LMFDB - Embedded newform 1470.4.a.d.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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +28.0000 q^{11} -12.0000 q^{12} -54.0000 q^{13} +15.0000 q^{15} +16.0000 q^{16} +46.0000 q^{17} -18.0000 q^{18} -12.0000 q^{19} -20.0000 q^{20} -56.0000 q^{22} +24.0000 q^{24} +25.0000 q^{25} +108.000 q^{26} -27.0000 q^{27} +6.00000 q^{29} -30.0000 q^{30} -296.000 q^{31} -32.0000 q^{32} -84.0000 q^{33} -92.0000 q^{34} +36.0000 q^{36} +134.000 q^{37} +24.0000 q^{38} +162.000 q^{39} +40.0000 q^{40} -146.000 q^{41} +556.000 q^{43} +112.000 q^{44} -45.0000 q^{45} +448.000 q^{47} -48.0000 q^{48} -50.0000 q^{50} -138.000 q^{51} -216.000 q^{52} +46.0000 q^{53} +54.0000 q^{54} -140.000 q^{55} +36.0000 q^{57} -12.0000 q^{58} -748.000 q^{59} +60.0000 q^{60} +50.0000 q^{61} +592.000 q^{62} +64.0000 q^{64} +270.000 q^{65} +168.000 q^{66} -156.000 q^{67} +184.000 q^{68} -1024.00 q^{71} -72.0000 q^{72} +310.000 q^{73} -268.000 q^{74} -75.0000 q^{75} -48.0000 q^{76} -324.000 q^{78} +856.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +292.000 q^{82} +628.000 q^{83} -230.000 q^{85} -1112.00 q^{86} -18.0000 q^{87} -224.000 q^{88} +590.000 q^{89} +90.0000 q^{90} +888.000 q^{93} -896.000 q^{94} +60.0000 q^{95} +96.0000 q^{96} +1390.00 q^{97} +252.000 q^{99} +O(q^{100})\)

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
$11$	28.0000	0.767483	0.383742	−	0.923440i	$-0.374635\pi$
$11$	28.0000	0.767483	0.383742	+	0.923440i	$0.374635\pi$
$12$	−12.0000	−0.288675
$13$	−54.0000	−1.15207	−0.576035	−	0.817425i	$-0.695401\pi$
$13$	−54.0000	−1.15207	−0.576035	+	0.817425i	$0.695401\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	46.0000	0.656273	0.328136	−	0.944630i	$-0.393579\pi$
$17$	46.0000	0.656273	0.328136	+	0.944630i	$0.393579\pi$
$18$	−18.0000	−0.235702
$19$	−12.0000	−0.144894	−0.0724471	−	0.997372i	$-0.523081\pi$
$19$	−12.0000	−0.144894	−0.0724471	+	0.997372i	$0.523081\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−56.0000	−0.542693
$23$	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
$26$	108.000	0.814636
$27$	−27.0000	−0.192450
$28$	0	0
$29$	6.00000	0.0384197	0.0192099	−	0.999815i	$-0.493885\pi$
$29$	6.00000	0.0384197	0.0192099	+	0.999815i	$0.493885\pi$
$30$	−30.0000	−0.182574
$31$	−296.000	−1.71494	−0.857470	−	0.514533i	$-0.827965\pi$
$31$	−296.000	−1.71494	−0.857470	+	0.514533i	$0.827965\pi$
$32$	−32.0000	−0.176777
$33$	−84.0000	−0.443107
$34$	−92.0000	−0.464055
$35$	0	0
$36$	36.0000	0.166667
$37$	134.000	0.595391	0.297695	−	0.954661i	$-0.403782\pi$
$37$	134.000	0.595391	0.297695	+	0.954661i	$0.403782\pi$
$38$	24.0000	0.102456
$39$	162.000	0.665148
$40$	40.0000	0.158114
$41$	−146.000	−0.556131	−0.278065	−	0.960562i	$-0.589693\pi$
$41$	−146.000	−0.556131	−0.278065	+	0.960562i	$0.589693\pi$
$42$	0	0
$43$	556.000	1.97184	0.985921	−	0.167212i	$-0.0534764\pi$
$43$	556.000	1.97184	0.985921	+	0.167212i	$0.0534764\pi$
$44$	112.000	0.383742
$45$	−45.0000	−0.149071
$46$	0	0
$47$	448.000	1.39037	0.695186	−	0.718830i	$-0.255322\pi$
$47$	448.000	1.39037	0.695186	+	0.718830i	$0.255322\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	−138.000	−0.378899
$52$	−216.000	−0.576035
$53$	46.0000	0.119219	0.0596093	−	0.998222i	$-0.481015\pi$
$53$	46.0000	0.119219	0.0596093	+	0.998222i	$0.481015\pi$
$54$	54.0000	0.136083
$55$	−140.000	−0.343229
$56$	0	0
$57$	36.0000	0.0836547
$58$	−12.0000	−0.0271668
$59$	−748.000	−1.65053	−0.825265	−	0.564745i	$-0.808974\pi$
$59$	−748.000	−1.65053	−0.825265	+	0.564745i	$0.808974\pi$
$60$	60.0000	0.129099
$61$	50.0000	0.104948	0.0524741	−	0.998622i	$-0.483289\pi$
$61$	50.0000	0.104948	0.0524741	+	0.998622i	$0.483289\pi$
$62$	592.000	1.21265
$63$	0	0
$64$	64.0000	0.125000
$65$	270.000	0.515221
$66$	168.000	0.313324
$67$	−156.000	−0.284454	−0.142227	−	0.989834i	$-0.545426\pi$
$67$	−156.000	−0.284454	−0.142227	+	0.989834i	$0.545426\pi$
$68$	184.000	0.328136
$69$	0	0
$70$	0	0
$71$	−1024.00	−1.71164	−0.855820	−	0.517274i	$-0.826947\pi$
$71$	−1024.00	−1.71164	−0.855820	+	0.517274i	$0.826947\pi$
$72$	−72.0000	−0.117851
$73$	310.000	0.497024	0.248512	−	0.968629i	$-0.420058\pi$
$73$	310.000	0.497024	0.248512	+	0.968629i	$0.420058\pi$
$74$	−268.000	−0.421005
$75$	−75.0000	−0.115470
$76$	−48.0000	−0.0724471
$77$	0	0
$78$	−324.000	−0.470330
$79$	856.000	1.21908	0.609541	−	0.792754i	$-0.291354\pi$
$79$	856.000	1.21908	0.609541	+	0.792754i	$0.291354\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	292.000	0.393244
$83$	628.000	0.830505	0.415253	−	0.909706i	$-0.363693\pi$
$83$	628.000	0.830505	0.415253	+	0.909706i	$0.363693\pi$
$84$	0	0
$85$	−230.000	−0.293494
$86$	−1112.00	−1.39430
$87$	−18.0000	−0.0221816
$88$	−224.000	−0.271346
$89$	590.000	0.702695	0.351348	−	0.936245i	$-0.385724\pi$
$89$	590.000	0.702695	0.351348	+	0.936245i	$0.385724\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	0	0
$93$	888.000	0.990122
$94$	−896.000	−0.983142
$95$	60.0000	0.0647986
$96$	96.0000	0.102062
$97$	1390.00	1.45498	0.727490	−	0.686118i	$-0.240687\pi$
$97$	1390.00	1.45498	0.727490	+	0.686118i	$0.240687\pi$
$98$	0	0
$99$	252.000	0.255828
$100$	100.000	0.100000
$101$	−270.000	−0.266000	−0.133000	−	0.991116i	$-0.542461\pi$
$101$	−270.000	−0.266000	−0.133000	+	0.991116i	$0.542461\pi$
$102$	276.000	0.267922
$103$	1640.00	1.56887	0.784437	−	0.620209i	$-0.212952\pi$
$103$	1640.00	1.56887	0.784437	+	0.620209i	$0.212952\pi$
$104$	432.000	0.407318
$105$	0	0
$106$	−92.0000	−0.0843003
$107$	−396.000	−0.357783	−0.178891	−	0.983869i	$-0.557251\pi$
$107$	−396.000	−0.357783	−0.178891	+	0.983869i	$0.557251\pi$
$108$	−108.000	−0.0962250
$109$	966.000	0.848863	0.424431	−	0.905460i	$-0.360474\pi$
$109$	966.000	0.848863	0.424431	+	0.905460i	$0.360474\pi$
$110$	280.000	0.242700
$111$	−402.000	−0.343749
$112$	0	0
$113$	−2038.00	−1.69663	−0.848314	−	0.529494i	$-0.822382\pi$
$113$	−2038.00	−1.69663	−0.848314	+	0.529494i	$0.822382\pi$
$114$	−72.0000	−0.0591528
$115$	0	0
$116$	24.0000	0.0192099
$117$	−486.000	−0.384023
$118$	1496.00	1.16710
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−547.000	−0.410969
$122$	−100.000	−0.0742096
$123$	438.000	0.321082
$124$	−1184.00	−0.857470
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−944.000	−0.659578	−0.329789	−	0.944055i	$-0.606978\pi$
$127$	−944.000	−0.659578	−0.329789	+	0.944055i	$0.606978\pi$
$128$	−128.000	−0.0883883
$129$	−1668.00	−1.13844
$130$	−540.000	−0.364316
$131$	−500.000	−0.333475	−0.166737	−	0.986001i	$-0.553323\pi$
$131$	−500.000	−0.333475	−0.166737	+	0.986001i	$0.553323\pi$
$132$	−336.000	−0.221553
$133$	0	0
$134$	312.000	0.201140
$135$	135.000	0.0860663
$136$	−368.000	−0.232027
$137$	−942.000	−0.587449	−0.293724	−	0.955890i	$-0.594895\pi$
$137$	−942.000	−0.587449	−0.293724	+	0.955890i	$0.594895\pi$
$138$	0	0
$139$	−772.000	−0.471080	−0.235540	−	0.971865i	$-0.575686\pi$
$139$	−772.000	−0.471080	−0.235540	+	0.971865i	$0.575686\pi$
$140$	0	0
$141$	−1344.00	−0.802732
$142$	2048.00	1.21031
$143$	−1512.00	−0.884194
$144$	144.000	0.0833333
$145$	−30.0000	−0.0171818
$146$	−620.000	−0.351449
$147$	0	0
$148$	536.000	0.297695
$149$	558.000	0.306800	0.153400	−	0.988164i	$-0.450978\pi$
$149$	558.000	0.306800	0.153400	+	0.988164i	$0.450978\pi$
$150$	150.000	0.0816497
$151$	368.000	0.198327	0.0991636	−	0.995071i	$-0.468383\pi$
$151$	368.000	0.198327	0.0991636	+	0.995071i	$0.468383\pi$
$152$	96.0000	0.0512278
$153$	414.000	0.218758
$154$	0	0
$155$	1480.00	0.766945
$156$	648.000	0.332574
$157$	−550.000	−0.279585	−0.139792	−	0.990181i	$-0.544643\pi$
$157$	−550.000	−0.279585	−0.139792	+	0.990181i	$0.544643\pi$
$158$	−1712.00	−0.862022
$159$	−138.000	−0.0688309
$160$	160.000	0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	740.000	0.355591	0.177795	−	0.984067i	$-0.443104\pi$
$163$	740.000	0.355591	0.177795	+	0.984067i	$0.443104\pi$
$164$	−584.000	−0.278065
$165$	420.000	0.198163
$166$	−1256.00	−0.587256
$167$	−1176.00	−0.544920	−0.272460	−	0.962167i	$-0.587837\pi$
$167$	−1176.00	−0.544920	−0.272460	+	0.962167i	$0.587837\pi$
$168$	0	0
$169$	719.000	0.327264
$170$	460.000	0.207532
$171$	−108.000	−0.0482980
$172$	2224.00	0.985921
$173$	−758.000	−0.333119	−0.166560	−	0.986031i	$-0.553266\pi$
$173$	−758.000	−0.333119	−0.166560	+	0.986031i	$0.553266\pi$
$174$	36.0000	0.0156848
$175$	0	0
$176$	448.000	0.191871
$177$	2244.00	0.952934
$178$	−1180.00	−0.496881
$179$	−2028.00	−0.846815	−0.423407	−	0.905939i	$-0.639166\pi$
$179$	−2028.00	−0.846815	−0.423407	+	0.905939i	$0.639166\pi$
$180$	−180.000	−0.0745356
$181$	3098.00	1.27222	0.636112	−	0.771597i	$-0.280542\pi$
$181$	3098.00	1.27222	0.636112	+	0.771597i	$0.280542\pi$
$182$	0	0
$183$	−150.000	−0.0605919
$184$	0	0
$185$	−670.000	−0.266267
$186$	−1776.00	−0.700122
$187$	1288.00	0.503679
$188$	1792.00	0.695186
$189$	0	0
$190$	−120.000	−0.0458196
$191$	1704.00	0.645535	0.322767	−	0.946478i	$-0.395387\pi$
$191$	1704.00	0.645535	0.322767	+	0.946478i	$0.395387\pi$
$192$	−192.000	−0.0721688
$193$	−3310.00	−1.23450	−0.617251	−	0.786766i	$-0.711754\pi$
$193$	−3310.00	−1.23450	−0.617251	+	0.786766i	$0.711754\pi$
$194$	−2780.00	−1.02883
$195$	−810.000	−0.297463
$196$	0	0
$197$	−1858.00	−0.671965	−0.335982	−	0.941868i	$-0.609068\pi$
$197$	−1858.00	−0.671965	−0.335982	+	0.941868i	$0.609068\pi$
$198$	−504.000	−0.180898
$199$	−4736.00	−1.68707	−0.843533	−	0.537077i	$-0.819528\pi$
$199$	−4736.00	−1.68707	−0.843533	+	0.537077i	$0.819528\pi$
$200$	−200.000	−0.0707107
$201$	468.000	0.164230
$202$	540.000	0.188090
$203$	0	0
$204$	−552.000	−0.189450
$205$	730.000	0.248709
$206$	−3280.00	−1.10936
$207$	0	0
$208$	−864.000	−0.288017
$209$	−336.000	−0.111204
$210$	0	0
$211$	−3308.00	−1.07930	−0.539650	−	0.841890i	$-0.681443\pi$
$211$	−3308.00	−1.07930	−0.539650	+	0.841890i	$0.681443\pi$
$212$	184.000	0.0596093
$213$	3072.00	0.988216
$214$	792.000	0.252991
$215$	−2780.00	−0.881835
$216$	216.000	0.0680414
$217$	0	0
$218$	−1932.00	−0.600236
$219$	−930.000	−0.286957
$220$	−560.000	−0.171615
$221$	−2484.00	−0.756072
$222$	804.000	0.243067
$223$	2192.00	0.658238	0.329119	−	0.944288i	$-0.393248\pi$
$223$	2192.00	0.658238	0.329119	+	0.944288i	$0.393248\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	4076.00	1.19970
$227$	−4796.00	−1.40230	−0.701149	−	0.713015i	$-0.747329\pi$
$227$	−4796.00	−1.40230	−0.701149	+	0.713015i	$0.747329\pi$
$228$	144.000	0.0418273
$229$	1946.00	0.561552	0.280776	−	0.959773i	$-0.409408\pi$
$229$	1946.00	0.561552	0.280776	+	0.959773i	$0.409408\pi$
$230$	0	0
$231$	0	0
$232$	−48.0000	−0.0135834
$233$	−1998.00	−0.561774	−0.280887	−	0.959741i	$-0.590629\pi$
$233$	−1998.00	−0.561774	−0.280887	+	0.959741i	$0.590629\pi$
$234$	972.000	0.271545
$235$	−2240.00	−0.621794
$236$	−2992.00	−0.825265
$237$	−2568.00	−0.703838
$238$	0	0
$239$	−3848.00	−1.04145	−0.520725	−	0.853725i	$-0.674338\pi$
$239$	−3848.00	−1.04145	−0.520725	+	0.853725i	$0.674338\pi$
$240$	240.000	0.0645497
$241$	4430.00	1.18407	0.592036	−	0.805911i	$-0.298324\pi$
$241$	4430.00	1.18407	0.592036	+	0.805911i	$0.298324\pi$
$242$	1094.00	0.290599
$243$	−243.000	−0.0641500
$244$	200.000	0.0524741
$245$	0	0
$246$	−876.000	−0.227040
$247$	648.000	0.166928
$248$	2368.00	0.606323
$249$	−1884.00	−0.479493
$250$	250.000	0.0632456
$251$	−4380.00	−1.10145	−0.550723	−	0.834688i	$-0.685648\pi$
$251$	−4380.00	−1.10145	−0.550723	+	0.834688i	$0.685648\pi$
$252$	0	0
$253$	0	0
$254$	1888.00	0.466392
$255$	690.000	0.169449
$256$	256.000	0.0625000
$257$	2110.00	0.512133	0.256067	−	0.966659i	$-0.417573\pi$
$257$	2110.00	0.512133	0.256067	+	0.966659i	$0.417573\pi$
$258$	3336.00	0.805001
$259$	0	0
$260$	1080.00	0.257611
$261$	54.0000	0.0128066
$262$	1000.00	0.235802
$263$	6512.00	1.52680	0.763398	−	0.645929i	$-0.223530\pi$
$263$	6512.00	1.52680	0.763398	+	0.645929i	$0.223530\pi$
$264$	672.000	0.156662
$265$	−230.000	−0.0533162
$266$	0	0
$267$	−1770.00	−0.405701
$268$	−624.000	−0.142227
$269$	−2886.00	−0.654136	−0.327068	−	0.945001i	$-0.606061\pi$
$269$	−2886.00	−0.654136	−0.327068	+	0.945001i	$0.606061\pi$
$270$	−270.000	−0.0608581
$271$	−3432.00	−0.769296	−0.384648	−	0.923063i	$-0.625677\pi$
$271$	−3432.00	−0.769296	−0.384648	+	0.923063i	$0.625677\pi$
$272$	736.000	0.164068
$273$	0	0
$274$	1884.00	0.415389
$275$	700.000	0.153497
$276$	0	0
$277$	−5514.00	−1.19604	−0.598022	−	0.801480i	$-0.704046\pi$
$277$	−5514.00	−1.19604	−0.598022	+	0.801480i	$0.704046\pi$
$278$	1544.00	0.333104
$279$	−2664.00	−0.571647
$280$	0	0
$281$	−3958.00	−0.840265	−0.420133	−	0.907463i	$-0.638016\pi$
$281$	−3958.00	−0.840265	−0.420133	+	0.907463i	$0.638016\pi$
$282$	2688.00	0.567617
$283$	−8948.00	−1.87952	−0.939759	−	0.341839i	$-0.888950\pi$
$283$	−8948.00	−1.87952	−0.939759	+	0.341839i	$0.888950\pi$
$284$	−4096.00	−0.855820
$285$	−180.000	−0.0374115
$286$	3024.00	0.625220
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−2797.00	−0.569306
$290$	60.0000	0.0121494
$291$	−4170.00	−0.840033
$292$	1240.00	0.248512
$293$	2.00000	0.000398776 0	0.000199388	−	1.00000i	$-0.499937\pi$
$293$	2.00000	0.000398776 0	0.000199388		1.00000i	$0.499937\pi$
$294$	0	0
$295$	3740.00	0.738140
$296$	−1072.00	−0.210502
$297$	−756.000	−0.147702
$298$	−1116.00	−0.216940
$299$	0	0
$300$	−300.000	−0.0577350
$301$	0	0
$302$	−736.000	−0.140239
$303$	810.000	0.153575
$304$	−192.000	−0.0362235
$305$	−250.000	−0.0469343
$306$	−828.000	−0.154685
$307$	−5884.00	−1.09387	−0.546934	−	0.837176i	$-0.684205\pi$
$307$	−5884.00	−1.09387	−0.546934	+	0.837176i	$0.684205\pi$
$308$	0	0
$309$	−4920.00	−0.905790
$310$	−2960.00	−0.542312
$311$	1608.00	0.293188	0.146594	−	0.989197i	$-0.453169\pi$
$311$	1608.00	0.293188	0.146594	+	0.989197i	$0.453169\pi$
$312$	−1296.00	−0.235165
$313$	−3290.00	−0.594127	−0.297064	−	0.954858i	$-0.596007\pi$
$313$	−3290.00	−0.594127	−0.297064	+	0.954858i	$0.596007\pi$
$314$	1100.00	0.197696
$315$	0	0
$316$	3424.00	0.609541
$317$	2374.00	0.420622	0.210311	−	0.977635i	$-0.432552\pi$
$317$	2374.00	0.420622	0.210311	+	0.977635i	$0.432552\pi$
$318$	276.000	0.0486708
$319$	168.000	0.0294865
$320$	−320.000	−0.0559017
$321$	1188.00	0.206566
$322$	0	0
$323$	−552.000	−0.0950901
$324$	324.000	0.0555556
$325$	−1350.00	−0.230414
$326$	−1480.00	−0.251441
$327$	−2898.00	−0.490091
$328$	1168.00	0.196622
$329$	0	0
$330$	−840.000	−0.140123
$331$	−4340.00	−0.720689	−0.360344	−	0.932819i	$-0.617341\pi$
$331$	−4340.00	−0.720689	−0.360344	+	0.932819i	$0.617341\pi$
$332$	2512.00	0.415253
$333$	1206.00	0.198464
$334$	2352.00	0.385317
$335$	780.000	0.127212
$336$	0	0
$337$	−9854.00	−1.59282	−0.796412	−	0.604755i	$-0.793271\pi$
$337$	−9854.00	−1.59282	−0.796412	+	0.604755i	$0.793271\pi$
$338$	−1438.00	−0.231411
$339$	6114.00	0.979548
$340$	−920.000	−0.146747
$341$	−8288.00	−1.31619
$342$	216.000	0.0341519
$343$	0	0
$344$	−4448.00	−0.697151
$345$	0	0
$346$	1516.00	0.235551
$347$	3172.00	0.490726	0.245363	−	0.969431i	$-0.421093\pi$
$347$	3172.00	0.490726	0.245363	+	0.969431i	$0.421093\pi$
$348$	−72.0000	−0.0110908
$349$	−9502.00	−1.45739	−0.728697	−	0.684836i	$-0.759874\pi$
$349$	−9502.00	−1.45739	−0.728697	+	0.684836i	$0.759874\pi$
$350$	0	0
$351$	1458.00	0.221716
$352$	−896.000	−0.135673
$353$	−11490.0	−1.73244	−0.866220	−	0.499664i	$-0.833457\pi$
$353$	−11490.0	−1.73244	−0.866220	+	0.499664i	$0.833457\pi$
$354$	−4488.00	−0.673826
$355$	5120.00	0.765469
$356$	2360.00	0.351348
$357$	0	0
$358$	4056.00	0.598788
$359$	−12064.0	−1.77358	−0.886788	−	0.462177i	$-0.847068\pi$
$359$	−12064.0	−1.77358	−0.886788	+	0.462177i	$0.847068\pi$
$360$	360.000	0.0527046
$361$	−6715.00	−0.979006
$362$	−6196.00	−0.899598
$363$	1641.00	0.237273
$364$	0	0
$365$	−1550.00	−0.222276
$366$	300.000	0.0428449
$367$	3056.00	0.434665	0.217332	−	0.976098i	$-0.430264\pi$
$367$	3056.00	0.434665	0.217332	+	0.976098i	$0.430264\pi$
$368$	0	0
$369$	−1314.00	−0.185377
$370$	1340.00	0.188279
$371$	0	0
$372$	3552.00	0.495061
$373$	−1258.00	−0.174629	−0.0873147	−	0.996181i	$-0.527829\pi$
$373$	−1258.00	−0.174629	−0.0873147	+	0.996181i	$0.527829\pi$
$374$	−2576.00	−0.356155
$375$	375.000	0.0516398
$376$	−3584.00	−0.491571
$377$	−324.000	−0.0442622
$378$	0	0
$379$	8508.00	1.15310	0.576552	−	0.817060i	$-0.304398\pi$
$379$	8508.00	1.15310	0.576552	+	0.817060i	$0.304398\pi$
$380$	240.000	0.0323993
$381$	2832.00	0.380808
$382$	−3408.00	−0.456462
$383$	−9360.00	−1.24876	−0.624378	−	0.781122i	$-0.714648\pi$
$383$	−9360.00	−1.24876	−0.624378	+	0.781122i	$0.714648\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	6620.00	0.872925
$387$	5004.00	0.657281
$388$	5560.00	0.727490
$389$	1214.00	0.158232	0.0791160	−	0.996865i	$-0.474790\pi$
$389$	1214.00	0.158232	0.0791160	+	0.996865i	$0.474790\pi$
$390$	1620.00	0.210338
$391$	0	0
$392$	0	0
$393$	1500.00	0.192532
$394$	3716.00	0.475151
$395$	−4280.00	−0.545190
$396$	1008.00	0.127914
$397$	11834.0	1.49605	0.748024	−	0.663671i	$-0.231003\pi$
$397$	11834.0	1.49605	0.748024	+	0.663671i	$0.231003\pi$
$398$	9472.00	1.19294
$399$	0	0
$400$	400.000	0.0500000
$401$	−8222.00	−1.02391	−0.511954	−	0.859013i	$-0.671078\pi$
$401$	−8222.00	−1.02391	−0.511954	+	0.859013i	$0.671078\pi$
$402$	−936.000	−0.116128
$403$	15984.0	1.97573
$404$	−1080.00	−0.133000
$405$	−405.000	−0.0496904
$406$	0	0
$407$	3752.00	0.456953
$408$	1104.00	0.133961
$409$	−7050.00	−0.852323	−0.426161	−	0.904647i	$-0.640134\pi$
$409$	−7050.00	−0.852323	−0.426161	+	0.904647i	$0.640134\pi$
$410$	−1460.00	−0.175864
$411$	2826.00	0.339164
$412$	6560.00	0.784437
$413$	0	0
$414$	0	0
$415$	−3140.00	−0.371413
$416$	1728.00	0.203659
$417$	2316.00	0.271978
$418$	672.000	0.0786330
$419$	15612.0	1.82028	0.910139	−	0.414304i	$-0.135975\pi$
$419$	15612.0	1.82028	0.910139	+	0.414304i	$0.135975\pi$
$420$	0	0
$421$	4910.00	0.568406	0.284203	−	0.958764i	$-0.408271\pi$
$421$	4910.00	0.568406	0.284203	+	0.958764i	$0.408271\pi$
$422$	6616.00	0.763180
$423$	4032.00	0.463458
$424$	−368.000	−0.0421501
$425$	1150.00	0.131255
$426$	−6144.00	−0.698774
$427$	0	0
$428$	−1584.00	−0.178891
$429$	4536.00	0.510490
$430$	5560.00	0.623551
$431$	13224.0	1.47791	0.738953	−	0.673757i	$-0.235320\pi$
$431$	13224.0	1.47791	0.738953	+	0.673757i	$0.235320\pi$
$432$	−432.000	−0.0481125
$433$	−11042.0	−1.22551	−0.612754	−	0.790274i	$-0.709938\pi$
$433$	−11042.0	−1.22551	−0.612754	+	0.790274i	$0.709938\pi$
$434$	0	0
$435$	90.0000	0.00991993
$436$	3864.00	0.424431
$437$	0	0
$438$	1860.00	0.202909
$439$	7616.00	0.828000	0.414000	−	0.910277i	$-0.364131\pi$
$439$	7616.00	0.828000	0.414000	+	0.910277i	$0.364131\pi$
$440$	1120.00	0.121350
$441$	0	0
$442$	4968.00	0.534624
$443$	−5708.00	−0.612179	−0.306089	−	0.952003i	$-0.599021\pi$
$443$	−5708.00	−0.612179	−0.306089	+	0.952003i	$0.599021\pi$
$444$	−1608.00	−0.171875
$445$	−2950.00	−0.314255
$446$	−4384.00	−0.465445
$447$	−1674.00	−0.177131
$448$	0	0
$449$	−990.000	−0.104056	−0.0520278	−	0.998646i	$-0.516568\pi$
$449$	−990.000	−0.104056	−0.0520278	+	0.998646i	$0.516568\pi$
$450$	−450.000	−0.0471405
$451$	−4088.00	−0.426821
$452$	−8152.00	−0.848314
$453$	−1104.00	−0.114504
$454$	9592.00	0.991575
$455$	0	0
$456$	−288.000	−0.0295764
$457$	−5414.00	−0.554171	−0.277086	−	0.960845i	$-0.589369\pi$
$457$	−5414.00	−0.554171	−0.277086	+	0.960845i	$0.589369\pi$
$458$	−3892.00	−0.397077
$459$	−1242.00	−0.126300
$460$	0	0
$461$	−11638.0	−1.17578	−0.587891	−	0.808940i	$-0.700042\pi$
$461$	−11638.0	−1.17578	−0.587891	+	0.808940i	$0.700042\pi$
$462$	0	0
$463$	19616.0	1.96897	0.984485	−	0.175470i	$-0.0561446\pi$
$463$	19616.0	1.96897	0.984485	+	0.175470i	$0.0561446\pi$
$464$	96.0000	0.00960493
$465$	−4440.00	−0.442796
$466$	3996.00	0.397234
$467$	−9788.00	−0.969881	−0.484941	−	0.874547i	$-0.661159\pi$
$467$	−9788.00	−0.969881	−0.484941	+	0.874547i	$0.661159\pi$
$468$	−1944.00	−0.192012
$469$	0	0
$470$	4480.00	0.439674
$471$	1650.00	0.161418
$472$	5984.00	0.583551
$473$	15568.0	1.51336
$474$	5136.00	0.497688
$475$	−300.000	−0.0289788
$476$	0	0
$477$	414.000	0.0397395
$478$	7696.00	0.736416
$479$	2688.00	0.256405	0.128202	−	0.991748i	$-0.459079\pi$
$479$	2688.00	0.256405	0.128202	+	0.991748i	$0.459079\pi$
$480$	−480.000	−0.0456435
$481$	−7236.00	−0.685932
$482$	−8860.00	−0.837265
$483$	0	0
$484$	−2188.00	−0.205485
$485$	−6950.00	−0.650687
$486$	486.000	0.0453609
$487$	7688.00	0.715352	0.357676	−	0.933846i	$-0.383569\pi$
$487$	7688.00	0.715352	0.357676	+	0.933846i	$0.383569\pi$
$488$	−400.000	−0.0371048
$489$	−2220.00	−0.205300
$490$	0	0
$491$	−14532.0	−1.33568	−0.667841	−	0.744304i	$-0.732781\pi$
$491$	−14532.0	−1.33568	−0.667841	+	0.744304i	$0.732781\pi$
$492$	1752.00	0.160541
$493$	276.000	0.0252138
$494$	−1296.00	−0.118036
$495$	−1260.00	−0.114410
$496$	−4736.00	−0.428735
$497$	0	0
$498$	3768.00	0.339052
$499$	1188.00	0.106578	0.0532888	−	0.998579i	$-0.483030\pi$
$499$	1188.00	0.106578	0.0532888	+	0.998579i	$0.483030\pi$
$500$	−500.000	−0.0447214
$501$	3528.00	0.314610
$502$	8760.00	0.778841
$503$	6552.00	0.580794	0.290397	−	0.956906i	$-0.406213\pi$
$503$	6552.00	0.580794	0.290397	+	0.956906i	$0.406213\pi$
$504$	0	0
$505$	1350.00	0.118959
$506$	0	0
$507$	−2157.00	−0.188946
$508$	−3776.00	−0.329789
$509$	6122.00	0.533110	0.266555	−	0.963820i	$-0.414115\pi$
$509$	6122.00	0.533110	0.266555	+	0.963820i	$0.414115\pi$
$510$	−1380.00	−0.119818
$511$	0	0
$512$	−512.000	−0.0441942
$513$	324.000	0.0278849
$514$	−4220.00	−0.362133
$515$	−8200.00	−0.701622
$516$	−6672.00	−0.569222
$517$	12544.0	1.06709
$518$	0	0
$519$	2274.00	0.192327
$520$	−2160.00	−0.182158
$521$	6766.00	0.568952	0.284476	−	0.958683i	$-0.408180\pi$
$521$	6766.00	0.568952	0.284476	+	0.958683i	$0.408180\pi$
$522$	−108.000	−0.00905562
$523$	9884.00	0.826381	0.413190	−	0.910645i	$-0.364414\pi$
$523$	9884.00	0.826381	0.413190	+	0.910645i	$0.364414\pi$
$524$	−2000.00	−0.166737
$525$	0	0
$526$	−13024.0	−1.07961
$527$	−13616.0	−1.12547
$528$	−1344.00	−0.110777
$529$	−12167.0	−1.00000
$530$	460.000	0.0377002
$531$	−6732.00	−0.550177
$532$	0	0
$533$	7884.00	0.640702
$534$	3540.00	0.286874
$535$	1980.00	0.160005
$536$	1248.00	0.100570
$537$	6084.00	0.488909
$538$	5772.00	0.462544
$539$	0	0
$540$	540.000	0.0430331
$541$	20358.0	1.61785	0.808927	−	0.587909i	$-0.200049\pi$
$541$	20358.0	1.61785	0.808927	+	0.587909i	$0.200049\pi$
$542$	6864.00	0.543974
$543$	−9294.00	−0.734519
$544$	−1472.00	−0.116014
$545$	−4830.00	−0.379623
$546$	0	0
$547$	−9420.00	−0.736326	−0.368163	−	0.929761i	$-0.620013\pi$
$547$	−9420.00	−0.736326	−0.368163	+	0.929761i	$0.620013\pi$
$548$	−3768.00	−0.293724
$549$	450.000	0.0349828
$550$	−1400.00	−0.108539
$551$	−72.0000	−0.00556679
$552$	0	0
$553$	0	0
$554$	11028.0	0.845731
$555$	2010.00	0.153729
$556$	−3088.00	−0.235540
$557$	8038.00	0.611456	0.305728	−	0.952119i	$-0.401100\pi$
$557$	8038.00	0.611456	0.305728	+	0.952119i	$0.401100\pi$
$558$	5328.00	0.404215
$559$	−30024.0	−2.27170
$560$	0	0
$561$	−3864.00	−0.290799
$562$	7916.00	0.594157
$563$	17476.0	1.30822	0.654108	−	0.756401i	$-0.273044\pi$
$563$	17476.0	1.30822	0.654108	+	0.756401i	$0.273044\pi$
$564$	−5376.00	−0.401366
$565$	10190.0	0.758755
$566$	17896.0	1.32902
$567$	0	0
$568$	8192.00	0.605156
$569$	−23238.0	−1.71210	−0.856052	−	0.516889i	$-0.827090\pi$
$569$	−23238.0	−1.71210	−0.856052	+	0.516889i	$0.827090\pi$
$570$	360.000	0.0264539
$571$	−2004.00	−0.146874	−0.0734368	−	0.997300i	$-0.523397\pi$
$571$	−2004.00	−0.146874	−0.0734368	+	0.997300i	$0.523397\pi$
$572$	−6048.00	−0.442097
$573$	−5112.00	−0.372700
$574$	0	0
$575$	0	0
$576$	576.000	0.0416667
$577$	2606.00	0.188023	0.0940114	−	0.995571i	$-0.470031\pi$
$577$	2606.00	0.188023	0.0940114	+	0.995571i	$0.470031\pi$
$578$	5594.00	0.402560
$579$	9930.00	0.712740
$580$	−120.000	−0.00859091
$581$	0	0
$582$	8340.00	0.593993
$583$	1288.00	0.0914983
$584$	−2480.00	−0.175725
$585$	2430.00	0.171740
$586$	−4.00000	−0.000281977 0
$587$	19948.0	1.40263	0.701314	−	0.712853i	$-0.252597\pi$
$587$	19948.0	1.40263	0.701314	+	0.712853i	$0.252597\pi$
$588$	0	0
$589$	3552.00	0.248485
$590$	−7480.00	−0.521944
$591$	5574.00	0.387959
$592$	2144.00	0.148848
$593$	14814.0	1.02587	0.512933	−	0.858429i	$-0.328559\pi$
$593$	14814.0	1.02587	0.512933	+	0.858429i	$0.328559\pi$
$594$	1512.00	0.104441
$595$	0	0
$596$	2232.00	0.153400
$597$	14208.0	0.974028
$598$	0	0
$599$	−14304.0	−0.975702	−0.487851	−	0.872927i	$-0.662219\pi$
$599$	−14304.0	−0.975702	−0.487851	+	0.872927i	$0.662219\pi$
$600$	600.000	0.0408248
$601$	−13578.0	−0.921561	−0.460781	−	0.887514i	$-0.652430\pi$
$601$	−13578.0	−0.921561	−0.460781	+	0.887514i	$0.652430\pi$
$602$	0	0
$603$	−1404.00	−0.0948181
$604$	1472.00	0.0991636
$605$	2735.00	0.183791
$606$	−1620.00	−0.108594
$607$	10208.0	0.682586	0.341293	−	0.939957i	$-0.389135\pi$
$607$	10208.0	0.682586	0.341293	+	0.939957i	$0.389135\pi$
$608$	384.000	0.0256139
$609$	0	0
$610$	500.000	0.0331876
$611$	−24192.0	−1.60181
$612$	1656.00	0.109379
$613$	25254.0	1.66395	0.831973	−	0.554815i	$-0.187211\pi$
$613$	25254.0	1.66395	0.831973	+	0.554815i	$0.187211\pi$
$614$	11768.0	0.773482
$615$	−2190.00	−0.143592
$616$	0	0
$617$	−26254.0	−1.71304	−0.856520	−	0.516113i	$-0.827378\pi$
$617$	−26254.0	−1.71304	−0.856520	+	0.516113i	$0.827378\pi$
$618$	9840.00	0.640490
$619$	28492.0	1.85006	0.925032	−	0.379888i	$-0.124038\pi$
$619$	28492.0	1.85006	0.925032	+	0.379888i	$0.124038\pi$
$620$	5920.00	0.383472
$621$	0	0
$622$	−3216.00	−0.207315
$623$	0	0
$624$	2592.00	0.166287
$625$	625.000	0.0400000
$626$	6580.00	0.420111
$627$	1008.00	0.0642036
$628$	−2200.00	−0.139792
$629$	6164.00	0.390739
$630$	0	0
$631$	17792.0	1.12249	0.561243	−	0.827651i	$-0.310323\pi$
$631$	17792.0	1.12249	0.561243	+	0.827651i	$0.310323\pi$
$632$	−6848.00	−0.431011
$633$	9924.00	0.623134
$634$	−4748.00	−0.297425
$635$	4720.00	0.294972
$636$	−552.000	−0.0344154
$637$	0	0
$638$	−336.000	−0.0208501
$639$	−9216.00	−0.570547
$640$	640.000	0.0395285
$641$	7490.00	0.461525	0.230762	−	0.973010i	$-0.425878\pi$
$641$	7490.00	0.461525	0.230762	+	0.973010i	$0.425878\pi$
$642$	−2376.00	−0.146064
$643$	15620.0	0.957998	0.478999	−	0.877815i	$-0.341000\pi$
$643$	15620.0	0.957998	0.478999	+	0.877815i	$0.341000\pi$
$644$	0	0
$645$	8340.00	0.509127
$646$	1104.00	0.0672389
$647$	−2968.00	−0.180346	−0.0901732	−	0.995926i	$-0.528742\pi$
$647$	−2968.00	−0.180346	−0.0901732	+	0.995926i	$0.528742\pi$
$648$	−648.000	−0.0392837
$649$	−20944.0	−1.26675
$650$	2700.00	0.162927
$651$	0	0
$652$	2960.00	0.177795
$653$	−2938.00	−0.176069	−0.0880343	−	0.996117i	$-0.528059\pi$
$653$	−2938.00	−0.176069	−0.0880343	+	0.996117i	$0.528059\pi$
$654$	5796.00	0.346547
$655$	2500.00	0.149134
$656$	−2336.00	−0.139033
$657$	2790.00	0.165675
$658$	0	0
$659$	−20924.0	−1.23685	−0.618424	−	0.785844i	$-0.712229\pi$
$659$	−20924.0	−1.23685	−0.618424	+	0.785844i	$0.712229\pi$
$660$	1680.00	0.0990817
$661$	22250.0	1.30927	0.654633	−	0.755947i	$-0.272823\pi$
$661$	22250.0	1.30927	0.654633	+	0.755947i	$0.272823\pi$
$662$	8680.00	0.509604
$663$	7452.00	0.436518
$664$	−5024.00	−0.293628
$665$	0	0
$666$	−2412.00	−0.140335
$667$	0	0
$668$	−4704.00	−0.272460
$669$	−6576.00	−0.380034
$670$	−1560.00	−0.0899523
$671$	1400.00	0.0805461
$672$	0	0
$673$	−2606.00	−0.149263	−0.0746314	−	0.997211i	$-0.523778\pi$
$673$	−2606.00	−0.149263	−0.0746314	+	0.997211i	$0.523778\pi$
$674$	19708.0	1.12630
$675$	−675.000	−0.0384900
$676$	2876.00	0.163632
$677$	−29310.0	−1.66392	−0.831961	−	0.554835i	$-0.812782\pi$
$677$	−29310.0	−1.66392	−0.831961	+	0.554835i	$0.812782\pi$
$678$	−12228.0	−0.692645
$679$	0	0
$680$	1840.00	0.103766
$681$	14388.0	0.809617
$682$	16576.0	0.930686
$683$	20276.0	1.13593	0.567965	−	0.823053i	$-0.307731\pi$
$683$	20276.0	1.13593	0.567965	+	0.823053i	$0.307731\pi$
$684$	−432.000	−0.0241490
$685$	4710.00	0.262715
$686$	0	0
$687$	−5838.00	−0.324212
$688$	8896.00	0.492960
$689$	−2484.00	−0.137348
$690$	0	0
$691$	3524.00	0.194008	0.0970038	−	0.995284i	$-0.469074\pi$
$691$	3524.00	0.194008	0.0970038	+	0.995284i	$0.469074\pi$
$692$	−3032.00	−0.166560
$693$	0	0
$694$	−6344.00	−0.346996
$695$	3860.00	0.210674
$696$	144.000	0.00784239
$697$	−6716.00	−0.364974
$698$	19004.0	1.03053
$699$	5994.00	0.324340
$700$	0	0
$701$	−31130.0	−1.67727	−0.838633	−	0.544696i	$-0.816645\pi$
$701$	−31130.0	−1.67727	−0.838633	+	0.544696i	$0.816645\pi$
$702$	−2916.00	−0.156777
$703$	−1608.00	−0.0862687
$704$	1792.00	0.0959354
$705$	6720.00	0.358993
$706$	22980.0	1.22502
$707$	0	0
$708$	8976.00	0.476467
$709$	2878.00	0.152448	0.0762239	−	0.997091i	$-0.475714\pi$
$709$	2878.00	0.152448	0.0762239	+	0.997091i	$0.475714\pi$
$710$	−10240.0	−0.541268
$711$	7704.00	0.406361
$712$	−4720.00	−0.248440
$713$	0	0
$714$	0	0
$715$	7560.00	0.395424
$716$	−8112.00	−0.423407
$717$	11544.0	0.601281
$718$	24128.0	1.25411
$719$	36240.0	1.87973	0.939864	−	0.341550i	$-0.110952\pi$
$719$	36240.0	1.87973	0.939864	+	0.341550i	$0.110952\pi$
$720$	−720.000	−0.0372678
$721$	0	0
$722$	13430.0	0.692262
$723$	−13290.0	−0.683624
$724$	12392.0	0.636112
$725$	150.000	0.00768395
$726$	−3282.00	−0.167777
$727$	−36648.0	−1.86960	−0.934800	−	0.355175i	$-0.884421\pi$
$727$	−36648.0	−1.86960	−0.934800	+	0.355175i	$0.884421\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	3100.00	0.157173
$731$	25576.0	1.29407
$732$	−600.000	−0.0302960
$733$	37370.0	1.88307	0.941536	−	0.336911i	$-0.109382\pi$
$733$	37370.0	1.88307	0.941536	+	0.336911i	$0.109382\pi$
$734$	−6112.00	−0.307354
$735$	0	0
$736$	0	0
$737$	−4368.00	−0.218314
$738$	2628.00	0.131081
$739$	13300.0	0.662041	0.331021	−	0.943624i	$-0.392607\pi$
$739$	13300.0	0.662041	0.331021	+	0.943624i	$0.392607\pi$
$740$	−2680.00	−0.133133
$741$	−1944.00	−0.0963760
$742$	0	0
$743$	38112.0	1.88182	0.940911	−	0.338654i	$-0.109972\pi$
$743$	38112.0	1.88182	0.940911	+	0.338654i	$0.109972\pi$
$744$	−7104.00	−0.350061
$745$	−2790.00	−0.137205
$746$	2516.00	0.123482
$747$	5652.00	0.276835
$748$	5152.00	0.251839
$749$	0	0
$750$	−750.000	−0.0365148
$751$	8024.00	0.389880	0.194940	−	0.980815i	$-0.437549\pi$
$751$	8024.00	0.389880	0.194940	+	0.980815i	$0.437549\pi$
$752$	7168.00	0.347593
$753$	13140.0	0.635921
$754$	648.000	0.0312981
$755$	−1840.00	−0.0886946
$756$	0	0
$757$	−13082.0	−0.628102	−0.314051	−	0.949406i	$-0.601686\pi$
$757$	−13082.0	−0.628102	−0.314051	+	0.949406i	$0.601686\pi$
$758$	−17016.0	−0.815368
$759$	0	0
$760$	−480.000	−0.0229098
$761$	−27186.0	−1.29500	−0.647498	−	0.762067i	$-0.724185\pi$
$761$	−27186.0	−1.29500	−0.647498	+	0.762067i	$0.724185\pi$
$762$	−5664.00	−0.269272
$763$	0	0
$764$	6816.00	0.322767
$765$	−2070.00	−0.0978314
$766$	18720.0	0.883004
$767$	40392.0	1.90153
$768$	−768.000	−0.0360844
$769$	−30802.0	−1.44441	−0.722203	−	0.691681i	$-0.756870\pi$
$769$	−30802.0	−1.44441	−0.722203	+	0.691681i	$0.756870\pi$
$770$	0	0
$771$	−6330.00	−0.295680
$772$	−13240.0	−0.617251
$773$	−22206.0	−1.03324	−0.516620	−	0.856215i	$-0.672810\pi$
$773$	−22206.0	−1.03324	−0.516620	+	0.856215i	$0.672810\pi$
$774$	−10008.0	−0.464768
$775$	−7400.00	−0.342988
$776$	−11120.0	−0.514413
$777$	0	0
$778$	−2428.00	−0.111887
$779$	1752.00	0.0805801
$780$	−3240.00	−0.148732
$781$	−28672.0	−1.31366
$782$	0	0
$783$	−162.000	−0.00739388
$784$	0	0
$785$	2750.00	0.125034
$786$	−3000.00	−0.136141
$787$	−10348.0	−0.468699	−0.234350	−	0.972152i	$-0.575296\pi$
$787$	−10348.0	−0.468699	−0.234350	+	0.972152i	$0.575296\pi$
$788$	−7432.00	−0.335982
$789$	−19536.0	−0.881496
$790$	8560.00	0.385508
$791$	0	0
$792$	−2016.00	−0.0904488
$793$	−2700.00	−0.120908
$794$	−23668.0	−1.05787
$795$	690.000	0.0307821
$796$	−18944.0	−0.843533
$797$	−25830.0	−1.14799	−0.573993	−	0.818860i	$-0.694607\pi$
$797$	−25830.0	−1.14799	−0.573993	+	0.818860i	$0.694607\pi$
$798$	0	0
$799$	20608.0	0.912464
$800$	−800.000	−0.0353553
$801$	5310.00	0.234232
$802$	16444.0	0.724012
$803$	8680.00	0.381458
$804$	1872.00	0.0821149
$805$	0	0
$806$	−31968.0	−1.39705
$807$	8658.00	0.377665
$808$	2160.00	0.0940452
$809$	33354.0	1.44952	0.724762	−	0.689000i	$-0.241950\pi$
$809$	33354.0	1.44952	0.724762	+	0.689000i	$0.241950\pi$
$810$	810.000	0.0351364
$811$	−36164.0	−1.56583	−0.782916	−	0.622127i	$-0.786269\pi$
$811$	−36164.0	−1.56583	−0.782916	+	0.622127i	$0.786269\pi$
$812$	0	0
$813$	10296.0	0.444153
$814$	−7504.00	−0.323114
$815$	−3700.00	−0.159025
$816$	−2208.00	−0.0947248
$817$	−6672.00	−0.285708
$818$	14100.0	0.602683
$819$	0	0
$820$	2920.00	0.124355
$821$	37134.0	1.57855	0.789273	−	0.614043i	$-0.210458\pi$
$821$	37134.0	1.57855	0.789273	+	0.614043i	$0.210458\pi$
$822$	−5652.00	−0.239825
$823$	−27368.0	−1.15916	−0.579580	−	0.814915i	$-0.696783\pi$
$823$	−27368.0	−1.15916	−0.579580	+	0.814915i	$0.696783\pi$
$824$	−13120.0	−0.554681
$825$	−2100.00	−0.0886214
$826$	0	0
$827$	34292.0	1.44190	0.720949	−	0.692988i	$-0.243706\pi$
$827$	34292.0	1.44190	0.720949	+	0.692988i	$0.243706\pi$
$828$	0	0
$829$	−9614.00	−0.402784	−0.201392	−	0.979511i	$-0.564547\pi$
$829$	−9614.00	−0.402784	−0.201392	+	0.979511i	$0.564547\pi$
$830$	6280.00	0.262629
$831$	16542.0	0.690536
$832$	−3456.00	−0.144009
$833$	0	0
$834$	−4632.00	−0.192318
$835$	5880.00	0.243696
$836$	−1344.00	−0.0556019
$837$	7992.00	0.330041
$838$	−31224.0	−1.28713
$839$	−40376.0	−1.66142	−0.830712	−	0.556703i	$-0.812066\pi$
$839$	−40376.0	−1.66142	−0.830712	+	0.556703i	$0.812066\pi$
$840$	0	0
$841$	−24353.0	−0.998524
$842$	−9820.00	−0.401923
$843$	11874.0	0.485127
$844$	−13232.0	−0.539650
$845$	−3595.00	−0.146357
$846$	−8064.00	−0.327714
$847$	0	0
$848$	736.000	0.0298047
$849$	26844.0	1.08514
$850$	−2300.00	−0.0928110
$851$	0	0
$852$	12288.0	0.494108
$853$	21250.0	0.852973	0.426487	−	0.904494i	$-0.359751\pi$
$853$	21250.0	0.852973	0.426487	+	0.904494i	$0.359751\pi$
$854$	0	0
$855$	540.000	0.0215995
$856$	3168.00	0.126495
$857$	−34170.0	−1.36199	−0.680995	−	0.732288i	$-0.738452\pi$
$857$	−34170.0	−1.36199	−0.680995	+	0.732288i	$0.738452\pi$
$858$	−9072.00	−0.360971
$859$	26604.0	1.05671	0.528357	−	0.849023i	$-0.322808\pi$
$859$	26604.0	1.05671	0.528357	+	0.849023i	$0.322808\pi$
$860$	−11120.0	−0.440917
$861$	0	0
$862$	−26448.0	−1.04504
$863$	−42104.0	−1.66076	−0.830381	−	0.557197i	$-0.811877\pi$
$863$	−42104.0	−1.66076	−0.830381	+	0.557197i	$0.811877\pi$
$864$	864.000	0.0340207
$865$	3790.00	0.148976
$866$	22084.0	0.866565
$867$	8391.00	0.328689
$868$	0	0
$869$	23968.0	0.935626
$870$	−180.000	−0.00701445
$871$	8424.00	0.327711
$872$	−7728.00	−0.300118
$873$	12510.0	0.484994
$874$	0	0
$875$	0	0
$876$	−3720.00	−0.143478
$877$	−22834.0	−0.879190	−0.439595	−	0.898196i	$-0.644878\pi$
$877$	−22834.0	−0.879190	−0.439595	+	0.898196i	$0.644878\pi$
$878$	−15232.0	−0.585484
$879$	−6.00000	−0.000230233 0
$880$	−2240.00	−0.0858073
$881$	15286.0	0.584561	0.292281	−	0.956333i	$-0.405586\pi$
$881$	15286.0	0.584561	0.292281	+	0.956333i	$0.405586\pi$
$882$	0	0
$883$	2004.00	0.0763760	0.0381880	−	0.999271i	$-0.487841\pi$
$883$	2004.00	0.0763760	0.0381880	+	0.999271i	$0.487841\pi$
$884$	−9936.00	−0.378036
$885$	−11220.0	−0.426165
$886$	11416.0	0.432876
$887$	−40328.0	−1.52659	−0.763293	−	0.646053i	$-0.776419\pi$
$887$	−40328.0	−1.52659	−0.763293	+	0.646053i	$0.776419\pi$
$888$	3216.00	0.121534
$889$	0	0
$890$	5900.00	0.222212
$891$	2268.00	0.0852759
$892$	8768.00	0.329119
$893$	−5376.00	−0.201457
$894$	3348.00	0.125250
$895$	10140.0	0.378707
$896$	0	0
$897$	0	0
$898$	1980.00	0.0735785
$899$	−1776.00	−0.0658876
$900$	900.000	0.0333333
$901$	2116.00	0.0782399
$902$	8176.00	0.301808
$903$	0	0
$904$	16304.0	0.599848
$905$	−15490.0	−0.568956
$906$	2208.00	0.0809668
$907$	−25732.0	−0.942025	−0.471013	−	0.882126i	$-0.656111\pi$
$907$	−25732.0	−0.942025	−0.471013	+	0.882126i	$0.656111\pi$
$908$	−19184.0	−0.701149
$909$	−2430.00	−0.0886667
$910$	0	0
$911$	−744.000	−0.0270580	−0.0135290	−	0.999908i	$-0.504307\pi$
$911$	−744.000	−0.0270580	−0.0135290	+	0.999908i	$0.504307\pi$
$912$	576.000	0.0209137
$913$	17584.0	0.637399
$914$	10828.0	0.391858
$915$	750.000	0.0270975
$916$	7784.00	0.280776
$917$	0	0
$918$	2484.00	0.0893074
$919$	6224.00	0.223407	0.111703	−	0.993742i	$-0.464369\pi$
$919$	6224.00	0.223407	0.111703	+	0.993742i	$0.464369\pi$
$920$	0	0
$921$	17652.0	0.631545
$922$	23276.0	0.831404
$923$	55296.0	1.97193
$924$	0	0
$925$	3350.00	0.119078
$926$	−39232.0	−1.39227
$927$	14760.0	0.522958
$928$	−192.000	−0.00679171
$929$	−27178.0	−0.959829	−0.479915	−	0.877315i	$-0.659332\pi$
$929$	−27178.0	−0.959829	−0.479915	+	0.877315i	$0.659332\pi$
$930$	8880.00	0.313104
$931$	0	0
$932$	−7992.00	−0.280887
$933$	−4824.00	−0.169272
$934$	19576.0	0.685810
$935$	−6440.00	−0.225252
$936$	3888.00	0.135773
$937$	10678.0	0.372289	0.186145	−	0.982522i	$-0.440401\pi$
$937$	10678.0	0.372289	0.186145	+	0.982522i	$0.440401\pi$
$938$	0	0
$939$	9870.00	0.343019
$940$	−8960.00	−0.310897
$941$	−16214.0	−0.561702	−0.280851	−	0.959751i	$-0.590617\pi$
$941$	−16214.0	−0.561702	−0.280851	+	0.959751i	$0.590617\pi$
$942$	−3300.00	−0.114140
$943$	0	0
$944$	−11968.0	−0.412633
$945$	0	0
$946$	−31136.0	−1.07010
$947$	−41764.0	−1.43310	−0.716551	−	0.697535i	$-0.754280\pi$
$947$	−41764.0	−1.43310	−0.716551	+	0.697535i	$0.754280\pi$
$948$	−10272.0	−0.351919
$949$	−16740.0	−0.572606
$950$	600.000	0.0204911
$951$	−7122.00	−0.242846
$952$	0	0
$953$	30354.0	1.03175	0.515877	−	0.856662i	$-0.327466\pi$
$953$	30354.0	1.03175	0.515877	+	0.856662i	$0.327466\pi$
$954$	−828.000	−0.0281001
$955$	−8520.00	−0.288692
$956$	−15392.0	−0.520725
$957$	−504.000	−0.0170240
$958$	−5376.00	−0.181306
$959$	0	0
$960$	960.000	0.0322749
$961$	57825.0	1.94102
$962$	14472.0	0.485027
$963$	−3564.00	−0.119261
$964$	17720.0	0.592036
$965$	16550.0	0.552086
$966$	0	0
$967$	−22952.0	−0.763275	−0.381637	−	0.924312i	$-0.624640\pi$
$967$	−22952.0	−0.763275	−0.381637	+	0.924312i	$0.624640\pi$
$968$	4376.00	0.145300
$969$	1656.00	0.0549003
$970$	13900.0	0.460105
$971$	−7404.00	−0.244702	−0.122351	−	0.992487i	$-0.539043\pi$
$971$	−7404.00	−0.244702	−0.122351	+	0.992487i	$0.539043\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	−15376.0	−0.505830
$975$	4050.00	0.133030
$976$	800.000	0.0262371
$977$	−54534.0	−1.78577	−0.892885	−	0.450285i	$-0.851322\pi$
$977$	−54534.0	−1.78577	−0.892885	+	0.450285i	$0.851322\pi$
$978$	4440.00	0.145169
$979$	16520.0	0.539307
$980$	0	0
$981$	8694.00	0.282954
$982$	29064.0	0.944470
$983$	7096.00	0.230241	0.115121	−	0.993352i	$-0.463275\pi$
$983$	7096.00	0.230241	0.115121	+	0.993352i	$0.463275\pi$
$984$	−3504.00	−0.113520
$985$	9290.00	0.300512
$986$	−552.000	−0.0178289
$987$	0	0
$988$	2592.00	0.0834641
$989$	0	0
$990$	2520.00	0.0808999
$991$	−41240.0	−1.32193	−0.660965	−	0.750417i	$-0.729853\pi$
$991$	−41240.0	−1.32193	−0.660965	+	0.750417i	$0.729853\pi$
$992$	9472.00	0.303162
$993$	13020.0	0.416090
$994$	0	0
$995$	23680.0	0.754479
$996$	−7536.00	−0.239746
$997$	−1646.00	−0.0522862	−0.0261431	−	0.999658i	$-0.508323\pi$
$997$	−1646.00	−0.0522862	−0.0261431	+	0.999658i	$0.508323\pi$
$998$	−2376.00	−0.0753617
$999$	−3618.00	−0.114583

Twists

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

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