Properties

Label 525.4.a.f.1.1
Level $525$
Weight $4$
Character 525.1
Self dual yes
Analytic conductor $30.976$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(30.9760027530\)
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 \(\chi\) \(=\) 525.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} -24.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} -24.0000 q^{8} +9.00000 q^{9} -21.0000 q^{11} +12.0000 q^{12} -24.0000 q^{13} +14.0000 q^{14} -16.0000 q^{16} +22.0000 q^{17} +18.0000 q^{18} +16.0000 q^{19} -21.0000 q^{21} -42.0000 q^{22} +25.0000 q^{23} +72.0000 q^{24} -48.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} +167.000 q^{29} +10.0000 q^{31} +160.000 q^{32} +63.0000 q^{33} +44.0000 q^{34} -36.0000 q^{36} +133.000 q^{37} +32.0000 q^{38} +72.0000 q^{39} -168.000 q^{41} -42.0000 q^{42} +97.0000 q^{43} +84.0000 q^{44} +50.0000 q^{46} +400.000 q^{47} +48.0000 q^{48} +49.0000 q^{49} -66.0000 q^{51} +96.0000 q^{52} +182.000 q^{53} -54.0000 q^{54} -168.000 q^{56} -48.0000 q^{57} +334.000 q^{58} +488.000 q^{59} +28.0000 q^{61} +20.0000 q^{62} +63.0000 q^{63} +448.000 q^{64} +126.000 q^{66} +967.000 q^{67} -88.0000 q^{68} -75.0000 q^{69} -285.000 q^{71} -216.000 q^{72} +838.000 q^{73} +266.000 q^{74} -64.0000 q^{76} -147.000 q^{77} +144.000 q^{78} -469.000 q^{79} +81.0000 q^{81} -336.000 q^{82} +406.000 q^{83} +84.0000 q^{84} +194.000 q^{86} -501.000 q^{87} +504.000 q^{88} +324.000 q^{89} -168.000 q^{91} -100.000 q^{92} -30.0000 q^{93} +800.000 q^{94} -480.000 q^{96} +114.000 q^{97} +98.0000 q^{98} -189.000 q^{99} +O(q^{100})\)

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 \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) −3.00000 −0.577350
\(4\) −4.00000 −0.500000
\(5\) 0 0
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) −24.0000 −1.06066
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −21.0000 −0.575613 −0.287806 0.957689i \(-0.592926\pi\)
−0.287806 + 0.957689i \(0.592926\pi\)
\(12\) 12.0000 0.288675
\(13\) −24.0000 −0.512031 −0.256015 0.966673i \(-0.582410\pi\)
−0.256015 + 0.966673i \(0.582410\pi\)
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) −16.0000 −0.250000
\(17\) 22.0000 0.313870 0.156935 0.987609i \(-0.449839\pi\)
0.156935 + 0.987609i \(0.449839\pi\)
\(18\) 18.0000 0.235702
\(19\) 16.0000 0.193192 0.0965961 0.995324i \(-0.469204\pi\)
0.0965961 + 0.995324i \(0.469204\pi\)
\(20\) 0 0
\(21\) −21.0000 −0.218218
\(22\) −42.0000 −0.407020
\(23\) 25.0000 0.226646 0.113323 0.993558i \(-0.463850\pi\)
0.113323 + 0.993558i \(0.463850\pi\)
\(24\) 72.0000 0.612372
\(25\) 0 0
\(26\) −48.0000 −0.362061
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) 167.000 1.06935 0.534675 0.845058i \(-0.320434\pi\)
0.534675 + 0.845058i \(0.320434\pi\)
\(30\) 0 0
\(31\) 10.0000 0.0579372 0.0289686 0.999580i \(-0.490778\pi\)
0.0289686 + 0.999580i \(0.490778\pi\)
\(32\) 160.000 0.883883
\(33\) 63.0000 0.332330
\(34\) 44.0000 0.221939
\(35\) 0 0
\(36\) −36.0000 −0.166667
\(37\) 133.000 0.590948 0.295474 0.955351i \(-0.404522\pi\)
0.295474 + 0.955351i \(0.404522\pi\)
\(38\) 32.0000 0.136608
\(39\) 72.0000 0.295621
\(40\) 0 0
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) −42.0000 −0.154303
\(43\) 97.0000 0.344008 0.172004 0.985096i \(-0.444976\pi\)
0.172004 + 0.985096i \(0.444976\pi\)
\(44\) 84.0000 0.287806
\(45\) 0 0
\(46\) 50.0000 0.160263
\(47\) 400.000 1.24140 0.620702 0.784046i \(-0.286848\pi\)
0.620702 + 0.784046i \(0.286848\pi\)
\(48\) 48.0000 0.144338
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) −66.0000 −0.181213
\(52\) 96.0000 0.256015
\(53\) 182.000 0.471691 0.235845 0.971791i \(-0.424214\pi\)
0.235845 + 0.971791i \(0.424214\pi\)
\(54\) −54.0000 −0.136083
\(55\) 0 0
\(56\) −168.000 −0.400892
\(57\) −48.0000 −0.111540
\(58\) 334.000 0.756144
\(59\) 488.000 1.07682 0.538408 0.842684i \(-0.319026\pi\)
0.538408 + 0.842684i \(0.319026\pi\)
\(60\) 0 0
\(61\) 28.0000 0.0587710 0.0293855 0.999568i \(-0.490645\pi\)
0.0293855 + 0.999568i \(0.490645\pi\)
\(62\) 20.0000 0.0409678
\(63\) 63.0000 0.125988
\(64\) 448.000 0.875000
\(65\) 0 0
\(66\) 126.000 0.234993
\(67\) 967.000 1.76325 0.881626 0.471949i \(-0.156449\pi\)
0.881626 + 0.471949i \(0.156449\pi\)
\(68\) −88.0000 −0.156935
\(69\) −75.0000 −0.130854
\(70\) 0 0
\(71\) −285.000 −0.476384 −0.238192 0.971218i \(-0.576555\pi\)
−0.238192 + 0.971218i \(0.576555\pi\)
\(72\) −216.000 −0.353553
\(73\) 838.000 1.34357 0.671784 0.740747i \(-0.265528\pi\)
0.671784 + 0.740747i \(0.265528\pi\)
\(74\) 266.000 0.417863
\(75\) 0 0
\(76\) −64.0000 −0.0965961
\(77\) −147.000 −0.217561
\(78\) 144.000 0.209036
\(79\) −469.000 −0.667932 −0.333966 0.942585i \(-0.608387\pi\)
−0.333966 + 0.942585i \(0.608387\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) −336.000 −0.452500
\(83\) 406.000 0.536919 0.268460 0.963291i \(-0.413485\pi\)
0.268460 + 0.963291i \(0.413485\pi\)
\(84\) 84.0000 0.109109
\(85\) 0 0
\(86\) 194.000 0.243251
\(87\) −501.000 −0.617389
\(88\) 504.000 0.610529
\(89\) 324.000 0.385887 0.192943 0.981210i \(-0.438197\pi\)
0.192943 + 0.981210i \(0.438197\pi\)
\(90\) 0 0
\(91\) −168.000 −0.193530
\(92\) −100.000 −0.113323
\(93\) −30.0000 −0.0334501
\(94\) 800.000 0.877805
\(95\) 0 0
\(96\) −480.000 −0.510310
\(97\) 114.000 0.119329 0.0596647 0.998218i \(-0.480997\pi\)
0.0596647 + 0.998218i \(0.480997\pi\)
\(98\) 98.0000 0.101015
\(99\) −189.000 −0.191871
\(100\) 0 0
\(101\) 34.0000 0.0334963 0.0167482 0.999860i \(-0.494669\pi\)
0.0167482 + 0.999860i \(0.494669\pi\)
\(102\) −132.000 −0.128137
\(103\) 1976.00 1.89030 0.945151 0.326634i \(-0.105915\pi\)
0.945151 + 0.326634i \(0.105915\pi\)
\(104\) 576.000 0.543091
\(105\) 0 0
\(106\) 364.000 0.333536
\(107\) −828.000 −0.748091 −0.374046 0.927410i \(-0.622030\pi\)
−0.374046 + 0.927410i \(0.622030\pi\)
\(108\) 108.000 0.0962250
\(109\) −1467.00 −1.28911 −0.644556 0.764557i \(-0.722958\pi\)
−0.644556 + 0.764557i \(0.722958\pi\)
\(110\) 0 0
\(111\) −399.000 −0.341184
\(112\) −112.000 −0.0944911
\(113\) −783.000 −0.651845 −0.325922 0.945397i \(-0.605675\pi\)
−0.325922 + 0.945397i \(0.605675\pi\)
\(114\) −96.0000 −0.0788704
\(115\) 0 0
\(116\) −668.000 −0.534675
\(117\) −216.000 −0.170677
\(118\) 976.000 0.761424
\(119\) 154.000 0.118632
\(120\) 0 0
\(121\) −890.000 −0.668670
\(122\) 56.0000 0.0415574
\(123\) 504.000 0.369465
\(124\) −40.0000 −0.0289686
\(125\) 0 0
\(126\) 126.000 0.0890871
\(127\) 515.000 0.359834 0.179917 0.983682i \(-0.442417\pi\)
0.179917 + 0.983682i \(0.442417\pi\)
\(128\) −384.000 −0.265165
\(129\) −291.000 −0.198613
\(130\) 0 0
\(131\) −1526.00 −1.01777 −0.508883 0.860836i \(-0.669941\pi\)
−0.508883 + 0.860836i \(0.669941\pi\)
\(132\) −252.000 −0.166165
\(133\) 112.000 0.0730198
\(134\) 1934.00 1.24681
\(135\) 0 0
\(136\) −528.000 −0.332909
\(137\) 1822.00 1.13623 0.568117 0.822948i \(-0.307672\pi\)
0.568117 + 0.822948i \(0.307672\pi\)
\(138\) −150.000 −0.0925279
\(139\) −3042.00 −1.85625 −0.928126 0.372266i \(-0.878581\pi\)
−0.928126 + 0.372266i \(0.878581\pi\)
\(140\) 0 0
\(141\) −1200.00 −0.716725
\(142\) −570.000 −0.336854
\(143\) 504.000 0.294731
\(144\) −144.000 −0.0833333
\(145\) 0 0
\(146\) 1676.00 0.950046
\(147\) −147.000 −0.0824786
\(148\) −532.000 −0.295474
\(149\) 349.000 0.191887 0.0959436 0.995387i \(-0.469413\pi\)
0.0959436 + 0.995387i \(0.469413\pi\)
\(150\) 0 0
\(151\) −2167.00 −1.16787 −0.583934 0.811801i \(-0.698487\pi\)
−0.583934 + 0.811801i \(0.698487\pi\)
\(152\) −384.000 −0.204911
\(153\) 198.000 0.104623
\(154\) −294.000 −0.153839
\(155\) 0 0
\(156\) −288.000 −0.147811
\(157\) 1204.00 0.612036 0.306018 0.952026i \(-0.401003\pi\)
0.306018 + 0.952026i \(0.401003\pi\)
\(158\) −938.000 −0.472299
\(159\) −546.000 −0.272331
\(160\) 0 0
\(161\) 175.000 0.0856642
\(162\) 162.000 0.0785674
\(163\) −3252.00 −1.56268 −0.781338 0.624108i \(-0.785463\pi\)
−0.781338 + 0.624108i \(0.785463\pi\)
\(164\) 672.000 0.319966
\(165\) 0 0
\(166\) 812.000 0.379659
\(167\) 1276.00 0.591257 0.295628 0.955303i \(-0.404471\pi\)
0.295628 + 0.955303i \(0.404471\pi\)
\(168\) 504.000 0.231455
\(169\) −1621.00 −0.737824
\(170\) 0 0
\(171\) 144.000 0.0643974
\(172\) −388.000 −0.172004
\(173\) −1140.00 −0.500998 −0.250499 0.968117i \(-0.580595\pi\)
−0.250499 + 0.968117i \(0.580595\pi\)
\(174\) −1002.00 −0.436560
\(175\) 0 0
\(176\) 336.000 0.143903
\(177\) −1464.00 −0.621700
\(178\) 648.000 0.272863
\(179\) 2724.00 1.13744 0.568719 0.822532i \(-0.307439\pi\)
0.568719 + 0.822532i \(0.307439\pi\)
\(180\) 0 0
\(181\) 4474.00 1.83729 0.918646 0.395082i \(-0.129284\pi\)
0.918646 + 0.395082i \(0.129284\pi\)
\(182\) −336.000 −0.136846
\(183\) −84.0000 −0.0339315
\(184\) −600.000 −0.240394
\(185\) 0 0
\(186\) −60.0000 −0.0236528
\(187\) −462.000 −0.180667
\(188\) −1600.00 −0.620702
\(189\) −189.000 −0.0727393
\(190\) 0 0
\(191\) 3932.00 1.48958 0.744789 0.667300i \(-0.232550\pi\)
0.744789 + 0.667300i \(0.232550\pi\)
\(192\) −1344.00 −0.505181
\(193\) −3441.00 −1.28336 −0.641680 0.766972i \(-0.721762\pi\)
−0.641680 + 0.766972i \(0.721762\pi\)
\(194\) 228.000 0.0843786
\(195\) 0 0
\(196\) −196.000 −0.0714286
\(197\) 201.000 0.0726937 0.0363468 0.999339i \(-0.488428\pi\)
0.0363468 + 0.999339i \(0.488428\pi\)
\(198\) −378.000 −0.135673
\(199\) −1384.00 −0.493011 −0.246505 0.969141i \(-0.579282\pi\)
−0.246505 + 0.969141i \(0.579282\pi\)
\(200\) 0 0
\(201\) −2901.00 −1.01801
\(202\) 68.0000 0.0236855
\(203\) 1169.00 0.404176
\(204\) 264.000 0.0906064
\(205\) 0 0
\(206\) 3952.00 1.33665
\(207\) 225.000 0.0755487
\(208\) 384.000 0.128008
\(209\) −336.000 −0.111204
\(210\) 0 0
\(211\) 3964.00 1.29333 0.646666 0.762773i \(-0.276163\pi\)
0.646666 + 0.762773i \(0.276163\pi\)
\(212\) −728.000 −0.235845
\(213\) 855.000 0.275041
\(214\) −1656.00 −0.528981
\(215\) 0 0
\(216\) 648.000 0.204124
\(217\) 70.0000 0.0218982
\(218\) −2934.00 −0.911539
\(219\) −2514.00 −0.775709
\(220\) 0 0
\(221\) −528.000 −0.160711
\(222\) −798.000 −0.241253
\(223\) 762.000 0.228822 0.114411 0.993434i \(-0.463502\pi\)
0.114411 + 0.993434i \(0.463502\pi\)
\(224\) 1120.00 0.334077
\(225\) 0 0
\(226\) −1566.00 −0.460924
\(227\) 5764.00 1.68533 0.842665 0.538437i \(-0.180985\pi\)
0.842665 + 0.538437i \(0.180985\pi\)
\(228\) 192.000 0.0557698
\(229\) 1510.00 0.435736 0.217868 0.975978i \(-0.430090\pi\)
0.217868 + 0.975978i \(0.430090\pi\)
\(230\) 0 0
\(231\) 441.000 0.125609
\(232\) −4008.00 −1.13422
\(233\) −5937.00 −1.66930 −0.834648 0.550784i \(-0.814329\pi\)
−0.834648 + 0.550784i \(0.814329\pi\)
\(234\) −432.000 −0.120687
\(235\) 0 0
\(236\) −1952.00 −0.538408
\(237\) 1407.00 0.385631
\(238\) 308.000 0.0838852
\(239\) 1456.00 0.394062 0.197031 0.980397i \(-0.436870\pi\)
0.197031 + 0.980397i \(0.436870\pi\)
\(240\) 0 0
\(241\) −588.000 −0.157164 −0.0785818 0.996908i \(-0.525039\pi\)
−0.0785818 + 0.996908i \(0.525039\pi\)
\(242\) −1780.00 −0.472821
\(243\) −243.000 −0.0641500
\(244\) −112.000 −0.0293855
\(245\) 0 0
\(246\) 1008.00 0.261251
\(247\) −384.000 −0.0989204
\(248\) −240.000 −0.0614517
\(249\) −1218.00 −0.309990
\(250\) 0 0
\(251\) 6510.00 1.63708 0.818541 0.574448i \(-0.194783\pi\)
0.818541 + 0.574448i \(0.194783\pi\)
\(252\) −252.000 −0.0629941
\(253\) −525.000 −0.130460
\(254\) 1030.00 0.254441
\(255\) 0 0
\(256\) −4352.00 −1.06250
\(257\) 2898.00 0.703394 0.351697 0.936114i \(-0.385605\pi\)
0.351697 + 0.936114i \(0.385605\pi\)
\(258\) −582.000 −0.140441
\(259\) 931.000 0.223357
\(260\) 0 0
\(261\) 1503.00 0.356450
\(262\) −3052.00 −0.719669
\(263\) −2953.00 −0.692357 −0.346178 0.938169i \(-0.612521\pi\)
−0.346178 + 0.938169i \(0.612521\pi\)
\(264\) −1512.00 −0.352489
\(265\) 0 0
\(266\) 224.000 0.0516328
\(267\) −972.000 −0.222792
\(268\) −3868.00 −0.881626
\(269\) 3394.00 0.769278 0.384639 0.923067i \(-0.374326\pi\)
0.384639 + 0.923067i \(0.374326\pi\)
\(270\) 0 0
\(271\) −1284.00 −0.287813 −0.143907 0.989591i \(-0.545967\pi\)
−0.143907 + 0.989591i \(0.545967\pi\)
\(272\) −352.000 −0.0784674
\(273\) 504.000 0.111734
\(274\) 3644.00 0.803438
\(275\) 0 0
\(276\) 300.000 0.0654271
\(277\) 3506.00 0.760488 0.380244 0.924886i \(-0.375840\pi\)
0.380244 + 0.924886i \(0.375840\pi\)
\(278\) −6084.00 −1.31257
\(279\) 90.0000 0.0193124
\(280\) 0 0
\(281\) 5823.00 1.23620 0.618098 0.786101i \(-0.287903\pi\)
0.618098 + 0.786101i \(0.287903\pi\)
\(282\) −2400.00 −0.506801
\(283\) 3830.00 0.804487 0.402244 0.915533i \(-0.368230\pi\)
0.402244 + 0.915533i \(0.368230\pi\)
\(284\) 1140.00 0.238192
\(285\) 0 0
\(286\) 1008.00 0.208407
\(287\) −1176.00 −0.241871
\(288\) 1440.00 0.294628
\(289\) −4429.00 −0.901486
\(290\) 0 0
\(291\) −342.000 −0.0688948
\(292\) −3352.00 −0.671784
\(293\) −3572.00 −0.712213 −0.356107 0.934445i \(-0.615896\pi\)
−0.356107 + 0.934445i \(0.615896\pi\)
\(294\) −294.000 −0.0583212
\(295\) 0 0
\(296\) −3192.00 −0.626795
\(297\) 567.000 0.110777
\(298\) 698.000 0.135685
\(299\) −600.000 −0.116050
\(300\) 0 0
\(301\) 679.000 0.130023
\(302\) −4334.00 −0.825807
\(303\) −102.000 −0.0193391
\(304\) −256.000 −0.0482980
\(305\) 0 0
\(306\) 396.000 0.0739798
\(307\) −7278.00 −1.35302 −0.676510 0.736433i \(-0.736509\pi\)
−0.676510 + 0.736433i \(0.736509\pi\)
\(308\) 588.000 0.108781
\(309\) −5928.00 −1.09137
\(310\) 0 0
\(311\) 3786.00 0.690303 0.345152 0.938547i \(-0.387827\pi\)
0.345152 + 0.938547i \(0.387827\pi\)
\(312\) −1728.00 −0.313554
\(313\) −448.000 −0.0809024 −0.0404512 0.999182i \(-0.512880\pi\)
−0.0404512 + 0.999182i \(0.512880\pi\)
\(314\) 2408.00 0.432775
\(315\) 0 0
\(316\) 1876.00 0.333966
\(317\) 4081.00 0.723066 0.361533 0.932359i \(-0.382254\pi\)
0.361533 + 0.932359i \(0.382254\pi\)
\(318\) −1092.00 −0.192567
\(319\) −3507.00 −0.615531
\(320\) 0 0
\(321\) 2484.00 0.431911
\(322\) 350.000 0.0605737
\(323\) 352.000 0.0606372
\(324\) −324.000 −0.0555556
\(325\) 0 0
\(326\) −6504.00 −1.10498
\(327\) 4401.00 0.744269
\(328\) 4032.00 0.678750
\(329\) 2800.00 0.469207
\(330\) 0 0
\(331\) 1071.00 0.177847 0.0889237 0.996038i \(-0.471657\pi\)
0.0889237 + 0.996038i \(0.471657\pi\)
\(332\) −1624.00 −0.268460
\(333\) 1197.00 0.196983
\(334\) 2552.00 0.418082
\(335\) 0 0
\(336\) 336.000 0.0545545
\(337\) −2102.00 −0.339772 −0.169886 0.985464i \(-0.554340\pi\)
−0.169886 + 0.985464i \(0.554340\pi\)
\(338\) −3242.00 −0.521721
\(339\) 2349.00 0.376343
\(340\) 0 0
\(341\) −210.000 −0.0333494
\(342\) 288.000 0.0455358
\(343\) 343.000 0.0539949
\(344\) −2328.00 −0.364876
\(345\) 0 0
\(346\) −2280.00 −0.354259
\(347\) 11471.0 1.77463 0.887313 0.461167i \(-0.152569\pi\)
0.887313 + 0.461167i \(0.152569\pi\)
\(348\) 2004.00 0.308694
\(349\) −6448.00 −0.988979 −0.494489 0.869184i \(-0.664645\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(350\) 0 0
\(351\) 648.000 0.0985404
\(352\) −3360.00 −0.508774
\(353\) 10050.0 1.51532 0.757659 0.652650i \(-0.226343\pi\)
0.757659 + 0.652650i \(0.226343\pi\)
\(354\) −2928.00 −0.439609
\(355\) 0 0
\(356\) −1296.00 −0.192943
\(357\) −462.000 −0.0684920
\(358\) 5448.00 0.804290
\(359\) −6597.00 −0.969851 −0.484925 0.874556i \(-0.661153\pi\)
−0.484925 + 0.874556i \(0.661153\pi\)
\(360\) 0 0
\(361\) −6603.00 −0.962677
\(362\) 8948.00 1.29916
\(363\) 2670.00 0.386057
\(364\) 672.000 0.0967648
\(365\) 0 0
\(366\) −168.000 −0.0239932
\(367\) −6500.00 −0.924516 −0.462258 0.886746i \(-0.652961\pi\)
−0.462258 + 0.886746i \(0.652961\pi\)
\(368\) −400.000 −0.0566615
\(369\) −1512.00 −0.213311
\(370\) 0 0
\(371\) 1274.00 0.178282
\(372\) 120.000 0.0167250
\(373\) −8665.00 −1.20283 −0.601416 0.798936i \(-0.705397\pi\)
−0.601416 + 0.798936i \(0.705397\pi\)
\(374\) −924.000 −0.127751
\(375\) 0 0
\(376\) −9600.00 −1.31671
\(377\) −4008.00 −0.547540
\(378\) −378.000 −0.0514344
\(379\) −217.000 −0.0294104 −0.0147052 0.999892i \(-0.504681\pi\)
−0.0147052 + 0.999892i \(0.504681\pi\)
\(380\) 0 0
\(381\) −1545.00 −0.207750
\(382\) 7864.00 1.05329
\(383\) 4640.00 0.619042 0.309521 0.950893i \(-0.399831\pi\)
0.309521 + 0.950893i \(0.399831\pi\)
\(384\) 1152.00 0.153093
\(385\) 0 0
\(386\) −6882.00 −0.907473
\(387\) 873.000 0.114669
\(388\) −456.000 −0.0596647
\(389\) −3021.00 −0.393755 −0.196878 0.980428i \(-0.563080\pi\)
−0.196878 + 0.980428i \(0.563080\pi\)
\(390\) 0 0
\(391\) 550.000 0.0711373
\(392\) −1176.00 −0.151523
\(393\) 4578.00 0.587607
\(394\) 402.000 0.0514022
\(395\) 0 0
\(396\) 756.000 0.0959354
\(397\) 7826.00 0.989359 0.494680 0.869075i \(-0.335285\pi\)
0.494680 + 0.869075i \(0.335285\pi\)
\(398\) −2768.00 −0.348611
\(399\) −336.000 −0.0421580
\(400\) 0 0
\(401\) −3405.00 −0.424034 −0.212017 0.977266i \(-0.568003\pi\)
−0.212017 + 0.977266i \(0.568003\pi\)
\(402\) −5802.00 −0.719844
\(403\) −240.000 −0.0296656
\(404\) −136.000 −0.0167482
\(405\) 0 0
\(406\) 2338.00 0.285796
\(407\) −2793.00 −0.340157
\(408\) 1584.00 0.192205
\(409\) 4052.00 0.489874 0.244937 0.969539i \(-0.421233\pi\)
0.244937 + 0.969539i \(0.421233\pi\)
\(410\) 0 0
\(411\) −5466.00 −0.656005
\(412\) −7904.00 −0.945151
\(413\) 3416.00 0.406998
\(414\) 450.000 0.0534210
\(415\) 0 0
\(416\) −3840.00 −0.452576
\(417\) 9126.00 1.07171
\(418\) −672.000 −0.0786330
\(419\) 11322.0 1.32009 0.660043 0.751228i \(-0.270538\pi\)
0.660043 + 0.751228i \(0.270538\pi\)
\(420\) 0 0
\(421\) −1757.00 −0.203399 −0.101699 0.994815i \(-0.532428\pi\)
−0.101699 + 0.994815i \(0.532428\pi\)
\(422\) 7928.00 0.914524
\(423\) 3600.00 0.413801
\(424\) −4368.00 −0.500304
\(425\) 0 0
\(426\) 1710.00 0.194483
\(427\) 196.000 0.0222134
\(428\) 3312.00 0.374046
\(429\) −1512.00 −0.170163
\(430\) 0 0
\(431\) −9304.00 −1.03981 −0.519905 0.854224i \(-0.674033\pi\)
−0.519905 + 0.854224i \(0.674033\pi\)
\(432\) 432.000 0.0481125
\(433\) 5752.00 0.638391 0.319196 0.947689i \(-0.396587\pi\)
0.319196 + 0.947689i \(0.396587\pi\)
\(434\) 140.000 0.0154844
\(435\) 0 0
\(436\) 5868.00 0.644556
\(437\) 400.000 0.0437863
\(438\) −5028.00 −0.548509
\(439\) 2344.00 0.254836 0.127418 0.991849i \(-0.459331\pi\)
0.127418 + 0.991849i \(0.459331\pi\)
\(440\) 0 0
\(441\) 441.000 0.0476190
\(442\) −1056.00 −0.113640
\(443\) 15132.0 1.62290 0.811448 0.584424i \(-0.198680\pi\)
0.811448 + 0.584424i \(0.198680\pi\)
\(444\) 1596.00 0.170592
\(445\) 0 0
\(446\) 1524.00 0.161802
\(447\) −1047.00 −0.110786
\(448\) 3136.00 0.330719
\(449\) −5055.00 −0.531314 −0.265657 0.964068i \(-0.585589\pi\)
−0.265657 + 0.964068i \(0.585589\pi\)
\(450\) 0 0
\(451\) 3528.00 0.368353
\(452\) 3132.00 0.325922
\(453\) 6501.00 0.674268
\(454\) 11528.0 1.19171
\(455\) 0 0
\(456\) 1152.00 0.118306
\(457\) 3795.00 0.388452 0.194226 0.980957i \(-0.437780\pi\)
0.194226 + 0.980957i \(0.437780\pi\)
\(458\) 3020.00 0.308112
\(459\) −594.000 −0.0604042
\(460\) 0 0
\(461\) 8300.00 0.838546 0.419273 0.907860i \(-0.362285\pi\)
0.419273 + 0.907860i \(0.362285\pi\)
\(462\) 882.000 0.0888189
\(463\) 5052.00 0.507098 0.253549 0.967323i \(-0.418402\pi\)
0.253549 + 0.967323i \(0.418402\pi\)
\(464\) −2672.00 −0.267337
\(465\) 0 0
\(466\) −11874.0 −1.18037
\(467\) −2482.00 −0.245938 −0.122969 0.992410i \(-0.539242\pi\)
−0.122969 + 0.992410i \(0.539242\pi\)
\(468\) 864.000 0.0853385
\(469\) 6769.00 0.666446
\(470\) 0 0
\(471\) −3612.00 −0.353359
\(472\) −11712.0 −1.14214
\(473\) −2037.00 −0.198016
\(474\) 2814.00 0.272682
\(475\) 0 0
\(476\) −616.000 −0.0593158
\(477\) 1638.00 0.157230
\(478\) 2912.00 0.278644
\(479\) 14176.0 1.35223 0.676115 0.736796i \(-0.263662\pi\)
0.676115 + 0.736796i \(0.263662\pi\)
\(480\) 0 0
\(481\) −3192.00 −0.302584
\(482\) −1176.00 −0.111131
\(483\) −525.000 −0.0494582
\(484\) 3560.00 0.334335
\(485\) 0 0
\(486\) −486.000 −0.0453609
\(487\) −1039.00 −0.0966768 −0.0483384 0.998831i \(-0.515393\pi\)
−0.0483384 + 0.998831i \(0.515393\pi\)
\(488\) −672.000 −0.0623361
\(489\) 9756.00 0.902212
\(490\) 0 0
\(491\) 9255.00 0.850656 0.425328 0.905039i \(-0.360159\pi\)
0.425328 + 0.905039i \(0.360159\pi\)
\(492\) −2016.00 −0.184732
\(493\) 3674.00 0.335636
\(494\) −768.000 −0.0699473
\(495\) 0 0
\(496\) −160.000 −0.0144843
\(497\) −1995.00 −0.180056
\(498\) −2436.00 −0.219196
\(499\) 14396.0 1.29149 0.645745 0.763553i \(-0.276547\pi\)
0.645745 + 0.763553i \(0.276547\pi\)
\(500\) 0 0
\(501\) −3828.00 −0.341362
\(502\) 13020.0 1.15759
\(503\) 6998.00 0.620329 0.310164 0.950683i \(-0.399616\pi\)
0.310164 + 0.950683i \(0.399616\pi\)
\(504\) −1512.00 −0.133631
\(505\) 0 0
\(506\) −1050.00 −0.0922494
\(507\) 4863.00 0.425983
\(508\) −2060.00 −0.179917
\(509\) −6400.00 −0.557318 −0.278659 0.960390i \(-0.589890\pi\)
−0.278659 + 0.960390i \(0.589890\pi\)
\(510\) 0 0
\(511\) 5866.00 0.507821
\(512\) −5632.00 −0.486136
\(513\) −432.000 −0.0371799
\(514\) 5796.00 0.497375
\(515\) 0 0
\(516\) 1164.00 0.0993067
\(517\) −8400.00 −0.714568
\(518\) 1862.00 0.157937
\(519\) 3420.00 0.289251
\(520\) 0 0
\(521\) 15158.0 1.27463 0.637317 0.770602i \(-0.280044\pi\)
0.637317 + 0.770602i \(0.280044\pi\)
\(522\) 3006.00 0.252048
\(523\) −4120.00 −0.344465 −0.172232 0.985056i \(-0.555098\pi\)
−0.172232 + 0.985056i \(0.555098\pi\)
\(524\) 6104.00 0.508883
\(525\) 0 0
\(526\) −5906.00 −0.489570
\(527\) 220.000 0.0181847
\(528\) −1008.00 −0.0830825
\(529\) −11542.0 −0.948632
\(530\) 0 0
\(531\) 4392.00 0.358939
\(532\) −448.000 −0.0365099
\(533\) 4032.00 0.327665
\(534\) −1944.00 −0.157538
\(535\) 0 0
\(536\) −23208.0 −1.87021
\(537\) −8172.00 −0.656700
\(538\) 6788.00 0.543962
\(539\) −1029.00 −0.0822304
\(540\) 0 0
\(541\) 3291.00 0.261536 0.130768 0.991413i \(-0.458256\pi\)
0.130768 + 0.991413i \(0.458256\pi\)
\(542\) −2568.00 −0.203515
\(543\) −13422.0 −1.06076
\(544\) 3520.00 0.277424
\(545\) 0 0
\(546\) 1008.00 0.0790081
\(547\) 20547.0 1.60608 0.803040 0.595924i \(-0.203214\pi\)
0.803040 + 0.595924i \(0.203214\pi\)
\(548\) −7288.00 −0.568117
\(549\) 252.000 0.0195903
\(550\) 0 0
\(551\) 2672.00 0.206590
\(552\) 1800.00 0.138792
\(553\) −3283.00 −0.252455
\(554\) 7012.00 0.537746
\(555\) 0 0
\(556\) 12168.0 0.928126
\(557\) 3169.00 0.241068 0.120534 0.992709i \(-0.461539\pi\)
0.120534 + 0.992709i \(0.461539\pi\)
\(558\) 180.000 0.0136559
\(559\) −2328.00 −0.176143
\(560\) 0 0
\(561\) 1386.00 0.104308
\(562\) 11646.0 0.874123
\(563\) 24878.0 1.86231 0.931157 0.364619i \(-0.118801\pi\)
0.931157 + 0.364619i \(0.118801\pi\)
\(564\) 4800.00 0.358363
\(565\) 0 0
\(566\) 7660.00 0.568858
\(567\) 567.000 0.0419961
\(568\) 6840.00 0.505282
\(569\) −1425.00 −0.104990 −0.0524948 0.998621i \(-0.516717\pi\)
−0.0524948 + 0.998621i \(0.516717\pi\)
\(570\) 0 0
\(571\) −14649.0 −1.07363 −0.536814 0.843701i \(-0.680372\pi\)
−0.536814 + 0.843701i \(0.680372\pi\)
\(572\) −2016.00 −0.147366
\(573\) −11796.0 −0.860009
\(574\) −2352.00 −0.171029
\(575\) 0 0
\(576\) 4032.00 0.291667
\(577\) −2108.00 −0.152092 −0.0760461 0.997104i \(-0.524230\pi\)
−0.0760461 + 0.997104i \(0.524230\pi\)
\(578\) −8858.00 −0.637447
\(579\) 10323.0 0.740949
\(580\) 0 0
\(581\) 2842.00 0.202936
\(582\) −684.000 −0.0487160
\(583\) −3822.00 −0.271511
\(584\) −20112.0 −1.42507
\(585\) 0 0
\(586\) −7144.00 −0.503611
\(587\) −24366.0 −1.71328 −0.856638 0.515919i \(-0.827451\pi\)
−0.856638 + 0.515919i \(0.827451\pi\)
\(588\) 588.000 0.0412393
\(589\) 160.000 0.0111930
\(590\) 0 0
\(591\) −603.000 −0.0419697
\(592\) −2128.00 −0.147737
\(593\) −17892.0 −1.23902 −0.619508 0.784990i \(-0.712668\pi\)
−0.619508 + 0.784990i \(0.712668\pi\)
\(594\) 1134.00 0.0783309
\(595\) 0 0
\(596\) −1396.00 −0.0959436
\(597\) 4152.00 0.284640
\(598\) −1200.00 −0.0820596
\(599\) 8077.00 0.550947 0.275474 0.961309i \(-0.411165\pi\)
0.275474 + 0.961309i \(0.411165\pi\)
\(600\) 0 0
\(601\) −7836.00 −0.531842 −0.265921 0.963995i \(-0.585676\pi\)
−0.265921 + 0.963995i \(0.585676\pi\)
\(602\) 1358.00 0.0919401
\(603\) 8703.00 0.587751
\(604\) 8668.00 0.583934
\(605\) 0 0
\(606\) −204.000 −0.0136748
\(607\) 24092.0 1.61098 0.805489 0.592610i \(-0.201903\pi\)
0.805489 + 0.592610i \(0.201903\pi\)
\(608\) 2560.00 0.170759
\(609\) −3507.00 −0.233351
\(610\) 0 0
\(611\) −9600.00 −0.635637
\(612\) −792.000 −0.0523116
\(613\) −13647.0 −0.899180 −0.449590 0.893235i \(-0.648430\pi\)
−0.449590 + 0.893235i \(0.648430\pi\)
\(614\) −14556.0 −0.956730
\(615\) 0 0
\(616\) 3528.00 0.230758
\(617\) −12813.0 −0.836032 −0.418016 0.908440i \(-0.637274\pi\)
−0.418016 + 0.908440i \(0.637274\pi\)
\(618\) −11856.0 −0.771712
\(619\) −300.000 −0.0194798 −0.00973992 0.999953i \(-0.503100\pi\)
−0.00973992 + 0.999953i \(0.503100\pi\)
\(620\) 0 0
\(621\) −675.000 −0.0436181
\(622\) 7572.00 0.488118
\(623\) 2268.00 0.145852
\(624\) −1152.00 −0.0739053
\(625\) 0 0
\(626\) −896.000 −0.0572066
\(627\) 1008.00 0.0642036
\(628\) −4816.00 −0.306018
\(629\) 2926.00 0.185481
\(630\) 0 0
\(631\) 24615.0 1.55294 0.776472 0.630152i \(-0.217007\pi\)
0.776472 + 0.630152i \(0.217007\pi\)
\(632\) 11256.0 0.708449
\(633\) −11892.0 −0.746705
\(634\) 8162.00 0.511285
\(635\) 0 0
\(636\) 2184.00 0.136165
\(637\) −1176.00 −0.0731473
\(638\) −7014.00 −0.435246
\(639\) −2565.00 −0.158795
\(640\) 0 0
\(641\) −24117.0 −1.48606 −0.743030 0.669258i \(-0.766612\pi\)
−0.743030 + 0.669258i \(0.766612\pi\)
\(642\) 4968.00 0.305407
\(643\) 14020.0 0.859868 0.429934 0.902860i \(-0.358537\pi\)
0.429934 + 0.902860i \(0.358537\pi\)
\(644\) −700.000 −0.0428321
\(645\) 0 0
\(646\) 704.000 0.0428769
\(647\) −2430.00 −0.147656 −0.0738278 0.997271i \(-0.523522\pi\)
−0.0738278 + 0.997271i \(0.523522\pi\)
\(648\) −1944.00 −0.117851
\(649\) −10248.0 −0.619829
\(650\) 0 0
\(651\) −210.000 −0.0126429
\(652\) 13008.0 0.781338
\(653\) 27514.0 1.64886 0.824430 0.565963i \(-0.191496\pi\)
0.824430 + 0.565963i \(0.191496\pi\)
\(654\) 8802.00 0.526277
\(655\) 0 0
\(656\) 2688.00 0.159983
\(657\) 7542.00 0.447856
\(658\) 5600.00 0.331779
\(659\) −20772.0 −1.22786 −0.613932 0.789359i \(-0.710413\pi\)
−0.613932 + 0.789359i \(0.710413\pi\)
\(660\) 0 0
\(661\) 32132.0 1.89076 0.945378 0.325976i \(-0.105693\pi\)
0.945378 + 0.325976i \(0.105693\pi\)
\(662\) 2142.00 0.125757
\(663\) 1584.00 0.0927865
\(664\) −9744.00 −0.569489
\(665\) 0 0
\(666\) 2394.00 0.139288
\(667\) 4175.00 0.242364
\(668\) −5104.00 −0.295628
\(669\) −2286.00 −0.132110
\(670\) 0 0
\(671\) −588.000 −0.0338293
\(672\) −3360.00 −0.192879
\(673\) −23542.0 −1.34841 −0.674203 0.738546i \(-0.735513\pi\)
−0.674203 + 0.738546i \(0.735513\pi\)
\(674\) −4204.00 −0.240255
\(675\) 0 0
\(676\) 6484.00 0.368912
\(677\) −30814.0 −1.74930 −0.874652 0.484752i \(-0.838910\pi\)
−0.874652 + 0.484752i \(0.838910\pi\)
\(678\) 4698.00 0.266114
\(679\) 798.000 0.0451023
\(680\) 0 0
\(681\) −17292.0 −0.973026
\(682\) −420.000 −0.0235816
\(683\) −9009.00 −0.504714 −0.252357 0.967634i \(-0.581206\pi\)
−0.252357 + 0.967634i \(0.581206\pi\)
\(684\) −576.000 −0.0321987
\(685\) 0 0
\(686\) 686.000 0.0381802
\(687\) −4530.00 −0.251572
\(688\) −1552.00 −0.0860021
\(689\) −4368.00 −0.241520
\(690\) 0 0
\(691\) −25860.0 −1.42368 −0.711838 0.702343i \(-0.752137\pi\)
−0.711838 + 0.702343i \(0.752137\pi\)
\(692\) 4560.00 0.250499
\(693\) −1323.00 −0.0725204
\(694\) 22942.0 1.25485
\(695\) 0 0
\(696\) 12024.0 0.654840
\(697\) −3696.00 −0.200855
\(698\) −12896.0 −0.699313
\(699\) 17811.0 0.963768
\(700\) 0 0
\(701\) 24170.0 1.30227 0.651133 0.758964i \(-0.274294\pi\)
0.651133 + 0.758964i \(0.274294\pi\)
\(702\) 1296.00 0.0696786
\(703\) 2128.00 0.114166
\(704\) −9408.00 −0.503661
\(705\) 0 0
\(706\) 20100.0 1.07149
\(707\) 238.000 0.0126604
\(708\) 5856.00 0.310850
\(709\) −8426.00 −0.446326 −0.223163 0.974781i \(-0.571638\pi\)
−0.223163 + 0.974781i \(0.571638\pi\)
\(710\) 0 0
\(711\) −4221.00 −0.222644
\(712\) −7776.00 −0.409295
\(713\) 250.000 0.0131312
\(714\) −924.000 −0.0484311
\(715\) 0 0
\(716\) −10896.0 −0.568719
\(717\) −4368.00 −0.227512
\(718\) −13194.0 −0.685788
\(719\) −30752.0 −1.59507 −0.797536 0.603272i \(-0.793863\pi\)
−0.797536 + 0.603272i \(0.793863\pi\)
\(720\) 0 0
\(721\) 13832.0 0.714467
\(722\) −13206.0 −0.680715
\(723\) 1764.00 0.0907384
\(724\) −17896.0 −0.918646
\(725\) 0 0
\(726\) 5340.00 0.272983
\(727\) −11570.0 −0.590244 −0.295122 0.955460i \(-0.595360\pi\)
−0.295122 + 0.955460i \(0.595360\pi\)
\(728\) 4032.00 0.205269
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 2134.00 0.107974
\(732\) 336.000 0.0169657
\(733\) −32836.0 −1.65460 −0.827302 0.561757i \(-0.810126\pi\)
−0.827302 + 0.561757i \(0.810126\pi\)
\(734\) −13000.0 −0.653731
\(735\) 0 0
\(736\) 4000.00 0.200329
\(737\) −20307.0 −1.01495
\(738\) −3024.00 −0.150833
\(739\) −22351.0 −1.11258 −0.556289 0.830989i \(-0.687775\pi\)
−0.556289 + 0.830989i \(0.687775\pi\)
\(740\) 0 0
\(741\) 1152.00 0.0571117
\(742\) 2548.00 0.126065
\(743\) 21720.0 1.07245 0.536224 0.844075i \(-0.319850\pi\)
0.536224 + 0.844075i \(0.319850\pi\)
\(744\) 720.000 0.0354791
\(745\) 0 0
\(746\) −17330.0 −0.850531
\(747\) 3654.00 0.178973
\(748\) 1848.00 0.0903337
\(749\) −5796.00 −0.282752
\(750\) 0 0
\(751\) −6352.00 −0.308639 −0.154319 0.988021i \(-0.549318\pi\)
−0.154319 + 0.988021i \(0.549318\pi\)
\(752\) −6400.00 −0.310351
\(753\) −19530.0 −0.945170
\(754\) −8016.00 −0.387169
\(755\) 0 0
\(756\) 756.000 0.0363696
\(757\) 7685.00 0.368978 0.184489 0.982835i \(-0.440937\pi\)
0.184489 + 0.982835i \(0.440937\pi\)
\(758\) −434.000 −0.0207963
\(759\) 1575.00 0.0753213
\(760\) 0 0
\(761\) −12.0000 −0.000571616 0 −0.000285808 1.00000i \(-0.500091\pi\)
−0.000285808 1.00000i \(0.500091\pi\)
\(762\) −3090.00 −0.146901
\(763\) −10269.0 −0.487238
\(764\) −15728.0 −0.744789
\(765\) 0 0
\(766\) 9280.00 0.437728
\(767\) −11712.0 −0.551364
\(768\) 13056.0 0.613435
\(769\) −24832.0 −1.16445 −0.582227 0.813026i \(-0.697818\pi\)
−0.582227 + 0.813026i \(0.697818\pi\)
\(770\) 0 0
\(771\) −8694.00 −0.406105
\(772\) 13764.0 0.641680
\(773\) −28242.0 −1.31409 −0.657047 0.753850i \(-0.728195\pi\)
−0.657047 + 0.753850i \(0.728195\pi\)
\(774\) 1746.00 0.0810836
\(775\) 0 0
\(776\) −2736.00 −0.126568
\(777\) −2793.00 −0.128955
\(778\) −6042.00 −0.278427
\(779\) −2688.00 −0.123630
\(780\) 0 0
\(781\) 5985.00 0.274213
\(782\) 1100.00 0.0503017
\(783\) −4509.00 −0.205796
\(784\) −784.000 −0.0357143
\(785\) 0 0
\(786\) 9156.00 0.415501
\(787\) −12542.0 −0.568074 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(788\) −804.000 −0.0363468
\(789\) 8859.00 0.399732
\(790\) 0 0
\(791\) −5481.00 −0.246374
\(792\) 4536.00 0.203510
\(793\) −672.000 −0.0300926
\(794\) 15652.0 0.699583
\(795\) 0 0
\(796\) 5536.00 0.246505
\(797\) −11058.0 −0.491461 −0.245731 0.969338i \(-0.579028\pi\)
−0.245731 + 0.969338i \(0.579028\pi\)
\(798\) −672.000 −0.0298102
\(799\) 8800.00 0.389639
\(800\) 0 0
\(801\) 2916.00 0.128629
\(802\) −6810.00 −0.299837
\(803\) −17598.0 −0.773375
\(804\) 11604.0 0.509007
\(805\) 0 0
\(806\) −480.000 −0.0209768
\(807\) −10182.0 −0.444143
\(808\) −816.000 −0.0355282
\(809\) −17307.0 −0.752141 −0.376070 0.926591i \(-0.622725\pi\)
−0.376070 + 0.926591i \(0.622725\pi\)
\(810\) 0 0
\(811\) −2706.00 −0.117165 −0.0585823 0.998283i \(-0.518658\pi\)
−0.0585823 + 0.998283i \(0.518658\pi\)
\(812\) −4676.00 −0.202088
\(813\) 3852.00 0.166169
\(814\) −5586.00 −0.240527
\(815\) 0 0
\(816\) 1056.00 0.0453032
\(817\) 1552.00 0.0664597
\(818\) 8104.00 0.346393
\(819\) −1512.00 −0.0645098
\(820\) 0 0
\(821\) −38862.0 −1.65200 −0.826001 0.563669i \(-0.809389\pi\)
−0.826001 + 0.563669i \(0.809389\pi\)
\(822\) −10932.0 −0.463865
\(823\) −27217.0 −1.15276 −0.576382 0.817180i \(-0.695536\pi\)
−0.576382 + 0.817180i \(0.695536\pi\)
\(824\) −47424.0 −2.00497
\(825\) 0 0
\(826\) 6832.00 0.287791
\(827\) −11301.0 −0.475181 −0.237590 0.971365i \(-0.576358\pi\)
−0.237590 + 0.971365i \(0.576358\pi\)
\(828\) −900.000 −0.0377744
\(829\) 6786.00 0.284303 0.142152 0.989845i \(-0.454598\pi\)
0.142152 + 0.989845i \(0.454598\pi\)
\(830\) 0 0
\(831\) −10518.0 −0.439068
\(832\) −10752.0 −0.448027
\(833\) 1078.00 0.0448385
\(834\) 18252.0 0.757812
\(835\) 0 0
\(836\) 1344.00 0.0556019
\(837\) −270.000 −0.0111500
\(838\) 22644.0 0.933442
\(839\) 8358.00 0.343922 0.171961 0.985104i \(-0.444990\pi\)
0.171961 + 0.985104i \(0.444990\pi\)
\(840\) 0 0
\(841\) 3500.00 0.143507
\(842\) −3514.00 −0.143825
\(843\) −17469.0 −0.713718
\(844\) −15856.0 −0.646666
\(845\) 0 0
\(846\) 7200.00 0.292602
\(847\) −6230.00 −0.252734
\(848\) −2912.00 −0.117923
\(849\) −11490.0 −0.464471
\(850\) 0 0
\(851\) 3325.00 0.133936
\(852\) −3420.00 −0.137520
\(853\) 16500.0 0.662309 0.331154 0.943577i \(-0.392562\pi\)
0.331154 + 0.943577i \(0.392562\pi\)
\(854\) 392.000 0.0157072
\(855\) 0 0
\(856\) 19872.0 0.793471
\(857\) −3372.00 −0.134405 −0.0672026 0.997739i \(-0.521407\pi\)
−0.0672026 + 0.997739i \(0.521407\pi\)
\(858\) −3024.00 −0.120324
\(859\) 39026.0 1.55012 0.775058 0.631890i \(-0.217721\pi\)
0.775058 + 0.631890i \(0.217721\pi\)
\(860\) 0 0
\(861\) 3528.00 0.139645
\(862\) −18608.0 −0.735256
\(863\) 41487.0 1.63642 0.818212 0.574917i \(-0.194966\pi\)
0.818212 + 0.574917i \(0.194966\pi\)
\(864\) −4320.00 −0.170103
\(865\) 0 0
\(866\) 11504.0 0.451411
\(867\) 13287.0 0.520473
\(868\) −280.000 −0.0109491
\(869\) 9849.00 0.384470
\(870\) 0 0
\(871\) −23208.0 −0.902839
\(872\) 35208.0 1.36731
\(873\) 1026.00 0.0397764
\(874\) 800.000 0.0309616
\(875\) 0 0
\(876\) 10056.0 0.387855
\(877\) 158.000 0.00608356 0.00304178 0.999995i \(-0.499032\pi\)
0.00304178 + 0.999995i \(0.499032\pi\)
\(878\) 4688.00 0.180196
\(879\) 10716.0 0.411196
\(880\) 0 0
\(881\) 36594.0 1.39941 0.699707 0.714430i \(-0.253314\pi\)
0.699707 + 0.714430i \(0.253314\pi\)
\(882\) 882.000 0.0336718
\(883\) 17839.0 0.679876 0.339938 0.940448i \(-0.389594\pi\)
0.339938 + 0.940448i \(0.389594\pi\)
\(884\) 2112.00 0.0803555
\(885\) 0 0
\(886\) 30264.0 1.14756
\(887\) −13996.0 −0.529808 −0.264904 0.964275i \(-0.585340\pi\)
−0.264904 + 0.964275i \(0.585340\pi\)
\(888\) 9576.00 0.361880
\(889\) 3605.00 0.136004
\(890\) 0 0
\(891\) −1701.00 −0.0639570
\(892\) −3048.00 −0.114411
\(893\) 6400.00 0.239830
\(894\) −2094.00 −0.0783376
\(895\) 0 0
\(896\) −2688.00 −0.100223
\(897\) 1800.00 0.0670014
\(898\) −10110.0 −0.375696
\(899\) 1670.00 0.0619551
\(900\) 0 0
\(901\) 4004.00 0.148049
\(902\) 7056.00 0.260465
\(903\) −2037.00 −0.0750688
\(904\) 18792.0 0.691386
\(905\) 0 0
\(906\) 13002.0 0.476780
\(907\) 31168.0 1.14103 0.570516 0.821286i \(-0.306743\pi\)
0.570516 + 0.821286i \(0.306743\pi\)
\(908\) −23056.0 −0.842665
\(909\) 306.000 0.0111654
\(910\) 0 0
\(911\) 1881.00 0.0684087 0.0342043 0.999415i \(-0.489110\pi\)
0.0342043 + 0.999415i \(0.489110\pi\)
\(912\) 768.000 0.0278849
\(913\) −8526.00 −0.309057
\(914\) 7590.00 0.274677
\(915\) 0 0
\(916\) −6040.00 −0.217868
\(917\) −10682.0 −0.384679
\(918\) −1188.00 −0.0427122
\(919\) 42447.0 1.52361 0.761805 0.647807i \(-0.224314\pi\)
0.761805 + 0.647807i \(0.224314\pi\)
\(920\) 0 0
\(921\) 21834.0 0.781167
\(922\) 16600.0 0.592941
\(923\) 6840.00 0.243923
\(924\) −1764.00 −0.0628045
\(925\) 0 0
\(926\) 10104.0 0.358572
\(927\) 17784.0 0.630101
\(928\) 26720.0 0.945180
\(929\) 7514.00 0.265367 0.132684 0.991158i \(-0.457641\pi\)
0.132684 + 0.991158i \(0.457641\pi\)
\(930\) 0 0
\(931\) 784.000 0.0275989
\(932\) 23748.0 0.834648
\(933\) −11358.0 −0.398547
\(934\) −4964.00 −0.173905
\(935\) 0 0
\(936\) 5184.00 0.181030
\(937\) −33284.0 −1.16045 −0.580225 0.814457i \(-0.697035\pi\)
−0.580225 + 0.814457i \(0.697035\pi\)
\(938\) 13538.0 0.471249
\(939\) 1344.00 0.0467090
\(940\) 0 0
\(941\) −10962.0 −0.379757 −0.189878 0.981808i \(-0.560809\pi\)
−0.189878 + 0.981808i \(0.560809\pi\)
\(942\) −7224.00 −0.249863
\(943\) −4200.00 −0.145038
\(944\) −7808.00 −0.269204
\(945\) 0 0
\(946\) −4074.00 −0.140018
\(947\) 6172.00 0.211788 0.105894 0.994377i \(-0.466230\pi\)
0.105894 + 0.994377i \(0.466230\pi\)
\(948\) −5628.00 −0.192815
\(949\) −20112.0 −0.687949
\(950\) 0 0
\(951\) −12243.0 −0.417462
\(952\) −3696.00 −0.125828
\(953\) −26263.0 −0.892699 −0.446349 0.894859i \(-0.647276\pi\)
−0.446349 + 0.894859i \(0.647276\pi\)
\(954\) 3276.00 0.111179
\(955\) 0 0
\(956\) −5824.00 −0.197031
\(957\) 10521.0 0.355377
\(958\) 28352.0 0.956171
\(959\) 12754.0 0.429456
\(960\) 0 0
\(961\) −29691.0 −0.996643
\(962\) −6384.00 −0.213959
\(963\) −7452.00 −0.249364
\(964\) 2352.00 0.0785818
\(965\) 0 0
\(966\) −1050.00 −0.0349723
\(967\) 5920.00 0.196871 0.0984356 0.995143i \(-0.468616\pi\)
0.0984356 + 0.995143i \(0.468616\pi\)
\(968\) 21360.0 0.709232
\(969\) −1056.00 −0.0350089
\(970\) 0 0
\(971\) 13372.0 0.441944 0.220972 0.975280i \(-0.429077\pi\)
0.220972 + 0.975280i \(0.429077\pi\)
\(972\) 972.000 0.0320750
\(973\) −21294.0 −0.701597
\(974\) −2078.00 −0.0683608
\(975\) 0 0
\(976\) −448.000 −0.0146928
\(977\) 35155.0 1.15119 0.575593 0.817737i \(-0.304771\pi\)
0.575593 + 0.817737i \(0.304771\pi\)
\(978\) 19512.0 0.637960
\(979\) −6804.00 −0.222121
\(980\) 0 0
\(981\) −13203.0 −0.429704
\(982\) 18510.0 0.601505
\(983\) 1858.00 0.0602859 0.0301429 0.999546i \(-0.490404\pi\)
0.0301429 + 0.999546i \(0.490404\pi\)
\(984\) −12096.0 −0.391876
\(985\) 0 0
\(986\) 7348.00 0.237331
\(987\) −8400.00 −0.270897
\(988\) 1536.00 0.0494602
\(989\) 2425.00 0.0779682
\(990\) 0 0
\(991\) −16401.0 −0.525726 −0.262863 0.964833i \(-0.584667\pi\)
−0.262863 + 0.964833i \(0.584667\pi\)
\(992\) 1600.00 0.0512097
\(993\) −3213.00 −0.102680
\(994\) −3990.00 −0.127319
\(995\) 0 0
\(996\) 4872.00 0.154995
\(997\) 22952.0 0.729084 0.364542 0.931187i \(-0.381225\pi\)
0.364542 + 0.931187i \(0.381225\pi\)
\(998\) 28792.0 0.913221
\(999\) −3591.00 −0.113728
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 525.4.a.f.1.1 yes 1
3.2 odd 2 1575.4.a.d.1.1 1
5.2 odd 4 525.4.d.e.274.2 2
5.3 odd 4 525.4.d.e.274.1 2
5.4 even 2 525.4.a.d.1.1 1
15.14 odd 2 1575.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.4.a.d.1.1 1 5.4 even 2
525.4.a.f.1.1 yes 1 1.1 even 1 trivial
525.4.d.e.274.1 2 5.3 odd 4
525.4.d.e.274.2 2 5.2 odd 4
1575.4.a.d.1.1 1 3.2 odd 2
1575.4.a.h.1.1 1 15.14 odd 2