LMFDB - Embedded newform 1078.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,4,Mod(1,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1078.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1078.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:	$63.6040589862$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1078.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} -18.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} -18.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} -36.0000 q^{10} -11.0000 q^{11} +8.00000 q^{12} -56.0000 q^{13} -36.0000 q^{15} +16.0000 q^{16} -36.0000 q^{17} -46.0000 q^{18} +28.0000 q^{19} -72.0000 q^{20} -22.0000 q^{22} +180.000 q^{23} +16.0000 q^{24} +199.000 q^{25} -112.000 q^{26} -100.000 q^{27} -54.0000 q^{29} -72.0000 q^{30} +334.000 q^{31} +32.0000 q^{32} -22.0000 q^{33} -72.0000 q^{34} -92.0000 q^{36} +386.000 q^{37} +56.0000 q^{38} -112.000 q^{39} -144.000 q^{40} +444.000 q^{41} -316.000 q^{43} -44.0000 q^{44} +414.000 q^{45} +360.000 q^{46} +402.000 q^{47} +32.0000 q^{48} +398.000 q^{50} -72.0000 q^{51} -224.000 q^{52} -486.000 q^{53} -200.000 q^{54} +198.000 q^{55} +56.0000 q^{57} -108.000 q^{58} +282.000 q^{59} -144.000 q^{60} -380.000 q^{61} +668.000 q^{62} +64.0000 q^{64} +1008.00 q^{65} -44.0000 q^{66} +176.000 q^{67} -144.000 q^{68} +360.000 q^{69} -324.000 q^{71} -184.000 q^{72} -800.000 q^{73} +772.000 q^{74} +398.000 q^{75} +112.000 q^{76} -224.000 q^{78} -1144.00 q^{79} -288.000 q^{80} +421.000 q^{81} +888.000 q^{82} -468.000 q^{83} +648.000 q^{85} -632.000 q^{86} -108.000 q^{87} -88.0000 q^{88} +870.000 q^{89} +828.000 q^{90} +720.000 q^{92} +668.000 q^{93} +804.000 q^{94} -504.000 q^{95} +64.0000 q^{96} +1330.00 q^{97} +253.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	2.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	2.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	4.00000	0.500000
$5$	−18.0000	−1.60997	−0.804984	−	0.593296i	$-0.797826\pi$
$5$	−18.0000	−1.60997	−0.804984	+	0.593296i	$0.797826\pi$
$6$	4.00000	0.272166
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	−36.0000	−1.13842
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	8.00000	0.192450
$13$	−56.0000	−1.19474	−0.597369	−	0.801966i	$-0.703787\pi$
$13$	−56.0000	−1.19474	−0.597369	+	0.801966i	$0.703787\pi$
$14$	0	0
$15$	−36.0000	−0.619677
$16$	16.0000	0.250000
$17$	−36.0000	−0.513605	−0.256802	−	0.966464i	$-0.582669\pi$
$17$	−36.0000	−0.513605	−0.256802	+	0.966464i	$0.582669\pi$
$18$	−46.0000	−0.602350
$19$	28.0000	0.338086	0.169043	−	0.985609i	$-0.445932\pi$
$19$	28.0000	0.338086	0.169043	+	0.985609i	$0.445932\pi$
$20$	−72.0000	−0.804984
$21$	0	0
$22$	−22.0000	−0.213201
$23$	180.000	1.63185	0.815926	−	0.578156i	$-0.196228\pi$
$23$	180.000	1.63185	0.815926	+	0.578156i	$0.196228\pi$
$24$	16.0000	0.136083
$25$	199.000	1.59200
$26$	−112.000	−0.844808
$27$	−100.000	−0.712778
$28$	0	0
$29$	−54.0000	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$29$	−54.0000	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$30$	−72.0000	−0.438178
$31$	334.000	1.93510	0.967551	−	0.252675i	$-0.0813104\pi$
$31$	334.000	1.93510	0.967551	+	0.252675i	$0.0813104\pi$
$32$	32.0000	0.176777
$33$	−22.0000	−0.116052
$34$	−72.0000	−0.363173
$35$	0	0
$36$	−92.0000	−0.425926
$37$	386.000	1.71508	0.857541	−	0.514416i	$-0.171991\pi$
$37$	386.000	1.71508	0.857541	+	0.514416i	$0.171991\pi$
$38$	56.0000	0.239063
$39$	−112.000	−0.459855
$40$	−144.000	−0.569210
$41$	444.000	1.69125	0.845624	−	0.533779i	$-0.179229\pi$
$41$	444.000	1.69125	0.845624	+	0.533779i	$0.179229\pi$
$42$	0	0
$43$	−316.000	−1.12069	−0.560344	−	0.828260i	$-0.689331\pi$
$43$	−316.000	−1.12069	−0.560344	+	0.828260i	$0.689331\pi$
$44$	−44.0000	−0.150756
$45$	414.000	1.37146
$46$	360.000	1.15389
$47$	402.000	1.24761	0.623806	−	0.781580i	$-0.285586\pi$
$47$	402.000	1.24761	0.623806	+	0.781580i	$0.285586\pi$
$48$	32.0000	0.0962250
$49$	0	0
$50$	398.000	1.12571
$51$	−72.0000	−0.197687
$52$	−224.000	−0.597369
$53$	−486.000	−1.25957	−0.629785	−	0.776769i	$-0.716857\pi$
$53$	−486.000	−1.25957	−0.629785	+	0.776769i	$0.716857\pi$
$54$	−200.000	−0.504010
$55$	198.000	0.485424
$56$	0	0
$57$	56.0000	0.130129
$58$	−108.000	−0.244502
$59$	282.000	0.622259	0.311129	−	0.950368i	$-0.399293\pi$
$59$	282.000	0.622259	0.311129	+	0.950368i	$0.399293\pi$
$60$	−144.000	−0.309839
$61$	−380.000	−0.797607	−0.398803	−	0.917036i	$-0.630574\pi$
$61$	−380.000	−0.797607	−0.398803	+	0.917036i	$0.630574\pi$
$62$	668.000	1.36832
$63$	0	0
$64$	64.0000	0.125000
$65$	1008.00	1.92349
$66$	−44.0000	−0.0820610
$67$	176.000	0.320923	0.160461	−	0.987042i	$-0.448702\pi$
$67$	176.000	0.320923	0.160461	+	0.987042i	$0.448702\pi$
$68$	−144.000	−0.256802
$69$	360.000	0.628100
$70$	0	0
$71$	−324.000	−0.541574	−0.270787	−	0.962639i	$-0.587284\pi$
$71$	−324.000	−0.541574	−0.270787	+	0.962639i	$0.587284\pi$
$72$	−184.000	−0.301175
$73$	−800.000	−1.28264	−0.641321	−	0.767272i	$-0.721613\pi$
$73$	−800.000	−1.28264	−0.641321	+	0.767272i	$0.721613\pi$
$74$	772.000	1.21275
$75$	398.000	0.612761
$76$	112.000	0.169043
$77$	0	0
$78$	−224.000	−0.325167
$79$	−1144.00	−1.62924	−0.814621	−	0.579994i	$-0.803055\pi$
$79$	−1144.00	−1.62924	−0.814621	+	0.579994i	$0.803055\pi$
$80$	−288.000	−0.402492
$81$	421.000	0.577503
$82$	888.000	1.19589
$83$	−468.000	−0.618912	−0.309456	−	0.950914i	$-0.600147\pi$
$83$	−468.000	−0.618912	−0.309456	+	0.950914i	$0.600147\pi$
$84$	0	0
$85$	648.000	0.826888
$86$	−632.000	−0.792445
$87$	−108.000	−0.133090
$88$	−88.0000	−0.106600
$89$	870.000	1.03618	0.518089	−	0.855327i	$-0.326644\pi$
$89$	870.000	1.03618	0.518089	+	0.855327i	$0.326644\pi$
$90$	828.000	0.969765
$91$	0	0
$92$	720.000	0.815926
$93$	668.000	0.744821
$94$	804.000	0.882194
$95$	−504.000	−0.544309
$96$	64.0000	0.0680414
$97$	1330.00	1.39218	0.696088	−	0.717957i	$-0.254922\pi$
$97$	1330.00	1.39218	0.696088	+	0.717957i	$0.254922\pi$
$98$	0	0
$99$	253.000	0.256843
$100$	796.000	0.796000
$101$	120.000	0.118222	0.0591111	−	0.998251i	$-0.481173\pi$
$101$	120.000	0.118222	0.0591111	+	0.998251i	$0.481173\pi$
$102$	−144.000	−0.139786
$103$	1210.00	1.15752	0.578761	−	0.815497i	$-0.303536\pi$
$103$	1210.00	1.15752	0.578761	+	0.815497i	$0.303536\pi$
$104$	−448.000	−0.422404
$105$	0	0
$106$	−972.000	−0.890651
$107$	1236.00	1.11672	0.558358	−	0.829600i	$-0.311432\pi$
$107$	1236.00	1.11672	0.558358	+	0.829600i	$0.311432\pi$
$108$	−400.000	−0.356389
$109$	−694.000	−0.609845	−0.304923	−	0.952377i	$-0.598631\pi$
$109$	−694.000	−0.609845	−0.304923	+	0.952377i	$0.598631\pi$
$110$	396.000	0.343247
$111$	772.000	0.660135
$112$	0	0
$113$	978.000	0.814181	0.407091	−	0.913388i	$-0.366543\pi$
$113$	978.000	0.814181	0.407091	+	0.913388i	$0.366543\pi$
$114$	112.000	0.0920154
$115$	−3240.00	−2.62723
$116$	−216.000	−0.172889
$117$	1288.00	1.01774
$118$	564.000	0.440003
$119$	0	0
$120$	−288.000	−0.219089
$121$	121.000	0.0909091
$122$	−760.000	−0.563993
$123$	888.000	0.650961
$124$	1336.00	0.967551
$125$	−1332.00	−0.953102
$126$	0	0
$127$	−1216.00	−0.849626	−0.424813	−	0.905281i	$-0.639660\pi$
$127$	−1216.00	−0.849626	−0.424813	+	0.905281i	$0.639660\pi$
$128$	128.000	0.0883883
$129$	−632.000	−0.431353
$130$	2016.00	1.36011
$131$	−1680.00	−1.12048	−0.560238	−	0.828332i	$-0.689290\pi$
$131$	−1680.00	−1.12048	−0.560238	+	0.828332i	$0.689290\pi$
$132$	−88.0000	−0.0580259
$133$	0	0
$134$	352.000	0.226927
$135$	1800.00	1.14755
$136$	−288.000	−0.181587
$137$	1062.00	0.662283	0.331142	−	0.943581i	$-0.392566\pi$
$137$	1062.00	0.662283	0.331142	+	0.943581i	$0.392566\pi$
$138$	720.000	0.444134
$139$	508.000	0.309986	0.154993	−	0.987916i	$-0.450465\pi$
$139$	508.000	0.309986	0.154993	+	0.987916i	$0.450465\pi$
$140$	0	0
$141$	804.000	0.480206
$142$	−648.000	−0.382950
$143$	616.000	0.360227
$144$	−368.000	−0.212963
$145$	972.000	0.556691
$146$	−1600.00	−0.906965
$147$	0	0
$148$	1544.00	0.857541
$149$	2598.00	1.42843	0.714216	−	0.699925i	$-0.246783\pi$
$149$	2598.00	1.42843	0.714216	+	0.699925i	$0.246783\pi$
$150$	796.000	0.433288
$151$	2648.00	1.42709	0.713547	−	0.700607i	$-0.247088\pi$
$151$	2648.00	1.42709	0.713547	+	0.700607i	$0.247088\pi$
$152$	224.000	0.119532
$153$	828.000	0.437515
$154$	0	0
$155$	−6012.00	−3.11545
$156$	−448.000	−0.229928
$157$	790.000	0.401585	0.200793	−	0.979634i	$-0.435648\pi$
$157$	790.000	0.401585	0.200793	+	0.979634i	$0.435648\pi$
$158$	−2288.00	−1.15205
$159$	−972.000	−0.484809
$160$	−576.000	−0.284605
$161$	0	0
$162$	842.000	0.408357
$163$	−160.000	−0.0768845	−0.0384422	−	0.999261i	$-0.512240\pi$
$163$	−160.000	−0.0768845	−0.0384422	+	0.999261i	$0.512240\pi$
$164$	1776.00	0.845624
$165$	396.000	0.186840
$166$	−936.000	−0.437637
$167$	−264.000	−0.122329	−0.0611645	−	0.998128i	$-0.519481\pi$
$167$	−264.000	−0.122329	−0.0611645	+	0.998128i	$0.519481\pi$
$168$	0	0
$169$	939.000	0.427401
$170$	1296.00	0.584698
$171$	−644.000	−0.287999
$172$	−1264.00	−0.560344
$173$	−1632.00	−0.717218	−0.358609	−	0.933488i	$-0.616749\pi$
$173$	−1632.00	−0.717218	−0.358609	+	0.933488i	$0.616749\pi$
$174$	−216.000	−0.0941087
$175$	0	0
$176$	−176.000	−0.0753778
$177$	564.000	0.239508
$178$	1740.00	0.732688
$179$	−708.000	−0.295634	−0.147817	−	0.989015i	$-0.547225\pi$
$179$	−708.000	−0.295634	−0.147817	+	0.989015i	$0.547225\pi$
$180$	1656.00	0.685728
$181$	−902.000	−0.370415	−0.185208	−	0.982699i	$-0.559296\pi$
$181$	−902.000	−0.370415	−0.185208	+	0.982699i	$0.559296\pi$
$182$	0	0
$183$	−760.000	−0.306999
$184$	1440.00	0.576947
$185$	−6948.00	−2.76123
$186$	1336.00	0.526668
$187$	396.000	0.154858
$188$	1608.00	0.623806
$189$	0	0
$190$	−1008.00	−0.384884
$191$	1824.00	0.690995	0.345497	−	0.938420i	$-0.387710\pi$
$191$	1824.00	0.690995	0.345497	+	0.938420i	$0.387710\pi$
$192$	128.000	0.0481125
$193$	2090.00	0.779490	0.389745	−	0.920923i	$-0.372563\pi$
$193$	2090.00	0.779490	0.389745	+	0.920923i	$0.372563\pi$
$194$	2660.00	0.984417
$195$	2016.00	0.740353
$196$	0	0
$197$	−1602.00	−0.579380	−0.289690	−	0.957121i	$-0.593552\pi$
$197$	−1602.00	−0.579380	−0.289690	+	0.957121i	$0.593552\pi$
$198$	506.000	0.181615
$199$	3274.00	1.16627	0.583135	−	0.812375i	$-0.301826\pi$
$199$	3274.00	1.16627	0.583135	+	0.812375i	$0.301826\pi$
$200$	1592.00	0.562857
$201$	352.000	0.123523
$202$	240.000	0.0835957
$203$	0	0
$204$	−288.000	−0.0988433
$205$	−7992.00	−2.72286
$206$	2420.00	0.818492
$207$	−4140.00	−1.39010
$208$	−896.000	−0.298685
$209$	−308.000	−0.101937
$210$	0	0
$211$	−4948.00	−1.61438	−0.807190	−	0.590291i	$-0.799013\pi$
$211$	−4948.00	−1.61438	−0.807190	+	0.590291i	$0.799013\pi$
$212$	−1944.00	−0.629785
$213$	−648.000	−0.208452
$214$	2472.00	0.789638
$215$	5688.00	1.80427
$216$	−800.000	−0.252005
$217$	0	0
$218$	−1388.00	−0.431226
$219$	−1600.00	−0.493689
$220$	792.000	0.242712
$221$	2016.00	0.613624
$222$	1544.00	0.466786
$223$	−2342.00	−0.703282	−0.351641	−	0.936135i	$-0.614376\pi$
$223$	−2342.00	−0.703282	−0.351641	+	0.936135i	$0.614376\pi$
$224$	0	0
$225$	−4577.00	−1.35615
$226$	1956.00	0.575713
$227$	−2064.00	−0.603491	−0.301746	−	0.953388i	$-0.597569\pi$
$227$	−2064.00	−0.603491	−0.301746	+	0.953388i	$0.597569\pi$
$228$	224.000	0.0650647
$229$	1666.00	0.480753	0.240376	−	0.970680i	$-0.422729\pi$
$229$	1666.00	0.480753	0.240376	+	0.970680i	$0.422729\pi$
$230$	−6480.00	−1.85773
$231$	0	0
$232$	−432.000	−0.122251
$233$	4158.00	1.16910	0.584549	−	0.811359i	$-0.301272\pi$
$233$	4158.00	1.16910	0.584549	+	0.811359i	$0.301272\pi$
$234$	2576.00	0.719651
$235$	−7236.00	−2.00862
$236$	1128.00	0.311129
$237$	−2288.00	−0.627095
$238$	0	0
$239$	72.0000	0.0194866	0.00974329	−	0.999953i	$-0.496899\pi$
$239$	72.0000	0.0194866	0.00974329	+	0.999953i	$0.496899\pi$
$240$	−576.000	−0.154919
$241$	−6860.00	−1.83357	−0.916787	−	0.399376i	$-0.869227\pi$
$241$	−6860.00	−1.83357	−0.916787	+	0.399376i	$0.869227\pi$
$242$	242.000	0.0642824
$243$	3542.00	0.935059
$244$	−1520.00	−0.398803
$245$	0	0
$246$	1776.00	0.460299
$247$	−1568.00	−0.403925
$248$	2672.00	0.684162
$249$	−936.000	−0.238219
$250$	−2664.00	−0.673945
$251$	150.000	0.0377208	0.0188604	−	0.999822i	$-0.493996\pi$
$251$	150.000	0.0377208	0.0188604	+	0.999822i	$0.493996\pi$
$252$	0	0
$253$	−1980.00	−0.492022
$254$	−2432.00	−0.600777
$255$	1296.00	0.318269
$256$	256.000	0.0625000
$257$	2430.00	0.589802	0.294901	−	0.955528i	$-0.404713\pi$
$257$	2430.00	0.589802	0.294901	+	0.955528i	$0.404713\pi$
$258$	−1264.00	−0.305012
$259$	0	0
$260$	4032.00	0.961746
$261$	1242.00	0.294551
$262$	−3360.00	−0.792296
$263$	3048.00	0.714630	0.357315	−	0.933984i	$-0.383692\pi$
$263$	3048.00	0.714630	0.357315	+	0.933984i	$0.383692\pi$
$264$	−176.000	−0.0410305
$265$	8748.00	2.02787
$266$	0	0
$267$	1740.00	0.398825
$268$	704.000	0.160461
$269$	3834.00	0.869008	0.434504	−	0.900670i	$-0.356924\pi$
$269$	3834.00	0.869008	0.434504	+	0.900670i	$0.356924\pi$
$270$	3600.00	0.811441
$271$	3508.00	0.786331	0.393166	−	0.919468i	$-0.371380\pi$
$271$	3508.00	0.786331	0.393166	+	0.919468i	$0.371380\pi$
$272$	−576.000	−0.128401
$273$	0	0
$274$	2124.00	0.468305
$275$	−2189.00	−0.480006
$276$	1440.00	0.314050
$277$	8294.00	1.79905	0.899527	−	0.436864i	$-0.143911\pi$
$277$	8294.00	1.79905	0.899527	+	0.436864i	$0.143911\pi$
$278$	1016.00	0.219193
$279$	−7682.00	−1.64842
$280$	0	0
$281$	8022.00	1.70303	0.851517	−	0.524327i	$-0.175683\pi$
$281$	8022.00	1.70303	0.851517	+	0.524327i	$0.175683\pi$
$282$	1608.00	0.339557
$283$	−392.000	−0.0823392	−0.0411696	−	0.999152i	$-0.513108\pi$
$283$	−392.000	−0.0823392	−0.0411696	+	0.999152i	$0.513108\pi$
$284$	−1296.00	−0.270787
$285$	−1008.00	−0.209504
$286$	1232.00	0.254719
$287$	0	0
$288$	−736.000	−0.150588
$289$	−3617.00	−0.736210
$290$	1944.00	0.393640
$291$	2660.00	0.535849
$292$	−3200.00	−0.641321
$293$	2748.00	0.547918	0.273959	−	0.961741i	$-0.411667\pi$
$293$	2748.00	0.547918	0.273959	+	0.961741i	$0.411667\pi$
$294$	0	0
$295$	−5076.00	−1.00182
$296$	3088.00	0.606373
$297$	1100.00	0.214911
$298$	5196.00	1.01005
$299$	−10080.0	−1.94964
$300$	1592.00	0.306381
$301$	0	0
$302$	5296.00	1.00911
$303$	240.000	0.0455038
$304$	448.000	0.0845216
$305$	6840.00	1.28412
$306$	1656.00	0.309370
$307$	3064.00	0.569615	0.284807	−	0.958585i	$-0.408070\pi$
$307$	3064.00	0.569615	0.284807	+	0.958585i	$0.408070\pi$
$308$	0	0
$309$	2420.00	0.445531
$310$	−12024.0	−2.20296
$311$	−4062.00	−0.740627	−0.370313	−	0.928907i	$-0.620750\pi$
$311$	−4062.00	−0.740627	−0.370313	+	0.928907i	$0.620750\pi$
$312$	−896.000	−0.162583
$313$	4870.00	0.879453	0.439726	−	0.898132i	$-0.355075\pi$
$313$	4870.00	0.879453	0.439726	+	0.898132i	$0.355075\pi$
$314$	1580.00	0.283964
$315$	0	0
$316$	−4576.00	−0.814621
$317$	4806.00	0.851520	0.425760	−	0.904836i	$-0.360007\pi$
$317$	4806.00	0.851520	0.425760	+	0.904836i	$0.360007\pi$
$318$	−1944.00	−0.342812
$319$	594.000	0.104256
$320$	−1152.00	−0.201246
$321$	2472.00	0.429824
$322$	0	0
$323$	−1008.00	−0.173643
$324$	1684.00	0.288752
$325$	−11144.0	−1.90202
$326$	−320.000	−0.0543655
$327$	−1388.00	−0.234730
$328$	3552.00	0.597946
$329$	0	0
$330$	792.000	0.132116
$331$	6620.00	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	6620.00	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−1872.00	−0.309456
$333$	−8878.00	−1.46100
$334$	−528.000	−0.0864996
$335$	−3168.00	−0.516676
$336$	0	0
$337$	1094.00	0.176837	0.0884184	−	0.996083i	$-0.471819\pi$
$337$	1094.00	0.176837	0.0884184	+	0.996083i	$0.471819\pi$
$338$	1878.00	0.302218
$339$	1956.00	0.313379
$340$	2592.00	0.413444
$341$	−3674.00	−0.583455
$342$	−1288.00	−0.203646
$343$	0	0
$344$	−2528.00	−0.396223
$345$	−6480.00	−1.01122
$346$	−3264.00	−0.507150
$347$	3468.00	0.536519	0.268259	−	0.963347i	$-0.413552\pi$
$347$	3468.00	0.536519	0.268259	+	0.963347i	$0.413552\pi$
$348$	−432.000	−0.0665449
$349$	8188.00	1.25586	0.627928	−	0.778272i	$-0.283903\pi$
$349$	8188.00	1.25586	0.627928	+	0.778272i	$0.283903\pi$
$350$	0	0
$351$	5600.00	0.851584
$352$	−352.000	−0.0533002
$353$	5070.00	0.764444	0.382222	−	0.924070i	$-0.375159\pi$
$353$	5070.00	0.764444	0.382222	+	0.924070i	$0.375159\pi$
$354$	1128.00	0.169357
$355$	5832.00	0.871917
$356$	3480.00	0.518089
$357$	0	0
$358$	−1416.00	−0.209044
$359$	1656.00	0.243455	0.121727	−	0.992564i	$-0.461157\pi$
$359$	1656.00	0.243455	0.121727	+	0.992564i	$0.461157\pi$
$360$	3312.00	0.484883
$361$	−6075.00	−0.885698
$362$	−1804.00	−0.261923
$363$	242.000	0.0349909
$364$	0	0
$365$	14400.0	2.06501
$366$	−1520.00	−0.217081
$367$	−10166.0	−1.44594	−0.722971	−	0.690878i	$-0.757224\pi$
$367$	−10166.0	−1.44594	−0.722971	+	0.690878i	$0.757224\pi$
$368$	2880.00	0.407963
$369$	−10212.0	−1.44069
$370$	−13896.0	−1.95248
$371$	0	0
$372$	2672.00	0.372411
$373$	−2722.00	−0.377855	−0.188927	−	0.981991i	$-0.560501\pi$
$373$	−2722.00	−0.377855	−0.188927	+	0.981991i	$0.560501\pi$
$374$	792.000	0.109501
$375$	−2664.00	−0.366849
$376$	3216.00	0.441097
$377$	3024.00	0.413114
$378$	0	0
$379$	−5872.00	−0.795843	−0.397921	−	0.917420i	$-0.630268\pi$
$379$	−5872.00	−0.795843	−0.397921	+	0.917420i	$0.630268\pi$
$380$	−2016.00	−0.272154
$381$	−2432.00	−0.327021
$382$	3648.00	0.488607
$383$	−12330.0	−1.64500	−0.822498	−	0.568768i	$-0.807420\pi$
$383$	−12330.0	−1.64500	−0.822498	+	0.568768i	$0.807420\pi$
$384$	256.000	0.0340207
$385$	0	0
$386$	4180.00	0.551182
$387$	7268.00	0.954659
$388$	5320.00	0.696088
$389$	−14586.0	−1.90113	−0.950565	−	0.310526i	$-0.899495\pi$
$389$	−14586.0	−1.90113	−0.950565	+	0.310526i	$0.899495\pi$
$390$	4032.00	0.523508
$391$	−6480.00	−0.838127
$392$	0	0
$393$	−3360.00	−0.431271
$394$	−3204.00	−0.409683
$395$	20592.0	2.62303
$396$	1012.00	0.128421
$397$	−1874.00	−0.236910	−0.118455	−	0.992959i	$-0.537794\pi$
$397$	−1874.00	−0.236910	−0.118455	+	0.992959i	$0.537794\pi$
$398$	6548.00	0.824677
$399$	0	0
$400$	3184.00	0.398000
$401$	13338.0	1.66102	0.830509	−	0.557006i	$-0.188050\pi$
$401$	13338.0	1.66102	0.830509	+	0.557006i	$0.188050\pi$
$402$	704.000	0.0873441
$403$	−18704.0	−2.31194
$404$	480.000	0.0591111
$405$	−7578.00	−0.929763
$406$	0	0
$407$	−4246.00	−0.517116
$408$	−576.000	−0.0698928
$409$	8200.00	0.991354	0.495677	−	0.868507i	$-0.334920\pi$
$409$	8200.00	0.991354	0.495677	+	0.868507i	$0.334920\pi$
$410$	−15984.0	−1.92535
$411$	2124.00	0.254913
$412$	4840.00	0.578761
$413$	0	0
$414$	−8280.00	−0.982946
$415$	8424.00	0.996429
$416$	−1792.00	−0.211202
$417$	1016.00	0.119314
$418$	−616.000	−0.0720803
$419$	7362.00	0.858370	0.429185	−	0.903216i	$-0.358801\pi$
$419$	7362.00	0.858370	0.429185	+	0.903216i	$0.358801\pi$
$420$	0	0
$421$	−11710.0	−1.35561	−0.677803	−	0.735243i	$-0.737068\pi$
$421$	−11710.0	−1.35561	−0.677803	+	0.735243i	$0.737068\pi$
$422$	−9896.00	−1.14154
$423$	−9246.00	−1.06278
$424$	−3888.00	−0.445325
$425$	−7164.00	−0.817659
$426$	−1296.00	−0.147398
$427$	0	0
$428$	4944.00	0.558358
$429$	1232.00	0.138652
$430$	11376.0	1.27581
$431$	−936.000	−0.104607	−0.0523034	−	0.998631i	$-0.516656\pi$
$431$	−936.000	−0.104607	−0.0523034	+	0.998631i	$0.516656\pi$
$432$	−1600.00	−0.178195
$433$	−9038.00	−1.00309	−0.501546	−	0.865131i	$-0.667235\pi$
$433$	−9038.00	−1.00309	−0.501546	+	0.865131i	$0.667235\pi$
$434$	0	0
$435$	1944.00	0.214270
$436$	−2776.00	−0.304923
$437$	5040.00	0.551707
$438$	−3200.00	−0.349091
$439$	−1964.00	−0.213523	−0.106762	−	0.994285i	$-0.534048\pi$
$439$	−1964.00	−0.213523	−0.106762	+	0.994285i	$0.534048\pi$
$440$	1584.00	0.171623
$441$	0	0
$442$	4032.00	0.433897
$443$	10068.0	1.07979	0.539893	−	0.841734i	$-0.318465\pi$
$443$	10068.0	1.07979	0.539893	+	0.841734i	$0.318465\pi$
$444$	3088.00	0.330068
$445$	−15660.0	−1.66821
$446$	−4684.00	−0.497296
$447$	5196.00	0.549804
$448$	0	0
$449$	3270.00	0.343699	0.171849	−	0.985123i	$-0.445026\pi$
$449$	3270.00	0.343699	0.171849	+	0.985123i	$0.445026\pi$
$450$	−9154.00	−0.958942
$451$	−4884.00	−0.509930
$452$	3912.00	0.407091
$453$	5296.00	0.549289
$454$	−4128.00	−0.426733
$455$	0	0
$456$	448.000	0.0460077
$457$	−15526.0	−1.58922	−0.794612	−	0.607117i	$-0.792326\pi$
$457$	−15526.0	−1.58922	−0.794612	+	0.607117i	$0.792326\pi$
$458$	3332.00	0.339944
$459$	3600.00	0.366086
$460$	−12960.0	−1.31362
$461$	−10548.0	−1.06566	−0.532830	−	0.846222i	$-0.678872\pi$
$461$	−10548.0	−1.06566	−0.532830	+	0.846222i	$0.678872\pi$
$462$	0	0
$463$	−3796.00	−0.381026	−0.190513	−	0.981685i	$-0.561015\pi$
$463$	−3796.00	−0.381026	−0.190513	+	0.981685i	$0.561015\pi$
$464$	−864.000	−0.0864444
$465$	−12024.0	−1.19914
$466$	8316.00	0.826677
$467$	−7122.00	−0.705711	−0.352855	−	0.935678i	$-0.614789\pi$
$467$	−7122.00	−0.705711	−0.352855	+	0.935678i	$0.614789\pi$
$468$	5152.00	0.508870
$469$	0	0
$470$	−14472.0	−1.42031
$471$	1580.00	0.154570
$472$	2256.00	0.220002
$473$	3476.00	0.337900
$474$	−4576.00	−0.443423
$475$	5572.00	0.538233
$476$	0	0
$477$	11178.0	1.07297
$478$	144.000	0.0137791
$479$	−2292.00	−0.218631	−0.109315	−	0.994007i	$-0.534866\pi$
$479$	−2292.00	−0.218631	−0.109315	+	0.994007i	$0.534866\pi$
$480$	−1152.00	−0.109545
$481$	−21616.0	−2.04907
$482$	−13720.0	−1.29653
$483$	0	0
$484$	484.000	0.0454545
$485$	−23940.0	−2.24136
$486$	7084.00	0.661187
$487$	5132.00	0.477522	0.238761	−	0.971078i	$-0.423259\pi$
$487$	5132.00	0.477522	0.238761	+	0.971078i	$0.423259\pi$
$488$	−3040.00	−0.281997
$489$	−320.000	−0.0295928
$490$	0	0
$491$	4188.00	0.384932	0.192466	−	0.981304i	$-0.438351\pi$
$491$	4188.00	0.384932	0.192466	+	0.981304i	$0.438351\pi$
$492$	3552.00	0.325481
$493$	1944.00	0.177593
$494$	−3136.00	−0.285618
$495$	−4554.00	−0.413509
$496$	5344.00	0.483776
$497$	0	0
$498$	−1872.00	−0.168446
$499$	3848.00	0.345211	0.172605	−	0.984991i	$-0.444781\pi$
$499$	3848.00	0.345211	0.172605	+	0.984991i	$0.444781\pi$
$500$	−5328.00	−0.476551
$501$	−528.000	−0.0470844
$502$	300.000	0.0266726
$503$	1068.00	0.0946715	0.0473358	−	0.998879i	$-0.484927\pi$
$503$	1068.00	0.0946715	0.0473358	+	0.998879i	$0.484927\pi$
$504$	0	0
$505$	−2160.00	−0.190334
$506$	−3960.00	−0.347912
$507$	1878.00	0.164507
$508$	−4864.00	−0.424813
$509$	6162.00	0.536593	0.268297	−	0.963336i	$-0.413539\pi$
$509$	6162.00	0.536593	0.268297	+	0.963336i	$0.413539\pi$
$510$	2592.00	0.225050
$511$	0	0
$512$	512.000	0.0441942
$513$	−2800.00	−0.240981
$514$	4860.00	0.417053
$515$	−21780.0	−1.86358
$516$	−2528.00	−0.215676
$517$	−4422.00	−0.376169
$518$	0	0
$519$	−3264.00	−0.276057
$520$	8064.00	0.680057
$521$	20946.0	1.76135	0.880673	−	0.473725i	$-0.157091\pi$
$521$	20946.0	1.76135	0.880673	+	0.473725i	$0.157091\pi$
$522$	2484.00	0.208279
$523$	4696.00	0.392623	0.196311	−	0.980542i	$-0.437104\pi$
$523$	4696.00	0.392623	0.196311	+	0.980542i	$0.437104\pi$
$524$	−6720.00	−0.560238
$525$	0	0
$526$	6096.00	0.505320
$527$	−12024.0	−0.993878
$528$	−352.000	−0.0290129
$529$	20233.0	1.66294
$530$	17496.0	1.43392
$531$	−6486.00	−0.530072
$532$	0	0
$533$	−24864.0	−2.02060
$534$	3480.00	0.282012
$535$	−22248.0	−1.79788
$536$	1408.00	0.113463
$537$	−1416.00	−0.113789
$538$	7668.00	0.614481
$539$	0	0
$540$	7200.00	0.573775
$541$	19358.0	1.53838	0.769192	−	0.639018i	$-0.220659\pi$
$541$	19358.0	1.53838	0.769192	+	0.639018i	$0.220659\pi$
$542$	7016.00	0.556020
$543$	−1804.00	−0.142573
$544$	−1152.00	−0.0907934
$545$	12492.0	0.981832
$546$	0	0
$547$	18020.0	1.40855	0.704277	−	0.709925i	$-0.251271\pi$
$547$	18020.0	1.40855	0.704277	+	0.709925i	$0.251271\pi$
$548$	4248.00	0.331142
$549$	8740.00	0.679443
$550$	−4378.00	−0.339416
$551$	−1512.00	−0.116903
$552$	2880.00	0.222067
$553$	0	0
$554$	16588.0	1.27212
$555$	−13896.0	−1.06280
$556$	2032.00	0.154993
$557$	14622.0	1.11231	0.556153	−	0.831080i	$-0.312277\pi$
$557$	14622.0	1.11231	0.556153	+	0.831080i	$0.312277\pi$
$558$	−15364.0	−1.16561
$559$	17696.0	1.33893
$560$	0	0
$561$	792.000	0.0596048
$562$	16044.0	1.20423
$563$	2244.00	0.167981	0.0839905	−	0.996467i	$-0.473233\pi$
$563$	2244.00	0.167981	0.0839905	+	0.996467i	$0.473233\pi$
$564$	3216.00	0.240103
$565$	−17604.0	−1.31081
$566$	−784.000	−0.0582226
$567$	0	0
$568$	−2592.00	−0.191475
$569$	−3258.00	−0.240039	−0.120020	−	0.992772i	$-0.538296\pi$
$569$	−3258.00	−0.240039	−0.120020	+	0.992772i	$0.538296\pi$
$570$	−2016.00	−0.148142
$571$	−6604.00	−0.484008	−0.242004	−	0.970275i	$-0.577805\pi$
$571$	−6604.00	−0.484008	−0.242004	+	0.970275i	$0.577805\pi$
$572$	2464.00	0.180114
$573$	3648.00	0.265964
$574$	0	0
$575$	35820.0	2.59791
$576$	−1472.00	−0.106481
$577$	16594.0	1.19726	0.598628	−	0.801027i	$-0.295713\pi$
$577$	16594.0	1.19726	0.598628	+	0.801027i	$0.295713\pi$
$578$	−7234.00	−0.520579
$579$	4180.00	0.300026
$580$	3888.00	0.278346
$581$	0	0
$582$	5320.00	0.378902
$583$	5346.00	0.379775
$584$	−6400.00	−0.453483
$585$	−23184.0	−1.63853
$586$	5496.00	0.387436
$587$	19062.0	1.34033	0.670164	−	0.742213i	$-0.266224\pi$
$587$	19062.0	1.34033	0.670164	+	0.742213i	$0.266224\pi$
$588$	0	0
$589$	9352.00	0.654232
$590$	−10152.0	−0.708392
$591$	−3204.00	−0.223003
$592$	6176.00	0.428770
$593$	4776.00	0.330737	0.165368	−	0.986232i	$-0.447119\pi$
$593$	4776.00	0.330737	0.165368	+	0.986232i	$0.447119\pi$
$594$	2200.00	0.151965
$595$	0	0
$596$	10392.0	0.714216
$597$	6548.00	0.448897
$598$	−20160.0	−1.37860
$599$	7956.00	0.542693	0.271347	−	0.962482i	$-0.412531\pi$
$599$	7956.00	0.542693	0.271347	+	0.962482i	$0.412531\pi$
$600$	3184.00	0.216644
$601$	−14348.0	−0.973822	−0.486911	−	0.873452i	$-0.661876\pi$
$601$	−14348.0	−0.973822	−0.486911	+	0.873452i	$0.661876\pi$
$602$	0	0
$603$	−4048.00	−0.273379
$604$	10592.0	0.713547
$605$	−2178.00	−0.146361
$606$	480.000	0.0321760
$607$	−24488.0	−1.63746	−0.818729	−	0.574180i	$-0.805321\pi$
$607$	−24488.0	−1.63746	−0.818729	+	0.574180i	$0.805321\pi$
$608$	896.000	0.0597658
$609$	0	0
$610$	13680.0	0.908011
$611$	−22512.0	−1.49057
$612$	3312.00	0.218758
$613$	−19654.0	−1.29497	−0.647486	−	0.762078i	$-0.724179\pi$
$613$	−19654.0	−1.29497	−0.647486	+	0.762078i	$0.724179\pi$
$614$	6128.00	0.402778
$615$	−15984.0	−1.04803
$616$	0	0
$617$	2694.00	0.175780	0.0878901	−	0.996130i	$-0.471988\pi$
$617$	2694.00	0.175780	0.0878901	+	0.996130i	$0.471988\pi$
$618$	4840.00	0.315038
$619$	−10178.0	−0.660886	−0.330443	−	0.943826i	$-0.607198\pi$
$619$	−10178.0	−0.660886	−0.330443	+	0.943826i	$0.607198\pi$
$620$	−24048.0	−1.55773
$621$	−18000.0	−1.16315
$622$	−8124.00	−0.523702
$623$	0	0
$624$	−1792.00	−0.114964
$625$	−899.000	−0.0575360
$626$	9740.00	0.621867
$627$	−616.000	−0.0392355
$628$	3160.00	0.200793
$629$	−13896.0	−0.880874
$630$	0	0
$631$	−7648.00	−0.482507	−0.241254	−	0.970462i	$-0.577559\pi$
$631$	−7648.00	−0.482507	−0.241254	+	0.970462i	$0.577559\pi$
$632$	−9152.00	−0.576024
$633$	−9896.00	−0.621375
$634$	9612.00	0.602116
$635$	21888.0	1.36787
$636$	−3888.00	−0.242404
$637$	0	0
$638$	1188.00	0.0737200
$639$	7452.00	0.461340
$640$	−2304.00	−0.142302
$641$	270.000	0.0166371	0.00831853	−	0.999965i	$-0.497352\pi$
$641$	270.000	0.0166371	0.00831853	+	0.999965i	$0.497352\pi$
$642$	4944.00	0.303932
$643$	−16250.0	−0.996637	−0.498318	−	0.866994i	$-0.666049\pi$
$643$	−16250.0	−0.996637	−0.498318	+	0.866994i	$0.666049\pi$
$644$	0	0
$645$	11376.0	0.694464
$646$	−2016.00	−0.122784
$647$	−10242.0	−0.622341	−0.311170	−	0.950354i	$-0.600721\pi$
$647$	−10242.0	−0.622341	−0.311170	+	0.950354i	$0.600721\pi$
$648$	3368.00	0.204178
$649$	−3102.00	−0.187618
$650$	−22288.0	−1.34493
$651$	0	0
$652$	−640.000	−0.0384422
$653$	−17322.0	−1.03807	−0.519037	−	0.854752i	$-0.673709\pi$
$653$	−17322.0	−1.03807	−0.519037	+	0.854752i	$0.673709\pi$
$654$	−2776.00	−0.165979
$655$	30240.0	1.80393
$656$	7104.00	0.422812
$657$	18400.0	1.09262
$658$	0	0
$659$	11676.0	0.690186	0.345093	−	0.938569i	$-0.387847\pi$
$659$	11676.0	0.690186	0.345093	+	0.938569i	$0.387847\pi$
$660$	1584.00	0.0934199
$661$	20710.0	1.21865	0.609323	−	0.792922i	$-0.291441\pi$
$661$	20710.0	1.21865	0.609323	+	0.792922i	$0.291441\pi$
$662$	13240.0	0.777322
$663$	4032.00	0.236184
$664$	−3744.00	−0.218818
$665$	0	0
$666$	−17756.0	−1.03308
$667$	−9720.00	−0.564258
$668$	−1056.00	−0.0611645
$669$	−4684.00	−0.270693
$670$	−6336.00	−0.365345
$671$	4180.00	0.240487
$672$	0	0
$673$	−10354.0	−0.593042	−0.296521	−	0.955026i	$-0.595827\pi$
$673$	−10354.0	−0.593042	−0.296521	+	0.955026i	$0.595827\pi$
$674$	2188.00	0.125042
$675$	−19900.0	−1.13474
$676$	3756.00	0.213701
$677$	10920.0	0.619926	0.309963	−	0.950749i	$-0.399683\pi$
$677$	10920.0	0.619926	0.309963	+	0.950749i	$0.399683\pi$
$678$	3912.00	0.221592
$679$	0	0
$680$	5184.00	0.292349
$681$	−4128.00	−0.232284
$682$	−7348.00	−0.412565
$683$	27804.0	1.55767	0.778836	−	0.627227i	$-0.215810\pi$
$683$	27804.0	1.55767	0.778836	+	0.627227i	$0.215810\pi$
$684$	−2576.00	−0.144000
$685$	−19116.0	−1.06626
$686$	0	0
$687$	3332.00	0.185042
$688$	−5056.00	−0.280172
$689$	27216.0	1.50486
$690$	−12960.0	−0.715042
$691$	25834.0	1.42225	0.711123	−	0.703068i	$-0.248187\pi$
$691$	25834.0	1.42225	0.711123	+	0.703068i	$0.248187\pi$
$692$	−6528.00	−0.358609
$693$	0	0
$694$	6936.00	0.379376
$695$	−9144.00	−0.499067
$696$	−864.000	−0.0470544
$697$	−15984.0	−0.868633
$698$	16376.0	0.888024
$699$	8316.00	0.449986
$700$	0	0
$701$	−10590.0	−0.570583	−0.285292	−	0.958441i	$-0.592090\pi$
$701$	−10590.0	−0.570583	−0.285292	+	0.958441i	$0.592090\pi$
$702$	11200.0	0.602161
$703$	10808.0	0.579846
$704$	−704.000	−0.0376889
$705$	−14472.0	−0.773116
$706$	10140.0	0.540544
$707$	0	0
$708$	2256.00	0.119754
$709$	−6802.00	−0.360302	−0.180151	−	0.983639i	$-0.557659\pi$
$709$	−6802.00	−0.360302	−0.180151	+	0.983639i	$0.557659\pi$
$710$	11664.0	0.616538
$711$	26312.0	1.38787
$712$	6960.00	0.366344
$713$	60120.0	3.15780
$714$	0	0
$715$	−11088.0	−0.579955
$716$	−2832.00	−0.147817
$717$	144.000	0.00750039
$718$	3312.00	0.172149
$719$	−23010.0	−1.19350	−0.596751	−	0.802426i	$-0.703542\pi$
$719$	−23010.0	−1.19350	−0.596751	+	0.802426i	$0.703542\pi$
$720$	6624.00	0.342864
$721$	0	0
$722$	−12150.0	−0.626283
$723$	−13720.0	−0.705743
$724$	−3608.00	−0.185208
$725$	−10746.0	−0.550478
$726$	484.000	0.0247423
$727$	−4682.00	−0.238853	−0.119426	−	0.992843i	$-0.538106\pi$
$727$	−4682.00	−0.238853	−0.119426	+	0.992843i	$0.538106\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	28800.0	1.46019
$731$	11376.0	0.575590
$732$	−3040.00	−0.153499
$733$	17860.0	0.899965	0.449982	−	0.893037i	$-0.351430\pi$
$733$	17860.0	0.899965	0.449982	+	0.893037i	$0.351430\pi$
$734$	−20332.0	−1.02244
$735$	0	0
$736$	5760.00	0.288473
$737$	−1936.00	−0.0967618
$738$	−20424.0	−1.01872
$739$	6860.00	0.341474	0.170737	−	0.985317i	$-0.445385\pi$
$739$	6860.00	0.341474	0.170737	+	0.985317i	$0.445385\pi$
$740$	−27792.0	−1.38061
$741$	−3136.00	−0.155471
$742$	0	0
$743$	−22752.0	−1.12341	−0.561703	−	0.827339i	$-0.689853\pi$
$743$	−22752.0	−1.12341	−0.561703	+	0.827339i	$0.689853\pi$
$744$	5344.00	0.263334
$745$	−46764.0	−2.29973
$746$	−5444.00	−0.267184
$747$	10764.0	0.527221
$748$	1584.00	0.0774288
$749$	0	0
$750$	−5328.00	−0.259401
$751$	7364.00	0.357811	0.178906	−	0.983866i	$-0.442744\pi$
$751$	7364.00	0.357811	0.178906	+	0.983866i	$0.442744\pi$
$752$	6432.00	0.311903
$753$	300.000	0.0145187
$754$	6048.00	0.292116
$755$	−47664.0	−2.29758
$756$	0	0
$757$	−34378.0	−1.65058	−0.825290	−	0.564709i	$-0.808989\pi$
$757$	−34378.0	−1.65058	−0.825290	+	0.564709i	$0.808989\pi$
$758$	−11744.0	−0.562746
$759$	−3960.00	−0.189379
$760$	−4032.00	−0.192442
$761$	−27456.0	−1.30786	−0.653929	−	0.756556i	$-0.726880\pi$
$761$	−27456.0	−1.30786	−0.653929	+	0.756556i	$0.726880\pi$
$762$	−4864.00	−0.231239
$763$	0	0
$764$	7296.00	0.345497
$765$	−14904.0	−0.704386
$766$	−24660.0	−1.16319
$767$	−15792.0	−0.743437
$768$	512.000	0.0240563
$769$	−7952.00	−0.372895	−0.186448	−	0.982465i	$-0.559697\pi$
$769$	−7952.00	−0.372895	−0.186448	+	0.982465i	$0.559697\pi$
$770$	0	0
$771$	4860.00	0.227015
$772$	8360.00	0.389745
$773$	4986.00	0.231997	0.115999	−	0.993249i	$-0.462993\pi$
$773$	4986.00	0.231997	0.115999	+	0.993249i	$0.462993\pi$
$774$	14536.0	0.675046
$775$	66466.0	3.08068
$776$	10640.0	0.492208
$777$	0	0
$778$	−29172.0	−1.34430
$779$	12432.0	0.571788
$780$	8064.00	0.370176
$781$	3564.00	0.163291
$782$	−12960.0	−0.592645
$783$	5400.00	0.246463
$784$	0	0
$785$	−14220.0	−0.646540
$786$	−6720.00	−0.304955
$787$	42748.0	1.93622	0.968108	−	0.250534i	$-0.0806062\pi$
$787$	42748.0	1.93622	0.968108	+	0.250534i	$0.0806062\pi$
$788$	−6408.00	−0.289690
$789$	6096.00	0.275061
$790$	41184.0	1.85476
$791$	0	0
$792$	2024.00	0.0908077
$793$	21280.0	0.952932
$794$	−3748.00	−0.167521
$795$	17496.0	0.780527
$796$	13096.0	0.583135
$797$	−35610.0	−1.58265	−0.791324	−	0.611397i	$-0.790608\pi$
$797$	−35610.0	−1.58265	−0.791324	+	0.611397i	$0.790608\pi$
$798$	0	0
$799$	−14472.0	−0.640779
$800$	6368.00	0.281428
$801$	−20010.0	−0.882670
$802$	26676.0	1.17452
$803$	8800.00	0.386731
$804$	1408.00	0.0617616
$805$	0	0
$806$	−37408.0	−1.63479
$807$	7668.00	0.334481
$808$	960.000	0.0417979
$809$	−17046.0	−0.740798	−0.370399	−	0.928873i	$-0.620779\pi$
$809$	−17046.0	−0.740798	−0.370399	+	0.928873i	$0.620779\pi$
$810$	−15156.0	−0.657441
$811$	2176.00	0.0942166	0.0471083	−	0.998890i	$-0.484999\pi$
$811$	2176.00	0.0942166	0.0471083	+	0.998890i	$0.484999\pi$
$812$	0	0
$813$	7016.00	0.302659
$814$	−8492.00	−0.365657
$815$	2880.00	0.123782
$816$	−1152.00	−0.0494217
$817$	−8848.00	−0.378889
$818$	16400.0	0.700993
$819$	0	0
$820$	−31968.0	−1.36143
$821$	2094.00	0.0890147	0.0445074	−	0.999009i	$-0.485828\pi$
$821$	2094.00	0.0890147	0.0445074	+	0.999009i	$0.485828\pi$
$822$	4248.00	0.180251
$823$	7328.00	0.310374	0.155187	−	0.987885i	$-0.450402\pi$
$823$	7328.00	0.310374	0.155187	+	0.987885i	$0.450402\pi$
$824$	9680.00	0.409246
$825$	−4378.00	−0.184754
$826$	0	0
$827$	−12492.0	−0.525259	−0.262630	−	0.964897i	$-0.584590\pi$
$827$	−12492.0	−0.525259	−0.262630	+	0.964897i	$0.584590\pi$
$828$	−16560.0	−0.695048
$829$	37486.0	1.57050	0.785249	−	0.619180i	$-0.212535\pi$
$829$	37486.0	1.57050	0.785249	+	0.619180i	$0.212535\pi$
$830$	16848.0	0.704581
$831$	16588.0	0.692456
$832$	−3584.00	−0.149342
$833$	0	0
$834$	2032.00	0.0843674
$835$	4752.00	0.196946
$836$	−1232.00	−0.0509684
$837$	−33400.0	−1.37930
$838$	14724.0	0.606960
$839$	17574.0	0.723149	0.361574	−	0.932343i	$-0.382239\pi$
$839$	17574.0	0.723149	0.361574	+	0.932343i	$0.382239\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	−23420.0	−0.958559
$843$	16044.0	0.655498
$844$	−19792.0	−0.807190
$845$	−16902.0	−0.688102
$846$	−18492.0	−0.751499
$847$	0	0
$848$	−7776.00	−0.314893
$849$	−784.000	−0.0316924
$850$	−14328.0	−0.578172
$851$	69480.0	2.79876
$852$	−2592.00	−0.104226
$853$	−9440.00	−0.378921	−0.189460	−	0.981888i	$-0.560674\pi$
$853$	−9440.00	−0.378921	−0.189460	+	0.981888i	$0.560674\pi$
$854$	0	0
$855$	11592.0	0.463670
$856$	9888.00	0.394819
$857$	28440.0	1.13360	0.566798	−	0.823857i	$-0.308182\pi$
$857$	28440.0	1.13360	0.566798	+	0.823857i	$0.308182\pi$
$858$	2464.00	0.0980415
$859$	24334.0	0.966549	0.483274	−	0.875469i	$-0.339447\pi$
$859$	24334.0	0.966549	0.483274	+	0.875469i	$0.339447\pi$
$860$	22752.0	0.902136
$861$	0	0
$862$	−1872.00	−0.0739682
$863$	39264.0	1.54874	0.774370	−	0.632733i	$-0.218067\pi$
$863$	39264.0	1.54874	0.774370	+	0.632733i	$0.218067\pi$
$864$	−3200.00	−0.126003
$865$	29376.0	1.15470
$866$	−18076.0	−0.709293
$867$	−7234.00	−0.283367
$868$	0	0
$869$	12584.0	0.491235
$870$	3888.00	0.151512
$871$	−9856.00	−0.383419
$872$	−5552.00	−0.215613
$873$	−30590.0	−1.18593
$874$	10080.0	0.390116
$875$	0	0
$876$	−6400.00	−0.246845
$877$	32114.0	1.23650	0.618251	−	0.785981i	$-0.287841\pi$
$877$	32114.0	1.23650	0.618251	+	0.785981i	$0.287841\pi$
$878$	−3928.00	−0.150984
$879$	5496.00	0.210894
$880$	3168.00	0.121356
$881$	−41454.0	−1.58527	−0.792634	−	0.609698i	$-0.791291\pi$
$881$	−41454.0	−1.58527	−0.792634	+	0.609698i	$0.791291\pi$
$882$	0	0
$883$	2876.00	0.109609	0.0548047	−	0.998497i	$-0.482546\pi$
$883$	2876.00	0.109609	0.0548047	+	0.998497i	$0.482546\pi$
$884$	8064.00	0.306812
$885$	−10152.0	−0.385600
$886$	20136.0	0.763524
$887$	−13932.0	−0.527385	−0.263693	−	0.964607i	$-0.584940\pi$
$887$	−13932.0	−0.527385	−0.263693	+	0.964607i	$0.584940\pi$
$888$	6176.00	0.233393
$889$	0	0
$890$	−31320.0	−1.17961
$891$	−4631.00	−0.174124
$892$	−9368.00	−0.351641
$893$	11256.0	0.421800
$894$	10392.0	0.388770
$895$	12744.0	0.475961
$896$	0	0
$897$	−20160.0	−0.750416
$898$	6540.00	0.243032
$899$	−18036.0	−0.669115
$900$	−18308.0	−0.678074
$901$	17496.0	0.646921
$902$	−9768.00	−0.360575
$903$	0	0
$904$	7824.00	0.287857
$905$	16236.0	0.596357
$906$	10592.0	0.388406
$907$	−19768.0	−0.723689	−0.361844	−	0.932239i	$-0.617853\pi$
$907$	−19768.0	−0.723689	−0.361844	+	0.932239i	$0.617853\pi$
$908$	−8256.00	−0.301746
$909$	−2760.00	−0.100708
$910$	0	0
$911$	43836.0	1.59424	0.797119	−	0.603822i	$-0.206356\pi$
$911$	43836.0	1.59424	0.797119	+	0.603822i	$0.206356\pi$
$912$	896.000	0.0325324
$913$	5148.00	0.186609
$914$	−31052.0	−1.12375
$915$	13680.0	0.494259
$916$	6664.00	0.240376
$917$	0	0
$918$	7200.00	0.258862
$919$	31544.0	1.13225	0.566127	−	0.824318i	$-0.308441\pi$
$919$	31544.0	1.13225	0.566127	+	0.824318i	$0.308441\pi$
$920$	−25920.0	−0.928866
$921$	6128.00	0.219245
$922$	−21096.0	−0.753536
$923$	18144.0	0.647039
$924$	0	0
$925$	76814.0	2.73041
$926$	−7592.00	−0.269426
$927$	−27830.0	−0.986038
$928$	−1728.00	−0.0611254
$929$	−11118.0	−0.392648	−0.196324	−	0.980539i	$-0.562900\pi$
$929$	−11118.0	−0.392648	−0.196324	+	0.980539i	$0.562900\pi$
$930$	−24048.0	−0.847919
$931$	0	0
$932$	16632.0	0.584549
$933$	−8124.00	−0.285067
$934$	−14244.0	−0.499013
$935$	−7128.00	−0.249316
$936$	10304.0	0.359826
$937$	−10568.0	−0.368454	−0.184227	−	0.982884i	$-0.558978\pi$
$937$	−10568.0	−0.368454	−0.184227	+	0.982884i	$0.558978\pi$
$938$	0	0
$939$	9740.00	0.338501
$940$	−28944.0	−1.00431
$941$	−14964.0	−0.518398	−0.259199	−	0.965824i	$-0.583459\pi$
$941$	−14964.0	−0.518398	−0.259199	+	0.965824i	$0.583459\pi$
$942$	3160.00	0.109298
$943$	79920.0	2.75987
$944$	4512.00	0.155565
$945$	0	0
$946$	6952.00	0.238931
$947$	3324.00	0.114061	0.0570304	−	0.998372i	$-0.481837\pi$
$947$	3324.00	0.114061	0.0570304	+	0.998372i	$0.481837\pi$
$948$	−9152.00	−0.313548
$949$	44800.0	1.53242
$950$	11144.0	0.380589
$951$	9612.00	0.327750
$952$	0	0
$953$	3906.00	0.132768	0.0663839	−	0.997794i	$-0.478854\pi$
$953$	3906.00	0.132768	0.0663839	+	0.997794i	$0.478854\pi$
$954$	22356.0	0.758703
$955$	−32832.0	−1.11248
$956$	288.000	0.00974329
$957$	1188.00	0.0401281
$958$	−4584.00	−0.154595
$959$	0	0
$960$	−2304.00	−0.0774597
$961$	81765.0	2.74462
$962$	−43232.0	−1.44891
$963$	−28428.0	−0.951277
$964$	−27440.0	−0.916787
$965$	−37620.0	−1.25495
$966$	0	0
$967$	−36448.0	−1.21209	−0.606044	−	0.795431i	$-0.707244\pi$
$967$	−36448.0	−1.21209	−0.606044	+	0.795431i	$0.707244\pi$
$968$	968.000	0.0321412
$969$	−2016.00	−0.0668351
$970$	−47880.0	−1.58488
$971$	20526.0	0.678384	0.339192	−	0.940717i	$-0.389846\pi$
$971$	20526.0	0.678384	0.339192	+	0.940717i	$0.389846\pi$
$972$	14168.0	0.467530
$973$	0	0
$974$	10264.0	0.337659
$975$	−22288.0	−0.732089
$976$	−6080.00	−0.199402
$977$	37434.0	1.22581	0.612907	−	0.790155i	$-0.290000\pi$
$977$	37434.0	1.22581	0.612907	+	0.790155i	$0.290000\pi$
$978$	−640.000	−0.0209253
$979$	−9570.00	−0.312419
$980$	0	0
$981$	15962.0	0.519498
$982$	8376.00	0.272188
$983$	52194.0	1.69352	0.846760	−	0.531975i	$-0.178550\pi$
$983$	52194.0	1.69352	0.846760	+	0.531975i	$0.178550\pi$
$984$	7104.00	0.230150
$985$	28836.0	0.932783
$986$	3888.00	0.125577
$987$	0	0
$988$	−6272.00	−0.201962
$989$	−56880.0	−1.82880
$990$	−9108.00	−0.292395
$991$	−15220.0	−0.487870	−0.243935	−	0.969792i	$-0.578438\pi$
$991$	−15220.0	−0.487870	−0.243935	+	0.969792i	$0.578438\pi$
$992$	10688.0	0.342081
$993$	13240.0	0.423121
$994$	0	0
$995$	−58932.0	−1.87766
$996$	−3744.00	−0.119110
$997$	−37664.0	−1.19642	−0.598210	−	0.801339i	$-0.704121\pi$
$997$	−37664.0	−1.19642	−0.598210	+	0.801339i	$0.704121\pi$
$998$	7696.00	0.244101
$999$	−38600.0	−1.22247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.4.a.g.1.1		1
7.6	odd	2		154.4.a.d.1.1	✓	1
21.20	even	2		1386.4.a.a.1.1		1
28.27	even	2		1232.4.a.f.1.1		1
77.76	even	2		1694.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.d.1.1	✓	1	7.6	odd	2
1078.4.a.g.1.1		1	1.1	even	1	trivial
1232.4.a.f.1.1		1	28.27	even	2
1386.4.a.a.1.1		1	21.20	even	2
1694.4.a.c.1.1		1	77.76	even	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1078.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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