LMFDB - Embedded newform 1274.4.a.g.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,4,Mod(1,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1274.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$75.1684333473$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1274.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} +10.0000 q^{10} -36.0000 q^{11} +8.00000 q^{12} +13.0000 q^{13} +10.0000 q^{15} +16.0000 q^{16} -26.0000 q^{17} -46.0000 q^{18} +47.0000 q^{19} +20.0000 q^{20} -72.0000 q^{22} -99.0000 q^{23} +16.0000 q^{24} -100.000 q^{25} +26.0000 q^{26} -100.000 q^{27} -61.0000 q^{29} +20.0000 q^{30} +23.0000 q^{31} +32.0000 q^{32} -72.0000 q^{33} -52.0000 q^{34} -92.0000 q^{36} -50.0000 q^{37} +94.0000 q^{38} +26.0000 q^{39} +40.0000 q^{40} -70.0000 q^{41} -19.0000 q^{43} -144.000 q^{44} -115.000 q^{45} -198.000 q^{46} -191.000 q^{47} +32.0000 q^{48} -200.000 q^{50} -52.0000 q^{51} +52.0000 q^{52} +195.000 q^{53} -200.000 q^{54} -180.000 q^{55} +94.0000 q^{57} -122.000 q^{58} -264.000 q^{59} +40.0000 q^{60} -310.000 q^{61} +46.0000 q^{62} +64.0000 q^{64} +65.0000 q^{65} -144.000 q^{66} -190.000 q^{67} -104.000 q^{68} -198.000 q^{69} -166.000 q^{71} -184.000 q^{72} -873.000 q^{73} -100.000 q^{74} -200.000 q^{75} +188.000 q^{76} +52.0000 q^{78} -1191.00 q^{79} +80.0000 q^{80} +421.000 q^{81} -140.000 q^{82} -259.000 q^{83} -130.000 q^{85} -38.0000 q^{86} -122.000 q^{87} -288.000 q^{88} +635.000 q^{89} -230.000 q^{90} -396.000 q^{92} +46.0000 q^{93} -382.000 q^{94} +235.000 q^{95} +64.0000 q^{96} -133.000 q^{97} +828.000 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	2.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	2.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	5.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	4.00000	0.272166
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	10.0000	0.316228
$11$	−36.0000	−0.986764	−0.493382	−	0.869813i	$-0.664240\pi$
$11$	−36.0000	−0.986764	−0.493382	+	0.869813i	$0.664240\pi$
$12$	8.00000	0.192450
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	10.0000	0.172133
$16$	16.0000	0.250000
$17$	−26.0000	−0.370937	−0.185468	−	0.982650i	$-0.559380\pi$
$17$	−26.0000	−0.370937	−0.185468	+	0.982650i	$0.559380\pi$
$18$	−46.0000	−0.602350
$19$	47.0000	0.567502	0.283751	−	0.958898i	$-0.408421\pi$
$19$	47.0000	0.567502	0.283751	+	0.958898i	$0.408421\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−72.0000	−0.697748
$23$	−99.0000	−0.897519	−0.448759	−	0.893653i	$-0.648134\pi$
$23$	−99.0000	−0.897519	−0.448759	+	0.893653i	$0.648134\pi$
$24$	16.0000	0.136083
$25$	−100.000	−0.800000
$26$	26.0000	0.196116
$27$	−100.000	−0.712778
$28$	0	0
$29$	−61.0000	−0.390601	−0.195300	−	0.980743i	$-0.562568\pi$
$29$	−61.0000	−0.390601	−0.195300	+	0.980743i	$0.562568\pi$
$30$	20.0000	0.121716
$31$	23.0000	0.133256	0.0666278	−	0.997778i	$-0.478776\pi$
$31$	23.0000	0.133256	0.0666278	+	0.997778i	$0.478776\pi$
$32$	32.0000	0.176777
$33$	−72.0000	−0.379806
$34$	−52.0000	−0.262292
$35$	0	0
$36$	−92.0000	−0.425926
$37$	−50.0000	−0.222161	−0.111080	−	0.993811i	$-0.535431\pi$
$37$	−50.0000	−0.222161	−0.111080	+	0.993811i	$0.535431\pi$
$38$	94.0000	0.401285
$39$	26.0000	0.106752
$40$	40.0000	0.158114
$41$	−70.0000	−0.266638	−0.133319	−	0.991073i	$-0.542564\pi$
$41$	−70.0000	−0.266638	−0.133319	+	0.991073i	$0.542564\pi$
$42$	0	0
$43$	−19.0000	−0.0673831	−0.0336915	−	0.999432i	$-0.510726\pi$
$43$	−19.0000	−0.0673831	−0.0336915	+	0.999432i	$0.510726\pi$
$44$	−144.000	−0.493382
$45$	−115.000	−0.380960
$46$	−198.000	−0.634641
$47$	−191.000	−0.592770	−0.296385	−	0.955068i	$-0.595781\pi$
$47$	−191.000	−0.592770	−0.296385	+	0.955068i	$0.595781\pi$
$48$	32.0000	0.0962250
$49$	0	0
$50$	−200.000	−0.565685
$51$	−52.0000	−0.142774
$52$	52.0000	0.138675
$53$	195.000	0.505383	0.252692	−	0.967547i	$-0.418684\pi$
$53$	195.000	0.505383	0.252692	+	0.967547i	$0.418684\pi$
$54$	−200.000	−0.504010
$55$	−180.000	−0.441294
$56$	0	0
$57$	94.0000	0.218432
$58$	−122.000	−0.276196
$59$	−264.000	−0.582540	−0.291270	−	0.956641i	$-0.594078\pi$
$59$	−264.000	−0.582540	−0.291270	+	0.956641i	$0.594078\pi$
$60$	40.0000	0.0860663
$61$	−310.000	−0.650679	−0.325340	−	0.945597i	$-0.605479\pi$
$61$	−310.000	−0.650679	−0.325340	+	0.945597i	$0.605479\pi$
$62$	46.0000	0.0942259
$63$	0	0
$64$	64.0000	0.125000
$65$	65.0000	0.124035
$66$	−144.000	−0.268563
$67$	−190.000	−0.346451	−0.173225	−	0.984882i	$-0.555419\pi$
$67$	−190.000	−0.346451	−0.173225	+	0.984882i	$0.555419\pi$
$68$	−104.000	−0.185468
$69$	−198.000	−0.345455
$70$	0	0
$71$	−166.000	−0.277473	−0.138736	−	0.990329i	$-0.544304\pi$
$71$	−166.000	−0.277473	−0.138736	+	0.990329i	$0.544304\pi$
$72$	−184.000	−0.301175
$73$	−873.000	−1.39968	−0.699842	−	0.714298i	$-0.746746\pi$
$73$	−873.000	−1.39968	−0.699842	+	0.714298i	$0.746746\pi$
$74$	−100.000	−0.157091
$75$	−200.000	−0.307920
$76$	188.000	0.283751
$77$	0	0
$78$	52.0000	0.0754851
$79$	−1191.00	−1.69618	−0.848088	−	0.529855i	$-0.822246\pi$
$79$	−1191.00	−1.69618	−0.848088	+	0.529855i	$0.822246\pi$
$80$	80.0000	0.111803
$81$	421.000	0.577503
$82$	−140.000	−0.188542
$83$	−259.000	−0.342517	−0.171259	−	0.985226i	$-0.554783\pi$
$83$	−259.000	−0.342517	−0.171259	+	0.985226i	$0.554783\pi$
$84$	0	0
$85$	−130.000	−0.165888
$86$	−38.0000	−0.0476470
$87$	−122.000	−0.150342
$88$	−288.000	−0.348874
$89$	635.000	0.756291	0.378145	−	0.925746i	$-0.376562\pi$
$89$	635.000	0.756291	0.378145	+	0.925746i	$0.376562\pi$
$90$	−230.000	−0.269379
$91$	0	0
$92$	−396.000	−0.448759
$93$	46.0000	0.0512901
$94$	−382.000	−0.419152
$95$	235.000	0.253795
$96$	64.0000	0.0680414
$97$	−133.000	−0.139218	−0.0696088	−	0.997574i	$-0.522175\pi$
$97$	−133.000	−0.139218	−0.0696088	+	0.997574i	$0.522175\pi$
$98$	0	0
$99$	828.000	0.840577
$100$	−400.000	−0.400000
$101$	−152.000	−0.149748	−0.0748741	−	0.997193i	$-0.523855\pi$
$101$	−152.000	−0.149748	−0.0748741	+	0.997193i	$0.523855\pi$
$102$	−104.000	−0.100956
$103$	1664.00	1.59183	0.795916	−	0.605406i	$-0.206989\pi$
$103$	1664.00	1.59183	0.795916	+	0.605406i	$0.206989\pi$
$104$	104.000	0.0980581
$105$	0	0
$106$	390.000	0.357360
$107$	−36.0000	−0.0325257	−0.0162629	−	0.999868i	$-0.505177\pi$
$107$	−36.0000	−0.0325257	−0.0162629	+	0.999868i	$0.505177\pi$
$108$	−400.000	−0.356389
$109$	−232.000	−0.203868	−0.101934	−	0.994791i	$-0.532503\pi$
$109$	−232.000	−0.203868	−0.101934	+	0.994791i	$0.532503\pi$
$110$	−360.000	−0.312042
$111$	−100.000	−0.0855097
$112$	0	0
$113$	1353.00	1.12637	0.563184	−	0.826332i	$-0.309576\pi$
$113$	1353.00	1.12637	0.563184	+	0.826332i	$0.309576\pi$
$114$	188.000	0.154455
$115$	−495.000	−0.401383
$116$	−244.000	−0.195300
$117$	−299.000	−0.236261
$118$	−528.000	−0.411918
$119$	0	0
$120$	80.0000	0.0608581
$121$	−35.0000	−0.0262960
$122$	−620.000	−0.460100
$123$	−140.000	−0.102629
$124$	92.0000	0.0666278
$125$	−1125.00	−0.804984
$126$	0	0
$127$	576.000	0.402455	0.201227	−	0.979545i	$-0.435507\pi$
$127$	576.000	0.402455	0.201227	+	0.979545i	$0.435507\pi$
$128$	128.000	0.0883883
$129$	−38.0000	−0.0259358
$130$	130.000	0.0877058
$131$	2056.00	1.37125	0.685624	−	0.727956i	$-0.259529\pi$
$131$	2056.00	1.37125	0.685624	+	0.727956i	$0.259529\pi$
$132$	−288.000	−0.189903
$133$	0	0
$134$	−380.000	−0.244978
$135$	−500.000	−0.318764
$136$	−208.000	−0.131146
$137$	−1842.00	−1.14871	−0.574353	−	0.818608i	$-0.694746\pi$
$137$	−1842.00	−1.14871	−0.574353	+	0.818608i	$0.694746\pi$
$138$	−396.000	−0.244274
$139$	1288.00	0.785948	0.392974	−	0.919550i	$-0.371446\pi$
$139$	1288.00	0.785948	0.392974	+	0.919550i	$0.371446\pi$
$140$	0	0
$141$	−382.000	−0.228157
$142$	−332.000	−0.196203
$143$	−468.000	−0.273679
$144$	−368.000	−0.212963
$145$	−305.000	−0.174682
$146$	−1746.00	−0.989726
$147$	0	0
$148$	−200.000	−0.111080
$149$	1196.00	0.657585	0.328792	−	0.944402i	$-0.393358\pi$
$149$	1196.00	0.657585	0.328792	+	0.944402i	$0.393358\pi$
$150$	−400.000	−0.217732
$151$	−890.000	−0.479650	−0.239825	−	0.970816i	$-0.577090\pi$
$151$	−890.000	−0.479650	−0.239825	+	0.970816i	$0.577090\pi$
$152$	376.000	0.200642
$153$	598.000	0.315983
$154$	0	0
$155$	115.000	0.0595937
$156$	104.000	0.0533761
$157$	−138.000	−0.0701503	−0.0350752	−	0.999385i	$-0.511167\pi$
$157$	−138.000	−0.0701503	−0.0350752	+	0.999385i	$0.511167\pi$
$158$	−2382.00	−1.19938
$159$	390.000	0.194522
$160$	160.000	0.0790569
$161$	0	0
$162$	842.000	0.408357
$163$	−3956.00	−1.90097	−0.950484	−	0.310773i	$-0.899412\pi$
$163$	−3956.00	−1.90097	−0.950484	+	0.310773i	$0.899412\pi$
$164$	−280.000	−0.133319
$165$	−360.000	−0.169854
$166$	−518.000	−0.242196
$167$	3675.00	1.70287	0.851437	−	0.524457i	$-0.175731\pi$
$167$	3675.00	1.70287	0.851437	+	0.524457i	$0.175731\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−260.000	−0.117301
$171$	−1081.00	−0.483428
$172$	−76.0000	−0.0336915
$173$	2826.00	1.24195	0.620973	−	0.783832i	$-0.286737\pi$
$173$	2826.00	1.24195	0.620973	+	0.783832i	$0.286737\pi$
$174$	−244.000	−0.106308
$175$	0	0
$176$	−576.000	−0.246691
$177$	−528.000	−0.224220
$178$	1270.00	0.534778
$179$	−3235.00	−1.35081	−0.675406	−	0.737446i	$-0.736031\pi$
$179$	−3235.00	−1.35081	−0.675406	+	0.737446i	$0.736031\pi$
$180$	−460.000	−0.190480
$181$	−1260.00	−0.517431	−0.258716	−	0.965954i	$-0.583299\pi$
$181$	−1260.00	−0.517431	−0.258716	+	0.965954i	$0.583299\pi$
$182$	0	0
$183$	−620.000	−0.250447
$184$	−792.000	−0.317321
$185$	−250.000	−0.0993533
$186$	92.0000	0.0362676
$187$	936.000	0.366027
$188$	−764.000	−0.296385
$189$	0	0
$190$	470.000	0.179460
$191$	−232.000	−0.0878897	−0.0439448	−	0.999034i	$-0.513993\pi$
$191$	−232.000	−0.0878897	−0.0439448	+	0.999034i	$0.513993\pi$
$192$	128.000	0.0481125
$193$	−5342.00	−1.99236	−0.996180	−	0.0873208i	$-0.972169\pi$
$193$	−5342.00	−1.99236	−0.996180	+	0.0873208i	$0.972169\pi$
$194$	−266.000	−0.0984417
$195$	130.000	0.0477410
$196$	0	0
$197$	1542.00	0.557680	0.278840	−	0.960338i	$-0.410050\pi$
$197$	1542.00	0.557680	0.278840	+	0.960338i	$0.410050\pi$
$198$	1656.00	0.594378
$199$	−2182.00	−0.777276	−0.388638	−	0.921391i	$-0.627054\pi$
$199$	−2182.00	−0.777276	−0.388638	+	0.921391i	$0.627054\pi$
$200$	−800.000	−0.282843
$201$	−380.000	−0.133349
$202$	−304.000	−0.105888
$203$	0	0
$204$	−208.000	−0.0713868
$205$	−350.000	−0.119244
$206$	3328.00	1.12560
$207$	2277.00	0.764553
$208$	208.000	0.0693375
$209$	−1692.00	−0.559991
$210$	0	0
$211$	−523.000	−0.170639	−0.0853194	−	0.996354i	$-0.527191\pi$
$211$	−523.000	−0.170639	−0.0853194	+	0.996354i	$0.527191\pi$
$212$	780.000	0.252692
$213$	−332.000	−0.106799
$214$	−72.0000	−0.0229992
$215$	−95.0000	−0.0301346
$216$	−800.000	−0.252005
$217$	0	0
$218$	−464.000	−0.144156
$219$	−1746.00	−0.538739
$220$	−720.000	−0.220647
$221$	−338.000	−0.102879
$222$	−200.000	−0.0604645
$223$	1981.00	0.594877	0.297439	−	0.954741i	$-0.403868\pi$
$223$	1981.00	0.594877	0.297439	+	0.954741i	$0.403868\pi$
$224$	0	0
$225$	2300.00	0.681481
$226$	2706.00	0.796462
$227$	−4352.00	−1.27248	−0.636239	−	0.771492i	$-0.719511\pi$
$227$	−4352.00	−1.27248	−0.636239	+	0.771492i	$0.719511\pi$
$228$	376.000	0.109216
$229$	−2130.00	−0.614648	−0.307324	−	0.951605i	$-0.599434\pi$
$229$	−2130.00	−0.614648	−0.307324	+	0.951605i	$0.599434\pi$
$230$	−990.000	−0.283820
$231$	0	0
$232$	−488.000	−0.138098
$233$	2687.00	0.755499	0.377749	−	0.925908i	$-0.376698\pi$
$233$	2687.00	0.755499	0.377749	+	0.925908i	$0.376698\pi$
$234$	−598.000	−0.167062
$235$	−955.000	−0.265095
$236$	−1056.00	−0.291270
$237$	−2382.00	−0.652859
$238$	0	0
$239$	3852.00	1.04253	0.521266	−	0.853394i	$-0.325460\pi$
$239$	3852.00	1.04253	0.521266	+	0.853394i	$0.325460\pi$
$240$	160.000	0.0430331
$241$	−1069.00	−0.285728	−0.142864	−	0.989742i	$-0.545631\pi$
$241$	−1069.00	−0.285728	−0.142864	+	0.989742i	$0.545631\pi$
$242$	−70.0000	−0.0185941
$243$	3542.00	0.935059
$244$	−1240.00	−0.325340
$245$	0	0
$246$	−280.000	−0.0725697
$247$	611.000	0.157397
$248$	184.000	0.0471130
$249$	−518.000	−0.131835
$250$	−2250.00	−0.569210
$251$	−5460.00	−1.37304	−0.686518	−	0.727113i	$-0.740862\pi$
$251$	−5460.00	−1.37304	−0.686518	+	0.727113i	$0.740862\pi$
$252$	0	0
$253$	3564.00	0.885639
$254$	1152.00	0.284578
$255$	−260.000	−0.0638503
$256$	256.000	0.0625000
$257$	−2172.00	−0.527181	−0.263591	−	0.964635i	$-0.584907\pi$
$257$	−2172.00	−0.527181	−0.263591	+	0.964635i	$0.584907\pi$
$258$	−76.0000	−0.0183394
$259$	0	0
$260$	260.000	0.0620174
$261$	1403.00	0.332734
$262$	4112.00	0.969619
$263$	−3417.00	−0.801145	−0.400573	−	0.916265i	$-0.631189\pi$
$263$	−3417.00	−0.801145	−0.400573	+	0.916265i	$0.631189\pi$
$264$	−576.000	−0.134282
$265$	975.000	0.226014
$266$	0	0
$267$	1270.00	0.291096
$268$	−760.000	−0.173225
$269$	−3792.00	−0.859488	−0.429744	−	0.902951i	$-0.641396\pi$
$269$	−3792.00	−0.859488	−0.429744	+	0.902951i	$0.641396\pi$
$270$	−1000.00	−0.225400
$271$	4408.00	0.988070	0.494035	−	0.869442i	$-0.335521\pi$
$271$	4408.00	0.988070	0.494035	+	0.869442i	$0.335521\pi$
$272$	−416.000	−0.0927342
$273$	0	0
$274$	−3684.00	−0.812258
$275$	3600.00	0.789412
$276$	−792.000	−0.172728
$277$	−1023.00	−0.221899	−0.110950	−	0.993826i	$-0.535389\pi$
$277$	−1023.00	−0.221899	−0.110950	+	0.993826i	$0.535389\pi$
$278$	2576.00	0.555749
$279$	−529.000	−0.113514
$280$	0	0
$281$	7912.00	1.67968	0.839840	−	0.542833i	$-0.182648\pi$
$281$	7912.00	1.67968	0.839840	+	0.542833i	$0.182648\pi$
$282$	−764.000	−0.161332
$283$	5336.00	1.12082	0.560410	−	0.828215i	$-0.310643\pi$
$283$	5336.00	1.12082	0.560410	+	0.828215i	$0.310643\pi$
$284$	−664.000	−0.138736
$285$	470.000	0.0976856
$286$	−936.000	−0.193520
$287$	0	0
$288$	−736.000	−0.150588
$289$	−4237.00	−0.862406
$290$	−610.000	−0.123519
$291$	−266.000	−0.0535849
$292$	−3492.00	−0.699842
$293$	−6615.00	−1.31895	−0.659475	−	0.751726i	$-0.729221\pi$
$293$	−6615.00	−1.31895	−0.659475	+	0.751726i	$0.729221\pi$
$294$	0	0
$295$	−1320.00	−0.260520
$296$	−400.000	−0.0785457
$297$	3600.00	0.703344
$298$	2392.00	0.464983
$299$	−1287.00	−0.248927
$300$	−800.000	−0.153960
$301$	0	0
$302$	−1780.00	−0.339164
$303$	−304.000	−0.0576381
$304$	752.000	0.141876
$305$	−1550.00	−0.290993
$306$	1196.00	0.223434
$307$	−3843.00	−0.714435	−0.357218	−	0.934021i	$-0.616275\pi$
$307$	−3843.00	−0.714435	−0.357218	+	0.934021i	$0.616275\pi$
$308$	0	0
$309$	3328.00	0.612697
$310$	230.000	0.0421391
$311$	−1748.00	−0.318714	−0.159357	−	0.987221i	$-0.550942\pi$
$311$	−1748.00	−0.318714	−0.159357	+	0.987221i	$0.550942\pi$
$312$	208.000	0.0377426
$313$	9392.00	1.69606	0.848031	−	0.529947i	$-0.177788\pi$
$313$	9392.00	1.69606	0.848031	+	0.529947i	$0.177788\pi$
$314$	−276.000	−0.0496038
$315$	0	0
$316$	−4764.00	−0.848088
$317$	10380.0	1.83911	0.919557	−	0.392958i	$-0.128548\pi$
$317$	10380.0	1.83911	0.919557	+	0.392958i	$0.128548\pi$
$318$	780.000	0.137548
$319$	2196.00	0.385431
$320$	320.000	0.0559017
$321$	−72.0000	−0.0125192
$322$	0	0
$323$	−1222.00	−0.210507
$324$	1684.00	0.288752
$325$	−1300.00	−0.221880
$326$	−7912.00	−1.34419
$327$	−464.000	−0.0784687
$328$	−560.000	−0.0942708
$329$	0	0
$330$	−720.000	−0.120105
$331$	6250.00	1.03786	0.518929	−	0.854817i	$-0.326331\pi$
$331$	6250.00	1.03786	0.518929	+	0.854817i	$0.326331\pi$
$332$	−1036.00	−0.171259
$333$	1150.00	0.189248
$334$	7350.00	1.20411
$335$	−950.000	−0.154937
$336$	0	0
$337$	−2315.00	−0.374202	−0.187101	−	0.982341i	$-0.559909\pi$
$337$	−2315.00	−0.374202	−0.187101	+	0.982341i	$0.559909\pi$
$338$	338.000	0.0543928
$339$	2706.00	0.433539
$340$	−520.000	−0.0829440
$341$	−828.000	−0.131492
$342$	−2162.00	−0.341835
$343$	0	0
$344$	−152.000	−0.0238235
$345$	−990.000	−0.154492
$346$	5652.00	0.878189
$347$	3296.00	0.509909	0.254955	−	0.966953i	$-0.417939\pi$
$347$	3296.00	0.509909	0.254955	+	0.966953i	$0.417939\pi$
$348$	−488.000	−0.0751711
$349$	5607.00	0.859988	0.429994	−	0.902832i	$-0.358516\pi$
$349$	5607.00	0.859988	0.429994	+	0.902832i	$0.358516\pi$
$350$	0	0
$351$	−1300.00	−0.197689
$352$	−1152.00	−0.174437
$353$	−3722.00	−0.561196	−0.280598	−	0.959825i	$-0.590533\pi$
$353$	−3722.00	−0.561196	−0.280598	+	0.959825i	$0.590533\pi$
$354$	−1056.00	−0.158547
$355$	−830.000	−0.124090
$356$	2540.00	0.378145
$357$	0	0
$358$	−6470.00	−0.955168
$359$	−2430.00	−0.357244	−0.178622	−	0.983918i	$-0.557164\pi$
$359$	−2430.00	−0.357244	−0.178622	+	0.983918i	$0.557164\pi$
$360$	−920.000	−0.134690
$361$	−4650.00	−0.677941
$362$	−2520.00	−0.365879
$363$	−70.0000	−0.0101213
$364$	0	0
$365$	−4365.00	−0.625958
$366$	−1240.00	−0.177092
$367$	8584.00	1.22093	0.610465	−	0.792043i	$-0.290983\pi$
$367$	8584.00	1.22093	0.610465	+	0.792043i	$0.290983\pi$
$368$	−1584.00	−0.224380
$369$	1610.00	0.227136
$370$	−500.000	−0.0702534
$371$	0	0
$372$	184.000	0.0256450
$373$	−7274.00	−1.00974	−0.504871	−	0.863195i	$-0.668460\pi$
$373$	−7274.00	−1.00974	−0.504871	+	0.863195i	$0.668460\pi$
$374$	1872.00	0.258820
$375$	−2250.00	−0.309839
$376$	−1528.00	−0.209576
$377$	−793.000	−0.108333
$378$	0	0
$379$	−1160.00	−0.157217	−0.0786084	−	0.996906i	$-0.525048\pi$
$379$	−1160.00	−0.157217	−0.0786084	+	0.996906i	$0.525048\pi$
$380$	940.000	0.126897
$381$	1152.00	0.154905
$382$	−464.000	−0.0621474
$383$	5528.00	0.737513	0.368757	−	0.929526i	$-0.379784\pi$
$383$	5528.00	0.737513	0.368757	+	0.929526i	$0.379784\pi$
$384$	256.000	0.0340207
$385$	0	0
$386$	−10684.0	−1.40881
$387$	437.000	0.0574004
$388$	−532.000	−0.0696088
$389$	9666.00	1.25986	0.629930	−	0.776652i	$-0.283084\pi$
$389$	9666.00	1.25986	0.629930	+	0.776652i	$0.283084\pi$
$390$	260.000	0.0337580
$391$	2574.00	0.332923
$392$	0	0
$393$	4112.00	0.527794
$394$	3084.00	0.394339
$395$	−5955.00	−0.758553
$396$	3312.00	0.420289
$397$	−4125.00	−0.521481	−0.260740	−	0.965409i	$-0.583967\pi$
$397$	−4125.00	−0.521481	−0.260740	+	0.965409i	$0.583967\pi$
$398$	−4364.00	−0.549617
$399$	0	0
$400$	−1600.00	−0.200000
$401$	−11796.0	−1.46899	−0.734494	−	0.678615i	$-0.762580\pi$
$401$	−11796.0	−1.46899	−0.734494	+	0.678615i	$0.762580\pi$
$402$	−760.000	−0.0942919
$403$	299.000	0.0369584
$404$	−608.000	−0.0748741
$405$	2105.00	0.258267
$406$	0	0
$407$	1800.00	0.219220
$408$	−416.000	−0.0504781
$409$	−8181.00	−0.989057	−0.494529	−	0.869161i	$-0.664659\pi$
$409$	−8181.00	−0.989057	−0.494529	+	0.869161i	$0.664659\pi$
$410$	−700.000	−0.0843184
$411$	−3684.00	−0.442137
$412$	6656.00	0.795916
$413$	0	0
$414$	4554.00	0.540621
$415$	−1295.00	−0.153178
$416$	416.000	0.0490290
$417$	2576.00	0.302511
$418$	−3384.00	−0.395973
$419$	9296.00	1.08386	0.541932	−	0.840422i	$-0.317693\pi$
$419$	9296.00	1.08386	0.541932	+	0.840422i	$0.317693\pi$
$420$	0	0
$421$	9074.00	1.05045	0.525225	−	0.850963i	$-0.323981\pi$
$421$	9074.00	1.05045	0.525225	+	0.850963i	$0.323981\pi$
$422$	−1046.00	−0.120660
$423$	4393.00	0.504953
$424$	1560.00	0.178680
$425$	2600.00	0.296749
$426$	−664.000	−0.0755186
$427$	0	0
$428$	−144.000	−0.0162629
$429$	−936.000	−0.105339
$430$	−190.000	−0.0213084
$431$	9358.00	1.04584	0.522922	−	0.852380i	$-0.324842\pi$
$431$	9358.00	1.04584	0.522922	+	0.852380i	$0.324842\pi$
$432$	−1600.00	−0.178195
$433$	14392.0	1.59731	0.798655	−	0.601789i	$-0.205545\pi$
$433$	14392.0	1.59731	0.798655	+	0.601789i	$0.205545\pi$
$434$	0	0
$435$	−610.000	−0.0672351
$436$	−928.000	−0.101934
$437$	−4653.00	−0.509344
$438$	−3492.00	−0.380946
$439$	6074.00	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$439$	6074.00	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$440$	−1440.00	−0.156021
$441$	0	0
$442$	−676.000	−0.0727467
$443$	−6483.00	−0.695297	−0.347649	−	0.937625i	$-0.613020\pi$
$443$	−6483.00	−0.695297	−0.347649	+	0.937625i	$0.613020\pi$
$444$	−400.000	−0.0427549
$445$	3175.00	0.338223
$446$	3962.00	0.420642
$447$	2392.00	0.253105
$448$	0	0
$449$	15388.0	1.61738	0.808691	−	0.588234i	$-0.200176\pi$
$449$	15388.0	1.61738	0.808691	+	0.588234i	$0.200176\pi$
$450$	4600.00	0.481880
$451$	2520.00	0.263109
$452$	5412.00	0.563184
$453$	−1780.00	−0.184617
$454$	−8704.00	−0.899777
$455$	0	0
$456$	752.000	0.0772273
$457$	−4642.00	−0.475150	−0.237575	−	0.971369i	$-0.576353\pi$
$457$	−4642.00	−0.475150	−0.237575	+	0.971369i	$0.576353\pi$
$458$	−4260.00	−0.434622
$459$	2600.00	0.264396
$460$	−1980.00	−0.200691
$461$	14266.0	1.44129	0.720644	−	0.693305i	$-0.243846\pi$
$461$	14266.0	1.44129	0.720644	+	0.693305i	$0.243846\pi$
$462$	0	0
$463$	1472.00	0.147753	0.0738765	−	0.997267i	$-0.476463\pi$
$463$	1472.00	0.147753	0.0738765	+	0.997267i	$0.476463\pi$
$464$	−976.000	−0.0976501
$465$	230.000	0.0229376
$466$	5374.00	0.534218
$467$	−1332.00	−0.131986	−0.0659932	−	0.997820i	$-0.521022\pi$
$467$	−1332.00	−0.131986	−0.0659932	+	0.997820i	$0.521022\pi$
$468$	−1196.00	−0.118131
$469$	0	0
$470$	−1910.00	−0.187450
$471$	−276.000	−0.0270009
$472$	−2112.00	−0.205959
$473$	684.000	0.0664912
$474$	−4764.00	−0.461641
$475$	−4700.00	−0.454002
$476$	0	0
$477$	−4485.00	−0.430512
$478$	7704.00	0.737182
$479$	−1629.00	−0.155388	−0.0776941	−	0.996977i	$-0.524756\pi$
$479$	−1629.00	−0.155388	−0.0776941	+	0.996977i	$0.524756\pi$
$480$	320.000	0.0304290
$481$	−650.000	−0.0616163
$482$	−2138.00	−0.202040
$483$	0	0
$484$	−140.000	−0.0131480
$485$	−665.000	−0.0622600
$486$	7084.00	0.661187
$487$	13754.0	1.27978	0.639890	−	0.768466i	$-0.278980\pi$
$487$	13754.0	1.27978	0.639890	+	0.768466i	$0.278980\pi$
$488$	−2480.00	−0.230050
$489$	−7912.00	−0.731683
$490$	0	0
$491$	−10904.0	−1.00222	−0.501111	−	0.865383i	$-0.667075\pi$
$491$	−10904.0	−1.00222	−0.501111	+	0.865383i	$0.667075\pi$
$492$	−560.000	−0.0513145
$493$	1586.00	0.144888
$494$	1222.00	0.111296
$495$	4140.00	0.375917
$496$	368.000	0.0333139
$497$	0	0
$498$	−1036.00	−0.0932214
$499$	10394.0	0.932464	0.466232	−	0.884663i	$-0.345611\pi$
$499$	10394.0	0.932464	0.466232	+	0.884663i	$0.345611\pi$
$500$	−4500.00	−0.402492
$501$	7350.00	0.655437
$502$	−10920.0	−0.970883
$503$	5754.00	0.510056	0.255028	−	0.966934i	$-0.417915\pi$
$503$	5754.00	0.510056	0.255028	+	0.966934i	$0.417915\pi$
$504$	0	0
$505$	−760.000	−0.0669694
$506$	7128.00	0.626242
$507$	338.000	0.0296077
$508$	2304.00	0.201227
$509$	−13547.0	−1.17969	−0.589843	−	0.807518i	$-0.700810\pi$
$509$	−13547.0	−1.17969	−0.589843	+	0.807518i	$0.700810\pi$
$510$	−520.000	−0.0451490
$511$	0	0
$512$	512.000	0.0441942
$513$	−4700.00	−0.404503
$514$	−4344.00	−0.372774
$515$	8320.00	0.711889
$516$	−152.000	−0.0129679
$517$	6876.00	0.584925
$518$	0	0
$519$	5652.00	0.478026
$520$	520.000	0.0438529
$521$	7044.00	0.592329	0.296164	−	0.955137i	$-0.404292\pi$
$521$	7044.00	0.592329	0.296164	+	0.955137i	$0.404292\pi$
$522$	2806.00	0.235278
$523$	−9858.00	−0.824207	−0.412103	−	0.911137i	$-0.635206\pi$
$523$	−9858.00	−0.824207	−0.412103	+	0.911137i	$0.635206\pi$
$524$	8224.00	0.685624
$525$	0	0
$526$	−6834.00	−0.566495
$527$	−598.000	−0.0494294
$528$	−1152.00	−0.0949514
$529$	−2366.00	−0.194460
$530$	1950.00	0.159816
$531$	6072.00	0.496238
$532$	0	0
$533$	−910.000	−0.0739521
$534$	2540.00	0.205836
$535$	−180.000	−0.0145459
$536$	−1520.00	−0.122489
$537$	−6470.00	−0.519928
$538$	−7584.00	−0.607750
$539$	0	0
$540$	−2000.00	−0.159382
$541$	−5650.00	−0.449006	−0.224503	−	0.974473i	$-0.572076\pi$
$541$	−5650.00	−0.449006	−0.224503	+	0.974473i	$0.572076\pi$
$542$	8816.00	0.698671
$543$	−2520.00	−0.199159
$544$	−832.000	−0.0655730
$545$	−1160.00	−0.0911724
$546$	0	0
$547$	−14285.0	−1.11660	−0.558302	−	0.829638i	$-0.688547\pi$
$547$	−14285.0	−1.11660	−0.558302	+	0.829638i	$0.688547\pi$
$548$	−7368.00	−0.574353
$549$	7130.00	0.554282
$550$	7200.00	0.558198
$551$	−2867.00	−0.221667
$552$	−1584.00	−0.122137
$553$	0	0
$554$	−2046.00	−0.156907
$555$	−500.000	−0.0382411
$556$	5152.00	0.392974
$557$	−2472.00	−0.188047	−0.0940233	−	0.995570i	$-0.529973\pi$
$557$	−2472.00	−0.188047	−0.0940233	+	0.995570i	$0.529973\pi$
$558$	−1058.00	−0.0802665
$559$	−247.000	−0.0186887
$560$	0	0
$561$	1872.00	0.140884
$562$	15824.0	1.18771
$563$	3936.00	0.294641	0.147320	−	0.989089i	$-0.452935\pi$
$563$	3936.00	0.294641	0.147320	+	0.989089i	$0.452935\pi$
$564$	−1528.00	−0.114079
$565$	6765.00	0.503727
$566$	10672.0	0.792540
$567$	0	0
$568$	−1328.00	−0.0981015
$569$	2995.00	0.220662	0.110331	−	0.993895i	$-0.464809\pi$
$569$	2995.00	0.220662	0.110331	+	0.993895i	$0.464809\pi$
$570$	940.000	0.0690742
$571$	19221.0	1.40871	0.704355	−	0.709848i	$-0.251236\pi$
$571$	19221.0	1.40871	0.704355	+	0.709848i	$0.251236\pi$
$572$	−1872.00	−0.136840
$573$	−464.000	−0.0338288
$574$	0	0
$575$	9900.00	0.718015
$576$	−1472.00	−0.106481
$577$	3166.00	0.228427	0.114213	−	0.993456i	$-0.463565\pi$
$577$	3166.00	0.228427	0.114213	+	0.993456i	$0.463565\pi$
$578$	−8474.00	−0.609813
$579$	−10684.0	−0.766860
$580$	−1220.00	−0.0873409
$581$	0	0
$582$	−532.000	−0.0378902
$583$	−7020.00	−0.498694
$584$	−6984.00	−0.494863
$585$	−1495.00	−0.105659
$586$	−13230.0	−0.932639
$587$	−13951.0	−0.980953	−0.490476	−	0.871454i	$-0.663177\pi$
$587$	−13951.0	−0.980953	−0.490476	+	0.871454i	$0.663177\pi$
$588$	0	0
$589$	1081.00	0.0756228
$590$	−2640.00	−0.184215
$591$	3084.00	0.214651
$592$	−800.000	−0.0555402
$593$	10645.0	0.737163	0.368582	−	0.929595i	$-0.379844\pi$
$593$	10645.0	0.737163	0.368582	+	0.929595i	$0.379844\pi$
$594$	7200.00	0.497339
$595$	0	0
$596$	4784.00	0.328792
$597$	−4364.00	−0.299174
$598$	−2574.00	−0.176018
$599$	6313.00	0.430621	0.215311	−	0.976546i	$-0.430924\pi$
$599$	6313.00	0.430621	0.215311	+	0.976546i	$0.430924\pi$
$600$	−1600.00	−0.108866
$601$	22162.0	1.50417	0.752086	−	0.659065i	$-0.229048\pi$
$601$	22162.0	1.50417	0.752086	+	0.659065i	$0.229048\pi$
$602$	0	0
$603$	4370.00	0.295125
$604$	−3560.00	−0.239825
$605$	−175.000	−0.0117599
$606$	−608.000	−0.0407563
$607$	−28716.0	−1.92018	−0.960088	−	0.279699i	$-0.909765\pi$
$607$	−28716.0	−1.92018	−0.960088	+	0.279699i	$0.909765\pi$
$608$	1504.00	0.100321
$609$	0	0
$610$	−3100.00	−0.205763
$611$	−2483.00	−0.164405
$612$	2392.00	0.157992
$613$	−5860.00	−0.386106	−0.193053	−	0.981188i	$-0.561839\pi$
$613$	−5860.00	−0.386106	−0.193053	+	0.981188i	$0.561839\pi$
$614$	−7686.00	−0.505182
$615$	−700.000	−0.0458971
$616$	0	0
$617$	−16154.0	−1.05403	−0.527014	−	0.849856i	$-0.676689\pi$
$617$	−16154.0	−1.05403	−0.527014	+	0.849856i	$0.676689\pi$
$618$	6656.00	0.433242
$619$	−9644.00	−0.626212	−0.313106	−	0.949718i	$-0.601369\pi$
$619$	−9644.00	−0.626212	−0.313106	+	0.949718i	$0.601369\pi$
$620$	460.000	0.0297968
$621$	9900.00	0.639732
$622$	−3496.00	−0.225365
$623$	0	0
$624$	416.000	0.0266880
$625$	6875.00	0.440000
$626$	18784.0	1.19930
$627$	−3384.00	−0.215541
$628$	−552.000	−0.0350752
$629$	1300.00	0.0824076
$630$	0	0
$631$	8682.00	0.547742	0.273871	−	0.961766i	$-0.411696\pi$
$631$	8682.00	0.547742	0.273871	+	0.961766i	$0.411696\pi$
$632$	−9528.00	−0.599689
$633$	−1046.00	−0.0656789
$634$	20760.0	1.30045
$635$	2880.00	0.179983
$636$	1560.00	0.0972610
$637$	0	0
$638$	4392.00	0.272541
$639$	3818.00	0.236366
$640$	640.000	0.0395285
$641$	−13791.0	−0.849784	−0.424892	−	0.905244i	$-0.639688\pi$
$641$	−13791.0	−0.849784	−0.424892	+	0.905244i	$0.639688\pi$
$642$	−144.000	−0.00885238
$643$	15316.0	0.939353	0.469677	−	0.882839i	$-0.344371\pi$
$643$	15316.0	0.939353	0.469677	+	0.882839i	$0.344371\pi$
$644$	0	0
$645$	−190.000	−0.0115988
$646$	−2444.00	−0.148851
$647$	−15244.0	−0.926280	−0.463140	−	0.886285i	$-0.653277\pi$
$647$	−15244.0	−0.926280	−0.463140	+	0.886285i	$0.653277\pi$
$648$	3368.00	0.204178
$649$	9504.00	0.574830
$650$	−2600.00	−0.156893
$651$	0	0
$652$	−15824.0	−0.950484
$653$	90.0000	0.00539353	0.00269676	−	0.999996i	$-0.499142\pi$
$653$	90.0000	0.00539353	0.00269676	+	0.999996i	$0.499142\pi$
$654$	−928.000	−0.0554857
$655$	10280.0	0.613241
$656$	−1120.00	−0.0666595
$657$	20079.0	1.19232
$658$	0	0
$659$	10887.0	0.643547	0.321773	−	0.946817i	$-0.395721\pi$
$659$	10887.0	0.643547	0.321773	+	0.946817i	$0.395721\pi$
$660$	−1440.00	−0.0849272
$661$	4475.00	0.263324	0.131662	−	0.991295i	$-0.457969\pi$
$661$	4475.00	0.263324	0.131662	+	0.991295i	$0.457969\pi$
$662$	12500.0	0.733877
$663$	−676.000	−0.0395983
$664$	−2072.00	−0.121098
$665$	0	0
$666$	2300.00	0.133819
$667$	6039.00	0.350571
$668$	14700.0	0.851437
$669$	3962.00	0.228968
$670$	−1900.00	−0.109557
$671$	11160.0	0.642067
$672$	0	0
$673$	−33451.0	−1.91596	−0.957980	−	0.286834i	$-0.907397\pi$
$673$	−33451.0	−1.91596	−0.957980	+	0.286834i	$0.907397\pi$
$674$	−4630.00	−0.264601
$675$	10000.0	0.570222
$676$	676.000	0.0384615
$677$	5556.00	0.315413	0.157706	−	0.987486i	$-0.449590\pi$
$677$	5556.00	0.315413	0.157706	+	0.987486i	$0.449590\pi$
$678$	5412.00	0.306558
$679$	0	0
$680$	−1040.00	−0.0586503
$681$	−8704.00	−0.489777
$682$	−1656.00	−0.0929788
$683$	−6504.00	−0.364376	−0.182188	−	0.983264i	$-0.558318\pi$
$683$	−6504.00	−0.364376	−0.182188	+	0.983264i	$0.558318\pi$
$684$	−4324.00	−0.241714
$685$	−9210.00	−0.513717
$686$	0	0
$687$	−4260.00	−0.236578
$688$	−304.000	−0.0168458
$689$	2535.00	0.140168
$690$	−1980.00	−0.109242
$691$	−16963.0	−0.933868	−0.466934	−	0.884292i	$-0.654641\pi$
$691$	−16963.0	−0.933868	−0.466934	+	0.884292i	$0.654641\pi$
$692$	11304.0	0.620973
$693$	0	0
$694$	6592.00	0.360560
$695$	6440.00	0.351487
$696$	−976.000	−0.0531540
$697$	1820.00	0.0989059
$698$	11214.0	0.608103
$699$	5374.00	0.290792
$700$	0	0
$701$	12805.0	0.689926	0.344963	−	0.938616i	$-0.387891\pi$
$701$	12805.0	0.689926	0.344963	+	0.938616i	$0.387891\pi$
$702$	−2600.00	−0.139787
$703$	−2350.00	−0.126077
$704$	−2304.00	−0.123346
$705$	−1910.00	−0.102035
$706$	−7444.00	−0.396825
$707$	0	0
$708$	−2112.00	−0.112110
$709$	10772.0	0.570594	0.285297	−	0.958439i	$-0.407908\pi$
$709$	10772.0	0.570594	0.285297	+	0.958439i	$0.407908\pi$
$710$	−1660.00	−0.0877446
$711$	27393.0	1.44489
$712$	5080.00	0.267389
$713$	−2277.00	−0.119599
$714$	0	0
$715$	−2340.00	−0.122393
$716$	−12940.0	−0.675406
$717$	7704.00	0.401271
$718$	−4860.00	−0.252609
$719$	22524.0	1.16829	0.584147	−	0.811648i	$-0.301429\pi$
$719$	22524.0	1.16829	0.584147	+	0.811648i	$0.301429\pi$
$720$	−1840.00	−0.0952399
$721$	0	0
$722$	−9300.00	−0.479377
$723$	−2138.00	−0.109977
$724$	−5040.00	−0.258716
$725$	6100.00	0.312480
$726$	−140.000	−0.00715687
$727$	5754.00	0.293541	0.146770	−	0.989171i	$-0.453112\pi$
$727$	5754.00	0.293541	0.146770	+	0.989171i	$0.453112\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	−8730.00	−0.442619
$731$	494.000	0.0249949
$732$	−2480.00	−0.125223
$733$	−31817.0	−1.60326	−0.801629	−	0.597822i	$-0.796033\pi$
$733$	−31817.0	−1.60326	−0.801629	+	0.597822i	$0.796033\pi$
$734$	17168.0	0.863328
$735$	0	0
$736$	−3168.00	−0.158660
$737$	6840.00	0.341865
$738$	3220.00	0.160610
$739$	30820.0	1.53414	0.767072	−	0.641561i	$-0.221713\pi$
$739$	30820.0	1.53414	0.767072	+	0.641561i	$0.221713\pi$
$740$	−1000.00	−0.0496767
$741$	1222.00	0.0605820
$742$	0	0
$743$	−5724.00	−0.282629	−0.141314	−	0.989965i	$-0.545133\pi$
$743$	−5724.00	−0.282629	−0.141314	+	0.989965i	$0.545133\pi$
$744$	368.000	0.0181338
$745$	5980.00	0.294081
$746$	−14548.0	−0.713995
$747$	5957.00	0.291774
$748$	3744.00	0.183014
$749$	0	0
$750$	−4500.00	−0.219089
$751$	20397.0	0.991075	0.495537	−	0.868587i	$-0.334971\pi$
$751$	20397.0	0.991075	0.495537	+	0.868587i	$0.334971\pi$
$752$	−3056.00	−0.148193
$753$	−10920.0	−0.528482
$754$	−1586.00	−0.0766031
$755$	−4450.00	−0.214506
$756$	0	0
$757$	−21103.0	−1.01321	−0.506606	−	0.862178i	$-0.669100\pi$
$757$	−21103.0	−1.01321	−0.506606	+	0.862178i	$0.669100\pi$
$758$	−2320.00	−0.111169
$759$	7128.00	0.340883
$760$	1880.00	0.0897300
$761$	22209.0	1.05792	0.528959	−	0.848647i	$-0.322583\pi$
$761$	22209.0	1.05792	0.528959	+	0.848647i	$0.322583\pi$
$762$	2304.00	0.109534
$763$	0	0
$764$	−928.000	−0.0439448
$765$	2990.00	0.141312
$766$	11056.0	0.521501
$767$	−3432.00	−0.161568
$768$	512.000	0.0240563
$769$	−27895.0	−1.30809	−0.654044	−	0.756457i	$-0.726929\pi$
$769$	−27895.0	−1.30809	−0.654044	+	0.756457i	$0.726929\pi$
$770$	0	0
$771$	−4344.00	−0.202912
$772$	−21368.0	−0.996180
$773$	−24722.0	−1.15031	−0.575154	−	0.818045i	$-0.695058\pi$
$773$	−24722.0	−1.15031	−0.575154	+	0.818045i	$0.695058\pi$
$774$	874.000	0.0405882
$775$	−2300.00	−0.106604
$776$	−1064.00	−0.0492208
$777$	0	0
$778$	19332.0	0.890856
$779$	−3290.00	−0.151318
$780$	520.000	0.0238705
$781$	5976.00	0.273800
$782$	5148.00	0.235412
$783$	6100.00	0.278412
$784$	0	0
$785$	−690.000	−0.0313722
$786$	8224.00	0.373207
$787$	40091.0	1.81587	0.907935	−	0.419111i	$-0.137658\pi$
$787$	40091.0	1.81587	0.907935	+	0.419111i	$0.137658\pi$
$788$	6168.00	0.278840
$789$	−6834.00	−0.308361
$790$	−11910.0	−0.536378
$791$	0	0
$792$	6624.00	0.297189
$793$	−4030.00	−0.180466
$794$	−8250.00	−0.368742
$795$	1950.00	0.0869929
$796$	−8728.00	−0.388638
$797$	−602.000	−0.0267552	−0.0133776	−	0.999911i	$-0.504258\pi$
$797$	−602.000	−0.0267552	−0.0133776	+	0.999911i	$0.504258\pi$
$798$	0	0
$799$	4966.00	0.219880
$800$	−3200.00	−0.141421
$801$	−14605.0	−0.644248
$802$	−23592.0	−1.03873
$803$	31428.0	1.38116
$804$	−1520.00	−0.0666745
$805$	0	0
$806$	598.000	0.0261336
$807$	−7584.00	−0.330817
$808$	−1216.00	−0.0529440
$809$	−38963.0	−1.69328	−0.846642	−	0.532163i	$-0.821379\pi$
$809$	−38963.0	−1.69328	−0.846642	+	0.532163i	$0.821379\pi$
$810$	4210.00	0.182623
$811$	−18116.0	−0.784388	−0.392194	−	0.919882i	$-0.628284\pi$
$811$	−18116.0	−0.784388	−0.392194	+	0.919882i	$0.628284\pi$
$812$	0	0
$813$	8816.00	0.380308
$814$	3600.00	0.155012
$815$	−19780.0	−0.850139
$816$	−832.000	−0.0356934
$817$	−893.000	−0.0382400
$818$	−16362.0	−0.699369
$819$	0	0
$820$	−1400.00	−0.0596221
$821$	8070.00	0.343051	0.171526	−	0.985180i	$-0.445130\pi$
$821$	8070.00	0.343051	0.171526	+	0.985180i	$0.445130\pi$
$822$	−7368.00	−0.312638
$823$	14664.0	0.621087	0.310544	−	0.950559i	$-0.399489\pi$
$823$	14664.0	0.621087	0.310544	+	0.950559i	$0.399489\pi$
$824$	13312.0	0.562798
$825$	7200.00	0.303845
$826$	0	0
$827$	−12836.0	−0.539724	−0.269862	−	0.962899i	$-0.586978\pi$
$827$	−12836.0	−0.539724	−0.269862	+	0.962899i	$0.586978\pi$
$828$	9108.00	0.382276
$829$	−22664.0	−0.949521	−0.474761	−	0.880115i	$-0.657465\pi$
$829$	−22664.0	−0.949521	−0.474761	+	0.880115i	$0.657465\pi$
$830$	−2590.00	−0.108314
$831$	−2046.00	−0.0854091
$832$	832.000	0.0346688
$833$	0	0
$834$	5152.00	0.213908
$835$	18375.0	0.761549
$836$	−6768.00	−0.279995
$837$	−2300.00	−0.0949816
$838$	18592.0	0.766408
$839$	420.000	0.0172825	0.00864125	−	0.999963i	$-0.497249\pi$
$839$	420.000	0.0172825	0.00864125	+	0.999963i	$0.497249\pi$
$840$	0	0
$841$	−20668.0	−0.847431
$842$	18148.0	0.742781
$843$	15824.0	0.646510
$844$	−2092.00	−0.0853194
$845$	845.000	0.0344010
$846$	8786.00	0.357055
$847$	0	0
$848$	3120.00	0.126346
$849$	10672.0	0.431404
$850$	5200.00	0.209834
$851$	4950.00	0.199393
$852$	−1328.00	−0.0533997
$853$	5425.00	0.217759	0.108880	−	0.994055i	$-0.465274\pi$
$853$	5425.00	0.217759	0.108880	+	0.994055i	$0.465274\pi$
$854$	0	0
$855$	−5405.00	−0.216195
$856$	−288.000	−0.0114996
$857$	33294.0	1.32707	0.663536	−	0.748144i	$-0.269055\pi$
$857$	33294.0	1.32707	0.663536	+	0.748144i	$0.269055\pi$
$858$	−1872.00	−0.0744860
$859$	−27386.0	−1.08777	−0.543887	−	0.839158i	$-0.683048\pi$
$859$	−27386.0	−1.08777	−0.543887	+	0.839158i	$0.683048\pi$
$860$	−380.000	−0.0150673
$861$	0	0
$862$	18716.0	0.739524
$863$	12004.0	0.473489	0.236744	−	0.971572i	$-0.423920\pi$
$863$	12004.0	0.473489	0.236744	+	0.971572i	$0.423920\pi$
$864$	−3200.00	−0.126003
$865$	14130.0	0.555416
$866$	28784.0	1.12947
$867$	−8474.00	−0.331940
$868$	0	0
$869$	42876.0	1.67373
$870$	−1220.00	−0.0475424
$871$	−2470.00	−0.0960881
$872$	−1856.00	−0.0720781
$873$	3059.00	0.118593
$874$	−9306.00	−0.360160
$875$	0	0
$876$	−6984.00	−0.269369
$877$	39346.0	1.51496	0.757480	−	0.652858i	$-0.226430\pi$
$877$	39346.0	1.51496	0.757480	+	0.652858i	$0.226430\pi$
$878$	12148.0	0.466942
$879$	−13230.0	−0.507664
$880$	−2880.00	−0.110324
$881$	−50806.0	−1.94290	−0.971452	−	0.237238i	$-0.923758\pi$
$881$	−50806.0	−1.94290	−0.971452	+	0.237238i	$0.923758\pi$
$882$	0	0
$883$	−34592.0	−1.31836	−0.659181	−	0.751984i	$-0.729097\pi$
$883$	−34592.0	−1.31836	−0.659181	+	0.751984i	$0.729097\pi$
$884$	−1352.00	−0.0514397
$885$	−2640.00	−0.100274
$886$	−12966.0	−0.491649
$887$	−34624.0	−1.31067	−0.655333	−	0.755340i	$-0.727472\pi$
$887$	−34624.0	−1.31067	−0.655333	+	0.755340i	$0.727472\pi$
$888$	−800.000	−0.0302323
$889$	0	0
$890$	6350.00	0.239160
$891$	−15156.0	−0.569860
$892$	7924.00	0.297439
$893$	−8977.00	−0.336398
$894$	4784.00	0.178972
$895$	−16175.0	−0.604101
$896$	0	0
$897$	−2574.00	−0.0958120
$898$	30776.0	1.14366
$899$	−1403.00	−0.0520497
$900$	9200.00	0.340741
$901$	−5070.00	−0.187465
$902$	5040.00	0.186046
$903$	0	0
$904$	10824.0	0.398231
$905$	−6300.00	−0.231402
$906$	−3560.00	−0.130544
$907$	10849.0	0.397172	0.198586	−	0.980083i	$-0.436365\pi$
$907$	10849.0	0.397172	0.198586	+	0.980083i	$0.436365\pi$
$908$	−17408.0	−0.636239
$909$	3496.00	0.127563
$910$	0	0
$911$	39671.0	1.44276	0.721382	−	0.692537i	$-0.243507\pi$
$911$	39671.0	1.44276	0.721382	+	0.692537i	$0.243507\pi$
$912$	1504.00	0.0546079
$913$	9324.00	0.337984
$914$	−9284.00	−0.335982
$915$	−3100.00	−0.112003
$916$	−8520.00	−0.307324
$917$	0	0
$918$	5200.00	0.186956
$919$	27208.0	0.976615	0.488307	−	0.872672i	$-0.337614\pi$
$919$	27208.0	0.976615	0.488307	+	0.872672i	$0.337614\pi$
$920$	−3960.00	−0.141910
$921$	−7686.00	−0.274986
$922$	28532.0	1.01914
$923$	−2158.00	−0.0769571
$924$	0	0
$925$	5000.00	0.177729
$926$	2944.00	0.104477
$927$	−38272.0	−1.35601
$928$	−1952.00	−0.0690491
$929$	27193.0	0.960359	0.480179	−	0.877170i	$-0.340572\pi$
$929$	27193.0	0.960359	0.480179	+	0.877170i	$0.340572\pi$
$930$	460.000	0.0162193
$931$	0	0
$932$	10748.0	0.377749
$933$	−3496.00	−0.122673
$934$	−2664.00	−0.0933284
$935$	4680.00	0.163692
$936$	−2392.00	−0.0835309
$937$	−24262.0	−0.845896	−0.422948	−	0.906154i	$-0.639005\pi$
$937$	−24262.0	−0.845896	−0.422948	+	0.906154i	$0.639005\pi$
$938$	0	0
$939$	18784.0	0.652814
$940$	−3820.00	−0.132548
$941$	303.000	0.0104968	0.00524842	−	0.999986i	$-0.498329\pi$
$941$	303.000	0.0104968	0.00524842	+	0.999986i	$0.498329\pi$
$942$	−552.000	−0.0190925
$943$	6930.00	0.239313
$944$	−4224.00	−0.145635
$945$	0	0
$946$	1368.00	0.0470164
$947$	−20098.0	−0.689649	−0.344824	−	0.938667i	$-0.612062\pi$
$947$	−20098.0	−0.689649	−0.344824	+	0.938667i	$0.612062\pi$
$948$	−9528.00	−0.326429
$949$	−11349.0	−0.388202
$950$	−9400.00	−0.321028
$951$	20760.0	0.707875
$952$	0	0
$953$	13477.0	0.458093	0.229047	−	0.973415i	$-0.426439\pi$
$953$	13477.0	0.458093	0.229047	+	0.973415i	$0.426439\pi$
$954$	−8970.00	−0.304418
$955$	−1160.00	−0.0393055
$956$	15408.0	0.521266
$957$	4392.00	0.148352
$958$	−3258.00	−0.109876
$959$	0	0
$960$	640.000	0.0215166
$961$	−29262.0	−0.982243
$962$	−1300.00	−0.0435693
$963$	828.000	0.0277071
$964$	−4276.00	−0.142864
$965$	−26710.0	−0.891011
$966$	0	0
$967$	−14488.0	−0.481802	−0.240901	−	0.970550i	$-0.577443\pi$
$967$	−14488.0	−0.481802	−0.240901	+	0.970550i	$0.577443\pi$
$968$	−280.000	−0.00929705
$969$	−2444.00	−0.0810243
$970$	−1330.00	−0.0440245
$971$	−2830.00	−0.0935314	−0.0467657	−	0.998906i	$-0.514891\pi$
$971$	−2830.00	−0.0935314	−0.0467657	+	0.998906i	$0.514891\pi$
$972$	14168.0	0.467530
$973$	0	0
$974$	27508.0	0.904942
$975$	−2600.00	−0.0854017
$976$	−4960.00	−0.162670
$977$	−36016.0	−1.17938	−0.589690	−	0.807630i	$-0.700750\pi$
$977$	−36016.0	−1.17938	−0.589690	+	0.807630i	$0.700750\pi$
$978$	−15824.0	−0.517378
$979$	−22860.0	−0.746281
$980$	0	0
$981$	5336.00	0.173665
$982$	−21808.0	−0.708677
$983$	16907.0	0.548575	0.274288	−	0.961648i	$-0.411558\pi$
$983$	16907.0	0.548575	0.274288	+	0.961648i	$0.411558\pi$
$984$	−1120.00	−0.0362849
$985$	7710.00	0.249402
$986$	3172.00	0.102451
$987$	0	0
$988$	2444.00	0.0786984
$989$	1881.00	0.0604776
$990$	8280.00	0.265814
$991$	−51528.0	−1.65171	−0.825853	−	0.563885i	$-0.809306\pi$
$991$	−51528.0	−1.65171	−0.825853	+	0.563885i	$0.809306\pi$
$992$	736.000	0.0235565
$993$	12500.0	0.399472
$994$	0	0
$995$	−10910.0	−0.347608
$996$	−2072.00	−0.0659175
$997$	−46492.0	−1.47685	−0.738423	−	0.674337i	$-0.764429\pi$
$997$	−46492.0	−1.47685	−0.738423	+	0.674337i	$0.764429\pi$
$998$	20788.0	0.659351
$999$	5000.00	0.158351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.4.a.g.1.1		1
7.6	odd	2		182.4.a.c.1.1	✓	1
21.20	even	2		1638.4.a.e.1.1		1
28.27	even	2		1456.4.a.f.1.1		1
91.90	odd	2		2366.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.a.c.1.1	✓	1	7.6	odd	2
1274.4.a.g.1.1		1	1.1	even	1	trivial
1456.4.a.f.1.1		1	28.27	even	2
1638.4.a.e.1.1		1	21.20	even	2
2366.4.a.b.1.1		1	91.90	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1274.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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