LMFDB - Embedded newform 64.24.a.c.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	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	$-0.191503\pi$
$3$	505908.	1.64883	0.824417	+	0.565982i	$0.191503\pi$
$4$	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	$-0.271904\pi$
$7$	6.87226e9	1.31363	0.656813	+	0.754053i	$0.271904\pi$
$8$	0	0
$9$	1.61800e11	1.71866
$10$	0	0
$11$	9.65329e11	1.02014	0.510070	−	0.860133i	$-0.329620\pi$
$11$	9.65329e11	1.02014	0.510070	+	0.860133i	$0.329620\pi$
$12$	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	$-0.684323\pi$
$19$	−5.55749e14	−1.09449	−0.547245	+	0.836972i	$0.684323\pi$
$20$	0	0
$21$	3.47673e15	2.16595
$22$	0	0
$23$	6.50864e15	1.42436	0.712180	−	0.701996i	$-0.247708\pi$
$23$	6.50864e15	1.42436	0.712180	+	0.701996i	$0.247708\pi$
$24$	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	$-0.360610\pi$
$31$	1.19978e17	0.848090	0.424045	+	0.905641i	$0.360610\pi$
$32$	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	$-0.741247\pi$
$43$	−8.37772e18	−1.37480	−0.687398	+	0.726281i	$0.741247\pi$
$44$	0	0
$45$	1.45839e19	1.41883
$46$	0	0
$47$	1.31005e19	0.772967	0.386484	−	0.922296i	$-0.373690\pi$
$47$	1.31005e19	0.772967	0.386484	+	0.922296i	$0.373690\pi$
$48$	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	$-0.448668\pi$
$59$	7.43839e19	0.321130	0.160565	+	0.987025i	$0.448668\pi$
$60$	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	$-0.838712\pi$
$67$	−1.74814e21	−1.74870	−0.874350	+	0.485296i	$0.838712\pi$
$68$	0	0
$69$	3.29277e21	2.34854
$70$	0	0
$71$	−2.71799e21	−1.39565	−0.697825	−	0.716269i	$-0.745849\pi$
$71$	−2.71799e21	−1.39565	−0.697825	+	0.716269i	$0.745849\pi$
$72$	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	$-0.412766\pi$
$79$	3.59856e21	0.541274	0.270637	+	0.962681i	$0.412766\pi$
$80$	0	0
$81$	2.08387e21	0.235122
$82$	0	0
$83$	2.25004e20	0.0191775	0.00958876	−	0.999954i	$-0.496948\pi$
$83$	2.25004e20	0.0191775	0.00958876	+	0.999954i	$0.496948\pi$
$84$	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	$-0.624411\pi$
$103$	−1.07041e23	−0.761946	−0.380973	+	0.924586i	$0.624411\pi$
$104$	0	0
$105$	3.13377e23	1.78809
$106$	0	0
$107$	−1.90048e23	−0.872872	−0.436436	−	0.899735i	$-0.643760\pi$
$107$	−1.90048e23	−0.872872	−0.436436	+	0.899735i	$0.643760\pi$
$108$	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	$-0.754659\pi$
$127$	−2.24142e24	−1.43476	−0.717381	+	0.696681i	$0.754659\pi$
$128$	0	0
$129$	−4.23835e24	−2.26681
$130$	0	0
$131$	−3.40494e24	−1.52577	−0.762887	−	0.646532i	$-0.776219\pi$
$131$	−3.40494e24	−1.52577	−0.762887	+	0.646532i	$0.776219\pi$
$132$	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	$-0.518713\pi$
$139$	−5.18506e23	−0.117512	−0.0587562	+	0.998272i	$0.518713\pi$
$140$	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	$-0.335565\pi$
$151$	1.12958e25	0.987832	0.493916	+	0.869509i	$0.335565\pi$
$152$	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	$-0.289203\pi$
$163$	3.38828e25	1.22977	0.614883	+	0.788619i	$0.289203\pi$
$164$	0	0
$165$	4.40193e25	1.38860
$166$	0	0
$167$	−2.60376e24	−0.0715092	−0.0357546	−	0.999361i	$-0.511383\pi$
$167$	−2.60376e24	−0.0715092	−0.0357546	+	0.999361i	$0.511383\pi$
$168$	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	$-0.411834\pi$
$179$	4.42305e25	0.546905	0.273453	+	0.961885i	$0.411834\pi$
$180$	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	$-0.451023\pi$
$191$	5.22803e25	0.306517	0.153258	+	0.988186i	$0.451023\pi$
$192$	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	$-0.509691\pi$
$199$	−1.66457e25	−0.0608823	−0.0304411	+	0.999537i	$0.509691\pi$
$200$	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	$-0.583999\pi$
$211$	−2.79674e26	−0.521680	−0.260840	+	0.965382i	$0.583999\pi$
$212$	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	$-0.586756\pi$
$223$	−5.45249e26	−0.538380	−0.269190	+	0.963087i	$0.586756\pi$
$224$	0	0
$225$	−6.14274e26	−0.547348
$226$	0	0
$227$	1.15345e27	0.928326	0.464163	−	0.885750i	$-0.346355\pi$
$227$	1.15345e27	0.928326	0.464163	+	0.885750i	$0.346355\pi$
$228$	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	$-0.521699\pi$
$239$	−3.06102e26	−0.136236	−0.0681178	+	0.997677i	$0.521699\pi$
$240$	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	$-0.429885\pi$
$251$	1.72473e27	0.436991	0.218495	+	0.975838i	$0.429885\pi$
$252$	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	$-0.195988\pi$
$263$	1.10256e28	1.63272	0.816360	+	0.577543i	$0.195988\pi$
$264$	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	$-0.229725\pi$
$271$	1.43098e28	1.50137	0.750683	+	0.660663i	$0.229725\pi$
$272$	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	$-0.452571\pi$
$283$	4.65761e27	0.296906	0.148453	+	0.988919i	$0.452571\pi$
$284$	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	$-0.636836\pi$
$307$	−3.33435e28	−0.833527	−0.416763	+	0.909015i	$0.636836\pi$
$308$	0	0
$309$	−5.41531e28	−1.25632
$310$	0	0
$311$	8.79341e28	1.89414	0.947072	−	0.321021i	$-0.104026\pi$
$311$	8.79341e28	1.89414	0.947072	+	0.321021i	$0.104026\pi$
$312$	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	$-0.307823\pi$
$331$	1.07942e29	1.13545	0.567727	+	0.823217i	$0.307823\pi$
$332$	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	$-0.383199\pi$
$347$	1.17389e29	0.717525	0.358763	+	0.933429i	$0.383199\pi$
$348$	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	$-0.459778\pi$
$359$	6.09639e28	0.252050	0.126025	+	0.992027i	$0.459778\pi$
$360$	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	$-0.558407\pi$
$367$	−1.13728e29	−0.364928	−0.182464	+	0.983213i	$0.558407\pi$
$368$	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	$-0.252721\pi$
$379$	6.32589e29	1.40207	0.701036	+	0.713126i	$0.252721\pi$
$380$	0	0
$381$	−1.13395e30	−2.36569
$382$	0	0
$383$	−6.48766e29	−1.27439	−0.637195	−	0.770703i	$-0.719905\pi$
$383$	−6.48766e29	−1.27439	−0.637195	+	0.770703i	$0.719905\pi$
$384$	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	$-0.606611\pi$
$419$	−9.40356e29	−0.657402	−0.328701	+	0.944434i	$0.606611\pi$
$420$	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	$-0.543315\pi$
$431$	−5.36984e29	−0.271315	−0.135657	+	0.990756i	$0.543315\pi$
$432$	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	$-0.619177\pi$
$439$	−1.78862e30	−0.731437	−0.365719	+	0.930725i	$0.619177\pi$
$440$	0	0
$441$	3.21320e30	1.24708
$442$	0	0
$443$	−3.61961e30	−1.33358	−0.666790	−	0.745246i	$-0.732332\pi$
$443$	−3.61961e30	−1.33358	−0.666790	+	0.745246i	$0.732332\pi$
$444$	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	$-0.355817\pi$
$463$	3.94748e30	0.875263	0.437631	+	0.899154i	$0.355817\pi$
$464$	0	0
$465$	5.47103e30	1.15441
$466$	0	0
$467$	−2.80285e30	−0.562931	−0.281466	−	0.959571i	$-0.590821\pi$
$467$	−2.80285e30	−0.562931	−0.281466	+	0.959571i	$0.590821\pi$
$468$	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	$-0.363275\pi$
$479$	5.55199e30	0.832895	0.416447	+	0.909160i	$0.363275\pi$
$480$	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	$-0.529121\pi$
$487$	−1.47354e30	−0.182716	−0.0913582	+	0.995818i	$0.529121\pi$
$488$	0	0
$489$	1.71416e31	2.02768
$490$	0	0
$491$	1.67709e29	0.0189287	0.00946433	−	0.999955i	$-0.496987\pi$
$491$	1.67709e29	0.0189287	0.00946433	+	0.999955i	$0.496987\pi$
$492$	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	$-0.295640\pi$
$499$	1.27784e31	1.19762	0.598810	+	0.800891i	$0.295640\pi$
$500$	0	0
$501$	−1.31726e30	−0.117907
$502$	0	0
$503$	6.62625e30	0.566547	0.283273	−	0.959039i	$-0.408580\pi$
$503$	6.62625e30	0.566547	0.283273	+	0.959039i	$0.408580\pi$
$504$	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	$-0.451111\pi$
$523$	5.60340e30	0.305972	0.152986	+	0.988228i	$0.451111\pi$
$524$	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	$-0.219101\pi$
$547$	4.73888e31	1.54462	0.772310	+	0.635246i	$0.219101\pi$
$548$	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	$-0.752401\pi$
$563$	−6.08993e31	−1.42484	−0.712419	+	0.701754i	$0.752401\pi$
$564$	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	$-0.616772\pi$
$571$	−3.60619e31	−0.717354	−0.358677	+	0.933462i	$0.616772\pi$
$572$	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	$-0.641380\pi$
$587$	−5.93652e31	−0.859397	−0.429698	+	0.902973i	$0.641380\pi$
$588$	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	$-0.322161\pi$
$599$	9.24234e31	1.06017	0.530083	+	0.847946i	$0.322161\pi$
$600$	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	$-0.667127\pi$
$607$	−1.01802e32	−1.00250	−0.501252	+	0.865301i	$0.667127\pi$
$608$	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	$-0.273299\pi$
$619$	1.66234e32	1.30701	0.653503	+	0.756924i	$0.273299\pi$
$620$	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	$-0.530981\pi$
$631$	−3.08263e31	−0.194350	−0.0971749	+	0.995267i	$0.530981\pi$
$632$	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	$-0.796781\pi$
$643$	−3.16365e32	−1.60606	−0.803032	+	0.595936i	$0.796781\pi$
$644$	0	0
$645$	−3.82026e32	−1.87136
$646$	0	0
$647$	−2.07765e32	−0.982141	−0.491070	−	0.871120i	$-0.663394\pi$
$647$	−2.07765e32	−0.982141	−0.491070	+	0.871120i	$0.663394\pi$
$648$	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	$-0.543798\pi$
$659$	−7.16883e31	−0.274325	−0.137163	+	0.990549i	$0.543798\pi$
$660$	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	$-0.166260\pi$
$683$	6.83468e32	1.73333	0.866663	+	0.498894i	$0.166260\pi$
$684$	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	$-0.734537\pi$
$691$	−6.05837e32	−1.34387	−0.671936	+	0.740609i	$0.734537\pi$
$692$	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	$-0.436951\pi$
$719$	2.80152e32	0.393561	0.196780	+	0.980448i	$0.436951\pi$
$720$	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	$-0.666559\pi$
$727$	−8.07964e32	−0.999416	−0.499708	+	0.866194i	$0.666559\pi$
$728$	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	$-0.475465\pi$
$739$	1.50297e32	0.154007	0.0770034	+	0.997031i	$0.475465\pi$
$740$	0	0
$741$	1.52489e32	0.151471
$742$	0	0
$743$	1.35193e33	1.30192	0.650958	−	0.759114i	$-0.274367\pi$
$743$	1.35193e33	1.30192	0.650958	+	0.759114i	$0.274367\pi$
$744$	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	$-0.577514\pi$
$751$	−5.66394e32	−0.482236	−0.241118	+	0.970496i	$0.577514\pi$
$752$	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	$-0.633325\pi$
$787$	−1.63692e33	−0.813427	−0.406714	+	0.913556i	$0.633325\pi$
$788$	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	$-0.688767\pi$
$811$	−3.17750e33	−1.11775	−0.558876	+	0.829251i	$0.688767\pi$
$812$	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	$-0.384549\pi$
$823$	2.38843e33	0.709600	0.354800	+	0.934942i	$0.384549\pi$
$824$	0	0
$825$	−1.85409e33	−0.535687
$826$	0	0
$827$	−8.06573e32	−0.226637	−0.113318	−	0.993559i	$-0.536148\pi$
$827$	−8.06573e32	−0.226637	−0.113318	+	0.993559i	$0.536148\pi$
$828$	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	$-0.562589\pi$
$839$	−1.64111e33	−0.390729	−0.195364	+	0.980731i	$0.562589\pi$
$840$	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	$-0.447200\pi$
$859$	1.81863e33	0.330235	0.165118	+	0.986274i	$0.447200\pi$
$860$	0	0
$861$	−5.52013e33	−0.975917
$862$	0	0
$863$	−3.75334e33	−0.646092	−0.323046	−	0.946383i	$-0.604707\pi$
$863$	−3.75334e33	−0.646092	−0.323046	+	0.946383i	$0.604707\pi$
$864$	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	$-0.533306\pi$
$883$	−1.57928e33	−0.208886	−0.104443	+	0.994531i	$0.533306\pi$
$884$	0	0
$885$	3.39193e33	0.437118
$886$	0	0
$887$	−1.49477e34	−1.87695	−0.938475	−	0.345348i	$-0.887761\pi$
$887$	−1.49477e34	−1.87695	−0.938475	+	0.345348i	$0.887761\pi$
$888$	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	$-0.503307\pi$
$907$	−2.13809e32	−0.0207751	−0.0103875	+	0.999946i	$0.503307\pi$
$908$	0	0
$909$	−2.30444e34	−2.18314
$910$	0	0
$911$	2.47006e33	0.228164	0.114082	−	0.993471i	$-0.463607\pi$
$911$	2.47006e33	0.228164	0.114082	+	0.993471i	$0.463607\pi$
$912$	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	$-0.391208\pi$
$919$	8.02451e33	0.670333	0.335166	+	0.942159i	$0.391208\pi$
$920$	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	$-0.543361\pi$
$947$	−4.59154e33	−0.271602	−0.135801	+	0.990736i	$0.543361\pi$
$948$	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	$-0.133219\pi$
$967$	3.92857e34	1.82738	0.913692	+	0.406407i	$0.133219\pi$
$968$	0	0
$969$	−2.30784e34	−1.04829
$970$	0	0
$971$	2.25313e34	0.999461	0.499730	−	0.866181i	$-0.333432\pi$
$971$	2.25313e34	0.999461	0.499730	+	0.866181i	$0.333432\pi$
$972$	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	$-0.302718\pi$
$983$	3.01623e34	1.16171	0.580857	+	0.814006i	$0.302718\pi$
$984$	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	$-0.649533\pi$
$991$	−2.58031e34	−0.905368	−0.452684	+	0.891671i	$0.649533\pi$
$992$	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.c.1.1		1
4.3	odd	2		64.24.a.a.1.1		1
8.3	odd	2		16.24.a.a.1.1		1
8.5	even	2		2.24.a.a.1.1	✓	1
24.5	odd	2		18.24.a.d.1.1		1
40.13	odd	4		50.24.b.a.49.2		2
40.29	even	2		50.24.a.a.1.1		1
40.37	odd	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	8.5	even	2
16.24.a.a.1.1		1	8.3	odd	2
18.24.a.d.1.1		1	24.5	odd	2
50.24.a.a.1.1		1	40.29	even	2
50.24.b.a.49.1		2	40.37	odd	4
50.24.b.a.49.2		2	40.13	odd	4
64.24.a.a.1.1		1	4.3	odd	2
64.24.a.c.1.1		1	1.1	even	1	trivial

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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