LMFDB - Embedded newform 2.24.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,24,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 24, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$6.70408074690$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2048.00 q^{2} -505908. q^{3} +4.19430e6 q^{4} -9.01356e7 q^{5} +1.03610e9 q^{6} +6.87226e9 q^{7} -8.58993e9 q^{8} +1.61800e11 q^{9} +O(q^{10})$

\(q-2048.00 q^{2} -505908. q^{3} +4.19430e6 q^{4} -9.01356e7 q^{5} +1.03610e9 q^{6} +6.87226e9 q^{7} -8.58993e9 q^{8} +1.61800e11 q^{9} +1.84598e11 q^{10} -9.65329e11 q^{11} -2.12193e12 q^{12} +5.42360e11 q^{13} -1.40744e13 q^{14} +4.56003e13 q^{15} +1.75922e13 q^{16} +8.20835e13 q^{17} -3.31366e14 q^{18} +5.55749e14 q^{19} -3.78056e14 q^{20} -3.47673e15 q^{21} +1.97699e15 q^{22} +6.50864e15 q^{23} +4.34572e15 q^{24} -3.79651e15 q^{25} -1.11075e15 q^{26} -3.42280e16 q^{27} +2.88243e16 q^{28} -1.22020e16 q^{29} -9.33894e16 q^{30} +1.19978e17 q^{31} -3.60288e16 q^{32} +4.88368e17 q^{33} -1.68107e17 q^{34} -6.19435e17 q^{35} +6.78637e17 q^{36} -6.19511e17 q^{37} -1.13817e18 q^{38} -2.74384e17 q^{39} +7.74259e17 q^{40} -1.58774e18 q^{41} +7.12034e18 q^{42} +8.37772e18 q^{43} -4.04888e18 q^{44} -1.45839e19 q^{45} -1.33297e19 q^{46} +1.31005e19 q^{47} -8.90003e18 q^{48} +1.98591e19 q^{49} +7.77525e18 q^{50} -4.15267e19 q^{51} +2.27482e18 q^{52} +4.17960e19 q^{53} +7.00989e19 q^{54} +8.70105e19 q^{55} -5.90322e19 q^{56} -2.81158e20 q^{57} +2.49898e19 q^{58} -7.43839e19 q^{59} +1.91262e20 q^{60} -2.71922e20 q^{61} -2.45715e20 q^{62} +1.11193e21 q^{63} +7.37870e19 q^{64} -4.88859e19 q^{65} -1.00018e21 q^{66} +1.74814e21 q^{67} +3.44283e20 q^{68} -3.29277e21 q^{69} +1.26860e21 q^{70} -2.71799e21 q^{71} -1.38985e21 q^{72} +4.31278e21 q^{73} +1.26876e21 q^{74} +1.92068e21 q^{75} +2.33098e21 q^{76} -6.63399e21 q^{77} +5.61939e20 q^{78} +3.59856e21 q^{79} -1.58568e21 q^{80} +2.08387e21 q^{81} +3.25168e21 q^{82} -2.25004e20 q^{83} -1.45825e22 q^{84} -7.39865e21 q^{85} -1.71576e22 q^{86} +6.17311e21 q^{87} +8.29211e21 q^{88} +3.38924e22 q^{89} +2.98678e22 q^{90} +3.72724e21 q^{91} +2.72992e22 q^{92} -6.06978e22 q^{93} -2.68297e22 q^{94} -5.00927e22 q^{95} +1.82273e22 q^{96} +9.21216e22 q^{97} -4.06715e22 q^{98} -1.56190e23 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−2048.00	−0.707107
$2$	−2048.00	−0.707107
$3$	−505908.	−1.64883	−0.824417	−	0.565982i	$-0.808497\pi$
$3$	−505908.	−1.64883	−0.824417	+	0.565982i	$0.808497\pi$
$4$	4.19430e6	0.500000
$5$	−9.01356e7	−0.825546	−0.412773	−	0.910834i	$-0.635440\pi$
$5$	−9.01356e7	−0.825546	−0.412773	+	0.910834i	$0.635440\pi$
$6$	1.03610e9	1.16590
$7$	6.87226e9	1.31363	0.656813	−	0.754053i	$-0.271904\pi$
$7$	6.87226e9	1.31363	0.656813	+	0.754053i	$0.271904\pi$
$8$	−8.58993e9	−0.353553
$9$	1.61800e11	1.71866
$10$	1.84598e11	0.583749
$11$	−9.65329e11	−1.02014	−0.510070	−	0.860133i	$-0.670380\pi$
$11$	−9.65329e11	−1.02014	−0.510070	+	0.860133i	$0.670380\pi$
$12$	−2.12193e12	−0.824417
$13$	5.42360e11	0.0839342	0.0419671	−	0.999119i	$-0.486638\pi$
$13$	5.42360e11	0.0839342	0.0419671	+	0.999119i	$0.486638\pi$
$14$	−1.40744e13	−0.928874
$15$	4.56003e13	1.36119
$16$	1.75922e13	0.250000
$17$	8.20835e13	0.580889	0.290445	−	0.956892i	$-0.406197\pi$
$17$	8.20835e13	0.580889	0.290445	+	0.956892i	$0.406197\pi$
$18$	−3.31366e14	−1.21527
$19$	5.55749e14	1.09449	0.547245	−	0.836972i	$-0.315677\pi$
$19$	5.55749e14	1.09449	0.547245	+	0.836972i	$0.315677\pi$
$20$	−3.78056e14	−0.412773
$21$	−3.47673e15	−2.16595
$22$	1.97699e15	0.721347
$23$	6.50864e15	1.42436	0.712180	−	0.701996i	$-0.247708\pi$
$23$	6.50864e15	1.42436	0.712180	+	0.701996i	$0.247708\pi$
$24$	4.34572e15	0.582951
$25$	−3.79651e15	−0.318474
$26$	−1.11075e15	−0.0593505
$27$	−3.42280e16	−1.18494
$28$	2.88243e16	0.656813
$29$	−1.22020e16	−0.185719	−0.0928593	−	0.995679i	$-0.529601\pi$
$29$	−1.22020e16	−0.185719	−0.0928593	+	0.995679i	$0.529601\pi$
$30$	−9.33894e16	−0.962506
$31$	1.19978e17	0.848090	0.424045	−	0.905641i	$-0.360610\pi$
$31$	1.19978e17	0.848090	0.424045	+	0.905641i	$0.360610\pi$
$32$	−3.60288e16	−0.176777
$33$	4.88368e17	1.68204
$34$	−1.68107e17	−0.410751
$35$	−6.19435e17	−1.08446
$36$	6.78637e17	0.859328
$37$	−6.19511e17	−0.572439	−0.286219	−	0.958164i	$-0.592399\pi$
$37$	−6.19511e17	−0.572439	−0.286219	+	0.958164i	$0.592399\pi$
$38$	−1.13817e18	−0.773922
$39$	−2.74384e17	−0.138394
$40$	7.74259e17	0.291875
$41$	−1.58774e18	−0.450572	−0.225286	−	0.974293i	$-0.572332\pi$
$41$	−1.58774e18	−0.450572	−0.225286	+	0.974293i	$0.572332\pi$
$42$	7.12034e18	1.53156
$43$	8.37772e18	1.37480	0.687398	−	0.726281i	$-0.258753\pi$
$43$	8.37772e18	1.37480	0.687398	+	0.726281i	$0.258753\pi$
$44$	−4.04888e18	−0.510070
$45$	−1.45839e19	−1.41883
$46$	−1.33297e19	−1.00718
$47$	1.31005e19	0.772967	0.386484	−	0.922296i	$-0.373690\pi$
$47$	1.31005e19	0.772967	0.386484	+	0.922296i	$0.373690\pi$
$48$	−8.90003e18	−0.412209
$49$	1.98591e19	0.725614
$50$	7.77525e18	0.225195
$51$	−4.15267e19	−0.957791
$52$	2.27482e18	0.0419671
$53$	4.17960e19	0.619387	0.309693	−	0.950836i	$-0.399774\pi$
$53$	4.17960e19	0.619387	0.309693	+	0.950836i	$0.399774\pi$
$54$	7.00989e19	0.837882
$55$	8.70105e19	0.842172
$56$	−5.90322e19	−0.464437
$57$	−2.81158e20	−1.80463
$58$	2.49898e19	0.131323
$59$	−7.43839e19	−0.321130	−0.160565	−	0.987025i	$-0.551332\pi$
$59$	−7.43839e19	−0.321130	−0.160565	+	0.987025i	$0.551332\pi$
$60$	1.91262e20	0.680594
$61$	−2.71922e20	−0.800113	−0.400056	−	0.916490i	$-0.631009\pi$
$61$	−2.71922e20	−0.800113	−0.400056	+	0.916490i	$0.631009\pi$
$62$	−2.45715e20	−0.599691
$63$	1.11193e21	2.25767
$64$	7.37870e19	0.125000
$65$	−4.88859e19	−0.0692915
$66$	−1.00018e21	−1.18938
$67$	1.74814e21	1.74870	0.874350	−	0.485296i	$-0.161288\pi$
$67$	1.74814e21	1.74870	0.874350	+	0.485296i	$0.161288\pi$
$68$	3.44283e20	0.290445
$69$	−3.29277e21	−2.34854
$70$	1.26860e21	0.766828
$71$	−2.71799e21	−1.39565	−0.697825	−	0.716269i	$-0.745849\pi$
$71$	−2.71799e21	−1.39565	−0.697825	+	0.716269i	$0.745849\pi$
$72$	−1.38985e21	−0.607637
$73$	4.31278e21	1.60896	0.804479	−	0.593982i	$-0.202445\pi$
$73$	4.31278e21	1.60896	0.804479	+	0.593982i	$0.202445\pi$
$74$	1.26876e21	0.404775
$75$	1.92068e21	0.525111
$76$	2.33098e21	0.547245
$77$	−6.63399e21	−1.34008
$78$	5.61939e20	0.0978591
$79$	3.59856e21	0.541274	0.270637	−	0.962681i	$-0.412766\pi$
$79$	3.59856e21	0.541274	0.270637	+	0.962681i	$0.412766\pi$
$80$	−1.58568e21	−0.206386
$81$	2.08387e21	0.235122
$82$	3.25168e21	0.318602
$83$	−2.25004e20	−0.0191775	−0.00958876	−	0.999954i	$-0.503052\pi$
$83$	−2.25004e20	−0.0191775	−0.00958876	+	0.999954i	$0.503052\pi$
$84$	−1.45825e22	−1.08298
$85$	−7.39865e21	−0.479551
$86$	−1.71576e22	−0.972128
$87$	6.17311e21	0.306219
$88$	8.29211e21	0.360674
$89$	3.38924e22	1.29455	0.647273	−	0.762258i	$-0.275909\pi$
$89$	3.38924e22	1.29455	0.647273	+	0.762258i	$0.275909\pi$
$90$	2.98678e22	1.00326
$91$	3.72724e21	0.110258
$92$	2.72992e22	0.712180
$93$	−6.06978e22	−1.39836
$94$	−2.68297e22	−0.546570
$95$	−5.00927e22	−0.903552
$96$	1.82273e22	0.291476
$97$	9.21216e22	1.30763	0.653817	−	0.756652i	$-0.273166\pi$
$97$	9.21216e22	1.30763	0.653817	+	0.756652i	$0.273166\pi$
$98$	−4.06715e22	−0.513086
$99$	−1.56190e23	−1.75327
$100$	−1.59237e22	−0.159237
$101$	1.42425e23	1.27026	0.635129	−	0.772406i	$-0.280947\pi$
$101$	1.42425e23	1.27026	0.635129	+	0.772406i	$0.280947\pi$
$102$	8.50467e22	0.677260
$103$	−1.07041e23	−0.761946	−0.380973	−	0.924586i	$-0.624411\pi$
$103$	−1.07041e23	−0.761946	−0.380973	+	0.924586i	$0.624411\pi$
$104$	−4.65884e21	−0.0296752
$105$	3.13377e23	1.78809
$106$	−8.55982e22	−0.437973
$107$	1.90048e23	0.872872	0.436436	−	0.899735i	$-0.356240\pi$
$107$	1.90048e23	0.872872	0.436436	+	0.899735i	$0.356240\pi$
$108$	−1.43563e23	−0.592472
$109$	−4.03432e23	−1.49750	−0.748749	−	0.662854i	$-0.769345\pi$
$109$	−4.03432e23	−1.49750	−0.748749	+	0.662854i	$0.769345\pi$
$110$	−1.78197e23	−0.595505
$111$	3.13416e23	0.943857
$112$	1.20898e23	0.328407
$113$	−4.80831e23	−1.17921	−0.589604	−	0.807693i	$-0.700716\pi$
$113$	−4.80831e23	−1.17921	−0.589604	+	0.807693i	$0.700716\pi$
$114$	5.75811e23	1.27607
$115$	−5.86660e23	−1.17588
$116$	−5.11791e22	−0.0928593
$117$	8.77537e22	0.144254
$118$	1.52338e23	0.227073
$119$	5.64099e23	0.763072
$120$	−3.91704e23	−0.481253
$121$	3.64294e22	0.0406837
$122$	5.56896e23	0.565765
$123$	8.03248e23	0.742918
$124$	5.03224e23	0.424045
$125$	1.41670e24	1.08846
$126$	−2.27723e24	−1.59641
$127$	−2.24142e24	−1.43476	−0.717381	−	0.696681i	$-0.754659\pi$
$127$	−2.24142e24	−1.43476	−0.717381	+	0.696681i	$0.754659\pi$
$128$	−1.51116e23	−0.0883883
$129$	−4.23835e24	−2.26681
$130$	1.00118e23	0.0489965
$131$	3.40494e24	1.52577	0.762887	−	0.646532i	$-0.223781\pi$
$131$	3.40494e24	1.52577	0.762887	+	0.646532i	$0.223781\pi$
$132$	2.04836e24	0.841020
$133$	3.81925e24	1.43775
$134$	−3.58018e24	−1.23652
$135$	3.08516e24	0.978226
$136$	−7.05092e23	−0.205375
$137$	−4.70653e24	−1.26013	−0.630063	−	0.776544i	$-0.716971\pi$
$137$	−4.70653e24	−1.26013	−0.630063	+	0.776544i	$0.716971\pi$
$138$	6.74360e24	1.66067
$139$	5.18506e23	0.117512	0.0587562	−	0.998272i	$-0.481287\pi$
$139$	5.18506e23	0.117512	0.0587562	+	0.998272i	$0.481287\pi$
$140$	−2.59810e24	−0.542229
$141$	−6.62763e24	−1.27450
$142$	5.56644e24	0.986873
$143$	−5.23556e23	−0.0856246
$144$	2.84641e24	0.429664
$145$	1.09984e24	0.153319
$146$	−8.83258e24	−1.13770
$147$	−1.00469e25	−1.19642
$148$	−2.59842e24	−0.286219
$149$	1.00676e25	1.02632	0.513160	−	0.858293i	$-0.328475\pi$
$149$	1.00676e25	1.02632	0.513160	+	0.858293i	$0.328475\pi$
$150$	−3.93356e24	−0.371310
$151$	1.12958e25	0.987832	0.493916	−	0.869509i	$-0.335565\pi$
$151$	1.12958e25	0.987832	0.493916	+	0.869509i	$0.335565\pi$
$152$	−4.77384e24	−0.386961
$153$	1.32811e25	0.998349
$154$	1.35864e25	0.947581
$155$	−1.08143e25	−0.700137
$156$	−1.15085e24	−0.0691968
$157$	4.49140e24	0.250920	0.125460	−	0.992099i	$-0.459959\pi$
$157$	4.49140e24	0.250920	0.125460	+	0.992099i	$0.459959\pi$
$158$	−7.36986e24	−0.382739
$159$	−2.11449e25	−1.02127
$160$	3.24748e24	0.145937
$161$	4.47290e25	1.87108
$162$	−4.26777e24	−0.166256
$163$	−3.38828e25	−1.22977	−0.614883	−	0.788619i	$-0.710797\pi$
$163$	−3.38828e25	−1.22977	−0.614883	+	0.788619i	$0.710797\pi$
$164$	−6.65945e24	−0.225286
$165$	−4.40193e25	−1.38860
$166$	4.60809e23	0.0135606
$167$	−2.60376e24	−0.0715092	−0.0357546	−	0.999361i	$-0.511383\pi$
$167$	−2.60376e24	−0.0715092	−0.0357546	+	0.999361i	$0.511383\pi$
$168$	2.98649e25	0.765780
$169$	−4.14598e25	−0.992955
$170$	1.51524e25	0.339094
$171$	8.99200e25	1.88105
$172$	3.51387e25	0.687398
$173$	3.96085e25	0.724866	0.362433	−	0.932010i	$-0.381946\pi$
$173$	3.96085e25	0.724866	0.362433	+	0.932010i	$0.381946\pi$
$174$	−1.26425e25	−0.216530
$175$	−2.60906e25	−0.418356
$176$	−1.69822e25	−0.255035
$177$	3.76314e25	0.529490
$178$	−6.94117e25	−0.915382
$179$	−4.42305e25	−0.546905	−0.273453	−	0.961885i	$-0.588166\pi$
$179$	−4.42305e25	−0.546905	−0.273453	+	0.961885i	$0.588166\pi$
$180$	−6.11694e25	−0.709415
$181$	−8.22310e25	−0.894813	−0.447406	−	0.894331i	$-0.647652\pi$
$181$	−8.22310e25	−0.894813	−0.447406	+	0.894331i	$0.647652\pi$
$182$	−7.63338e24	−0.0779643
$183$	1.37568e26	1.31925
$184$	−5.59088e25	−0.503588
$185$	5.58400e25	0.472575
$186$	1.24309e26	0.988791
$187$	−7.92376e25	−0.592588
$188$	5.49473e25	0.386484
$189$	−2.35223e26	−1.55657
$190$	1.02590e26	0.638908
$191$	5.22803e25	0.306517	0.153258	−	0.988186i	$-0.451023\pi$
$191$	5.22803e25	0.306517	0.153258	+	0.988186i	$0.451023\pi$
$192$	−3.73294e25	−0.206104
$193$	2.67638e26	1.39200	0.695999	−	0.718043i	$-0.254962\pi$
$193$	2.67638e26	1.39200	0.695999	+	0.718043i	$0.254962\pi$
$194$	−1.88665e26	−0.924637
$195$	2.47318e25	0.114250
$196$	8.32953e25	0.362807
$197$	8.45015e25	0.347139	0.173569	−	0.984822i	$-0.444470\pi$
$197$	8.45015e25	0.347139	0.173569	+	0.984822i	$0.444470\pi$
$198$	3.19877e26	1.23975
$199$	−1.66457e25	−0.0608823	−0.0304411	−	0.999537i	$-0.509691\pi$
$199$	−1.66457e25	−0.0608823	−0.0304411	+	0.999537i	$0.509691\pi$
$200$	3.26118e25	0.112598
$201$	−8.84397e26	−2.88332
$202$	−2.91687e26	−0.898208
$203$	−8.38555e25	−0.243965
$204$	−1.74176e26	−0.478895
$205$	1.43111e26	0.371967
$206$	2.19221e26	0.538777
$207$	1.05310e27	2.44799
$208$	9.54130e24	0.0209836
$209$	−5.36480e26	−1.11653
$210$	−6.41796e26	−1.26437
$211$	2.79674e26	0.521680	0.260840	−	0.965382i	$-0.416001\pi$
$211$	2.79674e26	0.521680	0.260840	+	0.965382i	$0.416001\pi$
$212$	1.75305e26	0.309693
$213$	1.37505e27	2.30120
$214$	−3.89219e26	−0.617214
$215$	−7.55130e26	−1.13496
$216$	2.94016e26	0.418941
$217$	8.24519e26	1.11407
$218$	8.26230e26	1.05889
$219$	−2.18187e27	−2.65290
$220$	3.64948e26	0.421086
$221$	4.45188e25	0.0487565
$222$	−6.41875e26	−0.667408
$223$	−5.45249e26	−0.538380	−0.269190	−	0.963087i	$-0.586756\pi$
$223$	−5.45249e26	−0.538380	−0.269190	+	0.963087i	$0.586756\pi$
$224$	−2.47599e26	−0.232219
$225$	−6.14274e26	−0.547348
$226$	9.84742e26	0.833826
$227$	−1.15345e27	−0.928326	−0.464163	−	0.885750i	$-0.653645\pi$
$227$	−1.15345e27	−0.928326	−0.464163	+	0.885750i	$0.653645\pi$
$228$	−1.17926e27	−0.902317
$229$	1.17499e27	0.854922	0.427461	−	0.904034i	$-0.359408\pi$
$229$	1.17499e27	0.854922	0.427461	+	0.904034i	$0.359408\pi$
$230$	1.20148e27	0.831469
$231$	3.35619e27	2.20957
$232$	1.04815e26	0.0656614
$233$	5.77127e26	0.344095	0.172048	−	0.985089i	$-0.444962\pi$
$233$	5.77127e26	0.344095	0.172048	+	0.985089i	$0.444962\pi$
$234$	−1.79720e26	−0.102003
$235$	−1.18082e27	−0.638120
$236$	−3.11989e26	−0.160565
$237$	−1.82054e27	−0.892472
$238$	−1.15527e27	−0.539573
$239$	−3.06102e26	−0.136236	−0.0681178	−	0.997677i	$-0.521699\pi$
$239$	−3.06102e26	−0.136236	−0.0681178	+	0.997677i	$0.521699\pi$
$240$	8.02209e26	0.340297
$241$	1.82530e27	0.738139	0.369070	−	0.929402i	$-0.379676\pi$
$241$	1.82530e27	0.738139	0.369070	+	0.929402i	$0.379676\pi$
$242$	−7.46075e25	−0.0287677
$243$	2.16808e27	0.797267
$244$	−1.14052e27	−0.400056
$245$	−1.79002e27	−0.599027
$246$	−1.64505e27	−0.525322
$247$	3.01416e26	0.0918652
$248$	−1.03060e27	−0.299845
$249$	1.13831e26	0.0316206
$250$	−2.90140e27	−0.769658
$251$	−1.72473e27	−0.436991	−0.218495	−	0.975838i	$-0.570115\pi$
$251$	−1.72473e27	−0.436991	−0.218495	+	0.975838i	$0.570115\pi$
$252$	4.66377e27	1.12884
$253$	−6.28298e27	−1.45305
$254$	4.59042e27	1.01453
$255$	3.74303e27	0.790700
$256$	3.09485e26	0.0625000
$257$	5.49958e27	1.06194	0.530968	−	0.847392i	$-0.321828\pi$
$257$	5.49958e27	1.06194	0.530968	+	0.847392i	$0.321828\pi$
$258$	8.68015e27	1.60288
$259$	−4.25744e27	−0.751971
$260$	−2.05042e26	−0.0346458
$261$	−1.97429e27	−0.319186
$262$	−6.97332e27	−1.07888
$263$	1.10256e28	1.63272	0.816360	−	0.577543i	$-0.195988\pi$
$263$	1.10256e28	1.63272	0.816360	+	0.577543i	$0.195988\pi$
$264$	−4.19505e27	−0.594691
$265$	−3.76730e27	−0.511332
$266$	−7.82182e27	−1.01664
$267$	−1.71464e28	−2.13449
$268$	7.33222e27	0.874350
$269$	5.47893e26	0.0625957	0.0312978	−	0.999510i	$-0.490036\pi$
$269$	5.47893e26	0.0625957	0.0312978	+	0.999510i	$0.490036\pi$
$270$	−6.31841e27	−0.691710
$271$	1.43098e28	1.50137	0.750683	−	0.660663i	$-0.229725\pi$
$271$	1.43098e28	1.50137	0.750683	+	0.660663i	$0.229725\pi$
$272$	1.44403e27	0.145222
$273$	−1.88564e27	−0.181798
$274$	9.63897e27	0.891044
$275$	3.66488e27	0.324888
$276$	−1.38109e28	−1.17427
$277$	−4.09302e27	−0.333831	−0.166915	−	0.985971i	$-0.553381\pi$
$277$	−4.09302e27	−0.333831	−0.166915	+	0.985971i	$0.553381\pi$
$278$	−1.06190e27	−0.0830938
$279$	1.94124e28	1.45758
$280$	5.32090e27	0.383414
$281$	−6.59576e27	−0.456186	−0.228093	−	0.973639i	$-0.573249\pi$
$281$	−6.59576e27	−0.456186	−0.228093	+	0.973639i	$0.573249\pi$
$282$	1.35734e28	0.901204
$283$	−4.65761e27	−0.296906	−0.148453	−	0.988919i	$-0.547429\pi$
$283$	−4.65761e27	−0.296906	−0.148453	+	0.988919i	$0.547429\pi$
$284$	−1.14001e28	−0.697825
$285$	2.53423e28	1.48981
$286$	1.07224e27	0.0605457
$287$	−1.09113e28	−0.591883
$288$	−5.82945e27	−0.303818
$289$	−1.32299e28	−0.662567
$290$	−2.25247e27	−0.108413
$291$	−4.66050e28	−2.15607
$292$	1.80891e28	0.804479
$293$	−2.37368e28	−1.01495	−0.507476	−	0.861666i	$-0.669421\pi$
$293$	−2.37368e28	−1.01495	−0.507476	+	0.861666i	$0.669421\pi$
$294$	2.05760e28	0.845995
$295$	6.70463e27	0.265107
$296$	5.32156e27	0.202388
$297$	3.30413e28	1.20881
$298$	−2.06184e28	−0.725718
$299$	3.53003e27	0.119553
$300$	8.05593e27	0.262556
$301$	5.75738e28	1.80597
$302$	−2.31339e28	−0.698503
$303$	−7.20542e28	−2.09445
$304$	9.77683e27	0.273623
$305$	2.45098e28	0.660530
$306$	−2.71997e28	−0.705939
$307$	3.33435e28	0.833527	0.416763	−	0.909015i	$-0.363164\pi$
$307$	3.33435e28	0.833527	0.416763	+	0.909015i	$0.363164\pi$
$308$	−2.78250e28	−0.670041
$309$	5.41531e28	1.25632
$310$	2.21477e28	0.495072
$311$	8.79341e28	1.89414	0.947072	−	0.321021i	$-0.104026\pi$
$311$	8.79341e28	1.89414	0.947072	+	0.321021i	$0.104026\pi$
$312$	2.35694e27	0.0489296
$313$	−9.00131e28	−1.80113	−0.900567	−	0.434718i	$-0.856848\pi$
$313$	−9.00131e28	−1.80113	−0.900567	+	0.434718i	$0.856848\pi$
$314$	−9.19839e27	−0.177427
$315$	−1.00224e29	−1.86381
$316$	1.50935e28	0.270637
$317$	−3.39800e28	−0.587545	−0.293773	−	0.955875i	$-0.594911\pi$
$317$	−3.39800e28	−0.587545	−0.293773	+	0.955875i	$0.594911\pi$
$318$	4.33048e28	0.722145
$319$	1.17790e28	0.189459
$320$	−6.65083e27	−0.103193
$321$	−9.61470e28	−1.43922
$322$	−9.16050e28	−1.32305
$323$	4.56178e28	0.635778
$324$	8.74040e27	0.117561
$325$	−2.05907e27	−0.0267309
$326$	6.93920e28	0.869575
$327$	2.04100e29	2.46913
$328$	1.36385e28	0.159301
$329$	9.00297e28	1.01539
$330$	9.01515e28	0.981890
$331$	−1.07942e29	−1.13545	−0.567727	−	0.823217i	$-0.692177\pi$
$331$	−1.07942e29	−1.13545	−0.567727	+	0.823217i	$0.692177\pi$
$332$	−9.43736e26	−0.00958876
$333$	−1.00237e29	−0.983826
$334$	5.33251e27	0.0505646
$335$	−1.57569e29	−1.44363
$336$	−6.11633e28	−0.541488
$337$	−2.54917e28	−0.218100	−0.109050	−	0.994036i	$-0.534781\pi$
$337$	−2.54917e28	−0.218100	−0.109050	+	0.994036i	$0.534781\pi$
$338$	8.49096e28	0.702125
$339$	2.43256e29	1.94432
$340$	−3.10322e28	−0.239775
$341$	−1.15818e29	−0.865170
$342$	−1.84156e29	−1.33010
$343$	−5.16079e28	−0.360441
$344$	−7.19640e28	−0.486064
$345$	2.96796e29	1.93882
$346$	−8.11182e28	−0.512558
$347$	−1.17389e29	−0.717525	−0.358763	−	0.933429i	$-0.616801\pi$
$347$	−1.17389e29	−0.717525	−0.358763	+	0.933429i	$0.616801\pi$
$348$	2.58919e28	0.153110
$349$	−2.03481e28	−0.116421	−0.0582104	−	0.998304i	$-0.518539\pi$
$349$	−2.03481e28	−0.116421	−0.0582104	+	0.998304i	$0.518539\pi$
$350$	5.34335e28	0.295822
$351$	−1.85639e28	−0.0994574
$352$	3.47796e28	0.180337
$353$	7.43192e28	0.372985	0.186493	−	0.982456i	$-0.440288\pi$
$353$	7.43192e28	0.372985	0.186493	+	0.982456i	$0.440288\pi$
$354$	−7.70691e28	−0.374406
$355$	2.44987e29	1.15217
$356$	1.42155e29	0.647273
$357$	−2.85382e29	−1.25818
$358$	9.05841e28	0.386721
$359$	6.09639e28	0.252050	0.126025	−	0.992027i	$-0.459778\pi$
$359$	6.09639e28	0.252050	0.126025	+	0.992027i	$0.459778\pi$
$360$	1.25275e29	0.501632
$361$	5.10268e28	0.197909
$362$	1.68409e29	0.632728
$363$	−1.84299e28	−0.0670808
$364$	1.56332e28	0.0551291
$365$	−3.88735e29	−1.32827
$366$	−2.81738e29	−0.932853
$367$	−1.13728e29	−0.364928	−0.182464	−	0.983213i	$-0.558407\pi$
$367$	−1.13728e29	−0.364928	−0.182464	+	0.983213i	$0.558407\pi$
$368$	1.14501e29	0.356090
$369$	−2.56895e29	−0.774378
$370$	−1.14360e29	−0.334161
$371$	2.87233e29	0.813643
$372$	−2.54585e29	−0.699180
$373$	7.16967e29	1.90918	0.954591	−	0.297920i	$-0.0962928\pi$
$373$	7.16967e29	1.90918	0.954591	+	0.297920i	$0.0962928\pi$
$374$	1.62279e29	0.419023
$375$	−7.16720e29	−1.79469
$376$	−1.12532e29	−0.273285
$377$	−6.61790e27	−0.0155881
$378$	4.81738e29	1.10066
$379$	−6.32589e29	−1.40207	−0.701036	−	0.713126i	$-0.747279\pi$
$379$	−6.32589e29	−1.40207	−0.701036	+	0.713126i	$0.747279\pi$
$380$	−2.10104e29	−0.451776
$381$	1.13395e30	2.36569
$382$	−1.07070e29	−0.216740
$383$	−6.48766e29	−1.27439	−0.637195	−	0.770703i	$-0.719905\pi$
$383$	−6.48766e29	−1.27439	−0.637195	+	0.770703i	$0.719905\pi$
$384$	7.64507e28	0.145738
$385$	5.97958e29	1.10630
$386$	−5.48122e29	−0.984291
$387$	1.35551e30	2.36280
$388$	3.86386e29	0.653817
$389$	1.78533e29	0.293291	0.146645	−	0.989189i	$-0.453152\pi$
$389$	1.78533e29	0.293291	0.146645	+	0.989189i	$0.453152\pi$
$390$	−5.06507e28	−0.0807872
$391$	5.34252e29	0.827396
$392$	−1.70589e29	−0.256543
$393$	−1.72259e30	−2.51575
$394$	−1.73059e29	−0.245464
$395$	−3.24359e29	−0.446847
$396$	−6.55108e29	−0.876634
$397$	−9.56321e28	−0.124312	−0.0621560	−	0.998066i	$-0.519798\pi$
$397$	−9.56321e28	−0.124312	−0.0621560	+	0.998066i	$0.519798\pi$
$398$	3.40903e28	0.0430503
$399$	−1.93219e30	−2.37061
$400$	−6.67889e28	−0.0796185
$401$	6.48450e29	0.751132	0.375566	−	0.926796i	$-0.377448\pi$
$401$	6.48450e29	0.751132	0.375566	+	0.926796i	$0.377448\pi$
$402$	1.81124e30	2.03881
$403$	6.50713e28	0.0711838
$404$	5.97376e29	0.635129
$405$	−1.87831e29	−0.194104
$406$	1.71736e29	0.172509
$407$	5.98032e29	0.583967
$408$	3.56712e29	0.338630
$409$	−6.20946e29	−0.573107	−0.286554	−	0.958064i	$-0.592510\pi$
$409$	−6.20946e29	−0.573107	−0.286554	+	0.958064i	$0.592510\pi$
$410$	−2.93092e29	−0.263021
$411$	2.38107e30	2.07774
$412$	−4.48965e29	−0.380973
$413$	−5.11185e29	−0.421845
$414$	−2.15674e30	−1.73099
$415$	2.02809e28	0.0158319
$416$	−1.95406e28	−0.0148376
$417$	−2.62316e29	−0.193758
$418$	1.09871e30	0.789508
$419$	9.40356e29	0.657402	0.328701	−	0.944434i	$-0.393389\pi$
$419$	9.40356e29	0.657402	0.328701	+	0.944434i	$0.393389\pi$
$420$	1.31440e30	0.894046
$421$	−1.63695e30	−1.08340	−0.541702	−	0.840571i	$-0.682220\pi$
$421$	−1.63695e30	−1.08340	−0.541702	+	0.840571i	$0.682220\pi$
$422$	−5.72773e29	−0.368883
$423$	2.11965e30	1.32846
$424$	−3.59025e29	−0.218986
$425$	−3.11631e29	−0.184998
$426$	−2.81610e30	−1.62719
$427$	−1.86872e30	−1.05105
$428$	7.97121e29	0.436436
$429$	2.64871e29	0.141181
$430$	1.54651e30	0.802536
$431$	−5.36984e29	−0.271315	−0.135657	−	0.990756i	$-0.543315\pi$
$431$	−5.36984e29	−0.271315	−0.135657	+	0.990756i	$0.543315\pi$
$432$	−6.02145e29	−0.296236
$433$	−7.10121e29	−0.340190	−0.170095	−	0.985428i	$-0.554407\pi$
$433$	−7.10121e29	−0.340190	−0.170095	+	0.985428i	$0.554407\pi$
$434$	−1.68862e30	−0.787769
$435$	−5.56417e29	−0.252798
$436$	−1.69212e30	−0.748749
$437$	3.61717e30	1.55895
$438$	4.46847e30	1.87589
$439$	−1.78862e30	−0.731437	−0.365719	−	0.930725i	$-0.619177\pi$
$439$	−1.78862e30	−0.731437	−0.365719	+	0.930725i	$0.619177\pi$
$440$	−7.47414e29	−0.297753
$441$	3.21320e30	1.24708
$442$	−9.11746e28	−0.0344761
$443$	3.61961e30	1.33358	0.666790	−	0.745246i	$-0.267668\pi$
$443$	3.61961e30	1.33358	0.666790	+	0.745246i	$0.267668\pi$
$444$	1.31456e30	0.471929
$445$	−3.05491e30	−1.06871
$446$	1.11667e30	0.380692
$447$	−5.09327e30	−1.69223
$448$	5.07083e29	0.164203
$449$	−1.09219e29	−0.0344720	−0.0172360	−	0.999851i	$-0.505487\pi$
$449$	−1.09219e29	−0.0344720	−0.0172360	+	0.999851i	$0.505487\pi$
$450$	1.25803e30	0.387033
$451$	1.53269e30	0.459646
$452$	−2.01675e30	−0.589604
$453$	−5.71465e30	−1.62877
$454$	2.36226e30	0.656426
$455$	−3.35957e29	−0.0910232
$456$	2.41513e30	0.638034
$457$	4.42972e30	1.14114	0.570571	−	0.821248i	$-0.306722\pi$
$457$	4.42972e30	1.14114	0.570571	+	0.821248i	$0.306722\pi$
$458$	−2.40638e30	−0.604521
$459$	−2.80955e30	−0.688322
$460$	−2.46063e30	−0.587938
$461$	−5.24784e30	−1.22298	−0.611491	−	0.791251i	$-0.709430\pi$
$461$	−5.24784e30	−1.22298	−0.611491	+	0.791251i	$0.709430\pi$
$462$	−6.87347e30	−1.56240
$463$	3.94748e30	0.875263	0.437631	−	0.899154i	$-0.355817\pi$
$463$	3.94748e30	0.875263	0.437631	+	0.899154i	$0.355817\pi$
$464$	−2.14661e29	−0.0464296
$465$	5.47103e30	1.15441
$466$	−1.18196e30	−0.243312
$467$	2.80285e30	0.562931	0.281466	−	0.959571i	$-0.409179\pi$
$467$	2.80285e30	0.562931	0.281466	+	0.959571i	$0.409179\pi$
$468$	3.68066e29	0.0721270
$469$	1.20136e31	2.29714
$470$	2.41831e30	0.451219
$471$	−2.27224e30	−0.413726
$472$	6.38953e29	0.113537
$473$	−8.08725e30	−1.40248
$474$	3.72847e30	0.631073
$475$	−2.10990e30	−0.348567
$476$	2.36600e30	0.381536
$477$	6.76258e30	1.06451
$478$	6.26897e29	0.0963331
$479$	5.55199e30	0.832895	0.416447	−	0.909160i	$-0.363275\pi$
$479$	5.55199e30	0.832895	0.416447	+	0.909160i	$0.363275\pi$
$480$	−1.64292e30	−0.240626
$481$	−3.35998e29	−0.0480472
$482$	−3.73821e30	−0.521943
$483$	−2.26288e31	−3.08510
$484$	1.52796e29	0.0203419
$485$	−8.30343e30	−1.07951
$486$	−4.44024e30	−0.563753
$487$	−1.47354e30	−0.182716	−0.0913582	−	0.995818i	$-0.529121\pi$
$487$	−1.47354e30	−0.182716	−0.0913582	+	0.995818i	$0.529121\pi$
$488$	2.33579e30	0.282883
$489$	1.71416e31	2.02768
$490$	3.66595e30	0.423576
$491$	−1.67709e29	−0.0189287	−0.00946433	−	0.999955i	$-0.503013\pi$
$491$	−1.67709e29	−0.0189287	−0.00946433	+	0.999955i	$0.503013\pi$
$492$	3.36907e30	0.371459
$493$	−1.00159e30	−0.107882
$494$	−6.17300e29	−0.0649585
$495$	1.40783e31	1.44740
$496$	2.11068e30	0.212023
$497$	−1.86787e31	−1.83336
$498$	−2.33127e29	−0.0223591
$499$	−1.27784e31	−1.19762	−0.598810	−	0.800891i	$-0.704360\pi$
$499$	−1.27784e31	−1.19762	−0.598810	+	0.800891i	$0.704360\pi$
$500$	5.94207e30	0.544230
$501$	1.31726e30	0.117907
$502$	3.53224e30	0.308999
$503$	6.62625e30	0.566547	0.283273	−	0.959039i	$-0.408580\pi$
$503$	6.62625e30	0.566547	0.283273	+	0.959039i	$0.408580\pi$
$504$	−9.55140e30	−0.798207
$505$	−1.28376e31	−1.04866
$506$	1.28675e31	1.02746
$507$	2.09748e31	1.63722
$508$	−9.40119e30	−0.717381
$509$	2.12937e31	1.58853	0.794266	−	0.607570i	$-0.207856\pi$
$509$	2.12937e31	1.58853	0.794266	+	0.607570i	$0.207856\pi$
$510$	−7.66573e30	−0.559109
$511$	2.96385e31	2.11357
$512$	−6.33825e29	−0.0441942
$513$	−1.90222e31	−1.29691
$514$	−1.12631e31	−0.750903
$515$	9.64825e30	0.629021
$516$	−1.77769e31	−1.13341
$517$	−1.26462e31	−0.788534
$518$	8.71923e30	0.531724
$519$	−2.00382e31	−1.19519
$520$	4.19927e29	0.0244983
$521$	−3.13459e31	−1.78874	−0.894368	−	0.447332i	$-0.852374\pi$
$521$	−3.13459e31	−1.78874	−0.894368	+	0.447332i	$0.852374\pi$
$522$	4.04334e30	0.225699
$523$	−5.60340e30	−0.305972	−0.152986	−	0.988228i	$-0.548889\pi$
$523$	−5.60340e30	−0.305972	−0.152986	+	0.988228i	$0.548889\pi$
$524$	1.42814e31	0.762887
$525$	1.31994e31	0.689800
$526$	−2.25805e31	−1.15451
$527$	9.84822e30	0.492647
$528$	8.59145e30	0.420510
$529$	2.14819e31	1.02880
$530$	7.71544e30	0.361566
$531$	−1.20353e31	−0.551912
$532$	1.60191e31	0.718876
$533$	−8.61124e29	−0.0378184
$534$	3.51159e31	1.50931
$535$	−1.71301e31	−0.720596
$536$	−1.50164e31	−0.618259
$537$	2.23766e31	0.901757
$538$	−1.12208e30	−0.0442618
$539$	−1.91706e31	−0.740227
$540$	1.29401e31	0.489113
$541$	−2.41300e30	−0.0892873	−0.0446436	−	0.999003i	$-0.514215\pi$
$541$	−2.41300e30	−0.0892873	−0.0446436	+	0.999003i	$0.514215\pi$
$542$	−2.93065e31	−1.06163
$543$	4.16013e31	1.47540
$544$	−2.95737e30	−0.102688
$545$	3.63636e31	1.23625
$546$	3.86179e30	0.128550
$547$	−4.73888e31	−1.54462	−0.772310	−	0.635246i	$-0.780899\pi$
$547$	−4.73888e31	−1.54462	−0.772310	+	0.635246i	$0.780899\pi$
$548$	−1.97406e31	−0.630063
$549$	−4.39969e31	−1.37512
$550$	−7.50567e30	−0.229730
$551$	−6.78126e30	−0.203267
$552$	2.82847e31	0.830333
$553$	2.47302e31	0.711032
$554$	8.38251e30	0.236054
$555$	−2.82499e31	−0.779197
$556$	2.17477e30	0.0587562
$557$	−4.15359e31	−1.09923	−0.549616	−	0.835417i	$-0.685226\pi$
$557$	−4.15359e31	−1.09923	−0.549616	+	0.835417i	$0.685226\pi$
$558$	−3.97566e31	−1.03066
$559$	4.54374e30	0.115392
$560$	−1.08972e31	−0.271115
$561$	4.00869e31	0.977080
$562$	1.35081e31	0.322572
$563$	6.08993e31	1.42484	0.712419	−	0.701754i	$-0.247599\pi$
$563$	6.08993e31	1.42484	0.712419	+	0.701754i	$0.247599\pi$
$564$	−2.77983e31	−0.637248
$565$	4.33400e31	0.973490
$566$	9.53878e30	0.209944
$567$	1.43209e31	0.308863
$568$	2.33473e31	0.493437
$569$	1.66042e31	0.343897	0.171948	−	0.985106i	$-0.444994\pi$
$569$	1.66042e31	0.343897	0.171948	+	0.985106i	$0.444994\pi$
$570$	−5.19010e31	−1.05345
$571$	3.60619e31	0.717354	0.358677	−	0.933462i	$-0.383228\pi$
$571$	3.60619e31	0.717354	0.358677	+	0.933462i	$0.383228\pi$
$572$	−2.19595e30	−0.0428123
$573$	−2.64490e31	−0.505395
$574$	2.23464e31	0.418524
$575$	−2.47101e31	−0.453622
$576$	1.19387e31	0.214832
$577$	−1.20260e31	−0.212129	−0.106064	−	0.994359i	$-0.533825\pi$
$577$	−1.20260e31	−0.212129	−0.106064	+	0.994359i	$0.533825\pi$
$578$	2.70948e31	0.468506
$579$	−1.35400e32	−2.29517
$580$	4.61305e30	0.0766596
$581$	−1.54629e30	−0.0251921
$582$	9.54471e31	1.52457
$583$	−4.03469e31	−0.631861
$584$	−3.70465e31	−0.568852
$585$	−7.90973e30	−0.119088
$586$	4.86130e31	0.717679
$587$	5.93652e31	0.859397	0.429698	−	0.902973i	$-0.358620\pi$
$587$	5.93652e31	0.859397	0.429698	+	0.902973i	$0.358620\pi$
$588$	−4.21397e31	−0.598209
$589$	6.66776e31	0.928227
$590$	−1.37311e31	−0.187459
$591$	−4.27500e31	−0.572374
$592$	−1.08986e31	−0.143110
$593$	−1.10327e32	−1.42087	−0.710433	−	0.703765i	$-0.751501\pi$
$593$	−1.10327e32	−1.42087	−0.710433	+	0.703765i	$0.751501\pi$
$594$	−6.76685e31	−0.854757
$595$	−5.08454e31	−0.629951
$596$	4.22265e31	0.513160
$597$	8.42118e30	0.100385
$598$	−7.22949e30	−0.0845365
$599$	9.24234e31	1.06017	0.530083	−	0.847946i	$-0.322161\pi$
$599$	9.24234e31	1.06017	0.530083	+	0.847946i	$0.322161\pi$
$600$	−1.64985e31	−0.185655
$601$	1.84593e31	0.203778	0.101889	−	0.994796i	$-0.467511\pi$
$601$	1.84593e31	0.203778	0.101889	+	0.994796i	$0.467511\pi$
$602$	−1.17911e32	−1.27701
$603$	2.82848e32	3.00541
$604$	4.73781e31	0.493916
$605$	−3.28359e30	−0.0335863
$606$	1.47567e32	1.48100
$607$	−1.01802e32	−1.00250	−0.501252	−	0.865301i	$-0.667127\pi$
$607$	−1.01802e32	−1.00250	−0.501252	+	0.865301i	$0.667127\pi$
$608$	−2.00230e31	−0.193480
$609$	4.24232e31	0.402258
$610$	−5.01962e31	−0.467065
$611$	7.10516e30	0.0648784
$612$	5.57049e31	0.499175
$613$	1.20531e32	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$613$	1.20531e32	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$614$	−6.82874e31	−0.589392
$615$	−7.24012e31	−0.613313
$616$	5.69855e31	0.473790
$617$	−1.30052e32	−1.06130	−0.530649	−	0.847592i	$-0.678052\pi$
$617$	−1.30052e32	−1.06130	−0.530649	+	0.847592i	$0.678052\pi$
$618$	−1.10906e32	−0.888354
$619$	−1.66234e32	−1.30701	−0.653503	−	0.756924i	$-0.726701\pi$
$619$	−1.66234e32	−1.30701	−0.653503	+	0.756924i	$0.726701\pi$
$620$	−4.53584e31	−0.350069
$621$	−2.22778e32	−1.68779
$622$	−1.80089e32	−1.33936
$623$	2.32917e32	1.70055
$624$	−4.82702e30	−0.0345984
$625$	−8.24372e31	−0.580100
$626$	1.84347e32	1.27359
$627$	2.71410e32	1.84098
$628$	1.88383e31	0.125460
$629$	−5.08517e31	−0.332524
$630$	2.05259e32	1.31791
$631$	−3.08263e31	−0.194350	−0.0971749	−	0.995267i	$-0.530981\pi$
$631$	−3.08263e31	−0.194350	−0.0971749	+	0.995267i	$0.530981\pi$
$632$	−3.09114e31	−0.191369
$633$	−1.41489e32	−0.860164
$634$	6.95909e31	0.415457
$635$	2.02032e32	1.18446
$636$	−8.86882e31	−0.510633
$637$	1.07708e31	0.0609038
$638$	−2.41233e31	−0.133968
$639$	−4.39769e32	−2.39864
$640$	1.36209e31	0.0729686
$641$	−8.22287e31	−0.432669	−0.216335	−	0.976319i	$-0.569410\pi$
$641$	−8.22287e31	−0.432669	−0.216335	+	0.976319i	$0.569410\pi$
$642$	1.96909e32	1.01768
$643$	3.16365e32	1.60606	0.803032	−	0.595936i	$-0.203219\pi$
$643$	3.16365e32	1.60606	0.803032	+	0.595936i	$0.203219\pi$
$644$	1.87607e32	0.935539
$645$	3.82026e32	1.87136
$646$	−9.34253e31	−0.449563
$647$	−2.07765e32	−0.982141	−0.491070	−	0.871120i	$-0.663394\pi$
$647$	−2.07765e32	−0.982141	−0.491070	+	0.871120i	$0.663394\pi$
$648$	−1.79003e31	−0.0831282
$649$	7.18049e31	0.327597
$650$	4.21698e30	0.0189016
$651$	−4.17131e32	−1.83692
$652$	−1.42115e32	−0.614883
$653$	2.36683e32	1.00616	0.503078	−	0.864241i	$-0.332201\pi$
$653$	2.36683e32	1.00616	0.503078	+	0.864241i	$0.332201\pi$
$654$	−4.17996e32	−1.74594
$655$	−3.06907e32	−1.25960
$656$	−2.79317e31	−0.112643
$657$	6.97807e32	2.76524
$658$	−1.84381e32	−0.717989
$659$	7.16883e31	0.274325	0.137163	−	0.990549i	$-0.456202\pi$
$659$	7.16883e31	0.274325	0.137163	+	0.990549i	$0.456202\pi$
$660$	−1.84630e32	−0.694301
$661$	−2.52957e32	−0.934824	−0.467412	−	0.884039i	$-0.654814\pi$
$661$	−2.52957e32	−0.934824	−0.467412	+	0.884039i	$0.654814\pi$
$662$	2.21066e32	0.802888
$663$	−2.25224e31	−0.0803914
$664$	1.93277e30	0.00678028
$665$	−3.44250e32	−1.18693
$666$	2.05285e32	0.695670
$667$	−7.94186e31	−0.264530
$668$	−1.09210e31	−0.0357546
$669$	2.75846e32	0.887700
$670$	3.22702e32	1.02080
$671$	2.62494e32	0.816226
$672$	1.25262e32	0.382890
$673$	−1.17871e32	−0.354188	−0.177094	−	0.984194i	$-0.556670\pi$
$673$	−1.17871e32	−0.354188	−0.177094	+	0.984194i	$0.556670\pi$
$674$	5.22070e31	0.154220
$675$	1.29947e32	0.377374
$676$	−1.73895e32	−0.496478
$677$	−6.75616e32	−1.89640	−0.948200	−	0.317674i	$-0.897098\pi$
$677$	−6.75616e32	−1.89640	−0.948200	+	0.317674i	$0.897098\pi$
$678$	−4.98189e32	−1.37484
$679$	6.33083e32	1.71774
$680$	6.35539e31	0.169547
$681$	5.83539e32	1.53066
$682$	2.37196e32	0.611768
$683$	−6.83468e32	−1.73333	−0.866663	−	0.498894i	$-0.833740\pi$
$683$	−6.83468e32	−1.73333	−0.866663	+	0.498894i	$0.833740\pi$
$684$	3.77152e32	0.940526
$685$	4.24226e32	1.04029
$686$	1.05693e32	0.254870
$687$	−5.94438e32	−1.40963
$688$	1.47382e32	0.343699
$689$	2.26685e31	0.0519878
$690$	−6.07838e32	−1.37096
$691$	6.05837e32	1.34387	0.671936	−	0.740609i	$-0.265463\pi$
$691$	6.05837e32	1.34387	0.671936	+	0.740609i	$0.265463\pi$
$692$	1.66130e32	0.362433
$693$	−1.07338e33	−2.30314
$694$	2.40412e32	0.507367
$695$	−4.67358e31	−0.0970118
$696$	−5.30266e31	−0.108265
$697$	−1.30327e32	−0.261732
$698$	4.16728e31	0.0823220
$699$	−2.91973e32	−0.567356
$700$	−1.09432e32	−0.209178
$701$	−7.67265e32	−1.44274	−0.721370	−	0.692550i	$-0.756487\pi$
$701$	−7.67265e32	−1.44274	−0.721370	+	0.692550i	$0.756487\pi$
$702$	3.80189e31	0.0703270
$703$	−3.44292e32	−0.626529
$704$	−7.12287e31	−0.127517
$705$	5.97385e32	1.05215
$706$	−1.52206e32	−0.263740
$707$	9.78784e32	1.66864
$708$	1.57838e32	0.264745
$709$	9.17188e32	1.51365	0.756827	−	0.653615i	$-0.226748\pi$
$709$	9.17188e32	1.51365	0.756827	+	0.653615i	$0.226748\pi$
$710$	−5.01734e32	−0.814709
$711$	5.82246e32	0.930265
$712$	−2.91134e32	−0.457691
$713$	7.80893e32	1.20799
$714$	5.84463e32	0.889667
$715$	4.71910e31	0.0706870
$716$	−1.85516e32	−0.273453
$717$	1.54860e32	0.224630
$718$	−1.24854e32	−0.178226
$719$	2.80152e32	0.393561	0.196780	−	0.980448i	$-0.436951\pi$
$719$	2.80152e32	0.393561	0.196780	+	0.980448i	$0.436951\pi$
$720$	−2.56563e32	−0.354707
$721$	−7.35616e32	−1.00091
$722$	−1.04503e32	−0.139943
$723$	−9.23434e32	−1.21707
$724$	−3.44902e32	−0.447406
$725$	4.63251e31	0.0591466
$726$	3.77445e31	0.0474333
$727$	−8.07964e32	−0.999416	−0.499708	−	0.866194i	$-0.666559\pi$
$727$	−8.07964e32	−0.999416	−0.499708	+	0.866194i	$0.666559\pi$
$728$	−3.20167e31	−0.0389822
$729$	−1.29303e33	−1.54968
$730$	7.96129e32	0.939227
$731$	6.87673e32	0.798605
$732$	5.77000e32	0.659627
$733$	1.23627e32	0.139129	0.0695645	−	0.997577i	$-0.477839\pi$
$733$	1.23627e32	0.139129	0.0695645	+	0.997577i	$0.477839\pi$
$734$	2.32914e32	0.258043
$735$	9.05583e32	0.987697
$736$	−2.34498e32	−0.251794
$737$	−1.68753e33	−1.78392
$738$	5.26121e32	0.547568
$739$	−1.50297e32	−0.154007	−0.0770034	−	0.997031i	$-0.524535\pi$
$739$	−1.50297e32	−0.154007	−0.0770034	+	0.997031i	$0.524535\pi$
$740$	2.34210e32	0.236287
$741$	−1.52489e32	−0.151471
$742$	−5.88252e32	−0.575332
$743$	1.35193e33	1.30192	0.650958	−	0.759114i	$-0.274367\pi$
$743$	1.35193e33	1.30192	0.650958	+	0.759114i	$0.274367\pi$
$744$	5.21390e32	0.494395
$745$	−9.07446e32	−0.847274
$746$	−1.46835e33	−1.35000
$747$	−3.64056e31	−0.0329596
$748$	−3.32347e32	−0.296294
$749$	1.30606e33	1.14663
$750$	1.46784e33	1.26904
$751$	−5.66394e32	−0.482236	−0.241118	−	0.970496i	$-0.577514\pi$
$751$	−5.66394e32	−0.482236	−0.241118	+	0.970496i	$0.577514\pi$
$752$	2.30466e32	0.193242
$753$	8.72552e32	0.720525
$754$	1.35535e31	0.0110225
$755$	−1.01816e33	−0.815501
$756$	−9.86599e32	−0.778287
$757$	7.79753e32	0.605835	0.302917	−	0.953017i	$-0.402039\pi$
$757$	7.79753e32	0.605835	0.302917	+	0.953017i	$0.402039\pi$
$758$	1.29554e33	0.991415
$759$	3.17861e33	2.39583
$760$	4.30293e32	0.319454
$761$	5.97338e32	0.436814	0.218407	−	0.975858i	$-0.429914\pi$
$761$	5.97338e32	0.436814	0.218407	+	0.975858i	$0.429914\pi$
$762$	−2.32233e33	−1.67279
$763$	−2.77249e33	−1.96715
$764$	2.19279e32	0.153258
$765$	−1.19710e33	−0.824183
$766$	1.32867e33	0.901130
$767$	−4.03428e31	−0.0269538
$768$	−1.56571e32	−0.103052
$769$	−7.32351e32	−0.474861	−0.237431	−	0.971405i	$-0.576305\pi$
$769$	−7.32351e32	−0.474861	−0.237431	+	0.971405i	$0.576305\pi$
$770$	−1.22462e33	−0.782271
$771$	−2.78228e33	−1.75096
$772$	1.12255e33	0.695999
$773$	3.08883e33	1.88682	0.943409	−	0.331633i	$-0.107599\pi$
$773$	3.08883e33	1.88682	0.943409	+	0.331633i	$0.107599\pi$
$774$	−2.77609e33	−1.67075
$775$	−4.55497e32	−0.270095
$776$	−7.91318e32	−0.462319
$777$	2.15387e33	1.23988
$778$	−3.65636e32	−0.207388
$779$	−8.82382e32	−0.493146
$780$	1.03733e32	0.0571252
$781$	2.62375e33	1.42376
$782$	−1.09415e33	−0.585057
$783$	4.17651e32	0.220066
$784$	3.49366e32	0.181403
$785$	−4.04835e32	−0.207146
$786$	3.52786e33	1.77890
$787$	1.63692e33	0.813427	0.406714	−	0.913556i	$-0.366675\pi$
$787$	1.63692e33	0.813427	0.406714	+	0.913556i	$0.366675\pi$
$788$	3.54425e32	0.173569
$789$	−5.57795e33	−2.69209
$790$	6.64286e32	0.315968
$791$	−3.30439e33	−1.54904
$792$	1.34166e33	0.619874
$793$	−1.47480e32	−0.0671569
$794$	1.95855e32	0.0879018
$795$	1.90591e33	0.843102
$796$	−6.98170e31	−0.0304411
$797$	3.06247e33	1.31614	0.658069	−	0.752957i	$-0.271373\pi$
$797$	3.06247e33	1.31614	0.658069	+	0.752957i	$0.271373\pi$
$798$	3.95712e33	1.67628
$799$	1.07533e33	0.449008
$800$	1.36784e32	0.0562988
$801$	5.48378e33	2.22488
$802$	−1.32803e33	−0.531131
$803$	−4.16325e33	−1.64136
$804$	−3.70943e33	−1.44166
$805$	−4.03168e33	−1.54466
$806$	−1.33266e32	−0.0503346
$807$	−2.77183e32	−0.103210
$808$	−1.22343e33	−0.449104
$809$	−4.44022e33	−1.60693	−0.803464	−	0.595353i	$-0.797012\pi$
$809$	−4.44022e33	−1.60693	−0.803464	+	0.595353i	$0.797012\pi$
$810$	3.84678e32	0.137252
$811$	3.17750e33	1.11775	0.558876	−	0.829251i	$-0.311233\pi$
$811$	3.17750e33	1.11775	0.558876	+	0.829251i	$0.311233\pi$
$812$	−3.51716e32	−0.121982
$813$	−7.23944e33	−2.47550
$814$	−1.22477e33	−0.412927
$815$	3.05405e33	1.01523
$816$	−7.30546e32	−0.239448
$817$	4.65590e33	1.50470
$818$	1.27170e33	0.405248
$819$	6.03066e32	0.189496
$820$	6.00253e32	0.185984
$821$	3.15264e33	0.963224	0.481612	−	0.876384i	$-0.340051\pi$
$821$	3.15264e33	0.963224	0.481612	+	0.876384i	$0.340051\pi$
$822$	−4.87643e33	−1.46918
$823$	2.38843e33	0.709600	0.354800	−	0.934942i	$-0.384549\pi$
$823$	2.38843e33	0.709600	0.354800	+	0.934942i	$0.384549\pi$
$824$	9.19479e32	0.269389
$825$	−1.85409e33	−0.535687
$826$	1.04691e33	0.298289
$827$	8.06573e32	0.226637	0.113318	−	0.993559i	$-0.463852\pi$
$827$	8.06573e32	0.226637	0.113318	+	0.993559i	$0.463852\pi$
$828$	4.41700e33	1.22399
$829$	5.77436e32	0.157807	0.0789036	−	0.996882i	$-0.474858\pi$
$829$	5.77436e32	0.157807	0.0789036	+	0.996882i	$0.474858\pi$
$830$	−4.15352e31	−0.0111949
$831$	2.07069e33	0.550432
$832$	4.00191e31	0.0104918
$833$	1.63011e33	0.421501
$834$	5.37224e32	0.137008
$835$	2.34692e32	0.0590341
$836$	−2.25016e33	−0.558266
$837$	−4.10661e33	−1.00494
$838$	−1.92585e33	−0.464853
$839$	−1.64111e33	−0.390729	−0.195364	−	0.980731i	$-0.562589\pi$
$839$	−1.64111e33	−0.390729	−0.195364	+	0.980731i	$0.562589\pi$
$840$	−2.69189e33	−0.632186
$841$	−4.16783e33	−0.965509
$842$	3.35246e33	0.766082
$843$	3.33685e33	0.752175
$844$	1.17304e33	0.260840
$845$	3.73700e33	0.819730
$846$	−4.34104e33	−0.939366
$847$	2.50352e32	0.0534432
$848$	7.35283e32	0.154847
$849$	2.35632e33	0.489549
$850$	6.38220e32	0.130814
$851$	−4.03217e33	−0.815360
$852$	5.76738e33	1.15060
$853$	1.64258e33	0.323306	0.161653	−	0.986848i	$-0.448318\pi$
$853$	1.64258e33	0.323306	0.161653	+	0.986848i	$0.448318\pi$
$854$	3.82713e33	0.743204
$855$	−8.10499e33	−1.55289
$856$	−1.63250e33	−0.308607
$857$	−1.00984e34	−1.88353	−0.941763	−	0.336277i	$-0.890832\pi$
$857$	−1.00984e34	−1.88353	−0.941763	+	0.336277i	$0.890832\pi$
$858$	−5.42456e32	−0.0998299
$859$	−1.81863e33	−0.330235	−0.165118	−	0.986274i	$-0.552800\pi$
$859$	−1.81863e33	−0.330235	−0.165118	+	0.986274i	$0.552800\pi$
$860$	−3.16725e33	−0.567479
$861$	5.52013e33	0.975917
$862$	1.09974e33	0.191848
$863$	−3.75334e33	−0.646092	−0.323046	−	0.946383i	$-0.604707\pi$
$863$	−3.75334e33	−0.646092	−0.323046	+	0.946383i	$0.604707\pi$
$864$	1.23319e33	0.209471
$865$	−3.57013e33	−0.598410
$866$	1.45433e33	0.240551
$867$	6.69309e33	1.09246
$868$	3.45829e33	0.557037
$869$	−3.47380e33	−0.552175
$870$	1.13954e33	0.178755
$871$	9.48120e32	0.146776
$872$	3.46546e33	0.529445
$873$	1.49052e34	2.24737
$874$	−7.40796e33	−1.10234
$875$	9.73592e33	1.42983
$876$	−9.15143e33	−1.32645
$877$	−3.70897e33	−0.530589	−0.265295	−	0.964167i	$-0.585469\pi$
$877$	−3.70897e33	−0.530589	−0.265295	+	0.964167i	$0.585469\pi$
$878$	3.66310e33	0.517204
$879$	1.20087e34	1.67349
$880$	1.53070e33	0.210543
$881$	4.79707e33	0.651259	0.325629	−	0.945498i	$-0.394424\pi$
$881$	4.79707e33	0.651259	0.325629	+	0.945498i	$0.394424\pi$
$882$	−6.58064e33	−0.881819
$883$	1.57928e33	0.208886	0.104443	−	0.994531i	$-0.466694\pi$
$883$	1.57928e33	0.208886	0.104443	+	0.994531i	$0.466694\pi$
$884$	1.86725e32	0.0243783
$885$	−3.39193e33	−0.437118
$886$	−7.41296e33	−0.942984
$887$	−1.49477e34	−1.87695	−0.938475	−	0.345348i	$-0.887761\pi$
$887$	−1.49477e34	−1.87695	−0.938475	+	0.345348i	$0.887761\pi$
$888$	−2.69222e33	−0.333704
$889$	−1.54036e34	−1.88474
$890$	6.25646e33	0.755690
$891$	−2.01162e33	−0.239857
$892$	−2.28694e33	−0.269190
$893$	7.28056e33	0.846005
$894$	1.04310e34	1.19659
$895$	3.98674e33	0.451495
$896$	−1.03851e33	−0.116109
$897$	−1.78587e33	−0.197123
$898$	2.23681e32	0.0243754
$899$	−1.46398e33	−0.157506
$900$	−2.57645e33	−0.273674
$901$	3.43076e33	0.359795
$902$	−3.13894e33	−0.325019
$903$	−2.91271e34	−2.97774
$904$	4.13031e33	0.416913
$905$	7.41194e33	0.738709
$906$	1.17036e34	1.15172
$907$	2.13809e32	0.0207751	0.0103875	−	0.999946i	$-0.496693\pi$
$907$	2.13809e32	0.0207751	0.0103875	+	0.999946i	$0.496693\pi$
$908$	−4.83791e33	−0.464163
$909$	2.30444e34	2.18314
$910$	6.88039e32	0.0643631
$911$	2.47006e33	0.228164	0.114082	−	0.993471i	$-0.463607\pi$
$911$	2.47006e33	0.228164	0.114082	+	0.993471i	$0.463607\pi$
$912$	−4.94618e33	−0.451158
$913$	2.17203e32	0.0195637
$914$	−9.07206e33	−0.806909
$915$	−1.23997e34	−1.08910
$916$	4.92827e33	0.427461
$917$	2.33996e34	2.00430
$918$	5.75397e33	0.486717
$919$	8.02451e33	0.670333	0.335166	−	0.942159i	$-0.391208\pi$
$919$	8.02451e33	0.670333	0.335166	+	0.942159i	$0.391208\pi$
$920$	5.03937e33	0.415735
$921$	−1.68687e34	−1.37435
$922$	1.07476e34	0.864779
$923$	−1.47413e33	−0.117143
$924$	1.40769e34	1.10479
$925$	2.35198e33	0.182307
$926$	−8.08444e33	−0.618904
$927$	−1.73193e34	−1.30952
$928$	4.39625e32	0.0328307
$929$	−3.89736e33	−0.287468	−0.143734	−	0.989616i	$-0.545911\pi$
$929$	−3.89736e33	−0.287468	−0.143734	+	0.989616i	$0.545911\pi$
$930$	−1.12047e34	−0.816292
$931$	1.10367e34	0.794177
$932$	2.42065e33	0.172048
$933$	−4.44866e34	−3.12313
$934$	−5.74023e33	−0.398052
$935$	7.14213e33	0.489209
$936$	−7.53799e32	−0.0510015
$937$	5.87024e33	0.392329	0.196165	−	0.980571i	$-0.437151\pi$
$937$	5.87024e33	0.392329	0.196165	+	0.980571i	$0.437151\pi$
$938$	−2.46039e34	−1.62432
$939$	4.55384e34	2.96977
$940$	−4.95271e33	−0.319060
$941$	−2.06023e34	−1.31110	−0.655549	−	0.755153i	$-0.727563\pi$
$941$	−2.06023e34	−1.31110	−0.655549	+	0.755153i	$0.727563\pi$
$942$	4.65354e33	0.292549
$943$	−1.03340e34	−0.641777
$944$	−1.30857e33	−0.0802824
$945$	2.12020e34	1.28502
$946$	1.65627e34	0.991706
$947$	4.59154e33	0.271602	0.135801	−	0.990736i	$-0.456639\pi$
$947$	4.59154e33	0.271602	0.135801	+	0.990736i	$0.456639\pi$
$948$	−7.63591e33	−0.446236
$949$	2.33908e33	0.135047
$950$	4.32108e33	0.246474
$951$	1.71907e34	0.968765
$952$	−4.84557e33	−0.269787
$953$	1.49358e34	0.821599	0.410799	−	0.911726i	$-0.365250\pi$
$953$	1.49358e34	0.821599	0.410799	+	0.911726i	$0.365250\pi$
$954$	−1.38498e34	−0.752724
$955$	−4.71231e33	−0.253044
$956$	−1.28389e33	−0.0681178
$957$	−5.95908e33	−0.312386
$958$	−1.13705e34	−0.588946
$959$	−3.23445e34	−1.65534
$960$	3.36471e33	0.170149
$961$	−5.61859e33	−0.280743
$962$	6.88124e32	0.0339745
$963$	3.07498e34	1.50017
$964$	7.65586e33	0.369070
$965$	−2.41237e34	−1.14916
$966$	4.63437e34	2.18149
$967$	3.92857e34	1.82738	0.913692	−	0.406407i	$-0.133219\pi$
$967$	3.92857e34	1.82738	0.913692	+	0.406407i	$0.133219\pi$
$968$	−3.12927e32	−0.0143839
$969$	−2.30784e34	−1.04829
$970$	1.70054e34	0.763330
$971$	−2.25313e34	−0.999461	−0.499730	−	0.866181i	$-0.666568\pi$
$971$	−2.25313e34	−0.999461	−0.499730	+	0.866181i	$0.666568\pi$
$972$	9.09360e33	0.398634
$973$	3.56330e33	0.154367
$974$	3.01780e33	0.129200
$975$	1.04170e33	0.0440748
$976$	−4.78370e33	−0.200028
$977$	2.96994e34	1.22732	0.613662	−	0.789569i	$-0.289696\pi$
$977$	2.96994e34	1.22732	0.613662	+	0.789569i	$0.289696\pi$
$978$	−3.51060e34	−1.43379
$979$	−3.27173e34	−1.32062
$980$	−7.50787e33	−0.299514
$981$	−6.52753e34	−2.57368
$982$	3.43469e32	0.0133846
$983$	3.01623e34	1.16171	0.580857	−	0.814006i	$-0.302718\pi$
$983$	3.01623e34	1.16171	0.580857	+	0.814006i	$0.302718\pi$
$984$	−6.89985e33	−0.262661
$985$	−7.61659e33	−0.286579
$986$	2.05125e33	0.0762841
$987$	−4.55467e34	−1.67421
$988$	1.26423e33	0.0459326
$989$	5.45275e34	1.95821
$990$	−2.88323e34	−1.02347
$991$	−2.58031e34	−0.905368	−0.452684	−	0.891671i	$-0.649533\pi$
$991$	−2.58031e34	−0.905368	−0.452684	+	0.891671i	$0.649533\pi$
$992$	−4.32266e33	−0.149923
$993$	5.46089e34	1.87218
$994$	3.82540e34	1.29638
$995$	1.50037e33	0.0502611
$996$	4.77444e32	0.0158103
$997$	−1.42567e34	−0.466685	−0.233342	−	0.972395i	$-0.574966\pi$
$997$	−1.42567e34	−0.466685	−0.233342	+	0.972395i	$0.574966\pi$
$998$	2.61701e34	0.846846
$999$	2.12046e34	0.678309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.24.a.a.1.1	✓	1
3.2	odd	2		18.24.a.d.1.1		1
4.3	odd	2		16.24.a.a.1.1		1
5.2	odd	4		50.24.b.a.49.1		2
5.3	odd	4		50.24.b.a.49.2		2
5.4	even	2		50.24.a.a.1.1		1
8.3	odd	2		64.24.a.a.1.1		1
8.5	even	2		64.24.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.24.a.a.1.1	✓	1	1.1	even	1	trivial
16.24.a.a.1.1		1	4.3	odd	2
18.24.a.d.1.1		1	3.2	odd	2
50.24.a.a.1.1		1	5.4	even	2
50.24.b.a.49.1		2	5.2	odd	4
50.24.b.a.49.2		2	5.3	odd	4
64.24.a.a.1.1		1	8.3	odd	2
64.24.a.c.1.1		1	8.5	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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