LMFDB - Embedded newform 490.4.a.i.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:	$1$
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	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{6} +8.00000 q^{8} +22.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{6} +8.00000 q^{8} +22.0000 q^{9} +10.0000 q^{10} -33.0000 q^{11} -28.0000 q^{12} +43.0000 q^{13} -35.0000 q^{15} +16.0000 q^{16} -111.000 q^{17} +44.0000 q^{18} +70.0000 q^{19} +20.0000 q^{20} -66.0000 q^{22} +42.0000 q^{23} -56.0000 q^{24} +25.0000 q^{25} +86.0000 q^{26} +35.0000 q^{27} -225.000 q^{29} -70.0000 q^{30} +88.0000 q^{31} +32.0000 q^{32} +231.000 q^{33} -222.000 q^{34} +88.0000 q^{36} -34.0000 q^{37} +140.000 q^{38} -301.000 q^{39} +40.0000 q^{40} -432.000 q^{41} -178.000 q^{43} -132.000 q^{44} +110.000 q^{45} +84.0000 q^{46} -411.000 q^{47} -112.000 q^{48} +50.0000 q^{50} +777.000 q^{51} +172.000 q^{52} -708.000 q^{53} +70.0000 q^{54} -165.000 q^{55} -490.000 q^{57} -450.000 q^{58} -480.000 q^{59} -140.000 q^{60} -812.000 q^{61} +176.000 q^{62} +64.0000 q^{64} +215.000 q^{65} +462.000 q^{66} +596.000 q^{67} -444.000 q^{68} -294.000 q^{69} +432.000 q^{71} +176.000 q^{72} +358.000 q^{73} -68.0000 q^{74} -175.000 q^{75} +280.000 q^{76} -602.000 q^{78} +425.000 q^{79} +80.0000 q^{80} -839.000 q^{81} -864.000 q^{82} -972.000 q^{83} -555.000 q^{85} -356.000 q^{86} +1575.00 q^{87} -264.000 q^{88} -960.000 q^{89} +220.000 q^{90} +168.000 q^{92} -616.000 q^{93} -822.000 q^{94} +350.000 q^{95} -224.000 q^{96} +709.000 q^{97} -726.000 q^{99} +O(q^{100})\)

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
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−14.0000	−0.952579
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	22.0000	0.814815
$10$	10.0000	0.316228
$11$	−33.0000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−33.0000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−28.0000	−0.673575
$13$	43.0000	0.917389	0.458694	−	0.888594i	$-0.348317\pi$
$13$	43.0000	0.917389	0.458694	+	0.888594i	$0.348317\pi$
$14$	0	0
$15$	−35.0000	−0.602464
$16$	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	$0.790860\pi$
$18$	44.0000	0.576161
$19$	70.0000	0.845216	0.422608	−	0.906313i	$-0.361115\pi$
$19$	70.0000	0.845216	0.422608	+	0.906313i	$0.361115\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−66.0000	−0.639602
$23$	42.0000	0.380765	0.190383	−	0.981710i	$-0.439027\pi$
$23$	42.0000	0.380765	0.190383	+	0.981710i	$0.439027\pi$
$24$	−56.0000	−0.476290
$25$	25.0000	0.200000
$26$	86.0000	0.648692
$27$	35.0000	0.249472
$28$	0	0
$29$	−225.000	−1.44074	−0.720370	−	0.693590i	$-0.756028\pi$
$29$	−225.000	−1.44074	−0.720370	+	0.693590i	$0.756028\pi$
$30$	−70.0000	−0.426006
$31$	88.0000	0.509847	0.254924	−	0.966961i	$-0.417950\pi$
$31$	88.0000	0.509847	0.254924	+	0.966961i	$0.417950\pi$
$32$	32.0000	0.176777
$33$	231.000	1.21854
$34$	−222.000	−1.11978
$35$	0	0
$36$	88.0000	0.407407
$37$	−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
$39$	−301.000	−1.23586
$40$	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
$45$	110.000	0.364396
$46$	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	$0.720144\pi$
$48$	−112.000	−0.336788
$49$	0	0
$50$	50.0000	0.141421
$51$	777.000	2.13337
$52$	172.000	0.458694
$53$	−708.000	−1.83493	−0.917465	−	0.397817i	$-0.869768\pi$
$53$	−708.000	−1.83493	−0.917465	+	0.397817i	$0.869768\pi$
$54$	70.0000	0.176404
$55$	−165.000	−0.404520
$56$	0	0
$57$	−490.000	−1.13863
$58$	−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	$0.677651\pi$
$60$	−140.000	−0.301232
$61$	−812.000	−1.70436	−0.852180	−	0.523249i	$-0.824720\pi$
$61$	−812.000	−1.70436	−0.852180	+	0.523249i	$0.824720\pi$
$62$	176.000	0.360516
$63$	0	0
$64$	64.0000	0.125000
$65$	215.000	0.410269
$66$	462.000	0.861640
$67$	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
$69$	−294.000	−0.512948
$70$	0	0
$71$	432.000	0.722098	0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000	0.722098	0.361049	+	0.932547i	$0.382419\pi$
$72$	176.000	0.288081
$73$	358.000	0.573983	0.286991	−	0.957933i	$-0.407345\pi$
$73$	358.000	0.573983	0.286991	+	0.957933i	$0.407345\pi$
$74$	−68.0000	−0.106822
$75$	−175.000	−0.269430
$76$	280.000	0.422608
$77$	0	0
$78$	−602.000	−0.873886
$79$	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
$81$	−839.000	−1.15089
$82$	−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
$87$	1575.00	1.94089
$88$	−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	$0.693710\pi$
$90$	220.000	0.257667
$91$	0	0
$92$	168.000	0.190383
$93$	−616.000	−0.686841
$94$	−822.000	−0.901945
$95$	350.000	0.377992
$96$	−224.000	−0.238145
$97$	709.000	0.742145	0.371072	−	0.928604i	$-0.378990\pi$
$97$	709.000	0.742145	0.371072	+	0.928604i	$0.378990\pi$
$98$	0	0
$99$	−726.000	−0.737028
$100$	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	$0.430779\pi$
$102$	1554.00	1.50852
$103$	1033.00	0.988199	0.494100	−	0.869405i	$-0.335498\pi$
$103$	1033.00	0.988199	0.494100	+	0.869405i	$0.335498\pi$
$104$	344.000	0.324346
$105$	0	0
$106$	−1416.00	−1.29749
$107$	906.000	0.818564	0.409282	−	0.912408i	$-0.365779\pi$
$107$	906.000	0.818564	0.409282	+	0.912408i	$0.365779\pi$
$108$	140.000	0.124736
$109$	−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
$111$	238.000	0.203513
$112$	0	0
$113$	−558.000	−0.464533	−0.232266	−	0.972652i	$-0.574614\pi$
$113$	−558.000	−0.464533	−0.232266	+	0.972652i	$0.574614\pi$
$114$	−980.000	−0.805135
$115$	210.000	0.170283
$116$	−900.000	−0.720370
$117$	946.000	0.747502
$118$	−960.000	−0.748942
$119$	0	0
$120$	−280.000	−0.213003
$121$	−242.000	−0.181818
$122$	−1624.00	−1.20516
$123$	3024.00	2.21679
$124$	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
$129$	1246.00	0.850420
$130$	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	$0.466181\pi$
$132$	924.000	0.609272
$133$	0	0
$134$	1192.00	0.768456
$135$	175.000	0.111567
$136$	−888.000	−0.559892
$137$	2496.00	1.55655	0.778276	−	0.627922i	$-0.216094\pi$
$137$	2496.00	1.55655	0.778276	+	0.627922i	$0.216094\pi$
$138$	−588.000	−0.362709
$139$	−1370.00	−0.835985	−0.417992	−	0.908451i	$-0.637266\pi$
$139$	−1370.00	−0.835985	−0.417992	+	0.908451i	$0.637266\pi$
$140$	0	0
$141$	2877.00	1.71835
$142$	864.000	0.510600
$143$	−1419.00	−0.829809
$144$	352.000	0.203704
$145$	−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	$-0.260009\pi$
$149$	2490.00	1.36905	0.684526	+	0.728988i	$0.260009\pi$
$150$	−350.000	−0.190516
$151$	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
$153$	−2442.00	−1.29035
$154$	0	0
$155$	440.000	0.228011
$156$	−1204.00	−0.617930
$157$	3274.00	1.66429	0.832145	−	0.554558i	$-0.187112\pi$
$157$	3274.00	1.66429	0.832145	+	0.554558i	$0.187112\pi$
$158$	850.000	0.427990
$159$	4956.00	2.47193
$160$	160.000	0.0790569
$161$	0	0
$162$	−1678.00	−0.813803
$163$	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
$165$	1155.00	0.544949
$166$	−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
$171$	1540.00	0.688694
$172$	−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	$0.377159\pi$
$174$	3150.00	1.37242
$175$	0	0
$176$	−528.000	−0.226134
$177$	3360.00	1.42685
$178$	−1920.00	−0.808484
$179$	−3660.00	−1.52828	−0.764138	−	0.645053i	$-0.776835\pi$
$179$	−3660.00	−1.52828	−0.764138	+	0.645053i	$0.776835\pi$
$180$	440.000	0.182198
$181$	1708.00	0.701407	0.350703	−	0.936487i	$-0.385943\pi$
$181$	1708.00	0.701407	0.350703	+	0.936487i	$0.385943\pi$
$182$	0	0
$183$	5684.00	2.29603
$184$	336.000	0.134621
$185$	−170.000	−0.0675603
$186$	−1232.00	−0.485670
$187$	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	$-0.628446\pi$
$191$	−2073.00	−0.785325	−0.392662	+	0.919683i	$0.628446\pi$
$192$	−448.000	−0.168394
$193$	−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
$195$	−1505.00	−0.552694
$196$	0	0
$197$	3276.00	1.18480	0.592399	−	0.805644i	$-0.298181\pi$
$197$	3276.00	1.18480	0.592399	+	0.805644i	$0.298181\pi$
$198$	−1452.00	−0.521157
$199$	−2360.00	−0.840683	−0.420342	−	0.907366i	$-0.638090\pi$
$199$	−2360.00	−0.840683	−0.420342	+	0.907366i	$0.638090\pi$
$200$	200.000	0.0707107
$201$	−4172.00	−1.46403
$202$	876.000	0.305124
$203$	0	0
$204$	3108.00	1.06668
$205$	−2160.00	−0.735907
$206$	2066.00	0.698762
$207$	924.000	0.310253
$208$	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
$213$	−3024.00	−0.972775
$214$	1812.00	0.578812
$215$	−890.000	−0.282314
$216$	280.000	0.0882018
$217$	0	0
$218$	−3830.00	−1.18991
$219$	−2506.00	−0.773241
$220$	−660.000	−0.202260
$221$	−4773.00	−1.45279
$222$	476.000	0.143906
$223$	−47.0000	−0.0141137	−0.00705684	−	0.999975i	$-0.502246\pi$
$223$	−47.0000	−0.0141137	−0.00705684	+	0.999975i	$0.502246\pi$
$224$	0	0
$225$	550.000	0.162963
$226$	−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	$0.845584\pi$
$228$	−1960.00	−0.569317
$229$	−3080.00	−0.888787	−0.444393	−	0.895832i	$-0.646581\pi$
$229$	−3080.00	−0.888787	−0.444393	+	0.895832i	$0.646581\pi$
$230$	420.000	0.120409
$231$	0	0
$232$	−1800.00	−0.509378
$233$	−3288.00	−0.924481	−0.462240	−	0.886755i	$-0.652954\pi$
$233$	−3288.00	−0.924481	−0.462240	+	0.886755i	$0.652954\pi$
$234$	1892.00	0.528564
$235$	−2055.00	−0.570440
$236$	−1920.00	−0.529582
$237$	−2975.00	−0.815388
$238$	0	0
$239$	−1755.00	−0.474985	−0.237493	−	0.971389i	$-0.576326\pi$
$239$	−1755.00	−0.474985	−0.237493	+	0.971389i	$0.576326\pi$
$240$	−560.000	−0.150616
$241$	−2.00000	−0.000534570 0	−0.000267285	−	1.00000i	$-0.500085\pi$
$241$	−2.00000	−0.000534570 0	−0.000267285		1.00000i	$0.500085\pi$
$242$	−484.000	−0.128565
$243$	4928.00	1.30095
$244$	−3248.00	−0.852180
$245$	0	0
$246$	6048.00	1.56751
$247$	3010.00	0.775392
$248$	704.000	0.180258
$249$	6804.00	1.73167
$250$	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
$255$	3885.00	0.954071
$256$	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	$0.415814\pi$
$258$	2492.00	0.601338
$259$	0	0
$260$	860.000	0.205134
$261$	−4950.00	−1.17394
$262$	636.000	0.149970
$263$	3882.00	0.910169	0.455084	−	0.890448i	$-0.349609\pi$
$263$	3882.00	0.910169	0.455084	+	0.890448i	$0.349609\pi$
$264$	1848.00	0.430820
$265$	−3540.00	−0.820606
$266$	0	0
$267$	6720.00	1.54029
$268$	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	$0.520576\pi$
$270$	350.000	0.0788901
$271$	−3332.00	−0.746880	−0.373440	−	0.927654i	$-0.621822\pi$
$271$	−3332.00	−0.746880	−0.373440	+	0.927654i	$0.621822\pi$
$272$	−1776.00	−0.395904
$273$	0	0
$274$	4992.00	1.10065
$275$	−825.000	−0.180907
$276$	−1176.00	−0.256474
$277$	−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
$279$	1936.00	0.415431
$280$	0	0
$281$	3267.00	0.693569	0.346784	−	0.937945i	$-0.387274\pi$
$281$	3267.00	0.693569	0.346784	+	0.937945i	$0.387274\pi$
$282$	5754.00	1.21506
$283$	−677.000	−0.142203	−0.0711015	−	0.997469i	$-0.522651\pi$
$283$	−677.000	−0.142203	−0.0711015	+	0.997469i	$0.522651\pi$
$284$	1728.00	0.361049
$285$	−2450.00	−0.509212
$286$	−2838.00	−0.586764
$287$	0	0
$288$	704.000	0.144040
$289$	7408.00	1.50784
$290$	−2250.00	−0.455602
$291$	−4963.00	−0.999781
$292$	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
$297$	−1155.00	−0.225656
$298$	4980.00	0.968066
$299$	1806.00	0.349310
$300$	−700.000	−0.134715
$301$	0	0
$302$	274.000	0.0522084
$303$	−3066.00	−0.581311
$304$	1120.00	0.211304
$305$	−4060.00	−0.762213
$306$	−4884.00	−0.912417
$307$	3499.00	0.650484	0.325242	−	0.945631i	$-0.394554\pi$
$307$	3499.00	0.650484	0.325242	+	0.945631i	$0.394554\pi$
$308$	0	0
$309$	−7231.00	−1.33125
$310$	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	$0.673324\pi$
$312$	−2408.00	−0.436943
$313$	−4097.00	−0.739860	−0.369930	−	0.929060i	$-0.620618\pi$
$313$	−4097.00	−0.739860	−0.369930	+	0.929060i	$0.620618\pi$
$314$	6548.00	1.17683
$315$	0	0
$316$	1700.00	0.302634
$317$	−4674.00	−0.828132	−0.414066	−	0.910247i	$-0.635892\pi$
$317$	−4674.00	−0.828132	−0.414066	+	0.910247i	$0.635892\pi$
$318$	9912.00	1.74792
$319$	7425.00	1.30320
$320$	320.000	0.0559017
$321$	−6342.00	−1.10273
$322$	0	0
$323$	−7770.00	−1.33850
$324$	−3356.00	−0.575446
$325$	1075.00	0.183478
$326$	1804.00	0.306486
$327$	13405.0	2.26697
$328$	−3456.00	−0.581786
$329$	0	0
$330$	2310.00	0.385337
$331$	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
$333$	−748.000	−0.123094
$334$	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
$339$	3906.00	0.625796
$340$	−2220.00	−0.354107
$341$	−2904.00	−0.461174
$342$	3080.00	0.486980
$343$	0	0
$344$	−1424.00	−0.223189
$345$	−1470.00	−0.229398
$346$	3426.00	0.532321
$347$	4566.00	0.706385	0.353193	−	0.935551i	$-0.385096\pi$
$347$	4566.00	0.706385	0.353193	+	0.935551i	$0.385096\pi$
$348$	6300.00	0.970447
$349$	6730.00	1.03223	0.516116	−	0.856519i	$-0.327378\pi$
$349$	6730.00	1.03223	0.516116	+	0.856519i	$0.327378\pi$
$350$	0	0
$351$	1505.00	0.228863
$352$	−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	$0.573285\pi$
$354$	6720.00	1.00894
$355$	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	$-0.434970\pi$
$359$	2760.00	0.405758	0.202879	+	0.979204i	$0.434970\pi$
$360$	880.000	0.128834
$361$	−1959.00	−0.285610
$362$	3416.00	0.495970
$363$	1694.00	0.244936
$364$	0	0
$365$	1790.00	0.256693
$366$	11368.0	1.62354
$367$	−6131.00	−0.872032	−0.436016	−	0.899939i	$-0.643611\pi$
$367$	−6131.00	−0.872032	−0.436016	+	0.899939i	$0.643611\pi$
$368$	672.000	0.0951914
$369$	−9504.00	−1.34081
$370$	−340.000	−0.0477723
$371$	0	0
$372$	−2464.00	−0.343421
$373$	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
$375$	−875.000	−0.120493
$376$	−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
$381$	12208.0	1.64156
$382$	−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	$0.525763\pi$
$384$	−896.000	−0.119072
$385$	0	0
$386$	−7376.00	−0.972613
$387$	−3916.00	−0.514371
$388$	2836.00	0.371072
$389$	4305.00	0.561111	0.280555	−	0.959838i	$-0.409481\pi$
$389$	4305.00	0.561111	0.280555	+	0.959838i	$0.409481\pi$
$390$	−3010.00	−0.390814
$391$	−4662.00	−0.602986
$392$	0	0
$393$	−2226.00	−0.285717
$394$	6552.00	0.837779
$395$	2125.00	0.270684
$396$	−2904.00	−0.368514
$397$	1609.00	0.203409	0.101705	−	0.994815i	$-0.467570\pi$
$397$	1609.00	0.203409	0.101705	+	0.994815i	$0.467570\pi$
$398$	−4720.00	−0.594453
$399$	0	0
$400$	400.000	0.0500000
$401$	−13503.0	−1.68157	−0.840783	−	0.541373i	$-0.817905\pi$
$401$	−13503.0	−1.68157	−0.840783	+	0.541373i	$0.817905\pi$
$402$	−8344.00	−1.03523
$403$	3784.00	0.467728
$404$	1752.00	0.215756
$405$	−4195.00	−0.514694
$406$	0	0
$407$	1122.00	0.136647
$408$	6216.00	0.754259
$409$	−470.000	−0.0568215	−0.0284108	−	0.999596i	$-0.509045\pi$
$409$	−470.000	−0.0568215	−0.0284108	+	0.999596i	$0.509045\pi$
$410$	−4320.00	−0.520365
$411$	−17472.0	−2.09691
$412$	4132.00	0.494100
$413$	0	0
$414$	1848.00	0.219382
$415$	−4860.00	−0.574863
$416$	1376.00	0.162173
$417$	9590.00	1.12620
$418$	−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
$423$	−9042.00	−1.03933
$424$	−5664.00	−0.648746
$425$	−2775.00	−0.316723
$426$	−6048.00	−0.687856
$427$	0	0
$428$	3624.00	0.409282
$429$	9933.00	1.11788
$430$	−1780.00	−0.199626
$431$	5187.00	0.579696	0.289848	−	0.957073i	$-0.406395\pi$
$431$	5187.00	0.579696	0.289848	+	0.957073i	$0.406395\pi$
$432$	560.000	0.0623681
$433$	−2882.00	−0.319862	−0.159931	−	0.987128i	$-0.551127\pi$
$433$	−2882.00	−0.319862	−0.159931	+	0.987128i	$0.551127\pi$
$434$	0	0
$435$	7875.00	0.867994
$436$	−7660.00	−0.841393
$437$	2940.00	0.321829
$438$	−5012.00	−0.546764
$439$	−9830.00	−1.06870	−0.534351	−	0.845263i	$-0.679444\pi$
$439$	−9830.00	−1.06870	−0.534351	+	0.845263i	$0.679444\pi$
$440$	−1320.00	−0.143019
$441$	0	0
$442$	−9546.00	−1.02728
$443$	−5178.00	−0.555337	−0.277668	−	0.960677i	$-0.589562\pi$
$443$	−5178.00	−0.555337	−0.277668	+	0.960677i	$0.589562\pi$
$444$	952.000	0.101757
$445$	−4800.00	−0.511330
$446$	−94.0000	−0.00997989
$447$	−17430.0	−1.84432
$448$	0	0
$449$	−4545.00	−0.477710	−0.238855	−	0.971055i	$-0.576772\pi$
$449$	−4545.00	−0.477710	−0.238855	+	0.971055i	$0.576772\pi$
$450$	1100.00	0.115232
$451$	14256.0	1.48845
$452$	−2232.00	−0.232266
$453$	−959.000	−0.0994652
$454$	−12102.0	−1.25105
$455$	0	0
$456$	−3920.00	−0.402568
$457$	−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
$459$	−3885.00	−0.395068
$460$	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
$465$	−3080.00	−0.307165
$466$	−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	$0.621542\pi$
$468$	3784.00	0.373751
$469$	0	0
$470$	−4110.00	−0.403362
$471$	−22918.0	−2.24205
$472$	−3840.00	−0.374471
$473$	5874.00	0.571008
$474$	−5950.00	−0.576567
$475$	1750.00	0.169043
$476$	0	0
$477$	−15576.0	−1.49513
$478$	−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	$0.638705\pi$
$480$	−1120.00	−0.106502
$481$	−1462.00	−0.138589
$482$	−4.00000	−0.000377998 0
$483$	0	0
$484$	−968.000	−0.0909091
$485$	3545.00	0.331897
$486$	9856.00	0.919912
$487$	−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
$489$	−6314.00	−0.583904
$490$	0	0
$491$	15237.0	1.40048	0.700241	−	0.713907i	$-0.253076\pi$
$491$	15237.0	1.40048	0.700241	+	0.713907i	$0.253076\pi$
$492$	12096.0	1.10839
$493$	24975.0	2.28158
$494$	6020.00	0.548285
$495$	−3630.00	−0.329609
$496$	1408.00	0.127462
$497$	0	0
$498$	13608.0	1.22448
$499$	−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
$501$	−27783.0	−2.47755
$502$	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
$507$	2436.00	0.213386
$508$	−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	$0.398063\pi$
$510$	7770.00	0.674630
$511$	0	0
$512$	512.000	0.0441942
$513$	2450.00	0.210858
$514$	4308.00	0.369684
$515$	5165.00	0.441936
$516$	4984.00	0.425210
$517$	13563.0	1.15377
$518$	0	0
$519$	−11991.0	−1.01416
$520$	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	$0.566899\pi$
$522$	−9900.00	−0.830098
$523$	−13772.0	−1.15145	−0.575724	−	0.817644i	$-0.695280\pi$
$523$	−13772.0	−1.15145	−0.575724	+	0.817644i	$0.695280\pi$
$524$	1272.00	0.106045
$525$	0	0
$526$	7764.00	0.643586
$527$	−9768.00	−0.807402
$528$	3696.00	0.304636
$529$	−10403.0	−0.855018
$530$	−7080.00	−0.580256
$531$	−10560.0	−0.863023
$532$	0	0
$533$	−18576.0	−1.50960
$534$	13440.0	1.08915
$535$	4530.00	0.366073
$536$	4768.00	0.384228
$537$	25620.0	2.05882
$538$	−1140.00	−0.0913548
$539$	0	0
$540$	700.000	0.0557837
$541$	−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
$543$	−11956.0	−0.944901
$544$	−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
$549$	−17864.0	−1.38874
$550$	−1650.00	−0.127920
$551$	−15750.0	−1.21774
$552$	−2352.00	−0.181355
$553$	0	0
$554$	−788.000	−0.0604312
$555$	1190.00	0.0910139
$556$	−5480.00	−0.417992
$557$	15096.0	1.14836	0.574181	−	0.818728i	$-0.305320\pi$
$557$	15096.0	1.14836	0.574181	+	0.818728i	$0.305320\pi$
$558$	3872.00	0.293754
$559$	−7654.00	−0.579123
$560$	0	0
$561$	−25641.0	−1.92970
$562$	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	$0.595948\pi$
$564$	11508.0	0.859174
$565$	−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	$-0.658831\pi$
$569$	−12990.0	−0.957063	−0.478532	+	0.878070i	$0.658831\pi$
$570$	−4900.00	−0.360067
$571$	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
$573$	14511.0	1.05795
$574$	0	0
$575$	1050.00	0.0761531
$576$	1408.00	0.101852
$577$	24379.0	1.75894	0.879472	−	0.475950i	$-0.157896\pi$
$577$	24379.0	1.75894	0.879472	+	0.475950i	$0.157896\pi$
$578$	14816.0	1.06620
$579$	25816.0	1.85298
$580$	−4500.00	−0.322159
$581$	0	0
$582$	−9926.00	−0.706952
$583$	23364.0	1.65976
$584$	2864.00	0.202933
$585$	4730.00	0.334293
$586$	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
$591$	−22932.0	−1.59610
$592$	−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	$0.576076\pi$
$594$	−2310.00	−0.159563
$595$	0	0
$596$	9960.00	0.684526
$597$	16520.0	1.13253
$598$	3612.00	0.246999
$599$	−8925.00	−0.608791	−0.304395	−	0.952546i	$-0.598454\pi$
$599$	−8925.00	−0.608791	−0.304395	+	0.952546i	$0.598454\pi$
$600$	−1400.00	−0.0952579
$601$	−20342.0	−1.38064	−0.690322	−	0.723502i	$-0.742531\pi$
$601$	−20342.0	−1.38064	−0.690322	+	0.723502i	$0.742531\pi$
$602$	0	0
$603$	13112.0	0.885509
$604$	548.000	0.0369169
$605$	−1210.00	−0.0813116
$606$	−6132.00	−0.411049
$607$	27439.0	1.83479	0.917393	−	0.397983i	$-0.130290\pi$
$607$	27439.0	1.83479	0.917393	+	0.397983i	$0.130290\pi$
$608$	2240.00	0.149414
$609$	0	0
$610$	−8120.00	−0.538966
$611$	−17673.0	−1.17017
$612$	−9768.00	−0.645176
$613$	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
$615$	15120.0	0.991378
$616$	0	0
$617$	−10494.0	−0.684720	−0.342360	−	0.939569i	$-0.611226\pi$
$617$	−10494.0	−0.684720	−0.342360	+	0.939569i	$0.611226\pi$
$618$	−14462.0	−0.941338
$619$	−22970.0	−1.49151	−0.745753	−	0.666223i	$-0.767910\pi$
$619$	−22970.0	−1.49151	−0.745753	+	0.666223i	$0.767910\pi$
$620$	1760.00	0.114005
$621$	1470.00	0.0949904
$622$	−11364.0	−0.732564
$623$	0	0
$624$	−4816.00	−0.308965
$625$	625.000	0.0400000
$626$	−8194.00	−0.523160
$627$	16170.0	1.02993
$628$	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
$633$	−18599.0	−1.16784
$634$	−9348.00	−0.585578
$635$	−8720.00	−0.544949
$636$	19824.0	1.23596
$637$	0	0
$638$	14850.0	0.921500
$639$	9504.00	0.588376
$640$	640.000	0.0395285
$641$	13602.0	0.838138	0.419069	−	0.907954i	$-0.362356\pi$
$641$	13602.0	0.838138	0.419069	+	0.907954i	$0.362356\pi$
$642$	−12684.0	−0.779747
$643$	−5807.00	−0.356152	−0.178076	−	0.984017i	$-0.556987\pi$
$643$	−5807.00	−0.356152	−0.178076	+	0.984017i	$0.556987\pi$
$644$	0	0
$645$	6230.00	0.380319
$646$	−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	$0.302891\pi$
$648$	−6712.00	−0.406902
$649$	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	$-0.463466\pi$
$653$	3822.00	0.229045	0.114523	+	0.993421i	$0.463466\pi$
$654$	26810.0	1.60299
$655$	1590.00	0.0948495
$656$	−6912.00	−0.411385
$657$	7876.00	0.467690
$658$	0	0
$659$	30555.0	1.80615	0.903076	−	0.429481i	$-0.141304\pi$
$659$	30555.0	1.80615	0.903076	+	0.429481i	$0.141304\pi$
$660$	4620.00	0.272475
$661$	−18632.0	−1.09637	−0.548185	−	0.836357i	$-0.684681\pi$
$661$	−18632.0	−1.09637	−0.548185	+	0.836357i	$0.684681\pi$
$662$	20344.0	1.19440
$663$	33411.0	1.95713
$664$	−7776.00	−0.454469
$665$	0	0
$666$	−1496.00	−0.0870403
$667$	−9450.00	−0.548584
$668$	15876.0	0.919552
$669$	329.000	0.0190133
$670$	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
$675$	875.000	0.0498945
$676$	−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	$0.858815\pi$
$678$	7812.00	0.442505
$679$	0	0
$680$	−4440.00	−0.250392
$681$	42357.0	2.38344
$682$	−5808.00	−0.326099
$683$	−25188.0	−1.41112	−0.705558	−	0.708652i	$-0.749304\pi$
$683$	−25188.0	−1.41112	−0.705558	+	0.708652i	$0.749304\pi$
$684$	6160.00	0.344347
$685$	12480.0	0.696111
$686$	0	0
$687$	21560.0	1.19733
$688$	−2848.00	−0.157818
$689$	−30444.0	−1.68334
$690$	−2940.00	−0.162209
$691$	2428.00	0.133669	0.0668346	−	0.997764i	$-0.478710\pi$
$691$	2428.00	0.133669	0.0668346	+	0.997764i	$0.478710\pi$
$692$	6852.00	0.376407
$693$	0	0
$694$	9132.00	0.499490
$695$	−6850.00	−0.373864
$696$	12600.0	0.686209
$697$	47952.0	2.60590
$698$	13460.0	0.729898
$699$	23016.0	1.24541
$700$	0	0
$701$	11187.0	0.602749	0.301375	−	0.953506i	$-0.402555\pi$
$701$	11187.0	0.602749	0.301375	+	0.953506i	$0.402555\pi$
$702$	3010.00	0.161831
$703$	−2380.00	−0.127686
$704$	−2112.00	−0.113067
$705$	14385.0	0.768469
$706$	−6054.00	−0.322727
$707$	0	0
$708$	13440.0	0.713427
$709$	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
$711$	9350.00	0.493182
$712$	−7680.00	−0.404242
$713$	3696.00	0.194132
$714$	0	0
$715$	−7095.00	−0.371102
$716$	−14640.0	−0.764138
$717$	12285.0	0.639877
$718$	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	$0.418629\pi$
$720$	1760.00	0.0910991
$721$	0	0
$722$	−3918.00	−0.201957
$723$	14.0000	0.000720146 0
$724$	6832.00	0.350703
$725$	−5625.00	−0.288148
$726$	3388.00	0.173196
$727$	17584.0	0.897049	0.448524	−	0.893771i	$-0.351950\pi$
$727$	17584.0	0.897049	0.448524	+	0.893771i	$0.351950\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	3580.00	0.181509
$731$	19758.0	0.999694
$732$	22736.0	1.14801
$733$	−20657.0	−1.04091	−0.520453	−	0.853890i	$-0.674237\pi$
$733$	−20657.0	−1.04091	−0.520453	+	0.853890i	$0.674237\pi$
$734$	−12262.0	−0.616619
$735$	0	0
$736$	1344.00	0.0673105
$737$	−19668.0	−0.983012
$738$	−19008.0	−0.948095
$739$	−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
$741$	−21070.0	−1.04457
$742$	0	0
$743$	−1548.00	−0.0764342	−0.0382171	−	0.999269i	$-0.512168\pi$
$743$	−1548.00	−0.0764342	−0.0382171	+	0.999269i	$0.512168\pi$
$744$	−4928.00	−0.242835
$745$	12450.0	0.612259
$746$	19264.0	0.945449
$747$	−21384.0	−1.04739
$748$	14652.0	0.716217
$749$	0	0
$750$	−1750.00	−0.0852013
$751$	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
$753$	−37926.0	−1.83546
$754$	−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
$759$	9702.00	0.463979
$760$	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	$0.368319\pi$
$762$	24416.0	1.16076
$763$	0	0
$764$	−8292.00	−0.392662
$765$	−12210.0	−0.577063
$766$	−2424.00	−0.114338
$767$	−20640.0	−0.971665
$768$	−1792.00	−0.0841969
$769$	−830.000	−0.0389214	−0.0194607	−	0.999811i	$-0.506195\pi$
$769$	−830.000	−0.0389214	−0.0194607	+	0.999811i	$0.506195\pi$
$770$	0	0
$771$	−15078.0	−0.704307
$772$	−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	$0.381752\pi$
$774$	−7832.00	−0.363715
$775$	2200.00	0.101969
$776$	5672.00	0.262388
$777$	0	0
$778$	8610.00	0.396765
$779$	−30240.0	−1.39083
$780$	−6020.00	−0.276347
$781$	−14256.0	−0.653162
$782$	−9324.00	−0.426375
$783$	−7875.00	−0.359425
$784$	0	0
$785$	16370.0	0.744293
$786$	−4452.00	−0.202033
$787$	12589.0	0.570203	0.285101	−	0.958497i	$-0.407973\pi$
$787$	12589.0	0.570203	0.285101	+	0.958497i	$0.407973\pi$
$788$	13104.0	0.592399
$789$	−27174.0	−1.22613
$790$	4250.00	0.191403
$791$	0	0
$792$	−5808.00	−0.260579
$793$	−34916.0	−1.56356
$794$	3218.00	0.143832
$795$	24780.0	1.10548
$796$	−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
$801$	−21120.0	−0.931634
$802$	−27006.0	−1.18905
$803$	−11814.0	−0.519187
$804$	−16688.0	−0.732015
$805$	0	0
$806$	7568.00	0.330734
$807$	3990.00	0.174045
$808$	3504.00	0.152562
$809$	3945.00	0.171445	0.0857224	−	0.996319i	$-0.472680\pi$
$809$	3945.00	0.171445	0.0857224	+	0.996319i	$0.472680\pi$
$810$	−8390.00	−0.363944
$811$	1618.00	0.0700563	0.0350282	−	0.999386i	$-0.488848\pi$
$811$	1618.00	0.0700563	0.0350282	+	0.999386i	$0.488848\pi$
$812$	0	0
$813$	23324.0	1.00616
$814$	2244.00	0.0966243
$815$	4510.00	0.193839
$816$	12432.0	0.533342
$817$	−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	$-0.335728\pi$
$821$	23217.0	0.986941	0.493471	+	0.869762i	$0.335728\pi$
$822$	−34944.0	−1.48274
$823$	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
$825$	5775.00	0.243709
$826$	0	0
$827$	−12654.0	−0.532071	−0.266035	−	0.963963i	$-0.585714\pi$
$827$	−12654.0	−0.532071	−0.266035	+	0.963963i	$0.585714\pi$
$828$	3696.00	0.155127
$829$	3400.00	0.142445	0.0712225	−	0.997460i	$-0.477310\pi$
$829$	3400.00	0.142445	0.0712225	+	0.997460i	$0.477310\pi$
$830$	−9720.00	−0.406489
$831$	2758.00	0.115131
$832$	2752.00	0.114674
$833$	0	0
$834$	19180.0	0.796342
$835$	19845.0	0.822473
$836$	−9240.00	−0.382263
$837$	3080.00	0.127193
$838$	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
$843$	−22869.0	−0.934342
$844$	10628.0	0.433449
$845$	−1740.00	−0.0708377
$846$	−18084.0	−0.734918
$847$	0	0
$848$	−11328.0	−0.458732
$849$	4739.00	0.191569
$850$	−5550.00	−0.223957
$851$	−1428.00	−0.0575220
$852$	−12096.0	−0.486387
$853$	−25022.0	−1.00438	−0.502190	−	0.864757i	$-0.667472\pi$
$853$	−25022.0	−1.00438	−0.502190	+	0.864757i	$0.667472\pi$
$854$	0	0
$855$	7700.00	0.307994
$856$	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	$0.486712\pi$
$858$	19866.0	0.790459
$859$	4300.00	0.170796	0.0853982	−	0.996347i	$-0.472784\pi$
$859$	4300.00	0.170796	0.0853982	+	0.996347i	$0.472784\pi$
$860$	−3560.00	−0.141157
$861$	0	0
$862$	10374.0	0.409907
$863$	−7428.00	−0.292992	−0.146496	−	0.989211i	$-0.546800\pi$
$863$	−7428.00	−0.292992	−0.146496	+	0.989211i	$0.546800\pi$
$864$	1120.00	0.0441009
$865$	8565.00	0.336669
$866$	−5764.00	−0.226176
$867$	−51856.0	−2.03128
$868$	0	0
$869$	−14025.0	−0.547486
$870$	15750.0	0.613764
$871$	25628.0	0.996982
$872$	−15320.0	−0.594955
$873$	15598.0	0.604711
$874$	5880.00	0.227567
$875$	0	0
$876$	−10024.0	−0.386621
$877$	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
$879$	−60291.0	−2.31350
$880$	−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
$885$	16800.0	0.638108
$886$	−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	$0.396844\pi$
$888$	1904.00	0.0719528
$889$	0	0
$890$	−9600.00	−0.361565
$891$	27687.0	1.04102
$892$	−188.000	−0.00705684
$893$	−28770.0	−1.07811
$894$	−34860.0	−1.30413
$895$	−18300.0	−0.683465
$896$	0	0
$897$	−12642.0	−0.470573
$898$	−9090.00	−0.337792
$899$	−19800.0	−0.734557
$900$	2200.00	0.0814815
$901$	78588.0	2.90582
$902$	28512.0	1.05249
$903$	0	0
$904$	−4464.00	−0.164237
$905$	8540.00	0.313679
$906$	−1918.00	−0.0703325
$907$	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
$909$	9636.00	0.351602
$910$	0	0
$911$	−21168.0	−0.769843	−0.384922	−	0.922949i	$-0.625772\pi$
$911$	−21168.0	−0.769843	−0.384922	+	0.922949i	$0.625772\pi$
$912$	−7840.00	−0.284658
$913$	32076.0	1.16272
$914$	−968.000	−0.0350313
$915$	28420.0	1.02682
$916$	−12320.0	−0.444393
$917$	0	0
$918$	−7770.00	−0.279355
$919$	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
$921$	−24493.0	−0.876299
$922$	2736.00	0.0977282
$923$	18576.0	0.662445
$924$	0	0
$925$	−850.000	−0.0302139
$926$	29704.0	1.05414
$927$	22726.0	0.805199
$928$	−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	$0.532771\pi$
$930$	−6160.00	−0.217198
$931$	0	0
$932$	−13152.0	−0.462240
$933$	39774.0	1.39565
$934$	−15042.0	−0.526969
$935$	18315.0	0.640604
$936$	7568.00	0.264282
$937$	1429.00	0.0498222	0.0249111	−	0.999690i	$-0.492070\pi$
$937$	1429.00	0.0498222	0.0249111	+	0.999690i	$0.492070\pi$
$938$	0	0
$939$	28679.0	0.996703
$940$	−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	$0.594749\pi$
$942$	−45836.0	−1.58537
$943$	−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	$-0.787782\pi$
$947$	−45804.0	−1.57173	−0.785866	+	0.618397i	$0.787782\pi$
$948$	−11900.0	−0.407694
$949$	15394.0	0.526565
$950$	3500.00	0.119532
$951$	32718.0	1.11562
$952$	0	0
$953$	−41508.0	−1.41089	−0.705444	−	0.708766i	$-0.749252\pi$
$953$	−41508.0	−1.41089	−0.705444	+	0.708766i	$0.749252\pi$
$954$	−31152.0	−1.05722
$955$	−10365.0	−0.351208
$956$	−7020.00	−0.237493
$957$	−51975.0	−1.75560
$958$	−17700.0	−0.596932
$959$	0	0
$960$	−2240.00	−0.0753080
$961$	−22047.0	−0.740056
$962$	−2924.00	−0.0979974
$963$	19932.0	0.666978
$964$	−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
$969$	54390.0	1.80316
$970$	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	$0.268812\pi$
$972$	19712.0	0.650476
$973$	0	0
$974$	−29228.0	−0.961525
$975$	−7525.00	−0.247172
$976$	−12992.0	−0.426090
$977$	−17214.0	−0.563690	−0.281845	−	0.959460i	$-0.590946\pi$
$977$	−17214.0	−0.563690	−0.281845	+	0.959460i	$0.590946\pi$
$978$	−12628.0	−0.412882
$979$	31680.0	1.03422
$980$	0	0
$981$	−42130.0	−1.37116
$982$	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	$0.565830\pi$
$984$	24192.0	0.783753
$985$	16380.0	0.529858
$986$	49950.0	1.61332
$987$	0	0
$988$	12040.0	0.387696
$989$	−7476.00	−0.240367
$990$	−7260.00	−0.233069
$991$	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
$993$	−71204.0	−2.27552
$994$	0	0
$995$	−11800.0	−0.375965
$996$	27216.0	0.865835
$997$	35269.0	1.12034	0.560171	−	0.828377i	$-0.310736\pi$
$997$	35269.0	1.12034	0.560171	+	0.828377i	$0.310736\pi$
$998$	−19130.0	−0.606763
$999$	−1190.00	−0.0376876

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.f.1.1	✓	1	7.6	odd	2
350.4.a.b.1.1		1	35.34	odd	2
350.4.c.l.99.1		2	35.13	even	4
350.4.c.l.99.2		2	35.27	even	4
490.4.a.i.1.1		1	1.1	even	1	trivial
490.4.e.b.361.1		2	7.5	odd	6
490.4.e.b.471.1		2	7.3	odd	6
490.4.e.h.361.1		2	7.2	even	3
490.4.e.h.471.1		2	7.4	even	3
560.4.a.c.1.1		1	28.27	even	2
630.4.a.j.1.1		1	21.20	even	2
2240.4.a.f.1.1		1	56.13	odd	2
2240.4.a.bh.1.1		1	56.27	even	2
2450.4.a.s.1.1		1	5.4	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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