LMFDB - Embedded newform 14.12.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,12,Mod(1,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$10.7568045278$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+32.0000 q^{2} -90.0000 q^{3} +1024.00 q^{4} -7480.00 q^{5} -2880.00 q^{6} -16807.0 q^{7} +32768.0 q^{8} -169047. q^{9} +O(q^{10})$

\(q+32.0000 q^{2} -90.0000 q^{3} +1024.00 q^{4} -7480.00 q^{5} -2880.00 q^{6} -16807.0 q^{7} +32768.0 q^{8} -169047. q^{9} -239360. q^{10} -294536. q^{11} -92160.0 q^{12} -210588. q^{13} -537824. q^{14} +673200. q^{15} +1.04858e6 q^{16} -6.96291e6 q^{17} -5.40950e6 q^{18} -9.34639e6 q^{19} -7.65952e6 q^{20} +1.51263e6 q^{21} -9.42515e6 q^{22} +5.11720e7 q^{23} -2.94912e6 q^{24} +7.12228e6 q^{25} -6.73882e6 q^{26} +3.11575e7 q^{27} -1.72104e7 q^{28} +1.66196e8 q^{29} +2.15424e7 q^{30} +1.19001e8 q^{31} +3.35544e7 q^{32} +2.65082e7 q^{33} -2.22813e8 q^{34} +1.25716e8 q^{35} -1.73104e8 q^{36} -2.75546e8 q^{37} -2.99084e8 q^{38} +1.89529e7 q^{39} -2.45105e8 q^{40} -1.97988e8 q^{41} +4.84042e7 q^{42} -8.09490e8 q^{43} -3.01605e8 q^{44} +1.26447e9 q^{45} +1.63750e9 q^{46} -2.60020e9 q^{47} -9.43718e7 q^{48} +2.82475e8 q^{49} +2.27913e8 q^{50} +6.26662e8 q^{51} -2.15642e8 q^{52} +7.33631e8 q^{53} +9.97039e8 q^{54} +2.20313e9 q^{55} -5.50732e8 q^{56} +8.41175e8 q^{57} +5.31828e9 q^{58} -4.65713e9 q^{59} +6.89357e8 q^{60} -5.13584e9 q^{61} +3.80803e9 q^{62} +2.84117e9 q^{63} +1.07374e9 q^{64} +1.57520e9 q^{65} +8.48264e8 q^{66} +8.81056e9 q^{67} -7.13002e9 q^{68} -4.60548e9 q^{69} +4.02292e9 q^{70} -3.84901e9 q^{71} -5.53933e9 q^{72} -1.86867e10 q^{73} -8.81746e9 q^{74} -6.41005e8 q^{75} -9.57070e9 q^{76} +4.95027e9 q^{77} +6.06493e8 q^{78} -2.98501e10 q^{79} -7.84335e9 q^{80} +2.71420e10 q^{81} -6.33563e9 q^{82} -5.87598e9 q^{83} +1.54893e9 q^{84} +5.20825e10 q^{85} -2.59037e10 q^{86} -1.49577e10 q^{87} -9.65136e9 q^{88} +8.30565e10 q^{89} +4.04631e10 q^{90} +3.53935e9 q^{91} +5.24001e10 q^{92} -1.07101e10 q^{93} -8.32063e10 q^{94} +6.99110e10 q^{95} -3.01990e9 q^{96} +1.49401e11 q^{97} +9.03921e9 q^{98} +4.97904e10 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	−90.0000	−0.213833	−0.106917	−	0.994268i	$-0.534098\pi$
$3$	−90.0000	−0.213833	−0.106917	+	0.994268i	$0.534098\pi$
$4$	1024.00	0.500000
$5$	−7480.00	−1.07045	−0.535225	−	0.844709i	$-0.679773\pi$
$5$	−7480.00	−1.07045	−0.535225	+	0.844709i	$0.679773\pi$
$6$	−2880.00	−0.151203
$7$	−16807.0	−0.377964
$7$	−16807.0	−0.377964
$8$	32768.0	0.353553
$9$	−169047.	−0.954275
$10$	−239360.	−0.756923
$11$	−294536.	−0.551415	−0.275708	−	0.961242i	$-0.588912\pi$
$11$	−294536.	−0.551415	−0.275708	+	0.961242i	$0.588912\pi$
$12$	−92160.0	−0.106917
$13$	−210588.	−0.157306	−0.0786530	−	0.996902i	$-0.525062\pi$
$13$	−210588.	−0.157306	−0.0786530	+	0.996902i	$0.525062\pi$
$14$	−537824.	−0.267261
$15$	673200.	0.228898
$16$	1.04858e6	0.250000
$17$	−6.96291e6	−1.18938	−0.594691	−	0.803954i	$-0.702726\pi$
$17$	−6.96291e6	−1.18938	−0.594691	+	0.803954i	$0.702726\pi$
$18$	−5.40950e6	−0.674775
$19$	−9.34639e6	−0.865963	−0.432981	−	0.901403i	$-0.642538\pi$
$19$	−9.34639e6	−0.865963	−0.432981	+	0.901403i	$0.642538\pi$
$20$	−7.65952e6	−0.535225
$21$	1.51263e6	0.0808214
$22$	−9.42515e6	−0.389909
$23$	5.11720e7	1.65779	0.828895	−	0.559405i	$-0.188970\pi$
$23$	5.11720e7	1.65779	0.828895	+	0.559405i	$0.188970\pi$
$24$	−2.94912e6	−0.0756015
$25$	7.12228e6	0.145864
$26$	−6.73882e6	−0.111232
$27$	3.11575e7	0.417889
$28$	−1.72104e7	−0.188982
$29$	1.66196e8	1.50464	0.752320	−	0.658798i	$-0.228935\pi$
$29$	1.66196e8	1.50464	0.752320	+	0.658798i	$0.228935\pi$
$30$	2.15424e7	0.161855
$31$	1.19001e8	0.746554	0.373277	−	0.927720i	$-0.378234\pi$
$31$	1.19001e8	0.746554	0.373277	+	0.927720i	$0.378234\pi$
$32$	3.35544e7	0.176777
$33$	2.65082e7	0.117911
$34$	−2.22813e8	−0.841020
$35$	1.25716e8	0.404592
$36$	−1.73104e8	−0.477138
$37$	−2.75546e8	−0.653257	−0.326628	−	0.945153i	$-0.605913\pi$
$37$	−2.75546e8	−0.653257	−0.326628	+	0.945153i	$0.605913\pi$
$38$	−2.99084e8	−0.612328
$39$	1.89529e7	0.0336373
$40$	−2.45105e8	−0.378461
$41$	−1.97988e8	−0.266888	−0.133444	−	0.991056i	$-0.542604\pi$
$41$	−1.97988e8	−0.266888	−0.133444	+	0.991056i	$0.542604\pi$
$42$	4.84042e7	0.0571494
$43$	−8.09490e8	−0.839721	−0.419860	−	0.907589i	$-0.637921\pi$
$43$	−8.09490e8	−0.839721	−0.419860	+	0.907589i	$0.637921\pi$
$44$	−3.01605e8	−0.275708
$45$	1.26447e9	1.02150
$46$	1.63750e9	1.17223
$47$	−2.60020e9	−1.65374	−0.826871	−	0.562391i	$-0.809882\pi$
$47$	−2.60020e9	−1.65374	−0.826871	+	0.562391i	$0.809882\pi$
$48$	−9.43718e7	−0.0534584
$49$	2.82475e8	0.142857
$50$	2.27913e8	0.103142
$51$	6.26662e8	0.254330
$52$	−2.15642e8	−0.0786530
$53$	7.33631e8	0.240969	0.120484	−	0.992715i	$-0.461555\pi$
$53$	7.33631e8	0.240969	0.120484	+	0.992715i	$0.461555\pi$
$54$	9.97039e8	0.295492
$55$	2.20313e9	0.590262
$56$	−5.50732e8	−0.133631
$57$	8.41175e8	0.185172
$58$	5.31828e9	1.06394
$59$	−4.65713e9	−0.848071	−0.424035	−	0.905646i	$-0.639387\pi$
$59$	−4.65713e9	−0.848071	−0.424035	+	0.905646i	$0.639387\pi$
$60$	6.89357e8	0.114449
$61$	−5.13584e9	−0.778569	−0.389285	−	0.921118i	$-0.627278\pi$
$61$	−5.13584e9	−0.778569	−0.389285	+	0.921118i	$0.627278\pi$
$62$	3.80803e9	0.527893
$63$	2.84117e9	0.360682
$64$	1.07374e9	0.125000
$65$	1.57520e9	0.168388
$66$	8.48264e8	0.0833756
$67$	8.81056e9	0.797246	0.398623	−	0.917115i	$-0.369488\pi$
$67$	8.81056e9	0.797246	0.398623	+	0.917115i	$0.369488\pi$
$68$	−7.13002e9	−0.594691
$69$	−4.60548e9	−0.354491
$70$	4.02292e9	0.286090
$71$	−3.84901e9	−0.253179	−0.126590	−	0.991955i	$-0.540403\pi$
$71$	−3.84901e9	−0.253179	−0.126590	+	0.991955i	$0.540403\pi$
$72$	−5.53933e9	−0.337387
$73$	−1.86867e10	−1.05501	−0.527507	−	0.849551i	$-0.676873\pi$
$73$	−1.86867e10	−1.05501	−0.527507	+	0.849551i	$0.676873\pi$
$74$	−8.81746e9	−0.461922
$75$	−6.41005e8	−0.0311906
$76$	−9.57070e9	−0.432981
$77$	4.95027e9	0.208415
$78$	6.06493e8	0.0237851
$79$	−2.98501e10	−1.09143	−0.545715	−	0.837971i	$-0.683742\pi$
$79$	−2.98501e10	−1.09143	−0.545715	+	0.837971i	$0.683742\pi$
$80$	−7.84335e9	−0.267613
$81$	2.71420e10	0.864917
$82$	−6.33563e9	−0.188718
$83$	−5.87598e9	−0.163739	−0.0818693	−	0.996643i	$-0.526089\pi$
$83$	−5.87598e9	−0.163739	−0.0818693	+	0.996643i	$0.526089\pi$
$84$	1.54893e9	0.0404107
$85$	5.20825e10	1.27317
$86$	−2.59037e10	−0.593772
$87$	−1.49577e10	−0.321742
$88$	−9.65136e9	−0.194955
$89$	8.30565e10	1.57663	0.788313	−	0.615274i	$-0.210955\pi$
$89$	8.30565e10	1.57663	0.788313	+	0.615274i	$0.210955\pi$
$90$	4.04631e10	0.722313
$91$	3.53935e9	0.0594561
$92$	5.24001e10	0.828895
$93$	−1.07101e10	−0.159638
$94$	−8.32063e10	−1.16937
$95$	6.99110e10	0.926970
$96$	−3.01990e9	−0.0378008
$97$	1.49401e11	1.76648	0.883239	−	0.468923i	$-0.155358\pi$
$97$	1.49401e11	1.76648	0.883239	+	0.468923i	$0.155358\pi$
$98$	9.03921e9	0.101015
$99$	4.97904e10	0.526202
$100$	7.29321e9	0.0729321
$101$	−1.94657e11	−1.84291	−0.921454	−	0.388488i	$-0.872997\pi$
$101$	−1.94657e11	−1.84291	−0.921454	+	0.388488i	$0.872997\pi$
$102$	2.00532e10	0.179838
$103$	−2.07935e11	−1.76735	−0.883674	−	0.468102i	$-0.844938\pi$
$103$	−2.07935e11	−1.76735	−0.883674	+	0.468102i	$0.844938\pi$
$104$	−6.90055e9	−0.0556161
$105$	−1.13145e10	−0.0865153
$106$	2.34762e10	0.170391
$107$	−2.13188e11	−1.46944	−0.734721	−	0.678369i	$-0.762687\pi$
$107$	−2.13188e11	−1.46944	−0.734721	+	0.678369i	$0.762687\pi$
$108$	3.19052e10	0.208945
$109$	−8.64802e10	−0.538358	−0.269179	−	0.963090i	$-0.586752\pi$
$109$	−8.64802e10	−0.538358	−0.269179	+	0.963090i	$0.586752\pi$
$110$	7.05001e10	0.417379
$111$	2.47991e10	0.139688
$112$	−1.76234e10	−0.0944911
$113$	2.73711e11	1.39753	0.698765	−	0.715351i	$-0.253733\pi$
$113$	2.73711e11	1.39753	0.698765	+	0.715351i	$0.253733\pi$
$114$	2.69176e10	0.130936
$115$	−3.82767e11	−1.77458
$116$	1.70185e11	0.752320
$117$	3.55993e10	0.150113
$118$	−1.49028e11	−0.599676
$119$	1.17026e11	0.449544
$120$	2.20594e10	0.0809277
$121$	−1.98560e11	−0.695941
$122$	−1.64347e11	−0.550532
$123$	1.78190e10	0.0570695
$124$	1.21857e11	0.373277
$125$	3.11960e11	0.914310
$126$	9.09175e10	0.255041
$127$	−1.50737e11	−0.404854	−0.202427	−	0.979297i	$-0.564883\pi$
$127$	−1.50737e11	−0.404854	−0.202427	+	0.979297i	$0.564883\pi$
$128$	3.43597e10	0.0883883
$129$	7.28541e10	0.179560
$130$	5.04063e10	0.119068
$131$	1.00555e11	0.227726	0.113863	−	0.993496i	$-0.463678\pi$
$131$	1.00555e11	0.227726	0.113863	+	0.993496i	$0.463678\pi$
$132$	2.71444e10	0.0589555
$133$	1.57085e11	0.327303
$134$	2.81938e11	0.563738
$135$	−2.33058e11	−0.447330
$136$	−2.28161e11	−0.420510
$137$	1.05164e12	1.86167	0.930834	−	0.365443i	$-0.119083\pi$
$137$	1.05164e12	1.86167	0.930834	+	0.365443i	$0.119083\pi$
$138$	−1.47375e11	−0.250663
$139$	−1.20260e11	−0.196579	−0.0982897	−	0.995158i	$-0.531337\pi$
$139$	−1.20260e11	−0.196579	−0.0982897	+	0.995158i	$0.531337\pi$
$140$	1.28734e11	0.202296
$141$	2.34018e11	0.353625
$142$	−1.23168e11	−0.179025
$143$	6.20257e10	0.0867409
$144$	−1.77259e11	−0.238569
$145$	−1.24315e12	−1.61064
$146$	−5.97976e11	−0.746007
$147$	−2.54228e10	−0.0305476
$148$	−2.82159e11	−0.326628
$149$	1.54109e12	1.71911	0.859555	−	0.511044i	$-0.170741\pi$
$149$	1.54109e12	1.71911	0.859555	+	0.511044i	$0.170741\pi$
$150$	−2.05122e10	−0.0220551
$151$	8.66822e10	0.0898580	0.0449290	−	0.998990i	$-0.485694\pi$
$151$	8.66822e10	0.0898580	0.0449290	+	0.998990i	$0.485694\pi$
$152$	−3.06263e11	−0.306164
$153$	1.17706e12	1.13500
$154$	1.58409e11	0.147372
$155$	−8.90127e11	−0.799149
$156$	1.94078e10	0.0168186
$157$	−2.81064e11	−0.235156	−0.117578	−	0.993064i	$-0.537513\pi$
$157$	−2.81064e11	−0.235156	−0.117578	+	0.993064i	$0.537513\pi$
$158$	−9.55202e11	−0.771758
$159$	−6.60268e10	−0.0515272
$160$	−2.50987e11	−0.189231
$161$	−8.60048e11	−0.626585
$162$	8.68544e11	0.611588
$163$	−1.93045e12	−1.31410	−0.657048	−	0.753849i	$-0.728195\pi$
$163$	−1.93045e12	−1.31410	−0.657048	+	0.753849i	$0.728195\pi$
$164$	−2.02740e11	−0.133444
$165$	−1.98282e11	−0.126218
$166$	−1.88031e11	−0.115781
$167$	−2.27036e11	−0.135255	−0.0676277	−	0.997711i	$-0.521543\pi$
$167$	−2.27036e11	−0.135255	−0.0676277	+	0.997711i	$0.521543\pi$
$168$	4.95659e10	0.0285747
$169$	−1.74781e12	−0.975255
$170$	1.66664e12	0.900271
$171$	1.57998e12	0.826367
$172$	−8.28917e11	−0.419860
$173$	3.42956e11	0.168262	0.0841308	−	0.996455i	$-0.473189\pi$
$173$	3.42956e11	0.168262	0.0841308	+	0.996455i	$0.473189\pi$
$174$	−4.78645e11	−0.227506
$175$	−1.19704e11	−0.0551315
$176$	−3.08843e11	−0.137854
$177$	4.19141e11	0.181346
$178$	2.65781e12	1.11484
$179$	2.20247e12	0.895813	0.447907	−	0.894080i	$-0.352170\pi$
$179$	2.20247e12	0.895813	0.447907	+	0.894080i	$0.352170\pi$
$180$	1.29482e12	0.510752
$181$	4.36015e11	0.166828	0.0834140	−	0.996515i	$-0.473418\pi$
$181$	4.36015e11	0.166828	0.0834140	+	0.996515i	$0.473418\pi$
$182$	1.13259e11	0.0420418
$183$	4.62225e11	0.166484
$184$	1.67680e12	0.586117
$185$	2.06108e12	0.699279
$186$	−3.42723e11	−0.112881
$187$	2.05083e12	0.655843
$188$	−2.66260e12	−0.826871
$189$	−5.23663e11	−0.157947
$190$	2.23715e12	0.655467
$191$	−3.46620e12	−0.986666	−0.493333	−	0.869841i	$-0.664222\pi$
$191$	−3.46620e12	−0.986666	−0.493333	+	0.869841i	$0.664222\pi$
$192$	−9.66368e10	−0.0267292
$193$	−4.78694e12	−1.28675	−0.643373	−	0.765553i	$-0.722465\pi$
$193$	−4.78694e12	−1.28675	−0.643373	+	0.765553i	$0.722465\pi$
$194$	4.78083e12	1.24909
$195$	−1.41768e11	−0.0360070
$196$	2.89255e11	0.0714286
$197$	−4.39904e12	−1.05632	−0.528158	−	0.849146i	$-0.677117\pi$
$197$	−4.39904e12	−1.05632	−0.528158	+	0.849146i	$0.677117\pi$
$198$	1.59329e12	0.372081
$199$	8.19877e12	1.86233	0.931166	−	0.364596i	$-0.118793\pi$
$199$	8.19877e12	1.86233	0.931166	+	0.364596i	$0.118793\pi$
$200$	2.33383e11	0.0515708
$201$	−7.92951e11	−0.170478
$202$	−6.22904e12	−1.30313
$203$	−2.79326e12	−0.568700
$204$	6.41701e11	0.127165
$205$	1.48095e12	0.285690
$206$	−6.65391e12	−1.24970
$207$	−8.65047e12	−1.58199
$208$	−2.20818e11	−0.0393265
$209$	2.75285e12	0.477505
$210$	−3.62063e11	−0.0611756
$211$	−6.08013e12	−1.00083	−0.500414	−	0.865786i	$-0.666819\pi$
$211$	−6.08013e12	−1.00083	−0.500414	+	0.865786i	$0.666819\pi$
$212$	7.51239e11	0.120484
$213$	3.46411e11	0.0541381
$214$	−6.82202e12	−1.03905
$215$	6.05498e12	0.898879
$216$	1.02097e12	0.147746
$217$	−2.00005e12	−0.282171
$218$	−2.76737e12	−0.380676
$219$	1.68181e12	0.225597
$220$	2.25600e12	0.295131
$221$	1.46630e12	0.187097
$222$	7.93571e11	0.0987744
$223$	1.25536e13	1.52437	0.762184	−	0.647360i	$-0.224127\pi$
$223$	1.25536e13	1.52437	0.762184	+	0.647360i	$0.224127\pi$
$224$	−5.63949e11	−0.0668153
$225$	−1.20400e12	−0.139195
$226$	8.75876e12	0.988203
$227$	7.58768e12	0.835539	0.417769	−	0.908553i	$-0.362812\pi$
$227$	7.58768e12	0.835539	0.417769	+	0.908553i	$0.362812\pi$
$228$	8.61363e11	0.0925859
$229$	−7.56606e12	−0.793916	−0.396958	−	0.917837i	$-0.629934\pi$
$229$	−7.56606e12	−0.793916	−0.396958	+	0.917837i	$0.629934\pi$
$230$	−1.22485e13	−1.25482
$231$	−4.45524e11	−0.0445662
$232$	5.44592e12	0.531970
$233$	−2.05048e12	−0.195613	−0.0978064	−	0.995205i	$-0.531183\pi$
$233$	−2.05048e12	−0.195613	−0.0978064	+	0.995205i	$0.531183\pi$
$234$	1.13918e12	0.106146
$235$	1.94495e13	1.77025
$236$	−4.76890e12	−0.424035
$237$	2.68651e12	0.233384
$238$	3.74482e12	0.317876
$239$	2.21167e12	0.183456	0.0917279	−	0.995784i	$-0.470761\pi$
$239$	2.21167e12	0.183456	0.0917279	+	0.995784i	$0.470761\pi$
$240$	7.05901e11	0.0572245
$241$	2.36692e12	0.187539	0.0937693	−	0.995594i	$-0.470108\pi$
$241$	2.36692e12	0.187539	0.0937693	+	0.995594i	$0.470108\pi$
$242$	−6.35393e12	−0.492105
$243$	−7.96223e12	−0.602837
$244$	−5.25910e12	−0.389285
$245$	−2.11291e12	−0.152921
$246$	5.70207e11	0.0403542
$247$	1.96824e12	0.136221
$248$	3.89942e12	0.263947
$249$	5.28838e11	0.0350128
$250$	9.98271e12	0.646515
$251$	5.02392e12	0.318301	0.159150	−	0.987254i	$-0.449125\pi$
$251$	5.02392e12	0.318301	0.159150	+	0.987254i	$0.449125\pi$
$252$	2.90936e12	0.180341
$253$	−1.50720e13	−0.914130
$254$	−4.82358e12	−0.286275
$255$	−4.68743e12	−0.272247
$256$	1.09951e12	0.0625000
$257$	2.05497e12	0.114333	0.0571666	−	0.998365i	$-0.481793\pi$
$257$	2.05497e12	0.114333	0.0571666	+	0.998365i	$0.481793\pi$
$258$	2.33133e12	0.126968
$259$	4.63109e12	0.246908
$260$	1.61300e12	0.0841941
$261$	−2.80950e13	−1.43584
$262$	3.21777e12	0.161027
$263$	2.35837e13	1.15573	0.577863	−	0.816134i	$-0.303887\pi$
$263$	2.35837e13	1.15573	0.577863	+	0.816134i	$0.303887\pi$
$264$	8.68622e11	0.0416878
$265$	−5.48756e12	−0.257945
$266$	5.02671e12	0.231438
$267$	−7.47509e12	−0.337135
$268$	9.02202e12	0.398623
$269$	−2.51656e13	−1.08936	−0.544678	−	0.838645i	$-0.683348\pi$
$269$	−2.51656e13	−1.08936	−0.544678	+	0.838645i	$0.683348\pi$
$270$	−7.45785e12	−0.316310
$271$	−3.35327e13	−1.39360	−0.696800	−	0.717266i	$-0.745393\pi$
$271$	−3.35327e13	−1.39360	−0.696800	+	0.717266i	$0.745393\pi$
$272$	−7.30114e12	−0.297346
$273$	−3.18542e11	−0.0127137
$274$	3.36523e13	1.31640
$275$	−2.09777e12	−0.0804317
$276$	−4.71601e12	−0.177245
$277$	5.32006e12	0.196010	0.0980048	−	0.995186i	$-0.468754\pi$
$277$	5.32006e12	0.196010	0.0980048	+	0.995186i	$0.468754\pi$
$278$	−3.84831e12	−0.139003
$279$	−2.01168e13	−0.712418
$280$	4.11947e12	0.143045
$281$	2.15974e13	0.735387	0.367693	−	0.929947i	$-0.380148\pi$
$281$	2.15974e13	0.735387	0.367693	+	0.929947i	$0.380148\pi$
$282$	7.48857e12	0.250051
$283$	−2.12679e13	−0.696464	−0.348232	−	0.937408i	$-0.613218\pi$
$283$	−2.12679e13	−0.696464	−0.348232	+	0.937408i	$0.613218\pi$
$284$	−3.94138e12	−0.126590
$285$	−6.29199e12	−0.198217
$286$	1.98482e12	0.0613351
$287$	3.32759e12	0.100874
$288$	−5.67228e12	−0.168694
$289$	1.42102e13	0.414630
$290$	−3.97808e13	−1.13890
$291$	−1.34461e13	−0.377732
$292$	−1.91352e13	−0.527507
$293$	6.21414e13	1.68116	0.840580	−	0.541687i	$-0.182214\pi$
$293$	6.21414e13	1.68116	0.840580	+	0.541687i	$0.182214\pi$
$294$	−8.13529e11	−0.0216004
$295$	3.48353e13	0.907818
$296$	−9.02908e12	−0.230961
$297$	−9.17699e12	−0.230430
$298$	4.93149e13	1.21559
$299$	−1.07762e13	−0.260780
$300$	−6.56389e11	−0.0155953
$301$	1.36051e13	0.317385
$302$	2.77383e12	0.0635392
$303$	1.75192e13	0.394075
$304$	−9.80040e12	−0.216491
$305$	3.84161e13	0.833420
$306$	3.76659e13	0.802565
$307$	6.26024e13	1.31018	0.655088	−	0.755552i	$-0.272631\pi$
$307$	6.26024e13	1.31018	0.655088	+	0.755552i	$0.272631\pi$
$308$	5.06907e12	0.104208
$309$	1.87141e13	0.377918
$310$	−2.84841e13	−0.565084
$311$	−5.45165e13	−1.06254	−0.531271	−	0.847202i	$-0.678285\pi$
$311$	−5.45165e13	−1.06254	−0.531271	+	0.847202i	$0.678285\pi$
$312$	6.21049e11	0.0118926
$313$	8.11167e13	1.52622	0.763108	−	0.646271i	$-0.223672\pi$
$313$	8.11167e13	1.52622	0.763108	+	0.646271i	$0.223672\pi$
$314$	−8.99404e12	−0.166281
$315$	−2.12520e13	−0.386092
$316$	−3.05665e13	−0.545715
$317$	−8.76302e13	−1.53754	−0.768772	−	0.639523i	$-0.779132\pi$
$317$	−8.76302e13	−1.53754	−0.768772	+	0.639523i	$0.779132\pi$
$318$	−2.11286e12	−0.0364352
$319$	−4.89508e13	−0.829681
$320$	−8.03159e12	−0.133806
$321$	1.91869e13	0.314216
$322$	−2.75215e13	−0.443063
$323$	6.50780e13	1.02996
$324$	2.77934e13	0.432458
$325$	−1.49987e12	−0.0229453
$326$	−6.17744e13	−0.929206
$327$	7.78322e12	0.115119
$328$	−6.48768e12	−0.0943590
$329$	4.37015e13	0.625056
$330$	−6.34501e12	−0.0892495
$331$	−7.95409e13	−1.10036	−0.550182	−	0.835045i	$-0.685442\pi$
$331$	−7.95409e13	−1.10036	−0.550182	+	0.835045i	$0.685442\pi$
$332$	−6.01700e12	−0.0818693
$333$	4.65801e13	0.623387
$334$	−7.26516e12	−0.0956400
$335$	−6.59030e13	−0.853412
$336$	1.58611e12	0.0202054
$337$	−6.74851e13	−0.845753	−0.422877	−	0.906187i	$-0.638980\pi$
$337$	−6.74851e13	−0.845753	−0.422877	+	0.906187i	$0.638980\pi$
$338$	−5.59300e13	−0.689609
$339$	−2.46340e13	−0.298839
$340$	5.33325e13	0.636587
$341$	−3.50501e13	−0.411661
$342$	5.05593e13	0.584329
$343$	−4.74756e12	−0.0539949
$344$	−2.65254e13	−0.296886
$345$	3.44490e13	0.379465
$346$	1.09746e13	0.118979
$347$	−6.91521e13	−0.737893	−0.368946	−	0.929451i	$-0.620281\pi$
$347$	−6.91521e13	−0.737893	−0.368946	+	0.929451i	$0.620281\pi$
$348$	−1.53167e13	−0.160871
$349$	−1.70296e14	−1.76062	−0.880310	−	0.474398i	$-0.842666\pi$
$349$	−1.70296e14	−1.76062	−0.880310	+	0.474398i	$0.842666\pi$
$350$	−3.83053e12	−0.0389838
$351$	−6.56139e12	−0.0657365
$352$	−9.88299e12	−0.0974773
$353$	1.06950e14	1.03854	0.519268	−	0.854611i	$-0.326205\pi$
$353$	1.06950e14	1.03854	0.519268	+	0.854611i	$0.326205\pi$
$354$	1.34125e13	0.128231
$355$	2.87906e13	0.271016
$356$	8.50499e13	0.788313
$357$	−1.05323e13	−0.0961276
$358$	7.04789e13	0.633435
$359$	1.26247e14	1.11738	0.558690	−	0.829377i	$-0.311304\pi$
$359$	1.26247e14	1.11738	0.558690	+	0.829377i	$0.311304\pi$
$360$	4.14342e13	0.361156
$361$	−2.91353e13	−0.250109
$362$	1.39525e13	0.117965
$363$	1.78704e13	0.148816
$364$	3.62430e12	0.0297280
$365$	1.39777e14	1.12934
$366$	1.47912e13	0.117722
$367$	−2.88682e13	−0.226337	−0.113169	−	0.993576i	$-0.536100\pi$
$367$	−2.88682e13	−0.226337	−0.113169	+	0.993576i	$0.536100\pi$
$368$	5.36577e13	0.414447
$369$	3.34693e13	0.254684
$370$	6.59546e13	0.494465
$371$	−1.23301e13	−0.0910776
$372$	−1.09671e13	−0.0798191
$373$	1.99029e14	1.42731	0.713653	−	0.700500i	$-0.247040\pi$
$373$	1.99029e14	1.42731	0.713653	+	0.700500i	$0.247040\pi$
$374$	6.56264e13	0.463751
$375$	−2.80764e13	−0.195510
$376$	−8.52032e13	−0.584686
$377$	−3.49990e13	−0.236689
$378$	−1.67572e13	−0.111686
$379$	−2.62273e14	−1.72281	−0.861405	−	0.507919i	$-0.830415\pi$
$379$	−2.62273e14	−1.72281	−0.861405	+	0.507919i	$0.830415\pi$
$380$	7.15889e13	0.463485
$381$	1.35663e13	0.0865714
$382$	−1.10918e14	−0.697678
$383$	2.06425e13	0.127988	0.0639939	−	0.997950i	$-0.479616\pi$
$383$	2.06425e13	0.127988	0.0639939	+	0.997950i	$0.479616\pi$
$384$	−3.09238e12	−0.0189004
$385$	−3.70280e13	−0.223098
$386$	−1.53182e14	−0.909866
$387$	1.36842e14	0.801325
$388$	1.52986e14	0.883239
$389$	−1.01229e14	−0.576213	−0.288106	−	0.957598i	$-0.593026\pi$
$389$	−1.01229e14	−0.576213	−0.288106	+	0.957598i	$0.593026\pi$
$390$	−4.53657e12	−0.0254608
$391$	−3.56306e14	−1.97175
$392$	9.25615e12	0.0505076
$393$	−9.04997e12	−0.0486954
$394$	−1.40769e14	−0.746928
$395$	2.23278e14	1.16832
$396$	5.09854e13	0.263101
$397$	1.49728e13	0.0762003	0.0381001	−	0.999274i	$-0.487869\pi$
$397$	1.49728e13	0.0762003	0.0381001	+	0.999274i	$0.487869\pi$
$398$	2.62361e14	1.31687
$399$	−1.41376e13	−0.0699883
$400$	7.46825e12	0.0364660
$401$	5.80482e13	0.279573	0.139786	−	0.990182i	$-0.455358\pi$
$401$	5.80482e13	0.279573	0.139786	+	0.990182i	$0.455358\pi$
$402$	−2.53744e13	−0.120546
$403$	−2.50602e13	−0.117437
$404$	−1.99329e14	−0.921454
$405$	−2.03022e14	−0.925850
$406$	−8.93844e13	−0.402132
$407$	8.11581e13	0.360216
$408$	2.05344e13	0.0899191
$409$	1.21939e14	0.526822	0.263411	−	0.964684i	$-0.415152\pi$
$409$	1.21939e14	0.526822	0.263411	+	0.964684i	$0.415152\pi$
$410$	4.73905e13	0.202013
$411$	−9.46472e13	−0.398087
$412$	−2.12925e14	−0.883674
$413$	7.82723e13	0.320541
$414$	−2.76815e14	−1.11863
$415$	4.39523e13	0.175274
$416$	−7.06616e12	−0.0278080
$417$	1.08234e13	0.0420353
$418$	8.80911e13	0.337647
$419$	1.11948e14	0.423487	0.211744	−	0.977325i	$-0.432086\pi$
$419$	1.11948e14	0.423487	0.211744	+	0.977325i	$0.432086\pi$
$420$	−1.15860e13	−0.0432577
$421$	−3.04456e14	−1.12195	−0.560974	−	0.827833i	$-0.689573\pi$
$421$	−3.04456e14	−1.12195	−0.560974	+	0.827833i	$0.689573\pi$
$422$	−1.94564e14	−0.707692
$423$	4.39555e14	1.57813
$424$	2.40396e13	0.0851953
$425$	−4.95917e13	−0.173488
$426$	1.10851e13	0.0382814
$427$	8.63180e13	0.294271
$428$	−2.18305e14	−0.734721
$429$	−5.58232e12	−0.0185481
$430$	1.93759e14	0.635604
$431$	3.15589e13	0.102211	0.0511054	−	0.998693i	$-0.483726\pi$
$431$	3.15589e13	0.102211	0.0511054	+	0.998693i	$0.483726\pi$
$432$	3.26710e13	0.104472
$433$	2.81113e14	0.887558	0.443779	−	0.896136i	$-0.353637\pi$
$433$	2.81113e14	0.887558	0.443779	+	0.896136i	$0.353637\pi$
$434$	−6.40016e13	−0.199525
$435$	1.11883e14	0.344409
$436$	−8.85557e13	−0.269179
$437$	−4.78273e14	−1.43558
$438$	5.38178e13	0.159521
$439$	5.46122e14	1.59858	0.799291	−	0.600944i	$-0.205208\pi$
$439$	5.46122e14	1.59858	0.799291	+	0.600944i	$0.205208\pi$
$440$	7.21921e13	0.208689
$441$	−4.77516e13	−0.136325
$442$	4.69217e13	0.132298
$443$	7.03218e12	0.0195826	0.00979128	−	0.999952i	$-0.496883\pi$
$443$	7.03218e12	0.0195826	0.00979128	+	0.999952i	$0.496883\pi$
$444$	2.53943e13	0.0698441
$445$	−6.21263e14	−1.68770
$446$	4.01714e14	1.07789
$447$	−1.38698e14	−0.367603
$448$	−1.80464e13	−0.0472456
$449$	3.43649e14	0.888710	0.444355	−	0.895851i	$-0.353433\pi$
$449$	3.43649e14	0.888710	0.444355	+	0.895851i	$0.353433\pi$
$450$	−3.85280e13	−0.0984254
$451$	5.83147e13	0.147166
$452$	2.80280e14	0.698765
$453$	−7.80140e12	−0.0192147
$454$	2.42806e14	0.590815
$455$	−2.64744e13	−0.0636448
$456$	2.75636e13	0.0654681
$457$	4.18796e14	0.982797	0.491399	−	0.870935i	$-0.336486\pi$
$457$	4.18796e14	0.982797	0.491399	+	0.870935i	$0.336486\pi$
$458$	−2.42114e14	−0.561383
$459$	−2.16946e14	−0.497030
$460$	−3.91953e14	−0.887291
$461$	−2.90732e14	−0.650336	−0.325168	−	0.945656i	$-0.605421\pi$
$461$	−2.90732e14	−0.650336	−0.325168	+	0.945656i	$0.605421\pi$
$462$	−1.42568e13	−0.0315130
$463$	5.54506e14	1.21119	0.605593	−	0.795774i	$-0.292936\pi$
$463$	5.54506e14	1.21119	0.605593	+	0.795774i	$0.292936\pi$
$464$	1.74270e14	0.376160
$465$	8.01115e13	0.170885
$466$	−6.56153e13	−0.138319
$467$	−3.59816e13	−0.0749614	−0.0374807	−	0.999297i	$-0.511933\pi$
$467$	−3.59816e13	−0.0749614	−0.0374807	+	0.999297i	$0.511933\pi$
$468$	3.64537e13	0.0750566
$469$	−1.48079e14	−0.301331
$470$	6.22383e14	1.25176
$471$	2.52957e13	0.0502843
$472$	−1.52605e14	−0.299838
$473$	2.38424e14	0.463035
$474$	8.59682e13	0.165028
$475$	−6.65676e13	−0.126313
$476$	1.19834e14	0.224772
$477$	−1.24018e14	−0.229950
$478$	7.07733e13	0.129723
$479$	−5.62704e14	−1.01961	−0.509805	−	0.860290i	$-0.670283\pi$
$479$	−5.62704e14	−1.01961	−0.509805	+	0.860290i	$0.670283\pi$
$480$	2.25888e13	0.0404638
$481$	5.80266e13	0.102761
$482$	7.57416e13	0.132610
$483$	7.74043e13	0.133985
$484$	−2.03326e14	−0.347971
$485$	−1.11752e15	−1.89093
$486$	−2.54791e14	−0.426270
$487$	−1.14346e13	−0.0189152	−0.00945762	−	0.999955i	$-0.503010\pi$
$487$	−1.14346e13	−0.0189152	−0.00945762	+	0.999955i	$0.503010\pi$
$488$	−1.68291e14	−0.275266
$489$	1.73741e14	0.280998
$490$	−6.76133e13	−0.108132
$491$	−8.16299e14	−1.29092	−0.645462	−	0.763792i	$-0.723335\pi$
$491$	−8.16299e14	−1.29092	−0.645462	+	0.763792i	$0.723335\pi$
$492$	1.82466e13	0.0285348
$493$	−1.15721e15	−1.78959
$494$	6.29836e13	0.0963228
$495$	−3.72432e14	−0.563273
$496$	1.24782e14	0.186639
$497$	6.46903e13	0.0956927
$498$	1.69228e13	0.0247578
$499$	−2.15006e13	−0.0311098	−0.0155549	−	0.999879i	$-0.504951\pi$
$499$	−2.15006e13	−0.0311098	−0.0155549	+	0.999879i	$0.504951\pi$
$500$	3.19447e14	0.457155
$501$	2.04333e13	0.0289221
$502$	1.60766e14	0.225073
$503$	−1.20521e14	−0.166893	−0.0834463	−	0.996512i	$-0.526593\pi$
$503$	−1.20521e14	−0.166893	−0.0834463	+	0.996512i	$0.526593\pi$
$504$	9.30996e13	0.127520
$505$	1.45604e15	1.97274
$506$	−4.82304e14	−0.646387
$507$	1.57303e14	0.208542
$508$	−1.54354e14	−0.202427
$509$	−6.45253e14	−0.837109	−0.418555	−	0.908192i	$-0.637463\pi$
$509$	−6.45253e14	−0.837109	−0.418555	+	0.908192i	$0.637463\pi$
$510$	−1.49998e14	−0.192508
$511$	3.14068e14	0.398758
$512$	3.51844e13	0.0441942
$513$	−2.91210e14	−0.361877
$514$	6.57589e13	0.0808458
$515$	1.55535e15	1.89186
$516$	7.46026e13	0.0897802
$517$	7.65851e14	0.911899
$518$	1.48195e14	0.174590
$519$	−3.08661e13	−0.0359800
$520$	5.16161e13	0.0595342
$521$	−1.26928e15	−1.44861	−0.724305	−	0.689480i	$-0.757839\pi$
$521$	−1.26928e15	−1.44861	−0.724305	+	0.689480i	$0.757839\pi$
$522$	−8.99040e14	−1.01529
$523$	1.25973e15	1.40773	0.703863	−	0.710336i	$-0.251457\pi$
$523$	1.25973e15	1.40773	0.703863	+	0.710336i	$0.251457\pi$
$524$	1.02969e14	0.113863
$525$	1.07734e13	0.0117890
$526$	7.54678e14	0.817222
$527$	−8.28593e14	−0.887938
$528$	2.77959e13	0.0294777
$529$	1.66576e15	1.74826
$530$	−1.75602e14	−0.182395
$531$	7.87273e14	0.809293
$532$	1.60855e14	0.163652
$533$	4.16940e13	0.0419830
$534$	−2.39203e14	−0.238391
$535$	1.59465e15	1.57296
$536$	2.88705e14	0.281869
$537$	−1.98222e14	−0.191555
$538$	−8.05300e14	−0.770291
$539$	−8.31991e13	−0.0787736
$540$	−2.38651e14	−0.223665
$541$	3.42258e14	0.317518	0.158759	−	0.987317i	$-0.449251\pi$
$541$	3.42258e14	0.317518	0.158759	+	0.987317i	$0.449251\pi$
$542$	−1.07305e15	−0.985423
$543$	−3.92413e13	−0.0356734
$544$	−2.33636e14	−0.210255
$545$	6.46872e14	0.576285
$546$	−1.01933e13	−0.00898994
$547$	−1.05395e15	−0.920212	−0.460106	−	0.887864i	$-0.652189\pi$
$547$	−1.05395e15	−0.920212	−0.460106	+	0.887864i	$0.652189\pi$
$548$	1.07687e15	0.930834
$549$	8.68198e14	0.742969
$550$	−6.71285e13	−0.0568738
$551$	−1.55334e15	−1.30296
$552$	−1.50912e14	−0.125331
$553$	5.01690e14	0.412522
$554$	1.70242e14	0.138600
$555$	−1.85497e14	−0.149529
$556$	−1.23146e14	−0.0982897
$557$	1.01399e15	0.801362	0.400681	−	0.916218i	$-0.368774\pi$
$557$	1.01399e15	0.801362	0.400681	+	0.916218i	$0.368774\pi$
$558$	−6.43736e14	−0.503756
$559$	1.70469e14	0.132093
$560$	1.31823e14	0.101148
$561$	−1.84574e14	−0.140241
$562$	6.91116e14	0.519997
$563$	−2.45239e15	−1.82723	−0.913616	−	0.406578i	$-0.866722\pi$
$563$	−2.45239e15	−1.82723	−0.913616	+	0.406578i	$0.866722\pi$
$564$	2.39634e14	0.176813
$565$	−2.04736e15	−1.49599
$566$	−6.80572e14	−0.492474
$567$	−4.56176e14	−0.326908
$568$	−1.26124e14	−0.0895123
$569$	8.80877e14	0.619153	0.309577	−	0.950875i	$-0.399813\pi$
$569$	8.80877e14	0.619153	0.309577	+	0.950875i	$0.399813\pi$
$570$	−2.01344e14	−0.140161
$571$	−2.33806e15	−1.61197	−0.805984	−	0.591937i	$-0.798363\pi$
$571$	−2.33806e15	−1.61197	−0.805984	+	0.591937i	$0.798363\pi$
$572$	6.35144e13	0.0433704
$573$	3.11958e14	0.210982
$574$	1.06483e14	0.0713287
$575$	3.64461e14	0.241812
$576$	−1.81513e14	−0.119284
$577$	7.50093e14	0.488257	0.244128	−	0.969743i	$-0.421498\pi$
$577$	7.50093e14	0.488257	0.244128	+	0.969743i	$0.421498\pi$
$578$	4.54725e14	0.293188
$579$	4.30824e14	0.275149
$580$	−1.27298e15	−0.805321
$581$	9.87576e13	0.0618873
$582$	−4.30274e14	−0.267097
$583$	−2.16081e14	−0.132874
$584$	−6.12327e14	−0.373004
$585$	−2.66283e14	−0.160689
$586$	1.98852e15	1.18876
$587$	8.50951e14	0.503958	0.251979	−	0.967733i	$-0.418919\pi$
$587$	8.50951e14	0.503958	0.251979	+	0.967733i	$0.418919\pi$
$588$	−2.60329e13	−0.0152738
$589$	−1.11223e15	−0.646488
$590$	1.11473e15	0.641924
$591$	3.95913e14	0.225875
$592$	−2.88930e14	−0.163314
$593$	1.30680e15	0.731829	0.365915	−	0.930648i	$-0.380756\pi$
$593$	1.30680e15	0.731829	0.365915	+	0.930648i	$0.380756\pi$
$594$	−2.93664e14	−0.162939
$595$	−8.75351e14	−0.481215
$596$	1.57808e15	0.859555
$597$	−7.37890e14	−0.398229
$598$	−3.44839e14	−0.184399
$599$	−1.29278e15	−0.684979	−0.342489	−	0.939522i	$-0.611270\pi$
$599$	−1.29278e15	−0.684979	−0.342489	+	0.939522i	$0.611270\pi$
$600$	−2.10044e13	−0.0110276
$601$	−5.68237e14	−0.295611	−0.147805	−	0.989016i	$-0.547221\pi$
$601$	−5.68237e14	−0.295611	−0.147805	+	0.989016i	$0.547221\pi$
$602$	4.35363e14	0.224425
$603$	−1.48940e15	−0.760792
$604$	8.87626e13	0.0449290
$605$	1.48523e15	0.744971
$606$	5.60613e14	0.278653
$607$	−1.21112e15	−0.596554	−0.298277	−	0.954479i	$-0.596412\pi$
$607$	−1.21112e15	−0.596554	−0.298277	+	0.954479i	$0.596412\pi$
$608$	−3.13613e14	−0.153082
$609$	2.51394e14	0.121607
$610$	1.22931e15	0.589317
$611$	5.47570e14	0.260144
$612$	1.20531e15	0.567499
$613$	9.95482e13	0.0464516	0.0232258	−	0.999730i	$-0.492606\pi$
$613$	9.95482e13	0.0464516	0.0232258	+	0.999730i	$0.492606\pi$
$614$	2.00328e15	0.926435
$615$	−1.33286e14	−0.0610901
$616$	1.62210e14	0.0736859
$617$	1.05369e15	0.474399	0.237199	−	0.971461i	$-0.423771\pi$
$617$	1.05369e15	0.474399	0.237199	+	0.971461i	$0.423771\pi$
$618$	5.98852e14	0.267229
$619$	3.01948e15	1.33547	0.667733	−	0.744401i	$-0.267265\pi$
$619$	3.01948e15	1.33547	0.667733	+	0.744401i	$0.267265\pi$
$620$	−9.11490e14	−0.399575
$621$	1.59439e15	0.692772
$622$	−1.74453e15	−0.751330
$623$	−1.39593e15	−0.595909
$624$	1.98736e13	0.00840932
$625$	−2.68123e15	−1.12459
$626$	2.59573e15	1.07920
$627$	−2.47756e14	−0.102106
$628$	−2.87809e14	−0.117578
$629$	1.91860e15	0.776972
$630$	−6.80063e14	−0.273009
$631$	−9.79096e14	−0.389640	−0.194820	−	0.980839i	$-0.562412\pi$
$631$	−9.79096e14	−0.389640	−0.194820	+	0.980839i	$0.562412\pi$
$632$	−9.78127e14	−0.385879
$633$	5.47212e14	0.214010
$634$	−2.80416e15	−1.08721
$635$	1.12751e15	0.433377
$636$	−6.76115e13	−0.0257636
$637$	−5.94859e13	−0.0224723
$638$	−1.56643e15	−0.586673
$639$	6.50663e14	0.241602
$640$	−2.57011e14	−0.0946153
$641$	1.97772e15	0.721847	0.360924	−	0.932595i	$-0.382462\pi$
$641$	1.97772e15	0.721847	0.360924	+	0.932595i	$0.382462\pi$
$642$	6.13982e14	0.222184
$643$	−2.16650e15	−0.777319	−0.388660	−	0.921381i	$-0.627062\pi$
$643$	−2.16650e15	−0.777319	−0.388660	+	0.921381i	$0.627062\pi$
$644$	−8.80689e14	−0.313293
$645$	−5.44948e14	−0.192210
$646$	2.08250e15	0.728292
$647$	4.14110e15	1.43596	0.717979	−	0.696064i	$-0.245067\pi$
$647$	4.14110e15	1.43596	0.717979	+	0.696064i	$0.245067\pi$
$648$	8.89389e14	0.305794
$649$	1.37169e15	0.467639
$650$	−4.79957e13	−0.0162248
$651$	1.80004e14	0.0603376
$652$	−1.97678e15	−0.657048
$653$	−3.49827e15	−1.15300	−0.576502	−	0.817096i	$-0.695583\pi$
$653$	−3.49827e15	−1.15300	−0.576502	+	0.817096i	$0.695583\pi$
$654$	2.49063e14	0.0814013
$655$	−7.52153e14	−0.243769
$656$	−2.07606e14	−0.0667219
$657$	3.15894e15	1.00677
$658$	1.39845e15	0.441981
$659$	−4.22412e15	−1.32394	−0.661968	−	0.749532i	$-0.730278\pi$
$659$	−4.22412e15	−1.32394	−0.661968	+	0.749532i	$0.730278\pi$
$660$	−2.03040e14	−0.0631089
$661$	−3.68234e15	−1.13505	−0.567526	−	0.823355i	$-0.692099\pi$
$661$	−3.68234e15	−1.13505	−0.567526	+	0.823355i	$0.692099\pi$
$662$	−2.54531e15	−0.778075
$663$	−1.31967e14	−0.0400076
$664$	−1.92544e14	−0.0578903
$665$	−1.17499e15	−0.350362
$666$	1.49056e15	0.440801
$667$	8.50460e15	2.49438
$668$	−2.32485e14	−0.0676277
$669$	−1.12982e15	−0.325961
$670$	−2.10890e15	−0.603454
$671$	1.51269e15	0.429315
$672$	5.07554e13	0.0142873
$673$	7.37970e14	0.206042	0.103021	−	0.994679i	$-0.467149\pi$
$673$	7.37970e14	0.206042	0.103021	+	0.994679i	$0.467149\pi$
$674$	−2.15952e15	−0.598038
$675$	2.21912e14	0.0609551
$676$	−1.78976e15	−0.487627
$677$	1.19823e15	0.323820	0.161910	−	0.986806i	$-0.448235\pi$
$677$	1.19823e15	0.323820	0.161910	+	0.986806i	$0.448235\pi$
$678$	−7.88288e14	−0.211311
$679$	−2.51098e15	−0.667666
$680$	1.70664e15	0.450135
$681$	−6.82891e14	−0.178666
$682$	−1.12160e15	−0.291088
$683$	−4.66464e15	−1.20089	−0.600447	−	0.799665i	$-0.705011\pi$
$683$	−4.66464e15	−1.20089	−0.600447	+	0.799665i	$0.705011\pi$
$684$	1.61790e15	0.413183
$685$	−7.86623e15	−1.99282
$686$	−1.51922e14	−0.0381802
$687$	6.80945e14	0.169766
$688$	−8.48812e14	−0.209930
$689$	−1.54494e14	−0.0379058
$690$	1.10237e15	0.268322
$691$	1.42740e15	0.344680	0.172340	−	0.985038i	$-0.444867\pi$
$691$	1.42740e15	0.344680	0.172340	+	0.985038i	$0.444867\pi$
$692$	3.51187e14	0.0841308
$693$	−8.36828e14	−0.198886
$694$	−2.21287e15	−0.521769
$695$	8.99541e14	0.210429
$696$	−4.90133e14	−0.113753
$697$	1.37857e15	0.317431
$698$	−5.44949e15	−1.24495
$699$	1.84543e14	0.0418286
$700$	−1.22577e14	−0.0275657
$701$	2.23166e15	0.497942	0.248971	−	0.968511i	$-0.419908\pi$
$701$	2.23166e15	0.497942	0.248971	+	0.968511i	$0.419908\pi$
$702$	−2.09964e14	−0.0464827
$703$	2.57536e15	0.565696
$704$	−3.16256e14	−0.0689269
$705$	−1.75045e15	−0.378539
$706$	3.42242e15	0.734356
$707$	3.27161e15	0.696553
$708$	4.29201e14	0.0906729
$709$	3.12103e15	0.654251	0.327125	−	0.944981i	$-0.393920\pi$
$709$	3.12103e15	0.654251	0.327125	+	0.944981i	$0.393920\pi$
$710$	9.21298e14	0.191637
$711$	5.04606e15	1.04153
$712$	2.72160e15	0.557422
$713$	6.08952e15	1.23763
$714$	−3.37034e14	−0.0679725
$715$	−4.63953e14	−0.0928518
$716$	2.25532e15	0.447907
$717$	−1.99050e14	−0.0392290
$718$	4.03990e15	0.790107
$719$	−5.95913e14	−0.115657	−0.0578287	−	0.998327i	$-0.518418\pi$
$719$	−5.95913e14	−0.115657	−0.0578287	+	0.998327i	$0.518418\pi$
$720$	1.32589e15	0.255376
$721$	3.49476e15	0.667995
$722$	−9.32328e14	−0.176854
$723$	−2.13023e14	−0.0401020
$724$	4.46479e14	0.0834140
$725$	1.18370e15	0.219473
$726$	5.71853e14	0.105228
$727$	−7.72455e15	−1.41070	−0.705349	−	0.708860i	$-0.749210\pi$
$727$	−7.72455e15	−1.41070	−0.705349	+	0.708860i	$0.749210\pi$
$728$	1.15978e14	0.0210209
$729$	−4.09152e15	−0.736010
$730$	4.47286e15	0.798564
$731$	5.63640e15	0.998749
$732$	4.73319e14	0.0832421
$733$	−5.16986e15	−0.902416	−0.451208	−	0.892419i	$-0.649007\pi$
$733$	−5.16986e15	−0.902416	−0.451208	+	0.892419i	$0.649007\pi$
$734$	−9.23782e14	−0.160045
$735$	1.90162e14	0.0326997
$736$	1.71705e15	0.293058
$737$	−2.59503e15	−0.439613
$738$	1.07102e15	0.180089
$739$	−2.69194e15	−0.449284	−0.224642	−	0.974441i	$-0.572121\pi$
$739$	−2.69194e15	−0.449284	−0.224642	+	0.974441i	$0.572121\pi$
$740$	2.11055e15	0.349639
$741$	−1.77141e14	−0.0291286
$742$	−3.94565e14	−0.0644016
$743$	−3.36315e13	−0.00544889	−0.00272444	−	0.999996i	$-0.500867\pi$
$743$	−3.36315e13	−0.00544889	−0.00272444	+	0.999996i	$0.500867\pi$
$744$	−3.50948e14	−0.0564406
$745$	−1.15274e16	−1.84022
$746$	6.36891e15	1.00926
$747$	9.93317e14	0.156252
$748$	2.10005e15	0.327922
$749$	3.58305e15	0.555397
$750$	−8.98444e14	−0.138246
$751$	−2.36355e15	−0.361032	−0.180516	−	0.983572i	$-0.557777\pi$
$751$	−2.36355e15	−0.361032	−0.180516	+	0.983572i	$0.557777\pi$
$752$	−2.72650e15	−0.413436
$753$	−4.52153e14	−0.0680633
$754$	−1.11997e15	−0.167364
$755$	−6.48383e14	−0.0961886
$756$	−5.36231e14	−0.0789737
$757$	1.22646e16	1.79320	0.896598	−	0.442846i	$-0.146031\pi$
$757$	1.22646e16	1.79320	0.896598	+	0.442846i	$0.146031\pi$
$758$	−8.39272e15	−1.21821
$759$	1.35648e15	0.195472
$760$	2.29084e15	0.327733
$761$	−5.76243e15	−0.818446	−0.409223	−	0.912434i	$-0.634200\pi$
$761$	−5.76243e15	−0.818446	−0.409223	+	0.912434i	$0.634200\pi$
$762$	4.34122e14	0.0612152
$763$	1.45347e15	0.203480
$764$	−3.54939e15	−0.493333
$765$	−8.80440e15	−1.21496
$766$	6.60559e14	0.0905010
$767$	9.80735e14	0.133407
$768$	−9.89560e13	−0.0133646
$769$	−9.00183e15	−1.20708	−0.603540	−	0.797333i	$-0.706244\pi$
$769$	−9.00183e15	−1.20708	−0.603540	+	0.797333i	$0.706244\pi$
$770$	−1.18490e15	−0.157754
$771$	−1.84947e14	−0.0244483
$772$	−4.90182e15	−0.643373
$773$	−1.44716e16	−1.88595	−0.942975	−	0.332865i	$-0.891985\pi$
$773$	−1.44716e16	−1.88595	−0.942975	+	0.332865i	$0.891985\pi$
$774$	4.37894e15	0.566622
$775$	8.47558e14	0.108896
$776$	4.89557e15	0.624545
$777$	−4.16798e14	−0.0527971
$778$	−3.23933e15	−0.407444
$779$	1.85048e15	0.231115
$780$	−1.45170e14	−0.0180035
$781$	1.13367e15	0.139607
$782$	−1.14018e16	−1.39423
$783$	5.17826e15	0.628773
$784$	2.96197e14	0.0357143
$785$	2.10236e15	0.251723
$786$	−2.89599e14	−0.0344329
$787$	−2.49279e15	−0.294323	−0.147162	−	0.989112i	$-0.547014\pi$
$787$	−2.49279e15	−0.294323	−0.147162	+	0.989112i	$0.547014\pi$
$788$	−4.50461e15	−0.528158
$789$	−2.12253e15	−0.247133
$790$	7.14491e15	0.826129
$791$	−4.60026e15	−0.528217
$792$	1.63153e15	0.186040
$793$	1.08155e15	0.122474
$794$	4.79131e14	0.0538817
$795$	4.93881e14	0.0551573
$796$	8.39555e15	0.931166
$797$	1.46284e16	1.61129	0.805647	−	0.592395i	$-0.201818\pi$
$797$	1.46284e16	1.61129	0.805647	+	0.592395i	$0.201818\pi$
$798$	−4.52404e14	−0.0494892
$799$	1.81049e16	1.96693
$800$	2.38984e14	0.0257854
$801$	−1.40405e16	−1.50454
$802$	1.85754e15	0.197688
$803$	5.50392e15	0.581750
$804$	−8.11982e14	−0.0852389
$805$	6.43316e15	0.670729
$806$	−8.01926e14	−0.0830408
$807$	2.26491e15	0.232941
$808$	−6.37854e15	−0.651566
$809$	3.62120e15	0.367397	0.183699	−	0.982983i	$-0.441193\pi$
$809$	3.62120e15	0.367397	0.183699	+	0.982983i	$0.441193\pi$
$810$	−6.49671e15	−0.654675
$811$	−6.30657e15	−0.631217	−0.315609	−	0.948889i	$-0.602209\pi$
$811$	−6.30657e15	−0.631217	−0.315609	+	0.948889i	$0.602209\pi$
$812$	−2.86030e15	−0.284350
$813$	3.01795e15	0.297998
$814$	2.59706e15	0.254711
$815$	1.44398e16	1.40667
$816$	6.57102e14	0.0635824
$817$	7.56581e15	0.727167
$818$	3.90205e15	0.372520
$819$	−5.98317e14	−0.0567375
$820$	1.51650e15	0.142845
$821$	1.39556e16	1.30576	0.652879	−	0.757462i	$-0.273561\pi$
$821$	1.39556e16	1.30576	0.652879	+	0.757462i	$0.273561\pi$
$822$	−3.02871e15	−0.281490
$823$	−9.59771e14	−0.0886071	−0.0443036	−	0.999018i	$-0.514107\pi$
$823$	−9.59771e14	−0.0886071	−0.0443036	+	0.999018i	$0.514107\pi$
$824$	−6.81361e15	−0.624852
$825$	1.88799e14	0.0171990
$826$	2.50471e15	0.226656
$827$	−1.03113e16	−0.926896	−0.463448	−	0.886124i	$-0.653388\pi$
$827$	−1.03113e16	−0.926896	−0.463448	+	0.886124i	$0.653388\pi$
$828$	−8.85808e15	−0.790994
$829$	−5.93557e15	−0.526517	−0.263259	−	0.964725i	$-0.584797\pi$
$829$	−5.93557e15	−0.526517	−0.263259	+	0.964725i	$0.584797\pi$
$830$	1.40647e15	0.123937
$831$	−4.78805e14	−0.0419134
$832$	−2.26117e14	−0.0196632
$833$	−1.96685e15	−0.169912
$834$	3.46348e14	0.0297234
$835$	1.69823e15	0.144784
$836$	2.81892e15	0.238752
$837$	3.70777e15	0.311977
$838$	3.58234e15	0.299451
$839$	−1.79816e16	−1.49327	−0.746635	−	0.665234i	$-0.768332\pi$
$839$	−1.79816e16	−1.49327	−0.746635	+	0.665234i	$0.768332\pi$
$840$	−3.70753e14	−0.0305878
$841$	1.54207e16	1.26394
$842$	−9.74259e15	−0.793338
$843$	−1.94376e15	−0.157250
$844$	−6.22605e15	−0.500414
$845$	1.30736e16	1.04396
$846$	1.40658e16	1.11590
$847$	3.33720e15	0.263041
$848$	7.69268e14	0.0602422
$849$	1.91411e15	0.148927
$850$	−1.58694e15	−0.122675
$851$	−1.41002e16	−1.08296
$852$	3.54724e14	0.0270691
$853$	3.79978e15	0.288097	0.144049	−	0.989571i	$-0.453988\pi$
$853$	3.79978e15	0.288097	0.144049	+	0.989571i	$0.453988\pi$
$854$	2.76218e15	0.208081
$855$	−1.18182e16	−0.884585
$856$	−6.98575e15	−0.519526
$857$	−6.63359e15	−0.490179	−0.245089	−	0.969501i	$-0.578817\pi$
$857$	−6.63359e15	−0.490179	−0.245089	+	0.969501i	$0.578817\pi$
$858$	−1.78634e14	−0.0131155
$859$	2.33958e16	1.70677	0.853387	−	0.521277i	$-0.174544\pi$
$859$	2.33958e16	1.70677	0.853387	+	0.521277i	$0.174544\pi$
$860$	6.20030e15	0.449440
$861$	−2.99483e14	−0.0215702
$862$	1.00988e15	0.0722739
$863$	−1.39490e16	−0.991939	−0.495970	−	0.868340i	$-0.665187\pi$
$863$	−1.39490e16	−0.991939	−0.495970	+	0.868340i	$0.665187\pi$
$864$	1.04547e15	0.0738731
$865$	−2.56531e15	−0.180116
$866$	8.99560e15	0.627599
$867$	−1.27891e15	−0.0886618
$868$	−2.04805e15	−0.141085
$869$	8.79192e15	0.601831
$870$	3.58027e15	0.243534
$871$	−1.85540e15	−0.125412
$872$	−2.83378e15	−0.190338
$873$	−2.52558e16	−1.68571
$874$	−1.53048e16	−1.01511
$875$	−5.24311e15	−0.345577
$876$	1.72217e15	0.112799
$877$	1.51152e15	0.0983822	0.0491911	−	0.998789i	$-0.484336\pi$
$877$	1.51152e15	0.0983822	0.0491911	+	0.998789i	$0.484336\pi$
$878$	1.74759e16	1.13037
$879$	−5.59273e15	−0.359488
$880$	2.31015e15	0.147566
$881$	−1.87000e16	−1.18706	−0.593532	−	0.804810i	$-0.702267\pi$
$881$	−1.87000e16	−1.18706	−0.593532	+	0.804810i	$0.702267\pi$
$882$	−1.52805e15	−0.0963964
$883$	−1.10862e16	−0.695026	−0.347513	−	0.937675i	$-0.612974\pi$
$883$	−1.10862e16	−0.695026	−0.347513	+	0.937675i	$0.612974\pi$
$884$	1.50150e15	0.0935485
$885$	−3.13518e15	−0.194122
$886$	2.25030e14	0.0138470
$887$	3.31195e14	0.0202537	0.0101269	−	0.999949i	$-0.496776\pi$
$887$	3.31195e14	0.0202537	0.0101269	+	0.999949i	$0.496776\pi$
$888$	8.12617e14	0.0493872
$889$	2.53343e15	0.153021
$890$	−1.98804e16	−1.19338
$891$	−7.99430e15	−0.476928
$892$	1.28548e16	0.762184
$893$	2.43024e16	1.43208
$894$	−4.43834e15	−0.259935
$895$	−1.64744e16	−0.958923
$896$	−5.77484e14	−0.0334077
$897$	9.69859e14	0.0557635
$898$	1.09968e16	0.628413
$899$	1.97775e16	1.12329
$900$	−1.23290e15	−0.0695973
$901$	−5.10821e15	−0.286604
$902$	1.86607e15	0.104062
$903$	−1.22446e15	−0.0678674
$904$	8.96897e15	0.494101
$905$	−3.26139e15	−0.178581
$906$	−2.49645e14	−0.0135868
$907$	−2.89755e16	−1.56744	−0.783720	−	0.621114i	$-0.786680\pi$
$907$	−2.89755e16	−1.56744	−0.783720	+	0.621114i	$0.786680\pi$
$908$	7.76978e15	0.417769
$909$	3.29063e16	1.75864
$910$	−8.47179e14	−0.0450037
$911$	−3.22915e16	−1.70505	−0.852526	−	0.522685i	$-0.824930\pi$
$911$	−3.22915e16	−1.70505	−0.852526	+	0.522685i	$0.824930\pi$
$912$	8.82036e14	0.0462929
$913$	1.73069e15	0.0902879
$914$	1.34015e16	0.694942
$915$	−3.45745e15	−0.178213
$916$	−7.74765e15	−0.396958
$917$	−1.69003e15	−0.0860723
$918$	−6.94229e15	−0.351453
$919$	3.29819e16	1.65974	0.829871	−	0.557955i	$-0.188414\pi$
$919$	3.29819e16	1.65974	0.829871	+	0.557955i	$0.188414\pi$
$920$	−1.25425e16	−0.627409
$921$	−5.63422e15	−0.280160
$922$	−9.30342e15	−0.459857
$923$	8.10555e14	0.0398266
$924$	−4.56217e14	−0.0222831
$925$	−1.96251e15	−0.0952868
$926$	1.77442e16	0.856438
$927$	3.51507e16	1.68654
$928$	5.57662e15	0.265985
$929$	−7.59250e15	−0.359997	−0.179998	−	0.983667i	$-0.557609\pi$
$929$	−7.59250e15	−0.359997	−0.179998	+	0.983667i	$0.557609\pi$
$930$	2.56357e15	0.120834
$931$	−2.64012e15	−0.123709
$932$	−2.09969e15	−0.0978064
$933$	4.90649e15	0.227207
$934$	−1.15141e15	−0.0530057
$935$	−1.53402e16	−0.702048
$936$	1.16652e15	0.0530730
$937$	−9.00877e15	−0.407472	−0.203736	−	0.979026i	$-0.565308\pi$
$937$	−9.00877e15	−0.407472	−0.203736	+	0.979026i	$0.565308\pi$
$938$	−4.73853e15	−0.213073
$939$	−7.30050e15	−0.326356
$940$	1.99163e16	0.885125
$941$	2.27504e16	1.00519	0.502594	−	0.864523i	$-0.332379\pi$
$941$	2.27504e16	1.00519	0.502594	+	0.864523i	$0.332379\pi$
$942$	8.09464e14	0.0355564
$943$	−1.01315e16	−0.442443
$944$	−4.88335e15	−0.212018
$945$	3.91700e15	0.169075
$946$	7.62956e15	0.327415
$947$	2.56044e16	1.09242	0.546211	−	0.837648i	$-0.316070\pi$
$947$	2.56044e16	1.09242	0.546211	+	0.837648i	$0.316070\pi$
$948$	2.75098e15	0.116692
$949$	3.93520e15	0.165960
$950$	−2.13016e15	−0.0893167
$951$	7.88671e15	0.328778
$952$	3.83469e15	0.158938
$953$	−9.59290e15	−0.395311	−0.197656	−	0.980272i	$-0.563333\pi$
$953$	−9.59290e15	−0.395311	−0.197656	+	0.980272i	$0.563333\pi$
$954$	−3.96858e15	−0.162600
$955$	2.59272e16	1.05618
$956$	2.26475e15	0.0917279
$957$	4.40557e15	0.177414
$958$	−1.80065e16	−0.720974
$959$	−1.76748e16	−0.703644
$960$	7.22843e14	0.0286123
$961$	−1.12472e16	−0.442657
$962$	1.85685e15	0.0726631
$963$	3.60388e16	1.40225
$964$	2.42373e15	0.0937693
$965$	3.58063e16	1.37740
$966$	2.47694e15	0.0947416
$967$	2.03618e16	0.774410	0.387205	−	0.921994i	$-0.373441\pi$
$967$	2.03618e16	0.774410	0.387205	+	0.921994i	$0.373441\pi$
$968$	−6.50642e15	−0.246052
$969$	−5.85702e15	−0.220240
$970$	−3.57606e16	−1.33709
$971$	−2.88942e16	−1.07425	−0.537124	−	0.843503i	$-0.680489\pi$
$971$	−2.88942e16	−1.07425	−0.537124	+	0.843503i	$0.680489\pi$
$972$	−8.15332e15	−0.301419
$973$	2.02120e15	0.0743001
$974$	−3.65907e14	−0.0133751
$975$	1.34988e14	0.00490647
$976$	−5.38532e15	−0.194642
$977$	2.61482e15	0.0939769	0.0469885	−	0.998895i	$-0.485038\pi$
$977$	2.61482e15	0.0939769	0.0469885	+	0.998895i	$0.485038\pi$
$978$	5.55970e15	0.198695
$979$	−2.44631e16	−0.869376
$980$	−2.16362e15	−0.0764607
$981$	1.46192e16	0.513741
$982$	−2.61216e16	−0.912821
$983$	2.93369e16	1.01946	0.509730	−	0.860334i	$-0.329745\pi$
$983$	2.93369e16	1.01946	0.509730	+	0.860334i	$0.329745\pi$
$984$	5.83891e14	0.0201771
$985$	3.29048e16	1.13073
$986$	−3.70307e16	−1.26543
$987$	−3.93313e15	−0.133658
$988$	2.01548e15	0.0681105
$989$	−4.14232e16	−1.39208
$990$	−1.19178e16	−0.398294
$991$	−4.57778e16	−1.52142	−0.760712	−	0.649090i	$-0.775150\pi$
$991$	−4.57778e16	−1.52142	−0.760712	+	0.649090i	$0.775150\pi$
$992$	3.99301e15	0.131973
$993$	7.15868e15	0.235295
$994$	2.07009e15	0.0676649
$995$	−6.13268e16	−1.99353
$996$	5.41530e14	0.0175064
$997$	−2.80206e16	−0.900855	−0.450427	−	0.892813i	$-0.648728\pi$
$997$	−2.80206e16	−0.900855	−0.450427	+	0.892813i	$0.648728\pi$
$998$	−6.88020e14	−0.0219980
$999$	−8.58530e15	−0.272989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.a.b.1.1	✓	1
3.2	odd	2		126.12.a.b.1.1		1
4.3	odd	2		112.12.a.a.1.1		1
7.2	even	3		98.12.c.b.67.1		2
7.3	odd	6		98.12.c.a.79.1		2
7.4	even	3		98.12.c.b.79.1		2
7.5	odd	6		98.12.c.a.67.1		2
7.6	odd	2		98.12.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.a.b.1.1	✓	1	1.1	even	1	trivial
98.12.a.b.1.1		1	7.6	odd	2
98.12.c.a.67.1		2	7.5	odd	6
98.12.c.a.79.1		2	7.3	odd	6
98.12.c.b.67.1		2	7.2	even	3
98.12.c.b.79.1		2	7.4	even	3
112.12.a.a.1.1		1	4.3	odd	2
126.12.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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