LMFDB - Embedded newform 1470.4.a.r.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 30)
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)

$f(q)$

$=$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -48.0000 q^{11} -12.0000 q^{12} -2.00000 q^{13} -15.0000 q^{15} +16.0000 q^{16} +114.000 q^{17} +18.0000 q^{18} -140.000 q^{19} +20.0000 q^{20} -96.0000 q^{22} +72.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} -4.00000 q^{26} -27.0000 q^{27} +210.000 q^{29} -30.0000 q^{30} -272.000 q^{31} +32.0000 q^{32} +144.000 q^{33} +228.000 q^{34} +36.0000 q^{36} -334.000 q^{37} -280.000 q^{38} +6.00000 q^{39} +40.0000 q^{40} +198.000 q^{41} -268.000 q^{43} -192.000 q^{44} +45.0000 q^{45} +144.000 q^{46} -216.000 q^{47} -48.0000 q^{48} +50.0000 q^{50} -342.000 q^{51} -8.00000 q^{52} -78.0000 q^{53} -54.0000 q^{54} -240.000 q^{55} +420.000 q^{57} +420.000 q^{58} -240.000 q^{59} -60.0000 q^{60} -302.000 q^{61} -544.000 q^{62} +64.0000 q^{64} -10.0000 q^{65} +288.000 q^{66} +596.000 q^{67} +456.000 q^{68} -216.000 q^{69} -768.000 q^{71} +72.0000 q^{72} +478.000 q^{73} -668.000 q^{74} -75.0000 q^{75} -560.000 q^{76} +12.0000 q^{78} -640.000 q^{79} +80.0000 q^{80} +81.0000 q^{81} +396.000 q^{82} +348.000 q^{83} +570.000 q^{85} -536.000 q^{86} -630.000 q^{87} -384.000 q^{88} -210.000 q^{89} +90.0000 q^{90} +288.000 q^{92} +816.000 q^{93} -432.000 q^{94} -700.000 q^{95} -96.0000 q^{96} +1534.00 q^{97} -432.000 q^{99} +O(q^{100})\)

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
$11$	−48.0000	−1.31569	−0.657843	−	0.753155i	$-0.728531\pi$
$11$	−48.0000	−1.31569	−0.657843	+	0.753155i	$0.728531\pi$
$12$	−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
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	18.0000	0.235702
$19$	−140.000	−1.69043	−0.845216	−	0.534425i	$-0.820528\pi$
$19$	−140.000	−1.69043	−0.845216	+	0.534425i	$0.820528\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−96.0000	−0.930330
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	−4.00000	−0.0301717
$27$	−27.0000	−0.192450
$28$	0	0
$29$	210.000	1.34469	0.672345	−	0.740238i	$-0.265287\pi$
$29$	210.000	1.34469	0.672345	+	0.740238i	$0.265287\pi$
$30$	−30.0000	−0.182574
$31$	−272.000	−1.57589	−0.787946	−	0.615745i	$-0.788855\pi$
$31$	−272.000	−1.57589	−0.787946	+	0.615745i	$0.788855\pi$
$32$	32.0000	0.176777
$33$	144.000	0.759612
$34$	228.000	1.15005
$35$	0	0
$36$	36.0000	0.166667
$37$	−334.000	−1.48403	−0.742017	−	0.670381i	$-0.766131\pi$
$37$	−334.000	−1.48403	−0.742017	+	0.670381i	$0.766131\pi$
$38$	−280.000	−1.19532
$39$	6.00000	0.0246351
$40$	40.0000	0.158114
$41$	198.000	0.754205	0.377102	−	0.926172i	$-0.376920\pi$
$41$	198.000	0.754205	0.377102	+	0.926172i	$0.376920\pi$
$42$	0	0
$43$	−268.000	−0.950456	−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000	−0.950456	−0.475228	+	0.879863i	$0.657634\pi$
$44$	−192.000	−0.657843
$45$	45.0000	0.149071
$46$	144.000	0.461557
$47$	−216.000	−0.670358	−0.335179	−	0.942154i	$-0.608797\pi$
$47$	−216.000	−0.670358	−0.335179	+	0.942154i	$0.608797\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	50.0000	0.141421
$51$	−342.000	−0.939011
$52$	−8.00000	−0.0213346
$53$	−78.0000	−0.202153	−0.101077	−	0.994879i	$-0.532229\pi$
$53$	−78.0000	−0.202153	−0.101077	+	0.994879i	$0.532229\pi$
$54$	−54.0000	−0.136083
$55$	−240.000	−0.588393
$56$	0	0
$57$	420.000	0.975971
$58$	420.000	0.950840
$59$	−240.000	−0.529582	−0.264791	−	0.964306i	$-0.585303\pi$
$59$	−240.000	−0.529582	−0.264791	+	0.964306i	$0.585303\pi$
$60$	−60.0000	−0.129099
$61$	−302.000	−0.633888	−0.316944	−	0.948444i	$-0.602657\pi$
$61$	−302.000	−0.633888	−0.316944	+	0.948444i	$0.602657\pi$
$62$	−544.000	−1.11432
$63$	0	0
$64$	64.0000	0.125000
$65$	−10.0000	−0.0190823
$66$	288.000	0.537127
$67$	596.000	1.08676	0.543381	−	0.839487i	$-0.317144\pi$
$67$	596.000	1.08676	0.543381	+	0.839487i	$0.317144\pi$
$68$	456.000	0.813208
$69$	−216.000	−0.376860
$70$	0	0
$71$	−768.000	−1.28373	−0.641865	−	0.766818i	$-0.721839\pi$
$71$	−768.000	−1.28373	−0.641865	+	0.766818i	$0.721839\pi$
$72$	72.0000	0.117851
$73$	478.000	0.766379	0.383190	−	0.923670i	$-0.374826\pi$
$73$	478.000	0.766379	0.383190	+	0.923670i	$0.374826\pi$
$74$	−668.000	−1.04937
$75$	−75.0000	−0.115470
$76$	−560.000	−0.845216
$77$	0	0
$78$	12.0000	0.0174196
$79$	−640.000	−0.911464	−0.455732	−	0.890117i	$-0.650622\pi$
$79$	−640.000	−0.911464	−0.455732	+	0.890117i	$0.650622\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	396.000	0.533303
$83$	348.000	0.460216	0.230108	−	0.973165i	$-0.426092\pi$
$83$	348.000	0.460216	0.230108	+	0.973165i	$0.426092\pi$
$84$	0	0
$85$	570.000	0.727355
$86$	−536.000	−0.672074
$87$	−630.000	−0.776357
$88$	−384.000	−0.465165
$89$	−210.000	−0.250112	−0.125056	−	0.992150i	$-0.539911\pi$
$89$	−210.000	−0.250112	−0.125056	+	0.992150i	$0.539911\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	288.000	0.326370
$93$	816.000	0.909841
$94$	−432.000	−0.474015
$95$	−700.000	−0.755984
$96$	−96.0000	−0.102062
$97$	1534.00	1.60571	0.802856	−	0.596173i	$-0.203313\pi$
$97$	1534.00	1.60571	0.802856	+	0.596173i	$0.203313\pi$
$98$	0	0
$99$	−432.000	−0.438562
$100$	100.000	0.100000
$101$	−1722.00	−1.69649	−0.848245	−	0.529605i	$-0.822340\pi$
$101$	−1722.00	−1.69649	−0.848245	+	0.529605i	$0.822340\pi$
$102$	−684.000	−0.663981
$103$	−1052.00	−1.00638	−0.503188	−	0.864177i	$-0.667840\pi$
$103$	−1052.00	−1.00638	−0.503188	+	0.864177i	$0.667840\pi$
$104$	−16.0000	−0.0150859
$105$	0	0
$106$	−156.000	−0.142944
$107$	−564.000	−0.509570	−0.254785	−	0.966998i	$-0.582005\pi$
$107$	−564.000	−0.509570	−0.254785	+	0.966998i	$0.582005\pi$
$108$	−108.000	−0.0962250
$109$	−610.000	−0.536031	−0.268016	−	0.963415i	$-0.586368\pi$
$109$	−610.000	−0.536031	−0.268016	+	0.963415i	$0.586368\pi$
$110$	−480.000	−0.416056
$111$	1002.00	0.856807
$112$	0	0
$113$	1302.00	1.08391	0.541955	−	0.840407i	$-0.317684\pi$
$113$	1302.00	1.08391	0.541955	+	0.840407i	$0.317684\pi$
$114$	840.000	0.690116
$115$	360.000	0.291915
$116$	840.000	0.672345
$117$	−18.0000	−0.0142231
$118$	−480.000	−0.374471
$119$	0	0
$120$	−120.000	−0.0912871
$121$	973.000	0.731029
$122$	−604.000	−0.448226
$123$	−594.000	−0.435440
$124$	−1088.00	−0.787946
$125$	125.000	0.0894427
$126$	0	0
$127$	−124.000	−0.0866395	−0.0433198	−	0.999061i	$-0.513793\pi$
$127$	−124.000	−0.0866395	−0.0433198	+	0.999061i	$0.513793\pi$
$128$	128.000	0.0883883
$129$	804.000	0.548746
$130$	−20.0000	−0.0134932
$131$	−192.000	−0.128054	−0.0640272	−	0.997948i	$-0.520394\pi$
$131$	−192.000	−0.128054	−0.0640272	+	0.997948i	$0.520394\pi$
$132$	576.000	0.379806
$133$	0	0
$134$	1192.00	0.768456
$135$	−135.000	−0.0860663
$136$	912.000	0.575025
$137$	−2514.00	−1.56778	−0.783889	−	0.620901i	$-0.786767\pi$
$137$	−2514.00	−1.56778	−0.783889	+	0.620901i	$0.786767\pi$
$138$	−432.000	−0.266480
$139$	−1340.00	−0.817679	−0.408839	−	0.912606i	$-0.634066\pi$
$139$	−1340.00	−0.817679	−0.408839	+	0.912606i	$0.634066\pi$
$140$	0	0
$141$	648.000	0.387032
$142$	−1536.00	−0.907734
$143$	96.0000	0.0561393
$144$	144.000	0.0833333
$145$	1050.00	0.601364
$146$	956.000	0.541912
$147$	0	0
$148$	−1336.00	−0.742017
$149$	1410.00	0.775246	0.387623	−	0.921818i	$-0.373296\pi$
$149$	1410.00	0.775246	0.387623	+	0.921818i	$0.373296\pi$
$150$	−150.000	−0.0816497
$151$	−2128.00	−1.14685	−0.573424	−	0.819258i	$-0.694385\pi$
$151$	−2128.00	−1.14685	−0.573424	+	0.819258i	$0.694385\pi$
$152$	−1120.00	−0.597658
$153$	1026.00	0.542138
$154$	0	0
$155$	−1360.00	−0.704760
$156$	24.0000	0.0123176
$157$	−3026.00	−1.53822	−0.769112	−	0.639114i	$-0.779301\pi$
$157$	−3026.00	−1.53822	−0.769112	+	0.639114i	$0.779301\pi$
$158$	−1280.00	−0.644502
$159$	234.000	0.116713
$160$	160.000	0.0790569
$161$	0	0
$162$	162.000	0.0785674
$163$	2612.00	1.25514	0.627569	−	0.778561i	$-0.284050\pi$
$163$	2612.00	1.25514	0.627569	+	0.778561i	$0.284050\pi$
$164$	792.000	0.377102
$165$	720.000	0.339709
$166$	696.000	0.325422
$167$	24.0000	0.0111208	0.00556041	−	0.999985i	$-0.498230\pi$
$167$	24.0000	0.0111208	0.00556041	+	0.999985i	$0.498230\pi$
$168$	0	0
$169$	−2193.00	−0.998179
$170$	1140.00	0.514318
$171$	−1260.00	−0.563477
$172$	−1072.00	−0.475228
$173$	−1962.00	−0.862243	−0.431122	−	0.902294i	$-0.641882\pi$
$173$	−1962.00	−0.862243	−0.431122	+	0.902294i	$0.641882\pi$
$174$	−1260.00	−0.548968
$175$	0	0
$176$	−768.000	−0.328921
$177$	720.000	0.305754
$178$	−420.000	−0.176856
$179$	−120.000	−0.0501074	−0.0250537	−	0.999686i	$-0.507976\pi$
$179$	−120.000	−0.0501074	−0.0250537	+	0.999686i	$0.507976\pi$
$180$	180.000	0.0745356
$181$	−902.000	−0.370415	−0.185208	−	0.982699i	$-0.559296\pi$
$181$	−902.000	−0.370415	−0.185208	+	0.982699i	$0.559296\pi$
$182$	0	0
$183$	906.000	0.365975
$184$	576.000	0.230779
$185$	−1670.00	−0.663680
$186$	1632.00	0.643355
$187$	−5472.00	−2.13985
$188$	−864.000	−0.335179
$189$	0	0
$190$	−1400.00	−0.534561
$191$	−168.000	−0.0636443	−0.0318221	−	0.999494i	$-0.510131\pi$
$191$	−168.000	−0.0636443	−0.0318221	+	0.999494i	$0.510131\pi$
$192$	−192.000	−0.0721688
$193$	−1318.00	−0.491563	−0.245782	−	0.969325i	$-0.579045\pi$
$193$	−1318.00	−0.491563	−0.245782	+	0.969325i	$0.579045\pi$
$194$	3068.00	1.13541
$195$	30.0000	0.0110172
$196$	0	0
$197$	−4014.00	−1.45170	−0.725852	−	0.687851i	$-0.758554\pi$
$197$	−4014.00	−1.45170	−0.725852	+	0.687851i	$0.758554\pi$
$198$	−864.000	−0.310110
$199$	−2000.00	−0.712443	−0.356222	−	0.934401i	$-0.615935\pi$
$199$	−2000.00	−0.712443	−0.356222	+	0.934401i	$0.615935\pi$
$200$	200.000	0.0707107
$201$	−1788.00	−0.627442
$202$	−3444.00	−1.19960
$203$	0	0
$204$	−1368.00	−0.469506
$205$	990.000	0.337291
$206$	−2104.00	−0.711615
$207$	648.000	0.217580
$208$	−32.0000	−0.0106673
$209$	6720.00	2.22408
$210$	0	0
$211$	−3868.00	−1.26201	−0.631005	−	0.775779i	$-0.717357\pi$
$211$	−3868.00	−1.26201	−0.631005	+	0.775779i	$0.717357\pi$
$212$	−312.000	−0.101077
$213$	2304.00	0.741162
$214$	−1128.00	−0.360320
$215$	−1340.00	−0.425057
$216$	−216.000	−0.0680414
$217$	0	0
$218$	−1220.00	−0.379031
$219$	−1434.00	−0.442469
$220$	−960.000	−0.294196
$221$	−228.000	−0.0693979
$222$	2004.00	0.605854
$223$	3148.00	0.945317	0.472658	−	0.881246i	$-0.343294\pi$
$223$	3148.00	0.945317	0.472658	+	0.881246i	$0.343294\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	2604.00	0.766440
$227$	−2556.00	−0.747347	−0.373673	−	0.927560i	$-0.621902\pi$
$227$	−2556.00	−0.747347	−0.373673	+	0.927560i	$0.621902\pi$
$228$	1680.00	0.487986
$229$	610.000	0.176026	0.0880130	−	0.996119i	$-0.471948\pi$
$229$	610.000	0.176026	0.0880130	+	0.996119i	$0.471948\pi$
$230$	720.000	0.206415
$231$	0	0
$232$	1680.00	0.475420
$233$	−2058.00	−0.578644	−0.289322	−	0.957232i	$-0.593430\pi$
$233$	−2058.00	−0.578644	−0.289322	+	0.957232i	$0.593430\pi$
$234$	−36.0000	−0.0100572
$235$	−1080.00	−0.299793
$236$	−960.000	−0.264791
$237$	1920.00	0.526234
$238$	0	0
$239$	4920.00	1.33158	0.665792	−	0.746138i	$-0.268094\pi$
$239$	4920.00	1.33158	0.665792	+	0.746138i	$0.268094\pi$
$240$	−240.000	−0.0645497
$241$	1438.00	0.384356	0.192178	−	0.981360i	$-0.438445\pi$
$241$	1438.00	0.384356	0.192178	+	0.981360i	$0.438445\pi$
$242$	1946.00	0.516916
$243$	−243.000	−0.0641500
$244$	−1208.00	−0.316944
$245$	0	0
$246$	−1188.00	−0.307903
$247$	280.000	0.0721294
$248$	−2176.00	−0.557162
$249$	−1044.00	−0.265706
$250$	250.000	0.0632456
$251$	−792.000	−0.199166	−0.0995829	−	0.995029i	$-0.531751\pi$
$251$	−792.000	−0.199166	−0.0995829	+	0.995029i	$0.531751\pi$
$252$	0	0
$253$	−3456.00	−0.858802
$254$	−248.000	−0.0612634
$255$	−1710.00	−0.419939
$256$	256.000	0.0625000
$257$	−2166.00	−0.525725	−0.262863	−	0.964833i	$-0.584667\pi$
$257$	−2166.00	−0.525725	−0.262863	+	0.964833i	$0.584667\pi$
$258$	1608.00	0.388022
$259$	0	0
$260$	−40.0000	−0.00954113
$261$	1890.00	0.448230
$262$	−384.000	−0.0905481
$263$	3192.00	0.748392	0.374196	−	0.927350i	$-0.377919\pi$
$263$	3192.00	0.748392	0.374196	+	0.927350i	$0.377919\pi$
$264$	1152.00	0.268563
$265$	−390.000	−0.0904057
$266$	0	0
$267$	630.000	0.144402
$268$	2384.00	0.543381
$269$	−5490.00	−1.24435	−0.622177	−	0.782877i	$-0.713752\pi$
$269$	−5490.00	−1.24435	−0.622177	+	0.782877i	$0.713752\pi$
$270$	−270.000	−0.0608581
$271$	6328.00	1.41845	0.709223	−	0.704985i	$-0.249046\pi$
$271$	6328.00	1.41845	0.709223	+	0.704985i	$0.249046\pi$
$272$	1824.00	0.406604
$273$	0	0
$274$	−5028.00	−1.10859
$275$	−1200.00	−0.263137
$276$	−864.000	−0.188430
$277$	−574.000	−0.124507	−0.0622533	−	0.998060i	$-0.519829\pi$
$277$	−574.000	−0.124507	−0.0622533	+	0.998060i	$0.519829\pi$
$278$	−2680.00	−0.578186
$279$	−2448.00	−0.525297
$280$	0	0
$281$	4242.00	0.900557	0.450278	−	0.892888i	$-0.351325\pi$
$281$	4242.00	0.900557	0.450278	+	0.892888i	$0.351325\pi$
$282$	1296.00	0.273673
$283$	628.000	0.131911	0.0659553	−	0.997823i	$-0.478991\pi$
$283$	628.000	0.131911	0.0659553	+	0.997823i	$0.478991\pi$
$284$	−3072.00	−0.641865
$285$	2100.00	0.436468
$286$	192.000	0.0396965
$287$	0	0
$288$	288.000	0.0589256
$289$	8083.00	1.64523
$290$	2100.00	0.425228
$291$	−4602.00	−0.927058
$292$	1912.00	0.383190
$293$	558.000	0.111258	0.0556292	−	0.998451i	$-0.482284\pi$
$293$	558.000	0.111258	0.0556292	+	0.998451i	$0.482284\pi$
$294$	0	0
$295$	−1200.00	−0.236836
$296$	−2672.00	−0.524685
$297$	1296.00	0.253204
$298$	2820.00	0.548182
$299$	−144.000	−0.0278520
$300$	−300.000	−0.0577350
$301$	0	0
$302$	−4256.00	−0.810945
$303$	5166.00	0.979468
$304$	−2240.00	−0.422608
$305$	−1510.00	−0.283483
$306$	2052.00	0.383350
$307$	6964.00	1.29465	0.647323	−	0.762216i	$-0.275888\pi$
$307$	6964.00	1.29465	0.647323	+	0.762216i	$0.275888\pi$
$308$	0	0
$309$	3156.00	0.581031
$310$	−2720.00	−0.498341
$311$	−2832.00	−0.516360	−0.258180	−	0.966097i	$-0.583123\pi$
$311$	−2832.00	−0.516360	−0.258180	+	0.966097i	$0.583123\pi$
$312$	48.0000	0.00870982
$313$	−8642.00	−1.56062	−0.780311	−	0.625392i	$-0.784939\pi$
$313$	−8642.00	−1.56062	−0.780311	+	0.625392i	$0.784939\pi$
$314$	−6052.00	−1.08769
$315$	0	0
$316$	−2560.00	−0.455732
$317$	−2214.00	−0.392273	−0.196137	−	0.980577i	$-0.562840\pi$
$317$	−2214.00	−0.392273	−0.196137	+	0.980577i	$0.562840\pi$
$318$	468.000	0.0825287
$319$	−10080.0	−1.76919
$320$	320.000	0.0559017
$321$	1692.00	0.294200
$322$	0	0
$323$	−15960.0	−2.74934
$324$	324.000	0.0555556
$325$	−50.0000	−0.00853385
$326$	5224.00	0.887517
$327$	1830.00	0.309478
$328$	1584.00	0.266652
$329$	0	0
$330$	1440.00	0.240210
$331$	10772.0	1.78877	0.894385	−	0.447299i	$-0.147614\pi$
$331$	10772.0	1.78877	0.894385	+	0.447299i	$0.147614\pi$
$332$	1392.00	0.230108
$333$	−3006.00	−0.494678
$334$	48.0000	0.00786360
$335$	2980.00	0.486014
$336$	0	0
$337$	−1654.00	−0.267356	−0.133678	−	0.991025i	$-0.542679\pi$
$337$	−1654.00	−0.267356	−0.133678	+	0.991025i	$0.542679\pi$
$338$	−4386.00	−0.705819
$339$	−3906.00	−0.625796
$340$	2280.00	0.363678
$341$	13056.0	2.07338
$342$	−2520.00	−0.398439
$343$	0	0
$344$	−2144.00	−0.336037
$345$	−1080.00	−0.168537
$346$	−3924.00	−0.609698
$347$	2196.00	0.339733	0.169867	−	0.985467i	$-0.445666\pi$
$347$	2196.00	0.339733	0.169867	+	0.985467i	$0.445666\pi$
$348$	−2520.00	−0.388179
$349$	−8270.00	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$349$	−8270.00	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$350$	0	0
$351$	54.0000	0.00821170
$352$	−1536.00	−0.232583
$353$	−10302.0	−1.55331	−0.776657	−	0.629923i	$-0.783086\pi$
$353$	−10302.0	−1.55331	−0.776657	+	0.629923i	$0.783086\pi$
$354$	1440.00	0.216201
$355$	−3840.00	−0.574102
$356$	−840.000	−0.125056
$357$	0	0
$358$	−240.000	−0.0354313
$359$	−2280.00	−0.335192	−0.167596	−	0.985856i	$-0.553600\pi$
$359$	−2280.00	−0.335192	−0.167596	+	0.985856i	$0.553600\pi$
$360$	360.000	0.0527046
$361$	12741.0	1.85756
$362$	−1804.00	−0.261923
$363$	−2919.00	−0.422060
$364$	0	0
$365$	2390.00	0.342735
$366$	1812.00	0.258783
$367$	8764.00	1.24653	0.623266	−	0.782010i	$-0.285805\pi$
$367$	8764.00	1.24653	0.623266	+	0.782010i	$0.285805\pi$
$368$	1152.00	0.163185
$369$	1782.00	0.251402
$370$	−3340.00	−0.469293
$371$	0	0
$372$	3264.00	0.454921
$373$	−1318.00	−0.182958	−0.0914792	−	0.995807i	$-0.529159\pi$
$373$	−1318.00	−0.182958	−0.0914792	+	0.995807i	$0.529159\pi$
$374$	−10944.0	−1.51310
$375$	−375.000	−0.0516398
$376$	−1728.00	−0.237007
$377$	−420.000	−0.0573769
$378$	0	0
$379$	1100.00	0.149085	0.0745425	−	0.997218i	$-0.476250\pi$
$379$	1100.00	0.149085	0.0745425	+	0.997218i	$0.476250\pi$
$380$	−2800.00	−0.377992
$381$	372.000	0.0500214
$382$	−336.000	−0.0450033
$383$	3528.00	0.470685	0.235343	−	0.971912i	$-0.424379\pi$
$383$	3528.00	0.470685	0.235343	+	0.971912i	$0.424379\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−2636.00	−0.347588
$387$	−2412.00	−0.316819
$388$	6136.00	0.802856
$389$	−9630.00	−1.25517	−0.627584	−	0.778549i	$-0.715956\pi$
$389$	−9630.00	−1.25517	−0.627584	+	0.778549i	$0.715956\pi$
$390$	60.0000	0.00779030
$391$	8208.00	1.06163
$392$	0	0
$393$	576.000	0.0739322
$394$	−8028.00	−1.02651
$395$	−3200.00	−0.407619
$396$	−1728.00	−0.219281
$397$	3094.00	0.391142	0.195571	−	0.980690i	$-0.437344\pi$
$397$	3094.00	0.391142	0.195571	+	0.980690i	$0.437344\pi$
$398$	−4000.00	−0.503774
$399$	0	0
$400$	400.000	0.0500000
$401$	−1638.00	−0.203985	−0.101992	−	0.994785i	$-0.532522\pi$
$401$	−1638.00	−0.203985	−0.101992	+	0.994785i	$0.532522\pi$
$402$	−3576.00	−0.443668
$403$	544.000	0.0672421
$404$	−6888.00	−0.848245
$405$	405.000	0.0496904
$406$	0	0
$407$	16032.0	1.95252
$408$	−2736.00	−0.331991
$409$	13750.0	1.66233	0.831166	−	0.556024i	$-0.187674\pi$
$409$	13750.0	1.66233	0.831166	+	0.556024i	$0.187674\pi$
$410$	1980.00	0.238501
$411$	7542.00	0.905157
$412$	−4208.00	−0.503188
$413$	0	0
$414$	1296.00	0.153852
$415$	1740.00	0.205815
$416$	−64.0000	−0.00754293
$417$	4020.00	0.472087
$418$	13440.0	1.57266
$419$	12480.0	1.45510	0.727551	−	0.686053i	$-0.240658\pi$
$419$	12480.0	1.45510	0.727551	+	0.686053i	$0.240658\pi$
$420$	0	0
$421$	7262.00	0.840685	0.420342	−	0.907366i	$-0.361910\pi$
$421$	7262.00	0.840685	0.420342	+	0.907366i	$0.361910\pi$
$422$	−7736.00	−0.892376
$423$	−1944.00	−0.223453
$424$	−624.000	−0.0714720
$425$	2850.00	0.325283
$426$	4608.00	0.524081
$427$	0	0
$428$	−2256.00	−0.254785
$429$	−288.000	−0.0324121
$430$	−2680.00	−0.300561
$431$	9792.00	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$432$	−432.000	−0.0481125
$433$	−1802.00	−0.199997	−0.0999984	−	0.994988i	$-0.531884\pi$
$433$	−1802.00	−0.199997	−0.0999984	+	0.994988i	$0.531884\pi$
$434$	0	0
$435$	−3150.00	−0.347198
$436$	−2440.00	−0.268016
$437$	−10080.0	−1.10341
$438$	−2868.00	−0.312873
$439$	2320.00	0.252227	0.126113	−	0.992016i	$-0.459750\pi$
$439$	2320.00	0.252227	0.126113	+	0.992016i	$0.459750\pi$
$440$	−1920.00	−0.208028
$441$	0	0
$442$	−456.000	−0.0490717
$443$	11172.0	1.19819	0.599095	−	0.800678i	$-0.295527\pi$
$443$	11172.0	1.19819	0.599095	+	0.800678i	$0.295527\pi$
$444$	4008.00	0.428404
$445$	−1050.00	−0.111853
$446$	6296.00	0.668440
$447$	−4230.00	−0.447589
$448$	0	0
$449$	6810.00	0.715777	0.357888	−	0.933764i	$-0.383497\pi$
$449$	6810.00	0.715777	0.357888	+	0.933764i	$0.383497\pi$
$450$	450.000	0.0471405
$451$	−9504.00	−0.992297
$452$	5208.00	0.541955
$453$	6384.00	0.662134
$454$	−5112.00	−0.528454
$455$	0	0
$456$	3360.00	0.345058
$457$	17066.0	1.74686	0.873429	−	0.486952i	$-0.161891\pi$
$457$	17066.0	1.74686	0.873429	+	0.486952i	$0.161891\pi$
$458$	1220.00	0.124469
$459$	−3078.00	−0.313004
$460$	1440.00	0.145957
$461$	18918.0	1.91128	0.955639	−	0.294541i	$-0.0951667\pi$
$461$	18918.0	1.91128	0.955639	+	0.294541i	$0.0951667\pi$
$462$	0	0
$463$	1052.00	0.105595	0.0527976	−	0.998605i	$-0.483186\pi$
$463$	1052.00	0.105595	0.0527976	+	0.998605i	$0.483186\pi$
$464$	3360.00	0.336173
$465$	4080.00	0.406893
$466$	−4116.00	−0.409163
$467$	−11076.0	−1.09751	−0.548754	−	0.835984i	$-0.684898\pi$
$467$	−11076.0	−1.09751	−0.548754	+	0.835984i	$0.684898\pi$
$468$	−72.0000	−0.00711154
$469$	0	0
$470$	−2160.00	−0.211986
$471$	9078.00	0.888094
$472$	−1920.00	−0.187236
$473$	12864.0	1.25050
$474$	3840.00	0.372103
$475$	−3500.00	−0.338086
$476$	0	0
$477$	−702.000	−0.0673844
$478$	9840.00	0.941571
$479$	9000.00	0.858498	0.429249	−	0.903186i	$-0.358778\pi$
$479$	9000.00	0.858498	0.429249	+	0.903186i	$0.358778\pi$
$480$	−480.000	−0.0456435
$481$	668.000	0.0633226
$482$	2876.00	0.271781
$483$	0	0
$484$	3892.00	0.365515
$485$	7670.00	0.718096
$486$	−486.000	−0.0453609
$487$	−8764.00	−0.815472	−0.407736	−	0.913100i	$-0.633682\pi$
$487$	−8764.00	−0.815472	−0.407736	+	0.913100i	$0.633682\pi$
$488$	−2416.00	−0.224113
$489$	−7836.00	−0.724655
$490$	0	0
$491$	5592.00	0.513978	0.256989	−	0.966414i	$-0.417270\pi$
$491$	5592.00	0.513978	0.256989	+	0.966414i	$0.417270\pi$
$492$	−2376.00	−0.217720
$493$	23940.0	2.18703
$494$	560.000	0.0510032
$495$	−2160.00	−0.196131
$496$	−4352.00	−0.393973
$497$	0	0
$498$	−2088.00	−0.187883
$499$	4700.00	0.421645	0.210823	−	0.977524i	$-0.432386\pi$
$499$	4700.00	0.421645	0.210823	+	0.977524i	$0.432386\pi$
$500$	500.000	0.0447214
$501$	−72.0000	−0.00642060
$502$	−1584.00	−0.140831
$503$	11808.0	1.04671	0.523353	−	0.852116i	$-0.324681\pi$
$503$	11808.0	1.04671	0.523353	+	0.852116i	$0.324681\pi$
$504$	0	0
$505$	−8610.00	−0.758693
$506$	−6912.00	−0.607265
$507$	6579.00	0.576299
$508$	−496.000	−0.0433198
$509$	−1170.00	−0.101885	−0.0509424	−	0.998702i	$-0.516222\pi$
$509$	−1170.00	−0.101885	−0.0509424	+	0.998702i	$0.516222\pi$
$510$	−3420.00	−0.296941
$511$	0	0
$512$	512.000	0.0441942
$513$	3780.00	0.325324
$514$	−4332.00	−0.371744
$515$	−5260.00	−0.450065
$516$	3216.00	0.274373
$517$	10368.0	0.881981
$518$	0	0
$519$	5886.00	0.497816
$520$	−80.0000	−0.00674660
$521$	16638.0	1.39909	0.699543	−	0.714590i	$-0.253387\pi$
$521$	16638.0	1.39909	0.699543	+	0.714590i	$0.253387\pi$
$522$	3780.00	0.316947
$523$	−15692.0	−1.31198	−0.655988	−	0.754771i	$-0.727748\pi$
$523$	−15692.0	−1.31198	−0.655988	+	0.754771i	$0.727748\pi$
$524$	−768.000	−0.0640272
$525$	0	0
$526$	6384.00	0.529193
$527$	−31008.0	−2.56305
$528$	2304.00	0.189903
$529$	−6983.00	−0.573929
$530$	−780.000	−0.0639265
$531$	−2160.00	−0.176527
$532$	0	0
$533$	−396.000	−0.0321814
$534$	1260.00	0.102108
$535$	−2820.00	−0.227886
$536$	4768.00	0.384228
$537$	360.000	0.0289295
$538$	−10980.0	−0.879891
$539$	0	0
$540$	−540.000	−0.0430331
$541$	−22018.0	−1.74977	−0.874887	−	0.484327i	$-0.839064\pi$
$541$	−22018.0	−1.74977	−0.874887	+	0.484327i	$0.839064\pi$
$542$	12656.0	1.00299
$543$	2706.00	0.213859
$544$	3648.00	0.287512
$545$	−3050.00	−0.239720
$546$	0	0
$547$	−4564.00	−0.356751	−0.178375	−	0.983963i	$-0.557084\pi$
$547$	−4564.00	−0.356751	−0.178375	+	0.983963i	$0.557084\pi$
$548$	−10056.0	−0.783889
$549$	−2718.00	−0.211296
$550$	−2400.00	−0.186066
$551$	−29400.0	−2.27311
$552$	−1728.00	−0.133240
$553$	0	0
$554$	−1148.00	−0.0880394
$555$	5010.00	0.383176
$556$	−5360.00	−0.408839
$557$	−7734.00	−0.588331	−0.294165	−	0.955755i	$-0.595042\pi$
$557$	−7734.00	−0.588331	−0.294165	+	0.955755i	$0.595042\pi$
$558$	−4896.00	−0.371441
$559$	536.000	0.0405552
$560$	0	0
$561$	16416.0	1.23544
$562$	8484.00	0.636790
$563$	20148.0	1.50824	0.754118	−	0.656739i	$-0.228065\pi$
$563$	20148.0	1.50824	0.754118	+	0.656739i	$0.228065\pi$
$564$	2592.00	0.193516
$565$	6510.00	0.484739
$566$	1256.00	0.0932749
$567$	0	0
$568$	−6144.00	−0.453867
$569$	−24030.0	−1.77046	−0.885228	−	0.465156i	$-0.845998\pi$
$569$	−24030.0	−1.77046	−0.885228	+	0.465156i	$0.845998\pi$
$570$	4200.00	0.308629
$571$	2372.00	0.173844	0.0869222	−	0.996215i	$-0.472297\pi$
$571$	2372.00	0.173844	0.0869222	+	0.996215i	$0.472297\pi$
$572$	384.000	0.0280697
$573$	504.000	0.0367450
$574$	0	0
$575$	1800.00	0.130548
$576$	576.000	0.0416667
$577$	−8546.00	−0.616594	−0.308297	−	0.951290i	$-0.599759\pi$
$577$	−8546.00	−0.616594	−0.308297	+	0.951290i	$0.599759\pi$
$578$	16166.0	1.16335
$579$	3954.00	0.283804
$580$	4200.00	0.300682
$581$	0	0
$582$	−9204.00	−0.655529
$583$	3744.00	0.265970
$584$	3824.00	0.270956
$585$	−90.0000	−0.00636076
$586$	1116.00	0.0786716
$587$	15444.0	1.08593	0.542966	−	0.839755i	$-0.317301\pi$
$587$	15444.0	1.08593	0.542966	+	0.839755i	$0.317301\pi$
$588$	0	0
$589$	38080.0	2.66394
$590$	−2400.00	−0.167469
$591$	12042.0	0.838142
$592$	−5344.00	−0.371009
$593$	−18342.0	−1.27018	−0.635089	−	0.772439i	$-0.719037\pi$
$593$	−18342.0	−1.27018	−0.635089	+	0.772439i	$0.719037\pi$
$594$	2592.00	0.179042
$595$	0	0
$596$	5640.00	0.387623
$597$	6000.00	0.411329
$598$	−288.000	−0.0196943
$599$	24600.0	1.67801	0.839006	−	0.544123i	$-0.183137\pi$
$599$	24600.0	1.67801	0.839006	+	0.544123i	$0.183137\pi$
$600$	−600.000	−0.0408248
$601$	8998.00	0.610709	0.305354	−	0.952239i	$-0.401225\pi$
$601$	8998.00	0.610709	0.305354	+	0.952239i	$0.401225\pi$
$602$	0	0
$603$	5364.00	0.362254
$604$	−8512.00	−0.573424
$605$	4865.00	0.326926
$606$	10332.0	0.692589
$607$	−4076.00	−0.272553	−0.136277	−	0.990671i	$-0.543514\pi$
$607$	−4076.00	−0.272553	−0.136277	+	0.990671i	$0.543514\pi$
$608$	−4480.00	−0.298829
$609$	0	0
$610$	−3020.00	−0.200453
$611$	432.000	0.0286037
$612$	4104.00	0.271069
$613$	−4078.00	−0.268693	−0.134347	−	0.990934i	$-0.542894\pi$
$613$	−4078.00	−0.268693	−0.134347	+	0.990934i	$0.542894\pi$
$614$	13928.0	0.915453
$615$	−2970.00	−0.194735
$616$	0	0
$617$	10086.0	0.658099	0.329049	−	0.944313i	$-0.393272\pi$
$617$	10086.0	0.658099	0.329049	+	0.944313i	$0.393272\pi$
$618$	6312.00	0.410851
$619$	−8780.00	−0.570110	−0.285055	−	0.958511i	$-0.592012\pi$
$619$	−8780.00	−0.570110	−0.285055	+	0.958511i	$0.592012\pi$
$620$	−5440.00	−0.352380
$621$	−1944.00	−0.125620
$622$	−5664.00	−0.365122
$623$	0	0
$624$	96.0000	0.00615878
$625$	625.000	0.0400000
$626$	−17284.0	−1.10353
$627$	−20160.0	−1.28407
$628$	−12104.0	−0.769112
$629$	−38076.0	−2.41366
$630$	0	0
$631$	2792.00	0.176145	0.0880727	−	0.996114i	$-0.471929\pi$
$631$	2792.00	0.176145	0.0880727	+	0.996114i	$0.471929\pi$
$632$	−5120.00	−0.322251
$633$	11604.0	0.728622
$634$	−4428.00	−0.277379
$635$	−620.000	−0.0387464
$636$	936.000	0.0583566
$637$	0	0
$638$	−20160.0	−1.25101
$639$	−6912.00	−0.427910
$640$	640.000	0.0395285
$641$	7602.00	0.468426	0.234213	−	0.972185i	$-0.424749\pi$
$641$	7602.00	0.468426	0.234213	+	0.972185i	$0.424749\pi$
$642$	3384.00	0.208031
$643$	−24212.0	−1.48496	−0.742479	−	0.669869i	$-0.766350\pi$
$643$	−24212.0	−1.48496	−0.742479	+	0.669869i	$0.766350\pi$
$644$	0	0
$645$	4020.00	0.245407
$646$	−31920.0	−1.94408
$647$	−9456.00	−0.574581	−0.287290	−	0.957844i	$-0.592754\pi$
$647$	−9456.00	−0.574581	−0.287290	+	0.957844i	$0.592754\pi$
$648$	648.000	0.0392837
$649$	11520.0	0.696764
$650$	−100.000	−0.00603434
$651$	0	0
$652$	10448.0	0.627569
$653$	−9558.00	−0.572792	−0.286396	−	0.958111i	$-0.592457\pi$
$653$	−9558.00	−0.572792	−0.286396	+	0.958111i	$0.592457\pi$
$654$	3660.00	0.218834
$655$	−960.000	−0.0572676
$656$	3168.00	0.188551
$657$	4302.00	0.255460
$658$	0	0
$659$	−29280.0	−1.73078	−0.865392	−	0.501095i	$-0.832931\pi$
$659$	−29280.0	−1.73078	−0.865392	+	0.501095i	$0.832931\pi$
$660$	2880.00	0.169854
$661$	29098.0	1.71223	0.856113	−	0.516789i	$-0.172873\pi$
$661$	29098.0	1.71223	0.856113	+	0.516789i	$0.172873\pi$
$662$	21544.0	1.26485
$663$	684.000	0.0400669
$664$	2784.00	0.162711
$665$	0	0
$666$	−6012.00	−0.349790
$667$	15120.0	0.877734
$668$	96.0000	0.00556041
$669$	−9444.00	−0.545779
$670$	5960.00	0.343664
$671$	14496.0	0.833997
$672$	0	0
$673$	−11638.0	−0.666585	−0.333293	−	0.942823i	$-0.608160\pi$
$673$	−11638.0	−0.666585	−0.333293	+	0.942823i	$0.608160\pi$
$674$	−3308.00	−0.189050
$675$	−675.000	−0.0384900
$676$	−8772.00	−0.499090
$677$	−3426.00	−0.194493	−0.0972466	−	0.995260i	$-0.531004\pi$
$677$	−3426.00	−0.194493	−0.0972466	+	0.995260i	$0.531004\pi$
$678$	−7812.00	−0.442505
$679$	0	0
$680$	4560.00	0.257159
$681$	7668.00	0.431481
$682$	26112.0	1.46610
$683$	−20148.0	−1.12876	−0.564379	−	0.825516i	$-0.690884\pi$
$683$	−20148.0	−1.12876	−0.564379	+	0.825516i	$0.690884\pi$
$684$	−5040.00	−0.281739
$685$	−12570.0	−0.701131
$686$	0	0
$687$	−1830.00	−0.101629
$688$	−4288.00	−0.237614
$689$	156.000	0.00862573
$690$	−2160.00	−0.119174
$691$	29428.0	1.62011	0.810053	−	0.586356i	$-0.199438\pi$
$691$	29428.0	1.62011	0.810053	+	0.586356i	$0.199438\pi$
$692$	−7848.00	−0.431122
$693$	0	0
$694$	4392.00	0.240228
$695$	−6700.00	−0.365677
$696$	−5040.00	−0.274484
$697$	22572.0	1.22665
$698$	−16540.0	−0.896917
$699$	6174.00	0.334080
$700$	0	0
$701$	16242.0	0.875110	0.437555	−	0.899192i	$-0.355845\pi$
$701$	16242.0	0.875110	0.437555	+	0.899192i	$0.355845\pi$
$702$	108.000	0.00580655
$703$	46760.0	2.50866
$704$	−3072.00	−0.164461
$705$	3240.00	0.173086
$706$	−20604.0	−1.09836
$707$	0	0
$708$	2880.00	0.152877
$709$	2030.00	0.107529	0.0537646	−	0.998554i	$-0.482878\pi$
$709$	2030.00	0.107529	0.0537646	+	0.998554i	$0.482878\pi$
$710$	−7680.00	−0.405951
$711$	−5760.00	−0.303821
$712$	−1680.00	−0.0884279
$713$	−19584.0	−1.02865
$714$	0	0
$715$	480.000	0.0251063
$716$	−480.000	−0.0250537
$717$	−14760.0	−0.768790
$718$	−4560.00	−0.237016
$719$	−6960.00	−0.361007	−0.180504	−	0.983574i	$-0.557773\pi$
$719$	−6960.00	−0.361007	−0.180504	+	0.983574i	$0.557773\pi$
$720$	720.000	0.0372678
$721$	0	0
$722$	25482.0	1.31349
$723$	−4314.00	−0.221908
$724$	−3608.00	−0.185208
$725$	5250.00	0.268938
$726$	−5838.00	−0.298441
$727$	−18596.0	−0.948676	−0.474338	−	0.880343i	$-0.657313\pi$
$727$	−18596.0	−0.948676	−0.474338	+	0.880343i	$0.657313\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	4780.00	0.242350
$731$	−30552.0	−1.54584
$732$	3624.00	0.182988
$733$	−21242.0	−1.07038	−0.535192	−	0.844731i	$-0.679761\pi$
$733$	−21242.0	−1.07038	−0.535192	+	0.844731i	$0.679761\pi$
$734$	17528.0	0.881431
$735$	0	0
$736$	2304.00	0.115389
$737$	−28608.0	−1.42984
$738$	3564.00	0.177768
$739$	−340.000	−0.0169244	−0.00846218	−	0.999964i	$-0.502694\pi$
$739$	−340.000	−0.0169244	−0.00846218	+	0.999964i	$0.502694\pi$
$740$	−6680.00	−0.331840
$741$	−840.000	−0.0416440
$742$	0	0
$743$	−21888.0	−1.08074	−0.540372	−	0.841426i	$-0.681716\pi$
$743$	−21888.0	−1.08074	−0.540372	+	0.841426i	$0.681716\pi$
$744$	6528.00	0.321678
$745$	7050.00	0.346701
$746$	−2636.00	−0.129371
$747$	3132.00	0.153405
$748$	−21888.0	−1.06993
$749$	0	0
$750$	−750.000	−0.0365148
$751$	17792.0	0.864500	0.432250	−	0.901754i	$-0.357720\pi$
$751$	17792.0	0.864500	0.432250	+	0.901754i	$0.357720\pi$
$752$	−3456.00	−0.167590
$753$	2376.00	0.114988
$754$	−840.000	−0.0405716
$755$	−10640.0	−0.512886
$756$	0	0
$757$	37346.0	1.79308	0.896541	−	0.442960i	$-0.146072\pi$
$757$	37346.0	1.79308	0.896541	+	0.442960i	$0.146072\pi$
$758$	2200.00	0.105419
$759$	10368.0	0.495829
$760$	−5600.00	−0.267281
$761$	11358.0	0.541034	0.270517	−	0.962715i	$-0.412805\pi$
$761$	11358.0	0.541034	0.270517	+	0.962715i	$0.412805\pi$
$762$	744.000	0.0353704
$763$	0	0
$764$	−672.000	−0.0318221
$765$	5130.00	0.242452
$766$	7056.00	0.332825
$767$	480.000	0.0225969
$768$	−768.000	−0.0360844
$769$	34270.0	1.60703	0.803516	−	0.595283i	$-0.202960\pi$
$769$	34270.0	1.60703	0.803516	+	0.595283i	$0.202960\pi$
$770$	0	0
$771$	6498.00	0.303528
$772$	−5272.00	−0.245782
$773$	13278.0	0.617822	0.308911	−	0.951091i	$-0.400035\pi$
$773$	13278.0	0.617822	0.308911	+	0.951091i	$0.400035\pi$
$774$	−4824.00	−0.224025
$775$	−6800.00	−0.315178
$776$	12272.0	0.567705
$777$	0	0
$778$	−19260.0	−0.887538
$779$	−27720.0	−1.27493
$780$	120.000	0.00550858
$781$	36864.0	1.68899
$782$	16416.0	0.750684
$783$	−5670.00	−0.258786
$784$	0	0
$785$	−15130.0	−0.687914
$786$	1152.00	0.0522780
$787$	11164.0	0.505659	0.252829	−	0.967511i	$-0.418639\pi$
$787$	11164.0	0.505659	0.252829	+	0.967511i	$0.418639\pi$
$788$	−16056.0	−0.725852
$789$	−9576.00	−0.432084
$790$	−6400.00	−0.288230
$791$	0	0
$792$	−3456.00	−0.155055
$793$	604.000	0.0270475
$794$	6188.00	0.276579
$795$	1170.00	0.0521958
$796$	−8000.00	−0.356222
$797$	5094.00	0.226397	0.113199	−	0.993572i	$-0.463890\pi$
$797$	5094.00	0.226397	0.113199	+	0.993572i	$0.463890\pi$
$798$	0	0
$799$	−24624.0	−1.09028
$800$	800.000	0.0353553
$801$	−1890.00	−0.0833706
$802$	−3276.00	−0.144239
$803$	−22944.0	−1.00831
$804$	−7152.00	−0.313721
$805$	0	0
$806$	1088.00	0.0475474
$807$	16470.0	0.718428
$808$	−13776.0	−0.599799
$809$	−8790.00	−0.382002	−0.191001	−	0.981590i	$-0.561173\pi$
$809$	−8790.00	−0.382002	−0.191001	+	0.981590i	$0.561173\pi$
$810$	810.000	0.0351364
$811$	−5852.00	−0.253380	−0.126690	−	0.991942i	$-0.540435\pi$
$811$	−5852.00	−0.253380	−0.126690	+	0.991942i	$0.540435\pi$
$812$	0	0
$813$	−18984.0	−0.818940
$814$	32064.0	1.38064
$815$	13060.0	0.561315
$816$	−5472.00	−0.234753
$817$	37520.0	1.60668
$818$	27500.0	1.17545
$819$	0	0
$820$	3960.00	0.168645
$821$	−29478.0	−1.25309	−0.626546	−	0.779384i	$-0.715532\pi$
$821$	−29478.0	−1.25309	−0.626546	+	0.779384i	$0.715532\pi$
$822$	15084.0	0.640042
$823$	39332.0	1.66589	0.832945	−	0.553356i	$-0.186653\pi$
$823$	39332.0	1.66589	0.832945	+	0.553356i	$0.186653\pi$
$824$	−8416.00	−0.355807
$825$	3600.00	0.151922
$826$	0	0
$827$	6756.00	0.284074	0.142037	−	0.989861i	$-0.454635\pi$
$827$	6756.00	0.284074	0.142037	+	0.989861i	$0.454635\pi$
$828$	2592.00	0.108790
$829$	−3950.00	−0.165488	−0.0827438	−	0.996571i	$-0.526368\pi$
$829$	−3950.00	−0.165488	−0.0827438	+	0.996571i	$0.526368\pi$
$830$	3480.00	0.145533
$831$	1722.00	0.0718839
$832$	−128.000	−0.00533366
$833$	0	0
$834$	8040.00	0.333816
$835$	120.000	0.00497338
$836$	26880.0	1.11204
$837$	7344.00	0.303280
$838$	24960.0	1.02891
$839$	−12360.0	−0.508599	−0.254300	−	0.967126i	$-0.581845\pi$
$839$	−12360.0	−0.508599	−0.254300	+	0.967126i	$0.581845\pi$
$840$	0	0
$841$	19711.0	0.808192
$842$	14524.0	0.594454
$843$	−12726.0	−0.519937
$844$	−15472.0	−0.631005
$845$	−10965.0	−0.446399
$846$	−3888.00	−0.158005
$847$	0	0
$848$	−1248.00	−0.0505383
$849$	−1884.00	−0.0761587
$850$	5700.00	0.230010
$851$	−24048.0	−0.968690
$852$	9216.00	0.370581
$853$	35998.0	1.44496	0.722478	−	0.691394i	$-0.243003\pi$
$853$	35998.0	1.44496	0.722478	+	0.691394i	$0.243003\pi$
$854$	0	0
$855$	−6300.00	−0.251995
$856$	−4512.00	−0.180160
$857$	21594.0	0.860720	0.430360	−	0.902657i	$-0.358387\pi$
$857$	21594.0	0.860720	0.430360	+	0.902657i	$0.358387\pi$
$858$	−576.000	−0.0229188
$859$	−9260.00	−0.367808	−0.183904	−	0.982944i	$-0.558874\pi$
$859$	−9260.00	−0.367808	−0.183904	+	0.982944i	$0.558874\pi$
$860$	−5360.00	−0.212528
$861$	0	0
$862$	19584.0	0.773821
$863$	31632.0	1.24770	0.623850	−	0.781544i	$-0.285567\pi$
$863$	31632.0	1.24770	0.623850	+	0.781544i	$0.285567\pi$
$864$	−864.000	−0.0340207
$865$	−9810.00	−0.385607
$866$	−3604.00	−0.141419
$867$	−24249.0	−0.949872
$868$	0	0
$869$	30720.0	1.19920
$870$	−6300.00	−0.245506
$871$	−1192.00	−0.0463713
$872$	−4880.00	−0.189516
$873$	13806.0	0.535237
$874$	−20160.0	−0.780231
$875$	0	0
$876$	−5736.00	−0.221235
$877$	−39694.0	−1.52836	−0.764180	−	0.645003i	$-0.776856\pi$
$877$	−39694.0	−1.52836	−0.764180	+	0.645003i	$0.776856\pi$
$878$	4640.00	0.178351
$879$	−1674.00	−0.0642351
$880$	−3840.00	−0.147098
$881$	−1242.00	−0.0474961	−0.0237480	−	0.999718i	$-0.507560\pi$
$881$	−1242.00	−0.0474961	−0.0237480	+	0.999718i	$0.507560\pi$
$882$	0	0
$883$	−2668.00	−0.101682	−0.0508411	−	0.998707i	$-0.516190\pi$
$883$	−2668.00	−0.101682	−0.0508411	+	0.998707i	$0.516190\pi$
$884$	−912.000	−0.0346990
$885$	3600.00	0.136737
$886$	22344.0	0.847248
$887$	4344.00	0.164439	0.0822194	−	0.996614i	$-0.473799\pi$
$887$	4344.00	0.164439	0.0822194	+	0.996614i	$0.473799\pi$
$888$	8016.00	0.302927
$889$	0	0
$890$	−2100.00	−0.0790923
$891$	−3888.00	−0.146187
$892$	12592.0	0.472658
$893$	30240.0	1.13319
$894$	−8460.00	−0.316493
$895$	−600.000	−0.0224087
$896$	0	0
$897$	432.000	0.0160803
$898$	13620.0	0.506131
$899$	−57120.0	−2.11909
$900$	900.000	0.0333333
$901$	−8892.00	−0.328785
$902$	−19008.0	−0.701660
$903$	0	0
$904$	10416.0	0.383220
$905$	−4510.00	−0.165655
$906$	12768.0	0.468199
$907$	4436.00	0.162398	0.0811990	−	0.996698i	$-0.474125\pi$
$907$	4436.00	0.162398	0.0811990	+	0.996698i	$0.474125\pi$
$908$	−10224.0	−0.373673
$909$	−15498.0	−0.565496
$910$	0	0
$911$	22752.0	0.827450	0.413725	−	0.910402i	$-0.364227\pi$
$911$	22752.0	0.827450	0.413725	+	0.910402i	$0.364227\pi$
$912$	6720.00	0.243993
$913$	−16704.0	−0.605500
$914$	34132.0	1.23521
$915$	4530.00	0.163669
$916$	2440.00	0.0880130
$917$	0	0
$918$	−6156.00	−0.221327
$919$	−27160.0	−0.974892	−0.487446	−	0.873153i	$-0.662071\pi$
$919$	−27160.0	−0.974892	−0.487446	+	0.873153i	$0.662071\pi$
$920$	2880.00	0.103207
$921$	−20892.0	−0.747465
$922$	37836.0	1.35148
$923$	1536.00	0.0547758
$924$	0	0
$925$	−8350.00	−0.296807
$926$	2104.00	0.0746671
$927$	−9468.00	−0.335458
$928$	6720.00	0.237710
$929$	33030.0	1.16650	0.583250	−	0.812292i	$-0.301781\pi$
$929$	33030.0	1.16650	0.583250	+	0.812292i	$0.301781\pi$
$930$	8160.00	0.287717
$931$	0	0
$932$	−8232.00	−0.289322
$933$	8496.00	0.298121
$934$	−22152.0	−0.776055
$935$	−27360.0	−0.956971
$936$	−144.000	−0.00502862
$937$	29974.0	1.04505	0.522523	−	0.852625i	$-0.324991\pi$
$937$	29974.0	1.04505	0.522523	+	0.852625i	$0.324991\pi$
$938$	0	0
$939$	25926.0	0.901026
$940$	−4320.00	−0.149897
$941$	−13962.0	−0.483686	−0.241843	−	0.970315i	$-0.577752\pi$
$941$	−13962.0	−0.483686	−0.241843	+	0.970315i	$0.577752\pi$
$942$	18156.0	0.627977
$943$	14256.0	0.492300
$944$	−3840.00	−0.132396
$945$	0	0
$946$	25728.0	0.884238
$947$	35196.0	1.20773	0.603863	−	0.797088i	$-0.293627\pi$
$947$	35196.0	1.20773	0.603863	+	0.797088i	$0.293627\pi$
$948$	7680.00	0.263117
$949$	−956.000	−0.0327008
$950$	−7000.00	−0.239063
$951$	6642.00	0.226479
$952$	0	0
$953$	−28338.0	−0.963230	−0.481615	−	0.876383i	$-0.659950\pi$
$953$	−28338.0	−0.963230	−0.481615	+	0.876383i	$0.659950\pi$
$954$	−1404.00	−0.0476480
$955$	−840.000	−0.0284626
$956$	19680.0	0.665792
$957$	30240.0	1.02144
$958$	18000.0	0.607050
$959$	0	0
$960$	−960.000	−0.0322749
$961$	44193.0	1.48343
$962$	1336.00	0.0447759
$963$	−5076.00	−0.169857
$964$	5752.00	0.192178
$965$	−6590.00	−0.219834
$966$	0	0
$967$	−17524.0	−0.582765	−0.291383	−	0.956607i	$-0.594115\pi$
$967$	−17524.0	−0.582765	−0.291383	+	0.956607i	$0.594115\pi$
$968$	7784.00	0.258458
$969$	47880.0	1.58733
$970$	15340.0	0.507771
$971$	26808.0	0.886004	0.443002	−	0.896521i	$-0.353913\pi$
$971$	26808.0	0.886004	0.443002	+	0.896521i	$0.353913\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	−17528.0	−0.576626
$975$	150.000	0.00492702
$976$	−4832.00	−0.158472
$977$	−10914.0	−0.357390	−0.178695	−	0.983905i	$-0.557187\pi$
$977$	−10914.0	−0.357390	−0.178695	+	0.983905i	$0.557187\pi$
$978$	−15672.0	−0.512408
$979$	10080.0	0.329069
$980$	0	0
$981$	−5490.00	−0.178677
$982$	11184.0	0.363438
$983$	−22272.0	−0.722652	−0.361326	−	0.932440i	$-0.617676\pi$
$983$	−22272.0	−0.722652	−0.361326	+	0.932440i	$0.617676\pi$
$984$	−4752.00	−0.153951
$985$	−20070.0	−0.649222
$986$	47880.0	1.54646
$987$	0	0
$988$	1120.00	0.0360647
$989$	−19296.0	−0.620402
$990$	−4320.00	−0.138685
$991$	14072.0	0.451071	0.225536	−	0.974235i	$-0.427587\pi$
$991$	14072.0	0.451071	0.225536	+	0.974235i	$0.427587\pi$
$992$	−8704.00	−0.278581
$993$	−32316.0	−1.03275
$994$	0	0
$995$	−10000.0	−0.318614
$996$	−4176.00	−0.132853
$997$	−4826.00	−0.153301	−0.0766504	−	0.997058i	$-0.524423\pi$
$997$	−4826.00	−0.153301	−0.0766504	+	0.997058i	$0.524423\pi$
$998$	9400.00	0.298148
$999$	9018.00	0.285602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.r.1.1		1
7.6	odd	2		30.4.a.b.1.1	✓	1
21.20	even	2		90.4.a.c.1.1		1
28.27	even	2		240.4.a.b.1.1		1
35.13	even	4		150.4.c.c.49.1		2
35.27	even	4		150.4.c.c.49.2		2
35.34	odd	2		150.4.a.b.1.1		1
56.13	odd	2		960.4.a.n.1.1		1
56.27	even	2		960.4.a.bg.1.1		1
63.13	odd	6		810.4.e.i.541.1		2
63.20	even	6		810.4.e.p.271.1		2
63.34	odd	6		810.4.e.i.271.1		2
63.41	even	6		810.4.e.p.541.1		2
84.83	odd	2		720.4.a.y.1.1		1
105.62	odd	4		450.4.c.j.199.1		2
105.83	odd	4		450.4.c.j.199.2		2
105.104	even	2		450.4.a.r.1.1		1
140.27	odd	4		1200.4.f.r.49.2		2
140.83	odd	4		1200.4.f.r.49.1		2
140.139	even	2		1200.4.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.a.b.1.1	✓	1	7.6	odd	2
90.4.a.c.1.1		1	21.20	even	2
150.4.a.b.1.1		1	35.34	odd	2
150.4.c.c.49.1		2	35.13	even	4
150.4.c.c.49.2		2	35.27	even	4
240.4.a.b.1.1		1	28.27	even	2
450.4.a.r.1.1		1	105.104	even	2
450.4.c.j.199.1		2	105.62	odd	4
450.4.c.j.199.2		2	105.83	odd	4
720.4.a.y.1.1		1	84.83	odd	2
810.4.e.i.271.1		2	63.34	odd	6
810.4.e.i.541.1		2	63.13	odd	6
810.4.e.p.271.1		2	63.20	even	6
810.4.e.p.541.1		2	63.41	even	6
960.4.a.n.1.1		1	56.13	odd	2
960.4.a.bg.1.1		1	56.27	even	2
1200.4.a.ba.1.1		1	140.139	even	2
1200.4.f.r.49.1		2	140.83	odd	4
1200.4.f.r.49.2		2	140.27	odd	4
1470.4.a.r.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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