LMFDB - Embedded newform 14.10.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,10,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.21050170629$
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	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+16.0000 q^{2} +170.000 q^{3} +256.000 q^{4} +544.000 q^{5} +2720.00 q^{6} -2401.00 q^{7} +4096.00 q^{8} +9217.00 q^{9} +8704.00 q^{10} +48824.0 q^{11} +43520.0 q^{12} -15876.0 q^{13} -38416.0 q^{14} +92480.0 q^{15} +65536.0 q^{16} -21418.0 q^{17} +147472. q^{18} -716410. q^{19} +139264. q^{20} -408170. q^{21} +781184. q^{22} -2.47000e6 q^{23} +696320. q^{24} -1.65719e6 q^{25} -254016. q^{26} -1.77922e6 q^{27} -614656. q^{28} +5.55683e6 q^{29} +1.47968e6 q^{30} +5.79935e6 q^{31} +1.04858e6 q^{32} +8.30008e6 q^{33} -342688. q^{34} -1.30614e6 q^{35} +2.35955e6 q^{36} -3.89443e6 q^{37} -1.14626e7 q^{38} -2.69892e6 q^{39} +2.22822e6 q^{40} -6.36086e6 q^{41} -6.53072e6 q^{42} -1.87013e7 q^{43} +1.24989e7 q^{44} +5.01405e6 q^{45} -3.95200e7 q^{46} +5.65391e7 q^{47} +1.11411e7 q^{48} +5.76480e6 q^{49} -2.65150e7 q^{50} -3.64106e6 q^{51} -4.06426e6 q^{52} -5.98947e7 q^{53} -2.84675e7 q^{54} +2.65603e7 q^{55} -9.83450e6 q^{56} -1.21790e8 q^{57} +8.89092e7 q^{58} +1.65630e8 q^{59} +2.36749e7 q^{60} +5.14190e7 q^{61} +9.27896e7 q^{62} -2.21300e7 q^{63} +1.67772e7 q^{64} -8.63654e6 q^{65} +1.32801e8 q^{66} +9.35465e7 q^{67} -5.48301e6 q^{68} -4.19900e8 q^{69} -2.08983e7 q^{70} -9.56335e7 q^{71} +3.77528e7 q^{72} +3.06496e8 q^{73} -6.23109e7 q^{74} -2.81722e8 q^{75} -1.83401e8 q^{76} -1.17226e8 q^{77} -4.31827e7 q^{78} +4.96474e8 q^{79} +3.56516e7 q^{80} -4.83886e8 q^{81} -1.01774e8 q^{82} -3.71487e8 q^{83} -1.04492e8 q^{84} -1.16514e7 q^{85} -2.99221e8 q^{86} +9.44660e8 q^{87} +1.99983e8 q^{88} -1.65483e8 q^{89} +8.02248e7 q^{90} +3.81183e7 q^{91} -6.32320e8 q^{92} +9.85889e8 q^{93} +9.04625e8 q^{94} -3.89727e8 q^{95} +1.78258e8 q^{96} +7.58017e8 q^{97} +9.22368e7 q^{98} +4.50011e8 q^{99} +O(q^{100})\)

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
$3$	170.000	1.21172	0.605861	−	0.795570i	$-0.292829\pi$
$3$	170.000	1.21172	0.605861	+	0.795570i	$0.292829\pi$
$4$	256.000	0.500000
$5$	544.000	0.389255	0.194627	−	0.980877i	$-0.437650\pi$
$5$	544.000	0.389255	0.194627	+	0.980877i	$0.437650\pi$
$6$	2720.00	0.856817
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	4096.00	0.353553
$9$	9217.00	0.468272
$10$	8704.00	0.275245
$11$	48824.0	1.00546	0.502732	−	0.864442i	$-0.332328\pi$
$11$	48824.0	1.00546	0.502732	+	0.864442i	$0.332328\pi$
$12$	43520.0	0.605861
$13$	−15876.0	−0.154169	−0.0770843	−	0.997025i	$-0.524561\pi$
$13$	−15876.0	−0.154169	−0.0770843	+	0.997025i	$0.524561\pi$
$14$	−38416.0	−0.267261
$15$	92480.0	0.471669
$16$	65536.0	0.250000
$17$	−21418.0	−0.0621955	−0.0310977	−	0.999516i	$-0.509900\pi$
$17$	−21418.0	−0.0621955	−0.0310977	+	0.999516i	$0.509900\pi$
$18$	147472.	0.331118
$19$	−716410.	−1.26116	−0.630580	−	0.776124i	$-0.717183\pi$
$19$	−716410.	−1.26116	−0.630580	+	0.776124i	$0.717183\pi$
$20$	139264.	0.194627
$21$	−408170.	−0.457988
$22$	781184.	0.710970
$23$	−2.47000e6	−1.84044	−0.920220	−	0.391401i	$-0.871990\pi$
$23$	−2.47000e6	−1.84044	−0.920220	+	0.391401i	$0.871990\pi$
$24$	696320.	0.428409
$25$	−1.65719e6	−0.848481
$26$	−254016.	−0.109014
$27$	−1.77922e6	−0.644307
$28$	−614656.	−0.188982
$29$	5.55683e6	1.45893	0.729467	−	0.684016i	$-0.239768\pi$
$29$	5.55683e6	1.45893	0.729467	+	0.684016i	$0.239768\pi$
$30$	1.47968e6	0.333520
$31$	5.79935e6	1.12785	0.563925	−	0.825826i	$-0.309291\pi$
$31$	5.79935e6	1.12785	0.563925	+	0.825826i	$0.309291\pi$
$32$	1.04858e6	0.176777
$33$	8.30008e6	1.21834
$34$	−342688.	−0.0439788
$35$	−1.30614e6	−0.147124
$36$	2.35955e6	0.234136
$37$	−3.89443e6	−0.341614	−0.170807	−	0.985304i	$-0.554638\pi$
$37$	−3.89443e6	−0.341614	−0.170807	+	0.985304i	$0.554638\pi$
$38$	−1.14626e7	−0.891775
$39$	−2.69892e6	−0.186810
$40$	2.22822e6	0.137622
$41$	−6.36086e6	−0.351551	−0.175776	−	0.984430i	$-0.556243\pi$
$41$	−6.36086e6	−0.351551	−0.175776	+	0.984430i	$0.556243\pi$
$42$	−6.53072e6	−0.323847
$43$	−1.87013e7	−0.834187	−0.417094	−	0.908863i	$-0.636951\pi$
$43$	−1.87013e7	−0.834187	−0.417094	+	0.908863i	$0.636951\pi$
$44$	1.24989e7	0.502732
$45$	5.01405e6	0.182277
$46$	−3.95200e7	−1.30139
$47$	5.65391e7	1.69008	0.845042	−	0.534700i	$-0.179575\pi$
$47$	5.65391e7	1.69008	0.845042	+	0.534700i	$0.179575\pi$
$48$	1.11411e7	0.302931
$49$	5.76480e6	0.142857
$50$	−2.65150e7	−0.599967
$51$	−3.64106e6	−0.0753637
$52$	−4.06426e6	−0.0770843
$53$	−5.98947e7	−1.04267	−0.521335	−	0.853352i	$-0.674566\pi$
$53$	−5.98947e7	−1.04267	−0.521335	+	0.853352i	$0.674566\pi$
$54$	−2.84675e7	−0.455594
$55$	2.65603e7	0.391381
$56$	−9.83450e6	−0.133631
$57$	−1.21790e8	−1.52818
$58$	8.89092e7	1.03162
$59$	1.65630e8	1.77952	0.889762	−	0.456424i	$-0.150870\pi$
$59$	1.65630e8	1.77952	0.889762	+	0.456424i	$0.150870\pi$
$60$	2.36749e7	0.235834
$61$	5.14190e7	0.475488	0.237744	−	0.971328i	$-0.423592\pi$
$61$	5.14190e7	0.475488	0.237744	+	0.971328i	$0.423592\pi$
$62$	9.27896e7	0.797511
$63$	−2.21300e7	−0.176990
$64$	1.67772e7	0.125000
$65$	−8.63654e6	−0.0600109
$66$	1.32801e8	0.861499
$67$	9.35465e7	0.567141	0.283570	−	0.958951i	$-0.408481\pi$
$67$	9.35465e7	0.567141	0.283570	+	0.958951i	$0.408481\pi$
$68$	−5.48301e6	−0.0310977
$69$	−4.19900e8	−2.23010
$70$	−2.08983e7	−0.104033
$71$	−9.56335e7	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$71$	−9.56335e7	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$72$	3.77528e7	0.165559
$73$	3.06496e8	1.26320	0.631601	−	0.775294i	$-0.282398\pi$
$73$	3.06496e8	1.26320	0.631601	+	0.775294i	$0.282398\pi$
$74$	−6.23109e7	−0.241558
$75$	−2.81722e8	−1.02812
$76$	−1.83401e8	−0.630580
$77$	−1.17226e8	−0.380029
$78$	−4.31827e7	−0.132094
$79$	4.96474e8	1.43408	0.717042	−	0.697030i	$-0.245495\pi$
$79$	4.96474e8	1.43408	0.717042	+	0.697030i	$0.245495\pi$
$80$	3.56516e7	0.0973137
$81$	−4.83886e8	−1.24899
$82$	−1.01774e8	−0.248584
$83$	−3.71487e8	−0.859196	−0.429598	−	0.903020i	$-0.641345\pi$
$83$	−3.71487e8	−0.859196	−0.429598	+	0.903020i	$0.641345\pi$
$84$	−1.04492e8	−0.228994
$85$	−1.16514e7	−0.0242099
$86$	−2.99221e8	−0.589860
$87$	9.44660e8	1.76782
$88$	1.99983e8	0.355485
$89$	−1.65483e8	−0.279574	−0.139787	−	0.990182i	$-0.544642\pi$
$89$	−1.65483e8	−0.279574	−0.139787	+	0.990182i	$0.544642\pi$
$90$	8.02248e7	0.128889
$91$	3.81183e7	0.0582703
$92$	−6.32320e8	−0.920220
$93$	9.85889e8	1.36664
$94$	9.04625e8	1.19507
$95$	−3.89727e8	−0.490913
$96$	1.78258e8	0.214204
$97$	7.58017e8	0.869373	0.434686	−	0.900582i	$-0.356859\pi$
$97$	7.58017e8	0.869373	0.434686	+	0.900582i	$0.356859\pi$
$98$	9.22368e7	0.101015
$99$	4.50011e8	0.470830
$100$	−4.24240e8	−0.424240
$101$	−9.04212e8	−0.864618	−0.432309	−	0.901726i	$-0.642301\pi$
$101$	−9.04212e8	−0.864618	−0.432309	+	0.901726i	$0.642301\pi$
$102$	−5.82570e7	−0.0532902
$103$	1.98157e9	1.73477	0.867384	−	0.497639i	$-0.165800\pi$
$103$	1.98157e9	1.73477	0.867384	+	0.497639i	$0.165800\pi$
$104$	−6.50281e7	−0.0545068
$105$	−2.22044e8	−0.178274
$106$	−9.58315e8	−0.737279
$107$	4.16379e8	0.307087	0.153544	−	0.988142i	$-0.450931\pi$
$107$	4.16379e8	0.307087	0.153544	+	0.988142i	$0.450931\pi$
$108$	−4.55480e8	−0.322153
$109$	−1.26921e9	−0.861220	−0.430610	−	0.902538i	$-0.641701\pi$
$109$	−1.26921e9	−0.861220	−0.430610	+	0.902538i	$0.641701\pi$
$110$	4.24964e8	0.276748
$111$	−6.62053e8	−0.413942
$112$	−1.57352e8	−0.0944911
$113$	−2.83528e9	−1.63585	−0.817923	−	0.575328i	$-0.804874\pi$
$113$	−2.83528e9	−1.63585	−0.817923	+	0.575328i	$0.804874\pi$
$114$	−1.94864e9	−1.08058
$115$	−1.34368e9	−0.716400
$116$	1.42255e9	0.729467
$117$	−1.46329e8	−0.0721929
$118$	2.65007e9	1.25831
$119$	5.14246e7	0.0235077
$120$	3.78798e8	0.166760
$121$	2.58353e7	0.0109567
$122$	8.22704e8	0.336221
$123$	−1.08135e9	−0.425982
$124$	1.48463e9	0.563925
$125$	−1.96401e9	−0.719530
$126$	−3.54080e8	−0.125151
$127$	5.44282e9	1.85655	0.928277	−	0.371889i	$-0.121290\pi$
$127$	5.44282e9	1.85655	0.928277	+	0.371889i	$0.121290\pi$
$128$	2.68435e8	0.0883883
$129$	−3.17922e9	−1.01080
$130$	−1.38185e8	−0.0424341
$131$	−6.44057e8	−0.191075	−0.0955374	−	0.995426i	$-0.530457\pi$
$131$	−6.44057e8	−0.191075	−0.0955374	+	0.995426i	$0.530457\pi$
$132$	2.12482e9	0.609171
$133$	1.72010e9	0.476674
$134$	1.49674e9	0.401029
$135$	−9.67896e8	−0.250799
$136$	−8.77281e7	−0.0219894
$137$	1.67376e9	0.405928	0.202964	−	0.979186i	$-0.434942\pi$
$137$	1.67376e9	0.405928	0.202964	+	0.979186i	$0.434942\pi$
$138$	−6.71840e9	−1.57692
$139$	−4.17330e9	−0.948229	−0.474115	−	0.880463i	$-0.657232\pi$
$139$	−4.17330e9	−0.948229	−0.474115	+	0.880463i	$0.657232\pi$
$140$	−3.34373e8	−0.0735622
$141$	9.61164e9	2.04791
$142$	−1.53014e9	−0.315815
$143$	−7.75130e8	−0.155011
$144$	6.04045e8	0.117068
$145$	3.02291e9	0.567897
$146$	4.90394e9	0.893218
$147$	9.80016e8	0.173103
$148$	−9.96974e8	−0.170807
$149$	−4.64096e8	−0.0771382	−0.0385691	−	0.999256i	$-0.512280\pi$
$149$	−4.64096e8	−0.0771382	−0.0385691	+	0.999256i	$0.512280\pi$
$150$	−4.50755e9	−0.726993
$151$	7.31929e9	1.14571	0.572853	−	0.819658i	$-0.305837\pi$
$151$	7.31929e9	1.14571	0.572853	+	0.819658i	$0.305837\pi$
$152$	−2.93442e9	−0.445888
$153$	−1.97410e8	−0.0291244
$154$	−1.87562e9	−0.268721
$155$	3.15485e9	0.439021
$156$	−6.90924e8	−0.0934048
$157$	−4.43050e9	−0.581975	−0.290987	−	0.956727i	$-0.593984\pi$
$157$	−4.43050e9	−0.581975	−0.290987	+	0.956727i	$0.593984\pi$
$158$	7.94359e9	1.01405
$159$	−1.01821e10	−1.26343
$160$	5.70425e8	0.0688112
$161$	5.93047e9	0.695621
$162$	−7.74217e9	−0.883172
$163$	−1.33645e10	−1.48289	−0.741446	−	0.671013i	$-0.765860\pi$
$163$	−1.33645e10	−1.48289	−0.741446	+	0.671013i	$0.765860\pi$
$164$	−1.62838e9	−0.175776
$165$	4.51524e9	0.474246
$166$	−5.94379e9	−0.607543
$167$	−1.24456e10	−1.23821	−0.619103	−	0.785310i	$-0.712504\pi$
$167$	−1.24456e10	−1.23821	−0.619103	+	0.785310i	$0.712504\pi$
$168$	−1.67186e9	−0.161923
$169$	−1.03525e10	−0.976232
$170$	−1.86422e8	−0.0171190
$171$	−6.60315e9	−0.590566
$172$	−4.78753e9	−0.417094
$173$	1.04544e10	0.887345	0.443672	−	0.896189i	$-0.353675\pi$
$173$	1.04544e10	0.887345	0.443672	+	0.896189i	$0.353675\pi$
$174$	1.51146e10	1.25004
$175$	3.97891e9	0.320696
$176$	3.19973e9	0.251366
$177$	2.81570e10	2.15629
$178$	−2.64772e9	−0.197689
$179$	−4.04391e9	−0.294417	−0.147208	−	0.989105i	$-0.547029\pi$
$179$	−4.04391e9	−0.294417	−0.147208	+	0.989105i	$0.547029\pi$
$180$	1.28360e9	0.0911386
$181$	1.24735e10	0.863843	0.431922	−	0.901911i	$-0.357836\pi$
$181$	1.24735e10	0.863843	0.431922	+	0.901911i	$0.357836\pi$
$182$	6.09892e8	0.0412033
$183$	8.74123e9	0.576160
$184$	−1.01171e10	−0.650694
$185$	−2.11857e9	−0.132975
$186$	1.57742e10	0.966362
$187$	−1.04571e9	−0.0625353
$188$	1.44740e10	0.845042
$189$	4.27191e9	0.243525
$190$	−6.23563e9	−0.347128
$191$	−3.81947e9	−0.207660	−0.103830	−	0.994595i	$-0.533110\pi$
$191$	−3.81947e9	−0.207660	−0.103830	+	0.994595i	$0.533110\pi$
$192$	2.85213e9	0.151465
$193$	−2.41193e10	−1.25129	−0.625644	−	0.780109i	$-0.715164\pi$
$193$	−2.41193e10	−1.25129	−0.625644	+	0.780109i	$0.715164\pi$
$194$	1.21283e10	0.614739
$195$	−1.46821e9	−0.0727165
$196$	1.47579e9	0.0714286
$197$	−1.24798e10	−0.590351	−0.295176	−	0.955443i	$-0.595378\pi$
$197$	−1.24798e10	−0.590351	−0.295176	+	0.955443i	$0.595378\pi$
$198$	7.20017e9	0.332927
$199$	−2.93127e9	−0.132500	−0.0662502	−	0.997803i	$-0.521104\pi$
$199$	−2.93127e9	−0.132500	−0.0662502	+	0.997803i	$0.521104\pi$
$200$	−6.78785e9	−0.299983
$201$	1.59029e10	0.687218
$202$	−1.44674e10	−0.611377
$203$	−1.33419e10	−0.551425
$204$	−9.32111e8	−0.0376818
$205$	−3.46031e9	−0.136843
$206$	3.17051e10	1.22667
$207$	−2.27660e10	−0.861827
$208$	−1.04045e9	−0.0385422
$209$	−3.49780e10	−1.26805
$210$	−3.55271e9	−0.126059
$211$	3.36978e10	1.17039	0.585195	−	0.810892i	$-0.301018\pi$
$211$	3.36978e10	1.17039	0.585195	+	0.810892i	$0.301018\pi$
$212$	−1.53330e10	−0.521335
$213$	−1.62577e10	−0.541191
$214$	6.66206e9	0.217143
$215$	−1.01735e10	−0.324711
$216$	−7.28769e9	−0.227797
$217$	−1.39242e10	−0.426287
$218$	−2.03073e10	−0.608974
$219$	5.21044e10	1.53065
$220$	6.79943e9	0.195691
$221$	3.40032e8	0.00958859
$222$	−1.05928e10	−0.292701
$223$	−3.87208e10	−1.04851	−0.524255	−	0.851561i	$-0.675656\pi$
$223$	−3.87208e10	−1.04851	−0.524255	+	0.851561i	$0.675656\pi$
$224$	−2.51763e9	−0.0668153
$225$	−1.52743e10	−0.397320
$226$	−4.53644e10	−1.15672
$227$	7.69011e10	1.92228	0.961139	−	0.276063i	$-0.0890299\pi$
$227$	7.69011e10	1.92228	0.961139	+	0.276063i	$0.0890299\pi$
$228$	−3.11782e10	−0.764089
$229$	4.35114e10	1.04555	0.522773	−	0.852472i	$-0.324897\pi$
$229$	4.35114e10	1.04555	0.522773	+	0.852472i	$0.324897\pi$
$230$	−2.14989e10	−0.506571
$231$	−1.99285e10	−0.460490
$232$	2.27608e10	0.515811
$233$	−2.07043e10	−0.460213	−0.230107	−	0.973165i	$-0.573907\pi$
$233$	−2.07043e10	−0.460213	−0.230107	+	0.973165i	$0.573907\pi$
$234$	−2.34127e9	−0.0510481
$235$	3.07573e10	0.657873
$236$	4.24012e10	0.889762
$237$	8.44006e10	1.73771
$238$	8.22794e8	0.0166224
$239$	2.16220e10	0.428653	0.214326	−	0.976762i	$-0.431244\pi$
$239$	2.16220e10	0.428653	0.214326	+	0.976762i	$0.431244\pi$
$240$	6.06077e9	0.117917
$241$	6.77789e10	1.29425	0.647124	−	0.762385i	$-0.275971\pi$
$241$	6.77789e10	1.29425	0.647124	+	0.762385i	$0.275971\pi$
$242$	4.13365e8	0.00774754
$243$	−4.72402e10	−0.869127
$244$	1.31633e10	0.237744
$245$	3.13605e9	0.0556078
$246$	−1.73015e10	−0.301215
$247$	1.13737e10	0.194431
$248$	2.37541e10	0.398755
$249$	−6.31528e10	−1.04111
$250$	−3.14242e10	−0.508784
$251$	4.87895e9	0.0775881	0.0387940	−	0.999247i	$-0.487648\pi$
$251$	4.87895e9	0.0775881	0.0387940	+	0.999247i	$0.487648\pi$
$252$	−5.66528e9	−0.0884951
$253$	−1.20595e11	−1.85050
$254$	8.70852e10	1.31278
$255$	−1.98074e9	−0.0293357
$256$	4.29497e9	0.0625000
$257$	−2.75029e10	−0.393259	−0.196630	−	0.980478i	$-0.563000\pi$
$257$	−2.75029e10	−0.393259	−0.196630	+	0.980478i	$0.563000\pi$
$258$	−5.08675e10	−0.714746
$259$	9.35053e9	0.129118
$260$	−2.21096e9	−0.0300054
$261$	5.12173e10	0.683178
$262$	−1.03049e10	−0.135110
$263$	−2.22595e10	−0.286889	−0.143445	−	0.989658i	$-0.545818\pi$
$263$	−2.22595e10	−0.286889	−0.143445	+	0.989658i	$0.545818\pi$
$264$	3.39971e10	0.430749
$265$	−3.25827e10	−0.405864
$266$	2.75216e10	0.337059
$267$	−2.81320e10	−0.338766
$268$	2.39479e10	0.283570
$269$	1.73017e10	0.201466	0.100733	−	0.994913i	$-0.467881\pi$
$269$	1.73017e10	0.201466	0.100733	+	0.994913i	$0.467881\pi$
$270$	−1.54863e10	−0.177342
$271$	4.81901e10	0.542745	0.271372	−	0.962474i	$-0.412523\pi$
$271$	4.81901e10	0.542745	0.271372	+	0.962474i	$0.412523\pi$
$272$	−1.40365e9	−0.0155489
$273$	6.48011e9	0.0706074
$274$	2.67801e10	0.287035
$275$	−8.09106e10	−0.853116
$276$	−1.07494e11	−1.11505
$277$	8.03834e10	0.820365	0.410183	−	0.912003i	$-0.365465\pi$
$277$	8.03834e10	0.820365	0.410183	+	0.912003i	$0.365465\pi$
$278$	−6.67728e10	−0.670499
$279$	5.34526e10	0.528141
$280$	−5.34997e9	−0.0520163
$281$	−1.95595e11	−1.87146	−0.935729	−	0.352719i	$-0.885257\pi$
$281$	−1.95595e11	−1.87146	−0.935729	+	0.352719i	$0.885257\pi$
$282$	1.53786e11	1.44809
$283$	−6.02802e10	−0.558645	−0.279322	−	0.960197i	$-0.590110\pi$
$283$	−6.02802e10	−0.558645	−0.279322	+	0.960197i	$0.590110\pi$
$284$	−2.44822e10	−0.223315
$285$	−6.62536e10	−0.594850
$286$	−1.24021e10	−0.109609
$287$	1.52724e10	0.132874
$288$	9.66472e9	0.0827796
$289$	−1.18129e11	−0.996132
$290$	4.83666e10	0.401564
$291$	1.28863e11	1.05344
$292$	7.84631e10	0.631601
$293$	−4.86743e10	−0.385830	−0.192915	−	0.981216i	$-0.561794\pi$
$293$	−4.86743e10	−0.385830	−0.192915	+	0.981216i	$0.561794\pi$
$294$	1.56803e10	0.122402
$295$	9.01025e10	0.692688
$296$	−1.59516e10	−0.120779
$297$	−8.68686e10	−0.647827
$298$	−7.42553e9	−0.0545449
$299$	3.92137e10	0.283738
$300$	−7.21209e10	−0.514062
$301$	4.49018e10	0.315293
$302$	1.17109e11	0.810136
$303$	−1.53716e11	−1.04768
$304$	−4.69506e10	−0.315290
$305$	2.79719e10	0.185086
$306$	−3.15856e9	−0.0205941
$307$	2.75178e11	1.76804	0.884018	−	0.467453i	$-0.154828\pi$
$307$	2.75178e11	1.76804	0.884018	+	0.467453i	$0.154828\pi$
$308$	−3.00100e10	−0.190015
$309$	3.36867e11	2.10206
$310$	5.04775e10	0.310435
$311$	1.12322e11	0.680835	0.340418	−	0.940274i	$-0.389432\pi$
$311$	1.12322e11	0.680835	0.340418	+	0.940274i	$0.389432\pi$
$312$	−1.10548e10	−0.0660472
$313$	−1.06140e11	−0.625069	−0.312535	−	0.949906i	$-0.601178\pi$
$313$	−1.06140e11	−0.625069	−0.312535	+	0.949906i	$0.601178\pi$
$314$	−7.08880e10	−0.411518
$315$	−1.20387e10	−0.0688943
$316$	1.27097e11	0.717042
$317$	2.31358e9	0.0128682	0.00643409	−	0.999979i	$-0.497952\pi$
$317$	2.31358e9	0.0128682	0.00643409	+	0.999979i	$0.497952\pi$
$318$	−1.62914e11	−0.893378
$319$	2.71306e11	1.46691
$320$	9.12681e9	0.0486568
$321$	7.07844e10	0.372105
$322$	9.48875e10	0.491878
$323$	1.53441e10	0.0784385
$324$	−1.23875e11	−0.624497
$325$	2.63095e10	0.130809
$326$	−2.13832e11	−1.04856
$327$	−2.15766e11	−1.04356
$328$	−2.60541e10	−0.124292
$329$	−1.35750e11	−0.638792
$330$	7.22439e10	0.335342
$331$	−2.16185e11	−0.989921	−0.494960	−	0.868916i	$-0.664817\pi$
$331$	−2.16185e11	−0.989921	−0.494960	+	0.868916i	$0.664817\pi$
$332$	−9.51007e10	−0.429598
$333$	−3.58950e10	−0.159968
$334$	−1.99130e11	−0.875544
$335$	5.08893e10	0.220762
$336$	−2.67498e10	−0.114497
$337$	5.00291e10	0.211294	0.105647	−	0.994404i	$-0.466309\pi$
$337$	5.00291e10	0.211294	0.105647	+	0.994404i	$0.466309\pi$
$338$	−1.65639e11	−0.690300
$339$	−4.81997e11	−1.98219
$340$	−2.98276e9	−0.0121049
$341$	2.83147e11	1.13401
$342$	−1.05650e11	−0.417594
$343$	−1.38413e10	−0.0539949
$344$	−7.66005e10	−0.294930
$345$	−2.28426e11	−0.868078
$346$	1.67271e11	0.627448
$347$	−1.84606e11	−0.683541	−0.341770	−	0.939784i	$-0.611026\pi$
$347$	−1.84606e11	−0.683541	−0.341770	+	0.939784i	$0.611026\pi$
$348$	2.41833e11	0.883912
$349$	2.74666e11	0.991039	0.495520	−	0.868597i	$-0.334978\pi$
$349$	2.74666e11	0.991039	0.495520	+	0.868597i	$0.334978\pi$
$350$	6.36626e10	0.226766
$351$	2.82469e10	0.0993319
$352$	5.11957e10	0.177743
$353$	−1.58053e11	−0.541774	−0.270887	−	0.962611i	$-0.587317\pi$
$353$	−1.58053e11	−0.541774	−0.270887	+	0.962611i	$0.587317\pi$
$354$	4.50513e11	1.52473
$355$	−5.20246e10	−0.173853
$356$	−4.23635e10	−0.139787
$357$	8.74219e9	0.0284848
$358$	−6.47025e10	−0.208184
$359$	3.40759e11	1.08274	0.541368	−	0.840786i	$-0.317907\pi$
$359$	3.40759e11	1.08274	0.541368	+	0.840786i	$0.317907\pi$
$360$	2.05375e10	0.0644447
$361$	1.90556e11	0.590526
$362$	1.99576e11	0.610829
$363$	4.39200e9	0.0132765
$364$	9.75828e9	0.0291351
$365$	1.66734e11	0.491707
$366$	1.39860e11	0.407406
$367$	−6.10216e11	−1.75584	−0.877922	−	0.478803i	$-0.841071\pi$
$367$	−6.10216e11	−1.75584	−0.877922	+	0.478803i	$0.841071\pi$
$368$	−1.61874e11	−0.460110
$369$	−5.86280e10	−0.164622
$370$	−3.38971e10	−0.0940275
$371$	1.43807e11	0.394092
$372$	2.52388e11	0.683321
$373$	4.34930e11	1.16340	0.581701	−	0.813402i	$-0.302387\pi$
$373$	4.34930e11	1.16340	0.581701	+	0.813402i	$0.302387\pi$
$374$	−1.67314e10	−0.0442191
$375$	−3.33882e11	−0.871871
$376$	2.31584e11	0.597535
$377$	−8.82202e10	−0.224922
$378$	6.83505e10	0.172198
$379$	−7.30677e11	−1.81907	−0.909534	−	0.415630i	$-0.863561\pi$
$379$	−7.30677e11	−1.81907	−0.909534	+	0.415630i	$0.863561\pi$
$380$	−9.97701e10	−0.245456
$381$	9.25280e11	2.24963
$382$	−6.11115e10	−0.146838
$383$	2.11074e11	0.501233	0.250617	−	0.968086i	$-0.419367\pi$
$383$	2.11074e11	0.501233	0.250617	+	0.968086i	$0.419367\pi$
$384$	4.56340e10	0.107102
$385$	−6.37712e10	−0.147928
$386$	−3.85909e11	−0.884794
$387$	−1.72370e11	−0.390627
$388$	1.94052e11	0.434686
$389$	7.21857e9	0.0159837	0.00799186	−	0.999968i	$-0.497456\pi$
$389$	7.21857e9	0.0159837	0.00799186	+	0.999968i	$0.497456\pi$
$390$	−2.34914e10	−0.0514184
$391$	5.29025e10	0.114467
$392$	2.36126e10	0.0505076
$393$	−1.09490e11	−0.231530
$394$	−1.99677e11	−0.417441
$395$	2.70082e11	0.558224
$396$	1.15203e11	0.235415
$397$	−6.99387e11	−1.41306	−0.706529	−	0.707684i	$-0.749740\pi$
$397$	−6.99387e11	−1.41306	−0.706529	+	0.707684i	$0.749740\pi$
$398$	−4.69004e10	−0.0936920
$399$	2.92417e11	0.577597
$400$	−1.08606e11	−0.212120
$401$	6.40644e11	1.23728	0.618638	−	0.785676i	$-0.287685\pi$
$401$	6.40644e11	1.23728	0.618638	+	0.785676i	$0.287685\pi$
$402$	2.54447e11	0.485936
$403$	−9.20704e10	−0.173879
$404$	−2.31478e11	−0.432309
$405$	−2.63234e11	−0.486177
$406$	−2.13471e11	−0.389917
$407$	−1.90142e11	−0.343481
$408$	−1.49138e10	−0.0266451
$409$	−1.31500e10	−0.0232365	−0.0116182	−	0.999933i	$-0.503698\pi$
$409$	−1.31500e10	−0.0232365	−0.0116182	+	0.999933i	$0.503698\pi$
$410$	−5.53649e10	−0.0967625
$411$	2.84538e11	0.491873
$412$	5.07281e11	0.867384
$413$	−3.97677e11	−0.672597
$414$	−3.64256e11	−0.609404
$415$	−2.02089e11	−0.334446
$416$	−1.66472e10	−0.0272534
$417$	−7.09461e11	−1.14899
$418$	−5.59648e11	−0.896647
$419$	−5.79915e11	−0.919182	−0.459591	−	0.888131i	$-0.652004\pi$
$419$	−5.79915e11	−0.919182	−0.459591	+	0.888131i	$0.652004\pi$
$420$	−5.68434e10	−0.0891370
$421$	1.66175e11	0.257808	0.128904	−	0.991657i	$-0.458854\pi$
$421$	1.66175e11	0.257808	0.128904	+	0.991657i	$0.458854\pi$
$422$	5.39165e11	0.827591
$423$	5.21121e11	0.791419
$424$	−2.45329e11	−0.368639
$425$	3.54937e10	0.0527717
$426$	−2.60123e11	−0.382680
$427$	−1.23457e11	−0.179718
$428$	1.06593e11	0.153544
$429$	−1.31772e11	−0.187830
$430$	−1.62776e11	−0.229606
$431$	7.57723e11	1.05770	0.528850	−	0.848715i	$-0.322623\pi$
$431$	7.57723e11	1.05770	0.528850	+	0.848715i	$0.322623\pi$
$432$	−1.16603e11	−0.161077
$433$	−1.07485e12	−1.46944	−0.734719	−	0.678371i	$-0.762686\pi$
$433$	−1.07485e12	−1.46944	−0.734719	+	0.678371i	$0.762686\pi$
$434$	−2.22788e11	−0.301431
$435$	5.13895e11	0.688134
$436$	−3.24918e11	−0.430610
$437$	1.76953e12	2.32109
$438$	8.33670e11	1.08233
$439$	1.70418e11	0.218991	0.109496	−	0.993987i	$-0.465076\pi$
$439$	1.70418e11	0.218991	0.109496	+	0.993987i	$0.465076\pi$
$440$	1.08791e11	0.138374
$441$	5.31342e10	0.0668960
$442$	5.44051e9	0.00678016
$443$	1.22937e12	1.51658	0.758290	−	0.651918i	$-0.226035\pi$
$443$	1.22937e12	1.51658	0.758290	+	0.651918i	$0.226035\pi$
$444$	−1.69486e11	−0.206971
$445$	−9.00225e10	−0.108826
$446$	−6.19533e11	−0.741409
$447$	−7.88963e10	−0.0934701
$448$	−4.02821e10	−0.0472456
$449$	−7.25792e10	−0.0842759	−0.0421380	−	0.999112i	$-0.513417\pi$
$449$	−7.25792e10	−0.0842759	−0.0421380	+	0.999112i	$0.513417\pi$
$450$	−2.44389e11	−0.280948
$451$	−3.10563e11	−0.353472
$452$	−7.25831e11	−0.817923
$453$	1.24428e12	1.38828
$454$	1.23042e12	1.35926
$455$	2.07363e10	0.0226820
$456$	−4.98851e11	−0.540292
$457$	−6.64172e11	−0.712291	−0.356146	−	0.934431i	$-0.615909\pi$
$457$	−6.64172e11	−0.712291	−0.356146	+	0.934431i	$0.615909\pi$
$458$	6.96183e11	0.739313
$459$	3.81073e10	0.0400730
$460$	−3.43982e11	−0.358200
$461$	−1.21501e12	−1.25293	−0.626463	−	0.779451i	$-0.715498\pi$
$461$	−1.21501e12	−1.25293	−0.626463	+	0.779451i	$0.715498\pi$
$462$	−3.18856e11	−0.325616
$463$	2.93878e11	0.297202	0.148601	−	0.988897i	$-0.452523\pi$
$463$	2.93878e11	0.297202	0.148601	+	0.988897i	$0.452523\pi$
$464$	3.64172e11	0.364734
$465$	5.36324e11	0.531972
$466$	−3.31269e11	−0.325420
$467$	4.73112e11	0.460297	0.230149	−	0.973155i	$-0.426079\pi$
$467$	4.73112e11	0.460297	0.230149	+	0.973155i	$0.426079\pi$
$468$	−3.74602e10	−0.0360964
$469$	−2.24605e11	−0.214359
$470$	4.92116e11	0.465187
$471$	−7.53185e11	−0.705192
$472$	6.78419e11	0.629157
$473$	−9.13072e11	−0.838745
$474$	1.35041e12	1.22875
$475$	1.18723e12	1.07007
$476$	1.31647e10	0.0117538
$477$	−5.52049e11	−0.488253
$478$	3.45952e11	0.303103
$479$	−2.05945e12	−1.78748	−0.893742	−	0.448582i	$-0.851929\pi$
$479$	−2.05945e12	−1.78748	−0.893742	+	0.448582i	$0.851929\pi$
$480$	9.69723e10	0.0833801
$481$	6.18280e10	0.0526662
$482$	1.08446e12	0.915172
$483$	1.00818e12	0.842900
$484$	6.61383e9	0.00547834
$485$	4.12361e11	0.338407
$486$	−7.55843e11	−0.614566
$487$	−1.22247e12	−0.984821	−0.492411	−	0.870363i	$-0.663884\pi$
$487$	−1.22247e12	−0.984821	−0.492411	+	0.870363i	$0.663884\pi$
$488$	2.10612e11	0.168110
$489$	−2.27197e12	−1.79685
$490$	5.01768e10	0.0393207
$491$	1.98225e11	0.153918	0.0769592	−	0.997034i	$-0.475479\pi$
$491$	1.98225e11	0.153918	0.0769592	+	0.997034i	$0.475479\pi$
$492$	−2.76825e11	−0.212991
$493$	−1.19016e11	−0.0907391
$494$	1.81980e11	0.137484
$495$	2.44806e11	0.183273
$496$	3.80066e11	0.281963
$497$	2.29616e11	0.168810
$498$	−1.01044e12	−0.736174
$499$	−3.00745e11	−0.217143	−0.108571	−	0.994089i	$-0.534628\pi$
$499$	−3.00745e11	−0.217143	−0.108571	+	0.994089i	$0.534628\pi$
$500$	−5.02787e11	−0.359765
$501$	−2.11576e12	−1.50036
$502$	7.80633e10	0.0548631
$503$	3.30194e11	0.229993	0.114996	−	0.993366i	$-0.463314\pi$
$503$	3.30194e11	0.229993	0.114996	+	0.993366i	$0.463314\pi$
$504$	−9.06445e10	−0.0625755
$505$	−4.91891e11	−0.336556
$506$	−1.92952e12	−1.30850
$507$	−1.75992e12	−1.18292
$508$	1.39336e12	0.928277
$509$	−6.32399e10	−0.0417600	−0.0208800	−	0.999782i	$-0.506647\pi$
$509$	−6.32399e10	−0.0417600	−0.0208800	+	0.999782i	$0.506647\pi$
$510$	−3.16918e10	−0.0207434
$511$	−7.35898e11	−0.477445
$512$	6.87195e10	0.0441942
$513$	1.27465e12	0.812574
$514$	−4.40046e11	−0.278076
$515$	1.07797e12	0.675267
$516$	−8.13880e11	−0.505402
$517$	2.76046e12	1.69932
$518$	1.49608e11	0.0913003
$519$	1.77725e12	1.07522
$520$	−3.53753e10	−0.0212170
$521$	−1.88994e12	−1.12377	−0.561886	−	0.827215i	$-0.689924\pi$
$521$	−1.88994e12	−1.12377	−0.561886	+	0.827215i	$0.689924\pi$
$522$	8.19476e11	0.483080
$523$	8.95863e11	0.523581	0.261791	−	0.965125i	$-0.415687\pi$
$523$	8.95863e11	0.523581	0.261791	+	0.965125i	$0.415687\pi$
$524$	−1.64879e11	−0.0955374
$525$	6.76415e11	0.388594
$526$	−3.56152e11	−0.202861
$527$	−1.24210e11	−0.0701472
$528$	5.43954e11	0.304586
$529$	4.29975e12	2.38722
$530$	−5.21323e11	−0.286989
$531$	1.52661e12	0.833302
$532$	4.40346e11	0.238337
$533$	1.00985e11	0.0541981
$534$	−4.50113e11	−0.239544
$535$	2.26510e11	0.119535
$536$	3.83166e11	0.200515
$537$	−6.87464e11	−0.356752
$538$	2.76826e11	0.142458
$539$	2.81461e11	0.143638
$540$	−2.47781e11	−0.125400
$541$	1.00221e12	0.503005	0.251502	−	0.967857i	$-0.419075\pi$
$541$	1.00221e12	0.503005	0.251502	+	0.967857i	$0.419075\pi$
$542$	7.71041e11	0.383778
$543$	2.12050e12	1.04674
$544$	−2.24584e10	−0.0109947
$545$	−6.90450e11	−0.335234
$546$	1.03682e11	0.0499270
$547$	2.73436e12	1.30591	0.652955	−	0.757396i	$-0.273529\pi$
$547$	2.73436e12	1.30591	0.652955	+	0.757396i	$0.273529\pi$
$548$	4.28481e11	0.202964
$549$	4.73929e11	0.222658
$550$	−1.29457e12	−0.603244
$551$	−3.98097e12	−1.83995
$552$	−1.71991e12	−0.788461
$553$	−1.19203e12	−0.542033
$554$	1.28613e12	0.580086
$555$	−3.60157e11	−0.161129
$556$	−1.06837e12	−0.474115
$557$	−4.22359e12	−1.85923	−0.929614	−	0.368534i	$-0.879860\pi$
$557$	−4.22359e12	−1.85923	−0.929614	+	0.368534i	$0.879860\pi$
$558$	8.55241e11	0.373452
$559$	2.96902e11	0.128606
$560$	−8.55995e10	−0.0367811
$561$	−1.77771e11	−0.0757754
$562$	−3.12953e12	−1.32332
$563$	−3.08311e12	−1.29330	−0.646652	−	0.762785i	$-0.723831\pi$
$563$	−3.08311e12	−1.29330	−0.646652	+	0.762785i	$0.723831\pi$
$564$	2.46058e12	1.02396
$565$	−1.54239e12	−0.636761
$566$	−9.64483e11	−0.395021
$567$	1.16181e12	0.472075
$568$	−3.91715e11	−0.157907
$569$	−2.74669e11	−0.109851	−0.0549256	−	0.998490i	$-0.517492\pi$
$569$	−2.74669e11	−0.109851	−0.0549256	+	0.998490i	$0.517492\pi$
$570$	−1.06006e12	−0.420623
$571$	2.82499e12	1.11213	0.556064	−	0.831140i	$-0.312311\pi$
$571$	2.82499e12	1.11213	0.556064	+	0.831140i	$0.312311\pi$
$572$	−1.98433e11	−0.0775055
$573$	−6.49310e11	−0.251626
$574$	2.44359e11	0.0939560
$575$	4.09326e12	1.56158
$576$	1.54636e11	0.0585340
$577$	3.76585e12	1.41440	0.707199	−	0.707014i	$-0.249958\pi$
$577$	3.76585e12	1.41440	0.707199	+	0.707014i	$0.249958\pi$
$578$	−1.89007e12	−0.704371
$579$	−4.10028e12	−1.51621
$580$	7.73866e11	0.283949
$581$	8.91940e11	0.324745
$582$	2.06181e12	0.744894
$583$	−2.92430e12	−1.04837
$584$	1.25541e12	0.446609
$585$	−7.96030e10	−0.0281014
$586$	−7.78789e11	−0.272823
$587$	−3.00831e12	−1.04580	−0.522902	−	0.852393i	$-0.675151\pi$
$587$	−3.00831e12	−1.04580	−0.522902	+	0.852393i	$0.675151\pi$
$588$	2.50884e11	0.0865516
$589$	−4.15471e12	−1.42240
$590$	1.44164e12	0.489805
$591$	−2.12157e12	−0.715342
$592$	−2.55225e11	−0.0854036
$593$	3.64775e12	1.21138	0.605688	−	0.795703i	$-0.292898\pi$
$593$	3.64775e12	1.21138	0.605688	+	0.795703i	$0.292898\pi$
$594$	−1.38990e12	−0.458083
$595$	2.79750e10	0.00915047
$596$	−1.18809e11	−0.0385691
$597$	−4.98316e11	−0.160554
$598$	6.27420e11	0.200633
$599$	4.17778e12	1.32594	0.662972	−	0.748644i	$-0.269295\pi$
$599$	4.17778e12	1.32594	0.662972	+	0.748644i	$0.269295\pi$
$600$	−1.15393e12	−0.363497
$601$	4.84445e12	1.51464	0.757321	−	0.653043i	$-0.226508\pi$
$601$	4.84445e12	1.51464	0.757321	+	0.653043i	$0.226508\pi$
$602$	7.18429e11	0.222946
$603$	8.62218e11	0.265576
$604$	1.87374e12	0.572853
$605$	1.40544e10	0.00426494
$606$	−2.45946e12	−0.740819
$607$	−1.58444e12	−0.473726	−0.236863	−	0.971543i	$-0.576119\pi$
$607$	−1.58444e12	−0.473726	−0.236863	+	0.971543i	$0.576119\pi$
$608$	−7.51210e11	−0.222944
$609$	−2.26813e12	−0.668175
$610$	4.47551e11	0.130876
$611$	−8.97614e11	−0.260558
$612$	−5.05369e10	−0.0145622
$613$	−2.79203e11	−0.0798635	−0.0399318	−	0.999202i	$-0.512714\pi$
$613$	−2.79203e11	−0.0798635	−0.0399318	+	0.999202i	$0.512714\pi$
$614$	4.40285e12	1.25019
$615$	−5.88252e11	−0.165816
$616$	−4.80159e11	−0.134361
$617$	−5.55576e12	−1.54333	−0.771667	−	0.636027i	$-0.780577\pi$
$617$	−5.55576e12	−1.54333	−0.771667	+	0.636027i	$0.780577\pi$
$618$	5.38986e12	1.48638
$619$	−2.70437e12	−0.740385	−0.370192	−	0.928955i	$-0.620708\pi$
$619$	−2.70437e12	−0.740385	−0.370192	+	0.928955i	$0.620708\pi$
$620$	8.07640e11	0.219511
$621$	4.39467e12	1.18581
$622$	1.79715e12	0.481423
$623$	3.97324e11	0.105669
$624$	−1.76876e11	−0.0467024
$625$	2.16828e12	0.568400
$626$	−1.69823e12	−0.441991
$627$	−5.94626e12	−1.53653
$628$	−1.13421e12	−0.290987
$629$	8.34109e10	0.0212469
$630$	−1.92620e11	−0.0487156
$631$	−4.73158e12	−1.18816	−0.594078	−	0.804407i	$-0.702483\pi$
$631$	−4.73158e12	−1.18816	−0.594078	+	0.804407i	$0.702483\pi$
$632$	2.03356e12	0.507025
$633$	5.72863e12	1.41819
$634$	3.70172e10	0.00909918
$635$	2.96090e12	0.722672
$636$	−2.60662e12	−0.631713
$637$	−9.15220e10	−0.0220241
$638$	4.34090e12	1.03726
$639$	−8.81454e11	−0.209144
$640$	1.46029e11	0.0344056
$641$	1.38865e12	0.324887	0.162444	−	0.986718i	$-0.448062\pi$
$641$	1.38865e12	0.324887	0.162444	+	0.986718i	$0.448062\pi$
$642$	1.13255e12	0.263118
$643$	3.09398e12	0.713786	0.356893	−	0.934145i	$-0.383836\pi$
$643$	3.09398e12	0.713786	0.356893	+	0.934145i	$0.383836\pi$
$644$	1.51820e12	0.347810
$645$	−1.72950e12	−0.393460
$646$	2.45505e11	0.0554644
$647$	2.31453e12	0.519270	0.259635	−	0.965707i	$-0.416398\pi$
$647$	2.31453e12	0.519270	0.259635	+	0.965707i	$0.416398\pi$
$648$	−1.98200e12	−0.441586
$649$	8.08670e12	1.78925
$650$	4.20953e11	0.0924960
$651$	−2.36712e12	−0.516542
$652$	−3.42132e12	−0.741446
$653$	−8.10575e11	−0.174455	−0.0872276	−	0.996188i	$-0.527801\pi$
$653$	−8.10575e11	−0.174455	−0.0872276	+	0.996188i	$0.527801\pi$
$654$	−3.45225e12	−0.737908
$655$	−3.50367e11	−0.0743768
$656$	−4.16865e11	−0.0878878
$657$	2.82498e12	0.591522
$658$	−2.17200e12	−0.451694
$659$	4.57355e11	0.0944645	0.0472323	−	0.998884i	$-0.484960\pi$
$659$	4.57355e11	0.0944645	0.0472323	+	0.998884i	$0.484960\pi$
$660$	1.15590e12	0.237123
$661$	7.94557e12	1.61889	0.809447	−	0.587193i	$-0.199767\pi$
$661$	7.94557e12	1.61889	0.809447	+	0.587193i	$0.199767\pi$
$662$	−3.45897e12	−0.699980
$663$	5.78055e10	0.0116187
$664$	−1.52161e12	−0.303772
$665$	9.35735e11	0.185548
$666$	−5.74319e11	−0.113115
$667$	−1.37254e13	−2.68508
$668$	−3.18608e12	−0.619103
$669$	−6.58254e12	−1.27050
$670$	8.14229e11	0.156102
$671$	2.51048e12	0.478086
$672$	−4.27997e11	−0.0809616
$673$	−8.92805e12	−1.67760	−0.838801	−	0.544439i	$-0.816743\pi$
$673$	−8.92805e12	−1.67760	−0.838801	+	0.544439i	$0.816743\pi$
$674$	8.00465e11	0.149408
$675$	2.94850e12	0.546682
$676$	−2.65023e12	−0.488116
$677$	−8.01730e12	−1.46683	−0.733414	−	0.679782i	$-0.762074\pi$
$677$	−8.01730e12	−1.46683	−0.733414	+	0.679782i	$0.762074\pi$
$678$	−7.71195e12	−1.40162
$679$	−1.82000e12	−0.328592
$680$	−4.77241e10	−0.00855949
$681$	1.30732e13	2.32927
$682$	4.53036e12	0.801868
$683$	4.14724e12	0.729233	0.364617	−	0.931158i	$-0.381200\pi$
$683$	4.14724e12	0.729233	0.364617	+	0.931158i	$0.381200\pi$
$684$	−1.69041e12	−0.295283
$685$	9.10523e11	0.158010
$686$	−2.21461e11	−0.0381802
$687$	7.39694e12	1.26691
$688$	−1.22561e12	−0.208547
$689$	9.50888e11	0.160747
$690$	−3.65481e12	−0.613824
$691$	−6.05580e12	−1.01046	−0.505231	−	0.862984i	$-0.668593\pi$
$691$	−6.05580e12	−1.01046	−0.505231	+	0.862984i	$0.668593\pi$
$692$	2.67633e12	0.443672
$693$	−1.08048e12	−0.177957
$694$	−2.95370e12	−0.483336
$695$	−2.27028e12	−0.369103
$696$	3.86933e12	0.625020
$697$	1.36237e11	0.0218649
$698$	4.39466e12	0.700771
$699$	−3.51973e12	−0.557651
$700$	1.01860e12	0.160348
$701$	1.88599e12	0.294990	0.147495	−	0.989063i	$-0.452879\pi$
$701$	1.88599e12	0.294990	0.147495	+	0.989063i	$0.452879\pi$
$702$	4.51950e11	0.0702383
$703$	2.79001e12	0.430831
$704$	8.19131e11	0.125683
$705$	5.22873e12	0.797160
$706$	−2.52886e12	−0.383092
$707$	2.17101e12	0.326795
$708$	7.20820e12	1.07815
$709$	−4.76210e12	−0.707767	−0.353884	−	0.935289i	$-0.615139\pi$
$709$	−4.76210e12	−0.707767	−0.353884	+	0.935289i	$0.615139\pi$
$710$	−8.32394e11	−0.122932
$711$	4.57600e12	0.671542
$712$	−6.77817e11	−0.0988444
$713$	−1.43244e13	−2.07574
$714$	1.39875e11	0.0201418
$715$	−4.21671e11	−0.0603387
$716$	−1.03524e12	−0.147208
$717$	3.67574e12	0.519408
$718$	5.45215e12	0.765610
$719$	5.34893e12	0.746427	0.373213	−	0.927746i	$-0.378256\pi$
$719$	5.34893e12	0.746427	0.373213	+	0.927746i	$0.378256\pi$
$720$	3.28601e11	0.0455693
$721$	−4.75774e12	−0.655681
$722$	3.04889e12	0.417565
$723$	1.15224e13	1.56827
$724$	3.19322e12	0.431922
$725$	−9.20871e12	−1.23788
$726$	7.02720e10	0.00938788
$727$	9.08222e12	1.20583	0.602917	−	0.797804i	$-0.294005\pi$
$727$	9.08222e12	1.20583	0.602917	+	0.797804i	$0.294005\pi$
$728$	1.56132e11	0.0206016
$729$	1.49349e12	0.195852
$730$	2.66774e12	0.347689
$731$	4.00544e11	0.0518827
$732$	2.23776e12	0.288080
$733$	−1.20547e13	−1.54237	−0.771185	−	0.636611i	$-0.780336\pi$
$733$	−1.20547e13	−1.54237	−0.771185	+	0.636611i	$0.780336\pi$
$734$	−9.76345e12	−1.24157
$735$	5.33129e11	0.0673813
$736$	−2.58998e12	−0.325347
$737$	4.56731e12	0.570239
$738$	−9.38048e11	−0.116405
$739$	1.08128e13	1.33364	0.666822	−	0.745217i	$-0.267654\pi$
$739$	1.08128e13	1.33364	0.666822	+	0.745217i	$0.267654\pi$
$740$	−5.42354e11	−0.0664875
$741$	1.93353e12	0.235597
$742$	2.30091e12	0.278665
$743$	6.39433e12	0.769742	0.384871	−	0.922970i	$-0.374246\pi$
$743$	6.39433e12	0.769742	0.384871	+	0.922970i	$0.374246\pi$
$744$	4.03820e12	0.483181
$745$	−2.52468e11	−0.0300264
$746$	6.95889e12	0.822650
$747$	−3.42400e12	−0.402337
$748$	−2.67702e11	−0.0312676
$749$	−9.99726e11	−0.116068
$750$	−5.34211e12	−0.616506
$751$	−2.30580e12	−0.264510	−0.132255	−	0.991216i	$-0.542222\pi$
$751$	−2.30580e12	−0.264510	−0.132255	+	0.991216i	$0.542222\pi$
$752$	3.70534e12	0.422521
$753$	8.29422e11	0.0940152
$754$	−1.41152e12	−0.159044
$755$	3.98170e12	0.445971
$756$	1.09361e12	0.121763
$757$	−6.85316e12	−0.758507	−0.379253	−	0.925293i	$-0.623819\pi$
$757$	−6.85316e12	−0.758507	−0.379253	+	0.925293i	$0.623819\pi$
$758$	−1.16908e13	−1.28628
$759$	−2.05012e13	−2.24229
$760$	−1.59632e12	−0.173564
$761$	−1.55520e12	−0.168095	−0.0840474	−	0.996462i	$-0.526785\pi$
$761$	−1.55520e12	−0.168095	−0.0840474	+	0.996462i	$0.526785\pi$
$762$	1.48045e13	1.59073
$763$	3.04737e12	0.325510
$764$	−9.77784e11	−0.103830
$765$	−1.07391e11	−0.0113368
$766$	3.37718e12	0.354425
$767$	−2.62954e12	−0.274347
$768$	7.30144e11	0.0757327
$769$	−1.31148e12	−0.135236	−0.0676179	−	0.997711i	$-0.521540\pi$
$769$	−1.31148e12	−0.135236	−0.0676179	+	0.997711i	$0.521540\pi$
$770$	−1.02034e12	−0.104601
$771$	−4.67549e12	−0.476521
$772$	−6.17454e12	−0.625644
$773$	−9.82010e12	−0.989255	−0.494627	−	0.869105i	$-0.664695\pi$
$773$	−9.82010e12	−0.989255	−0.494627	+	0.869105i	$0.664695\pi$
$774$	−2.75792e12	−0.276215
$775$	−9.61062e12	−0.956959
$776$	3.10484e12	0.307370
$777$	1.58959e12	0.156455
$778$	1.15497e11	0.0113022
$779$	4.55698e12	0.443362
$780$	−3.75862e11	−0.0363583
$781$	−4.66921e12	−0.449070
$782$	8.46439e11	0.0809404
$783$	−9.88682e12	−0.940001
$784$	3.77802e11	0.0357143
$785$	−2.41019e12	−0.226536
$786$	−1.75184e12	−0.163716
$787$	−4.81658e12	−0.447562	−0.223781	−	0.974639i	$-0.571840\pi$
$787$	−4.81658e12	−0.447562	−0.223781	+	0.974639i	$0.571840\pi$
$788$	−3.19484e12	−0.295176
$789$	−3.78411e12	−0.347630
$790$	4.32131e12	0.394724
$791$	6.80750e12	0.618292
$792$	1.84324e12	0.166464
$793$	−8.16328e11	−0.0733053
$794$	−1.11902e13	−0.999183
$795$	−5.53906e12	−0.491795
$796$	−7.50406e11	−0.0662502
$797$	7.71344e12	0.677151	0.338575	−	0.940939i	$-0.390055\pi$
$797$	7.71344e12	0.677151	0.338575	+	0.940939i	$0.390055\pi$
$798$	4.67867e12	0.408423
$799$	−1.21095e12	−0.105116
$800$	−1.73769e12	−0.149992
$801$	−1.52525e12	−0.130917
$802$	1.02503e13	0.874887
$803$	1.49644e13	1.27010
$804$	4.07114e12	0.343609
$805$	3.22618e12	0.270774
$806$	−1.47313e12	−0.122951
$807$	2.94128e12	0.244121
$808$	−3.70365e12	−0.305688
$809$	2.12869e13	1.74721	0.873604	−	0.486637i	$-0.161777\pi$
$809$	2.12869e13	1.74721	0.873604	+	0.486637i	$0.161777\pi$
$810$	−4.21174e12	−0.343779
$811$	2.45053e13	1.98914	0.994570	−	0.104067i	$-0.0331856\pi$
$811$	2.45053e13	1.98914	0.994570	+	0.104067i	$0.0331856\pi$
$812$	−3.41554e12	−0.275713
$813$	8.19231e12	0.657656
$814$	−3.04227e12	−0.242878
$815$	−7.27030e12	−0.577223
$816$	−2.38621e11	−0.0188409
$817$	1.33978e13	1.05204
$818$	−2.10400e11	−0.0164307
$819$	3.51336e11	0.0272863
$820$	−8.85839e11	−0.0684214
$821$	−9.72826e12	−0.747293	−0.373646	−	0.927571i	$-0.621893\pi$
$821$	−9.72826e12	−0.747293	−0.373646	+	0.927571i	$0.621893\pi$
$822$	4.55261e12	0.347807
$823$	−8.28745e11	−0.0629683	−0.0314841	−	0.999504i	$-0.510023\pi$
$823$	−8.28745e11	−0.0629683	−0.0314841	+	0.999504i	$0.510023\pi$
$824$	8.11650e12	0.613333
$825$	−1.37548e13	−1.03374
$826$	−6.36283e12	−0.475598
$827$	2.42842e13	1.80530	0.902649	−	0.430376i	$-0.141619\pi$
$827$	2.42842e13	1.80530	0.902649	+	0.430376i	$0.141619\pi$
$828$	−5.82809e12	−0.430913
$829$	1.95570e13	1.43816	0.719078	−	0.694929i	$-0.244564\pi$
$829$	1.95570e13	1.43816	0.719078	+	0.694929i	$0.244564\pi$
$830$	−3.23342e12	−0.236489
$831$	1.36652e13	0.994055
$832$	−2.66355e11	−0.0192711
$833$	−1.23471e11	−0.00888507
$834$	−1.13514e13	−0.812459
$835$	−6.77043e12	−0.481978
$836$	−8.95437e12	−0.634025
$837$	−1.03183e13	−0.726682
$838$	−9.27865e12	−0.649960
$839$	−7.69577e12	−0.536196	−0.268098	−	0.963392i	$-0.586395\pi$
$839$	−7.69577e12	−0.536196	−0.268098	+	0.963392i	$0.586395\pi$
$840$	−9.09494e11	−0.0630294
$841$	1.63712e13	1.12849
$842$	2.65880e12	0.182298
$843$	−3.32512e13	−2.26769
$844$	8.62664e12	0.585195
$845$	−5.63173e12	−0.380003
$846$	8.33793e12	0.559618
$847$	−6.20305e10	−0.00414124
$848$	−3.92526e12	−0.260667
$849$	−1.02476e13	−0.676923
$850$	5.67899e11	0.0373152
$851$	9.61924e12	0.628721
$852$	−4.16197e12	−0.270596
$853$	−2.79895e12	−0.181019	−0.0905097	−	0.995896i	$-0.528850\pi$
$853$	−2.79895e12	−0.181019	−0.0905097	+	0.995896i	$0.528850\pi$
$854$	−1.97531e12	−0.127079
$855$	−3.59211e12	−0.229881
$856$	1.70549e12	0.108572
$857$	−5.56141e12	−0.352185	−0.176093	−	0.984374i	$-0.556346\pi$
$857$	−5.56141e12	−0.352185	−0.176093	+	0.984374i	$0.556346\pi$
$858$	−2.10835e12	−0.132816
$859$	3.51052e12	0.219989	0.109995	−	0.993932i	$-0.464917\pi$
$859$	3.51052e12	0.219989	0.109995	+	0.993932i	$0.464917\pi$
$860$	−2.60442e12	−0.162356
$861$	2.59631e12	0.161006
$862$	1.21236e13	0.747908
$863$	1.43838e13	0.882721	0.441361	−	0.897330i	$-0.354496\pi$
$863$	1.43838e13	0.882721	0.441361	+	0.897330i	$0.354496\pi$
$864$	−1.86565e12	−0.113898
$865$	5.68720e12	0.345403
$866$	−1.71976e13	−1.03905
$867$	−2.00820e13	−1.20704
$868$	−3.56460e12	−0.213144
$869$	2.42399e13	1.44192
$870$	8.22232e12	0.486584
$871$	−1.48514e12	−0.0874353
$872$	−5.19868e12	−0.304487
$873$	6.98664e12	0.407103
$874$	2.83125e13	1.64126
$875$	4.71559e12	0.271957
$876$	1.33387e13	0.765325
$877$	−6.34278e12	−0.362061	−0.181030	−	0.983477i	$-0.557943\pi$
$877$	−6.34278e12	−0.362061	−0.181030	+	0.983477i	$0.557943\pi$
$878$	2.72670e12	0.154850
$879$	−8.27463e12	−0.467519
$880$	1.74065e12	0.0978453
$881$	−2.89282e13	−1.61782	−0.808910	−	0.587933i	$-0.799942\pi$
$881$	−2.89282e13	−1.61782	−0.808910	+	0.587933i	$0.799942\pi$
$882$	8.50147e11	0.0473026
$883$	−7.17154e12	−0.396999	−0.198500	−	0.980101i	$-0.563607\pi$
$883$	−7.17154e12	−0.396999	−0.198500	+	0.980101i	$0.563607\pi$
$884$	8.70482e10	0.00479430
$885$	1.53174e13	0.839346
$886$	1.96699e13	1.07238
$887$	−1.68020e13	−0.911389	−0.455695	−	0.890136i	$-0.650609\pi$
$887$	−1.68020e13	−0.911389	−0.455695	+	0.890136i	$0.650609\pi$
$888$	−2.71177e12	−0.146351
$889$	−1.30682e13	−0.701711
$890$	−1.44036e12	−0.0769513
$891$	−2.36252e13	−1.25582
$892$	−9.91254e12	−0.524255
$893$	−4.05052e13	−2.13147
$894$	−1.26234e12	−0.0660933
$895$	−2.19989e12	−0.114603
$896$	−6.44514e11	−0.0334077
$897$	6.66633e12	0.343812
$898$	−1.16127e12	−0.0595921
$899$	3.22260e13	1.64546
$900$	−3.91022e12	−0.198660
$901$	1.28282e12	0.0648493
$902$	−4.96900e12	−0.249942
$903$	7.63331e12	0.382048
$904$	−1.16133e13	−0.578359
$905$	6.78559e12	0.336255
$906$	1.99085e13	0.981660
$907$	−1.87924e13	−0.922038	−0.461019	−	0.887390i	$-0.652516\pi$
$907$	−1.87924e13	−0.922038	−0.461019	+	0.887390i	$0.652516\pi$
$908$	1.96867e13	0.961139
$909$	−8.33412e12	−0.404876
$910$	3.31781e11	0.0160386
$911$	−3.39496e13	−1.63306	−0.816529	−	0.577304i	$-0.804105\pi$
$911$	−3.39496e13	−1.63306	−0.816529	+	0.577304i	$0.804105\pi$
$912$	−7.98161e12	−0.382044
$913$	−1.81375e13	−0.863890
$914$	−1.06267e13	−0.503666
$915$	4.75523e12	0.224273
$916$	1.11389e13	0.522773
$917$	1.54638e12	0.0722195
$918$	6.09717e11	0.0283359
$919$	1.03287e13	0.477667	0.238833	−	0.971061i	$-0.423235\pi$
$919$	1.03287e13	0.477667	0.238833	+	0.971061i	$0.423235\pi$
$920$	−5.50371e12	−0.253286
$921$	4.67803e13	2.14237
$922$	−1.94401e13	−0.885952
$923$	1.51828e12	0.0688563
$924$	−5.10169e12	−0.230245
$925$	6.45381e12	0.289853
$926$	4.70205e12	0.210154
$927$	1.82641e13	0.812344
$928$	5.82675e12	0.257906
$929$	−2.79767e13	−1.23233	−0.616163	−	0.787619i	$-0.711314\pi$
$929$	−2.79767e13	−1.23233	−0.616163	+	0.787619i	$0.711314\pi$
$930$	8.58118e12	0.376161
$931$	−4.12996e12	−0.180166
$932$	−5.30030e12	−0.230107
$933$	1.90947e13	0.824984
$934$	7.56980e12	0.325479
$935$	−5.68868e11	−0.0243421
$936$	−5.99364e11	−0.0255240
$937$	3.31649e13	1.40556	0.702782	−	0.711406i	$-0.251941\pi$
$937$	3.31649e13	1.40556	0.702782	+	0.711406i	$0.251941\pi$
$938$	−3.59368e12	−0.151575
$939$	−1.80437e13	−0.757411
$940$	7.87386e12	0.328937
$941$	3.19309e13	1.32757	0.663786	−	0.747923i	$-0.268949\pi$
$941$	3.19309e13	1.32757	0.663786	+	0.747923i	$0.268949\pi$
$942$	−1.20510e13	−0.498646
$943$	1.57113e13	0.647009
$944$	1.08547e13	0.444881
$945$	2.32392e12	0.0947933
$946$	−1.46092e13	−0.593082
$947$	3.56921e13	1.44210	0.721052	−	0.692881i	$-0.243659\pi$
$947$	3.56921e13	1.44210	0.721052	+	0.692881i	$0.243659\pi$
$948$	2.16066e13	0.868856
$949$	−4.86594e12	−0.194746
$950$	1.89956e13	0.756654
$951$	3.93308e11	0.0155927
$952$	2.10635e11	0.00831122
$953$	−3.04923e13	−1.19749	−0.598745	−	0.800940i	$-0.704334\pi$
$953$	−3.04923e13	−1.19749	−0.598745	+	0.800940i	$0.704334\pi$
$954$	−8.83279e12	−0.345247
$955$	−2.07779e12	−0.0808327
$956$	5.53524e12	0.214326
$957$	4.61221e13	1.77748
$958$	−3.29512e13	−1.26394
$959$	−4.01869e12	−0.153427
$960$	1.55156e12	0.0589586
$961$	7.19282e12	0.272047
$962$	9.89248e11	0.0372406
$963$	3.83776e12	0.143800
$964$	1.73514e13	0.647124
$965$	−1.31209e13	−0.487069
$966$	1.61309e13	0.596020
$967$	−3.45533e13	−1.27078	−0.635389	−	0.772192i	$-0.719160\pi$
$967$	−3.45533e13	−1.27078	−0.635389	+	0.772192i	$0.719160\pi$
$968$	1.05821e11	0.00387377
$969$	2.60849e12	0.0950457
$970$	6.59778e12	0.239290
$971$	−2.06708e13	−0.746225	−0.373112	−	0.927786i	$-0.621709\pi$
$971$	−2.06708e13	−0.746225	−0.373112	+	0.927786i	$0.621709\pi$
$972$	−1.20935e13	−0.434563
$973$	1.00201e13	0.358397
$974$	−1.95595e13	−0.696374
$975$	4.47262e12	0.158504
$976$	3.36980e12	0.118872
$977$	1.78789e11	0.00627791	0.00313896	−	0.999995i	$-0.499001\pi$
$977$	1.78789e11	0.00627791	0.00313896	+	0.999995i	$0.499001\pi$
$978$	−3.63515e13	−1.27057
$979$	−8.07952e12	−0.281102
$980$	8.02829e11	0.0278039
$981$	−1.16983e13	−0.403285
$982$	3.17159e12	0.108837
$983$	−1.42657e13	−0.487305	−0.243652	−	0.969863i	$-0.578346\pi$
$983$	−1.42657e13	−0.487305	−0.243652	+	0.969863i	$0.578346\pi$
$984$	−4.42919e12	−0.150608
$985$	−6.78902e12	−0.229797
$986$	−1.90426e12	−0.0641622
$987$	−2.30776e13	−0.774038
$988$	2.91167e12	0.0972157
$989$	4.61922e13	1.53527
$990$	3.91689e12	0.129594
$991$	−2.71296e13	−0.893537	−0.446768	−	0.894650i	$-0.647425\pi$
$991$	−2.71296e13	−0.893537	−0.446768	+	0.894650i	$0.647425\pi$
$992$	6.08106e12	0.199378
$993$	−3.67515e13	−1.19951
$994$	3.67386e12	0.119367
$995$	−1.59461e12	−0.0515764
$996$	−1.61671e13	−0.520554
$997$	−3.86723e12	−0.123957	−0.0619787	−	0.998077i	$-0.519741\pi$
$997$	−3.86723e12	−0.123957	−0.0619787	+	0.998077i	$0.519741\pi$
$998$	−4.81191e12	−0.153543
$999$	6.92905e12	0.220104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.10.a.b.1.1	✓	1
3.2	odd	2		126.10.a.a.1.1		1
4.3	odd	2		112.10.a.a.1.1		1
5.2	odd	4		350.10.c.d.99.2		2
5.3	odd	4		350.10.c.d.99.1		2
5.4	even	2		350.10.a.a.1.1		1
7.2	even	3		98.10.c.a.67.1		2
7.3	odd	6		98.10.c.d.79.1		2
7.4	even	3		98.10.c.a.79.1		2
7.5	odd	6		98.10.c.d.67.1		2
7.6	odd	2		98.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.b.1.1	✓	1	1.1	even	1	trivial
98.10.a.b.1.1		1	7.6	odd	2
98.10.c.a.67.1		2	7.2	even	3
98.10.c.a.79.1		2	7.4	even	3
98.10.c.d.67.1		2	7.5	odd	6
98.10.c.d.79.1		2	7.3	odd	6
112.10.a.a.1.1		1	4.3	odd	2
126.10.a.a.1.1		1	3.2	odd	2
350.10.a.a.1.1		1	5.4	even	2
350.10.c.d.99.1		2	5.3	odd	4
350.10.c.d.99.2		2	5.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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