LMFDB - Embedded newform 64.24.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,24,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, 24, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 24 $
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:	$214.530583901$
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)

$f(q)$

$=$

$q-505908. q^{3} +9.01356e7 q^{5} -6.87226e9 q^{7} +1.61800e11 q^{9} +O(q^{10})$

$q-505908. q^{3} +9.01356e7 q^{5} -6.87226e9 q^{7} +1.61800e11 q^{9} -9.65329e11 q^{11} -5.42360e11 q^{13} -4.56003e13 q^{15} +8.20835e13 q^{17} +5.55749e14 q^{19} +3.47673e15 q^{21} -6.50864e15 q^{23} -3.79651e15 q^{25} -3.42280e16 q^{27} +1.22020e16 q^{29} -1.19978e17 q^{31} +4.88368e17 q^{33} -6.19435e17 q^{35} +6.19511e17 q^{37} +2.74384e17 q^{39} -1.58774e18 q^{41} +8.37772e18 q^{43} +1.45839e19 q^{45} -1.31005e19 q^{47} +1.98591e19 q^{49} -4.15267e19 q^{51} -4.17960e19 q^{53} -8.70105e19 q^{55} -2.81158e20 q^{57} -7.43839e19 q^{59} +2.71922e20 q^{61} -1.11193e21 q^{63} -4.88859e19 q^{65} +1.74814e21 q^{67} +3.29277e21 q^{69} +2.71799e21 q^{71} +4.31278e21 q^{73} +1.92068e21 q^{75} +6.63399e21 q^{77} -3.59856e21 q^{79} +2.08387e21 q^{81} -2.25004e20 q^{83} +7.39865e21 q^{85} -6.17311e21 q^{87} +3.38924e22 q^{89} +3.72724e21 q^{91} +6.06978e22 q^{93} +5.00927e22 q^{95} +9.21216e22 q^{97} -1.56190e23 q^{99} +O(q^{100})$

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
$3$	−505908.	−1.64883	−0.824417	−	0.565982i	$-0.808497\pi$
$3$	−505908.	−1.64883	−0.824417	+	0.565982i	$0.808497\pi$
$4$	0	0
$5$	9.01356e7	0.825546	0.412773	−	0.910834i	$-0.364560\pi$
$5$	9.01356e7	0.825546	0.412773	+	0.910834i	$0.364560\pi$
$6$	0	0
$7$	−6.87226e9	−1.31363	−0.656813	−	0.754053i	$-0.728096\pi$
$7$	−6.87226e9	−1.31363	−0.656813	+	0.754053i	$0.728096\pi$
$8$	0	0
$9$	1.61800e11	1.71866
$10$	0	0
$11$	−9.65329e11	−1.02014	−0.510070	−	0.860133i	$-0.670380\pi$
$11$	−9.65329e11	−1.02014	−0.510070	+	0.860133i	$0.670380\pi$
$12$	0	0
$13$	−5.42360e11	−0.0839342	−0.0419671	−	0.999119i	$-0.513362\pi$
$13$	−5.42360e11	−0.0839342	−0.0419671	+	0.999119i	$0.513362\pi$
$14$	0	0
$15$	−4.56003e13	−1.36119
$16$	0	0
$17$	8.20835e13	0.580889	0.290445	−	0.956892i	$-0.406197\pi$
$17$	8.20835e13	0.580889	0.290445	+	0.956892i	$0.406197\pi$
$18$	0	0
$19$	5.55749e14	1.09449	0.547245	−	0.836972i	$-0.315677\pi$
$19$	5.55749e14	1.09449	0.547245	+	0.836972i	$0.315677\pi$
$20$	0	0
$21$	3.47673e15	2.16595
$22$	0	0
$23$	−6.50864e15	−1.42436	−0.712180	−	0.701996i	$-0.752292\pi$
$23$	−6.50864e15	−1.42436	−0.712180	+	0.701996i	$0.752292\pi$
$24$	0	0
$25$	−3.79651e15	−0.318474
$26$	0	0
$27$	−3.42280e16	−1.18494
$28$	0	0
$29$	1.22020e16	0.185719	0.0928593	−	0.995679i	$-0.470399\pi$
$29$	1.22020e16	0.185719	0.0928593	+	0.995679i	$0.470399\pi$
$30$	0	0
$31$	−1.19978e17	−0.848090	−0.424045	−	0.905641i	$-0.639390\pi$
$31$	−1.19978e17	−0.848090	−0.424045	+	0.905641i	$0.639390\pi$
$32$	0	0
$33$	4.88368e17	1.68204
$34$	0	0
$35$	−6.19435e17	−1.08446
$36$	0	0
$37$	6.19511e17	0.572439	0.286219	−	0.958164i	$-0.407601\pi$
$37$	6.19511e17	0.572439	0.286219	+	0.958164i	$0.407601\pi$
$38$	0	0
$39$	2.74384e17	0.138394
$40$	0	0
$41$	−1.58774e18	−0.450572	−0.225286	−	0.974293i	$-0.572332\pi$
$41$	−1.58774e18	−0.450572	−0.225286	+	0.974293i	$0.572332\pi$
$42$	0	0
$43$	8.37772e18	1.37480	0.687398	−	0.726281i	$-0.258753\pi$
$43$	8.37772e18	1.37480	0.687398	+	0.726281i	$0.258753\pi$
$44$	0	0
$45$	1.45839e19	1.41883
$46$	0	0
$47$	−1.31005e19	−0.772967	−0.386484	−	0.922296i	$-0.626310\pi$
$47$	−1.31005e19	−0.772967	−0.386484	+	0.922296i	$0.626310\pi$
$48$	0	0
$49$	1.98591e19	0.725614
$50$	0	0
$51$	−4.15267e19	−0.957791
$52$	0	0
$53$	−4.17960e19	−0.619387	−0.309693	−	0.950836i	$-0.600226\pi$
$53$	−4.17960e19	−0.619387	−0.309693	+	0.950836i	$0.600226\pi$
$54$	0	0
$55$	−8.70105e19	−0.842172
$56$	0	0
$57$	−2.81158e20	−1.80463
$58$	0	0
$59$	−7.43839e19	−0.321130	−0.160565	−	0.987025i	$-0.551332\pi$
$59$	−7.43839e19	−0.321130	−0.160565	+	0.987025i	$0.551332\pi$
$60$	0	0
$61$	2.71922e20	0.800113	0.400056	−	0.916490i	$-0.368991\pi$
$61$	2.71922e20	0.800113	0.400056	+	0.916490i	$0.368991\pi$
$62$	0	0
$63$	−1.11193e21	−2.25767
$64$	0	0
$65$	−4.88859e19	−0.0692915
$66$	0	0
$67$	1.74814e21	1.74870	0.874350	−	0.485296i	$-0.161288\pi$
$67$	1.74814e21	1.74870	0.874350	+	0.485296i	$0.161288\pi$
$68$	0	0
$69$	3.29277e21	2.34854
$70$	0	0
$71$	2.71799e21	1.39565	0.697825	−	0.716269i	$-0.254151\pi$
$71$	2.71799e21	1.39565	0.697825	+	0.716269i	$0.254151\pi$
$72$	0	0
$73$	4.31278e21	1.60896	0.804479	−	0.593982i	$-0.202445\pi$
$73$	4.31278e21	1.60896	0.804479	+	0.593982i	$0.202445\pi$
$74$	0	0
$75$	1.92068e21	0.525111
$76$	0	0
$77$	6.63399e21	1.34008
$78$	0	0
$79$	−3.59856e21	−0.541274	−0.270637	−	0.962681i	$-0.587234\pi$
$79$	−3.59856e21	−0.541274	−0.270637	+	0.962681i	$0.587234\pi$
$80$	0	0
$81$	2.08387e21	0.235122
$82$	0	0
$83$	−2.25004e20	−0.0191775	−0.00958876	−	0.999954i	$-0.503052\pi$
$83$	−2.25004e20	−0.0191775	−0.00958876	+	0.999954i	$0.503052\pi$
$84$	0	0
$85$	7.39865e21	0.479551
$86$	0	0
$87$	−6.17311e21	−0.306219
$88$	0	0
$89$	3.38924e22	1.29455	0.647273	−	0.762258i	$-0.275909\pi$
$89$	3.38924e22	1.29455	0.647273	+	0.762258i	$0.275909\pi$
$90$	0	0
$91$	3.72724e21	0.110258
$92$	0	0
$93$	6.06978e22	1.39836
$94$	0	0
$95$	5.00927e22	0.903552
$96$	0	0
$97$	9.21216e22	1.30763	0.653817	−	0.756652i	$-0.273166\pi$
$97$	9.21216e22	1.30763	0.653817	+	0.756652i	$0.273166\pi$
$98$	0	0
$99$	−1.56190e23	−1.75327
$100$	0	0
$101$	−1.42425e23	−1.27026	−0.635129	−	0.772406i	$-0.719053\pi$
$101$	−1.42425e23	−1.27026	−0.635129	+	0.772406i	$0.719053\pi$
$102$	0	0
$103$	1.07041e23	0.761946	0.380973	−	0.924586i	$-0.375589\pi$
$103$	1.07041e23	0.761946	0.380973	+	0.924586i	$0.375589\pi$
$104$	0	0
$105$	3.13377e23	1.78809
$106$	0	0
$107$	1.90048e23	0.872872	0.436436	−	0.899735i	$-0.356240\pi$
$107$	1.90048e23	0.872872	0.436436	+	0.899735i	$0.356240\pi$
$108$	0	0
$109$	4.03432e23	1.49750	0.748749	−	0.662854i	$-0.230655\pi$
$109$	4.03432e23	1.49750	0.748749	+	0.662854i	$0.230655\pi$
$110$	0	0
$111$	−3.13416e23	−0.943857
$112$	0	0
$113$	−4.80831e23	−1.17921	−0.589604	−	0.807693i	$-0.700716\pi$
$113$	−4.80831e23	−1.17921	−0.589604	+	0.807693i	$0.700716\pi$
$114$	0	0
$115$	−5.86660e23	−1.17588
$116$	0	0
$117$	−8.77537e22	−0.144254
$118$	0	0
$119$	−5.64099e23	−0.763072
$120$	0	0
$121$	3.64294e22	0.0406837
$122$	0	0
$123$	8.03248e23	0.742918
$124$	0	0
$125$	−1.41670e24	−1.08846
$126$	0	0
$127$	2.24142e24	1.43476	0.717381	−	0.696681i	$-0.245341\pi$
$127$	2.24142e24	1.43476	0.717381	+	0.696681i	$0.245341\pi$
$128$	0	0
$129$	−4.23835e24	−2.26681
$130$	0	0
$131$	3.40494e24	1.52577	0.762887	−	0.646532i	$-0.223781\pi$
$131$	3.40494e24	1.52577	0.762887	+	0.646532i	$0.223781\pi$
$132$	0	0
$133$	−3.81925e24	−1.43775
$134$	0	0
$135$	−3.08516e24	−0.978226
$136$	0	0
$137$	−4.70653e24	−1.26013	−0.630063	−	0.776544i	$-0.716971\pi$
$137$	−4.70653e24	−1.26013	−0.630063	+	0.776544i	$0.716971\pi$
$138$	0	0
$139$	5.18506e23	0.117512	0.0587562	−	0.998272i	$-0.481287\pi$
$139$	5.18506e23	0.117512	0.0587562	+	0.998272i	$0.481287\pi$
$140$	0	0
$141$	6.62763e24	1.27450
$142$	0	0
$143$	5.23556e23	0.0856246
$144$	0	0
$145$	1.09984e24	0.153319
$146$	0	0
$147$	−1.00469e25	−1.19642
$148$	0	0
$149$	−1.00676e25	−1.02632	−0.513160	−	0.858293i	$-0.671525\pi$
$149$	−1.00676e25	−1.02632	−0.513160	+	0.858293i	$0.671525\pi$
$150$	0	0
$151$	−1.12958e25	−0.987832	−0.493916	−	0.869509i	$-0.664435\pi$
$151$	−1.12958e25	−0.987832	−0.493916	+	0.869509i	$0.664435\pi$
$152$	0	0
$153$	1.32811e25	0.998349
$154$	0	0
$155$	−1.08143e25	−0.700137
$156$	0	0
$157$	−4.49140e24	−0.250920	−0.125460	−	0.992099i	$-0.540041\pi$
$157$	−4.49140e24	−0.250920	−0.125460	+	0.992099i	$0.540041\pi$
$158$	0	0
$159$	2.11449e25	1.02127
$160$	0	0
$161$	4.47290e25	1.87108
$162$	0	0
$163$	−3.38828e25	−1.22977	−0.614883	−	0.788619i	$-0.710797\pi$
$163$	−3.38828e25	−1.22977	−0.614883	+	0.788619i	$0.710797\pi$
$164$	0	0
$165$	4.40193e25	1.38860
$166$	0	0
$167$	2.60376e24	0.0715092	0.0357546	−	0.999361i	$-0.488617\pi$
$167$	2.60376e24	0.0715092	0.0357546	+	0.999361i	$0.488617\pi$
$168$	0	0
$169$	−4.14598e25	−0.992955
$170$	0	0
$171$	8.99200e25	1.88105
$172$	0	0
$173$	−3.96085e25	−0.724866	−0.362433	−	0.932010i	$-0.618054\pi$
$173$	−3.96085e25	−0.724866	−0.362433	+	0.932010i	$0.618054\pi$
$174$	0	0
$175$	2.60906e25	0.418356
$176$	0	0
$177$	3.76314e25	0.529490
$178$	0	0
$179$	−4.42305e25	−0.546905	−0.273453	−	0.961885i	$-0.588166\pi$
$179$	−4.42305e25	−0.546905	−0.273453	+	0.961885i	$0.588166\pi$
$180$	0	0
$181$	8.22310e25	0.894813	0.447406	−	0.894331i	$-0.352348\pi$
$181$	8.22310e25	0.894813	0.447406	+	0.894331i	$0.352348\pi$
$182$	0	0
$183$	−1.37568e26	−1.31925
$184$	0	0
$185$	5.58400e25	0.472575
$186$	0	0
$187$	−7.92376e25	−0.592588
$188$	0	0
$189$	2.35223e26	1.55657
$190$	0	0
$191$	−5.22803e25	−0.306517	−0.153258	−	0.988186i	$-0.548977\pi$
$191$	−5.22803e25	−0.306517	−0.153258	+	0.988186i	$0.548977\pi$
$192$	0	0
$193$	2.67638e26	1.39200	0.695999	−	0.718043i	$-0.254962\pi$
$193$	2.67638e26	1.39200	0.695999	+	0.718043i	$0.254962\pi$
$194$	0	0
$195$	2.47318e25	0.114250
$196$	0	0
$197$	−8.45015e25	−0.347139	−0.173569	−	0.984822i	$-0.555530\pi$
$197$	−8.45015e25	−0.347139	−0.173569	+	0.984822i	$0.555530\pi$
$198$	0	0
$199$	1.66457e25	0.0608823	0.0304411	−	0.999537i	$-0.490309\pi$
$199$	1.66457e25	0.0608823	0.0304411	+	0.999537i	$0.490309\pi$
$200$	0	0
$201$	−8.84397e26	−2.88332
$202$	0	0
$203$	−8.38555e25	−0.243965
$204$	0	0
$205$	−1.43111e26	−0.371967
$206$	0	0
$207$	−1.05310e27	−2.44799
$208$	0	0
$209$	−5.36480e26	−1.11653
$210$	0	0
$211$	2.79674e26	0.521680	0.260840	−	0.965382i	$-0.416001\pi$
$211$	2.79674e26	0.521680	0.260840	+	0.965382i	$0.416001\pi$
$212$	0	0
$213$	−1.37505e27	−2.30120
$214$	0	0
$215$	7.55130e26	1.13496
$216$	0	0
$217$	8.24519e26	1.11407
$218$	0	0
$219$	−2.18187e27	−2.65290
$220$	0	0
$221$	−4.45188e25	−0.0487565
$222$	0	0
$223$	5.45249e26	0.538380	0.269190	−	0.963087i	$-0.413244\pi$
$223$	5.45249e26	0.538380	0.269190	+	0.963087i	$0.413244\pi$
$224$	0	0
$225$	−6.14274e26	−0.547348
$226$	0	0
$227$	−1.15345e27	−0.928326	−0.464163	−	0.885750i	$-0.653645\pi$
$227$	−1.15345e27	−0.928326	−0.464163	+	0.885750i	$0.653645\pi$
$228$	0	0
$229$	−1.17499e27	−0.854922	−0.427461	−	0.904034i	$-0.640592\pi$
$229$	−1.17499e27	−0.854922	−0.427461	+	0.904034i	$0.640592\pi$
$230$	0	0
$231$	−3.35619e27	−2.20957
$232$	0	0
$233$	5.77127e26	0.344095	0.172048	−	0.985089i	$-0.444962\pi$
$233$	5.77127e26	0.344095	0.172048	+	0.985089i	$0.444962\pi$
$234$	0	0
$235$	−1.18082e27	−0.638120
$236$	0	0
$237$	1.82054e27	0.892472
$238$	0	0
$239$	3.06102e26	0.136236	0.0681178	−	0.997677i	$-0.478301\pi$
$239$	3.06102e26	0.136236	0.0681178	+	0.997677i	$0.478301\pi$
$240$	0	0
$241$	1.82530e27	0.738139	0.369070	−	0.929402i	$-0.379676\pi$
$241$	1.82530e27	0.738139	0.369070	+	0.929402i	$0.379676\pi$
$242$	0	0
$243$	2.16808e27	0.797267
$244$	0	0
$245$	1.79002e27	0.599027
$246$	0	0
$247$	−3.01416e26	−0.0918652
$248$	0	0
$249$	1.13831e26	0.0316206
$250$	0	0
$251$	−1.72473e27	−0.436991	−0.218495	−	0.975838i	$-0.570115\pi$
$251$	−1.72473e27	−0.436991	−0.218495	+	0.975838i	$0.570115\pi$
$252$	0	0
$253$	6.28298e27	1.45305
$254$	0	0
$255$	−3.74303e27	−0.790700
$256$	0	0
$257$	5.49958e27	1.06194	0.530968	−	0.847392i	$-0.321828\pi$
$257$	5.49958e27	1.06194	0.530968	+	0.847392i	$0.321828\pi$
$258$	0	0
$259$	−4.25744e27	−0.751971
$260$	0	0
$261$	1.97429e27	0.319186
$262$	0	0
$263$	−1.10256e28	−1.63272	−0.816360	−	0.577543i	$-0.804012\pi$
$263$	−1.10256e28	−1.63272	−0.816360	+	0.577543i	$0.804012\pi$
$264$	0	0
$265$	−3.76730e27	−0.511332
$266$	0	0
$267$	−1.71464e28	−2.13449
$268$	0	0
$269$	−5.47893e26	−0.0625957	−0.0312978	−	0.999510i	$-0.509964\pi$
$269$	−5.47893e26	−0.0625957	−0.0312978	+	0.999510i	$0.509964\pi$
$270$	0	0
$271$	−1.43098e28	−1.50137	−0.750683	−	0.660663i	$-0.770275\pi$
$271$	−1.43098e28	−1.50137	−0.750683	+	0.660663i	$0.770275\pi$
$272$	0	0
$273$	−1.88564e27	−0.181798
$274$	0	0
$275$	3.66488e27	0.324888
$276$	0	0
$277$	4.09302e27	0.333831	0.166915	−	0.985971i	$-0.446619\pi$
$277$	4.09302e27	0.333831	0.166915	+	0.985971i	$0.446619\pi$
$278$	0	0
$279$	−1.94124e28	−1.45758
$280$	0	0
$281$	−6.59576e27	−0.456186	−0.228093	−	0.973639i	$-0.573249\pi$
$281$	−6.59576e27	−0.456186	−0.228093	+	0.973639i	$0.573249\pi$
$282$	0	0
$283$	−4.65761e27	−0.296906	−0.148453	−	0.988919i	$-0.547429\pi$
$283$	−4.65761e27	−0.296906	−0.148453	+	0.988919i	$0.547429\pi$
$284$	0	0
$285$	−2.53423e28	−1.48981
$286$	0	0
$287$	1.09113e28	0.591883
$288$	0	0
$289$	−1.32299e28	−0.662567
$290$	0	0
$291$	−4.66050e28	−2.15607
$292$	0	0
$293$	2.37368e28	1.01495	0.507476	−	0.861666i	$-0.330579\pi$
$293$	2.37368e28	1.01495	0.507476	+	0.861666i	$0.330579\pi$
$294$	0	0
$295$	−6.70463e27	−0.265107
$296$	0	0
$297$	3.30413e28	1.20881
$298$	0	0
$299$	3.53003e27	0.119553
$300$	0	0
$301$	−5.75738e28	−1.80597
$302$	0	0
$303$	7.20542e28	2.09445
$304$	0	0
$305$	2.45098e28	0.660530
$306$	0	0
$307$	3.33435e28	0.833527	0.416763	−	0.909015i	$-0.363164\pi$
$307$	3.33435e28	0.833527	0.416763	+	0.909015i	$0.363164\pi$
$308$	0	0
$309$	−5.41531e28	−1.25632
$310$	0	0
$311$	−8.79341e28	−1.89414	−0.947072	−	0.321021i	$-0.895974\pi$
$311$	−8.79341e28	−1.89414	−0.947072	+	0.321021i	$0.895974\pi$
$312$	0	0
$313$	−9.00131e28	−1.80113	−0.900567	−	0.434718i	$-0.856848\pi$
$313$	−9.00131e28	−1.80113	−0.900567	+	0.434718i	$0.856848\pi$
$314$	0	0
$315$	−1.00224e29	−1.86381
$316$	0	0
$317$	3.39800e28	0.587545	0.293773	−	0.955875i	$-0.405089\pi$
$317$	3.39800e28	0.587545	0.293773	+	0.955875i	$0.405089\pi$
$318$	0	0
$319$	−1.17790e28	−0.189459
$320$	0	0
$321$	−9.61470e28	−1.43922
$322$	0	0
$323$	4.56178e28	0.635778
$324$	0	0
$325$	2.05907e27	0.0267309
$326$	0	0
$327$	−2.04100e29	−2.46913
$328$	0	0
$329$	9.00297e28	1.01539
$330$	0	0
$331$	−1.07942e29	−1.13545	−0.567727	−	0.823217i	$-0.692177\pi$
$331$	−1.07942e29	−1.13545	−0.567727	+	0.823217i	$0.692177\pi$
$332$	0	0
$333$	1.00237e29	0.983826
$334$	0	0
$335$	1.57569e29	1.44363
$336$	0	0
$337$	−2.54917e28	−0.218100	−0.109050	−	0.994036i	$-0.534781\pi$
$337$	−2.54917e28	−0.218100	−0.109050	+	0.994036i	$0.534781\pi$
$338$	0	0
$339$	2.43256e29	1.94432
$340$	0	0
$341$	1.15818e29	0.865170
$342$	0	0
$343$	5.16079e28	0.360441
$344$	0	0
$345$	2.96796e29	1.93882
$346$	0	0
$347$	−1.17389e29	−0.717525	−0.358763	−	0.933429i	$-0.616801\pi$
$347$	−1.17389e29	−0.717525	−0.358763	+	0.933429i	$0.616801\pi$
$348$	0	0
$349$	2.03481e28	0.116421	0.0582104	−	0.998304i	$-0.481461\pi$
$349$	2.03481e28	0.116421	0.0582104	+	0.998304i	$0.481461\pi$
$350$	0	0
$351$	1.85639e28	0.0994574
$352$	0	0
$353$	7.43192e28	0.372985	0.186493	−	0.982456i	$-0.440288\pi$
$353$	7.43192e28	0.372985	0.186493	+	0.982456i	$0.440288\pi$
$354$	0	0
$355$	2.44987e29	1.15217
$356$	0	0
$357$	2.85382e29	1.25818
$358$	0	0
$359$	−6.09639e28	−0.252050	−0.126025	−	0.992027i	$-0.540222\pi$
$359$	−6.09639e28	−0.252050	−0.126025	+	0.992027i	$0.540222\pi$
$360$	0	0
$361$	5.10268e28	0.197909
$362$	0	0
$363$	−1.84299e28	−0.0670808
$364$	0	0
$365$	3.88735e29	1.32827
$366$	0	0
$367$	1.13728e29	0.364928	0.182464	−	0.983213i	$-0.441593\pi$
$367$	1.13728e29	0.364928	0.182464	+	0.983213i	$0.441593\pi$
$368$	0	0
$369$	−2.56895e29	−0.774378
$370$	0	0
$371$	2.87233e29	0.813643
$372$	0	0
$373$	−7.16967e29	−1.90918	−0.954591	−	0.297920i	$-0.903707\pi$
$373$	−7.16967e29	−1.90918	−0.954591	+	0.297920i	$0.903707\pi$
$374$	0	0
$375$	7.16720e29	1.79469
$376$	0	0
$377$	−6.61790e27	−0.0155881
$378$	0	0
$379$	−6.32589e29	−1.40207	−0.701036	−	0.713126i	$-0.747279\pi$
$379$	−6.32589e29	−1.40207	−0.701036	+	0.713126i	$0.747279\pi$
$380$	0	0
$381$	−1.13395e30	−2.36569
$382$	0	0
$383$	6.48766e29	1.27439	0.637195	−	0.770703i	$-0.280095\pi$
$383$	6.48766e29	1.27439	0.637195	+	0.770703i	$0.280095\pi$
$384$	0	0
$385$	5.97958e29	1.10630
$386$	0	0
$387$	1.35551e30	2.36280
$388$	0	0
$389$	−1.78533e29	−0.293291	−0.146645	−	0.989189i	$-0.546848\pi$
$389$	−1.78533e29	−0.293291	−0.146645	+	0.989189i	$0.546848\pi$
$390$	0	0
$391$	−5.34252e29	−0.827396
$392$	0	0
$393$	−1.72259e30	−2.51575
$394$	0	0
$395$	−3.24359e29	−0.446847
$396$	0	0
$397$	9.56321e28	0.124312	0.0621560	−	0.998066i	$-0.480202\pi$
$397$	9.56321e28	0.124312	0.0621560	+	0.998066i	$0.480202\pi$
$398$	0	0
$399$	1.93219e30	2.37061
$400$	0	0
$401$	6.48450e29	0.751132	0.375566	−	0.926796i	$-0.377448\pi$
$401$	6.48450e29	0.751132	0.375566	+	0.926796i	$0.377448\pi$
$402$	0	0
$403$	6.50713e28	0.0711838
$404$	0	0
$405$	1.87831e29	0.194104
$406$	0	0
$407$	−5.98032e29	−0.583967
$408$	0	0
$409$	−6.20946e29	−0.573107	−0.286554	−	0.958064i	$-0.592510\pi$
$409$	−6.20946e29	−0.573107	−0.286554	+	0.958064i	$0.592510\pi$
$410$	0	0
$411$	2.38107e30	2.07774
$412$	0	0
$413$	5.11185e29	0.421845
$414$	0	0
$415$	−2.02809e28	−0.0158319
$416$	0	0
$417$	−2.62316e29	−0.193758
$418$	0	0
$419$	9.40356e29	0.657402	0.328701	−	0.944434i	$-0.393389\pi$
$419$	9.40356e29	0.657402	0.328701	+	0.944434i	$0.393389\pi$
$420$	0	0
$421$	1.63695e30	1.08340	0.541702	−	0.840571i	$-0.317780\pi$
$421$	1.63695e30	1.08340	0.541702	+	0.840571i	$0.317780\pi$
$422$	0	0
$423$	−2.11965e30	−1.32846
$424$	0	0
$425$	−3.11631e29	−0.184998
$426$	0	0
$427$	−1.86872e30	−1.05105
$428$	0	0
$429$	−2.64871e29	−0.141181
$430$	0	0
$431$	5.36984e29	0.271315	0.135657	−	0.990756i	$-0.456685\pi$
$431$	5.36984e29	0.271315	0.135657	+	0.990756i	$0.456685\pi$
$432$	0	0
$433$	−7.10121e29	−0.340190	−0.170095	−	0.985428i	$-0.554407\pi$
$433$	−7.10121e29	−0.340190	−0.170095	+	0.985428i	$0.554407\pi$
$434$	0	0
$435$	−5.56417e29	−0.252798
$436$	0	0
$437$	−3.61717e30	−1.55895
$438$	0	0
$439$	1.78862e30	0.731437	0.365719	−	0.930725i	$-0.380823\pi$
$439$	1.78862e30	0.731437	0.365719	+	0.930725i	$0.380823\pi$
$440$	0	0
$441$	3.21320e30	1.24708
$442$	0	0
$443$	3.61961e30	1.33358	0.666790	−	0.745246i	$-0.267668\pi$
$443$	3.61961e30	1.33358	0.666790	+	0.745246i	$0.267668\pi$
$444$	0	0
$445$	3.05491e30	1.06871
$446$	0	0
$447$	5.09327e30	1.69223
$448$	0	0
$449$	−1.09219e29	−0.0344720	−0.0172360	−	0.999851i	$-0.505487\pi$
$449$	−1.09219e29	−0.0344720	−0.0172360	+	0.999851i	$0.505487\pi$
$450$	0	0
$451$	1.53269e30	0.459646
$452$	0	0
$453$	5.71465e30	1.62877
$454$	0	0
$455$	3.35957e29	0.0910232
$456$	0	0
$457$	4.42972e30	1.14114	0.570571	−	0.821248i	$-0.306722\pi$
$457$	4.42972e30	1.14114	0.570571	+	0.821248i	$0.306722\pi$
$458$	0	0
$459$	−2.80955e30	−0.688322
$460$	0	0
$461$	5.24784e30	1.22298	0.611491	−	0.791251i	$-0.290570\pi$
$461$	5.24784e30	1.22298	0.611491	+	0.791251i	$0.290570\pi$
$462$	0	0
$463$	−3.94748e30	−0.875263	−0.437631	−	0.899154i	$-0.644183\pi$
$463$	−3.94748e30	−0.875263	−0.437631	+	0.899154i	$0.644183\pi$
$464$	0	0
$465$	5.47103e30	1.15441
$466$	0	0
$467$	2.80285e30	0.562931	0.281466	−	0.959571i	$-0.409179\pi$
$467$	2.80285e30	0.562931	0.281466	+	0.959571i	$0.409179\pi$
$468$	0	0
$469$	−1.20136e31	−2.29714
$470$	0	0
$471$	2.27224e30	0.413726
$472$	0	0
$473$	−8.08725e30	−1.40248
$474$	0	0
$475$	−2.10990e30	−0.348567
$476$	0	0
$477$	−6.76258e30	−1.06451
$478$	0	0
$479$	−5.55199e30	−0.832895	−0.416447	−	0.909160i	$-0.636725\pi$
$479$	−5.55199e30	−0.832895	−0.416447	+	0.909160i	$0.636725\pi$
$480$	0	0
$481$	−3.35998e29	−0.0480472
$482$	0	0
$483$	−2.26288e31	−3.08510
$484$	0	0
$485$	8.30343e30	1.07951
$486$	0	0
$487$	1.47354e30	0.182716	0.0913582	−	0.995818i	$-0.470879\pi$
$487$	1.47354e30	0.182716	0.0913582	+	0.995818i	$0.470879\pi$
$488$	0	0
$489$	1.71416e31	2.02768
$490$	0	0
$491$	−1.67709e29	−0.0189287	−0.00946433	−	0.999955i	$-0.503013\pi$
$491$	−1.67709e29	−0.0189287	−0.00946433	+	0.999955i	$0.503013\pi$
$492$	0	0
$493$	1.00159e30	0.107882
$494$	0	0
$495$	−1.40783e31	−1.44740
$496$	0	0
$497$	−1.86787e31	−1.83336
$498$	0	0
$499$	−1.27784e31	−1.19762	−0.598810	−	0.800891i	$-0.704360\pi$
$499$	−1.27784e31	−1.19762	−0.598810	+	0.800891i	$0.704360\pi$
$500$	0	0
$501$	−1.31726e30	−0.117907
$502$	0	0
$503$	−6.62625e30	−0.566547	−0.283273	−	0.959039i	$-0.591420\pi$
$503$	−6.62625e30	−0.566547	−0.283273	+	0.959039i	$0.591420\pi$
$504$	0	0
$505$	−1.28376e31	−1.04866
$506$	0	0
$507$	2.09748e31	1.63722
$508$	0	0
$509$	−2.12937e31	−1.58853	−0.794266	−	0.607570i	$-0.792144\pi$
$509$	−2.12937e31	−1.58853	−0.794266	+	0.607570i	$0.792144\pi$
$510$	0	0
$511$	−2.96385e31	−2.11357
$512$	0	0
$513$	−1.90222e31	−1.29691
$514$	0	0
$515$	9.64825e30	0.629021
$516$	0	0
$517$	1.26462e31	0.788534
$518$	0	0
$519$	2.00382e31	1.19519
$520$	0	0
$521$	−3.13459e31	−1.78874	−0.894368	−	0.447332i	$-0.852374\pi$
$521$	−3.13459e31	−1.78874	−0.894368	+	0.447332i	$0.852374\pi$
$522$	0	0
$523$	−5.60340e30	−0.305972	−0.152986	−	0.988228i	$-0.548889\pi$
$523$	−5.60340e30	−0.305972	−0.152986	+	0.988228i	$0.548889\pi$
$524$	0	0
$525$	−1.31994e31	−0.689800
$526$	0	0
$527$	−9.84822e30	−0.492647
$528$	0	0
$529$	2.14819e31	1.02880
$530$	0	0
$531$	−1.20353e31	−0.551912
$532$	0	0
$533$	8.61124e29	0.0378184
$534$	0	0
$535$	1.71301e31	0.720596
$536$	0	0
$537$	2.23766e31	0.901757
$538$	0	0
$539$	−1.91706e31	−0.740227
$540$	0	0
$541$	2.41300e30	0.0892873	0.0446436	−	0.999003i	$-0.485785\pi$
$541$	2.41300e30	0.0892873	0.0446436	+	0.999003i	$0.485785\pi$
$542$	0	0
$543$	−4.16013e31	−1.47540
$544$	0	0
$545$	3.63636e31	1.23625
$546$	0	0
$547$	−4.73888e31	−1.54462	−0.772310	−	0.635246i	$-0.780899\pi$
$547$	−4.73888e31	−1.54462	−0.772310	+	0.635246i	$0.780899\pi$
$548$	0	0
$549$	4.39969e31	1.37512
$550$	0	0
$551$	6.78126e30	0.203267
$552$	0	0
$553$	2.47302e31	0.711032
$554$	0	0
$555$	−2.82499e31	−0.779197
$556$	0	0
$557$	4.15359e31	1.09923	0.549616	−	0.835417i	$-0.314774\pi$
$557$	4.15359e31	1.09923	0.549616	+	0.835417i	$0.314774\pi$
$558$	0	0
$559$	−4.54374e30	−0.115392
$560$	0	0
$561$	4.00869e31	0.977080
$562$	0	0
$563$	6.08993e31	1.42484	0.712419	−	0.701754i	$-0.247599\pi$
$563$	6.08993e31	1.42484	0.712419	+	0.701754i	$0.247599\pi$
$564$	0	0
$565$	−4.33400e31	−0.973490
$566$	0	0
$567$	−1.43209e31	−0.308863
$568$	0	0
$569$	1.66042e31	0.343897	0.171948	−	0.985106i	$-0.444994\pi$
$569$	1.66042e31	0.343897	0.171948	+	0.985106i	$0.444994\pi$
$570$	0	0
$571$	3.60619e31	0.717354	0.358677	−	0.933462i	$-0.383228\pi$
$571$	3.60619e31	0.717354	0.358677	+	0.933462i	$0.383228\pi$
$572$	0	0
$573$	2.64490e31	0.505395
$574$	0	0
$575$	2.47101e31	0.453622
$576$	0	0
$577$	−1.20260e31	−0.212129	−0.106064	−	0.994359i	$-0.533825\pi$
$577$	−1.20260e31	−0.212129	−0.106064	+	0.994359i	$0.533825\pi$
$578$	0	0
$579$	−1.35400e32	−2.29517
$580$	0	0
$581$	1.54629e30	0.0251921
$582$	0	0
$583$	4.03469e31	0.631861
$584$	0	0
$585$	−7.90973e30	−0.119088
$586$	0	0
$587$	5.93652e31	0.859397	0.429698	−	0.902973i	$-0.358620\pi$
$587$	5.93652e31	0.859397	0.429698	+	0.902973i	$0.358620\pi$
$588$	0	0
$589$	−6.66776e31	−0.928227
$590$	0	0
$591$	4.27500e31	0.572374
$592$	0	0
$593$	−1.10327e32	−1.42087	−0.710433	−	0.703765i	$-0.751501\pi$
$593$	−1.10327e32	−1.42087	−0.710433	+	0.703765i	$0.751501\pi$
$594$	0	0
$595$	−5.08454e31	−0.629951
$596$	0	0
$597$	−8.42118e30	−0.100385
$598$	0	0
$599$	−9.24234e31	−1.06017	−0.530083	−	0.847946i	$-0.677839\pi$
$599$	−9.24234e31	−1.06017	−0.530083	+	0.847946i	$0.677839\pi$
$600$	0	0
$601$	1.84593e31	0.203778	0.101889	−	0.994796i	$-0.467511\pi$
$601$	1.84593e31	0.203778	0.101889	+	0.994796i	$0.467511\pi$
$602$	0	0
$603$	2.82848e32	3.00541
$604$	0	0
$605$	3.28359e30	0.0335863
$606$	0	0
$607$	1.01802e32	1.00250	0.501252	−	0.865301i	$-0.332873\pi$
$607$	1.01802e32	1.00250	0.501252	+	0.865301i	$0.332873\pi$
$608$	0	0
$609$	4.24232e31	0.402258
$610$	0	0
$611$	7.10516e30	0.0648784
$612$	0	0
$613$	−1.20531e32	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$613$	−1.20531e32	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$614$	0	0
$615$	7.24012e31	0.613313
$616$	0	0
$617$	−1.30052e32	−1.06130	−0.530649	−	0.847592i	$-0.678052\pi$
$617$	−1.30052e32	−1.06130	−0.530649	+	0.847592i	$0.678052\pi$
$618$	0	0
$619$	−1.66234e32	−1.30701	−0.653503	−	0.756924i	$-0.726701\pi$
$619$	−1.66234e32	−1.30701	−0.653503	+	0.756924i	$0.726701\pi$
$620$	0	0
$621$	2.22778e32	1.68779
$622$	0	0
$623$	−2.32917e32	−1.70055
$624$	0	0
$625$	−8.24372e31	−0.580100
$626$	0	0
$627$	2.71410e32	1.84098
$628$	0	0
$629$	5.08517e31	0.332524
$630$	0	0
$631$	3.08263e31	0.194350	0.0971749	−	0.995267i	$-0.469019\pi$
$631$	3.08263e31	0.194350	0.0971749	+	0.995267i	$0.469019\pi$
$632$	0	0
$633$	−1.41489e32	−0.860164
$634$	0	0
$635$	2.02032e32	1.18446
$636$	0	0
$637$	−1.07708e31	−0.0609038
$638$	0	0
$639$	4.39769e32	2.39864
$640$	0	0
$641$	−8.22287e31	−0.432669	−0.216335	−	0.976319i	$-0.569410\pi$
$641$	−8.22287e31	−0.432669	−0.216335	+	0.976319i	$0.569410\pi$
$642$	0	0
$643$	3.16365e32	1.60606	0.803032	−	0.595936i	$-0.203219\pi$
$643$	3.16365e32	1.60606	0.803032	+	0.595936i	$0.203219\pi$
$644$	0	0
$645$	−3.82026e32	−1.87136
$646$	0	0
$647$	2.07765e32	0.982141	0.491070	−	0.871120i	$-0.336606\pi$
$647$	2.07765e32	0.982141	0.491070	+	0.871120i	$0.336606\pi$
$648$	0	0
$649$	7.18049e31	0.327597
$650$	0	0
$651$	−4.17131e32	−1.83692
$652$	0	0
$653$	−2.36683e32	−1.00616	−0.503078	−	0.864241i	$-0.667799\pi$
$653$	−2.36683e32	−1.00616	−0.503078	+	0.864241i	$0.667799\pi$
$654$	0	0
$655$	3.06907e32	1.25960
$656$	0	0
$657$	6.97807e32	2.76524
$658$	0	0
$659$	7.16883e31	0.274325	0.137163	−	0.990549i	$-0.456202\pi$
$659$	7.16883e31	0.274325	0.137163	+	0.990549i	$0.456202\pi$
$660$	0	0
$661$	2.52957e32	0.934824	0.467412	−	0.884039i	$-0.345186\pi$
$661$	2.52957e32	0.934824	0.467412	+	0.884039i	$0.345186\pi$
$662$	0	0
$663$	2.25224e31	0.0803914
$664$	0	0
$665$	−3.44250e32	−1.18693
$666$	0	0
$667$	−7.94186e31	−0.264530
$668$	0	0
$669$	−2.75846e32	−0.887700
$670$	0	0
$671$	−2.62494e32	−0.816226
$672$	0	0
$673$	−1.17871e32	−0.354188	−0.177094	−	0.984194i	$-0.556670\pi$
$673$	−1.17871e32	−0.354188	−0.177094	+	0.984194i	$0.556670\pi$
$674$	0	0
$675$	1.29947e32	0.377374
$676$	0	0
$677$	6.75616e32	1.89640	0.948200	−	0.317674i	$-0.102902\pi$
$677$	6.75616e32	1.89640	0.948200	+	0.317674i	$0.102902\pi$
$678$	0	0
$679$	−6.33083e32	−1.71774
$680$	0	0
$681$	5.83539e32	1.53066
$682$	0	0
$683$	−6.83468e32	−1.73333	−0.866663	−	0.498894i	$-0.833740\pi$
$683$	−6.83468e32	−1.73333	−0.866663	+	0.498894i	$0.833740\pi$
$684$	0	0
$685$	−4.24226e32	−1.04029
$686$	0	0
$687$	5.94438e32	1.40963
$688$	0	0
$689$	2.26685e31	0.0519878
$690$	0	0
$691$	6.05837e32	1.34387	0.671936	−	0.740609i	$-0.265463\pi$
$691$	6.05837e32	1.34387	0.671936	+	0.740609i	$0.265463\pi$
$692$	0	0
$693$	1.07338e33	2.30314
$694$	0	0
$695$	4.67358e31	0.0970118
$696$	0	0
$697$	−1.30327e32	−0.261732
$698$	0	0
$699$	−2.91973e32	−0.567356
$700$	0	0
$701$	7.67265e32	1.44274	0.721370	−	0.692550i	$-0.243513\pi$
$701$	7.67265e32	1.44274	0.721370	+	0.692550i	$0.243513\pi$
$702$	0	0
$703$	3.44292e32	0.626529
$704$	0	0
$705$	5.97385e32	1.05215
$706$	0	0
$707$	9.78784e32	1.66864
$708$	0	0
$709$	−9.17188e32	−1.51365	−0.756827	−	0.653615i	$-0.773252\pi$
$709$	−9.17188e32	−1.51365	−0.756827	+	0.653615i	$0.773252\pi$
$710$	0	0
$711$	−5.82246e32	−0.930265
$712$	0	0
$713$	7.80893e32	1.20799
$714$	0	0
$715$	4.71910e31	0.0706870
$716$	0	0
$717$	−1.54860e32	−0.224630
$718$	0	0
$719$	−2.80152e32	−0.393561	−0.196780	−	0.980448i	$-0.563049\pi$
$719$	−2.80152e32	−0.393561	−0.196780	+	0.980448i	$0.563049\pi$
$720$	0	0
$721$	−7.35616e32	−1.00091
$722$	0	0
$723$	−9.23434e32	−1.21707
$724$	0	0
$725$	−4.63251e31	−0.0591466
$726$	0	0
$727$	8.07964e32	0.999416	0.499708	−	0.866194i	$-0.333441\pi$
$727$	8.07964e32	0.999416	0.499708	+	0.866194i	$0.333441\pi$
$728$	0	0
$729$	−1.29303e33	−1.54968
$730$	0	0
$731$	6.87673e32	0.798605
$732$	0	0
$733$	−1.23627e32	−0.139129	−0.0695645	−	0.997577i	$-0.522161\pi$
$733$	−1.23627e32	−0.139129	−0.0695645	+	0.997577i	$0.522161\pi$
$734$	0	0
$735$	−9.05583e32	−0.987697
$736$	0	0
$737$	−1.68753e33	−1.78392
$738$	0	0
$739$	−1.50297e32	−0.154007	−0.0770034	−	0.997031i	$-0.524535\pi$
$739$	−1.50297e32	−0.154007	−0.0770034	+	0.997031i	$0.524535\pi$
$740$	0	0
$741$	1.52489e32	0.151471
$742$	0	0
$743$	−1.35193e33	−1.30192	−0.650958	−	0.759114i	$-0.725633\pi$
$743$	−1.35193e33	−1.30192	−0.650958	+	0.759114i	$0.725633\pi$
$744$	0	0
$745$	−9.07446e32	−0.847274
$746$	0	0
$747$	−3.64056e31	−0.0329596
$748$	0	0
$749$	−1.30606e33	−1.14663
$750$	0	0
$751$	5.66394e32	0.482236	0.241118	−	0.970496i	$-0.422486\pi$
$751$	5.66394e32	0.482236	0.241118	+	0.970496i	$0.422486\pi$
$752$	0	0
$753$	8.72552e32	0.720525
$754$	0	0
$755$	−1.01816e33	−0.815501
$756$	0	0
$757$	−7.79753e32	−0.605835	−0.302917	−	0.953017i	$-0.597961\pi$
$757$	−7.79753e32	−0.605835	−0.302917	+	0.953017i	$0.597961\pi$
$758$	0	0
$759$	−3.17861e33	−2.39583
$760$	0	0
$761$	5.97338e32	0.436814	0.218407	−	0.975858i	$-0.429914\pi$
$761$	5.97338e32	0.436814	0.218407	+	0.975858i	$0.429914\pi$
$762$	0	0
$763$	−2.77249e33	−1.96715
$764$	0	0
$765$	1.19710e33	0.824183
$766$	0	0
$767$	4.03428e31	0.0269538
$768$	0	0
$769$	−7.32351e32	−0.474861	−0.237431	−	0.971405i	$-0.576305\pi$
$769$	−7.32351e32	−0.474861	−0.237431	+	0.971405i	$0.576305\pi$
$770$	0	0
$771$	−2.78228e33	−1.75096
$772$	0	0
$773$	−3.08883e33	−1.88682	−0.943409	−	0.331633i	$-0.892401\pi$
$773$	−3.08883e33	−1.88682	−0.943409	+	0.331633i	$0.892401\pi$
$774$	0	0
$775$	4.55497e32	0.270095
$776$	0	0
$777$	2.15387e33	1.23988
$778$	0	0
$779$	−8.82382e32	−0.493146
$780$	0	0
$781$	−2.62375e33	−1.42376
$782$	0	0
$783$	−4.17651e32	−0.220066
$784$	0	0
$785$	−4.04835e32	−0.207146
$786$	0	0
$787$	1.63692e33	0.813427	0.406714	−	0.913556i	$-0.366675\pi$
$787$	1.63692e33	0.813427	0.406714	+	0.913556i	$0.366675\pi$
$788$	0	0
$789$	5.57795e33	2.69209
$790$	0	0
$791$	3.30439e33	1.54904
$792$	0	0
$793$	−1.47480e32	−0.0671569
$794$	0	0
$795$	1.90591e33	0.843102
$796$	0	0
$797$	−3.06247e33	−1.31614	−0.658069	−	0.752957i	$-0.728627\pi$
$797$	−3.06247e33	−1.31614	−0.658069	+	0.752957i	$0.728627\pi$
$798$	0	0
$799$	−1.07533e33	−0.449008
$800$	0	0
$801$	5.48378e33	2.22488
$802$	0	0
$803$	−4.16325e33	−1.64136
$804$	0	0
$805$	4.03168e33	1.54466
$806$	0	0
$807$	2.77183e32	0.103210
$808$	0	0
$809$	−4.44022e33	−1.60693	−0.803464	−	0.595353i	$-0.797012\pi$
$809$	−4.44022e33	−1.60693	−0.803464	+	0.595353i	$0.797012\pi$
$810$	0	0
$811$	3.17750e33	1.11775	0.558876	−	0.829251i	$-0.311233\pi$
$811$	3.17750e33	1.11775	0.558876	+	0.829251i	$0.311233\pi$
$812$	0	0
$813$	7.23944e33	2.47550
$814$	0	0
$815$	−3.05405e33	−1.01523
$816$	0	0
$817$	4.65590e33	1.50470
$818$	0	0
$819$	6.03066e32	0.189496
$820$	0	0
$821$	−3.15264e33	−0.963224	−0.481612	−	0.876384i	$-0.659949\pi$
$821$	−3.15264e33	−0.963224	−0.481612	+	0.876384i	$0.659949\pi$
$822$	0	0
$823$	−2.38843e33	−0.709600	−0.354800	−	0.934942i	$-0.615451\pi$
$823$	−2.38843e33	−0.709600	−0.354800	+	0.934942i	$0.615451\pi$
$824$	0	0
$825$	−1.85409e33	−0.535687
$826$	0	0
$827$	8.06573e32	0.226637	0.113318	−	0.993559i	$-0.463852\pi$
$827$	8.06573e32	0.226637	0.113318	+	0.993559i	$0.463852\pi$
$828$	0	0
$829$	−5.77436e32	−0.157807	−0.0789036	−	0.996882i	$-0.525142\pi$
$829$	−5.77436e32	−0.157807	−0.0789036	+	0.996882i	$0.525142\pi$
$830$	0	0
$831$	−2.07069e33	−0.550432
$832$	0	0
$833$	1.63011e33	0.421501
$834$	0	0
$835$	2.34692e32	0.0590341
$836$	0	0
$837$	4.10661e33	1.00494
$838$	0	0
$839$	1.64111e33	0.390729	0.195364	−	0.980731i	$-0.437411\pi$
$839$	1.64111e33	0.390729	0.195364	+	0.980731i	$0.437411\pi$
$840$	0	0
$841$	−4.16783e33	−0.965509
$842$	0	0
$843$	3.33685e33	0.752175
$844$	0	0
$845$	−3.73700e33	−0.819730
$846$	0	0
$847$	−2.50352e32	−0.0534432
$848$	0	0
$849$	2.35632e33	0.489549
$850$	0	0
$851$	−4.03217e33	−0.815360
$852$	0	0
$853$	−1.64258e33	−0.323306	−0.161653	−	0.986848i	$-0.551682\pi$
$853$	−1.64258e33	−0.323306	−0.161653	+	0.986848i	$0.551682\pi$
$854$	0	0
$855$	8.10499e33	1.55289
$856$	0	0
$857$	−1.00984e34	−1.88353	−0.941763	−	0.336277i	$-0.890832\pi$
$857$	−1.00984e34	−1.88353	−0.941763	+	0.336277i	$0.890832\pi$
$858$	0	0
$859$	−1.81863e33	−0.330235	−0.165118	−	0.986274i	$-0.552800\pi$
$859$	−1.81863e33	−0.330235	−0.165118	+	0.986274i	$0.552800\pi$
$860$	0	0
$861$	−5.52013e33	−0.975917
$862$	0	0
$863$	3.75334e33	0.646092	0.323046	−	0.946383i	$-0.395293\pi$
$863$	3.75334e33	0.646092	0.323046	+	0.946383i	$0.395293\pi$
$864$	0	0
$865$	−3.57013e33	−0.598410
$866$	0	0
$867$	6.69309e33	1.09246
$868$	0	0
$869$	3.47380e33	0.552175
$870$	0	0
$871$	−9.48120e32	−0.146776
$872$	0	0
$873$	1.49052e34	2.24737
$874$	0	0
$875$	9.73592e33	1.42983
$876$	0	0
$877$	3.70897e33	0.530589	0.265295	−	0.964167i	$-0.414531\pi$
$877$	3.70897e33	0.530589	0.265295	+	0.964167i	$0.414531\pi$
$878$	0	0
$879$	−1.20087e34	−1.67349
$880$	0	0
$881$	4.79707e33	0.651259	0.325629	−	0.945498i	$-0.394424\pi$
$881$	4.79707e33	0.651259	0.325629	+	0.945498i	$0.394424\pi$
$882$	0	0
$883$	1.57928e33	0.208886	0.104443	−	0.994531i	$-0.466694\pi$
$883$	1.57928e33	0.208886	0.104443	+	0.994531i	$0.466694\pi$
$884$	0	0
$885$	3.39193e33	0.437118
$886$	0	0
$887$	1.49477e34	1.87695	0.938475	−	0.345348i	$-0.112239\pi$
$887$	1.49477e34	1.87695	0.938475	+	0.345348i	$0.112239\pi$
$888$	0	0
$889$	−1.54036e34	−1.88474
$890$	0	0
$891$	−2.01162e33	−0.239857
$892$	0	0
$893$	−7.28056e33	−0.846005
$894$	0	0
$895$	−3.98674e33	−0.451495
$896$	0	0
$897$	−1.78587e33	−0.197123
$898$	0	0
$899$	−1.46398e33	−0.157506
$900$	0	0
$901$	−3.43076e33	−0.359795
$902$	0	0
$903$	2.91271e34	2.97774
$904$	0	0
$905$	7.41194e33	0.738709
$906$	0	0
$907$	2.13809e32	0.0207751	0.0103875	−	0.999946i	$-0.496693\pi$
$907$	2.13809e32	0.0207751	0.0103875	+	0.999946i	$0.496693\pi$
$908$	0	0
$909$	−2.30444e34	−2.18314
$910$	0	0
$911$	−2.47006e33	−0.228164	−0.114082	−	0.993471i	$-0.536393\pi$
$911$	−2.47006e33	−0.228164	−0.114082	+	0.993471i	$0.536393\pi$
$912$	0	0
$913$	2.17203e32	0.0195637
$914$	0	0
$915$	−1.23997e34	−1.08910
$916$	0	0
$917$	−2.33996e34	−2.00430
$918$	0	0
$919$	−8.02451e33	−0.670333	−0.335166	−	0.942159i	$-0.608792\pi$
$919$	−8.02451e33	−0.670333	−0.335166	+	0.942159i	$0.608792\pi$
$920$	0	0
$921$	−1.68687e34	−1.37435
$922$	0	0
$923$	−1.47413e33	−0.117143
$924$	0	0
$925$	−2.35198e33	−0.182307
$926$	0	0
$927$	1.73193e34	1.30952
$928$	0	0
$929$	−3.89736e33	−0.287468	−0.143734	−	0.989616i	$-0.545911\pi$
$929$	−3.89736e33	−0.287468	−0.143734	+	0.989616i	$0.545911\pi$
$930$	0	0
$931$	1.10367e34	0.794177
$932$	0	0
$933$	4.44866e34	3.12313
$934$	0	0
$935$	−7.14213e33	−0.489209
$936$	0	0
$937$	5.87024e33	0.392329	0.196165	−	0.980571i	$-0.437151\pi$
$937$	5.87024e33	0.392329	0.196165	+	0.980571i	$0.437151\pi$
$938$	0	0
$939$	4.55384e34	2.96977
$940$	0	0
$941$	2.06023e34	1.31110	0.655549	−	0.755153i	$-0.272437\pi$
$941$	2.06023e34	1.31110	0.655549	+	0.755153i	$0.272437\pi$
$942$	0	0
$943$	1.03340e34	0.641777
$944$	0	0
$945$	2.12020e34	1.28502
$946$	0	0
$947$	4.59154e33	0.271602	0.135801	−	0.990736i	$-0.456639\pi$
$947$	4.59154e33	0.271602	0.135801	+	0.990736i	$0.456639\pi$
$948$	0	0
$949$	−2.33908e33	−0.135047
$950$	0	0
$951$	−1.71907e34	−0.968765
$952$	0	0
$953$	1.49358e34	0.821599	0.410799	−	0.911726i	$-0.365250\pi$
$953$	1.49358e34	0.821599	0.410799	+	0.911726i	$0.365250\pi$
$954$	0	0
$955$	−4.71231e33	−0.253044
$956$	0	0
$957$	5.95908e33	0.312386
$958$	0	0
$959$	3.23445e34	1.65534
$960$	0	0
$961$	−5.61859e33	−0.280743
$962$	0	0
$963$	3.07498e34	1.50017
$964$	0	0
$965$	2.41237e34	1.14916
$966$	0	0
$967$	−3.92857e34	−1.82738	−0.913692	−	0.406407i	$-0.866781\pi$
$967$	−3.92857e34	−1.82738	−0.913692	+	0.406407i	$0.866781\pi$
$968$	0	0
$969$	−2.30784e34	−1.04829
$970$	0	0
$971$	−2.25313e34	−0.999461	−0.499730	−	0.866181i	$-0.666568\pi$
$971$	−2.25313e34	−0.999461	−0.499730	+	0.866181i	$0.666568\pi$
$972$	0	0
$973$	−3.56330e33	−0.154367
$974$	0	0
$975$	−1.04170e33	−0.0440748
$976$	0	0
$977$	2.96994e34	1.22732	0.613662	−	0.789569i	$-0.289696\pi$
$977$	2.96994e34	1.22732	0.613662	+	0.789569i	$0.289696\pi$
$978$	0	0
$979$	−3.27173e34	−1.32062
$980$	0	0
$981$	6.52753e34	2.57368
$982$	0	0
$983$	−3.01623e34	−1.16171	−0.580857	−	0.814006i	$-0.697282\pi$
$983$	−3.01623e34	−1.16171	−0.580857	+	0.814006i	$0.697282\pi$
$984$	0	0
$985$	−7.61659e33	−0.286579
$986$	0	0
$987$	−4.55467e34	−1.67421
$988$	0	0
$989$	−5.45275e34	−1.95821
$990$	0	0
$991$	2.58031e34	0.905368	0.452684	−	0.891671i	$-0.350467\pi$
$991$	2.58031e34	0.905368	0.452684	+	0.891671i	$0.350467\pi$
$992$	0	0
$993$	5.46089e34	1.87218
$994$	0	0
$995$	1.50037e33	0.0502611
$996$	0	0
$997$	1.42567e34	0.466685	0.233342	−	0.972395i	$-0.425034\pi$
$997$	1.42567e34	0.466685	0.233342	+	0.972395i	$0.425034\pi$
$998$	0	0
$999$	−2.12046e34	−0.678309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.24.a.a.1.1		1
4.3	odd	2		64.24.a.c.1.1		1
8.3	odd	2		2.24.a.a.1.1	✓	1
8.5	even	2		16.24.a.a.1.1		1
24.11	even	2		18.24.a.d.1.1		1
40.3	even	4		50.24.b.a.49.2		2
40.19	odd	2		50.24.a.a.1.1		1
40.27	even	4		50.24.b.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.24.a.a.1.1	✓	1	8.3	odd	2
16.24.a.a.1.1		1	8.5	even	2
18.24.a.d.1.1		1	24.11	even	2
50.24.a.a.1.1		1	40.19	odd	2
50.24.b.a.49.1		2	40.27	even	4
50.24.b.a.49.2		2	40.3	even	4
64.24.a.a.1.1		1	1.1	even	1	trivial
64.24.a.c.1.1		1	4.3	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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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