Properties

Label 435.4.a.a.1.1
Level $435$
Weight $4$
Character 435.1
Self dual yes
Analytic conductor $25.666$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [435,4,Mod(1,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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);
 
Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 435.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: \(25.6658308525\)
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)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +29.0000 q^{7} +24.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +29.0000 q^{7} +24.0000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -15.0000 q^{11} +12.0000 q^{12} +3.00000 q^{13} -58.0000 q^{14} -15.0000 q^{15} -16.0000 q^{16} +121.000 q^{17} -18.0000 q^{18} -40.0000 q^{19} -20.0000 q^{20} -87.0000 q^{21} +30.0000 q^{22} -116.000 q^{23} -72.0000 q^{24} +25.0000 q^{25} -6.00000 q^{26} -27.0000 q^{27} -116.000 q^{28} +29.0000 q^{29} +30.0000 q^{30} -116.000 q^{31} -160.000 q^{32} +45.0000 q^{33} -242.000 q^{34} +145.000 q^{35} -36.0000 q^{36} +36.0000 q^{37} +80.0000 q^{38} -9.00000 q^{39} +120.000 q^{40} -170.000 q^{41} +174.000 q^{42} +230.000 q^{43} +60.0000 q^{44} +45.0000 q^{45} +232.000 q^{46} +231.000 q^{47} +48.0000 q^{48} +498.000 q^{49} -50.0000 q^{50} -363.000 q^{51} -12.0000 q^{52} +456.000 q^{53} +54.0000 q^{54} -75.0000 q^{55} +696.000 q^{56} +120.000 q^{57} -58.0000 q^{58} +576.000 q^{59} +60.0000 q^{60} +342.000 q^{61} +232.000 q^{62} +261.000 q^{63} +448.000 q^{64} +15.0000 q^{65} -90.0000 q^{66} -269.000 q^{67} -484.000 q^{68} +348.000 q^{69} -290.000 q^{70} +302.000 q^{71} +216.000 q^{72} -372.000 q^{73} -72.0000 q^{74} -75.0000 q^{75} +160.000 q^{76} -435.000 q^{77} +18.0000 q^{78} -348.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +340.000 q^{82} -512.000 q^{83} +348.000 q^{84} +605.000 q^{85} -460.000 q^{86} -87.0000 q^{87} -360.000 q^{88} +1525.00 q^{89} -90.0000 q^{90} +87.0000 q^{91} +464.000 q^{92} +348.000 q^{93} -462.000 q^{94} -200.000 q^{95} +480.000 q^{96} -560.000 q^{97} -996.000 q^{98} -135.000 q^{99} +O(q^{100})\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −3.00000 −0.577350
\(4\) −4.00000 −0.500000
\(5\) 5.00000 0.447214
\(6\) 6.00000 0.408248
\(7\) 29.0000 1.56585 0.782926 0.622114i \(-0.213726\pi\)
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 \(-0.565907\pi\)
−0.205576 + 0.978641i \(0.565907\pi\)
\(12\) 12.0000 0.288675
\(13\) 3.00000 0.0640039 0.0320019 0.999488i \(-0.489812\pi\)
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 \(-0.168494\pi\)
0.863141 + 0.504962i \(0.168494\pi\)
\(18\) −18.0000 −0.235702
\(19\) −40.0000 −0.482980 −0.241490 0.970403i \(-0.577636\pi\)
−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 \(-0.676241\pi\)
−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
\(30\) 30.0000 0.182574
\(31\) −116.000 −0.672071 −0.336036 0.941849i \(-0.609086\pi\)
−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 \(-0.474515\pi\)
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 \(-0.604952\pi\)
−0.323775 + 0.946134i \(0.604952\pi\)
\(42\) 174.000 0.639257
\(43\) 230.000 0.815690 0.407845 0.913051i \(-0.366280\pi\)
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 \(-0.383303\pi\)
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 \(-0.298769\pi\)
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 \(-0.280795\pi\)
0.635498 + 0.772102i \(0.280795\pi\)
\(60\) 60.0000 0.129099
\(61\) 342.000 0.717846 0.358923 0.933367i \(-0.383144\pi\)
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 \(-0.578870\pi\)
−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 \(-0.418780\pi\)
0.252400 + 0.967623i \(0.418780\pi\)
\(72\) 216.000 0.353553
\(73\) −372.000 −0.596429 −0.298214 0.954499i \(-0.596391\pi\)
−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 \(-0.579709\pi\)
−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 \(-0.609936\pi\)
−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 \(-0.137499\pi\)
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 \(-0.594683\pi\)
−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 \(-0.247435\pi\)
0.712782 + 0.701386i \(0.247435\pi\)
\(102\) 726.000 0.704752
\(103\) 556.000 0.531886 0.265943 0.963989i \(-0.414317\pi\)
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 \(-0.251476\pi\)
0.703820 + 0.710378i \(0.251476\pi\)
\(108\) 108.000 0.0962250
\(109\) −881.000 −0.774170 −0.387085 0.922044i \(-0.626518\pi\)
−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 \(-0.458411\pi\)
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 \(-0.555210\pi\)
−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 \(-0.733399\pi\)
−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 \(-0.407594\pi\)
0.286241 + 0.958158i \(0.407594\pi\)
\(138\) −696.000 −0.429329
\(139\) 1619.00 0.987927 0.493963 0.869483i \(-0.335548\pi\)
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 \(-0.184089\pi\)
0.837376 + 0.546627i \(0.184089\pi\)
\(150\) 150.000 0.0816497
\(151\) 1576.00 0.849358 0.424679 0.905344i \(-0.360387\pi\)
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 \(-0.856998\pi\)
−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 \(-0.559074\pi\)
−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 \(-0.622788\pi\)
−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 \(-0.378140\pi\)
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 \(-0.200560\pi\)
0.807982 + 0.589208i \(0.200560\pi\)
\(180\) −180.000 −0.0745356
\(181\) 1757.00 0.721529 0.360765 0.932657i \(-0.382516\pi\)
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 \(-0.626809\pi\)
−0.387927 + 0.921690i \(0.626809\pi\)
\(192\) −1344.00 −0.505181
\(193\) −2398.00 −0.894362 −0.447181 0.894444i \(-0.647572\pi\)
−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 \(-0.245436\pi\)
0.717172 + 0.696896i \(0.245436\pi\)
\(198\) 270.000 0.0969094
\(199\) 641.000 0.228338 0.114169 0.993461i \(-0.463579\pi\)
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 \(-0.152698\pi\)
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 \(-0.361940\pi\)
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 \(-0.430007\pi\)
0.218122 + 0.975921i \(0.430007\pi\)
\(228\) −480.000 −0.139424
\(229\) 4622.00 1.33376 0.666879 0.745166i \(-0.267630\pi\)
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 \(-0.300609\pi\)
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 \(-0.426731\pi\)
0.228155 + 0.973625i \(0.426731\pi\)
\(240\) 240.000 0.0645497
\(241\) −3925.00 −1.04909 −0.524547 0.851382i \(-0.675765\pi\)
−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 \(-0.758681\pi\)
−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 \(-0.624694\pi\)
−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 \(-0.736365\pi\)
−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 \(-0.812775\pi\)
−0.831949 + 0.554852i \(0.812775\pi\)
\(270\) 270.000 0.0608581
\(271\) −14.0000 −0.00313815 −0.00156908 0.999999i \(-0.500499\pi\)
−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 \(-0.367772\pi\)
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 \(-0.468730\pi\)
0.0980805 + 0.995178i \(0.468730\pi\)
\(282\) 1386.00 0.292678
\(283\) 1940.00 0.407495 0.203747 0.979023i \(-0.434688\pi\)
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 \(-0.324032\pi\)
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 \(-0.280058\pi\)
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 \(-0.571612\pi\)
−0.223081 + 0.974800i \(0.571612\pi\)
\(312\) −216.000 −0.0391942
\(313\) 511.000 0.0922793 0.0461397 0.998935i \(-0.485308\pi\)
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 \(-0.281033\pi\)
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 \(-0.767123\pi\)
−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 \(-0.429818\pi\)
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 \(-0.444767\pi\)
0.172651 + 0.984983i \(0.444767\pi\)
\(348\) 348.000 0.0536056
\(349\) 9742.00 1.49420 0.747102 0.664709i \(-0.231445\pi\)
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 \(-0.565101\pi\)
−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 \(-0.522481\pi\)
−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 \(-0.606851\pi\)
−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 \(-0.653508\pi\)
−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 \(-0.223370\pi\)
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 \(-0.478410\pi\)
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 \(-0.578095\pi\)
−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 \(-0.459854\pi\)
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 \(-0.363104\pi\)
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 \(-0.495151\pi\)
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 \(-0.357649\pi\)
0.432450 + 0.901658i \(0.357649\pi\)
\(420\) 1740.00 0.202151
\(421\) 11268.0 1.30444 0.652219 0.758030i \(-0.273838\pi\)
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 \(-0.724480\pi\)
−0.648205 + 0.761466i \(0.724480\pi\)
\(432\) 432.000 0.0481125
\(433\) 1072.00 0.118977 0.0594885 0.998229i \(-0.481053\pi\)
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 \(-0.734023\pi\)
−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 \(-0.805179\pi\)
−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 \(-0.303410\pi\)
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 \(-0.612607\pi\)
−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 \(-0.589850\pi\)
−0.278539 + 0.960425i \(0.589850\pi\)
\(462\) −2610.00 −0.262832
\(463\) −14205.0 −1.42584 −0.712918 0.701247i \(-0.752627\pi\)
−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 \(-0.658855\pi\)
−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 \(-0.618982\pi\)
−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 \(-0.766548\pi\)
−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 \(-0.437636\pi\)
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 \(-0.774754\pi\)
−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 \(-0.526228\pi\)
−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 \(-0.543040\pi\)
−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 \(-0.397459\pi\)
0.316598 + 0.948560i \(0.397459\pi\)
\(522\) −522.000 −0.0437688
\(523\) −5767.00 −0.482167 −0.241083 0.970504i \(-0.577503\pi\)
−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 \(-0.817026\pi\)
−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 \(-0.254115\pi\)
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 \(-0.426215\pi\)
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 \(-0.695123\pi\)
−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 \(-0.270791\pi\)
0.659445 + 0.751752i \(0.270791\pi\)
\(570\) −1200.00 −0.0881798
\(571\) −10056.0 −0.737006 −0.368503 0.929627i \(-0.620130\pi\)
−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 \(-0.464698\pi\)
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 \(-0.533455\pi\)
−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 \(-0.433927\pi\)
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 \(-0.646208\pi\)
−0.443343 + 0.896352i \(0.646208\pi\)
\(600\) −1800.00 −0.122474
\(601\) 23398.0 1.58806 0.794030 0.607878i \(-0.207979\pi\)
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 \(-0.162067\pi\)
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 \(-0.793452\pi\)
−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 \(-0.476988\pi\)
0.0722304 + 0.997388i \(0.476988\pi\)
\(618\) 3336.00 0.217142
\(619\) −19586.0 −1.27177 −0.635887 0.771782i \(-0.719365\pi\)
−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 \(-0.455910\pi\)
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 \(-0.765121\pi\)
−0.739887 + 0.672731i \(0.765121\pi\)
\(642\) 9348.00 0.574667
\(643\) −19465.0 −1.19382 −0.596909 0.802309i \(-0.703605\pi\)
−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 \(-0.707322\pi\)
−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 \(-0.736762\pi\)
−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 \(-0.429168\pi\)
0.220693 + 0.975343i \(0.429168\pi\)
\(660\) −900.000 −0.0530795
\(661\) 16601.0 0.976859 0.488430 0.872603i \(-0.337570\pi\)
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 \(-0.264129\pi\)
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 \(-0.659905\pi\)
−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 \(-0.444944\pi\)
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 \(-0.330323\pi\)
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 \(-0.565198\pi\)
−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 \(-0.219555\pi\)
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 \(-0.806775\pi\)
−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 \(-0.319294\pi\)
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 \(-0.794869\pi\)
−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 \(-0.836759\pi\)
−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 \(-0.859532\pi\)
−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 \(-0.434423\pi\)
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 \(-0.612388\pi\)
−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 \(-0.445082\pi\)
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 \(-0.766030\pi\)
−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 \(-0.506888\pi\)
−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 \(-0.447952\pi\)
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 \(-0.751663\pi\)
−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 \(-0.442733\pi\)
0.178941 + 0.983860i \(0.442733\pi\)
\(810\) −810.000 −0.0351364
\(811\) −9031.00 −0.391025 −0.195513 0.980701i \(-0.562637\pi\)
−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 \(-0.158743\pi\)
0.878202 + 0.478289i \(0.158743\pi\)
\(822\) 5508.00 0.233715
\(823\) 31150.0 1.31934 0.659672 0.751553i \(-0.270695\pi\)
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 \(-0.449030\pi\)
0.159445 + 0.987207i \(0.449030\pi\)
\(828\) 4176.00 0.175273
\(829\) −28316.0 −1.18632 −0.593158 0.805086i \(-0.702119\pi\)
−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 \(-0.684454\pi\)
−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 \(-0.264960\pi\)
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 \(-0.676317\pi\)
−0.526022 + 0.850471i \(0.676317\pi\)
\(858\) −270.000 −0.0107432
\(859\) −12076.0 −0.479660 −0.239830 0.970815i \(-0.577092\pi\)
−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 \(-0.515386\pi\)
−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 \(-0.596878\pi\)
−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 \(-0.270721\pi\)
0.659610 + 0.751608i \(0.270721\pi\)
\(882\) −8964.00 −0.342215
\(883\) 17044.0 0.649577 0.324788 0.945787i \(-0.394707\pi\)
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 \(-0.603658\pi\)
−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 \(-0.234159\pi\)
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 \(-0.586632\pi\)
−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 \(-0.226124\pi\)
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 \(-0.330923\pi\)
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 \(-0.875954\pi\)
−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 \(-0.592503\pi\)
−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 \(-0.322526\pi\)
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 \(-0.211569\pi\)
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 \(-0.568833\pi\)
−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 \(-0.504734\pi\)
−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 \(-0.608269\pi\)
−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 \(-0.429949\pi\)
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 \(-0.643840\pi\)
−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 \(-0.507847\pi\)
−0.0246501 + 0.999696i \(0.507847\pi\)
\(998\) 33882.0 1.07467
\(999\) −972.000 −0.0307835
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 \(a_p\))

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