LMFDB - Embedded newform 930.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(1,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.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:	$54.8717763053$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -18.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -18.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +12.0000 q^{12} +28.0000 q^{13} -36.0000 q^{14} -15.0000 q^{15} +16.0000 q^{16} +10.0000 q^{17} +18.0000 q^{18} -120.000 q^{19} -20.0000 q^{20} -54.0000 q^{21} -152.000 q^{23} +24.0000 q^{24} +25.0000 q^{25} +56.0000 q^{26} +27.0000 q^{27} -72.0000 q^{28} -28.0000 q^{29} -30.0000 q^{30} +31.0000 q^{31} +32.0000 q^{32} +20.0000 q^{34} +90.0000 q^{35} +36.0000 q^{36} -204.000 q^{37} -240.000 q^{38} +84.0000 q^{39} -40.0000 q^{40} -94.0000 q^{41} -108.000 q^{42} +88.0000 q^{43} -45.0000 q^{45} -304.000 q^{46} +296.000 q^{47} +48.0000 q^{48} -19.0000 q^{49} +50.0000 q^{50} +30.0000 q^{51} +112.000 q^{52} -714.000 q^{53} +54.0000 q^{54} -144.000 q^{56} -360.000 q^{57} -56.0000 q^{58} -390.000 q^{59} -60.0000 q^{60} -134.000 q^{61} +62.0000 q^{62} -162.000 q^{63} +64.0000 q^{64} -140.000 q^{65} -442.000 q^{67} +40.0000 q^{68} -456.000 q^{69} +180.000 q^{70} -574.000 q^{71} +72.0000 q^{72} -1072.00 q^{73} -408.000 q^{74} +75.0000 q^{75} -480.000 q^{76} +168.000 q^{78} +1160.00 q^{79} -80.0000 q^{80} +81.0000 q^{81} -188.000 q^{82} -12.0000 q^{83} -216.000 q^{84} -50.0000 q^{85} +176.000 q^{86} -84.0000 q^{87} +212.000 q^{89} -90.0000 q^{90} -504.000 q^{91} -608.000 q^{92} +93.0000 q^{93} +592.000 q^{94} +600.000 q^{95} +96.0000 q^{96} -226.000 q^{97} -38.0000 q^{98} +O(q^{100})\)

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
$7$	−18.0000	−0.971909	−0.485954	−	0.873984i	$-0.661528\pi$
$7$	−18.0000	−0.971909	−0.485954	+	0.873984i	$0.661528\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	12.0000	0.288675
$13$	28.0000	0.597369	0.298685	−	0.954352i	$-0.403452\pi$
$13$	28.0000	0.597369	0.298685	+	0.954352i	$0.403452\pi$
$14$	−36.0000	−0.687243
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	10.0000	0.142668	0.0713340	−	0.997452i	$-0.477274\pi$
$17$	10.0000	0.142668	0.0713340	+	0.997452i	$0.477274\pi$
$18$	18.0000	0.235702
$19$	−120.000	−1.44894	−0.724471	−	0.689306i	$-0.757916\pi$
$19$	−120.000	−1.44894	−0.724471	+	0.689306i	$0.757916\pi$
$20$	−20.0000	−0.223607
$21$	−54.0000	−0.561132
$22$	0	0
$23$	−152.000	−1.37801	−0.689004	−	0.724757i	$-0.741952\pi$
$23$	−152.000	−1.37801	−0.689004	+	0.724757i	$0.741952\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	56.0000	0.422404
$27$	27.0000	0.192450
$28$	−72.0000	−0.485954
$29$	−28.0000	−0.179292	−0.0896460	−	0.995974i	$-0.528574\pi$
$29$	−28.0000	−0.179292	−0.0896460	+	0.995974i	$0.528574\pi$
$30$	−30.0000	−0.182574
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	32.0000	0.176777
$33$	0	0
$34$	20.0000	0.100882
$35$	90.0000	0.434651
$36$	36.0000	0.166667
$37$	−204.000	−0.906416	−0.453208	−	0.891405i	$-0.649721\pi$
$37$	−204.000	−0.906416	−0.453208	+	0.891405i	$0.649721\pi$
$38$	−240.000	−1.02456
$39$	84.0000	0.344891
$40$	−40.0000	−0.158114
$41$	−94.0000	−0.358057	−0.179028	−	0.983844i	$-0.557295\pi$
$41$	−94.0000	−0.358057	−0.179028	+	0.983844i	$0.557295\pi$
$42$	−108.000	−0.396780
$43$	88.0000	0.312090	0.156045	−	0.987750i	$-0.450125\pi$
$43$	88.0000	0.312090	0.156045	+	0.987750i	$0.450125\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	−304.000	−0.974399
$47$	296.000	0.918639	0.459320	−	0.888271i	$-0.348093\pi$
$47$	296.000	0.918639	0.459320	+	0.888271i	$0.348093\pi$
$48$	48.0000	0.144338
$49$	−19.0000	−0.0553936
$50$	50.0000	0.141421
$51$	30.0000	0.0823694
$52$	112.000	0.298685
$53$	−714.000	−1.85048	−0.925240	−	0.379382i	$-0.876137\pi$
$53$	−714.000	−1.85048	−0.925240	+	0.379382i	$0.876137\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	−144.000	−0.343622
$57$	−360.000	−0.836547
$58$	−56.0000	−0.126779
$59$	−390.000	−0.860571	−0.430285	−	0.902693i	$-0.641587\pi$
$59$	−390.000	−0.860571	−0.430285	+	0.902693i	$0.641587\pi$
$60$	−60.0000	−0.129099
$61$	−134.000	−0.281261	−0.140631	−	0.990062i	$-0.544913\pi$
$61$	−134.000	−0.281261	−0.140631	+	0.990062i	$0.544913\pi$
$62$	62.0000	0.127000
$63$	−162.000	−0.323970
$64$	64.0000	0.125000
$65$	−140.000	−0.267152
$66$	0	0
$67$	−442.000	−0.805954	−0.402977	−	0.915210i	$-0.632024\pi$
$67$	−442.000	−0.805954	−0.402977	+	0.915210i	$0.632024\pi$
$68$	40.0000	0.0713340
$69$	−456.000	−0.795593
$70$	180.000	0.307344
$71$	−574.000	−0.959454	−0.479727	−	0.877418i	$-0.659264\pi$
$71$	−574.000	−0.959454	−0.479727	+	0.877418i	$0.659264\pi$
$72$	72.0000	0.117851
$73$	−1072.00	−1.71874	−0.859371	−	0.511353i	$-0.829144\pi$
$73$	−1072.00	−1.71874	−0.859371	+	0.511353i	$0.829144\pi$
$74$	−408.000	−0.640933
$75$	75.0000	0.115470
$76$	−480.000	−0.724471
$77$	0	0
$78$	168.000	0.243875
$79$	1160.00	1.65203	0.826014	−	0.563650i	$-0.190603\pi$
$79$	1160.00	1.65203	0.826014	+	0.563650i	$0.190603\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−188.000	−0.253184
$83$	−12.0000	−0.0158695	−0.00793477	−	0.999969i	$-0.502526\pi$
$83$	−12.0000	−0.0158695	−0.00793477	+	0.999969i	$0.502526\pi$
$84$	−216.000	−0.280566
$85$	−50.0000	−0.0638031
$86$	176.000	0.220681
$87$	−84.0000	−0.103514
$88$	0	0
$89$	212.000	0.252494	0.126247	−	0.991999i	$-0.459707\pi$
$89$	212.000	0.252494	0.126247	+	0.991999i	$0.459707\pi$
$90$	−90.0000	−0.105409
$91$	−504.000	−0.580589
$92$	−608.000	−0.689004
$93$	93.0000	0.103695
$94$	592.000	0.649576
$95$	600.000	0.647986
$96$	96.0000	0.102062
$97$	−226.000	−0.236565	−0.118283	−	0.992980i	$-0.537739\pi$
$97$	−226.000	−0.236565	−0.118283	+	0.992980i	$0.537739\pi$
$98$	−38.0000	−0.0391692
$99$	0	0
$100$	100.000	0.100000
$101$	−902.000	−0.888637	−0.444319	−	0.895869i	$-0.646554\pi$
$101$	−902.000	−0.888637	−0.444319	+	0.895869i	$0.646554\pi$
$102$	60.0000	0.0582440
$103$	994.000	0.950891	0.475445	−	0.879745i	$-0.342287\pi$
$103$	994.000	0.950891	0.475445	+	0.879745i	$0.342287\pi$
$104$	224.000	0.211202
$105$	270.000	0.250946
$106$	−1428.00	−1.30849
$107$	1212.00	1.09503	0.547516	−	0.836795i	$-0.315573\pi$
$107$	1212.00	1.09503	0.547516	+	0.836795i	$0.315573\pi$
$108$	108.000	0.0962250
$109$	−598.000	−0.525486	−0.262743	−	0.964866i	$-0.584627\pi$
$109$	−598.000	−0.525486	−0.262743	+	0.964866i	$0.584627\pi$
$110$	0	0
$111$	−612.000	−0.523320
$112$	−288.000	−0.242977
$113$	414.000	0.344653	0.172327	−	0.985040i	$-0.444872\pi$
$113$	414.000	0.344653	0.172327	+	0.985040i	$0.444872\pi$
$114$	−720.000	−0.591528
$115$	760.000	0.616264
$116$	−112.000	−0.0896460
$117$	252.000	0.199123
$118$	−780.000	−0.608515
$119$	−180.000	−0.138660
$120$	−120.000	−0.0912871
$121$	−1331.00	−1.00000
$122$	−268.000	−0.198882
$123$	−282.000	−0.206724
$124$	124.000	0.0898027
$125$	−125.000	−0.0894427
$126$	−324.000	−0.229081
$127$	680.000	0.475120	0.237560	−	0.971373i	$-0.423652\pi$
$127$	680.000	0.475120	0.237560	+	0.971373i	$0.423652\pi$
$128$	128.000	0.0883883
$129$	264.000	0.180185
$130$	−280.000	−0.188905
$131$	−246.000	−0.164070	−0.0820348	−	0.996629i	$-0.526142\pi$
$131$	−246.000	−0.164070	−0.0820348	+	0.996629i	$0.526142\pi$
$132$	0	0
$133$	2160.00	1.40824
$134$	−884.000	−0.569895
$135$	−135.000	−0.0860663
$136$	80.0000	0.0504408
$137$	1054.00	0.657294	0.328647	−	0.944453i	$-0.393407\pi$
$137$	1054.00	0.657294	0.328647	+	0.944453i	$0.393407\pi$
$138$	−912.000	−0.562570
$139$	−2156.00	−1.31561	−0.657804	−	0.753189i	$-0.728515\pi$
$139$	−2156.00	−1.31561	−0.657804	+	0.753189i	$0.728515\pi$
$140$	360.000	0.217325
$141$	888.000	0.530377
$142$	−1148.00	−0.678437
$143$	0	0
$144$	144.000	0.0833333
$145$	140.000	0.0801818
$146$	−2144.00	−1.21533
$147$	−57.0000	−0.0319815
$148$	−816.000	−0.453208
$149$	2498.00	1.37345	0.686725	−	0.726917i	$-0.259048\pi$
$149$	2498.00	1.37345	0.686725	+	0.726917i	$0.259048\pi$
$150$	150.000	0.0816497
$151$	1680.00	0.905407	0.452704	−	0.891661i	$-0.350460\pi$
$151$	1680.00	0.905407	0.452704	+	0.891661i	$0.350460\pi$
$152$	−960.000	−0.512278
$153$	90.0000	0.0475560
$154$	0	0
$155$	−155.000	−0.0803219
$156$	336.000	0.172446
$157$	2086.00	1.06039	0.530194	−	0.847876i	$-0.322119\pi$
$157$	2086.00	1.06039	0.530194	+	0.847876i	$0.322119\pi$
$158$	2320.00	1.16816
$159$	−2142.00	−1.06838
$160$	−160.000	−0.0790569
$161$	2736.00	1.33930
$162$	162.000	0.0785674
$163$	−178.000	−0.0855340	−0.0427670	−	0.999085i	$-0.513617\pi$
$163$	−178.000	−0.0855340	−0.0427670	+	0.999085i	$0.513617\pi$
$164$	−376.000	−0.179028
$165$	0	0
$166$	−24.0000	−0.0112215
$167$	−1088.00	−0.504144	−0.252072	−	0.967709i	$-0.581112\pi$
$167$	−1088.00	−0.504144	−0.252072	+	0.967709i	$0.581112\pi$
$168$	−432.000	−0.198390
$169$	−1413.00	−0.643150
$170$	−100.000	−0.0451156
$171$	−1080.00	−0.482980
$172$	352.000	0.156045
$173$	−2438.00	−1.07143	−0.535716	−	0.844398i	$-0.679958\pi$
$173$	−2438.00	−1.07143	−0.535716	+	0.844398i	$0.679958\pi$
$174$	−168.000	−0.0731957
$175$	−450.000	−0.194382
$176$	0	0
$177$	−1170.00	−0.496851
$178$	424.000	0.178540
$179$	1376.00	0.574565	0.287282	−	0.957846i	$-0.407248\pi$
$179$	1376.00	0.574565	0.287282	+	0.957846i	$0.407248\pi$
$180$	−180.000	−0.0745356
$181$	−2158.00	−0.886204	−0.443102	−	0.896471i	$-0.646122\pi$
$181$	−2158.00	−0.886204	−0.443102	+	0.896471i	$0.646122\pi$
$182$	−1008.00	−0.410538
$183$	−402.000	−0.162386
$184$	−1216.00	−0.487200
$185$	1020.00	0.405362
$186$	186.000	0.0733236
$187$	0	0
$188$	1184.00	0.459320
$189$	−486.000	−0.187044
$190$	1200.00	0.458196
$191$	3038.00	1.15090	0.575450	−	0.817837i	$-0.304827\pi$
$191$	3038.00	1.15090	0.575450	+	0.817837i	$0.304827\pi$
$192$	192.000	0.0721688
$193$	−1146.00	−0.427414	−0.213707	−	0.976898i	$-0.568554\pi$
$193$	−1146.00	−0.427414	−0.213707	+	0.976898i	$0.568554\pi$
$194$	−452.000	−0.167277
$195$	−420.000	−0.154240
$196$	−76.0000	−0.0276968
$197$	4050.00	1.46472	0.732362	−	0.680916i	$-0.238418\pi$
$197$	4050.00	1.46472	0.732362	+	0.680916i	$0.238418\pi$
$198$	0	0
$199$	16.0000	0.00569955	0.00284977	−	0.999996i	$-0.499093\pi$
$199$	16.0000	0.00569955	0.00284977	+	0.999996i	$0.499093\pi$
$200$	200.000	0.0707107
$201$	−1326.00	−0.465318
$202$	−1804.00	−0.628361
$203$	504.000	0.174255
$204$	120.000	0.0411847
$205$	470.000	0.160128
$206$	1988.00	0.672381
$207$	−1368.00	−0.459336
$208$	448.000	0.149342
$209$	0	0
$210$	540.000	0.177445
$211$	−688.000	−0.224473	−0.112237	−	0.993682i	$-0.535801\pi$
$211$	−688.000	−0.224473	−0.112237	+	0.993682i	$0.535801\pi$
$212$	−2856.00	−0.925240
$213$	−1722.00	−0.553941
$214$	2424.00	0.774305
$215$	−440.000	−0.139571
$216$	216.000	0.0680414
$217$	−558.000	−0.174560
$218$	−1196.00	−0.371575
$219$	−3216.00	−0.992316
$220$	0	0
$221$	280.000	0.0852255
$222$	−1224.00	−0.370043
$223$	2388.00	0.717096	0.358548	−	0.933511i	$-0.383272\pi$
$223$	2388.00	0.717096	0.358548	+	0.933511i	$0.383272\pi$
$224$	−576.000	−0.171811
$225$	225.000	0.0666667
$226$	828.000	0.243707
$227$	−1200.00	−0.350867	−0.175433	−	0.984491i	$-0.556133\pi$
$227$	−1200.00	−0.350867	−0.175433	+	0.984491i	$0.556133\pi$
$228$	−1440.00	−0.418273
$229$	−1586.00	−0.457667	−0.228834	−	0.973466i	$-0.573491\pi$
$229$	−1586.00	−0.457667	−0.228834	+	0.973466i	$0.573491\pi$
$230$	1520.00	0.435764
$231$	0	0
$232$	−224.000	−0.0633893
$233$	−5238.00	−1.47276	−0.736379	−	0.676569i	$-0.763466\pi$
$233$	−5238.00	−1.47276	−0.736379	+	0.676569i	$0.763466\pi$
$234$	504.000	0.140801
$235$	−1480.00	−0.410828
$236$	−1560.00	−0.430285
$237$	3480.00	0.953799
$238$	−360.000	−0.0980476
$239$	636.000	0.172131	0.0860657	−	0.996289i	$-0.472570\pi$
$239$	636.000	0.172131	0.0860657	+	0.996289i	$0.472570\pi$
$240$	−240.000	−0.0645497
$241$	1914.00	0.511583	0.255792	−	0.966732i	$-0.417664\pi$
$241$	1914.00	0.511583	0.255792	+	0.966732i	$0.417664\pi$
$242$	−2662.00	−0.707107
$243$	243.000	0.0641500
$244$	−536.000	−0.140631
$245$	95.0000	0.0247728
$246$	−564.000	−0.146176
$247$	−3360.00	−0.865553
$248$	248.000	0.0635001
$249$	−36.0000	−0.00916228
$250$	−250.000	−0.0632456
$251$	4032.00	1.01393	0.506967	−	0.861965i	$-0.330766\pi$
$251$	4032.00	1.01393	0.506967	+	0.861965i	$0.330766\pi$
$252$	−648.000	−0.161985
$253$	0	0
$254$	1360.00	0.335961
$255$	−150.000	−0.0368367
$256$	256.000	0.0625000
$257$	4346.00	1.05485	0.527424	−	0.849602i	$-0.323158\pi$
$257$	4346.00	1.05485	0.527424	+	0.849602i	$0.323158\pi$
$258$	528.000	0.127410
$259$	3672.00	0.880954
$260$	−560.000	−0.133576
$261$	−252.000	−0.0597640
$262$	−492.000	−0.116015
$263$	−3744.00	−0.877813	−0.438907	−	0.898533i	$-0.644634\pi$
$263$	−3744.00	−0.877813	−0.438907	+	0.898533i	$0.644634\pi$
$264$	0	0
$265$	3570.00	0.827560
$266$	4320.00	0.995775
$267$	636.000	0.145777
$268$	−1768.00	−0.402977
$269$	4012.00	0.909353	0.454677	−	0.890657i	$-0.349755\pi$
$269$	4012.00	0.909353	0.454677	+	0.890657i	$0.349755\pi$
$270$	−270.000	−0.0608581
$271$	3880.00	0.869717	0.434858	−	0.900499i	$-0.356798\pi$
$271$	3880.00	0.869717	0.434858	+	0.900499i	$0.356798\pi$
$272$	160.000	0.0356670
$273$	−1512.00	−0.335203
$274$	2108.00	0.464777
$275$	0	0
$276$	−1824.00	−0.397797
$277$	2136.00	0.463321	0.231660	−	0.972797i	$-0.425584\pi$
$277$	2136.00	0.463321	0.231660	+	0.972797i	$0.425584\pi$
$278$	−4312.00	−0.930275
$279$	279.000	0.0598684
$280$	720.000	0.153672
$281$	−2938.00	−0.623724	−0.311862	−	0.950127i	$-0.600953\pi$
$281$	−2938.00	−0.623724	−0.311862	+	0.950127i	$0.600953\pi$
$282$	1776.00	0.375033
$283$	3558.00	0.747354	0.373677	−	0.927559i	$-0.378097\pi$
$283$	3558.00	0.747354	0.373677	+	0.927559i	$0.378097\pi$
$284$	−2296.00	−0.479727
$285$	1800.00	0.374115
$286$	0	0
$287$	1692.00	0.347999
$288$	288.000	0.0589256
$289$	−4813.00	−0.979646
$290$	280.000	0.0566971
$291$	−678.000	−0.136581
$292$	−4288.00	−0.859371
$293$	−1362.00	−0.271566	−0.135783	−	0.990739i	$-0.543355\pi$
$293$	−1362.00	−0.271566	−0.135783	+	0.990739i	$0.543355\pi$
$294$	−114.000	−0.0226143
$295$	1950.00	0.384859
$296$	−1632.00	−0.320466
$297$	0	0
$298$	4996.00	0.971176
$299$	−4256.00	−0.823180
$300$	300.000	0.0577350
$301$	−1584.00	−0.303323
$302$	3360.00	0.640219
$303$	−2706.00	−0.513055
$304$	−1920.00	−0.362235
$305$	670.000	0.125784
$306$	180.000	0.0336272
$307$	154.000	0.0286295	0.0143147	−	0.999898i	$-0.495443\pi$
$307$	154.000	0.0286295	0.0143147	+	0.999898i	$0.495443\pi$
$308$	0	0
$309$	2982.00	0.548997
$310$	−310.000	−0.0567962
$311$	4542.00	0.828145	0.414073	−	0.910244i	$-0.364106\pi$
$311$	4542.00	0.828145	0.414073	+	0.910244i	$0.364106\pi$
$312$	672.000	0.121938
$313$	−2832.00	−0.511419	−0.255709	−	0.966754i	$-0.582309\pi$
$313$	−2832.00	−0.511419	−0.255709	+	0.966754i	$0.582309\pi$
$314$	4172.00	0.749808
$315$	810.000	0.144884
$316$	4640.00	0.826014
$317$	−4042.00	−0.716156	−0.358078	−	0.933692i	$-0.616568\pi$
$317$	−4042.00	−0.716156	−0.358078	+	0.933692i	$0.616568\pi$
$318$	−4284.00	−0.755455
$319$	0	0
$320$	−320.000	−0.0559017
$321$	3636.00	0.632217
$322$	5472.00	0.947027
$323$	−1200.00	−0.206718
$324$	324.000	0.0555556
$325$	700.000	0.119474
$326$	−356.000	−0.0604816
$327$	−1794.00	−0.303390
$328$	−752.000	−0.126592
$329$	−5328.00	−0.892833
$330$	0	0
$331$	996.000	0.165393	0.0826965	−	0.996575i	$-0.473647\pi$
$331$	996.000	0.165393	0.0826965	+	0.996575i	$0.473647\pi$
$332$	−48.0000	−0.00793477
$333$	−1836.00	−0.302139
$334$	−2176.00	−0.356483
$335$	2210.00	0.360433
$336$	−864.000	−0.140283
$337$	3484.00	0.563162	0.281581	−	0.959537i	$-0.409141\pi$
$337$	3484.00	0.563162	0.281581	+	0.959537i	$0.409141\pi$
$338$	−2826.00	−0.454776
$339$	1242.00	0.198986
$340$	−200.000	−0.0319015
$341$	0	0
$342$	−2160.00	−0.341519
$343$	6516.00	1.02575
$344$	704.000	0.110341
$345$	2280.00	0.355800
$346$	−4876.00	−0.757617
$347$	−6316.00	−0.977120	−0.488560	−	0.872530i	$-0.662478\pi$
$347$	−6316.00	−0.977120	−0.488560	+	0.872530i	$0.662478\pi$
$348$	−336.000	−0.0517572
$349$	−7974.00	−1.22303	−0.611516	−	0.791232i	$-0.709440\pi$
$349$	−7974.00	−1.22303	−0.611516	+	0.791232i	$0.709440\pi$
$350$	−900.000	−0.137449
$351$	756.000	0.114964
$352$	0	0
$353$	11298.0	1.70349	0.851745	−	0.523957i	$-0.175545\pi$
$353$	11298.0	1.70349	0.851745	+	0.523957i	$0.175545\pi$
$354$	−2340.00	−0.351327
$355$	2870.00	0.429081
$356$	848.000	0.126247
$357$	−540.000	−0.0800555
$358$	2752.00	0.406279
$359$	−3906.00	−0.574236	−0.287118	−	0.957895i	$-0.592697\pi$
$359$	−3906.00	−0.574236	−0.287118	+	0.957895i	$0.592697\pi$
$360$	−360.000	−0.0527046
$361$	7541.00	1.09943
$362$	−4316.00	−0.626641
$363$	−3993.00	−0.577350
$364$	−2016.00	−0.290294
$365$	5360.00	0.768644
$366$	−804.000	−0.114824
$367$	1076.00	0.153043	0.0765214	−	0.997068i	$-0.475619\pi$
$367$	1076.00	0.153043	0.0765214	+	0.997068i	$0.475619\pi$
$368$	−2432.00	−0.344502
$369$	−846.000	−0.119352
$370$	2040.00	0.286634
$371$	12852.0	1.79850
$372$	372.000	0.0518476
$373$	8838.00	1.22685	0.613424	−	0.789754i	$-0.289792\pi$
$373$	8838.00	1.22685	0.613424	+	0.789754i	$0.289792\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	2368.00	0.324788
$377$	−784.000	−0.107104
$378$	−972.000	−0.132260
$379$	−1944.00	−0.263474	−0.131737	−	0.991285i	$-0.542055\pi$
$379$	−1944.00	−0.263474	−0.131737	+	0.991285i	$0.542055\pi$
$380$	2400.00	0.323993
$381$	2040.00	0.274311
$382$	6076.00	0.813809
$383$	−5064.00	−0.675609	−0.337805	−	0.941216i	$-0.609684\pi$
$383$	−5064.00	−0.675609	−0.337805	+	0.941216i	$0.609684\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	−2292.00	−0.302227
$387$	792.000	0.104030
$388$	−904.000	−0.118283
$389$	14996.0	1.95457	0.977285	−	0.211931i	$-0.0679753\pi$
$389$	14996.0	1.95457	0.977285	+	0.211931i	$0.0679753\pi$
$390$	−840.000	−0.109064
$391$	−1520.00	−0.196598
$392$	−152.000	−0.0195846
$393$	−738.000	−0.0947256
$394$	8100.00	1.03572
$395$	−5800.00	−0.738809
$396$	0	0
$397$	−8206.00	−1.03740	−0.518699	−	0.854957i	$-0.673584\pi$
$397$	−8206.00	−1.03740	−0.518699	+	0.854957i	$0.673584\pi$
$398$	32.0000	0.00403019
$399$	6480.00	0.813047
$400$	400.000	0.0500000
$401$	13880.0	1.72851	0.864257	−	0.503051i	$-0.167789\pi$
$401$	13880.0	1.72851	0.864257	+	0.503051i	$0.167789\pi$
$402$	−2652.00	−0.329029
$403$	868.000	0.107291
$404$	−3608.00	−0.444319
$405$	−405.000	−0.0496904
$406$	1008.00	0.123217
$407$	0	0
$408$	240.000	0.0291220
$409$	−13642.0	−1.64928	−0.824638	−	0.565662i	$-0.808621\pi$
$409$	−13642.0	−1.64928	−0.824638	+	0.565662i	$0.808621\pi$
$410$	940.000	0.113228
$411$	3162.00	0.379489
$412$	3976.00	0.475445
$413$	7020.00	0.836396
$414$	−2736.00	−0.324800
$415$	60.0000	0.00709707
$416$	896.000	0.105601
$417$	−6468.00	−0.759567
$418$	0	0
$419$	13470.0	1.57053	0.785266	−	0.619159i	$-0.212526\pi$
$419$	13470.0	1.57053	0.785266	+	0.619159i	$0.212526\pi$
$420$	1080.00	0.125473
$421$	−14926.0	−1.72791	−0.863953	−	0.503572i	$-0.832019\pi$
$421$	−14926.0	−1.72791	−0.863953	+	0.503572i	$0.832019\pi$
$422$	−1376.00	−0.158727
$423$	2664.00	0.306213
$424$	−5712.00	−0.654243
$425$	250.000	0.0285336
$426$	−3444.00	−0.391696
$427$	2412.00	0.273360
$428$	4848.00	0.547516
$429$	0	0
$430$	−880.000	−0.0986916
$431$	−2962.00	−0.331031	−0.165516	−	0.986207i	$-0.552929\pi$
$431$	−2962.00	−0.331031	−0.165516	+	0.986207i	$0.552929\pi$
$432$	432.000	0.0481125
$433$	−448.000	−0.0497217	−0.0248609	−	0.999691i	$-0.507914\pi$
$433$	−448.000	−0.0497217	−0.0248609	+	0.999691i	$0.507914\pi$
$434$	−1116.00	−0.123433
$435$	420.000	0.0462930
$436$	−2392.00	−0.262743
$437$	18240.0	1.99665
$438$	−6432.00	−0.701673
$439$	−17880.0	−1.94389	−0.971943	−	0.235217i	$-0.924420\pi$
$439$	−17880.0	−1.94389	−0.971943	+	0.235217i	$0.924420\pi$
$440$	0	0
$441$	−171.000	−0.0184645
$442$	560.000	0.0602635
$443$	−2256.00	−0.241954	−0.120977	−	0.992655i	$-0.538603\pi$
$443$	−2256.00	−0.241954	−0.120977	+	0.992655i	$0.538603\pi$
$444$	−2448.00	−0.261660
$445$	−1060.00	−0.112919
$446$	4776.00	0.507063
$447$	7494.00	0.792962
$448$	−1152.00	−0.121489
$449$	3904.00	0.410337	0.205168	−	0.978727i	$-0.434226\pi$
$449$	3904.00	0.410337	0.205168	+	0.978727i	$0.434226\pi$
$450$	450.000	0.0471405
$451$	0	0
$452$	1656.00	0.172327
$453$	5040.00	0.522737
$454$	−2400.00	−0.248100
$455$	2520.00	0.259647
$456$	−2880.00	−0.295764
$457$	−7184.00	−0.735346	−0.367673	−	0.929955i	$-0.619846\pi$
$457$	−7184.00	−0.735346	−0.367673	+	0.929955i	$0.619846\pi$
$458$	−3172.00	−0.323620
$459$	270.000	0.0274565
$460$	3040.00	0.308132
$461$	3936.00	0.397652	0.198826	−	0.980035i	$-0.436287\pi$
$461$	3936.00	0.397652	0.198826	+	0.980035i	$0.436287\pi$
$462$	0	0
$463$	−13160.0	−1.32094	−0.660472	−	0.750851i	$-0.729644\pi$
$463$	−13160.0	−1.32094	−0.660472	+	0.750851i	$0.729644\pi$
$464$	−448.000	−0.0448230
$465$	−465.000	−0.0463739
$466$	−10476.0	−1.04140
$467$	16020.0	1.58740	0.793701	−	0.608307i	$-0.208151\pi$
$467$	16020.0	1.58740	0.793701	+	0.608307i	$0.208151\pi$
$468$	1008.00	0.0995616
$469$	7956.00	0.783313
$470$	−2960.00	−0.290499
$471$	6258.00	0.612215
$472$	−3120.00	−0.304258
$473$	0	0
$474$	6960.00	0.674438
$475$	−3000.00	−0.289788
$476$	−720.000	−0.0693301
$477$	−6426.00	−0.616827
$478$	1272.00	0.121715
$479$	2946.00	0.281015	0.140507	−	0.990080i	$-0.455127\pi$
$479$	2946.00	0.281015	0.140507	+	0.990080i	$0.455127\pi$
$480$	−480.000	−0.0456435
$481$	−5712.00	−0.541465
$482$	3828.00	0.361744
$483$	8208.00	0.773244
$484$	−5324.00	−0.500000
$485$	1130.00	0.105795
$486$	486.000	0.0453609
$487$	12608.0	1.17315	0.586574	−	0.809896i	$-0.300476\pi$
$487$	12608.0	1.17315	0.586574	+	0.809896i	$0.300476\pi$
$488$	−1072.00	−0.0994409
$489$	−534.000	−0.0493831
$490$	190.000	0.0175170
$491$	−2420.00	−0.222430	−0.111215	−	0.993796i	$-0.535474\pi$
$491$	−2420.00	−0.222430	−0.111215	+	0.993796i	$0.535474\pi$
$492$	−1128.00	−0.103362
$493$	−280.000	−0.0255792
$494$	−6720.00	−0.612039
$495$	0	0
$496$	496.000	0.0449013
$497$	10332.0	0.932502
$498$	−72.0000	−0.00647871
$499$	−13556.0	−1.21613	−0.608066	−	0.793886i	$-0.708054\pi$
$499$	−13556.0	−1.21613	−0.608066	+	0.793886i	$0.708054\pi$
$500$	−500.000	−0.0447214
$501$	−3264.00	−0.291067
$502$	8064.00	0.716960
$503$	12496.0	1.10769	0.553846	−	0.832619i	$-0.313160\pi$
$503$	12496.0	1.10769	0.553846	+	0.832619i	$0.313160\pi$
$504$	−1296.00	−0.114541
$505$	4510.00	0.397411
$506$	0	0
$507$	−4239.00	−0.371323
$508$	2720.00	0.237560
$509$	−9240.00	−0.804628	−0.402314	−	0.915502i	$-0.631794\pi$
$509$	−9240.00	−0.804628	−0.402314	+	0.915502i	$0.631794\pi$
$510$	−300.000	−0.0260475
$511$	19296.0	1.67046
$512$	512.000	0.0441942
$513$	−3240.00	−0.278849
$514$	8692.00	0.745890
$515$	−4970.00	−0.425251
$516$	1056.00	0.0900927
$517$	0	0
$518$	7344.00	0.622928
$519$	−7314.00	−0.618591
$520$	−1120.00	−0.0944524
$521$	18114.0	1.52320	0.761601	−	0.648046i	$-0.224413\pi$
$521$	18114.0	1.52320	0.761601	+	0.648046i	$0.224413\pi$
$522$	−504.000	−0.0422595
$523$	−9544.00	−0.797954	−0.398977	−	0.916961i	$-0.630635\pi$
$523$	−9544.00	−0.797954	−0.398977	+	0.916961i	$0.630635\pi$
$524$	−984.000	−0.0820348
$525$	−1350.00	−0.112226
$526$	−7488.00	−0.620708
$527$	310.000	0.0256239
$528$	0	0
$529$	10937.0	0.898907
$530$	7140.00	0.585173
$531$	−3510.00	−0.286857
$532$	8640.00	0.704119
$533$	−2632.00	−0.213892
$534$	1272.00	0.103080
$535$	−6060.00	−0.489713
$536$	−3536.00	−0.284948
$537$	4128.00	0.331725
$538$	8024.00	0.643010
$539$	0	0
$540$	−540.000	−0.0430331
$541$	2410.00	0.191523	0.0957615	−	0.995404i	$-0.469471\pi$
$541$	2410.00	0.191523	0.0957615	+	0.995404i	$0.469471\pi$
$542$	7760.00	0.614983
$543$	−6474.00	−0.511650
$544$	320.000	0.0252204
$545$	2990.00	0.235005
$546$	−3024.00	−0.237024
$547$	2662.00	0.208078	0.104039	−	0.994573i	$-0.466823\pi$
$547$	2662.00	0.208078	0.104039	+	0.994573i	$0.466823\pi$
$548$	4216.00	0.328647
$549$	−1206.00	−0.0937538
$550$	0	0
$551$	3360.00	0.259784
$552$	−3648.00	−0.281285
$553$	−20880.0	−1.60562
$554$	4272.00	0.327617
$555$	3060.00	0.234036
$556$	−8624.00	−0.657804
$557$	14014.0	1.06605	0.533027	−	0.846098i	$-0.321054\pi$
$557$	14014.0	1.06605	0.533027	+	0.846098i	$0.321054\pi$
$558$	558.000	0.0423334
$559$	2464.00	0.186433
$560$	1440.00	0.108663
$561$	0	0
$562$	−5876.00	−0.441039
$563$	−10892.0	−0.815352	−0.407676	−	0.913127i	$-0.633661\pi$
$563$	−10892.0	−0.815352	−0.407676	+	0.913127i	$0.633661\pi$
$564$	3552.00	0.265188
$565$	−2070.00	−0.154134
$566$	7116.00	0.528459
$567$	−1458.00	−0.107990
$568$	−4592.00	−0.339218
$569$	−16264.0	−1.19828	−0.599141	−	0.800644i	$-0.704491\pi$
$569$	−16264.0	−1.19828	−0.599141	+	0.800644i	$0.704491\pi$
$570$	3600.00	0.264539
$571$	4180.00	0.306353	0.153176	−	0.988199i	$-0.451050\pi$
$571$	4180.00	0.306353	0.153176	+	0.988199i	$0.451050\pi$
$572$	0	0
$573$	9114.00	0.664473
$574$	3384.00	0.246072
$575$	−3800.00	−0.275602
$576$	576.000	0.0416667
$577$	−7454.00	−0.537806	−0.268903	−	0.963167i	$-0.586661\pi$
$577$	−7454.00	−0.537806	−0.268903	+	0.963167i	$0.586661\pi$
$578$	−9626.00	−0.692714
$579$	−3438.00	−0.246768
$580$	560.000	0.0400909
$581$	216.000	0.0154237
$582$	−1356.00	−0.0965773
$583$	0	0
$584$	−8576.00	−0.607667
$585$	−1260.00	−0.0890506
$586$	−2724.00	−0.192026
$587$	22948.0	1.61357	0.806785	−	0.590845i	$-0.201206\pi$
$587$	22948.0	1.61357	0.806785	+	0.590845i	$0.201206\pi$
$588$	−228.000	−0.0159908
$589$	−3720.00	−0.260238
$590$	3900.00	0.272136
$591$	12150.0	0.845659
$592$	−3264.00	−0.226604
$593$	−8770.00	−0.607320	−0.303660	−	0.952780i	$-0.598209\pi$
$593$	−8770.00	−0.607320	−0.303660	+	0.952780i	$0.598209\pi$
$594$	0	0
$595$	900.000	0.0620108
$596$	9992.00	0.686725
$597$	48.0000	0.00329064
$598$	−8512.00	−0.582076
$599$	−2346.00	−0.160025	−0.0800125	−	0.996794i	$-0.525496\pi$
$599$	−2346.00	−0.160025	−0.0800125	+	0.996794i	$0.525496\pi$
$600$	600.000	0.0408248
$601$	198.000	0.0134386	0.00671929	−	0.999977i	$-0.497861\pi$
$601$	198.000	0.0134386	0.00671929	+	0.999977i	$0.497861\pi$
$602$	−3168.00	−0.214482
$603$	−3978.00	−0.268651
$604$	6720.00	0.452704
$605$	6655.00	0.447214
$606$	−5412.00	−0.362785
$607$	13706.0	0.916490	0.458245	−	0.888826i	$-0.348478\pi$
$607$	13706.0	0.916490	0.458245	+	0.888826i	$0.348478\pi$
$608$	−3840.00	−0.256139
$609$	1512.00	0.100606
$610$	1340.00	0.0889426
$611$	8288.00	0.548767
$612$	360.000	0.0237780
$613$	12032.0	0.792770	0.396385	−	0.918084i	$-0.370265\pi$
$613$	12032.0	0.792770	0.396385	+	0.918084i	$0.370265\pi$
$614$	308.000	0.0202441
$615$	1410.00	0.0924499
$616$	0	0
$617$	6318.00	0.412242	0.206121	−	0.978527i	$-0.433916\pi$
$617$	6318.00	0.412242	0.206121	+	0.978527i	$0.433916\pi$
$618$	5964.00	0.388199
$619$	−17996.0	−1.16853	−0.584265	−	0.811563i	$-0.698617\pi$
$619$	−17996.0	−1.16853	−0.584265	+	0.811563i	$0.698617\pi$
$620$	−620.000	−0.0401610
$621$	−4104.00	−0.265198
$622$	9084.00	0.585587
$623$	−3816.00	−0.245401
$624$	1344.00	0.0862229
$625$	625.000	0.0400000
$626$	−5664.00	−0.361628
$627$	0	0
$628$	8344.00	0.530194
$629$	−2040.00	−0.129317
$630$	1620.00	0.102448
$631$	−20704.0	−1.30620	−0.653101	−	0.757271i	$-0.726532\pi$
$631$	−20704.0	−1.30620	−0.653101	+	0.757271i	$0.726532\pi$
$632$	9280.00	0.584080
$633$	−2064.00	−0.129600
$634$	−8084.00	−0.506399
$635$	−3400.00	−0.212480
$636$	−8568.00	−0.534188
$637$	−532.000	−0.0330904
$638$	0	0
$639$	−5166.00	−0.319818
$640$	−640.000	−0.0395285
$641$	−12512.0	−0.770974	−0.385487	−	0.922713i	$-0.625967\pi$
$641$	−12512.0	−0.770974	−0.385487	+	0.922713i	$0.625967\pi$
$642$	7272.00	0.447045
$643$	−21440.0	−1.31495	−0.657474	−	0.753478i	$-0.728375\pi$
$643$	−21440.0	−1.31495	−0.657474	+	0.753478i	$0.728375\pi$
$644$	10944.0	0.669649
$645$	−1320.00	−0.0805813
$646$	−2400.00	−0.146171
$647$	15840.0	0.962496	0.481248	−	0.876585i	$-0.340184\pi$
$647$	15840.0	0.962496	0.481248	+	0.876585i	$0.340184\pi$
$648$	648.000	0.0392837
$649$	0	0
$650$	1400.00	0.0844808
$651$	−1674.00	−0.100782
$652$	−712.000	−0.0427670
$653$	−11386.0	−0.682341	−0.341170	−	0.940001i	$-0.610823\pi$
$653$	−11386.0	−0.682341	−0.341170	+	0.940001i	$0.610823\pi$
$654$	−3588.00	−0.214529
$655$	1230.00	0.0733742
$656$	−1504.00	−0.0895142
$657$	−9648.00	−0.572914
$658$	−10656.0	−0.631328
$659$	−12290.0	−0.726480	−0.363240	−	0.931696i	$-0.618330\pi$
$659$	−12290.0	−0.726480	−0.363240	+	0.931696i	$0.618330\pi$
$660$	0	0
$661$	478.000	0.0281271	0.0140636	−	0.999901i	$-0.495523\pi$
$661$	478.000	0.0281271	0.0140636	+	0.999901i	$0.495523\pi$
$662$	1992.00	0.116951
$663$	840.000	0.0492050
$664$	−96.0000	−0.00561073
$665$	−10800.0	−0.629784
$666$	−3672.00	−0.213644
$667$	4256.00	0.247066
$668$	−4352.00	−0.252072
$669$	7164.00	0.414015
$670$	4420.00	0.254865
$671$	0	0
$672$	−1728.00	−0.0991950
$673$	−28756.0	−1.64705	−0.823523	−	0.567282i	$-0.807995\pi$
$673$	−28756.0	−1.64705	−0.823523	+	0.567282i	$0.807995\pi$
$674$	6968.00	0.398216
$675$	675.000	0.0384900
$676$	−5652.00	−0.321575
$677$	1062.00	0.0602895	0.0301447	−	0.999546i	$-0.490403\pi$
$677$	1062.00	0.0602895	0.0301447	+	0.999546i	$0.490403\pi$
$678$	2484.00	0.140704
$679$	4068.00	0.229920
$680$	−400.000	−0.0225578
$681$	−3600.00	−0.202573
$682$	0	0
$683$	18064.0	1.01201	0.506003	−	0.862532i	$-0.331123\pi$
$683$	18064.0	1.01201	0.506003	+	0.862532i	$0.331123\pi$
$684$	−4320.00	−0.241490
$685$	−5270.00	−0.293951
$686$	13032.0	0.725312
$687$	−4758.00	−0.264234
$688$	1408.00	0.0780225
$689$	−19992.0	−1.10542
$690$	4560.00	0.251589
$691$	−6868.00	−0.378106	−0.189053	−	0.981967i	$-0.560542\pi$
$691$	−6868.00	−0.378106	−0.189053	+	0.981967i	$0.560542\pi$
$692$	−9752.00	−0.535716
$693$	0	0
$694$	−12632.0	−0.690928
$695$	10780.0	0.588358
$696$	−672.000	−0.0365978
$697$	−940.000	−0.0510833
$698$	−15948.0	−0.864815
$699$	−15714.0	−0.850298
$700$	−1800.00	−0.0971909
$701$	−22026.0	−1.18675	−0.593374	−	0.804927i	$-0.702205\pi$
$701$	−22026.0	−1.18675	−0.593374	+	0.804927i	$0.702205\pi$
$702$	1512.00	0.0812917
$703$	24480.0	1.31334
$704$	0	0
$705$	−4440.00	−0.237192
$706$	22596.0	1.20455
$707$	16236.0	0.863674
$708$	−4680.00	−0.248425
$709$	−20698.0	−1.09637	−0.548187	−	0.836356i	$-0.684682\pi$
$709$	−20698.0	−1.09637	−0.548187	+	0.836356i	$0.684682\pi$
$710$	5740.00	0.303406
$711$	10440.0	0.550676
$712$	1696.00	0.0892701
$713$	−4712.00	−0.247498
$714$	−1080.00	−0.0566078
$715$	0	0
$716$	5504.00	0.287282
$717$	1908.00	0.0993801
$718$	−7812.00	−0.406046
$719$	−4520.00	−0.234447	−0.117224	−	0.993106i	$-0.537399\pi$
$719$	−4520.00	−0.234447	−0.117224	+	0.993106i	$0.537399\pi$
$720$	−720.000	−0.0372678
$721$	−17892.0	−0.924179
$722$	15082.0	0.777415
$723$	5742.00	0.295363
$724$	−8632.00	−0.443102
$725$	−700.000	−0.0358584
$726$	−7986.00	−0.408248
$727$	25062.0	1.27854	0.639270	−	0.768983i	$-0.279237\pi$
$727$	25062.0	1.27854	0.639270	+	0.768983i	$0.279237\pi$
$728$	−4032.00	−0.205269
$729$	729.000	0.0370370
$730$	10720.0	0.543514
$731$	880.000	0.0445253
$732$	−1608.00	−0.0811932
$733$	23898.0	1.20422	0.602110	−	0.798413i	$-0.294327\pi$
$733$	23898.0	1.20422	0.602110	+	0.798413i	$0.294327\pi$
$734$	2152.00	0.108218
$735$	285.000	0.0143026
$736$	−4864.00	−0.243600
$737$	0	0
$738$	−1692.00	−0.0843948
$739$	−2900.00	−0.144355	−0.0721774	−	0.997392i	$-0.522995\pi$
$739$	−2900.00	−0.144355	−0.0721774	+	0.997392i	$0.522995\pi$
$740$	4080.00	0.202681
$741$	−10080.0	−0.499727
$742$	25704.0	1.27173
$743$	24616.0	1.21544	0.607721	−	0.794151i	$-0.292084\pi$
$743$	24616.0	1.21544	0.607721	+	0.794151i	$0.292084\pi$
$744$	744.000	0.0366618
$745$	−12490.0	−0.614226
$746$	17676.0	0.867513
$747$	−108.000	−0.00528984
$748$	0	0
$749$	−21816.0	−1.06427
$750$	−750.000	−0.0365148
$751$	−17552.0	−0.852838	−0.426419	−	0.904526i	$-0.640225\pi$
$751$	−17552.0	−0.852838	−0.426419	+	0.904526i	$0.640225\pi$
$752$	4736.00	0.229660
$753$	12096.0	0.585395
$754$	−1568.00	−0.0757337
$755$	−8400.00	−0.404910
$756$	−1944.00	−0.0935220
$757$	−12340.0	−0.592477	−0.296238	−	0.955114i	$-0.595732\pi$
$757$	−12340.0	−0.592477	−0.296238	+	0.955114i	$0.595732\pi$
$758$	−3888.00	−0.186304
$759$	0	0
$760$	4800.00	0.229098
$761$	18720.0	0.891721	0.445860	−	0.895103i	$-0.352898\pi$
$761$	18720.0	0.891721	0.445860	+	0.895103i	$0.352898\pi$
$762$	4080.00	0.193967
$763$	10764.0	0.510725
$764$	12152.0	0.575450
$765$	−450.000	−0.0212677
$766$	−10128.0	−0.477728
$767$	−10920.0	−0.514079
$768$	768.000	0.0360844
$769$	−14610.0	−0.685111	−0.342555	−	0.939498i	$-0.611292\pi$
$769$	−14610.0	−0.685111	−0.342555	+	0.939498i	$0.611292\pi$
$770$	0	0
$771$	13038.0	0.609017
$772$	−4584.00	−0.213707
$773$	19774.0	0.920079	0.460040	−	0.887898i	$-0.347835\pi$
$773$	19774.0	0.920079	0.460040	+	0.887898i	$0.347835\pi$
$774$	1584.00	0.0735603
$775$	775.000	0.0359211
$776$	−1808.00	−0.0836384
$777$	11016.0	0.508619
$778$	29992.0	1.38209
$779$	11280.0	0.518804
$780$	−1680.00	−0.0771201
$781$	0	0
$782$	−3040.00	−0.139016
$783$	−756.000	−0.0345048
$784$	−304.000	−0.0138484
$785$	−10430.0	−0.474220
$786$	−1476.00	−0.0669811
$787$	15484.0	0.701328	0.350664	−	0.936501i	$-0.385956\pi$
$787$	15484.0	0.701328	0.350664	+	0.936501i	$0.385956\pi$
$788$	16200.0	0.732362
$789$	−11232.0	−0.506806
$790$	−11600.0	−0.522417
$791$	−7452.00	−0.334972
$792$	0	0
$793$	−3752.00	−0.168017
$794$	−16412.0	−0.733552
$795$	10710.0	0.477792
$796$	64.0000	0.00284977
$797$	10186.0	0.452706	0.226353	−	0.974045i	$-0.427320\pi$
$797$	10186.0	0.452706	0.226353	+	0.974045i	$0.427320\pi$
$798$	12960.0	0.574911
$799$	2960.00	0.131060
$800$	800.000	0.0353553
$801$	1908.00	0.0841646
$802$	27760.0	1.22224
$803$	0	0
$804$	−5304.00	−0.232659
$805$	−13680.0	−0.598952
$806$	1736.00	0.0758660
$807$	12036.0	0.525015
$808$	−7216.00	−0.314181
$809$	−17840.0	−0.775304	−0.387652	−	0.921806i	$-0.626714\pi$
$809$	−17840.0	−0.775304	−0.387652	+	0.921806i	$0.626714\pi$
$810$	−810.000	−0.0351364
$811$	−17280.0	−0.748191	−0.374095	−	0.927390i	$-0.622047\pi$
$811$	−17280.0	−0.748191	−0.374095	+	0.927390i	$0.622047\pi$
$812$	2016.00	0.0871277
$813$	11640.0	0.502131
$814$	0	0
$815$	890.000	0.0382520
$816$	480.000	0.0205924
$817$	−10560.0	−0.452200
$818$	−27284.0	−1.16621
$819$	−4536.00	−0.193530
$820$	1880.00	0.0800640
$821$	26588.0	1.13024	0.565120	−	0.825008i	$-0.308830\pi$
$821$	26588.0	1.13024	0.565120	+	0.825008i	$0.308830\pi$
$822$	6324.00	0.268339
$823$	−30456.0	−1.28995	−0.644975	−	0.764203i	$-0.723132\pi$
$823$	−30456.0	−1.28995	−0.644975	+	0.764203i	$0.723132\pi$
$824$	7952.00	0.336191
$825$	0	0
$826$	14040.0	0.591421
$827$	−2372.00	−0.0997370	−0.0498685	−	0.998756i	$-0.515880\pi$
$827$	−2372.00	−0.0997370	−0.0498685	+	0.998756i	$0.515880\pi$
$828$	−5472.00	−0.229668
$829$	−12854.0	−0.538526	−0.269263	−	0.963067i	$-0.586780\pi$
$829$	−12854.0	−0.538526	−0.269263	+	0.963067i	$0.586780\pi$
$830$	120.000	0.00501839
$831$	6408.00	0.267498
$832$	1792.00	0.0746712
$833$	−190.000	−0.00790289
$834$	−12936.0	−0.537095
$835$	5440.00	0.225460
$836$	0	0
$837$	837.000	0.0345651
$838$	26940.0	1.11053
$839$	−20274.0	−0.834251	−0.417125	−	0.908849i	$-0.636962\pi$
$839$	−20274.0	−0.834251	−0.417125	+	0.908849i	$0.636962\pi$
$840$	2160.00	0.0887227
$841$	−23605.0	−0.967854
$842$	−29852.0	−1.22181
$843$	−8814.00	−0.360107
$844$	−2752.00	−0.112237
$845$	7065.00	0.287625
$846$	5328.00	0.216525
$847$	23958.0	0.971909
$848$	−11424.0	−0.462620
$849$	10674.0	0.431485
$850$	500.000	0.0201763
$851$	31008.0	1.24905
$852$	−6888.00	−0.276971
$853$	−27062.0	−1.08627	−0.543133	−	0.839647i	$-0.682762\pi$
$853$	−27062.0	−1.08627	−0.543133	+	0.839647i	$0.682762\pi$
$854$	4824.00	0.193295
$855$	5400.00	0.215995
$856$	9696.00	0.387152
$857$	−19050.0	−0.759318	−0.379659	−	0.925126i	$-0.623959\pi$
$857$	−19050.0	−0.759318	−0.379659	+	0.925126i	$0.623959\pi$
$858$	0	0
$859$	−21580.0	−0.857160	−0.428580	−	0.903504i	$-0.640986\pi$
$859$	−21580.0	−0.857160	−0.428580	+	0.903504i	$0.640986\pi$
$860$	−1760.00	−0.0697855
$861$	5076.00	0.200917
$862$	−5924.00	−0.234075
$863$	−44488.0	−1.75480	−0.877398	−	0.479763i	$-0.840723\pi$
$863$	−44488.0	−1.75480	−0.877398	+	0.479763i	$0.840723\pi$
$864$	864.000	0.0340207
$865$	12190.0	0.479159
$866$	−896.000	−0.0351586
$867$	−14439.0	−0.565599
$868$	−2232.00	−0.0872800
$869$	0	0
$870$	840.000	0.0327341
$871$	−12376.0	−0.481452
$872$	−4784.00	−0.185787
$873$	−2034.00	−0.0788551
$874$	36480.0	1.41185
$875$	2250.00	0.0869302
$876$	−12864.0	−0.496158
$877$	−34382.0	−1.32383	−0.661914	−	0.749580i	$-0.730256\pi$
$877$	−34382.0	−1.32383	−0.661914	+	0.749580i	$0.730256\pi$
$878$	−35760.0	−1.37453
$879$	−4086.00	−0.156789
$880$	0	0
$881$	−25004.0	−0.956193	−0.478097	−	0.878307i	$-0.658673\pi$
$881$	−25004.0	−0.956193	−0.478097	+	0.878307i	$0.658673\pi$
$882$	−342.000	−0.0130564
$883$	3044.00	0.116012	0.0580061	−	0.998316i	$-0.481526\pi$
$883$	3044.00	0.116012	0.0580061	+	0.998316i	$0.481526\pi$
$884$	1120.00	0.0426128
$885$	5850.00	0.222198
$886$	−4512.00	−0.171088
$887$	−16004.0	−0.605819	−0.302910	−	0.953019i	$-0.597958\pi$
$887$	−16004.0	−0.605819	−0.302910	+	0.953019i	$0.597958\pi$
$888$	−4896.00	−0.185021
$889$	−12240.0	−0.461773
$890$	−2120.00	−0.0798456
$891$	0	0
$892$	9552.00	0.358548
$893$	−35520.0	−1.33105
$894$	14988.0	0.560709
$895$	−6880.00	−0.256953
$896$	−2304.00	−0.0859054
$897$	−12768.0	−0.475263
$898$	7808.00	0.290152
$899$	−868.000	−0.0322018
$900$	900.000	0.0333333
$901$	−7140.00	−0.264004
$902$	0	0
$903$	−4752.00	−0.175124
$904$	3312.00	0.121853
$905$	10790.0	0.396322
$906$	10080.0	0.369631
$907$	13538.0	0.495614	0.247807	−	0.968809i	$-0.420290\pi$
$907$	13538.0	0.495614	0.247807	+	0.968809i	$0.420290\pi$
$908$	−4800.00	−0.175433
$909$	−8118.00	−0.296212
$910$	5040.00	0.183598
$911$	−40952.0	−1.48935	−0.744676	−	0.667426i	$-0.767396\pi$
$911$	−40952.0	−1.48935	−0.744676	+	0.667426i	$0.767396\pi$
$912$	−5760.00	−0.209137
$913$	0	0
$914$	−14368.0	−0.519968
$915$	2010.00	0.0726214
$916$	−6344.00	−0.228834
$917$	4428.00	0.159461
$918$	540.000	0.0194147
$919$	39508.0	1.41812	0.709058	−	0.705150i	$-0.249120\pi$
$919$	39508.0	1.41812	0.709058	+	0.705150i	$0.249120\pi$
$920$	6080.00	0.217882
$921$	462.000	0.0165292
$922$	7872.00	0.281183
$923$	−16072.0	−0.573149
$924$	0	0
$925$	−5100.00	−0.181283
$926$	−26320.0	−0.934048
$927$	8946.00	0.316964
$928$	−896.000	−0.0316947
$929$	−55204.0	−1.94961	−0.974803	−	0.223066i	$-0.928393\pi$
$929$	−55204.0	−1.94961	−0.974803	+	0.223066i	$0.928393\pi$
$930$	−930.000	−0.0327913
$931$	2280.00	0.0802621
$932$	−20952.0	−0.736379
$933$	13626.0	0.478130
$934$	32040.0	1.12246
$935$	0	0
$936$	2016.00	0.0704007
$937$	−45058.0	−1.57095	−0.785475	−	0.618893i	$-0.787581\pi$
$937$	−45058.0	−1.57095	−0.785475	+	0.618893i	$0.787581\pi$
$938$	15912.0	0.553886
$939$	−8496.00	−0.295268
$940$	−5920.00	−0.205414
$941$	−38548.0	−1.33542	−0.667709	−	0.744422i	$-0.732725\pi$
$941$	−38548.0	−1.33542	−0.667709	+	0.744422i	$0.732725\pi$
$942$	12516.0	0.432902
$943$	14288.0	0.493405
$944$	−6240.00	−0.215143
$945$	2430.00	0.0836486
$946$	0	0
$947$	−27540.0	−0.945016	−0.472508	−	0.881326i	$-0.656651\pi$
$947$	−27540.0	−0.945016	−0.472508	+	0.881326i	$0.656651\pi$
$948$	13920.0	0.476899
$949$	−30016.0	−1.02672
$950$	−6000.00	−0.204911
$951$	−12126.0	−0.413473
$952$	−1440.00	−0.0490238
$953$	−18266.0	−0.620875	−0.310437	−	0.950594i	$-0.600476\pi$
$953$	−18266.0	−0.620875	−0.310437	+	0.950594i	$0.600476\pi$
$954$	−12852.0	−0.436162
$955$	−15190.0	−0.514698
$956$	2544.00	0.0860657
$957$	0	0
$958$	5892.00	0.198708
$959$	−18972.0	−0.638830
$960$	−960.000	−0.0322749
$961$	961.000	0.0322581
$962$	−11424.0	−0.382874
$963$	10908.0	0.365011
$964$	7656.00	0.255792
$965$	5730.00	0.191145
$966$	16416.0	0.546766
$967$	40620.0	1.35083	0.675414	−	0.737439i	$-0.263965\pi$
$967$	40620.0	1.35083	0.675414	+	0.737439i	$0.263965\pi$
$968$	−10648.0	−0.353553
$969$	−3600.00	−0.119348
$970$	2260.00	0.0748085
$971$	−27138.0	−0.896910	−0.448455	−	0.893805i	$-0.648026\pi$
$971$	−27138.0	−0.896910	−0.448455	+	0.893805i	$0.648026\pi$
$972$	972.000	0.0320750
$973$	38808.0	1.27865
$974$	25216.0	0.829541
$975$	2100.00	0.0689783
$976$	−2144.00	−0.0703153
$977$	−33386.0	−1.09326	−0.546629	−	0.837375i	$-0.684089\pi$
$977$	−33386.0	−1.09326	−0.546629	+	0.837375i	$0.684089\pi$
$978$	−1068.00	−0.0349191
$979$	0	0
$980$	380.000	0.0123864
$981$	−5382.00	−0.175162
$982$	−4840.00	−0.157282
$983$	11144.0	0.361585	0.180793	−	0.983521i	$-0.442134\pi$
$983$	11144.0	0.361585	0.180793	+	0.983521i	$0.442134\pi$
$984$	−2256.00	−0.0730881
$985$	−20250.0	−0.655044
$986$	−560.000	−0.0180873
$987$	−15984.0	−0.515478
$988$	−13440.0	−0.432777
$989$	−13376.0	−0.430063
$990$	0	0
$991$	27272.0	0.874191	0.437096	−	0.899415i	$-0.356007\pi$
$991$	27272.0	0.874191	0.437096	+	0.899415i	$0.356007\pi$
$992$	992.000	0.0317500
$993$	2988.00	0.0954897
$994$	20664.0	0.659379
$995$	−80.0000	−0.00254892
$996$	−144.000	−0.00458114
$997$	35814.0	1.13765	0.568827	−	0.822457i	$-0.307397\pi$
$997$	35814.0	1.13765	0.568827	+	0.822457i	$0.307397\pi$
$998$	−27112.0	−0.859935
$999$	−5508.00	−0.174440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.a.b.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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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