LMFDB - Embedded newform 570.4.a.f.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:	$1$
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -8.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -20.0000 q^{11} +12.0000 q^{12} -82.0000 q^{13} -16.0000 q^{14} -15.0000 q^{15} +16.0000 q^{16} -18.0000 q^{17} +18.0000 q^{18} +19.0000 q^{19} -20.0000 q^{20} -24.0000 q^{21} -40.0000 q^{22} -88.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -164.000 q^{26} +27.0000 q^{27} -32.0000 q^{28} -186.000 q^{29} -30.0000 q^{30} -248.000 q^{31} +32.0000 q^{32} -60.0000 q^{33} -36.0000 q^{34} +40.0000 q^{35} +36.0000 q^{36} +262.000 q^{37} +38.0000 q^{38} -246.000 q^{39} -40.0000 q^{40} +246.000 q^{41} -48.0000 q^{42} +288.000 q^{43} -80.0000 q^{44} -45.0000 q^{45} -176.000 q^{46} -168.000 q^{47} +48.0000 q^{48} -279.000 q^{49} +50.0000 q^{50} -54.0000 q^{51} -328.000 q^{52} -302.000 q^{53} +54.0000 q^{54} +100.000 q^{55} -64.0000 q^{56} +57.0000 q^{57} -372.000 q^{58} +72.0000 q^{59} -60.0000 q^{60} -546.000 q^{61} -496.000 q^{62} -72.0000 q^{63} +64.0000 q^{64} +410.000 q^{65} -120.000 q^{66} -804.000 q^{67} -72.0000 q^{68} -264.000 q^{69} +80.0000 q^{70} +240.000 q^{71} +72.0000 q^{72} +602.000 q^{73} +524.000 q^{74} +75.0000 q^{75} +76.0000 q^{76} +160.000 q^{77} -492.000 q^{78} -800.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +492.000 q^{82} -116.000 q^{83} -96.0000 q^{84} +90.0000 q^{85} +576.000 q^{86} -558.000 q^{87} -160.000 q^{88} +766.000 q^{89} -90.0000 q^{90} +656.000 q^{91} -352.000 q^{92} -744.000 q^{93} -336.000 q^{94} -95.0000 q^{95} +96.0000 q^{96} +790.000 q^{97} -558.000 q^{98} -180.000 q^{99} +O(q^{100})\)

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
$7$	−8.00000	−0.431959	−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−8.00000	−0.431959	−0.215980	+	0.976398i	$0.569295\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	−20.0000	−0.548202	−0.274101	−	0.961701i	$-0.588380\pi$
$11$	−20.0000	−0.548202	−0.274101	+	0.961701i	$0.588380\pi$
$12$	12.0000	0.288675
$13$	−82.0000	−1.74944	−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000	−1.74944	−0.874720	+	0.484629i	$0.838954\pi$
$14$	−16.0000	−0.305441
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−18.0000	−0.256802	−0.128401	−	0.991722i	$-0.540985\pi$
$17$	−18.0000	−0.256802	−0.128401	+	0.991722i	$0.540985\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−20.0000	−0.223607
$21$	−24.0000	−0.249392
$22$	−40.0000	−0.387638
$23$	−88.0000	−0.797794	−0.398897	−	0.916996i	$-0.630607\pi$
$23$	−88.0000	−0.797794	−0.398897	+	0.916996i	$0.630607\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−164.000	−1.23704
$27$	27.0000	0.192450
$28$	−32.0000	−0.215980
$29$	−186.000	−1.19101	−0.595506	−	0.803351i	$-0.703048\pi$
$29$	−186.000	−1.19101	−0.595506	+	0.803351i	$0.703048\pi$
$30$	−30.0000	−0.182574
$31$	−248.000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−248.000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	32.0000	0.176777
$33$	−60.0000	−0.316505
$34$	−36.0000	−0.181587
$35$	40.0000	0.193178
$36$	36.0000	0.166667
$37$	262.000	1.16412	0.582061	−	0.813145i	$-0.302246\pi$
$37$	262.000	1.16412	0.582061	+	0.813145i	$0.302246\pi$
$38$	38.0000	0.162221
$39$	−246.000	−1.01004
$40$	−40.0000	−0.158114
$41$	246.000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	246.000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−48.0000	−0.176347
$43$	288.000	1.02139	0.510693	−	0.859763i	$-0.329389\pi$
$43$	288.000	1.02139	0.510693	+	0.859763i	$0.329389\pi$
$44$	−80.0000	−0.274101
$45$	−45.0000	−0.149071
$46$	−176.000	−0.564126
$47$	−168.000	−0.521390	−0.260695	−	0.965421i	$-0.583952\pi$
$47$	−168.000	−0.521390	−0.260695	+	0.965421i	$0.583952\pi$
$48$	48.0000	0.144338
$49$	−279.000	−0.813411
$50$	50.0000	0.141421
$51$	−54.0000	−0.148265
$52$	−328.000	−0.874720
$53$	−302.000	−0.782696	−0.391348	−	0.920243i	$-0.627991\pi$
$53$	−302.000	−0.782696	−0.391348	+	0.920243i	$0.627991\pi$
$54$	54.0000	0.136083
$55$	100.000	0.245164
$56$	−64.0000	−0.152721
$57$	57.0000	0.132453
$58$	−372.000	−0.842172
$59$	72.0000	0.158875	0.0794373	−	0.996840i	$-0.474688\pi$
$59$	72.0000	0.158875	0.0794373	+	0.996840i	$0.474688\pi$
$60$	−60.0000	−0.129099
$61$	−546.000	−1.14604	−0.573018	−	0.819543i	$-0.694227\pi$
$61$	−546.000	−1.14604	−0.573018	+	0.819543i	$0.694227\pi$
$62$	−496.000	−1.01600
$63$	−72.0000	−0.143986
$64$	64.0000	0.125000
$65$	410.000	0.782373
$66$	−120.000	−0.223803
$67$	−804.000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−804.000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−72.0000	−0.128401
$69$	−264.000	−0.460607
$70$	80.0000	0.136598
$71$	240.000	0.401166	0.200583	−	0.979677i	$-0.435716\pi$
$71$	240.000	0.401166	0.200583	+	0.979677i	$0.435716\pi$
$72$	72.0000	0.117851
$73$	602.000	0.965189	0.482594	−	0.875844i	$-0.339695\pi$
$73$	602.000	0.965189	0.482594	+	0.875844i	$0.339695\pi$
$74$	524.000	0.823159
$75$	75.0000	0.115470
$76$	76.0000	0.114708
$77$	160.000	0.236801
$78$	−492.000	−0.714206
$79$	−800.000	−1.13933	−0.569665	−	0.821877i	$-0.692927\pi$
$79$	−800.000	−1.13933	−0.569665	+	0.821877i	$0.692927\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	492.000	0.662589
$83$	−116.000	−0.153405	−0.0767027	−	0.997054i	$-0.524439\pi$
$83$	−116.000	−0.153405	−0.0767027	+	0.997054i	$0.524439\pi$
$84$	−96.0000	−0.124696
$85$	90.0000	0.114846
$86$	576.000	0.722229
$87$	−558.000	−0.687631
$88$	−160.000	−0.193819
$89$	766.000	0.912313	0.456156	−	0.889900i	$-0.349226\pi$
$89$	766.000	0.912313	0.456156	+	0.889900i	$0.349226\pi$
$90$	−90.0000	−0.105409
$91$	656.000	0.755687
$92$	−352.000	−0.398897
$93$	−744.000	−0.829561
$94$	−336.000	−0.368678
$95$	−95.0000	−0.102598
$96$	96.0000	0.102062
$97$	790.000	0.826931	0.413466	−	0.910520i	$-0.364318\pi$
$97$	790.000	0.826931	0.413466	+	0.910520i	$0.364318\pi$
$98$	−558.000	−0.575168
$99$	−180.000	−0.182734
$100$	100.000	0.100000
$101$	290.000	0.285704	0.142852	−	0.989744i	$-0.454373\pi$
$101$	290.000	0.285704	0.142852	+	0.989744i	$0.454373\pi$
$102$	−108.000	−0.104839
$103$	1540.00	1.47321	0.736605	−	0.676323i	$-0.236428\pi$
$103$	1540.00	1.47321	0.736605	+	0.676323i	$0.236428\pi$
$104$	−656.000	−0.618520
$105$	120.000	0.111531
$106$	−604.000	−0.553450
$107$	1564.00	1.41306	0.706531	−	0.707682i	$-0.250259\pi$
$107$	1564.00	1.41306	0.706531	+	0.707682i	$0.250259\pi$
$108$	108.000	0.0962250
$109$	−554.000	−0.486822	−0.243411	−	0.969923i	$-0.578266\pi$
$109$	−554.000	−0.486822	−0.243411	+	0.969923i	$0.578266\pi$
$110$	200.000	0.173357
$111$	786.000	0.672106
$112$	−128.000	−0.107990
$113$	−834.000	−0.694302	−0.347151	−	0.937809i	$-0.612851\pi$
$113$	−834.000	−0.694302	−0.347151	+	0.937809i	$0.612851\pi$
$114$	114.000	0.0936586
$115$	440.000	0.356784
$116$	−744.000	−0.595506
$117$	−738.000	−0.583146
$118$	144.000	0.112341
$119$	144.000	0.110928
$120$	−120.000	−0.0912871
$121$	−931.000	−0.699474
$122$	−1092.00	−0.810369
$123$	738.000	0.541002
$124$	−992.000	−0.718421
$125$	−125.000	−0.0894427
$126$	−144.000	−0.101814
$127$	−876.000	−0.612066	−0.306033	−	0.952021i	$-0.599002\pi$
$127$	−876.000	−0.612066	−0.306033	+	0.952021i	$0.599002\pi$
$128$	128.000	0.0883883
$129$	864.000	0.589697
$130$	820.000	0.553221
$131$	−508.000	−0.338810	−0.169405	−	0.985546i	$-0.554185\pi$
$131$	−508.000	−0.338810	−0.169405	+	0.985546i	$0.554185\pi$
$132$	−240.000	−0.158252
$133$	−152.000	−0.0990983
$134$	−1608.00	−1.03664
$135$	−135.000	−0.0860663
$136$	−144.000	−0.0907934
$137$	−1506.00	−0.939170	−0.469585	−	0.882887i	$-0.655596\pi$
$137$	−1506.00	−0.939170	−0.469585	+	0.882887i	$0.655596\pi$
$138$	−528.000	−0.325698
$139$	−620.000	−0.378329	−0.189164	−	0.981945i	$-0.560578\pi$
$139$	−620.000	−0.378329	−0.189164	+	0.981945i	$0.560578\pi$
$140$	160.000	0.0965891
$141$	−504.000	−0.301025
$142$	480.000	0.283667
$143$	1640.00	0.959047
$144$	144.000	0.0833333
$145$	930.000	0.532637
$146$	1204.00	0.682491
$147$	−837.000	−0.469623
$148$	1048.00	0.582061
$149$	1738.00	0.955587	0.477794	−	0.878472i	$-0.341437\pi$
$149$	1738.00	0.955587	0.477794	+	0.878472i	$0.341437\pi$
$150$	150.000	0.0816497
$151$	−1720.00	−0.926964	−0.463482	−	0.886106i	$-0.653400\pi$
$151$	−1720.00	−0.926964	−0.463482	+	0.886106i	$0.653400\pi$
$152$	152.000	0.0811107
$153$	−162.000	−0.0856008
$154$	320.000	0.167444
$155$	1240.00	0.642575
$156$	−984.000	−0.505020
$157$	−1446.00	−0.735053	−0.367527	−	0.930013i	$-0.619795\pi$
$157$	−1446.00	−0.735053	−0.367527	+	0.930013i	$0.619795\pi$
$158$	−1600.00	−0.805628
$159$	−906.000	−0.451890
$160$	−160.000	−0.0790569
$161$	704.000	0.344615
$162$	162.000	0.0785674
$163$	−392.000	−0.188367	−0.0941835	−	0.995555i	$-0.530024\pi$
$163$	−392.000	−0.188367	−0.0941835	+	0.995555i	$0.530024\pi$
$164$	984.000	0.468521
$165$	300.000	0.141545
$166$	−232.000	−0.108474
$167$	−544.000	−0.252072	−0.126036	−	0.992026i	$-0.540225\pi$
$167$	−544.000	−0.252072	−0.126036	+	0.992026i	$0.540225\pi$
$168$	−192.000	−0.0881733
$169$	4527.00	2.06054
$170$	180.000	0.0812081
$171$	171.000	0.0764719
$172$	1152.00	0.510693
$173$	1154.00	0.507150	0.253575	−	0.967316i	$-0.418393\pi$
$173$	1154.00	0.507150	0.253575	+	0.967316i	$0.418393\pi$
$174$	−1116.00	−0.486228
$175$	−200.000	−0.0863919
$176$	−320.000	−0.137051
$177$	216.000	0.0917263
$178$	1532.00	0.645103
$179$	2528.00	1.05560	0.527798	−	0.849370i	$-0.323018\pi$
$179$	2528.00	1.05560	0.527798	+	0.849370i	$0.323018\pi$
$180$	−180.000	−0.0745356
$181$	1454.00	0.597099	0.298550	−	0.954394i	$-0.403497\pi$
$181$	1454.00	0.597099	0.298550	+	0.954394i	$0.403497\pi$
$182$	1312.00	0.534351
$183$	−1638.00	−0.661664
$184$	−704.000	−0.282063
$185$	−1310.00	−0.520611
$186$	−1488.00	−0.586588
$187$	360.000	0.140780
$188$	−672.000	−0.260695
$189$	−216.000	−0.0831306
$190$	−190.000	−0.0725476
$191$	−4332.00	−1.64111	−0.820556	−	0.571566i	$-0.806336\pi$
$191$	−4332.00	−1.64111	−0.820556	+	0.571566i	$0.806336\pi$
$192$	192.000	0.0721688
$193$	−2330.00	−0.869000	−0.434500	−	0.900672i	$-0.643075\pi$
$193$	−2330.00	−0.869000	−0.434500	+	0.900672i	$0.643075\pi$
$194$	1580.00	0.584729
$195$	1230.00	0.451703
$196$	−1116.00	−0.406706
$197$	1714.00	0.619886	0.309943	−	0.950755i	$-0.399690\pi$
$197$	1714.00	0.619886	0.309943	+	0.950755i	$0.399690\pi$
$198$	−360.000	−0.129213
$199$	1320.00	0.470213	0.235106	−	0.971970i	$-0.424456\pi$
$199$	1320.00	0.470213	0.235106	+	0.971970i	$0.424456\pi$
$200$	200.000	0.0707107
$201$	−2412.00	−0.846415
$202$	580.000	0.202023
$203$	1488.00	0.514469
$204$	−216.000	−0.0741325
$205$	−1230.00	−0.419058
$206$	3080.00	1.04172
$207$	−792.000	−0.265931
$208$	−1312.00	−0.437360
$209$	−380.000	−0.125766
$210$	240.000	0.0788646
$211$	196.000	0.0639488	0.0319744	−	0.999489i	$-0.489820\pi$
$211$	196.000	0.0639488	0.0319744	+	0.999489i	$0.489820\pi$
$212$	−1208.00	−0.391348
$213$	720.000	0.231613
$214$	3128.00	0.999185
$215$	−1440.00	−0.456778
$216$	216.000	0.0680414
$217$	1984.00	0.620658
$218$	−1108.00	−0.344235
$219$	1806.00	0.557252
$220$	400.000	0.122582
$221$	1476.00	0.449260
$222$	1572.00	0.475251
$223$	−1076.00	−0.323113	−0.161557	−	0.986863i	$-0.551651\pi$
$223$	−1076.00	−0.323113	−0.161557	+	0.986863i	$0.551651\pi$
$224$	−256.000	−0.0763604
$225$	225.000	0.0666667
$226$	−1668.00	−0.490946
$227$	1684.00	0.492383	0.246192	−	0.969221i	$-0.420821\pi$
$227$	1684.00	0.492383	0.246192	+	0.969221i	$0.420821\pi$
$228$	228.000	0.0662266
$229$	3150.00	0.908986	0.454493	−	0.890750i	$-0.349820\pi$
$229$	3150.00	0.908986	0.454493	+	0.890750i	$0.349820\pi$
$230$	880.000	0.252285
$231$	480.000	0.136717
$232$	−1488.00	−0.421086
$233$	1622.00	0.456055	0.228027	−	0.973655i	$-0.426772\pi$
$233$	1622.00	0.456055	0.228027	+	0.973655i	$0.426772\pi$
$234$	−1476.00	−0.412347
$235$	840.000	0.233173
$236$	288.000	0.0794373
$237$	−2400.00	−0.657792
$238$	288.000	0.0784381
$239$	5708.00	1.54485	0.772426	−	0.635104i	$-0.219043\pi$
$239$	5708.00	1.54485	0.772426	+	0.635104i	$0.219043\pi$
$240$	−240.000	−0.0645497
$241$	1314.00	0.351212	0.175606	−	0.984460i	$-0.443811\pi$
$241$	1314.00	0.351212	0.175606	+	0.984460i	$0.443811\pi$
$242$	−1862.00	−0.494603
$243$	243.000	0.0641500
$244$	−2184.00	−0.573018
$245$	1395.00	0.363768
$246$	1476.00	0.382546
$247$	−1558.00	−0.401349
$248$	−1984.00	−0.508001
$249$	−348.000	−0.0885687
$250$	−250.000	−0.0632456
$251$	3732.00	0.938493	0.469247	−	0.883067i	$-0.344526\pi$
$251$	3732.00	0.938493	0.469247	+	0.883067i	$0.344526\pi$
$252$	−288.000	−0.0719932
$253$	1760.00	0.437353
$254$	−1752.00	−0.432796
$255$	270.000	0.0663061
$256$	256.000	0.0625000
$257$	−994.000	−0.241261	−0.120630	−	0.992697i	$-0.538492\pi$
$257$	−994.000	−0.241261	−0.120630	+	0.992697i	$0.538492\pi$
$258$	1728.00	0.416979
$259$	−2096.00	−0.502854
$260$	1640.00	0.391186
$261$	−1674.00	−0.397004
$262$	−1016.00	−0.239575
$263$	6256.00	1.46677	0.733387	−	0.679812i	$-0.237938\pi$
$263$	6256.00	1.46677	0.733387	+	0.679812i	$0.237938\pi$
$264$	−480.000	−0.111901
$265$	1510.00	0.350032
$266$	−304.000	−0.0700731
$267$	2298.00	0.526724
$268$	−3216.00	−0.733017
$269$	3766.00	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	3766.00	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−270.000	−0.0608581
$271$	−6240.00	−1.39872	−0.699360	−	0.714770i	$-0.746531\pi$
$271$	−6240.00	−1.39872	−0.699360	+	0.714770i	$0.746531\pi$
$272$	−288.000	−0.0642006
$273$	1968.00	0.436296
$274$	−3012.00	−0.664093
$275$	−500.000	−0.109640
$276$	−1056.00	−0.230303
$277$	6010.00	1.30363	0.651816	−	0.758377i	$-0.274008\pi$
$277$	6010.00	1.30363	0.651816	+	0.758377i	$0.274008\pi$
$278$	−1240.00	−0.267519
$279$	−2232.00	−0.478947
$280$	320.000	0.0682988
$281$	−1098.00	−0.233100	−0.116550	−	0.993185i	$-0.537184\pi$
$281$	−1098.00	−0.233100	−0.116550	+	0.993185i	$0.537184\pi$
$282$	−1008.00	−0.212856
$283$	688.000	0.144514	0.0722568	−	0.997386i	$-0.476980\pi$
$283$	688.000	0.144514	0.0722568	+	0.997386i	$0.476980\pi$
$284$	960.000	0.200583
$285$	−285.000	−0.0592349
$286$	3280.00	0.678148
$287$	−1968.00	−0.404764
$288$	288.000	0.0589256
$289$	−4589.00	−0.934053
$290$	1860.00	0.376631
$291$	2370.00	0.477429
$292$	2408.00	0.482594
$293$	8442.00	1.68323	0.841616	−	0.540077i	$-0.181605\pi$
$293$	8442.00	1.68323	0.841616	+	0.540077i	$0.181605\pi$
$294$	−1674.00	−0.332074
$295$	−360.000	−0.0710509
$296$	2096.00	0.411579
$297$	−540.000	−0.105502
$298$	3476.00	0.675702
$299$	7216.00	1.39569
$300$	300.000	0.0577350
$301$	−2304.00	−0.441197
$302$	−3440.00	−0.655463
$303$	870.000	0.164951
$304$	304.000	0.0573539
$305$	2730.00	0.512522
$306$	−324.000	−0.0605289
$307$	1588.00	0.295218	0.147609	−	0.989046i	$-0.452842\pi$
$307$	1588.00	0.295218	0.147609	+	0.989046i	$0.452842\pi$
$308$	640.000	0.118401
$309$	4620.00	0.850559
$310$	2480.00	0.454369
$311$	−8260.00	−1.50605	−0.753025	−	0.657992i	$-0.771406\pi$
$311$	−8260.00	−1.50605	−0.753025	+	0.657992i	$0.771406\pi$
$312$	−1968.00	−0.357103
$313$	−9790.00	−1.76793	−0.883967	−	0.467549i	$-0.845137\pi$
$313$	−9790.00	−1.76793	−0.883967	+	0.467549i	$0.845137\pi$
$314$	−2892.00	−0.519761
$315$	360.000	0.0643927
$316$	−3200.00	−0.569665
$317$	−3654.00	−0.647410	−0.323705	−	0.946158i	$-0.604929\pi$
$317$	−3654.00	−0.647410	−0.323705	+	0.946158i	$0.604929\pi$
$318$	−1812.00	−0.319534
$319$	3720.00	0.652915
$320$	−320.000	−0.0559017
$321$	4692.00	0.815831
$322$	1408.00	0.243679
$323$	−342.000	−0.0589145
$324$	324.000	0.0555556
$325$	−2050.00	−0.349888
$326$	−784.000	−0.133196
$327$	−1662.00	−0.281067
$328$	1968.00	0.331295
$329$	1344.00	0.225219
$330$	600.000	0.100088
$331$	−4132.00	−0.686149	−0.343074	−	0.939308i	$-0.611468\pi$
$331$	−4132.00	−0.686149	−0.343074	+	0.939308i	$0.611468\pi$
$332$	−464.000	−0.0767027
$333$	2358.00	0.388041
$334$	−1088.00	−0.178242
$335$	4020.00	0.655630
$336$	−384.000	−0.0623480
$337$	−7506.00	−1.21329	−0.606644	−	0.794974i	$-0.707485\pi$
$337$	−7506.00	−1.21329	−0.606644	+	0.794974i	$0.707485\pi$
$338$	9054.00	1.45702
$339$	−2502.00	−0.400855
$340$	360.000	0.0574228
$341$	4960.00	0.787681
$342$	342.000	0.0540738
$343$	4976.00	0.783320
$344$	2304.00	0.361114
$345$	1320.00	0.205990
$346$	2308.00	0.358609
$347$	−8292.00	−1.28282	−0.641409	−	0.767199i	$-0.721650\pi$
$347$	−8292.00	−1.28282	−0.641409	+	0.767199i	$0.721650\pi$
$348$	−2232.00	−0.343815
$349$	−11362.0	−1.74268	−0.871338	−	0.490683i	$-0.836747\pi$
$349$	−11362.0	−1.74268	−0.871338	+	0.490683i	$0.836747\pi$
$350$	−400.000	−0.0610883
$351$	−2214.00	−0.336680
$352$	−640.000	−0.0969094
$353$	11102.0	1.67394	0.836969	−	0.547251i	$-0.184326\pi$
$353$	11102.0	1.67394	0.836969	+	0.547251i	$0.184326\pi$
$354$	432.000	0.0648603
$355$	−1200.00	−0.179407
$356$	3064.00	0.456156
$357$	432.000	0.0640444
$358$	5056.00	0.746419
$359$	2036.00	0.299320	0.149660	−	0.988738i	$-0.452182\pi$
$359$	2036.00	0.299320	0.149660	+	0.988738i	$0.452182\pi$
$360$	−360.000	−0.0527046
$361$	361.000	0.0526316
$362$	2908.00	0.422213
$363$	−2793.00	−0.403842
$364$	2624.00	0.377843
$365$	−3010.00	−0.431645
$366$	−3276.00	−0.467867
$367$	1592.00	0.226435	0.113218	−	0.993570i	$-0.463884\pi$
$367$	1592.00	0.226435	0.113218	+	0.993570i	$0.463884\pi$
$368$	−1408.00	−0.199449
$369$	2214.00	0.312348
$370$	−2620.00	−0.368128
$371$	2416.00	0.338093
$372$	−2976.00	−0.414781
$373$	−7082.00	−0.983089	−0.491544	−	0.870853i	$-0.663567\pi$
$373$	−7082.00	−0.983089	−0.491544	+	0.870853i	$0.663567\pi$
$374$	720.000	0.0995463
$375$	−375.000	−0.0516398
$376$	−1344.00	−0.184339
$377$	15252.0	2.08360
$378$	−432.000	−0.0587822
$379$	−12588.0	−1.70607	−0.853037	−	0.521850i	$-0.825242\pi$
$379$	−12588.0	−1.70607	−0.853037	+	0.521850i	$0.825242\pi$
$380$	−380.000	−0.0512989
$381$	−2628.00	−0.353377
$382$	−8664.00	−1.16044
$383$	10552.0	1.40779	0.703893	−	0.710306i	$-0.251443\pi$
$383$	10552.0	1.40779	0.703893	+	0.710306i	$0.251443\pi$
$384$	384.000	0.0510310
$385$	−800.000	−0.105901
$386$	−4660.00	−0.614476
$387$	2592.00	0.340462
$388$	3160.00	0.413466
$389$	−2174.00	−0.283358	−0.141679	−	0.989913i	$-0.545250\pi$
$389$	−2174.00	−0.283358	−0.141679	+	0.989913i	$0.545250\pi$
$390$	2460.00	0.319402
$391$	1584.00	0.204876
$392$	−2232.00	−0.287584
$393$	−1524.00	−0.195612
$394$	3428.00	0.438325
$395$	4000.00	0.509524
$396$	−720.000	−0.0913671
$397$	−12718.0	−1.60780	−0.803902	−	0.594762i	$-0.797246\pi$
$397$	−12718.0	−1.60780	−0.803902	+	0.594762i	$0.797246\pi$
$398$	2640.00	0.332491
$399$	−456.000	−0.0572144
$400$	400.000	0.0500000
$401$	−3330.00	−0.414694	−0.207347	−	0.978267i	$-0.566483\pi$
$401$	−3330.00	−0.414694	−0.207347	+	0.978267i	$0.566483\pi$
$402$	−4824.00	−0.598506
$403$	20336.0	2.51367
$404$	1160.00	0.142852
$405$	−405.000	−0.0496904
$406$	2976.00	0.363784
$407$	−5240.00	−0.638175
$408$	−432.000	−0.0524196
$409$	−4334.00	−0.523967	−0.261984	−	0.965072i	$-0.584377\pi$
$409$	−4334.00	−0.523967	−0.261984	+	0.965072i	$0.584377\pi$
$410$	−2460.00	−0.296319
$411$	−4518.00	−0.542230
$412$	6160.00	0.736605
$413$	−576.000	−0.0686274
$414$	−1584.00	−0.188042
$415$	580.000	0.0686050
$416$	−2624.00	−0.309260
$417$	−1860.00	−0.218428
$418$	−760.000	−0.0889302
$419$	13420.0	1.56470	0.782351	−	0.622838i	$-0.214020\pi$
$419$	13420.0	1.56470	0.782351	+	0.622838i	$0.214020\pi$
$420$	480.000	0.0557657
$421$	−16418.0	−1.90063	−0.950314	−	0.311293i	$-0.899238\pi$
$421$	−16418.0	−1.90063	−0.950314	+	0.311293i	$0.899238\pi$
$422$	392.000	0.0452186
$423$	−1512.00	−0.173797
$424$	−2416.00	−0.276725
$425$	−450.000	−0.0513605
$426$	1440.00	0.163775
$427$	4368.00	0.495041
$428$	6256.00	0.706531
$429$	4920.00	0.553706
$430$	−2880.00	−0.322991
$431$	−14232.0	−1.59056	−0.795280	−	0.606242i	$-0.792676\pi$
$431$	−14232.0	−1.59056	−0.795280	+	0.606242i	$0.792676\pi$
$432$	432.000	0.0481125
$433$	−17530.0	−1.94558	−0.972792	−	0.231679i	$-0.925578\pi$
$433$	−17530.0	−1.94558	−0.972792	+	0.231679i	$0.925578\pi$
$434$	3968.00	0.438871
$435$	2790.00	0.307518
$436$	−2216.00	−0.243411
$437$	−1672.00	−0.183027
$438$	3612.00	0.394037
$439$	6464.00	0.702756	0.351378	−	0.936234i	$-0.385713\pi$
$439$	6464.00	0.702756	0.351378	+	0.936234i	$0.385713\pi$
$440$	800.000	0.0866784
$441$	−2511.00	−0.271137
$442$	2952.00	0.317675
$443$	3732.00	0.400254	0.200127	−	0.979770i	$-0.435864\pi$
$443$	3732.00	0.400254	0.200127	+	0.979770i	$0.435864\pi$
$444$	3144.00	0.336053
$445$	−3830.00	−0.407999
$446$	−2152.00	−0.228476
$447$	5214.00	0.551709
$448$	−512.000	−0.0539949
$449$	−2330.00	−0.244899	−0.122449	−	0.992475i	$-0.539075\pi$
$449$	−2330.00	−0.244899	−0.122449	+	0.992475i	$0.539075\pi$
$450$	450.000	0.0471405
$451$	−4920.00	−0.513689
$452$	−3336.00	−0.347151
$453$	−5160.00	−0.535183
$454$	3368.00	0.348168
$455$	−3280.00	−0.337953
$456$	456.000	0.0468293
$457$	7594.00	0.777314	0.388657	−	0.921383i	$-0.372939\pi$
$457$	7594.00	0.777314	0.388657	+	0.921383i	$0.372939\pi$
$458$	6300.00	0.642750
$459$	−486.000	−0.0494217
$460$	1760.00	0.178392
$461$	−9678.00	−0.977764	−0.488882	−	0.872350i	$-0.662595\pi$
$461$	−9678.00	−0.977764	−0.488882	+	0.872350i	$0.662595\pi$
$462$	960.000	0.0966737
$463$	17728.0	1.77946	0.889730	−	0.456487i	$-0.150893\pi$
$463$	17728.0	1.77946	0.889730	+	0.456487i	$0.150893\pi$
$464$	−2976.00	−0.297753
$465$	3720.00	0.370991
$466$	3244.00	0.322479
$467$	−2572.00	−0.254856	−0.127428	−	0.991848i	$-0.540672\pi$
$467$	−2572.00	−0.254856	−0.127428	+	0.991848i	$0.540672\pi$
$468$	−2952.00	−0.291573
$469$	6432.00	0.633267
$470$	1680.00	0.164878
$471$	−4338.00	−0.424383
$472$	576.000	0.0561707
$473$	−5760.00	−0.559926
$474$	−4800.00	−0.465129
$475$	475.000	0.0458831
$476$	576.000	0.0554641
$477$	−2718.00	−0.260899
$478$	11416.0	1.09238
$479$	−11244.0	−1.07255	−0.536275	−	0.844043i	$-0.680169\pi$
$479$	−11244.0	−1.07255	−0.536275	+	0.844043i	$0.680169\pi$
$480$	−480.000	−0.0456435
$481$	−21484.0	−2.03656
$482$	2628.00	0.248345
$483$	2112.00	0.198963
$484$	−3724.00	−0.349737
$485$	−3950.00	−0.369815
$486$	486.000	0.0453609
$487$	2236.00	0.208055	0.104028	−	0.994574i	$-0.466827\pi$
$487$	2236.00	0.208055	0.104028	+	0.994574i	$0.466827\pi$
$488$	−4368.00	−0.405185
$489$	−1176.00	−0.108754
$490$	2790.00	0.257223
$491$	−15924.0	−1.46363	−0.731813	−	0.681506i	$-0.761325\pi$
$491$	−15924.0	−1.46363	−0.731813	+	0.681506i	$0.761325\pi$
$492$	2952.00	0.270501
$493$	3348.00	0.305855
$494$	−3116.00	−0.283796
$495$	900.000	0.0817212
$496$	−3968.00	−0.359211
$497$	−1920.00	−0.173287
$498$	−696.000	−0.0626275
$499$	7284.00	0.653460	0.326730	−	0.945118i	$-0.394053\pi$
$499$	7284.00	0.653460	0.326730	+	0.945118i	$0.394053\pi$
$500$	−500.000	−0.0447214
$501$	−1632.00	−0.145534
$502$	7464.00	0.663615
$503$	16488.0	1.46156	0.730779	−	0.682614i	$-0.239157\pi$
$503$	16488.0	1.46156	0.730779	+	0.682614i	$0.239157\pi$
$504$	−576.000	−0.0509069
$505$	−1450.00	−0.127771
$506$	3520.00	0.309255
$507$	13581.0	1.18965
$508$	−3504.00	−0.306033
$509$	−11954.0	−1.04097	−0.520483	−	0.853872i	$-0.674248\pi$
$509$	−11954.0	−1.04097	−0.520483	+	0.853872i	$0.674248\pi$
$510$	540.000	0.0468855
$511$	−4816.00	−0.416922
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	−1988.00	−0.170597
$515$	−7700.00	−0.658840
$516$	3456.00	0.294849
$517$	3360.00	0.285827
$518$	−4192.00	−0.355571
$519$	3462.00	0.292803
$520$	3280.00	0.276611
$521$	15750.0	1.32441	0.662207	−	0.749321i	$-0.269620\pi$
$521$	15750.0	1.32441	0.662207	+	0.749321i	$0.269620\pi$
$522$	−3348.00	−0.280724
$523$	7884.00	0.659165	0.329582	−	0.944127i	$-0.393092\pi$
$523$	7884.00	0.659165	0.329582	+	0.944127i	$0.393092\pi$
$524$	−2032.00	−0.169405
$525$	−600.000	−0.0498784
$526$	12512.0	1.03717
$527$	4464.00	0.368985
$528$	−960.000	−0.0791262
$529$	−4423.00	−0.363524
$530$	3020.00	0.247510
$531$	648.000	0.0529582
$532$	−608.000	−0.0495491
$533$	−20172.0	−1.63930
$534$	4596.00	0.372450
$535$	−7820.00	−0.631940
$536$	−6432.00	−0.518321
$537$	7584.00	0.609448
$538$	7532.00	0.603583
$539$	5580.00	0.445914
$540$	−540.000	−0.0430331
$541$	−14402.0	−1.14453	−0.572265	−	0.820069i	$-0.693935\pi$
$541$	−14402.0	−1.14453	−0.572265	+	0.820069i	$0.693935\pi$
$542$	−12480.0	−0.989044
$543$	4362.00	0.344735
$544$	−576.000	−0.0453967
$545$	2770.00	0.217713
$546$	3936.00	0.308508
$547$	−9676.00	−0.756336	−0.378168	−	0.925737i	$-0.623446\pi$
$547$	−9676.00	−0.756336	−0.378168	+	0.925737i	$0.623446\pi$
$548$	−6024.00	−0.469585
$549$	−4914.00	−0.382012
$550$	−1000.00	−0.0775275
$551$	−3534.00	−0.273237
$552$	−2112.00	−0.162849
$553$	6400.00	0.492144
$554$	12020.0	0.921807
$555$	−3930.00	−0.300575
$556$	−2480.00	−0.189164
$557$	−20406.0	−1.55230	−0.776149	−	0.630550i	$-0.782830\pi$
$557$	−20406.0	−1.55230	−0.776149	+	0.630550i	$0.782830\pi$
$558$	−4464.00	−0.338667
$559$	−23616.0	−1.78685
$560$	640.000	0.0482945
$561$	1080.00	0.0812792
$562$	−2196.00	−0.164827
$563$	−18428.0	−1.37948	−0.689740	−	0.724057i	$-0.742275\pi$
$563$	−18428.0	−1.37948	−0.689740	+	0.724057i	$0.742275\pi$
$564$	−2016.00	−0.150512
$565$	4170.00	0.310501
$566$	1376.00	0.102187
$567$	−648.000	−0.0479955
$568$	1920.00	0.141833
$569$	−24162.0	−1.78018	−0.890091	−	0.455783i	$-0.849359\pi$
$569$	−24162.0	−1.78018	−0.890091	+	0.455783i	$0.849359\pi$
$570$	−570.000	−0.0418854
$571$	−9828.00	−0.720296	−0.360148	−	0.932895i	$-0.617274\pi$
$571$	−9828.00	−0.720296	−0.360148	+	0.932895i	$0.617274\pi$
$572$	6560.00	0.479523
$573$	−12996.0	−0.947497
$574$	−3936.00	−0.286212
$575$	−2200.00	−0.159559
$576$	576.000	0.0416667
$577$	−25966.0	−1.87345	−0.936723	−	0.350071i	$-0.886158\pi$
$577$	−25966.0	−1.87345	−0.936723	+	0.350071i	$0.886158\pi$
$578$	−9178.00	−0.660475
$579$	−6990.00	−0.501718
$580$	3720.00	0.266318
$581$	928.000	0.0662649
$582$	4740.00	0.337593
$583$	6040.00	0.429076
$584$	4816.00	0.341246
$585$	3690.00	0.260791
$586$	16884.0	1.19022
$587$	7020.00	0.493605	0.246803	−	0.969066i	$-0.420620\pi$
$587$	7020.00	0.493605	0.246803	+	0.969066i	$0.420620\pi$
$588$	−3348.00	−0.234812
$589$	−4712.00	−0.329634
$590$	−720.000	−0.0502406
$591$	5142.00	0.357891
$592$	4192.00	0.291031
$593$	−4698.00	−0.325335	−0.162668	−	0.986681i	$-0.552010\pi$
$593$	−4698.00	−0.325335	−0.162668	+	0.986681i	$0.552010\pi$
$594$	−1080.00	−0.0746009
$595$	−720.000	−0.0496086
$596$	6952.00	0.477794
$597$	3960.00	0.271477
$598$	14432.0	0.986904
$599$	−1408.00	−0.0960423	−0.0480211	−	0.998846i	$-0.515291\pi$
$599$	−1408.00	−0.0960423	−0.0480211	+	0.998846i	$0.515291\pi$
$600$	600.000	0.0408248
$601$	−18942.0	−1.28562	−0.642812	−	0.766024i	$-0.722232\pi$
$601$	−18942.0	−1.28562	−0.642812	+	0.766024i	$0.722232\pi$
$602$	−4608.00	−0.311974
$603$	−7236.00	−0.488678
$604$	−6880.00	−0.463482
$605$	4655.00	0.312814
$606$	1740.00	0.116638
$607$	−4268.00	−0.285392	−0.142696	−	0.989767i	$-0.545577\pi$
$607$	−4268.00	−0.285392	−0.142696	+	0.989767i	$0.545577\pi$
$608$	608.000	0.0405554
$609$	4464.00	0.297029
$610$	5460.00	0.362408
$611$	13776.0	0.912140
$612$	−648.000	−0.0428004
$613$	106.000	0.00698418	0.00349209	−	0.999994i	$-0.498888\pi$
$613$	106.000	0.00698418	0.00349209	+	0.999994i	$0.498888\pi$
$614$	3176.00	0.208751
$615$	−3690.00	−0.241943
$616$	1280.00	0.0837219
$617$	−4250.00	−0.277307	−0.138654	−	0.990341i	$-0.544277\pi$
$617$	−4250.00	−0.277307	−0.138654	+	0.990341i	$0.544277\pi$
$618$	9240.00	0.601436
$619$	−11436.0	−0.742571	−0.371286	−	0.928519i	$-0.621083\pi$
$619$	−11436.0	−0.742571	−0.371286	+	0.928519i	$0.621083\pi$
$620$	4960.00	0.321288
$621$	−2376.00	−0.153536
$622$	−16520.0	−1.06494
$623$	−6128.00	−0.394082
$624$	−3936.00	−0.252510
$625$	625.000	0.0400000
$626$	−19580.0	−1.25012
$627$	−1140.00	−0.0726112
$628$	−5784.00	−0.367527
$629$	−4716.00	−0.298949
$630$	720.000	0.0455325
$631$	−1528.00	−0.0964005	−0.0482003	−	0.998838i	$-0.515349\pi$
$631$	−1528.00	−0.0964005	−0.0482003	+	0.998838i	$0.515349\pi$
$632$	−6400.00	−0.402814
$633$	588.000	0.0369209
$634$	−7308.00	−0.457788
$635$	4380.00	0.273724
$636$	−3624.00	−0.225945
$637$	22878.0	1.42301
$638$	7440.00	0.461681
$639$	2160.00	0.133722
$640$	−640.000	−0.0395285
$641$	−11186.0	−0.689267	−0.344634	−	0.938737i	$-0.611997\pi$
$641$	−11186.0	−0.689267	−0.344634	+	0.938737i	$0.611997\pi$
$642$	9384.00	0.576880
$643$	18968.0	1.16334	0.581668	−	0.813426i	$-0.302400\pi$
$643$	18968.0	1.16334	0.581668	+	0.813426i	$0.302400\pi$
$644$	2816.00	0.172307
$645$	−4320.00	−0.263721
$646$	−684.000	−0.0416589
$647$	−21192.0	−1.28770	−0.643851	−	0.765151i	$-0.722664\pi$
$647$	−21192.0	−1.28770	−0.643851	+	0.765151i	$0.722664\pi$
$648$	648.000	0.0392837
$649$	−1440.00	−0.0870954
$650$	−4100.00	−0.247408
$651$	5952.00	0.358337
$652$	−1568.00	−0.0941835
$653$	18538.0	1.11095	0.555473	−	0.831534i	$-0.312537\pi$
$653$	18538.0	1.11095	0.555473	+	0.831534i	$0.312537\pi$
$654$	−3324.00	−0.198744
$655$	2540.00	0.151521
$656$	3936.00	0.234261
$657$	5418.00	0.321730
$658$	2688.00	0.159254
$659$	12192.0	0.720687	0.360344	−	0.932820i	$-0.382659\pi$
$659$	12192.0	0.720687	0.360344	+	0.932820i	$0.382659\pi$
$660$	1200.00	0.0707726
$661$	16926.0	0.995984	0.497992	−	0.867182i	$-0.334071\pi$
$661$	16926.0	0.995984	0.497992	+	0.867182i	$0.334071\pi$
$662$	−8264.00	−0.485180
$663$	4428.00	0.259380
$664$	−928.000	−0.0542370
$665$	760.000	0.0443181
$666$	4716.00	0.274386
$667$	16368.0	0.950182
$668$	−2176.00	−0.126036
$669$	−3228.00	−0.186550
$670$	8040.00	0.463600
$671$	10920.0	0.628259
$672$	−768.000	−0.0440867
$673$	14830.0	0.849412	0.424706	−	0.905331i	$-0.360377\pi$
$673$	14830.0	0.849412	0.424706	+	0.905331i	$0.360377\pi$
$674$	−15012.0	−0.857924
$675$	675.000	0.0384900
$676$	18108.0	1.03027
$677$	−21246.0	−1.20613	−0.603065	−	0.797692i	$-0.706054\pi$
$677$	−21246.0	−1.20613	−0.603065	+	0.797692i	$0.706054\pi$
$678$	−5004.00	−0.283448
$679$	−6320.00	−0.357201
$680$	720.000	0.0406040
$681$	5052.00	0.284278
$682$	9920.00	0.556974
$683$	2924.00	0.163812	0.0819061	−	0.996640i	$-0.473899\pi$
$683$	2924.00	0.163812	0.0819061	+	0.996640i	$0.473899\pi$
$684$	684.000	0.0382360
$685$	7530.00	0.420010
$686$	9952.00	0.553891
$687$	9450.00	0.524803
$688$	4608.00	0.255346
$689$	24764.0	1.36928
$690$	2640.00	0.145657
$691$	33732.0	1.85706	0.928528	−	0.371262i	$-0.121075\pi$
$691$	33732.0	1.85706	0.928528	+	0.371262i	$0.121075\pi$
$692$	4616.00	0.253575
$693$	1440.00	0.0789337
$694$	−16584.0	−0.907089
$695$	3100.00	0.169194
$696$	−4464.00	−0.243114
$697$	−4428.00	−0.240635
$698$	−22724.0	−1.23226
$699$	4866.00	0.263303
$700$	−800.000	−0.0431959
$701$	−19398.0	−1.04515	−0.522577	−	0.852592i	$-0.675029\pi$
$701$	−19398.0	−1.04515	−0.522577	+	0.852592i	$0.675029\pi$
$702$	−4428.00	−0.238069
$703$	4978.00	0.267068
$704$	−1280.00	−0.0685253
$705$	2520.00	0.134622
$706$	22204.0	1.18365
$707$	−2320.00	−0.123412
$708$	864.000	0.0458631
$709$	−21250.0	−1.12561	−0.562807	−	0.826588i	$-0.690279\pi$
$709$	−21250.0	−1.12561	−0.562807	+	0.826588i	$0.690279\pi$
$710$	−2400.00	−0.126860
$711$	−7200.00	−0.379777
$712$	6128.00	0.322551
$713$	21824.0	1.14630
$714$	864.000	0.0452863
$715$	−8200.00	−0.428899
$716$	10112.0	0.527798
$717$	17124.0	0.891921
$718$	4072.00	0.211651
$719$	24708.0	1.28158	0.640788	−	0.767718i	$-0.278608\pi$
$719$	24708.0	1.28158	0.640788	+	0.767718i	$0.278608\pi$
$720$	−720.000	−0.0372678
$721$	−12320.0	−0.636367
$722$	722.000	0.0372161
$723$	3942.00	0.202773
$724$	5816.00	0.298550
$725$	−4650.00	−0.238202
$726$	−5586.00	−0.285559
$727$	9176.00	0.468114	0.234057	−	0.972223i	$-0.424800\pi$
$727$	9176.00	0.468114	0.234057	+	0.972223i	$0.424800\pi$
$728$	5248.00	0.267176
$729$	729.000	0.0370370
$730$	−6020.00	−0.305219
$731$	−5184.00	−0.262294
$732$	−6552.00	−0.330832
$733$	−18870.0	−0.950859	−0.475429	−	0.879754i	$-0.657707\pi$
$733$	−18870.0	−0.950859	−0.475429	+	0.879754i	$0.657707\pi$
$734$	3184.00	0.160114
$735$	4185.00	0.210022
$736$	−2816.00	−0.141031
$737$	16080.0	0.803683
$738$	4428.00	0.220863
$739$	−15076.0	−0.750446	−0.375223	−	0.926935i	$-0.622434\pi$
$739$	−15076.0	−0.750446	−0.375223	+	0.926935i	$0.622434\pi$
$740$	−5240.00	−0.260306
$741$	−4674.00	−0.231719
$742$	4832.00	0.239068
$743$	−4656.00	−0.229895	−0.114948	−	0.993372i	$-0.536670\pi$
$743$	−4656.00	−0.229895	−0.114948	+	0.993372i	$0.536670\pi$
$744$	−5952.00	−0.293294
$745$	−8690.00	−0.427352
$746$	−14164.0	−0.695149
$747$	−1044.00	−0.0511352
$748$	1440.00	0.0703899
$749$	−12512.0	−0.610385
$750$	−750.000	−0.0365148
$751$	20920.0	1.01649	0.508243	−	0.861213i	$-0.330295\pi$
$751$	20920.0	1.01649	0.508243	+	0.861213i	$0.330295\pi$
$752$	−2688.00	−0.130347
$753$	11196.0	0.541839
$754$	30504.0	1.47333
$755$	8600.00	0.414551
$756$	−864.000	−0.0415653
$757$	34578.0	1.66018	0.830092	−	0.557627i	$-0.188288\pi$
$757$	34578.0	1.66018	0.830092	+	0.557627i	$0.188288\pi$
$758$	−25176.0	−1.20638
$759$	5280.00	0.252506
$760$	−760.000	−0.0362738
$761$	−28214.0	−1.34396	−0.671982	−	0.740567i	$-0.734557\pi$
$761$	−28214.0	−1.34396	−0.671982	+	0.740567i	$0.734557\pi$
$762$	−5256.00	−0.249875
$763$	4432.00	0.210287
$764$	−17328.0	−0.820556
$765$	810.000	0.0382818
$766$	21104.0	0.995455
$767$	−5904.00	−0.277941
$768$	768.000	0.0360844
$769$	−36734.0	−1.72258	−0.861289	−	0.508116i	$-0.830342\pi$
$769$	−36734.0	−1.72258	−0.861289	+	0.508116i	$0.830342\pi$
$770$	−1600.00	−0.0748831
$771$	−2982.00	−0.139292
$772$	−9320.00	−0.434500
$773$	21762.0	1.01258	0.506290	−	0.862363i	$-0.331016\pi$
$773$	21762.0	1.01258	0.506290	+	0.862363i	$0.331016\pi$
$774$	5184.00	0.240743
$775$	−6200.00	−0.287368
$776$	6320.00	0.292364
$777$	−6288.00	−0.290323
$778$	−4348.00	−0.200364
$779$	4674.00	0.214972
$780$	4920.00	0.225852
$781$	−4800.00	−0.219920
$782$	3168.00	0.144869
$783$	−5022.00	−0.229210
$784$	−4464.00	−0.203353
$785$	7230.00	0.328726
$786$	−3048.00	−0.138319
$787$	28260.0	1.28000	0.640000	−	0.768375i	$-0.278934\pi$
$787$	28260.0	1.28000	0.640000	+	0.768375i	$0.278934\pi$
$788$	6856.00	0.309943
$789$	18768.0	0.846842
$790$	8000.00	0.360288
$791$	6672.00	0.299910
$792$	−1440.00	−0.0646063
$793$	44772.0	2.00492
$794$	−25436.0	−1.13689
$795$	4530.00	0.202091
$796$	5280.00	0.235106
$797$	−29854.0	−1.32683	−0.663415	−	0.748252i	$-0.730893\pi$
$797$	−29854.0	−1.32683	−0.663415	+	0.748252i	$0.730893\pi$
$798$	−912.000	−0.0404567
$799$	3024.00	0.133894
$800$	800.000	0.0353553
$801$	6894.00	0.304104
$802$	−6660.00	−0.293233
$803$	−12040.0	−0.529119
$804$	−9648.00	−0.423207
$805$	−3520.00	−0.154116
$806$	40672.0	1.77743
$807$	11298.0	0.492823
$808$	2320.00	0.101012
$809$	21482.0	0.933581	0.466790	−	0.884368i	$-0.345410\pi$
$809$	21482.0	0.933581	0.466790	+	0.884368i	$0.345410\pi$
$810$	−810.000	−0.0351364
$811$	−14756.0	−0.638907	−0.319453	−	0.947602i	$-0.603499\pi$
$811$	−14756.0	−0.638907	−0.319453	+	0.947602i	$0.603499\pi$
$812$	5952.00	0.257234
$813$	−18720.0	−0.807551
$814$	−10480.0	−0.451258
$815$	1960.00	0.0842403
$816$	−864.000	−0.0370662
$817$	5472.00	0.234322
$818$	−8668.00	−0.370501
$819$	5904.00	0.251896
$820$	−4920.00	−0.209529
$821$	−13214.0	−0.561720	−0.280860	−	0.959749i	$-0.590620\pi$
$821$	−13214.0	−0.561720	−0.280860	+	0.959749i	$0.590620\pi$
$822$	−9036.00	−0.383414
$823$	19256.0	0.815580	0.407790	−	0.913076i	$-0.366300\pi$
$823$	19256.0	0.815580	0.407790	+	0.913076i	$0.366300\pi$
$824$	12320.0	0.520859
$825$	−1500.00	−0.0633010
$826$	−1152.00	−0.0485269
$827$	25356.0	1.06616	0.533080	−	0.846065i	$-0.321034\pi$
$827$	25356.0	1.06616	0.533080	+	0.846065i	$0.321034\pi$
$828$	−3168.00	−0.132966
$829$	37286.0	1.56212	0.781059	−	0.624457i	$-0.214680\pi$
$829$	37286.0	1.56212	0.781059	+	0.624457i	$0.214680\pi$
$830$	1160.00	0.0485111
$831$	18030.0	0.752652
$832$	−5248.00	−0.218680
$833$	5022.00	0.208886
$834$	−3720.00	−0.154452
$835$	2720.00	0.112730
$836$	−1520.00	−0.0628831
$837$	−6696.00	−0.276520
$838$	26840.0	1.10641
$839$	−35816.0	−1.47379	−0.736893	−	0.676010i	$-0.763708\pi$
$839$	−35816.0	−1.47379	−0.736893	+	0.676010i	$0.763708\pi$
$840$	960.000	0.0394323
$841$	10207.0	0.418508
$842$	−32836.0	−1.34395
$843$	−3294.00	−0.134581
$844$	784.000	0.0319744
$845$	−22635.0	−0.921500
$846$	−3024.00	−0.122893
$847$	7448.00	0.302144
$848$	−4832.00	−0.195674
$849$	2064.00	0.0834350
$850$	−900.000	−0.0363173
$851$	−23056.0	−0.928730
$852$	2880.00	0.115807
$853$	−4206.00	−0.168828	−0.0844142	−	0.996431i	$-0.526902\pi$
$853$	−4206.00	−0.168828	−0.0844142	+	0.996431i	$0.526902\pi$
$854$	8736.00	0.350047
$855$	−855.000	−0.0341993
$856$	12512.0	0.499593
$857$	29446.0	1.17369	0.586847	−	0.809698i	$-0.300369\pi$
$857$	29446.0	1.17369	0.586847	+	0.809698i	$0.300369\pi$
$858$	9840.00	0.391529
$859$	−5572.00	−0.221320	−0.110660	−	0.993858i	$-0.535297\pi$
$859$	−5572.00	−0.221320	−0.110660	+	0.993858i	$0.535297\pi$
$860$	−5760.00	−0.228389
$861$	−5904.00	−0.233691
$862$	−28464.0	−1.12470
$863$	11056.0	0.436096	0.218048	−	0.975938i	$-0.430031\pi$
$863$	11056.0	0.436096	0.218048	+	0.975938i	$0.430031\pi$
$864$	864.000	0.0340207
$865$	−5770.00	−0.226804
$866$	−35060.0	−1.37574
$867$	−13767.0	−0.539275
$868$	7936.00	0.310329
$869$	16000.0	0.624583
$870$	5580.00	0.217448
$871$	65928.0	2.56474
$872$	−4432.00	−0.172117
$873$	7110.00	0.275644
$874$	−3344.00	−0.129419
$875$	1000.00	0.0386356
$876$	7224.00	0.278626
$877$	−2322.00	−0.0894052	−0.0447026	−	0.999000i	$-0.514234\pi$
$877$	−2322.00	−0.0894052	−0.0447026	+	0.999000i	$0.514234\pi$
$878$	12928.0	0.496924
$879$	25326.0	0.971814
$880$	1600.00	0.0612909
$881$	−12910.0	−0.493699	−0.246850	−	0.969054i	$-0.579395\pi$
$881$	−12910.0	−0.493699	−0.246850	+	0.969054i	$0.579395\pi$
$882$	−5022.00	−0.191723
$883$	−4440.00	−0.169216	−0.0846081	−	0.996414i	$-0.526964\pi$
$883$	−4440.00	−0.169216	−0.0846081	+	0.996414i	$0.526964\pi$
$884$	5904.00	0.224630
$885$	−1080.00	−0.0410212
$886$	7464.00	0.283023
$887$	−6056.00	−0.229245	−0.114623	−	0.993409i	$-0.536566\pi$
$887$	−6056.00	−0.229245	−0.114623	+	0.993409i	$0.536566\pi$
$888$	6288.00	0.237626
$889$	7008.00	0.264388
$890$	−7660.00	−0.288499
$891$	−1620.00	−0.0609114
$892$	−4304.00	−0.161557
$893$	−3192.00	−0.119615
$894$	10428.0	0.390117
$895$	−12640.0	−0.472077
$896$	−1024.00	−0.0381802
$897$	21648.0	0.805803
$898$	−4660.00	−0.173170
$899$	46128.0	1.71130
$900$	900.000	0.0333333
$901$	5436.00	0.200998
$902$	−9840.00	−0.363233
$903$	−6912.00	−0.254725
$904$	−6672.00	−0.245473
$905$	−7270.00	−0.267031
$906$	−10320.0	−0.378432
$907$	25076.0	0.918010	0.459005	−	0.888434i	$-0.348206\pi$
$907$	25076.0	0.918010	0.459005	+	0.888434i	$0.348206\pi$
$908$	6736.00	0.246192
$909$	2610.00	0.0952346
$910$	−6560.00	−0.238969
$911$	−20208.0	−0.734930	−0.367465	−	0.930037i	$-0.619774\pi$
$911$	−20208.0	−0.734930	−0.367465	+	0.930037i	$0.619774\pi$
$912$	912.000	0.0331133
$913$	2320.00	0.0840973
$914$	15188.0	0.549644
$915$	8190.00	0.295905
$916$	12600.0	0.454493
$917$	4064.00	0.146352
$918$	−972.000	−0.0349464
$919$	30136.0	1.08171	0.540857	−	0.841115i	$-0.318100\pi$
$919$	30136.0	1.08171	0.540857	+	0.841115i	$0.318100\pi$
$920$	3520.00	0.126142
$921$	4764.00	0.170444
$922$	−19356.0	−0.691384
$923$	−19680.0	−0.701815
$924$	1920.00	0.0683586
$925$	6550.00	0.232825
$926$	35456.0	1.25827
$927$	13860.0	0.491070
$928$	−5952.00	−0.210543
$929$	15594.0	0.550724	0.275362	−	0.961341i	$-0.411202\pi$
$929$	15594.0	0.550724	0.275362	+	0.961341i	$0.411202\pi$
$930$	7440.00	0.262330
$931$	−5301.00	−0.186609
$932$	6488.00	0.228027
$933$	−24780.0	−0.869519
$934$	−5144.00	−0.180211
$935$	−1800.00	−0.0629586
$936$	−5904.00	−0.206173
$937$	25634.0	0.893731	0.446866	−	0.894601i	$-0.352540\pi$
$937$	25634.0	0.893731	0.446866	+	0.894601i	$0.352540\pi$
$938$	12864.0	0.447787
$939$	−29370.0	−1.02072
$940$	3360.00	0.116586
$941$	37758.0	1.30805	0.654025	−	0.756473i	$-0.273079\pi$
$941$	37758.0	1.30805	0.654025	+	0.756473i	$0.273079\pi$
$942$	−8676.00	−0.300084
$943$	−21648.0	−0.747567
$944$	1152.00	0.0397187
$945$	1080.00	0.0371771
$946$	−11520.0	−0.395928
$947$	40356.0	1.38479	0.692394	−	0.721520i	$-0.256556\pi$
$947$	40356.0	1.38479	0.692394	+	0.721520i	$0.256556\pi$
$948$	−9600.00	−0.328896
$949$	−49364.0	−1.68854
$950$	950.000	0.0324443
$951$	−10962.0	−0.373783
$952$	1152.00	0.0392190
$953$	−27978.0	−0.950993	−0.475496	−	0.879718i	$-0.657732\pi$
$953$	−27978.0	−0.950993	−0.475496	+	0.879718i	$0.657732\pi$
$954$	−5436.00	−0.184483
$955$	21660.0	0.733928
$956$	22832.0	0.772426
$957$	11160.0	0.376961
$958$	−22488.0	−0.758407
$959$	12048.0	0.405683
$960$	−960.000	−0.0322749
$961$	31713.0	1.06452
$962$	−42968.0	−1.44007
$963$	14076.0	0.471021
$964$	5256.00	0.175606
$965$	11650.0	0.388629
$966$	4224.00	0.140688
$967$	−19616.0	−0.652335	−0.326168	−	0.945312i	$-0.605757\pi$
$967$	−19616.0	−0.652335	−0.326168	+	0.945312i	$0.605757\pi$
$968$	−7448.00	−0.247301
$969$	−1026.00	−0.0340143
$970$	−7900.00	−0.261499
$971$	8648.00	0.285816	0.142908	−	0.989736i	$-0.454355\pi$
$971$	8648.00	0.285816	0.142908	+	0.989736i	$0.454355\pi$
$972$	972.000	0.0320750
$973$	4960.00	0.163423
$974$	4472.00	0.147117
$975$	−6150.00	−0.202008
$976$	−8736.00	−0.286509
$977$	−5746.00	−0.188158	−0.0940792	−	0.995565i	$-0.529991\pi$
$977$	−5746.00	−0.188158	−0.0940792	+	0.995565i	$0.529991\pi$
$978$	−2352.00	−0.0769005
$979$	−15320.0	−0.500132
$980$	5580.00	0.181884
$981$	−4986.00	−0.162274
$982$	−31848.0	−1.03494
$983$	−5304.00	−0.172097	−0.0860485	−	0.996291i	$-0.527424\pi$
$983$	−5304.00	−0.172097	−0.0860485	+	0.996291i	$0.527424\pi$
$984$	5904.00	0.191273
$985$	−8570.00	−0.277221
$986$	6696.00	0.216272
$987$	4032.00	0.130030
$988$	−6232.00	−0.200674
$989$	−25344.0	−0.814856
$990$	1800.00	0.0577856
$991$	7416.00	0.237716	0.118858	−	0.992911i	$-0.462077\pi$
$991$	7416.00	0.237716	0.118858	+	0.992911i	$0.462077\pi$
$992$	−7936.00	−0.254000
$993$	−12396.0	−0.396148
$994$	−3840.00	−0.122533
$995$	−6600.00	−0.210285
$996$	−1392.00	−0.0442843
$997$	−13358.0	−0.424325	−0.212163	−	0.977234i	$-0.568051\pi$
$997$	−13358.0	−0.424325	−0.212163	+	0.977234i	$0.568051\pi$
$998$	14568.0	0.462066
$999$	7074.00	0.224035

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.a.f.1.1	✓	1	1.1	even	1	trivial
1710.4.a.f.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

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