LMFDB - Embedded newform 1470.4.a.u.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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -6.00000 q^{11} -12.0000 q^{12} +19.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} -12.0000 q^{17} +18.0000 q^{18} -119.000 q^{19} +20.0000 q^{20} -12.0000 q^{22} -12.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +38.0000 q^{26} -27.0000 q^{27} -252.000 q^{29} -30.0000 q^{30} -251.000 q^{31} +32.0000 q^{32} +18.0000 q^{33} -24.0000 q^{34} +36.0000 q^{36} +359.000 q^{37} -238.000 q^{38} -57.0000 q^{39} +40.0000 q^{40} -54.0000 q^{41} -37.0000 q^{43} -24.0000 q^{44} +45.0000 q^{45} -24.0000 q^{46} +246.000 q^{47} -48.0000 q^{48} +50.0000 q^{50} +36.0000 q^{51} +76.0000 q^{52} +552.000 q^{53} -54.0000 q^{54} -30.0000 q^{55} +357.000 q^{57} -504.000 q^{58} -408.000 q^{59} -60.0000 q^{60} -386.000 q^{61} -502.000 q^{62} +64.0000 q^{64} +95.0000 q^{65} +36.0000 q^{66} -811.000 q^{67} -48.0000 q^{68} +36.0000 q^{69} -54.0000 q^{71} +72.0000 q^{72} -173.000 q^{73} +718.000 q^{74} -75.0000 q^{75} -476.000 q^{76} -114.000 q^{78} +1061.00 q^{79} +80.0000 q^{80} +81.0000 q^{81} -108.000 q^{82} -1206.00 q^{83} -60.0000 q^{85} -74.0000 q^{86} +756.000 q^{87} -48.0000 q^{88} -672.000 q^{89} +90.0000 q^{90} -48.0000 q^{92} +753.000 q^{93} +492.000 q^{94} -595.000 q^{95} -96.0000 q^{96} -818.000 q^{97} -54.0000 q^{99} +O(q^{100})\)

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
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	−12.0000	−0.288675
$13$	19.0000	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$13$	19.0000	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−12.0000	−0.171202	−0.0856008	−	0.996330i	$-0.527281\pi$
$17$	−12.0000	−0.171202	−0.0856008	+	0.996330i	$0.527281\pi$
$18$	18.0000	0.235702
$19$	−119.000	−1.43687	−0.718433	−	0.695596i	$-0.755141\pi$
$19$	−119.000	−1.43687	−0.718433	+	0.695596i	$0.755141\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−12.0000	−0.116291
$23$	−12.0000	−0.108790	−0.0543951	−	0.998519i	$-0.517323\pi$
$23$	−12.0000	−0.108790	−0.0543951	+	0.998519i	$0.517323\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	38.0000	0.286631
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−252.000	−1.61363	−0.806814	−	0.590805i	$-0.798810\pi$
$29$	−252.000	−1.61363	−0.806814	+	0.590805i	$0.798810\pi$
$30$	−30.0000	−0.182574
$31$	−251.000	−1.45422	−0.727112	−	0.686519i	$-0.759138\pi$
$31$	−251.000	−1.45422	−0.727112	+	0.686519i	$0.759138\pi$
$32$	32.0000	0.176777
$33$	18.0000	0.0949514
$34$	−24.0000	−0.121058
$35$	0	0
$36$	36.0000	0.166667
$37$	359.000	1.59511	0.797557	−	0.603243i	$-0.206125\pi$
$37$	359.000	1.59511	0.797557	+	0.603243i	$0.206125\pi$
$38$	−238.000	−1.01602
$39$	−57.0000	−0.234033
$40$	40.0000	0.158114
$41$	−54.0000	−0.205692	−0.102846	−	0.994697i	$-0.532795\pi$
$41$	−54.0000	−0.205692	−0.102846	+	0.994697i	$0.532795\pi$
$42$	0	0
$43$	−37.0000	−0.131220	−0.0656099	−	0.997845i	$-0.520899\pi$
$43$	−37.0000	−0.131220	−0.0656099	+	0.997845i	$0.520899\pi$
$44$	−24.0000	−0.0822304
$45$	45.0000	0.149071
$46$	−24.0000	−0.0769262
$47$	246.000	0.763464	0.381732	−	0.924273i	$-0.375328\pi$
$47$	246.000	0.763464	0.381732	+	0.924273i	$0.375328\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	50.0000	0.141421
$51$	36.0000	0.0988433
$52$	76.0000	0.202679
$53$	552.000	1.43062	0.715312	−	0.698806i	$-0.246285\pi$
$53$	552.000	1.43062	0.715312	+	0.698806i	$0.246285\pi$
$54$	−54.0000	−0.136083
$55$	−30.0000	−0.0735491
$56$	0	0
$57$	357.000	0.829576
$58$	−504.000	−1.14101
$59$	−408.000	−0.900289	−0.450145	−	0.892956i	$-0.648628\pi$
$59$	−408.000	−0.900289	−0.450145	+	0.892956i	$0.648628\pi$
$60$	−60.0000	−0.129099
$61$	−386.000	−0.810201	−0.405100	−	0.914272i	$-0.632763\pi$
$61$	−386.000	−0.810201	−0.405100	+	0.914272i	$0.632763\pi$
$62$	−502.000	−1.02829
$63$	0	0
$64$	64.0000	0.125000
$65$	95.0000	0.181282
$66$	36.0000	0.0671408
$67$	−811.000	−1.47880	−0.739399	−	0.673268i	$-0.764890\pi$
$67$	−811.000	−1.47880	−0.739399	+	0.673268i	$0.764890\pi$
$68$	−48.0000	−0.0856008
$69$	36.0000	0.0628100
$70$	0	0
$71$	−54.0000	−0.0902623	−0.0451311	−	0.998981i	$-0.514371\pi$
$71$	−54.0000	−0.0902623	−0.0451311	+	0.998981i	$0.514371\pi$
$72$	72.0000	0.117851
$73$	−173.000	−0.277371	−0.138686	−	0.990336i	$-0.544288\pi$
$73$	−173.000	−0.277371	−0.138686	+	0.990336i	$0.544288\pi$
$74$	718.000	1.12792
$75$	−75.0000	−0.115470
$76$	−476.000	−0.718433
$77$	0	0
$78$	−114.000	−0.165487
$79$	1061.00	1.51104	0.755518	−	0.655128i	$-0.227385\pi$
$79$	1061.00	1.51104	0.755518	+	0.655128i	$0.227385\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	−108.000	−0.145446
$83$	−1206.00	−1.59489	−0.797444	−	0.603393i	$-0.793815\pi$
$83$	−1206.00	−1.59489	−0.797444	+	0.603393i	$0.793815\pi$
$84$	0	0
$85$	−60.0000	−0.0765637
$86$	−74.0000	−0.0927863
$87$	756.000	0.931629
$88$	−48.0000	−0.0581456
$89$	−672.000	−0.800358	−0.400179	−	0.916437i	$-0.631052\pi$
$89$	−672.000	−0.800358	−0.400179	+	0.916437i	$0.631052\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	−48.0000	−0.0543951
$93$	753.000	0.839596
$94$	492.000	0.539850
$95$	−595.000	−0.642586
$96$	−96.0000	−0.102062
$97$	−818.000	−0.856240	−0.428120	−	0.903722i	$-0.640824\pi$
$97$	−818.000	−0.856240	−0.428120	+	0.903722i	$0.640824\pi$
$98$	0	0
$99$	−54.0000	−0.0548202
$100$	100.000	0.100000
$101$	−210.000	−0.206889	−0.103444	−	0.994635i	$-0.532986\pi$
$101$	−210.000	−0.206889	−0.103444	+	0.994635i	$0.532986\pi$
$102$	72.0000	0.0698928
$103$	397.000	0.379782	0.189891	−	0.981805i	$-0.439186\pi$
$103$	397.000	0.379782	0.189891	+	0.981805i	$0.439186\pi$
$104$	152.000	0.143316
$105$	0	0
$106$	1104.00	1.01160
$107$	−1236.00	−1.11672	−0.558358	−	0.829600i	$-0.688568\pi$
$107$	−1236.00	−1.11672	−0.558358	+	0.829600i	$0.688568\pi$
$108$	−108.000	−0.0962250
$109$	125.000	0.109842	0.0549212	−	0.998491i	$-0.482509\pi$
$109$	125.000	0.109842	0.0549212	+	0.998491i	$0.482509\pi$
$110$	−60.0000	−0.0520071
$111$	−1077.00	−0.920940
$112$	0	0
$113$	−378.000	−0.314684	−0.157342	−	0.987544i	$-0.550292\pi$
$113$	−378.000	−0.314684	−0.157342	+	0.987544i	$0.550292\pi$
$114$	714.000	0.586598
$115$	−60.0000	−0.0486524
$116$	−1008.00	−0.806814
$117$	171.000	0.135119
$118$	−816.000	−0.636601
$119$	0	0
$120$	−120.000	−0.0912871
$121$	−1295.00	−0.972953
$122$	−772.000	−0.572898
$123$	162.000	0.118756
$124$	−1004.00	−0.727112
$125$	125.000	0.0894427
$126$	0	0
$127$	−1405.00	−0.981682	−0.490841	−	0.871249i	$-0.663310\pi$
$127$	−1405.00	−0.981682	−0.490841	+	0.871249i	$0.663310\pi$
$128$	128.000	0.0883883
$129$	111.000	0.0757597
$130$	190.000	0.128185
$131$	858.000	0.572243	0.286121	−	0.958193i	$-0.407634\pi$
$131$	858.000	0.572243	0.286121	+	0.958193i	$0.407634\pi$
$132$	72.0000	0.0474757
$133$	0	0
$134$	−1622.00	−1.04567
$135$	−135.000	−0.0860663
$136$	−96.0000	−0.0605289
$137$	2316.00	1.44430	0.722150	−	0.691736i	$-0.243154\pi$
$137$	2316.00	1.44430	0.722150	+	0.691736i	$0.243154\pi$
$138$	72.0000	0.0444134
$139$	−899.000	−0.548577	−0.274288	−	0.961647i	$-0.588442\pi$
$139$	−899.000	−0.548577	−0.274288	+	0.961647i	$0.588442\pi$
$140$	0	0
$141$	−738.000	−0.440786
$142$	−108.000	−0.0638251
$143$	−114.000	−0.0666654
$144$	144.000	0.0833333
$145$	−1260.00	−0.721637
$146$	−346.000	−0.196131
$147$	0	0
$148$	1436.00	0.797557
$149$	1284.00	0.705969	0.352984	−	0.935629i	$-0.385167\pi$
$149$	1284.00	0.705969	0.352984	+	0.935629i	$0.385167\pi$
$150$	−150.000	−0.0816497
$151$	3248.00	1.75045	0.875227	−	0.483713i	$-0.160712\pi$
$151$	3248.00	1.75045	0.875227	+	0.483713i	$0.160712\pi$
$152$	−952.000	−0.508009
$153$	−108.000	−0.0570672
$154$	0	0
$155$	−1255.00	−0.650349
$156$	−228.000	−0.117017
$157$	−3530.00	−1.79442	−0.897212	−	0.441599i	$-0.854411\pi$
$157$	−3530.00	−1.79442	−0.897212	+	0.441599i	$0.854411\pi$
$158$	2122.00	1.06846
$159$	−1656.00	−0.825971
$160$	160.000	0.0790569
$161$	0	0
$162$	162.000	0.0785674
$163$	−1756.00	−0.843807	−0.421903	−	0.906641i	$-0.638638\pi$
$163$	−1756.00	−0.843807	−0.421903	+	0.906641i	$0.638638\pi$
$164$	−216.000	−0.102846
$165$	90.0000	0.0424636
$166$	−2412.00	−1.12776
$167$	−4050.00	−1.87664	−0.938319	−	0.345772i	$-0.887617\pi$
$167$	−4050.00	−1.87664	−0.938319	+	0.345772i	$0.887617\pi$
$168$	0	0
$169$	−1836.00	−0.835685
$170$	−120.000	−0.0541387
$171$	−1071.00	−0.478956
$172$	−148.000	−0.0656099
$173$	2028.00	0.891248	0.445624	−	0.895220i	$-0.352982\pi$
$173$	2028.00	0.891248	0.445624	+	0.895220i	$0.352982\pi$
$174$	1512.00	0.658761
$175$	0	0
$176$	−96.0000	−0.0411152
$177$	1224.00	0.519782
$178$	−1344.00	−0.565939
$179$	−78.0000	−0.0325698	−0.0162849	−	0.999867i	$-0.505184\pi$
$179$	−78.0000	−0.0325698	−0.0162849	+	0.999867i	$0.505184\pi$
$180$	180.000	0.0745356
$181$	1807.00	0.742062	0.371031	−	0.928620i	$-0.379004\pi$
$181$	1807.00	0.742062	0.371031	+	0.928620i	$0.379004\pi$
$182$	0	0
$183$	1158.00	0.467770
$184$	−96.0000	−0.0384631
$185$	1795.00	0.713357
$186$	1506.00	0.593684
$187$	72.0000	0.0281559
$188$	984.000	0.381732
$189$	0	0
$190$	−1190.00	−0.454377
$191$	−1470.00	−0.556887	−0.278444	−	0.960453i	$-0.589819\pi$
$191$	−1470.00	−0.556887	−0.278444	+	0.960453i	$0.589819\pi$
$192$	−192.000	−0.0721688
$193$	−37.0000	−0.0137996	−0.00689979	−	0.999976i	$-0.502196\pi$
$193$	−37.0000	−0.0137996	−0.00689979	+	0.999976i	$0.502196\pi$
$194$	−1636.00	−0.605453
$195$	−285.000	−0.104663
$196$	0	0
$197$	−3636.00	−1.31500	−0.657498	−	0.753456i	$-0.728385\pi$
$197$	−3636.00	−1.31500	−0.657498	+	0.753456i	$0.728385\pi$
$198$	−108.000	−0.0387638
$199$	−152.000	−0.0541457	−0.0270729	−	0.999633i	$-0.508619\pi$
$199$	−152.000	−0.0541457	−0.0270729	+	0.999633i	$0.508619\pi$
$200$	200.000	0.0707107
$201$	2433.00	0.853784
$202$	−420.000	−0.146293
$203$	0	0
$204$	144.000	0.0494217
$205$	−270.000	−0.0919884
$206$	794.000	0.268547
$207$	−108.000	−0.0362634
$208$	304.000	0.101339
$209$	714.000	0.236308
$210$	0	0
$211$	1340.00	0.437201	0.218600	−	0.975814i	$-0.429851\pi$
$211$	1340.00	0.437201	0.218600	+	0.975814i	$0.429851\pi$
$212$	2208.00	0.715312
$213$	162.000	0.0521129
$214$	−2472.00	−0.789638
$215$	−185.000	−0.0586832
$216$	−216.000	−0.0680414
$217$	0	0
$218$	250.000	0.0776704
$219$	519.000	0.160141
$220$	−120.000	−0.0367745
$221$	−228.000	−0.0693979
$222$	−2154.00	−0.651203
$223$	−128.000	−0.0384373	−0.0192186	−	0.999815i	$-0.506118\pi$
$223$	−128.000	−0.0384373	−0.0192186	+	0.999815i	$0.506118\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−756.000	−0.222515
$227$	−750.000	−0.219292	−0.109646	−	0.993971i	$-0.534972\pi$
$227$	−750.000	−0.219292	−0.109646	+	0.993971i	$0.534972\pi$
$228$	1428.00	0.414788
$229$	−2897.00	−0.835979	−0.417989	−	0.908452i	$-0.637265\pi$
$229$	−2897.00	−0.835979	−0.417989	+	0.908452i	$0.637265\pi$
$230$	−120.000	−0.0344025
$231$	0	0
$232$	−2016.00	−0.570504
$233$	−2982.00	−0.838443	−0.419222	−	0.907884i	$-0.637697\pi$
$233$	−2982.00	−0.838443	−0.419222	+	0.907884i	$0.637697\pi$
$234$	342.000	0.0955438
$235$	1230.00	0.341431
$236$	−1632.00	−0.450145
$237$	−3183.00	−0.872397
$238$	0	0
$239$	−2934.00	−0.794078	−0.397039	−	0.917802i	$-0.629962\pi$
$239$	−2934.00	−0.794078	−0.397039	+	0.917802i	$0.629962\pi$
$240$	−240.000	−0.0645497
$241$	−1502.00	−0.401462	−0.200731	−	0.979646i	$-0.564332\pi$
$241$	−1502.00	−0.401462	−0.200731	+	0.979646i	$0.564332\pi$
$242$	−2590.00	−0.687981
$243$	−243.000	−0.0641500
$244$	−1544.00	−0.405100
$245$	0	0
$246$	324.000	0.0839735
$247$	−2261.00	−0.582445
$248$	−2008.00	−0.514146
$249$	3618.00	0.920809
$250$	250.000	0.0632456
$251$	−4572.00	−1.14973	−0.574865	−	0.818248i	$-0.694945\pi$
$251$	−4572.00	−1.14973	−0.574865	+	0.818248i	$0.694945\pi$
$252$	0	0
$253$	72.0000	0.0178917
$254$	−2810.00	−0.694154
$255$	180.000	0.0442041
$256$	256.000	0.0625000
$257$	1866.00	0.452910	0.226455	−	0.974022i	$-0.427286\pi$
$257$	1866.00	0.452910	0.226455	+	0.974022i	$0.427286\pi$
$258$	222.000	0.0535702
$259$	0	0
$260$	380.000	0.0906408
$261$	−2268.00	−0.537876
$262$	1716.00	0.404637
$263$	−3948.00	−0.925643	−0.462822	−	0.886451i	$-0.653163\pi$
$263$	−3948.00	−0.925643	−0.462822	+	0.886451i	$0.653163\pi$
$264$	144.000	0.0335704
$265$	2760.00	0.639794
$266$	0	0
$267$	2016.00	0.462087
$268$	−3244.00	−0.739399
$269$	5010.00	1.13556	0.567779	−	0.823181i	$-0.307803\pi$
$269$	5010.00	1.13556	0.567779	+	0.823181i	$0.307803\pi$
$270$	−270.000	−0.0608581
$271$	784.000	0.175737	0.0878683	−	0.996132i	$-0.471995\pi$
$271$	784.000	0.175737	0.0878683	+	0.996132i	$0.471995\pi$
$272$	−192.000	−0.0428004
$273$	0	0
$274$	4632.00	1.02128
$275$	−150.000	−0.0328921
$276$	144.000	0.0314050
$277$	5201.00	1.12815	0.564075	−	0.825723i	$-0.309233\pi$
$277$	5201.00	1.12815	0.564075	+	0.825723i	$0.309233\pi$
$278$	−1798.00	−0.387902
$279$	−2259.00	−0.484741
$280$	0	0
$281$	1008.00	0.213994	0.106997	−	0.994259i	$-0.465877\pi$
$281$	1008.00	0.213994	0.106997	+	0.994259i	$0.465877\pi$
$282$	−1476.00	−0.311683
$283$	3421.00	0.718577	0.359289	−	0.933227i	$-0.383019\pi$
$283$	3421.00	0.718577	0.359289	+	0.933227i	$0.383019\pi$
$284$	−216.000	−0.0451311
$285$	1785.00	0.370997
$286$	−228.000	−0.0471396
$287$	0	0
$288$	288.000	0.0589256
$289$	−4769.00	−0.970690
$290$	−2520.00	−0.510274
$291$	2454.00	0.494351
$292$	−692.000	−0.138686
$293$	−2592.00	−0.516813	−0.258407	−	0.966036i	$-0.583197\pi$
$293$	−2592.00	−0.516813	−0.258407	+	0.966036i	$0.583197\pi$
$294$	0	0
$295$	−2040.00	−0.402622
$296$	2872.00	0.563958
$297$	162.000	0.0316505
$298$	2568.00	0.499195
$299$	−228.000	−0.0440989
$300$	−300.000	−0.0577350
$301$	0	0
$302$	6496.00	1.23776
$303$	630.000	0.119447
$304$	−1904.00	−0.359217
$305$	−1930.00	−0.362333
$306$	−216.000	−0.0403526
$307$	8119.00	1.50937	0.754684	−	0.656089i	$-0.227790\pi$
$307$	8119.00	1.50937	0.754684	+	0.656089i	$0.227790\pi$
$308$	0	0
$309$	−1191.00	−0.219267
$310$	−2510.00	−0.459866
$311$	9474.00	1.72740	0.863700	−	0.504007i	$-0.168141\pi$
$311$	9474.00	1.72740	0.863700	+	0.504007i	$0.168141\pi$
$312$	−456.000	−0.0827433
$313$	−2783.00	−0.502570	−0.251285	−	0.967913i	$-0.580853\pi$
$313$	−2783.00	−0.502570	−0.251285	+	0.967913i	$0.580853\pi$
$314$	−7060.00	−1.26885
$315$	0	0
$316$	4244.00	0.755518
$317$	600.000	0.106307	0.0531536	−	0.998586i	$-0.483073\pi$
$317$	600.000	0.106307	0.0531536	+	0.998586i	$0.483073\pi$
$318$	−3312.00	−0.584049
$319$	1512.00	0.265379
$320$	320.000	0.0559017
$321$	3708.00	0.644736
$322$	0	0
$323$	1428.00	0.245994
$324$	324.000	0.0555556
$325$	475.000	0.0810716
$326$	−3512.00	−0.596662
$327$	−375.000	−0.0634176
$328$	−432.000	−0.0727232
$329$	0	0
$330$	180.000	0.0300263
$331$	−3319.00	−0.551144	−0.275572	−	0.961280i	$-0.588867\pi$
$331$	−3319.00	−0.551144	−0.275572	+	0.961280i	$0.588867\pi$
$332$	−4824.00	−0.797444
$333$	3231.00	0.531705
$334$	−8100.00	−1.32698
$335$	−4055.00	−0.661338
$336$	0	0
$337$	−5875.00	−0.949649	−0.474824	−	0.880081i	$-0.657488\pi$
$337$	−5875.00	−0.949649	−0.474824	+	0.880081i	$0.657488\pi$
$338$	−3672.00	−0.590919
$339$	1134.00	0.181683
$340$	−240.000	−0.0382818
$341$	1506.00	0.239163
$342$	−2142.00	−0.338673
$343$	0	0
$344$	−296.000	−0.0463932
$345$	180.000	0.0280895
$346$	4056.00	0.630208
$347$	−10068.0	−1.55758	−0.778788	−	0.627288i	$-0.784165\pi$
$347$	−10068.0	−1.55758	−0.778788	+	0.627288i	$0.784165\pi$
$348$	3024.00	0.465814
$349$	−8018.00	−1.22978	−0.614891	−	0.788612i	$-0.710800\pi$
$349$	−8018.00	−1.22978	−0.614891	+	0.788612i	$0.710800\pi$
$350$	0	0
$351$	−513.000	−0.0780112
$352$	−192.000	−0.0290728
$353$	−4926.00	−0.742732	−0.371366	−	0.928486i	$-0.621111\pi$
$353$	−4926.00	−0.742732	−0.371366	+	0.928486i	$0.621111\pi$
$354$	2448.00	0.367542
$355$	−270.000	−0.0403665
$356$	−2688.00	−0.400179
$357$	0	0
$358$	−156.000	−0.0230303
$359$	−516.000	−0.0758592	−0.0379296	−	0.999280i	$-0.512076\pi$
$359$	−516.000	−0.0758592	−0.0379296	+	0.999280i	$0.512076\pi$
$360$	360.000	0.0527046
$361$	7302.00	1.06459
$362$	3614.00	0.524717
$363$	3885.00	0.561734
$364$	0	0
$365$	−865.000	−0.124044
$366$	2316.00	0.330763
$367$	−6293.00	−0.895073	−0.447537	−	0.894266i	$-0.647699\pi$
$367$	−6293.00	−0.895073	−0.447537	+	0.894266i	$0.647699\pi$
$368$	−192.000	−0.0271975
$369$	−486.000	−0.0685641
$370$	3590.00	0.504419
$371$	0	0
$372$	3012.00	0.419798
$373$	8363.00	1.16091	0.580455	−	0.814292i	$-0.302875\pi$
$373$	8363.00	1.16091	0.580455	+	0.814292i	$0.302875\pi$
$374$	144.000	0.0199093
$375$	−375.000	−0.0516398
$376$	1968.00	0.269925
$377$	−4788.00	−0.654097
$378$	0	0
$379$	−3331.00	−0.451456	−0.225728	−	0.974190i	$-0.572476\pi$
$379$	−3331.00	−0.451456	−0.225728	+	0.974190i	$0.572476\pi$
$380$	−2380.00	−0.321293
$381$	4215.00	0.566774
$382$	−2940.00	−0.393779
$383$	−4704.00	−0.627580	−0.313790	−	0.949492i	$-0.601599\pi$
$383$	−4704.00	−0.627580	−0.313790	+	0.949492i	$0.601599\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−74.0000	−0.00975777
$387$	−333.000	−0.0437399
$388$	−3272.00	−0.428120
$389$	8094.00	1.05497	0.527483	−	0.849565i	$-0.323136\pi$
$389$	8094.00	1.05497	0.527483	+	0.849565i	$0.323136\pi$
$390$	−570.000	−0.0740079
$391$	144.000	0.0186250
$392$	0	0
$393$	−2574.00	−0.330385
$394$	−7272.00	−0.929843
$395$	5305.00	0.675756
$396$	−216.000	−0.0274101
$397$	−2051.00	−0.259286	−0.129643	−	0.991561i	$-0.541383\pi$
$397$	−2051.00	−0.259286	−0.129643	+	0.991561i	$0.541383\pi$
$398$	−304.000	−0.0382868
$399$	0	0
$400$	400.000	0.0500000
$401$	7728.00	0.962389	0.481194	−	0.876614i	$-0.340203\pi$
$401$	7728.00	0.962389	0.481194	+	0.876614i	$0.340203\pi$
$402$	4866.00	0.603716
$403$	−4769.00	−0.589481
$404$	−840.000	−0.103444
$405$	405.000	0.0496904
$406$	0	0
$407$	−2154.00	−0.262334
$408$	288.000	0.0349464
$409$	14275.0	1.72580	0.862901	−	0.505372i	$-0.168645\pi$
$409$	14275.0	1.72580	0.862901	+	0.505372i	$0.168645\pi$
$410$	−540.000	−0.0650456
$411$	−6948.00	−0.833868
$412$	1588.00	0.189891
$413$	0	0
$414$	−216.000	−0.0256421
$415$	−6030.00	−0.713256
$416$	608.000	0.0716578
$417$	2697.00	0.316721
$418$	1428.00	0.167095
$419$	5886.00	0.686277	0.343138	−	0.939285i	$-0.388510\pi$
$419$	5886.00	0.686277	0.343138	+	0.939285i	$0.388510\pi$
$420$	0	0
$421$	7661.00	0.886875	0.443437	−	0.896305i	$-0.353759\pi$
$421$	7661.00	0.886875	0.443437	+	0.896305i	$0.353759\pi$
$422$	2680.00	0.309148
$423$	2214.00	0.254488
$424$	4416.00	0.505802
$425$	−300.000	−0.0342403
$426$	324.000	0.0368494
$427$	0	0
$428$	−4944.00	−0.558358
$429$	342.000	0.0384893
$430$	−370.000	−0.0414953
$431$	15798.0	1.76558	0.882788	−	0.469772i	$-0.155664\pi$
$431$	15798.0	1.76558	0.882788	+	0.469772i	$0.155664\pi$
$432$	−432.000	−0.0481125
$433$	15985.0	1.77411	0.887056	−	0.461663i	$-0.152747\pi$
$433$	15985.0	1.77411	0.887056	+	0.461663i	$0.152747\pi$
$434$	0	0
$435$	3780.00	0.416637
$436$	500.000	0.0549212
$437$	1428.00	0.156317
$438$	1038.00	0.113236
$439$	14416.0	1.56729	0.783643	−	0.621212i	$-0.213359\pi$
$439$	14416.0	1.56729	0.783643	+	0.621212i	$0.213359\pi$
$440$	−240.000	−0.0260035
$441$	0	0
$442$	−456.000	−0.0490717
$443$	5712.00	0.612608	0.306304	−	0.951934i	$-0.400908\pi$
$443$	5712.00	0.612608	0.306304	+	0.951934i	$0.400908\pi$
$444$	−4308.00	−0.460470
$445$	−3360.00	−0.357931
$446$	−256.000	−0.0271793
$447$	−3852.00	−0.407591
$448$	0	0
$449$	−9990.00	−1.05002	−0.525008	−	0.851097i	$-0.675938\pi$
$449$	−9990.00	−1.05002	−0.525008	+	0.851097i	$0.675938\pi$
$450$	450.000	0.0471405
$451$	324.000	0.0338283
$452$	−1512.00	−0.157342
$453$	−9744.00	−1.01062
$454$	−1500.00	−0.155063
$455$	0	0
$456$	2856.00	0.293299
$457$	17045.0	1.74471	0.872354	−	0.488875i	$-0.162593\pi$
$457$	17045.0	1.74471	0.872354	+	0.488875i	$0.162593\pi$
$458$	−5794.00	−0.591126
$459$	324.000	0.0329478
$460$	−240.000	−0.0243262
$461$	6948.00	0.701954	0.350977	−	0.936384i	$-0.385850\pi$
$461$	6948.00	0.701954	0.350977	+	0.936384i	$0.385850\pi$
$462$	0	0
$463$	6869.00	0.689481	0.344740	−	0.938698i	$-0.387967\pi$
$463$	6869.00	0.689481	0.344740	+	0.938698i	$0.387967\pi$
$464$	−4032.00	−0.403407
$465$	3765.00	0.375479
$466$	−5964.00	−0.592869
$467$	16266.0	1.61178	0.805889	−	0.592066i	$-0.201688\pi$
$467$	16266.0	1.61178	0.805889	+	0.592066i	$0.201688\pi$
$468$	684.000	0.0675596
$469$	0	0
$470$	2460.00	0.241428
$471$	10590.0	1.03601
$472$	−3264.00	−0.318300
$473$	222.000	0.0215805
$474$	−6366.00	−0.616878
$475$	−2975.00	−0.287373
$476$	0	0
$477$	4968.00	0.476874
$478$	−5868.00	−0.561498
$479$	−9984.00	−0.952360	−0.476180	−	0.879348i	$-0.657979\pi$
$479$	−9984.00	−0.952360	−0.476180	+	0.879348i	$0.657979\pi$
$480$	−480.000	−0.0456435
$481$	6821.00	0.646592
$482$	−3004.00	−0.283876
$483$	0	0
$484$	−5180.00	−0.486476
$485$	−4090.00	−0.382922
$486$	−486.000	−0.0453609
$487$	20909.0	1.94554	0.972769	−	0.231776i	$-0.0744536\pi$
$487$	20909.0	1.94554	0.972769	+	0.231776i	$0.0744536\pi$
$488$	−3088.00	−0.286449
$489$	5268.00	0.487172
$490$	0	0
$491$	−4572.00	−0.420227	−0.210114	−	0.977677i	$-0.567383\pi$
$491$	−4572.00	−0.420227	−0.210114	+	0.977677i	$0.567383\pi$
$492$	648.000	0.0593782
$493$	3024.00	0.276256
$494$	−4522.00	−0.411851
$495$	−270.000	−0.0245164
$496$	−4016.00	−0.363556
$497$	0	0
$498$	7236.00	0.651110
$499$	−10189.0	−0.914073	−0.457036	−	0.889448i	$-0.651089\pi$
$499$	−10189.0	−0.914073	−0.457036	+	0.889448i	$0.651089\pi$
$500$	500.000	0.0447214
$501$	12150.0	1.08348
$502$	−9144.00	−0.812981
$503$	18486.0	1.63867	0.819334	−	0.573316i	$-0.194343\pi$
$503$	18486.0	1.63867	0.819334	+	0.573316i	$0.194343\pi$
$504$	0	0
$505$	−1050.00	−0.0925235
$506$	144.000	0.0126513
$507$	5508.00	0.482483
$508$	−5620.00	−0.490841
$509$	18570.0	1.61709	0.808547	−	0.588432i	$-0.200254\pi$
$509$	18570.0	1.61709	0.808547	+	0.588432i	$0.200254\pi$
$510$	360.000	0.0312570
$511$	0	0
$512$	512.000	0.0441942
$513$	3213.00	0.276525
$514$	3732.00	0.320256
$515$	1985.00	0.169844
$516$	444.000	0.0378799
$517$	−1476.00	−0.125560
$518$	0	0
$519$	−6084.00	−0.514563
$520$	760.000	0.0640927
$521$	−9444.00	−0.794144	−0.397072	−	0.917787i	$-0.629974\pi$
$521$	−9444.00	−0.794144	−0.397072	+	0.917787i	$0.629974\pi$
$522$	−4536.00	−0.380336
$523$	−10673.0	−0.892347	−0.446174	−	0.894946i	$-0.647214\pi$
$523$	−10673.0	−0.892347	−0.446174	+	0.894946i	$0.647214\pi$
$524$	3432.00	0.286121
$525$	0	0
$526$	−7896.00	−0.654528
$527$	3012.00	0.248965
$528$	288.000	0.0237379
$529$	−12023.0	−0.988165
$530$	5520.00	0.452403
$531$	−3672.00	−0.300096
$532$	0	0
$533$	−1026.00	−0.0833790
$534$	4032.00	0.326745
$535$	−6180.00	−0.499411
$536$	−6488.00	−0.522834
$537$	234.000	0.0188042
$538$	10020.0	0.802961
$539$	0	0
$540$	−540.000	−0.0430331
$541$	17777.0	1.41274	0.706371	−	0.707842i	$-0.250331\pi$
$541$	17777.0	1.41274	0.706371	+	0.707842i	$0.250331\pi$
$542$	1568.00	0.124265
$543$	−5421.00	−0.428430
$544$	−384.000	−0.0302645
$545$	625.000	0.0491230
$546$	0	0
$547$	−5068.00	−0.396146	−0.198073	−	0.980187i	$-0.563468\pi$
$547$	−5068.00	−0.396146	−0.198073	+	0.980187i	$0.563468\pi$
$548$	9264.00	0.722150
$549$	−3474.00	−0.270067
$550$	−300.000	−0.0232583
$551$	29988.0	2.31857
$552$	288.000	0.0222067
$553$	0	0
$554$	10402.0	0.797723
$555$	−5385.00	−0.411857
$556$	−3596.00	−0.274288
$557$	−14370.0	−1.09314	−0.546568	−	0.837415i	$-0.684066\pi$
$557$	−14370.0	−1.09314	−0.546568	+	0.837415i	$0.684066\pi$
$558$	−4518.00	−0.342764
$559$	−703.000	−0.0531909
$560$	0	0
$561$	−216.000	−0.0162558
$562$	2016.00	0.151316
$563$	−4422.00	−0.331021	−0.165511	−	0.986208i	$-0.552927\pi$
$563$	−4422.00	−0.331021	−0.165511	+	0.986208i	$0.552927\pi$
$564$	−2952.00	−0.220393
$565$	−1890.00	−0.140731
$566$	6842.00	0.508111
$567$	0	0
$568$	−432.000	−0.0319125
$569$	582.000	0.0428800	0.0214400	−	0.999770i	$-0.493175\pi$
$569$	582.000	0.0428800	0.0214400	+	0.999770i	$0.493175\pi$
$570$	3570.00	0.262335
$571$	−6973.00	−0.511052	−0.255526	−	0.966802i	$-0.582249\pi$
$571$	−6973.00	−0.511052	−0.255526	+	0.966802i	$0.582249\pi$
$572$	−456.000	−0.0333327
$573$	4410.00	0.321519
$574$	0	0
$575$	−300.000	−0.0217580
$576$	576.000	0.0416667
$577$	6553.00	0.472799	0.236399	−	0.971656i	$-0.424033\pi$
$577$	6553.00	0.472799	0.236399	+	0.971656i	$0.424033\pi$
$578$	−9538.00	−0.686381
$579$	111.000	0.00796719
$580$	−5040.00	−0.360818
$581$	0	0
$582$	4908.00	0.349559
$583$	−3312.00	−0.235281
$584$	−1384.00	−0.0980656
$585$	855.000	0.0604272
$586$	−5184.00	−0.365442
$587$	−27144.0	−1.90861	−0.954304	−	0.298838i	$-0.903401\pi$
$587$	−27144.0	−1.90861	−0.954304	+	0.298838i	$0.903401\pi$
$588$	0	0
$589$	29869.0	2.08953
$590$	−4080.00	−0.284697
$591$	10908.0	0.759213
$592$	5744.00	0.398779
$593$	28614.0	1.98151	0.990756	−	0.135659i	$-0.0433151\pi$
$593$	28614.0	1.98151	0.990756	+	0.135659i	$0.0433151\pi$
$594$	324.000	0.0223803
$595$	0	0
$596$	5136.00	0.352984
$597$	456.000	0.0312610
$598$	−456.000	−0.0311827
$599$	−26556.0	−1.81143	−0.905717	−	0.423883i	$-0.860667\pi$
$599$	−26556.0	−1.81143	−0.905717	+	0.423883i	$0.860667\pi$
$600$	−600.000	−0.0408248
$601$	2593.00	0.175991	0.0879956	−	0.996121i	$-0.471954\pi$
$601$	2593.00	0.175991	0.0879956	+	0.996121i	$0.471954\pi$
$602$	0	0
$603$	−7299.00	−0.492932
$604$	12992.0	0.875227
$605$	−6475.00	−0.435118
$606$	1260.00	0.0844620
$607$	16315.0	1.09095	0.545474	−	0.838128i	$-0.316350\pi$
$607$	16315.0	1.09095	0.545474	+	0.838128i	$0.316350\pi$
$608$	−3808.00	−0.254005
$609$	0	0
$610$	−3860.00	−0.256208
$611$	4674.00	0.309476
$612$	−432.000	−0.0285336
$613$	−28270.0	−1.86267	−0.931333	−	0.364168i	$-0.881353\pi$
$613$	−28270.0	−1.86267	−0.931333	+	0.364168i	$0.881353\pi$
$614$	16238.0	1.06728
$615$	810.000	0.0531095
$616$	0	0
$617$	−7974.00	−0.520294	−0.260147	−	0.965569i	$-0.583771\pi$
$617$	−7974.00	−0.520294	−0.260147	+	0.965569i	$0.583771\pi$
$618$	−2382.00	−0.155045
$619$	13123.0	0.852113	0.426056	−	0.904697i	$-0.359902\pi$
$619$	13123.0	0.852113	0.426056	+	0.904697i	$0.359902\pi$
$620$	−5020.00	−0.325174
$621$	324.000	0.0209367
$622$	18948.0	1.22146
$623$	0	0
$624$	−912.000	−0.0585084
$625$	625.000	0.0400000
$626$	−5566.00	−0.355371
$627$	−2142.00	−0.136433
$628$	−14120.0	−0.897212
$629$	−4308.00	−0.273086
$630$	0	0
$631$	5984.00	0.377527	0.188763	−	0.982023i	$-0.439552\pi$
$631$	5984.00	0.377527	0.188763	+	0.982023i	$0.439552\pi$
$632$	8488.00	0.534232
$633$	−4020.00	−0.252418
$634$	1200.00	0.0751705
$635$	−7025.00	−0.439021
$636$	−6624.00	−0.412985
$637$	0	0
$638$	3024.00	0.187651
$639$	−486.000	−0.0300874
$640$	640.000	0.0395285
$641$	−14028.0	−0.864388	−0.432194	−	0.901781i	$-0.642260\pi$
$641$	−14028.0	−0.864388	−0.432194	+	0.901781i	$0.642260\pi$
$642$	7416.00	0.455897
$643$	8317.00	0.510094	0.255047	−	0.966929i	$-0.417909\pi$
$643$	8317.00	0.510094	0.255047	+	0.966929i	$0.417909\pi$
$644$	0	0
$645$	555.000	0.0338808
$646$	2856.00	0.173944
$647$	−17310.0	−1.05182	−0.525909	−	0.850541i	$-0.676275\pi$
$647$	−17310.0	−1.05182	−0.525909	+	0.850541i	$0.676275\pi$
$648$	648.000	0.0392837
$649$	2448.00	0.148062
$650$	950.000	0.0573263
$651$	0	0
$652$	−7024.00	−0.421903
$653$	−20478.0	−1.22721	−0.613603	−	0.789614i	$-0.710281\pi$
$653$	−20478.0	−1.22721	−0.613603	+	0.789614i	$0.710281\pi$
$654$	−750.000	−0.0448430
$655$	4290.00	0.255915
$656$	−864.000	−0.0514231
$657$	−1557.00	−0.0924572
$658$	0	0
$659$	−29448.0	−1.74072	−0.870358	−	0.492420i	$-0.836112\pi$
$659$	−29448.0	−1.74072	−0.870358	+	0.492420i	$0.836112\pi$
$660$	360.000	0.0212318
$661$	24037.0	1.41442	0.707209	−	0.707004i	$-0.249954\pi$
$661$	24037.0	1.41442	0.707209	+	0.707004i	$0.249954\pi$
$662$	−6638.00	−0.389718
$663$	684.000	0.0400669
$664$	−9648.00	−0.563878
$665$	0	0
$666$	6462.00	0.375972
$667$	3024.00	0.175547
$668$	−16200.0	−0.938319
$669$	384.000	0.0221918
$670$	−8110.00	−0.467637
$671$	2316.00	0.133246
$672$	0	0
$673$	23159.0	1.32647	0.663235	−	0.748412i	$-0.269183\pi$
$673$	23159.0	1.32647	0.663235	+	0.748412i	$0.269183\pi$
$674$	−11750.0	−0.671503
$675$	−675.000	−0.0384900
$676$	−7344.00	−0.417843
$677$	−17412.0	−0.988475	−0.494237	−	0.869327i	$-0.664553\pi$
$677$	−17412.0	−0.988475	−0.494237	+	0.869327i	$0.664553\pi$
$678$	2268.00	0.128469
$679$	0	0
$680$	−480.000	−0.0270694
$681$	2250.00	0.126608
$682$	3012.00	0.169114
$683$	−15864.0	−0.888754	−0.444377	−	0.895840i	$-0.646575\pi$
$683$	−15864.0	−0.888754	−0.444377	+	0.895840i	$0.646575\pi$
$684$	−4284.00	−0.239478
$685$	11580.0	0.645911
$686$	0	0
$687$	8691.00	0.482653
$688$	−592.000	−0.0328049
$689$	10488.0	0.579914
$690$	360.000	0.0198623
$691$	−18557.0	−1.02162	−0.510812	−	0.859693i	$-0.670655\pi$
$691$	−18557.0	−1.02162	−0.510812	+	0.859693i	$0.670655\pi$
$692$	8112.00	0.445624
$693$	0	0
$694$	−20136.0	−1.10137
$695$	−4495.00	−0.245331
$696$	6048.00	0.329381
$697$	648.000	0.0352148
$698$	−16036.0	−0.869587
$699$	8946.00	0.484076
$700$	0	0
$701$	9396.00	0.506251	0.253126	−	0.967433i	$-0.418541\pi$
$701$	9396.00	0.506251	0.253126	+	0.967433i	$0.418541\pi$
$702$	−1026.00	−0.0551622
$703$	−42721.0	−2.29197
$704$	−384.000	−0.0205576
$705$	−3690.00	−0.197125
$706$	−9852.00	−0.525191
$707$	0	0
$708$	4896.00	0.259891
$709$	9926.00	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	9926.00	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−540.000	−0.0285434
$711$	9549.00	0.503679
$712$	−5376.00	−0.282969
$713$	3012.00	0.158205
$714$	0	0
$715$	−570.000	−0.0298137
$716$	−312.000	−0.0162849
$717$	8802.00	0.458461
$718$	−1032.00	−0.0536405
$719$	−17754.0	−0.920880	−0.460440	−	0.887691i	$-0.652308\pi$
$719$	−17754.0	−0.920880	−0.460440	+	0.887691i	$0.652308\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	14604.0	0.752776
$723$	4506.00	0.231784
$724$	7228.00	0.371031
$725$	−6300.00	−0.322726
$726$	7770.00	0.397206
$727$	24391.0	1.24431	0.622154	−	0.782895i	$-0.286258\pi$
$727$	24391.0	1.24431	0.622154	+	0.782895i	$0.286258\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−1730.00	−0.0877126
$731$	444.000	0.0224650
$732$	4632.00	0.233885
$733$	34219.0	1.72429	0.862147	−	0.506658i	$-0.169119\pi$
$733$	34219.0	1.72429	0.862147	+	0.506658i	$0.169119\pi$
$734$	−12586.0	−0.632912
$735$	0	0
$736$	−384.000	−0.0192316
$737$	4866.00	0.243204
$738$	−972.000	−0.0484821
$739$	12239.0	0.609227	0.304614	−	0.952476i	$-0.401473\pi$
$739$	12239.0	0.609227	0.304614	+	0.952476i	$0.401473\pi$
$740$	7180.00	0.356678
$741$	6783.00	0.336275
$742$	0	0
$743$	−16722.0	−0.825667	−0.412834	−	0.910806i	$-0.635461\pi$
$743$	−16722.0	−0.825667	−0.412834	+	0.910806i	$0.635461\pi$
$744$	6024.00	0.296842
$745$	6420.00	0.315719
$746$	16726.0	0.820888
$747$	−10854.0	−0.531629
$748$	288.000	0.0140780
$749$	0	0
$750$	−750.000	−0.0365148
$751$	24239.0	1.17775	0.588877	−	0.808222i	$-0.299570\pi$
$751$	24239.0	1.17775	0.588877	+	0.808222i	$0.299570\pi$
$752$	3936.00	0.190866
$753$	13716.0	0.663797
$754$	−9576.00	−0.462516
$755$	16240.0	0.782827
$756$	0	0
$757$	−14734.0	−0.707419	−0.353710	−	0.935355i	$-0.615080\pi$
$757$	−14734.0	−0.707419	−0.353710	+	0.935355i	$0.615080\pi$
$758$	−6662.00	−0.319228
$759$	−216.000	−0.0103298
$760$	−4760.00	−0.227189
$761$	38532.0	1.83546	0.917729	−	0.397207i	$-0.130020\pi$
$761$	38532.0	1.83546	0.917729	+	0.397207i	$0.130020\pi$
$762$	8430.00	0.400770
$763$	0	0
$764$	−5880.00	−0.278444
$765$	−540.000	−0.0255212
$766$	−9408.00	−0.443766
$767$	−7752.00	−0.364939
$768$	−768.000	−0.0360844
$769$	−23879.0	−1.11976	−0.559882	−	0.828572i	$-0.689154\pi$
$769$	−23879.0	−1.11976	−0.559882	+	0.828572i	$0.689154\pi$
$770$	0	0
$771$	−5598.00	−0.261488
$772$	−148.000	−0.00689979
$773$	−16374.0	−0.761878	−0.380939	−	0.924600i	$-0.624399\pi$
$773$	−16374.0	−0.761878	−0.380939	+	0.924600i	$0.624399\pi$
$774$	−666.000	−0.0309288
$775$	−6275.00	−0.290845
$776$	−6544.00	−0.302727
$777$	0	0
$778$	16188.0	0.745974
$779$	6426.00	0.295552
$780$	−1140.00	−0.0523315
$781$	324.000	0.0148446
$782$	288.000	0.0131699
$783$	6804.00	0.310543
$784$	0	0
$785$	−17650.0	−0.802491
$786$	−5148.00	−0.233617
$787$	11584.0	0.524682	0.262341	−	0.964975i	$-0.415505\pi$
$787$	11584.0	0.524682	0.262341	+	0.964975i	$0.415505\pi$
$788$	−14544.0	−0.657498
$789$	11844.0	0.534420
$790$	10610.0	0.477831
$791$	0	0
$792$	−432.000	−0.0193819
$793$	−7334.00	−0.328421
$794$	−4102.00	−0.183343
$795$	−8280.00	−0.369385
$796$	−608.000	−0.0270729
$797$	6732.00	0.299197	0.149598	−	0.988747i	$-0.452202\pi$
$797$	6732.00	0.299197	0.149598	+	0.988747i	$0.452202\pi$
$798$	0	0
$799$	−2952.00	−0.130706
$800$	800.000	0.0353553
$801$	−6048.00	−0.266786
$802$	15456.0	0.680512
$803$	1038.00	0.0456167
$804$	9732.00	0.426892
$805$	0	0
$806$	−9538.00	−0.416826
$807$	−15030.0	−0.655615
$808$	−1680.00	−0.0731463
$809$	−42558.0	−1.84952	−0.924759	−	0.380554i	$-0.875733\pi$
$809$	−42558.0	−1.84952	−0.924759	+	0.380554i	$0.875733\pi$
$810$	810.000	0.0351364
$811$	2968.00	0.128509	0.0642544	−	0.997934i	$-0.479533\pi$
$811$	2968.00	0.128509	0.0642544	+	0.997934i	$0.479533\pi$
$812$	0	0
$813$	−2352.00	−0.101462
$814$	−4308.00	−0.185498
$815$	−8780.00	−0.377362
$816$	576.000	0.0247108
$817$	4403.00	0.188545
$818$	28550.0	1.22033
$819$	0	0
$820$	−1080.00	−0.0459942
$821$	36294.0	1.54284	0.771419	−	0.636328i	$-0.219548\pi$
$821$	36294.0	1.54284	0.771419	+	0.636328i	$0.219548\pi$
$822$	−13896.0	−0.589633
$823$	16064.0	0.680384	0.340192	−	0.940356i	$-0.389508\pi$
$823$	16064.0	0.680384	0.340192	+	0.940356i	$0.389508\pi$
$824$	3176.00	0.134273
$825$	450.000	0.0189903
$826$	0	0
$827$	−1350.00	−0.0567643	−0.0283822	−	0.999597i	$-0.509036\pi$
$827$	−1350.00	−0.0567643	−0.0283822	+	0.999597i	$0.509036\pi$
$828$	−432.000	−0.0181317
$829$	−32573.0	−1.36466	−0.682332	−	0.731042i	$-0.739034\pi$
$829$	−32573.0	−1.36466	−0.682332	+	0.731042i	$0.739034\pi$
$830$	−12060.0	−0.504348
$831$	−15603.0	−0.651338
$832$	1216.00	0.0506697
$833$	0	0
$834$	5394.00	0.223956
$835$	−20250.0	−0.839258
$836$	2856.00	0.118154
$837$	6777.00	0.279865
$838$	11772.0	0.485271
$839$	28044.0	1.15398	0.576988	−	0.816752i	$-0.304228\pi$
$839$	28044.0	1.15398	0.576988	+	0.816752i	$0.304228\pi$
$840$	0	0
$841$	39115.0	1.60380
$842$	15322.0	0.627115
$843$	−3024.00	−0.123549
$844$	5360.00	0.218600
$845$	−9180.00	−0.373730
$846$	4428.00	0.179950
$847$	0	0
$848$	8832.00	0.357656
$849$	−10263.0	−0.414871
$850$	−600.000	−0.0242116
$851$	−4308.00	−0.173533
$852$	648.000	0.0260565
$853$	34297.0	1.37668	0.688339	−	0.725389i	$-0.258340\pi$
$853$	34297.0	1.37668	0.688339	+	0.725389i	$0.258340\pi$
$854$	0	0
$855$	−5355.00	−0.214195
$856$	−9888.00	−0.394819
$857$	2904.00	0.115751	0.0578756	−	0.998324i	$-0.481567\pi$
$857$	2904.00	0.115751	0.0578756	+	0.998324i	$0.481567\pi$
$858$	684.000	0.0272161
$859$	−28160.0	−1.11852	−0.559259	−	0.828993i	$-0.688914\pi$
$859$	−28160.0	−1.11852	−0.559259	+	0.828993i	$0.688914\pi$
$860$	−740.000	−0.0293416
$861$	0	0
$862$	31596.0	1.24845
$863$	−48378.0	−1.90823	−0.954117	−	0.299433i	$-0.903202\pi$
$863$	−48378.0	−1.90823	−0.954117	+	0.299433i	$0.903202\pi$
$864$	−864.000	−0.0340207
$865$	10140.0	0.398578
$866$	31970.0	1.25449
$867$	14307.0	0.560428
$868$	0	0
$869$	−6366.00	−0.248506
$870$	7560.00	0.294607
$871$	−15409.0	−0.599442
$872$	1000.00	0.0388352
$873$	−7362.00	−0.285413
$874$	2856.00	0.110533
$875$	0	0
$876$	2076.00	0.0800703
$877$	26666.0	1.02674	0.513368	−	0.858169i	$-0.328398\pi$
$877$	26666.0	1.02674	0.513368	+	0.858169i	$0.328398\pi$
$878$	28832.0	1.10824
$879$	7776.00	0.298382
$880$	−480.000	−0.0183873
$881$	−41940.0	−1.60385	−0.801927	−	0.597423i	$-0.796191\pi$
$881$	−41940.0	−1.60385	−0.801927	+	0.597423i	$0.796191\pi$
$882$	0	0
$883$	461.000	0.0175695	0.00878476	−	0.999961i	$-0.497204\pi$
$883$	461.000	0.0175695	0.00878476	+	0.999961i	$0.497204\pi$
$884$	−912.000	−0.0346990
$885$	6120.00	0.232454
$886$	11424.0	0.433179
$887$	16230.0	0.614374	0.307187	−	0.951649i	$-0.400612\pi$
$887$	16230.0	0.614374	0.307187	+	0.951649i	$0.400612\pi$
$888$	−8616.00	−0.325601
$889$	0	0
$890$	−6720.00	−0.253095
$891$	−486.000	−0.0182734
$892$	−512.000	−0.0192186
$893$	−29274.0	−1.09700
$894$	−7704.00	−0.288211
$895$	−390.000	−0.0145657
$896$	0	0
$897$	684.000	0.0254605
$898$	−19980.0	−0.742474
$899$	63252.0	2.34658
$900$	900.000	0.0333333
$901$	−6624.00	−0.244925
$902$	648.000	0.0239202
$903$	0	0
$904$	−3024.00	−0.111257
$905$	9035.00	0.331860
$906$	−19488.0	−0.714620
$907$	32597.0	1.19335	0.596673	−	0.802484i	$-0.296489\pi$
$907$	32597.0	1.19335	0.596673	+	0.802484i	$0.296489\pi$
$908$	−3000.00	−0.109646
$909$	−1890.00	−0.0689630
$910$	0	0
$911$	−33948.0	−1.23463	−0.617315	−	0.786716i	$-0.711779\pi$
$911$	−33948.0	−1.23463	−0.617315	+	0.786716i	$0.711779\pi$
$912$	5712.00	0.207394
$913$	7236.00	0.262296
$914$	34090.0	1.23369
$915$	5790.00	0.209193
$916$	−11588.0	−0.417989
$917$	0	0
$918$	648.000	0.0232976
$919$	22589.0	0.810819	0.405409	−	0.914135i	$-0.367129\pi$
$919$	22589.0	0.810819	0.405409	+	0.914135i	$0.367129\pi$
$920$	−480.000	−0.0172012
$921$	−24357.0	−0.871434
$922$	13896.0	0.496356
$923$	−1026.00	−0.0365885
$924$	0	0
$925$	8975.00	0.319023
$926$	13738.0	0.487536
$927$	3573.00	0.126594
$928$	−8064.00	−0.285252
$929$	−14514.0	−0.512582	−0.256291	−	0.966600i	$-0.582501\pi$
$929$	−14514.0	−0.512582	−0.256291	+	0.966600i	$0.582501\pi$
$930$	7530.00	0.265504
$931$	0	0
$932$	−11928.0	−0.419222
$933$	−28422.0	−0.997315
$934$	32532.0	1.13970
$935$	360.000	0.0125917
$936$	1368.00	0.0477719
$937$	−5327.00	−0.185726	−0.0928631	−	0.995679i	$-0.529602\pi$
$937$	−5327.00	−0.185726	−0.0928631	+	0.995679i	$0.529602\pi$
$938$	0	0
$939$	8349.00	0.290159
$940$	4920.00	0.170716
$941$	22200.0	0.769075	0.384537	−	0.923109i	$-0.374361\pi$
$941$	22200.0	0.769075	0.384537	+	0.923109i	$0.374361\pi$
$942$	21180.0	0.732571
$943$	648.000	0.0223773
$944$	−6528.00	−0.225072
$945$	0	0
$946$	444.000	0.0152597
$947$	30282.0	1.03911	0.519553	−	0.854438i	$-0.326099\pi$
$947$	30282.0	1.03911	0.519553	+	0.854438i	$0.326099\pi$
$948$	−12732.0	−0.436198
$949$	−3287.00	−0.112435
$950$	−5950.00	−0.203204
$951$	−1800.00	−0.0613764
$952$	0	0
$953$	18072.0	0.614281	0.307140	−	0.951664i	$-0.400628\pi$
$953$	18072.0	0.614281	0.307140	+	0.951664i	$0.400628\pi$
$954$	9936.00	0.337201
$955$	−7350.00	−0.249048
$956$	−11736.0	−0.397039
$957$	−4536.00	−0.153216
$958$	−19968.0	−0.673420
$959$	0	0
$960$	−960.000	−0.0322749
$961$	33210.0	1.11477
$962$	13642.0	0.457210
$963$	−11124.0	−0.372239
$964$	−6008.00	−0.200731
$965$	−185.000	−0.00617136
$966$	0	0
$967$	50705.0	1.68621	0.843104	−	0.537751i	$-0.180726\pi$
$967$	50705.0	1.68621	0.843104	+	0.537751i	$0.180726\pi$
$968$	−10360.0	−0.343991
$969$	−4284.00	−0.142025
$970$	−8180.00	−0.270767
$971$	−44088.0	−1.45711	−0.728554	−	0.684989i	$-0.759807\pi$
$971$	−44088.0	−1.45711	−0.728554	+	0.684989i	$0.759807\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	41818.0	1.37570
$975$	−1425.00	−0.0468067
$976$	−6176.00	−0.202550
$977$	−23514.0	−0.769989	−0.384995	−	0.922919i	$-0.625797\pi$
$977$	−23514.0	−0.769989	−0.384995	+	0.922919i	$0.625797\pi$
$978$	10536.0	0.344483
$979$	4032.00	0.131627
$980$	0	0
$981$	1125.00	0.0366142
$982$	−9144.00	−0.297145
$983$	744.000	0.0241403	0.0120701	−	0.999927i	$-0.496158\pi$
$983$	744.000	0.0241403	0.0120701	+	0.999927i	$0.496158\pi$
$984$	1296.00	0.0419868
$985$	−18180.0	−0.588084
$986$	6048.00	0.195342
$987$	0	0
$988$	−9044.00	−0.291223
$989$	444.000	0.0142754
$990$	−540.000	−0.0173357
$991$	54035.0	1.73207	0.866033	−	0.499986i	$-0.166662\pi$
$991$	54035.0	1.73207	0.866033	+	0.499986i	$0.166662\pi$
$992$	−8032.00	−0.257073
$993$	9957.00	0.318203
$994$	0	0
$995$	−760.000	−0.0242147
$996$	14472.0	0.460404
$997$	41185.0	1.30827	0.654133	−	0.756379i	$-0.273033\pi$
$997$	41185.0	1.30827	0.654133	+	0.756379i	$0.273033\pi$
$998$	−20378.0	−0.646347
$999$	−9693.00	−0.306980

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.c.121.1	✓	2	7.3	odd	6
210.4.i.c.151.1	yes	2	7.5	odd	6
630.4.k.h.361.1		2	21.5	even	6
630.4.k.h.541.1		2	21.17	even	6
1470.4.a.u.1.1		1	1.1	even	1	trivial
1470.4.a.y.1.1		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

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