$	−3.44280e15	−0.262721
$853$	2.76334e15	0.209515	0.104757	−	0.994498i	$-0.466593\pi$
$853$	2.76334e15	0.209515	0.104757	+	0.994498i	$0.466593\pi$
$854$	−1.24541e16	−0.938198
$855$	0	0
$856$	8.11832e15	0.603755
$857$	5.65045e15	0.417531	0.208766	−	0.977966i	$-0.433055\pi$
$857$	5.65045e15	0.417531	0.208766	+	0.977966i	$0.433055\pi$
$858$	−3.46750e15	−0.254587
$859$	−2.06725e16	−1.50810	−0.754052	−	0.656815i	$-0.771903\pi$
$859$	−2.06725e16	−1.50810	−0.754052	+	0.656815i	$0.771903\pi$
$860$	0	0
$861$	−1.44793e16	−1.04287
$862$	1.46415e16	1.04784
$863$	−9.23100e15	−0.656431	−0.328216	−	0.944603i	$-0.606447\pi$
$863$	−9.23100e15	−0.656431	−0.328216	+	0.944603i	$0.606447\pi$
$864$	4.81469e14	0.0340207
$865$	0	0
$866$	−4.62903e15	−0.322955
$867$	−7.52514e15	−0.521687
$868$	−3.80555e15	−0.262156
$869$	1.61062e16	1.10252
$870$	0	0
$871$	8.80541e15	0.595182
$872$	7.21943e15	0.484911
$873$	5.72360e15	0.382024
$874$	7.43608e15	0.493209
$875$	0	0
$876$	8.11157e15	0.531291
$877$	−6.03959e15	−0.393106	−0.196553	−	0.980493i	$-0.562975\pi$
$877$	−6.03959e15	−0.393106	−0.196553	+	0.980493i	$0.562975\pi$
$878$	9.90916e15	0.640939
$879$	−2.87505e15	−0.184802
$880$	0	0
$881$	−7.34004e15	−0.465941	−0.232971	−	0.972484i	$-0.574845\pi$
$881$	−7.34004e15	−0.465941	−0.232971	+	0.972484i	$0.574845\pi$
$882$	−6.82183e15	−0.430352
$883$	−2.80456e16	−1.75825	−0.879127	−	0.476588i	$-0.841874\pi$
$883$	−2.80456e16	−1.75825	−0.879127	+	0.476588i	$0.841874\pi$
$884$	4.59773e15	0.286455
$885$	0	0
$886$	3.69900e15	0.227614
$887$	−1.99237e16	−1.21840	−0.609200	−	0.793017i	$-0.708509\pi$
$887$	−1.99237e16	−1.21840	−0.609200	+	0.793017i	$0.708509\pi$
$888$	−1.42495e15	−0.0866021
$889$	1.02585e16	0.619620
$890$	0	0
$891$	2.79703e15	0.166867
$892$	−1.05780e16	−0.627187
$893$	1.49605e16	0.881584
$894$	−1.35123e16	−0.791359
$895$	0	0
$896$	−2.56840e15	−0.148583
$897$	3.03608e15	0.174564
$898$	−1.09168e15	−0.0623846
$899$	7.41702e15	0.421261
$900$	0	0
$901$	−2.54877e16	−1.43003
$902$	−2.04622e16	−1.14108
$903$	3.47652e16	1.92691
$904$	2.44198e15	0.134529
$905$	0	0
$906$	3.90171e15	0.212349
$907$	−5.41309e14	−0.0292823	−0.0146412	−	0.999893i	$-0.504661\pi$
$907$	−5.41309e14	−0.0292823	−0.0146412	+	0.999893i	$0.504661\pi$
$908$	8.00024e15	0.430161
$909$	2.14267e15	0.114513
$910$	0	0
$911$	−1.91638e16	−1.01188	−0.505941	−	0.862568i	$-0.668855\pi$
$911$	−1.91638e16	−1.01188	−0.505941	+	0.862568i	$0.668855\pi$
$912$	2.63440e15	0.138264
$913$	4.70702e15	0.245560
$914$	1.30537e16	0.676906
$915$	0	0
$916$	−1.42644e16	−0.730848
$917$	5.95451e15	0.303260
$918$	−3.70872e15	−0.187754
$919$	3.88332e16	1.95420	0.977099	−	0.212787i	$-0.0682539\pi$
$919$	3.88332e16	1.95420	0.977099	+	0.212787i	$0.0682539\pi$
$920$	0	0
$921$	−5.73043e15	−0.284944
$922$	−3.82261e15	−0.188947
$923$	−7.69120e15	−0.377907
$924$	−1.49207e16	−0.728777
$925$	0	0
$926$	2.24259e16	1.08240
$927$	−7.28529e15	−0.349549
$928$	5.00580e15	0.238759
$929$	−3.51219e16	−1.66530	−0.832648	−	0.553803i	$-0.813176\pi$
$929$	−3.51219e16	−1.66530	−0.832648	+	0.553803i	$0.813176\pi$
$930$	0	0
$931$	−3.73262e16	−1.74900
$932$	1.90403e15	0.0886921
$933$	1.72075e16	0.796835
$934$	2.26673e16	1.04350
$935$	0	0
$936$	1.07560e15	0.0489366
$937$	1.27459e16	0.576504	0.288252	−	0.957555i	$-0.406926\pi$
$937$	1.27459e16	0.576504	0.288252	+	0.957555i	$0.406926\pi$
$938$	3.78899e16	1.70376
$939$	1.11263e16	0.497383
$940$	0	0
$941$	1.69186e16	0.747519	0.373759	−	0.927526i	$-0.378069\pi$
$941$	1.69186e16	0.747519	0.373759	+	0.927526i	$0.378069\pi$
$942$	3.13486e15	0.137701
$943$	1.79163e16	0.782409
$944$	−3.57720e15	−0.155309
$945$	0	0
$946$	4.91301e16	2.10837
$947$	1.11373e16	0.475175	0.237587	−	0.971366i	$-0.423643\pi$
$947$	1.11373e16	0.475175	0.237587	+	0.971366i	$0.423643\pi$
$948$	−4.99607e15	−0.211925
$949$	1.81212e16	0.764228
$950$	0	0
$951$	−8.47584e15	−0.353338
$952$	1.97842e16	0.820001
$953$	2.38806e16	0.984091	0.492045	−	0.870570i	$-0.336249\pi$
$953$	2.38806e16	0.984091	0.492045	+	0.870570i	$0.336249\pi$
$954$	−5.96262e15	−0.244299
$955$	0	0
$956$	1.19441e16	0.483765
$957$	2.90805e16	1.17108
$958$	−3.03160e15	−0.121384
$959$	−5.14494e15	−0.204823
$960$	0	0
$961$	−2.29367e16	−0.902718
$962$	−3.18333e15	−0.124572
$963$	−1.46295e16	−0.569226
$964$	3.53219e15	0.136654
$965$	0	0
$966$	1.30643e16	0.499704
$967$	4.36732e16	1.66100	0.830499	−	0.557020i	$-0.188055\pi$
$967$	4.36732e16	1.66100	0.830499	+	0.557020i	$0.188055\pi$
$968$	−1.17369e16	−0.443852
$969$	−2.02926e16	−0.763056
$970$	0	0
$971$	−2.17127e16	−0.807251	−0.403626	−	0.914924i	$-0.632250\pi$
$971$	−2.17127e16	−0.807251	−0.403626	+	0.914924i	$0.632250\pi$
$972$	−8.67624e14	−0.0320750
$973$	−2.50008e16	−0.919038
$974$	2.61160e16	0.954623
$975$	0	0
$976$	5.45947e15	0.197323
$977$	−5.23688e16	−1.88214	−0.941071	−	0.338210i	$-0.890178\pi$
$977$	−5.23688e16	−1.88214	−0.941071	+	0.338210i	$0.890178\pi$
$978$	2.46337e15	0.0880370
$979$	5.11201e16	1.81672
$980$	0	0
$981$	−1.30097e16	−0.457179
$982$	−3.79488e16	−1.32612
$983$	3.67253e15	0.127621	0.0638103	−	0.997962i	$-0.479675\pi$
$983$	3.67253e15	0.127621	0.0638103	+	0.997962i	$0.479675\pi$
$984$	6.34725e15	0.219337
$985$	0	0
$986$	−3.85593e16	−1.31767
$987$	2.62839e16	0.893193
$988$	5.88523e15	0.198884
$989$	−4.30174e16	−1.44566
$990$	0	0
$991$	4.81435e16	1.60005	0.800023	−	0.599969i	$-0.204820\pi$
$991$	4.81435e16	1.60005	0.800023	+	0.599969i	$0.204820\pi$
$992$	1.66823e15	0.0551368
$993$	3.02228e16	0.993378
$994$	−3.30954e16	−1.08179
$995$	0	0
$996$	−1.46009e15	−0.0472013
$997$	−8.11665e15	−0.260948	−0.130474	−	0.991452i	$-0.541650\pi$
$997$	−8.11665e15	−0.260948	−0.130474	+	0.991452i	$0.541650\pi$
$998$	3.91231e16	1.25088
$999$	2.56781e15	0.0816492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.12.a.j.1.2	✓	2
5.2	odd	4		150.12.c.m.49.2		4
5.3	odd	4		150.12.c.m.49.3		4
5.4	even	2		150.12.a.s.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.12.a.j.1.2	✓	2	1.1	even	1	trivial
150.12.a.s.1.1	yes	2	5.4	even	2
150.12.c.m.49.2		4	5.2	odd	4
150.12.c.m.49.3		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +7776.00 q^{6} +74750.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} +802180. q^{11} -248832. q^{12} -555889. q^{13} -2.39201e6 q^{14} +1.04858e6 q^{16} -8.07710e6 q^{17} -1.88957e6 q^{18} -1.03389e7 q^{19} -1.81643e7 q^{21} -2.56698e7 q^{22} +2.24760e7 q^{23} +7.96262e6 q^{24} +1.77885e7 q^{26} -1.43489e7 q^{27} +7.65442e7 q^{28} -1.49185e8 q^{29} -4.97171e7 q^{31} -3.35544e7 q^{32} -1.94930e8 q^{33} +2.58467e8 q^{34} +6.04662e7 q^{36} -1.78955e8 q^{37} +3.30846e8 q^{38} +1.35081e8 q^{39} +7.97131e8 q^{41} +5.81257e8 q^{42} -1.91393e9 q^{43} +8.21432e8 q^{44} -7.19231e8 q^{46} -1.44701e9 q^{47} -2.54804e8 q^{48} +3.61026e9 q^{49} +1.96274e9 q^{51} -5.69231e8 q^{52} +3.15555e9 q^{53} +4.59165e8 q^{54} -2.44941e9 q^{56} +2.51236e9 q^{57} +4.77390e9 q^{58} -3.41149e9 q^{59} +5.20656e9 q^{61} +1.59095e9 q^{62} +4.41392e9 q^{63} +1.07374e9 q^{64} +6.23775e9 q^{66} -1.58402e10 q^{67} -8.27095e9 q^{68} -5.46166e9 q^{69} +1.38358e10 q^{71} -1.93492e9 q^{72} -3.25986e10 q^{73} +5.72655e9 q^{74} -1.05871e10 q^{76} +5.99631e10 q^{77} -4.32260e9 q^{78} +2.00781e10 q^{79} +3.48678e9 q^{81} -2.55082e10 q^{82} +5.86779e9 q^{83} -1.86002e10 q^{84} +6.12457e10 q^{86} +3.62518e10 q^{87} -2.62858e10 q^{88} +6.37265e10 q^{89} -4.15528e10 q^{91} +2.30154e10 q^{92} +1.20813e10 q^{93} +4.63043e10 q^{94} +8.15373e9 q^{96} +9.69296e10 q^{97} -1.15528e11 q^{98} +4.73679e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 64 q^{2} - 486 q^{3} + 2048 q^{4} + 15552 q^{6} + 24058 q^{7} - 65536 q^{8} + 118098 q^{9} + 726264 q^{11} - 497664 q^{12} - 860894 q^{13} - 769856 q^{14} + 2097152 q^{16} - 6996912 q^{17} - 3779136 q^{18}+ \cdots + 42885162936 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more