LMFDB - Embedded newform 16.26.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,26,Mod(1,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("16.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	16.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:	$63.3594847924$
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	$\chi$	$=$	16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-97956.0 q^{3} +3.41005e8 q^{5} +4.08826e10 q^{7} -8.37693e11 q^{9} +O(q^{10})$

$q-97956.0 q^{3} +3.41005e8 q^{5} +4.08826e10 q^{7} -8.37693e11 q^{9} +1.45062e13 q^{11} +8.78440e13 q^{13} -3.34035e13 q^{15} -2.65543e15 q^{17} +1.39994e16 q^{19} -4.00470e15 q^{21} -8.58528e16 q^{23} -1.81739e17 q^{25} +1.65054e17 q^{27} +2.08023e18 q^{29} -2.66353e18 q^{31} -1.42097e18 q^{33} +1.39412e19 q^{35} -5.13796e19 q^{37} -8.60485e18 q^{39} +2.33560e20 q^{41} +4.01336e19 q^{43} -2.85658e20 q^{45} -2.79826e20 q^{47} +3.30321e20 q^{49} +2.60115e20 q^{51} +4.25070e20 q^{53} +4.94670e21 q^{55} -1.37133e21 q^{57} +8.33891e21 q^{59} +2.42979e22 q^{61} -3.42471e22 q^{63} +2.99553e22 q^{65} +1.24700e23 q^{67} +8.40979e21 q^{69} +9.30490e22 q^{71} +4.04218e22 q^{73} +1.78024e22 q^{75} +5.93053e23 q^{77} +8.05270e23 q^{79} +6.93600e23 q^{81} -8.98335e21 q^{83} -9.05514e23 q^{85} -2.03771e23 q^{87} +3.55600e24 q^{89} +3.59129e24 q^{91} +2.60909e23 q^{93} +4.77388e24 q^{95} -8.66049e24 q^{97} -1.21518e25 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−97956.0	−0.106418	−0.0532090	−	0.998583i	$-0.516945\pi$
$3$	−97956.0	−0.106418	−0.0532090	+	0.998583i	$0.516945\pi$
$4$	0	0
$5$	3.41005e8	0.624649	0.312325	−	0.949975i	$-0.398892\pi$
$5$	3.41005e8	0.624649	0.312325	+	0.949975i	$0.398892\pi$
$6$	0	0
$7$	4.08826e10	1.11638	0.558192	−	0.829712i	$-0.311495\pi$
$7$	4.08826e10	1.11638	0.558192	+	0.829712i	$0.311495\pi$
$8$	0	0
$9$	−8.37693e11	−0.988675
$10$	0	0
$11$	1.45062e13	1.39362	0.696812	−	0.717254i	$-0.254601\pi$
$11$	1.45062e13	1.39362	0.696812	+	0.717254i	$0.254601\pi$
$12$	0	0
$13$	8.78440e13	1.04573	0.522866	−	0.852415i	$-0.324863\pi$
$13$	8.78440e13	1.04573	0.522866	+	0.852415i	$0.324863\pi$
$14$	0	0
$15$	−3.34035e13	−0.0664740
$16$	0	0
$17$	−2.65543e15	−1.10541	−0.552704	−	0.833378i	$-0.686404\pi$
$17$	−2.65543e15	−1.10541	−0.552704	+	0.833378i	$0.686404\pi$
$18$	0	0
$19$	1.39994e16	1.45108	0.725538	−	0.688182i	$-0.241591\pi$
$19$	1.39994e16	1.45108	0.725538	+	0.688182i	$0.241591\pi$
$20$	0	0
$21$	−4.00470e15	−0.118803
$22$	0	0
$23$	−8.58528e16	−0.816877	−0.408438	−	0.912786i	$-0.633926\pi$
$23$	−8.58528e16	−0.816877	−0.408438	+	0.912786i	$0.633926\pi$
$24$	0	0
$25$	−1.81739e17	−0.609813
$26$	0	0
$27$	1.65054e17	0.211631
$28$	0	0
$29$	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	$-0.598213\pi$
$31$	−2.66353e18	−0.607347	−0.303673	+	0.952776i	$0.598213\pi$
$32$	0	0
$33$	−1.42097e18	−0.148307
$34$	0	0
$35$	1.39412e19	0.697348
$36$	0	0
$37$	−5.13796e19	−1.28313	−0.641563	−	0.767070i	$-0.721714\pi$
$37$	−5.13796e19	−1.28313	−0.641563	+	0.767070i	$0.721714\pi$
$38$	0	0
$39$	−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	$0.200391\pi$
$42$	0	0
$43$	4.01336e19	0.153162	0.0765812	−	0.997063i	$-0.475600\pi$
$43$	4.01336e19	0.153162	0.0765812	+	0.997063i	$0.475600\pi$
$44$	0	0
$45$	−2.85658e20	−0.617575
$46$	0	0
$47$	−2.79826e20	−0.351290	−0.175645	−	0.984454i	$-0.556201\pi$
$47$	−2.79826e20	−0.351290	−0.175645	+	0.984454i	$0.556201\pi$
$48$	0	0
$49$	3.30321e20	0.246312
$50$	0	0
$51$	2.60115e20	0.117635
$52$	0	0
$53$	4.25070e20	0.118854	0.0594268	−	0.998233i	$-0.481073\pi$
$53$	4.25070e20	0.118854	0.0594268	+	0.998233i	$0.481073\pi$
$54$	0	0
$55$	4.94670e21	0.870526
$56$	0	0
$57$	−1.37133e21	−0.154421
$58$	0	0
$59$	8.33891e21	0.610181	0.305091	−	0.952323i	$-0.401313\pi$
$59$	8.33891e21	0.610181	0.305091	+	0.952323i	$0.401313\pi$
$60$	0	0
$61$	2.42979e22	1.17205	0.586026	−	0.810292i	$-0.300692\pi$
$61$	2.42979e22	1.17205	0.586026	+	0.810292i	$0.300692\pi$
$62$	0	0
$63$	−3.42471e22	−1.10374
$64$	0	0
$65$	2.99553e22	0.653215
$66$	0	0
$67$	1.24700e23	1.86179	0.930897	−	0.365282i	$-0.119027\pi$
$67$	1.24700e23	1.86179	0.930897	+	0.365282i	$0.119027\pi$
$68$	0	0
$69$	8.40979e21	0.0869304
$70$	0	0
$71$	9.30490e22	0.672949	0.336475	−	0.941693i	$-0.390765\pi$
$71$	9.30490e22	0.672949	0.336475	+	0.941693i	$0.390765\pi$
$72$	0	0
$73$	4.04218e22	0.206576	0.103288	−	0.994651i	$-0.467064\pi$
$73$	4.04218e22	0.206576	0.103288	+	0.994651i	$0.467064\pi$
$74$	0	0
$75$	1.78024e22	0.0648952
$76$	0	0
$77$	5.93053e23	1.55582
$78$	0	0
$79$	8.05270e23	1.53321	0.766607	−	0.642116i	$-0.221943\pi$
$79$	8.05270e23	1.53321	0.766607	+	0.642116i	$0.221943\pi$
$80$	0	0
$81$	6.93600e23	0.966154
$82$	0	0
$83$	−8.98335e21	−0.00922491	−0.00461245	−	0.999989i	$-0.501468\pi$
$83$	−8.98335e21	−0.00922491	−0.00461245	+	0.999989i	$0.501468\pi$
$84$	0	0
$85$	−9.05514e23	−0.690492
$86$	0	0
$87$	−2.03771e23	−0.116185
$88$	0	0
$89$	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
$92$	0	0
$93$	2.60909e23	0.0646327
$94$	0	0
$95$	4.77388e24	0.906413
$96$	0	0
$97$	−8.66049e24	−1.26735	−0.633674	−	0.773600i	$-0.718454\pi$
$97$	−8.66049e24	−1.26735	−0.633674	+	0.773600i	$0.718454\pi$
$98$	0	0
$99$	−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	$0.395781\pi$
$102$	0	0
$103$	−1.52392e25	−1.05317	−0.526583	−	0.850123i	$-0.676527\pi$
$103$	−1.52392e25	−1.05317	−0.526583	+	0.850123i	$0.676527\pi$
$104$	0	0
$105$	−1.36562e24	−0.0742104
$106$	0	0
$107$	6.27006e24	0.269138	0.134569	−	0.990904i	$-0.457035\pi$
$107$	6.27006e24	0.269138	0.134569	+	0.990904i	$0.457035\pi$
$108$	0	0
$109$	−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
$112$	0	0
$113$	−4.59044e25	−0.996263	−0.498131	−	0.867102i	$-0.665980\pi$
$113$	−4.59044e25	−0.996263	−0.498131	+	0.867102i	$0.665980\pi$
$114$	0	0
$115$	−2.92763e25	−0.510261
$116$	0	0
$117$	−7.35863e25	−1.03389
$118$	0	0
$119$	−1.08561e26	−1.23406
$120$	0	0
$121$	1.02083e26	0.942189
$122$	0	0
$123$	−2.28786e25	−0.172034
$124$	0	0
$125$	−1.63601e26	−1.00557
$126$	0	0
$127$	3.66137e24	0.0184543	0.00922713	−	0.999957i	$-0.497063\pi$
$127$	3.66137e24	0.0184543	0.00922713	+	0.999957i	$0.497063\pi$
$128$	0	0
$129$	−3.93133e24	−0.0162993
$130$	0	0
$131$	1.37888e26	0.471667	0.235833	−	0.971793i	$-0.424218\pi$
$131$	1.37888e26	0.471667	0.235833	+	0.971793i	$0.424218\pi$
$132$	0	0
$133$	5.72333e26	1.61996
$134$	0	0
$135$	5.62843e25	0.132195
$136$	0	0
$137$	−4.32281e26	−0.844810	−0.422405	−	0.906407i	$-0.638814\pi$
$137$	−4.32281e26	−0.844810	−0.422405	+	0.906407i	$0.638814\pi$
$138$	0	0
$139$	4.00646e25	0.0653245	0.0326622	−	0.999466i	$-0.489601\pi$
$139$	4.00646e25	0.0653245	0.0326622	+	0.999466i	$0.489601\pi$
$140$	0	0
$141$	2.74107e25	0.0373836
$142$	0	0
$143$	1.27428e27	1.45736
$144$	0	0
$145$	7.09370e26	0.681982
$146$	0	0
$147$	−3.23570e25	−0.0262121
$148$	0	0
$149$	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	$-0.475533\pi$
$151$	2.65183e26	0.153580	0.0767900	+	0.997047i	$0.475533\pi$
$152$	0	0
$153$	2.22443e27	1.09289
$154$	0	0
$155$	−9.08279e26	−0.379379
$156$	0	0
$157$	−8.32328e26	−0.296175	−0.148088	−	0.988974i	$-0.547312\pi$
$157$	−8.32328e26	−0.296175	−0.148088	+	0.988974i	$0.547312\pi$
$158$	0	0
$159$	−4.16382e25	−0.0126482
$160$	0	0
$161$	−3.50989e27	−0.911947
$162$	0	0
$163$	7.22281e27	1.60828	0.804139	−	0.594442i	$-0.202627\pi$
$163$	7.22281e27	1.60828	0.804139	+	0.594442i	$0.202627\pi$
$164$	0	0
$165$	−4.84559e26	−0.0926397
$166$	0	0
$167$	−3.82503e27	−0.629041	−0.314520	−	0.949251i	$-0.601844\pi$
$167$	−3.82503e27	−0.629041	−0.314520	+	0.949251i	$0.601844\pi$
$168$	0	0
$169$	6.60156e26	0.0935542
$170$	0	0
$171$	−1.17272e28	−1.43464
$172$	0	0
$173$	−4.74370e27	−0.501812	−0.250906	−	0.968012i	$-0.580728\pi$
$173$	−4.74370e27	−0.501812	−0.250906	+	0.968012i	$0.580728\pi$
$174$	0	0
$175$	−7.42995e27	−0.680786
$176$	0	0
$177$	−8.16846e26	−0.0649343
$178$	0	0
$179$	6.99171e27	0.482970	0.241485	−	0.970405i	$-0.422365\pi$
$179$	6.99171e27	0.482970	0.241485	+	0.970405i	$0.422365\pi$
$180$	0	0
$181$	−6.34714e27	−0.381589	−0.190794	−	0.981630i	$-0.561106\pi$
$181$	−6.34714e27	−0.381589	−0.190794	+	0.981630i	$0.561106\pi$
$182$	0	0
$183$	−2.38013e27	−0.124727
$184$	0	0
$185$	−1.75207e28	−0.801503
$186$	0	0
$187$	−3.85202e28	−1.54052
$188$	0	0
$189$	6.74785e27	0.236261
$190$	0	0
$191$	3.59244e28	1.10274	0.551369	−	0.834261i	$-0.314106\pi$
$191$	3.59244e28	1.10274	0.551369	+	0.834261i	$0.314106\pi$
$192$	0	0
$193$	−3.76264e27	−0.101397	−0.0506987	−	0.998714i	$-0.516145\pi$
$193$	−3.76264e27	−0.101397	−0.0506987	+	0.998714i	$0.516145\pi$
$194$	0	0
$195$	−2.93430e27	−0.0695139
$196$	0	0
$197$	−1.84478e28	−0.384696	−0.192348	−	0.981327i	$-0.561610\pi$
$197$	−1.84478e28	−0.384696	−0.192348	+	0.981327i	$0.561610\pi$
$198$	0	0
$199$	−3.23533e28	−0.594641	−0.297321	−	0.954778i	$-0.596093\pi$
$199$	−3.23533e28	−0.594641	−0.297321	+	0.954778i	$0.596093\pi$
$200$	0	0
$201$	−1.22151e28	−0.198129
$202$	0	0
$203$	8.50453e28	1.21885
$204$	0	0
$205$	7.96451e28	1.00980
$206$	0	0
$207$	7.19183e28	0.807626
$208$	0	0
$209$	2.03079e29	2.02226
$210$	0	0
$211$	−7.34820e28	−0.649607	−0.324803	−	0.945782i	$-0.605298\pi$
$211$	−7.34820e28	−0.649607	−0.324803	+	0.945782i	$0.605298\pi$
$212$	0	0
$213$	−9.11471e27	−0.0716140
$214$	0	0
$215$	1.36858e28	0.0956728
$216$	0	0
$217$	−1.08892e29	−0.678032
$218$	0	0
$219$	−3.95956e27	−0.0219834
$220$	0	0
$221$	−2.33263e29	−1.15596
$222$	0	0
$223$	3.83771e29	1.69927	0.849634	−	0.527373i	$-0.176823\pi$
$223$	3.83771e29	1.69927	0.849634	+	0.527373i	$0.176823\pi$
$224$	0	0
$225$	1.52241e29	0.602907
$226$	0	0
$227$	−2.86396e28	−0.101541	−0.0507707	−	0.998710i	$-0.516168\pi$
$227$	−2.86396e28	−0.101541	−0.0507707	+	0.998710i	$0.516168\pi$
$228$	0	0
$229$	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
$232$	0	0
$233$	−1.11488e29	−0.285285	−0.142643	−	0.989774i	$-0.545560\pi$
$233$	−1.11488e29	−0.285285	−0.142643	+	0.989774i	$0.545560\pi$
$234$	0	0
$235$	−9.54223e28	−0.219433
$236$	0	0
$237$	−7.88810e28	−0.163162
$238$	0	0
$239$	−9.81417e29	−1.82759	−0.913797	−	0.406170i	$-0.866864\pi$
$239$	−9.81417e29	−1.82759	−0.913797	+	0.406170i	$0.866864\pi$
$240$	0	0
$241$	−1.00294e30	−1.68292	−0.841459	−	0.540320i	$-0.818303\pi$
$241$	−1.00294e30	−1.68292	−0.841459	+	0.540320i	$0.818303\pi$
$242$	0	0
$243$	−2.07791e29	−0.314447
$244$	0	0
$245$	1.12641e29	0.153859
$246$	0	0
$247$	1.22977e30	1.51744
$248$	0	0
$249$	8.79973e26	0.000981697 0
$250$	0	0
$251$	−1.14894e30	−1.15978	−0.579892	−	0.814694i	$-0.696905\pi$
$251$	−1.14894e30	−1.15978	−0.579892	+	0.814694i	$0.696905\pi$
$252$	0	0
$253$	−1.24540e30	−1.13842
$254$	0	0
$255$	8.87006e28	0.0734808
$256$	0	0
$257$	1.28454e30	0.965123	0.482562	−	0.875862i	$-0.339706\pi$
$257$	1.28454e30	0.965123	0.482562	+	0.875862i	$0.339706\pi$
$258$	0	0
$259$	−2.10053e30	−1.43246
$260$	0	0
$261$	−1.74259e30	−1.07942
$262$	0	0
$263$	2.47079e30	1.39120	0.695598	−	0.718431i	$-0.255140\pi$
$263$	2.47079e30	1.39120	0.695598	+	0.718431i	$0.255140\pi$
$264$	0	0
$265$	1.44951e29	0.0742418
$266$	0	0
$267$	−3.48332e29	−0.162406
$268$	0	0
$269$	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	$-0.475956\pi$
$271$	3.89840e29	0.150928	0.0754641	+	0.997149i	$0.475956\pi$
$272$	0	0
$273$	−3.51789e29	−0.124236
$274$	0	0
$275$	−2.63634e30	−0.849851
$276$	0	0
$277$	5.75822e30	1.69548	0.847738	−	0.530416i	$-0.177964\pi$
$277$	5.75822e30	1.69548	0.847738	+	0.530416i	$0.177964\pi$
$278$	0	0
$279$	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	$0.528822\pi$
$282$	0	0
$283$	1.15692e30	0.260600	0.130300	−	0.991475i	$-0.458406\pi$
$283$	1.15692e30	0.260600	0.130300	+	0.991475i	$0.458406\pi$
$284$	0	0
$285$	−4.67630e29	−0.0964588
$286$	0	0
$287$	9.54854e30	1.80473
$288$	0	0
$289$	1.28066e30	0.221927
$290$	0	0
$291$	8.48347e29	0.134869
$292$	0	0
$293$	−9.96443e29	−0.145414	−0.0727072	−	0.997353i	$-0.523164\pi$
$293$	−9.96443e29	−0.145414	−0.0727072	+	0.997353i	$0.523164\pi$
$294$	0	0
$295$	2.84361e30	0.381149
$296$	0	0
$297$	2.39431e30	0.294934
$298$	0	0
$299$	−7.54165e30	−0.854233
$300$	0	0
$301$	1.64077e30	0.170988
$302$	0	0
$303$	−7.13492e29	−0.0684473
$304$	0	0
$305$	8.28573e30	0.732121
$306$	0	0
$307$	−1.11603e31	−0.908755	−0.454378	−	0.890809i	$-0.650138\pi$
$307$	−1.11603e31	−0.908755	−0.454378	+	0.890809i	$0.650138\pi$
$308$	0	0
$309$	1.49277e30	0.112076
$310$	0	0
$311$	8.47315e30	0.586867	0.293434	−	0.955979i	$-0.405202\pi$
$311$	8.47315e30	0.586867	0.293434	+	0.955979i	$0.405202\pi$
$312$	0	0
$313$	−1.15783e31	−0.740184	−0.370092	−	0.928995i	$-0.620674\pi$
$313$	−1.15783e31	−0.740184	−0.370092	+	0.928995i	$0.620674\pi$
$314$	0	0
$315$	−1.16784e31	−0.689451
$316$	0	0
$317$	−1.97191e31	−1.07559	−0.537796	−	0.843075i	$-0.680743\pi$
$317$	−1.97191e31	−1.07559	−0.537796	+	0.843075i	$0.680743\pi$
$318$	0	0
$319$	3.01763e31	1.52154
$320$	0	0
$321$	−6.14190e29	−0.0286411
$322$	0	0
$323$	−3.71744e31	−1.60403
$324$	0	0
$325$	−1.59646e31	−0.637701
$326$	0	0
$327$	1.62823e30	0.0602376
$328$	0	0
$329$	−1.14400e31	−0.392174
$330$	0	0
$331$	−4.77112e31	−1.51625	−0.758124	−	0.652110i	$-0.773884\pi$
$331$	−4.77112e31	−1.51625	−0.758124	+	0.652110i	$0.773884\pi$
$332$	0	0
$333$	4.30403e31	1.26859
$334$	0	0
$335$	4.25234e31	1.16297
$336$	0	0
$337$	−3.28717e31	−0.834542	−0.417271	−	0.908782i	$-0.637013\pi$
$337$	−3.28717e31	−0.834542	−0.417271	+	0.908782i	$0.637013\pi$
$338$	0	0
$339$	4.49661e30	0.106020
$340$	0	0
$341$	−3.86378e31	−0.846413
$342$	0	0
$343$	−4.13220e31	−0.841405
$344$	0	0
$345$	2.86779e30	0.0543010
$346$	0	0
$347$	−3.13233e31	−0.551759	−0.275879	−	0.961192i	$-0.588969\pi$
$347$	−3.13233e31	−0.551759	−0.275879	+	0.961192i	$0.588969\pi$
$348$	0	0
$349$	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
$352$	0	0
$353$	4.38482e31	0.623401	0.311701	−	0.950180i	$-0.399101\pi$
$353$	4.38482e31	0.623401	0.311701	+	0.950180i	$0.399101\pi$
$354$	0	0
$355$	3.17302e31	0.420357
$356$	0	0
$357$	1.06342e31	0.131326
$358$	0	0
$359$	1.50427e32	1.73239	0.866193	−	0.499710i	$-0.166560\pi$
$359$	1.50427e32	1.73239	0.866193	+	0.499710i	$0.166560\pi$
$360$	0	0
$361$	1.02907e32	1.10562
$362$	0	0
$363$	−9.99968e30	−0.100266
$364$	0	0
$365$	1.37840e31	0.129038
$366$	0	0
$367$	6.93296e31	0.606168	0.303084	−	0.952964i	$-0.401984\pi$
$367$	6.93296e31	0.606168	0.303084	+	0.952964i	$0.401984\pi$
$368$	0	0
$369$	−1.95651e32	−1.59828
$370$	0	0
$371$	1.73780e31	0.132686
$372$	0	0
$373$	6.14410e31	0.438630	0.219315	−	0.975654i	$-0.429618\pi$
$373$	6.14410e31	0.438630	0.219315	+	0.975654i	$0.429618\pi$
$374$	0	0
$375$	1.60257e31	0.107011
$376$	0	0
$377$	1.82736e32	1.14171
$378$	0	0
$379$	−6.25980e31	−0.366075	−0.183038	−	0.983106i	$-0.558593\pi$
$379$	−6.25980e31	−0.366075	−0.183038	+	0.983106i	$0.558593\pi$
$380$	0	0
$381$	−3.58653e29	−0.00196387
$382$	0	0
$383$	−1.95859e32	−1.00452	−0.502260	−	0.864716i	$-0.667498\pi$
$383$	−1.95859e32	−1.00452	−0.502260	+	0.864716i	$0.667498\pi$
$384$	0	0
$385$	2.02234e32	0.971841
$386$	0	0
$387$	−3.36196e31	−0.151428
$388$	0	0
$389$	−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
$392$	0	0
$393$	−1.35070e31	−0.0501939
$394$	0	0
$395$	2.74601e32	0.957721
$396$	0	0
$397$	−4.00706e32	−1.31203	−0.656017	−	0.754746i	$-0.727760\pi$
$397$	−4.00706e32	−1.31203	−0.656017	+	0.754746i	$0.727760\pi$
$398$	0	0
$399$	−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	$0.632425\pi$
$402$	0	0
$403$	−2.33975e32	−0.635122
$404$	0	0
$405$	2.36521e32	0.603507
$406$	0	0
$407$	−7.45324e32	−1.78820
$408$	0	0
$409$	−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
$412$	0	0
$413$	3.40916e32	0.681196
$414$	0	0
$415$	−3.06337e30	−0.00576233
$416$	0	0
$417$	−3.92457e30	−0.00695170
$418$	0	0
$419$	−5.13071e32	−0.856057	−0.428028	−	0.903765i	$-0.640792\pi$
$419$	−5.13071e32	−0.856057	−0.428028	+	0.903765i	$0.640792\pi$
$420$	0	0
$421$	−1.30991e32	−0.205927	−0.102964	−	0.994685i	$-0.532833\pi$
$421$	−1.30991e32	−0.205927	−0.102964	+	0.994685i	$0.532833\pi$
$422$	0	0
$423$	2.34409e32	0.347311
$424$	0	0
$425$	4.82593e32	0.674093
$426$	0	0
$427$	9.93364e32	1.30846
$428$	0	0
$429$	−1.24824e32	−0.155089
$430$	0	0
$431$	−4.25042e32	−0.498271	−0.249135	−	0.968469i	$-0.580146\pi$
$431$	−4.25042e32	−0.498271	−0.249135	+	0.968469i	$0.580146\pi$
$432$	0	0
$433$	2.18224e32	0.241437	0.120719	−	0.992687i	$-0.461480\pi$
$433$	2.18224e32	0.241437	0.120719	+	0.992687i	$0.461480\pi$
$434$	0	0
$435$	−6.94870e31	−0.0725752
$436$	0	0
$437$	−1.20189e33	−1.18535
$438$	0	0
$439$	−1.96041e33	−1.82617	−0.913084	−	0.407771i	$-0.866306\pi$
$439$	−1.96041e33	−1.82617	−0.913084	+	0.407771i	$0.866306\pi$
$440$	0	0
$441$	−2.76708e32	−0.243523
$442$	0	0
$443$	1.81076e33	1.50596	0.752980	−	0.658043i	$-0.228615\pi$
$443$	1.81076e33	1.50596	0.752980	+	0.658043i	$0.228615\pi$
$444$	0	0
$445$	1.21262e33	0.953286
$446$	0	0
$447$	−1.09899e32	−0.0816866
$448$	0	0
$449$	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
$452$	0	0
$453$	−2.59763e31	−0.0163437
$454$	0	0
$455$	1.22465e33	0.729239
$456$	0	0
$457$	−6.51681e32	−0.367352	−0.183676	−	0.982987i	$-0.558800\pi$
$457$	−6.51681e32	−0.367352	−0.183676	+	0.982987i	$0.558800\pi$
$458$	0	0
$459$	−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	$0.530083\pi$
$462$	0	0
$463$	−3.92901e33	−1.88157	−0.940787	−	0.338999i	$-0.889912\pi$
$463$	−3.92901e33	−1.88157	−0.940787	+	0.338999i	$0.889912\pi$
$464$	0	0
$465$	8.89714e31	0.0403727
$466$	0	0
$467$	2.19321e33	0.943235	0.471618	−	0.881803i	$-0.343670\pi$
$467$	2.19321e33	0.943235	0.471618	+	0.881803i	$0.343670\pi$
$468$	0	0
$469$	5.09807e33	2.07848
$470$	0	0
$471$	8.15315e31	0.0315184
$472$	0	0
$473$	5.82187e32	0.213451
$474$	0	0
$475$	−2.54424e33	−0.884886
$476$	0	0
$477$	−3.56079e32	−0.117508
$478$	0	0
$479$	4.26617e33	1.33612	0.668058	−	0.744110i	$-0.267126\pi$
$479$	4.26617e33	1.33612	0.668058	+	0.744110i	$0.267126\pi$
$480$	0	0
$481$	−4.51339e33	−1.34180
$482$	0	0
$483$	3.43815e32	0.0970477
$484$	0	0
$485$	−2.95327e33	−0.791648
$486$	0	0
$487$	−2.19049e33	−0.557737	−0.278869	−	0.960329i	$-0.589959\pi$
$487$	−2.19049e33	−0.557737	−0.278869	+	0.960329i	$0.589959\pi$
$488$	0	0
$489$	−7.07517e32	−0.171150
$490$	0	0
$491$	1.06443e32	0.0244681	0.0122340	−	0.999925i	$-0.496106\pi$
$491$	1.06443e32	0.0244681	0.0122340	+	0.999925i	$0.496106\pi$
$492$	0	0
$493$	−5.52390e33	−1.20687
$494$	0	0
$495$	−4.14382e33	−0.860668
$496$	0	0
$497$	3.80409e33	0.751269
$498$	0	0
$499$	3.46371e33	0.650555	0.325278	−	0.945619i	$-0.394542\pi$
$499$	3.46371e33	0.650555	0.325278	+	0.945619i	$0.394542\pi$
$500$	0	0
$501$	3.74684e32	0.0669413
$502$	0	0
$503$	−1.02261e34	−1.73824	−0.869121	−	0.494599i	$-0.835315\pi$
$503$	−1.02261e34	−1.73824	−0.869121	+	0.494599i	$0.835315\pi$
$504$	0	0
$505$	2.48382e33	0.401770
$506$	0	0
$507$	−6.46663e31	−0.00995585
$508$	0	0
$509$	−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
$512$	0	0
$513$	2.31066e33	0.307093
$514$	0	0
$515$	−5.19665e33	−0.657860
$516$	0	0
$517$	−4.05922e33	−0.489566
$518$	0	0
$519$	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	$0.672123\pi$
$522$	0	0
$523$	4.23584e33	0.442250	0.221125	−	0.975245i	$-0.429027\pi$
$523$	4.23584e33	0.442250	0.221125	+	0.975245i	$0.429027\pi$
$524$	0	0
$525$	7.27808e32	0.0724479
$526$	0	0
$527$	7.07281e33	0.671366
$528$	0	0
$529$	−3.67507e33	−0.332713
$530$	0	0
$531$	−6.98544e33	−0.603271
$532$	0	0
$533$	2.05168e34	1.69052
$534$	0	0
$535$	2.13813e33	0.168117
$536$	0	0
$537$	−6.84880e32	−0.0513968
$538$	0	0
$539$	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	$0.463339\pi$
$542$	0	0
$543$	6.21740e32	0.0406080
$544$	0	0
$545$	−5.66820e33	−0.353581
$546$	0	0
$547$	1.80091e33	0.107313	0.0536563	−	0.998559i	$-0.482912\pi$
$547$	1.80091e33	0.107313	0.0536563	+	0.998559i	$0.482912\pi$
$548$	0	0
$549$	−2.03542e34	−1.15878
$550$	0	0
$551$	2.91220e34	1.58426
$552$	0	0
$553$	3.29216e34	1.71166
$554$	0	0
$555$	1.71626e33	0.0852944
$556$	0	0
$557$	3.61276e34	1.71652	0.858261	−	0.513214i	$-0.171545\pi$
$557$	3.61276e34	1.71652	0.858261	+	0.513214i	$0.171545\pi$
$558$	0	0
$559$	3.52550e33	0.160167
$560$	0	0
$561$	3.77328e33	0.163940
$562$	0	0
$563$	−2.65943e34	−1.10518	−0.552591	−	0.833452i	$-0.686361\pi$
$563$	−2.65943e34	−1.10518	−0.552591	+	0.833452i	$0.686361\pi$
$564$	0	0
$565$	−1.56537e34	−0.622315
$566$	0	0
$567$	2.83562e34	1.07860
$568$	0	0
$569$	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	$-0.756176\pi$
$571$	−4.13744e34	−1.44139	−0.720693	+	0.693254i	$0.756176\pi$
$572$	0	0
$573$	−3.51901e33	−0.117351
$574$	0	0
$575$	1.56028e34	0.498142
$576$	0	0
$577$	−3.07665e34	−0.940548	−0.470274	−	0.882520i	$-0.655845\pi$
$577$	−3.07665e34	−0.940548	−0.470274	+	0.882520i	$0.655845\pi$
$578$	0	0
$579$	3.68573e32	0.0107905
$580$	0	0
$581$	−3.67263e32	−0.0102985
$582$	0	0
$583$	6.16617e33	0.165637
$584$	0	0
$585$	−2.50933e34	−0.645818
$586$	0	0
$587$	2.58213e34	0.636798	0.318399	−	0.947957i	$-0.396855\pi$
$587$	2.58213e34	0.636798	0.318399	+	0.947957i	$0.396855\pi$
$588$	0	0
$589$	−3.72879e34	−0.881307
$590$	0	0
$591$	1.80708e33	0.0409386
$592$	0	0
$593$	4.00098e34	0.868925	0.434463	−	0.900690i	$-0.356938\pi$
$593$	4.00098e34	0.868925	0.434463	+	0.900690i	$0.356938\pi$
$594$	0	0
$595$	−3.70198e34	−0.770854
$596$	0	0
$597$	3.16920e33	0.0632806
$598$	0	0
$599$	2.84196e34	0.544230	0.272115	−	0.962265i	$-0.412277\pi$
$599$	2.84196e34	0.544230	0.272115	+	0.962265i	$0.412277\pi$
$600$	0	0
$601$	−1.02008e34	−0.187371	−0.0936856	−	0.995602i	$-0.529865\pi$
$601$	−1.02008e34	−0.187371	−0.0936856	+	0.995602i	$0.529865\pi$
$602$	0	0
$603$	−1.04460e35	−1.84071
$604$	0	0
$605$	3.48110e34	0.588538
$606$	0	0
$607$	−7.37377e34	−1.19628	−0.598138	−	0.801393i	$-0.704092\pi$
$607$	−7.37377e34	−1.19628	−0.598138	+	0.801393i	$0.704092\pi$
$608$	0	0
$609$	−8.33070e33	−0.129708
$610$	0	0
$611$	−2.45811e34	−0.367355
$612$	0	0
$613$	−9.86145e34	−1.41477	−0.707384	−	0.706830i	$-0.750125\pi$
$613$	−9.86145e34	−1.41477	−0.707384	+	0.706830i	$0.750125\pi$
$614$	0	0
$615$	−7.80172e33	−0.107461
$616$	0	0
$617$	−6.22897e34	−0.823857	−0.411928	−	0.911216i	$-0.635145\pi$
$617$	−6.22897e34	−0.823857	−0.411928	+	0.911216i	$0.635145\pi$
$618$	0	0
$619$	1.66187e34	0.211089	0.105544	−	0.994415i	$-0.466341\pi$
$619$	1.66187e34	0.211089	0.105544	+	0.994415i	$0.466341\pi$
$620$	0	0
$621$	−1.41704e34	−0.172876
$622$	0	0
$623$	1.45379e35	1.70373
$624$	0	0
$625$	−1.62662e33	−0.0183141
$626$	0	0
$627$	−1.98928e34	−0.215204
$628$	0	0
$629$	1.36435e35	1.41838
$630$	0	0
$631$	5.71133e34	0.570650	0.285325	−	0.958431i	$-0.407898\pi$
$631$	5.71133e34	0.570650	0.285325	+	0.958431i	$0.407898\pi$
$632$	0	0
$633$	7.19801e33	0.0691299
$634$	0	0
$635$	1.24855e33	0.0115274
$636$	0	0
$637$	2.90168e34	0.257576
$638$	0	0
$639$	−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	$0.483229\pi$
$642$	0	0
$643$	1.37614e35	1.08649	0.543246	−	0.839574i	$-0.317195\pi$
$643$	1.37614e35	1.08649	0.543246	+	0.839574i	$0.317195\pi$
$644$	0	0
$645$	−1.34060e33	−0.0101813
$646$	0	0
$647$	−9.39917e34	−0.686730	−0.343365	−	0.939202i	$-0.611567\pi$
$647$	−9.39917e34	−0.686730	−0.343365	+	0.939202i	$0.611567\pi$
$648$	0	0
$649$	1.20966e35	0.850364
$650$	0	0
$651$	1.06666e34	0.0721549
$652$	0	0
$653$	−1.48718e35	−0.968164	−0.484082	−	0.875023i	$-0.660846\pi$
$653$	−1.48718e35	−0.968164	−0.484082	+	0.875023i	$0.660846\pi$
$654$	0	0
$655$	4.70206e34	0.294626
$656$	0	0
$657$	−3.38611e34	−0.204237
$658$	0	0
$659$	1.21873e35	0.707683	0.353842	−	0.935305i	$-0.384875\pi$
$659$	1.21873e35	0.707683	0.353842	+	0.935305i	$0.384875\pi$
$660$	0	0
$661$	2.07522e35	1.16023	0.580117	−	0.814533i	$-0.303007\pi$
$661$	2.07522e35	1.16023	0.580117	+	0.814533i	$0.303007\pi$
$662$	0	0
$663$	2.28495e34	0.123015
$664$	0	0
$665$	1.95169e35	1.01190
$666$	0	0
$667$	−1.78594e35	−0.891852
$668$	0	0
$669$	−3.75927e34	−0.180833
$670$	0	0
$671$	3.52471e35	1.63340
$672$	0	0
$673$	−2.63064e34	−0.117455	−0.0587277	−	0.998274i	$-0.518704\pi$
$673$	−2.63064e34	−0.117455	−0.0587277	+	0.998274i	$0.518704\pi$
$674$	0	0
$675$	−2.99967e34	−0.129055
$676$	0	0
$677$	1.31255e35	0.544198	0.272099	−	0.962269i	$-0.412282\pi$
$677$	1.31255e35	0.544198	0.272099	+	0.962269i	$0.412282\pi$
$678$	0	0
$679$	−3.54064e35	−1.41485
$680$	0	0
$681$	2.80542e33	0.0108058
$682$	0	0
$683$	4.53998e35	1.68576	0.842879	−	0.538104i	$-0.180859\pi$
$683$	4.53998e35	1.68576	0.842879	+	0.538104i	$0.180859\pi$
$684$	0	0
$685$	−1.47410e35	−0.527710
$686$	0	0
$687$	−5.07426e34	−0.175151
$688$	0	0
$689$	3.73399e34	0.124289
$690$	0	0
$691$	−1.42914e35	−0.458773	−0.229387	−	0.973335i	$-0.573672\pi$
$691$	−1.42914e35	−0.458773	−0.229387	+	0.973335i	$0.573672\pi$
$692$	0	0
$693$	−4.96796e35	−1.53820
$694$	0	0
$695$	1.36622e34	0.0408049
$696$	0	0
$697$	−6.20201e35	−1.78699
$698$	0	0
$699$	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	$0.299771\pi$
$702$	0	0
$703$	−7.19285e35	−1.86191
$704$	0	0
$705$	9.34719e33	0.0233516
$706$	0	0
$707$	2.97781e35	0.718050
$708$	0	0
$709$	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
$712$	0	0
$713$	2.28672e35	0.496127
$714$	0	0
$715$	4.34538e35	0.910337
$716$	0	0
$717$	9.61357e34	0.194489
$718$	0	0
$719$	−8.06410e35	−1.57560	−0.787798	−	0.615934i	$-0.788779\pi$
$719$	−8.06410e35	−1.57560	−0.787798	+	0.615934i	$0.788779\pi$
$720$	0	0
$721$	−6.23019e35	−1.17574
$722$	0	0
$723$	9.82443e34	0.179093
$724$	0	0
$725$	−3.78058e35	−0.665784
$726$	0	0
$727$	4.49933e35	0.765539	0.382770	−	0.923844i	$-0.374970\pi$
$727$	4.49933e35	0.765539	0.382770	+	0.923844i	$0.374970\pi$
$728$	0	0
$729$	−5.67325e35	−0.932691
$730$	0	0
$731$	−1.06572e35	−0.169307
$732$	0	0
$733$	−1.09791e36	−1.68565	−0.842827	−	0.538185i	$-0.819110\pi$
$733$	−1.09791e36	−1.68565	−0.842827	+	0.538185i	$0.819110\pi$
$734$	0	0
$735$	−1.10339e34	−0.0163733
$736$	0	0
$737$	1.80893e36	2.59464
$738$	0	0
$739$	6.34879e35	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$739$	6.34879e35	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$740$	0	0
$741$	−1.20463e35	−0.161483
$742$	0	0
$743$	6.17895e35	0.800856	0.400428	−	0.916328i	$-0.368861\pi$
$743$	6.17895e35	0.800856	0.400428	+	0.916328i	$0.368861\pi$
$744$	0	0
$745$	3.82583e35	0.479481
$746$	0	0
$747$	7.52529e33	0.00912044
$748$	0	0
$749$	2.56337e35	0.300461
$750$	0	0
$751$	−6.31220e35	−0.715619	−0.357809	−	0.933795i	$-0.616476\pi$
$751$	−6.31220e35	−0.715619	−0.357809	+	0.933795i	$0.616476\pi$
$752$	0	0
$753$	1.12546e35	0.123422
$754$	0	0
$755$	9.04290e34	0.0959336
$756$	0	0
$757$	2.78268e35	0.285605	0.142802	−	0.989751i	$-0.454389\pi$
$757$	2.78268e35	0.285605	0.142802	+	0.989751i	$0.454389\pi$
$758$	0	0
$759$	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	$0.455289\pi$
$762$	0	0
$763$	−6.79552e35	−0.631926
$764$	0	0
$765$	7.58543e35	0.682673
$766$	0	0
$767$	7.32523e35	0.638086
$768$	0	0
$769$	−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
$772$	0	0
$773$	1.26764e36	1.00173	0.500866	−	0.865525i	$-0.333015\pi$
$773$	1.26764e36	1.00173	0.500866	+	0.865525i	$0.333015\pi$
$774$	0	0
$775$	4.84067e35	0.370368
$776$	0	0
$777$	2.05760e35	0.152440
$778$	0	0
$779$	3.26970e36	2.34580
$780$	0	0
$781$	1.34979e36	0.937838
$782$	0	0
$783$	3.43351e35	0.231055
$784$	0	0
$785$	−2.83828e35	−0.185006
$786$	0	0
$787$	−1.69750e36	−1.07183	−0.535915	−	0.844272i	$-0.680033\pi$
$787$	−1.69750e36	−1.07183	−0.535915	+	0.844272i	$0.680033\pi$
$788$	0	0
$789$	−2.42028e35	−0.148048
$790$	0	0
$791$	−1.87669e36	−1.11221
$792$	0	0
$793$	2.13443e36	1.22565
$794$	0	0
$795$	−1.41988e34	−0.00790067
$796$	0	0
$797$	−1.94040e36	−1.04631	−0.523157	−	0.852236i	$-0.675246\pi$
$797$	−1.94040e36	−1.04631	−0.523157	+	0.852236i	$0.675246\pi$
$798$	0	0
$799$	7.43058e35	0.388319
$800$	0	0
$801$	−2.97884e36	−1.50883
$802$	0	0
$803$	5.86368e35	0.287889
$804$	0	0
$805$	−1.19689e36	−0.569647
$806$	0	0
$807$	−8.15908e34	−0.0376463
$808$	0	0
$809$	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	$-0.586225\pi$
$811$	−1.23381e36	−0.535165	−0.267583	+	0.963535i	$0.586225\pi$
$812$	0	0
$813$	−3.81872e34	−0.0160615
$814$	0	0
$815$	2.46302e36	1.00461
$816$	0	0
$817$	5.61847e35	0.222250
$818$	0	0
$819$	−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	$0.503560\pi$
$822$	0	0
$823$	−1.64344e36	−0.593274	−0.296637	−	0.954990i	$-0.595865\pi$
$823$	−1.64344e36	−0.593274	−0.296637	+	0.954990i	$0.595865\pi$
$824$	0	0
$825$	2.58245e35	0.0904395
$826$	0	0
$827$	−4.86438e36	−1.65276	−0.826378	−	0.563116i	$-0.809602\pi$
$827$	−4.86438e36	−1.65276	−0.826378	+	0.563116i	$0.809602\pi$
$828$	0	0
$829$	−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
$832$	0	0
$833$	−8.77144e35	−0.272275
$834$	0	0
$835$	−1.30435e36	−0.392930
$836$	0	0
$837$	−4.39627e35	−0.128533
$838$	0	0
$839$	3.56272e36	1.01101	0.505506	−	0.862823i	$-0.331306\pi$
$839$	3.56272e36	1.01101	0.505506	+	0.862823i	$0.331306\pi$
$840$	0	0
$841$	6.96997e35	0.191991
$842$	0	0
$843$	7.19727e34	0.0192452
$844$	0	0
$845$	2.25117e35	0.0584385
$846$	0	0
$847$	4.17344e36	1.05184
$848$	0	0
$849$	−1.13328e35	−0.0277325
$850$	0	0
$851$	4.41108e36	1.04816
$852$	0	0
$853$	−2.91289e36	−0.672142	−0.336071	−	0.941837i	$-0.609098\pi$
$853$	−2.91289e36	−0.672142	−0.336071	+	0.941837i	$0.609098\pi$
$854$	0	0
$855$	−3.99905e36	−0.896148
$856$	0	0
$857$	−6.85495e36	−1.49192	−0.745958	−	0.665993i	$-0.768008\pi$
$857$	−6.85495e36	−1.49192	−0.745958	+	0.665993i	$0.768008\pi$
$858$	0	0
$859$	−6.94361e36	−1.46781	−0.733907	−	0.679250i	$-0.762305\pi$
$859$	−6.94361e36	−1.46781	−0.733907	+	0.679250i	$0.762305\pi$
$860$	0	0
$861$	−9.35337e35	−0.192056
$862$	0	0
$863$	5.37478e35	0.107208	0.0536038	−	0.998562i	$-0.482929\pi$
$863$	5.37478e35	0.107208	0.0536038	+	0.998562i	$0.482929\pi$
$864$	0	0
$865$	−1.61763e36	−0.313456
$866$	0	0
$867$	−1.25448e35	−0.0236171
$868$	0	0
$869$	1.16814e37	2.13673
$870$	0	0
$871$	1.09542e37	1.94694
$872$	0	0
$873$	7.25483e36	1.25300
$874$	0	0
$875$	−6.68845e36	−1.12260
$876$	0	0
$877$	1.45532e36	0.237391	0.118695	−	0.992931i	$-0.462129\pi$
$877$	1.45532e36	0.237391	0.118695	+	0.992931i	$0.462129\pi$
$878$	0	0
$879$	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	$0.296613\pi$
$882$	0	0
$883$	1.08821e35	0.0163006	0.00815031	−	0.999967i	$-0.497406\pi$
$883$	1.08821e35	0.0163006	0.00815031	+	0.999967i	$0.497406\pi$
$884$	0	0
$885$	−2.78549e35	−0.0405612
$886$	0	0
$887$	7.82913e36	1.10833	0.554164	−	0.832407i	$-0.313038\pi$
$887$	7.82913e36	1.10833	0.554164	+	0.832407i	$0.313038\pi$
$888$	0	0
$889$	1.49686e35	0.0206020
$890$	0	0
$891$	1.00615e37	1.34646
$892$	0	0
$893$	−3.91741e36	−0.509748
$894$	0	0
$895$	2.38421e36	0.301687
$896$	0	0
$897$	7.38750e35	0.0909059
$898$	0	0
$899$	−5.54076e36	−0.663091
$900$	0	0
$901$	−1.12874e36	−0.131382
$902$	0	0
$903$	−1.60723e35	−0.0181962
$904$	0	0
$905$	−2.16441e36	−0.238359
$906$	0	0
$907$	−1.06412e36	−0.113999	−0.0569993	−	0.998374i	$-0.518153\pi$
$907$	−1.06412e36	−0.113999	−0.0569993	+	0.998374i	$0.518153\pi$
$908$	0	0
$909$	−6.10159e36	−0.635909
$910$	0	0
$911$	−7.34268e36	−0.744517	−0.372259	−	0.928129i	$-0.621417\pi$
$911$	−7.34268e36	−0.744517	−0.372259	+	0.928129i	$0.621417\pi$
$912$	0	0
$913$	−1.30314e35	−0.0128561
$914$	0	0
$915$	−8.11637e35	−0.0779109
$916$	0	0
$917$	5.63723e36	0.526561
$918$	0	0
$919$	−5.22115e36	−0.474594	−0.237297	−	0.971437i	$-0.576262\pi$
$919$	−5.22115e36	−0.474594	−0.237297	+	0.971437i	$0.576262\pi$
$920$	0	0
$921$	1.09322e36	0.0967080
$922$	0	0
$923$	8.17379e36	0.703724
$924$	0	0
$925$	9.33766e36	0.782467
$926$	0	0
$927$	1.27658e37	1.04124
$928$	0	0
$929$	−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
$932$	0	0
$933$	−8.29996e35	−0.0624533
$934$	0	0
$935$	−1.31356e37	−0.962287
$936$	0	0
$937$	5.72513e36	0.408358	0.204179	−	0.978934i	$-0.434548\pi$
$937$	5.72513e36	0.408358	0.204179	+	0.978934i	$0.434548\pi$
$938$	0	0
$939$	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	$0.788341\pi$
$942$	0	0
$943$	−2.00518e37	−1.32055
$944$	0	0
$945$	2.30105e36	0.147580
$946$	0	0
$947$	−2.10624e37	−1.31563	−0.657814	−	0.753180i	$-0.728519\pi$
$947$	−2.10624e37	−1.31563	−0.657814	+	0.753180i	$0.728519\pi$
$948$	0	0
$949$	3.55081e36	0.216023
$950$	0	0
$951$	1.93161e36	0.114462
$952$	0	0
$953$	−1.00956e36	−0.0582736	−0.0291368	−	0.999575i	$-0.509276\pi$
$953$	−1.00956e36	−0.0582736	−0.0291368	+	0.999575i	$0.509276\pi$
$954$	0	0
$955$	1.22504e37	0.688825
$956$	0	0
$957$	−2.95595e36	−0.161919
$958$	0	0
$959$	−1.76728e37	−0.943131
$960$	0	0
$961$	−1.21384e37	−0.631130
$962$	0	0
$963$	−5.25239e36	−0.266090
$964$	0	0
$965$	−1.28308e36	−0.0633378
$966$	0	0
$967$	−5.41536e36	−0.260493	−0.130247	−	0.991482i	$-0.541577\pi$
$967$	−5.41536e36	−0.260493	−0.130247	+	0.991482i	$0.541577\pi$
$968$	0	0
$969$	3.64146e36	0.170698
$970$	0	0
$971$	5.44528e36	0.248759	0.124380	−	0.992235i	$-0.460306\pi$
$971$	5.44528e36	0.248759	0.124380	+	0.992235i	$0.460306\pi$
$972$	0	0
$973$	1.63795e36	0.0729271
$974$	0	0
$975$	1.56383e36	0.0678629
$976$	0	0
$977$	−3.00155e37	−1.26959	−0.634794	−	0.772681i	$-0.718915\pi$
$977$	−3.00155e37	−1.26959	−0.634794	+	0.772681i	$0.718915\pi$
$978$	0	0
$979$	5.15842e37	2.12683
$980$	0	0
$981$	1.39242e37	0.559637
$982$	0	0
$983$	−2.29888e36	−0.0900737	−0.0450368	−	0.998985i	$-0.514341\pi$
$983$	−2.29888e36	−0.0900737	−0.0450368	+	0.998985i	$0.514341\pi$
$984$	0	0
$985$	−6.29081e36	−0.240300
$986$	0	0
$987$	1.12062e36	0.0417344
$988$	0	0
$989$	−3.44558e36	−0.125115
$990$	0	0
$991$	−9.88586e36	−0.350021	−0.175010	−	0.984567i	$-0.555996\pi$
$991$	−9.88586e36	−0.350021	−0.175010	+	0.984567i	$0.555996\pi$
$992$	0	0
$993$	4.67360e36	0.161356
$994$	0	0
$995$	−1.10326e37	−0.371442
$996$	0	0
$997$	2.20132e37	0.722759	0.361380	−	0.932419i	$-0.382306\pi$
$997$	2.20132e37	0.722759	0.361380	+	0.932419i	$0.382306\pi$
$998$	0	0
$999$	−8.48041e36	−0.271549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.26.a.a.1.1		1
4.3	odd	2		2.26.a.a.1.1	✓	1
12.11	even	2		18.26.a.c.1.1		1
20.3	even	4		50.26.b.a.49.2		2
20.7	even	4		50.26.b.a.49.1		2
20.19	odd	2		50.26.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.a.1.1	✓	1	4.3	odd	2
16.26.a.a.1.1		1	1.1	even	1	trivial
18.26.a.c.1.1		1	12.11	even	2
50.26.a.b.1.1		1	20.19	odd	2
50.26.b.a.49.1		2	20.7	even	4
50.26.b.a.49.2		2	20.3	even	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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