LMFDB - Embedded newform 490.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	490.1

$q$ -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} -5.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -10.0000 q^{6} +8.00000 q^{8} -2.00000 q^{9} -10.0000 q^{10} -1.00000 q^{11} -20.0000 q^{12} -7.00000 q^{13} +25.0000 q^{15} +16.0000 q^{16} +51.0000 q^{17} -4.00000 q^{18} -30.0000 q^{19} -20.0000 q^{20} -2.00000 q^{22} -50.0000 q^{23} -40.0000 q^{24} +25.0000 q^{25} -14.0000 q^{26} +145.000 q^{27} +79.0000 q^{29} +50.0000 q^{30} +212.000 q^{31} +32.0000 q^{32} +5.00000 q^{33} +102.000 q^{34} -8.00000 q^{36} -190.000 q^{37} -60.0000 q^{38} +35.0000 q^{39} -40.0000 q^{40} +308.000 q^{41} +422.000 q^{43} -4.00000 q^{44} +10.0000 q^{45} -100.000 q^{46} -121.000 q^{47} -80.0000 q^{48} +50.0000 q^{50} -255.000 q^{51} -28.0000 q^{52} +664.000 q^{53} +290.000 q^{54} +5.00000 q^{55} +150.000 q^{57} +158.000 q^{58} -628.000 q^{59} +100.000 q^{60} +684.000 q^{61} +424.000 q^{62} +64.0000 q^{64} +35.0000 q^{65} +10.0000 q^{66} +1056.00 q^{67} +204.000 q^{68} +250.000 q^{69} +744.000 q^{71} -16.0000 q^{72} -726.000 q^{73} -380.000 q^{74} -125.000 q^{75} -120.000 q^{76} +70.0000 q^{78} -407.000 q^{79} -80.0000 q^{80} -671.000 q^{81} +616.000 q^{82} -644.000 q^{83} -255.000 q^{85} +844.000 q^{86} -395.000 q^{87} -8.00000 q^{88} +880.000 q^{89} +20.0000 q^{90} -200.000 q^{92} -1060.00 q^{93} -242.000 q^{94} +150.000 q^{95} -160.000 q^{96} +1351.00 q^{97} +2.00000 q^{99} +O(q^{100})

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
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−10.0000	−0.680414
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−2.00000	−0.0740741
$10$	−10.0000	−0.316228
$11$	−1.00000	−0.0274101	−0.0137051	−	0.999906i	$-0.504363\pi$
$11$	−1.00000	−0.0274101	−0.0137051	+	0.999906i	$0.504363\pi$
$12$	−20.0000	−0.481125
$13$	−7.00000	−0.149342	−0.0746712	−	0.997208i	$-0.523791\pi$
$13$	−7.00000	−0.149342	−0.0746712	+	0.997208i	$0.523791\pi$
$14$	0	0
$15$	25.0000	0.430331
$16$	16.0000	0.250000
$17$	51.0000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	51.0000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−4.00000	−0.0523783
$19$	−30.0000	−0.362235	−0.181118	−	0.983461i	$-0.557971\pi$
$19$	−30.0000	−0.362235	−0.181118	+	0.983461i	$0.557971\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−2.00000	−0.0193819
$23$	−50.0000	−0.453292	−0.226646	−	0.973977i	$-0.572776\pi$
$23$	−50.0000	−0.453292	−0.226646	+	0.973977i	$0.572776\pi$
$24$	−40.0000	−0.340207
$25$	25.0000	0.200000
$26$	−14.0000	−0.105601
$27$	145.000	1.03353
$28$	0	0
$29$	79.0000	0.505860	0.252930	−	0.967485i	$-0.418606\pi$
$29$	79.0000	0.505860	0.252930	+	0.967485i	$0.418606\pi$
$30$	50.0000	0.304290
$31$	212.000	1.22827	0.614134	−	0.789202i	$-0.289505\pi$
$31$	212.000	1.22827	0.614134	+	0.789202i	$0.289505\pi$
$32$	32.0000	0.176777
$33$	5.00000	0.0263754
$34$	102.000	0.514496
$35$	0	0
$36$	−8.00000	−0.0370370
$37$	−190.000	−0.844211	−0.422106	−	0.906547i	$-0.638709\pi$
$37$	−190.000	−0.844211	−0.422106	+	0.906547i	$0.638709\pi$
$38$	−60.0000	−0.256139
$39$	35.0000	0.143705
$40$	−40.0000	−0.158114
$41$	308.000	1.17321	0.586604	−	0.809874i	$-0.300465\pi$
$41$	308.000	1.17321	0.586604	+	0.809874i	$0.300465\pi$
$42$	0	0
$43$	422.000	1.49661	0.748307	−	0.663353i	$-0.230867\pi$
$43$	422.000	1.49661	0.748307	+	0.663353i	$0.230867\pi$
$44$	−4.00000	−0.0137051
$45$	10.0000	0.0331269
$46$	−100.000	−0.320526
$47$	−121.000	−0.375525	−0.187762	−	0.982214i	$-0.560123\pi$
$47$	−121.000	−0.375525	−0.187762	+	0.982214i	$0.560123\pi$
$48$	−80.0000	−0.240563
$49$	0	0
$50$	50.0000	0.141421
$51$	−255.000	−0.700140
$52$	−28.0000	−0.0746712
$53$	664.000	1.72089	0.860447	−	0.509539i	$-0.170184\pi$
$53$	664.000	1.72089	0.860447	+	0.509539i	$0.170184\pi$
$54$	290.000	0.730815
$55$	5.00000	0.0122582
$56$	0	0
$57$	150.000	0.348561
$58$	158.000	0.357697
$59$	−628.000	−1.38574	−0.692870	−	0.721063i	$-0.743654\pi$
$59$	−628.000	−1.38574	−0.692870	+	0.721063i	$0.743654\pi$
$60$	100.000	0.215166
$61$	684.000	1.43569	0.717846	−	0.696202i	$-0.245128\pi$
$61$	684.000	1.43569	0.717846	+	0.696202i	$0.245128\pi$
$62$	424.000	0.868517
$63$	0	0
$64$	64.0000	0.125000
$65$	35.0000	0.0667879
$66$	10.0000	0.0186502
$67$	1056.00	1.92554	0.962768	−	0.270328i	$-0.0871323\pi$
$67$	1056.00	1.92554	0.962768	+	0.270328i	$0.0871323\pi$
$68$	204.000	0.363803
$69$	250.000	0.436181
$70$	0	0
$71$	744.000	1.24361	0.621807	−	0.783171i	$-0.286399\pi$
$71$	744.000	1.24361	0.621807	+	0.783171i	$0.286399\pi$
$72$	−16.0000	−0.0261891
$73$	−726.000	−1.16400	−0.581999	−	0.813189i	$-0.697729\pi$
$73$	−726.000	−1.16400	−0.581999	+	0.813189i	$0.697729\pi$
$74$	−380.000	−0.596947
$75$	−125.000	−0.192450
$76$	−120.000	−0.181118
$77$	0	0
$78$	70.0000	0.101615
$79$	−407.000	−0.579634	−0.289817	−	0.957082i	$-0.593594\pi$
$79$	−407.000	−0.579634	−0.289817	+	0.957082i	$0.593594\pi$
$80$	−80.0000	−0.111803
$81$	−671.000	−0.920439
$82$	616.000	0.829583
$83$	−644.000	−0.851665	−0.425832	−	0.904802i	$-0.640019\pi$
$83$	−644.000	−0.851665	−0.425832	+	0.904802i	$0.640019\pi$
$84$	0	0
$85$	−255.000	−0.325396
$86$	844.000	1.05827
$87$	−395.000	−0.486764
$88$	−8.00000	−0.00969094
$89$	880.000	1.04809	0.524044	−	0.851691i	$-0.324423\pi$
$89$	880.000	1.04809	0.524044	+	0.851691i	$0.324423\pi$
$90$	20.0000	0.0234243
$91$	0	0
$92$	−200.000	−0.226646
$93$	−1060.00	−1.18190
$94$	−242.000	−0.265536
$95$	150.000	0.161997
$96$	−160.000	−0.170103
$97$	1351.00	1.41416	0.707079	−	0.707135i	$-0.250013\pi$
$97$	1351.00	1.41416	0.707079	+	0.707135i	$0.250013\pi$
$98$	0	0
$99$	2.00000	0.00203038
$100$	100.000	0.100000
$101$	−54.0000	−0.0532000	−0.0266000	−	0.999646i	$-0.508468\pi$
$101$	−54.0000	−0.0532000	−0.0266000	+	0.999646i	$0.508468\pi$
$102$	−510.000	−0.495074
$103$	1027.00	0.982459	0.491230	−	0.871030i	$-0.336548\pi$
$103$	1027.00	0.982459	0.491230	+	0.871030i	$0.336548\pi$
$104$	−56.0000	−0.0528005
$105$	0	0
$106$	1328.00	1.21686
$107$	314.000	0.283697	0.141848	−	0.989888i	$-0.454695\pi$
$107$	314.000	0.283697	0.141848	+	0.989888i	$0.454695\pi$
$108$	580.000	0.516764
$109$	−1611.00	−1.41565	−0.707825	−	0.706388i	$-0.750323\pi$
$109$	−1611.00	−1.41565	−0.707825	+	0.706388i	$0.750323\pi$
$110$	10.0000	0.00866784
$111$	950.000	0.812342
$112$	0	0
$113$	366.000	0.304694	0.152347	−	0.988327i	$-0.451317\pi$
$113$	366.000	0.304694	0.152347	+	0.988327i	$0.451317\pi$
$114$	300.000	0.246470
$115$	250.000	0.202718
$116$	316.000	0.252930
$117$	14.0000	0.0110624
$118$	−1256.00	−0.979866
$119$	0	0
$120$	200.000	0.152145
$121$	−1330.00	−0.999249
$122$	1368.00	1.01519
$123$	−1540.00	−1.12892
$124$	848.000	0.614134
$125$	−125.000	−0.0894427
$126$	0	0
$127$	604.000	0.422018	0.211009	−	0.977484i	$-0.432325\pi$
$127$	604.000	0.422018	0.211009	+	0.977484i	$0.432325\pi$
$128$	128.000	0.0883883
$129$	−2110.00	−1.44012
$130$	70.0000	0.0472262
$131$	−2914.00	−1.94349	−0.971746	−	0.236030i	$-0.924153\pi$
$131$	−2914.00	−1.94349	−0.971746	+	0.236030i	$0.924153\pi$
$132$	20.0000	0.0131877
$133$	0	0
$134$	2112.00	1.36156
$135$	−725.000	−0.462208
$136$	408.000	0.257248
$137$	2568.00	1.60145	0.800726	−	0.599030i	$-0.204447\pi$
$137$	2568.00	1.60145	0.800726	+	0.599030i	$0.204447\pi$
$138$	500.000	0.308426
$139$	−1274.00	−0.777405	−0.388702	−	0.921363i	$-0.627077\pi$
$139$	−1274.00	−0.777405	−0.388702	+	0.921363i	$0.627077\pi$
$140$	0	0
$141$	605.000	0.361349
$142$	1488.00	0.879368
$143$	7.00000	0.00409349
$144$	−32.0000	−0.0185185
$145$	−395.000	−0.226227
$146$	−1452.00	−0.823071
$147$	0	0
$148$	−760.000	−0.422106
$149$	594.000	0.326593	0.163297	−	0.986577i	$-0.447787\pi$
$149$	594.000	0.326593	0.163297	+	0.986577i	$0.447787\pi$
$150$	−250.000	−0.136083
$151$	−1527.00	−0.822950	−0.411475	−	0.911421i	$-0.634986\pi$
$151$	−1527.00	−0.822950	−0.411475	+	0.911421i	$0.634986\pi$
$152$	−240.000	−0.128070
$153$	−102.000	−0.0538968
$154$	0	0
$155$	−1060.00	−0.549298
$156$	140.000	0.0718524
$157$	−530.000	−0.269418	−0.134709	−	0.990885i	$-0.543010\pi$
$157$	−530.000	−0.269418	−0.134709	+	0.990885i	$0.543010\pi$
$158$	−814.000	−0.409863
$159$	−3320.00	−1.65593
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−1342.00	−0.650849
$163$	−3662.00	−1.75969	−0.879847	−	0.475258i	$-0.842355\pi$
$163$	−3662.00	−1.75969	−0.879847	+	0.475258i	$0.842355\pi$
$164$	1232.00	0.586604
$165$	−25.0000	−0.0117954
$166$	−1288.00	−0.602218
$167$	315.000	0.145961	0.0729803	−	0.997333i	$-0.476749\pi$
$167$	315.000	0.145961	0.0729803	+	0.997333i	$0.476749\pi$
$168$	0	0
$169$	−2148.00	−0.977697
$170$	−510.000	−0.230089
$171$	60.0000	0.0268322
$172$	1688.00	0.748307
$173$	1251.00	0.549779	0.274890	−	0.961476i	$-0.411359\pi$
$173$	1251.00	0.549779	0.274890	+	0.961476i	$0.411359\pi$
$174$	−790.000	−0.344194
$175$	0	0
$176$	−16.0000	−0.00685253
$177$	3140.00	1.33343
$178$	1760.00	0.741110
$179$	−148.000	−0.0617991	−0.0308996	−	0.999522i	$-0.509837\pi$
$179$	−148.000	−0.0617991	−0.0308996	+	0.999522i	$0.509837\pi$
$180$	40.0000	0.0165635
$181$	1344.00	0.551927	0.275963	−	0.961168i	$-0.411003\pi$
$181$	1344.00	0.551927	0.275963	+	0.961168i	$0.411003\pi$
$182$	0	0
$183$	−3420.00	−1.38150
$184$	−400.000	−0.160263
$185$	950.000	0.377543
$186$	−2120.00	−0.835731
$187$	−51.0000	−0.0199438
$188$	−484.000	−0.187762
$189$	0	0
$190$	300.000	0.114549
$191$	−561.000	−0.212526	−0.106263	−	0.994338i	$-0.533889\pi$
$191$	−561.000	−0.212526	−0.106263	+	0.994338i	$0.533889\pi$
$192$	−320.000	−0.120281
$193$	3016.00	1.12485	0.562426	−	0.826848i	$-0.309868\pi$
$193$	3016.00	1.12485	0.562426	+	0.826848i	$0.309868\pi$
$194$	2702.00	0.999960
$195$	−175.000	−0.0642667
$196$	0	0
$197$	−3232.00	−1.16889	−0.584443	−	0.811435i	$-0.698687\pi$
$197$	−3232.00	−1.16889	−0.584443	+	0.811435i	$0.698687\pi$
$198$	4.00000	0.00143570
$199$	1164.00	0.414642	0.207321	−	0.978273i	$-0.433526\pi$
$199$	1164.00	0.414642	0.207321	+	0.978273i	$0.433526\pi$
$200$	200.000	0.0707107
$201$	−5280.00	−1.85285
$202$	−108.000	−0.0376181
$203$	0	0
$204$	−1020.00	−0.350070
$205$	−1540.00	−0.524674
$206$	2054.00	0.694704
$207$	100.000	0.0335772
$208$	−112.000	−0.0373356
$209$	30.0000	0.00992892
$210$	0	0
$211$	569.000	0.185647	0.0928236	−	0.995683i	$-0.470411\pi$
$211$	569.000	0.185647	0.0928236	+	0.995683i	$0.470411\pi$
$212$	2656.00	0.860447
$213$	−3720.00	−1.19667
$214$	628.000	0.200604
$215$	−2110.00	−0.669306
$216$	1160.00	0.365407
$217$	0	0
$218$	−3222.00	−1.00102
$219$	3630.00	1.12006
$220$	20.0000	0.00612909
$221$	−357.000	−0.108663
$222$	1900.00	0.574413
$223$	−693.000	−0.208102	−0.104051	−	0.994572i	$-0.533180\pi$
$223$	−693.000	−0.208102	−0.104051	+	0.994572i	$0.533180\pi$
$224$	0	0
$225$	−50.0000	−0.0148148
$226$	732.000	0.215451
$227$	4279.00	1.25113	0.625567	−	0.780171i	$-0.284868\pi$
$227$	4279.00	1.25113	0.625567	+	0.780171i	$0.284868\pi$
$228$	600.000	0.174281
$229$	3316.00	0.956888	0.478444	−	0.878118i	$-0.341201\pi$
$229$	3316.00	0.956888	0.478444	+	0.878118i	$0.341201\pi$
$230$	500.000	0.143344
$231$	0	0
$232$	632.000	0.178848
$233$	3912.00	1.09993	0.549965	−	0.835188i	$-0.314641\pi$
$233$	3912.00	1.09993	0.549965	+	0.835188i	$0.314641\pi$
$234$	28.0000	0.00782230
$235$	605.000	0.167940
$236$	−2512.00	−0.692870
$237$	2035.00	0.557753
$238$	0	0
$239$	−5451.00	−1.47530	−0.737648	−	0.675185i	$-0.764064\pi$
$239$	−5451.00	−1.47530	−0.737648	+	0.675185i	$0.764064\pi$
$240$	400.000	0.107583
$241$	−250.000	−0.0668212	−0.0334106	−	0.999442i	$-0.510637\pi$
$241$	−250.000	−0.0668212	−0.0334106	+	0.999442i	$0.510637\pi$
$242$	−2660.00	−0.706576
$243$	−560.000	−0.147835
$244$	2736.00	0.717846
$245$	0	0
$246$	−3080.00	−0.798267
$247$	210.000	0.0540971
$248$	1696.00	0.434258
$249$	3220.00	0.819515
$250$	−250.000	−0.0632456
$251$	−910.000	−0.228839	−0.114420	−	0.993432i	$-0.536501\pi$
$251$	−910.000	−0.228839	−0.114420	+	0.993432i	$0.536501\pi$
$252$	0	0
$253$	50.0000	0.0124248
$254$	1208.00	0.298412
$255$	1275.00	0.313112
$256$	256.000	0.0625000
$257$	6494.00	1.57620	0.788102	−	0.615544i	$-0.211064\pi$
$257$	6494.00	1.57620	0.788102	+	0.615544i	$0.211064\pi$
$258$	−4220.00	−1.01832
$259$	0	0
$260$	140.000	0.0333940
$261$	−158.000	−0.0374711
$262$	−5828.00	−1.37426
$263$	1434.00	0.336214	0.168107	−	0.985769i	$-0.446235\pi$
$263$	1434.00	0.336214	0.168107	+	0.985769i	$0.446235\pi$
$264$	40.0000	0.00932511
$265$	−3320.00	−0.769607
$266$	0	0
$267$	−4400.00	−1.00852
$268$	4224.00	0.962768
$269$	5014.00	1.13646	0.568232	−	0.822868i	$-0.307627\pi$
$269$	5014.00	1.13646	0.568232	+	0.822868i	$0.307627\pi$
$270$	−1450.00	−0.326830
$271$	−5420.00	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−5420.00	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	816.000	0.181902
$273$	0	0
$274$	5136.00	1.13240
$275$	−25.0000	−0.00548202
$276$	1000.00	0.218090
$277$	3674.00	0.796929	0.398464	−	0.917184i	$-0.369543\pi$
$277$	3674.00	0.796929	0.398464	+	0.917184i	$0.369543\pi$
$278$	−2548.00	−0.549708
$279$	−424.000	−0.0909829
$280$	0	0
$281$	7331.00	1.55634	0.778169	−	0.628055i	$-0.216149\pi$
$281$	7331.00	1.55634	0.778169	+	0.628055i	$0.216149\pi$
$282$	1210.00	0.255512
$283$	−271.000	−0.0569232	−0.0284616	−	0.999595i	$-0.509061\pi$
$283$	−271.000	−0.0569232	−0.0284616	+	0.999595i	$0.509061\pi$
$284$	2976.00	0.621807
$285$	−750.000	−0.155881
$286$	14.0000	0.00289454
$287$	0	0
$288$	−64.0000	−0.0130946
$289$	−2312.00	−0.470588
$290$	−790.000	−0.159967
$291$	−6755.00	−1.36077
$292$	−2904.00	−0.581999
$293$	−4305.00	−0.858364	−0.429182	−	0.903218i	$-0.641198\pi$
$293$	−4305.00	−0.858364	−0.429182	+	0.903218i	$0.641198\pi$
$294$	0	0
$295$	3140.00	0.619722
$296$	−1520.00	−0.298474
$297$	−145.000	−0.0283291
$298$	1188.00	0.230936
$299$	350.000	0.0676957
$300$	−500.000	−0.0962250
$301$	0	0
$302$	−3054.00	−0.581914
$303$	270.000	0.0511917
$304$	−480.000	−0.0905588
$305$	−3420.00	−0.642061
$306$	−204.000	−0.0381108
$307$	−2639.00	−0.490605	−0.245302	−	0.969447i	$-0.578887\pi$
$307$	−2639.00	−0.490605	−0.245302	+	0.969447i	$0.578887\pi$
$308$	0	0
$309$	−5135.00	−0.945372
$310$	−2120.00	−0.388413
$311$	8514.00	1.55236	0.776181	−	0.630510i	$-0.217154\pi$
$311$	8514.00	1.55236	0.776181	+	0.630510i	$0.217154\pi$
$312$	280.000	0.0508073
$313$	−219.000	−0.0395483	−0.0197741	−	0.999804i	$-0.506295\pi$
$313$	−219.000	−0.0395483	−0.0197741	+	0.999804i	$0.506295\pi$
$314$	−1060.00	−0.190507
$315$	0	0
$316$	−1628.00	−0.289817
$317$	−4026.00	−0.713321	−0.356660	−	0.934234i	$-0.616085\pi$
$317$	−4026.00	−0.713321	−0.356660	+	0.934234i	$0.616085\pi$
$318$	−6640.00	−1.17092
$319$	−79.0000	−0.0138657
$320$	−320.000	−0.0559017
$321$	−1570.00	−0.272987
$322$	0	0
$323$	−1530.00	−0.263565
$324$	−2684.00	−0.460219
$325$	−175.000	−0.0298685
$326$	−7324.00	−1.24429
$327$	8055.00	1.36221
$328$	2464.00	0.414792
$329$	0	0
$330$	−50.0000	−0.00834063
$331$	−7036.00	−1.16838	−0.584190	−	0.811617i	$-0.698588\pi$
$331$	−7036.00	−1.16838	−0.584190	+	0.811617i	$0.698588\pi$
$332$	−2576.00	−0.425832
$333$	380.000	0.0625341
$334$	630.000	0.103210
$335$	−5280.00	−0.861126
$336$	0	0
$337$	10362.0	1.67494	0.837469	−	0.546485i	$-0.184034\pi$
$337$	10362.0	1.67494	0.837469	+	0.546485i	$0.184034\pi$
$338$	−4296.00	−0.691336
$339$	−1830.00	−0.293192
$340$	−1020.00	−0.162698
$341$	−212.000	−0.0336670
$342$	120.000	0.0189733
$343$	0	0
$344$	3376.00	0.529133
$345$	−1250.00	−0.195066
$346$	2502.00	0.388752
$347$	−8422.00	−1.30293	−0.651465	−	0.758679i	$-0.725845\pi$
$347$	−8422.00	−1.30293	−0.651465	+	0.758679i	$0.725845\pi$
$348$	−1580.00	−0.243382
$349$	7350.00	1.12733	0.563663	−	0.826005i	$-0.309392\pi$
$349$	7350.00	1.12733	0.563663	+	0.826005i	$0.309392\pi$
$350$	0	0
$351$	−1015.00	−0.154350
$352$	−32.0000	−0.00484547
$353$	−3057.00	−0.460928	−0.230464	−	0.973081i	$-0.574024\pi$
$353$	−3057.00	−0.460928	−0.230464	+	0.973081i	$0.574024\pi$
$354$	6280.00	0.942876
$355$	−3720.00	−0.556161
$356$	3520.00	0.524044
$357$	0	0
$358$	−296.000	−0.0436986
$359$	8392.00	1.23374	0.616870	−	0.787065i	$-0.288400\pi$
$359$	8392.00	1.23374	0.616870	+	0.787065i	$0.288400\pi$
$360$	80.0000	0.0117121
$361$	−5959.00	−0.868786
$362$	2688.00	0.390271
$363$	6650.00	0.961527
$364$	0	0
$365$	3630.00	0.520556
$366$	−6840.00	−0.976865
$367$	−8377.00	−1.19149	−0.595744	−	0.803175i	$-0.703143\pi$
$367$	−8377.00	−1.19149	−0.595744	+	0.803175i	$0.703143\pi$
$368$	−800.000	−0.113323
$369$	−616.000	−0.0869043
$370$	1900.00	0.266963
$371$	0	0
$372$	−4240.00	−0.590951
$373$	−1968.00	−0.273188	−0.136594	−	0.990627i	$-0.543616\pi$
$373$	−1968.00	−0.273188	−0.136594	+	0.990627i	$0.543616\pi$
$374$	−102.000	−0.0141024
$375$	625.000	0.0860663
$376$	−968.000	−0.132768
$377$	−553.000	−0.0755463
$378$	0	0
$379$	1052.00	0.142579	0.0712897	−	0.997456i	$-0.477289\pi$
$379$	1052.00	0.142579	0.0712897	+	0.997456i	$0.477289\pi$
$380$	600.000	0.0809983
$381$	−3020.00	−0.406087
$382$	−1122.00	−0.150279
$383$	2308.00	0.307920	0.153960	−	0.988077i	$-0.450797\pi$
$383$	2308.00	0.307920	0.153960	+	0.988077i	$0.450797\pi$
$384$	−640.000	−0.0850517
$385$	0	0
$386$	6032.00	0.795390
$387$	−844.000	−0.110860
$388$	5404.00	0.707079
$389$	2281.00	0.297304	0.148652	−	0.988890i	$-0.452507\pi$
$389$	2281.00	0.297304	0.148652	+	0.988890i	$0.452507\pi$
$390$	−350.000	−0.0454434
$391$	−2550.00	−0.329819
$392$	0	0
$393$	14570.0	1.87013
$394$	−6464.00	−0.826527
$395$	2035.00	0.259220
$396$	8.00000	0.00101519
$397$	14635.0	1.85015	0.925075	−	0.379784i	$-0.124002\pi$
$397$	14635.0	1.85015	0.925075	+	0.379784i	$0.124002\pi$
$398$	2328.00	0.293196
$399$	0	0
$400$	400.000	0.0500000
$401$	5641.00	0.702489	0.351245	−	0.936284i	$-0.385759\pi$
$401$	5641.00	0.702489	0.351245	+	0.936284i	$0.385759\pi$
$402$	−10560.0	−1.31016
$403$	−1484.00	−0.183433
$404$	−216.000	−0.0266000
$405$	3355.00	0.411633
$406$	0	0
$407$	190.000	0.0231399
$408$	−2040.00	−0.247537
$409$	−6410.00	−0.774949	−0.387474	−	0.921880i	$-0.626652\pi$
$409$	−6410.00	−0.774949	−0.387474	+	0.921880i	$0.626652\pi$
$410$	−3080.00	−0.371001
$411$	−12840.0	−1.54100
$412$	4108.00	0.491230
$413$	0	0
$414$	200.000	0.0237427
$415$	3220.00	0.380876
$416$	−224.000	−0.0264002
$417$	6370.00	0.748058
$418$	60.0000	0.00702080
$419$	−4816.00	−0.561520	−0.280760	−	0.959778i	$-0.590587\pi$
$419$	−4816.00	−0.561520	−0.280760	+	0.959778i	$0.590587\pi$
$420$	0	0
$421$	15325.0	1.77410	0.887048	−	0.461676i	$-0.152752\pi$
$421$	15325.0	1.77410	0.887048	+	0.461676i	$0.152752\pi$
$422$	1138.00	0.131272
$423$	242.000	0.0278166
$424$	5312.00	0.608428
$425$	1275.00	0.145521
$426$	−7440.00	−0.846172
$427$	0	0
$428$	1256.00	0.141848
$429$	−35.0000	−0.00393896
$430$	−4220.00	−0.473271
$431$	1875.00	0.209549	0.104774	−	0.994496i	$-0.466588\pi$
$431$	1875.00	0.209549	0.104774	+	0.994496i	$0.466588\pi$
$432$	2320.00	0.258382
$433$	13874.0	1.53982	0.769910	−	0.638153i	$-0.220301\pi$
$433$	13874.0	1.53982	0.769910	+	0.638153i	$0.220301\pi$
$434$	0	0
$435$	1975.00	0.217687
$436$	−6444.00	−0.707825
$437$	1500.00	0.164198
$438$	7260.00	0.792000
$439$	3442.00	0.374209	0.187104	−	0.982340i	$-0.440090\pi$
$439$	3442.00	0.374209	0.187104	+	0.982340i	$0.440090\pi$
$440$	40.0000	0.00433392
$441$	0	0
$442$	−714.000	−0.0768360
$443$	16750.0	1.79643	0.898213	−	0.439561i	$-0.144866\pi$
$443$	16750.0	1.79643	0.898213	+	0.439561i	$0.144866\pi$
$444$	3800.00	0.406171
$445$	−4400.00	−0.468719
$446$	−1386.00	−0.147150
$447$	−2970.00	−0.314264
$448$	0	0
$449$	695.000	0.0730492	0.0365246	−	0.999333i	$-0.488371\pi$
$449$	695.000	0.0730492	0.0365246	+	0.999333i	$0.488371\pi$
$450$	−100.000	−0.0104757
$451$	−308.000	−0.0321578
$452$	1464.00	0.152347
$453$	7635.00	0.791884
$454$	8558.00	0.884685
$455$	0	0
$456$	1200.00	0.123235
$457$	5760.00	0.589587	0.294794	−	0.955561i	$-0.404749\pi$
$457$	5760.00	0.589587	0.294794	+	0.955561i	$0.404749\pi$
$458$	6632.00	0.676622
$459$	7395.00	0.752002
$460$	1000.00	0.101359
$461$	−13440.0	−1.35784	−0.678919	−	0.734213i	$-0.737551\pi$
$461$	−13440.0	−1.35784	−0.678919	+	0.734213i	$0.737551\pi$
$462$	0	0
$463$	−7348.00	−0.737561	−0.368780	−	0.929517i	$-0.620225\pi$
$463$	−7348.00	−0.737561	−0.368780	+	0.929517i	$0.620225\pi$
$464$	1264.00	0.126465
$465$	5300.00	0.528563
$466$	7824.00	0.777768
$467$	17925.0	1.77617	0.888084	−	0.459682i	$-0.152037\pi$
$467$	17925.0	1.77617	0.888084	+	0.459682i	$0.152037\pi$
$468$	56.0000	0.00553120
$469$	0	0
$470$	1210.00	0.118751
$471$	2650.00	0.259247
$472$	−5024.00	−0.489933
$473$	−422.000	−0.0410224
$474$	4070.00	0.394391
$475$	−750.000	−0.0724471
$476$	0	0
$477$	−1328.00	−0.127474
$478$	−10902.0	−1.04319
$479$	−12346.0	−1.17767	−0.588834	−	0.808254i	$-0.700413\pi$
$479$	−12346.0	−1.17767	−0.588834	+	0.808254i	$0.700413\pi$
$480$	800.000	0.0760726
$481$	1330.00	0.126076
$482$	−500.000	−0.0472497
$483$	0	0
$484$	−5320.00	−0.499624
$485$	−6755.00	−0.632430
$486$	−1120.00	−0.104535
$487$	15014.0	1.39702	0.698511	−	0.715600i	$-0.253847\pi$
$487$	15014.0	1.39702	0.698511	+	0.715600i	$0.253847\pi$
$488$	5472.00	0.507594
$489$	18310.0	1.69327
$490$	0	0
$491$	−4723.00	−0.434106	−0.217053	−	0.976160i	$-0.569644\pi$
$491$	−4723.00	−0.434106	−0.217053	+	0.976160i	$0.569644\pi$
$492$	−6160.00	−0.564460
$493$	4029.00	0.368067
$494$	420.000	0.0382524
$495$	−10.0000	−0.000908013 0
$496$	3392.00	0.307067
$497$	0	0
$498$	6440.00	0.579485
$499$	11227.0	1.00719	0.503597	−	0.863939i	$-0.332010\pi$
$499$	11227.0	1.00719	0.503597	+	0.863939i	$0.332010\pi$
$500$	−500.000	−0.0447214
$501$	−1575.00	−0.140451
$502$	−1820.00	−0.161814
$503$	4557.00	0.403949	0.201975	−	0.979391i	$-0.435264\pi$
$503$	4557.00	0.403949	0.201975	+	0.979391i	$0.435264\pi$
$504$	0	0
$505$	270.000	0.0237918
$506$	100.000	0.00878566
$507$	10740.0	0.940789
$508$	2416.00	0.211009
$509$	14110.0	1.22871	0.614356	−	0.789029i	$-0.289416\pi$
$509$	14110.0	1.22871	0.614356	+	0.789029i	$0.289416\pi$
$510$	2550.00	0.221404
$511$	0	0
$512$	512.000	0.0441942
$513$	−4350.00	−0.374380
$514$	12988.0	1.11454
$515$	−5135.00	−0.439369
$516$	−8440.00	−0.720059
$517$	121.000	0.0102932
$518$	0	0
$519$	−6255.00	−0.529025
$520$	280.000	0.0236131
$521$	−1902.00	−0.159939	−0.0799694	−	0.996797i	$-0.525482\pi$
$521$	−1902.00	−0.159939	−0.0799694	+	0.996797i	$0.525482\pi$
$522$	−316.000	−0.0264961
$523$	1972.00	0.164875	0.0824374	−	0.996596i	$-0.473730\pi$
$523$	1972.00	0.164875	0.0824374	+	0.996596i	$0.473730\pi$
$524$	−11656.0	−0.971746
$525$	0	0
$526$	2868.00	0.237739
$527$	10812.0	0.893697
$528$	80.0000	0.00659385
$529$	−9667.00	−0.794526
$530$	−6640.00	−0.544195
$531$	1256.00	0.102647
$532$	0	0
$533$	−2156.00	−0.175210
$534$	−8800.00	−0.713133
$535$	−1570.00	−0.126873
$536$	8448.00	0.680780
$537$	740.000	0.0594662
$538$	10028.0	0.803602
$539$	0	0
$540$	−2900.00	−0.231104
$541$	−25033.0	−1.98938	−0.994688	−	0.102933i	$-0.967177\pi$
$541$	−25033.0	−1.98938	−0.994688	+	0.102933i	$0.967177\pi$
$542$	−10840.0	−0.859074
$543$	−6720.00	−0.531092
$544$	1632.00	0.128624
$545$	8055.00	0.633098
$546$	0	0
$547$	−236.000	−0.0184472	−0.00922361	−	0.999957i	$-0.502936\pi$
$547$	−236.000	−0.0184472	−0.00922361	+	0.999957i	$0.502936\pi$
$548$	10272.0	0.800726
$549$	−1368.00	−0.106348
$550$	−50.0000	−0.00387638
$551$	−2370.00	−0.183240
$552$	2000.00	0.154213
$553$	0	0
$554$	7348.00	0.563514
$555$	−4750.00	−0.363291
$556$	−5096.00	−0.388702
$557$	15504.0	1.17940	0.589700	−	0.807623i	$-0.299246\pi$
$557$	15504.0	1.17940	0.589700	+	0.807623i	$0.299246\pi$
$558$	−848.000	−0.0643346
$559$	−2954.00	−0.223508
$560$	0	0
$561$	255.000	0.0191909
$562$	14662.0	1.10050
$563$	8948.00	0.669828	0.334914	−	0.942249i	$-0.391293\pi$
$563$	8948.00	0.669828	0.334914	+	0.942249i	$0.391293\pi$
$564$	2420.00	0.180674
$565$	−1830.00	−0.136263
$566$	−542.000	−0.0402508
$567$	0	0
$568$	5952.00	0.439684
$569$	13866.0	1.02160	0.510802	−	0.859698i	$-0.329348\pi$
$569$	13866.0	1.02160	0.510802	+	0.859698i	$0.329348\pi$
$570$	−1500.00	−0.110225
$571$	9988.00	0.732022	0.366011	−	0.930610i	$-0.380723\pi$
$571$	9988.00	0.732022	0.366011	+	0.930610i	$0.380723\pi$
$572$	28.0000	0.00204675
$573$	2805.00	0.204504
$574$	0	0
$575$	−1250.00	−0.0906584
$576$	−128.000	−0.00925926
$577$	2585.00	0.186508	0.0932539	−	0.995642i	$-0.470273\pi$
$577$	2585.00	0.186508	0.0932539	+	0.995642i	$0.470273\pi$
$578$	−4624.00	−0.332756
$579$	−15080.0	−1.08239
$580$	−1580.00	−0.113114
$581$	0	0
$582$	−13510.0	−0.962212
$583$	−664.000	−0.0471699
$584$	−5808.00	−0.411536
$585$	−70.0000	−0.00494725
$586$	−8610.00	−0.606955
$587$	−19656.0	−1.38210	−0.691048	−	0.722809i	$-0.742851\pi$
$587$	−19656.0	−1.38210	−0.691048	+	0.722809i	$0.742851\pi$
$588$	0	0
$589$	−6360.00	−0.444922
$590$	6280.00	0.438209
$591$	16160.0	1.12476
$592$	−3040.00	−0.211053
$593$	−21247.0	−1.47135	−0.735674	−	0.677335i	$-0.763135\pi$
$593$	−21247.0	−1.47135	−0.735674	+	0.677335i	$0.763135\pi$
$594$	−290.000	−0.0200317
$595$	0	0
$596$	2376.00	0.163297
$597$	−5820.00	−0.398990
$598$	700.000	0.0478681
$599$	−9325.00	−0.636075	−0.318038	−	0.948078i	$-0.603024\pi$
$599$	−9325.00	−0.636075	−0.318038	+	0.948078i	$0.603024\pi$
$600$	−1000.00	−0.0680414
$601$	−5362.00	−0.363928	−0.181964	−	0.983305i	$-0.558245\pi$
$601$	−5362.00	−0.363928	−0.181964	+	0.983305i	$0.558245\pi$
$602$	0	0
$603$	−2112.00	−0.142632
$604$	−6108.00	−0.411475
$605$	6650.00	0.446878
$606$	540.000	0.0361980
$607$	−15731.0	−1.05190	−0.525949	−	0.850516i	$-0.676290\pi$
$607$	−15731.0	−1.05190	−0.525949	+	0.850516i	$0.676290\pi$
$608$	−960.000	−0.0640348
$609$	0	0
$610$	−6840.00	−0.454006
$611$	847.000	0.0560818
$612$	−408.000	−0.0269484
$613$	−13742.0	−0.905439	−0.452720	−	0.891653i	$-0.649546\pi$
$613$	−13742.0	−0.905439	−0.452720	+	0.891653i	$0.649546\pi$
$614$	−5278.00	−0.346910
$615$	7700.00	0.504868
$616$	0	0
$617$	18286.0	1.19314	0.596569	−	0.802561i	$-0.296530\pi$
$617$	18286.0	1.19314	0.596569	+	0.802561i	$0.296530\pi$
$618$	−10270.0	−0.668479
$619$	−24722.0	−1.60527	−0.802634	−	0.596472i	$-0.796569\pi$
$619$	−24722.0	−1.60527	−0.802634	+	0.596472i	$0.796569\pi$
$620$	−4240.00	−0.274649
$621$	−7250.00	−0.468490
$622$	17028.0	1.09769
$623$	0	0
$624$	560.000	0.0359262
$625$	625.000	0.0400000
$626$	−438.000	−0.0279649
$627$	−150.000	−0.00955410
$628$	−2120.00	−0.134709
$629$	−9690.00	−0.614254
$630$	0	0
$631$	−22181.0	−1.39938	−0.699692	−	0.714444i	$-0.746680\pi$
$631$	−22181.0	−1.39938	−0.699692	+	0.714444i	$0.746680\pi$
$632$	−3256.00	−0.204932
$633$	−2845.00	−0.178639
$634$	−8052.00	−0.504394
$635$	−3020.00	−0.188732
$636$	−13280.0	−0.827966
$637$	0	0
$638$	−158.000	−0.00980451
$639$	−1488.00	−0.0921195
$640$	−640.000	−0.0395285
$641$	−23598.0	−1.45408	−0.727040	−	0.686595i	$-0.759104\pi$
$641$	−23598.0	−1.45408	−0.727040	+	0.686595i	$0.759104\pi$
$642$	−3140.00	−0.193031
$643$	−13349.0	−0.818714	−0.409357	−	0.912374i	$-0.634247\pi$
$643$	−13349.0	−0.818714	−0.409357	+	0.912374i	$0.634247\pi$
$644$	0	0
$645$	10550.0	0.644040
$646$	−3060.00	−0.186369
$647$	24488.0	1.48798	0.743990	−	0.668191i	$-0.232931\pi$
$647$	24488.0	1.48798	0.743990	+	0.668191i	$0.232931\pi$
$648$	−5368.00	−0.325424
$649$	628.000	0.0379833
$650$	−350.000	−0.0211202
$651$	0	0
$652$	−14648.0	−0.879847
$653$	21622.0	1.29576	0.647882	−	0.761740i	$-0.275655\pi$
$653$	21622.0	1.29576	0.647882	+	0.761740i	$0.275655\pi$
$654$	16110.0	0.963228
$655$	14570.0	0.869156
$656$	4928.00	0.293302
$657$	1452.00	0.0862221
$658$	0	0
$659$	−2973.00	−0.175738	−0.0878692	−	0.996132i	$-0.528006\pi$
$659$	−2973.00	−0.175738	−0.0878692	+	0.996132i	$0.528006\pi$
$660$	−100.000	−0.00589772
$661$	−18912.0	−1.11285	−0.556423	−	0.830899i	$-0.687827\pi$
$661$	−18912.0	−1.11285	−0.556423	+	0.830899i	$0.687827\pi$
$662$	−14072.0	−0.826169
$663$	1785.00	0.104561
$664$	−5152.00	−0.301109
$665$	0	0
$666$	760.000	0.0442183
$667$	−3950.00	−0.229302
$668$	1260.00	0.0729803
$669$	3465.00	0.200246
$670$	−10560.0	−0.608908
$671$	−684.000	−0.0393525
$672$	0	0
$673$	688.000	0.0394063	0.0197032	−	0.999806i	$-0.493728\pi$
$673$	688.000	0.0394063	0.0197032	+	0.999806i	$0.493728\pi$
$674$	20724.0	1.18436
$675$	3625.00	0.206706
$676$	−8592.00	−0.488848
$677$	−12791.0	−0.726142	−0.363071	−	0.931761i	$-0.618272\pi$
$677$	−12791.0	−0.726142	−0.363071	+	0.931761i	$0.618272\pi$
$678$	−3660.00	−0.207318
$679$	0	0
$680$	−2040.00	−0.115045
$681$	−21395.0	−1.20390
$682$	−424.000	−0.0238062
$683$	−7652.00	−0.428691	−0.214345	−	0.976758i	$-0.568762\pi$
$683$	−7652.00	−0.428691	−0.214345	+	0.976758i	$0.568762\pi$
$684$	240.000	0.0134161
$685$	−12840.0	−0.716192
$686$	0	0
$687$	−16580.0	−0.920766
$688$	6752.00	0.374153
$689$	−4648.00	−0.257002
$690$	−2500.00	−0.137932
$691$	2532.00	0.139395	0.0696974	−	0.997568i	$-0.477797\pi$
$691$	2532.00	0.139395	0.0696974	+	0.997568i	$0.477797\pi$
$692$	5004.00	0.274890
$693$	0	0
$694$	−16844.0	−0.921311
$695$	6370.00	0.347666
$696$	−3160.00	−0.172097
$697$	15708.0	0.853634
$698$	14700.0	0.797139
$699$	−19560.0	−1.05841
$700$	0	0
$701$	−2133.00	−0.114925	−0.0574624	−	0.998348i	$-0.518301\pi$
$701$	−2133.00	−0.114925	−0.0574624	+	0.998348i	$0.518301\pi$
$702$	−2030.00	−0.109142
$703$	5700.00	0.305803
$704$	−64.0000	−0.00342627
$705$	−3025.00	−0.161600
$706$	−6114.00	−0.325926
$707$	0	0
$708$	12560.0	0.666714
$709$	−19153.0	−1.01454	−0.507268	−	0.861788i	$-0.669345\pi$
$709$	−19153.0	−1.01454	−0.507268	+	0.861788i	$0.669345\pi$
$710$	−7440.00	−0.393265
$711$	814.000	0.0429358
$712$	7040.00	0.370555
$713$	−10600.0	−0.556765
$714$	0	0
$715$	−35.0000	−0.00183067
$716$	−592.000	−0.0308996
$717$	27255.0	1.41960
$718$	16784.0	0.872386
$719$	21334.0	1.10657	0.553285	−	0.832992i	$-0.313374\pi$
$719$	21334.0	1.10657	0.553285	+	0.832992i	$0.313374\pi$
$720$	160.000	0.00828173
$721$	0	0
$722$	−11918.0	−0.614324
$723$	1250.00	0.0642988
$724$	5376.00	0.275963
$725$	1975.00	0.101172
$726$	13300.0	0.679903
$727$	−11480.0	−0.585653	−0.292826	−	0.956166i	$-0.594596\pi$
$727$	−11480.0	−0.585653	−0.292826	+	0.956166i	$0.594596\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	7260.00	0.368089
$731$	21522.0	1.08895
$732$	−13680.0	−0.690748
$733$	−19763.0	−0.995857	−0.497928	−	0.867218i	$-0.665906\pi$
$733$	−19763.0	−0.995857	−0.497928	+	0.867218i	$0.665906\pi$
$734$	−16754.0	−0.842509
$735$	0	0
$736$	−1600.00	−0.0801315
$737$	−1056.00	−0.0527792
$738$	−1232.00	−0.0614506
$739$	−40153.0	−1.99872	−0.999359	−	0.0358110i	$-0.988599\pi$
$739$	−40153.0	−1.99872	−0.999359	+	0.0358110i	$0.988599\pi$
$740$	3800.00	0.188771
$741$	−1050.00	−0.0520549
$742$	0	0
$743$	−30896.0	−1.52552	−0.762762	−	0.646679i	$-0.776157\pi$
$743$	−30896.0	−1.52552	−0.762762	+	0.646679i	$0.776157\pi$
$744$	−8480.00	−0.417865
$745$	−2970.00	−0.146057
$746$	−3936.00	−0.193173
$747$	1288.00	0.0630863
$748$	−204.000	−0.00997190
$749$	0	0
$750$	1250.00	0.0608581
$751$	11969.0	0.581565	0.290782	−	0.956789i	$-0.406084\pi$
$751$	11969.0	0.581565	0.290782	+	0.956789i	$0.406084\pi$
$752$	−1936.00	−0.0938812
$753$	4550.00	0.220201
$754$	−1106.00	−0.0534193
$755$	7635.00	0.368035
$756$	0	0
$757$	−10456.0	−0.502021	−0.251010	−	0.967984i	$-0.580763\pi$
$757$	−10456.0	−0.502021	−0.251010	+	0.967984i	$0.580763\pi$
$758$	2104.00	0.100819
$759$	−250.000	−0.0119558
$760$	1200.00	0.0572744
$761$	28782.0	1.37102	0.685510	−	0.728063i	$-0.259579\pi$
$761$	28782.0	1.37102	0.685510	+	0.728063i	$0.259579\pi$
$762$	−6040.00	−0.287147
$763$	0	0
$764$	−2244.00	−0.106263
$765$	510.000	0.0241034
$766$	4616.00	0.217732
$767$	4396.00	0.206950
$768$	−1280.00	−0.0601407
$769$	14630.0	0.686048	0.343024	−	0.939327i	$-0.388549\pi$
$769$	14630.0	0.686048	0.343024	+	0.939327i	$0.388549\pi$
$770$	0	0
$771$	−32470.0	−1.51670
$772$	12064.0	0.562426
$773$	−24351.0	−1.13305	−0.566523	−	0.824046i	$-0.691712\pi$
$773$	−24351.0	−1.13305	−0.566523	+	0.824046i	$0.691712\pi$
$774$	−1688.00	−0.0783901
$775$	5300.00	0.245654
$776$	10808.0	0.499980
$777$	0	0
$778$	4562.00	0.210226
$779$	−9240.00	−0.424977
$780$	−700.000	−0.0321334
$781$	−744.000	−0.0340876
$782$	−5100.00	−0.233217
$783$	11455.0	0.522820
$784$	0	0
$785$	2650.00	0.120487
$786$	29140.0	1.32238
$787$	−2329.00	−0.105489	−0.0527445	−	0.998608i	$-0.516797\pi$
$787$	−2329.00	−0.105489	−0.0527445	+	0.998608i	$0.516797\pi$
$788$	−12928.0	−0.584443
$789$	−7170.00	−0.323522
$790$	4070.00	0.183296
$791$	0	0
$792$	16.0000	0.000717848 0
$793$	−4788.00	−0.214410
$794$	29270.0	1.30825
$795$	16600.0	0.740555
$796$	4656.00	0.207321
$797$	11067.0	0.491861	0.245931	−	0.969287i	$-0.420906\pi$
$797$	11067.0	0.491861	0.245931	+	0.969287i	$0.420906\pi$
$798$	0	0
$799$	−6171.00	−0.273234
$800$	800.000	0.0353553
$801$	−1760.00	−0.0776361
$802$	11282.0	0.496735
$803$	726.000	0.0319053
$804$	−21120.0	−0.926424
$805$	0	0
$806$	−2968.00	−0.129706
$807$	−25070.0	−1.09356
$808$	−432.000	−0.0188090
$809$	−3879.00	−0.168576	−0.0842882	−	0.996441i	$-0.526862\pi$
$809$	−3879.00	−0.168576	−0.0842882	+	0.996441i	$0.526862\pi$
$810$	6710.00	0.291068
$811$	−7518.00	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$811$	−7518.00	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$812$	0	0
$813$	27100.0	1.16905
$814$	380.000	0.0163624
$815$	18310.0	0.786959
$816$	−4080.00	−0.175035
$817$	−12660.0	−0.542126
$818$	−12820.0	−0.547972
$819$	0	0
$820$	−6160.00	−0.262337
$821$	39801.0	1.69192	0.845959	−	0.533248i	$-0.179029\pi$
$821$	39801.0	1.69192	0.845959	+	0.533248i	$0.179029\pi$
$822$	−25680.0	−1.08965
$823$	−3564.00	−0.150952	−0.0754758	−	0.997148i	$-0.524048\pi$
$823$	−3564.00	−0.150952	−0.0754758	+	0.997148i	$0.524048\pi$
$824$	8216.00	0.347352
$825$	125.000	0.00527508
$826$	0	0
$827$	10838.0	0.455712	0.227856	−	0.973695i	$-0.426828\pi$
$827$	10838.0	0.455712	0.227856	+	0.973695i	$0.426828\pi$
$828$	400.000	0.0167886
$829$	−41956.0	−1.75777	−0.878885	−	0.477033i	$-0.841712\pi$
$829$	−41956.0	−1.75777	−0.878885	+	0.477033i	$0.841712\pi$
$830$	6440.00	0.269320
$831$	−18370.0	−0.766845
$832$	−448.000	−0.0186678
$833$	0	0
$834$	12740.0	0.528957
$835$	−1575.00	−0.0652756
$836$	120.000	0.00496446
$837$	30740.0	1.26945
$838$	−9632.00	−0.397055
$839$	28714.0	1.18155	0.590773	−	0.806838i	$-0.298823\pi$
$839$	28714.0	1.18155	0.590773	+	0.806838i	$0.298823\pi$
$840$	0	0
$841$	−18148.0	−0.744106
$842$	30650.0	1.25448
$843$	−36655.0	−1.49759
$844$	2276.00	0.0928236
$845$	10740.0	0.437239
$846$	484.000	0.0196693
$847$	0	0
$848$	10624.0	0.430224
$849$	1355.00	0.0547744
$850$	2550.00	0.102899
$851$	9500.00	0.382674
$852$	−14880.0	−0.598334
$853$	−15442.0	−0.619841	−0.309920	−	0.950763i	$-0.600302\pi$
$853$	−15442.0	−0.619841	−0.309920	+	0.950763i	$0.600302\pi$
$854$	0	0
$855$	−300.000	−0.0119997
$856$	2512.00	0.100302
$857$	17978.0	0.716589	0.358295	−	0.933609i	$-0.383358\pi$
$857$	17978.0	0.716589	0.358295	+	0.933609i	$0.383358\pi$
$858$	−70.0000	−0.00278527
$859$	−19308.0	−0.766916	−0.383458	−	0.923558i	$-0.625267\pi$
$859$	−19308.0	−0.766916	−0.383458	+	0.923558i	$0.625267\pi$
$860$	−8440.00	−0.334653
$861$	0	0
$862$	3750.00	0.148173
$863$	17464.0	0.688855	0.344427	−	0.938813i	$-0.388073\pi$
$863$	17464.0	0.688855	0.344427	+	0.938813i	$0.388073\pi$
$864$	4640.00	0.182704
$865$	−6255.00	−0.245869
$866$	27748.0	1.08882
$867$	11560.0	0.452824
$868$	0	0
$869$	407.000	0.0158878
$870$	3950.00	0.153928
$871$	−7392.00	−0.287564
$872$	−12888.0	−0.500508
$873$	−2702.00	−0.104752
$874$	3000.00	0.116106
$875$	0	0
$876$	14520.0	0.560029
$877$	−23962.0	−0.922622	−0.461311	−	0.887239i	$-0.652621\pi$
$877$	−23962.0	−0.922622	−0.461311	+	0.887239i	$0.652621\pi$
$878$	6884.00	0.264606
$879$	21525.0	0.825962
$880$	80.0000	0.00306454
$881$	35168.0	1.34488	0.672440	−	0.740151i	$-0.265246\pi$
$881$	35168.0	1.34488	0.672440	+	0.740151i	$0.265246\pi$
$882$	0	0
$883$	−37896.0	−1.44428	−0.722142	−	0.691745i	$-0.756842\pi$
$883$	−37896.0	−1.44428	−0.722142	+	0.691745i	$0.756842\pi$
$884$	−1428.00	−0.0543313
$885$	−15700.0	−0.596327
$886$	33500.0	1.27026
$887$	−30368.0	−1.14956	−0.574779	−	0.818309i	$-0.694912\pi$
$887$	−30368.0	−1.14956	−0.574779	+	0.818309i	$0.694912\pi$
$888$	7600.00	0.287206
$889$	0	0
$890$	−8800.00	−0.331434
$891$	671.000	0.0252293
$892$	−2772.00	−0.104051
$893$	3630.00	0.136028
$894$	−5940.00	−0.222218
$895$	740.000	0.0276374
$896$	0	0
$897$	−1750.00	−0.0651402
$898$	1390.00	0.0516536
$899$	16748.0	0.621332
$900$	−200.000	−0.00740741
$901$	33864.0	1.25213
$902$	−616.000	−0.0227390
$903$	0	0
$904$	2928.00	0.107725
$905$	−6720.00	−0.246829
$906$	15270.0	0.559947
$907$	−33874.0	−1.24010	−0.620048	−	0.784564i	$-0.712887\pi$
$907$	−33874.0	−1.24010	−0.620048	+	0.784564i	$0.712887\pi$
$908$	17116.0	0.625567
$909$	108.000	0.00394074
$910$	0	0
$911$	24880.0	0.904842	0.452421	−	0.891804i	$-0.350560\pi$
$911$	24880.0	0.904842	0.452421	+	0.891804i	$0.350560\pi$
$912$	2400.00	0.0871403
$913$	644.000	0.0233442
$914$	11520.0	0.416901
$915$	17100.0	0.617824
$916$	13264.0	0.478444
$917$	0	0
$918$	14790.0	0.531746
$919$	−25299.0	−0.908092	−0.454046	−	0.890978i	$-0.650020\pi$
$919$	−25299.0	−0.908092	−0.454046	+	0.890978i	$0.650020\pi$
$920$	2000.00	0.0716718
$921$	13195.0	0.472085
$922$	−26880.0	−0.960136
$923$	−5208.00	−0.185724
$924$	0	0
$925$	−4750.00	−0.168842
$926$	−14696.0	−0.521534
$927$	−2054.00	−0.0727748
$928$	2528.00	0.0894242
$929$	−6792.00	−0.239869	−0.119934	−	0.992782i	$-0.538268\pi$
$929$	−6792.00	−0.239869	−0.119934	+	0.992782i	$0.538268\pi$
$930$	10600.0	0.373750
$931$	0	0
$932$	15648.0	0.549965
$933$	−42570.0	−1.49376
$934$	35850.0	1.25594
$935$	255.000	0.00891914
$936$	112.000	0.00391115
$937$	43575.0	1.51925	0.759623	−	0.650364i	$-0.225384\pi$
$937$	43575.0	1.51925	0.759623	+	0.650364i	$0.225384\pi$
$938$	0	0
$939$	1095.00	0.0380554
$940$	2420.00	0.0839699
$941$	−45372.0	−1.57182	−0.785911	−	0.618339i	$-0.787806\pi$
$941$	−45372.0	−1.57182	−0.785911	+	0.618339i	$0.787806\pi$
$942$	5300.00	0.183316
$943$	−15400.0	−0.531806
$944$	−10048.0	−0.346435
$945$	0	0
$946$	−844.000	−0.0290072
$947$	−39152.0	−1.34347	−0.671737	−	0.740790i	$-0.734451\pi$
$947$	−39152.0	−1.34347	−0.671737	+	0.740790i	$0.734451\pi$
$948$	8140.00	0.278876
$949$	5082.00	0.173834
$950$	−1500.00	−0.0512278
$951$	20130.0	0.686393
$952$	0	0
$953$	−18632.0	−0.633316	−0.316658	−	0.948540i	$-0.602561\pi$
$953$	−18632.0	−0.633316	−0.316658	+	0.948540i	$0.602561\pi$
$954$	−2656.00	−0.0901375
$955$	2805.00	0.0950447
$956$	−21804.0	−0.737648
$957$	395.000	0.0133423
$958$	−24692.0	−0.832737
$959$	0	0
$960$	1600.00	0.0537914
$961$	15153.0	0.508644
$962$	2660.00	0.0891495
$963$	−628.000	−0.0210146
$964$	−1000.00	−0.0334106
$965$	−15080.0	−0.503049
$966$	0	0
$967$	48862.0	1.62492	0.812459	−	0.583018i	$-0.198128\pi$
$967$	48862.0	1.62492	0.812459	+	0.583018i	$0.198128\pi$
$968$	−10640.0	−0.353288
$969$	7650.00	0.253615
$970$	−13510.0	−0.447196
$971$	−19896.0	−0.657562	−0.328781	−	0.944406i	$-0.606638\pi$
$971$	−19896.0	−0.657562	−0.328781	+	0.944406i	$0.606638\pi$
$972$	−2240.00	−0.0739177
$973$	0	0
$974$	30028.0	0.987843
$975$	875.000	0.0287410
$976$	10944.0	0.358923
$977$	5130.00	0.167987	0.0839935	−	0.996466i	$-0.473233\pi$
$977$	5130.00	0.167987	0.0839935	+	0.996466i	$0.473233\pi$
$978$	36620.0	1.19732
$979$	−880.000	−0.0287282
$980$	0	0
$981$	3222.00	0.104863
$982$	−9446.00	−0.306959
$983$	11573.0	0.375505	0.187752	−	0.982216i	$-0.439880\pi$
$983$	11573.0	0.375505	0.187752	+	0.982216i	$0.439880\pi$
$984$	−12320.0	−0.399133
$985$	16160.0	0.522742
$986$	8058.00	0.260263
$987$	0	0
$988$	840.000	0.0270485
$989$	−21100.0	−0.678403
$990$	−20.0000	−0.000642062 0
$991$	34600.0	1.10909	0.554544	−	0.832155i	$-0.312893\pi$
$991$	34600.0	1.10909	0.554544	+	0.832155i	$0.312893\pi$
$992$	6784.00	0.217129
$993$	35180.0	1.12427
$994$	0	0
$995$	−5820.00	−0.185434
$996$	12880.0	0.409757
$997$	15199.0	0.482806	0.241403	−	0.970425i	$-0.422393\pi$
$997$	15199.0	0.482806	0.241403	+	0.970425i	$0.422393\pi$
$998$	22454.0	0.712193
$999$	−27550.0	−0.872516

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.j.1.1		1
5.4	even	2		2450.4.a.r.1.1		1
7.2	even	3		490.4.e.g.361.1		2
7.3	odd	6		490.4.e.c.471.1		2
7.4	even	3		490.4.e.g.471.1		2
7.5	odd	6		490.4.e.c.361.1		2
7.6	odd	2		70.4.a.e.1.1	✓	1
21.20	even	2		630.4.a.b.1.1		1
28.27	even	2		560.4.a.f.1.1		1
35.13	even	4		350.4.c.k.99.1		2
35.27	even	4		350.4.c.k.99.2		2
35.34	odd	2		350.4.a.c.1.1		1
56.13	odd	2		2240.4.a.h.1.1		1
56.27	even	2		2240.4.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.e.1.1	✓	1	7.6	odd	2
350.4.a.c.1.1		1	35.34	odd	2
350.4.c.k.99.1		2	35.13	even	4
350.4.c.k.99.2		2	35.27	even	4
490.4.a.j.1.1		1	1.1	even	1	trivial
490.4.e.c.361.1		2	7.5	odd	6
490.4.e.c.471.1		2	7.3	odd	6
490.4.e.g.361.1		2	7.2	even	3
490.4.e.g.471.1		2	7.4	even	3
560.4.a.f.1.1		1	28.27	even	2
630.4.a.b.1.1		1	21.20	even	2
2240.4.a.h.1.1		1	56.13	odd	2
2240.4.a.bc.1.1		1	56.27	even	2
2450.4.a.r.1.1		1	5.4	even	2

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Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

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Groups

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	490.4.a.j.1.1

Level	$490$
Weight	$4$
Character	490.1
Self dual	yes
Analytic conductor	$28.911$
Analytic rank	$0$
Dimension	$1$
CM	no
Inner twists	$1$