LMFDB - Embedded newform 2.36.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,36,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 36, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	2.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:	$15.5190261267$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+131072. q^{2} +1.59934e8 q^{3} +1.71799e10 q^{4} -2.83874e12 q^{5} +2.09628e13 q^{6} -7.82282e14 q^{7} +2.25180e15 q^{8} -2.44527e16 q^{9} +O(q^{10})$

\(q+131072. q^{2} +1.59934e8 q^{3} +1.71799e10 q^{4} -2.83874e12 q^{5} +2.09628e13 q^{6} -7.82282e14 q^{7} +2.25180e15 q^{8} -2.44527e16 q^{9} -3.72080e17 q^{10} +7.38502e17 q^{11} +2.74764e18 q^{12} +1.22500e19 q^{13} -1.02535e20 q^{14} -4.54011e20 q^{15} +2.95148e20 q^{16} -5.84069e21 q^{17} -3.20507e21 q^{18} -1.00983e22 q^{19} -4.87692e22 q^{20} -1.25113e23 q^{21} +9.67969e22 q^{22} +4.89050e23 q^{23} +3.60139e23 q^{24} +5.14808e24 q^{25} +1.60563e24 q^{26} -1.19126e25 q^{27} -1.34395e25 q^{28} +5.76807e25 q^{29} -5.95081e25 q^{30} -1.92021e26 q^{31} +3.86856e25 q^{32} +1.18111e26 q^{33} -7.65551e26 q^{34} +2.22070e27 q^{35} -4.20094e26 q^{36} +3.01023e27 q^{37} -1.32361e27 q^{38} +1.95918e27 q^{39} -6.39228e27 q^{40} -1.17797e28 q^{41} -1.63989e28 q^{42} -1.50493e28 q^{43} +1.26874e28 q^{44} +6.94149e28 q^{45} +6.41008e28 q^{46} -1.39394e29 q^{47} +4.72041e28 q^{48} +2.33146e29 q^{49} +6.74769e29 q^{50} -9.34125e29 q^{51} +2.10453e29 q^{52} -1.64138e29 q^{53} -1.56140e30 q^{54} -2.09642e30 q^{55} -1.76154e30 q^{56} -1.61506e30 q^{57} +7.56032e30 q^{58} +1.84597e31 q^{59} -7.79985e30 q^{60} +9.15885e30 q^{61} -2.51686e31 q^{62} +1.91289e31 q^{63} +5.07060e30 q^{64} -3.47745e31 q^{65} +1.54811e31 q^{66} -1.04342e32 q^{67} -1.00342e32 q^{68} +7.82156e31 q^{69} +2.91071e32 q^{70} -8.24274e31 q^{71} -5.50626e31 q^{72} -2.41533e32 q^{73} +3.94557e32 q^{74} +8.23352e32 q^{75} -1.73488e32 q^{76} -5.77717e32 q^{77} +2.56794e32 q^{78} -5.14148e32 q^{79} -8.37849e32 q^{80} -6.81814e32 q^{81} -1.54398e33 q^{82} -4.80338e33 q^{83} -2.14943e33 q^{84} +1.65802e34 q^{85} -1.97255e33 q^{86} +9.22509e33 q^{87} +1.66296e33 q^{88} -1.20305e34 q^{89} +9.09836e33 q^{90} -9.58291e33 q^{91} +8.40181e33 q^{92} -3.07107e34 q^{93} -1.82707e34 q^{94} +2.86665e34 q^{95} +6.18714e33 q^{96} -6.58288e34 q^{97} +3.05589e34 q^{98} -1.80584e34 q^{99} +O(q^{100})\)

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 $

$2$	131072.	0.707107
$2$	131072.	0.707107
$3$	1.59934e8	0.715020	0.357510	−	0.933909i	$-0.383626\pi$
$3$	1.59934e8	0.715020	0.357510	+	0.933909i	$0.383626\pi$
$4$	1.71799e10	0.500000
$5$	−2.83874e12	−1.66399	−0.831995	−	0.554782i	$-0.812801\pi$
$5$	−2.83874e12	−1.66399	−0.831995	+	0.554782i	$0.812801\pi$
$6$	2.09628e13	0.505596
$7$	−7.82282e14	−1.27101	−0.635503	−	0.772098i	$-0.719207\pi$
$7$	−7.82282e14	−1.27101	−0.635503	+	0.772098i	$0.719207\pi$
$8$	2.25180e15	0.353553
$9$	−2.44527e16	−0.488746
$10$	−3.72080e17	−1.17662
$11$	7.38502e17	0.440534	0.220267	−	0.975440i	$-0.429307\pi$
$11$	7.38502e17	0.440534	0.220267	+	0.975440i	$0.429307\pi$
$12$	2.74764e18	0.357510
$13$	1.22500e19	0.392759	0.196379	−	0.980528i	$-0.437082\pi$
$13$	1.22500e19	0.392759	0.196379	+	0.980528i	$0.437082\pi$
$14$	−1.02535e20	−0.898737
$15$	−4.54011e20	−1.18979
$16$	2.95148e20	0.250000
$17$	−5.84069e21	−1.71241	−0.856206	−	0.516635i	$-0.827185\pi$
$17$	−5.84069e21	−1.71241	−0.856206	+	0.516635i	$0.827185\pi$
$18$	−3.20507e21	−0.345595
$19$	−1.00983e22	−0.422728	−0.211364	−	0.977407i	$-0.567790\pi$
$19$	−1.00983e22	−0.422728	−0.211364	+	0.977407i	$0.567790\pi$
$20$	−4.87692e22	−0.831995
$21$	−1.25113e23	−0.908795
$22$	9.67969e22	0.311505
$23$	4.89050e23	0.722963	0.361482	−	0.932379i	$-0.382271\pi$
$23$	4.89050e23	0.722963	0.361482	+	0.932379i	$0.382271\pi$
$24$	3.60139e23	0.252798
$25$	5.14808e24	1.76887
$26$	1.60563e24	0.277722
$27$	−1.19126e25	−1.06448
$28$	−1.34395e25	−0.635503
$29$	5.76807e25	1.47593	0.737964	−	0.674840i	$-0.235787\pi$
$29$	5.76807e25	1.47593	0.737964	+	0.674840i	$0.235787\pi$
$30$	−5.95081e25	−0.841307
$31$	−1.92021e26	−1.52939	−0.764697	−	0.644390i	$-0.777111\pi$
$31$	−1.92021e26	−1.52939	−0.764697	+	0.644390i	$0.777111\pi$
$32$	3.86856e25	0.176777
$33$	1.18111e26	0.314991
$34$	−7.65551e26	−1.21086
$35$	2.22070e27	2.11494
$36$	−4.20094e26	−0.244373
$37$	3.01023e27	1.08410	0.542051	−	0.840346i	$-0.317648\pi$
$37$	3.01023e27	1.08410	0.542051	+	0.840346i	$0.317648\pi$
$38$	−1.32361e27	−0.298914
$39$	1.95918e27	0.280830
$40$	−6.39228e27	−0.588310
$41$	−1.17797e28	−0.703745	−0.351872	−	0.936048i	$-0.614455\pi$
$41$	−1.17797e28	−0.703745	−0.351872	+	0.936048i	$0.614455\pi$
$42$	−1.63989e28	−0.642615
$43$	−1.50493e28	−0.390679	−0.195339	−	0.980736i	$-0.562581\pi$
$43$	−1.50493e28	−0.390679	−0.195339	+	0.980736i	$0.562581\pi$
$44$	1.26874e28	0.220267
$45$	6.94149e28	0.813269
$46$	6.41008e28	0.511212
$47$	−1.39394e29	−0.763014	−0.381507	−	0.924366i	$-0.624595\pi$
$47$	−1.39394e29	−0.763014	−0.381507	+	0.924366i	$0.624595\pi$
$48$	4.72041e28	0.178755
$49$	2.33146e29	0.615456
$50$	6.74769e29	1.25078
$51$	−9.34125e29	−1.22441
$52$	2.10453e29	0.196379
$53$	−1.64138e29	−0.109744	−0.0548720	−	0.998493i	$-0.517475\pi$
$53$	−1.64138e29	−0.109744	−0.0548720	+	0.998493i	$0.517475\pi$
$54$	−1.56140e30	−0.752704
$55$	−2.09642e30	−0.733045
$56$	−1.76154e30	−0.449368
$57$	−1.61506e30	−0.302259
$58$	7.56032e30	1.04364
$59$	1.84597e31	1.88936	0.944681	−	0.327991i	$-0.106371\pi$
$59$	1.84597e31	1.88936	0.944681	+	0.327991i	$0.106371\pi$
$60$	−7.79985e30	−0.594894
$61$	9.15885e30	0.523081	0.261540	−	0.965193i	$-0.415770\pi$
$61$	9.15885e30	0.523081	0.261540	+	0.965193i	$0.415770\pi$
$62$	−2.51686e31	−1.08144
$63$	1.91289e31	0.621199
$64$	5.07060e30	0.125000
$65$	−3.47745e31	−0.653547
$66$	1.54811e31	0.222732
$67$	−1.04342e32	−1.15385	−0.576924	−	0.816798i	$-0.695747\pi$
$67$	−1.04342e32	−1.15385	−0.576924	+	0.816798i	$0.695747\pi$
$68$	−1.00342e32	−0.856206
$69$	7.82156e31	0.516933
$70$	2.91071e32	1.49549
$71$	−8.24274e31	−0.330408	−0.165204	−	0.986259i	$-0.552828\pi$
$71$	−8.24274e31	−0.330408	−0.165204	+	0.986259i	$0.552828\pi$
$72$	−5.50626e31	−0.172798
$73$	−2.41533e32	−0.595425	−0.297712	−	0.954656i	$-0.596224\pi$
$73$	−2.41533e32	−0.595425	−0.297712	+	0.954656i	$0.596224\pi$
$74$	3.94557e32	0.766576
$75$	8.23352e32	1.26477
$76$	−1.73488e32	−0.211364
$77$	−5.77717e32	−0.559922
$78$	2.56794e32	0.198577
$79$	−5.14148e32	−0.318137	−0.159069	−	0.987268i	$-0.550849\pi$
$79$	−5.14148e32	−0.318137	−0.159069	+	0.987268i	$0.550849\pi$
$80$	−8.37849e32	−0.415998
$81$	−6.81814e32	−0.272382
$82$	−1.54398e33	−0.497623
$83$	−4.80338e33	−1.25222	−0.626110	−	0.779735i	$-0.715354\pi$
$83$	−4.80338e33	−1.25222	−0.626110	+	0.779735i	$0.715354\pi$
$84$	−2.14943e33	−0.454398
$85$	1.65802e34	2.84944
$86$	−1.97255e33	−0.276251
$87$	9.22509e33	1.05532
$88$	1.66296e33	0.155752
$89$	−1.20305e34	−0.924609	−0.462304	−	0.886721i	$-0.652977\pi$
$89$	−1.20305e34	−0.924609	−0.462304	+	0.886721i	$0.652977\pi$
$90$	9.09836e33	0.575068
$91$	−9.58291e33	−0.499198
$92$	8.40181e33	0.361482
$93$	−3.07107e34	−1.09355
$94$	−1.82707e34	−0.539532
$95$	2.86665e34	0.703415
$96$	6.18714e33	0.126399
$97$	−6.58288e34	−1.12179	−0.560894	−	0.827888i	$-0.689542\pi$
$97$	−6.58288e34	−1.12179	−0.560894	+	0.827888i	$0.689542\pi$
$98$	3.05589e34	0.435193
$99$	−1.80584e34	−0.215309
$100$	8.84433e34	0.884433
$101$	1.98120e34	0.166457	0.0832287	−	0.996530i	$-0.473477\pi$
$101$	1.98120e34	0.166457	0.0832287	+	0.996530i	$0.473477\pi$
$102$	−1.22438e35	−0.865788
$103$	1.21712e35	0.725575	0.362788	−	0.931872i	$-0.381825\pi$
$103$	1.21712e35	0.725575	0.362788	+	0.931872i	$0.381825\pi$
$104$	2.75844e34	0.138861
$105$	3.55165e35	1.51223
$106$	−2.15139e34	−0.0776007
$107$	−1.83871e35	−0.562726	−0.281363	−	0.959601i	$-0.590786\pi$
$107$	−1.83871e35	−0.562726	−0.281363	+	0.959601i	$0.590786\pi$
$108$	−2.04656e35	−0.532242
$109$	−4.04185e35	−0.894575	−0.447287	−	0.894390i	$-0.647610\pi$
$109$	−4.04185e35	−0.894575	−0.447287	+	0.894390i	$0.647610\pi$
$110$	−2.74782e35	−0.518341
$111$	4.81438e35	0.775155
$112$	−2.30889e35	−0.317751
$113$	3.56343e34	0.0419755	0.0209877	−	0.999780i	$-0.493319\pi$
$113$	3.56343e34	0.0419755	0.0209877	+	0.999780i	$0.493319\pi$
$114$	−2.11689e35	−0.213729
$115$	−1.38829e36	−1.20300
$116$	9.90947e35	0.737964
$117$	−2.99544e35	−0.191959
$118$	2.41955e36	1.33598
$119$	4.56907e36	2.17649
$120$	−1.02234e36	−0.420653
$121$	−2.26486e36	−0.805930
$122$	1.20047e36	0.369874
$123$	−1.88397e36	−0.503192
$124$	−3.29890e36	−0.764697
$125$	−6.35224e36	−1.27939
$126$	2.50726e36	0.439254
$127$	2.79269e36	0.426047	0.213024	−	0.977047i	$-0.431669\pi$
$127$	2.79269e36	0.426047	0.213024	+	0.977047i	$0.431669\pi$
$128$	6.64614e35	0.0883883
$129$	−2.40690e36	−0.279343
$130$	−4.55796e36	−0.462127
$131$	3.63027e36	0.321878	0.160939	−	0.986964i	$-0.448548\pi$
$131$	3.63027e36	0.321878	0.160939	+	0.986964i	$0.448548\pi$
$132$	2.02914e36	0.157496
$133$	7.89972e36	0.537289
$134$	−1.36763e37	−0.815894
$135$	3.38167e37	1.77129
$136$	−1.31521e37	−0.605429
$137$	−1.79623e37	−0.727366	−0.363683	−	0.931523i	$-0.618481\pi$
$137$	−1.79623e37	−0.727366	−0.363683	+	0.931523i	$0.618481\pi$
$138$	1.02519e37	0.365527
$139$	1.63067e37	0.512398	0.256199	−	0.966624i	$-0.417530\pi$
$139$	1.63067e37	0.512398	0.256199	+	0.966624i	$0.417530\pi$
$140$	3.81513e37	1.05747
$141$	−2.22939e37	−0.545570
$142$	−1.08039e37	−0.233634
$143$	9.04661e36	0.173024
$144$	−7.21717e36	−0.122186
$145$	−1.63741e38	−2.45593
$146$	−3.16582e37	−0.421029
$147$	3.72880e37	0.440064
$148$	5.17154e37	0.542051
$149$	4.54931e37	0.423824	0.211912	−	0.977289i	$-0.432031\pi$
$149$	4.54931e37	0.423824	0.211912	+	0.977289i	$0.432031\pi$
$150$	1.07918e38	0.894331
$151$	−1.40963e38	−1.03994	−0.519972	−	0.854183i	$-0.674058\pi$
$151$	−1.40963e38	−1.03994	−0.519972	+	0.854183i	$0.674058\pi$
$152$	−2.27394e37	−0.149457
$153$	1.42821e38	0.836934
$154$	−7.57225e37	−0.395924
$155$	5.45099e38	2.54490
$156$	3.36585e37	0.140415
$157$	−3.23003e38	−1.20493	−0.602467	−	0.798144i	$-0.705815\pi$
$157$	−3.23003e38	−1.20493	−0.602467	+	0.798144i	$0.705815\pi$
$158$	−6.73905e37	−0.224957
$159$	−2.62512e37	−0.0784691
$160$	−1.09819e38	−0.294155
$161$	−3.82575e38	−0.918890
$162$	−8.93667e37	−0.192603
$163$	2.92365e38	0.565774	0.282887	−	0.959153i	$-0.408708\pi$
$163$	2.92365e38	0.565774	0.282887	+	0.959153i	$0.408708\pi$
$164$	−2.02373e38	−0.351872
$165$	−3.35288e38	−0.524142
$166$	−6.29589e38	−0.885453
$167$	1.13812e39	1.44095	0.720477	−	0.693479i	$-0.243923\pi$
$167$	1.13812e39	1.44095	0.720477	+	0.693479i	$0.243923\pi$
$168$	−2.81730e38	−0.321308
$169$	−8.22725e38	−0.845741
$170$	2.17320e39	2.01486
$171$	2.46931e38	0.206606
$172$	−2.58546e38	−0.195339
$173$	9.60388e38	0.655602	0.327801	−	0.944747i	$-0.393693\pi$
$173$	9.60388e38	0.655602	0.327801	+	0.944747i	$0.393693\pi$
$174$	1.20915e39	0.746223
$175$	−4.02725e39	−2.24824
$176$	2.17967e38	0.110134
$177$	2.95234e39	1.35093
$178$	−1.57686e39	−0.653797
$179$	−1.67000e39	−0.627753	−0.313876	−	0.949464i	$-0.601628\pi$
$179$	−1.67000e39	−0.627753	−0.313876	+	0.949464i	$0.601628\pi$
$180$	1.19254e39	0.406634
$181$	1.71820e39	0.531740	0.265870	−	0.964009i	$-0.414341\pi$
$181$	1.71820e39	0.531740	0.265870	+	0.964009i	$0.414341\pi$
$182$	−1.25605e39	−0.352987
$183$	1.46481e39	0.374013
$184$	1.10124e39	0.255606
$185$	−8.54528e39	−1.80394
$186$	−4.02531e39	−0.773255
$187$	−4.31336e39	−0.754376
$188$	−2.39478e39	−0.381507
$189$	9.31897e39	1.35296
$190$	3.75737e39	0.497389
$191$	1.54856e40	1.87000	0.935002	−	0.354641i	$-0.115397\pi$
$191$	1.54856e40	1.87000	0.935002	+	0.354641i	$0.115397\pi$
$192$	8.10961e38	0.0893776
$193$	4.81790e39	0.484847	0.242423	−	0.970171i	$-0.422058\pi$
$193$	4.81790e39	0.484847	0.242423	+	0.970171i	$0.422058\pi$
$194$	−8.62831e39	−0.793224
$195$	−5.56161e39	−0.467299
$196$	4.00542e39	0.307728
$197$	1.64634e40	1.15707	0.578535	−	0.815657i	$-0.303625\pi$
$197$	1.64634e40	1.15707	0.578535	+	0.815657i	$0.303625\pi$
$198$	−2.36695e39	−0.152247
$199$	−2.17621e40	−1.28166	−0.640829	−	0.767684i	$-0.721409\pi$
$199$	−2.17621e40	−1.28166	−0.640829	+	0.767684i	$0.721409\pi$
$200$	1.15924e40	0.625388
$201$	−1.66878e40	−0.825025
$202$	2.59679e39	0.117703
$203$	−4.51226e40	−1.87591
$204$	−1.60481e40	−0.612205
$205$	3.34394e40	1.17103
$206$	1.59531e40	0.513059
$207$	−1.19586e40	−0.353345
$208$	3.61555e39	0.0981896
$209$	−7.45762e39	−0.186226
$210$	4.65521e40	1.06931
$211$	1.96990e40	0.416391	0.208196	−	0.978087i	$-0.433241\pi$
$211$	1.96990e40	0.416391	0.208196	+	0.978087i	$0.433241\pi$
$212$	−2.81986e39	−0.0548720
$213$	−1.31829e40	−0.236248
$214$	−2.41003e40	−0.397907
$215$	4.27212e40	0.650086
$216$	−2.68247e40	−0.376352
$217$	1.50215e41	1.94387
$218$	−5.29774e40	−0.632560
$219$	−3.86293e40	−0.425741
$220$	−3.60162e40	−0.366523
$221$	−7.15482e40	−0.672564
$222$	6.31031e40	0.548117
$223$	−8.16161e40	−0.655301	−0.327650	−	0.944799i	$-0.606257\pi$
$223$	−8.16161e40	−0.655301	−0.327650	+	0.944799i	$0.606257\pi$
$224$	−3.02631e40	−0.224684
$225$	−1.25884e41	−0.864526
$226$	4.67066e39	0.0296811
$227$	1.94330e41	1.14311	0.571553	−	0.820565i	$-0.306341\pi$
$227$	1.94330e41	1.14311	0.571553	+	0.820565i	$0.306341\pi$
$228$	−2.77465e40	−0.151129
$229$	9.53092e40	0.480855	0.240427	−	0.970667i	$-0.422712\pi$
$229$	9.53092e40	0.480855	0.240427	+	0.970667i	$0.422712\pi$
$230$	−1.81966e41	−0.850652
$231$	−9.23965e40	−0.400355
$232$	1.29885e41	0.521820
$233$	−2.43764e41	−0.908325	−0.454163	−	0.890919i	$-0.650061\pi$
$233$	−2.43764e41	−0.908325	−0.454163	+	0.890919i	$0.650061\pi$
$234$	−3.92619e40	−0.135736
$235$	3.95704e41	1.26965
$236$	3.17136e41	0.944681
$237$	−8.22297e40	−0.227475
$238$	5.98877e41	1.53901
$239$	−1.46611e41	−0.350110	−0.175055	−	0.984559i	$-0.556010\pi$
$239$	−1.46611e41	−0.350110	−0.175055	+	0.984559i	$0.556010\pi$
$240$	−1.34000e41	−0.297447
$241$	−2.24059e41	−0.462450	−0.231225	−	0.972900i	$-0.574273\pi$
$241$	−2.24059e41	−0.462450	−0.231225	+	0.972900i	$0.574273\pi$
$242$	−2.96860e41	−0.569878
$243$	4.86958e41	0.869725
$244$	1.57348e41	0.261540
$245$	−6.61842e41	−1.02411
$246$	−2.46935e41	−0.355810
$247$	−1.23704e41	−0.166030
$248$	−4.32393e41	−0.540722
$249$	−7.68224e41	−0.895363
$250$	−8.32600e41	−0.904662
$251$	1.59733e41	0.161847	0.0809235	−	0.996720i	$-0.474213\pi$
$251$	1.59733e41	0.161847	0.0809235	+	0.996720i	$0.474213\pi$
$252$	3.28632e41	0.310599
$253$	3.61164e41	0.318490
$254$	3.66044e41	0.301261
$255$	2.65174e42	2.03741
$256$	8.71123e40	0.0625000
$257$	2.36934e42	1.58781	0.793905	−	0.608042i	$-0.208045\pi$
$257$	2.36934e42	1.58781	0.793905	+	0.608042i	$0.208045\pi$
$258$	−3.15477e41	−0.197525
$259$	−2.35485e42	−1.37790
$260$	−5.97421e41	−0.326773
$261$	−1.41045e42	−0.721354
$262$	4.75826e41	0.227602
$263$	1.22012e42	0.545979	0.272989	−	0.962017i	$-0.411988\pi$
$263$	1.22012e42	0.545979	0.272989	+	0.962017i	$0.411988\pi$
$264$	2.65963e41	0.111366
$265$	4.65945e41	0.182613
$266$	1.03543e42	0.379921
$267$	−1.92408e42	−0.661114
$268$	−1.79258e42	−0.576924
$269$	−1.12335e42	−0.338729	−0.169364	−	0.985554i	$-0.554171\pi$
$269$	−1.12335e42	−0.338729	−0.169364	+	0.985554i	$0.554171\pi$
$270$	4.43242e42	1.25249
$271$	−4.25945e42	−1.12821	−0.564106	−	0.825702i	$-0.690779\pi$
$271$	−4.25945e42	−1.12821	−0.564106	+	0.825702i	$0.690779\pi$
$272$	−1.72387e42	−0.428103
$273$	−1.53263e42	−0.356937
$274$	−2.35436e42	−0.514325
$275$	3.80187e42	0.779246
$276$	1.34373e42	0.258467
$277$	−5.33232e42	−0.962766	−0.481383	−	0.876510i	$-0.659865\pi$
$277$	−5.33232e42	−0.962766	−0.481383	+	0.876510i	$0.659865\pi$
$278$	2.13735e42	0.362320
$279$	4.69544e42	0.747485
$280$	5.00056e42	0.747745
$281$	6.03182e42	0.847398	0.423699	−	0.905803i	$-0.360731\pi$
$281$	6.03182e42	0.847398	0.423699	+	0.905803i	$0.360731\pi$
$282$	−2.92210e42	−0.385777
$283$	−8.32656e42	−1.03324	−0.516622	−	0.856213i	$-0.672811\pi$
$283$	−8.32656e42	−1.03324	−0.516622	+	0.856213i	$0.672811\pi$
$284$	−1.41609e42	−0.165204
$285$	4.58474e42	0.502956
$286$	1.18576e42	0.122346
$287$	9.21501e42	0.894464
$288$	−9.45968e41	−0.0863989
$289$	2.24801e43	1.93235
$290$	−2.14618e43	−1.73661
$291$	−1.05283e43	−0.802101
$292$	−4.14951e42	−0.297712
$293$	1.38889e43	0.938609	0.469304	−	0.883036i	$-0.344505\pi$
$293$	1.38889e43	0.938609	0.469304	+	0.883036i	$0.344505\pi$
$294$	4.88741e42	0.311172
$295$	−5.24024e43	−3.14388
$296$	6.77844e42	0.383288
$297$	−8.79745e42	−0.468942
$298$	5.96287e42	0.299689
$299$	5.99084e42	0.283950
$300$	1.41451e43	0.632387
$301$	1.17728e43	0.496555
$302$	−1.84764e43	−0.735351
$303$	3.16860e42	0.119020
$304$	−2.98049e42	−0.105682
$305$	−2.59996e43	−0.870402
$306$	1.87198e43	0.591802
$307$	6.36819e43	1.90149	0.950745	−	0.309973i	$-0.100320\pi$
$307$	6.36819e43	1.90149	0.950745	+	0.309973i	$0.100320\pi$
$308$	−9.92510e42	−0.279961
$309$	1.94659e43	0.518801
$310$	7.14472e43	1.79951
$311$	−5.90309e42	−0.140531	−0.0702656	−	0.997528i	$-0.522385\pi$
$311$	−5.90309e42	−0.140531	−0.0702656	+	0.997528i	$0.522385\pi$
$312$	4.41169e42	0.0992885
$313$	−4.90346e43	−1.04346	−0.521731	−	0.853110i	$-0.674714\pi$
$313$	−4.90346e43	−1.04346	−0.521731	+	0.853110i	$0.674714\pi$
$314$	−4.23367e43	−0.852017
$315$	−5.43021e43	−1.03367
$316$	−8.83300e42	−0.159069
$317$	−3.17530e43	−0.541063	−0.270532	−	0.962711i	$-0.587199\pi$
$317$	−3.17530e43	−0.541063	−0.270532	+	0.962711i	$0.587199\pi$
$318$	−3.44079e42	−0.0554861
$319$	4.25973e43	0.650197
$320$	−1.43941e43	−0.207999
$321$	−2.94072e43	−0.402360
$322$	−5.01449e43	−0.649754
$323$	5.89811e43	0.723884
$324$	−1.17135e43	−0.136191
$325$	6.30637e43	0.694737
$326$	3.83209e43	0.400062
$327$	−6.46429e43	−0.639639
$328$	−2.65254e43	−0.248811
$329$	1.09046e44	0.969795
$330$	−4.39469e43	−0.370624
$331$	1.45939e43	0.116730	0.0583651	−	0.998295i	$-0.481411\pi$
$331$	1.45939e43	0.116730	0.0583651	+	0.998295i	$0.481411\pi$
$332$	−8.25215e43	−0.626110
$333$	−7.36084e43	−0.529850
$334$	1.49176e44	1.01891
$335$	2.96199e44	1.91999
$336$	−3.69269e43	−0.227199
$337$	−1.60396e44	−0.936852	−0.468426	−	0.883503i	$-0.655179\pi$
$337$	−1.60396e44	−0.936852	−0.468426	+	0.883503i	$0.655179\pi$
$338$	−1.07836e44	−0.598029
$339$	5.69913e42	0.0300133
$340$	2.84846e44	1.42472
$341$	−1.41808e44	−0.673751
$342$	3.23657e43	0.146093
$343$	1.13957e44	0.488758
$344$	−3.38881e43	−0.138126
$345$	−2.22034e44	−0.860172
$346$	1.25880e44	0.463580
$347$	−3.26343e44	−1.14264	−0.571319	−	0.820728i	$-0.693568\pi$
$347$	−3.26343e44	−1.14264	−0.571319	+	0.820728i	$0.693568\pi$
$348$	1.58486e44	0.527660
$349$	−3.30747e44	−1.04725	−0.523625	−	0.851949i	$-0.675421\pi$
$349$	−3.30747e44	−1.04725	−0.523625	+	0.851949i	$0.675421\pi$
$350$	−5.27859e44	−1.58974
$351$	−1.45928e44	−0.418085
$352$	2.85694e43	0.0778762
$353$	3.24878e44	0.842679	0.421340	−	0.906903i	$-0.361560\pi$
$353$	3.24878e44	0.842679	0.421340	+	0.906903i	$0.361560\pi$
$354$	3.86969e44	0.955253
$355$	2.33990e44	0.549796
$356$	−2.06682e44	−0.462304
$357$	7.30749e44	1.55623
$358$	−2.18890e44	−0.443888
$359$	2.83284e44	0.547104	0.273552	−	0.961857i	$-0.411801\pi$
$359$	2.83284e44	0.547104	0.273552	+	0.961857i	$0.411801\pi$
$360$	1.56309e44	0.287534
$361$	−4.68682e44	−0.821301
$362$	2.25208e44	0.375997
$363$	−3.62228e44	−0.576256
$364$	−1.64633e44	−0.249599
$365$	6.85650e44	0.990781
$366$	1.91996e44	0.264467
$367$	5.59849e44	0.735215	0.367608	−	0.929981i	$-0.380177\pi$
$367$	5.59849e44	0.735215	0.367608	+	0.929981i	$0.380177\pi$
$368$	1.44342e44	0.180741
$369$	2.88045e44	0.343952
$370$	−1.12005e45	−1.27558
$371$	1.28402e44	0.139485
$372$	−5.27605e44	−0.546774
$373$	−1.56597e45	−1.54839	−0.774193	−	0.632949i	$-0.781844\pi$
$373$	−1.56597e45	−1.54839	−0.774193	+	0.632949i	$0.781844\pi$
$374$	−5.65361e44	−0.533425
$375$	−1.01594e45	−0.914787
$376$	−3.13888e44	−0.269766
$377$	7.06586e44	0.579684
$378$	1.22146e45	0.956691
$379$	−2.57898e44	−0.192869	−0.0964343	−	0.995339i	$-0.530744\pi$
$379$	−2.57898e44	−0.192869	−0.0964343	+	0.995339i	$0.530744\pi$
$380$	4.92487e44	0.351707
$381$	4.46646e44	0.304633
$382$	2.02972e45	1.32229
$383$	−2.53251e45	−1.57606	−0.788029	−	0.615638i	$-0.788899\pi$
$383$	−2.53251e45	−1.57606	−0.788029	+	0.615638i	$0.788899\pi$
$384$	1.06294e44	0.0631995
$385$	1.63999e45	0.931705
$386$	6.31491e44	0.342838
$387$	3.67997e44	0.190943
$388$	−1.13093e45	−0.560894
$389$	2.99420e45	1.41959	0.709795	−	0.704408i	$-0.248788\pi$
$389$	2.99420e45	1.41959	0.709795	+	0.704408i	$0.248788\pi$
$390$	−7.28972e44	−0.330430
$391$	−2.85639e45	−1.23801
$392$	5.24999e44	0.217597
$393$	5.80602e44	0.230149
$394$	2.15789e45	0.818172
$395$	1.45953e45	0.529377
$396$	−3.10241e44	−0.107655
$397$	−4.85667e45	−1.61252	−0.806260	−	0.591562i	$-0.798512\pi$
$397$	−4.85667e45	−1.61252	−0.806260	+	0.591562i	$0.798512\pi$
$398$	−2.85240e45	−0.906269
$399$	1.26343e45	0.384173
$400$	1.51944e45	0.442216
$401$	3.04283e45	0.847717	0.423858	−	0.905728i	$-0.360675\pi$
$401$	3.04283e45	0.847717	0.423858	+	0.905728i	$0.360675\pi$
$402$	−2.18730e45	−0.583381
$403$	−2.35225e45	−0.600683
$404$	3.40367e44	0.0832287
$405$	1.93549e45	0.453241
$406$	−5.91430e45	−1.32647
$407$	2.22306e45	0.477584
$408$	−2.10346e45	−0.432894
$409$	1.45173e45	0.286239	0.143119	−	0.989705i	$-0.454287\pi$
$409$	1.45173e45	0.286239	0.143119	+	0.989705i	$0.454287\pi$
$410$	4.38297e45	0.828040
$411$	−2.87279e45	−0.520081
$412$	2.09100e45	0.362788
$413$	−1.44407e46	−2.40139
$414$	−1.56744e45	−0.249853
$415$	1.36356e46	2.08368
$416$	4.73897e44	0.0694306
$417$	2.60799e45	0.366375
$418$	−9.77485e44	−0.131682
$419$	6.00808e45	0.776230	0.388115	−	0.921611i	$-0.373126\pi$
$419$	6.00808e45	0.776230	0.388115	+	0.921611i	$0.373126\pi$
$420$	6.10168e45	0.756113
$421$	1.54583e46	1.83749	0.918745	−	0.394851i	$-0.129204\pi$
$421$	1.54583e46	1.83749	0.918745	+	0.394851i	$0.129204\pi$
$422$	2.58199e45	0.294433
$423$	3.40857e45	0.372920
$424$	−3.69605e44	−0.0388003
$425$	−3.00683e46	−3.02903
$426$	−1.72791e45	−0.167053
$427$	−7.16480e45	−0.664839
$428$	−3.15888e45	−0.281363
$429$	1.44686e45	0.123715
$430$	5.59956e45	0.459680
$431$	−9.17869e45	−0.723483	−0.361742	−	0.932278i	$-0.617818\pi$
$431$	−9.17869e45	−0.723483	−0.361742	+	0.932278i	$0.617818\pi$
$432$	−3.51597e45	−0.266121
$433$	1.61852e45	0.117647	0.0588235	−	0.998268i	$-0.481265\pi$
$433$	1.61852e45	0.117647	0.0588235	+	0.998268i	$0.481265\pi$
$434$	1.96889e46	1.37452
$435$	−2.61877e46	−1.75604
$436$	−6.94385e45	−0.447287
$437$	−4.93858e45	−0.305616
$438$	−5.06322e45	−0.301044
$439$	3.23512e46	1.84825	0.924125	−	0.382090i	$-0.124795\pi$
$439$	3.23512e46	1.84825	0.924125	+	0.382090i	$0.124795\pi$
$440$	−4.72071e45	−0.259171
$441$	−5.70106e45	−0.300802
$442$	−9.37797e45	−0.475575
$443$	1.76802e46	0.861831	0.430915	−	0.902392i	$-0.358191\pi$
$443$	1.76802e46	0.861831	0.430915	+	0.902392i	$0.358191\pi$
$444$	8.27105e45	0.387577
$445$	3.41514e46	1.53854
$446$	−1.06976e46	−0.463368
$447$	7.27588e45	0.303043
$448$	−3.96664e45	−0.158876
$449$	1.47636e46	0.568696	0.284348	−	0.958721i	$-0.408223\pi$
$449$	1.47636e46	0.568696	0.284348	+	0.958721i	$0.408223\pi$
$450$	−1.64999e46	−0.611312
$451$	−8.69930e45	−0.310024
$452$	6.12193e44	0.0209877
$453$	−2.25448e46	−0.743581
$454$	2.54712e46	0.808298
$455$	2.72034e46	0.830662
$456$	−3.63679e45	−0.106865
$457$	−6.00910e46	−1.69932	−0.849661	−	0.527329i	$-0.823194\pi$
$457$	−6.00910e46	−1.69932	−0.849661	+	0.527329i	$0.823194\pi$
$458$	1.24924e46	0.340016
$459$	6.95776e46	1.82283
$460$	−2.38506e46	−0.601502
$461$	−6.33149e46	−1.53723	−0.768617	−	0.639709i	$-0.779055\pi$
$461$	−6.33149e46	−1.53723	−0.768617	+	0.639709i	$0.779055\pi$
$462$	−1.21106e46	−0.283094
$463$	−8.42279e46	−1.89578	−0.947892	−	0.318592i	$-0.896790\pi$
$463$	−8.42279e46	−1.89578	−0.947892	+	0.318592i	$0.896790\pi$
$464$	1.70243e46	0.368982
$465$	8.71797e46	1.81965
$466$	−3.19507e46	−0.642283
$467$	−5.40173e46	−1.04589	−0.522947	−	0.852365i	$-0.675167\pi$
$467$	−5.40173e46	−1.04589	−0.522947	+	0.852365i	$0.675167\pi$
$468$	−5.14613e45	−0.0959796
$469$	8.16246e46	1.46655
$470$	5.18658e46	0.897777
$471$	−5.16592e46	−0.861552
$472$	4.15676e46	0.667990
$473$	−1.11140e46	−0.172107
$474$	−1.07780e46	−0.160849
$475$	−5.19869e46	−0.747748
$476$	7.84960e46	1.08824
$477$	4.01361e45	0.0536369
$478$	−1.92166e46	−0.247565
$479$	2.14848e46	0.266846	0.133423	−	0.991059i	$-0.457403\pi$
$479$	2.14848e46	0.266846	0.133423	+	0.991059i	$0.457403\pi$
$480$	−1.75637e46	−0.210327
$481$	3.68752e46	0.425790
$482$	−2.93679e46	−0.327002
$483$	−6.11867e46	−0.657025
$484$	−3.89100e46	−0.402965
$485$	1.86871e47	1.86664
$486$	6.38266e46	0.614989
$487$	1.25456e47	1.16609	0.583047	−	0.812439i	$-0.301861\pi$
$487$	1.25456e47	1.16609	0.583047	+	0.812439i	$0.301861\pi$
$488$	2.06239e46	0.184937
$489$	4.67591e46	0.404540
$490$	−8.67490e46	−0.724157
$491$	−1.88807e47	−1.52087	−0.760433	−	0.649416i	$-0.775013\pi$
$491$	−1.88807e47	−1.52087	−0.760433	+	0.649416i	$0.775013\pi$
$492$	−3.23663e46	−0.251596
$493$	−3.36895e47	−2.52740
$494$	−1.62141e46	−0.117401
$495$	5.12631e46	0.358273
$496$	−5.66746e46	−0.382348
$497$	6.44815e46	0.419950
$498$	−1.00693e47	−0.633117
$499$	9.74630e46	0.591671	0.295835	−	0.955239i	$-0.404402\pi$
$499$	9.74630e46	0.591671	0.295835	+	0.955239i	$0.404402\pi$
$500$	−1.09131e47	−0.639693
$501$	1.82024e47	1.03031
$502$	2.09365e46	0.114443
$503$	5.22114e46	0.275630	0.137815	−	0.990458i	$-0.455992\pi$
$503$	5.22114e46	0.275630	0.137815	+	0.990458i	$0.455992\pi$
$504$	4.30745e46	0.219627
$505$	−5.62410e46	−0.276984
$506$	4.73385e46	0.225206
$507$	−1.31582e47	−0.604722
$508$	4.79781e46	0.213024
$509$	7.69687e46	0.330182	0.165091	−	0.986278i	$-0.447208\pi$
$509$	7.69687e46	0.330182	0.165091	+	0.986278i	$0.447208\pi$
$510$	3.47569e47	1.44066
$511$	1.88947e47	0.756788
$512$	1.14180e46	0.0441942
$513$	1.20297e47	0.449987
$514$	3.10555e47	1.12275
$515$	−3.45509e47	−1.20735
$516$	−4.13502e46	−0.139672
$517$	−1.02943e47	−0.336134
$518$	−3.08655e47	−0.974322
$519$	1.53599e47	0.468769
$520$	−7.83051e46	−0.231064
$521$	−2.80116e47	−0.799241	−0.399620	−	0.916681i	$-0.630858\pi$
$521$	−2.80116e47	−0.799241	−0.399620	+	0.916681i	$0.630858\pi$
$522$	−1.84870e47	−0.510074
$523$	−2.35376e47	−0.628032	−0.314016	−	0.949418i	$-0.601675\pi$
$523$	−2.35376e47	−0.628032	−0.314016	+	0.949418i	$0.601675\pi$
$524$	6.23675e46	0.160939
$525$	−6.44093e47	−1.60754
$526$	1.59923e47	0.386065
$527$	1.12154e48	2.61895
$528$	3.48604e46	0.0787478
$529$	−2.18418e47	−0.477324
$530$	6.10723e46	0.129127
$531$	−4.51390e47	−0.923418
$532$	1.35716e47	0.268645
$533$	−1.44300e47	−0.276402
$534$	−2.52193e47	−0.467478
$535$	5.21962e47	0.936370
$536$	−2.34957e47	−0.407947
$537$	−2.67090e47	−0.448856
$538$	−1.47240e47	−0.239517
$539$	1.72179e47	0.271129
$540$	5.80966e47	0.885646
$541$	4.65471e47	0.686974	0.343487	−	0.939157i	$-0.388392\pi$
$541$	4.65471e47	0.686974	0.343487	+	0.939157i	$0.388392\pi$
$542$	−5.58295e47	−0.797767
$543$	2.74799e47	0.380205
$544$	−2.25951e47	−0.302715
$545$	1.14738e48	1.48856
$546$	−2.00885e47	−0.252393
$547$	6.56213e47	0.798485	0.399243	−	0.916845i	$-0.369273\pi$
$547$	6.56213e47	0.798485	0.399243	+	0.916845i	$0.369273\pi$
$548$	−3.08591e47	−0.363683
$549$	−2.23959e47	−0.255654
$550$	4.98318e47	0.551010
$551$	−5.82477e47	−0.623916
$552$	1.76126e47	0.182764
$553$	4.02209e47	0.404354
$554$	−6.98918e47	−0.680778
$555$	−1.36668e48	−1.28985
$556$	2.80147e47	0.256199
$557$	−8.73979e47	−0.774524	−0.387262	−	0.921970i	$-0.626579\pi$
$557$	−8.73979e47	−0.774524	−0.387262	+	0.921970i	$0.626579\pi$
$558$	6.15440e47	0.528552
$559$	−1.84354e47	−0.153442
$560$	6.55434e47	0.528736
$561$	−6.89853e47	−0.539394
$562$	7.90602e47	0.599201
$563$	−3.92549e47	−0.288401	−0.144201	−	0.989548i	$-0.546061\pi$
$563$	−3.92549e47	−0.288401	−0.144201	+	0.989548i	$0.546061\pi$
$564$	−3.83006e47	−0.272785
$565$	−1.01157e47	−0.0698468
$566$	−1.09138e48	−0.730614
$567$	5.33371e47	0.346199
$568$	−1.85610e47	−0.116817
$569$	−1.94519e48	−1.18713	−0.593564	−	0.804787i	$-0.702280\pi$
$569$	−1.94519e48	−1.18713	−0.593564	+	0.804787i	$0.702280\pi$
$570$	6.00931e47	0.355644
$571$	−1.16130e48	−0.666517	−0.333258	−	0.942836i	$-0.608148\pi$
$571$	−1.16130e48	−0.666517	−0.333258	+	0.942836i	$0.608148\pi$
$572$	1.55420e47	0.0865118
$573$	2.47666e48	1.33709
$574$	1.20783e48	0.632481
$575$	2.51767e48	1.27882
$576$	−1.23990e47	−0.0610932
$577$	−1.65122e48	−0.789275	−0.394638	−	0.918837i	$-0.629130\pi$
$577$	−1.65122e48	−0.789275	−0.394638	+	0.918837i	$0.629130\pi$
$578$	2.94652e48	1.36638
$579$	7.70545e47	0.346675
$580$	−2.81304e48	−1.22797
$581$	3.75760e48	1.59158
$582$	−1.37996e48	−0.567171
$583$	−1.21216e47	−0.0483460
$584$	−5.43884e47	−0.210514
$585$	8.50330e47	0.319418
$586$	1.82045e48	0.663697
$587$	−3.35250e48	−1.18632	−0.593160	−	0.805085i	$-0.702120\pi$
$587$	−3.35250e48	−1.18632	−0.593160	+	0.805085i	$0.702120\pi$
$588$	6.40603e47	0.220032
$589$	1.93909e48	0.646517
$590$	−6.86849e48	−2.22306
$591$	2.63305e48	0.827329
$592$	8.88464e47	0.271025
$593$	1.07473e48	0.318305	0.159152	−	0.987254i	$-0.449124\pi$
$593$	1.07473e48	0.318305	0.159152	+	0.987254i	$0.449124\pi$
$594$	−1.15310e48	−0.331592
$595$	−1.29704e49	−3.62165
$596$	7.81565e47	0.211912
$597$	−3.48050e48	−0.916411
$598$	7.85231e47	0.200783
$599$	8.24010e47	0.204627	0.102313	−	0.994752i	$-0.467376\pi$
$599$	8.24010e47	0.204627	0.102313	+	0.994752i	$0.467376\pi$
$600$	1.85402e48	0.447165
$601$	7.68431e48	1.80012	0.900060	−	0.435765i	$-0.143522\pi$
$601$	7.68431e48	1.80012	0.900060	+	0.435765i	$0.143522\pi$
$602$	1.54309e48	0.351117
$603$	2.55144e48	0.563939
$604$	−2.42173e48	−0.519972
$605$	6.42935e48	1.34106
$606$	4.15315e47	0.0841602
$607$	4.69477e48	0.924298	0.462149	−	0.886802i	$-0.347079\pi$
$607$	4.69477e48	0.924298	0.462149	+	0.886802i	$0.347079\pi$
$608$	−3.90659e47	−0.0747284
$609$	−7.21662e48	−1.34132
$610$	−3.40782e48	−0.615467
$611$	−1.70757e48	−0.299680
$612$	2.45364e48	0.418467
$613$	−6.38797e48	−1.05878	−0.529389	−	0.848379i	$-0.677579\pi$
$613$	−6.38797e48	−1.05878	−0.529389	+	0.848379i	$0.677579\pi$
$614$	8.34691e48	1.34456
$615$	5.34810e48	0.837307
$616$	−1.30090e48	−0.197962
$617$	2.42807e48	0.359146	0.179573	−	0.983745i	$-0.442528\pi$
$617$	2.42807e48	0.359146	0.179573	+	0.983745i	$0.442528\pi$
$618$	2.55143e48	0.366848
$619$	−1.28640e49	−1.79800	−0.898999	−	0.437951i	$-0.855704\pi$
$619$	−1.28640e49	−1.79800	−0.898999	+	0.437951i	$0.855704\pi$
$620$	9.36472e48	1.27245
$621$	−5.82583e48	−0.769582
$622$	−7.73730e47	−0.0993706
$623$	9.41123e48	1.17518
$624$	5.78248e47	0.0702076
$625$	3.04949e48	0.360020
$626$	−6.42706e48	−0.737839
$627$	−1.19273e48	−0.133155
$628$	−5.54916e48	−0.602467
$629$	−1.75819e49	−1.85643
$630$	−7.11748e48	−0.730914
$631$	1.93961e49	1.93731	0.968656	−	0.248405i	$-0.0799064\pi$
$631$	1.93961e49	1.93731	0.968656	+	0.248405i	$0.0799064\pi$
$632$	−1.15776e48	−0.112478
$633$	3.15054e48	0.297728
$634$	−4.16193e48	−0.382589
$635$	−7.92774e48	−0.708939
$636$	−4.50992e47	−0.0392346
$637$	2.85603e48	0.241726
$638$	5.58331e48	0.459759
$639$	2.01557e48	0.161486
$640$	−1.88667e48	−0.147077
$641$	−1.58642e49	−1.20338	−0.601688	−	0.798731i	$-0.705505\pi$
$641$	−1.58642e49	−1.20338	−0.601688	+	0.798731i	$0.705505\pi$
$642$	−3.85446e48	−0.284512
$643$	1.86954e49	1.34289	0.671447	−	0.741053i	$-0.265673\pi$
$643$	1.86954e49	1.34289	0.671447	+	0.741053i	$0.265673\pi$
$644$	−6.57259e48	−0.459445
$645$	6.83257e48	0.464824
$646$	7.73077e48	0.511863
$647$	−8.57393e48	−0.552529	−0.276264	−	0.961082i	$-0.589097\pi$
$647$	−8.57393e48	−0.552529	−0.276264	+	0.961082i	$0.589097\pi$
$648$	−1.53531e48	−0.0963015
$649$	1.36326e49	0.832329
$650$	8.26588e48	0.491253
$651$	2.40244e49	1.38991
$652$	5.02280e48	0.282887
$653$	1.29072e49	0.707705	0.353852	−	0.935301i	$-0.384872\pi$
$653$	1.29072e49	0.707705	0.353852	+	0.935301i	$0.384872\pi$
$654$	−8.47287e48	−0.452293
$655$	−1.03054e49	−0.535601
$656$	−3.47674e48	−0.175936
$657$	5.90614e48	0.291011
$658$	1.42928e49	0.685749
$659$	−3.09167e49	−1.44444	−0.722219	−	0.691664i	$-0.756878\pi$
$659$	−3.09167e49	−1.44444	−0.722219	+	0.691664i	$0.756878\pi$
$660$	−5.76021e48	−0.262071
$661$	−2.39279e49	−1.06018	−0.530090	−	0.847941i	$-0.677842\pi$
$661$	−2.39279e49	−1.06018	−0.530090	+	0.847941i	$0.677842\pi$
$662$	1.91286e48	0.0825407
$663$	−1.14430e49	−0.480897
$664$	−1.08163e49	−0.442727
$665$	−2.24253e49	−0.894044
$666$	−9.64800e48	−0.374661
$667$	2.82087e49	1.06704
$668$	1.95528e49	0.720477
$669$	−1.30532e49	−0.468553
$670$	3.88234e49	1.35764
$671$	6.76383e48	0.230435
$672$	−4.84009e48	−0.160654
$673$	−2.90249e49	−0.938659	−0.469329	−	0.883023i	$-0.655504\pi$
$673$	−2.90249e49	−0.938659	−0.469329	+	0.883023i	$0.655504\pi$
$674$	−2.10235e49	−0.662454
$675$	−6.13267e49	−1.88293
$676$	−1.41343e49	−0.422870
$677$	1.16732e49	0.340321	0.170160	−	0.985416i	$-0.445571\pi$
$677$	1.16732e49	0.340321	0.170160	+	0.985416i	$0.445571\pi$
$678$	7.46996e47	0.0212226
$679$	5.14967e49	1.42580
$680$	3.73353e49	1.00743
$681$	3.10799e49	0.817344
$682$	−1.85871e49	−0.476414
$683$	3.31156e49	0.827313	0.413657	−	0.910433i	$-0.364251\pi$
$683$	3.31156e49	0.827313	0.413657	+	0.910433i	$0.364251\pi$
$684$	4.24224e48	0.103303
$685$	5.09904e49	1.21033
$686$	1.49366e49	0.345604
$687$	1.52432e49	0.343821
$688$	−4.44178e48	−0.0976696
$689$	−2.01068e48	−0.0431029
$690$	−2.91025e49	−0.608234
$691$	−5.24688e49	−1.06914	−0.534571	−	0.845124i	$-0.679527\pi$
$691$	−5.24688e49	−1.06914	−0.534571	+	0.845124i	$0.679527\pi$
$692$	1.64993e49	0.327801
$693$	1.41267e49	0.273659
$694$	−4.27744e49	−0.807967
$695$	−4.62905e49	−0.852625
$696$	2.07731e49	0.373112
$697$	6.88014e49	1.20510
$698$	−4.33516e49	−0.740518
$699$	−3.89862e49	−0.649471
$700$	−6.91876e49	−1.12412
$701$	2.28536e49	0.362150	0.181075	−	0.983469i	$-0.442042\pi$
$701$	2.28536e49	0.362150	0.181075	+	0.983469i	$0.442042\pi$
$702$	−1.91271e49	−0.295631
$703$	−3.03983e49	−0.458280
$704$	3.74465e48	0.0550668
$705$	6.32865e49	0.907824
$706$	4.25823e49	0.595864
$707$	−1.54985e49	−0.211568
$708$	5.07207e49	0.675466
$709$	−8.39589e49	−1.09083	−0.545416	−	0.838166i	$-0.683628\pi$
$709$	−8.39589e49	−1.09083	−0.545416	+	0.838166i	$0.683628\pi$
$710$	3.06696e49	0.388764
$711$	1.25723e49	0.155488
$712$	−2.70902e49	−0.326898
$713$	−9.39079e49	−1.10570
$714$	9.57807e49	1.10042
$715$	−2.56810e49	−0.287910
$716$	−2.86904e49	−0.313876
$717$	−2.34481e49	−0.250335
$718$	3.71307e49	0.386861
$719$	1.29619e50	1.31799	0.658994	−	0.752148i	$-0.270982\pi$
$719$	1.29619e50	1.31799	0.658994	+	0.752148i	$0.270982\pi$
$720$	2.04877e49	0.203317
$721$	−9.52132e49	−0.922210
$722$	−6.14311e49	−0.580748
$723$	−3.58347e49	−0.330661
$724$	2.95185e49	0.265870
$725$	2.96945e50	2.61072
$726$	−4.74779e49	−0.407475
$727$	−1.26624e50	−1.06087	−0.530436	−	0.847725i	$-0.677972\pi$
$727$	−1.26624e50	−1.06087	−0.530436	+	0.847725i	$0.677972\pi$
$728$	−2.15788e49	−0.176493
$729$	1.11993e50	0.894253
$730$	8.98696e49	0.700588
$731$	8.78986e49	0.669003
$732$	2.51652e49	0.187007
$733$	−1.54415e50	−1.12039	−0.560197	−	0.828359i	$-0.689275\pi$
$733$	−1.54415e50	−1.12039	−0.560197	+	0.828359i	$0.689275\pi$
$734$	7.33805e49	0.519876
$735$	−1.05851e50	−0.732262
$736$	1.89192e49	0.127803
$737$	−7.70565e49	−0.508310
$738$	3.77546e49	0.243211
$739$	1.25930e50	0.792233	0.396116	−	0.918200i	$-0.370358\pi$
$739$	1.25930e50	0.792233	0.396116	+	0.918200i	$0.370358\pi$
$740$	−1.46807e50	−0.901968
$741$	−1.97844e49	−0.118715
$742$	1.68299e49	0.0986309
$743$	−3.01647e50	−1.72661	−0.863305	−	0.504682i	$-0.831610\pi$
$743$	−3.01647e50	−1.72661	−0.863305	+	0.504682i	$0.831610\pi$
$744$	−6.91543e49	−0.386628
$745$	−1.29143e50	−0.705239
$746$	−2.05255e50	−1.09487
$747$	1.17456e50	0.612017
$748$	−7.41030e49	−0.377188
$749$	1.43839e50	0.715228
$750$	−1.33161e50	−0.646852
$751$	2.05672e50	0.976060	0.488030	−	0.872827i	$-0.337716\pi$
$751$	2.05672e50	0.976060	0.488030	+	0.872827i	$0.337716\pi$
$752$	−4.11419e49	−0.190753
$753$	2.55467e49	0.115724
$754$	9.26136e49	0.409898
$755$	4.00159e50	1.73046
$756$	1.60099e50	0.676482
$757$	−1.91499e49	−0.0790657	−0.0395328	−	0.999218i	$-0.512587\pi$
$757$	−1.91499e49	−0.0790657	−0.0395328	+	0.999218i	$0.512587\pi$
$758$	−3.38032e49	−0.136379
$759$	5.77624e49	0.227727
$760$	6.45512e49	0.248695
$761$	−4.27936e50	−1.61119	−0.805595	−	0.592466i	$-0.798154\pi$
$761$	−4.27936e50	−1.61119	−0.805595	+	0.592466i	$0.798154\pi$
$762$	5.85428e49	0.215408
$763$	3.16187e50	1.13701
$764$	2.66040e50	0.935002
$765$	−4.05431e50	−1.39265
$766$	−3.31941e50	−1.11444
$767$	2.26131e50	0.742063
$768$	1.39322e49	0.0446888
$769$	5.09724e50	1.59818	0.799088	−	0.601214i	$-0.205316\pi$
$769$	5.09724e50	1.59818	0.799088	+	0.601214i	$0.205316\pi$
$770$	2.14957e50	0.658815
$771$	3.78938e50	1.13532
$772$	8.27708e49	0.242423
$773$	−4.89690e50	−1.40210	−0.701052	−	0.713110i	$-0.747286\pi$
$773$	−4.89690e50	−1.40210	−0.701052	+	0.713110i	$0.747286\pi$
$774$	4.82341e49	0.135017
$775$	−9.88539e50	−2.70529
$776$	−1.48233e50	−0.396612
$777$	−3.76620e50	−0.985227
$778$	3.92456e50	1.00380
$779$	1.18955e50	0.297492
$780$	−9.55478e49	−0.233650
$781$	−6.08728e49	−0.145556
$782$	−3.74393e50	−0.875406
$783$	−6.87124e50	−1.57110
$784$	6.88126e49	0.153864
$785$	9.16924e50	2.00500
$786$	7.61007e49	0.162740
$787$	−2.57689e50	−0.538937	−0.269469	−	0.963009i	$-0.586848\pi$
$787$	−2.57689e50	−0.538937	−0.269469	+	0.963009i	$0.586848\pi$
$788$	2.82839e50	0.578535
$789$	1.95138e50	0.390386
$790$	1.91304e50	0.374326
$791$	−2.78761e49	−0.0533511
$792$	−4.06638e49	−0.0761233
$793$	1.12195e50	0.205444
$794$	−6.36574e50	−1.14022
$795$	7.45203e49	0.130572
$796$	−3.73870e50	−0.640829
$797$	−9.90388e49	−0.166068	−0.0830338	−	0.996547i	$-0.526461\pi$
$797$	−9.90388e49	−0.166068	−0.0830338	+	0.996547i	$0.526461\pi$
$798$	1.65601e50	0.271651
$799$	8.14159e50	1.30659
$800$	1.99157e50	0.312694
$801$	2.94178e50	0.451899
$802$	3.98830e50	0.599426
$803$	−1.78373e50	−0.262305
$804$	−2.86694e50	−0.412513
$805$	1.08603e51	1.52903
$806$	−3.08314e50	−0.424747
$807$	−1.79662e50	−0.242198
$808$	4.46126e49	0.0588516
$809$	−5.00297e50	−0.645845	−0.322923	−	0.946425i	$-0.604665\pi$
$809$	−5.00297e50	−0.645845	−0.322923	+	0.946425i	$0.604665\pi$
$810$	2.53689e50	0.320490
$811$	6.27960e50	0.776367	0.388183	−	0.921582i	$-0.373103\pi$
$811$	6.27960e50	0.776367	0.388183	+	0.921582i	$0.373103\pi$
$812$	−7.75200e50	−0.937957
$813$	−6.81230e50	−0.806695
$814$	2.91381e50	0.337703
$815$	−8.29950e50	−0.941442
$816$	−2.75705e50	−0.306102
$817$	1.51973e50	0.165151
$818$	1.90282e50	0.202402
$819$	2.34328e50	0.243981
$820$	5.74485e50	0.585513
$821$	1.97304e50	0.196848	0.0984241	−	0.995145i	$-0.468620\pi$
$821$	1.97304e50	0.196848	0.0984241	+	0.995145i	$0.468620\pi$
$822$	−3.76542e50	−0.367753
$823$	−4.17931e50	−0.399584	−0.199792	−	0.979838i	$-0.564027\pi$
$823$	−4.17931e50	−0.399584	−0.199792	+	0.979838i	$0.564027\pi$
$824$	2.74071e50	0.256530
$825$	6.08047e50	0.557177
$826$	−1.89277e51	−1.69804
$827$	8.79074e50	0.772110	0.386055	−	0.922476i	$-0.373838\pi$
$827$	8.79074e50	0.772110	0.386055	+	0.922476i	$0.373838\pi$
$828$	−2.05447e50	−0.176673
$829$	−1.26305e51	−1.06345	−0.531725	−	0.846917i	$-0.678456\pi$
$829$	−1.26305e51	−1.06345	−0.531725	+	0.846917i	$0.678456\pi$
$830$	1.78724e51	1.47339
$831$	−8.52819e50	−0.688397
$832$	6.21146e49	0.0490948
$833$	−1.36174e51	−1.05391
$834$	3.41835e50	0.259066
$835$	−3.23083e51	−2.39773
$836$	−1.28121e50	−0.0931130
$837$	2.28746e51	1.62801
$838$	7.87491e50	0.548877
$839$	−1.16482e51	−0.795106	−0.397553	−	0.917579i	$-0.630141\pi$
$839$	−1.16482e51	−0.795106	−0.397553	+	0.917579i	$0.630141\pi$
$840$	7.99760e50	0.534653
$841$	1.79974e51	1.17837
$842$	2.02615e51	1.29930
$843$	9.64692e50	0.605907
$844$	3.38426e50	0.208196
$845$	2.33550e51	1.40730
$846$	4.46768e50	0.263694
$847$	1.77176e51	1.02434
$848$	−4.84449e49	−0.0274360
$849$	−1.33170e51	−0.738791
$850$	−3.94112e51	−2.14185
$851$	1.47215e51	0.783766
$852$	−2.26481e50	−0.118124
$853$	−6.89209e50	−0.352162	−0.176081	−	0.984376i	$-0.556342\pi$
$853$	−6.89209e50	−0.352162	−0.176081	+	0.984376i	$0.556342\pi$
$854$	−9.39105e50	−0.470112
$855$	−7.00973e50	−0.343791
$856$	−4.14040e50	−0.198954
$857$	−2.11545e51	−0.995952	−0.497976	−	0.867191i	$-0.665923\pi$
$857$	−2.11545e51	−0.995952	−0.497976	+	0.867191i	$0.665923\pi$
$858$	1.89643e50	0.0874800
$859$	1.05851e51	0.478428	0.239214	−	0.970967i	$-0.423110\pi$
$859$	1.05851e51	0.478428	0.239214	+	0.970967i	$0.423110\pi$
$860$	7.33945e50	0.325043
$861$	1.47379e51	0.639560
$862$	−1.20307e51	−0.511580
$863$	−4.37424e51	−1.82269	−0.911347	−	0.411639i	$-0.864956\pi$
$863$	−4.37424e51	−1.82269	−0.911347	+	0.411639i	$0.864956\pi$
$864$	−4.60845e50	−0.188176
$865$	−2.72630e51	−1.09092
$866$	2.12143e50	0.0831889
$867$	3.59534e51	1.38167
$868$	2.58067e51	0.971934
$869$	−3.79700e50	−0.140150
$870$	−3.43247e51	−1.24171
$871$	−1.27818e51	−0.453184
$872$	−9.10144e50	−0.316280
$873$	1.60969e51	0.548269
$874$	−6.47309e50	−0.216103
$875$	4.96924e51	1.62611
$876$	−6.63647e50	−0.212870
$877$	−2.39914e51	−0.754334	−0.377167	−	0.926145i	$-0.623102\pi$
$877$	−2.39914e51	−0.754334	−0.377167	+	0.926145i	$0.623102\pi$
$878$	4.24033e51	1.30691
$879$	2.22131e51	0.671124
$880$	−6.18753e50	−0.183261
$881$	3.95100e51	1.14717	0.573585	−	0.819146i	$-0.305552\pi$
$881$	3.95100e51	1.14717	0.573585	+	0.819146i	$0.305552\pi$
$882$	−7.47249e50	−0.212699
$883$	2.60490e51	0.726906	0.363453	−	0.931613i	$-0.381598\pi$
$883$	2.60490e51	0.726906	0.363453	+	0.931613i	$0.381598\pi$
$884$	−1.22919e51	−0.336282
$885$	−8.38092e51	−2.24794
$886$	2.31738e51	0.609406
$887$	−1.14555e50	−0.0295359	−0.0147680	−	0.999891i	$-0.504701\pi$
$887$	−1.14555e50	−0.0295359	−0.0147680	+	0.999891i	$0.504701\pi$
$888$	1.08410e51	0.274059
$889$	−2.18467e51	−0.541509
$890$	4.47630e51	1.08791
$891$	−5.03521e50	−0.119993
$892$	−1.40215e51	−0.327650
$893$	1.40765e51	0.322547
$894$	9.53664e50	0.214284
$895$	4.74070e51	1.04457
$896$	−5.19915e50	−0.112342
$897$	9.58138e50	0.203030
$898$	1.93509e51	0.402129
$899$	−1.10759e52	−2.25728
$900$	−2.16268e51	−0.432263
$901$	9.58678e50	0.187927
$902$	−1.14024e51	−0.219220
$903$	1.88287e51	0.355047
$904$	8.02413e49	0.0148406
$905$	−4.87754e51	−0.884811
$906$	−2.95500e51	−0.525791
$907$	−6.78274e50	−0.118380	−0.0591899	−	0.998247i	$-0.518852\pi$
$907$	−6.78274e50	−0.118380	−0.0591899	+	0.998247i	$0.518852\pi$
$908$	3.33856e51	0.571553
$909$	−4.84456e50	−0.0813554
$910$	3.56561e51	0.587367
$911$	1.67446e51	0.270584	0.135292	−	0.990806i	$-0.456803\pi$
$911$	1.67446e51	0.270584	0.135292	+	0.990806i	$0.456803\pi$
$912$	−4.76682e50	−0.0755647
$913$	−3.54731e51	−0.551646
$914$	−7.87625e51	−1.20160
$915$	−4.15822e51	−0.622355
$916$	1.63740e51	0.240427
$917$	−2.83989e51	−0.409108
$918$	9.11967e51	1.28894
$919$	9.04719e51	1.25456	0.627281	−	0.778793i	$-0.284168\pi$
$919$	9.04719e51	1.25456	0.627281	+	0.778793i	$0.284168\pi$
$920$	−3.12614e51	−0.425326
$921$	1.01849e52	1.35960
$922$	−8.29882e51	−1.08699
$923$	−1.00973e51	−0.129771
$924$	−1.58736e51	−0.200178
$925$	1.54969e52	1.91763
$926$	−1.10399e52	−1.34052
$927$	−2.97619e51	−0.354622
$928$	2.23141e51	0.260910
$929$	−2.19935e51	−0.252359	−0.126180	−	0.992007i	$-0.540272\pi$
$929$	−2.19935e51	−0.252359	−0.126180	+	0.992007i	$0.540272\pi$
$930$	1.14268e52	1.28669
$931$	−2.35438e51	−0.260170
$932$	−4.18784e51	−0.454163
$933$	−9.44104e50	−0.100483
$934$	−7.08016e51	−0.739558
$935$	1.22445e52	1.25528
$936$	−6.74514e50	−0.0678678
$937$	1.62026e52	1.60008	0.800041	−	0.599945i	$-0.204811\pi$
$937$	1.62026e52	1.60008	0.800041	+	0.599945i	$0.204811\pi$
$938$	1.06987e52	1.03701
$939$	−7.84229e51	−0.746097
$940$	6.79815e51	0.634824
$941$	−1.96636e51	−0.180237	−0.0901186	−	0.995931i	$-0.528725\pi$
$941$	−1.96636e51	−0.180237	−0.0901186	+	0.995931i	$0.528725\pi$
$942$	−6.77107e51	−0.609210
$943$	−5.76084e51	−0.508782
$944$	5.44835e51	0.472341
$945$	−2.64542e52	−2.25132
$946$	−1.45673e51	−0.121698
$947$	−7.17568e51	−0.588489	−0.294244	−	0.955730i	$-0.595068\pi$
$947$	−7.17568e51	−0.588489	−0.294244	+	0.955730i	$0.595068\pi$
$948$	−1.41270e51	−0.113737
$949$	−2.95877e51	−0.233858
$950$	−6.81402e51	−0.528738
$951$	−5.07838e51	−0.386871
$952$	1.02886e52	0.769504
$953$	1.57698e52	1.15798	0.578991	−	0.815334i	$-0.303447\pi$
$953$	1.57698e52	1.15798	0.578991	+	0.815334i	$0.303447\pi$
$954$	5.26072e50	0.0379270
$955$	−4.39595e52	−3.11167
$956$	−2.51876e51	−0.175055
$957$	6.81275e51	0.464904
$958$	2.81606e51	0.188689
$959$	1.40516e52	0.924486
$960$	−2.30211e51	−0.148723
$961$	2.11084e52	1.33905
$962$	4.83331e51	0.301079
$963$	4.49614e51	0.275030
$964$	−3.84931e51	−0.231225
$965$	−1.36768e52	−0.806781
$966$	−8.01986e51	−0.464587
$967$	−1.33548e51	−0.0759755	−0.0379878	−	0.999278i	$-0.512095\pi$
$967$	−1.33548e51	−0.0759755	−0.0379878	+	0.999278i	$0.512095\pi$
$968$	−5.10001e51	−0.284939
$969$	9.43308e51	0.517592
$970$	2.44936e52	1.31992
$971$	2.61448e52	1.38372	0.691861	−	0.722031i	$-0.256791\pi$
$971$	2.61448e52	1.38372	0.691861	+	0.722031i	$0.256791\pi$
$972$	8.36588e51	0.434863
$973$	−1.27564e52	−0.651260
$974$	1.64437e52	0.824552
$975$	1.00860e52	0.496751
$976$	2.70321e51	0.130770
$977$	9.78014e51	0.464719	0.232359	−	0.972630i	$-0.425355\pi$
$977$	9.78014e51	0.464719	0.232359	+	0.972630i	$0.425355\pi$
$978$	6.12881e51	0.286053
$979$	−8.88454e51	−0.407322
$980$	−1.13704e52	−0.512057
$981$	9.88342e51	0.437220
$982$	−2.47473e52	−1.07541
$983$	−1.35974e52	−0.580454	−0.290227	−	0.956958i	$-0.593731\pi$
$983$	−1.35974e52	−0.580454	−0.290227	+	0.956958i	$0.593731\pi$
$984$	−4.24231e51	−0.177905
$985$	−4.67353e52	−1.92535
$986$	−4.41575e52	−1.78714
$987$	1.74401e52	0.693423
$988$	−2.12521e51	−0.0830149
$989$	−7.35988e51	−0.282446
$990$	6.71915e51	0.253337
$991$	2.83806e52	1.05131	0.525656	−	0.850697i	$-0.323820\pi$
$991$	2.83806e52	1.05131	0.525656	+	0.850697i	$0.323820\pi$
$992$	−7.42846e51	−0.270361
$993$	2.33407e51	0.0834644
$994$	8.45171e51	0.296950
$995$	6.17770e52	2.13267
$996$	−1.31980e52	−0.447682
$997$	1.05150e52	0.350463	0.175232	−	0.984527i	$-0.443933\pi$
$997$	1.05150e52	0.350463	0.175232	+	0.984527i	$0.443933\pi$
$998$	1.27747e52	0.418374
$999$	−3.58596e52	−1.15401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.36.a.b.1.1	✓	1
3.2	odd	2		18.36.a.b.1.1		1
4.3	odd	2		16.36.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.36.a.b.1.1	✓	1	1.1	even	1	trivial
16.36.a.a.1.1		1	4.3	odd	2
18.36.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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