Properties

Label 1575.4.a.d.1.1
Level $1575$
Weight $4$
Character 1575.1
Self dual yes
Analytic conductor $92.928$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(92.9280082590\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 525)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1575.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -4.00000 q^{4} +7.00000 q^{7} +24.0000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} -4.00000 q^{4} +7.00000 q^{7} +24.0000 q^{8} +21.0000 q^{11} -24.0000 q^{13} -14.0000 q^{14} -16.0000 q^{16} -22.0000 q^{17} +16.0000 q^{19} -42.0000 q^{22} -25.0000 q^{23} +48.0000 q^{26} -28.0000 q^{28} -167.000 q^{29} +10.0000 q^{31} -160.000 q^{32} +44.0000 q^{34} +133.000 q^{37} -32.0000 q^{38} +168.000 q^{41} +97.0000 q^{43} -84.0000 q^{44} +50.0000 q^{46} -400.000 q^{47} +49.0000 q^{49} +96.0000 q^{52} -182.000 q^{53} +168.000 q^{56} +334.000 q^{58} -488.000 q^{59} +28.0000 q^{61} -20.0000 q^{62} +448.000 q^{64} +967.000 q^{67} +88.0000 q^{68} +285.000 q^{71} +838.000 q^{73} -266.000 q^{74} -64.0000 q^{76} +147.000 q^{77} -469.000 q^{79} -336.000 q^{82} -406.000 q^{83} -194.000 q^{86} +504.000 q^{88} -324.000 q^{89} -168.000 q^{91} +100.000 q^{92} +800.000 q^{94} +114.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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 \(0.615027\pi\)
\(3\) 0 0
\(4\) −4.00000 −0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 24.0000 1.06066
\(9\) 0 0
\(10\) 0 0
\(11\) 21.0000 0.575613 0.287806 0.957689i \(-0.407074\pi\)
0.287806 + 0.957689i \(0.407074\pi\)
\(12\) 0 0
\(13\) −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 \(-0.550161\pi\)
−0.156935 + 0.987609i \(0.550161\pi\)
\(18\) 0 0
\(19\) 16.0000 0.193192 0.0965961 0.995324i \(-0.469204\pi\)
0.0965961 + 0.995324i \(0.469204\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −42.0000 −0.407020
\(23\) −25.0000 −0.226646 −0.113323 0.993558i \(-0.536150\pi\)
−0.113323 + 0.993558i \(0.536150\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 48.0000 0.362061
\(27\) 0 0
\(28\) −28.0000 −0.188982
\(29\) −167.000 −1.06935 −0.534675 0.845058i \(-0.679566\pi\)
−0.534675 + 0.845058i \(0.679566\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 44.0000 0.221939
\(35\) 0 0
\(36\) 0 0
\(37\) 133.000 0.590948 0.295474 0.955351i \(-0.404522\pi\)
0.295474 + 0.955351i \(0.404522\pi\)
\(38\) −32.0000 −0.136608
\(39\) 0 0
\(40\) 0 0
\(41\) 168.000 0.639932 0.319966 0.947429i \(-0.396329\pi\)
0.319966 + 0.947429i \(0.396329\pi\)
\(42\) 0 0
\(43\) 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 \(-0.713152\pi\)
−0.620702 + 0.784046i \(0.713152\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 96.0000 0.256015
\(53\) −182.000 −0.471691 −0.235845 0.971791i \(-0.575786\pi\)
−0.235845 + 0.971791i \(0.575786\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 168.000 0.400892
\(57\) 0 0
\(58\) 334.000 0.756144
\(59\) −488.000 −1.07682 −0.538408 0.842684i \(-0.680974\pi\)
−0.538408 + 0.842684i \(0.680974\pi\)
\(60\) 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
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) 967.000 1.76325 0.881626 0.471949i \(-0.156449\pi\)
0.881626 + 0.471949i \(0.156449\pi\)
\(68\) 88.0000 0.156935
\(69\) 0 0
\(70\) 0 0
\(71\) 285.000 0.476384 0.238192 0.971218i \(-0.423445\pi\)
0.238192 + 0.971218i \(0.423445\pi\)
\(72\) 0 0
\(73\) 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
\(78\) 0 0
\(79\) −469.000 −0.667932 −0.333966 0.942585i \(-0.608387\pi\)
−0.333966 + 0.942585i \(0.608387\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −336.000 −0.452500
\(83\) −406.000 −0.536919 −0.268460 0.963291i \(-0.586515\pi\)
−0.268460 + 0.963291i \(0.586515\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −194.000 −0.243251
\(87\) 0 0
\(88\) 504.000 0.610529
\(89\) −324.000 −0.385887 −0.192943 0.981210i \(-0.561803\pi\)
−0.192943 + 0.981210i \(0.561803\pi\)
\(90\) 0 0
\(91\) −168.000 −0.193530
\(92\) 100.000 0.113323
\(93\) 0 0
\(94\) 800.000 0.877805
\(95\) 0 0
\(96\) 0 0
\(97\) 114.000 0.119329 0.0596647 0.998218i \(-0.480997\pi\)
0.0596647 + 0.998218i \(0.480997\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) −34.0000 −0.0334963 −0.0167482 0.999860i \(-0.505331\pi\)
−0.0167482 + 0.999860i \(0.505331\pi\)
\(102\) 0 0
\(103\) 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 \(-0.377970\pi\)
0.374046 + 0.927410i \(0.377970\pi\)
\(108\) 0 0
\(109\) −1467.00 −1.28911 −0.644556 0.764557i \(-0.722958\pi\)
−0.644556 + 0.764557i \(0.722958\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −112.000 −0.0944911
\(113\) 783.000 0.651845 0.325922 0.945397i \(-0.394325\pi\)
0.325922 + 0.945397i \(0.394325\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 668.000 0.534675
\(117\) 0 0
\(118\) 976.000 0.761424
\(119\) −154.000 −0.118632
\(120\) 0 0
\(121\) −890.000 −0.668670
\(122\) −56.0000 −0.0415574
\(123\) 0 0
\(124\) −40.0000 −0.0289686
\(125\) 0 0
\(126\) 0 0
\(127\) 515.000 0.359834 0.179917 0.983682i \(-0.442417\pi\)
0.179917 + 0.983682i \(0.442417\pi\)
\(128\) 384.000 0.265165
\(129\) 0 0
\(130\) 0 0
\(131\) 1526.00 1.01777 0.508883 0.860836i \(-0.330059\pi\)
0.508883 + 0.860836i \(0.330059\pi\)
\(132\) 0 0
\(133\) 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 \(-0.692328\pi\)
−0.568117 + 0.822948i \(0.692328\pi\)
\(138\) 0 0
\(139\) −3042.00 −1.85625 −0.928126 0.372266i \(-0.878581\pi\)
−0.928126 + 0.372266i \(0.878581\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −570.000 −0.336854
\(143\) −504.000 −0.294731
\(144\) 0 0
\(145\) 0 0
\(146\) −1676.00 −0.950046
\(147\) 0 0
\(148\) −532.000 −0.295474
\(149\) −349.000 −0.191887 −0.0959436 0.995387i \(-0.530587\pi\)
−0.0959436 + 0.995387i \(0.530587\pi\)
\(150\) 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
\(153\) 0 0
\(154\) −294.000 −0.153839
\(155\) 0 0
\(156\) 0 0
\(157\) 1204.00 0.612036 0.306018 0.952026i \(-0.401003\pi\)
0.306018 + 0.952026i \(0.401003\pi\)
\(158\) 938.000 0.472299
\(159\) 0 0
\(160\) 0 0
\(161\) −175.000 −0.0856642
\(162\) 0 0
\(163\) −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 \(-0.595529\pi\)
−0.295628 + 0.955303i \(0.595529\pi\)
\(168\) 0 0
\(169\) −1621.00 −0.737824
\(170\) 0 0
\(171\) 0 0
\(172\) −388.000 −0.172004
\(173\) 1140.00 0.500998 0.250499 0.968117i \(-0.419405\pi\)
0.250499 + 0.968117i \(0.419405\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −336.000 −0.143903
\(177\) 0 0
\(178\) 648.000 0.272863
\(179\) −2724.00 −1.13744 −0.568719 0.822532i \(-0.692561\pi\)
−0.568719 + 0.822532i \(0.692561\pi\)
\(180\) 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
\(183\) 0 0
\(184\) −600.000 −0.240394
\(185\) 0 0
\(186\) 0 0
\(187\) −462.000 −0.180667
\(188\) 1600.00 0.620702
\(189\) 0 0
\(190\) 0 0
\(191\) −3932.00 −1.48958 −0.744789 0.667300i \(-0.767450\pi\)
−0.744789 + 0.667300i \(0.767450\pi\)
\(192\) 0 0
\(193\) −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 \(-0.511572\pi\)
−0.0363468 + 0.999339i \(0.511572\pi\)
\(198\) 0 0
\(199\) −1384.00 −0.493011 −0.246505 0.969141i \(-0.579282\pi\)
−0.246505 + 0.969141i \(0.579282\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 68.0000 0.0236855
\(203\) −1169.00 −0.404176
\(204\) 0 0
\(205\) 0 0
\(206\) −3952.00 −1.33665
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) −1656.00 −0.528981
\(215\) 0 0
\(216\) 0 0
\(217\) 70.0000 0.0218982
\(218\) 2934.00 0.911539
\(219\) 0 0
\(220\) 0 0
\(221\) 528.000 0.160711
\(222\) 0 0
\(223\) 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 \(-0.819015\pi\)
−0.842665 + 0.538437i \(0.819015\pi\)
\(228\) 0 0
\(229\) 1510.00 0.435736 0.217868 0.975978i \(-0.430090\pi\)
0.217868 + 0.975978i \(0.430090\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4008.00 −1.13422
\(233\) 5937.00 1.66930 0.834648 0.550784i \(-0.185671\pi\)
0.834648 + 0.550784i \(0.185671\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1952.00 0.538408
\(237\) 0 0
\(238\) 308.000 0.0838852
\(239\) −1456.00 −0.394062 −0.197031 0.980397i \(-0.563130\pi\)
−0.197031 + 0.980397i \(0.563130\pi\)
\(240\) 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
\(243\) 0 0
\(244\) −112.000 −0.0293855
\(245\) 0 0
\(246\) 0 0
\(247\) −384.000 −0.0989204
\(248\) 240.000 0.0614517
\(249\) 0 0
\(250\) 0 0
\(251\) −6510.00 −1.63708 −0.818541 0.574448i \(-0.805217\pi\)
−0.818541 + 0.574448i \(0.805217\pi\)
\(252\) 0 0
\(253\) −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 \(-0.614395\pi\)
−0.351697 + 0.936114i \(0.614395\pi\)
\(258\) 0 0
\(259\) 931.000 0.223357
\(260\) 0 0
\(261\) 0 0
\(262\) −3052.00 −0.719669
\(263\) 2953.00 0.692357 0.346178 0.938169i \(-0.387479\pi\)
0.346178 + 0.938169i \(0.387479\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −224.000 −0.0516328
\(267\) 0 0
\(268\) −3868.00 −0.881626
\(269\) −3394.00 −0.769278 −0.384639 0.923067i \(-0.625674\pi\)
−0.384639 + 0.923067i \(0.625674\pi\)
\(270\) 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
\(273\) 0 0
\(274\) 3644.00 0.803438
\(275\) 0 0
\(276\) 0 0
\(277\) 3506.00 0.760488 0.380244 0.924886i \(-0.375840\pi\)
0.380244 + 0.924886i \(0.375840\pi\)
\(278\) 6084.00 1.31257
\(279\) 0 0
\(280\) 0 0
\(281\) −5823.00 −1.23620 −0.618098 0.786101i \(-0.712097\pi\)
−0.618098 + 0.786101i \(0.712097\pi\)
\(282\) 0 0
\(283\) 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
\(288\) 0 0
\(289\) −4429.00 −0.901486
\(290\) 0 0
\(291\) 0 0
\(292\) −3352.00 −0.671784
\(293\) 3572.00 0.712213 0.356107 0.934445i \(-0.384104\pi\)
0.356107 + 0.934445i \(0.384104\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3192.00 0.626795
\(297\) 0 0
\(298\) 698.000 0.135685
\(299\) 600.000 0.116050
\(300\) 0 0
\(301\) 679.000 0.130023
\(302\) 4334.00 0.825807
\(303\) 0 0
\(304\) −256.000 −0.0482980
\(305\) 0 0
\(306\) 0 0
\(307\) −7278.00 −1.35302 −0.676510 0.736433i \(-0.736509\pi\)
−0.676510 + 0.736433i \(0.736509\pi\)
\(308\) −588.000 −0.108781
\(309\) 0 0
\(310\) 0 0
\(311\) −3786.00 −0.690303 −0.345152 0.938547i \(-0.612173\pi\)
−0.345152 + 0.938547i \(0.612173\pi\)
\(312\) 0 0
\(313\) −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 \(-0.617746\pi\)
−0.361533 + 0.932359i \(0.617746\pi\)
\(318\) 0 0
\(319\) −3507.00 −0.615531
\(320\) 0 0
\(321\) 0 0
\(322\) 350.000 0.0605737
\(323\) −352.000 −0.0606372
\(324\) 0 0
\(325\) 0 0
\(326\) 6504.00 1.10498
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) 2552.00 0.418082
\(335\) 0 0
\(336\) 0 0
\(337\) −2102.00 −0.339772 −0.169886 0.985464i \(-0.554340\pi\)
−0.169886 + 0.985464i \(0.554340\pi\)
\(338\) 3242.00 0.521721
\(339\) 0 0
\(340\) 0 0
\(341\) 210.000 0.0333494
\(342\) 0 0
\(343\) 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 \(-0.847431\pi\)
−0.887313 + 0.461167i \(0.847431\pi\)
\(348\) 0 0
\(349\) −6448.00 −0.988979 −0.494489 0.869184i \(-0.664645\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3360.00 −0.508774
\(353\) −10050.0 −1.51532 −0.757659 0.652650i \(-0.773657\pi\)
−0.757659 + 0.652650i \(0.773657\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1296.00 0.192943
\(357\) 0 0
\(358\) 5448.00 0.804290
\(359\) 6597.00 0.969851 0.484925 0.874556i \(-0.338847\pi\)
0.484925 + 0.874556i \(0.338847\pi\)
\(360\) 0 0
\(361\) −6603.00 −0.962677
\(362\) −8948.00 −1.29916
\(363\) 0 0
\(364\) 672.000 0.0967648
\(365\) 0 0
\(366\) 0 0
\(367\) −6500.00 −0.924516 −0.462258 0.886746i \(-0.652961\pi\)
−0.462258 + 0.886746i \(0.652961\pi\)
\(368\) 400.000 0.0566615
\(369\) 0 0
\(370\) 0 0
\(371\) −1274.00 −0.178282
\(372\) 0 0
\(373\) −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
\(378\) 0 0
\(379\) −217.000 −0.0294104 −0.0147052 0.999892i \(-0.504681\pi\)
−0.0147052 + 0.999892i \(0.504681\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7864.00 1.05329
\(383\) −4640.00 −0.619042 −0.309521 0.950893i \(-0.600169\pi\)
−0.309521 + 0.950893i \(0.600169\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6882.00 0.907473
\(387\) 0 0
\(388\) −456.000 −0.0596647
\(389\) 3021.00 0.393755 0.196878 0.980428i \(-0.436920\pi\)
0.196878 + 0.980428i \(0.436920\pi\)
\(390\) 0 0
\(391\) 550.000 0.0711373
\(392\) 1176.00 0.151523
\(393\) 0 0
\(394\) 402.000 0.0514022
\(395\) 0 0
\(396\) 0 0
\(397\) 7826.00 0.989359 0.494680 0.869075i \(-0.335285\pi\)
0.494680 + 0.869075i \(0.335285\pi\)
\(398\) 2768.00 0.348611
\(399\) 0 0
\(400\) 0 0
\(401\) 3405.00 0.424034 0.212017 0.977266i \(-0.431997\pi\)
0.212017 + 0.977266i \(0.431997\pi\)
\(402\) 0 0
\(403\) −240.000 −0.0296656
\(404\) 136.000 0.0167482
\(405\) 0 0
\(406\) 2338.00 0.285796
\(407\) 2793.00 0.340157
\(408\) 0 0
\(409\) 4052.00 0.489874 0.244937 0.969539i \(-0.421233\pi\)
0.244937 + 0.969539i \(0.421233\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7904.00 −0.945151
\(413\) −3416.00 −0.406998
\(414\) 0 0
\(415\) 0 0
\(416\) 3840.00 0.452576
\(417\) 0 0
\(418\) −672.000 −0.0786330
\(419\) −11322.0 −1.32009 −0.660043 0.751228i \(-0.729462\pi\)
−0.660043 + 0.751228i \(0.729462\pi\)
\(420\) 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
\(423\) 0 0
\(424\) −4368.00 −0.500304
\(425\) 0 0
\(426\) 0 0
\(427\) 196.000 0.0222134
\(428\) −3312.00 −0.374046
\(429\) 0 0
\(430\) 0 0
\(431\) 9304.00 1.03981 0.519905 0.854224i \(-0.325967\pi\)
0.519905 + 0.854224i \(0.325967\pi\)
\(432\) 0 0
\(433\) 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
\(438\) 0 0
\(439\) 2344.00 0.254836 0.127418 0.991849i \(-0.459331\pi\)
0.127418 + 0.991849i \(0.459331\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1056.00 −0.113640
\(443\) −15132.0 −1.62290 −0.811448 0.584424i \(-0.801320\pi\)
−0.811448 + 0.584424i \(0.801320\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1524.00 −0.161802
\(447\) 0 0
\(448\) 3136.00 0.330719
\(449\) 5055.00 0.531314 0.265657 0.964068i \(-0.414411\pi\)
0.265657 + 0.964068i \(0.414411\pi\)
\(450\) 0 0
\(451\) 3528.00 0.368353
\(452\) −3132.00 −0.325922
\(453\) 0 0
\(454\) 11528.0 1.19171
\(455\) 0 0
\(456\) 0 0
\(457\) 3795.00 0.388452 0.194226 0.980957i \(-0.437780\pi\)
0.194226 + 0.980957i \(0.437780\pi\)
\(458\) −3020.00 −0.308112
\(459\) 0 0
\(460\) 0 0
\(461\) −8300.00 −0.838546 −0.419273 0.907860i \(-0.637715\pi\)
−0.419273 + 0.907860i \(0.637715\pi\)
\(462\) 0 0
\(463\) 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 \(-0.460758\pi\)
0.122969 + 0.992410i \(0.460758\pi\)
\(468\) 0 0
\(469\) 6769.00 0.666446
\(470\) 0 0
\(471\) 0 0
\(472\) −11712.0 −1.14214
\(473\) 2037.00 0.198016
\(474\) 0 0
\(475\) 0 0
\(476\) 616.000 0.0593158
\(477\) 0 0
\(478\) 2912.00 0.278644
\(479\) −14176.0 −1.35223 −0.676115 0.736796i \(-0.736338\pi\)
−0.676115 + 0.736796i \(0.736338\pi\)
\(480\) 0 0
\(481\) −3192.00 −0.302584
\(482\) 1176.00 0.111131
\(483\) 0 0
\(484\) 3560.00 0.334335
\(485\) 0 0
\(486\) 0 0
\(487\) −1039.00 −0.0966768 −0.0483384 0.998831i \(-0.515393\pi\)
−0.0483384 + 0.998831i \(0.515393\pi\)
\(488\) 672.000 0.0623361
\(489\) 0 0
\(490\) 0 0
\(491\) −9255.00 −0.850656 −0.425328 0.905039i \(-0.639841\pi\)
−0.425328 + 0.905039i \(0.639841\pi\)
\(492\) 0 0
\(493\) 3674.00 0.335636
\(494\) 768.000 0.0699473
\(495\) 0 0
\(496\) −160.000 −0.0144843
\(497\) 1995.00 0.180056
\(498\) 0 0
\(499\) 14396.0 1.29149 0.645745 0.763553i \(-0.276547\pi\)
0.645745 + 0.763553i \(0.276547\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 13020.0 1.15759
\(503\) −6998.00 −0.620329 −0.310164 0.950683i \(-0.600384\pi\)
−0.310164 + 0.950683i \(0.600384\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1050.00 0.0922494
\(507\) 0 0
\(508\) −2060.00 −0.179917
\(509\) 6400.00 0.557318 0.278659 0.960390i \(-0.410110\pi\)
0.278659 + 0.960390i \(0.410110\pi\)
\(510\) 0 0
\(511\) 5866.00 0.507821
\(512\) 5632.00 0.486136
\(513\) 0 0
\(514\) 5796.00 0.497375
\(515\) 0 0
\(516\) 0 0
\(517\) −8400.00 −0.714568
\(518\) −1862.00 −0.157937
\(519\) 0 0
\(520\) 0 0
\(521\) −15158.0 −1.27463 −0.637317 0.770602i \(-0.719956\pi\)
−0.637317 + 0.770602i \(0.719956\pi\)
\(522\) 0 0
\(523\) −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
\(528\) 0 0
\(529\) −11542.0 −0.948632
\(530\) 0 0
\(531\) 0 0
\(532\) −448.000 −0.0365099
\(533\) −4032.00 −0.327665
\(534\) 0 0
\(535\) 0 0
\(536\) 23208.0 1.87021
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 3520.00 0.277424
\(545\) 0 0
\(546\) 0 0
\(547\) 20547.0 1.60608 0.803040 0.595924i \(-0.203214\pi\)
0.803040 + 0.595924i \(0.203214\pi\)
\(548\) 7288.00 0.568117
\(549\) 0 0
\(550\) 0 0
\(551\) −2672.00 −0.206590
\(552\) 0 0
\(553\) −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 \(-0.538461\pi\)
−0.120534 + 0.992709i \(0.538461\pi\)
\(558\) 0 0
\(559\) −2328.00 −0.176143
\(560\) 0 0
\(561\) 0 0
\(562\) 11646.0 0.874123
\(563\) −24878.0 −1.86231 −0.931157 0.364619i \(-0.881199\pi\)
−0.931157 + 0.364619i \(0.881199\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −7660.00 −0.568858
\(567\) 0 0
\(568\) 6840.00 0.505282
\(569\) 1425.00 0.104990 0.0524948 0.998621i \(-0.483283\pi\)
0.0524948 + 0.998621i \(0.483283\pi\)
\(570\) 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
\(573\) 0 0
\(574\) −2352.00 −0.171029
\(575\) 0 0
\(576\) 0 0
\(577\) −2108.00 −0.152092 −0.0760461 0.997104i \(-0.524230\pi\)
−0.0760461 + 0.997104i \(0.524230\pi\)
\(578\) 8858.00 0.637447
\(579\) 0 0
\(580\) 0 0
\(581\) −2842.00 −0.202936
\(582\) 0 0
\(583\) −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 \(-0.172549\pi\)
0.856638 + 0.515919i \(0.172549\pi\)
\(588\) 0 0
\(589\) 160.000 0.0111930
\(590\) 0 0
\(591\) 0 0
\(592\) −2128.00 −0.147737
\(593\) 17892.0 1.23902 0.619508 0.784990i \(-0.287332\pi\)
0.619508 + 0.784990i \(0.287332\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1396.00 0.0959436
\(597\) 0 0
\(598\) −1200.00 −0.0820596
\(599\) −8077.00 −0.550947 −0.275474 0.961309i \(-0.588835\pi\)
−0.275474 + 0.961309i \(0.588835\pi\)
\(600\) 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
\(603\) 0 0
\(604\) 8668.00 0.583934
\(605\) 0 0
\(606\) 0 0
\(607\) 24092.0 1.61098 0.805489 0.592610i \(-0.201903\pi\)
0.805489 + 0.592610i \(0.201903\pi\)
\(608\) −2560.00 −0.170759
\(609\) 0 0
\(610\) 0 0
\(611\) 9600.00 0.635637
\(612\) 0 0
\(613\) −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 \(-0.362726\pi\)
0.418016 + 0.908440i \(0.362726\pi\)
\(618\) 0 0
\(619\) −300.000 −0.0194798 −0.00973992 0.999953i \(-0.503100\pi\)
−0.00973992 + 0.999953i \(0.503100\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 7572.00 0.488118
\(623\) −2268.00 −0.145852
\(624\) 0 0
\(625\) 0 0
\(626\) 896.000 0.0572066
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) 8162.00 0.511285
\(635\) 0 0
\(636\) 0 0
\(637\) −1176.00 −0.0731473
\(638\) 7014.00 0.435246
\(639\) 0 0
\(640\) 0 0
\(641\) 24117.0 1.48606 0.743030 0.669258i \(-0.233388\pi\)
0.743030 + 0.669258i \(0.233388\pi\)
\(642\) 0 0
\(643\) 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 \(-0.476478\pi\)
0.0738278 + 0.997271i \(0.476478\pi\)
\(648\) 0 0
\(649\) −10248.0 −0.619829
\(650\) 0 0
\(651\) 0 0
\(652\) 13008.0 0.781338
\(653\) −27514.0 −1.64886 −0.824430 0.565963i \(-0.808504\pi\)
−0.824430 + 0.565963i \(0.808504\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2688.00 −0.159983
\(657\) 0 0
\(658\) 5600.00 0.331779
\(659\) 20772.0 1.22786 0.613932 0.789359i \(-0.289587\pi\)
0.613932 + 0.789359i \(0.289587\pi\)
\(660\) 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
\(663\) 0 0
\(664\) −9744.00 −0.569489
\(665\) 0 0
\(666\) 0 0
\(667\) 4175.00 0.242364
\(668\) 5104.00 0.295628
\(669\) 0 0
\(670\) 0 0
\(671\) 588.000 0.0338293
\(672\) 0 0
\(673\) −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 \(-0.161090\pi\)
0.874652 + 0.484752i \(0.161090\pi\)
\(678\) 0 0
\(679\) 798.000 0.0451023
\(680\) 0 0
\(681\) 0 0
\(682\) −420.000 −0.0235816
\(683\) 9009.00 0.504714 0.252357 0.967634i \(-0.418794\pi\)
0.252357 + 0.967634i \(0.418794\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −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
\(693\) 0 0
\(694\) 22942.0 1.25485
\(695\) 0 0
\(696\) 0 0
\(697\) −3696.00 −0.200855
\(698\) 12896.0 0.699313
\(699\) 0 0
\(700\) 0 0
\(701\) −24170.0 −1.30227 −0.651133 0.758964i \(-0.725706\pi\)
−0.651133 + 0.758964i \(0.725706\pi\)
\(702\) 0 0
\(703\) 2128.00 0.114166
\(704\) 9408.00 0.503661
\(705\) 0 0
\(706\) 20100.0 1.07149
\(707\) −238.000 −0.0126604
\(708\) 0 0
\(709\) −8426.00 −0.446326 −0.223163 0.974781i \(-0.571638\pi\)
−0.223163 + 0.974781i \(0.571638\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7776.00 −0.409295
\(713\) −250.000 −0.0131312
\(714\) 0 0
\(715\) 0 0
\(716\) 10896.0 0.568719
\(717\) 0 0
\(718\) −13194.0 −0.685788
\(719\) 30752.0 1.59507 0.797536 0.603272i \(-0.206137\pi\)
0.797536 + 0.603272i \(0.206137\pi\)
\(720\) 0 0
\(721\) 13832.0 0.714467
\(722\) 13206.0 0.680715
\(723\) 0 0
\(724\) −17896.0 −0.918646
\(725\) 0 0
\(726\) 0 0
\(727\) −11570.0 −0.590244 −0.295122 0.955460i \(-0.595360\pi\)
−0.295122 + 0.955460i \(0.595360\pi\)
\(728\) −4032.00 −0.205269
\(729\) 0 0
\(730\) 0 0
\(731\) −2134.00 −0.107974
\(732\) 0 0
\(733\) −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
\(738\) 0 0
\(739\) −22351.0 −1.11258 −0.556289 0.830989i \(-0.687775\pi\)
−0.556289 + 0.830989i \(0.687775\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2548.00 0.126065
\(743\) −21720.0 −1.07245 −0.536224 0.844075i \(-0.680150\pi\)
−0.536224 + 0.844075i \(0.680150\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 17330.0 0.850531
\(747\) 0 0
\(748\) 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
\(753\) 0 0
\(754\) −8016.00 −0.387169
\(755\) 0 0
\(756\) 0 0
\(757\) 7685.00 0.368978 0.184489 0.982835i \(-0.440937\pi\)
0.184489 + 0.982835i \(0.440937\pi\)
\(758\) 434.000 0.0207963
\(759\) 0 0
\(760\) 0 0
\(761\) 12.0000 0.000571616 0 0.000285808 1.00000i \(-0.499909\pi\)
0.000285808 1.00000i \(0.499909\pi\)
\(762\) 0 0
\(763\) −10269.0 −0.487238
\(764\) 15728.0 0.744789
\(765\) 0 0
\(766\) 9280.00 0.437728
\(767\) 11712.0 0.551364
\(768\) 0 0
\(769\) −24832.0 −1.16445 −0.582227 0.813026i \(-0.697818\pi\)
−0.582227 + 0.813026i \(0.697818\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13764.0 0.641680
\(773\) 28242.0 1.31409 0.657047 0.753850i \(-0.271805\pi\)
0.657047 + 0.753850i \(0.271805\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 2736.00 0.126568
\(777\) 0 0
\(778\) −6042.00 −0.278427
\(779\) 2688.00 0.123630
\(780\) 0 0
\(781\) 5985.00 0.274213
\(782\) −1100.00 −0.0503017
\(783\) 0 0
\(784\) −784.000 −0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −12542.0 −0.568074 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(788\) 804.000 0.0363468
\(789\) 0 0
\(790\) 0 0
\(791\) 5481.00 0.246374
\(792\) 0 0
\(793\) −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 \(-0.420972\pi\)
0.245731 + 0.969338i \(0.420972\pi\)
\(798\) 0 0
\(799\) 8800.00 0.389639
\(800\) 0 0
\(801\) 0 0
\(802\) −6810.00 −0.299837
\(803\) 17598.0 0.773375
\(804\) 0 0
\(805\) 0 0
\(806\) 480.000 0.0209768
\(807\) 0 0
\(808\) −816.000 −0.0355282
\(809\) 17307.0 0.752141 0.376070 0.926591i \(-0.377275\pi\)
0.376070 + 0.926591i \(0.377275\pi\)
\(810\) 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
\(813\) 0 0
\(814\) −5586.00 −0.240527
\(815\) 0 0
\(816\) 0 0
\(817\) 1552.00 0.0664597
\(818\) −8104.00 −0.346393
\(819\) 0 0
\(820\) 0 0
\(821\) 38862.0 1.65200 0.826001 0.563669i \(-0.190611\pi\)
0.826001 + 0.563669i \(0.190611\pi\)
\(822\) 0 0
\(823\) −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 \(-0.423642\pi\)
0.237590 + 0.971365i \(0.423642\pi\)
\(828\) 0 0
\(829\) 6786.00 0.284303 0.142152 0.989845i \(-0.454598\pi\)
0.142152 + 0.989845i \(0.454598\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −10752.0 −0.448027
\(833\) −1078.00 −0.0448385
\(834\) 0 0
\(835\) 0 0
\(836\) −1344.00 −0.0556019
\(837\) 0 0
\(838\) 22644.0 0.933442
\(839\) −8358.00 −0.343922 −0.171961 0.985104i \(-0.555010\pi\)
−0.171961 + 0.985104i \(0.555010\pi\)
\(840\) 0 0
\(841\) 3500.00 0.143507
\(842\) 3514.00 0.143825
\(843\) 0 0
\(844\) −15856.0 −0.646666
\(845\) 0 0
\(846\) 0 0
\(847\) −6230.00 −0.252734
\(848\) 2912.00 0.117923
\(849\) 0 0
\(850\) 0 0
\(851\) −3325.00 −0.133936
\(852\) 0 0
\(853\) 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 \(-0.478593\pi\)
0.0672026 + 0.997739i \(0.478593\pi\)
\(858\) 0 0
\(859\) 39026.0 1.55012 0.775058 0.631890i \(-0.217721\pi\)
0.775058 + 0.631890i \(0.217721\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −18608.0 −0.735256
\(863\) −41487.0 −1.63642 −0.818212 0.574917i \(-0.805034\pi\)
−0.818212 + 0.574917i \(0.805034\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −11504.0 −0.451411
\(867\) 0 0
\(868\) −280.000 −0.0109491
\(869\) −9849.00 −0.384470
\(870\) 0 0
\(871\) −23208.0 −0.902839
\(872\) −35208.0 −1.36731
\(873\) 0 0
\(874\) 800.000 0.0309616
\(875\) 0 0
\(876\) 0 0
\(877\) 158.000 0.00608356 0.00304178 0.999995i \(-0.499032\pi\)
0.00304178 + 0.999995i \(0.499032\pi\)
\(878\) −4688.00 −0.180196
\(879\) 0 0
\(880\) 0 0
\(881\) −36594.0 −1.39941 −0.699707 0.714430i \(-0.746686\pi\)
−0.699707 + 0.714430i \(0.746686\pi\)
\(882\) 0 0
\(883\) 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 \(-0.414660\pi\)
0.264904 + 0.964275i \(0.414660\pi\)
\(888\) 0 0
\(889\) 3605.00 0.136004
\(890\) 0 0
\(891\) 0 0
\(892\) −3048.00 −0.114411
\(893\) −6400.00 −0.239830
\(894\) 0 0
\(895\) 0 0
\(896\) 2688.00 0.100223
\(897\) 0 0
\(898\) −10110.0 −0.375696
\(899\) −1670.00 −0.0619551
\(900\) 0 0
\(901\) 4004.00 0.148049
\(902\) −7056.00 −0.260465
\(903\) 0 0
\(904\) 18792.0 0.691386
\(905\) 0 0
\(906\) 0 0
\(907\) 31168.0 1.14103 0.570516 0.821286i \(-0.306743\pi\)
0.570516 + 0.821286i \(0.306743\pi\)
\(908\) 23056.0 0.842665
\(909\) 0 0
\(910\) 0 0
\(911\) −1881.00 −0.0684087 −0.0342043 0.999415i \(-0.510890\pi\)
−0.0342043 + 0.999415i \(0.510890\pi\)
\(912\) 0 0
\(913\) −8526.00 −0.309057
\(914\) −7590.00 −0.274677
\(915\) 0 0
\(916\) −6040.00 −0.217868
\(917\) 10682.0 0.384679
\(918\) 0 0
\(919\) 42447.0 1.52361 0.761805 0.647807i \(-0.224314\pi\)
0.761805 + 0.647807i \(0.224314\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 16600.0 0.592941
\(923\) −6840.00 −0.243923
\(924\) 0 0
\(925\) 0 0
\(926\) −10104.0 −0.358572
\(927\) 0 0
\(928\) 26720.0 0.945180
\(929\) −7514.00 −0.265367 −0.132684 0.991158i \(-0.542359\pi\)
−0.132684 + 0.991158i \(0.542359\pi\)
\(930\) 0 0
\(931\) 784.000 0.0275989
\(932\) −23748.0 −0.834648
\(933\) 0 0
\(934\) −4964.00 −0.173905
\(935\) 0 0
\(936\) 0 0
\(937\) −33284.0 −1.16045 −0.580225 0.814457i \(-0.697035\pi\)
−0.580225 + 0.814457i \(0.697035\pi\)
\(938\) −13538.0 −0.471249
\(939\) 0 0
\(940\) 0 0
\(941\) 10962.0 0.379757 0.189878 0.981808i \(-0.439191\pi\)
0.189878 + 0.981808i \(0.439191\pi\)
\(942\) 0 0
\(943\) −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 \(-0.533770\pi\)
−0.105894 + 0.994377i \(0.533770\pi\)
\(948\) 0 0
\(949\) −20112.0 −0.687949
\(950\) 0 0
\(951\) 0 0
\(952\) −3696.00 −0.125828
\(953\) 26263.0 0.892699 0.446349 0.894859i \(-0.352724\pi\)
0.446349 + 0.894859i \(0.352724\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 5824.00 0.197031
\(957\) 0 0
\(958\) 28352.0 0.956171
\(959\) −12754.0 −0.429456
\(960\) 0 0
\(961\) −29691.0 −0.996643
\(962\) 6384.00 0.213959
\(963\) 0 0
\(964\) 2352.00 0.0785818
\(965\) 0 0
\(966\) 0 0
\(967\) 5920.00 0.196871 0.0984356 0.995143i \(-0.468616\pi\)
0.0984356 + 0.995143i \(0.468616\pi\)
\(968\) −21360.0 −0.709232
\(969\) 0 0
\(970\) 0 0
\(971\) −13372.0 −0.441944 −0.220972 0.975280i \(-0.570923\pi\)
−0.220972 + 0.975280i \(0.570923\pi\)
\(972\) 0 0
\(973\) −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 \(-0.695229\pi\)
−0.575593 + 0.817737i \(0.695229\pi\)
\(978\) 0 0
\(979\) −6804.00 −0.222121
\(980\) 0 0
\(981\) 0 0
\(982\) 18510.0 0.601505
\(983\) −1858.00 −0.0602859 −0.0301429 0.999546i \(-0.509596\pi\)
−0.0301429 + 0.999546i \(0.509596\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −7348.00 −0.237331
\(987\) 0 0
\(988\) 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
\(993\) 0 0
\(994\) −3990.00 −0.127319
\(995\) 0 0
\(996\) 0 0
\(997\) 22952.0 0.729084 0.364542 0.931187i \(-0.381225\pi\)
0.364542 + 0.931187i \(0.381225\pi\)
\(998\) −28792.0 −0.913221
\(999\) 0 0
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 1575.4.a.d.1.1 1
3.2 odd 2 525.4.a.f.1.1 yes 1
5.4 even 2 1575.4.a.h.1.1 1
15.2 even 4 525.4.d.e.274.2 2
15.8 even 4 525.4.d.e.274.1 2
15.14 odd 2 525.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.4.a.d.1.1 1 15.14 odd 2
525.4.a.f.1.1 yes 1 3.2 odd 2
525.4.d.e.274.1 2 15.8 even 4
525.4.d.e.274.2 2 15.2 even 4
1575.4.a.d.1.1 1 1.1 even 1 trivial
1575.4.a.h.1.1 1 5.4 even 2