LMFDB - Embedded newform 1470.4.a.z.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:	$1$
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +16.0000 q^{11} +12.0000 q^{12} -58.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} -34.0000 q^{17} +18.0000 q^{18} -64.0000 q^{19} -20.0000 q^{20} +32.0000 q^{22} -16.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -116.000 q^{26} +27.0000 q^{27} +62.0000 q^{29} -30.0000 q^{30} -60.0000 q^{31} +32.0000 q^{32} +48.0000 q^{33} -68.0000 q^{34} +36.0000 q^{36} +150.000 q^{37} -128.000 q^{38} -174.000 q^{39} -40.0000 q^{40} -474.000 q^{41} -292.000 q^{43} +64.0000 q^{44} -45.0000 q^{45} -32.0000 q^{46} -240.000 q^{47} +48.0000 q^{48} +50.0000 q^{50} -102.000 q^{51} -232.000 q^{52} -662.000 q^{53} +54.0000 q^{54} -80.0000 q^{55} -192.000 q^{57} +124.000 q^{58} +324.000 q^{59} -60.0000 q^{60} +514.000 q^{61} -120.000 q^{62} +64.0000 q^{64} +290.000 q^{65} +96.0000 q^{66} -372.000 q^{67} -136.000 q^{68} -48.0000 q^{69} -412.000 q^{71} +72.0000 q^{72} +770.000 q^{73} +300.000 q^{74} +75.0000 q^{75} -256.000 q^{76} -348.000 q^{78} -560.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} -948.000 q^{82} +852.000 q^{83} +170.000 q^{85} -584.000 q^{86} +186.000 q^{87} +128.000 q^{88} -1466.00 q^{89} -90.0000 q^{90} -64.0000 q^{92} -180.000 q^{93} -480.000 q^{94} +320.000 q^{95} +96.0000 q^{96} +178.000 q^{97} +144.000 q^{99} +O(q^{100})\)

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
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	16.0000	0.438562	0.219281	−	0.975662i	$-0.429629\pi$
$11$	16.0000	0.438562	0.219281	+	0.975662i	$0.429629\pi$
$12$	12.0000	0.288675
$13$	−58.0000	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$13$	−58.0000	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−34.0000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−34.0000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	18.0000	0.235702
$19$	−64.0000	−0.772769	−0.386384	−	0.922338i	$-0.626276\pi$
$19$	−64.0000	−0.772769	−0.386384	+	0.922338i	$0.626276\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	32.0000	0.310110
$23$	−16.0000	−0.145054	−0.0725268	−	0.997366i	$-0.523106\pi$
$23$	−16.0000	−0.145054	−0.0725268	+	0.997366i	$0.523106\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−116.000	−0.874980
$27$	27.0000	0.192450
$28$	0	0
$29$	62.0000	0.397004	0.198502	−	0.980101i	$-0.436392\pi$
$29$	62.0000	0.397004	0.198502	+	0.980101i	$0.436392\pi$
$30$	−30.0000	−0.182574
$31$	−60.0000	−0.347623	−0.173812	−	0.984779i	$-0.555608\pi$
$31$	−60.0000	−0.347623	−0.173812	+	0.984779i	$0.555608\pi$
$32$	32.0000	0.176777
$33$	48.0000	0.253204
$34$	−68.0000	−0.342997
$35$	0	0
$36$	36.0000	0.166667
$37$	150.000	0.666482	0.333241	−	0.942842i	$-0.391858\pi$
$37$	150.000	0.666482	0.333241	+	0.942842i	$0.391858\pi$
$38$	−128.000	−0.546430
$39$	−174.000	−0.714418
$40$	−40.0000	−0.158114
$41$	−474.000	−1.80552	−0.902761	−	0.430144i	$-0.858463\pi$
$41$	−474.000	−1.80552	−0.902761	+	0.430144i	$0.858463\pi$
$42$	0	0
$43$	−292.000	−1.03557	−0.517786	−	0.855510i	$-0.673244\pi$
$43$	−292.000	−1.03557	−0.517786	+	0.855510i	$0.673244\pi$
$44$	64.0000	0.219281
$45$	−45.0000	−0.149071
$46$	−32.0000	−0.102568
$47$	−240.000	−0.744843	−0.372421	−	0.928064i	$-0.621472\pi$
$47$	−240.000	−0.744843	−0.372421	+	0.928064i	$0.621472\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	50.0000	0.141421
$51$	−102.000	−0.280056
$52$	−232.000	−0.618704
$53$	−662.000	−1.71571	−0.857856	−	0.513891i	$-0.828204\pi$
$53$	−662.000	−1.71571	−0.857856	+	0.513891i	$0.828204\pi$
$54$	54.0000	0.136083
$55$	−80.0000	−0.196131
$56$	0	0
$57$	−192.000	−0.446158
$58$	124.000	0.280724
$59$	324.000	0.714936	0.357468	−	0.933925i	$-0.383640\pi$
$59$	324.000	0.714936	0.357468	+	0.933925i	$0.383640\pi$
$60$	−60.0000	−0.129099
$61$	514.000	1.07887	0.539434	−	0.842028i	$-0.318638\pi$
$61$	514.000	1.07887	0.539434	+	0.842028i	$0.318638\pi$
$62$	−120.000	−0.245807
$63$	0	0
$64$	64.0000	0.125000
$65$	290.000	0.553386
$66$	96.0000	0.179042
$67$	−372.000	−0.678314	−0.339157	−	0.940730i	$-0.610142\pi$
$67$	−372.000	−0.678314	−0.339157	+	0.940730i	$0.610142\pi$
$68$	−136.000	−0.242536
$69$	−48.0000	−0.0837467
$70$	0	0
$71$	−412.000	−0.688668	−0.344334	−	0.938847i	$-0.611895\pi$
$71$	−412.000	−0.688668	−0.344334	+	0.938847i	$0.611895\pi$
$72$	72.0000	0.117851
$73$	770.000	1.23454	0.617272	−	0.786750i	$-0.288238\pi$
$73$	770.000	1.23454	0.617272	+	0.786750i	$0.288238\pi$
$74$	300.000	0.471274
$75$	75.0000	0.115470
$76$	−256.000	−0.386384
$77$	0	0
$78$	−348.000	−0.505170
$79$	−560.000	−0.797531	−0.398765	−	0.917053i	$-0.630561\pi$
$79$	−560.000	−0.797531	−0.398765	+	0.917053i	$0.630561\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−948.000	−1.27670
$83$	852.000	1.12674	0.563368	−	0.826206i	$-0.309505\pi$
$83$	852.000	1.12674	0.563368	+	0.826206i	$0.309505\pi$
$84$	0	0
$85$	170.000	0.216930
$86$	−584.000	−0.732260
$87$	186.000	0.229210
$88$	128.000	0.155055
$89$	−1466.00	−1.74602	−0.873009	−	0.487703i	$-0.837835\pi$
$89$	−1466.00	−1.74602	−0.873009	+	0.487703i	$0.837835\pi$
$90$	−90.0000	−0.105409
$91$	0	0
$92$	−64.0000	−0.0725268
$93$	−180.000	−0.200700
$94$	−480.000	−0.526683
$95$	320.000	0.345593
$96$	96.0000	0.102062
$97$	178.000	0.186321	0.0931606	−	0.995651i	$-0.470303\pi$
$97$	178.000	0.186321	0.0931606	+	0.995651i	$0.470303\pi$
$98$	0	0
$99$	144.000	0.146187
$100$	100.000	0.100000
$101$	−1278.00	−1.25907	−0.629533	−	0.776973i	$-0.716754\pi$
$101$	−1278.00	−1.25907	−0.629533	+	0.776973i	$0.716754\pi$
$102$	−204.000	−0.198030
$103$	296.000	0.283163	0.141581	−	0.989927i	$-0.454781\pi$
$103$	296.000	0.283163	0.141581	+	0.989927i	$0.454781\pi$
$104$	−464.000	−0.437490
$105$	0	0
$106$	−1324.00	−1.21319
$107$	1164.00	1.05166	0.525832	−	0.850588i	$-0.323754\pi$
$107$	1164.00	1.05166	0.525832	+	0.850588i	$0.323754\pi$
$108$	108.000	0.0962250
$109$	−778.000	−0.683659	−0.341830	−	0.939762i	$-0.611047\pi$
$109$	−778.000	−0.683659	−0.341830	+	0.939762i	$0.611047\pi$
$110$	−160.000	−0.138685
$111$	450.000	0.384794
$112$	0	0
$113$	−42.0000	−0.0349648	−0.0174824	−	0.999847i	$-0.505565\pi$
$113$	−42.0000	−0.0349648	−0.0174824	+	0.999847i	$0.505565\pi$
$114$	−384.000	−0.315482
$115$	80.0000	0.0648699
$116$	248.000	0.198502
$117$	−522.000	−0.412469
$118$	648.000	0.505536
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−1075.00	−0.807663
$122$	1028.00	0.762875
$123$	−1422.00	−1.04242
$124$	−240.000	−0.173812
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−280.000	−0.195638	−0.0978188	−	0.995204i	$-0.531187\pi$
$127$	−280.000	−0.195638	−0.0978188	+	0.995204i	$0.531187\pi$
$128$	128.000	0.0883883
$129$	−876.000	−0.597888
$130$	580.000	0.391303
$131$	−1180.00	−0.787001	−0.393500	−	0.919324i	$-0.628736\pi$
$131$	−1180.00	−0.787001	−0.393500	+	0.919324i	$0.628736\pi$
$132$	192.000	0.126602
$133$	0	0
$134$	−744.000	−0.479640
$135$	−135.000	−0.0860663
$136$	−272.000	−0.171499
$137$	−730.000	−0.455242	−0.227621	−	0.973750i	$-0.573095\pi$
$137$	−730.000	−0.455242	−0.227621	+	0.973750i	$0.573095\pi$
$138$	−96.0000	−0.0592178
$139$	664.000	0.405178	0.202589	−	0.979264i	$-0.435064\pi$
$139$	664.000	0.405178	0.202589	+	0.979264i	$0.435064\pi$
$140$	0	0
$141$	−720.000	−0.430035
$142$	−824.000	−0.486962
$143$	−928.000	−0.542680
$144$	144.000	0.0833333
$145$	−310.000	−0.177546
$146$	1540.00	0.872954
$147$	0	0
$148$	600.000	0.333241
$149$	2974.00	1.63516	0.817582	−	0.575812i	$-0.195314\pi$
$149$	2974.00	1.63516	0.817582	+	0.575812i	$0.195314\pi$
$150$	150.000	0.0816497
$151$	−2768.00	−1.49177	−0.745883	−	0.666077i	$-0.767972\pi$
$151$	−2768.00	−1.49177	−0.745883	+	0.666077i	$0.767972\pi$
$152$	−512.000	−0.273215
$153$	−306.000	−0.161690
$154$	0	0
$155$	300.000	0.155462
$156$	−696.000	−0.357209
$157$	−1890.00	−0.960754	−0.480377	−	0.877062i	$-0.659500\pi$
$157$	−1890.00	−0.960754	−0.480377	+	0.877062i	$0.659500\pi$
$158$	−1120.00	−0.563939
$159$	−1986.00	−0.990566
$160$	−160.000	−0.0790569
$161$	0	0
$162$	162.000	0.0785674
$163$	−1180.00	−0.567023	−0.283511	−	0.958969i	$-0.591499\pi$
$163$	−1180.00	−0.567023	−0.283511	+	0.958969i	$0.591499\pi$
$164$	−1896.00	−0.902761
$165$	−240.000	−0.113236
$166$	1704.00	0.796723
$167$	1216.00	0.563455	0.281727	−	0.959495i	$-0.409093\pi$
$167$	1216.00	0.563455	0.281727	+	0.959495i	$0.409093\pi$
$168$	0	0
$169$	1167.00	0.531179
$170$	340.000	0.153393
$171$	−576.000	−0.257590
$172$	−1168.00	−0.517786
$173$	−126.000	−0.0553734	−0.0276867	−	0.999617i	$-0.508814\pi$
$173$	−126.000	−0.0553734	−0.0276867	+	0.999617i	$0.508814\pi$
$174$	372.000	0.162076
$175$	0	0
$176$	256.000	0.109640
$177$	972.000	0.412768
$178$	−2932.00	−1.23462
$179$	872.000	0.364114	0.182057	−	0.983288i	$-0.441725\pi$
$179$	872.000	0.364114	0.182057	+	0.983288i	$0.441725\pi$
$180$	−180.000	−0.0745356
$181$	18.0000	0.00739188	0.00369594	−	0.999993i	$-0.498824\pi$
$181$	18.0000	0.00739188	0.00369594	+	0.999993i	$0.498824\pi$
$182$	0	0
$183$	1542.00	0.622885
$184$	−128.000	−0.0512842
$185$	−750.000	−0.298060
$186$	−360.000	−0.141917
$187$	−544.000	−0.212734
$188$	−960.000	−0.372421
$189$	0	0
$190$	640.000	0.244371
$191$	4420.00	1.67445	0.837225	−	0.546858i	$-0.184176\pi$
$191$	4420.00	1.67445	0.837225	+	0.546858i	$0.184176\pi$
$192$	192.000	0.0721688
$193$	−2254.00	−0.840655	−0.420328	−	0.907372i	$-0.638085\pi$
$193$	−2254.00	−0.840655	−0.420328	+	0.907372i	$0.638085\pi$
$194$	356.000	0.131749
$195$	870.000	0.319497
$196$	0	0
$197$	−750.000	−0.271245	−0.135623	−	0.990761i	$-0.543303\pi$
$197$	−750.000	−0.271245	−0.135623	+	0.990761i	$0.543303\pi$
$198$	288.000	0.103370
$199$	−3732.00	−1.32942	−0.664710	−	0.747102i	$-0.731445\pi$
$199$	−3732.00	−1.32942	−0.664710	+	0.747102i	$0.731445\pi$
$200$	200.000	0.0707107
$201$	−1116.00	−0.391625
$202$	−2556.00	−0.890295
$203$	0	0
$204$	−408.000	−0.140028
$205$	2370.00	0.807454
$206$	592.000	0.200226
$207$	−144.000	−0.0483512
$208$	−928.000	−0.309352
$209$	−1024.00	−0.338907
$210$	0	0
$211$	1980.00	0.646013	0.323007	−	0.946397i	$-0.395306\pi$
$211$	1980.00	0.646013	0.323007	+	0.946397i	$0.395306\pi$
$212$	−2648.00	−0.857856
$213$	−1236.00	−0.397602
$214$	2328.00	0.743639
$215$	1460.00	0.463122
$216$	216.000	0.0680414
$217$	0	0
$218$	−1556.00	−0.483420
$219$	2310.00	0.712764
$220$	−320.000	−0.0980654
$221$	1972.00	0.600231
$222$	900.000	0.272090
$223$	6328.00	1.90024	0.950122	−	0.311880i	$-0.100959\pi$
$223$	6328.00	1.90024	0.950122	+	0.311880i	$0.100959\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−84.0000	−0.0247239
$227$	2596.00	0.759042	0.379521	−	0.925183i	$-0.376089\pi$
$227$	2596.00	0.759042	0.379521	+	0.925183i	$0.376089\pi$
$228$	−768.000	−0.223079
$229$	−4742.00	−1.36839	−0.684193	−	0.729301i	$-0.739845\pi$
$229$	−4742.00	−1.36839	−0.684193	+	0.729301i	$0.739845\pi$
$230$	160.000	0.0458699
$231$	0	0
$232$	496.000	0.140362
$233$	1294.00	0.363832	0.181916	−	0.983314i	$-0.441770\pi$
$233$	1294.00	0.363832	0.181916	+	0.983314i	$0.441770\pi$
$234$	−1044.00	−0.291660
$235$	1200.00	0.333104
$236$	1296.00	0.357468
$237$	−1680.00	−0.460455
$238$	0	0
$239$	−2340.00	−0.633314	−0.316657	−	0.948540i	$-0.602560\pi$
$239$	−2340.00	−0.633314	−0.316657	+	0.948540i	$0.602560\pi$
$240$	−240.000	−0.0645497
$241$	−5962.00	−1.59355	−0.796776	−	0.604274i	$-0.793463\pi$
$241$	−5962.00	−1.59355	−0.796776	+	0.604274i	$0.793463\pi$
$242$	−2150.00	−0.571104
$243$	243.000	0.0641500
$244$	2056.00	0.539434
$245$	0	0
$246$	−2844.00	−0.737101
$247$	3712.00	0.956230
$248$	−480.000	−0.122903
$249$	2556.00	0.650522
$250$	−250.000	−0.0632456
$251$	1572.00	0.395314	0.197657	−	0.980271i	$-0.436667\pi$
$251$	1572.00	0.395314	0.197657	+	0.980271i	$0.436667\pi$
$252$	0	0
$253$	−256.000	−0.0636149
$254$	−560.000	−0.138337
$255$	510.000	0.125245
$256$	256.000	0.0625000
$257$	3910.00	0.949024	0.474512	−	0.880249i	$-0.342625\pi$
$257$	3910.00	0.949024	0.474512	+	0.880249i	$0.342625\pi$
$258$	−1752.00	−0.422770
$259$	0	0
$260$	1160.00	0.276693
$261$	558.000	0.132335
$262$	−2360.00	−0.556493
$263$	−5672.00	−1.32985	−0.664925	−	0.746910i	$-0.731536\pi$
$263$	−5672.00	−1.32985	−0.664925	+	0.746910i	$0.731536\pi$
$264$	384.000	0.0895211
$265$	3310.00	0.767289
$266$	0	0
$267$	−4398.00	−1.00806
$268$	−1488.00	−0.339157
$269$	1002.00	0.227112	0.113556	−	0.993532i	$-0.463776\pi$
$269$	1002.00	0.227112	0.113556	+	0.993532i	$0.463776\pi$
$270$	−270.000	−0.0608581
$271$	6140.00	1.37630	0.688152	−	0.725566i	$-0.258422\pi$
$271$	6140.00	1.37630	0.688152	+	0.725566i	$0.258422\pi$
$272$	−544.000	−0.121268
$273$	0	0
$274$	−1460.00	−0.321904
$275$	400.000	0.0877124
$276$	−192.000	−0.0418733
$277$	70.0000	0.0151837	0.00759186	−	0.999971i	$-0.497583\pi$
$277$	70.0000	0.0151837	0.00759186	+	0.999971i	$0.497583\pi$
$278$	1328.00	0.286504
$279$	−540.000	−0.115874
$280$	0	0
$281$	−3294.00	−0.699301	−0.349650	−	0.936880i	$-0.613700\pi$
$281$	−3294.00	−0.699301	−0.349650	+	0.936880i	$0.613700\pi$
$282$	−1440.00	−0.304081
$283$	−1852.00	−0.389011	−0.194505	−	0.980901i	$-0.562310\pi$
$283$	−1852.00	−0.389011	−0.194505	+	0.980901i	$0.562310\pi$
$284$	−1648.00	−0.344334
$285$	960.000	0.199528
$286$	−1856.00	−0.383733
$287$	0	0
$288$	288.000	0.0589256
$289$	−3757.00	−0.764706
$290$	−620.000	−0.125544
$291$	534.000	0.107573
$292$	3080.00	0.617272
$293$	5130.00	1.02286	0.511430	−	0.859325i	$-0.329116\pi$
$293$	5130.00	1.02286	0.511430	+	0.859325i	$0.329116\pi$
$294$	0	0
$295$	−1620.00	−0.319729
$296$	1200.00	0.235637
$297$	432.000	0.0844013
$298$	5948.00	1.15624
$299$	928.000	0.179490
$300$	300.000	0.0577350
$301$	0	0
$302$	−5536.00	−1.05484
$303$	−3834.00	−0.726923
$304$	−1024.00	−0.193192
$305$	−2570.00	−0.482484
$306$	−612.000	−0.114332
$307$	−956.000	−0.177726	−0.0888629	−	0.996044i	$-0.528323\pi$
$307$	−956.000	−0.177726	−0.0888629	+	0.996044i	$0.528323\pi$
$308$	0	0
$309$	888.000	0.163484
$310$	600.000	0.109928
$311$	3448.00	0.628676	0.314338	−	0.949311i	$-0.398218\pi$
$311$	3448.00	0.628676	0.314338	+	0.949311i	$0.398218\pi$
$312$	−1392.00	−0.252585
$313$	5850.00	1.05643	0.528213	−	0.849112i	$-0.322862\pi$
$313$	5850.00	1.05643	0.528213	+	0.849112i	$0.322862\pi$
$314$	−3780.00	−0.679356
$315$	0	0
$316$	−2240.00	−0.398765
$317$	3794.00	0.672215	0.336108	−	0.941824i	$-0.390889\pi$
$317$	3794.00	0.672215	0.336108	+	0.941824i	$0.390889\pi$
$318$	−3972.00	−0.700436
$319$	992.000	0.174111
$320$	−320.000	−0.0559017
$321$	3492.00	0.607179
$322$	0	0
$323$	2176.00	0.374848
$324$	324.000	0.0555556
$325$	−1450.00	−0.247482
$326$	−2360.00	−0.400946
$327$	−2334.00	−0.394711
$328$	−3792.00	−0.638348
$329$	0	0
$330$	−480.000	−0.0800701
$331$	4116.00	0.683492	0.341746	−	0.939792i	$-0.388982\pi$
$331$	4116.00	0.683492	0.341746	+	0.939792i	$0.388982\pi$
$332$	3408.00	0.563368
$333$	1350.00	0.222161
$334$	2432.00	0.398423
$335$	1860.00	0.303351
$336$	0	0
$337$	7506.00	1.21329	0.606644	−	0.794974i	$-0.292515\pi$
$337$	7506.00	1.21329	0.606644	+	0.794974i	$0.292515\pi$
$338$	2334.00	0.375600
$339$	−126.000	−0.0201870
$340$	680.000	0.108465
$341$	−960.000	−0.152454
$342$	−1152.00	−0.182143
$343$	0	0
$344$	−2336.00	−0.366130
$345$	240.000	0.0374527
$346$	−252.000	−0.0391549
$347$	−11516.0	−1.78159	−0.890794	−	0.454407i	$-0.849851\pi$
$347$	−11516.0	−1.78159	−0.890794	+	0.454407i	$0.849851\pi$
$348$	744.000	0.114605
$349$	11362.0	1.74268	0.871338	−	0.490683i	$-0.163253\pi$
$349$	11362.0	1.74268	0.871338	+	0.490683i	$0.163253\pi$
$350$	0	0
$351$	−1566.00	−0.238139
$352$	512.000	0.0775275
$353$	−3890.00	−0.586526	−0.293263	−	0.956032i	$-0.594741\pi$
$353$	−3890.00	−0.586526	−0.293263	+	0.956032i	$0.594741\pi$
$354$	1944.00	0.291871
$355$	2060.00	0.307982
$356$	−5864.00	−0.873009
$357$	0	0
$358$	1744.00	0.257467
$359$	−1332.00	−0.195822	−0.0979112	−	0.995195i	$-0.531216\pi$
$359$	−1332.00	−0.195822	−0.0979112	+	0.995195i	$0.531216\pi$
$360$	−360.000	−0.0527046
$361$	−2763.00	−0.402828
$362$	36.0000	0.00522685
$363$	−3225.00	−0.466305
$364$	0	0
$365$	−3850.00	−0.552105
$366$	3084.00	0.440446
$367$	−10264.0	−1.45988	−0.729941	−	0.683511i	$-0.760452\pi$
$367$	−10264.0	−1.45988	−0.729941	+	0.683511i	$0.760452\pi$
$368$	−256.000	−0.0362634
$369$	−4266.00	−0.601840
$370$	−1500.00	−0.210760
$371$	0	0
$372$	−720.000	−0.100350
$373$	−7714.00	−1.07082	−0.535410	−	0.844592i	$-0.679843\pi$
$373$	−7714.00	−1.07082	−0.535410	+	0.844592i	$0.679843\pi$
$374$	−1088.00	−0.150426
$375$	−375.000	−0.0516398
$376$	−1920.00	−0.263342
$377$	−3596.00	−0.491256
$378$	0	0
$379$	−6020.00	−0.815901	−0.407951	−	0.913004i	$-0.633756\pi$
$379$	−6020.00	−0.815901	−0.407951	+	0.913004i	$0.633756\pi$
$380$	1280.00	0.172796
$381$	−840.000	−0.112951
$382$	8840.00	1.18402
$383$	5368.00	0.716167	0.358084	−	0.933690i	$-0.383430\pi$
$383$	5368.00	0.716167	0.358084	+	0.933690i	$0.383430\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	−4508.00	−0.594433
$387$	−2628.00	−0.345191
$388$	712.000	0.0931606
$389$	10526.0	1.37195	0.685976	−	0.727624i	$-0.259375\pi$
$389$	10526.0	1.37195	0.685976	+	0.727624i	$0.259375\pi$
$390$	1740.00	0.225919
$391$	544.000	0.0703613
$392$	0	0
$393$	−3540.00	−0.454375
$394$	−1500.00	−0.191799
$395$	2800.00	0.356667
$396$	576.000	0.0730937
$397$	−15642.0	−1.97745	−0.988727	−	0.149728i	$-0.952160\pi$
$397$	−15642.0	−1.97745	−0.988727	+	0.149728i	$0.952160\pi$
$398$	−7464.00	−0.940041
$399$	0	0
$400$	400.000	0.0500000
$401$	14498.0	1.80548	0.902738	−	0.430192i	$-0.141554\pi$
$401$	14498.0	1.80548	0.902738	+	0.430192i	$0.141554\pi$
$402$	−2232.00	−0.276921
$403$	3480.00	0.430152
$404$	−5112.00	−0.629533
$405$	−405.000	−0.0496904
$406$	0	0
$407$	2400.00	0.292294
$408$	−816.000	−0.0990148
$409$	13718.0	1.65846	0.829232	−	0.558905i	$-0.188778\pi$
$409$	13718.0	1.65846	0.829232	+	0.558905i	$0.188778\pi$
$410$	4740.00	0.570956
$411$	−2190.00	−0.262834
$412$	1184.00	0.141581
$413$	0	0
$414$	−288.000	−0.0341894
$415$	−4260.00	−0.503892
$416$	−1856.00	−0.218745
$417$	1992.00	0.233930
$418$	−2048.00	−0.239643
$419$	10484.0	1.22238	0.611190	−	0.791484i	$-0.290691\pi$
$419$	10484.0	1.22238	0.611190	+	0.791484i	$0.290691\pi$
$420$	0	0
$421$	−8594.00	−0.994883	−0.497442	−	0.867497i	$-0.665727\pi$
$421$	−8594.00	−0.994883	−0.497442	+	0.867497i	$0.665727\pi$
$422$	3960.00	0.456800
$423$	−2160.00	−0.248281
$424$	−5296.00	−0.606596
$425$	−850.000	−0.0970143
$426$	−2472.00	−0.281147
$427$	0	0
$428$	4656.00	0.525832
$429$	−2784.00	−0.313317
$430$	2920.00	0.327477
$431$	−420.000	−0.0469390	−0.0234695	−	0.999725i	$-0.507471\pi$
$431$	−420.000	−0.0469390	−0.0234695	+	0.999725i	$0.507471\pi$
$432$	432.000	0.0481125
$433$	9794.00	1.08700	0.543498	−	0.839410i	$-0.317099\pi$
$433$	9794.00	1.08700	0.543498	+	0.839410i	$0.317099\pi$
$434$	0	0
$435$	−930.000	−0.102506
$436$	−3112.00	−0.341830
$437$	1024.00	0.112093
$438$	4620.00	0.504000
$439$	1436.00	0.156120	0.0780598	−	0.996949i	$-0.475127\pi$
$439$	1436.00	0.156120	0.0780598	+	0.996949i	$0.475127\pi$
$440$	−640.000	−0.0693427
$441$	0	0
$442$	3944.00	0.424427
$443$	12228.0	1.31144	0.655722	−	0.755002i	$-0.272364\pi$
$443$	12228.0	1.31144	0.655722	+	0.755002i	$0.272364\pi$
$444$	1800.00	0.192397
$445$	7330.00	0.780843
$446$	12656.0	1.34367
$447$	8922.00	0.944063
$448$	0	0
$449$	−6734.00	−0.707789	−0.353894	−	0.935285i	$-0.615143\pi$
$449$	−6734.00	−0.707789	−0.353894	+	0.935285i	$0.615143\pi$
$450$	450.000	0.0471405
$451$	−7584.00	−0.791833
$452$	−168.000	−0.0174824
$453$	−8304.00	−0.861271
$454$	5192.00	0.536724
$455$	0	0
$456$	−1536.00	−0.157741
$457$	10690.0	1.09422	0.547108	−	0.837062i	$-0.315729\pi$
$457$	10690.0	1.09422	0.547108	+	0.837062i	$0.315729\pi$
$458$	−9484.00	−0.967594
$459$	−918.000	−0.0933520
$460$	320.000	0.0324349
$461$	−14902.0	−1.50554	−0.752772	−	0.658282i	$-0.771283\pi$
$461$	−14902.0	−1.50554	−0.752772	+	0.658282i	$0.771283\pi$
$462$	0	0
$463$	17064.0	1.71281	0.856405	−	0.516304i	$-0.172693\pi$
$463$	17064.0	1.71281	0.856405	+	0.516304i	$0.172693\pi$
$464$	992.000	0.0992510
$465$	900.000	0.0897559
$466$	2588.00	0.257268
$467$	−3036.00	−0.300834	−0.150417	−	0.988623i	$-0.548062\pi$
$467$	−3036.00	−0.300834	−0.150417	+	0.988623i	$0.548062\pi$
$468$	−2088.00	−0.206235
$469$	0	0
$470$	2400.00	0.235540
$471$	−5670.00	−0.554692
$472$	2592.00	0.252768
$473$	−4672.00	−0.454162
$474$	−3360.00	−0.325591
$475$	−1600.00	−0.154554
$476$	0	0
$477$	−5958.00	−0.571904
$478$	−4680.00	−0.447821
$479$	13664.0	1.30339	0.651695	−	0.758481i	$-0.274058\pi$
$479$	13664.0	1.30339	0.651695	+	0.758481i	$0.274058\pi$
$480$	−480.000	−0.0456435
$481$	−8700.00	−0.824711
$482$	−11924.0	−1.12681
$483$	0	0
$484$	−4300.00	−0.403832
$485$	−890.000	−0.0833254
$486$	486.000	0.0453609
$487$	−11744.0	−1.09275	−0.546377	−	0.837539i	$-0.683994\pi$
$487$	−11744.0	−1.09275	−0.546377	+	0.837539i	$0.683994\pi$
$488$	4112.00	0.381437
$489$	−3540.00	−0.327371
$490$	0	0
$491$	−48.0000	−0.00441183	−0.00220592	−	0.999998i	$-0.500702\pi$
$491$	−48.0000	−0.00441183	−0.00220592	+	0.999998i	$0.500702\pi$
$492$	−5688.00	−0.521209
$493$	−2108.00	−0.192575
$494$	7424.00	0.676157
$495$	−720.000	−0.0653770
$496$	−960.000	−0.0869058
$497$	0	0
$498$	5112.00	0.459988
$499$	1044.00	0.0936590	0.0468295	−	0.998903i	$-0.485088\pi$
$499$	1044.00	0.0936590	0.0468295	+	0.998903i	$0.485088\pi$
$500$	−500.000	−0.0447214
$501$	3648.00	0.325311
$502$	3144.00	0.279529
$503$	−14432.0	−1.27931	−0.639653	−	0.768664i	$-0.720922\pi$
$503$	−14432.0	−1.27931	−0.639653	+	0.768664i	$0.720922\pi$
$504$	0	0
$505$	6390.00	0.563072
$506$	−512.000	−0.0449826
$507$	3501.00	0.306676
$508$	−1120.00	−0.0978188
$509$	6426.00	0.559582	0.279791	−	0.960061i	$-0.409735\pi$
$509$	6426.00	0.559582	0.279791	+	0.960061i	$0.409735\pi$
$510$	1020.00	0.0885615
$511$	0	0
$512$	512.000	0.0441942
$513$	−1728.00	−0.148719
$514$	7820.00	0.671061
$515$	−1480.00	−0.126634
$516$	−3504.00	−0.298944
$517$	−3840.00	−0.326660
$518$	0	0
$519$	−378.000	−0.0319699
$520$	2320.00	0.195651
$521$	11766.0	0.989401	0.494700	−	0.869064i	$-0.335278\pi$
$521$	11766.0	0.989401	0.494700	+	0.869064i	$0.335278\pi$
$522$	1116.00	0.0935747
$523$	11900.0	0.994934	0.497467	−	0.867483i	$-0.334263\pi$
$523$	11900.0	0.994934	0.497467	+	0.867483i	$0.334263\pi$
$524$	−4720.00	−0.393500
$525$	0	0
$526$	−11344.0	−0.940346
$527$	2040.00	0.168622
$528$	768.000	0.0633010
$529$	−11911.0	−0.978959
$530$	6620.00	0.542556
$531$	2916.00	0.238312
$532$	0	0
$533$	27492.0	2.23417
$534$	−8796.00	−0.712809
$535$	−5820.00	−0.470319
$536$	−2976.00	−0.239820
$537$	2616.00	0.210221
$538$	2004.00	0.160592
$539$	0	0
$540$	−540.000	−0.0430331
$541$	−22330.0	−1.77457	−0.887284	−	0.461223i	$-0.847411\pi$
$541$	−22330.0	−1.77457	−0.887284	+	0.461223i	$0.847411\pi$
$542$	12280.0	0.973194
$543$	54.0000	0.00426770
$544$	−1088.00	−0.0857493
$545$	3890.00	0.305742
$546$	0	0
$547$	18396.0	1.43795	0.718973	−	0.695038i	$-0.244613\pi$
$547$	18396.0	1.43795	0.718973	+	0.695038i	$0.244613\pi$
$548$	−2920.00	−0.227621
$549$	4626.00	0.359623
$550$	800.000	0.0620220
$551$	−3968.00	−0.306792
$552$	−384.000	−0.0296089
$553$	0	0
$554$	140.000	0.0107365
$555$	−2250.00	−0.172085
$556$	2656.00	0.202589
$557$	−3774.00	−0.287091	−0.143545	−	0.989644i	$-0.545850\pi$
$557$	−3774.00	−0.287091	−0.143545	+	0.989644i	$0.545850\pi$
$558$	−1080.00	−0.0819356
$559$	16936.0	1.28142
$560$	0	0
$561$	−1632.00	−0.122822
$562$	−6588.00	−0.494480
$563$	−9412.00	−0.704562	−0.352281	−	0.935894i	$-0.614594\pi$
$563$	−9412.00	−0.704562	−0.352281	+	0.935894i	$0.614594\pi$
$564$	−2880.00	−0.215018
$565$	210.000	0.0156368
$566$	−3704.00	−0.275072
$567$	0	0
$568$	−3296.00	−0.243481
$569$	11146.0	0.821203	0.410602	−	0.911815i	$-0.365319\pi$
$569$	11146.0	0.821203	0.410602	+	0.911815i	$0.365319\pi$
$570$	1920.00	0.141088
$571$	15292.0	1.12075	0.560377	−	0.828238i	$-0.310656\pi$
$571$	15292.0	1.12075	0.560377	+	0.828238i	$0.310656\pi$
$572$	−3712.00	−0.271340
$573$	13260.0	0.966744
$574$	0	0
$575$	−400.000	−0.0290107
$576$	576.000	0.0416667
$577$	22322.0	1.61053	0.805266	−	0.592914i	$-0.202022\pi$
$577$	22322.0	1.61053	0.805266	+	0.592914i	$0.202022\pi$
$578$	−7514.00	−0.540729
$579$	−6762.00	−0.485353
$580$	−1240.00	−0.0887728
$581$	0	0
$582$	1068.00	0.0760653
$583$	−10592.0	−0.752446
$584$	6160.00	0.436477
$585$	2610.00	0.184462
$586$	10260.0	0.723271
$587$	−684.000	−0.0480949	−0.0240474	−	0.999711i	$-0.507655\pi$
$587$	−684.000	−0.0480949	−0.0240474	+	0.999711i	$0.507655\pi$
$588$	0	0
$589$	3840.00	0.268632
$590$	−3240.00	−0.226083
$591$	−2250.00	−0.156603
$592$	2400.00	0.166621
$593$	7806.00	0.540563	0.270282	−	0.962781i	$-0.412883\pi$
$593$	7806.00	0.540563	0.270282	+	0.962781i	$0.412883\pi$
$594$	864.000	0.0596807
$595$	0	0
$596$	11896.0	0.817582
$597$	−11196.0	−0.767541
$598$	1856.00	0.126919
$599$	−1284.00	−0.0875840	−0.0437920	−	0.999041i	$-0.513944\pi$
$599$	−1284.00	−0.0875840	−0.0437920	+	0.999041i	$0.513944\pi$
$600$	600.000	0.0408248
$601$	−12706.0	−0.862377	−0.431188	−	0.902262i	$-0.641906\pi$
$601$	−12706.0	−0.862377	−0.431188	+	0.902262i	$0.641906\pi$
$602$	0	0
$603$	−3348.00	−0.226105
$604$	−11072.0	−0.745883
$605$	5375.00	0.361198
$606$	−7668.00	−0.514012
$607$	−9016.00	−0.602880	−0.301440	−	0.953485i	$-0.597467\pi$
$607$	−9016.00	−0.602880	−0.301440	+	0.953485i	$0.597467\pi$
$608$	−2048.00	−0.136608
$609$	0	0
$610$	−5140.00	−0.341168
$611$	13920.0	0.921674
$612$	−1224.00	−0.0808452
$613$	−19386.0	−1.27731	−0.638657	−	0.769492i	$-0.720510\pi$
$613$	−19386.0	−1.27731	−0.638657	+	0.769492i	$0.720510\pi$
$614$	−1912.00	−0.125671
$615$	7110.00	0.466184
$616$	0	0
$617$	14206.0	0.926924	0.463462	−	0.886117i	$-0.346607\pi$
$617$	14206.0	0.926924	0.463462	+	0.886117i	$0.346607\pi$
$618$	1776.00	0.115601
$619$	−344.000	−0.0223369	−0.0111684	−	0.999938i	$-0.503555\pi$
$619$	−344.000	−0.0223369	−0.0111684	+	0.999938i	$0.503555\pi$
$620$	1200.00	0.0777309
$621$	−432.000	−0.0279156
$622$	6896.00	0.444541
$623$	0	0
$624$	−2784.00	−0.178604
$625$	625.000	0.0400000
$626$	11700.0	0.747006
$627$	−3072.00	−0.195668
$628$	−7560.00	−0.480377
$629$	−5100.00	−0.323291
$630$	0	0
$631$	3608.00	0.227626	0.113813	−	0.993502i	$-0.463693\pi$
$631$	3608.00	0.227626	0.113813	+	0.993502i	$0.463693\pi$
$632$	−4480.00	−0.281970
$633$	5940.00	0.372976
$634$	7588.00	0.475328
$635$	1400.00	0.0874918
$636$	−7944.00	−0.495283
$637$	0	0
$638$	1984.00	0.123115
$639$	−3708.00	−0.229556
$640$	−640.000	−0.0395285
$641$	−18838.0	−1.16077	−0.580387	−	0.814341i	$-0.697099\pi$
$641$	−18838.0	−1.16077	−0.580387	+	0.814341i	$0.697099\pi$
$642$	6984.00	0.429340
$643$	−27068.0	−1.66012	−0.830060	−	0.557673i	$-0.811694\pi$
$643$	−27068.0	−1.66012	−0.830060	+	0.557673i	$0.811694\pi$
$644$	0	0
$645$	4380.00	0.267383
$646$	4352.00	0.265058
$647$	18912.0	1.14916	0.574581	−	0.818448i	$-0.305165\pi$
$647$	18912.0	1.14916	0.574581	+	0.818448i	$0.305165\pi$
$648$	648.000	0.0392837
$649$	5184.00	0.313544
$650$	−2900.00	−0.174996
$651$	0	0
$652$	−4720.00	−0.283511
$653$	−614.000	−0.0367958	−0.0183979	−	0.999831i	$-0.505857\pi$
$653$	−614.000	−0.0367958	−0.0183979	+	0.999831i	$0.505857\pi$
$654$	−4668.00	−0.279103
$655$	5900.00	0.351957
$656$	−7584.00	−0.451380
$657$	6930.00	0.411515
$658$	0	0
$659$	31248.0	1.84712	0.923558	−	0.383459i	$-0.125267\pi$
$659$	31248.0	1.84712	0.923558	+	0.383459i	$0.125267\pi$
$660$	−960.000	−0.0566181
$661$	19882.0	1.16992	0.584962	−	0.811060i	$-0.301109\pi$
$661$	19882.0	1.16992	0.584962	+	0.811060i	$0.301109\pi$
$662$	8232.00	0.483302
$663$	5916.00	0.346544
$664$	6816.00	0.398362
$665$	0	0
$666$	2700.00	0.157091
$667$	−992.000	−0.0575868
$668$	4864.00	0.281727
$669$	18984.0	1.09711
$670$	3720.00	0.214502
$671$	8224.00	0.473151
$672$	0	0
$673$	31866.0	1.82518	0.912588	−	0.408879i	$-0.134080\pi$
$673$	31866.0	1.82518	0.912588	+	0.408879i	$0.134080\pi$
$674$	15012.0	0.857924
$675$	675.000	0.0384900
$676$	4668.00	0.265589
$677$	−19574.0	−1.11121	−0.555606	−	0.831446i	$-0.687514\pi$
$677$	−19574.0	−1.11121	−0.555606	+	0.831446i	$0.687514\pi$
$678$	−252.000	−0.0142743
$679$	0	0
$680$	1360.00	0.0766965
$681$	7788.00	0.438233
$682$	−1920.00	−0.107801
$683$	24036.0	1.34658	0.673288	−	0.739380i	$-0.264881\pi$
$683$	24036.0	1.34658	0.673288	+	0.739380i	$0.264881\pi$
$684$	−2304.00	−0.128795
$685$	3650.00	0.203590
$686$	0	0
$687$	−14226.0	−0.790037
$688$	−4672.00	−0.258893
$689$	38396.0	2.12303
$690$	480.000	0.0264830
$691$	−29496.0	−1.62385	−0.811925	−	0.583761i	$-0.801580\pi$
$691$	−29496.0	−1.62385	−0.811925	+	0.583761i	$0.801580\pi$
$692$	−504.000	−0.0276867
$693$	0	0
$694$	−23032.0	−1.25977
$695$	−3320.00	−0.181201
$696$	1488.00	0.0810381
$697$	16116.0	0.875806
$698$	22724.0	1.23226
$699$	3882.00	0.210058
$700$	0	0
$701$	−10242.0	−0.551833	−0.275917	−	0.961182i	$-0.588981\pi$
$701$	−10242.0	−0.551833	−0.275917	+	0.961182i	$0.588981\pi$
$702$	−3132.00	−0.168390
$703$	−9600.00	−0.515037
$704$	1024.00	0.0548202
$705$	3600.00	0.192318
$706$	−7780.00	−0.414737
$707$	0	0
$708$	3888.00	0.206384
$709$	−13730.0	−0.727279	−0.363640	−	0.931540i	$-0.618466\pi$
$709$	−13730.0	−0.727279	−0.363640	+	0.931540i	$0.618466\pi$
$710$	4120.00	0.217776
$711$	−5040.00	−0.265844
$712$	−11728.0	−0.617311
$713$	960.000	0.0504240
$714$	0	0
$715$	4640.00	0.242694
$716$	3488.00	0.182057
$717$	−7020.00	−0.365644
$718$	−2664.00	−0.138467
$719$	14840.0	0.769734	0.384867	−	0.922972i	$-0.374247\pi$
$719$	14840.0	0.769734	0.384867	+	0.922972i	$0.374247\pi$
$720$	−720.000	−0.0372678
$721$	0	0
$722$	−5526.00	−0.284843
$723$	−17886.0	−0.920038
$724$	72.0000	0.00369594
$725$	1550.00	0.0794008
$726$	−6450.00	−0.329727
$727$	3616.00	0.184470	0.0922352	−	0.995737i	$-0.470599\pi$
$727$	3616.00	0.184470	0.0922352	+	0.995737i	$0.470599\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−7700.00	−0.390397
$731$	9928.00	0.502326
$732$	6168.00	0.311442
$733$	24182.0	1.21853	0.609265	−	0.792967i	$-0.291465\pi$
$733$	24182.0	1.21853	0.609265	+	0.792967i	$0.291465\pi$
$734$	−20528.0	−1.03229
$735$	0	0
$736$	−512.000	−0.0256421
$737$	−5952.00	−0.297483
$738$	−8532.00	−0.425565
$739$	34052.0	1.69502	0.847512	−	0.530776i	$-0.178099\pi$
$739$	34052.0	1.69502	0.847512	+	0.530776i	$0.178099\pi$
$740$	−3000.00	−0.149030
$741$	11136.0	0.552080
$742$	0	0
$743$	21192.0	1.04638	0.523189	−	0.852217i	$-0.324742\pi$
$743$	21192.0	1.04638	0.523189	+	0.852217i	$0.324742\pi$
$744$	−1440.00	−0.0709583
$745$	−14870.0	−0.731268
$746$	−15428.0	−0.757184
$747$	7668.00	0.375579
$748$	−2176.00	−0.106367
$749$	0	0
$750$	−750.000	−0.0365148
$751$	−2192.00	−0.106508	−0.0532538	−	0.998581i	$-0.516959\pi$
$751$	−2192.00	−0.106508	−0.0532538	+	0.998581i	$0.516959\pi$
$752$	−3840.00	−0.186211
$753$	4716.00	0.228235
$754$	−7192.00	−0.347370
$755$	13840.0	0.667138
$756$	0	0
$757$	−39458.0	−1.89449	−0.947243	−	0.320517i	$-0.896143\pi$
$757$	−39458.0	−1.89449	−0.947243	+	0.320517i	$0.896143\pi$
$758$	−12040.0	−0.576929
$759$	−768.000	−0.0367281
$760$	2560.00	0.122185
$761$	−458.000	−0.0218167	−0.0109083	−	0.999941i	$-0.503472\pi$
$761$	−458.000	−0.0218167	−0.0109083	+	0.999941i	$0.503472\pi$
$762$	−1680.00	−0.0798687
$763$	0	0
$764$	17680.0	0.837225
$765$	1530.00	0.0723102
$766$	10736.0	0.506407
$767$	−18792.0	−0.884667
$768$	768.000	0.0360844
$769$	−25354.0	−1.18893	−0.594466	−	0.804121i	$-0.702636\pi$
$769$	−25354.0	−1.18893	−0.594466	+	0.804121i	$0.702636\pi$
$770$	0	0
$771$	11730.0	0.547919
$772$	−9016.00	−0.420328
$773$	25306.0	1.17748	0.588741	−	0.808322i	$-0.299624\pi$
$773$	25306.0	1.17748	0.588741	+	0.808322i	$0.299624\pi$
$774$	−5256.00	−0.244087
$775$	−1500.00	−0.0695246
$776$	1424.00	0.0658745
$777$	0	0
$778$	21052.0	0.970117
$779$	30336.0	1.39525
$780$	3480.00	0.159749
$781$	−6592.00	−0.302023
$782$	1088.00	0.0497529
$783$	1674.00	0.0764034
$784$	0	0
$785$	9450.00	0.429662
$786$	−7080.00	−0.321292
$787$	−26588.0	−1.20427	−0.602135	−	0.798395i	$-0.705683\pi$
$787$	−26588.0	−1.20427	−0.602135	+	0.798395i	$0.705683\pi$
$788$	−3000.00	−0.135623
$789$	−17016.0	−0.767789
$790$	5600.00	0.252201
$791$	0	0
$792$	1152.00	0.0516850
$793$	−29812.0	−1.33500
$794$	−31284.0	−1.39827
$795$	9930.00	0.442995
$796$	−14928.0	−0.664710
$797$	−38862.0	−1.72718	−0.863590	−	0.504194i	$-0.831789\pi$
$797$	−38862.0	−1.72718	−0.863590	+	0.504194i	$0.831789\pi$
$798$	0	0
$799$	8160.00	0.361302
$800$	800.000	0.0353553
$801$	−13194.0	−0.582006
$802$	28996.0	1.27666
$803$	12320.0	0.541424
$804$	−4464.00	−0.195812
$805$	0	0
$806$	6960.00	0.304163
$807$	3006.00	0.131123
$808$	−10224.0	−0.445147
$809$	6610.00	0.287262	0.143631	−	0.989631i	$-0.454122\pi$
$809$	6610.00	0.287262	0.143631	+	0.989631i	$0.454122\pi$
$810$	−810.000	−0.0351364
$811$	−4696.00	−0.203328	−0.101664	−	0.994819i	$-0.532417\pi$
$811$	−4696.00	−0.203328	−0.101664	+	0.994819i	$0.532417\pi$
$812$	0	0
$813$	18420.0	0.794610
$814$	4800.00	0.206683
$815$	5900.00	0.253580
$816$	−1632.00	−0.0700140
$817$	18688.0	0.800257
$818$	27436.0	1.17271
$819$	0	0
$820$	9480.00	0.403727
$821$	−20362.0	−0.865577	−0.432788	−	0.901495i	$-0.642470\pi$
$821$	−20362.0	−0.865577	−0.432788	+	0.901495i	$0.642470\pi$
$822$	−4380.00	−0.185852
$823$	−9888.00	−0.418802	−0.209401	−	0.977830i	$-0.567151\pi$
$823$	−9888.00	−0.418802	−0.209401	+	0.977830i	$0.567151\pi$
$824$	2368.00	0.100113
$825$	1200.00	0.0506408
$826$	0	0
$827$	−19252.0	−0.809501	−0.404751	−	0.914427i	$-0.632642\pi$
$827$	−19252.0	−0.809501	−0.404751	+	0.914427i	$0.632642\pi$
$828$	−576.000	−0.0241756
$829$	12954.0	0.542715	0.271358	−	0.962479i	$-0.412527\pi$
$829$	12954.0	0.542715	0.271358	+	0.962479i	$0.412527\pi$
$830$	−8520.00	−0.356305
$831$	210.000	0.00876633
$832$	−3712.00	−0.154676
$833$	0	0
$834$	3984.00	0.165413
$835$	−6080.00	−0.251985
$836$	−4096.00	−0.169453
$837$	−1620.00	−0.0669001
$838$	20968.0	0.864353
$839$	−18784.0	−0.772939	−0.386469	−	0.922302i	$-0.626306\pi$
$839$	−18784.0	−0.772939	−0.386469	+	0.922302i	$0.626306\pi$
$840$	0	0
$841$	−20545.0	−0.842388
$842$	−17188.0	−0.703489
$843$	−9882.00	−0.403742
$844$	7920.00	0.323007
$845$	−5835.00	−0.237550
$846$	−4320.00	−0.175561
$847$	0	0
$848$	−10592.0	−0.428928
$849$	−5556.00	−0.224595
$850$	−1700.00	−0.0685994
$851$	−2400.00	−0.0966756
$852$	−4944.00	−0.198801
$853$	4958.00	0.199014	0.0995069	−	0.995037i	$-0.468273\pi$
$853$	4958.00	0.199014	0.0995069	+	0.995037i	$0.468273\pi$
$854$	0	0
$855$	2880.00	0.115198
$856$	9312.00	0.371820
$857$	15326.0	0.610882	0.305441	−	0.952211i	$-0.401196\pi$
$857$	15326.0	0.610882	0.305441	+	0.952211i	$0.401196\pi$
$858$	−5568.00	−0.221548
$859$	−49840.0	−1.97965	−0.989825	−	0.142292i	$-0.954553\pi$
$859$	−49840.0	−1.97965	−0.989825	+	0.142292i	$0.954553\pi$
$860$	5840.00	0.231561
$861$	0	0
$862$	−840.000	−0.0331909
$863$	13384.0	0.527922	0.263961	−	0.964533i	$-0.414971\pi$
$863$	13384.0	0.527922	0.263961	+	0.964533i	$0.414971\pi$
$864$	864.000	0.0340207
$865$	630.000	0.0247637
$866$	19588.0	0.768623
$867$	−11271.0	−0.441503
$868$	0	0
$869$	−8960.00	−0.349767
$870$	−1860.00	−0.0724827
$871$	21576.0	0.839351
$872$	−6224.00	−0.241710
$873$	1602.00	0.0621071
$874$	2048.00	0.0792616
$875$	0	0
$876$	9240.00	0.356382
$877$	5006.00	0.192749	0.0963743	−	0.995345i	$-0.469275\pi$
$877$	5006.00	0.192749	0.0963743	+	0.995345i	$0.469275\pi$
$878$	2872.00	0.110393
$879$	15390.0	0.590548
$880$	−1280.00	−0.0490327
$881$	−14098.0	−0.539130	−0.269565	−	0.962982i	$-0.586880\pi$
$881$	−14098.0	−0.539130	−0.269565	+	0.962982i	$0.586880\pi$
$882$	0	0
$883$	13580.0	0.517558	0.258779	−	0.965937i	$-0.416680\pi$
$883$	13580.0	0.517558	0.258779	+	0.965937i	$0.416680\pi$
$884$	7888.00	0.300116
$885$	−4860.00	−0.184596
$886$	24456.0	0.927331
$887$	14648.0	0.554489	0.277244	−	0.960799i	$-0.410579\pi$
$887$	14648.0	0.554489	0.277244	+	0.960799i	$0.410579\pi$
$888$	3600.00	0.136045
$889$	0	0
$890$	14660.0	0.552140
$891$	1296.00	0.0487291
$892$	25312.0	0.950122
$893$	15360.0	0.575591
$894$	17844.0	0.667553
$895$	−4360.00	−0.162837
$896$	0	0
$897$	2784.00	0.103629
$898$	−13468.0	−0.500482
$899$	−3720.00	−0.138008
$900$	900.000	0.0333333
$901$	22508.0	0.832242
$902$	−15168.0	−0.559910
$903$	0	0
$904$	−336.000	−0.0123619
$905$	−90.0000	−0.00330575
$906$	−16608.0	−0.609011
$907$	−17996.0	−0.658817	−0.329409	−	0.944187i	$-0.606849\pi$
$907$	−17996.0	−0.658817	−0.329409	+	0.944187i	$0.606849\pi$
$908$	10384.0	0.379521
$909$	−11502.0	−0.419689
$910$	0	0
$911$	−41420.0	−1.50637	−0.753187	−	0.657807i	$-0.771484\pi$
$911$	−41420.0	−1.50637	−0.753187	+	0.657807i	$0.771484\pi$
$912$	−3072.00	−0.111540
$913$	13632.0	0.494144
$914$	21380.0	0.773728
$915$	−7710.00	−0.278563
$916$	−18968.0	−0.684193
$917$	0	0
$918$	−1836.00	−0.0660098
$919$	33640.0	1.20749	0.603744	−	0.797178i	$-0.293675\pi$
$919$	33640.0	1.20749	0.603744	+	0.797178i	$0.293675\pi$
$920$	640.000	0.0229350
$921$	−2868.00	−0.102610
$922$	−29804.0	−1.06458
$923$	23896.0	0.852163
$924$	0	0
$925$	3750.00	0.133296
$926$	34128.0	1.21114
$927$	2664.00	0.0943875
$928$	1984.00	0.0701810
$929$	37918.0	1.33913	0.669564	−	0.742755i	$-0.266481\pi$
$929$	37918.0	1.33913	0.669564	+	0.742755i	$0.266481\pi$
$930$	1800.00	0.0634670
$931$	0	0
$932$	5176.00	0.181916
$933$	10344.0	0.362966
$934$	−6072.00	−0.212722
$935$	2720.00	0.0951374
$936$	−4176.00	−0.145830
$937$	5954.00	0.207587	0.103793	−	0.994599i	$-0.466902\pi$
$937$	5954.00	0.207587	0.103793	+	0.994599i	$0.466902\pi$
$938$	0	0
$939$	17550.0	0.609928
$940$	4800.00	0.166552
$941$	33066.0	1.14551	0.572753	−	0.819728i	$-0.305875\pi$
$941$	33066.0	1.14551	0.572753	+	0.819728i	$0.305875\pi$
$942$	−11340.0	−0.392226
$943$	7584.00	0.261897
$944$	5184.00	0.178734
$945$	0	0
$946$	−9344.00	−0.321141
$947$	28508.0	0.978232	0.489116	−	0.872219i	$-0.337320\pi$
$947$	28508.0	0.978232	0.489116	+	0.872219i	$0.337320\pi$
$948$	−6720.00	−0.230227
$949$	−44660.0	−1.52763
$950$	−3200.00	−0.109286
$951$	11382.0	0.388104
$952$	0	0
$953$	24718.0	0.840183	0.420092	−	0.907482i	$-0.361998\pi$
$953$	24718.0	0.840183	0.420092	+	0.907482i	$0.361998\pi$
$954$	−11916.0	−0.404397
$955$	−22100.0	−0.748837
$956$	−9360.00	−0.316657
$957$	2976.00	0.100523
$958$	27328.0	0.921636
$959$	0	0
$960$	−960.000	−0.0322749
$961$	−26191.0	−0.879158
$962$	−17400.0	−0.583159
$963$	10476.0	0.350555
$964$	−23848.0	−0.796776
$965$	11270.0	0.375952
$966$	0	0
$967$	−52424.0	−1.74337	−0.871687	−	0.490063i	$-0.836974\pi$
$967$	−52424.0	−1.74337	−0.871687	+	0.490063i	$0.836974\pi$
$968$	−8600.00	−0.285552
$969$	6528.00	0.216419
$970$	−1780.00	−0.0589200
$971$	−10988.0	−0.363153	−0.181577	−	0.983377i	$-0.558120\pi$
$971$	−10988.0	−0.363153	−0.181577	+	0.983377i	$0.558120\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	−23488.0	−0.772694
$975$	−4350.00	−0.142884
$976$	8224.00	0.269717
$977$	31446.0	1.02973	0.514865	−	0.857271i	$-0.327842\pi$
$977$	31446.0	1.02973	0.514865	+	0.857271i	$0.327842\pi$
$978$	−7080.00	−0.231486
$979$	−23456.0	−0.765737
$980$	0	0
$981$	−7002.00	−0.227886
$982$	−96.0000	−0.00311964
$983$	−33528.0	−1.08787	−0.543935	−	0.839127i	$-0.683066\pi$
$983$	−33528.0	−1.08787	−0.543935	+	0.839127i	$0.683066\pi$
$984$	−11376.0	−0.368550
$985$	3750.00	0.121305
$986$	−4216.00	−0.136171
$987$	0	0
$988$	14848.0	0.478115
$989$	4672.00	0.150213
$990$	−1440.00	−0.0462285
$991$	−49856.0	−1.59811	−0.799056	−	0.601257i	$-0.794667\pi$
$991$	−49856.0	−1.59811	−0.799056	+	0.601257i	$0.794667\pi$
$992$	−1920.00	−0.0614517
$993$	12348.0	0.394614
$994$	0	0
$995$	18660.0	0.594534
$996$	10224.0	0.325261
$997$	−9298.00	−0.295357	−0.147678	−	0.989035i	$-0.547180\pi$
$997$	−9298.00	−0.295357	−0.147678	+	0.989035i	$0.547180\pi$
$998$	2088.00	0.0662269
$999$	4050.00	0.128265

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.i.1.1	✓	1	7.6	odd	2
630.4.a.a.1.1		1	21.20	even	2
1050.4.a.l.1.1		1	35.34	odd	2
1050.4.g.f.799.1		2	35.13	even	4
1050.4.g.f.799.2		2	35.27	even	4
1470.4.a.z.1.1		1	1.1	even	1	trivial
1680.4.a.w.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

Related objects

Downloads

Learn more