LMFDB - Embedded newform 1470.4.a.n.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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +12.0000 q^{11} +12.0000 q^{12} -2.00000 q^{13} +15.0000 q^{15} +16.0000 q^{16} +18.0000 q^{17} -18.0000 q^{18} -56.0000 q^{19} +20.0000 q^{20} -24.0000 q^{22} -156.000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +4.00000 q^{26} +27.0000 q^{27} -186.000 q^{29} -30.0000 q^{30} +52.0000 q^{31} -32.0000 q^{32} +36.0000 q^{33} -36.0000 q^{34} +36.0000 q^{36} -178.000 q^{37} +112.000 q^{38} -6.00000 q^{39} -40.0000 q^{40} +138.000 q^{41} -412.000 q^{43} +48.0000 q^{44} +45.0000 q^{45} +312.000 q^{46} +456.000 q^{47} +48.0000 q^{48} -50.0000 q^{50} +54.0000 q^{51} -8.00000 q^{52} -198.000 q^{53} -54.0000 q^{54} +60.0000 q^{55} -168.000 q^{57} +372.000 q^{58} -348.000 q^{59} +60.0000 q^{60} -110.000 q^{61} -104.000 q^{62} +64.0000 q^{64} -10.0000 q^{65} -72.0000 q^{66} -196.000 q^{67} +72.0000 q^{68} -468.000 q^{69} -936.000 q^{71} -72.0000 q^{72} -542.000 q^{73} +356.000 q^{74} +75.0000 q^{75} -224.000 q^{76} +12.0000 q^{78} +992.000 q^{79} +80.0000 q^{80} +81.0000 q^{81} -276.000 q^{82} +276.000 q^{83} +90.0000 q^{85} +824.000 q^{86} -558.000 q^{87} -96.0000 q^{88} -630.000 q^{89} -90.0000 q^{90} -624.000 q^{92} +156.000 q^{93} -912.000 q^{94} -280.000 q^{95} -96.0000 q^{96} -110.000 q^{97} +108.000 q^{99} +O(q^{100})\)

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
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	12.0000	0.288675
$13$	−2.00000	−0.0426692	−0.0213346	−	0.999772i	$-0.506792\pi$
$13$	−2.00000	−0.0426692	−0.0213346	+	0.999772i	$0.506792\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	18.0000	0.256802	0.128401	−	0.991722i	$-0.459015\pi$
$17$	18.0000	0.256802	0.128401	+	0.991722i	$0.459015\pi$
$18$	−18.0000	−0.235702
$19$	−56.0000	−0.676173	−0.338086	−	0.941115i	$-0.609780\pi$
$19$	−56.0000	−0.676173	−0.338086	+	0.941115i	$0.609780\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−24.0000	−0.232583
$23$	−156.000	−1.41427	−0.707136	−	0.707078i	$-0.750013\pi$
$23$	−156.000	−1.41427	−0.707136	+	0.707078i	$0.750013\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	4.00000	0.0301717
$27$	27.0000	0.192450
$28$	0	0
$29$	−186.000	−1.19101	−0.595506	−	0.803351i	$-0.703048\pi$
$29$	−186.000	−1.19101	−0.595506	+	0.803351i	$0.703048\pi$
$30$	−30.0000	−0.182574
$31$	52.0000	0.301273	0.150637	−	0.988589i	$-0.451868\pi$
$31$	52.0000	0.301273	0.150637	+	0.988589i	$0.451868\pi$
$32$	−32.0000	−0.176777
$33$	36.0000	0.189903
$34$	−36.0000	−0.181587
$35$	0	0
$36$	36.0000	0.166667
$37$	−178.000	−0.790892	−0.395446	−	0.918489i	$-0.629410\pi$
$37$	−178.000	−0.790892	−0.395446	+	0.918489i	$0.629410\pi$
$38$	112.000	0.478126
$39$	−6.00000	−0.0246351
$40$	−40.0000	−0.158114
$41$	138.000	0.525658	0.262829	−	0.964842i	$-0.415344\pi$
$41$	138.000	0.525658	0.262829	+	0.964842i	$0.415344\pi$
$42$	0	0
$43$	−412.000	−1.46115	−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000	−1.46115	−0.730575	+	0.682833i	$0.760748\pi$
$44$	48.0000	0.164461
$45$	45.0000	0.149071
$46$	312.000	1.00004
$47$	456.000	1.41520	0.707600	−	0.706613i	$-0.249778\pi$
$47$	456.000	1.41520	0.707600	+	0.706613i	$0.249778\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	54.0000	0.148265
$52$	−8.00000	−0.0213346
$53$	−198.000	−0.513158	−0.256579	−	0.966523i	$-0.582595\pi$
$53$	−198.000	−0.513158	−0.256579	+	0.966523i	$0.582595\pi$
$54$	−54.0000	−0.136083
$55$	60.0000	0.147098
$56$	0	0
$57$	−168.000	−0.390388
$58$	372.000	0.842172
$59$	−348.000	−0.767894	−0.383947	−	0.923355i	$-0.625435\pi$
$59$	−348.000	−0.767894	−0.383947	+	0.923355i	$0.625435\pi$
$60$	60.0000	0.129099
$61$	−110.000	−0.230886	−0.115443	−	0.993314i	$-0.536829\pi$
$61$	−110.000	−0.230886	−0.115443	+	0.993314i	$0.536829\pi$
$62$	−104.000	−0.213032
$63$	0	0
$64$	64.0000	0.125000
$65$	−10.0000	−0.0190823
$66$	−72.0000	−0.134282
$67$	−196.000	−0.357391	−0.178696	−	0.983904i	$-0.557188\pi$
$67$	−196.000	−0.357391	−0.178696	+	0.983904i	$0.557188\pi$
$68$	72.0000	0.128401
$69$	−468.000	−0.816530
$70$	0	0
$71$	−936.000	−1.56455	−0.782273	−	0.622936i	$-0.785940\pi$
$71$	−936.000	−1.56455	−0.782273	+	0.622936i	$0.785940\pi$
$72$	−72.0000	−0.117851
$73$	−542.000	−0.868990	−0.434495	−	0.900674i	$-0.643073\pi$
$73$	−542.000	−0.868990	−0.434495	+	0.900674i	$0.643073\pi$
$74$	356.000	0.559245
$75$	75.0000	0.115470
$76$	−224.000	−0.338086
$77$	0	0
$78$	12.0000	0.0174196
$79$	992.000	1.41277	0.706384	−	0.707829i	$-0.250325\pi$
$79$	992.000	1.41277	0.706384	+	0.707829i	$0.250325\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	−276.000	−0.371696
$83$	276.000	0.364999	0.182500	−	0.983206i	$-0.441581\pi$
$83$	276.000	0.364999	0.182500	+	0.983206i	$0.441581\pi$
$84$	0	0
$85$	90.0000	0.114846
$86$	824.000	1.03319
$87$	−558.000	−0.687631
$88$	−96.0000	−0.116291
$89$	−630.000	−0.750336	−0.375168	−	0.926957i	$-0.622415\pi$
$89$	−630.000	−0.750336	−0.375168	+	0.926957i	$0.622415\pi$
$90$	−90.0000	−0.105409
$91$	0	0
$92$	−624.000	−0.707136
$93$	156.000	0.173940
$94$	−912.000	−1.00070
$95$	−280.000	−0.302394
$96$	−96.0000	−0.102062
$97$	−110.000	−0.115142	−0.0575712	−	0.998341i	$-0.518336\pi$
$97$	−110.000	−0.115142	−0.0575712	+	0.998341i	$0.518336\pi$
$98$	0	0
$99$	108.000	0.109640
$100$	100.000	0.100000
$101$	−570.000	−0.561556	−0.280778	−	0.959773i	$-0.590592\pi$
$101$	−570.000	−0.561556	−0.280778	+	0.959773i	$0.590592\pi$
$102$	−108.000	−0.104839
$103$	304.000	0.290816	0.145408	−	0.989372i	$-0.453551\pi$
$103$	304.000	0.290816	0.145408	+	0.989372i	$0.453551\pi$
$104$	16.0000	0.0150859
$105$	0	0
$106$	396.000	0.362858
$107$	216.000	0.195154	0.0975771	−	0.995228i	$-0.468891\pi$
$107$	216.000	0.195154	0.0975771	+	0.995228i	$0.468891\pi$
$108$	108.000	0.0962250
$109$	614.000	0.539546	0.269773	−	0.962924i	$-0.413051\pi$
$109$	614.000	0.539546	0.269773	+	0.962924i	$0.413051\pi$
$110$	−120.000	−0.104014
$111$	−534.000	−0.456622
$112$	0	0
$113$	−498.000	−0.414583	−0.207292	−	0.978279i	$-0.566465\pi$
$113$	−498.000	−0.414583	−0.207292	+	0.978279i	$0.566465\pi$
$114$	336.000	0.276046
$115$	−780.000	−0.632482
$116$	−744.000	−0.595506
$117$	−18.0000	−0.0142231
$118$	696.000	0.542983
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−1187.00	−0.891811
$122$	220.000	0.163261
$123$	414.000	0.303489
$124$	208.000	0.150637
$125$	125.000	0.0894427
$126$	0	0
$127$	−1888.00	−1.31916	−0.659578	−	0.751636i	$-0.729265\pi$
$127$	−1888.00	−1.31916	−0.659578	+	0.751636i	$0.729265\pi$
$128$	−128.000	−0.0883883
$129$	−1236.00	−0.843595
$130$	20.0000	0.0134932
$131$	2892.00	1.92882	0.964409	−	0.264414i	$-0.0851786\pi$
$131$	2892.00	1.92882	0.964409	+	0.264414i	$0.0851786\pi$
$132$	144.000	0.0949514
$133$	0	0
$134$	392.000	0.252714
$135$	135.000	0.0860663
$136$	−144.000	−0.0907934
$137$	822.000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	822.000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	936.000	0.577374
$139$	376.000	0.229438	0.114719	−	0.993398i	$-0.463403\pi$
$139$	376.000	0.229438	0.114719	+	0.993398i	$0.463403\pi$
$140$	0	0
$141$	1368.00	0.817067
$142$	1872.00	1.10630
$143$	−24.0000	−0.0140348
$144$	144.000	0.0833333
$145$	−930.000	−0.532637
$146$	1084.00	0.614469
$147$	0	0
$148$	−712.000	−0.395446
$149$	3390.00	1.86389	0.931945	−	0.362600i	$-0.118111\pi$
$149$	3390.00	1.86389	0.931945	+	0.362600i	$0.118111\pi$
$150$	−150.000	−0.0816497
$151$	−2968.00	−1.59955	−0.799776	−	0.600298i	$-0.795049\pi$
$151$	−2968.00	−1.59955	−0.799776	+	0.600298i	$0.795049\pi$
$152$	448.000	0.239063
$153$	162.000	0.0856008
$154$	0	0
$155$	260.000	0.134734
$156$	−24.0000	−0.0123176
$157$	−1874.00	−0.952621	−0.476310	−	0.879277i	$-0.658026\pi$
$157$	−1874.00	−0.952621	−0.476310	+	0.879277i	$0.658026\pi$
$158$	−1984.00	−0.998978
$159$	−594.000	−0.296272
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	452.000	0.217199	0.108599	−	0.994086i	$-0.465363\pi$
$163$	452.000	0.217199	0.108599	+	0.994086i	$0.465363\pi$
$164$	552.000	0.262829
$165$	180.000	0.0849272
$166$	−552.000	−0.258093
$167$	1416.00	0.656128	0.328064	−	0.944656i	$-0.393604\pi$
$167$	1416.00	0.656128	0.328064	+	0.944656i	$0.393604\pi$
$168$	0	0
$169$	−2193.00	−0.998179
$170$	−180.000	−0.0812081
$171$	−504.000	−0.225391
$172$	−1648.00	−0.730575
$173$	−426.000	−0.187215	−0.0936075	−	0.995609i	$-0.529840\pi$
$173$	−426.000	−0.187215	−0.0936075	+	0.995609i	$0.529840\pi$
$174$	1116.00	0.486228
$175$	0	0
$176$	192.000	0.0822304
$177$	−1044.00	−0.443344
$178$	1260.00	0.530567
$179$	2700.00	1.12742	0.563708	−	0.825974i	$-0.309374\pi$
$179$	2700.00	1.12742	0.563708	+	0.825974i	$0.309374\pi$
$180$	180.000	0.0745356
$181$	1978.00	0.812285	0.406142	−	0.913810i	$-0.366874\pi$
$181$	1978.00	0.812285	0.406142	+	0.913810i	$0.366874\pi$
$182$	0	0
$183$	−330.000	−0.133302
$184$	1248.00	0.500021
$185$	−890.000	−0.353698
$186$	−312.000	−0.122994
$187$	216.000	0.0844678
$188$	1824.00	0.707600
$189$	0	0
$190$	560.000	0.213825
$191$	−2328.00	−0.881928	−0.440964	−	0.897525i	$-0.645363\pi$
$191$	−2328.00	−0.881928	−0.440964	+	0.897525i	$0.645363\pi$
$192$	192.000	0.0721688
$193$	−3166.00	−1.18080	−0.590398	−	0.807112i	$-0.701029\pi$
$193$	−3166.00	−1.18080	−0.590398	+	0.807112i	$0.701029\pi$
$194$	220.000	0.0814179
$195$	−30.0000	−0.0110172
$196$	0	0
$197$	−414.000	−0.149727	−0.0748637	−	0.997194i	$-0.523852\pi$
$197$	−414.000	−0.149727	−0.0748637	+	0.997194i	$0.523852\pi$
$198$	−216.000	−0.0775275
$199$	1636.00	0.582779	0.291389	−	0.956605i	$-0.405882\pi$
$199$	1636.00	0.582779	0.291389	+	0.956605i	$0.405882\pi$
$200$	−200.000	−0.0707107
$201$	−588.000	−0.206340
$202$	1140.00	0.397080
$203$	0	0
$204$	216.000	0.0741325
$205$	690.000	0.235081
$206$	−608.000	−0.205638
$207$	−1404.00	−0.471424
$208$	−32.0000	−0.0106673
$209$	−672.000	−0.222408
$210$	0	0
$211$	−2860.00	−0.933130	−0.466565	−	0.884487i	$-0.654509\pi$
$211$	−2860.00	−0.933130	−0.466565	+	0.884487i	$0.654509\pi$
$212$	−792.000	−0.256579
$213$	−2808.00	−0.903291
$214$	−432.000	−0.137995
$215$	−2060.00	−0.653446
$216$	−216.000	−0.0680414
$217$	0	0
$218$	−1228.00	−0.381517
$219$	−1626.00	−0.501712
$220$	240.000	0.0735491
$221$	−36.0000	−0.0109576
$222$	1068.00	0.322880
$223$	1096.00	0.329119	0.164560	−	0.986367i	$-0.447380\pi$
$223$	1096.00	0.329119	0.164560	+	0.986367i	$0.447380\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	996.000	0.293155
$227$	−6276.00	−1.83503	−0.917517	−	0.397696i	$-0.869810\pi$
$227$	−6276.00	−1.83503	−0.917517	+	0.397696i	$0.869810\pi$
$228$	−672.000	−0.195194
$229$	754.000	0.217580	0.108790	−	0.994065i	$-0.465302\pi$
$229$	754.000	0.217580	0.108790	+	0.994065i	$0.465302\pi$
$230$	1560.00	0.447232
$231$	0	0
$232$	1488.00	0.421086
$233$	3870.00	1.08812	0.544060	−	0.839046i	$-0.316886\pi$
$233$	3870.00	1.08812	0.544060	+	0.839046i	$0.316886\pi$
$234$	36.0000	0.0100572
$235$	2280.00	0.632897
$236$	−1392.00	−0.383947
$237$	2976.00	0.815662
$238$	0	0
$239$	744.000	0.201361	0.100681	−	0.994919i	$-0.467898\pi$
$239$	744.000	0.201361	0.100681	+	0.994919i	$0.467898\pi$
$240$	240.000	0.0645497
$241$	−5474.00	−1.46312	−0.731559	−	0.681778i	$-0.761207\pi$
$241$	−5474.00	−1.46312	−0.731559	+	0.681778i	$0.761207\pi$
$242$	2374.00	0.630605
$243$	243.000	0.0641500
$244$	−440.000	−0.115443
$245$	0	0
$246$	−828.000	−0.214599
$247$	112.000	0.0288518
$248$	−416.000	−0.106516
$249$	828.000	0.210732
$250$	−250.000	−0.0632456
$251$	−1980.00	−0.497914	−0.248957	−	0.968514i	$-0.580088\pi$
$251$	−1980.00	−0.497914	−0.248957	+	0.968514i	$0.580088\pi$
$252$	0	0
$253$	−1872.00	−0.465184
$254$	3776.00	0.932785
$255$	270.000	0.0663061
$256$	256.000	0.0625000
$257$	210.000	0.0509706	0.0254853	−	0.999675i	$-0.491887\pi$
$257$	210.000	0.0509706	0.0254853	+	0.999675i	$0.491887\pi$
$258$	2472.00	0.596512
$259$	0	0
$260$	−40.0000	−0.00954113
$261$	−1674.00	−0.397004
$262$	−5784.00	−1.36388
$263$	−1428.00	−0.334807	−0.167404	−	0.985888i	$-0.553538\pi$
$263$	−1428.00	−0.334807	−0.167404	+	0.985888i	$0.553538\pi$
$264$	−288.000	−0.0671408
$265$	−990.000	−0.229491
$266$	0	0
$267$	−1890.00	−0.433206
$268$	−784.000	−0.178696
$269$	−4122.00	−0.934285	−0.467143	−	0.884182i	$-0.654717\pi$
$269$	−4122.00	−0.934285	−0.467143	+	0.884182i	$0.654717\pi$
$270$	−270.000	−0.0608581
$271$	−5780.00	−1.29561	−0.647804	−	0.761807i	$-0.724313\pi$
$271$	−5780.00	−1.29561	−0.647804	+	0.761807i	$0.724313\pi$
$272$	288.000	0.0642006
$273$	0	0
$274$	−1644.00	−0.362473
$275$	300.000	0.0657843
$276$	−1872.00	−0.408265
$277$	4574.00	0.992148	0.496074	−	0.868280i	$-0.334774\pi$
$277$	4574.00	0.992148	0.496074	+	0.868280i	$0.334774\pi$
$278$	−752.000	−0.162237
$279$	468.000	0.100424
$280$	0	0
$281$	3450.00	0.732419	0.366210	−	0.930532i	$-0.380655\pi$
$281$	3450.00	0.732419	0.366210	+	0.930532i	$0.380655\pi$
$282$	−2736.00	−0.577753
$283$	700.000	0.147034	0.0735171	−	0.997294i	$-0.476578\pi$
$283$	700.000	0.147034	0.0735171	+	0.997294i	$0.476578\pi$
$284$	−3744.00	−0.782273
$285$	−840.000	−0.174587
$286$	48.0000	0.00992412
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−4589.00	−0.934053
$290$	1860.00	0.376631
$291$	−330.000	−0.0664775
$292$	−2168.00	−0.434495
$293$	−7170.00	−1.42961	−0.714805	−	0.699324i	$-0.753485\pi$
$293$	−7170.00	−1.42961	−0.714805	+	0.699324i	$0.753485\pi$
$294$	0	0
$295$	−1740.00	−0.343413
$296$	1424.00	0.279623
$297$	324.000	0.0633010
$298$	−6780.00	−1.31797
$299$	312.000	0.0603459
$300$	300.000	0.0577350
$301$	0	0
$302$	5936.00	1.13105
$303$	−1710.00	−0.324214
$304$	−896.000	−0.169043
$305$	−550.000	−0.103255
$306$	−324.000	−0.0605289
$307$	−6644.00	−1.23516	−0.617578	−	0.786509i	$-0.711886\pi$
$307$	−6644.00	−1.23516	−0.617578	+	0.786509i	$0.711886\pi$
$308$	0	0
$309$	912.000	0.167902
$310$	−520.000	−0.0952710
$311$	5376.00	0.980209	0.490104	−	0.871664i	$-0.336959\pi$
$311$	5376.00	0.980209	0.490104	+	0.871664i	$0.336959\pi$
$312$	48.0000	0.00870982
$313$	−2126.00	−0.383925	−0.191963	−	0.981402i	$-0.561485\pi$
$313$	−2126.00	−0.383925	−0.191963	+	0.981402i	$0.561485\pi$
$314$	3748.00	0.673605
$315$	0	0
$316$	3968.00	0.706384
$317$	1074.00	0.190290	0.0951449	−	0.995463i	$-0.469669\pi$
$317$	1074.00	0.190290	0.0951449	+	0.995463i	$0.469669\pi$
$318$	1188.00	0.209496
$319$	−2232.00	−0.391749
$320$	320.000	0.0559017
$321$	648.000	0.112672
$322$	0	0
$323$	−1008.00	−0.173643
$324$	324.000	0.0555556
$325$	−50.0000	−0.00853385
$326$	−904.000	−0.153583
$327$	1842.00	0.311507
$328$	−1104.00	−0.185848
$329$	0	0
$330$	−360.000	−0.0600526
$331$	−2788.00	−0.462968	−0.231484	−	0.972839i	$-0.574358\pi$
$331$	−2788.00	−0.462968	−0.231484	+	0.972839i	$0.574358\pi$
$332$	1104.00	0.182500
$333$	−1602.00	−0.263631
$334$	−2832.00	−0.463953
$335$	−980.000	−0.159830
$336$	0	0
$337$	−6334.00	−1.02384	−0.511921	−	0.859032i	$-0.671066\pi$
$337$	−6334.00	−1.02384	−0.511921	+	0.859032i	$0.671066\pi$
$338$	4386.00	0.705819
$339$	−1494.00	−0.239360
$340$	360.000	0.0574228
$341$	624.000	0.0990953
$342$	1008.00	0.159375
$343$	0	0
$344$	3296.00	0.516594
$345$	−2340.00	−0.365163
$346$	852.000	0.132381
$347$	−7032.00	−1.08789	−0.543945	−	0.839121i	$-0.683070\pi$
$347$	−7032.00	−1.08789	−0.543945	+	0.839121i	$0.683070\pi$
$348$	−2232.00	−0.343815
$349$	1474.00	0.226079	0.113039	−	0.993591i	$-0.463941\pi$
$349$	1474.00	0.226079	0.113039	+	0.993591i	$0.463941\pi$
$350$	0	0
$351$	−54.0000	−0.00821170
$352$	−384.000	−0.0581456
$353$	−7950.00	−1.19868	−0.599342	−	0.800493i	$-0.704571\pi$
$353$	−7950.00	−1.19868	−0.599342	+	0.800493i	$0.704571\pi$
$354$	2088.00	0.313491
$355$	−4680.00	−0.699686
$356$	−2520.00	−0.375168
$357$	0	0
$358$	−5400.00	−0.797204
$359$	6624.00	0.973820	0.486910	−	0.873452i	$-0.338124\pi$
$359$	6624.00	0.973820	0.486910	+	0.873452i	$0.338124\pi$
$360$	−360.000	−0.0527046
$361$	−3723.00	−0.542790
$362$	−3956.00	−0.574372
$363$	−3561.00	−0.514887
$364$	0	0
$365$	−2710.00	−0.388624
$366$	660.000	0.0942589
$367$	−1784.00	−0.253744	−0.126872	−	0.991919i	$-0.540494\pi$
$367$	−1784.00	−0.253744	−0.126872	+	0.991919i	$0.540494\pi$
$368$	−2496.00	−0.353568
$369$	1242.00	0.175219
$370$	1780.00	0.250102
$371$	0	0
$372$	624.000	0.0869701
$373$	−1978.00	−0.274576	−0.137288	−	0.990531i	$-0.543839\pi$
$373$	−1978.00	−0.274576	−0.137288	+	0.990531i	$0.543839\pi$
$374$	−432.000	−0.0597278
$375$	375.000	0.0516398
$376$	−3648.00	−0.500349
$377$	372.000	0.0508196
$378$	0	0
$379$	−10780.0	−1.46103	−0.730516	−	0.682895i	$-0.760721\pi$
$379$	−10780.0	−1.46103	−0.730516	+	0.682895i	$0.760721\pi$
$380$	−1120.00	−0.151197
$381$	−5664.00	−0.761616
$382$	4656.00	0.623617
$383$	5880.00	0.784475	0.392238	−	0.919864i	$-0.371701\pi$
$383$	5880.00	0.784475	0.392238	+	0.919864i	$0.371701\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	6332.00	0.834949
$387$	−3708.00	−0.487050
$388$	−440.000	−0.0575712
$389$	6438.00	0.839125	0.419562	−	0.907726i	$-0.362184\pi$
$389$	6438.00	0.839125	0.419562	+	0.907726i	$0.362184\pi$
$390$	60.0000	0.00779030
$391$	−2808.00	−0.363188
$392$	0	0
$393$	8676.00	1.11360
$394$	828.000	0.105873
$395$	4960.00	0.631809
$396$	432.000	0.0548202
$397$	−2954.00	−0.373443	−0.186722	−	0.982413i	$-0.559786\pi$
$397$	−2954.00	−0.373443	−0.186722	+	0.982413i	$0.559786\pi$
$398$	−3272.00	−0.412087
$399$	0	0
$400$	400.000	0.0500000
$401$	−5574.00	−0.694145	−0.347073	−	0.937838i	$-0.612824\pi$
$401$	−5574.00	−0.694145	−0.347073	+	0.937838i	$0.612824\pi$
$402$	1176.00	0.145904
$403$	−104.000	−0.0128551
$404$	−2280.00	−0.280778
$405$	405.000	0.0496904
$406$	0	0
$407$	−2136.00	−0.260141
$408$	−432.000	−0.0524196
$409$	15406.0	1.86254	0.931269	−	0.364333i	$-0.118703\pi$
$409$	15406.0	1.86254	0.931269	+	0.364333i	$0.118703\pi$
$410$	−1380.00	−0.166228
$411$	2466.00	0.295958
$412$	1216.00	0.145408
$413$	0	0
$414$	2808.00	0.333347
$415$	1380.00	0.163233
$416$	64.0000	0.00754293
$417$	1128.00	0.132466
$418$	1344.00	0.157266
$419$	−2940.00	−0.342789	−0.171394	−	0.985203i	$-0.554827\pi$
$419$	−2940.00	−0.342789	−0.171394	+	0.985203i	$0.554827\pi$
$420$	0	0
$421$	254.000	0.0294043	0.0147021	−	0.999892i	$-0.495320\pi$
$421$	254.000	0.0294043	0.0147021	+	0.999892i	$0.495320\pi$
$422$	5720.00	0.659823
$423$	4104.00	0.471734
$424$	1584.00	0.181429
$425$	450.000	0.0513605
$426$	5616.00	0.638723
$427$	0	0
$428$	864.000	0.0975771
$429$	−72.0000	−0.00810301
$430$	4120.00	0.462056
$431$	−13248.0	−1.48059	−0.740294	−	0.672283i	$-0.765314\pi$
$431$	−13248.0	−1.48059	−0.740294	+	0.672283i	$0.765314\pi$
$432$	432.000	0.0481125
$433$	−16598.0	−1.84215	−0.921073	−	0.389391i	$-0.872686\pi$
$433$	−16598.0	−1.84215	−0.921073	+	0.389391i	$0.872686\pi$
$434$	0	0
$435$	−2790.00	−0.307518
$436$	2456.00	0.269773
$437$	8736.00	0.956292
$438$	3252.00	0.354764
$439$	6532.00	0.710149	0.355074	−	0.934838i	$-0.384456\pi$
$439$	6532.00	0.710149	0.355074	+	0.934838i	$0.384456\pi$
$440$	−480.000	−0.0520071
$441$	0	0
$442$	72.0000	0.00774817
$443$	12216.0	1.31016	0.655079	−	0.755561i	$-0.272635\pi$
$443$	12216.0	1.31016	0.655079	+	0.755561i	$0.272635\pi$
$444$	−2136.00	−0.228311
$445$	−3150.00	−0.335560
$446$	−2192.00	−0.232722
$447$	10170.0	1.07612
$448$	0	0
$449$	306.000	0.0321627	0.0160813	−	0.999871i	$-0.494881\pi$
$449$	306.000	0.0321627	0.0160813	+	0.999871i	$0.494881\pi$
$450$	−450.000	−0.0471405
$451$	1656.00	0.172900
$452$	−1992.00	−0.207292
$453$	−8904.00	−0.923502
$454$	12552.0	1.29757
$455$	0	0
$456$	1344.00	0.138023
$457$	−6046.00	−0.618862	−0.309431	−	0.950922i	$-0.600139\pi$
$457$	−6046.00	−0.618862	−0.309431	+	0.950922i	$0.600139\pi$
$458$	−1508.00	−0.153852
$459$	486.000	0.0494217
$460$	−3120.00	−0.316241
$461$	−7122.00	−0.719533	−0.359766	−	0.933042i	$-0.617144\pi$
$461$	−7122.00	−0.719533	−0.359766	+	0.933042i	$0.617144\pi$
$462$	0	0
$463$	−11248.0	−1.12903	−0.564513	−	0.825424i	$-0.690936\pi$
$463$	−11248.0	−1.12903	−0.564513	+	0.825424i	$0.690936\pi$
$464$	−2976.00	−0.297753
$465$	780.000	0.0777885
$466$	−7740.00	−0.769418
$467$	18252.0	1.80857	0.904285	−	0.426930i	$-0.140405\pi$
$467$	18252.0	1.80857	0.904285	+	0.426930i	$0.140405\pi$
$468$	−72.0000	−0.00711154
$469$	0	0
$470$	−4560.00	−0.447526
$471$	−5622.00	−0.549996
$472$	2784.00	0.271491
$473$	−4944.00	−0.480603
$474$	−5952.00	−0.576760
$475$	−1400.00	−0.135235
$476$	0	0
$477$	−1782.00	−0.171053
$478$	−1488.00	−0.142384
$479$	18168.0	1.73302	0.866511	−	0.499159i	$-0.166358\pi$
$479$	18168.0	1.73302	0.866511	+	0.499159i	$0.166358\pi$
$480$	−480.000	−0.0456435
$481$	356.000	0.0337468
$482$	10948.0	1.03458
$483$	0	0
$484$	−4748.00	−0.445905
$485$	−550.000	−0.0514932
$486$	−486.000	−0.0453609
$487$	19856.0	1.84756	0.923780	−	0.382925i	$-0.125083\pi$
$487$	19856.0	1.84756	0.923780	+	0.382925i	$0.125083\pi$
$488$	880.000	0.0816306
$489$	1356.00	0.125400
$490$	0	0
$491$	11220.0	1.03127	0.515633	−	0.856810i	$-0.327557\pi$
$491$	11220.0	1.03127	0.515633	+	0.856810i	$0.327557\pi$
$492$	1656.00	0.151744
$493$	−3348.00	−0.305855
$494$	−224.000	−0.0204013
$495$	540.000	0.0490327
$496$	832.000	0.0753184
$497$	0	0
$498$	−1656.00	−0.149010
$499$	−9268.00	−0.831448	−0.415724	−	0.909491i	$-0.636472\pi$
$499$	−9268.00	−0.831448	−0.415724	+	0.909491i	$0.636472\pi$
$500$	500.000	0.0447214
$501$	4248.00	0.378816
$502$	3960.00	0.352079
$503$	−18576.0	−1.64665	−0.823323	−	0.567573i	$-0.807882\pi$
$503$	−18576.0	−1.64665	−0.823323	+	0.567573i	$0.807882\pi$
$504$	0	0
$505$	−2850.00	−0.251135
$506$	3744.00	0.328935
$507$	−6579.00	−0.576299
$508$	−7552.00	−0.659578
$509$	11190.0	0.974436	0.487218	−	0.873280i	$-0.338012\pi$
$509$	11190.0	0.974436	0.487218	+	0.873280i	$0.338012\pi$
$510$	−540.000	−0.0468855
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−1512.00	−0.130129
$514$	−420.000	−0.0360416
$515$	1520.00	0.130057
$516$	−4944.00	−0.421797
$517$	5472.00	0.465490
$518$	0	0
$519$	−1278.00	−0.108089
$520$	80.0000	0.00674660
$521$	306.000	0.0257315	0.0128657	−	0.999917i	$-0.495905\pi$
$521$	306.000	0.0257315	0.0128657	+	0.999917i	$0.495905\pi$
$522$	3348.00	0.280724
$523$	−17444.0	−1.45846	−0.729228	−	0.684270i	$-0.760121\pi$
$523$	−17444.0	−1.45846	−0.729228	+	0.684270i	$0.760121\pi$
$524$	11568.0	0.964409
$525$	0	0
$526$	2856.00	0.236744
$527$	936.000	0.0773677
$528$	576.000	0.0474757
$529$	12169.0	1.00016
$530$	1980.00	0.162275
$531$	−3132.00	−0.255965
$532$	0	0
$533$	−276.000	−0.0224294
$534$	3780.00	0.306323
$535$	1080.00	0.0872756
$536$	1568.00	0.126357
$537$	8100.00	0.650914
$538$	8244.00	0.660640
$539$	0	0
$540$	540.000	0.0430331
$541$	−538.000	−0.0427549	−0.0213775	−	0.999771i	$-0.506805\pi$
$541$	−538.000	−0.0427549	−0.0213775	+	0.999771i	$0.506805\pi$
$542$	11560.0	0.916134
$543$	5934.00	0.468973
$544$	−576.000	−0.0453967
$545$	3070.00	0.241292
$546$	0	0
$547$	19820.0	1.54925	0.774627	−	0.632418i	$-0.217938\pi$
$547$	19820.0	1.54925	0.774627	+	0.632418i	$0.217938\pi$
$548$	3288.00	0.256307
$549$	−990.000	−0.0769621
$550$	−600.000	−0.0465165
$551$	10416.0	0.805329
$552$	3744.00	0.288687
$553$	0	0
$554$	−9148.00	−0.701555
$555$	−2670.00	−0.204208
$556$	1504.00	0.114719
$557$	−16686.0	−1.26932	−0.634658	−	0.772794i	$-0.718859\pi$
$557$	−16686.0	−1.26932	−0.634658	+	0.772794i	$0.718859\pi$
$558$	−936.000	−0.0710108
$559$	824.000	0.0623461
$560$	0	0
$561$	648.000	0.0487675
$562$	−6900.00	−0.517898
$563$	16788.0	1.25671	0.628357	−	0.777925i	$-0.283728\pi$
$563$	16788.0	1.25671	0.628357	+	0.777925i	$0.283728\pi$
$564$	5472.00	0.408533
$565$	−2490.00	−0.185407
$566$	−1400.00	−0.103969
$567$	0	0
$568$	7488.00	0.553151
$569$	15906.0	1.17191	0.585953	−	0.810345i	$-0.300720\pi$
$569$	15906.0	1.17191	0.585953	+	0.810345i	$0.300720\pi$
$570$	1680.00	0.123452
$571$	17084.0	1.25209	0.626045	−	0.779787i	$-0.284673\pi$
$571$	17084.0	1.25209	0.626045	+	0.779787i	$0.284673\pi$
$572$	−96.0000	−0.00701742
$573$	−6984.00	−0.509181
$574$	0	0
$575$	−3900.00	−0.282854
$576$	576.000	0.0416667
$577$	−25382.0	−1.83131	−0.915656	−	0.401964i	$-0.868328\pi$
$577$	−25382.0	−1.83131	−0.915656	+	0.401964i	$0.868328\pi$
$578$	9178.00	0.660475
$579$	−9498.00	−0.681733
$580$	−3720.00	−0.266318
$581$	0	0
$582$	660.000	0.0470067
$583$	−2376.00	−0.168789
$584$	4336.00	0.307235
$585$	−90.0000	−0.00636076
$586$	14340.0	1.01089
$587$	−13764.0	−0.967804	−0.483902	−	0.875122i	$-0.660781\pi$
$587$	−13764.0	−0.967804	−0.483902	+	0.875122i	$0.660781\pi$
$588$	0	0
$589$	−2912.00	−0.203713
$590$	3480.00	0.242829
$591$	−1242.00	−0.0864451
$592$	−2848.00	−0.197723
$593$	13266.0	0.918667	0.459333	−	0.888264i	$-0.348088\pi$
$593$	13266.0	0.918667	0.459333	+	0.888264i	$0.348088\pi$
$594$	−648.000	−0.0447605
$595$	0	0
$596$	13560.0	0.931945
$597$	4908.00	0.336467
$598$	−624.000	−0.0426710
$599$	9600.00	0.654834	0.327417	−	0.944880i	$-0.393822\pi$
$599$	9600.00	0.654834	0.327417	+	0.944880i	$0.393822\pi$
$600$	−600.000	−0.0408248
$601$	19582.0	1.32906	0.664531	−	0.747261i	$-0.268631\pi$
$601$	19582.0	1.32906	0.664531	+	0.747261i	$0.268631\pi$
$602$	0	0
$603$	−1764.00	−0.119130
$604$	−11872.0	−0.799776
$605$	−5935.00	−0.398830
$606$	3420.00	0.229254
$607$	−3944.00	−0.263727	−0.131863	−	0.991268i	$-0.542096\pi$
$607$	−3944.00	−0.263727	−0.131863	+	0.991268i	$0.542096\pi$
$608$	1792.00	0.119532
$609$	0	0
$610$	1100.00	0.0730126
$611$	−912.000	−0.0603855
$612$	648.000	0.0428004
$613$	20846.0	1.37351	0.686755	−	0.726889i	$-0.259034\pi$
$613$	20846.0	1.37351	0.686755	+	0.726889i	$0.259034\pi$
$614$	13288.0	0.873388
$615$	2070.00	0.135724
$616$	0	0
$617$	15342.0	1.00105	0.500523	−	0.865723i	$-0.333141\pi$
$617$	15342.0	1.00105	0.500523	+	0.865723i	$0.333141\pi$
$618$	−1824.00	−0.118725
$619$	5128.00	0.332975	0.166488	−	0.986044i	$-0.446757\pi$
$619$	5128.00	0.332975	0.166488	+	0.986044i	$0.446757\pi$
$620$	1040.00	0.0673668
$621$	−4212.00	−0.272177
$622$	−10752.0	−0.693112
$623$	0	0
$624$	−96.0000	−0.00615878
$625$	625.000	0.0400000
$626$	4252.00	0.271476
$627$	−2016.00	−0.128407
$628$	−7496.00	−0.476310
$629$	−3204.00	−0.203103
$630$	0	0
$631$	31016.0	1.95678	0.978389	−	0.206771i	$-0.0662954\pi$
$631$	31016.0	1.95678	0.978389	+	0.206771i	$0.0662954\pi$
$632$	−7936.00	−0.499489
$633$	−8580.00	−0.538743
$634$	−2148.00	−0.134555
$635$	−9440.00	−0.589945
$636$	−2376.00	−0.148136
$637$	0	0
$638$	4464.00	0.277009
$639$	−8424.00	−0.521515
$640$	−640.000	−0.0395285
$641$	15474.0	0.953489	0.476744	−	0.879042i	$-0.341817\pi$
$641$	15474.0	0.953489	0.476744	+	0.879042i	$0.341817\pi$
$642$	−1296.00	−0.0796714
$643$	−24644.0	−1.51145	−0.755727	−	0.654887i	$-0.772716\pi$
$643$	−24644.0	−1.51145	−0.755727	+	0.654887i	$0.772716\pi$
$644$	0	0
$645$	−6180.00	−0.377267
$646$	2016.00	0.122784
$647$	16632.0	1.01062	0.505310	−	0.862938i	$-0.331378\pi$
$647$	16632.0	1.01062	0.505310	+	0.862938i	$0.331378\pi$
$648$	−648.000	−0.0392837
$649$	−4176.00	−0.252577
$650$	100.000	0.00603434
$651$	0	0
$652$	1808.00	0.108599
$653$	−10542.0	−0.631762	−0.315881	−	0.948799i	$-0.602300\pi$
$653$	−10542.0	−0.631762	−0.315881	+	0.948799i	$0.602300\pi$
$654$	−3684.00	−0.220269
$655$	14460.0	0.862594
$656$	2208.00	0.131415
$657$	−4878.00	−0.289663
$658$	0	0
$659$	15276.0	0.902987	0.451494	−	0.892274i	$-0.350891\pi$
$659$	15276.0	0.902987	0.451494	+	0.892274i	$0.350891\pi$
$660$	720.000	0.0424636
$661$	−1478.00	−0.0869706	−0.0434853	−	0.999054i	$-0.513846\pi$
$661$	−1478.00	−0.0869706	−0.0434853	+	0.999054i	$0.513846\pi$
$662$	5576.00	0.327368
$663$	−108.000	−0.00632635
$664$	−2208.00	−0.129047
$665$	0	0
$666$	3204.00	0.186415
$667$	29016.0	1.68441
$668$	5664.00	0.328064
$669$	3288.00	0.190017
$670$	1960.00	0.113017
$671$	−1320.00	−0.0759434
$672$	0	0
$673$	−19366.0	−1.10922	−0.554610	−	0.832111i	$-0.687132\pi$
$673$	−19366.0	−1.10922	−0.554610	+	0.832111i	$0.687132\pi$
$674$	12668.0	0.723966
$675$	675.000	0.0384900
$676$	−8772.00	−0.499090
$677$	21390.0	1.21430	0.607152	−	0.794585i	$-0.292312\pi$
$677$	21390.0	1.21430	0.607152	+	0.794585i	$0.292312\pi$
$678$	2988.00	0.169253
$679$	0	0
$680$	−720.000	−0.0406040
$681$	−18828.0	−1.05946
$682$	−1248.00	−0.0700710
$683$	−21672.0	−1.21414	−0.607069	−	0.794649i	$-0.707655\pi$
$683$	−21672.0	−1.21414	−0.607069	+	0.794649i	$0.707655\pi$
$684$	−2016.00	−0.112695
$685$	4110.00	0.229248
$686$	0	0
$687$	2262.00	0.125620
$688$	−6592.00	−0.365287
$689$	396.000	0.0218961
$690$	4680.00	0.258210
$691$	5992.00	0.329879	0.164940	−	0.986304i	$-0.447257\pi$
$691$	5992.00	0.329879	0.164940	+	0.986304i	$0.447257\pi$
$692$	−1704.00	−0.0936075
$693$	0	0
$694$	14064.0	0.769254
$695$	1880.00	0.102608
$696$	4464.00	0.243114
$697$	2484.00	0.134990
$698$	−2948.00	−0.159862
$699$	11610.0	0.628227
$700$	0	0
$701$	17766.0	0.957222	0.478611	−	0.878027i	$-0.341140\pi$
$701$	17766.0	0.957222	0.478611	+	0.878027i	$0.341140\pi$
$702$	108.000	0.00580655
$703$	9968.00	0.534780
$704$	768.000	0.0411152
$705$	6840.00	0.365403
$706$	15900.0	0.847598
$707$	0	0
$708$	−4176.00	−0.221672
$709$	−24514.0	−1.29851	−0.649254	−	0.760571i	$-0.724919\pi$
$709$	−24514.0	−1.29851	−0.649254	+	0.760571i	$0.724919\pi$
$710$	9360.00	0.494753
$711$	8928.00	0.470923
$712$	5040.00	0.265284
$713$	−8112.00	−0.426082
$714$	0	0
$715$	−120.000	−0.00627657
$716$	10800.0	0.563708
$717$	2232.00	0.116256
$718$	−13248.0	−0.688595
$719$	13176.0	0.683424	0.341712	−	0.939805i	$-0.388993\pi$
$719$	13176.0	0.683424	0.341712	+	0.939805i	$0.388993\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	7446.00	0.383811
$723$	−16422.0	−0.844731
$724$	7912.00	0.406142
$725$	−4650.00	−0.238202
$726$	7122.00	0.364080
$727$	−20792.0	−1.06071	−0.530353	−	0.847777i	$-0.677940\pi$
$727$	−20792.0	−1.06071	−0.530353	+	0.847777i	$0.677940\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	5420.00	0.274799
$731$	−7416.00	−0.375227
$732$	−1320.00	−0.0666511
$733$	21742.0	1.09558	0.547789	−	0.836616i	$-0.315470\pi$
$733$	21742.0	1.09558	0.547789	+	0.836616i	$0.315470\pi$
$734$	3568.00	0.179424
$735$	0	0
$736$	4992.00	0.250010
$737$	−2352.00	−0.117554
$738$	−2484.00	−0.123899
$739$	39044.0	1.94351	0.971757	−	0.235984i	$-0.0758313\pi$
$739$	39044.0	1.94351	0.971757	+	0.235984i	$0.0758313\pi$
$740$	−3560.00	−0.176849
$741$	336.000	0.0166576
$742$	0	0
$743$	−31116.0	−1.53639	−0.768193	−	0.640218i	$-0.778844\pi$
$743$	−31116.0	−1.53639	−0.768193	+	0.640218i	$0.778844\pi$
$744$	−1248.00	−0.0614972
$745$	16950.0	0.833557
$746$	3956.00	0.194155
$747$	2484.00	0.121666
$748$	864.000	0.0422339
$749$	0	0
$750$	−750.000	−0.0365148
$751$	−29320.0	−1.42464	−0.712318	−	0.701857i	$-0.752355\pi$
$751$	−29320.0	−1.42464	−0.712318	+	0.701857i	$0.752355\pi$
$752$	7296.00	0.353800
$753$	−5940.00	−0.287471
$754$	−744.000	−0.0359349
$755$	−14840.0	−0.715342
$756$	0	0
$757$	−2266.00	−0.108797	−0.0543984	−	0.998519i	$-0.517324\pi$
$757$	−2266.00	−0.108797	−0.0543984	+	0.998519i	$0.517324\pi$
$758$	21560.0	1.03311
$759$	−5616.00	−0.268574
$760$	2240.00	0.106912
$761$	29946.0	1.42647	0.713234	−	0.700926i	$-0.247230\pi$
$761$	29946.0	1.42647	0.713234	+	0.700926i	$0.247230\pi$
$762$	11328.0	0.538543
$763$	0	0
$764$	−9312.00	−0.440964
$765$	810.000	0.0382818
$766$	−11760.0	−0.554708
$767$	696.000	0.0327655
$768$	768.000	0.0360844
$769$	23110.0	1.08370	0.541852	−	0.840474i	$-0.317723\pi$
$769$	23110.0	1.08370	0.541852	+	0.840474i	$0.317723\pi$
$770$	0	0
$771$	630.000	0.0294279
$772$	−12664.0	−0.590398
$773$	31950.0	1.48663	0.743313	−	0.668944i	$-0.233253\pi$
$773$	31950.0	1.48663	0.743313	+	0.668944i	$0.233253\pi$
$774$	7416.00	0.344396
$775$	1300.00	0.0602547
$776$	880.000	0.0407090
$777$	0	0
$778$	−12876.0	−0.593351
$779$	−7728.00	−0.355436
$780$	−120.000	−0.00550858
$781$	−11232.0	−0.514613
$782$	5616.00	0.256813
$783$	−5022.00	−0.229210
$784$	0	0
$785$	−9370.00	−0.426025
$786$	−17352.0	−0.787437
$787$	−6284.00	−0.284626	−0.142313	−	0.989822i	$-0.545454\pi$
$787$	−6284.00	−0.284626	−0.142313	+	0.989822i	$0.545454\pi$
$788$	−1656.00	−0.0748637
$789$	−4284.00	−0.193301
$790$	−9920.00	−0.446757
$791$	0	0
$792$	−864.000	−0.0387638
$793$	220.000	0.00985174
$794$	5908.00	0.264064
$795$	−2970.00	−0.132497
$796$	6544.00	0.291389
$797$	−5946.00	−0.264264	−0.132132	−	0.991232i	$-0.542182\pi$
$797$	−5946.00	−0.264264	−0.132132	+	0.991232i	$0.542182\pi$
$798$	0	0
$799$	8208.00	0.363427
$800$	−800.000	−0.0353553
$801$	−5670.00	−0.250112
$802$	11148.0	0.490835
$803$	−6504.00	−0.285830
$804$	−2352.00	−0.103170
$805$	0	0
$806$	208.000	0.00908993
$807$	−12366.0	−0.539410
$808$	4560.00	0.198540
$809$	27090.0	1.17730	0.588649	−	0.808389i	$-0.299660\pi$
$809$	27090.0	1.17730	0.588649	+	0.808389i	$0.299660\pi$
$810$	−810.000	−0.0351364
$811$	20104.0	0.870465	0.435232	−	0.900318i	$-0.356666\pi$
$811$	20104.0	0.870465	0.435232	+	0.900318i	$0.356666\pi$
$812$	0	0
$813$	−17340.0	−0.748020
$814$	4272.00	0.183948
$815$	2260.00	0.0971342
$816$	864.000	0.0370662
$817$	23072.0	0.987989
$818$	−30812.0	−1.31701
$819$	0	0
$820$	2760.00	0.117541
$821$	7302.00	0.310404	0.155202	−	0.987883i	$-0.450397\pi$
$821$	7302.00	0.310404	0.155202	+	0.987883i	$0.450397\pi$
$822$	−4932.00	−0.209274
$823$	−24136.0	−1.02227	−0.511135	−	0.859500i	$-0.670775\pi$
$823$	−24136.0	−1.02227	−0.511135	+	0.859500i	$0.670775\pi$
$824$	−2432.00	−0.102819
$825$	900.000	0.0379806
$826$	0	0
$827$	22680.0	0.953641	0.476820	−	0.879001i	$-0.341789\pi$
$827$	22680.0	0.953641	0.476820	+	0.879001i	$0.341789\pi$
$828$	−5616.00	−0.235712
$829$	20338.0	0.852072	0.426036	−	0.904706i	$-0.359910\pi$
$829$	20338.0	0.852072	0.426036	+	0.904706i	$0.359910\pi$
$830$	−2760.00	−0.115423
$831$	13722.0	0.572817
$832$	−128.000	−0.00533366
$833$	0	0
$834$	−2256.00	−0.0936677
$835$	7080.00	0.293429
$836$	−2688.00	−0.111204
$837$	1404.00	0.0579801
$838$	5880.00	0.242388
$839$	−6600.00	−0.271582	−0.135791	−	0.990738i	$-0.543358\pi$
$839$	−6600.00	−0.271582	−0.135791	+	0.990738i	$0.543358\pi$
$840$	0	0
$841$	10207.0	0.418508
$842$	−508.000	−0.0207920
$843$	10350.0	0.422862
$844$	−11440.0	−0.466565
$845$	−10965.0	−0.446399
$846$	−8208.00	−0.333566
$847$	0	0
$848$	−3168.00	−0.128290
$849$	2100.00	0.0848902
$850$	−900.000	−0.0363173
$851$	27768.0	1.11854
$852$	−11232.0	−0.451646
$853$	40174.0	1.61258	0.806290	−	0.591520i	$-0.201472\pi$
$853$	40174.0	1.61258	0.806290	+	0.591520i	$0.201472\pi$
$854$	0	0
$855$	−2520.00	−0.100798
$856$	−1728.00	−0.0689975
$857$	20778.0	0.828195	0.414097	−	0.910233i	$-0.364097\pi$
$857$	20778.0	0.828195	0.414097	+	0.910233i	$0.364097\pi$
$858$	144.000	0.00572970
$859$	−7400.00	−0.293929	−0.146964	−	0.989142i	$-0.546950\pi$
$859$	−7400.00	−0.293929	−0.146964	+	0.989142i	$0.546950\pi$
$860$	−8240.00	−0.326723
$861$	0	0
$862$	26496.0	1.04693
$863$	684.000	0.0269799	0.0134899	−	0.999909i	$-0.495706\pi$
$863$	684.000	0.0269799	0.0134899	+	0.999909i	$0.495706\pi$
$864$	−864.000	−0.0340207
$865$	−2130.00	−0.0837251
$866$	33196.0	1.30259
$867$	−13767.0	−0.539275
$868$	0	0
$869$	11904.0	0.464690
$870$	5580.00	0.217448
$871$	392.000	0.0152496
$872$	−4912.00	−0.190758
$873$	−990.000	−0.0383808
$874$	−17472.0	−0.676200
$875$	0	0
$876$	−6504.00	−0.250856
$877$	−9754.00	−0.375563	−0.187782	−	0.982211i	$-0.560130\pi$
$877$	−9754.00	−0.375563	−0.187782	+	0.982211i	$0.560130\pi$
$878$	−13064.0	−0.502151
$879$	−21510.0	−0.825386
$880$	960.000	0.0367745
$881$	−14310.0	−0.547237	−0.273619	−	0.961838i	$-0.588221\pi$
$881$	−14310.0	−0.547237	−0.273619	+	0.961838i	$0.588221\pi$
$882$	0	0
$883$	−14092.0	−0.537071	−0.268535	−	0.963270i	$-0.586540\pi$
$883$	−14092.0	−0.537071	−0.268535	+	0.963270i	$0.586540\pi$
$884$	−144.000	−0.00547878
$885$	−5220.00	−0.198269
$886$	−24432.0	−0.926421
$887$	−45600.0	−1.72615	−0.863077	−	0.505073i	$-0.831466\pi$
$887$	−45600.0	−1.72615	−0.863077	+	0.505073i	$0.831466\pi$
$888$	4272.00	0.161440
$889$	0	0
$890$	6300.00	0.237277
$891$	972.000	0.0365468
$892$	4384.00	0.164560
$893$	−25536.0	−0.956920
$894$	−20340.0	−0.760930
$895$	13500.0	0.504196
$896$	0	0
$897$	936.000	0.0348407
$898$	−612.000	−0.0227424
$899$	−9672.00	−0.358820
$900$	900.000	0.0333333
$901$	−3564.00	−0.131780
$902$	−3312.00	−0.122259
$903$	0	0
$904$	3984.00	0.146577
$905$	9890.00	0.363265
$906$	17808.0	0.653015
$907$	8012.00	0.293312	0.146656	−	0.989188i	$-0.453149\pi$
$907$	8012.00	0.293312	0.146656	+	0.989188i	$0.453149\pi$
$908$	−25104.0	−0.917517
$909$	−5130.00	−0.187185
$910$	0	0
$911$	2136.00	0.0776826	0.0388413	−	0.999245i	$-0.487633\pi$
$911$	2136.00	0.0776826	0.0388413	+	0.999245i	$0.487633\pi$
$912$	−2688.00	−0.0975971
$913$	3312.00	0.120056
$914$	12092.0	0.437602
$915$	−1650.00	−0.0596146
$916$	3016.00	0.108790
$917$	0	0
$918$	−972.000	−0.0349464
$919$	−15280.0	−0.548466	−0.274233	−	0.961663i	$-0.588424\pi$
$919$	−15280.0	−0.548466	−0.274233	+	0.961663i	$0.588424\pi$
$920$	6240.00	0.223616
$921$	−19932.0	−0.713118
$922$	14244.0	0.508787
$923$	1872.00	0.0667580
$924$	0	0
$925$	−4450.00	−0.158178
$926$	22496.0	0.798342
$927$	2736.00	0.0969385
$928$	5952.00	0.210543
$929$	−20910.0	−0.738466	−0.369233	−	0.929337i	$-0.620380\pi$
$929$	−20910.0	−0.738466	−0.369233	+	0.929337i	$0.620380\pi$
$930$	−1560.00	−0.0550047
$931$	0	0
$932$	15480.0	0.544060
$933$	16128.0	0.565924
$934$	−36504.0	−1.27885
$935$	1080.00	0.0377752
$936$	144.000	0.00502862
$937$	38122.0	1.32913	0.664563	−	0.747232i	$-0.268618\pi$
$937$	38122.0	1.32913	0.664563	+	0.747232i	$0.268618\pi$
$938$	0	0
$939$	−6378.00	−0.221659
$940$	9120.00	0.316449
$941$	−42810.0	−1.48307	−0.741534	−	0.670916i	$-0.765901\pi$
$941$	−42810.0	−1.48307	−0.741534	+	0.670916i	$0.765901\pi$
$942$	11244.0	0.388906
$943$	−21528.0	−0.743423
$944$	−5568.00	−0.191973
$945$	0	0
$946$	9888.00	0.339838
$947$	39864.0	1.36790	0.683952	−	0.729527i	$-0.260260\pi$
$947$	39864.0	1.36790	0.683952	+	0.729527i	$0.260260\pi$
$948$	11904.0	0.407831
$949$	1084.00	0.0370792
$950$	2800.00	0.0956253
$951$	3222.00	0.109864
$952$	0	0
$953$	−23850.0	−0.810679	−0.405340	−	0.914166i	$-0.632847\pi$
$953$	−23850.0	−0.810679	−0.405340	+	0.914166i	$0.632847\pi$
$954$	3564.00	0.120953
$955$	−11640.0	−0.394410
$956$	2976.00	0.100681
$957$	−6696.00	−0.226177
$958$	−36336.0	−1.22543
$959$	0	0
$960$	960.000	0.0322749
$961$	−27087.0	−0.909234
$962$	−712.000	−0.0238626
$963$	1944.00	0.0650514
$964$	−21896.0	−0.731559
$965$	−15830.0	−0.528068
$966$	0	0
$967$	−12832.0	−0.426731	−0.213366	−	0.976972i	$-0.568443\pi$
$967$	−12832.0	−0.426731	−0.213366	+	0.976972i	$0.568443\pi$
$968$	9496.00	0.315303
$969$	−3024.00	−0.100253
$970$	1100.00	0.0364112
$971$	15804.0	0.522322	0.261161	−	0.965295i	$-0.415895\pi$
$971$	15804.0	0.522322	0.261161	+	0.965295i	$0.415895\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	−39712.0	−1.30642
$975$	−150.000	−0.00492702
$976$	−1760.00	−0.0577215
$977$	−33114.0	−1.08435	−0.542175	−	0.840265i	$-0.682399\pi$
$977$	−33114.0	−1.08435	−0.542175	+	0.840265i	$0.682399\pi$
$978$	−2712.00	−0.0886710
$979$	−7560.00	−0.246801
$980$	0	0
$981$	5526.00	0.179849
$982$	−22440.0	−0.729215
$983$	58632.0	1.90241	0.951206	−	0.308558i	$-0.0998462\pi$
$983$	58632.0	1.90241	0.951206	+	0.308558i	$0.0998462\pi$
$984$	−3312.00	−0.107299
$985$	−2070.00	−0.0669601
$986$	6696.00	0.216272
$987$	0	0
$988$	448.000	0.0144259
$989$	64272.0	2.06646
$990$	−1080.00	−0.0346714
$991$	55784.0	1.78813	0.894065	−	0.447937i	$-0.147841\pi$
$991$	55784.0	1.78813	0.894065	+	0.447937i	$0.147841\pi$
$992$	−1664.00	−0.0532581
$993$	−8364.00	−0.267295
$994$	0	0
$995$	8180.00	0.260627
$996$	3312.00	0.105366
$997$	23326.0	0.740965	0.370482	−	0.928840i	$-0.379192\pi$
$997$	23326.0	0.740965	0.370482	+	0.928840i	$0.379192\pi$
$998$	18536.0	0.587923
$999$	−4806.00	−0.152207

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.a.1.1	✓	1	7.6	odd	2
630.4.a.v.1.1		1	21.20	even	2
1050.4.a.t.1.1		1	35.34	odd	2
1050.4.g.o.799.1		2	35.27	even	4
1050.4.g.o.799.2		2	35.13	even	4
1470.4.a.n.1.1		1	1.1	even	1	trivial
1680.4.a.n.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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