LMFDB - Embedded newform 6.26.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,26,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, 26, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 26 $
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:	$23.7598067971$
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)

$f(q)$

$=$

$q+4096.00 q^{2} -531441. q^{3} +1.67772e7 q^{4} -7.99328e8 q^{5} -2.17678e9 q^{6} +7.96241e9 q^{7} +6.87195e10 q^{8} +2.82430e11 q^{9} +O(q^{10})$

\(q+4096.00 q^{2} -531441. q^{3} +1.67772e7 q^{4} -7.99328e8 q^{5} -2.17678e9 q^{6} +7.96241e9 q^{7} +6.87195e10 q^{8} +2.82430e11 q^{9} -3.27405e12 q^{10} -1.76017e12 q^{11} -8.91610e12 q^{12} +1.64198e14 q^{13} +3.26140e13 q^{14} +4.24795e14 q^{15} +2.81475e14 q^{16} -2.37749e15 q^{17} +1.15683e15 q^{18} +1.06285e16 q^{19} -1.34105e16 q^{20} -4.23155e15 q^{21} -7.20965e15 q^{22} +7.66363e16 q^{23} -3.65203e16 q^{24} +3.40901e17 q^{25} +6.72554e17 q^{26} -1.50095e17 q^{27} +1.33587e17 q^{28} +2.40929e18 q^{29} +1.73996e18 q^{30} +5.30029e18 q^{31} +1.15292e18 q^{32} +9.35426e17 q^{33} -9.73818e18 q^{34} -6.36457e18 q^{35} +4.73838e18 q^{36} +8.42228e18 q^{37} +4.35342e19 q^{38} -8.72614e19 q^{39} -5.49294e19 q^{40} +9.69499e19 q^{41} -1.73324e19 q^{42} -3.66142e20 q^{43} -2.95307e19 q^{44} -2.25754e20 q^{45} +3.13902e20 q^{46} -1.09612e21 q^{47} -1.49587e20 q^{48} -1.27767e21 q^{49} +1.39633e21 q^{50} +1.26349e21 q^{51} +2.75478e21 q^{52} +6.64388e21 q^{53} -6.14788e20 q^{54} +1.40695e21 q^{55} +5.47173e20 q^{56} -5.64840e21 q^{57} +9.86844e21 q^{58} -1.85710e22 q^{59} +7.12689e21 q^{60} +1.81091e20 q^{61} +2.17100e22 q^{62} +2.24882e21 q^{63} +4.72237e21 q^{64} -1.31248e23 q^{65} +3.83151e21 q^{66} +4.27227e22 q^{67} -3.98876e22 q^{68} -4.07277e22 q^{69} -2.60693e22 q^{70} +9.75118e22 q^{71} +1.94084e22 q^{72} +2.13279e22 q^{73} +3.44977e22 q^{74} -1.81169e23 q^{75} +1.78316e23 q^{76} -1.40152e22 q^{77} -3.57423e23 q^{78} +8.51443e23 q^{79} -2.24991e23 q^{80} +7.97664e22 q^{81} +3.97107e23 q^{82} +7.75507e23 q^{83} -7.09936e22 q^{84} +1.90039e24 q^{85} -1.49972e24 q^{86} -1.28039e24 q^{87} -1.20958e23 q^{88} -1.40038e23 q^{89} -9.24687e23 q^{90} +1.30741e24 q^{91} +1.28574e24 q^{92} -2.81679e24 q^{93} -4.48971e24 q^{94} -8.49562e24 q^{95} -6.12710e23 q^{96} +5.08788e24 q^{97} -5.23333e24 q^{98} -4.97124e23 q^{99} +O(q^{100})\)

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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	−531441.	−0.577350
$3$	−531441.	−0.577350
$4$	1.67772e7	0.500000
$5$	−7.99328e8	−1.46420	−0.732099	−	0.681198i	$-0.761459\pi$
$5$	−7.99328e8	−1.46420	−0.732099	+	0.681198i	$0.761459\pi$
$6$	−2.17678e9	−0.408248
$7$	7.96241e9	0.217430	0.108715	−	0.994073i	$-0.465326\pi$
$7$	7.96241e9	0.217430	0.108715	+	0.994073i	$0.465326\pi$
$8$	6.87195e10	0.353553
$9$	2.82430e11	0.333333
$10$	−3.27405e12	−1.03534
$11$	−1.76017e12	−0.169101	−0.0845504	−	0.996419i	$-0.526945\pi$
$11$	−1.76017e12	−0.169101	−0.0845504	+	0.996419i	$0.526945\pi$
$12$	−8.91610e12	−0.288675
$13$	1.64198e14	1.95468	0.977339	−	0.211679i	$-0.0678931\pi$
$13$	1.64198e14	1.95468	0.977339	+	0.211679i	$0.0678931\pi$
$14$	3.26140e13	0.153746
$15$	4.24795e14	0.845355
$16$	2.81475e14	0.250000
$17$	−2.37749e15	−0.989706	−0.494853	−	0.868977i	$-0.664778\pi$
$17$	−2.37749e15	−0.989706	−0.494853	+	0.868977i	$0.664778\pi$
$18$	1.15683e15	0.235702
$19$	1.06285e16	1.10167	0.550833	−	0.834615i	$-0.314310\pi$
$19$	1.06285e16	1.10167	0.550833	+	0.834615i	$0.314310\pi$
$20$	−1.34105e16	−0.732099
$21$	−4.23155e15	−0.125533
$22$	−7.20965e15	−0.119572
$23$	7.66363e16	0.729183	0.364591	−	0.931168i	$-0.381209\pi$
$23$	7.66363e16	0.729183	0.364591	+	0.931168i	$0.381209\pi$
$24$	−3.65203e16	−0.204124
$25$	3.40901e17	1.14388
$26$	6.72554e17	1.38217
$27$	−1.50095e17	−0.192450
$28$	1.33587e17	0.108715
$29$	2.40929e18	1.26448	0.632242	−	0.774771i	$-0.282135\pi$
$29$	2.40929e18	1.26448	0.632242	+	0.774771i	$0.282135\pi$
$30$	1.73996e18	0.597756
$31$	5.30029e18	1.20859	0.604295	−	0.796761i	$-0.293455\pi$
$31$	5.30029e18	1.20859	0.604295	+	0.796761i	$0.293455\pi$
$32$	1.15292e18	0.176777
$33$	9.35426e17	0.0976304
$34$	−9.73818e18	−0.699828
$35$	−6.36457e18	−0.318360
$36$	4.73838e18	0.166667
$37$	8.42228e18	0.210333	0.105167	−	0.994455i	$-0.466462\pi$
$37$	8.42228e18	0.210333	0.105167	+	0.994455i	$0.466462\pi$
$38$	4.35342e19	0.778996
$39$	−8.72614e19	−1.12853
$40$	−5.49294e19	−0.517672
$41$	9.69499e19	0.671041	0.335521	−	0.942033i	$-0.391088\pi$
$41$	9.69499e19	0.671041	0.335521	+	0.942033i	$0.391088\pi$
$42$	−1.73324e19	−0.0887653
$43$	−3.66142e20	−1.39731	−0.698657	−	0.715457i	$-0.746219\pi$
$43$	−3.66142e20	−1.39731	−0.698657	+	0.715457i	$0.746219\pi$
$44$	−2.95307e19	−0.0845504
$45$	−2.25754e20	−0.488066
$46$	3.13902e20	0.515610
$47$	−1.09612e21	−1.37605	−0.688026	−	0.725686i	$-0.741523\pi$
$47$	−1.09612e21	−1.37605	−0.688026	+	0.725686i	$0.741523\pi$
$48$	−1.49587e20	−0.144338
$49$	−1.27767e21	−0.952724
$50$	1.39633e21	0.808842
$51$	1.26349e21	0.571407
$52$	2.75478e21	0.977339
$53$	6.64388e21	1.85769	0.928845	−	0.370468i	$-0.120803\pi$
$53$	6.64388e21	1.85769	0.928845	+	0.370468i	$0.120803\pi$
$54$	−6.14788e20	−0.136083
$55$	1.40695e21	0.247597
$56$	5.47173e20	0.0768730
$57$	−5.64840e21	−0.636047
$58$	9.86844e21	0.894125
$59$	−1.85710e22	−1.35889	−0.679445	−	0.733726i	$-0.737780\pi$
$59$	−1.85710e22	−1.35889	−0.679445	+	0.733726i	$0.737780\pi$
$60$	7.12689e21	0.422678
$61$	1.81091e20	0.00873520	0.00436760	−	0.999990i	$-0.498610\pi$
$61$	1.81091e20	0.00873520	0.00436760	+	0.999990i	$0.498610\pi$
$62$	2.17100e22	0.854602
$63$	2.24882e21	0.0724766
$64$	4.72237e21	0.125000
$65$	−1.31248e23	−2.86204
$66$	3.83151e21	0.0690352
$67$	4.27227e22	0.637858	0.318929	−	0.947779i	$-0.396677\pi$
$67$	4.27227e22	0.637858	0.318929	+	0.947779i	$0.396677\pi$
$68$	−3.98876e22	−0.494853
$69$	−4.07277e22	−0.420994
$70$	−2.60693e22	−0.225115
$71$	9.75118e22	0.705225	0.352613	−	0.935769i	$-0.385293\pi$
$71$	9.75118e22	0.705225	0.352613	+	0.935769i	$0.385293\pi$
$72$	1.94084e22	0.117851
$73$	2.13279e22	0.108996	0.0544981	−	0.998514i	$-0.482644\pi$
$73$	2.13279e22	0.108996	0.0544981	+	0.998514i	$0.482644\pi$
$74$	3.44977e22	0.148728
$75$	−1.81169e23	−0.660417
$76$	1.78316e23	0.550833
$77$	−1.40152e22	−0.0367676
$78$	−3.57423e23	−0.797994
$79$	8.51443e23	1.62113	0.810563	−	0.585651i	$-0.199161\pi$
$79$	8.51443e23	1.62113	0.810563	+	0.585651i	$0.199161\pi$
$80$	−2.24991e23	−0.366049
$81$	7.97664e22	0.111111
$82$	3.97107e23	0.474498
$83$	7.75507e23	0.796361	0.398180	−	0.917307i	$-0.369642\pi$
$83$	7.75507e23	0.796361	0.398180	+	0.917307i	$0.369642\pi$
$84$	−7.09936e22	−0.0627666
$85$	1.90039e24	1.44913
$86$	−1.49972e24	−0.988050
$87$	−1.28039e24	−0.730050
$88$	−1.20958e23	−0.0597862
$89$	−1.40038e23	−0.0600995	−0.0300497	−	0.999548i	$-0.509567\pi$
$89$	−1.40038e23	−0.0600995	−0.0300497	+	0.999548i	$0.509567\pi$
$90$	−9.24687e23	−0.345115
$91$	1.30741e24	0.425005
$92$	1.28574e24	0.364591
$93$	−2.81679e24	−0.697779
$94$	−4.48971e24	−0.973016
$95$	−8.49562e24	−1.61306
$96$	−6.12710e23	−0.102062
$97$	5.08788e24	0.744543	0.372272	−	0.928124i	$-0.378579\pi$
$97$	5.08788e24	0.744543	0.372272	+	0.928124i	$0.378579\pi$
$98$	−5.23333e24	−0.673678
$99$	−4.97124e23	−0.0563670
$100$	5.71938e24	0.571938
$101$	−1.00228e25	−0.885055	−0.442528	−	0.896755i	$-0.645918\pi$
$101$	−1.00228e25	−0.885055	−0.442528	+	0.896755i	$0.645918\pi$
$102$	5.17527e24	0.404046
$103$	2.48025e25	1.71408	0.857039	−	0.515252i	$-0.172302\pi$
$103$	2.48025e25	1.71408	0.857039	+	0.515252i	$0.172302\pi$
$104$	1.12836e25	0.691083
$105$	3.38240e24	0.183805
$106$	2.72133e25	1.31359
$107$	−2.18556e24	−0.0938133	−0.0469067	−	0.998899i	$-0.514936\pi$
$107$	−2.18556e24	−0.0938133	−0.0469067	+	0.998899i	$0.514936\pi$
$108$	−2.51817e24	−0.0962250
$109$	−3.57638e25	−1.21790	−0.608951	−	0.793208i	$-0.708409\pi$
$109$	−3.57638e25	−1.21790	−0.608951	+	0.793208i	$0.708409\pi$
$110$	5.76288e24	0.175078
$111$	−4.47594e24	−0.121436
$112$	2.24122e24	0.0543574
$113$	4.32478e25	0.938607	0.469304	−	0.883037i	$-0.344505\pi$
$113$	4.32478e25	0.938607	0.469304	+	0.883037i	$0.344505\pi$
$114$	−2.31358e25	−0.449753
$115$	−6.12575e25	−1.06767
$116$	4.04211e25	0.632242
$117$	4.63743e25	0.651560
$118$	−7.60667e25	−0.960881
$119$	−1.89305e25	−0.215192
$120$	2.91917e25	0.298878
$121$	−1.05249e26	−0.971405
$122$	7.41747e23	0.00617672
$123$	−5.15232e25	−0.387426
$124$	8.89242e25	0.604295
$125$	−3.42738e25	−0.210662
$126$	9.21117e24	0.0512487
$127$	−4.41074e25	−0.222313	−0.111156	−	0.993803i	$-0.535455\pi$
$127$	−4.41074e25	−0.222313	−0.111156	+	0.993803i	$0.535455\pi$
$128$	1.93428e25	0.0883883
$129$	1.94583e26	0.806739
$130$	−5.37591e26	−2.02377
$131$	4.57870e25	0.156621	0.0783106	−	0.996929i	$-0.475047\pi$
$131$	4.57870e25	0.156621	0.0783106	+	0.996929i	$0.475047\pi$
$132$	1.56938e25	0.0488152
$133$	8.46281e25	0.239535
$134$	1.74992e26	0.451034
$135$	1.19975e26	0.281785
$136$	−1.63380e26	−0.349914
$137$	6.23484e26	1.21848	0.609240	−	0.792986i	$-0.291475\pi$
$137$	6.23484e26	1.21848	0.609240	+	0.792986i	$0.291475\pi$
$138$	−1.66820e26	−0.297688
$139$	8.43369e26	1.37509	0.687547	−	0.726139i	$-0.258687\pi$
$139$	8.43369e26	1.37509	0.687547	+	0.726139i	$0.258687\pi$
$140$	−1.06780e26	−0.159180
$141$	5.82523e26	0.794464
$142$	3.99408e26	0.498669
$143$	−2.89016e26	−0.330538
$144$	7.94968e25	0.0833333
$145$	−1.92581e27	−1.85146
$146$	8.73589e25	0.0770720
$147$	6.79006e26	0.550056
$148$	1.41302e26	0.105167
$149$	−1.96211e27	−1.34244	−0.671219	−	0.741259i	$-0.734229\pi$
$149$	−1.96211e27	−1.34244	−0.671219	+	0.741259i	$0.734229\pi$
$150$	−7.42068e26	−0.466985
$151$	3.30732e27	1.91542	0.957711	−	0.287732i	$-0.0929012\pi$
$151$	3.30732e27	1.91542	0.957711	+	0.287732i	$0.0929012\pi$
$152$	7.30382e26	0.389498
$153$	−6.71472e26	−0.329902
$154$	−5.74062e25	−0.0259986
$155$	−4.23667e27	−1.76961
$156$	−1.46400e27	−0.564267
$157$	−3.25702e27	−1.15898	−0.579489	−	0.814980i	$-0.696748\pi$
$157$	−3.25702e27	−1.15898	−0.579489	+	0.814980i	$0.696748\pi$
$158$	3.48751e27	1.14631
$159$	−3.53083e27	−1.07254
$160$	−9.21562e26	−0.258836
$161$	6.10209e26	0.158546
$162$	3.26723e26	0.0785674
$163$	2.19500e27	0.488753	0.244376	−	0.969680i	$-0.421417\pi$
$163$	2.19500e27	0.488753	0.244376	+	0.969680i	$0.421417\pi$
$164$	1.62655e27	0.335521
$165$	−7.47712e26	−0.142950
$166$	3.17648e27	0.563112
$167$	1.09361e27	0.179849	0.0899246	−	0.995949i	$-0.471337\pi$
$167$	1.09361e27	0.179849	0.0899246	+	0.995949i	$0.471337\pi$
$168$	−2.90790e26	−0.0443827
$169$	1.99045e28	2.82077
$170$	7.78400e27	1.02469
$171$	3.00179e27	0.367222
$172$	−6.14284e27	−0.698657
$173$	−1.71336e28	−1.81248	−0.906238	−	0.422768i	$-0.861059\pi$
$173$	−1.71336e28	−1.81248	−0.906238	+	0.422768i	$0.861059\pi$
$174$	−5.24449e27	−0.516224
$175$	2.71440e27	0.248713
$176$	−4.95444e26	−0.0422752
$177$	9.86938e27	0.784556
$178$	−5.73595e26	−0.0424967
$179$	−5.15937e27	−0.356397	−0.178199	−	0.983995i	$-0.557027\pi$
$179$	−5.15937e27	−0.356397	−0.178199	+	0.983995i	$0.557027\pi$
$180$	−3.78752e27	−0.244033
$181$	−8.19291e27	−0.492556	−0.246278	−	0.969199i	$-0.579208\pi$
$181$	−8.19291e27	−0.492556	−0.246278	+	0.969199i	$0.579208\pi$
$182$	5.35515e27	0.300524
$183$	−9.62390e25	−0.00504327
$184$	5.26640e27	0.257805
$185$	−6.73216e27	−0.307970
$186$	−1.15376e28	−0.493404
$187$	4.18478e27	0.167360
$188$	−1.83899e28	−0.688026
$189$	−1.19511e27	−0.0418444
$190$	−3.47981e28	−1.14060
$191$	1.76729e28	0.542489	0.271244	−	0.962511i	$-0.412565\pi$
$191$	1.76729e28	0.542489	0.271244	+	0.962511i	$0.412565\pi$
$192$	−2.50966e27	−0.0721688
$193$	−1.41256e28	−0.380662	−0.190331	−	0.981720i	$-0.560956\pi$
$193$	−1.41256e28	−0.380662	−0.190331	+	0.981720i	$0.560956\pi$
$194$	2.08399e28	0.526472
$195$	6.97505e28	1.65240
$196$	−2.14357e28	−0.476362
$197$	−2.79711e28	−0.583286	−0.291643	−	0.956527i	$-0.594202\pi$
$197$	−2.79711e28	−0.583286	−0.291643	+	0.956527i	$0.594202\pi$
$198$	−2.03622e27	−0.0398575
$199$	1.17150e27	0.0215317	0.0107659	−	0.999942i	$-0.496573\pi$
$199$	1.17150e27	0.0215317	0.0107659	+	0.999942i	$0.496573\pi$
$200$	2.34266e28	0.404421
$201$	−2.27046e28	−0.368267
$202$	−4.10532e28	−0.625829
$203$	1.91837e28	0.274937
$204$	2.11979e28	0.285704
$205$	−7.74948e28	−0.982537
$206$	1.01591e29	1.21204
$207$	2.16443e28	0.243061
$208$	4.62176e28	0.488670
$209$	−1.87079e28	−0.186293
$210$	1.38543e28	0.129970
$211$	1.56649e28	0.138483	0.0692414	−	0.997600i	$-0.477942\pi$
$211$	1.56649e28	0.138483	0.0692414	+	0.997600i	$0.477942\pi$
$212$	1.11466e29	0.928845
$213$	−5.18218e28	−0.407162
$214$	−8.95203e27	−0.0663360
$215$	2.92667e29	2.04594
$216$	−1.03144e28	−0.0680414
$217$	4.22031e28	0.262783
$218$	−1.46488e29	−0.861186
$219$	−1.13345e28	−0.0629290
$220$	2.36047e28	0.123799
$221$	−3.90378e29	−1.93456
$222$	−1.83335e28	−0.0858682
$223$	−2.91739e29	−1.29177	−0.645884	−	0.763436i	$-0.723511\pi$
$223$	−2.91739e29	−1.29177	−0.645884	+	0.763436i	$0.723511\pi$
$224$	9.18003e27	0.0384365
$225$	9.62806e28	0.381292
$226$	1.77143e29	0.663696
$227$	−2.71265e29	−0.961768	−0.480884	−	0.876784i	$-0.659684\pi$
$227$	−2.71265e29	−0.961768	−0.480884	+	0.876784i	$0.659684\pi$
$228$	−9.47644e28	−0.318024
$229$	−1.04565e29	−0.332235	−0.166117	−	0.986106i	$-0.553123\pi$
$229$	−1.04565e29	−0.332235	−0.166117	+	0.986106i	$0.553123\pi$
$230$	−2.50911e29	−0.754955
$231$	7.44825e27	0.0212278
$232$	1.65565e29	0.447063
$233$	−2.43186e29	−0.622285	−0.311142	−	0.950363i	$-0.600712\pi$
$233$	−2.43186e29	−0.622285	−0.311142	+	0.950363i	$0.600712\pi$
$234$	1.89949e29	0.460722
$235$	8.76159e29	2.01481
$236$	−3.11569e29	−0.679445
$237$	−4.52492e29	−0.935958
$238$	−7.75394e28	−0.152163
$239$	8.21362e29	1.52954	0.764770	−	0.644303i	$-0.222852\pi$
$239$	8.21362e29	1.52954	0.764770	+	0.644303i	$0.222852\pi$
$240$	1.19569e29	0.211339
$241$	−2.05427e29	−0.344702	−0.172351	−	0.985036i	$-0.555136\pi$
$241$	−2.05427e29	−0.344702	−0.172351	+	0.985036i	$0.555136\pi$
$242$	−4.31099e29	−0.686887
$243$	−4.23912e28	−0.0641500
$244$	3.03820e27	0.00436760
$245$	1.02128e30	1.39498
$246$	−2.11039e29	−0.273952
$247$	1.74517e30	2.15340
$248$	3.64233e29	0.427301
$249$	−4.12136e29	−0.459779
$250$	−1.40385e29	−0.148961
$251$	−7.25306e28	−0.0732149	−0.0366075	−	0.999330i	$-0.511655\pi$
$251$	−7.25306e28	−0.0732149	−0.0366075	+	0.999330i	$0.511655\pi$
$252$	3.77289e28	0.0362383
$253$	−1.34893e29	−0.123305
$254$	−1.80664e29	−0.157199
$255$	−1.00995e30	−0.836653
$256$	7.92282e28	0.0625000
$257$	−6.73707e29	−0.506183	−0.253091	−	0.967442i	$-0.581447\pi$
$257$	−6.73707e29	−0.506183	−0.253091	+	0.967442i	$0.581447\pi$
$258$	7.97012e29	0.570451
$259$	6.70616e28	0.0457327
$260$	−2.20197e30	−1.43102
$261$	6.80454e29	0.421495
$262$	1.87543e29	0.110748
$263$	1.68079e30	0.946380	0.473190	−	0.880960i	$-0.343102\pi$
$263$	1.68079e30	0.946380	0.473190	+	0.880960i	$0.343102\pi$
$264$	6.42820e28	0.0345176
$265$	−5.31064e30	−2.72003
$266$	3.46637e29	0.169377
$267$	7.44219e28	0.0346984
$268$	7.16768e29	0.318929
$269$	1.14096e30	0.484582	0.242291	−	0.970204i	$-0.422101\pi$
$269$	1.14096e30	0.484582	0.242291	+	0.970204i	$0.422101\pi$
$270$	4.91417e29	0.199252
$271$	−3.12111e30	−1.20835	−0.604175	−	0.796852i	$-0.706497\pi$
$271$	−3.12111e30	−1.20835	−0.604175	+	0.796852i	$0.706497\pi$
$272$	−6.69203e29	−0.247427
$273$	−6.94811e29	−0.245377
$274$	2.55379e30	0.861595
$275$	−6.00044e29	−0.193430
$276$	−6.83297e29	−0.210497
$277$	−3.28440e28	−0.00967073	−0.00483537	−	0.999988i	$-0.501539\pi$
$277$	−3.28440e28	−0.00967073	−0.00483537	+	0.999988i	$0.501539\pi$
$278$	3.45444e30	0.972339
$279$	1.49696e30	0.402863
$280$	−4.37370e29	−0.112557
$281$	7.32716e29	0.180346	0.0901730	−	0.995926i	$-0.471258\pi$
$281$	7.32716e29	0.180346	0.0901730	+	0.995926i	$0.471258\pi$
$282$	2.38602e30	0.561771
$283$	−1.94247e30	−0.437546	−0.218773	−	0.975776i	$-0.570205\pi$
$283$	−1.94247e30	−0.437546	−0.218773	+	0.975776i	$0.570205\pi$
$284$	1.63598e30	0.352613
$285$	4.51492e30	0.931299
$286$	−1.18381e30	−0.233726
$287$	7.71955e29	0.145904
$288$	3.25619e29	0.0589256
$289$	−1.18189e29	−0.0204811
$290$	−7.88811e30	−1.30918
$291$	−2.70391e30	−0.429862
$292$	3.57822e29	0.0544981
$293$	−5.98650e30	−0.873630	−0.436815	−	0.899551i	$-0.643894\pi$
$293$	−5.98650e30	−0.873630	−0.436815	+	0.899551i	$0.643894\pi$
$294$	2.78121e30	0.388948
$295$	1.48443e31	1.98969
$296$	5.78775e29	0.0743641
$297$	2.64192e29	0.0325435
$298$	−8.03679e30	−0.949247
$299$	1.25835e31	1.42532
$300$	−3.03951e30	−0.330208
$301$	−2.91537e30	−0.303818
$302$	1.35468e31	1.35441
$303$	5.32651e30	0.510987
$304$	2.99164e30	0.275417
$305$	−1.44751e29	−0.0127901
$306$	−2.75035e30	−0.233276
$307$	−1.91484e31	−1.55920	−0.779602	−	0.626275i	$-0.784579\pi$
$307$	−1.91484e31	−1.55920	−0.779602	+	0.626275i	$0.784579\pi$
$308$	−2.35136e29	−0.0183838
$309$	−1.31811e31	−0.989623
$310$	−1.73534e31	−1.25131
$311$	−2.18310e31	−1.51206	−0.756030	−	0.654537i	$-0.772863\pi$
$311$	−2.18310e31	−1.51206	−0.756030	+	0.654537i	$0.772863\pi$
$312$	−5.99656e30	−0.398997
$313$	2.05365e31	1.31287	0.656434	−	0.754383i	$-0.272064\pi$
$313$	2.05365e31	1.31287	0.656434	+	0.754383i	$0.272064\pi$
$314$	−1.33408e31	−0.819521
$315$	−1.79754e30	−0.106120
$316$	1.42848e31	0.810563
$317$	1.58483e31	0.864457	0.432228	−	0.901764i	$-0.357727\pi$
$317$	1.58483e31	0.864457	0.432228	+	0.901764i	$0.357727\pi$
$318$	−1.44623e31	−0.758399
$319$	−4.24075e30	−0.213825
$320$	−3.77472e30	−0.183025
$321$	1.16149e30	0.0541632
$322$	2.49942e30	0.112109
$323$	−2.52690e31	−1.09033
$324$	1.33826e30	0.0555556
$325$	5.59753e31	2.23591
$326$	8.99071e30	0.345600
$327$	1.90063e31	0.703156
$328$	6.66235e30	0.237249
$329$	−8.72776e30	−0.299195
$330$	−3.06263e30	−0.101081
$331$	−4.16688e30	−0.132422	−0.0662112	−	0.997806i	$-0.521091\pi$
$331$	−4.16688e30	−0.132422	−0.0662112	+	0.997806i	$0.521091\pi$
$332$	1.30109e31	0.398180
$333$	2.37870e30	0.0701111
$334$	4.47944e30	0.127173
$335$	−3.41495e31	−0.933950
$336$	−1.19108e30	−0.0313833
$337$	4.74117e31	1.20368	0.601841	−	0.798616i	$-0.294434\pi$
$337$	4.74117e31	1.20368	0.601841	+	0.798616i	$0.294434\pi$
$338$	8.15288e31	1.99458
$339$	−2.29837e31	−0.541905
$340$	3.18833e31	0.724563
$341$	−9.32941e30	−0.204374
$342$	1.22953e31	0.259665
$343$	−2.08515e31	−0.424580
$344$	−2.51611e31	−0.494025
$345$	3.25547e31	0.616418
$346$	−7.01792e31	−1.28161
$347$	−4.63683e31	−0.816776	−0.408388	−	0.912809i	$-0.633909\pi$
$347$	−4.63683e31	−0.816776	−0.408388	+	0.912809i	$0.633909\pi$
$348$	−2.14814e31	−0.365025
$349$	−6.34598e31	−1.04035	−0.520176	−	0.854059i	$-0.674134\pi$
$349$	−6.34598e31	−1.04035	−0.520176	+	0.854059i	$0.674134\pi$
$350$	1.11182e31	0.175866
$351$	−2.46452e31	−0.376178
$352$	−2.02934e30	−0.0298931
$353$	−2.12528e31	−0.302157	−0.151079	−	0.988522i	$-0.548275\pi$
$353$	−2.12528e31	−0.302157	−0.151079	+	0.988522i	$0.548275\pi$
$354$	4.04250e31	0.554765
$355$	−7.79439e31	−1.03259
$356$	−2.34945e30	−0.0300497
$357$	1.00605e31	0.124241
$358$	−2.11328e31	−0.252011
$359$	6.38661e31	0.735512	0.367756	−	0.929922i	$-0.380126\pi$
$359$	6.38661e31	0.735512	0.367756	+	0.929922i	$0.380126\pi$
$360$	−1.55137e31	−0.172557
$361$	1.98876e31	0.213669
$362$	−3.35581e31	−0.348290
$363$	5.59336e31	0.560841
$364$	2.19347e31	0.212503
$365$	−1.70480e31	−0.159592
$366$	−3.94195e29	−0.00356613
$367$	1.67899e31	0.146799	0.0733993	−	0.997303i	$-0.476615\pi$
$367$	1.67899e31	0.146799	0.0733993	+	0.997303i	$0.476615\pi$
$368$	2.15712e31	0.182296
$369$	2.73815e31	0.223680
$370$	−2.75749e31	−0.217767
$371$	5.29013e31	0.403917
$372$	−4.72579e31	−0.348890
$373$	−2.15396e32	−1.53772	−0.768859	−	0.639419i	$-0.779175\pi$
$373$	−2.15396e32	−1.53772	−0.768859	+	0.639419i	$0.779175\pi$
$374$	1.71408e31	0.118342
$375$	1.82145e31	0.121626
$376$	−7.53248e31	−0.486508
$377$	3.95599e32	2.47166
$378$	−4.89519e30	−0.0295884
$379$	9.22117e31	0.539257	0.269629	−	0.962964i	$-0.413099\pi$
$379$	9.22117e31	0.539257	0.269629	+	0.962964i	$0.413099\pi$
$380$	−1.42533e32	−0.806529
$381$	2.34405e31	0.128352
$382$	7.23882e31	0.383597
$383$	1.91940e32	0.984423	0.492211	−	0.870476i	$-0.336189\pi$
$383$	1.91940e32	0.984423	0.492211	+	0.870476i	$0.336189\pi$
$384$	−1.02796e31	−0.0510310
$385$	1.12027e31	0.0538350
$386$	−5.78583e31	−0.269169
$387$	−1.03409e32	−0.465771
$388$	8.53604e31	0.372272
$389$	1.99017e32	0.840464	0.420232	−	0.907417i	$-0.361949\pi$
$389$	1.99017e32	0.840464	0.420232	+	0.907417i	$0.361949\pi$
$390$	2.85698e32	1.16842
$391$	−1.82202e32	−0.721677
$392$	−8.78007e31	−0.336839
$393$	−2.43331e31	−0.0904253
$394$	−1.14570e32	−0.412446
$395$	−6.80582e32	−2.37365
$396$	−8.34035e30	−0.0281835
$397$	2.21227e32	0.724364	0.362182	−	0.932107i	$-0.382032\pi$
$397$	2.21227e32	0.724364	0.362182	+	0.932107i	$0.382032\pi$
$398$	4.79846e30	0.0152252
$399$	−4.49749e31	−0.138296
$400$	9.59552e31	0.285969
$401$	−3.65964e32	−1.05714	−0.528571	−	0.848889i	$-0.677272\pi$
$401$	−3.65964e32	−1.05714	−0.528571	+	0.848889i	$0.677272\pi$
$402$	−9.29981e31	−0.260404
$403$	8.70296e32	2.36240
$404$	−1.68154e32	−0.442528
$405$	−6.37595e31	−0.162689
$406$	7.85765e31	0.194409
$407$	−1.48246e31	−0.0355676
$408$	8.68266e31	0.202023
$409$	−5.04541e32	−1.13856	−0.569279	−	0.822145i	$-0.692777\pi$
$409$	−5.04541e32	−1.13856	−0.569279	+	0.822145i	$0.692777\pi$
$410$	−3.17419e32	−0.694759
$411$	−3.31345e32	−0.703490
$412$	4.16117e32	0.857039
$413$	−1.47870e32	−0.295463
$414$	8.86552e31	0.171870
$415$	−6.19884e32	−1.16603
$416$	1.89307e32	0.345542
$417$	−4.48201e32	−0.793911
$418$	−7.66275e31	−0.131729
$419$	9.21971e32	1.53830	0.769151	−	0.639067i	$-0.220679\pi$
$419$	9.21971e32	1.53830	0.769151	+	0.639067i	$0.220679\pi$
$420$	5.67472e31	0.0919027
$421$	7.64796e31	0.120232	0.0601159	−	0.998191i	$-0.480853\pi$
$421$	7.64796e31	0.120232	0.0601159	+	0.998191i	$0.480853\pi$
$422$	6.41632e31	0.0979221
$423$	−3.09577e32	−0.458684
$424$	4.56564e32	0.656793
$425$	−8.10488e32	−1.13210
$426$	−2.12262e32	−0.287907
$427$	1.44192e30	0.00189929
$428$	−3.66675e31	−0.0469067
$429$	1.53595e32	0.190836
$430$	1.19877e33	1.44670
$431$	1.05168e33	1.23287	0.616434	−	0.787406i	$-0.288577\pi$
$431$	1.05168e33	1.23287	0.616434	+	0.787406i	$0.288577\pi$
$432$	−4.22479e31	−0.0481125
$433$	1.67254e31	0.0185045	0.00925226	−	0.999957i	$-0.497055\pi$
$433$	1.67254e31	0.0185045	0.00925226	+	0.999957i	$0.497055\pi$
$434$	1.72864e32	0.185816
$435$	1.02345e33	1.06894
$436$	−6.00017e32	−0.608951
$437$	8.14525e32	0.803316
$438$	−4.64261e31	−0.0444975
$439$	1.10688e33	1.03109	0.515543	−	0.856864i	$-0.327590\pi$
$439$	1.10688e33	1.03109	0.515543	+	0.856864i	$0.327590\pi$
$440$	9.66850e31	0.0875388
$441$	−3.60851e32	−0.317575
$442$	−1.59899e33	−1.36794
$443$	4.29049e32	0.356829	0.178415	−	0.983955i	$-0.442903\pi$
$443$	4.29049e32	0.356829	0.178415	+	0.983955i	$0.442903\pi$
$444$	−7.50939e31	−0.0607180
$445$	1.11936e32	0.0879975
$446$	−1.19496e33	−0.913417
$447$	1.04274e33	0.775057
$448$	3.76014e31	0.0271787
$449$	−7.54140e32	−0.530118	−0.265059	−	0.964232i	$-0.585391\pi$
$449$	−7.54140e32	−0.530118	−0.265059	+	0.964232i	$0.585391\pi$
$450$	3.94366e32	0.269614
$451$	−1.70648e32	−0.113474
$452$	7.25578e32	0.469304
$453$	−1.75765e33	−1.10587
$454$	−1.11110e33	−0.680073
$455$	−1.04505e33	−0.622292
$456$	−3.88155e32	−0.224877
$457$	−1.60283e33	−0.903515	−0.451758	−	0.892141i	$-0.649203\pi$
$457$	−1.60283e33	−0.903515	−0.451758	+	0.892141i	$0.649203\pi$
$458$	−4.28300e32	−0.234925
$459$	3.56848e32	0.190469
$460$	−1.02773e33	−0.533834
$461$	−4.68625e32	−0.236899	−0.118450	−	0.992960i	$-0.537792\pi$
$461$	−4.68625e32	−0.236899	−0.118450	+	0.992960i	$0.537792\pi$
$462$	3.05080e31	0.0150103
$463$	−2.26778e33	−1.08602	−0.543011	−	0.839726i	$-0.682716\pi$
$463$	−2.26778e33	−1.08602	−0.543011	+	0.839726i	$0.682716\pi$
$464$	6.78154e32	0.316121
$465$	2.25154e33	1.02169
$466$	−9.96089e32	−0.440022
$467$	−1.03293e33	−0.444232	−0.222116	−	0.975020i	$-0.571296\pi$
$467$	−1.03293e33	−0.444232	−0.222116	+	0.975020i	$0.571296\pi$
$468$	7.78032e32	0.325780
$469$	3.40176e32	0.138689
$470$	3.58875e33	1.42469
$471$	1.73092e33	0.669136
$472$	−1.27619e33	−0.480440
$473$	6.44472e32	0.236287
$474$	−1.85341e33	−0.661822
$475$	3.62326e33	1.26017
$476$	−3.17601e32	−0.107596
$477$	1.87643e33	0.619230
$478$	3.36430e33	1.08155
$479$	−2.76902e32	−0.0867226	−0.0433613	−	0.999059i	$-0.513807\pi$
$479$	−2.76902e32	−0.0867226	−0.0433613	+	0.999059i	$0.513807\pi$
$480$	4.89756e32	0.149439
$481$	1.38292e33	0.411134
$482$	−8.41427e32	−0.243741
$483$	−3.24290e32	−0.0915366
$484$	−1.76578e33	−0.485702
$485$	−4.06688e33	−1.09016
$486$	−1.73634e32	−0.0453609
$487$	−2.55940e33	−0.651668	−0.325834	−	0.945427i	$-0.605645\pi$
$487$	−2.55940e33	−0.651668	−0.325834	+	0.945427i	$0.605645\pi$
$488$	1.24445e31	0.00308836
$489$	−1.16651e33	−0.282181
$490$	4.18315e33	0.986398
$491$	4.20891e33	0.967499	0.483749	−	0.875207i	$-0.339275\pi$
$491$	4.20891e33	0.967499	0.483749	+	0.875207i	$0.339275\pi$
$492$	−8.64415e32	−0.193713
$493$	−5.72804e33	−1.25147
$494$	7.14821e33	1.52269
$495$	3.97365e32	0.0825324
$496$	1.49190e33	0.302147
$497$	7.76429e32	0.153337
$498$	−1.68811e33	−0.325113
$499$	2.66094e33	0.499779	0.249889	−	0.968274i	$-0.419606\pi$
$499$	2.66094e33	0.499779	0.249889	+	0.968274i	$0.419606\pi$
$500$	−5.75018e32	−0.105331
$501$	−5.81192e32	−0.103836
$502$	−2.97085e32	−0.0517708
$503$	−5.35065e33	−0.909509	−0.454754	−	0.890617i	$-0.650273\pi$
$503$	−5.35065e33	−0.909509	−0.454754	+	0.890617i	$0.650273\pi$
$504$	1.54538e32	0.0256243
$505$	8.01147e33	1.29590
$506$	−5.52521e32	−0.0871901
$507$	−1.05781e34	−1.62857
$508$	−7.39999e32	−0.111156
$509$	3.29461e33	0.482872	0.241436	−	0.970417i	$-0.422382\pi$
$509$	3.29461e33	0.482872	0.241436	+	0.970417i	$0.422382\pi$
$510$	−4.13674e33	−0.591603
$511$	1.69821e32	0.0236990
$512$	3.24519e32	0.0441942
$513$	−1.59527e33	−0.212016
$514$	−2.75950e33	−0.357925
$515$	−1.98253e34	−2.50975
$516$	3.26456e33	0.403370
$517$	1.92936e33	0.232692
$518$	2.74684e32	0.0323379
$519$	9.10550e33	1.04643
$520$	−9.01928e33	−1.01188
$521$	9.31092e33	1.01981	0.509907	−	0.860229i	$-0.329680\pi$
$521$	9.31092e33	1.01981	0.509907	+	0.860229i	$0.329680\pi$
$522$	2.78714e33	0.298042
$523$	1.25896e34	1.31444	0.657222	−	0.753697i	$-0.271732\pi$
$523$	1.25896e34	1.31444	0.657222	+	0.753697i	$0.271732\pi$
$524$	7.68178e32	0.0783106
$525$	−1.44254e33	−0.143594
$526$	6.88450e33	0.669192
$527$	−1.26014e34	−1.19615
$528$	2.63299e32	0.0244076
$529$	−5.17265e33	−0.468292
$530$	−2.17524e34	−1.92335
$531$	−5.24499e33	−0.452964
$532$	1.41982e33	0.119768
$533$	1.59190e34	1.31167
$534$	3.04832e32	0.0245355
$535$	1.74697e33	0.137361
$536$	2.93588e33	0.225517
$537$	2.74190e33	0.205766
$538$	4.67337e33	0.342651
$539$	2.24891e33	0.161107
$540$	2.01284e33	0.140893
$541$	6.31367e33	0.431833	0.215917	−	0.976412i	$-0.430726\pi$
$541$	6.31367e33	0.431833	0.215917	+	0.976412i	$0.430726\pi$
$542$	−1.27841e34	−0.854432
$543$	4.35405e33	0.284377
$544$	−2.74105e33	−0.174957
$545$	2.85870e34	1.78325
$546$	−2.84595e33	−0.173508
$547$	1.24089e33	0.0739420	0.0369710	−	0.999316i	$-0.488229\pi$
$547$	1.24089e33	0.0739420	0.0369710	+	0.999316i	$0.488229\pi$
$548$	1.04603e34	0.609240
$549$	5.11453e31	0.00291173
$550$	−2.45778e33	−0.136776
$551$	2.56070e34	1.39304
$552$	−2.79878e33	−0.148844
$553$	6.77954e33	0.352481
$554$	−1.34529e32	−0.00683824
$555$	3.57775e33	0.177806
$556$	1.41494e34	0.687547
$557$	−1.09634e34	−0.520900	−0.260450	−	0.965487i	$-0.583871\pi$
$557$	−1.09634e34	−0.520900	−0.260450	+	0.965487i	$0.583871\pi$
$558$	6.13154e33	0.284867
$559$	−6.01197e34	−2.73130
$560$	−1.79147e33	−0.0795901
$561$	−2.22396e33	−0.0966255
$562$	3.00121e33	0.127524
$563$	−2.17888e34	−0.905481	−0.452740	−	0.891642i	$-0.649554\pi$
$563$	−2.17888e34	−0.905481	−0.452740	+	0.891642i	$0.649554\pi$
$564$	9.77312e33	0.397232
$565$	−3.45692e34	−1.37431
$566$	−7.95636e33	−0.309392
$567$	6.35133e32	0.0241589
$568$	6.70096e33	0.249335
$569$	4.32215e33	0.157325	0.0786623	−	0.996901i	$-0.474935\pi$
$569$	4.32215e33	0.157325	0.0786623	+	0.996901i	$0.474935\pi$
$570$	1.84931e34	0.658528
$571$	5.12902e33	0.178683	0.0893414	−	0.996001i	$-0.471524\pi$
$571$	5.12902e33	0.178683	0.0893414	+	0.996001i	$0.471524\pi$
$572$	−4.84888e33	−0.165269
$573$	−9.39210e33	−0.313206
$574$	3.16193e33	0.103170
$575$	2.61254e34	0.834094
$576$	1.33374e33	0.0416667
$577$	−4.84747e34	−1.48189	−0.740947	−	0.671564i	$-0.765623\pi$
$577$	−4.84747e34	−1.48189	−0.740947	+	0.671564i	$0.765623\pi$
$578$	−4.84101e32	−0.0144823
$579$	7.50691e33	0.219775
$580$	−3.23097e34	−0.925728
$581$	6.17491e33	0.173152
$582$	−1.10752e34	−0.303959
$583$	−1.16944e34	−0.314137
$584$	1.46564e33	0.0385360
$585$	−3.70683e34	−0.954012
$586$	−2.45207e34	−0.617750
$587$	−2.64989e34	−0.653509	−0.326754	−	0.945109i	$-0.605955\pi$
$587$	−2.64989e34	−0.653509	−0.326754	+	0.945109i	$0.605955\pi$
$588$	1.13918e34	0.275028
$589$	5.63339e34	1.33146
$590$	6.08022e34	1.40692
$591$	1.48650e34	0.336760
$592$	2.37066e33	0.0525833
$593$	4.79232e32	0.0104079	0.00520394	−	0.999986i	$-0.498344\pi$
$593$	4.79232e32	0.0104079	0.00520394	+	0.999986i	$0.498344\pi$
$594$	1.08213e33	0.0230117
$595$	1.51317e34	0.315083
$596$	−3.29187e34	−0.671219
$597$	−6.22583e32	−0.0124313
$598$	5.15420e34	1.00785
$599$	4.24367e34	0.812656	0.406328	−	0.913727i	$-0.366809\pi$
$599$	4.24367e34	0.812656	0.406328	+	0.913727i	$0.366809\pi$
$600$	−1.24498e34	−0.233493
$601$	4.84516e34	0.889975	0.444987	−	0.895537i	$-0.353208\pi$
$601$	4.84516e34	0.889975	0.444987	+	0.895537i	$0.353208\pi$
$602$	−1.19414e34	−0.214831
$603$	1.20662e34	0.212619
$604$	5.54876e34	0.957711
$605$	8.41283e34	1.42233
$606$	2.18174e34	0.361322
$607$	9.47666e33	0.153743	0.0768717	−	0.997041i	$-0.475507\pi$
$607$	9.47666e33	0.153743	0.0768717	+	0.997041i	$0.475507\pi$
$608$	1.22538e34	0.194749
$609$	−1.01950e34	−0.158735
$610$	−5.92899e32	−0.00904394
$611$	−1.79981e35	−2.68974
$612$	−1.12654e34	−0.164951
$613$	4.82718e34	0.692528	0.346264	−	0.938137i	$-0.387450\pi$
$613$	4.82718e34	0.692528	0.346264	+	0.938137i	$0.387450\pi$
$614$	−7.84319e34	−1.10252
$615$	4.11839e34	0.567268
$616$	−9.63117e32	−0.0129993
$617$	−4.73363e34	−0.626080	−0.313040	−	0.949740i	$-0.601347\pi$
$617$	−4.73363e34	−0.626080	−0.313040	+	0.949740i	$0.601347\pi$
$618$	−5.39897e34	−0.699769
$619$	1.05288e35	1.33736	0.668678	−	0.743552i	$-0.266860\pi$
$619$	1.05288e35	1.33736	0.668678	+	0.743552i	$0.266860\pi$
$620$	−7.10795e34	−0.884807
$621$	−1.15027e34	−0.140331
$622$	−8.94198e34	−1.06919
$623$	−1.11504e33	−0.0130674
$624$	−2.45619e34	−0.282134
$625$	−7.42006e34	−0.835424
$626$	8.41173e34	0.928338
$627$	9.94214e33	0.107556
$628$	−5.46438e34	−0.579489
$629$	−2.00239e34	−0.208168
$630$	−7.36274e33	−0.0750382
$631$	1.21038e35	1.20935	0.604677	−	0.796471i	$-0.293302\pi$
$631$	1.21038e35	1.20935	0.604677	+	0.796471i	$0.293302\pi$
$632$	5.85107e34	0.573155
$633$	−8.32495e33	−0.0799530
$634$	6.49148e34	0.611263
$635$	3.52562e34	0.325510
$636$	−5.92375e34	−0.536269
$637$	−2.09790e35	−1.86227
$638$	−1.73701e34	−0.151197
$639$	2.75402e34	0.235075
$640$	−1.54612e34	−0.129418
$641$	4.47319e34	0.367191	0.183596	−	0.983002i	$-0.441226\pi$
$641$	4.47319e34	0.367191	0.183596	+	0.983002i	$0.441226\pi$
$642$	4.75748e33	0.0382991
$643$	1.98318e35	1.56576	0.782881	−	0.622172i	$-0.213749\pi$
$643$	1.98318e35	1.56576	0.782881	+	0.622172i	$0.213749\pi$
$644$	1.02376e34	0.0792730
$645$	−1.55535e35	−1.18123
$646$	−1.03502e35	−0.770977
$647$	−1.56561e35	−1.14388	−0.571938	−	0.820297i	$-0.693808\pi$
$647$	−1.56561e35	−1.14388	−0.571938	+	0.820297i	$0.693808\pi$
$648$	5.48151e33	0.0392837
$649$	3.26881e34	0.229790
$650$	2.29275e35	1.58103
$651$	−2.24285e34	−0.151718
$652$	3.68260e34	0.244376
$653$	−5.70499e34	−0.371399	−0.185699	−	0.982607i	$-0.559455\pi$
$653$	−5.70499e34	−0.371399	−0.185699	+	0.982607i	$0.559455\pi$
$654$	7.78500e34	0.497206
$655$	−3.65988e34	−0.229324
$656$	2.72890e34	0.167760
$657$	6.02362e33	0.0363321
$658$	−3.57489e34	−0.211563
$659$	9.83548e34	0.571121	0.285560	−	0.958361i	$-0.407820\pi$
$659$	9.83548e34	0.571121	0.285560	+	0.958361i	$0.407820\pi$
$660$	−1.25445e34	−0.0714751
$661$	−2.45689e35	−1.37362	−0.686810	−	0.726837i	$-0.740990\pi$
$661$	−2.45689e35	−1.37362	−0.686810	+	0.726837i	$0.740990\pi$
$662$	−1.70675e34	−0.0936367
$663$	2.07463e35	1.11692
$664$	5.32925e34	0.281556
$665$	−6.76456e34	−0.350727
$666$	9.74316e33	0.0495760
$667$	1.84639e35	0.922040
$668$	1.83478e34	0.0899246
$669$	1.55042e35	0.745802
$670$	−1.39876e35	−0.660403
$671$	−3.18750e32	−0.00147713
$672$	−4.87865e33	−0.0221913
$673$	−2.79717e34	−0.124891	−0.0624453	−	0.998048i	$-0.519890\pi$
$673$	−2.79717e34	−0.124891	−0.0624453	+	0.998048i	$0.519890\pi$
$674$	1.94198e35	0.851132
$675$	−5.11675e34	−0.220139
$676$	3.33942e35	1.41038
$677$	−8.21963e34	−0.340796	−0.170398	−	0.985375i	$-0.554505\pi$
$677$	−8.21963e34	−0.340796	−0.170398	+	0.985375i	$0.554505\pi$
$678$	−9.41411e34	−0.383185
$679$	4.05118e34	0.161886
$680$	1.30594e35	0.512343
$681$	1.44161e35	0.555277
$682$	−3.82133e34	−0.144514
$683$	−1.88130e35	−0.698553	−0.349276	−	0.937020i	$-0.613573\pi$
$683$	−1.88130e35	−0.698553	−0.349276	+	0.937020i	$0.613573\pi$
$684$	5.03617e34	0.183611
$685$	−4.98368e35	−1.78410
$686$	−8.54076e34	−0.300224
$687$	5.55704e34	0.191816
$688$	−1.03060e35	−0.349328
$689$	1.09091e36	3.63119
$690$	1.33344e35	0.435874
$691$	−3.60460e35	−1.15713	−0.578564	−	0.815637i	$-0.696387\pi$
$691$	−3.60460e35	−1.15713	−0.578564	+	0.815637i	$0.696387\pi$
$692$	−2.87454e35	−0.906238
$693$	−3.95830e33	−0.0122559
$694$	−1.89925e35	−0.577548
$695$	−6.74128e35	−2.01341
$696$	−8.79880e34	−0.258112
$697$	−2.30497e35	−0.664134
$698$	−2.59931e35	−0.735641
$699$	1.29239e35	0.359276
$700$	4.55400e34	0.124356
$701$	−1.42171e35	−0.381361	−0.190680	−	0.981652i	$-0.561069\pi$
$701$	−1.42171e35	−0.381361	−0.190680	+	0.981652i	$0.561069\pi$
$702$	−1.00947e35	−0.265998
$703$	8.95158e34	0.231717
$704$	−8.31217e33	−0.0211376
$705$	−4.65627e35	−1.16325
$706$	−8.70516e34	−0.213658
$707$	−7.98054e34	−0.192437
$708$	1.65581e35	0.392278
$709$	7.86988e35	1.83185	0.915925	−	0.401349i	$-0.131458\pi$
$709$	7.86988e35	1.83185	0.915925	+	0.401349i	$0.131458\pi$
$710$	−3.19258e35	−0.730151
$711$	2.40473e35	0.540375
$712$	−9.62333e33	−0.0212484
$713$	4.06195e35	0.881282
$714$	4.12076e34	0.0878516
$715$	2.31018e35	0.483973
$716$	−8.65599e34	−0.178199
$717$	−4.36506e35	−0.883081
$718$	2.61595e35	0.520085
$719$	−6.28316e35	−1.22763	−0.613814	−	0.789451i	$-0.710366\pi$
$719$	−6.28316e35	−1.22763	−0.613814	+	0.789451i	$0.710366\pi$
$720$	−6.35440e34	−0.122016
$721$	1.97488e35	0.372691
$722$	8.14595e34	0.151087
$723$	1.09172e35	0.199014
$724$	−1.37454e35	−0.246278
$725$	8.21329e35	1.44641
$726$	2.29104e35	0.396574
$727$	6.67907e34	0.113641	0.0568206	−	0.998384i	$-0.481904\pi$
$727$	6.67907e34	0.113641	0.0568206	+	0.998384i	$0.481904\pi$
$728$	8.98445e34	0.150262
$729$	2.25284e34	0.0370370
$730$	−6.98284e34	−0.112849
$731$	8.70497e35	1.38293
$732$	−1.61462e33	−0.00252164
$733$	1.62081e35	0.248847	0.124423	−	0.992229i	$-0.460292\pi$
$733$	1.62081e35	0.248847	0.124423	+	0.992229i	$0.460292\pi$
$734$	6.87714e34	0.103802
$735$	−5.42748e35	−0.805390
$736$	8.83556e34	0.128903
$737$	−7.51992e34	−0.107862
$738$	1.12155e35	0.158166
$739$	4.45403e34	0.0617586	0.0308793	−	0.999523i	$-0.490169\pi$
$739$	4.45403e34	0.0617586	0.0308793	+	0.999523i	$0.490169\pi$
$740$	−1.12947e35	−0.153985
$741$	−9.27454e35	−1.24327
$742$	2.16684e35	0.285613
$743$	1.44384e36	1.87137	0.935683	−	0.352841i	$-0.114784\pi$
$743$	1.44384e36	1.87137	0.935683	+	0.352841i	$0.114784\pi$
$744$	−1.93569e35	−0.246702
$745$	1.56837e36	1.96560
$746$	−8.82261e35	−1.08733
$747$	2.19026e35	0.265454
$748$	7.02089e34	0.0836801
$749$	−1.74023e34	−0.0203978
$750$	7.46065e34	0.0860025
$751$	−1.30627e36	−1.48093	−0.740463	−	0.672098i	$-0.765394\pi$
$751$	−1.30627e36	−1.48093	−0.740463	+	0.672098i	$0.765394\pi$
$752$	−3.08530e35	−0.344013
$753$	3.85457e34	0.0422707
$754$	1.62038e36	1.74773
$755$	−2.64363e36	−2.80456
$756$	−2.00507e34	−0.0209222
$757$	−1.88629e36	−1.93602	−0.968008	−	0.250918i	$-0.919267\pi$
$757$	−1.88629e36	−1.93602	−0.968008	+	0.250918i	$0.919267\pi$
$758$	3.77699e35	0.381312
$759$	7.16876e34	0.0711904
$760$	−5.83814e35	−0.570302
$761$	1.11272e35	0.106924	0.0534622	−	0.998570i	$-0.482974\pi$
$761$	1.11272e35	0.106924	0.0534622	+	0.998570i	$0.482974\pi$
$762$	9.60121e34	0.0907588
$763$	−2.84766e35	−0.264808
$764$	2.96502e35	0.271244
$765$	5.36726e35	0.483042
$766$	7.86188e35	0.696092
$767$	−3.04931e36	−2.65619
$768$	−4.21051e34	−0.0360844
$769$	−1.49222e35	−0.125822	−0.0629108	−	0.998019i	$-0.520038\pi$
$769$	−1.49222e35	−0.125822	−0.0629108	+	0.998019i	$0.520038\pi$
$770$	4.58864e34	0.0380671
$771$	3.58036e35	0.292245
$772$	−2.36988e35	−0.190331
$773$	2.44702e35	0.193372	0.0966859	−	0.995315i	$-0.469176\pi$
$773$	2.44702e35	0.193372	0.0966859	+	0.995315i	$0.469176\pi$
$774$	−4.23565e35	−0.329350
$775$	1.80688e36	1.38248
$776$	3.49636e35	0.263236
$777$	−3.56393e34	−0.0264038
$778$	8.15172e35	0.594298
$779$	1.03043e36	0.739264
$780$	1.17022e36	0.826199
$781$	−1.71637e35	−0.119254
$782$	−7.46298e35	−0.510303
$783$	−3.61621e35	−0.243350
$784$	−3.59632e35	−0.238181
$785$	2.60343e36	1.69697
$786$	−9.96682e34	−0.0639403
$787$	−2.60952e36	−1.64770	−0.823848	−	0.566811i	$-0.808177\pi$
$787$	−2.60952e36	−1.64770	−0.823848	+	0.566811i	$0.808177\pi$
$788$	−4.69277e35	−0.291643
$789$	−8.93238e35	−0.546393
$790$	−2.78766e36	−1.67842
$791$	3.44357e35	0.204081
$792$	−3.41621e34	−0.0199287
$793$	2.97347e34	0.0170745
$794$	9.06145e35	0.512202
$795$	2.82229e36	1.57041
$796$	1.96545e34	0.0107659
$797$	2.46627e36	1.32988	0.664939	−	0.746898i	$-0.268458\pi$
$797$	2.46627e36	1.32988	0.664939	+	0.746898i	$0.268458\pi$
$798$	−1.84217e35	−0.0977898
$799$	2.60601e36	1.36189
$800$	3.93033e35	0.202211
$801$	−3.95508e34	−0.0200332
$802$	−1.49899e36	−0.747513
$803$	−3.75407e34	−0.0184314
$804$	−3.80920e35	−0.184134
$805$	−4.87757e35	−0.232143
$806$	3.56473e36	1.67047
$807$	−6.06353e35	−0.279773
$808$	−6.88759e35	−0.312914
$809$	−2.02484e36	−0.905805	−0.452903	−	0.891560i	$-0.649611\pi$
$809$	−2.02484e36	−0.905805	−0.452903	+	0.891560i	$0.649611\pi$
$810$	−2.61159e35	−0.115038
$811$	9.73398e35	0.422211	0.211106	−	0.977463i	$-0.432294\pi$
$811$	9.73398e35	0.422211	0.211106	+	0.977463i	$0.432294\pi$
$812$	3.21849e35	0.137468
$813$	1.65868e36	0.697641
$814$	−6.07217e34	−0.0251501
$815$	−1.75452e36	−0.715631
$816$	3.55642e35	0.142852
$817$	−3.89152e36	−1.53937
$818$	−2.06660e36	−0.805082
$819$	3.69251e35	0.141668
$820$	−1.30015e36	−0.491269
$821$	2.06497e36	0.768464	0.384232	−	0.923237i	$-0.374466\pi$
$821$	2.06497e36	0.768464	0.384232	+	0.923237i	$0.374466\pi$
$822$	−1.35719e36	−0.497442
$823$	3.82250e36	1.37990	0.689952	−	0.723855i	$-0.257631\pi$
$823$	3.82250e36	1.37990	0.689952	+	0.723855i	$0.257631\pi$
$824$	1.70442e36	0.606018
$825$	3.18888e35	0.111677
$826$	−6.05674e35	−0.208924
$827$	−2.79897e36	−0.950996	−0.475498	−	0.879717i	$-0.657732\pi$
$827$	−2.79897e36	−0.950996	−0.475498	+	0.879717i	$0.657732\pi$
$828$	3.63132e35	0.121530
$829$	−9.30579e35	−0.306776	−0.153388	−	0.988166i	$-0.549018\pi$
$829$	−9.30579e35	−0.306776	−0.153388	+	0.988166i	$0.549018\pi$
$830$	−2.53905e36	−0.824507
$831$	1.74547e34	0.00558340
$832$	7.75402e35	0.244335
$833$	3.03764e36	0.942917
$834$	−1.83583e36	−0.561380
$835$	−8.74156e35	−0.263335
$836$	−3.13866e35	−0.0931464
$837$	−7.95546e35	−0.232593
$838$	3.77639e36	1.08774
$839$	4.59554e36	1.30410	0.652052	−	0.758174i	$-0.273908\pi$
$839$	4.59554e36	1.30410	0.652052	+	0.758174i	$0.273908\pi$
$840$	2.32436e35	0.0649850
$841$	2.17430e36	0.598921
$842$	3.13261e35	0.0850168
$843$	−3.89395e35	−0.104123
$844$	2.62813e35	0.0692414
$845$	−1.59102e37	−4.13016
$846$	−1.26803e36	−0.324339
$847$	−8.38035e35	−0.211212
$848$	1.87009e36	0.464423
$849$	1.03231e36	0.252618
$850$	−3.31976e36	−0.800516
$851$	6.45452e35	0.153371
$852$	−8.69425e35	−0.203581
$853$	−8.31965e36	−1.91974	−0.959869	−	0.280448i	$-0.909517\pi$
$853$	−8.31965e36	−1.91974	−0.959869	+	0.280448i	$0.909517\pi$
$854$	5.90610e33	0.00134300
$855$	−2.39941e36	−0.537686
$856$	−1.50190e35	−0.0331680
$857$	2.17022e36	0.472328	0.236164	−	0.971713i	$-0.424110\pi$
$857$	2.17022e36	0.472328	0.236164	+	0.971713i	$0.424110\pi$
$858$	6.29125e35	0.134942
$859$	4.20196e36	0.888253	0.444127	−	0.895964i	$-0.353514\pi$
$859$	4.20196e36	0.888253	0.444127	+	0.895964i	$0.353514\pi$
$860$	4.91014e36	1.02297
$861$	−4.10249e35	−0.0842379
$862$	4.30767e36	0.871770
$863$	−5.42765e36	−1.08262	−0.541311	−	0.840823i	$-0.682072\pi$
$863$	−5.42765e36	−1.08262	−0.541311	+	0.840823i	$0.682072\pi$
$864$	−1.73047e35	−0.0340207
$865$	1.36954e37	2.65382
$866$	6.85072e34	0.0130847
$867$	6.28104e34	0.0118248
$868$	7.08051e35	0.131392
$869$	−1.49868e36	−0.274134
$870$	4.19207e36	0.755853
$871$	7.01498e36	1.24681
$872$	−2.45767e36	−0.430593
$873$	1.43697e36	0.248181
$874$	3.33630e36	0.568030
$875$	−2.72902e35	−0.0458042
$876$	−1.90161e35	−0.0314645
$877$	1.50413e36	0.245352	0.122676	−	0.992447i	$-0.460852\pi$
$877$	1.50413e36	0.245352	0.122676	+	0.992447i	$0.460852\pi$
$878$	4.53379e36	0.729088
$879$	3.18147e36	0.504391
$880$	3.96022e35	0.0618993
$881$	6.99433e36	1.07782	0.538912	−	0.842362i	$-0.318836\pi$
$881$	6.99433e36	1.07782	0.538912	+	0.842362i	$0.318836\pi$
$882$	−1.47805e36	−0.224559
$883$	−5.09980e36	−0.763913	−0.381957	−	0.924180i	$-0.624750\pi$
$883$	−5.09980e36	−0.763913	−0.381957	+	0.924180i	$0.624750\pi$
$884$	−6.54945e36	−0.967279
$885$	−7.88887e36	−1.14875
$886$	1.75738e36	0.252316
$887$	3.95574e35	0.0559993	0.0279997	−	0.999608i	$-0.491086\pi$
$887$	3.95574e35	0.0559993	0.0279997	+	0.999608i	$0.491086\pi$
$888$	−3.07585e35	−0.0429341
$889$	−3.51201e35	−0.0483374
$890$	4.58491e35	0.0622236
$891$	−1.40402e35	−0.0187890
$892$	−4.89457e36	−0.645884
$893$	−1.16501e37	−1.51595
$894$	4.27108e36	0.548048
$895$	4.12403e36	0.521836
$896$	1.54015e35	0.0192183
$897$	−6.68739e36	−0.822908
$898$	−3.08896e36	−0.374850
$899$	1.27699e37	1.52824
$900$	1.61532e36	0.190646
$901$	−1.57957e37	−1.83857
$902$	−6.98975e35	−0.0802380
$903$	1.54935e36	0.175409
$904$	2.97197e36	0.331848
$905$	6.54882e36	0.721200
$906$	−7.19932e36	−0.781968
$907$	−4.89142e36	−0.524015	−0.262008	−	0.965066i	$-0.584385\pi$
$907$	−4.89142e36	−0.524015	−0.262008	+	0.965066i	$0.584385\pi$
$908$	−4.55107e36	−0.480884
$909$	−2.83073e36	−0.295018
$910$	−4.28052e36	−0.440027
$911$	8.47560e36	0.859390	0.429695	−	0.902974i	$-0.358621\pi$
$911$	8.47560e36	0.859390	0.429695	+	0.902974i	$0.358621\pi$
$912$	−1.58988e36	−0.159012
$913$	−1.36502e36	−0.134665
$914$	−6.56520e36	−0.638882
$915$	7.69265e34	0.00738435
$916$	−1.75432e36	−0.166117
$917$	3.64575e35	0.0340541
$918$	1.46165e36	0.134682
$919$	−1.82311e37	−1.65717	−0.828587	−	0.559861i	$-0.810855\pi$
$919$	−1.82311e37	−1.65717	−0.828587	+	0.559861i	$0.810855\pi$
$920$	−4.20958e36	−0.377478
$921$	1.01762e37	0.900207
$922$	−1.91949e36	−0.167513
$923$	1.60112e37	1.37849
$924$	1.24961e35	0.0106139
$925$	2.87117e36	0.240595
$926$	−9.28883e36	−0.767933
$927$	7.00496e36	0.571359
$928$	2.77772e36	0.223531
$929$	1.06321e37	0.844155	0.422077	−	0.906560i	$-0.361301\pi$
$929$	1.06321e37	0.844155	0.422077	+	0.906560i	$0.361301\pi$
$930$	9.22231e36	0.722442
$931$	−1.35796e37	−1.04958
$932$	−4.07998e36	−0.311142
$933$	1.16019e37	0.872988
$934$	−4.23088e36	−0.314120
$935$	−3.34501e36	−0.245049
$936$	3.18682e36	0.230361
$937$	1.66137e37	1.18501	0.592504	−	0.805567i	$-0.298139\pi$
$937$	1.66137e37	1.18501	0.592504	+	0.805567i	$0.298139\pi$
$938$	1.39336e36	0.0980681
$939$	−1.09139e37	−0.757985
$940$	1.46995e37	1.00741
$941$	−4.12190e36	−0.278758	−0.139379	−	0.990239i	$-0.544511\pi$
$941$	−4.12190e36	−0.278758	−0.139379	+	0.990239i	$0.544511\pi$
$942$	7.08983e36	0.473151
$943$	7.42988e36	0.489312
$944$	−5.22726e36	−0.339723
$945$	9.55288e35	0.0612685
$946$	2.63976e36	0.167080
$947$	2.38912e36	0.149233	0.0746164	−	0.997212i	$-0.476227\pi$
$947$	2.38912e36	0.149233	0.0746164	+	0.997212i	$0.476227\pi$
$948$	−7.59155e36	−0.467979
$949$	3.50199e36	0.213053
$950$	1.48409e37	0.891074
$951$	−8.42246e36	−0.499094
$952$	−1.30090e36	−0.0760817
$953$	−1.81231e37	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$953$	−1.81231e37	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$954$	7.68585e36	0.437862
$955$	−1.41264e37	−0.794311
$956$	1.37802e37	0.764770
$957$	2.25371e36	0.123452
$958$	−1.13419e36	−0.0613222
$959$	4.96444e36	0.264934
$960$	2.00604e36	0.105669
$961$	8.86031e36	0.460688
$962$	5.66444e36	0.290716
$963$	−6.17265e35	−0.0312711
$964$	−3.44648e36	−0.172351
$965$	1.12910e37	0.557365
$966$	−1.32829e36	−0.0647262
$967$	−9.72478e36	−0.467788	−0.233894	−	0.972262i	$-0.575147\pi$
$967$	−9.72478e36	−0.467788	−0.233894	+	0.972262i	$0.575147\pi$
$968$	−7.23265e36	−0.343443
$969$	1.34290e37	0.629500
$970$	−1.66579e37	−0.770859
$971$	−1.70444e37	−0.778651	−0.389325	−	0.921100i	$-0.627292\pi$
$971$	−1.70444e37	−0.778651	−0.389325	+	0.921100i	$0.627292\pi$
$972$	−7.11206e35	−0.0320750
$973$	6.71525e36	0.298987
$974$	−1.04833e37	−0.460799
$975$	−2.97475e37	−1.29090
$976$	5.09725e34	0.00218380
$977$	1.94120e37	0.821084	0.410542	−	0.911842i	$-0.365340\pi$
$977$	1.94120e37	0.821084	0.410542	+	0.911842i	$0.365340\pi$
$978$	−4.77803e36	−0.199532
$979$	2.46490e35	0.0101629
$980$	1.71342e37	0.697488
$981$	−1.01007e37	−0.405967
$982$	1.72397e37	0.684125
$983$	−4.70164e37	−1.84217	−0.921087	−	0.389358i	$-0.872697\pi$
$983$	−4.70164e37	−1.84217	−0.921087	+	0.389358i	$0.872697\pi$
$984$	−3.54065e36	−0.136976
$985$	2.23581e37	0.854046
$986$	−2.34621e37	−0.884922
$987$	4.63829e36	0.172740
$988$	2.92791e37	1.07670
$989$	−2.80598e37	−1.01890
$990$	1.62761e36	0.0583592
$991$	−2.01760e37	−0.714354	−0.357177	−	0.934037i	$-0.616261\pi$
$991$	−2.01760e37	−0.714354	−0.357177	+	0.934037i	$0.616261\pi$
$992$	6.11082e36	0.213650
$993$	2.21445e36	0.0764541
$994$	3.18025e36	0.108426
$995$	−9.36412e35	−0.0315267
$996$	−6.91450e36	−0.229889
$997$	−3.05159e37	−1.00193	−0.500965	−	0.865468i	$-0.667021\pi$
$997$	−3.05159e37	−1.00193	−0.500965	+	0.865468i	$0.667021\pi$
$998$	1.08992e37	0.353397
$999$	−1.26414e36	−0.0404787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.26.a.c.1.1	✓	1
3.2	odd	2		18.26.a.a.1.1		1
4.3	odd	2		48.26.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.26.a.c.1.1	✓	1	1.1	even	1	trivial
18.26.a.a.1.1		1	3.2	odd	2
48.26.a.b.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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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