LMFDB - Embedded newform 1470.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,4,Mod(1,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, 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("1470.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1470.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:	$86.7328077084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -12.0000 q^{12} -26.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} -18.0000 q^{17} -18.0000 q^{18} -92.0000 q^{19} +20.0000 q^{20} +24.0000 q^{24} +25.0000 q^{25} +52.0000 q^{26} -27.0000 q^{27} -6.00000 q^{29} +30.0000 q^{30} +4.00000 q^{31} -32.0000 q^{32} +36.0000 q^{34} +36.0000 q^{36} +410.000 q^{37} +184.000 q^{38} +78.0000 q^{39} -40.0000 q^{40} -174.000 q^{41} +248.000 q^{43} +45.0000 q^{45} -420.000 q^{47} -48.0000 q^{48} -50.0000 q^{50} +54.0000 q^{51} -104.000 q^{52} +102.000 q^{53} +54.0000 q^{54} +276.000 q^{57} +12.0000 q^{58} +588.000 q^{59} -60.0000 q^{60} -650.000 q^{61} -8.00000 q^{62} +64.0000 q^{64} -130.000 q^{65} +152.000 q^{67} -72.0000 q^{68} -168.000 q^{71} -72.0000 q^{72} +610.000 q^{73} -820.000 q^{74} -75.0000 q^{75} -368.000 q^{76} -156.000 q^{78} -1048.00 q^{79} +80.0000 q^{80} +81.0000 q^{81} +348.000 q^{82} +684.000 q^{83} -90.0000 q^{85} -496.000 q^{86} +18.0000 q^{87} +834.000 q^{89} -90.0000 q^{90} -12.0000 q^{93} +840.000 q^{94} -460.000 q^{95} +96.0000 q^{96} -110.000 q^{97} +O(q^{100})\)

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
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−12.0000	−0.288675
$13$	−26.0000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−26.0000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−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
$19$	−92.0000	−1.11086	−0.555428	−	0.831565i	$-0.687445\pi$
$19$	−92.0000	−1.11086	−0.555428	+	0.831565i	$0.687445\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	52.0000	0.392232
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−6.00000	−0.0384197	−0.0192099	−	0.999815i	$-0.506115\pi$
$29$	−6.00000	−0.0384197	−0.0192099	+	0.999815i	$0.506115\pi$
$30$	30.0000	0.182574
$31$	4.00000	0.0231749	0.0115874	−	0.999933i	$-0.496312\pi$
$31$	4.00000	0.0231749	0.0115874	+	0.999933i	$0.496312\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	36.0000	0.181587
$35$	0	0
$36$	36.0000	0.166667
$37$	410.000	1.82172	0.910859	−	0.412717i	$-0.135420\pi$
$37$	410.000	1.82172	0.910859	+	0.412717i	$0.135420\pi$
$38$	184.000	0.785493
$39$	78.0000	0.320256
$40$	−40.0000	−0.158114
$41$	−174.000	−0.662786	−0.331393	−	0.943493i	$-0.607519\pi$
$41$	−174.000	−0.662786	−0.331393	+	0.943493i	$0.607519\pi$
$42$	0	0
$43$	248.000	0.879527	0.439763	−	0.898114i	$-0.355062\pi$
$43$	248.000	0.879527	0.439763	+	0.898114i	$0.355062\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	0	0
$47$	−420.000	−1.30347	−0.651737	−	0.758445i	$-0.725959\pi$
$47$	−420.000	−1.30347	−0.651737	+	0.758445i	$0.725959\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	54.0000	0.148265
$52$	−104.000	−0.277350
$53$	102.000	0.264354	0.132177	−	0.991226i	$-0.457803\pi$
$53$	102.000	0.264354	0.132177	+	0.991226i	$0.457803\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	0	0
$57$	276.000	0.641353
$58$	12.0000	0.0271668
$59$	588.000	1.29748	0.648738	−	0.761012i	$-0.275297\pi$
$59$	588.000	1.29748	0.648738	+	0.761012i	$0.275297\pi$
$60$	−60.0000	−0.129099
$61$	−650.000	−1.36433	−0.682164	−	0.731199i	$-0.738961\pi$
$61$	−650.000	−1.36433	−0.682164	+	0.731199i	$0.738961\pi$
$62$	−8.00000	−0.0163871
$63$	0	0
$64$	64.0000	0.125000
$65$	−130.000	−0.248069
$66$	0	0
$67$	152.000	0.277161	0.138580	−	0.990351i	$-0.455746\pi$
$67$	152.000	0.277161	0.138580	+	0.990351i	$0.455746\pi$
$68$	−72.0000	−0.128401
$69$	0	0
$70$	0	0
$71$	−168.000	−0.280816	−0.140408	−	0.990094i	$-0.544841\pi$
$71$	−168.000	−0.280816	−0.140408	+	0.990094i	$0.544841\pi$
$72$	−72.0000	−0.117851
$73$	610.000	0.978015	0.489008	−	0.872280i	$-0.337359\pi$
$73$	610.000	0.978015	0.489008	+	0.872280i	$0.337359\pi$
$74$	−820.000	−1.28815
$75$	−75.0000	−0.115470
$76$	−368.000	−0.555428
$77$	0	0
$78$	−156.000	−0.226455
$79$	−1048.00	−1.49252	−0.746261	−	0.665654i	$-0.768153\pi$
$79$	−1048.00	−1.49252	−0.746261	+	0.665654i	$0.768153\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	348.000	0.468661
$83$	684.000	0.904563	0.452282	−	0.891875i	$-0.350610\pi$
$83$	684.000	0.904563	0.452282	+	0.891875i	$0.350610\pi$
$84$	0	0
$85$	−90.0000	−0.114846
$86$	−496.000	−0.621919
$87$	18.0000	0.0221816
$88$	0	0
$89$	834.000	0.993301	0.496651	−	0.867951i	$-0.334563\pi$
$89$	834.000	0.993301	0.496651	+	0.867951i	$0.334563\pi$
$90$	−90.0000	−0.105409
$91$	0	0
$92$	0	0
$93$	−12.0000	−0.0133800
$94$	840.000	0.921696
$95$	−460.000	−0.496790
$96$	96.0000	0.102062
$97$	−110.000	−0.115142	−0.0575712	−	0.998341i	$-0.518336\pi$
$97$	−110.000	−0.115142	−0.0575712	+	0.998341i	$0.518336\pi$
$98$	0	0
$99$	0	0
$100$	100.000	0.100000
$101$	1374.00	1.35364	0.676822	−	0.736146i	$-0.263357\pi$
$101$	1374.00	1.35364	0.676822	+	0.736146i	$0.263357\pi$
$102$	−108.000	−0.104839
$103$	−1184.00	−1.13265	−0.566325	−	0.824182i	$-0.691635\pi$
$103$	−1184.00	−1.13265	−0.566325	+	0.824182i	$0.691635\pi$
$104$	208.000	0.196116
$105$	0	0
$106$	−204.000	−0.186927
$107$	−276.000	−0.249364	−0.124682	−	0.992197i	$-0.539791\pi$
$107$	−276.000	−0.249364	−0.124682	+	0.992197i	$0.539791\pi$
$108$	−108.000	−0.0962250
$109$	−1594.00	−1.40071	−0.700356	−	0.713794i	$-0.746975\pi$
$109$	−1594.00	−1.40071	−0.700356	+	0.713794i	$0.746975\pi$
$110$	0	0
$111$	−1230.00	−1.05177
$112$	0	0
$113$	738.000	0.614382	0.307191	−	0.951648i	$-0.400611\pi$
$113$	738.000	0.614382	0.307191	+	0.951648i	$0.400611\pi$
$114$	−552.000	−0.453505
$115$	0	0
$116$	−24.0000	−0.0192099
$117$	−234.000	−0.184900
$118$	−1176.00	−0.917454
$119$	0	0
$120$	120.000	0.0912871
$121$	−1331.00	−1.00000
$122$	1300.00	0.964725
$123$	522.000	0.382660
$124$	16.0000	0.0115874
$125$	125.000	0.0894427
$126$	0	0
$127$	776.000	0.542196	0.271098	−	0.962552i	$-0.412613\pi$
$127$	776.000	0.542196	0.271098	+	0.962552i	$0.412613\pi$
$128$	−128.000	−0.0883883
$129$	−744.000	−0.507795
$130$	260.000	0.175412
$131$	−588.000	−0.392166	−0.196083	−	0.980587i	$-0.562822\pi$
$131$	−588.000	−0.392166	−0.196083	+	0.980587i	$0.562822\pi$
$132$	0	0
$133$	0	0
$134$	−304.000	−0.195982
$135$	−135.000	−0.0860663
$136$	144.000	0.0907934
$137$	1242.00	0.774534	0.387267	−	0.921968i	$-0.373419\pi$
$137$	1242.00	0.774534	0.387267	+	0.921968i	$0.373419\pi$
$138$	0	0
$139$	724.000	0.441790	0.220895	−	0.975298i	$-0.429102\pi$
$139$	724.000	0.441790	0.220895	+	0.975298i	$0.429102\pi$
$140$	0	0
$141$	1260.00	0.752561
$142$	336.000	0.198567
$143$	0	0
$144$	144.000	0.0833333
$145$	−30.0000	−0.0171818
$146$	−1220.00	−0.691561
$147$	0	0
$148$	1640.00	0.910859
$149$	−1566.00	−0.861018	−0.430509	−	0.902586i	$-0.641666\pi$
$149$	−1566.00	−0.861018	−0.430509	+	0.902586i	$0.641666\pi$
$150$	150.000	0.0816497
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	736.000	0.392747
$153$	−162.000	−0.0856008
$154$	0	0
$155$	20.0000	0.0103641
$156$	312.000	0.160128
$157$	2374.00	1.20679	0.603394	−	0.797443i	$-0.293815\pi$
$157$	2374.00	1.20679	0.603394	+	0.797443i	$0.293815\pi$
$158$	2096.00	1.05537
$159$	−306.000	−0.152625
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	−400.000	−0.192211	−0.0961056	−	0.995371i	$-0.530639\pi$
$163$	−400.000	−0.192211	−0.0961056	+	0.995371i	$0.530639\pi$
$164$	−696.000	−0.331393
$165$	0	0
$166$	−1368.00	−0.639623
$167$	−1260.00	−0.583843	−0.291921	−	0.956442i	$-0.594295\pi$
$167$	−1260.00	−0.583843	−0.291921	+	0.956442i	$0.594295\pi$
$168$	0	0
$169$	−1521.00	−0.692308
$170$	180.000	0.0812081
$171$	−828.000	−0.370285
$172$	992.000	0.439763
$173$	−258.000	−0.113384	−0.0566918	−	0.998392i	$-0.518055\pi$
$173$	−258.000	−0.113384	−0.0566918	+	0.998392i	$0.518055\pi$
$174$	−36.0000	−0.0156848
$175$	0	0
$176$	0	0
$177$	−1764.00	−0.749098
$178$	−1668.00	−0.702370
$179$	2784.00	1.16249	0.581246	−	0.813728i	$-0.302566\pi$
$179$	2784.00	1.16249	0.581246	+	0.813728i	$0.302566\pi$
$180$	180.000	0.0745356
$181$	70.0000	0.0287462	0.0143731	−	0.999897i	$-0.495425\pi$
$181$	70.0000	0.0287462	0.0143731	+	0.999897i	$0.495425\pi$
$182$	0	0
$183$	1950.00	0.787695
$184$	0	0
$185$	2050.00	0.814697
$186$	24.0000	0.00946110
$187$	0	0
$188$	−1680.00	−0.651737
$189$	0	0
$190$	920.000	0.351283
$191$	792.000	0.300037	0.150019	−	0.988683i	$-0.452067\pi$
$191$	792.000	0.300037	0.150019	+	0.988683i	$0.452067\pi$
$192$	−192.000	−0.0721688
$193$	−214.000	−0.0798138	−0.0399069	−	0.999203i	$-0.512706\pi$
$193$	−214.000	−0.0798138	−0.0399069	+	0.999203i	$0.512706\pi$
$194$	220.000	0.0814179
$195$	390.000	0.143223
$196$	0	0
$197$	2766.00	1.00035	0.500176	−	0.865924i	$-0.333269\pi$
$197$	2766.00	1.00035	0.500176	+	0.865924i	$0.333269\pi$
$198$	0	0
$199$	2020.00	0.719568	0.359784	−	0.933036i	$-0.382850\pi$
$199$	2020.00	0.719568	0.359784	+	0.933036i	$0.382850\pi$
$200$	−200.000	−0.0707107
$201$	−456.000	−0.160019
$202$	−2748.00	−0.957171
$203$	0	0
$204$	216.000	0.0741325
$205$	−870.000	−0.296407
$206$	2368.00	0.800905
$207$	0	0
$208$	−416.000	−0.138675
$209$	0	0
$210$	0	0
$211$	356.000	0.116152	0.0580759	−	0.998312i	$-0.481503\pi$
$211$	356.000	0.116152	0.0580759	+	0.998312i	$0.481503\pi$
$212$	408.000	0.132177
$213$	504.000	0.162129
$214$	552.000	0.176327
$215$	1240.00	0.393336
$216$	216.000	0.0680414
$217$	0	0
$218$	3188.00	0.990452
$219$	−1830.00	−0.564657
$220$	0	0
$221$	468.000	0.142448
$222$	2460.00	0.743713
$223$	2176.00	0.653434	0.326717	−	0.945122i	$-0.394058\pi$
$223$	2176.00	0.653434	0.326717	+	0.945122i	$0.394058\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−1476.00	−0.434434
$227$	1716.00	0.501740	0.250870	−	0.968021i	$-0.419283\pi$
$227$	1716.00	0.501740	0.250870	+	0.968021i	$0.419283\pi$
$228$	1104.00	0.320676
$229$	5734.00	1.65464	0.827322	−	0.561728i	$-0.189863\pi$
$229$	5734.00	1.65464	0.827322	+	0.561728i	$0.189863\pi$
$230$	0	0
$231$	0	0
$232$	48.0000	0.0135834
$233$	1770.00	0.497668	0.248834	−	0.968546i	$-0.419953\pi$
$233$	1770.00	0.497668	0.248834	+	0.968546i	$0.419953\pi$
$234$	468.000	0.130744
$235$	−2100.00	−0.582931
$236$	2352.00	0.648738
$237$	3144.00	0.861708
$238$	0	0
$239$	6072.00	1.64337	0.821684	−	0.569943i	$-0.193035\pi$
$239$	6072.00	1.64337	0.821684	+	0.569943i	$0.193035\pi$
$240$	−240.000	−0.0645497
$241$	4054.00	1.08357	0.541787	−	0.840516i	$-0.317748\pi$
$241$	4054.00	1.08357	0.541787	+	0.840516i	$0.317748\pi$
$242$	2662.00	0.707107
$243$	−243.000	−0.0641500
$244$	−2600.00	−0.682164
$245$	0	0
$246$	−1044.00	−0.270581
$247$	2392.00	0.616192
$248$	−32.0000	−0.00819356
$249$	−2052.00	−0.522250
$250$	−250.000	−0.0632456
$251$	−1788.00	−0.449632	−0.224816	−	0.974401i	$-0.572178\pi$
$251$	−1788.00	−0.449632	−0.224816	+	0.974401i	$0.572178\pi$
$252$	0	0
$253$	0	0
$254$	−1552.00	−0.383390
$255$	270.000	0.0663061
$256$	256.000	0.0625000
$257$	5550.00	1.34708	0.673540	−	0.739151i	$-0.264773\pi$
$257$	5550.00	1.34708	0.673540	+	0.739151i	$0.264773\pi$
$258$	1488.00	0.359065
$259$	0	0
$260$	−520.000	−0.124035
$261$	−54.0000	−0.0128066
$262$	1176.00	0.277304
$263$	4368.00	1.02412	0.512058	−	0.858951i	$-0.328883\pi$
$263$	4368.00	1.02412	0.512058	+	0.858951i	$0.328883\pi$
$264$	0	0
$265$	510.000	0.118223
$266$	0	0
$267$	−2502.00	−0.573483
$268$	608.000	0.138580
$269$	102.000	0.0231191	0.0115596	−	0.999933i	$-0.496320\pi$
$269$	102.000	0.0231191	0.0115596	+	0.999933i	$0.496320\pi$
$270$	270.000	0.0608581
$271$	−8180.00	−1.83358	−0.916789	−	0.399372i	$-0.869228\pi$
$271$	−8180.00	−1.83358	−0.916789	+	0.399372i	$0.869228\pi$
$272$	−288.000	−0.0642006
$273$	0	0
$274$	−2484.00	−0.547679
$275$	0	0
$276$	0	0
$277$	3410.00	0.739664	0.369832	−	0.929099i	$-0.379415\pi$
$277$	3410.00	0.739664	0.369832	+	0.929099i	$0.379415\pi$
$278$	−1448.00	−0.312393
$279$	36.0000	0.00772496
$280$	0	0
$281$	5058.00	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	5058.00	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	−2520.00	−0.532141
$283$	5572.00	1.17039	0.585196	−	0.810892i	$-0.301018\pi$
$283$	5572.00	1.17039	0.585196	+	0.810892i	$0.301018\pi$
$284$	−672.000	−0.140408
$285$	1380.00	0.286822
$286$	0	0
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−4589.00	−0.934053
$290$	60.0000	0.0121494
$291$	330.000	0.0664775
$292$	2440.00	0.489008
$293$	5790.00	1.15446	0.577228	−	0.816583i	$-0.304135\pi$
$293$	5790.00	1.15446	0.577228	+	0.816583i	$0.304135\pi$
$294$	0	0
$295$	2940.00	0.580249
$296$	−3280.00	−0.644075
$297$	0	0
$298$	3132.00	0.608832
$299$	0	0
$300$	−300.000	−0.0577350
$301$	0	0
$302$	−2416.00	−0.460348
$303$	−4122.00	−0.781527
$304$	−1472.00	−0.277714
$305$	−3250.00	−0.610146
$306$	324.000	0.0605289
$307$	−3452.00	−0.641746	−0.320873	−	0.947122i	$-0.603976\pi$
$307$	−3452.00	−0.641746	−0.320873	+	0.947122i	$0.603976\pi$
$308$	0	0
$309$	3552.00	0.653936
$310$	−40.0000	−0.00732854
$311$	3696.00	0.673894	0.336947	−	0.941524i	$-0.390606\pi$
$311$	3696.00	0.673894	0.336947	+	0.941524i	$0.390606\pi$
$312$	−624.000	−0.113228
$313$	7018.00	1.26735	0.633675	−	0.773599i	$-0.281545\pi$
$313$	7018.00	1.26735	0.633675	+	0.773599i	$0.281545\pi$
$314$	−4748.00	−0.853328
$315$	0	0
$316$	−4192.00	−0.746261
$317$	9486.00	1.68072	0.840358	−	0.542032i	$-0.182345\pi$
$317$	9486.00	1.68072	0.840358	+	0.542032i	$0.182345\pi$
$318$	612.000	0.107922
$319$	0	0
$320$	320.000	0.0559017
$321$	828.000	0.143970
$322$	0	0
$323$	1656.00	0.285270
$324$	324.000	0.0555556
$325$	−650.000	−0.110940
$326$	800.000	0.135914
$327$	4782.00	0.808701
$328$	1392.00	0.234330
$329$	0	0
$330$	0	0
$331$	5852.00	0.971767	0.485884	−	0.874023i	$-0.338498\pi$
$331$	5852.00	0.971767	0.485884	+	0.874023i	$0.338498\pi$
$332$	2736.00	0.452282
$333$	3690.00	0.607240
$334$	2520.00	0.412839
$335$	760.000	0.123950
$336$	0	0
$337$	−5686.00	−0.919098	−0.459549	−	0.888152i	$-0.651989\pi$
$337$	−5686.00	−0.919098	−0.459549	+	0.888152i	$0.651989\pi$
$338$	3042.00	0.489535
$339$	−2214.00	−0.354714
$340$	−360.000	−0.0574228
$341$	0	0
$342$	1656.00	0.261831
$343$	0	0
$344$	−1984.00	−0.310960
$345$	0	0
$346$	516.000	0.0801744
$347$	−7764.00	−1.20113	−0.600567	−	0.799575i	$-0.705058\pi$
$347$	−7764.00	−1.20113	−0.600567	+	0.799575i	$0.705058\pi$
$348$	72.0000	0.0110908
$349$	3070.00	0.470869	0.235435	−	0.971890i	$-0.424349\pi$
$349$	3070.00	0.470869	0.235435	+	0.971890i	$0.424349\pi$
$350$	0	0
$351$	702.000	0.106752
$352$	0	0
$353$	4518.00	0.681215	0.340607	−	0.940206i	$-0.389367\pi$
$353$	4518.00	0.681215	0.340607	+	0.940206i	$0.389367\pi$
$354$	3528.00	0.529692
$355$	−840.000	−0.125585
$356$	3336.00	0.496651
$357$	0	0
$358$	−5568.00	−0.822005
$359$	12552.0	1.84532	0.922659	−	0.385617i	$-0.126011\pi$
$359$	12552.0	1.84532	0.922659	+	0.385617i	$0.126011\pi$
$360$	−360.000	−0.0527046
$361$	1605.00	0.233999
$362$	−140.000	−0.0203266
$363$	3993.00	0.577350
$364$	0	0
$365$	3050.00	0.437382
$366$	−3900.00	−0.556984
$367$	−5096.00	−0.724820	−0.362410	−	0.932019i	$-0.618046\pi$
$367$	−5096.00	−0.724820	−0.362410	+	0.932019i	$0.618046\pi$
$368$	0	0
$369$	−1566.00	−0.220929
$370$	−4100.00	−0.576078
$371$	0	0
$372$	−48.0000	−0.00669001
$373$	−8782.00	−1.21907	−0.609537	−	0.792757i	$-0.708645\pi$
$373$	−8782.00	−1.21907	−0.609537	+	0.792757i	$0.708645\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	3360.00	0.460848
$377$	156.000	0.0213114
$378$	0	0
$379$	−3196.00	−0.433160	−0.216580	−	0.976265i	$-0.569490\pi$
$379$	−3196.00	−0.433160	−0.216580	+	0.976265i	$0.569490\pi$
$380$	−1840.00	−0.248395
$381$	−2328.00	−0.313037
$382$	−1584.00	−0.212158
$383$	8148.00	1.08706	0.543529	−	0.839390i	$-0.317088\pi$
$383$	8148.00	1.08706	0.543529	+	0.839390i	$0.317088\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	428.000	0.0564369
$387$	2232.00	0.293176
$388$	−440.000	−0.0575712
$389$	354.000	0.0461401	0.0230701	−	0.999734i	$-0.492656\pi$
$389$	354.000	0.0461401	0.0230701	+	0.999734i	$0.492656\pi$
$390$	−780.000	−0.101274
$391$	0	0
$392$	0	0
$393$	1764.00	0.226417
$394$	−5532.00	−0.707356
$395$	−5240.00	−0.667476
$396$	0	0
$397$	−9914.00	−1.25332	−0.626662	−	0.779291i	$-0.715579\pi$
$397$	−9914.00	−1.25332	−0.626662	+	0.779291i	$0.715579\pi$
$398$	−4040.00	−0.508811
$399$	0	0
$400$	400.000	0.0500000
$401$	5490.00	0.683685	0.341842	−	0.939757i	$-0.388949\pi$
$401$	5490.00	0.683685	0.341842	+	0.939757i	$0.388949\pi$
$402$	912.000	0.113150
$403$	−104.000	−0.0128551
$404$	5496.00	0.676822
$405$	405.000	0.0496904
$406$	0	0
$407$	0	0
$408$	−432.000	−0.0524196
$409$	6166.00	0.745450	0.372725	−	0.927942i	$-0.378423\pi$
$409$	6166.00	0.745450	0.372725	+	0.927942i	$0.378423\pi$
$410$	1740.00	0.209591
$411$	−3726.00	−0.447178
$412$	−4736.00	−0.566325
$413$	0	0
$414$	0	0
$415$	3420.00	0.404533
$416$	832.000	0.0980581
$417$	−2172.00	−0.255068
$418$	0	0
$419$	−6132.00	−0.714959	−0.357479	−	0.933921i	$-0.616364\pi$
$419$	−6132.00	−0.714959	−0.357479	+	0.933921i	$0.616364\pi$
$420$	0	0
$421$	−3202.00	−0.370679	−0.185340	−	0.982675i	$-0.559339\pi$
$421$	−3202.00	−0.370679	−0.185340	+	0.982675i	$0.559339\pi$
$422$	−712.000	−0.0821318
$423$	−3780.00	−0.434491
$424$	−816.000	−0.0934634
$425$	−450.000	−0.0513605
$426$	−1008.00	−0.114643
$427$	0	0
$428$	−1104.00	−0.124682
$429$	0	0
$430$	−2480.00	−0.278131
$431$	−5712.00	−0.638370	−0.319185	−	0.947692i	$-0.603409\pi$
$431$	−5712.00	−0.638370	−0.319185	+	0.947692i	$0.603409\pi$
$432$	−432.000	−0.0481125
$433$	9490.00	1.05326	0.526629	−	0.850096i	$-0.323456\pi$
$433$	9490.00	1.05326	0.526629	+	0.850096i	$0.323456\pi$
$434$	0	0
$435$	90.0000	0.00991993
$436$	−6376.00	−0.700356
$437$	0	0
$438$	3660.00	0.399273
$439$	−11828.0	−1.28592	−0.642961	−	0.765899i	$-0.722294\pi$
$439$	−11828.0	−1.28592	−0.642961	+	0.765899i	$0.722294\pi$
$440$	0	0
$441$	0	0
$442$	−936.000	−0.100726
$443$	7164.00	0.768334	0.384167	−	0.923264i	$-0.374489\pi$
$443$	7164.00	0.768334	0.384167	+	0.923264i	$0.374489\pi$
$444$	−4920.00	−0.525885
$445$	4170.00	0.444218
$446$	−4352.00	−0.462047
$447$	4698.00	0.497109
$448$	0	0
$449$	7722.00	0.811634	0.405817	−	0.913954i	$-0.366987\pi$
$449$	7722.00	0.811634	0.405817	+	0.913954i	$0.366987\pi$
$450$	−450.000	−0.0471405
$451$	0	0
$452$	2952.00	0.307191
$453$	−3624.00	−0.375873
$454$	−3432.00	−0.354784
$455$	0	0
$456$	−2208.00	−0.226752
$457$	13394.0	1.37100	0.685498	−	0.728075i	$-0.259585\pi$
$457$	13394.0	1.37100	0.685498	+	0.728075i	$0.259585\pi$
$458$	−11468.0	−1.17001
$459$	486.000	0.0494217
$460$	0	0
$461$	−8682.00	−0.877139	−0.438569	−	0.898697i	$-0.644515\pi$
$461$	−8682.00	−0.877139	−0.438569	+	0.898697i	$0.644515\pi$
$462$	0	0
$463$	−6640.00	−0.666495	−0.333247	−	0.942839i	$-0.608144\pi$
$463$	−6640.00	−0.666495	−0.333247	+	0.942839i	$0.608144\pi$
$464$	−96.0000	−0.00960493
$465$	−60.0000	−0.00598373
$466$	−3540.00	−0.351904
$467$	3372.00	0.334128	0.167064	−	0.985946i	$-0.446571\pi$
$467$	3372.00	0.334128	0.167064	+	0.985946i	$0.446571\pi$
$468$	−936.000	−0.0924500
$469$	0	0
$470$	4200.00	0.412195
$471$	−7122.00	−0.696740
$472$	−4704.00	−0.458727
$473$	0	0
$474$	−6288.00	−0.609319
$475$	−2300.00	−0.222171
$476$	0	0
$477$	918.000	0.0881181
$478$	−12144.0	−1.16204
$479$	−14040.0	−1.33926	−0.669628	−	0.742696i	$-0.733547\pi$
$479$	−14040.0	−1.33926	−0.669628	+	0.742696i	$0.733547\pi$
$480$	480.000	0.0456435
$481$	−10660.0	−1.01051
$482$	−8108.00	−0.766202
$483$	0	0
$484$	−5324.00	−0.500000
$485$	−550.000	−0.0514932
$486$	486.000	0.0453609
$487$	18704.0	1.74037	0.870184	−	0.492727i	$-0.164000\pi$
$487$	18704.0	1.74037	0.870184	+	0.492727i	$0.164000\pi$
$488$	5200.00	0.482363
$489$	1200.00	0.110973
$490$	0	0
$491$	−16440.0	−1.51105	−0.755526	−	0.655118i	$-0.772619\pi$
$491$	−16440.0	−1.51105	−0.755526	+	0.655118i	$0.772619\pi$
$492$	2088.00	0.191330
$493$	108.000	0.00986628
$494$	−4784.00	−0.435713
$495$	0	0
$496$	64.0000	0.00579372
$497$	0	0
$498$	4104.00	0.369286
$499$	−5860.00	−0.525711	−0.262855	−	0.964835i	$-0.584664\pi$
$499$	−5860.00	−0.525711	−0.262855	+	0.964835i	$0.584664\pi$
$500$	500.000	0.0447214
$501$	3780.00	0.337082
$502$	3576.00	0.317938
$503$	13380.0	1.18605	0.593027	−	0.805183i	$-0.297933\pi$
$503$	13380.0	1.18605	0.593027	+	0.805183i	$0.297933\pi$
$504$	0	0
$505$	6870.00	0.605368
$506$	0	0
$507$	4563.00	0.399704
$508$	3104.00	0.271098
$509$	7590.00	0.660945	0.330472	−	0.943816i	$-0.392792\pi$
$509$	7590.00	0.660945	0.330472	+	0.943816i	$0.392792\pi$
$510$	−540.000	−0.0468855
$511$	0	0
$512$	−512.000	−0.0441942
$513$	2484.00	0.213784
$514$	−11100.0	−0.952529
$515$	−5920.00	−0.506537
$516$	−2976.00	−0.253897
$517$	0	0
$518$	0	0
$519$	774.000	0.0654621
$520$	1040.00	0.0877058
$521$	22626.0	1.90262	0.951308	−	0.308242i	$-0.0997405\pi$
$521$	22626.0	1.90262	0.951308	+	0.308242i	$0.0997405\pi$
$522$	108.000	0.00905562
$523$	−12476.0	−1.04309	−0.521546	−	0.853223i	$-0.674645\pi$
$523$	−12476.0	−1.04309	−0.521546	+	0.853223i	$0.674645\pi$
$524$	−2352.00	−0.196083
$525$	0	0
$526$	−8736.00	−0.724159
$527$	−72.0000	−0.00595136
$528$	0	0
$529$	−12167.0	−1.00000
$530$	−1020.00	−0.0835962
$531$	5292.00	0.432492
$532$	0	0
$533$	4524.00	0.367648
$534$	5004.00	0.405514
$535$	−1380.00	−0.111519
$536$	−1216.00	−0.0979910
$537$	−8352.00	−0.671165
$538$	−204.000	−0.0163477
$539$	0	0
$540$	−540.000	−0.0430331
$541$	10046.0	0.798357	0.399179	−	0.916873i	$-0.369295\pi$
$541$	10046.0	0.798357	0.399179	+	0.916873i	$0.369295\pi$
$542$	16360.0	1.29654
$543$	−210.000	−0.0165966
$544$	576.000	0.0453967
$545$	−7970.00	−0.626417
$546$	0	0
$547$	−14392.0	−1.12497	−0.562484	−	0.826808i	$-0.690154\pi$
$547$	−14392.0	−1.12497	−0.562484	+	0.826808i	$0.690154\pi$
$548$	4968.00	0.387267
$549$	−5850.00	−0.454776
$550$	0	0
$551$	552.000	0.0426787
$552$	0	0
$553$	0	0
$554$	−6820.00	−0.523022
$555$	−6150.00	−0.470366
$556$	2896.00	0.220895
$557$	−21474.0	−1.63354	−0.816771	−	0.576962i	$-0.804238\pi$
$557$	−21474.0	−1.63354	−0.816771	+	0.576962i	$0.804238\pi$
$558$	−72.0000	−0.00546237
$559$	−6448.00	−0.487874
$560$	0	0
$561$	0	0
$562$	−10116.0	−0.759284
$563$	16332.0	1.22258	0.611289	−	0.791407i	$-0.290651\pi$
$563$	16332.0	1.22258	0.611289	+	0.791407i	$0.290651\pi$
$564$	5040.00	0.376281
$565$	3690.00	0.274760
$566$	−11144.0	−0.827592
$567$	0	0
$568$	1344.00	0.0992834
$569$	19146.0	1.41062	0.705309	−	0.708900i	$-0.250808\pi$
$569$	19146.0	1.41062	0.705309	+	0.708900i	$0.250808\pi$
$570$	−2760.00	−0.202813
$571$	−18484.0	−1.35470	−0.677348	−	0.735663i	$-0.736871\pi$
$571$	−18484.0	−1.35470	−0.677348	+	0.735663i	$0.736871\pi$
$572$	0	0
$573$	−2376.00	−0.173227
$574$	0	0
$575$	0	0
$576$	576.000	0.0416667
$577$	−24590.0	−1.77417	−0.887084	−	0.461608i	$-0.847273\pi$
$577$	−24590.0	−1.77417	−0.887084	+	0.461608i	$0.847273\pi$
$578$	9178.00	0.660475
$579$	642.000	0.0460805
$580$	−120.000	−0.00859091
$581$	0	0
$582$	−660.000	−0.0470067
$583$	0	0
$584$	−4880.00	−0.345781
$585$	−1170.00	−0.0826898
$586$	−11580.0	−0.816323
$587$	19476.0	1.36944	0.684719	−	0.728807i	$-0.259925\pi$
$587$	19476.0	1.36944	0.684719	+	0.728807i	$0.259925\pi$
$588$	0	0
$589$	−368.000	−0.0257439
$590$	−5880.00	−0.410298
$591$	−8298.00	−0.577553
$592$	6560.00	0.455430
$593$	19758.0	1.36824	0.684118	−	0.729371i	$-0.260187\pi$
$593$	19758.0	1.36824	0.684118	+	0.729371i	$0.260187\pi$
$594$	0	0
$595$	0	0
$596$	−6264.00	−0.430509
$597$	−6060.00	−0.415443
$598$	0	0
$599$	−26976.0	−1.84008	−0.920041	−	0.391821i	$-0.871845\pi$
$599$	−26976.0	−1.84008	−0.920041	+	0.391821i	$0.871845\pi$
$600$	600.000	0.0408248
$601$	22798.0	1.54734	0.773669	−	0.633590i	$-0.218419\pi$
$601$	22798.0	1.54734	0.773669	+	0.633590i	$0.218419\pi$
$602$	0	0
$603$	1368.00	0.0923868
$604$	4832.00	0.325515
$605$	−6655.00	−0.447214
$606$	8244.00	0.552623
$607$	−11936.0	−0.798134	−0.399067	−	0.916922i	$-0.630666\pi$
$607$	−11936.0	−0.798134	−0.399067	+	0.916922i	$0.630666\pi$
$608$	2944.00	0.196373
$609$	0	0
$610$	6500.00	0.431438
$611$	10920.0	0.723038
$612$	−648.000	−0.0428004
$613$	19034.0	1.25412	0.627060	−	0.778971i	$-0.284258\pi$
$613$	19034.0	1.25412	0.627060	+	0.778971i	$0.284258\pi$
$614$	6904.00	0.453783
$615$	2610.00	0.171131
$616$	0	0
$617$	954.000	0.0622473	0.0311237	−	0.999516i	$-0.490091\pi$
$617$	954.000	0.0622473	0.0311237	+	0.999516i	$0.490091\pi$
$618$	−7104.00	−0.462403
$619$	−11108.0	−0.721273	−0.360637	−	0.932706i	$-0.617441\pi$
$619$	−11108.0	−0.721273	−0.360637	+	0.932706i	$0.617441\pi$
$620$	80.0000	0.00518206
$621$	0	0
$622$	−7392.00	−0.476515
$623$	0	0
$624$	1248.00	0.0800641
$625$	625.000	0.0400000
$626$	−14036.0	−0.896152
$627$	0	0
$628$	9496.00	0.603394
$629$	−7380.00	−0.467822
$630$	0	0
$631$	−8536.00	−0.538531	−0.269265	−	0.963066i	$-0.586781\pi$
$631$	−8536.00	−0.538531	−0.269265	+	0.963066i	$0.586781\pi$
$632$	8384.00	0.527686
$633$	−1068.00	−0.0670603
$634$	−18972.0	−1.18845
$635$	3880.00	0.242477
$636$	−1224.00	−0.0763125
$637$	0	0
$638$	0	0
$639$	−1512.00	−0.0936053
$640$	−640.000	−0.0395285
$641$	−10158.0	−0.625923	−0.312962	−	0.949766i	$-0.601321\pi$
$641$	−10158.0	−0.625923	−0.312962	+	0.949766i	$0.601321\pi$
$642$	−1656.00	−0.101802
$643$	22732.0	1.39419	0.697094	−	0.716980i	$-0.254476\pi$
$643$	22732.0	1.39419	0.697094	+	0.716980i	$0.254476\pi$
$644$	0	0
$645$	−3720.00	−0.227093
$646$	−3312.00	−0.201717
$647$	19500.0	1.18489	0.592445	−	0.805611i	$-0.298163\pi$
$647$	19500.0	1.18489	0.592445	+	0.805611i	$0.298163\pi$
$648$	−648.000	−0.0392837
$649$	0	0
$650$	1300.00	0.0784465
$651$	0	0
$652$	−1600.00	−0.0961056
$653$	−16218.0	−0.971913	−0.485957	−	0.873983i	$-0.661529\pi$
$653$	−16218.0	−0.971913	−0.485957	+	0.873983i	$0.661529\pi$
$654$	−9564.00	−0.571838
$655$	−2940.00	−0.175382
$656$	−2784.00	−0.165697
$657$	5490.00	0.326005
$658$	0	0
$659$	−1968.00	−0.116331	−0.0581657	−	0.998307i	$-0.518525\pi$
$659$	−1968.00	−0.116331	−0.0581657	+	0.998307i	$0.518525\pi$
$660$	0	0
$661$	15694.0	0.923488	0.461744	−	0.887013i	$-0.347224\pi$
$661$	15694.0	0.923488	0.461744	+	0.887013i	$0.347224\pi$
$662$	−11704.0	−0.687143
$663$	−1404.00	−0.0822426
$664$	−5472.00	−0.319811
$665$	0	0
$666$	−7380.00	−0.429383
$667$	0	0
$668$	−5040.00	−0.291921
$669$	−6528.00	−0.377260
$670$	−1520.00	−0.0876459
$671$	0	0
$672$	0	0
$673$	20018.0	1.14656	0.573282	−	0.819358i	$-0.305670\pi$
$673$	20018.0	1.14656	0.573282	+	0.819358i	$0.305670\pi$
$674$	11372.0	0.649901
$675$	−675.000	−0.0384900
$676$	−6084.00	−0.346154
$677$	−3834.00	−0.217655	−0.108828	−	0.994061i	$-0.534710\pi$
$677$	−3834.00	−0.217655	−0.108828	+	0.994061i	$0.534710\pi$
$678$	4428.00	0.250821
$679$	0	0
$680$	720.000	0.0406040
$681$	−5148.00	−0.289680
$682$	0	0
$683$	−26172.0	−1.46624	−0.733121	−	0.680098i	$-0.761937\pi$
$683$	−26172.0	−1.46624	−0.733121	+	0.680098i	$0.761937\pi$
$684$	−3312.00	−0.185143
$685$	6210.00	0.346382
$686$	0	0
$687$	−17202.0	−0.955309
$688$	3968.00	0.219882
$689$	−2652.00	−0.146637
$690$	0	0
$691$	−10244.0	−0.563965	−0.281983	−	0.959419i	$-0.590992\pi$
$691$	−10244.0	−0.563965	−0.281983	+	0.959419i	$0.590992\pi$
$692$	−1032.00	−0.0566918
$693$	0	0
$694$	15528.0	0.849330
$695$	3620.00	0.197575
$696$	−144.000	−0.00784239
$697$	3132.00	0.170205
$698$	−6140.00	−0.332955
$699$	−5310.00	−0.287329
$700$	0	0
$701$	7386.00	0.397953	0.198977	−	0.980004i	$-0.436238\pi$
$701$	7386.00	0.397953	0.198977	+	0.980004i	$0.436238\pi$
$702$	−1404.00	−0.0754851
$703$	−37720.0	−2.02367
$704$	0	0
$705$	6300.00	0.336556
$706$	−9036.00	−0.481692
$707$	0	0
$708$	−7056.00	−0.374549
$709$	−28330.0	−1.50064	−0.750321	−	0.661073i	$-0.770101\pi$
$709$	−28330.0	−1.50064	−0.750321	+	0.661073i	$0.770101\pi$
$710$	1680.00	0.0888018
$711$	−9432.00	−0.497507
$712$	−6672.00	−0.351185
$713$	0	0
$714$	0	0
$715$	0	0
$716$	11136.0	0.581246
$717$	−18216.0	−0.948799
$718$	−25104.0	−1.30484
$719$	−3024.00	−0.156851	−0.0784257	−	0.996920i	$-0.524989\pi$
$719$	−3024.00	−0.156851	−0.0784257	+	0.996920i	$0.524989\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	−3210.00	−0.165462
$723$	−12162.0	−0.625601
$724$	280.000	0.0143731
$725$	−150.000	−0.00768395
$726$	−7986.00	−0.408248
$727$	12376.0	0.631362	0.315681	−	0.948865i	$-0.397767\pi$
$727$	12376.0	0.631362	0.315681	+	0.948865i	$0.397767\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−6100.00	−0.309276
$731$	−4464.00	−0.225865
$732$	7800.00	0.393847
$733$	−506.000	−0.0254973	−0.0127487	−	0.999919i	$-0.504058\pi$
$733$	−506.000	−0.0254973	−0.0127487	+	0.999919i	$0.504058\pi$
$734$	10192.0	0.512525
$735$	0	0
$736$	0	0
$737$	0	0
$738$	3132.00	0.156220
$739$	6428.00	0.319970	0.159985	−	0.987119i	$-0.448855\pi$
$739$	6428.00	0.319970	0.159985	+	0.987119i	$0.448855\pi$
$740$	8200.00	0.407349
$741$	−7176.00	−0.355758
$742$	0	0
$743$	32568.0	1.60808	0.804040	−	0.594575i	$-0.202680\pi$
$743$	32568.0	1.60808	0.804040	+	0.594575i	$0.202680\pi$
$744$	96.0000	0.00473055
$745$	−7830.00	−0.385059
$746$	17564.0	0.862016
$747$	6156.00	0.301521
$748$	0	0
$749$	0	0
$750$	750.000	0.0365148
$751$	28928.0	1.40559	0.702795	−	0.711393i	$-0.251935\pi$
$751$	28928.0	1.40559	0.702795	+	0.711393i	$0.251935\pi$
$752$	−6720.00	−0.325869
$753$	5364.00	0.259595
$754$	−312.000	−0.0150695
$755$	6040.00	0.291150
$756$	0	0
$757$	5042.00	0.242080	0.121040	−	0.992648i	$-0.461377\pi$
$757$	5042.00	0.242080	0.121040	+	0.992648i	$0.461377\pi$
$758$	6392.00	0.306290
$759$	0	0
$760$	3680.00	0.175642
$761$	−29574.0	−1.40875	−0.704374	−	0.709829i	$-0.748772\pi$
$761$	−29574.0	−1.40875	−0.704374	+	0.709829i	$0.748772\pi$
$762$	4656.00	0.221351
$763$	0	0
$764$	3168.00	0.150019
$765$	−810.000	−0.0382818
$766$	−16296.0	−0.768666
$767$	−15288.0	−0.719710
$768$	−768.000	−0.0360844
$769$	8206.00	0.384806	0.192403	−	0.981316i	$-0.438372\pi$
$769$	8206.00	0.384806	0.192403	+	0.981316i	$0.438372\pi$
$770$	0	0
$771$	−16650.0	−0.777737
$772$	−856.000	−0.0399069
$773$	−30786.0	−1.43247	−0.716233	−	0.697862i	$-0.754135\pi$
$773$	−30786.0	−1.43247	−0.716233	+	0.697862i	$0.754135\pi$
$774$	−4464.00	−0.207306
$775$	100.000	0.00463498
$776$	880.000	0.0407090
$777$	0	0
$778$	−708.000	−0.0326260
$779$	16008.0	0.736259
$780$	1560.00	0.0716115
$781$	0	0
$782$	0	0
$783$	162.000	0.00739388
$784$	0	0
$785$	11870.0	0.539692
$786$	−3528.00	−0.160101
$787$	−19532.0	−0.884677	−0.442338	−	0.896848i	$-0.645851\pi$
$787$	−19532.0	−0.884677	−0.442338	+	0.896848i	$0.645851\pi$
$788$	11064.0	0.500176
$789$	−13104.0	−0.591273
$790$	10480.0	0.471977
$791$	0	0
$792$	0	0
$793$	16900.0	0.756793
$794$	19828.0	0.886233
$795$	−1530.00	−0.0682560
$796$	8080.00	0.359784
$797$	−12546.0	−0.557594	−0.278797	−	0.960350i	$-0.589936\pi$
$797$	−12546.0	−0.557594	−0.278797	+	0.960350i	$0.589936\pi$
$798$	0	0
$799$	7560.00	0.334735
$800$	−800.000	−0.0353553
$801$	7506.00	0.331100
$802$	−10980.0	−0.483438
$803$	0	0
$804$	−1824.00	−0.0800094
$805$	0	0
$806$	208.000	0.00908993
$807$	−306.000	−0.0133478
$808$	−10992.0	−0.478586
$809$	9570.00	0.415900	0.207950	−	0.978139i	$-0.433321\pi$
$809$	9570.00	0.415900	0.207950	+	0.978139i	$0.433321\pi$
$810$	−810.000	−0.0351364
$811$	−1964.00	−0.0850374	−0.0425187	−	0.999096i	$-0.513538\pi$
$811$	−1964.00	−0.0850374	−0.0425187	+	0.999096i	$0.513538\pi$
$812$	0	0
$813$	24540.0	1.05862
$814$	0	0
$815$	−2000.00	−0.0859594
$816$	864.000	0.0370662
$817$	−22816.0	−0.977027
$818$	−12332.0	−0.527113
$819$	0	0
$820$	−3480.00	−0.148204
$821$	37122.0	1.57803	0.789017	−	0.614371i	$-0.210590\pi$
$821$	37122.0	1.57803	0.789017	+	0.614371i	$0.210590\pi$
$822$	7452.00	0.316202
$823$	36536.0	1.54747	0.773733	−	0.633512i	$-0.218387\pi$
$823$	36536.0	1.54747	0.773733	+	0.633512i	$0.218387\pi$
$824$	9472.00	0.400452
$825$	0	0
$826$	0	0
$827$	−32412.0	−1.36285	−0.681424	−	0.731889i	$-0.738639\pi$
$827$	−32412.0	−1.36285	−0.681424	+	0.731889i	$0.738639\pi$
$828$	0	0
$829$	23686.0	0.992339	0.496169	−	0.868226i	$-0.334740\pi$
$829$	23686.0	0.992339	0.496169	+	0.868226i	$0.334740\pi$
$830$	−6840.00	−0.286048
$831$	−10230.0	−0.427045
$832$	−1664.00	−0.0693375
$833$	0	0
$834$	4344.00	0.180360
$835$	−6300.00	−0.261102
$836$	0	0
$837$	−108.000	−0.00446001
$838$	12264.0	0.505552
$839$	−25680.0	−1.05670	−0.528350	−	0.849026i	$-0.677189\pi$
$839$	−25680.0	−1.05670	−0.528350	+	0.849026i	$0.677189\pi$
$840$	0	0
$841$	−24353.0	−0.998524
$842$	6404.00	0.262110
$843$	−15174.0	−0.619953
$844$	1424.00	0.0580759
$845$	−7605.00	−0.309609
$846$	7560.00	0.307232
$847$	0	0
$848$	1632.00	0.0660886
$849$	−16716.0	−0.675726
$850$	900.000	0.0363173
$851$	0	0
$852$	2016.00	0.0810646
$853$	29662.0	1.19063	0.595315	−	0.803492i	$-0.297027\pi$
$853$	29662.0	1.19063	0.595315	+	0.803492i	$0.297027\pi$
$854$	0	0
$855$	−4140.00	−0.165597
$856$	2208.00	0.0881634
$857$	−17418.0	−0.694268	−0.347134	−	0.937816i	$-0.612845\pi$
$857$	−17418.0	−0.694268	−0.347134	+	0.937816i	$0.612845\pi$
$858$	0	0
$859$	22420.0	0.890524	0.445262	−	0.895400i	$-0.353110\pi$
$859$	22420.0	0.890524	0.445262	+	0.895400i	$0.353110\pi$
$860$	4960.00	0.196668
$861$	0	0
$862$	11424.0	0.451396
$863$	37008.0	1.45975	0.729877	−	0.683579i	$-0.239578\pi$
$863$	37008.0	1.45975	0.729877	+	0.683579i	$0.239578\pi$
$864$	864.000	0.0340207
$865$	−1290.00	−0.0507067
$866$	−18980.0	−0.744765
$867$	13767.0	0.539275
$868$	0	0
$869$	0	0
$870$	−180.000	−0.00701445
$871$	−3952.00	−0.153741
$872$	12752.0	0.495226
$873$	−990.000	−0.0383808
$874$	0	0
$875$	0	0
$876$	−7320.00	−0.282329
$877$	−37222.0	−1.43318	−0.716589	−	0.697495i	$-0.754298\pi$
$877$	−37222.0	−1.43318	−0.716589	+	0.697495i	$0.754298\pi$
$878$	23656.0	0.909284
$879$	−17370.0	−0.666525
$880$	0	0
$881$	−48270.0	−1.84592	−0.922961	−	0.384893i	$-0.874238\pi$
$881$	−48270.0	−1.84592	−0.922961	+	0.384893i	$0.874238\pi$
$882$	0	0
$883$	35192.0	1.34123	0.670614	−	0.741806i	$-0.266031\pi$
$883$	35192.0	1.34123	0.670614	+	0.741806i	$0.266031\pi$
$884$	1872.00	0.0712242
$885$	−8820.00	−0.335007
$886$	−14328.0	−0.543294
$887$	−50148.0	−1.89831	−0.949157	−	0.314802i	$-0.898062\pi$
$887$	−50148.0	−1.89831	−0.949157	+	0.314802i	$0.898062\pi$
$888$	9840.00	0.371857
$889$	0	0
$890$	−8340.00	−0.314109
$891$	0	0
$892$	8704.00	0.326717
$893$	38640.0	1.44797
$894$	−9396.00	−0.351509
$895$	13920.0	0.519882
$896$	0	0
$897$	0	0
$898$	−15444.0	−0.573912
$899$	−24.0000	−0.000890372 0
$900$	900.000	0.0333333
$901$	−1836.00	−0.0678868
$902$	0	0
$903$	0	0
$904$	−5904.00	−0.217217
$905$	350.000	0.0128557
$906$	7248.00	0.265782
$907$	−18976.0	−0.694694	−0.347347	−	0.937737i	$-0.612917\pi$
$907$	−18976.0	−0.694694	−0.347347	+	0.937737i	$0.612917\pi$
$908$	6864.00	0.250870
$909$	12366.0	0.451215
$910$	0	0
$911$	−52968.0	−1.92635	−0.963177	−	0.268869i	$-0.913350\pi$
$911$	−52968.0	−1.92635	−0.963177	+	0.268869i	$0.913350\pi$
$912$	4416.00	0.160338
$913$	0	0
$914$	−26788.0	−0.969440
$915$	9750.00	0.352268
$916$	22936.0	0.827322
$917$	0	0
$918$	−972.000	−0.0349464
$919$	−4792.00	−0.172006	−0.0860030	−	0.996295i	$-0.527409\pi$
$919$	−4792.00	−0.172006	−0.0860030	+	0.996295i	$0.527409\pi$
$920$	0	0
$921$	10356.0	0.370512
$922$	17364.0	0.620231
$923$	4368.00	0.155769
$924$	0	0
$925$	10250.0	0.364344
$926$	13280.0	0.471283
$927$	−10656.0	−0.377550
$928$	192.000	0.00679171
$929$	32370.0	1.14319	0.571596	−	0.820535i	$-0.306324\pi$
$929$	32370.0	1.14319	0.571596	+	0.820535i	$0.306324\pi$
$930$	120.000	0.00423113
$931$	0	0
$932$	7080.00	0.248834
$933$	−11088.0	−0.389073
$934$	−6744.00	−0.236264
$935$	0	0
$936$	1872.00	0.0653720
$937$	−4286.00	−0.149432	−0.0747159	−	0.997205i	$-0.523805\pi$
$937$	−4286.00	−0.149432	−0.0747159	+	0.997205i	$0.523805\pi$
$938$	0	0
$939$	−21054.0	−0.731705
$940$	−8400.00	−0.291466
$941$	18678.0	0.647062	0.323531	−	0.946218i	$-0.395130\pi$
$941$	18678.0	0.647062	0.323531	+	0.946218i	$0.395130\pi$
$942$	14244.0	0.492669
$943$	0	0
$944$	9408.00	0.324369
$945$	0	0
$946$	0	0
$947$	−21012.0	−0.721012	−0.360506	−	0.932757i	$-0.617396\pi$
$947$	−21012.0	−0.721012	−0.360506	+	0.932757i	$0.617396\pi$
$948$	12576.0	0.430854
$949$	−15860.0	−0.542505
$950$	4600.00	0.157099
$951$	−28458.0	−0.970362
$952$	0	0
$953$	21930.0	0.745417	0.372708	−	0.927948i	$-0.378429\pi$
$953$	21930.0	0.745417	0.372708	+	0.927948i	$0.378429\pi$
$954$	−1836.00	−0.0623089
$955$	3960.00	0.134181
$956$	24288.0	0.821684
$957$	0	0
$958$	28080.0	0.946998
$959$	0	0
$960$	−960.000	−0.0322749
$961$	−29775.0	−0.999463
$962$	21320.0	0.714537
$963$	−2484.00	−0.0831213
$964$	16216.0	0.541787
$965$	−1070.00	−0.0356938
$966$	0	0
$967$	−49144.0	−1.63430	−0.817148	−	0.576428i	$-0.804446\pi$
$967$	−49144.0	−1.63430	−0.817148	+	0.576428i	$0.804446\pi$
$968$	10648.0	0.353553
$969$	−4968.00	−0.164701
$970$	1100.00	0.0364112
$971$	52884.0	1.74781	0.873907	−	0.486092i	$-0.161578\pi$
$971$	52884.0	1.74781	0.873907	+	0.486092i	$0.161578\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	−37408.0	−1.23063
$975$	1950.00	0.0640513
$976$	−10400.0	−0.341082
$977$	22722.0	0.744054	0.372027	−	0.928222i	$-0.378663\pi$
$977$	22722.0	0.744054	0.372027	+	0.928222i	$0.378663\pi$
$978$	−2400.00	−0.0784699
$979$	0	0
$980$	0	0
$981$	−14346.0	−0.466904
$982$	32880.0	1.06848
$983$	−11772.0	−0.381962	−0.190981	−	0.981594i	$-0.561167\pi$
$983$	−11772.0	−0.381962	−0.190981	+	0.981594i	$0.561167\pi$
$984$	−4176.00	−0.135291
$985$	13830.0	0.447371
$986$	−216.000	−0.00697651
$987$	0	0
$988$	9568.00	0.308096
$989$	0	0
$990$	0	0
$991$	17408.0	0.558005	0.279003	−	0.960290i	$-0.409996\pi$
$991$	17408.0	0.558005	0.279003	+	0.960290i	$0.409996\pi$
$992$	−128.000	−0.00409678
$993$	−17556.0	−0.561050
$994$	0	0
$995$	10100.0	0.321801
$996$	−8208.00	−0.261125
$997$	24478.0	0.777559	0.388779	−	0.921331i	$-0.372897\pi$
$997$	24478.0	0.777559	0.388779	+	0.921331i	$0.372897\pi$
$998$	11720.0	0.371734
$999$	−11070.0	−0.350590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.g.1.1		1
7.6	odd	2		210.4.a.e.1.1	✓	1
21.20	even	2		630.4.a.w.1.1		1
28.27	even	2		1680.4.a.a.1.1		1
35.13	even	4		1050.4.g.d.799.2		2
35.27	even	4		1050.4.g.d.799.1		2
35.34	odd	2		1050.4.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.e.1.1	✓	1	7.6	odd	2
630.4.a.w.1.1		1	21.20	even	2
1050.4.a.n.1.1		1	35.34	odd	2
1050.4.g.d.799.1		2	35.27	even	4
1050.4.g.d.799.2		2	35.13	even	4
1470.4.a.g.1.1		1	1.1	even	1	trivial
1680.4.a.a.1.1		1	28.27	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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