LMFDB - Embedded newform 9.26.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,26,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, 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("9.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	9.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:	$35.6397101957$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+48.0000 q^{2} -3.35521e7 q^{4} +7.41990e8 q^{5} +3.90806e10 q^{7} -3.22111e9 q^{8} +O(q^{10})$

\(q+48.0000 q^{2} -3.35521e7 q^{4} +7.41990e8 q^{5} +3.90806e10 q^{7} -3.22111e9 q^{8} +3.56155e10 q^{10} -8.41952e12 q^{11} -8.16510e13 q^{13} +1.87587e12 q^{14} +1.12567e15 q^{16} +2.51990e15 q^{17} -6.08206e15 q^{19} -2.48953e16 q^{20} -4.04137e14 q^{22} +9.49953e16 q^{23} +2.52526e17 q^{25} -3.91925e15 q^{26} -1.31124e18 q^{28} +2.71247e17 q^{29} +4.29167e18 q^{31} +1.62115e17 q^{32} +1.20955e17 q^{34} +2.89974e19 q^{35} +2.03015e19 q^{37} -2.91939e17 q^{38} -2.39003e18 q^{40} +1.83744e20 q^{41} +3.00902e20 q^{43} +2.82493e20 q^{44} +4.55977e18 q^{46} +9.24361e20 q^{47} +1.86224e20 q^{49} +1.21212e19 q^{50} +2.73957e21 q^{52} +9.90292e20 q^{53} -6.24719e21 q^{55} -1.25883e20 q^{56} +1.30199e19 q^{58} -1.30526e22 q^{59} +9.01545e21 q^{61} +2.06000e20 q^{62} -3.77634e22 q^{64} -6.05842e22 q^{65} -2.66891e22 q^{67} -8.45480e22 q^{68} +1.39188e21 q^{70} +1.92391e23 q^{71} +4.24046e22 q^{73} +9.74471e20 q^{74} +2.04066e23 q^{76} -3.29040e23 q^{77} -2.71681e23 q^{79} +8.35234e23 q^{80} +8.81972e21 q^{82} +9.31454e23 q^{83} +1.86974e24 q^{85} +1.44433e22 q^{86} +2.71202e22 q^{88} +1.76364e24 q^{89} -3.19097e24 q^{91} -3.18729e24 q^{92} +4.43693e22 q^{94} -4.51282e24 q^{95} +2.82924e24 q^{97} +8.93877e21 q^{98} +O(q^{100})\)

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 $

$2$	48.0000	0.00828641	0.00414320	−	0.999991i	$-0.498681\pi$
$2$	48.0000	0.00828641	0.00414320	+	0.999991i	$0.498681\pi$
$3$	0	0
$3$	0	0
$4$	−3.35521e7	−0.999931
$5$	7.41990e8	1.35917	0.679584	−	0.733598i	$-0.262160\pi$
$5$	7.41990e8	1.35917	0.679584	+	0.733598i	$0.262160\pi$
$6$	0	0
$7$	3.90806e10	1.06718	0.533588	−	0.845745i	$-0.320843\pi$
$7$	3.90806e10	1.06718	0.533588	+	0.845745i	$0.320843\pi$
$8$	−3.22111e9	−0.0165722
$9$	0	0
$10$	3.56155e10	0.0112626
$11$	−8.41952e12	−0.808870	−0.404435	−	0.914567i	$-0.632532\pi$
$11$	−8.41952e12	−0.808870	−0.404435	+	0.914567i	$0.632532\pi$
$12$	0	0
$13$	−8.16510e13	−0.972008	−0.486004	−	0.873957i	$-0.661546\pi$
$13$	−8.16510e13	−0.972008	−0.486004	+	0.873957i	$0.661546\pi$
$14$	1.87587e12	0.00884305
$15$	0	0
$16$	1.12567e15	0.999794
$17$	2.51990e15	1.04899	0.524496	−	0.851413i	$-0.324254\pi$
$17$	2.51990e15	1.04899	0.524496	+	0.851413i	$0.324254\pi$
$18$	0	0
$19$	−6.08206e15	−0.630421	−0.315210	−	0.949022i	$-0.602075\pi$
$19$	−6.08206e15	−0.630421	−0.315210	+	0.949022i	$0.602075\pi$
$20$	−2.48953e16	−1.35907
$21$	0	0
$22$	−4.04137e14	−0.00670262
$23$	9.49953e16	0.903866	0.451933	−	0.892052i	$-0.350735\pi$
$23$	9.49953e16	0.903866	0.451933	+	0.892052i	$0.350735\pi$
$24$	0	0
$25$	2.52526e17	0.847336
$26$	−3.91925e15	−0.00805445
$27$	0	0
$28$	−1.31124e18	−1.06710
$29$	2.71247e17	0.142361	0.0711803	−	0.997463i	$-0.477323\pi$
$29$	2.71247e17	0.142361	0.0711803	+	0.997463i	$0.477323\pi$
$30$	0	0
$31$	4.29167e18	0.978599	0.489299	−	0.872116i	$-0.337253\pi$
$31$	4.29167e18	0.978599	0.489299	+	0.872116i	$0.337253\pi$
$32$	1.62115e17	0.0248569
$33$	0	0
$34$	1.20955e17	0.00869237
$35$	2.89974e19	1.45047
$36$	0	0
$37$	2.03015e19	0.506998	0.253499	−	0.967336i	$-0.418419\pi$
$37$	2.03015e19	0.506998	0.253499	+	0.967336i	$0.418419\pi$
$38$	−2.91939e17	−0.00522392
$39$	0	0
$40$	−2.39003e18	−0.0225245
$41$	1.83744e20	1.27179	0.635895	−	0.771775i	$-0.280631\pi$
$41$	1.83744e20	1.27179	0.635895	+	0.771775i	$0.280631\pi$
$42$	0	0
$43$	3.00902e20	1.14834	0.574168	−	0.818737i	$-0.305326\pi$
$43$	3.00902e20	1.14834	0.574168	+	0.818737i	$0.305326\pi$
$44$	2.82493e20	0.808814
$45$	0	0
$46$	4.55977e18	0.00748980
$47$	9.24361e20	1.16043	0.580214	−	0.814464i	$-0.302969\pi$
$47$	9.24361e20	1.16043	0.580214	+	0.814464i	$0.302969\pi$
$48$	0	0
$49$	1.86224e20	0.138863
$50$	1.21212e19	0.00702137
$51$	0	0
$52$	2.73957e21	0.971941
$53$	9.90292e20	0.276895	0.138447	−	0.990370i	$-0.455789\pi$
$53$	9.90292e20	0.276895	0.138447	+	0.990370i	$0.455789\pi$
$54$	0	0
$55$	−6.24719e21	−1.09939
$56$	−1.25883e20	−0.0176855
$57$	0	0
$58$	1.30199e19	0.00117966
$59$	−1.30526e22	−0.955093	−0.477547	−	0.878606i	$-0.658474\pi$
$59$	−1.30526e22	−0.955093	−0.477547	+	0.878606i	$0.658474\pi$
$60$	0	0
$61$	9.01545e21	0.434875	0.217438	−	0.976074i	$-0.430230\pi$
$61$	9.01545e21	0.434875	0.217438	+	0.976074i	$0.430230\pi$
$62$	2.06000e20	0.00810907
$63$	0	0
$64$	−3.77634e22	−0.999588
$65$	−6.05842e22	−1.32112
$66$	0	0
$67$	−2.66891e22	−0.398473	−0.199236	−	0.979951i	$-0.563846\pi$
$67$	−2.66891e22	−0.398473	−0.199236	+	0.979951i	$0.563846\pi$
$68$	−8.45480e22	−1.04892
$69$	0	0
$70$	1.39188e21	0.0120192
$71$	1.92391e23	1.39141	0.695704	−	0.718329i	$-0.255093\pi$
$71$	1.92391e23	1.39141	0.695704	+	0.718329i	$0.255093\pi$
$72$	0	0
$73$	4.24046e22	0.216709	0.108355	−	0.994112i	$-0.465442\pi$
$73$	4.24046e22	0.216709	0.108355	+	0.994112i	$0.465442\pi$
$74$	9.74471e20	0.00420119
$75$	0	0
$76$	2.04066e23	0.630377
$77$	−3.29040e23	−0.863206
$78$	0	0
$79$	−2.71681e23	−0.517274	−0.258637	−	0.965975i	$-0.583273\pi$
$79$	−2.71681e23	−0.517274	−0.258637	+	0.965975i	$0.583273\pi$
$80$	8.35234e23	1.35889
$81$	0	0
$82$	8.81972e21	0.0105386
$83$	9.31454e23	0.956501	0.478251	−	0.878223i	$-0.341271\pi$
$83$	9.31454e23	0.956501	0.478251	+	0.878223i	$0.341271\pi$
$84$	0	0
$85$	1.86974e24	1.42575
$86$	1.44433e22	0.00951558
$87$	0	0
$88$	2.71202e22	0.0134048
$89$	1.76364e24	0.756892	0.378446	−	0.925623i	$-0.376459\pi$
$89$	1.76364e24	0.756892	0.378446	+	0.925623i	$0.376459\pi$
$90$	0	0
$91$	−3.19097e24	−1.03730
$92$	−3.18729e24	−0.903804
$93$	0	0
$94$	4.43693e22	0.00961578
$95$	−4.51282e24	−0.856847
$96$	0	0
$97$	2.82924e24	0.414022	0.207011	−	0.978339i	$-0.433626\pi$
$97$	2.82924e24	0.414022	0.207011	+	0.978339i	$0.433626\pi$
$98$	8.93877e21	0.00115067
$99$	0	0
$100$	−8.47278e24	−0.847278
$101$	−1.86342e24	−0.164549	−0.0822744	−	0.996610i	$-0.526218\pi$
$101$	−1.86342e24	−0.164549	−0.0822744	+	0.996610i	$0.526218\pi$
$102$	0	0
$103$	4.85812e24	0.335740	0.167870	−	0.985809i	$-0.446311\pi$
$103$	4.85812e24	0.335740	0.167870	+	0.985809i	$0.446311\pi$
$104$	2.63007e23	0.0161084
$105$	0	0
$106$	4.75340e22	0.00229446
$107$	−3.58304e25	−1.53799	−0.768997	−	0.639252i	$-0.779244\pi$
$107$	−3.58304e25	−1.53799	−0.768997	+	0.639252i	$0.779244\pi$
$108$	0	0
$109$	−4.77795e25	−1.62709	−0.813543	−	0.581505i	$-0.802464\pi$
$109$	−4.77795e25	−1.62709	−0.813543	+	0.581505i	$0.802464\pi$
$110$	−2.99865e23	−0.00910999
$111$	0	0
$112$	4.39918e25	1.06696
$113$	7.46476e25	1.62008	0.810038	−	0.586378i	$-0.199447\pi$
$113$	7.46476e25	1.62008	0.810038	+	0.586378i	$0.199447\pi$
$114$	0	0
$115$	7.04855e25	1.22851
$116$	−9.10091e24	−0.142351
$117$	0	0
$118$	−6.26523e23	−0.00791429
$119$	9.84792e25	1.11946
$120$	0	0
$121$	−3.74588e25	−0.345730
$122$	4.32742e23	0.00360355
$123$	0	0
$124$	−1.43995e26	−0.978532
$125$	−3.37587e25	−0.207496
$126$	0	0
$127$	3.35905e26	1.69305	0.846524	−	0.532350i	$-0.178691\pi$
$127$	3.35905e26	1.69305	0.846524	+	0.532350i	$0.178691\pi$
$128$	−7.25231e24	−0.0331399
$129$	0	0
$130$	−2.90804e24	−0.0109474
$131$	1.74971e26	0.598513	0.299257	−	0.954173i	$-0.403261\pi$
$131$	1.74971e26	0.598513	0.299257	+	0.954173i	$0.403261\pi$
$132$	0	0
$133$	−2.37690e26	−0.672769
$134$	−1.28108e24	−0.00330191
$135$	0	0
$136$	−8.11689e24	−0.0173841
$137$	−6.18313e26	−1.20837	−0.604187	−	0.796843i	$-0.706502\pi$
$137$	−6.18313e26	−1.20837	−0.604187	+	0.796843i	$0.706502\pi$
$138$	0	0
$139$	−4.84462e26	−0.789905	−0.394952	−	0.918702i	$-0.629239\pi$
$139$	−4.84462e26	−0.789905	−0.394952	+	0.918702i	$0.629239\pi$
$140$	−9.72925e26	−1.45037
$141$	0	0
$142$	9.23474e24	0.0115298
$143$	6.87462e26	0.786228
$144$	0	0
$145$	2.01262e26	0.193492
$146$	2.03542e24	0.00179574
$147$	0	0
$148$	−6.81158e26	−0.506963
$149$	−9.05569e26	−0.619574	−0.309787	−	0.950806i	$-0.600258\pi$
$149$	−9.05569e26	−0.619574	−0.309787	+	0.950806i	$0.600258\pi$
$150$	0	0
$151$	1.16190e27	0.672907	0.336454	−	0.941700i	$-0.390772\pi$
$151$	1.16190e27	0.672907	0.336454	+	0.941700i	$0.390772\pi$
$152$	1.95910e25	0.0104475
$153$	0	0
$154$	−1.57939e25	−0.00715287
$155$	3.18437e27	1.33008
$156$	0	0
$157$	−3.41505e26	−0.121521	−0.0607605	−	0.998152i	$-0.519353\pi$
$157$	−3.41505e26	−0.121521	−0.0607605	+	0.998152i	$0.519353\pi$
$158$	−1.30407e25	−0.00428634
$159$	0	0
$160$	1.20287e26	0.0337847
$161$	3.71247e27	0.964583
$162$	0	0
$163$	4.63202e27	1.03140	0.515698	−	0.856771i	$-0.327533\pi$
$163$	4.63202e27	1.03140	0.515698	+	0.856771i	$0.327533\pi$
$164$	−6.16501e27	−1.27170
$165$	0	0
$166$	4.47098e25	0.00792596
$167$	8.26470e27	1.35916	0.679581	−	0.733600i	$-0.262162\pi$
$167$	8.26470e27	1.35916	0.679581	+	0.733600i	$0.262162\pi$
$168$	0	0
$169$	−3.89517e26	−0.0552004
$170$	8.97475e25	0.0118144
$171$	0	0
$172$	−1.00959e28	−1.14826
$173$	6.02602e27	0.637462	0.318731	−	0.947845i	$-0.396743\pi$
$173$	6.02602e27	0.637462	0.318731	+	0.947845i	$0.396743\pi$
$174$	0	0
$175$	9.86886e27	0.904256
$176$	−9.47758e27	−0.808703
$177$	0	0
$178$	8.46545e25	0.00627191
$179$	−2.41023e28	−1.66493	−0.832463	−	0.554081i	$-0.813070\pi$
$179$	−2.41023e28	−1.66493	−0.832463	+	0.554081i	$0.813070\pi$
$180$	0	0
$181$	−8.19193e27	−0.492498	−0.246249	−	0.969207i	$-0.579198\pi$
$181$	−8.19193e27	−0.492498	−0.246249	+	0.969207i	$0.579198\pi$
$182$	−1.53167e26	−0.00859551
$183$	0	0
$184$	−3.05991e26	−0.0149791
$185$	1.50635e28	0.689095
$186$	0	0
$187$	−2.12163e28	−0.848497
$188$	−3.10143e28	−1.16035
$189$	0	0
$190$	−2.16616e26	−0.00710018
$191$	−5.50602e27	−0.169013	−0.0845066	−	0.996423i	$-0.526931\pi$
$191$	−5.50602e27	−0.169013	−0.0845066	+	0.996423i	$0.526931\pi$
$192$	0	0
$193$	2.08716e28	0.562457	0.281228	−	0.959641i	$-0.409258\pi$
$193$	2.08716e28	0.562457	0.281228	+	0.959641i	$0.409258\pi$
$194$	1.35804e26	0.00343075
$195$	0	0
$196$	−6.24823e27	−0.138853
$197$	5.99370e28	1.24988	0.624938	−	0.780674i	$-0.285124\pi$
$197$	5.99370e28	1.24988	0.624938	+	0.780674i	$0.285124\pi$
$198$	0	0
$199$	2.24042e27	0.0411782	0.0205891	−	0.999788i	$-0.493446\pi$
$199$	2.24042e27	0.0411782	0.0205891	+	0.999788i	$0.493446\pi$
$200$	−8.13414e26	−0.0140423
$201$	0	0
$202$	−8.94444e25	−0.00136352
$203$	1.06005e28	0.151924
$204$	0	0
$205$	1.36336e29	1.72858
$206$	2.33190e26	0.00278208
$207$	0	0
$208$	−9.19120e28	−0.971808
$209$	5.12080e28	0.509928
$210$	0	0
$211$	−7.52475e28	−0.665214	−0.332607	−	0.943066i	$-0.607928\pi$
$211$	−7.52475e28	−0.665214	−0.332607	+	0.943066i	$0.607928\pi$
$212$	−3.32264e28	−0.276876
$213$	0	0
$214$	−1.71986e27	−0.0127444
$215$	2.23266e29	1.56078
$216$	0	0
$217$	1.67721e29	1.04434
$218$	−2.29342e27	−0.0134827
$219$	0	0
$220$	2.09607e29	1.09931
$221$	−2.05752e29	−1.01963
$222$	0	0
$223$	−3.16696e29	−1.40227	−0.701135	−	0.713029i	$-0.747323\pi$
$223$	−3.16696e29	−1.40227	−0.701135	+	0.713029i	$0.747323\pi$
$224$	6.33554e27	0.0265267
$225$	0	0
$226$	3.58308e27	0.0134246
$227$	−3.85094e29	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$227$	−3.85094e29	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$228$	0	0
$229$	−5.68261e29	−1.80553	−0.902765	−	0.430134i	$-0.858466\pi$
$229$	−5.68261e29	−1.80553	−0.902765	+	0.430134i	$0.858466\pi$
$230$	3.38331e27	0.0101799
$231$	0	0
$232$	−8.73718e26	−0.00235924
$233$	−4.95586e29	−1.26815	−0.634075	−	0.773272i	$-0.718619\pi$
$233$	−4.95586e29	−1.26815	−0.634075	+	0.773272i	$0.718619\pi$
$234$	0	0
$235$	6.85867e29	1.57722
$236$	4.37941e29	0.955028
$237$	0	0
$238$	4.72700e27	0.00927628
$239$	1.44023e29	0.268200	0.134100	−	0.990968i	$-0.457186\pi$
$239$	1.44023e29	0.268200	0.134100	+	0.990968i	$0.457186\pi$
$240$	0	0
$241$	−3.19456e29	−0.536041	−0.268020	−	0.963413i	$-0.586369\pi$
$241$	−3.19456e29	−0.536041	−0.268020	+	0.963413i	$0.586369\pi$
$242$	−1.79802e27	−0.00286486
$243$	0	0
$244$	−3.02488e29	−0.434845
$245$	1.38177e29	0.188738
$246$	0	0
$247$	4.96606e29	0.612774
$248$	−1.38239e28	−0.0162176
$249$	0	0
$250$	−1.62042e27	−0.00171940
$251$	−6.21677e29	−0.627543	−0.313771	−	0.949499i	$-0.601593\pi$
$251$	−6.21677e29	−0.627543	−0.313771	+	0.949499i	$0.601593\pi$
$252$	0	0
$253$	−7.99814e29	−0.731110
$254$	1.61234e28	0.0140293
$255$	0	0
$256$	1.26678e30	0.999313
$257$	2.29446e30	1.72392	0.861960	−	0.506977i	$-0.169237\pi$
$257$	2.29446e30	1.72392	0.861960	+	0.506977i	$0.169237\pi$
$258$	0	0
$259$	7.93394e29	0.541056
$260$	2.03273e30	1.32103
$261$	0	0
$262$	8.39859e27	0.00495952
$263$	−7.73316e29	−0.435422	−0.217711	−	0.976013i	$-0.569859\pi$
$263$	−7.73316e29	−0.435422	−0.217711	+	0.976013i	$0.569859\pi$
$264$	0	0
$265$	7.34787e29	0.376347
$266$	−1.14091e28	−0.00557484
$267$	0	0
$268$	8.95475e29	0.398445
$269$	−3.62259e30	−1.53856	−0.769282	−	0.638910i	$-0.779386\pi$
$269$	−3.62259e30	−1.53856	−0.769282	+	0.638910i	$0.779386\pi$
$270$	0	0
$271$	−3.62767e30	−1.40447	−0.702234	−	0.711946i	$-0.747814\pi$
$271$	−3.62767e30	−1.40447	−0.702234	+	0.711946i	$0.747814\pi$
$272$	2.83657e30	1.04877
$273$	0	0
$274$	−2.96790e28	−0.0100131
$275$	−2.12614e30	−0.685384
$276$	0	0
$277$	−2.54808e30	−0.750266	−0.375133	−	0.926971i	$-0.622403\pi$
$277$	−2.54808e30	−0.750266	−0.375133	+	0.926971i	$0.622403\pi$
$278$	−2.32542e28	−0.00654547
$279$	0	0
$280$	−9.34040e28	−0.0240375
$281$	−3.59817e30	−0.885631	−0.442816	−	0.896613i	$-0.646020\pi$
$281$	−3.59817e30	−0.885631	−0.442816	+	0.896613i	$0.646020\pi$
$282$	0	0
$283$	3.82265e30	0.861061	0.430530	−	0.902576i	$-0.358327\pi$
$283$	3.82265e30	0.861061	0.430530	+	0.902576i	$0.358327\pi$
$284$	−6.45511e30	−1.39131
$285$	0	0
$286$	3.29982e28	0.00651500
$287$	7.18084e30	1.35722
$288$	0	0
$289$	5.79269e29	0.100382
$290$	9.66060e27	0.00160335
$291$	0	0
$292$	−1.42276e30	−0.216694
$293$	−1.30007e29	−0.0189723	−0.00948615	−	0.999955i	$-0.503020\pi$
$293$	−1.30007e29	−0.0189723	−0.00948615	+	0.999955i	$0.503020\pi$
$294$	0	0
$295$	−9.68487e30	−1.29813
$296$	−6.53934e28	−0.00840210
$297$	0	0
$298$	−4.34673e28	−0.00513404
$299$	−7.75646e30	−0.878565
$300$	0	0
$301$	1.17594e31	1.22548
$302$	5.57710e28	0.00557599
$303$	0	0
$304$	−6.84638e30	−0.630291
$305$	6.68937e30	0.591068
$306$	0	0
$307$	1.43602e31	1.16931	0.584657	−	0.811281i	$-0.301229\pi$
$307$	1.43602e31	1.16931	0.584657	+	0.811281i	$0.301229\pi$
$308$	1.10400e31	0.863146
$309$	0	0
$310$	1.52850e29	0.0110216
$311$	2.24630e31	1.55584	0.777918	−	0.628366i	$-0.216276\pi$
$311$	2.24630e31	1.55584	0.777918	+	0.628366i	$0.216276\pi$
$312$	0	0
$313$	−1.37956e30	−0.0881934	−0.0440967	−	0.999027i	$-0.514041\pi$
$313$	−1.37956e30	−0.0881934	−0.0440967	+	0.999027i	$0.514041\pi$
$314$	−1.63922e28	−0.00100697
$315$	0	0
$316$	9.11548e30	0.517239
$317$	1.02787e31	0.560655	0.280327	−	0.959904i	$-0.409557\pi$
$317$	1.02787e31	0.560655	0.280327	+	0.959904i	$0.409557\pi$
$318$	0	0
$319$	−2.28377e30	−0.115151
$320$	−2.80200e31	−1.35861
$321$	0	0
$322$	1.78199e29	0.00799293
$323$	−1.53262e31	−0.661306
$324$	0	0
$325$	−2.06190e31	−0.823617
$326$	2.22337e29	0.00854656
$327$	0	0
$328$	−5.91861e29	−0.0210764
$329$	3.61246e31	1.23838
$330$	0	0
$331$	−5.75356e30	−0.182847	−0.0914233	−	0.995812i	$-0.529142\pi$
$331$	−5.75356e30	−0.182847	−0.0914233	+	0.995812i	$0.529142\pi$
$332$	−3.12523e31	−0.956435
$333$	0	0
$334$	3.96706e29	0.0112626
$335$	−1.98030e31	−0.541591
$336$	0	0
$337$	6.69268e31	1.69913	0.849564	−	0.527485i	$-0.176865\pi$
$337$	6.69268e31	1.69913	0.849564	+	0.527485i	$0.176865\pi$
$338$	−1.86968e28	−0.000457413 0
$339$	0	0
$340$	−6.27338e31	−1.42566
$341$	−3.61337e31	−0.791559
$342$	0	0
$343$	−4.51320e31	−0.918984
$344$	−9.69239e29	−0.0190305
$345$	0	0
$346$	2.89249e29	0.00528227
$347$	−9.41781e29	−0.0165894	−0.00829472	−	0.999966i	$-0.502640\pi$
$347$	−9.41781e29	−0.0165894	−0.00829472	+	0.999966i	$0.502640\pi$
$348$	0	0
$349$	−3.39081e31	−0.555886	−0.277943	−	0.960598i	$-0.589653\pi$
$349$	−3.39081e31	−0.555886	−0.277943	+	0.960598i	$0.589653\pi$
$350$	4.73705e29	0.00749303
$351$	0	0
$352$	−1.36493e30	−0.0201060
$353$	−1.30313e31	−0.185269	−0.0926346	−	0.995700i	$-0.529529\pi$
$353$	−1.30313e31	−0.185269	−0.0926346	+	0.995700i	$0.529529\pi$
$354$	0	0
$355$	1.42752e32	1.89116
$356$	−5.91737e31	−0.756840
$357$	0	0
$358$	−1.15691e30	−0.0137963
$359$	1.30336e32	1.50101	0.750506	−	0.660864i	$-0.229810\pi$
$359$	1.30336e32	1.50101	0.750506	+	0.660864i	$0.229810\pi$
$360$	0	0
$361$	−5.60851e31	−0.602570
$362$	−3.93213e29	−0.00408104
$363$	0	0
$364$	1.07064e32	1.03723
$365$	3.14638e31	0.294544
$366$	0	0
$367$	−2.06294e32	−1.80369	−0.901844	−	0.432061i	$-0.857786\pi$
$367$	−2.06294e32	−1.80369	−0.901844	+	0.432061i	$0.857786\pi$
$368$	1.06933e32	0.903680
$369$	0	0
$370$	7.23048e29	0.00571012
$371$	3.87012e31	0.295495
$372$	0	0
$373$	2.46051e32	1.75657	0.878283	−	0.478142i	$-0.158689\pi$
$373$	2.46051e32	1.75657	0.878283	+	0.478142i	$0.158689\pi$
$374$	−1.01838e30	−0.00703099
$375$	0	0
$376$	−2.97747e30	−0.0192309
$377$	−2.21476e31	−0.138376
$378$	0	0
$379$	7.12743e31	0.416815	0.208407	−	0.978042i	$-0.433172\pi$
$379$	7.12743e31	0.416815	0.208407	+	0.978042i	$0.433172\pi$
$380$	1.51415e32	0.856788
$381$	0	0
$382$	−2.64289e29	−0.00140051
$383$	−1.33051e32	−0.682393	−0.341196	−	0.939992i	$-0.610832\pi$
$383$	−1.33051e32	−0.682393	−0.341196	+	0.939992i	$0.610832\pi$
$384$	0	0
$385$	−2.44144e32	−1.17324
$386$	1.00184e30	0.00466075
$387$	0	0
$388$	−9.49271e31	−0.413993
$389$	−2.40509e32	−1.01569	−0.507844	−	0.861449i	$-0.669557\pi$
$389$	−2.40509e32	−1.01569	−0.507844	+	0.861449i	$0.669557\pi$
$390$	0	0
$391$	2.39379e32	0.948147
$392$	−5.99850e29	−0.00230127
$393$	0	0
$394$	2.87698e30	0.0103570
$395$	−2.01585e32	−0.703062
$396$	0	0
$397$	−4.12137e32	−1.34946	−0.674730	−	0.738065i	$-0.735740\pi$
$397$	−4.12137e32	−1.34946	−0.674730	+	0.738065i	$0.735740\pi$
$398$	1.07540e29	0.000341219 0
$399$	0	0
$400$	2.84260e32	0.847161
$401$	7.16647e31	0.207014	0.103507	−	0.994629i	$-0.466994\pi$
$401$	7.16647e31	0.207014	0.103507	+	0.994629i	$0.466994\pi$
$402$	0	0
$403$	−3.50419e32	−0.951206
$404$	6.25219e31	0.164537
$405$	0	0
$406$	5.08824e29	0.00125890
$407$	−1.70929e32	−0.410095
$408$	0	0
$409$	1.34430e32	0.303358	0.151679	−	0.988430i	$-0.451532\pi$
$409$	1.34430e32	0.303358	0.151679	+	0.988430i	$0.451532\pi$
$410$	6.54415e30	0.0143237
$411$	0	0
$412$	−1.63000e32	−0.335717
$413$	−5.10102e32	−1.01925
$414$	0	0
$415$	6.91130e32	1.30004
$416$	−1.32368e31	−0.0241612
$417$	0	0
$418$	2.45798e30	0.00422547
$419$	1.71876e32	0.286774	0.143387	−	0.989667i	$-0.454201\pi$
$419$	1.71876e32	0.286774	0.143387	+	0.989667i	$0.454201\pi$
$420$	0	0
$421$	−8.27664e32	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$421$	−8.27664e32	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$422$	−3.61188e30	−0.00551223
$423$	0	0
$424$	−3.18984e30	−0.00458877
$425$	6.36340e32	0.888848
$426$	0	0
$427$	3.52329e32	0.464088
$428$	1.20219e33	1.53789
$429$	0	0
$430$	1.07168e31	0.0129333
$431$	7.83836e31	0.0918881	0.0459441	−	0.998944i	$-0.485370\pi$
$431$	7.83836e31	0.0918881	0.0459441	+	0.998944i	$0.485370\pi$
$432$	0	0
$433$	6.33273e32	0.700635	0.350318	−	0.936631i	$-0.386074\pi$
$433$	6.33273e32	0.700635	0.350318	+	0.936631i	$0.386074\pi$
$434$	8.05060e30	0.00865380
$435$	0	0
$436$	1.60310e33	1.62697
$437$	−5.77767e32	−0.569816
$438$	0	0
$439$	−1.48299e33	−1.38144	−0.690718	−	0.723124i	$-0.742705\pi$
$439$	−1.48299e33	−1.38144	−0.690718	+	0.723124i	$0.742705\pi$
$440$	2.01229e31	0.0182193
$441$	0	0
$442$	−9.87612e30	−0.00844905
$443$	1.20901e33	1.00551	0.502753	−	0.864430i	$-0.332321\pi$
$443$	1.20901e33	1.00551	0.502753	+	0.864430i	$0.332321\pi$
$444$	0	0
$445$	1.30860e33	1.02874
$446$	−1.52014e31	−0.0116198
$447$	0	0
$448$	−1.47581e33	−1.06674
$449$	9.48861e32	0.666996	0.333498	−	0.942751i	$-0.391771\pi$
$449$	9.48861e32	0.666996	0.333498	+	0.942751i	$0.391771\pi$
$450$	0	0
$451$	−1.54704e33	−1.02871
$452$	−2.50459e33	−1.61996
$453$	0	0
$454$	−1.84845e31	−0.0113138
$455$	−2.36767e33	−1.40987
$456$	0	0
$457$	1.90644e33	1.07466	0.537329	−	0.843373i	$-0.319433\pi$
$457$	1.90644e33	1.07466	0.537329	+	0.843373i	$0.319433\pi$
$458$	−2.72765e31	−0.0149614
$459$	0	0
$460$	−2.36494e33	−1.22842
$461$	4.56270e31	0.0230653	0.0115327	−	0.999933i	$-0.496329\pi$
$461$	4.56270e31	0.0230653	0.0115327	+	0.999933i	$0.496329\pi$
$462$	0	0
$463$	2.13521e33	1.02254	0.511269	−	0.859421i	$-0.329176\pi$
$463$	2.13521e33	1.02254	0.511269	+	0.859421i	$0.329176\pi$
$464$	3.05334e32	0.142331
$465$	0	0
$466$	−2.37882e31	−0.0105084
$467$	2.67225e33	1.14926	0.574628	−	0.818415i	$-0.305147\pi$
$467$	2.67225e33	1.14926	0.574628	+	0.818415i	$0.305147\pi$
$468$	0	0
$469$	−1.04302e33	−0.425240
$470$	3.29216e31	0.0130695
$471$	0	0
$472$	4.20438e31	0.0158280
$473$	−2.53345e33	−0.928854
$474$	0	0
$475$	−1.53588e33	−0.534178
$476$	−3.30419e33	−1.11938
$477$	0	0
$478$	6.91313e30	0.00222242
$479$	−1.97240e33	−0.617733	−0.308867	−	0.951105i	$-0.599950\pi$
$479$	−1.97240e33	−0.617733	−0.308867	+	0.951105i	$0.599950\pi$
$480$	0	0
$481$	−1.65764e33	−0.492806
$482$	−1.53339e31	−0.00444185
$483$	0	0
$484$	1.25682e33	0.345706
$485$	2.09927e33	0.562725
$486$	0	0
$487$	−3.96366e32	−0.100922	−0.0504608	−	0.998726i	$-0.516069\pi$
$487$	−3.96366e32	−0.100922	−0.0504608	+	0.998726i	$0.516069\pi$
$488$	−2.90398e31	−0.00720686
$489$	0	0
$490$	6.63248e30	0.00156396
$491$	7.22626e33	1.66110	0.830548	−	0.556947i	$-0.188027\pi$
$491$	7.22626e33	1.66110	0.830548	+	0.556947i	$0.188027\pi$
$492$	0	0
$493$	6.83515e32	0.149335
$494$	2.38371e31	0.00507769
$495$	0	0
$496$	4.83099e33	0.978397
$497$	7.51874e33	1.48488
$498$	0	0
$499$	8.19830e33	1.53981	0.769905	−	0.638159i	$-0.220304\pi$
$499$	8.19830e33	1.53981	0.769905	+	0.638159i	$0.220304\pi$
$500$	1.13268e33	0.207482
$501$	0	0
$502$	−2.98405e31	−0.00520008
$503$	−4.72562e33	−0.803265	−0.401633	−	0.915801i	$-0.631557\pi$
$503$	−4.72562e33	−0.803265	−0.401633	+	0.915801i	$0.631557\pi$
$504$	0	0
$505$	−1.38264e33	−0.223649
$506$	−3.83911e31	−0.00605827
$507$	0	0
$508$	−1.12703e34	−1.69293
$509$	−1.96955e33	−0.288665	−0.144332	−	0.989529i	$-0.546103\pi$
$509$	−1.96955e33	−0.288665	−0.144332	+	0.989529i	$0.546103\pi$
$510$	0	0
$511$	1.65720e33	0.231267
$512$	3.04153e32	0.0414207
$513$	0	0
$514$	1.10134e32	0.0142851
$515$	3.60468e33	0.456327
$516$	0	0
$517$	−7.78267e33	−0.938635
$518$	3.80829e31	0.00448341
$519$	0	0
$520$	1.95149e32	0.0218940
$521$	−7.39782e33	−0.810274	−0.405137	−	0.914256i	$-0.632776\pi$
$521$	−7.39782e33	−0.810274	−0.405137	+	0.914256i	$0.632776\pi$
$522$	0	0
$523$	1.70332e34	1.77838	0.889191	−	0.457535i	$-0.151268\pi$
$523$	1.70332e34	1.77838	0.889191	+	0.457535i	$0.151268\pi$
$524$	−5.87063e33	−0.598472
$525$	0	0
$526$	−3.71192e31	−0.00360808
$527$	1.08146e34	1.02654
$528$	0	0
$529$	−2.02166e33	−0.183026
$530$	3.52698e31	0.00311856
$531$	0	0
$532$	7.97502e33	0.672723
$533$	−1.50029e34	−1.23619
$534$	0	0
$535$	−2.65858e34	−2.09039
$536$	8.59686e31	0.00660358
$537$	0	0
$538$	−1.73884e32	−0.0127492
$539$	−1.56792e33	−0.112322
$540$	0	0
$541$	−1.28681e34	−0.880134	−0.440067	−	0.897965i	$-0.645045\pi$
$541$	−1.28681e34	−0.880134	−0.440067	+	0.897965i	$0.645045\pi$
$542$	−1.74128e32	−0.0116380
$543$	0	0
$544$	4.08513e32	0.0260747
$545$	−3.54519e34	−2.21148
$546$	0	0
$547$	2.06624e34	1.23123	0.615616	−	0.788046i	$-0.288907\pi$
$547$	2.06624e34	1.23123	0.615616	+	0.788046i	$0.288907\pi$
$548$	2.07457e34	1.20829
$549$	0	0
$550$	−1.02055e32	−0.00567937
$551$	−1.64974e33	−0.0897471
$552$	0	0
$553$	−1.06175e34	−0.552022
$554$	−1.22308e32	−0.00621701
$555$	0	0
$556$	1.62547e34	0.789851
$557$	3.28751e33	0.156198	0.0780992	−	0.996946i	$-0.475115\pi$
$557$	3.28751e33	0.156198	0.0780992	+	0.996946i	$0.475115\pi$
$558$	0	0
$559$	−2.45689e34	−1.11619
$560$	3.26415e34	1.45017
$561$	0	0
$562$	−1.72712e32	−0.00733870
$563$	1.80804e34	0.751371	0.375685	−	0.926747i	$-0.377407\pi$
$563$	1.80804e34	0.751371	0.375685	+	0.926747i	$0.377407\pi$
$564$	0	0
$565$	5.53878e34	2.20195
$566$	1.83487e32	0.00713510
$567$	0	0
$568$	−6.19712e32	−0.0230587
$569$	3.05967e33	0.111371	0.0556854	−	0.998448i	$-0.482266\pi$
$569$	3.05967e33	0.111371	0.0556854	+	0.998448i	$0.482266\pi$
$570$	0	0
$571$	−1.29884e34	−0.452486	−0.226243	−	0.974071i	$-0.572644\pi$
$571$	−1.29884e34	−0.452486	−0.226243	+	0.974071i	$0.572644\pi$
$572$	−2.30658e34	−0.786174
$573$	0	0
$574$	3.44680e32	0.0112465
$575$	2.39888e34	0.765878
$576$	0	0
$577$	−7.31490e31	−0.00223620	−0.00111810	−	0.999999i	$-0.500356\pi$
$577$	−7.31490e31	−0.00223620	−0.00111810	+	0.999999i	$0.500356\pi$
$578$	2.78049e31	0.000831808 0
$579$	0	0
$580$	−6.75278e33	−0.193479
$581$	3.64018e34	1.02075
$582$	0	0
$583$	−8.33778e33	−0.223972
$584$	−1.36590e32	−0.00359136
$585$	0	0
$586$	−6.24031e30	−0.000157212 0
$587$	−5.16226e34	−1.27310	−0.636551	−	0.771234i	$-0.719640\pi$
$587$	−5.16226e34	−1.27310	−0.636551	+	0.771234i	$0.719640\pi$
$588$	0	0
$589$	−2.61022e34	−0.616929
$590$	−4.64874e32	−0.0107568
$591$	0	0
$592$	2.28527e34	0.506894
$593$	−2.40705e34	−0.522758	−0.261379	−	0.965236i	$-0.584177\pi$
$593$	−2.40705e34	−0.522758	−0.261379	+	0.965236i	$0.584177\pi$
$594$	0	0
$595$	7.30706e34	1.52153
$596$	3.03838e34	0.619531
$597$	0	0
$598$	−3.72310e32	−0.00728015
$599$	8.30672e33	0.159072	0.0795361	−	0.996832i	$-0.474656\pi$
$599$	8.30672e33	0.159072	0.0795361	+	0.996832i	$0.474656\pi$
$600$	0	0
$601$	−3.00405e34	−0.551792	−0.275896	−	0.961187i	$-0.588975\pi$
$601$	−3.00405e34	−0.551792	−0.275896	+	0.961187i	$0.588975\pi$
$602$	5.64452e32	0.0101548
$603$	0	0
$604$	−3.89841e34	−0.672861
$605$	−2.77941e34	−0.469905
$606$	0	0
$607$	−1.00963e35	−1.63796	−0.818978	−	0.573825i	$-0.805459\pi$
$607$	−1.00963e35	−1.63796	−0.818978	+	0.573825i	$0.805459\pi$
$608$	−9.85991e32	−0.0156703
$609$	0	0
$610$	3.21090e32	0.00489783
$611$	−7.54750e34	−1.12795
$612$	0	0
$613$	−1.02453e33	−0.0146983	−0.00734915	−	0.999973i	$-0.502339\pi$
$613$	−1.02453e33	−0.0146983	−0.00734915	+	0.999973i	$0.502339\pi$
$614$	6.89290e32	0.00968941
$615$	0	0
$616$	1.05987e33	0.0143053
$617$	−4.53271e34	−0.599505	−0.299753	−	0.954017i	$-0.596904\pi$
$617$	−4.53271e34	−0.599505	−0.299753	+	0.954017i	$0.596904\pi$
$618$	0	0
$619$	1.24784e35	1.58499	0.792496	−	0.609878i	$-0.208781\pi$
$619$	1.24784e35	1.58499	0.792496	+	0.609878i	$0.208781\pi$
$620$	−1.06842e35	−1.32999
$621$	0	0
$622$	1.07823e33	0.0128923
$623$	6.89239e34	0.807736
$624$	0	0
$625$	−1.00307e35	−1.12936
$626$	−6.62189e31	−0.000730807 0
$627$	0	0
$628$	1.14582e34	0.121513
$629$	5.11577e34	0.531836
$630$	0	0
$631$	4.83338e34	0.482930	0.241465	−	0.970410i	$-0.422372\pi$
$631$	4.83338e34	0.482930	0.241465	+	0.970410i	$0.422372\pi$
$632$	8.75116e32	0.00857239
$633$	0	0
$634$	4.93375e32	0.00464581
$635$	2.49238e35	2.30114
$636$	0	0
$637$	−1.52054e34	−0.134976
$638$	−1.09621e32	−0.000954190 0
$639$	0	0
$640$	−5.38114e33	−0.0450427
$641$	−8.30494e34	−0.681728	−0.340864	−	0.940113i	$-0.610720\pi$
$641$	−8.30494e34	−0.681728	−0.340864	+	0.940113i	$0.610720\pi$
$642$	0	0
$643$	5.25724e34	0.415069	0.207535	−	0.978228i	$-0.433456\pi$
$643$	5.25724e34	0.415069	0.207535	+	0.978228i	$0.433456\pi$
$644$	−1.24561e35	−0.964517
$645$	0	0
$646$	−7.35656e32	−0.00547985
$647$	2.03021e35	1.48333	0.741665	−	0.670770i	$-0.234036\pi$
$647$	2.03021e35	1.48333	0.741665	+	0.670770i	$0.234036\pi$
$648$	0	0
$649$	1.09896e35	0.772546
$650$	−9.89711e32	−0.00682483
$651$	0	0
$652$	−1.55414e35	−1.03132
$653$	−1.67657e35	−1.09146	−0.545728	−	0.837962i	$-0.683747\pi$
$653$	−1.67657e35	−1.09146	−0.545728	+	0.837962i	$0.683747\pi$
$654$	0	0
$655$	1.29826e35	0.813479
$656$	2.06835e35	1.27153
$657$	0	0
$658$	1.73398e33	0.0102617
$659$	2.92521e35	1.69859	0.849296	−	0.527917i	$-0.177027\pi$
$659$	2.92521e35	1.69859	0.849296	+	0.527917i	$0.177027\pi$
$660$	0	0
$661$	8.30227e34	0.464172	0.232086	−	0.972695i	$-0.425445\pi$
$661$	8.30227e34	0.464172	0.232086	+	0.972695i	$0.425445\pi$
$662$	−2.76171e32	−0.00151514
$663$	0	0
$664$	−3.00032e33	−0.0158514
$665$	−1.76364e35	−0.914406
$666$	0	0
$667$	2.57672e34	0.128675
$668$	−2.77298e35	−1.35907
$669$	0	0
$670$	−9.50545e32	−0.00448784
$671$	−7.59057e34	−0.351757
$672$	0	0
$673$	−3.23598e35	−1.44483	−0.722417	−	0.691458i	$-0.756969\pi$
$673$	−3.23598e35	−1.44483	−0.722417	+	0.691458i	$0.756969\pi$
$674$	3.21249e33	0.0140797
$675$	0	0
$676$	1.30691e34	0.0551966
$677$	−7.76333e34	−0.321877	−0.160938	−	0.986964i	$-0.551452\pi$
$677$	−7.76333e34	−0.321877	−0.160938	+	0.986964i	$0.551452\pi$
$678$	0	0
$679$	1.10568e35	0.441834
$680$	−6.02265e33	−0.0236280
$681$	0	0
$682$	−1.73442e33	−0.00655918
$683$	2.49909e35	0.927945	0.463973	−	0.885850i	$-0.346424\pi$
$683$	2.49909e35	0.927945	0.463973	+	0.885850i	$0.346424\pi$
$684$	0	0
$685$	−4.58782e35	−1.64238
$686$	−2.16634e33	−0.00761508
$687$	0	0
$688$	3.38716e35	1.14810
$689$	−8.08584e34	−0.269144
$690$	0	0
$691$	−8.56964e34	−0.275098	−0.137549	−	0.990495i	$-0.543922\pi$
$691$	−8.56964e34	−0.275098	−0.137549	+	0.990495i	$0.543922\pi$
$692$	−2.02186e35	−0.637419
$693$	0	0
$694$	−4.52055e31	−0.000137467 0
$695$	−3.59466e35	−1.07361
$696$	0	0
$697$	4.63017e35	1.33410
$698$	−1.62759e33	−0.00460630
$699$	0	0
$700$	−3.31121e35	−0.904193
$701$	−4.53464e35	−1.21637	−0.608187	−	0.793793i	$-0.708103\pi$
$701$	−4.53464e35	−1.21637	−0.608187	+	0.793793i	$0.708103\pi$
$702$	0	0
$703$	−1.23475e35	−0.319622
$704$	3.17949e35	0.808536
$705$	0	0
$706$	−6.25502e32	−0.00153522
$707$	−7.28238e34	−0.175602
$708$	0	0
$709$	−4.93254e35	−1.14813	−0.574067	−	0.818808i	$-0.694635\pi$
$709$	−4.93254e35	−1.14813	−0.574067	+	0.818808i	$0.694635\pi$
$710$	6.85209e33	0.0156709
$711$	0	0
$712$	−5.68087e33	−0.0125434
$713$	4.07688e35	0.884522
$714$	0	0
$715$	5.10090e35	1.06862
$716$	8.08682e35	1.66481
$717$	0	0
$718$	6.25613e33	0.0124380
$719$	−2.13499e35	−0.417142	−0.208571	−	0.978007i	$-0.566881\pi$
$719$	−2.13499e35	−0.417142	−0.208571	+	0.978007i	$0.566881\pi$
$720$	0	0
$721$	1.89858e35	0.358293
$722$	−2.69208e33	−0.00499314
$723$	0	0
$724$	2.74857e35	0.492464
$725$	6.84968e34	0.120627
$726$	0	0
$727$	5.12190e35	0.871467	0.435734	−	0.900076i	$-0.356489\pi$
$727$	5.12190e35	0.871467	0.435734	+	0.900076i	$0.356489\pi$
$728$	1.02785e34	0.0171904
$729$	0	0
$730$	1.51026e33	0.00244071
$731$	7.58243e35	1.20459
$732$	0	0
$733$	1.77366e35	0.272315	0.136157	−	0.990687i	$-0.456525\pi$
$733$	1.77366e35	0.272315	0.136157	+	0.990687i	$0.456525\pi$
$734$	−9.90213e33	−0.0149461
$735$	0	0
$736$	1.54001e34	0.0224674
$737$	2.24709e35	0.322312
$738$	0	0
$739$	−1.13535e36	−1.57425	−0.787124	−	0.616794i	$-0.788431\pi$
$739$	−1.13535e36	−1.57425	−0.787124	+	0.616794i	$0.788431\pi$
$740$	−5.05412e35	−0.689048
$741$	0	0
$742$	1.85766e33	0.00244860
$743$	−4.03749e34	−0.0523301	−0.0261651	−	0.999658i	$-0.508330\pi$
$743$	−4.03749e34	−0.0523301	−0.0261651	+	0.999658i	$0.508330\pi$
$744$	0	0
$745$	−6.71923e35	−0.842104
$746$	1.18104e34	0.0145556
$747$	0	0
$748$	7.11853e35	0.848439
$749$	−1.40027e36	−1.64131
$750$	0	0
$751$	7.72405e35	0.875681	0.437840	−	0.899053i	$-0.355744\pi$
$751$	7.72405e35	0.875681	0.437840	+	0.899053i	$0.355744\pi$
$752$	1.04052e36	1.16019
$753$	0	0
$754$	−1.06308e33	−0.00114664
$755$	8.62115e35	0.914594
$756$	0	0
$757$	3.31585e35	0.340327	0.170163	−	0.985416i	$-0.445570\pi$
$757$	3.31585e35	0.340327	0.170163	+	0.985416i	$0.445570\pi$
$758$	3.42117e33	0.00345390
$759$	0	0
$760$	1.45363e34	0.0141999
$761$	−2.02230e36	−1.94329	−0.971646	−	0.236440i	$-0.924019\pi$
$761$	−2.02230e36	−1.94329	−0.971646	+	0.236440i	$0.924019\pi$
$762$	0	0
$763$	−1.86725e36	−1.73639
$764$	1.84739e35	0.169002
$765$	0	0
$766$	−6.38646e33	−0.00565458
$767$	1.06576e36	0.928358
$768$	0	0
$769$	7.71193e35	0.650255	0.325128	−	0.945670i	$-0.394593\pi$
$769$	7.71193e35	0.650255	0.325128	+	0.945670i	$0.394593\pi$
$770$	−1.17189e34	−0.00972195
$771$	0	0
$772$	−7.00286e35	−0.562418
$773$	−1.96060e36	−1.54934	−0.774668	−	0.632368i	$-0.782083\pi$
$773$	−1.96060e36	−1.54934	−0.774668	+	0.632368i	$0.782083\pi$
$774$	0	0
$775$	1.08376e36	0.829202
$776$	−9.11331e33	−0.00686127
$777$	0	0
$778$	−1.15444e34	−0.00841641
$779$	−1.11754e36	−0.801763
$780$	0	0
$781$	−1.61983e36	−1.12547
$782$	1.14902e34	0.00785674
$783$	0	0
$784$	2.09627e35	0.138834
$785$	−2.53393e35	−0.165167
$786$	0	0
$787$	−8.92654e35	−0.563637	−0.281818	−	0.959468i	$-0.590938\pi$
$787$	−8.92654e35	−0.563637	−0.281818	+	0.959468i	$0.590938\pi$
$788$	−2.01101e36	−1.24979
$789$	0	0
$790$	−9.67606e33	−0.00582586
$791$	2.91727e36	1.72890
$792$	0	0
$793$	−7.36121e35	−0.422702
$794$	−1.97826e34	−0.0111822
$795$	0	0
$796$	−7.51710e34	−0.0411753
$797$	2.35494e36	1.26984	0.634921	−	0.772577i	$-0.281032\pi$
$797$	2.35494e36	1.26984	0.634921	+	0.772577i	$0.281032\pi$
$798$	0	0
$799$	2.32930e36	1.21728
$800$	4.09381e34	0.0210622
$801$	0	0
$802$	3.43990e33	0.00171541
$803$	−3.57026e35	−0.175289
$804$	0	0
$805$	2.75462e36	1.31103
$806$	−1.68201e34	−0.00788208
$807$	0	0
$808$	6.00231e33	0.00272694
$809$	1.29617e36	0.579834	0.289917	−	0.957052i	$-0.406372\pi$
$809$	1.29617e36	0.579834	0.289917	+	0.957052i	$0.406372\pi$
$810$	0	0
$811$	2.63606e36	1.14339	0.571695	−	0.820467i	$-0.306286\pi$
$811$	2.63606e36	1.14339	0.571695	+	0.820467i	$0.306286\pi$
$812$	−3.55669e35	−0.151913
$813$	0	0
$814$	−8.20458e33	−0.00339822
$815$	3.43691e36	1.40184
$816$	0	0
$817$	−1.83010e36	−0.723935
$818$	6.45265e33	0.00251375
$819$	0	0
$820$	−4.57438e36	−1.72846
$821$	5.92271e35	0.220410	0.110205	−	0.993909i	$-0.464849\pi$
$821$	5.92271e35	0.220410	0.110205	+	0.993909i	$0.464849\pi$
$822$	0	0
$823$	4.76928e35	0.172169	0.0860845	−	0.996288i	$-0.472564\pi$
$823$	4.76928e35	0.172169	0.0860845	+	0.996288i	$0.472564\pi$
$824$	−1.56486e34	−0.00556396
$825$	0	0
$826$	−2.44849e34	−0.00844594
$827$	−4.17794e36	−1.41953	−0.709763	−	0.704440i	$-0.751198\pi$
$827$	−4.17794e36	−1.41953	−0.709763	+	0.704440i	$0.751198\pi$
$828$	0	0
$829$	−3.18023e36	−1.04840	−0.524199	−	0.851596i	$-0.675635\pi$
$829$	−3.18023e36	−1.04840	−0.524199	+	0.851596i	$0.675635\pi$
$830$	3.31742e34	0.0107727
$831$	0	0
$832$	3.08342e36	0.971608
$833$	4.69267e35	0.145666
$834$	0	0
$835$	6.13232e36	1.84733
$836$	−1.71814e36	−0.509893
$837$	0	0
$838$	8.25006e33	0.00237633
$839$	3.57270e36	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$839$	3.57270e36	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$840$	0	0
$841$	−3.55679e36	−0.979733
$842$	−3.97279e34	−0.0107819
$843$	0	0
$844$	2.52471e36	0.665168
$845$	−2.89018e35	−0.0750266
$846$	0	0
$847$	−1.46391e36	−0.368954
$848$	1.11474e36	0.276838
$849$	0	0
$850$	3.05443e34	0.00736535
$851$	1.92855e36	0.458258
$852$	0	0
$853$	−1.75466e36	−0.404884	−0.202442	−	0.979294i	$-0.564888\pi$
$853$	−1.75466e36	−0.404884	−0.202442	+	0.979294i	$0.564888\pi$
$854$	1.69118e34	0.00384562
$855$	0	0
$856$	1.15414e35	0.0254880
$857$	−7.10324e36	−1.54595	−0.772976	−	0.634435i	$-0.781233\pi$
$857$	−7.10324e36	−1.54595	−0.772976	+	0.634435i	$0.781233\pi$
$858$	0	0
$859$	−7.56695e36	−1.59958	−0.799791	−	0.600279i	$-0.795056\pi$
$859$	−7.56695e36	−1.59958	−0.799791	+	0.600279i	$0.795056\pi$
$860$	−7.49105e36	−1.56067
$861$	0	0
$862$	3.76241e33	0.000761423 0
$863$	−5.72195e36	−1.14132	−0.570662	−	0.821185i	$-0.693313\pi$
$863$	−5.72195e36	−1.14132	−0.570662	+	0.821185i	$0.693313\pi$
$864$	0	0
$865$	4.47125e36	0.866418
$866$	3.03971e34	0.00580575
$867$	0	0
$868$	−5.62739e36	−1.04426
$869$	2.28742e36	0.418407
$870$	0	0
$871$	2.17919e36	0.387318
$872$	1.53903e35	0.0269645
$873$	0	0
$874$	−2.77328e34	−0.00472173
$875$	−1.31931e36	−0.221435
$876$	0	0
$877$	3.21926e36	0.525123	0.262561	−	0.964915i	$-0.415433\pi$
$877$	3.21926e36	0.525123	0.262561	+	0.964915i	$0.415433\pi$
$878$	−7.11834e34	−0.0114471
$879$	0	0
$880$	−7.03227e36	−1.09916
$881$	1.04633e37	1.61238	0.806191	−	0.591655i	$-0.201525\pi$
$881$	1.04633e37	1.61238	0.806191	+	0.591655i	$0.201525\pi$
$882$	0	0
$883$	4.11745e36	0.616765	0.308382	−	0.951263i	$-0.400212\pi$
$883$	4.11745e36	0.616765	0.308382	+	0.951263i	$0.400212\pi$
$884$	6.90343e36	1.01956
$885$	0	0
$886$	5.80326e34	0.00833202
$887$	2.52904e36	0.358022	0.179011	−	0.983847i	$-0.442710\pi$
$887$	2.52904e36	0.358022	0.179011	+	0.983847i	$0.442710\pi$
$888$	0	0
$889$	1.31273e37	1.80678
$890$	6.28128e34	0.00852458
$891$	0	0
$892$	1.06258e37	1.40217
$893$	−5.62202e36	−0.731558
$894$	0	0
$895$	−1.78836e37	−2.26291
$896$	−2.83425e35	−0.0353661
$897$	0	0
$898$	4.55453e34	0.00552700
$899$	1.16410e36	0.139314
$900$	0	0
$901$	2.49544e36	0.290460
$902$	−7.42578e34	−0.00852433
$903$	0	0
$904$	−2.40448e35	−0.0268483
$905$	−6.07833e36	−0.669387
$906$	0	0
$907$	−4.93129e36	−0.528286	−0.264143	−	0.964484i	$-0.585089\pi$
$907$	−4.93129e36	−0.528286	−0.264143	+	0.964484i	$0.585089\pi$
$908$	1.29207e37	1.36525
$909$	0	0
$910$	−1.13648e35	−0.0116827
$911$	7.10548e36	0.720466	0.360233	−	0.932862i	$-0.382697\pi$
$911$	7.10548e36	0.720466	0.360233	+	0.932862i	$0.382697\pi$
$912$	0	0
$913$	−7.84240e36	−0.773685
$914$	9.15090e34	0.00890505
$915$	0	0
$916$	1.90664e37	1.80541
$917$	6.83795e36	0.638718
$918$	0	0
$919$	2.64155e36	0.240112	0.120056	−	0.992767i	$-0.461693\pi$
$919$	2.64155e36	0.240112	0.120056	+	0.992767i	$0.461693\pi$
$920$	−2.27042e35	−0.0203591
$921$	0	0
$922$	2.19009e33	0.000191129 0
$923$	−1.57089e37	−1.35246
$924$	0	0
$925$	5.12665e36	0.429597
$926$	1.02490e35	0.00847316
$927$	0	0
$928$	4.39731e34	0.00353865
$929$	−5.01934e36	−0.398520	−0.199260	−	0.979947i	$-0.563854\pi$
$929$	−5.01934e36	−0.398520	−0.199260	+	0.979947i	$0.563854\pi$
$930$	0	0
$931$	−1.13263e36	−0.0875419
$932$	1.66280e37	1.26806
$933$	0	0
$934$	1.28268e35	0.00952320
$935$	−1.57423e37	−1.15325
$936$	0	0
$937$	−1.70189e37	−1.21391	−0.606956	−	0.794735i	$-0.707610\pi$
$937$	−1.70189e37	−1.21391	−0.606956	+	0.794735i	$0.707610\pi$
$938$	−5.00652e34	−0.00352371
$939$	0	0
$940$	−2.30123e37	−1.57711
$941$	1.51254e37	1.02291	0.511455	−	0.859310i	$-0.329107\pi$
$941$	1.51254e37	1.02291	0.511455	+	0.859310i	$0.329107\pi$
$942$	0	0
$943$	1.74548e37	1.14953
$944$	−1.46929e37	−0.954897
$945$	0	0
$946$	−1.21605e35	−0.00769687
$947$	−1.65329e36	−0.103270	−0.0516351	−	0.998666i	$-0.516443\pi$
$947$	−1.65329e36	−0.103270	−0.0516351	+	0.998666i	$0.516443\pi$
$948$	0	0
$949$	−3.46238e36	−0.210643
$950$	−7.37220e34	−0.00442642
$951$	0	0
$952$	−3.17213e35	−0.0185519
$953$	−2.77784e37	−1.60341	−0.801706	−	0.597718i	$-0.796074\pi$
$953$	−2.77784e37	−1.60341	−0.801706	+	0.597718i	$0.796074\pi$
$954$	0	0
$955$	−4.08541e36	−0.229717
$956$	−4.83229e36	−0.268182
$957$	0	0
$958$	−9.46752e34	−0.00511879
$959$	−2.41640e37	−1.28955
$960$	0	0
$961$	−8.14395e35	−0.0423441
$962$	−7.95666e34	−0.00408359
$963$	0	0
$964$	1.07184e37	0.536004
$965$	1.54865e37	0.764473
$966$	0	0
$967$	3.82441e36	0.183965	0.0919823	−	0.995761i	$-0.470680\pi$
$967$	3.82441e36	0.183965	0.0919823	+	0.995761i	$0.470680\pi$
$968$	1.20659e35	0.00572952
$969$	0	0
$970$	1.00765e35	0.00466297
$971$	1.67087e37	0.763311	0.381655	−	0.924305i	$-0.375354\pi$
$971$	1.67087e37	0.763311	0.381655	+	0.924305i	$0.375354\pi$
$972$	0	0
$973$	−1.89331e37	−0.842967
$974$	−1.90256e34	−0.000836277 0
$975$	0	0
$976$	1.01484e37	0.434786
$977$	3.54376e37	1.49893	0.749466	−	0.662043i	$-0.230310\pi$
$977$	3.54376e37	1.49893	0.749466	+	0.662043i	$0.230310\pi$
$978$	0	0
$979$	−1.48490e37	−0.612227
$980$	−4.63612e36	−0.188725
$981$	0	0
$982$	3.46860e35	0.0137645
$983$	−2.26759e37	−0.888476	−0.444238	−	0.895909i	$-0.646525\pi$
$983$	−2.26759e37	−0.888476	−0.444238	+	0.895909i	$0.646525\pi$
$984$	0	0
$985$	4.44726e37	1.69879
$986$	3.28087e34	0.00123745
$987$	0	0
$988$	−1.66622e37	−0.612732
$989$	2.85843e37	1.03794
$990$	0	0
$991$	−1.82706e36	−0.0646891	−0.0323445	−	0.999477i	$-0.510297\pi$
$991$	−1.82706e36	−0.0646891	−0.0323445	+	0.999477i	$0.510297\pi$
$992$	6.95742e35	0.0243250
$993$	0	0
$994$	3.60899e35	0.0123043
$995$	1.66237e36	0.0559680
$996$	0	0
$997$	2.34599e37	0.770260	0.385130	−	0.922862i	$-0.374157\pi$
$997$	2.34599e37	0.770260	0.385130	+	0.922862i	$0.374157\pi$
$998$	3.93518e35	0.0127595
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.26.a.a.1.1		1
3.2	odd	2		1.26.a.a.1.1	✓	1
12.11	even	2		16.26.a.b.1.1		1
15.2	even	4		25.26.b.a.24.1		2
15.8	even	4		25.26.b.a.24.2		2
15.14	odd	2		25.26.a.a.1.1		1
21.20	even	2		49.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.26.a.a.1.1	✓	1	3.2	odd	2
9.26.a.a.1.1		1	1.1	even	1	trivial
16.26.a.b.1.1		1	12.11	even	2
25.26.a.a.1.1		1	15.14	odd	2
25.26.b.a.24.1		2	15.2	even	4
25.26.b.a.24.2		2	15.8	even	4
49.26.a.a.1.1		1	21.20	even	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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