Properties

Label 4028.2.a.d.1.10
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.0800487\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0800487 q^{3} +0.442813 q^{5} +2.60518 q^{7} -2.99359 q^{9} +O(q^{10})\) \(q+0.0800487 q^{3} +0.442813 q^{5} +2.60518 q^{7} -2.99359 q^{9} -2.05333 q^{11} +2.33968 q^{13} +0.0354466 q^{15} +2.04003 q^{17} -1.00000 q^{19} +0.208542 q^{21} -6.75394 q^{23} -4.80392 q^{25} -0.479779 q^{27} -0.161496 q^{29} -7.92315 q^{31} -0.164366 q^{33} +1.15361 q^{35} +3.74579 q^{37} +0.187289 q^{39} -5.17031 q^{41} -4.07281 q^{43} -1.32560 q^{45} +2.84920 q^{47} -0.213017 q^{49} +0.163302 q^{51} +1.00000 q^{53} -0.909239 q^{55} -0.0800487 q^{57} +8.26122 q^{59} -4.20321 q^{61} -7.79886 q^{63} +1.03604 q^{65} -10.7790 q^{67} -0.540644 q^{69} -4.25972 q^{71} +2.99568 q^{73} -0.384547 q^{75} -5.34930 q^{77} +1.77749 q^{79} +8.94237 q^{81} +13.1358 q^{83} +0.903350 q^{85} -0.0129275 q^{87} -8.31561 q^{89} +6.09530 q^{91} -0.634237 q^{93} -0.442813 q^{95} -13.1455 q^{97} +6.14683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0800487 0.0462161 0.0231081 0.999733i \(-0.492644\pi\)
0.0231081 + 0.999733i \(0.492644\pi\)
\(4\) 0 0
\(5\) 0.442813 0.198032 0.0990159 0.995086i \(-0.468431\pi\)
0.0990159 + 0.995086i \(0.468431\pi\)
\(6\) 0 0
\(7\) 2.60518 0.984667 0.492333 0.870407i \(-0.336144\pi\)
0.492333 + 0.870407i \(0.336144\pi\)
\(8\) 0 0
\(9\) −2.99359 −0.997864
\(10\) 0 0
\(11\) −2.05333 −0.619102 −0.309551 0.950883i \(-0.600179\pi\)
−0.309551 + 0.950883i \(0.600179\pi\)
\(12\) 0 0
\(13\) 2.33968 0.648911 0.324456 0.945901i \(-0.394819\pi\)
0.324456 + 0.945901i \(0.394819\pi\)
\(14\) 0 0
\(15\) 0.0354466 0.00915226
\(16\) 0 0
\(17\) 2.04003 0.494779 0.247390 0.968916i \(-0.420427\pi\)
0.247390 + 0.968916i \(0.420427\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0.208542 0.0455075
\(22\) 0 0
\(23\) −6.75394 −1.40829 −0.704147 0.710054i \(-0.748670\pi\)
−0.704147 + 0.710054i \(0.748670\pi\)
\(24\) 0 0
\(25\) −4.80392 −0.960783
\(26\) 0 0
\(27\) −0.479779 −0.0923335
\(28\) 0 0
\(29\) −0.161496 −0.0299890 −0.0149945 0.999888i \(-0.504773\pi\)
−0.0149945 + 0.999888i \(0.504773\pi\)
\(30\) 0 0
\(31\) −7.92315 −1.42304 −0.711520 0.702666i \(-0.751993\pi\)
−0.711520 + 0.702666i \(0.751993\pi\)
\(32\) 0 0
\(33\) −0.164366 −0.0286125
\(34\) 0 0
\(35\) 1.15361 0.194995
\(36\) 0 0
\(37\) 3.74579 0.615804 0.307902 0.951418i \(-0.400373\pi\)
0.307902 + 0.951418i \(0.400373\pi\)
\(38\) 0 0
\(39\) 0.187289 0.0299902
\(40\) 0 0
\(41\) −5.17031 −0.807467 −0.403734 0.914877i \(-0.632288\pi\)
−0.403734 + 0.914877i \(0.632288\pi\)
\(42\) 0 0
\(43\) −4.07281 −0.621097 −0.310549 0.950557i \(-0.600513\pi\)
−0.310549 + 0.950557i \(0.600513\pi\)
\(44\) 0 0
\(45\) −1.32560 −0.197609
\(46\) 0 0
\(47\) 2.84920 0.415598 0.207799 0.978172i \(-0.433370\pi\)
0.207799 + 0.978172i \(0.433370\pi\)
\(48\) 0 0
\(49\) −0.213017 −0.0304310
\(50\) 0 0
\(51\) 0.163302 0.0228668
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −0.909239 −0.122602
\(56\) 0 0
\(57\) −0.0800487 −0.0106027
\(58\) 0 0
\(59\) 8.26122 1.07552 0.537759 0.843098i \(-0.319271\pi\)
0.537759 + 0.843098i \(0.319271\pi\)
\(60\) 0 0
\(61\) −4.20321 −0.538165 −0.269083 0.963117i \(-0.586721\pi\)
−0.269083 + 0.963117i \(0.586721\pi\)
\(62\) 0 0
\(63\) −7.79886 −0.982564
\(64\) 0 0
\(65\) 1.03604 0.128505
\(66\) 0 0
\(67\) −10.7790 −1.31687 −0.658434 0.752638i \(-0.728781\pi\)
−0.658434 + 0.752638i \(0.728781\pi\)
\(68\) 0 0
\(69\) −0.540644 −0.0650859
\(70\) 0 0
\(71\) −4.25972 −0.505535 −0.252768 0.967527i \(-0.581341\pi\)
−0.252768 + 0.967527i \(0.581341\pi\)
\(72\) 0 0
\(73\) 2.99568 0.350618 0.175309 0.984513i \(-0.443908\pi\)
0.175309 + 0.984513i \(0.443908\pi\)
\(74\) 0 0
\(75\) −0.384547 −0.0444037
\(76\) 0 0
\(77\) −5.34930 −0.609609
\(78\) 0 0
\(79\) 1.77749 0.199983 0.0999915 0.994988i \(-0.468118\pi\)
0.0999915 + 0.994988i \(0.468118\pi\)
\(80\) 0 0
\(81\) 8.94237 0.993597
\(82\) 0 0
\(83\) 13.1358 1.44184 0.720920 0.693018i \(-0.243719\pi\)
0.720920 + 0.693018i \(0.243719\pi\)
\(84\) 0 0
\(85\) 0.903350 0.0979821
\(86\) 0 0
\(87\) −0.0129275 −0.00138597
\(88\) 0 0
\(89\) −8.31561 −0.881453 −0.440727 0.897641i \(-0.645279\pi\)
−0.440727 + 0.897641i \(0.645279\pi\)
\(90\) 0 0
\(91\) 6.09530 0.638962
\(92\) 0 0
\(93\) −0.634237 −0.0657674
\(94\) 0 0
\(95\) −0.442813 −0.0454316
\(96\) 0 0
\(97\) −13.1455 −1.33472 −0.667360 0.744736i \(-0.732576\pi\)
−0.667360 + 0.744736i \(0.732576\pi\)
\(98\) 0 0
\(99\) 6.14683 0.617779
\(100\) 0 0
\(101\) 0.0172236 0.00171381 0.000856907 1.00000i \(-0.499727\pi\)
0.000856907 1.00000i \(0.499727\pi\)
\(102\) 0 0
\(103\) 4.31935 0.425598 0.212799 0.977096i \(-0.431742\pi\)
0.212799 + 0.977096i \(0.431742\pi\)
\(104\) 0 0
\(105\) 0.0923448 0.00901193
\(106\) 0 0
\(107\) −13.5615 −1.31104 −0.655519 0.755179i \(-0.727550\pi\)
−0.655519 + 0.755179i \(0.727550\pi\)
\(108\) 0 0
\(109\) 4.87340 0.466787 0.233394 0.972382i \(-0.425017\pi\)
0.233394 + 0.972382i \(0.425017\pi\)
\(110\) 0 0
\(111\) 0.299846 0.0284601
\(112\) 0 0
\(113\) −10.5045 −0.988184 −0.494092 0.869410i \(-0.664499\pi\)
−0.494092 + 0.869410i \(0.664499\pi\)
\(114\) 0 0
\(115\) −2.99073 −0.278887
\(116\) 0 0
\(117\) −7.00406 −0.647525
\(118\) 0 0
\(119\) 5.31465 0.487193
\(120\) 0 0
\(121\) −6.78385 −0.616713
\(122\) 0 0
\(123\) −0.413877 −0.0373180
\(124\) 0 0
\(125\) −4.34130 −0.388298
\(126\) 0 0
\(127\) 2.11653 0.187812 0.0939058 0.995581i \(-0.470065\pi\)
0.0939058 + 0.995581i \(0.470065\pi\)
\(128\) 0 0
\(129\) −0.326023 −0.0287047
\(130\) 0 0
\(131\) −5.17455 −0.452102 −0.226051 0.974115i \(-0.572582\pi\)
−0.226051 + 0.974115i \(0.572582\pi\)
\(132\) 0 0
\(133\) −2.60518 −0.225898
\(134\) 0 0
\(135\) −0.212452 −0.0182850
\(136\) 0 0
\(137\) 11.5877 0.990004 0.495002 0.868892i \(-0.335167\pi\)
0.495002 + 0.868892i \(0.335167\pi\)
\(138\) 0 0
\(139\) −22.1807 −1.88135 −0.940673 0.339315i \(-0.889805\pi\)
−0.940673 + 0.339315i \(0.889805\pi\)
\(140\) 0 0
\(141\) 0.228074 0.0192073
\(142\) 0 0
\(143\) −4.80414 −0.401742
\(144\) 0 0
\(145\) −0.0715123 −0.00593877
\(146\) 0 0
\(147\) −0.0170517 −0.00140640
\(148\) 0 0
\(149\) 11.1654 0.914703 0.457352 0.889286i \(-0.348798\pi\)
0.457352 + 0.889286i \(0.348798\pi\)
\(150\) 0 0
\(151\) −21.8788 −1.78047 −0.890237 0.455497i \(-0.849461\pi\)
−0.890237 + 0.455497i \(0.849461\pi\)
\(152\) 0 0
\(153\) −6.10701 −0.493723
\(154\) 0 0
\(155\) −3.50847 −0.281807
\(156\) 0 0
\(157\) −7.15969 −0.571405 −0.285703 0.958318i \(-0.592227\pi\)
−0.285703 + 0.958318i \(0.592227\pi\)
\(158\) 0 0
\(159\) 0.0800487 0.00634827
\(160\) 0 0
\(161\) −17.5953 −1.38670
\(162\) 0 0
\(163\) 17.1676 1.34467 0.672334 0.740248i \(-0.265292\pi\)
0.672334 + 0.740248i \(0.265292\pi\)
\(164\) 0 0
\(165\) −0.0727834 −0.00566618
\(166\) 0 0
\(167\) 17.2803 1.33719 0.668595 0.743627i \(-0.266896\pi\)
0.668595 + 0.743627i \(0.266896\pi\)
\(168\) 0 0
\(169\) −7.52588 −0.578914
\(170\) 0 0
\(171\) 2.99359 0.228926
\(172\) 0 0
\(173\) 13.1836 1.00233 0.501164 0.865352i \(-0.332905\pi\)
0.501164 + 0.865352i \(0.332905\pi\)
\(174\) 0 0
\(175\) −12.5151 −0.946052
\(176\) 0 0
\(177\) 0.661299 0.0497063
\(178\) 0 0
\(179\) 5.00811 0.374324 0.187162 0.982329i \(-0.440071\pi\)
0.187162 + 0.982329i \(0.440071\pi\)
\(180\) 0 0
\(181\) 2.15207 0.159962 0.0799810 0.996796i \(-0.474514\pi\)
0.0799810 + 0.996796i \(0.474514\pi\)
\(182\) 0 0
\(183\) −0.336461 −0.0248719
\(184\) 0 0
\(185\) 1.65868 0.121949
\(186\) 0 0
\(187\) −4.18884 −0.306319
\(188\) 0 0
\(189\) −1.24991 −0.0909178
\(190\) 0 0
\(191\) 21.9716 1.58981 0.794905 0.606734i \(-0.207521\pi\)
0.794905 + 0.606734i \(0.207521\pi\)
\(192\) 0 0
\(193\) 3.78614 0.272533 0.136266 0.990672i \(-0.456490\pi\)
0.136266 + 0.990672i \(0.456490\pi\)
\(194\) 0 0
\(195\) 0.0829337 0.00593901
\(196\) 0 0
\(197\) 7.05465 0.502623 0.251312 0.967906i \(-0.419138\pi\)
0.251312 + 0.967906i \(0.419138\pi\)
\(198\) 0 0
\(199\) −17.2692 −1.22418 −0.612091 0.790788i \(-0.709671\pi\)
−0.612091 + 0.790788i \(0.709671\pi\)
\(200\) 0 0
\(201\) −0.862847 −0.0608606
\(202\) 0 0
\(203\) −0.420726 −0.0295292
\(204\) 0 0
\(205\) −2.28948 −0.159904
\(206\) 0 0
\(207\) 20.2185 1.40529
\(208\) 0 0
\(209\) 2.05333 0.142032
\(210\) 0 0
\(211\) −23.5576 −1.62177 −0.810886 0.585204i \(-0.801014\pi\)
−0.810886 + 0.585204i \(0.801014\pi\)
\(212\) 0 0
\(213\) −0.340985 −0.0233639
\(214\) 0 0
\(215\) −1.80349 −0.122997
\(216\) 0 0
\(217\) −20.6413 −1.40122
\(218\) 0 0
\(219\) 0.239800 0.0162042
\(220\) 0 0
\(221\) 4.77302 0.321068
\(222\) 0 0
\(223\) 17.2802 1.15717 0.578584 0.815623i \(-0.303605\pi\)
0.578584 + 0.815623i \(0.303605\pi\)
\(224\) 0 0
\(225\) 14.3810 0.958731
\(226\) 0 0
\(227\) −0.177530 −0.0117831 −0.00589155 0.999983i \(-0.501875\pi\)
−0.00589155 + 0.999983i \(0.501875\pi\)
\(228\) 0 0
\(229\) −11.8364 −0.782171 −0.391086 0.920354i \(-0.627900\pi\)
−0.391086 + 0.920354i \(0.627900\pi\)
\(230\) 0 0
\(231\) −0.428204 −0.0281738
\(232\) 0 0
\(233\) 21.5076 1.40901 0.704505 0.709699i \(-0.251169\pi\)
0.704505 + 0.709699i \(0.251169\pi\)
\(234\) 0 0
\(235\) 1.26166 0.0823016
\(236\) 0 0
\(237\) 0.142286 0.00924244
\(238\) 0 0
\(239\) −8.78149 −0.568027 −0.284014 0.958820i \(-0.591666\pi\)
−0.284014 + 0.958820i \(0.591666\pi\)
\(240\) 0 0
\(241\) −21.2194 −1.36686 −0.683432 0.730014i \(-0.739513\pi\)
−0.683432 + 0.730014i \(0.739513\pi\)
\(242\) 0 0
\(243\) 2.15516 0.138254
\(244\) 0 0
\(245\) −0.0943265 −0.00602630
\(246\) 0 0
\(247\) −2.33968 −0.148870
\(248\) 0 0
\(249\) 1.05150 0.0666363
\(250\) 0 0
\(251\) −30.5509 −1.92836 −0.964179 0.265252i \(-0.914545\pi\)
−0.964179 + 0.265252i \(0.914545\pi\)
\(252\) 0 0
\(253\) 13.8681 0.871877
\(254\) 0 0
\(255\) 0.0723120 0.00452835
\(256\) 0 0
\(257\) −11.2946 −0.704535 −0.352268 0.935899i \(-0.614589\pi\)
−0.352268 + 0.935899i \(0.614589\pi\)
\(258\) 0 0
\(259\) 9.75848 0.606362
\(260\) 0 0
\(261\) 0.483452 0.0299249
\(262\) 0 0
\(263\) −0.0775000 −0.00477885 −0.00238943 0.999997i \(-0.500761\pi\)
−0.00238943 + 0.999997i \(0.500761\pi\)
\(264\) 0 0
\(265\) 0.442813 0.0272018
\(266\) 0 0
\(267\) −0.665654 −0.0407374
\(268\) 0 0
\(269\) −21.5966 −1.31677 −0.658385 0.752681i \(-0.728760\pi\)
−0.658385 + 0.752681i \(0.728760\pi\)
\(270\) 0 0
\(271\) 6.03169 0.366399 0.183199 0.983076i \(-0.441355\pi\)
0.183199 + 0.983076i \(0.441355\pi\)
\(272\) 0 0
\(273\) 0.487921 0.0295303
\(274\) 0 0
\(275\) 9.86401 0.594822
\(276\) 0 0
\(277\) 27.7533 1.66753 0.833766 0.552117i \(-0.186180\pi\)
0.833766 + 0.552117i \(0.186180\pi\)
\(278\) 0 0
\(279\) 23.7187 1.42000
\(280\) 0 0
\(281\) 12.4658 0.743647 0.371824 0.928303i \(-0.378733\pi\)
0.371824 + 0.928303i \(0.378733\pi\)
\(282\) 0 0
\(283\) 28.6112 1.70076 0.850378 0.526172i \(-0.176373\pi\)
0.850378 + 0.526172i \(0.176373\pi\)
\(284\) 0 0
\(285\) −0.0354466 −0.00209967
\(286\) 0 0
\(287\) −13.4696 −0.795086
\(288\) 0 0
\(289\) −12.8383 −0.755193
\(290\) 0 0
\(291\) −1.05228 −0.0616856
\(292\) 0 0
\(293\) 1.23617 0.0722178 0.0361089 0.999348i \(-0.488504\pi\)
0.0361089 + 0.999348i \(0.488504\pi\)
\(294\) 0 0
\(295\) 3.65817 0.212987
\(296\) 0 0
\(297\) 0.985144 0.0571638
\(298\) 0 0
\(299\) −15.8021 −0.913858
\(300\) 0 0
\(301\) −10.6104 −0.611574
\(302\) 0 0
\(303\) 0.00137873 7.92059e−5 0
\(304\) 0 0
\(305\) −1.86123 −0.106574
\(306\) 0 0
\(307\) −31.5868 −1.80275 −0.901376 0.433038i \(-0.857442\pi\)
−0.901376 + 0.433038i \(0.857442\pi\)
\(308\) 0 0
\(309\) 0.345758 0.0196695
\(310\) 0 0
\(311\) −26.1076 −1.48043 −0.740213 0.672373i \(-0.765275\pi\)
−0.740213 + 0.672373i \(0.765275\pi\)
\(312\) 0 0
\(313\) 11.9883 0.677618 0.338809 0.940855i \(-0.389976\pi\)
0.338809 + 0.940855i \(0.389976\pi\)
\(314\) 0 0
\(315\) −3.45343 −0.194579
\(316\) 0 0
\(317\) 11.2848 0.633817 0.316909 0.948456i \(-0.397355\pi\)
0.316909 + 0.948456i \(0.397355\pi\)
\(318\) 0 0
\(319\) 0.331603 0.0185662
\(320\) 0 0
\(321\) −1.08558 −0.0605911
\(322\) 0 0
\(323\) −2.04003 −0.113510
\(324\) 0 0
\(325\) −11.2396 −0.623463
\(326\) 0 0
\(327\) 0.390109 0.0215731
\(328\) 0 0
\(329\) 7.42268 0.409226
\(330\) 0 0
\(331\) −33.5123 −1.84200 −0.921002 0.389558i \(-0.872628\pi\)
−0.921002 + 0.389558i \(0.872628\pi\)
\(332\) 0 0
\(333\) −11.2134 −0.614489
\(334\) 0 0
\(335\) −4.77309 −0.260782
\(336\) 0 0
\(337\) 4.52540 0.246514 0.123257 0.992375i \(-0.460666\pi\)
0.123257 + 0.992375i \(0.460666\pi\)
\(338\) 0 0
\(339\) −0.840875 −0.0456701
\(340\) 0 0
\(341\) 16.2688 0.881006
\(342\) 0 0
\(343\) −18.7912 −1.01463
\(344\) 0 0
\(345\) −0.239404 −0.0128891
\(346\) 0 0
\(347\) −34.4767 −1.85081 −0.925403 0.378985i \(-0.876273\pi\)
−0.925403 + 0.378985i \(0.876273\pi\)
\(348\) 0 0
\(349\) 15.3968 0.824173 0.412086 0.911145i \(-0.364800\pi\)
0.412086 + 0.911145i \(0.364800\pi\)
\(350\) 0 0
\(351\) −1.12253 −0.0599163
\(352\) 0 0
\(353\) −7.39183 −0.393427 −0.196714 0.980461i \(-0.563027\pi\)
−0.196714 + 0.980461i \(0.563027\pi\)
\(354\) 0 0
\(355\) −1.88626 −0.100112
\(356\) 0 0
\(357\) 0.425430 0.0225162
\(358\) 0 0
\(359\) −31.8118 −1.67896 −0.839481 0.543389i \(-0.817141\pi\)
−0.839481 + 0.543389i \(0.817141\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −0.543038 −0.0285021
\(364\) 0 0
\(365\) 1.32653 0.0694335
\(366\) 0 0
\(367\) −2.60800 −0.136136 −0.0680682 0.997681i \(-0.521684\pi\)
−0.0680682 + 0.997681i \(0.521684\pi\)
\(368\) 0 0
\(369\) 15.4778 0.805743
\(370\) 0 0
\(371\) 2.60518 0.135254
\(372\) 0 0
\(373\) 0.546587 0.0283012 0.0141506 0.999900i \(-0.495496\pi\)
0.0141506 + 0.999900i \(0.495496\pi\)
\(374\) 0 0
\(375\) −0.347515 −0.0179456
\(376\) 0 0
\(377\) −0.377848 −0.0194602
\(378\) 0 0
\(379\) −34.5170 −1.77302 −0.886510 0.462709i \(-0.846878\pi\)
−0.886510 + 0.462709i \(0.846878\pi\)
\(380\) 0 0
\(381\) 0.169425 0.00867993
\(382\) 0 0
\(383\) 10.5252 0.537813 0.268906 0.963166i \(-0.413338\pi\)
0.268906 + 0.963166i \(0.413338\pi\)
\(384\) 0 0
\(385\) −2.36874 −0.120722
\(386\) 0 0
\(387\) 12.1923 0.619771
\(388\) 0 0
\(389\) −35.1600 −1.78268 −0.891342 0.453331i \(-0.850236\pi\)
−0.891342 + 0.453331i \(0.850236\pi\)
\(390\) 0 0
\(391\) −13.7782 −0.696795
\(392\) 0 0
\(393\) −0.414216 −0.0208944
\(394\) 0 0
\(395\) 0.787094 0.0396030
\(396\) 0 0
\(397\) −28.6583 −1.43832 −0.719158 0.694846i \(-0.755472\pi\)
−0.719158 + 0.694846i \(0.755472\pi\)
\(398\) 0 0
\(399\) −0.208542 −0.0104401
\(400\) 0 0
\(401\) 32.8079 1.63835 0.819175 0.573544i \(-0.194432\pi\)
0.819175 + 0.573544i \(0.194432\pi\)
\(402\) 0 0
\(403\) −18.5377 −0.923426
\(404\) 0 0
\(405\) 3.95979 0.196764
\(406\) 0 0
\(407\) −7.69134 −0.381245
\(408\) 0 0
\(409\) −16.2118 −0.801620 −0.400810 0.916161i \(-0.631271\pi\)
−0.400810 + 0.916161i \(0.631271\pi\)
\(410\) 0 0
\(411\) 0.927580 0.0457541
\(412\) 0 0
\(413\) 21.5220 1.05903
\(414\) 0 0
\(415\) 5.81670 0.285530
\(416\) 0 0
\(417\) −1.77554 −0.0869485
\(418\) 0 0
\(419\) −14.8854 −0.727200 −0.363600 0.931555i \(-0.618452\pi\)
−0.363600 + 0.931555i \(0.618452\pi\)
\(420\) 0 0
\(421\) 24.6578 1.20175 0.600874 0.799344i \(-0.294819\pi\)
0.600874 + 0.799344i \(0.294819\pi\)
\(422\) 0 0
\(423\) −8.52933 −0.414710
\(424\) 0 0
\(425\) −9.80012 −0.475376
\(426\) 0 0
\(427\) −10.9501 −0.529914
\(428\) 0 0
\(429\) −0.384565 −0.0185670
\(430\) 0 0
\(431\) 37.3628 1.79970 0.899850 0.436199i \(-0.143676\pi\)
0.899850 + 0.436199i \(0.143676\pi\)
\(432\) 0 0
\(433\) 8.55750 0.411247 0.205624 0.978631i \(-0.434078\pi\)
0.205624 + 0.978631i \(0.434078\pi\)
\(434\) 0 0
\(435\) −0.00572446 −0.000274467 0
\(436\) 0 0
\(437\) 6.75394 0.323085
\(438\) 0 0
\(439\) 34.9645 1.66876 0.834382 0.551187i \(-0.185825\pi\)
0.834382 + 0.551187i \(0.185825\pi\)
\(440\) 0 0
\(441\) 0.637685 0.0303660
\(442\) 0 0
\(443\) 22.2168 1.05555 0.527777 0.849383i \(-0.323026\pi\)
0.527777 + 0.849383i \(0.323026\pi\)
\(444\) 0 0
\(445\) −3.68226 −0.174556
\(446\) 0 0
\(447\) 0.893774 0.0422740
\(448\) 0 0
\(449\) 12.2221 0.576795 0.288397 0.957511i \(-0.406878\pi\)
0.288397 + 0.957511i \(0.406878\pi\)
\(450\) 0 0
\(451\) 10.6163 0.499904
\(452\) 0 0
\(453\) −1.75137 −0.0822866
\(454\) 0 0
\(455\) 2.69908 0.126535
\(456\) 0 0
\(457\) 19.3167 0.903597 0.451798 0.892120i \(-0.350783\pi\)
0.451798 + 0.892120i \(0.350783\pi\)
\(458\) 0 0
\(459\) −0.978763 −0.0456847
\(460\) 0 0
\(461\) 7.75002 0.360954 0.180477 0.983579i \(-0.442236\pi\)
0.180477 + 0.983579i \(0.442236\pi\)
\(462\) 0 0
\(463\) −12.6871 −0.589622 −0.294811 0.955556i \(-0.595257\pi\)
−0.294811 + 0.955556i \(0.595257\pi\)
\(464\) 0 0
\(465\) −0.280848 −0.0130240
\(466\) 0 0
\(467\) 9.81309 0.454095 0.227048 0.973884i \(-0.427093\pi\)
0.227048 + 0.973884i \(0.427093\pi\)
\(468\) 0 0
\(469\) −28.0814 −1.29668
\(470\) 0 0
\(471\) −0.573123 −0.0264081
\(472\) 0 0
\(473\) 8.36281 0.384522
\(474\) 0 0
\(475\) 4.80392 0.220419
\(476\) 0 0
\(477\) −2.99359 −0.137067
\(478\) 0 0
\(479\) −29.7465 −1.35915 −0.679576 0.733605i \(-0.737836\pi\)
−0.679576 + 0.733605i \(0.737836\pi\)
\(480\) 0 0
\(481\) 8.76396 0.399602
\(482\) 0 0
\(483\) −1.40848 −0.0640879
\(484\) 0 0
\(485\) −5.82098 −0.264317
\(486\) 0 0
\(487\) 20.1548 0.913299 0.456650 0.889647i \(-0.349049\pi\)
0.456650 + 0.889647i \(0.349049\pi\)
\(488\) 0 0
\(489\) 1.37424 0.0621454
\(490\) 0 0
\(491\) −25.9467 −1.17096 −0.585480 0.810687i \(-0.699094\pi\)
−0.585480 + 0.810687i \(0.699094\pi\)
\(492\) 0 0
\(493\) −0.329455 −0.0148379
\(494\) 0 0
\(495\) 2.72189 0.122340
\(496\) 0 0
\(497\) −11.0973 −0.497784
\(498\) 0 0
\(499\) 41.1611 1.84262 0.921312 0.388823i \(-0.127118\pi\)
0.921312 + 0.388823i \(0.127118\pi\)
\(500\) 0 0
\(501\) 1.38327 0.0617997
\(502\) 0 0
\(503\) −0.0598213 −0.00266730 −0.00133365 0.999999i \(-0.500425\pi\)
−0.00133365 + 0.999999i \(0.500425\pi\)
\(504\) 0 0
\(505\) 0.00762684 0.000339390 0
\(506\) 0 0
\(507\) −0.602437 −0.0267552
\(508\) 0 0
\(509\) 40.9387 1.81458 0.907289 0.420508i \(-0.138148\pi\)
0.907289 + 0.420508i \(0.138148\pi\)
\(510\) 0 0
\(511\) 7.80430 0.345242
\(512\) 0 0
\(513\) 0.479779 0.0211828
\(514\) 0 0
\(515\) 1.91266 0.0842820
\(516\) 0 0
\(517\) −5.85033 −0.257297
\(518\) 0 0
\(519\) 1.05533 0.0463237
\(520\) 0 0
\(521\) 41.3009 1.80943 0.904714 0.426021i \(-0.140085\pi\)
0.904714 + 0.426021i \(0.140085\pi\)
\(522\) 0 0
\(523\) −2.06733 −0.0903981 −0.0451991 0.998978i \(-0.514392\pi\)
−0.0451991 + 0.998978i \(0.514392\pi\)
\(524\) 0 0
\(525\) −1.00182 −0.0437228
\(526\) 0 0
\(527\) −16.1634 −0.704090
\(528\) 0 0
\(529\) 22.6157 0.983293
\(530\) 0 0
\(531\) −24.7307 −1.07322
\(532\) 0 0
\(533\) −12.0969 −0.523975
\(534\) 0 0
\(535\) −6.00520 −0.259627
\(536\) 0 0
\(537\) 0.400893 0.0172998
\(538\) 0 0
\(539\) 0.437393 0.0188399
\(540\) 0 0
\(541\) −24.6525 −1.05989 −0.529946 0.848031i \(-0.677788\pi\)
−0.529946 + 0.848031i \(0.677788\pi\)
\(542\) 0 0
\(543\) 0.172270 0.00739282
\(544\) 0 0
\(545\) 2.15800 0.0924387
\(546\) 0 0
\(547\) −15.6190 −0.667819 −0.333909 0.942605i \(-0.608368\pi\)
−0.333909 + 0.942605i \(0.608368\pi\)
\(548\) 0 0
\(549\) 12.5827 0.537016
\(550\) 0 0
\(551\) 0.161496 0.00687994
\(552\) 0 0
\(553\) 4.63068 0.196917
\(554\) 0 0
\(555\) 0.132775 0.00563600
\(556\) 0 0
\(557\) 28.0983 1.19056 0.595281 0.803518i \(-0.297041\pi\)
0.595281 + 0.803518i \(0.297041\pi\)
\(558\) 0 0
\(559\) −9.52908 −0.403037
\(560\) 0 0
\(561\) −0.335311 −0.0141569
\(562\) 0 0
\(563\) 1.62749 0.0685904 0.0342952 0.999412i \(-0.489081\pi\)
0.0342952 + 0.999412i \(0.489081\pi\)
\(564\) 0 0
\(565\) −4.65155 −0.195692
\(566\) 0 0
\(567\) 23.2965 0.978362
\(568\) 0 0
\(569\) −26.9361 −1.12922 −0.564610 0.825358i \(-0.690973\pi\)
−0.564610 + 0.825358i \(0.690973\pi\)
\(570\) 0 0
\(571\) −39.2736 −1.64355 −0.821775 0.569811i \(-0.807016\pi\)
−0.821775 + 0.569811i \(0.807016\pi\)
\(572\) 0 0
\(573\) 1.75880 0.0734748
\(574\) 0 0
\(575\) 32.4454 1.35307
\(576\) 0 0
\(577\) 14.9871 0.623923 0.311961 0.950095i \(-0.399014\pi\)
0.311961 + 0.950095i \(0.399014\pi\)
\(578\) 0 0
\(579\) 0.303076 0.0125954
\(580\) 0 0
\(581\) 34.2212 1.41973
\(582\) 0 0
\(583\) −2.05333 −0.0850401
\(584\) 0 0
\(585\) −3.10148 −0.128231
\(586\) 0 0
\(587\) 38.9297 1.60680 0.803400 0.595439i \(-0.203022\pi\)
0.803400 + 0.595439i \(0.203022\pi\)
\(588\) 0 0
\(589\) 7.92315 0.326468
\(590\) 0 0
\(591\) 0.564716 0.0232293
\(592\) 0 0
\(593\) −23.6009 −0.969174 −0.484587 0.874743i \(-0.661030\pi\)
−0.484587 + 0.874743i \(0.661030\pi\)
\(594\) 0 0
\(595\) 2.35339 0.0964797
\(596\) 0 0
\(597\) −1.38238 −0.0565769
\(598\) 0 0
\(599\) −36.9916 −1.51144 −0.755718 0.654897i \(-0.772712\pi\)
−0.755718 + 0.654897i \(0.772712\pi\)
\(600\) 0 0
\(601\) 39.7323 1.62071 0.810357 0.585936i \(-0.199273\pi\)
0.810357 + 0.585936i \(0.199273\pi\)
\(602\) 0 0
\(603\) 32.2680 1.31406
\(604\) 0 0
\(605\) −3.00397 −0.122129
\(606\) 0 0
\(607\) 42.9832 1.74464 0.872318 0.488939i \(-0.162616\pi\)
0.872318 + 0.488939i \(0.162616\pi\)
\(608\) 0 0
\(609\) −0.0336785 −0.00136472
\(610\) 0 0
\(611\) 6.66622 0.269686
\(612\) 0 0
\(613\) 20.2633 0.818428 0.409214 0.912438i \(-0.365803\pi\)
0.409214 + 0.912438i \(0.365803\pi\)
\(614\) 0 0
\(615\) −0.183270 −0.00739015
\(616\) 0 0
\(617\) 43.4290 1.74839 0.874193 0.485579i \(-0.161391\pi\)
0.874193 + 0.485579i \(0.161391\pi\)
\(618\) 0 0
\(619\) −28.6938 −1.15330 −0.576651 0.816991i \(-0.695641\pi\)
−0.576651 + 0.816991i \(0.695641\pi\)
\(620\) 0 0
\(621\) 3.24040 0.130033
\(622\) 0 0
\(623\) −21.6637 −0.867938
\(624\) 0 0
\(625\) 22.0972 0.883888
\(626\) 0 0
\(627\) 0.164366 0.00656415
\(628\) 0 0
\(629\) 7.64152 0.304687
\(630\) 0 0
\(631\) 34.0787 1.35665 0.678326 0.734761i \(-0.262706\pi\)
0.678326 + 0.734761i \(0.262706\pi\)
\(632\) 0 0
\(633\) −1.88575 −0.0749520
\(634\) 0 0
\(635\) 0.937226 0.0371927
\(636\) 0 0
\(637\) −0.498392 −0.0197470
\(638\) 0 0
\(639\) 12.7519 0.504456
\(640\) 0 0
\(641\) 49.8468 1.96883 0.984414 0.175864i \(-0.0562720\pi\)
0.984414 + 0.175864i \(0.0562720\pi\)
\(642\) 0 0
\(643\) −35.7487 −1.40979 −0.704896 0.709311i \(-0.749006\pi\)
−0.704896 + 0.709311i \(0.749006\pi\)
\(644\) 0 0
\(645\) −0.144367 −0.00568445
\(646\) 0 0
\(647\) −26.6225 −1.04664 −0.523319 0.852137i \(-0.675307\pi\)
−0.523319 + 0.852137i \(0.675307\pi\)
\(648\) 0 0
\(649\) −16.9630 −0.665855
\(650\) 0 0
\(651\) −1.65231 −0.0647589
\(652\) 0 0
\(653\) −16.5839 −0.648977 −0.324488 0.945890i \(-0.605192\pi\)
−0.324488 + 0.945890i \(0.605192\pi\)
\(654\) 0 0
\(655\) −2.29136 −0.0895307
\(656\) 0 0
\(657\) −8.96785 −0.349869
\(658\) 0 0
\(659\) 19.7302 0.768580 0.384290 0.923212i \(-0.374446\pi\)
0.384290 + 0.923212i \(0.374446\pi\)
\(660\) 0 0
\(661\) 24.3031 0.945283 0.472641 0.881255i \(-0.343301\pi\)
0.472641 + 0.881255i \(0.343301\pi\)
\(662\) 0 0
\(663\) 0.382074 0.0148385
\(664\) 0 0
\(665\) −1.15361 −0.0447350
\(666\) 0 0
\(667\) 1.09073 0.0422333
\(668\) 0 0
\(669\) 1.38326 0.0534798
\(670\) 0 0
\(671\) 8.63056 0.333179
\(672\) 0 0
\(673\) −8.92628 −0.344083 −0.172041 0.985090i \(-0.555036\pi\)
−0.172041 + 0.985090i \(0.555036\pi\)
\(674\) 0 0
\(675\) 2.30482 0.0887125
\(676\) 0 0
\(677\) −26.3563 −1.01295 −0.506477 0.862254i \(-0.669052\pi\)
−0.506477 + 0.862254i \(0.669052\pi\)
\(678\) 0 0
\(679\) −34.2463 −1.31425
\(680\) 0 0
\(681\) −0.0142111 −0.000544569 0
\(682\) 0 0
\(683\) 4.89120 0.187157 0.0935783 0.995612i \(-0.470169\pi\)
0.0935783 + 0.995612i \(0.470169\pi\)
\(684\) 0 0
\(685\) 5.13118 0.196052
\(686\) 0 0
\(687\) −0.947488 −0.0361489
\(688\) 0 0
\(689\) 2.33968 0.0891348
\(690\) 0 0
\(691\) 18.2422 0.693965 0.346982 0.937872i \(-0.387206\pi\)
0.346982 + 0.937872i \(0.387206\pi\)
\(692\) 0 0
\(693\) 16.0136 0.608307
\(694\) 0 0
\(695\) −9.82191 −0.372566
\(696\) 0 0
\(697\) −10.5476 −0.399518
\(698\) 0 0
\(699\) 1.72166 0.0651190
\(700\) 0 0
\(701\) 33.4734 1.26427 0.632136 0.774857i \(-0.282178\pi\)
0.632136 + 0.774857i \(0.282178\pi\)
\(702\) 0 0
\(703\) −3.74579 −0.141275
\(704\) 0 0
\(705\) 0.100994 0.00380366
\(706\) 0 0
\(707\) 0.0448707 0.00168754
\(708\) 0 0
\(709\) 7.77292 0.291918 0.145959 0.989291i \(-0.453373\pi\)
0.145959 + 0.989291i \(0.453373\pi\)
\(710\) 0 0
\(711\) −5.32108 −0.199556
\(712\) 0 0
\(713\) 53.5125 2.00406
\(714\) 0 0
\(715\) −2.12733 −0.0795577
\(716\) 0 0
\(717\) −0.702947 −0.0262520
\(718\) 0 0
\(719\) −6.23898 −0.232675 −0.116337 0.993210i \(-0.537115\pi\)
−0.116337 + 0.993210i \(0.537115\pi\)
\(720\) 0 0
\(721\) 11.2527 0.419072
\(722\) 0 0
\(723\) −1.69859 −0.0631711
\(724\) 0 0
\(725\) 0.775811 0.0288129
\(726\) 0 0
\(727\) 14.6584 0.543651 0.271826 0.962347i \(-0.412373\pi\)
0.271826 + 0.962347i \(0.412373\pi\)
\(728\) 0 0
\(729\) −26.6546 −0.987207
\(730\) 0 0
\(731\) −8.30864 −0.307306
\(732\) 0 0
\(733\) 6.06986 0.224195 0.112098 0.993697i \(-0.464243\pi\)
0.112098 + 0.993697i \(0.464243\pi\)
\(734\) 0 0
\(735\) −0.00755071 −0.000278512 0
\(736\) 0 0
\(737\) 22.1329 0.815275
\(738\) 0 0
\(739\) 4.49102 0.165205 0.0826025 0.996583i \(-0.473677\pi\)
0.0826025 + 0.996583i \(0.473677\pi\)
\(740\) 0 0
\(741\) −0.187289 −0.00688022
\(742\) 0 0
\(743\) −10.7290 −0.393607 −0.196804 0.980443i \(-0.563056\pi\)
−0.196804 + 0.980443i \(0.563056\pi\)
\(744\) 0 0
\(745\) 4.94417 0.181140
\(746\) 0 0
\(747\) −39.3232 −1.43876
\(748\) 0 0
\(749\) −35.3302 −1.29094
\(750\) 0 0
\(751\) 48.8939 1.78416 0.892081 0.451875i \(-0.149245\pi\)
0.892081 + 0.451875i \(0.149245\pi\)
\(752\) 0 0
\(753\) −2.44556 −0.0891213
\(754\) 0 0
\(755\) −9.68822 −0.352591
\(756\) 0 0
\(757\) −11.7495 −0.427041 −0.213521 0.976939i \(-0.568493\pi\)
−0.213521 + 0.976939i \(0.568493\pi\)
\(758\) 0 0
\(759\) 1.11012 0.0402948
\(760\) 0 0
\(761\) −9.70454 −0.351789 −0.175895 0.984409i \(-0.556282\pi\)
−0.175895 + 0.984409i \(0.556282\pi\)
\(762\) 0 0
\(763\) 12.6961 0.459630
\(764\) 0 0
\(765\) −2.70426 −0.0977728
\(766\) 0 0
\(767\) 19.3286 0.697916
\(768\) 0 0
\(769\) −14.8869 −0.536834 −0.268417 0.963303i \(-0.586500\pi\)
−0.268417 + 0.963303i \(0.586500\pi\)
\(770\) 0 0
\(771\) −0.904114 −0.0325609
\(772\) 0 0
\(773\) −2.74773 −0.0988289 −0.0494145 0.998778i \(-0.515736\pi\)
−0.0494145 + 0.998778i \(0.515736\pi\)
\(774\) 0 0
\(775\) 38.0621 1.36723
\(776\) 0 0
\(777\) 0.781153 0.0280237
\(778\) 0 0
\(779\) 5.17031 0.185246
\(780\) 0 0
\(781\) 8.74660 0.312978
\(782\) 0 0
\(783\) 0.0774822 0.00276899
\(784\) 0 0
\(785\) −3.17040 −0.113156
\(786\) 0 0
\(787\) −4.24788 −0.151421 −0.0757103 0.997130i \(-0.524122\pi\)
−0.0757103 + 0.997130i \(0.524122\pi\)
\(788\) 0 0
\(789\) −0.00620377 −0.000220860 0
\(790\) 0 0
\(791\) −27.3663 −0.973033
\(792\) 0 0
\(793\) −9.83417 −0.349222
\(794\) 0 0
\(795\) 0.0354466 0.00125716
\(796\) 0 0
\(797\) 3.42079 0.121171 0.0605854 0.998163i \(-0.480703\pi\)
0.0605854 + 0.998163i \(0.480703\pi\)
\(798\) 0 0
\(799\) 5.81244 0.205629
\(800\) 0 0
\(801\) 24.8936 0.879571
\(802\) 0 0
\(803\) −6.15111 −0.217068
\(804\) 0 0
\(805\) −7.79140 −0.274611
\(806\) 0 0
\(807\) −1.72878 −0.0608560
\(808\) 0 0
\(809\) 20.2668 0.712543 0.356272 0.934382i \(-0.384048\pi\)
0.356272 + 0.934382i \(0.384048\pi\)
\(810\) 0 0
\(811\) −16.6631 −0.585121 −0.292561 0.956247i \(-0.594507\pi\)
−0.292561 + 0.956247i \(0.594507\pi\)
\(812\) 0 0
\(813\) 0.482829 0.0169335
\(814\) 0 0
\(815\) 7.60202 0.266287
\(816\) 0 0
\(817\) 4.07281 0.142489
\(818\) 0 0
\(819\) −18.2469 −0.637597
\(820\) 0 0
\(821\) 40.5886 1.41655 0.708277 0.705935i \(-0.249473\pi\)
0.708277 + 0.705935i \(0.249473\pi\)
\(822\) 0 0
\(823\) 28.3801 0.989267 0.494634 0.869102i \(-0.335302\pi\)
0.494634 + 0.869102i \(0.335302\pi\)
\(824\) 0 0
\(825\) 0.789601 0.0274904
\(826\) 0 0
\(827\) −38.6329 −1.34340 −0.671699 0.740824i \(-0.734435\pi\)
−0.671699 + 0.740824i \(0.734435\pi\)
\(828\) 0 0
\(829\) −24.0546 −0.835449 −0.417725 0.908574i \(-0.637172\pi\)
−0.417725 + 0.908574i \(0.637172\pi\)
\(830\) 0 0
\(831\) 2.22161 0.0770669
\(832\) 0 0
\(833\) −0.434560 −0.0150566
\(834\) 0 0
\(835\) 7.65194 0.264806
\(836\) 0 0
\(837\) 3.80136 0.131394
\(838\) 0 0
\(839\) −12.5322 −0.432660 −0.216330 0.976320i \(-0.569409\pi\)
−0.216330 + 0.976320i \(0.569409\pi\)
\(840\) 0 0
\(841\) −28.9739 −0.999101
\(842\) 0 0
\(843\) 0.997871 0.0343685
\(844\) 0 0
\(845\) −3.33256 −0.114643
\(846\) 0 0
\(847\) −17.6732 −0.607257
\(848\) 0 0
\(849\) 2.29029 0.0786024
\(850\) 0 0
\(851\) −25.2989 −0.867234
\(852\) 0 0
\(853\) 18.0175 0.616908 0.308454 0.951239i \(-0.400188\pi\)
0.308454 + 0.951239i \(0.400188\pi\)
\(854\) 0 0
\(855\) 1.32560 0.0453346
\(856\) 0 0
\(857\) −27.4522 −0.937748 −0.468874 0.883265i \(-0.655340\pi\)
−0.468874 + 0.883265i \(0.655340\pi\)
\(858\) 0 0
\(859\) 35.8818 1.22427 0.612136 0.790753i \(-0.290311\pi\)
0.612136 + 0.790753i \(0.290311\pi\)
\(860\) 0 0
\(861\) −1.07823 −0.0367458
\(862\) 0 0
\(863\) 35.0943 1.19463 0.597313 0.802008i \(-0.296235\pi\)
0.597313 + 0.802008i \(0.296235\pi\)
\(864\) 0 0
\(865\) 5.83785 0.198493
\(866\) 0 0
\(867\) −1.02769 −0.0349021
\(868\) 0 0
\(869\) −3.64977 −0.123810
\(870\) 0 0
\(871\) −25.2195 −0.854531
\(872\) 0 0
\(873\) 39.3522 1.33187
\(874\) 0 0
\(875\) −11.3099 −0.382344
\(876\) 0 0
\(877\) 32.5063 1.09766 0.548829 0.835934i \(-0.315074\pi\)
0.548829 + 0.835934i \(0.315074\pi\)
\(878\) 0 0
\(879\) 0.0989537 0.00333763
\(880\) 0 0
\(881\) −28.6801 −0.966259 −0.483129 0.875549i \(-0.660500\pi\)
−0.483129 + 0.875549i \(0.660500\pi\)
\(882\) 0 0
\(883\) −6.16251 −0.207385 −0.103692 0.994609i \(-0.533066\pi\)
−0.103692 + 0.994609i \(0.533066\pi\)
\(884\) 0 0
\(885\) 0.292832 0.00984343
\(886\) 0 0
\(887\) 0.262178 0.00880309 0.00440154 0.999990i \(-0.498599\pi\)
0.00440154 + 0.999990i \(0.498599\pi\)
\(888\) 0 0
\(889\) 5.51395 0.184932
\(890\) 0 0
\(891\) −18.3616 −0.615137
\(892\) 0 0
\(893\) −2.84920 −0.0953447
\(894\) 0 0
\(895\) 2.21765 0.0741280
\(896\) 0 0
\(897\) −1.26494 −0.0422350
\(898\) 0 0
\(899\) 1.27955 0.0426755
\(900\) 0 0
\(901\) 2.04003 0.0679632
\(902\) 0 0
\(903\) −0.849349 −0.0282646
\(904\) 0 0
\(905\) 0.952963 0.0316775
\(906\) 0 0
\(907\) 38.5866 1.28125 0.640624 0.767855i \(-0.278676\pi\)
0.640624 + 0.767855i \(0.278676\pi\)
\(908\) 0 0
\(909\) −0.0515605 −0.00171015
\(910\) 0 0
\(911\) 11.7598 0.389619 0.194810 0.980841i \(-0.437591\pi\)
0.194810 + 0.980841i \(0.437591\pi\)
\(912\) 0 0
\(913\) −26.9721 −0.892646
\(914\) 0 0
\(915\) −0.148989 −0.00492543
\(916\) 0 0
\(917\) −13.4807 −0.445170
\(918\) 0 0
\(919\) −11.4742 −0.378500 −0.189250 0.981929i \(-0.560606\pi\)
−0.189250 + 0.981929i \(0.560606\pi\)
\(920\) 0 0
\(921\) −2.52848 −0.0833162
\(922\) 0 0
\(923\) −9.96639 −0.328048
\(924\) 0 0
\(925\) −17.9945 −0.591655
\(926\) 0 0
\(927\) −12.9304 −0.424689
\(928\) 0 0
\(929\) 26.1220 0.857035 0.428517 0.903534i \(-0.359036\pi\)
0.428517 + 0.903534i \(0.359036\pi\)
\(930\) 0 0
\(931\) 0.213017 0.00698134
\(932\) 0 0
\(933\) −2.08988 −0.0684195
\(934\) 0 0
\(935\) −1.85487 −0.0606608
\(936\) 0 0
\(937\) 3.58835 0.117226 0.0586131 0.998281i \(-0.481332\pi\)
0.0586131 + 0.998281i \(0.481332\pi\)
\(938\) 0 0
\(939\) 0.959646 0.0313169
\(940\) 0 0
\(941\) −55.1725 −1.79857 −0.899287 0.437359i \(-0.855914\pi\)
−0.899287 + 0.437359i \(0.855914\pi\)
\(942\) 0 0
\(943\) 34.9200 1.13715
\(944\) 0 0
\(945\) −0.553477 −0.0180046
\(946\) 0 0
\(947\) 26.9388 0.875393 0.437697 0.899123i \(-0.355794\pi\)
0.437697 + 0.899123i \(0.355794\pi\)
\(948\) 0 0
\(949\) 7.00894 0.227520
\(950\) 0 0
\(951\) 0.903333 0.0292926
\(952\) 0 0
\(953\) −41.4776 −1.34359 −0.671796 0.740737i \(-0.734477\pi\)
−0.671796 + 0.740737i \(0.734477\pi\)
\(954\) 0 0
\(955\) 9.72930 0.314833
\(956\) 0 0
\(957\) 0.0265444 0.000858059 0
\(958\) 0 0
\(959\) 30.1881 0.974824
\(960\) 0 0
\(961\) 31.7763 1.02504
\(962\) 0 0
\(963\) 40.5975 1.30824
\(964\) 0 0
\(965\) 1.67655 0.0539701
\(966\) 0 0
\(967\) −32.2835 −1.03817 −0.519084 0.854723i \(-0.673727\pi\)
−0.519084 + 0.854723i \(0.673727\pi\)
\(968\) 0 0
\(969\) −0.163302 −0.00524600
\(970\) 0 0
\(971\) 1.53014 0.0491045 0.0245522 0.999699i \(-0.492184\pi\)
0.0245522 + 0.999699i \(0.492184\pi\)
\(972\) 0 0
\(973\) −57.7849 −1.85250
\(974\) 0 0
\(975\) −0.899719 −0.0288141
\(976\) 0 0
\(977\) 46.5952 1.49071 0.745357 0.666666i \(-0.232279\pi\)
0.745357 + 0.666666i \(0.232279\pi\)
\(978\) 0 0
\(979\) 17.0747 0.545709
\(980\) 0 0
\(981\) −14.5890 −0.465790
\(982\) 0 0
\(983\) 20.0055 0.638076 0.319038 0.947742i \(-0.396640\pi\)
0.319038 + 0.947742i \(0.396640\pi\)
\(984\) 0 0
\(985\) 3.12389 0.0995354
\(986\) 0 0
\(987\) 0.594176 0.0189128
\(988\) 0 0
\(989\) 27.5075 0.874688
\(990\) 0 0
\(991\) 8.00418 0.254261 0.127131 0.991886i \(-0.459423\pi\)
0.127131 + 0.991886i \(0.459423\pi\)
\(992\) 0 0
\(993\) −2.68262 −0.0851303
\(994\) 0 0
\(995\) −7.64702 −0.242427
\(996\) 0 0
\(997\) −3.35634 −0.106296 −0.0531482 0.998587i \(-0.516926\pi\)
−0.0531482 + 0.998587i \(0.516926\pi\)
\(998\) 0 0
\(999\) −1.79715 −0.0568594
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 \(a_p\))