LMFDB - Embedded newform 64.18.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,18,Mod(1,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	64.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:	$117.262135901$
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	$\chi$	$=$	64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-6084.00 q^{3} -1.25511e6 q^{5} -2.24659e7 q^{7} -9.21251e7 q^{9} +O(q^{10})$

$q-6084.00 q^{3} -1.25511e6 q^{5} -2.24659e7 q^{7} -9.21251e7 q^{9} -1.72400e8 q^{11} +2.18015e9 q^{13} +7.63609e9 q^{15} +3.01639e10 q^{17} +7.62758e10 q^{19} +1.36683e11 q^{21} +1.30467e11 q^{23} +8.12362e11 q^{25} +1.34618e12 q^{27} -8.03134e11 q^{29} +2.04534e12 q^{31} +1.04888e12 q^{33} +2.81972e13 q^{35} -3.38554e13 q^{37} -1.32640e13 q^{39} +5.32064e13 q^{41} -2.65904e13 q^{43} +1.15627e14 q^{45} -2.32565e14 q^{47} +2.72087e14 q^{49} -1.83517e14 q^{51} +1.63278e14 q^{53} +2.16381e14 q^{55} -4.64062e14 q^{57} -6.97821e14 q^{59} +8.98968e14 q^{61} +2.06967e15 q^{63} -2.73633e15 q^{65} +2.66700e15 q^{67} -7.93759e14 q^{69} +3.91064e15 q^{71} +5.85593e15 q^{73} -4.94241e15 q^{75} +3.87312e15 q^{77} -2.38217e16 q^{79} +3.70690e15 q^{81} +1.39157e16 q^{83} -3.78591e16 q^{85} +4.88627e15 q^{87} -3.07227e16 q^{89} -4.89790e16 q^{91} -1.24438e16 q^{93} -9.57345e16 q^{95} +5.76491e16 q^{97} +1.58823e16 q^{99} +O(q^{100})$

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
$3$	−6084.00	−0.535376	−0.267688	−	0.963506i	$-0.586260\pi$
$3$	−6084.00	−0.535376	−0.267688	+	0.963506i	$0.586260\pi$
$4$	0	0
$5$	−1.25511e6	−1.43693	−0.718467	−	0.695561i	$-0.755156\pi$
$5$	−1.25511e6	−1.43693	−0.718467	+	0.695561i	$0.755156\pi$
$6$	0	0
$7$	−2.24659e7	−1.47296	−0.736480	−	0.676460i	$-0.763513\pi$
$7$	−2.24659e7	−1.47296	−0.736480	+	0.676460i	$0.763513\pi$
$8$	0	0
$9$	−9.21251e7	−0.713373
$10$	0	0
$11$	−1.72400e8	−0.242493	−0.121246	−	0.992622i	$-0.538689\pi$
$11$	−1.72400e8	−0.242493	−0.121246	+	0.992622i	$0.538689\pi$
$12$	0	0
$13$	2.18015e9	0.741255	0.370628	−	0.928782i	$-0.379143\pi$
$13$	2.18015e9	0.741255	0.370628	+	0.928782i	$0.379143\pi$
$14$	0	0
$15$	7.63609e9	0.769299
$16$	0	0
$17$	3.01639e10	1.04875	0.524375	−	0.851487i	$-0.324299\pi$
$17$	3.01639e10	1.04875	0.524375	+	0.851487i	$0.324299\pi$
$18$	0	0
$19$	7.62758e10	1.03034	0.515170	−	0.857088i	$-0.327729\pi$
$19$	7.62758e10	1.03034	0.515170	+	0.857088i	$0.327729\pi$
$20$	0	0
$21$	1.36683e11	0.788586
$22$	0	0
$23$	1.30467e11	0.347386	0.173693	−	0.984800i	$-0.444430\pi$
$23$	1.30467e11	0.347386	0.173693	+	0.984800i	$0.444430\pi$
$24$	0	0
$25$	8.12362e11	1.06478
$26$	0	0
$27$	1.34618e12	0.917298
$28$	0	0
$29$	−8.03134e11	−0.298130	−0.149065	−	0.988827i	$-0.547626\pi$
$29$	−8.03134e11	−0.298130	−0.149065	+	0.988827i	$0.547626\pi$
$30$	0	0
$31$	2.04534e12	0.430715	0.215358	−	0.976535i	$-0.430908\pi$
$31$	2.04534e12	0.430715	0.215358	+	0.976535i	$0.430908\pi$
$32$	0	0
$33$	1.04888e12	0.129825
$34$	0	0
$35$	2.81972e13	2.11654
$36$	0	0
$37$	−3.38554e13	−1.58458	−0.792288	−	0.610148i	$-0.791110\pi$
$37$	−3.38554e13	−1.58458	−0.792288	+	0.610148i	$0.791110\pi$
$38$	0	0
$39$	−1.32640e13	−0.396850
$40$	0	0
$41$	5.32064e13	1.04064	0.520321	−	0.853971i	$-0.325812\pi$
$41$	5.32064e13	1.04064	0.520321	+	0.853971i	$0.325812\pi$
$42$	0	0
$43$	−2.65904e13	−0.346930	−0.173465	−	0.984840i	$-0.555496\pi$
$43$	−2.65904e13	−0.346930	−0.173465	+	0.984840i	$0.555496\pi$
$44$	0	0
$45$	1.15627e14	1.02507
$46$	0	0
$47$	−2.32565e14	−1.42467	−0.712333	−	0.701841i	$-0.752362\pi$
$47$	−2.32565e14	−1.42467	−0.712333	+	0.701841i	$0.752362\pi$
$48$	0	0
$49$	2.72087e14	1.16961
$50$	0	0
$51$	−1.83517e14	−0.561475
$52$	0	0
$53$	1.63278e14	0.360232	0.180116	−	0.983645i	$-0.442353\pi$
$53$	1.63278e14	0.360232	0.180116	+	0.983645i	$0.442353\pi$
$54$	0	0
$55$	2.16381e14	0.348446
$56$	0	0
$57$	−4.64062e14	−0.551619
$58$	0	0
$59$	−6.97821e14	−0.618731	−0.309365	−	0.950943i	$-0.600117\pi$
$59$	−6.97821e14	−0.618731	−0.309365	+	0.950943i	$0.600117\pi$
$60$	0	0
$61$	8.98968e14	0.600400	0.300200	−	0.953876i	$-0.402947\pi$
$61$	8.98968e14	0.600400	0.300200	+	0.953876i	$0.402947\pi$
$62$	0	0
$63$	2.06967e15	1.05077
$64$	0	0
$65$	−2.73633e15	−1.06513
$66$	0	0
$67$	2.66700e15	0.802394	0.401197	−	0.915992i	$-0.368594\pi$
$67$	2.66700e15	0.802394	0.401197	+	0.915992i	$0.368594\pi$
$68$	0	0
$69$	−7.93759e14	−0.185982
$70$	0	0
$71$	3.91064e15	0.718707	0.359353	−	0.933202i	$-0.382997\pi$
$71$	3.91064e15	0.718707	0.359353	+	0.933202i	$0.382997\pi$
$72$	0	0
$73$	5.85593e15	0.849868	0.424934	−	0.905224i	$-0.360297\pi$
$73$	5.85593e15	0.849868	0.424934	+	0.905224i	$0.360297\pi$
$74$	0	0
$75$	−4.94241e15	−0.570056
$76$	0	0
$77$	3.87312e15	0.357182
$78$	0	0
$79$	−2.38217e16	−1.76662	−0.883310	−	0.468789i	$-0.844690\pi$
$79$	−2.38217e16	−1.76662	−0.883310	+	0.468789i	$0.844690\pi$
$80$	0	0
$81$	3.70690e15	0.222274
$82$	0	0
$83$	1.39157e16	0.678176	0.339088	−	0.940755i	$-0.389881\pi$
$83$	1.39157e16	0.678176	0.339088	+	0.940755i	$0.389881\pi$
$84$	0	0
$85$	−3.78591e16	−1.50698
$86$	0	0
$87$	4.88627e15	0.159611
$88$	0	0
$89$	−3.07227e16	−0.827266	−0.413633	−	0.910444i	$-0.635740\pi$
$89$	−3.07227e16	−0.827266	−0.413633	+	0.910444i	$0.635740\pi$
$90$	0	0
$91$	−4.89790e16	−1.09184
$92$	0	0
$93$	−1.24438e16	−0.230594
$94$	0	0
$95$	−9.57345e16	−1.48053
$96$	0	0
$97$	5.76491e16	0.746849	0.373424	−	0.927661i	$-0.378183\pi$
$97$	5.76491e16	0.746849	0.373424	+	0.927661i	$0.378183\pi$
$98$	0	0
$99$	1.58823e16	0.172988
$100$	0	0
$101$	3.80153e16	0.349323	0.174661	−	0.984629i	$-0.444117\pi$
$101$	3.80153e16	0.349323	0.174661	+	0.984629i	$0.444117\pi$
$102$	0	0
$103$	1.43913e17	1.11940	0.559700	−	0.828696i	$-0.310917\pi$
$103$	1.43913e17	1.11940	0.559700	+	0.828696i	$0.310917\pi$
$104$	0	0
$105$	−1.71552e17	−1.13315
$106$	0	0
$107$	−9.14309e16	−0.514435	−0.257218	−	0.966353i	$-0.582806\pi$
$107$	−9.14309e16	−0.514435	−0.257218	+	0.966353i	$0.582806\pi$
$108$	0	0
$109$	3.74881e17	1.80205	0.901027	−	0.433762i	$-0.142814\pi$
$109$	3.74881e17	1.80205	0.901027	+	0.433762i	$0.142814\pi$
$110$	0	0
$111$	2.05976e17	0.848343
$112$	0	0
$113$	4.32401e17	1.53010	0.765051	−	0.643970i	$-0.222714\pi$
$113$	4.32401e17	1.53010	0.765051	+	0.643970i	$0.222714\pi$
$114$	0	0
$115$	−1.63750e17	−0.499171
$116$	0	0
$117$	−2.00846e17	−0.528791
$118$	0	0
$119$	−6.77660e17	−1.54477
$120$	0	0
$121$	−4.75725e17	−0.941197
$122$	0	0
$123$	−3.23708e17	−0.557134
$124$	0	0
$125$	−6.20303e16	−0.0930827
$126$	0	0
$127$	−1.20057e18	−1.57418	−0.787091	−	0.616836i	$-0.788414\pi$
$127$	−1.20057e18	−1.57418	−0.787091	+	0.616836i	$0.788414\pi$
$128$	0	0
$129$	1.61776e17	0.185738
$130$	0	0
$131$	−1.75544e18	−1.76840	−0.884198	−	0.467112i	$-0.845295\pi$
$131$	−1.75544e18	−1.76840	−0.884198	+	0.467112i	$0.845295\pi$
$132$	0	0
$133$	−1.71360e18	−1.51765
$134$	0	0
$135$	−1.68960e18	−1.31810
$136$	0	0
$137$	4.29231e17	0.295506	0.147753	−	0.989024i	$-0.452796\pi$
$137$	4.29231e17	0.295506	0.147753	+	0.989024i	$0.452796\pi$
$138$	0	0
$139$	8.28362e17	0.504190	0.252095	−	0.967702i	$-0.418880\pi$
$139$	8.28362e17	0.504190	0.252095	+	0.967702i	$0.418880\pi$
$140$	0	0
$141$	1.41493e18	0.762732
$142$	0	0
$143$	−3.75857e17	−0.179749
$144$	0	0
$145$	1.00802e18	0.428393
$146$	0	0
$147$	−1.65538e18	−0.626180
$148$	0	0
$149$	3.84279e17	0.129587	0.0647937	−	0.997899i	$-0.479361\pi$
$149$	3.84279e17	0.129587	0.0647937	+	0.997899i	$0.479361\pi$
$150$	0	0
$151$	−8.97916e17	−0.270353	−0.135177	−	0.990822i	$-0.543160\pi$
$151$	−8.97916e17	−0.270353	−0.135177	+	0.990822i	$0.543160\pi$
$152$	0	0
$153$	−2.77886e18	−0.748150
$154$	0	0
$155$	−2.56712e18	−0.618909
$156$	0	0
$157$	−3.59596e16	−0.00777442	−0.00388721	−	0.999992i	$-0.501237\pi$
$157$	−3.59596e16	−0.00777442	−0.00388721	+	0.999992i	$0.501237\pi$
$158$	0	0
$159$	−9.93383e17	−0.192859
$160$	0	0
$161$	−2.93105e18	−0.511686
$162$	0	0
$163$	−1.15191e19	−1.81060	−0.905301	−	0.424771i	$-0.860354\pi$
$163$	−1.15191e19	−1.81060	−0.905301	+	0.424771i	$0.860354\pi$
$164$	0	0
$165$	−1.31646e18	−0.186549
$166$	0	0
$167$	−4.51883e18	−0.578011	−0.289006	−	0.957327i	$-0.593325\pi$
$167$	−4.51883e18	−0.578011	−0.289006	+	0.957327i	$0.593325\pi$
$168$	0	0
$169$	−3.89736e18	−0.450541
$170$	0	0
$171$	−7.02691e18	−0.735017
$172$	0	0
$173$	6.30747e18	0.597673	0.298837	−	0.954304i	$-0.403401\pi$
$173$	6.30747e18	0.597673	0.298837	+	0.954304i	$0.403401\pi$
$174$	0	0
$175$	−1.82504e19	−1.56838
$176$	0	0
$177$	4.24554e18	0.331253
$178$	0	0
$179$	−4.69485e18	−0.332944	−0.166472	−	0.986046i	$-0.553237\pi$
$179$	−4.69485e18	−0.332944	−0.166472	+	0.986046i	$0.553237\pi$
$180$	0	0
$181$	7.61795e18	0.491553	0.245776	−	0.969327i	$-0.420957\pi$
$181$	7.61795e18	0.491553	0.245776	+	0.969327i	$0.420957\pi$
$182$	0	0
$183$	−5.46932e18	−0.321440
$184$	0	0
$185$	4.24922e19	2.27693
$186$	0	0
$187$	−5.20025e18	−0.254314
$188$	0	0
$189$	−3.02431e19	−1.35114
$190$	0	0
$191$	−3.26501e19	−1.33383	−0.666916	−	0.745133i	$-0.732386\pi$
$191$	−3.26501e19	−1.33383	−0.666916	+	0.745133i	$0.732386\pi$
$192$	0	0
$193$	−2.16468e19	−0.809386	−0.404693	−	0.914453i	$-0.632622\pi$
$193$	−2.16468e19	−0.809386	−0.404693	+	0.914453i	$0.632622\pi$
$194$	0	0
$195$	1.66478e19	0.570247
$196$	0	0
$197$	4.59530e19	1.44328	0.721641	−	0.692268i	$-0.243388\pi$
$197$	4.59530e19	1.44328	0.721641	+	0.692268i	$0.243388\pi$
$198$	0	0
$199$	5.74258e19	1.65522	0.827610	−	0.561303i	$-0.189700\pi$
$199$	5.74258e19	1.65522	0.827610	+	0.561303i	$0.189700\pi$
$200$	0	0
$201$	−1.62260e19	−0.429582
$202$	0	0
$203$	1.80431e19	0.439133
$204$	0	0
$205$	−6.67799e19	−1.49533
$206$	0	0
$207$	−1.20192e19	−0.247816
$208$	0	0
$209$	−1.31499e19	−0.249850
$210$	0	0
$211$	2.94651e19	0.516305	0.258153	−	0.966104i	$-0.416886\pi$
$211$	2.94651e19	0.516305	0.258153	+	0.966104i	$0.416886\pi$
$212$	0	0
$213$	−2.37923e19	−0.384778
$214$	0	0
$215$	3.33738e19	0.498516
$216$	0	0
$217$	−4.59503e19	−0.634426
$218$	0	0
$219$	−3.56275e19	−0.454999
$220$	0	0
$221$	6.57619e19	0.777392
$222$	0	0
$223$	1.27173e20	1.39252	0.696262	−	0.717788i	$-0.254845\pi$
$223$	1.27173e20	1.39252	0.696262	+	0.717788i	$0.254845\pi$
$224$	0	0
$225$	−7.48389e19	−0.759584
$226$	0	0
$227$	−8.30214e19	−0.781574	−0.390787	−	0.920481i	$-0.627797\pi$
$227$	−8.30214e19	−0.781574	−0.390787	+	0.920481i	$0.627797\pi$
$228$	0	0
$229$	6.40290e19	0.559468	0.279734	−	0.960078i	$-0.409754\pi$
$229$	6.40290e19	0.559468	0.279734	+	0.960078i	$0.409754\pi$
$230$	0	0
$231$	−2.35640e19	−0.191226
$232$	0	0
$233$	1.53412e20	1.15700	0.578501	−	0.815682i	$-0.303638\pi$
$233$	1.53412e20	1.15700	0.578501	+	0.815682i	$0.303638\pi$
$234$	0	0
$235$	2.91895e20	2.04715
$236$	0	0
$237$	1.44931e20	0.945805
$238$	0	0
$239$	−5.35334e19	−0.325269	−0.162635	−	0.986686i	$-0.551999\pi$
$239$	−5.35334e19	−0.325269	−0.162635	+	0.986686i	$0.551999\pi$
$240$	0	0
$241$	7.12230e19	0.403158	0.201579	−	0.979472i	$-0.435393\pi$
$241$	7.12230e19	0.403158	0.201579	+	0.979472i	$0.435393\pi$
$242$	0	0
$243$	−1.96398e20	−1.03630
$244$	0	0
$245$	−3.41499e20	−1.68065
$246$	0	0
$247$	1.66293e20	0.763746
$248$	0	0
$249$	−8.46634e19	−0.363079
$250$	0	0
$251$	3.66706e20	1.46924	0.734618	−	0.678481i	$-0.237361\pi$
$251$	3.66706e20	1.46924	0.734618	+	0.678481i	$0.237361\pi$
$252$	0	0
$253$	−2.24924e19	−0.0842386
$254$	0	0
$255$	2.30334e20	0.806803
$256$	0	0
$257$	2.48604e20	0.814849	0.407425	−	0.913239i	$-0.366427\pi$
$257$	2.48604e20	0.814849	0.407425	+	0.913239i	$0.366427\pi$
$258$	0	0
$259$	7.60592e20	2.33401
$260$	0	0
$261$	7.39888e19	0.212678
$262$	0	0
$263$	9.04042e19	0.243537	0.121768	−	0.992559i	$-0.461143\pi$
$263$	9.04042e19	0.243537	0.121768	+	0.992559i	$0.461143\pi$
$264$	0	0
$265$	−2.04932e20	−0.517630
$266$	0	0
$267$	1.86917e20	0.442898
$268$	0	0
$269$	−2.89996e19	−0.0644908	−0.0322454	−	0.999480i	$-0.510266\pi$
$269$	−2.89996e19	−0.0644908	−0.0322454	+	0.999480i	$0.510266\pi$
$270$	0	0
$271$	7.70455e20	1.60882	0.804412	−	0.594072i	$-0.202481\pi$
$271$	7.70455e20	1.60882	0.804412	+	0.594072i	$0.202481\pi$
$272$	0	0
$273$	2.97989e20	0.584544
$274$	0	0
$275$	−1.40051e20	−0.258201
$276$	0	0
$277$	1.55171e20	0.268988	0.134494	−	0.990914i	$-0.457059\pi$
$277$	1.55171e20	0.268988	0.134494	+	0.990914i	$0.457059\pi$
$278$	0	0
$279$	−1.88427e20	−0.307261
$280$	0	0
$281$	−4.97825e20	−0.763964	−0.381982	−	0.924170i	$-0.624758\pi$
$281$	−4.97825e20	−0.763964	−0.381982	+	0.924170i	$0.624758\pi$
$282$	0	0
$283$	−1.19056e21	−1.72016	−0.860078	−	0.510163i	$-0.829585\pi$
$283$	−1.19056e21	−1.72016	−0.860078	+	0.510163i	$0.829585\pi$
$284$	0	0
$285$	5.82449e20	0.792641
$286$	0	0
$287$	−1.19533e21	−1.53282
$288$	0	0
$289$	8.26226e19	0.0998774
$290$	0	0
$291$	−3.50737e20	−0.399845
$292$	0	0
$293$	−5.21973e20	−0.561401	−0.280701	−	0.959795i	$-0.590567\pi$
$293$	−5.21973e20	−0.561401	−0.280701	+	0.959795i	$0.590567\pi$
$294$	0	0
$295$	8.75842e20	0.889075
$296$	0	0
$297$	−2.32081e20	−0.222438
$298$	0	0
$299$	2.84437e20	0.257502
$300$	0	0
$301$	5.97377e20	0.511014
$302$	0	0
$303$	−2.31285e20	−0.187019
$304$	0	0
$305$	−1.12830e21	−0.862735
$306$	0	0
$307$	1.85651e20	0.134283	0.0671416	−	0.997743i	$-0.478612\pi$
$307$	1.85651e20	0.134283	0.0671416	+	0.997743i	$0.478612\pi$
$308$	0	0
$309$	−8.75569e20	−0.599299
$310$	0	0
$311$	−1.00184e21	−0.649136	−0.324568	−	0.945862i	$-0.605219\pi$
$311$	−1.00184e21	−0.649136	−0.324568	+	0.945862i	$0.605219\pi$
$312$	0	0
$313$	−4.18947e20	−0.257059	−0.128529	−	0.991706i	$-0.541026\pi$
$313$	−4.18947e20	−0.257059	−0.128529	+	0.991706i	$0.541026\pi$
$314$	0	0
$315$	−2.59767e21	−1.50989
$316$	0	0
$317$	−3.02177e21	−1.66440	−0.832199	−	0.554478i	$-0.812918\pi$
$317$	−3.02177e21	−1.66440	−0.832199	+	0.554478i	$0.812918\pi$
$318$	0	0
$319$	1.38460e20	0.0722943
$320$	0	0
$321$	5.56266e20	0.275416
$322$	0	0
$323$	2.30078e21	1.08057
$324$	0	0
$325$	1.77107e21	0.789273
$326$	0	0
$327$	−2.28077e21	−0.964776
$328$	0	0
$329$	5.22479e21	2.09848
$330$	0	0
$331$	1.94091e21	0.740401	0.370200	−	0.928952i	$-0.379289\pi$
$331$	1.94091e21	0.740401	0.370200	+	0.928952i	$0.379289\pi$
$332$	0	0
$333$	3.11893e21	1.13039
$334$	0	0
$335$	−3.34738e21	−1.15299
$336$	0	0
$337$	−1.79576e20	−0.0588022	−0.0294011	−	0.999568i	$-0.509360\pi$
$337$	−1.79576e20	−0.0588022	−0.0294011	+	0.999568i	$0.509360\pi$
$338$	0	0
$339$	−2.63073e21	−0.819179
$340$	0	0
$341$	−3.52615e20	−0.104445
$342$	0	0
$343$	−8.86419e20	−0.249827
$344$	0	0
$345$	9.96255e20	0.267244
$346$	0	0
$347$	−7.43959e21	−1.89998	−0.949989	−	0.312283i	$-0.898906\pi$
$347$	−7.43959e21	−1.89998	−0.949989	+	0.312283i	$0.898906\pi$
$348$	0	0
$349$	−6.07435e20	−0.147735	−0.0738675	−	0.997268i	$-0.523534\pi$
$349$	−6.07435e20	−0.147735	−0.0738675	+	0.997268i	$0.523534\pi$
$350$	0	0
$351$	2.93487e21	0.679952
$352$	0	0
$353$	−5.66609e21	−1.25083	−0.625416	−	0.780292i	$-0.715071\pi$
$353$	−5.66609e21	−1.25083	−0.625416	+	0.780292i	$0.715071\pi$
$354$	0	0
$355$	−4.90828e21	−1.03273
$356$	0	0
$357$	4.12289e21	0.827030
$358$	0	0
$359$	−7.99486e21	−1.52935	−0.764677	−	0.644414i	$-0.777101\pi$
$359$	−7.99486e21	−1.52935	−0.764677	+	0.644414i	$0.777101\pi$
$360$	0	0
$361$	3.37606e20	0.0616025
$362$	0	0
$363$	2.89431e21	0.503894
$364$	0	0
$365$	−7.34984e21	−1.22120
$366$	0	0
$367$	1.36525e21	0.216547	0.108273	−	0.994121i	$-0.465468\pi$
$367$	1.36525e21	0.216547	0.108273	+	0.994121i	$0.465468\pi$
$368$	0	0
$369$	−4.90165e21	−0.742366
$370$	0	0
$371$	−3.66819e21	−0.530607
$372$	0	0
$373$	1.82317e21	0.251942	0.125971	−	0.992034i	$-0.459795\pi$
$373$	1.82317e21	0.251942	0.125971	+	0.992034i	$0.459795\pi$
$374$	0	0
$375$	3.77392e20	0.0498342
$376$	0	0
$377$	−1.75095e21	−0.220990
$378$	0	0
$379$	−5.95497e21	−0.718532	−0.359266	−	0.933235i	$-0.616973\pi$
$379$	−5.95497e21	−0.718532	−0.359266	+	0.933235i	$0.616973\pi$
$380$	0	0
$381$	7.30426e21	0.842779
$382$	0	0
$383$	2.83557e21	0.312933	0.156466	−	0.987683i	$-0.449990\pi$
$383$	2.83557e21	0.312933	0.156466	+	0.987683i	$0.449990\pi$
$384$	0	0
$385$	−4.86119e21	−0.513247
$386$	0	0
$387$	2.44964e21	0.247491
$388$	0	0
$389$	−1.16641e22	−1.12793	−0.563963	−	0.825800i	$-0.690724\pi$
$389$	−1.16641e22	−1.12793	−0.563963	+	0.825800i	$0.690724\pi$
$390$	0	0
$391$	3.93539e21	0.364322
$392$	0	0
$393$	1.06801e22	0.946756
$394$	0	0
$395$	2.98989e22	2.53852
$396$	0	0
$397$	2.09530e21	0.170423	0.0852113	−	0.996363i	$-0.472843\pi$
$397$	2.09530e21	0.170423	0.0852113	+	0.996363i	$0.472843\pi$
$398$	0	0
$399$	1.04256e22	0.812513
$400$	0	0
$401$	2.60385e22	1.94486	0.972430	−	0.233194i	$-0.0749176\pi$
$401$	2.60385e22	1.94486	0.972430	+	0.233194i	$0.0749176\pi$
$402$	0	0
$403$	4.45914e21	0.319270
$404$	0	0
$405$	−4.65257e21	−0.319393
$406$	0	0
$407$	5.83665e21	0.384248
$408$	0	0
$409$	−2.74091e22	−1.73080	−0.865400	−	0.501082i	$-0.832935\pi$
$409$	−2.74091e22	−1.73080	−0.865400	+	0.501082i	$0.832935\pi$
$410$	0	0
$411$	−2.61144e21	−0.158207
$412$	0	0
$413$	1.56772e22	0.911365
$414$	0	0
$415$	−1.74658e22	−0.974495
$416$	0	0
$417$	−5.03975e21	−0.269931
$418$	0	0
$419$	3.15789e22	1.62397	0.811985	−	0.583679i	$-0.198387\pi$
$419$	3.15789e22	1.62397	0.811985	+	0.583679i	$0.198387\pi$
$420$	0	0
$421$	−2.96704e22	−1.46530	−0.732648	−	0.680608i	$-0.761716\pi$
$421$	−2.96704e22	−1.46530	−0.732648	+	0.680608i	$0.761716\pi$
$422$	0	0
$423$	2.14251e22	1.01632
$424$	0	0
$425$	2.45040e22	1.11669
$426$	0	0
$427$	−2.01961e22	−0.884365
$428$	0	0
$429$	2.28671e21	0.0962332
$430$	0	0
$431$	−1.92658e21	−0.0779346	−0.0389673	−	0.999240i	$-0.512407\pi$
$431$	−1.92658e21	−0.0779346	−0.0389673	+	0.999240i	$0.512407\pi$
$432$	0	0
$433$	3.02417e21	0.117614	0.0588070	−	0.998269i	$-0.481270\pi$
$433$	3.02417e21	0.117614	0.0588070	+	0.998269i	$0.481270\pi$
$434$	0	0
$435$	−6.13281e21	−0.229351
$436$	0	0
$437$	9.95144e21	0.357926
$438$	0	0
$439$	2.18819e22	0.757071	0.378536	−	0.925587i	$-0.376428\pi$
$439$	2.18819e22	0.757071	0.378536	+	0.925587i	$0.376428\pi$
$440$	0	0
$441$	−2.50660e22	−0.834367
$442$	0	0
$443$	2.01050e21	0.0643979	0.0321990	−	0.999481i	$-0.489749\pi$
$443$	2.01050e21	0.0643979	0.0321990	+	0.999481i	$0.489749\pi$
$444$	0	0
$445$	3.85604e22	1.18873
$446$	0	0
$447$	−2.33795e21	−0.0693779
$448$	0	0
$449$	−4.78968e22	−1.36840	−0.684200	−	0.729295i	$-0.739848\pi$
$449$	−4.78968e22	−1.36840	−0.684200	+	0.729295i	$0.739848\pi$
$450$	0	0
$451$	−9.17277e21	−0.252348
$452$	0	0
$453$	5.46292e21	0.144740
$454$	0	0
$455$	6.14741e22	1.56890
$456$	0	0
$457$	6.48444e22	1.59435	0.797177	−	0.603746i	$-0.206326\pi$
$457$	6.48444e22	1.59435	0.797177	+	0.603746i	$0.206326\pi$
$458$	0	0
$459$	4.06060e22	0.962017
$460$	0	0
$461$	4.94636e22	1.12935	0.564674	−	0.825314i	$-0.309002\pi$
$461$	4.94636e22	1.12935	0.564674	+	0.825314i	$0.309002\pi$
$462$	0	0
$463$	3.26536e21	0.0718609	0.0359305	−	0.999354i	$-0.488561\pi$
$463$	3.26536e21	0.0718609	0.0359305	+	0.999354i	$0.488561\pi$
$464$	0	0
$465$	1.56184e22	0.331349
$466$	0	0
$467$	1.09833e22	0.224667	0.112333	−	0.993671i	$-0.464168\pi$
$467$	1.09833e22	0.224667	0.112333	+	0.993671i	$0.464168\pi$
$468$	0	0
$469$	−5.99166e22	−1.18189
$470$	0	0
$471$	2.18778e20	0.00416223
$472$	0	0
$473$	4.58417e21	0.0841281
$474$	0	0
$475$	6.19635e22	1.09709
$476$	0	0
$477$	−1.50420e22	−0.256980
$478$	0	0
$479$	5.84533e22	0.963734	0.481867	−	0.876244i	$-0.339959\pi$
$479$	5.84533e22	0.963734	0.481867	+	0.876244i	$0.339959\pi$
$480$	0	0
$481$	−7.38098e22	−1.17457
$482$	0	0
$483$	1.78325e22	0.273944
$484$	0	0
$485$	−7.23560e22	−1.07317
$486$	0	0
$487$	−8.54084e22	−1.22322	−0.611610	−	0.791160i	$-0.709478\pi$
$487$	−8.54084e22	−1.22322	−0.611610	+	0.791160i	$0.709478\pi$
$488$	0	0
$489$	7.00820e22	0.969352
$490$	0	0
$491$	−4.73139e22	−0.632115	−0.316058	−	0.948740i	$-0.602359\pi$
$491$	−4.73139e22	−0.632115	−0.316058	+	0.948740i	$0.602359\pi$
$492$	0	0
$493$	−2.42257e22	−0.312664
$494$	0	0
$495$	−1.99341e22	−0.248572
$496$	0	0
$497$	−8.78560e22	−1.05863
$498$	0	0
$499$	−7.86063e22	−0.915382	−0.457691	−	0.889111i	$-0.651323\pi$
$499$	−7.86063e22	−0.915382	−0.457691	+	0.889111i	$0.651323\pi$
$500$	0	0
$501$	2.74926e22	0.309453
$502$	0	0
$503$	−1.44291e23	−1.57004	−0.785022	−	0.619468i	$-0.787348\pi$
$503$	−1.44291e23	−1.57004	−0.785022	+	0.619468i	$0.787348\pi$
$504$	0	0
$505$	−4.77134e22	−0.501953
$506$	0	0
$507$	2.37116e22	0.241208
$508$	0	0
$509$	−8.61175e22	−0.847208	−0.423604	−	0.905847i	$-0.639235\pi$
$509$	−8.61175e22	−0.847208	−0.423604	+	0.905847i	$0.639235\pi$
$510$	0	0
$511$	−1.31559e23	−1.25182
$512$	0	0
$513$	1.02681e23	0.945130
$514$	0	0
$515$	−1.80627e23	−1.60850
$516$	0	0
$517$	4.00942e22	0.345471
$518$	0	0
$519$	−3.83747e22	−0.319980
$520$	0	0
$521$	1.98567e23	1.60246	0.801229	−	0.598358i	$-0.204180\pi$
$521$	1.98567e23	1.60246	0.801229	+	0.598358i	$0.204180\pi$
$522$	0	0
$523$	−1.21175e23	−0.946563	−0.473282	−	0.880911i	$-0.656931\pi$
$523$	−1.21175e23	−0.946563	−0.473282	+	0.880911i	$0.656931\pi$
$524$	0	0
$525$	1.11036e23	0.839670
$526$	0	0
$527$	6.16954e22	0.451713
$528$	0	0
$529$	−1.24029e23	−0.879323
$530$	0	0
$531$	6.42868e22	0.441386
$532$	0	0
$533$	1.15998e23	0.771381
$534$	0	0
$535$	1.14756e23	0.739210
$536$	0	0
$537$	2.85635e22	0.178250
$538$	0	0
$539$	−4.69077e22	−0.283622
$540$	0	0
$541$	1.67082e23	0.978932	0.489466	−	0.872022i	$-0.337192\pi$
$541$	1.67082e23	0.978932	0.489466	+	0.872022i	$0.337192\pi$
$542$	0	0
$543$	−4.63476e22	−0.263165
$544$	0	0
$545$	−4.70517e23	−2.58943
$546$	0	0
$547$	−4.10773e22	−0.219134	−0.109567	−	0.993979i	$-0.534946\pi$
$547$	−4.10773e22	−0.219134	−0.109567	+	0.993979i	$0.534946\pi$
$548$	0	0
$549$	−8.28176e22	−0.428309
$550$	0	0
$551$	−6.12597e22	−0.307175
$552$	0	0
$553$	5.35177e23	2.60216
$554$	0	0
$555$	−2.58523e23	−1.21901
$556$	0	0
$557$	1.50464e23	0.688118	0.344059	−	0.938948i	$-0.388198\pi$
$557$	1.50464e23	0.688118	0.344059	+	0.938948i	$0.388198\pi$
$558$	0	0
$559$	−5.79710e22	−0.257164
$560$	0	0
$561$	3.16383e22	0.136154
$562$	0	0
$563$	1.14744e22	0.0479082	0.0239541	−	0.999713i	$-0.492374\pi$
$563$	1.14744e22	0.0479082	0.0239541	+	0.999713i	$0.492374\pi$
$564$	0	0
$565$	−5.42711e23	−2.19865
$566$	0	0
$567$	−8.32790e22	−0.327401
$568$	0	0
$569$	−4.09528e23	−1.56253	−0.781267	−	0.624197i	$-0.785426\pi$
$569$	−4.09528e23	−1.56253	−0.781267	+	0.624197i	$0.785426\pi$
$570$	0	0
$571$	2.45795e23	0.910260	0.455130	−	0.890425i	$-0.349593\pi$
$571$	2.45795e23	0.910260	0.455130	+	0.890425i	$0.349593\pi$
$572$	0	0
$573$	1.98643e23	0.714101
$574$	0	0
$575$	1.05986e23	0.369890
$576$	0	0
$577$	−8.68049e22	−0.294137	−0.147069	−	0.989126i	$-0.546984\pi$
$577$	−8.68049e22	−0.294137	−0.147069	+	0.989126i	$0.546984\pi$
$578$	0	0
$579$	1.31699e23	0.433326
$580$	0	0
$581$	−3.12630e23	−0.998926
$582$	0	0
$583$	−2.81491e22	−0.0873537
$584$	0	0
$585$	2.52084e23	0.759838
$586$	0	0
$587$	−3.99552e23	−1.16990	−0.584951	−	0.811069i	$-0.698886\pi$
$587$	−3.99552e23	−1.16990	−0.584951	+	0.811069i	$0.698886\pi$
$588$	0	0
$589$	1.56010e23	0.443784
$590$	0	0
$591$	−2.79578e23	−0.772698
$592$	0	0
$593$	2.25692e23	0.606110	0.303055	−	0.952973i	$-0.401993\pi$
$593$	2.25692e23	0.606110	0.303055	+	0.952973i	$0.401993\pi$
$594$	0	0
$595$	8.50538e23	2.21973
$596$	0	0
$597$	−3.49379e23	−0.886165
$598$	0	0
$599$	−3.25464e23	−0.802370	−0.401185	−	0.915997i	$-0.631402\pi$
$599$	−3.25464e23	−0.802370	−0.401185	+	0.915997i	$0.631402\pi$
$600$	0	0
$601$	3.08585e23	0.739506	0.369753	−	0.929130i	$-0.379442\pi$
$601$	3.08585e23	0.739506	0.369753	+	0.929130i	$0.379442\pi$
$602$	0	0
$603$	−2.45698e23	−0.572406
$604$	0	0
$605$	5.97088e23	1.35244
$606$	0	0
$607$	4.99444e22	0.109998	0.0549988	−	0.998486i	$-0.482485\pi$
$607$	4.99444e22	0.109998	0.0549988	+	0.998486i	$0.482485\pi$
$608$	0	0
$609$	−1.09775e23	−0.235101
$610$	0	0
$611$	−5.07027e23	−1.05604
$612$	0	0
$613$	−5.20372e22	−0.105414	−0.0527072	−	0.998610i	$-0.516785\pi$
$613$	−5.20372e22	−0.105414	−0.0527072	+	0.998610i	$0.516785\pi$
$614$	0	0
$615$	4.06289e23	0.800565
$616$	0	0
$617$	−1.26687e23	−0.242833	−0.121416	−	0.992602i	$-0.538744\pi$
$617$	−1.26687e23	−0.242833	−0.121416	+	0.992602i	$0.538744\pi$
$618$	0	0
$619$	7.40213e22	0.138034	0.0690170	−	0.997615i	$-0.478014\pi$
$619$	7.40213e22	0.138034	0.0690170	+	0.997615i	$0.478014\pi$
$620$	0	0
$621$	1.75631e23	0.318657
$622$	0	0
$623$	6.90214e23	1.21853
$624$	0	0
$625$	−5.41928e23	−0.931025
$626$	0	0
$627$	8.00041e22	0.133764
$628$	0	0
$629$	−1.02121e24	−1.66182
$630$	0	0
$631$	8.00054e23	1.26727	0.633636	−	0.773631i	$-0.281562\pi$
$631$	8.00054e23	1.26727	0.633636	+	0.773631i	$0.281562\pi$
$632$	0	0
$633$	−1.79266e23	−0.276417
$634$	0	0
$635$	1.50685e24	2.26200
$636$	0	0
$637$	5.93190e23	0.866979
$638$	0	0
$639$	−3.60268e23	−0.512706
$640$	0	0
$641$	−2.73379e23	−0.378854	−0.189427	−	0.981895i	$-0.560663\pi$
$641$	−2.73379e23	−0.378854	−0.189427	+	0.981895i	$0.560663\pi$
$642$	0	0
$643$	4.94746e23	0.667712	0.333856	−	0.942624i	$-0.391650\pi$
$643$	4.94746e23	0.667712	0.333856	+	0.942624i	$0.391650\pi$
$644$	0	0
$645$	−2.03046e23	−0.266893
$646$	0	0
$647$	5.85656e23	0.749818	0.374909	−	0.927062i	$-0.377674\pi$
$647$	5.85656e23	0.749818	0.374909	+	0.927062i	$0.377674\pi$
$648$	0	0
$649$	1.20304e23	0.150038
$650$	0	0
$651$	2.79562e23	0.339656
$652$	0	0
$653$	1.33857e24	1.58446	0.792229	−	0.610224i	$-0.208921\pi$
$653$	1.33857e24	1.58446	0.792229	+	0.610224i	$0.208921\pi$
$654$	0	0
$655$	2.20327e24	2.54107
$656$	0	0
$657$	−5.39478e23	−0.606273
$658$	0	0
$659$	−9.95800e23	−1.09055	−0.545276	−	0.838257i	$-0.683575\pi$
$659$	−9.95800e23	−1.09055	−0.545276	+	0.838257i	$0.683575\pi$
$660$	0	0
$661$	3.55898e23	0.379851	0.189925	−	0.981799i	$-0.439175\pi$
$661$	3.55898e23	0.379851	0.189925	+	0.981799i	$0.439175\pi$
$662$	0	0
$663$	−4.00095e23	−0.416197
$664$	0	0
$665$	2.15076e24	2.18076
$666$	0	0
$667$	−1.04782e23	−0.103566
$668$	0	0
$669$	−7.73719e23	−0.745523
$670$	0	0
$671$	−1.54982e23	−0.145593
$672$	0	0
$673$	−8.19644e23	−0.750753	−0.375377	−	0.926872i	$-0.622487\pi$
$673$	−8.19644e23	−0.750753	−0.375377	+	0.926872i	$0.622487\pi$
$674$	0	0
$675$	1.09358e24	0.976719
$676$	0	0
$677$	3.76541e23	0.327950	0.163975	−	0.986464i	$-0.447568\pi$
$677$	3.76541e23	0.327950	0.163975	+	0.986464i	$0.447568\pi$
$678$	0	0
$679$	−1.29514e24	−1.10008
$680$	0	0
$681$	5.05102e23	0.418436
$682$	0	0
$683$	1.24736e24	1.00789	0.503946	−	0.863735i	$-0.331881\pi$
$683$	1.24736e24	1.00789	0.503946	+	0.863735i	$0.331881\pi$
$684$	0	0
$685$	−5.38732e23	−0.424622
$686$	0	0
$687$	−3.89552e23	−0.299525
$688$	0	0
$689$	3.55970e23	0.267024
$690$	0	0
$691$	−9.48314e23	−0.694047	−0.347023	−	0.937856i	$-0.612808\pi$
$691$	−9.48314e23	−0.694047	−0.347023	+	0.937856i	$0.612808\pi$
$692$	0	0
$693$	−3.56811e23	−0.254804
$694$	0	0
$695$	−1.03969e24	−0.724488
$696$	0	0
$697$	1.60492e24	1.09137
$698$	0	0
$699$	−9.33359e23	−0.619431
$700$	0	0
$701$	1.86029e23	0.120498	0.0602488	−	0.998183i	$-0.480811\pi$
$701$	1.86029e23	0.120498	0.0602488	+	0.998183i	$0.480811\pi$
$702$	0	0
$703$	−2.58234e24	−1.63265
$704$	0	0
$705$	−1.77589e24	−1.09600
$706$	0	0
$707$	−8.54048e23	−0.514538
$708$	0	0
$709$	−1.93226e24	−1.13651	−0.568253	−	0.822854i	$-0.692381\pi$
$709$	−1.93226e24	−1.13651	−0.568253	+	0.822854i	$0.692381\pi$
$710$	0	0
$711$	2.19458e24	1.26026
$712$	0	0
$713$	2.66848e23	0.149625
$714$	0	0
$715$	4.71742e23	0.258287
$716$	0	0
$717$	3.25697e23	0.174141
$718$	0	0
$719$	−1.37714e24	−0.719089	−0.359545	−	0.933128i	$-0.617068\pi$
$719$	−1.37714e24	−0.719089	−0.359545	+	0.933128i	$0.617068\pi$
$720$	0	0
$721$	−3.23315e24	−1.64883
$722$	0	0
$723$	−4.33321e23	−0.215841
$724$	0	0
$725$	−6.52436e23	−0.317442
$726$	0	0
$727$	2.26138e24	1.07481	0.537404	−	0.843325i	$-0.319405\pi$
$727$	2.26138e24	1.07481	0.537404	+	0.843325i	$0.319405\pi$
$728$	0	0
$729$	7.16178e23	0.332535
$730$	0	0
$731$	−8.02070e23	−0.363843
$732$	0	0
$733$	2.27165e23	0.100683	0.0503416	−	0.998732i	$-0.483969\pi$
$733$	2.27165e23	0.100683	0.0503416	+	0.998732i	$0.483969\pi$
$734$	0	0
$735$	2.07768e24	0.899779
$736$	0	0
$737$	−4.59790e23	−0.194575
$738$	0	0
$739$	6.37558e23	0.263659	0.131829	−	0.991272i	$-0.457915\pi$
$739$	6.37558e23	0.263659	0.131829	+	0.991272i	$0.457915\pi$
$740$	0	0
$741$	−1.01172e24	−0.408891
$742$	0	0
$743$	−1.43514e24	−0.566876	−0.283438	−	0.958991i	$-0.591475\pi$
$743$	−1.43514e24	−0.566876	−0.283438	+	0.958991i	$0.591475\pi$
$744$	0	0
$745$	−4.82312e23	−0.186209
$746$	0	0
$747$	−1.28199e24	−0.483793
$748$	0	0
$749$	2.05408e24	0.757742
$750$	0	0
$751$	−3.45967e24	−1.24766	−0.623829	−	0.781561i	$-0.714424\pi$
$751$	−3.45967e24	−1.24766	−0.623829	+	0.781561i	$0.714424\pi$
$752$	0	0
$753$	−2.23104e24	−0.786593
$754$	0	0
$755$	1.12698e24	0.388480
$756$	0	0
$757$	4.54182e24	1.53079	0.765395	−	0.643561i	$-0.222544\pi$
$757$	4.54182e24	1.53079	0.765395	+	0.643561i	$0.222544\pi$
$758$	0	0
$759$	1.36844e23	0.0450993
$760$	0	0
$761$	3.84040e24	1.23768	0.618838	−	0.785519i	$-0.287604\pi$
$761$	3.84040e24	1.23768	0.618838	+	0.785519i	$0.287604\pi$
$762$	0	0
$763$	−8.42204e24	−2.65435
$764$	0	0
$765$	3.48777e24	1.07504
$766$	0	0
$767$	−1.52135e24	−0.458637
$768$	0	0
$769$	5.15334e24	1.51955	0.759775	−	0.650186i	$-0.225309\pi$
$769$	5.15334e24	1.51955	0.759775	+	0.650186i	$0.225309\pi$
$770$	0	0
$771$	−1.51251e24	−0.436250
$772$	0	0
$773$	−5.28998e24	−1.49255	−0.746274	−	0.665639i	$-0.768159\pi$
$773$	−5.28998e24	−1.49255	−0.746274	+	0.665639i	$0.768159\pi$
$774$	0	0
$775$	1.66155e24	0.458616
$776$	0	0
$777$	−4.62744e24	−1.24957
$778$	0	0
$779$	4.05836e24	1.07222
$780$	0	0
$781$	−6.74193e23	−0.174281
$782$	0	0
$783$	−1.08116e24	−0.273474
$784$	0	0
$785$	4.51333e22	0.0111713
$786$	0	0
$787$	−5.81069e24	−1.40748	−0.703740	−	0.710457i	$-0.748488\pi$
$787$	−5.81069e24	−1.40748	−0.703740	+	0.710457i	$0.748488\pi$
$788$	0	0
$789$	−5.50019e23	−0.130384
$790$	0	0
$791$	−9.71429e24	−2.25378
$792$	0	0
$793$	1.95989e24	0.445050
$794$	0	0
$795$	1.24680e24	0.277126
$796$	0	0
$797$	−1.38132e24	−0.300538	−0.150269	−	0.988645i	$-0.548014\pi$
$797$	−1.38132e24	−0.300538	−0.150269	+	0.988645i	$0.548014\pi$
$798$	0	0
$799$	−7.01509e24	−1.49412
$800$	0	0
$801$	2.83034e24	0.590149
$802$	0	0
$803$	−1.00956e24	−0.206087
$804$	0	0
$805$	3.67879e24	0.735259
$806$	0	0
$807$	1.76434e23	0.0345268
$808$	0	0
$809$	−3.50030e24	−0.670723	−0.335362	−	0.942089i	$-0.608858\pi$
$809$	−3.50030e24	−0.670723	−0.335362	+	0.942089i	$0.608858\pi$
$810$	0	0
$811$	2.96509e24	0.556365	0.278183	−	0.960528i	$-0.410268\pi$
$811$	2.96509e24	0.556365	0.278183	+	0.960528i	$0.410268\pi$
$812$	0	0
$813$	−4.68745e24	−0.861325
$814$	0	0
$815$	1.44577e25	2.60171
$816$	0	0
$817$	−2.02820e24	−0.357457
$818$	0	0
$819$	4.51220e24	0.778888
$820$	0	0
$821$	−8.29888e24	−1.40315	−0.701573	−	0.712598i	$-0.747518\pi$
$821$	−8.29888e24	−1.40315	−0.701573	+	0.712598i	$0.747518\pi$
$822$	0	0
$823$	−1.89319e24	−0.313541	−0.156771	−	0.987635i	$-0.550108\pi$
$823$	−1.89319e24	−0.313541	−0.156771	+	0.987635i	$0.550108\pi$
$824$	0	0
$825$	8.52070e23	0.138235
$826$	0	0
$827$	1.23165e24	0.195745	0.0978724	−	0.995199i	$-0.468796\pi$
$827$	1.23165e24	0.195745	0.0978724	+	0.995199i	$0.468796\pi$
$828$	0	0
$829$	3.32086e24	0.517055	0.258528	−	0.966004i	$-0.416763\pi$
$829$	3.32086e24	0.517055	0.258528	+	0.966004i	$0.416763\pi$
$830$	0	0
$831$	−9.44062e23	−0.144010
$832$	0	0
$833$	8.20720e24	1.22663
$834$	0	0
$835$	5.67163e24	0.830564
$836$	0	0
$837$	2.75339e24	0.395094
$838$	0	0
$839$	−7.24116e23	−0.101820	−0.0509098	−	0.998703i	$-0.516212\pi$
$839$	−7.24116e23	−0.101820	−0.0509098	+	0.998703i	$0.516212\pi$
$840$	0	0
$841$	−6.61212e24	−0.911119
$842$	0	0
$843$	3.02877e24	0.409007
$844$	0	0
$845$	4.89162e24	0.647397
$846$	0	0
$847$	1.06876e25	1.38635
$848$	0	0
$849$	7.24338e24	0.920929
$850$	0	0
$851$	−4.41699e24	−0.550460
$852$	0	0
$853$	8.97587e23	0.109650	0.0548251	−	0.998496i	$-0.482540\pi$
$853$	8.97587e23	0.109650	0.0548251	+	0.998496i	$0.482540\pi$
$854$	0	0
$855$	8.81955e24	1.05617
$856$	0	0
$857$	−1.01446e25	−1.19097	−0.595483	−	0.803368i	$-0.703039\pi$
$857$	−1.01446e25	−1.19097	−0.595483	+	0.803368i	$0.703039\pi$
$858$	0	0
$859$	−8.66799e23	−0.0997646	−0.0498823	−	0.998755i	$-0.515885\pi$
$859$	−8.66799e23	−0.0997646	−0.0498823	+	0.998755i	$0.515885\pi$
$860$	0	0
$861$	7.27240e24	0.820636
$862$	0	0
$863$	2.24930e24	0.248860	0.124430	−	0.992228i	$-0.460290\pi$
$863$	2.24930e24	0.248860	0.124430	+	0.992228i	$0.460290\pi$
$864$	0	0
$865$	−7.91657e24	−0.858817
$866$	0	0
$867$	−5.02676e23	−0.0534719
$868$	0	0
$869$	4.10686e24	0.428393
$870$	0	0
$871$	5.81446e24	0.594779
$872$	0	0
$873$	−5.31093e24	−0.532782
$874$	0	0
$875$	1.39357e24	0.137107
$876$	0	0
$877$	−7.32275e24	−0.706606	−0.353303	−	0.935509i	$-0.614942\pi$
$877$	−7.32275e24	−0.706606	−0.353303	+	0.935509i	$0.614942\pi$
$878$	0	0
$879$	3.17568e24	0.300560
$880$	0	0
$881$	−8.73491e24	−0.810893	−0.405446	−	0.914119i	$-0.632884\pi$
$881$	−8.73491e24	−0.810893	−0.405446	+	0.914119i	$0.632884\pi$
$882$	0	0
$883$	1.80866e25	1.64699	0.823496	−	0.567323i	$-0.192021\pi$
$883$	1.80866e25	1.64699	0.823496	+	0.567323i	$0.192021\pi$
$884$	0	0
$885$	−5.32862e24	−0.475989
$886$	0	0
$887$	−2.95323e24	−0.258790	−0.129395	−	0.991593i	$-0.541303\pi$
$887$	−2.95323e24	−0.258790	−0.129395	+	0.991593i	$0.541303\pi$
$888$	0	0
$889$	2.69719e25	2.31871
$890$	0	0
$891$	−6.39069e23	−0.0538998
$892$	0	0
$893$	−1.77391e25	−1.46789
$894$	0	0
$895$	5.89255e24	0.478418
$896$	0	0
$897$	−1.73051e24	−0.137860
$898$	0	0
$899$	−1.64268e24	−0.128409
$900$	0	0
$901$	4.92510e24	0.377794
$902$	0	0
$903$	−3.63444e24	−0.273585
$904$	0	0
$905$	−9.56137e24	−0.706329
$906$	0	0
$907$	−1.14361e25	−0.829116	−0.414558	−	0.910023i	$-0.636064\pi$
$907$	−1.14361e25	−0.829116	−0.414558	+	0.910023i	$0.636064\pi$
$908$	0	0
$909$	−3.50216e24	−0.249197
$910$	0	0
$911$	−7.42471e24	−0.518529	−0.259265	−	0.965806i	$-0.583480\pi$
$911$	−7.42471e24	−0.518529	−0.259265	+	0.965806i	$0.583480\pi$
$912$	0	0
$913$	−2.39907e24	−0.164453
$914$	0	0
$915$	6.86460e24	0.461887
$916$	0	0
$917$	3.94375e25	2.60478
$918$	0	0
$919$	2.07572e24	0.134582	0.0672910	−	0.997733i	$-0.478564\pi$
$919$	2.07572e24	0.134582	0.0672910	+	0.997733i	$0.478564\pi$
$920$	0	0
$921$	−1.12950e24	−0.0718920
$922$	0	0
$923$	8.52577e24	0.532745
$924$	0	0
$925$	−2.75028e25	−1.68722
$926$	0	0
$927$	−1.32580e25	−0.798549
$928$	0	0
$929$	2.31300e25	1.36786	0.683930	−	0.729548i	$-0.260269\pi$
$929$	2.31300e25	1.36786	0.683930	+	0.729548i	$0.260269\pi$
$930$	0	0
$931$	2.07536e25	1.20510
$932$	0	0
$933$	6.09520e24	0.347532
$934$	0	0
$935$	6.52689e24	0.365433
$936$	0	0
$937$	6.85999e24	0.377170	0.188585	−	0.982057i	$-0.439610\pi$
$937$	6.85999e24	0.377170	0.188585	+	0.982057i	$0.439610\pi$
$938$	0	0
$939$	2.54887e24	0.137623
$940$	0	0
$941$	−1.00555e25	−0.533204	−0.266602	−	0.963807i	$-0.585901\pi$
$941$	−1.00555e25	−0.533204	−0.266602	+	0.963807i	$0.585901\pi$
$942$	0	0
$943$	6.94166e24	0.361505
$944$	0	0
$945$	3.79584e25	1.94150
$946$	0	0
$947$	−2.54151e25	−1.27678	−0.638392	−	0.769712i	$-0.720400\pi$
$947$	−2.54151e25	−1.27678	−0.638392	+	0.769712i	$0.720400\pi$
$948$	0	0
$949$	1.27668e25	0.629969
$950$	0	0
$951$	1.83844e25	0.891078
$952$	0	0
$953$	−1.52541e25	−0.726266	−0.363133	−	0.931737i	$-0.618293\pi$
$953$	−1.52541e25	−0.726266	−0.363133	+	0.931737i	$0.618293\pi$
$954$	0	0
$955$	4.09795e25	1.91663
$956$	0	0
$957$	−8.42391e23	−0.0387046
$958$	0	0
$959$	−9.64306e24	−0.435268
$960$	0	0
$961$	−1.83667e25	−0.814484
$962$	0	0
$963$	8.42308e24	0.366984
$964$	0	0
$965$	2.71691e25	1.16303
$966$	0	0
$967$	2.94437e25	1.23842	0.619209	−	0.785226i	$-0.287453\pi$
$967$	2.94437e25	1.23842	0.619209	+	0.785226i	$0.287453\pi$
$968$	0	0
$969$	−1.39979e25	−0.578511
$970$	0	0
$971$	−4.42559e25	−1.79725	−0.898623	−	0.438722i	$-0.855431\pi$
$971$	−4.42559e25	−1.79725	−0.898623	+	0.438722i	$0.855431\pi$
$972$	0	0
$973$	−1.86099e25	−0.742651
$974$	0	0
$975$	−1.07752e25	−0.422557
$976$	0	0
$977$	−4.39121e24	−0.169231	−0.0846157	−	0.996414i	$-0.526966\pi$
$977$	−4.39121e24	−0.169231	−0.0846157	+	0.996414i	$0.526966\pi$
$978$	0	0
$979$	5.29659e24	0.200606
$980$	0	0
$981$	−3.45359e25	−1.28554
$982$	0	0
$983$	−3.24550e25	−1.18734	−0.593672	−	0.804707i	$-0.702322\pi$
$983$	−3.24550e25	−1.18734	−0.593672	+	0.804707i	$0.702322\pi$
$984$	0	0
$985$	−5.76761e25	−2.07390
$986$	0	0
$987$	−3.17876e25	−1.12347
$988$	0	0
$989$	−3.46915e24	−0.120519
$990$	0	0
$991$	−1.34212e25	−0.458315	−0.229157	−	0.973389i	$-0.573597\pi$
$991$	−1.34212e25	−0.458315	−0.229157	+	0.973389i	$0.573597\pi$
$992$	0	0
$993$	−1.18085e25	−0.396393
$994$	0	0
$995$	−7.20757e25	−2.37844
$996$	0	0
$997$	2.02909e25	0.658252	0.329126	−	0.944286i	$-0.393246\pi$
$997$	2.02909e25	0.658252	0.329126	+	0.944286i	$0.393246\pi$
$998$	0	0
$999$	−4.55753e25	−1.45353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.18.a.a.1.1		1
4.3	odd	2		64.18.a.e.1.1		1
8.3	odd	2		16.18.a.a.1.1		1
8.5	even	2		2.18.a.a.1.1	✓	1
24.5	odd	2		18.18.a.a.1.1		1
40.13	odd	4		50.18.b.b.49.1		2
40.29	even	2		50.18.a.a.1.1		1
40.37	odd	4		50.18.b.b.49.2		2
56.13	odd	2		98.18.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.18.a.a.1.1	✓	1	8.5	even	2
16.18.a.a.1.1		1	8.3	odd	2
18.18.a.a.1.1		1	24.5	odd	2
50.18.a.a.1.1		1	40.29	even	2
50.18.b.b.49.1		2	40.13	odd	4
50.18.b.b.49.2		2	40.37	odd	4
64.18.a.a.1.1		1	1.1	even	1	trivial
64.18.a.e.1.1		1	4.3	odd	2
98.18.a.a.1.1		1	56.13	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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