LMFDB - Embedded newform 1470.4.a.k.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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +12.0000 q^{11} +12.0000 q^{12} +58.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} -42.0000 q^{17} -18.0000 q^{18} +4.00000 q^{19} -20.0000 q^{20} -24.0000 q^{22} +24.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} -116.000 q^{26} +27.0000 q^{27} +294.000 q^{29} +30.0000 q^{30} -128.000 q^{31} -32.0000 q^{32} +36.0000 q^{33} +84.0000 q^{34} +36.0000 q^{36} -58.0000 q^{37} -8.00000 q^{38} +174.000 q^{39} +40.0000 q^{40} -282.000 q^{41} +428.000 q^{43} +48.0000 q^{44} -45.0000 q^{45} -48.0000 q^{46} -384.000 q^{47} +48.0000 q^{48} -50.0000 q^{50} -126.000 q^{51} +232.000 q^{52} -138.000 q^{53} -54.0000 q^{54} -60.0000 q^{55} +12.0000 q^{57} -588.000 q^{58} -468.000 q^{59} -60.0000 q^{60} +250.000 q^{61} +256.000 q^{62} +64.0000 q^{64} -290.000 q^{65} -72.0000 q^{66} -556.000 q^{67} -168.000 q^{68} +72.0000 q^{69} +624.000 q^{71} -72.0000 q^{72} +958.000 q^{73} +116.000 q^{74} +75.0000 q^{75} +16.0000 q^{76} -348.000 q^{78} +632.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +564.000 q^{82} -84.0000 q^{83} +210.000 q^{85} -856.000 q^{86} +882.000 q^{87} -96.0000 q^{88} -810.000 q^{89} +90.0000 q^{90} +96.0000 q^{92} -384.000 q^{93} +768.000 q^{94} -20.0000 q^{95} -96.0000 q^{96} +790.000 q^{97} +108.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	12.0000	0.288675
$13$	58.0000	1.23741	0.618704	−	0.785624i	$-0.287658\pi$
$13$	58.0000	1.23741	0.618704	+	0.785624i	$0.287658\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−42.0000	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$18$	−18.0000	−0.235702
$19$	4.00000	0.0482980	0.0241490	−	0.999708i	$-0.492312\pi$
$19$	4.00000	0.0482980	0.0241490	+	0.999708i	$0.492312\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−24.0000	−0.232583
$23$	24.0000	0.217580	0.108790	−	0.994065i	$-0.465302\pi$
$23$	24.0000	0.217580	0.108790	+	0.994065i	$0.465302\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	−116.000	−0.874980
$27$	27.0000	0.192450
$28$	0	0
$29$	294.000	1.88257	0.941283	−	0.337618i	$-0.109621\pi$
$29$	294.000	1.88257	0.941283	+	0.337618i	$0.109621\pi$
$30$	30.0000	0.182574
$31$	−128.000	−0.741596	−0.370798	−	0.928714i	$-0.620916\pi$
$31$	−128.000	−0.741596	−0.370798	+	0.928714i	$0.620916\pi$
$32$	−32.0000	−0.176777
$33$	36.0000	0.189903
$34$	84.0000	0.423702
$35$	0	0
$36$	36.0000	0.166667
$37$	−58.0000	−0.257707	−0.128853	−	0.991664i	$-0.541130\pi$
$37$	−58.0000	−0.257707	−0.128853	+	0.991664i	$0.541130\pi$
$38$	−8.00000	−0.0341519
$39$	174.000	0.714418
$40$	40.0000	0.158114
$41$	−282.000	−1.07417	−0.537085	−	0.843528i	$-0.680475\pi$
$41$	−282.000	−1.07417	−0.537085	+	0.843528i	$0.680475\pi$
$42$	0	0
$43$	428.000	1.51789	0.758946	−	0.651153i	$-0.225714\pi$
$43$	428.000	1.51789	0.758946	+	0.651153i	$0.225714\pi$
$44$	48.0000	0.164461
$45$	−45.0000	−0.149071
$46$	−48.0000	−0.153852
$47$	−384.000	−1.19175	−0.595874	−	0.803078i	$-0.703194\pi$
$47$	−384.000	−1.19175	−0.595874	+	0.803078i	$0.703194\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	−126.000	−0.345952
$52$	232.000	0.618704
$53$	−138.000	−0.357656	−0.178828	−	0.983880i	$-0.557231\pi$
$53$	−138.000	−0.357656	−0.178828	+	0.983880i	$0.557231\pi$
$54$	−54.0000	−0.136083
$55$	−60.0000	−0.147098
$56$	0	0
$57$	12.0000	0.0278849
$58$	−588.000	−1.33118
$59$	−468.000	−1.03268	−0.516342	−	0.856382i	$-0.672707\pi$
$59$	−468.000	−1.03268	−0.516342	+	0.856382i	$0.672707\pi$
$60$	−60.0000	−0.129099
$61$	250.000	0.524741	0.262371	−	0.964967i	$-0.415496\pi$
$61$	250.000	0.524741	0.262371	+	0.964967i	$0.415496\pi$
$62$	256.000	0.524388
$63$	0	0
$64$	64.0000	0.125000
$65$	−290.000	−0.553386
$66$	−72.0000	−0.134282
$67$	−556.000	−1.01382	−0.506912	−	0.861998i	$-0.669213\pi$
$67$	−556.000	−1.01382	−0.506912	+	0.861998i	$0.669213\pi$
$68$	−168.000	−0.299603
$69$	72.0000	0.125620
$70$	0	0
$71$	624.000	1.04303	0.521515	−	0.853242i	$-0.325367\pi$
$71$	624.000	1.04303	0.521515	+	0.853242i	$0.325367\pi$
$72$	−72.0000	−0.117851
$73$	958.000	1.53596	0.767982	−	0.640471i	$-0.221261\pi$
$73$	958.000	1.53596	0.767982	+	0.640471i	$0.221261\pi$
$74$	116.000	0.182226
$75$	75.0000	0.115470
$76$	16.0000	0.0241490
$77$	0	0
$78$	−348.000	−0.505170
$79$	632.000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	632.000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	564.000	0.759553
$83$	−84.0000	−0.111087	−0.0555434	−	0.998456i	$-0.517689\pi$
$83$	−84.0000	−0.111087	−0.0555434	+	0.998456i	$0.517689\pi$
$84$	0	0
$85$	210.000	0.267973
$86$	−856.000	−1.07331
$87$	882.000	1.08690
$88$	−96.0000	−0.116291
$89$	−810.000	−0.964717	−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000	−0.964717	−0.482359	+	0.875974i	$0.660220\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	96.0000	0.108790
$93$	−384.000	−0.428161
$94$	768.000	0.842693
$95$	−20.0000	−0.0215995
$96$	−96.0000	−0.102062
$97$	790.000	0.826931	0.413466	−	0.910520i	$-0.364318\pi$
$97$	790.000	0.826931	0.413466	+	0.910520i	$0.364318\pi$
$98$	0	0
$99$	108.000	0.109640
$100$	100.000	0.100000
$101$	1890.00	1.86200	0.931000	−	0.365019i	$-0.118937\pi$
$101$	1890.00	1.86200	0.931000	+	0.365019i	$0.118937\pi$
$102$	252.000	0.244625
$103$	−296.000	−0.283163	−0.141581	−	0.989927i	$-0.545219\pi$
$103$	−296.000	−0.283163	−0.141581	+	0.989927i	$0.545219\pi$
$104$	−464.000	−0.437490
$105$	0	0
$106$	276.000	0.252901
$107$	−324.000	−0.292731	−0.146366	−	0.989231i	$-0.546758\pi$
$107$	−324.000	−0.292731	−0.146366	+	0.989231i	$0.546758\pi$
$108$	108.000	0.0962250
$109$	854.000	0.750444	0.375222	−	0.926935i	$-0.377567\pi$
$109$	854.000	0.750444	0.375222	+	0.926935i	$0.377567\pi$
$110$	120.000	0.104014
$111$	−174.000	−0.148787
$112$	0	0
$113$	402.000	0.334664	0.167332	−	0.985901i	$-0.446485\pi$
$113$	402.000	0.334664	0.167332	+	0.985901i	$0.446485\pi$
$114$	−24.0000	−0.0197176
$115$	−120.000	−0.0973048
$116$	1176.00	0.941283
$117$	522.000	0.412469
$118$	936.000	0.730219
$119$	0	0
$120$	120.000	0.0912871
$121$	−1187.00	−0.891811
$122$	−500.000	−0.371048
$123$	−846.000	−0.620173
$124$	−512.000	−0.370798
$125$	−125.000	−0.0894427
$126$	0	0
$127$	2192.00	1.53156	0.765782	−	0.643101i	$-0.222352\pi$
$127$	2192.00	1.53156	0.765782	+	0.643101i	$0.222352\pi$
$128$	−128.000	−0.0883883
$129$	1284.00	0.876356
$130$	580.000	0.391303
$131$	1572.00	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	1572.00	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	144.000	0.0949514
$133$	0	0
$134$	1112.00	0.716882
$135$	−135.000	−0.0860663
$136$	336.000	0.211851
$137$	−198.000	−0.123477	−0.0617383	−	0.998092i	$-0.519664\pi$
$137$	−198.000	−0.123477	−0.0617383	+	0.998092i	$0.519664\pi$
$138$	−144.000	−0.0888268
$139$	−1364.00	−0.832324	−0.416162	−	0.909291i	$-0.636625\pi$
$139$	−1364.00	−0.832324	−0.416162	+	0.909291i	$0.636625\pi$
$140$	0	0
$141$	−1152.00	−0.688056
$142$	−1248.00	−0.737534
$143$	696.000	0.407010
$144$	144.000	0.0833333
$145$	−1470.00	−0.841909
$146$	−1916.00	−1.08609
$147$	0	0
$148$	−232.000	−0.128853
$149$	1470.00	0.808236	0.404118	−	0.914707i	$-0.367579\pi$
$149$	1470.00	0.808236	0.404118	+	0.914707i	$0.367579\pi$
$150$	−150.000	−0.0816497
$151$	−1888.00	−1.01751	−0.508753	−	0.860913i	$-0.669893\pi$
$151$	−1888.00	−1.01751	−0.508753	+	0.860913i	$0.669893\pi$
$152$	−32.0000	−0.0170759
$153$	−378.000	−0.199735
$154$	0	0
$155$	640.000	0.331652
$156$	696.000	0.357209
$157$	106.000	0.0538836	0.0269418	−	0.999637i	$-0.491423\pi$
$157$	106.000	0.0538836	0.0269418	+	0.999637i	$0.491423\pi$
$158$	−1264.00	−0.636446
$159$	−414.000	−0.206493
$160$	160.000	0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	1172.00	0.563179	0.281589	−	0.959535i	$-0.409138\pi$
$163$	1172.00	0.563179	0.281589	+	0.959535i	$0.409138\pi$
$164$	−1128.00	−0.537085
$165$	−180.000	−0.0849272
$166$	168.000	0.0785502
$167$	−2664.00	−1.23441	−0.617205	−	0.786802i	$-0.711735\pi$
$167$	−2664.00	−1.23441	−0.617205	+	0.786802i	$0.711735\pi$
$168$	0	0
$169$	1167.00	0.531179
$170$	−420.000	−0.189485
$171$	36.0000	0.0160993
$172$	1712.00	0.758946
$173$	1914.00	0.841149	0.420574	−	0.907258i	$-0.361829\pi$
$173$	1914.00	0.841149	0.420574	+	0.907258i	$0.361829\pi$
$174$	−1764.00	−0.768555
$175$	0	0
$176$	192.000	0.0822304
$177$	−1404.00	−0.596221
$178$	1620.00	0.682158
$179$	3300.00	1.37795	0.688976	−	0.724784i	$-0.258060\pi$
$179$	3300.00	1.37795	0.688976	+	0.724784i	$0.258060\pi$
$180$	−180.000	−0.0745356
$181$	−302.000	−0.124019	−0.0620096	−	0.998076i	$-0.519751\pi$
$181$	−302.000	−0.124019	−0.0620096	+	0.998076i	$0.519751\pi$
$182$	0	0
$183$	750.000	0.302960
$184$	−192.000	−0.0769262
$185$	290.000	0.115250
$186$	768.000	0.302755
$187$	−504.000	−0.197092
$188$	−1536.00	−0.595874
$189$	0	0
$190$	40.0000	0.0152732
$191$	−4248.00	−1.60929	−0.804645	−	0.593756i	$-0.797645\pi$
$191$	−4248.00	−1.60929	−0.804645	+	0.593756i	$0.797645\pi$
$192$	192.000	0.0721688
$193$	2354.00	0.877951	0.438976	−	0.898499i	$-0.355341\pi$
$193$	2354.00	0.877951	0.438976	+	0.898499i	$0.355341\pi$
$194$	−1580.00	−0.584729
$195$	−870.000	−0.319497
$196$	0	0
$197$	−3114.00	−1.12621	−0.563105	−	0.826385i	$-0.690393\pi$
$197$	−3114.00	−1.12621	−0.563105	+	0.826385i	$0.690393\pi$
$198$	−216.000	−0.0775275
$199$	3256.00	1.15986	0.579929	−	0.814667i	$-0.303080\pi$
$199$	3256.00	1.15986	0.579929	+	0.814667i	$0.303080\pi$
$200$	−200.000	−0.0707107
$201$	−1668.00	−0.585332
$202$	−3780.00	−1.31663
$203$	0	0
$204$	−504.000	−0.172976
$205$	1410.00	0.480384
$206$	592.000	0.200226
$207$	216.000	0.0725268
$208$	928.000	0.309352
$209$	48.0000	0.0158863
$210$	0	0
$211$	5780.00	1.88584	0.942919	−	0.333024i	$-0.108069\pi$
$211$	5780.00	1.88584	0.942919	+	0.333024i	$0.108069\pi$
$212$	−552.000	−0.178828
$213$	1872.00	0.602194
$214$	648.000	0.206992
$215$	−2140.00	−0.678822
$216$	−216.000	−0.0680414
$217$	0	0
$218$	−1708.00	−0.530644
$219$	2874.00	0.886790
$220$	−240.000	−0.0735491
$221$	−2436.00	−0.741462
$222$	348.000	0.105208
$223$	1456.00	0.437224	0.218612	−	0.975812i	$-0.429847\pi$
$223$	1456.00	0.437224	0.218612	+	0.975812i	$0.429847\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−804.000	−0.236643
$227$	2604.00	0.761381	0.380691	−	0.924702i	$-0.375686\pi$
$227$	2604.00	0.761381	0.380691	+	0.924702i	$0.375686\pi$
$228$	48.0000	0.0139424
$229$	4354.00	1.25642	0.628211	−	0.778043i	$-0.283788\pi$
$229$	4354.00	1.25642	0.628211	+	0.778043i	$0.283788\pi$
$230$	240.000	0.0688049
$231$	0	0
$232$	−2352.00	−0.665588
$233$	−2070.00	−0.582018	−0.291009	−	0.956720i	$-0.593991\pi$
$233$	−2070.00	−0.582018	−0.291009	+	0.956720i	$0.593991\pi$
$234$	−1044.00	−0.291660
$235$	1920.00	0.532966
$236$	−1872.00	−0.516342
$237$	1896.00	0.519656
$238$	0	0
$239$	744.000	0.201361	0.100681	−	0.994919i	$-0.467898\pi$
$239$	744.000	0.201361	0.100681	+	0.994919i	$0.467898\pi$
$240$	−240.000	−0.0645497
$241$	1726.00	0.461334	0.230667	−	0.973033i	$-0.425909\pi$
$241$	1726.00	0.461334	0.230667	+	0.973033i	$0.425909\pi$
$242$	2374.00	0.630605
$243$	243.000	0.0641500
$244$	1000.00	0.262371
$245$	0	0
$246$	1692.00	0.438528
$247$	232.000	0.0597644
$248$	1024.00	0.262194
$249$	−252.000	−0.0641359
$250$	250.000	0.0632456
$251$	6060.00	1.52392	0.761960	−	0.647624i	$-0.224237\pi$
$251$	6060.00	1.52392	0.761960	+	0.647624i	$0.224237\pi$
$252$	0	0
$253$	288.000	0.0715668
$254$	−4384.00	−1.08298
$255$	630.000	0.154714
$256$	256.000	0.0625000
$257$	150.000	0.0364076	0.0182038	−	0.999834i	$-0.494205\pi$
$257$	150.000	0.0364076	0.0182038	+	0.999834i	$0.494205\pi$
$258$	−2568.00	−0.619677
$259$	0	0
$260$	−1160.00	−0.276693
$261$	2646.00	0.627522
$262$	−3144.00	−0.741362
$263$	−3288.00	−0.770900	−0.385450	−	0.922729i	$-0.625954\pi$
$263$	−3288.00	−0.770900	−0.385450	+	0.922729i	$0.625954\pi$
$264$	−288.000	−0.0671408
$265$	690.000	0.159949
$266$	0	0
$267$	−2430.00	−0.556980
$268$	−2224.00	−0.506912
$269$	6378.00	1.44563	0.722813	−	0.691043i	$-0.242849\pi$
$269$	6378.00	1.44563	0.722813	+	0.691043i	$0.242849\pi$
$270$	270.000	0.0608581
$271$	1600.00	0.358646	0.179323	−	0.983790i	$-0.442609\pi$
$271$	1600.00	0.358646	0.179323	+	0.983790i	$0.442609\pi$
$272$	−672.000	−0.149801
$273$	0	0
$274$	396.000	0.0873111
$275$	300.000	0.0657843
$276$	288.000	0.0628100
$277$	4934.00	1.07024	0.535118	−	0.844777i	$-0.320267\pi$
$277$	4934.00	1.07024	0.535118	+	0.844777i	$0.320267\pi$
$278$	2728.00	0.588542
$279$	−1152.00	−0.247199
$280$	0	0
$281$	−630.000	−0.133746	−0.0668730	−	0.997761i	$-0.521302\pi$
$281$	−630.000	−0.133746	−0.0668730	+	0.997761i	$0.521302\pi$
$282$	2304.00	0.486529
$283$	5380.00	1.13006	0.565031	−	0.825069i	$-0.308864\pi$
$283$	5380.00	1.13006	0.565031	+	0.825069i	$0.308864\pi$
$284$	2496.00	0.521515
$285$	−60.0000	−0.0124705
$286$	−1392.00	−0.287800
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−3149.00	−0.640953
$290$	2940.00	0.595320
$291$	2370.00	0.477429
$292$	3832.00	0.767982
$293$	−1470.00	−0.293100	−0.146550	−	0.989203i	$-0.546817\pi$
$293$	−1470.00	−0.293100	−0.146550	+	0.989203i	$0.546817\pi$
$294$	0	0
$295$	2340.00	0.461831
$296$	464.000	0.0911130
$297$	324.000	0.0633010
$298$	−2940.00	−0.571509
$299$	1392.00	0.269236
$300$	300.000	0.0577350
$301$	0	0
$302$	3776.00	0.719485
$303$	5670.00	1.07503
$304$	64.0000	0.0120745
$305$	−1250.00	−0.234671
$306$	756.000	0.141234
$307$	1036.00	0.192598	0.0962991	−	0.995352i	$-0.469299\pi$
$307$	1036.00	0.192598	0.0962991	+	0.995352i	$0.469299\pi$
$308$	0	0
$309$	−888.000	−0.163484
$310$	−1280.00	−0.234513
$311$	216.000	0.0393834	0.0196917	−	0.999806i	$-0.493732\pi$
$311$	216.000	0.0393834	0.0196917	+	0.999806i	$0.493732\pi$
$312$	−1392.00	−0.252585
$313$	1534.00	0.277019	0.138509	−	0.990361i	$-0.455769\pi$
$313$	1534.00	0.277019	0.138509	+	0.990361i	$0.455769\pi$
$314$	−212.000	−0.0381014
$315$	0	0
$316$	2528.00	0.450035
$317$	−6546.00	−1.15981	−0.579905	−	0.814684i	$-0.696910\pi$
$317$	−6546.00	−1.15981	−0.579905	+	0.814684i	$0.696910\pi$
$318$	828.000	0.146012
$319$	3528.00	0.619217
$320$	−320.000	−0.0559017
$321$	−972.000	−0.169009
$322$	0	0
$323$	−168.000	−0.0289405
$324$	324.000	0.0555556
$325$	1450.00	0.247482
$326$	−2344.00	−0.398227
$327$	2562.00	0.433269
$328$	2256.00	0.379777
$329$	0	0
$330$	360.000	0.0600526
$331$	92.0000	0.0152773	0.00763864	−	0.999971i	$-0.497569\pi$
$331$	92.0000	0.0152773	0.00763864	+	0.999971i	$0.497569\pi$
$332$	−336.000	−0.0555434
$333$	−522.000	−0.0859022
$334$	5328.00	0.872860
$335$	2780.00	0.453396
$336$	0	0
$337$	8546.00	1.38140	0.690698	−	0.723144i	$-0.257304\pi$
$337$	8546.00	1.38140	0.690698	+	0.723144i	$0.257304\pi$
$338$	−2334.00	−0.375600
$339$	1206.00	0.193218
$340$	840.000	0.133986
$341$	−1536.00	−0.243927
$342$	−72.0000	−0.0113840
$343$	0	0
$344$	−3424.00	−0.536656
$345$	−360.000	−0.0561790
$346$	−3828.00	−0.594782
$347$	6588.00	1.01920	0.509600	−	0.860411i	$-0.329793\pi$
$347$	6588.00	1.01920	0.509600	+	0.860411i	$0.329793\pi$
$348$	3528.00	0.543450
$349$	6874.00	1.05432	0.527159	−	0.849767i	$-0.323257\pi$
$349$	6874.00	1.05432	0.527159	+	0.849767i	$0.323257\pi$
$350$	0	0
$351$	1566.00	0.238139
$352$	−384.000	−0.0581456
$353$	−7530.00	−1.13536	−0.567679	−	0.823250i	$-0.692159\pi$
$353$	−7530.00	−1.13536	−0.567679	+	0.823250i	$0.692159\pi$
$354$	2808.00	0.421592
$355$	−3120.00	−0.466457
$356$	−3240.00	−0.482359
$357$	0	0
$358$	−6600.00	−0.974360
$359$	9264.00	1.36194	0.680968	−	0.732313i	$-0.261559\pi$
$359$	9264.00	1.36194	0.680968	+	0.732313i	$0.261559\pi$
$360$	360.000	0.0527046
$361$	−6843.00	−0.997667
$362$	604.000	0.0876948
$363$	−3561.00	−0.514887
$364$	0	0
$365$	−4790.00	−0.686904
$366$	−1500.00	−0.214225
$367$	−12944.0	−1.84107	−0.920533	−	0.390665i	$-0.872245\pi$
$367$	−12944.0	−1.84107	−0.920533	+	0.390665i	$0.872245\pi$
$368$	384.000	0.0543951
$369$	−2538.00	−0.358057
$370$	−580.000	−0.0814940
$371$	0	0
$372$	−1536.00	−0.214080
$373$	7862.00	1.09136	0.545682	−	0.837992i	$-0.316271\pi$
$373$	7862.00	1.09136	0.545682	+	0.837992i	$0.316271\pi$
$374$	1008.00	0.139365
$375$	−375.000	−0.0516398
$376$	3072.00	0.421347
$377$	17052.0	2.32950
$378$	0	0
$379$	−2980.00	−0.403885	−0.201942	−	0.979397i	$-0.564725\pi$
$379$	−2980.00	−0.403885	−0.201942	+	0.979397i	$0.564725\pi$
$380$	−80.0000	−0.0107998
$381$	6576.00	0.884249
$382$	8496.00	1.13794
$383$	−9840.00	−1.31280	−0.656398	−	0.754415i	$-0.727921\pi$
$383$	−9840.00	−1.31280	−0.656398	+	0.754415i	$0.727921\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−4708.00	−0.620805
$387$	3852.00	0.505964
$388$	3160.00	0.413466
$389$	6318.00	0.823484	0.411742	−	0.911300i	$-0.364920\pi$
$389$	6318.00	0.823484	0.411742	+	0.911300i	$0.364920\pi$
$390$	1740.00	0.225919
$391$	−1008.00	−0.130375
$392$	0	0
$393$	4716.00	0.605320
$394$	6228.00	0.796351
$395$	−3160.00	−0.402524
$396$	432.000	0.0548202
$397$	10906.0	1.37873	0.689366	−	0.724413i	$-0.257889\pi$
$397$	10906.0	1.37873	0.689366	+	0.724413i	$0.257889\pi$
$398$	−6512.00	−0.820143
$399$	0	0
$400$	400.000	0.0500000
$401$	−9294.00	−1.15741	−0.578704	−	0.815538i	$-0.696441\pi$
$401$	−9294.00	−1.15741	−0.578704	+	0.815538i	$0.696441\pi$
$402$	3336.00	0.413892
$403$	−7424.00	−0.917657
$404$	7560.00	0.931000
$405$	−405.000	−0.0496904
$406$	0	0
$407$	−696.000	−0.0847652
$408$	1008.00	0.122312
$409$	6166.00	0.745450	0.372725	−	0.927942i	$-0.378423\pi$
$409$	6166.00	0.745450	0.372725	+	0.927942i	$0.378423\pi$
$410$	−2820.00	−0.339683
$411$	−594.000	−0.0712892
$412$	−1184.00	−0.141581
$413$	0	0
$414$	−432.000	−0.0512842
$415$	420.000	0.0496795
$416$	−1856.00	−0.218745
$417$	−4092.00	−0.480542
$418$	−96.0000	−0.0112333
$419$	10740.0	1.25223	0.626114	−	0.779732i	$-0.284645\pi$
$419$	10740.0	1.25223	0.626114	+	0.779732i	$0.284645\pi$
$420$	0	0
$421$	13454.0	1.55750	0.778750	−	0.627334i	$-0.215854\pi$
$421$	13454.0	1.55750	0.778750	+	0.627334i	$0.215854\pi$
$422$	−11560.0	−1.33349
$423$	−3456.00	−0.397249
$424$	1104.00	0.126450
$425$	−1050.00	−0.119841
$426$	−3744.00	−0.425815
$427$	0	0
$428$	−1296.00	−0.146366
$429$	2088.00	0.234987
$430$	4280.00	0.480000
$431$	10152.0	1.13458	0.567291	−	0.823518i	$-0.307992\pi$
$431$	10152.0	1.13458	0.567291	+	0.823518i	$0.307992\pi$
$432$	432.000	0.0481125
$433$	−15818.0	−1.75558	−0.877788	−	0.479049i	$-0.840982\pi$
$433$	−15818.0	−1.75558	−0.877788	+	0.479049i	$0.840982\pi$
$434$	0	0
$435$	−4410.00	−0.486077
$436$	3416.00	0.375222
$437$	96.0000	0.0105087
$438$	−5748.00	−0.627055
$439$	7432.00	0.807995	0.403998	−	0.914760i	$-0.367620\pi$
$439$	7432.00	0.807995	0.403998	+	0.914760i	$0.367620\pi$
$440$	480.000	0.0520071
$441$	0	0
$442$	4872.00	0.524293
$443$	5916.00	0.634487	0.317243	−	0.948344i	$-0.397243\pi$
$443$	5916.00	0.634487	0.317243	+	0.948344i	$0.397243\pi$
$444$	−696.000	−0.0743935
$445$	4050.00	0.431435
$446$	−2912.00	−0.309164
$447$	4410.00	0.466635
$448$	0	0
$449$	2466.00	0.259193	0.129597	−	0.991567i	$-0.458632\pi$
$449$	2466.00	0.259193	0.129597	+	0.991567i	$0.458632\pi$
$450$	−450.000	−0.0471405
$451$	−3384.00	−0.353318
$452$	1608.00	0.167332
$453$	−5664.00	−0.587457
$454$	−5208.00	−0.538378
$455$	0	0
$456$	−96.0000	−0.00985880
$457$	13994.0	1.43241	0.716205	−	0.697890i	$-0.245877\pi$
$457$	13994.0	1.43241	0.716205	+	0.697890i	$0.245877\pi$
$458$	−8708.00	−0.888424
$459$	−1134.00	−0.115317
$460$	−480.000	−0.0486524
$461$	3978.00	0.401896	0.200948	−	0.979602i	$-0.435598\pi$
$461$	3978.00	0.401896	0.200948	+	0.979602i	$0.435598\pi$
$462$	0	0
$463$	10352.0	1.03909	0.519545	−	0.854443i	$-0.326102\pi$
$463$	10352.0	1.03909	0.519545	+	0.854443i	$0.326102\pi$
$464$	4704.00	0.470642
$465$	1920.00	0.191479
$466$	4140.00	0.411549
$467$	−1428.00	−0.141499	−0.0707494	−	0.997494i	$-0.522539\pi$
$467$	−1428.00	−0.141499	−0.0707494	+	0.997494i	$0.522539\pi$
$468$	2088.00	0.206235
$469$	0	0
$470$	−3840.00	−0.376864
$471$	318.000	0.0311097
$472$	3744.00	0.365109
$473$	5136.00	0.499268
$474$	−3792.00	−0.367452
$475$	100.000	0.00965961
$476$	0	0
$477$	−1242.00	−0.119219
$478$	−1488.00	−0.142384
$479$	−8832.00	−0.842473	−0.421236	−	0.906951i	$-0.638404\pi$
$479$	−8832.00	−0.842473	−0.421236	+	0.906951i	$0.638404\pi$
$480$	480.000	0.0456435
$481$	−3364.00	−0.318888
$482$	−3452.00	−0.326212
$483$	0	0
$484$	−4748.00	−0.445905
$485$	−3950.00	−0.369815
$486$	−486.000	−0.0453609
$487$	−9064.00	−0.843386	−0.421693	−	0.906739i	$-0.638564\pi$
$487$	−9064.00	−0.843386	−0.421693	+	0.906739i	$0.638564\pi$
$488$	−2000.00	−0.185524
$489$	3516.00	0.325151
$490$	0	0
$491$	12780.0	1.17465	0.587325	−	0.809351i	$-0.300181\pi$
$491$	12780.0	1.17465	0.587325	+	0.809351i	$0.300181\pi$
$492$	−3384.00	−0.310086
$493$	−12348.0	−1.12804
$494$	−464.000	−0.0422598
$495$	−540.000	−0.0490327
$496$	−2048.00	−0.185399
$497$	0	0
$498$	504.000	0.0453510
$499$	−15628.0	−1.40201	−0.701007	−	0.713154i	$-0.747266\pi$
$499$	−15628.0	−1.40201	−0.701007	+	0.713154i	$0.747266\pi$
$500$	−500.000	−0.0447214
$501$	−7992.00	−0.712687
$502$	−12120.0	−1.07757
$503$	−3096.00	−0.274441	−0.137220	−	0.990541i	$-0.543817\pi$
$503$	−3096.00	−0.274441	−0.137220	+	0.990541i	$0.543817\pi$
$504$	0	0
$505$	−9450.00	−0.832712
$506$	−576.000	−0.0506054
$507$	3501.00	0.306676
$508$	8768.00	0.765782
$509$	−17190.0	−1.49692	−0.748461	−	0.663179i	$-0.769207\pi$
$509$	−17190.0	−1.49692	−0.748461	+	0.663179i	$0.769207\pi$
$510$	−1260.00	−0.109399
$511$	0	0
$512$	−512.000	−0.0441942
$513$	108.000	0.00929496
$514$	−300.000	−0.0257440
$515$	1480.00	0.126634
$516$	5136.00	0.438178
$517$	−4608.00	−0.391992
$518$	0	0
$519$	5742.00	0.485637
$520$	2320.00	0.195651
$521$	−17034.0	−1.43239	−0.716193	−	0.697902i	$-0.754117\pi$
$521$	−17034.0	−1.43239	−0.716193	+	0.697902i	$0.754117\pi$
$522$	−5292.00	−0.443725
$523$	10516.0	0.879221	0.439610	−	0.898189i	$-0.355116\pi$
$523$	10516.0	0.879221	0.439610	+	0.898189i	$0.355116\pi$
$524$	6288.00	0.524222
$525$	0	0
$526$	6576.00	0.545109
$527$	5376.00	0.444369
$528$	576.000	0.0474757
$529$	−11591.0	−0.952659
$530$	−1380.00	−0.113101
$531$	−4212.00	−0.344228
$532$	0	0
$533$	−16356.0	−1.32919
$534$	4860.00	0.393844
$535$	1620.00	0.130913
$536$	4448.00	0.358441
$537$	9900.00	0.795562
$538$	−12756.0	−1.02221
$539$	0	0
$540$	−540.000	−0.0430331
$541$	−538.000	−0.0427549	−0.0213775	−	0.999771i	$-0.506805\pi$
$541$	−538.000	−0.0427549	−0.0213775	+	0.999771i	$0.506805\pi$
$542$	−3200.00	−0.253601
$543$	−906.000	−0.0716025
$544$	1344.00	0.105926
$545$	−4270.00	−0.335609
$546$	0	0
$547$	−1420.00	−0.110996	−0.0554980	−	0.998459i	$-0.517675\pi$
$547$	−1420.00	−0.110996	−0.0554980	+	0.998459i	$0.517675\pi$
$548$	−792.000	−0.0617383
$549$	2250.00	0.174914
$550$	−600.000	−0.0465165
$551$	1176.00	0.0909243
$552$	−576.000	−0.0444134
$553$	0	0
$554$	−9868.00	−0.756771
$555$	870.000	0.0665395
$556$	−5456.00	−0.416162
$557$	−17106.0	−1.30126	−0.650632	−	0.759393i	$-0.725496\pi$
$557$	−17106.0	−1.30126	−0.650632	+	0.759393i	$0.725496\pi$
$558$	2304.00	0.174796
$559$	24824.0	1.87825
$560$	0	0
$561$	−1512.00	−0.113791
$562$	1260.00	0.0945728
$563$	−3252.00	−0.243438	−0.121719	−	0.992565i	$-0.538841\pi$
$563$	−3252.00	−0.243438	−0.121719	+	0.992565i	$0.538841\pi$
$564$	−4608.00	−0.344028
$565$	−2010.00	−0.149666
$566$	−10760.0	−0.799075
$567$	0	0
$568$	−4992.00	−0.368767
$569$	−7254.00	−0.534453	−0.267226	−	0.963634i	$-0.586107\pi$
$569$	−7254.00	−0.534453	−0.267226	+	0.963634i	$0.586107\pi$
$570$	120.000	0.00881798
$571$	−24676.0	−1.80851	−0.904254	−	0.426994i	$-0.859572\pi$
$571$	−24676.0	−1.80851	−0.904254	+	0.426994i	$0.859572\pi$
$572$	2784.00	0.203505
$573$	−12744.0	−0.929124
$574$	0	0
$575$	600.000	0.0435161
$576$	576.000	0.0416667
$577$	−5162.00	−0.372438	−0.186219	−	0.982508i	$-0.559623\pi$
$577$	−5162.00	−0.372438	−0.186219	+	0.982508i	$0.559623\pi$
$578$	6298.00	0.453222
$579$	7062.00	0.506885
$580$	−5880.00	−0.420955
$581$	0	0
$582$	−4740.00	−0.337593
$583$	−1656.00	−0.117641
$584$	−7664.00	−0.543046
$585$	−2610.00	−0.184462
$586$	2940.00	0.207253
$587$	17556.0	1.23444	0.617218	−	0.786792i	$-0.288260\pi$
$587$	17556.0	1.23444	0.617218	+	0.786792i	$0.288260\pi$
$588$	0	0
$589$	−512.000	−0.0358176
$590$	−4680.00	−0.326564
$591$	−9342.00	−0.650217
$592$	−928.000	−0.0644266
$593$	−23274.0	−1.61172	−0.805859	−	0.592108i	$-0.798296\pi$
$593$	−23274.0	−1.61172	−0.805859	+	0.592108i	$0.798296\pi$
$594$	−648.000	−0.0447605
$595$	0	0
$596$	5880.00	0.404118
$597$	9768.00	0.669644
$598$	−2784.00	−0.190378
$599$	12000.0	0.818542	0.409271	−	0.912413i	$-0.365783\pi$
$599$	12000.0	0.818542	0.409271	+	0.912413i	$0.365783\pi$
$600$	−600.000	−0.0408248
$601$	24742.0	1.67928	0.839640	−	0.543143i	$-0.182766\pi$
$601$	24742.0	1.67928	0.839640	+	0.543143i	$0.182766\pi$
$602$	0	0
$603$	−5004.00	−0.337941
$604$	−7552.00	−0.508753
$605$	5935.00	0.398830
$606$	−11340.0	−0.760158
$607$	4096.00	0.273890	0.136945	−	0.990579i	$-0.456272\pi$
$607$	4096.00	0.273890	0.136945	+	0.990579i	$0.456272\pi$
$608$	−128.000	−0.00853797
$609$	0	0
$610$	2500.00	0.165938
$611$	−22272.0	−1.47468
$612$	−1512.00	−0.0998676
$613$	−28474.0	−1.87611	−0.938054	−	0.346489i	$-0.887374\pi$
$613$	−28474.0	−1.87611	−0.938054	+	0.346489i	$0.887374\pi$
$614$	−2072.00	−0.136187
$615$	4230.00	0.277350
$616$	0	0
$617$	−5238.00	−0.341773	−0.170886	−	0.985291i	$-0.554663\pi$
$617$	−5238.00	−0.341773	−0.170886	+	0.985291i	$0.554663\pi$
$618$	1776.00	0.115601
$619$	21388.0	1.38878	0.694391	−	0.719598i	$-0.255674\pi$
$619$	21388.0	1.38878	0.694391	+	0.719598i	$0.255674\pi$
$620$	2560.00	0.165826
$621$	648.000	0.0418733
$622$	−432.000	−0.0278483
$623$	0	0
$624$	2784.00	0.178604
$625$	625.000	0.0400000
$626$	−3068.00	−0.195882
$627$	144.000	0.00917194
$628$	424.000	0.0269418
$629$	2436.00	0.154419
$630$	0	0
$631$	−18304.0	−1.15479	−0.577394	−	0.816466i	$-0.695930\pi$
$631$	−18304.0	−1.15479	−0.577394	+	0.816466i	$0.695930\pi$
$632$	−5056.00	−0.318223
$633$	17340.0	1.08879
$634$	13092.0	0.820110
$635$	−10960.0	−0.684936
$636$	−1656.00	−0.103246
$637$	0	0
$638$	−7056.00	−0.437852
$639$	5616.00	0.347677
$640$	640.000	0.0395285
$641$	5634.00	0.347160	0.173580	−	0.984820i	$-0.444466\pi$
$641$	5634.00	0.347160	0.173580	+	0.984820i	$0.444466\pi$
$642$	1944.00	0.119507
$643$	8476.00	0.519846	0.259923	−	0.965629i	$-0.416303\pi$
$643$	8476.00	0.519846	0.259923	+	0.965629i	$0.416303\pi$
$644$	0	0
$645$	−6420.00	−0.391918
$646$	336.000	0.0204640
$647$	−22728.0	−1.38104	−0.690518	−	0.723316i	$-0.742617\pi$
$647$	−22728.0	−1.38104	−0.690518	+	0.723316i	$0.742617\pi$
$648$	−648.000	−0.0392837
$649$	−5616.00	−0.339672
$650$	−2900.00	−0.174996
$651$	0	0
$652$	4688.00	0.281589
$653$	−11682.0	−0.700080	−0.350040	−	0.936735i	$-0.613832\pi$
$653$	−11682.0	−0.700080	−0.350040	+	0.936735i	$0.613832\pi$
$654$	−5124.00	−0.306367
$655$	−7860.00	−0.468879
$656$	−4512.00	−0.268543
$657$	8622.00	0.511988
$658$	0	0
$659$	−19644.0	−1.16119	−0.580593	−	0.814194i	$-0.697179\pi$
$659$	−19644.0	−1.16119	−0.580593	+	0.814194i	$0.697179\pi$
$660$	−720.000	−0.0424636
$661$	−2318.00	−0.136399	−0.0681995	−	0.997672i	$-0.521725\pi$
$661$	−2318.00	−0.136399	−0.0681995	+	0.997672i	$0.521725\pi$
$662$	−184.000	−0.0108027
$663$	−7308.00	−0.428083
$664$	672.000	0.0392751
$665$	0	0
$666$	1044.00	0.0607420
$667$	7056.00	0.409609
$668$	−10656.0	−0.617205
$669$	4368.00	0.252431
$670$	−5560.00	−0.320599
$671$	3000.00	0.172599
$672$	0	0
$673$	−29086.0	−1.66595	−0.832974	−	0.553312i	$-0.813364\pi$
$673$	−29086.0	−1.66595	−0.832974	+	0.553312i	$0.813364\pi$
$674$	−17092.0	−0.976794
$675$	675.000	0.0384900
$676$	4668.00	0.265589
$677$	−15630.0	−0.887311	−0.443656	−	0.896197i	$-0.646319\pi$
$677$	−15630.0	−0.887311	−0.443656	+	0.896197i	$0.646319\pi$
$678$	−2412.00	−0.136626
$679$	0	0
$680$	−1680.00	−0.0947427
$681$	7812.00	0.439584
$682$	3072.00	0.172482
$683$	−20292.0	−1.13683	−0.568413	−	0.822744i	$-0.692442\pi$
$683$	−20292.0	−1.13683	−0.568413	+	0.822744i	$0.692442\pi$
$684$	144.000	0.00804967
$685$	990.000	0.0552204
$686$	0	0
$687$	13062.0	0.725395
$688$	6848.00	0.379473
$689$	−8004.00	−0.442566
$690$	720.000	0.0397245
$691$	532.000	0.0292883	0.0146442	−	0.999893i	$-0.495338\pi$
$691$	532.000	0.0292883	0.0146442	+	0.999893i	$0.495338\pi$
$692$	7656.00	0.420574
$693$	0	0
$694$	−13176.0	−0.720683
$695$	6820.00	0.372226
$696$	−7056.00	−0.384277
$697$	11844.0	0.643649
$698$	−13748.0	−0.745515
$699$	−6210.00	−0.336028
$700$	0	0
$701$	24486.0	1.31929	0.659646	−	0.751577i	$-0.270706\pi$
$701$	24486.0	1.31929	0.659646	+	0.751577i	$0.270706\pi$
$702$	−3132.00	−0.168390
$703$	−232.000	−0.0124467
$704$	768.000	0.0411152
$705$	5760.00	0.307708
$706$	15060.0	0.802820
$707$	0	0
$708$	−5616.00	−0.298110
$709$	30926.0	1.63815	0.819076	−	0.573684i	$-0.194486\pi$
$709$	30926.0	1.63815	0.819076	+	0.573684i	$0.194486\pi$
$710$	6240.00	0.329835
$711$	5688.00	0.300023
$712$	6480.00	0.341079
$713$	−3072.00	−0.161357
$714$	0	0
$715$	−3480.00	−0.182020
$716$	13200.0	0.688976
$717$	2232.00	0.116256
$718$	−18528.0	−0.963035
$719$	−27504.0	−1.42660	−0.713300	−	0.700858i	$-0.752801\pi$
$719$	−27504.0	−1.42660	−0.713300	+	0.700858i	$0.752801\pi$
$720$	−720.000	−0.0372678
$721$	0	0
$722$	13686.0	0.705457
$723$	5178.00	0.266351
$724$	−1208.00	−0.0620096
$725$	7350.00	0.376513
$726$	7122.00	0.364080
$727$	−29192.0	−1.48923	−0.744616	−	0.667493i	$-0.767367\pi$
$727$	−29192.0	−1.48923	−0.744616	+	0.667493i	$0.767367\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	9580.00	0.485715
$731$	−17976.0	−0.909530
$732$	3000.00	0.151480
$733$	−22118.0	−1.11453	−0.557263	−	0.830336i	$-0.688148\pi$
$733$	−22118.0	−1.11453	−0.557263	+	0.830336i	$0.688148\pi$
$734$	25888.0	1.30183
$735$	0	0
$736$	−768.000	−0.0384631
$737$	−6672.00	−0.333468
$738$	5076.00	0.253184
$739$	−23836.0	−1.18650	−0.593249	−	0.805019i	$-0.702155\pi$
$739$	−23836.0	−1.18650	−0.593249	+	0.805019i	$0.702155\pi$
$740$	1160.00	0.0576249
$741$	696.000	0.0345050
$742$	0	0
$743$	−33576.0	−1.65785	−0.828926	−	0.559358i	$-0.811048\pi$
$743$	−33576.0	−1.65785	−0.828926	+	0.559358i	$0.811048\pi$
$744$	3072.00	0.151378
$745$	−7350.00	−0.361454
$746$	−15724.0	−0.771711
$747$	−756.000	−0.0370289
$748$	−2016.00	−0.0985458
$749$	0	0
$750$	750.000	0.0365148
$751$	22040.0	1.07091	0.535453	−	0.844565i	$-0.320141\pi$
$751$	22040.0	1.07091	0.535453	+	0.844565i	$0.320141\pi$
$752$	−6144.00	−0.297937
$753$	18180.0	0.879835
$754$	−34104.0	−1.64721
$755$	9440.00	0.455042
$756$	0	0
$757$	2774.00	0.133187	0.0665936	−	0.997780i	$-0.478787\pi$
$757$	2774.00	0.133187	0.0665936	+	0.997780i	$0.478787\pi$
$758$	5960.00	0.285590
$759$	864.000	0.0413191
$760$	160.000	0.00763659
$761$	−9594.00	−0.457007	−0.228503	−	0.973543i	$-0.573383\pi$
$761$	−9594.00	−0.457007	−0.228503	+	0.973543i	$0.573383\pi$
$762$	−13152.0	−0.625258
$763$	0	0
$764$	−16992.0	−0.804645
$765$	1890.00	0.0893243
$766$	19680.0	0.928286
$767$	−27144.0	−1.27785
$768$	768.000	0.0360844
$769$	−29330.0	−1.37538	−0.687690	−	0.726005i	$-0.741375\pi$
$769$	−29330.0	−1.37538	−0.687690	+	0.726005i	$0.741375\pi$
$770$	0	0
$771$	450.000	0.0210199
$772$	9416.00	0.438976
$773$	33090.0	1.53967	0.769835	−	0.638243i	$-0.220339\pi$
$773$	33090.0	1.53967	0.769835	+	0.638243i	$0.220339\pi$
$774$	−7704.00	−0.357771
$775$	−3200.00	−0.148319
$776$	−6320.00	−0.292364
$777$	0	0
$778$	−12636.0	−0.582291
$779$	−1128.00	−0.0518804
$780$	−3480.00	−0.159749
$781$	7488.00	0.343075
$782$	2016.00	0.0921893
$783$	7938.00	0.362300
$784$	0	0
$785$	−530.000	−0.0240975
$786$	−9432.00	−0.428026
$787$	−32564.0	−1.47494	−0.737472	−	0.675377i	$-0.763981\pi$
$787$	−32564.0	−1.47494	−0.737472	+	0.675377i	$0.763981\pi$
$788$	−12456.0	−0.563105
$789$	−9864.00	−0.445079
$790$	6320.00	0.284627
$791$	0	0
$792$	−864.000	−0.0387638
$793$	14500.0	0.649319
$794$	−21812.0	−0.974910
$795$	2070.00	0.0923463
$796$	13024.0	0.579929
$797$	−14646.0	−0.650926	−0.325463	−	0.945555i	$-0.605520\pi$
$797$	−14646.0	−0.650926	−0.325463	+	0.945555i	$0.605520\pi$
$798$	0	0
$799$	16128.0	0.714102
$800$	−800.000	−0.0353553
$801$	−7290.00	−0.321572
$802$	18588.0	0.818410
$803$	11496.0	0.505212
$804$	−6672.00	−0.292666
$805$	0	0
$806$	14848.0	0.648882
$807$	19134.0	0.834633
$808$	−15120.0	−0.658317
$809$	41850.0	1.81875	0.909374	−	0.415979i	$-0.136561\pi$
$809$	41850.0	1.81875	0.909374	+	0.415979i	$0.136561\pi$
$810$	810.000	0.0351364
$811$	39004.0	1.68880	0.844399	−	0.535714i	$-0.179958\pi$
$811$	39004.0	1.68880	0.844399	+	0.535714i	$0.179958\pi$
$812$	0	0
$813$	4800.00	0.207064
$814$	1392.00	0.0599381
$815$	−5860.00	−0.251861
$816$	−2016.00	−0.0864879
$817$	1712.00	0.0733113
$818$	−12332.0	−0.527113
$819$	0	0
$820$	5640.00	0.240192
$821$	−13458.0	−0.572092	−0.286046	−	0.958216i	$-0.592341\pi$
$821$	−13458.0	−0.572092	−0.286046	+	0.958216i	$0.592341\pi$
$822$	1188.00	0.0504091
$823$	−40696.0	−1.72366	−0.861831	−	0.507196i	$-0.830682\pi$
$823$	−40696.0	−1.72366	−0.861831	+	0.507196i	$0.830682\pi$
$824$	2368.00	0.100113
$825$	900.000	0.0379806
$826$	0	0
$827$	22140.0	0.930935	0.465467	−	0.885065i	$-0.345886\pi$
$827$	22140.0	0.930935	0.465467	+	0.885065i	$0.345886\pi$
$828$	864.000	0.0362634
$829$	20698.0	0.867155	0.433577	−	0.901116i	$-0.357251\pi$
$829$	20698.0	0.867155	0.433577	+	0.901116i	$0.357251\pi$
$830$	−840.000	−0.0351287
$831$	14802.0	0.617901
$832$	3712.00	0.154676
$833$	0	0
$834$	8184.00	0.339795
$835$	13320.0	0.552045
$836$	192.000	0.00794313
$837$	−3456.00	−0.142720
$838$	−21480.0	−0.885459
$839$	15480.0	0.636983	0.318492	−	0.947926i	$-0.396824\pi$
$839$	15480.0	0.636983	0.318492	+	0.947926i	$0.396824\pi$
$840$	0	0
$841$	62047.0	2.54406
$842$	−26908.0	−1.10132
$843$	−1890.00	−0.0772183
$844$	23120.0	0.942919
$845$	−5835.00	−0.237550
$846$	6912.00	0.280898
$847$	0	0
$848$	−2208.00	−0.0894140
$849$	16140.0	0.652442
$850$	2100.00	0.0847405
$851$	−1392.00	−0.0560719
$852$	7488.00	0.301097
$853$	−47486.0	−1.90608	−0.953042	−	0.302838i	$-0.902066\pi$
$853$	−47486.0	−1.90608	−0.953042	+	0.302838i	$0.902066\pi$
$854$	0	0
$855$	−180.000	−0.00719985
$856$	2592.00	0.103496
$857$	15438.0	0.615347	0.307673	−	0.951492i	$-0.400450\pi$
$857$	15438.0	0.615347	0.307673	+	0.951492i	$0.400450\pi$
$858$	−4176.00	−0.166161
$859$	15100.0	0.599773	0.299887	−	0.953975i	$-0.403051\pi$
$859$	15100.0	0.599773	0.299887	+	0.953975i	$0.403051\pi$
$860$	−8560.00	−0.339411
$861$	0	0
$862$	−20304.0	−0.802270
$863$	−7056.00	−0.278319	−0.139159	−	0.990270i	$-0.544440\pi$
$863$	−7056.00	−0.278319	−0.139159	+	0.990270i	$0.544440\pi$
$864$	−864.000	−0.0340207
$865$	−9570.00	−0.376173
$866$	31636.0	1.24138
$867$	−9447.00	−0.370054
$868$	0	0
$869$	7584.00	0.296052
$870$	8820.00	0.343708
$871$	−32248.0	−1.25451
$872$	−6832.00	−0.265322
$873$	7110.00	0.275644
$874$	−192.000	−0.00743077
$875$	0	0
$876$	11496.0	0.443395
$877$	23726.0	0.913535	0.456767	−	0.889586i	$-0.349007\pi$
$877$	23726.0	0.913535	0.456767	+	0.889586i	$0.349007\pi$
$878$	−14864.0	−0.571339
$879$	−4410.00	−0.169221
$880$	−960.000	−0.0367745
$881$	38190.0	1.46045	0.730223	−	0.683208i	$-0.239416\pi$
$881$	38190.0	1.46045	0.730223	+	0.683208i	$0.239416\pi$
$882$	0	0
$883$	−46732.0	−1.78104	−0.890519	−	0.454946i	$-0.849659\pi$
$883$	−46732.0	−1.78104	−0.890519	+	0.454946i	$0.849659\pi$
$884$	−9744.00	−0.370731
$885$	7020.00	0.266638
$886$	−11832.0	−0.448650
$887$	−13800.0	−0.522389	−0.261194	−	0.965286i	$-0.584116\pi$
$887$	−13800.0	−0.522389	−0.261194	+	0.965286i	$0.584116\pi$
$888$	1392.00	0.0526041
$889$	0	0
$890$	−8100.00	−0.305070
$891$	972.000	0.0365468
$892$	5824.00	0.218612
$893$	−1536.00	−0.0575591
$894$	−8820.00	−0.329961
$895$	−16500.0	−0.616239
$896$	0	0
$897$	4176.00	0.155443
$898$	−4932.00	−0.183277
$899$	−37632.0	−1.39610
$900$	900.000	0.0333333
$901$	5796.00	0.214309
$902$	6768.00	0.249833
$903$	0	0
$904$	−3216.00	−0.118321
$905$	1510.00	0.0554631
$906$	11328.0	0.415395
$907$	−5668.00	−0.207500	−0.103750	−	0.994603i	$-0.533084\pi$
$907$	−5668.00	−0.207500	−0.103750	+	0.994603i	$0.533084\pi$
$908$	10416.0	0.380691
$909$	17010.0	0.620667
$910$	0	0
$911$	−1464.00	−0.0532431	−0.0266216	−	0.999646i	$-0.508475\pi$
$911$	−1464.00	−0.0532431	−0.0266216	+	0.999646i	$0.508475\pi$
$912$	192.000	0.00697122
$913$	−1008.00	−0.0365388
$914$	−27988.0	−1.01287
$915$	−3750.00	−0.135488
$916$	17416.0	0.628211
$917$	0	0
$918$	2268.00	0.0815416
$919$	−28000.0	−1.00504	−0.502522	−	0.864565i	$-0.667594\pi$
$919$	−28000.0	−1.00504	−0.502522	+	0.864565i	$0.667594\pi$
$920$	960.000	0.0344025
$921$	3108.00	0.111197
$922$	−7956.00	−0.284183
$923$	36192.0	1.29065
$924$	0	0
$925$	−1450.00	−0.0515413
$926$	−20704.0	−0.734747
$927$	−2664.00	−0.0943875
$928$	−9408.00	−0.332794
$929$	45870.0	1.61996	0.809982	−	0.586455i	$-0.199477\pi$
$929$	45870.0	1.61996	0.809982	+	0.586455i	$0.199477\pi$
$930$	−3840.00	−0.135396
$931$	0	0
$932$	−8280.00	−0.291009
$933$	648.000	0.0227380
$934$	2856.00	0.100055
$935$	2520.00	0.0881420
$936$	−4176.00	−0.145830
$937$	−7058.00	−0.246078	−0.123039	−	0.992402i	$-0.539264\pi$
$937$	−7058.00	−0.246078	−0.123039	+	0.992402i	$0.539264\pi$
$938$	0	0
$939$	4602.00	0.159937
$940$	7680.00	0.266483
$941$	−35670.0	−1.23572	−0.617858	−	0.786290i	$-0.711999\pi$
$941$	−35670.0	−1.23572	−0.617858	+	0.786290i	$0.711999\pi$
$942$	−636.000	−0.0219979
$943$	−6768.00	−0.233718
$944$	−7488.00	−0.258171
$945$	0	0
$946$	−10272.0	−0.353035
$947$	−15996.0	−0.548891	−0.274446	−	0.961603i	$-0.588494\pi$
$947$	−15996.0	−0.548891	−0.274446	+	0.961603i	$0.588494\pi$
$948$	7584.00	0.259828
$949$	55564.0	1.90062
$950$	−200.000	−0.00683038
$951$	−19638.0	−0.669617
$952$	0	0
$953$	−31110.0	−1.05745	−0.528726	−	0.848793i	$-0.677330\pi$
$953$	−31110.0	−1.05745	−0.528726	+	0.848793i	$0.677330\pi$
$954$	2484.00	0.0843003
$955$	21240.0	0.719697
$956$	2976.00	0.100681
$957$	10584.0	0.357505
$958$	17664.0	0.595718
$959$	0	0
$960$	−960.000	−0.0322749
$961$	−13407.0	−0.450035
$962$	6728.00	0.225488
$963$	−2916.00	−0.0975771
$964$	6904.00	0.230667
$965$	−11770.0	−0.392632
$966$	0	0
$967$	5768.00	0.191816	0.0959082	−	0.995390i	$-0.469424\pi$
$967$	5768.00	0.191816	0.0959082	+	0.995390i	$0.469424\pi$
$968$	9496.00	0.315303
$969$	−504.000	−0.0167088
$970$	7900.00	0.261499
$971$	39324.0	1.29966	0.649829	−	0.760081i	$-0.274841\pi$
$971$	39324.0	1.29966	0.649829	+	0.760081i	$0.274841\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	18128.0	0.596364
$975$	4350.00	0.142884
$976$	4000.00	0.131185
$977$	−8334.00	−0.272905	−0.136453	−	0.990647i	$-0.543570\pi$
$977$	−8334.00	−0.272905	−0.136453	+	0.990647i	$0.543570\pi$
$978$	−7032.00	−0.229917
$979$	−9720.00	−0.317316
$980$	0	0
$981$	7686.00	0.250148
$982$	−25560.0	−0.830603
$983$	17352.0	0.563014	0.281507	−	0.959559i	$-0.409166\pi$
$983$	17352.0	0.563014	0.281507	+	0.959559i	$0.409166\pi$
$984$	6768.00	0.219264
$985$	15570.0	0.503656
$986$	24696.0	0.797648
$987$	0	0
$988$	928.000	0.0298822
$989$	10272.0	0.330263
$990$	1080.00	0.0346714
$991$	35384.0	1.13422	0.567109	−	0.823643i	$-0.308062\pi$
$991$	35384.0	1.13422	0.567109	+	0.823643i	$0.308062\pi$
$992$	4096.00	0.131097
$993$	276.000	0.00882034
$994$	0	0
$995$	−16280.0	−0.518704
$996$	−1008.00	−0.0320680
$997$	48706.0	1.54718	0.773588	−	0.633689i	$-0.218460\pi$
$997$	48706.0	1.54718	0.773588	+	0.633689i	$0.218460\pi$
$998$	31256.0	0.991374
$999$	−1566.00	−0.0495956

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.c.1.1	✓	1	7.6	odd	2
630.4.a.q.1.1		1	21.20	even	2
1050.4.a.u.1.1		1	35.34	odd	2
1050.4.g.p.799.1		2	35.27	even	4
1050.4.g.p.799.2		2	35.13	even	4
1470.4.a.k.1.1		1	1.1	even	1	trivial
1680.4.a.t.1.1		1	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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