LMFDB - Embedded newform 435.4.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] 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("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$25.6658308525$
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	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +29.0000 q^{7} +24.0000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -15.0000 q^{11} +12.0000 q^{12} +3.00000 q^{13} -58.0000 q^{14} -15.0000 q^{15} -16.0000 q^{16} +121.000 q^{17} -18.0000 q^{18} -40.0000 q^{19} -20.0000 q^{20} -87.0000 q^{21} +30.0000 q^{22} -116.000 q^{23} -72.0000 q^{24} +25.0000 q^{25} -6.00000 q^{26} -27.0000 q^{27} -116.000 q^{28} +29.0000 q^{29} +30.0000 q^{30} -116.000 q^{31} -160.000 q^{32} +45.0000 q^{33} -242.000 q^{34} +145.000 q^{35} -36.0000 q^{36} +36.0000 q^{37} +80.0000 q^{38} -9.00000 q^{39} +120.000 q^{40} -170.000 q^{41} +174.000 q^{42} +230.000 q^{43} +60.0000 q^{44} +45.0000 q^{45} +232.000 q^{46} +231.000 q^{47} +48.0000 q^{48} +498.000 q^{49} -50.0000 q^{50} -363.000 q^{51} -12.0000 q^{52} +456.000 q^{53} +54.0000 q^{54} -75.0000 q^{55} +696.000 q^{56} +120.000 q^{57} -58.0000 q^{58} +576.000 q^{59} +60.0000 q^{60} +342.000 q^{61} +232.000 q^{62} +261.000 q^{63} +448.000 q^{64} +15.0000 q^{65} -90.0000 q^{66} -269.000 q^{67} -484.000 q^{68} +348.000 q^{69} -290.000 q^{70} +302.000 q^{71} +216.000 q^{72} -372.000 q^{73} -72.0000 q^{74} -75.0000 q^{75} +160.000 q^{76} -435.000 q^{77} +18.0000 q^{78} -348.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +340.000 q^{82} -512.000 q^{83} +348.000 q^{84} +605.000 q^{85} -460.000 q^{86} -87.0000 q^{87} -360.000 q^{88} +1525.00 q^{89} -90.0000 q^{90} +87.0000 q^{91} +464.000 q^{92} +348.000 q^{93} -462.000 q^{94} -200.000 q^{95} +480.000 q^{96} -560.000 q^{97} -996.000 q^{98} -135.000 q^{99} +O(q^{100})\)

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−2.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−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
$7$	29.0000	1.56585	0.782926	−	0.622114i	$-0.213726\pi$
$7$	29.0000	1.56585	0.782926	+	0.622114i	$0.213726\pi$
$8$	24.0000	1.06066
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	−15.0000	−0.411152	−0.205576	−	0.978641i	$-0.565907\pi$
$11$	−15.0000	−0.411152	−0.205576	+	0.978641i	$0.565907\pi$
$12$	12.0000	0.288675
$13$	3.00000	0.0640039	0.0320019	−	0.999488i	$-0.489812\pi$
$13$	3.00000	0.0640039	0.0320019	+	0.999488i	$0.489812\pi$
$14$	−58.0000	−1.10723
$15$	−15.0000	−0.258199
$16$	−16.0000	−0.250000
$17$	121.000	1.72628	0.863141	−	0.504962i	$-0.168494\pi$
$17$	121.000	1.72628	0.863141	+	0.504962i	$0.168494\pi$
$18$	−18.0000	−0.235702
$19$	−40.0000	−0.482980	−0.241490	−	0.970403i	$-0.577636\pi$
$19$	−40.0000	−0.482980	−0.241490	+	0.970403i	$0.577636\pi$
$20$	−20.0000	−0.223607
$21$	−87.0000	−0.904046
$22$	30.0000	0.290728
$23$	−116.000	−1.05164	−0.525819	−	0.850597i	$-0.676241\pi$
$23$	−116.000	−1.05164	−0.525819	+	0.850597i	$0.676241\pi$
$24$	−72.0000	−0.612372
$25$	25.0000	0.200000
$26$	−6.00000	−0.0452576
$27$	−27.0000	−0.192450
$28$	−116.000	−0.782926
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	30.0000	0.182574
$31$	−116.000	−0.672071	−0.336036	−	0.941849i	$-0.609086\pi$
$31$	−116.000	−0.672071	−0.336036	+	0.941849i	$0.609086\pi$
$32$	−160.000	−0.883883
$33$	45.0000	0.237379
$34$	−242.000	−1.22067
$35$	145.000	0.700271
$36$	−36.0000	−0.166667
$37$	36.0000	0.159956	0.0799779	−	0.996797i	$-0.474515\pi$
$37$	36.0000	0.159956	0.0799779	+	0.996797i	$0.474515\pi$
$38$	80.0000	0.341519
$39$	−9.00000	−0.0369527
$40$	120.000	0.474342
$41$	−170.000	−0.647550	−0.323775	−	0.946134i	$-0.604952\pi$
$41$	−170.000	−0.647550	−0.323775	+	0.946134i	$0.604952\pi$
$42$	174.000	0.639257
$43$	230.000	0.815690	0.407845	−	0.913051i	$-0.366280\pi$
$43$	230.000	0.815690	0.407845	+	0.913051i	$0.366280\pi$
$44$	60.0000	0.205576
$45$	45.0000	0.149071
$46$	232.000	0.743620
$47$	231.000	0.716911	0.358455	−	0.933547i	$-0.383303\pi$
$47$	231.000	0.716911	0.358455	+	0.933547i	$0.383303\pi$
$48$	48.0000	0.144338
$49$	498.000	1.45190
$50$	−50.0000	−0.141421
$51$	−363.000	−0.996670
$52$	−12.0000	−0.0320019
$53$	456.000	1.18182	0.590910	−	0.806738i	$-0.298769\pi$
$53$	456.000	1.18182	0.590910	+	0.806738i	$0.298769\pi$
$54$	54.0000	0.136083
$55$	−75.0000	−0.183873
$56$	696.000	1.66084
$57$	120.000	0.278849
$58$	−58.0000	−0.131306
$59$	576.000	1.27100	0.635498	−	0.772102i	$-0.280795\pi$
$59$	576.000	1.27100	0.635498	+	0.772102i	$0.280795\pi$
$60$	60.0000	0.129099
$61$	342.000	0.717846	0.358923	−	0.933367i	$-0.383144\pi$
$61$	342.000	0.717846	0.358923	+	0.933367i	$0.383144\pi$
$62$	232.000	0.475226
$63$	261.000	0.521951
$64$	448.000	0.875000
$65$	15.0000	0.0286234
$66$	−90.0000	−0.167852
$67$	−269.000	−0.490501	−0.245251	−	0.969460i	$-0.578870\pi$
$67$	−269.000	−0.490501	−0.245251	+	0.969460i	$0.578870\pi$
$68$	−484.000	−0.863141
$69$	348.000	0.607163
$70$	−290.000	−0.495166
$71$	302.000	0.504800	0.252400	−	0.967623i	$-0.418780\pi$
$71$	302.000	0.504800	0.252400	+	0.967623i	$0.418780\pi$
$72$	216.000	0.353553
$73$	−372.000	−0.596429	−0.298214	−	0.954499i	$-0.596391\pi$
$73$	−372.000	−0.596429	−0.298214	+	0.954499i	$0.596391\pi$
$74$	−72.0000	−0.113106
$75$	−75.0000	−0.115470
$76$	160.000	0.241490
$77$	−435.000	−0.643803
$78$	18.0000	0.0261295
$79$	−348.000	−0.495608	−0.247804	−	0.968810i	$-0.579709\pi$
$79$	−348.000	−0.495608	−0.247804	+	0.968810i	$0.579709\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	340.000	0.457887
$83$	−512.000	−0.677100	−0.338550	−	0.940948i	$-0.609936\pi$
$83$	−512.000	−0.677100	−0.338550	+	0.940948i	$0.609936\pi$
$84$	348.000	0.452023
$85$	605.000	0.772017
$86$	−460.000	−0.576780
$87$	−87.0000	−0.107211
$88$	−360.000	−0.436092
$89$	1525.00	1.81629	0.908144	−	0.418657i	$-0.137499\pi$
$89$	1525.00	1.81629	0.908144	+	0.418657i	$0.137499\pi$
$90$	−90.0000	−0.105409
$91$	87.0000	0.100221
$92$	464.000	0.525819
$93$	348.000	0.388021
$94$	−462.000	−0.506933
$95$	−200.000	−0.215995
$96$	480.000	0.510310
$97$	−560.000	−0.586179	−0.293090	−	0.956085i	$-0.594683\pi$
$97$	−560.000	−0.586179	−0.293090	+	0.956085i	$0.594683\pi$
$98$	−996.000	−1.02664
$99$	−135.000	−0.137051
$100$	−100.000	−0.100000
$101$	1447.00	1.42556	0.712782	−	0.701386i	$-0.247435\pi$
$101$	1447.00	1.42556	0.712782	+	0.701386i	$0.247435\pi$
$102$	726.000	0.704752
$103$	556.000	0.531886	0.265943	−	0.963989i	$-0.414317\pi$
$103$	556.000	0.531886	0.265943	+	0.963989i	$0.414317\pi$
$104$	72.0000	0.0678864
$105$	−435.000	−0.404301
$106$	−912.000	−0.835672
$107$	1558.00	1.40764	0.703820	−	0.710378i	$-0.251476\pi$
$107$	1558.00	1.40764	0.703820	+	0.710378i	$0.251476\pi$
$108$	108.000	0.0962250
$109$	−881.000	−0.774170	−0.387085	−	0.922044i	$-0.626518\pi$
$109$	−881.000	−0.774170	−0.387085	+	0.922044i	$0.626518\pi$
$110$	150.000	0.130018
$111$	−108.000	−0.0923505
$112$	−464.000	−0.391463
$113$	313.000	0.260571	0.130286	−	0.991476i	$-0.458411\pi$
$113$	313.000	0.260571	0.130286	+	0.991476i	$0.458411\pi$
$114$	−240.000	−0.197176
$115$	−580.000	−0.470307
$116$	−116.000	−0.0928477
$117$	27.0000	0.0213346
$118$	−1152.00	−0.898730
$119$	3509.00	2.70311
$120$	−360.000	−0.273861
$121$	−1106.00	−0.830954
$122$	−684.000	−0.507594
$123$	510.000	0.373863
$124$	464.000	0.336036
$125$	125.000	0.0894427
$126$	−522.000	−0.369075
$127$	−494.000	−0.345161	−0.172580	−	0.984995i	$-0.555210\pi$
$127$	−494.000	−0.345161	−0.172580	+	0.984995i	$0.555210\pi$
$128$	384.000	0.265165
$129$	−690.000	−0.470939
$130$	−30.0000	−0.0202398
$131$	−2007.00	−1.33857	−0.669284	−	0.743007i	$-0.733399\pi$
$131$	−2007.00	−1.33857	−0.669284	+	0.743007i	$0.733399\pi$
$132$	−180.000	−0.118689
$133$	−1160.00	−0.756276
$134$	538.000	0.346837
$135$	−135.000	−0.0860663
$136$	2904.00	1.83100
$137$	918.000	0.572482	0.286241	−	0.958158i	$-0.407594\pi$
$137$	918.000	0.572482	0.286241	+	0.958158i	$0.407594\pi$
$138$	−696.000	−0.429329
$139$	1619.00	0.987927	0.493963	−	0.869483i	$-0.335548\pi$
$139$	1619.00	0.987927	0.493963	+	0.869483i	$0.335548\pi$
$140$	−580.000	−0.350135
$141$	−693.000	−0.413909
$142$	−604.000	−0.356948
$143$	−45.0000	−0.0263153
$144$	−144.000	−0.0833333
$145$	145.000	0.0830455
$146$	744.000	0.421739
$147$	−1494.00	−0.838252
$148$	−144.000	−0.0799779
$149$	3046.00	1.67475	0.837376	−	0.546627i	$-0.184089\pi$
$149$	3046.00	1.67475	0.837376	+	0.546627i	$0.184089\pi$
$150$	150.000	0.0816497
$151$	1576.00	0.849358	0.424679	−	0.905344i	$-0.360387\pi$
$151$	1576.00	0.849358	0.424679	+	0.905344i	$0.360387\pi$
$152$	−960.000	−0.512278
$153$	1089.00	0.575428
$154$	870.000	0.455238
$155$	−580.000	−0.300559
$156$	36.0000	0.0184763
$157$	−3544.00	−1.80154	−0.900771	−	0.434295i	$-0.856998\pi$
$157$	−3544.00	−1.80154	−0.900771	+	0.434295i	$0.856998\pi$
$158$	696.000	0.350448
$159$	−1368.00	−0.682324
$160$	−800.000	−0.395285
$161$	−3364.00	−1.64671
$162$	−162.000	−0.0785674
$163$	−768.000	−0.369045	−0.184523	−	0.982828i	$-0.559074\pi$
$163$	−768.000	−0.369045	−0.184523	+	0.982828i	$0.559074\pi$
$164$	680.000	0.323775
$165$	225.000	0.106159
$166$	1024.00	0.478782
$167$	−1624.00	−0.752508	−0.376254	−	0.926516i	$-0.622788\pi$
$167$	−1624.00	−0.752508	−0.376254	+	0.926516i	$0.622788\pi$
$168$	−2088.00	−0.958885
$169$	−2188.00	−0.995904
$170$	−1210.00	−0.545899
$171$	−360.000	−0.160993
$172$	−920.000	−0.407845
$173$	1700.00	0.747102	0.373551	−	0.927610i	$-0.378140\pi$
$173$	1700.00	0.747102	0.373551	+	0.927610i	$0.378140\pi$
$174$	174.000	0.0758098
$175$	725.000	0.313171
$176$	240.000	0.102788
$177$	−1728.00	−0.733810
$178$	−3050.00	−1.28431
$179$	3870.00	1.61596	0.807982	−	0.589208i	$-0.200560\pi$
$179$	3870.00	1.61596	0.807982	+	0.589208i	$0.200560\pi$
$180$	−180.000	−0.0745356
$181$	1757.00	0.721529	0.360765	−	0.932657i	$-0.382516\pi$
$181$	1757.00	0.721529	0.360765	+	0.932657i	$0.382516\pi$
$182$	−174.000	−0.0708667
$183$	−1026.00	−0.414449
$184$	−2784.00	−1.11543
$185$	180.000	0.0715344
$186$	−696.000	−0.274372
$187$	−1815.00	−0.709764
$188$	−924.000	−0.358455
$189$	−783.000	−0.301349
$190$	400.000	0.152732
$191$	−2048.00	−0.775854	−0.387927	−	0.921690i	$-0.626809\pi$
$191$	−2048.00	−0.775854	−0.387927	+	0.921690i	$0.626809\pi$
$192$	−1344.00	−0.505181
$193$	−2398.00	−0.894362	−0.447181	−	0.894444i	$-0.647572\pi$
$193$	−2398.00	−0.894362	−0.447181	+	0.894444i	$0.647572\pi$
$194$	1120.00	0.414491
$195$	−45.0000	−0.0165257
$196$	−1992.00	−0.725948
$197$	3966.00	1.43434	0.717172	−	0.696896i	$-0.245436\pi$
$197$	3966.00	1.43434	0.717172	+	0.696896i	$0.245436\pi$
$198$	270.000	0.0969094
$199$	641.000	0.228338	0.114169	−	0.993461i	$-0.463579\pi$
$199$	641.000	0.228338	0.114169	+	0.993461i	$0.463579\pi$
$200$	600.000	0.212132
$201$	807.000	0.283191
$202$	−2894.00	−1.00803
$203$	841.000	0.290772
$204$	1452.00	0.498335
$205$	−850.000	−0.289593
$206$	−1112.00	−0.376101
$207$	−1044.00	−0.350546
$208$	−48.0000	−0.0160010
$209$	600.000	0.198578
$210$	870.000	0.285884
$211$	5438.00	1.77425	0.887126	−	0.461526i	$-0.152698\pi$
$211$	5438.00	1.77425	0.887126	+	0.461526i	$0.152698\pi$
$212$	−1824.00	−0.590910
$213$	−906.000	−0.291446
$214$	−3116.00	−0.995352
$215$	1150.00	0.364788
$216$	−648.000	−0.204124
$217$	−3364.00	−1.05236
$218$	1762.00	0.547421
$219$	1116.00	0.344348
$220$	300.000	0.0919363
$221$	363.000	0.110489
$222$	216.000	0.0653017
$223$	2799.00	0.840515	0.420258	−	0.907405i	$-0.361940\pi$
$223$	2799.00	0.840515	0.420258	+	0.907405i	$0.361940\pi$
$224$	−4640.00	−1.38403
$225$	225.000	0.0666667
$226$	−626.000	−0.184252
$227$	1492.00	0.436245	0.218122	−	0.975921i	$-0.430007\pi$
$227$	1492.00	0.436245	0.218122	+	0.975921i	$0.430007\pi$
$228$	−480.000	−0.139424
$229$	4622.00	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$229$	4622.00	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$230$	1160.00	0.332557
$231$	1305.00	0.371700
$232$	696.000	0.196960
$233$	4170.00	1.17247	0.586236	−	0.810141i	$-0.300609\pi$
$233$	4170.00	1.17247	0.586236	+	0.810141i	$0.300609\pi$
$234$	−54.0000	−0.0150859
$235$	1155.00	0.320612
$236$	−2304.00	−0.635498
$237$	1044.00	0.286140
$238$	−7018.00	−1.91138
$239$	1686.00	0.456311	0.228155	−	0.973625i	$-0.426731\pi$
$239$	1686.00	0.456311	0.228155	+	0.973625i	$0.426731\pi$
$240$	240.000	0.0645497
$241$	−3925.00	−1.04909	−0.524547	−	0.851382i	$-0.675765\pi$
$241$	−3925.00	−1.04909	−0.524547	+	0.851382i	$0.675765\pi$
$242$	2212.00	0.587573
$243$	−243.000	−0.0641500
$244$	−1368.00	−0.358923
$245$	2490.00	0.649307
$246$	−1020.00	−0.264361
$247$	−120.000	−0.0309126
$248$	−2784.00	−0.712839
$249$	1536.00	0.390924
$250$	−250.000	−0.0632456
$251$	−5775.00	−1.45225	−0.726125	−	0.687563i	$-0.758681\pi$
$251$	−5775.00	−1.45225	−0.726125	+	0.687563i	$0.758681\pi$
$252$	−1044.00	−0.260975
$253$	1740.00	0.432383
$254$	988.000	0.244065
$255$	−1815.00	−0.445724
$256$	−4352.00	−1.06250
$257$	−3146.00	−0.763588	−0.381794	−	0.924247i	$-0.624694\pi$
$257$	−3146.00	−0.763588	−0.381794	+	0.924247i	$0.624694\pi$
$258$	1380.00	0.333004
$259$	1044.00	0.250467
$260$	−60.0000	−0.0143117
$261$	261.000	0.0618984
$262$	4014.00	0.946510
$263$	−5768.00	−1.35236	−0.676179	−	0.736737i	$-0.736365\pi$
$263$	−5768.00	−1.35236	−0.676179	+	0.736737i	$0.736365\pi$
$264$	1080.00	0.251778
$265$	2280.00	0.528526
$266$	2320.00	0.534768
$267$	−4575.00	−1.04863
$268$	1076.00	0.245251
$269$	−7341.00	−1.66390	−0.831949	−	0.554852i	$-0.812775\pi$
$269$	−7341.00	−1.66390	−0.831949	+	0.554852i	$0.812775\pi$
$270$	270.000	0.0608581
$271$	−14.0000	−0.00313815	−0.00156908	−	0.999999i	$-0.500499\pi$
$271$	−14.0000	−0.00313815	−0.00156908	+	0.999999i	$0.500499\pi$
$272$	−1936.00	−0.431571
$273$	−261.000	−0.0578624
$274$	−1836.00	−0.404806
$275$	−375.000	−0.0822304
$276$	−1392.00	−0.303582
$277$	3721.00	0.807124	0.403562	−	0.914952i	$-0.367772\pi$
$277$	3721.00	0.807124	0.403562	+	0.914952i	$0.367772\pi$
$278$	−3238.00	−0.698570
$279$	−1044.00	−0.224024
$280$	3480.00	0.742749
$281$	924.000	0.196161	0.0980805	−	0.995178i	$-0.468730\pi$
$281$	924.000	0.196161	0.0980805	+	0.995178i	$0.468730\pi$
$282$	1386.00	0.292678
$283$	1940.00	0.407495	0.203747	−	0.979023i	$-0.434688\pi$
$283$	1940.00	0.407495	0.203747	+	0.979023i	$0.434688\pi$
$284$	−1208.00	−0.252400
$285$	600.000	0.124705
$286$	90.0000	0.0186077
$287$	−4930.00	−1.01397
$288$	−1440.00	−0.294628
$289$	9728.00	1.98005
$290$	−290.000	−0.0587220
$291$	1680.00	0.338431
$292$	1488.00	0.298214
$293$	5267.00	1.05018	0.525088	−	0.851048i	$-0.324032\pi$
$293$	5267.00	1.05018	0.525088	+	0.851048i	$0.324032\pi$
$294$	2988.00	0.592734
$295$	2880.00	0.568407
$296$	864.000	0.169659
$297$	405.000	0.0791262
$298$	−6092.00	−1.18423
$299$	−348.000	−0.0673089
$300$	300.000	0.0577350
$301$	6670.00	1.27725
$302$	−3152.00	−0.600587
$303$	−4341.00	−0.823049
$304$	640.000	0.120745
$305$	1710.00	0.321031
$306$	−2178.00	−0.406889
$307$	6856.00	1.27457	0.637284	−	0.770629i	$-0.280058\pi$
$307$	6856.00	1.27457	0.637284	+	0.770629i	$0.280058\pi$
$308$	1740.00	0.321902
$309$	−1668.00	−0.307085
$310$	1160.00	0.212528
$311$	−2447.00	−0.446163	−0.223081	−	0.974800i	$-0.571612\pi$
$311$	−2447.00	−0.446163	−0.223081	+	0.974800i	$0.571612\pi$
$312$	−216.000	−0.0391942
$313$	511.000	0.0922793	0.0461397	−	0.998935i	$-0.485308\pi$
$313$	511.000	0.0922793	0.0461397	+	0.998935i	$0.485308\pi$
$314$	7088.00	1.27388
$315$	1305.00	0.233424
$316$	1392.00	0.247804
$317$	7167.00	1.26984	0.634919	−	0.772578i	$-0.281033\pi$
$317$	7167.00	1.26984	0.634919	+	0.772578i	$0.281033\pi$
$318$	2736.00	0.482476
$319$	−435.000	−0.0763490
$320$	2240.00	0.391312
$321$	−4674.00	−0.812702
$322$	6728.00	1.16440
$323$	−4840.00	−0.833761
$324$	−324.000	−0.0555556
$325$	75.0000	0.0128008
$326$	1536.00	0.260955
$327$	2643.00	0.446967
$328$	−4080.00	−0.686830
$329$	6699.00	1.12258
$330$	−450.000	−0.0750657
$331$	−8962.00	−1.48821	−0.744103	−	0.668065i	$-0.767123\pi$
$331$	−8962.00	−1.48821	−0.744103	+	0.668065i	$0.767123\pi$
$332$	2048.00	0.338550
$333$	324.000	0.0533186
$334$	3248.00	0.532104
$335$	−1345.00	−0.219359
$336$	1392.00	0.226011
$337$	2706.00	0.437404	0.218702	−	0.975792i	$-0.429818\pi$
$337$	2706.00	0.437404	0.218702	+	0.975792i	$0.429818\pi$
$338$	4376.00	0.704210
$339$	−939.000	−0.150441
$340$	−2420.00	−0.386009
$341$	1740.00	0.276323
$342$	720.000	0.113840
$343$	4495.00	0.707601
$344$	5520.00	0.865170
$345$	1740.00	0.271532
$346$	−3400.00	−0.528281
$347$	2232.00	0.345303	0.172651	−	0.984983i	$-0.444767\pi$
$347$	2232.00	0.345303	0.172651	+	0.984983i	$0.444767\pi$
$348$	348.000	0.0536056
$349$	9742.00	1.49420	0.747102	−	0.664709i	$-0.231445\pi$
$349$	9742.00	1.49420	0.747102	+	0.664709i	$0.231445\pi$
$350$	−1450.00	−0.221445
$351$	−81.0000	−0.0123176
$352$	2400.00	0.363410
$353$	−2694.00	−0.406196	−0.203098	−	0.979158i	$-0.565101\pi$
$353$	−2694.00	−0.406196	−0.203098	+	0.979158i	$0.565101\pi$
$354$	3456.00	0.518882
$355$	1510.00	0.225753
$356$	−6100.00	−0.908144
$357$	−10527.0	−1.56064
$358$	−7740.00	−1.14266
$359$	−960.000	−0.141133	−0.0705667	−	0.997507i	$-0.522481\pi$
$359$	−960.000	−0.141133	−0.0705667	+	0.997507i	$0.522481\pi$
$360$	1080.00	0.158114
$361$	−5259.00	−0.766730
$362$	−3514.00	−0.510198
$363$	3318.00	0.479752
$364$	−348.000	−0.0501103
$365$	−1860.00	−0.266731
$366$	2052.00	0.293059
$367$	−4632.00	−0.658824	−0.329412	−	0.944186i	$-0.606851\pi$
$367$	−4632.00	−0.658824	−0.329412	+	0.944186i	$0.606851\pi$
$368$	1856.00	0.262909
$369$	−1530.00	−0.215850
$370$	−360.000	−0.0505825
$371$	13224.0	1.85055
$372$	−1392.00	−0.194010
$373$	−6682.00	−0.927563	−0.463781	−	0.885950i	$-0.653508\pi$
$373$	−6682.00	−0.927563	−0.463781	+	0.885950i	$0.653508\pi$
$374$	3630.00	0.501879
$375$	−375.000	−0.0516398
$376$	5544.00	0.760399
$377$	87.0000	0.0118852
$378$	1566.00	0.213086
$379$	11270.0	1.52744	0.763722	−	0.645546i	$-0.223370\pi$
$379$	11270.0	1.52744	0.763722	+	0.645546i	$0.223370\pi$
$380$	800.000	0.107998
$381$	1482.00	0.199279
$382$	4096.00	0.548611
$383$	1016.00	0.135549	0.0677744	−	0.997701i	$-0.478410\pi$
$383$	1016.00	0.135549	0.0677744	+	0.997701i	$0.478410\pi$
$384$	−1152.00	−0.153093
$385$	−2175.00	−0.287918
$386$	4796.00	0.632409
$387$	2070.00	0.271897
$388$	2240.00	0.293090
$389$	−3727.00	−0.485775	−0.242887	−	0.970054i	$-0.578095\pi$
$389$	−3727.00	−0.485775	−0.242887	+	0.970054i	$0.578095\pi$
$390$	90.0000	0.0116855
$391$	−14036.0	−1.81542
$392$	11952.0	1.53997
$393$	6021.00	0.772823
$394$	−7932.00	−1.01423
$395$	−1740.00	−0.221643
$396$	540.000	0.0685253
$397$	1990.00	0.251575	0.125787	−	0.992057i	$-0.459854\pi$
$397$	1990.00	0.251575	0.125787	+	0.992057i	$0.459854\pi$
$398$	−1282.00	−0.161459
$399$	3480.00	0.436636
$400$	−400.000	−0.0500000
$401$	6696.00	0.833871	0.416936	−	0.908936i	$-0.363104\pi$
$401$	6696.00	0.833871	0.416936	+	0.908936i	$0.363104\pi$
$402$	−1614.00	−0.200246
$403$	−348.000	−0.0430152
$404$	−5788.00	−0.712782
$405$	405.000	0.0496904
$406$	−1682.00	−0.205607
$407$	−540.000	−0.0657661
$408$	−8712.00	−1.05713
$409$	252.000	0.0304660	0.0152330	−	0.999884i	$-0.495151\pi$
$409$	252.000	0.0304660	0.0152330	+	0.999884i	$0.495151\pi$
$410$	1700.00	0.204773
$411$	−2754.00	−0.330523
$412$	−2224.00	−0.265943
$413$	16704.0	1.99019
$414$	2088.00	0.247873
$415$	−2560.00	−0.302808
$416$	−480.000	−0.0565720
$417$	−4857.00	−0.570380
$418$	−1200.00	−0.140416
$419$	7418.00	0.864900	0.432450	−	0.901658i	$-0.357649\pi$
$419$	7418.00	0.864900	0.432450	+	0.901658i	$0.357649\pi$
$420$	1740.00	0.202151
$421$	11268.0	1.30444	0.652219	−	0.758030i	$-0.273838\pi$
$421$	11268.0	1.30444	0.652219	+	0.758030i	$0.273838\pi$
$422$	−10876.0	−1.25459
$423$	2079.00	0.238970
$424$	10944.0	1.25351
$425$	3025.00	0.345257
$426$	1812.00	0.206084
$427$	9918.00	1.12404
$428$	−6232.00	−0.703820
$429$	135.000	0.0151932
$430$	−2300.00	−0.257944
$431$	−11600.0	−1.29641	−0.648205	−	0.761466i	$-0.724480\pi$
$431$	−11600.0	−1.29641	−0.648205	+	0.761466i	$0.724480\pi$
$432$	432.000	0.0481125
$433$	1072.00	0.118977	0.0594885	−	0.998229i	$-0.481053\pi$
$433$	1072.00	0.118977	0.0594885	+	0.998229i	$0.481053\pi$
$434$	6728.00	0.744134
$435$	−435.000	−0.0479463
$436$	3524.00	0.387085
$437$	4640.00	0.507921
$438$	−2232.00	−0.243491
$439$	−12339.0	−1.34148	−0.670738	−	0.741694i	$-0.734023\pi$
$439$	−12339.0	−1.34148	−0.670738	+	0.741694i	$0.734023\pi$
$440$	−1800.00	−0.195026
$441$	4482.00	0.483965
$442$	−726.000	−0.0781274
$443$	−15263.0	−1.63695	−0.818473	−	0.574545i	$-0.805179\pi$
$443$	−15263.0	−1.63695	−0.818473	+	0.574545i	$0.805179\pi$
$444$	432.000	0.0461753
$445$	7625.00	0.812269
$446$	−5598.00	−0.594334
$447$	−9138.00	−0.966918
$448$	12992.0	1.37012
$449$	11019.0	1.15817	0.579085	−	0.815267i	$-0.303410\pi$
$449$	11019.0	1.15817	0.579085	+	0.815267i	$0.303410\pi$
$450$	−450.000	−0.0471405
$451$	2550.00	0.266241
$452$	−1252.00	−0.130286
$453$	−4728.00	−0.490377
$454$	−2984.00	−0.308471
$455$	435.000	0.0448200
$456$	2880.00	0.295764
$457$	−6769.00	−0.692868	−0.346434	−	0.938074i	$-0.612607\pi$
$457$	−6769.00	−0.692868	−0.346434	+	0.938074i	$0.612607\pi$
$458$	−9244.00	−0.943109
$459$	−3267.00	−0.332223
$460$	2320.00	0.235153
$461$	−5514.00	−0.557077	−0.278539	−	0.960425i	$-0.589850\pi$
$461$	−5514.00	−0.557077	−0.278539	+	0.960425i	$0.589850\pi$
$462$	−2610.00	−0.262832
$463$	−14205.0	−1.42584	−0.712918	−	0.701247i	$-0.752627\pi$
$463$	−14205.0	−1.42584	−0.712918	+	0.701247i	$0.752627\pi$
$464$	−464.000	−0.0464238
$465$	1740.00	0.173528
$466$	−8340.00	−0.829062
$467$	−9660.00	−0.957198	−0.478599	−	0.878034i	$-0.658855\pi$
$467$	−9660.00	−0.957198	−0.478599	+	0.878034i	$0.658855\pi$
$468$	−108.000	−0.0106673
$469$	−7801.00	−0.768053
$470$	−2310.00	−0.226707
$471$	10632.0	1.04012
$472$	13824.0	1.34810
$473$	−3450.00	−0.335372
$474$	−2088.00	−0.202331
$475$	−1000.00	−0.0965961
$476$	−14036.0	−1.35155
$477$	4104.00	0.393940
$478$	−3372.00	−0.322660
$479$	−7656.00	−0.730296	−0.365148	−	0.930950i	$-0.618982\pi$
$479$	−7656.00	−0.730296	−0.365148	+	0.930950i	$0.618982\pi$
$480$	2400.00	0.228218
$481$	108.000	0.0102378
$482$	7850.00	0.741821
$483$	10092.0	0.950729
$484$	4424.00	0.415477
$485$	−2800.00	−0.262147
$486$	486.000	0.0453609
$487$	−15968.0	−1.48579	−0.742894	−	0.669409i	$-0.766548\pi$
$487$	−15968.0	−1.48579	−0.742894	+	0.669409i	$0.766548\pi$
$488$	8208.00	0.761391
$489$	2304.00	0.213068
$490$	−4980.00	−0.459130
$491$	4236.00	0.389344	0.194672	−	0.980868i	$-0.437636\pi$
$491$	4236.00	0.389344	0.194672	+	0.980868i	$0.437636\pi$
$492$	−2040.00	−0.186932
$493$	3509.00	0.320563
$494$	240.000	0.0218585
$495$	−675.000	−0.0612909
$496$	1856.00	0.168018
$497$	8758.00	0.790443
$498$	−3072.00	−0.276425
$499$	−16941.0	−1.51981	−0.759903	−	0.650036i	$-0.774754\pi$
$499$	−16941.0	−1.51981	−0.759903	+	0.650036i	$0.774754\pi$
$500$	−500.000	−0.0447214
$501$	4872.00	0.434461
$502$	11550.0	1.02690
$503$	−1857.00	−0.164611	−0.0823057	−	0.996607i	$-0.526228\pi$
$503$	−1857.00	−0.164611	−0.0823057	+	0.996607i	$0.526228\pi$
$504$	6264.00	0.553613
$505$	7235.00	0.637531
$506$	−3480.00	−0.305741
$507$	6564.00	0.574985
$508$	1976.00	0.172580
$509$	−3096.00	−0.269603	−0.134801	−	0.990873i	$-0.543040\pi$
$509$	−3096.00	−0.269603	−0.134801	+	0.990873i	$0.543040\pi$
$510$	3630.00	0.315175
$511$	−10788.0	−0.933920
$512$	5632.00	0.486136
$513$	1080.00	0.0929496
$514$	6292.00	0.539938
$515$	2780.00	0.237867
$516$	2760.00	0.235469
$517$	−3465.00	−0.294759
$518$	−2088.00	−0.177107
$519$	−5100.00	−0.431339
$520$	360.000	0.0303597
$521$	7530.00	0.633196	0.316598	−	0.948560i	$-0.397459\pi$
$521$	7530.00	0.633196	0.316598	+	0.948560i	$0.397459\pi$
$522$	−522.000	−0.0437688
$523$	−5767.00	−0.482167	−0.241083	−	0.970504i	$-0.577503\pi$
$523$	−5767.00	−0.482167	−0.241083	+	0.970504i	$0.577503\pi$
$524$	8028.00	0.669284
$525$	−2175.00	−0.180809
$526$	11536.0	0.956261
$527$	−14036.0	−1.16019
$528$	−720.000	−0.0593447
$529$	1289.00	0.105942
$530$	−4560.00	−0.373724
$531$	5184.00	0.423666
$532$	4640.00	0.378138
$533$	−510.000	−0.0414457
$534$	9150.00	0.741497
$535$	7790.00	0.629516
$536$	−6456.00	−0.520255
$537$	−11610.0	−0.932977
$538$	14682.0	1.17655
$539$	−7470.00	−0.596949
$540$	540.000	0.0430331
$541$	−21122.0	−1.67857	−0.839284	−	0.543693i	$-0.817026\pi$
$541$	−21122.0	−1.67857	−0.839284	+	0.543693i	$0.817026\pi$
$542$	28.0000	0.00221901
$543$	−5271.00	−0.416575
$544$	−19360.0	−1.52583
$545$	−4405.00	−0.346219
$546$	522.000	0.0409149
$547$	17857.0	1.39581	0.697907	−	0.716188i	$-0.254115\pi$
$547$	17857.0	1.39581	0.697907	+	0.716188i	$0.254115\pi$
$548$	−3672.00	−0.286241
$549$	3078.00	0.239282
$550$	750.000	0.0581456
$551$	−1160.00	−0.0896872
$552$	8352.00	0.643994
$553$	−10092.0	−0.776050
$554$	−7442.00	−0.570723
$555$	−540.000	−0.0413004
$556$	−6476.00	−0.493963
$557$	6040.00	0.459467	0.229733	−	0.973254i	$-0.426215\pi$
$557$	6040.00	0.459467	0.229733	+	0.973254i	$0.426215\pi$
$558$	2088.00	0.158409
$559$	690.000	0.0522073
$560$	−2320.00	−0.175068
$561$	5445.00	0.409783
$562$	−1848.00	−0.138707
$563$	−15371.0	−1.15064	−0.575320	−	0.817928i	$-0.695123\pi$
$563$	−15371.0	−1.15064	−0.575320	+	0.817928i	$0.695123\pi$
$564$	2772.00	0.206954
$565$	1565.00	0.116531
$566$	−3880.00	−0.288142
$567$	2349.00	0.173984
$568$	7248.00	0.535421
$569$	17901.0	1.31889	0.659445	−	0.751752i	$-0.270791\pi$
$569$	17901.0	1.31889	0.659445	+	0.751752i	$0.270791\pi$
$570$	−1200.00	−0.0881798
$571$	−10056.0	−0.737006	−0.368503	−	0.929627i	$-0.620130\pi$
$571$	−10056.0	−0.737006	−0.368503	+	0.929627i	$0.620130\pi$
$572$	180.000	0.0131577
$573$	6144.00	0.447939
$574$	9860.00	0.716983
$575$	−2900.00	−0.210328
$576$	4032.00	0.291667
$577$	3068.00	0.221356	0.110678	−	0.993856i	$-0.464698\pi$
$577$	3068.00	0.221356	0.110678	+	0.993856i	$0.464698\pi$
$578$	−19456.0	−1.40011
$579$	7194.00	0.516360
$580$	−580.000	−0.0415227
$581$	−14848.0	−1.06024
$582$	−3360.00	−0.239307
$583$	−6840.00	−0.485907
$584$	−8928.00	−0.632608
$585$	135.000	0.00954113
$586$	−10534.0	−0.742586
$587$	−2984.00	−0.209817	−0.104909	−	0.994482i	$-0.533455\pi$
$587$	−2984.00	−0.209817	−0.104909	+	0.994482i	$0.533455\pi$
$588$	5976.00	0.419126
$589$	4640.00	0.324597
$590$	−5760.00	−0.401924
$591$	−11898.0	−0.828119
$592$	−576.000	−0.0399889
$593$	5952.00	0.412174	0.206087	−	0.978534i	$-0.433927\pi$
$593$	5952.00	0.412174	0.206087	+	0.978534i	$0.433927\pi$
$594$	−810.000	−0.0559507
$595$	17545.0	1.20887
$596$	−12184.0	−0.837376
$597$	−1923.00	−0.131831
$598$	696.000	0.0475946
$599$	−12999.0	−0.886686	−0.443343	−	0.896352i	$-0.646208\pi$
$599$	−12999.0	−0.886686	−0.443343	+	0.896352i	$0.646208\pi$
$600$	−1800.00	−0.122474
$601$	23398.0	1.58806	0.794030	−	0.607878i	$-0.207979\pi$
$601$	23398.0	1.58806	0.794030	+	0.607878i	$0.207979\pi$
$602$	−13340.0	−0.903153
$603$	−2421.00	−0.163500
$604$	−6304.00	−0.424679
$605$	−5530.00	−0.371614
$606$	8682.00	0.581984
$607$	26116.0	1.74632	0.873160	−	0.487434i	$-0.162067\pi$
$607$	26116.0	1.74632	0.873160	+	0.487434i	$0.162067\pi$
$608$	6400.00	0.426898
$609$	−2523.00	−0.167877
$610$	−3420.00	−0.227003
$611$	693.000	0.0458851
$612$	−4356.00	−0.287714
$613$	−24185.0	−1.59351	−0.796756	−	0.604301i	$-0.793452\pi$
$613$	−24185.0	−1.59351	−0.796756	+	0.604301i	$0.793452\pi$
$614$	−13712.0	−0.901256
$615$	2550.00	0.167197
$616$	−10440.0	−0.682856
$617$	2214.00	0.144461	0.0722304	−	0.997388i	$-0.476988\pi$
$617$	2214.00	0.144461	0.0722304	+	0.997388i	$0.476988\pi$
$618$	3336.00	0.217142
$619$	−19586.0	−1.27177	−0.635887	−	0.771782i	$-0.719365\pi$
$619$	−19586.0	−1.27177	−0.635887	+	0.771782i	$0.719365\pi$
$620$	2320.00	0.150280
$621$	3132.00	0.202388
$622$	4894.00	0.315485
$623$	44225.0	2.84404
$624$	144.000	0.00923816
$625$	625.000	0.0400000
$626$	−1022.00	−0.0652513
$627$	−1800.00	−0.114649
$628$	14176.0	0.900771
$629$	4356.00	0.276129
$630$	−2610.00	−0.165055
$631$	4377.00	0.276142	0.138071	−	0.990422i	$-0.455910\pi$
$631$	4377.00	0.276142	0.138071	+	0.990422i	$0.455910\pi$
$632$	−8352.00	−0.525672
$633$	−16314.0	−1.02437
$634$	−14334.0	−0.897911
$635$	−2470.00	−0.154361
$636$	5472.00	0.341162
$637$	1494.00	0.0929269
$638$	870.000	0.0539869
$639$	2718.00	0.168267
$640$	1920.00	0.118585
$641$	−24015.0	−1.47977	−0.739887	−	0.672731i	$-0.765121\pi$
$641$	−24015.0	−1.47977	−0.739887	+	0.672731i	$0.765121\pi$
$642$	9348.00	0.574667
$643$	−19465.0	−1.19382	−0.596909	−	0.802309i	$-0.703605\pi$
$643$	−19465.0	−1.19382	−0.596909	+	0.802309i	$0.703605\pi$
$644$	13456.0	0.823355
$645$	−3450.00	−0.210610
$646$	9680.00	0.589558
$647$	−19954.0	−1.21248	−0.606239	−	0.795283i	$-0.707322\pi$
$647$	−19954.0	−1.21248	−0.606239	+	0.795283i	$0.707322\pi$
$648$	1944.00	0.117851
$649$	−8640.00	−0.522573
$650$	−150.000	−0.00905151
$651$	10092.0	0.607583
$652$	3072.00	0.184523
$653$	−22597.0	−1.35419	−0.677097	−	0.735894i	$-0.736762\pi$
$653$	−22597.0	−1.35419	−0.677097	+	0.735894i	$0.736762\pi$
$654$	−5286.00	−0.316053
$655$	−10035.0	−0.598626
$656$	2720.00	0.161887
$657$	−3348.00	−0.198810
$658$	−13398.0	−0.793782
$659$	7467.00	0.441385	0.220693	−	0.975343i	$-0.429168\pi$
$659$	7467.00	0.441385	0.220693	+	0.975343i	$0.429168\pi$
$660$	−900.000	−0.0530795
$661$	16601.0	0.976859	0.488430	−	0.872603i	$-0.337570\pi$
$661$	16601.0	0.976859	0.488430	+	0.872603i	$0.337570\pi$
$662$	17924.0	1.05232
$663$	−1089.00	−0.0637907
$664$	−12288.0	−0.718173
$665$	−5800.00	−0.338217
$666$	−648.000	−0.0377019
$667$	−3364.00	−0.195284
$668$	6496.00	0.376254
$669$	−8397.00	−0.485272
$670$	2690.00	0.155110
$671$	−5130.00	−0.295144
$672$	13920.0	0.799071
$673$	23571.0	1.35007	0.675034	−	0.737787i	$-0.264129\pi$
$673$	23571.0	1.35007	0.675034	+	0.737787i	$0.264129\pi$
$674$	−5412.00	−0.309291
$675$	−675.000	−0.0384900
$676$	8752.00	0.497952
$677$	−16963.0	−0.962985	−0.481493	−	0.876450i	$-0.659905\pi$
$677$	−16963.0	−0.962985	−0.481493	+	0.876450i	$0.659905\pi$
$678$	1878.00	0.106378
$679$	−16240.0	−0.917870
$680$	14520.0	0.818848
$681$	−4476.00	−0.251866
$682$	−3480.00	−0.195390
$683$	6144.00	0.344207	0.172104	−	0.985079i	$-0.444944\pi$
$683$	6144.00	0.344207	0.172104	+	0.985079i	$0.444944\pi$
$684$	1440.00	0.0804967
$685$	4590.00	0.256022
$686$	−8990.00	−0.500350
$687$	−13866.0	−0.770045
$688$	−3680.00	−0.203923
$689$	1368.00	0.0756410
$690$	−3480.00	−0.192002
$691$	18461.0	1.01634	0.508169	−	0.861257i	$-0.330323\pi$
$691$	18461.0	1.01634	0.508169	+	0.861257i	$0.330323\pi$
$692$	−6800.00	−0.373551
$693$	−3915.00	−0.214601
$694$	−4464.00	−0.244166
$695$	8095.00	0.441814
$696$	−2088.00	−0.113715
$697$	−20570.0	−1.11785
$698$	−19484.0	−1.05656
$699$	−12510.0	−0.676927
$700$	−2900.00	−0.156585
$701$	−7550.00	−0.406790	−0.203395	−	0.979097i	$-0.565198\pi$
$701$	−7550.00	−0.406790	−0.203395	+	0.979097i	$0.565198\pi$
$702$	162.000	0.00870982
$703$	−1440.00	−0.0772555
$704$	−6720.00	−0.359758
$705$	−3465.00	−0.185106
$706$	5388.00	0.287224
$707$	41963.0	2.23222
$708$	6912.00	0.366905
$709$	29126.0	1.54281	0.771403	−	0.636347i	$-0.219555\pi$
$709$	29126.0	1.54281	0.771403	+	0.636347i	$0.219555\pi$
$710$	−3020.00	−0.159632
$711$	−3132.00	−0.165203
$712$	36600.0	1.92646
$713$	13456.0	0.706776
$714$	21054.0	1.10354
$715$	−225.000	−0.0117686
$716$	−15480.0	−0.807982
$717$	−5058.00	−0.263451
$718$	1920.00	0.0997963
$719$	−31670.0	−1.64269	−0.821343	−	0.570434i	$-0.806775\pi$
$719$	−31670.0	−1.64269	−0.821343	+	0.570434i	$0.806775\pi$
$720$	−720.000	−0.0372678
$721$	16124.0	0.832856
$722$	10518.0	0.542160
$723$	11775.0	0.605694
$724$	−7028.00	−0.360765
$725$	725.000	0.0371391
$726$	−6636.00	−0.339236
$727$	21080.0	1.07540	0.537699	−	0.843137i	$-0.319294\pi$
$727$	21080.0	1.07540	0.537699	+	0.843137i	$0.319294\pi$
$728$	2088.00	0.106300
$729$	729.000	0.0370370
$730$	3720.00	0.188607
$731$	27830.0	1.40811
$732$	4104.00	0.207224
$733$	−31730.0	−1.59887	−0.799437	−	0.600750i	$-0.794869\pi$
$733$	−31730.0	−1.59887	−0.799437	+	0.600750i	$0.794869\pi$
$734$	9264.00	0.465859
$735$	−7470.00	−0.374878
$736$	18560.0	0.929525
$737$	4035.00	0.201670
$738$	3060.00	0.152629
$739$	−35010.0	−1.74271	−0.871356	−	0.490652i	$-0.836759\pi$
$739$	−35010.0	−1.74271	−0.871356	+	0.490652i	$0.836759\pi$
$740$	−720.000	−0.0357672
$741$	360.000	0.0178474
$742$	−26448.0	−1.30854
$743$	−36625.0	−1.80840	−0.904200	−	0.427110i	$-0.859532\pi$
$743$	−36625.0	−1.80840	−0.904200	+	0.427110i	$0.859532\pi$
$744$	8352.00	0.411558
$745$	15230.0	0.748972
$746$	13364.0	0.655886
$747$	−4608.00	−0.225700
$748$	7260.00	0.354882
$749$	45182.0	2.20416
$750$	750.000	0.0365148
$751$	8420.00	0.409121	0.204561	−	0.978854i	$-0.434423\pi$
$751$	8420.00	0.409121	0.204561	+	0.978854i	$0.434423\pi$
$752$	−3696.00	−0.179228
$753$	17325.0	0.838457
$754$	−174.000	−0.00840412
$755$	7880.00	0.379844
$756$	3132.00	0.150674
$757$	−14404.0	−0.691575	−0.345788	−	0.938313i	$-0.612388\pi$
$757$	−14404.0	−0.691575	−0.345788	+	0.938313i	$0.612388\pi$
$758$	−22540.0	−1.08007
$759$	−5220.00	−0.249636
$760$	−4800.00	−0.229098
$761$	7208.00	0.343351	0.171675	−	0.985154i	$-0.445082\pi$
$761$	7208.00	0.343351	0.171675	+	0.985154i	$0.445082\pi$
$762$	−2964.00	−0.140911
$763$	−25549.0	−1.21224
$764$	8192.00	0.387927
$765$	5445.00	0.257339
$766$	−2032.00	−0.0958474
$767$	1728.00	0.0813487
$768$	13056.0	0.613435
$769$	−31638.0	−1.48361	−0.741805	−	0.670616i	$-0.766030\pi$
$769$	−31638.0	−1.48361	−0.741805	+	0.670616i	$0.766030\pi$
$770$	4350.00	0.203588
$771$	9438.00	0.440858
$772$	9592.00	0.447181
$773$	−930.000	−0.0432727	−0.0216363	−	0.999766i	$-0.506888\pi$
$773$	−930.000	−0.0432727	−0.0216363	+	0.999766i	$0.506888\pi$
$774$	−4140.00	−0.192260
$775$	−2900.00	−0.134414
$776$	−13440.0	−0.621737
$777$	−3132.00	−0.144607
$778$	7454.00	0.343495
$779$	6800.00	0.312754
$780$	180.000	0.00826286
$781$	−4530.00	−0.207549
$782$	28072.0	1.28370
$783$	−783.000	−0.0357371
$784$	−7968.00	−0.362974
$785$	−17720.0	−0.805674
$786$	−12042.0	−0.546468
$787$	7188.00	0.325571	0.162786	−	0.986661i	$-0.447952\pi$
$787$	7188.00	0.325571	0.162786	+	0.986661i	$0.447952\pi$
$788$	−15864.0	−0.717172
$789$	17304.0	0.780784
$790$	3480.00	0.156725
$791$	9077.00	0.408016
$792$	−3240.00	−0.145364
$793$	1026.00	0.0459449
$794$	−3980.00	−0.177890
$795$	−6840.00	−0.305144
$796$	−2564.00	−0.114169
$797$	−31986.0	−1.42158	−0.710792	−	0.703402i	$-0.751663\pi$
$797$	−31986.0	−1.42158	−0.710792	+	0.703402i	$0.751663\pi$
$798$	−6960.00	−0.308749
$799$	27951.0	1.23759
$800$	−4000.00	−0.176777
$801$	13725.0	0.605430
$802$	−13392.0	−0.589636
$803$	5580.00	0.245223
$804$	−3228.00	−0.141596
$805$	−16820.0	−0.736431
$806$	696.000	0.0304163
$807$	22023.0	0.960652
$808$	34728.0	1.51204
$809$	8235.00	0.357883	0.178941	−	0.983860i	$-0.442733\pi$
$809$	8235.00	0.357883	0.178941	+	0.983860i	$0.442733\pi$
$810$	−810.000	−0.0351364
$811$	−9031.00	−0.391025	−0.195513	−	0.980701i	$-0.562637\pi$
$811$	−9031.00	−0.391025	−0.195513	+	0.980701i	$0.562637\pi$
$812$	−3364.00	−0.145386
$813$	42.0000	0.00181181
$814$	1080.00	0.0465037
$815$	−3840.00	−0.165042
$816$	5808.00	0.249167
$817$	−9200.00	−0.393962
$818$	−504.000	−0.0215427
$819$	783.000	0.0334069
$820$	3400.00	0.144797
$821$	41318.0	1.75640	0.878202	−	0.478289i	$-0.158743\pi$
$821$	41318.0	1.75640	0.878202	+	0.478289i	$0.158743\pi$
$822$	5508.00	0.233715
$823$	31150.0	1.31934	0.659672	−	0.751553i	$-0.270695\pi$
$823$	31150.0	1.31934	0.659672	+	0.751553i	$0.270695\pi$
$824$	13344.0	0.564151
$825$	1125.00	0.0474757
$826$	−33408.0	−1.40728
$827$	7584.00	0.318889	0.159445	−	0.987207i	$-0.449030\pi$
$827$	7584.00	0.318889	0.159445	+	0.987207i	$0.449030\pi$
$828$	4176.00	0.175273
$829$	−28316.0	−1.18632	−0.593158	−	0.805086i	$-0.702119\pi$
$829$	−28316.0	−1.18632	−0.593158	+	0.805086i	$0.702119\pi$
$830$	5120.00	0.214118
$831$	−11163.0	−0.465993
$832$	1344.00	0.0560034
$833$	60258.0	2.50638
$834$	9714.00	0.403319
$835$	−8120.00	−0.336532
$836$	−2400.00	−0.0992892
$837$	3132.00	0.129340
$838$	−14836.0	−0.611577
$839$	−26615.0	−1.09518	−0.547588	−	0.836748i	$-0.684454\pi$
$839$	−26615.0	−1.09518	−0.547588	+	0.836748i	$0.684454\pi$
$840$	−10440.0	−0.428826
$841$	841.000	0.0344828
$842$	−22536.0	−0.922377
$843$	−2772.00	−0.113254
$844$	−21752.0	−0.887126
$845$	−10940.0	−0.445382
$846$	−4158.00	−0.168978
$847$	−32074.0	−1.30115
$848$	−7296.00	−0.295455
$849$	−5820.00	−0.235267
$850$	−6050.00	−0.244133
$851$	−4176.00	−0.168216
$852$	3624.00	0.145723
$853$	33538.0	1.34621	0.673106	−	0.739546i	$-0.264960\pi$
$853$	33538.0	1.34621	0.673106	+	0.739546i	$0.264960\pi$
$854$	−19836.0	−0.794817
$855$	−1800.00	−0.0719985
$856$	37392.0	1.49303
$857$	−26394.0	−1.05204	−0.526022	−	0.850471i	$-0.676317\pi$
$857$	−26394.0	−1.05204	−0.526022	+	0.850471i	$0.676317\pi$
$858$	−270.000	−0.0107432
$859$	−12076.0	−0.479660	−0.239830	−	0.970815i	$-0.577092\pi$
$859$	−12076.0	−0.479660	−0.239830	+	0.970815i	$0.577092\pi$
$860$	−4600.00	−0.182394
$861$	14790.0	0.585414
$862$	23200.0	0.916700
$863$	−2450.00	−0.0966384	−0.0483192	−	0.998832i	$-0.515386\pi$
$863$	−2450.00	−0.0966384	−0.0483192	+	0.998832i	$0.515386\pi$
$864$	4320.00	0.170103
$865$	8500.00	0.334114
$866$	−2144.00	−0.0841294
$867$	−29184.0	−1.14318
$868$	13456.0	0.526182
$869$	5220.00	0.203770
$870$	870.000	0.0339032
$871$	−807.000	−0.0313940
$872$	−21144.0	−0.821131
$873$	−5040.00	−0.195393
$874$	−9280.00	−0.359154
$875$	3625.00	0.140054
$876$	−4464.00	−0.172174
$877$	−15566.0	−0.599346	−0.299673	−	0.954042i	$-0.596878\pi$
$877$	−15566.0	−0.599346	−0.299673	+	0.954042i	$0.596878\pi$
$878$	24678.0	0.948567
$879$	−15801.0	−0.606319
$880$	1200.00	0.0459682
$881$	34497.0	1.31922	0.659610	−	0.751608i	$-0.270721\pi$
$881$	34497.0	1.31922	0.659610	+	0.751608i	$0.270721\pi$
$882$	−8964.00	−0.342215
$883$	17044.0	0.649577	0.324788	−	0.945787i	$-0.394707\pi$
$883$	17044.0	0.649577	0.324788	+	0.945787i	$0.394707\pi$
$884$	−1452.00	−0.0552444
$885$	−8640.00	−0.328170
$886$	30526.0	1.15750
$887$	−16903.0	−0.639850	−0.319925	−	0.947443i	$-0.603658\pi$
$887$	−16903.0	−0.639850	−0.319925	+	0.947443i	$0.603658\pi$
$888$	−2592.00	−0.0979525
$889$	−14326.0	−0.540471
$890$	−15250.0	−0.574361
$891$	−1215.00	−0.0456835
$892$	−11196.0	−0.420258
$893$	−9240.00	−0.346254
$894$	18276.0	0.683715
$895$	19350.0	0.722681
$896$	11136.0	0.415209
$897$	1044.00	0.0388608
$898$	−22038.0	−0.818951
$899$	−3364.00	−0.124801
$900$	−900.000	−0.0333333
$901$	55176.0	2.04015
$902$	−5100.00	−0.188261
$903$	−20010.0	−0.737421
$904$	7512.00	0.276378
$905$	8785.00	0.322678
$906$	9456.00	0.346749
$907$	40504.0	1.48282	0.741408	−	0.671055i	$-0.234159\pi$
$907$	40504.0	1.48282	0.741408	+	0.671055i	$0.234159\pi$
$908$	−5968.00	−0.218122
$909$	13023.0	0.475188
$910$	−870.000	−0.0316925
$911$	−14783.0	−0.537632	−0.268816	−	0.963192i	$-0.586632\pi$
$911$	−14783.0	−0.537632	−0.268816	+	0.963192i	$0.586632\pi$
$912$	−1920.00	−0.0697122
$913$	7680.00	0.278391
$914$	13538.0	0.489931
$915$	−5130.00	−0.185347
$916$	−18488.0	−0.666879
$917$	−58203.0	−2.09600
$918$	6534.00	0.234917
$919$	42241.0	1.51622	0.758108	−	0.652129i	$-0.226124\pi$
$919$	42241.0	1.51622	0.758108	+	0.652129i	$0.226124\pi$
$920$	−13920.0	−0.498836
$921$	−20568.0	−0.735873
$922$	11028.0	0.393913
$923$	906.000	0.0323092
$924$	−5220.00	−0.185850
$925$	900.000	0.0319912
$926$	28410.0	1.00822
$927$	5004.00	0.177295
$928$	−4640.00	−0.164133
$929$	28686.0	1.01309	0.506543	−	0.862215i	$-0.330923\pi$
$929$	28686.0	1.01309	0.506543	+	0.862215i	$0.330923\pi$
$930$	−3480.00	−0.122703
$931$	−19920.0	−0.701237
$932$	−16680.0	−0.586236
$933$	7341.00	0.257592
$934$	19320.0	0.676841
$935$	−9075.00	−0.317416
$936$	648.000	0.0226288
$937$	−53063.0	−1.85005	−0.925023	−	0.379912i	$-0.875954\pi$
$937$	−53063.0	−1.85005	−0.925023	+	0.379912i	$0.875954\pi$
$938$	15602.0	0.543095
$939$	−1533.00	−0.0532775
$940$	−4620.00	−0.160306
$941$	−16542.0	−0.573065	−0.286532	−	0.958071i	$-0.592503\pi$
$941$	−16542.0	−0.573065	−0.286532	+	0.958071i	$0.592503\pi$
$942$	−21264.0	−0.735476
$943$	19720.0	0.680988
$944$	−9216.00	−0.317749
$945$	−3915.00	−0.134767
$946$	6900.00	0.237144
$947$	30839.0	1.05822	0.529109	−	0.848554i	$-0.322526\pi$
$947$	30839.0	1.05822	0.529109	+	0.848554i	$0.322526\pi$
$948$	−4176.00	−0.143070
$949$	−1116.00	−0.0381738
$950$	2000.00	0.0683038
$951$	−21501.0	−0.733142
$952$	84216.0	2.86708
$953$	46314.0	1.57425	0.787124	−	0.616795i	$-0.211569\pi$
$953$	46314.0	1.57425	0.787124	+	0.616795i	$0.211569\pi$
$954$	−8208.00	−0.278557
$955$	−10240.0	−0.346972
$956$	−6744.00	−0.228155
$957$	1305.00	0.0440801
$958$	15312.0	0.516397
$959$	26622.0	0.896423
$960$	−6720.00	−0.225924
$961$	−16335.0	−0.548320
$962$	−216.000	−0.00723921
$963$	14022.0	0.469214
$964$	15700.0	0.524547
$965$	−11990.0	−0.399971
$966$	−20184.0	−0.672267
$967$	−12904.0	−0.429126	−0.214563	−	0.976710i	$-0.568833\pi$
$967$	−12904.0	−0.429126	−0.214563	+	0.976710i	$0.568833\pi$
$968$	−26544.0	−0.881360
$969$	14520.0	0.481372
$970$	5600.00	0.185366
$971$	−900.000	−0.0297450	−0.0148725	−	0.999889i	$-0.504734\pi$
$971$	−900.000	−0.0297450	−0.0148725	+	0.999889i	$0.504734\pi$
$972$	972.000	0.0320750
$973$	46951.0	1.54695
$974$	31936.0	1.05061
$975$	−225.000	−0.00739053
$976$	−5472.00	−0.179462
$977$	−20376.0	−0.667232	−0.333616	−	0.942709i	$-0.608269\pi$
$977$	−20376.0	−0.667232	−0.333616	+	0.942709i	$0.608269\pi$
$978$	−4608.00	−0.150662
$979$	−22875.0	−0.746770
$980$	−9960.00	−0.324654
$981$	−7929.00	−0.258057
$982$	−8472.00	−0.275308
$983$	13456.0	0.436602	0.218301	−	0.975881i	$-0.429949\pi$
$983$	13456.0	0.436602	0.218301	+	0.975881i	$0.429949\pi$
$984$	12240.0	0.396542
$985$	19830.0	0.641458
$986$	−7018.00	−0.226672
$987$	−20097.0	−0.648120
$988$	480.000	0.0154563
$989$	−26680.0	−0.857811
$990$	1350.00	0.0433392
$991$	−27245.0	−0.873326	−0.436663	−	0.899625i	$-0.643840\pi$
$991$	−27245.0	−0.873326	−0.436663	+	0.899625i	$0.643840\pi$
$992$	18560.0	0.594033
$993$	26886.0	0.859216
$994$	−17516.0	−0.558927
$995$	3205.00	0.102116
$996$	−6144.00	−0.195462
$997$	−1552.00	−0.0493002	−0.0246501	−	0.999696i	$-0.507847\pi$
$997$	−1552.00	−0.0493002	−0.0246501	+	0.999696i	$0.507847\pi$
$998$	33882.0	1.07467
$999$	−972.000	−0.0307835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.a.1.1	✓	1
3.2	odd	2		1305.4.a.d.1.1		1
5.4	even	2		2175.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.a.1.1	✓	1	1.1	even	1	trivial
1305.4.a.d.1.1		1	3.2	odd	2
2175.4.a.c.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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