LMFDB - Embedded newform 570.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +54.0000 q^{11} -12.0000 q^{12} +32.0000 q^{13} -52.0000 q^{14} -15.0000 q^{15} +16.0000 q^{16} +78.0000 q^{17} -18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} -78.0000 q^{21} -108.000 q^{22} +12.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -64.0000 q^{26} -27.0000 q^{27} +104.000 q^{28} +204.000 q^{29} +30.0000 q^{30} -256.000 q^{31} -32.0000 q^{32} -162.000 q^{33} -156.000 q^{34} +130.000 q^{35} +36.0000 q^{36} -340.000 q^{37} -38.0000 q^{38} -96.0000 q^{39} -40.0000 q^{40} -156.000 q^{41} +156.000 q^{42} +326.000 q^{43} +216.000 q^{44} +45.0000 q^{45} -24.0000 q^{46} -132.000 q^{47} -48.0000 q^{48} +333.000 q^{49} -50.0000 q^{50} -234.000 q^{51} +128.000 q^{52} +90.0000 q^{53} +54.0000 q^{54} +270.000 q^{55} -208.000 q^{56} -57.0000 q^{57} -408.000 q^{58} -360.000 q^{59} -60.0000 q^{60} -838.000 q^{61} +512.000 q^{62} +234.000 q^{63} +64.0000 q^{64} +160.000 q^{65} +324.000 q^{66} -16.0000 q^{67} +312.000 q^{68} -36.0000 q^{69} -260.000 q^{70} +888.000 q^{71} -72.0000 q^{72} +854.000 q^{73} +680.000 q^{74} -75.0000 q^{75} +76.0000 q^{76} +1404.00 q^{77} +192.000 q^{78} -640.000 q^{79} +80.0000 q^{80} +81.0000 q^{81} +312.000 q^{82} -84.0000 q^{83} -312.000 q^{84} +390.000 q^{85} -652.000 q^{86} -612.000 q^{87} -432.000 q^{88} +828.000 q^{89} -90.0000 q^{90} +832.000 q^{91} +48.0000 q^{92} +768.000 q^{93} +264.000 q^{94} +95.0000 q^{95} +96.0000 q^{96} +1424.00 q^{97} -666.000 q^{98} +486.000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	6.00000	0.408248
$7$	26.0000	1.40387	0.701934	−	0.712242i	$-0.252320\pi$
$7$	26.0000	1.40387	0.701934	+	0.712242i	$0.252320\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	54.0000	1.48015	0.740073	−	0.672526i	$-0.234791\pi$
$11$	54.0000	1.48015	0.740073	+	0.672526i	$0.234791\pi$
$12$	−12.0000	−0.288675
$13$	32.0000	0.682708	0.341354	−	0.939935i	$-0.389115\pi$
$13$	32.0000	0.682708	0.341354	+	0.939935i	$0.389115\pi$
$14$	−52.0000	−0.992685
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	78.0000	1.11281	0.556405	−	0.830911i	$-0.312180\pi$
$17$	78.0000	1.11281	0.556405	+	0.830911i	$0.312180\pi$
$18$	−18.0000	−0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	20.0000	0.223607
$21$	−78.0000	−0.810524
$22$	−108.000	−1.04662
$23$	12.0000	0.108790	0.0543951	−	0.998519i	$-0.482677\pi$
$23$	12.0000	0.108790	0.0543951	+	0.998519i	$0.482677\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−64.0000	−0.482747
$27$	−27.0000	−0.192450
$28$	104.000	0.701934
$29$	204.000	1.30627	0.653135	−	0.757241i	$-0.273453\pi$
$29$	204.000	1.30627	0.653135	+	0.757241i	$0.273453\pi$
$30$	30.0000	0.182574
$31$	−256.000	−1.48319	−0.741596	−	0.670847i	$-0.765931\pi$
$31$	−256.000	−1.48319	−0.741596	+	0.670847i	$0.765931\pi$
$32$	−32.0000	−0.176777
$33$	−162.000	−0.854563
$34$	−156.000	−0.786876
$35$	130.000	0.627829
$36$	36.0000	0.166667
$37$	−340.000	−1.51069	−0.755347	−	0.655325i	$-0.772532\pi$
$37$	−340.000	−1.51069	−0.755347	+	0.655325i	$0.772532\pi$
$38$	−38.0000	−0.162221
$39$	−96.0000	−0.394162
$40$	−40.0000	−0.158114
$41$	−156.000	−0.594222	−0.297111	−	0.954843i	$-0.596023\pi$
$41$	−156.000	−0.594222	−0.297111	+	0.954843i	$0.596023\pi$
$42$	156.000	0.573127
$43$	326.000	1.15615	0.578076	−	0.815983i	$-0.303804\pi$
$43$	326.000	1.15615	0.578076	+	0.815983i	$0.303804\pi$
$44$	216.000	0.740073
$45$	45.0000	0.149071
$46$	−24.0000	−0.0769262
$47$	−132.000	−0.409663	−0.204832	−	0.978797i	$-0.565665\pi$
$47$	−132.000	−0.409663	−0.204832	+	0.978797i	$0.565665\pi$
$48$	−48.0000	−0.144338
$49$	333.000	0.970845
$50$	−50.0000	−0.141421
$51$	−234.000	−0.642481
$52$	128.000	0.341354
$53$	90.0000	0.233254	0.116627	−	0.993176i	$-0.462792\pi$
$53$	90.0000	0.233254	0.116627	+	0.993176i	$0.462792\pi$
$54$	54.0000	0.136083
$55$	270.000	0.661942
$56$	−208.000	−0.496342
$57$	−57.0000	−0.132453
$58$	−408.000	−0.923673
$59$	−360.000	−0.794373	−0.397187	−	0.917738i	$-0.630013\pi$
$59$	−360.000	−0.794373	−0.397187	+	0.917738i	$0.630013\pi$
$60$	−60.0000	−0.129099
$61$	−838.000	−1.75893	−0.879466	−	0.475961i	$-0.842100\pi$
$61$	−838.000	−1.75893	−0.879466	+	0.475961i	$0.842100\pi$
$62$	512.000	1.04878
$63$	234.000	0.467956
$64$	64.0000	0.125000
$65$	160.000	0.305316
$66$	324.000	0.604267
$67$	−16.0000	−0.0291748	−0.0145874	−	0.999894i	$-0.504643\pi$
$67$	−16.0000	−0.0291748	−0.0145874	+	0.999894i	$0.504643\pi$
$68$	312.000	0.556405
$69$	−36.0000	−0.0628100
$70$	−260.000	−0.443942
$71$	888.000	1.48431	0.742156	−	0.670227i	$-0.233803\pi$
$71$	888.000	1.48431	0.742156	+	0.670227i	$0.233803\pi$
$72$	−72.0000	−0.117851
$73$	854.000	1.36922	0.684611	−	0.728909i	$-0.259972\pi$
$73$	854.000	1.36922	0.684611	+	0.728909i	$0.259972\pi$
$74$	680.000	1.06822
$75$	−75.0000	−0.115470
$76$	76.0000	0.114708
$77$	1404.00	2.07793
$78$	192.000	0.278714
$79$	−640.000	−0.911464	−0.455732	−	0.890117i	$-0.650622\pi$
$79$	−640.000	−0.911464	−0.455732	+	0.890117i	$0.650622\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	312.000	0.420178
$83$	−84.0000	−0.111087	−0.0555434	−	0.998456i	$-0.517689\pi$
$83$	−84.0000	−0.111087	−0.0555434	+	0.998456i	$0.517689\pi$
$84$	−312.000	−0.405262
$85$	390.000	0.497664
$86$	−652.000	−0.817523
$87$	−612.000	−0.754176
$88$	−432.000	−0.523311
$89$	828.000	0.986155	0.493078	−	0.869985i	$-0.335872\pi$
$89$	828.000	0.986155	0.493078	+	0.869985i	$0.335872\pi$
$90$	−90.0000	−0.105409
$91$	832.000	0.958432
$92$	48.0000	0.0543951
$93$	768.000	0.856321
$94$	264.000	0.289676
$95$	95.0000	0.102598
$96$	96.0000	0.102062
$97$	1424.00	1.49057	0.745285	−	0.666746i	$-0.232313\pi$
$97$	1424.00	1.49057	0.745285	+	0.666746i	$0.232313\pi$
$98$	−666.000	−0.686491
$99$	486.000	0.493382
$100$	100.000	0.100000
$101$	−750.000	−0.738889	−0.369445	−	0.929253i	$-0.620452\pi$
$101$	−750.000	−0.738889	−0.369445	+	0.929253i	$0.620452\pi$
$102$	468.000	0.454303
$103$	−676.000	−0.646682	−0.323341	−	0.946282i	$-0.604806\pi$
$103$	−676.000	−0.646682	−0.323341	+	0.946282i	$0.604806\pi$
$104$	−256.000	−0.241374
$105$	−390.000	−0.362477
$106$	−180.000	−0.164935
$107$	1476.00	1.33355	0.666777	−	0.745257i	$-0.267673\pi$
$107$	1476.00	1.33355	0.666777	+	0.745257i	$0.267673\pi$
$108$	−108.000	−0.0962250
$109$	−1294.00	−1.13709	−0.568545	−	0.822652i	$-0.692493\pi$
$109$	−1294.00	−1.13709	−0.568545	+	0.822652i	$0.692493\pi$
$110$	−540.000	−0.468063
$111$	1020.00	0.872199
$112$	416.000	0.350967
$113$	498.000	0.414583	0.207292	−	0.978279i	$-0.433535\pi$
$113$	498.000	0.414583	0.207292	+	0.978279i	$0.433535\pi$
$114$	114.000	0.0936586
$115$	60.0000	0.0486524
$116$	816.000	0.653135
$117$	288.000	0.227569
$118$	720.000	0.561707
$119$	2028.00	1.56224
$120$	120.000	0.0912871
$121$	1585.00	1.19083
$122$	1676.00	1.24375
$123$	468.000	0.343074
$124$	−1024.00	−0.741596
$125$	125.000	0.0894427
$126$	−468.000	−0.330895
$127$	920.000	0.642809	0.321405	−	0.946942i	$-0.395845\pi$
$127$	920.000	0.642809	0.321405	+	0.946942i	$0.395845\pi$
$128$	−128.000	−0.0883883
$129$	−978.000	−0.667505
$130$	−320.000	−0.215891
$131$	−678.000	−0.452192	−0.226096	−	0.974105i	$-0.572596\pi$
$131$	−678.000	−0.452192	−0.226096	+	0.974105i	$0.572596\pi$
$132$	−648.000	−0.427282
$133$	494.000	0.322069
$134$	32.0000	0.0206297
$135$	−135.000	−0.0860663
$136$	−624.000	−0.393438
$137$	−630.000	−0.392880	−0.196440	−	0.980516i	$-0.562938\pi$
$137$	−630.000	−0.392880	−0.196440	+	0.980516i	$0.562938\pi$
$138$	72.0000	0.0444134
$139$	−376.000	−0.229438	−0.114719	−	0.993398i	$-0.536597\pi$
$139$	−376.000	−0.229438	−0.114719	+	0.993398i	$0.536597\pi$
$140$	520.000	0.313914
$141$	396.000	0.236519
$142$	−1776.00	−1.04957
$143$	1728.00	1.01051
$144$	144.000	0.0833333
$145$	1020.00	0.584182
$146$	−1708.00	−0.968186
$147$	−999.000	−0.560518
$148$	−1360.00	−0.755347
$149$	1386.00	0.762051	0.381025	−	0.924565i	$-0.375571\pi$
$149$	1386.00	0.762051	0.381025	+	0.924565i	$0.375571\pi$
$150$	150.000	0.0816497
$151$	−592.000	−0.319048	−0.159524	−	0.987194i	$-0.550996\pi$
$151$	−592.000	−0.319048	−0.159524	+	0.987194i	$0.550996\pi$
$152$	−152.000	−0.0811107
$153$	702.000	0.370937
$154$	−2808.00	−1.46932
$155$	−1280.00	−0.663304
$156$	−384.000	−0.197081
$157$	−1726.00	−0.877387	−0.438694	−	0.898637i	$-0.644559\pi$
$157$	−1726.00	−0.877387	−0.438694	+	0.898637i	$0.644559\pi$
$158$	1280.00	0.644502
$159$	−270.000	−0.134669
$160$	−160.000	−0.0790569
$161$	312.000	0.152727
$162$	−162.000	−0.0785674
$163$	2402.00	1.15423	0.577114	−	0.816664i	$-0.304179\pi$
$163$	2402.00	1.15423	0.577114	+	0.816664i	$0.304179\pi$
$164$	−624.000	−0.297111
$165$	−810.000	−0.382172
$166$	168.000	0.0785502
$167$	−2832.00	−1.31226	−0.656128	−	0.754650i	$-0.727807\pi$
$167$	−2832.00	−1.31226	−0.656128	+	0.754650i	$0.727807\pi$
$168$	624.000	0.286563
$169$	−1173.00	−0.533910
$170$	−780.000	−0.351902
$171$	171.000	0.0764719
$172$	1304.00	0.578076
$173$	1446.00	0.635476	0.317738	−	0.948179i	$-0.397077\pi$
$173$	1446.00	0.635476	0.317738	+	0.948179i	$0.397077\pi$
$174$	1224.00	0.533283
$175$	650.000	0.280774
$176$	864.000	0.370037
$177$	1080.00	0.458631
$178$	−1656.00	−0.697317
$179$	3192.00	1.33286	0.666428	−	0.745569i	$-0.267822\pi$
$179$	3192.00	1.33286	0.666428	+	0.745569i	$0.267822\pi$
$180$	180.000	0.0745356
$181$	−2950.00	−1.21145	−0.605723	−	0.795675i	$-0.707116\pi$
$181$	−2950.00	−1.21145	−0.605723	+	0.795675i	$0.707116\pi$
$182$	−1664.00	−0.677714
$183$	2514.00	1.01552
$184$	−96.0000	−0.0384631
$185$	−1700.00	−0.675603
$186$	−1536.00	−0.605511
$187$	4212.00	1.64712
$188$	−528.000	−0.204832
$189$	−702.000	−0.270175
$190$	−190.000	−0.0725476
$191$	2322.00	0.879655	0.439827	−	0.898082i	$-0.355040\pi$
$191$	2322.00	0.879655	0.439827	+	0.898082i	$0.355040\pi$
$192$	−192.000	−0.0721688
$193$	572.000	0.213334	0.106667	−	0.994295i	$-0.465982\pi$
$193$	572.000	0.213334	0.106667	+	0.994295i	$0.465982\pi$
$194$	−2848.00	−1.05399
$195$	−480.000	−0.176274
$196$	1332.00	0.485423
$197$	−1206.00	−0.436162	−0.218081	−	0.975931i	$-0.569980\pi$
$197$	−1206.00	−0.436162	−0.218081	+	0.975931i	$0.569980\pi$
$198$	−972.000	−0.348874
$199$	−2836.00	−1.01024	−0.505122	−	0.863048i	$-0.668553\pi$
$199$	−2836.00	−1.01024	−0.505122	+	0.863048i	$0.668553\pi$
$200$	−200.000	−0.0707107
$201$	48.0000	0.0168441
$202$	1500.00	0.522473
$203$	5304.00	1.83383
$204$	−936.000	−0.321241
$205$	−780.000	−0.265744
$206$	1352.00	0.457273
$207$	108.000	0.0362634
$208$	512.000	0.170677
$209$	1026.00	0.339569
$210$	780.000	0.256310
$211$	−4708.00	−1.53608	−0.768038	−	0.640404i	$-0.778767\pi$
$211$	−4708.00	−1.53608	−0.768038	+	0.640404i	$0.778767\pi$
$212$	360.000	0.116627
$213$	−2664.00	−0.856968
$214$	−2952.00	−0.942965
$215$	1630.00	0.517047
$216$	216.000	0.0680414
$217$	−6656.00	−2.08221
$218$	2588.00	0.804043
$219$	−2562.00	−0.790520
$220$	1080.00	0.330971
$221$	2496.00	0.759725
$222$	−2040.00	−0.616738
$223$	4172.00	1.25282	0.626408	−	0.779496i	$-0.284525\pi$
$223$	4172.00	1.25282	0.626408	+	0.779496i	$0.284525\pi$
$224$	−832.000	−0.248171
$225$	225.000	0.0666667
$226$	−996.000	−0.293155
$227$	−420.000	−0.122803	−0.0614017	−	0.998113i	$-0.519557\pi$
$227$	−420.000	−0.122803	−0.0614017	+	0.998113i	$0.519557\pi$
$228$	−228.000	−0.0662266
$229$	−2494.00	−0.719686	−0.359843	−	0.933013i	$-0.617170\pi$
$229$	−2494.00	−0.719686	−0.359843	+	0.933013i	$0.617170\pi$
$230$	−120.000	−0.0344025
$231$	−4212.00	−1.19969
$232$	−1632.00	−0.461836
$233$	−2166.00	−0.609010	−0.304505	−	0.952511i	$-0.598491\pi$
$233$	−2166.00	−0.609010	−0.304505	+	0.952511i	$0.598491\pi$
$234$	−576.000	−0.160916
$235$	−660.000	−0.183207
$236$	−1440.00	−0.397187
$237$	1920.00	0.526234
$238$	−4056.00	−1.10467
$239$	−4890.00	−1.32346	−0.661732	−	0.749741i	$-0.730178\pi$
$239$	−4890.00	−1.32346	−0.661732	+	0.749741i	$0.730178\pi$
$240$	−240.000	−0.0645497
$241$	−6430.00	−1.71864	−0.859321	−	0.511437i	$-0.829113\pi$
$241$	−6430.00	−1.71864	−0.859321	+	0.511437i	$0.829113\pi$
$242$	−3170.00	−0.842047
$243$	−243.000	−0.0641500
$244$	−3352.00	−0.879466
$245$	1665.00	0.434175
$246$	−936.000	−0.242590
$247$	608.000	0.156624
$248$	2048.00	0.524388
$249$	252.000	0.0641359
$250$	−250.000	−0.0632456
$251$	5910.00	1.48620	0.743099	−	0.669181i	$-0.233355\pi$
$251$	5910.00	1.48620	0.743099	+	0.669181i	$0.233355\pi$
$252$	936.000	0.233978
$253$	648.000	0.161025
$254$	−1840.00	−0.454535
$255$	−1170.00	−0.287326
$256$	256.000	0.0625000
$257$	−1206.00	−0.292717	−0.146358	−	0.989232i	$-0.546755\pi$
$257$	−1206.00	−0.292717	−0.146358	+	0.989232i	$0.546755\pi$
$258$	1956.00	0.471997
$259$	−8840.00	−2.12081
$260$	640.000	0.152658
$261$	1836.00	0.435424
$262$	1356.00	0.319748
$263$	5976.00	1.40113	0.700563	−	0.713591i	$-0.252932\pi$
$263$	5976.00	1.40113	0.700563	+	0.713591i	$0.252932\pi$
$264$	1296.00	0.302134
$265$	450.000	0.104314
$266$	−988.000	−0.227737
$267$	−2484.00	−0.569357
$268$	−64.0000	−0.0145874
$269$	2076.00	0.470543	0.235271	−	0.971930i	$-0.424402\pi$
$269$	2076.00	0.470543	0.235271	+	0.971930i	$0.424402\pi$
$270$	270.000	0.0608581
$271$	−340.000	−0.0762123	−0.0381061	−	0.999274i	$-0.512132\pi$
$271$	−340.000	−0.0762123	−0.0381061	+	0.999274i	$0.512132\pi$
$272$	1248.00	0.278203
$273$	−2496.00	−0.553351
$274$	1260.00	0.277808
$275$	1350.00	0.296029
$276$	−144.000	−0.0314050
$277$	−3454.00	−0.749208	−0.374604	−	0.927185i	$-0.622221\pi$
$277$	−3454.00	−0.749208	−0.374604	+	0.927185i	$0.622221\pi$
$278$	752.000	0.162237
$279$	−2304.00	−0.494397
$280$	−1040.00	−0.221971
$281$	−7776.00	−1.65081	−0.825404	−	0.564542i	$-0.809053\pi$
$281$	−7776.00	−1.65081	−0.825404	+	0.564542i	$0.809053\pi$
$282$	−792.000	−0.167244
$283$	8354.00	1.75475	0.877374	−	0.479807i	$-0.159293\pi$
$283$	8354.00	1.75475	0.877374	+	0.479807i	$0.159293\pi$
$284$	3552.00	0.742156
$285$	−285.000	−0.0592349
$286$	−3456.00	−0.714537
$287$	−4056.00	−0.834209
$288$	−288.000	−0.0589256
$289$	1171.00	0.238347
$290$	−2040.00	−0.413079
$291$	−4272.00	−0.860581
$292$	3416.00	0.684611
$293$	−474.000	−0.0945098	−0.0472549	−	0.998883i	$-0.515047\pi$
$293$	−474.000	−0.0945098	−0.0472549	+	0.998883i	$0.515047\pi$
$294$	1998.00	0.396346
$295$	−1800.00	−0.355254
$296$	2720.00	0.534111
$297$	−1458.00	−0.284854
$298$	−2772.00	−0.538851
$299$	384.000	0.0742719
$300$	−300.000	−0.0577350
$301$	8476.00	1.62308
$302$	1184.00	0.225601
$303$	2250.00	0.426598
$304$	304.000	0.0573539
$305$	−4190.00	−0.786619
$306$	−1404.00	−0.262292
$307$	8696.00	1.61663	0.808317	−	0.588747i	$-0.200379\pi$
$307$	8696.00	1.61663	0.808317	+	0.588747i	$0.200379\pi$
$308$	5616.00	1.03897
$309$	2028.00	0.373362
$310$	2560.00	0.469027
$311$	−1134.00	−0.206763	−0.103381	−	0.994642i	$-0.532966\pi$
$311$	−1134.00	−0.206763	−0.103381	+	0.994642i	$0.532966\pi$
$312$	768.000	0.139357
$313$	−6982.00	−1.26085	−0.630425	−	0.776250i	$-0.717119\pi$
$313$	−6982.00	−1.26085	−0.630425	+	0.776250i	$0.717119\pi$
$314$	3452.00	0.620406
$315$	1170.00	0.209276
$316$	−2560.00	−0.455732
$317$	−414.000	−0.0733519	−0.0366760	−	0.999327i	$-0.511677\pi$
$317$	−414.000	−0.0733519	−0.0366760	+	0.999327i	$0.511677\pi$
$318$	540.000	0.0952255
$319$	11016.0	1.93347
$320$	320.000	0.0559017
$321$	−4428.00	−0.769928
$322$	−624.000	−0.107994
$323$	1482.00	0.255296
$324$	324.000	0.0555556
$325$	800.000	0.136542
$326$	−4804.00	−0.816162
$327$	3882.00	0.656499
$328$	1248.00	0.210089
$329$	−3432.00	−0.575113
$330$	1620.00	0.270237
$331$	8468.00	1.40617	0.703087	−	0.711104i	$-0.251805\pi$
$331$	8468.00	1.40617	0.703087	+	0.711104i	$0.251805\pi$
$332$	−336.000	−0.0555434
$333$	−3060.00	−0.503564
$334$	5664.00	0.927905
$335$	−80.0000	−0.0130474
$336$	−1248.00	−0.202631
$337$	−2488.00	−0.402166	−0.201083	−	0.979574i	$-0.564446\pi$
$337$	−2488.00	−0.402166	−0.201083	+	0.979574i	$0.564446\pi$
$338$	2346.00	0.377531
$339$	−1494.00	−0.239360
$340$	1560.00	0.248832
$341$	−13824.0	−2.19534
$342$	−342.000	−0.0540738
$343$	−260.000	−0.0409291
$344$	−2608.00	−0.408761
$345$	−180.000	−0.0280895
$346$	−2892.00	−0.449349
$347$	−9444.00	−1.46104	−0.730519	−	0.682892i	$-0.760722\pi$
$347$	−9444.00	−1.46104	−0.730519	+	0.682892i	$0.760722\pi$
$348$	−2448.00	−0.377088
$349$	1118.00	0.171476	0.0857381	−	0.996318i	$-0.472675\pi$
$349$	1118.00	0.171476	0.0857381	+	0.996318i	$0.472675\pi$
$350$	−1300.00	−0.198537
$351$	−864.000	−0.131387
$352$	−1728.00	−0.261655
$353$	−870.000	−0.131177	−0.0655884	−	0.997847i	$-0.520892\pi$
$353$	−870.000	−0.131177	−0.0655884	+	0.997847i	$0.520892\pi$
$354$	−2160.00	−0.324301
$355$	4440.00	0.663805
$356$	3312.00	0.493078
$357$	−6084.00	−0.901959
$358$	−6384.00	−0.942472
$359$	2010.00	0.295498	0.147749	−	0.989025i	$-0.452797\pi$
$359$	2010.00	0.295498	0.147749	+	0.989025i	$0.452797\pi$
$360$	−360.000	−0.0527046
$361$	361.000	0.0526316
$362$	5900.00	0.856622
$363$	−4755.00	−0.687528
$364$	3328.00	0.479216
$365$	4270.00	0.612334
$366$	−5028.00	−0.718081
$367$	−3274.00	−0.465671	−0.232836	−	0.972516i	$-0.574800\pi$
$367$	−3274.00	−0.465671	−0.232836	+	0.972516i	$0.574800\pi$
$368$	192.000	0.0271975
$369$	−1404.00	−0.198074
$370$	3400.00	0.477723
$371$	2340.00	0.327458
$372$	3072.00	0.428161
$373$	−8008.00	−1.11163	−0.555816	−	0.831306i	$-0.687594\pi$
$373$	−8008.00	−1.11163	−0.555816	+	0.831306i	$0.687594\pi$
$374$	−8424.00	−1.16469
$375$	−375.000	−0.0516398
$376$	1056.00	0.144838
$377$	6528.00	0.891801
$378$	1404.00	0.191042
$379$	8132.00	1.10214	0.551072	−	0.834458i	$-0.314219\pi$
$379$	8132.00	1.10214	0.551072	+	0.834458i	$0.314219\pi$
$380$	380.000	0.0512989
$381$	−2760.00	−0.371126
$382$	−4644.00	−0.622010
$383$	11592.0	1.54654	0.773268	−	0.634079i	$-0.218621\pi$
$383$	11592.0	1.54654	0.773268	+	0.634079i	$0.218621\pi$
$384$	384.000	0.0510310
$385$	7020.00	0.929279
$386$	−1144.00	−0.150850
$387$	2934.00	0.385384
$388$	5696.00	0.745285
$389$	−1530.00	−0.199419	−0.0997096	−	0.995017i	$-0.531791\pi$
$389$	−1530.00	−0.199419	−0.0997096	+	0.995017i	$0.531791\pi$
$390$	960.000	0.124645
$391$	936.000	0.121063
$392$	−2664.00	−0.343246
$393$	2034.00	0.261073
$394$	2412.00	0.308413
$395$	−3200.00	−0.407619
$396$	1944.00	0.246691
$397$	1562.00	0.197467	0.0987337	−	0.995114i	$-0.468521\pi$
$397$	1562.00	0.197467	0.0987337	+	0.995114i	$0.468521\pi$
$398$	5672.00	0.714351
$399$	−1482.00	−0.185947
$400$	400.000	0.0500000
$401$	14976.0	1.86500	0.932501	−	0.361168i	$-0.117622\pi$
$401$	14976.0	1.86500	0.932501	+	0.361168i	$0.117622\pi$
$402$	−96.0000	−0.0119106
$403$	−8192.00	−1.01259
$404$	−3000.00	−0.369445
$405$	405.000	0.0496904
$406$	−10608.0	−1.29671
$407$	−18360.0	−2.23605
$408$	1872.00	0.227151
$409$	8246.00	0.996916	0.498458	−	0.866914i	$-0.333900\pi$
$409$	8246.00	0.996916	0.498458	+	0.866914i	$0.333900\pi$
$410$	1560.00	0.187910
$411$	1890.00	0.226829
$412$	−2704.00	−0.323341
$413$	−9360.00	−1.11519
$414$	−216.000	−0.0256421
$415$	−420.000	−0.0496795
$416$	−1024.00	−0.120687
$417$	1128.00	0.132466
$418$	−2052.00	−0.240111
$419$	12630.0	1.47259	0.736296	−	0.676660i	$-0.236573\pi$
$419$	12630.0	1.47259	0.736296	+	0.676660i	$0.236573\pi$
$420$	−1560.00	−0.181239
$421$	10262.0	1.18798	0.593990	−	0.804473i	$-0.297552\pi$
$421$	10262.0	1.18798	0.593990	+	0.804473i	$0.297552\pi$
$422$	9416.00	1.08617
$423$	−1188.00	−0.136554
$424$	−720.000	−0.0824677
$425$	1950.00	0.222562
$426$	5328.00	0.605968
$427$	−21788.0	−2.46931
$428$	5904.00	0.666777
$429$	−5184.00	−0.583417
$430$	−3260.00	−0.365607
$431$	−3900.00	−0.435862	−0.217931	−	0.975964i	$-0.569931\pi$
$431$	−3900.00	−0.435862	−0.217931	+	0.975964i	$0.569931\pi$
$432$	−432.000	−0.0481125
$433$	9380.00	1.04105	0.520524	−	0.853847i	$-0.325737\pi$
$433$	9380.00	1.04105	0.520524	+	0.853847i	$0.325737\pi$
$434$	13312.0	1.47234
$435$	−3060.00	−0.337278
$436$	−5176.00	−0.568545
$437$	228.000	0.0249582
$438$	5124.00	0.558982
$439$	9608.00	1.04457	0.522283	−	0.852772i	$-0.325080\pi$
$439$	9608.00	1.04457	0.522283	+	0.852772i	$0.325080\pi$
$440$	−2160.00	−0.234032
$441$	2997.00	0.323615
$442$	−4992.00	−0.537206
$443$	−5112.00	−0.548258	−0.274129	−	0.961693i	$-0.588390\pi$
$443$	−5112.00	−0.548258	−0.274129	+	0.961693i	$0.588390\pi$
$444$	4080.00	0.436100
$445$	4140.00	0.441022
$446$	−8344.00	−0.885874
$447$	−4158.00	−0.439970
$448$	1664.00	0.175484
$449$	−12612.0	−1.32561	−0.662803	−	0.748794i	$-0.730633\pi$
$449$	−12612.0	−1.32561	−0.662803	+	0.748794i	$0.730633\pi$
$450$	−450.000	−0.0471405
$451$	−8424.00	−0.879536
$452$	1992.00	0.207292
$453$	1776.00	0.184203
$454$	840.000	0.0868351
$455$	4160.00	0.428624
$456$	456.000	0.0468293
$457$	−15214.0	−1.55729	−0.778644	−	0.627466i	$-0.784092\pi$
$457$	−15214.0	−1.55729	−0.778644	+	0.627466i	$0.784092\pi$
$458$	4988.00	0.508895
$459$	−2106.00	−0.214160
$460$	240.000	0.0243262
$461$	10098.0	1.02020	0.510098	−	0.860116i	$-0.329609\pi$
$461$	10098.0	1.02020	0.510098	+	0.860116i	$0.329609\pi$
$462$	8424.00	0.848312
$463$	16766.0	1.68290	0.841449	−	0.540336i	$-0.181703\pi$
$463$	16766.0	1.68290	0.841449	+	0.540336i	$0.181703\pi$
$464$	3264.00	0.326568
$465$	3840.00	0.382959
$466$	4332.00	0.430635
$467$	−8904.00	−0.882287	−0.441143	−	0.897437i	$-0.645427\pi$
$467$	−8904.00	−0.882287	−0.441143	+	0.897437i	$0.645427\pi$
$468$	1152.00	0.113785
$469$	−416.000	−0.0409576
$470$	1320.00	0.129547
$471$	5178.00	0.506560
$472$	2880.00	0.280853
$473$	17604.0	1.71127
$474$	−3840.00	−0.372103
$475$	475.000	0.0458831
$476$	8112.00	0.781120
$477$	810.000	0.0777513
$478$	9780.00	0.935830
$479$	−12966.0	−1.23681	−0.618405	−	0.785860i	$-0.712221\pi$
$479$	−12966.0	−1.23681	−0.618405	+	0.785860i	$0.712221\pi$
$480$	480.000	0.0456435
$481$	−10880.0	−1.03136
$482$	12860.0	1.21526
$483$	−936.000	−0.0881770
$484$	6340.00	0.595417
$485$	7120.00	0.666603
$486$	486.000	0.0453609
$487$	1460.00	0.135850	0.0679250	−	0.997690i	$-0.478362\pi$
$487$	1460.00	0.135850	0.0679250	+	0.997690i	$0.478362\pi$
$488$	6704.00	0.621877
$489$	−7206.00	−0.666394
$490$	−3330.00	−0.307008
$491$	−1038.00	−0.0954059	−0.0477029	−	0.998862i	$-0.515190\pi$
$491$	−1038.00	−0.0954059	−0.0477029	+	0.998862i	$0.515190\pi$
$492$	1872.00	0.171537
$493$	15912.0	1.45363
$494$	−1216.00	−0.110750
$495$	2430.00	0.220647
$496$	−4096.00	−0.370798
$497$	23088.0	2.08378
$498$	−504.000	−0.0453510
$499$	−16096.0	−1.44400	−0.722000	−	0.691893i	$-0.756777\pi$
$499$	−16096.0	−1.44400	−0.722000	+	0.691893i	$0.756777\pi$
$500$	500.000	0.0447214
$501$	8496.00	0.757631
$502$	−11820.0	−1.05090
$503$	19296.0	1.71047	0.855235	−	0.518241i	$-0.173413\pi$
$503$	19296.0	1.71047	0.855235	+	0.518241i	$0.173413\pi$
$504$	−1872.00	−0.165447
$505$	−3750.00	−0.330441
$506$	−1296.00	−0.113862
$507$	3519.00	0.308253
$508$	3680.00	0.321405
$509$	2472.00	0.215264	0.107632	−	0.994191i	$-0.465673\pi$
$509$	2472.00	0.215264	0.107632	+	0.994191i	$0.465673\pi$
$510$	2340.00	0.203170
$511$	22204.0	1.92221
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	2412.00	0.206982
$515$	−3380.00	−0.289205
$516$	−3912.00	−0.333752
$517$	−7128.00	−0.606362
$518$	17680.0	1.49964
$519$	−4338.00	−0.366892
$520$	−1280.00	−0.107946
$521$	−19320.0	−1.62462	−0.812308	−	0.583229i	$-0.801789\pi$
$521$	−19320.0	−1.62462	−0.812308	+	0.583229i	$0.801789\pi$
$522$	−3672.00	−0.307891
$523$	−1468.00	−0.122736	−0.0613682	−	0.998115i	$-0.519546\pi$
$523$	−1468.00	−0.122736	−0.0613682	+	0.998115i	$0.519546\pi$
$524$	−2712.00	−0.226096
$525$	−1950.00	−0.162105
$526$	−11952.0	−0.990745
$527$	−19968.0	−1.65051
$528$	−2592.00	−0.213641
$529$	−12023.0	−0.988165
$530$	−900.000	−0.0737613
$531$	−3240.00	−0.264791
$532$	1976.00	0.161035
$533$	−4992.00	−0.405680
$534$	4968.00	0.402596
$535$	7380.00	0.596384
$536$	128.000	0.0103148
$537$	−9576.00	−0.769525
$538$	−4152.00	−0.332724
$539$	17982.0	1.43699
$540$	−540.000	−0.0430331
$541$	17078.0	1.35719	0.678596	−	0.734512i	$-0.262589\pi$
$541$	17078.0	1.35719	0.678596	+	0.734512i	$0.262589\pi$
$542$	680.000	0.0538902
$543$	8850.00	0.699429
$544$	−2496.00	−0.196719
$545$	−6470.00	−0.508522
$546$	4992.00	0.391278
$547$	22712.0	1.77531	0.887655	−	0.460508i	$-0.152333\pi$
$547$	22712.0	1.77531	0.887655	+	0.460508i	$0.152333\pi$
$548$	−2520.00	−0.196440
$549$	−7542.00	−0.586311
$550$	−2700.00	−0.209324
$551$	3876.00	0.299679
$552$	288.000	0.0222067
$553$	−16640.0	−1.27957
$554$	6908.00	0.529770
$555$	5100.00	0.390059
$556$	−1504.00	−0.114719
$557$	4590.00	0.349164	0.174582	−	0.984643i	$-0.444143\pi$
$557$	4590.00	0.349164	0.174582	+	0.984643i	$0.444143\pi$
$558$	4608.00	0.349592
$559$	10432.0	0.789314
$560$	2080.00	0.156957
$561$	−12636.0	−0.950967
$562$	15552.0	1.16730
$563$	−13668.0	−1.02316	−0.511579	−	0.859236i	$-0.670939\pi$
$563$	−13668.0	−1.02316	−0.511579	+	0.859236i	$0.670939\pi$
$564$	1584.00	0.118260
$565$	2490.00	0.185407
$566$	−16708.0	−1.24079
$567$	2106.00	0.155985
$568$	−7104.00	−0.524784
$569$	11148.0	0.821351	0.410675	−	0.911782i	$-0.365293\pi$
$569$	11148.0	0.821351	0.410675	+	0.911782i	$0.365293\pi$
$570$	570.000	0.0418854
$571$	19112.0	1.40072	0.700361	−	0.713789i	$-0.253022\pi$
$571$	19112.0	1.40072	0.700361	+	0.713789i	$0.253022\pi$
$572$	6912.00	0.505254
$573$	−6966.00	−0.507869
$574$	8112.00	0.589875
$575$	300.000	0.0217580
$576$	576.000	0.0416667
$577$	18650.0	1.34560	0.672799	−	0.739826i	$-0.265092\pi$
$577$	18650.0	1.34560	0.672799	+	0.739826i	$0.265092\pi$
$578$	−2342.00	−0.168537
$579$	−1716.00	−0.123168
$580$	4080.00	0.292091
$581$	−2184.00	−0.155951
$582$	8544.00	0.608523
$583$	4860.00	0.345250
$584$	−6832.00	−0.484093
$585$	1440.00	0.101772
$586$	948.000	0.0668285
$587$	6504.00	0.457323	0.228662	−	0.973506i	$-0.426565\pi$
$587$	6504.00	0.457323	0.228662	+	0.973506i	$0.426565\pi$
$588$	−3996.00	−0.280259
$589$	−4864.00	−0.340268
$590$	3600.00	0.251203
$591$	3618.00	0.251818
$592$	−5440.00	−0.377673
$593$	−17934.0	−1.24192	−0.620962	−	0.783841i	$-0.713258\pi$
$593$	−17934.0	−1.24192	−0.620962	+	0.783841i	$0.713258\pi$
$594$	2916.00	0.201422
$595$	10140.0	0.698655
$596$	5544.00	0.381025
$597$	8508.00	0.583265
$598$	−768.000	−0.0525182
$599$	−5412.00	−0.369162	−0.184581	−	0.982817i	$-0.559093\pi$
$599$	−5412.00	−0.369162	−0.184581	+	0.982817i	$0.559093\pi$
$600$	600.000	0.0408248
$601$	−25306.0	−1.71756	−0.858780	−	0.512345i	$-0.828777\pi$
$601$	−25306.0	−1.71756	−0.858780	+	0.512345i	$0.828777\pi$
$602$	−16952.0	−1.14769
$603$	−144.000	−0.00972493
$604$	−2368.00	−0.159524
$605$	7925.00	0.532557
$606$	−4500.00	−0.301650
$607$	−18916.0	−1.26487	−0.632436	−	0.774613i	$-0.717945\pi$
$607$	−18916.0	−1.26487	−0.632436	+	0.774613i	$0.717945\pi$
$608$	−608.000	−0.0405554
$609$	−15912.0	−1.05876
$610$	8380.00	0.556223
$611$	−4224.00	−0.279680
$612$	2808.00	0.185468
$613$	29882.0	1.96888	0.984439	−	0.175725i	$-0.0562269\pi$
$613$	29882.0	1.96888	0.984439	+	0.175725i	$0.0562269\pi$
$614$	−17392.0	−1.14313
$615$	2340.00	0.153427
$616$	−11232.0	−0.734659
$617$	−23466.0	−1.53113	−0.765564	−	0.643360i	$-0.777540\pi$
$617$	−23466.0	−1.53113	−0.765564	+	0.643360i	$0.777540\pi$
$618$	−4056.00	−0.264007
$619$	11456.0	0.743870	0.371935	−	0.928259i	$-0.378694\pi$
$619$	11456.0	0.743870	0.371935	+	0.928259i	$0.378694\pi$
$620$	−5120.00	−0.331652
$621$	−324.000	−0.0209367
$622$	2268.00	0.146203
$623$	21528.0	1.38443
$624$	−1536.00	−0.0985404
$625$	625.000	0.0400000
$626$	13964.0	0.891555
$627$	−3078.00	−0.196050
$628$	−6904.00	−0.438694
$629$	−26520.0	−1.68112
$630$	−2340.00	−0.147981
$631$	−19432.0	−1.22595	−0.612976	−	0.790102i	$-0.710028\pi$
$631$	−19432.0	−1.22595	−0.612976	+	0.790102i	$0.710028\pi$
$632$	5120.00	0.322251
$633$	14124.0	0.886854
$634$	828.000	0.0518676
$635$	4600.00	0.287473
$636$	−1080.00	−0.0673346
$637$	10656.0	0.662804
$638$	−22032.0	−1.36717
$639$	7992.00	0.494771
$640$	−640.000	−0.0395285
$641$	−22500.0	−1.38642	−0.693211	−	0.720735i	$-0.743805\pi$
$641$	−22500.0	−1.38642	−0.693211	+	0.720735i	$0.743805\pi$
$642$	8856.00	0.544421
$643$	−16270.0	−0.997863	−0.498932	−	0.866641i	$-0.666274\pi$
$643$	−16270.0	−0.997863	−0.498932	+	0.866641i	$0.666274\pi$
$644$	1248.00	0.0763635
$645$	−4890.00	−0.298517
$646$	−2964.00	−0.180522
$647$	−19968.0	−1.21333	−0.606664	−	0.794958i	$-0.707493\pi$
$647$	−19968.0	−1.21333	−0.606664	+	0.794958i	$0.707493\pi$
$648$	−648.000	−0.0392837
$649$	−19440.0	−1.17579
$650$	−1600.00	−0.0965495
$651$	19968.0	1.20216
$652$	9608.00	0.577114
$653$	−2358.00	−0.141310	−0.0706552	−	0.997501i	$-0.522509\pi$
$653$	−2358.00	−0.141310	−0.0706552	+	0.997501i	$0.522509\pi$
$654$	−7764.00	−0.464215
$655$	−3390.00	−0.202226
$656$	−2496.00	−0.148556
$657$	7686.00	0.456407
$658$	6864.00	0.406667
$659$	15588.0	0.921430	0.460715	−	0.887548i	$-0.347593\pi$
$659$	15588.0	0.921430	0.460715	+	0.887548i	$0.347593\pi$
$660$	−3240.00	−0.191086
$661$	8642.00	0.508525	0.254262	−	0.967135i	$-0.418167\pi$
$661$	8642.00	0.508525	0.254262	+	0.967135i	$0.418167\pi$
$662$	−16936.0	−0.994315
$663$	−7488.00	−0.438627
$664$	672.000	0.0392751
$665$	2470.00	0.144034
$666$	6120.00	0.356074
$667$	2448.00	0.142109
$668$	−11328.0	−0.656128
$669$	−12516.0	−0.723313
$670$	160.000	0.00922588
$671$	−45252.0	−2.60348
$672$	2496.00	0.143282
$673$	4928.00	0.282259	0.141130	−	0.989991i	$-0.454927\pi$
$673$	4928.00	0.282259	0.141130	+	0.989991i	$0.454927\pi$
$674$	4976.00	0.284374
$675$	−675.000	−0.0384900
$676$	−4692.00	−0.266955
$677$	−462.000	−0.0262276	−0.0131138	−	0.999914i	$-0.504174\pi$
$677$	−462.000	−0.0262276	−0.0131138	+	0.999914i	$0.504174\pi$
$678$	2988.00	0.169253
$679$	37024.0	2.09256
$680$	−3120.00	−0.175951
$681$	1260.00	0.0709006
$682$	27648.0	1.55234
$683$	−16356.0	−0.916318	−0.458159	−	0.888870i	$-0.651491\pi$
$683$	−16356.0	−0.916318	−0.458159	+	0.888870i	$0.651491\pi$
$684$	684.000	0.0382360
$685$	−3150.00	−0.175701
$686$	520.000	0.0289412
$687$	7482.00	0.415511
$688$	5216.00	0.289038
$689$	2880.00	0.159244
$690$	360.000	0.0198623
$691$	−18736.0	−1.03148	−0.515739	−	0.856746i	$-0.672483\pi$
$691$	−18736.0	−1.03148	−0.515739	+	0.856746i	$0.672483\pi$
$692$	5784.00	0.317738
$693$	12636.0	0.692644
$694$	18888.0	1.03311
$695$	−1880.00	−0.102608
$696$	4896.00	0.266641
$697$	−12168.0	−0.661257
$698$	−2236.00	−0.121252
$699$	6498.00	0.351612
$700$	2600.00	0.140387
$701$	−4590.00	−0.247307	−0.123653	−	0.992325i	$-0.539461\pi$
$701$	−4590.00	−0.247307	−0.123653	+	0.992325i	$0.539461\pi$
$702$	1728.00	0.0929048
$703$	−6460.00	−0.346577
$704$	3456.00	0.185018
$705$	1980.00	0.105775
$706$	1740.00	0.0927560
$707$	−19500.0	−1.03730
$708$	4320.00	0.229316
$709$	−2014.00	−0.106682	−0.0533409	−	0.998576i	$-0.516987\pi$
$709$	−2014.00	−0.106682	−0.0533409	+	0.998576i	$0.516987\pi$
$710$	−8880.00	−0.469381
$711$	−5760.00	−0.303821
$712$	−6624.00	−0.348659
$713$	−3072.00	−0.161357
$714$	12168.0	0.637781
$715$	8640.00	0.451913
$716$	12768.0	0.666428
$717$	14670.0	0.764102
$718$	−4020.00	−0.208949
$719$	−7170.00	−0.371900	−0.185950	−	0.982559i	$-0.559536\pi$
$719$	−7170.00	−0.371900	−0.185950	+	0.982559i	$0.559536\pi$
$720$	720.000	0.0372678
$721$	−17576.0	−0.907856
$722$	−722.000	−0.0372161
$723$	19290.0	0.992258
$724$	−11800.0	−0.605723
$725$	5100.00	0.261254
$726$	9510.00	0.486156
$727$	422.000	0.0215284	0.0107642	−	0.999942i	$-0.496574\pi$
$727$	422.000	0.0215284	0.0107642	+	0.999942i	$0.496574\pi$
$728$	−6656.00	−0.338857
$729$	729.000	0.0370370
$730$	−8540.00	−0.432986
$731$	25428.0	1.28658
$732$	10056.0	0.507760
$733$	−30274.0	−1.52551	−0.762753	−	0.646690i	$-0.776153\pi$
$733$	−30274.0	−1.52551	−0.762753	+	0.646690i	$0.776153\pi$
$734$	6548.00	0.329279
$735$	−4995.00	−0.250671
$736$	−384.000	−0.0192316
$737$	−864.000	−0.0431830
$738$	2808.00	0.140059
$739$	−4540.00	−0.225990	−0.112995	−	0.993596i	$-0.536044\pi$
$739$	−4540.00	−0.225990	−0.112995	+	0.993596i	$0.536044\pi$
$740$	−6800.00	−0.337801
$741$	−1824.00	−0.0904269
$742$	−4680.00	−0.231547
$743$	1704.00	0.0841369	0.0420684	−	0.999115i	$-0.486605\pi$
$743$	1704.00	0.0841369	0.0420684	+	0.999115i	$0.486605\pi$
$744$	−6144.00	−0.302755
$745$	6930.00	0.340799
$746$	16016.0	0.786042
$747$	−756.000	−0.0370289
$748$	16848.0	0.823561
$749$	38376.0	1.87213
$750$	750.000	0.0365148
$751$	−15568.0	−0.756437	−0.378219	−	0.925716i	$-0.623463\pi$
$751$	−15568.0	−0.756437	−0.378219	+	0.925716i	$0.623463\pi$
$752$	−2112.00	−0.102416
$753$	−17730.0	−0.858057
$754$	−13056.0	−0.630599
$755$	−2960.00	−0.142683
$756$	−2808.00	−0.135087
$757$	−21034.0	−1.00990	−0.504950	−	0.863149i	$-0.668489\pi$
$757$	−21034.0	−1.00990	−0.504950	+	0.863149i	$0.668489\pi$
$758$	−16264.0	−0.779334
$759$	−1944.00	−0.0929680
$760$	−760.000	−0.0362738
$761$	−33834.0	−1.61167	−0.805835	−	0.592140i	$-0.798283\pi$
$761$	−33834.0	−1.61167	−0.805835	+	0.592140i	$0.798283\pi$
$762$	5520.00	0.262426
$763$	−33644.0	−1.59632
$764$	9288.00	0.439827
$765$	3510.00	0.165888
$766$	−23184.0	−1.09357
$767$	−11520.0	−0.542325
$768$	−768.000	−0.0360844
$769$	13298.0	0.623587	0.311793	−	0.950150i	$-0.399070\pi$
$769$	13298.0	0.623587	0.311793	+	0.950150i	$0.399070\pi$
$770$	−14040.0	−0.657099
$771$	3618.00	0.169000
$772$	2288.00	0.106667
$773$	−24702.0	−1.14938	−0.574689	−	0.818372i	$-0.694877\pi$
$773$	−24702.0	−1.14938	−0.574689	+	0.818372i	$0.694877\pi$
$774$	−5868.00	−0.272508
$775$	−6400.00	−0.296638
$776$	−11392.0	−0.526996
$777$	26520.0	1.22445
$778$	3060.00	0.141011
$779$	−2964.00	−0.136324
$780$	−1920.00	−0.0881372
$781$	47952.0	2.19700
$782$	−1872.00	−0.0856043
$783$	−5508.00	−0.251392
$784$	5328.00	0.242711
$785$	−8630.00	−0.392380
$786$	−4068.00	−0.184607
$787$	−2692.00	−0.121931	−0.0609653	−	0.998140i	$-0.519418\pi$
$787$	−2692.00	−0.121931	−0.0609653	+	0.998140i	$0.519418\pi$
$788$	−4824.00	−0.218081
$789$	−17928.0	−0.808940
$790$	6400.00	0.288230
$791$	12948.0	0.582020
$792$	−3888.00	−0.174437
$793$	−26816.0	−1.20084
$794$	−3124.00	−0.139630
$795$	−1350.00	−0.0602259
$796$	−11344.0	−0.505122
$797$	−19866.0	−0.882923	−0.441462	−	0.897280i	$-0.645540\pi$
$797$	−19866.0	−0.882923	−0.441462	+	0.897280i	$0.645540\pi$
$798$	2964.00	0.131484
$799$	−10296.0	−0.455878
$800$	−800.000	−0.0353553
$801$	7452.00	0.328718
$802$	−29952.0	−1.31876
$803$	46116.0	2.02665
$804$	192.000	0.00842204
$805$	1560.00	0.0683016
$806$	16384.0	0.716007
$807$	−6228.00	−0.271668
$808$	6000.00	0.261237
$809$	−25758.0	−1.11941	−0.559705	−	0.828692i	$-0.689086\pi$
$809$	−25758.0	−1.11941	−0.559705	+	0.828692i	$0.689086\pi$
$810$	−810.000	−0.0351364
$811$	−44548.0	−1.92884	−0.964422	−	0.264369i	$-0.914836\pi$
$811$	−44548.0	−1.92884	−0.964422	+	0.264369i	$0.914836\pi$
$812$	21216.0	0.916916
$813$	1020.00	0.0440012
$814$	36720.0	1.58112
$815$	12010.0	0.516186
$816$	−3744.00	−0.160620
$817$	6194.00	0.265239
$818$	−16492.0	−0.704926
$819$	7488.00	0.319477
$820$	−3120.00	−0.132872
$821$	30618.0	1.30155	0.650777	−	0.759269i	$-0.274443\pi$
$821$	30618.0	1.30155	0.650777	+	0.759269i	$0.274443\pi$
$822$	−3780.00	−0.160393
$823$	−23578.0	−0.998636	−0.499318	−	0.866419i	$-0.666416\pi$
$823$	−23578.0	−0.998636	−0.499318	+	0.866419i	$0.666416\pi$
$824$	5408.00	0.228637
$825$	−4050.00	−0.170913
$826$	18720.0	0.788562
$827$	31236.0	1.31340	0.656700	−	0.754152i	$-0.271952\pi$
$827$	31236.0	1.31340	0.656700	+	0.754152i	$0.271952\pi$
$828$	432.000	0.0181317
$829$	28850.0	1.20869	0.604344	−	0.796724i	$-0.293435\pi$
$829$	28850.0	1.20869	0.604344	+	0.796724i	$0.293435\pi$
$830$	840.000	0.0351287
$831$	10362.0	0.432556
$832$	2048.00	0.0853385
$833$	25974.0	1.08037
$834$	−2256.00	−0.0936677
$835$	−14160.0	−0.586859
$836$	4104.00	0.169784
$837$	6912.00	0.285440
$838$	−25260.0	−1.04128
$839$	−360.000	−0.0148136	−0.00740678	−	0.999973i	$-0.502358\pi$
$839$	−360.000	−0.0148136	−0.00740678	+	0.999973i	$0.502358\pi$
$840$	3120.00	0.128155
$841$	17227.0	0.706343
$842$	−20524.0	−0.840028
$843$	23328.0	0.953095
$844$	−18832.0	−0.768038
$845$	−5865.00	−0.238772
$846$	2376.00	0.0965586
$847$	41210.0	1.67177
$848$	1440.00	0.0583134
$849$	−25062.0	−1.01310
$850$	−3900.00	−0.157375
$851$	−4080.00	−0.164349
$852$	−10656.0	−0.428484
$853$	−12778.0	−0.512908	−0.256454	−	0.966556i	$-0.582554\pi$
$853$	−12778.0	−0.512908	−0.256454	+	0.966556i	$0.582554\pi$
$854$	43576.0	1.74607
$855$	855.000	0.0341993
$856$	−11808.0	−0.471483
$857$	−2730.00	−0.108816	−0.0544078	−	0.998519i	$-0.517327\pi$
$857$	−2730.00	−0.108816	−0.0544078	+	0.998519i	$0.517327\pi$
$858$	10368.0	0.412538
$859$	12116.0	0.481249	0.240624	−	0.970618i	$-0.422648\pi$
$859$	12116.0	0.481249	0.240624	+	0.970618i	$0.422648\pi$
$860$	6520.00	0.258523
$861$	12168.0	0.481631
$862$	7800.00	0.308201
$863$	−24624.0	−0.971275	−0.485638	−	0.874160i	$-0.661413\pi$
$863$	−24624.0	−0.971275	−0.485638	+	0.874160i	$0.661413\pi$
$864$	864.000	0.0340207
$865$	7230.00	0.284193
$866$	−18760.0	−0.736133
$867$	−3513.00	−0.137610
$868$	−26624.0	−1.04110
$869$	−34560.0	−1.34910
$870$	6120.00	0.238491
$871$	−512.000	−0.0199179
$872$	10352.0	0.402022
$873$	12816.0	0.496857
$874$	−456.000	−0.0176481
$875$	3250.00	0.125566
$876$	−10248.0	−0.395260
$877$	−17248.0	−0.664109	−0.332054	−	0.943260i	$-0.607742\pi$
$877$	−17248.0	−0.664109	−0.332054	+	0.943260i	$0.607742\pi$
$878$	−19216.0	−0.738620
$879$	1422.00	0.0545653
$880$	4320.00	0.165485
$881$	−8202.00	−0.313658	−0.156829	−	0.987626i	$-0.550127\pi$
$881$	−8202.00	−0.313658	−0.156829	+	0.987626i	$0.550127\pi$
$882$	−5994.00	−0.228830
$883$	−19942.0	−0.760025	−0.380012	−	0.924981i	$-0.624080\pi$
$883$	−19942.0	−0.760025	−0.380012	+	0.924981i	$0.624080\pi$
$884$	9984.00	0.379862
$885$	5400.00	0.205106
$886$	10224.0	0.387677
$887$	−46944.0	−1.77703	−0.888515	−	0.458848i	$-0.848262\pi$
$887$	−46944.0	−1.77703	−0.888515	+	0.458848i	$0.848262\pi$
$888$	−8160.00	−0.308369
$889$	23920.0	0.902420
$890$	−8280.00	−0.311850
$891$	4374.00	0.164461
$892$	16688.0	0.626408
$893$	−2508.00	−0.0939832
$894$	8316.00	0.311106
$895$	15960.0	0.596071
$896$	−3328.00	−0.124086
$897$	−1152.00	−0.0428809
$898$	25224.0	0.937345
$899$	−52224.0	−1.93745
$900$	900.000	0.0333333
$901$	7020.00	0.259567
$902$	16848.0	0.621926
$903$	−25428.0	−0.937088
$904$	−3984.00	−0.146577
$905$	−14750.0	−0.541775
$906$	−3552.00	−0.130251
$907$	9020.00	0.330214	0.165107	−	0.986276i	$-0.447203\pi$
$907$	9020.00	0.330214	0.165107	+	0.986276i	$0.447203\pi$
$908$	−1680.00	−0.0614017
$909$	−6750.00	−0.246296
$910$	−8320.00	−0.303083
$911$	46032.0	1.67410	0.837052	−	0.547124i	$-0.184277\pi$
$911$	46032.0	1.67410	0.837052	+	0.547124i	$0.184277\pi$
$912$	−912.000	−0.0331133
$913$	−4536.00	−0.164425
$914$	30428.0	1.10117
$915$	12570.0	0.454155
$916$	−9976.00	−0.359843
$917$	−17628.0	−0.634818
$918$	4212.00	0.151434
$919$	50984.0	1.83004	0.915020	−	0.403408i	$-0.132175\pi$
$919$	50984.0	1.83004	0.915020	+	0.403408i	$0.132175\pi$
$920$	−480.000	−0.0172012
$921$	−26088.0	−0.933365
$922$	−20196.0	−0.721388
$923$	28416.0	1.01335
$924$	−16848.0	−0.599847
$925$	−8500.00	−0.302139
$926$	−33532.0	−1.18999
$927$	−6084.00	−0.215561
$928$	−6528.00	−0.230918
$929$	−39582.0	−1.39789	−0.698947	−	0.715174i	$-0.746348\pi$
$929$	−39582.0	−1.39789	−0.698947	+	0.715174i	$0.746348\pi$
$930$	−7680.00	−0.270793
$931$	6327.00	0.222727
$932$	−8664.00	−0.304505
$933$	3402.00	0.119375
$934$	17808.0	0.623871
$935$	21060.0	0.736616
$936$	−2304.00	−0.0804579
$937$	17222.0	0.600446	0.300223	−	0.953869i	$-0.402939\pi$
$937$	17222.0	0.600446	0.300223	+	0.953869i	$0.402939\pi$
$938$	832.000	0.0289614
$939$	20946.0	0.727952
$940$	−2640.00	−0.0916035
$941$	−43020.0	−1.49034	−0.745171	−	0.666873i	$-0.767632\pi$
$941$	−43020.0	−1.49034	−0.745171	+	0.666873i	$0.767632\pi$
$942$	−10356.0	−0.358192
$943$	−1872.00	−0.0646455
$944$	−5760.00	−0.198593
$945$	−3510.00	−0.120826
$946$	−35208.0	−1.21005
$947$	27924.0	0.958192	0.479096	−	0.877762i	$-0.340965\pi$
$947$	27924.0	0.958192	0.479096	+	0.877762i	$0.340965\pi$
$948$	7680.00	0.263117
$949$	27328.0	0.934778
$950$	−950.000	−0.0324443
$951$	1242.00	0.0423497
$952$	−16224.0	−0.552335
$953$	41418.0	1.40783	0.703914	−	0.710285i	$-0.251434\pi$
$953$	41418.0	1.40783	0.703914	+	0.710285i	$0.251434\pi$
$954$	−1620.00	−0.0549784
$955$	11610.0	0.393393
$956$	−19560.0	−0.661732
$957$	−33048.0	−1.11629
$958$	25932.0	0.874556
$959$	−16380.0	−0.551551
$960$	−960.000	−0.0322749
$961$	35745.0	1.19986
$962$	21760.0	0.729283
$963$	13284.0	0.444518
$964$	−25720.0	−0.859321
$965$	2860.00	0.0954059
$966$	1872.00	0.0623505
$967$	24974.0	0.830517	0.415258	−	0.909704i	$-0.363691\pi$
$967$	24974.0	0.830517	0.415258	+	0.909704i	$0.363691\pi$
$968$	−12680.0	−0.421023
$969$	−4446.00	−0.147395
$970$	−14240.0	−0.471360
$971$	55548.0	1.83586	0.917930	−	0.396742i	$-0.129859\pi$
$971$	55548.0	1.83586	0.917930	+	0.396742i	$0.129859\pi$
$972$	−972.000	−0.0320750
$973$	−9776.00	−0.322101
$974$	−2920.00	−0.0960604
$975$	−2400.00	−0.0788323
$976$	−13408.0	−0.439733
$977$	−5514.00	−0.180561	−0.0902807	−	0.995916i	$-0.528776\pi$
$977$	−5514.00	−0.180561	−0.0902807	+	0.995916i	$0.528776\pi$
$978$	14412.0	0.471212
$979$	44712.0	1.45965
$980$	6660.00	0.217088
$981$	−11646.0	−0.379030
$982$	2076.00	0.0674621
$983$	−15648.0	−0.507725	−0.253863	−	0.967240i	$-0.581701\pi$
$983$	−15648.0	−0.507725	−0.253863	+	0.967240i	$0.581701\pi$
$984$	−3744.00	−0.121295
$985$	−6030.00	−0.195058
$986$	−31824.0	−1.02787
$987$	10296.0	0.332042
$988$	2432.00	0.0783120
$989$	3912.00	0.125778
$990$	−4860.00	−0.156021
$991$	10088.0	0.323366	0.161683	−	0.986843i	$-0.448308\pi$
$991$	10088.0	0.323366	0.161683	+	0.986843i	$0.448308\pi$
$992$	8192.00	0.262194
$993$	−25404.0	−0.811855
$994$	−46176.0	−1.47345
$995$	−14180.0	−0.451795
$996$	1008.00	0.0320680
$997$	62066.0	1.97156	0.985782	−	0.168027i	$-0.0537397\pi$
$997$	62066.0	1.97156	0.985782	+	0.168027i	$0.0537397\pi$
$998$	32192.0	1.02106
$999$	9180.00	0.290733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.a.b.1.1	✓	1
3.2	odd	2		1710.4.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.a.b.1.1	✓	1	1.1	even	1	trivial
1710.4.a.j.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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