LMFDB - Embedded newform 6.28.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,28,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	6.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:	$27.7113344903$
Analytic rank:	$0$
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	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+8192.00 q^{2} +1.59432e6 q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} +1.30607e10 q^{6} +9.68892e10 q^{7} +5.49756e11 q^{8} +2.54187e12 q^{9} +O(q^{10})$

\(q+8192.00 q^{2} +1.59432e6 q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} +1.30607e10 q^{6} +9.68892e10 q^{7} +5.49756e11 q^{8} +2.54187e12 q^{9} +1.00000e13 q^{10} +3.44951e13 q^{11} +1.06993e14 q^{12} +3.00893e14 q^{13} +7.93716e14 q^{14} +1.94620e15 q^{15} +4.50360e15 q^{16} +1.14065e16 q^{17} +2.08230e16 q^{18} +6.26944e16 q^{19} +8.19200e16 q^{20} +1.54473e17 q^{21} +2.82584e17 q^{22} -8.94750e17 q^{23} +8.76488e17 q^{24} -5.96046e18 q^{25} +2.46491e18 q^{26} +4.05256e18 q^{27} +6.50212e18 q^{28} +1.04978e20 q^{29} +1.59432e19 q^{30} +2.42605e20 q^{31} +3.68935e19 q^{32} +5.49963e19 q^{33} +9.34421e19 q^{34} +1.18273e20 q^{35} +1.70582e20 q^{36} +1.61530e21 q^{37} +5.13593e20 q^{38} +4.79720e20 q^{39} +6.71089e20 q^{40} -3.84523e21 q^{41} +1.26544e21 q^{42} -4.57280e20 q^{43} +2.31492e21 q^{44} +3.10286e21 q^{45} -7.32980e21 q^{46} -4.80403e22 q^{47} +7.18019e21 q^{48} -5.63248e22 q^{49} -4.88281e22 q^{50} +1.81857e22 q^{51} +2.01926e22 q^{52} -2.77437e23 q^{53} +3.31985e22 q^{54} +4.21082e22 q^{55} +5.32654e22 q^{56} +9.99552e22 q^{57} +8.59979e23 q^{58} +2.57780e23 q^{59} +1.30607e23 q^{60} +1.43522e23 q^{61} +1.98742e24 q^{62} +2.46279e23 q^{63} +3.02231e23 q^{64} +3.67300e23 q^{65} +4.50529e23 q^{66} -5.98904e24 q^{67} +7.65478e23 q^{68} -1.42652e24 q^{69} +9.68892e23 q^{70} -5.16701e24 q^{71} +1.39741e24 q^{72} -1.25580e25 q^{73} +1.32325e25 q^{74} -9.50291e24 q^{75} +4.20735e24 q^{76} +3.34220e24 q^{77} +3.92987e24 q^{78} -6.07834e25 q^{79} +5.49756e24 q^{80} +6.46108e24 q^{81} -3.15001e25 q^{82} +3.97116e24 q^{83} +1.03665e25 q^{84} +1.39240e25 q^{85} -3.74603e24 q^{86} +1.67369e26 q^{87} +1.89639e25 q^{88} +3.12461e26 q^{89} +2.54187e25 q^{90} +2.91532e25 q^{91} -6.00457e25 q^{92} +3.86790e26 q^{93} -3.93546e26 q^{94} +7.65313e25 q^{95} +5.88201e25 q^{96} -5.48672e26 q^{97} -4.61413e26 q^{98} +8.76818e25 q^{99} +O(q^{100})\)

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 $

$2$	8192.00	0.707107
$2$	8192.00	0.707107
$3$	1.59432e6	0.577350
$3$	1.59432e6	0.577350
$4$	6.71089e7	0.500000
$5$	1.22070e9	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.22070e9	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.30607e10	0.408248
$7$	9.68892e10	0.377965	0.188983	−	0.981980i	$-0.439481\pi$
$7$	9.68892e10	0.377965	0.188983	+	0.981980i	$0.439481\pi$
$8$	5.49756e11	0.353553
$9$	2.54187e12	0.333333
$10$	1.00000e13	0.316228
$11$	3.44951e13	0.301270	0.150635	−	0.988589i	$-0.451868\pi$
$11$	3.44951e13	0.301270	0.150635	+	0.988589i	$0.451868\pi$
$12$	1.06993e14	0.288675
$13$	3.00893e14	0.275535	0.137767	−	0.990465i	$-0.456007\pi$
$13$	3.00893e14	0.275535	0.137767	+	0.990465i	$0.456007\pi$
$14$	7.93716e14	0.267262
$15$	1.94620e15	0.258199
$16$	4.50360e15	0.250000
$17$	1.14065e16	0.279314	0.139657	−	0.990200i	$-0.455400\pi$
$17$	1.14065e16	0.279314	0.139657	+	0.990200i	$0.455400\pi$
$18$	2.08230e16	0.235702
$19$	6.26944e16	0.342023	0.171012	−	0.985269i	$-0.445296\pi$
$19$	6.26944e16	0.342023	0.171012	+	0.985269i	$0.445296\pi$
$20$	8.19200e16	0.223607
$21$	1.54473e17	0.218218
$22$	2.82584e17	0.213030
$23$	−8.94750e17	−0.370149	−0.185074	−	0.982725i	$-0.559253\pi$
$23$	−8.94750e17	−0.370149	−0.185074	+	0.982725i	$0.559253\pi$
$24$	8.76488e17	0.204124
$25$	−5.96046e18	−0.800000
$26$	2.46491e18	0.194832
$27$	4.05256e18	0.192450
$28$	6.50212e18	0.188983
$29$	1.04978e20	1.89987	0.949937	−	0.312441i	$-0.101147\pi$
$29$	1.04978e20	1.89987	0.949937	+	0.312441i	$0.101147\pi$
$30$	1.59432e19	0.182574
$31$	2.42605e20	1.78450	0.892249	−	0.451543i	$-0.149126\pi$
$31$	2.42605e20	1.78450	0.892249	+	0.451543i	$0.149126\pi$
$32$	3.68935e19	0.176777
$33$	5.49963e19	0.173938
$34$	9.34421e19	0.197505
$35$	1.18273e20	0.169031
$36$	1.70582e20	0.166667
$37$	1.61530e21	1.09026	0.545129	−	0.838352i	$-0.316481\pi$
$37$	1.61530e21	1.09026	0.545129	+	0.838352i	$0.316481\pi$
$38$	5.13593e20	0.241847
$39$	4.79720e20	0.159080
$40$	6.71089e20	0.158114
$41$	−3.84523e21	−0.649142	−0.324571	−	0.945861i	$-0.605220\pi$
$41$	−3.84523e21	−0.649142	−0.324571	+	0.945861i	$0.605220\pi$
$42$	1.26544e21	0.154304
$43$	−4.57280e20	−0.0405843	−0.0202921	−	0.999794i	$-0.506460\pi$
$43$	−4.57280e20	−0.0405843	−0.0202921	+	0.999794i	$0.506460\pi$
$44$	2.31492e21	0.150635
$45$	3.10286e21	0.149071
$46$	−7.32980e21	−0.261735
$47$	−4.80403e22	−1.28317	−0.641585	−	0.767052i	$-0.721723\pi$
$47$	−4.80403e22	−1.28317	−0.641585	+	0.767052i	$0.721723\pi$
$48$	7.18019e21	0.144338
$49$	−5.63248e22	−0.857142
$50$	−4.88281e22	−0.565685
$51$	1.81857e22	0.161262
$52$	2.01926e22	0.137767
$53$	−2.77437e23	−1.46366	−0.731829	−	0.681488i	$-0.761333\pi$
$53$	−2.77437e23	−1.46366	−0.731829	+	0.681488i	$0.761333\pi$
$54$	3.31985e22	0.136083
$55$	4.21082e22	0.134732
$56$	5.32654e22	0.133631
$57$	9.99552e22	0.197467
$58$	8.59979e23	1.34341
$59$	2.57780e23	0.319704	0.159852	−	0.987141i	$-0.448898\pi$
$59$	2.57780e23	0.319704	0.159852	+	0.987141i	$0.448898\pi$
$60$	1.30607e23	0.129099
$61$	1.43522e23	0.113492	0.0567460	−	0.998389i	$-0.481927\pi$
$61$	1.43522e23	0.113492	0.0567460	+	0.998389i	$0.481927\pi$
$62$	1.98742e24	1.26183
$63$	2.46279e23	0.125988
$64$	3.02231e23	0.125000
$65$	3.67300e23	0.123223
$66$	4.50529e23	0.122993
$67$	−5.98904e24	−1.33459	−0.667294	−	0.744794i	$-0.732548\pi$
$67$	−5.98904e24	−1.33459	−0.667294	+	0.744794i	$0.732548\pi$
$68$	7.65478e23	0.139657
$69$	−1.42652e24	−0.213705
$70$	9.68892e23	0.119523
$71$	−5.16701e24	−0.526322	−0.263161	−	0.964752i	$-0.584765\pi$
$71$	−5.16701e24	−0.526322	−0.263161	+	0.964752i	$0.584765\pi$
$72$	1.39741e24	0.117851
$73$	−1.25580e25	−0.879149	−0.439575	−	0.898206i	$-0.644871\pi$
$73$	−1.25580e25	−0.879149	−0.439575	+	0.898206i	$0.644871\pi$
$74$	1.32325e25	0.770928
$75$	−9.50291e24	−0.461880
$76$	4.20735e24	0.171012
$77$	3.34220e24	0.113870
$78$	3.92987e24	0.112487
$79$	−6.07834e25	−1.46494	−0.732468	−	0.680801i	$-0.761632\pi$
$79$	−6.07834e25	−1.46494	−0.732468	+	0.680801i	$0.761632\pi$
$80$	5.49756e24	0.111803
$81$	6.46108e24	0.111111
$82$	−3.15001e25	−0.459013
$83$	3.97116e24	0.0491318	0.0245659	−	0.999698i	$-0.492180\pi$
$83$	3.97116e24	0.0491318	0.0245659	+	0.999698i	$0.492180\pi$
$84$	1.03665e25	0.109109
$85$	1.39240e25	0.124913
$86$	−3.74603e24	−0.0286974
$87$	1.67369e26	1.09689
$88$	1.89639e25	0.106515
$89$	3.12461e26	1.50671	0.753356	−	0.657613i	$-0.228434\pi$
$89$	3.12461e26	1.50671	0.753356	+	0.657613i	$0.228434\pi$
$90$	2.54187e25	0.105409
$91$	2.91532e25	0.104143
$92$	−6.00457e25	−0.185074
$93$	3.86790e26	1.03028
$94$	−3.93546e26	−0.907339
$95$	7.65313e25	0.152957
$96$	5.88201e25	0.102062
$97$	−5.48672e26	−0.827741	−0.413870	−	0.910336i	$-0.635823\pi$
$97$	−5.48672e26	−0.827741	−0.413870	+	0.910336i	$0.635823\pi$
$98$	−4.61413e26	−0.606091
$99$	8.76818e25	0.100423
$100$	−4.00000e26	−0.400000
$101$	2.36258e26	0.206561	0.103281	−	0.994652i	$-0.467066\pi$
$101$	2.36258e26	0.206561	0.103281	+	0.994652i	$0.467066\pi$
$102$	1.48977e26	0.114029
$103$	−2.02899e27	−1.36137	−0.680686	−	0.732575i	$-0.738318\pi$
$103$	−2.02899e27	−1.36137	−0.680686	+	0.732575i	$0.738318\pi$
$104$	1.65417e26	0.0974162
$105$	1.88565e26	0.0975902
$106$	−2.27276e27	−1.03496
$107$	1.17972e27	0.473260	0.236630	−	0.971600i	$-0.423957\pi$
$107$	1.17972e27	0.473260	0.236630	+	0.971600i	$0.423957\pi$
$108$	2.71962e26	0.0962250
$109$	−2.78339e27	−0.869594	−0.434797	−	0.900529i	$-0.643180\pi$
$109$	−2.78339e27	−0.869594	−0.434797	+	0.900529i	$0.643180\pi$
$110$	3.44951e26	0.0952699
$111$	2.57530e27	0.629460
$112$	4.36350e26	0.0944913
$113$	7.39772e27	1.42082	0.710410	−	0.703788i	$-0.248510\pi$
$113$	7.39772e27	1.42082	0.710410	+	0.703788i	$0.248510\pi$
$114$	8.18833e26	0.139630
$115$	−1.09222e27	−0.165535
$116$	7.04495e27	0.949937
$117$	7.64829e26	0.0918449
$118$	2.11174e27	0.226065
$119$	1.10517e27	0.105571
$120$	1.06993e27	0.0912871
$121$	−1.19201e28	−0.909236
$122$	1.17573e27	0.0802509
$123$	−6.13053e27	−0.374782
$124$	1.62809e28	0.892249
$125$	−1.63709e28	−0.804984
$126$	2.01752e27	0.0890873
$127$	4.56858e27	0.181314	0.0906568	−	0.995882i	$-0.471103\pi$
$127$	4.56858e27	0.181314	0.0906568	+	0.995882i	$0.471103\pi$
$128$	2.47588e27	0.0883883
$129$	−7.29051e26	−0.0234313
$130$	3.00893e27	0.0871317
$131$	−2.81737e28	−0.735666	−0.367833	−	0.929892i	$-0.619900\pi$
$131$	−2.81737e28	−0.735666	−0.367833	+	0.929892i	$0.619900\pi$
$132$	3.69074e27	0.0869691
$133$	6.07441e27	0.129273
$134$	−4.90622e28	−0.943696
$135$	4.94697e27	0.0860663
$136$	6.27080e27	0.0987523
$137$	−5.51326e28	−0.786467	−0.393234	−	0.919439i	$-0.628644\pi$
$137$	−5.51326e28	−0.786467	−0.393234	+	0.919439i	$0.628644\pi$
$138$	−1.16861e28	−0.151113
$139$	7.00269e28	0.821420	0.410710	−	0.911766i	$-0.365281\pi$
$139$	7.00269e28	0.821420	0.410710	+	0.911766i	$0.365281\pi$
$140$	7.93716e27	0.0845156
$141$	−7.65917e28	−0.740839
$142$	−4.23281e28	−0.372166
$143$	1.03793e28	0.0830103
$144$	1.14475e28	0.0833333
$145$	1.28147e29	0.849650
$146$	−1.02875e29	−0.621652
$147$	−8.98000e28	−0.494871
$148$	1.08401e29	0.545129
$149$	2.78083e29	1.27691	0.638454	−	0.769660i	$-0.279574\pi$
$149$	2.78083e29	1.27691	0.638454	+	0.769660i	$0.279574\pi$
$150$	−7.78478e28	−0.326599
$151$	4.54602e29	1.74358	0.871792	−	0.489876i	$-0.162958\pi$
$151$	4.54602e29	1.74358	0.871792	+	0.489876i	$0.162958\pi$
$152$	3.44666e28	0.120923
$153$	2.89938e28	0.0931046
$154$	2.73793e28	0.0805179
$155$	2.96148e29	0.798052
$156$	3.21935e28	0.0795400
$157$	5.05735e28	0.114625	0.0573123	−	0.998356i	$-0.481747\pi$
$157$	5.05735e28	0.114625	0.0573123	+	0.998356i	$0.481747\pi$
$158$	−4.97937e29	−1.03587
$159$	−4.42324e29	−0.845043
$160$	4.50360e28	0.0790569
$161$	−8.66917e28	−0.139903
$162$	5.29292e28	0.0785674
$163$	−1.02522e30	−1.40051	−0.700253	−	0.713894i	$-0.746930\pi$
$163$	−1.02522e30	−1.40051	−0.700253	+	0.713894i	$0.746930\pi$
$164$	−2.58049e29	−0.324571
$165$	6.71341e28	0.0777875
$166$	3.25317e28	0.0347415
$167$	−4.82712e29	−0.475352	−0.237676	−	0.971344i	$-0.576386\pi$
$167$	−4.82712e29	−0.475352	−0.237676	+	0.971344i	$0.576386\pi$
$168$	8.49223e28	0.0771518
$169$	−1.10200e30	−0.924081
$170$	1.14065e29	0.0883268
$171$	1.59361e29	0.114008
$172$	−3.06875e28	−0.0202921
$173$	4.32361e29	0.264377	0.132189	−	0.991225i	$-0.457800\pi$
$173$	4.32361e29	0.264377	0.132189	+	0.991225i	$0.457800\pi$
$174$	1.37108e30	0.775620
$175$	−5.77505e29	−0.302372
$176$	1.55352e29	0.0753175
$177$	4.10985e29	0.184581
$178$	2.55968e30	1.06541
$179$	6.11216e29	0.235873	0.117937	−	0.993021i	$-0.462372\pi$
$179$	6.11216e29	0.235873	0.117937	+	0.993021i	$0.462372\pi$
$180$	2.08230e29	0.0745356
$181$	−2.12911e30	−0.707193	−0.353597	−	0.935398i	$-0.615041\pi$
$181$	−2.12911e30	−0.707193	−0.353597	+	0.935398i	$0.615041\pi$
$182$	2.38823e29	0.0736399
$183$	2.28820e29	0.0655246
$184$	−4.91894e29	−0.130867
$185$	1.97180e30	0.487578
$186$	3.16859e30	0.728519
$187$	3.93468e29	0.0841488
$188$	−3.22393e30	−0.641585
$189$	3.92649e29	0.0727394
$190$	6.26944e29	0.108157
$191$	1.17916e31	1.89505	0.947526	−	0.319679i	$-0.103575\pi$
$191$	1.17916e31	1.89505	0.947526	+	0.319679i	$0.103575\pi$
$192$	4.81855e29	0.0721688
$193$	−1.05614e31	−1.47468	−0.737340	−	0.675522i	$-0.763918\pi$
$193$	−1.05614e31	−1.47468	−0.737340	+	0.675522i	$0.763918\pi$
$194$	−4.49472e30	−0.585301
$195$	5.85596e29	0.0711427
$196$	−3.77990e30	−0.428571
$197$	5.36786e30	0.568208	0.284104	−	0.958794i	$-0.408304\pi$
$197$	5.36786e30	0.568208	0.284104	+	0.958794i	$0.408304\pi$
$198$	7.18290e29	0.0710100
$199$	−8.87988e30	−0.820145	−0.410072	−	0.912053i	$-0.634497\pi$
$199$	−8.87988e30	−0.820145	−0.410072	+	0.912053i	$0.634497\pi$
$200$	−3.27680e30	−0.282843
$201$	−9.54846e30	−0.770525
$202$	1.93543e30	0.146061
$203$	1.01712e31	0.718086
$204$	1.22042e30	0.0806309
$205$	−4.69388e30	−0.290305
$206$	−1.66215e31	−0.962636
$207$	−2.27434e30	−0.123383
$208$	1.35510e30	0.0688837
$209$	2.16265e30	0.103041
$210$	1.54473e30	0.0690067
$211$	2.43935e31	1.02203	0.511013	−	0.859573i	$-0.329271\pi$
$211$	2.43935e31	1.02203	0.511013	+	0.859573i	$0.329271\pi$
$212$	−1.86185e31	−0.731829
$213$	−8.23788e30	−0.303872
$214$	9.66431e30	0.334645
$215$	−5.58203e29	−0.0181498
$216$	2.22792e30	0.0680414
$217$	2.35058e31	0.674479
$218$	−2.28015e31	−0.614896
$219$	−2.00215e31	−0.507577
$220$	2.82584e30	0.0673660
$221$	3.43213e30	0.0769606
$222$	2.10969e31	0.445096
$223$	5.57763e31	1.10748	0.553738	−	0.832691i	$-0.313201\pi$
$223$	5.57763e31	1.10748	0.553738	+	0.832691i	$0.313201\pi$
$224$	3.57458e30	0.0668154
$225$	−1.51507e31	−0.266667
$226$	6.06021e31	1.00467
$227$	5.73808e31	0.896226	0.448113	−	0.893977i	$-0.352096\pi$
$227$	5.73808e31	0.896226	0.448113	+	0.893977i	$0.352096\pi$
$228$	6.70788e30	0.0987336
$229$	1.27510e31	0.176915	0.0884573	−	0.996080i	$-0.471806\pi$
$229$	1.27510e31	0.176915	0.0884573	+	0.996080i	$0.471806\pi$
$230$	−8.94750e30	−0.117051
$231$	5.32855e30	0.0657426
$232$	5.77122e31	0.671707
$233$	−1.19492e32	−1.31230	−0.656152	−	0.754629i	$-0.727817\pi$
$233$	−1.19492e32	−1.31230	−0.656152	+	0.754629i	$0.727817\pi$
$234$	6.26548e30	0.0649441
$235$	−5.86429e31	−0.573851
$236$	1.72993e31	0.159852
$237$	−9.69083e31	−0.845782
$238$	9.05353e30	0.0746499
$239$	−8.18060e31	−0.637402	−0.318701	−	0.947855i	$-0.603247\pi$
$239$	−8.18060e31	−0.637402	−0.318701	+	0.947855i	$0.603247\pi$
$240$	8.76488e30	0.0645497
$241$	−1.91244e32	−1.33155	−0.665775	−	0.746152i	$-0.731899\pi$
$241$	−1.91244e32	−1.33155	−0.665775	+	0.746152i	$0.731899\pi$
$242$	−9.76493e31	−0.642927
$243$	1.03011e31	0.0641500
$244$	9.63159e30	0.0567460
$245$	−6.87559e31	−0.383326
$246$	−5.02213e31	−0.265011
$247$	1.88643e31	0.0942392
$248$	1.33373e32	0.630916
$249$	6.33131e30	0.0283663
$250$	−1.34110e32	−0.569210
$251$	3.66784e32	1.47508	0.737540	−	0.675304i	$-0.235987\pi$
$251$	3.66784e32	1.47508	0.737540	+	0.675304i	$0.235987\pi$
$252$	1.65275e31	0.0629942
$253$	−3.08645e31	−0.111515
$254$	3.74258e31	0.128208
$255$	2.21993e31	0.0721185
$256$	2.02824e31	0.0625000
$257$	1.65993e32	0.485279	0.242640	−	0.970117i	$-0.421987\pi$
$257$	1.65993e32	0.485279	0.242640	+	0.970117i	$0.421987\pi$
$258$	−5.97239e30	−0.0165685
$259$	1.56505e32	0.412079
$260$	2.46491e31	0.0616114
$261$	2.66840e32	0.633291
$262$	−2.30799e32	−0.520195
$263$	6.69843e32	1.43407	0.717035	−	0.697037i	$-0.245499\pi$
$263$	6.69843e32	1.43407	0.717035	+	0.697037i	$0.245499\pi$
$264$	3.02345e31	0.0614965
$265$	−3.38668e32	−0.654568
$266$	4.97616e31	0.0914097
$267$	4.98163e32	0.869901
$268$	−4.01918e32	−0.667294
$269$	−7.62437e32	−1.20378	−0.601891	−	0.798578i	$-0.705586\pi$
$269$	−7.62437e32	−1.20378	−0.601891	+	0.798578i	$0.705586\pi$
$270$	4.05256e31	0.0608581
$271$	3.29031e32	0.470058	0.235029	−	0.971988i	$-0.424481\pi$
$271$	3.29031e32	0.470058	0.235029	+	0.971988i	$0.424481\pi$
$272$	5.13704e31	0.0698284
$273$	4.64797e31	0.0601267
$274$	−4.51646e32	−0.556116
$275$	−2.05607e32	−0.241016
$276$	−9.57322e31	−0.106853
$277$	−6.76124e32	−0.718703	−0.359352	−	0.933202i	$-0.617002\pi$
$277$	−6.76124e32	−0.718703	−0.359352	+	0.933202i	$0.617002\pi$
$278$	5.73660e32	0.580831
$279$	6.16669e32	0.594833
$280$	6.50212e31	0.0597616
$281$	−1.34817e33	−1.18089	−0.590446	−	0.807077i	$-0.701048\pi$
$281$	−1.34817e33	−1.18089	−0.590446	+	0.807077i	$0.701048\pi$
$282$	−6.27439e32	−0.523852
$283$	1.66365e33	1.32417	0.662087	−	0.749427i	$-0.269671\pi$
$283$	1.66365e33	1.32417	0.662087	+	0.749427i	$0.269671\pi$
$284$	−3.46752e32	−0.263161
$285$	1.22016e32	0.0883100
$286$	8.50273e31	0.0586971
$287$	−3.72561e32	−0.245353
$288$	9.37783e31	0.0589256
$289$	−1.53760e33	−0.921984
$290$	1.04978e33	0.600793
$291$	−8.74760e32	−0.477896
$292$	−8.42754e32	−0.439575
$293$	−1.69131e33	−0.842385	−0.421193	−	0.906971i	$-0.638388\pi$
$293$	−1.69131e33	−0.842385	−0.421193	+	0.906971i	$0.638388\pi$
$294$	−7.35642e32	−0.349927
$295$	3.14673e32	0.142976
$296$	8.88019e32	0.385464
$297$	1.39793e32	0.0579794
$298$	2.27806e33	0.902911
$299$	−2.69224e32	−0.101989
$300$	−6.37729e32	−0.230940
$301$	−4.43055e31	−0.0153394
$302$	3.72410e33	1.23290
$303$	3.76672e32	0.119258
$304$	2.82351e32	0.0855058
$305$	1.75198e32	0.0507552
$306$	2.37517e32	0.0658349
$307$	4.93547e33	1.30906	0.654531	−	0.756035i	$-0.272866\pi$
$307$	4.93547e33	1.30906	0.654531	+	0.756035i	$0.272866\pi$
$308$	2.24291e32	0.0569348
$309$	−3.23486e33	−0.785989
$310$	2.42605e33	0.564308
$311$	−2.20475e33	−0.491014	−0.245507	−	0.969395i	$-0.578954\pi$
$311$	−2.20475e33	−0.491014	−0.245507	+	0.969395i	$0.578954\pi$
$312$	2.63729e32	0.0562433
$313$	5.07005e33	1.03553	0.517766	−	0.855522i	$-0.326764\pi$
$313$	5.07005e33	1.03553	0.517766	+	0.855522i	$0.326764\pi$
$314$	4.14298e32	0.0810519
$315$	3.00634e32	0.0563437
$316$	−4.07910e33	−0.732468
$317$	−1.74494e33	−0.300248	−0.150124	−	0.988667i	$-0.547967\pi$
$317$	−1.74494e33	−0.300248	−0.150124	+	0.988667i	$0.547967\pi$
$318$	−3.62352e33	−0.597536
$319$	3.62122e33	0.572375
$320$	3.68935e32	0.0559017
$321$	1.88086e33	0.273237
$322$	−7.10178e32	−0.0989266
$323$	7.15125e32	0.0955318
$324$	4.33596e32	0.0555556
$325$	−1.79346e33	−0.220428
$326$	−8.39862e33	−0.990308
$327$	−4.43762e33	−0.502060
$328$	−2.11394e33	−0.229506
$329$	−4.65458e33	−0.484994
$330$	5.49963e32	0.0550041
$331$	−6.34472e33	−0.609165	−0.304582	−	0.952486i	$-0.598517\pi$
$331$	−6.34472e33	−0.609165	−0.304582	+	0.952486i	$0.598517\pi$
$332$	2.66500e32	0.0245659
$333$	4.10587e33	0.363419
$334$	−3.95438e33	−0.336125
$335$	−7.31084e33	−0.596846
$336$	6.95683e32	0.0545546
$337$	−2.23148e32	−0.0168109	−0.00840543	−	0.999965i	$-0.502676\pi$
$337$	−2.23148e32	−0.0168109	−0.00840543	+	0.999965i	$0.502676\pi$
$338$	−9.02756e33	−0.653424
$339$	1.17944e34	0.820311
$340$	9.34421e32	0.0624565
$341$	8.36866e33	0.537616
$342$	1.30548e33	0.0806156
$343$	−1.18241e34	−0.701935
$344$	−2.51392e32	−0.0143487
$345$	−1.74136e33	−0.0955720
$346$	3.54190e33	0.186943
$347$	3.41729e34	1.73474	0.867369	−	0.497665i	$-0.165809\pi$
$347$	3.41729e34	1.73474	0.867369	+	0.497665i	$0.165809\pi$
$348$	1.12319e34	0.548446
$349$	2.14957e33	0.100974	0.0504868	−	0.998725i	$-0.483923\pi$
$349$	2.14957e33	0.100974	0.0504868	+	0.998725i	$0.483923\pi$
$350$	−4.73092e33	−0.213809
$351$	1.21938e33	0.0530267
$352$	1.27264e33	0.0532575
$353$	3.18480e34	1.28269	0.641347	−	0.767251i	$-0.278376\pi$
$353$	3.18480e34	1.28269	0.641347	+	0.767251i	$0.278376\pi$
$354$	3.36679e33	0.130518
$355$	−6.30738e33	−0.235378
$356$	2.09689e34	0.753356
$357$	1.76199e33	0.0609514
$358$	5.00708e33	0.166788
$359$	1.63087e34	0.523171	0.261586	−	0.965180i	$-0.415755\pi$
$359$	1.63087e34	0.523171	0.261586	+	0.965180i	$0.415755\pi$
$360$	1.70582e33	0.0527046
$361$	−2.96700e34	−0.883020
$362$	−1.74417e34	−0.500061
$363$	−1.90045e34	−0.524948
$364$	1.95644e33	0.0520713
$365$	−1.53296e34	−0.393167
$366$	1.87449e33	0.0463329
$367$	−7.33607e34	−1.74772	−0.873860	−	0.486178i	$-0.838391\pi$
$367$	−7.33607e34	−1.74772	−0.873860	+	0.486178i	$0.838391\pi$
$368$	−4.02960e33	−0.0925371
$369$	−9.77405e33	−0.216381
$370$	1.61530e34	0.344770
$371$	−2.68806e34	−0.553212
$372$	2.59571e34	0.515140
$373$	1.73575e34	0.332214	0.166107	−	0.986108i	$-0.446880\pi$
$373$	1.73575e34	0.332214	0.166107	+	0.986108i	$0.446880\pi$
$374$	3.22329e33	0.0595022
$375$	−2.61005e34	−0.464758
$376$	−2.64104e34	−0.453669
$377$	3.15871e34	0.523481
$378$	3.21658e33	0.0514346
$379$	−7.14293e33	−0.110217	−0.0551083	−	0.998480i	$-0.517550\pi$
$379$	−7.14293e33	−0.110217	−0.0551083	+	0.998480i	$0.517550\pi$
$380$	5.13593e33	0.0764787
$381$	7.28379e33	0.104682
$382$	9.65965e34	1.34000
$383$	−7.85416e34	−1.05176	−0.525880	−	0.850559i	$-0.676264\pi$
$383$	−7.85416e34	−1.05176	−0.525880	+	0.850559i	$0.676264\pi$
$384$	3.94735e33	0.0510310
$385$	4.07983e33	0.0509240
$386$	−8.65189e34	−1.04276
$387$	−1.16234e33	−0.0135281
$388$	−3.68207e34	−0.413870
$389$	1.06081e35	1.15165	0.575824	−	0.817574i	$-0.304681\pi$
$389$	1.06081e35	1.15165	0.575824	+	0.817574i	$0.304681\pi$
$390$	4.79720e33	0.0503055
$391$	−1.02060e34	−0.103388
$392$	−3.09649e34	−0.303046
$393$	−4.49179e34	−0.424737
$394$	4.39735e34	0.401783
$395$	−7.41984e34	−0.655140
$396$	5.88423e33	0.0502116
$397$	2.31367e35	1.90822	0.954112	−	0.299451i	$-0.0968036\pi$
$397$	2.31367e35	1.90822	0.954112	+	0.299451i	$0.0968036\pi$
$398$	−7.27440e34	−0.579930
$399$	9.68458e33	0.0746357
$400$	−2.68435e34	−0.200000
$401$	3.29848e34	0.237610	0.118805	−	0.992918i	$-0.462094\pi$
$401$	3.29848e34	0.237610	0.118805	+	0.992918i	$0.462094\pi$
$402$	−7.82210e34	−0.544843
$403$	7.29979e34	0.491691
$404$	1.58550e34	0.103281
$405$	7.88706e33	0.0496904
$406$	8.33227e34	0.507764
$407$	5.57198e34	0.328462
$408$	9.99767e33	0.0570147
$409$	3.56464e35	1.96676	0.983379	−	0.181563i	$-0.0581155\pi$
$409$	3.56464e35	1.96676	0.983379	+	0.181563i	$0.0581155\pi$
$410$	−3.84523e34	−0.205277
$411$	−8.78991e34	−0.454067
$412$	−1.36163e35	−0.680686
$413$	2.49761e34	0.120837
$414$	−1.86314e34	−0.0872449
$415$	4.84761e33	0.0219724
$416$	1.11010e34	0.0487081
$417$	1.11645e35	0.474247
$418$	1.77164e34	0.0728612
$419$	−8.12999e34	−0.323743	−0.161872	−	0.986812i	$-0.551753\pi$
$419$	−8.12999e34	−0.323743	−0.161872	+	0.986812i	$0.551753\pi$
$420$	1.26544e34	0.0487951
$421$	−4.71631e35	−1.76114	−0.880571	−	0.473914i	$-0.842841\pi$
$421$	−4.71631e35	−1.76114	−0.880571	+	0.473914i	$0.842841\pi$
$422$	1.99832e35	0.722681
$423$	−1.22112e35	−0.427724
$424$	−1.52522e35	−0.517481
$425$	−6.79881e34	−0.223451
$426$	−6.74847e34	−0.214870
$427$	1.39057e34	0.0428960
$428$	7.91700e34	0.236630
$429$	1.65480e34	0.0479260
$430$	−4.57280e33	−0.0128339
$431$	−3.31026e35	−0.900366	−0.450183	−	0.892936i	$-0.648641\pi$
$431$	−3.31026e35	−0.900366	−0.450183	+	0.892936i	$0.648641\pi$
$432$	1.82511e34	0.0481125
$433$	−5.01044e35	−1.28023	−0.640117	−	0.768277i	$-0.721114\pi$
$433$	−5.01044e35	−1.28023	−0.640117	+	0.768277i	$0.721114\pi$
$434$	1.92559e35	0.476928
$435$	2.04307e35	0.490545
$436$	−1.86790e35	−0.434797
$437$	−5.60959e34	−0.126599
$438$	−1.64016e35	−0.358911
$439$	−2.17216e35	−0.460914	−0.230457	−	0.973082i	$-0.574022\pi$
$439$	−2.17216e35	−0.460914	−0.230457	+	0.973082i	$0.574022\pi$
$440$	2.31492e34	0.0476350
$441$	−1.43170e35	−0.285714
$442$	2.81160e34	0.0544194
$443$	2.95266e35	0.554323	0.277161	−	0.960823i	$-0.410606\pi$
$443$	2.95266e35	0.554323	0.277161	+	0.960823i	$0.410606\pi$
$444$	1.72826e35	0.314730
$445$	3.81422e35	0.673822
$446$	4.56919e35	0.783103
$447$	4.43354e35	0.737224
$448$	2.92830e34	0.0472457
$449$	−6.02841e34	−0.0943795	−0.0471897	−	0.998886i	$-0.515027\pi$
$449$	−6.02841e34	−0.0943795	−0.0471897	+	0.998886i	$0.515027\pi$
$450$	−1.24115e35	−0.188562
$451$	−1.32641e35	−0.195567
$452$	4.96453e35	0.710410
$453$	7.24783e35	1.00666
$454$	4.70064e35	0.633727
$455$	3.55875e34	0.0465739
$456$	5.49509e34	0.0698152
$457$	−2.15103e35	−0.265325	−0.132662	−	0.991161i	$-0.542353\pi$
$457$	−2.15103e35	−0.265325	−0.132662	+	0.991161i	$0.542353\pi$
$458$	1.04456e35	0.125098
$459$	4.62255e34	0.0537540
$460$	−7.32980e34	−0.0827677
$461$	−1.30614e36	−1.43228	−0.716140	−	0.697957i	$-0.754093\pi$
$461$	−1.30614e36	−1.43228	−0.716140	+	0.697957i	$0.754093\pi$
$462$	4.36514e34	0.0464870
$463$	8.41706e35	0.870596	0.435298	−	0.900286i	$-0.356643\pi$
$463$	8.41706e35	0.870596	0.435298	+	0.900286i	$0.356643\pi$
$464$	4.72778e35	0.474969
$465$	4.72156e35	0.460756
$466$	−9.78879e35	−0.927939
$467$	2.34162e35	0.215644	0.107822	−	0.994170i	$-0.465612\pi$
$467$	2.34162e35	0.215644	0.107822	+	0.994170i	$0.465612\pi$
$468$	5.13268e34	0.0459224
$469$	−5.80273e35	−0.504428
$470$	−4.80403e35	−0.405774
$471$	8.06305e34	0.0661786
$472$	1.41716e35	0.113032
$473$	−1.57739e34	−0.0122268
$474$	−7.93873e35	−0.598058
$475$	−3.73688e35	−0.273618
$476$	7.41666e34	0.0527854
$477$	−7.05207e35	−0.487886
$478$	−6.70155e35	−0.450711
$479$	6.18533e35	0.404421	0.202210	−	0.979342i	$-0.435188\pi$
$479$	6.18533e35	0.404421	0.202210	+	0.979342i	$0.435188\pi$
$480$	7.18019e34	0.0456435
$481$	4.86031e35	0.300404
$482$	−1.56667e36	−0.941548
$483$	−1.38214e35	−0.0807732
$484$	−7.99943e35	−0.454618
$485$	−6.69765e35	−0.370177
$486$	8.43862e34	0.0453609
$487$	7.82358e35	0.409039	0.204519	−	0.978863i	$-0.434437\pi$
$487$	7.82358e35	0.409039	0.204519	+	0.978863i	$0.434437\pi$
$488$	7.89020e34	0.0401255
$489$	−1.63453e36	−0.808583
$490$	−5.63248e35	−0.271052
$491$	5.20847e35	0.243843	0.121922	−	0.992540i	$-0.461094\pi$
$491$	5.20847e35	0.243843	0.121922	+	0.992540i	$0.461094\pi$
$492$	−4.11413e35	−0.187391
$493$	1.19743e36	0.530661
$494$	1.54536e35	0.0666372
$495$	1.07033e35	0.0449107
$496$	1.09259e36	0.446125
$497$	−5.00627e35	−0.198931
$498$	5.18661e34	0.0200580
$499$	3.67348e36	1.38267	0.691337	−	0.722532i	$-0.257022\pi$
$499$	3.67348e36	1.38267	0.691337	+	0.722532i	$0.257022\pi$
$500$	−1.09863e36	−0.402492
$501$	−7.69599e35	−0.274445
$502$	3.00470e36	1.04304
$503$	3.63527e36	1.22848	0.614242	−	0.789118i	$-0.289462\pi$
$503$	3.63527e36	1.22848	0.614242	+	0.789118i	$0.289462\pi$
$504$	1.35394e35	0.0445436
$505$	2.88401e35	0.0923769
$506$	−2.52842e35	−0.0788527
$507$	−1.75694e36	−0.533518
$508$	3.06592e35	0.0906568
$509$	−1.15664e36	−0.333049	−0.166524	−	0.986037i	$-0.553254\pi$
$509$	−1.15664e36	−0.333049	−0.166524	+	0.986037i	$0.553254\pi$
$510$	1.81857e35	0.0509955
$511$	−1.21674e36	−0.332288
$512$	1.66153e35	0.0441942
$513$	2.54073e35	0.0658224
$514$	1.35981e36	0.343144
$515$	−2.47679e36	−0.608824
$516$	−4.89258e34	−0.0117157
$517$	−1.65715e36	−0.386581
$518$	1.28209e36	0.291384
$519$	6.89323e35	0.152638
$520$	2.01926e35	0.0435659
$521$	1.14451e36	0.240607	0.120304	−	0.992737i	$-0.461613\pi$
$521$	1.14451e36	0.240607	0.120304	+	0.992737i	$0.461613\pi$
$522$	2.18595e36	0.447805
$523$	−1.04105e36	−0.207825	−0.103912	−	0.994586i	$-0.533136\pi$
$523$	−1.04105e36	−0.207825	−0.103912	+	0.994586i	$0.533136\pi$
$524$	−1.89070e36	−0.367833
$525$	−9.20729e35	−0.174575
$526$	5.48735e36	1.01404
$527$	2.76727e36	0.498435
$528$	2.47681e35	0.0434846
$529$	−5.04263e36	−0.862990
$530$	−2.77437e36	−0.462849
$531$	6.55243e35	0.106568
$532$	4.07647e35	0.0646364
$533$	−1.15700e36	−0.178861
$534$	4.08095e36	0.615113
$535$	1.44009e36	0.211648
$536$	−3.29251e36	−0.471848
$537$	9.74476e35	0.136182
$538$	−6.24588e36	−0.851203
$539$	−1.94293e36	−0.258231
$540$	3.31985e35	0.0430331
$541$	−4.09753e36	−0.518035	−0.259018	−	0.965873i	$-0.583399\pi$
$541$	−4.09753e36	−0.518035	−0.259018	+	0.965873i	$0.583399\pi$
$542$	2.69543e36	0.332382
$543$	−3.39449e36	−0.408298
$544$	4.20826e35	0.0493762
$545$	−3.39769e36	−0.388894
$546$	3.80762e35	0.0425160
$547$	−1.15878e37	−1.26233	−0.631164	−	0.775650i	$-0.717422\pi$
$547$	−1.15878e37	−1.26233	−0.631164	+	0.775650i	$0.717422\pi$
$548$	−3.69988e36	−0.393234
$549$	3.64813e35	0.0378307
$550$	−1.68433e36	−0.170424
$551$	6.58153e36	0.649801
$552$	−7.84238e35	−0.0755563
$553$	−5.88925e36	−0.553695
$554$	−5.53881e36	−0.508200
$555$	3.14368e36	0.281503
$556$	4.69943e36	0.410710
$557$	6.70845e36	0.572238	0.286119	−	0.958194i	$-0.407635\pi$
$557$	6.70845e36	0.572238	0.286119	+	0.958194i	$0.407635\pi$
$558$	5.05175e36	0.420610
$559$	−1.37592e35	−0.0111824
$560$	5.32654e35	0.0422578
$561$	6.27316e35	0.0485833
$562$	−1.10442e37	−0.835017
$563$	2.13431e37	1.57541	0.787706	−	0.616051i	$-0.211268\pi$
$563$	2.13431e37	1.57541	0.787706	+	0.616051i	$0.211268\pi$
$564$	−5.13998e36	−0.370419
$565$	9.03042e36	0.635410
$566$	1.36286e37	0.936333
$567$	6.26009e35	0.0419961
$568$	−2.84059e36	−0.186083
$569$	2.12293e37	1.35806	0.679032	−	0.734109i	$-0.262400\pi$
$569$	2.12293e37	1.35806	0.679032	+	0.734109i	$0.262400\pi$
$570$	9.99552e35	0.0624446
$571$	4.26569e35	0.0260257	0.0130128	−	0.999915i	$-0.495858\pi$
$571$	4.26569e35	0.0260257	0.0130128	+	0.999915i	$0.495858\pi$
$572$	6.96544e35	0.0415051
$573$	1.87996e37	1.09411
$574$	−3.05202e36	−0.173491
$575$	5.33313e36	0.296119
$576$	7.68232e35	0.0416667
$577$	1.07242e37	0.568187	0.284093	−	0.958797i	$-0.408307\pi$
$577$	1.07242e37	0.568187	0.284093	+	0.958797i	$0.408307\pi$
$578$	−1.25960e37	−0.651941
$579$	−1.68383e37	−0.851406
$580$	8.59979e36	0.424825
$581$	3.84762e35	0.0185701
$582$	−7.16604e36	−0.337924
$583$	−9.57019e36	−0.440956
$584$	−6.90384e36	−0.310826
$585$	9.33629e35	0.0410743
$586$	−1.38552e37	−0.595656
$587$	−4.07635e37	−1.71260	−0.856302	−	0.516476i	$-0.827244\pi$
$587$	−4.07635e37	−1.71260	−0.856302	+	0.516476i	$0.827244\pi$
$588$	−6.02638e36	−0.247436
$589$	1.52100e37	0.610340
$590$	2.57780e36	0.101099
$591$	8.55810e36	0.328055
$592$	7.27465e36	0.272564
$593$	−2.65397e37	−0.971982	−0.485991	−	0.873964i	$-0.661541\pi$
$593$	−2.65397e37	−0.971982	−0.485991	+	0.873964i	$0.661541\pi$
$594$	1.14519e36	0.0409976
$595$	1.34908e36	0.0472127
$596$	1.86618e37	0.638454
$597$	−1.41574e37	−0.473511
$598$	−2.20548e36	−0.0721169
$599$	−5.47539e37	−1.75046	−0.875232	−	0.483703i	$-0.839291\pi$
$599$	−5.47539e37	−1.75046	−0.875232	+	0.483703i	$0.839291\pi$
$600$	−5.22428e36	−0.163299
$601$	3.81934e37	1.16730	0.583651	−	0.812005i	$-0.301624\pi$
$601$	3.81934e37	1.16730	0.583651	+	0.812005i	$0.301624\pi$
$602$	−3.62950e35	−0.0108466
$603$	−1.52233e37	−0.444863
$604$	3.05078e37	0.871792
$605$	−1.45509e37	−0.406623
$606$	3.08570e36	0.0843282
$607$	−5.59979e37	−1.49666	−0.748332	−	0.663324i	$-0.769145\pi$
$607$	−5.59979e37	−1.49666	−0.748332	+	0.663324i	$0.769145\pi$
$608$	2.31302e36	0.0604617
$609$	1.62162e37	0.414587
$610$	1.43522e36	0.0358893
$611$	−1.44550e37	−0.353558
$612$	1.94574e36	0.0465523
$613$	3.41746e37	0.799810	0.399905	−	0.916556i	$-0.369043\pi$
$613$	3.41746e37	0.799810	0.399905	+	0.916556i	$0.369043\pi$
$614$	4.04314e37	0.925647
$615$	−7.48356e36	−0.167608
$616$	1.83739e36	0.0402590
$617$	−4.09863e37	−0.878595	−0.439298	−	0.898342i	$-0.644773\pi$
$617$	−4.09863e37	−0.878595	−0.439298	+	0.898342i	$0.644773\pi$
$618$	−2.65000e37	−0.555778
$619$	8.21032e37	1.68475	0.842376	−	0.538890i	$-0.181156\pi$
$619$	8.21032e37	1.68475	0.842376	+	0.538890i	$0.181156\pi$
$620$	1.98742e37	0.399026
$621$	−3.62603e36	−0.0712351
$622$	−1.80613e37	−0.347199
$623$	3.02741e37	0.569485
$624$	2.16047e36	0.0397700
$625$	2.44249e37	0.440000
$626$	4.15338e37	0.732231
$627$	3.44796e36	0.0594909
$628$	3.39393e36	0.0573123
$629$	1.84249e37	0.304524
$630$	2.46279e36	0.0398410
$631$	−1.32062e37	−0.209114	−0.104557	−	0.994519i	$-0.533342\pi$
$631$	−1.32062e37	−0.209114	−0.104557	+	0.994519i	$0.533342\pi$
$632$	−3.34160e37	−0.517933
$633$	3.88912e37	0.590066
$634$	−1.42945e37	−0.212307
$635$	5.57688e36	0.0810860
$636$	−2.96838e37	−0.422522
$637$	−1.69477e37	−0.236172
$638$	2.96650e37	0.404730
$639$	−1.31338e37	−0.175441
$640$	3.02231e36	0.0395285
$641$	2.31400e36	0.0296333	0.0148166	−	0.999890i	$-0.495284\pi$
$641$	2.31400e36	0.0296333	0.0148166	+	0.999890i	$0.495284\pi$
$642$	1.54080e37	0.193208
$643$	−5.12051e37	−0.628731	−0.314366	−	0.949302i	$-0.601792\pi$
$643$	−5.12051e37	−0.628731	−0.314366	+	0.949302i	$0.601792\pi$
$644$	−5.81778e36	−0.0699517
$645$	−8.89955e35	−0.0104788
$646$	5.85830e36	0.0675512
$647$	6.39865e37	0.722571	0.361285	−	0.932455i	$-0.382338\pi$
$647$	6.39865e37	0.722571	0.361285	+	0.932455i	$0.382338\pi$
$648$	3.55202e36	0.0392837
$649$	8.89215e36	0.0963171
$650$	−1.46920e37	−0.155866
$651$	3.74758e37	0.389410
$652$	−6.88015e37	−0.700253
$653$	−3.67195e37	−0.366074	−0.183037	−	0.983106i	$-0.558593\pi$
$653$	−3.67195e37	−0.366074	−0.183037	+	0.983106i	$0.558593\pi$
$654$	−3.63530e37	−0.355010
$655$	−3.43917e37	−0.329000
$656$	−1.73174e37	−0.162286
$657$	−3.19208e37	−0.293050
$658$	−3.81304e37	−0.342942
$659$	1.28742e38	1.13440	0.567200	−	0.823580i	$-0.308027\pi$
$659$	1.28742e38	1.13440	0.567200	+	0.823580i	$0.308027\pi$
$660$	4.50529e36	0.0388938
$661$	−1.03496e38	−0.875391	−0.437696	−	0.899123i	$-0.644205\pi$
$661$	−1.03496e38	−0.875391	−0.437696	+	0.899123i	$0.644205\pi$
$662$	−5.19760e37	−0.430744
$663$	5.47193e36	0.0444332
$664$	2.18317e36	0.0173707
$665$	7.41506e36	0.0578126
$666$	3.36353e37	0.256976
$667$	−9.39290e37	−0.703236
$668$	−3.23942e37	−0.237676
$669$	8.89254e37	0.639401
$670$	−5.98904e37	−0.422034
$671$	4.95079e36	0.0341917
$672$	5.69904e36	0.0385759
$673$	7.31978e37	0.485618	0.242809	−	0.970074i	$-0.421931\pi$
$673$	7.31978e37	0.485618	0.242809	+	0.970074i	$0.421931\pi$
$674$	−1.82803e36	−0.0118871
$675$	−2.41551e37	−0.153960
$676$	−7.39538e37	−0.462040
$677$	−2.18861e38	−1.34036	−0.670180	−	0.742198i	$-0.733783\pi$
$677$	−2.18861e38	−1.34036	−0.670180	+	0.742198i	$0.733783\pi$
$678$	9.66194e37	0.580047
$679$	−5.31604e37	−0.312857
$680$	7.65478e36	0.0441634
$681$	9.14835e37	0.517436
$682$	6.85561e37	0.380152
$683$	2.80256e38	1.52362	0.761808	−	0.647803i	$-0.224312\pi$
$683$	2.80256e38	1.52362	0.761808	+	0.647803i	$0.224312\pi$
$684$	1.06945e37	0.0570038
$685$	−6.73005e37	−0.351719
$686$	−9.68629e37	−0.496343
$687$	2.03291e37	0.102142
$688$	−2.05940e36	−0.0101461
$689$	−8.34786e37	−0.403288
$690$	−1.42652e37	−0.0675796
$691$	1.02659e38	0.476918	0.238459	−	0.971153i	$-0.423358\pi$
$691$	1.02659e38	0.476918	0.238459	+	0.971153i	$0.423358\pi$
$692$	2.90153e37	0.132189
$693$	8.49542e36	0.0379565
$694$	2.79944e38	1.22665
$695$	8.54820e37	0.367350
$696$	9.20119e37	0.387810
$697$	−4.38606e37	−0.181314
$698$	1.76093e37	0.0713991
$699$	−1.90509e38	−0.757659
$700$	−3.87557e37	−0.151186
$701$	1.43700e38	0.549873	0.274936	−	0.961462i	$-0.411343\pi$
$701$	1.43700e38	0.549873	0.274936	+	0.961462i	$0.411343\pi$
$702$	9.98919e36	0.0374955
$703$	1.01270e38	0.372893
$704$	1.04255e37	0.0376587
$705$	−9.34958e37	−0.331313
$706$	2.60899e38	0.907002
$707$	2.28909e37	0.0780729
$708$	2.75807e37	0.0922905
$709$	8.89829e37	0.292134	0.146067	−	0.989275i	$-0.453338\pi$
$709$	8.89829e37	0.292134	0.146067	+	0.989275i	$0.453338\pi$
$710$	−5.16701e37	−0.166438
$711$	−1.54503e38	−0.488312
$712$	1.71777e38	0.532703
$713$	−2.17071e38	−0.660530
$714$	1.44343e37	0.0430991
$715$	1.26701e37	0.0371233
$716$	4.10180e37	0.117937
$717$	−1.30425e38	−0.368004
$718$	1.33601e38	0.369938
$719$	4.55640e38	1.23817	0.619087	−	0.785322i	$-0.287503\pi$
$719$	4.55640e38	1.23817	0.619087	+	0.785322i	$0.287503\pi$
$720$	1.39741e37	0.0372678
$721$	−1.96587e38	−0.514552
$722$	−2.43057e38	−0.624390
$723$	−3.04905e38	−0.768771
$724$	−1.42882e38	−0.353597
$725$	−6.25717e38	−1.51990
$726$	−1.55685e38	−0.371194
$727$	−4.44330e38	−1.03990	−0.519949	−	0.854197i	$-0.674049\pi$
$727$	−4.44330e38	−1.03990	−0.519949	+	0.854197i	$0.674049\pi$
$728$	1.60272e37	0.0368199
$729$	1.64232e37	0.0370370
$730$	−1.25580e38	−0.278011
$731$	−5.21596e36	−0.0113357
$732$	1.53559e37	0.0327623
$733$	−1.70169e38	−0.356432	−0.178216	−	0.983991i	$-0.557033\pi$
$733$	−1.70169e38	−0.356432	−0.178216	+	0.983991i	$0.557033\pi$
$734$	−6.00971e38	−1.23582
$735$	−1.09619e38	−0.221313
$736$	−3.30105e37	−0.0654336
$737$	−2.06592e38	−0.402071
$738$	−8.00690e37	−0.153004
$739$	7.84015e38	1.47104	0.735520	−	0.677503i	$-0.236938\pi$
$739$	7.84015e38	1.47104	0.735520	+	0.677503i	$0.236938\pi$
$740$	1.32325e38	0.243789
$741$	3.00758e37	0.0544090
$742$	−2.20206e38	−0.391180
$743$	6.91082e38	1.20554	0.602769	−	0.797916i	$-0.294064\pi$
$743$	6.91082e38	1.20554	0.602769	+	0.797916i	$0.294064\pi$
$744$	2.12640e38	0.364259
$745$	3.39457e38	0.571051
$746$	1.42193e38	0.234911
$747$	1.00942e37	0.0163773
$748$	2.64052e37	0.0420744
$749$	1.14303e38	0.178876
$750$	−2.13815e38	−0.328634
$751$	5.92509e38	0.894449	0.447225	−	0.894422i	$-0.352412\pi$
$751$	5.92509e38	0.894449	0.447225	+	0.894422i	$0.352412\pi$
$752$	−2.16354e38	−0.320793
$753$	5.84772e38	0.851637
$754$	2.58761e38	0.370157
$755$	5.54934e38	0.779754
$756$	2.63502e37	0.0363697
$757$	5.23346e38	0.709569	0.354785	−	0.934948i	$-0.384554\pi$
$757$	5.23346e38	0.709569	0.354785	+	0.934948i	$0.384554\pi$
$758$	−5.85149e37	−0.0779349
$759$	−4.92079e37	−0.0643830
$760$	4.20735e37	0.0540786
$761$	−9.61949e38	−1.21467	−0.607336	−	0.794445i	$-0.707762\pi$
$761$	−9.61949e38	−1.21467	−0.607336	+	0.794445i	$0.707762\pi$
$762$	5.96688e37	0.0740210
$763$	−2.69681e38	−0.328676
$764$	7.91319e38	0.947526
$765$	3.53928e37	0.0416376
$766$	−6.43413e38	−0.743706
$767$	7.75642e37	0.0880894
$768$	3.23367e37	0.0360844
$769$	7.52098e38	0.824649	0.412324	−	0.911037i	$-0.364717\pi$
$769$	7.52098e38	0.824649	0.412324	+	0.911037i	$0.364717\pi$
$770$	3.34220e37	0.0360087
$771$	2.64646e38	0.280176
$772$	−7.08763e38	−0.737340
$773$	7.81318e37	0.0798738	0.0399369	−	0.999202i	$-0.487284\pi$
$773$	7.81318e37	0.0798738	0.0399369	+	0.999202i	$0.487284\pi$
$774$	−9.52192e36	−0.00956580
$775$	−1.44604e39	−1.42760
$776$	−3.01636e38	−0.292651
$777$	2.49519e38	0.237914
$778$	8.69019e38	0.814338
$779$	−2.41074e38	−0.222022
$780$	3.92987e37	0.0355714
$781$	−1.78236e38	−0.158565
$782$	−8.36074e37	−0.0731061
$783$	4.25429e38	0.365631
$784$	−2.53665e38	−0.214286
$785$	6.17353e37	0.0512617
$786$	−3.67968e38	−0.300334
$787$	−1.90701e39	−1.53001	−0.765005	−	0.644024i	$-0.777264\pi$
$787$	−1.90701e39	−1.53001	−0.765005	+	0.644024i	$0.777264\pi$
$788$	3.60231e38	0.284104
$789$	1.06795e39	0.827961
$790$	−6.07834e38	−0.463254
$791$	7.16759e38	0.537020
$792$	4.82036e37	0.0355050
$793$	4.31846e37	0.0312710
$794$	1.89536e39	1.34932
$795$	−5.39946e38	−0.377915
$796$	−5.95919e38	−0.410072
$797$	−2.85595e39	−1.93225	−0.966124	−	0.258079i	$-0.916911\pi$
$797$	−2.85595e39	−1.93225	−0.966124	+	0.258079i	$0.916911\pi$
$798$	7.93361e37	0.0527754
$799$	−5.47972e38	−0.358407
$800$	−2.19902e38	−0.141421
$801$	7.94233e38	0.502237
$802$	2.70211e38	0.168015
$803$	−4.33190e38	−0.264861
$804$	−6.40786e38	−0.385262
$805$	−1.05825e38	−0.0625667
$806$	5.97999e38	0.347678
$807$	−1.21557e39	−0.695004
$808$	1.29884e38	0.0730304
$809$	2.51764e39	1.39216	0.696079	−	0.717965i	$-0.254926\pi$
$809$	2.51764e39	1.39216	0.696079	+	0.717965i	$0.254926\pi$
$810$	6.46108e37	0.0351364
$811$	−2.67985e39	−1.43327	−0.716635	−	0.697448i	$-0.754319\pi$
$811$	−2.67985e39	−1.43327	−0.716635	+	0.697448i	$0.754319\pi$
$812$	6.82579e38	0.359043
$813$	5.24582e38	0.271388
$814$	4.56456e38	0.232258
$815$	−1.25149e39	−0.626326
$816$	8.19009e37	0.0403155
$817$	−2.86689e37	−0.0138808
$818$	2.92015e39	1.39071
$819$	7.41036e37	0.0347142
$820$	−3.15001e38	−0.145153
$821$	−2.26876e39	−1.02838	−0.514192	−	0.857675i	$-0.671908\pi$
$821$	−2.26876e39	−1.02838	−0.514192	+	0.857675i	$0.671908\pi$
$822$	−7.20070e38	−0.321074
$823$	2.01600e39	0.884285	0.442143	−	0.896945i	$-0.354218\pi$
$823$	2.01600e39	0.884285	0.442143	+	0.896945i	$0.354218\pi$
$824$	−1.11545e39	−0.481318
$825$	−3.27803e38	−0.139151
$826$	2.04605e38	0.0854446
$827$	1.90457e39	0.782480	0.391240	−	0.920289i	$-0.372046\pi$
$827$	1.90457e39	0.782480	0.391240	+	0.920289i	$0.372046\pi$
$828$	−1.52628e38	−0.0616914
$829$	4.29630e39	1.70847	0.854236	−	0.519885i	$-0.174025\pi$
$829$	4.29630e39	1.70847	0.854236	+	0.519885i	$0.174025\pi$
$830$	3.97116e37	0.0155369
$831$	−1.07796e39	−0.414943
$832$	9.09392e37	0.0344418
$833$	−6.42470e38	−0.239412
$834$	9.14600e38	0.335343
$835$	−5.89248e38	−0.212584
$836$	1.45133e38	0.0515206
$837$	9.83169e38	0.343427
$838$	−6.66009e38	−0.228921
$839$	1.84551e39	0.624208	0.312104	−	0.950048i	$-0.398966\pi$
$839$	1.84551e39	0.624208	0.312104	+	0.950048i	$0.398966\pi$
$840$	1.03665e38	0.0345033
$841$	7.96722e39	2.60952
$842$	−3.86360e39	−1.24532
$843$	−2.14942e39	−0.681789
$844$	1.63702e39	0.511013
$845$	−1.34521e39	−0.413261
$846$	−1.00034e39	−0.302446
$847$	−1.15493e39	−0.343660
$848$	−1.24946e39	−0.365914
$849$	2.65240e39	0.764512
$850$	−5.56959e38	−0.158004
$851$	−1.44529e39	−0.403557
$852$	−5.52835e38	−0.151936
$853$	−2.91353e38	−0.0788147	−0.0394074	−	0.999223i	$-0.512547\pi$
$853$	−2.91353e38	−0.0788147	−0.0394074	+	0.999223i	$0.512547\pi$
$854$	1.13916e38	0.0303321
$855$	1.94532e38	0.0509858
$856$	6.48561e38	0.167323
$857$	−3.74975e39	−0.952272	−0.476136	−	0.879372i	$-0.657963\pi$
$857$	−3.74975e39	−0.952272	−0.476136	+	0.879372i	$0.657963\pi$
$858$	1.35561e38	0.0338888
$859$	1.25499e39	0.308839	0.154419	−	0.988005i	$-0.450649\pi$
$859$	1.25499e39	0.308839	0.154419	+	0.988005i	$0.450649\pi$
$860$	−3.74603e37	−0.00907492
$861$	−5.93983e38	−0.141655
$862$	−2.71177e39	−0.636655
$863$	5.25992e39	1.21572	0.607860	−	0.794044i	$-0.292028\pi$
$863$	5.25992e39	1.21572	0.607860	+	0.794044i	$0.292028\pi$
$864$	1.49513e38	0.0340207
$865$	5.27785e38	0.118233
$866$	−4.10455e39	−0.905262
$867$	−2.45144e39	−0.532308
$868$	1.57745e39	0.337239
$869$	−2.09673e39	−0.441341
$870$	1.67369e39	0.346868
$871$	−1.80206e39	−0.367725
$872$	−1.53019e39	−0.307448
$873$	−1.39465e39	−0.275914
$874$	−4.59537e38	−0.0895193
$875$	−1.58616e39	−0.304256
$876$	−1.34362e39	−0.253789
$877$	−8.12884e39	−1.51194	−0.755969	−	0.654608i	$-0.772834\pi$
$877$	−8.12884e39	−1.51194	−0.755969	+	0.654608i	$0.772834\pi$
$878$	−1.77943e39	−0.325916
$879$	−2.69650e39	−0.486351
$880$	1.89639e38	0.0336830
$881$	6.92412e39	1.21113	0.605564	−	0.795797i	$-0.292948\pi$
$881$	6.92412e39	1.21113	0.605564	+	0.795797i	$0.292948\pi$
$882$	−1.17285e39	−0.202030
$883$	1.75435e39	0.297609	0.148805	−	0.988867i	$-0.452457\pi$
$883$	1.75435e39	0.297609	0.148805	+	0.988867i	$0.452457\pi$
$884$	2.30327e38	0.0384803
$885$	5.01691e38	0.0825471
$886$	2.41882e39	0.391965
$887$	−6.78450e39	−1.08280	−0.541401	−	0.840764i	$-0.682106\pi$
$887$	−6.78450e39	−1.08280	−0.541401	+	0.840764i	$0.682106\pi$
$888$	1.41579e39	0.222548
$889$	4.42646e38	0.0685303
$890$	3.12461e39	0.476464
$891$	2.22875e38	0.0334744
$892$	3.74308e39	0.553738
$893$	−3.01186e39	−0.438874
$894$	3.63196e39	0.521296
$895$	7.46113e38	0.105486
$896$	2.39886e38	0.0334077
$897$	−4.29230e38	−0.0588832
$898$	−4.93848e38	−0.0667364
$899$	2.54681e40	3.39032
$900$	−1.01675e39	−0.133333
$901$	−3.16458e39	−0.408820
$902$	−1.08660e39	−0.138287
$903$	−7.06372e37	−0.00885623
$904$	4.06694e39	0.502336
$905$	−2.59902e39	−0.316266
$906$	5.93742e39	0.711815
$907$	−8.83788e39	−1.04388	−0.521939	−	0.852983i	$-0.674791\pi$
$907$	−8.83788e39	−1.04388	−0.521939	+	0.852983i	$0.674791\pi$
$908$	3.85076e39	0.448113
$909$	6.00537e38	0.0688537
$910$	2.91532e38	0.0329328
$911$	1.16724e40	1.29916	0.649580	−	0.760293i	$-0.274945\pi$
$911$	1.16724e40	1.29916	0.649580	+	0.760293i	$0.274945\pi$
$912$	4.50158e38	0.0493668
$913$	1.36985e38	0.0148019
$914$	−1.76212e39	−0.187613
$915$	2.79321e38	0.0293035
$916$	8.55702e38	0.0884573
$917$	−2.72972e39	−0.278056
$918$	3.78679e38	0.0380098
$919$	−4.23340e39	−0.418726	−0.209363	−	0.977838i	$-0.567139\pi$
$919$	−4.23340e39	−0.418726	−0.209363	+	0.977838i	$0.567139\pi$
$920$	−6.00457e38	−0.0585256
$921$	7.86873e39	0.755787
$922$	−1.06999e40	−1.01278
$923$	−1.55471e39	−0.145020
$924$	3.57593e38	0.0328713
$925$	−9.62792e39	−0.872206
$926$	6.89525e39	0.615605
$927$	−5.15742e39	−0.453791
$928$	3.87300e39	0.335853
$929$	−3.19134e39	−0.272747	−0.136374	−	0.990657i	$-0.543545\pi$
$929$	−3.19134e39	−0.272747	−0.136374	+	0.990657i	$0.543545\pi$
$930$	3.86790e39	0.325803
$931$	−3.53125e39	−0.293162
$932$	−8.01898e39	−0.656152
$933$	−3.51508e39	−0.283487
$934$	1.91825e39	0.152483
$935$	4.80308e38	0.0376325
$936$	4.20469e38	0.0324721
$937$	−1.17365e40	−0.893417	−0.446709	−	0.894679i	$-0.647404\pi$
$937$	−1.17365e40	−0.893417	−0.446709	+	0.894679i	$0.647404\pi$
$938$	−4.75360e39	−0.356684
$939$	8.08329e39	0.597864
$940$	−3.93546e39	−0.286926
$941$	−2.49572e40	−1.79364	−0.896821	−	0.442394i	$-0.854129\pi$
$941$	−2.49572e40	−1.79364	−0.896821	+	0.442394i	$0.854129\pi$
$942$	6.60525e38	0.0467953
$943$	3.44052e39	0.240279
$944$	1.16094e39	0.0799259
$945$	4.79308e38	0.0325301
$946$	−1.29220e38	−0.00864566
$947$	−7.66374e39	−0.505494	−0.252747	−	0.967532i	$-0.581334\pi$
$947$	−7.66374e39	−0.505494	−0.252747	+	0.967532i	$0.581334\pi$
$948$	−6.50341e39	−0.422891
$949$	−3.77861e39	−0.242236
$950$	−3.06125e39	−0.193477
$951$	−2.78199e39	−0.173348
$952$	6.07572e38	0.0373249
$953$	2.42435e40	1.46839	0.734194	−	0.678940i	$-0.237560\pi$
$953$	2.42435e40	1.46839	0.734194	+	0.678940i	$0.237560\pi$
$954$	−5.77705e39	−0.344987
$955$	1.43940e40	0.847493
$956$	−5.48991e39	−0.318701
$957$	5.77339e39	0.330461
$958$	5.06702e39	0.285969
$959$	−5.34175e39	−0.297257
$960$	5.88201e38	0.0322749
$961$	4.03743e40	2.18444
$962$	3.98156e39	0.212417
$963$	2.99870e39	0.157753
$964$	−1.28342e40	−0.665775
$965$	−1.28923e40	−0.659497
$966$	−1.13225e39	−0.0571153
$967$	2.03153e39	0.101057	0.0505285	−	0.998723i	$-0.483909\pi$
$967$	2.03153e39	0.101057	0.0505285	+	0.998723i	$0.483909\pi$
$968$	−6.55314e39	−0.321464
$969$	1.14014e39	0.0551553
$970$	−5.48672e39	−0.261755
$971$	3.00765e40	1.41504	0.707518	−	0.706695i	$-0.249815\pi$
$971$	3.00765e40	1.41504	0.707518	+	0.706695i	$0.249815\pi$
$972$	6.91292e38	0.0320750
$973$	6.78485e39	0.310468
$974$	6.40908e39	0.289234
$975$	−2.85935e39	−0.127264
$976$	6.46365e38	0.0283730
$977$	−3.29295e40	−1.42564	−0.712818	−	0.701349i	$-0.752581\pi$
$977$	−3.29295e40	−1.42564	−0.712818	+	0.701349i	$0.752581\pi$
$978$	−1.33901e40	−0.571754
$979$	1.07783e40	0.453927
$980$	−4.61413e39	−0.191663
$981$	−7.07501e39	−0.289865
$982$	4.26678e39	0.172423
$983$	1.93189e40	0.770035	0.385018	−	0.922909i	$-0.374195\pi$
$983$	1.93189e40	0.770035	0.385018	+	0.922909i	$0.374195\pi$
$984$	−3.37030e39	−0.132506
$985$	6.55256e39	0.254110
$986$	9.80936e39	0.375234
$987$	−7.42091e39	−0.280011
$988$	1.26596e39	0.0471196
$989$	4.09151e38	0.0150222
$990$	8.76818e38	0.0317566
$991$	1.22554e40	0.437857	0.218928	−	0.975741i	$-0.429744\pi$
$991$	1.22554e40	0.437857	0.218928	+	0.975741i	$0.429744\pi$
$992$	8.95053e39	0.315458
$993$	−1.01155e40	−0.351701
$994$	−4.10114e39	−0.140666
$995$	−1.08397e40	−0.366780
$996$	4.24887e38	0.0141831
$997$	−3.35817e38	−0.0110590	−0.00552952	−	0.999985i	$-0.501760\pi$
$997$	−3.35817e38	−0.0110590	−0.00552952	+	0.999985i	$0.501760\pi$
$998$	3.00931e40	0.977698
$999$	6.54608e39	0.209820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.28.a.c.1.1	✓	1
3.2	odd	2		18.28.a.b.1.1		1
4.3	odd	2		48.28.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.28.a.c.1.1	✓	1	1.1	even	1	trivial
18.28.a.b.1.1		1	3.2	odd	2
48.28.a.a.1.1		1	4.3	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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