LMFDB - Embedded newform 10.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,12,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	10.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:	$7.68343180560$
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	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-32.0000 q^{2} -12.0000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +384.000 q^{6} -14176.0 q^{7} -32768.0 q^{8} -177003. q^{9} +O(q^{10})$

\(q-32.0000 q^{2} -12.0000 q^{3} +1024.00 q^{4} +3125.00 q^{5} +384.000 q^{6} -14176.0 q^{7} -32768.0 q^{8} -177003. q^{9} -100000. q^{10} -756348. q^{11} -12288.0 q^{12} -905482. q^{13} +453632. q^{14} -37500.0 q^{15} +1.04858e6 q^{16} +2.80379e6 q^{17} +5.66410e6 q^{18} -5.42866e6 q^{19} +3.20000e6 q^{20} +170112. q^{21} +2.42031e7 q^{22} -1.02367e7 q^{23} +393216. q^{24} +9.76562e6 q^{25} +2.89754e7 q^{26} +4.24980e6 q^{27} -1.45162e7 q^{28} -1.97498e8 q^{29} +1.20000e6 q^{30} -4.43623e7 q^{31} -3.35544e7 q^{32} +9.07618e6 q^{33} -8.97214e7 q^{34} -4.43000e7 q^{35} -1.81251e8 q^{36} +5.76737e8 q^{37} +1.73717e8 q^{38} +1.08658e7 q^{39} -1.02400e8 q^{40} +9.30058e8 q^{41} -5.44358e6 q^{42} +1.60560e9 q^{43} -7.74500e8 q^{44} -5.53134e8 q^{45} +3.27574e8 q^{46} -1.80368e9 q^{47} -1.25829e7 q^{48} -1.77637e9 q^{49} -3.12500e8 q^{50} -3.36455e7 q^{51} -9.27214e8 q^{52} +1.55867e9 q^{53} -1.35994e8 q^{54} -2.36359e9 q^{55} +4.64519e8 q^{56} +6.51439e7 q^{57} +6.31994e9 q^{58} -9.50200e9 q^{59} -3.84000e7 q^{60} +6.73632e9 q^{61} +1.41959e9 q^{62} +2.50919e9 q^{63} +1.07374e9 q^{64} -2.82963e9 q^{65} -2.90438e8 q^{66} +8.40291e9 q^{67} +2.87109e9 q^{68} +1.22840e8 q^{69} +1.41760e9 q^{70} -4.80631e9 q^{71} +5.80003e9 q^{72} +7.46271e9 q^{73} -1.84556e10 q^{74} -1.17188e8 q^{75} -5.55895e9 q^{76} +1.07220e10 q^{77} -3.47705e8 q^{78} -2.06445e10 q^{79} +3.27680e9 q^{80} +3.13046e10 q^{81} -2.97619e10 q^{82} -6.80133e10 q^{83} +1.74195e8 q^{84} +8.76186e9 q^{85} -5.13792e10 q^{86} +2.36998e9 q^{87} +2.47840e10 q^{88} +6.98713e10 q^{89} +1.77003e10 q^{90} +1.28361e10 q^{91} -1.04824e10 q^{92} +5.32347e8 q^{93} +5.77179e10 q^{94} -1.69646e10 q^{95} +4.02653e8 q^{96} +3.99610e10 q^{97} +5.68438e10 q^{98} +1.33876e11 q^{99} +O(q^{100})\)

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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	−12.0000	−0.0285111	−0.0142556	−	0.999898i	$-0.504538\pi$
$3$	−12.0000	−0.0285111	−0.0142556	+	0.999898i	$0.504538\pi$
$4$	1024.00	0.500000
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	384.000	0.0201604
$7$	−14176.0	−0.318797	−0.159399	−	0.987214i	$-0.550956\pi$
$7$	−14176.0	−0.318797	−0.159399	+	0.987214i	$0.550956\pi$
$8$	−32768.0	−0.353553
$9$	−177003.	−0.999187
$10$	−100000.	−0.316228
$11$	−756348.	−1.41600	−0.707998	−	0.706215i	$-0.750401\pi$
$11$	−756348.	−1.41600	−0.707998	+	0.706215i	$0.750401\pi$
$12$	−12288.0	−0.0142556
$13$	−905482.	−0.676381	−0.338190	−	0.941078i	$-0.609815\pi$
$13$	−905482.	−0.676381	−0.338190	+	0.941078i	$0.609815\pi$
$14$	453632.	0.225424
$15$	−37500.0	−0.0127506
$16$	1.04858e6	0.250000
$17$	2.80379e6	0.478936	0.239468	−	0.970904i	$-0.423027\pi$
$17$	2.80379e6	0.478936	0.239468	+	0.970904i	$0.423027\pi$
$18$	5.66410e6	0.706532
$19$	−5.42866e6	−0.502977	−0.251488	−	0.967860i	$-0.580920\pi$
$19$	−5.42866e6	−0.502977	−0.251488	+	0.967860i	$0.580920\pi$
$20$	3.20000e6	0.223607
$21$	170112.	0.00908927
$22$	2.42031e7	1.00126
$23$	−1.02367e7	−0.331631	−0.165816	−	0.986157i	$-0.553026\pi$
$23$	−1.02367e7	−0.331631	−0.165816	+	0.986157i	$0.553026\pi$
$24$	393216.	0.0100802
$25$	9.76562e6	0.200000
$26$	2.89754e7	0.478274
$27$	4.24980e6	0.0569991
$28$	−1.45162e7	−0.159399
$29$	−1.97498e8	−1.78803	−0.894013	−	0.448041i	$-0.852122\pi$
$29$	−1.97498e8	−1.78803	−0.894013	+	0.448041i	$0.852122\pi$
$30$	1.20000e6	0.00901601
$31$	−4.43623e7	−0.278307	−0.139154	−	0.990271i	$-0.544438\pi$
$31$	−4.43623e7	−0.278307	−0.139154	+	0.990271i	$0.544438\pi$
$32$	−3.35544e7	−0.176777
$33$	9.07618e6	0.0403716
$34$	−8.97214e7	−0.338659
$35$	−4.43000e7	−0.142570
$36$	−1.81251e8	−0.499594
$37$	5.76737e8	1.36731	0.683657	−	0.729803i	$-0.260388\pi$
$37$	5.76737e8	1.36731	0.683657	+	0.729803i	$0.260388\pi$
$38$	1.73717e8	0.355658
$39$	1.08658e7	0.0192844
$40$	−1.02400e8	−0.158114
$41$	9.30058e8	1.25372	0.626858	−	0.779134i	$-0.284341\pi$
$41$	9.30058e8	1.25372	0.626858	+	0.779134i	$0.284341\pi$
$42$	−5.44358e6	−0.00642708
$43$	1.60560e9	1.66556	0.832781	−	0.553603i	$-0.186748\pi$
$43$	1.60560e9	1.66556	0.832781	+	0.553603i	$0.186748\pi$
$44$	−7.74500e8	−0.707998
$45$	−5.53134e8	−0.446850
$46$	3.27574e8	0.234499
$47$	−1.80368e9	−1.14716	−0.573578	−	0.819151i	$-0.694445\pi$
$47$	−1.80368e9	−1.14716	−0.573578	+	0.819151i	$0.694445\pi$
$48$	−1.25829e7	−0.00712778
$49$	−1.77637e9	−0.898368
$50$	−3.12500e8	−0.141421
$51$	−3.36455e7	−0.0136550
$52$	−9.27214e8	−0.338190
$53$	1.55867e9	0.511963	0.255981	−	0.966682i	$-0.417601\pi$
$53$	1.55867e9	0.511963	0.255981	+	0.966682i	$0.417601\pi$
$54$	−1.35994e8	−0.0403044
$55$	−2.36359e9	−0.633252
$56$	4.64519e8	0.112712
$57$	6.51439e7	0.0143404
$58$	6.31994e9	1.26433
$59$	−9.50200e9	−1.73033	−0.865165	−	0.501488i	$-0.832786\pi$
$59$	−9.50200e9	−1.73033	−0.865165	+	0.501488i	$0.832786\pi$
$60$	−3.84000e7	−0.00637528
$61$	6.73632e9	1.02119	0.510597	−	0.859820i	$-0.329424\pi$
$61$	6.73632e9	1.02119	0.510597	+	0.859820i	$0.329424\pi$
$62$	1.41959e9	0.196793
$63$	2.50919e9	0.318538
$64$	1.07374e9	0.125000
$65$	−2.82963e9	−0.302487
$66$	−2.90438e8	−0.0285471
$67$	8.40291e9	0.760358	0.380179	−	0.924913i	$-0.375862\pi$
$67$	8.40291e9	0.760358	0.380179	+	0.924913i	$0.375862\pi$
$68$	2.87109e9	0.239468
$69$	1.22840e8	0.00945519
$70$	1.41760e9	0.100813
$71$	−4.80631e9	−0.316148	−0.158074	−	0.987427i	$-0.550528\pi$
$71$	−4.80631e9	−0.316148	−0.158074	+	0.987427i	$0.550528\pi$
$72$	5.80003e9	0.353266
$73$	7.46271e9	0.421329	0.210664	−	0.977558i	$-0.432437\pi$
$73$	7.46271e9	0.421329	0.210664	+	0.977558i	$0.432437\pi$
$74$	−1.84556e10	−0.966837
$75$	−1.17188e8	−0.00570222
$76$	−5.55895e9	−0.251488
$77$	1.07220e10	0.451415
$78$	−3.47705e8	−0.0136361
$79$	−2.06445e10	−0.754842	−0.377421	−	0.926042i	$-0.623189\pi$
$79$	−2.06445e10	−0.754842	−0.377421	+	0.926042i	$0.623189\pi$
$80$	3.27680e9	0.111803
$81$	3.13046e10	0.997562
$82$	−2.97619e10	−0.886511
$83$	−6.80133e10	−1.89524	−0.947621	−	0.319397i	$-0.896520\pi$
$83$	−6.80133e10	−1.89524	−0.947621	+	0.319397i	$0.896520\pi$
$84$	1.74195e8	0.00454463
$85$	8.76186e9	0.214186
$86$	−5.13792e10	−1.17773
$87$	2.36998e9	0.0509786
$88$	2.47840e10	0.500630
$89$	6.98713e10	1.32634	0.663169	−	0.748470i	$-0.269211\pi$
$89$	6.98713e10	1.32634	0.663169	+	0.748470i	$0.269211\pi$
$90$	1.77003e10	0.315971
$91$	1.28361e10	0.215628
$92$	−1.04824e10	−0.165816
$93$	5.32347e8	0.00793485
$94$	5.77179e10	0.811162
$95$	−1.69646e10	−0.224938
$96$	4.02653e8	0.00504010
$97$	3.99610e10	0.472489	0.236244	−	0.971694i	$-0.424083\pi$
$97$	3.99610e10	0.472489	0.236244	+	0.971694i	$0.424083\pi$
$98$	5.68438e10	0.635242
$99$	1.33876e11	1.41484
$100$	1.00000e10	0.100000
$101$	−3.21212e10	−0.304106	−0.152053	−	0.988372i	$-0.548588\pi$
$101$	−3.21212e10	−0.304106	−0.152053	+	0.988372i	$0.548588\pi$
$102$	1.07666e9	0.00965554
$103$	−1.92061e11	−1.63243	−0.816214	−	0.577750i	$-0.803931\pi$
$103$	−1.92061e11	−1.63243	−0.816214	+	0.577750i	$0.803931\pi$
$104$	2.96708e10	0.239137
$105$	5.31600e8	0.00406484
$106$	−4.98776e10	−0.362012
$107$	−2.31013e11	−1.59230	−0.796152	−	0.605097i	$-0.793134\pi$
$107$	−2.31013e11	−1.59230	−0.796152	+	0.605097i	$0.793134\pi$
$108$	4.35180e9	0.0284995
$109$	9.27682e10	0.577502	0.288751	−	0.957404i	$-0.406760\pi$
$109$	9.27682e10	0.577502	0.288751	+	0.957404i	$0.406760\pi$
$110$	7.56348e10	0.447777
$111$	−6.92084e9	−0.0389837
$112$	−1.48646e10	−0.0796993
$113$	−3.15799e11	−1.61243	−0.806213	−	0.591626i	$-0.798486\pi$
$113$	−3.15799e11	−1.61243	−0.806213	+	0.591626i	$0.798486\pi$
$114$	−2.08461e9	−0.0101402
$115$	−3.19896e10	−0.148310
$116$	−2.02238e11	−0.894013
$117$	1.60273e11	0.675831
$118$	3.04064e11	1.22353
$119$	−3.97466e10	−0.152683
$120$	1.22880e9	0.00450800
$121$	2.86751e11	1.00504
$122$	−2.15562e11	−0.722094
$123$	−1.11607e10	−0.0357448
$124$	−4.54270e10	−0.139154
$125$	3.05176e10	0.0894427
$126$	−8.02942e10	−0.225240
$127$	4.96182e11	1.33266	0.666332	−	0.745656i	$-0.267864\pi$
$127$	4.96182e11	1.33266	0.666332	+	0.745656i	$0.267864\pi$
$128$	−3.43597e10	−0.0883883
$129$	−1.92672e10	−0.0474870
$130$	9.05482e10	0.213890
$131$	2.85841e11	0.647339	0.323669	−	0.946170i	$-0.395083\pi$
$131$	2.85841e11	0.647339	0.323669	+	0.946170i	$0.395083\pi$
$132$	9.29400e9	0.0201858
$133$	7.69567e10	0.160348
$134$	−2.68893e11	−0.537654
$135$	1.32806e10	0.0254908
$136$	−9.18747e10	−0.169329
$137$	2.64739e11	0.468657	0.234329	−	0.972157i	$-0.424711\pi$
$137$	2.64739e11	0.468657	0.234329	+	0.972157i	$0.424711\pi$
$138$	−3.93088e9	−0.00668583
$139$	−5.52202e11	−0.902644	−0.451322	−	0.892361i	$-0.649047\pi$
$139$	−5.52202e11	−0.902644	−0.451322	+	0.892361i	$0.649047\pi$
$140$	−4.53632e10	−0.0712852
$141$	2.16442e10	0.0327067
$142$	1.53802e11	0.223550
$143$	6.84859e11	0.957752
$144$	−1.85601e11	−0.249797
$145$	−6.17181e11	−0.799629
$146$	−2.38807e11	−0.297924
$147$	2.13164e10	0.0256135
$148$	5.90579e11	0.683657
$149$	−9.05012e11	−1.00955	−0.504777	−	0.863250i	$-0.668425\pi$
$149$	−9.05012e11	−1.00955	−0.504777	+	0.863250i	$0.668425\pi$
$150$	3.75000e9	0.00403208
$151$	2.10556e11	0.218271	0.109135	−	0.994027i	$-0.465192\pi$
$151$	2.10556e11	0.218271	0.109135	+	0.994027i	$0.465192\pi$
$152$	1.77886e11	0.177829
$153$	−4.96280e11	−0.478546
$154$	−3.43104e11	−0.319199
$155$	−1.38632e11	−0.124463
$156$	1.11266e10	0.00964219
$157$	−1.79683e12	−1.50335	−0.751673	−	0.659536i	$-0.770753\pi$
$157$	−1.79683e12	−1.50335	−0.751673	+	0.659536i	$0.770753\pi$
$158$	6.60625e11	0.533754
$159$	−1.87041e10	−0.0145966
$160$	−1.04858e11	−0.0790569
$161$	1.45115e11	0.105723
$162$	−1.00175e12	−0.705383
$163$	4.99980e11	0.340346	0.170173	−	0.985414i	$-0.445567\pi$
$163$	4.99980e11	0.340346	0.170173	+	0.985414i	$0.445567\pi$
$164$	9.52380e11	0.626858
$165$	2.83630e10	0.0180547
$166$	2.17643e12	1.34014
$167$	9.07923e11	0.540889	0.270445	−	0.962736i	$-0.412829\pi$
$167$	9.07923e11	0.540889	0.270445	+	0.962736i	$0.412829\pi$
$168$	−5.57423e9	−0.00321354
$169$	−9.72263e11	−0.542509
$170$	−2.80379e11	−0.151453
$171$	9.60889e11	0.502568
$172$	1.64413e12	0.832781
$173$	2.87865e12	1.41233	0.706163	−	0.708050i	$-0.250425\pi$
$173$	2.87865e12	1.41233	0.706163	+	0.708050i	$0.250425\pi$
$174$	−7.58392e10	−0.0360473
$175$	−1.38438e11	−0.0637594
$176$	−7.93088e11	−0.353999
$177$	1.14024e11	0.0493336
$178$	−2.23588e12	−0.937862
$179$	2.91517e12	1.18569	0.592847	−	0.805315i	$-0.298004\pi$
$179$	2.91517e12	1.18569	0.592847	+	0.805315i	$0.298004\pi$
$180$	−5.66410e11	−0.223425
$181$	−3.52122e12	−1.34729	−0.673644	−	0.739056i	$-0.735272\pi$
$181$	−3.52122e12	−1.34729	−0.673644	+	0.739056i	$0.735272\pi$
$182$	−4.10756e11	−0.152472
$183$	−8.08358e10	−0.0291154
$184$	3.35435e11	0.117249
$185$	1.80230e12	0.611482
$186$	−1.70351e10	−0.00561079
$187$	−2.12064e12	−0.678171
$188$	−1.84697e12	−0.573578
$189$	−6.02452e10	−0.0181711
$190$	5.42866e11	0.159055
$191$	−1.30901e12	−0.372615	−0.186307	−	0.982491i	$-0.559652\pi$
$191$	−1.30901e12	−0.372615	−0.186307	+	0.982491i	$0.559652\pi$
$192$	−1.28849e10	−0.00356389
$193$	−4.59519e12	−1.23520	−0.617601	−	0.786491i	$-0.711895\pi$
$193$	−4.59519e12	−1.23520	−0.617601	+	0.786491i	$0.711895\pi$
$194$	−1.27875e12	−0.334100
$195$	3.39556e10	0.00862424
$196$	−1.81900e12	−0.449184
$197$	2.16578e12	0.520056	0.260028	−	0.965601i	$-0.416268\pi$
$197$	2.16578e12	0.520056	0.260028	+	0.965601i	$0.416268\pi$
$198$	−4.28403e12	−1.00045
$199$	1.28938e12	0.292879	0.146439	−	0.989220i	$-0.453219\pi$
$199$	1.28938e12	0.292879	0.146439	+	0.989220i	$0.453219\pi$
$200$	−3.20000e11	−0.0707107
$201$	−1.00835e11	−0.0216787
$202$	1.02788e12	0.215035
$203$	2.79973e12	0.570018
$204$	−3.44530e10	−0.00682749
$205$	2.90643e12	0.560679
$206$	6.14594e12	1.15430
$207$	1.81192e12	0.331362
$208$	−9.49467e11	−0.169095
$209$	4.10596e12	0.712213
$210$	−1.70112e10	−0.00287428
$211$	−6.25366e12	−1.02939	−0.514696	−	0.857373i	$-0.672095\pi$
$211$	−6.25366e12	−1.02939	−0.514696	+	0.857373i	$0.672095\pi$
$212$	1.59608e12	0.255981
$213$	5.76757e10	0.00901374
$214$	7.39242e12	1.12593
$215$	5.01750e12	0.744862
$216$	−1.39257e11	−0.0201522
$217$	6.28880e11	0.0887236
$218$	−2.96858e12	−0.408356
$219$	−8.95526e10	−0.0120126
$220$	−2.42031e12	−0.316626
$221$	−2.53878e12	−0.323943
$222$	2.21467e11	0.0275656
$223$	−4.03630e12	−0.490125	−0.245062	−	0.969507i	$-0.578808\pi$
$223$	−4.03630e12	−0.490125	−0.245062	+	0.969507i	$0.578808\pi$
$224$	4.75668e11	0.0563559
$225$	−1.72854e12	−0.199837
$226$	1.01056e13	1.14016
$227$	−1.64271e13	−1.80892	−0.904458	−	0.426562i	$-0.859725\pi$
$227$	−1.64271e13	−1.80892	−0.904458	+	0.426562i	$0.859725\pi$
$228$	6.67074e10	0.00717022
$229$	2.45577e12	0.257687	0.128843	−	0.991665i	$-0.458874\pi$
$229$	2.45577e12	0.257687	0.128843	+	0.991665i	$0.458874\pi$
$230$	1.02367e12	0.104871
$231$	−1.28664e11	−0.0128704
$232$	6.47161e12	0.632163
$233$	1.02275e13	0.975692	0.487846	−	0.872930i	$-0.337783\pi$
$233$	1.02275e13	0.975692	0.487846	+	0.872930i	$0.337783\pi$
$234$	−5.12874e12	−0.477885
$235$	−5.63651e12	−0.513024
$236$	−9.73004e12	−0.865165
$237$	2.47734e11	0.0215214
$238$	1.27189e12	0.107963
$239$	−7.15584e12	−0.593571	−0.296785	−	0.954944i	$-0.595915\pi$
$239$	−7.15584e12	−0.593571	−0.296785	+	0.954944i	$0.595915\pi$
$240$	−3.93216e10	−0.00318764
$241$	1.53304e12	0.121468	0.0607338	−	0.998154i	$-0.480656\pi$
$241$	1.53304e12	0.121468	0.0607338	+	0.998154i	$0.480656\pi$
$242$	−9.17602e12	−0.710673
$243$	−1.12849e12	−0.0854407
$244$	6.89799e12	0.510597
$245$	−5.55115e12	−0.401763
$246$	3.57142e11	0.0252754
$247$	4.91555e12	0.340204
$248$	1.45366e12	0.0983965
$249$	8.16160e11	0.0540355
$250$	−9.76562e11	−0.0632456
$251$	−9.90332e12	−0.627445	−0.313722	−	0.949515i	$-0.601576\pi$
$251$	−9.90332e12	−0.627445	−0.313722	+	0.949515i	$0.601576\pi$
$252$	2.56942e12	0.159269
$253$	7.74249e12	0.469589
$254$	−1.58778e13	−0.942335
$255$	−1.05142e11	−0.00610670
$256$	1.09951e12	0.0625000
$257$	7.77981e12	0.432849	0.216425	−	0.976299i	$-0.430560\pi$
$257$	7.77981e12	0.432849	0.216425	+	0.976299i	$0.430560\pi$
$258$	6.16550e11	0.0335784
$259$	−8.17582e12	−0.435896
$260$	−2.89754e12	−0.151243
$261$	3.49577e13	1.78657
$262$	−9.14690e12	−0.457738
$263$	2.79805e13	1.37119	0.685596	−	0.727982i	$-0.259542\pi$
$263$	2.79805e13	1.37119	0.685596	+	0.727982i	$0.259542\pi$
$264$	−2.97408e11	−0.0142735
$265$	4.87086e12	0.228957
$266$	−2.46261e12	−0.113383
$267$	−8.38456e11	−0.0378154
$268$	8.60458e12	0.380179
$269$	−3.06020e13	−1.32469	−0.662343	−	0.749201i	$-0.730438\pi$
$269$	−3.06020e13	−1.32469	−0.662343	+	0.749201i	$0.730438\pi$
$270$	−4.24980e11	−0.0180247
$271$	2.95584e13	1.22843	0.614213	−	0.789140i	$-0.289473\pi$
$271$	2.95584e13	1.22843	0.614213	+	0.789140i	$0.289473\pi$
$272$	2.93999e12	0.119734
$273$	−1.54033e11	−0.00614781
$274$	−8.47166e12	−0.331391
$275$	−7.38621e12	−0.283199
$276$	1.25788e11	0.00472759
$277$	3.83655e13	1.41352	0.706761	−	0.707453i	$-0.250156\pi$
$277$	3.83655e13	1.41352	0.706761	+	0.707453i	$0.250156\pi$
$278$	1.76705e13	0.638265
$279$	7.85226e12	0.278081
$280$	1.45162e12	0.0504063
$281$	−2.28736e13	−0.778841	−0.389421	−	0.921060i	$-0.627325\pi$
$281$	−2.28736e13	−0.778841	−0.389421	+	0.921060i	$0.627325\pi$
$282$	−6.92615e11	−0.0231271
$283$	−3.83555e13	−1.25604	−0.628018	−	0.778199i	$-0.716134\pi$
$283$	−3.83555e13	−1.25604	−0.628018	+	0.778199i	$0.716134\pi$
$284$	−4.92166e12	−0.158074
$285$	2.03575e11	0.00641324
$286$	−2.19155e13	−0.677233
$287$	−1.31845e13	−0.399681
$288$	5.93924e12	0.176633
$289$	−2.64106e13	−0.770621
$290$	1.97498e13	0.565423
$291$	−4.79531e11	−0.0134712
$292$	7.64182e12	0.210664
$293$	−4.96190e13	−1.34238	−0.671191	−	0.741285i	$-0.734217\pi$
$293$	−4.96190e13	−1.34238	−0.671191	+	0.741285i	$0.734217\pi$
$294$	−6.82125e11	−0.0181115
$295$	−2.96937e13	−0.773827
$296$	−1.88985e13	−0.483419
$297$	−3.21433e12	−0.0807104
$298$	2.89604e13	0.713863
$299$	9.26912e12	0.224309
$300$	−1.20000e11	−0.00285111
$301$	−2.27610e13	−0.530976
$302$	−6.73780e12	−0.154341
$303$	3.85455e11	0.00867039
$304$	−5.69236e12	−0.125744
$305$	2.10510e13	0.456692
$306$	1.58810e13	0.338383
$307$	−7.46045e12	−0.156136	−0.0780681	−	0.996948i	$-0.524875\pi$
$307$	−7.46045e12	−0.156136	−0.0780681	+	0.996948i	$0.524875\pi$
$308$	1.09793e13	0.225708
$309$	2.30473e12	0.0465423
$310$	4.43623e12	0.0880085
$311$	5.16368e13	1.00641	0.503207	−	0.864166i	$-0.332153\pi$
$311$	5.16368e13	1.00641	0.503207	+	0.864166i	$0.332153\pi$
$312$	−3.56050e11	−0.00681806
$313$	−1.19326e13	−0.224513	−0.112257	−	0.993679i	$-0.535808\pi$
$313$	−1.19326e13	−0.224513	−0.112257	+	0.993679i	$0.535808\pi$
$314$	5.74986e13	1.06303
$315$	7.84123e12	0.142455
$316$	−2.11400e13	−0.377421
$317$	−7.60383e12	−0.133415	−0.0667077	−	0.997773i	$-0.521250\pi$
$317$	−7.60383e12	−0.133415	−0.0667077	+	0.997773i	$0.521250\pi$
$318$	5.98531e11	0.0103214
$319$	1.49377e14	2.53184
$320$	3.35544e12	0.0559017
$321$	2.77216e12	0.0453984
$322$	−4.64368e12	−0.0747576
$323$	−1.52208e13	−0.240893
$324$	3.20559e13	0.498781
$325$	−8.84260e12	−0.135276
$326$	−1.59994e13	−0.240661
$327$	−1.11322e12	−0.0164652
$328$	−3.04762e13	−0.443255
$329$	2.55690e13	0.365710
$330$	−9.07618e11	−0.0127666
$331$	−2.41900e13	−0.334643	−0.167321	−	0.985902i	$-0.553512\pi$
$331$	−2.41900e13	−0.334643	−0.167321	+	0.985902i	$0.553512\pi$
$332$	−6.96457e13	−0.947621
$333$	−1.02084e14	−1.36620
$334$	−2.90535e13	−0.382466
$335$	2.62591e13	0.340042
$336$	1.78375e11	0.00227232
$337$	2.29753e13	0.287937	0.143969	−	0.989582i	$-0.454014\pi$
$337$	2.29753e13	0.287937	0.143969	+	0.989582i	$0.454014\pi$
$338$	3.11124e13	0.383612
$339$	3.78959e12	0.0459721
$340$	8.97214e12	0.107093
$341$	3.35533e13	0.394082
$342$	−3.07485e13	−0.355369
$343$	5.32124e13	0.605194
$344$	−5.26123e13	−0.588865
$345$	3.83875e11	0.00422849
$346$	−9.21167e13	−0.998665
$347$	−7.47631e13	−0.797765	−0.398883	−	0.917002i	$-0.630602\pi$
$347$	−7.47631e13	−0.797765	−0.398883	+	0.917002i	$0.630602\pi$
$348$	2.42686e12	0.0254893
$349$	4.00382e12	0.0413937	0.0206969	−	0.999786i	$-0.493412\pi$
$349$	4.00382e12	0.0413937	0.0206969	+	0.999786i	$0.493412\pi$
$350$	4.43000e12	0.0450847
$351$	−3.84812e12	−0.0385531
$352$	2.53788e13	0.250315
$353$	−6.95139e13	−0.675011	−0.337505	−	0.941324i	$-0.609583\pi$
$353$	−6.95139e13	−0.675011	−0.337505	+	0.941324i	$0.609583\pi$
$354$	−3.64877e12	−0.0348842
$355$	−1.50197e13	−0.141386
$356$	7.15482e13	0.663169
$357$	4.76959e11	0.00435317
$358$	−9.32855e13	−0.838412
$359$	1.01987e14	0.902664	0.451332	−	0.892356i	$-0.350949\pi$
$359$	1.01987e14	0.902664	0.451332	+	0.892356i	$0.350949\pi$
$360$	1.81251e13	0.157985
$361$	−8.70199e13	−0.747014
$362$	1.12679e14	0.952677
$363$	−3.44101e12	−0.0286549
$364$	1.31442e13	0.107814
$365$	2.33210e13	0.188424
$366$	2.58675e12	0.0205877
$367$	7.93405e13	0.622059	0.311029	−	0.950400i	$-0.399326\pi$
$367$	7.93405e13	0.622059	0.311029	+	0.950400i	$0.399326\pi$
$368$	−1.07339e13	−0.0829079
$369$	−1.64623e14	−1.25270
$370$	−5.76737e13	−0.432383
$371$	−2.20958e13	−0.163212
$372$	5.45124e11	0.00396743
$373$	1.54096e14	1.10508	0.552539	−	0.833487i	$-0.313659\pi$
$373$	1.54096e14	1.10508	0.552539	+	0.833487i	$0.313659\pi$
$374$	6.78606e13	0.479539
$375$	−3.66211e11	−0.00255011
$376$	5.91031e13	0.405581
$377$	1.78831e14	1.20939
$378$	1.92785e12	0.0128489
$379$	−1.69882e14	−1.11592	−0.557958	−	0.829869i	$-0.688415\pi$
$379$	−1.69882e14	−1.11592	−0.557958	+	0.829869i	$0.688415\pi$
$380$	−1.73717e13	−0.112469
$381$	−5.95418e12	−0.0379957
$382$	4.18884e13	0.263478
$383$	2.11674e14	1.31243	0.656213	−	0.754575i	$-0.272157\pi$
$383$	2.11674e14	1.31243	0.656213	+	0.754575i	$0.272157\pi$
$384$	4.12317e11	0.00252005
$385$	3.35062e13	0.201879
$386$	1.47046e14	0.873420
$387$	−2.84196e14	−1.66421
$388$	4.09200e13	0.236244
$389$	−2.17282e14	−1.23680	−0.618402	−	0.785862i	$-0.712220\pi$
$389$	−2.17282e14	−1.23680	−0.618402	+	0.785862i	$0.712220\pi$
$390$	−1.08658e12	−0.00609826
$391$	−2.87015e13	−0.158830
$392$	5.82080e13	0.317621
$393$	−3.43009e12	−0.0184564
$394$	−6.93049e13	−0.367735
$395$	−6.45142e13	−0.337576
$396$	1.37089e14	0.707422
$397$	3.00248e14	1.52803	0.764017	−	0.645196i	$-0.223224\pi$
$397$	3.00248e14	1.52803	0.764017	+	0.645196i	$0.223224\pi$
$398$	−4.12601e13	−0.207097
$399$	−9.23480e11	−0.00457169
$400$	1.02400e13	0.0500000
$401$	1.24274e14	0.598533	0.299266	−	0.954170i	$-0.403258\pi$
$401$	1.24274e14	0.598533	0.299266	+	0.954170i	$0.403258\pi$
$402$	3.22672e12	0.0153291
$403$	4.01693e13	0.188242
$404$	−3.28921e13	−0.152053
$405$	9.78267e13	0.446123
$406$	−8.95914e13	−0.403063
$407$	−4.36214e14	−1.93611
$408$	1.10250e12	0.00482777
$409$	−7.41716e13	−0.320449	−0.160225	−	0.987081i	$-0.551222\pi$
$409$	−7.41716e13	−0.320449	−0.160225	+	0.987081i	$0.551222\pi$
$410$	−9.30058e13	−0.396460
$411$	−3.17687e12	−0.0133620
$412$	−1.96670e14	−0.816214
$413$	1.34700e14	0.551624
$414$	−5.79815e13	−0.234308
$415$	−2.12542e14	−0.847578
$416$	3.03829e13	0.119568
$417$	6.62642e12	0.0257354
$418$	−1.31391e14	−0.503610
$419$	−1.97541e13	−0.0747273	−0.0373637	−	0.999302i	$-0.511896\pi$
$419$	−1.97541e13	−0.0747273	−0.0373637	+	0.999302i	$0.511896\pi$
$420$	5.44358e11	0.00203242
$421$	−4.20530e14	−1.54969	−0.774846	−	0.632150i	$-0.782173\pi$
$421$	−4.20530e14	−1.54969	−0.774846	+	0.632150i	$0.782173\pi$
$422$	2.00117e14	0.727890
$423$	3.19258e14	1.14622
$424$	−5.10747e13	−0.181006
$425$	2.73808e13	0.0957871
$426$	−1.84562e12	−0.00637367
$427$	−9.54941e13	−0.325554
$428$	−2.36557e14	−0.796152
$429$	−8.21831e12	−0.0273066
$430$	−1.60560e14	−0.526697
$431$	2.75584e14	0.892541	0.446271	−	0.894898i	$-0.352752\pi$
$431$	2.75584e14	0.892541	0.446271	+	0.894898i	$0.352752\pi$
$432$	4.45624e12	0.0142498
$433$	3.60639e14	1.13865	0.569323	−	0.822114i	$-0.307205\pi$
$433$	3.60639e14	1.13865	0.569323	+	0.822114i	$0.307205\pi$
$434$	−2.01242e13	−0.0627371
$435$	7.40618e12	0.0227983
$436$	9.49946e13	0.288751
$437$	5.55714e13	0.166803
$438$	2.86568e12	0.00849416
$439$	6.71717e14	1.96622	0.983108	−	0.183024i	$-0.0585887\pi$
$439$	6.71717e14	1.96622	0.983108	+	0.183024i	$0.0585887\pi$
$440$	7.74500e13	0.223889
$441$	3.14422e14	0.897638
$442$	8.12411e13	0.229062
$443$	−2.02306e14	−0.563363	−0.281682	−	0.959508i	$-0.590892\pi$
$443$	−2.02306e14	−0.563363	−0.281682	+	0.959508i	$0.590892\pi$
$444$	−7.08694e12	−0.0194918
$445$	2.18348e14	0.593156
$446$	1.29162e14	0.346571
$447$	1.08601e13	0.0287835
$448$	−1.52214e13	−0.0398496
$449$	−1.08827e14	−0.281438	−0.140719	−	0.990050i	$-0.544941\pi$
$449$	−1.08827e14	−0.281438	−0.140719	+	0.990050i	$0.544941\pi$
$450$	5.53134e13	0.141306
$451$	−7.03448e14	−1.77526
$452$	−3.23378e14	−0.806213
$453$	−2.52668e12	−0.00622314
$454$	5.25667e14	1.27910
$455$	4.01129e13	0.0964319
$456$	−2.13464e12	−0.00507011
$457$	6.26717e14	1.47073	0.735365	−	0.677672i	$-0.237011\pi$
$457$	6.26717e14	1.47073	0.735365	+	0.677672i	$0.237011\pi$
$458$	−7.85846e13	−0.182212
$459$	1.19156e13	0.0272989
$460$	−3.27574e13	−0.0741550
$461$	2.33223e14	0.521695	0.260848	−	0.965380i	$-0.415998\pi$
$461$	2.33223e14	0.521695	0.260848	+	0.965380i	$0.415998\pi$
$462$	4.11724e12	0.00910072
$463$	−3.78029e14	−0.825714	−0.412857	−	0.910796i	$-0.635469\pi$
$463$	−3.78029e14	−0.825714	−0.412857	+	0.910796i	$0.635469\pi$
$464$	−2.07092e14	−0.447006
$465$	1.66359e12	0.00354857
$466$	−3.27280e14	−0.689918
$467$	−4.52620e14	−0.942955	−0.471477	−	0.881878i	$-0.656279\pi$
$467$	−4.52620e14	−0.942955	−0.471477	+	0.881878i	$0.656279\pi$
$468$	1.64120e14	0.337916
$469$	−1.19120e14	−0.242400
$470$	1.80368e14	0.362762
$471$	2.15620e13	0.0428621
$472$	3.11361e14	0.611764
$473$	−1.21439e15	−2.35843
$474$	−7.92750e12	−0.0152179
$475$	−5.30143e13	−0.100595
$476$	−4.07005e13	−0.0763416
$477$	−2.75890e14	−0.511546
$478$	2.28987e14	0.419718
$479$	−1.13587e14	−0.205819	−0.102909	−	0.994691i	$-0.532815\pi$
$479$	−1.13587e14	−0.205819	−0.102909	+	0.994691i	$0.532815\pi$
$480$	1.25829e12	0.00225400
$481$	−5.22225e14	−0.924825
$482$	−4.90573e13	−0.0858905
$483$	−1.74138e12	−0.00301429
$484$	2.93633e14	0.502522
$485$	1.24878e14	0.211303
$486$	3.61118e13	0.0604157
$487$	1.95281e13	0.0323035	0.0161518	−	0.999870i	$-0.494859\pi$
$487$	1.95281e13	0.0323035	0.0161518	+	0.999870i	$0.494859\pi$
$488$	−2.20736e14	−0.361047
$489$	−5.99976e12	−0.00970365
$490$	1.77637e14	0.284089
$491$	3.79883e14	0.600761	0.300381	−	0.953819i	$-0.402886\pi$
$491$	3.79883e14	0.600761	0.300381	+	0.953819i	$0.402886\pi$
$492$	−1.14286e13	−0.0178724
$493$	−5.53744e14	−0.856349
$494$	−1.57298e14	−0.240560
$495$	4.18362e14	0.632738
$496$	−4.65172e13	−0.0695768
$497$	6.81342e13	0.100787
$498$	−2.61171e13	−0.0382089
$499$	1.29221e15	1.86973	0.934867	−	0.354998i	$-0.115518\pi$
$499$	1.29221e15	1.86973	0.934867	+	0.354998i	$0.115518\pi$
$500$	3.12500e13	0.0447214
$501$	−1.08951e13	−0.0154214
$502$	3.16906e14	0.443670
$503$	2.13775e14	0.296029	0.148014	−	0.988985i	$-0.452712\pi$
$503$	2.13775e14	0.296029	0.148014	+	0.988985i	$0.452712\pi$
$504$	−8.22213e13	−0.112620
$505$	−1.00379e14	−0.136000
$506$	−2.47760e14	−0.332049
$507$	1.16672e13	0.0154675
$508$	5.08090e14	0.666332
$509$	−4.21457e13	−0.0546771	−0.0273386	−	0.999626i	$-0.508703\pi$
$509$	−4.21457e13	−0.0546771	−0.0273386	+	0.999626i	$0.508703\pi$
$510$	3.36455e12	0.00431809
$511$	−1.05791e14	−0.134318
$512$	−3.51844e13	−0.0441942
$513$	−2.30707e13	−0.0286692
$514$	−2.48954e14	−0.306071
$515$	−6.00190e14	−0.730044
$516$	−1.97296e13	−0.0237435
$517$	1.36421e15	1.62437
$518$	2.61626e14	0.308225
$519$	−3.45438e13	−0.0402670
$520$	9.27214e13	0.106945
$521$	3.64128e14	0.415572	0.207786	−	0.978174i	$-0.433374\pi$
$521$	3.64128e14	0.415572	0.207786	+	0.978174i	$0.433374\pi$
$522$	−1.11865e15	−1.26330
$523$	7.11541e14	0.795135	0.397567	−	0.917573i	$-0.369854\pi$
$523$	7.11541e14	0.795135	0.397567	+	0.917573i	$0.369854\pi$
$524$	2.92701e14	0.323669
$525$	1.66125e12	0.00181785
$526$	−8.95375e14	−0.969579
$527$	−1.24383e14	−0.133291
$528$	9.51706e12	0.0100929
$529$	−8.48020e14	−0.890021
$530$	−1.55867e14	−0.161897
$531$	1.68188e15	1.72892
$532$	7.88036e13	0.0801738
$533$	−8.42151e14	−0.847989
$534$	2.68306e13	0.0267395
$535$	−7.21916e14	−0.712100
$536$	−2.75346e14	−0.268827
$537$	−3.49820e13	−0.0338054
$538$	9.79265e14	0.936694
$539$	1.34355e15	1.27209
$540$	1.35994e13	0.0127454
$541$	−2.24644e14	−0.208405	−0.104203	−	0.994556i	$-0.533229\pi$
$541$	−2.24644e14	−0.208405	−0.104203	+	0.994556i	$0.533229\pi$
$542$	−9.45867e14	−0.868629
$543$	4.22546e13	0.0384127
$544$	−9.40797e13	−0.0846646
$545$	2.89901e14	0.258267
$546$	4.92907e12	0.00434716
$547$	−1.36574e15	−1.19244	−0.596220	−	0.802821i	$-0.703331\pi$
$547$	−1.36574e15	−1.19244	−0.596220	+	0.802821i	$0.703331\pi$
$548$	2.71093e14	0.234329
$549$	−1.19235e15	−1.02036
$550$	2.36359e14	0.200252
$551$	1.07215e15	0.899335
$552$	−4.02522e12	−0.00334291
$553$	2.92657e14	0.240642
$554$	−1.22770e15	−0.999510
$555$	−2.16276e13	−0.0174340
$556$	−5.65455e14	−0.451322
$557$	−2.26109e14	−0.178695	−0.0893477	−	0.996000i	$-0.528478\pi$
$557$	−2.26109e14	−0.178695	−0.0893477	+	0.996000i	$0.528478\pi$
$558$	−2.51272e14	−0.196633
$559$	−1.45384e15	−1.12655
$560$	−4.64519e13	−0.0356426
$561$	2.54477e13	0.0193354
$562$	7.31954e14	0.550724
$563$	1.43177e15	1.06678	0.533391	−	0.845869i	$-0.320917\pi$
$563$	1.43177e15	1.06678	0.533391	+	0.845869i	$0.320917\pi$
$564$	2.21637e13	0.0163533
$565$	−9.86873e14	−0.721098
$566$	1.22738e15	0.888152
$567$	−4.43773e14	−0.318020
$568$	1.57493e14	0.111775
$569$	−1.53241e15	−1.07710	−0.538552	−	0.842592i	$-0.681028\pi$
$569$	−1.53241e15	−1.07710	−0.538552	+	0.842592i	$0.681028\pi$
$570$	−6.51439e12	−0.00453484
$571$	−1.43911e15	−0.992195	−0.496097	−	0.868267i	$-0.665234\pi$
$571$	−1.43911e15	−0.992195	−0.496097	+	0.868267i	$0.665234\pi$
$572$	7.01296e14	0.478876
$573$	1.57081e13	0.0106237
$574$	4.21904e14	0.282617
$575$	−9.99675e13	−0.0663263
$576$	−1.90056e14	−0.124898
$577$	1.48513e15	0.966712	0.483356	−	0.875424i	$-0.339418\pi$
$577$	1.48513e15	0.966712	0.483356	+	0.875424i	$0.339418\pi$
$578$	8.45140e14	0.544911
$579$	5.51423e13	0.0352170
$580$	−6.31994e14	−0.399815
$581$	9.64157e14	0.604198
$582$	1.53450e13	0.00952556
$583$	−1.17890e15	−0.724937
$584$	−2.44538e14	−0.148962
$585$	5.00853e14	0.302241
$586$	1.58781e15	0.949207
$587$	1.31107e15	0.776458	0.388229	−	0.921563i	$-0.373087\pi$
$587$	1.31107e15	0.776458	0.388229	+	0.921563i	$0.373087\pi$
$588$	2.18280e13	0.0128067
$589$	2.40828e14	0.139982
$590$	9.50200e14	0.547178
$591$	−2.59893e13	−0.0148274
$592$	6.04753e14	0.341829
$593$	2.32109e15	1.29984	0.649921	−	0.760002i	$-0.274802\pi$
$593$	2.32109e15	1.29984	0.649921	+	0.760002i	$0.274802\pi$
$594$	1.02858e14	0.0570709
$595$	−1.24208e14	−0.0682820
$596$	−9.26732e14	−0.504777
$597$	−1.54725e13	−0.00835031
$598$	−2.96612e14	−0.158611
$599$	7.44744e14	0.394602	0.197301	−	0.980343i	$-0.436782\pi$
$599$	7.44744e14	0.394602	0.197301	+	0.980343i	$0.436782\pi$
$600$	3.84000e12	0.00201604
$601$	−1.61148e15	−0.838330	−0.419165	−	0.907910i	$-0.637677\pi$
$601$	−1.61148e15	−0.838330	−0.419165	+	0.907910i	$0.637677\pi$
$602$	7.28351e14	0.375457
$603$	−1.48734e15	−0.759740
$604$	2.15610e14	0.109135
$605$	8.96096e14	0.449469
$606$	−1.23345e13	−0.00613089
$607$	8.74853e14	0.430921	0.215460	−	0.976513i	$-0.430875\pi$
$607$	8.74853e14	0.430921	0.215460	+	0.976513i	$0.430875\pi$
$608$	1.82156e14	0.0889146
$609$	−3.35968e13	−0.0162518
$610$	−6.73632e14	−0.322930
$611$	1.63320e15	0.775914
$612$	−5.08191e14	−0.239273
$613$	−5.18906e14	−0.242134	−0.121067	−	0.992644i	$-0.538632\pi$
$613$	−5.18906e14	−0.242134	−0.121067	+	0.992644i	$0.538632\pi$
$614$	2.38734e14	0.110405
$615$	−3.48772e13	−0.0159856
$616$	−3.51338e14	−0.159599
$617$	−1.80298e15	−0.811752	−0.405876	−	0.913928i	$-0.633033\pi$
$617$	−1.80298e15	−0.811752	−0.405876	+	0.913928i	$0.633033\pi$
$618$	−7.37513e13	−0.0329104
$619$	−2.73518e15	−1.20973	−0.604864	−	0.796329i	$-0.706772\pi$
$619$	−2.73518e15	−1.20973	−0.604864	+	0.796329i	$0.706772\pi$
$620$	−1.41959e14	−0.0622314
$621$	−4.35038e13	−0.0189027
$622$	−1.65238e15	−0.711643
$623$	−9.90496e14	−0.422833
$624$	1.13936e13	0.00482110
$625$	9.53674e13	0.0400000
$626$	3.81844e14	0.158755
$627$	−4.92715e13	−0.0203060
$628$	−1.83995e15	−0.751673
$629$	1.61705e15	0.654855
$630$	−2.50919e14	−0.100731
$631$	−4.52954e15	−1.80257	−0.901287	−	0.433224i	$-0.857376\pi$
$631$	−4.52954e15	−1.80257	−0.901287	+	0.433224i	$0.857376\pi$
$632$	6.76480e14	0.266877
$633$	7.50439e13	0.0293491
$634$	2.43322e14	0.0943390
$635$	1.55057e15	0.595985
$636$	−1.91530e13	−0.00729831
$637$	1.60847e15	0.607639
$638$	−4.78007e15	−1.79028
$639$	8.50731e14	0.315891
$640$	−1.07374e14	−0.0395285
$641$	−9.22535e14	−0.336716	−0.168358	−	0.985726i	$-0.553846\pi$
$641$	−9.22535e14	−0.336716	−0.168358	+	0.985726i	$0.553846\pi$
$642$	−8.87090e13	−0.0321015
$643$	1.91900e15	0.688517	0.344258	−	0.938875i	$-0.388130\pi$
$643$	1.91900e15	0.688517	0.344258	+	0.938875i	$0.388130\pi$
$644$	1.48598e14	0.0528616
$645$	−6.02100e13	−0.0212368
$646$	4.87067e14	0.170337
$647$	−5.10676e15	−1.77081	−0.885405	−	0.464821i	$-0.846119\pi$
$647$	−5.10676e15	−1.77081	−0.885405	+	0.464821i	$0.846119\pi$
$648$	−1.02579e15	−0.352691
$649$	7.18682e15	2.45014
$650$	2.82963e14	0.0956547
$651$	−7.54656e12	−0.00252961
$652$	5.11980e14	0.170173
$653$	1.71910e15	0.566604	0.283302	−	0.959031i	$-0.408570\pi$
$653$	1.71910e15	0.566604	0.283302	+	0.959031i	$0.408570\pi$
$654$	3.56230e13	0.0116427
$655$	8.93252e14	0.289499
$656$	9.75237e14	0.313429
$657$	−1.32092e15	−0.420986
$658$	−8.18209e14	−0.258596
$659$	2.75909e15	0.864762	0.432381	−	0.901691i	$-0.357674\pi$
$659$	2.75909e15	0.864762	0.432381	+	0.901691i	$0.357674\pi$
$660$	2.90438e13	0.00902737
$661$	4.74724e15	1.46330	0.731650	−	0.681681i	$-0.238751\pi$
$661$	4.74724e15	1.46330	0.731650	+	0.681681i	$0.238751\pi$
$662$	7.74079e14	0.236628
$663$	3.04654e13	0.00923598
$664$	2.22866e15	0.670069
$665$	2.40490e14	0.0717096
$666$	3.26669e15	0.966051
$667$	2.02172e15	0.592965
$668$	9.29713e14	0.270445
$669$	4.84356e13	0.0139740
$670$	−8.40291e14	−0.240446
$671$	−5.09500e15	−1.44601
$672$	−5.70801e12	−0.00160677
$673$	−1.84642e15	−0.515524	−0.257762	−	0.966208i	$-0.582985\pi$
$673$	−1.84642e15	−0.515524	−0.257762	+	0.966208i	$0.582985\pi$
$674$	−7.35211e14	−0.203602
$675$	4.15020e13	0.0113998
$676$	−9.95597e14	−0.271254
$677$	−3.07379e15	−0.830686	−0.415343	−	0.909665i	$-0.636338\pi$
$677$	−3.07379e15	−0.830686	−0.415343	+	0.909665i	$0.636338\pi$
$678$	−1.21267e14	−0.0325072
$679$	−5.66486e14	−0.150628
$680$	−2.87109e14	−0.0757264
$681$	1.97125e14	0.0515743
$682$	−1.07371e15	−0.278658
$683$	2.73187e15	0.703308	0.351654	−	0.936130i	$-0.385619\pi$
$683$	2.73187e15	0.703308	0.351654	+	0.936130i	$0.385619\pi$
$684$	9.83950e14	0.251284
$685$	8.27311e14	0.209590
$686$	−1.70280e15	−0.427937
$687$	−2.94692e13	−0.00734695
$688$	1.68359e15	0.416390
$689$	−1.41135e15	−0.346282
$690$	−1.22840e13	−0.00298999
$691$	−1.00765e15	−0.243320	−0.121660	−	0.992572i	$-0.538822\pi$
$691$	−1.00765e15	−0.243320	−0.121660	+	0.992572i	$0.538822\pi$
$692$	2.94773e15	0.706163
$693$	−1.89782e15	−0.451048
$694$	2.39242e15	0.564105
$695$	−1.72563e15	−0.403675
$696$	−7.76594e13	−0.0180237
$697$	2.60769e15	0.600449
$698$	−1.28122e14	−0.0292698
$699$	−1.22730e14	−0.0278181
$700$	−1.41760e14	−0.0318797
$701$	−8.74882e15	−1.95209	−0.976046	−	0.217564i	$-0.930189\pi$
$701$	−8.74882e15	−1.95209	−0.976046	+	0.217564i	$0.930189\pi$
$702$	1.23140e14	0.0272612
$703$	−3.13091e15	−0.687727
$704$	−8.12122e14	−0.176999
$705$	6.76382e13	0.0146269
$706$	2.22444e15	0.477305
$707$	4.55350e14	0.0969480
$708$	1.16761e14	0.0246668
$709$	−2.77232e15	−0.581151	−0.290576	−	0.956852i	$-0.593847\pi$
$709$	−2.77232e15	−0.581151	−0.290576	+	0.956852i	$0.593847\pi$
$710$	4.80631e14	0.0999748
$711$	3.65415e15	0.754229
$712$	−2.28954e15	−0.468931
$713$	4.54122e14	0.0922955
$714$	−1.52627e13	−0.00307816
$715$	2.14019e15	0.428320
$716$	2.98513e15	0.592847
$717$	8.58701e13	0.0169234
$718$	−3.26359e15	−0.638280
$719$	−7.95270e15	−1.54350	−0.771749	−	0.635928i	$-0.780618\pi$
$719$	−7.95270e15	−1.54350	−0.771749	+	0.635928i	$0.780618\pi$
$720$	−5.80003e14	−0.111713
$721$	2.72265e15	0.520413
$722$	2.78464e15	0.528219
$723$	−1.83965e13	−0.00346318
$724$	−3.60573e15	−0.673644
$725$	−1.92869e15	−0.357605
$726$	1.10112e14	0.0202621
$727$	1.34232e15	0.245141	0.122571	−	0.992460i	$-0.460886\pi$
$727$	1.34232e15	0.245141	0.122571	+	0.992460i	$0.460886\pi$
$728$	−4.20614e14	−0.0762361
$729$	−5.53197e15	−0.995126
$730$	−7.46271e14	−0.133236
$731$	4.50177e15	0.797696
$732$	−8.27759e13	−0.0145577
$733$	1.01134e16	1.76533	0.882663	−	0.470007i	$-0.155749\pi$
$733$	1.01134e16	1.76533	0.882663	+	0.470007i	$0.155749\pi$
$734$	−2.53890e15	−0.439862
$735$	6.66138e13	0.0114547
$736$	3.43486e14	0.0586247
$737$	−6.35552e15	−1.07666
$738$	5.26794e15	0.885790
$739$	−9.57608e14	−0.159824	−0.0799122	−	0.996802i	$-0.525464\pi$
$739$	−9.57608e14	−0.159824	−0.0799122	+	0.996802i	$0.525464\pi$
$740$	1.84556e15	0.305741
$741$	−5.89866e13	−0.00969959
$742$	7.07065e14	0.115408
$743$	1.82930e15	0.296379	0.148189	−	0.988959i	$-0.452655\pi$
$743$	1.82930e15	0.296379	0.148189	+	0.988959i	$0.452655\pi$
$744$	−1.74440e13	−0.00280539
$745$	−2.82816e15	−0.451487
$746$	−4.93108e15	−0.781408
$747$	1.20386e16	1.89370
$748$	−2.17154e15	−0.339085
$749$	3.27484e15	0.507622
$750$	1.17188e13	0.00180320
$751$	6.44053e15	0.983788	0.491894	−	0.870655i	$-0.336305\pi$
$751$	6.44053e15	0.983788	0.491894	+	0.870655i	$0.336305\pi$
$752$	−1.89130e15	−0.286789
$753$	1.18840e14	0.0178892
$754$	−5.72259e15	−0.855165
$755$	6.57989e14	0.0976136
$756$	−6.16910e13	−0.00908557
$757$	−2.59826e15	−0.379888	−0.189944	−	0.981795i	$-0.560831\pi$
$757$	−2.59826e15	−0.379888	−0.189944	+	0.981795i	$0.560831\pi$
$758$	5.43622e15	0.789072
$759$	−9.29098e13	−0.0133885
$760$	5.55895e14	0.0795276
$761$	5.42627e15	0.770701	0.385350	−	0.922770i	$-0.374081\pi$
$761$	5.42627e15	0.770701	0.385350	+	0.922770i	$0.374081\pi$
$762$	1.90534e14	0.0268670
$763$	−1.31508e15	−0.184106
$764$	−1.34043e15	−0.186307
$765$	−1.55087e15	−0.214012
$766$	−6.77358e15	−0.928026
$767$	8.60389e15	1.17036
$768$	−1.31941e13	−0.00178195
$769$	3.36300e15	0.450954	0.225477	−	0.974249i	$-0.427606\pi$
$769$	3.36300e15	0.450954	0.225477	+	0.974249i	$0.427606\pi$
$770$	−1.07220e15	−0.142750
$771$	−9.33577e13	−0.0123410
$772$	−4.70547e15	−0.617601
$773$	−4.07367e14	−0.0530882	−0.0265441	−	0.999648i	$-0.508450\pi$
$773$	−4.07367e14	−0.0530882	−0.0265441	+	0.999648i	$0.508450\pi$
$774$	9.09427e15	1.17677
$775$	−4.33225e14	−0.0556615
$776$	−1.30944e15	−0.167050
$777$	9.81099e13	0.0124279
$778$	6.95303e15	0.874553
$779$	−5.04897e15	−0.630590
$780$	3.47705e13	0.00431212
$781$	3.63524e15	0.447664
$782$	9.18449e14	0.112310
$783$	−8.39327e14	−0.101916
$784$	−1.86266e15	−0.224592
$785$	−5.61510e15	−0.672317
$786$	1.09763e14	0.0130506
$787$	1.64875e15	0.194667	0.0973337	−	0.995252i	$-0.468969\pi$
$787$	1.64875e15	0.194667	0.0973337	+	0.995252i	$0.468969\pi$
$788$	2.21776e15	0.260028
$789$	−3.35766e14	−0.0390942
$790$	2.06445e15	0.238702
$791$	4.47677e15	0.514037
$792$	−4.38684e15	−0.500223
$793$	−6.09962e15	−0.690717
$794$	−9.60795e15	−1.08048
$795$	−5.84503e13	−0.00652781
$796$	1.32032e15	0.146439
$797$	−1.64609e16	−1.81314	−0.906571	−	0.422053i	$-0.861310\pi$
$797$	−1.64609e16	−1.81314	−0.906571	+	0.422053i	$0.861310\pi$
$798$	2.95514e13	0.00323267
$799$	−5.05716e15	−0.549414
$800$	−3.27680e14	−0.0353553
$801$	−1.23674e16	−1.32526
$802$	−3.97678e15	−0.423227
$803$	−5.64441e15	−0.596600
$804$	−1.03255e14	−0.0108393
$805$	4.53485e14	0.0472808
$806$	−1.28542e15	−0.133107
$807$	3.67225e14	0.0377683
$808$	1.05255e15	0.107518
$809$	1.47123e16	1.49267	0.746334	−	0.665572i	$-0.231812\pi$
$809$	1.47123e16	1.49267	0.746334	+	0.665572i	$0.231812\pi$
$810$	−3.13046e15	−0.315457
$811$	−4.23707e15	−0.424083	−0.212042	−	0.977261i	$-0.568011\pi$
$811$	−4.23707e15	−0.424083	−0.212042	+	0.977261i	$0.568011\pi$
$812$	2.86693e15	0.285009
$813$	−3.54700e14	−0.0350238
$814$	1.39588e16	1.36904
$815$	1.56244e15	0.152207
$816$	−3.52799e13	−0.00341375
$817$	−8.71625e15	−0.837738
$818$	2.37349e15	0.226592
$819$	−2.27203e15	−0.215453
$820$	2.97619e15	0.280339
$821$	−1.49805e15	−0.140165	−0.0700825	−	0.997541i	$-0.522326\pi$
$821$	−1.49805e15	−0.140165	−0.0700825	+	0.997541i	$0.522326\pi$
$822$	1.01660e14	0.00944833
$823$	−1.02890e16	−0.949894	−0.474947	−	0.880014i	$-0.657533\pi$
$823$	−1.02890e16	−0.949894	−0.474947	+	0.880014i	$0.657533\pi$
$824$	6.29345e15	0.577150
$825$	8.86345e13	0.00807433
$826$	−4.31041e15	−0.390057
$827$	1.06945e16	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$827$	1.06945e16	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$828$	1.85541e15	0.165681
$829$	6.98954e15	0.620010	0.310005	−	0.950735i	$-0.399669\pi$
$829$	6.98954e15	0.620010	0.310005	+	0.950735i	$0.399669\pi$
$830$	6.80133e15	0.599328
$831$	−4.60386e14	−0.0403011
$832$	−9.72254e14	−0.0845476
$833$	−4.98057e15	−0.430261
$834$	−2.12045e14	−0.0181977
$835$	2.83726e15	0.241893
$836$	4.20450e15	0.356106
$837$	−1.88531e14	−0.0158633
$838$	6.32130e14	0.0528402
$839$	1.67921e16	1.39448	0.697242	−	0.716836i	$-0.254410\pi$
$839$	1.67921e16	1.39448	0.697242	+	0.716836i	$0.254410\pi$
$840$	−1.74195e13	−0.00143714
$841$	2.68050e16	2.19704
$842$	1.34570e16	1.09580
$843$	2.74483e14	0.0222056
$844$	−6.40374e15	−0.514696
$845$	−3.03832e15	−0.242617
$846$	−1.02162e16	−0.810502
$847$	−4.06498e15	−0.320405
$848$	1.63439e15	0.127991
$849$	4.60266e14	0.0358110
$850$	−8.76186e14	−0.0677317
$851$	−5.90387e15	−0.453444
$852$	5.90599e13	0.00450687
$853$	−1.01151e16	−0.766924	−0.383462	−	0.923557i	$-0.625268\pi$
$853$	−1.01151e16	−0.766924	−0.383462	+	0.923557i	$0.625268\pi$
$854$	3.05581e15	0.230201
$855$	3.00278e15	0.224755
$856$	7.56984e15	0.562964
$857$	9.16392e15	0.677153	0.338576	−	0.940939i	$-0.390055\pi$
$857$	9.16392e15	0.677153	0.338576	+	0.940939i	$0.390055\pi$
$858$	2.62986e14	0.0193087
$859$	−1.57002e16	−1.14536	−0.572680	−	0.819779i	$-0.694096\pi$
$859$	−1.57002e16	−1.14536	−0.572680	+	0.819779i	$0.694096\pi$
$860$	5.13792e15	0.372431
$861$	1.58214e14	0.0113954
$862$	−8.81867e15	−0.631122
$863$	−1.40705e15	−0.100058	−0.0500289	−	0.998748i	$-0.515931\pi$
$863$	−1.40705e15	−0.100058	−0.0500289	+	0.998748i	$0.515931\pi$
$864$	−1.42600e14	−0.0100761
$865$	8.99577e15	0.631611
$866$	−1.15404e16	−0.805145
$867$	3.16928e14	0.0219713
$868$	6.43973e14	0.0443618
$869$	1.56145e16	1.06885
$870$	−2.36998e14	−0.0161209
$871$	−7.60868e15	−0.514292
$872$	−3.03983e15	−0.204178
$873$	−7.07321e15	−0.472104
$874$	−1.77829e15	−0.117947
$875$	−4.32617e14	−0.0285141
$876$	−9.17018e13	−0.00600628
$877$	1.03861e16	0.676010	0.338005	−	0.941144i	$-0.390248\pi$
$877$	1.03861e16	0.676010	0.338005	+	0.941144i	$0.390248\pi$
$878$	−2.14949e16	−1.39033
$879$	5.95428e14	0.0382728
$880$	−2.47840e15	−0.158313
$881$	−1.45130e16	−0.921277	−0.460639	−	0.887588i	$-0.652380\pi$
$881$	−1.45130e16	−0.921277	−0.460639	+	0.887588i	$0.652380\pi$
$882$	−1.00615e16	−0.634726
$883$	−1.27565e16	−0.799736	−0.399868	−	0.916573i	$-0.630944\pi$
$883$	−1.27565e16	−0.799736	−0.399868	+	0.916573i	$0.630944\pi$
$884$	−2.59972e15	−0.161971
$885$	3.56325e14	0.0220627
$886$	6.47380e15	0.398358
$887$	1.45276e16	0.888413	0.444207	−	0.895924i	$-0.353486\pi$
$887$	1.45276e16	0.888413	0.444207	+	0.895924i	$0.353486\pi$
$888$	2.26782e14	0.0137828
$889$	−7.03387e15	−0.424849
$890$	−6.98713e15	−0.419425
$891$	−2.36771e16	−1.41254
$892$	−4.13317e15	−0.245062
$893$	9.79159e15	0.576993
$894$	−3.47525e14	−0.0203530
$895$	9.10991e15	0.530258
$896$	4.87084e14	0.0281780
$897$	−1.11229e14	−0.00639531
$898$	3.48247e15	0.199006
$899$	8.76146e15	0.497621
$900$	−1.77003e15	−0.0999187
$901$	4.37020e15	0.245197
$902$	2.25103e16	1.25530
$903$	2.73132e14	0.0151387
$904$	1.03481e16	0.570078
$905$	−1.10038e16	−0.602526
$906$	8.08536e13	0.00440042
$907$	−3.00432e16	−1.62520	−0.812599	−	0.582823i	$-0.801948\pi$
$907$	−3.00432e16	−1.62520	−0.812599	+	0.582823i	$0.801948\pi$
$908$	−1.68213e16	−0.904458
$909$	5.68555e15	0.303858
$910$	−1.28361e15	−0.0681877
$911$	1.41333e16	0.746264	0.373132	−	0.927778i	$-0.378284\pi$
$911$	1.41333e16	0.746264	0.373132	+	0.927778i	$0.378284\pi$
$912$	6.83084e13	0.00358511
$913$	5.14418e16	2.68365
$914$	−2.00550e16	−1.03996
$915$	−2.52612e14	−0.0130208
$916$	2.51471e15	0.128843
$917$	−4.05208e15	−0.206370
$918$	−3.81298e14	−0.0193032
$919$	−3.46543e16	−1.74390	−0.871952	−	0.489592i	$-0.837146\pi$
$919$	−3.46543e16	−1.74390	−0.871952	+	0.489592i	$0.837146\pi$
$920$	1.04824e15	0.0524355
$921$	8.95254e13	0.00445162
$922$	−7.46315e15	−0.368894
$923$	4.35202e15	0.213837
$924$	−1.31752e14	−0.00643518
$925$	5.63220e15	0.273463
$926$	1.20969e16	0.583868
$927$	3.39953e16	1.63110
$928$	6.62693e15	0.316081
$929$	7.33539e15	0.347806	0.173903	−	0.984763i	$-0.444362\pi$
$929$	7.33539e15	0.347806	0.173903	+	0.984763i	$0.444362\pi$
$930$	−5.32347e13	−0.00250922
$931$	9.64330e15	0.451858
$932$	1.04730e16	0.487846
$933$	−6.19641e14	−0.0286940
$934$	1.44838e16	0.666770
$935$	−6.62701e15	−0.303287
$936$	−5.25183e15	−0.238942
$937$	−3.44345e16	−1.55749	−0.778747	−	0.627338i	$-0.784145\pi$
$937$	−3.44345e16	−1.55749	−0.778747	+	0.627338i	$0.784145\pi$
$938$	3.81183e15	0.171403
$939$	1.43191e14	0.00640112
$940$	−5.77179e15	−0.256512
$941$	1.75999e16	0.777620	0.388810	−	0.921318i	$-0.372886\pi$
$941$	1.75999e16	0.777620	0.388810	+	0.921318i	$0.372886\pi$
$942$	−6.89983e14	−0.0303081
$943$	−9.52070e15	−0.415771
$944$	−9.96357e15	−0.432582
$945$	−1.88266e14	−0.00812638
$946$	3.88605e16	1.66766
$947$	−3.45143e16	−1.47256	−0.736282	−	0.676675i	$-0.763420\pi$
$947$	−3.45143e16	−1.47256	−0.736282	+	0.676675i	$0.763420\pi$
$948$	2.53680e14	0.0107607
$949$	−6.75735e15	−0.284979
$950$	1.69646e15	0.0711316
$951$	9.12459e13	0.00380383
$952$	1.30242e15	0.0539817
$953$	1.69927e16	0.700248	0.350124	−	0.936703i	$-0.386139\pi$
$953$	1.69927e16	0.700248	0.350124	+	0.936703i	$0.386139\pi$
$954$	8.82848e15	0.361718
$955$	−4.09066e15	−0.166638
$956$	−7.32758e15	−0.296785
$957$	−1.79253e15	−0.0721855
$958$	3.63479e15	0.145536
$959$	−3.75295e15	−0.149407
$960$	−4.02653e13	−0.00159382
$961$	−2.34405e16	−0.922545
$962$	1.67112e16	0.653950
$963$	4.08900e16	1.59101
$964$	1.56984e15	0.0607338
$965$	−1.43600e16	−0.552399
$966$	5.57242e13	0.00213142
$967$	3.38514e16	1.28745	0.643726	−	0.765256i	$-0.277387\pi$
$967$	3.38514e16	1.28745	0.643726	+	0.765256i	$0.277387\pi$
$968$	−9.39624e15	−0.355337
$969$	1.82650e14	0.00686814
$970$	−3.99610e15	−0.149414
$971$	−1.97060e16	−0.732644	−0.366322	−	0.930488i	$-0.619383\pi$
$971$	−1.97060e16	−0.732644	−0.366322	+	0.930488i	$0.619383\pi$
$972$	−1.15558e15	−0.0427203
$973$	7.82801e15	0.287760
$974$	−6.24898e14	−0.0228420
$975$	1.06111e14	0.00385688
$976$	7.06354e15	0.255299
$977$	−1.84324e16	−0.662464	−0.331232	−	0.943549i	$-0.607464\pi$
$977$	−1.84324e16	−0.662464	−0.331232	+	0.943549i	$0.607464\pi$
$978$	1.91992e14	0.00686152
$979$	−5.28470e16	−1.87809
$980$	−5.68438e15	−0.200881
$981$	−1.64203e16	−0.577032
$982$	−1.21563e16	−0.424802
$983$	2.40762e16	0.836649	0.418324	−	0.908298i	$-0.362618\pi$
$983$	2.40762e16	0.836649	0.418324	+	0.908298i	$0.362618\pi$
$984$	3.65714e14	0.0126377
$985$	6.76806e15	0.232576
$986$	1.77198e16	0.605530
$987$	−3.06828e14	−0.0104268
$988$	5.03353e15	0.170102
$989$	−1.64360e16	−0.552352
$990$	−1.33876e16	−0.447413
$991$	1.41288e16	0.469569	0.234785	−	0.972047i	$-0.424562\pi$
$991$	1.41288e16	0.469569	0.234785	+	0.972047i	$0.424562\pi$
$992$	1.48855e15	0.0491982
$993$	2.90280e14	0.00954104
$994$	−2.18029e15	−0.0712673
$995$	4.02930e15	0.130979
$996$	8.35748e14	0.0270177
$997$	−1.24862e16	−0.401427	−0.200714	−	0.979650i	$-0.564326\pi$
$997$	−1.24862e16	−0.401427	−0.200714	+	0.979650i	$0.564326\pi$
$998$	−4.13507e16	−1.32210
$999$	2.45102e15	0.0779356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.a.a.1.1	✓	1
3.2	odd	2		90.12.a.g.1.1		1
4.3	odd	2		80.12.a.d.1.1		1
5.2	odd	4		50.12.b.c.49.1		2
5.3	odd	4		50.12.b.c.49.2		2
5.4	even	2		50.12.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.a.a.1.1	✓	1	1.1	even	1	trivial
50.12.a.d.1.1		1	5.4	even	2
50.12.b.c.49.1		2	5.2	odd	4
50.12.b.c.49.2		2	5.3	odd	4
80.12.a.d.1.1		1	4.3	odd	2
90.12.a.g.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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more