LMFDB - Embedded newform 2.32.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,32,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, 32, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 32 $
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:	$12.1754265638$
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	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+32768.0 q^{2} -1.99842e7 q^{3} +1.07374e9 q^{4} +4.29517e10 q^{5} -6.54843e11 q^{6} -1.68354e13 q^{7} +3.51844e13 q^{8} -2.18305e14 q^{9} +O(q^{10})$

\(q+32768.0 q^{2} -1.99842e7 q^{3} +1.07374e9 q^{4} +4.29517e10 q^{5} -6.54843e11 q^{6} -1.68354e13 q^{7} +3.51844e13 q^{8} -2.18305e14 q^{9} +1.40744e15 q^{10} -7.20783e15 q^{11} -2.14579e16 q^{12} -2.70054e17 q^{13} -5.51661e17 q^{14} -8.58356e17 q^{15} +1.15292e18 q^{16} -1.62755e19 q^{17} -7.15341e18 q^{18} +1.09087e20 q^{19} +4.61190e19 q^{20} +3.36441e20 q^{21} -2.36186e20 q^{22} -3.05935e20 q^{23} -7.03132e20 q^{24} -2.81176e21 q^{25} -8.84912e21 q^{26} +1.67064e22 q^{27} -1.80768e22 q^{28} +3.42166e22 q^{29} -2.81266e22 q^{30} +1.62779e23 q^{31} +3.77789e22 q^{32} +1.44043e23 q^{33} -5.33315e23 q^{34} -7.23107e23 q^{35} -2.34403e23 q^{36} -2.50895e24 q^{37} +3.57457e24 q^{38} +5.39681e24 q^{39} +1.51123e24 q^{40} -9.29498e24 q^{41} +1.10245e25 q^{42} +5.86009e24 q^{43} -7.73935e24 q^{44} -9.37656e24 q^{45} -1.00249e25 q^{46} -9.16365e25 q^{47} -2.30402e25 q^{48} +1.25654e26 q^{49} -9.21359e25 q^{50} +3.25253e26 q^{51} -2.89968e26 q^{52} +5.88384e26 q^{53} +5.47434e26 q^{54} -3.09589e26 q^{55} -5.92342e26 q^{56} -2.18002e27 q^{57} +1.12121e27 q^{58} -3.22410e27 q^{59} -9.21653e26 q^{60} +4.04424e27 q^{61} +5.33394e27 q^{62} +3.67524e27 q^{63} +1.23794e27 q^{64} -1.15993e28 q^{65} +4.72000e27 q^{66} +1.64520e28 q^{67} -1.74757e28 q^{68} +6.11388e27 q^{69} -2.36948e28 q^{70} -6.89178e27 q^{71} -7.68091e27 q^{72} -2.34635e28 q^{73} -8.22132e28 q^{74} +5.61909e28 q^{75} +1.17132e29 q^{76} +1.21346e29 q^{77} +1.76843e29 q^{78} -6.35600e28 q^{79} +4.95199e28 q^{80} -1.99023e29 q^{81} -3.04578e29 q^{82} -2.80657e29 q^{83} +3.61251e29 q^{84} -6.99060e29 q^{85} +1.92023e29 q^{86} -6.83792e29 q^{87} -2.53603e29 q^{88} +1.97625e30 q^{89} -3.07251e29 q^{90} +4.54645e30 q^{91} -3.28496e29 q^{92} -3.25301e30 q^{93} -3.00274e30 q^{94} +4.68549e30 q^{95} -7.54982e29 q^{96} -7.78054e30 q^{97} +4.11743e30 q^{98} +1.57350e30 q^{99} +O(q^{100})\)

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 $

$2$	32768.0	0.707107
$2$	32768.0	0.707107
$3$	−1.99842e7	−0.804095	−0.402048	−	0.915619i	$-0.631701\pi$
$3$	−1.99842e7	−0.804095	−0.402048	+	0.915619i	$0.631701\pi$
$4$	1.07374e9	0.500000
$5$	4.29517e10	0.629427	0.314714	−	0.949187i	$-0.398092\pi$
$5$	4.29517e10	0.629427	0.314714	+	0.949187i	$0.398092\pi$
$6$	−6.54843e11	−0.568581
$7$	−1.68354e13	−1.34030	−0.670151	−	0.742225i	$-0.733771\pi$
$7$	−1.68354e13	−1.34030	−0.670151	+	0.742225i	$0.733771\pi$
$8$	3.51844e13	0.353553
$9$	−2.18305e14	−0.353431
$10$	1.40744e15	0.445072
$11$	−7.20783e15	−0.520257	−0.260129	−	0.965574i	$-0.583765\pi$
$11$	−7.20783e15	−0.520257	−0.260129	+	0.965574i	$0.583765\pi$
$12$	−2.14579e16	−0.402048
$13$	−2.70054e17	−1.46328	−0.731641	−	0.681690i	$-0.761245\pi$
$13$	−2.70054e17	−1.46328	−0.731641	+	0.681690i	$0.761245\pi$
$14$	−5.51661e17	−0.947737
$15$	−8.58356e17	−0.506119
$16$	1.15292e18	0.250000
$17$	−1.62755e19	−1.37904	−0.689518	−	0.724269i	$-0.742178\pi$
$17$	−1.62755e19	−1.37904	−0.689518	+	0.724269i	$0.742178\pi$
$18$	−7.15341e18	−0.249913
$19$	1.09087e20	1.64852	0.824259	−	0.566214i	$-0.191592\pi$
$19$	1.09087e20	1.64852	0.824259	+	0.566214i	$0.191592\pi$
$20$	4.61190e19	0.314714
$21$	3.36441e20	1.07773
$22$	−2.36186e20	−0.367877
$23$	−3.05935e20	−0.239248	−0.119624	−	0.992819i	$-0.538169\pi$
$23$	−3.05935e20	−0.239248	−0.119624	+	0.992819i	$0.538169\pi$
$24$	−7.03132e20	−0.284291
$25$	−2.81176e21	−0.603822
$26$	−8.84912e21	−1.03470
$27$	1.67064e22	1.08829
$28$	−1.80768e22	−0.670151
$29$	3.42166e22	0.736322	0.368161	−	0.929762i	$-0.379988\pi$
$29$	3.42166e22	0.736322	0.368161	+	0.929762i	$0.379988\pi$
$30$	−2.81266e22	−0.357880
$31$	1.62779e23	1.24593	0.622963	−	0.782251i	$-0.285929\pi$
$31$	1.62779e23	1.24593	0.622963	+	0.782251i	$0.285929\pi$
$32$	3.77789e22	0.176777
$33$	1.44043e23	0.418336
$34$	−5.33315e23	−0.975126
$35$	−7.23107e23	−0.843622
$36$	−2.34403e23	−0.176715
$37$	−2.50895e24	−1.23699	−0.618493	−	0.785790i	$-0.712257\pi$
$37$	−2.50895e24	−1.23699	−0.618493	+	0.785790i	$0.712257\pi$
$38$	3.57457e24	1.16568
$39$	5.39681e24	1.17662
$40$	1.51123e24	0.222536
$41$	−9.29498e24	−0.933466	−0.466733	−	0.884398i	$-0.654569\pi$
$41$	−9.29498e24	−0.933466	−0.466733	+	0.884398i	$0.654569\pi$
$42$	1.10245e25	0.762071
$43$	5.86009e24	0.281283	0.140641	−	0.990061i	$-0.455084\pi$
$43$	5.86009e24	0.281283	0.140641	+	0.990061i	$0.455084\pi$
$44$	−7.73935e24	−0.260129
$45$	−9.37656e24	−0.222459
$46$	−1.00249e25	−0.169174
$47$	−9.16365e25	−1.10803	−0.554015	−	0.832507i	$-0.686905\pi$
$47$	−9.16365e25	−1.10803	−0.554015	+	0.832507i	$0.686905\pi$
$48$	−2.30402e25	−0.201024
$49$	1.25654e26	0.796410
$50$	−9.21359e25	−0.426966
$51$	3.25253e26	1.10888
$52$	−2.89968e26	−0.731641
$53$	5.88384e26	1.10506	0.552528	−	0.833494i	$-0.313663\pi$
$53$	5.88384e26	1.10506	0.552528	+	0.833494i	$0.313663\pi$
$54$	5.47434e26	0.769535
$55$	−3.09589e26	−0.327464
$56$	−5.92342e26	−0.473868
$57$	−2.18002e27	−1.32556
$58$	1.12121e27	0.520658
$59$	−3.22410e27	−1.14869	−0.574344	−	0.818614i	$-0.694743\pi$
$59$	−3.22410e27	−1.14869	−0.574344	+	0.818614i	$0.694743\pi$
$60$	−9.21653e26	−0.253060
$61$	4.04424e27	0.859458	0.429729	−	0.902958i	$-0.358609\pi$
$61$	4.04424e27	0.859458	0.429729	+	0.902958i	$0.358609\pi$
$62$	5.33394e27	0.881003
$63$	3.67524e27	0.473704
$64$	1.23794e27	0.125000
$65$	−1.15993e28	−0.921029
$66$	4.72000e27	0.295809
$67$	1.64520e28	0.816692	0.408346	−	0.912827i	$-0.366106\pi$
$67$	1.64520e28	0.816692	0.408346	+	0.912827i	$0.366106\pi$
$68$	−1.74757e28	−0.689518
$69$	6.11388e27	0.192378
$70$	−2.36948e28	−0.596531
$71$	−6.89178e27	−0.139260	−0.0696301	−	0.997573i	$-0.522182\pi$
$71$	−6.89178e27	−0.139260	−0.0696301	+	0.997573i	$0.522182\pi$
$72$	−7.68091e27	−0.124957
$73$	−2.34635e28	−0.308240	−0.154120	−	0.988052i	$-0.549254\pi$
$73$	−2.34635e28	−0.308240	−0.154120	+	0.988052i	$0.549254\pi$
$74$	−8.22132e28	−0.874681
$75$	5.61909e28	0.485530
$76$	1.17132e29	0.824259
$77$	1.21346e29	0.697302
$78$	1.76843e29	0.831995
$79$	−6.35600e28	−0.245451	−0.122725	−	0.992441i	$-0.539163\pi$
$79$	−6.35600e28	−0.245451	−0.122725	+	0.992441i	$0.539163\pi$
$80$	4.95199e28	0.157357
$81$	−1.99023e29	−0.521656
$82$	−3.04578e29	−0.660060
$83$	−2.80657e29	−0.504041	−0.252020	−	0.967722i	$-0.581095\pi$
$83$	−2.80657e29	−0.504041	−0.252020	+	0.967722i	$0.581095\pi$
$84$	3.61251e29	0.538865
$85$	−6.99060e29	−0.868003
$86$	1.92023e29	0.198897
$87$	−6.83792e29	−0.592073
$88$	−2.53603e29	−0.183939
$89$	1.97625e30	1.20308	0.601542	−	0.798841i	$-0.294553\pi$
$89$	1.97625e30	1.20308	0.601542	+	0.798841i	$0.294553\pi$
$90$	−3.07251e29	−0.157302
$91$	4.54645e30	1.96124
$92$	−3.28496e29	−0.119624
$93$	−3.25301e30	−1.00184
$94$	−3.00274e30	−0.783496
$95$	4.68549e30	1.03762
$96$	−7.54982e29	−0.142145
$97$	−7.78054e30	−1.24752	−0.623760	−	0.781616i	$-0.714396\pi$
$97$	−7.78054e30	−1.24752	−0.623760	+	0.781616i	$0.714396\pi$
$98$	4.11743e30	0.563147
$99$	1.57350e30	0.183875
$100$	−3.01911e30	−0.301911
$101$	−7.73050e30	−0.662562	−0.331281	−	0.943532i	$-0.607481\pi$
$101$	−7.73050e30	−0.662562	−0.331281	+	0.943532i	$0.607481\pi$
$102$	1.06579e31	0.784094
$103$	−1.41437e31	−0.894512	−0.447256	−	0.894406i	$-0.647599\pi$
$103$	−1.41437e31	−0.894512	−0.447256	+	0.894406i	$0.647599\pi$
$104$	−9.50167e30	−0.517348
$105$	1.44507e31	0.678353
$106$	1.92802e31	0.781393
$107$	3.26395e31	1.14365	0.571827	−	0.820374i	$-0.306235\pi$
$107$	3.26395e31	1.14365	0.571827	+	0.820374i	$0.306235\pi$
$108$	1.79383e31	0.544144
$109$	−3.26173e31	−0.857704	−0.428852	−	0.903375i	$-0.641082\pi$
$109$	−3.26173e31	−0.857704	−0.428852	+	0.903375i	$0.641082\pi$
$110$	−1.01446e31	−0.231552
$111$	5.01393e31	0.994655
$112$	−1.94098e31	−0.335076
$113$	−1.08807e32	−1.63659	−0.818293	−	0.574801i	$-0.805080\pi$
$113$	−1.08807e32	−1.63659	−0.818293	+	0.574801i	$0.805080\pi$
$114$	−7.14350e31	−0.937316
$115$	−1.31404e31	−0.150589
$116$	3.67398e31	0.368161
$117$	5.89540e31	0.517169
$118$	−1.05647e32	−0.812245
$119$	2.74004e32	1.84833
$120$	−3.02007e31	−0.178940
$121$	−1.39991e32	−0.729332
$122$	1.32522e32	0.607729
$123$	1.85753e32	0.750596
$124$	1.74783e32	0.622963
$125$	−3.20780e32	−1.00949
$126$	1.20430e32	0.334959
$127$	−2.53110e32	−0.622805	−0.311403	−	0.950278i	$-0.600799\pi$
$127$	−2.53110e32	−0.622805	−0.311403	+	0.950278i	$0.600799\pi$
$128$	4.05648e31	0.0883883
$129$	−1.17109e32	−0.226178
$130$	−3.80085e32	−0.651266
$131$	4.62256e32	0.703360	0.351680	−	0.936120i	$-0.385611\pi$
$131$	4.62256e32	0.703360	0.351680	+	0.936120i	$0.385611\pi$
$132$	1.54665e32	0.209168
$133$	−1.83652e33	−2.20951
$134$	5.39098e32	0.577488
$135$	7.17567e32	0.684997
$136$	−5.72643e32	−0.487563
$137$	2.41393e33	1.83466	0.917332	−	0.398123i	$-0.130338\pi$
$137$	2.41393e33	1.83466	0.917332	+	0.398123i	$0.130338\pi$
$138$	2.00340e32	0.136032
$139$	−1.53762e33	−0.933510	−0.466755	−	0.884387i	$-0.654577\pi$
$139$	−1.53762e33	−0.933510	−0.466755	+	0.884387i	$0.654577\pi$
$140$	−7.76431e32	−0.421811
$141$	1.83128e33	0.890962
$142$	−2.25830e32	−0.0984718
$143$	1.94650e33	0.761283
$144$	−2.51688e32	−0.0883576
$145$	1.46966e33	0.463461
$146$	−7.68852e32	−0.217958
$147$	−2.51109e33	−0.640390
$148$	−2.69396e33	−0.618493
$149$	−7.06717e33	−1.46170	−0.730850	−	0.682538i	$-0.760876\pi$
$149$	−7.06717e33	−1.46170	−0.730850	+	0.682538i	$0.760876\pi$
$150$	1.84126e33	0.343322
$151$	−6.31239e33	−1.06182	−0.530911	−	0.847428i	$-0.678150\pi$
$151$	−6.31239e33	−1.06182	−0.530911	+	0.847428i	$0.678150\pi$
$152$	3.83817e33	0.582839
$153$	3.55301e33	0.487393
$154$	3.97628e33	0.493067
$155$	6.99164e33	0.784219
$156$	5.79478e33	0.588309
$157$	9.11534e33	0.838163	0.419082	−	0.907949i	$-0.362352\pi$
$157$	9.11534e33	0.838163	0.419082	+	0.907949i	$0.362352\pi$
$158$	−2.08273e33	−0.173560
$159$	−1.17584e34	−0.888571
$160$	1.62267e33	0.111268
$161$	5.15053e33	0.320665
$162$	−6.52157e33	−0.368867
$163$	−4.96877e33	−0.255471	−0.127735	−	0.991808i	$-0.540771\pi$
$163$	−4.96877e33	−0.255471	−0.127735	+	0.991808i	$0.540771\pi$
$164$	−9.98041e33	−0.466733
$165$	6.18689e33	0.263312
$166$	−9.19657e33	−0.356411
$167$	−2.74735e34	−0.970082	−0.485041	−	0.874491i	$-0.661195\pi$
$167$	−2.74735e34	−0.970082	−0.485041	+	0.874491i	$0.661195\pi$
$168$	1.18375e34	0.381035
$169$	3.88690e34	1.14119
$170$	−2.29068e34	−0.613770
$171$	−2.38143e34	−0.582636
$172$	6.29222e33	0.140641
$173$	1.32315e34	0.270331	0.135165	−	0.990823i	$-0.456843\pi$
$173$	1.32315e34	0.270331	0.135165	+	0.990823i	$0.456843\pi$
$174$	−2.24065e34	−0.418659
$175$	4.73370e34	0.809304
$176$	−8.31007e33	−0.130064
$177$	6.44311e34	0.923655
$178$	6.47576e34	0.850708
$179$	−5.48512e34	−0.660639	−0.330319	−	0.943869i	$-0.607156\pi$
$179$	−5.48512e34	−0.660639	−0.330319	+	0.943869i	$0.607156\pi$
$180$	−1.00680e34	−0.111229
$181$	−6.85442e34	−0.694949	−0.347475	−	0.937689i	$-0.612961\pi$
$181$	−6.85442e34	−0.694949	−0.347475	+	0.937689i	$0.612961\pi$
$182$	1.48978e35	1.38681
$183$	−8.08210e34	−0.691086
$184$	−1.07641e34	−0.0845869
$185$	−1.07764e35	−0.778593
$186$	−1.06595e35	−0.708410
$187$	1.17311e35	0.717453
$188$	−9.83939e34	−0.554015
$189$	−2.81258e35	−1.45863
$190$	1.53534e35	0.733709
$191$	2.17438e35	0.957895	0.478947	−	0.877844i	$-0.341018\pi$
$191$	2.17438e35	0.957895	0.478947	+	0.877844i	$0.341018\pi$
$192$	−2.47393e34	−0.100512
$193$	3.50352e34	0.131331	0.0656653	−	0.997842i	$-0.479083\pi$
$193$	3.50352e34	0.131331	0.0656653	+	0.997842i	$0.479083\pi$
$194$	−2.54953e35	−0.882130
$195$	2.31802e35	0.740595
$196$	1.34920e35	0.398205
$197$	4.67654e35	1.27555	0.637776	−	0.770222i	$-0.279855\pi$
$197$	4.67654e35	1.27555	0.637776	+	0.770222i	$0.279855\pi$
$198$	5.15606e34	0.130019
$199$	3.55886e35	0.830020	0.415010	−	0.909817i	$-0.363778\pi$
$199$	3.55886e35	0.830020	0.415010	+	0.909817i	$0.363778\pi$
$200$	−9.89301e34	−0.213483
$201$	−3.28780e35	−0.656698
$202$	−2.53313e35	−0.468502
$203$	−5.76049e35	−0.986894
$204$	3.49237e35	0.554438
$205$	−3.99235e35	−0.587549
$206$	−4.63461e35	−0.632515
$207$	6.67871e34	0.0845575
$208$	−3.11351e35	−0.365821
$209$	−7.86283e35	−0.857653
$210$	4.73522e35	0.479668
$211$	9.00169e35	0.847122	0.423561	−	0.905868i	$-0.360780\pi$
$211$	9.00169e35	0.847122	0.423561	+	0.905868i	$0.360780\pi$
$212$	6.31772e35	0.552528
$213$	1.37727e35	0.111978
$214$	1.06953e36	0.808685
$215$	2.51701e35	0.177047
$216$	5.87803e35	0.384768
$217$	−2.74044e36	−1.66992
$218$	−1.06880e36	−0.606489
$219$	4.68900e35	0.247854
$220$	−3.32418e35	−0.163732
$221$	4.39525e36	2.01792
$222$	1.64297e36	0.703327
$223$	−1.53232e36	−0.611820	−0.305910	−	0.952060i	$-0.598961\pi$
$223$	−1.53232e36	−0.611820	−0.305910	+	0.952060i	$0.598961\pi$
$224$	−6.36022e35	−0.236934
$225$	6.13821e35	0.213409
$226$	−3.56537e36	−1.15724
$227$	1.78639e36	0.541470	0.270735	−	0.962654i	$-0.412733\pi$
$227$	1.78639e36	0.541470	0.270735	+	0.962654i	$0.412733\pi$
$228$	−2.34078e36	−0.662782
$229$	−4.03297e36	−1.06703	−0.533514	−	0.845791i	$-0.679129\pi$
$229$	−4.03297e36	−1.06703	−0.533514	+	0.845791i	$0.679129\pi$
$230$	−4.30586e35	−0.106483
$231$	−2.42501e36	−0.560697
$232$	1.20389e36	0.260329
$233$	4.83929e36	0.978959	0.489480	−	0.872015i	$-0.337187\pi$
$233$	4.83929e36	0.978959	0.489480	+	0.872015i	$0.337187\pi$
$234$	1.93180e36	0.365693
$235$	−3.93594e36	−0.697424
$236$	−3.46185e36	−0.574344
$237$	1.27020e36	0.197366
$238$	8.97855e36	1.30696
$239$	7.98646e36	1.08940	0.544699	−	0.838632i	$-0.316644\pi$
$239$	7.98646e36	1.08940	0.544699	+	0.838632i	$0.316644\pi$
$240$	−9.89617e35	−0.126530
$241$	5.53361e36	0.663353	0.331676	−	0.943393i	$-0.392386\pi$
$241$	5.53361e36	0.663353	0.331676	+	0.943393i	$0.392386\pi$
$242$	−4.58721e36	−0.515716
$243$	−6.34177e36	−0.668826
$244$	4.34247e36	0.429729
$245$	5.39705e36	0.501282
$246$	6.08675e36	0.530752
$247$	−2.94594e37	−2.41225
$248$	5.72728e36	0.440501
$249$	5.60871e36	0.405297
$250$	−1.05113e37	−0.713816
$251$	−1.82546e37	−1.16528	−0.582640	−	0.812730i	$-0.697980\pi$
$251$	−1.82546e37	−1.16528	−0.582640	+	0.812730i	$0.697980\pi$
$252$	3.94626e36	0.236852
$253$	2.20513e36	0.124470
$254$	−8.29392e36	−0.440390
$255$	1.39702e37	0.697957
$256$	1.32923e36	0.0625000
$257$	−3.53190e36	−0.156331	−0.0781654	−	0.996940i	$-0.524906\pi$
$257$	−3.53190e36	−0.156331	−0.0781654	+	0.996940i	$0.524906\pi$
$258$	−3.83744e36	−0.159932
$259$	4.22390e37	1.65794
$260$	−1.24546e37	−0.460515
$261$	−7.46964e36	−0.260239
$262$	1.51472e37	0.497350
$263$	3.77552e37	1.16859	0.584296	−	0.811541i	$-0.301371\pi$
$263$	3.77552e37	1.16859	0.584296	+	0.811541i	$0.301371\pi$
$264$	5.06806e36	0.147904
$265$	2.52721e37	0.695553
$266$	−6.01792e37	−1.56236
$267$	−3.94937e37	−0.967394
$268$	1.76652e37	0.408346
$269$	−1.73593e37	−0.378767	−0.189384	−	0.981903i	$-0.560649\pi$
$269$	−1.73593e37	−0.378767	−0.189384	+	0.981903i	$0.560649\pi$
$270$	2.35132e37	0.484366
$271$	6.46880e36	0.125835	0.0629173	−	0.998019i	$-0.479960\pi$
$271$	6.46880e36	0.125835	0.0629173	+	0.998019i	$0.479960\pi$
$272$	−1.87644e37	−0.344759
$273$	−9.08572e37	−1.57702
$274$	7.90998e37	1.29730
$275$	2.02667e37	0.314143
$276$	6.56473e36	0.0961891
$277$	−1.98649e37	−0.275201	−0.137601	−	0.990488i	$-0.543939\pi$
$277$	−1.98649e37	−0.275201	−0.137601	+	0.990488i	$0.543939\pi$
$278$	−5.03846e37	−0.660091
$279$	−3.55354e37	−0.440348
$280$	−2.54421e37	−0.298266
$281$	5.48253e37	0.608181	0.304091	−	0.952643i	$-0.401647\pi$
$281$	5.48253e37	0.608181	0.304091	+	0.952643i	$0.401647\pi$
$282$	6.00075e37	0.630005
$283$	−2.62737e37	−0.261115	−0.130557	−	0.991441i	$-0.541677\pi$
$283$	−2.62737e37	−0.261115	−0.130557	+	0.991441i	$0.541677\pi$
$284$	−7.39999e36	−0.0696301
$285$	−9.36358e37	−0.834346
$286$	6.37830e37	0.538308
$287$	1.56484e38	1.25113
$288$	−8.24732e36	−0.0624783
$289$	1.25602e38	0.901740
$290$	4.81579e37	0.327716
$291$	1.55488e38	1.00313
$292$	−2.51937e37	−0.154120
$293$	−1.33198e38	−0.772768	−0.386384	−	0.922338i	$-0.626276\pi$
$293$	−1.33198e38	−0.772768	−0.386384	+	0.922338i	$0.626276\pi$
$294$	−8.22836e37	−0.452824
$295$	−1.38481e38	−0.723016
$296$	−8.82757e37	−0.437341
$297$	−1.20417e38	−0.566189
$298$	−2.31577e38	−1.03358
$299$	8.26190e37	0.350087
$300$	6.03345e37	0.242765
$301$	−9.86567e37	−0.377004
$302$	−2.06844e38	−0.750821
$303$	1.54488e38	0.532763
$304$	1.25769e38	0.412129
$305$	1.73707e38	0.540966
$306$	1.16425e38	0.344639
$307$	−4.38543e37	−0.123415	−0.0617075	−	0.998094i	$-0.519655\pi$
$307$	−4.38543e37	−0.123415	−0.0617075	+	0.998094i	$0.519655\pi$
$308$	1.30295e38	0.348651
$309$	2.82651e38	0.719273
$310$	2.29102e38	0.554527
$311$	−2.86015e38	−0.658571	−0.329285	−	0.944230i	$-0.606808\pi$
$311$	−2.86015e38	−0.658571	−0.329285	+	0.944230i	$0.606808\pi$
$312$	1.89883e38	0.415997
$313$	−6.01224e38	−1.25343	−0.626714	−	0.779250i	$-0.715600\pi$
$313$	−6.01224e38	−1.25343	−0.626714	+	0.779250i	$0.715600\pi$
$314$	2.98692e38	0.592671
$315$	1.57858e38	0.298162
$316$	−6.82470e37	−0.122725
$317$	9.02679e38	1.54566	0.772831	−	0.634612i	$-0.218840\pi$
$317$	9.02679e38	1.54566	0.772831	+	0.634612i	$0.218840\pi$
$318$	−3.85299e38	−0.628315
$319$	−2.46627e38	−0.383077
$320$	5.31716e37	0.0786784
$321$	−6.52274e38	−0.919607
$322$	1.68773e38	0.226744
$323$	−1.77545e39	−2.27336
$324$	−2.13699e38	−0.260828
$325$	7.59327e38	0.883561
$326$	−1.62817e38	−0.180645
$327$	6.51832e38	0.689676
$328$	−3.27038e38	−0.330030
$329$	1.54273e39	1.48510
$330$	2.02732e38	0.186190
$331$	−1.37329e39	−1.20345	−0.601725	−	0.798704i	$-0.705520\pi$
$331$	−1.37329e39	−1.20345	−0.601725	+	0.798704i	$0.705520\pi$
$332$	−3.01353e38	−0.252020
$333$	5.47715e38	0.437189
$334$	−9.00252e38	−0.685952
$335$	7.06640e38	0.514048
$336$	3.87891e38	0.269433
$337$	1.29341e37	0.00857975	0.00428987	−	0.999991i	$-0.498634\pi$
$337$	1.29341e37	0.00857975	0.00428987	+	0.999991i	$0.498634\pi$
$338$	1.27366e39	0.806946
$339$	2.17441e39	1.31597
$340$	−7.50610e38	−0.434001
$341$	−1.17328e39	−0.648202
$342$	−7.80346e38	−0.411986
$343$	5.40776e38	0.272872
$344$	2.06183e38	0.0994485
$345$	2.62601e38	0.121088
$346$	4.33571e38	0.191153
$347$	−1.27078e39	−0.535753	−0.267876	−	0.963453i	$-0.586322\pi$
$347$	−1.27078e39	−0.535753	−0.267876	+	0.963453i	$0.586322\pi$
$348$	−7.34216e38	−0.296037
$349$	1.38237e39	0.533128	0.266564	−	0.963817i	$-0.414112\pi$
$349$	1.38237e39	0.533128	0.266564	+	0.963817i	$0.414112\pi$
$350$	1.55114e39	0.572264
$351$	−4.51161e39	−1.59247
$352$	−2.72304e38	−0.0919693
$353$	−5.17037e39	−1.67114	−0.835571	−	0.549382i	$-0.814863\pi$
$353$	−5.17037e39	−1.67114	−0.835571	+	0.549382i	$0.814863\pi$
$354$	2.11128e39	0.653123
$355$	−2.96014e38	−0.0876541
$356$	2.12198e39	0.601542
$357$	−5.47575e39	−1.48623
$358$	−1.79736e39	−0.467142
$359$	6.53823e39	1.62741	0.813704	−	0.581279i	$-0.197448\pi$
$359$	6.53823e39	1.62741	0.813704	+	0.581279i	$0.197448\pi$
$360$	−3.29908e38	−0.0786510
$361$	7.52118e39	1.71761
$362$	−2.24606e39	−0.491403
$363$	2.79760e39	0.586453
$364$	4.88171e39	0.980620
$365$	−1.00780e39	−0.194014
$366$	−2.64834e39	−0.488672
$367$	7.94764e39	1.40577	0.702885	−	0.711304i	$-0.251895\pi$
$367$	7.94764e39	1.40577	0.702885	+	0.711304i	$0.251895\pi$
$368$	−3.52719e38	−0.0598120
$369$	2.02914e39	0.329916
$370$	−3.53120e39	−0.550548
$371$	−9.90565e39	−1.48111
$372$	−3.49289e39	−0.500922
$373$	−7.09424e39	−0.975931	−0.487966	−	0.872863i	$-0.662261\pi$
$373$	−7.09424e39	−0.975931	−0.487966	+	0.872863i	$0.662261\pi$
$374$	3.84405e39	0.507316
$375$	6.41053e39	0.811725
$376$	−3.22417e39	−0.391748
$377$	−9.24032e39	−1.07745
$378$	−9.21625e39	−1.03141
$379$	8.95619e39	0.962089	0.481045	−	0.876696i	$-0.340257\pi$
$379$	8.95619e39	0.962089	0.481045	+	0.876696i	$0.340257\pi$
$380$	5.03100e39	0.518811
$381$	5.05821e39	0.500795
$382$	7.12500e39	0.677334
$383$	−1.43173e40	−1.30702	−0.653509	−	0.756919i	$-0.726704\pi$
$383$	−1.43173e40	−1.30702	−0.653509	+	0.756919i	$0.726704\pi$
$384$	−8.10656e38	−0.0710727
$385$	5.21204e39	0.438901
$386$	1.14803e39	0.0928647
$387$	−1.27928e39	−0.0994139
$388$	−8.35429e39	−0.623760
$389$	7.93003e39	0.568926	0.284463	−	0.958687i	$-0.408185\pi$
$389$	7.93003e39	0.568926	0.284463	+	0.958687i	$0.408185\pi$
$390$	7.59569e39	0.523680
$391$	4.97925e39	0.329932
$392$	4.42105e39	0.281574
$393$	−9.23782e39	−0.565568
$394$	1.53241e40	0.901951
$395$	−2.73001e39	−0.154493
$396$	1.68954e39	0.0919374
$397$	−2.07260e40	−1.08458	−0.542292	−	0.840190i	$-0.682444\pi$
$397$	−2.07260e40	−1.08458	−0.542292	+	0.840190i	$0.682444\pi$
$398$	1.16617e40	0.586913
$399$	3.67015e40	1.77666
$400$	−3.24174e39	−0.150955
$401$	3.44745e38	0.0154440	0.00772201	−	0.999970i	$-0.497542\pi$
$401$	3.44745e38	0.0154440	0.00772201	+	0.999970i	$0.497542\pi$
$402$	−1.07734e40	−0.464356
$403$	−4.39591e40	−1.82314
$404$	−8.30056e39	−0.331281
$405$	−8.54836e39	−0.328345
$406$	−1.88760e40	−0.697840
$407$	1.80841e40	0.643551
$408$	1.14438e40	0.392047
$409$	2.68695e40	0.886235	0.443118	−	0.896463i	$-0.353872\pi$
$409$	2.68695e40	0.886235	0.443118	+	0.896463i	$0.353872\pi$
$410$	−1.30821e40	−0.415460
$411$	−4.82406e40	−1.47525
$412$	−1.51867e40	−0.447256
$413$	5.42789e40	1.53959
$414$	2.18848e39	0.0597912
$415$	−1.20547e40	−0.317257
$416$	−1.02023e40	−0.258674
$417$	3.07281e40	0.750631
$418$	−2.57649e40	−0.606452
$419$	−1.18872e40	−0.269627	−0.134814	−	0.990871i	$-0.543044\pi$
$419$	−1.18872e40	−0.269627	−0.134814	+	0.990871i	$0.543044\pi$
$420$	1.55164e40	0.339176
$421$	3.74735e40	0.789499	0.394749	−	0.918789i	$-0.370831\pi$
$421$	3.74735e40	0.789499	0.394749	+	0.918789i	$0.370831\pi$
$422$	2.94967e40	0.599005
$423$	2.00047e40	0.391612
$424$	2.07019e40	0.390697
$425$	4.57628e40	0.832692
$426$	4.51303e39	0.0791807
$427$	−6.80863e40	−1.15193
$428$	3.50464e40	0.571827
$429$	−3.88993e40	−0.612144
$430$	8.24773e39	0.125191
$431$	2.80334e40	0.410466	0.205233	−	0.978713i	$-0.434205\pi$
$431$	2.80334e40	0.410466	0.205233	+	0.978713i	$0.434205\pi$
$432$	1.92611e40	0.272072
$433$	−1.18599e41	−1.61629	−0.808146	−	0.588982i	$-0.799529\pi$
$433$	−1.18599e41	−1.61629	−0.808146	+	0.588982i	$0.799529\pi$
$434$	−8.97989e40	−1.18081
$435$	−2.93700e40	−0.372667
$436$	−3.50226e40	−0.428852
$437$	−3.33737e40	−0.394404
$438$	1.53649e40	0.175259
$439$	2.22996e40	0.245526	0.122763	−	0.992436i	$-0.460825\pi$
$439$	2.22996e40	0.245526	0.122763	+	0.992436i	$0.460825\pi$
$440$	−1.08927e40	−0.115776
$441$	−2.74308e40	−0.281476
$442$	1.44024e41	1.42688
$443$	−4.19902e40	−0.401689	−0.200845	−	0.979623i	$-0.564369\pi$
$443$	−4.19902e40	−0.401689	−0.200845	+	0.979623i	$0.564369\pi$
$444$	5.38367e40	0.497327
$445$	8.48831e40	0.757253
$446$	−5.02111e40	−0.432622
$447$	1.41232e41	1.17535
$448$	−2.08412e40	−0.167538
$449$	−9.25651e40	−0.718835	−0.359417	−	0.933177i	$-0.617025\pi$
$449$	−9.25651e40	−0.718835	−0.359417	+	0.933177i	$0.617025\pi$
$450$	2.01137e40	0.150903
$451$	6.69967e40	0.485643
$452$	−1.16830e41	−0.818293
$453$	1.26148e41	0.853805
$454$	5.85363e40	0.382877
$455$	1.95278e41	1.23446
$456$	−7.67028e40	−0.468658
$457$	−4.96857e40	−0.293447	−0.146724	−	0.989178i	$-0.546873\pi$
$457$	−4.96857e40	−0.293447	−0.146724	+	0.989178i	$0.546873\pi$
$458$	−1.32153e41	−0.754502
$459$	−2.71904e41	−1.50079
$460$	−1.41094e40	−0.0752946
$461$	−1.25763e40	−0.0648916	−0.0324458	−	0.999473i	$-0.510330\pi$
$461$	−1.25763e40	−0.0648916	−0.0324458	+	0.999473i	$0.510330\pi$
$462$	−7.94628e40	−0.396473
$463$	2.97996e41	1.43782	0.718912	−	0.695102i	$-0.244641\pi$
$463$	2.97996e41	1.43782	0.718912	+	0.695102i	$0.244641\pi$
$464$	3.94490e40	0.184081
$465$	−1.39722e41	−0.630587
$466$	1.58574e41	0.692229
$467$	1.08239e41	0.457060	0.228530	−	0.973537i	$-0.426608\pi$
$467$	1.08239e41	0.457060	0.228530	+	0.973537i	$0.426608\pi$
$468$	6.33013e40	0.258584
$469$	−2.76975e41	−1.09461
$470$	−1.28973e41	−0.493153
$471$	−1.82163e41	−0.673963
$472$	−1.13438e41	−0.406123
$473$	−4.22385e40	−0.146339
$474$	4.16218e40	0.139559
$475$	−3.06728e41	−0.995410
$476$	2.94209e41	0.924163
$477$	−1.28447e41	−0.390561
$478$	2.61700e41	0.770321
$479$	2.71815e41	0.774591	0.387296	−	0.921956i	$-0.373409\pi$
$479$	2.71815e41	0.774591	0.387296	+	0.921956i	$0.373409\pi$
$480$	−3.24278e40	−0.0894701
$481$	6.77550e41	1.81006
$482$	1.81325e41	0.469061
$483$	−1.02929e41	−0.257845
$484$	−1.50314e41	−0.364666
$485$	−3.34187e41	−0.785223
$486$	−2.07807e41	−0.472931
$487$	6.38745e41	1.40808	0.704042	−	0.710158i	$-0.251376\pi$
$487$	6.38745e41	1.40808	0.704042	+	0.710158i	$0.251376\pi$
$488$	1.42294e41	0.303864
$489$	9.92970e40	0.205423
$490$	1.76851e41	0.354460
$491$	−3.73865e41	−0.726025	−0.363012	−	0.931784i	$-0.618252\pi$
$491$	−3.73865e41	−0.726025	−0.363012	+	0.931784i	$0.618252\pi$
$492$	1.99451e41	0.375298
$493$	−5.56892e41	−1.01541
$494$	−9.65326e41	−1.70572
$495$	6.75847e40	0.115736
$496$	1.87671e41	0.311481
$497$	1.16026e41	0.186651
$498$	1.83786e41	0.286588
$499$	−9.33430e41	−1.41099	−0.705494	−	0.708716i	$-0.749275\pi$
$499$	−9.33430e41	−1.41099	−0.705494	+	0.708716i	$0.749275\pi$
$500$	−3.44434e41	−0.504744
$501$	5.49036e41	0.780039
$502$	−5.98168e41	−0.823978
$503$	9.86263e41	1.31731	0.658657	−	0.752443i	$-0.271125\pi$
$503$	9.86263e41	1.31731	0.658657	+	0.752443i	$0.271125\pi$
$504$	1.29311e41	0.167480
$505$	−3.32038e41	−0.417034
$506$	7.22577e40	0.0880139
$507$	−7.76767e41	−0.917629
$508$	−2.71775e41	−0.311403
$509$	7.59362e41	0.843962	0.421981	−	0.906605i	$-0.361335\pi$
$509$	7.59362e41	0.843962	0.421981	+	0.906605i	$0.361335\pi$
$510$	4.57774e41	0.493530
$511$	3.95017e41	0.413134
$512$	4.35561e40	0.0441942
$513$	1.82245e42	1.79406
$514$	−1.15733e41	−0.110543
$515$	−6.07496e41	−0.563030
$516$	−1.25745e41	−0.113089
$517$	6.60500e41	0.576461
$518$	1.38409e42	1.17234
$519$	−2.64422e41	−0.217372
$520$	−4.08113e41	−0.325633
$521$	−1.05689e42	−0.818553	−0.409277	−	0.912410i	$-0.634219\pi$
$521$	−1.05689e42	−0.818553	−0.409277	+	0.912410i	$0.634219\pi$
$522$	−2.44765e41	−0.184017
$523$	−1.00854e42	−0.736064	−0.368032	−	0.929813i	$-0.619968\pi$
$523$	−1.00854e42	−0.736064	−0.368032	+	0.929813i	$0.619968\pi$
$524$	4.96344e41	0.351680
$525$	−9.45994e41	−0.650757
$526$	1.23716e42	0.826319
$527$	−2.64931e42	−1.71818
$528$	1.66070e41	0.104584
$529$	−1.54157e42	−0.942760
$530$	8.28116e41	0.491830
$531$	7.03836e41	0.405982
$532$	−1.97195e42	−1.10476
$533$	2.51014e42	1.36592
$534$	−1.29413e42	−0.684051
$535$	1.40192e42	0.719847
$536$	5.78852e41	0.288744
$537$	1.09616e42	0.531216
$538$	−5.68830e41	−0.267829
$539$	−9.05693e41	−0.414338
$540$	7.70482e41	0.342499
$541$	−5.23504e41	−0.226132	−0.113066	−	0.993587i	$-0.536067\pi$
$541$	−5.23504e41	−0.226132	−0.113066	+	0.993587i	$0.536067\pi$
$542$	2.11970e41	0.0889785
$543$	1.36980e42	0.558805
$544$	−6.14870e41	−0.243781
$545$	−1.40097e42	−0.539862
$546$	−2.97721e42	−1.11512
$547$	2.05991e42	0.749970	0.374985	−	0.927031i	$-0.377648\pi$
$547$	2.05991e42	0.749970	0.374985	+	0.927031i	$0.377648\pi$
$548$	2.59194e42	0.917332
$549$	−8.82877e41	−0.303759
$550$	6.64100e41	0.222132
$551$	3.73260e42	1.21384
$552$	2.15113e41	0.0680160
$553$	1.07006e42	0.328978
$554$	−6.50934e41	−0.194597
$555$	2.15357e42	0.626063
$556$	−1.65100e42	−0.466755
$557$	1.26865e40	0.00348807	0.00174404	−	0.999998i	$-0.499445\pi$
$557$	1.26865e40	0.00348807	0.00174404	+	0.999998i	$0.499445\pi$
$558$	−1.16442e42	−0.311373
$559$	−1.58254e42	−0.411596
$560$	−8.33686e41	−0.210906
$561$	−2.34437e42	−0.576901
$562$	1.79652e42	0.430049
$563$	−4.54148e42	−1.05759	−0.528795	−	0.848749i	$-0.677356\pi$
$563$	−4.54148e42	−1.05759	−0.528795	+	0.848749i	$0.677356\pi$
$564$	1.96632e42	0.445481
$565$	−4.67343e42	−1.03011
$566$	−8.60937e41	−0.184636
$567$	3.35062e42	0.699177
$568$	−2.42483e41	−0.0492359
$569$	−7.78015e42	−1.53726	−0.768631	−	0.639693i	$-0.779062\pi$
$569$	−7.78015e42	−1.53726	−0.768631	+	0.639693i	$0.779062\pi$
$570$	−3.06826e42	−0.589972
$571$	4.96641e42	0.929357	0.464679	−	0.885479i	$-0.346170\pi$
$571$	4.96641e42	0.929357	0.464679	+	0.885479i	$0.346170\pi$
$572$	2.09004e42	0.380642
$573$	−4.34532e42	−0.770239
$574$	5.12768e42	0.884680
$575$	8.60218e41	0.144463
$576$	−2.70248e41	−0.0441788
$577$	8.08612e42	1.28681	0.643406	−	0.765525i	$-0.277521\pi$
$577$	8.08612e42	1.28681	0.643406	+	0.765525i	$0.277521\pi$
$578$	4.11574e42	0.637627
$579$	−7.00150e41	−0.105602
$580$	1.57804e42	0.231731
$581$	4.72496e42	0.675567
$582$	5.09503e42	0.709317
$583$	−4.24097e42	−0.574914
$584$	−8.25549e41	−0.108979
$585$	2.53217e42	0.325520
$586$	−4.36463e42	−0.546429
$587$	−3.64148e42	−0.444005	−0.222003	−	0.975046i	$-0.571259\pi$
$587$	−3.64148e42	−0.444005	−0.222003	+	0.975046i	$0.571259\pi$
$588$	−2.69627e42	−0.320195
$589$	1.77571e43	2.05393
$590$	−4.53773e42	−0.511249
$591$	−9.34569e42	−1.02566
$592$	−2.89262e42	−0.309247
$593$	−1.59482e43	−1.66098	−0.830491	−	0.557032i	$-0.811940\pi$
$593$	−1.59482e43	−1.66098	−0.830491	+	0.557032i	$0.811940\pi$
$594$	−3.94581e42	−0.400356
$595$	1.17689e43	1.16339
$596$	−7.58832e42	−0.730850
$597$	−7.11211e42	−0.667415
$598$	2.70726e42	0.247549
$599$	1.05341e43	0.938600	0.469300	−	0.883039i	$-0.344506\pi$
$599$	1.05341e43	0.938600	0.469300	+	0.883039i	$0.344506\pi$
$600$	1.97704e42	0.171661
$601$	4.64301e42	0.392867	0.196434	−	0.980517i	$-0.437064\pi$
$601$	4.64301e42	0.392867	0.196434	+	0.980517i	$0.437064\pi$
$602$	−3.23278e42	−0.266582
$603$	−3.59154e42	−0.288644
$604$	−6.77788e42	−0.530911
$605$	−6.01283e42	−0.459062
$606$	5.06226e42	0.376720
$607$	−2.17421e43	−1.57717	−0.788583	−	0.614929i	$-0.789185\pi$
$607$	−2.17421e43	−1.57717	−0.788583	+	0.614929i	$0.789185\pi$
$608$	4.12120e42	0.291419
$609$	1.15119e43	0.793557
$610$	5.69204e42	0.382521
$611$	2.47468e43	1.62136
$612$	3.81502e42	0.243697
$613$	−1.21288e43	−0.755409	−0.377704	−	0.925926i	$-0.623286\pi$
$613$	−1.21288e43	−0.755409	−0.377704	+	0.925926i	$0.623286\pi$
$614$	−1.43702e42	−0.0872675
$615$	7.97840e42	0.472445
$616$	4.26950e42	0.246533
$617$	3.00516e43	1.69219	0.846093	−	0.533036i	$-0.178949\pi$
$617$	3.00516e43	1.69219	0.846093	+	0.533036i	$0.178949\pi$
$618$	9.26190e42	0.508603
$619$	−2.57828e43	−1.38078	−0.690391	−	0.723436i	$-0.742562\pi$
$619$	−2.57828e43	−1.38078	−0.690391	+	0.723436i	$0.742562\pi$
$620$	7.50721e42	0.392110
$621$	−5.11107e42	−0.260371
$622$	−9.37213e42	−0.465680
$623$	−3.32708e43	−1.61250
$624$	6.22210e42	0.294155
$625$	−6.84734e41	−0.0315778
$626$	−1.97009e43	−0.886307
$627$	1.57132e43	0.689635
$628$	9.78753e42	0.419082
$629$	4.08343e43	1.70585
$630$	5.17268e42	0.210832
$631$	−4.05493e43	−1.61261	−0.806303	−	0.591503i	$-0.798535\pi$
$631$	−4.05493e43	−1.61261	−0.806303	+	0.591503i	$0.798535\pi$
$632$	−2.23632e42	−0.0867799
$633$	−1.79892e43	−0.681167
$634$	2.95790e43	1.09295
$635$	−1.08715e43	−0.392011
$636$	−1.26255e43	−0.444286
$637$	−3.39333e43	−1.16537
$638$	−8.08149e42	−0.270876
$639$	1.50451e42	0.0492188
$640$	1.74233e42	0.0556340
$641$	2.77200e43	0.863960	0.431980	−	0.901883i	$-0.357815\pi$
$641$	2.77200e43	0.863960	0.431980	+	0.901883i	$0.357815\pi$
$642$	−2.13737e43	−0.650260
$643$	4.13799e43	1.22891	0.614454	−	0.788952i	$-0.289376\pi$
$643$	4.13799e43	1.22891	0.614454	+	0.788952i	$0.289376\pi$
$644$	5.53034e42	0.160332
$645$	−5.03004e42	−0.142363
$646$	−5.81779e43	−1.60751
$647$	−1.37833e43	−0.371823	−0.185912	−	0.982566i	$-0.559524\pi$
$647$	−1.37833e43	−0.371823	−0.185912	+	0.982566i	$0.559524\pi$
$648$	−7.00248e42	−0.184433
$649$	2.32388e43	0.597613
$650$	2.48816e43	0.624772
$651$	5.47656e43	1.34277
$652$	−5.33518e42	−0.127735
$653$	1.72282e43	0.402797	0.201398	−	0.979509i	$-0.435451\pi$
$653$	1.72282e43	0.402797	0.201398	+	0.979509i	$0.435451\pi$
$654$	2.13592e43	0.487675
$655$	1.98547e43	0.442714
$656$	−1.07164e43	−0.233367
$657$	5.12219e42	0.108941
$658$	5.05523e43	1.05012
$659$	8.45482e43	1.71546	0.857730	−	0.514101i	$-0.171874\pi$
$659$	8.45482e43	1.71546	0.857730	+	0.514101i	$0.171874\pi$
$660$	6.64312e42	0.131656
$661$	−6.65139e43	−1.28763	−0.643813	−	0.765183i	$-0.722648\pi$
$661$	−6.65139e43	−1.28763	−0.643813	+	0.765183i	$0.722648\pi$
$662$	−4.49999e43	−0.850967
$663$	−8.78357e43	−1.62260
$664$	−9.87474e42	−0.178205
$665$	−7.88818e43	−1.39073
$666$	1.79475e43	0.309139
$667$	−1.04681e43	−0.176164
$668$	−2.94994e43	−0.485041
$669$	3.06222e43	0.491962
$670$	2.31552e43	0.363487
$671$	−2.91502e43	−0.447139
$672$	1.27104e43	0.190518
$673$	−8.33123e43	−1.22033	−0.610163	−	0.792276i	$-0.708896\pi$
$673$	−8.33123e43	−1.22033	−0.610163	+	0.792276i	$0.708896\pi$
$674$	4.23826e41	0.00606680
$675$	−4.69743e43	−0.657131
$676$	4.17353e43	0.570597
$677$	−1.76795e42	−0.0236235	−0.0118118	−	0.999930i	$-0.503760\pi$
$677$	−1.76795e42	−0.0236235	−0.0118118	+	0.999930i	$0.503760\pi$
$678$	7.12512e43	0.930533
$679$	1.30988e44	1.67205
$680$	−2.45960e43	−0.306885
$681$	−3.56995e43	−0.435394
$682$	−3.84462e43	−0.458348
$683$	3.16064e43	0.368344	0.184172	−	0.982894i	$-0.441040\pi$
$683$	3.16064e43	0.368344	0.184172	+	0.982894i	$0.441040\pi$
$684$	−2.55704e43	−0.291318
$685$	1.03683e44	1.15479
$686$	1.77202e43	0.192950
$687$	8.05958e43	0.857992
$688$	6.75622e42	0.0703207
$689$	−1.58895e44	−1.61701
$690$	8.60493e42	0.0856222
$691$	1.14213e44	1.11124	0.555618	−	0.831438i	$-0.312482\pi$
$691$	1.14213e44	1.11124	0.555618	+	0.831438i	$0.312482\pi$
$692$	1.42073e43	0.135165
$693$	−2.64905e43	−0.246448
$694$	−4.16410e43	−0.378834
$695$	−6.60433e43	−0.587576
$696$	−2.40588e43	−0.209329
$697$	1.51280e44	1.28728
$698$	4.52977e43	0.376979
$699$	−9.67093e43	−0.787177
$700$	5.08278e43	0.404652
$701$	1.40003e44	1.09020	0.545102	−	0.838370i	$-0.316491\pi$
$701$	1.40003e44	1.09020	0.545102	+	0.838370i	$0.316491\pi$
$702$	−1.47837e44	−1.12605
$703$	−2.73694e44	−2.03919
$704$	−8.92286e42	−0.0650321
$705$	7.86567e43	0.560796
$706$	−1.69423e44	−1.18168
$707$	1.30146e44	0.888033
$708$	6.91824e43	0.461828
$709$	−3.96655e43	−0.259057	−0.129529	−	0.991576i	$-0.541346\pi$
$709$	−3.96655e43	−0.259057	−0.129529	+	0.991576i	$0.541346\pi$
$710$	−9.69977e42	−0.0619808
$711$	1.38754e43	0.0867497
$712$	6.95329e43	0.425354
$713$	−4.97999e43	−0.298085
$714$	−1.79429e44	−1.05092
$715$	8.36056e43	0.479172
$716$	−5.88960e43	−0.330319
$717$	−1.59603e44	−0.875980
$718$	2.14245e44	1.15075
$719$	−1.62203e44	−0.852629	−0.426314	−	0.904575i	$-0.640188\pi$
$719$	−1.62203e44	−0.852629	−0.426314	+	0.904575i	$0.640188\pi$
$720$	−1.08104e43	−0.0556147
$721$	2.38114e44	1.19892
$722$	2.46454e44	1.21453
$723$	−1.10585e44	−0.533399
$724$	−7.35988e43	−0.347475
$725$	−9.62090e43	−0.444607
$726$	9.16718e43	0.414685
$727$	1.45218e44	0.643036	0.321518	−	0.946903i	$-0.395807\pi$
$727$	1.45218e44	0.643036	0.321518	+	0.946903i	$0.395807\pi$
$728$	1.59964e44	0.693403
$729$	2.49666e44	1.05946
$730$	−3.30235e43	−0.137189
$731$	−9.53758e43	−0.387899
$732$	−8.67809e43	−0.345543
$733$	−1.34214e44	−0.523222	−0.261611	−	0.965173i	$-0.584254\pi$
$733$	−1.34214e44	−0.523222	−0.261611	+	0.965173i	$0.584254\pi$
$734$	2.60428e44	0.994029
$735$	−1.07856e44	−0.403079
$736$	−1.15579e43	−0.0422935
$737$	−1.18583e44	−0.424890
$738$	6.64908e43	0.233286
$739$	−3.10772e44	−1.06771	−0.533855	−	0.845576i	$-0.679257\pi$
$739$	−3.10772e44	−1.06771	−0.533855	+	0.845576i	$0.679257\pi$
$740$	−1.15710e44	−0.389296
$741$	5.88723e44	1.93968
$742$	−3.24588e44	−1.04730
$743$	3.12688e44	0.988062	0.494031	−	0.869444i	$-0.335523\pi$
$743$	3.12688e44	0.988062	0.494031	+	0.869444i	$0.335523\pi$
$744$	−1.14455e44	−0.354205
$745$	−3.03547e44	−0.920034
$746$	−2.32464e44	−0.690088
$747$	6.12687e43	0.178143
$748$	1.25962e44	0.358727
$749$	−5.49497e44	−1.53284
$750$	2.10060e44	0.573976
$751$	−3.16352e44	−0.846742	−0.423371	−	0.905956i	$-0.639153\pi$
$751$	−3.16352e44	−0.846742	−0.423371	+	0.905956i	$0.639153\pi$
$752$	−1.05650e44	−0.277008
$753$	3.64804e44	0.936997
$754$	−3.02787e44	−0.761870
$755$	−2.71128e44	−0.668339
$756$	−3.01998e44	−0.729317
$757$	4.10509e44	0.971263	0.485632	−	0.874164i	$-0.338590\pi$
$757$	4.10509e44	0.971263	0.485632	+	0.874164i	$0.338590\pi$
$758$	2.93476e44	0.680300
$759$	−4.40678e43	−0.100086
$760$	1.64856e44	0.366854
$761$	3.57723e44	0.779982	0.389991	−	0.920819i	$-0.372478\pi$
$761$	3.57723e44	0.779982	0.389991	+	0.920819i	$0.372478\pi$
$762$	1.65747e44	0.354115
$763$	5.49124e44	1.14958
$764$	2.33472e44	0.478947
$765$	1.52608e44	0.306779
$766$	−4.69151e44	−0.924201
$767$	8.70680e44	1.68086
$768$	−2.65636e43	−0.0502560
$769$	−1.12924e44	−0.209377	−0.104689	−	0.994505i	$-0.533385\pi$
$769$	−1.12924e44	−0.209377	−0.104689	+	0.994505i	$0.533385\pi$
$770$	1.70788e44	0.310350
$771$	7.05822e43	0.125705
$772$	3.76187e43	0.0656653
$773$	−4.52518e44	−0.774201	−0.387100	−	0.922038i	$-0.626523\pi$
$773$	−4.52518e44	−0.774201	−0.387100	+	0.922038i	$0.626523\pi$
$774$	−4.19196e43	−0.0702962
$775$	−4.57696e44	−0.752317
$776$	−2.73753e44	−0.441065
$777$	−8.44114e44	−1.33314
$778$	2.59851e44	0.402291
$779$	−1.01396e45	−1.53884
$780$	2.48896e44	0.370298
$781$	4.96748e43	0.0724511
$782$	1.63160e44	0.233297
$783$	5.71635e44	0.801330
$784$	1.44869e44	0.199103
$785$	3.91520e44	0.527562
$786$	−3.02705e44	−0.399917
$787$	−8.95840e44	−1.16044	−0.580219	−	0.814460i	$-0.697033\pi$
$787$	−8.95840e44	−1.16044	−0.580219	+	0.814460i	$0.697033\pi$
$788$	5.02139e44	0.637776
$789$	−7.54508e44	−0.939659
$790$	−8.94570e43	−0.109243
$791$	1.83180e45	2.19352
$792$	5.53627e43	0.0650096
$793$	−1.09216e45	−1.25763
$794$	−6.79151e44	−0.766917
$795$	−5.05043e44	−0.559291
$796$	3.82130e44	0.415010
$797$	−4.97034e44	−0.529398	−0.264699	−	0.964331i	$-0.585273\pi$
$797$	−4.97034e44	−0.529398	−0.264699	+	0.964331i	$0.585273\pi$
$798$	1.20263e45	1.25629
$799$	1.49143e45	1.52801
$800$	−1.06225e44	−0.106742
$801$	−4.31424e44	−0.425206
$802$	1.12966e43	0.0109206
$803$	1.69121e44	0.160364
$804$	−3.53024e44	−0.328349
$805$	2.21224e44	0.201835
$806$	−1.44045e45	−1.28916
$807$	3.46912e44	0.304565
$808$	−2.71993e44	−0.234251
$809$	1.66443e45	1.40625	0.703127	−	0.711064i	$-0.251786\pi$
$809$	1.66443e45	1.40625	0.703127	+	0.711064i	$0.251786\pi$
$810$	−2.80113e44	−0.232175
$811$	1.88658e45	1.53409	0.767046	−	0.641592i	$-0.221726\pi$
$811$	1.88658e45	1.53409	0.767046	+	0.641592i	$0.221726\pi$
$812$	−6.18528e44	−0.493447
$813$	−1.29274e44	−0.101183
$814$	5.92579e44	0.455059
$815$	−2.13417e44	−0.160800
$816$	3.74991e44	0.277219
$817$	6.39261e44	0.463699
$818$	8.80461e44	0.626663
$819$	−9.92511e44	−0.693162
$820$	−4.28676e44	−0.293774
$821$	−8.30695e44	−0.558628	−0.279314	−	0.960200i	$-0.590107\pi$
$821$	−8.30695e44	−0.558628	−0.279314	+	0.960200i	$0.590107\pi$
$822$	−1.58075e45	−1.04316
$823$	−2.11118e45	−1.36719	−0.683594	−	0.729862i	$-0.739584\pi$
$823$	−2.11118e45	−1.36719	−0.683594	+	0.729862i	$0.739584\pi$
$824$	−4.97637e44	−0.316258
$825$	−4.05014e44	−0.252601
$826$	1.77861e45	1.08865
$827$	−2.31980e45	−1.39353	−0.696764	−	0.717301i	$-0.745377\pi$
$827$	−2.31980e45	−1.39353	−0.696764	+	0.717301i	$0.745377\pi$
$828$	7.17121e43	0.0422788
$829$	2.73984e45	1.58537	0.792684	−	0.609633i	$-0.208683\pi$
$829$	2.73984e45	1.58537	0.792684	+	0.609633i	$0.208683\pi$
$830$	−3.95008e44	−0.224334
$831$	3.96985e44	0.221288
$832$	−3.34310e44	−0.182910
$833$	−2.04508e45	−1.09828
$834$	1.00690e45	0.530776
$835$	−1.18003e45	−0.610596
$836$	−8.44265e44	−0.428826
$837$	2.71945e45	1.35593
$838$	−3.89521e44	−0.190655
$839$	−2.08003e44	−0.0999444	−0.0499722	−	0.998751i	$-0.515913\pi$
$839$	−2.08003e44	−0.0999444	−0.0499722	+	0.998751i	$0.515913\pi$
$840$	5.08440e44	0.239834
$841$	−9.88649e44	−0.457830
$842$	1.22793e45	0.558260
$843$	−1.09564e45	−0.489036
$844$	9.66549e44	0.423561
$845$	1.66949e45	0.718299
$846$	6.55513e44	0.276911
$847$	2.35679e45	0.977526
$848$	6.78360e44	0.276264
$849$	5.25059e44	0.209961
$850$	1.49956e45	0.588802
$851$	7.67576e44	0.295946
$852$	1.47883e44	0.0559892
$853$	−8.05595e44	−0.299507	−0.149753	−	0.988723i	$-0.547848\pi$
$853$	−8.05595e44	−0.299507	−0.149753	+	0.988723i	$0.547848\pi$
$854$	−2.23105e45	−0.814540
$855$	−1.02286e45	−0.366727
$856$	1.14840e45	0.404343
$857$	8.81281e44	0.304728	0.152364	−	0.988324i	$-0.451311\pi$
$857$	8.81281e44	0.304728	0.152364	+	0.988324i	$0.451311\pi$
$858$	−1.27465e45	−0.432851
$859$	−3.21045e45	−1.07071	−0.535356	−	0.844627i	$-0.679822\pi$
$859$	−3.21045e45	−1.07071	−0.535356	+	0.844627i	$0.679822\pi$
$860$	2.70262e44	0.0885235
$861$	−3.12722e45	−1.00603
$862$	9.18597e44	0.290243
$863$	3.88645e45	1.20611	0.603053	−	0.797701i	$-0.293951\pi$
$863$	3.88645e45	1.20611	0.603053	+	0.797701i	$0.293951\pi$
$864$	6.31149e44	0.192384
$865$	5.68317e44	0.170154
$866$	−3.88626e45	−1.14289
$867$	−2.51007e45	−0.725085
$868$	−2.94253e45	−0.834959
$869$	4.58130e44	0.127697
$870$	−9.62397e44	−0.263515
$871$	−4.44291e45	−1.19505
$872$	−1.14762e45	−0.303244
$873$	1.69853e45	0.440912
$874$	−1.09359e45	−0.278886
$875$	5.40044e45	1.35302
$876$	5.03477e44	0.123927
$877$	2.77423e45	0.670886	0.335443	−	0.942061i	$-0.391114\pi$
$877$	2.77423e45	0.670886	0.335443	+	0.942061i	$0.391114\pi$
$878$	7.30714e44	0.173613
$879$	2.66185e45	0.621379
$880$	−3.56932e44	−0.0818660
$881$	1.10273e45	0.248508	0.124254	−	0.992250i	$-0.460346\pi$
$881$	1.10273e45	0.248508	0.124254	+	0.992250i	$0.460346\pi$
$882$	−8.98854e44	−0.199033
$883$	−4.69663e45	−1.02187	−0.510935	−	0.859619i	$-0.670701\pi$
$883$	−4.69663e45	−1.02187	−0.510935	+	0.859619i	$0.670701\pi$
$884$	4.71937e45	1.00896
$885$	2.76743e45	0.581373
$886$	−1.37594e45	−0.284037
$887$	1.19670e45	0.242755	0.121378	−	0.992606i	$-0.461269\pi$
$887$	1.19670e45	0.242755	0.121378	+	0.992606i	$0.461269\pi$
$888$	1.76412e45	0.351664
$889$	4.26120e45	0.834747
$890$	2.78145e45	0.535459
$891$	1.43452e45	0.271395
$892$	−1.64532e45	−0.305910
$893$	−9.99638e45	−1.82661
$894$	4.62788e45	0.831096
$895$	−2.35595e45	−0.415824
$896$	−6.82923e44	−0.118467
$897$	−1.65107e45	−0.281504
$898$	−3.03317e45	−0.508293
$899$	5.56974e45	0.917403
$900$	6.59085e44	0.106705
$901$	−9.57623e45	−1.52391
$902$	2.19535e45	0.343401
$903$	1.97158e45	0.303147
$904$	−3.82829e45	−0.578621
$905$	−2.94409e45	−0.437420
$906$	4.13362e45	0.603732
$907$	3.04922e45	0.437800	0.218900	−	0.975747i	$-0.429753\pi$
$907$	3.04922e45	0.437800	0.218900	+	0.975747i	$0.429753\pi$
$908$	1.91812e45	0.270735
$909$	1.68760e45	0.234170
$910$	6.39886e45	0.872893
$911$	−3.67350e45	−0.492657	−0.246329	−	0.969186i	$-0.579224\pi$
$911$	−3.67350e45	−0.492657	−0.246329	+	0.969186i	$0.579224\pi$
$912$	−2.51340e45	−0.331391
$913$	2.02293e45	0.262231
$914$	−1.62810e45	−0.207499
$915$	−3.47140e45	−0.434988
$916$	−4.33037e45	−0.533514
$917$	−7.78224e45	−0.942714
$918$	−8.90975e45	−1.06122
$919$	−1.23482e45	−0.144614	−0.0723072	−	0.997382i	$-0.523036\pi$
$919$	−1.23482e45	−0.144614	−0.0723072	+	0.997382i	$0.523036\pi$
$920$	−4.62338e44	−0.0532413
$921$	8.76394e44	0.0992374
$922$	−4.12100e44	−0.0458853
$923$	1.86115e45	0.203777
$924$	−2.60384e45	−0.280349
$925$	7.05457e45	0.746919
$926$	9.76474e45	1.01669
$927$	3.08764e45	0.316148
$928$	1.29267e45	0.130165
$929$	−1.71673e44	−0.0170003	−0.00850017	−	0.999964i	$-0.502706\pi$
$929$	−1.71673e44	−0.0170003	−0.00850017	+	0.999964i	$0.502706\pi$
$930$	−4.57842e45	−0.445893
$931$	1.37072e46	1.31290
$932$	5.19615e45	0.489480
$933$	5.71578e45	0.529554
$934$	3.54679e45	0.323191
$935$	5.03871e45	0.451585
$936$	2.07426e45	0.182847
$937$	−2.90729e45	−0.252072	−0.126036	−	0.992026i	$-0.540226\pi$
$937$	−2.90729e45	−0.252072	−0.126036	+	0.992026i	$0.540226\pi$
$938$	−9.07591e45	−0.774009
$939$	1.20150e46	1.00787
$940$	−4.22619e45	−0.348712
$941$	−2.30709e45	−0.187251	−0.0936257	−	0.995607i	$-0.529846\pi$
$941$	−2.30709e45	−0.187251	−0.0936257	+	0.995607i	$0.529846\pi$
$942$	−5.96912e45	−0.476564
$943$	2.84366e45	0.223330
$944$	−3.71713e45	−0.287172
$945$	−1.20805e46	−0.918104
$946$	−1.38407e45	−0.103478
$947$	−1.36872e45	−0.100668	−0.0503340	−	0.998732i	$-0.516029\pi$
$947$	−1.36872e45	−0.100668	−0.0503340	+	0.998732i	$0.516029\pi$
$948$	1.36386e45	0.0986828
$949$	6.33641e45	0.451042
$950$	−1.00509e46	−0.703861
$951$	−1.80393e46	−1.24286
$952$	9.64064e45	0.653482
$953$	−2.04354e46	−1.36284	−0.681418	−	0.731894i	$-0.738637\pi$
$953$	−2.04354e46	−1.36284	−0.681418	+	0.731894i	$0.738637\pi$
$954$	−4.20895e45	−0.276168
$955$	9.33932e45	0.602925
$956$	8.57539e45	0.544699
$957$	4.92866e45	0.308030
$958$	8.90683e45	0.547719
$959$	−4.06394e46	−2.45900
$960$	−1.06259e45	−0.0632649
$961$	9.42784e45	0.552332
$962$	2.22020e46	1.27991
$963$	−7.12535e45	−0.404202
$964$	5.94167e45	0.331676
$965$	1.50482e45	0.0826630
$966$	−3.37279e45	−0.182324
$967$	−2.05882e46	−1.09524	−0.547619	−	0.836728i	$-0.684466\pi$
$967$	−2.05882e46	−1.09524	−0.547619	+	0.836728i	$0.684466\pi$
$968$	−4.92548e45	−0.257858
$969$	3.54809e46	1.82800
$970$	−1.09507e46	−0.555237
$971$	3.11280e46	1.55329	0.776647	−	0.629937i	$-0.216919\pi$
$971$	3.11280e46	1.55329	0.776647	+	0.629937i	$0.216919\pi$
$972$	−6.80942e45	−0.334413
$973$	2.58863e46	1.25119
$974$	2.09304e46	0.995666
$975$	−1.51746e46	−0.710468
$976$	4.66269e45	0.214865
$977$	−2.53889e46	−1.15154	−0.575769	−	0.817613i	$-0.695297\pi$
$977$	−2.53889e46	−1.15154	−0.575769	+	0.817613i	$0.695297\pi$
$978$	3.25376e45	0.145256
$979$	−1.42444e46	−0.625913
$980$	5.79504e45	0.250641
$981$	7.12051e45	0.303139
$982$	−1.22508e46	−0.513377
$983$	4.44662e46	1.83422	0.917109	−	0.398637i	$-0.130517\pi$
$983$	4.44662e46	1.83422	0.917109	+	0.398637i	$0.130517\pi$
$984$	6.53560e45	0.265376
$985$	2.00865e46	0.802866
$986$	−1.82482e46	−0.718007
$987$	−3.08303e46	−1.19416
$988$	−3.16318e46	−1.20612
$989$	−1.79281e45	−0.0672963
$990$	2.21461e45	0.0818375
$991$	−3.72910e46	−1.35663	−0.678317	−	0.734769i	$-0.737291\pi$
$991$	−3.72910e46	−1.35663	−0.678317	+	0.734769i	$0.737291\pi$
$992$	6.14962e45	0.220251
$993$	2.74441e46	0.967688
$994$	3.80192e45	0.131982
$995$	1.52859e46	0.522437
$996$	6.02231e45	0.202648
$997$	−9.69190e45	−0.321095	−0.160548	−	0.987028i	$-0.551326\pi$
$997$	−9.69190e45	−0.321095	−0.160548	+	0.987028i	$0.551326\pi$
$998$	−3.05866e46	−0.997719
$999$	−4.19154e46	−1.34620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.32.a.a.1.1	✓	1
3.2	odd	2		18.32.a.a.1.1		1
4.3	odd	2		16.32.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.32.a.a.1.1	✓	1	1.1	even	1	trivial
16.32.a.a.1.1		1	4.3	odd	2
18.32.a.a.1.1		1	3.2	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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