LMFDB - Embedded newform 3.20.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,20,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	3.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:	$6.86450089669$
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	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1104.00 q^{2} +19683.0 q^{3} +694528. q^{4} +3.51627e6 q^{5} -2.17300e7 q^{6} -1.95591e8 q^{7} -1.87945e8 q^{8} +3.87420e8 q^{9} +O(q^{10})$

\(q-1104.00 q^{2} +19683.0 q^{3} +694528. q^{4} +3.51627e6 q^{5} -2.17300e7 q^{6} -1.95591e8 q^{7} -1.87945e8 q^{8} +3.87420e8 q^{9} -3.88196e9 q^{10} -2.74686e9 q^{11} +1.36704e10 q^{12} -4.44004e10 q^{13} +2.15932e11 q^{14} +6.92107e10 q^{15} -1.56641e11 q^{16} -7.85983e11 q^{17} -4.27712e11 q^{18} +3.15410e11 q^{19} +2.44215e12 q^{20} -3.84981e12 q^{21} +3.03253e12 q^{22} +4.90056e12 q^{23} -3.69932e12 q^{24} -6.70933e12 q^{25} +4.90181e13 q^{26} +7.62560e12 q^{27} -1.35843e14 q^{28} +1.21885e13 q^{29} -7.64087e13 q^{30} -4.27137e13 q^{31} +2.71469e14 q^{32} -5.40664e13 q^{33} +8.67725e14 q^{34} -6.87749e14 q^{35} +2.69074e14 q^{36} -4.23452e14 q^{37} -3.48213e14 q^{38} -8.73934e14 q^{39} -6.60865e14 q^{40} -1.11392e15 q^{41} +4.25019e15 q^{42} +1.13610e15 q^{43} -1.90777e15 q^{44} +1.36228e15 q^{45} -5.41022e15 q^{46} +1.53137e15 q^{47} -3.08317e15 q^{48} +2.68568e16 q^{49} +7.40710e15 q^{50} -1.54705e16 q^{51} -3.08374e16 q^{52} -1.80593e16 q^{53} -8.41866e15 q^{54} -9.65869e15 q^{55} +3.67603e16 q^{56} +6.20822e15 q^{57} -1.34561e16 q^{58} +9.27004e16 q^{59} +4.80688e16 q^{60} +2.13530e16 q^{61} +4.71559e16 q^{62} -7.57758e16 q^{63} -2.17577e17 q^{64} -1.56124e17 q^{65} +5.96893e16 q^{66} +2.68065e17 q^{67} -5.45887e17 q^{68} +9.64577e16 q^{69} +7.59275e17 q^{70} -1.13274e17 q^{71} -7.28137e16 q^{72} -5.45956e17 q^{73} +4.67491e17 q^{74} -1.32060e17 q^{75} +2.19061e17 q^{76} +5.37260e17 q^{77} +9.64823e17 q^{78} -1.80761e18 q^{79} -5.50794e17 q^{80} +1.50095e17 q^{81} +1.22977e18 q^{82} +1.46996e18 q^{83} -2.67380e18 q^{84} -2.76373e18 q^{85} -1.25425e18 q^{86} +2.39907e17 q^{87} +5.16258e17 q^{88} +2.97404e18 q^{89} -1.50395e18 q^{90} +8.68431e18 q^{91} +3.40358e18 q^{92} -8.40733e17 q^{93} -1.69063e18 q^{94} +1.10907e18 q^{95} +5.34333e18 q^{96} -6.92569e18 q^{97} -2.96499e19 q^{98} -1.06419e18 q^{99} +O(q^{100})\)

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 $

$2$	−1104.00	−1.52470	−0.762349	−	0.647166i	$-0.775954\pi$
$2$	−1104.00	−1.52470	−0.762349	+	0.647166i	$0.775954\pi$
$3$	19683.0	0.577350
$3$	19683.0	0.577350
$4$	694528.	1.32471
$5$	3.51627e6	0.805132	0.402566	−	0.915391i	$-0.368118\pi$
$5$	3.51627e6	0.805132	0.402566	+	0.915391i	$0.368118\pi$
$6$	−2.17300e7	−0.880285
$7$	−1.95591e8	−1.83196	−0.915981	−	0.401221i	$-0.868586\pi$
$7$	−1.95591e8	−1.83196	−0.915981	+	0.401221i	$0.868586\pi$
$8$	−1.87945e8	−0.495080
$9$	3.87420e8	0.333333
$10$	−3.88196e9	−1.22758
$11$	−2.74686e9	−0.351241	−0.175621	−	0.984458i	$-0.556193\pi$
$11$	−2.74686e9	−0.351241	−0.175621	+	0.984458i	$0.556193\pi$
$12$	1.36704e10	0.764820
$13$	−4.44004e10	−1.16125	−0.580625	−	0.814171i	$-0.697192\pi$
$13$	−4.44004e10	−1.16125	−0.580625	+	0.814171i	$0.697192\pi$
$14$	2.15932e11	2.79319
$15$	6.92107e10	0.464843
$16$	−1.56641e11	−0.569858
$17$	−7.85983e11	−1.60749	−0.803745	−	0.594974i	$-0.797162\pi$
$17$	−7.85983e11	−1.60749	−0.803745	+	0.594974i	$0.797162\pi$
$18$	−4.27712e11	−0.508233
$19$	3.15410e11	0.224242	0.112121	−	0.993695i	$-0.464236\pi$
$19$	3.15410e11	0.224242	0.112121	+	0.993695i	$0.464236\pi$
$20$	2.44215e12	1.06656
$21$	−3.84981e12	−1.05768
$22$	3.03253e12	0.535537
$23$	4.90056e12	0.567324	0.283662	−	0.958924i	$-0.408451\pi$
$23$	4.90056e12	0.567324	0.283662	+	0.958924i	$0.408451\pi$
$24$	−3.69932e12	−0.285835
$25$	−6.70933e12	−0.351762
$26$	4.90181e13	1.77056
$27$	7.62560e12	0.192450
$28$	−1.35843e14	−2.42681
$29$	1.21885e13	0.156016	0.0780082	−	0.996953i	$-0.475144\pi$
$29$	1.21885e13	0.156016	0.0780082	+	0.996953i	$0.475144\pi$
$30$	−7.64087e13	−0.708746
$31$	−4.27137e13	−0.290155	−0.145078	−	0.989420i	$-0.546343\pi$
$31$	−4.27137e13	−0.290155	−0.145078	+	0.989420i	$0.546343\pi$
$32$	2.71469e14	1.36394
$33$	−5.40664e13	−0.202789
$34$	8.67725e14	2.45094
$35$	−6.87749e14	−1.47497
$36$	2.69074e14	0.441569
$37$	−4.23452e14	−0.535659	−0.267829	−	0.963466i	$-0.586306\pi$
$37$	−4.23452e14	−0.535659	−0.267829	+	0.963466i	$0.586306\pi$
$38$	−3.48213e14	−0.341901
$39$	−8.73934e14	−0.670448
$40$	−6.60865e14	−0.398605
$41$	−1.11392e15	−0.531383	−0.265691	−	0.964058i	$-0.585600\pi$
$41$	−1.11392e15	−0.531383	−0.265691	+	0.964058i	$0.585600\pi$
$42$	4.25019e15	1.61265
$43$	1.13610e15	0.344720	0.172360	−	0.985034i	$-0.444861\pi$
$43$	1.13610e15	0.344720	0.172360	+	0.985034i	$0.444861\pi$
$44$	−1.90777e15	−0.465292
$45$	1.36228e15	0.268377
$46$	−5.41022e15	−0.864999
$47$	1.53137e15	0.199596	0.0997978	−	0.995008i	$-0.468180\pi$
$47$	1.53137e15	0.199596	0.0997978	+	0.995008i	$0.468180\pi$
$48$	−3.08317e15	−0.329008
$49$	2.68568e16	2.35609
$50$	7.40710e15	0.536331
$51$	−1.54705e16	−0.928084
$52$	−3.08374e16	−1.53832
$53$	−1.80593e16	−0.751762	−0.375881	−	0.926668i	$-0.622660\pi$
$53$	−1.80593e16	−0.751762	−0.375881	+	0.926668i	$0.622660\pi$
$54$	−8.41866e15	−0.293428
$55$	−9.65869e15	−0.282796
$56$	3.67603e16	0.906969
$57$	6.20822e15	0.129466
$58$	−1.34561e16	−0.237878
$59$	9.27004e16	1.39312	0.696559	−	0.717500i	$-0.254714\pi$
$59$	9.27004e16	1.39312	0.696559	+	0.717500i	$0.254714\pi$
$60$	4.80688e16	0.615781
$61$	2.13530e16	0.233789	0.116895	−	0.993144i	$-0.462706\pi$
$61$	2.13530e16	0.233789	0.116895	+	0.993144i	$0.462706\pi$
$62$	4.71559e16	0.442400
$63$	−7.57758e16	−0.610654
$64$	−2.17577e17	−1.50974
$65$	−1.56124e17	−0.934959
$66$	5.96893e16	0.309193
$67$	2.68065e17	1.20373	0.601866	−	0.798597i	$-0.294424\pi$
$67$	2.68065e17	1.20373	0.601866	+	0.798597i	$0.294424\pi$
$68$	−5.45887e17	−2.12945
$69$	9.64577e16	0.327545
$70$	7.59275e17	2.24889
$71$	−1.13274e17	−0.293207	−0.146603	−	0.989195i	$-0.546834\pi$
$71$	−1.13274e17	−0.293207	−0.146603	+	0.989195i	$0.546834\pi$
$72$	−7.28137e16	−0.165027
$73$	−5.45956e17	−1.08540	−0.542701	−	0.839926i	$-0.682598\pi$
$73$	−5.45956e17	−1.08540	−0.542701	+	0.839926i	$0.682598\pi$
$74$	4.67491e17	0.816718
$75$	−1.32060e17	−0.203090
$76$	2.19061e17	0.297055
$77$	5.37260e17	0.643461
$78$	9.64823e17	1.02223
$79$	−1.80761e18	−1.69687	−0.848433	−	0.529303i	$-0.822453\pi$
$79$	−1.80761e18	−1.69687	−0.848433	+	0.529303i	$0.822453\pi$
$80$	−5.50794e17	−0.458811
$81$	1.50095e17	0.111111
$82$	1.22977e18	0.810199
$83$	1.46996e18	0.863104	0.431552	−	0.902088i	$-0.357966\pi$
$83$	1.46996e18	0.863104	0.431552	+	0.902088i	$0.357966\pi$
$84$	−2.67380e18	−1.40112
$85$	−2.76373e18	−1.29424
$86$	−1.25425e18	−0.525594
$87$	2.39907e17	0.0900761
$88$	5.16258e17	0.173893
$89$	2.97404e18	0.899791	0.449896	−	0.893081i	$-0.351461\pi$
$89$	2.97404e18	0.899791	0.449896	+	0.893081i	$0.351461\pi$
$90$	−1.50395e18	−0.409195
$91$	8.68431e18	2.12737
$92$	3.40358e18	0.751538
$93$	−8.40733e17	−0.167521
$94$	−1.69063e18	−0.304323
$95$	1.10907e18	0.180544
$96$	5.34333e18	0.787473
$97$	−6.92569e18	−0.924978	−0.462489	−	0.886625i	$-0.653043\pi$
$97$	−6.92569e18	−0.924978	−0.462489	+	0.886625i	$0.653043\pi$
$98$	−2.96499e19	−3.59232
$99$	−1.06419e18	−0.117080
$100$	−4.65982e18	−0.465982
$101$	1.78746e19	1.62623	0.813117	−	0.582100i	$-0.197769\pi$
$101$	1.78746e19	1.62623	0.813117	+	0.582100i	$0.197769\pi$
$102$	1.70794e19	1.41505
$103$	−7.05681e18	−0.532911	−0.266456	−	0.963847i	$-0.585853\pi$
$103$	−7.05681e18	−0.532911	−0.266456	+	0.963847i	$0.585853\pi$
$104$	8.34484e18	0.574912
$105$	−1.35370e19	−0.851575
$106$	1.99375e19	1.14621
$107$	−1.77197e19	−0.931772	−0.465886	−	0.884845i	$-0.654264\pi$
$107$	−1.77197e19	−0.931772	−0.465886	+	0.884845i	$0.654264\pi$
$108$	5.29619e18	0.254940
$109$	8.11766e18	0.357997	0.178998	−	0.983849i	$-0.442714\pi$
$109$	8.11766e18	0.357997	0.178998	+	0.983849i	$0.442714\pi$
$110$	1.06632e19	0.431178
$111$	−8.33481e18	−0.309263
$112$	3.06376e19	1.04396
$113$	−4.38285e19	−1.37250	−0.686249	−	0.727367i	$-0.740744\pi$
$113$	−4.38285e19	−1.37250	−0.686249	+	0.727367i	$0.740744\pi$
$114$	−6.85388e18	−0.197397
$115$	1.72317e19	0.456771
$116$	8.46527e18	0.206676
$117$	−1.72016e19	−0.387083
$118$	−1.02341e20	−2.12408
$119$	1.53731e20	2.94486
$120$	−1.30078e19	−0.230135
$121$	−5.36139e19	−0.876629
$122$	−2.35737e19	−0.356458
$123$	−2.19253e19	−0.306794
$124$	−2.96658e19	−0.384371
$125$	−9.06593e19	−1.08835
$126$	8.36565e19	0.931064
$127$	2.94833e19	0.304398	0.152199	−	0.988350i	$-0.451365\pi$
$127$	2.94833e19	0.304398	0.152199	+	0.988350i	$0.451365\pi$
$128$	9.78769e19	0.937962
$129$	2.23619e19	0.199024
$130$	1.72361e20	1.42553
$131$	1.29096e20	0.992738	0.496369	−	0.868112i	$-0.334666\pi$
$131$	1.29096e20	0.992738	0.496369	+	0.868112i	$0.334666\pi$
$132$	−3.75506e19	−0.268636
$133$	−6.16913e19	−0.410803
$134$	−2.95944e20	−1.83533
$135$	2.68137e19	0.154948
$136$	1.47721e20	0.795837
$137$	−1.15732e20	−0.581576	−0.290788	−	0.956788i	$-0.593917\pi$
$137$	−1.15732e20	−0.581576	−0.290788	+	0.956788i	$0.593917\pi$
$138$	−1.06489e20	−0.499407
$139$	−5.77640e19	−0.252939	−0.126470	−	0.991970i	$-0.540365\pi$
$139$	−5.77640e19	−0.252939	−0.126470	+	0.991970i	$0.540365\pi$
$140$	−4.77661e20	−1.95391
$141$	3.01420e19	0.115237
$142$	1.25054e20	0.447052
$143$	1.21962e20	0.407879
$144$	−6.06861e19	−0.189953
$145$	4.28581e19	0.125614
$146$	6.02736e20	1.65491
$147$	5.28622e20	1.36029
$148$	−2.94100e20	−0.709591
$149$	9.58388e19	0.216906	0.108453	−	0.994102i	$-0.465410\pi$
$149$	9.58388e19	0.216906	0.108453	+	0.994102i	$0.465410\pi$
$150$	1.45794e20	0.309651
$151$	1.32704e20	0.264608	0.132304	−	0.991209i	$-0.457763\pi$
$151$	1.32704e20	0.264608	0.132304	+	0.991209i	$0.457763\pi$
$152$	−5.92798e19	−0.111018
$153$	−3.04506e20	−0.535830
$154$	−5.93135e20	−0.981084
$155$	−1.50193e20	−0.233613
$156$	−6.06972e20	−0.888147
$157$	−9.90999e20	−1.36467	−0.682333	−	0.731041i	$-0.739035\pi$
$157$	−9.90999e20	−1.36467	−0.682333	+	0.731041i	$0.739035\pi$
$158$	1.99560e21	2.58721
$159$	−3.55462e20	−0.434030
$160$	9.54560e20	1.09815
$161$	−9.58503e20	−1.03932
$162$	−1.65704e20	−0.169411
$163$	1.74144e21	1.67929	0.839647	−	0.543133i	$-0.182762\pi$
$163$	1.74144e21	1.67929	0.839647	+	0.543133i	$0.182762\pi$
$164$	−7.73649e20	−0.703927
$165$	−1.90112e20	−0.163272
$166$	−1.62283e21	−1.31597
$167$	−2.34167e21	−1.79357	−0.896785	−	0.442466i	$-0.854104\pi$
$167$	−2.34167e21	−1.79357	−0.896785	+	0.442466i	$0.854104\pi$
$168$	7.23552e20	0.523639
$169$	5.09479e20	0.348500
$170$	3.05115e21	1.97333
$171$	1.22196e20	0.0747473
$172$	7.89053e20	0.456653
$173$	−5.36374e20	−0.293785	−0.146892	−	0.989152i	$-0.546927\pi$
$173$	−5.36374e20	−0.293785	−0.146892	+	0.989152i	$0.546927\pi$
$174$	−2.64857e20	−0.137339
$175$	1.31228e21	0.644415
$176$	4.30272e20	0.200158
$177$	1.82462e21	0.804317
$178$	−3.28334e21	−1.37191
$179$	3.33179e21	1.32000	0.660000	−	0.751266i	$-0.270556\pi$
$179$	3.33179e21	1.32000	0.660000	+	0.751266i	$0.270556\pi$
$180$	9.46138e20	0.355521
$181$	−3.97005e20	−0.141530	−0.0707652	−	0.997493i	$-0.522544\pi$
$181$	−3.97005e20	−0.141530	−0.0707652	+	0.997493i	$0.522544\pi$
$182$	−9.58748e21	−3.24359
$183$	4.20290e20	0.134978
$184$	−9.21036e20	−0.280871
$185$	−1.48897e21	−0.431276
$186$	9.28169e20	0.255420
$187$	2.15898e21	0.564617
$188$	1.06358e21	0.264406
$189$	−1.49150e21	−0.352561
$190$	−1.22441e21	−0.275276
$191$	1.18297e20	0.0253022	0.0126511	−	0.999920i	$-0.495973\pi$
$191$	1.18297e20	0.0253022	0.0126511	+	0.999920i	$0.495973\pi$
$192$	−4.28257e21	−0.871651
$193$	3.76434e21	0.729281	0.364640	−	0.931148i	$-0.381192\pi$
$193$	3.76434e21	0.729281	0.364640	+	0.931148i	$0.381192\pi$
$194$	7.64596e21	1.41031
$195$	−3.07299e21	−0.539799
$196$	1.86528e22	3.12112
$197$	4.37987e21	0.698283	0.349142	−	0.937070i	$-0.386473\pi$
$197$	4.37987e21	0.698283	0.349142	+	0.937070i	$0.386473\pi$
$198$	1.17486e21	0.178512
$199$	−1.32104e22	−1.91343	−0.956715	−	0.291025i	$-0.906004\pi$
$199$	−1.32104e22	−1.91343	−0.956715	+	0.291025i	$0.906004\pi$
$200$	1.26099e21	0.174151
$201$	5.27632e21	0.694975
$202$	−1.97335e22	−2.47952
$203$	−2.38396e21	−0.285816
$204$	−1.07447e22	−1.22944
$205$	−3.91685e21	−0.427834
$206$	7.79072e21	0.812530
$207$	1.89858e21	0.189108
$208$	6.95495e21	0.661748
$209$	−8.66388e20	−0.0787631
$210$	1.49448e22	1.29840
$211$	−1.55480e22	−1.29120	−0.645598	−	0.763678i	$-0.723392\pi$
$211$	−1.55480e22	−1.29120	−0.645598	+	0.763678i	$0.723392\pi$
$212$	−1.25427e22	−0.995865
$213$	−2.22956e21	−0.169283
$214$	1.95625e22	1.42067
$215$	3.99484e21	0.277545
$216$	−1.43319e21	−0.0952783
$217$	8.35439e21	0.531554
$218$	−8.96190e21	−0.545837
$219$	−1.07461e22	−0.626657
$220$	−6.70823e21	−0.374622
$221$	3.48980e22	1.86670
$222$	9.20163e21	0.471533
$223$	−1.04802e21	−0.0514602	−0.0257301	−	0.999669i	$-0.508191\pi$
$223$	−1.04802e21	−0.0514602	−0.0257301	+	0.999669i	$0.508191\pi$
$224$	−5.30969e22	−2.49869
$225$	−2.59933e21	−0.117254
$226$	4.83867e22	2.09265
$227$	−4.90340e21	−0.203354	−0.101677	−	0.994817i	$-0.532421\pi$
$227$	−4.90340e21	−0.203354	−0.101677	+	0.994817i	$0.532421\pi$
$228$	4.31179e21	0.171505
$229$	1.69013e22	0.644885	0.322443	−	0.946589i	$-0.395496\pi$
$229$	1.69013e22	0.644885	0.322443	+	0.946589i	$0.395496\pi$
$230$	−1.90238e22	−0.696438
$231$	1.05749e22	0.371502
$232$	−2.29077e21	−0.0772406
$233$	−2.94863e22	−0.954418	−0.477209	−	0.878790i	$-0.658352\pi$
$233$	−2.94863e22	−0.954418	−0.477209	+	0.878790i	$0.658352\pi$
$234$	1.89906e22	0.590185
$235$	5.38472e21	0.160701
$236$	6.43831e22	1.84547
$237$	−3.55792e22	−0.979686
$238$	−1.69719e23	−4.49003
$239$	−3.48672e22	−0.886415	−0.443208	−	0.896419i	$-0.646160\pi$
$239$	−3.48672e22	−0.886415	−0.443208	+	0.896419i	$0.646160\pi$
$240$	−1.08413e22	−0.264895
$241$	3.10412e22	0.729083	0.364542	−	0.931187i	$-0.381226\pi$
$241$	3.10412e22	0.729083	0.364542	+	0.931187i	$0.381226\pi$
$242$	5.91897e22	1.33660
$243$	2.95431e21	0.0641500
$244$	1.48302e22	0.309702
$245$	9.44357e22	1.89696
$246$	2.42055e22	0.467769
$247$	−1.40044e22	−0.260401
$248$	8.02782e21	0.143650
$249$	2.89332e22	0.498313
$250$	1.00088e23	1.65940
$251$	2.43352e21	0.0388449	0.0194224	−	0.999811i	$-0.493817\pi$
$251$	2.43352e21	0.0388449	0.0194224	+	0.999811i	$0.493817\pi$
$252$	−5.26284e22	−0.808938
$253$	−1.34611e22	−0.199268
$254$	−3.25496e22	−0.464115
$255$	−5.43984e22	−0.747231
$256$	6.01696e21	0.0796338
$257$	−7.09300e22	−0.904618	−0.452309	−	0.891861i	$-0.649400\pi$
$257$	−7.09300e22	−0.904618	−0.452309	+	0.891861i	$0.649400\pi$
$258$	−2.46875e22	−0.303452
$259$	8.28233e22	0.981307
$260$	−1.08432e23	−1.23855
$261$	4.72208e21	0.0520054
$262$	−1.42522e23	−1.51363
$263$	8.10179e22	0.829854	0.414927	−	0.909855i	$-0.363807\pi$
$263$	8.10179e22	0.829854	0.414927	+	0.909855i	$0.363807\pi$
$264$	1.01615e22	0.100397
$265$	−6.35014e22	−0.605268
$266$	6.81072e22	0.626351
$267$	5.85380e22	0.519495
$268$	1.86179e23	1.59459
$269$	−2.10267e23	−1.73830	−0.869150	−	0.494549i	$-0.835333\pi$
$269$	−2.10267e23	−1.73830	−0.869150	+	0.494549i	$0.835333\pi$
$270$	−2.96023e22	−0.236249
$271$	−9.67500e22	−0.745491	−0.372746	−	0.927934i	$-0.621584\pi$
$271$	−9.67500e22	−0.745491	−0.372746	+	0.927934i	$0.621584\pi$
$272$	1.23117e23	0.916041
$273$	1.70933e23	1.22823
$274$	1.27768e23	0.886728
$275$	1.84296e22	0.123553
$276$	6.69926e22	0.433901
$277$	−1.50223e23	−0.940112	−0.470056	−	0.882637i	$-0.655766\pi$
$277$	−1.50223e23	−0.940112	−0.470056	+	0.882637i	$0.655766\pi$
$278$	6.37714e22	0.385656
$279$	−1.65481e22	−0.0967185
$280$	1.29259e23	0.730230
$281$	−2.78843e23	−1.52282	−0.761412	−	0.648268i	$-0.775494\pi$
$281$	−2.78843e23	−1.52282	−0.761412	+	0.648268i	$0.775494\pi$
$282$	−3.32768e22	−0.175701
$283$	−9.74687e22	−0.497615	−0.248808	−	0.968553i	$-0.580039\pi$
$283$	−9.74687e22	−0.497615	−0.248808	+	0.968553i	$0.580039\pi$
$284$	−7.86716e22	−0.388413
$285$	2.18298e22	0.104237
$286$	−1.34646e23	−0.621892
$287$	2.17872e23	0.973474
$288$	1.05173e23	0.454648
$289$	3.78696e23	1.58402
$290$	−4.73154e22	−0.191523
$291$	−1.36318e23	−0.534036
$292$	−3.79182e23	−1.43784
$293$	2.78548e23	1.02249	0.511243	−	0.859436i	$-0.329185\pi$
$293$	2.78548e23	1.02249	0.511243	+	0.859436i	$0.329185\pi$
$294$	−5.83599e23	−2.07403
$295$	3.25960e23	1.12164
$296$	7.95857e22	0.265194
$297$	−2.09464e22	−0.0675964
$298$	−1.05806e23	−0.330716
$299$	−2.17587e23	−0.658805
$300$	−9.17192e22	−0.269035
$301$	−2.22211e23	−0.631514
$302$	−1.46505e23	−0.403447
$303$	3.51826e23	0.938907
$304$	−4.94064e22	−0.127786
$305$	7.50828e22	0.188231
$306$	3.36174e23	0.816979
$307$	4.84526e23	1.14157	0.570785	−	0.821099i	$-0.306639\pi$
$307$	4.84526e23	1.14157	0.570785	+	0.821099i	$0.306639\pi$
$308$	3.73142e23	0.852397
$309$	−1.38899e23	−0.307677
$310$	1.65813e23	0.356190
$311$	5.63561e23	1.17413	0.587067	−	0.809539i	$-0.300283\pi$
$311$	5.63561e23	1.17413	0.587067	+	0.809539i	$0.300283\pi$
$312$	1.64251e23	0.331926
$313$	−5.79355e23	−1.13573	−0.567863	−	0.823123i	$-0.692230\pi$
$313$	−5.79355e23	−1.13573	−0.567863	+	0.823123i	$0.692230\pi$
$314$	1.09406e24	2.08071
$315$	−2.66448e23	−0.491657
$316$	−1.25544e24	−2.24785
$317$	−1.07037e24	−1.85982	−0.929909	−	0.367791i	$-0.880114\pi$
$317$	−1.07037e24	−1.85982	−0.929909	+	0.367791i	$0.880114\pi$
$318$	3.92430e23	0.661766
$319$	−3.34801e22	−0.0547994
$320$	−7.65060e23	−1.21554
$321$	−3.48776e23	−0.537959
$322$	1.05819e24	1.58465
$323$	−2.47907e23	−0.360467
$324$	1.04245e23	0.147190
$325$	2.97897e23	0.408484
$326$	−1.92255e24	−2.56042
$327$	1.59780e23	0.206690
$328$	2.09356e23	0.263077
$329$	−2.99522e23	−0.365652
$330$	2.09884e23	0.248941
$331$	−3.07182e23	−0.354022	−0.177011	−	0.984209i	$-0.556643\pi$
$331$	−3.07182e23	−0.354022	−0.177011	+	0.984209i	$0.556643\pi$
$332$	1.02093e24	1.14336
$333$	−1.64054e23	−0.178553
$334$	2.58520e24	2.73465
$335$	9.42589e23	0.969163
$336$	6.03040e23	0.602730
$337$	1.59649e24	1.55125	0.775625	−	0.631194i	$-0.217435\pi$
$337$	1.59649e24	1.55125	0.775625	+	0.631194i	$0.217435\pi$
$338$	−5.62465e23	−0.531358
$339$	−8.62677e23	−0.792412
$340$	−1.91949e24	−1.71449
$341$	1.17328e23	0.101915
$342$	−1.34905e23	−0.113967
$343$	−3.02342e24	−2.48430
$344$	−2.13524e23	−0.170664
$345$	3.39171e23	0.263717
$346$	5.92157e23	0.447934
$347$	1.89344e24	1.39354	0.696772	−	0.717292i	$-0.254619\pi$
$347$	1.89344e24	1.39354	0.696772	+	0.717292i	$0.254619\pi$
$348$	1.66622e23	0.119324
$349$	3.19249e23	0.222478	0.111239	−	0.993794i	$-0.464518\pi$
$349$	3.19249e23	0.222478	0.111239	+	0.993794i	$0.464518\pi$
$350$	−1.44876e24	−0.982539
$351$	−3.38580e23	−0.223483
$352$	−7.45688e23	−0.479073
$353$	2.10677e24	1.31752	0.658761	−	0.752352i	$-0.271081\pi$
$353$	2.10677e24	1.31752	0.658761	+	0.752352i	$0.271081\pi$
$354$	−2.01438e24	−1.22634
$355$	−3.98300e23	−0.236070
$356$	2.06555e24	1.19196
$357$	3.02588e24	1.70022
$358$	−3.67830e24	−2.01260
$359$	−1.45227e24	−0.773836	−0.386918	−	0.922114i	$-0.626460\pi$
$359$	−1.45227e24	−0.773836	−0.386918	+	0.922114i	$0.626460\pi$
$360$	−2.56033e23	−0.132868
$361$	−1.87894e24	−0.949716
$362$	4.38294e23	0.215791
$363$	−1.05528e24	−0.506122
$364$	6.03150e24	2.81814
$365$	−1.91973e24	−0.873892
$366$	−4.64001e23	−0.205801
$367$	−3.52842e23	−0.152494	−0.0762470	−	0.997089i	$-0.524294\pi$
$367$	−3.52842e23	−0.152494	−0.0762470	+	0.997089i	$0.524294\pi$
$368$	−7.67631e23	−0.323294
$369$	−4.31556e23	−0.177128
$370$	1.64383e24	0.657566
$371$	3.53223e24	1.37720
$372$	−5.83913e23	−0.221917
$373$	3.12604e24	1.15814	0.579069	−	0.815278i	$-0.303416\pi$
$373$	3.12604e24	1.15814	0.579069	+	0.815278i	$0.303416\pi$
$374$	−2.38352e24	−0.860871
$375$	−1.78445e24	−0.628358
$376$	−2.87814e23	−0.0988159
$377$	−5.41176e23	−0.181174
$378$	1.64661e24	0.537550
$379$	5.18388e23	0.165037	0.0825187	−	0.996590i	$-0.473704\pi$
$379$	5.18388e23	0.165037	0.0825187	+	0.996590i	$0.473704\pi$
$380$	7.70279e23	0.239168
$381$	5.80321e23	0.175744
$382$	−1.30600e23	−0.0385782
$383$	2.12429e23	0.0612106	0.0306053	−	0.999532i	$-0.490257\pi$
$383$	2.12429e23	0.0612106	0.0306053	+	0.999532i	$0.490257\pi$
$384$	1.92651e24	0.541533
$385$	1.88915e24	0.518071
$386$	−4.15583e24	−1.11193
$387$	4.40149e23	0.114907
$388$	−4.81008e24	−1.22532
$389$	−4.43856e24	−1.10337	−0.551685	−	0.834053i	$-0.686015\pi$
$389$	−4.43856e24	−1.10337	−0.551685	+	0.834053i	$0.686015\pi$
$390$	3.39258e24	0.823031
$391$	−3.85175e24	−0.911968
$392$	−5.04760e24	−1.16645
$393$	2.54099e24	0.573158
$394$	−4.83537e24	−1.06467
$395$	−6.35604e24	−1.36620
$396$	−7.39109e23	−0.155097
$397$	4.22183e24	0.864951	0.432475	−	0.901646i	$-0.357640\pi$
$397$	4.22183e24	0.864951	0.432475	+	0.901646i	$0.357640\pi$
$398$	1.45843e25	2.91741
$399$	−1.21427e24	−0.237177
$400$	1.05096e24	0.200455
$401$	3.29680e24	0.614075	0.307037	−	0.951697i	$-0.400662\pi$
$401$	3.29680e24	0.614075	0.307037	+	0.951697i	$0.400662\pi$
$402$	−5.82506e24	−1.05963
$403$	1.89651e24	0.336943
$404$	1.24144e25	2.15428
$405$	5.27773e23	0.0894591
$406$	2.63189e24	0.435783
$407$	1.16316e24	0.188146
$408$	2.90760e24	0.459477
$409$	3.40224e24	0.525284	0.262642	−	0.964893i	$-0.415406\pi$
$409$	3.40224e24	0.525284	0.262642	+	0.964893i	$0.415406\pi$
$410$	4.32420e24	0.652317
$411$	−2.27794e24	−0.335773
$412$	−4.90116e24	−0.705952
$413$	−1.81313e25	−2.55214
$414$	−2.09603e24	−0.288333
$415$	5.16877e24	0.694913
$416$	−1.20534e25	−1.58388
$417$	−1.13697e24	−0.146035
$418$	9.56492e23	0.120090
$419$	2.53386e24	0.310992	0.155496	−	0.987837i	$-0.450302\pi$
$419$	2.53386e24	0.310992	0.155496	+	0.987837i	$0.450302\pi$
$420$	−9.40180e24	−1.12809
$421$	−1.07229e25	−1.25786	−0.628930	−	0.777462i	$-0.716507\pi$
$421$	−1.07229e25	−1.25786	−0.628930	+	0.777462i	$0.716507\pi$
$422$	1.71650e25	1.96868
$423$	5.93285e23	0.0665319
$424$	3.39416e24	0.372183
$425$	5.27342e24	0.565454
$426$	2.46144e24	0.258106
$427$	−4.17644e24	−0.428293
$428$	−1.23068e25	−1.23433
$429$	2.40057e24	0.235489
$430$	−4.41030e24	−0.423173
$431$	1.57678e25	1.47992	0.739960	−	0.672651i	$-0.234845\pi$
$431$	1.57678e25	1.47992	0.739960	+	0.672651i	$0.234845\pi$
$432$	−1.19448e24	−0.109669
$433$	7.64728e24	0.686866	0.343433	−	0.939177i	$-0.388410\pi$
$433$	7.64728e24	0.686866	0.343433	+	0.939177i	$0.388410\pi$
$434$	−9.22325e24	−0.810460
$435$	8.43577e23	0.0725231
$436$	5.63794e24	0.474241
$437$	1.54569e24	0.127218
$438$	1.18636e25	0.955464
$439$	−6.56625e24	−0.517493	−0.258747	−	0.965945i	$-0.583309\pi$
$439$	−6.56625e24	−0.517493	−0.258747	+	0.965945i	$0.583309\pi$
$440$	1.81530e24	0.140007
$441$	1.04049e25	0.785362
$442$	−3.85274e25	−2.84615
$443$	7.45718e24	0.539187	0.269594	−	0.962974i	$-0.413111\pi$
$443$	7.45718e24	0.539187	0.269594	+	0.962974i	$0.413111\pi$
$444$	−5.78876e24	−0.409683
$445$	1.04575e25	0.724451
$446$	1.15701e24	0.0784614
$447$	1.88639e24	0.125231
$448$	4.25560e25	2.76579
$449$	−2.64059e25	−1.68020	−0.840101	−	0.542430i	$-0.817504\pi$
$449$	−2.64059e25	−1.68020	−0.840101	+	0.542430i	$0.817504\pi$
$450$	2.86966e24	0.178777
$451$	3.05978e24	0.186644
$452$	−3.04401e25	−1.81816
$453$	2.61201e24	0.152771
$454$	5.41336e24	0.310053
$455$	3.05364e25	1.71281
$456$	−1.16680e24	−0.0640962
$457$	1.31845e25	0.709347	0.354674	−	0.934990i	$-0.384592\pi$
$457$	1.31845e25	0.709347	0.354674	+	0.934990i	$0.384592\pi$
$458$	−1.86590e25	−0.983256
$459$	−5.99359e24	−0.309361
$460$	1.19679e25	0.605088
$461$	−3.04421e25	−1.50770	−0.753851	−	0.657046i	$-0.771806\pi$
$461$	−3.04421e25	−1.50770	−0.753851	+	0.657046i	$0.771806\pi$
$462$	−1.16747e25	−0.566429
$463$	−3.64943e25	−1.73463	−0.867313	−	0.497764i	$-0.834155\pi$
$463$	−3.64943e25	−1.73463	−0.867313	+	0.497764i	$0.834155\pi$
$464$	−1.90923e24	−0.0889072
$465$	−2.95624e24	−0.134877
$466$	3.25529e25	1.45520
$467$	3.33264e25	1.45975	0.729875	−	0.683581i	$-0.239578\pi$
$467$	3.33264e25	1.45975	0.729875	+	0.683581i	$0.239578\pi$
$468$	−1.19470e25	−0.512772
$469$	−5.24310e25	−2.20519
$470$	−5.94473e24	−0.245020
$471$	−1.95058e25	−0.787890
$472$	−1.74226e25	−0.689705
$473$	−3.12071e24	−0.121080
$474$	3.92794e25	1.49373
$475$	−2.11619e24	−0.0788798
$476$	1.06770e26	3.90108
$477$	−6.99655e24	−0.250587
$478$	3.84934e25	1.35152
$479$	8.10234e24	0.278884	0.139442	−	0.990230i	$-0.455469\pi$
$479$	8.10234e24	0.278884	0.139442	+	0.990230i	$0.455469\pi$
$480$	1.87886e25	0.634020
$481$	1.88015e25	0.622033
$482$	−3.42695e25	−1.11163
$483$	−1.88662e25	−0.600050
$484$	−3.72363e25	−1.16128
$485$	−2.43526e25	−0.744729
$486$	−3.26156e24	−0.0978095
$487$	4.90469e25	1.44240	0.721202	−	0.692725i	$-0.243590\pi$
$487$	4.90469e25	1.44240	0.721202	+	0.692725i	$0.243590\pi$
$488$	−4.01318e24	−0.115745
$489$	3.42768e25	0.969541
$490$	−1.04257e26	−2.89229
$491$	4.15501e25	1.13057	0.565285	−	0.824895i	$-0.308766\pi$
$491$	4.15501e25	1.13057	0.565285	+	0.824895i	$0.308766\pi$
$492$	−1.52277e25	−0.406412
$493$	−9.57996e24	−0.250795
$494$	1.54608e25	0.397033
$495$	−3.74198e24	−0.0942652
$496$	6.69073e24	0.165347
$497$	2.21552e25	0.537144
$498$	−3.19423e25	−0.759778
$499$	−2.09237e25	−0.488297	−0.244148	−	0.969738i	$-0.578508\pi$
$499$	−2.09237e25	−0.488297	−0.244148	+	0.969738i	$0.578508\pi$
$500$	−6.29655e25	−1.44174
$501$	−4.60910e25	−1.03552
$502$	−2.68660e24	−0.0592267
$503$	−8.92504e25	−1.93070	−0.965349	−	0.260963i	$-0.915960\pi$
$503$	−8.92504e25	−1.93070	−0.965349	+	0.260963i	$0.915960\pi$
$504$	1.42417e25	0.302323
$505$	6.28519e25	1.30933
$506$	1.48611e25	0.303823
$507$	1.00281e25	0.201207
$508$	2.04770e25	0.403238
$509$	7.25766e25	1.40274	0.701371	−	0.712797i	$-0.252572\pi$
$509$	7.25766e25	1.40274	0.701371	+	0.712797i	$0.252572\pi$
$510$	6.00559e25	1.13930
$511$	1.06784e26	1.98842
$512$	−5.79584e25	−1.05938
$513$	2.40519e24	0.0431554
$514$	7.83067e25	1.37927
$515$	−2.48137e25	−0.429064
$516$	1.55309e25	0.263649
$517$	−4.20646e24	−0.0701063
$518$	−9.14369e25	−1.49620
$519$	−1.05574e25	−0.169617
$520$	2.93427e25	0.462880
$521$	−4.13657e25	−0.640741	−0.320370	−	0.947292i	$-0.603807\pi$
$521$	−4.13657e25	−0.640741	−0.320370	+	0.947292i	$0.603807\pi$
$522$	−5.21318e24	−0.0792926
$523$	−1.17484e26	−1.75475	−0.877373	−	0.479810i	$-0.840706\pi$
$523$	−1.17484e26	−1.75475	−0.877373	+	0.479810i	$0.840706\pi$
$524$	8.96607e25	1.31509
$525$	2.58296e25	0.372053
$526$	−8.94438e25	−1.26528
$527$	3.35722e25	0.466422
$528$	8.46904e24	0.115561
$529$	−5.06000e25	−0.678143
$530$	7.01056e25	0.922852
$531$	3.59140e25	0.464372
$532$	−4.28463e25	−0.544193
$533$	4.94586e25	0.617068
$534$	−6.46260e25	−0.792073
$535$	−6.23071e25	−0.750200
$536$	−5.03815e25	−0.595944
$537$	6.55796e25	0.762102
$538$	2.32135e26	2.65038
$539$	−7.37718e25	−0.827555
$540$	1.86228e25	0.205260
$541$	−4.86212e25	−0.526565	−0.263282	−	0.964719i	$-0.584805\pi$
$541$	−4.86212e25	−0.526565	−0.263282	+	0.964719i	$0.584805\pi$
$542$	1.06812e26	1.13665
$543$	−7.81425e24	−0.0817126
$544$	−2.13370e26	−2.19252
$545$	2.85439e25	0.288235
$546$	−1.88710e26	−1.87269
$547$	−3.16162e25	−0.308340	−0.154170	−	0.988044i	$-0.549270\pi$
$547$	−3.16162e25	−0.308340	−0.154170	+	0.988044i	$0.549270\pi$
$548$	−8.03788e25	−0.770417
$549$	8.27258e24	0.0779298
$550$	−2.03463e25	−0.188382
$551$	3.84439e24	0.0349854
$552$	−1.81287e25	−0.162161
$553$	3.53551e26	3.10859
$554$	1.65847e26	1.43339
$555$	−2.93075e25	−0.248997
$556$	−4.01187e25	−0.335071
$557$	−1.82242e26	−1.49632	−0.748158	−	0.663520i	$-0.769062\pi$
$557$	−1.82242e26	−1.49632	−0.748158	+	0.663520i	$0.769062\pi$
$558$	1.82692e25	0.147467
$559$	−5.04434e25	−0.400306
$560$	1.07730e26	0.840525
$561$	4.24952e25	0.325982
$562$	3.07843e26	2.32185
$563$	−3.15854e25	−0.234237	−0.117119	−	0.993118i	$-0.537366\pi$
$563$	−3.15854e25	−0.234237	−0.117119	+	0.993118i	$0.537366\pi$
$564$	2.09345e25	0.152655
$565$	−1.54113e26	−1.10504
$566$	1.07605e26	0.758714
$567$	−2.93571e25	−0.203551
$568$	2.12892e25	0.145161
$569$	1.47589e26	0.989666	0.494833	−	0.868988i	$-0.335229\pi$
$569$	1.47589e26	0.989666	0.494833	+	0.868988i	$0.335229\pi$
$570$	−2.41001e25	−0.158931
$571$	−1.69593e26	−1.09993	−0.549966	−	0.835187i	$-0.685359\pi$
$571$	−1.69593e26	−1.09993	−0.549966	+	0.835187i	$0.685359\pi$
$572$	8.47058e25	0.540320
$573$	2.32844e24	0.0146082
$574$	−2.40531e26	−1.48425
$575$	−3.28795e25	−0.199563
$576$	−8.42938e25	−0.503248
$577$	7.03834e25	0.413333	0.206667	−	0.978411i	$-0.433738\pi$
$577$	7.03834e25	0.413333	0.206667	+	0.978411i	$0.433738\pi$
$578$	−4.18080e26	−2.41516
$579$	7.40936e25	0.421050
$580$	2.97662e25	0.166401
$581$	−2.87510e26	−1.58117
$582$	1.50495e26	0.814244
$583$	4.96064e25	0.264050
$584$	1.02610e26	0.537361
$585$	−6.04856e25	−0.311653
$586$	−3.07517e26	−1.55898
$587$	3.43137e25	0.171162	0.0855808	−	0.996331i	$-0.472725\pi$
$587$	3.43137e25	0.171162	0.0855808	+	0.996331i	$0.472725\pi$
$588$	3.67143e26	1.80198
$589$	−1.34723e25	−0.0650650
$590$	−3.59860e26	−1.71017
$591$	8.62089e25	0.403154
$592$	6.63302e25	0.305250
$593$	3.21922e26	1.45791	0.728955	−	0.684562i	$-0.240007\pi$
$593$	3.21922e26	1.45791	0.728955	+	0.684562i	$0.240007\pi$
$594$	2.31249e25	0.103064
$595$	5.40559e26	2.37100
$596$	6.65627e25	0.287337
$597$	−2.60021e26	−1.10472
$598$	2.40216e26	1.00448
$599$	6.71773e25	0.276483	0.138241	−	0.990399i	$-0.455855\pi$
$599$	6.71773e25	0.276483	0.138241	+	0.990399i	$0.455855\pi$
$600$	2.48200e25	0.100546
$601$	−1.65737e26	−0.660863	−0.330432	−	0.943830i	$-0.607194\pi$
$601$	−1.65737e26	−0.660863	−0.330432	+	0.943830i	$0.607194\pi$
$602$	2.45320e26	0.962869
$603$	1.03854e26	0.401244
$604$	9.21666e25	0.350528
$605$	−1.88521e26	−0.705803
$606$	−3.88415e26	−1.43155
$607$	−1.07010e26	−0.388267	−0.194133	−	0.980975i	$-0.562189\pi$
$607$	−1.07010e26	−0.388267	−0.194133	+	0.980975i	$0.562189\pi$
$608$	8.56243e25	0.305853
$609$	−4.69235e25	−0.165016
$610$	−8.28914e25	−0.286996
$611$	−6.79936e25	−0.231780
$612$	−2.11488e26	−0.709818
$613$	1.05520e26	0.348708	0.174354	−	0.984683i	$-0.444216\pi$
$613$	1.05520e26	0.348708	0.174354	+	0.984683i	$0.444216\pi$
$614$	−5.34917e26	−1.74055
$615$	−7.70953e25	−0.247010
$616$	−1.00975e26	−0.318565
$617$	5.70260e26	1.77159	0.885796	−	0.464074i	$-0.153613\pi$
$617$	5.70260e26	1.77159	0.885796	+	0.464074i	$0.153613\pi$
$618$	1.53345e26	0.469114
$619$	5.68518e26	1.71271	0.856353	−	0.516390i	$-0.172725\pi$
$619$	5.68518e26	1.71271	0.856353	+	0.516390i	$0.172725\pi$
$620$	−1.04313e26	−0.309469
$621$	3.73697e25	0.109182
$622$	−6.22172e26	−1.79020
$623$	−5.81694e26	−1.64838
$624$	1.36894e26	0.382060
$625$	−1.90812e26	−0.524501
$626$	6.39608e26	1.73164
$627$	−1.70531e25	−0.0454739
$628$	−6.88276e26	−1.80778
$629$	3.32826e26	0.861066
$630$	2.94159e26	0.749629
$631$	−2.31534e26	−0.581214	−0.290607	−	0.956842i	$-0.593857\pi$
$631$	−2.31534e26	−0.581214	−0.290607	+	0.956842i	$0.593857\pi$
$632$	3.39731e26	0.840085
$633$	−3.06032e26	−0.745472
$634$	1.18169e27	2.83566
$635$	1.03671e26	0.245080
$636$	−2.46878e26	−0.574963
$637$	−1.19245e27	−2.73600
$638$	3.69621e25	0.0835526
$639$	−4.38845e25	−0.0977356
$640$	3.44162e26	0.755184
$641$	6.84136e26	1.47908	0.739539	−	0.673114i	$-0.235044\pi$
$641$	6.84136e26	1.47908	0.739539	+	0.673114i	$0.235044\pi$
$642$	3.85049e26	0.820225
$643$	−4.41658e26	−0.927004	−0.463502	−	0.886096i	$-0.653407\pi$
$643$	−4.41658e26	−0.927004	−0.463502	+	0.886096i	$0.653407\pi$
$644$	−6.65708e26	−1.37679
$645$	7.86303e25	0.160241
$646$	2.73689e26	0.549603
$647$	2.91842e26	0.577507	0.288754	−	0.957403i	$-0.406759\pi$
$647$	2.91842e26	0.577507	0.288754	+	0.957403i	$0.406759\pi$
$648$	−2.82095e25	−0.0550089
$649$	−2.54635e26	−0.489320
$650$	−3.28879e26	−0.622815
$651$	1.64439e26	0.306893
$652$	1.20948e27	2.22457
$653$	−9.04573e26	−1.63972	−0.819858	−	0.572567i	$-0.805948\pi$
$653$	−9.04573e26	−1.63972	−0.819858	+	0.572567i	$0.805948\pi$
$654$	−1.76397e26	−0.315139
$655$	4.53936e26	0.799286
$656$	1.74486e26	0.302813
$657$	−2.11515e26	−0.361801
$658$	3.30672e26	0.557509
$659$	−2.65595e26	−0.441375	−0.220688	−	0.975345i	$-0.570830\pi$
$659$	−2.65595e26	−0.441375	−0.220688	+	0.975345i	$0.570830\pi$
$660$	−1.32038e26	−0.216288
$661$	3.55026e26	0.573253	0.286627	−	0.958042i	$-0.407466\pi$
$661$	3.55026e26	0.573253	0.286627	+	0.958042i	$0.407466\pi$
$662$	3.39129e26	0.539777
$663$	6.86897e26	1.07774
$664$	−2.76271e26	−0.427306
$665$	−2.16923e26	−0.330751
$666$	1.81116e26	0.272239
$667$	5.97306e25	0.0885118
$668$	−1.62635e27	−2.37595
$669$	−2.06281e25	−0.0297106
$670$	−1.04062e27	−1.47768
$671$	−5.86536e25	−0.0821165
$672$	−1.04511e27	−1.44262
$673$	−3.58165e26	−0.487461	−0.243731	−	0.969843i	$-0.578371\pi$
$673$	−3.58165e26	−0.487461	−0.243731	+	0.969843i	$0.578371\pi$
$674$	−1.76252e27	−2.36519
$675$	−5.11627e25	−0.0676967
$676$	3.53848e26	0.461660
$677$	4.80665e26	0.618373	0.309186	−	0.951001i	$-0.399943\pi$
$677$	4.80665e26	0.618373	0.309186	+	0.951001i	$0.399943\pi$
$678$	9.52395e26	1.20819
$679$	1.35460e27	1.69452
$680$	5.19429e26	0.640754
$681$	−9.65137e25	−0.117406
$682$	−1.29531e26	−0.155389
$683$	9.71565e26	1.14941	0.574705	−	0.818360i	$-0.305117\pi$
$683$	9.71565e26	1.14941	0.574705	+	0.818360i	$0.305117\pi$
$684$	8.48689e25	0.0990183
$685$	−4.06943e26	−0.468245
$686$	3.33785e27	3.78781
$687$	3.32668e26	0.372325
$688$	−1.77960e26	−0.196441
$689$	8.01842e26	0.872984
$690$	−3.74445e26	−0.402089
$691$	−6.78820e26	−0.718975	−0.359487	−	0.933150i	$-0.617048\pi$
$691$	−6.78820e26	−0.718975	−0.359487	+	0.933150i	$0.617048\pi$
$692$	−3.72527e26	−0.389179
$693$	2.08145e26	0.214487
$694$	−2.09035e27	−2.12474
$695$	−2.03114e26	−0.203650
$696$	−4.50892e25	−0.0445949
$697$	8.75522e26	0.854193
$698$	−3.52451e26	−0.339212
$699$	−5.80379e26	−0.551034
$700$	9.11417e26	0.853661
$701$	−1.64884e26	−0.152355	−0.0761776	−	0.997094i	$-0.524272\pi$
$701$	−1.64884e26	−0.152355	−0.0761776	+	0.997094i	$0.524272\pi$
$702$	3.73792e26	0.340744
$703$	−1.33561e26	−0.120117
$704$	5.97653e26	0.530285
$705$	1.05987e26	0.0927807
$706$	−2.32588e27	−2.00882
$707$	−3.49610e27	−2.97920
$708$	1.26725e27	1.06548
$709$	1.52342e27	1.26381	0.631904	−	0.775047i	$-0.282274\pi$
$709$	1.52342e27	1.26381	0.631904	+	0.775047i	$0.282274\pi$
$710$	4.39724e26	0.359936
$711$	−7.00305e26	−0.565622
$712$	−5.58956e26	−0.445469
$713$	−2.09321e26	−0.164612
$714$	−3.34057e27	−2.59232
$715$	4.28850e26	0.328396
$716$	2.31402e27	1.74861
$717$	−6.86291e26	−0.511772
$718$	1.60330e27	1.17987
$719$	−2.54571e26	−0.184878	−0.0924390	−	0.995718i	$-0.529466\pi$
$719$	−2.54571e26	−0.184878	−0.0924390	+	0.995718i	$0.529466\pi$
$720$	−2.13389e26	−0.152937
$721$	1.38025e27	0.976274
$722$	2.07435e27	1.44803
$723$	6.10985e26	0.420936
$724$	−2.75731e26	−0.187486
$725$	−8.17768e25	−0.0548806
$726$	1.16503e27	0.771684
$727$	−2.12348e27	−1.38826	−0.694132	−	0.719847i	$-0.744212\pi$
$727$	−2.12348e27	−1.38826	−0.694132	+	0.719847i	$0.744212\pi$
$728$	−1.63217e27	−1.05322
$729$	5.81497e25	0.0370370
$730$	2.11938e27	1.33242
$731$	−8.92955e26	−0.554134
$732$	2.91903e26	0.178807
$733$	−1.37369e27	−0.830619	−0.415309	−	0.909680i	$-0.636327\pi$
$733$	−1.37369e27	−0.830619	−0.415309	+	0.909680i	$0.636327\pi$
$734$	3.89538e26	0.232507
$735$	1.85878e27	1.09521
$736$	1.33035e27	0.773798
$737$	−7.36336e26	−0.422800
$738$	4.76437e26	0.270066
$739$	2.36197e27	1.32176	0.660880	−	0.750492i	$-0.270183\pi$
$739$	2.36197e27	1.32176	0.660880	+	0.750492i	$0.270183\pi$
$740$	−1.03413e27	−0.571314
$741$	−2.75648e26	−0.150342
$742$	−3.89959e27	−2.09982
$743$	−2.96849e26	−0.157813	−0.0789063	−	0.996882i	$-0.525143\pi$
$743$	−2.96849e26	−0.157813	−0.0789063	+	0.996882i	$0.525143\pi$
$744$	1.58012e26	0.0829365
$745$	3.36995e26	0.174638
$746$	−3.45115e27	−1.76581
$747$	5.69492e26	0.287701
$748$	1.49947e27	0.747952
$749$	3.46580e27	1.70697
$750$	1.97003e27	0.958056
$751$	−2.22426e27	−1.06808	−0.534042	−	0.845458i	$-0.679327\pi$
$751$	−2.22426e27	−1.06808	−0.534042	+	0.845458i	$0.679327\pi$
$752$	−2.39876e26	−0.113741
$753$	4.78989e25	0.0224271
$754$	5.97458e26	0.276236
$755$	4.66623e26	0.213044
$756$	−1.03589e27	−0.467040
$757$	−1.92178e26	−0.0855643	−0.0427822	−	0.999084i	$-0.513622\pi$
$757$	−1.92178e26	−0.0855643	−0.0427822	+	0.999084i	$0.513622\pi$
$758$	−5.72300e26	−0.251632
$759$	−2.64956e26	−0.115047
$760$	−2.08444e26	−0.0893840
$761$	1.93340e27	0.818778	0.409389	−	0.912360i	$-0.365742\pi$
$761$	1.93340e27	0.818778	0.409389	+	0.912360i	$0.365742\pi$
$762$	−6.40674e26	−0.267957
$763$	−1.58774e27	−0.655837
$764$	8.21607e25	0.0335179
$765$	−1.07072e27	−0.431414
$766$	−2.34522e26	−0.0933277
$767$	−4.11594e27	−1.61776
$768$	1.18432e26	0.0459766
$769$	−1.55642e27	−0.596796	−0.298398	−	0.954442i	$-0.596452\pi$
$769$	−1.55642e27	−0.596796	−0.298398	+	0.954442i	$0.596452\pi$
$770$	−2.08562e27	−0.789903
$771$	−1.39611e27	−0.522281
$772$	2.61444e27	0.966083
$773$	2.79822e27	1.02136	0.510678	−	0.859772i	$-0.329394\pi$
$773$	2.79822e27	1.02136	0.510678	+	0.859772i	$0.329394\pi$
$774$	−4.85924e26	−0.175198
$775$	2.86580e26	0.102066
$776$	1.30165e27	0.457938
$777$	1.63021e27	0.566558
$778$	4.90017e27	1.68231
$779$	−3.51342e26	−0.119158
$780$	−2.13428e27	−0.715075
$781$	3.11146e26	0.102986
$782$	4.25234e27	1.39048
$783$	9.29448e25	0.0300254
$784$	−4.20689e27	−1.34264
$785$	−3.48462e27	−1.09874
$786$	−2.80526e27	−0.873893
$787$	3.80897e27	1.17232	0.586161	−	0.810194i	$-0.300639\pi$
$787$	3.80897e27	1.17232	0.586161	+	0.810194i	$0.300639\pi$
$788$	3.04194e27	0.925021
$789$	1.59468e27	0.479116
$790$	7.01707e27	2.08304
$791$	8.57244e27	2.51436
$792$	2.00009e26	0.0579643
$793$	−9.48081e26	−0.271488
$794$	−4.66090e27	−1.31879
$795$	−1.24990e27	−0.349452
$796$	−9.17501e27	−2.53474
$797$	3.90140e26	0.106504	0.0532521	−	0.998581i	$-0.483041\pi$
$797$	3.90140e26	0.106504	0.0532521	+	0.998581i	$0.483041\pi$
$798$	1.34055e27	0.361624
$799$	−1.20363e27	−0.320848
$800$	−1.82138e27	−0.479784
$801$	1.15220e27	0.299930
$802$	−3.63967e27	−0.936279
$803$	1.49966e27	0.381238
$804$	3.66455e27	0.920638
$805$	−3.37036e27	−0.836787
$806$	−2.09374e27	−0.513736
$807$	−4.13869e27	−1.00361
$808$	−3.35944e27	−0.805117
$809$	−8.85420e26	−0.209719	−0.104860	−	0.994487i	$-0.533439\pi$
$809$	−8.85420e26	−0.209719	−0.104860	+	0.994487i	$0.533439\pi$
$810$	−5.82662e26	−0.136398
$811$	−2.17253e27	−0.502651	−0.251326	−	0.967903i	$-0.580866\pi$
$811$	−2.17253e27	−0.502651	−0.251326	+	0.967903i	$0.580866\pi$
$812$	−1.65573e27	−0.378623
$813$	−1.90433e27	−0.430410
$814$	−1.28413e27	−0.286865
$815$	6.12338e27	1.35205
$816$	2.42332e27	0.528877
$817$	3.58338e26	0.0773007
$818$	−3.75608e27	−0.800900
$819$	3.36448e27	0.709122
$820$	−2.72036e27	−0.566754
$821$	−2.60443e27	−0.536355	−0.268177	−	0.963370i	$-0.586421\pi$
$821$	−2.60443e27	−0.536355	−0.268177	+	0.963370i	$0.586421\pi$
$822$	2.51485e27	0.511953
$823$	3.71169e27	0.746919	0.373459	−	0.927647i	$-0.378172\pi$
$823$	3.71169e27	0.746919	0.373459	+	0.927647i	$0.378172\pi$
$824$	1.32629e27	0.263834
$825$	3.62749e26	0.0713336
$826$	2.00170e28	3.89124
$827$	5.98762e27	1.15067	0.575336	−	0.817917i	$-0.304871\pi$
$827$	5.98762e27	1.15067	0.575336	+	0.817917i	$0.304871\pi$
$828$	1.31862e27	0.250513
$829$	9.15991e27	1.72038	0.860188	−	0.509977i	$-0.170346\pi$
$829$	9.15991e27	1.72038	0.860188	+	0.509977i	$0.170346\pi$
$830$	−5.70632e27	−1.05953
$831$	−2.95685e27	−0.542774
$832$	9.66052e27	1.75319
$833$	−2.11090e28	−3.78738
$834$	1.25521e27	0.222659
$835$	−8.23393e27	−1.44406
$836$	−6.01731e26	−0.104338
$837$	−3.25717e26	−0.0558404
$838$	−2.79738e27	−0.474169
$839$	−1.90995e27	−0.320099	−0.160049	−	0.987109i	$-0.551165\pi$
$839$	−1.90995e27	−0.320099	−0.160049	+	0.987109i	$0.551165\pi$
$840$	2.54421e27	0.421598
$841$	−5.95470e27	−0.975659
$842$	1.18381e28	1.91786
$843$	−5.48847e27	−0.879203
$844$	−1.07985e28	−1.71046
$845$	1.79147e27	0.280589
$846$	−6.54987e26	−0.101441
$847$	1.04864e28	1.60595
$848$	2.82884e27	0.428398
$849$	−1.91848e27	−0.287298
$850$	−5.82185e27	−0.862147
$851$	−2.07515e27	−0.303892
$852$	−1.54849e27	−0.224250
$853$	2.96003e27	0.423917	0.211958	−	0.977279i	$-0.432016\pi$
$853$	2.96003e27	0.423917	0.211958	+	0.977279i	$0.432016\pi$
$854$	4.61079e27	0.653018
$855$	4.29676e26	0.0601815
$856$	3.33032e27	0.461302
$857$	6.39793e27	0.876439	0.438219	−	0.898868i	$-0.355609\pi$
$857$	6.39793e27	0.876439	0.438219	+	0.898868i	$0.355609\pi$
$858$	−2.65023e27	−0.359050
$859$	1.49963e27	0.200932	0.100466	−	0.994941i	$-0.467967\pi$
$859$	1.49963e27	0.200932	0.100466	+	0.994941i	$0.467967\pi$
$860$	2.77452e27	0.367666
$861$	4.28838e27	0.562035
$862$	−1.74077e28	−2.25643
$863$	−1.16811e28	−1.49755	−0.748774	−	0.662825i	$-0.769357\pi$
$863$	−1.16811e28	−1.49755	−0.748774	+	0.662825i	$0.769357\pi$
$864$	2.07012e27	0.262491
$865$	−1.88604e27	−0.236536
$866$	−8.44260e27	−1.04726
$867$	7.45387e27	0.914536
$868$	5.80236e27	0.704153
$869$	4.96525e27	0.596009
$870$	−9.31309e26	−0.110576
$871$	−1.19022e28	−1.39783
$872$	−1.52567e27	−0.177237
$873$	−2.68315e27	−0.308326
$874$	−1.70644e27	−0.193969
$875$	1.77321e28	1.99381
$876$	−7.46344e27	−0.830137
$877$	3.36367e27	0.370098	0.185049	−	0.982729i	$-0.440756\pi$
$877$	3.36367e27	0.370098	0.185049	+	0.982729i	$0.440756\pi$
$878$	7.24914e27	0.789021
$879$	5.48265e27	0.590332
$880$	1.51295e27	0.161154
$881$	−8.62862e27	−0.909222	−0.454611	−	0.890690i	$-0.650222\pi$
$881$	−8.62862e27	−0.909222	−0.454611	+	0.890690i	$0.650222\pi$
$882$	−1.14870e28	−1.19744
$883$	3.09180e27	0.318849	0.159425	−	0.987210i	$-0.449036\pi$
$883$	3.09180e27	0.318849	0.159425	+	0.987210i	$0.449036\pi$
$884$	2.42376e28	2.47283
$885$	6.41587e27	0.647581
$886$	−8.23273e27	−0.822098
$887$	1.06571e28	1.05285	0.526423	−	0.850223i	$-0.323533\pi$
$887$	1.06571e28	1.05285	0.526423	+	0.850223i	$0.323533\pi$
$888$	1.56649e27	0.153110
$889$	−5.76666e27	−0.557645
$890$	−1.15451e28	−1.10457
$891$	−4.12289e26	−0.0390268
$892$	−7.27876e26	−0.0681697
$893$	4.83011e26	0.0447577
$894$	−2.08258e27	−0.190939
$895$	1.17155e28	1.06277
$896$	−1.91438e28	−1.71831
$897$	−4.28277e27	−0.380361
$898$	2.91522e28	2.56180
$899$	−5.20616e26	−0.0452690
$900$	−1.80531e27	−0.155327
$901$	1.41943e28	1.20845
$902$	−3.37800e27	−0.284575
$903$	−4.37377e27	−0.364605
$904$	8.23735e27	0.679497
$905$	−1.39598e27	−0.113951
$906$	−2.88366e27	−0.232930
$907$	−1.19240e28	−0.953133	−0.476567	−	0.879138i	$-0.658119\pi$
$907$	−1.19240e28	−0.953133	−0.476567	+	0.879138i	$0.658119\pi$
$908$	−3.40555e27	−0.269384
$909$	6.92498e27	0.542078
$910$	−3.37122e28	−2.61152
$911$	−1.44243e28	−1.10578	−0.552890	−	0.833254i	$-0.686475\pi$
$911$	−1.44243e28	−1.10578	−0.552890	+	0.833254i	$0.686475\pi$
$912$	−9.72465e26	−0.0737774
$913$	−4.03777e27	−0.303158
$914$	−1.45557e28	−1.08154
$915$	1.47785e27	0.108675
$916$	1.17384e28	0.854284
$917$	−2.52499e28	−1.81866
$918$	6.61692e27	0.471683
$919$	−2.45481e28	−1.73189	−0.865946	−	0.500138i	$-0.833283\pi$
$919$	−2.45481e28	−1.73189	−0.865946	+	0.500138i	$0.833283\pi$
$920$	−3.23861e27	−0.226138
$921$	9.53693e27	0.659086
$922$	3.36080e28	2.29879
$923$	5.02940e27	0.340486
$924$	7.34455e27	0.492132
$925$	2.84108e27	0.188425
$926$	4.02897e28	2.64478
$927$	−2.73395e27	−0.177637
$928$	3.30881e27	0.212797
$929$	2.24631e27	0.142995	0.0714974	−	0.997441i	$-0.477222\pi$
$929$	2.24631e27	0.142995	0.0714974	+	0.997441i	$0.477222\pi$
$930$	3.26369e27	0.205647
$931$	8.47091e27	0.528333
$932$	−2.04790e28	−1.26432
$933$	1.10926e28	0.677886
$934$	−3.67924e28	−2.22568
$935$	7.59156e27	0.454591
$936$	3.23296e27	0.191637
$937$	5.69436e27	0.334132	0.167066	−	0.985946i	$-0.446571\pi$
$937$	5.69436e27	0.334132	0.167066	+	0.985946i	$0.446571\pi$
$938$	5.78838e28	3.36225
$939$	−1.14034e28	−0.655712
$940$	3.73984e27	0.212882
$941$	−4.99691e27	−0.281579	−0.140790	−	0.990040i	$-0.544964\pi$
$941$	−4.99691e27	−0.281579	−0.140790	+	0.990040i	$0.544964\pi$
$942$	2.15344e28	1.20130
$943$	−5.45884e27	−0.301466
$944$	−1.45207e28	−0.793879
$945$	−5.24450e27	−0.283858
$946$	3.44526e27	0.184610
$947$	−1.38781e28	−0.736214	−0.368107	−	0.929783i	$-0.619994\pi$
$947$	−1.38781e28	−0.736214	−0.368107	+	0.929783i	$0.619994\pi$
$948$	−2.47107e28	−1.29780
$949$	2.42407e28	1.26042
$950$	2.33628e27	0.120268
$951$	−2.10681e28	−1.07377
$952$	−2.88929e28	−1.45794
$953$	−3.71993e27	−0.185846	−0.0929228	−	0.995673i	$-0.529621\pi$
$953$	−3.71993e27	−0.185846	−0.0929228	+	0.995673i	$0.529621\pi$
$954$	7.72419e27	0.382070
$955$	4.15965e26	0.0203716
$956$	−2.42163e28	−1.17424
$957$	−6.58989e26	−0.0316384
$958$	−8.94498e27	−0.425213
$959$	2.26360e28	1.06542
$960$	−1.50587e28	−0.701794
$961$	−1.98462e28	−0.915810
$962$	−2.07568e28	−0.948414
$963$	−6.86496e27	−0.310591
$964$	2.15590e28	0.965822
$965$	1.32364e28	0.587167
$966$	2.08283e28	0.914895
$967$	1.20501e28	0.524132	0.262066	−	0.965050i	$-0.415596\pi$
$967$	1.20501e28	0.524132	0.262066	+	0.965050i	$0.415596\pi$
$968$	1.00765e28	0.434002
$969$	−4.87956e27	−0.208115
$970$	2.68853e28	1.13549
$971$	−8.01489e27	−0.335208	−0.167604	−	0.985854i	$-0.553603\pi$
$971$	−8.01489e27	−0.335208	−0.167604	+	0.985854i	$0.553603\pi$
$972$	2.05185e27	0.0849800
$973$	1.12981e28	0.463375
$974$	−5.41478e28	−2.19923
$975$	5.86351e27	0.235838
$976$	−3.34476e27	−0.133227
$977$	3.97949e28	1.56975	0.784873	−	0.619656i	$-0.212728\pi$
$977$	3.97949e28	1.56975	0.784873	+	0.619656i	$0.212728\pi$
$978$	−3.78416e28	−1.47826
$979$	−8.16927e27	−0.316044
$980$	6.55882e28	2.51292
$981$	3.14495e27	0.119332
$982$	−4.58713e28	−1.72378
$983$	1.67921e28	0.624950	0.312475	−	0.949926i	$-0.398842\pi$
$983$	1.67921e28	0.624950	0.312475	+	0.949926i	$0.398842\pi$
$984$	4.12075e27	0.151888
$985$	1.54008e28	0.562210
$986$	1.05763e28	0.382386
$987$	−5.89549e27	−0.211109
$988$	−9.72642e27	−0.344955
$989$	5.56753e27	0.195568
$990$	4.13114e27	0.143726
$991$	1.18105e28	0.406975	0.203488	−	0.979078i	$-0.434772\pi$
$991$	1.18105e28	0.406975	0.203488	+	0.979078i	$0.434772\pi$
$992$	−1.15955e28	−0.395755
$993$	−6.04627e27	−0.204395
$994$	−2.44594e28	−0.818983
$995$	−4.64514e28	−1.54056
$996$	2.00949e28	0.660119
$997$	−4.34119e27	−0.141255	−0.0706277	−	0.997503i	$-0.522500\pi$
$997$	−4.34119e27	−0.141255	−0.0706277	+	0.997503i	$0.522500\pi$
$998$	2.30998e28	0.744506
$999$	−3.22908e27	−0.103088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.20.a.a.1.1	✓	1
3.2	odd	2		9.20.a.b.1.1		1
4.3	odd	2		48.20.a.c.1.1		1
5.2	odd	4		75.20.b.a.49.1		2
5.3	odd	4		75.20.b.a.49.2		2
5.4	even	2		75.20.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.a.1.1	✓	1	1.1	even	1	trivial
9.20.a.b.1.1		1	3.2	odd	2
48.20.a.c.1.1		1	4.3	odd	2
75.20.a.a.1.1		1	5.4	even	2
75.20.b.a.49.1		2	5.2	odd	4
75.20.b.a.49.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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