LMFDB - Embedded newform 169.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,12,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, 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("169.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	169.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:	$129.849997515$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+24.0000 q^{2} +252.000 q^{3} -1472.00 q^{4} -4830.00 q^{5} +6048.00 q^{6} +16744.0 q^{7} -84480.0 q^{8} -113643. q^{9} +O(q^{10})$

\(q+24.0000 q^{2} +252.000 q^{3} -1472.00 q^{4} -4830.00 q^{5} +6048.00 q^{6} +16744.0 q^{7} -84480.0 q^{8} -113643. q^{9} -115920. q^{10} -534612. q^{11} -370944. q^{12} +401856. q^{14} -1.21716e6 q^{15} +987136. q^{16} -6.90593e6 q^{17} -2.72743e6 q^{18} -1.06614e7 q^{19} +7.10976e6 q^{20} +4.21949e6 q^{21} -1.28307e7 q^{22} +1.86433e7 q^{23} -2.12890e7 q^{24} -2.54992e7 q^{25} -7.32791e7 q^{27} -2.46472e7 q^{28} +1.28407e8 q^{29} -2.92118e7 q^{30} +5.28432e7 q^{31} +1.96706e8 q^{32} -1.34722e8 q^{33} -1.65742e8 q^{34} -8.08735e7 q^{35} +1.67282e8 q^{36} +1.82213e8 q^{37} -2.55874e8 q^{38} +4.08038e8 q^{40} -3.08120e8 q^{41} +1.01268e8 q^{42} -1.71257e7 q^{43} +7.86949e8 q^{44} +5.48896e8 q^{45} +4.47439e8 q^{46} -2.68735e9 q^{47} +2.48758e8 q^{48} -1.69697e9 q^{49} -6.11981e8 q^{50} -1.74030e9 q^{51} -1.59606e9 q^{53} -1.75870e9 q^{54} +2.58218e9 q^{55} -1.41453e9 q^{56} -2.68668e9 q^{57} +3.08176e9 q^{58} +5.18920e9 q^{59} +1.79166e9 q^{60} +6.95648e9 q^{61} +1.26824e9 q^{62} -1.90284e9 q^{63} +2.69930e9 q^{64} -3.23333e9 q^{66} +1.54818e10 q^{67} +1.01655e10 q^{68} +4.69810e9 q^{69} -1.94096e9 q^{70} -9.79149e9 q^{71} +9.60056e9 q^{72} -1.46379e9 q^{73} +4.37312e9 q^{74} -6.42580e9 q^{75} +1.56936e10 q^{76} -8.95154e9 q^{77} +3.81168e10 q^{79} -4.76787e9 q^{80} +1.66519e9 q^{81} -7.39489e9 q^{82} +2.93351e10 q^{83} -6.21109e9 q^{84} +3.33557e10 q^{85} -4.11017e8 q^{86} +3.23585e10 q^{87} +4.51640e10 q^{88} +2.49929e10 q^{89} +1.31735e10 q^{90} -2.74429e10 q^{92} +1.33165e10 q^{93} -6.44964e10 q^{94} +5.14947e10 q^{95} +4.95700e10 q^{96} -7.50136e10 q^{97} -4.07272e10 q^{98} +6.07549e10 q^{99} +O(q^{100})\)

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 $

$2$	24.0000	0.530330	0.265165	−	0.964203i	$-0.414574\pi$
$2$	24.0000	0.530330	0.265165	+	0.964203i	$0.414574\pi$
$3$	252.000	0.598734	0.299367	−	0.954138i	$-0.403225\pi$
$3$	252.000	0.598734	0.299367	+	0.954138i	$0.403225\pi$
$4$	−1472.00	−0.718750
$5$	−4830.00	−0.691213	−0.345607	−	0.938379i	$-0.612327\pi$
$5$	−4830.00	−0.691213	−0.345607	+	0.938379i	$0.612327\pi$
$6$	6048.00	0.317526
$7$	16744.0	0.376548	0.188274	−	0.982117i	$-0.439711\pi$
$7$	16744.0	0.376548	0.188274	+	0.982117i	$0.439711\pi$
$8$	−84480.0	−0.911505
$9$	−113643.	−0.641518
$10$	−115920.	−0.366571
$11$	−534612.	−1.00087	−0.500436	−	0.865773i	$-0.666827\pi$
$11$	−534612.	−1.00087	−0.500436	+	0.865773i	$0.666827\pi$
$12$	−370944.	−0.430340
$13$	0	0
$13$	0	0
$14$	401856.	0.199695
$15$	−1.21716e6	−0.413853
$16$	987136.	0.235352
$17$	−6.90593e6	−1.17965	−0.589825	−	0.807531i	$-0.700803\pi$
$17$	−6.90593e6	−1.17965	−0.589825	+	0.807531i	$0.700803\pi$
$18$	−2.72743e6	−0.340216
$19$	−1.06614e7	−0.987803	−0.493901	−	0.869518i	$-0.664430\pi$
$19$	−1.06614e7	−0.987803	−0.493901	+	0.869518i	$0.664430\pi$
$20$	7.10976e6	0.496810
$21$	4.21949e6	0.225452
$22$	−1.28307e7	−0.530793
$23$	1.86433e7	0.603975	0.301988	−	0.953312i	$-0.402350\pi$
$23$	1.86433e7	0.603975	0.301988	+	0.953312i	$0.402350\pi$
$24$	−2.12890e7	−0.545749
$25$	−2.54992e7	−0.522224
$26$	0	0
$27$	−7.32791e7	−0.982832
$28$	−2.46472e7	−0.270644
$29$	1.28407e8	1.16251	0.581257	−	0.813720i	$-0.302561\pi$
$29$	1.28407e8	1.16251	0.581257	+	0.813720i	$0.302561\pi$
$30$	−2.92118e7	−0.219479
$31$	5.28432e7	0.331512	0.165756	−	0.986167i	$-0.446994\pi$
$31$	5.28432e7	0.331512	0.165756	+	0.986167i	$0.446994\pi$
$32$	1.96706e8	1.03632
$33$	−1.34722e8	−0.599256
$34$	−1.65742e8	−0.625604
$35$	−8.08735e7	−0.260275
$36$	1.67282e8	0.461091
$37$	1.82213e8	0.431987	0.215993	−	0.976395i	$-0.430701\pi$
$37$	1.82213e8	0.431987	0.215993	+	0.976395i	$0.430701\pi$
$38$	−2.55874e8	−0.523862
$39$	0	0
$40$	4.08038e8	0.630044
$41$	−3.08120e8	−0.415345	−0.207673	−	0.978198i	$-0.566589\pi$
$41$	−3.08120e8	−0.415345	−0.207673	+	0.978198i	$0.566589\pi$
$42$	1.01268e8	0.119564
$43$	−1.71257e7	−0.0177653	−0.00888264	−	0.999961i	$-0.502827\pi$
$43$	−1.71257e7	−0.0177653	−0.00888264	+	0.999961i	$0.502827\pi$
$44$	7.86949e8	0.719377
$45$	5.48896e8	0.443426
$46$	4.47439e8	0.320306
$47$	−2.68735e9	−1.70917	−0.854586	−	0.519310i	$-0.826189\pi$
$47$	−2.68735e9	−1.70917	−0.854586	+	0.519310i	$0.826189\pi$
$48$	2.48758e8	0.140913
$49$	−1.69697e9	−0.858212
$50$	−6.11981e8	−0.276951
$51$	−1.74030e9	−0.706296
$52$	0	0
$53$	−1.59606e9	−0.524241	−0.262120	−	0.965035i	$-0.584422\pi$
$53$	−1.59606e9	−0.524241	−0.262120	+	0.965035i	$0.584422\pi$
$54$	−1.75870e9	−0.521225
$55$	2.58218e9	0.691817
$56$	−1.41453e9	−0.343225
$57$	−2.68668e9	−0.591431
$58$	3.08176e9	0.616517
$59$	5.18920e9	0.944963	0.472481	−	0.881341i	$-0.343358\pi$
$59$	5.18920e9	0.944963	0.472481	+	0.881341i	$0.343358\pi$
$60$	1.79166e9	0.297457
$61$	6.95648e9	1.05457	0.527285	−	0.849689i	$-0.323210\pi$
$61$	6.95648e9	1.05457	0.527285	+	0.849689i	$0.323210\pi$
$62$	1.26824e9	0.175811
$63$	−1.90284e9	−0.241562
$64$	2.69930e9	0.314240
$65$	0	0
$66$	−3.23333e9	−0.317804
$67$	1.54818e10	1.40091	0.700456	−	0.713696i	$-0.252980\pi$
$67$	1.54818e10	1.40091	0.700456	+	0.713696i	$0.252980\pi$
$68$	1.01655e10	0.847874
$69$	4.69810e9	0.361620
$70$	−1.94096e9	−0.138032
$71$	−9.79149e9	−0.644062	−0.322031	−	0.946729i	$-0.604366\pi$
$71$	−9.79149e9	−0.644062	−0.322031	+	0.946729i	$0.604366\pi$
$72$	9.60056e9	0.584747
$73$	−1.46379e9	−0.0826425	−0.0413212	−	0.999146i	$-0.513157\pi$
$73$	−1.46379e9	−0.0826425	−0.0413212	+	0.999146i	$0.513157\pi$
$74$	4.37312e9	0.229096
$75$	−6.42580e9	−0.312673
$76$	1.56936e10	0.709983
$77$	−8.95154e9	−0.376876
$78$	0	0
$79$	3.81168e10	1.39370	0.696848	−	0.717219i	$-0.254585\pi$
$79$	3.81168e10	1.39370	0.696848	+	0.717219i	$0.254585\pi$
$80$	−4.76787e9	−0.162678
$81$	1.66519e9	0.0530635
$82$	−7.39489e9	−0.220270
$83$	2.93351e10	0.817444	0.408722	−	0.912659i	$-0.365975\pi$
$83$	2.93351e10	0.817444	0.408722	+	0.912659i	$0.365975\pi$
$84$	−6.21109e9	−0.162043
$85$	3.33557e10	0.815390
$86$	−4.11017e8	−0.00942146
$87$	3.23585e10	0.696037
$88$	4.51640e10	0.912300
$89$	2.49929e10	0.474430	0.237215	−	0.971457i	$-0.423765\pi$
$89$	2.49929e10	0.474430	0.237215	+	0.971457i	$0.423765\pi$
$90$	1.31735e10	0.235162
$91$	0	0
$92$	−2.74429e10	−0.434107
$93$	1.33165e10	0.198488
$94$	−6.44964e10	−0.906425
$95$	5.14947e10	0.682782
$96$	4.95700e10	0.620479
$97$	−7.50136e10	−0.886942	−0.443471	−	0.896289i	$-0.646253\pi$
$97$	−7.50136e10	−0.886942	−0.443471	+	0.896289i	$0.646253\pi$
$98$	−4.07272e10	−0.455136
$99$	6.07549e10	0.642078
$100$	3.75349e10	0.375349
$101$	8.17430e10	0.773896	0.386948	−	0.922101i	$-0.373529\pi$
$101$	8.17430e10	0.773896	0.386948	+	0.922101i	$0.373529\pi$
$102$	−4.17671e10	−0.374570
$103$	−2.25755e11	−1.91881	−0.959407	−	0.282025i	$-0.908994\pi$
$103$	−2.25755e11	−1.91881	−0.959407	+	0.282025i	$0.908994\pi$
$104$	0	0
$105$	−2.03801e10	−0.155835
$106$	−3.83053e10	−0.278021
$107$	9.02413e10	0.622006	0.311003	−	0.950409i	$-0.399335\pi$
$107$	9.02413e10	0.622006	0.311003	+	0.950409i	$0.399335\pi$
$108$	1.07867e11	0.706411
$109$	−7.34827e10	−0.457445	−0.228723	−	0.973492i	$-0.573455\pi$
$109$	−7.34827e10	−0.457445	−0.228723	+	0.973492i	$0.573455\pi$
$110$	6.19722e10	0.366891
$111$	4.59178e10	0.258645
$112$	1.65286e10	0.0886211
$113$	−8.51469e10	−0.434748	−0.217374	−	0.976088i	$-0.569749\pi$
$113$	−8.51469e10	−0.434748	−0.217374	+	0.976088i	$0.569749\pi$
$114$	−6.44803e10	−0.313654
$115$	−9.00470e10	−0.417476
$116$	−1.89015e11	−0.835557
$117$	0	0
$118$	1.24541e11	0.501142
$119$	−1.15633e11	−0.444195
$120$	1.02826e11	0.377229
$121$	4.98320e8	0.00174658
$122$	1.66955e11	0.559270
$123$	−7.76464e10	−0.248681
$124$	−7.77851e10	−0.238274
$125$	3.59001e11	1.05218
$126$	−4.56681e10	−0.128108
$127$	−2.62717e11	−0.705615	−0.352808	−	0.935696i	$-0.614773\pi$
$127$	−2.62717e11	−0.705615	−0.352808	+	0.935696i	$0.614773\pi$
$128$	−3.38071e11	−0.869668
$129$	−4.31568e9	−0.0106367
$130$	0	0
$131$	6.31529e11	1.43021	0.715107	−	0.699015i	$-0.246378\pi$
$131$	6.31529e11	1.43021	0.715107	+	0.699015i	$0.246378\pi$
$132$	1.98311e11	0.430715
$133$	−1.78515e11	−0.371955
$134$	3.71564e11	0.742946
$135$	3.53938e11	0.679347
$136$	5.83413e11	1.07526
$137$	2.97199e11	0.526119	0.263059	−	0.964780i	$-0.415268\pi$
$137$	2.97199e11	0.526119	0.263059	+	0.964780i	$0.415268\pi$
$138$	1.12755e11	0.191778
$139$	5.96794e11	0.975535	0.487767	−	0.872974i	$-0.337811\pi$
$139$	5.96794e11	0.975535	0.487767	+	0.872974i	$0.337811\pi$
$140$	1.19046e11	0.187073
$141$	−6.77212e11	−1.02334
$142$	−2.34996e11	−0.341565
$143$	0	0
$144$	−1.12181e11	−0.150982
$145$	−6.20204e11	−0.803546
$146$	−3.51310e10	−0.0438278
$147$	−4.27635e11	−0.513840
$148$	−2.68218e11	−0.310491
$149$	1.11543e12	1.24428	0.622142	−	0.782905i	$-0.286263\pi$
$149$	1.11543e12	1.24428	0.622142	+	0.782905i	$0.286263\pi$
$150$	−1.54219e11	−0.165820
$151$	8.24447e11	0.854653	0.427326	−	0.904097i	$-0.359456\pi$
$151$	8.24447e11	0.854653	0.427326	+	0.904097i	$0.359456\pi$
$152$	9.00677e11	0.900387
$153$	7.84811e11	0.756767
$154$	−2.14837e11	−0.199869
$155$	−2.55233e11	−0.229146
$156$	0	0
$157$	1.31512e12	1.10031	0.550156	−	0.835062i	$-0.314568\pi$
$157$	1.31512e12	1.10031	0.550156	+	0.835062i	$0.314568\pi$
$158$	9.14804e11	0.739119
$159$	−4.02206e11	−0.313881
$160$	−9.50091e11	−0.716317
$161$	3.12163e11	0.227425
$162$	3.99645e10	0.0281412
$163$	3.57833e11	0.243584	0.121792	−	0.992556i	$-0.461136\pi$
$163$	3.57833e11	0.243584	0.121792	+	0.992556i	$0.461136\pi$
$164$	4.53553e11	0.298529
$165$	6.50708e11	0.414214
$166$	7.04042e11	0.433515
$167$	−2.75483e12	−1.64117	−0.820587	−	0.571521i	$-0.806354\pi$
$167$	−2.75483e12	−1.64117	−0.820587	+	0.571521i	$0.806354\pi$
$168$	−3.56462e11	−0.205500
$169$	0	0
$170$	8.00536e11	0.432426
$171$	1.21160e12	0.633693
$172$	2.52090e10	0.0127688
$173$	−9.50387e11	−0.466280	−0.233140	−	0.972443i	$-0.574900\pi$
$173$	−9.50387e11	−0.466280	−0.233140	+	0.972443i	$0.574900\pi$
$174$	7.76603e11	0.369129
$175$	−4.26959e11	−0.196642
$176$	−5.27735e11	−0.235557
$177$	1.30768e12	0.565781
$178$	5.99830e11	0.251604
$179$	1.68138e12	0.683873	0.341936	−	0.939723i	$-0.388917\pi$
$179$	1.68138e12	0.683873	0.341936	+	0.939723i	$0.388917\pi$
$180$	−8.07974e11	−0.318712
$181$	−9.96774e11	−0.381386	−0.190693	−	0.981650i	$-0.561073\pi$
$181$	−9.96774e11	−0.381386	−0.190693	+	0.981650i	$0.561073\pi$
$182$	0	0
$183$	1.75303e12	0.631406
$184$	−1.57498e12	−0.550526
$185$	−8.80090e11	−0.298595
$186$	3.19595e11	0.105264
$187$	3.69200e12	1.18068
$188$	3.95578e12	1.22847
$189$	−1.22698e12	−0.370083
$190$	1.23587e12	0.362100
$191$	2.76240e12	0.786328	0.393164	−	0.919468i	$-0.371381\pi$
$191$	2.76240e12	0.786328	0.393164	+	0.919468i	$0.371381\pi$
$192$	6.80223e11	0.188146
$193$	−5.44239e12	−1.46293	−0.731466	−	0.681878i	$-0.761164\pi$
$193$	−5.44239e12	−1.46293	−0.731466	+	0.681878i	$0.761164\pi$
$194$	−1.80033e12	−0.470372
$195$	0	0
$196$	2.49793e12	0.616840
$197$	2.87609e12	0.690619	0.345309	−	0.938489i	$-0.387774\pi$
$197$	2.87609e12	0.690619	0.345309	+	0.938489i	$0.387774\pi$
$198$	1.45812e12	0.340513
$199$	7.28391e11	0.165452	0.0827262	−	0.996572i	$-0.473637\pi$
$199$	7.28391e11	0.165452	0.0827262	+	0.996572i	$0.473637\pi$
$200$	2.15417e12	0.476010
$201$	3.90142e12	0.838773
$202$	1.96183e12	0.410421
$203$	2.15004e12	0.437742
$204$	2.56171e12	0.507651
$205$	1.48822e12	0.287092
$206$	−5.41812e12	−1.01760
$207$	−2.11868e12	−0.387461
$208$	0	0
$209$	5.69972e12	0.988665
$210$	−4.89123e11	−0.0826441
$211$	−6.79317e12	−1.11820	−0.559099	−	0.829101i	$-0.688853\pi$
$211$	−6.79317e12	−1.11820	−0.559099	+	0.829101i	$0.688853\pi$
$212$	2.34939e12	0.376798
$213$	−2.46745e12	−0.385622
$214$	2.16579e12	0.329868
$215$	8.27172e10	0.0122796
$216$	6.19062e12	0.895856
$217$	8.84806e11	0.124830
$218$	−1.76358e12	−0.242597
$219$	−3.68875e11	−0.0494808
$220$	−3.80096e12	−0.497243
$221$	0	0
$222$	1.10203e12	0.137167
$223$	−7.33486e12	−0.890667	−0.445333	−	0.895365i	$-0.646915\pi$
$223$	−7.33486e12	−0.890667	−0.445333	+	0.895365i	$0.646915\pi$
$224$	3.29365e12	0.390223
$225$	2.89781e12	0.335016
$226$	−2.04352e12	−0.230560
$227$	1.35984e12	0.149743	0.0748713	−	0.997193i	$-0.476145\pi$
$227$	1.35984e12	0.149743	0.0748713	+	0.997193i	$0.476145\pi$
$228$	3.95479e12	0.425091
$229$	1.18244e13	1.24075	0.620375	−	0.784305i	$-0.286980\pi$
$229$	1.18244e13	1.24075	0.620375	+	0.784305i	$0.286980\pi$
$230$	−2.16113e12	−0.221400
$231$	−2.25579e12	−0.225649
$232$	−1.08478e13	−1.05964
$233$	−1.75634e13	−1.67552	−0.837761	−	0.546038i	$-0.816135\pi$
$233$	−1.75634e13	−1.67552	−0.837761	+	0.546038i	$0.816135\pi$
$234$	0	0
$235$	1.29799e13	1.18140
$236$	−7.63851e12	−0.679192
$237$	9.60545e12	0.834452
$238$	−2.77519e12	−0.235570
$239$	7.13958e12	0.592221	0.296111	−	0.955154i	$-0.404310\pi$
$239$	7.13958e12	0.592221	0.296111	+	0.955154i	$0.404310\pi$
$240$	−1.20150e12	−0.0974009
$241$	2.31307e11	0.0183271	0.00916357	−	0.999958i	$-0.497083\pi$
$241$	2.31307e11	0.0183271	0.00916357	+	0.999958i	$0.497083\pi$
$242$	1.19597e10	0.000926264 0
$243$	1.34008e13	1.01460
$244$	−1.02399e13	−0.757972
$245$	8.19634e12	0.593207
$246$	−1.86351e12	−0.131883
$247$	0	0
$248$	−4.46419e12	−0.302175
$249$	7.39245e12	0.489431
$250$	8.61603e12	0.558004
$251$	1.29831e13	0.822567	0.411284	−	0.911507i	$-0.365081\pi$
$251$	1.29831e13	0.822567	0.411284	+	0.911507i	$0.365081\pi$
$252$	2.80098e12	0.173623
$253$	−9.96692e12	−0.604502
$254$	−6.30521e12	−0.374209
$255$	8.40563e12	0.488201
$256$	−1.36419e13	−0.775451
$257$	2.39612e13	1.33314	0.666571	−	0.745442i	$-0.267761\pi$
$257$	2.39612e13	1.33314	0.666571	+	0.745442i	$0.267761\pi$
$258$	−1.03576e11	−0.00564095
$259$	3.05098e12	0.162664
$260$	0	0
$261$	−1.45925e13	−0.745774
$262$	1.51567e13	0.758485
$263$	−2.42737e13	−1.18954	−0.594771	−	0.803895i	$-0.702757\pi$
$263$	−2.42737e13	−1.18954	−0.594771	+	0.803895i	$0.702757\pi$
$264$	1.13813e13	0.546225
$265$	7.70895e12	0.362362
$266$	−4.28436e12	−0.197259
$267$	6.29822e12	0.284057
$268$	−2.27892e13	−1.00691
$269$	2.58377e13	1.11845	0.559225	−	0.829016i	$-0.311099\pi$
$269$	2.58377e13	1.11845	0.559225	+	0.829016i	$0.311099\pi$
$270$	8.49451e12	0.360278
$271$	3.76793e12	0.156593	0.0782964	−	0.996930i	$-0.475052\pi$
$271$	3.76793e12	0.156593	0.0782964	+	0.996930i	$0.475052\pi$
$272$	−6.81710e12	−0.277633
$273$	0	0
$274$	7.13277e12	0.279017
$275$	1.36322e13	0.522680
$276$	−6.91561e12	−0.259915
$277$	−1.64189e13	−0.604931	−0.302466	−	0.953160i	$-0.597810\pi$
$277$	−1.64189e13	−0.604931	−0.302466	+	0.953160i	$0.597810\pi$
$278$	1.43230e13	0.517355
$279$	−6.00526e12	−0.212671
$280$	6.83219e12	0.237242
$281$	−2.10357e13	−0.716263	−0.358132	−	0.933671i	$-0.616586\pi$
$281$	−2.10357e13	−0.716263	−0.358132	+	0.933671i	$0.616586\pi$
$282$	−1.62531e13	−0.542707
$283$	1.67132e13	0.547310	0.273655	−	0.961828i	$-0.411767\pi$
$283$	1.67132e13	0.547310	0.273655	+	0.961828i	$0.411767\pi$
$284$	1.44131e13	0.462920
$285$	1.29767e13	0.408805
$286$	0	0
$287$	−5.15917e12	−0.156397
$288$	−2.23543e13	−0.664817
$289$	1.34200e13	0.391575
$290$	−1.48849e13	−0.426144
$291$	−1.89034e13	−0.531042
$292$	2.15470e12	0.0593993
$293$	2.39269e13	0.647312	0.323656	−	0.946175i	$-0.395088\pi$
$293$	2.39269e13	0.647312	0.323656	+	0.946175i	$0.395088\pi$
$294$	−1.02632e13	−0.272505
$295$	−2.50639e13	−0.653171
$296$	−1.53934e13	−0.393758
$297$	3.91759e13	0.983690
$298$	2.67704e13	0.659881
$299$	0	0
$300$	9.45878e12	0.224734
$301$	−2.86753e11	−0.00668947
$302$	1.97867e13	0.453248
$303$	2.05992e13	0.463358
$304$	−1.05243e13	−0.232481
$305$	−3.35998e13	−0.728933
$306$	1.88355e13	0.401336
$307$	−1.53111e13	−0.320439	−0.160219	−	0.987081i	$-0.551220\pi$
$307$	−1.53111e13	−0.320439	−0.160219	+	0.987081i	$0.551220\pi$
$308$	1.31767e13	0.270880
$309$	−5.68903e13	−1.14886
$310$	−6.12558e12	−0.121523
$311$	4.98752e13	0.972080	0.486040	−	0.873936i	$-0.338441\pi$
$311$	4.98752e13	0.972080	0.486040	+	0.873936i	$0.338441\pi$
$312$	0	0
$313$	−9.94808e13	−1.87174	−0.935870	−	0.352345i	$-0.885384\pi$
$313$	−9.94808e13	−1.87174	−0.935870	+	0.352345i	$0.885384\pi$
$314$	3.15628e13	0.583529
$315$	9.19071e12	0.166971
$316$	−5.61080e13	−1.00172
$317$	−8.33692e13	−1.46278	−0.731392	−	0.681958i	$-0.761129\pi$
$317$	−8.33692e13	−1.46278	−0.731392	+	0.681958i	$0.761129\pi$
$318$	−9.65294e12	−0.166460
$319$	−6.86477e13	−1.16353
$320$	−1.30376e13	−0.217207
$321$	2.27408e13	0.372416
$322$	7.49191e12	0.120611
$323$	7.36271e13	1.16526
$324$	−2.45116e12	−0.0381394
$325$	0	0
$326$	8.58799e12	0.129180
$327$	−1.85176e13	−0.273888
$328$	2.60300e13	0.378589
$329$	−4.49970e13	−0.643585
$330$	1.56170e13	0.219670
$331$	6.35840e13	0.879618	0.439809	−	0.898091i	$-0.355046\pi$
$331$	6.35840e13	0.879618	0.439809	+	0.898091i	$0.355046\pi$
$332$	−4.31813e13	−0.587538
$333$	−2.07073e13	−0.277127
$334$	−6.61160e13	−0.870364
$335$	−7.47772e13	−0.968329
$336$	4.16521e12	0.0530604
$337$	1.21001e14	1.51644	0.758221	−	0.651997i	$-0.226069\pi$
$337$	1.21001e14	1.51644	0.758221	+	0.651997i	$0.226069\pi$
$338$	0	0
$339$	−2.14570e13	−0.260298
$340$	−4.90995e13	−0.586062
$341$	−2.82506e13	−0.331802
$342$	2.90783e13	0.336067
$343$	−6.15223e13	−0.699705
$344$	1.44678e12	0.0161931
$345$	−2.26918e13	−0.249957
$346$	−2.28093e13	−0.247283
$347$	−1.55662e14	−1.66100	−0.830499	−	0.557020i	$-0.811945\pi$
$347$	−1.55662e14	−1.66100	−0.830499	+	0.557020i	$0.811945\pi$
$348$	−4.76317e13	−0.500276
$349$	2.56430e13	0.265112	0.132556	−	0.991176i	$-0.457682\pi$
$349$	2.56430e13	0.265112	0.132556	+	0.991176i	$0.457682\pi$
$350$	−1.02470e13	−0.104285
$351$	0	0
$352$	−1.05162e14	−1.03722
$353$	−2.49098e13	−0.241885	−0.120943	−	0.992659i	$-0.538592\pi$
$353$	−2.49098e13	−0.241885	−0.120943	+	0.992659i	$0.538592\pi$
$354$	3.13843e13	0.300051
$355$	4.72929e13	0.445184
$356$	−3.67896e13	−0.340996
$357$	−2.91395e13	−0.265954
$358$	4.03532e13	0.362678
$359$	−1.57584e14	−1.39474	−0.697370	−	0.716712i	$-0.745646\pi$
$359$	−1.57584e14	−1.39474	−0.697370	+	0.716712i	$0.745646\pi$
$360$	−4.63707e13	−0.404185
$361$	−2.82438e12	−0.0242457
$362$	−2.39226e13	−0.202260
$363$	1.25577e11	0.00104574
$364$	0	0
$365$	7.07011e12	0.0571236
$366$	4.20728e13	0.334854
$367$	−1.77901e14	−1.39481	−0.697406	−	0.716676i	$-0.745662\pi$
$367$	−1.77901e14	−1.39481	−0.697406	+	0.716676i	$0.745662\pi$
$368$	1.84034e13	0.142146
$369$	3.50157e13	0.266452
$370$	−2.11222e13	−0.158354
$371$	−2.67244e13	−0.197402
$372$	−1.96019e13	−0.142663
$373$	−5.51617e13	−0.395585	−0.197792	−	0.980244i	$-0.563377\pi$
$373$	−5.51617e13	−0.395585	−0.197792	+	0.980244i	$0.563377\pi$
$374$	8.86079e13	0.626150
$375$	9.04683e13	0.629976
$376$	2.27027e14	1.55792
$377$	0	0
$378$	−2.94476e13	−0.196266
$379$	−1.46463e14	−0.962083	−0.481042	−	0.876698i	$-0.659741\pi$
$379$	−1.46463e14	−0.962083	−0.481042	+	0.876698i	$0.659741\pi$
$380$	−7.58001e13	−0.490750
$381$	−6.62047e13	−0.422476
$382$	6.62977e13	0.417013
$383$	−2.31450e14	−1.43504	−0.717519	−	0.696539i	$-0.754722\pi$
$383$	−2.31450e14	−1.43504	−0.717519	+	0.696539i	$0.754722\pi$
$384$	−8.51940e13	−0.520700
$385$	4.32360e13	0.260502
$386$	−1.30617e14	−0.775837
$387$	1.94622e12	0.0113967
$388$	1.10420e14	0.637490
$389$	−1.49872e14	−0.853093	−0.426547	−	0.904466i	$-0.640270\pi$
$389$	−1.49872e14	−0.853093	−0.426547	+	0.904466i	$0.640270\pi$
$390$	0	0
$391$	−1.28749e14	−0.712480
$392$	1.43360e14	0.782264
$393$	1.59145e14	0.856317
$394$	6.90262e13	0.366256
$395$	−1.84104e14	−0.963341
$396$	−8.94312e13	−0.461494
$397$	−2.08111e14	−1.05912	−0.529562	−	0.848271i	$-0.677644\pi$
$397$	−2.08111e14	−1.05912	−0.529562	+	0.848271i	$0.677644\pi$
$398$	1.74814e13	0.0877443
$399$	−4.49857e13	−0.222702
$400$	−2.51712e13	−0.122906
$401$	1.33408e14	0.642521	0.321261	−	0.946991i	$-0.395893\pi$
$401$	1.33408e14	0.642521	0.321261	+	0.946991i	$0.395893\pi$
$402$	9.36341e13	0.444827
$403$	0	0
$404$	−1.20326e14	−0.556238
$405$	−8.04286e12	−0.0366782
$406$	5.16010e13	0.232148
$407$	−9.74134e13	−0.432364
$408$	1.47020e14	0.643793
$409$	2.06168e14	0.890722	0.445361	−	0.895351i	$-0.353075\pi$
$409$	2.06168e14	0.890722	0.445361	+	0.895351i	$0.353075\pi$
$410$	3.57173e13	0.152254
$411$	7.48941e13	0.315005
$412$	3.32312e14	1.37915
$413$	8.68880e13	0.355824
$414$	−5.08483e13	−0.205482
$415$	−1.41689e14	−0.565028
$416$	0	0
$417$	1.50392e14	0.584085
$418$	1.36793e14	0.524319
$419$	7.34035e13	0.277677	0.138838	−	0.990315i	$-0.455663\pi$
$419$	7.34035e13	0.277677	0.138838	+	0.990315i	$0.455663\pi$
$420$	2.99995e13	0.112007
$421$	−1.71112e14	−0.630563	−0.315282	−	0.948998i	$-0.602099\pi$
$421$	−1.71112e14	−0.630563	−0.315282	+	0.948998i	$0.602099\pi$
$422$	−1.63036e14	−0.593014
$423$	3.05398e14	1.09646
$424$	1.34835e14	0.477848
$425$	1.76096e14	0.616042
$426$	−5.92189e13	−0.204507
$427$	1.16479e14	0.397096
$428$	−1.32835e14	−0.447067
$429$	0	0
$430$	1.98521e12	0.00651224
$431$	7.17758e13	0.232463	0.116231	−	0.993222i	$-0.462919\pi$
$431$	7.17758e13	0.232463	0.116231	+	0.993222i	$0.462919\pi$
$432$	−7.23364e13	−0.231311
$433$	9.98812e13	0.315356	0.157678	−	0.987491i	$-0.449599\pi$
$433$	9.98812e13	0.315356	0.157678	+	0.987491i	$0.449599\pi$
$434$	2.12353e13	0.0662012
$435$	−1.56291e14	−0.481110
$436$	1.08166e14	0.328789
$437$	−1.98764e14	−0.596608
$438$	−8.85301e12	−0.0262412
$439$	−2.90312e13	−0.0849788	−0.0424894	−	0.999097i	$-0.513529\pi$
$439$	−2.90312e13	−0.0849788	−0.0424894	+	0.999097i	$0.513529\pi$
$440$	−2.18142e14	−0.630594
$441$	1.92848e14	0.550558
$442$	0	0
$443$	3.28370e14	0.914414	0.457207	−	0.889360i	$-0.348850\pi$
$443$	3.28370e14	0.914414	0.457207	+	0.889360i	$0.348850\pi$
$444$	−6.75909e13	−0.185901
$445$	−1.20716e14	−0.327932
$446$	−1.76037e14	−0.472347
$447$	2.81089e14	0.744994
$448$	4.51970e13	0.118326
$449$	6.12368e14	1.58364	0.791822	−	0.610752i	$-0.209133\pi$
$449$	6.12368e14	1.58364	0.791822	+	0.610752i	$0.209133\pi$
$450$	6.95474e13	0.177669
$451$	1.64725e14	0.415708
$452$	1.25336e14	0.312475
$453$	2.07761e14	0.511709
$454$	3.26361e13	0.0794130
$455$	0	0
$456$	2.26971e14	0.539092
$457$	−3.03483e14	−0.712189	−0.356095	−	0.934450i	$-0.615892\pi$
$457$	−3.03483e14	−0.712189	−0.356095	+	0.934450i	$0.615892\pi$
$458$	2.83786e14	0.658007
$459$	5.06060e14	1.15940
$460$	1.32549e14	0.300061
$461$	7.29308e14	1.63138	0.815691	−	0.578487i	$-0.196357\pi$
$461$	7.29308e14	1.63138	0.815691	+	0.578487i	$0.196357\pi$
$462$	−5.41389e13	−0.119668
$463$	−1.22188e14	−0.266891	−0.133445	−	0.991056i	$-0.542604\pi$
$463$	−1.22188e14	−0.266891	−0.133445	+	0.991056i	$0.542604\pi$
$464$	1.26755e14	0.273600
$465$	−6.43186e13	−0.137197
$466$	−4.21520e14	−0.888579
$467$	−6.17381e14	−1.28621	−0.643103	−	0.765780i	$-0.722353\pi$
$467$	−6.17381e14	−1.28621	−0.643103	+	0.765780i	$0.722353\pi$
$468$	0	0
$469$	2.59228e14	0.527510
$470$	3.11517e14	0.626533
$471$	3.31409e14	0.658794
$472$	−4.38384e14	−0.861338
$473$	9.15561e12	0.0177808
$474$	2.30531e14	0.442535
$475$	2.71858e14	0.515854
$476$	1.70212e14	0.319265
$477$	1.81381e14	0.336310
$478$	1.71350e14	0.314073
$479$	−1.05084e15	−1.90410	−0.952052	−	0.305938i	$-0.901030\pi$
$479$	−1.05084e15	−1.90410	−0.952052	+	0.305938i	$0.901030\pi$
$480$	−2.39423e14	−0.428883
$481$	0	0
$482$	5.55137e12	0.00971944
$483$	7.86651e13	0.136167
$484$	−7.33527e11	−0.00125536
$485$	3.62316e14	0.613066
$486$	3.21619e14	0.538074
$487$	2.19910e14	0.363777	0.181889	−	0.983319i	$-0.441779\pi$
$487$	2.19910e14	0.363777	0.181889	+	0.983319i	$0.441779\pi$
$488$	−5.87683e14	−0.961246
$489$	9.01739e13	0.145842
$490$	1.96712e14	0.314596
$491$	−4.83863e14	−0.765199	−0.382599	−	0.923914i	$-0.624971\pi$
$491$	−4.83863e14	−0.765199	−0.382599	+	0.923914i	$0.624971\pi$
$492$	1.14295e14	0.178740
$493$	−8.86768e14	−1.37136
$494$	0	0
$495$	−2.93446e14	−0.443813
$496$	5.21634e13	0.0780219
$497$	−1.63949e14	−0.242520
$498$	1.77419e14	0.259560
$499$	1.08878e14	0.157538	0.0787691	−	0.996893i	$-0.474901\pi$
$499$	1.08878e14	0.157538	0.0787691	+	0.996893i	$0.474901\pi$
$500$	−5.28450e14	−0.756256
$501$	−6.94218e14	−0.982626
$502$	3.11593e14	0.436232
$503$	5.06588e14	0.701506	0.350753	−	0.936468i	$-0.385926\pi$
$503$	5.06588e14	0.701506	0.350753	+	0.936468i	$0.385926\pi$
$504$	1.60752e14	0.220185
$505$	−3.94818e14	−0.534927
$506$	−2.39206e14	−0.320586
$507$	0	0
$508$	3.86720e14	0.507161
$509$	−8.57534e13	−0.111251	−0.0556254	−	0.998452i	$-0.517715\pi$
$509$	−8.57534e13	−0.111251	−0.0556254	+	0.998452i	$0.517715\pi$
$510$	2.01735e14	0.258908
$511$	−2.45097e13	−0.0311188
$512$	3.64965e14	0.458423
$513$	7.81259e14	0.970844
$514$	5.75069e14	0.707005
$515$	1.09040e15	1.32631
$516$	6.35268e12	0.00764511
$517$	1.43669e15	1.71066
$518$	7.32235e13	0.0862654
$519$	−2.39498e14	−0.279178
$520$	0	0
$521$	9.27575e14	1.05862	0.529312	−	0.848428i	$-0.322450\pi$
$521$	9.27575e14	1.05862	0.529312	+	0.848428i	$0.322450\pi$
$522$	−3.50220e14	−0.395506
$523$	−2.18187e13	−0.0243820	−0.0121910	−	0.999926i	$-0.503881\pi$
$523$	−2.18187e13	−0.0243820	−0.0121910	+	0.999926i	$0.503881\pi$
$524$	−9.29610e14	−1.02797
$525$	−1.07594e14	−0.117736
$526$	−5.82569e14	−0.630850
$527$	−3.64931e14	−0.391069
$528$	−1.32989e14	−0.141036
$529$	−6.05238e14	−0.635214
$530$	1.85015e14	0.192172
$531$	−5.89717e14	−0.606211
$532$	2.62774e14	0.267343
$533$	0	0
$534$	1.51157e14	0.150644
$535$	−4.35865e14	−0.429939
$536$	−1.30790e15	−1.27694
$537$	4.23709e14	0.409458
$538$	6.20105e14	0.593147
$539$	9.07218e14	0.858961
$540$	−5.20997e14	−0.488280
$541$	1.69527e15	1.57273	0.786363	−	0.617765i	$-0.211962\pi$
$541$	1.69527e15	1.57273	0.786363	+	0.617765i	$0.211962\pi$
$542$	9.04304e13	0.0830459
$543$	−2.51187e14	−0.228349
$544$	−1.35844e15	−1.22249
$545$	3.54921e14	0.316192
$546$	0	0
$547$	7.52145e14	0.656706	0.328353	−	0.944555i	$-0.393506\pi$
$547$	7.52145e14	0.656706	0.328353	+	0.944555i	$0.393506\pi$
$548$	−4.37477e14	−0.378148
$549$	−7.90555e14	−0.676526
$550$	3.27173e14	0.277193
$551$	−1.36900e15	−1.14834
$552$	−3.96896e14	−0.329619
$553$	6.38228e14	0.524793
$554$	−3.94054e14	−0.320813
$555$	−2.21783e14	−0.178779
$556$	−8.78480e14	−0.701166
$557$	−1.87489e14	−0.148174	−0.0740870	−	0.997252i	$-0.523604\pi$
$557$	−1.87489e14	−0.148174	−0.0740870	+	0.997252i	$0.523604\pi$
$558$	−1.44126e14	−0.112786
$559$	0	0
$560$	−7.98332e13	−0.0612561
$561$	9.30383e14	0.706913
$562$	−5.04857e14	−0.379856
$563$	2.44971e14	0.182524	0.0912618	−	0.995827i	$-0.470910\pi$
$563$	2.44971e14	0.182524	0.0912618	+	0.995827i	$0.470910\pi$
$564$	9.96856e14	0.735525
$565$	4.11259e14	0.300503
$566$	4.01116e14	0.290255
$567$	2.78819e13	0.0199809
$568$	8.27185e14	0.587066
$569$	1.35243e15	0.950596	0.475298	−	0.879825i	$-0.342340\pi$
$569$	1.35243e15	0.950596	0.475298	+	0.879825i	$0.342340\pi$
$570$	3.11440e14	0.216801
$571$	1.43223e15	0.987447	0.493723	−	0.869619i	$-0.335636\pi$
$571$	1.43223e15	0.987447	0.493723	+	0.869619i	$0.335636\pi$
$572$	0	0
$573$	6.96126e14	0.470801
$574$	−1.23820e14	−0.0829422
$575$	−4.75389e14	−0.315410
$576$	−3.06756e14	−0.201590
$577$	8.77659e14	0.571293	0.285647	−	0.958335i	$-0.407792\pi$
$577$	8.77659e14	0.571293	0.285647	+	0.958335i	$0.407792\pi$
$578$	3.22081e14	0.207664
$579$	−1.37148e15	−0.875907
$580$	9.12940e14	0.577548
$581$	4.91187e14	0.307807
$582$	−4.53682e14	−0.281628
$583$	8.53271e14	0.524698
$584$	1.23661e14	0.0753290
$585$	0	0
$586$	5.74245e14	0.343289
$587$	2.43425e15	1.44164	0.720818	−	0.693124i	$-0.243766\pi$
$587$	2.43425e15	1.44164	0.720818	+	0.693124i	$0.243766\pi$
$588$	6.29479e14	0.369323
$589$	−5.63383e14	−0.327469
$590$	−6.01532e14	−0.346396
$591$	7.24775e14	0.413497
$592$	1.79869e14	0.101669
$593$	3.03318e14	0.169863	0.0849313	−	0.996387i	$-0.472933\pi$
$593$	3.03318e14	0.169863	0.0849313	+	0.996387i	$0.472933\pi$
$594$	9.40221e14	0.521680
$595$	5.58507e14	0.307033
$596$	−1.64192e15	−0.894329
$597$	1.83555e14	0.0990619
$598$	0	0
$599$	−1.70198e15	−0.901795	−0.450898	−	0.892576i	$-0.648896\pi$
$599$	−1.70198e15	−0.901795	−0.450898	+	0.892576i	$0.648896\pi$
$600$	5.42852e14	0.285003
$601$	2.33922e15	1.21692	0.608458	−	0.793586i	$-0.291788\pi$
$601$	2.33922e15	1.21692	0.608458	+	0.793586i	$0.291788\pi$
$602$	−6.88207e12	−0.00354763
$603$	−1.75940e15	−0.898710
$604$	−1.21359e15	−0.614282
$605$	−2.40689e12	−0.00120726
$606$	4.94381e14	0.245733
$607$	−2.49607e15	−1.22947	−0.614737	−	0.788732i	$-0.710738\pi$
$607$	−2.49607e15	−1.22947	−0.614737	+	0.788732i	$0.710738\pi$
$608$	−2.09717e15	−1.02368
$609$	5.41810e14	0.262091
$610$	−8.06395e14	−0.386575
$611$	0	0
$612$	−1.15524e15	−0.543926
$613$	−2.47301e15	−1.15397	−0.576983	−	0.816756i	$-0.695770\pi$
$613$	−2.47301e15	−1.15397	−0.576983	+	0.816756i	$0.695770\pi$
$614$	−3.67466e14	−0.169938
$615$	3.75032e14	0.171892
$616$	7.56226e14	0.343525
$617$	−2.43368e13	−0.0109571	−0.00547854	−	0.999985i	$-0.501744\pi$
$617$	−2.43368e13	−0.0109571	−0.00547854	+	0.999985i	$0.501744\pi$
$618$	−1.36537e15	−0.609274
$619$	−4.22545e15	−1.86885	−0.934425	−	0.356160i	$-0.884086\pi$
$619$	−4.22545e15	−1.86885	−0.934425	+	0.356160i	$0.884086\pi$
$620$	3.75702e14	0.164698
$621$	−1.36616e15	−0.593606
$622$	1.19700e15	0.515523
$623$	4.18481e14	0.178645
$624$	0	0
$625$	−4.88896e14	−0.205058
$626$	−2.38754e15	−0.992640
$627$	1.43633e15	0.591947
$628$	−1.93585e15	−0.790850
$629$	−1.25835e15	−0.509594
$630$	2.20577e14	0.0885497
$631$	4.26326e15	1.69660	0.848302	−	0.529513i	$-0.177625\pi$
$631$	4.26326e15	1.69660	0.848302	+	0.529513i	$0.177625\pi$
$632$	−3.22011e15	−1.27036
$633$	−1.71188e15	−0.669503
$634$	−2.00086e15	−0.775758
$635$	1.26892e15	0.487731
$636$	5.92047e14	0.225602
$637$	0	0
$638$	−1.64755e15	−0.617055
$639$	1.11273e15	0.413177
$640$	1.63288e15	0.601126
$641$	1.00830e15	0.368018	0.184009	−	0.982925i	$-0.441092\pi$
$641$	1.00830e15	0.368018	0.184009	+	0.982925i	$0.441092\pi$
$642$	5.45779e14	0.197503
$643$	−3.03982e14	−0.109066	−0.0545328	−	0.998512i	$-0.517367\pi$
$643$	−3.03982e14	−0.109066	−0.0545328	+	0.998512i	$0.517367\pi$
$644$	−4.59504e14	−0.163462
$645$	2.08447e13	0.00735221
$646$	1.76705e15	0.617974
$647$	3.43583e15	1.19140	0.595700	−	0.803207i	$-0.296875\pi$
$647$	3.43583e15	1.19140	0.595700	+	0.803207i	$0.296875\pi$
$648$	−1.40675e14	−0.0483676
$649$	−2.77421e15	−0.945788
$650$	0	0
$651$	2.22971e14	0.0747400
$652$	−5.26730e14	−0.175076
$653$	−1.18539e15	−0.390695	−0.195347	−	0.980734i	$-0.562583\pi$
$653$	−1.18539e15	−0.390695	−0.195347	+	0.980734i	$0.562583\pi$
$654$	−4.44423e14	−0.145251
$655$	−3.05028e15	−0.988583
$656$	−3.04157e14	−0.0977522
$657$	1.66350e14	0.0530167
$658$	−1.07993e15	−0.341312
$659$	−2.26510e15	−0.709934	−0.354967	−	0.934879i	$-0.615508\pi$
$659$	−2.26510e15	−0.709934	−0.354967	+	0.934879i	$0.615508\pi$
$660$	−9.57843e14	−0.297716
$661$	5.33012e15	1.64297	0.821484	−	0.570232i	$-0.193147\pi$
$661$	5.33012e15	1.64297	0.821484	+	0.570232i	$0.193147\pi$
$662$	1.52602e15	0.466488
$663$	0	0
$664$	−2.47823e15	−0.745104
$665$	8.62227e14	0.257100
$666$	−4.96974e14	−0.146969
$667$	2.39392e15	0.702130
$668$	4.05512e15	1.17959
$669$	−1.84839e15	−0.533272
$670$	−1.79465e15	−0.513534
$671$	−3.71902e15	−1.05549
$672$	8.30000e14	0.233640
$673$	4.74120e15	1.32375	0.661874	−	0.749615i	$-0.269761\pi$
$673$	4.74120e15	1.32375	0.661874	+	0.749615i	$0.269761\pi$
$674$	2.90403e15	0.804215
$675$	1.86856e15	0.513259
$676$	0	0
$677$	−1.41307e15	−0.381880	−0.190940	−	0.981602i	$-0.561154\pi$
$677$	−1.41307e15	−0.381880	−0.190940	+	0.981602i	$0.561154\pi$
$678$	−5.14968e14	−0.138044
$679$	−1.25603e15	−0.333976
$680$	−2.81789e15	−0.743232
$681$	3.42680e14	0.0896559
$682$	−6.78014e14	−0.175964
$683$	3.03116e15	0.780359	0.390180	−	0.920739i	$-0.372413\pi$
$683$	3.03116e15	0.780359	0.390180	+	0.920739i	$0.372413\pi$
$684$	−1.78347e15	−0.455467
$685$	−1.43547e15	−0.363660
$686$	−1.47654e15	−0.371075
$687$	2.97975e15	0.742879
$688$	−1.69054e13	−0.00418109
$689$	0	0
$690$	−5.44604e14	−0.132560
$691$	2.74731e15	0.663405	0.331703	−	0.943384i	$-0.392377\pi$
$691$	2.74731e15	0.663405	0.331703	+	0.943384i	$0.392377\pi$
$692$	1.39897e15	0.335139
$693$	1.01728e15	0.241773
$694$	−3.73588e15	−0.880878
$695$	−2.88251e15	−0.674303
$696$	−2.73364e15	−0.634441
$697$	2.12786e15	0.489962
$698$	6.15433e14	0.140597
$699$	−4.42597e15	−1.00319
$700$	6.28484e14	0.141337
$701$	5.72747e15	1.27795	0.638974	−	0.769228i	$-0.279359\pi$
$701$	5.72747e15	1.27795	0.638974	+	0.769228i	$0.279359\pi$
$702$	0	0
$703$	−1.94265e15	−0.426718
$704$	−1.44308e15	−0.314514
$705$	3.27093e15	0.707345
$706$	−5.97836e14	−0.128279
$707$	1.36870e15	0.291409
$708$	−1.92490e15	−0.406655
$709$	−6.98326e14	−0.146388	−0.0731938	−	0.997318i	$-0.523319\pi$
$709$	−6.98326e14	−0.146388	−0.0731938	+	0.997318i	$0.523319\pi$
$710$	1.13503e15	0.236095
$711$	−4.33171e15	−0.894081
$712$	−2.11140e15	−0.432445
$713$	9.85170e14	0.200225
$714$	−6.99348e14	−0.141044
$715$	0	0
$716$	−2.47500e15	−0.491534
$717$	1.79917e15	0.354583
$718$	−3.78202e15	−0.739672
$719$	9.70979e15	1.88452	0.942260	−	0.334882i	$-0.108696\pi$
$719$	9.70979e15	1.88452	0.942260	+	0.334882i	$0.108696\pi$
$720$	5.41835e14	0.104361
$721$	−3.78004e15	−0.722525
$722$	−6.77852e13	−0.0128582
$723$	5.82893e13	0.0109731
$724$	1.46725e15	0.274121
$725$	−3.27427e15	−0.607093
$726$	3.01384e12	0.000554586 0
$727$	2.46469e15	0.450114	0.225057	−	0.974346i	$-0.427743\pi$
$727$	2.46469e15	0.450114	0.225057	+	0.974346i	$0.427743\pi$
$728$	0	0
$729$	3.08202e15	0.554413
$730$	1.69683e14	0.0302944
$731$	1.18269e14	0.0209568
$732$	−2.58046e15	−0.453823
$733$	−7.91285e15	−1.38121	−0.690607	−	0.723230i	$-0.742657\pi$
$733$	−7.91285e15	−1.38121	−0.690607	+	0.723230i	$0.742657\pi$
$734$	−4.26963e15	−0.739711
$735$	2.06548e15	0.355173
$736$	3.66725e15	0.625911
$737$	−8.27677e15	−1.40213
$738$	8.40378e14	0.141307
$739$	8.40694e15	1.40312	0.701558	−	0.712613i	$-0.252488\pi$
$739$	8.40694e15	1.40312	0.701558	+	0.712613i	$0.252488\pi$
$740$	1.29549e15	0.214615
$741$	0	0
$742$	−6.41385e14	−0.104688
$743$	−1.36287e15	−0.220809	−0.110404	−	0.993887i	$-0.535215\pi$
$743$	−1.36287e15	−0.220809	−0.110404	+	0.993887i	$0.535215\pi$
$744$	−1.12498e15	−0.180922
$745$	−5.38754e15	−0.860065
$746$	−1.32388e15	−0.209790
$747$	−3.33373e15	−0.524405
$748$	−5.43462e15	−0.848614
$749$	1.51100e15	0.234215
$750$	2.17124e15	0.334095
$751$	6.81722e15	1.04133	0.520664	−	0.853762i	$-0.325684\pi$
$751$	6.81722e15	1.04133	0.520664	+	0.853762i	$0.325684\pi$
$752$	−2.65278e15	−0.402256
$753$	3.27173e15	0.492499
$754$	0	0
$755$	−3.98208e15	−0.590747
$756$	1.80612e15	0.265997
$757$	−6.67049e14	−0.0975282	−0.0487641	−	0.998810i	$-0.515528\pi$
$757$	−6.67049e14	−0.0975282	−0.0487641	+	0.998810i	$0.515528\pi$
$758$	−3.51511e15	−0.510222
$759$	−2.51166e15	−0.361936
$760$	−4.35027e15	−0.622360
$761$	7.74408e15	1.09990	0.549951	−	0.835197i	$-0.314646\pi$
$761$	7.74408e15	1.09990	0.549951	+	0.835197i	$0.314646\pi$
$762$	−1.58891e15	−0.224052
$763$	−1.23039e15	−0.172250
$764$	−4.06626e15	−0.565173
$765$	−3.79064e15	−0.523088
$766$	−5.55479e15	−0.761043
$767$	0	0
$768$	−3.43775e15	−0.464288
$769$	−2.52411e15	−0.338465	−0.169232	−	0.985576i	$-0.554129\pi$
$769$	−2.52411e15	−0.338465	−0.169232	+	0.985576i	$0.554129\pi$
$770$	1.03766e15	0.138152
$771$	6.03822e15	0.798197
$772$	8.01119e15	1.05148
$773$	1.11453e16	1.45246	0.726229	−	0.687453i	$-0.241271\pi$
$773$	1.11453e16	1.45246	0.726229	+	0.687453i	$0.241271\pi$
$774$	4.67092e13	0.00604404
$775$	−1.34746e15	−0.173124
$776$	6.33715e15	0.808452
$777$	7.68847e14	0.0973922
$778$	−3.59692e15	−0.452421
$779$	3.28500e15	0.410279
$780$	0	0
$781$	5.23465e15	0.644624
$782$	−3.08998e15	−0.377849
$783$	−9.40952e15	−1.14256
$784$	−1.67514e15	−0.201981
$785$	−6.35201e15	−0.760551
$786$	3.81949e15	0.454131
$787$	−1.32271e16	−1.56172	−0.780861	−	0.624705i	$-0.785219\pi$
$787$	−1.32271e16	−1.56172	−0.780861	+	0.624705i	$0.785219\pi$
$788$	−4.23361e15	−0.496382
$789$	−6.11698e15	−0.712219
$790$	−4.41850e15	−0.510889
$791$	−1.42570e15	−0.163703
$792$	−5.13257e15	−0.585257
$793$	0	0
$794$	−4.99466e15	−0.561685
$795$	1.94266e15	0.216958
$796$	−1.07219e15	−0.118919
$797$	2.30248e15	0.253615	0.126807	−	0.991927i	$-0.459527\pi$
$797$	2.30248e15	0.253615	0.126807	+	0.991927i	$0.459527\pi$
$798$	−1.07966e15	−0.118106
$799$	1.85587e16	2.01623
$800$	−5.01586e15	−0.541191
$801$	−2.84027e15	−0.304355
$802$	3.20179e15	0.340748
$803$	7.82560e14	0.0827146
$804$	−5.74289e15	−0.602868
$805$	−1.50775e15	−0.157199
$806$	0	0
$807$	6.51110e15	0.669653
$808$	−6.90565e15	−0.705410
$809$	5.60472e15	0.568639	0.284320	−	0.958730i	$-0.408232\pi$
$809$	5.60472e15	0.568639	0.284320	+	0.958730i	$0.408232\pi$
$810$	−1.93029e14	−0.0194515
$811$	5.08516e15	0.508968	0.254484	−	0.967077i	$-0.418094\pi$
$811$	5.08516e15	0.508968	0.254484	+	0.967077i	$0.418094\pi$
$812$	−3.16486e15	−0.314627
$813$	9.49519e14	0.0937574
$814$	−2.33792e15	−0.229296
$815$	−1.72833e15	−0.168368
$816$	−1.71791e15	−0.166228
$817$	1.82584e14	0.0175486
$818$	4.94802e15	0.472377
$819$	0	0
$820$	−2.19066e15	−0.206348
$821$	−2.79111e14	−0.0261150	−0.0130575	−	0.999915i	$-0.504156\pi$
$821$	−2.79111e14	−0.0261150	−0.0130575	+	0.999915i	$0.504156\pi$
$822$	1.79746e15	0.167057
$823$	−1.35265e16	−1.24878	−0.624391	−	0.781112i	$-0.714653\pi$
$823$	−1.35265e16	−1.24878	−0.624391	+	0.781112i	$0.714653\pi$
$824$	1.90718e16	1.74901
$825$	3.43531e15	0.312946
$826$	2.08531e15	0.188704
$827$	−2.72544e14	−0.0244994	−0.0122497	−	0.999925i	$-0.503899\pi$
$827$	−2.72544e14	−0.0244994	−0.0122497	+	0.999925i	$0.503899\pi$
$828$	3.11869e15	0.278488
$829$	1.80459e16	1.60077	0.800385	−	0.599486i	$-0.204628\pi$
$829$	1.80459e16	1.60077	0.800385	+	0.599486i	$0.204628\pi$
$830$	−3.40052e15	−0.299651
$831$	−4.13757e15	−0.362193
$832$	0	0
$833$	1.17191e16	1.01239
$834$	3.60941e15	0.309758
$835$	1.33058e16	1.13440
$836$	−8.38999e15	−0.710603
$837$	−3.87230e15	−0.325821
$838$	1.76168e15	0.147260
$839$	7.96183e15	0.661184	0.330592	−	0.943774i	$-0.392752\pi$
$839$	7.96183e15	0.661184	0.330592	+	0.943774i	$0.392752\pi$
$840$	1.72171e15	0.142045
$841$	4.28775e15	0.351440
$842$	−4.10669e15	−0.334407
$843$	−5.30100e15	−0.428851
$844$	9.99954e15	0.803705
$845$	0	0
$846$	7.32956e15	0.581488
$847$	8.34387e12	0.000657671 0
$848$	−1.57552e15	−0.123381
$849$	4.21172e15	0.327693
$850$	4.22630e15	0.326706
$851$	3.39705e15	0.260909
$852$	3.63209e15	0.277165
$853$	1.49826e16	1.13598	0.567988	−	0.823037i	$-0.307722\pi$
$853$	1.49826e16	1.13598	0.567988	+	0.823037i	$0.307722\pi$
$854$	2.79550e15	0.210592
$855$	−5.85201e15	−0.438017
$856$	−7.62358e15	−0.566961
$857$	−2.22561e16	−1.64458	−0.822290	−	0.569068i	$-0.807304\pi$
$857$	−2.22561e16	−1.64458	−0.822290	+	0.569068i	$0.807304\pi$
$858$	0	0
$859$	5.44237e15	0.397032	0.198516	−	0.980098i	$-0.436388\pi$
$859$	5.44237e15	0.397032	0.198516	+	0.980098i	$0.436388\pi$
$860$	−1.21760e14	−0.00882596
$861$	−1.30011e15	−0.0936403
$862$	1.72262e15	0.123282
$863$	−1.08110e16	−0.768787	−0.384393	−	0.923169i	$-0.625589\pi$
$863$	−1.08110e16	−0.768787	−0.384393	+	0.923169i	$0.625589\pi$
$864$	−1.44145e16	−1.01853
$865$	4.59037e15	0.322299
$866$	2.39715e15	0.167243
$867$	3.38185e15	0.234449
$868$	−1.30243e15	−0.0897217
$869$	−2.03777e16	−1.39491
$870$	−3.75099e15	−0.255147
$871$	0	0
$872$	6.20782e15	0.416964
$873$	8.52477e15	0.568989
$874$	−4.77033e15	−0.316399
$875$	6.01111e15	0.396197
$876$	5.42985e14	0.0355644
$877$	2.81024e16	1.82914	0.914568	−	0.404431i	$-0.132530\pi$
$877$	2.81024e16	1.82914	0.914568	+	0.404431i	$0.132530\pi$
$878$	−6.96749e14	−0.0450668
$879$	6.02957e15	0.387568
$880$	2.54896e15	0.162820
$881$	4.22209e15	0.268016	0.134008	−	0.990980i	$-0.457215\pi$
$881$	4.22209e15	0.268016	0.134008	+	0.990980i	$0.457215\pi$
$882$	4.62836e15	0.291978
$883$	5.16092e14	0.0323551	0.0161776	−	0.999869i	$-0.494850\pi$
$883$	5.16092e14	0.0323551	0.0161776	+	0.999869i	$0.494850\pi$
$884$	0	0
$885$	−6.31609e15	−0.391075
$886$	7.88088e15	0.484941
$887$	5.71906e15	0.349740	0.174870	−	0.984592i	$-0.444050\pi$
$887$	5.71906e15	0.349740	0.174870	+	0.984592i	$0.444050\pi$
$888$	−3.87913e15	−0.235756
$889$	−4.39894e15	−0.265698
$890$	−2.89718e15	−0.173912
$891$	−8.90230e14	−0.0531098
$892$	1.07969e16	0.640167
$893$	2.86510e16	1.68832
$894$	6.74614e15	0.395093
$895$	−8.12109e15	−0.472702
$896$	−5.66067e15	−0.327472
$897$	0	0
$898$	1.46968e16	0.839854
$899$	6.78541e15	0.385388
$900$	−4.26557e15	−0.240793
$901$	1.10223e16	0.618421
$902$	3.95340e15	0.220462
$903$	−7.22617e13	−0.00400521
$904$	7.19321e15	0.396275
$905$	4.81442e15	0.263619
$906$	4.98626e15	0.271375
$907$	−8.43778e13	−0.00456445	−0.00228222	−	0.999997i	$-0.500726\pi$
$907$	−8.43778e13	−0.00456445	−0.00228222	+	0.999997i	$0.500726\pi$
$908$	−2.00168e15	−0.107628
$909$	−9.28952e15	−0.496468
$910$	0	0
$911$	−1.10091e16	−0.581298	−0.290649	−	0.956830i	$-0.593871\pi$
$911$	−1.10091e16	−0.581298	−0.290649	+	0.956830i	$0.593871\pi$
$912$	−2.65212e15	−0.139194
$913$	−1.56829e16	−0.818158
$914$	−7.28359e15	−0.377695
$915$	−8.46715e15	−0.436437
$916$	−1.74055e16	−0.891789
$917$	1.05743e16	0.538544
$918$	1.21455e16	0.614864
$919$	−4.86351e15	−0.244746	−0.122373	−	0.992484i	$-0.539050\pi$
$919$	−4.86351e15	−0.244746	−0.122373	+	0.992484i	$0.539050\pi$
$920$	7.60717e15	0.380531
$921$	−3.85840e15	−0.191857
$922$	1.75034e16	0.865171
$923$	0	0
$924$	3.32052e15	0.162185
$925$	−4.64630e15	−0.225594
$926$	−2.93252e15	−0.141540
$927$	2.56555e16	1.23095
$928$	2.52584e16	1.20474
$929$	−3.57534e15	−0.169524	−0.0847620	−	0.996401i	$-0.527013\pi$
$929$	−3.57534e15	−0.169524	−0.0847620	+	0.996401i	$0.527013\pi$
$930$	−1.54365e15	−0.0727598
$931$	1.80921e16	0.847744
$932$	2.58533e16	1.20428
$933$	1.25685e16	0.582017
$934$	−1.48171e16	−0.682113
$935$	−1.78323e16	−0.816102
$936$	0	0
$937$	3.86373e16	1.74759	0.873795	−	0.486295i	$-0.161652\pi$
$937$	3.86373e16	1.74759	0.873795	+	0.486295i	$0.161652\pi$
$938$	6.22147e15	0.279754
$939$	−2.50692e16	−1.12067
$940$	−1.91064e16	−0.849133
$941$	3.48997e16	1.54198	0.770991	−	0.636846i	$-0.219761\pi$
$941$	3.48997e16	1.54198	0.770991	+	0.636846i	$0.219761\pi$
$942$	7.95383e15	0.349378
$943$	−5.74437e15	−0.250858
$944$	5.12245e15	0.222398
$945$	5.92634e15	0.255806
$946$	2.19735e14	0.00942969
$947$	2.85123e16	1.21649	0.608243	−	0.793751i	$-0.291875\pi$
$947$	2.85123e16	1.21649	0.608243	+	0.793751i	$0.291875\pi$
$948$	−1.41392e16	−0.599763
$949$	0	0
$950$	6.52459e15	0.273573
$951$	−2.10091e16	−0.875817
$952$	9.76867e15	0.404886
$953$	4.00334e16	1.64973	0.824863	−	0.565332i	$-0.191252\pi$
$953$	4.00334e16	1.64973	0.824863	+	0.565332i	$0.191252\pi$
$954$	4.35313e15	0.178355
$955$	−1.33424e16	−0.543520
$956$	−1.05095e16	−0.425659
$957$	−1.72992e16	−0.696644
$958$	−2.52201e16	−1.00980
$959$	4.97630e15	0.198109
$960$	−3.28548e15	−0.130049
$961$	−2.26161e16	−0.890100
$962$	0	0
$963$	−1.02553e16	−0.399028
$964$	−3.40484e14	−0.0131726
$965$	2.62867e16	1.01120
$966$	1.88796e15	0.0722136
$967$	−1.84953e16	−0.703422	−0.351711	−	0.936109i	$-0.614400\pi$
$967$	−1.84953e16	−0.703422	−0.351711	+	0.936109i	$0.614400\pi$
$968$	−4.20981e13	−0.00159202
$969$	1.85540e16	0.697682
$970$	8.69557e15	0.325127
$971$	−2.14877e16	−0.798884	−0.399442	−	0.916759i	$-0.630796\pi$
$971$	−2.14877e16	−0.798884	−0.399442	+	0.916759i	$0.630796\pi$
$972$	−1.97260e16	−0.729246
$973$	9.99271e15	0.367335
$974$	5.27784e15	0.192922
$975$	0	0
$976$	6.86699e15	0.248195
$977$	8.73880e15	0.314074	0.157037	−	0.987593i	$-0.449806\pi$
$977$	8.73880e15	0.314074	0.157037	+	0.987593i	$0.449806\pi$
$978$	2.16417e15	0.0773443
$979$	−1.33615e16	−0.474844
$980$	−1.20650e16	−0.426368
$981$	8.35079e15	0.293459
$982$	−1.16127e16	−0.405808
$983$	−1.18924e16	−0.413263	−0.206631	−	0.978419i	$-0.566250\pi$
$983$	−1.18924e16	−0.413263	−0.206631	+	0.978419i	$0.566250\pi$
$984$	6.55956e15	0.226674
$985$	−1.38915e16	−0.477365
$986$	−2.12824e16	−0.727274
$987$	−1.13392e16	−0.385336
$988$	0	0
$989$	−3.19279e14	−0.0107298
$990$	−7.04271e15	−0.235367
$991$	2.34409e16	0.779056	0.389528	−	0.921015i	$-0.372638\pi$
$991$	2.34409e16	0.779056	0.389528	+	0.921015i	$0.372638\pi$
$992$	1.03946e16	0.343552
$993$	1.60232e16	0.526657
$994$	−3.93477e15	−0.128616
$995$	−3.51813e15	−0.114363
$996$	−1.08817e16	−0.351779
$997$	−2.14004e16	−0.688016	−0.344008	−	0.938967i	$-0.611785\pi$
$997$	−2.14004e16	−0.688016	−0.344008	+	0.938967i	$0.611785\pi$
$998$	2.61307e15	0.0835473
$999$	−1.33524e16	−0.424571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.12.a.a.1.1		1
13.12	even	2		1.12.a.a.1.1	✓	1
39.38	odd	2		9.12.a.b.1.1		1
52.51	odd	2		16.12.a.a.1.1		1
65.12	odd	4		25.12.b.b.24.1		2
65.38	odd	4		25.12.b.b.24.2		2
65.64	even	2		25.12.a.b.1.1		1
91.12	odd	6		49.12.c.c.18.1		2
91.25	even	6		49.12.c.b.30.1		2
91.38	odd	6		49.12.c.c.30.1		2
91.51	even	6		49.12.c.b.18.1		2
91.90	odd	2		49.12.a.a.1.1		1
104.51	odd	2		64.12.a.f.1.1		1
104.77	even	2		64.12.a.b.1.1		1
117.25	even	6		81.12.c.d.28.1		2
117.38	odd	6		81.12.c.b.28.1		2
117.77	odd	6		81.12.c.b.55.1		2
117.103	even	6		81.12.c.d.55.1		2
143.142	odd	2		121.12.a.b.1.1		1
156.155	even	2		144.12.a.d.1.1		1
195.38	even	4		225.12.b.d.199.1		2
195.77	even	4		225.12.b.d.199.2		2
195.194	odd	2		225.12.a.b.1.1		1
208.51	odd	4		256.12.b.c.129.1		2
208.77	even	4		256.12.b.e.129.2		2
208.155	odd	4		256.12.b.c.129.2		2
208.181	even	4		256.12.b.e.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.12.a.a.1.1	✓	1	13.12	even	2
9.12.a.b.1.1		1	39.38	odd	2
16.12.a.a.1.1		1	52.51	odd	2
25.12.a.b.1.1		1	65.64	even	2
25.12.b.b.24.1		2	65.12	odd	4
25.12.b.b.24.2		2	65.38	odd	4
49.12.a.a.1.1		1	91.90	odd	2
49.12.c.b.18.1		2	91.51	even	6
49.12.c.b.30.1		2	91.25	even	6
49.12.c.c.18.1		2	91.12	odd	6
49.12.c.c.30.1		2	91.38	odd	6
64.12.a.b.1.1		1	104.77	even	2
64.12.a.f.1.1		1	104.51	odd	2
81.12.c.b.28.1		2	117.38	odd	6
81.12.c.b.55.1		2	117.77	odd	6
81.12.c.d.28.1		2	117.25	even	6
81.12.c.d.55.1		2	117.103	even	6
121.12.a.b.1.1		1	143.142	odd	2
144.12.a.d.1.1		1	156.155	even	2
169.12.a.a.1.1		1	1.1	even	1	trivial
225.12.a.b.1.1		1	195.194	odd	2
225.12.b.d.199.1		2	195.38	even	4
225.12.b.d.199.2		2	195.77	even	4
256.12.b.c.129.1		2	208.51	odd	4
256.12.b.c.129.2		2	208.155	odd	4
256.12.b.e.129.1		2	208.181	even	4
256.12.b.e.129.2		2	208.77	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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