LMFDB - Embedded newform 16.16.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,16,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, 16, names="a")

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

chi := DirichletCharacter("16.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 16 $
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:	$22.8309608160$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
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)

$f(q)$

$=$

$q+276.000 q^{3} -132210. q^{5} +3.58574e6 q^{7} -1.42727e7 q^{9} +O(q^{10})$

$q+276.000 q^{3} -132210. q^{5} +3.58574e6 q^{7} -1.42727e7 q^{9} -4.78017e7 q^{11} +2.47785e8 q^{13} -3.64900e7 q^{15} -2.12768e9 q^{17} +1.07486e9 q^{19} +9.89663e8 q^{21} -2.49829e10 q^{23} -1.30381e10 q^{25} -7.89957e9 q^{27} -1.65100e11 q^{29} -1.00736e11 q^{31} -1.31933e10 q^{33} -4.74070e11 q^{35} +4.24904e10 q^{37} +6.83887e10 q^{39} -1.38878e12 q^{41} +1.16878e12 q^{43} +1.88700e12 q^{45} +1.64566e12 q^{47} +8.10994e12 q^{49} -5.87240e11 q^{51} -4.46963e12 q^{53} +6.31986e12 q^{55} +2.96662e11 q^{57} +2.87948e13 q^{59} +1.57199e13 q^{61} -5.11782e13 q^{63} -3.27597e13 q^{65} -6.16271e13 q^{67} -6.89528e12 q^{69} +6.67804e13 q^{71} -5.77496e13 q^{73} -3.59851e12 q^{75} -1.71404e14 q^{77} -1.98700e14 q^{79} +2.02618e14 q^{81} +1.13345e14 q^{83} +2.81301e14 q^{85} -4.55675e13 q^{87} -4.82309e13 q^{89} +8.88491e14 q^{91} -2.78032e13 q^{93} -1.42108e14 q^{95} +9.51217e13 q^{97} +6.82261e14 q^{99} +O(q^{100})$

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
$3$	276.000	0.0728618	0.0364309	−	0.999336i	$-0.488401\pi$
$3$	276.000	0.0728618	0.0364309	+	0.999336i	$0.488401\pi$
$4$	0	0
$5$	−132210.	−0.756814	−0.378407	−	0.925639i	$-0.623528\pi$
$5$	−132210.	−0.756814	−0.378407	+	0.925639i	$0.623528\pi$
$6$	0	0
$7$	3.58574e6	1.64567	0.822835	−	0.568280i	$-0.192391\pi$
$7$	3.58574e6	1.64567	0.822835	+	0.568280i	$0.192391\pi$
$8$	0	0
$9$	−1.42727e7	−0.994691
$10$	0	0
$11$	−4.78017e7	−0.739602	−0.369801	−	0.929111i	$-0.620574\pi$
$11$	−4.78017e7	−0.739602	−0.369801	+	0.929111i	$0.620574\pi$
$12$	0	0
$13$	2.47785e8	1.09522	0.547608	−	0.836735i	$-0.315539\pi$
$13$	2.47785e8	1.09522	0.547608	+	0.836735i	$0.315539\pi$
$14$	0	0
$15$	−3.64900e7	−0.0551428
$16$	0	0
$17$	−2.12768e9	−1.25759	−0.628796	−	0.777570i	$-0.716452\pi$
$17$	−2.12768e9	−1.25759	−0.628796	+	0.777570i	$0.716452\pi$
$18$	0	0
$19$	1.07486e9	0.275868	0.137934	−	0.990441i	$-0.455954\pi$
$19$	1.07486e9	0.275868	0.137934	+	0.990441i	$0.455954\pi$
$20$	0	0
$21$	9.89663e8	0.119906
$22$	0	0
$23$	−2.49829e10	−1.52997	−0.764987	−	0.644046i	$-0.777255\pi$
$23$	−2.49829e10	−1.52997	−0.764987	+	0.644046i	$0.777255\pi$
$24$	0	0
$25$	−1.30381e10	−0.427232
$26$	0	0
$27$	−7.89957e9	−0.145337
$28$	0	0
$29$	−1.65100e11	−1.77730	−0.888651	−	0.458584i	$-0.848357\pi$
$29$	−1.65100e11	−1.77730	−0.888651	+	0.458584i	$0.848357\pi$
$30$	0	0
$31$	−1.00736e11	−0.657618	−0.328809	−	0.944397i	$-0.606647\pi$
$31$	−1.00736e11	−0.657618	−0.328809	+	0.944397i	$0.606647\pi$
$32$	0	0
$33$	−1.31933e10	−0.0538887
$34$	0	0
$35$	−4.74070e11	−1.24547
$36$	0	0
$37$	4.24904e10	0.0735831	0.0367916	−	0.999323i	$-0.488286\pi$
$37$	4.24904e10	0.0735831	0.0367916	+	0.999323i	$0.488286\pi$
$38$	0	0
$39$	6.83887e10	0.0797994
$40$	0	0
$41$	−1.38878e12	−1.11366	−0.556832	−	0.830625i	$-0.687983\pi$
$41$	−1.38878e12	−1.11366	−0.556832	+	0.830625i	$0.687983\pi$
$42$	0	0
$43$	1.16878e12	0.655723	0.327862	−	0.944726i	$-0.393672\pi$
$43$	1.16878e12	0.655723	0.327862	+	0.944726i	$0.393672\pi$
$44$	0	0
$45$	1.88700e12	0.752796
$46$	0	0
$47$	1.64566e12	0.473811	0.236905	−	0.971533i	$-0.423867\pi$
$47$	1.64566e12	0.473811	0.236905	+	0.971533i	$0.423867\pi$
$48$	0	0
$49$	8.10994e12	1.70823
$50$	0	0
$51$	−5.87240e11	−0.0916304
$52$	0	0
$53$	−4.46963e12	−0.522640	−0.261320	−	0.965252i	$-0.584158\pi$
$53$	−4.46963e12	−0.522640	−0.261320	+	0.965252i	$0.584158\pi$
$54$	0	0
$55$	6.31986e12	0.559741
$56$	0	0
$57$	2.96662e11	0.0201002
$58$	0	0
$59$	2.87948e13	1.50634	0.753172	−	0.657824i	$-0.228523\pi$
$59$	2.87948e13	1.50634	0.753172	+	0.657824i	$0.228523\pi$
$60$	0	0
$61$	1.57199e13	0.640438	0.320219	−	0.947344i	$-0.396243\pi$
$61$	1.57199e13	0.640438	0.320219	+	0.947344i	$0.396243\pi$
$62$	0	0
$63$	−5.11782e13	−1.63693
$64$	0	0
$65$	−3.27597e13	−0.828875
$66$	0	0
$67$	−6.16271e13	−1.24225	−0.621127	−	0.783710i	$-0.713325\pi$
$67$	−6.16271e13	−1.24225	−0.621127	+	0.783710i	$0.713325\pi$
$68$	0	0
$69$	−6.89528e12	−0.111477
$70$	0	0
$71$	6.67804e13	0.871388	0.435694	−	0.900095i	$-0.356503\pi$
$71$	6.67804e13	0.871388	0.435694	+	0.900095i	$0.356503\pi$
$72$	0	0
$73$	−5.77496e13	−0.611826	−0.305913	−	0.952059i	$-0.598962\pi$
$73$	−5.77496e13	−0.611826	−0.305913	+	0.952059i	$0.598962\pi$
$74$	0	0
$75$	−3.59851e12	−0.0311289
$76$	0	0
$77$	−1.71404e14	−1.21714
$78$	0	0
$79$	−1.98700e14	−1.16411	−0.582056	−	0.813148i	$-0.697752\pi$
$79$	−1.98700e14	−1.16411	−0.582056	+	0.813148i	$0.697752\pi$
$80$	0	0
$81$	2.02618e14	0.984102
$82$	0	0
$83$	1.13345e14	0.458477	0.229238	−	0.973370i	$-0.426376\pi$
$83$	1.13345e14	0.458477	0.229238	+	0.973370i	$0.426376\pi$
$84$	0	0
$85$	2.81301e14	0.951764
$86$	0	0
$87$	−4.55675e13	−0.129497
$88$	0	0
$89$	−4.82309e13	−0.115585	−0.0577923	−	0.998329i	$-0.518406\pi$
$89$	−4.82309e13	−0.115585	−0.0577923	+	0.998329i	$0.518406\pi$
$90$	0	0
$91$	8.88491e14	1.80237
$92$	0	0
$93$	−2.78032e13	−0.0479152
$94$	0	0
$95$	−1.42108e14	−0.208781
$96$	0	0
$97$	9.51217e13	0.119534	0.0597670	−	0.998212i	$-0.480964\pi$
$97$	9.51217e13	0.119534	0.0597670	+	0.998212i	$0.480964\pi$
$98$	0	0
$99$	6.82261e14	0.735676
$100$	0	0
$101$	1.15833e15	1.07503	0.537517	−	0.843253i	$-0.319363\pi$
$101$	1.15833e15	1.07503	0.537517	+	0.843253i	$0.319363\pi$
$102$	0	0
$103$	−1.61757e15	−1.29594	−0.647969	−	0.761667i	$-0.724381\pi$
$103$	−1.61757e15	−1.29594	−0.647969	+	0.761667i	$0.724381\pi$
$104$	0	0
$105$	−1.30843e14	−0.0907469
$106$	0	0
$107$	−3.70312e14	−0.222941	−0.111471	−	0.993768i	$-0.535556\pi$
$107$	−3.70312e14	−0.222941	−0.111471	+	0.993768i	$0.535556\pi$
$108$	0	0
$109$	−2.17152e15	−1.13780	−0.568898	−	0.822408i	$-0.692630\pi$
$109$	−2.17152e15	−1.13780	−0.568898	+	0.822408i	$0.692630\pi$
$110$	0	0
$111$	1.17274e13	0.00536139
$112$	0	0
$113$	1.52160e14	0.0608433	0.0304216	−	0.999537i	$-0.490315\pi$
$113$	1.52160e14	0.0608433	0.0304216	+	0.999537i	$0.490315\pi$
$114$	0	0
$115$	3.30299e15	1.15791
$116$	0	0
$117$	−3.53657e15	−1.08940
$118$	0	0
$119$	−7.62931e15	−2.06958
$120$	0	0
$121$	−1.89225e15	−0.452989
$122$	0	0
$123$	−3.83303e14	−0.0811435
$124$	0	0
$125$	5.75850e15	1.08015
$126$	0	0
$127$	−4.07637e15	−0.678806	−0.339403	−	0.940641i	$-0.610225\pi$
$127$	−4.07637e15	−0.678806	−0.339403	+	0.940641i	$0.610225\pi$
$128$	0	0
$129$	3.22584e14	0.0477772
$130$	0	0
$131$	1.11695e16	1.47401	0.737005	−	0.675888i	$-0.236240\pi$
$131$	1.11695e16	1.47401	0.737005	+	0.675888i	$0.236240\pi$
$132$	0	0
$133$	3.85417e15	0.453988
$134$	0	0
$135$	1.04440e15	0.109993
$136$	0	0
$137$	−6.36477e15	−0.600314	−0.300157	−	0.953890i	$-0.597039\pi$
$137$	−6.36477e15	−0.600314	−0.300157	+	0.953890i	$0.597039\pi$
$138$	0	0
$139$	1.64991e16	1.39589	0.697943	−	0.716154i	$-0.254099\pi$
$139$	1.64991e16	1.39589	0.697943	+	0.716154i	$0.254099\pi$
$140$	0	0
$141$	4.54201e14	0.0345227
$142$	0	0
$143$	−1.18445e16	−0.810024
$144$	0	0
$145$	2.18278e16	1.34509
$146$	0	0
$147$	2.23834e15	0.124465
$148$	0	0
$149$	−3.30220e15	−0.165923	−0.0829614	−	0.996553i	$-0.526438\pi$
$149$	−3.30220e15	−0.165923	−0.0829614	+	0.996553i	$0.526438\pi$
$150$	0	0
$151$	−4.31473e15	−0.196167	−0.0980836	−	0.995178i	$-0.531271\pi$
$151$	−4.31473e15	−0.196167	−0.0980836	+	0.995178i	$0.531271\pi$
$152$	0	0
$153$	3.03678e16	1.25092
$154$	0	0
$155$	1.33184e16	0.497694
$156$	0	0
$157$	−1.74769e16	−0.593220	−0.296610	−	0.954999i	$-0.595856\pi$
$157$	−1.74769e16	−0.593220	−0.296610	+	0.954999i	$0.595856\pi$
$158$	0	0
$159$	−1.23362e15	−0.0380804
$160$	0	0
$161$	−8.95821e16	−2.51783
$162$	0	0
$163$	−4.95169e16	−1.26866	−0.634331	−	0.773061i	$-0.718724\pi$
$163$	−4.95169e16	−1.26866	−0.634331	+	0.773061i	$0.718724\pi$
$164$	0	0
$165$	1.74428e15	0.0407837
$166$	0	0
$167$	2.33915e16	0.499671	0.249836	−	0.968288i	$-0.419623\pi$
$167$	2.33915e16	0.499671	0.249836	+	0.968288i	$0.419623\pi$
$168$	0	0
$169$	1.02115e16	0.199498
$170$	0	0
$171$	−1.53412e16	−0.274403
$172$	0	0
$173$	5.33179e16	0.874032	0.437016	−	0.899454i	$-0.356035\pi$
$173$	5.33179e16	0.874032	0.437016	+	0.899454i	$0.356035\pi$
$174$	0	0
$175$	−4.67512e16	−0.703084
$176$	0	0
$177$	7.94737e15	0.109755
$178$	0	0
$179$	−4.41727e16	−0.560733	−0.280366	−	0.959893i	$-0.590456\pi$
$179$	−4.41727e16	−0.560733	−0.280366	+	0.959893i	$0.590456\pi$
$180$	0	0
$181$	−8.52336e16	−0.995455	−0.497728	−	0.867333i	$-0.665832\pi$
$181$	−8.52336e16	−0.995455	−0.497728	+	0.867333i	$0.665832\pi$
$182$	0	0
$183$	4.33870e15	0.0466634
$184$	0	0
$185$	−5.61766e15	−0.0556887
$186$	0	0
$187$	1.01707e17	0.930118
$188$	0	0
$189$	−2.83258e16	−0.239176
$190$	0	0
$191$	1.64872e17	1.28646	0.643231	−	0.765672i	$-0.277594\pi$
$191$	1.64872e17	1.28646	0.643231	+	0.765672i	$0.277594\pi$
$192$	0	0
$193$	1.67090e17	1.20579	0.602894	−	0.797821i	$-0.294014\pi$
$193$	1.67090e17	1.20579	0.602894	+	0.797821i	$0.294014\pi$
$194$	0	0
$195$	−9.04166e15	−0.0603933
$196$	0	0
$197$	1.06538e17	0.659189	0.329594	−	0.944123i	$-0.393088\pi$
$197$	1.06538e17	0.659189	0.329594	+	0.944123i	$0.393088\pi$
$198$	0	0
$199$	1.97125e17	1.13069	0.565346	−	0.824854i	$-0.308743\pi$
$199$	1.97125e17	1.13069	0.565346	+	0.824854i	$0.308743\pi$
$200$	0	0
$201$	−1.70091e16	−0.0905129
$202$	0	0
$203$	−5.92004e17	−2.92485
$204$	0	0
$205$	1.83611e17	0.842837
$206$	0	0
$207$	3.56574e17	1.52185
$208$	0	0
$209$	−5.13803e16	−0.204032
$210$	0	0
$211$	2.03916e17	0.753933	0.376967	−	0.926227i	$-0.376967\pi$
$211$	2.03916e17	0.753933	0.376967	+	0.926227i	$0.376967\pi$
$212$	0	0
$213$	1.84314e16	0.0634909
$214$	0	0
$215$	−1.54525e17	−0.496261
$216$	0	0
$217$	−3.61214e17	−1.08222
$218$	0	0
$219$	−1.59389e16	−0.0445787
$220$	0	0
$221$	−5.27208e17	−1.37734
$222$	0	0
$223$	−1.24699e16	−0.0304493	−0.0152247	−	0.999884i	$-0.504846\pi$
$223$	−1.24699e16	−0.0304493	−0.0152247	+	0.999884i	$0.504846\pi$
$224$	0	0
$225$	1.86089e17	0.424964
$226$	0	0
$227$	−5.90160e17	−1.26118	−0.630588	−	0.776118i	$-0.717186\pi$
$227$	−5.90160e17	−1.26118	−0.630588	+	0.776118i	$0.717186\pi$
$228$	0	0
$229$	1.89415e17	0.379007	0.189503	−	0.981880i	$-0.439312\pi$
$229$	1.89415e17	0.379007	0.189503	+	0.981880i	$0.439312\pi$
$230$	0	0
$231$	−4.73076e16	−0.0886831
$232$	0	0
$233$	1.25116e17	0.219858	0.109929	−	0.993939i	$-0.464938\pi$
$233$	1.25116e17	0.219858	0.109929	+	0.993939i	$0.464938\pi$
$234$	0	0
$235$	−2.17572e17	−0.358587
$236$	0	0
$237$	−5.48412e16	−0.0848193
$238$	0	0
$239$	−2.62041e17	−0.380526	−0.190263	−	0.981733i	$-0.560934\pi$
$239$	−2.62041e17	−0.380526	−0.190263	+	0.981733i	$0.560934\pi$
$240$	0	0
$241$	1.32765e15	0.00181115	0.000905577	−	1.00000i	$-0.499712\pi$
$241$	1.32765e15	0.00181115	0.000905577		1.00000i	$0.499712\pi$
$242$	0	0
$243$	1.69273e17	0.217040
$244$	0	0
$245$	−1.07222e18	−1.29281
$246$	0	0
$247$	2.66335e17	0.302135
$248$	0	0
$249$	3.12833e16	0.0334054
$250$	0	0
$251$	1.47445e18	1.48278	0.741390	−	0.671074i	$-0.234167\pi$
$251$	1.47445e18	1.48278	0.741390	+	0.671074i	$0.234167\pi$
$252$	0	0
$253$	1.19422e18	1.13157
$254$	0	0
$255$	7.76390e16	0.0693472
$256$	0	0
$257$	−2.24341e17	−0.188978	−0.0944889	−	0.995526i	$-0.530122\pi$
$257$	−2.24341e17	−0.188978	−0.0944889	+	0.995526i	$0.530122\pi$
$258$	0	0
$259$	1.52359e17	0.121094
$260$	0	0
$261$	2.35642e18	1.76787
$262$	0	0
$263$	−2.10162e17	−0.148897	−0.0744486	−	0.997225i	$-0.523720\pi$
$263$	−2.10162e17	−0.148897	−0.0744486	+	0.997225i	$0.523720\pi$
$264$	0	0
$265$	5.90929e17	0.395541
$266$	0	0
$267$	−1.33117e16	−0.00842170
$268$	0	0
$269$	−1.11450e18	−0.666712	−0.333356	−	0.942801i	$-0.608181\pi$
$269$	−1.11450e18	−0.666712	−0.333356	+	0.942801i	$0.608181\pi$
$270$	0	0
$271$	−1.39617e18	−0.790076	−0.395038	−	0.918665i	$-0.629269\pi$
$271$	−1.39617e18	−0.790076	−0.395038	+	0.918665i	$0.629269\pi$
$272$	0	0
$273$	2.45224e17	0.131324
$274$	0	0
$275$	6.23243e17	0.315982
$276$	0	0
$277$	−7.25940e17	−0.348580	−0.174290	−	0.984694i	$-0.555763\pi$
$277$	−7.25940e17	−0.348580	−0.174290	+	0.984694i	$0.555763\pi$
$278$	0	0
$279$	1.43778e18	0.654126
$280$	0	0
$281$	−1.38854e18	−0.598772	−0.299386	−	0.954132i	$-0.596782\pi$
$281$	−1.38854e18	−0.598772	−0.299386	+	0.954132i	$0.596782\pi$
$282$	0	0
$283$	4.17187e18	1.70582	0.852909	−	0.522059i	$-0.174836\pi$
$283$	4.17187e18	1.70582	0.852909	+	0.522059i	$0.174836\pi$
$284$	0	0
$285$	−3.92217e16	−0.0152121
$286$	0	0
$287$	−4.97980e18	−1.83272
$288$	0	0
$289$	1.66461e18	0.581538
$290$	0	0
$291$	2.62536e16	0.00870946
$292$	0	0
$293$	−5.97698e18	−1.88354	−0.941770	−	0.336258i	$-0.890839\pi$
$293$	−5.97698e18	−1.88354	−0.941770	+	0.336258i	$0.890839\pi$
$294$	0	0
$295$	−3.80696e18	−1.14002
$296$	0	0
$297$	3.77613e17	0.107491
$298$	0	0
$299$	−6.19039e18	−1.67565
$300$	0	0
$301$	4.19095e18	1.07910
$302$	0	0
$303$	3.19699e17	0.0783288
$304$	0	0
$305$	−2.07833e18	−0.484693
$306$	0	0
$307$	7.16291e18	1.59057	0.795283	−	0.606238i	$-0.207322\pi$
$307$	7.16291e18	1.59057	0.795283	+	0.606238i	$0.207322\pi$
$308$	0	0
$309$	−4.46449e17	−0.0944243
$310$	0	0
$311$	−5.55387e18	−1.11916	−0.559581	−	0.828776i	$-0.689038\pi$
$311$	−5.55387e18	−1.11916	−0.559581	+	0.828776i	$0.689038\pi$
$312$	0	0
$313$	−5.23128e18	−1.00467	−0.502337	−	0.864672i	$-0.667526\pi$
$313$	−5.23128e18	−1.00467	−0.502337	+	0.864672i	$0.667526\pi$
$314$	0	0
$315$	6.76628e18	1.23886
$316$	0	0
$317$	6.51227e18	1.13707	0.568536	−	0.822658i	$-0.307510\pi$
$317$	6.51227e18	1.13707	0.568536	+	0.822658i	$0.307510\pi$
$318$	0	0
$319$	7.89204e18	1.31450
$320$	0	0
$321$	−1.02206e17	−0.0162439
$322$	0	0
$323$	−2.28697e18	−0.346929
$324$	0	0
$325$	−3.23064e18	−0.467912
$326$	0	0
$327$	−5.99338e17	−0.0829018
$328$	0	0
$329$	5.90089e18	0.779737
$330$	0	0
$331$	−1.14330e19	−1.44361	−0.721805	−	0.692097i	$-0.756687\pi$
$331$	−1.14330e19	−1.44361	−0.721805	+	0.692097i	$0.756687\pi$
$332$	0	0
$333$	−6.06454e17	−0.0731925
$334$	0	0
$335$	8.14772e18	0.940156
$336$	0	0
$337$	1.54167e19	1.70125	0.850626	−	0.525772i	$-0.176223\pi$
$337$	1.54167e19	1.70125	0.850626	+	0.525772i	$0.176223\pi$
$338$	0	0
$339$	4.19962e16	0.00443315
$340$	0	0
$341$	4.81537e18	0.486375
$342$	0	0
$343$	1.20566e19	1.16552
$344$	0	0
$345$	9.11625e17	0.0843671
$346$	0	0
$347$	4.17759e18	0.370216	0.185108	−	0.982718i	$-0.440737\pi$
$347$	4.17759e18	0.370216	0.185108	+	0.982718i	$0.440737\pi$
$348$	0	0
$349$	−9.17864e18	−0.779090	−0.389545	−	0.921007i	$-0.627368\pi$
$349$	−9.17864e18	−0.779090	−0.389545	+	0.921007i	$0.627368\pi$
$350$	0	0
$351$	−1.95740e18	−0.159175
$352$	0	0
$353$	−1.65269e19	−1.28790	−0.643950	−	0.765068i	$-0.722705\pi$
$353$	−1.65269e19	−1.28790	−0.643950	+	0.765068i	$0.722705\pi$
$354$	0	0
$355$	−8.82904e18	−0.659479
$356$	0	0
$357$	−2.10569e18	−0.150793
$358$	0	0
$359$	−3.35789e17	−0.0230599	−0.0115300	−	0.999934i	$-0.503670\pi$
$359$	−3.35789e17	−0.0230599	−0.0115300	+	0.999934i	$0.503670\pi$
$360$	0	0
$361$	−1.40258e19	−0.923897
$362$	0	0
$363$	−5.22260e17	−0.0330055
$364$	0	0
$365$	7.63508e18	0.463039
$366$	0	0
$367$	−1.00766e19	−0.586566	−0.293283	−	0.956026i	$-0.594748\pi$
$367$	−1.00766e19	−0.586566	−0.293283	+	0.956026i	$0.594748\pi$
$368$	0	0
$369$	1.98217e19	1.10775
$370$	0	0
$371$	−1.60269e19	−0.860093
$372$	0	0
$373$	9.00462e18	0.464140	0.232070	−	0.972699i	$-0.425450\pi$
$373$	9.00462e18	0.464140	0.232070	+	0.972699i	$0.425450\pi$
$374$	0	0
$375$	1.58934e18	0.0787016
$376$	0	0
$377$	−4.09092e19	−1.94653
$378$	0	0
$379$	−2.82432e19	−1.29157	−0.645787	−	0.763518i	$-0.723470\pi$
$379$	−2.82432e19	−1.29157	−0.645787	+	0.763518i	$0.723470\pi$
$380$	0	0
$381$	−1.12508e18	−0.0494590
$382$	0	0
$383$	1.21539e19	0.513720	0.256860	−	0.966449i	$-0.417312\pi$
$383$	1.21539e19	0.513720	0.256860	+	0.966449i	$0.417312\pi$
$384$	0	0
$385$	2.26614e19	0.921150
$386$	0	0
$387$	−1.66817e19	−0.652242
$388$	0	0
$389$	−4.18075e19	−1.57265	−0.786325	−	0.617814i	$-0.788019\pi$
$389$	−4.18075e19	−1.57265	−0.786325	+	0.617814i	$0.788019\pi$
$390$	0	0
$391$	5.31557e19	1.92408
$392$	0	0
$393$	3.08279e18	0.107399
$394$	0	0
$395$	2.62701e19	0.881017
$396$	0	0
$397$	1.37012e19	0.442416	0.221208	−	0.975227i	$-0.429000\pi$
$397$	1.37012e19	0.442416	0.221208	+	0.975227i	$0.429000\pi$
$398$	0	0
$399$	1.06375e18	0.0330783
$400$	0	0
$401$	4.53299e19	1.35770	0.678848	−	0.734279i	$-0.262480\pi$
$401$	4.53299e19	1.35770	0.678848	+	0.734279i	$0.262480\pi$
$402$	0	0
$403$	−2.49609e19	−0.720233
$404$	0	0
$405$	−2.67881e19	−0.744782
$406$	0	0
$407$	−2.03111e18	−0.0544222
$408$	0	0
$409$	−1.53151e19	−0.395545	−0.197772	−	0.980248i	$-0.563371\pi$
$409$	−1.53151e19	−0.395545	−0.197772	+	0.980248i	$0.563371\pi$
$410$	0	0
$411$	−1.75668e18	−0.0437399
$412$	0	0
$413$	1.03251e20	2.47895
$414$	0	0
$415$	−1.49854e19	−0.346982
$416$	0	0
$417$	4.55376e18	0.101707
$418$	0	0
$419$	5.44494e19	1.17324	0.586622	−	0.809861i	$-0.300457\pi$
$419$	5.44494e19	1.17324	0.586622	+	0.809861i	$0.300457\pi$
$420$	0	0
$421$	−2.33400e19	−0.485271	−0.242636	−	0.970117i	$-0.578012\pi$
$421$	−2.33400e19	−0.485271	−0.242636	+	0.970117i	$0.578012\pi$
$422$	0	0
$423$	−2.34880e19	−0.471295
$424$	0	0
$425$	2.77409e19	0.537284
$426$	0	0
$427$	5.63676e19	1.05395
$428$	0	0
$429$	−3.26909e18	−0.0590198
$430$	0	0
$431$	4.14548e19	0.722761	0.361381	−	0.932418i	$-0.382305\pi$
$431$	4.14548e19	0.722761	0.361381	+	0.932418i	$0.382305\pi$
$432$	0	0
$433$	−5.43924e19	−0.915965	−0.457982	−	0.888961i	$-0.651428\pi$
$433$	−5.43924e19	−0.915965	−0.457982	+	0.888961i	$0.651428\pi$
$434$	0	0
$435$	6.02448e18	0.0980054
$436$	0	0
$437$	−2.68532e19	−0.422071
$438$	0	0
$439$	−8.80718e19	−1.33768	−0.668841	−	0.743405i	$-0.733210\pi$
$439$	−8.80718e19	−1.33768	−0.668841	+	0.743405i	$0.733210\pi$
$440$	0	0
$441$	−1.15751e20	−1.69916
$442$	0	0
$443$	−7.78245e19	−1.10430	−0.552152	−	0.833744i	$-0.686193\pi$
$443$	−7.78245e19	−1.10430	−0.552152	+	0.833744i	$0.686193\pi$
$444$	0	0
$445$	6.37661e18	0.0874761
$446$	0	0
$447$	−9.11407e17	−0.0120894
$448$	0	0
$449$	1.27118e20	1.63065	0.815325	−	0.579003i	$-0.196558\pi$
$449$	1.27118e20	1.63065	0.815325	+	0.579003i	$0.196558\pi$
$450$	0	0
$451$	6.63860e19	0.823669
$452$	0	0
$453$	−1.19087e18	−0.0142931
$454$	0	0
$455$	−1.17467e20	−1.36406
$456$	0	0
$457$	−6.20016e18	−0.0696676	−0.0348338	−	0.999393i	$-0.511090\pi$
$457$	−6.20016e18	−0.0696676	−0.0348338	+	0.999393i	$0.511090\pi$
$458$	0	0
$459$	1.68078e19	0.182774
$460$	0	0
$461$	1.65070e19	0.173745	0.0868723	−	0.996219i	$-0.472313\pi$
$461$	1.65070e19	0.173745	0.0868723	+	0.996219i	$0.472313\pi$
$462$	0	0
$463$	−1.28678e20	−1.31114	−0.655569	−	0.755135i	$-0.727571\pi$
$463$	−1.28678e20	−1.31114	−0.655569	+	0.755135i	$0.727571\pi$
$464$	0	0
$465$	3.67586e18	0.0362629
$466$	0	0
$467$	1.11384e20	1.06402	0.532008	−	0.846739i	$-0.321438\pi$
$467$	1.11384e20	1.06402	0.532008	+	0.846739i	$0.321438\pi$
$468$	0	0
$469$	−2.20979e20	−2.04434
$470$	0	0
$471$	−4.82361e18	−0.0432231
$472$	0	0
$473$	−5.58698e19	−0.484974
$474$	0	0
$475$	−1.40142e19	−0.117860
$476$	0	0
$477$	6.37938e19	0.519865
$478$	0	0
$479$	7.43442e19	0.587125	0.293563	−	0.955940i	$-0.405159\pi$
$479$	7.43442e19	0.587125	0.293563	+	0.955940i	$0.405159\pi$
$480$	0	0
$481$	1.05285e19	0.0805894
$482$	0	0
$483$	−2.47247e19	−0.183454
$484$	0	0
$485$	−1.25760e19	−0.0904651
$486$	0	0
$487$	9.10325e19	0.634935	0.317467	−	0.948269i	$-0.397168\pi$
$487$	9.10325e19	0.634935	0.317467	+	0.948269i	$0.397168\pi$
$488$	0	0
$489$	−1.36667e19	−0.0924370
$490$	0	0
$491$	1.54954e20	1.01646	0.508232	−	0.861220i	$-0.330299\pi$
$491$	1.54954e20	1.01646	0.508232	+	0.861220i	$0.330299\pi$
$492$	0	0
$493$	3.51280e20	2.23512
$494$	0	0
$495$	−9.02017e19	−0.556770
$496$	0	0
$497$	2.39457e20	1.43402
$498$	0	0
$499$	−7.98004e19	−0.463715	−0.231858	−	0.972750i	$-0.574480\pi$
$499$	−7.98004e19	−0.463715	−0.231858	+	0.972750i	$0.574480\pi$
$500$	0	0
$501$	6.45605e18	0.0364069
$502$	0	0
$503$	1.35801e20	0.743267	0.371633	−	0.928380i	$-0.378798\pi$
$503$	1.35801e20	0.743267	0.371633	+	0.928380i	$0.378798\pi$
$504$	0	0
$505$	−1.53143e20	−0.813600
$506$	0	0
$507$	2.81837e18	0.0145358
$508$	0	0
$509$	−1.98988e19	−0.0996420	−0.0498210	−	0.998758i	$-0.515865\pi$
$509$	−1.98988e19	−0.0996420	−0.0498210	+	0.998758i	$0.515865\pi$
$510$	0	0
$511$	−2.07075e20	−1.00686
$512$	0	0
$513$	−8.49096e18	−0.0400937
$514$	0	0
$515$	2.13859e20	0.980784
$516$	0	0
$517$	−7.86651e19	−0.350432
$518$	0	0
$519$	1.47157e19	0.0636835
$520$	0	0
$521$	−2.13098e20	−0.895974	−0.447987	−	0.894040i	$-0.647859\pi$
$521$	−2.13098e20	−0.895974	−0.447987	+	0.894040i	$0.647859\pi$
$522$	0	0
$523$	2.23159e20	0.911700	0.455850	−	0.890057i	$-0.349335\pi$
$523$	2.23159e20	0.911700	0.455850	+	0.890057i	$0.349335\pi$
$524$	0	0
$525$	−1.29033e19	−0.0512279
$526$	0	0
$527$	2.14335e20	0.827015
$528$	0	0
$529$	3.57510e20	1.34082
$530$	0	0
$531$	−4.10981e20	−1.49835
$532$	0	0
$533$	−3.44119e20	−1.21970
$534$	0	0
$535$	4.89590e19	0.168725
$536$	0	0
$537$	−1.21917e19	−0.0408560
$538$	0	0
$539$	−3.87669e20	−1.26341
$540$	0	0
$541$	3.73861e19	0.118503	0.0592517	−	0.998243i	$-0.481129\pi$
$541$	3.73861e19	0.118503	0.0592517	+	0.998243i	$0.481129\pi$
$542$	0	0
$543$	−2.35245e19	−0.0725306
$544$	0	0
$545$	2.87096e20	0.861100
$546$	0	0
$547$	−4.35348e20	−1.27037	−0.635187	−	0.772358i	$-0.719077\pi$
$547$	−4.35348e20	−1.27037	−0.635187	+	0.772358i	$0.719077\pi$
$548$	0	0
$549$	−2.24366e20	−0.637038
$550$	0	0
$551$	−1.77459e20	−0.490300
$552$	0	0
$553$	−7.12486e20	−1.91575
$554$	0	0
$555$	−1.55047e18	−0.00405758
$556$	0	0
$557$	3.85862e20	0.982919	0.491460	−	0.870900i	$-0.336463\pi$
$557$	3.85862e20	0.982919	0.491460	+	0.870900i	$0.336463\pi$
$558$	0	0
$559$	2.89607e20	0.718159
$560$	0	0
$561$	2.80711e19	0.0677700
$562$	0	0
$563$	−1.54528e20	−0.363241	−0.181621	−	0.983369i	$-0.558134\pi$
$563$	−1.54528e20	−0.363241	−0.181621	+	0.983369i	$0.558134\pi$
$564$	0	0
$565$	−2.01171e19	−0.0460471
$566$	0	0
$567$	7.26534e20	1.61951
$568$	0	0
$569$	−6.21279e20	−1.34879	−0.674395	−	0.738371i	$-0.735596\pi$
$569$	−6.21279e20	−1.34879	−0.674395	+	0.738371i	$0.735596\pi$
$570$	0	0
$571$	−1.89079e20	−0.399828	−0.199914	−	0.979813i	$-0.564066\pi$
$571$	−1.89079e20	−0.399828	−0.199914	+	0.979813i	$0.564066\pi$
$572$	0	0
$573$	4.55047e19	0.0937339
$574$	0	0
$575$	3.25729e20	0.653654
$576$	0	0
$577$	3.30668e20	0.646508	0.323254	−	0.946312i	$-0.395223\pi$
$577$	3.30668e20	0.646508	0.323254	+	0.946312i	$0.395223\pi$
$578$	0	0
$579$	4.61169e19	0.0878559
$580$	0	0
$581$	4.06426e20	0.754502
$582$	0	0
$583$	2.13656e20	0.386545
$584$	0	0
$585$	4.67570e20	0.824475
$586$	0	0
$587$	−9.95916e20	−1.71174	−0.855869	−	0.517193i	$-0.826977\pi$
$587$	−9.95916e20	−1.71174	−0.855869	+	0.517193i	$0.826977\pi$
$588$	0	0
$589$	−1.08278e20	−0.181416
$590$	0	0
$591$	2.94046e19	0.0480296
$592$	0	0
$593$	1.74283e19	0.0277552	0.0138776	−	0.999904i	$-0.495582\pi$
$593$	1.74283e19	0.0277552	0.0138776	+	0.999904i	$0.495582\pi$
$594$	0	0
$595$	1.00867e21	1.56629
$596$	0	0
$597$	5.44066e19	0.0823843
$598$	0	0
$599$	−1.08247e21	−1.59850	−0.799251	−	0.600997i	$-0.794770\pi$
$599$	−1.08247e21	−1.59850	−0.799251	+	0.600997i	$0.794770\pi$
$600$	0	0
$601$	1.36215e21	1.96186	0.980930	−	0.194362i	$-0.0622637\pi$
$601$	1.36215e21	1.96186	0.980930	+	0.194362i	$0.0622637\pi$
$602$	0	0
$603$	8.79587e20	1.23566
$604$	0	0
$605$	2.50174e20	0.342828
$606$	0	0
$607$	8.40943e20	1.12422	0.562110	−	0.827062i	$-0.309990\pi$
$607$	8.40943e20	1.12422	0.562110	+	0.827062i	$0.309990\pi$
$608$	0	0
$609$	−1.63393e20	−0.213110
$610$	0	0
$611$	4.07769e20	0.518925
$612$	0	0
$613$	−1.36910e21	−1.70012	−0.850062	−	0.526683i	$-0.823435\pi$
$613$	−1.36910e21	−1.70012	−0.850062	+	0.526683i	$0.823435\pi$
$614$	0	0
$615$	5.06765e19	0.0614106
$616$	0	0
$617$	−6.11863e20	−0.723629	−0.361814	−	0.932250i	$-0.617843\pi$
$617$	−6.11863e20	−0.723629	−0.361814	+	0.932250i	$0.617843\pi$
$618$	0	0
$619$	−8.48529e20	−0.979461	−0.489730	−	0.871874i	$-0.662905\pi$
$619$	−8.48529e20	−0.979461	−0.489730	+	0.871874i	$0.662905\pi$
$620$	0	0
$621$	1.97354e20	0.222361
$622$	0	0
$623$	−1.72943e20	−0.190214
$624$	0	0
$625$	−3.63440e20	−0.390240
$626$	0	0
$627$	−1.41810e19	−0.0148662
$628$	0	0
$629$	−9.04061e19	−0.0925375
$630$	0	0
$631$	2.46175e20	0.246050	0.123025	−	0.992404i	$-0.460740\pi$
$631$	2.46175e20	0.246050	0.123025	+	0.992404i	$0.460740\pi$
$632$	0	0
$633$	5.62808e19	0.0549329
$634$	0	0
$635$	5.38937e20	0.513730
$636$	0	0
$637$	2.00952e21	1.87088
$638$	0	0
$639$	−9.53139e20	−0.866762
$640$	0	0
$641$	−7.97105e20	−0.708077	−0.354039	−	0.935231i	$-0.615192\pi$
$641$	−7.97105e20	−0.708077	−0.354039	+	0.935231i	$0.615192\pi$
$642$	0	0
$643$	−1.97437e21	−1.71335	−0.856674	−	0.515858i	$-0.827473\pi$
$643$	−1.97437e21	−1.71335	−0.856674	+	0.515858i	$0.827473\pi$
$644$	0	0
$645$	−4.26489e19	−0.0361584
$646$	0	0
$647$	−6.95727e20	−0.576311	−0.288155	−	0.957584i	$-0.593042\pi$
$647$	−6.95727e20	−0.576311	−0.288155	+	0.957584i	$0.593042\pi$
$648$	0	0
$649$	−1.37644e21	−1.11410
$650$	0	0
$651$	−9.96950e19	−0.0788526
$652$	0	0
$653$	−1.72385e21	−1.33245	−0.666225	−	0.745751i	$-0.732091\pi$
$653$	−1.72385e21	−1.33245	−0.666225	+	0.745751i	$0.732091\pi$
$654$	0	0
$655$	−1.47672e21	−1.11555
$656$	0	0
$657$	8.24245e20	0.608578
$658$	0	0
$659$	1.18711e21	0.856743	0.428372	−	0.903603i	$-0.359087\pi$
$659$	1.18711e21	0.856743	0.428372	+	0.903603i	$0.359087\pi$
$660$	0	0
$661$	−5.33810e20	−0.376596	−0.188298	−	0.982112i	$-0.560297\pi$
$661$	−5.33810e20	−0.376596	−0.188298	+	0.982112i	$0.560297\pi$
$662$	0	0
$663$	−1.45509e20	−0.100355
$664$	0	0
$665$	−5.09560e20	−0.343584
$666$	0	0
$667$	4.12467e21	2.71923
$668$	0	0
$669$	−3.44170e18	−0.00221859
$670$	0	0
$671$	−7.51440e20	−0.473669
$672$	0	0
$673$	2.17188e21	1.33882	0.669412	−	0.742892i	$-0.266546\pi$
$673$	2.17188e21	1.33882	0.669412	+	0.742892i	$0.266546\pi$
$674$	0	0
$675$	1.02995e20	0.0620925
$676$	0	0
$677$	−6.65673e20	−0.392506	−0.196253	−	0.980553i	$-0.562877\pi$
$677$	−6.65673e20	−0.392506	−0.196253	+	0.980553i	$0.562877\pi$
$678$	0	0
$679$	3.41081e20	0.196714
$680$	0	0
$681$	−1.62884e20	−0.0918916
$682$	0	0
$683$	−5.80477e20	−0.320354	−0.160177	−	0.987088i	$-0.551206\pi$
$683$	−5.80477e20	−0.320354	−0.160177	+	0.987088i	$0.551206\pi$
$684$	0	0
$685$	8.41486e20	0.454326
$686$	0	0
$687$	5.22784e19	0.0276151
$688$	0	0
$689$	−1.10751e21	−0.572403
$690$	0	0
$691$	−7.03253e20	−0.355653	−0.177826	−	0.984062i	$-0.556907\pi$
$691$	−7.03253e20	−0.355653	−0.177826	+	0.984062i	$0.556907\pi$
$692$	0	0
$693$	2.44641e21	1.21068
$694$	0	0
$695$	−2.18135e21	−1.05643
$696$	0	0
$697$	2.95488e21	1.40054
$698$	0	0
$699$	3.45320e19	0.0160193
$700$	0	0
$701$	−2.35895e21	−1.07111	−0.535555	−	0.844500i	$-0.679898\pi$
$701$	−2.35895e21	−1.07111	−0.535555	+	0.844500i	$0.679898\pi$
$702$	0	0
$703$	4.56714e19	0.0202992
$704$	0	0
$705$	−6.00499e19	−0.0261273
$706$	0	0
$707$	4.15346e21	1.76915
$708$	0	0
$709$	2.25453e21	0.940178	0.470089	−	0.882619i	$-0.344222\pi$
$709$	2.25453e21	0.940178	0.470089	+	0.882619i	$0.344222\pi$
$710$	0	0
$711$	2.83599e21	1.15793
$712$	0	0
$713$	2.51669e21	1.00614
$714$	0	0
$715$	1.56597e21	0.613038
$716$	0	0
$717$	−7.23232e19	−0.0277258
$718$	0	0
$719$	−1.60661e21	−0.603176	−0.301588	−	0.953438i	$-0.597517\pi$
$719$	−1.60661e21	−0.603176	−0.301588	+	0.953438i	$0.597517\pi$
$720$	0	0
$721$	−5.80018e21	−2.13269
$722$	0	0
$723$	3.66431e17	0.000131964 0
$724$	0	0
$725$	2.15259e21	0.759321
$726$	0	0
$727$	1.86781e21	0.645395	0.322697	−	0.946502i	$-0.395410\pi$
$727$	1.86781e21	0.645395	0.322697	+	0.946502i	$0.395410\pi$
$728$	0	0
$729$	−2.86062e21	−0.968288
$730$	0	0
$731$	−2.48680e21	−0.824633
$732$	0	0
$733$	−3.05032e21	−0.990983	−0.495491	−	0.868613i	$-0.665012\pi$
$733$	−3.05032e21	−0.990983	−0.495491	+	0.868613i	$0.665012\pi$
$734$	0	0
$735$	−2.95931e20	−0.0941968
$736$	0	0
$737$	2.94588e21	0.918775
$738$	0	0
$739$	−4.19047e21	−1.28065	−0.640323	−	0.768106i	$-0.721200\pi$
$739$	−4.19047e21	−1.28065	−0.640323	+	0.768106i	$0.721200\pi$
$740$	0	0
$741$	7.35084e19	0.0220141
$742$	0	0
$743$	−4.43470e21	−1.30151	−0.650756	−	0.759287i	$-0.725548\pi$
$743$	−4.43470e21	−1.30151	−0.650756	+	0.759287i	$0.725548\pi$
$744$	0	0
$745$	4.36584e20	0.125573
$746$	0	0
$747$	−1.61775e21	−0.456043
$748$	0	0
$749$	−1.32784e21	−0.366888
$750$	0	0
$751$	2.92003e21	0.790840	0.395420	−	0.918500i	$-0.370599\pi$
$751$	2.92003e21	0.790840	0.395420	+	0.918500i	$0.370599\pi$
$752$	0	0
$753$	4.06948e20	0.108038
$754$	0	0
$755$	5.70450e20	0.148462
$756$	0	0
$757$	7.26556e20	0.185374	0.0926872	−	0.995695i	$-0.470454\pi$
$757$	7.26556e20	0.185374	0.0926872	+	0.995695i	$0.470454\pi$
$758$	0	0
$759$	3.29606e20	0.0824483
$760$	0	0
$761$	4.27961e21	1.04959	0.524795	−	0.851229i	$-0.324142\pi$
$761$	4.27961e21	1.04959	0.524795	+	0.851229i	$0.324142\pi$
$762$	0	0
$763$	−7.78648e21	−1.87244
$764$	0	0
$765$	−4.01493e21	−0.946711
$766$	0	0
$767$	7.13492e21	1.64977
$768$	0	0
$769$	−8.11710e21	−1.84057	−0.920287	−	0.391244i	$-0.872045\pi$
$769$	−8.11710e21	−1.84057	−0.920287	+	0.391244i	$0.872045\pi$
$770$	0	0
$771$	−6.19182e19	−0.0137692
$772$	0	0
$773$	−2.50509e20	−0.0546358	−0.0273179	−	0.999627i	$-0.508697\pi$
$773$	−2.50509e20	−0.0546358	−0.0273179	+	0.999627i	$0.508697\pi$
$774$	0	0
$775$	1.31341e21	0.280955
$776$	0	0
$777$	4.20512e19	0.00882309
$778$	0	0
$779$	−1.49275e21	−0.307224
$780$	0	0
$781$	−3.19222e21	−0.644480
$782$	0	0
$783$	1.30422e21	0.258307
$784$	0	0
$785$	2.31061e21	0.448957
$786$	0	0
$787$	1.41837e21	0.270383	0.135191	−	0.990819i	$-0.456835\pi$
$787$	1.41837e21	0.270383	0.135191	+	0.990819i	$0.456835\pi$
$788$	0	0
$789$	−5.80048e19	−0.0108489
$790$	0	0
$791$	5.45606e20	0.100128
$792$	0	0
$793$	3.89517e21	0.701418
$794$	0	0
$795$	1.63097e20	0.0288198
$796$	0	0
$797$	5.73312e21	0.994154	0.497077	−	0.867707i	$-0.334407\pi$
$797$	5.73312e21	0.994154	0.497077	+	0.867707i	$0.334407\pi$
$798$	0	0
$799$	−3.50143e21	−0.595861
$800$	0	0
$801$	6.88386e20	0.114971
$802$	0	0
$803$	2.76053e21	0.452508
$804$	0	0
$805$	1.18436e22	1.90553
$806$	0	0
$807$	−3.07602e20	−0.0485778
$808$	0	0
$809$	−1.91138e21	−0.296301	−0.148150	−	0.988965i	$-0.547332\pi$
$809$	−1.91138e21	−0.296301	−0.148150	+	0.988965i	$0.547332\pi$
$810$	0	0
$811$	5.22815e21	0.795594	0.397797	−	0.917473i	$-0.369775\pi$
$811$	5.22815e21	0.795594	0.397797	+	0.917473i	$0.369775\pi$
$812$	0	0
$813$	−3.85343e20	−0.0575663
$814$	0	0
$815$	6.54663e21	0.960142
$816$	0	0
$817$	1.25628e21	0.180893
$818$	0	0
$819$	−1.26812e22	−1.79280
$820$	0	0
$821$	2.67624e21	0.371493	0.185747	−	0.982598i	$-0.440530\pi$
$821$	2.67624e21	0.371493	0.185747	+	0.982598i	$0.440530\pi$
$822$	0	0
$823$	7.87824e21	1.07382	0.536909	−	0.843640i	$-0.319592\pi$
$823$	7.87824e21	1.07382	0.536909	+	0.843640i	$0.319592\pi$
$824$	0	0
$825$	1.72015e20	0.0230230
$826$	0	0
$827$	5.82948e21	0.766193	0.383097	−	0.923708i	$-0.374858\pi$
$827$	5.82948e21	0.766193	0.383097	+	0.923708i	$0.374858\pi$
$828$	0	0
$829$	−8.01369e21	−1.03436	−0.517182	−	0.855875i	$-0.673019\pi$
$829$	−8.01369e21	−1.03436	−0.517182	+	0.855875i	$0.673019\pi$
$830$	0	0
$831$	−2.00360e20	−0.0253982
$832$	0	0
$833$	−1.72554e22	−2.14826
$834$	0	0
$835$	−3.09259e21	−0.378158
$836$	0	0
$837$	7.95774e20	0.0955760
$838$	0	0
$839$	8.32442e21	0.982063	0.491031	−	0.871142i	$-0.336620\pi$
$839$	8.32442e21	0.982063	0.491031	+	0.871142i	$0.336620\pi$
$840$	0	0
$841$	1.86287e22	2.15880
$842$	0	0
$843$	−3.83237e20	−0.0436276
$844$	0	0
$845$	−1.35006e21	−0.150983
$846$	0	0
$847$	−6.78509e21	−0.745470
$848$	0	0
$849$	1.15144e21	0.124289
$850$	0	0
$851$	−1.06153e21	−0.112580
$852$	0	0
$853$	−1.52798e22	−1.59221	−0.796105	−	0.605159i	$-0.793110\pi$
$853$	−1.52798e22	−1.59221	−0.796105	+	0.605159i	$0.793110\pi$
$854$	0	0
$855$	2.02826e21	0.207672
$856$	0	0
$857$	1.01566e22	1.02186	0.510929	−	0.859623i	$-0.329301\pi$
$857$	1.01566e22	1.02186	0.510929	+	0.859623i	$0.329301\pi$
$858$	0	0
$859$	−1.38374e22	−1.36806	−0.684031	−	0.729453i	$-0.739775\pi$
$859$	−1.38374e22	−1.36806	−0.684031	+	0.729453i	$0.739775\pi$
$860$	0	0
$861$	−1.37442e21	−0.133536
$862$	0	0
$863$	−1.44757e22	−1.38216	−0.691081	−	0.722778i	$-0.742865\pi$
$863$	−1.44757e22	−1.38216	−0.691081	+	0.722778i	$0.742865\pi$
$864$	0	0
$865$	−7.04916e21	−0.661480
$866$	0	0
$867$	4.59432e20	0.0423719
$868$	0	0
$869$	9.49820e21	0.860980
$870$	0	0
$871$	−1.52703e22	−1.36054
$872$	0	0
$873$	−1.35765e21	−0.118899
$874$	0	0
$875$	2.06484e22	1.77757
$876$	0	0
$877$	−4.82674e21	−0.408467	−0.204234	−	0.978922i	$-0.565470\pi$
$877$	−4.82674e21	−0.408467	−0.204234	+	0.978922i	$0.565470\pi$
$878$	0	0
$879$	−1.64965e21	−0.137238
$880$	0	0
$881$	−1.19939e22	−0.980934	−0.490467	−	0.871460i	$-0.663174\pi$
$881$	−1.19939e22	−0.980934	−0.490467	+	0.871460i	$0.663174\pi$
$882$	0	0
$883$	7.57807e21	0.609331	0.304666	−	0.952459i	$-0.401455\pi$
$883$	7.57807e21	0.609331	0.304666	+	0.952459i	$0.401455\pi$
$884$	0	0
$885$	−1.05072e21	−0.0830640
$886$	0	0
$887$	−4.60362e21	−0.357826	−0.178913	−	0.983865i	$-0.557258\pi$
$887$	−4.60362e21	−0.357826	−0.178913	+	0.983865i	$0.557258\pi$
$888$	0	0
$889$	−1.46168e22	−1.11709
$890$	0	0
$891$	−9.68548e21	−0.727844
$892$	0	0
$893$	1.76885e21	0.130709
$894$	0	0
$895$	5.84007e21	0.424371
$896$	0	0
$897$	−1.70855e21	−0.122091
$898$	0	0
$899$	1.66315e22	1.16879
$900$	0	0
$901$	9.50995e21	0.657267
$902$	0	0
$903$	1.15670e21	0.0786255
$904$	0	0
$905$	1.12687e22	0.753375
$906$	0	0
$907$	1.22617e22	0.806302	0.403151	−	0.915133i	$-0.367915\pi$
$907$	1.22617e22	0.806302	0.403151	+	0.915133i	$0.367915\pi$
$908$	0	0
$909$	−1.65325e22	−1.06933
$910$	0	0
$911$	−2.67560e22	−1.70229	−0.851146	−	0.524929i	$-0.824092\pi$
$911$	−2.67560e22	−1.70229	−0.851146	+	0.524929i	$0.824092\pi$
$912$	0	0
$913$	−5.41809e21	−0.339090
$914$	0	0
$915$	−5.73620e20	−0.0353156
$916$	0	0
$917$	4.00510e22	2.42573
$918$	0	0
$919$	−1.63829e22	−0.976171	−0.488085	−	0.872796i	$-0.662304\pi$
$919$	−1.63829e22	−0.976171	−0.488085	+	0.872796i	$0.662304\pi$
$920$	0	0
$921$	1.97696e21	0.115891
$922$	0	0
$923$	1.65472e22	0.954358
$924$	0	0
$925$	−5.53994e20	−0.0314371
$926$	0	0
$927$	2.30871e22	1.28906
$928$	0	0
$929$	3.04477e22	1.67277	0.836387	−	0.548140i	$-0.184664\pi$
$929$	3.04477e22	1.67277	0.836387	+	0.548140i	$0.184664\pi$
$930$	0	0
$931$	8.71707e21	0.471246
$932$	0	0
$933$	−1.53287e21	−0.0815441
$934$	0	0
$935$	−1.34467e22	−0.703926
$936$	0	0
$937$	1.77203e22	0.912903	0.456451	−	0.889748i	$-0.349120\pi$
$937$	1.77203e22	0.912903	0.456451	+	0.889748i	$0.349120\pi$
$938$	0	0
$939$	−1.44383e21	−0.0732024
$940$	0	0
$941$	−2.63345e22	−1.31402	−0.657011	−	0.753881i	$-0.728179\pi$
$941$	−2.63345e22	−1.31402	−0.657011	+	0.753881i	$0.728179\pi$
$942$	0	0
$943$	3.46957e22	1.70388
$944$	0	0
$945$	3.74495e21	0.181012
$946$	0	0
$947$	6.91872e21	0.329155	0.164578	−	0.986364i	$-0.447374\pi$
$947$	6.91872e21	0.329155	0.164578	+	0.986364i	$0.447374\pi$
$948$	0	0
$949$	−1.43095e22	−0.670082
$950$	0	0
$951$	1.79739e21	0.0828491
$952$	0	0
$953$	−2.25013e22	−1.02097	−0.510483	−	0.859888i	$-0.670533\pi$
$953$	−2.25013e22	−1.02097	−0.510483	+	0.859888i	$0.670533\pi$
$954$	0	0
$955$	−2.17977e22	−0.973612
$956$	0	0
$957$	2.17820e21	0.0957765
$958$	0	0
$959$	−2.28224e22	−0.987920
$960$	0	0
$961$	−1.33175e22	−0.567539
$962$	0	0
$963$	5.28537e21	0.221757
$964$	0	0
$965$	−2.20910e22	−0.912558
$966$	0	0
$967$	1.96165e22	0.797853	0.398926	−	0.916983i	$-0.369383\pi$
$967$	1.96165e22	0.797853	0.398926	+	0.916983i	$0.369383\pi$
$968$	0	0
$969$	−6.31203e20	−0.0252779
$970$	0	0
$971$	1.13903e21	0.0449148	0.0224574	−	0.999748i	$-0.492851\pi$
$971$	1.13903e21	0.0449148	0.0224574	+	0.999748i	$0.492851\pi$
$972$	0	0
$973$	5.91615e22	2.29717
$974$	0	0
$975$	−8.91658e20	−0.0340929
$976$	0	0
$977$	6.23540e21	0.234777	0.117388	−	0.993086i	$-0.462548\pi$
$977$	6.23540e21	0.234777	0.117388	+	0.993086i	$0.462548\pi$
$978$	0	0
$979$	2.30552e21	0.0854867
$980$	0	0
$981$	3.09935e22	1.13176
$982$	0	0
$983$	−5.13857e22	−1.84795	−0.923977	−	0.382448i	$-0.875081\pi$
$983$	−5.13857e22	−1.84795	−0.923977	+	0.382448i	$0.875081\pi$
$984$	0	0
$985$	−1.40854e22	−0.498883
$986$	0	0
$987$	1.62864e21	0.0568130
$988$	0	0
$989$	−2.91996e22	−1.00324
$990$	0	0
$991$	3.04476e21	0.103039	0.0515194	−	0.998672i	$-0.483594\pi$
$991$	3.04476e21	0.103039	0.0515194	+	0.998672i	$0.483594\pi$
$992$	0	0
$993$	−3.15550e21	−0.105184
$994$	0	0
$995$	−2.60620e22	−0.855724
$996$	0	0
$997$	−3.60430e22	−1.16576	−0.582878	−	0.812560i	$-0.698073\pi$
$997$	−3.60430e22	−1.16576	−0.582878	+	0.812560i	$0.698073\pi$
$998$	0	0
$999$	−3.35656e20	−0.0106943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.16.a.c.1.1		1
3.2	odd	2		144.16.a.k.1.1		1
4.3	odd	2		4.16.a.a.1.1	✓	1
8.3	odd	2		64.16.a.g.1.1		1
8.5	even	2		64.16.a.e.1.1		1
12.11	even	2		36.16.a.b.1.1		1
20.3	even	4		100.16.c.a.49.1		2
20.7	even	4		100.16.c.a.49.2		2
20.19	odd	2		100.16.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.16.a.a.1.1	✓	1	4.3	odd	2
16.16.a.c.1.1		1	1.1	even	1	trivial
36.16.a.b.1.1		1	12.11	even	2
64.16.a.e.1.1		1	8.5	even	2
64.16.a.g.1.1		1	8.3	odd	2
100.16.a.a.1.1		1	20.19	odd	2
100.16.c.a.49.1		2	20.3	even	4
100.16.c.a.49.2		2	20.7	even	4
144.16.a.k.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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