LMFDB - Embedded newform 1470.4.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1470.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$86.7328077084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -15.0000 q^{11} +12.0000 q^{12} -77.0000 q^{13} +15.0000 q^{15} +16.0000 q^{16} +96.0000 q^{17} +18.0000 q^{18} +37.0000 q^{19} +20.0000 q^{20} -30.0000 q^{22} -99.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -154.000 q^{26} +27.0000 q^{27} +240.000 q^{29} +30.0000 q^{30} +166.000 q^{31} +32.0000 q^{32} -45.0000 q^{33} +192.000 q^{34} +36.0000 q^{36} +335.000 q^{37} +74.0000 q^{38} -231.000 q^{39} +40.0000 q^{40} -21.0000 q^{41} -40.0000 q^{43} -60.0000 q^{44} +45.0000 q^{45} -198.000 q^{46} +639.000 q^{47} +48.0000 q^{48} +50.0000 q^{50} +288.000 q^{51} -308.000 q^{52} +153.000 q^{53} +54.0000 q^{54} -75.0000 q^{55} +111.000 q^{57} +480.000 q^{58} +684.000 q^{59} +60.0000 q^{60} -488.000 q^{61} +332.000 q^{62} +64.0000 q^{64} -385.000 q^{65} -90.0000 q^{66} +608.000 q^{67} +384.000 q^{68} -297.000 q^{69} +198.000 q^{71} +72.0000 q^{72} -338.000 q^{73} +670.000 q^{74} +75.0000 q^{75} +148.000 q^{76} -462.000 q^{78} -736.000 q^{79} +80.0000 q^{80} +81.0000 q^{81} -42.0000 q^{82} +480.000 q^{85} -80.0000 q^{86} +720.000 q^{87} -120.000 q^{88} +1290.00 q^{89} +90.0000 q^{90} -396.000 q^{92} +498.000 q^{93} +1278.00 q^{94} +185.000 q^{95} +96.0000 q^{96} +1456.00 q^{97} -135.000 q^{99} +O(q^{100})\)

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
$11$	−15.0000	−0.411152	−0.205576	−	0.978641i	$-0.565907\pi$
$11$	−15.0000	−0.411152	−0.205576	+	0.978641i	$0.565907\pi$
$12$	12.0000	0.288675
$13$	−77.0000	−1.64277	−0.821383	−	0.570377i	$-0.806797\pi$
$13$	−77.0000	−1.64277	−0.821383	+	0.570377i	$0.806797\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	96.0000	1.36961	0.684806	−	0.728725i	$-0.259887\pi$
$17$	96.0000	1.36961	0.684806	+	0.728725i	$0.259887\pi$
$18$	18.0000	0.235702
$19$	37.0000	0.446757	0.223378	−	0.974732i	$-0.428291\pi$
$19$	37.0000	0.446757	0.223378	+	0.974732i	$0.428291\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−30.0000	−0.290728
$23$	−99.0000	−0.897519	−0.448759	−	0.893653i	$-0.648134\pi$
$23$	−99.0000	−0.897519	−0.448759	+	0.893653i	$0.648134\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−154.000	−1.16161
$27$	27.0000	0.192450
$28$	0	0
$29$	240.000	1.53679	0.768395	−	0.639976i	$-0.221056\pi$
$29$	240.000	1.53679	0.768395	+	0.639976i	$0.221056\pi$
$30$	30.0000	0.182574
$31$	166.000	0.961757	0.480879	−	0.876787i	$-0.340318\pi$
$31$	166.000	0.961757	0.480879	+	0.876787i	$0.340318\pi$
$32$	32.0000	0.176777
$33$	−45.0000	−0.237379
$34$	192.000	0.968463
$35$	0	0
$36$	36.0000	0.166667
$37$	335.000	1.48848	0.744239	−	0.667914i	$-0.232813\pi$
$37$	335.000	1.48848	0.744239	+	0.667914i	$0.232813\pi$
$38$	74.0000	0.315905
$39$	−231.000	−0.948451
$40$	40.0000	0.158114
$41$	−21.0000	−0.0799914	−0.0399957	−	0.999200i	$-0.512734\pi$
$41$	−21.0000	−0.0799914	−0.0399957	+	0.999200i	$0.512734\pi$
$42$	0	0
$43$	−40.0000	−0.141859	−0.0709296	−	0.997481i	$-0.522597\pi$
$43$	−40.0000	−0.141859	−0.0709296	+	0.997481i	$0.522597\pi$
$44$	−60.0000	−0.205576
$45$	45.0000	0.149071
$46$	−198.000	−0.634641
$47$	639.000	1.98314	0.991572	−	0.129560i	$-0.0413565\pi$
$47$	639.000	1.98314	0.991572	+	0.129560i	$0.0413565\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	50.0000	0.141421
$51$	288.000	0.790746
$52$	−308.000	−0.821383
$53$	153.000	0.396531	0.198266	−	0.980148i	$-0.436469\pi$
$53$	153.000	0.396531	0.198266	+	0.980148i	$0.436469\pi$
$54$	54.0000	0.136083
$55$	−75.0000	−0.183873
$56$	0	0
$57$	111.000	0.257935
$58$	480.000	1.08667
$59$	684.000	1.50931	0.754654	−	0.656123i	$-0.227805\pi$
$59$	684.000	1.50931	0.754654	+	0.656123i	$0.227805\pi$
$60$	60.0000	0.129099
$61$	−488.000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−488.000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	332.000	0.680065
$63$	0	0
$64$	64.0000	0.125000
$65$	−385.000	−0.734667
$66$	−90.0000	−0.167852
$67$	608.000	1.10864	0.554321	−	0.832303i	$-0.312978\pi$
$67$	608.000	1.10864	0.554321	+	0.832303i	$0.312978\pi$
$68$	384.000	0.684806
$69$	−297.000	−0.518183
$70$	0	0
$71$	198.000	0.330962	0.165481	−	0.986213i	$-0.447082\pi$
$71$	198.000	0.330962	0.165481	+	0.986213i	$0.447082\pi$
$72$	72.0000	0.117851
$73$	−338.000	−0.541917	−0.270958	−	0.962591i	$-0.587341\pi$
$73$	−338.000	−0.541917	−0.270958	+	0.962591i	$0.587341\pi$
$74$	670.000	1.05251
$75$	75.0000	0.115470
$76$	148.000	0.223378
$77$	0	0
$78$	−462.000	−0.670656
$79$	−736.000	−1.04818	−0.524092	−	0.851662i	$-0.675595\pi$
$79$	−736.000	−1.04818	−0.524092	+	0.851662i	$0.675595\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	−42.0000	−0.0565625
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	480.000	0.612510
$86$	−80.0000	−0.100310
$87$	720.000	0.887266
$88$	−120.000	−0.145364
$89$	1290.00	1.53640	0.768201	−	0.640209i	$-0.221152\pi$
$89$	1290.00	1.53640	0.768201	+	0.640209i	$0.221152\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	−396.000	−0.448759
$93$	498.000	0.555271
$94$	1278.00	1.40229
$95$	185.000	0.199796
$96$	96.0000	0.102062
$97$	1456.00	1.52407	0.762033	−	0.647538i	$-0.224201\pi$
$97$	1456.00	1.52407	0.762033	+	0.647538i	$0.224201\pi$
$98$	0	0
$99$	−135.000	−0.137051
$100$	100.000	0.100000
$101$	−408.000	−0.401956	−0.200978	−	0.979596i	$-0.564412\pi$
$101$	−408.000	−0.401956	−0.200978	+	0.979596i	$0.564412\pi$
$102$	576.000	0.559142
$103$	520.000	0.497448	0.248724	−	0.968574i	$-0.419989\pi$
$103$	520.000	0.497448	0.248724	+	0.968574i	$0.419989\pi$
$104$	−616.000	−0.580805
$105$	0	0
$106$	306.000	0.280390
$107$	−1254.00	−1.13298	−0.566490	−	0.824069i	$-0.691699\pi$
$107$	−1254.00	−1.13298	−0.566490	+	0.824069i	$0.691699\pi$
$108$	108.000	0.0962250
$109$	−2122.00	−1.86469	−0.932343	−	0.361575i	$-0.882239\pi$
$109$	−2122.00	−1.86469	−0.932343	+	0.361575i	$0.882239\pi$
$110$	−150.000	−0.130018
$111$	1005.00	0.859373
$112$	0	0
$113$	−1818.00	−1.51348	−0.756739	−	0.653717i	$-0.773209\pi$
$113$	−1818.00	−1.51348	−0.756739	+	0.653717i	$0.773209\pi$
$114$	222.000	0.182388
$115$	−495.000	−0.401383
$116$	960.000	0.768395
$117$	−693.000	−0.547589
$118$	1368.00	1.06724
$119$	0	0
$120$	120.000	0.0912871
$121$	−1106.00	−0.830954
$122$	−976.000	−0.724286
$123$	−63.0000	−0.0461831
$124$	664.000	0.480879
$125$	125.000	0.0894427
$126$	0	0
$127$	−523.000	−0.365423	−0.182712	−	0.983167i	$-0.558487\pi$
$127$	−523.000	−0.365423	−0.182712	+	0.983167i	$0.558487\pi$
$128$	128.000	0.0883883
$129$	−120.000	−0.0819024
$130$	−770.000	−0.519488
$131$	−453.000	−0.302128	−0.151064	−	0.988524i	$-0.548270\pi$
$131$	−453.000	−0.302128	−0.151064	+	0.988524i	$0.548270\pi$
$132$	−180.000	−0.118689
$133$	0	0
$134$	1216.00	0.783928
$135$	135.000	0.0860663
$136$	768.000	0.484231
$137$	−1842.00	−1.14871	−0.574353	−	0.818608i	$-0.694746\pi$
$137$	−1842.00	−1.14871	−0.574353	+	0.818608i	$0.694746\pi$
$138$	−594.000	−0.366410
$139$	−308.000	−0.187944	−0.0939720	−	0.995575i	$-0.529956\pi$
$139$	−308.000	−0.187944	−0.0939720	+	0.995575i	$0.529956\pi$
$140$	0	0
$141$	1917.00	1.14497
$142$	396.000	0.234025
$143$	1155.00	0.675426
$144$	144.000	0.0833333
$145$	1200.00	0.687273
$146$	−676.000	−0.383193
$147$	0	0
$148$	1340.00	0.744239
$149$	1056.00	0.580610	0.290305	−	0.956934i	$-0.406243\pi$
$149$	1056.00	0.580610	0.290305	+	0.956934i	$0.406243\pi$
$150$	150.000	0.0816497
$151$	−862.000	−0.464560	−0.232280	−	0.972649i	$-0.574619\pi$
$151$	−862.000	−0.464560	−0.232280	+	0.972649i	$0.574619\pi$
$152$	296.000	0.157952
$153$	864.000	0.456538
$154$	0	0
$155$	830.000	0.430111
$156$	−924.000	−0.474226
$157$	691.000	0.351260	0.175630	−	0.984456i	$-0.443804\pi$
$157$	691.000	0.351260	0.175630	+	0.984456i	$0.443804\pi$
$158$	−1472.00	−0.741177
$159$	459.000	0.228938
$160$	160.000	0.0790569
$161$	0	0
$162$	162.000	0.0785674
$163$	776.000	0.372890	0.186445	−	0.982465i	$-0.440303\pi$
$163$	776.000	0.372890	0.186445	+	0.982465i	$0.440303\pi$
$164$	−84.0000	−0.0399957
$165$	−225.000	−0.106159
$166$	0	0
$167$	1617.00	0.749265	0.374632	−	0.927173i	$-0.377769\pi$
$167$	1617.00	0.749265	0.374632	+	0.927173i	$0.377769\pi$
$168$	0	0
$169$	3732.00	1.69868
$170$	960.000	0.433110
$171$	333.000	0.148919
$172$	−160.000	−0.0709296
$173$	891.000	0.391569	0.195785	−	0.980647i	$-0.437275\pi$
$173$	891.000	0.391569	0.195785	+	0.980647i	$0.437275\pi$
$174$	1440.00	0.627391
$175$	0	0
$176$	−240.000	−0.102788
$177$	2052.00	0.871400
$178$	2580.00	1.08640
$179$	−2829.00	−1.18128	−0.590641	−	0.806935i	$-0.701125\pi$
$179$	−2829.00	−1.18128	−0.590641	+	0.806935i	$0.701125\pi$
$180$	180.000	0.0745356
$181$	3472.00	1.42581	0.712905	−	0.701260i	$-0.247379\pi$
$181$	3472.00	1.42581	0.712905	+	0.701260i	$0.247379\pi$
$182$	0	0
$183$	−1464.00	−0.591377
$184$	−792.000	−0.317321
$185$	1675.00	0.665667
$186$	996.000	0.392636
$187$	−1440.00	−0.563119
$188$	2556.00	0.991572
$189$	0	0
$190$	370.000	0.141277
$191$	2694.00	1.02058	0.510291	−	0.860002i	$-0.329538\pi$
$191$	2694.00	1.02058	0.510291	+	0.860002i	$0.329538\pi$
$192$	192.000	0.0721688
$193$	−946.000	−0.352822	−0.176411	−	0.984317i	$-0.556449\pi$
$193$	−946.000	−0.352822	−0.176411	+	0.984317i	$0.556449\pi$
$194$	2912.00	1.07768
$195$	−1155.00	−0.424160
$196$	0	0
$197$	3579.00	1.29438	0.647191	−	0.762328i	$-0.275944\pi$
$197$	3579.00	1.29438	0.647191	+	0.762328i	$0.275944\pi$
$198$	−270.000	−0.0969094
$199$	−4664.00	−1.66142	−0.830709	−	0.556707i	$-0.812065\pi$
$199$	−4664.00	−1.66142	−0.830709	+	0.556707i	$0.812065\pi$
$200$	200.000	0.0707107
$201$	1824.00	0.640075
$202$	−816.000	−0.284226
$203$	0	0
$204$	1152.00	0.395373
$205$	−105.000	−0.0357733
$206$	1040.00	0.351749
$207$	−891.000	−0.299173
$208$	−1232.00	−0.410691
$209$	−555.000	−0.183685
$210$	0	0
$211$	−2581.00	−0.842101	−0.421051	−	0.907037i	$-0.638339\pi$
$211$	−2581.00	−0.842101	−0.421051	+	0.907037i	$0.638339\pi$
$212$	612.000	0.198266
$213$	594.000	0.191081
$214$	−2508.00	−0.801137
$215$	−200.000	−0.0634413
$216$	216.000	0.0680414
$217$	0	0
$218$	−4244.00	−1.31853
$219$	−1014.00	−0.312876
$220$	−300.000	−0.0919363
$221$	−7392.00	−2.24995
$222$	2010.00	0.607668
$223$	4228.00	1.26963	0.634816	−	0.772664i	$-0.281076\pi$
$223$	4228.00	1.26963	0.634816	+	0.772664i	$0.281076\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−3636.00	−1.07019
$227$	−1752.00	−0.512266	−0.256133	−	0.966642i	$-0.582448\pi$
$227$	−1752.00	−0.512266	−0.256133	+	0.966642i	$0.582448\pi$
$228$	444.000	0.128968
$229$	−3134.00	−0.904369	−0.452185	−	0.891924i	$-0.649355\pi$
$229$	−3134.00	−0.904369	−0.452185	+	0.891924i	$0.649355\pi$
$230$	−990.000	−0.283820
$231$	0	0
$232$	1920.00	0.543337
$233$	−1590.00	−0.447057	−0.223529	−	0.974697i	$-0.571758\pi$
$233$	−1590.00	−0.447057	−0.223529	+	0.974697i	$0.571758\pi$
$234$	−1386.00	−0.387204
$235$	3195.00	0.886889
$236$	2736.00	0.754654
$237$	−2208.00	−0.605169
$238$	0	0
$239$	−1230.00	−0.332896	−0.166448	−	0.986050i	$-0.553230\pi$
$239$	−1230.00	−0.332896	−0.166448	+	0.986050i	$0.553230\pi$
$240$	240.000	0.0645497
$241$	1321.00	0.353083	0.176542	−	0.984293i	$-0.443509\pi$
$241$	1321.00	0.353083	0.176542	+	0.984293i	$0.443509\pi$
$242$	−2212.00	−0.587573
$243$	243.000	0.0641500
$244$	−1952.00	−0.512148
$245$	0	0
$246$	−126.000	−0.0326564
$247$	−2849.00	−0.733917
$248$	1328.00	0.340033
$249$	0	0
$250$	250.000	0.0632456
$251$	7413.00	1.86416	0.932081	−	0.362251i	$-0.117992\pi$
$251$	7413.00	1.86416	0.932081	+	0.362251i	$0.117992\pi$
$252$	0	0
$253$	1485.00	0.369016
$254$	−1046.00	−0.258393
$255$	1440.00	0.353633
$256$	256.000	0.0625000
$257$	−5220.00	−1.26698	−0.633492	−	0.773750i	$-0.718379\pi$
$257$	−5220.00	−1.26698	−0.633492	+	0.773750i	$0.718379\pi$
$258$	−240.000	−0.0579137
$259$	0	0
$260$	−1540.00	−0.367334
$261$	2160.00	0.512263
$262$	−906.000	−0.213637
$263$	1728.00	0.405145	0.202572	−	0.979267i	$-0.435070\pi$
$263$	1728.00	0.405145	0.202572	+	0.979267i	$0.435070\pi$
$264$	−360.000	−0.0839260
$265$	765.000	0.177334
$266$	0	0
$267$	3870.00	0.887042
$268$	2432.00	0.554321
$269$	−4356.00	−0.987323	−0.493662	−	0.869654i	$-0.664342\pi$
$269$	−4356.00	−0.987323	−0.493662	+	0.869654i	$0.664342\pi$
$270$	270.000	0.0608581
$271$	−488.000	−0.109387	−0.0546935	−	0.998503i	$-0.517418\pi$
$271$	−488.000	−0.109387	−0.0546935	+	0.998503i	$0.517418\pi$
$272$	1536.00	0.342403
$273$	0	0
$274$	−3684.00	−0.812258
$275$	−375.000	−0.0822304
$276$	−1188.00	−0.259091
$277$	146.000	0.0316689	0.0158345	−	0.999875i	$-0.494960\pi$
$277$	146.000	0.0316689	0.0158345	+	0.999875i	$0.494960\pi$
$278$	−616.000	−0.132896
$279$	1494.00	0.320586
$280$	0	0
$281$	−1881.00	−0.399328	−0.199664	−	0.979864i	$-0.563985\pi$
$281$	−1881.00	−0.399328	−0.199664	+	0.979864i	$0.563985\pi$
$282$	3834.00	0.809615
$283$	−8822.00	−1.85305	−0.926526	−	0.376232i	$-0.877220\pi$
$283$	−8822.00	−1.85305	−0.926526	+	0.376232i	$0.877220\pi$
$284$	792.000	0.165481
$285$	555.000	0.115352
$286$	2310.00	0.477598
$287$	0	0
$288$	288.000	0.0589256
$289$	4303.00	0.875840
$290$	2400.00	0.485975
$291$	4368.00	0.879920
$292$	−1352.00	−0.270958
$293$	−8127.00	−1.62042	−0.810212	−	0.586137i	$-0.800648\pi$
$293$	−8127.00	−1.62042	−0.810212	+	0.586137i	$0.800648\pi$
$294$	0	0
$295$	3420.00	0.674983
$296$	2680.00	0.526256
$297$	−405.000	−0.0791262
$298$	2112.00	0.410553
$299$	7623.00	1.47441
$300$	300.000	0.0577350
$301$	0	0
$302$	−1724.00	−0.328494
$303$	−1224.00	−0.232069
$304$	592.000	0.111689
$305$	−2440.00	−0.458079
$306$	1728.00	0.322821
$307$	10444.0	1.94160	0.970799	−	0.239895i	$-0.0771129\pi$
$307$	10444.0	1.94160	0.970799	+	0.239895i	$0.0771129\pi$
$308$	0	0
$309$	1560.00	0.287202
$310$	1660.00	0.304134
$311$	6396.00	1.16619	0.583093	−	0.812405i	$-0.301842\pi$
$311$	6396.00	1.16619	0.583093	+	0.812405i	$0.301842\pi$
$312$	−1848.00	−0.335328
$313$	6820.00	1.23159	0.615797	−	0.787905i	$-0.288834\pi$
$313$	6820.00	1.23159	0.615797	+	0.787905i	$0.288834\pi$
$314$	1382.00	0.248378
$315$	0	0
$316$	−2944.00	−0.524092
$317$	5046.00	0.894043	0.447021	−	0.894523i	$-0.352485\pi$
$317$	5046.00	0.894043	0.447021	+	0.894523i	$0.352485\pi$
$318$	918.000	0.161883
$319$	−3600.00	−0.631854
$320$	320.000	0.0559017
$321$	−3762.00	−0.654126
$322$	0	0
$323$	3552.00	0.611884
$324$	324.000	0.0555556
$325$	−1925.00	−0.328553
$326$	1552.00	0.263673
$327$	−6366.00	−1.07658
$328$	−168.000	−0.0282812
$329$	0	0
$330$	−450.000	−0.0750657
$331$	−5755.00	−0.955660	−0.477830	−	0.878452i	$-0.658576\pi$
$331$	−5755.00	−0.955660	−0.477830	+	0.878452i	$0.658576\pi$
$332$	0	0
$333$	3015.00	0.496159
$334$	3234.00	0.529810
$335$	3040.00	0.495800
$336$	0	0
$337$	−6172.00	−0.997657	−0.498828	−	0.866701i	$-0.666236\pi$
$337$	−6172.00	−0.997657	−0.498828	+	0.866701i	$0.666236\pi$
$338$	7464.00	1.20115
$339$	−5454.00	−0.873807
$340$	1920.00	0.306255
$341$	−2490.00	−0.395428
$342$	666.000	0.105302
$343$	0	0
$344$	−320.000	−0.0501548
$345$	−1485.00	−0.231738
$346$	1782.00	0.276881
$347$	−5958.00	−0.921735	−0.460868	−	0.887469i	$-0.652462\pi$
$347$	−5958.00	−0.921735	−0.460868	+	0.887469i	$0.652462\pi$
$348$	2880.00	0.443633
$349$	5236.00	0.803085	0.401542	−	0.915840i	$-0.368474\pi$
$349$	5236.00	0.803085	0.401542	+	0.915840i	$0.368474\pi$
$350$	0	0
$351$	−2079.00	−0.316150
$352$	−480.000	−0.0726821
$353$	3120.00	0.470427	0.235214	−	0.971944i	$-0.424421\pi$
$353$	3120.00	0.470427	0.235214	+	0.971944i	$0.424421\pi$
$354$	4104.00	0.616173
$355$	990.000	0.148011
$356$	5160.00	0.768201
$357$	0	0
$358$	−5658.00	−0.835292
$359$	5508.00	0.809752	0.404876	−	0.914372i	$-0.367315\pi$
$359$	5508.00	0.809752	0.404876	+	0.914372i	$0.367315\pi$
$360$	360.000	0.0527046
$361$	−5490.00	−0.800408
$362$	6944.00	1.00820
$363$	−3318.00	−0.479752
$364$	0	0
$365$	−1690.00	−0.242352
$366$	−2928.00	−0.418167
$367$	−7499.00	−1.06661	−0.533303	−	0.845924i	$-0.679050\pi$
$367$	−7499.00	−1.06661	−0.533303	+	0.845924i	$0.679050\pi$
$368$	−1584.00	−0.224380
$369$	−189.000	−0.0266638
$370$	3350.00	0.470698
$371$	0	0
$372$	1992.00	0.277635
$373$	5102.00	0.708235	0.354117	−	0.935201i	$-0.384781\pi$
$373$	5102.00	0.708235	0.354117	+	0.935201i	$0.384781\pi$
$374$	−2880.00	−0.398185
$375$	375.000	0.0516398
$376$	5112.00	0.701147
$377$	−18480.0	−2.52458
$378$	0	0
$379$	9851.00	1.33512	0.667562	−	0.744554i	$-0.267338\pi$
$379$	9851.00	1.33512	0.667562	+	0.744554i	$0.267338\pi$
$380$	740.000	0.0998979
$381$	−1569.00	−0.210977
$382$	5388.00	0.721660
$383$	303.000	0.0404245	0.0202122	−	0.999796i	$-0.493566\pi$
$383$	303.000	0.0404245	0.0202122	+	0.999796i	$0.493566\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	−1892.00	−0.249483
$387$	−360.000	−0.0472864
$388$	5824.00	0.762033
$389$	2274.00	0.296392	0.148196	−	0.988958i	$-0.452653\pi$
$389$	2274.00	0.296392	0.148196	+	0.988958i	$0.452653\pi$
$390$	−2310.00	−0.299927
$391$	−9504.00	−1.22925
$392$	0	0
$393$	−1359.00	−0.174434
$394$	7158.00	0.915266
$395$	−3680.00	−0.468762
$396$	−540.000	−0.0685253
$397$	1066.00	0.134763	0.0673816	−	0.997727i	$-0.478536\pi$
$397$	1066.00	0.134763	0.0673816	+	0.997727i	$0.478536\pi$
$398$	−9328.00	−1.17480
$399$	0	0
$400$	400.000	0.0500000
$401$	−10557.0	−1.31469	−0.657346	−	0.753589i	$-0.728321\pi$
$401$	−10557.0	−1.31469	−0.657346	+	0.753589i	$0.728321\pi$
$402$	3648.00	0.452601
$403$	−12782.0	−1.57994
$404$	−1632.00	−0.200978
$405$	405.000	0.0496904
$406$	0	0
$407$	−5025.00	−0.611990
$408$	2304.00	0.279571
$409$	10750.0	1.29964	0.649821	−	0.760088i	$-0.274844\pi$
$409$	10750.0	1.29964	0.649821	+	0.760088i	$0.274844\pi$
$410$	−210.000	−0.0252955
$411$	−5526.00	−0.663206
$412$	2080.00	0.248724
$413$	0	0
$414$	−1782.00	−0.211547
$415$	0	0
$416$	−2464.00	−0.290403
$417$	−924.000	−0.108510
$418$	−1110.00	−0.129885
$419$	3843.00	0.448074	0.224037	−	0.974581i	$-0.428076\pi$
$419$	3843.00	0.448074	0.224037	+	0.974581i	$0.428076\pi$
$420$	0	0
$421$	10670.0	1.23521	0.617606	−	0.786488i	$-0.288103\pi$
$421$	10670.0	1.23521	0.617606	+	0.786488i	$0.288103\pi$
$422$	−5162.00	−0.595456
$423$	5751.00	0.661048
$424$	1224.00	0.140195
$425$	2400.00	0.273923
$426$	1188.00	0.135115
$427$	0	0
$428$	−5016.00	−0.566490
$429$	3465.00	0.389958
$430$	−400.000	−0.0448598
$431$	−10032.0	−1.12117	−0.560585	−	0.828097i	$-0.689424\pi$
$431$	−10032.0	−1.12117	−0.560585	+	0.828097i	$0.689424\pi$
$432$	432.000	0.0481125
$433$	−7448.00	−0.826624	−0.413312	−	0.910590i	$-0.635628\pi$
$433$	−7448.00	−0.826624	−0.413312	+	0.910590i	$0.635628\pi$
$434$	0	0
$435$	3600.00	0.396797
$436$	−8488.00	−0.932343
$437$	−3663.00	−0.400973
$438$	−2028.00	−0.221237
$439$	−7040.00	−0.765378	−0.382689	−	0.923877i	$-0.625002\pi$
$439$	−7040.00	−0.765378	−0.382689	+	0.923877i	$0.625002\pi$
$440$	−600.000	−0.0650088
$441$	0	0
$442$	−14784.0	−1.59096
$443$	−2472.00	−0.265120	−0.132560	−	0.991175i	$-0.542320\pi$
$443$	−2472.00	−0.265120	−0.132560	+	0.991175i	$0.542320\pi$
$444$	4020.00	0.429686
$445$	6450.00	0.687100
$446$	8456.00	0.897765
$447$	3168.00	0.335215
$448$	0	0
$449$	−5829.00	−0.612667	−0.306334	−	0.951924i	$-0.599102\pi$
$449$	−5829.00	−0.612667	−0.306334	+	0.951924i	$0.599102\pi$
$450$	450.000	0.0471405
$451$	315.000	0.0328886
$452$	−7272.00	−0.756739
$453$	−2586.00	−0.268214
$454$	−3504.00	−0.362227
$455$	0	0
$456$	888.000	0.0911939
$457$	−1954.00	−0.200009	−0.100005	−	0.994987i	$-0.531886\pi$
$457$	−1954.00	−0.200009	−0.100005	+	0.994987i	$0.531886\pi$
$458$	−6268.00	−0.639486
$459$	2592.00	0.263582
$460$	−1980.00	−0.200691
$461$	−1428.00	−0.144270	−0.0721351	−	0.997395i	$-0.522981\pi$
$461$	−1428.00	−0.144270	−0.0721351	+	0.997395i	$0.522981\pi$
$462$	0	0
$463$	16025.0	1.60852	0.804260	−	0.594277i	$-0.202562\pi$
$463$	16025.0	1.60852	0.804260	+	0.594277i	$0.202562\pi$
$464$	3840.00	0.384197
$465$	2490.00	0.248325
$466$	−3180.00	−0.316117
$467$	744.000	0.0737221	0.0368610	−	0.999320i	$-0.488264\pi$
$467$	744.000	0.0737221	0.0368610	+	0.999320i	$0.488264\pi$
$468$	−2772.00	−0.273794
$469$	0	0
$470$	6390.00	0.627125
$471$	2073.00	0.202800
$472$	5472.00	0.533621
$473$	600.000	0.0583256
$474$	−4416.00	−0.427919
$475$	925.000	0.0893514
$476$	0	0
$477$	1377.00	0.132177
$478$	−2460.00	−0.235393
$479$	−14562.0	−1.38905	−0.694525	−	0.719469i	$-0.744385\pi$
$479$	−14562.0	−1.38905	−0.694525	+	0.719469i	$0.744385\pi$
$480$	480.000	0.0456435
$481$	−25795.0	−2.44522
$482$	2642.00	0.249668
$483$	0	0
$484$	−4424.00	−0.415477
$485$	7280.00	0.681583
$486$	486.000	0.0453609
$487$	17912.0	1.66667	0.833337	−	0.552765i	$-0.186427\pi$
$487$	17912.0	1.66667	0.833337	+	0.552765i	$0.186427\pi$
$488$	−3904.00	−0.362143
$489$	2328.00	0.215288
$490$	0	0
$491$	5364.00	0.493022	0.246511	−	0.969140i	$-0.420716\pi$
$491$	5364.00	0.493022	0.246511	+	0.969140i	$0.420716\pi$
$492$	−252.000	−0.0230915
$493$	23040.0	2.10481
$494$	−5698.00	−0.518958
$495$	−675.000	−0.0612909
$496$	2656.00	0.240439
$497$	0	0
$498$	0	0
$499$	4808.00	0.431334	0.215667	−	0.976467i	$-0.430807\pi$
$499$	4808.00	0.431334	0.215667	+	0.976467i	$0.430807\pi$
$500$	500.000	0.0447214
$501$	4851.00	0.432588
$502$	14826.0	1.31816
$503$	−16548.0	−1.46688	−0.733438	−	0.679756i	$-0.762086\pi$
$503$	−16548.0	−1.46688	−0.733438	+	0.679756i	$0.762086\pi$
$504$	0	0
$505$	−2040.00	−0.179760
$506$	2970.00	0.260934
$507$	11196.0	0.980733
$508$	−2092.00	−0.182712
$509$	114.000	0.00992723	0.00496362	−	0.999988i	$-0.498420\pi$
$509$	114.000	0.00992723	0.00496362	+	0.999988i	$0.498420\pi$
$510$	2880.00	0.250056
$511$	0	0
$512$	512.000	0.0441942
$513$	999.000	0.0859784
$514$	−10440.0	−0.895892
$515$	2600.00	0.222465
$516$	−480.000	−0.0409512
$517$	−9585.00	−0.815373
$518$	0	0
$519$	2673.00	0.226073
$520$	−3080.00	−0.259744
$521$	−13575.0	−1.14152	−0.570760	−	0.821117i	$-0.693351\pi$
$521$	−13575.0	−1.14152	−0.570760	+	0.821117i	$0.693351\pi$
$522$	4320.00	0.362225
$523$	−9854.00	−0.823873	−0.411936	−	0.911213i	$-0.635147\pi$
$523$	−9854.00	−0.823873	−0.411936	+	0.911213i	$0.635147\pi$
$524$	−1812.00	−0.151064
$525$	0	0
$526$	3456.00	0.286481
$527$	15936.0	1.31724
$528$	−720.000	−0.0593447
$529$	−2366.00	−0.194460
$530$	1530.00	0.125394
$531$	6156.00	0.503103
$532$	0	0
$533$	1617.00	0.131407
$534$	7740.00	0.627233
$535$	−6270.00	−0.506684
$536$	4864.00	0.391964
$537$	−8487.00	−0.682013
$538$	−8712.00	−0.698143
$539$	0	0
$540$	540.000	0.0430331
$541$	−13546.0	−1.07650	−0.538251	−	0.842784i	$-0.680915\pi$
$541$	−13546.0	−1.07650	−0.538251	+	0.842784i	$0.680915\pi$
$542$	−976.000	−0.0773483
$543$	10416.0	0.823192
$544$	3072.00	0.242116
$545$	−10610.0	−0.833913
$546$	0	0
$547$	−7432.00	−0.580931	−0.290466	−	0.956885i	$-0.593810\pi$
$547$	−7432.00	−0.580931	−0.290466	+	0.956885i	$0.593810\pi$
$548$	−7368.00	−0.574353
$549$	−4392.00	−0.341432
$550$	−750.000	−0.0581456
$551$	8880.00	0.686571
$552$	−2376.00	−0.183205
$553$	0	0
$554$	292.000	0.0223933
$555$	5025.00	0.384323
$556$	−1232.00	−0.0939720
$557$	12123.0	0.922205	0.461102	−	0.887347i	$-0.347454\pi$
$557$	12123.0	0.922205	0.461102	+	0.887347i	$0.347454\pi$
$558$	2988.00	0.226688
$559$	3080.00	0.233041
$560$	0	0
$561$	−4320.00	−0.325117
$562$	−3762.00	−0.282367
$563$	−5910.00	−0.442410	−0.221205	−	0.975227i	$-0.570999\pi$
$563$	−5910.00	−0.442410	−0.221205	+	0.975227i	$0.570999\pi$
$564$	7668.00	0.572484
$565$	−9090.00	−0.676848
$566$	−17644.0	−1.31031
$567$	0	0
$568$	1584.00	0.117013
$569$	−8457.00	−0.623086	−0.311543	−	0.950232i	$-0.600846\pi$
$569$	−8457.00	−0.623086	−0.311543	+	0.950232i	$0.600846\pi$
$570$	1110.00	0.0815663
$571$	−568.000	−0.0416288	−0.0208144	−	0.999783i	$-0.506626\pi$
$571$	−568.000	−0.0416288	−0.0208144	+	0.999783i	$0.506626\pi$
$572$	4620.00	0.337713
$573$	8082.00	0.589233
$574$	0	0
$575$	−2475.00	−0.179504
$576$	576.000	0.0416667
$577$	−26882.0	−1.93954	−0.969768	−	0.244029i	$-0.921531\pi$
$577$	−26882.0	−1.93954	−0.969768	+	0.244029i	$0.921531\pi$
$578$	8606.00	0.619312
$579$	−2838.00	−0.203702
$580$	4800.00	0.343636
$581$	0	0
$582$	8736.00	0.622197
$583$	−2295.00	−0.163035
$584$	−2704.00	−0.191596
$585$	−3465.00	−0.244889
$586$	−16254.0	−1.14581
$587$	−4746.00	−0.333711	−0.166856	−	0.985981i	$-0.553361\pi$
$587$	−4746.00	−0.333711	−0.166856	+	0.985981i	$0.553361\pi$
$588$	0	0
$589$	6142.00	0.429672
$590$	6840.00	0.477285
$591$	10737.0	0.747312
$592$	5360.00	0.372119
$593$	15528.0	1.07531	0.537655	−	0.843165i	$-0.319310\pi$
$593$	15528.0	1.07531	0.537655	+	0.843165i	$0.319310\pi$
$594$	−810.000	−0.0559507
$595$	0	0
$596$	4224.00	0.290305
$597$	−13992.0	−0.959220
$598$	15246.0	1.04257
$599$	678.000	0.0462476	0.0231238	−	0.999733i	$-0.492639\pi$
$599$	678.000	0.0462476	0.0231238	+	0.999733i	$0.492639\pi$
$600$	600.000	0.0408248
$601$	24010.0	1.62960	0.814799	−	0.579744i	$-0.196847\pi$
$601$	24010.0	1.62960	0.814799	+	0.579744i	$0.196847\pi$
$602$	0	0
$603$	5472.00	0.369547
$604$	−3448.00	−0.232280
$605$	−5530.00	−0.371614
$606$	−2448.00	−0.164098
$607$	−16889.0	−1.12933	−0.564665	−	0.825320i	$-0.690995\pi$
$607$	−16889.0	−1.12933	−0.564665	+	0.825320i	$0.690995\pi$
$608$	1184.00	0.0789762
$609$	0	0
$610$	−4880.00	−0.323911
$611$	−49203.0	−3.25784
$612$	3456.00	0.228269
$613$	30323.0	1.99794	0.998968	−	0.0454255i	$-0.0144644\pi$
$613$	30323.0	1.99794	0.998968	+	0.0454255i	$0.0144644\pi$
$614$	20888.0	1.37292
$615$	−315.000	−0.0206537
$616$	0	0
$617$	7380.00	0.481536	0.240768	−	0.970583i	$-0.422601\pi$
$617$	7380.00	0.481536	0.240768	+	0.970583i	$0.422601\pi$
$618$	3120.00	0.203082
$619$	3925.00	0.254861	0.127431	−	0.991847i	$-0.459327\pi$
$619$	3925.00	0.254861	0.127431	+	0.991847i	$0.459327\pi$
$620$	3320.00	0.215055
$621$	−2673.00	−0.172728
$622$	12792.0	0.824618
$623$	0	0
$624$	−3696.00	−0.237113
$625$	625.000	0.0400000
$626$	13640.0	0.870869
$627$	−1665.00	−0.106051
$628$	2764.00	0.175630
$629$	32160.0	2.03864
$630$	0	0
$631$	−8062.00	−0.508626	−0.254313	−	0.967122i	$-0.581849\pi$
$631$	−8062.00	−0.508626	−0.254313	+	0.967122i	$0.581849\pi$
$632$	−5888.00	−0.370589
$633$	−7743.00	−0.486187
$634$	10092.0	0.632184
$635$	−2615.00	−0.163422
$636$	1836.00	0.114469
$637$	0	0
$638$	−7200.00	−0.446788
$639$	1782.00	0.110321
$640$	640.000	0.0395285
$641$	−3123.00	−0.192435	−0.0962177	−	0.995360i	$-0.530674\pi$
$641$	−3123.00	−0.192435	−0.0962177	+	0.995360i	$0.530674\pi$
$642$	−7524.00	−0.462537
$643$	−28826.0	−1.76794	−0.883971	−	0.467542i	$-0.845140\pi$
$643$	−28826.0	−1.76794	−0.883971	+	0.467542i	$0.845140\pi$
$644$	0	0
$645$	−600.000	−0.0366279
$646$	7104.00	0.432667
$647$	8643.00	0.525180	0.262590	−	0.964908i	$-0.415423\pi$
$647$	8643.00	0.525180	0.262590	+	0.964908i	$0.415423\pi$
$648$	648.000	0.0392837
$649$	−10260.0	−0.620555
$650$	−3850.00	−0.232322
$651$	0	0
$652$	3104.00	0.186445
$653$	−24165.0	−1.44816	−0.724081	−	0.689715i	$-0.757736\pi$
$653$	−24165.0	−1.44816	−0.724081	+	0.689715i	$0.757736\pi$
$654$	−12732.0	−0.761255
$655$	−2265.00	−0.135116
$656$	−336.000	−0.0199979
$657$	−3042.00	−0.180639
$658$	0	0
$659$	−2364.00	−0.139740	−0.0698698	−	0.997556i	$-0.522258\pi$
$659$	−2364.00	−0.139740	−0.0698698	+	0.997556i	$0.522258\pi$
$660$	−900.000	−0.0530795
$661$	5080.00	0.298925	0.149462	−	0.988767i	$-0.452246\pi$
$661$	5080.00	0.298925	0.149462	+	0.988767i	$0.452246\pi$
$662$	−11510.0	−0.675754
$663$	−22176.0	−1.29901
$664$	0	0
$665$	0	0
$666$	6030.00	0.350837
$667$	−23760.0	−1.37930
$668$	6468.00	0.374632
$669$	12684.0	0.733022
$670$	6080.00	0.350583
$671$	7320.00	0.421141
$672$	0	0
$673$	−27508.0	−1.57557	−0.787783	−	0.615953i	$-0.788771\pi$
$673$	−27508.0	−1.57557	−0.787783	+	0.615953i	$0.788771\pi$
$674$	−12344.0	−0.705450
$675$	675.000	0.0384900
$676$	14928.0	0.849340
$677$	−3519.00	−0.199773	−0.0998864	−	0.994999i	$-0.531848\pi$
$677$	−3519.00	−0.199773	−0.0998864	+	0.994999i	$0.531848\pi$
$678$	−10908.0	−0.617875
$679$	0	0
$680$	3840.00	0.216555
$681$	−5256.00	−0.295757
$682$	−4980.00	−0.279610
$683$	−13308.0	−0.745559	−0.372779	−	0.927920i	$-0.621595\pi$
$683$	−13308.0	−0.745559	−0.372779	+	0.927920i	$0.621595\pi$
$684$	1332.00	0.0744595
$685$	−9210.00	−0.513717
$686$	0	0
$687$	−9402.00	−0.522138
$688$	−640.000	−0.0354648
$689$	−11781.0	−0.651408
$690$	−2970.00	−0.163864
$691$	12700.0	0.699176	0.349588	−	0.936903i	$-0.386322\pi$
$691$	12700.0	0.699176	0.349588	+	0.936903i	$0.386322\pi$
$692$	3564.00	0.195785
$693$	0	0
$694$	−11916.0	−0.651765
$695$	−1540.00	−0.0840511
$696$	5760.00	0.313696
$697$	−2016.00	−0.109557
$698$	10472.0	0.567867
$699$	−4770.00	−0.258109
$700$	0	0
$701$	−35922.0	−1.93546	−0.967728	−	0.251996i	$-0.918913\pi$
$701$	−35922.0	−1.93546	−0.967728	+	0.251996i	$0.918913\pi$
$702$	−4158.00	−0.223552
$703$	12395.0	0.664988
$704$	−960.000	−0.0513940
$705$	9585.00	0.512045
$706$	6240.00	0.332642
$707$	0	0
$708$	8208.00	0.435700
$709$	13124.0	0.695179	0.347590	−	0.937647i	$-0.387000\pi$
$709$	13124.0	0.695179	0.347590	+	0.937647i	$0.387000\pi$
$710$	1980.00	0.104659
$711$	−6624.00	−0.349394
$712$	10320.0	0.543200
$713$	−16434.0	−0.863195
$714$	0	0
$715$	5775.00	0.302060
$716$	−11316.0	−0.590641
$717$	−3690.00	−0.192197
$718$	11016.0	0.572581
$719$	−18702.0	−0.970051	−0.485026	−	0.874500i	$-0.661190\pi$
$719$	−18702.0	−0.970051	−0.485026	+	0.874500i	$0.661190\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	−10980.0	−0.565974
$723$	3963.00	0.203853
$724$	13888.0	0.712905
$725$	6000.00	0.307358
$726$	−6636.00	−0.339236
$727$	23191.0	1.18309	0.591545	−	0.806272i	$-0.298518\pi$
$727$	23191.0	1.18309	0.591545	+	0.806272i	$0.298518\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−3380.00	−0.171369
$731$	−3840.00	−0.194292
$732$	−5856.00	−0.295689
$733$	−21383.0	−1.07749	−0.538744	−	0.842469i	$-0.681101\pi$
$733$	−21383.0	−1.07749	−0.538744	+	0.842469i	$0.681101\pi$
$734$	−14998.0	−0.754205
$735$	0	0
$736$	−3168.00	−0.158660
$737$	−9120.00	−0.455820
$738$	−378.000	−0.0188542
$739$	24443.0	1.21671	0.608356	−	0.793664i	$-0.291829\pi$
$739$	24443.0	1.21671	0.608356	+	0.793664i	$0.291829\pi$
$740$	6700.00	0.332834
$741$	−8547.00	−0.423727
$742$	0	0
$743$	−12717.0	−0.627916	−0.313958	−	0.949437i	$-0.601655\pi$
$743$	−12717.0	−0.627916	−0.313958	+	0.949437i	$0.601655\pi$
$744$	3984.00	0.196318
$745$	5280.00	0.259657
$746$	10204.0	0.500798
$747$	0	0
$748$	−5760.00	−0.281559
$749$	0	0
$750$	750.000	0.0365148
$751$	20894.0	1.01522	0.507612	−	0.861586i	$-0.330528\pi$
$751$	20894.0	1.01522	0.507612	+	0.861586i	$0.330528\pi$
$752$	10224.0	0.495786
$753$	22239.0	1.07627
$754$	−36960.0	−1.78515
$755$	−4310.00	−0.207758
$756$	0	0
$757$	32762.0	1.57299	0.786496	−	0.617595i	$-0.211893\pi$
$757$	32762.0	1.57299	0.786496	+	0.617595i	$0.211893\pi$
$758$	19702.0	0.944075
$759$	4455.00	0.213052
$760$	1480.00	0.0706385
$761$	6813.00	0.324535	0.162267	−	0.986747i	$-0.448119\pi$
$761$	6813.00	0.324535	0.162267	+	0.986747i	$0.448119\pi$
$762$	−3138.00	−0.149183
$763$	0	0
$764$	10776.0	0.510291
$765$	4320.00	0.204170
$766$	606.000	0.0285844
$767$	−52668.0	−2.47944
$768$	768.000	0.0360844
$769$	−31619.0	−1.48272	−0.741359	−	0.671109i	$-0.765818\pi$
$769$	−31619.0	−1.48272	−0.741359	+	0.671109i	$0.765818\pi$
$770$	0	0
$771$	−15660.0	−0.731493
$772$	−3784.00	−0.176411
$773$	31659.0	1.47309	0.736543	−	0.676391i	$-0.236457\pi$
$773$	31659.0	1.47309	0.736543	+	0.676391i	$0.236457\pi$
$774$	−720.000	−0.0334365
$775$	4150.00	0.192351
$776$	11648.0	0.538839
$777$	0	0
$778$	4548.00	0.209581
$779$	−777.000	−0.0357367
$780$	−4620.00	−0.212080
$781$	−2970.00	−0.136075
$782$	−19008.0	−0.869213
$783$	6480.00	0.295755
$784$	0	0
$785$	3455.00	0.157088
$786$	−2718.00	−0.123343
$787$	16126.0	0.730406	0.365203	−	0.930928i	$-0.381000\pi$
$787$	16126.0	0.730406	0.365203	+	0.930928i	$0.381000\pi$
$788$	14316.0	0.647191
$789$	5184.00	0.233910
$790$	−7360.00	−0.331465
$791$	0	0
$792$	−1080.00	−0.0484547
$793$	37576.0	1.68268
$794$	2132.00	0.0952920
$795$	2295.00	0.102384
$796$	−18656.0	−0.830709
$797$	−27510.0	−1.22265	−0.611326	−	0.791379i	$-0.709364\pi$
$797$	−27510.0	−1.22265	−0.611326	+	0.791379i	$0.709364\pi$
$798$	0	0
$799$	61344.0	2.71614
$800$	800.000	0.0353553
$801$	11610.0	0.512134
$802$	−21114.0	−0.929628
$803$	5070.00	0.222810
$804$	7296.00	0.320037
$805$	0	0
$806$	−25564.0	−1.11719
$807$	−13068.0	−0.570031
$808$	−3264.00	−0.142113
$809$	−351.000	−0.0152540	−0.00762701	−	0.999971i	$-0.502428\pi$
$809$	−351.000	−0.0152540	−0.00762701	+	0.999971i	$0.502428\pi$
$810$	810.000	0.0351364
$811$	5929.00	0.256714	0.128357	−	0.991728i	$-0.459030\pi$
$811$	5929.00	0.256714	0.128357	+	0.991728i	$0.459030\pi$
$812$	0	0
$813$	−1464.00	−0.0631546
$814$	−10050.0	−0.432742
$815$	3880.00	0.166761
$816$	4608.00	0.197687
$817$	−1480.00	−0.0633766
$818$	21500.0	0.918985
$819$	0	0
$820$	−420.000	−0.0178866
$821$	−12174.0	−0.517510	−0.258755	−	0.965943i	$-0.583312\pi$
$821$	−12174.0	−0.517510	−0.258755	+	0.965943i	$0.583312\pi$
$822$	−11052.0	−0.468957
$823$	−15856.0	−0.671574	−0.335787	−	0.941938i	$-0.609002\pi$
$823$	−15856.0	−0.671574	−0.335787	+	0.941938i	$0.609002\pi$
$824$	4160.00	0.175874
$825$	−1125.00	−0.0474757
$826$	0	0
$827$	−27606.0	−1.16077	−0.580384	−	0.814343i	$-0.697097\pi$
$827$	−27606.0	−1.16077	−0.580384	+	0.814343i	$0.697097\pi$
$828$	−3564.00	−0.149586
$829$	−36248.0	−1.51863	−0.759315	−	0.650723i	$-0.774466\pi$
$829$	−36248.0	−1.51863	−0.759315	+	0.650723i	$0.774466\pi$
$830$	0	0
$831$	438.000	0.0182841
$832$	−4928.00	−0.205346
$833$	0	0
$834$	−1848.00	−0.0767278
$835$	8085.00	0.335081
$836$	−2220.00	−0.0918425
$837$	4482.00	0.185090
$838$	7686.00	0.316836
$839$	−7728.00	−0.317998	−0.158999	−	0.987279i	$-0.550827\pi$
$839$	−7728.00	−0.317998	−0.158999	+	0.987279i	$0.550827\pi$
$840$	0	0
$841$	33211.0	1.36172
$842$	21340.0	0.873426
$843$	−5643.00	−0.230552
$844$	−10324.0	−0.421051
$845$	18660.0	0.759673
$846$	11502.0	0.467431
$847$	0	0
$848$	2448.00	0.0991329
$849$	−26466.0	−1.06986
$850$	4800.00	0.193693
$851$	−33165.0	−1.33594
$852$	2376.00	0.0955404
$853$	2653.00	0.106491	0.0532456	−	0.998581i	$-0.483043\pi$
$853$	2653.00	0.106491	0.0532456	+	0.998581i	$0.483043\pi$
$854$	0	0
$855$	1665.00	0.0665986
$856$	−10032.0	−0.400569
$857$	−32202.0	−1.28355	−0.641773	−	0.766894i	$-0.721801\pi$
$857$	−32202.0	−1.28355	−0.641773	+	0.766894i	$0.721801\pi$
$858$	6930.00	0.275742
$859$	44116.0	1.75229	0.876146	−	0.482046i	$-0.160106\pi$
$859$	44116.0	1.75229	0.876146	+	0.482046i	$0.160106\pi$
$860$	−800.000	−0.0317207
$861$	0	0
$862$	−20064.0	−0.792787
$863$	41145.0	1.62293	0.811467	−	0.584398i	$-0.198669\pi$
$863$	41145.0	1.62293	0.811467	+	0.584398i	$0.198669\pi$
$864$	864.000	0.0340207
$865$	4455.00	0.175115
$866$	−14896.0	−0.584511
$867$	12909.0	0.505666
$868$	0	0
$869$	11040.0	0.430962
$870$	7200.00	0.280578
$871$	−46816.0	−1.82124
$872$	−16976.0	−0.659266
$873$	13104.0	0.508022
$874$	−7326.00	−0.283530
$875$	0	0
$876$	−4056.00	−0.156438
$877$	−11131.0	−0.428583	−0.214291	−	0.976770i	$-0.568744\pi$
$877$	−11131.0	−0.428583	−0.214291	+	0.976770i	$0.568744\pi$
$878$	−14080.0	−0.541204
$879$	−24381.0	−0.935553
$880$	−1200.00	−0.0459682
$881$	−48867.0	−1.86875	−0.934376	−	0.356288i	$-0.884042\pi$
$881$	−48867.0	−1.86875	−0.934376	+	0.356288i	$0.884042\pi$
$882$	0	0
$883$	−5374.00	−0.204813	−0.102406	−	0.994743i	$-0.532654\pi$
$883$	−5374.00	−0.204813	−0.102406	+	0.994743i	$0.532654\pi$
$884$	−29568.0	−1.12498
$885$	10260.0	0.389702
$886$	−4944.00	−0.187468
$887$	−17484.0	−0.661844	−0.330922	−	0.943658i	$-0.607360\pi$
$887$	−17484.0	−0.661844	−0.330922	+	0.943658i	$0.607360\pi$
$888$	8040.00	0.303834
$889$	0	0
$890$	12900.0	0.485853
$891$	−1215.00	−0.0456835
$892$	16912.0	0.634816
$893$	23643.0	0.885983
$894$	6336.00	0.237033
$895$	−14145.0	−0.528285
$896$	0	0
$897$	22869.0	0.851253
$898$	−11658.0	−0.433221
$899$	39840.0	1.47802
$900$	900.000	0.0333333
$901$	14688.0	0.543095
$902$	630.000	0.0232558
$903$	0	0
$904$	−14544.0	−0.535095
$905$	17360.0	0.637642
$906$	−5172.00	−0.189656
$907$	47522.0	1.73974	0.869869	−	0.493283i	$-0.164203\pi$
$907$	47522.0	1.73974	0.869869	+	0.493283i	$0.164203\pi$
$908$	−7008.00	−0.256133
$909$	−3672.00	−0.133985
$910$	0	0
$911$	−47766.0	−1.73717	−0.868583	−	0.495544i	$-0.834969\pi$
$911$	−47766.0	−1.73717	−0.868583	+	0.495544i	$0.834969\pi$
$912$	1776.00	0.0644838
$913$	0	0
$914$	−3908.00	−0.141428
$915$	−7320.00	−0.264472
$916$	−12536.0	−0.452185
$917$	0	0
$918$	5184.00	0.186381
$919$	−31396.0	−1.12694	−0.563470	−	0.826136i	$-0.690534\pi$
$919$	−31396.0	−1.12694	−0.563470	+	0.826136i	$0.690534\pi$
$920$	−3960.00	−0.141910
$921$	31332.0	1.12098
$922$	−2856.00	−0.102014
$923$	−15246.0	−0.543693
$924$	0	0
$925$	8375.00	0.297695
$926$	32050.0	1.13740
$927$	4680.00	0.165816
$928$	7680.00	0.271668
$929$	−14187.0	−0.501034	−0.250517	−	0.968112i	$-0.580601\pi$
$929$	−14187.0	−0.501034	−0.250517	+	0.968112i	$0.580601\pi$
$930$	4980.00	0.175592
$931$	0	0
$932$	−6360.00	−0.223529
$933$	19188.0	0.673298
$934$	1488.00	0.0521294
$935$	−7200.00	−0.251834
$936$	−5544.00	−0.193602
$937$	10612.0	0.369988	0.184994	−	0.982740i	$-0.440773\pi$
$937$	10612.0	0.369988	0.184994	+	0.982740i	$0.440773\pi$
$938$	0	0
$939$	20460.0	0.711062
$940$	12780.0	0.443444
$941$	−27750.0	−0.961343	−0.480672	−	0.876901i	$-0.659607\pi$
$941$	−27750.0	−0.961343	−0.480672	+	0.876901i	$0.659607\pi$
$942$	4146.00	0.143401
$943$	2079.00	0.0717938
$944$	10944.0	0.377327
$945$	0	0
$946$	1200.00	0.0412425
$947$	−23934.0	−0.821278	−0.410639	−	0.911798i	$-0.634694\pi$
$947$	−23934.0	−0.821278	−0.410639	+	0.911798i	$0.634694\pi$
$948$	−8832.00	−0.302584
$949$	26026.0	0.890242
$950$	1850.00	0.0631810
$951$	15138.0	0.516176
$952$	0	0
$953$	−18828.0	−0.639978	−0.319989	−	0.947421i	$-0.603679\pi$
$953$	−18828.0	−0.639978	−0.319989	+	0.947421i	$0.603679\pi$
$954$	2754.00	0.0934634
$955$	13470.0	0.456418
$956$	−4920.00	−0.166448
$957$	−10800.0	−0.364801
$958$	−29124.0	−0.982206
$959$	0	0
$960$	960.000	0.0322749
$961$	−2235.00	−0.0750227
$962$	−51590.0	−1.72903
$963$	−11286.0	−0.377660
$964$	5284.00	0.176542
$965$	−4730.00	−0.157787
$966$	0	0
$967$	6428.00	0.213765	0.106882	−	0.994272i	$-0.465913\pi$
$967$	6428.00	0.213765	0.106882	+	0.994272i	$0.465913\pi$
$968$	−8848.00	−0.293787
$969$	10656.0	0.353271
$970$	14560.0	0.481952
$971$	23571.0	0.779021	0.389510	−	0.921022i	$-0.372644\pi$
$971$	23571.0	0.779021	0.389510	+	0.921022i	$0.372644\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	35824.0	1.17852
$975$	−5775.00	−0.189690
$976$	−7808.00	−0.256074
$977$	−18474.0	−0.604949	−0.302475	−	0.953157i	$-0.597813\pi$
$977$	−18474.0	−0.604949	−0.302475	+	0.953157i	$0.597813\pi$
$978$	4656.00	0.152232
$979$	−19350.0	−0.631694
$980$	0	0
$981$	−19098.0	−0.621562
$982$	10728.0	0.348619
$983$	13389.0	0.434428	0.217214	−	0.976124i	$-0.430303\pi$
$983$	13389.0	0.434428	0.217214	+	0.976124i	$0.430303\pi$
$984$	−504.000	−0.0163282
$985$	17895.0	0.578865
$986$	46080.0	1.48832
$987$	0	0
$988$	−11396.0	−0.366959
$989$	3960.00	0.127321
$990$	−1350.00	−0.0433392
$991$	−32446.0	−1.04004	−0.520021	−	0.854154i	$-0.674076\pi$
$991$	−32446.0	−1.04004	−0.520021	+	0.854154i	$0.674076\pi$
$992$	5312.00	0.170016
$993$	−17265.0	−0.551750
$994$	0	0
$995$	−23320.0	−0.743009
$996$	0	0
$997$	23770.0	0.755069	0.377534	−	0.925996i	$-0.376772\pi$
$997$	23770.0	0.755069	0.377534	+	0.925996i	$0.376772\pi$
$998$	9616.00	0.304999
$999$	9045.00	0.286458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.ba.1.1		1
7.3	odd	6		210.4.i.d.121.1	✓	2
7.5	odd	6		210.4.i.d.151.1	yes	2
7.6	odd	2		1470.4.a.p.1.1		1
21.5	even	6		630.4.k.f.361.1		2
21.17	even	6		630.4.k.f.541.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.d.121.1	✓	2	7.3	odd	6
210.4.i.d.151.1	yes	2	7.5	odd	6
630.4.k.f.361.1		2	21.5	even	6
630.4.k.f.541.1		2	21.17	even	6
1470.4.a.p.1.1		1	7.6	odd	2
1470.4.a.ba.1.1		1	1.1	even	1	trivial

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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