LMFDB - Embedded newform 714.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,4,Mod(1,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, 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("714.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	714.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:	$42.1273637441$
Analytic rank:	$0$
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	$\chi$	$=$	714.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -2.00000 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -2.00000 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -4.00000 q^{10} +28.0000 q^{11} -12.0000 q^{12} +30.0000 q^{13} -14.0000 q^{14} +6.00000 q^{15} +16.0000 q^{16} +17.0000 q^{17} +18.0000 q^{18} -56.0000 q^{19} -8.00000 q^{20} +21.0000 q^{21} +56.0000 q^{22} -80.0000 q^{23} -24.0000 q^{24} -121.000 q^{25} +60.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -126.000 q^{29} +12.0000 q^{30} +272.000 q^{31} +32.0000 q^{32} -84.0000 q^{33} +34.0000 q^{34} +14.0000 q^{35} +36.0000 q^{36} +134.000 q^{37} -112.000 q^{38} -90.0000 q^{39} -16.0000 q^{40} +402.000 q^{41} +42.0000 q^{42} +412.000 q^{43} +112.000 q^{44} -18.0000 q^{45} -160.000 q^{46} +272.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -242.000 q^{50} -51.0000 q^{51} +120.000 q^{52} +294.000 q^{53} -54.0000 q^{54} -56.0000 q^{55} -56.0000 q^{56} +168.000 q^{57} -252.000 q^{58} +100.000 q^{59} +24.0000 q^{60} +706.000 q^{61} +544.000 q^{62} -63.0000 q^{63} +64.0000 q^{64} -60.0000 q^{65} -168.000 q^{66} -244.000 q^{67} +68.0000 q^{68} +240.000 q^{69} +28.0000 q^{70} +304.000 q^{71} +72.0000 q^{72} +638.000 q^{73} +268.000 q^{74} +363.000 q^{75} -224.000 q^{76} -196.000 q^{77} -180.000 q^{78} -760.000 q^{79} -32.0000 q^{80} +81.0000 q^{81} +804.000 q^{82} -444.000 q^{83} +84.0000 q^{84} -34.0000 q^{85} +824.000 q^{86} +378.000 q^{87} +224.000 q^{88} +138.000 q^{89} -36.0000 q^{90} -210.000 q^{91} -320.000 q^{92} -816.000 q^{93} +544.000 q^{94} +112.000 q^{95} -96.0000 q^{96} +1150.00 q^{97} +98.0000 q^{98} +252.000 q^{99} +O(q^{100})\)

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
$5$	−2.00000	−0.178885	−0.0894427	−	0.995992i	$-0.528509\pi$
$5$	−2.00000	−0.178885	−0.0894427	+	0.995992i	$0.528509\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−4.00000	−0.126491
$11$	28.0000	0.767483	0.383742	−	0.923440i	$-0.374635\pi$
$11$	28.0000	0.767483	0.383742	+	0.923440i	$0.374635\pi$
$12$	−12.0000	−0.288675
$13$	30.0000	0.640039	0.320019	−	0.947411i	$-0.396311\pi$
$13$	30.0000	0.640039	0.320019	+	0.947411i	$0.396311\pi$
$14$	−14.0000	−0.267261
$15$	6.00000	0.103280
$16$	16.0000	0.250000
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	18.0000	0.235702
$19$	−56.0000	−0.676173	−0.338086	−	0.941115i	$-0.609780\pi$
$19$	−56.0000	−0.676173	−0.338086	+	0.941115i	$0.609780\pi$
$20$	−8.00000	−0.0894427
$21$	21.0000	0.218218
$22$	56.0000	0.542693
$23$	−80.0000	−0.725268	−0.362634	−	0.931932i	$-0.618122\pi$
$23$	−80.0000	−0.725268	−0.362634	+	0.931932i	$0.618122\pi$
$24$	−24.0000	−0.204124
$25$	−121.000	−0.968000
$26$	60.0000	0.452576
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−126.000	−0.806814	−0.403407	−	0.915021i	$-0.632174\pi$
$29$	−126.000	−0.806814	−0.403407	+	0.915021i	$0.632174\pi$
$30$	12.0000	0.0730297
$31$	272.000	1.57589	0.787946	−	0.615745i	$-0.211145\pi$
$31$	272.000	1.57589	0.787946	+	0.615745i	$0.211145\pi$
$32$	32.0000	0.176777
$33$	−84.0000	−0.443107
$34$	34.0000	0.171499
$35$	14.0000	0.0676123
$36$	36.0000	0.166667
$37$	134.000	0.595391	0.297695	−	0.954661i	$-0.403782\pi$
$37$	134.000	0.595391	0.297695	+	0.954661i	$0.403782\pi$
$38$	−112.000	−0.478126
$39$	−90.0000	−0.369527
$40$	−16.0000	−0.0632456
$41$	402.000	1.53126	0.765632	−	0.643278i	$-0.222426\pi$
$41$	402.000	1.53126	0.765632	+	0.643278i	$0.222426\pi$
$42$	42.0000	0.154303
$43$	412.000	1.46115	0.730575	−	0.682833i	$-0.239252\pi$
$43$	412.000	1.46115	0.730575	+	0.682833i	$0.239252\pi$
$44$	112.000	0.383742
$45$	−18.0000	−0.0596285
$46$	−160.000	−0.512842
$47$	272.000	0.844155	0.422077	−	0.906560i	$-0.361301\pi$
$47$	272.000	0.844155	0.422077	+	0.906560i	$0.361301\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−242.000	−0.684479
$51$	−51.0000	−0.140028
$52$	120.000	0.320019
$53$	294.000	0.761962	0.380981	−	0.924583i	$-0.375586\pi$
$53$	294.000	0.761962	0.380981	+	0.924583i	$0.375586\pi$
$54$	−54.0000	−0.136083
$55$	−56.0000	−0.137292
$56$	−56.0000	−0.133631
$57$	168.000	0.390388
$58$	−252.000	−0.570504
$59$	100.000	0.220659	0.110330	−	0.993895i	$-0.464809\pi$
$59$	100.000	0.220659	0.110330	+	0.993895i	$0.464809\pi$
$60$	24.0000	0.0516398
$61$	706.000	1.48187	0.740935	−	0.671577i	$-0.234383\pi$
$61$	706.000	1.48187	0.740935	+	0.671577i	$0.234383\pi$
$62$	544.000	1.11432
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−60.0000	−0.114494
$66$	−168.000	−0.313324
$67$	−244.000	−0.444916	−0.222458	−	0.974942i	$-0.571408\pi$
$67$	−244.000	−0.444916	−0.222458	+	0.974942i	$0.571408\pi$
$68$	68.0000	0.121268
$69$	240.000	0.418733
$70$	28.0000	0.0478091
$71$	304.000	0.508143	0.254072	−	0.967185i	$-0.418230\pi$
$71$	304.000	0.508143	0.254072	+	0.967185i	$0.418230\pi$
$72$	72.0000	0.117851
$73$	638.000	1.02291	0.511454	−	0.859311i	$-0.329107\pi$
$73$	638.000	1.02291	0.511454	+	0.859311i	$0.329107\pi$
$74$	268.000	0.421005
$75$	363.000	0.558875
$76$	−224.000	−0.338086
$77$	−196.000	−0.290081
$78$	−180.000	−0.261295
$79$	−760.000	−1.08236	−0.541182	−	0.840906i	$-0.682023\pi$
$79$	−760.000	−1.08236	−0.541182	+	0.840906i	$0.682023\pi$
$80$	−32.0000	−0.0447214
$81$	81.0000	0.111111
$82$	804.000	1.08277
$83$	−444.000	−0.587173	−0.293586	−	0.955933i	$-0.594849\pi$
$83$	−444.000	−0.587173	−0.293586	+	0.955933i	$0.594849\pi$
$84$	84.0000	0.109109
$85$	−34.0000	−0.0433861
$86$	824.000	1.03319
$87$	378.000	0.465814
$88$	224.000	0.271346
$89$	138.000	0.164359	0.0821796	−	0.996618i	$-0.473812\pi$
$89$	138.000	0.164359	0.0821796	+	0.996618i	$0.473812\pi$
$90$	−36.0000	−0.0421637
$91$	−210.000	−0.241912
$92$	−320.000	−0.362634
$93$	−816.000	−0.909841
$94$	544.000	0.596908
$95$	112.000	0.120957
$96$	−96.0000	−0.102062
$97$	1150.00	1.20376	0.601880	−	0.798586i	$-0.294418\pi$
$97$	1150.00	1.20376	0.601880	+	0.798586i	$0.294418\pi$
$98$	98.0000	0.101015
$99$	252.000	0.255828
$100$	−484.000	−0.484000
$101$	910.000	0.896519	0.448259	−	0.893904i	$-0.352044\pi$
$101$	910.000	0.896519	0.448259	+	0.893904i	$0.352044\pi$
$102$	−102.000	−0.0990148
$103$	−772.000	−0.738519	−0.369259	−	0.929326i	$-0.620389\pi$
$103$	−772.000	−0.738519	−0.369259	+	0.929326i	$0.620389\pi$
$104$	240.000	0.226288
$105$	−42.0000	−0.0390360
$106$	588.000	0.538789
$107$	708.000	0.639672	0.319836	−	0.947473i	$-0.396372\pi$
$107$	708.000	0.639672	0.319836	+	0.947473i	$0.396372\pi$
$108$	−108.000	−0.0962250
$109$	−490.000	−0.430582	−0.215291	−	0.976550i	$-0.569070\pi$
$109$	−490.000	−0.430582	−0.215291	+	0.976550i	$0.569070\pi$
$110$	−112.000	−0.0970798
$111$	−402.000	−0.343749
$112$	−112.000	−0.0944911
$113$	−626.000	−0.521143	−0.260571	−	0.965455i	$-0.583911\pi$
$113$	−626.000	−0.521143	−0.260571	+	0.965455i	$0.583911\pi$
$114$	336.000	0.276046
$115$	160.000	0.129740
$116$	−504.000	−0.403407
$117$	270.000	0.213346
$118$	200.000	0.156030
$119$	−119.000	−0.0916698
$120$	48.0000	0.0365148
$121$	−547.000	−0.410969
$122$	1412.00	1.04784
$123$	−1206.00	−0.884076
$124$	1088.00	0.787946
$125$	492.000	0.352047
$126$	−126.000	−0.0890871
$127$	−216.000	−0.150920	−0.0754602	−	0.997149i	$-0.524043\pi$
$127$	−216.000	−0.150920	−0.0754602	+	0.997149i	$0.524043\pi$
$128$	128.000	0.0883883
$129$	−1236.00	−0.843595
$130$	−120.000	−0.0809592
$131$	2124.00	1.41660	0.708301	−	0.705911i	$-0.249462\pi$
$131$	2124.00	1.41660	0.708301	+	0.705911i	$0.249462\pi$
$132$	−336.000	−0.221553
$133$	392.000	0.255569
$134$	−488.000	−0.314603
$135$	54.0000	0.0344265
$136$	136.000	0.0857493
$137$	1394.00	0.869325	0.434662	−	0.900594i	$-0.356868\pi$
$137$	1394.00	0.869325	0.434662	+	0.900594i	$0.356868\pi$
$138$	480.000	0.296089
$139$	−564.000	−0.344157	−0.172079	−	0.985083i	$-0.555048\pi$
$139$	−564.000	−0.344157	−0.172079	+	0.985083i	$0.555048\pi$
$140$	56.0000	0.0338062
$141$	−816.000	−0.487373
$142$	608.000	0.359311
$143$	840.000	0.491219
$144$	144.000	0.0833333
$145$	252.000	0.144327
$146$	1276.00	0.723305
$147$	−147.000	−0.0824786
$148$	536.000	0.297695
$149$	1294.00	0.711467	0.355734	−	0.934587i	$-0.384231\pi$
$149$	1294.00	0.711467	0.355734	+	0.934587i	$0.384231\pi$
$150$	726.000	0.395184
$151$	3008.00	1.62111	0.810555	−	0.585663i	$-0.199166\pi$
$151$	3008.00	1.62111	0.810555	+	0.585663i	$0.199166\pi$
$152$	−448.000	−0.239063
$153$	153.000	0.0808452
$154$	−392.000	−0.205119
$155$	−544.000	−0.281904
$156$	−360.000	−0.184763
$157$	−3610.00	−1.83509	−0.917546	−	0.397630i	$-0.869833\pi$
$157$	−3610.00	−1.83509	−0.917546	+	0.397630i	$0.869833\pi$
$158$	−1520.00	−0.765346
$159$	−882.000	−0.439919
$160$	−64.0000	−0.0316228
$161$	560.000	0.274125
$162$	162.000	0.0785674
$163$	1188.00	0.570867	0.285434	−	0.958398i	$-0.407862\pi$
$163$	1188.00	0.570867	0.285434	+	0.958398i	$0.407862\pi$
$164$	1608.00	0.765632
$165$	168.000	0.0792653
$166$	−888.000	−0.415194
$167$	−1912.00	−0.885958	−0.442979	−	0.896532i	$-0.646078\pi$
$167$	−1912.00	−0.885958	−0.442979	+	0.896532i	$0.646078\pi$
$168$	168.000	0.0771517
$169$	−1297.00	−0.590350
$170$	−68.0000	−0.0306786
$171$	−504.000	−0.225391
$172$	1648.00	0.730575
$173$	−258.000	−0.113384	−0.0566918	−	0.998392i	$-0.518055\pi$
$173$	−258.000	−0.113384	−0.0566918	+	0.998392i	$0.518055\pi$
$174$	756.000	0.329381
$175$	847.000	0.365870
$176$	448.000	0.191871
$177$	−300.000	−0.127398
$178$	276.000	0.116220
$179$	−1640.00	−0.684801	−0.342400	−	0.939554i	$-0.611240\pi$
$179$	−1640.00	−0.684801	−0.342400	+	0.939554i	$0.611240\pi$
$180$	−72.0000	−0.0298142
$181$	1050.00	0.431193	0.215596	−	0.976483i	$-0.430830\pi$
$181$	1050.00	0.431193	0.215596	+	0.976483i	$0.430830\pi$
$182$	−420.000	−0.171058
$183$	−2118.00	−0.855558
$184$	−640.000	−0.256421
$185$	−268.000	−0.106507
$186$	−1632.00	−0.643355
$187$	476.000	0.186142
$188$	1088.00	0.422077
$189$	189.000	0.0727393
$190$	224.000	0.0855298
$191$	−3612.00	−1.36835	−0.684176	−	0.729317i	$-0.739838\pi$
$191$	−3612.00	−1.36835	−0.684176	+	0.729317i	$0.739838\pi$
$192$	−192.000	−0.0721688
$193$	530.000	0.197670	0.0988348	−	0.995104i	$-0.468488\pi$
$193$	530.000	0.197670	0.0988348	+	0.995104i	$0.468488\pi$
$194$	2300.00	0.851188
$195$	180.000	0.0661029
$196$	196.000	0.0714286
$197$	1594.00	0.576486	0.288243	−	0.957557i	$-0.406929\pi$
$197$	1594.00	0.576486	0.288243	+	0.957557i	$0.406929\pi$
$198$	504.000	0.180898
$199$	3360.00	1.19690	0.598452	−	0.801158i	$-0.295783\pi$
$199$	3360.00	1.19690	0.598452	+	0.801158i	$0.295783\pi$
$200$	−968.000	−0.342240
$201$	732.000	0.256872
$202$	1820.00	0.633934
$203$	882.000	0.304947
$204$	−204.000	−0.0700140
$205$	−804.000	−0.273921
$206$	−1544.00	−0.522212
$207$	−720.000	−0.241756
$208$	480.000	0.160010
$209$	−1568.00	−0.518951
$210$	−84.0000	−0.0276026
$211$	−3028.00	−0.987944	−0.493972	−	0.869478i	$-0.664455\pi$
$211$	−3028.00	−0.987944	−0.493972	+	0.869478i	$0.664455\pi$
$212$	1176.00	0.380981
$213$	−912.000	−0.293377
$214$	1416.00	0.452317
$215$	−824.000	−0.261378
$216$	−216.000	−0.0680414
$217$	−1904.00	−0.595631
$218$	−980.000	−0.304468
$219$	−1914.00	−0.590576
$220$	−224.000	−0.0686458
$221$	510.000	0.155232
$222$	−804.000	−0.243067
$223$	−3828.00	−1.14951	−0.574757	−	0.818324i	$-0.694904\pi$
$223$	−3828.00	−1.14951	−0.574757	+	0.818324i	$0.694904\pi$
$224$	−224.000	−0.0668153
$225$	−1089.00	−0.322667
$226$	−1252.00	−0.368504
$227$	−1764.00	−0.515774	−0.257887	−	0.966175i	$-0.583026\pi$
$227$	−1764.00	−0.515774	−0.257887	+	0.966175i	$0.583026\pi$
$228$	672.000	0.195194
$229$	−1666.00	−0.480753	−0.240376	−	0.970680i	$-0.577271\pi$
$229$	−1666.00	−0.480753	−0.240376	+	0.970680i	$0.577271\pi$
$230$	320.000	0.0917399
$231$	588.000	0.167479
$232$	−1008.00	−0.285252
$233$	−2378.00	−0.668618	−0.334309	−	0.942464i	$-0.608503\pi$
$233$	−2378.00	−0.668618	−0.334309	+	0.942464i	$0.608503\pi$
$234$	540.000	0.150859
$235$	−544.000	−0.151007
$236$	400.000	0.110330
$237$	2280.00	0.624903
$238$	−238.000	−0.0648204
$239$	−1732.00	−0.468761	−0.234380	−	0.972145i	$-0.575306\pi$
$239$	−1732.00	−0.468761	−0.234380	+	0.972145i	$0.575306\pi$
$240$	96.0000	0.0258199
$241$	−546.000	−0.145938	−0.0729688	−	0.997334i	$-0.523247\pi$
$241$	−546.000	−0.145938	−0.0729688	+	0.997334i	$0.523247\pi$
$242$	−1094.00	−0.290599
$243$	−243.000	−0.0641500
$244$	2824.00	0.740935
$245$	−98.0000	−0.0255551
$246$	−2412.00	−0.625136
$247$	−1680.00	−0.432777
$248$	2176.00	0.557162
$249$	1332.00	0.339004
$250$	984.000	0.248934
$251$	−4036.00	−1.01494	−0.507470	−	0.861669i	$-0.669419\pi$
$251$	−4036.00	−1.01494	−0.507470	+	0.861669i	$0.669419\pi$
$252$	−252.000	−0.0629941
$253$	−2240.00	−0.556631
$254$	−432.000	−0.106717
$255$	102.000	0.0250490
$256$	256.000	0.0625000
$257$	2546.00	0.617958	0.308979	−	0.951069i	$-0.400013\pi$
$257$	2546.00	0.617958	0.308979	+	0.951069i	$0.400013\pi$
$258$	−2472.00	−0.596512
$259$	−938.000	−0.225037
$260$	−240.000	−0.0572468
$261$	−1134.00	−0.268938
$262$	4248.00	1.00169
$263$	588.000	0.137862	0.0689309	−	0.997621i	$-0.478041\pi$
$263$	588.000	0.137862	0.0689309	+	0.997621i	$0.478041\pi$
$264$	−672.000	−0.156662
$265$	−588.000	−0.136304
$266$	784.000	0.180715
$267$	−414.000	−0.0948928
$268$	−976.000	−0.222458
$269$	7126.00	1.61517	0.807583	−	0.589753i	$-0.200775\pi$
$269$	7126.00	1.61517	0.807583	+	0.589753i	$0.200775\pi$
$270$	108.000	0.0243432
$271$	−7036.00	−1.57715	−0.788573	−	0.614941i	$-0.789180\pi$
$271$	−7036.00	−1.57715	−0.788573	+	0.614941i	$0.789180\pi$
$272$	272.000	0.0606339
$273$	630.000	0.139668
$274$	2788.00	0.614705
$275$	−3388.00	−0.742924
$276$	960.000	0.209367
$277$	−7834.00	−1.69928	−0.849638	−	0.527366i	$-0.823180\pi$
$277$	−7834.00	−1.69928	−0.849638	+	0.527366i	$0.823180\pi$
$278$	−1128.00	−0.243356
$279$	2448.00	0.525297
$280$	112.000	0.0239046
$281$	−174.000	−0.0369394	−0.0184697	−	0.999829i	$-0.505879\pi$
$281$	−174.000	−0.0369394	−0.0184697	+	0.999829i	$0.505879\pi$
$282$	−1632.00	−0.344625
$283$	5260.00	1.10486	0.552429	−	0.833560i	$-0.313701\pi$
$283$	5260.00	1.10486	0.552429	+	0.833560i	$0.313701\pi$
$284$	1216.00	0.254072
$285$	−336.000	−0.0698348
$286$	1680.00	0.347344
$287$	−2814.00	−0.578764
$288$	288.000	0.0589256
$289$	289.000	0.0588235
$290$	504.000	0.102055
$291$	−3450.00	−0.694992
$292$	2552.00	0.511454
$293$	7582.00	1.51176	0.755879	−	0.654711i	$-0.227210\pi$
$293$	7582.00	1.51176	0.755879	+	0.654711i	$0.227210\pi$
$294$	−294.000	−0.0583212
$295$	−200.000	−0.0394727
$296$	1072.00	0.210502
$297$	−756.000	−0.147702
$298$	2588.00	0.503083
$299$	−2400.00	−0.464199
$300$	1452.00	0.279438
$301$	−2884.00	−0.552262
$302$	6016.00	1.14630
$303$	−2730.00	−0.517605
$304$	−896.000	−0.169043
$305$	−1412.00	−0.265085
$306$	306.000	0.0571662
$307$	−7520.00	−1.39801	−0.699005	−	0.715117i	$-0.746373\pi$
$307$	−7520.00	−1.39801	−0.699005	+	0.715117i	$0.746373\pi$
$308$	−784.000	−0.145041
$309$	2316.00	0.426384
$310$	−1088.00	−0.199336
$311$	3912.00	0.713277	0.356639	−	0.934242i	$-0.383923\pi$
$311$	3912.00	0.713277	0.356639	+	0.934242i	$0.383923\pi$
$312$	−720.000	−0.130647
$313$	3054.00	0.551509	0.275754	−	0.961228i	$-0.411072\pi$
$313$	3054.00	0.551509	0.275754	+	0.961228i	$0.411072\pi$
$314$	−7220.00	−1.29761
$315$	126.000	0.0225374
$316$	−3040.00	−0.541182
$317$	1026.00	0.181785	0.0908926	−	0.995861i	$-0.471028\pi$
$317$	1026.00	0.181785	0.0908926	+	0.995861i	$0.471028\pi$
$318$	−1764.00	−0.311070
$319$	−3528.00	−0.619217
$320$	−128.000	−0.0223607
$321$	−2124.00	−0.369315
$322$	1120.00	0.193836
$323$	−952.000	−0.163996
$324$	324.000	0.0555556
$325$	−3630.00	−0.619557
$326$	2376.00	0.403664
$327$	1470.00	0.248597
$328$	3216.00	0.541384
$329$	−1904.00	−0.319061
$330$	336.000	0.0560491
$331$	5380.00	0.893388	0.446694	−	0.894687i	$-0.352601\pi$
$331$	5380.00	0.893388	0.446694	+	0.894687i	$0.352601\pi$
$332$	−1776.00	−0.293586
$333$	1206.00	0.198464
$334$	−3824.00	−0.626467
$335$	488.000	0.0795889
$336$	336.000	0.0545545
$337$	4690.00	0.758103	0.379051	−	0.925376i	$-0.376250\pi$
$337$	4690.00	0.758103	0.379051	+	0.925376i	$0.376250\pi$
$338$	−2594.00	−0.417441
$339$	1878.00	0.300882
$340$	−136.000	−0.0216930
$341$	7616.00	1.20947
$342$	−1008.00	−0.159375
$343$	−343.000	−0.0539949
$344$	3296.00	0.516594
$345$	−480.000	−0.0749053
$346$	−516.000	−0.0801744
$347$	3980.00	0.615728	0.307864	−	0.951430i	$-0.400386\pi$
$347$	3980.00	0.615728	0.307864	+	0.951430i	$0.400386\pi$
$348$	1512.00	0.232907
$349$	1566.00	0.240189	0.120095	−	0.992762i	$-0.461680\pi$
$349$	1566.00	0.240189	0.120095	+	0.992762i	$0.461680\pi$
$350$	1694.00	0.258709
$351$	−810.000	−0.123176
$352$	896.000	0.135673
$353$	7970.00	1.20170	0.600850	−	0.799362i	$-0.294829\pi$
$353$	7970.00	1.20170	0.600850	+	0.799362i	$0.294829\pi$
$354$	−600.000	−0.0900837
$355$	−608.000	−0.0908994
$356$	552.000	0.0821796
$357$	357.000	0.0529256
$358$	−3280.00	−0.484227
$359$	9980.00	1.46720	0.733599	−	0.679582i	$-0.237839\pi$
$359$	9980.00	1.46720	0.733599	+	0.679582i	$0.237839\pi$
$360$	−144.000	−0.0210819
$361$	−3723.00	−0.542790
$362$	2100.00	0.304899
$363$	1641.00	0.237273
$364$	−840.000	−0.120956
$365$	−1276.00	−0.182983
$366$	−4236.00	−0.604971
$367$	−12528.0	−1.78190	−0.890949	−	0.454104i	$-0.849959\pi$
$367$	−12528.0	−1.78190	−0.890949	+	0.454104i	$0.849959\pi$
$368$	−1280.00	−0.181317
$369$	3618.00	0.510422
$370$	−536.000	−0.0753117
$371$	−2058.00	−0.287995
$372$	−3264.00	−0.454921
$373$	−338.000	−0.0469195	−0.0234598	−	0.999725i	$-0.507468\pi$
$373$	−338.000	−0.0469195	−0.0234598	+	0.999725i	$0.507468\pi$
$374$	952.000	0.131622
$375$	−1476.00	−0.203254
$376$	2176.00	0.298454
$377$	−3780.00	−0.516392
$378$	378.000	0.0514344
$379$	−8924.00	−1.20949	−0.604743	−	0.796421i	$-0.706724\pi$
$379$	−8924.00	−1.20949	−0.604743	+	0.796421i	$0.706724\pi$
$380$	448.000	0.0604787
$381$	648.000	0.0871340
$382$	−7224.00	−0.967571
$383$	−872.000	−0.116337	−0.0581686	−	0.998307i	$-0.518526\pi$
$383$	−872.000	−0.116337	−0.0581686	+	0.998307i	$0.518526\pi$
$384$	−384.000	−0.0510310
$385$	392.000	0.0518914
$386$	1060.00	0.139774
$387$	3708.00	0.487050
$388$	4600.00	0.601880
$389$	6846.00	0.892303	0.446152	−	0.894957i	$-0.352794\pi$
$389$	6846.00	0.892303	0.446152	+	0.894957i	$0.352794\pi$
$390$	360.000	0.0467418
$391$	−1360.00	−0.175903
$392$	392.000	0.0505076
$393$	−6372.00	−0.817875
$394$	3188.00	0.407637
$395$	1520.00	0.193619
$396$	1008.00	0.127914
$397$	−2710.00	−0.342597	−0.171298	−	0.985219i	$-0.554796\pi$
$397$	−2710.00	−0.342597	−0.171298	+	0.985219i	$0.554796\pi$
$398$	6720.00	0.846340
$399$	−1176.00	−0.147553
$400$	−1936.00	−0.242000
$401$	−7538.00	−0.938728	−0.469364	−	0.883005i	$-0.655517\pi$
$401$	−7538.00	−0.938728	−0.469364	+	0.883005i	$0.655517\pi$
$402$	1464.00	0.181636
$403$	8160.00	1.00863
$404$	3640.00	0.448259
$405$	−162.000	−0.0198762
$406$	1764.00	0.215630
$407$	3752.00	0.456953
$408$	−408.000	−0.0495074
$409$	3914.00	0.473190	0.236595	−	0.971608i	$-0.423968\pi$
$409$	3914.00	0.473190	0.236595	+	0.971608i	$0.423968\pi$
$410$	−1608.00	−0.193691
$411$	−4182.00	−0.501905
$412$	−3088.00	−0.369259
$413$	−700.000	−0.0834013
$414$	−1440.00	−0.170947
$415$	888.000	0.105037
$416$	960.000	0.113144
$417$	1692.00	0.198699
$418$	−3136.00	−0.366954
$419$	14028.0	1.63559	0.817796	−	0.575509i	$-0.195196\pi$
$419$	14028.0	1.63559	0.817796	+	0.575509i	$0.195196\pi$
$420$	−168.000	−0.0195180
$421$	−1554.00	−0.179899	−0.0899493	−	0.995946i	$-0.528671\pi$
$421$	−1554.00	−0.179899	−0.0899493	+	0.995946i	$0.528671\pi$
$422$	−6056.00	−0.698582
$423$	2448.00	0.281385
$424$	2352.00	0.269394
$425$	−2057.00	−0.234774
$426$	−1824.00	−0.207449
$427$	−4942.00	−0.560094
$428$	2832.00	0.319836
$429$	−2520.00	−0.283605
$430$	−1648.00	−0.184822
$431$	13568.0	1.51635	0.758176	−	0.652050i	$-0.226091\pi$
$431$	13568.0	1.51635	0.758176	+	0.652050i	$0.226091\pi$
$432$	−432.000	−0.0481125
$433$	−11070.0	−1.22861	−0.614307	−	0.789067i	$-0.710565\pi$
$433$	−11070.0	−1.22861	−0.614307	+	0.789067i	$0.710565\pi$
$434$	−3808.00	−0.421175
$435$	−756.000	−0.0833274
$436$	−1960.00	−0.215291
$437$	4480.00	0.490406
$438$	−3828.00	−0.417600
$439$	−9704.00	−1.05500	−0.527502	−	0.849554i	$-0.676871\pi$
$439$	−9704.00	−1.05500	−0.527502	+	0.849554i	$0.676871\pi$
$440$	−448.000	−0.0485399
$441$	441.000	0.0476190
$442$	1020.00	0.109766
$443$	−17616.0	−1.88930	−0.944652	−	0.328075i	$-0.893600\pi$
$443$	−17616.0	−1.88930	−0.944652	+	0.328075i	$0.893600\pi$
$444$	−1608.00	−0.171875
$445$	−276.000	−0.0294015
$446$	−7656.00	−0.812830
$447$	−3882.00	−0.410766
$448$	−448.000	−0.0472456
$449$	−9306.00	−0.978123	−0.489062	−	0.872249i	$-0.662661\pi$
$449$	−9306.00	−0.978123	−0.489062	+	0.872249i	$0.662661\pi$
$450$	−2178.00	−0.228160
$451$	11256.0	1.17522
$452$	−2504.00	−0.260571
$453$	−9024.00	−0.935948
$454$	−3528.00	−0.364708
$455$	420.000	0.0432745
$456$	1344.00	0.138023
$457$	−6070.00	−0.621319	−0.310659	−	0.950521i	$-0.600550\pi$
$457$	−6070.00	−0.621319	−0.310659	+	0.950521i	$0.600550\pi$
$458$	−3332.00	−0.339944
$459$	−459.000	−0.0466760
$460$	640.000	0.0648699
$461$	12550.0	1.26792	0.633961	−	0.773365i	$-0.281428\pi$
$461$	12550.0	1.26792	0.633961	+	0.773365i	$0.281428\pi$
$462$	1176.00	0.118425
$463$	−16288.0	−1.63492	−0.817460	−	0.575986i	$-0.804618\pi$
$463$	−16288.0	−1.63492	−0.817460	+	0.575986i	$0.804618\pi$
$464$	−2016.00	−0.201704
$465$	1632.00	0.162757
$466$	−4756.00	−0.472784
$467$	−6444.00	−0.638528	−0.319264	−	0.947666i	$-0.603436\pi$
$467$	−6444.00	−0.638528	−0.319264	+	0.947666i	$0.603436\pi$
$468$	1080.00	0.106673
$469$	1708.00	0.168162
$470$	−1088.00	−0.106778
$471$	10830.0	1.05949
$472$	800.000	0.0780148
$473$	11536.0	1.12141
$474$	4560.00	0.441873
$475$	6776.00	0.654535
$476$	−476.000	−0.0458349
$477$	2646.00	0.253987
$478$	−3464.00	−0.331464
$479$	8760.00	0.835605	0.417802	−	0.908538i	$-0.362800\pi$
$479$	8760.00	0.835605	0.417802	+	0.908538i	$0.362800\pi$
$480$	192.000	0.0182574
$481$	4020.00	0.381073
$482$	−1092.00	−0.103193
$483$	−1680.00	−0.158266
$484$	−2188.00	−0.205485
$485$	−2300.00	−0.215335
$486$	−486.000	−0.0453609
$487$	17984.0	1.67337	0.836687	−	0.547682i	$-0.184490\pi$
$487$	17984.0	1.67337	0.836687	+	0.547682i	$0.184490\pi$
$488$	5648.00	0.523920
$489$	−3564.00	−0.329590
$490$	−196.000	−0.0180702
$491$	−17072.0	−1.56914	−0.784571	−	0.620039i	$-0.787117\pi$
$491$	−17072.0	−1.56914	−0.784571	+	0.620039i	$0.787117\pi$
$492$	−4824.00	−0.442038
$493$	−2142.00	−0.195681
$494$	−3360.00	−0.306019
$495$	−504.000	−0.0457639
$496$	4352.00	0.393973
$497$	−2128.00	−0.192060
$498$	2664.00	0.239712
$499$	−11276.0	−1.01159	−0.505795	−	0.862654i	$-0.668801\pi$
$499$	−11276.0	−1.01159	−0.505795	+	0.862654i	$0.668801\pi$
$500$	1968.00	0.176023
$501$	5736.00	0.511508
$502$	−8072.00	−0.717671
$503$	−8592.00	−0.761627	−0.380813	−	0.924652i	$-0.624356\pi$
$503$	−8592.00	−0.761627	−0.380813	+	0.924652i	$0.624356\pi$
$504$	−504.000	−0.0445435
$505$	−1820.00	−0.160374
$506$	−4480.00	−0.393597
$507$	3891.00	0.340839
$508$	−864.000	−0.0754602
$509$	−730.000	−0.0635691	−0.0317846	−	0.999495i	$-0.510119\pi$
$509$	−730.000	−0.0635691	−0.0317846	+	0.999495i	$0.510119\pi$
$510$	204.000	0.0177123
$511$	−4466.00	−0.386623
$512$	512.000	0.0441942
$513$	1512.00	0.130129
$514$	5092.00	0.436962
$515$	1544.00	0.132110
$516$	−4944.00	−0.421797
$517$	7616.00	0.647875
$518$	−1876.00	−0.159125
$519$	774.000	0.0654621
$520$	−480.000	−0.0404796
$521$	16314.0	1.37184	0.685921	−	0.727676i	$-0.259400\pi$
$521$	16314.0	1.37184	0.685921	+	0.727676i	$0.259400\pi$
$522$	−2268.00	−0.190168
$523$	−7208.00	−0.602646	−0.301323	−	0.953522i	$-0.597428\pi$
$523$	−7208.00	−0.602646	−0.301323	+	0.953522i	$0.597428\pi$
$524$	8496.00	0.708301
$525$	−2541.00	−0.211235
$526$	1176.00	0.0974830
$527$	4624.00	0.382210
$528$	−1344.00	−0.110777
$529$	−5767.00	−0.473987
$530$	−1176.00	−0.0963815
$531$	900.000	0.0735531
$532$	1568.00	0.127785
$533$	12060.0	0.980069
$534$	−828.000	−0.0670994
$535$	−1416.00	−0.114428
$536$	−1952.00	−0.157301
$537$	4920.00	0.395370
$538$	14252.0	1.14210
$539$	1372.00	0.109640
$540$	216.000	0.0172133
$541$	−194.000	−0.0154172	−0.00770861	−	0.999970i	$-0.502454\pi$
$541$	−194.000	−0.0154172	−0.00770861	+	0.999970i	$0.502454\pi$
$542$	−14072.0	−1.11521
$543$	−3150.00	−0.248949
$544$	544.000	0.0428746
$545$	980.000	0.0770249
$546$	1260.00	0.0987601
$547$	−18052.0	−1.41106	−0.705528	−	0.708682i	$-0.749290\pi$
$547$	−18052.0	−1.41106	−0.705528	+	0.708682i	$0.749290\pi$
$548$	5576.00	0.434662
$549$	6354.00	0.493956
$550$	−6776.00	−0.525327
$551$	7056.00	0.545546
$552$	1920.00	0.148045
$553$	5320.00	0.409095
$554$	−15668.0	−1.20157
$555$	804.000	0.0614917
$556$	−2256.00	−0.172079
$557$	3918.00	0.298045	0.149022	−	0.988834i	$-0.452387\pi$
$557$	3918.00	0.298045	0.149022	+	0.988834i	$0.452387\pi$
$558$	4896.00	0.371441
$559$	12360.0	0.935192
$560$	224.000	0.0169031
$561$	−1428.00	−0.107469
$562$	−348.000	−0.0261201
$563$	−4340.00	−0.324883	−0.162442	−	0.986718i	$-0.551937\pi$
$563$	−4340.00	−0.324883	−0.162442	+	0.986718i	$0.551937\pi$
$564$	−3264.00	−0.243687
$565$	1252.00	0.0932248
$566$	10520.0	0.781252
$567$	−567.000	−0.0419961
$568$	2432.00	0.179656
$569$	16962.0	1.24971	0.624854	−	0.780741i	$-0.285158\pi$
$569$	16962.0	1.24971	0.624854	+	0.780741i	$0.285158\pi$
$570$	−672.000	−0.0493807
$571$	−26404.0	−1.93515	−0.967577	−	0.252576i	$-0.918722\pi$
$571$	−26404.0	−1.93515	−0.967577	+	0.252576i	$0.918722\pi$
$572$	3360.00	0.245610
$573$	10836.0	0.790018
$574$	−5628.00	−0.409248
$575$	9680.00	0.702059
$576$	576.000	0.0416667
$577$	−2326.00	−0.167821	−0.0839104	−	0.996473i	$-0.526741\pi$
$577$	−2326.00	−0.167821	−0.0839104	+	0.996473i	$0.526741\pi$
$578$	578.000	0.0415945
$579$	−1590.00	−0.114125
$580$	1008.00	0.0721637
$581$	3108.00	0.221930
$582$	−6900.00	−0.491433
$583$	8232.00	0.584793
$584$	5104.00	0.361652
$585$	−540.000	−0.0381645
$586$	15164.0	1.06897
$587$	−7636.00	−0.536919	−0.268459	−	0.963291i	$-0.586515\pi$
$587$	−7636.00	−0.536919	−0.268459	+	0.963291i	$0.586515\pi$
$588$	−588.000	−0.0412393
$589$	−15232.0	−1.06557
$590$	−400.000	−0.0279114
$591$	−4782.00	−0.332835
$592$	2144.00	0.148848
$593$	4962.00	0.343617	0.171809	−	0.985130i	$-0.445039\pi$
$593$	4962.00	0.343617	0.171809	+	0.985130i	$0.445039\pi$
$594$	−1512.00	−0.104441
$595$	238.000	0.0163984
$596$	5176.00	0.355734
$597$	−10080.0	−0.691033
$598$	−4800.00	−0.328238
$599$	2340.00	0.159616	0.0798079	−	0.996810i	$-0.474569\pi$
$599$	2340.00	0.159616	0.0798079	+	0.996810i	$0.474569\pi$
$600$	2904.00	0.197592
$601$	19910.0	1.35132	0.675662	−	0.737211i	$-0.263858\pi$
$601$	19910.0	1.35132	0.675662	+	0.737211i	$0.263858\pi$
$602$	−5768.00	−0.390509
$603$	−2196.00	−0.148305
$604$	12032.0	0.810555
$605$	1094.00	0.0735164
$606$	−5460.00	−0.366002
$607$	−25816.0	−1.72626	−0.863129	−	0.504983i	$-0.831499\pi$
$607$	−25816.0	−1.72626	−0.863129	+	0.504983i	$0.831499\pi$
$608$	−1792.00	−0.119532
$609$	−2646.00	−0.176061
$610$	−2824.00	−0.187443
$611$	8160.00	0.540292
$612$	612.000	0.0404226
$613$	5822.00	0.383603	0.191801	−	0.981434i	$-0.438567\pi$
$613$	5822.00	0.383603	0.191801	+	0.981434i	$0.438567\pi$
$614$	−15040.0	−0.988542
$615$	2412.00	0.158148
$616$	−1568.00	−0.102559
$617$	10534.0	0.687330	0.343665	−	0.939092i	$-0.388331\pi$
$617$	10534.0	0.687330	0.343665	+	0.939092i	$0.388331\pi$
$618$	4632.00	0.301499
$619$	−7868.00	−0.510891	−0.255446	−	0.966823i	$-0.582222\pi$
$619$	−7868.00	−0.510891	−0.255446	+	0.966823i	$0.582222\pi$
$620$	−2176.00	−0.140952
$621$	2160.00	0.139578
$622$	7824.00	0.504363
$623$	−966.000	−0.0621219
$624$	−1440.00	−0.0923816
$625$	14141.0	0.905024
$626$	6108.00	0.389976
$627$	4704.00	0.299617
$628$	−14440.0	−0.917546
$629$	2278.00	0.144404
$630$	252.000	0.0159364
$631$	13424.0	0.846911	0.423456	−	0.905917i	$-0.360817\pi$
$631$	13424.0	0.846911	0.423456	+	0.905917i	$0.360817\pi$
$632$	−6080.00	−0.382673
$633$	9084.00	0.570390
$634$	2052.00	0.128542
$635$	432.000	0.0269975
$636$	−3528.00	−0.219960
$637$	1470.00	0.0914341
$638$	−7056.00	−0.437852
$639$	2736.00	0.169381
$640$	−256.000	−0.0158114
$641$	20518.0	1.26429	0.632147	−	0.774849i	$-0.282174\pi$
$641$	20518.0	1.26429	0.632147	+	0.774849i	$0.282174\pi$
$642$	−4248.00	−0.261145
$643$	16644.0	1.02080	0.510401	−	0.859937i	$-0.329497\pi$
$643$	16644.0	1.02080	0.510401	+	0.859937i	$0.329497\pi$
$644$	2240.00	0.137063
$645$	2472.00	0.150907
$646$	−1904.00	−0.115963
$647$	−3872.00	−0.235277	−0.117638	−	0.993057i	$-0.537532\pi$
$647$	−3872.00	−0.235277	−0.117638	+	0.993057i	$0.537532\pi$
$648$	648.000	0.0392837
$649$	2800.00	0.169352
$650$	−7260.00	−0.438093
$651$	5712.00	0.343888
$652$	4752.00	0.285434
$653$	13690.0	0.820415	0.410208	−	0.911992i	$-0.365456\pi$
$653$	13690.0	0.820415	0.410208	+	0.911992i	$0.365456\pi$
$654$	2940.00	0.175785
$655$	−4248.00	−0.253409
$656$	6432.00	0.382816
$657$	5742.00	0.340969
$658$	−3808.00	−0.225610
$659$	−17896.0	−1.05786	−0.528930	−	0.848666i	$-0.677406\pi$
$659$	−17896.0	−1.05786	−0.528930	+	0.848666i	$0.677406\pi$
$660$	672.000	0.0396327
$661$	15990.0	0.940906	0.470453	−	0.882425i	$-0.344091\pi$
$661$	15990.0	0.940906	0.470453	+	0.882425i	$0.344091\pi$
$662$	10760.0	0.631721
$663$	−1530.00	−0.0896233
$664$	−3552.00	−0.207597
$665$	−784.000	−0.0457176
$666$	2412.00	0.140335
$667$	10080.0	0.585156
$668$	−7648.00	−0.442979
$669$	11484.0	0.663673
$670$	976.000	0.0562779
$671$	19768.0	1.13731
$672$	672.000	0.0385758
$673$	2410.00	0.138037	0.0690183	−	0.997615i	$-0.478013\pi$
$673$	2410.00	0.138037	0.0690183	+	0.997615i	$0.478013\pi$
$674$	9380.00	0.536059
$675$	3267.00	0.186292
$676$	−5188.00	−0.295175
$677$	−16554.0	−0.939766	−0.469883	−	0.882729i	$-0.655704\pi$
$677$	−16554.0	−0.939766	−0.469883	+	0.882729i	$0.655704\pi$
$678$	3756.00	0.212756
$679$	−8050.00	−0.454979
$680$	−272.000	−0.0153393
$681$	5292.00	0.297782
$682$	15232.0	0.855225
$683$	24660.0	1.38154	0.690768	−	0.723077i	$-0.257273\pi$
$683$	24660.0	1.38154	0.690768	+	0.723077i	$0.257273\pi$
$684$	−2016.00	−0.112695
$685$	−2788.00	−0.155509
$686$	−686.000	−0.0381802
$687$	4998.00	0.277563
$688$	6592.00	0.365287
$689$	8820.00	0.487685
$690$	−960.000	−0.0529661
$691$	19900.0	1.09556	0.547780	−	0.836623i	$-0.315473\pi$
$691$	19900.0	1.09556	0.547780	+	0.836623i	$0.315473\pi$
$692$	−1032.00	−0.0566918
$693$	−1764.00	−0.0966938
$694$	7960.00	0.435385
$695$	1128.00	0.0615647
$696$	3024.00	0.164690
$697$	6834.00	0.371386
$698$	3132.00	0.169839
$699$	7134.00	0.386027
$700$	3388.00	0.182935
$701$	−22434.0	−1.20873	−0.604366	−	0.796707i	$-0.706573\pi$
$701$	−22434.0	−1.20873	−0.604366	+	0.796707i	$0.706573\pi$
$702$	−1620.00	−0.0870982
$703$	−7504.00	−0.402587
$704$	1792.00	0.0959354
$705$	1632.00	0.0871839
$706$	15940.0	0.849731
$707$	−6370.00	−0.338852
$708$	−1200.00	−0.0636988
$709$	10702.0	0.566886	0.283443	−	0.958989i	$-0.408523\pi$
$709$	10702.0	0.566886	0.283443	+	0.958989i	$0.408523\pi$
$710$	−1216.00	−0.0642756
$711$	−6840.00	−0.360788
$712$	1104.00	0.0581098
$713$	−21760.0	−1.14294
$714$	714.000	0.0374241
$715$	−1680.00	−0.0878719
$716$	−6560.00	−0.342400
$717$	5196.00	0.270639
$718$	19960.0	1.03747
$719$	−18696.0	−0.969740	−0.484870	−	0.874586i	$-0.661133\pi$
$719$	−18696.0	−0.969740	−0.484870	+	0.874586i	$0.661133\pi$
$720$	−288.000	−0.0149071
$721$	5404.00	0.279134
$722$	−7446.00	−0.383811
$723$	1638.00	0.0842571
$724$	4200.00	0.215596
$725$	15246.0	0.780996
$726$	3282.00	0.167777
$727$	34204.0	1.74492	0.872460	−	0.488686i	$-0.162524\pi$
$727$	34204.0	1.74492	0.872460	+	0.488686i	$0.162524\pi$
$728$	−1680.00	−0.0855288
$729$	729.000	0.0370370
$730$	−2552.00	−0.129389
$731$	7004.00	0.354381
$732$	−8472.00	−0.427779
$733$	19454.0	0.980286	0.490143	−	0.871642i	$-0.336944\pi$
$733$	19454.0	0.980286	0.490143	+	0.871642i	$0.336944\pi$
$734$	−25056.0	−1.25999
$735$	294.000	0.0147542
$736$	−2560.00	−0.128210
$737$	−6832.00	−0.341465
$738$	7236.00	0.360923
$739$	33020.0	1.64365	0.821827	−	0.569737i	$-0.192955\pi$
$739$	33020.0	1.64365	0.821827	+	0.569737i	$0.192955\pi$
$740$	−1072.00	−0.0532534
$741$	5040.00	0.249864
$742$	−4116.00	−0.203643
$743$	22536.0	1.11274	0.556370	−	0.830935i	$-0.312194\pi$
$743$	22536.0	1.11274	0.556370	+	0.830935i	$0.312194\pi$
$744$	−6528.00	−0.321678
$745$	−2588.00	−0.127271
$746$	−676.000	−0.0331771
$747$	−3996.00	−0.195724
$748$	1904.00	0.0930710
$749$	−4956.00	−0.241773
$750$	−2952.00	−0.143722
$751$	−7720.00	−0.375109	−0.187554	−	0.982254i	$-0.560056\pi$
$751$	−7720.00	−0.375109	−0.187554	+	0.982254i	$0.560056\pi$
$752$	4352.00	0.211039
$753$	12108.0	0.585976
$754$	−7560.00	−0.365145
$755$	−6016.00	−0.289993
$756$	756.000	0.0363696
$757$	−23986.0	−1.15163	−0.575816	−	0.817579i	$-0.695316\pi$
$757$	−23986.0	−1.15163	−0.575816	+	0.817579i	$0.695316\pi$
$758$	−17848.0	−0.855236
$759$	6720.00	0.321371
$760$	896.000	0.0427649
$761$	−22374.0	−1.06578	−0.532889	−	0.846185i	$-0.678894\pi$
$761$	−22374.0	−1.06578	−0.532889	+	0.846185i	$0.678894\pi$
$762$	1296.00	0.0616130
$763$	3430.00	0.162745
$764$	−14448.0	−0.684176
$765$	−306.000	−0.0144620
$766$	−1744.00	−0.0822628
$767$	3000.00	0.141230
$768$	−768.000	−0.0360844
$769$	14314.0	0.671230	0.335615	−	0.941999i	$-0.391056\pi$
$769$	14314.0	0.671230	0.335615	+	0.941999i	$0.391056\pi$
$770$	784.000	0.0366927
$771$	−7638.00	−0.356778
$772$	2120.00	0.0988348
$773$	−38370.0	−1.78535	−0.892673	−	0.450704i	$-0.851173\pi$
$773$	−38370.0	−1.78535	−0.892673	+	0.450704i	$0.851173\pi$
$774$	7416.00	0.344396
$775$	−32912.0	−1.52546
$776$	9200.00	0.425594
$777$	2814.00	0.129925
$778$	13692.0	0.630954
$779$	−22512.0	−1.03540
$780$	720.000	0.0330515
$781$	8512.00	0.389991
$782$	−2720.00	−0.124382
$783$	3402.00	0.155271
$784$	784.000	0.0357143
$785$	7220.00	0.328271
$786$	−12744.0	−0.578325
$787$	4892.00	0.221577	0.110788	−	0.993844i	$-0.464662\pi$
$787$	4892.00	0.221577	0.110788	+	0.993844i	$0.464662\pi$
$788$	6376.00	0.288243
$789$	−1764.00	−0.0795945
$790$	3040.00	0.136909
$791$	4382.00	0.196973
$792$	2016.00	0.0904488
$793$	21180.0	0.948454
$794$	−5420.00	−0.242253
$795$	1764.00	0.0786951
$796$	13440.0	0.598452
$797$	41270.0	1.83420	0.917101	−	0.398656i	$-0.130523\pi$
$797$	41270.0	1.83420	0.917101	+	0.398656i	$0.130523\pi$
$798$	−2352.00	−0.104336
$799$	4624.00	0.204738
$800$	−3872.00	−0.171120
$801$	1242.00	0.0547864
$802$	−15076.0	−0.663781
$803$	17864.0	0.785065
$804$	2928.00	0.128436
$805$	−1120.00	−0.0490370
$806$	16320.0	0.713210
$807$	−21378.0	−0.932517
$808$	7280.00	0.316967
$809$	19374.0	0.841970	0.420985	−	0.907068i	$-0.361685\pi$
$809$	19374.0	0.841970	0.420985	+	0.907068i	$0.361685\pi$
$810$	−324.000	−0.0140546
$811$	21548.0	0.932987	0.466494	−	0.884525i	$-0.345517\pi$
$811$	21548.0	0.932987	0.466494	+	0.884525i	$0.345517\pi$
$812$	3528.00	0.152474
$813$	21108.0	0.910566
$814$	7504.00	0.323114
$815$	−2376.00	−0.102120
$816$	−816.000	−0.0350070
$817$	−23072.0	−0.987989
$818$	7828.00	0.334596
$819$	−1890.00	−0.0806373
$820$	−3216.00	−0.136960
$821$	−9462.00	−0.402224	−0.201112	−	0.979568i	$-0.564456\pi$
$821$	−9462.00	−0.402224	−0.201112	+	0.979568i	$0.564456\pi$
$822$	−8364.00	−0.354900
$823$	5384.00	0.228037	0.114018	−	0.993479i	$-0.463628\pi$
$823$	5384.00	0.228037	0.114018	+	0.993479i	$0.463628\pi$
$824$	−6176.00	−0.261106
$825$	10164.0	0.428927
$826$	−1400.00	−0.0589736
$827$	16692.0	0.701859	0.350930	−	0.936402i	$-0.385866\pi$
$827$	16692.0	0.701859	0.350930	+	0.936402i	$0.385866\pi$
$828$	−2880.00	−0.120878
$829$	−7322.00	−0.306759	−0.153380	−	0.988167i	$-0.549016\pi$
$829$	−7322.00	−0.306759	−0.153380	+	0.988167i	$0.549016\pi$
$830$	1776.00	0.0742721
$831$	23502.0	0.981077
$832$	1920.00	0.0800048
$833$	833.000	0.0346479
$834$	3384.00	0.140502
$835$	3824.00	0.158485
$836$	−6272.00	−0.259476
$837$	−7344.00	−0.303280
$838$	28056.0	1.15654
$839$	−36144.0	−1.48728	−0.743641	−	0.668579i	$-0.766903\pi$
$839$	−36144.0	−1.48728	−0.743641	+	0.668579i	$0.766903\pi$
$840$	−336.000	−0.0138013
$841$	−8513.00	−0.349051
$842$	−3108.00	−0.127208
$843$	522.000	0.0213270
$844$	−12112.0	−0.493972
$845$	2594.00	0.105605
$846$	4896.00	0.198969
$847$	3829.00	0.155332
$848$	4704.00	0.190491
$849$	−15780.0	−0.637890
$850$	−4114.00	−0.166011
$851$	−10720.0	−0.431818
$852$	−3648.00	−0.146688
$853$	9722.00	0.390240	0.195120	−	0.980779i	$-0.437490\pi$
$853$	9722.00	0.390240	0.195120	+	0.980779i	$0.437490\pi$
$854$	−9884.00	−0.396046
$855$	1008.00	0.0403191
$856$	5664.00	0.226158
$857$	30994.0	1.23540	0.617698	−	0.786415i	$-0.288065\pi$
$857$	30994.0	1.23540	0.617698	+	0.786415i	$0.288065\pi$
$858$	−5040.00	−0.200539
$859$	−42560.0	−1.69049	−0.845244	−	0.534381i	$-0.820545\pi$
$859$	−42560.0	−1.69049	−0.845244	+	0.534381i	$0.820545\pi$
$860$	−3296.00	−0.130689
$861$	8442.00	0.334149
$862$	27136.0	1.07222
$863$	12116.0	0.477907	0.238953	−	0.971031i	$-0.423196\pi$
$863$	12116.0	0.477907	0.238953	+	0.971031i	$0.423196\pi$
$864$	−864.000	−0.0340207
$865$	516.000	0.0202827
$866$	−22140.0	−0.868762
$867$	−867.000	−0.0339618
$868$	−7616.00	−0.297816
$869$	−21280.0	−0.830696
$870$	−1512.00	−0.0589214
$871$	−7320.00	−0.284763
$872$	−3920.00	−0.152234
$873$	10350.0	0.401254
$874$	8960.00	0.346769
$875$	−3444.00	−0.133061
$876$	−7656.00	−0.295288
$877$	−29826.0	−1.14841	−0.574203	−	0.818713i	$-0.694688\pi$
$877$	−29826.0	−1.14841	−0.574203	+	0.818713i	$0.694688\pi$
$878$	−19408.0	−0.746000
$879$	−22746.0	−0.872814
$880$	−896.000	−0.0343229
$881$	−9726.00	−0.371938	−0.185969	−	0.982556i	$-0.559542\pi$
$881$	−9726.00	−0.371938	−0.185969	+	0.982556i	$0.559542\pi$
$882$	882.000	0.0336718
$883$	−40508.0	−1.54383	−0.771915	−	0.635725i	$-0.780701\pi$
$883$	−40508.0	−1.54383	−0.771915	+	0.635725i	$0.780701\pi$
$884$	2040.00	0.0776161
$885$	600.000	0.0227896
$886$	−35232.0	−1.33594
$887$	−30056.0	−1.13775	−0.568874	−	0.822425i	$-0.692621\pi$
$887$	−30056.0	−1.13775	−0.568874	+	0.822425i	$0.692621\pi$
$888$	−3216.00	−0.121534
$889$	1512.00	0.0570426
$890$	−552.000	−0.0207900
$891$	2268.00	0.0852759
$892$	−15312.0	−0.574757
$893$	−15232.0	−0.570794
$894$	−7764.00	−0.290455
$895$	3280.00	0.122501
$896$	−896.000	−0.0334077
$897$	7200.00	0.268006
$898$	−18612.0	−0.691638
$899$	−34272.0	−1.27145
$900$	−4356.00	−0.161333
$901$	4998.00	0.184803
$902$	22512.0	0.831006
$903$	8652.00	0.318849
$904$	−5008.00	−0.184252
$905$	−2100.00	−0.0771341
$906$	−18048.0	−0.661815
$907$	−27588.0	−1.00997	−0.504986	−	0.863128i	$-0.668502\pi$
$907$	−27588.0	−1.00997	−0.504986	+	0.863128i	$0.668502\pi$
$908$	−7056.00	−0.257887
$909$	8190.00	0.298840
$910$	840.000	0.0305997
$911$	−26528.0	−0.964777	−0.482389	−	0.875957i	$-0.660231\pi$
$911$	−26528.0	−0.964777	−0.482389	+	0.875957i	$0.660231\pi$
$912$	2688.00	0.0975971
$913$	−12432.0	−0.450645
$914$	−12140.0	−0.439339
$915$	4236.00	0.153047
$916$	−6664.00	−0.240376
$917$	−14868.0	−0.535425
$918$	−918.000	−0.0330049
$919$	3080.00	0.110555	0.0552774	−	0.998471i	$-0.482396\pi$
$919$	3080.00	0.110555	0.0552774	+	0.998471i	$0.482396\pi$
$920$	1280.00	0.0458699
$921$	22560.0	0.807141
$922$	25100.0	0.896556
$923$	9120.00	0.325231
$924$	2352.00	0.0837393
$925$	−16214.0	−0.576338
$926$	−32576.0	−1.15606
$927$	−6948.00	−0.246173
$928$	−4032.00	−0.142626
$929$	33322.0	1.17681	0.588407	−	0.808565i	$-0.299755\pi$
$929$	33322.0	1.17681	0.588407	+	0.808565i	$0.299755\pi$
$930$	3264.00	0.115087
$931$	−2744.00	−0.0965961
$932$	−9512.00	−0.334309
$933$	−11736.0	−0.411811
$934$	−12888.0	−0.451508
$935$	−952.000	−0.0332981
$936$	2160.00	0.0754293
$937$	−4654.00	−0.162262	−0.0811310	−	0.996703i	$-0.525853\pi$
$937$	−4654.00	−0.162262	−0.0811310	+	0.996703i	$0.525853\pi$
$938$	3416.00	0.118909
$939$	−9162.00	−0.318414
$940$	−2176.00	−0.0755035
$941$	−2154.00	−0.0746210	−0.0373105	−	0.999304i	$-0.511879\pi$
$941$	−2154.00	−0.0746210	−0.0373105	+	0.999304i	$0.511879\pi$
$942$	21660.0	0.749173
$943$	−32160.0	−1.11058
$944$	1600.00	0.0551648
$945$	−378.000	−0.0130120
$946$	23072.0	0.792955
$947$	−47076.0	−1.61538	−0.807690	−	0.589608i	$-0.799282\pi$
$947$	−47076.0	−1.61538	−0.807690	+	0.589608i	$0.799282\pi$
$948$	9120.00	0.312451
$949$	19140.0	0.654700
$950$	13552.0	0.462826
$951$	−3078.00	−0.104954
$952$	−952.000	−0.0324102
$953$	−35694.0	−1.21327	−0.606633	−	0.794982i	$-0.707480\pi$
$953$	−35694.0	−1.21327	−0.606633	+	0.794982i	$0.707480\pi$
$954$	5292.00	0.179596
$955$	7224.00	0.244778
$956$	−6928.00	−0.234380
$957$	10584.0	0.357505
$958$	17520.0	0.590862
$959$	−9758.00	−0.328574
$960$	384.000	0.0129099
$961$	44193.0	1.48343
$962$	8040.00	0.269459
$963$	6372.00	0.213224
$964$	−2184.00	−0.0729688
$965$	−1060.00	−0.0353602
$966$	−3360.00	−0.111911
$967$	52928.0	1.76013	0.880067	−	0.474849i	$-0.157497\pi$
$967$	52928.0	1.76013	0.880067	+	0.474849i	$0.157497\pi$
$968$	−4376.00	−0.145300
$969$	2856.00	0.0946831
$970$	−4600.00	−0.152265
$971$	−14412.0	−0.476316	−0.238158	−	0.971226i	$-0.576544\pi$
$971$	−14412.0	−0.476316	−0.238158	+	0.971226i	$0.576544\pi$
$972$	−972.000	−0.0320750
$973$	3948.00	0.130079
$974$	35968.0	1.18325
$975$	10890.0	0.357702
$976$	11296.0	0.370467
$977$	−3302.00	−0.108127	−0.0540636	−	0.998537i	$-0.517217\pi$
$977$	−3302.00	−0.108127	−0.0540636	+	0.998537i	$0.517217\pi$
$978$	−7128.00	−0.233056
$979$	3864.00	0.126143
$980$	−392.000	−0.0127775
$981$	−4410.00	−0.143527
$982$	−34144.0	−1.10955
$983$	2672.00	0.0866974	0.0433487	−	0.999060i	$-0.486197\pi$
$983$	2672.00	0.0866974	0.0433487	+	0.999060i	$0.486197\pi$
$984$	−9648.00	−0.312568
$985$	−3188.00	−0.103125
$986$	−4284.00	−0.138367
$987$	5712.00	0.184210
$988$	−6720.00	−0.216388
$989$	−32960.0	−1.05972
$990$	−1008.00	−0.0323599
$991$	38176.0	1.22371	0.611857	−	0.790968i	$-0.290423\pi$
$991$	38176.0	1.22371	0.611857	+	0.790968i	$0.290423\pi$
$992$	8704.00	0.278581
$993$	−16140.0	−0.515798
$994$	−4256.00	−0.135807
$995$	−6720.00	−0.214109
$996$	5328.00	0.169502
$997$	−46230.0	−1.46852	−0.734262	−	0.678866i	$-0.762472\pi$
$997$	−46230.0	−1.46852	−0.734262	+	0.678866i	$0.762472\pi$
$998$	−22552.0	−0.715302
$999$	−3618.00	−0.114583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.4.a.d.1.1	✓	1
3.2	odd	2		2142.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.4.a.d.1.1	✓	1	1.1	even	1	trivial
2142.4.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	714.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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