LMFDB - Embedded newform 3.24.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,24,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	3.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:	$10.0561211204$
Analytic rank:	$1$
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	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1128.00 q^{2} +177147. q^{3} -7.11622e6 q^{4} -4.88637e7 q^{5} +1.99822e8 q^{6} -1.72369e9 q^{7} -1.74895e10 q^{8} +3.13811e10 q^{9} +O(q^{10})$

\(q+1128.00 q^{2} +177147. q^{3} -7.11622e6 q^{4} -4.88637e7 q^{5} +1.99822e8 q^{6} -1.72369e9 q^{7} -1.74895e10 q^{8} +3.13811e10 q^{9} -5.51183e10 q^{10} -1.42826e12 q^{11} -1.26062e12 q^{12} -8.22096e12 q^{13} -1.94432e12 q^{14} -8.65606e12 q^{15} +3.99671e13 q^{16} -5.98921e12 q^{17} +3.53978e13 q^{18} +6.80005e14 q^{19} +3.47725e14 q^{20} -3.05346e14 q^{21} -1.61108e15 q^{22} +1.54406e13 q^{23} -3.09820e15 q^{24} -9.53326e15 q^{25} -9.27325e15 q^{26} +5.55906e15 q^{27} +1.22662e16 q^{28} +1.15094e17 q^{29} -9.76404e15 q^{30} -9.08297e16 q^{31} +1.91795e17 q^{32} -2.53013e17 q^{33} -6.75583e15 q^{34} +8.42259e16 q^{35} -2.23315e17 q^{36} -1.29787e18 q^{37} +7.67046e17 q^{38} -1.45632e18 q^{39} +8.54600e17 q^{40} +5.21404e18 q^{41} -3.44431e17 q^{42} -2.41043e18 q^{43} +1.01638e19 q^{44} -1.53340e18 q^{45} +1.74171e16 q^{46} -2.31327e19 q^{47} +7.08005e18 q^{48} -2.43976e19 q^{49} -1.07535e19 q^{50} -1.06097e18 q^{51} +5.85022e19 q^{52} -4.45126e19 q^{53} +6.27062e18 q^{54} +6.97903e19 q^{55} +3.01464e19 q^{56} +1.20461e20 q^{57} +1.29826e20 q^{58} -3.23974e20 q^{59} +6.15985e19 q^{60} -1.99406e20 q^{61} -1.02456e20 q^{62} -5.40912e19 q^{63} -1.18924e20 q^{64} +4.01707e20 q^{65} -2.85398e20 q^{66} -6.46393e20 q^{67} +4.26206e19 q^{68} +2.73526e18 q^{69} +9.50068e19 q^{70} +3.55146e21 q^{71} -5.48837e20 q^{72} +3.35319e21 q^{73} -1.46400e21 q^{74} -1.68879e21 q^{75} -4.83907e21 q^{76} +2.46188e21 q^{77} -1.64273e21 q^{78} -6.87213e21 q^{79} -1.95294e21 q^{80} +9.84771e20 q^{81} +5.88143e21 q^{82} -1.16977e21 q^{83} +2.17291e21 q^{84} +2.92655e20 q^{85} -2.71897e21 q^{86} +2.03886e22 q^{87} +2.49795e22 q^{88} -2.34572e22 q^{89} -1.72967e21 q^{90} +1.41704e22 q^{91} -1.09879e20 q^{92} -1.60902e22 q^{93} -2.60937e22 q^{94} -3.32276e22 q^{95} +3.39759e22 q^{96} -3.06039e22 q^{97} -2.75205e22 q^{98} -4.48204e22 q^{99} +O(q^{100})\)

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 $

$2$	1128.00	0.389461	0.194731	−	0.980857i	$-0.437617\pi$
$2$	1128.00	0.389461	0.194731	+	0.980857i	$0.437617\pi$
$3$	177147.	0.577350
$3$	177147.	0.577350
$4$	−7.11622e6	−0.848320
$5$	−4.88637e7	−0.447540	−0.223770	−	0.974642i	$-0.571836\pi$
$5$	−4.88637e7	−0.447540	−0.223770	+	0.974642i	$0.571836\pi$
$6$	1.99822e8	0.224856
$7$	−1.72369e9	−0.329482	−0.164741	−	0.986337i	$-0.552679\pi$
$7$	−1.72369e9	−0.329482	−0.164741	+	0.986337i	$0.552679\pi$
$8$	−1.74895e10	−0.719849
$9$	3.13811e10	0.333333
$10$	−5.51183e10	−0.174299
$11$	−1.42826e12	−1.50936	−0.754679	−	0.656094i	$-0.772207\pi$
$11$	−1.42826e12	−1.50936	−0.754679	+	0.656094i	$0.772207\pi$
$12$	−1.26062e12	−0.489778
$13$	−8.22096e12	−1.27226	−0.636128	−	0.771584i	$-0.719465\pi$
$13$	−8.22096e12	−1.27226	−0.636128	+	0.771584i	$0.719465\pi$
$14$	−1.94432e12	−0.128320
$15$	−8.65606e12	−0.258387
$16$	3.99671e13	0.567967
$17$	−5.98921e12	−0.0423845	−0.0211922	−	0.999775i	$-0.506746\pi$
$17$	−5.98921e12	−0.0423845	−0.0211922	+	0.999775i	$0.506746\pi$
$18$	3.53978e13	0.129820
$19$	6.80005e14	1.33920	0.669601	−	0.742721i	$-0.266465\pi$
$19$	6.80005e14	1.33920	0.669601	+	0.742721i	$0.266465\pi$
$20$	3.47725e14	0.379657
$21$	−3.05346e14	−0.190226
$22$	−1.61108e15	−0.587836
$23$	1.54406e13	0.00337906	0.00168953	−	0.999999i	$-0.499462\pi$
$23$	1.54406e13	0.00337906	0.00168953	+	0.999999i	$0.499462\pi$
$24$	−3.09820e15	−0.415605
$25$	−9.53326e15	−0.799708
$26$	−9.27325e15	−0.495494
$27$	5.55906e15	0.192450
$28$	1.22662e16	0.279506
$29$	1.15094e17	1.75177	0.875884	−	0.482522i	$-0.160279\pi$
$29$	1.15094e17	1.75177	0.875884	+	0.482522i	$0.160279\pi$
$30$	−9.76404e15	−0.100632
$31$	−9.08297e16	−0.642050	−0.321025	−	0.947071i	$-0.604027\pi$
$31$	−9.08297e16	−0.642050	−0.321025	+	0.947071i	$0.604027\pi$
$32$	1.91795e17	0.941050
$33$	−2.53013e17	−0.871428
$34$	−6.75583e15	−0.0165071
$35$	8.42259e16	0.147456
$36$	−2.23315e17	−0.282773
$37$	−1.29787e18	−1.19926	−0.599629	−	0.800278i	$-0.704685\pi$
$37$	−1.29787e18	−1.19926	−0.599629	+	0.800278i	$0.704685\pi$
$38$	7.67046e17	0.521567
$39$	−1.45632e18	−0.734537
$40$	8.54600e17	0.322161
$41$	5.21404e18	1.47965	0.739826	−	0.672798i	$-0.234908\pi$
$41$	5.21404e18	1.47965	0.739826	+	0.672798i	$0.234908\pi$
$42$	−3.44431e17	−0.0740858
$43$	−2.41043e18	−0.395556	−0.197778	−	0.980247i	$-0.563373\pi$
$43$	−2.41043e18	−0.395556	−0.197778	+	0.980247i	$0.563373\pi$
$44$	1.01638e19	1.28042
$45$	−1.53340e18	−0.149180
$46$	1.74171e16	0.00131601
$47$	−2.31327e19	−1.36490	−0.682449	−	0.730933i	$-0.739085\pi$
$47$	−2.31327e19	−1.36490	−0.682449	+	0.730933i	$0.739085\pi$
$48$	7.08005e18	0.327916
$49$	−2.43976e19	−0.891442
$50$	−1.07535e19	−0.311455
$51$	−1.06097e18	−0.0244707
$52$	5.85022e19	1.07928
$53$	−4.45126e19	−0.659646	−0.329823	−	0.944043i	$-0.606989\pi$
$53$	−4.45126e19	−0.659646	−0.329823	+	0.944043i	$0.606989\pi$
$54$	6.27062e18	0.0749518
$55$	6.97903e19	0.675498
$56$	3.01464e19	0.237177
$57$	1.20461e20	0.773188
$58$	1.29826e20	0.682245
$59$	−3.23974e20	−1.39866	−0.699331	−	0.714798i	$-0.746519\pi$
$59$	−3.23974e20	−1.39866	−0.699331	+	0.714798i	$0.746519\pi$
$60$	6.15985e19	0.219195
$61$	−1.99406e20	−0.586740	−0.293370	−	0.955999i	$-0.594777\pi$
$61$	−1.99406e20	−0.586740	−0.293370	+	0.955999i	$0.594777\pi$
$62$	−1.02456e20	−0.250053
$63$	−5.40912e19	−0.109827
$64$	−1.18924e20	−0.201464
$65$	4.01707e20	0.569385
$66$	−2.85398e20	−0.339388
$67$	−6.46393e20	−0.646601	−0.323300	−	0.946296i	$-0.604792\pi$
$67$	−6.46393e20	−0.646601	−0.323300	+	0.946296i	$0.604792\pi$
$68$	4.26206e19	0.0359556
$69$	2.73526e18	0.00195090
$70$	9.50068e19	0.0574284
$71$	3.55146e21	1.82363	0.911814	−	0.410604i	$-0.134682\pi$
$71$	3.55146e21	1.82363	0.911814	+	0.410604i	$0.134682\pi$
$72$	−5.48837e20	−0.239950
$73$	3.35319e21	1.25096	0.625482	−	0.780238i	$-0.284902\pi$
$73$	3.35319e21	1.25096	0.625482	+	0.780238i	$0.284902\pi$
$74$	−1.46400e21	−0.467064
$75$	−1.68879e21	−0.461712
$76$	−4.83907e21	−1.13607
$77$	2.46188e21	0.497306
$78$	−1.64273e21	−0.286074
$79$	−6.87213e21	−1.03367	−0.516833	−	0.856086i	$-0.672889\pi$
$79$	−6.87213e21	−1.03367	−0.516833	+	0.856086i	$0.672889\pi$
$80$	−1.95294e21	−0.254188
$81$	9.84771e20	0.111111
$82$	5.88143e21	0.576267
$83$	−1.16977e21	−0.0997016	−0.0498508	−	0.998757i	$-0.515875\pi$
$83$	−1.16977e21	−0.0997016	−0.0498508	+	0.998757i	$0.515875\pi$
$84$	2.17291e21	0.161373
$85$	2.92655e20	0.0189687
$86$	−2.71897e21	−0.154054
$87$	2.03886e22	1.01138
$88$	2.49795e22	1.08651
$89$	−2.34572e22	−0.895966	−0.447983	−	0.894042i	$-0.647857\pi$
$89$	−2.34572e22	−0.895966	−0.447983	+	0.894042i	$0.647857\pi$
$90$	−1.72967e21	−0.0580998
$91$	1.41704e22	0.419185
$92$	−1.09879e20	−0.00286652
$93$	−1.60902e22	−0.370687
$94$	−2.60937e22	−0.531575
$95$	−3.32276e22	−0.599346
$96$	3.39759e22	0.543315
$97$	−3.06039e22	−0.434412	−0.217206	−	0.976126i	$-0.569694\pi$
$97$	−3.06039e22	−0.434412	−0.217206	+	0.976126i	$0.569694\pi$
$98$	−2.75205e22	−0.347182
$99$	−4.48204e22	−0.503119
$100$	6.78408e22	0.678408
$101$	−2.39411e21	−0.0213525	−0.0106762	−	0.999943i	$-0.503398\pi$
$101$	−2.39411e21	−0.0213525	−0.0106762	+	0.999943i	$0.503398\pi$
$102$	−1.19677e21	−0.00953039
$103$	−2.98735e22	−0.212646	−0.106323	−	0.994332i	$-0.533908\pi$
$103$	−2.98735e22	−0.212646	−0.106323	+	0.994332i	$0.533908\pi$
$104$	1.43780e23	0.915831
$105$	1.49204e22	0.0851339
$106$	−5.02102e22	−0.256906
$107$	3.52639e23	1.61963	0.809817	−	0.586683i	$-0.199567\pi$
$107$	3.52639e23	1.61963	0.809817	+	0.586683i	$0.199567\pi$
$108$	−3.95595e22	−0.163259
$109$	−1.52076e23	−0.564489	−0.282245	−	0.959342i	$-0.591079\pi$
$109$	−1.52076e23	−0.564489	−0.282245	+	0.959342i	$0.591079\pi$
$110$	7.87234e22	0.263080
$111$	−2.29914e23	−0.692392
$112$	−6.88909e22	−0.187135
$113$	5.18685e22	0.127204	0.0636021	−	0.997975i	$-0.479741\pi$
$113$	5.18685e22	0.127204	0.0636021	+	0.997975i	$0.479741\pi$
$114$	1.35880e23	0.301127
$115$	−7.54488e20	−0.00151226
$116$	−8.19036e23	−1.48606
$117$	−2.57983e23	−0.424085
$118$	−3.65443e23	−0.544724
$119$	1.03235e22	0.0139649
$120$	1.51390e23	0.186000
$121$	1.14451e24	1.27816
$122$	−2.24930e23	−0.228512
$123$	9.23651e23	0.854278
$124$	6.46365e23	0.544663
$125$	1.04833e24	0.805441
$126$	−6.10148e22	−0.0427734
$127$	−3.34992e23	−0.214433	−0.107217	−	0.994236i	$-0.534194\pi$
$127$	−3.34992e23	−0.214433	−0.107217	+	0.994236i	$0.534194\pi$
$128$	−1.74304e24	−1.01951
$129$	−4.27001e23	−0.228374
$130$	4.53125e23	0.221753
$131$	−8.94767e23	−0.400950	−0.200475	−	0.979699i	$-0.564248\pi$
$131$	−8.94767e23	−0.400950	−0.200475	+	0.979699i	$0.564248\pi$
$132$	1.80049e24	0.739250
$133$	−1.17212e24	−0.441243
$134$	−7.29131e23	−0.251826
$135$	−2.71636e23	−0.0861291
$136$	1.04748e23	0.0305104
$137$	−1.52550e24	−0.408437	−0.204219	−	0.978925i	$-0.565465\pi$
$137$	−1.52550e24	−0.408437	−0.204219	+	0.978925i	$0.565465\pi$
$138$	3.08538e21	0.000759799 0
$139$	−2.87052e24	−0.650565	−0.325283	−	0.945617i	$-0.605459\pi$
$139$	−2.87052e24	−0.650565	−0.325283	+	0.945617i	$0.605459\pi$
$140$	−5.99370e23	−0.125090
$141$	−4.09788e24	−0.788025
$142$	4.00605e24	0.710232
$143$	1.17417e25	1.92029
$144$	1.25421e24	0.189322
$145$	−5.62393e24	−0.783985
$146$	3.78240e24	0.487202
$147$	−4.32197e24	−0.514674
$148$	9.23596e24	1.01735
$149$	7.06708e24	0.720440	0.360220	−	0.932867i	$-0.382702\pi$
$149$	7.06708e24	0.720440	0.360220	+	0.932867i	$0.382702\pi$
$150$	−1.90495e24	−0.179819
$151$	−5.44882e24	−0.476505	−0.238253	−	0.971203i	$-0.576575\pi$
$151$	−5.44882e24	−0.476505	−0.238253	+	0.971203i	$0.576575\pi$
$152$	−1.18929e25	−0.964023
$153$	−1.87948e23	−0.0141282
$154$	2.77700e24	0.193681
$155$	4.43828e24	0.287343
$156$	1.03635e25	0.623122
$157$	−2.79179e25	−1.55968	−0.779841	−	0.625977i	$-0.784700\pi$
$157$	−2.79179e25	−1.55968	−0.779841	+	0.625977i	$0.784700\pi$
$158$	−7.75177e24	−0.402573
$159$	−7.88528e24	−0.380847
$160$	−9.37182e24	−0.421157
$161$	−2.66149e22	−0.00111334
$162$	1.11082e24	0.0432735
$163$	4.83707e25	1.75560	0.877799	−	0.479029i	$-0.159011\pi$
$163$	4.83707e25	1.75560	0.877799	+	0.479029i	$0.159011\pi$
$164$	−3.71042e25	−1.25522
$165$	1.23631e25	0.389999
$166$	−1.31950e24	−0.0388299
$167$	3.59666e25	0.987779	0.493890	−	0.869525i	$-0.335575\pi$
$167$	3.59666e25	0.987779	0.493890	+	0.869525i	$0.335575\pi$
$168$	5.34034e24	0.136934
$169$	2.58303e25	0.618633
$170$	3.30115e23	0.00738759
$171$	2.13393e25	0.446401
$172$	1.71532e25	0.335558
$173$	−6.18040e25	−1.13106	−0.565531	−	0.824727i	$-0.691329\pi$
$173$	−6.18040e25	−1.13106	−0.565531	+	0.824727i	$0.691329\pi$
$174$	2.29983e25	0.393895
$175$	1.64324e25	0.263489
$176$	−5.70836e25	−0.857265
$177$	−5.73911e25	−0.807518
$178$	−2.64597e25	−0.348944
$179$	4.18182e25	0.517077	0.258539	−	0.966001i	$-0.416759\pi$
$179$	4.18182e25	0.517077	0.258539	+	0.966001i	$0.416759\pi$
$180$	1.09120e25	0.126552
$181$	−1.04652e26	−1.13879	−0.569394	−	0.822065i	$-0.692822\pi$
$181$	−1.04652e26	−1.13879	−0.569394	+	0.822065i	$0.692822\pi$
$182$	1.59842e25	0.163256
$183$	−3.53242e25	−0.338754
$184$	−2.70048e23	−0.00243241
$185$	6.34189e25	0.536715
$186$	−1.81498e25	−0.144368
$187$	8.55417e24	0.0639734
$188$	1.64617e26	1.15787
$189$	−9.58209e24	−0.0634088
$190$	−3.74807e25	−0.233422
$191$	1.25691e26	0.736923	0.368461	−	0.929643i	$-0.379885\pi$
$191$	1.25691e26	0.736923	0.368461	+	0.929643i	$0.379885\pi$
$192$	−2.10670e25	−0.116316
$193$	−8.55418e25	−0.444907	−0.222453	−	0.974943i	$-0.571407\pi$
$193$	−8.55418e25	−0.444907	−0.222453	+	0.974943i	$0.571407\pi$
$194$	−3.45212e25	−0.169187
$195$	7.11612e25	0.328734
$196$	1.73619e26	0.756228
$197$	−9.41370e25	−0.386722	−0.193361	−	0.981128i	$-0.561939\pi$
$197$	−9.41370e25	−0.386722	−0.193361	+	0.981128i	$0.561939\pi$
$198$	−5.05574e25	−0.195945
$199$	7.46484e25	0.273030	0.136515	−	0.990638i	$-0.456410\pi$
$199$	7.46484e25	0.273030	0.136515	+	0.990638i	$0.456410\pi$
$200$	1.66732e26	0.575669
$201$	−1.14506e26	−0.373315
$202$	−2.70056e24	−0.00831597
$203$	−1.98387e26	−0.577175
$204$	7.55010e24	0.0207590
$205$	−2.54777e26	−0.662203
$206$	−3.36973e25	−0.0828175
$207$	4.84544e23	0.00112635
$208$	−3.28568e26	−0.722599
$209$	−9.71227e26	−2.02134
$210$	1.68302e25	0.0331563
$211$	6.91338e26	1.28956	0.644781	−	0.764368i	$-0.276949\pi$
$211$	6.91338e26	1.28956	0.644781	+	0.764368i	$0.276949\pi$
$212$	3.16762e26	0.559591
$213$	6.29131e26	1.05287
$214$	3.97777e26	0.630784
$215$	1.17783e26	0.177027
$216$	−9.72249e25	−0.138535
$217$	1.56562e26	0.211544
$218$	−1.71542e26	−0.219847
$219$	5.94007e26	0.722245
$220$	−4.96643e26	−0.573038
$221$	4.92371e25	0.0539239
$222$	−2.59343e26	−0.269660
$223$	7.98521e26	0.788462	0.394231	−	0.919011i	$-0.371011\pi$
$223$	7.98521e26	0.788462	0.394231	+	0.919011i	$0.371011\pi$
$224$	−3.30595e26	−0.310059
$225$	−2.99164e26	−0.266569
$226$	5.85077e25	0.0495411
$227$	1.19285e27	0.960042	0.480021	−	0.877257i	$-0.340629\pi$
$227$	1.19285e27	0.960042	0.480021	+	0.877257i	$0.340629\pi$
$228$	−8.57227e26	−0.655911
$229$	−1.64063e27	−1.19372	−0.596860	−	0.802345i	$-0.703585\pi$
$229$	−1.64063e27	−1.19372	−0.596860	+	0.802345i	$0.703585\pi$
$230$	−8.51062e23	−0.000588967 0
$231$	4.36115e26	0.287120
$232$	−2.01293e27	−1.26101
$233$	−1.47808e27	−0.881263	−0.440632	−	0.897688i	$-0.645246\pi$
$233$	−1.47808e27	−0.881263	−0.440632	+	0.897688i	$0.645246\pi$
$234$	−2.91004e26	−0.165165
$235$	1.13035e27	0.610846
$236$	2.30547e27	1.18651
$237$	−1.21738e27	−0.596787
$238$	1.16449e25	0.00543879
$239$	−1.00529e26	−0.0447421	−0.0223711	−	0.999750i	$-0.507122\pi$
$239$	−1.00529e26	−0.0447421	−0.0223711	+	0.999750i	$0.507122\pi$
$240$	−3.45958e26	−0.146755
$241$	2.89067e27	1.16897	0.584483	−	0.811406i	$-0.301297\pi$
$241$	2.89067e27	1.16897	0.584483	+	0.811406i	$0.301297\pi$
$242$	1.29100e27	0.497795
$243$	1.74449e26	0.0641500
$244$	1.41902e27	0.497743
$245$	1.19216e27	0.398956
$246$	1.04188e27	0.332708
$247$	−5.59030e27	−1.70381
$248$	1.58856e27	0.462179
$249$	−2.07221e26	−0.0575628
$250$	1.18252e27	0.313688
$251$	−3.03848e26	−0.0769855	−0.0384928	−	0.999259i	$-0.512256\pi$
$251$	−3.03848e26	−0.0769855	−0.0384928	+	0.999259i	$0.512256\pi$
$252$	3.84925e26	0.0931687
$253$	−2.20533e25	−0.00510021
$254$	−3.77872e26	−0.0835134
$255$	5.18430e25	0.0109516
$256$	−9.68545e26	−0.195596
$257$	−5.74761e27	−1.10983	−0.554915	−	0.831907i	$-0.687249\pi$
$257$	−5.74761e27	−1.10983	−0.554915	+	0.831907i	$0.687249\pi$
$258$	−4.81657e26	−0.0889430
$259$	2.23713e27	0.395134
$260$	−2.85864e27	−0.483020
$261$	3.61178e27	0.583922
$262$	−1.00930e27	−0.156154
$263$	−9.08470e27	−1.34530	−0.672650	−	0.739961i	$-0.734844\pi$
$263$	−9.08470e27	−1.34530	−0.672650	+	0.739961i	$0.734844\pi$
$264$	4.42505e27	0.627297
$265$	2.17505e27	0.295218
$266$	−1.32215e27	−0.171847
$267$	−4.15537e27	−0.517286
$268$	4.59987e27	0.548524
$269$	2.45445e27	0.280416	0.140208	−	0.990122i	$-0.455223\pi$
$269$	2.45445e27	0.280416	0.140208	+	0.990122i	$0.455223\pi$
$270$	−3.06406e26	−0.0335439
$271$	5.65329e27	0.593136	0.296568	−	0.955012i	$-0.404158\pi$
$271$	5.65329e27	0.593136	0.296568	+	0.955012i	$0.404158\pi$
$272$	−2.39371e26	−0.0240730
$273$	2.51024e27	0.242016
$274$	−1.72076e27	−0.159070
$275$	1.36160e28	1.20705
$276$	−1.94648e25	−0.00165499
$277$	3.55531e27	0.289975	0.144987	−	0.989433i	$-0.453686\pi$
$277$	3.55531e27	0.289975	0.144987	+	0.989433i	$0.453686\pi$
$278$	−3.23795e27	−0.253370
$279$	−2.85033e27	−0.214017
$280$	−1.47306e27	−0.106146
$281$	2.83906e28	1.96359	0.981797	−	0.189931i	$-0.0608265\pi$
$281$	2.83906e28	1.96359	0.981797	+	0.189931i	$0.0608265\pi$
$282$	−4.62241e27	−0.306905
$283$	−2.29202e28	−1.46108	−0.730542	−	0.682868i	$-0.760732\pi$
$283$	−2.29202e28	−1.46108	−0.730542	+	0.682868i	$0.760732\pi$
$284$	−2.52730e28	−1.54702
$285$	−5.88617e27	−0.346033
$286$	1.32446e28	0.747878
$287$	−8.98738e27	−0.487518
$288$	6.01873e27	0.313683
$289$	−1.99317e28	−0.998204
$290$	−6.34379e27	−0.305332
$291$	−5.42139e27	−0.250808
$292$	−2.38620e28	−1.06122
$293$	3.43109e28	1.46708	0.733542	−	0.679644i	$-0.237866\pi$
$293$	3.43109e28	1.46708	0.733542	+	0.679644i	$0.237866\pi$
$294$	−4.87518e27	−0.200446
$295$	1.58306e28	0.625957
$296$	2.26991e28	0.863284
$297$	−7.93980e27	−0.290476
$298$	7.97167e27	0.280584
$299$	−1.26937e26	−0.00429902
$300$	1.20178e28	0.391679
$301$	4.15484e27	0.130329
$302$	−6.14627e27	−0.185580
$303$	−4.24110e26	−0.0123279
$304$	2.71779e28	0.760622
$305$	9.74373e27	0.262589
$306$	−2.12005e26	−0.00550237
$307$	−1.16886e28	−0.292195	−0.146097	−	0.989270i	$-0.546671\pi$
$307$	−1.16886e28	−0.292195	−0.146097	+	0.989270i	$0.546671\pi$
$308$	−1.75193e28	−0.421875
$309$	−5.29200e27	−0.122771
$310$	5.00638e27	0.111909
$311$	−2.49825e28	−0.538135	−0.269067	−	0.963121i	$-0.586715\pi$
$311$	−2.49825e28	−0.538135	−0.269067	+	0.963121i	$0.586715\pi$
$312$	2.54702e28	0.528755
$313$	6.03885e28	1.20835	0.604177	−	0.796850i	$-0.293502\pi$
$313$	6.03885e28	1.20835	0.604177	+	0.796850i	$0.293502\pi$
$314$	−3.14914e28	−0.607436
$315$	2.64310e27	0.0491521
$316$	4.89036e28	0.876879
$317$	−1.04255e29	−1.80266	−0.901330	−	0.433133i	$-0.857408\pi$
$317$	−1.04255e29	−1.80266	−0.901330	+	0.433133i	$0.857408\pi$
$318$	−8.89459e27	−0.148325
$319$	−1.64385e29	−2.64404
$320$	5.81105e27	0.0901633
$321$	6.24689e28	0.935096
$322$	−3.00216e25	−0.000433602 0
$323$	−4.07270e27	−0.0567614
$324$	−7.00785e27	−0.0942578
$325$	7.83726e28	1.01743
$326$	5.45622e28	0.683737
$327$	−2.69398e28	−0.325908
$328$	−9.11906e28	−1.06513
$329$	3.98735e28	0.449709
$330$	1.39456e28	0.151889
$331$	1.38759e29	1.45962	0.729809	−	0.683651i	$-0.239609\pi$
$331$	1.38759e29	1.45962	0.729809	+	0.683651i	$0.239609\pi$
$332$	8.32434e27	0.0845789
$333$	−4.07286e28	−0.399753
$334$	4.05703e28	0.384702
$335$	3.15851e28	0.289379
$336$	−1.22038e28	−0.108042
$337$	−1.50795e29	−1.29016	−0.645078	−	0.764117i	$-0.723175\pi$
$337$	−1.50795e29	−1.29016	−0.645078	+	0.764117i	$0.723175\pi$
$338$	2.91366e28	0.240934
$339$	9.18835e27	0.0734414
$340$	−2.08260e27	−0.0160916
$341$	1.29729e29	0.969083
$342$	2.40707e28	0.173856
$343$	8.92291e28	0.623196
$344$	4.21572e28	0.284741
$345$	−1.33655e26	−0.000873105 0
$346$	−6.97149e28	−0.440504
$347$	−1.45030e29	−0.886482	−0.443241	−	0.896403i	$-0.646171\pi$
$347$	−1.45030e29	−0.886482	−0.443241	+	0.896403i	$0.646171\pi$
$348$	−1.45090e29	−0.857977
$349$	1.03224e29	0.590592	0.295296	−	0.955406i	$-0.404582\pi$
$349$	1.03224e29	0.590592	0.295296	+	0.955406i	$0.404582\pi$
$350$	1.85357e28	0.102619
$351$	−4.57008e28	−0.244846
$352$	−2.73934e29	−1.42038
$353$	−9.96681e28	−0.500204	−0.250102	−	0.968220i	$-0.580464\pi$
$353$	−9.96681e28	−0.500204	−0.250102	+	0.968220i	$0.580464\pi$
$354$	−6.47372e28	−0.314497
$355$	−1.73538e29	−0.816146
$356$	1.66927e29	0.760066
$357$	1.82878e27	0.00806265
$358$	4.71709e28	0.201381
$359$	1.99929e29	0.826589	0.413294	−	0.910597i	$-0.364378\pi$
$359$	1.99929e29	0.826589	0.413294	+	0.910597i	$0.364378\pi$
$360$	2.68182e28	0.107387
$361$	2.04578e29	0.793461
$362$	−1.18047e29	−0.443514
$363$	2.02746e29	0.737948
$364$	−1.00840e29	−0.355603
$365$	−1.63849e29	−0.559856
$366$	−3.98457e28	−0.131932
$367$	5.60764e29	1.79937	0.899684	−	0.436541i	$-0.143797\pi$
$367$	5.60764e29	1.79937	0.899684	+	0.436541i	$0.143797\pi$
$368$	6.17118e26	0.00191919
$369$	1.63622e29	0.493217
$370$	7.15366e28	0.209030
$371$	7.67259e28	0.217341
$372$	1.14502e29	0.314462
$373$	−4.46930e29	−1.19011	−0.595056	−	0.803684i	$-0.702870\pi$
$373$	−4.46930e29	−1.19011	−0.595056	+	0.803684i	$0.702870\pi$
$374$	9.64910e27	0.0249151
$375$	1.85709e29	0.465022
$376$	4.04578e29	0.982521
$377$	−9.46185e29	−2.22869
$378$	−1.08086e28	−0.0246953
$379$	−3.66574e29	−0.812477	−0.406239	−	0.913767i	$-0.633160\pi$
$379$	−3.66574e29	−0.812477	−0.406239	+	0.913767i	$0.633160\pi$
$380$	2.36455e29	0.508437
$381$	−5.93429e28	−0.123803
$382$	1.41780e29	0.287003
$383$	−1.49291e29	−0.293257	−0.146628	−	0.989192i	$-0.546842\pi$
$383$	−1.49291e29	−0.293257	−0.146628	+	0.989192i	$0.546842\pi$
$384$	−3.08774e29	−0.588616
$385$	−1.20297e29	−0.222564
$386$	−9.64911e28	−0.173274
$387$	−7.56420e28	−0.131852
$388$	2.17784e29	0.368520
$389$	−1.97534e29	−0.324506	−0.162253	−	0.986749i	$-0.551876\pi$
$389$	−1.97534e29	−0.324506	−0.162253	+	0.986749i	$0.551876\pi$
$390$	8.02698e28	0.128029
$391$	−9.24773e25	−0.000143220 0
$392$	4.26701e29	0.641703
$393$	−1.58505e29	−0.231488
$394$	−1.06187e29	−0.150613
$395$	3.35798e29	0.462606
$396$	3.18952e29	0.426806
$397$	−2.62393e28	−0.0341084	−0.0170542	−	0.999855i	$-0.505429\pi$
$397$	−2.62393e28	−0.0341084	−0.0170542	+	0.999855i	$0.505429\pi$
$398$	8.42034e28	0.106334
$399$	−2.07637e29	−0.254751
$400$	−3.81017e29	−0.454208
$401$	4.34375e29	0.503159	0.251579	−	0.967837i	$-0.419050\pi$
$401$	4.34375e29	0.503159	0.251579	+	0.967837i	$0.419050\pi$
$402$	−1.29163e29	−0.145392
$403$	7.46708e29	0.816851
$404$	1.70370e28	0.0181137
$405$	−4.81196e28	−0.0497266
$406$	−2.23780e29	−0.224787
$407$	1.85370e30	1.81011
$408$	1.85558e28	0.0176152
$409$	−8.14589e29	−0.751832	−0.375916	−	0.926654i	$-0.622672\pi$
$409$	−8.14589e29	−0.751832	−0.375916	+	0.926654i	$0.622672\pi$
$410$	−2.87389e29	−0.257902
$411$	−2.70238e29	−0.235811
$412$	2.12586e29	0.180392
$413$	5.58431e29	0.460833
$414$	5.46566e26	0.000438670 0
$415$	5.71593e28	0.0446204
$416$	−1.57674e30	−1.19726
$417$	−5.08505e29	−0.375604
$418$	−1.09554e30	−0.787232
$419$	1.28769e29	0.0900221	0.0450111	−	0.998986i	$-0.485668\pi$
$419$	1.28769e29	0.0900221	0.0450111	+	0.998986i	$0.485668\pi$
$420$	−1.06177e29	−0.0722208
$421$	−1.44725e30	−0.957852	−0.478926	−	0.877855i	$-0.658974\pi$
$421$	−1.44725e30	−0.957852	−0.478926	+	0.877855i	$0.658974\pi$
$422$	7.79829e29	0.502234
$423$	−7.25928e29	−0.454966
$424$	7.78501e29	0.474845
$425$	5.70967e28	0.0338952
$426$	7.09659e29	0.410053
$427$	3.43714e29	0.193320
$428$	−2.50946e30	−1.37397
$429$	2.08001e30	1.10868
$430$	1.32859e29	0.0689452
$431$	−1.55229e30	−0.784303	−0.392152	−	0.919901i	$-0.628269\pi$
$431$	−1.55229e30	−0.784303	−0.392152	+	0.919901i	$0.628269\pi$
$432$	2.22180e29	0.109305
$433$	3.69055e30	1.76799	0.883997	−	0.467493i	$-0.154843\pi$
$433$	3.69055e30	1.76799	0.883997	+	0.467493i	$0.154843\pi$
$434$	1.76602e29	0.0823880
$435$	−9.96263e29	−0.452634
$436$	1.08221e30	0.478867
$437$	1.04997e28	0.00452524
$438$	6.70040e29	0.281286
$439$	4.37828e29	0.179045	0.0895223	−	0.995985i	$-0.471466\pi$
$439$	4.37828e29	0.179045	0.0895223	+	0.995985i	$0.471466\pi$
$440$	−1.22059e30	−0.486256
$441$	−7.65624e29	−0.297147
$442$	5.55394e28	0.0210013
$443$	1.47008e30	0.541624	0.270812	−	0.962632i	$-0.412708\pi$
$443$	1.47008e30	0.541624	0.270812	+	0.962632i	$0.412708\pi$
$444$	1.63612e30	0.587370
$445$	1.14621e30	0.400980
$446$	9.00732e29	0.307075
$447$	1.25191e30	0.415946
$448$	2.04987e29	0.0663789
$449$	−2.17842e29	−0.0687558	−0.0343779	−	0.999409i	$-0.510945\pi$
$449$	−2.17842e29	−0.0687558	−0.0343779	+	0.999409i	$0.510945\pi$
$450$	−3.37457e29	−0.103818
$451$	−7.44702e30	−2.23333
$452$	−3.69108e29	−0.107910
$453$	−9.65243e29	−0.275111
$454$	1.34554e30	0.373899
$455$	−6.92418e29	−0.187602
$456$	−2.10680e30	−0.556579
$457$	−1.90386e30	−0.490454	−0.245227	−	0.969466i	$-0.578862\pi$
$457$	−1.90386e30	−0.490454	−0.245227	+	0.969466i	$0.578862\pi$
$458$	−1.85063e30	−0.464908
$459$	−3.32944e28	−0.00815690
$460$	5.36910e27	0.00128288
$461$	−4.96919e30	−1.15804	−0.579022	−	0.815312i	$-0.696566\pi$
$461$	−4.96919e30	−1.15804	−0.579022	+	0.815312i	$0.696566\pi$
$462$	4.91938e29	0.111822
$463$	1.11956e30	0.248237	0.124118	−	0.992267i	$-0.460390\pi$
$463$	1.11956e30	0.248237	0.124118	+	0.992267i	$0.460390\pi$
$464$	4.59998e30	0.994946
$465$	7.86228e29	0.165897
$466$	−1.66728e30	−0.343218
$467$	8.69961e30	1.74725	0.873626	−	0.486598i	$-0.161762\pi$
$467$	8.69961e30	1.74725	0.873626	+	0.486598i	$0.161762\pi$
$468$	1.83586e30	0.359760
$469$	1.11418e30	0.213043
$470$	1.27503e30	0.237901
$471$	−4.94557e30	−0.900483
$472$	5.66614e30	1.00682
$473$	3.44273e30	0.597036
$474$	−1.37320e30	−0.232425
$475$	−6.48267e30	−1.07097
$476$	−7.34646e28	−0.0118467
$477$	−1.39685e30	−0.219882
$478$	−1.13397e29	−0.0174253
$479$	−6.06140e29	−0.0909315	−0.0454658	−	0.998966i	$-0.514477\pi$
$479$	−6.06140e29	−0.0909315	−0.0454658	+	0.998966i	$0.514477\pi$
$480$	−1.66019e30	−0.243155
$481$	1.06698e31	1.52576
$482$	3.26067e30	0.455267
$483$	−4.71474e27	−0.000642786 0
$484$	−8.14456e30	−1.08429
$485$	1.49542e30	0.194417
$486$	1.96779e29	0.0249839
$487$	−4.30348e30	−0.533626	−0.266813	−	0.963748i	$-0.585971\pi$
$487$	−4.30348e30	−0.533626	−0.266813	+	0.963748i	$0.585971\pi$
$488$	3.48750e30	0.422364
$489$	8.56873e30	1.01360
$490$	1.34476e30	0.155378
$491$	−1.13566e31	−1.28177	−0.640885	−	0.767637i	$-0.721432\pi$
$491$	−1.13566e31	−1.28177	−0.640885	+	0.767637i	$0.721432\pi$
$492$	−6.57291e30	−0.724701
$493$	−6.89323e29	−0.0742478
$494$	−6.30586e30	−0.663566
$495$	2.19009e30	0.225166
$496$	−3.63020e30	−0.364663
$497$	−6.12161e30	−0.600852
$498$	−2.33746e29	−0.0224185
$499$	9.99815e30	0.937052	0.468526	−	0.883450i	$-0.344785\pi$
$499$	9.99815e30	0.937052	0.468526	+	0.883450i	$0.344785\pi$
$500$	−7.46016e30	−0.683272
$501$	6.37137e30	0.570295
$502$	−3.42741e29	−0.0299829
$503$	−6.16806e30	−0.527372	−0.263686	−	0.964609i	$-0.584938\pi$
$503$	−6.16806e30	−0.527372	−0.263686	+	0.964609i	$0.584938\pi$
$504$	9.46025e29	0.0790590
$505$	1.16985e29	0.00955609
$506$	−2.48761e28	−0.00198633
$507$	4.57577e30	0.357168
$508$	2.38388e30	0.181908
$509$	2.98637e30	0.222786	0.111393	−	0.993776i	$-0.464469\pi$
$509$	2.98637e30	0.222786	0.111393	+	0.993776i	$0.464469\pi$
$510$	5.84789e28	0.00426523
$511$	−5.77985e30	−0.412170
$512$	1.35292e31	0.943335
$513$	3.78019e30	0.257729
$514$	−6.48331e30	−0.432236
$515$	1.45973e30	0.0951677
$516$	3.03864e30	0.193735
$517$	3.30395e31	2.06012
$518$	2.52348e30	0.153889
$519$	−1.09484e31	−0.653019
$520$	−7.02563e30	−0.409871
$521$	−8.51705e30	−0.486022	−0.243011	−	0.970024i	$-0.578135\pi$
$521$	−8.51705e30	−0.486022	−0.243011	+	0.970024i	$0.578135\pi$
$522$	4.07409e30	0.227415
$523$	1.27472e31	0.696059	0.348029	−	0.937484i	$-0.386851\pi$
$523$	1.27472e31	0.696059	0.348029	+	0.937484i	$0.386851\pi$
$524$	6.36736e30	0.340134
$525$	2.91095e30	0.152126
$526$	−1.02475e31	−0.523942
$527$	5.43998e29	0.0272129
$528$	−1.01122e31	−0.494942
$529$	−2.08802e31	−0.999989
$530$	2.45346e30	0.114976
$531$	−1.01667e31	−0.466221
$532$	8.34105e30	0.374315
$533$	−4.28644e31	−1.88250
$534$	−4.68726e30	−0.201463
$535$	−1.72312e31	−0.724850
$536$	1.13050e31	0.465455
$537$	7.40796e30	0.298535
$538$	2.76862e30	0.109211
$539$	3.48463e31	1.34551
$540$	1.93303e30	0.0730650
$541$	−1.00626e31	−0.372342	−0.186171	−	0.982517i	$-0.559608\pi$
$541$	−1.00626e31	−0.372342	−0.186171	+	0.982517i	$0.559608\pi$
$542$	6.37691e30	0.231004
$543$	−1.85387e31	−0.657479
$544$	−1.14870e30	−0.0398859
$545$	7.43099e30	0.252631
$546$	2.83155e30	0.0942560
$547$	−4.27216e31	−1.39249	−0.696247	−	0.717802i	$-0.745148\pi$
$547$	−4.27216e31	−1.39249	−0.696247	+	0.717802i	$0.745148\pi$
$548$	1.08558e31	0.346485
$549$	−6.25758e30	−0.195580
$550$	1.53589e31	0.470098
$551$	7.82647e31	2.34597
$552$	−4.78383e28	−0.00140435
$553$	1.18454e31	0.340574
$554$	4.01039e30	0.112934
$555$	1.12345e31	0.309873
$556$	2.04273e31	0.551887
$557$	−6.81696e31	−1.80408	−0.902040	−	0.431652i	$-0.857931\pi$
$557$	−6.81696e31	−1.80408	−0.902040	+	0.431652i	$0.857931\pi$
$558$	−3.21518e30	−0.0833511
$559$	1.98161e31	0.503248
$560$	3.36626e30	0.0837502
$561$	1.51535e30	0.0369351
$562$	3.20246e31	0.764744
$563$	6.17906e30	0.144569	0.0722846	−	0.997384i	$-0.476971\pi$
$563$	6.17906e30	0.144569	0.0722846	+	0.997384i	$0.476971\pi$
$564$	2.91615e31	0.668497
$565$	−2.53449e30	−0.0569289
$566$	−2.58540e31	−0.569035
$567$	−1.69744e30	−0.0366091
$568$	−6.21131e31	−1.31274
$569$	−1.87031e31	−0.387366	−0.193683	−	0.981064i	$-0.562043\pi$
$569$	−1.87031e31	−0.387366	−0.193683	+	0.981064i	$0.562043\pi$
$570$	−6.63960e30	−0.134766
$571$	2.56599e31	0.510433	0.255217	−	0.966884i	$-0.417853\pi$
$571$	2.56599e31	0.510433	0.255217	+	0.966884i	$0.417853\pi$
$572$	−8.35566e31	−1.62902
$573$	2.22659e31	0.425463
$574$	−1.01378e31	−0.189870
$575$	−1.47200e29	−0.00270226
$576$	−3.73195e30	−0.0671548
$577$	−2.35477e31	−0.415362	−0.207681	−	0.978197i	$-0.566592\pi$
$577$	−2.35477e31	−0.415362	−0.207681	+	0.978197i	$0.566592\pi$
$578$	−2.24830e31	−0.388762
$579$	−1.51535e31	−0.256867
$580$	4.00212e31	0.665071
$581$	2.01632e30	0.0328499
$582$	−6.11532e30	−0.0976799
$583$	6.35758e31	0.995642
$584$	−5.86454e31	−0.900505
$585$	1.26060e31	0.189795
$586$	3.87027e31	0.571372
$587$	7.54955e31	1.09291	0.546453	−	0.837490i	$-0.315978\pi$
$587$	7.54955e31	1.09291	0.546453	+	0.837490i	$0.315978\pi$
$588$	3.07561e31	0.436608
$589$	−6.17647e31	−0.859834
$590$	1.78569e31	0.243786
$591$	−1.66761e31	−0.223274
$592$	−5.18723e31	−0.681139
$593$	3.26412e31	0.420376	0.210188	−	0.977661i	$-0.432592\pi$
$593$	3.26412e31	0.420376	0.210188	+	0.977661i	$0.432592\pi$
$594$	−8.95610e30	−0.113129
$595$	−5.04446e29	−0.00624985
$596$	−5.02909e31	−0.611164
$597$	1.32237e31	0.157634
$598$	−1.43185e29	−0.00167430
$599$	5.33038e31	0.611434	0.305717	−	0.952122i	$-0.401104\pi$
$599$	5.33038e31	0.611434	0.305717	+	0.952122i	$0.401104\pi$
$600$	2.95360e31	0.332363
$601$	1.42622e32	1.57446	0.787229	−	0.616661i	$-0.211515\pi$
$601$	1.42622e32	1.57446	0.787229	+	0.616661i	$0.211515\pi$
$602$	4.68666e30	0.0507579
$603$	−2.02845e31	−0.215534
$604$	3.87750e31	0.404229
$605$	−5.59248e31	−0.572029
$606$	−4.78396e29	−0.00480123
$607$	−1.51222e32	−1.48917	−0.744586	−	0.667526i	$-0.767353\pi$
$607$	−1.51222e32	−1.48917	−0.744586	+	0.667526i	$0.767353\pi$
$608$	1.30422e32	1.26026
$609$	−3.51436e31	−0.333232
$610$	1.09909e31	0.102268
$611$	1.90173e32	1.73650
$612$	1.33748e30	0.0119852
$613$	−1.24132e32	−1.09166	−0.545831	−	0.837895i	$-0.683786\pi$
$613$	−1.24132e32	−1.09166	−0.545831	+	0.837895i	$0.683786\pi$
$614$	−1.31848e31	−0.113798
$615$	−4.51330e31	−0.382323
$616$	−4.30569e31	−0.357985
$617$	−1.89291e32	−1.54472	−0.772361	−	0.635184i	$-0.780924\pi$
$617$	−1.89291e32	−1.54472	−0.772361	+	0.635184i	$0.780924\pi$
$618$	−5.96937e30	−0.0478147
$619$	−1.33375e32	−1.04865	−0.524327	−	0.851517i	$-0.675683\pi$
$619$	−1.33375e32	−1.04865	−0.524327	+	0.851517i	$0.675683\pi$
$620$	−3.15838e31	−0.243759
$621$	8.58355e28	0.000650300 0
$622$	−2.81802e31	−0.209583
$623$	4.04329e31	0.295204
$624$	−5.82049e31	−0.417193
$625$	6.24200e31	0.439241
$626$	6.81182e31	0.470607
$627$	−1.72050e32	−1.16702
$628$	1.98670e32	1.32311
$629$	7.77324e30	0.0508299
$630$	2.98141e30	0.0191428
$631$	2.80913e31	0.177107	0.0885533	−	0.996071i	$-0.471776\pi$
$631$	2.80913e31	0.177107	0.0885533	+	0.996071i	$0.471776\pi$
$632$	1.20190e32	0.744083
$633$	1.22468e32	0.744529
$634$	−1.17599e32	−0.702066
$635$	1.63690e31	0.0959674
$636$	5.61134e31	0.323080
$637$	2.00572e32	1.13414
$638$	−1.85426e32	−1.02975
$639$	1.11449e32	0.607876
$640$	8.51714e31	0.456272
$641$	−3.78628e31	−0.199225	−0.0996127	−	0.995026i	$-0.531760\pi$
$641$	−3.78628e31	−0.199225	−0.0996127	+	0.995026i	$0.531760\pi$
$642$	7.04649e31	0.364183
$643$	−1.43262e32	−0.727283	−0.363641	−	0.931539i	$-0.618467\pi$
$643$	−1.43262e32	−0.727283	−0.363641	+	0.931539i	$0.618467\pi$
$644$	1.89397e29	0.000944466 0
$645$	2.08649e31	0.102207
$646$	−4.59400e30	−0.0221064
$647$	−2.32752e31	−0.110026	−0.0550129	−	0.998486i	$-0.517520\pi$
$647$	−2.32752e31	−0.110026	−0.0550129	+	0.998486i	$0.517520\pi$
$648$	−1.72231e31	−0.0799832
$649$	4.62721e32	2.11108
$650$	8.84043e31	0.396251
$651$	2.77345e31	0.122135
$652$	−3.44217e32	−1.48931
$653$	−4.07291e32	−1.73142	−0.865712	−	0.500543i	$-0.833134\pi$
$653$	−4.07291e32	−1.73142	−0.865712	+	0.500543i	$0.833134\pi$
$654$	−3.03881e31	−0.126928
$655$	4.37216e31	0.179441
$656$	2.08390e32	0.840393
$657$	1.05227e32	0.416988
$658$	4.49773e31	0.175144
$659$	−4.35631e32	−1.66700	−0.833501	−	0.552518i	$-0.813667\pi$
$659$	−4.35631e32	−1.66700	−0.833501	+	0.552518i	$0.813667\pi$
$660$	−8.79788e31	−0.330844
$661$	−4.22347e32	−1.56082	−0.780410	−	0.625268i	$-0.784990\pi$
$661$	−4.22347e32	−1.56082	−0.780410	+	0.625268i	$0.784990\pi$
$662$	1.56520e32	0.568465
$663$	8.72220e30	0.0311330
$664$	2.04586e31	0.0717701
$665$	5.72740e31	0.197474
$666$	−4.59419e31	−0.155688
$667$	1.77713e30	0.00591932
$668$	−2.55946e32	−0.837953
$669$	1.41456e32	0.455218
$670$	3.56280e31	0.112702
$671$	2.84805e32	0.885601
$672$	−5.85639e31	−0.179013
$673$	3.27631e32	0.984491	0.492245	−	0.870456i	$-0.336176\pi$
$673$	3.27631e32	0.984491	0.492245	+	0.870456i	$0.336176\pi$
$674$	−1.70096e32	−0.502466
$675$	−5.29960e31	−0.153904
$676$	−1.83815e32	−0.524799
$677$	1.65241e32	0.463820	0.231910	−	0.972737i	$-0.425503\pi$
$677$	1.65241e32	0.463820	0.231910	+	0.972737i	$0.425503\pi$
$678$	1.03645e31	0.0286026
$679$	5.27516e31	0.143131
$680$	−5.11838e30	−0.0136546
$681$	2.11311e32	0.554281
$682$	1.46334e32	0.377420
$683$	1.17826e32	0.298816	0.149408	−	0.988776i	$-0.452263\pi$
$683$	1.17826e32	0.298816	0.149408	+	0.988776i	$0.452263\pi$
$684$	−1.51855e32	−0.378691
$685$	7.45416e31	0.182792
$686$	1.00650e32	0.242710
$687$	−2.90633e32	−0.689194
$688$	−9.63381e31	−0.224663
$689$	3.65937e32	0.839238
$690$	−1.50763e29	−0.000340040 0
$691$	2.43790e32	0.540778	0.270389	−	0.962751i	$-0.412848\pi$
$691$	2.43790e32	0.540778	0.270389	+	0.962751i	$0.412848\pi$
$692$	4.39811e32	0.959502
$693$	7.72564e31	0.165769
$694$	−1.63594e32	−0.345250
$695$	1.40264e32	0.291154
$696$	−3.56585e32	−0.728043
$697$	−3.12280e31	−0.0627143
$698$	1.16437e32	0.230013
$699$	−2.61838e32	−0.508798
$700$	−1.16937e32	−0.223523
$701$	−3.79931e32	−0.714409	−0.357205	−	0.934026i	$-0.616270\pi$
$701$	−3.79931e32	−0.714409	−0.357205	+	0.934026i	$0.616270\pi$
$702$	−5.15505e31	−0.0953579
$703$	−8.82561e32	−1.60605
$704$	1.69854e32	0.304082
$705$	2.00238e32	0.352672
$706$	−1.12426e32	−0.194810
$707$	4.12670e30	0.00703526
$708$	4.08408e32	0.685033
$709$	−1.44569e31	−0.0238586	−0.0119293	−	0.999929i	$-0.503797\pi$
$709$	−1.44569e31	−0.0238586	−0.0119293	+	0.999929i	$0.503797\pi$
$710$	−1.95750e32	−0.317857
$711$	−2.15655e32	−0.344555
$712$	4.10254e32	0.644960
$713$	−1.40247e30	−0.00216952
$714$	2.06287e30	0.00314009
$715$	−5.73743e32	−0.859405
$716$	−2.97588e32	−0.438647
$717$	−1.78085e31	−0.0258319
$718$	2.25520e32	0.321924
$719$	−1.33387e32	−0.187383	−0.0936915	−	0.995601i	$-0.529867\pi$
$719$	−1.33387e32	−0.187383	−0.0936915	+	0.995601i	$0.529867\pi$
$720$	−6.12854e31	−0.0847292
$721$	5.14926e31	0.0700631
$722$	2.30764e32	0.309022
$723$	5.12073e32	0.674903
$724$	7.44725e32	0.966057
$725$	−1.09722e33	−1.40090
$726$	2.28697e32	0.287402
$727$	4.93859e31	0.0610882	0.0305441	−	0.999533i	$-0.490276\pi$
$727$	4.93859e31	0.0610882	0.0305441	+	0.999533i	$0.490276\pi$
$728$	−2.47832e32	−0.301750
$729$	3.09032e31	0.0370370
$730$	−1.84822e32	−0.218042
$731$	1.44366e31	0.0167654
$732$	2.51375e32	0.287372
$733$	1.05389e33	1.18604	0.593019	−	0.805189i	$-0.297936\pi$
$733$	1.05389e33	1.18604	0.593019	+	0.805189i	$0.297936\pi$
$734$	6.32541e32	0.700784
$735$	2.11188e32	0.230337
$736$	2.96144e30	0.00317986
$737$	9.23219e32	0.975952
$738$	1.84566e32	0.192089
$739$	1.09776e33	1.12486	0.562428	−	0.826846i	$-0.309867\pi$
$739$	1.09776e33	1.12486	0.562428	+	0.826846i	$0.309867\pi$
$740$	−4.51303e32	−0.455306
$741$	−9.90305e32	−0.983693
$742$	8.65468e31	0.0846460
$743$	−5.60678e32	−0.539936	−0.269968	−	0.962869i	$-0.587013\pi$
$743$	−5.60678e32	−0.539936	−0.269968	+	0.962869i	$0.587013\pi$
$744$	2.81409e32	0.266839
$745$	−3.45324e32	−0.322426
$746$	−5.04137e32	−0.463502
$747$	−3.67086e31	−0.0332339
$748$	−6.08734e31	−0.0542699
$749$	−6.07840e32	−0.533640
$750$	2.09480e32	0.181108
$751$	−1.01215e33	−0.861759	−0.430880	−	0.902409i	$-0.641797\pi$
$751$	−1.01215e33	−0.861759	−0.430880	+	0.902409i	$0.641797\pi$
$752$	−9.24546e32	−0.775217
$753$	−5.38258e31	−0.0444476
$754$	−1.06730e33	−0.867990
$755$	2.66250e32	0.213255
$756$	6.81883e31	0.0537909
$757$	−9.48447e32	−0.736903	−0.368452	−	0.929647i	$-0.620112\pi$
$757$	−9.48447e32	−0.736903	−0.368452	+	0.929647i	$0.620112\pi$
$758$	−4.13496e32	−0.316428
$759$	−3.90668e30	−0.00294461
$760$	5.81133e32	0.431438
$761$	9.81408e32	0.717672	0.358836	−	0.933401i	$-0.383174\pi$
$761$	9.81408e32	0.717672	0.358836	+	0.933401i	$0.383174\pi$
$762$	−6.69388e31	−0.0482165
$763$	2.62131e32	0.185989
$764$	−8.94448e32	−0.625146
$765$	9.18383e30	0.00632291
$766$	−1.68400e32	−0.114212
$767$	2.66338e33	1.77945
$768$	−1.71575e32	−0.112927
$769$	8.57155e32	0.555785	0.277892	−	0.960612i	$-0.410364\pi$
$769$	8.57155e32	0.555785	0.277892	+	0.960612i	$0.410364\pi$
$770$	−1.35695e32	−0.0866801
$771$	−1.01817e33	−0.640761
$772$	6.08734e32	0.377423
$773$	−9.41593e31	−0.0575174	−0.0287587	−	0.999586i	$-0.509155\pi$
$773$	−9.41593e31	−0.0575174	−0.0287587	+	0.999586i	$0.509155\pi$
$774$	−8.53242e31	−0.0513512
$775$	8.65904e32	0.513452
$776$	5.35245e32	0.312711
$777$	3.96301e32	0.228130
$778$	−2.22819e32	−0.126382
$779$	3.54557e33	1.98155
$780$	−5.06399e32	−0.278872
$781$	−5.07242e33	−2.75251
$782$	−1.04314e29	−5.57785e−5 0
$783$	6.39816e32	0.337128
$784$	−9.75103e32	−0.506309
$785$	1.36417e33	0.698020
$786$	−1.78794e32	−0.0901557
$787$	2.72161e33	1.35243	0.676216	−	0.736703i	$-0.263618\pi$
$787$	2.72161e33	1.35243	0.676216	+	0.736703i	$0.263618\pi$
$788$	6.69900e32	0.328064
$789$	−1.60933e33	−0.776710
$790$	3.78780e32	0.180167
$791$	−8.94051e31	−0.0419115
$792$	7.83884e32	0.362170
$793$	1.63931e33	0.746483
$794$	−2.95979e31	−0.0132839
$795$	3.85304e32	0.170444
$796$	−5.31215e32	−0.231617
$797$	−3.49544e33	−1.50221	−0.751106	−	0.660182i	$-0.770479\pi$
$797$	−3.49544e33	−1.50221	−0.751106	+	0.660182i	$0.770479\pi$
$798$	−2.34215e32	−0.0992158
$799$	1.38546e32	0.0578505
$800$	−1.82843e33	−0.752565
$801$	−7.36112e32	−0.298655
$802$	4.89975e32	0.195961
$803$	−4.78923e33	−1.88815
$804$	8.14854e32	0.316691
$805$	1.30050e30	0.000498263 0
$806$	8.42287e32	0.318132
$807$	4.34799e32	0.161898
$808$	4.18717e31	0.0153706
$809$	1.04226e33	0.377196	0.188598	−	0.982054i	$-0.439606\pi$
$809$	1.04226e33	0.377196	0.188598	+	0.982054i	$0.439606\pi$
$810$	−5.42789e31	−0.0193666
$811$	−2.22771e33	−0.783643	−0.391821	−	0.920041i	$-0.628155\pi$
$811$	−2.22771e33	−0.783643	−0.391821	+	0.920041i	$0.628155\pi$
$812$	1.41176e33	0.489629
$813$	1.00146e33	0.342447
$814$	2.09098e33	0.704967
$815$	−2.36357e33	−0.785700
$816$	−4.24039e31	−0.0138985
$817$	−1.63911e33	−0.529729
$818$	−9.18857e32	−0.292809
$819$	4.44682e32	0.139728
$820$	1.81305e33	0.561760
$821$	−7.36864e31	−0.0225134	−0.0112567	−	0.999937i	$-0.503583\pi$
$821$	−7.36864e31	−0.0225134	−0.0112567	+	0.999937i	$0.503583\pi$
$822$	−3.04828e32	−0.0918394
$823$	4.08369e33	1.21326	0.606631	−	0.794984i	$-0.292521\pi$
$823$	4.08369e33	1.21326	0.606631	+	0.794984i	$0.292521\pi$
$824$	5.22471e32	0.153073
$825$	2.41204e33	0.696888
$826$	6.29910e32	0.179477
$827$	6.73455e32	0.189232	0.0946161	−	0.995514i	$-0.469838\pi$
$827$	6.73455e32	0.189232	0.0946161	+	0.995514i	$0.469838\pi$
$828$	−3.44812e30	−0.000955507 0
$829$	−3.77086e33	−1.03054	−0.515268	−	0.857029i	$-0.672308\pi$
$829$	−3.77086e33	−1.03054	−0.515268	+	0.857029i	$0.672308\pi$
$830$	6.44757e31	0.0173779
$831$	6.29813e32	0.167417
$832$	9.77667e32	0.256314
$833$	1.46123e32	0.0377833
$834$	−5.73593e32	−0.146283
$835$	−1.75746e33	−0.442070
$836$	6.91147e33	1.71474
$837$	−5.04928e32	−0.123562
$838$	1.45251e32	0.0350601
$839$	−4.99200e33	−1.18853	−0.594267	−	0.804268i	$-0.702558\pi$
$839$	−4.99200e33	−1.18853	−0.594267	+	0.804268i	$0.702558\pi$
$840$	−2.60949e32	−0.0612835
$841$	8.92995e33	2.06869
$842$	−1.63249e33	−0.373046
$843$	5.02931e33	1.13368
$844$	−4.91971e33	−1.09396
$845$	−1.26217e33	−0.276863
$846$	−8.18846e32	−0.177192
$847$	−1.97277e33	−0.421131
$848$	−1.77904e33	−0.374657
$849$	−4.06025e33	−0.843557
$850$	6.44051e31	0.0132009
$851$	−2.00400e31	−0.00405236
$852$	−4.47704e33	−0.893172
$853$	−2.52826e33	−0.497631	−0.248815	−	0.968551i	$-0.580041\pi$
$853$	−2.52826e33	−0.497631	−0.248815	+	0.968551i	$0.580041\pi$
$854$	3.87710e32	0.0752907
$855$	−1.04272e33	−0.199782
$856$	−6.16746e33	−1.16589
$857$	7.45015e33	1.38959	0.694793	−	0.719209i	$-0.255496\pi$
$857$	7.45015e33	1.38959	0.694793	+	0.719209i	$0.255496\pi$
$858$	2.34625e33	0.431788
$859$	−5.27466e32	−0.0957797	−0.0478898	−	0.998853i	$-0.515250\pi$
$859$	−5.27466e32	−0.0957797	−0.0478898	+	0.998853i	$0.515250\pi$
$860$	−8.38169e32	−0.150176
$861$	−1.59209e33	−0.281469
$862$	−1.75098e33	−0.305456
$863$	−6.72847e33	−1.15822	−0.579112	−	0.815248i	$-0.696600\pi$
$863$	−6.72847e33	−1.15822	−0.579112	+	0.815248i	$0.696600\pi$
$864$	1.06620e33	0.181105
$865$	3.01997e33	0.506195
$866$	4.16294e33	0.688565
$867$	−3.53084e33	−0.576313
$868$	−1.11413e33	−0.179457
$869$	9.81522e33	1.56017
$870$	−1.12378e33	−0.176283
$871$	5.31397e33	0.822641
$872$	2.65972e33	0.406347
$873$	−9.60382e32	−0.144804
$874$	1.18437e31	0.00176240
$875$	−1.80700e33	−0.265378
$876$	−4.22709e33	−0.612695
$877$	−7.45124e33	−1.06594	−0.532970	−	0.846134i	$-0.678924\pi$
$877$	−7.45124e33	−1.06594	−0.532970	+	0.846134i	$0.678924\pi$
$878$	4.93870e32	0.0697310
$879$	6.07808e33	0.847021
$880$	2.78932e33	0.383660
$881$	1.17245e34	1.59174	0.795870	−	0.605468i	$-0.207014\pi$
$881$	1.17245e34	1.59174	0.795870	+	0.605468i	$0.207014\pi$
$882$	−8.63624e32	−0.115727
$883$	1.05295e34	1.39271	0.696353	−	0.717699i	$-0.254805\pi$
$883$	1.05295e34	1.39271	0.696353	+	0.717699i	$0.254805\pi$
$884$	−3.50382e32	−0.0457447
$885$	2.80434e33	0.361396
$886$	1.65825e33	0.210941
$887$	−6.86475e33	−0.861992	−0.430996	−	0.902354i	$-0.641838\pi$
$887$	−6.86475e33	−0.861992	−0.430996	+	0.902354i	$0.641838\pi$
$888$	4.02108e33	0.498417
$889$	5.77423e32	0.0706519
$890$	1.29292e33	0.156166
$891$	−1.40651e33	−0.167706
$892$	−5.68246e33	−0.668868
$893$	−1.57303e34	−1.82787
$894$	1.41216e33	0.161995
$895$	−2.04339e33	−0.231412
$896$	3.00446e33	0.335911
$897$	−2.24865e31	−0.00248204
$898$	−2.45726e32	−0.0267777
$899$	−1.04540e34	−1.12472
$900$	2.12892e33	0.226136
$901$	2.66596e32	0.0279587
$902$	−8.40023e33	−0.869794
$903$	7.36017e32	0.0752452
$904$	−9.07152e32	−0.0915678
$905$	5.11367e33	0.509653
$906$	−1.08879e33	−0.107145
$907$	−9.01545e33	−0.875999	−0.438000	−	0.898975i	$-0.644313\pi$
$907$	−9.01545e33	−0.875999	−0.438000	+	0.898975i	$0.644313\pi$
$908$	−8.48862e33	−0.814423
$909$	−7.51298e31	−0.00711750
$910$	−7.81047e32	−0.0730636
$911$	1.54259e34	1.42492	0.712459	−	0.701714i	$-0.247582\pi$
$911$	1.54259e34	1.42492	0.712459	+	0.701714i	$0.247582\pi$
$912$	4.81448e33	0.439145
$913$	1.67074e33	0.150486
$914$	−2.14755e33	−0.191013
$915$	1.72607e33	0.151606
$916$	1.16751e34	1.01266
$917$	1.54230e33	0.132106
$918$	−3.75561e31	−0.00317680
$919$	3.21779e32	0.0268800	0.0134400	−	0.999910i	$-0.495722\pi$
$919$	3.21779e32	0.0268800	0.0134400	+	0.999910i	$0.495722\pi$
$920$	1.31956e31	0.00108860
$921$	−2.07060e33	−0.168699
$922$	−5.60525e33	−0.451013
$923$	−2.91964e34	−2.32012
$924$	−3.10349e33	−0.243569
$925$	1.23730e34	0.959056
$926$	1.26286e33	0.0966786
$927$	−9.37462e32	−0.0708821
$928$	2.20745e34	1.64850
$929$	6.89145e33	0.508311	0.254156	−	0.967163i	$-0.418202\pi$
$929$	6.89145e33	0.508311	0.254156	+	0.967163i	$0.418202\pi$
$930$	8.86865e32	0.0646106
$931$	−1.65905e34	−1.19382
$932$	1.05184e34	0.747593
$933$	−4.42557e33	−0.310692
$934$	9.81316e33	0.680487
$935$	−4.17989e32	−0.0286306
$936$	4.51197e33	0.305277
$937$	6.25703e32	0.0418180	0.0209090	−	0.999781i	$-0.493344\pi$
$937$	6.25703e32	0.0418180	0.0209090	+	0.999781i	$0.493344\pi$
$938$	1.25679e33	0.0829720
$939$	1.06976e34	0.697644
$940$	−8.04381e33	−0.518193
$941$	2.43281e34	1.54820	0.774101	−	0.633062i	$-0.218202\pi$
$941$	2.43281e34	1.54820	0.774101	+	0.633062i	$0.218202\pi$
$942$	−5.57860e33	−0.350703
$943$	8.05081e31	0.00499983
$944$	−1.29483e34	−0.794393
$945$	4.68217e32	0.0283780
$946$	3.88340e33	0.232522
$947$	1.95908e34	1.15885	0.579424	−	0.815026i	$-0.303277\pi$
$947$	1.95908e34	1.15885	0.579424	+	0.815026i	$0.303277\pi$
$948$	8.66313e33	0.506266
$949$	−2.75664e34	−1.59155
$950$	−7.31245e33	−0.417101
$951$	−1.84684e34	−1.04077
$952$	−1.80553e32	−0.0100526
$953$	2.99818e33	0.164926	0.0824632	−	0.996594i	$-0.473721\pi$
$953$	2.99818e33	0.164926	0.0824632	+	0.996594i	$0.473721\pi$
$954$	−1.57565e33	−0.0856355
$955$	−6.14175e33	−0.329802
$956$	7.15389e32	0.0379556
$957$	−2.91203e34	−1.52654
$958$	−6.83726e32	−0.0354143
$959$	2.62948e33	0.134573
$960$	1.02941e33	0.0520558
$961$	−1.17633e34	−0.587772
$962$	1.20355e34	0.594225
$963$	1.10662e34	0.539878
$964$	−2.05706e34	−0.991658
$965$	4.17989e33	0.199114
$966$	−5.31823e30	−0.000250340 0
$967$	5.37477e33	0.250009	0.125004	−	0.992156i	$-0.460106\pi$
$967$	5.37477e33	0.250009	0.125004	+	0.992156i	$0.460106\pi$
$968$	−2.00168e34	−0.920084
$969$	−7.21466e32	−0.0327712
$970$	1.68683e33	0.0757177
$971$	1.12238e34	0.497872	0.248936	−	0.968520i	$-0.419919\pi$
$971$	1.12238e34	0.497872	0.248936	+	0.968520i	$0.419919\pi$
$972$	−1.24142e33	−0.0544198
$973$	4.94789e33	0.214349
$974$	−4.85433e33	−0.207827
$975$	1.38835e34	0.587415
$976$	−7.96969e33	−0.333249
$977$	2.41460e34	0.997831	0.498915	−	0.866651i	$-0.333732\pi$
$977$	2.41460e34	0.997831	0.498915	+	0.866651i	$0.333732\pi$
$978$	9.66553e33	0.394756
$979$	3.35031e34	1.35233
$980$	−8.48368e33	−0.338442
$981$	−4.77230e33	−0.188163
$982$	−1.28102e34	−0.499199
$983$	−1.21263e34	−0.467048	−0.233524	−	0.972351i	$-0.575026\pi$
$983$	−1.21263e34	−0.467048	−0.233524	+	0.972351i	$0.575026\pi$
$984$	−1.61541e34	−0.614951
$985$	4.59989e33	0.173073
$986$	−7.77557e32	−0.0289166
$987$	7.06347e33	0.259640
$988$	3.97818e34	1.44537
$989$	−3.72187e31	−0.00133661
$990$	2.47042e33	0.0876934
$991$	1.83350e34	0.643329	0.321664	−	0.946854i	$-0.395758\pi$
$991$	1.83350e34	0.643329	0.321664	+	0.946854i	$0.395758\pi$
$992$	−1.74207e34	−0.604201
$993$	2.45807e34	0.842711
$994$	−6.90518e33	−0.234008
$995$	−3.64760e33	−0.122192
$996$	1.47463e33	0.0488316
$997$	1.59227e34	0.521222	0.260611	−	0.965444i	$-0.416076\pi$
$997$	1.59227e34	0.521222	0.260611	+	0.965444i	$0.416076\pi$
$998$	1.12779e34	0.364945
$999$	−7.21496e33	−0.230797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.24.a.a.1.1	✓	1
3.2	odd	2		9.24.a.a.1.1		1
4.3	odd	2		48.24.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.24.a.a.1.1	✓	1	1.1	even	1	trivial
9.24.a.a.1.1		1	3.2	odd	2
48.24.a.a.1.1		1	4.3	odd	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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