LMFDB - Embedded newform 1470.4.a.c.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:	yes
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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -4.00000 q^{11} -12.0000 q^{12} +62.0000 q^{13} +15.0000 q^{15} +16.0000 q^{16} -70.0000 q^{17} -18.0000 q^{18} +6.00000 q^{19} -20.0000 q^{20} +8.00000 q^{22} -70.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -124.000 q^{26} -27.0000 q^{27} -162.000 q^{29} -30.0000 q^{30} -62.0000 q^{31} -32.0000 q^{32} +12.0000 q^{33} +140.000 q^{34} +36.0000 q^{36} +218.000 q^{37} -12.0000 q^{38} -186.000 q^{39} +40.0000 q^{40} +130.000 q^{41} +232.000 q^{43} -16.0000 q^{44} -45.0000 q^{45} +140.000 q^{46} +304.000 q^{47} -48.0000 q^{48} -50.0000 q^{50} +210.000 q^{51} +248.000 q^{52} -380.000 q^{53} +54.0000 q^{54} +20.0000 q^{55} -18.0000 q^{57} +324.000 q^{58} +376.000 q^{59} +60.0000 q^{60} +56.0000 q^{61} +124.000 q^{62} +64.0000 q^{64} -310.000 q^{65} -24.0000 q^{66} -952.000 q^{67} -280.000 q^{68} +210.000 q^{69} +708.000 q^{71} -72.0000 q^{72} +682.000 q^{73} -436.000 q^{74} -75.0000 q^{75} +24.0000 q^{76} +372.000 q^{78} -632.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} -260.000 q^{82} +244.000 q^{83} +350.000 q^{85} -464.000 q^{86} +486.000 q^{87} +32.0000 q^{88} -1198.00 q^{89} +90.0000 q^{90} -280.000 q^{92} +186.000 q^{93} -608.000 q^{94} -30.0000 q^{95} +96.0000 q^{96} +1206.00 q^{97} -36.0000 q^{99} +O(q^{100})\)

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
$11$	−4.00000	−0.109640	−0.0548202	−	0.998496i	$-0.517459\pi$
$11$	−4.00000	−0.109640	−0.0548202	+	0.998496i	$0.517459\pi$
$12$	−12.0000	−0.288675
$13$	62.0000	1.32275	0.661373	−	0.750057i	$-0.269974\pi$
$13$	62.0000	1.32275	0.661373	+	0.750057i	$0.269974\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	−70.0000	−0.998676	−0.499338	−	0.866407i	$-0.666423\pi$
$17$	−70.0000	−0.998676	−0.499338	+	0.866407i	$0.666423\pi$
$18$	−18.0000	−0.235702
$19$	6.00000	0.0724471	0.0362235	−	0.999344i	$-0.488467\pi$
$19$	6.00000	0.0724471	0.0362235	+	0.999344i	$0.488467\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	8.00000	0.0775275
$23$	−70.0000	−0.634609	−0.317305	−	0.948324i	$-0.602778\pi$
$23$	−70.0000	−0.634609	−0.317305	+	0.948324i	$0.602778\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−124.000	−0.935323
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−162.000	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$30$	−30.0000	−0.182574
$31$	−62.0000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−62.0000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−32.0000	−0.176777
$33$	12.0000	0.0633010
$34$	140.000	0.706171
$35$	0	0
$36$	36.0000	0.166667
$37$	218.000	0.968621	0.484311	−	0.874896i	$-0.339070\pi$
$37$	218.000	0.968621	0.484311	+	0.874896i	$0.339070\pi$
$38$	−12.0000	−0.0512278
$39$	−186.000	−0.763688
$40$	40.0000	0.158114
$41$	130.000	0.495185	0.247593	−	0.968864i	$-0.420361\pi$
$41$	130.000	0.495185	0.247593	+	0.968864i	$0.420361\pi$
$42$	0	0
$43$	232.000	0.822783	0.411391	−	0.911459i	$-0.365043\pi$
$43$	232.000	0.822783	0.411391	+	0.911459i	$0.365043\pi$
$44$	−16.0000	−0.0548202
$45$	−45.0000	−0.149071
$46$	140.000	0.448736
$47$	304.000	0.943467	0.471734	−	0.881741i	$-0.343628\pi$
$47$	304.000	0.943467	0.471734	+	0.881741i	$0.343628\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	210.000	0.576586
$52$	248.000	0.661373
$53$	−380.000	−0.984849	−0.492425	−	0.870355i	$-0.663889\pi$
$53$	−380.000	−0.984849	−0.492425	+	0.870355i	$0.663889\pi$
$54$	54.0000	0.136083
$55$	20.0000	0.0490327
$56$	0	0
$57$	−18.0000	−0.0418273
$58$	324.000	0.733505
$59$	376.000	0.829678	0.414839	−	0.909895i	$-0.363838\pi$
$59$	376.000	0.829678	0.414839	+	0.909895i	$0.363838\pi$
$60$	60.0000	0.129099
$61$	56.0000	0.117542	0.0587710	−	0.998271i	$-0.481282\pi$
$61$	56.0000	0.117542	0.0587710	+	0.998271i	$0.481282\pi$
$62$	124.000	0.254000
$63$	0	0
$64$	64.0000	0.125000
$65$	−310.000	−0.591550
$66$	−24.0000	−0.0447605
$67$	−952.000	−1.73590	−0.867950	−	0.496651i	$-0.834563\pi$
$67$	−952.000	−1.73590	−0.867950	+	0.496651i	$0.834563\pi$
$68$	−280.000	−0.499338
$69$	210.000	0.366392
$70$	0	0
$71$	708.000	1.18344	0.591719	−	0.806144i	$-0.298449\pi$
$71$	708.000	1.18344	0.591719	+	0.806144i	$0.298449\pi$
$72$	−72.0000	−0.117851
$73$	682.000	1.09345	0.546726	−	0.837311i	$-0.315874\pi$
$73$	682.000	1.09345	0.546726	+	0.837311i	$0.315874\pi$
$74$	−436.000	−0.684919
$75$	−75.0000	−0.115470
$76$	24.0000	0.0362235
$77$	0	0
$78$	372.000	0.540009
$79$	−632.000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−632.000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−260.000	−0.350149
$83$	244.000	0.322680	0.161340	−	0.986899i	$-0.448418\pi$
$83$	244.000	0.322680	0.161340	+	0.986899i	$0.448418\pi$
$84$	0	0
$85$	350.000	0.446622
$86$	−464.000	−0.581795
$87$	486.000	0.598904
$88$	32.0000	0.0387638
$89$	−1198.00	−1.42683	−0.713414	−	0.700742i	$-0.752852\pi$
$89$	−1198.00	−1.42683	−0.713414	+	0.700742i	$0.752852\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	−280.000	−0.317305
$93$	186.000	0.207390
$94$	−608.000	−0.667132
$95$	−30.0000	−0.0323993
$96$	96.0000	0.102062
$97$	1206.00	1.26238	0.631189	−	0.775629i	$-0.282567\pi$
$97$	1206.00	1.26238	0.631189	+	0.775629i	$0.282567\pi$
$98$	0	0
$99$	−36.0000	−0.0365468
$100$	100.000	0.100000
$101$	−266.000	−0.262059	−0.131030	−	0.991378i	$-0.541828\pi$
$101$	−266.000	−0.262059	−0.131030	+	0.991378i	$0.541828\pi$
$102$	−420.000	−0.407708
$103$	676.000	0.646682	0.323341	−	0.946282i	$-0.395194\pi$
$103$	676.000	0.646682	0.323341	+	0.946282i	$0.395194\pi$
$104$	−496.000	−0.467662
$105$	0	0
$106$	760.000	0.696394
$107$	918.000	0.829406	0.414703	−	0.909957i	$-0.363886\pi$
$107$	918.000	0.829406	0.414703	+	0.909957i	$0.363886\pi$
$108$	−108.000	−0.0962250
$109$	−746.000	−0.655540	−0.327770	−	0.944758i	$-0.606297\pi$
$109$	−746.000	−0.655540	−0.327770	+	0.944758i	$0.606297\pi$
$110$	−40.0000	−0.0346714
$111$	−654.000	−0.559234
$112$	0	0
$113$	748.000	0.622707	0.311354	−	0.950294i	$-0.399218\pi$
$113$	748.000	0.622707	0.311354	+	0.950294i	$0.399218\pi$
$114$	36.0000	0.0295764
$115$	350.000	0.283806
$116$	−648.000	−0.518666
$117$	558.000	0.440916
$118$	−752.000	−0.586671
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−1315.00	−0.987979
$122$	−112.000	−0.0831148
$123$	−390.000	−0.285895
$124$	−248.000	−0.179605
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1488.00	1.03967	0.519837	−	0.854265i	$-0.325993\pi$
$127$	1488.00	1.03967	0.519837	+	0.854265i	$0.325993\pi$
$128$	−128.000	−0.0883883
$129$	−696.000	−0.475034
$130$	620.000	0.418289
$131$	528.000	0.352149	0.176075	−	0.984377i	$-0.443660\pi$
$131$	528.000	0.352149	0.176075	+	0.984377i	$0.443660\pi$
$132$	48.0000	0.0316505
$133$	0	0
$134$	1904.00	1.22747
$135$	135.000	0.0860663
$136$	560.000	0.353085
$137$	−2060.00	−1.28465	−0.642327	−	0.766430i	$-0.722031\pi$
$137$	−2060.00	−1.28465	−0.642327	+	0.766430i	$0.722031\pi$
$138$	−420.000	−0.259078
$139$	218.000	0.133025	0.0665127	−	0.997786i	$-0.478813\pi$
$139$	218.000	0.133025	0.0665127	+	0.997786i	$0.478813\pi$
$140$	0	0
$141$	−912.000	−0.544711
$142$	−1416.00	−0.836817
$143$	−248.000	−0.145027
$144$	144.000	0.0833333
$145$	810.000	0.463909
$146$	−1364.00	−0.773188
$147$	0	0
$148$	872.000	0.484311
$149$	350.000	0.192437	0.0962185	−	0.995360i	$-0.469325\pi$
$149$	350.000	0.192437	0.0962185	+	0.995360i	$0.469325\pi$
$150$	150.000	0.0816497
$151$	−648.000	−0.349228	−0.174614	−	0.984637i	$-0.555868\pi$
$151$	−648.000	−0.349228	−0.174614	+	0.984637i	$0.555868\pi$
$152$	−48.0000	−0.0256139
$153$	−630.000	−0.332892
$154$	0	0
$155$	310.000	0.160644
$156$	−744.000	−0.381844
$157$	518.000	0.263318	0.131659	−	0.991295i	$-0.457970\pi$
$157$	518.000	0.263318	0.131659	+	0.991295i	$0.457970\pi$
$158$	1264.00	0.636446
$159$	1140.00	0.568603
$160$	160.000	0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	−2404.00	−1.15519	−0.577595	−	0.816324i	$-0.696009\pi$
$163$	−2404.00	−1.15519	−0.577595	+	0.816324i	$0.696009\pi$
$164$	520.000	0.247593
$165$	−60.0000	−0.0283091
$166$	−488.000	−0.228170
$167$	−1824.00	−0.845182	−0.422591	−	0.906321i	$-0.638879\pi$
$167$	−1824.00	−0.845182	−0.422591	+	0.906321i	$0.638879\pi$
$168$	0	0
$169$	1647.00	0.749659
$170$	−700.000	−0.315809
$171$	54.0000	0.0241490
$172$	928.000	0.411391
$173$	−1482.00	−0.651297	−0.325648	−	0.945491i	$-0.605583\pi$
$173$	−1482.00	−0.651297	−0.325648	+	0.945491i	$0.605583\pi$
$174$	−972.000	−0.423489
$175$	0	0
$176$	−64.0000	−0.0274101
$177$	−1128.00	−0.479015
$178$	2396.00	1.00892
$179$	−1952.00	−0.815080	−0.407540	−	0.913187i	$-0.633613\pi$
$179$	−1952.00	−0.815080	−0.407540	+	0.913187i	$0.633613\pi$
$180$	−180.000	−0.0745356
$181$	920.000	0.377807	0.188903	−	0.981996i	$-0.439507\pi$
$181$	920.000	0.377807	0.188903	+	0.981996i	$0.439507\pi$
$182$	0	0
$183$	−168.000	−0.0678629
$184$	560.000	0.224368
$185$	−1090.00	−0.433181
$186$	−372.000	−0.146647
$187$	280.000	0.109495
$188$	1216.00	0.471734
$189$	0	0
$190$	60.0000	0.0229098
$191$	−600.000	−0.227301	−0.113650	−	0.993521i	$-0.536254\pi$
$191$	−600.000	−0.227301	−0.113650	+	0.993521i	$0.536254\pi$
$192$	−192.000	−0.0721688
$193$	−654.000	−0.243917	−0.121958	−	0.992535i	$-0.538917\pi$
$193$	−654.000	−0.243917	−0.121958	+	0.992535i	$0.538917\pi$
$194$	−2412.00	−0.892637
$195$	930.000	0.341532
$196$	0	0
$197$	3072.00	1.11102	0.555510	−	0.831510i	$-0.312523\pi$
$197$	3072.00	1.11102	0.555510	+	0.831510i	$0.312523\pi$
$198$	72.0000	0.0258425
$199$	502.000	0.178823	0.0894116	−	0.995995i	$-0.471501\pi$
$199$	502.000	0.178823	0.0894116	+	0.995995i	$0.471501\pi$
$200$	−200.000	−0.0707107
$201$	2856.00	1.00222
$202$	532.000	0.185304
$203$	0	0
$204$	840.000	0.288293
$205$	−650.000	−0.221454
$206$	−1352.00	−0.457273
$207$	−630.000	−0.211536
$208$	992.000	0.330687
$209$	−24.0000	−0.00794313
$210$	0	0
$211$	−2788.00	−0.909639	−0.454820	−	0.890584i	$-0.650296\pi$
$211$	−2788.00	−0.909639	−0.454820	+	0.890584i	$0.650296\pi$
$212$	−1520.00	−0.492425
$213$	−2124.00	−0.683259
$214$	−1836.00	−0.586478
$215$	−1160.00	−0.367960
$216$	216.000	0.0680414
$217$	0	0
$218$	1492.00	0.463537
$219$	−2046.00	−0.631305
$220$	80.0000	0.0245164
$221$	−4340.00	−1.32100
$222$	1308.00	0.395438
$223$	772.000	0.231825	0.115912	−	0.993259i	$-0.463021\pi$
$223$	772.000	0.231825	0.115912	+	0.993259i	$0.463021\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−1496.00	−0.440321
$227$	−4260.00	−1.24558	−0.622789	−	0.782390i	$-0.714000\pi$
$227$	−4260.00	−1.24558	−0.622789	+	0.782390i	$0.714000\pi$
$228$	−72.0000	−0.0209137
$229$	−4004.00	−1.15542	−0.577711	−	0.816241i	$-0.696054\pi$
$229$	−4004.00	−1.15542	−0.577711	+	0.816241i	$0.696054\pi$
$230$	−700.000	−0.200681
$231$	0	0
$232$	1296.00	0.366752
$233$	−5480.00	−1.54080	−0.770401	−	0.637560i	$-0.779944\pi$
$233$	−5480.00	−1.54080	−0.770401	+	0.637560i	$0.779944\pi$
$234$	−1116.00	−0.311774
$235$	−1520.00	−0.421931
$236$	1504.00	0.414839
$237$	1896.00	0.519656
$238$	0	0
$239$	−536.000	−0.145067	−0.0725334	−	0.997366i	$-0.523108\pi$
$239$	−536.000	−0.145067	−0.0725334	+	0.997366i	$0.523108\pi$
$240$	240.000	0.0645497
$241$	−5432.00	−1.45189	−0.725946	−	0.687752i	$-0.758598\pi$
$241$	−5432.00	−1.45189	−0.725946	+	0.687752i	$0.758598\pi$
$242$	2630.00	0.698607
$243$	−243.000	−0.0641500
$244$	224.000	0.0587710
$245$	0	0
$246$	780.000	0.202158
$247$	372.000	0.0958291
$248$	496.000	0.127000
$249$	−732.000	−0.186300
$250$	250.000	0.0632456
$251$	−3800.00	−0.955593	−0.477797	−	0.878471i	$-0.658564\pi$
$251$	−3800.00	−0.955593	−0.477797	+	0.878471i	$0.658564\pi$
$252$	0	0
$253$	280.000	0.0695789
$254$	−2976.00	−0.735161
$255$	−1050.00	−0.257857
$256$	256.000	0.0625000
$257$	3246.00	0.787860	0.393930	−	0.919141i	$-0.371115\pi$
$257$	3246.00	0.787860	0.393930	+	0.919141i	$0.371115\pi$
$258$	1392.00	0.335900
$259$	0	0
$260$	−1240.00	−0.295775
$261$	−1458.00	−0.345778
$262$	−1056.00	−0.249007
$263$	−4146.00	−0.972066	−0.486033	−	0.873941i	$-0.661556\pi$
$263$	−4146.00	−0.972066	−0.486033	+	0.873941i	$0.661556\pi$
$264$	−96.0000	−0.0223803
$265$	1900.00	0.440438
$266$	0	0
$267$	3594.00	0.823780
$268$	−3808.00	−0.867950
$269$	−3118.00	−0.706721	−0.353360	−	0.935487i	$-0.614961\pi$
$269$	−3118.00	−0.706721	−0.353360	+	0.935487i	$0.614961\pi$
$270$	−270.000	−0.0608581
$271$	−2402.00	−0.538417	−0.269209	−	0.963082i	$-0.586762\pi$
$271$	−2402.00	−0.538417	−0.269209	+	0.963082i	$0.586762\pi$
$272$	−1120.00	−0.249669
$273$	0	0
$274$	4120.00	0.908388
$275$	−100.000	−0.0219281
$276$	840.000	0.183196
$277$	−5926.00	−1.28541	−0.642705	−	0.766113i	$-0.722188\pi$
$277$	−5926.00	−1.28541	−0.642705	+	0.766113i	$0.722188\pi$
$278$	−436.000	−0.0940631
$279$	−558.000	−0.119737
$280$	0	0
$281$	−9094.00	−1.93061	−0.965307	−	0.261117i	$-0.915909\pi$
$281$	−9094.00	−1.93061	−0.965307	+	0.261117i	$0.915909\pi$
$282$	1824.00	0.385169
$283$	8176.00	1.71736	0.858680	−	0.512512i	$-0.171285\pi$
$283$	8176.00	1.71736	0.858680	+	0.512512i	$0.171285\pi$
$284$	2832.00	0.591719
$285$	90.0000	0.0187058
$286$	496.000	0.102549
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−13.0000	−0.00264604
$290$	−1620.00	−0.328033
$291$	−3618.00	−0.728835
$292$	2728.00	0.546726
$293$	−5886.00	−1.17360	−0.586798	−	0.809733i	$-0.699612\pi$
$293$	−5886.00	−1.17360	−0.586798	+	0.809733i	$0.699612\pi$
$294$	0	0
$295$	−1880.00	−0.371043
$296$	−1744.00	−0.342459
$297$	108.000	0.0211003
$298$	−700.000	−0.136074
$299$	−4340.00	−0.839427
$300$	−300.000	−0.0577350
$301$	0	0
$302$	1296.00	0.246942
$303$	798.000	0.151300
$304$	96.0000	0.0181118
$305$	−280.000	−0.0525664
$306$	1260.00	0.235390
$307$	6700.00	1.24557	0.622784	−	0.782394i	$-0.286002\pi$
$307$	6700.00	1.24557	0.622784	+	0.782394i	$0.286002\pi$
$308$	0	0
$309$	−2028.00	−0.373362
$310$	−620.000	−0.113592
$311$	5692.00	1.03783	0.518913	−	0.854827i	$-0.326337\pi$
$311$	5692.00	1.03783	0.518913	+	0.854827i	$0.326337\pi$
$312$	1488.00	0.270005
$313$	9082.00	1.64008	0.820040	−	0.572306i	$-0.193951\pi$
$313$	9082.00	1.64008	0.820040	+	0.572306i	$0.193951\pi$
$314$	−1036.00	−0.186194
$315$	0	0
$316$	−2528.00	−0.450035
$317$	−6420.00	−1.13749	−0.568743	−	0.822515i	$-0.692570\pi$
$317$	−6420.00	−1.13749	−0.568743	+	0.822515i	$0.692570\pi$
$318$	−2280.00	−0.402063
$319$	648.000	0.113734
$320$	−320.000	−0.0559017
$321$	−2754.00	−0.478858
$322$	0	0
$323$	−420.000	−0.0723512
$324$	324.000	0.0555556
$325$	1550.00	0.264549
$326$	4808.00	0.816842
$327$	2238.00	0.378476
$328$	−1040.00	−0.175074
$329$	0	0
$330$	120.000	0.0200175
$331$	−8020.00	−1.33178	−0.665890	−	0.746050i	$-0.731948\pi$
$331$	−8020.00	−1.33178	−0.665890	+	0.746050i	$0.731948\pi$
$332$	976.000	0.161340
$333$	1962.00	0.322874
$334$	3648.00	0.597634
$335$	4760.00	0.776318
$336$	0	0
$337$	−5822.00	−0.941082	−0.470541	−	0.882378i	$-0.655941\pi$
$337$	−5822.00	−0.941082	−0.470541	+	0.882378i	$0.655941\pi$
$338$	−3294.00	−0.530089
$339$	−2244.00	−0.359520
$340$	1400.00	0.223311
$341$	248.000	0.0393840
$342$	−108.000	−0.0170759
$343$	0	0
$344$	−1856.00	−0.290898
$345$	−1050.00	−0.163855
$346$	2964.00	0.460536
$347$	−3346.00	−0.517645	−0.258822	−	0.965925i	$-0.583334\pi$
$347$	−3346.00	−0.517645	−0.258822	+	0.965925i	$0.583334\pi$
$348$	1944.00	0.299452
$349$	1192.00	0.182826	0.0914130	−	0.995813i	$-0.470862\pi$
$349$	1192.00	0.182826	0.0914130	+	0.995813i	$0.470862\pi$
$350$	0	0
$351$	−1674.00	−0.254563
$352$	128.000	0.0193819
$353$	9438.00	1.42304	0.711521	−	0.702665i	$-0.248007\pi$
$353$	9438.00	1.42304	0.711521	+	0.702665i	$0.248007\pi$
$354$	2256.00	0.338715
$355$	−3540.00	−0.529250
$356$	−4792.00	−0.713414
$357$	0	0
$358$	3904.00	0.576349
$359$	−776.000	−0.114083	−0.0570414	−	0.998372i	$-0.518167\pi$
$359$	−776.000	−0.114083	−0.0570414	+	0.998372i	$0.518167\pi$
$360$	360.000	0.0527046
$361$	−6823.00	−0.994751
$362$	−1840.00	−0.267150
$363$	3945.00	0.570410
$364$	0	0
$365$	−3410.00	−0.489007
$366$	336.000	0.0479863
$367$	908.000	0.129148	0.0645739	−	0.997913i	$-0.479431\pi$
$367$	908.000	0.129148	0.0645739	+	0.997913i	$0.479431\pi$
$368$	−1120.00	−0.158652
$369$	1170.00	0.165062
$370$	2180.00	0.306305
$371$	0	0
$372$	744.000	0.103695
$373$	6606.00	0.917013	0.458506	−	0.888691i	$-0.348385\pi$
$373$	6606.00	0.917013	0.458506	+	0.888691i	$0.348385\pi$
$374$	−560.000	−0.0774249
$375$	375.000	0.0516398
$376$	−2432.00	−0.333566
$377$	−10044.0	−1.37213
$378$	0	0
$379$	−10036.0	−1.36020	−0.680099	−	0.733121i	$-0.738063\pi$
$379$	−10036.0	−1.36020	−0.680099	+	0.733121i	$0.738063\pi$
$380$	−120.000	−0.0161997
$381$	−4464.00	−0.600256
$382$	1200.00	0.160726
$383$	−7168.00	−0.956313	−0.478156	−	0.878275i	$-0.658695\pi$
$383$	−7168.00	−0.956313	−0.478156	+	0.878275i	$0.658695\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	1308.00	0.172475
$387$	2088.00	0.274261
$388$	4824.00	0.631189
$389$	−7254.00	−0.945482	−0.472741	−	0.881201i	$-0.656735\pi$
$389$	−7254.00	−0.945482	−0.472741	+	0.881201i	$0.656735\pi$
$390$	−1860.00	−0.241499
$391$	4900.00	0.633769
$392$	0	0
$393$	−1584.00	−0.203314
$394$	−6144.00	−0.785610
$395$	3160.00	0.402524
$396$	−144.000	−0.0182734
$397$	−4942.00	−0.624765	−0.312383	−	0.949956i	$-0.601127\pi$
$397$	−4942.00	−0.624765	−0.312383	+	0.949956i	$0.601127\pi$
$398$	−1004.00	−0.126447
$399$	0	0
$400$	400.000	0.0500000
$401$	−1298.00	−0.161643	−0.0808217	−	0.996729i	$-0.525754\pi$
$401$	−1298.00	−0.161643	−0.0808217	+	0.996729i	$0.525754\pi$
$402$	−5712.00	−0.708678
$403$	−3844.00	−0.475145
$404$	−1064.00	−0.131030
$405$	−405.000	−0.0496904
$406$	0	0
$407$	−872.000	−0.106200
$408$	−1680.00	−0.203854
$409$	−1436.00	−0.173608	−0.0868039	−	0.996225i	$-0.527665\pi$
$409$	−1436.00	−0.173608	−0.0868039	+	0.996225i	$0.527665\pi$
$410$	1300.00	0.156591
$411$	6180.00	0.741696
$412$	2704.00	0.323341
$413$	0	0
$414$	1260.00	0.149579
$415$	−1220.00	−0.144307
$416$	−1984.00	−0.233831
$417$	−654.000	−0.0768022
$418$	48.0000	0.00561664
$419$	−11748.0	−1.36976	−0.684878	−	0.728658i	$-0.740144\pi$
$419$	−11748.0	−1.36976	−0.684878	+	0.728658i	$0.740144\pi$
$420$	0	0
$421$	3746.00	0.433655	0.216828	−	0.976210i	$-0.430429\pi$
$421$	3746.00	0.433655	0.216828	+	0.976210i	$0.430429\pi$
$422$	5576.00	0.643212
$423$	2736.00	0.314489
$424$	3040.00	0.348197
$425$	−1750.00	−0.199735
$426$	4248.00	0.483137
$427$	0	0
$428$	3672.00	0.414703
$429$	744.000	0.0837311
$430$	2320.00	0.260187
$431$	11340.0	1.26735	0.633676	−	0.773599i	$-0.281545\pi$
$431$	11340.0	1.26735	0.633676	+	0.773599i	$0.281545\pi$
$432$	−432.000	−0.0481125
$433$	12506.0	1.38799	0.693995	−	0.719979i	$-0.255849\pi$
$433$	12506.0	1.38799	0.693995	+	0.719979i	$0.255849\pi$
$434$	0	0
$435$	−2430.00	−0.267838
$436$	−2984.00	−0.327770
$437$	−420.000	−0.0459756
$438$	4092.00	0.446400
$439$	−16850.0	−1.83191	−0.915953	−	0.401286i	$-0.868563\pi$
$439$	−16850.0	−1.83191	−0.915953	+	0.401286i	$0.868563\pi$
$440$	−160.000	−0.0173357
$441$	0	0
$442$	8680.00	0.934085
$443$	17014.0	1.82474	0.912370	−	0.409367i	$-0.134251\pi$
$443$	17014.0	1.82474	0.912370	+	0.409367i	$0.134251\pi$
$444$	−2616.00	−0.279617
$445$	5990.00	0.638097
$446$	−1544.00	−0.163925
$447$	−1050.00	−0.111104
$448$	0	0
$449$	6570.00	0.690551	0.345276	−	0.938501i	$-0.387785\pi$
$449$	6570.00	0.690551	0.345276	+	0.938501i	$0.387785\pi$
$450$	−450.000	−0.0471405
$451$	−520.000	−0.0542923
$452$	2992.00	0.311354
$453$	1944.00	0.201627
$454$	8520.00	0.880756
$455$	0	0
$456$	144.000	0.0147882
$457$	4206.00	0.430522	0.215261	−	0.976557i	$-0.430940\pi$
$457$	4206.00	0.430522	0.215261	+	0.976557i	$0.430940\pi$
$458$	8008.00	0.817007
$459$	1890.00	0.192195
$460$	1400.00	0.141903
$461$	−14058.0	−1.42027	−0.710137	−	0.704063i	$-0.751367\pi$
$461$	−14058.0	−1.42027	−0.710137	+	0.704063i	$0.751367\pi$
$462$	0	0
$463$	−17576.0	−1.76420	−0.882102	−	0.471059i	$-0.843872\pi$
$463$	−17576.0	−1.76420	−0.882102	+	0.471059i	$0.843872\pi$
$464$	−2592.00	−0.259333
$465$	−930.000	−0.0927478
$466$	10960.0	1.08951
$467$	−4060.00	−0.402301	−0.201150	−	0.979560i	$-0.564468\pi$
$467$	−4060.00	−0.402301	−0.201150	+	0.979560i	$0.564468\pi$
$468$	2232.00	0.220458
$469$	0	0
$470$	3040.00	0.298351
$471$	−1554.00	−0.152027
$472$	−3008.00	−0.293336
$473$	−928.000	−0.0902103
$474$	−3792.00	−0.367452
$475$	150.000	0.0144894
$476$	0	0
$477$	−3420.00	−0.328283
$478$	1072.00	0.102578
$479$	−956.000	−0.0911916	−0.0455958	−	0.998960i	$-0.514519\pi$
$479$	−956.000	−0.0911916	−0.0455958	+	0.998960i	$0.514519\pi$
$480$	−480.000	−0.0456435
$481$	13516.0	1.28124
$482$	10864.0	1.02664
$483$	0	0
$484$	−5260.00	−0.493989
$485$	−6030.00	−0.564553
$486$	486.000	0.0453609
$487$	−10676.0	−0.993379	−0.496690	−	0.867928i	$-0.665451\pi$
$487$	−10676.0	−0.993379	−0.496690	+	0.867928i	$0.665451\pi$
$488$	−448.000	−0.0415574
$489$	7212.00	0.666949
$490$	0	0
$491$	−792.000	−0.0727952	−0.0363976	−	0.999337i	$-0.511588\pi$
$491$	−792.000	−0.0727952	−0.0363976	+	0.999337i	$0.511588\pi$
$492$	−1560.00	−0.142948
$493$	11340.0	1.03596
$494$	−744.000	−0.0677614
$495$	180.000	0.0163442
$496$	−992.000	−0.0898027
$497$	0	0
$498$	1464.00	0.131734
$499$	18052.0	1.61948	0.809738	−	0.586792i	$-0.199609\pi$
$499$	18052.0	1.61948	0.809738	+	0.586792i	$0.199609\pi$
$500$	−500.000	−0.0447214
$501$	5472.00	0.487966
$502$	7600.00	0.675706
$503$	−10368.0	−0.919058	−0.459529	−	0.888163i	$-0.651982\pi$
$503$	−10368.0	−0.919058	−0.459529	+	0.888163i	$0.651982\pi$
$504$	0	0
$505$	1330.00	0.117196
$506$	−560.000	−0.0491997
$507$	−4941.00	−0.432816
$508$	5952.00	0.519837
$509$	−6246.00	−0.543908	−0.271954	−	0.962310i	$-0.587670\pi$
$509$	−6246.00	−0.543908	−0.271954	+	0.962310i	$0.587670\pi$
$510$	2100.00	0.182332
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−162.000	−0.0139424
$514$	−6492.00	−0.557101
$515$	−3380.00	−0.289205
$516$	−2784.00	−0.237517
$517$	−1216.00	−0.103442
$518$	0	0
$519$	4446.00	0.376026
$520$	2480.00	0.209145
$521$	2862.00	0.240665	0.120333	−	0.992734i	$-0.461604\pi$
$521$	2862.00	0.240665	0.120333	+	0.992734i	$0.461604\pi$
$522$	2916.00	0.244502
$523$	−2608.00	−0.218049	−0.109025	−	0.994039i	$-0.534773\pi$
$523$	−2608.00	−0.218049	−0.109025	+	0.994039i	$0.534773\pi$
$524$	2112.00	0.176075
$525$	0	0
$526$	8292.00	0.687354
$527$	4340.00	0.358735
$528$	192.000	0.0158252
$529$	−7267.00	−0.597271
$530$	−3800.00	−0.311437
$531$	3384.00	0.276559
$532$	0	0
$533$	8060.00	0.655004
$534$	−7188.00	−0.582500
$535$	−4590.00	−0.370922
$536$	7616.00	0.613733
$537$	5856.00	0.470587
$538$	6236.00	0.499727
$539$	0	0
$540$	540.000	0.0430331
$541$	218.000	0.0173245	0.00866225	−	0.999962i	$-0.497243\pi$
$541$	218.000	0.0173245	0.00866225	+	0.999962i	$0.497243\pi$
$542$	4804.00	0.380719
$543$	−2760.00	−0.218127
$544$	2240.00	0.176543
$545$	3730.00	0.293166
$546$	0	0
$547$	5560.00	0.434604	0.217302	−	0.976104i	$-0.430274\pi$
$547$	5560.00	0.434604	0.217302	+	0.976104i	$0.430274\pi$
$548$	−8240.00	−0.642327
$549$	504.000	0.0391807
$550$	200.000	0.0155055
$551$	−972.000	−0.0751517
$552$	−1680.00	−0.129539
$553$	0	0
$554$	11852.0	0.908923
$555$	3270.00	0.250097
$556$	872.000	0.0665127
$557$	5244.00	0.398915	0.199457	−	0.979907i	$-0.436082\pi$
$557$	5244.00	0.398915	0.199457	+	0.979907i	$0.436082\pi$
$558$	1116.00	0.0846668
$559$	14384.0	1.08833
$560$	0	0
$561$	−840.000	−0.0632172
$562$	18188.0	1.36515
$563$	24708.0	1.84959	0.924794	−	0.380468i	$-0.124237\pi$
$563$	24708.0	1.84959	0.924794	+	0.380468i	$0.124237\pi$
$564$	−3648.00	−0.272356
$565$	−3740.00	−0.278483
$566$	−16352.0	−1.21436
$567$	0	0
$568$	−5664.00	−0.418409
$569$	24454.0	1.80170	0.900848	−	0.434135i	$-0.142946\pi$
$569$	24454.0	1.80170	0.900848	+	0.434135i	$0.142946\pi$
$570$	−180.000	−0.0132270
$571$	24876.0	1.82317	0.911583	−	0.411115i	$-0.134861\pi$
$571$	24876.0	1.82317	0.911583	+	0.411115i	$0.134861\pi$
$572$	−992.000	−0.0725133
$573$	1800.00	0.131232
$574$	0	0
$575$	−1750.00	−0.126922
$576$	576.000	0.0416667
$577$	−20342.0	−1.46768	−0.733838	−	0.679325i	$-0.762273\pi$
$577$	−20342.0	−1.46768	−0.733838	+	0.679325i	$0.762273\pi$
$578$	26.0000	0.00187103
$579$	1962.00	0.140825
$580$	3240.00	0.231955
$581$	0	0
$582$	7236.00	0.515364
$583$	1520.00	0.107979
$584$	−5456.00	−0.386594
$585$	−2790.00	−0.197183
$586$	11772.0	0.829858
$587$	−27604.0	−1.94095	−0.970476	−	0.241197i	$-0.922460\pi$
$587$	−27604.0	−1.94095	−0.970476	+	0.241197i	$0.922460\pi$
$588$	0	0
$589$	−372.000	−0.0260238
$590$	3760.00	0.262367
$591$	−9216.00	−0.641448
$592$	3488.00	0.242155
$593$	9838.00	0.681279	0.340639	−	0.940194i	$-0.389357\pi$
$593$	9838.00	0.681279	0.340639	+	0.940194i	$0.389357\pi$
$594$	−216.000	−0.0149202
$595$	0	0
$596$	1400.00	0.0962185
$597$	−1506.00	−0.103244
$598$	8680.00	0.593565
$599$	10256.0	0.699581	0.349790	−	0.936828i	$-0.386253\pi$
$599$	10256.0	0.699581	0.349790	+	0.936828i	$0.386253\pi$
$600$	600.000	0.0408248
$601$	−3572.00	−0.242437	−0.121219	−	0.992626i	$-0.538680\pi$
$601$	−3572.00	−0.242437	−0.121219	+	0.992626i	$0.538680\pi$
$602$	0	0
$603$	−8568.00	−0.578633
$604$	−2592.00	−0.174614
$605$	6575.00	0.441838
$606$	−1596.00	−0.106985
$607$	11540.0	0.771654	0.385827	−	0.922571i	$-0.373916\pi$
$607$	11540.0	0.771654	0.385827	+	0.922571i	$0.373916\pi$
$608$	−192.000	−0.0128070
$609$	0	0
$610$	560.000	0.0371701
$611$	18848.0	1.24797
$612$	−2520.00	−0.166446
$613$	−1382.00	−0.0910578	−0.0455289	−	0.998963i	$-0.514497\pi$
$613$	−1382.00	−0.0910578	−0.0455289	+	0.998963i	$0.514497\pi$
$614$	−13400.0	−0.880749
$615$	1950.00	0.127856
$616$	0	0
$617$	−22176.0	−1.44696	−0.723478	−	0.690347i	$-0.757458\pi$
$617$	−22176.0	−1.44696	−0.723478	+	0.690347i	$0.757458\pi$
$618$	4056.00	0.264007
$619$	−15390.0	−0.999316	−0.499658	−	0.866223i	$-0.666541\pi$
$619$	−15390.0	−0.999316	−0.499658	+	0.866223i	$0.666541\pi$
$620$	1240.00	0.0803219
$621$	1890.00	0.122131
$622$	−11384.0	−0.733853
$623$	0	0
$624$	−2976.00	−0.190922
$625$	625.000	0.0400000
$626$	−18164.0	−1.15971
$627$	72.0000	0.00458597
$628$	2072.00	0.131659
$629$	−15260.0	−0.967339
$630$	0	0
$631$	520.000	0.0328065	0.0164032	−	0.999865i	$-0.494778\pi$
$631$	520.000	0.0328065	0.0164032	+	0.999865i	$0.494778\pi$
$632$	5056.00	0.318223
$633$	8364.00	0.525180
$634$	12840.0	0.804324
$635$	−7440.00	−0.464957
$636$	4560.00	0.284302
$637$	0	0
$638$	−1296.00	−0.0804218
$639$	6372.00	0.394480
$640$	640.000	0.0395285
$641$	−11982.0	−0.738316	−0.369158	−	0.929367i	$-0.620354\pi$
$641$	−11982.0	−0.738316	−0.369158	+	0.929367i	$0.620354\pi$
$642$	5508.00	0.338603
$643$	24972.0	1.53157	0.765785	−	0.643097i	$-0.222351\pi$
$643$	24972.0	1.53157	0.765785	+	0.643097i	$0.222351\pi$
$644$	0	0
$645$	3480.00	0.212442
$646$	840.000	0.0511600
$647$	20872.0	1.26826	0.634129	−	0.773227i	$-0.281359\pi$
$647$	20872.0	1.26826	0.634129	+	0.773227i	$0.281359\pi$
$648$	−648.000	−0.0392837
$649$	−1504.00	−0.0909664
$650$	−3100.00	−0.187065
$651$	0	0
$652$	−9616.00	−0.577595
$653$	9212.00	0.552057	0.276029	−	0.961149i	$-0.410982\pi$
$653$	9212.00	0.552057	0.276029	+	0.961149i	$0.410982\pi$
$654$	−4476.00	−0.267623
$655$	−2640.00	−0.157486
$656$	2080.00	0.123796
$657$	6138.00	0.364484
$658$	0	0
$659$	2696.00	0.159365	0.0796823	−	0.996820i	$-0.474609\pi$
$659$	2696.00	0.159365	0.0796823	+	0.996820i	$0.474609\pi$
$660$	−240.000	−0.0141545
$661$	−19952.0	−1.17404	−0.587022	−	0.809571i	$-0.699700\pi$
$661$	−19952.0	−1.17404	−0.587022	+	0.809571i	$0.699700\pi$
$662$	16040.0	0.941710
$663$	13020.0	0.762677
$664$	−1952.00	−0.114085
$665$	0	0
$666$	−3924.00	−0.228306
$667$	11340.0	0.658301
$668$	−7296.00	−0.422591
$669$	−2316.00	−0.133844
$670$	−9520.00	−0.548940
$671$	−224.000	−0.0128874
$672$	0	0
$673$	18718.0	1.07210	0.536052	−	0.844185i	$-0.319915\pi$
$673$	18718.0	1.07210	0.536052	+	0.844185i	$0.319915\pi$
$674$	11644.0	0.665445
$675$	−675.000	−0.0384900
$676$	6588.00	0.374829
$677$	−12406.0	−0.704286	−0.352143	−	0.935946i	$-0.614547\pi$
$677$	−12406.0	−0.704286	−0.352143	+	0.935946i	$0.614547\pi$
$678$	4488.00	0.254219
$679$	0	0
$680$	−2800.00	−0.157905
$681$	12780.0	0.719135
$682$	−496.000	−0.0278487
$683$	7758.00	0.434629	0.217315	−	0.976102i	$-0.430270\pi$
$683$	7758.00	0.434629	0.217315	+	0.976102i	$0.430270\pi$
$684$	216.000	0.0120745
$685$	10300.0	0.574515
$686$	0	0
$687$	12012.0	0.667084
$688$	3712.00	0.205696
$689$	−23560.0	−1.30271
$690$	2100.00	0.115863
$691$	26750.0	1.47267	0.736337	−	0.676615i	$-0.236554\pi$
$691$	26750.0	1.47267	0.736337	+	0.676615i	$0.236554\pi$
$692$	−5928.00	−0.325648
$693$	0	0
$694$	6692.00	0.366030
$695$	−1090.00	−0.0594907
$696$	−3888.00	−0.211745
$697$	−9100.00	−0.494530
$698$	−2384.00	−0.129278
$699$	16440.0	0.889582
$700$	0	0
$701$	−20066.0	−1.08114	−0.540572	−	0.841298i	$-0.681792\pi$
$701$	−20066.0	−1.08114	−0.540572	+	0.841298i	$0.681792\pi$
$702$	3348.00	0.180003
$703$	1308.00	0.0701738
$704$	−256.000	−0.0137051
$705$	4560.00	0.243602
$706$	−18876.0	−1.00624
$707$	0	0
$708$	−4512.00	−0.239508
$709$	10938.0	0.579387	0.289693	−	0.957120i	$-0.406447\pi$
$709$	10938.0	0.579387	0.289693	+	0.957120i	$0.406447\pi$
$710$	7080.00	0.374236
$711$	−5688.00	−0.300023
$712$	9584.00	0.504460
$713$	4340.00	0.227958
$714$	0	0
$715$	1240.00	0.0648579
$716$	−7808.00	−0.407540
$717$	1608.00	0.0837543
$718$	1552.00	0.0806687
$719$	−8796.00	−0.456238	−0.228119	−	0.973633i	$-0.573258\pi$
$719$	−8796.00	−0.456238	−0.228119	+	0.973633i	$0.573258\pi$
$720$	−720.000	−0.0372678
$721$	0	0
$722$	13646.0	0.703395
$723$	16296.0	0.838250
$724$	3680.00	0.188903
$725$	−4050.00	−0.207467
$726$	−7890.00	−0.403341
$727$	−11176.0	−0.570144	−0.285072	−	0.958506i	$-0.592018\pi$
$727$	−11176.0	−0.570144	−0.285072	+	0.958506i	$0.592018\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	6820.00	0.345780
$731$	−16240.0	−0.821694
$732$	−672.000	−0.0339315
$733$	−36282.0	−1.82825	−0.914124	−	0.405434i	$-0.867120\pi$
$733$	−36282.0	−1.82825	−0.914124	+	0.405434i	$0.867120\pi$
$734$	−1816.00	−0.0913212
$735$	0	0
$736$	2240.00	0.112184
$737$	3808.00	0.190325
$738$	−2340.00	−0.116716
$739$	15660.0	0.779516	0.389758	−	0.920917i	$-0.372559\pi$
$739$	15660.0	0.779516	0.389758	+	0.920917i	$0.372559\pi$
$740$	−4360.00	−0.216590
$741$	−1116.00	−0.0553270
$742$	0	0
$743$	−31710.0	−1.56572	−0.782858	−	0.622200i	$-0.786239\pi$
$743$	−31710.0	−1.56572	−0.782858	+	0.622200i	$0.786239\pi$
$744$	−1488.00	−0.0733236
$745$	−1750.00	−0.0860605
$746$	−13212.0	−0.648426
$747$	2196.00	0.107560
$748$	1120.00	0.0547477
$749$	0	0
$750$	−750.000	−0.0365148
$751$	26680.0	1.29636	0.648180	−	0.761487i	$-0.275530\pi$
$751$	26680.0	1.29636	0.648180	+	0.761487i	$0.275530\pi$
$752$	4864.00	0.235867
$753$	11400.0	0.551712
$754$	20088.0	0.970241
$755$	3240.00	0.156180
$756$	0	0
$757$	11230.0	0.539183	0.269591	−	0.962975i	$-0.413111\pi$
$757$	11230.0	0.539183	0.269591	+	0.962975i	$0.413111\pi$
$758$	20072.0	0.961805
$759$	−840.000	−0.0401714
$760$	240.000	0.0114549
$761$	11706.0	0.557611	0.278806	−	0.960348i	$-0.410061\pi$
$761$	11706.0	0.557611	0.278806	+	0.960348i	$0.410061\pi$
$762$	8928.00	0.424445
$763$	0	0
$764$	−2400.00	−0.113650
$765$	3150.00	0.148874
$766$	14336.0	0.676215
$767$	23312.0	1.09745
$768$	−768.000	−0.0360844
$769$	6340.00	0.297303	0.148652	−	0.988890i	$-0.452507\pi$
$769$	6340.00	0.297303	0.148652	+	0.988890i	$0.452507\pi$
$770$	0	0
$771$	−9738.00	−0.454871
$772$	−2616.00	−0.121958
$773$	38718.0	1.80154	0.900770	−	0.434297i	$-0.143003\pi$
$773$	38718.0	1.80154	0.900770	+	0.434297i	$0.143003\pi$
$774$	−4176.00	−0.193932
$775$	−1550.00	−0.0718421
$776$	−9648.00	−0.446318
$777$	0	0
$778$	14508.0	0.668557
$779$	780.000	0.0358747
$780$	3720.00	0.170766
$781$	−2832.00	−0.129753
$782$	−9800.00	−0.448142
$783$	4374.00	0.199635
$784$	0	0
$785$	−2590.00	−0.117759
$786$	3168.00	0.143764
$787$	16320.0	0.739193	0.369597	−	0.929192i	$-0.379496\pi$
$787$	16320.0	0.739193	0.369597	+	0.929192i	$0.379496\pi$
$788$	12288.0	0.555510
$789$	12438.0	0.561222
$790$	−6320.00	−0.284627
$791$	0	0
$792$	288.000	0.0129213
$793$	3472.00	0.155478
$794$	9884.00	0.441776
$795$	−5700.00	−0.254287
$796$	2008.00	0.0894116
$797$	−23866.0	−1.06070	−0.530349	−	0.847779i	$-0.677939\pi$
$797$	−23866.0	−1.06070	−0.530349	+	0.847779i	$0.677939\pi$
$798$	0	0
$799$	−21280.0	−0.942218
$800$	−800.000	−0.0353553
$801$	−10782.0	−0.475610
$802$	2596.00	0.114299
$803$	−2728.00	−0.119887
$804$	11424.0	0.501111
$805$	0	0
$806$	7688.00	0.335978
$807$	9354.00	0.408025
$808$	2128.00	0.0926520
$809$	278.000	0.0120815	0.00604077	−	0.999982i	$-0.498077\pi$
$809$	278.000	0.0120815	0.00604077	+	0.999982i	$0.498077\pi$
$810$	810.000	0.0351364
$811$	−34414.0	−1.49006	−0.745030	−	0.667031i	$-0.767565\pi$
$811$	−34414.0	−1.49006	−0.745030	+	0.667031i	$0.767565\pi$
$812$	0	0
$813$	7206.00	0.310855
$814$	1744.00	0.0750948
$815$	12020.0	0.516616
$816$	3360.00	0.144146
$817$	1392.00	0.0596082
$818$	2872.00	0.122759
$819$	0	0
$820$	−2600.00	−0.110727
$821$	11970.0	0.508838	0.254419	−	0.967094i	$-0.418116\pi$
$821$	11970.0	0.508838	0.254419	+	0.967094i	$0.418116\pi$
$822$	−12360.0	−0.524458
$823$	−18352.0	−0.777291	−0.388646	−	0.921387i	$-0.627057\pi$
$823$	−18352.0	−0.777291	−0.388646	+	0.921387i	$0.627057\pi$
$824$	−5408.00	−0.228637
$825$	300.000	0.0126602
$826$	0	0
$827$	−4378.00	−0.184085	−0.0920423	−	0.995755i	$-0.529340\pi$
$827$	−4378.00	−0.184085	−0.0920423	+	0.995755i	$0.529340\pi$
$828$	−2520.00	−0.105768
$829$	−34408.0	−1.44154	−0.720772	−	0.693173i	$-0.756212\pi$
$829$	−34408.0	−1.44154	−0.720772	+	0.693173i	$0.756212\pi$
$830$	2440.00	0.102041
$831$	17778.0	0.742132
$832$	3968.00	0.165343
$833$	0	0
$834$	1308.00	0.0543074
$835$	9120.00	0.377977
$836$	−96.0000	−0.00397157
$837$	1674.00	0.0691301
$838$	23496.0	0.968563
$839$	−4104.00	−0.168875	−0.0844373	−	0.996429i	$-0.526909\pi$
$839$	−4104.00	−0.168875	−0.0844373	+	0.996429i	$0.526909\pi$
$840$	0	0
$841$	1855.00	0.0760589
$842$	−7492.00	−0.306641
$843$	27282.0	1.11464
$844$	−11152.0	−0.454820
$845$	−8235.00	−0.335258
$846$	−5472.00	−0.222377
$847$	0	0
$848$	−6080.00	−0.246212
$849$	−24528.0	−0.991518
$850$	3500.00	0.141234
$851$	−15260.0	−0.614696
$852$	−8496.00	−0.341629
$853$	16106.0	0.646493	0.323247	−	0.946315i	$-0.395226\pi$
$853$	16106.0	0.646493	0.323247	+	0.946315i	$0.395226\pi$
$854$	0	0
$855$	−270.000	−0.0107998
$856$	−7344.00	−0.293239
$857$	−22470.0	−0.895637	−0.447818	−	0.894125i	$-0.647799\pi$
$857$	−22470.0	−0.895637	−0.447818	+	0.894125i	$0.647799\pi$
$858$	−1488.00	−0.0592069
$859$	6626.00	0.263185	0.131593	−	0.991304i	$-0.457991\pi$
$859$	6626.00	0.263185	0.131593	+	0.991304i	$0.457991\pi$
$860$	−4640.00	−0.183980
$861$	0	0
$862$	−22680.0	−0.896153
$863$	3114.00	0.122829	0.0614147	−	0.998112i	$-0.480439\pi$
$863$	3114.00	0.122829	0.0614147	+	0.998112i	$0.480439\pi$
$864$	864.000	0.0340207
$865$	7410.00	0.291269
$866$	−25012.0	−0.981458
$867$	39.0000	0.00152769
$868$	0	0
$869$	2528.00	0.0986842
$870$	4860.00	0.189390
$871$	−59024.0	−2.29616
$872$	5968.00	0.231768
$873$	10854.0	0.420793
$874$	840.000	0.0325096
$875$	0	0
$876$	−8184.00	−0.315653
$877$	−28134.0	−1.08326	−0.541629	−	0.840617i	$-0.682192\pi$
$877$	−28134.0	−1.08326	−0.541629	+	0.840617i	$0.682192\pi$
$878$	33700.0	1.29535
$879$	17658.0	0.677576
$880$	320.000	0.0122582
$881$	−37978.0	−1.45234	−0.726170	−	0.687515i	$-0.758701\pi$
$881$	−37978.0	−1.45234	−0.726170	+	0.687515i	$0.758701\pi$
$882$	0	0
$883$	−5348.00	−0.203822	−0.101911	−	0.994794i	$-0.532496\pi$
$883$	−5348.00	−0.203822	−0.101911	+	0.994794i	$0.532496\pi$
$884$	−17360.0	−0.660498
$885$	5640.00	0.214222
$886$	−34028.0	−1.29029
$887$	−12632.0	−0.478175	−0.239087	−	0.970998i	$-0.576848\pi$
$887$	−12632.0	−0.478175	−0.239087	+	0.970998i	$0.576848\pi$
$888$	5232.00	0.197719
$889$	0	0
$890$	−11980.0	−0.451203
$891$	−324.000	−0.0121823
$892$	3088.00	0.115912
$893$	1824.00	0.0683514
$894$	2100.00	0.0785621
$895$	9760.00	0.364515
$896$	0	0
$897$	13020.0	0.484643
$898$	−13140.0	−0.488293
$899$	10044.0	0.372621
$900$	900.000	0.0333333
$901$	26600.0	0.983545
$902$	1040.00	0.0383905
$903$	0	0
$904$	−5984.00	−0.220160
$905$	−4600.00	−0.168960
$906$	−3888.00	−0.142572
$907$	30340.0	1.11072	0.555360	−	0.831610i	$-0.312580\pi$
$907$	30340.0	1.11072	0.555360	+	0.831610i	$0.312580\pi$
$908$	−17040.0	−0.622789
$909$	−2394.00	−0.0873531
$910$	0	0
$911$	28432.0	1.03402	0.517011	−	0.855979i	$-0.327045\pi$
$911$	28432.0	1.03402	0.517011	+	0.855979i	$0.327045\pi$
$912$	−288.000	−0.0104568
$913$	−976.000	−0.0353788
$914$	−8412.00	−0.304425
$915$	840.000	0.0303492
$916$	−16016.0	−0.577711
$917$	0	0
$918$	−3780.00	−0.135903
$919$	22328.0	0.801450	0.400725	−	0.916198i	$-0.368758\pi$
$919$	22328.0	0.801450	0.400725	+	0.916198i	$0.368758\pi$
$920$	−2800.00	−0.100341
$921$	−20100.0	−0.719129
$922$	28116.0	1.00429
$923$	43896.0	1.56539
$924$	0	0
$925$	5450.00	0.193724
$926$	35152.0	1.24748
$927$	6084.00	0.215561
$928$	5184.00	0.183376
$929$	−51198.0	−1.80813	−0.904065	−	0.427396i	$-0.859431\pi$
$929$	−51198.0	−1.80813	−0.904065	+	0.427396i	$0.859431\pi$
$930$	1860.00	0.0655826
$931$	0	0
$932$	−21920.0	−0.770401
$933$	−17076.0	−0.599189
$934$	8120.00	0.284470
$935$	−1400.00	−0.0489678
$936$	−4464.00	−0.155887
$937$	−31050.0	−1.08256	−0.541280	−	0.840842i	$-0.682060\pi$
$937$	−31050.0	−1.08256	−0.541280	+	0.840842i	$0.682060\pi$
$938$	0	0
$939$	−27246.0	−0.946901
$940$	−6080.00	−0.210966
$941$	−12382.0	−0.428950	−0.214475	−	0.976730i	$-0.568804\pi$
$941$	−12382.0	−0.428950	−0.214475	+	0.976730i	$0.568804\pi$
$942$	3108.00	0.107499
$943$	−9100.00	−0.314249
$944$	6016.00	0.207420
$945$	0	0
$946$	1856.00	0.0637883
$947$	−39366.0	−1.35082	−0.675408	−	0.737444i	$-0.736033\pi$
$947$	−39366.0	−1.35082	−0.675408	+	0.737444i	$0.736033\pi$
$948$	7584.00	0.259828
$949$	42284.0	1.44636
$950$	−300.000	−0.0102456
$951$	19260.0	0.656728
$952$	0	0
$953$	31172.0	1.05956	0.529780	−	0.848135i	$-0.322275\pi$
$953$	31172.0	1.05956	0.529780	+	0.848135i	$0.322275\pi$
$954$	6840.00	0.232131
$955$	3000.00	0.101652
$956$	−2144.00	−0.0725334
$957$	−1944.00	−0.0656642
$958$	1912.00	0.0644822
$959$	0	0
$960$	960.000	0.0322749
$961$	−25947.0	−0.870968
$962$	−27032.0	−0.905974
$963$	8262.00	0.276469
$964$	−21728.0	−0.725946
$965$	3270.00	0.109083
$966$	0	0
$967$	−3436.00	−0.114265	−0.0571325	−	0.998367i	$-0.518196\pi$
$967$	−3436.00	−0.114265	−0.0571325	+	0.998367i	$0.518196\pi$
$968$	10520.0	0.349303
$969$	1260.00	0.0417720
$970$	12060.0	0.399199
$971$	−4796.00	−0.158508	−0.0792538	−	0.996854i	$-0.525254\pi$
$971$	−4796.00	−0.158508	−0.0792538	+	0.996854i	$0.525254\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	21352.0	0.702425
$975$	−4650.00	−0.152738
$976$	896.000	0.0293855
$977$	−25152.0	−0.823627	−0.411814	−	0.911268i	$-0.635105\pi$
$977$	−25152.0	−0.823627	−0.411814	+	0.911268i	$0.635105\pi$
$978$	−14424.0	−0.471604
$979$	4792.00	0.156438
$980$	0	0
$981$	−6714.00	−0.218513
$982$	1584.00	0.0514740
$983$	46256.0	1.50085	0.750426	−	0.660955i	$-0.229848\pi$
$983$	46256.0	1.50085	0.750426	+	0.660955i	$0.229848\pi$
$984$	3120.00	0.101079
$985$	−15360.0	−0.496863
$986$	−22680.0	−0.732534
$987$	0	0
$988$	1488.00	0.0479146
$989$	−16240.0	−0.522146
$990$	−360.000	−0.0115571
$991$	25848.0	0.828546	0.414273	−	0.910153i	$-0.364036\pi$
$991$	25848.0	0.828546	0.414273	+	0.910153i	$0.364036\pi$
$992$	1984.00	0.0635001
$993$	24060.0	0.768903
$994$	0	0
$995$	−2510.00	−0.0799722
$996$	−2928.00	−0.0931498
$997$	−28854.0	−0.916565	−0.458283	−	0.888807i	$-0.651535\pi$
$997$	−28854.0	−0.916565	−0.458283	+	0.888807i	$0.651535\pi$
$998$	−36104.0	−1.14514
$999$	−5886.00	−0.186411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.c.1.1	✓	1
7.6	odd	2		1470.4.a.m.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.4.a.c.1.1	✓	1	1.1	even	1	trivial
1470.4.a.m.1.1	yes	1	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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