LMFDB - Embedded newform 10.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,10,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, 10, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
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:	$5.15035836164$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-16.0000 q^{2} -204.000 q^{3} +256.000 q^{4} +625.000 q^{5} +3264.00 q^{6} +5432.00 q^{7} -4096.00 q^{8} +21933.0 q^{9} +O(q^{10})$

\(q-16.0000 q^{2} -204.000 q^{3} +256.000 q^{4} +625.000 q^{5} +3264.00 q^{6} +5432.00 q^{7} -4096.00 q^{8} +21933.0 q^{9} -10000.0 q^{10} +73932.0 q^{11} -52224.0 q^{12} -114514. q^{13} -86912.0 q^{14} -127500. q^{15} +65536.0 q^{16} +41682.0 q^{17} -350928. q^{18} +1.05746e6 q^{19} +160000. q^{20} -1.10813e6 q^{21} -1.18291e6 q^{22} +1.59934e6 q^{23} +835584. q^{24} +390625. q^{25} +1.83222e6 q^{26} -459000. q^{27} +1.39059e6 q^{28} +2.18451e6 q^{29} +2.04000e6 q^{30} -9.61965e6 q^{31} -1.04858e6 q^{32} -1.50821e7 q^{33} -666912. q^{34} +3.39500e6 q^{35} +5.61485e6 q^{36} +4.79994e6 q^{37} -1.69194e7 q^{38} +2.33609e7 q^{39} -2.56000e6 q^{40} +9.53188e6 q^{41} +1.77300e7 q^{42} -1.34645e7 q^{43} +1.89266e7 q^{44} +1.37081e7 q^{45} -2.55894e7 q^{46} +1.14420e7 q^{47} -1.33693e7 q^{48} -1.08470e7 q^{49} -6.25000e6 q^{50} -8.50313e6 q^{51} -2.93156e7 q^{52} +5.36158e7 q^{53} +7.34400e6 q^{54} +4.62075e7 q^{55} -2.22495e7 q^{56} -2.15722e8 q^{57} -3.49522e7 q^{58} +8.18626e7 q^{59} -3.26400e7 q^{60} -1.04691e8 q^{61} +1.53914e8 q^{62} +1.19140e8 q^{63} +1.67772e7 q^{64} -7.15712e7 q^{65} +2.41314e8 q^{66} +1.40571e8 q^{67} +1.06706e7 q^{68} -3.26265e8 q^{69} -5.43200e7 q^{70} +9.70988e7 q^{71} -8.98376e7 q^{72} +1.71849e8 q^{73} -7.67991e7 q^{74} -7.96875e7 q^{75} +2.70710e8 q^{76} +4.01599e8 q^{77} -3.73774e8 q^{78} -1.17380e8 q^{79} +4.09600e7 q^{80} -3.38071e8 q^{81} -1.52510e8 q^{82} +3.23638e8 q^{83} -2.83681e8 q^{84} +2.60512e7 q^{85} +2.15432e8 q^{86} -4.45640e8 q^{87} -3.02825e8 q^{88} -8.94379e8 q^{89} -2.19330e8 q^{90} -6.22040e8 q^{91} +4.09430e8 q^{92} +1.96241e9 q^{93} -1.83071e8 q^{94} +6.60912e8 q^{95} +2.13910e8 q^{96} +2.32679e8 q^{97} +1.73552e8 q^{98} +1.62155e9 q^{99} +O(q^{100})\)

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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	−204.000	−1.45407	−0.727034	−	0.686602i	$-0.759102\pi$
$3$	−204.000	−1.45407	−0.727034	+	0.686602i	$0.759102\pi$
$4$	256.000	0.500000
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	3264.00	1.02818
$7$	5432.00	0.855103	0.427552	−	0.903991i	$-0.359376\pi$
$7$	5432.00	0.855103	0.427552	+	0.903991i	$0.359376\pi$
$8$	−4096.00	−0.353553
$9$	21933.0	1.11431
$10$	−10000.0	−0.316228
$11$	73932.0	1.52253	0.761264	−	0.648442i	$-0.224579\pi$
$11$	73932.0	1.52253	0.761264	+	0.648442i	$0.224579\pi$
$12$	−52224.0	−0.727034
$13$	−114514.	−1.11202	−0.556011	−	0.831175i	$-0.687669\pi$
$13$	−114514.	−1.11202	−0.556011	+	0.831175i	$0.687669\pi$
$14$	−86912.0	−0.604649
$15$	−127500.	−0.650279
$16$	65536.0	0.250000
$17$	41682.0	0.121040	0.0605199	−	0.998167i	$-0.480724\pi$
$17$	41682.0	0.121040	0.0605199	+	0.998167i	$0.480724\pi$
$18$	−350928.	−0.787937
$19$	1.05746e6	1.86154	0.930771	−	0.365603i	$-0.119137\pi$
$19$	1.05746e6	1.86154	0.930771	+	0.365603i	$0.119137\pi$
$20$	160000.	0.223607
$21$	−1.10813e6	−1.24338
$22$	−1.18291e6	−1.07659
$23$	1.59934e6	1.19169	0.595847	−	0.803098i	$-0.296817\pi$
$23$	1.59934e6	1.19169	0.595847	+	0.803098i	$0.296817\pi$
$24$	835584.	0.514090
$25$	390625.	0.200000
$26$	1.83222e6	0.786319
$27$	−459000.	−0.166217
$28$	1.39059e6	0.427552
$29$	2.18451e6	0.573539	0.286770	−	0.958000i	$-0.407419\pi$
$29$	2.18451e6	0.573539	0.286770	+	0.958000i	$0.407419\pi$
$30$	2.04000e6	0.459816
$31$	−9.61965e6	−1.87082	−0.935409	−	0.353567i	$-0.884968\pi$
$31$	−9.61965e6	−1.87082	−0.935409	+	0.353567i	$0.884968\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.50821e7	−2.21386
$34$	−666912.	−0.0855881
$35$	3.39500e6	0.382414
$36$	5.61485e6	0.557156
$37$	4.79994e6	0.421045	0.210522	−	0.977589i	$-0.432484\pi$
$37$	4.79994e6	0.421045	0.210522	+	0.977589i	$0.432484\pi$
$38$	−1.69194e7	−1.31631
$39$	2.33609e7	1.61696
$40$	−2.56000e6	−0.158114
$41$	9.53188e6	0.526807	0.263403	−	0.964686i	$-0.415155\pi$
$41$	9.53188e6	0.526807	0.263403	+	0.964686i	$0.415155\pi$
$42$	1.77300e7	0.879201
$43$	−1.34645e7	−0.600595	−0.300297	−	0.953846i	$-0.597086\pi$
$43$	−1.34645e7	−0.600595	−0.300297	+	0.953846i	$0.597086\pi$
$44$	1.89266e7	0.761264
$45$	1.37081e7	0.498335
$46$	−2.55894e7	−0.842654
$47$	1.14420e7	0.342027	0.171013	−	0.985269i	$-0.445296\pi$
$47$	1.14420e7	0.342027	0.171013	+	0.985269i	$0.445296\pi$
$48$	−1.33693e7	−0.363517
$49$	−1.08470e7	−0.268798
$50$	−6.25000e6	−0.141421
$51$	−8.50313e6	−0.176000
$52$	−2.93156e7	−0.556011
$53$	5.36158e7	0.933364	0.466682	−	0.884425i	$-0.345449\pi$
$53$	5.36158e7	0.933364	0.466682	+	0.884425i	$0.345449\pi$
$54$	7.34400e6	0.117533
$55$	4.62075e7	0.680895
$56$	−2.22495e7	−0.302325
$57$	−2.15722e8	−2.70681
$58$	−3.49522e7	−0.405553
$59$	8.18626e7	0.879532	0.439766	−	0.898112i	$-0.355061\pi$
$59$	8.18626e7	0.879532	0.439766	+	0.898112i	$0.355061\pi$
$60$	−3.26400e7	−0.325139
$61$	−1.04691e8	−0.968114	−0.484057	−	0.875037i	$-0.660837\pi$
$61$	−1.04691e8	−0.968114	−0.484057	+	0.875037i	$0.660837\pi$
$62$	1.53914e8	1.32287
$63$	1.19140e8	0.952852
$64$	1.67772e7	0.125000
$65$	−7.15712e7	−0.497311
$66$	2.41314e8	1.56543
$67$	1.40571e8	0.852235	0.426118	−	0.904668i	$-0.359881\pi$
$67$	1.40571e8	0.852235	0.426118	+	0.904668i	$0.359881\pi$
$68$	1.06706e7	0.0605199
$69$	−3.26265e8	−1.73280
$70$	−5.43200e7	−0.270407
$71$	9.70988e7	0.453473	0.226736	−	0.973956i	$-0.427194\pi$
$71$	9.70988e7	0.453473	0.226736	+	0.973956i	$0.427194\pi$
$72$	−8.98376e7	−0.393969
$73$	1.71849e8	0.708262	0.354131	−	0.935196i	$-0.384777\pi$
$73$	1.71849e8	0.708262	0.354131	+	0.935196i	$0.384777\pi$
$74$	−7.67991e7	−0.297724
$75$	−7.96875e7	−0.290813
$76$	2.70710e8	0.930771
$77$	4.01599e8	1.30192
$78$	−3.73774e8	−1.14336
$79$	−1.17380e8	−0.339057	−0.169528	−	0.985525i	$-0.554224\pi$
$79$	−1.17380e8	−0.339057	−0.169528	+	0.985525i	$0.554224\pi$
$80$	4.09600e7	0.111803
$81$	−3.38071e8	−0.872621
$82$	−1.52510e8	−0.372509
$83$	3.23638e8	0.748527	0.374264	−	0.927322i	$-0.377896\pi$
$83$	3.23638e8	0.748527	0.374264	+	0.927322i	$0.377896\pi$
$84$	−2.83681e8	−0.621689
$85$	2.60512e7	0.0541307
$86$	2.15432e8	0.424685
$87$	−4.45640e8	−0.833965
$88$	−3.02825e8	−0.538295
$89$	−8.94379e8	−1.51101	−0.755504	−	0.655144i	$-0.772608\pi$
$89$	−8.94379e8	−1.51101	−0.755504	+	0.655144i	$0.772608\pi$
$90$	−2.19330e8	−0.352376
$91$	−6.22040e8	−0.950894
$92$	4.09430e8	0.595847
$93$	1.96241e9	2.72030
$94$	−1.83071e8	−0.241849
$95$	6.60912e8	0.832507
$96$	2.13910e8	0.257045
$97$	2.32679e8	0.266860	0.133430	−	0.991058i	$-0.457401\pi$
$97$	2.32679e8	0.266860	0.133430	+	0.991058i	$0.457401\pi$
$98$	1.73552e8	0.190069
$99$	1.62155e9	1.69657
$100$	1.00000e8	0.100000
$101$	6.51288e8	0.622769	0.311384	−	0.950284i	$-0.399207\pi$
$101$	6.51288e8	0.622769	0.311384	+	0.950284i	$0.399207\pi$
$102$	1.36050e8	0.124451
$103$	−1.71129e9	−1.49815	−0.749076	−	0.662484i	$-0.769502\pi$
$103$	−1.71129e9	−1.49815	−0.749076	+	0.662484i	$0.769502\pi$
$104$	4.69049e8	0.393159
$105$	−6.92580e8	−0.556055
$106$	−8.57852e8	−0.659988
$107$	−1.31553e9	−0.970228	−0.485114	−	0.874451i	$-0.661222\pi$
$107$	−1.31553e9	−0.970228	−0.485114	+	0.874451i	$0.661222\pi$
$108$	−1.17504e8	−0.0831086
$109$	3.10670e8	0.210805	0.105402	−	0.994430i	$-0.466387\pi$
$109$	3.10670e8	0.210805	0.105402	+	0.994430i	$0.466387\pi$
$110$	−7.39320e8	−0.481466
$111$	−9.79188e8	−0.612227
$112$	3.55992e8	0.213776
$113$	−2.74850e9	−1.58578	−0.792889	−	0.609366i	$-0.791424\pi$
$113$	−2.74850e9	−1.58578	−0.792889	+	0.609366i	$0.791424\pi$
$114$	3.45155e9	1.91400
$115$	9.99585e8	0.532941
$116$	5.59235e8	0.286770
$117$	−2.51164e9	−1.23914
$118$	−1.30980e9	−0.621923
$119$	2.26417e8	0.103502
$120$	5.22240e8	0.229908
$121$	3.10799e9	1.31809
$122$	1.67506e9	0.684560
$123$	−1.94450e9	−0.766012
$124$	−2.46263e9	−0.935409
$125$	2.44141e8	0.0894427
$126$	−1.90624e9	−0.673768
$127$	2.64323e9	0.901608	0.450804	−	0.892623i	$-0.351137\pi$
$127$	2.64323e9	0.901608	0.450804	+	0.892623i	$0.351137\pi$
$128$	−2.68435e8	−0.0883883
$129$	2.74675e9	0.873305
$130$	1.14514e9	0.351652
$131$	−2.63724e9	−0.782401	−0.391201	−	0.920305i	$-0.627940\pi$
$131$	−2.63724e9	−0.782401	−0.391201	+	0.920305i	$0.627940\pi$
$132$	−3.86102e9	−1.10693
$133$	5.74412e9	1.59181
$134$	−2.24914e9	−0.602621
$135$	−2.86875e8	−0.0743346
$136$	−1.70729e8	−0.0427941
$137$	5.16539e9	1.25274	0.626370	−	0.779526i	$-0.284540\pi$
$137$	5.16539e9	1.25274	0.626370	+	0.779526i	$0.284540\pi$
$138$	5.22023e9	1.22528
$139$	2.76751e9	0.628815	0.314407	−	0.949288i	$-0.398194\pi$
$139$	2.76751e9	0.628815	0.314407	+	0.949288i	$0.398194\pi$
$140$	8.69120e8	0.191207
$141$	−2.33416e9	−0.497330
$142$	−1.55358e9	−0.320654
$143$	−8.46625e9	−1.69309
$144$	1.43740e9	0.278578
$145$	1.36532e9	0.256494
$146$	−2.74958e9	−0.500817
$147$	2.21278e9	0.390851
$148$	1.22879e9	0.210522
$149$	−6.04151e9	−1.00417	−0.502085	−	0.864818i	$-0.667434\pi$
$149$	−6.04151e9	−1.00417	−0.502085	+	0.864818i	$0.667434\pi$
$150$	1.27500e9	0.205636
$151$	4.07206e8	0.0637408	0.0318704	−	0.999492i	$-0.489854\pi$
$151$	4.07206e8	0.0637408	0.0318704	+	0.999492i	$0.489854\pi$
$152$	−4.33136e9	−0.658154
$153$	9.14211e8	0.134876
$154$	−6.42558e9	−0.920596
$155$	−6.01228e9	−0.836655
$156$	5.98038e9	0.808478
$157$	1.80938e8	0.0237674	0.0118837	−	0.999929i	$-0.496217\pi$
$157$	1.80938e8	0.0237674	0.0118837	+	0.999929i	$0.496217\pi$
$158$	1.87808e9	0.239749
$159$	−1.09376e10	−1.35717
$160$	−6.55360e8	−0.0790569
$161$	8.68759e9	1.01902
$162$	5.40914e9	0.617036
$163$	5.88002e9	0.652432	0.326216	−	0.945295i	$-0.394226\pi$
$163$	5.88002e9	0.652432	0.326216	+	0.945295i	$0.394226\pi$
$164$	2.44016e9	0.263403
$165$	−9.42633e9	−0.990068
$166$	−5.17820e9	−0.529289
$167$	1.36197e9	0.135501	0.0677507	−	0.997702i	$-0.478418\pi$
$167$	1.36197e9	0.135501	0.0677507	+	0.997702i	$0.478418\pi$
$168$	4.53889e9	0.439600
$169$	2.50896e9	0.236594
$170$	−4.16820e8	−0.0382762
$171$	2.31933e10	2.07434
$172$	−3.44691e9	−0.300297
$173$	−1.41778e10	−1.20338	−0.601688	−	0.798731i	$-0.705505\pi$
$173$	−1.41778e10	−1.20338	−0.601688	+	0.798731i	$0.705505\pi$
$174$	7.13024e9	0.589702
$175$	2.12188e9	0.171021
$176$	4.84521e9	0.380632
$177$	−1.67000e10	−1.27890
$178$	1.43101e10	1.06844
$179$	2.66456e9	0.193993	0.0969967	−	0.995285i	$-0.469076\pi$
$179$	2.66456e9	0.193993	0.0969967	+	0.995285i	$0.469076\pi$
$180$	3.50928e9	0.249168
$181$	−4.05446e9	−0.280789	−0.140394	−	0.990096i	$-0.544837\pi$
$181$	−4.05446e9	−0.280789	−0.140394	+	0.990096i	$0.544837\pi$
$182$	9.95264e9	0.672384
$183$	2.13570e10	1.40770
$184$	−6.55088e9	−0.421327
$185$	2.99996e9	0.188297
$186$	−3.13985e10	−1.92354
$187$	3.08163e9	0.184287
$188$	2.92914e9	0.171013
$189$	−2.49329e9	−0.142133
$190$	−1.05746e10	−0.588671
$191$	−1.01385e10	−0.551216	−0.275608	−	0.961270i	$-0.588879\pi$
$191$	−1.01385e10	−0.551216	−0.275608	+	0.961270i	$0.588879\pi$
$192$	−3.42255e9	−0.181758
$193$	−7.57686e9	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$193$	−7.57686e9	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$194$	−3.72286e9	−0.188699
$195$	1.46005e10	0.723124
$196$	−2.77683e9	−0.134399
$197$	−2.20768e8	−0.0104433	−0.00522166	−	0.999986i	$-0.501662\pi$
$197$	−2.20768e8	−0.0104433	−0.00522166	+	0.999986i	$0.501662\pi$
$198$	−2.59448e10	−1.19966
$199$	−2.99296e10	−1.35289	−0.676445	−	0.736493i	$-0.736481\pi$
$199$	−2.99296e10	−1.35289	−0.676445	+	0.736493i	$0.736481\pi$
$200$	−1.60000e9	−0.0707107
$201$	−2.86765e10	−1.23921
$202$	−1.04206e10	−0.440364
$203$	1.18663e10	0.490435
$204$	−2.17680e9	−0.0880001
$205$	5.95743e9	0.235595
$206$	2.73806e10	1.05935
$207$	3.50782e10	1.32792
$208$	−7.50479e9	−0.278006
$209$	7.81801e10	2.83425
$210$	1.10813e10	0.393191
$211$	2.92533e10	1.01602	0.508012	−	0.861350i	$-0.330381\pi$
$211$	2.92533e10	1.01602	0.508012	+	0.861350i	$0.330381\pi$
$212$	1.37256e10	0.466682
$213$	−1.98082e10	−0.659380
$214$	2.10485e10	0.686055
$215$	−8.41530e9	−0.268594
$216$	1.88006e9	0.0587666
$217$	−5.22539e10	−1.59974
$218$	−4.97072e9	−0.149061
$219$	−3.50572e10	−1.02986
$220$	1.18291e10	0.340448
$221$	−4.77317e9	−0.134599
$222$	1.56670e10	0.432910
$223$	−5.18482e10	−1.40398	−0.701991	−	0.712186i	$-0.747705\pi$
$223$	−5.18482e10	−1.40398	−0.701991	+	0.712186i	$0.747705\pi$
$224$	−5.69586e9	−0.151162
$225$	8.56758e9	0.222862
$226$	4.39760e10	1.12131
$227$	4.56273e10	1.14053	0.570267	−	0.821460i	$-0.306840\pi$
$227$	4.56273e10	1.14053	0.570267	+	0.821460i	$0.306840\pi$
$228$	−5.52248e10	−1.35340
$229$	6.21495e10	1.49341	0.746703	−	0.665158i	$-0.231636\pi$
$229$	6.21495e10	1.49341	0.746703	+	0.665158i	$0.231636\pi$
$230$	−1.59934e10	−0.376846
$231$	−8.19261e10	−1.89308
$232$	−8.94775e9	−0.202777
$233$	−3.72165e9	−0.0827245	−0.0413623	−	0.999144i	$-0.513170\pi$
$233$	−3.72165e9	−0.0827245	−0.0413623	+	0.999144i	$0.513170\pi$
$234$	4.01862e10	0.876204
$235$	7.15122e9	0.152959
$236$	2.09568e10	0.439766
$237$	2.39455e10	0.493011
$238$	−3.62267e9	−0.0731867
$239$	3.62221e9	0.0718098	0.0359049	−	0.999355i	$-0.488569\pi$
$239$	3.62221e9	0.0718098	0.0359049	+	0.999355i	$0.488569\pi$
$240$	−8.35584e9	−0.162570
$241$	−3.36556e10	−0.642660	−0.321330	−	0.946967i	$-0.604130\pi$
$241$	−3.36556e10	−0.642660	−0.321330	+	0.946967i	$0.604130\pi$
$242$	−4.97279e10	−0.932032
$243$	7.80010e10	1.43507
$244$	−2.68010e10	−0.484057
$245$	−6.77936e9	−0.120210
$246$	3.11121e10	0.541653
$247$	−1.21094e11	−2.07008
$248$	3.94021e10	0.661434
$249$	−6.60221e10	−1.08841
$250$	−3.90625e9	−0.0632456
$251$	−5.88110e10	−0.935248	−0.467624	−	0.883928i	$-0.654890\pi$
$251$	−5.88110e10	−0.935248	−0.467624	+	0.883928i	$0.654890\pi$
$252$	3.04999e10	0.476426
$253$	1.18242e11	1.81439
$254$	−4.22917e10	−0.637533
$255$	−5.31446e9	−0.0787096
$256$	4.29497e9	0.0625000
$257$	−7.52072e10	−1.07538	−0.537688	−	0.843144i	$-0.680702\pi$
$257$	−7.52072e10	−1.07538	−0.537688	+	0.843144i	$0.680702\pi$
$258$	−4.39481e10	−0.617520
$259$	2.60733e10	0.360037
$260$	−1.83222e10	−0.248656
$261$	4.79129e10	0.639101
$262$	4.21959e10	0.553241
$263$	−1.16316e10	−0.149913	−0.0749565	−	0.997187i	$-0.523882\pi$
$263$	−1.16316e10	−0.149913	−0.0749565	+	0.997187i	$0.523882\pi$
$264$	6.17764e10	0.782717
$265$	3.35099e10	0.417413
$266$	−9.19060e10	−1.12558
$267$	1.82453e11	2.19711
$268$	3.59862e10	0.426118
$269$	2.83871e10	0.330549	0.165275	−	0.986248i	$-0.447149\pi$
$269$	2.83871e10	0.330549	0.165275	+	0.986248i	$0.447149\pi$
$270$	4.59000e9	0.0525625
$271$	1.47987e11	1.66672	0.833361	−	0.552729i	$-0.186414\pi$
$271$	1.47987e11	1.66672	0.833361	+	0.552729i	$0.186414\pi$
$272$	2.73167e9	0.0302600
$273$	1.26896e11	1.38266
$274$	−8.26463e10	−0.885820
$275$	2.88797e10	0.304506
$276$	−8.35237e10	−0.866401
$277$	−7.58857e10	−0.774464	−0.387232	−	0.921982i	$-0.626569\pi$
$277$	−7.58857e10	−0.774464	−0.387232	+	0.921982i	$0.626569\pi$
$278$	−4.42802e10	−0.444639
$279$	−2.10988e11	−2.08467
$280$	−1.39059e10	−0.135204
$281$	1.72151e11	1.64714	0.823570	−	0.567215i	$-0.191979\pi$
$281$	1.72151e11	1.64714	0.823570	+	0.567215i	$0.191979\pi$
$282$	3.73465e10	0.351665
$283$	−1.49932e11	−1.38949	−0.694745	−	0.719256i	$-0.744483\pi$
$283$	−1.49932e11	−1.38949	−0.694745	+	0.719256i	$0.744483\pi$
$284$	2.48573e10	0.226736
$285$	−1.34826e11	−1.21052
$286$	1.35460e11	1.19719
$287$	5.17772e10	0.450474
$288$	−2.29984e10	−0.196984
$289$	−1.16850e11	−0.985349
$290$	−2.18451e10	−0.181369
$291$	−4.74664e10	−0.388032
$292$	4.39933e10	0.354131
$293$	9.51745e9	0.0754426	0.0377213	−	0.999288i	$-0.487990\pi$
$293$	9.51745e9	0.0754426	0.0377213	+	0.999288i	$0.487990\pi$
$294$	−3.54046e10	−0.276373
$295$	5.11641e10	0.393339
$296$	−1.96606e10	−0.148862
$297$	−3.39348e10	−0.253070
$298$	9.66642e10	0.710056
$299$	−1.83146e11	−1.32519
$300$	−2.04000e10	−0.145407
$301$	−7.31391e10	−0.513571
$302$	−6.51529e9	−0.0450716
$303$	−1.32863e11	−0.905547
$304$	6.93017e10	0.465385
$305$	−6.54321e10	−0.432954
$306$	−1.46274e10	−0.0953718
$307$	9.05900e10	0.582046	0.291023	−	0.956716i	$-0.406004\pi$
$307$	9.05900e10	0.582046	0.291023	+	0.956716i	$0.406004\pi$
$308$	1.02809e11	0.650959
$309$	3.49103e11	2.17841
$310$	9.61965e10	0.591605
$311$	−2.81285e11	−1.70500	−0.852501	−	0.522726i	$-0.824915\pi$
$311$	−2.81285e11	−1.70500	−0.852501	+	0.522726i	$0.824915\pi$
$312$	−9.56861e10	−0.571680
$313$	−9.11248e10	−0.536645	−0.268323	−	0.963329i	$-0.586469\pi$
$313$	−9.11248e10	−0.536645	−0.268323	+	0.963329i	$0.586469\pi$
$314$	−2.89501e9	−0.0168061
$315$	7.44625e10	0.426128
$316$	−3.00493e10	−0.169528
$317$	1.03167e11	0.573819	0.286909	−	0.957958i	$-0.407372\pi$
$317$	1.03167e11	0.573819	0.286909	+	0.957958i	$0.407372\pi$
$318$	1.75002e11	0.959667
$319$	1.61505e11	0.873230
$320$	1.04858e10	0.0559017
$321$	2.68368e11	1.41078
$322$	−1.39001e11	−0.720556
$323$	4.40770e10	0.225321
$324$	−8.65462e10	−0.436310
$325$	−4.47320e10	−0.222404
$326$	−9.40804e10	−0.461339
$327$	−6.33767e10	−0.306524
$328$	−3.90426e10	−0.186254
$329$	6.21527e10	0.292468
$330$	1.50821e11	0.700084
$331$	2.51080e11	1.14970	0.574851	−	0.818258i	$-0.305060\pi$
$331$	2.51080e11	1.14970	0.574851	+	0.818258i	$0.305060\pi$
$332$	8.28512e10	0.374264
$333$	1.05277e11	0.469175
$334$	−2.17916e10	−0.0958140
$335$	8.78569e10	0.381131
$336$	−7.26223e10	−0.310844
$337$	−4.04967e11	−1.71035	−0.855175	−	0.518339i	$-0.826550\pi$
$337$	−4.04967e11	−1.71035	−0.855175	+	0.518339i	$0.826550\pi$
$338$	−4.01433e10	−0.167297
$339$	5.60694e11	2.30583
$340$	6.66912e9	0.0270653
$341$	−7.11200e11	−2.84837
$342$	−3.71092e11	−1.46678
$343$	−2.78122e11	−1.08495
$344$	5.51505e10	0.212342
$345$	−2.03915e11	−0.774933
$346$	2.26845e11	0.850916
$347$	4.20848e11	1.55827	0.779134	−	0.626857i	$-0.215659\pi$
$347$	4.20848e11	1.55827	0.779134	+	0.626857i	$0.215659\pi$
$348$	−1.14084e11	−0.416982
$349$	−3.99383e11	−1.44104	−0.720518	−	0.693436i	$-0.756096\pi$
$349$	−3.99383e11	−1.44104	−0.720518	+	0.693436i	$0.756096\pi$
$350$	−3.39500e10	−0.120930
$351$	5.25619e10	0.184837
$352$	−7.75233e10	−0.269148
$353$	−7.88806e10	−0.270386	−0.135193	−	0.990819i	$-0.543165\pi$
$353$	−7.88806e10	−0.270386	−0.135193	+	0.990819i	$0.543165\pi$
$354$	2.67200e11	0.904318
$355$	6.06867e10	0.202799
$356$	−2.28961e11	−0.755504
$357$	−4.61890e10	−0.150498
$358$	−4.26330e10	−0.137174
$359$	1.39842e11	0.444337	0.222168	−	0.975008i	$-0.428686\pi$
$359$	1.39842e11	0.444337	0.222168	+	0.975008i	$0.428686\pi$
$360$	−5.61485e10	−0.176188
$361$	7.95534e11	2.46534
$362$	6.48714e10	0.198547
$363$	−6.34031e11	−1.91660
$364$	−1.59242e11	−0.475447
$365$	1.07406e11	0.316744
$366$	−3.41712e11	−0.995396
$367$	5.08662e11	1.46363	0.731816	−	0.681502i	$-0.238673\pi$
$367$	5.08662e11	1.46363	0.731816	+	0.681502i	$0.238673\pi$
$368$	1.04814e11	0.297923
$369$	2.09063e11	0.587027
$370$	−4.79994e10	−0.133146
$371$	2.91241e11	0.798123
$372$	5.02376e11	1.36015
$373$	−2.96761e11	−0.793810	−0.396905	−	0.917860i	$-0.629916\pi$
$373$	−2.96761e11	−0.793810	−0.396905	+	0.917860i	$0.629916\pi$
$374$	−4.93061e10	−0.130310
$375$	−4.98047e10	−0.130056
$376$	−4.68662e10	−0.120925
$377$	−2.50157e11	−0.637788
$378$	3.98926e10	0.100503
$379$	−4.53918e11	−1.13006	−0.565030	−	0.825071i	$-0.691135\pi$
$379$	−4.53918e11	−1.13006	−0.565030	+	0.825071i	$0.691135\pi$
$380$	1.69194e11	0.416253
$381$	−5.39219e11	−1.31100
$382$	1.62215e11	0.389768
$383$	2.67567e11	0.635387	0.317694	−	0.948193i	$-0.397092\pi$
$383$	2.67567e11	0.635387	0.317694	+	0.948193i	$0.397092\pi$
$384$	5.47608e10	0.128523
$385$	2.50999e11	0.582236
$386$	1.21230e11	0.277950
$387$	−2.95317e11	−0.669250
$388$	5.95657e10	0.133430
$389$	3.34750e11	0.741221	0.370610	−	0.928788i	$-0.379148\pi$
$389$	3.34750e11	0.741221	0.370610	+	0.928788i	$0.379148\pi$
$390$	−2.33609e11	−0.511326
$391$	6.66635e10	0.144242
$392$	4.44292e10	0.0950346
$393$	5.37998e11	1.13766
$394$	3.53229e9	0.00738454
$395$	−7.33626e10	−0.151631
$396$	4.15117e11	0.848286
$397$	−4.55573e11	−0.920451	−0.460226	−	0.887802i	$-0.652231\pi$
$397$	−4.55573e11	−0.920451	−0.460226	+	0.887802i	$0.652231\pi$
$398$	4.78874e11	0.956638
$399$	−1.17180e12	−2.31460
$400$	2.56000e10	0.0500000
$401$	2.18973e11	0.422904	0.211452	−	0.977388i	$-0.432181\pi$
$401$	2.18973e11	0.422904	0.211452	+	0.977388i	$0.432181\pi$
$402$	4.58824e11	0.876252
$403$	1.10158e12	2.08039
$404$	1.66730e11	0.311384
$405$	−2.11295e11	−0.390248
$406$	−1.89860e11	−0.346790
$407$	3.54869e11	0.641053
$408$	3.48288e10	0.0622254
$409$	−3.63048e11	−0.641519	−0.320760	−	0.947161i	$-0.603938\pi$
$409$	−3.63048e11	−0.641519	−0.320760	+	0.947161i	$0.603938\pi$
$410$	−9.53188e10	−0.166591
$411$	−1.05374e12	−1.82157
$412$	−4.38090e11	−0.749076
$413$	4.44678e11	0.752091
$414$	−5.61252e11	−0.938980
$415$	2.02274e11	0.334752
$416$	1.20077e11	0.196580
$417$	−5.64572e11	−0.914339
$418$	−1.25088e12	−2.00412
$419$	−1.14340e12	−1.81232	−0.906158	−	0.422939i	$-0.860999\pi$
$419$	−1.14340e12	−1.81232	−0.906158	+	0.422939i	$0.860999\pi$
$420$	−1.77300e11	−0.278028
$421$	6.58288e11	1.02128	0.510642	−	0.859793i	$-0.329408\pi$
$421$	6.58288e11	1.02128	0.510642	+	0.859793i	$0.329408\pi$
$422$	−4.68053e11	−0.718437
$423$	2.50956e11	0.381124
$424$	−2.19610e11	−0.329994
$425$	1.62820e10	0.0242080
$426$	3.16930e11	0.466252
$427$	−5.68683e11	−0.827837
$428$	−3.36776e11	−0.485114
$429$	1.72711e12	2.46186
$430$	1.34645e11	0.189925
$431$	−1.27825e11	−0.178430	−0.0892152	−	0.996012i	$-0.528436\pi$
$431$	−1.27825e11	−0.178430	−0.0892152	+	0.996012i	$0.528436\pi$
$432$	−3.00810e10	−0.0415543
$433$	−5.76786e10	−0.0788531	−0.0394266	−	0.999222i	$-0.512553\pi$
$433$	−5.76786e10	−0.0788531	−0.0394266	+	0.999222i	$0.512553\pi$
$434$	8.36063e11	1.13119
$435$	−2.78525e11	−0.372960
$436$	7.95315e10	0.105402
$437$	1.69123e12	2.21839
$438$	5.60915e11	0.728221
$439$	4.11418e11	0.528681	0.264340	−	0.964429i	$-0.414846\pi$
$439$	4.11418e11	0.528681	0.264340	+	0.964429i	$0.414846\pi$
$440$	−1.89266e11	−0.240733
$441$	−2.37907e11	−0.299525
$442$	7.63708e10	0.0951759
$443$	1.17254e11	0.144647	0.0723237	−	0.997381i	$-0.476959\pi$
$443$	1.17254e11	0.144647	0.0723237	+	0.997381i	$0.476959\pi$
$444$	−2.50672e11	−0.306114
$445$	−5.58987e11	−0.675743
$446$	8.29571e11	0.992766
$447$	1.23247e12	1.46013
$448$	9.11338e10	0.106888
$449$	9.15676e10	0.106325	0.0531623	−	0.998586i	$-0.483070\pi$
$449$	9.15676e10	0.106325	0.0531623	+	0.998586i	$0.483070\pi$
$450$	−1.37081e11	−0.157587
$451$	7.04711e11	0.802078
$452$	−7.03615e11	−0.792889
$453$	−8.30700e10	−0.0926834
$454$	−7.30036e11	−0.806479
$455$	−3.88775e11	−0.425253
$456$	8.83597e11	0.957001
$457$	−1.55029e12	−1.66261	−0.831305	−	0.555816i	$-0.812406\pi$
$457$	−1.55029e12	−1.66261	−0.831305	+	0.555816i	$0.812406\pi$
$458$	−9.94392e11	−1.05600
$459$	−1.91320e10	−0.0201189
$460$	2.55894e11	0.266471
$461$	−1.61825e12	−1.66875	−0.834374	−	0.551198i	$-0.814171\pi$
$461$	−1.61825e12	−1.66875	−0.834374	+	0.551198i	$0.814171\pi$
$462$	1.31082e12	1.33861
$463$	9.04370e11	0.914601	0.457301	−	0.889312i	$-0.348816\pi$
$463$	9.04370e11	0.914601	0.457301	+	0.889312i	$0.348816\pi$
$464$	1.43164e11	0.143385
$465$	1.22651e12	1.21655
$466$	5.95465e10	0.0584951
$467$	−1.28255e12	−1.24781	−0.623903	−	0.781502i	$-0.714454\pi$
$467$	−1.28255e12	−1.24781	−0.623903	+	0.781502i	$0.714454\pi$
$468$	−6.42979e11	−0.619570
$469$	7.63582e11	0.728749
$470$	−1.14420e11	−0.108158
$471$	−3.69113e10	−0.0345594
$472$	−3.35309e11	−0.310961
$473$	−9.95456e11	−0.914423
$474$	−3.83129e11	−0.348612
$475$	4.13070e11	0.372308
$476$	5.79627e10	0.0517508
$477$	1.17595e12	1.04006
$478$	−5.79554e10	−0.0507772
$479$	−5.31423e11	−0.461244	−0.230622	−	0.973043i	$-0.574076\pi$
$479$	−5.31423e11	−0.461244	−0.230622	+	0.973043i	$0.574076\pi$
$480$	1.33693e11	0.114954
$481$	−5.49661e11	−0.468211
$482$	5.38490e11	0.454429
$483$	−1.77227e12	−1.48172
$484$	7.95646e11	0.659046
$485$	1.45424e11	0.119343
$486$	−1.24802e12	−1.01475
$487$	−1.10916e12	−0.893539	−0.446770	−	0.894649i	$-0.647426\pi$
$487$	−1.10916e12	−0.893539	−0.446770	+	0.894649i	$0.647426\pi$
$488$	4.28816e11	0.342280
$489$	−1.19953e12	−0.948679
$490$	1.08470e11	0.0850015
$491$	−9.04143e11	−0.702054	−0.351027	−	0.936365i	$-0.614168\pi$
$491$	−9.04143e11	−0.702054	−0.351027	+	0.936365i	$0.614168\pi$
$492$	−4.97793e11	−0.383006
$493$	9.10547e10	0.0694211
$494$	1.93750e12	1.46376
$495$	1.01347e12	0.758730
$496$	−6.30433e11	−0.467705
$497$	5.27441e11	0.387766
$498$	1.05635e12	0.769621
$499$	1.01146e12	0.730290	0.365145	−	0.930951i	$-0.381019\pi$
$499$	1.01146e12	0.730290	0.365145	+	0.930951i	$0.381019\pi$
$500$	6.25000e10	0.0447214
$501$	−2.77842e11	−0.197028
$502$	9.40975e11	0.661320
$503$	1.26417e11	0.0880538	0.0440269	−	0.999030i	$-0.485981\pi$
$503$	1.26417e11	0.0880538	0.0440269	+	0.999030i	$0.485981\pi$
$504$	−4.87998e11	−0.336884
$505$	4.07055e11	0.278511
$506$	−1.89187e12	−1.28297
$507$	−5.11827e11	−0.344023
$508$	6.76666e11	0.450804
$509$	−4.08226e11	−0.269569	−0.134785	−	0.990875i	$-0.543034\pi$
$509$	−4.08226e11	−0.269569	−0.134785	+	0.990875i	$0.543034\pi$
$510$	8.50313e10	0.0556561
$511$	9.33483e11	0.605637
$512$	−6.87195e10	−0.0441942
$513$	−4.85374e11	−0.309420
$514$	1.20332e12	0.760406
$515$	−1.06956e12	−0.669994
$516$	7.03169e11	0.436653
$517$	8.45926e11	0.520745
$518$	−4.17173e11	−0.254584
$519$	2.89227e12	1.74979
$520$	2.93156e11	0.175826
$521$	2.96958e12	1.76573	0.882867	−	0.469624i	$-0.155610\pi$
$521$	2.96958e12	1.76573	0.882867	+	0.469624i	$0.155610\pi$
$522$	−7.66606e11	−0.451913
$523$	−4.01653e11	−0.234743	−0.117372	−	0.993088i	$-0.537447\pi$
$523$	−4.01653e11	−0.234743	−0.117372	+	0.993088i	$0.537447\pi$
$524$	−6.75134e11	−0.391201
$525$	−4.32862e11	−0.248676
$526$	1.86106e11	0.106004
$527$	−4.00966e11	−0.226444
$528$	−9.88422e11	−0.553465
$529$	7.56723e11	0.420133
$530$	−5.36158e11	−0.295156
$531$	1.79549e12	0.980073
$532$	1.47050e12	0.795905
$533$	−1.09153e12	−0.585821
$534$	−2.91925e12	−1.55359
$535$	−8.22206e11	−0.433899
$536$	−5.75779e11	−0.301311
$537$	−5.43571e11	−0.282080
$538$	−4.54194e11	−0.233734
$539$	−8.01939e11	−0.409253
$540$	−7.34400e10	−0.0371673
$541$	−6.35088e11	−0.318747	−0.159374	−	0.987218i	$-0.550947\pi$
$541$	−6.35088e11	−0.318747	−0.159374	+	0.987218i	$0.550947\pi$
$542$	−2.36780e12	−1.17855
$543$	8.27110e11	0.408285
$544$	−4.37067e10	−0.0213970
$545$	1.94169e11	0.0942747
$546$	−2.03034e12	−0.977691
$547$	2.74387e12	1.31045	0.655224	−	0.755434i	$-0.272574\pi$
$547$	2.74387e12	1.31045	0.655224	+	0.755434i	$0.272574\pi$
$548$	1.32234e12	0.626370
$549$	−2.29619e12	−1.07878
$550$	−4.62075e11	−0.215318
$551$	2.31003e12	1.06767
$552$	1.33638e12	0.612638
$553$	−6.37609e11	−0.289929
$554$	1.21417e12	0.547629
$555$	−6.11993e11	−0.273796
$556$	7.08483e11	0.314407
$557$	−1.31358e12	−0.578238	−0.289119	−	0.957293i	$-0.593362\pi$
$557$	−1.31358e12	−0.578238	−0.289119	+	0.957293i	$0.593362\pi$
$558$	3.37580e12	1.47409
$559$	1.54187e12	0.667875
$560$	2.22495e11	0.0956035
$561$	−6.28653e11	−0.267965
$562$	−2.75441e12	−1.16470
$563$	−3.11100e12	−1.30500	−0.652502	−	0.757787i	$-0.726281\pi$
$563$	−3.11100e12	−1.30500	−0.652502	+	0.757787i	$0.726281\pi$
$564$	−5.97545e11	−0.248665
$565$	−1.71781e12	−0.709182
$566$	2.39891e12	0.982518
$567$	−1.83640e12	−0.746181
$568$	−3.97717e11	−0.160327
$569$	−1.45889e12	−0.583470	−0.291735	−	0.956499i	$-0.594233\pi$
$569$	−1.45889e12	−0.583470	−0.291735	+	0.956499i	$0.594233\pi$
$570$	2.15722e12	0.855967
$571$	−3.94710e12	−1.55387	−0.776936	−	0.629579i	$-0.783227\pi$
$571$	−3.94710e12	−1.55387	−0.776936	+	0.629579i	$0.783227\pi$
$572$	−2.16736e12	−0.846543
$573$	2.06824e12	0.801505
$574$	−8.28435e11	−0.318533
$575$	6.24741e11	0.238339
$576$	3.67975e11	0.139289
$577$	−5.27904e11	−0.198273	−0.0991365	−	0.995074i	$-0.531608\pi$
$577$	−5.27904e11	−0.198273	−0.0991365	+	0.995074i	$0.531608\pi$
$578$	1.86961e12	0.696747
$579$	1.54568e12	0.571565
$580$	3.49522e11	0.128247
$581$	1.75800e12	0.640068
$582$	7.59463e11	0.274380
$583$	3.96392e12	1.42107
$584$	−7.03893e11	−0.250408
$585$	−1.56977e12	−0.554160
$586$	−1.52279e11	−0.0533460
$587$	4.56943e12	1.58851	0.794255	−	0.607584i	$-0.207861\pi$
$587$	4.56943e12	1.58851	0.794255	+	0.607584i	$0.207861\pi$
$588$	5.66473e11	0.195425
$589$	−1.01724e13	−3.48261
$590$	−8.18626e11	−0.278132
$591$	4.50367e10	0.0151853
$592$	3.14569e11	0.105261
$593$	3.19168e12	1.05992	0.529960	−	0.848022i	$-0.322207\pi$
$593$	3.19168e12	1.05992	0.529960	+	0.848022i	$0.322207\pi$
$594$	5.42957e11	0.178948
$595$	1.41510e11	0.0462873
$596$	−1.54663e12	−0.502085
$597$	6.10565e12	1.96719
$598$	2.93034e12	0.937050
$599$	2.72611e12	0.865211	0.432605	−	0.901583i	$-0.357594\pi$
$599$	2.72611e12	0.865211	0.432605	+	0.901583i	$0.357594\pi$
$600$	3.26400e11	0.102818
$601$	1.16094e11	0.0362974	0.0181487	−	0.999835i	$-0.494223\pi$
$601$	1.16094e11	0.0362974	0.0181487	+	0.999835i	$0.494223\pi$
$602$	1.17023e12	0.363149
$603$	3.08315e12	0.949656
$604$	1.04245e11	0.0318704
$605$	1.94250e12	0.589469
$606$	2.12580e12	0.640319
$607$	−3.81951e12	−1.14198	−0.570990	−	0.820957i	$-0.693441\pi$
$607$	−3.81951e12	−1.14198	−0.570990	+	0.820957i	$0.693441\pi$
$608$	−1.10883e12	−0.329077
$609$	−2.42072e12	−0.713126
$610$	1.04691e12	0.306144
$611$	−1.31026e12	−0.380341
$612$	2.34038e11	0.0674381
$613$	−3.74021e12	−1.06985	−0.534926	−	0.844899i	$-0.679660\pi$
$613$	−3.74021e12	−1.06985	−0.534926	+	0.844899i	$0.679660\pi$
$614$	−1.44944e12	−0.411569
$615$	−1.21531e12	−0.342571
$616$	−1.64495e12	−0.460298
$617$	6.24435e12	1.73462	0.867310	−	0.497769i	$-0.165847\pi$
$617$	6.24435e12	1.73462	0.867310	+	0.497769i	$0.165847\pi$
$618$	−5.58565e12	−1.54037
$619$	4.46634e12	1.22277	0.611383	−	0.791335i	$-0.290613\pi$
$619$	4.46634e12	1.22277	0.611383	+	0.791335i	$0.290613\pi$
$620$	−1.53914e12	−0.418328
$621$	−7.34095e11	−0.198080
$622$	4.50056e12	1.20562
$623$	−4.85827e12	−1.29207
$624$	1.53098e12	0.404239
$625$	1.52588e11	0.0400000
$626$	1.45800e12	0.379465
$627$	−1.59487e13	−4.12119
$628$	4.63201e10	0.0118837
$629$	2.00071e11	0.0509632
$630$	−1.19140e12	−0.301318
$631$	−3.08003e12	−0.773434	−0.386717	−	0.922198i	$-0.626391\pi$
$631$	−3.08003e12	−0.773434	−0.386717	+	0.922198i	$0.626391\pi$
$632$	4.80789e11	0.119875
$633$	−5.96767e12	−1.47737
$634$	−1.65067e12	−0.405751
$635$	1.65202e12	0.403212
$636$	−2.80003e12	−0.678587
$637$	1.24213e12	0.298910
$638$	−2.58408e12	−0.617467
$639$	2.12967e12	0.505310
$640$	−1.67772e11	−0.0395285
$641$	7.87684e12	1.84285	0.921427	−	0.388552i	$-0.127025\pi$
$641$	7.87684e12	1.84285	0.921427	+	0.388552i	$0.127025\pi$
$642$	−4.29389e12	−0.997570
$643$	−2.80833e12	−0.647886	−0.323943	−	0.946077i	$-0.605009\pi$
$643$	−2.80833e12	−0.647886	−0.323943	+	0.946077i	$0.605009\pi$
$644$	2.22402e12	0.509510
$645$	1.71672e12	0.390554
$646$	−7.05233e11	−0.159326
$647$	2.03365e12	0.456254	0.228127	−	0.973631i	$-0.426740\pi$
$647$	2.03365e12	0.456254	0.228127	+	0.973631i	$0.426740\pi$
$648$	1.38474e12	0.308518
$649$	6.05227e12	1.33911
$650$	7.15712e11	0.157264
$651$	1.06598e13	2.32613
$652$	1.50529e12	0.326216
$653$	5.29056e12	1.13865	0.569327	−	0.822111i	$-0.307204\pi$
$653$	5.29056e12	1.13865	0.569327	+	0.822111i	$0.307204\pi$
$654$	1.01403e12	0.216745
$655$	−1.64828e12	−0.349900
$656$	6.24681e11	0.131702
$657$	3.76916e12	0.789225
$658$	−9.94443e11	−0.206806
$659$	−5.06766e12	−1.04670	−0.523351	−	0.852117i	$-0.675318\pi$
$659$	−5.06766e12	−1.04670	−0.523351	+	0.852117i	$0.675318\pi$
$660$	−2.41314e12	−0.495034
$661$	−6.05804e12	−1.23431	−0.617157	−	0.786840i	$-0.711716\pi$
$661$	−6.05804e12	−1.23431	−0.617157	+	0.786840i	$0.711716\pi$
$662$	−4.01728e12	−0.812963
$663$	9.73727e11	0.195716
$664$	−1.32562e12	−0.264644
$665$	3.59008e12	0.711879
$666$	−1.68443e12	−0.331757
$667$	3.49377e12	0.683483
$668$	3.48665e11	0.0677507
$669$	1.05770e13	2.04149
$670$	−1.40571e12	−0.269500
$671$	−7.74004e12	−1.47398
$672$	1.16196e12	0.219800
$673$	5.03218e12	0.945559	0.472779	−	0.881181i	$-0.343251\pi$
$673$	5.03218e12	0.945559	0.472779	+	0.881181i	$0.343251\pi$
$674$	6.47947e12	1.20940
$675$	−1.79297e11	−0.0332434
$676$	6.42293e11	0.118297
$677$	−8.61276e12	−1.57577	−0.787886	−	0.615821i	$-0.788824\pi$
$677$	−8.61276e12	−1.57577	−0.787886	+	0.615821i	$0.788824\pi$
$678$	−8.97110e12	−1.63047
$679$	1.26391e12	0.228193
$680$	−1.06706e11	−0.0191381
$681$	−9.30796e12	−1.65841
$682$	1.13792e13	2.01410
$683$	−3.37706e11	−0.0593807	−0.0296903	−	0.999559i	$-0.509452\pi$
$683$	−3.37706e11	−0.0593807	−0.0296903	+	0.999559i	$0.509452\pi$
$684$	5.93748e12	1.03717
$685$	3.22837e12	0.560242
$686$	4.44995e12	0.767178
$687$	−1.26785e13	−2.17151
$688$	−8.82408e11	−0.150149
$689$	−6.13976e12	−1.03792
$690$	3.26265e12	0.547960
$691$	1.74896e11	0.0291830	0.0145915	−	0.999894i	$-0.495355\pi$
$691$	1.74896e11	0.0291830	0.0145915	+	0.999894i	$0.495355\pi$
$692$	−3.62952e12	−0.601688
$693$	8.80826e12	1.45074
$694$	−6.73356e12	−1.10186
$695$	1.72969e12	0.281214
$696$	1.82534e12	0.294851
$697$	3.97308e11	0.0637646
$698$	6.39012e12	1.01897
$699$	7.59217e11	0.120287
$700$	5.43200e11	0.0855103
$701$	−5.36577e12	−0.839269	−0.419634	−	0.907693i	$-0.637842\pi$
$701$	−5.36577e12	−0.839269	−0.419634	+	0.907693i	$0.637842\pi$
$702$	−8.40991e11	−0.130700
$703$	5.07575e12	0.783792
$704$	1.24037e12	0.190316
$705$	−1.45885e12	−0.222413
$706$	1.26209e12	0.191192
$707$	3.53779e12	0.532531
$708$	−4.27519e12	−0.639449
$709$	5.45452e12	0.810679	0.405339	−	0.914166i	$-0.367153\pi$
$709$	5.45452e12	0.810679	0.405339	+	0.914166i	$0.367153\pi$
$710$	−9.70988e11	−0.143401
$711$	−2.57450e12	−0.377815
$712$	3.66338e12	0.534222
$713$	−1.53850e13	−2.22944
$714$	7.39024e11	0.106418
$715$	−5.29141e12	−0.757171
$716$	6.82128e11	0.0969967
$717$	−7.38932e11	−0.104416
$718$	−2.23747e12	−0.314194
$719$	−6.60953e12	−0.922339	−0.461169	−	0.887312i	$-0.652570\pi$
$719$	−6.60953e12	−0.922339	−0.461169	+	0.887312i	$0.652570\pi$
$720$	8.98376e11	0.124584
$721$	−9.29572e12	−1.28107
$722$	−1.27285e13	−1.74326
$723$	6.86575e12	0.934471
$724$	−1.03794e12	−0.140394
$725$	8.53324e11	0.114708
$726$	1.01445e13	1.35524
$727$	1.12652e13	1.49566	0.747832	−	0.663888i	$-0.231095\pi$
$727$	1.12652e13	1.49566	0.747832	+	0.663888i	$0.231095\pi$
$728$	2.54788e12	0.336192
$729$	−9.25795e12	−1.21406
$730$	−1.71849e12	−0.223972
$731$	−5.61227e11	−0.0726959
$732$	5.46740e12	0.703851
$733$	−1.55010e13	−1.98332	−0.991659	−	0.128890i	$-0.958859\pi$
$733$	−1.55010e13	−1.98332	−0.991659	+	0.128890i	$0.958859\pi$
$734$	−8.13859e12	−1.03494
$735$	1.38299e12	0.174794
$736$	−1.67703e12	−0.210664
$737$	1.03927e13	1.29755
$738$	−3.34500e12	−0.415091
$739$	8.86702e12	1.09365	0.546824	−	0.837247i	$-0.315837\pi$
$739$	8.86702e12	1.09365	0.546824	+	0.837247i	$0.315837\pi$
$740$	7.67991e11	0.0941485
$741$	2.47032e13	3.01003
$742$	−4.65985e12	−0.564358
$743$	1.04586e13	1.25900	0.629500	−	0.777001i	$-0.283260\pi$
$743$	1.04586e13	1.25900	0.629500	+	0.777001i	$0.283260\pi$
$744$	−8.03802e12	−0.961770
$745$	−3.77595e12	−0.449079
$746$	4.74817e12	0.561309
$747$	7.09834e12	0.834093
$748$	7.88898e11	0.0921433
$749$	−7.14596e12	−0.829645
$750$	7.96875e11	0.0919633
$751$	3.37332e11	0.0386971	0.0193485	−	0.999813i	$-0.493841\pi$
$751$	3.37332e11	0.0386971	0.0193485	+	0.999813i	$0.493841\pi$
$752$	7.49860e11	0.0855066
$753$	1.19974e13	1.35991
$754$	4.00251e12	0.450984
$755$	2.54504e11	0.0285058
$756$	−6.38282e11	−0.0710664
$757$	1.61864e12	0.179151	0.0895756	−	0.995980i	$-0.471449\pi$
$757$	1.61864e12	0.179151	0.0895756	+	0.995980i	$0.471449\pi$
$758$	7.26269e12	0.799073
$759$	−2.41214e13	−2.63824
$760$	−2.70710e12	−0.294336
$761$	−3.16676e12	−0.342282	−0.171141	−	0.985247i	$-0.554745\pi$
$761$	−3.16676e12	−0.342282	−0.171141	+	0.985247i	$0.554745\pi$
$762$	8.62750e12	0.927016
$763$	1.68756e12	0.180260
$764$	−2.59544e12	−0.275608
$765$	5.71382e11	0.0603184
$766$	−4.28108e12	−0.449287
$767$	−9.37442e12	−0.978059
$768$	−8.76173e11	−0.0908792
$769$	9.41136e12	0.970474	0.485237	−	0.874383i	$-0.338733\pi$
$769$	9.41136e12	0.970474	0.485237	+	0.874383i	$0.338733\pi$
$770$	−4.01599e12	−0.411703
$771$	1.53423e13	1.56367
$772$	−1.93967e12	−0.196540
$773$	−3.00421e12	−0.302638	−0.151319	−	0.988485i	$-0.548352\pi$
$773$	−3.00421e12	−0.302638	−0.151319	+	0.988485i	$0.548352\pi$
$774$	4.72506e12	0.473231
$775$	−3.75768e12	−0.374164
$776$	−9.53051e11	−0.0943493
$777$	−5.31895e12	−0.523518
$778$	−5.35600e12	−0.524122
$779$	1.00796e13	0.980673
$780$	3.73774e12	0.361562
$781$	7.17871e12	0.690425
$782$	−1.06662e12	−0.101995
$783$	−1.00269e12	−0.0953320
$784$	−7.10868e11	−0.0671996
$785$	1.13086e11	0.0106291
$786$	−8.60796e12	−0.804450
$787$	4.78765e12	0.444873	0.222436	−	0.974947i	$-0.428599\pi$
$787$	4.78765e12	0.444873	0.222436	+	0.974947i	$0.428599\pi$
$788$	−5.65167e10	−0.00522166
$789$	2.37285e12	0.217983
$790$	1.17380e12	0.107219
$791$	−1.49298e13	−1.35600
$792$	−6.64187e12	−0.599829
$793$	1.19886e13	1.07656
$794$	7.28917e12	0.650857
$795$	−6.83601e12	−0.606947
$796$	−7.66199e12	−0.676445
$797$	−8.82657e12	−0.774871	−0.387436	−	0.921897i	$-0.626639\pi$
$797$	−8.82657e12	−0.774871	−0.387436	+	0.921897i	$0.626639\pi$
$798$	1.87488e13	1.63667
$799$	4.76923e11	0.0413988
$800$	−4.09600e11	−0.0353553
$801$	−1.96164e13	−1.68373
$802$	−3.50358e12	−0.299038
$803$	1.27051e13	1.07835
$804$	−7.34118e12	−0.619604
$805$	5.42975e12	0.455720
$806$	−1.76253e13	−1.47106
$807$	−5.79097e12	−0.480641
$808$	−2.66767e12	−0.220182
$809$	−4.75875e12	−0.390593	−0.195296	−	0.980744i	$-0.562567\pi$
$809$	−4.75875e12	−0.390593	−0.195296	+	0.980744i	$0.562567\pi$
$810$	3.38071e12	0.275947
$811$	1.32270e13	1.07366	0.536831	−	0.843690i	$-0.319621\pi$
$811$	1.32270e13	1.07366	0.536831	+	0.843690i	$0.319621\pi$
$812$	3.03776e12	0.245218
$813$	−3.01894e13	−2.42353
$814$	−5.67791e12	−0.453293
$815$	3.67502e12	0.291776
$816$	−5.57261e11	−0.0440000
$817$	−1.42382e13	−1.11803
$818$	5.80877e12	0.453623
$819$	−1.36432e13	−1.05959
$820$	1.52510e12	0.117798
$821$	1.96204e13	1.50717	0.753587	−	0.657348i	$-0.228322\pi$
$821$	1.96204e13	1.50717	0.753587	+	0.657348i	$0.228322\pi$
$822$	1.68598e13	1.28804
$823$	1.44369e12	0.109692	0.0548461	−	0.998495i	$-0.482533\pi$
$823$	1.44369e12	0.109692	0.0548461	+	0.998495i	$0.482533\pi$
$824$	7.00944e12	0.529677
$825$	−5.89146e12	−0.442772
$826$	−7.11484e12	−0.531808
$827$	−6.15968e12	−0.457913	−0.228957	−	0.973437i	$-0.573531\pi$
$827$	−6.15968e12	−0.457913	−0.228957	+	0.973437i	$0.573531\pi$
$828$	8.98003e12	0.663959
$829$	−7.89482e12	−0.580560	−0.290280	−	0.956942i	$-0.593748\pi$
$829$	−7.89482e12	−0.580560	−0.290280	+	0.956942i	$0.593748\pi$
$830$	−3.23638e12	−0.236705
$831$	1.54807e13	1.12612
$832$	−1.92123e12	−0.139003
$833$	−4.52124e11	−0.0325353
$834$	9.03315e12	0.646535
$835$	8.51232e11	0.0605981
$836$	2.00141e13	1.41712
$837$	4.41542e12	0.310962
$838$	1.82944e13	1.28150
$839$	1.39455e13	0.971642	0.485821	−	0.874058i	$-0.338521\pi$
$839$	1.39455e13	0.971642	0.485821	+	0.874058i	$0.338521\pi$
$840$	2.83681e12	0.196595
$841$	−9.73506e12	−0.671053
$842$	−1.05326e13	−0.722157
$843$	−3.51188e13	−2.39505
$844$	7.48884e12	0.508012
$845$	1.56810e12	0.105808
$846$	−4.01530e12	−0.269495
$847$	1.68826e13	1.12711
$848$	3.51376e12	0.233341
$849$	3.05861e13	2.02041
$850$	−2.60512e11	−0.0171176
$851$	7.67672e12	0.501756
$852$	−5.07089e12	−0.329690
$853$	2.06868e12	0.133789	0.0668947	−	0.997760i	$-0.478691\pi$
$853$	2.06868e12	0.133789	0.0668947	+	0.997760i	$0.478691\pi$
$854$	9.09893e12	0.585369
$855$	1.44958e13	0.927672
$856$	5.38841e12	0.343027
$857$	1.27749e13	0.808989	0.404494	−	0.914540i	$-0.367447\pi$
$857$	1.27749e13	0.808989	0.404494	+	0.914540i	$0.367447\pi$
$858$	−2.76338e13	−1.74080
$859$	2.44751e13	1.53376	0.766878	−	0.641793i	$-0.221809\pi$
$859$	2.44751e13	1.53376	0.766878	+	0.641793i	$0.221809\pi$
$860$	−2.15432e12	−0.134297
$861$	−1.05625e13	−0.655020
$862$	2.04520e12	0.126169
$863$	−3.04987e13	−1.87169	−0.935843	−	0.352417i	$-0.885360\pi$
$863$	−3.04987e13	−1.87169	−0.935843	+	0.352417i	$0.885360\pi$
$864$	4.81296e11	0.0293833
$865$	−8.86113e12	−0.538167
$866$	9.22857e11	0.0557576
$867$	2.38375e13	1.43276
$868$	−1.33770e13	−0.799871
$869$	−8.67814e12	−0.516224
$870$	4.45640e12	0.263723
$871$	−1.60974e13	−0.947704
$872$	−1.27250e12	−0.0745307
$873$	5.10334e12	0.297365
$874$	−2.70597e13	−1.56864
$875$	1.32617e12	0.0764828
$876$	−8.97464e12	−0.514930
$877$	−3.32305e13	−1.89688	−0.948439	−	0.316960i	$-0.897338\pi$
$877$	−3.32305e13	−1.89688	−0.948439	+	0.316960i	$0.897338\pi$
$878$	−6.58270e12	−0.373834
$879$	−1.94156e12	−0.109699
$880$	3.02825e12	0.170224
$881$	1.65219e13	0.923995	0.461998	−	0.886881i	$-0.347133\pi$
$881$	1.65219e13	0.923995	0.461998	+	0.886881i	$0.347133\pi$
$882$	3.80651e12	0.211796
$883$	−2.19061e13	−1.21267	−0.606333	−	0.795211i	$-0.707360\pi$
$883$	−2.19061e13	−1.21267	−0.606333	+	0.795211i	$0.707360\pi$
$884$	−1.22193e12	−0.0672995
$885$	−1.04375e13	−0.571941
$886$	−1.87606e12	−0.102281
$887$	1.63192e13	0.885203	0.442601	−	0.896718i	$-0.354056\pi$
$887$	1.63192e13	0.885203	0.442601	+	0.896718i	$0.354056\pi$
$888$	4.01075e12	0.216455
$889$	1.43580e13	0.770968
$890$	8.94379e12	0.477823
$891$	−2.49943e13	−1.32859
$892$	−1.32731e13	−0.701991
$893$	1.20994e13	0.636697
$894$	−1.97195e13	−1.03247
$895$	1.66535e12	0.0867565
$896$	−1.45814e12	−0.0755812
$897$	3.73619e13	1.92691
$898$	−1.46508e12	−0.0751828
$899$	−2.10142e13	−1.07299
$900$	2.19330e12	0.111431
$901$	2.23481e12	0.112974
$902$	−1.12754e13	−0.567155
$903$	1.49204e13	0.746766
$904$	1.12578e13	0.560657
$905$	−2.53404e12	−0.125572
$906$	1.32912e12	0.0655371
$907$	−1.98103e12	−0.0971980	−0.0485990	−	0.998818i	$-0.515476\pi$
$907$	−1.98103e12	−0.0971980	−0.0485990	+	0.998818i	$0.515476\pi$
$908$	1.16806e13	0.570267
$909$	1.42847e13	0.693958
$910$	6.22040e12	0.300699
$911$	−1.60376e12	−0.0771446	−0.0385723	−	0.999256i	$-0.512281\pi$
$911$	−1.60376e12	−0.0771446	−0.0385723	+	0.999256i	$0.512281\pi$
$912$	−1.41375e13	−0.676702
$913$	2.39272e13	1.13965
$914$	2.48047e13	1.17564
$915$	1.33481e13	0.629544
$916$	1.59103e13	0.746703
$917$	−1.43255e13	−0.669034
$918$	3.06113e11	0.0142262
$919$	−2.81428e13	−1.30151	−0.650755	−	0.759288i	$-0.725548\pi$
$919$	−2.81428e13	−1.30151	−0.650755	+	0.759288i	$0.725548\pi$
$920$	−4.09430e12	−0.188423
$921$	−1.84804e13	−0.846335
$922$	2.58920e13	1.17998
$923$	−1.11192e13	−0.504272
$924$	−2.09731e13	−0.946539
$925$	1.87498e12	0.0842089
$926$	−1.44699e13	−0.646721
$927$	−3.75337e13	−1.66941
$928$	−2.29062e12	−0.101388
$929$	−5.39418e12	−0.237605	−0.118802	−	0.992918i	$-0.537905\pi$
$929$	−5.39418e12	−0.237605	−0.118802	+	0.992918i	$0.537905\pi$
$930$	−1.96241e13	−0.860233
$931$	−1.14703e13	−0.500379
$932$	−9.52743e11	−0.0413623
$933$	5.73821e13	2.47919
$934$	2.05208e13	0.882333
$935$	1.92602e12	0.0824155
$936$	1.02877e13	0.438102
$937$	−1.25051e13	−0.529978	−0.264989	−	0.964251i	$-0.585368\pi$
$937$	−1.25051e13	−0.529978	−0.264989	+	0.964251i	$0.585368\pi$
$938$	−1.22173e13	−0.515303
$939$	1.85895e13	0.780318
$940$	1.83071e12	0.0764795
$941$	9.23095e12	0.383789	0.191895	−	0.981416i	$-0.438537\pi$
$941$	9.23095e12	0.383789	0.191895	+	0.981416i	$0.438537\pi$
$942$	5.90582e11	0.0244372
$943$	1.52447e13	0.627792
$944$	5.36495e12	0.219883
$945$	−1.55830e12	−0.0635637
$946$	1.59273e13	0.646595
$947$	4.13417e13	1.67037	0.835186	−	0.549967i	$-0.185360\pi$
$947$	4.13417e13	1.67037	0.835186	+	0.549967i	$0.185360\pi$
$948$	6.13006e12	0.246506
$949$	−1.96791e13	−0.787603
$950$	−6.60912e12	−0.263262
$951$	−2.10461e13	−0.834371
$952$	−9.27402e11	−0.0365933
$953$	1.05715e13	0.415162	0.207581	−	0.978218i	$-0.433441\pi$
$953$	1.05715e13	0.415162	0.207581	+	0.978218i	$0.433441\pi$
$954$	−1.88153e13	−0.735433
$955$	−6.33653e12	−0.246511
$956$	9.27287e11	0.0359049
$957$	−3.29471e13	−1.26973
$958$	8.50277e12	0.326149
$959$	2.80584e13	1.07122
$960$	−2.13910e12	−0.0812848
$961$	6.60980e13	2.49996
$962$	8.79457e12	0.331075
$963$	−2.88535e13	−1.08114
$964$	−8.61585e12	−0.321330
$965$	−4.73553e12	−0.175791
$966$	2.83563e13	1.04774
$967$	−4.28128e13	−1.57454	−0.787271	−	0.616607i	$-0.788507\pi$
$967$	−4.28128e13	−1.57454	−0.787271	+	0.616607i	$0.788507\pi$
$968$	−1.27303e13	−0.466016
$969$	−8.99172e12	−0.327632
$970$	−2.32679e12	−0.0843886
$971$	5.22930e12	0.188780	0.0943902	−	0.995535i	$-0.469910\pi$
$971$	5.22930e12	0.188780	0.0943902	+	0.995535i	$0.469910\pi$
$972$	1.99683e13	0.717533
$973$	1.50331e13	0.537702
$974$	1.77466e13	0.631828
$975$	9.12533e12	0.323391
$976$	−6.86105e12	−0.242028
$977$	3.56421e12	0.125152	0.0625760	−	0.998040i	$-0.480068\pi$
$977$	3.56421e12	0.125152	0.0625760	+	0.998040i	$0.480068\pi$
$978$	1.91924e13	0.670818
$979$	−6.61232e13	−2.30055
$980$	−1.73552e12	−0.0601051
$981$	6.81393e12	0.234902
$982$	1.44663e13	0.496427
$983$	1.92286e13	0.656837	0.328418	−	0.944532i	$-0.393484\pi$
$983$	1.92286e13	0.656837	0.328418	+	0.944532i	$0.393484\pi$
$984$	7.96469e12	0.270826
$985$	−1.37980e11	−0.00467039
$986$	−1.45688e12	−0.0490881
$987$	−1.26791e13	−0.425268
$988$	−3.10001e13	−1.03504
$989$	−2.15342e13	−0.715725
$990$	−1.62155e13	−0.536503
$991$	−3.28794e13	−1.08291	−0.541454	−	0.840730i	$-0.682126\pi$
$991$	−3.28794e13	−1.08291	−0.541454	+	0.840730i	$0.682126\pi$
$992$	1.00869e13	0.330717
$993$	−5.12203e13	−1.67175
$994$	−8.43905e12	−0.274192
$995$	−1.87060e13	−0.605031
$996$	−1.69017e13	−0.544205
$997$	1.66280e13	0.532982	0.266491	−	0.963837i	$-0.414136\pi$
$997$	1.66280e13	0.532982	0.266491	+	0.963837i	$0.414136\pi$
$998$	−1.61833e13	−0.516393
$999$	−2.20317e12	−0.0699848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.10.a.a.1.1	✓	1
3.2	odd	2		90.10.a.g.1.1		1
4.3	odd	2		80.10.a.e.1.1		1
5.2	odd	4		50.10.b.e.49.1		2
5.3	odd	4		50.10.b.e.49.2		2
5.4	even	2		50.10.a.f.1.1		1
8.3	odd	2		320.10.a.a.1.1		1
8.5	even	2		320.10.a.j.1.1		1
20.3	even	4		400.10.c.b.49.2		2
20.7	even	4		400.10.c.b.49.1		2
20.19	odd	2		400.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.a.a.1.1	✓	1	1.1	even	1	trivial
50.10.a.f.1.1		1	5.4	even	2
50.10.b.e.49.1		2	5.2	odd	4
50.10.b.e.49.2		2	5.3	odd	4
80.10.a.e.1.1		1	4.3	odd	2
90.10.a.g.1.1		1	3.2	odd	2
320.10.a.a.1.1		1	8.3	odd	2
320.10.a.j.1.1		1	8.5	even	2
400.10.a.a.1.1		1	20.19	odd	2
400.10.c.b.49.1		2	20.7	even	4
400.10.c.b.49.2		2	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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