LMFDB - Embedded newform 18.26.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,26,Mod(1,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, 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("18.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	18.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:	$71.2794203914$
Analytic rank:	$1$
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	$\chi$	$=$	18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4096.00 q^{2} +1.67772e7 q^{4} -3.41005e8 q^{5} -4.08826e10 q^{7} +6.87195e10 q^{8} -1.39676e12 q^{10} +1.45062e13 q^{11} +8.78440e13 q^{13} -1.67455e14 q^{14} +2.81475e14 q^{16} +2.65543e15 q^{17} -1.39994e16 q^{19} -5.72112e15 q^{20} +5.94175e16 q^{22} -8.58528e16 q^{23} -1.81739e17 q^{25} +3.59809e17 q^{26} -6.85897e17 q^{28} -2.08023e18 q^{29} +2.66353e18 q^{31} +1.15292e18 q^{32} +1.08766e19 q^{34} +1.39412e19 q^{35} -5.13796e19 q^{37} -5.73416e19 q^{38} -2.34337e19 q^{40} -2.33560e20 q^{41} -4.01336e19 q^{43} +2.43374e20 q^{44} -3.51653e20 q^{46} -2.79826e20 q^{47} +3.30321e20 q^{49} -7.44401e20 q^{50} +1.47378e21 q^{52} -4.25070e20 q^{53} -4.94670e21 q^{55} -2.80943e21 q^{56} -8.52062e21 q^{58} +8.33891e21 q^{59} +2.42979e22 q^{61} +1.09098e22 q^{62} +4.72237e21 q^{64} -2.99553e22 q^{65} -1.24700e23 q^{67} +4.45507e22 q^{68} +5.71031e22 q^{70} +9.30490e22 q^{71} +4.04218e22 q^{73} -2.10451e23 q^{74} -2.34871e23 q^{76} -5.93053e23 q^{77} -8.05270e23 q^{79} -9.59845e22 q^{80} -9.56661e23 q^{82} -8.98335e21 q^{83} -9.05514e23 q^{85} -1.64387e23 q^{86} +9.96860e23 q^{88} -3.55600e24 q^{89} -3.59129e24 q^{91} -1.44037e24 q^{92} -1.14617e24 q^{94} +4.77388e24 q^{95} -8.66049e24 q^{97} +1.35300e24 q^{98} +O(q^{100})\)

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
$3$	0	0
$3$	0	0
$4$	1.67772e7	0.500000
$5$	−3.41005e8	−0.624649	−0.312325	−	0.949975i	$-0.601108\pi$
$5$	−3.41005e8	−0.624649	−0.312325	+	0.949975i	$0.601108\pi$
$6$	0	0
$7$	−4.08826e10	−1.11638	−0.558192	−	0.829712i	$-0.688505\pi$
$7$	−4.08826e10	−1.11638	−0.558192	+	0.829712i	$0.688505\pi$
$8$	6.87195e10	0.353553
$9$	0	0
$10$	−1.39676e12	−0.441694
$11$	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	$0.324863\pi$
$14$	−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	$0.313596\pi$
$18$	0	0
$19$	−1.39994e16	−1.45108	−0.725538	−	0.688182i	$-0.758409\pi$
$19$	−1.39994e16	−1.45108	−0.725538	+	0.688182i	$0.758409\pi$
$20$	−5.72112e15	−0.312325
$21$	0	0
$22$	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	$0.633926\pi$
$24$	0	0
$25$	−1.81739e17	−0.609813
$26$	3.59809e17	0.739444
$27$	0	0
$28$	−6.85897e17	−0.558192
$29$	−2.08023e18	−1.09178	−0.545892	−	0.837856i	$-0.683809\pi$
$29$	−2.08023e18	−1.09178	−0.545892	+	0.837856i	$0.683809\pi$
$30$	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
$33$	0	0
$34$	1.08766e19	0.781642
$35$	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	$0.721714\pi$
$38$	−5.73416e19	−1.02607
$39$	0	0
$40$	−2.34337e19	−0.220847
$41$	−2.33560e20	−1.61659	−0.808295	−	0.588778i	$-0.799609\pi$
$41$	−2.33560e20	−1.61659	−0.808295	+	0.588778i	$0.799609\pi$
$42$	0	0
$43$	−4.01336e19	−0.153162	−0.0765812	−	0.997063i	$-0.524400\pi$
$43$	−4.01336e19	−0.153162	−0.0765812	+	0.997063i	$0.524400\pi$
$44$	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	$0.556201\pi$
$48$	0	0
$49$	3.30321e20	0.246312
$50$	−7.44401e20	−0.431203
$51$	0	0
$52$	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	$0.518927\pi$
$54$	0	0
$55$	−4.94670e21	−0.870526
$56$	−2.80943e21	−0.394701
$57$	0	0
$58$	−8.52062e21	−0.772007
$59$	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	$0.300692\pi$
$62$	1.09098e22	0.429459
$63$	0	0
$64$	4.72237e21	0.125000
$65$	−2.99553e22	−0.653215
$66$	0	0
$67$	−1.24700e23	−1.86179	−0.930897	−	0.365282i	$-0.880973\pi$
$67$	−1.24700e23	−1.86179	−0.930897	+	0.365282i	$0.880973\pi$
$68$	4.45507e22	0.552704
$69$	0	0
$70$	5.71031e22	0.493099
$71$	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	$0.467064\pi$
$74$	−2.10451e23	−0.907307
$75$	0	0
$76$	−2.34871e23	−0.725538
$77$	−5.93053e23	−1.55582
$78$	0	0
$79$	−8.05270e23	−1.53321	−0.766607	−	0.642116i	$-0.778057\pi$
$79$	−8.05270e23	−1.53321	−0.766607	+	0.642116i	$0.778057\pi$
$80$	−9.59845e22	−0.156162
$81$	0	0
$82$	−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	$0.501468\pi$
$84$	0	0
$85$	−9.05514e23	−0.690492
$86$	−1.64387e23	−0.108302
$87$	0	0
$88$	9.96860e23	0.492721
$89$	−3.55600e24	−1.52611	−0.763057	−	0.646331i	$-0.776303\pi$
$89$	−3.55600e24	−1.52611	−0.763057	+	0.646331i	$0.776303\pi$
$90$	0	0
$91$	−3.59129e24	−1.16744
$92$	−1.44037e24	−0.408438
$93$	0	0
$94$	−1.14617e24	−0.248399
$95$	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	$0.718454\pi$
$98$	1.35300e24	0.174169
$99$	0	0
$100$	−3.04907e24	−0.304907
$101$	−7.28380e24	−0.643193	−0.321596	−	0.946877i	$-0.604219\pi$
$101$	−7.28380e24	−0.643193	−0.321596	+	0.946877i	$0.604219\pi$
$102$	0	0
$103$	1.52392e25	1.05317	0.526583	−	0.850123i	$-0.323473\pi$
$103$	1.52392e25	1.05317	0.526583	+	0.850123i	$0.323473\pi$
$104$	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	$0.457035\pi$
$108$	0	0
$109$	−1.66220e25	−0.566047	−0.283024	−	0.959113i	$-0.591337\pi$
$109$	−1.66220e25	−0.566047	−0.283024	+	0.959113i	$0.591337\pi$
$110$	−2.02617e25	−0.615555
$111$	0	0
$112$	−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	$0.334020\pi$
$114$	0	0
$115$	2.92763e25	0.510261
$116$	−3.49005e25	−0.545892
$117$	0	0
$118$	3.41562e25	0.431463
$119$	−1.08561e26	−1.23406
$120$	0	0
$121$	1.02083e26	0.942189
$122$	9.95244e25	0.828766
$123$	0	0
$124$	4.46867e25	0.303673
$125$	1.63601e26	1.00557
$126$	0	0
$127$	−3.66137e24	−0.0184543	−0.00922713	−	0.999957i	$-0.502937\pi$
$127$	−3.66137e24	−0.0184543	−0.00922713	+	0.999957i	$0.502937\pi$
$128$	1.93428e25	0.0883883
$129$	0	0
$130$	−1.22697e26	−0.461893
$131$	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
$134$	−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	$0.361186\pi$
$138$	0	0
$139$	−4.00646e25	−0.0653245	−0.0326622	−	0.999466i	$-0.510399\pi$
$139$	−4.00646e25	−0.0653245	−0.0326622	+	0.999466i	$0.510399\pi$
$140$	2.33894e26	0.348674
$141$	0	0
$142$	3.81129e26	0.475847
$143$	1.27428e27	1.45736
$144$	0	0
$145$	7.09370e26	0.681982
$146$	1.65568e26	0.146071
$147$	0	0
$148$	−8.62007e26	−0.641563
$149$	−1.12193e27	−0.767601	−0.383801	−	0.923416i	$-0.625385\pi$
$149$	−1.12193e27	−0.767601	−0.383801	+	0.923416i	$0.625385\pi$
$150$	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
$153$	0	0
$154$	−2.42914e27	−1.10013
$155$	−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	$0.547312\pi$
$158$	−3.29839e27	−1.08415
$159$	0	0
$160$	−3.93152e26	−0.110423
$161$	3.50989e27	0.911947
$162$	0	0
$163$	−7.22281e27	−1.60828	−0.804139	−	0.594442i	$-0.797373\pi$
$163$	−7.22281e27	−1.60828	−0.804139	+	0.594442i	$0.797373\pi$
$164$	−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	$0.601844\pi$
$168$	0	0
$169$	6.60156e26	0.0935542
$170$	−3.70899e27	−0.488252
$171$	0	0
$172$	−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	$0.419272\pi$
$174$	0	0
$175$	7.42995e27	0.680786
$176$	4.08314e27	0.348406
$177$	0	0
$178$	−1.45654e28	−1.07913
$179$	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	$0.561106\pi$
$182$	−1.47099e28	−0.825503
$183$	0	0
$184$	−5.89976e27	−0.288809
$185$	1.75207e28	0.801503
$186$	0	0
$187$	3.85202e28	1.54052
$188$	−4.69471e27	−0.175645
$189$	0	0
$190$	1.95538e28	0.640931
$191$	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	$0.516145\pi$
$194$	−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	$0.438390\pi$
$198$	0	0
$199$	3.23533e28	0.594641	0.297321	−	0.954778i	$-0.403907\pi$
$199$	3.23533e28	0.594641	0.297321	+	0.954778i	$0.403907\pi$
$200$	−1.24890e28	−0.215602
$201$	0	0
$202$	−2.98345e28	−0.454806
$203$	8.50453e28	1.21885
$204$	0	0
$205$	7.96451e28	1.00980
$206$	6.24198e28	0.744701
$207$	0	0
$208$	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
$213$	0	0
$214$	2.56822e28	0.190309
$215$	1.36858e28	0.0956728
$216$	0	0
$217$	−1.08892e29	−0.678032
$218$	−6.80838e28	−0.400256
$219$	0	0
$220$	−8.29918e28	−0.435263
$221$	2.33263e29	1.15596
$222$	0	0
$223$	−3.83771e29	−1.69927	−0.849634	−	0.527373i	$-0.823177\pi$
$223$	−3.83771e29	−1.69927	−0.849634	+	0.527373i	$0.823177\pi$
$224$	−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	$0.516168\pi$
$228$	0	0
$229$	5.18014e29	1.64588	0.822939	−	0.568129i	$-0.192333\pi$
$229$	5.18014e29	1.64588	0.822939	+	0.568129i	$0.192333\pi$
$230$	1.19916e29	0.360809
$231$	0	0
$232$	−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	$0.454440\pi$
$234$	0	0
$235$	9.54223e28	0.219433
$236$	1.39904e29	0.305091
$237$	0	0
$238$	−4.44665e29	−0.872612
$239$	−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	$0.818303\pi$
$242$	4.18134e29	0.666228
$243$	0	0
$244$	4.07652e29	0.586026
$245$	−1.12641e29	−0.153859
$246$	0	0
$247$	−1.22977e30	−1.51744
$248$	1.83037e29	0.214730
$249$	0	0
$250$	6.70111e29	0.711044
$251$	−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
$254$	−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	$0.660294\pi$
$258$	0	0
$259$	2.10053e30	1.43246
$260$	−5.02566e29	−0.326608
$261$	0	0
$262$	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	$0.255140\pi$
$264$	0	0
$265$	1.44951e29	0.0742418
$266$	2.34428e30	1.14548
$267$	0	0
$268$	−2.09212e30	−0.930897
$269$	−8.32933e29	−0.353758	−0.176879	−	0.984233i	$-0.556600\pi$
$269$	−8.32933e29	−0.353758	−0.176879	+	0.984233i	$0.556600\pi$
$270$	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
$273$	0	0
$274$	1.77062e30	0.597371
$275$	−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	$0.177964\pi$
$278$	−1.64105e29	−0.0461914
$279$	0	0
$280$	9.58032e29	0.246550
$281$	7.34745e29	0.180846	0.0904228	−	0.995903i	$-0.471178\pi$
$281$	7.34745e29	0.180846	0.0904228	+	0.995903i	$0.471178\pi$
$282$	0	0
$283$	−1.15692e30	−0.260600	−0.130300	−	0.991475i	$-0.541594\pi$
$283$	−1.15692e30	−0.260600	−0.130300	+	0.991475i	$0.541594\pi$
$284$	1.56110e30	0.336475
$285$	0	0
$286$	5.21947e30	1.03051
$287$	9.54854e30	1.80473
$288$	0	0
$289$	1.28066e30	0.221927
$290$	2.90558e30	0.482234
$291$	0	0
$292$	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	$0.476836\pi$
$294$	0	0
$295$	−2.84361e30	−0.381149
$296$	−3.53078e30	−0.453653
$297$	0	0
$298$	−4.59541e30	−0.542776
$299$	−7.54165e30	−0.854233
$300$	0	0
$301$	1.64077e30	0.170988
$302$	−1.08619e30	−0.108597
$303$	0	0
$304$	−3.94049e30	−0.362769
$305$	−8.28573e30	−0.732121
$306$	0	0
$307$	1.11603e31	0.908755	0.454378	−	0.890809i	$-0.349862\pi$
$307$	1.11603e31	0.908755	0.454378	+	0.890809i	$0.349862\pi$
$308$	−9.94977e30	−0.777910
$309$	0	0
$310$	−3.72031e30	−0.268261
$311$	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	$0.620674\pi$
$314$	−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	$0.319257\pi$
$318$	0	0
$319$	−3.01763e31	−1.52154
$320$	−1.61035e30	−0.0780811
$321$	0	0
$322$	1.43765e31	0.644844
$323$	−3.71744e31	−1.60403
$324$	0	0
$325$	−1.59646e31	−0.637701
$326$	−2.95846e31	−1.13722
$327$	0	0
$328$	−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
$333$	0	0
$334$	−1.56673e31	−0.444799
$335$	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	$0.637013\pi$
$338$	2.70400e30	0.0661528
$339$	0	0
$340$	−1.51920e31	−0.345246
$341$	3.86378e31	0.846413
$342$	0	0
$343$	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	$0.588969\pi$
$348$	0	0
$349$	3.37807e31	0.553796	0.276898	−	0.960899i	$-0.410694\pi$
$349$	3.37807e31	0.553796	0.276898	+	0.960899i	$0.410694\pi$
$350$	3.04331e31	0.481388
$351$	0	0
$352$	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	$0.600899\pi$
$354$	0	0
$355$	−3.17302e31	−0.420357
$356$	−5.96599e31	−0.763057
$357$	0	0
$358$	2.86380e31	0.341512
$359$	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
$362$	−2.59979e31	−0.269824
$363$	0	0
$364$	−6.02519e31	−0.583719
$365$	−1.37840e31	−0.129038
$366$	0	0
$367$	−6.93296e31	−0.606168	−0.303084	−	0.952964i	$-0.598016\pi$
$367$	−6.93296e31	−0.606168	−0.303084	+	0.952964i	$0.598016\pi$
$368$	−2.41654e31	−0.204219
$369$	0	0
$370$	7.17649e31	0.566748
$371$	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	$0.429618\pi$
$374$	1.57779e32	1.08931
$375$	0	0
$376$	−1.92295e31	−0.124200
$377$	−1.82736e32	−1.14171
$378$	0	0
$379$	6.25980e31	0.366075	0.183038	−	0.983106i	$-0.441407\pi$
$379$	6.25980e31	0.366075	0.183038	+	0.983106i	$0.441407\pi$
$380$	8.00924e31	0.453207
$381$	0	0
$382$	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	$0.667498\pi$
$384$	0	0
$385$	2.02234e32	0.971841
$386$	−1.54118e31	−0.0716988
$387$	0	0
$388$	−1.45299e32	−0.633674
$389$	5.55896e31	0.234760	0.117380	−	0.993087i	$-0.462550\pi$
$389$	5.55896e31	0.234760	0.117380	+	0.993087i	$0.462550\pi$
$390$	0	0
$391$	−2.27976e32	−0.902982
$392$	2.26995e31	0.0870845
$393$	0	0
$394$	7.55624e31	0.272021
$395$	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	$0.727760\pi$
$398$	1.32519e32	0.420475
$399$	0	0
$400$	−5.11549e31	−0.152453
$401$	2.79804e32	0.808258	0.404129	−	0.914702i	$-0.367575\pi$
$401$	2.79804e32	0.808258	0.404129	+	0.914702i	$0.367575\pi$
$402$	0	0
$403$	2.33975e32	0.635122
$404$	−1.22202e32	−0.321596
$405$	0	0
$406$	3.48346e32	0.861856
$407$	−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	$0.803164\pi$
$410$	3.26227e32	0.714038
$411$	0	0
$412$	2.55672e32	0.526583
$413$	−3.40916e32	−0.681196
$414$	0	0
$415$	3.06337e30	0.00576233
$416$	1.01277e32	0.184861
$417$	0	0
$418$	−8.31811e32	−1.42995
$419$	−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	$0.532833\pi$
$422$	3.00982e32	0.459341
$423$	0	0
$424$	−2.92106e31	−0.0420211
$425$	−4.82593e32	−0.674093
$426$	0	0
$427$	−9.93364e32	−1.30846
$428$	1.05194e32	0.134569
$429$	0	0
$430$	5.60569e31	0.0676509
$431$	−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	$0.461480\pi$
$434$	−4.46023e32	−0.479441
$435$	0	0
$436$	−2.78871e32	−0.283024
$437$	1.20189e33	1.18535
$438$	0	0
$439$	1.96041e33	1.82617	0.913084	−	0.407771i	$-0.133694\pi$
$439$	1.96041e33	1.82617	0.913084	+	0.407771i	$0.133694\pi$
$440$	−3.39935e32	−0.307778
$441$	0	0
$442$	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	$0.228615\pi$
$444$	0	0
$445$	1.21262e33	0.953286
$446$	−1.57193e33	−1.20156
$447$	0	0
$448$	−1.93063e32	−0.139548
$449$	−1.96738e33	−1.38296	−0.691480	−	0.722396i	$-0.743041\pi$
$449$	−1.96738e33	−1.38296	−0.691480	+	0.722396i	$0.743041\pi$
$450$	0	0
$451$	−3.38807e33	−2.25292
$452$	7.70148e32	0.498131
$453$	0	0
$454$	−1.17308e32	−0.0718006
$455$	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	$0.558800\pi$
$458$	2.12178e33	1.16381
$459$	0	0
$460$	4.91174e32	0.255131
$461$	3.73344e32	0.188733	0.0943666	−	0.995538i	$-0.469917\pi$
$461$	3.73344e32	0.188733	0.0943666	+	0.995538i	$0.469917\pi$
$462$	0	0
$463$	3.92901e33	1.88157	0.940787	−	0.338999i	$-0.110088\pi$
$463$	3.92901e33	1.88157	0.940787	+	0.338999i	$0.110088\pi$
$464$	−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	$0.343670\pi$
$468$	0	0
$469$	5.09807e33	2.07848
$470$	3.90850e32	0.155162
$471$	0	0
$472$	5.73045e32	0.215732
$473$	−5.82187e32	−0.213451
$474$	0	0
$475$	2.54424e33	0.884886
$476$	−1.82135e33	−0.617030
$477$	0	0
$478$	−4.01989e33	−1.29230
$479$	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
$482$	−4.10805e33	−1.19000
$483$	0	0
$484$	1.71268e33	0.471095
$485$	2.95327e33	0.791648
$486$	0	0
$487$	2.19049e33	0.557737	0.278869	−	0.960329i	$-0.410041\pi$
$487$	2.19049e33	0.557737	0.278869	+	0.960329i	$0.410041\pi$
$488$	1.66974e33	0.414383
$489$	0	0
$490$	−4.61379e32	−0.108794
$491$	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
$494$	−5.03712e33	−1.07299
$495$	0	0
$496$	7.49718e32	0.151837
$497$	−3.80409e33	−0.751269
$498$	0	0
$499$	−3.46371e33	−0.650555	−0.325278	−	0.945619i	$-0.605458\pi$
$499$	−3.46371e33	−0.650555	−0.325278	+	0.945619i	$0.605458\pi$
$500$	2.74478e33	0.502784
$501$	0	0
$502$	−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	$0.835315\pi$
$504$	0	0
$505$	2.48382e33	0.401770
$506$	−5.10116e33	−0.804984
$507$	0	0
$508$	−6.14275e31	−0.00922713
$509$	2.69685e33	0.395261	0.197630	−	0.980277i	$-0.436675\pi$
$509$	2.69685e33	0.395261	0.197630	+	0.980277i	$0.436675\pi$
$510$	0	0
$511$	−1.65255e33	−0.230618
$512$	3.24519e32	0.0441942
$513$	0	0
$514$	−5.26147e33	−0.682445
$515$	−5.19665e33	−0.657860
$516$	0	0
$517$	−4.05922e33	−0.489566
$518$	8.60379e33	1.01290
$519$	0	0
$520$	−2.05851e33	−0.230946
$521$	9.39972e33	1.02954	0.514770	−	0.857328i	$-0.327877\pi$
$521$	9.39972e33	1.02954	0.514770	+	0.857328i	$0.327877\pi$
$522$	0	0
$523$	−4.23584e33	−0.442250	−0.221125	−	0.975245i	$-0.570973\pi$
$523$	−4.23584e33	−0.442250	−0.221125	+	0.975245i	$0.570973\pi$
$524$	2.31338e33	0.235833
$525$	0	0
$526$	1.01203e34	0.983724
$527$	7.07281e33	0.671366
$528$	0	0
$529$	−3.67507e33	−0.332713
$530$	5.93721e32	0.0524969
$531$	0	0
$532$	9.60216e33	0.809979
$533$	−2.05168e34	−1.69052
$534$	0	0
$535$	−2.13813e33	−0.168117
$536$	−8.56932e33	−0.658244
$537$	0	0
$538$	−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
$543$	0	0
$544$	3.06150e33	0.195410
$545$	5.66820e33	0.353581
$546$	0	0
$547$	−1.80091e33	−0.107313	−0.0536563	−	0.998559i	$-0.517088\pi$
$547$	−1.80091e33	−0.107313	−0.0536563	+	0.998559i	$0.517088\pi$
$548$	7.25247e33	0.422405
$549$	0	0
$550$	−1.07984e34	−0.600935
$551$	2.91220e34	1.58426
$552$	0	0
$553$	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	$0.828455\pi$
$558$	0	0
$559$	−3.52550e33	−0.160167
$560$	3.92410e33	0.174337
$561$	0	0
$562$	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	$0.686361\pi$
$564$	0	0
$565$	−1.56537e34	−0.622315
$566$	−4.73876e33	−0.184272
$567$	0	0
$568$	6.39428e33	0.237923
$569$	−7.96966e33	−0.290093	−0.145046	−	0.989425i	$-0.546333\pi$
$569$	−7.96966e33	−0.290093	−0.145046	+	0.989425i	$0.546333\pi$
$570$	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
$573$	0	0
$574$	3.91108e34	1.27614
$575$	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	$0.655845\pi$
$578$	5.24558e33	0.156926
$579$	0	0
$580$	1.19012e34	0.340991
$581$	3.67263e32	0.0102985
$582$	0	0
$583$	−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	$0.396855\pi$
$588$	0	0
$589$	−3.72879e34	−0.881307
$590$	−1.16474e34	−0.269513
$591$	0	0
$592$	−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	$0.643062\pi$
$594$	0	0
$595$	3.70198e34	0.770854
$596$	−1.88228e34	−0.383801
$597$	0	0
$598$	−3.08906e34	−0.604034
$599$	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	$0.529865\pi$
$602$	6.72058e33	0.120907
$603$	0	0
$604$	−4.44904e33	−0.0767900
$605$	−3.48110e34	−0.588538
$606$	0	0
$607$	7.37377e34	1.19628	0.598138	−	0.801393i	$-0.295908\pi$
$607$	7.37377e34	1.19628	0.598138	+	0.801393i	$0.295908\pi$
$608$	−1.61402e34	−0.256516
$609$	0	0
$610$	−3.39384e34	−0.517688
$611$	−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	$0.750125\pi$
$614$	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	$0.364855\pi$
$618$	0	0
$619$	−1.66187e34	−0.211089	−0.105544	−	0.994415i	$-0.533659\pi$
$619$	−1.66187e34	−0.211089	−0.105544	+	0.994415i	$0.533659\pi$
$620$	−1.52384e34	−0.189689
$621$	0	0
$622$	3.47060e34	0.414978
$623$	1.45379e35	1.70373
$624$	0	0
$625$	−1.62662e33	−0.0183141
$626$	−4.74246e34	−0.523389
$627$	0	0
$628$	−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
$633$	0	0
$634$	8.07696e34	0.760558
$635$	1.24855e33	0.0115274
$636$	0	0
$637$	2.90168e34	0.257576
$638$	−1.23602e35	−1.07589
$639$	0	0
$640$	−6.59600e33	−0.0552117
$641$	−1.28313e34	−0.105329	−0.0526643	−	0.998612i	$-0.516771\pi$
$641$	−1.28313e34	−0.105329	−0.0526643	+	0.998612i	$0.516771\pi$
$642$	0	0
$643$	−1.37614e35	−1.08649	−0.543246	−	0.839574i	$-0.682805\pi$
$643$	−1.37614e35	−1.08649	−0.543246	+	0.839574i	$0.682805\pi$
$644$	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	$0.611567\pi$
$648$	0	0
$649$	1.20966e35	0.850364
$650$	−6.53912e34	−0.450923
$651$	0	0
$652$	−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	$0.339154\pi$
$654$	0	0
$655$	−4.70206e34	−0.294626
$656$	−6.57412e34	−0.404148
$657$	0	0
$658$	4.68584e34	0.277309
$659$	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	$0.303007\pi$
$662$	1.95425e35	1.07215
$663$	0	0
$664$	−6.17331e32	−0.00326150
$665$	−1.95169e35	−1.01190
$666$	0	0
$667$	1.78594e35	0.891852
$668$	−6.41733e34	−0.314520
$669$	0	0
$670$	1.74176e35	0.822343
$671$	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	$0.518704\pi$
$674$	−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	$0.587718\pi$
$678$	0	0
$679$	3.54064e35	1.41485
$680$	−6.22265e34	−0.244126
$681$	0	0
$682$	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	$0.180859\pi$
$684$	0	0
$685$	−1.47410e35	−0.527710
$686$	1.69255e35	0.594963
$687$	0	0
$688$	−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
$693$	0	0
$694$	−1.28300e35	−0.390152
$695$	1.36622e34	0.0408049
$696$	0	0
$697$	−6.20201e35	−1.78699
$698$	1.38366e35	0.391593
$699$	0	0
$700$	1.24654e35	0.340393
$701$	−4.38686e35	−1.17673	−0.588367	−	0.808594i	$-0.700229\pi$
$701$	−4.38686e35	−1.17673	−0.588367	+	0.808594i	$0.700229\pi$
$702$	0	0
$703$	7.19285e35	1.86191
$704$	6.85037e34	0.174203
$705$	0	0
$706$	−1.79602e35	−0.440811
$707$	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	$0.365046\pi$
$710$	−1.29967e35	−0.297237
$711$	0	0
$712$	−2.44367e35	−0.539563
$713$	−2.28672e35	−0.496127
$714$	0	0
$715$	−4.34538e35	−0.910337
$716$	1.17301e35	0.241485
$717$	0	0
$718$	6.16148e35	1.22498
$719$	−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
$722$	4.21509e35	0.781793
$723$	0	0
$724$	−1.06487e35	−0.190794
$725$	3.78058e35	0.665784
$726$	0	0
$727$	−4.49933e35	−0.765539	−0.382770	−	0.923844i	$-0.625030\pi$
$727$	−4.49933e35	−0.765539	−0.382770	+	0.923844i	$0.625030\pi$
$728$	−2.46792e35	−0.412751
$729$	0	0
$730$	−5.64595e34	−0.0912433
$731$	−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	$0.819110\pi$
$734$	−2.83974e35	−0.428626
$735$	0	0
$736$	−9.89815e34	−0.144405
$737$	−1.80893e36	−2.59464
$738$	0	0
$739$	−6.34879e35	−0.880309	−0.440155	−	0.897922i	$-0.645076\pi$
$739$	−6.34879e35	−0.880309	−0.440155	+	0.897922i	$0.645076\pi$
$740$	2.93949e35	0.400752
$741$	0	0
$742$	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	$0.368861\pi$
$744$	0	0
$745$	3.82583e35	0.479481
$746$	2.51662e35	0.310158
$747$	0	0
$748$	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
$753$	0	0
$754$	−7.48486e35	−0.807312
$755$	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	$0.454389\pi$
$758$	2.56401e35	0.258854
$759$	0	0
$760$	3.28058e35	0.320466
$761$	−2.91390e35	−0.280005	−0.140003	−	0.990151i	$-0.544711\pi$
$761$	−2.91390e35	−0.280005	−0.140003	+	0.990151i	$0.544711\pi$
$762$	0	0
$763$	6.79552e35	0.631926
$764$	6.02712e35	0.551369
$765$	0	0
$766$	−8.02238e35	−0.710303
$767$	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	$0.735075\pi$
$770$	8.28351e35	0.687196
$771$	0	0
$772$	−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	$0.666985\pi$
$774$	0	0
$775$	−4.84067e35	−0.370368
$776$	−5.95144e35	−0.448075
$777$	0	0
$778$	2.27695e35	0.166000
$779$	3.26970e36	2.34580
$780$	0	0
$781$	1.34979e36	0.937838
$782$	−9.33788e35	−0.638505
$783$	0	0
$784$	9.29772e34	0.0615780
$785$	2.83828e35	0.185006
$786$	0	0
$787$	1.69750e36	1.07183	0.535915	−	0.844272i	$-0.319967\pi$
$787$	1.69750e36	1.07183	0.535915	+	0.844272i	$0.319967\pi$
$788$	3.09503e35	0.192348
$789$	0	0
$790$	1.12477e36	0.677211
$791$	−1.87669e36	−1.11221
$792$	0	0
$793$	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	$0.324754\pi$
$798$	0	0
$799$	−7.43058e35	−0.388319
$800$	−2.09530e35	−0.107801
$801$	0	0
$802$	1.14608e36	0.571525
$803$	5.86368e35	0.287889
$804$	0	0
$805$	−1.19689e36	−0.569647
$806$	9.58363e35	0.449099
$807$	0	0
$808$	−5.00539e35	−0.227403
$809$	−8.07086e35	−0.361047	−0.180523	−	0.983571i	$-0.557779\pi$
$809$	−8.07086e35	−0.361047	−0.180523	+	0.983571i	$0.557779\pi$
$810$	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
$813$	0	0
$814$	−3.05285e36	−1.26445
$815$	2.46302e36	1.00461
$816$	0	0
$817$	5.61847e35	0.222250
$818$	−2.95796e36	−1.15233
$819$	0	0
$820$	1.33622e36	0.504901
$821$	6.01008e34	0.0223661	0.0111831	−	0.999937i	$-0.496440\pi$
$821$	6.01008e34	0.0223661	0.0111831	+	0.999937i	$0.496440\pi$
$822$	0	0
$823$	1.64344e36	0.593274	0.296637	−	0.954990i	$-0.404135\pi$
$823$	1.64344e36	0.593274	0.296637	+	0.954990i	$0.404135\pi$
$824$	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	$0.809602\pi$
$828$	0	0
$829$	−1.30083e36	−0.428834	−0.214417	−	0.976742i	$-0.568785\pi$
$829$	−1.30083e36	−0.428834	−0.214417	+	0.976742i	$0.568785\pi$
$830$	1.25476e34	0.00407458
$831$	0	0
$832$	4.14832e35	0.130716
$833$	8.77144e35	0.272275
$834$	0	0
$835$	1.30435e36	0.392930
$836$	−3.40710e36	−1.01113
$837$	0	0
$838$	−2.10154e36	−0.605323
$839$	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
$842$	−5.36538e35	−0.145613
$843$	0	0
$844$	1.23282e36	0.324803
$845$	−2.25117e35	−0.0584385
$846$	0	0
$847$	−4.17344e36	−1.05184
$848$	−1.19647e35	−0.0297134
$849$	0	0
$850$	−1.97670e36	−0.476656
$851$	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	$0.609098\pi$
$854$	−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	$0.231992\pi$
$858$	0	0
$859$	6.94361e36	1.46781	0.733907	−	0.679250i	$-0.237695\pi$
$859$	6.94361e36	1.46781	0.733907	+	0.679250i	$0.237695\pi$
$860$	2.29609e35	0.0478364
$861$	0	0
$862$	−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	$0.482929\pi$
$864$	0	0
$865$	−1.61763e36	−0.313456
$866$	8.93846e35	0.170722
$867$	0	0
$868$	−1.82691e36	−0.339016
$869$	−1.16814e37	−2.13673
$870$	0	0
$871$	−1.09542e37	−1.94694
$872$	−1.14226e36	−0.200128
$873$	0	0
$874$	4.92294e36	0.838169
$875$	−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	$0.462129\pi$
$878$	8.02985e36	1.29130
$879$	0	0
$880$	−1.39237e36	−0.217632
$881$	−7.73993e36	−1.19272	−0.596360	−	0.802717i	$-0.703387\pi$
$881$	−7.73993e36	−1.19272	−0.596360	+	0.802717i	$0.703387\pi$
$882$	0	0
$883$	−1.08821e35	−0.0163006	−0.00815031	−	0.999967i	$-0.502594\pi$
$883$	−1.08821e35	−0.0163006	−0.00815031	+	0.999967i	$0.502594\pi$
$884$	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	$0.313038\pi$
$888$	0	0
$889$	1.49686e35	0.0206020
$890$	4.96688e36	0.674075
$891$	0	0
$892$	−6.43861e36	−0.849634
$893$	3.91741e36	0.509748
$894$	0	0
$895$	−2.38421e36	−0.301687
$896$	−7.90785e35	−0.0986753
$897$	0	0
$898$	−8.05840e36	−0.977900
$899$	−5.54076e36	−0.663091
$900$	0	0
$901$	−1.12874e36	−0.131382
$902$	−1.38775e37	−1.59305
$903$	0	0
$904$	3.15453e36	0.352232
$905$	2.16441e36	0.238359
$906$	0	0
$907$	1.06412e36	0.113999	0.0569993	−	0.998374i	$-0.481847\pi$
$907$	1.06412e36	0.113999	0.0569993	+	0.998374i	$0.481847\pi$
$908$	−4.80492e35	−0.0507707
$909$	0	0
$910$	5.01617e36	0.515650
$911$	−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
$914$	−2.66928e36	−0.259757
$915$	0	0
$916$	8.69083e36	0.822939
$917$	−5.63723e36	−0.526561
$918$	0	0
$919$	5.22115e36	0.474594	0.237297	−	0.971437i	$-0.423738\pi$
$919$	5.22115e36	0.474594	0.237297	+	0.971437i	$0.423738\pi$
$920$	2.01185e36	0.180405
$921$	0	0
$922$	1.52922e36	0.133454
$923$	8.17379e36	0.703724
$924$	0	0
$925$	9.33766e36	0.782467
$926$	1.60932e37	1.33047
$927$	0	0
$928$	−2.39834e36	−0.193002
$929$	1.16329e37	0.923618	0.461809	−	0.886979i	$-0.347201\pi$
$929$	1.16329e37	0.923618	0.461809	+	0.886979i	$0.347201\pi$
$930$	0	0
$931$	−4.62431e36	−0.357418
$932$	1.87046e36	0.142643
$933$	0	0
$934$	8.98341e36	0.666968
$935$	−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	$0.434548\pi$
$938$	2.08817e37	1.46970
$939$	0	0
$940$	1.60092e36	0.109716
$941$	2.32727e37	1.57390	0.786950	−	0.617016i	$-0.211659\pi$
$941$	2.32727e37	1.57390	0.786950	+	0.617016i	$0.211659\pi$
$942$	0	0
$943$	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	$0.728519\pi$
$948$	0	0
$949$	3.55081e36	0.216023
$950$	1.04212e37	0.625709
$951$	0	0
$952$	−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	$0.490724\pi$
$954$	0	0
$955$	−1.22504e37	−0.688825
$956$	−1.64654e37	−0.913797
$957$	0	0
$958$	1.74742e37	0.944776
$959$	−1.76728e37	−0.943131
$960$	0	0
$961$	−1.21384e37	−0.631130
$962$	−1.84868e37	−0.948799
$963$	0	0
$964$	−1.68266e37	−0.841459
$965$	1.28308e36	0.0633378
$966$	0	0
$967$	5.41536e36	0.260493	0.130247	−	0.991482i	$-0.458423\pi$
$967$	5.41536e36	0.260493	0.130247	+	0.991482i	$0.458423\pi$
$968$	7.01512e36	0.333114
$969$	0	0
$970$	1.20966e37	0.559779
$971$	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
$974$	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	$0.281085\pi$
$978$	0	0
$979$	−5.15842e37	−2.12683
$980$	−1.88981e36	−0.0769293
$981$	0	0
$982$	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	$0.514341\pi$
$984$	0	0
$985$	−6.29081e36	−0.240300
$986$	−2.26259e37	−0.853383
$987$	0	0
$988$	−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
$993$	0	0
$994$	−1.55815e37	−0.531228
$995$	−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	$0.382306\pi$
$998$	−1.41873e37	−0.460012
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.26.a.c.1.1		1
3.2	odd	2		2.26.a.a.1.1	✓	1
12.11	even	2		16.26.a.a.1.1		1
15.2	even	4		50.26.b.a.49.1		2
15.8	even	4		50.26.b.a.49.2		2
15.14	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	3.2	odd	2
16.26.a.a.1.1		1	12.11	even	2
18.26.a.c.1.1		1	1.1	even	1	trivial
50.26.a.b.1.1		1	15.14	odd	2
50.26.b.a.49.1		2	15.2	even	4
50.26.b.a.49.2		2	15.8	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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