LMFDB - Embedded newform 50.26.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(1,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, 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("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4096.00 q^{2} -97956.0 q^{3} +1.67772e7 q^{4} -4.01228e8 q^{6} +4.08826e10 q^{7} +6.87195e10 q^{8} -8.37693e11 q^{9} -1.45062e13 q^{11} -1.64343e12 q^{12} -8.78440e13 q^{13} +1.67455e14 q^{14} +2.81475e14 q^{16} +2.65543e15 q^{17} -3.43119e15 q^{18} -1.39994e16 q^{19} -4.00470e15 q^{21} -5.94175e16 q^{22} -8.58528e16 q^{23} -6.73149e15 q^{24} -3.59809e17 q^{26} +1.65054e17 q^{27} +6.85897e17 q^{28} +2.08023e18 q^{29} +2.66353e18 q^{31} +1.15292e18 q^{32} +1.42097e18 q^{33} +1.08766e19 q^{34} -1.40542e19 q^{36} +5.13796e19 q^{37} -5.73416e19 q^{38} +8.60485e18 q^{39} +2.33560e20 q^{41} -1.64032e19 q^{42} +4.01336e19 q^{43} -2.43374e20 q^{44} -3.51653e20 q^{46} -2.79826e20 q^{47} -2.75722e19 q^{48} +3.30321e20 q^{49} -2.60115e20 q^{51} -1.47378e21 q^{52} -4.25070e20 q^{53} +6.76062e20 q^{54} +2.80943e21 q^{56} +1.37133e21 q^{57} +8.52062e21 q^{58} -8.33891e21 q^{59} +2.42979e22 q^{61} +1.09098e22 q^{62} -3.42471e22 q^{63} +4.72237e21 q^{64} +5.82030e21 q^{66} +1.24700e23 q^{67} +4.45507e22 q^{68} +8.40979e21 q^{69} -9.30490e22 q^{71} -5.75658e22 q^{72} -4.04218e22 q^{73} +2.10451e23 q^{74} -2.34871e23 q^{76} -5.93053e23 q^{77} +3.52454e22 q^{78} -8.05270e23 q^{79} +6.93600e23 q^{81} +9.56661e23 q^{82} -8.98335e21 q^{83} -6.71877e22 q^{84} +1.64387e23 q^{86} -2.03771e23 q^{87} -9.96860e23 q^{88} +3.55600e24 q^{89} -3.59129e24 q^{91} -1.44037e24 q^{92} -2.60909e23 q^{93} -1.14617e24 q^{94} -1.12936e23 q^{96} +8.66049e24 q^{97} +1.35300e24 q^{98} +1.21518e25 q^{99} +O(q^{100})\)

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
$3$	−97956.0	−0.106418	−0.0532090	−	0.998583i	$-0.516945\pi$
$3$	−97956.0	−0.106418	−0.0532090	+	0.998583i	$0.516945\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−4.01228e8	−0.0752489
$7$	4.08826e10	1.11638	0.558192	−	0.829712i	$-0.311495\pi$
$7$	4.08826e10	1.11638	0.558192	+	0.829712i	$0.311495\pi$
$8$	6.87195e10	0.353553
$9$	−8.37693e11	−0.988675
$10$	0	0
$11$	−1.45062e13	−1.39362	−0.696812	−	0.717254i	$-0.745399\pi$
$11$	−1.45062e13	−1.39362	−0.696812	+	0.717254i	$0.745399\pi$
$12$	−1.64343e12	−0.0532090
$13$	−8.78440e13	−1.04573	−0.522866	−	0.852415i	$-0.675137\pi$
$13$	−8.78440e13	−1.04573	−0.522866	+	0.852415i	$0.675137\pi$
$14$	1.67455e14	0.789402
$15$	0	0
$16$	2.81475e14	0.250000
$17$	2.65543e15	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$17$	2.65543e15	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$18$	−3.43119e15	−0.699099
$19$	−1.39994e16	−1.45108	−0.725538	−	0.688182i	$-0.758409\pi$
$19$	−1.39994e16	−1.45108	−0.725538	+	0.688182i	$0.758409\pi$
$20$	0	0
$21$	−4.00470e15	−0.118803
$22$	−5.94175e16	−0.985441
$23$	−8.58528e16	−0.816877	−0.408438	−	0.912786i	$-0.633926\pi$
$23$	−8.58528e16	−0.816877	−0.408438	+	0.912786i	$0.633926\pi$
$24$	−6.73149e15	−0.0376245
$25$	0	0
$26$	−3.59809e17	−0.739444
$27$	1.65054e17	0.211631
$28$	6.85897e17	0.558192
$29$	2.08023e18	1.09178	0.545892	−	0.837856i	$-0.316191\pi$
$29$	2.08023e18	1.09178	0.545892	+	0.837856i	$0.316191\pi$
$30$	0	0
$31$	2.66353e18	0.607347	0.303673	−	0.952776i	$-0.401787\pi$
$31$	2.66353e18	0.607347	0.303673	+	0.952776i	$0.401787\pi$
$32$	1.15292e18	0.176777
$33$	1.42097e18	0.148307
$34$	1.08766e19	0.781642
$35$	0	0
$36$	−1.40542e19	−0.494338
$37$	5.13796e19	1.28313	0.641563	−	0.767070i	$-0.278286\pi$
$37$	5.13796e19	1.28313	0.641563	+	0.767070i	$0.278286\pi$
$38$	−5.73416e19	−1.02607
$39$	8.60485e18	0.111285
$40$	0	0
$41$	2.33560e20	1.61659	0.808295	−	0.588778i	$-0.200391\pi$
$41$	2.33560e20	1.61659	0.808295	+	0.588778i	$0.200391\pi$
$42$	−1.64032e19	−0.0840067
$43$	4.01336e19	0.153162	0.0765812	−	0.997063i	$-0.475600\pi$
$43$	4.01336e19	0.153162	0.0765812	+	0.997063i	$0.475600\pi$
$44$	−2.43374e20	−0.696812
$45$	0	0
$46$	−3.51653e20	−0.577619
$47$	−2.79826e20	−0.351290	−0.175645	−	0.984454i	$-0.556201\pi$
$47$	−2.79826e20	−0.351290	−0.175645	+	0.984454i	$0.556201\pi$
$48$	−2.75722e19	−0.0266045
$49$	3.30321e20	0.246312
$50$	0	0
$51$	−2.60115e20	−0.117635
$52$	−1.47378e21	−0.522866
$53$	−4.25070e20	−0.118854	−0.0594268	−	0.998233i	$-0.518927\pi$
$53$	−4.25070e20	−0.118854	−0.0594268	+	0.998233i	$0.518927\pi$
$54$	6.76062e20	0.149646
$55$	0	0
$56$	2.80943e21	0.394701
$57$	1.37133e21	0.154421
$58$	8.52062e21	0.772007
$59$	−8.33891e21	−0.610181	−0.305091	−	0.952323i	$-0.598687\pi$
$59$	−8.33891e21	−0.610181	−0.305091	+	0.952323i	$0.598687\pi$
$60$	0	0
$61$	2.42979e22	1.17205	0.586026	−	0.810292i	$-0.300692\pi$
$61$	2.42979e22	1.17205	0.586026	+	0.810292i	$0.300692\pi$
$62$	1.09098e22	0.429459
$63$	−3.42471e22	−1.10374
$64$	4.72237e21	0.125000
$65$	0	0
$66$	5.82030e21	0.104869
$67$	1.24700e23	1.86179	0.930897	−	0.365282i	$-0.119027\pi$
$67$	1.24700e23	1.86179	0.930897	+	0.365282i	$0.119027\pi$
$68$	4.45507e22	0.552704
$69$	8.40979e21	0.0869304
$70$	0	0
$71$	−9.30490e22	−0.672949	−0.336475	−	0.941693i	$-0.609235\pi$
$71$	−9.30490e22	−0.672949	−0.336475	+	0.941693i	$0.609235\pi$
$72$	−5.75658e22	−0.349549
$73$	−4.04218e22	−0.206576	−0.103288	−	0.994651i	$-0.532936\pi$
$73$	−4.04218e22	−0.206576	−0.103288	+	0.994651i	$0.532936\pi$
$74$	2.10451e23	0.907307
$75$	0	0
$76$	−2.34871e23	−0.725538
$77$	−5.93053e23	−1.55582
$78$	3.52454e22	0.0786902
$79$	−8.05270e23	−1.53321	−0.766607	−	0.642116i	$-0.778057\pi$
$79$	−8.05270e23	−1.53321	−0.766607	+	0.642116i	$0.778057\pi$
$80$	0	0
$81$	6.93600e23	0.966154
$82$	9.56661e23	1.14310
$83$	−8.98335e21	−0.00922491	−0.00461245	−	0.999989i	$-0.501468\pi$
$83$	−8.98335e21	−0.00922491	−0.00461245	+	0.999989i	$0.501468\pi$
$84$	−6.71877e22	−0.0594017
$85$	0	0
$86$	1.64387e23	0.108302
$87$	−2.03771e23	−0.116185
$88$	−9.96860e23	−0.492721
$89$	3.55600e24	1.52611	0.763057	−	0.646331i	$-0.223697\pi$
$89$	3.55600e24	1.52611	0.763057	+	0.646331i	$0.223697\pi$
$90$	0	0
$91$	−3.59129e24	−1.16744
$92$	−1.44037e24	−0.408438
$93$	−2.60909e23	−0.0646327
$94$	−1.14617e24	−0.248399
$95$	0	0
$96$	−1.12936e23	−0.0188122
$97$	8.66049e24	1.26735	0.633674	−	0.773600i	$-0.281546\pi$
$97$	8.66049e24	1.26735	0.633674	+	0.773600i	$0.281546\pi$
$98$	1.35300e24	0.174169
$99$	1.21518e25	1.37784
$100$	0	0
$101$	7.28380e24	0.643193	0.321596	−	0.946877i	$-0.395781\pi$
$101$	7.28380e24	0.643193	0.321596	+	0.946877i	$0.395781\pi$
$102$	−1.06543e24	−0.0831808
$103$	−1.52392e25	−1.05317	−0.526583	−	0.850123i	$-0.676527\pi$
$103$	−1.52392e25	−1.05317	−0.526583	+	0.850123i	$0.676527\pi$
$104$	−6.03659e24	−0.369722
$105$	0	0
$106$	−1.74109e24	−0.0840422
$107$	6.27006e24	0.269138	0.134569	−	0.990904i	$-0.457035\pi$
$107$	6.27006e24	0.269138	0.134569	+	0.990904i	$0.457035\pi$
$108$	2.76915e24	0.105815
$109$	−1.66220e25	−0.566047	−0.283024	−	0.959113i	$-0.591337\pi$
$109$	−1.66220e25	−0.566047	−0.283024	+	0.959113i	$0.591337\pi$
$110$	0	0
$111$	−5.03294e24	−0.136548
$112$	1.15074e25	0.279096
$113$	4.59044e25	0.996263	0.498131	−	0.867102i	$-0.334020\pi$
$113$	4.59044e25	0.996263	0.498131	+	0.867102i	$0.334020\pi$
$114$	5.61696e24	0.109192
$115$	0	0
$116$	3.49005e25	0.545892
$117$	7.35863e25	1.03389
$118$	−3.41562e25	−0.431463
$119$	1.08561e26	1.23406
$120$	0	0
$121$	1.02083e26	0.942189
$122$	9.95244e25	0.828766
$123$	−2.28786e25	−0.172034
$124$	4.46867e25	0.303673
$125$	0	0
$126$	−1.40276e26	−0.780463
$127$	3.66137e24	0.0184543	0.00922713	−	0.999957i	$-0.497063\pi$
$127$	3.66137e24	0.0184543	0.00922713	+	0.999957i	$0.497063\pi$
$128$	1.93428e25	0.0883883
$129$	−3.93133e24	−0.0162993
$130$	0	0
$131$	−1.37888e26	−0.471667	−0.235833	−	0.971793i	$-0.575782\pi$
$131$	−1.37888e26	−0.471667	−0.235833	+	0.971793i	$0.575782\pi$
$132$	2.38399e25	0.0741534
$133$	−5.72333e26	−1.61996
$134$	5.10772e26	1.31649
$135$	0	0
$136$	1.82479e26	0.390821
$137$	4.32281e26	0.844810	0.422405	−	0.906407i	$-0.361186\pi$
$137$	4.32281e26	0.844810	0.422405	+	0.906407i	$0.361186\pi$
$138$	3.44465e25	0.0614691
$139$	−4.00646e25	−0.0653245	−0.0326622	−	0.999466i	$-0.510399\pi$
$139$	−4.00646e25	−0.0653245	−0.0326622	+	0.999466i	$0.510399\pi$
$140$	0	0
$141$	2.74107e25	0.0373836
$142$	−3.81129e26	−0.475847
$143$	1.27428e27	1.45736
$144$	−2.35790e26	−0.247169
$145$	0	0
$146$	−1.65568e26	−0.146071
$147$	−3.23570e25	−0.0262121
$148$	8.62007e26	0.641563
$149$	1.12193e27	0.767601	0.383801	−	0.923416i	$-0.374615\pi$
$149$	1.12193e27	0.767601	0.383801	+	0.923416i	$0.374615\pi$
$150$	0	0
$151$	−2.65183e26	−0.153580	−0.0767900	−	0.997047i	$-0.524467\pi$
$151$	−2.65183e26	−0.153580	−0.0767900	+	0.997047i	$0.524467\pi$
$152$	−9.62033e26	−0.513033
$153$	−2.22443e27	−1.09289
$154$	−2.42914e27	−1.10013
$155$	0	0
$156$	1.44365e26	0.0556424
$157$	8.32328e26	0.296175	0.148088	−	0.988974i	$-0.452688\pi$
$157$	8.32328e26	0.296175	0.148088	+	0.988974i	$0.452688\pi$
$158$	−3.29839e27	−1.08415
$159$	4.16382e25	0.0126482
$160$	0	0
$161$	−3.50989e27	−0.911947
$162$	2.84099e27	0.683174
$163$	7.22281e27	1.60828	0.804139	−	0.594442i	$-0.202627\pi$
$163$	7.22281e27	1.60828	0.804139	+	0.594442i	$0.202627\pi$
$164$	3.91848e27	0.808295
$165$	0	0
$166$	−3.67958e25	−0.00652300
$167$	−3.82503e27	−0.629041	−0.314520	−	0.949251i	$-0.601844\pi$
$167$	−3.82503e27	−0.629041	−0.314520	+	0.949251i	$0.601844\pi$
$168$	−2.75201e26	−0.0420033
$169$	6.60156e26	0.0935542
$170$	0	0
$171$	1.17272e28	1.43464
$172$	6.73330e26	0.0765812
$173$	4.74370e27	0.501812	0.250906	−	0.968012i	$-0.419272\pi$
$173$	4.74370e27	0.501812	0.250906	+	0.968012i	$0.419272\pi$
$174$	−8.34646e26	−0.0821555
$175$	0	0
$176$	−4.08314e27	−0.348406
$177$	8.16846e26	0.0649343
$178$	1.45654e28	1.07913
$179$	−6.99171e27	−0.482970	−0.241485	−	0.970405i	$-0.577635\pi$
$179$	−6.99171e27	−0.482970	−0.241485	+	0.970405i	$0.577635\pi$
$180$	0	0
$181$	−6.34714e27	−0.381589	−0.190794	−	0.981630i	$-0.561106\pi$
$181$	−6.34714e27	−0.381589	−0.190794	+	0.981630i	$0.561106\pi$
$182$	−1.47099e28	−0.825503
$183$	−2.38013e27	−0.124727
$184$	−5.89976e27	−0.288809
$185$	0	0
$186$	−1.06868e27	−0.0457022
$187$	−3.85202e28	−1.54052
$188$	−4.69471e27	−0.175645
$189$	6.74785e27	0.236261
$190$	0	0
$191$	−3.59244e28	−1.10274	−0.551369	−	0.834261i	$-0.685894\pi$
$191$	−3.59244e28	−1.10274	−0.551369	+	0.834261i	$0.685894\pi$
$192$	−4.62584e26	−0.0133023
$193$	3.76264e27	0.101397	0.0506987	−	0.998714i	$-0.483855\pi$
$193$	3.76264e27	0.101397	0.0506987	+	0.998714i	$0.483855\pi$
$194$	3.54734e28	0.896150
$195$	0	0
$196$	5.54187e27	0.123156
$197$	1.84478e28	0.384696	0.192348	−	0.981327i	$-0.438390\pi$
$197$	1.84478e28	0.384696	0.192348	+	0.981327i	$0.438390\pi$
$198$	4.97736e28	0.974281
$199$	3.23533e28	0.594641	0.297321	−	0.954778i	$-0.403907\pi$
$199$	3.23533e28	0.594641	0.297321	+	0.954778i	$0.403907\pi$
$200$	0	0
$201$	−1.22151e28	−0.198129
$202$	2.98345e28	0.454806
$203$	8.50453e28	1.21885
$204$	−4.36400e27	−0.0588177
$205$	0	0
$206$	−6.24198e28	−0.744701
$207$	7.19183e28	0.807626
$208$	−2.47259e28	−0.261433
$209$	2.03079e29	2.02226
$210$	0	0
$211$	7.34820e28	0.649607	0.324803	−	0.945782i	$-0.394702\pi$
$211$	7.34820e28	0.649607	0.324803	+	0.945782i	$0.394702\pi$
$212$	−7.13150e27	−0.0594268
$213$	9.11471e27	0.0716140
$214$	2.56822e28	0.190309
$215$	0	0
$216$	1.13424e28	0.0748228
$217$	1.08892e29	0.678032
$218$	−6.80838e28	−0.400256
$219$	3.95956e27	0.0219834
$220$	0	0
$221$	−2.33263e29	−1.15596
$222$	−2.06149e28	−0.0965539
$223$	3.83771e29	1.69927	0.849634	−	0.527373i	$-0.176823\pi$
$223$	3.83771e29	1.69927	0.849634	+	0.527373i	$0.176823\pi$
$224$	4.71345e28	0.197351
$225$	0	0
$226$	1.88024e29	0.704464
$227$	−2.86396e28	−0.101541	−0.0507707	−	0.998710i	$-0.516168\pi$
$227$	−2.86396e28	−0.101541	−0.0507707	+	0.998710i	$0.516168\pi$
$228$	2.30071e28	0.0772104
$229$	5.18014e29	1.64588	0.822939	−	0.568129i	$-0.192333\pi$
$229$	5.18014e29	1.64588	0.822939	+	0.568129i	$0.192333\pi$
$230$	0	0
$231$	5.80931e28	0.165567
$232$	1.42952e29	0.386004
$233$	1.11488e29	0.285285	0.142643	−	0.989774i	$-0.454440\pi$
$233$	1.11488e29	0.285285	0.142643	+	0.989774i	$0.454440\pi$
$234$	3.01410e29	0.731070
$235$	0	0
$236$	−1.39904e29	−0.305091
$237$	7.88810e28	0.163162
$238$	4.44665e29	0.872612
$239$	9.81417e29	1.82759	0.913797	−	0.406170i	$-0.133136\pi$
$239$	9.81417e29	1.82759	0.913797	+	0.406170i	$0.133136\pi$
$240$	0	0
$241$	−1.00294e30	−1.68292	−0.841459	−	0.540320i	$-0.818303\pi$
$241$	−1.00294e30	−1.68292	−0.841459	+	0.540320i	$0.818303\pi$
$242$	4.18134e29	0.666228
$243$	−2.07791e29	−0.314447
$244$	4.07652e29	0.586026
$245$	0	0
$246$	−9.37107e28	−0.121647
$247$	1.22977e30	1.51744
$248$	1.83037e29	0.214730
$249$	8.79973e26	0.000981697 0
$250$	0	0
$251$	1.14894e30	1.15978	0.579892	−	0.814694i	$-0.303095\pi$
$251$	1.14894e30	1.15978	0.579892	+	0.814694i	$0.303095\pi$
$252$	−5.74571e29	−0.551870
$253$	1.24540e30	1.13842
$254$	1.49970e28	0.0130491
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.28454e30	−0.965123	−0.482562	−	0.875862i	$-0.660294\pi$
$257$	−1.28454e30	−0.965123	−0.482562	+	0.875862i	$0.660294\pi$
$258$	−1.61027e28	−0.0115253
$259$	2.10053e30	1.43246
$260$	0	0
$261$	−1.74259e30	−1.07942
$262$	−5.64789e29	−0.333519
$263$	2.47079e30	1.39120	0.695598	−	0.718431i	$-0.255140\pi$
$263$	2.47079e30	1.39120	0.695598	+	0.718431i	$0.255140\pi$
$264$	9.76484e28	0.0524344
$265$	0	0
$266$	−2.34428e30	−1.14548
$267$	−3.48332e29	−0.162406
$268$	2.09212e30	0.930897
$269$	8.32933e29	0.353758	0.176879	−	0.984233i	$-0.443400\pi$
$269$	8.32933e29	0.353758	0.176879	+	0.984233i	$0.443400\pi$
$270$	0	0
$271$	−3.89840e29	−0.150928	−0.0754641	−	0.997149i	$-0.524044\pi$
$271$	−3.89840e29	−0.150928	−0.0754641	+	0.997149i	$0.524044\pi$
$272$	7.47436e29	0.276352
$273$	3.51789e29	0.124236
$274$	1.77062e30	0.597371
$275$	0	0
$276$	1.41093e29	0.0434652
$277$	−5.75822e30	−1.69548	−0.847738	−	0.530416i	$-0.822036\pi$
$277$	−5.75822e30	−1.69548	−0.847738	+	0.530416i	$0.822036\pi$
$278$	−1.64105e29	−0.0461914
$279$	−2.23122e30	−0.600469
$280$	0	0
$281$	−7.34745e29	−0.180846	−0.0904228	−	0.995903i	$-0.528822\pi$
$281$	−7.34745e29	−0.180846	−0.0904228	+	0.995903i	$0.528822\pi$
$282$	1.12274e29	0.0264342
$283$	1.15692e30	0.260600	0.130300	−	0.991475i	$-0.458406\pi$
$283$	1.15692e30	0.260600	0.130300	+	0.991475i	$0.458406\pi$
$284$	−1.56110e30	−0.336475
$285$	0	0
$286$	5.21947e30	1.03051
$287$	9.54854e30	1.80473
$288$	−9.65795e29	−0.174775
$289$	1.28066e30	0.221927
$290$	0	0
$291$	−8.48347e29	−0.134869
$292$	−6.78165e29	−0.103288
$293$	9.96443e29	0.145414	0.0727072	−	0.997353i	$-0.476836\pi$
$293$	9.96443e29	0.145414	0.0727072	+	0.997353i	$0.476836\pi$
$294$	−1.32534e29	−0.0185347
$295$	0	0
$296$	3.53078e30	0.453653
$297$	−2.39431e30	−0.294934
$298$	4.59541e30	0.542776
$299$	7.54165e30	0.854233
$300$	0	0
$301$	1.64077e30	0.170988
$302$	−1.08619e30	−0.108597
$303$	−7.13492e29	−0.0684473
$304$	−3.94049e30	−0.362769
$305$	0	0
$306$	−9.11127e30	−0.772790
$307$	−1.11603e31	−0.908755	−0.454378	−	0.890809i	$-0.650138\pi$
$307$	−1.11603e31	−0.908755	−0.454378	+	0.890809i	$0.650138\pi$
$308$	−9.94977e30	−0.777910
$309$	1.49277e30	0.112076
$310$	0	0
$311$	−8.47315e30	−0.586867	−0.293434	−	0.955979i	$-0.594798\pi$
$311$	−8.47315e30	−0.586867	−0.293434	+	0.955979i	$0.594798\pi$
$312$	5.91321e29	0.0393451
$313$	1.15783e31	0.740184	0.370092	−	0.928995i	$-0.379326\pi$
$313$	1.15783e31	0.740184	0.370092	+	0.928995i	$0.379326\pi$
$314$	3.40921e30	0.209427
$315$	0	0
$316$	−1.35102e31	−0.766607
$317$	1.97191e31	1.07559	0.537796	−	0.843075i	$-0.319257\pi$
$317$	1.97191e31	1.07559	0.537796	+	0.843075i	$0.319257\pi$
$318$	1.70550e29	0.00894361
$319$	−3.01763e31	−1.52154
$320$	0	0
$321$	−6.14190e29	−0.0286411
$322$	−1.43765e31	−0.644844
$323$	−3.71744e31	−1.60403
$324$	1.16367e31	0.483077
$325$	0	0
$326$	2.95846e31	1.13722
$327$	1.62823e30	0.0602376
$328$	1.60501e31	0.571551
$329$	−1.14400e31	−0.392174
$330$	0	0
$331$	4.77112e31	1.51625	0.758124	−	0.652110i	$-0.226116\pi$
$331$	4.77112e31	1.51625	0.758124	+	0.652110i	$0.226116\pi$
$332$	−1.50716e29	−0.00461245
$333$	−4.30403e31	−1.26859
$334$	−1.56673e31	−0.444799
$335$	0	0
$336$	−1.12722e30	−0.0297008
$337$	3.28717e31	0.834542	0.417271	−	0.908782i	$-0.362987\pi$
$337$	3.28717e31	0.834542	0.417271	+	0.908782i	$0.362987\pi$
$338$	2.70400e30	0.0661528
$339$	−4.49661e30	−0.106020
$340$	0	0
$341$	−3.86378e31	−0.846413
$342$	4.80347e31	1.01445
$343$	−4.13220e31	−0.841405
$344$	2.75796e30	0.0541511
$345$	0	0
$346$	1.94302e31	0.354834
$347$	−3.13233e31	−0.551759	−0.275879	−	0.961192i	$-0.588969\pi$
$347$	−3.13233e31	−0.551759	−0.275879	+	0.961192i	$0.588969\pi$
$348$	−3.41871e30	−0.0580927
$349$	3.37807e31	0.553796	0.276898	−	0.960899i	$-0.410694\pi$
$349$	3.37807e31	0.553796	0.276898	+	0.960899i	$0.410694\pi$
$350$	0	0
$351$	−1.44990e31	−0.221309
$352$	−1.67245e31	−0.246360
$353$	−4.38482e31	−0.623401	−0.311701	−	0.950180i	$-0.600899\pi$
$353$	−4.38482e31	−0.623401	−0.311701	+	0.950180i	$0.600899\pi$
$354$	3.34580e30	0.0459155
$355$	0	0
$356$	5.96599e31	0.763057
$357$	−1.06342e31	−0.131326
$358$	−2.86380e31	−0.341512
$359$	−1.50427e32	−1.73239	−0.866193	−	0.499710i	$-0.833440\pi$
$359$	−1.50427e32	−1.73239	−0.866193	+	0.499710i	$0.833440\pi$
$360$	0	0
$361$	1.02907e32	1.10562
$362$	−2.59979e31	−0.269824
$363$	−9.99968e30	−0.100266
$364$	−6.02519e31	−0.583719
$365$	0	0
$366$	−9.74901e30	−0.0881956
$367$	6.93296e31	0.606168	0.303084	−	0.952964i	$-0.401984\pi$
$367$	6.93296e31	0.606168	0.303084	+	0.952964i	$0.401984\pi$
$368$	−2.41654e31	−0.204219
$369$	−1.95651e32	−1.59828
$370$	0	0
$371$	−1.73780e31	−0.132686
$372$	−4.37733e30	−0.0323163
$373$	−6.14410e31	−0.438630	−0.219315	−	0.975654i	$-0.570382\pi$
$373$	−6.14410e31	−0.438630	−0.219315	+	0.975654i	$0.570382\pi$
$374$	−1.57779e32	−1.08931
$375$	0	0
$376$	−1.92295e31	−0.124200
$377$	−1.82736e32	−1.14171
$378$	2.76392e31	0.167062
$379$	6.25980e31	0.366075	0.183038	−	0.983106i	$-0.441407\pi$
$379$	6.25980e31	0.366075	0.183038	+	0.983106i	$0.441407\pi$
$380$	0	0
$381$	−3.58653e29	−0.00196387
$382$	−1.47146e32	−0.779754
$383$	−1.95859e32	−1.00452	−0.502260	−	0.864716i	$-0.667498\pi$
$383$	−1.95859e32	−1.00452	−0.502260	+	0.864716i	$0.667498\pi$
$384$	−1.89474e30	−0.00940612
$385$	0	0
$386$	1.54118e31	0.0716988
$387$	−3.36196e31	−0.151428
$388$	1.45299e32	0.633674
$389$	−5.55896e31	−0.234760	−0.117380	−	0.993087i	$-0.537450\pi$
$389$	−5.55896e31	−0.234760	−0.117380	+	0.993087i	$0.537450\pi$
$390$	0	0
$391$	−2.27976e32	−0.902982
$392$	2.26995e31	0.0870845
$393$	1.35070e31	0.0501939
$394$	7.55624e31	0.272021
$395$	0	0
$396$	2.03873e32	0.688921
$397$	4.00706e32	1.31203	0.656017	−	0.754746i	$-0.272240\pi$
$397$	4.00706e32	1.31203	0.656017	+	0.754746i	$0.272240\pi$
$398$	1.32519e32	0.420475
$399$	5.60635e31	0.172393
$400$	0	0
$401$	−2.79804e32	−0.808258	−0.404129	−	0.914702i	$-0.632425\pi$
$401$	−2.79804e32	−0.808258	−0.404129	+	0.914702i	$0.632425\pi$
$402$	−5.00331e31	−0.140098
$403$	−2.33975e32	−0.635122
$404$	1.22202e32	0.321596
$405$	0	0
$406$	3.48346e32	0.861856
$407$	−7.45324e32	−1.78820
$408$	−1.78750e31	−0.0415904
$409$	−7.22159e32	−1.62964	−0.814820	−	0.579715i	$-0.803164\pi$
$409$	−7.22159e32	−1.62964	−0.814820	+	0.579715i	$0.803164\pi$
$410$	0	0
$411$	−4.23445e31	−0.0899030
$412$	−2.55672e32	−0.526583
$413$	−3.40916e32	−0.681196
$414$	2.94577e32	0.571078
$415$	0	0
$416$	−1.01277e32	−0.184861
$417$	3.92457e30	0.00695170
$418$	8.31811e32	1.42995
$419$	5.13071e32	0.856057	0.428028	−	0.903765i	$-0.359208\pi$
$419$	5.13071e32	0.856057	0.428028	+	0.903765i	$0.359208\pi$
$420$	0	0
$421$	−1.30991e32	−0.205927	−0.102964	−	0.994685i	$-0.532833\pi$
$421$	−1.30991e32	−0.205927	−0.102964	+	0.994685i	$0.532833\pi$
$422$	3.00982e32	0.459341
$423$	2.34409e32	0.347311
$424$	−2.92106e31	−0.0420211
$425$	0	0
$426$	3.73338e31	0.0506387
$427$	9.93364e32	1.30846
$428$	1.05194e32	0.134569
$429$	−1.24824e32	−0.155089
$430$	0	0
$431$	4.25042e32	0.498271	0.249135	−	0.968469i	$-0.419854\pi$
$431$	4.25042e32	0.498271	0.249135	+	0.968469i	$0.419854\pi$
$432$	4.64586e31	0.0529077
$433$	−2.18224e32	−0.241437	−0.120719	−	0.992687i	$-0.538520\pi$
$433$	−2.18224e32	−0.241437	−0.120719	+	0.992687i	$0.538520\pi$
$434$	4.46023e32	0.479441
$435$	0	0
$436$	−2.78871e32	−0.283024
$437$	1.20189e33	1.18535
$438$	1.62183e31	0.0155446
$439$	1.96041e33	1.82617	0.913084	−	0.407771i	$-0.133694\pi$
$439$	1.96041e33	1.82617	0.913084	+	0.407771i	$0.133694\pi$
$440$	0	0
$441$	−2.76708e32	−0.243523
$442$	−9.55446e32	−0.817387
$443$	1.81076e33	1.50596	0.752980	−	0.658043i	$-0.228615\pi$
$443$	1.81076e33	1.50596	0.752980	+	0.658043i	$0.228615\pi$
$444$	−8.44387e31	−0.0682739
$445$	0	0
$446$	1.57193e33	1.20156
$447$	−1.09899e32	−0.0816866
$448$	1.93063e32	0.139548
$449$	1.96738e33	1.38296	0.691480	−	0.722396i	$-0.256959\pi$
$449$	1.96738e33	1.38296	0.691480	+	0.722396i	$0.256959\pi$
$450$	0	0
$451$	−3.38807e33	−2.25292
$452$	7.70148e32	0.498131
$453$	2.59763e31	0.0163437
$454$	−1.17308e32	−0.0718006
$455$	0	0
$456$	9.42369e31	0.0545960
$457$	6.51681e32	0.367352	0.183676	−	0.982987i	$-0.441200\pi$
$457$	6.51681e32	0.367352	0.183676	+	0.982987i	$0.441200\pi$
$458$	2.12178e33	1.16381
$459$	4.38289e32	0.233939
$460$	0	0
$461$	−3.73344e32	−0.188733	−0.0943666	−	0.995538i	$-0.530083\pi$
$461$	−3.73344e32	−0.188733	−0.0943666	+	0.995538i	$0.530083\pi$
$462$	2.37949e32	0.117074
$463$	−3.92901e33	−1.88157	−0.940787	−	0.338999i	$-0.889912\pi$
$463$	−3.92901e33	−1.88157	−0.940787	+	0.338999i	$0.889912\pi$
$464$	5.85533e32	0.272946
$465$	0	0
$466$	4.56655e32	0.201727
$467$	2.19321e33	0.943235	0.471618	−	0.881803i	$-0.343670\pi$
$467$	2.19321e33	0.943235	0.471618	+	0.881803i	$0.343670\pi$
$468$	1.23457e33	0.516944
$469$	5.09807e33	2.07848
$470$	0	0
$471$	−8.15315e31	−0.0315184
$472$	−5.73045e32	−0.215732
$473$	−5.82187e32	−0.213451
$474$	3.23097e32	0.115373
$475$	0	0
$476$	1.82135e33	0.617030
$477$	3.56079e32	0.117508
$478$	4.01989e33	1.29230
$479$	−4.26617e33	−1.33612	−0.668058	−	0.744110i	$-0.732874\pi$
$479$	−4.26617e33	−1.33612	−0.668058	+	0.744110i	$0.732874\pi$
$480$	0	0
$481$	−4.51339e33	−1.34180
$482$	−4.10805e33	−1.19000
$483$	3.43815e32	0.0970477
$484$	1.71268e33	0.471095
$485$	0	0
$486$	−8.51111e32	−0.222348
$487$	−2.19049e33	−0.557737	−0.278869	−	0.960329i	$-0.589959\pi$
$487$	−2.19049e33	−0.557737	−0.278869	+	0.960329i	$0.589959\pi$
$488$	1.66974e33	0.414383
$489$	−7.07517e32	−0.171150
$490$	0	0
$491$	−1.06443e32	−0.0244681	−0.0122340	−	0.999925i	$-0.503894\pi$
$491$	−1.06443e32	−0.0244681	−0.0122340	+	0.999925i	$0.503894\pi$
$492$	−3.83839e32	−0.0860172
$493$	5.52390e33	1.20687
$494$	5.03712e33	1.07299
$495$	0	0
$496$	7.49718e32	0.151837
$497$	−3.80409e33	−0.751269
$498$	3.60437e30	0.000694165 0
$499$	−3.46371e33	−0.650555	−0.325278	−	0.945619i	$-0.605458\pi$
$499$	−3.46371e33	−0.650555	−0.325278	+	0.945619i	$0.605458\pi$
$500$	0	0
$501$	3.74684e32	0.0669413
$502$	4.70607e33	0.820090
$503$	−1.02261e34	−1.73824	−0.869121	−	0.494599i	$-0.835315\pi$
$503$	−1.02261e34	−1.73824	−0.869121	+	0.494599i	$0.835315\pi$
$504$	−2.35344e33	−0.390231
$505$	0	0
$506$	5.10116e33	0.804984
$507$	−6.46663e31	−0.00995585
$508$	6.14275e31	0.00922713
$509$	−2.69685e33	−0.395261	−0.197630	−	0.980277i	$-0.563325\pi$
$509$	−2.69685e33	−0.395261	−0.197630	+	0.980277i	$0.563325\pi$
$510$	0	0
$511$	−1.65255e33	−0.230618
$512$	3.24519e32	0.0441942
$513$	−2.31066e33	−0.307093
$514$	−5.26147e33	−0.682445
$515$	0	0
$516$	−6.59567e31	−0.00814963
$517$	4.05922e33	0.489566
$518$	8.60379e33	1.01290
$519$	−4.64674e32	−0.0534018
$520$	0	0
$521$	−9.39972e33	−1.02954	−0.514770	−	0.857328i	$-0.672123\pi$
$521$	−9.39972e33	−1.02954	−0.514770	+	0.857328i	$0.672123\pi$
$522$	−7.13767e33	−0.763265
$523$	4.23584e33	0.442250	0.221125	−	0.975245i	$-0.429027\pi$
$523$	4.23584e33	0.442250	0.221125	+	0.975245i	$0.429027\pi$
$524$	−2.31338e33	−0.235833
$525$	0	0
$526$	1.01203e34	0.983724
$527$	7.07281e33	0.671366
$528$	3.99968e32	0.0370767
$529$	−3.67507e33	−0.332713
$530$	0	0
$531$	6.98544e33	0.603271
$532$	−9.60216e33	−0.809979
$533$	−2.05168e34	−1.69052
$534$	−1.42677e33	−0.114839
$535$	0	0
$536$	8.56932e33	0.658244
$537$	6.84880e32	0.0513968
$538$	3.41170e33	0.250145
$539$	−4.79172e33	−0.343267
$540$	0	0
$541$	3.36042e33	0.229841	0.114921	−	0.993375i	$-0.463339\pi$
$541$	3.36042e33	0.229841	0.114921	+	0.993375i	$0.463339\pi$
$542$	−1.59678e33	−0.106722
$543$	6.21740e32	0.0406080
$544$	3.06150e33	0.195410
$545$	0	0
$546$	1.44093e33	0.0878484
$547$	1.80091e33	0.107313	0.0536563	−	0.998559i	$-0.482912\pi$
$547$	1.80091e33	0.107313	0.0536563	+	0.998559i	$0.482912\pi$
$548$	7.25247e33	0.422405
$549$	−2.03542e34	−1.15878
$550$	0	0
$551$	−2.91220e34	−1.58426
$552$	5.77917e32	0.0307345
$553$	−3.29216e34	−1.71166
$554$	−2.35857e34	−1.19888
$555$	0	0
$556$	−6.72172e32	−0.0326622
$557$	−3.61276e34	−1.71652	−0.858261	−	0.513214i	$-0.828455\pi$
$557$	−3.61276e34	−1.71652	−0.858261	+	0.513214i	$0.828455\pi$
$558$	−9.13909e33	−0.424596
$559$	−3.52550e33	−0.160167
$560$	0	0
$561$	3.77328e33	0.163940
$562$	−3.00952e33	−0.127877
$563$	−2.65943e34	−1.10518	−0.552591	−	0.833452i	$-0.686361\pi$
$563$	−2.65943e34	−1.10518	−0.552591	+	0.833452i	$0.686361\pi$
$564$	4.59875e32	0.0186918
$565$	0	0
$566$	4.73876e33	0.184272
$567$	2.83562e34	1.07860
$568$	−6.39428e33	−0.237923
$569$	7.96966e33	0.290093	0.145046	−	0.989425i	$-0.453667\pi$
$569$	7.96966e33	0.290093	0.145046	+	0.989425i	$0.453667\pi$
$570$	0	0
$571$	4.13744e34	1.44139	0.720693	−	0.693254i	$-0.243824\pi$
$571$	4.13744e34	1.44139	0.720693	+	0.693254i	$0.243824\pi$
$572$	2.13789e34	0.728678
$573$	3.51901e33	0.117351
$574$	3.91108e34	1.27614
$575$	0	0
$576$	−3.95589e33	−0.123584
$577$	3.07665e34	0.940548	0.470274	−	0.882520i	$-0.344155\pi$
$577$	3.07665e34	0.940548	0.470274	+	0.882520i	$0.344155\pi$
$578$	5.24558e33	0.156926
$579$	−3.68573e32	−0.0107905
$580$	0	0
$581$	−3.67263e32	−0.0102985
$582$	−3.47483e33	−0.0953666
$583$	6.16617e33	0.165637
$584$	−2.77776e33	−0.0730356
$585$	0	0
$586$	4.08143e33	0.102824
$587$	2.58213e34	0.636798	0.318399	−	0.947957i	$-0.396855\pi$
$587$	2.58213e34	0.636798	0.318399	+	0.947957i	$0.396855\pi$
$588$	−5.42860e32	−0.0131060
$589$	−3.72879e34	−0.881307
$590$	0	0
$591$	−1.80708e33	−0.0409386
$592$	1.44621e34	0.320781
$593$	−4.00098e34	−0.868925	−0.434463	−	0.900690i	$-0.643062\pi$
$593$	−4.00098e34	−0.868925	−0.434463	+	0.900690i	$0.643062\pi$
$594$	−9.80710e33	−0.208550
$595$	0	0
$596$	1.88228e34	0.383801
$597$	−3.16920e33	−0.0632806
$598$	3.08906e34	0.604034
$599$	−2.84196e34	−0.544230	−0.272115	−	0.962265i	$-0.587723\pi$
$599$	−2.84196e34	−0.544230	−0.272115	+	0.962265i	$0.587723\pi$
$600$	0	0
$601$	−1.02008e34	−0.187371	−0.0936856	−	0.995602i	$-0.529865\pi$
$601$	−1.02008e34	−0.187371	−0.0936856	+	0.995602i	$0.529865\pi$
$602$	6.72058e33	0.120907
$603$	−1.04460e35	−1.84071
$604$	−4.44904e33	−0.0767900
$605$	0	0
$606$	−2.92246e33	−0.0483996
$607$	−7.37377e34	−1.19628	−0.598138	−	0.801393i	$-0.704092\pi$
$607$	−7.37377e34	−1.19628	−0.598138	+	0.801393i	$0.704092\pi$
$608$	−1.61402e34	−0.256516
$609$	−8.33070e33	−0.129708
$610$	0	0
$611$	2.45811e34	0.367355
$612$	−3.73198e34	−0.546445
$613$	9.86145e34	1.41477	0.707384	−	0.706830i	$-0.249875\pi$
$613$	9.86145e34	1.41477	0.707384	+	0.706830i	$0.249875\pi$
$614$	−4.57127e34	−0.642587
$615$	0	0
$616$	−4.07543e34	−0.550065
$617$	6.22897e34	0.823857	0.411928	−	0.911216i	$-0.364855\pi$
$617$	6.22897e34	0.823857	0.411928	+	0.911216i	$0.364855\pi$
$618$	6.11440e33	0.0792497
$619$	−1.66187e34	−0.211089	−0.105544	−	0.994415i	$-0.533659\pi$
$619$	−1.66187e34	−0.211089	−0.105544	+	0.994415i	$0.533659\pi$
$620$	0	0
$621$	−1.41704e34	−0.172876
$622$	−3.47060e34	−0.414978
$623$	1.45379e35	1.70373
$624$	2.42205e33	0.0278212
$625$	0	0
$626$	4.74246e34	0.523389
$627$	−1.98928e34	−0.215204
$628$	1.39641e34	0.148088
$629$	1.36435e35	1.41838
$630$	0	0
$631$	−5.71133e34	−0.570650	−0.285325	−	0.958431i	$-0.592102\pi$
$631$	−5.71133e34	−0.570650	−0.285325	+	0.958431i	$0.592102\pi$
$632$	−5.53377e34	−0.542073
$633$	−7.19801e33	−0.0691299
$634$	8.07696e34	0.760558
$635$	0	0
$636$	6.98573e32	0.00632409
$637$	−2.90168e34	−0.257576
$638$	−1.23602e35	−1.07589
$639$	7.79465e34	0.665328
$640$	0	0
$641$	1.28313e34	0.105329	0.0526643	−	0.998612i	$-0.483229\pi$
$641$	1.28313e34	0.105329	0.0526643	+	0.998612i	$0.483229\pi$
$642$	−2.51572e33	−0.0202523
$643$	1.37614e35	1.08649	0.543246	−	0.839574i	$-0.317195\pi$
$643$	1.37614e35	1.08649	0.543246	+	0.839574i	$0.317195\pi$
$644$	−5.88862e34	−0.455974
$645$	0	0
$646$	−1.52266e35	−1.13422
$647$	−9.39917e34	−0.686730	−0.343365	−	0.939202i	$-0.611567\pi$
$647$	−9.39917e34	−0.686730	−0.343365	+	0.939202i	$0.611567\pi$
$648$	4.76638e34	0.341587
$649$	1.20966e35	0.850364
$650$	0	0
$651$	−1.06666e34	−0.0721549
$652$	1.21179e35	0.804139
$653$	1.48718e35	0.968164	0.484082	−	0.875023i	$-0.339154\pi$
$653$	1.48718e35	0.968164	0.484082	+	0.875023i	$0.339154\pi$
$654$	6.66921e33	0.0425944
$655$	0	0
$656$	6.57412e34	0.404148
$657$	3.38611e34	0.204237
$658$	−4.68584e34	−0.277309
$659$	−1.21873e35	−0.707683	−0.353842	−	0.935305i	$-0.615125\pi$
$659$	−1.21873e35	−0.707683	−0.353842	+	0.935305i	$0.615125\pi$
$660$	0	0
$661$	2.07522e35	1.16023	0.580117	−	0.814533i	$-0.303007\pi$
$661$	2.07522e35	1.16023	0.580117	+	0.814533i	$0.303007\pi$
$662$	1.95425e35	1.07215
$663$	2.28495e34	0.123015
$664$	−6.17331e32	−0.00326150
$665$	0	0
$666$	−1.76293e35	−0.897032
$667$	−1.78594e35	−0.891852
$668$	−6.41733e34	−0.314520
$669$	−3.75927e34	−0.180833
$670$	0	0
$671$	−3.52471e35	−1.63340
$672$	−4.61710e33	−0.0210017
$673$	2.63064e34	0.117455	0.0587277	−	0.998274i	$-0.481296\pi$
$673$	2.63064e34	0.117455	0.0587277	+	0.998274i	$0.481296\pi$
$674$	1.34642e35	0.590110
$675$	0	0
$676$	1.10756e34	0.0467771
$677$	−1.31255e35	−0.544198	−0.272099	−	0.962269i	$-0.587718\pi$
$677$	−1.31255e35	−0.544198	−0.272099	+	0.962269i	$0.587718\pi$
$678$	−1.84181e34	−0.0749677
$679$	3.54064e35	1.41485
$680$	0	0
$681$	2.80542e33	0.0108058
$682$	−1.58260e35	−0.598505
$683$	4.53998e35	1.68576	0.842879	−	0.538104i	$-0.180859\pi$
$683$	4.53998e35	1.68576	0.842879	+	0.538104i	$0.180859\pi$
$684$	1.96750e35	0.717321
$685$	0	0
$686$	−1.69255e35	−0.594963
$687$	−5.07426e34	−0.175151
$688$	1.12966e34	0.0382906
$689$	3.73399e34	0.124289
$690$	0	0
$691$	1.42914e35	0.458773	0.229387	−	0.973335i	$-0.426328\pi$
$691$	1.42914e35	0.458773	0.229387	+	0.973335i	$0.426328\pi$
$692$	7.95860e34	0.250906
$693$	4.96796e35	1.53820
$694$	−1.28300e35	−0.390152
$695$	0	0
$696$	−1.40030e34	−0.0410778
$697$	6.20201e35	1.78699
$698$	1.38366e35	0.391593
$699$	−1.09209e34	−0.0303595
$700$	0	0
$701$	4.38686e35	1.17673	0.588367	−	0.808594i	$-0.299771\pi$
$701$	4.38686e35	1.17673	0.588367	+	0.808594i	$0.299771\pi$
$702$	−5.93879e34	−0.156489
$703$	−7.19285e35	−1.86191
$704$	−6.85037e34	−0.174203
$705$	0	0
$706$	−1.79602e35	−0.440811
$707$	2.97781e35	0.718050
$708$	1.37044e34	0.0324672
$709$	3.53471e35	0.822766	0.411383	−	0.911463i	$-0.365046\pi$
$709$	3.53471e35	0.822766	0.411383	+	0.911463i	$0.365046\pi$
$710$	0	0
$711$	6.74569e35	1.51585
$712$	2.44367e35	0.539563
$713$	−2.28672e35	−0.496127
$714$	−4.35576e34	−0.0928617
$715$	0	0
$716$	−1.17301e35	−0.241485
$717$	−9.61357e34	−0.194489
$718$	−6.16148e35	−1.22498
$719$	8.06410e35	1.57560	0.787798	−	0.615934i	$-0.211221\pi$
$719$	8.06410e35	1.57560	0.787798	+	0.615934i	$0.211221\pi$
$720$	0	0
$721$	−6.23019e35	−1.17574
$722$	4.21509e35	0.781793
$723$	9.82443e34	0.179093
$724$	−1.06487e35	−0.190794
$725$	0	0
$726$	−4.09587e34	−0.0708987
$727$	4.49933e35	0.765539	0.382770	−	0.923844i	$-0.374970\pi$
$727$	4.49933e35	0.765539	0.382770	+	0.923844i	$0.374970\pi$
$728$	−2.46792e35	−0.412751
$729$	−5.67325e35	−0.932691
$730$	0	0
$731$	1.06572e35	0.169307
$732$	−3.99320e34	−0.0623637
$733$	1.09791e36	1.68565	0.842827	−	0.538185i	$-0.180890\pi$
$733$	1.09791e36	1.68565	0.842827	+	0.538185i	$0.180890\pi$
$734$	2.83974e35	0.428626
$735$	0	0
$736$	−9.89815e34	−0.144405
$737$	−1.80893e36	−2.59464
$738$	−8.01388e35	−1.13016
$739$	−6.34879e35	−0.880309	−0.440155	−	0.897922i	$-0.645076\pi$
$739$	−6.34879e35	−0.880309	−0.440155	+	0.897922i	$0.645076\pi$
$740$	0	0
$741$	−1.20463e35	−0.161483
$742$	−7.11803e34	−0.0938234
$743$	6.17895e35	0.800856	0.400428	−	0.916328i	$-0.368861\pi$
$743$	6.17895e35	0.800856	0.400428	+	0.916328i	$0.368861\pi$
$744$	−1.79295e34	−0.0228511
$745$	0	0
$746$	−2.51662e35	−0.310158
$747$	7.52529e33	0.00912044
$748$	−6.46262e35	−0.770262
$749$	2.56337e35	0.300461
$750$	0	0
$751$	6.31220e35	0.715619	0.357809	−	0.933795i	$-0.383524\pi$
$751$	6.31220e35	0.715619	0.357809	+	0.933795i	$0.383524\pi$
$752$	−7.87641e34	−0.0878224
$753$	−1.12546e35	−0.123422
$754$	−7.48486e35	−0.807312
$755$	0	0
$756$	1.13210e35	0.118131
$757$	−2.78268e35	−0.285605	−0.142802	−	0.989751i	$-0.545611\pi$
$757$	−2.78268e35	−0.285605	−0.142802	+	0.989751i	$0.545611\pi$
$758$	2.56401e35	0.258854
$759$	−1.21994e35	−0.121148
$760$	0	0
$761$	2.91390e35	0.280005	0.140003	−	0.990151i	$-0.455289\pi$
$761$	2.91390e35	0.280005	0.140003	+	0.990151i	$0.455289\pi$
$762$	−1.46904e33	−0.00138866
$763$	−6.79552e35	−0.631926
$764$	−6.02712e35	−0.551369
$765$	0	0
$766$	−8.02238e35	−0.710303
$767$	7.32523e35	0.638086
$768$	−7.76087e33	−0.00665113
$769$	−1.59678e36	−1.34637	−0.673187	−	0.739473i	$-0.735075\pi$
$769$	−1.59678e36	−1.34637	−0.673187	+	0.739473i	$0.735075\pi$
$770$	0	0
$771$	1.25828e35	0.102707
$772$	6.31267e34	0.0506987
$773$	−1.26764e36	−1.00173	−0.500866	−	0.865525i	$-0.666985\pi$
$773$	−1.26764e36	−1.00173	−0.500866	+	0.865525i	$0.666985\pi$
$774$	−1.37706e35	−0.107076
$775$	0	0
$776$	5.95144e35	0.448075
$777$	−2.05760e35	−0.152440
$778$	−2.27695e35	−0.166000
$779$	−3.26970e36	−2.34580
$780$	0	0
$781$	1.34979e36	0.937838
$782$	−9.33788e35	−0.638505
$783$	3.43351e35	0.231055
$784$	9.29772e34	0.0615780
$785$	0	0
$786$	5.53245e34	0.0354924
$787$	−1.69750e36	−1.07183	−0.535915	−	0.844272i	$-0.680033\pi$
$787$	−1.69750e36	−1.07183	−0.535915	+	0.844272i	$0.680033\pi$
$788$	3.09503e35	0.192348
$789$	−2.42028e35	−0.148048
$790$	0	0
$791$	1.87669e36	1.11221
$792$	8.35063e35	0.487141
$793$	−2.13443e36	−1.22565
$794$	1.64129e36	0.927748
$795$	0	0
$796$	5.42798e35	0.297321
$797$	1.94040e36	1.04631	0.523157	−	0.852236i	$-0.324754\pi$
$797$	1.94040e36	1.04631	0.523157	+	0.852236i	$0.324754\pi$
$798$	2.29636e35	0.121900
$799$	−7.43058e35	−0.388319
$800$	0	0
$801$	−2.97884e36	−1.50883
$802$	−1.14608e36	−0.571525
$803$	5.86368e35	0.287889
$804$	−2.04936e35	−0.0990643
$805$	0	0
$806$	−9.58363e35	−0.449099
$807$	−8.15908e34	−0.0376463
$808$	5.00539e35	0.227403
$809$	8.07086e35	0.361047	0.180523	−	0.983571i	$-0.442221\pi$
$809$	8.07086e35	0.361047	0.180523	+	0.983571i	$0.442221\pi$
$810$	0	0
$811$	1.23381e36	0.535165	0.267583	−	0.963535i	$-0.413775\pi$
$811$	1.23381e36	0.535165	0.267583	+	0.963535i	$0.413775\pi$
$812$	1.42682e36	0.609424
$813$	3.81872e34	0.0160615
$814$	−3.05285e36	−1.26445
$815$	0	0
$816$	−7.32158e34	−0.0294088
$817$	−5.61847e35	−0.222250
$818$	−2.95796e36	−1.15233
$819$	3.00840e36	1.15422
$820$	0	0
$821$	−6.01008e34	−0.0223661	−0.0111831	−	0.999937i	$-0.503560\pi$
$821$	−6.01008e34	−0.0223661	−0.0111831	+	0.999937i	$0.503560\pi$
$822$	−1.73443e35	−0.0635710
$823$	−1.64344e36	−0.593274	−0.296637	−	0.954990i	$-0.595865\pi$
$823$	−1.64344e36	−0.593274	−0.296637	+	0.954990i	$0.595865\pi$
$824$	−1.04723e36	−0.372351
$825$	0	0
$826$	−1.39639e36	−0.481679
$827$	−4.86438e36	−1.65276	−0.826378	−	0.563116i	$-0.809602\pi$
$827$	−4.86438e36	−1.65276	−0.826378	+	0.563116i	$0.809602\pi$
$828$	1.20659e36	0.403813
$829$	−1.30083e36	−0.428834	−0.214417	−	0.976742i	$-0.568785\pi$
$829$	−1.30083e36	−0.428834	−0.214417	+	0.976742i	$0.568785\pi$
$830$	0	0
$831$	5.64053e35	0.180429
$832$	−4.14832e35	−0.130716
$833$	8.77144e35	0.272275
$834$	1.60750e34	0.00491560
$835$	0	0
$836$	3.40710e36	1.01113
$837$	4.39627e35	0.128533
$838$	2.10154e36	0.605323
$839$	−3.56272e36	−1.01101	−0.505506	−	0.862823i	$-0.668694\pi$
$839$	−3.56272e36	−1.01101	−0.505506	+	0.862823i	$0.668694\pi$
$840$	0	0
$841$	6.96997e35	0.191991
$842$	−5.36538e35	−0.145613
$843$	7.19727e34	0.0192452
$844$	1.23282e36	0.324803
$845$	0	0
$846$	9.60138e35	0.245586
$847$	4.17344e36	1.05184
$848$	−1.19647e35	−0.0297134
$849$	−1.13328e35	−0.0277325
$850$	0	0
$851$	−4.41108e36	−1.04816
$852$	1.52919e35	0.0358070
$853$	2.91289e36	0.672142	0.336071	−	0.941837i	$-0.390902\pi$
$853$	2.91289e36	0.672142	0.336071	+	0.941837i	$0.390902\pi$
$854$	4.06882e36	0.925220
$855$	0	0
$856$	4.30876e35	0.0951546
$857$	6.85495e36	1.49192	0.745958	−	0.665993i	$-0.231992\pi$
$857$	6.85495e36	1.49192	0.745958	+	0.665993i	$0.231992\pi$
$858$	−5.11278e35	−0.109665
$859$	6.94361e36	1.46781	0.733907	−	0.679250i	$-0.237695\pi$
$859$	6.94361e36	1.46781	0.733907	+	0.679250i	$0.237695\pi$
$860$	0	0
$861$	−9.35337e35	−0.192056
$862$	1.74097e36	0.352331
$863$	5.37478e35	0.107208	0.0536038	−	0.998562i	$-0.482929\pi$
$863$	5.37478e35	0.107208	0.0536038	+	0.998562i	$0.482929\pi$
$864$	1.90294e35	0.0374114
$865$	0	0
$866$	−8.93846e35	−0.170722
$867$	−1.25448e35	−0.0236171
$868$	1.82691e36	0.339016
$869$	1.16814e37	2.13673
$870$	0	0
$871$	−1.09542e37	−1.94694
$872$	−1.14226e36	−0.200128
$873$	−7.25483e36	−1.25300
$874$	4.92294e36	0.838169
$875$	0	0
$876$	6.64304e34	0.0109917
$877$	−1.45532e36	−0.237391	−0.118695	−	0.992931i	$-0.537871\pi$
$877$	−1.45532e36	−0.237391	−0.118695	+	0.992931i	$0.537871\pi$
$878$	8.02985e36	1.29130
$879$	−9.76076e34	−0.0154747
$880$	0	0
$881$	7.73993e36	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$881$	7.73993e36	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$882$	−1.13340e36	−0.172197
$883$	1.08821e35	0.0163006	0.00815031	−	0.999967i	$-0.497406\pi$
$883$	1.08821e35	0.0163006	0.00815031	+	0.999967i	$0.497406\pi$
$884$	−3.91351e36	−0.577980
$885$	0	0
$886$	7.41686e36	1.06488
$887$	7.82913e36	1.10833	0.554164	−	0.832407i	$-0.313038\pi$
$887$	7.82913e36	1.10833	0.554164	+	0.832407i	$0.313038\pi$
$888$	−3.45861e35	−0.0482769
$889$	1.49686e35	0.0206020
$890$	0	0
$891$	−1.00615e37	−1.34646
$892$	6.43861e36	0.849634
$893$	3.91741e36	0.509748
$894$	−4.50148e35	−0.0577612
$895$	0	0
$896$	7.90785e35	0.0986753
$897$	−7.38750e35	−0.0909059
$898$	8.05840e36	0.977900
$899$	5.54076e36	0.663091
$900$	0	0
$901$	−1.12874e36	−0.131382
$902$	−1.38775e37	−1.59305
$903$	−1.60723e35	−0.0181962
$904$	3.15453e36	0.352232
$905$	0	0
$906$	1.06399e35	0.0115567
$907$	−1.06412e36	−0.113999	−0.0569993	−	0.998374i	$-0.518153\pi$
$907$	−1.06412e36	−0.113999	−0.0569993	+	0.998374i	$0.518153\pi$
$908$	−4.80492e35	−0.0507707
$909$	−6.10159e36	−0.635909
$910$	0	0
$911$	7.34268e36	0.744517	0.372259	−	0.928129i	$-0.378583\pi$
$911$	7.34268e36	0.744517	0.372259	+	0.928129i	$0.378583\pi$
$912$	3.85994e35	0.0386052
$913$	1.30314e35	0.0128561
$914$	2.66928e36	0.259757
$915$	0	0
$916$	8.69083e36	0.822939
$917$	−5.63723e36	−0.526561
$918$	1.79523e36	0.165420
$919$	5.22115e36	0.474594	0.237297	−	0.971437i	$-0.423738\pi$
$919$	5.22115e36	0.474594	0.237297	+	0.971437i	$0.423738\pi$
$920$	0	0
$921$	1.09322e36	0.0967080
$922$	−1.52922e36	−0.133454
$923$	8.17379e36	0.703724
$924$	9.74640e35	0.0827836
$925$	0	0
$926$	−1.60932e37	−1.33047
$927$	1.27658e37	1.04124
$928$	2.39834e36	0.193002
$929$	−1.16329e37	−0.923618	−0.461809	−	0.886979i	$-0.652799\pi$
$929$	−1.16329e37	−0.923618	−0.461809	+	0.886979i	$0.652799\pi$
$930$	0	0
$931$	−4.62431e36	−0.357418
$932$	1.87046e36	0.142643
$933$	8.29996e35	0.0624533
$934$	8.98341e36	0.666968
$935$	0	0
$936$	5.05681e36	0.365535
$937$	−5.72513e36	−0.408358	−0.204179	−	0.978934i	$-0.565452\pi$
$937$	−5.72513e36	−0.408358	−0.204179	+	0.978934i	$0.565452\pi$
$938$	2.08817e37	1.46970
$939$	−1.13416e36	−0.0787690
$940$	0	0
$941$	−2.32727e37	−1.57390	−0.786950	−	0.617016i	$-0.788341\pi$
$941$	−2.32727e37	−1.57390	−0.786950	+	0.617016i	$0.788341\pi$
$942$	−3.33953e35	−0.0222869
$943$	−2.00518e37	−1.32055
$944$	−2.34719e36	−0.152545
$945$	0	0
$946$	−2.38464e36	−0.150933
$947$	−2.10624e37	−1.31563	−0.657814	−	0.753180i	$-0.728519\pi$
$947$	−2.10624e37	−1.31563	−0.657814	+	0.753180i	$0.728519\pi$
$948$	1.32340e36	0.0815809
$949$	3.55081e36	0.216023
$950$	0	0
$951$	−1.93161e36	−0.114462
$952$	7.46024e36	0.436306
$953$	1.00956e36	0.0582736	0.0291368	−	0.999575i	$-0.490724\pi$
$953$	1.00956e36	0.0582736	0.0291368	+	0.999575i	$0.490724\pi$
$954$	1.45850e36	0.0830905
$955$	0	0
$956$	1.64654e37	0.913797
$957$	2.95595e36	0.161919
$958$	−1.74742e37	−0.944776
$959$	1.76728e37	0.943131
$960$	0	0
$961$	−1.21384e37	−0.631130
$962$	−1.84868e37	−0.948799
$963$	−5.25239e36	−0.266090
$964$	−1.68266e37	−0.841459
$965$	0	0
$966$	1.40826e36	0.0686231
$967$	−5.41536e36	−0.260493	−0.130247	−	0.991482i	$-0.541577\pi$
$967$	−5.41536e36	−0.260493	−0.130247	+	0.991482i	$0.541577\pi$
$968$	7.01512e36	0.333114
$969$	3.64146e36	0.170698
$970$	0	0
$971$	−5.44528e36	−0.248759	−0.124380	−	0.992235i	$-0.539694\pi$
$971$	−5.44528e36	−0.248759	−0.124380	+	0.992235i	$0.539694\pi$
$972$	−3.48615e36	−0.157224
$973$	−1.63795e36	−0.0729271
$974$	−8.97226e36	−0.394380
$975$	0	0
$976$	6.83926e36	0.293013
$977$	3.00155e37	1.26959	0.634794	−	0.772681i	$-0.281085\pi$
$977$	3.00155e37	1.26959	0.634794	+	0.772681i	$0.281085\pi$
$978$	−2.89799e36	−0.121021
$979$	−5.15842e37	−2.12683
$980$	0	0
$981$	1.39242e37	0.559637
$982$	−4.35992e35	−0.0173015
$983$	−2.29888e36	−0.0900737	−0.0450368	−	0.998985i	$-0.514341\pi$
$983$	−2.29888e36	−0.0900737	−0.0450368	+	0.998985i	$0.514341\pi$
$984$	−1.57220e36	−0.0608233
$985$	0	0
$986$	2.26259e37	0.853383
$987$	1.12062e36	0.0417344
$988$	2.06320e37	0.758718
$989$	−3.44558e36	−0.125115
$990$	0	0
$991$	9.88586e36	0.350021	0.175010	−	0.984567i	$-0.444004\pi$
$991$	9.88586e36	0.350021	0.175010	+	0.984567i	$0.444004\pi$
$992$	3.07084e36	0.107365
$993$	−4.67360e36	−0.161356
$994$	−1.55815e37	−0.531228
$995$	0	0
$996$	1.47635e34	0.000490848 0
$997$	−2.20132e37	−0.722759	−0.361380	−	0.932419i	$-0.617694\pi$
$997$	−2.20132e37	−0.722759	−0.361380	+	0.932419i	$0.617694\pi$
$998$	−1.41873e37	−0.460012
$999$	8.48041e36	0.271549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.b.1.1		1
5.2	odd	4		50.26.b.a.49.2		2
5.3	odd	4		50.26.b.a.49.1		2
5.4	even	2		2.26.a.a.1.1	✓	1
15.14	odd	2		18.26.a.c.1.1		1
20.19	odd	2		16.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.a.1.1	✓	1	5.4	even	2
16.26.a.a.1.1		1	20.19	odd	2
18.26.a.c.1.1		1	15.14	odd	2
50.26.a.b.1.1		1	1.1	even	1	trivial
50.26.b.a.49.1		2	5.3	odd	4
50.26.b.a.49.2		2	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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