LMFDB - Embedded newform 630.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(1,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("630.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.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:	$37.1712033036$
Analytic rank:	$1$
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	$\chi$	$=$	630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +33.0000 q^{11} -43.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -111.000 q^{17} -70.0000 q^{19} +20.0000 q^{20} -66.0000 q^{22} -42.0000 q^{23} +25.0000 q^{25} +86.0000 q^{26} +28.0000 q^{28} +225.000 q^{29} -88.0000 q^{31} -32.0000 q^{32} +222.000 q^{34} +35.0000 q^{35} -34.0000 q^{37} +140.000 q^{38} -40.0000 q^{40} -432.000 q^{41} -178.000 q^{43} +132.000 q^{44} +84.0000 q^{46} -411.000 q^{47} +49.0000 q^{49} -50.0000 q^{50} -172.000 q^{52} +708.000 q^{53} +165.000 q^{55} -56.0000 q^{56} -450.000 q^{58} -480.000 q^{59} +812.000 q^{61} +176.000 q^{62} +64.0000 q^{64} -215.000 q^{65} +596.000 q^{67} -444.000 q^{68} -70.0000 q^{70} -432.000 q^{71} -358.000 q^{73} +68.0000 q^{74} -280.000 q^{76} +231.000 q^{77} +425.000 q^{79} +80.0000 q^{80} +864.000 q^{82} -972.000 q^{83} -555.000 q^{85} +356.000 q^{86} -264.000 q^{88} -960.000 q^{89} -301.000 q^{91} -168.000 q^{92} +822.000 q^{94} -350.000 q^{95} -709.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	33.0000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	33.0000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	−43.0000	−0.917389	−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−43.0000	−0.917389	−0.458694	+	0.888594i	$0.651683\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−111.000	−1.58361	−0.791807	−	0.610771i	$-0.790860\pi$
$17$	−111.000	−1.58361	−0.791807	+	0.610771i	$0.790860\pi$
$18$	0	0
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−66.0000	−0.639602
$23$	−42.0000	−0.380765	−0.190383	−	0.981710i	$-0.560973\pi$
$23$	−42.0000	−0.380765	−0.190383	+	0.981710i	$0.560973\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	86.0000	0.648692
$27$	0	0
$28$	28.0000	0.188982
$29$	225.000	1.44074	0.720370	−	0.693590i	$-0.243972\pi$
$29$	225.000	1.44074	0.720370	+	0.693590i	$0.243972\pi$
$30$	0	0
$31$	−88.0000	−0.509847	−0.254924	−	0.966961i	$-0.582050\pi$
$31$	−88.0000	−0.509847	−0.254924	+	0.966961i	$0.582050\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	222.000	1.11978
$35$	35.0000	0.169031
$36$	0	0
$37$	−34.0000	−0.151069	−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000	−0.151069	−0.0755347	+	0.997143i	$0.524066\pi$
$38$	140.000	0.597658
$39$	0	0
$40$	−40.0000	−0.158114
$41$	−432.000	−1.64554	−0.822769	−	0.568376i	$-0.807572\pi$
$41$	−432.000	−1.64554	−0.822769	+	0.568376i	$0.807572\pi$
$42$	0	0
$43$	−178.000	−0.631273	−0.315637	−	0.948880i	$-0.602218\pi$
$43$	−178.000	−0.631273	−0.315637	+	0.948880i	$0.602218\pi$
$44$	132.000	0.452267
$45$	0	0
$46$	84.0000	0.269242
$47$	−411.000	−1.27554	−0.637771	−	0.770226i	$-0.720144\pi$
$47$	−411.000	−1.27554	−0.637771	+	0.770226i	$0.720144\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	0	0
$52$	−172.000	−0.458694
$53$	708.000	1.83493	0.917465	−	0.397817i	$-0.130232\pi$
$53$	708.000	1.83493	0.917465	+	0.397817i	$0.130232\pi$
$54$	0	0
$55$	165.000	0.404520
$56$	−56.0000	−0.133631
$57$	0	0
$58$	−450.000	−1.01876
$59$	−480.000	−1.05916	−0.529582	−	0.848259i	$-0.677651\pi$
$59$	−480.000	−1.05916	−0.529582	+	0.848259i	$0.677651\pi$
$60$	0	0
$61$	812.000	1.70436	0.852180	−	0.523249i	$-0.175280\pi$
$61$	812.000	1.70436	0.852180	+	0.523249i	$0.175280\pi$
$62$	176.000	0.360516
$63$	0	0
$64$	64.0000	0.125000
$65$	−215.000	−0.410269
$66$	0	0
$67$	596.000	1.08676	0.543381	−	0.839487i	$-0.317144\pi$
$67$	596.000	1.08676	0.543381	+	0.839487i	$0.317144\pi$
$68$	−444.000	−0.791807
$69$	0	0
$70$	−70.0000	−0.119523
$71$	−432.000	−0.722098	−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000	−0.722098	−0.361049	+	0.932547i	$0.617581\pi$
$72$	0	0
$73$	−358.000	−0.573983	−0.286991	−	0.957933i	$-0.592655\pi$
$73$	−358.000	−0.573983	−0.286991	+	0.957933i	$0.592655\pi$
$74$	68.0000	0.106822
$75$	0	0
$76$	−280.000	−0.422608
$77$	231.000	0.341882
$78$	0	0
$79$	425.000	0.605269	0.302634	−	0.953107i	$-0.402134\pi$
$79$	425.000	0.605269	0.302634	+	0.953107i	$0.402134\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	864.000	1.16357
$83$	−972.000	−1.28543	−0.642716	−	0.766105i	$-0.722192\pi$
$83$	−972.000	−1.28543	−0.642716	+	0.766105i	$0.722192\pi$
$84$	0	0
$85$	−555.000	−0.708214
$86$	356.000	0.446378
$87$	0	0
$88$	−264.000	−0.319801
$89$	−960.000	−1.14337	−0.571684	−	0.820474i	$-0.693710\pi$
$89$	−960.000	−1.14337	−0.571684	+	0.820474i	$0.693710\pi$
$90$	0	0
$91$	−301.000	−0.346740
$92$	−168.000	−0.190383
$93$	0	0
$94$	822.000	0.901945
$95$	−350.000	−0.377992
$96$	0	0
$97$	−709.000	−0.742145	−0.371072	−	0.928604i	$-0.621010\pi$
$97$	−709.000	−0.742145	−0.371072	+	0.928604i	$0.621010\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	438.000	0.431511	0.215756	−	0.976447i	$-0.430779\pi$
$101$	438.000	0.431511	0.215756	+	0.976447i	$0.430779\pi$
$102$	0	0
$103$	−1033.00	−0.988199	−0.494100	−	0.869405i	$-0.664502\pi$
$103$	−1033.00	−0.988199	−0.494100	+	0.869405i	$0.664502\pi$
$104$	344.000	0.324346
$105$	0	0
$106$	−1416.00	−1.29749
$107$	−906.000	−0.818564	−0.409282	−	0.912408i	$-0.634221\pi$
$107$	−906.000	−0.818564	−0.409282	+	0.912408i	$0.634221\pi$
$108$	0	0
$109$	−1915.00	−1.68279	−0.841393	−	0.540423i	$-0.818264\pi$
$109$	−1915.00	−1.68279	−0.841393	+	0.540423i	$0.818264\pi$
$110$	−330.000	−0.286039
$111$	0	0
$112$	112.000	0.0944911
$113$	558.000	0.464533	0.232266	−	0.972652i	$-0.425386\pi$
$113$	558.000	0.464533	0.232266	+	0.972652i	$0.425386\pi$
$114$	0	0
$115$	−210.000	−0.170283
$116$	900.000	0.720370
$117$	0	0
$118$	960.000	0.748942
$119$	−777.000	−0.598550
$120$	0	0
$121$	−242.000	−0.181818
$122$	−1624.00	−1.20516
$123$	0	0
$124$	−352.000	−0.254924
$125$	125.000	0.0894427
$126$	0	0
$127$	−1744.00	−1.21854	−0.609272	−	0.792962i	$-0.708538\pi$
$127$	−1744.00	−1.21854	−0.609272	+	0.792962i	$0.708538\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	430.000	0.290104
$131$	318.000	0.212090	0.106045	−	0.994361i	$-0.466181\pi$
$131$	318.000	0.212090	0.106045	+	0.994361i	$0.466181\pi$
$132$	0	0
$133$	−490.000	−0.319462
$134$	−1192.00	−0.768456
$135$	0	0
$136$	888.000	0.559892
$137$	−2496.00	−1.55655	−0.778276	−	0.627922i	$-0.783906\pi$
$137$	−2496.00	−1.55655	−0.778276	+	0.627922i	$0.783906\pi$
$138$	0	0
$139$	1370.00	0.835985	0.417992	−	0.908451i	$-0.362734\pi$
$139$	1370.00	0.835985	0.417992	+	0.908451i	$0.362734\pi$
$140$	140.000	0.0845154
$141$	0	0
$142$	864.000	0.510600
$143$	−1419.00	−0.829809
$144$	0	0
$145$	1125.00	0.644318
$146$	716.000	0.405867
$147$	0	0
$148$	−136.000	−0.0755347
$149$	−2490.00	−1.36905	−0.684526	−	0.728988i	$-0.739991\pi$
$149$	−2490.00	−1.36905	−0.684526	+	0.728988i	$0.739991\pi$
$150$	0	0
$151$	137.000	0.0738338	0.0369169	−	0.999318i	$-0.488246\pi$
$151$	137.000	0.0738338	0.0369169	+	0.999318i	$0.488246\pi$
$152$	560.000	0.298829
$153$	0	0
$154$	−462.000	−0.241747
$155$	−440.000	−0.228011
$156$	0	0
$157$	−3274.00	−1.66429	−0.832145	−	0.554558i	$-0.812888\pi$
$157$	−3274.00	−1.66429	−0.832145	+	0.554558i	$0.812888\pi$
$158$	−850.000	−0.427990
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−294.000	−0.143916
$162$	0	0
$163$	902.000	0.433436	0.216718	−	0.976234i	$-0.430465\pi$
$163$	902.000	0.433436	0.216718	+	0.976234i	$0.430465\pi$
$164$	−1728.00	−0.822769
$165$	0	0
$166$	1944.00	0.908938
$167$	3969.00	1.83910	0.919552	−	0.392968i	$-0.128552\pi$
$167$	3969.00	1.83910	0.919552	+	0.392968i	$0.128552\pi$
$168$	0	0
$169$	−348.000	−0.158398
$170$	1110.00	0.500783
$171$	0	0
$172$	−712.000	−0.315637
$173$	1713.00	0.752815	0.376407	−	0.926454i	$-0.377159\pi$
$173$	1713.00	0.752815	0.376407	+	0.926454i	$0.377159\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	528.000	0.226134
$177$	0	0
$178$	1920.00	0.808484
$179$	3660.00	1.52828	0.764138	−	0.645053i	$-0.223165\pi$
$179$	3660.00	1.52828	0.764138	+	0.645053i	$0.223165\pi$
$180$	0	0
$181$	−1708.00	−0.701407	−0.350703	−	0.936487i	$-0.614057\pi$
$181$	−1708.00	−0.701407	−0.350703	+	0.936487i	$0.614057\pi$
$182$	602.000	0.245182
$183$	0	0
$184$	336.000	0.134621
$185$	−170.000	−0.0675603
$186$	0	0
$187$	−3663.00	−1.43243
$188$	−1644.00	−0.637771
$189$	0	0
$190$	700.000	0.267281
$191$	2073.00	0.785325	0.392662	−	0.919683i	$-0.371554\pi$
$191$	2073.00	0.785325	0.392662	+	0.919683i	$0.371554\pi$
$192$	0	0
$193$	−3688.00	−1.37548	−0.687741	−	0.725956i	$-0.741398\pi$
$193$	−3688.00	−1.37548	−0.687741	+	0.725956i	$0.741398\pi$
$194$	1418.00	0.524776
$195$	0	0
$196$	196.000	0.0714286
$197$	−3276.00	−1.18480	−0.592399	−	0.805644i	$-0.701819\pi$
$197$	−3276.00	−1.18480	−0.592399	+	0.805644i	$0.701819\pi$
$198$	0	0
$199$	2360.00	0.840683	0.420342	−	0.907366i	$-0.361910\pi$
$199$	2360.00	0.840683	0.420342	+	0.907366i	$0.361910\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−876.000	−0.305124
$203$	1575.00	0.544548
$204$	0	0
$205$	−2160.00	−0.735907
$206$	2066.00	0.698762
$207$	0	0
$208$	−688.000	−0.229347
$209$	−2310.00	−0.764527
$210$	0	0
$211$	2657.00	0.866898	0.433449	−	0.901178i	$-0.357296\pi$
$211$	2657.00	0.866898	0.433449	+	0.901178i	$0.357296\pi$
$212$	2832.00	0.917465
$213$	0	0
$214$	1812.00	0.578812
$215$	−890.000	−0.282314
$216$	0	0
$217$	−616.000	−0.192704
$218$	3830.00	1.18991
$219$	0	0
$220$	660.000	0.202260
$221$	4773.00	1.45279
$222$	0	0
$223$	47.0000	0.0141137	0.00705684	−	0.999975i	$-0.497754\pi$
$223$	47.0000	0.0141137	0.00705684	+	0.999975i	$0.497754\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−1116.00	−0.328474
$227$	−6051.00	−1.76925	−0.884623	−	0.466306i	$-0.845584\pi$
$227$	−6051.00	−1.76925	−0.884623	+	0.466306i	$0.845584\pi$
$228$	0	0
$229$	3080.00	0.888787	0.444393	−	0.895832i	$-0.353419\pi$
$229$	3080.00	0.888787	0.444393	+	0.895832i	$0.353419\pi$
$230$	420.000	0.120409
$231$	0	0
$232$	−1800.00	−0.509378
$233$	3288.00	0.924481	0.462240	−	0.886755i	$-0.347046\pi$
$233$	3288.00	0.924481	0.462240	+	0.886755i	$0.347046\pi$
$234$	0	0
$235$	−2055.00	−0.570440
$236$	−1920.00	−0.529582
$237$	0	0
$238$	1554.00	0.423239
$239$	1755.00	0.474985	0.237493	−	0.971389i	$-0.423674\pi$
$239$	1755.00	0.474985	0.237493	+	0.971389i	$0.423674\pi$
$240$	0	0
$241$	2.00000	0.000534570 0	0.000267285	−	1.00000i	$-0.499915\pi$
$241$	2.00000	0.000534570 0	0.000267285		1.00000i	$0.499915\pi$
$242$	484.000	0.128565
$243$	0	0
$244$	3248.00	0.852180
$245$	245.000	0.0638877
$246$	0	0
$247$	3010.00	0.775392
$248$	704.000	0.180258
$249$	0	0
$250$	−250.000	−0.0632456
$251$	5418.00	1.36247	0.681237	−	0.732063i	$-0.261442\pi$
$251$	5418.00	1.36247	0.681237	+	0.732063i	$0.261442\pi$
$252$	0	0
$253$	−1386.00	−0.344415
$254$	3488.00	0.861640
$255$	0	0
$256$	256.000	0.0625000
$257$	2154.00	0.522813	0.261406	−	0.965229i	$-0.415814\pi$
$257$	2154.00	0.522813	0.261406	+	0.965229i	$0.415814\pi$
$258$	0	0
$259$	−238.000	−0.0570988
$260$	−860.000	−0.205134
$261$	0	0
$262$	−636.000	−0.149970
$263$	−3882.00	−0.910169	−0.455084	−	0.890448i	$-0.650391\pi$
$263$	−3882.00	−0.910169	−0.455084	+	0.890448i	$0.650391\pi$
$264$	0	0
$265$	3540.00	0.820606
$266$	980.000	0.225893
$267$	0	0
$268$	2384.00	0.543381
$269$	−570.000	−0.129195	−0.0645976	−	0.997911i	$-0.520576\pi$
$269$	−570.000	−0.129195	−0.0645976	+	0.997911i	$0.520576\pi$
$270$	0	0
$271$	3332.00	0.746880	0.373440	−	0.927654i	$-0.378178\pi$
$271$	3332.00	0.746880	0.373440	+	0.927654i	$0.378178\pi$
$272$	−1776.00	−0.395904
$273$	0	0
$274$	4992.00	1.10065
$275$	825.000	0.180907
$276$	0	0
$277$	−394.000	−0.0854627	−0.0427313	−	0.999087i	$-0.513606\pi$
$277$	−394.000	−0.0854627	−0.0427313	+	0.999087i	$0.513606\pi$
$278$	−2740.00	−0.591131
$279$	0	0
$280$	−280.000	−0.0597614
$281$	−3267.00	−0.693569	−0.346784	−	0.937945i	$-0.612726\pi$
$281$	−3267.00	−0.693569	−0.346784	+	0.937945i	$0.612726\pi$
$282$	0	0
$283$	677.000	0.142203	0.0711015	−	0.997469i	$-0.477349\pi$
$283$	677.000	0.142203	0.0711015	+	0.997469i	$0.477349\pi$
$284$	−1728.00	−0.361049
$285$	0	0
$286$	2838.00	0.586764
$287$	−3024.00	−0.621955
$288$	0	0
$289$	7408.00	1.50784
$290$	−2250.00	−0.455602
$291$	0	0
$292$	−1432.00	−0.286991
$293$	8613.00	1.71733	0.858664	−	0.512540i	$-0.171295\pi$
$293$	8613.00	1.71733	0.858664	+	0.512540i	$0.171295\pi$
$294$	0	0
$295$	−2400.00	−0.473673
$296$	272.000	0.0534111
$297$	0	0
$298$	4980.00	0.968066
$299$	1806.00	0.349310
$300$	0	0
$301$	−1246.00	−0.238599
$302$	−274.000	−0.0522084
$303$	0	0
$304$	−1120.00	−0.211304
$305$	4060.00	0.762213
$306$	0	0
$307$	−3499.00	−0.650484	−0.325242	−	0.945631i	$-0.605446\pi$
$307$	−3499.00	−0.650484	−0.325242	+	0.945631i	$0.605446\pi$
$308$	924.000	0.170941
$309$	0	0
$310$	880.000	0.161228
$311$	−5682.00	−1.03600	−0.518001	−	0.855380i	$-0.673324\pi$
$311$	−5682.00	−1.03600	−0.518001	+	0.855380i	$0.673324\pi$
$312$	0	0
$313$	4097.00	0.739860	0.369930	−	0.929060i	$-0.379382\pi$
$313$	4097.00	0.739860	0.369930	+	0.929060i	$0.379382\pi$
$314$	6548.00	1.17683
$315$	0	0
$316$	1700.00	0.302634
$317$	4674.00	0.828132	0.414066	−	0.910247i	$-0.364108\pi$
$317$	4674.00	0.828132	0.414066	+	0.910247i	$0.364108\pi$
$318$	0	0
$319$	7425.00	1.30320
$320$	320.000	0.0559017
$321$	0	0
$322$	588.000	0.101764
$323$	7770.00	1.33850
$324$	0	0
$325$	−1075.00	−0.183478
$326$	−1804.00	−0.306486
$327$	0	0
$328$	3456.00	0.581786
$329$	−2877.00	−0.482110
$330$	0	0
$331$	10172.0	1.68913	0.844567	−	0.535449i	$-0.179858\pi$
$331$	10172.0	1.68913	0.844567	+	0.535449i	$0.179858\pi$
$332$	−3888.00	−0.642716
$333$	0	0
$334$	−7938.00	−1.30044
$335$	2980.00	0.486014
$336$	0	0
$337$	−9394.00	−1.51847	−0.759234	−	0.650818i	$-0.774426\pi$
$337$	−9394.00	−1.51847	−0.759234	+	0.650818i	$0.774426\pi$
$338$	696.000	0.112004
$339$	0	0
$340$	−2220.00	−0.354107
$341$	−2904.00	−0.461174
$342$	0	0
$343$	343.000	0.0539949
$344$	1424.00	0.223189
$345$	0	0
$346$	−3426.00	−0.532321
$347$	−4566.00	−0.706385	−0.353193	−	0.935551i	$-0.614904\pi$
$347$	−4566.00	−0.706385	−0.353193	+	0.935551i	$0.614904\pi$
$348$	0	0
$349$	−6730.00	−1.03223	−0.516116	−	0.856519i	$-0.672622\pi$
$349$	−6730.00	−1.03223	−0.516116	+	0.856519i	$0.672622\pi$
$350$	−350.000	−0.0534522
$351$	0	0
$352$	−1056.00	−0.159901
$353$	−3027.00	−0.456405	−0.228202	−	0.973614i	$-0.573285\pi$
$353$	−3027.00	−0.456405	−0.228202	+	0.973614i	$0.573285\pi$
$354$	0	0
$355$	−2160.00	−0.322932
$356$	−3840.00	−0.571684
$357$	0	0
$358$	−7320.00	−1.08065
$359$	−2760.00	−0.405758	−0.202879	−	0.979204i	$-0.565030\pi$
$359$	−2760.00	−0.405758	−0.202879	+	0.979204i	$0.565030\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	3416.00	0.495970
$363$	0	0
$364$	−1204.00	−0.173370
$365$	−1790.00	−0.256693
$366$	0	0
$367$	6131.00	0.872032	0.436016	−	0.899939i	$-0.356389\pi$
$367$	6131.00	0.872032	0.436016	+	0.899939i	$0.356389\pi$
$368$	−672.000	−0.0951914
$369$	0	0
$370$	340.000	0.0477723
$371$	4956.00	0.693538
$372$	0	0
$373$	9632.00	1.33707	0.668534	−	0.743682i	$-0.266922\pi$
$373$	9632.00	1.33707	0.668534	+	0.743682i	$0.266922\pi$
$374$	7326.00	1.01288
$375$	0	0
$376$	3288.00	0.450972
$377$	−9675.00	−1.32172
$378$	0	0
$379$	−9700.00	−1.31466	−0.657329	−	0.753604i	$-0.728314\pi$
$379$	−9700.00	−1.31466	−0.657329	+	0.753604i	$0.728314\pi$
$380$	−1400.00	−0.188996
$381$	0	0
$382$	−4146.00	−0.555308
$383$	−1212.00	−0.161698	−0.0808490	−	0.996726i	$-0.525763\pi$
$383$	−1212.00	−0.161698	−0.0808490	+	0.996726i	$0.525763\pi$
$384$	0	0
$385$	1155.00	0.152894
$386$	7376.00	0.972613
$387$	0	0
$388$	−2836.00	−0.371072
$389$	−4305.00	−0.561111	−0.280555	−	0.959838i	$-0.590519\pi$
$389$	−4305.00	−0.561111	−0.280555	+	0.959838i	$0.590519\pi$
$390$	0	0
$391$	4662.00	0.602986
$392$	−392.000	−0.0505076
$393$	0	0
$394$	6552.00	0.837779
$395$	2125.00	0.270684
$396$	0	0
$397$	−1609.00	−0.203409	−0.101705	−	0.994815i	$-0.532430\pi$
$397$	−1609.00	−0.203409	−0.101705	+	0.994815i	$0.532430\pi$
$398$	−4720.00	−0.594453
$399$	0	0
$400$	400.000	0.0500000
$401$	13503.0	1.68157	0.840783	−	0.541373i	$-0.182095\pi$
$401$	13503.0	1.68157	0.840783	+	0.541373i	$0.182095\pi$
$402$	0	0
$403$	3784.00	0.467728
$404$	1752.00	0.215756
$405$	0	0
$406$	−3150.00	−0.385054
$407$	−1122.00	−0.136647
$408$	0	0
$409$	470.000	0.0568215	0.0284108	−	0.999596i	$-0.490955\pi$
$409$	470.000	0.0568215	0.0284108	+	0.999596i	$0.490955\pi$
$410$	4320.00	0.520365
$411$	0	0
$412$	−4132.00	−0.494100
$413$	−3360.00	−0.400326
$414$	0	0
$415$	−4860.00	−0.574863
$416$	1376.00	0.162173
$417$	0	0
$418$	4620.00	0.540602
$419$	11700.0	1.36416	0.682079	−	0.731278i	$-0.261076\pi$
$419$	11700.0	1.36416	0.682079	+	0.731278i	$0.261076\pi$
$420$	0	0
$421$	−6163.00	−0.713459	−0.356730	−	0.934208i	$-0.616108\pi$
$421$	−6163.00	−0.713459	−0.356730	+	0.934208i	$0.616108\pi$
$422$	−5314.00	−0.612989
$423$	0	0
$424$	−5664.00	−0.648746
$425$	−2775.00	−0.316723
$426$	0	0
$427$	5684.00	0.644187
$428$	−3624.00	−0.409282
$429$	0	0
$430$	1780.00	0.199626
$431$	−5187.00	−0.579696	−0.289848	−	0.957073i	$-0.593605\pi$
$431$	−5187.00	−0.579696	−0.289848	+	0.957073i	$0.593605\pi$
$432$	0	0
$433$	2882.00	0.319862	0.159931	−	0.987128i	$-0.448873\pi$
$433$	2882.00	0.319862	0.159931	+	0.987128i	$0.448873\pi$
$434$	1232.00	0.136262
$435$	0	0
$436$	−7660.00	−0.841393
$437$	2940.00	0.321829
$438$	0	0
$439$	9830.00	1.06870	0.534351	−	0.845263i	$-0.320556\pi$
$439$	9830.00	1.06870	0.534351	+	0.845263i	$0.320556\pi$
$440$	−1320.00	−0.143019
$441$	0	0
$442$	−9546.00	−1.02728
$443$	5178.00	0.555337	0.277668	−	0.960677i	$-0.410438\pi$
$443$	5178.00	0.555337	0.277668	+	0.960677i	$0.410438\pi$
$444$	0	0
$445$	−4800.00	−0.511330
$446$	−94.0000	−0.00997989
$447$	0	0
$448$	448.000	0.0472456
$449$	4545.00	0.477710	0.238855	−	0.971055i	$-0.423228\pi$
$449$	4545.00	0.477710	0.238855	+	0.971055i	$0.423228\pi$
$450$	0	0
$451$	−14256.0	−1.48845
$452$	2232.00	0.232266
$453$	0	0
$454$	12102.0	1.25105
$455$	−1505.00	−0.155067
$456$	0	0
$457$	−484.000	−0.0495417	−0.0247709	−	0.999693i	$-0.507886\pi$
$457$	−484.000	−0.0495417	−0.0247709	+	0.999693i	$0.507886\pi$
$458$	−6160.00	−0.628467
$459$	0	0
$460$	−840.000	−0.0851417
$461$	1368.00	0.138208	0.0691042	−	0.997609i	$-0.477986\pi$
$461$	1368.00	0.138208	0.0691042	+	0.997609i	$0.477986\pi$
$462$	0	0
$463$	14852.0	1.49078	0.745390	−	0.666629i	$-0.232263\pi$
$463$	14852.0	1.49078	0.745390	+	0.666629i	$0.232263\pi$
$464$	3600.00	0.360185
$465$	0	0
$466$	−6576.00	−0.653707
$467$	−7521.00	−0.745247	−0.372624	−	0.927983i	$-0.621542\pi$
$467$	−7521.00	−0.745247	−0.372624	+	0.927983i	$0.621542\pi$
$468$	0	0
$469$	4172.00	0.410757
$470$	4110.00	0.403362
$471$	0	0
$472$	3840.00	0.374471
$473$	−5874.00	−0.571008
$474$	0	0
$475$	−1750.00	−0.169043
$476$	−3108.00	−0.299275
$477$	0	0
$478$	−3510.00	−0.335865
$479$	−8850.00	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$479$	−8850.00	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$480$	0	0
$481$	1462.00	0.138589
$482$	−4.00000	−0.000377998 0
$483$	0	0
$484$	−968.000	−0.0909091
$485$	−3545.00	−0.331897
$486$	0	0
$487$	−14614.0	−1.35980	−0.679901	−	0.733304i	$-0.737977\pi$
$487$	−14614.0	−1.35980	−0.679901	+	0.733304i	$0.737977\pi$
$488$	−6496.00	−0.602582
$489$	0	0
$490$	−490.000	−0.0451754
$491$	−15237.0	−1.40048	−0.700241	−	0.713907i	$-0.746924\pi$
$491$	−15237.0	−1.40048	−0.700241	+	0.713907i	$0.746924\pi$
$492$	0	0
$493$	−24975.0	−2.28158
$494$	−6020.00	−0.548285
$495$	0	0
$496$	−1408.00	−0.127462
$497$	−3024.00	−0.272927
$498$	0	0
$499$	−9565.00	−0.858093	−0.429046	−	0.903282i	$-0.641150\pi$
$499$	−9565.00	−0.858093	−0.429046	+	0.903282i	$0.641150\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	−10836.0	−0.963415
$503$	7263.00	0.643819	0.321910	−	0.946770i	$-0.395675\pi$
$503$	7263.00	0.643819	0.321910	+	0.946770i	$0.395675\pi$
$504$	0	0
$505$	2190.00	0.192978
$506$	2772.00	0.243538
$507$	0	0
$508$	−6976.00	−0.609272
$509$	7230.00	0.629596	0.314798	−	0.949159i	$-0.398063\pi$
$509$	7230.00	0.629596	0.314798	+	0.949159i	$0.398063\pi$
$510$	0	0
$511$	−2506.00	−0.216945
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−4308.00	−0.369684
$515$	−5165.00	−0.441936
$516$	0	0
$517$	−13563.0	−1.15377
$518$	476.000	0.0403750
$519$	0	0
$520$	1720.00	0.145052
$521$	−4962.00	−0.417254	−0.208627	−	0.977995i	$-0.566899\pi$
$521$	−4962.00	−0.417254	−0.208627	+	0.977995i	$0.566899\pi$
$522$	0	0
$523$	13772.0	1.15145	0.575724	−	0.817644i	$-0.304720\pi$
$523$	13772.0	1.15145	0.575724	+	0.817644i	$0.304720\pi$
$524$	1272.00	0.106045
$525$	0	0
$526$	7764.00	0.643586
$527$	9768.00	0.807402
$528$	0	0
$529$	−10403.0	−0.855018
$530$	−7080.00	−0.580256
$531$	0	0
$532$	−1960.00	−0.159731
$533$	18576.0	1.50960
$534$	0	0
$535$	−4530.00	−0.366073
$536$	−4768.00	−0.384228
$537$	0	0
$538$	1140.00	0.0913548
$539$	1617.00	0.129219
$540$	0	0
$541$	−3193.00	−0.253748	−0.126874	−	0.991919i	$-0.540494\pi$
$541$	−3193.00	−0.253748	−0.126874	+	0.991919i	$0.540494\pi$
$542$	−6664.00	−0.528124
$543$	0	0
$544$	3552.00	0.279946
$545$	−9575.00	−0.752565
$546$	0	0
$547$	22916.0	1.79126	0.895628	−	0.444803i	$-0.146726\pi$
$547$	22916.0	1.79126	0.895628	+	0.444803i	$0.146726\pi$
$548$	−9984.00	−0.778276
$549$	0	0
$550$	−1650.00	−0.127920
$551$	−15750.0	−1.21774
$552$	0	0
$553$	2975.00	0.228770
$554$	788.000	0.0604312
$555$	0	0
$556$	5480.00	0.417992
$557$	−15096.0	−1.14836	−0.574181	−	0.818728i	$-0.694680\pi$
$557$	−15096.0	−1.14836	−0.574181	+	0.818728i	$0.694680\pi$
$558$	0	0
$559$	7654.00	0.579123
$560$	560.000	0.0422577
$561$	0	0
$562$	6534.00	0.490427
$563$	−7932.00	−0.593773	−0.296886	−	0.954913i	$-0.595948\pi$
$563$	−7932.00	−0.593773	−0.296886	+	0.954913i	$0.595948\pi$
$564$	0	0
$565$	2790.00	0.207745
$566$	−1354.00	−0.100553
$567$	0	0
$568$	3456.00	0.255300
$569$	12990.0	0.957063	0.478532	−	0.878070i	$-0.341169\pi$
$569$	12990.0	0.957063	0.478532	+	0.878070i	$0.341169\pi$
$570$	0	0
$571$	20252.0	1.48427	0.742136	−	0.670249i	$-0.233813\pi$
$571$	20252.0	1.48427	0.742136	+	0.670249i	$0.233813\pi$
$572$	−5676.00	−0.414905
$573$	0	0
$574$	6048.00	0.439789
$575$	−1050.00	−0.0761531
$576$	0	0
$577$	−24379.0	−1.75894	−0.879472	−	0.475950i	$-0.842104\pi$
$577$	−24379.0	−1.75894	−0.879472	+	0.475950i	$0.842104\pi$
$578$	−14816.0	−1.06620
$579$	0	0
$580$	4500.00	0.322159
$581$	−6804.00	−0.485848
$582$	0	0
$583$	23364.0	1.65976
$584$	2864.00	0.202933
$585$	0	0
$586$	−17226.0	−1.21433
$587$	2304.00	0.162004	0.0810019	−	0.996714i	$-0.474188\pi$
$587$	2304.00	0.162004	0.0810019	+	0.996714i	$0.474188\pi$
$588$	0	0
$589$	6160.00	0.430931
$590$	4800.00	0.334937
$591$	0	0
$592$	−544.000	−0.0377673
$593$	−6837.00	−0.473460	−0.236730	−	0.971575i	$-0.576076\pi$
$593$	−6837.00	−0.473460	−0.236730	+	0.971575i	$0.576076\pi$
$594$	0	0
$595$	−3885.00	−0.267680
$596$	−9960.00	−0.684526
$597$	0	0
$598$	−3612.00	−0.246999
$599$	8925.00	0.608791	0.304395	−	0.952546i	$-0.401546\pi$
$599$	8925.00	0.608791	0.304395	+	0.952546i	$0.401546\pi$
$600$	0	0
$601$	20342.0	1.38064	0.690322	−	0.723502i	$-0.257469\pi$
$601$	20342.0	1.38064	0.690322	+	0.723502i	$0.257469\pi$
$602$	2492.00	0.168715
$603$	0	0
$604$	548.000	0.0369169
$605$	−1210.00	−0.0813116
$606$	0	0
$607$	−27439.0	−1.83479	−0.917393	−	0.397983i	$-0.869710\pi$
$607$	−27439.0	−1.83479	−0.917393	+	0.397983i	$0.869710\pi$
$608$	2240.00	0.149414
$609$	0	0
$610$	−8120.00	−0.538966
$611$	17673.0	1.17017
$612$	0	0
$613$	6842.00	0.450809	0.225404	−	0.974265i	$-0.427630\pi$
$613$	6842.00	0.450809	0.225404	+	0.974265i	$0.427630\pi$
$614$	6998.00	0.459961
$615$	0	0
$616$	−1848.00	−0.120873
$617$	10494.0	0.684720	0.342360	−	0.939569i	$-0.388774\pi$
$617$	10494.0	0.684720	0.342360	+	0.939569i	$0.388774\pi$
$618$	0	0
$619$	22970.0	1.49151	0.745753	−	0.666223i	$-0.232090\pi$
$619$	22970.0	1.49151	0.745753	+	0.666223i	$0.232090\pi$
$620$	−1760.00	−0.114005
$621$	0	0
$622$	11364.0	0.732564
$623$	−6720.00	−0.432153
$624$	0	0
$625$	625.000	0.0400000
$626$	−8194.00	−0.523160
$627$	0	0
$628$	−13096.0	−0.832145
$629$	3774.00	0.239236
$630$	0	0
$631$	6347.00	0.400428	0.200214	−	0.979752i	$-0.435836\pi$
$631$	6347.00	0.400428	0.200214	+	0.979752i	$0.435836\pi$
$632$	−3400.00	−0.213995
$633$	0	0
$634$	−9348.00	−0.585578
$635$	−8720.00	−0.544949
$636$	0	0
$637$	−2107.00	−0.131056
$638$	−14850.0	−0.921500
$639$	0	0
$640$	−640.000	−0.0395285
$641$	−13602.0	−0.838138	−0.419069	−	0.907954i	$-0.637644\pi$
$641$	−13602.0	−0.838138	−0.419069	+	0.907954i	$0.637644\pi$
$642$	0	0
$643$	5807.00	0.356152	0.178076	−	0.984017i	$-0.443013\pi$
$643$	5807.00	0.356152	0.178076	+	0.984017i	$0.443013\pi$
$644$	−1176.00	−0.0719579
$645$	0	0
$646$	−15540.0	−0.946460
$647$	19104.0	1.16083	0.580414	−	0.814322i	$-0.302891\pi$
$647$	19104.0	1.16083	0.580414	+	0.814322i	$0.302891\pi$
$648$	0	0
$649$	−15840.0	−0.958050
$650$	2150.00	0.129738
$651$	0	0
$652$	3608.00	0.216718
$653$	−3822.00	−0.229045	−0.114523	−	0.993421i	$-0.536534\pi$
$653$	−3822.00	−0.229045	−0.114523	+	0.993421i	$0.536534\pi$
$654$	0	0
$655$	1590.00	0.0948495
$656$	−6912.00	−0.411385
$657$	0	0
$658$	5754.00	0.340903
$659$	−30555.0	−1.80615	−0.903076	−	0.429481i	$-0.858696\pi$
$659$	−30555.0	−1.80615	−0.903076	+	0.429481i	$0.858696\pi$
$660$	0	0
$661$	18632.0	1.09637	0.548185	−	0.836357i	$-0.315319\pi$
$661$	18632.0	1.09637	0.548185	+	0.836357i	$0.315319\pi$
$662$	−20344.0	−1.19440
$663$	0	0
$664$	7776.00	0.454469
$665$	−2450.00	−0.142868
$666$	0	0
$667$	−9450.00	−0.548584
$668$	15876.0	0.919552
$669$	0	0
$670$	−5960.00	−0.343664
$671$	26796.0	1.54165
$672$	0	0
$673$	−15568.0	−0.891682	−0.445841	−	0.895112i	$-0.647095\pi$
$673$	−15568.0	−0.891682	−0.445841	+	0.895112i	$0.647095\pi$
$674$	18788.0	1.07372
$675$	0	0
$676$	−1392.00	−0.0791989
$677$	−31821.0	−1.80647	−0.903235	−	0.429146i	$-0.858815\pi$
$677$	−31821.0	−1.80647	−0.903235	+	0.429146i	$0.858815\pi$
$678$	0	0
$679$	−4963.00	−0.280504
$680$	4440.00	0.250392
$681$	0	0
$682$	5808.00	0.326099
$683$	25188.0	1.41112	0.705558	−	0.708652i	$-0.250696\pi$
$683$	25188.0	1.41112	0.705558	+	0.708652i	$0.250696\pi$
$684$	0	0
$685$	−12480.0	−0.696111
$686$	−686.000	−0.0381802
$687$	0	0
$688$	−2848.00	−0.157818
$689$	−30444.0	−1.68334
$690$	0	0
$691$	−2428.00	−0.133669	−0.0668346	−	0.997764i	$-0.521290\pi$
$691$	−2428.00	−0.133669	−0.0668346	+	0.997764i	$0.521290\pi$
$692$	6852.00	0.376407
$693$	0	0
$694$	9132.00	0.499490
$695$	6850.00	0.373864
$696$	0	0
$697$	47952.0	2.60590
$698$	13460.0	0.729898
$699$	0	0
$700$	700.000	0.0377964
$701$	−11187.0	−0.602749	−0.301375	−	0.953506i	$-0.597445\pi$
$701$	−11187.0	−0.602749	−0.301375	+	0.953506i	$0.597445\pi$
$702$	0	0
$703$	2380.00	0.127686
$704$	2112.00	0.113067
$705$	0	0
$706$	6054.00	0.322727
$707$	3066.00	0.163096
$708$	0	0
$709$	22655.0	1.20004	0.600019	−	0.799986i	$-0.295160\pi$
$709$	22655.0	1.20004	0.600019	+	0.799986i	$0.295160\pi$
$710$	4320.00	0.228347
$711$	0	0
$712$	7680.00	0.404242
$713$	3696.00	0.194132
$714$	0	0
$715$	−7095.00	−0.371102
$716$	14640.0	0.764138
$717$	0	0
$718$	5520.00	0.286914
$719$	9750.00	0.505721	0.252861	−	0.967503i	$-0.418629\pi$
$719$	9750.00	0.505721	0.252861	+	0.967503i	$0.418629\pi$
$720$	0	0
$721$	−7231.00	−0.373504
$722$	3918.00	0.201957
$723$	0	0
$724$	−6832.00	−0.350703
$725$	5625.00	0.288148
$726$	0	0
$727$	−17584.0	−0.897049	−0.448524	−	0.893771i	$-0.648050\pi$
$727$	−17584.0	−0.897049	−0.448524	+	0.893771i	$0.648050\pi$
$728$	2408.00	0.122591
$729$	0	0
$730$	3580.00	0.181509
$731$	19758.0	0.999694
$732$	0	0
$733$	20657.0	1.04091	0.520453	−	0.853890i	$-0.325763\pi$
$733$	20657.0	1.04091	0.520453	+	0.853890i	$0.325763\pi$
$734$	−12262.0	−0.616619
$735$	0	0
$736$	1344.00	0.0673105
$737$	19668.0	0.983012
$738$	0	0
$739$	−15505.0	−0.771801	−0.385900	−	0.922540i	$-0.626109\pi$
$739$	−15505.0	−0.771801	−0.385900	+	0.922540i	$0.626109\pi$
$740$	−680.000	−0.0337801
$741$	0	0
$742$	−9912.00	−0.490406
$743$	1548.00	0.0764342	0.0382171	−	0.999269i	$-0.487832\pi$
$743$	1548.00	0.0764342	0.0382171	+	0.999269i	$0.487832\pi$
$744$	0	0
$745$	−12450.0	−0.612259
$746$	−19264.0	−0.945449
$747$	0	0
$748$	−14652.0	−0.716217
$749$	−6342.00	−0.309388
$750$	0	0
$751$	8417.00	0.408976	0.204488	−	0.978869i	$-0.434447\pi$
$751$	8417.00	0.408976	0.204488	+	0.978869i	$0.434447\pi$
$752$	−6576.00	−0.318886
$753$	0	0
$754$	19350.0	0.934596
$755$	685.000	0.0330195
$756$	0	0
$757$	4376.00	0.210104	0.105052	−	0.994467i	$-0.466499\pi$
$757$	4376.00	0.210104	0.105052	+	0.994467i	$0.466499\pi$
$758$	19400.0	0.929604
$759$	0	0
$760$	2800.00	0.133640
$761$	16878.0	0.803978	0.401989	−	0.915645i	$-0.368319\pi$
$761$	16878.0	0.803978	0.401989	+	0.915645i	$0.368319\pi$
$762$	0	0
$763$	−13405.0	−0.636034
$764$	8292.00	0.392662
$765$	0	0
$766$	2424.00	0.114338
$767$	20640.0	0.971665
$768$	0	0
$769$	830.000	0.0389214	0.0194607	−	0.999811i	$-0.493805\pi$
$769$	830.000	0.0389214	0.0194607	+	0.999811i	$0.493805\pi$
$770$	−2310.00	−0.108112
$771$	0	0
$772$	−14752.0	−0.687741
$773$	15603.0	0.726004	0.363002	−	0.931788i	$-0.381752\pi$
$773$	15603.0	0.726004	0.363002	+	0.931788i	$0.381752\pi$
$774$	0	0
$775$	−2200.00	−0.101969
$776$	5672.00	0.262388
$777$	0	0
$778$	8610.00	0.396765
$779$	30240.0	1.39083
$780$	0	0
$781$	−14256.0	−0.653162
$782$	−9324.00	−0.426375
$783$	0	0
$784$	784.000	0.0357143
$785$	−16370.0	−0.744293
$786$	0	0
$787$	−12589.0	−0.570203	−0.285101	−	0.958497i	$-0.592027\pi$
$787$	−12589.0	−0.570203	−0.285101	+	0.958497i	$0.592027\pi$
$788$	−13104.0	−0.592399
$789$	0	0
$790$	−4250.00	−0.191403
$791$	3906.00	0.175577
$792$	0	0
$793$	−34916.0	−1.56356
$794$	3218.00	0.143832
$795$	0	0
$796$	9440.00	0.420342
$797$	5769.00	0.256397	0.128199	−	0.991749i	$-0.459081\pi$
$797$	5769.00	0.256397	0.128199	+	0.991749i	$0.459081\pi$
$798$	0	0
$799$	45621.0	2.01997
$800$	−800.000	−0.0353553
$801$	0	0
$802$	−27006.0	−1.18905
$803$	−11814.0	−0.519187
$804$	0	0
$805$	−1470.00	−0.0643611
$806$	−7568.00	−0.330734
$807$	0	0
$808$	−3504.00	−0.152562
$809$	−3945.00	−0.171445	−0.0857224	−	0.996319i	$-0.527320\pi$
$809$	−3945.00	−0.171445	−0.0857224	+	0.996319i	$0.527320\pi$
$810$	0	0
$811$	−1618.00	−0.0700563	−0.0350282	−	0.999386i	$-0.511152\pi$
$811$	−1618.00	−0.0700563	−0.0350282	+	0.999386i	$0.511152\pi$
$812$	6300.00	0.272274
$813$	0	0
$814$	2244.00	0.0966243
$815$	4510.00	0.193839
$816$	0	0
$817$	12460.0	0.533562
$818$	−940.000	−0.0401789
$819$	0	0
$820$	−8640.00	−0.367954
$821$	−23217.0	−0.986941	−0.493471	−	0.869762i	$-0.664272\pi$
$821$	−23217.0	−0.986941	−0.493471	+	0.869762i	$0.664272\pi$
$822$	0	0
$823$	15032.0	0.636674	0.318337	−	0.947978i	$-0.396876\pi$
$823$	15032.0	0.636674	0.318337	+	0.947978i	$0.396876\pi$
$824$	8264.00	0.349381
$825$	0	0
$826$	6720.00	0.283073
$827$	12654.0	0.532071	0.266035	−	0.963963i	$-0.414286\pi$
$827$	12654.0	0.532071	0.266035	+	0.963963i	$0.414286\pi$
$828$	0	0
$829$	−3400.00	−0.142445	−0.0712225	−	0.997460i	$-0.522690\pi$
$829$	−3400.00	−0.142445	−0.0712225	+	0.997460i	$0.522690\pi$
$830$	9720.00	0.406489
$831$	0	0
$832$	−2752.00	−0.114674
$833$	−5439.00	−0.226231
$834$	0	0
$835$	19845.0	0.822473
$836$	−9240.00	−0.382263
$837$	0	0
$838$	−23400.0	−0.964606
$839$	−16830.0	−0.692534	−0.346267	−	0.938136i	$-0.612551\pi$
$839$	−16830.0	−0.692534	−0.346267	+	0.938136i	$0.612551\pi$
$840$	0	0
$841$	26236.0	1.07573
$842$	12326.0	0.504492
$843$	0	0
$844$	10628.0	0.433449
$845$	−1740.00	−0.0708377
$846$	0	0
$847$	−1694.00	−0.0687208
$848$	11328.0	0.458732
$849$	0	0
$850$	5550.00	0.223957
$851$	1428.00	0.0575220
$852$	0	0
$853$	25022.0	1.00438	0.502190	−	0.864757i	$-0.332528\pi$
$853$	25022.0	1.00438	0.502190	+	0.864757i	$0.332528\pi$
$854$	−11368.0	−0.455509
$855$	0	0
$856$	7248.00	0.289406
$857$	2094.00	0.0834652	0.0417326	−	0.999129i	$-0.486712\pi$
$857$	2094.00	0.0834652	0.0417326	+	0.999129i	$0.486712\pi$
$858$	0	0
$859$	−4300.00	−0.170796	−0.0853982	−	0.996347i	$-0.527216\pi$
$859$	−4300.00	−0.170796	−0.0853982	+	0.996347i	$0.527216\pi$
$860$	−3560.00	−0.141157
$861$	0	0
$862$	10374.0	0.409907
$863$	7428.00	0.292992	0.146496	−	0.989211i	$-0.453200\pi$
$863$	7428.00	0.292992	0.146496	+	0.989211i	$0.453200\pi$
$864$	0	0
$865$	8565.00	0.336669
$866$	−5764.00	−0.226176
$867$	0	0
$868$	−2464.00	−0.0963521
$869$	14025.0	0.547486
$870$	0	0
$871$	−25628.0	−0.996982
$872$	15320.0	0.594955
$873$	0	0
$874$	−5880.00	−0.227567
$875$	875.000	0.0338062
$876$	0	0
$877$	33446.0	1.28779	0.643895	−	0.765114i	$-0.277318\pi$
$877$	33446.0	1.28779	0.643895	+	0.765114i	$0.277318\pi$
$878$	−19660.0	−0.755687
$879$	0	0
$880$	2640.00	0.101130
$881$	−20592.0	−0.787471	−0.393736	−	0.919224i	$-0.628817\pi$
$881$	−20592.0	−0.787471	−0.393736	+	0.919224i	$0.628817\pi$
$882$	0	0
$883$	−47248.0	−1.80070	−0.900352	−	0.435162i	$-0.856691\pi$
$883$	−47248.0	−1.80070	−0.900352	+	0.435162i	$0.856691\pi$
$884$	19092.0	0.726395
$885$	0	0
$886$	−10356.0	−0.392682
$887$	16824.0	0.636860	0.318430	−	0.947946i	$-0.396844\pi$
$887$	16824.0	0.636860	0.318430	+	0.947946i	$0.396844\pi$
$888$	0	0
$889$	−12208.0	−0.460566
$890$	9600.00	0.361565
$891$	0	0
$892$	188.000	0.00705684
$893$	28770.0	1.07811
$894$	0	0
$895$	18300.0	0.683465
$896$	−896.000	−0.0334077
$897$	0	0
$898$	−9090.00	−0.337792
$899$	−19800.0	−0.734557
$900$	0	0
$901$	−78588.0	−2.90582
$902$	28512.0	1.05249
$903$	0	0
$904$	−4464.00	−0.164237
$905$	−8540.00	−0.313679
$906$	0	0
$907$	8066.00	0.295289	0.147645	−	0.989040i	$-0.452831\pi$
$907$	8066.00	0.295289	0.147645	+	0.989040i	$0.452831\pi$
$908$	−24204.0	−0.884623
$909$	0	0
$910$	3010.00	0.109649
$911$	21168.0	0.769843	0.384922	−	0.922949i	$-0.374228\pi$
$911$	21168.0	0.769843	0.384922	+	0.922949i	$0.374228\pi$
$912$	0	0
$913$	−32076.0	−1.16272
$914$	968.000	0.0350313
$915$	0	0
$916$	12320.0	0.444393
$917$	2226.00	0.0801625
$918$	0	0
$919$	10685.0	0.383532	0.191766	−	0.981441i	$-0.438579\pi$
$919$	10685.0	0.383532	0.191766	+	0.981441i	$0.438579\pi$
$920$	1680.00	0.0602043
$921$	0	0
$922$	−2736.00	−0.0977282
$923$	18576.0	0.662445
$924$	0	0
$925$	−850.000	−0.0302139
$926$	−29704.0	−1.05414
$927$	0	0
$928$	−7200.00	−0.254689
$929$	−5820.00	−0.205541	−0.102771	−	0.994705i	$-0.532771\pi$
$929$	−5820.00	−0.205541	−0.102771	+	0.994705i	$0.532771\pi$
$930$	0	0
$931$	−3430.00	−0.120745
$932$	13152.0	0.462240
$933$	0	0
$934$	15042.0	0.526969
$935$	−18315.0	−0.640604
$936$	0	0
$937$	−1429.00	−0.0498222	−0.0249111	−	0.999690i	$-0.507930\pi$
$937$	−1429.00	−0.0498222	−0.0249111	+	0.999690i	$0.507930\pi$
$938$	−8344.00	−0.290449
$939$	0	0
$940$	−8220.00	−0.285220
$941$	−16932.0	−0.586575	−0.293288	−	0.956024i	$-0.594749\pi$
$941$	−16932.0	−0.586575	−0.293288	+	0.956024i	$0.594749\pi$
$942$	0	0
$943$	18144.0	0.626564
$944$	−7680.00	−0.264791
$945$	0	0
$946$	11748.0	0.403764
$947$	45804.0	1.57173	0.785866	−	0.618397i	$-0.212218\pi$
$947$	45804.0	1.57173	0.785866	+	0.618397i	$0.212218\pi$
$948$	0	0
$949$	15394.0	0.526565
$950$	3500.00	0.119532
$951$	0	0
$952$	6216.00	0.211619
$953$	41508.0	1.41089	0.705444	−	0.708766i	$-0.250748\pi$
$953$	41508.0	1.41089	0.705444	+	0.708766i	$0.250748\pi$
$954$	0	0
$955$	10365.0	0.351208
$956$	7020.00	0.237493
$957$	0	0
$958$	17700.0	0.596932
$959$	−17472.0	−0.588321
$960$	0	0
$961$	−22047.0	−0.740056
$962$	−2924.00	−0.0979974
$963$	0	0
$964$	8.00000	0.000267285 0
$965$	−18440.0	−0.615134
$966$	0	0
$967$	39566.0	1.31578	0.657889	−	0.753115i	$-0.271450\pi$
$967$	39566.0	1.31578	0.657889	+	0.753115i	$0.271450\pi$
$968$	1936.00	0.0642824
$969$	0	0
$970$	7090.00	0.234687
$971$	40188.0	1.32821	0.664106	−	0.747638i	$-0.268812\pi$
$971$	40188.0	1.32821	0.664106	+	0.747638i	$0.268812\pi$
$972$	0	0
$973$	9590.00	0.315973
$974$	29228.0	0.961525
$975$	0	0
$976$	12992.0	0.426090
$977$	17214.0	0.563690	0.281845	−	0.959460i	$-0.409054\pi$
$977$	17214.0	0.563690	0.281845	+	0.959460i	$0.409054\pi$
$978$	0	0
$979$	−31680.0	−1.03422
$980$	980.000	0.0319438
$981$	0	0
$982$	30474.0	0.990290
$983$	−12657.0	−0.410677	−0.205339	−	0.978691i	$-0.565830\pi$
$983$	−12657.0	−0.410677	−0.205339	+	0.978691i	$0.565830\pi$
$984$	0	0
$985$	−16380.0	−0.529858
$986$	49950.0	1.61332
$987$	0	0
$988$	12040.0	0.387696
$989$	7476.00	0.240367
$990$	0	0
$991$	38072.0	1.22038	0.610190	−	0.792255i	$-0.291093\pi$
$991$	38072.0	1.22038	0.610190	+	0.792255i	$0.291093\pi$
$992$	2816.00	0.0901291
$993$	0	0
$994$	6048.00	0.192989
$995$	11800.0	0.375965
$996$	0	0
$997$	−35269.0	−1.12034	−0.560171	−	0.828377i	$-0.689264\pi$
$997$	−35269.0	−1.12034	−0.560171	+	0.828377i	$0.689264\pi$
$998$	19130.0	0.606763
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.a.j.1.1		1
3.2	odd	2		70.4.a.f.1.1	✓	1
12.11	even	2		560.4.a.c.1.1		1
15.2	even	4		350.4.c.l.99.2		2
15.8	even	4		350.4.c.l.99.1		2
15.14	odd	2		350.4.a.b.1.1		1
21.2	odd	6		490.4.e.b.361.1		2
21.5	even	6		490.4.e.h.361.1		2
21.11	odd	6		490.4.e.b.471.1		2
21.17	even	6		490.4.e.h.471.1		2
21.20	even	2		490.4.a.i.1.1		1
24.5	odd	2		2240.4.a.f.1.1		1
24.11	even	2		2240.4.a.bh.1.1		1
105.104	even	2		2450.4.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.f.1.1	✓	1	3.2	odd	2
350.4.a.b.1.1		1	15.14	odd	2
350.4.c.l.99.1		2	15.8	even	4
350.4.c.l.99.2		2	15.2	even	4
490.4.a.i.1.1		1	21.20	even	2
490.4.e.b.361.1		2	21.2	odd	6
490.4.e.b.471.1		2	21.11	odd	6
490.4.e.h.361.1		2	21.5	even	6
490.4.e.h.471.1		2	21.17	even	6
560.4.a.c.1.1		1	12.11	even	2
630.4.a.j.1.1		1	1.1	even	1	trivial
2240.4.a.f.1.1		1	24.5	odd	2
2240.4.a.bh.1.1		1	24.11	even	2
2450.4.a.s.1.1		1	105.104	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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