Properties

Label 1470.4.a.w.1.1
Level $1470$
Weight $4$
Character 1470.1
Self dual yes
Analytic conductor $86.733$
Analytic rank $1$
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] = [1470,4,Mod(1,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, 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("1470.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1470.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: \(86.7328077084\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1470.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -20.0000 q^{11} +12.0000 q^{12} -26.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} +26.0000 q^{17} +18.0000 q^{18} +42.0000 q^{19} -20.0000 q^{20} -40.0000 q^{22} -194.000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -52.0000 q^{26} +27.0000 q^{27} -42.0000 q^{29} -30.0000 q^{30} -274.000 q^{31} +32.0000 q^{32} -60.0000 q^{33} +52.0000 q^{34} +36.0000 q^{36} +2.00000 q^{37} +84.0000 q^{38} -78.0000 q^{39} -40.0000 q^{40} +250.000 q^{41} -296.000 q^{43} -80.0000 q^{44} -45.0000 q^{45} -388.000 q^{46} +328.000 q^{47} +48.0000 q^{48} +50.0000 q^{50} +78.0000 q^{51} -104.000 q^{52} -148.000 q^{53} +54.0000 q^{54} +100.000 q^{55} +126.000 q^{57} -84.0000 q^{58} -488.000 q^{59} -60.0000 q^{60} -272.000 q^{61} -548.000 q^{62} +64.0000 q^{64} +130.000 q^{65} -120.000 q^{66} +8.00000 q^{67} +104.000 q^{68} -582.000 q^{69} -684.000 q^{71} +72.0000 q^{72} -310.000 q^{73} +4.00000 q^{74} +75.0000 q^{75} +168.000 q^{76} -156.000 q^{78} -584.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +500.000 q^{82} -404.000 q^{83} -130.000 q^{85} -592.000 q^{86} -126.000 q^{87} -160.000 q^{88} +266.000 q^{89} -90.0000 q^{90} -776.000 q^{92} -822.000 q^{93} +656.000 q^{94} -210.000 q^{95} +96.0000 q^{96} +678.000 q^{97} -180.000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −10.0000 −0.316228
\(11\) −20.0000 −0.548202 −0.274101 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 12.0000 0.288675
\(13\) −26.0000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −15.0000 −0.258199
\(16\) 16.0000 0.250000
\(17\) 26.0000 0.370937 0.185468 0.982650i \(-0.440620\pi\)
0.185468 + 0.982650i \(0.440620\pi\)
\(18\) 18.0000 0.235702
\(19\) 42.0000 0.507130 0.253565 0.967318i \(-0.418397\pi\)
0.253565 + 0.967318i \(0.418397\pi\)
\(20\) −20.0000 −0.223607
\(21\) 0 0
\(22\) −40.0000 −0.387638
\(23\) −194.000 −1.75877 −0.879387 0.476108i \(-0.842047\pi\)
−0.879387 + 0.476108i \(0.842047\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) −52.0000 −0.392232
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −42.0000 −0.268938 −0.134469 0.990918i \(-0.542933\pi\)
−0.134469 + 0.990918i \(0.542933\pi\)
\(30\) −30.0000 −0.182574
\(31\) −274.000 −1.58748 −0.793740 0.608258i \(-0.791869\pi\)
−0.793740 + 0.608258i \(0.791869\pi\)
\(32\) 32.0000 0.176777
\(33\) −60.0000 −0.316505
\(34\) 52.0000 0.262292
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) 2.00000 0.00888643 0.00444322 0.999990i \(-0.498586\pi\)
0.00444322 + 0.999990i \(0.498586\pi\)
\(38\) 84.0000 0.358595
\(39\) −78.0000 −0.320256
\(40\) −40.0000 −0.158114
\(41\) 250.000 0.952279 0.476140 0.879370i \(-0.342036\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(42\) 0 0
\(43\) −296.000 −1.04976 −0.524879 0.851177i \(-0.675889\pi\)
−0.524879 + 0.851177i \(0.675889\pi\)
\(44\) −80.0000 −0.274101
\(45\) −45.0000 −0.149071
\(46\) −388.000 −1.24364
\(47\) 328.000 1.01795 0.508976 0.860781i \(-0.330024\pi\)
0.508976 + 0.860781i \(0.330024\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) 50.0000 0.141421
\(51\) 78.0000 0.214160
\(52\) −104.000 −0.277350
\(53\) −148.000 −0.383573 −0.191786 0.981437i \(-0.561428\pi\)
−0.191786 + 0.981437i \(0.561428\pi\)
\(54\) 54.0000 0.136083
\(55\) 100.000 0.245164
\(56\) 0 0
\(57\) 126.000 0.292791
\(58\) −84.0000 −0.190168
\(59\) −488.000 −1.07682 −0.538408 0.842684i \(-0.680974\pi\)
−0.538408 + 0.842684i \(0.680974\pi\)
\(60\) −60.0000 −0.129099
\(61\) −272.000 −0.570919 −0.285459 0.958391i \(-0.592146\pi\)
−0.285459 + 0.958391i \(0.592146\pi\)
\(62\) −548.000 −1.12252
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 130.000 0.248069
\(66\) −120.000 −0.223803
\(67\) 8.00000 0.0145874 0.00729370 0.999973i \(-0.497678\pi\)
0.00729370 + 0.999973i \(0.497678\pi\)
\(68\) 104.000 0.185468
\(69\) −582.000 −1.01543
\(70\) 0 0
\(71\) −684.000 −1.14332 −0.571661 0.820490i \(-0.693701\pi\)
−0.571661 + 0.820490i \(0.693701\pi\)
\(72\) 72.0000 0.117851
\(73\) −310.000 −0.497024 −0.248512 0.968629i \(-0.579942\pi\)
−0.248512 + 0.968629i \(0.579942\pi\)
\(74\) 4.00000 0.00628366
\(75\) 75.0000 0.115470
\(76\) 168.000 0.253565
\(77\) 0 0
\(78\) −156.000 −0.226455
\(79\) −584.000 −0.831711 −0.415855 0.909431i \(-0.636518\pi\)
−0.415855 + 0.909431i \(0.636518\pi\)
\(80\) −80.0000 −0.111803
\(81\) 81.0000 0.111111
\(82\) 500.000 0.673363
\(83\) −404.000 −0.534274 −0.267137 0.963659i \(-0.586078\pi\)
−0.267137 + 0.963659i \(0.586078\pi\)
\(84\) 0 0
\(85\) −130.000 −0.165888
\(86\) −592.000 −0.742291
\(87\) −126.000 −0.155271
\(88\) −160.000 −0.193819
\(89\) 266.000 0.316808 0.158404 0.987374i \(-0.449365\pi\)
0.158404 + 0.987374i \(0.449365\pi\)
\(90\) −90.0000 −0.105409
\(91\) 0 0
\(92\) −776.000 −0.879387
\(93\) −822.000 −0.916531
\(94\) 656.000 0.719800
\(95\) −210.000 −0.226795
\(96\) 96.0000 0.102062
\(97\) 678.000 0.709696 0.354848 0.934924i \(-0.384533\pi\)
0.354848 + 0.934924i \(0.384533\pi\)
\(98\) 0 0
\(99\) −180.000 −0.182734
\(100\) 100.000 0.100000
\(101\) 406.000 0.399985 0.199993 0.979797i \(-0.435908\pi\)
0.199993 + 0.979797i \(0.435908\pi\)
\(102\) 156.000 0.151434
\(103\) −292.000 −0.279336 −0.139668 0.990198i \(-0.544604\pi\)
−0.139668 + 0.990198i \(0.544604\pi\)
\(104\) −208.000 −0.196116
\(105\) 0 0
\(106\) −296.000 −0.271227
\(107\) −1950.00 −1.76181 −0.880905 0.473294i \(-0.843065\pi\)
−0.880905 + 0.473294i \(0.843065\pi\)
\(108\) 108.000 0.0962250
\(109\) −218.000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 200.000 0.173357
\(111\) 6.00000 0.00513058
\(112\) 0 0
\(113\) 1820.00 1.51514 0.757572 0.652752i \(-0.226386\pi\)
0.757572 + 0.652752i \(0.226386\pi\)
\(114\) 252.000 0.207035
\(115\) 970.000 0.786548
\(116\) −168.000 −0.134469
\(117\) −234.000 −0.184900
\(118\) −976.000 −0.761424
\(119\) 0 0
\(120\) −120.000 −0.0912871
\(121\) −931.000 −0.699474
\(122\) −544.000 −0.403700
\(123\) 750.000 0.549799
\(124\) −1096.00 −0.793740
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −96.0000 −0.0670758 −0.0335379 0.999437i \(-0.510677\pi\)
−0.0335379 + 0.999437i \(0.510677\pi\)
\(128\) 128.000 0.0883883
\(129\) −888.000 −0.606078
\(130\) 260.000 0.175412
\(131\) 1872.00 1.24853 0.624265 0.781213i \(-0.285399\pi\)
0.624265 + 0.781213i \(0.285399\pi\)
\(132\) −240.000 −0.158252
\(133\) 0 0
\(134\) 16.0000 0.0103148
\(135\) −135.000 −0.0860663
\(136\) 208.000 0.131146
\(137\) −316.000 −0.197064 −0.0985318 0.995134i \(-0.531415\pi\)
−0.0985318 + 0.995134i \(0.531415\pi\)
\(138\) −1164.00 −0.718016
\(139\) 262.000 0.159874 0.0799372 0.996800i \(-0.474528\pi\)
0.0799372 + 0.996800i \(0.474528\pi\)
\(140\) 0 0
\(141\) 984.000 0.587715
\(142\) −1368.00 −0.808451
\(143\) 520.000 0.304088
\(144\) 144.000 0.0833333
\(145\) 210.000 0.120273
\(146\) −620.000 −0.351449
\(147\) 0 0
\(148\) 8.00000 0.00444322
\(149\) −2090.00 −1.14912 −0.574562 0.818461i \(-0.694828\pi\)
−0.574562 + 0.818461i \(0.694828\pi\)
\(150\) 150.000 0.0816497
\(151\) −2520.00 −1.35811 −0.679055 0.734087i \(-0.737610\pi\)
−0.679055 + 0.734087i \(0.737610\pi\)
\(152\) 336.000 0.179297
\(153\) 234.000 0.123646
\(154\) 0 0
\(155\) 1370.00 0.709942
\(156\) −312.000 −0.160128
\(157\) −866.000 −0.440219 −0.220109 0.975475i \(-0.570641\pi\)
−0.220109 + 0.975475i \(0.570641\pi\)
\(158\) −1168.00 −0.588108
\(159\) −444.000 −0.221456
\(160\) −160.000 −0.0790569
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) −3436.00 −1.65109 −0.825547 0.564334i \(-0.809133\pi\)
−0.825547 + 0.564334i \(0.809133\pi\)
\(164\) 1000.00 0.476140
\(165\) 300.000 0.141545
\(166\) −808.000 −0.377789
\(167\) 1656.00 0.767336 0.383668 0.923471i \(-0.374661\pi\)
0.383668 + 0.923471i \(0.374661\pi\)
\(168\) 0 0
\(169\) −1521.00 −0.692308
\(170\) −260.000 −0.117301
\(171\) 378.000 0.169043
\(172\) −1184.00 −0.524879
\(173\) −2154.00 −0.946622 −0.473311 0.880895i \(-0.656941\pi\)
−0.473311 + 0.880895i \(0.656941\pi\)
\(174\) −252.000 −0.109794
\(175\) 0 0
\(176\) −320.000 −0.137051
\(177\) −1464.00 −0.621700
\(178\) 532.000 0.224017
\(179\) 1112.00 0.464328 0.232164 0.972677i \(-0.425419\pi\)
0.232164 + 0.972677i \(0.425419\pi\)
\(180\) −180.000 −0.0745356
\(181\) −512.000 −0.210258 −0.105129 0.994459i \(-0.533526\pi\)
−0.105129 + 0.994459i \(0.533526\pi\)
\(182\) 0 0
\(183\) −816.000 −0.329620
\(184\) −1552.00 −0.621820
\(185\) −10.0000 −0.00397413
\(186\) −1644.00 −0.648086
\(187\) −520.000 −0.203348
\(188\) 1312.00 0.508976
\(189\) 0 0
\(190\) −420.000 −0.160368
\(191\) −1008.00 −0.381866 −0.190933 0.981603i \(-0.561151\pi\)
−0.190933 + 0.981603i \(0.561151\pi\)
\(192\) 192.000 0.0721688
\(193\) 1650.00 0.615387 0.307693 0.951486i \(-0.400443\pi\)
0.307693 + 0.951486i \(0.400443\pi\)
\(194\) 1356.00 0.501831
\(195\) 390.000 0.143223
\(196\) 0 0
\(197\) 312.000 0.112838 0.0564190 0.998407i \(-0.482032\pi\)
0.0564190 + 0.998407i \(0.482032\pi\)
\(198\) −360.000 −0.129213
\(199\) 1706.00 0.607714 0.303857 0.952718i \(-0.401725\pi\)
0.303857 + 0.952718i \(0.401725\pi\)
\(200\) 200.000 0.0707107
\(201\) 24.0000 0.00842204
\(202\) 812.000 0.282832
\(203\) 0 0
\(204\) 312.000 0.107080
\(205\) −1250.00 −0.425872
\(206\) −584.000 −0.197520
\(207\) −1746.00 −0.586258
\(208\) −416.000 −0.138675
\(209\) −840.000 −0.278010
\(210\) 0 0
\(211\) 5036.00 1.64309 0.821546 0.570142i \(-0.193112\pi\)
0.821546 + 0.570142i \(0.193112\pi\)
\(212\) −592.000 −0.191786
\(213\) −2052.00 −0.660097
\(214\) −3900.00 −1.24579
\(215\) 1480.00 0.469466
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) −436.000 −0.135457
\(219\) −930.000 −0.286957
\(220\) 400.000 0.122582
\(221\) −676.000 −0.205759
\(222\) 12.0000 0.00362787
\(223\) 3740.00 1.12309 0.561545 0.827446i \(-0.310207\pi\)
0.561545 + 0.827446i \(0.310207\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 3640.00 1.07137
\(227\) −2652.00 −0.775416 −0.387708 0.921782i \(-0.626733\pi\)
−0.387708 + 0.921782i \(0.626733\pi\)
\(228\) 504.000 0.146396
\(229\) 20.0000 0.00577134 0.00288567 0.999996i \(-0.499081\pi\)
0.00288567 + 0.999996i \(0.499081\pi\)
\(230\) 1940.00 0.556173
\(231\) 0 0
\(232\) −336.000 −0.0950840
\(233\) −1288.00 −0.362145 −0.181072 0.983470i \(-0.557957\pi\)
−0.181072 + 0.983470i \(0.557957\pi\)
\(234\) −468.000 −0.130744
\(235\) −1640.00 −0.455242
\(236\) −1952.00 −0.538408
\(237\) −1752.00 −0.480188
\(238\) 0 0
\(239\) 3632.00 0.982990 0.491495 0.870880i \(-0.336451\pi\)
0.491495 + 0.870880i \(0.336451\pi\)
\(240\) −240.000 −0.0645497
\(241\) 2216.00 0.592303 0.296152 0.955141i \(-0.404297\pi\)
0.296152 + 0.955141i \(0.404297\pi\)
\(242\) −1862.00 −0.494603
\(243\) 243.000 0.0641500
\(244\) −1088.00 −0.285459
\(245\) 0 0
\(246\) 1500.00 0.388766
\(247\) −1092.00 −0.281305
\(248\) −2192.00 −0.561259
\(249\) −1212.00 −0.308463
\(250\) −250.000 −0.0632456
\(251\) 1576.00 0.396320 0.198160 0.980170i \(-0.436503\pi\)
0.198160 + 0.980170i \(0.436503\pi\)
\(252\) 0 0
\(253\) 3880.00 0.964164
\(254\) −192.000 −0.0474297
\(255\) −390.000 −0.0957755
\(256\) 256.000 0.0625000
\(257\) 7710.00 1.87135 0.935674 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) −1776.00 −0.428562
\(259\) 0 0
\(260\) 520.000 0.124035
\(261\) −378.000 −0.0896460
\(262\) 3744.00 0.882844
\(263\) −3990.00 −0.935490 −0.467745 0.883863i \(-0.654933\pi\)
−0.467745 + 0.883863i \(0.654933\pi\)
\(264\) −480.000 −0.111901
\(265\) 740.000 0.171539
\(266\) 0 0
\(267\) 798.000 0.182909
\(268\) 32.0000 0.00729370
\(269\) 4370.00 0.990497 0.495248 0.868751i \(-0.335077\pi\)
0.495248 + 0.868751i \(0.335077\pi\)
\(270\) −270.000 −0.0608581
\(271\) −7630.00 −1.71029 −0.855147 0.518386i \(-0.826533\pi\)
−0.855147 + 0.518386i \(0.826533\pi\)
\(272\) 416.000 0.0927342
\(273\) 0 0
\(274\) −632.000 −0.139345
\(275\) −500.000 −0.109640
\(276\) −2328.00 −0.507714
\(277\) 434.000 0.0941391 0.0470696 0.998892i \(-0.485012\pi\)
0.0470696 + 0.998892i \(0.485012\pi\)
\(278\) 524.000 0.113048
\(279\) −2466.00 −0.529160
\(280\) 0 0
\(281\) 4858.00 1.03133 0.515665 0.856790i \(-0.327545\pi\)
0.515665 + 0.856790i \(0.327545\pi\)
\(282\) 1968.00 0.415577
\(283\) 9200.00 1.93245 0.966225 0.257701i \(-0.0829648\pi\)
0.966225 + 0.257701i \(0.0829648\pi\)
\(284\) −2736.00 −0.571661
\(285\) −630.000 −0.130940
\(286\) 1040.00 0.215023
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) −4237.00 −0.862406
\(290\) 420.000 0.0850457
\(291\) 2034.00 0.409743
\(292\) −1240.00 −0.248512
\(293\) 6162.00 1.22863 0.614314 0.789062i \(-0.289433\pi\)
0.614314 + 0.789062i \(0.289433\pi\)
\(294\) 0 0
\(295\) 2440.00 0.481567
\(296\) 16.0000 0.00314183
\(297\) −540.000 −0.105502
\(298\) −4180.00 −0.812553
\(299\) 5044.00 0.975592
\(300\) 300.000 0.0577350
\(301\) 0 0
\(302\) −5040.00 −0.960329
\(303\) 1218.00 0.230932
\(304\) 672.000 0.126782
\(305\) 1360.00 0.255323
\(306\) 468.000 0.0874307
\(307\) 3956.00 0.735442 0.367721 0.929936i \(-0.380138\pi\)
0.367721 + 0.929936i \(0.380138\pi\)
\(308\) 0 0
\(309\) −876.000 −0.161275
\(310\) 2740.00 0.502005
\(311\) −9068.00 −1.65337 −0.826687 0.562663i \(-0.809777\pi\)
−0.826687 + 0.562663i \(0.809777\pi\)
\(312\) −624.000 −0.113228
\(313\) −7318.00 −1.32153 −0.660763 0.750594i \(-0.729767\pi\)
−0.660763 + 0.750594i \(0.729767\pi\)
\(314\) −1732.00 −0.311282
\(315\) 0 0
\(316\) −2336.00 −0.415855
\(317\) −4188.00 −0.742024 −0.371012 0.928628i \(-0.620989\pi\)
−0.371012 + 0.928628i \(0.620989\pi\)
\(318\) −888.000 −0.156593
\(319\) 840.000 0.147433
\(320\) −320.000 −0.0559017
\(321\) −5850.00 −1.01718
\(322\) 0 0
\(323\) 1092.00 0.188113
\(324\) 324.000 0.0555556
\(325\) −650.000 −0.110940
\(326\) −6872.00 −1.16750
\(327\) −654.000 −0.110600
\(328\) 2000.00 0.336681
\(329\) 0 0
\(330\) 600.000 0.100088
\(331\) −3172.00 −0.526734 −0.263367 0.964696i \(-0.584833\pi\)
−0.263367 + 0.964696i \(0.584833\pi\)
\(332\) −1616.00 −0.267137
\(333\) 18.0000 0.00296214
\(334\) 3312.00 0.542589
\(335\) −40.0000 −0.00652368
\(336\) 0 0
\(337\) 2434.00 0.393437 0.196719 0.980460i \(-0.436971\pi\)
0.196719 + 0.980460i \(0.436971\pi\)
\(338\) −3042.00 −0.489535
\(339\) 5460.00 0.874768
\(340\) −520.000 −0.0829440
\(341\) 5480.00 0.870260
\(342\) 756.000 0.119532
\(343\) 0 0
\(344\) −2368.00 −0.371145
\(345\) 2910.00 0.454113
\(346\) −4308.00 −0.669363
\(347\) −1766.00 −0.273210 −0.136605 0.990626i \(-0.543619\pi\)
−0.136605 + 0.990626i \(0.543619\pi\)
\(348\) −504.000 −0.0776357
\(349\) −8320.00 −1.27610 −0.638051 0.769994i \(-0.720259\pi\)
−0.638051 + 0.769994i \(0.720259\pi\)
\(350\) 0 0
\(351\) −702.000 −0.106752
\(352\) −640.000 −0.0969094
\(353\) −4818.00 −0.726448 −0.363224 0.931702i \(-0.618324\pi\)
−0.363224 + 0.931702i \(0.618324\pi\)
\(354\) −2928.00 −0.439609
\(355\) 3420.00 0.511309
\(356\) 1064.00 0.158404
\(357\) 0 0
\(358\) 2224.00 0.328330
\(359\) 464.000 0.0682144 0.0341072 0.999418i \(-0.489141\pi\)
0.0341072 + 0.999418i \(0.489141\pi\)
\(360\) −360.000 −0.0527046
\(361\) −5095.00 −0.742820
\(362\) −1024.00 −0.148675
\(363\) −2793.00 −0.403842
\(364\) 0 0
\(365\) 1550.00 0.222276
\(366\) −1632.00 −0.233077
\(367\) −2492.00 −0.354445 −0.177223 0.984171i \(-0.556711\pi\)
−0.177223 + 0.984171i \(0.556711\pi\)
\(368\) −3104.00 −0.439693
\(369\) 2250.00 0.317426
\(370\) −20.0000 −0.00281014
\(371\) 0 0
\(372\) −3288.00 −0.458266
\(373\) 5766.00 0.800408 0.400204 0.916426i \(-0.368939\pi\)
0.400204 + 0.916426i \(0.368939\pi\)
\(374\) −1040.00 −0.143789
\(375\) −375.000 −0.0516398
\(376\) 2624.00 0.359900
\(377\) 1092.00 0.149180
\(378\) 0 0
\(379\) 7148.00 0.968781 0.484391 0.874852i \(-0.339041\pi\)
0.484391 + 0.874852i \(0.339041\pi\)
\(380\) −840.000 −0.113398
\(381\) −288.000 −0.0387262
\(382\) −2016.00 −0.270020
\(383\) 728.000 0.0971255 0.0485627 0.998820i \(-0.484536\pi\)
0.0485627 + 0.998820i \(0.484536\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) 3300.00 0.435144
\(387\) −2664.00 −0.349919
\(388\) 2712.00 0.354848
\(389\) 114.000 0.0148587 0.00742934 0.999972i \(-0.497635\pi\)
0.00742934 + 0.999972i \(0.497635\pi\)
\(390\) 780.000 0.101274
\(391\) −5044.00 −0.652394
\(392\) 0 0
\(393\) 5616.00 0.720839
\(394\) 624.000 0.0797885
\(395\) 2920.00 0.371952
\(396\) −720.000 −0.0913671
\(397\) −7574.00 −0.957502 −0.478751 0.877951i \(-0.658910\pi\)
−0.478751 + 0.877951i \(0.658910\pi\)
\(398\) 3412.00 0.429719
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) 13790.0 1.71731 0.858653 0.512557i \(-0.171302\pi\)
0.858653 + 0.512557i \(0.171302\pi\)
\(402\) 48.0000 0.00595528
\(403\) 7124.00 0.880575
\(404\) 1624.00 0.199993
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) −40.0000 −0.00487156
\(408\) 624.000 0.0757172
\(409\) 5444.00 0.658163 0.329081 0.944302i \(-0.393261\pi\)
0.329081 + 0.944302i \(0.393261\pi\)
\(410\) −2500.00 −0.301137
\(411\) −948.000 −0.113775
\(412\) −1168.00 −0.139668
\(413\) 0 0
\(414\) −3492.00 −0.414547
\(415\) 2020.00 0.238935
\(416\) −832.000 −0.0980581
\(417\) 786.000 0.0923036
\(418\) −1680.00 −0.196583
\(419\) 2052.00 0.239252 0.119626 0.992819i \(-0.461830\pi\)
0.119626 + 0.992819i \(0.461830\pi\)
\(420\) 0 0
\(421\) 4322.00 0.500336 0.250168 0.968202i \(-0.419514\pi\)
0.250168 + 0.968202i \(0.419514\pi\)
\(422\) 10072.0 1.16184
\(423\) 2952.00 0.339317
\(424\) −1184.00 −0.135613
\(425\) 650.000 0.0741874
\(426\) −4104.00 −0.466759
\(427\) 0 0
\(428\) −7800.00 −0.880905
\(429\) 1560.00 0.175565
\(430\) 2960.00 0.331963
\(431\) 3660.00 0.409039 0.204520 0.978862i \(-0.434437\pi\)
0.204520 + 0.978862i \(0.434437\pi\)
\(432\) 432.000 0.0481125
\(433\) 682.000 0.0756924 0.0378462 0.999284i \(-0.487950\pi\)
0.0378462 + 0.999284i \(0.487950\pi\)
\(434\) 0 0
\(435\) 630.000 0.0694395
\(436\) −872.000 −0.0957826
\(437\) −8148.00 −0.891926
\(438\) −1860.00 −0.202909
\(439\) 914.000 0.0993687 0.0496843 0.998765i \(-0.484178\pi\)
0.0496843 + 0.998765i \(0.484178\pi\)
\(440\) 800.000 0.0866784
\(441\) 0 0
\(442\) −1352.00 −0.145493
\(443\) −6958.00 −0.746241 −0.373120 0.927783i \(-0.621712\pi\)
−0.373120 + 0.927783i \(0.621712\pi\)
\(444\) 24.0000 0.00256529
\(445\) −1330.00 −0.141681
\(446\) 7480.00 0.794144
\(447\) −6270.00 −0.663447
\(448\) 0 0
\(449\) 5466.00 0.574513 0.287257 0.957854i \(-0.407257\pi\)
0.287257 + 0.957854i \(0.407257\pi\)
\(450\) 450.000 0.0471405
\(451\) −5000.00 −0.522042
\(452\) 7280.00 0.757572
\(453\) −7560.00 −0.784105
\(454\) −5304.00 −0.548302
\(455\) 0 0
\(456\) 1008.00 0.103517
\(457\) −13986.0 −1.43159 −0.715796 0.698310i \(-0.753936\pi\)
−0.715796 + 0.698310i \(0.753936\pi\)
\(458\) 40.0000 0.00408095
\(459\) 702.000 0.0713868
\(460\) 3880.00 0.393274
\(461\) −11946.0 −1.20690 −0.603450 0.797401i \(-0.706208\pi\)
−0.603450 + 0.797401i \(0.706208\pi\)
\(462\) 0 0
\(463\) −7208.00 −0.723508 −0.361754 0.932274i \(-0.617822\pi\)
−0.361754 + 0.932274i \(0.617822\pi\)
\(464\) −672.000 −0.0672345
\(465\) 4110.00 0.409885
\(466\) −2576.00 −0.256075
\(467\) −3988.00 −0.395166 −0.197583 0.980286i \(-0.563309\pi\)
−0.197583 + 0.980286i \(0.563309\pi\)
\(468\) −936.000 −0.0924500
\(469\) 0 0
\(470\) −3280.00 −0.321905
\(471\) −2598.00 −0.254160
\(472\) −3904.00 −0.380712
\(473\) 5920.00 0.575480
\(474\) −3504.00 −0.339544
\(475\) 1050.00 0.101426
\(476\) 0 0
\(477\) −1332.00 −0.127858
\(478\) 7264.00 0.695079
\(479\) −7796.00 −0.743650 −0.371825 0.928303i \(-0.621268\pi\)
−0.371825 + 0.928303i \(0.621268\pi\)
\(480\) −480.000 −0.0456435
\(481\) −52.0000 −0.00492931
\(482\) 4432.00 0.418822
\(483\) 0 0
\(484\) −3724.00 −0.349737
\(485\) −3390.00 −0.317386
\(486\) 486.000 0.0453609
\(487\) 16324.0 1.51891 0.759457 0.650558i \(-0.225465\pi\)
0.759457 + 0.650558i \(0.225465\pi\)
\(488\) −2176.00 −0.201850
\(489\) −10308.0 −0.953259
\(490\) 0 0
\(491\) 17856.0 1.64120 0.820601 0.571502i \(-0.193639\pi\)
0.820601 + 0.571502i \(0.193639\pi\)
\(492\) 3000.00 0.274899
\(493\) −1092.00 −0.0997590
\(494\) −2184.00 −0.198913
\(495\) 900.000 0.0817212
\(496\) −4384.00 −0.396870
\(497\) 0 0
\(498\) −2424.00 −0.218117
\(499\) 3412.00 0.306096 0.153048 0.988219i \(-0.451091\pi\)
0.153048 + 0.988219i \(0.451091\pi\)
\(500\) −500.000 −0.0447214
\(501\) 4968.00 0.443022
\(502\) 3152.00 0.280240
\(503\) 15912.0 1.41050 0.705250 0.708959i \(-0.250835\pi\)
0.705250 + 0.708959i \(0.250835\pi\)
\(504\) 0 0
\(505\) −2030.00 −0.178879
\(506\) 7760.00 0.681767
\(507\) −4563.00 −0.399704
\(508\) −384.000 −0.0335379
\(509\) 13434.0 1.16985 0.584923 0.811089i \(-0.301125\pi\)
0.584923 + 0.811089i \(0.301125\pi\)
\(510\) −780.000 −0.0677235
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 1134.00 0.0975971
\(514\) 15420.0 1.32324
\(515\) 1460.00 0.124923
\(516\) −3552.00 −0.303039
\(517\) −6560.00 −0.558043
\(518\) 0 0
\(519\) −6462.00 −0.546532
\(520\) 1040.00 0.0877058
\(521\) −19578.0 −1.64631 −0.823155 0.567816i \(-0.807788\pi\)
−0.823155 + 0.567816i \(0.807788\pi\)
\(522\) −756.000 −0.0633893
\(523\) −20288.0 −1.69624 −0.848119 0.529806i \(-0.822265\pi\)
−0.848119 + 0.529806i \(0.822265\pi\)
\(524\) 7488.00 0.624265
\(525\) 0 0
\(526\) −7980.00 −0.661492
\(527\) −7124.00 −0.588854
\(528\) −960.000 −0.0791262
\(529\) 25469.0 2.09329
\(530\) 1480.00 0.121296
\(531\) −4392.00 −0.358939
\(532\) 0 0
\(533\) −6500.00 −0.528229
\(534\) 1596.00 0.129336
\(535\) 9750.00 0.787905
\(536\) 64.0000 0.00515742
\(537\) 3336.00 0.268080
\(538\) 8740.00 0.700387
\(539\) 0 0
\(540\) −540.000 −0.0430331
\(541\) 12170.0 0.967152 0.483576 0.875302i \(-0.339338\pi\)
0.483576 + 0.875302i \(0.339338\pi\)
\(542\) −15260.0 −1.20936
\(543\) −1536.00 −0.121392
\(544\) 832.000 0.0655730
\(545\) 1090.00 0.0856706
\(546\) 0 0
\(547\) 11368.0 0.888593 0.444297 0.895880i \(-0.353454\pi\)
0.444297 + 0.895880i \(0.353454\pi\)
\(548\) −1264.00 −0.0985318
\(549\) −2448.00 −0.190306
\(550\) −1000.00 −0.0775275
\(551\) −1764.00 −0.136386
\(552\) −4656.00 −0.359008
\(553\) 0 0
\(554\) 868.000 0.0665664
\(555\) −30.0000 −0.00229447
\(556\) 1048.00 0.0799372
\(557\) 9444.00 0.718411 0.359206 0.933258i \(-0.383048\pi\)
0.359206 + 0.933258i \(0.383048\pi\)
\(558\) −4932.00 −0.374172
\(559\) 7696.00 0.582301
\(560\) 0 0
\(561\) −1560.00 −0.117403
\(562\) 9716.00 0.729261
\(563\) 3708.00 0.277573 0.138786 0.990322i \(-0.455680\pi\)
0.138786 + 0.990322i \(0.455680\pi\)
\(564\) 3936.00 0.293857
\(565\) −9100.00 −0.677593
\(566\) 18400.0 1.36645
\(567\) 0 0
\(568\) −5472.00 −0.404225
\(569\) 17270.0 1.27240 0.636200 0.771524i \(-0.280505\pi\)
0.636200 + 0.771524i \(0.280505\pi\)
\(570\) −1260.00 −0.0925888
\(571\) 8364.00 0.612999 0.306500 0.951871i \(-0.400842\pi\)
0.306500 + 0.951871i \(0.400842\pi\)
\(572\) 2080.00 0.152044
\(573\) −3024.00 −0.220470
\(574\) 0 0
\(575\) −4850.00 −0.351755
\(576\) 576.000 0.0416667
\(577\) 4682.00 0.337806 0.168903 0.985633i \(-0.445977\pi\)
0.168903 + 0.985633i \(0.445977\pi\)
\(578\) −8474.00 −0.609813
\(579\) 4950.00 0.355294
\(580\) 840.000 0.0601364
\(581\) 0 0
\(582\) 4068.00 0.289732
\(583\) 2960.00 0.210276
\(584\) −2480.00 −0.175725
\(585\) 1170.00 0.0826898
\(586\) 12324.0 0.868771
\(587\) 27620.0 1.94208 0.971039 0.238922i \(-0.0767941\pi\)
0.971039 + 0.238922i \(0.0767941\pi\)
\(588\) 0 0
\(589\) −11508.0 −0.805058
\(590\) 4880.00 0.340519
\(591\) 936.000 0.0651470
\(592\) 32.0000 0.00222161
\(593\) −6578.00 −0.455525 −0.227762 0.973717i \(-0.573141\pi\)
−0.227762 + 0.973717i \(0.573141\pi\)
\(594\) −1080.00 −0.0746009
\(595\) 0 0
\(596\) −8360.00 −0.574562
\(597\) 5118.00 0.350864
\(598\) 10088.0 0.689848
\(599\) 23704.0 1.61689 0.808447 0.588569i \(-0.200309\pi\)
0.808447 + 0.588569i \(0.200309\pi\)
\(600\) 600.000 0.0408248
\(601\) −388.000 −0.0263342 −0.0131671 0.999913i \(-0.504191\pi\)
−0.0131671 + 0.999913i \(0.504191\pi\)
\(602\) 0 0
\(603\) 72.0000 0.00486247
\(604\) −10080.0 −0.679055
\(605\) 4655.00 0.312814
\(606\) 2436.00 0.163293
\(607\) 5644.00 0.377402 0.188701 0.982035i \(-0.439572\pi\)
0.188701 + 0.982035i \(0.439572\pi\)
\(608\) 1344.00 0.0896487
\(609\) 0 0
\(610\) 2720.00 0.180540
\(611\) −8528.00 −0.564658
\(612\) 936.000 0.0618228
\(613\) 14290.0 0.941546 0.470773 0.882254i \(-0.343975\pi\)
0.470773 + 0.882254i \(0.343975\pi\)
\(614\) 7912.00 0.520036
\(615\) −3750.00 −0.245877
\(616\) 0 0
\(617\) −23808.0 −1.55344 −0.776721 0.629845i \(-0.783119\pi\)
−0.776721 + 0.629845i \(0.783119\pi\)
\(618\) −1752.00 −0.114038
\(619\) 12798.0 0.831010 0.415505 0.909591i \(-0.363605\pi\)
0.415505 + 0.909591i \(0.363605\pi\)
\(620\) 5480.00 0.354971
\(621\) −5238.00 −0.338476
\(622\) −18136.0 −1.16911
\(623\) 0 0
\(624\) −1248.00 −0.0800641
\(625\) 625.000 0.0400000
\(626\) −14636.0 −0.934460
\(627\) −2520.00 −0.160509
\(628\) −3464.00 −0.220109
\(629\) 52.0000 0.00329630
\(630\) 0 0
\(631\) −8744.00 −0.551653 −0.275827 0.961207i \(-0.588952\pi\)
−0.275827 + 0.961207i \(0.588952\pi\)
\(632\) −4672.00 −0.294054
\(633\) 15108.0 0.948640
\(634\) −8376.00 −0.524690
\(635\) 480.000 0.0299972
\(636\) −1776.00 −0.110728
\(637\) 0 0
\(638\) 1680.00 0.104251
\(639\) −6156.00 −0.381107
\(640\) −640.000 −0.0395285
\(641\) 24738.0 1.52432 0.762162 0.647386i \(-0.224138\pi\)
0.762162 + 0.647386i \(0.224138\pi\)
\(642\) −11700.0 −0.719256
\(643\) 3828.00 0.234777 0.117388 0.993086i \(-0.462548\pi\)
0.117388 + 0.993086i \(0.462548\pi\)
\(644\) 0 0
\(645\) 4440.00 0.271046
\(646\) 2184.00 0.133016
\(647\) 14272.0 0.867218 0.433609 0.901101i \(-0.357240\pi\)
0.433609 + 0.901101i \(0.357240\pi\)
\(648\) 648.000 0.0392837
\(649\) 9760.00 0.590314
\(650\) −1300.00 −0.0784465
\(651\) 0 0
\(652\) −13744.0 −0.825547
\(653\) 16468.0 0.986895 0.493448 0.869775i \(-0.335736\pi\)
0.493448 + 0.869775i \(0.335736\pi\)
\(654\) −1308.00 −0.0782062
\(655\) −9360.00 −0.558359
\(656\) 4000.00 0.238070
\(657\) −2790.00 −0.165675
\(658\) 0 0
\(659\) −18416.0 −1.08860 −0.544299 0.838892i \(-0.683204\pi\)
−0.544299 + 0.838892i \(0.683204\pi\)
\(660\) 1200.00 0.0707726
\(661\) −30568.0 −1.79873 −0.899363 0.437203i \(-0.855969\pi\)
−0.899363 + 0.437203i \(0.855969\pi\)
\(662\) −6344.00 −0.372457
\(663\) −2028.00 −0.118795
\(664\) −3232.00 −0.188894
\(665\) 0 0
\(666\) 36.0000 0.00209455
\(667\) 8148.00 0.473001
\(668\) 6624.00 0.383668
\(669\) 11220.0 0.648416
\(670\) −80.0000 −0.00461294
\(671\) 5440.00 0.312979
\(672\) 0 0
\(673\) −7970.00 −0.456495 −0.228247 0.973603i \(-0.573299\pi\)
−0.228247 + 0.973603i \(0.573299\pi\)
\(674\) 4868.00 0.278202
\(675\) 675.000 0.0384900
\(676\) −6084.00 −0.346154
\(677\) 34394.0 1.95254 0.976269 0.216559i \(-0.0694835\pi\)
0.976269 + 0.216559i \(0.0694835\pi\)
\(678\) 10920.0 0.618555
\(679\) 0 0
\(680\) −1040.00 −0.0586503
\(681\) −7956.00 −0.447687
\(682\) 10960.0 0.615367
\(683\) 1818.00 0.101850 0.0509252 0.998702i \(-0.483783\pi\)
0.0509252 + 0.998702i \(0.483783\pi\)
\(684\) 1512.00 0.0845216
\(685\) 1580.00 0.0881295
\(686\) 0 0
\(687\) 60.0000 0.00333209
\(688\) −4736.00 −0.262439
\(689\) 3848.00 0.212768
\(690\) 5820.00 0.321107
\(691\) −11774.0 −0.648197 −0.324098 0.946023i \(-0.605061\pi\)
−0.324098 + 0.946023i \(0.605061\pi\)
\(692\) −8616.00 −0.473311
\(693\) 0 0
\(694\) −3532.00 −0.193189
\(695\) −1310.00 −0.0714980
\(696\) −1008.00 −0.0548968
\(697\) 6500.00 0.353235
\(698\) −16640.0 −0.902340
\(699\) −3864.00 −0.209084
\(700\) 0 0
\(701\) −28138.0 −1.51606 −0.758030 0.652220i \(-0.773838\pi\)
−0.758030 + 0.652220i \(0.773838\pi\)
\(702\) −1404.00 −0.0754851
\(703\) 84.0000 0.00450657
\(704\) −1280.00 −0.0685253
\(705\) −4920.00 −0.262834
\(706\) −9636.00 −0.513677
\(707\) 0 0
\(708\) −5856.00 −0.310850
\(709\) 5754.00 0.304790 0.152395 0.988320i \(-0.451301\pi\)
0.152395 + 0.988320i \(0.451301\pi\)
\(710\) 6840.00 0.361550
\(711\) −5256.00 −0.277237
\(712\) 2128.00 0.112009
\(713\) 53156.0 2.79202
\(714\) 0 0
\(715\) −2600.00 −0.135992
\(716\) 4448.00 0.232164
\(717\) 10896.0 0.567529
\(718\) 928.000 0.0482349
\(719\) 34428.0 1.78574 0.892870 0.450314i \(-0.148688\pi\)
0.892870 + 0.450314i \(0.148688\pi\)
\(720\) −720.000 −0.0372678
\(721\) 0 0
\(722\) −10190.0 −0.525253
\(723\) 6648.00 0.341967
\(724\) −2048.00 −0.105129
\(725\) −1050.00 −0.0537876
\(726\) −5586.00 −0.285559
\(727\) −28472.0 −1.45250 −0.726250 0.687430i \(-0.758739\pi\)
−0.726250 + 0.687430i \(0.758739\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 3100.00 0.157173
\(731\) −7696.00 −0.389394
\(732\) −3264.00 −0.164810
\(733\) −23586.0 −1.18850 −0.594249 0.804281i \(-0.702551\pi\)
−0.594249 + 0.804281i \(0.702551\pi\)
\(734\) −4984.00 −0.250631
\(735\) 0 0
\(736\) −6208.00 −0.310910
\(737\) −160.000 −0.00799685
\(738\) 4500.00 0.224454
\(739\) −28116.0 −1.39955 −0.699773 0.714366i \(-0.746715\pi\)
−0.699773 + 0.714366i \(0.746715\pi\)
\(740\) −40.0000 −0.00198707
\(741\) −3276.00 −0.162411
\(742\) 0 0
\(743\) 25446.0 1.25642 0.628212 0.778042i \(-0.283787\pi\)
0.628212 + 0.778042i \(0.283787\pi\)
\(744\) −6576.00 −0.324043
\(745\) 10450.0 0.513904
\(746\) 11532.0 0.565974
\(747\) −3636.00 −0.178091
\(748\) −2080.00 −0.101674
\(749\) 0 0
\(750\) −750.000 −0.0365148
\(751\) 18856.0 0.916199 0.458099 0.888901i \(-0.348530\pi\)
0.458099 + 0.888901i \(0.348530\pi\)
\(752\) 5248.00 0.254488
\(753\) 4728.00 0.228815
\(754\) 2184.00 0.105486
\(755\) 12600.0 0.607365
\(756\) 0 0
\(757\) 3382.00 0.162379 0.0811895 0.996699i \(-0.474128\pi\)
0.0811895 + 0.996699i \(0.474128\pi\)
\(758\) 14296.0 0.685032
\(759\) 11640.0 0.556660
\(760\) −1680.00 −0.0801842
\(761\) 4434.00 0.211212 0.105606 0.994408i \(-0.466322\pi\)
0.105606 + 0.994408i \(0.466322\pi\)
\(762\) −576.000 −0.0273836
\(763\) 0 0
\(764\) −4032.00 −0.190933
\(765\) −1170.00 −0.0552960
\(766\) 1456.00 0.0686781
\(767\) 12688.0 0.597310
\(768\) 768.000 0.0360844
\(769\) −10540.0 −0.494255 −0.247128 0.968983i \(-0.579487\pi\)
−0.247128 + 0.968983i \(0.579487\pi\)
\(770\) 0 0
\(771\) 23130.0 1.08042
\(772\) 6600.00 0.307693
\(773\) 19902.0 0.926035 0.463018 0.886349i \(-0.346767\pi\)
0.463018 + 0.886349i \(0.346767\pi\)
\(774\) −5328.00 −0.247430
\(775\) −6850.00 −0.317496
\(776\) 5424.00 0.250915
\(777\) 0 0
\(778\) 228.000 0.0105067
\(779\) 10500.0 0.482929
\(780\) 1560.00 0.0716115
\(781\) 13680.0 0.626772
\(782\) −10088.0 −0.461312
\(783\) −1134.00 −0.0517572
\(784\) 0 0
\(785\) 4330.00 0.196872
\(786\) 11232.0 0.509710
\(787\) −32304.0 −1.46317 −0.731584 0.681751i \(-0.761219\pi\)
−0.731584 + 0.681751i \(0.761219\pi\)
\(788\) 1248.00 0.0564190
\(789\) −11970.0 −0.540106
\(790\) 5840.00 0.263010
\(791\) 0 0
\(792\) −1440.00 −0.0646063
\(793\) 7072.00 0.316689
\(794\) −15148.0 −0.677056
\(795\) 2220.00 0.0990381
\(796\) 6824.00 0.303857
\(797\) −20410.0 −0.907101 −0.453550 0.891231i \(-0.649843\pi\)
−0.453550 + 0.891231i \(0.649843\pi\)
\(798\) 0 0
\(799\) 8528.00 0.377596
\(800\) 800.000 0.0353553
\(801\) 2394.00 0.105603
\(802\) 27580.0 1.21432
\(803\) 6200.00 0.272470
\(804\) 96.0000 0.00421102
\(805\) 0 0
\(806\) 14248.0 0.622661
\(807\) 13110.0 0.571864
\(808\) 3248.00 0.141416
\(809\) −14138.0 −0.614420 −0.307210 0.951642i \(-0.599395\pi\)
−0.307210 + 0.951642i \(0.599395\pi\)
\(810\) −810.000 −0.0351364
\(811\) −43442.0 −1.88096 −0.940478 0.339855i \(-0.889622\pi\)
−0.940478 + 0.339855i \(0.889622\pi\)
\(812\) 0 0
\(813\) −22890.0 −0.987438
\(814\) −80.0000 −0.00344472
\(815\) 17180.0 0.738392
\(816\) 1248.00 0.0535401
\(817\) −12432.0 −0.532363
\(818\) 10888.0 0.465391
\(819\) 0 0
\(820\) −5000.00 −0.212936
\(821\) −21750.0 −0.924580 −0.462290 0.886729i \(-0.652972\pi\)
−0.462290 + 0.886729i \(0.652972\pi\)
\(822\) −1896.00 −0.0804508
\(823\) 3632.00 0.153832 0.0769159 0.997038i \(-0.475493\pi\)
0.0769159 + 0.997038i \(0.475493\pi\)
\(824\) −2336.00 −0.0987602
\(825\) −1500.00 −0.0633010
\(826\) 0 0
\(827\) −9806.00 −0.412319 −0.206160 0.978518i \(-0.566097\pi\)
−0.206160 + 0.978518i \(0.566097\pi\)
\(828\) −6984.00 −0.293129
\(829\) −18128.0 −0.759483 −0.379742 0.925093i \(-0.623987\pi\)
−0.379742 + 0.925093i \(0.623987\pi\)
\(830\) 4040.00 0.168952
\(831\) 1302.00 0.0543512
\(832\) −1664.00 −0.0693375
\(833\) 0 0
\(834\) 1572.00 0.0652685
\(835\) −8280.00 −0.343163
\(836\) −3360.00 −0.139005
\(837\) −7398.00 −0.305510
\(838\) 4104.00 0.169177
\(839\) 35544.0 1.46259 0.731296 0.682060i \(-0.238916\pi\)
0.731296 + 0.682060i \(0.238916\pi\)
\(840\) 0 0
\(841\) −22625.0 −0.927672
\(842\) 8644.00 0.353791
\(843\) 14574.0 0.595439
\(844\) 20144.0 0.821546
\(845\) 7605.00 0.309609
\(846\) 5904.00 0.239933
\(847\) 0 0
\(848\) −2368.00 −0.0958932
\(849\) 27600.0 1.11570
\(850\) 1300.00 0.0524584
\(851\) −388.000 −0.0156292
\(852\) −8208.00 −0.330049
\(853\) 39490.0 1.58513 0.792563 0.609791i \(-0.208746\pi\)
0.792563 + 0.609791i \(0.208746\pi\)
\(854\) 0 0
\(855\) −1890.00 −0.0755984
\(856\) −15600.0 −0.622894
\(857\) −39990.0 −1.59397 −0.796985 0.603999i \(-0.793573\pi\)
−0.796985 + 0.603999i \(0.793573\pi\)
\(858\) 3120.00 0.124143
\(859\) −6098.00 −0.242213 −0.121107 0.992640i \(-0.538644\pi\)
−0.121107 + 0.992640i \(0.538644\pi\)
\(860\) 5920.00 0.234733
\(861\) 0 0
\(862\) 7320.00 0.289235
\(863\) 13614.0 0.536994 0.268497 0.963280i \(-0.413473\pi\)
0.268497 + 0.963280i \(0.413473\pi\)
\(864\) 864.000 0.0340207
\(865\) 10770.0 0.423342
\(866\) 1364.00 0.0535226
\(867\) −12711.0 −0.497910
\(868\) 0 0
\(869\) 11680.0 0.455946
\(870\) 1260.00 0.0491012
\(871\) −208.000 −0.00809163
\(872\) −1744.00 −0.0677285
\(873\) 6102.00 0.236565
\(874\) −16296.0 −0.630687
\(875\) 0 0
\(876\) −3720.00 −0.143478
\(877\) 32994.0 1.27039 0.635193 0.772354i \(-0.280921\pi\)
0.635193 + 0.772354i \(0.280921\pi\)
\(878\) 1828.00 0.0702643
\(879\) 18486.0 0.709348
\(880\) 1600.00 0.0612909
\(881\) −9202.00 −0.351899 −0.175950 0.984399i \(-0.556300\pi\)
−0.175950 + 0.984399i \(0.556300\pi\)
\(882\) 0 0
\(883\) −41420.0 −1.57859 −0.789294 0.614015i \(-0.789553\pi\)
−0.789294 + 0.614015i \(0.789553\pi\)
\(884\) −2704.00 −0.102879
\(885\) 7320.00 0.278033
\(886\) −13916.0 −0.527672
\(887\) 2320.00 0.0878218 0.0439109 0.999035i \(-0.486018\pi\)
0.0439109 + 0.999035i \(0.486018\pi\)
\(888\) 48.0000 0.00181394
\(889\) 0 0
\(890\) −2660.00 −0.100184
\(891\) −1620.00 −0.0609114
\(892\) 14960.0 0.561545
\(893\) 13776.0 0.516233
\(894\) −12540.0 −0.469128
\(895\) −5560.00 −0.207654
\(896\) 0 0
\(897\) 15132.0 0.563258
\(898\) 10932.0 0.406242
\(899\) 11508.0 0.426934
\(900\) 900.000 0.0333333
\(901\) −3848.00 −0.142281
\(902\) −10000.0 −0.369139
\(903\) 0 0
\(904\) 14560.0 0.535684
\(905\) 2560.00 0.0940301
\(906\) −15120.0 −0.554446
\(907\) −46244.0 −1.69295 −0.846476 0.532427i \(-0.821280\pi\)
−0.846476 + 0.532427i \(0.821280\pi\)
\(908\) −10608.0 −0.387708
\(909\) 3654.00 0.133328
\(910\) 0 0
\(911\) 3992.00 0.145182 0.0725910 0.997362i \(-0.476873\pi\)
0.0725910 + 0.997362i \(0.476873\pi\)
\(912\) 2016.00 0.0731978
\(913\) 8080.00 0.292890
\(914\) −27972.0 −1.01229
\(915\) 4080.00 0.147411
\(916\) 80.0000 0.00288567
\(917\) 0 0
\(918\) 1404.00 0.0504781
\(919\) −31864.0 −1.14374 −0.571870 0.820345i \(-0.693782\pi\)
−0.571870 + 0.820345i \(0.693782\pi\)
\(920\) 7760.00 0.278087
\(921\) 11868.0 0.424608
\(922\) −23892.0 −0.853407
\(923\) 17784.0 0.634201
\(924\) 0 0
\(925\) 50.0000 0.00177729
\(926\) −14416.0 −0.511597
\(927\) −2628.00 −0.0931120
\(928\) −1344.00 −0.0475420
\(929\) 24762.0 0.874505 0.437252 0.899339i \(-0.355952\pi\)
0.437252 + 0.899339i \(0.355952\pi\)
\(930\) 8220.00 0.289833
\(931\) 0 0
\(932\) −5152.00 −0.181072
\(933\) −27204.0 −0.954576
\(934\) −7976.00 −0.279425
\(935\) 2600.00 0.0909402
\(936\) −1872.00 −0.0653720
\(937\) 5334.00 0.185970 0.0929852 0.995667i \(-0.470359\pi\)
0.0929852 + 0.995667i \(0.470359\pi\)
\(938\) 0 0
\(939\) −21954.0 −0.762984
\(940\) −6560.00 −0.227621
\(941\) −16894.0 −0.585259 −0.292629 0.956226i \(-0.594530\pi\)
−0.292629 + 0.956226i \(0.594530\pi\)
\(942\) −5196.00 −0.179719
\(943\) −48500.0 −1.67484
\(944\) −7808.00 −0.269204
\(945\) 0 0
\(946\) 11840.0 0.406926
\(947\) −21378.0 −0.733571 −0.366785 0.930306i \(-0.619542\pi\)
−0.366785 + 0.930306i \(0.619542\pi\)
\(948\) −7008.00 −0.240094
\(949\) 8060.00 0.275699
\(950\) 2100.00 0.0717189
\(951\) −12564.0 −0.428408
\(952\) 0 0
\(953\) 29188.0 0.992122 0.496061 0.868288i \(-0.334779\pi\)
0.496061 + 0.868288i \(0.334779\pi\)
\(954\) −2664.00 −0.0904090
\(955\) 5040.00 0.170775
\(956\) 14528.0 0.491495
\(957\) 2520.00 0.0851202
\(958\) −15592.0 −0.525840
\(959\) 0 0
\(960\) −960.000 −0.0322749
\(961\) 45285.0 1.52009
\(962\) −104.000 −0.00348555
\(963\) −17550.0 −0.587270
\(964\) 8864.00 0.296152
\(965\) −8250.00 −0.275209
\(966\) 0 0
\(967\) 49676.0 1.65199 0.825994 0.563679i \(-0.190614\pi\)
0.825994 + 0.563679i \(0.190614\pi\)
\(968\) −7448.00 −0.247301
\(969\) 3276.00 0.108607
\(970\) −6780.00 −0.224425
\(971\) 49660.0 1.64126 0.820631 0.571459i \(-0.193622\pi\)
0.820631 + 0.571459i \(0.193622\pi\)
\(972\) 972.000 0.0320750
\(973\) 0 0
\(974\) 32648.0 1.07403
\(975\) −1950.00 −0.0640513
\(976\) −4352.00 −0.142730
\(977\) −15408.0 −0.504550 −0.252275 0.967656i \(-0.581179\pi\)
−0.252275 + 0.967656i \(0.581179\pi\)
\(978\) −20616.0 −0.674056
\(979\) −5320.00 −0.173675
\(980\) 0 0
\(981\) −1962.00 −0.0638551
\(982\) 35712.0 1.16050
\(983\) 37784.0 1.22596 0.612982 0.790097i \(-0.289970\pi\)
0.612982 + 0.790097i \(0.289970\pi\)
\(984\) 6000.00 0.194383
\(985\) −1560.00 −0.0504627
\(986\) −2184.00 −0.0705403
\(987\) 0 0
\(988\) −4368.00 −0.140652
\(989\) 57424.0 1.84629
\(990\) 1800.00 0.0577856
\(991\) −23784.0 −0.762385 −0.381193 0.924496i \(-0.624487\pi\)
−0.381193 + 0.924496i \(0.624487\pi\)
\(992\) −8768.00 −0.280629
\(993\) −9516.00 −0.304110
\(994\) 0 0
\(995\) −8530.00 −0.271778
\(996\) −4848.00 −0.154232
\(997\) −49998.0 −1.58822 −0.794109 0.607776i \(-0.792062\pi\)
−0.794109 + 0.607776i \(0.792062\pi\)
\(998\) 6824.00 0.216443
\(999\) 54.0000 0.00171019
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 1470.4.a.w.1.1 yes 1
7.6 odd 2 1470.4.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.4.a.s.1.1 1 7.6 odd 2
1470.4.a.w.1.1 yes 1 1.1 even 1 trivial