LMFDB - Embedded newform 6.30.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,30,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, 30, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 30 $
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:	$31.9668254298$
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	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+16384.0 q^{2} +4.78297e6 q^{3} +2.68435e8 q^{4} -2.10039e10 q^{5} +7.83642e10 q^{6} +1.54063e12 q^{7} +4.39805e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$

\(q+16384.0 q^{2} +4.78297e6 q^{3} +2.68435e8 q^{4} -2.10039e10 q^{5} +7.83642e10 q^{6} +1.54063e12 q^{7} +4.39805e12 q^{8} +2.28768e13 q^{9} -3.44127e14 q^{10} -1.76512e15 q^{11} +1.28392e15 q^{12} -2.81753e15 q^{13} +2.52417e16 q^{14} -1.00461e17 q^{15} +7.20576e16 q^{16} -1.21734e18 q^{17} +3.74813e17 q^{18} +2.69682e18 q^{19} -5.63818e18 q^{20} +7.36878e18 q^{21} -2.89197e19 q^{22} -8.30916e19 q^{23} +2.10357e19 q^{24} +2.54898e20 q^{25} -4.61625e19 q^{26} +1.09419e20 q^{27} +4.13559e20 q^{28} -3.73822e20 q^{29} -1.64595e21 q^{30} -2.50324e21 q^{31} +1.18059e21 q^{32} -8.44252e21 q^{33} -1.99450e22 q^{34} -3.23592e22 q^{35} +6.14094e21 q^{36} -5.54528e22 q^{37} +4.41848e22 q^{38} -1.34762e22 q^{39} -9.23760e22 q^{40} -3.97796e23 q^{41} +1.20730e23 q^{42} +2.10619e23 q^{43} -4.73821e23 q^{44} -4.80501e23 q^{45} -1.36137e24 q^{46} +2.59431e24 q^{47} +3.44649e23 q^{48} -8.46368e23 q^{49} +4.17625e24 q^{50} -5.82252e24 q^{51} -7.56326e23 q^{52} +5.77744e24 q^{53} +1.79272e24 q^{54} +3.70744e25 q^{55} +6.77576e24 q^{56} +1.28988e25 q^{57} -6.12470e24 q^{58} +6.49020e25 q^{59} -2.69673e25 q^{60} -1.12175e26 q^{61} -4.10131e25 q^{62} +3.52447e25 q^{63} +1.93428e25 q^{64} +5.91791e25 q^{65} -1.38322e26 q^{66} -2.48738e26 q^{67} -3.26778e26 q^{68} -3.97425e26 q^{69} -5.30173e26 q^{70} +6.12934e26 q^{71} +1.00613e26 q^{72} +1.45554e27 q^{73} -9.08538e26 q^{74} +1.21917e27 q^{75} +7.23923e26 q^{76} -2.71940e27 q^{77} -2.20794e26 q^{78} +2.43598e27 q^{79} -1.51349e27 q^{80} +5.23348e26 q^{81} -6.51748e27 q^{82} +5.28372e27 q^{83} +1.97804e27 q^{84} +2.55689e28 q^{85} +3.45079e27 q^{86} -1.78798e27 q^{87} -7.76309e27 q^{88} +6.17585e27 q^{89} -7.87253e27 q^{90} -4.34077e27 q^{91} -2.23047e28 q^{92} -1.19729e28 q^{93} +4.25052e28 q^{94} -5.66438e28 q^{95} +5.64673e27 q^{96} -6.25178e28 q^{97} -1.38669e28 q^{98} -4.03803e28 q^{99} +O(q^{100})\)

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 $

$2$	16384.0	0.707107
$2$	16384.0	0.707107
$3$	4.78297e6	0.577350
$3$	4.78297e6	0.577350
$4$	2.68435e8	0.500000
$5$	−2.10039e10	−1.53898	−0.769492	−	0.638656i	$-0.779491\pi$
$5$	−2.10039e10	−1.53898	−0.769492	+	0.638656i	$0.779491\pi$
$6$	7.83642e10	0.408248
$7$	1.54063e12	0.858572	0.429286	−	0.903169i	$-0.358765\pi$
$7$	1.54063e12	0.858572	0.429286	+	0.903169i	$0.358765\pi$
$8$	4.39805e12	0.353553
$9$	2.28768e13	0.333333
$10$	−3.44127e14	−1.08823
$11$	−1.76512e15	−1.40146	−0.700730	−	0.713427i	$-0.747142\pi$
$11$	−1.76512e15	−1.40146	−0.700730	+	0.713427i	$0.747142\pi$
$12$	1.28392e15	0.288675
$13$	−2.81753e15	−0.198468	−0.0992340	−	0.995064i	$-0.531639\pi$
$13$	−2.81753e15	−0.198468	−0.0992340	+	0.995064i	$0.531639\pi$
$14$	2.52417e16	0.607102
$15$	−1.00461e17	−0.888533
$16$	7.20576e16	0.250000
$17$	−1.21734e18	−1.75349	−0.876746	−	0.480953i	$-0.840291\pi$
$17$	−1.21734e18	−1.75349	−0.876746	+	0.480953i	$0.840291\pi$
$18$	3.74813e17	0.235702
$19$	2.69682e18	0.774329	0.387164	−	0.922011i	$-0.373455\pi$
$19$	2.69682e18	0.774329	0.387164	+	0.922011i	$0.373455\pi$
$20$	−5.63818e18	−0.769492
$21$	7.36878e18	0.495697
$22$	−2.89197e19	−0.990982
$23$	−8.30916e19	−1.49453	−0.747263	−	0.664528i	$-0.768633\pi$
$23$	−8.30916e19	−1.49453	−0.747263	+	0.664528i	$0.768633\pi$
$24$	2.10357e19	0.204124
$25$	2.54898e20	1.36847
$26$	−4.61625e19	−0.140338
$27$	1.09419e20	0.192450
$28$	4.13559e20	0.429286
$29$	−3.73822e20	−0.233289	−0.116644	−	0.993174i	$-0.537214\pi$
$29$	−3.73822e20	−0.233289	−0.116644	+	0.993174i	$0.537214\pi$
$30$	−1.64595e21	−0.628288
$31$	−2.50324e21	−0.593961	−0.296981	−	0.954884i	$-0.595980\pi$
$31$	−2.50324e21	−0.593961	−0.296981	+	0.954884i	$0.595980\pi$
$32$	1.18059e21	0.176777
$33$	−8.44252e21	−0.809133
$34$	−1.99450e22	−1.23991
$35$	−3.23592e22	−1.32133
$36$	6.14094e21	0.166667
$37$	−5.54528e22	−1.01158	−0.505788	−	0.862658i	$-0.668798\pi$
$37$	−5.54528e22	−1.01158	−0.505788	+	0.862658i	$0.668798\pi$
$38$	4.41848e22	0.547533
$39$	−1.34762e22	−0.114586
$40$	−9.23760e22	−0.544113
$41$	−3.97796e23	−1.63793	−0.818963	−	0.573847i	$-0.805450\pi$
$41$	−3.97796e23	−1.63793	−0.818963	+	0.573847i	$0.805450\pi$
$42$	1.20730e23	0.350510
$43$	2.10619e23	0.434716	0.217358	−	0.976092i	$-0.430256\pi$
$43$	2.10619e23	0.434716	0.217358	+	0.976092i	$0.430256\pi$
$44$	−4.73821e23	−0.700730
$45$	−4.80501e23	−0.512995
$46$	−1.36137e24	−1.05679
$47$	2.59431e24	1.47436	0.737180	−	0.675697i	$-0.236157\pi$
$47$	2.59431e24	1.47436	0.737180	+	0.675697i	$0.236157\pi$
$48$	3.44649e23	0.144338
$49$	−8.46368e23	−0.262855
$50$	4.17625e24	0.967657
$51$	−5.82252e24	−1.01238
$52$	−7.56326e23	−0.0992340
$53$	5.77744e24	0.575089	0.287545	−	0.957767i	$-0.407161\pi$
$53$	5.77744e24	0.575089	0.287545	+	0.957767i	$0.407161\pi$
$54$	1.79272e24	0.136083
$55$	3.70744e25	2.15683
$56$	6.77576e24	0.303551
$57$	1.28988e25	0.447059
$58$	−6.12470e24	−0.164960
$59$	6.49020e25	1.36428	0.682141	−	0.731221i	$-0.261049\pi$
$59$	6.49020e25	1.36428	0.682141	+	0.731221i	$0.261049\pi$
$60$	−2.69673e25	−0.444267
$61$	−1.12175e26	−1.45416	−0.727082	−	0.686551i	$-0.759124\pi$
$61$	−1.12175e26	−1.45416	−0.727082	+	0.686551i	$0.759124\pi$
$62$	−4.10131e25	−0.419994
$63$	3.52447e25	0.286191
$64$	1.93428e25	0.125000
$65$	5.91791e25	0.305439
$66$	−1.38322e26	−0.572144
$67$	−2.48738e26	−0.827289	−0.413645	−	0.910438i	$-0.635744\pi$
$67$	−2.48738e26	−0.827289	−0.413645	+	0.910438i	$0.635744\pi$
$68$	−3.26778e26	−0.876746
$69$	−3.97425e26	−0.862865
$70$	−5.30173e26	−0.934320
$71$	6.12934e26	0.879362	0.439681	−	0.898154i	$-0.355091\pi$
$71$	6.12934e26	0.879362	0.439681	+	0.898154i	$0.355091\pi$
$72$	1.00613e26	0.117851
$73$	1.45554e27	1.39586	0.697931	−	0.716165i	$-0.254104\pi$
$73$	1.45554e27	1.39586	0.697931	+	0.716165i	$0.254104\pi$
$74$	−9.08538e26	−0.715292
$75$	1.21917e27	0.790089
$76$	7.23923e26	0.387164
$77$	−2.71940e27	−1.20325
$78$	−2.20794e26	−0.0810242
$79$	2.43598e27	0.743158	0.371579	−	0.928401i	$-0.378816\pi$
$79$	2.43598e27	0.743158	0.371579	+	0.928401i	$0.378816\pi$
$80$	−1.51349e27	−0.384746
$81$	5.23348e26	0.111111
$82$	−6.51748e27	−1.15819
$83$	5.28372e27	0.787603	0.393802	−	0.919195i	$-0.371160\pi$
$83$	5.28372e27	0.787603	0.393802	+	0.919195i	$0.371160\pi$
$84$	1.97804e27	0.247848
$85$	2.55689e28	2.69860
$86$	3.45079e27	0.307391
$87$	−1.78798e27	−0.134689
$88$	−7.76309e27	−0.495491
$89$	6.17585e27	0.334612	0.167306	−	0.985905i	$-0.446493\pi$
$89$	6.17585e27	0.334612	0.167306	+	0.985905i	$0.446493\pi$
$90$	−7.87253e27	−0.362742
$91$	−4.34077e27	−0.170399
$92$	−2.23047e28	−0.747263
$93$	−1.19729e28	−0.342924
$94$	4.25052e28	1.04253
$95$	−5.66438e28	−1.19168
$96$	5.64673e27	0.102062
$97$	−6.25178e28	−0.972329	−0.486165	−	0.873867i	$-0.661604\pi$
$97$	−6.25178e28	−0.972329	−0.486165	+	0.873867i	$0.661604\pi$
$98$	−1.38669e28	−0.185866
$99$	−4.03803e28	−0.467153
$100$	6.84237e28	0.684237
$101$	−1.15780e29	−1.00225	−0.501124	−	0.865375i	$-0.667080\pi$
$101$	−1.15780e29	−1.00225	−0.501124	+	0.865375i	$0.667080\pi$
$102$	−9.53962e28	−0.715860
$103$	1.10577e29	0.720323	0.360161	−	0.932890i	$-0.382722\pi$
$103$	1.10577e29	0.720323	0.360161	+	0.932890i	$0.382722\pi$
$104$	−1.23916e28	−0.0701690
$105$	−1.54773e29	−0.762869
$106$	9.46576e28	0.406650
$107$	4.12693e29	1.54726	0.773628	−	0.633640i	$-0.218440\pi$
$107$	4.12693e29	1.54726	0.773628	+	0.633640i	$0.218440\pi$
$108$	2.93719e28	0.0962250
$109$	7.15616e28	0.205114	0.102557	−	0.994727i	$-0.467298\pi$
$109$	7.15616e28	0.205114	0.102557	+	0.994727i	$0.467298\pi$
$110$	6.07427e29	1.52511
$111$	−2.65229e29	−0.584033
$112$	1.11014e29	0.214643
$113$	−9.56049e29	−1.62496	−0.812480	−	0.582989i	$-0.801883\pi$
$113$	−9.56049e29	−1.62496	−0.812480	+	0.582989i	$0.801883\pi$
$114$	2.11334e29	0.316118
$115$	1.74525e30	2.30005
$116$	−1.00347e29	−0.116644
$117$	−6.44561e28	−0.0661560
$118$	1.06335e30	0.964693
$119$	−1.87548e30	−1.50550
$120$	−4.41832e29	−0.314144
$121$	1.52934e30	0.964089
$122$	−1.83788e30	−1.02825
$123$	−1.90264e30	−0.945657
$124$	−6.71959e29	−0.296981
$125$	−1.44157e30	−0.567076
$126$	5.77448e29	0.202367
$127$	−3.42698e29	−0.107092	−0.0535461	−	0.998565i	$-0.517052\pi$
$127$	−3.42698e29	−0.107092	−0.0535461	+	0.998565i	$0.517052\pi$
$128$	3.16913e29	0.0883883
$129$	1.00739e30	0.250983
$130$	9.69591e29	0.215978
$131$	5.31150e29	0.105873	0.0529363	−	0.998598i	$-0.483142\pi$
$131$	5.31150e29	0.105873	0.0529363	+	0.998598i	$0.483142\pi$
$132$	−2.26627e30	−0.404567
$133$	4.15481e30	0.664817
$134$	−4.07532e30	−0.584982
$135$	−2.29822e30	−0.296178
$136$	−5.35394e30	−0.619953
$137$	6.39076e30	0.665433	0.332717	−	0.943027i	$-0.392035\pi$
$137$	6.39076e30	0.665433	0.332717	+	0.943027i	$0.392035\pi$
$138$	−6.51140e30	−0.610138
$139$	3.95472e29	0.0333735	0.0166867	−	0.999861i	$-0.494688\pi$
$139$	3.95472e29	0.0333735	0.0166867	+	0.999861i	$0.494688\pi$
$140$	−8.68635e30	−0.660664
$141$	1.24085e31	0.851222
$142$	1.00423e31	0.621803
$143$	4.97329e30	0.278145
$144$	1.64845e30	0.0833333
$145$	7.85170e30	0.359028
$146$	2.38475e31	0.987023
$147$	−4.04815e30	−0.151759
$148$	−1.48855e31	−0.505788
$149$	2.11770e31	0.652625	0.326313	−	0.945262i	$-0.394194\pi$
$149$	2.11770e31	0.652625	0.326313	+	0.945262i	$0.394194\pi$
$150$	1.99749e31	0.558677
$151$	1.50020e31	0.381050	0.190525	−	0.981682i	$-0.438981\pi$
$151$	1.50020e31	0.381050	0.190525	+	0.981682i	$0.438981\pi$
$152$	1.18608e31	0.273767
$153$	−2.78489e31	−0.584498
$154$	−4.45546e31	−0.850829
$155$	5.25778e31	0.914097
$156$	−3.61748e30	−0.0572928
$157$	−1.12788e32	−1.62824	−0.814119	−	0.580698i	$-0.802780\pi$
$157$	−1.12788e32	−1.62824	−0.814119	+	0.580698i	$0.802780\pi$
$158$	3.99111e31	0.525492
$159$	2.76333e31	0.332028
$160$	−2.47970e31	−0.272057
$161$	−1.28013e32	−1.28316
$162$	8.57453e30	0.0785674
$163$	−1.80626e32	−1.51377	−0.756885	−	0.653548i	$-0.773280\pi$
$163$	−1.80626e32	−1.51377	−0.756885	+	0.653548i	$0.773280\pi$
$164$	−1.06782e32	−0.818963
$165$	1.77326e32	1.24524
$166$	8.65685e31	0.556920
$167$	−2.98724e32	−1.76149	−0.880746	−	0.473589i	$-0.842958\pi$
$167$	−2.98724e32	−1.76149	−0.880746	+	0.473589i	$0.842958\pi$
$168$	3.24082e31	0.175255
$169$	−1.93600e32	−0.960610
$170$	4.18922e32	1.90820
$171$	6.16947e31	0.258110
$172$	5.65377e31	0.217358
$173$	3.21201e32	1.13530	0.567648	−	0.823272i	$-0.307854\pi$
$173$	3.21201e32	1.13530	0.567648	+	0.823272i	$0.307854\pi$
$174$	−2.92942e31	−0.0952397
$175$	3.92703e32	1.17493
$176$	−1.27190e32	−0.350365
$177$	3.10424e32	0.787668
$178$	1.01185e32	0.236606
$179$	−1.82373e31	−0.0393180	−0.0196590	−	0.999807i	$-0.506258\pi$
$179$	−1.82373e31	−0.0393180	−0.0196590	+	0.999807i	$0.506258\pi$
$180$	−1.28984e32	−0.256497
$181$	−7.18953e32	−1.31935	−0.659677	−	0.751550i	$-0.729307\pi$
$181$	−7.18953e32	−1.31935	−0.659677	+	0.751550i	$0.729307\pi$
$182$	−7.11192e31	−0.120490
$183$	−5.36530e32	−0.839562
$184$	−3.65441e32	−0.528395
$185$	1.16472e33	1.55680
$186$	−1.96164e32	−0.242484
$187$	2.14876e33	2.45745
$188$	6.96406e32	0.737180
$189$	1.68574e32	0.165232
$190$	−9.28051e32	−0.842645
$191$	−1.76080e33	−1.48159	−0.740794	−	0.671732i	$-0.765551\pi$
$191$	−1.76080e33	−1.48159	−0.740794	+	0.671732i	$0.765551\pi$
$192$	9.25161e31	0.0721688
$193$	−1.30567e33	−0.944606	−0.472303	−	0.881436i	$-0.656577\pi$
$193$	−1.30567e33	−0.944606	−0.472303	+	0.881436i	$0.656577\pi$
$194$	−1.02429e33	−0.687541
$195$	2.83052e32	0.176345
$196$	−2.27195e32	−0.131427
$197$	−1.59354e33	−0.856252	−0.428126	−	0.903719i	$-0.640826\pi$
$197$	−1.59354e33	−0.856252	−0.428126	+	0.903719i	$0.640826\pi$
$198$	−6.61591e32	−0.330327
$199$	1.69188e33	0.785234	0.392617	−	0.919702i	$-0.371570\pi$
$199$	1.69188e33	0.785234	0.392617	+	0.919702i	$0.371570\pi$
$200$	1.12105e33	0.483829
$201$	−1.18971e33	−0.477636
$202$	−1.89695e33	−0.708697
$203$	−5.75921e32	−0.200295
$204$	−1.56297e33	−0.506190
$205$	8.35525e33	2.52074
$206$	1.81170e33	0.509345
$207$	−1.90087e33	−0.498175
$208$	−2.03025e32	−0.0496170
$209$	−4.76022e33	−1.08519
$210$	−2.53580e33	−0.539430
$211$	−9.79887e32	−0.194572	−0.0972860	−	0.995256i	$-0.531016\pi$
$211$	−9.79887e32	−0.194572	−0.0972860	+	0.995256i	$0.531016\pi$
$212$	1.55087e33	0.287545
$213$	2.93164e33	0.507700
$214$	6.76156e33	1.09408
$215$	−4.42382e33	−0.669021
$216$	4.81230e32	0.0680414
$217$	−3.85657e33	−0.509958
$218$	1.17247e33	0.145038
$219$	6.96180e33	0.805901
$220$	9.95208e33	1.07841
$221$	3.42991e33	0.348012
$222$	−4.34551e33	−0.412974
$223$	1.30814e34	1.16476	0.582378	−	0.812918i	$-0.302123\pi$
$223$	1.30814e34	1.16476	0.582378	+	0.812918i	$0.302123\pi$
$224$	1.81885e33	0.151775
$225$	5.83125e33	0.456158
$226$	−1.56639e34	−1.14902
$227$	−2.48788e34	−1.71181	−0.855904	−	0.517135i	$-0.826999\pi$
$227$	−2.48788e34	−1.71181	−0.855904	+	0.517135i	$0.826999\pi$
$228$	3.46250e33	0.223529
$229$	1.41639e34	0.858162	0.429081	−	0.903266i	$-0.358838\pi$
$229$	1.41639e34	0.858162	0.429081	+	0.903266i	$0.358838\pi$
$230$	2.85941e34	1.62638
$231$	−1.30068e34	−0.694699
$232$	−1.64409e33	−0.0824800
$233$	−1.49931e34	−0.706691	−0.353345	−	0.935493i	$-0.614956\pi$
$233$	−1.49931e34	−0.706691	−0.353345	+	0.935493i	$0.614956\pi$
$234$	−1.05605e33	−0.0467794
$235$	−5.44906e34	−2.26902
$236$	1.74220e34	0.682141
$237$	1.16512e34	0.429063
$238$	−3.07278e34	−1.06455
$239$	−1.21727e34	−0.396843	−0.198422	−	0.980117i	$-0.563581\pi$
$239$	−1.21727e34	−0.396843	−0.198422	+	0.980117i	$0.563581\pi$
$240$	−7.23897e33	−0.222133
$241$	−1.84878e34	−0.534118	−0.267059	−	0.963680i	$-0.586052\pi$
$241$	−1.84878e34	−0.534118	−0.267059	+	0.963680i	$0.586052\pi$
$242$	2.50568e34	0.681714
$243$	2.50316e33	0.0641500
$244$	−3.01117e34	−0.727082
$245$	1.77770e34	0.404530
$246$	−3.11729e34	−0.668680
$247$	−7.59839e33	−0.153680
$248$	−1.10094e34	−0.209997
$249$	2.52719e34	0.454723
$250$	−2.36187e34	−0.400983
$251$	1.02152e35	1.63673	0.818366	−	0.574698i	$-0.194880\pi$
$251$	1.02152e35	1.63673	0.818366	+	0.574698i	$0.194880\pi$
$252$	9.46091e33	0.143095
$253$	1.46667e35	2.09452
$254$	−5.61477e33	−0.0757256
$255$	1.22295e35	1.55804
$256$	5.19230e33	0.0625000
$257$	−7.12073e34	−0.810017	−0.405009	−	0.914313i	$-0.632732\pi$
$257$	−7.12073e34	−0.810017	−0.405009	+	0.914313i	$0.632732\pi$
$258$	1.65050e34	0.177472
$259$	−8.54322e34	−0.868510
$260$	1.58858e34	0.152720
$261$	−8.55184e33	−0.0777629
$262$	8.70236e33	0.0748632
$263$	−1.38648e33	−0.0112864	−0.00564318	−	0.999984i	$-0.501796\pi$
$263$	−1.38648e33	−0.0112864	−0.00564318	+	0.999984i	$0.501796\pi$
$264$	−3.71306e34	−0.286072
$265$	−1.21349e35	−0.885054
$266$	6.80723e34	0.470096
$267$	2.95389e34	0.193188
$268$	−6.67701e34	−0.413645
$269$	1.55345e35	0.911780	0.455890	−	0.890036i	$-0.349321\pi$
$269$	1.55345e35	0.911780	0.455890	+	0.890036i	$0.349321\pi$
$270$	−3.76541e34	−0.209429
$271$	−6.57202e32	−0.00346453	−0.00173226	−	0.999998i	$-0.500551\pi$
$271$	−6.57202e32	−0.00346453	−0.00173226	+	0.999998i	$0.500551\pi$
$272$	−8.77189e34	−0.438373
$273$	−2.07618e34	−0.0983799
$274$	1.04706e35	0.470532
$275$	−4.49926e35	−1.91786
$276$	−1.06683e35	−0.431433
$277$	3.83138e35	1.47028	0.735138	−	0.677917i	$-0.237117\pi$
$277$	3.83138e35	1.47028	0.735138	+	0.677917i	$0.237117\pi$
$278$	6.47942e33	0.0235986
$279$	−5.72661e34	−0.197987
$280$	−1.42317e35	−0.467160
$281$	−2.50822e35	−0.781850	−0.390925	−	0.920423i	$-0.627845\pi$
$281$	−2.50822e35	−0.781850	−0.390925	+	0.920423i	$0.627845\pi$
$282$	2.03301e35	0.601905
$283$	−1.40452e35	−0.395024	−0.197512	−	0.980300i	$-0.563286\pi$
$283$	−1.40452e35	−0.395024	−0.197512	+	0.980300i	$0.563286\pi$
$284$	1.64533e35	0.439681
$285$	−2.70925e35	−0.688017
$286$	8.14824e34	0.196678
$287$	−6.12855e35	−1.40628
$288$	2.70081e34	0.0589256
$289$	9.99958e35	2.07474
$290$	1.28642e35	0.253871
$291$	−2.99021e35	−0.561375
$292$	3.90718e35	0.697931
$293$	6.03242e35	1.02544	0.512721	−	0.858555i	$-0.328637\pi$
$293$	6.03242e35	1.02544	0.512721	+	0.858555i	$0.328637\pi$
$294$	−6.63249e34	−0.107310
$295$	−1.36319e36	−2.09961
$296$	−2.43884e35	−0.357646
$297$	−1.93138e35	−0.269711
$298$	3.46964e35	0.461476
$299$	2.34113e35	0.296616
$300$	3.27268e35	0.395044
$301$	3.24486e35	0.373235
$302$	2.45792e35	0.269443
$303$	−5.53774e35	−0.578648
$304$	1.94327e35	0.193582
$305$	2.35611e36	2.23794
$306$	−4.56277e35	−0.413302
$307$	1.20834e36	1.04396	0.521980	−	0.852958i	$-0.325194\pi$
$307$	1.20834e36	1.04396	0.521980	+	0.852958i	$0.325194\pi$
$308$	−7.29983e35	−0.601627
$309$	5.28889e35	0.415878
$310$	8.61434e35	0.646364
$311$	1.38359e35	0.0990792	0.0495396	−	0.998772i	$-0.484225\pi$
$311$	1.38359e35	0.0990792	0.0495396	+	0.998772i	$0.484225\pi$
$312$	−5.92689e34	−0.0405121
$313$	−1.62851e36	−1.06267	−0.531335	−	0.847162i	$-0.678309\pi$
$313$	−1.62851e36	−1.06267	−0.531335	+	0.847162i	$0.678309\pi$
$314$	−1.84792e36	−1.15134
$315$	−7.40274e35	−0.440443
$316$	6.53904e35	0.371579
$317$	−8.85592e35	−0.480700	−0.240350	−	0.970686i	$-0.577262\pi$
$317$	−8.85592e35	−0.480700	−0.240350	+	0.970686i	$0.577262\pi$
$318$	4.52744e35	0.234779
$319$	6.59841e35	0.326945
$320$	−4.06274e35	−0.192373
$321$	1.97390e36	0.893309
$322$	−2.09737e36	−0.907330
$323$	−3.28296e36	−1.35778
$324$	1.40485e35	0.0555556
$325$	−7.18184e35	−0.271598
$326$	−2.95938e36	−1.07040
$327$	3.42277e35	0.118423
$328$	−1.74952e36	−0.579094
$329$	3.99687e36	1.26584
$330$	2.90530e36	0.880520
$331$	−1.66672e36	−0.483455	−0.241727	−	0.970344i	$-0.577714\pi$
$331$	−1.66672e36	−0.483455	−0.241727	+	0.970344i	$0.577714\pi$
$332$	1.41834e36	0.393802
$333$	−1.26858e36	−0.337192
$334$	−4.89429e36	−1.24556
$335$	5.22446e36	1.27319
$336$	5.30977e35	0.123924
$337$	−4.32988e36	−0.967926	−0.483963	−	0.875089i	$-0.660803\pi$
$337$	−4.32988e36	−0.967926	−0.483963	+	0.875089i	$0.660803\pi$
$338$	−3.17194e36	−0.679254
$339$	−4.57275e36	−0.938171
$340$	6.86361e36	1.34930
$341$	4.41852e36	0.832413
$342$	1.01081e36	0.182511
$343$	−6.26462e36	−1.08425
$344$	9.26314e35	0.153695
$345$	8.34746e36	1.32794
$346$	5.26256e36	0.802775
$347$	−1.89621e35	−0.0277401	−0.0138701	−	0.999904i	$-0.504415\pi$
$347$	−1.89621e35	−0.0277401	−0.0138701	+	0.999904i	$0.504415\pi$
$348$	−4.79957e35	−0.0673446
$349$	1.02720e37	1.38256	0.691282	−	0.722585i	$-0.257046\pi$
$349$	1.02720e37	1.38256	0.691282	+	0.722585i	$0.257046\pi$
$350$	6.43405e36	0.830803
$351$	−3.08292e35	−0.0381952
$352$	−2.08389e36	−0.247745
$353$	1.50625e37	1.71856	0.859280	−	0.511505i	$-0.170912\pi$
$353$	1.50625e37	1.71856	0.859280	+	0.511505i	$0.170912\pi$
$354$	5.08599e36	0.556966
$355$	−1.28740e37	−1.35332
$356$	1.65782e36	0.167306
$357$	−8.97034e36	−0.869200
$358$	−2.98800e35	−0.0278020
$359$	−7.19268e36	−0.642719	−0.321360	−	0.946957i	$-0.604140\pi$
$359$	−7.19268e36	−0.642719	−0.321360	+	0.946957i	$0.604140\pi$
$360$	−2.11327e36	−0.181371
$361$	−4.85696e36	−0.400415
$362$	−1.17793e37	−0.932923
$363$	7.31480e36	0.556617
$364$	−1.16522e36	−0.0851995
$365$	−3.05719e37	−2.14821
$366$	−8.79050e36	−0.593660
$367$	9.84591e36	0.639143	0.319571	−	0.947562i	$-0.396461\pi$
$367$	9.84591e36	0.639143	0.319571	+	0.947562i	$0.396461\pi$
$368$	−5.98738e36	−0.373632
$369$	−9.10029e36	−0.545975
$370$	1.90828e37	1.10082
$371$	8.90089e36	0.493755
$372$	−3.21396e36	−0.171462
$373$	−1.39369e37	−0.715134	−0.357567	−	0.933887i	$-0.616394\pi$
$373$	−1.39369e37	−0.715134	−0.357567	+	0.933887i	$0.616394\pi$
$374$	3.52053e37	1.73768
$375$	−6.89499e36	−0.327401
$376$	1.14099e37	0.521265
$377$	1.05326e36	0.0463003
$378$	2.76192e36	0.116837
$379$	−1.20993e37	−0.492596	−0.246298	−	0.969194i	$-0.579214\pi$
$379$	−1.20993e37	−0.492596	−0.246298	+	0.969194i	$0.579214\pi$
$380$	−1.52052e37	−0.595840
$381$	−1.63911e36	−0.0618297
$382$	−2.88490e37	−1.04764
$383$	−2.32997e37	−0.814645	−0.407322	−	0.913284i	$-0.633537\pi$
$383$	−2.32997e37	−0.814645	−0.407322	+	0.913284i	$0.633537\pi$
$384$	1.51578e36	0.0510310
$385$	5.71179e37	1.85179
$386$	−2.13920e37	−0.667937
$387$	4.81830e36	0.144905
$388$	−1.67820e37	−0.486165
$389$	7.76444e36	0.216691	0.108346	−	0.994113i	$-0.465445\pi$
$389$	7.76444e36	0.216691	0.108346	+	0.994113i	$0.465445\pi$
$390$	4.63752e36	0.124695
$391$	1.01151e38	2.62064
$392$	−3.72237e36	−0.0929332
$393$	2.54047e36	0.0611256
$394$	−2.61085e37	−0.605461
$395$	−5.11651e37	−1.14371
$396$	−1.08395e37	−0.233577
$397$	5.69627e37	1.18339	0.591696	−	0.806162i	$-0.298459\pi$
$397$	5.69627e37	1.18339	0.591696	+	0.806162i	$0.298459\pi$
$398$	2.77197e37	0.555244
$399$	1.98723e37	0.383832
$400$	1.83673e37	0.342118
$401$	−6.60341e37	−1.18625	−0.593123	−	0.805112i	$-0.702105\pi$
$401$	−6.60341e37	−1.18625	−0.593123	+	0.805112i	$0.702105\pi$
$402$	−1.94921e37	−0.337739
$403$	7.05297e36	0.117882
$404$	−3.10796e37	−0.501124
$405$	−1.09923e37	−0.170998
$406$	−9.43588e36	−0.141630
$407$	9.78809e37	1.41768
$408$	−2.56077e37	−0.357930
$409$	−5.09366e37	−0.687135	−0.343567	−	0.939128i	$-0.611635\pi$
$409$	−5.09366e37	−0.687135	−0.343567	+	0.939128i	$0.611635\pi$
$410$	1.36892e38	1.78243
$411$	3.05668e37	0.384188
$412$	2.96829e37	0.360161
$413$	9.99899e37	1.17133
$414$	−3.11438e37	−0.352263
$415$	−1.10979e38	−1.21211
$416$	−3.32636e36	−0.0350845
$417$	1.89153e36	0.0192682
$418$	−7.79915e37	−0.767346
$419$	−8.63770e36	−0.0820908	−0.0410454	−	0.999157i	$-0.513069\pi$
$419$	−8.63770e36	−0.0820908	−0.0410454	+	0.999157i	$0.513069\pi$
$420$	−4.15465e37	−0.381435
$421$	−1.16342e38	−1.03192	−0.515960	−	0.856612i	$-0.672565\pi$
$421$	−1.16342e38	−1.03192	−0.515960	+	0.856612i	$0.672565\pi$
$422$	−1.60545e37	−0.137583
$423$	5.93496e37	0.491453
$424$	2.54095e37	0.203325
$425$	−3.10299e38	−2.39961
$426$	4.80321e37	0.358998
$427$	−1.72820e38	−1.24850
$428$	1.10781e38	0.773628
$429$	2.37871e37	0.160587
$430$	−7.24799e37	−0.473070
$431$	1.65300e38	1.04316	0.521580	−	0.853202i	$-0.325343\pi$
$431$	1.65300e38	1.04316	0.521580	+	0.853202i	$0.325343\pi$
$432$	7.88447e36	0.0481125
$433$	−4.56608e37	−0.269444	−0.134722	−	0.990883i	$-0.543014\pi$
$433$	−4.56608e37	−0.269444	−0.134722	+	0.990883i	$0.543014\pi$
$434$	−6.31860e37	−0.360595
$435$	3.75545e37	0.207285
$436$	1.92097e37	0.102557
$437$	−2.24083e38	−1.15725
$438$	1.14062e38	0.569858
$439$	1.34814e38	0.651627	0.325813	−	0.945434i	$-0.394362\pi$
$439$	1.34814e38	0.651627	0.325813	+	0.945434i	$0.394362\pi$
$440$	1.63055e38	0.762553
$441$	−1.93622e37	−0.0876183
$442$	5.61956e37	0.246082
$443$	1.97853e38	0.838471	0.419235	−	0.907878i	$-0.362298\pi$
$443$	1.97853e38	0.838471	0.419235	+	0.907878i	$0.362298\pi$
$444$	−7.11968e37	−0.292017
$445$	−1.29717e38	−0.514963
$446$	2.14326e38	0.823606
$447$	1.01289e38	0.376793
$448$	2.98001e37	0.107321
$449$	−1.06384e38	−0.370939	−0.185470	−	0.982650i	$-0.559381\pi$
$449$	−1.06384e38	−0.370939	−0.185470	+	0.982650i	$0.559381\pi$
$450$	9.55392e37	0.322552
$451$	7.02157e38	2.29549
$452$	−2.56637e38	−0.812480
$453$	7.17539e37	0.219999
$454$	−4.07615e38	−1.21043
$455$	9.11731e37	0.262241
$456$	5.67296e37	0.158059
$457$	−4.03702e38	−1.08962	−0.544811	−	0.838559i	$-0.683399\pi$
$457$	−4.03702e38	−1.08962	−0.544811	+	0.838559i	$0.683399\pi$
$458$	2.32062e38	0.606812
$459$	−1.33201e38	−0.337460
$460$	4.68486e38	1.15003
$461$	6.35426e38	1.51148	0.755738	−	0.654874i	$-0.227278\pi$
$461$	6.35426e38	1.51148	0.755738	+	0.654874i	$0.227278\pi$
$462$	−2.13103e38	−0.491226
$463$	5.73481e37	0.128113	0.0640567	−	0.997946i	$-0.479596\pi$
$463$	5.73481e37	0.128113	0.0640567	+	0.997946i	$0.479596\pi$
$464$	−2.69367e37	−0.0583222
$465$	2.51478e38	0.527754
$466$	−2.45646e38	−0.499706
$467$	−6.34998e38	−1.25221	−0.626106	−	0.779738i	$-0.715352\pi$
$467$	−6.34998e38	−1.25221	−0.626106	+	0.779738i	$0.715352\pi$
$468$	−1.73023e37	−0.0330780
$469$	−3.83213e38	−0.710287
$470$	−8.92774e38	−1.60444
$471$	−5.39462e38	−0.940064
$472$	2.85442e38	0.482346
$473$	−3.71769e38	−0.609237
$474$	1.90894e38	0.303393
$475$	6.87416e38	1.05965
$476$	−5.03444e38	−0.752750
$477$	1.32169e38	0.191696
$478$	−1.99438e38	−0.280610
$479$	−1.05569e38	−0.144103	−0.0720514	−	0.997401i	$-0.522955\pi$
$479$	−1.05569e38	−0.144103	−0.0720514	+	0.997401i	$0.522955\pi$
$480$	−1.18603e38	−0.157072
$481$	1.56240e38	0.200765
$482$	−3.02903e38	−0.377678
$483$	−6.12284e38	−0.740831
$484$	4.10530e38	0.482045
$485$	1.31312e39	1.49640
$486$	4.10117e37	0.0453609
$487$	−4.00602e38	−0.430075	−0.215037	−	0.976606i	$-0.568987\pi$
$487$	−4.00602e38	−0.430075	−0.215037	+	0.976606i	$0.568987\pi$
$488$	−4.93351e38	−0.514125
$489$	−8.63929e38	−0.873976
$490$	2.91258e38	0.286046
$491$	1.16900e39	1.11464	0.557320	−	0.830298i	$-0.311830\pi$
$491$	1.16900e39	1.11464	0.557320	+	0.830298i	$0.311830\pi$
$492$	−5.10737e38	−0.472828
$493$	4.55070e38	0.409070
$494$	−1.24492e38	−0.108668
$495$	8.48143e38	0.718942
$496$	−1.80378e38	−0.148490
$497$	9.44304e38	0.754995
$498$	4.14054e38	0.321538
$499$	−9.74755e38	−0.735254	−0.367627	−	0.929973i	$-0.619830\pi$
$499$	−9.74755e38	−0.735254	−0.367627	+	0.929973i	$0.619830\pi$
$500$	−3.86969e38	−0.283538
$501$	−1.42879e39	−1.01700
$502$	1.67366e39	1.15734
$503$	−6.18103e38	−0.415264	−0.207632	−	0.978207i	$-0.566576\pi$
$503$	−6.18103e38	−0.415264	−0.207632	+	0.978207i	$0.566576\pi$
$504$	1.55008e38	0.101184
$505$	2.43184e39	1.54245
$506$	2.40299e39	1.48105
$507$	−9.25981e38	−0.554609
$508$	−9.19923e37	−0.0535461
$509$	−1.70393e39	−0.963924	−0.481962	−	0.876192i	$-0.660076\pi$
$509$	−1.70393e39	−0.963924	−0.481962	+	0.876192i	$0.660076\pi$
$510$	2.00369e39	1.10170
$511$	2.24245e39	1.19845
$512$	8.50706e37	0.0441942
$513$	2.95084e38	0.149020
$514$	−1.16666e39	−0.572769
$515$	−2.32256e39	−1.10857
$516$	2.70418e38	0.125492
$517$	−4.57928e39	−2.06626
$518$	−1.39972e39	−0.614129
$519$	1.53630e39	0.655463
$520$	2.60273e38	0.107989
$521$	3.29159e38	0.132819	0.0664094	−	0.997792i	$-0.478846\pi$
$521$	3.29159e38	0.132819	0.0664094	+	0.997792i	$0.478846\pi$
$522$	−1.40113e38	−0.0549867
$523$	−3.31488e39	−1.26530	−0.632650	−	0.774438i	$-0.718033\pi$
$523$	−3.31488e39	−1.26530	−0.632650	+	0.774438i	$0.718033\pi$
$524$	1.42579e38	0.0529363
$525$	1.87829e39	0.678348
$526$	−2.27160e37	−0.00798066
$527$	3.04731e39	1.04151
$528$	−6.08348e38	−0.202283
$529$	3.81316e39	1.23361
$530$	−1.98818e39	−0.625828
$531$	1.48475e39	0.454760
$532$	1.11530e39	0.332408
$533$	1.12080e39	0.325076
$534$	4.83965e38	0.136605
$535$	−8.66815e39	−2.38120
$536$	−1.09396e39	−0.292491
$537$	−8.72285e37	−0.0227003
$538$	2.54518e39	0.644726
$539$	1.49394e39	0.368381
$540$	−6.16924e38	−0.148089
$541$	−2.48809e39	−0.581442	−0.290721	−	0.956808i	$-0.593895\pi$
$541$	−2.48809e39	−0.581442	−0.290721	+	0.956808i	$0.593895\pi$
$542$	−1.07676e37	−0.00244979
$543$	−3.43873e39	−0.761729
$544$	−1.43719e39	−0.309977
$545$	−1.50307e39	−0.315668
$546$	−3.40161e38	−0.0695651
$547$	−2.53457e39	−0.504763	−0.252382	−	0.967628i	$-0.581214\pi$
$547$	−2.53457e39	−0.504763	−0.252382	+	0.967628i	$0.581214\pi$
$548$	1.71551e39	0.332717
$549$	−2.56620e39	−0.484721
$550$	−7.37159e39	−1.35613
$551$	−1.00813e39	−0.180642
$552$	−1.74789e39	−0.305069
$553$	3.75295e39	0.638055
$554$	6.27734e39	1.03964
$555$	5.57083e39	0.898818
$556$	1.06159e38	0.0166867
$557$	7.12040e39	1.09045	0.545223	−	0.838291i	$-0.316445\pi$
$557$	7.12040e39	1.09045	0.545223	+	0.838291i	$0.316445\pi$
$558$	−9.38248e38	−0.139998
$559$	−5.93427e38	−0.0862772
$560$	−2.33172e39	−0.330332
$561$	1.02775e40	1.41881
$562$	−4.10946e39	−0.552851
$563$	2.52834e39	0.331484	0.165742	−	0.986169i	$-0.446998\pi$
$563$	2.52834e39	0.331484	0.165742	+	0.986169i	$0.446998\pi$
$564$	3.33089e39	0.425611
$565$	2.00807e40	2.50079
$566$	−2.30116e39	−0.279324
$567$	8.06285e38	0.0953968
$568$	2.69571e39	0.310901
$569$	4.03857e39	0.454046	0.227023	−	0.973889i	$-0.427101\pi$
$569$	4.03857e39	0.454046	0.227023	+	0.973889i	$0.427101\pi$
$570$	−4.43884e39	−0.486501
$571$	6.40562e39	0.684443	0.342222	−	0.939619i	$-0.388821\pi$
$571$	6.40562e39	0.684443	0.342222	+	0.939619i	$0.388821\pi$
$572$	1.33501e39	0.139072
$573$	−8.42188e39	−0.855395
$574$	−1.00410e40	−0.994387
$575$	−2.11799e40	−2.04522
$576$	4.42502e38	0.0416667
$577$	2.98901e39	0.274459	0.137230	−	0.990539i	$-0.456180\pi$
$577$	2.98901e39	0.274459	0.137230	+	0.990539i	$0.456180\pi$
$578$	1.63833e40	1.46706
$579$	−6.24496e39	−0.545369
$580$	2.10768e39	0.179514
$581$	8.14025e39	0.676214
$582$	−4.89915e39	−0.396952
$583$	−1.01979e40	−0.805965
$584$	6.40153e39	0.493511
$585$	1.35383e39	0.101813
$586$	9.88352e39	0.725097
$587$	−1.56819e40	−1.12239	−0.561197	−	0.827682i	$-0.689659\pi$
$587$	−1.56819e40	−1.12239	−0.561197	+	0.827682i	$0.689659\pi$
$588$	−1.08667e39	−0.0758797
$589$	−6.75080e39	−0.459921
$590$	−2.23346e40	−1.48465
$591$	−7.62183e39	−0.494357
$592$	−3.99579e39	−0.252894
$593$	−2.86074e40	−1.76679	−0.883395	−	0.468628i	$-0.844748\pi$
$593$	−2.86074e40	−1.76679	−0.883395	+	0.468628i	$0.844748\pi$
$594$	−3.16437e39	−0.190715
$595$	3.93923e40	2.31694
$596$	5.68466e39	0.326313
$597$	8.09219e39	0.453355
$598$	3.83571e39	0.209739
$599$	−1.92969e39	−0.102991	−0.0514954	−	0.998673i	$-0.516399\pi$
$599$	−1.92969e39	−0.102991	−0.0514954	+	0.998673i	$0.516399\pi$
$600$	5.36197e39	0.279339
$601$	−3.11888e40	−1.58606	−0.793029	−	0.609184i	$-0.791497\pi$
$601$	−3.11888e40	−1.58606	−0.793029	+	0.609184i	$0.791497\pi$
$602$	5.31638e39	0.263917
$603$	−5.69033e39	−0.275763
$604$	4.02706e39	0.190525
$605$	−3.21221e40	−1.48372
$606$	−9.07304e39	−0.409166
$607$	2.57778e39	0.113503	0.0567517	−	0.998388i	$-0.481926\pi$
$607$	2.57778e39	0.113503	0.0567517	+	0.998388i	$0.481926\pi$
$608$	3.18385e39	0.136883
$609$	−2.75461e39	−0.115640
$610$	3.86025e40	1.58246
$611$	−7.30957e39	−0.292613
$612$	−7.47564e39	−0.292249
$613$	1.83756e40	0.701561	0.350780	−	0.936458i	$-0.385916\pi$
$613$	1.83756e40	0.701561	0.350780	+	0.936458i	$0.385916\pi$
$614$	1.97975e40	0.738191
$615$	3.99629e40	1.45535
$616$	−1.19600e40	−0.425414
$617$	2.25261e40	0.782622	0.391311	−	0.920259i	$-0.372022\pi$
$617$	2.25261e40	0.782622	0.391311	+	0.920259i	$0.372022\pi$
$618$	8.66531e39	0.294070
$619$	1.38777e40	0.460048	0.230024	−	0.973185i	$-0.426120\pi$
$619$	1.38777e40	0.460048	0.230024	+	0.973185i	$0.426120\pi$
$620$	1.41137e40	0.457049
$621$	−9.09180e39	−0.287622
$622$	2.26688e39	0.0700596
$623$	9.51469e39	0.287288
$624$	−9.71061e38	−0.0286464
$625$	−1.71999e40	−0.495753
$626$	−2.66816e40	−0.751421
$627$	−2.27680e40	−0.626535
$628$	−3.02763e40	−0.814119
$629$	6.75051e40	1.77379
$630$	−1.21287e40	−0.311440
$631$	−2.69624e40	−0.676601	−0.338300	−	0.941038i	$-0.609852\pi$
$631$	−2.69624e40	−0.676601	−0.338300	+	0.941038i	$0.609852\pi$
$632$	1.07136e40	0.262746
$633$	−4.68677e39	−0.112336
$634$	−1.45095e40	−0.339907
$635$	7.19799e39	0.164813
$636$	7.41776e39	0.166014
$637$	2.38467e39	0.0521683
$638$	1.08108e40	0.231185
$639$	1.40220e40	0.293121
$640$	−6.65639e39	−0.136028
$641$	3.91551e40	0.782252	0.391126	−	0.920337i	$-0.372086\pi$
$641$	3.91551e40	0.782252	0.391126	+	0.920337i	$0.372086\pi$
$642$	3.23403e40	0.631665
$643$	5.79155e40	1.10595	0.552975	−	0.833198i	$-0.313492\pi$
$643$	5.79155e40	1.10595	0.552975	+	0.833198i	$0.313492\pi$
$644$	−3.43633e40	−0.641579
$645$	−2.11590e40	−0.386260
$646$	−5.37881e40	−0.960096
$647$	5.38714e40	0.940257	0.470128	−	0.882598i	$-0.344208\pi$
$647$	5.38714e40	0.940257	0.470128	+	0.882598i	$0.344208\pi$
$648$	2.30171e39	0.0392837
$649$	−1.14560e41	−1.91199
$650$	−1.17667e40	−0.192049
$651$	−1.84458e40	−0.294424
$652$	−4.84864e40	−0.756885
$653$	−3.92899e40	−0.599847	−0.299923	−	0.953963i	$-0.596961\pi$
$653$	−3.92899e40	−0.599847	−0.299923	+	0.953963i	$0.596961\pi$
$654$	5.60787e39	0.0837375
$655$	−1.11562e40	−0.162936
$656$	−2.86642e40	−0.409481
$657$	3.32981e40	0.465287
$658$	6.54848e40	0.895086
$659$	−4.51992e40	−0.604355	−0.302177	−	0.953252i	$-0.597713\pi$
$659$	−4.51992e40	−0.604355	−0.302177	+	0.953252i	$0.597713\pi$
$660$	4.76005e40	0.622622
$661$	−5.49534e40	−0.703191	−0.351595	−	0.936152i	$-0.614361\pi$
$661$	−5.49534e40	−0.703191	−0.351595	+	0.936152i	$0.614361\pi$
$662$	−2.73075e40	−0.341854
$663$	1.64051e40	0.200925
$664$	2.32381e40	0.278460
$665$	−8.72670e40	−1.02314
$666$	−2.07844e40	−0.238431
$667$	3.10614e40	0.348656
$668$	−8.01880e40	−0.880746
$669$	6.25681e40	0.672472
$670$	8.55975e40	0.900278
$671$	1.98002e41	2.03795
$672$	8.69952e39	0.0876276
$673$	−3.70785e40	−0.365514	−0.182757	−	0.983158i	$-0.558502\pi$
$673$	−3.70785e40	−0.365514	−0.182757	+	0.983158i	$0.558502\pi$
$674$	−7.09407e40	−0.684427
$675$	2.78907e40	0.263363
$676$	−5.19690e40	−0.480305
$677$	4.63793e40	0.419555	0.209777	−	0.977749i	$-0.432726\pi$
$677$	4.63793e40	0.419555	0.209777	+	0.977749i	$0.432726\pi$
$678$	−7.49200e40	−0.663387
$679$	−9.63167e40	−0.834814
$680$	1.12453e41	0.954099
$681$	−1.18995e41	−0.988313
$682$	7.23931e40	0.588605
$683$	5.51349e40	0.438860	0.219430	−	0.975628i	$-0.429580\pi$
$683$	5.51349e40	0.438860	0.219430	+	0.975628i	$0.429580\pi$
$684$	1.65610e40	0.129055
$685$	−1.34231e41	−1.02409
$686$	−1.02640e41	−0.766681
$687$	6.77456e40	0.495460
$688$	1.51767e40	0.108679
$689$	−1.62781e40	−0.114137
$690$	1.36765e41	0.938993
$691$	1.20626e41	0.810976	0.405488	−	0.914100i	$-0.367102\pi$
$691$	1.20626e41	0.810976	0.405488	+	0.914100i	$0.367102\pi$
$692$	8.62218e40	0.567648
$693$	−6.22111e40	−0.401084
$694$	−3.10675e39	−0.0196152
$695$	−8.30645e39	−0.0513613
$696$	−7.86361e39	−0.0476198
$697$	4.84254e41	2.87209
$698$	1.68296e41	0.977620
$699$	−7.17113e40	−0.408008
$700$	1.05416e41	0.587466
$701$	−1.75260e41	−0.956690	−0.478345	−	0.878172i	$-0.658763\pi$
$701$	−1.75260e41	−0.956690	−0.478345	+	0.878172i	$0.658763\pi$
$702$	−5.05105e39	−0.0270081
$703$	−1.49546e41	−0.783292
$704$	−3.41424e40	−0.175182
$705$	−2.60627e41	−1.31002
$706$	2.46785e41	1.21521
$707$	−1.78375e41	−0.860502
$708$	8.33289e40	0.393834
$709$	3.70352e40	0.171492	0.0857461	−	0.996317i	$-0.472673\pi$
$709$	3.70352e40	0.171492	0.0857461	+	0.996317i	$0.472673\pi$
$710$	−2.10927e41	−0.956945
$711$	5.57275e40	0.247719
$712$	2.71617e40	0.118303
$713$	2.07998e41	0.887691
$714$	−1.46970e41	−0.614617
$715$	−1.04458e41	−0.428061
$716$	−4.89554e39	−0.0196590
$717$	−5.82218e40	−0.229117
$718$	−1.17845e41	−0.454471
$719$	−8.54414e40	−0.322923	−0.161462	−	0.986879i	$-0.551621\pi$
$719$	−8.54414e40	−0.322923	−0.161462	+	0.986879i	$0.551621\pi$
$720$	−3.46238e40	−0.128249
$721$	1.70359e41	0.618448
$722$	−7.95764e40	−0.283136
$723$	−8.84264e40	−0.308373
$724$	−1.92992e41	−0.659677
$725$	−9.52865e40	−0.319249
$726$	1.19846e41	0.393588
$727$	−1.15556e41	−0.372002	−0.186001	−	0.982550i	$-0.559553\pi$
$727$	−1.15556e41	−0.372002	−0.186001	+	0.982550i	$0.559553\pi$
$728$	−1.90909e40	−0.0602451
$729$	1.19725e40	0.0370370
$730$	−5.00891e41	−1.51901
$731$	−2.56396e41	−0.762272
$732$	−1.44024e41	−0.419781
$733$	−2.20124e41	−0.629013	−0.314507	−	0.949255i	$-0.601839\pi$
$733$	−2.20124e41	−0.629013	−0.314507	+	0.949255i	$0.601839\pi$
$734$	1.61315e41	0.451942
$735$	8.50269e40	0.233555
$736$	−9.80973e40	−0.264197
$737$	4.39053e41	1.15941
$738$	−1.49099e41	−0.386063
$739$	4.90700e41	1.24587	0.622933	−	0.782275i	$-0.285941\pi$
$739$	4.90700e41	1.24587	0.622933	+	0.782275i	$0.285941\pi$
$740$	3.12653e41	0.778400
$741$	−3.63429e40	−0.0887269
$742$	1.45832e41	0.349138
$743$	−2.52884e41	−0.593723	−0.296861	−	0.954921i	$-0.595940\pi$
$743$	−2.52884e41	−0.593723	−0.296861	+	0.954921i	$0.595940\pi$
$744$	−5.26575e40	−0.121242
$745$	−4.44799e41	−1.00438
$746$	−2.28342e41	−0.505676
$747$	1.20875e41	0.262534
$748$	5.76803e41	1.22872
$749$	6.35807e41	1.32843
$750$	−1.12968e41	−0.231508
$751$	8.10589e41	1.62938	0.814689	−	0.579898i	$-0.196908\pi$
$751$	8.10589e41	1.62938	0.814689	+	0.579898i	$0.196908\pi$
$752$	1.86940e41	0.368590
$753$	4.88589e41	0.944967
$754$	1.72565e40	0.0327393
$755$	−3.15099e41	−0.586430
$756$	4.52513e40	0.0826161
$757$	3.97652e41	0.712218	0.356109	−	0.934444i	$-0.384103\pi$
$757$	3.97652e41	0.712218	0.356109	+	0.934444i	$0.384103\pi$
$758$	−1.98234e41	−0.348318
$759$	7.01503e41	1.20927
$760$	−2.49122e41	−0.421323
$761$	−1.86467e41	−0.309403	−0.154701	−	0.987961i	$-0.549442\pi$
$761$	−1.86467e41	−0.309403	−0.154701	+	0.987961i	$0.549442\pi$
$762$	−2.68553e40	−0.0437202
$763$	1.10250e41	0.176105
$764$	−4.72662e41	−0.740794
$765$	5.84935e41	0.899533
$766$	−3.81742e41	−0.576041
$767$	−1.82864e41	−0.270766
$768$	2.48346e40	0.0360844
$769$	−1.02676e42	−1.46398	−0.731991	−	0.681315i	$-0.761409\pi$
$769$	−1.02676e42	−1.46398	−0.731991	+	0.681315i	$0.761409\pi$
$770$	9.35819e41	1.30941
$771$	−3.40582e41	−0.467664
$772$	−3.50487e41	−0.472303
$773$	−3.59602e41	−0.475576	−0.237788	−	0.971317i	$-0.576422\pi$
$773$	−3.59602e41	−0.475576	−0.237788	+	0.971317i	$0.576422\pi$
$774$	7.89430e40	0.102464
$775$	−6.38071e41	−0.812820
$776$	−2.74956e41	−0.343770
$777$	−4.08619e41	−0.501434
$778$	1.27213e41	0.153224
$779$	−1.07278e42	−1.26829
$780$	7.59812e40	0.0881727
$781$	−1.08190e42	−1.23239
$782$	1.65726e42	1.85307
$783$	−4.09032e40	−0.0448964
$784$	−6.09872e40	−0.0657137
$785$	2.36898e42	2.50583
$786$	4.16231e40	0.0432223
$787$	8.99339e41	0.916832	0.458416	−	0.888738i	$-0.348417\pi$
$787$	8.99339e41	0.916832	0.458416	+	0.888738i	$0.348417\pi$
$788$	−4.27761e41	−0.428126
$789$	−6.63147e39	−0.00651618
$790$	−8.38288e41	−0.808725
$791$	−1.47292e42	−1.39514
$792$	−1.77594e41	−0.165164
$793$	3.16057e41	0.288605
$794$	9.33277e41	0.836784
$795$	−5.80407e41	−0.510986
$796$	4.54160e41	0.392617
$797$	8.99287e41	0.763401	0.381701	−	0.924286i	$-0.375339\pi$
$797$	8.99287e41	0.763401	0.381701	+	0.924286i	$0.375339\pi$
$798$	3.25588e41	0.271410
$799$	−3.15817e42	−2.58528
$800$	3.00931e41	0.241914
$801$	1.41284e41	0.111537
$802$	−1.08190e42	−0.838803
$803$	−2.56920e42	−1.95624
$804$	−3.19359e41	−0.238818
$805$	2.68878e42	1.97476
$806$	1.15556e41	0.0833554
$807$	7.43012e41	0.526417
$808$	−5.09208e41	−0.354348
$809$	−1.96667e42	−1.34424	−0.672122	−	0.740440i	$-0.734617\pi$
$809$	−1.96667e42	−1.34424	−0.672122	+	0.740440i	$0.734617\pi$
$810$	−1.80098e41	−0.120914
$811$	1.05714e41	0.0697154	0.0348577	−	0.999392i	$-0.488902\pi$
$811$	1.05714e41	0.0697154	0.0348577	+	0.999392i	$0.488902\pi$
$812$	−1.54598e41	−0.100147
$813$	−3.14338e39	−0.00200025
$814$	1.60368e42	1.00245
$815$	3.79385e42	2.32967
$816$	−4.19557e41	−0.253095
$817$	5.68003e41	0.336613
$818$	−8.34545e41	−0.485878
$819$	−9.93030e40	−0.0567997
$820$	2.24284e42	1.26037
$821$	1.26744e42	0.699767	0.349883	−	0.936793i	$-0.386221\pi$
$821$	1.26744e42	0.699767	0.349883	+	0.936793i	$0.386221\pi$
$822$	5.00807e41	0.271662
$823$	−1.14353e42	−0.609469	−0.304734	−	0.952437i	$-0.598568\pi$
$823$	−1.14353e42	−0.609469	−0.304734	+	0.952437i	$0.598568\pi$
$824$	4.86325e41	0.254672
$825$	−2.15198e42	−1.10728
$826$	1.63823e42	0.828258
$827$	−2.26203e42	−1.12375	−0.561874	−	0.827223i	$-0.689919\pi$
$827$	−2.26203e42	−1.12375	−0.561874	+	0.827223i	$0.689919\pi$
$828$	−5.10261e41	−0.249088
$829$	2.88043e41	0.138171	0.0690855	−	0.997611i	$-0.477992\pi$
$829$	2.88043e41	0.138171	0.0690855	+	0.997611i	$0.477992\pi$
$830$	−1.81827e42	−0.857091
$831$	1.83254e42	0.848864
$832$	−5.44990e40	−0.0248085
$833$	1.03032e42	0.460914
$834$	3.09909e40	0.0136247
$835$	6.27435e42	2.71091
$836$	−1.27781e42	−0.542595
$837$	−2.73902e41	−0.114308
$838$	−1.41520e41	−0.0580470
$839$	−1.52172e42	−0.613459	−0.306729	−	0.951797i	$-0.599235\pi$
$839$	−1.52172e42	−0.613459	−0.306729	+	0.951797i	$0.599235\pi$
$840$	−6.80699e41	−0.269715
$841$	−2.42794e42	−0.945576
$842$	−1.90615e42	−0.729678
$843$	−1.19967e42	−0.451401
$844$	−2.63036e41	−0.0972860
$845$	4.06634e42	1.47836
$846$	9.72383e41	0.347510
$847$	2.35615e42	0.827740
$848$	4.16308e41	0.143772
$849$	−6.71776e41	−0.228067
$850$	−5.08393e42	−1.69678
$851$	4.60766e42	1.51183
$852$	7.86957e41	0.253850
$853$	2.95528e42	0.937212	0.468606	−	0.883407i	$-0.344756\pi$
$853$	2.95528e42	0.937212	0.468606	+	0.883407i	$0.344756\pi$
$854$	−2.83148e42	−0.882826
$855$	−1.29583e42	−0.397227
$856$	1.81504e42	0.547038
$857$	−2.32070e42	−0.687698	−0.343849	−	0.939025i	$-0.611731\pi$
$857$	−2.32070e42	−0.687698	−0.343849	+	0.939025i	$0.611731\pi$
$858$	3.89728e41	0.113552
$859$	−3.32442e41	−0.0952390	−0.0476195	−	0.998866i	$-0.515163\pi$
$859$	−3.32442e41	−0.0952390	−0.0476195	+	0.998866i	$0.515163\pi$
$860$	−1.18751e42	−0.334511
$861$	−2.93127e42	−0.811914
$862$	2.70827e42	0.737626
$863$	−5.16488e42	−1.38326	−0.691630	−	0.722252i	$-0.743107\pi$
$863$	−5.16488e42	−1.38326	−0.691630	+	0.722252i	$0.743107\pi$
$864$	1.29179e41	0.0340207
$865$	−6.74647e42	−1.74720
$866$	−7.48106e41	−0.190526
$867$	4.78277e42	1.19785
$868$	−1.03524e42	−0.254979
$869$	−4.29980e42	−1.04151
$870$	6.15292e41	0.146572
$871$	7.00828e41	0.164190
$872$	3.14731e41	0.0725188
$873$	−1.43021e42	−0.324110
$874$	−3.67138e42	−0.818303
$875$	−2.22093e42	−0.486875
$876$	1.86879e42	0.402950
$877$	−2.41449e42	−0.512072	−0.256036	−	0.966667i	$-0.582417\pi$
$877$	−2.41449e42	−0.512072	−0.256036	+	0.966667i	$0.582417\pi$
$878$	2.20879e42	0.460770
$879$	2.88529e42	0.592039
$880$	2.67149e42	0.539206
$881$	4.81771e42	0.956512	0.478256	−	0.878220i	$-0.341269\pi$
$881$	4.81771e42	0.956512	0.478256	+	0.878220i	$0.341269\pi$
$882$	−3.17230e41	−0.0619555
$883$	−2.91349e42	−0.559737	−0.279868	−	0.960038i	$-0.590291\pi$
$883$	−2.91349e42	−0.559737	−0.279868	+	0.960038i	$0.590291\pi$
$884$	9.20709e41	0.174006
$885$	−6.52011e42	−1.21221
$886$	3.24162e42	0.592888
$887$	6.40710e42	1.15284	0.576420	−	0.817154i	$-0.304449\pi$
$887$	6.40710e42	1.15284	0.576420	+	0.817154i	$0.304449\pi$
$888$	−1.16649e42	−0.206487
$889$	−5.27971e41	−0.0919463
$890$	−2.12528e42	−0.364134
$891$	−9.23772e41	−0.155718
$892$	3.51152e42	0.582378
$893$	6.99641e42	1.14164
$894$	1.65952e42	0.266433
$895$	3.83054e41	0.0605098
$896$	4.88245e41	0.0758877
$897$	1.11976e42	0.171251
$898$	−1.74299e42	−0.262294
$899$	9.35766e41	0.138564
$900$	1.56531e42	0.228079
$901$	−7.03313e42	−1.00842
$902$	1.15041e43	1.62315
$903$	1.55201e42	0.215487
$904$	−4.20475e42	−0.574510
$905$	1.51008e43	2.03046
$906$	1.17562e42	0.155563
$907$	1.89188e42	0.246370	0.123185	−	0.992384i	$-0.460689\pi$
$907$	1.89188e42	0.246370	0.123185	+	0.992384i	$0.460689\pi$
$908$	−6.67836e42	−0.855904
$909$	−2.64869e42	−0.334083
$910$	1.49378e42	0.185433
$911$	−5.64197e41	−0.0689309	−0.0344655	−	0.999406i	$-0.510973\pi$
$911$	−5.64197e41	−0.0689309	−0.0344655	+	0.999406i	$0.510973\pi$
$912$	9.29458e41	0.111765
$913$	−9.32641e42	−1.10379
$914$	−6.61425e42	−0.770479
$915$	1.12692e43	1.29207
$916$	3.80210e42	0.429081
$917$	8.18305e41	0.0908992
$918$	−2.18236e42	−0.238620
$919$	−5.19829e42	−0.559481	−0.279741	−	0.960076i	$-0.590248\pi$
$919$	−5.19829e42	−0.559481	−0.279741	+	0.960076i	$0.590248\pi$
$920$	7.67567e42	0.813192
$921$	5.77947e42	0.602731
$922$	1.04108e43	1.06878
$923$	−1.72696e42	−0.174525
$924$	−3.49148e42	−0.347349
$925$	−1.41348e43	−1.38431
$926$	9.39591e41	0.0905898
$927$	2.52966e42	0.240108
$928$	−4.41331e41	−0.0412400
$929$	−1.98115e43	−1.82260	−0.911298	−	0.411748i	$-0.864918\pi$
$929$	−1.98115e43	−1.82260	−0.911298	+	0.411748i	$0.864918\pi$
$930$	4.12021e42	0.373179
$931$	−2.28251e42	−0.203536
$932$	−4.02467e42	−0.353345
$933$	6.61768e41	0.0572034
$934$	−1.04038e43	−0.885447
$935$	−4.51323e43	−3.78198
$936$	−2.83481e41	−0.0233897
$937$	1.66202e43	1.35025	0.675123	−	0.737705i	$-0.264090\pi$
$937$	1.66202e43	1.35025	0.675123	+	0.737705i	$0.264090\pi$
$938$	−6.27856e42	−0.502249
$939$	−7.78913e42	−0.613533
$940$	−1.46272e43	−1.13451
$941$	1.60082e43	1.22262	0.611312	−	0.791390i	$-0.290642\pi$
$941$	1.60082e43	1.22262	0.611312	+	0.791390i	$0.290642\pi$
$942$	−8.83854e42	−0.664725
$943$	3.30535e43	2.44792
$944$	4.67668e42	0.341070
$945$	−3.54071e42	−0.254290
$946$	−6.09106e42	−0.430796
$947$	1.90894e43	1.32959	0.664796	−	0.747025i	$-0.268518\pi$
$947$	1.90894e43	1.32959	0.664796	+	0.747025i	$0.268518\pi$
$948$	3.12760e42	0.214531
$949$	−4.10103e42	−0.277034
$950$	1.12626e43	0.749285
$951$	−4.23576e42	−0.277533
$952$	−8.24843e42	−0.532274
$953$	−2.09108e43	−1.32899	−0.664497	−	0.747291i	$-0.731354\pi$
$953$	−2.09108e43	−1.32899	−0.664497	+	0.747291i	$0.731354\pi$
$954$	2.16546e42	0.135550
$955$	3.69837e43	2.28014
$956$	−3.26760e42	−0.198422
$957$	3.15600e42	0.188762
$958$	−1.72965e42	−0.101896
$959$	9.84579e42	0.571322
$960$	−1.94320e42	−0.111067
$961$	−1.14957e43	−0.647210
$962$	2.55984e42	0.141963
$963$	9.44109e42	0.515752
$964$	−4.96277e42	−0.267059
$965$	2.74240e43	1.45373
$966$	−1.00317e43	−0.523847
$967$	5.08124e42	0.261388	0.130694	−	0.991423i	$-0.458279\pi$
$967$	5.08124e42	0.261388	0.130694	+	0.991423i	$0.458279\pi$
$968$	6.72613e42	0.340857
$969$	−1.57023e43	−0.783915
$970$	2.15141e43	1.05811
$971$	−3.87761e43	−1.87882	−0.939410	−	0.342795i	$-0.888626\pi$
$971$	−3.87761e43	−1.87882	−0.939410	+	0.342795i	$0.888626\pi$
$972$	6.71936e41	0.0320750
$973$	6.09276e41	0.0286535
$974$	−6.56347e42	−0.304109
$975$	−3.43505e42	−0.156807
$976$	−8.08306e42	−0.363541
$977$	3.20220e43	1.41898	0.709492	−	0.704713i	$-0.248924\pi$
$977$	3.20220e43	1.41898	0.709492	+	0.704713i	$0.248924\pi$
$978$	−1.41546e43	−0.617994
$979$	−1.09011e43	−0.468945
$980$	4.77198e42	0.202265
$981$	1.63710e42	0.0683714
$982$	1.91530e43	0.788169
$983$	−1.11454e43	−0.451930	−0.225965	−	0.974135i	$-0.572553\pi$
$983$	−1.11454e43	−0.451930	−0.225965	+	0.974135i	$0.572553\pi$
$984$	−8.36792e42	−0.334340
$985$	3.34704e43	1.31776
$986$	7.45586e42	0.289256
$987$	1.91169e43	0.730835
$988$	−2.03968e42	−0.0768398
$989$	−1.75007e43	−0.649695
$990$	1.38960e43	0.508369
$991$	3.00225e43	1.08238	0.541188	−	0.840901i	$-0.317975\pi$
$991$	3.00225e43	1.08238	0.541188	+	0.840901i	$0.317975\pi$
$992$	−2.95531e42	−0.104998
$993$	−7.97186e42	−0.279123
$994$	1.54715e43	0.533862
$995$	−3.55360e43	−1.20846
$996$	6.78387e42	0.227362
$997$	6.73357e42	0.222416	0.111208	−	0.993797i	$-0.464528\pi$
$997$	6.73357e42	0.222416	0.111208	+	0.993797i	$0.464528\pi$
$998$	−1.59704e43	−0.519903
$999$	−6.06759e42	−0.194678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.30.a.c.1.1	✓	1
3.2	odd	2		18.30.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.30.a.c.1.1	✓	1	1.1	even	1	trivial
18.30.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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