LMFDB - Embedded newform 147.12.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,12,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	147.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:	$112.946447542$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+78.0000 q^{2} +243.000 q^{3} +4036.00 q^{4} +5370.00 q^{5} +18954.0 q^{6} +155064. q^{8} +59049.0 q^{9} +O(q^{10})$

\(q+78.0000 q^{2} +243.000 q^{3} +4036.00 q^{4} +5370.00 q^{5} +18954.0 q^{6} +155064. q^{8} +59049.0 q^{9} +418860. q^{10} +637836. q^{11} +980748. q^{12} -766214. q^{13} +1.30491e6 q^{15} +3.82926e6 q^{16} -3.08435e6 q^{17} +4.60582e6 q^{18} +1.95114e7 q^{19} +2.16733e7 q^{20} +4.97512e7 q^{22} +1.53124e7 q^{23} +3.76806e7 q^{24} -1.99912e7 q^{25} -5.97647e7 q^{26} +1.43489e7 q^{27} +1.07513e7 q^{29} +1.01783e8 q^{30} +5.09374e7 q^{31} -1.88885e7 q^{32} +1.54994e8 q^{33} -2.40580e8 q^{34} +2.38322e8 q^{36} +6.64741e8 q^{37} +1.52189e9 q^{38} -1.86190e8 q^{39} +8.32694e8 q^{40} -8.98833e8 q^{41} -9.57947e8 q^{43} +2.57431e9 q^{44} +3.17093e8 q^{45} +1.19436e9 q^{46} +1.55574e9 q^{47} +9.30511e8 q^{48} -1.55932e9 q^{50} -7.49498e8 q^{51} -3.09244e9 q^{52} +3.79242e9 q^{53} +1.11921e9 q^{54} +3.42518e9 q^{55} +4.74127e9 q^{57} +8.38598e8 q^{58} -5.55307e8 q^{59} +5.26662e9 q^{60} -4.95042e9 q^{61} +3.97312e9 q^{62} -9.31563e9 q^{64} -4.11457e9 q^{65} +1.20895e10 q^{66} +5.29240e9 q^{67} -1.24485e10 q^{68} +3.72090e9 q^{69} -1.48311e10 q^{71} +9.15637e9 q^{72} -1.39710e10 q^{73} +5.18498e10 q^{74} -4.85787e9 q^{75} +7.87480e10 q^{76} -1.45228e10 q^{78} +3.72054e9 q^{79} +2.05631e10 q^{80} +3.48678e9 q^{81} -7.01090e10 q^{82} -8.76845e9 q^{83} -1.65630e10 q^{85} -7.47199e10 q^{86} +2.61256e9 q^{87} +9.89054e10 q^{88} +2.54728e10 q^{89} +2.47333e10 q^{90} +6.18007e10 q^{92} +1.23778e10 q^{93} +1.21348e11 q^{94} +1.04776e11 q^{95} -4.58990e9 q^{96} +3.90925e10 q^{97} +3.76636e10 q^{99} +O(q^{100})\)

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 $

$2$	78.0000	1.72357	0.861786	−	0.507271i	$-0.169346\pi$
$2$	78.0000	1.72357	0.861786	+	0.507271i	$0.169346\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	4036.00	1.97070
$5$	5370.00	0.768492	0.384246	−	0.923231i	$-0.374461\pi$
$5$	5370.00	0.768492	0.384246	+	0.923231i	$0.374461\pi$
$6$	18954.0	0.995105
$7$	0	0
$7$	0	0
$8$	155064.	1.67308
$9$	59049.0	0.333333
$10$	418860.	1.32455
$11$	637836.	1.19412	0.597062	−	0.802195i	$-0.296335\pi$
$11$	637836.	1.19412	0.597062	+	0.802195i	$0.296335\pi$
$12$	980748.	1.13779
$13$	−766214.	−0.572350	−0.286175	−	0.958177i	$-0.592384\pi$
$13$	−766214.	−0.572350	−0.286175	+	0.958177i	$0.592384\pi$
$14$	0	0
$15$	1.30491e6	0.443689
$16$	3.82926e6	0.912968
$17$	−3.08435e6	−0.526860	−0.263430	−	0.964679i	$-0.584854\pi$
$17$	−3.08435e6	−0.526860	−0.263430	+	0.964679i	$0.584854\pi$
$18$	4.60582e6	0.574524
$19$	1.95114e7	1.80777	0.903886	−	0.427773i	$-0.140702\pi$
$19$	1.95114e7	1.80777	0.903886	+	0.427773i	$0.140702\pi$
$20$	2.16733e7	1.51447
$21$	0	0
$22$	4.97512e7	2.05816
$23$	1.53124e7	0.496066	0.248033	−	0.968752i	$-0.420216\pi$
$23$	1.53124e7	0.496066	0.248033	+	0.968752i	$0.420216\pi$
$24$	3.76806e7	0.965952
$25$	−1.99912e7	−0.409420
$26$	−5.97647e7	−0.986487
$27$	1.43489e7	0.192450
$28$	0	0
$29$	1.07513e7	0.0973353	0.0486677	−	0.998815i	$-0.484502\pi$
$29$	1.07513e7	0.0973353	0.0486677	+	0.998815i	$0.484502\pi$
$30$	1.01783e8	0.764730
$31$	5.09374e7	0.319556	0.159778	−	0.987153i	$-0.448922\pi$
$31$	5.09374e7	0.319556	0.159778	+	0.987153i	$0.448922\pi$
$32$	−1.88885e7	−0.0995112
$33$	1.54994e8	0.689428
$34$	−2.40580e8	−0.908081
$35$	0	0
$36$	2.38322e8	0.656901
$37$	6.64741e8	1.57595	0.787976	−	0.615706i	$-0.211129\pi$
$37$	6.64741e8	1.57595	0.787976	+	0.615706i	$0.211129\pi$
$38$	1.52189e9	3.11583
$39$	−1.86190e8	−0.330446
$40$	8.32694e8	1.28575
$41$	−8.98833e8	−1.21162	−0.605812	−	0.795608i	$-0.707152\pi$
$41$	−8.98833e8	−1.21162	−0.605812	+	0.795608i	$0.707152\pi$
$42$	0	0
$43$	−9.57947e8	−0.993722	−0.496861	−	0.867830i	$-0.665514\pi$
$43$	−9.57947e8	−0.993722	−0.496861	+	0.867830i	$0.665514\pi$
$44$	2.57431e9	2.35326
$45$	3.17093e8	0.256164
$46$	1.19436e9	0.855005
$47$	1.55574e9	0.989462	0.494731	−	0.869046i	$-0.335267\pi$
$47$	1.55574e9	0.989462	0.494731	+	0.869046i	$0.335267\pi$
$48$	9.30511e8	0.527102
$49$	0	0
$50$	−1.55932e9	−0.705666
$51$	−7.49498e8	−0.304183
$52$	−3.09244e9	−1.12793
$53$	3.79242e9	1.24566	0.622829	−	0.782358i	$-0.285983\pi$
$53$	3.79242e9	1.24566	0.622829	+	0.782358i	$0.285983\pi$
$54$	1.11921e9	0.331702
$55$	3.42518e9	0.917674
$56$	0	0
$57$	4.74127e9	1.04372
$58$	8.38598e8	0.167765
$59$	−5.55307e8	−0.101122	−0.0505612	−	0.998721i	$-0.516101\pi$
$59$	−5.55307e8	−0.101122	−0.0505612	+	0.998721i	$0.516101\pi$
$60$	5.26662e9	0.874379
$61$	−4.95042e9	−0.750461	−0.375230	−	0.926932i	$-0.622436\pi$
$61$	−4.95042e9	−0.750461	−0.375230	+	0.926932i	$0.622436\pi$
$62$	3.97312e9	0.550779
$63$	0	0
$64$	−9.31563e9	−1.08448
$65$	−4.11457e9	−0.439846
$66$	1.20895e10	1.18828
$67$	5.29240e9	0.478896	0.239448	−	0.970909i	$-0.423034\pi$
$67$	5.29240e9	0.478896	0.239448	+	0.970909i	$0.423034\pi$
$68$	−1.24485e10	−1.03828
$69$	3.72090e9	0.286404
$70$	0	0
$71$	−1.48311e10	−0.975556	−0.487778	−	0.872968i	$-0.662192\pi$
$71$	−1.48311e10	−0.975556	−0.487778	+	0.872968i	$0.662192\pi$
$72$	9.15637e9	0.557692
$73$	−1.39710e10	−0.788773	−0.394386	−	0.918945i	$-0.629043\pi$
$73$	−1.39710e10	−0.788773	−0.394386	+	0.918945i	$0.629043\pi$
$74$	5.18498e10	2.71627
$75$	−4.85787e9	−0.236379
$76$	7.87480e10	3.56258
$77$	0	0
$78$	−1.45228e10	−0.569548
$79$	3.72054e9	0.136037	0.0680185	−	0.997684i	$-0.478332\pi$
$79$	3.72054e9	0.136037	0.0680185	+	0.997684i	$0.478332\pi$
$80$	2.05631e10	0.701608
$81$	3.48678e9	0.111111
$82$	−7.01090e10	−2.08832
$83$	−8.76845e9	−0.244339	−0.122170	−	0.992509i	$-0.538985\pi$
$83$	−8.76845e9	−0.244339	−0.122170	+	0.992509i	$0.538985\pi$
$84$	0	0
$85$	−1.65630e10	−0.404888
$86$	−7.47199e10	−1.71275
$87$	2.61256e9	0.0561966
$88$	9.89054e10	1.99786
$89$	2.54728e10	0.483539	0.241769	−	0.970334i	$-0.422272\pi$
$89$	2.54728e10	0.483539	0.241769	+	0.970334i	$0.422272\pi$
$90$	2.47333e10	0.441517
$91$	0	0
$92$	6.18007e10	0.977598
$93$	1.23778e10	0.184496
$94$	1.21348e11	1.70541
$95$	1.04776e11	1.38926
$96$	−4.58990e9	−0.0574528
$97$	3.90925e10	0.462220	0.231110	−	0.972928i	$-0.425764\pi$
$97$	3.90925e10	0.462220	0.231110	+	0.972928i	$0.425764\pi$
$98$	0	0
$99$	3.76636e10	0.398041
$100$	−8.06846e10	−0.806846
$101$	−9.31078e9	−0.0881492	−0.0440746	−	0.999028i	$-0.514034\pi$
$101$	−9.31078e9	−0.0881492	−0.0440746	+	0.999028i	$0.514034\pi$
$102$	−5.84608e10	−0.524281
$103$	−4.85751e10	−0.412865	−0.206433	−	0.978461i	$-0.566185\pi$
$103$	−4.85751e10	−0.412865	−0.206433	+	0.978461i	$0.566185\pi$
$104$	−1.18812e11	−0.957586
$105$	0	0
$106$	2.95809e11	2.14698
$107$	2.25596e11	1.55496	0.777482	−	0.628906i	$-0.216497\pi$
$107$	2.25596e11	1.55496	0.777482	+	0.628906i	$0.216497\pi$
$108$	5.79122e10	0.379262
$109$	−6.94512e10	−0.432348	−0.216174	−	0.976355i	$-0.569358\pi$
$109$	−6.94512e10	−0.432348	−0.216174	+	0.976355i	$0.569358\pi$
$110$	2.67164e11	1.58168
$111$	1.61532e11	0.909876
$112$	0	0
$113$	−3.59665e11	−1.83640	−0.918198	−	0.396122i	$-0.870356\pi$
$113$	−3.59665e11	−1.83640	−0.918198	+	0.396122i	$0.870356\pi$
$114$	3.69819e11	1.79892
$115$	8.22274e10	0.381222
$116$	4.33921e10	0.191819
$117$	−4.52442e10	−0.190783
$118$	−4.33139e10	−0.174292
$119$	0	0
$120$	2.02345e11	0.742326
$121$	1.21523e11	0.425931
$122$	−3.86133e11	−1.29347
$123$	−2.18417e11	−0.699532
$124$	2.05583e11	0.629751
$125$	−3.69560e11	−1.08313
$126$	0	0
$127$	2.50273e11	0.672192	0.336096	−	0.941828i	$-0.390893\pi$
$127$	2.50273e11	0.672192	0.336096	+	0.941828i	$0.390893\pi$
$128$	−6.87936e11	−1.76967
$129$	−2.32781e11	−0.573726
$130$	−3.20936e11	−0.758107
$131$	9.78918e10	0.221694	0.110847	−	0.993837i	$-0.464644\pi$
$131$	9.78918e10	0.221694	0.110847	+	0.993837i	$0.464644\pi$
$132$	6.25556e11	1.35866
$133$	0	0
$134$	4.12807e11	0.825412
$135$	7.70536e10	0.147896
$136$	−4.78272e11	−0.881477
$137$	−1.55015e11	−0.274416	−0.137208	−	0.990542i	$-0.543813\pi$
$137$	−1.55015e11	−0.274416	−0.137208	+	0.990542i	$0.543813\pi$
$138$	2.90230e11	0.493637
$139$	1.12627e12	1.84102	0.920512	−	0.390715i	$-0.127772\pi$
$139$	1.12627e12	1.84102	0.920512	+	0.390715i	$0.127772\pi$
$140$	0	0
$141$	3.78045e11	0.571266
$142$	−1.15682e12	−1.68144
$143$	−4.88719e11	−0.683457
$144$	2.26114e11	0.304323
$145$	5.77343e10	0.0748014
$146$	−1.08974e12	−1.35951
$147$	0	0
$148$	2.68289e12	3.10573
$149$	−1.38458e12	−1.54452	−0.772261	−	0.635306i	$-0.780874\pi$
$149$	−1.38458e12	−1.54452	−0.772261	+	0.635306i	$0.780874\pi$
$150$	−3.78914e11	−0.407416
$151$	−6.98601e11	−0.724196	−0.362098	−	0.932140i	$-0.617939\pi$
$151$	−6.98601e11	−0.724196	−0.362098	+	0.932140i	$0.617939\pi$
$152$	3.02552e12	3.02454
$153$	−1.82128e11	−0.175620
$154$	0	0
$155$	2.73534e11	0.245576
$156$	−7.51463e11	−0.651212
$157$	−2.13127e12	−1.78316	−0.891580	−	0.452863i	$-0.850403\pi$
$157$	−2.13127e12	−1.78316	−0.891580	+	0.452863i	$0.850403\pi$
$158$	2.90202e11	0.234470
$159$	9.21557e11	0.719181
$160$	−1.01431e11	−0.0764736
$161$	0	0
$162$	2.71969e11	0.191508
$163$	−1.63564e11	−0.111342	−0.0556708	−	0.998449i	$-0.517730\pi$
$163$	−1.63564e11	−0.111342	−0.0556708	+	0.998449i	$0.517730\pi$
$164$	−3.62769e12	−2.38775
$165$	8.32319e11	0.529819
$166$	−6.83939e11	−0.421137
$167$	8.80943e9	0.00524816	0.00262408	−	0.999997i	$-0.499165\pi$
$167$	8.80943e9	0.00524816	0.00262408	+	0.999997i	$0.499165\pi$
$168$	0	0
$169$	−1.20508e12	−0.672416
$170$	−1.29191e12	−0.697853
$171$	1.15213e12	0.602591
$172$	−3.86627e12	−1.95833
$173$	7.30852e11	0.358571	0.179286	−	0.983797i	$-0.442621\pi$
$173$	7.30852e11	0.358571	0.179286	+	0.983797i	$0.442621\pi$
$174$	2.03779e11	0.0968589
$175$	0	0
$176$	2.44244e12	1.09020
$177$	−1.34940e11	−0.0583830
$178$	1.98688e12	0.833414
$179$	3.92371e12	1.59590	0.797950	−	0.602724i	$-0.205918\pi$
$179$	3.92371e12	1.59590	0.797950	+	0.602724i	$0.205918\pi$
$180$	1.27979e12	0.504823
$181$	−2.27931e12	−0.872110	−0.436055	−	0.899920i	$-0.643625\pi$
$181$	−2.27931e12	−0.872110	−0.436055	+	0.899920i	$0.643625\pi$
$182$	0	0
$183$	−1.20295e12	−0.433279
$184$	2.37440e12	0.829956
$185$	3.56966e12	1.21111
$186$	9.65467e11	0.317992
$187$	−1.96731e12	−0.629136
$188$	6.27897e12	1.94994
$189$	0	0
$190$	8.17255e12	2.39449
$191$	3.38709e12	0.964147	0.482073	−	0.876131i	$-0.339884\pi$
$191$	3.38709e12	0.964147	0.482073	+	0.876131i	$0.339884\pi$
$192$	−2.26370e12	−0.626126
$193$	−4.92921e12	−1.32499	−0.662494	−	0.749067i	$-0.730502\pi$
$193$	−4.92921e12	−1.32499	−0.662494	+	0.749067i	$0.730502\pi$
$194$	3.04921e12	0.796670
$195$	−9.99840e11	−0.253945
$196$	0	0
$197$	6.35785e12	1.52667	0.763337	−	0.646001i	$-0.223560\pi$
$197$	6.35785e12	1.52667	0.763337	+	0.646001i	$0.223560\pi$
$198$	2.93776e12	0.686053
$199$	3.78554e12	0.859875	0.429938	−	0.902859i	$-0.358536\pi$
$199$	3.78554e12	0.859875	0.429938	+	0.902859i	$0.358536\pi$
$200$	−3.09992e12	−0.684992
$201$	1.28605e12	0.276491
$202$	−7.26241e11	−0.151932
$203$	0	0
$204$	−3.02497e12	−0.599454
$205$	−4.82674e12	−0.931123
$206$	−3.78885e12	−0.711604
$207$	9.04180e11	0.165355
$208$	−2.93404e12	−0.522537
$209$	1.24451e13	2.15870
$210$	0	0
$211$	1.79494e11	0.0295458	0.0147729	−	0.999891i	$-0.495297\pi$
$211$	1.79494e11	0.0295458	0.0147729	+	0.999891i	$0.495297\pi$
$212$	1.53062e13	2.45482
$213$	−3.60395e12	−0.563237
$214$	1.75965e13	2.68009
$215$	−5.14418e12	−0.763668
$216$	2.22500e12	0.321984
$217$	0	0
$218$	−5.41719e12	−0.745184
$219$	−3.39495e12	−0.455398
$220$	1.38240e13	1.80846
$221$	2.36328e12	0.301548
$222$	1.25995e13	1.56824
$223$	−2.22568e12	−0.270263	−0.135132	−	0.990828i	$-0.543146\pi$
$223$	−2.22568e12	−0.270263	−0.135132	+	0.990828i	$0.543146\pi$
$224$	0	0
$225$	−1.18046e12	−0.136473
$226$	−2.80538e13	−3.16516
$227$	4.15848e11	0.0457923	0.0228961	−	0.999738i	$-0.492711\pi$
$227$	4.15848e11	0.0457923	0.0228961	+	0.999738i	$0.492711\pi$
$228$	1.91358e13	2.05686
$229$	−1.81248e13	−1.90186	−0.950928	−	0.309414i	$-0.899867\pi$
$229$	−1.81248e13	−1.90186	−0.950928	+	0.309414i	$0.899867\pi$
$230$	6.41374e12	0.657064
$231$	0	0
$232$	1.66713e12	0.162850
$233$	−1.87641e10	−0.00179007	−0.000895033	−	1.00000i	$-0.500285\pi$
$233$	−1.87641e10	−0.00179007	−0.000895033		1.00000i	$0.500285\pi$
$234$	−3.52905e12	−0.328829
$235$	8.35433e12	0.760394
$236$	−2.24122e12	−0.199282
$237$	9.04092e11	0.0785410
$238$	0	0
$239$	−1.76252e13	−1.46200	−0.730999	−	0.682379i	$-0.760946\pi$
$239$	−1.76252e13	−1.46200	−0.730999	+	0.682379i	$0.760946\pi$
$240$	4.99684e12	0.405074
$241$	8.90117e11	0.0705267	0.0352633	−	0.999378i	$-0.488773\pi$
$241$	8.90117e11	0.0705267	0.0352633	+	0.999378i	$0.488773\pi$
$242$	9.47880e12	0.734123
$243$	8.47289e11	0.0641500
$244$	−1.99799e13	−1.47894
$245$	0	0
$246$	−1.70365e13	−1.20569
$247$	−1.49499e13	−1.03468
$248$	7.89856e12	0.534643
$249$	−2.13073e12	−0.141069
$250$	−2.88257e13	−1.86685
$251$	2.42280e13	1.53502	0.767508	−	0.641040i	$-0.221497\pi$
$251$	2.42280e13	1.53502	0.767508	+	0.641040i	$0.221497\pi$
$252$	0	0
$253$	9.76677e12	0.592364
$254$	1.95213e13	1.15857
$255$	−4.02480e12	−0.233762
$256$	−3.45806e13	−1.96568
$257$	−7.80492e12	−0.434246	−0.217123	−	0.976144i	$-0.569667\pi$
$257$	−7.80492e12	−0.434246	−0.217123	+	0.976144i	$0.569667\pi$
$258$	−1.81569e13	−0.988858
$259$	0	0
$260$	−1.66064e13	−0.866806
$261$	6.34851e11	0.0324451
$262$	7.63556e12	0.382106
$263$	1.65956e13	0.813272	0.406636	−	0.913590i	$-0.366702\pi$
$263$	1.65956e13	0.813272	0.406636	+	0.913590i	$0.366702\pi$
$264$	2.40340e13	1.15347
$265$	2.03653e13	0.957278
$266$	0	0
$267$	6.18988e12	0.279171
$268$	2.13601e13	0.943762
$269$	−2.85236e13	−1.23471	−0.617357	−	0.786683i	$-0.711797\pi$
$269$	−2.85236e13	−1.23471	−0.617357	+	0.786683i	$0.711797\pi$
$270$	6.01018e12	0.254910
$271$	−2.33800e13	−0.971658	−0.485829	−	0.874054i	$-0.661482\pi$
$271$	−2.33800e13	−0.971658	−0.485829	+	0.874054i	$0.661482\pi$
$272$	−1.18108e13	−0.481006
$273$	0	0
$274$	−1.20911e13	−0.472976
$275$	−1.27511e13	−0.488898
$276$	1.50176e13	0.564416
$277$	−3.03641e13	−1.11872	−0.559361	−	0.828924i	$-0.688953\pi$
$277$	−3.03641e13	−1.11872	−0.559361	+	0.828924i	$0.688953\pi$
$278$	8.78487e13	3.17314
$279$	3.00780e12	0.106519
$280$	0	0
$281$	1.59749e13	0.543942	0.271971	−	0.962306i	$-0.412325\pi$
$281$	1.59749e13	0.543942	0.271971	+	0.962306i	$0.412325\pi$
$282$	2.94875e13	0.984619
$283$	−2.87045e13	−0.939993	−0.469997	−	0.882668i	$-0.655745\pi$
$283$	−2.87045e13	−0.939993	−0.469997	+	0.882668i	$0.655745\pi$
$284$	−5.98583e13	−1.92253
$285$	2.54606e13	0.802089
$286$	−3.81201e13	−1.17799
$287$	0	0
$288$	−1.11535e12	−0.0331704
$289$	−2.47587e13	−0.722419
$290$	4.50327e12	0.128926
$291$	9.49948e12	0.266863
$292$	−5.63870e13	−1.55444
$293$	−4.81754e13	−1.30333	−0.651663	−	0.758508i	$-0.725929\pi$
$293$	−4.81754e13	−1.30333	−0.651663	+	0.758508i	$0.725929\pi$
$294$	0	0
$295$	−2.98200e12	−0.0777117
$296$	1.03077e14	2.63669
$297$	9.15225e12	0.229809
$298$	−1.07997e14	−2.66209
$299$	−1.17325e13	−0.283923
$300$	−1.96064e13	−0.465833
$301$	0	0
$302$	−5.44909e13	−1.24820
$303$	−2.26252e12	−0.0508930
$304$	7.47143e13	1.65044
$305$	−2.65838e13	−0.576723
$306$	−1.42060e13	−0.302694
$307$	−2.57350e13	−0.538597	−0.269298	−	0.963057i	$-0.586792\pi$
$307$	−2.57350e13	−0.538597	−0.269298	+	0.963057i	$0.586792\pi$
$308$	0	0
$309$	−1.18037e13	−0.238368
$310$	2.13356e13	0.423269
$311$	−3.46043e13	−0.674446	−0.337223	−	0.941425i	$-0.609488\pi$
$311$	−3.46043e13	−0.674446	−0.337223	+	0.941425i	$0.609488\pi$
$312$	−2.88714e13	−0.552862
$313$	−1.26066e13	−0.237194	−0.118597	−	0.992942i	$-0.537840\pi$
$313$	−1.26066e13	−0.237194	−0.118597	+	0.992942i	$0.537840\pi$
$314$	−1.66239e14	−3.07341
$315$	0	0
$316$	1.50161e13	0.268089
$317$	−8.18243e13	−1.43568	−0.717838	−	0.696210i	$-0.754868\pi$
$317$	−8.18243e13	−1.43568	−0.717838	+	0.696210i	$0.754868\pi$
$318$	7.18815e13	1.23956
$319$	6.85754e12	0.116230
$320$	−5.00250e13	−0.833416
$321$	5.48198e13	0.897758
$322$	0	0
$323$	−6.01801e13	−0.952443
$324$	1.40727e13	0.218967
$325$	1.53176e13	0.234332
$326$	−1.27580e13	−0.191905
$327$	−1.68766e13	−0.249616
$328$	−1.39377e14	−2.02714
$329$	0	0
$330$	6.49208e13	0.913182
$331$	−3.40115e13	−0.470513	−0.235256	−	0.971933i	$-0.575593\pi$
$331$	−3.40115e13	−0.470513	−0.235256	+	0.971933i	$0.575593\pi$
$332$	−3.53895e13	−0.481520
$333$	3.92523e13	0.525317
$334$	6.87135e11	0.00904558
$335$	2.84202e13	0.368028
$336$	0	0
$337$	−5.99439e13	−0.751244	−0.375622	−	0.926773i	$-0.622571\pi$
$337$	−5.99439e13	−0.751244	−0.375622	+	0.926773i	$0.622571\pi$
$338$	−9.39960e13	−1.15896
$339$	−8.73985e13	−1.06024
$340$	−6.68482e13	−0.797913
$341$	3.24897e13	0.381590
$342$	8.98661e13	1.03861
$343$	0	0
$344$	−1.48543e14	−1.66257
$345$	1.99813e13	0.220099
$346$	5.70064e13	0.618024
$347$	9.78685e13	1.04431	0.522157	−	0.852850i	$-0.325128\pi$
$347$	9.78685e13	1.04431	0.522157	+	0.852850i	$0.325128\pi$
$348$	1.05443e13	0.110747
$349$	1.42790e14	1.47624	0.738120	−	0.674670i	$-0.235714\pi$
$349$	1.42790e14	1.47624	0.738120	+	0.674670i	$0.235714\pi$
$350$	0	0
$351$	−1.09943e13	−0.110149
$352$	−1.20478e13	−0.118829
$353$	−1.44246e14	−1.40069	−0.700346	−	0.713804i	$-0.746971\pi$
$353$	−1.44246e14	−1.40069	−0.700346	+	0.713804i	$0.746971\pi$
$354$	−1.05253e13	−0.100627
$355$	−7.96429e13	−0.749707
$356$	1.02808e14	0.952911
$357$	0	0
$358$	3.06050e14	2.75065
$359$	−1.24349e14	−1.10059	−0.550293	−	0.834972i	$-0.685484\pi$
$359$	−1.24349e14	−1.10059	−0.550293	+	0.834972i	$0.685484\pi$
$360$	4.91697e13	0.428582
$361$	2.64205e14	2.26804
$362$	−1.77786e14	−1.50314
$363$	2.95301e13	0.245911
$364$	0	0
$365$	−7.50243e13	−0.606165
$366$	−9.38303e13	−0.746788
$367$	1.60110e14	1.25532	0.627659	−	0.778488i	$-0.284013\pi$
$367$	1.60110e14	1.25532	0.627659	+	0.778488i	$0.284013\pi$
$368$	5.86351e13	0.452892
$369$	−5.30752e13	−0.403875
$370$	2.78433e14	2.08743
$371$	0	0
$372$	4.99568e13	0.363587
$373$	−3.47258e13	−0.249031	−0.124516	−	0.992218i	$-0.539738\pi$
$373$	−3.47258e13	−0.249031	−0.124516	+	0.992218i	$0.539738\pi$
$374$	−1.53450e14	−1.08436
$375$	−8.98031e13	−0.625344
$376$	2.41239e14	1.65545
$377$	−8.23777e12	−0.0557099
$378$	0	0
$379$	−1.46500e14	−0.962327	−0.481163	−	0.876631i	$-0.659786\pi$
$379$	−1.46500e14	−0.962327	−0.481163	+	0.876631i	$0.659786\pi$
$380$	4.22877e14	2.73782
$381$	6.08164e13	0.388090
$382$	2.64193e14	1.66178
$383$	−6.43419e13	−0.398933	−0.199467	−	0.979905i	$-0.563921\pi$
$383$	−6.43419e13	−0.398933	−0.199467	+	0.979905i	$0.563921\pi$
$384$	−1.67168e14	−1.02172
$385$	0	0
$386$	−3.84478e14	−2.28371
$387$	−5.65658e13	−0.331241
$388$	1.57777e14	0.910899
$389$	−3.98900e13	−0.227061	−0.113530	−	0.993535i	$-0.536216\pi$
$389$	−3.98900e13	−0.227061	−0.113530	+	0.993535i	$0.536216\pi$
$390$	−7.79875e13	−0.437693
$391$	−4.72287e13	−0.261357
$392$	0	0
$393$	2.37877e13	0.127995
$394$	4.95912e14	2.63133
$395$	1.99793e13	0.104543
$396$	1.52010e14	0.784421
$397$	−1.06552e14	−0.542268	−0.271134	−	0.962542i	$-0.587399\pi$
$397$	−1.06552e14	−0.542268	−0.271134	+	0.962542i	$0.587399\pi$
$398$	2.95272e14	1.48206
$399$	0	0
$400$	−7.65517e13	−0.373787
$401$	3.41445e13	0.164447	0.0822236	−	0.996614i	$-0.473798\pi$
$401$	3.41445e13	0.164447	0.0822236	+	0.996614i	$0.473798\pi$
$402$	1.00312e14	0.476552
$403$	−3.90289e13	−0.182898
$404$	−3.75783e13	−0.173716
$405$	1.87240e13	0.0853880
$406$	0	0
$407$	4.23996e14	1.88188
$408$	−1.16220e14	−0.508921
$409$	−5.33349e13	−0.230427	−0.115213	−	0.993341i	$-0.536755\pi$
$409$	−5.33349e13	−0.230427	−0.115213	+	0.993341i	$0.536755\pi$
$410$	−3.76485e14	−1.60486
$411$	−3.76686e13	−0.158434
$412$	−1.96049e14	−0.813635
$413$	0	0
$414$	7.05260e13	0.285002
$415$	−4.70866e13	−0.187773
$416$	1.44726e13	0.0569553
$417$	2.73682e14	1.06292
$418$	9.70716e14	3.72068
$419$	1.01288e14	0.383159	0.191580	−	0.981477i	$-0.438639\pi$
$419$	1.01288e14	0.383159	0.191580	+	0.981477i	$0.438639\pi$
$420$	0	0
$421$	−1.57928e14	−0.581981	−0.290991	−	0.956726i	$-0.593985\pi$
$421$	−1.57928e14	−0.581981	−0.290991	+	0.956726i	$0.593985\pi$
$422$	1.40005e13	0.0509244
$423$	9.18650e13	0.329821
$424$	5.88067e14	2.08408
$425$	6.16600e13	0.215707
$426$	−2.81108e14	−0.970780
$427$	0	0
$428$	9.10504e14	3.06437
$429$	−1.18759e14	−0.394594
$430$	−4.01246e14	−1.31624
$431$	5.13171e14	1.66202	0.831012	−	0.556254i	$-0.187762\pi$
$431$	5.13171e14	1.66202	0.831012	+	0.556254i	$0.187762\pi$
$432$	5.49458e13	0.175701
$433$	7.49248e13	0.236560	0.118280	−	0.992980i	$-0.462262\pi$
$433$	7.49248e13	0.236560	0.118280	+	0.992980i	$0.462262\pi$
$434$	0	0
$435$	1.40294e13	0.0431866
$436$	−2.80305e14	−0.852030
$437$	2.98766e14	0.896773
$438$	−2.64806e14	−0.784912
$439$	3.68335e14	1.07817	0.539086	−	0.842250i	$-0.318770\pi$
$439$	3.68335e14	1.07817	0.539086	+	0.842250i	$0.318770\pi$
$440$	5.31122e14	1.53534
$441$	0	0
$442$	1.84335e14	0.519740
$443$	−1.11248e14	−0.309793	−0.154896	−	0.987931i	$-0.549504\pi$
$443$	−1.11248e14	−0.309793	−0.154896	+	0.987931i	$0.549504\pi$
$444$	6.51943e14	1.79310
$445$	1.36789e14	0.371595
$446$	−1.73603e14	−0.465818
$447$	−3.36453e14	−0.891730
$448$	0	0
$449$	−8.83314e13	−0.228434	−0.114217	−	0.993456i	$-0.536436\pi$
$449$	−8.83314e13	−0.228434	−0.114217	+	0.993456i	$0.536436\pi$
$450$	−9.20760e13	−0.235222
$451$	−5.73308e14	−1.44683
$452$	−1.45161e15	−3.61899
$453$	−1.69760e14	−0.418115
$454$	3.24361e13	0.0789263
$455$	0	0
$456$	7.35200e14	1.74622
$457$	−9.42094e12	−0.0221083	−0.0110541	−	0.999939i	$-0.503519\pi$
$457$	−9.42094e12	−0.0221083	−0.0110541	+	0.999939i	$0.503519\pi$
$458$	−1.41373e15	−3.27799
$459$	−4.42571e13	−0.101394
$460$	3.31870e14	0.751276
$461$	6.97134e14	1.55941	0.779706	−	0.626146i	$-0.215369\pi$
$461$	6.97134e14	1.55941	0.779706	+	0.626146i	$0.215369\pi$
$462$	0	0
$463$	−1.87941e14	−0.410513	−0.205256	−	0.978708i	$-0.565803\pi$
$463$	−1.87941e14	−0.410513	−0.205256	+	0.978708i	$0.565803\pi$
$464$	4.11694e13	0.0888640
$465$	6.64687e13	0.141784
$466$	−1.46360e12	−0.00308531
$467$	−3.20007e14	−0.666678	−0.333339	−	0.942807i	$-0.608175\pi$
$467$	−3.20007e14	−0.666678	−0.333339	+	0.942807i	$0.608175\pi$
$468$	−1.82605e14	−0.375977
$469$	0	0
$470$	6.51638e14	1.31059
$471$	−5.17899e14	−1.02951
$472$	−8.61081e13	−0.169185
$473$	−6.11013e14	−1.18663
$474$	7.05192e13	0.135371
$475$	−3.90057e14	−0.740139
$476$	0	0
$477$	2.23938e14	0.415219
$478$	−1.37477e15	−2.51986
$479$	1.50382e14	0.272491	0.136245	−	0.990675i	$-0.456496\pi$
$479$	1.50382e14	0.272491	0.136245	+	0.990675i	$0.456496\pi$
$480$	−2.46478e13	−0.0441520
$481$	−5.09334e14	−0.901996
$482$	6.94291e13	0.121558
$483$	0	0
$484$	4.90467e14	0.839384
$485$	2.09927e14	0.355212
$486$	6.60885e13	0.110567
$487$	1.76546e14	0.292045	0.146022	−	0.989281i	$-0.453353\pi$
$487$	1.76546e14	0.292045	0.146022	+	0.989281i	$0.453353\pi$
$488$	−7.67632e14	−1.25558
$489$	−3.97462e13	−0.0642831
$490$	0	0
$491$	−8.60958e14	−1.36155	−0.680775	−	0.732492i	$-0.738357\pi$
$491$	−8.60958e14	−1.36155	−0.680775	+	0.732492i	$0.738357\pi$
$492$	−8.81529e14	−1.37857
$493$	−3.31607e13	−0.0512821
$494$	−1.16609e15	−1.78334
$495$	2.02253e14	0.305891
$496$	1.95053e14	0.291745
$497$	0	0
$498$	−1.66197e14	−0.243143
$499$	6.01209e14	0.869907	0.434953	−	0.900453i	$-0.356765\pi$
$499$	6.01209e14	0.869907	0.434953	+	0.900453i	$0.356765\pi$
$500$	−1.49154e15	−2.13452
$501$	2.14069e12	0.00303003
$502$	1.88979e15	2.64571
$503$	−1.09203e15	−1.51221	−0.756103	−	0.654453i	$-0.772899\pi$
$503$	−1.09203e15	−1.51221	−0.756103	+	0.654453i	$0.772899\pi$
$504$	0	0
$505$	−4.99989e13	−0.0677420
$506$	7.61808e14	1.02098
$507$	−2.92834e14	−0.388219
$508$	1.01010e15	1.32469
$509$	−8.76371e14	−1.13695	−0.568474	−	0.822702i	$-0.692466\pi$
$509$	−8.76371e14	−1.13695	−0.568474	+	0.822702i	$0.692466\pi$
$510$	−3.13935e14	−0.402906
$511$	0	0
$512$	−1.28839e15	−1.61832
$513$	2.79967e14	0.347906
$514$	−6.08784e14	−0.748455
$515$	−2.60848e14	−0.317284
$516$	−9.39505e14	−1.13064
$517$	9.92308e14	1.18154
$518$	0	0
$519$	1.77597e14	0.207021
$520$	−6.38022e14	−0.735897
$521$	3.71989e14	0.424544	0.212272	−	0.977211i	$-0.431914\pi$
$521$	3.71989e14	0.424544	0.212272	+	0.977211i	$0.431914\pi$
$522$	4.95184e13	0.0559215
$523$	9.73507e14	1.08788	0.543939	−	0.839125i	$-0.316932\pi$
$523$	9.73507e14	1.08788	0.543939	+	0.839125i	$0.316932\pi$
$524$	3.95091e14	0.436893
$525$	0	0
$526$	1.29445e15	1.40173
$527$	−1.57109e14	−0.168361
$528$	5.93514e14	0.629425
$529$	−7.18341e14	−0.753919
$530$	1.58849e15	1.64994
$531$	−3.27903e13	−0.0337074
$532$	0	0
$533$	6.88699e14	0.693473
$534$	4.82811e14	0.481172
$535$	1.21145e15	1.19498
$536$	8.20661e14	0.801230
$537$	9.53463e14	0.921393
$538$	−2.22484e15	−2.12812
$539$	0	0
$540$	3.10988e14	0.291460
$541$	1.74606e15	1.61985	0.809925	−	0.586533i	$-0.199508\pi$
$541$	1.74606e15	1.61985	0.809925	+	0.586533i	$0.199508\pi$
$542$	−1.82364e15	−1.67472
$543$	−5.53872e14	−0.503513
$544$	5.82588e13	0.0524285
$545$	−3.72953e14	−0.332256
$546$	0	0
$547$	1.74624e14	0.152467	0.0762333	−	0.997090i	$-0.475711\pi$
$547$	1.74624e14	0.152467	0.0762333	+	0.997090i	$0.475711\pi$
$548$	−6.25639e14	−0.540793
$549$	−2.92317e14	−0.250154
$550$	−9.94588e14	−0.842652
$551$	2.09772e14	0.175960
$552$	5.76978e14	0.479175
$553$	0	0
$554$	−2.36840e15	−1.92820
$555$	8.67427e14	0.699232
$556$	4.54561e15	3.62811
$557$	1.58365e15	1.25157	0.625785	−	0.779995i	$-0.284779\pi$
$557$	1.58365e15	1.25157	0.625785	+	0.779995i	$0.284779\pi$
$558$	2.34609e14	0.183593
$559$	7.33993e14	0.568757
$560$	0	0
$561$	−4.78057e14	−0.363232
$562$	1.24604e15	0.937523
$563$	9.75798e14	0.727049	0.363525	−	0.931585i	$-0.381573\pi$
$563$	9.75798e14	0.727049	0.363525	+	0.931585i	$0.381573\pi$
$564$	1.52579e15	1.12580
$565$	−1.93140e15	−1.41125
$566$	−2.23895e15	−1.62015
$567$	0	0
$568$	−2.29977e15	−1.63218
$569$	1.92427e15	1.35254	0.676269	−	0.736655i	$-0.263596\pi$
$569$	1.92427e15	1.35254	0.676269	+	0.736655i	$0.263596\pi$
$570$	1.98593e15	1.38246
$571$	1.61132e15	1.11092	0.555461	−	0.831543i	$-0.312542\pi$
$571$	1.61132e15	1.11092	0.555461	+	0.831543i	$0.312542\pi$
$572$	−1.97247e15	−1.34689
$573$	8.23063e14	0.556650
$574$	0	0
$575$	−3.06113e14	−0.203099
$576$	−5.50079e14	−0.361494
$577$	2.53250e15	1.64848	0.824239	−	0.566242i	$-0.191603\pi$
$577$	2.53250e15	1.64848	0.824239	+	0.566242i	$0.191603\pi$
$578$	−1.93118e15	−1.24514
$579$	−1.19780e15	−0.764982
$580$	2.33016e14	0.147411
$581$	0	0
$582$	7.40959e14	0.459958
$583$	2.41894e15	1.48747
$584$	−2.16640e15	−1.31968
$585$	−2.42961e14	−0.146615
$586$	−3.75768e15	−2.24638
$587$	3.11508e15	1.84484	0.922421	−	0.386186i	$-0.126208\pi$
$587$	3.11508e15	1.84484	0.922421	+	0.386186i	$0.126208\pi$
$588$	0	0
$589$	9.93860e14	0.577685
$590$	−2.32596e14	−0.133942
$591$	1.54496e15	0.881425
$592$	2.54547e15	1.43879
$593$	2.20723e15	1.23608	0.618040	−	0.786146i	$-0.287927\pi$
$593$	2.20723e15	1.23608	0.618040	+	0.786146i	$0.287927\pi$
$594$	7.13875e14	0.396093
$595$	0	0
$596$	−5.58817e15	−3.04379
$597$	9.19885e14	0.496449
$598$	−9.15138e14	−0.489362
$599$	3.41159e15	1.80763	0.903813	−	0.427927i	$-0.140756\pi$
$599$	3.41159e15	1.80763	0.903813	+	0.427927i	$0.140756\pi$
$600$	−7.53280e14	−0.395480
$601$	1.57545e15	0.819588	0.409794	−	0.912178i	$-0.365601\pi$
$601$	1.57545e15	0.819588	0.409794	+	0.912178i	$0.365601\pi$
$602$	0	0
$603$	3.12511e14	0.159632
$604$	−2.81956e15	−1.42718
$605$	6.52579e14	0.327325
$606$	−1.76477e14	−0.0877178
$607$	5.05592e14	0.249036	0.124518	−	0.992217i	$-0.460262\pi$
$607$	5.05592e14	0.249036	0.124518	+	0.992217i	$0.460262\pi$
$608$	−3.68541e14	−0.179894
$609$	0	0
$610$	−2.07353e15	−0.994024
$611$	−1.19203e15	−0.566319
$612$	−7.35069e14	−0.346095
$613$	−1.98375e15	−0.925665	−0.462832	−	0.886446i	$-0.653167\pi$
$613$	−1.98375e15	−0.925665	−0.462832	+	0.886446i	$0.653167\pi$
$614$	−2.00733e15	−0.928310
$615$	−1.17290e15	−0.537584
$616$	0	0
$617$	−1.93099e15	−0.869382	−0.434691	−	0.900580i	$-0.643142\pi$
$617$	−1.93099e15	−0.869382	−0.434691	+	0.900580i	$0.643142\pi$
$618$	−9.20692e14	−0.410845
$619$	−9.47689e14	−0.419148	−0.209574	−	0.977793i	$-0.567208\pi$
$619$	−9.47689e14	−0.419148	−0.209574	+	0.977793i	$0.567208\pi$
$620$	1.10398e15	0.483958
$621$	2.19716e14	0.0954679
$622$	−2.69913e15	−1.16246
$623$	0	0
$624$	−7.12971e14	−0.301687
$625$	−1.00840e15	−0.422955
$626$	−9.83314e14	−0.408821
$627$	3.02415e15	1.24633
$628$	−8.60181e15	−3.51408
$629$	−2.05030e15	−0.830306
$630$	0	0
$631$	1.00593e15	0.400318	0.200159	−	0.979763i	$-0.435854\pi$
$631$	1.00593e15	0.400318	0.200159	+	0.979763i	$0.435854\pi$
$632$	5.76922e14	0.227601
$633$	4.36170e13	0.0170583
$634$	−6.38230e15	−2.47449
$635$	1.34397e15	0.516574
$636$	3.71941e15	1.41729
$637$	0	0
$638$	5.34888e14	0.200332
$639$	−8.75761e14	−0.325185
$640$	−3.69422e15	−1.35998
$641$	1.13144e15	0.412966	0.206483	−	0.978450i	$-0.433798\pi$
$641$	1.13144e15	0.412966	0.206483	+	0.978450i	$0.433798\pi$
$642$	4.27594e15	1.54735
$643$	8.68306e14	0.311539	0.155769	−	0.987793i	$-0.450214\pi$
$643$	8.68306e14	0.311539	0.155769	+	0.987793i	$0.450214\pi$
$644$	0	0
$645$	−1.25003e15	−0.440904
$646$	−4.69405e15	−1.64160
$647$	1.37636e15	0.477265	0.238633	−	0.971110i	$-0.423301\pi$
$647$	1.37636e15	0.477265	0.238633	+	0.971110i	$0.423301\pi$
$648$	5.40675e14	0.185897
$649$	−3.54195e14	−0.120753
$650$	1.19477e15	0.403888
$651$	0	0
$652$	−6.60146e14	−0.219421
$653$	2.55276e15	0.841370	0.420685	−	0.907207i	$-0.361790\pi$
$653$	2.55276e15	0.841370	0.420685	+	0.907207i	$0.361790\pi$
$654$	−1.31638e15	−0.430232
$655$	5.25679e14	0.170370
$656$	−3.44187e15	−1.10617
$657$	−8.24974e14	−0.262924
$658$	0	0
$659$	9.26792e14	0.290478	0.145239	−	0.989397i	$-0.453605\pi$
$659$	9.26792e14	0.290478	0.145239	+	0.989397i	$0.453605\pi$
$660$	3.35924e15	1.04412
$661$	1.90332e15	0.586683	0.293342	−	0.956008i	$-0.405233\pi$
$661$	1.90332e15	0.586683	0.293342	+	0.956008i	$0.405233\pi$
$662$	−2.65289e15	−0.810963
$663$	5.74276e14	0.174099
$664$	−1.35967e15	−0.408799
$665$	0	0
$666$	3.06168e15	0.905422
$667$	1.64627e14	0.0482847
$668$	3.55548e13	0.0103426
$669$	−5.40841e14	−0.156037
$670$	2.21677e15	0.634322
$671$	−3.15756e15	−0.896143
$672$	0	0
$673$	4.92990e15	1.37643	0.688217	−	0.725505i	$-0.258394\pi$
$673$	4.92990e15	1.37643	0.688217	+	0.725505i	$0.258394\pi$
$674$	−4.67563e15	−1.29482
$675$	−2.86852e14	−0.0787930
$676$	−4.86369e15	−1.32513
$677$	−4.30293e14	−0.116286	−0.0581429	−	0.998308i	$-0.518518\pi$
$677$	−4.30293e14	−0.116286	−0.0581429	+	0.998308i	$0.518518\pi$
$678$	−6.81708e15	−1.82741
$679$	0	0
$680$	−2.56832e15	−0.677408
$681$	1.01051e14	0.0264382
$682$	2.53420e15	0.657698
$683$	−3.81244e15	−0.981498	−0.490749	−	0.871301i	$-0.663277\pi$
$683$	−3.81244e15	−0.981498	−0.490749	+	0.871301i	$0.663277\pi$
$684$	4.64999e15	1.18753
$685$	−8.32429e14	−0.210887
$686$	0	0
$687$	−4.40432e15	−1.09804
$688$	−3.66823e15	−0.907236
$689$	−2.90580e15	−0.712952
$690$	1.55854e15	0.379356
$691$	−4.03729e15	−0.974901	−0.487450	−	0.873151i	$-0.662073\pi$
$691$	−4.03729e15	−0.974901	−0.487450	+	0.873151i	$0.662073\pi$
$692$	2.94972e15	0.706638
$693$	0	0
$694$	7.63374e15	1.79995
$695$	6.04805e15	1.41481
$696$	4.05113e14	0.0940212
$697$	2.77232e15	0.638356
$698$	1.11376e16	2.54441
$699$	−4.55967e12	−0.00103350
$700$	0	0
$701$	−4.71267e15	−1.05152	−0.525761	−	0.850632i	$-0.676219\pi$
$701$	−4.71267e15	−1.05152	−0.525761	+	0.850632i	$0.676219\pi$
$702$	−8.57558e14	−0.189849
$703$	1.29700e16	2.84896
$704$	−5.94185e15	−1.29501
$705$	2.03010e15	0.439013
$706$	−1.12512e16	−2.41419
$707$	0	0
$708$	−5.44616e14	−0.115056
$709$	8.66706e14	0.181684	0.0908422	−	0.995865i	$-0.471044\pi$
$709$	8.66706e14	0.181684	0.0908422	+	0.995865i	$0.471044\pi$
$710$	−6.21215e15	−1.29217
$711$	2.19694e14	0.0453457
$712$	3.94991e15	0.808997
$713$	7.79972e14	0.158521
$714$	0	0
$715$	−2.62442e15	−0.525231
$716$	1.58361e16	3.14505
$717$	−4.28293e15	−0.844085
$718$	−9.69924e15	−1.89694
$719$	−2.62666e13	−0.00509795	−0.00254897	−	0.999997i	$-0.500811\pi$
$719$	−2.62666e13	−0.00509795	−0.00254897	+	0.999997i	$0.500811\pi$
$720$	1.21423e15	0.233869
$721$	0	0
$722$	2.06080e16	3.90913
$723$	2.16298e14	0.0407186
$724$	−9.19929e15	−1.71867
$725$	−2.14931e14	−0.0398511
$726$	2.30335e15	0.423846
$727$	5.68018e15	1.03734	0.518672	−	0.854973i	$-0.326427\pi$
$727$	5.68018e15	1.03734	0.518672	+	0.854973i	$0.326427\pi$
$728$	0	0
$729$	2.05891e14	0.0370370
$730$	−5.85190e15	−1.04477
$731$	2.95465e15	0.523552
$732$	−4.85512e15	−0.853864
$733$	1.62312e15	0.283320	0.141660	−	0.989915i	$-0.454756\pi$
$733$	1.62312e15	0.283320	0.141660	+	0.989915i	$0.454756\pi$
$734$	1.24885e16	2.16363
$735$	0	0
$736$	−2.89227e14	−0.0493641
$737$	3.37568e15	0.571861
$738$	−4.13987e15	−0.696108
$739$	3.64794e15	0.608840	0.304420	−	0.952538i	$-0.401537\pi$
$739$	3.64794e15	0.608840	0.304420	+	0.952538i	$0.401537\pi$
$740$	1.44071e16	2.38673
$741$	−3.63283e15	−0.597372
$742$	0	0
$743$	6.76045e15	1.09531	0.547655	−	0.836704i	$-0.315521\pi$
$743$	6.76045e15	1.09531	0.547655	+	0.836704i	$0.315521\pi$
$744$	1.91935e15	0.308676
$745$	−7.43520e15	−1.18695
$746$	−2.70861e15	−0.429224
$747$	−5.17768e14	−0.0814465
$748$	−7.94007e15	−1.23984
$749$	0	0
$750$	−7.00464e15	−1.07783
$751$	2.64833e13	0.00404532	0.00202266	−	0.999998i	$-0.499356\pi$
$751$	2.64833e13	0.00404532	0.00202266	+	0.999998i	$0.499356\pi$
$752$	5.95734e15	0.903347
$753$	5.88741e15	0.886242
$754$	−6.42546e14	−0.0960200
$755$	−3.75149e15	−0.556539
$756$	0	0
$757$	7.37364e15	1.07809	0.539045	−	0.842277i	$-0.318785\pi$
$757$	7.37364e15	1.07809	0.539045	+	0.842277i	$0.318785\pi$
$758$	−1.14270e16	−1.65864
$759$	2.37333e15	0.342001
$760$	1.62470e16	2.32434
$761$	−6.20983e15	−0.881991	−0.440996	−	0.897509i	$-0.645375\pi$
$761$	−6.20983e15	−0.881991	−0.440996	+	0.897509i	$0.645375\pi$
$762$	4.74368e15	0.668902
$763$	0	0
$764$	1.36703e16	1.90005
$765$	−9.78027e14	−0.134963
$766$	−5.01866e15	−0.687591
$767$	4.25484e14	0.0578774
$768$	−8.40308e15	−1.13488
$769$	8.86195e15	1.18832	0.594162	−	0.804346i	$-0.297484\pi$
$769$	8.86195e15	1.18832	0.594162	+	0.804346i	$0.297484\pi$
$770$	0	0
$771$	−1.89659e15	−0.250712
$772$	−1.98943e16	−2.61116
$773$	2.95047e15	0.384507	0.192254	−	0.981345i	$-0.438420\pi$
$773$	2.95047e15	0.384507	0.192254	+	0.981345i	$0.438420\pi$
$774$	−4.41213e15	−0.570918
$775$	−1.01830e15	−0.130833
$776$	6.06184e15	0.773330
$777$	0	0
$778$	−3.11142e15	−0.391355
$779$	−1.75375e16	−2.19034
$780$	−4.03536e15	−0.500451
$781$	−9.45980e15	−1.16493
$782$	−3.68384e15	−0.450468
$783$	1.54269e14	0.0187322
$784$	0	0
$785$	−1.14449e16	−1.37034
$786$	1.85544e15	0.220609
$787$	−1.35545e16	−1.60038	−0.800190	−	0.599746i	$-0.795268\pi$
$787$	−1.35545e16	−1.60038	−0.800190	+	0.599746i	$0.795268\pi$
$788$	2.56603e16	3.00862
$789$	4.03272e15	0.469543
$790$	1.55839e15	0.180188
$791$	0	0
$792$	5.84027e15	0.665954
$793$	3.79308e15	0.429526
$794$	−8.31105e15	−0.934638
$795$	4.94876e15	0.552685
$796$	1.52784e16	1.69456
$797$	1.59922e16	1.76152	0.880762	−	0.473558i	$-0.157031\pi$
$797$	1.59922e16	1.76152	0.880762	+	0.473558i	$0.157031\pi$
$798$	0	0
$799$	−4.79846e15	−0.521308
$800$	3.77604e14	0.0407419
$801$	1.50414e15	0.161180
$802$	2.66327e15	0.283437
$803$	−8.91121e15	−0.941892
$804$	5.19051e15	0.544881
$805$	0	0
$806$	−3.04426e15	−0.315238
$807$	−6.93123e15	−0.712863
$808$	−1.44377e15	−0.147481
$809$	9.45859e15	0.959643	0.479821	−	0.877366i	$-0.340701\pi$
$809$	9.45859e15	0.959643	0.479821	+	0.877366i	$0.340701\pi$
$810$	1.46047e15	0.147172
$811$	1.07996e16	1.08092	0.540461	−	0.841369i	$-0.318250\pi$
$811$	1.07996e16	1.08092	0.540461	+	0.841369i	$0.318250\pi$
$812$	0	0
$813$	−5.68134e15	−0.560987
$814$	3.30717e16	3.24356
$815$	−8.78341e14	−0.0855651
$816$	−2.87003e15	−0.277709
$817$	−1.86909e16	−1.79642
$818$	−4.16012e15	−0.397158
$819$	0	0
$820$	−1.94807e16	−1.83497
$821$	−1.10411e16	−1.03306	−0.516529	−	0.856270i	$-0.672776\pi$
$821$	−1.10411e16	−1.03306	−0.516529	+	0.856270i	$0.672776\pi$
$822$	−2.93815e15	−0.273073
$823$	1.26104e16	1.16420	0.582101	−	0.813117i	$-0.302231\pi$
$823$	1.26104e16	1.16420	0.582101	+	0.813117i	$0.302231\pi$
$824$	−7.53224e15	−0.690756
$825$	−3.09852e15	−0.282266
$826$	0	0
$827$	−7.86172e14	−0.0706704	−0.0353352	−	0.999376i	$-0.511250\pi$
$827$	−7.86172e14	−0.0706704	−0.0353352	+	0.999376i	$0.511250\pi$
$828$	3.64927e15	0.325866
$829$	5.92589e15	0.525659	0.262829	−	0.964842i	$-0.415344\pi$
$829$	5.92589e15	0.525659	0.262829	+	0.964842i	$0.415344\pi$
$830$	−3.67275e15	−0.323640
$831$	−7.37848e15	−0.645894
$832$	7.13777e15	0.620704
$833$	0	0
$834$	2.13472e16	1.83201
$835$	4.73066e13	0.00403317
$836$	5.02283e16	4.25416
$837$	7.30896e14	0.0614986
$838$	7.90044e15	0.660403
$839$	−2.10209e16	−1.74566	−0.872831	−	0.488022i	$-0.837718\pi$
$839$	−2.10209e16	−1.74566	−0.872831	+	0.488022i	$0.837718\pi$
$840$	0	0
$841$	−1.20849e16	−0.990526
$842$	−1.23184e16	−1.00309
$843$	3.88189e15	0.314045
$844$	7.24437e14	0.0582260
$845$	−6.47126e15	−0.516746
$846$	7.16547e15	0.568470
$847$	0	0
$848$	1.45222e16	1.13725
$849$	−6.97520e15	−0.542705
$850$	4.80948e15	0.371787
$851$	1.01788e16	0.781775
$852$	−1.45456e16	−1.10997
$853$	1.98378e16	1.50409	0.752046	−	0.659110i	$-0.229067\pi$
$853$	1.98378e16	1.50409	0.752046	+	0.659110i	$0.229067\pi$
$854$	0	0
$855$	6.18693e15	0.463086
$856$	3.49818e16	2.60157
$857$	−7.96639e15	−0.588663	−0.294332	−	0.955703i	$-0.595097\pi$
$857$	−7.96639e15	−0.588663	−0.294332	+	0.955703i	$0.595097\pi$
$858$	−9.26318e15	−0.680111
$859$	1.59749e16	1.16540	0.582701	−	0.812687i	$-0.301996\pi$
$859$	1.59749e16	1.16540	0.582701	+	0.812687i	$0.301996\pi$
$860$	−2.07619e16	−1.50496
$861$	0	0
$862$	4.00274e16	2.86462
$863$	−4.02926e15	−0.286527	−0.143264	−	0.989685i	$-0.545760\pi$
$863$	−4.02926e15	−0.286527	−0.143264	+	0.989685i	$0.545760\pi$
$864$	−2.71029e14	−0.0191509
$865$	3.92467e15	0.275559
$866$	5.84413e15	0.407729
$867$	−6.01635e15	−0.417089
$868$	0	0
$869$	2.37310e15	0.162445
$870$	1.09430e15	0.0744353
$871$	−4.05511e15	−0.274096
$872$	−1.07694e16	−0.723352
$873$	2.30837e15	0.154073
$874$	2.33037e16	1.54565
$875$	0	0
$876$	−1.37020e16	−0.897455
$877$	9.76958e15	0.635884	0.317942	−	0.948110i	$-0.397008\pi$
$877$	9.76958e15	0.635884	0.317942	+	0.948110i	$0.397008\pi$
$878$	2.87301e16	1.85831
$879$	−1.17066e16	−0.752476
$880$	1.31159e16	0.837807
$881$	−1.62583e16	−1.03207	−0.516033	−	0.856569i	$-0.672592\pi$
$881$	−1.62583e16	−1.03207	−0.516033	+	0.856569i	$0.672592\pi$
$882$	0	0
$883$	1.66061e16	1.04108	0.520540	−	0.853837i	$-0.325731\pi$
$883$	1.66061e16	1.04108	0.520540	+	0.853837i	$0.325731\pi$
$884$	9.53818e15	0.594262
$885$	−7.24626e14	−0.0448669
$886$	−8.67733e15	−0.533950
$887$	1.91314e16	1.16995	0.584975	−	0.811051i	$-0.301104\pi$
$887$	1.91314e16	1.16995	0.584975	+	0.811051i	$0.301104\pi$
$888$	2.50478e16	1.52229
$889$	0	0
$890$	1.06695e16	0.640472
$891$	2.22400e15	0.132680
$892$	−8.98286e15	−0.532608
$893$	3.03547e16	1.78872
$894$	−2.62433e16	−1.53696
$895$	2.10703e16	1.22644
$896$	0	0
$897$	−2.85101e15	−0.163923
$898$	−6.88985e15	−0.393722
$899$	5.47641e14	0.0311041
$900$	−4.76434e15	−0.268949
$901$	−1.16972e16	−0.656287
$902$	−4.47180e16	−2.49372
$903$	0	0
$904$	−5.57710e16	−3.07243
$905$	−1.22399e16	−0.670209
$906$	−1.32413e16	−0.720651
$907$	−1.07252e16	−0.580182	−0.290091	−	0.956999i	$-0.593686\pi$
$907$	−1.07252e16	−0.580182	−0.290091	+	0.956999i	$0.593686\pi$
$908$	1.67836e15	0.0902430
$909$	−5.49792e14	−0.0293831
$910$	0	0
$911$	−2.82249e16	−1.49032	−0.745162	−	0.666883i	$-0.767628\pi$
$911$	−2.82249e16	−1.49032	−0.745162	+	0.666883i	$0.767628\pi$
$912$	1.81556e16	0.952881
$913$	−5.59284e15	−0.291771
$914$	−7.34833e14	−0.0381052
$915$	−6.45985e15	−0.332971
$916$	−7.31516e16	−3.74799
$917$	0	0
$918$	−3.45205e15	−0.174760
$919$	1.83551e16	0.923679	0.461839	−	0.886964i	$-0.347190\pi$
$919$	1.83551e16	0.923679	0.461839	+	0.886964i	$0.347190\pi$
$920$	1.27505e16	0.637814
$921$	−6.25361e15	−0.310959
$922$	5.43764e16	2.68776
$923$	1.13638e16	0.558359
$924$	0	0
$925$	−1.32890e16	−0.645227
$926$	−1.46594e16	−0.707549
$927$	−2.86831e15	−0.137622
$928$	−2.03075e14	−0.00968596
$929$	1.10125e16	0.522155	0.261078	−	0.965318i	$-0.415922\pi$
$929$	1.10125e16	0.522155	0.261078	+	0.965318i	$0.415922\pi$
$930$	5.18456e15	0.244374
$931$	0	0
$932$	−7.57317e13	−0.00352769
$933$	−8.40884e15	−0.389392
$934$	−2.49605e16	−1.14907
$935$	−1.05645e16	−0.483486
$936$	−7.01574e15	−0.319195
$937$	−8.36357e15	−0.378289	−0.189145	−	0.981949i	$-0.560571\pi$
$937$	−8.36357e15	−0.378289	−0.189145	+	0.981949i	$0.560571\pi$
$938$	0	0
$939$	−3.06340e15	−0.136944
$940$	3.37181e16	1.49851
$941$	−2.22942e16	−0.985028	−0.492514	−	0.870305i	$-0.663922\pi$
$941$	−2.22942e16	−0.985028	−0.492514	+	0.870305i	$0.663922\pi$
$942$	−4.03961e16	−1.77443
$943$	−1.37633e16	−0.601045
$944$	−2.12642e15	−0.0923214
$945$	0	0
$946$	−4.76590e16	−2.04524
$947$	−3.78038e16	−1.61291	−0.806457	−	0.591293i	$-0.798618\pi$
$947$	−3.78038e16	−1.61291	−0.806457	+	0.591293i	$0.798618\pi$
$948$	3.64891e15	0.154781
$949$	1.07048e16	0.451454
$950$	−3.04244e16	−1.27568
$951$	−1.98833e16	−0.828888
$952$	0	0
$953$	4.79568e15	0.197624	0.0988119	−	0.995106i	$-0.468496\pi$
$953$	4.79568e15	0.197624	0.0988119	+	0.995106i	$0.468496\pi$
$954$	1.74672e16	0.715661
$955$	1.81887e16	0.740939
$956$	−7.11355e16	−2.88116
$957$	1.66638e15	0.0671057
$958$	1.17298e16	0.469657
$959$	0	0
$960$	−1.21561e16	−0.481173
$961$	−2.28139e16	−0.897884
$962$	−3.97280e16	−1.55466
$963$	1.33212e16	0.518321
$964$	3.59251e15	0.138987
$965$	−2.64698e16	−1.01824
$966$	0	0
$967$	3.37420e16	1.28329	0.641645	−	0.767002i	$-0.278252\pi$
$967$	3.37420e16	1.28329	0.641645	+	0.767002i	$0.278252\pi$
$968$	1.88439e16	0.712616
$969$	−1.46238e16	−0.549893
$970$	1.63743e16	0.612234
$971$	−3.58587e16	−1.33318	−0.666590	−	0.745425i	$-0.732247\pi$
$971$	−3.58587e16	−1.33318	−0.666590	+	0.745425i	$0.732247\pi$
$972$	3.41966e15	0.126421
$973$	0	0
$974$	1.37706e16	0.503360
$975$	3.72217e15	0.135291
$976$	−1.89565e16	−0.685147
$977$	−1.20023e16	−0.431366	−0.215683	−	0.976463i	$-0.569198\pi$
$977$	−1.20023e16	−0.431366	−0.215683	+	0.976463i	$0.569198\pi$
$978$	−3.10020e15	−0.110797
$979$	1.62474e16	0.577405
$980$	0	0
$981$	−4.10102e15	−0.144116
$982$	−6.71547e16	−2.34673
$983$	4.42687e15	0.153834	0.0769170	−	0.997038i	$-0.475492\pi$
$983$	4.42687e15	0.153834	0.0769170	+	0.997038i	$0.475492\pi$
$984$	−3.38685e16	−1.17037
$985$	3.41417e16	1.17324
$986$	−2.58653e15	−0.0883884
$987$	0	0
$988$	−6.03378e16	−2.03904
$989$	−1.46684e16	−0.492951
$990$	1.57758e16	0.527226
$991$	−3.79167e16	−1.26016	−0.630080	−	0.776530i	$-0.716978\pi$
$991$	−3.79167e16	−1.26016	−0.630080	+	0.776530i	$0.716978\pi$
$992$	−9.62130e14	−0.0317994
$993$	−8.26479e15	−0.271651
$994$	0	0
$995$	2.03283e16	0.660807
$996$	−8.59964e15	−0.278006
$997$	−5.76003e13	−0.00185183	−0.000925915	−	1.00000i	$-0.500295\pi$
$997$	−5.76003e13	−0.00185183	−0.000925915		1.00000i	$0.500295\pi$
$998$	4.68943e16	1.49935
$999$	9.53830e15	0.303292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.12.a.c.1.1		1
7.6	odd	2		3.12.a.a.1.1	✓	1
21.20	even	2		9.12.a.a.1.1		1
28.27	even	2		48.12.a.f.1.1		1
35.13	even	4		75.12.b.a.49.1		2
35.27	even	4		75.12.b.a.49.2		2
35.34	odd	2		75.12.a.a.1.1		1
56.13	odd	2		192.12.a.q.1.1		1
56.27	even	2		192.12.a.g.1.1		1
63.13	odd	6		81.12.c.a.55.1		2
63.20	even	6		81.12.c.e.28.1		2
63.34	odd	6		81.12.c.a.28.1		2
63.41	even	6		81.12.c.e.55.1		2
84.83	odd	2		144.12.a.l.1.1		1
105.62	odd	4		225.12.b.a.199.1		2
105.83	odd	4		225.12.b.a.199.2		2
105.104	even	2		225.12.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.12.a.a.1.1	✓	1	7.6	odd	2
9.12.a.a.1.1		1	21.20	even	2
48.12.a.f.1.1		1	28.27	even	2
75.12.a.a.1.1		1	35.34	odd	2
75.12.b.a.49.1		2	35.13	even	4
75.12.b.a.49.2		2	35.27	even	4
81.12.c.a.28.1		2	63.34	odd	6
81.12.c.a.55.1		2	63.13	odd	6
81.12.c.e.28.1		2	63.20	even	6
81.12.c.e.55.1		2	63.41	even	6
144.12.a.l.1.1		1	84.83	odd	2
147.12.a.c.1.1		1	1.1	even	1	trivial
192.12.a.g.1.1		1	56.27	even	2
192.12.a.q.1.1		1	56.13	odd	2
225.12.a.f.1.1		1	105.104	even	2
225.12.b.a.199.1		2	105.62	odd	4
225.12.b.a.199.2		2	105.83	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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