Properties

Label 8004.2.a.j.1.5
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.86734\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.86734 q^{5}\) \(-4.84365 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.86734 q^{5}\) \(-4.84365 q^{7}\) \(+1.00000 q^{9}\) \(-4.93713 q^{11}\) \(+2.86190 q^{13}\) \(-1.86734 q^{15}\) \(+3.10878 q^{17}\) \(-1.94897 q^{19}\) \(-4.84365 q^{21}\) \(+1.00000 q^{23}\) \(-1.51304 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-5.41813 q^{31}\) \(-4.93713 q^{33}\) \(+9.04474 q^{35}\) \(-6.81511 q^{37}\) \(+2.86190 q^{39}\) \(+10.1828 q^{41}\) \(-3.21385 q^{43}\) \(-1.86734 q^{45}\) \(-12.3322 q^{47}\) \(+16.4610 q^{49}\) \(+3.10878 q^{51}\) \(-13.4625 q^{53}\) \(+9.21930 q^{55}\) \(-1.94897 q^{57}\) \(+1.37852 q^{59}\) \(-5.44631 q^{61}\) \(-4.84365 q^{63}\) \(-5.34413 q^{65}\) \(-4.14327 q^{67}\) \(+1.00000 q^{69}\) \(-10.2781 q^{71}\) \(-4.90515 q^{73}\) \(-1.51304 q^{75}\) \(+23.9138 q^{77}\) \(+10.3997 q^{79}\) \(+1.00000 q^{81}\) \(+13.7262 q^{83}\) \(-5.80514 q^{85}\) \(-1.00000 q^{87}\) \(-1.89306 q^{89}\) \(-13.8620 q^{91}\) \(-5.41813 q^{93}\) \(+3.63939 q^{95}\) \(+6.06388 q^{97}\) \(-4.93713 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.86734 −0.835100 −0.417550 0.908654i \(-0.637111\pi\)
−0.417550 + 0.908654i \(0.637111\pi\)
\(6\) 0 0
\(7\) −4.84365 −1.83073 −0.915364 0.402627i \(-0.868097\pi\)
−0.915364 + 0.402627i \(0.868097\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.93713 −1.48860 −0.744301 0.667844i \(-0.767217\pi\)
−0.744301 + 0.667844i \(0.767217\pi\)
\(12\) 0 0
\(13\) 2.86190 0.793747 0.396873 0.917873i \(-0.370095\pi\)
0.396873 + 0.917873i \(0.370095\pi\)
\(14\) 0 0
\(15\) −1.86734 −0.482145
\(16\) 0 0
\(17\) 3.10878 0.753989 0.376995 0.926215i \(-0.376958\pi\)
0.376995 + 0.926215i \(0.376958\pi\)
\(18\) 0 0
\(19\) −1.94897 −0.447124 −0.223562 0.974690i \(-0.571769\pi\)
−0.223562 + 0.974690i \(0.571769\pi\)
\(20\) 0 0
\(21\) −4.84365 −1.05697
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −1.51304 −0.302609
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −5.41813 −0.973126 −0.486563 0.873646i \(-0.661750\pi\)
−0.486563 + 0.873646i \(0.661750\pi\)
\(32\) 0 0
\(33\) −4.93713 −0.859445
\(34\) 0 0
\(35\) 9.04474 1.52884
\(36\) 0 0
\(37\) −6.81511 −1.12040 −0.560198 0.828358i \(-0.689275\pi\)
−0.560198 + 0.828358i \(0.689275\pi\)
\(38\) 0 0
\(39\) 2.86190 0.458270
\(40\) 0 0
\(41\) 10.1828 1.59029 0.795145 0.606420i \(-0.207395\pi\)
0.795145 + 0.606420i \(0.207395\pi\)
\(42\) 0 0
\(43\) −3.21385 −0.490108 −0.245054 0.969509i \(-0.578806\pi\)
−0.245054 + 0.969509i \(0.578806\pi\)
\(44\) 0 0
\(45\) −1.86734 −0.278367
\(46\) 0 0
\(47\) −12.3322 −1.79884 −0.899420 0.437085i \(-0.856011\pi\)
−0.899420 + 0.437085i \(0.856011\pi\)
\(48\) 0 0
\(49\) 16.4610 2.35157
\(50\) 0 0
\(51\) 3.10878 0.435316
\(52\) 0 0
\(53\) −13.4625 −1.84922 −0.924610 0.380915i \(-0.875609\pi\)
−0.924610 + 0.380915i \(0.875609\pi\)
\(54\) 0 0
\(55\) 9.21930 1.24313
\(56\) 0 0
\(57\) −1.94897 −0.258147
\(58\) 0 0
\(59\) 1.37852 0.179468 0.0897342 0.995966i \(-0.471398\pi\)
0.0897342 + 0.995966i \(0.471398\pi\)
\(60\) 0 0
\(61\) −5.44631 −0.697329 −0.348664 0.937248i \(-0.613365\pi\)
−0.348664 + 0.937248i \(0.613365\pi\)
\(62\) 0 0
\(63\) −4.84365 −0.610243
\(64\) 0 0
\(65\) −5.34413 −0.662858
\(66\) 0 0
\(67\) −4.14327 −0.506181 −0.253090 0.967443i \(-0.581447\pi\)
−0.253090 + 0.967443i \(0.581447\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −10.2781 −1.21979 −0.609895 0.792482i \(-0.708788\pi\)
−0.609895 + 0.792482i \(0.708788\pi\)
\(72\) 0 0
\(73\) −4.90515 −0.574105 −0.287052 0.957915i \(-0.592675\pi\)
−0.287052 + 0.957915i \(0.592675\pi\)
\(74\) 0 0
\(75\) −1.51304 −0.174711
\(76\) 0 0
\(77\) 23.9138 2.72523
\(78\) 0 0
\(79\) 10.3997 1.17006 0.585029 0.811013i \(-0.301083\pi\)
0.585029 + 0.811013i \(0.301083\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 13.7262 1.50665 0.753324 0.657649i \(-0.228449\pi\)
0.753324 + 0.657649i \(0.228449\pi\)
\(84\) 0 0
\(85\) −5.80514 −0.629656
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −1.89306 −0.200664 −0.100332 0.994954i \(-0.531991\pi\)
−0.100332 + 0.994954i \(0.531991\pi\)
\(90\) 0 0
\(91\) −13.8620 −1.45313
\(92\) 0 0
\(93\) −5.41813 −0.561834
\(94\) 0 0
\(95\) 3.63939 0.373393
\(96\) 0 0
\(97\) 6.06388 0.615693 0.307847 0.951436i \(-0.400392\pi\)
0.307847 + 0.951436i \(0.400392\pi\)
\(98\) 0 0
\(99\) −4.93713 −0.496201
\(100\) 0 0
\(101\) 7.91628 0.787699 0.393850 0.919175i \(-0.371143\pi\)
0.393850 + 0.919175i \(0.371143\pi\)
\(102\) 0 0
\(103\) 9.03978 0.890716 0.445358 0.895353i \(-0.353076\pi\)
0.445358 + 0.895353i \(0.353076\pi\)
\(104\) 0 0
\(105\) 9.04474 0.882676
\(106\) 0 0
\(107\) −9.79071 −0.946504 −0.473252 0.880927i \(-0.656920\pi\)
−0.473252 + 0.880927i \(0.656920\pi\)
\(108\) 0 0
\(109\) 14.4248 1.38164 0.690822 0.723025i \(-0.257249\pi\)
0.690822 + 0.723025i \(0.257249\pi\)
\(110\) 0 0
\(111\) −6.81511 −0.646861
\(112\) 0 0
\(113\) 6.00311 0.564725 0.282363 0.959308i \(-0.408882\pi\)
0.282363 + 0.959308i \(0.408882\pi\)
\(114\) 0 0
\(115\) −1.86734 −0.174130
\(116\) 0 0
\(117\) 2.86190 0.264582
\(118\) 0 0
\(119\) −15.0578 −1.38035
\(120\) 0 0
\(121\) 13.3753 1.21594
\(122\) 0 0
\(123\) 10.1828 0.918154
\(124\) 0 0
\(125\) 12.1621 1.08781
\(126\) 0 0
\(127\) −4.05286 −0.359633 −0.179816 0.983700i \(-0.557550\pi\)
−0.179816 + 0.983700i \(0.557550\pi\)
\(128\) 0 0
\(129\) −3.21385 −0.282964
\(130\) 0 0
\(131\) 3.69396 0.322742 0.161371 0.986894i \(-0.448408\pi\)
0.161371 + 0.986894i \(0.448408\pi\)
\(132\) 0 0
\(133\) 9.44013 0.818563
\(134\) 0 0
\(135\) −1.86734 −0.160715
\(136\) 0 0
\(137\) −14.8480 −1.26855 −0.634274 0.773109i \(-0.718701\pi\)
−0.634274 + 0.773109i \(0.718701\pi\)
\(138\) 0 0
\(139\) −0.753509 −0.0639118 −0.0319559 0.999489i \(-0.510174\pi\)
−0.0319559 + 0.999489i \(0.510174\pi\)
\(140\) 0 0
\(141\) −12.3322 −1.03856
\(142\) 0 0
\(143\) −14.1296 −1.18157
\(144\) 0 0
\(145\) 1.86734 0.155074
\(146\) 0 0
\(147\) 16.4610 1.35768
\(148\) 0 0
\(149\) 19.0823 1.56328 0.781641 0.623729i \(-0.214383\pi\)
0.781641 + 0.623729i \(0.214383\pi\)
\(150\) 0 0
\(151\) 11.9551 0.972895 0.486448 0.873710i \(-0.338292\pi\)
0.486448 + 0.873710i \(0.338292\pi\)
\(152\) 0 0
\(153\) 3.10878 0.251330
\(154\) 0 0
\(155\) 10.1175 0.812657
\(156\) 0 0
\(157\) 0.855906 0.0683088 0.0341544 0.999417i \(-0.489126\pi\)
0.0341544 + 0.999417i \(0.489126\pi\)
\(158\) 0 0
\(159\) −13.4625 −1.06765
\(160\) 0 0
\(161\) −4.84365 −0.381733
\(162\) 0 0
\(163\) 18.9613 1.48516 0.742580 0.669757i \(-0.233602\pi\)
0.742580 + 0.669757i \(0.233602\pi\)
\(164\) 0 0
\(165\) 9.21930 0.717722
\(166\) 0 0
\(167\) −16.5645 −1.28180 −0.640900 0.767625i \(-0.721439\pi\)
−0.640900 + 0.767625i \(0.721439\pi\)
\(168\) 0 0
\(169\) −4.80956 −0.369966
\(170\) 0 0
\(171\) −1.94897 −0.149041
\(172\) 0 0
\(173\) 23.8644 1.81438 0.907189 0.420723i \(-0.138224\pi\)
0.907189 + 0.420723i \(0.138224\pi\)
\(174\) 0 0
\(175\) 7.32865 0.553994
\(176\) 0 0
\(177\) 1.37852 0.103616
\(178\) 0 0
\(179\) 12.2293 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(180\) 0 0
\(181\) 11.6427 0.865393 0.432696 0.901540i \(-0.357562\pi\)
0.432696 + 0.901540i \(0.357562\pi\)
\(182\) 0 0
\(183\) −5.44631 −0.402603
\(184\) 0 0
\(185\) 12.7261 0.935643
\(186\) 0 0
\(187\) −15.3484 −1.12239
\(188\) 0 0
\(189\) −4.84365 −0.352324
\(190\) 0 0
\(191\) −22.9093 −1.65766 −0.828829 0.559502i \(-0.810992\pi\)
−0.828829 + 0.559502i \(0.810992\pi\)
\(192\) 0 0
\(193\) 19.0630 1.37219 0.686094 0.727513i \(-0.259324\pi\)
0.686094 + 0.727513i \(0.259324\pi\)
\(194\) 0 0
\(195\) −5.34413 −0.382701
\(196\) 0 0
\(197\) −12.4760 −0.888880 −0.444440 0.895809i \(-0.646597\pi\)
−0.444440 + 0.895809i \(0.646597\pi\)
\(198\) 0 0
\(199\) −20.5233 −1.45486 −0.727428 0.686184i \(-0.759284\pi\)
−0.727428 + 0.686184i \(0.759284\pi\)
\(200\) 0 0
\(201\) −4.14327 −0.292244
\(202\) 0 0
\(203\) 4.84365 0.339958
\(204\) 0 0
\(205\) −19.0148 −1.32805
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 9.62233 0.665590
\(210\) 0 0
\(211\) 17.5670 1.20936 0.604682 0.796467i \(-0.293300\pi\)
0.604682 + 0.796467i \(0.293300\pi\)
\(212\) 0 0
\(213\) −10.2781 −0.704246
\(214\) 0 0
\(215\) 6.00136 0.409289
\(216\) 0 0
\(217\) 26.2436 1.78153
\(218\) 0 0
\(219\) −4.90515 −0.331460
\(220\) 0 0
\(221\) 8.89699 0.598477
\(222\) 0 0
\(223\) 14.8503 0.994451 0.497225 0.867621i \(-0.334352\pi\)
0.497225 + 0.867621i \(0.334352\pi\)
\(224\) 0 0
\(225\) −1.51304 −0.100870
\(226\) 0 0
\(227\) −8.04076 −0.533684 −0.266842 0.963740i \(-0.585980\pi\)
−0.266842 + 0.963740i \(0.585980\pi\)
\(228\) 0 0
\(229\) 12.8993 0.852409 0.426204 0.904627i \(-0.359850\pi\)
0.426204 + 0.904627i \(0.359850\pi\)
\(230\) 0 0
\(231\) 23.9138 1.57341
\(232\) 0 0
\(233\) 24.3045 1.59224 0.796120 0.605138i \(-0.206882\pi\)
0.796120 + 0.605138i \(0.206882\pi\)
\(234\) 0 0
\(235\) 23.0285 1.50221
\(236\) 0 0
\(237\) 10.3997 0.675533
\(238\) 0 0
\(239\) −4.62036 −0.298867 −0.149433 0.988772i \(-0.547745\pi\)
−0.149433 + 0.988772i \(0.547745\pi\)
\(240\) 0 0
\(241\) 10.3930 0.669472 0.334736 0.942312i \(-0.391353\pi\)
0.334736 + 0.942312i \(0.391353\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −30.7382 −1.96379
\(246\) 0 0
\(247\) −5.57775 −0.354904
\(248\) 0 0
\(249\) 13.7262 0.869864
\(250\) 0 0
\(251\) 3.33210 0.210320 0.105160 0.994455i \(-0.466464\pi\)
0.105160 + 0.994455i \(0.466464\pi\)
\(252\) 0 0
\(253\) −4.93713 −0.310395
\(254\) 0 0
\(255\) −5.80514 −0.363532
\(256\) 0 0
\(257\) −13.5424 −0.844749 −0.422375 0.906421i \(-0.638803\pi\)
−0.422375 + 0.906421i \(0.638803\pi\)
\(258\) 0 0
\(259\) 33.0100 2.05114
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 23.2268 1.43222 0.716112 0.697986i \(-0.245920\pi\)
0.716112 + 0.697986i \(0.245920\pi\)
\(264\) 0 0
\(265\) 25.1391 1.54428
\(266\) 0 0
\(267\) −1.89306 −0.115854
\(268\) 0 0
\(269\) 16.5605 1.00971 0.504855 0.863204i \(-0.331546\pi\)
0.504855 + 0.863204i \(0.331546\pi\)
\(270\) 0 0
\(271\) 28.2844 1.71815 0.859077 0.511847i \(-0.171038\pi\)
0.859077 + 0.511847i \(0.171038\pi\)
\(272\) 0 0
\(273\) −13.8620 −0.838968
\(274\) 0 0
\(275\) 7.47010 0.450464
\(276\) 0 0
\(277\) 11.3786 0.683675 0.341838 0.939759i \(-0.388951\pi\)
0.341838 + 0.939759i \(0.388951\pi\)
\(278\) 0 0
\(279\) −5.41813 −0.324375
\(280\) 0 0
\(281\) 8.08816 0.482499 0.241249 0.970463i \(-0.422443\pi\)
0.241249 + 0.970463i \(0.422443\pi\)
\(282\) 0 0
\(283\) 7.42987 0.441660 0.220830 0.975312i \(-0.429123\pi\)
0.220830 + 0.975312i \(0.429123\pi\)
\(284\) 0 0
\(285\) 3.63939 0.215579
\(286\) 0 0
\(287\) −49.3220 −2.91139
\(288\) 0 0
\(289\) −7.33551 −0.431500
\(290\) 0 0
\(291\) 6.06388 0.355471
\(292\) 0 0
\(293\) −11.1144 −0.649312 −0.324656 0.945832i \(-0.605249\pi\)
−0.324656 + 0.945832i \(0.605249\pi\)
\(294\) 0 0
\(295\) −2.57417 −0.149874
\(296\) 0 0
\(297\) −4.93713 −0.286482
\(298\) 0 0
\(299\) 2.86190 0.165508
\(300\) 0 0
\(301\) 15.5668 0.897255
\(302\) 0 0
\(303\) 7.91628 0.454778
\(304\) 0 0
\(305\) 10.1701 0.582339
\(306\) 0 0
\(307\) 6.59206 0.376229 0.188114 0.982147i \(-0.439762\pi\)
0.188114 + 0.982147i \(0.439762\pi\)
\(308\) 0 0
\(309\) 9.03978 0.514255
\(310\) 0 0
\(311\) 1.87943 0.106573 0.0532863 0.998579i \(-0.483030\pi\)
0.0532863 + 0.998579i \(0.483030\pi\)
\(312\) 0 0
\(313\) 25.4792 1.44017 0.720086 0.693885i \(-0.244102\pi\)
0.720086 + 0.693885i \(0.244102\pi\)
\(314\) 0 0
\(315\) 9.04474 0.509613
\(316\) 0 0
\(317\) −12.0671 −0.677755 −0.338878 0.940830i \(-0.610047\pi\)
−0.338878 + 0.940830i \(0.610047\pi\)
\(318\) 0 0
\(319\) 4.93713 0.276426
\(320\) 0 0
\(321\) −9.79071 −0.546464
\(322\) 0 0
\(323\) −6.05891 −0.337127
\(324\) 0 0
\(325\) −4.33017 −0.240195
\(326\) 0 0
\(327\) 14.4248 0.797693
\(328\) 0 0
\(329\) 59.7330 3.29319
\(330\) 0 0
\(331\) −34.5193 −1.89735 −0.948676 0.316251i \(-0.897576\pi\)
−0.948676 + 0.316251i \(0.897576\pi\)
\(332\) 0 0
\(333\) −6.81511 −0.373466
\(334\) 0 0
\(335\) 7.73689 0.422711
\(336\) 0 0
\(337\) −24.8494 −1.35364 −0.676818 0.736151i \(-0.736641\pi\)
−0.676818 + 0.736151i \(0.736641\pi\)
\(338\) 0 0
\(339\) 6.00311 0.326044
\(340\) 0 0
\(341\) 26.7501 1.44860
\(342\) 0 0
\(343\) −45.8256 −2.47435
\(344\) 0 0
\(345\) −1.86734 −0.100534
\(346\) 0 0
\(347\) 15.8748 0.852205 0.426103 0.904675i \(-0.359886\pi\)
0.426103 + 0.904675i \(0.359886\pi\)
\(348\) 0 0
\(349\) 15.4659 0.827873 0.413936 0.910306i \(-0.364154\pi\)
0.413936 + 0.910306i \(0.364154\pi\)
\(350\) 0 0
\(351\) 2.86190 0.152757
\(352\) 0 0
\(353\) −0.502338 −0.0267368 −0.0133684 0.999911i \(-0.504255\pi\)
−0.0133684 + 0.999911i \(0.504255\pi\)
\(354\) 0 0
\(355\) 19.1928 1.01865
\(356\) 0 0
\(357\) −15.0578 −0.796945
\(358\) 0 0
\(359\) −25.7686 −1.36001 −0.680007 0.733205i \(-0.738023\pi\)
−0.680007 + 0.733205i \(0.738023\pi\)
\(360\) 0 0
\(361\) −15.2015 −0.800080
\(362\) 0 0
\(363\) 13.3753 0.702021
\(364\) 0 0
\(365\) 9.15959 0.479435
\(366\) 0 0
\(367\) 27.9152 1.45716 0.728581 0.684960i \(-0.240180\pi\)
0.728581 + 0.684960i \(0.240180\pi\)
\(368\) 0 0
\(369\) 10.1828 0.530096
\(370\) 0 0
\(371\) 65.2078 3.38542
\(372\) 0 0
\(373\) −35.6994 −1.84844 −0.924222 0.381856i \(-0.875285\pi\)
−0.924222 + 0.381856i \(0.875285\pi\)
\(374\) 0 0
\(375\) 12.1621 0.628046
\(376\) 0 0
\(377\) −2.86190 −0.147395
\(378\) 0 0
\(379\) 1.69150 0.0868864 0.0434432 0.999056i \(-0.486167\pi\)
0.0434432 + 0.999056i \(0.486167\pi\)
\(380\) 0 0
\(381\) −4.05286 −0.207634
\(382\) 0 0
\(383\) −9.91105 −0.506431 −0.253216 0.967410i \(-0.581488\pi\)
−0.253216 + 0.967410i \(0.581488\pi\)
\(384\) 0 0
\(385\) −44.6551 −2.27583
\(386\) 0 0
\(387\) −3.21385 −0.163369
\(388\) 0 0
\(389\) 23.1451 1.17350 0.586752 0.809767i \(-0.300406\pi\)
0.586752 + 0.809767i \(0.300406\pi\)
\(390\) 0 0
\(391\) 3.10878 0.157218
\(392\) 0 0
\(393\) 3.69396 0.186335
\(394\) 0 0
\(395\) −19.4198 −0.977115
\(396\) 0 0
\(397\) −13.4833 −0.676708 −0.338354 0.941019i \(-0.609870\pi\)
−0.338354 + 0.941019i \(0.609870\pi\)
\(398\) 0 0
\(399\) 9.44013 0.472598
\(400\) 0 0
\(401\) −39.5347 −1.97427 −0.987133 0.159900i \(-0.948883\pi\)
−0.987133 + 0.159900i \(0.948883\pi\)
\(402\) 0 0
\(403\) −15.5061 −0.772415
\(404\) 0 0
\(405\) −1.86734 −0.0927888
\(406\) 0 0
\(407\) 33.6471 1.66782
\(408\) 0 0
\(409\) 8.56923 0.423721 0.211860 0.977300i \(-0.432048\pi\)
0.211860 + 0.977300i \(0.432048\pi\)
\(410\) 0 0
\(411\) −14.8480 −0.732396
\(412\) 0 0
\(413\) −6.67708 −0.328558
\(414\) 0 0
\(415\) −25.6315 −1.25820
\(416\) 0 0
\(417\) −0.753509 −0.0368995
\(418\) 0 0
\(419\) −18.1207 −0.885254 −0.442627 0.896706i \(-0.645953\pi\)
−0.442627 + 0.896706i \(0.645953\pi\)
\(420\) 0 0
\(421\) −22.8733 −1.11477 −0.557387 0.830253i \(-0.688196\pi\)
−0.557387 + 0.830253i \(0.688196\pi\)
\(422\) 0 0
\(423\) −12.3322 −0.599614
\(424\) 0 0
\(425\) −4.70371 −0.228164
\(426\) 0 0
\(427\) 26.3800 1.27662
\(428\) 0 0
\(429\) −14.1296 −0.682182
\(430\) 0 0
\(431\) −16.8383 −0.811074 −0.405537 0.914079i \(-0.632916\pi\)
−0.405537 + 0.914079i \(0.632916\pi\)
\(432\) 0 0
\(433\) 33.6268 1.61600 0.808001 0.589181i \(-0.200550\pi\)
0.808001 + 0.589181i \(0.200550\pi\)
\(434\) 0 0
\(435\) 1.86734 0.0895321
\(436\) 0 0
\(437\) −1.94897 −0.0932319
\(438\) 0 0
\(439\) −18.3416 −0.875396 −0.437698 0.899122i \(-0.644206\pi\)
−0.437698 + 0.899122i \(0.644206\pi\)
\(440\) 0 0
\(441\) 16.4610 0.783855
\(442\) 0 0
\(443\) −24.0952 −1.14480 −0.572400 0.819975i \(-0.693987\pi\)
−0.572400 + 0.819975i \(0.693987\pi\)
\(444\) 0 0
\(445\) 3.53499 0.167575
\(446\) 0 0
\(447\) 19.0823 0.902561
\(448\) 0 0
\(449\) 4.45100 0.210056 0.105028 0.994469i \(-0.466507\pi\)
0.105028 + 0.994469i \(0.466507\pi\)
\(450\) 0 0
\(451\) −50.2739 −2.36731
\(452\) 0 0
\(453\) 11.9551 0.561701
\(454\) 0 0
\(455\) 25.8851 1.21351
\(456\) 0 0
\(457\) −23.6804 −1.10772 −0.553860 0.832610i \(-0.686846\pi\)
−0.553860 + 0.832610i \(0.686846\pi\)
\(458\) 0 0
\(459\) 3.10878 0.145105
\(460\) 0 0
\(461\) −0.913736 −0.0425569 −0.0212785 0.999774i \(-0.506774\pi\)
−0.0212785 + 0.999774i \(0.506774\pi\)
\(462\) 0 0
\(463\) 12.5722 0.584279 0.292139 0.956376i \(-0.405633\pi\)
0.292139 + 0.956376i \(0.405633\pi\)
\(464\) 0 0
\(465\) 10.1175 0.469188
\(466\) 0 0
\(467\) −13.2992 −0.615415 −0.307708 0.951481i \(-0.599562\pi\)
−0.307708 + 0.951481i \(0.599562\pi\)
\(468\) 0 0
\(469\) 20.0686 0.926680
\(470\) 0 0
\(471\) 0.855906 0.0394381
\(472\) 0 0
\(473\) 15.8672 0.729576
\(474\) 0 0
\(475\) 2.94888 0.135304
\(476\) 0 0
\(477\) −13.4625 −0.616407
\(478\) 0 0
\(479\) 29.7874 1.36102 0.680512 0.732737i \(-0.261758\pi\)
0.680512 + 0.732737i \(0.261758\pi\)
\(480\) 0 0
\(481\) −19.5041 −0.889312
\(482\) 0 0
\(483\) −4.84365 −0.220394
\(484\) 0 0
\(485\) −11.3233 −0.514165
\(486\) 0 0
\(487\) −1.21942 −0.0552574 −0.0276287 0.999618i \(-0.508796\pi\)
−0.0276287 + 0.999618i \(0.508796\pi\)
\(488\) 0 0
\(489\) 18.9613 0.857458
\(490\) 0 0
\(491\) 35.5778 1.60560 0.802802 0.596246i \(-0.203342\pi\)
0.802802 + 0.596246i \(0.203342\pi\)
\(492\) 0 0
\(493\) −3.10878 −0.140012
\(494\) 0 0
\(495\) 9.21930 0.414377
\(496\) 0 0
\(497\) 49.7837 2.23310
\(498\) 0 0
\(499\) −12.1010 −0.541716 −0.270858 0.962619i \(-0.587307\pi\)
−0.270858 + 0.962619i \(0.587307\pi\)
\(500\) 0 0
\(501\) −16.5645 −0.740047
\(502\) 0 0
\(503\) 2.26150 0.100835 0.0504176 0.998728i \(-0.483945\pi\)
0.0504176 + 0.998728i \(0.483945\pi\)
\(504\) 0 0
\(505\) −14.7824 −0.657807
\(506\) 0 0
\(507\) −4.80956 −0.213600
\(508\) 0 0
\(509\) −31.5346 −1.39775 −0.698874 0.715245i \(-0.746315\pi\)
−0.698874 + 0.715245i \(0.746315\pi\)
\(510\) 0 0
\(511\) 23.7589 1.05103
\(512\) 0 0
\(513\) −1.94897 −0.0860491
\(514\) 0 0
\(515\) −16.8803 −0.743837
\(516\) 0 0
\(517\) 60.8859 2.67776
\(518\) 0 0
\(519\) 23.8644 1.04753
\(520\) 0 0
\(521\) 12.6095 0.552434 0.276217 0.961095i \(-0.410919\pi\)
0.276217 + 0.961095i \(0.410919\pi\)
\(522\) 0 0
\(523\) −27.7998 −1.21560 −0.607800 0.794090i \(-0.707948\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(524\) 0 0
\(525\) 7.32865 0.319849
\(526\) 0 0
\(527\) −16.8438 −0.733726
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 1.37852 0.0598228
\(532\) 0 0
\(533\) 29.1422 1.26229
\(534\) 0 0
\(535\) 18.2826 0.790425
\(536\) 0 0
\(537\) 12.2293 0.527734
\(538\) 0 0
\(539\) −81.2699 −3.50054
\(540\) 0 0
\(541\) −33.3620 −1.43435 −0.717173 0.696895i \(-0.754564\pi\)
−0.717173 + 0.696895i \(0.754564\pi\)
\(542\) 0 0
\(543\) 11.6427 0.499635
\(544\) 0 0
\(545\) −26.9360 −1.15381
\(546\) 0 0
\(547\) 39.9906 1.70988 0.854938 0.518731i \(-0.173595\pi\)
0.854938 + 0.518731i \(0.173595\pi\)
\(548\) 0 0
\(549\) −5.44631 −0.232443
\(550\) 0 0
\(551\) 1.94897 0.0830289
\(552\) 0 0
\(553\) −50.3725 −2.14206
\(554\) 0 0
\(555\) 12.7261 0.540194
\(556\) 0 0
\(557\) −6.84277 −0.289937 −0.144969 0.989436i \(-0.546308\pi\)
−0.144969 + 0.989436i \(0.546308\pi\)
\(558\) 0 0
\(559\) −9.19771 −0.389022
\(560\) 0 0
\(561\) −15.3484 −0.648012
\(562\) 0 0
\(563\) 14.9084 0.628313 0.314156 0.949371i \(-0.398278\pi\)
0.314156 + 0.949371i \(0.398278\pi\)
\(564\) 0 0
\(565\) −11.2099 −0.471602
\(566\) 0 0
\(567\) −4.84365 −0.203414
\(568\) 0 0
\(569\) 28.3870 1.19004 0.595022 0.803709i \(-0.297143\pi\)
0.595022 + 0.803709i \(0.297143\pi\)
\(570\) 0 0
\(571\) −24.9532 −1.04426 −0.522129 0.852866i \(-0.674862\pi\)
−0.522129 + 0.852866i \(0.674862\pi\)
\(572\) 0 0
\(573\) −22.9093 −0.957049
\(574\) 0 0
\(575\) −1.51304 −0.0630983
\(576\) 0 0
\(577\) 36.5385 1.52112 0.760558 0.649270i \(-0.224925\pi\)
0.760558 + 0.649270i \(0.224925\pi\)
\(578\) 0 0
\(579\) 19.0630 0.792233
\(580\) 0 0
\(581\) −66.4850 −2.75826
\(582\) 0 0
\(583\) 66.4663 2.75275
\(584\) 0 0
\(585\) −5.34413 −0.220953
\(586\) 0 0
\(587\) −22.4432 −0.926331 −0.463166 0.886272i \(-0.653286\pi\)
−0.463166 + 0.886272i \(0.653286\pi\)
\(588\) 0 0
\(589\) 10.5598 0.435108
\(590\) 0 0
\(591\) −12.4760 −0.513195
\(592\) 0 0
\(593\) −37.3577 −1.53410 −0.767049 0.641589i \(-0.778276\pi\)
−0.767049 + 0.641589i \(0.778276\pi\)
\(594\) 0 0
\(595\) 28.1181 1.15273
\(596\) 0 0
\(597\) −20.5233 −0.839961
\(598\) 0 0
\(599\) 4.50787 0.184187 0.0920933 0.995750i \(-0.470644\pi\)
0.0920933 + 0.995750i \(0.470644\pi\)
\(600\) 0 0
\(601\) −19.9181 −0.812476 −0.406238 0.913767i \(-0.633160\pi\)
−0.406238 + 0.913767i \(0.633160\pi\)
\(602\) 0 0
\(603\) −4.14327 −0.168727
\(604\) 0 0
\(605\) −24.9762 −1.01543
\(606\) 0 0
\(607\) 15.3046 0.621193 0.310596 0.950542i \(-0.399471\pi\)
0.310596 + 0.950542i \(0.399471\pi\)
\(608\) 0 0
\(609\) 4.84365 0.196275
\(610\) 0 0
\(611\) −35.2936 −1.42782
\(612\) 0 0
\(613\) −38.9131 −1.57168 −0.785842 0.618427i \(-0.787770\pi\)
−0.785842 + 0.618427i \(0.787770\pi\)
\(614\) 0 0
\(615\) −19.0148 −0.766750
\(616\) 0 0
\(617\) −36.8410 −1.48316 −0.741581 0.670863i \(-0.765924\pi\)
−0.741581 + 0.670863i \(0.765924\pi\)
\(618\) 0 0
\(619\) 47.7922 1.92093 0.960464 0.278403i \(-0.0898050\pi\)
0.960464 + 0.278403i \(0.0898050\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 9.16935 0.367362
\(624\) 0 0
\(625\) −15.1455 −0.605819
\(626\) 0 0
\(627\) 9.62233 0.384279
\(628\) 0 0
\(629\) −21.1866 −0.844767
\(630\) 0 0
\(631\) −13.4766 −0.536495 −0.268248 0.963350i \(-0.586445\pi\)
−0.268248 + 0.963350i \(0.586445\pi\)
\(632\) 0 0
\(633\) 17.5670 0.698226
\(634\) 0 0
\(635\) 7.56806 0.300329
\(636\) 0 0
\(637\) 47.1095 1.86655
\(638\) 0 0
\(639\) −10.2781 −0.406597
\(640\) 0 0
\(641\) −38.8240 −1.53345 −0.766727 0.641973i \(-0.778116\pi\)
−0.766727 + 0.641973i \(0.778116\pi\)
\(642\) 0 0
\(643\) 42.2647 1.66676 0.833379 0.552702i \(-0.186403\pi\)
0.833379 + 0.552702i \(0.186403\pi\)
\(644\) 0 0
\(645\) 6.00136 0.236303
\(646\) 0 0
\(647\) 12.5267 0.492475 0.246237 0.969210i \(-0.420806\pi\)
0.246237 + 0.969210i \(0.420806\pi\)
\(648\) 0 0
\(649\) −6.80595 −0.267157
\(650\) 0 0
\(651\) 26.2436 1.02857
\(652\) 0 0
\(653\) −12.1492 −0.475436 −0.237718 0.971334i \(-0.576399\pi\)
−0.237718 + 0.971334i \(0.576399\pi\)
\(654\) 0 0
\(655\) −6.89787 −0.269522
\(656\) 0 0
\(657\) −4.90515 −0.191368
\(658\) 0 0
\(659\) −40.9303 −1.59442 −0.797210 0.603703i \(-0.793691\pi\)
−0.797210 + 0.603703i \(0.793691\pi\)
\(660\) 0 0
\(661\) −5.80196 −0.225670 −0.112835 0.993614i \(-0.535993\pi\)
−0.112835 + 0.993614i \(0.535993\pi\)
\(662\) 0 0
\(663\) 8.89699 0.345531
\(664\) 0 0
\(665\) −17.6279 −0.683582
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 14.8503 0.574146
\(670\) 0 0
\(671\) 26.8892 1.03804
\(672\) 0 0
\(673\) −27.0266 −1.04180 −0.520899 0.853618i \(-0.674403\pi\)
−0.520899 + 0.853618i \(0.674403\pi\)
\(674\) 0 0
\(675\) −1.51304 −0.0582371
\(676\) 0 0
\(677\) −12.3630 −0.475148 −0.237574 0.971369i \(-0.576352\pi\)
−0.237574 + 0.971369i \(0.576352\pi\)
\(678\) 0 0
\(679\) −29.3713 −1.12717
\(680\) 0 0
\(681\) −8.04076 −0.308123
\(682\) 0 0
\(683\) 17.8193 0.681836 0.340918 0.940093i \(-0.389262\pi\)
0.340918 + 0.940093i \(0.389262\pi\)
\(684\) 0 0
\(685\) 27.7262 1.05936
\(686\) 0 0
\(687\) 12.8993 0.492138
\(688\) 0 0
\(689\) −38.5283 −1.46781
\(690\) 0 0
\(691\) 2.55059 0.0970290 0.0485145 0.998822i \(-0.484551\pi\)
0.0485145 + 0.998822i \(0.484551\pi\)
\(692\) 0 0
\(693\) 23.9138 0.908408
\(694\) 0 0
\(695\) 1.40706 0.0533727
\(696\) 0 0
\(697\) 31.6561 1.19906
\(698\) 0 0
\(699\) 24.3045 0.919281
\(700\) 0 0
\(701\) −5.99753 −0.226524 −0.113262 0.993565i \(-0.536130\pi\)
−0.113262 + 0.993565i \(0.536130\pi\)
\(702\) 0 0
\(703\) 13.2824 0.500957
\(704\) 0 0
\(705\) 23.0285 0.867302
\(706\) 0 0
\(707\) −38.3437 −1.44206
\(708\) 0 0
\(709\) −20.3497 −0.764250 −0.382125 0.924111i \(-0.624808\pi\)
−0.382125 + 0.924111i \(0.624808\pi\)
\(710\) 0 0
\(711\) 10.3997 0.390019
\(712\) 0 0
\(713\) −5.41813 −0.202911
\(714\) 0 0
\(715\) 26.3847 0.986731
\(716\) 0 0
\(717\) −4.62036 −0.172551
\(718\) 0 0
\(719\) −18.7200 −0.698139 −0.349069 0.937097i \(-0.613502\pi\)
−0.349069 + 0.937097i \(0.613502\pi\)
\(720\) 0 0
\(721\) −43.7855 −1.63066
\(722\) 0 0
\(723\) 10.3930 0.386520
\(724\) 0 0
\(725\) 1.51304 0.0561930
\(726\) 0 0
\(727\) 22.6322 0.839381 0.419691 0.907667i \(-0.362139\pi\)
0.419691 + 0.907667i \(0.362139\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −9.99115 −0.369536
\(732\) 0 0
\(733\) 28.5871 1.05589 0.527945 0.849279i \(-0.322963\pi\)
0.527945 + 0.849279i \(0.322963\pi\)
\(734\) 0 0
\(735\) −30.7382 −1.13380
\(736\) 0 0
\(737\) 20.4559 0.753502
\(738\) 0 0
\(739\) 24.0224 0.883679 0.441839 0.897094i \(-0.354326\pi\)
0.441839 + 0.897094i \(0.354326\pi\)
\(740\) 0 0
\(741\) −5.57775 −0.204904
\(742\) 0 0
\(743\) −30.7880 −1.12950 −0.564752 0.825261i \(-0.691028\pi\)
−0.564752 + 0.825261i \(0.691028\pi\)
\(744\) 0 0
\(745\) −35.6331 −1.30550
\(746\) 0 0
\(747\) 13.7262 0.502216
\(748\) 0 0
\(749\) 47.4228 1.73279
\(750\) 0 0
\(751\) 37.5105 1.36878 0.684388 0.729118i \(-0.260070\pi\)
0.684388 + 0.729118i \(0.260070\pi\)
\(752\) 0 0
\(753\) 3.33210 0.121429
\(754\) 0 0
\(755\) −22.3243 −0.812464
\(756\) 0 0
\(757\) −1.92889 −0.0701067 −0.0350533 0.999385i \(-0.511160\pi\)
−0.0350533 + 0.999385i \(0.511160\pi\)
\(758\) 0 0
\(759\) −4.93713 −0.179207
\(760\) 0 0
\(761\) −13.2430 −0.480059 −0.240030 0.970766i \(-0.577157\pi\)
−0.240030 + 0.970766i \(0.577157\pi\)
\(762\) 0 0
\(763\) −69.8687 −2.52942
\(764\) 0 0
\(765\) −5.80514 −0.209885
\(766\) 0 0
\(767\) 3.94519 0.142452
\(768\) 0 0
\(769\) 20.5343 0.740485 0.370242 0.928935i \(-0.379275\pi\)
0.370242 + 0.928935i \(0.379275\pi\)
\(770\) 0 0
\(771\) −13.5424 −0.487716
\(772\) 0 0
\(773\) 0.422817 0.0152077 0.00760384 0.999971i \(-0.497580\pi\)
0.00760384 + 0.999971i \(0.497580\pi\)
\(774\) 0 0
\(775\) 8.19787 0.294476
\(776\) 0 0
\(777\) 33.0100 1.18423
\(778\) 0 0
\(779\) −19.8460 −0.711057
\(780\) 0 0
\(781\) 50.7445 1.81578
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −1.59827 −0.0570446
\(786\) 0 0
\(787\) 50.8110 1.81122 0.905608 0.424116i \(-0.139415\pi\)
0.905608 + 0.424116i \(0.139415\pi\)
\(788\) 0 0
\(789\) 23.2268 0.826895
\(790\) 0 0
\(791\) −29.0770 −1.03386
\(792\) 0 0
\(793\) −15.5868 −0.553502
\(794\) 0 0
\(795\) 25.1391 0.891592
\(796\) 0 0
\(797\) −15.0840 −0.534303 −0.267151 0.963655i \(-0.586082\pi\)
−0.267151 + 0.963655i \(0.586082\pi\)
\(798\) 0 0
\(799\) −38.3382 −1.35631
\(800\) 0 0
\(801\) −1.89306 −0.0668882
\(802\) 0 0
\(803\) 24.2174 0.854613
\(804\) 0 0
\(805\) 9.04474 0.318785
\(806\) 0 0
\(807\) 16.5605 0.582957
\(808\) 0 0
\(809\) −28.8924 −1.01580 −0.507902 0.861415i \(-0.669579\pi\)
−0.507902 + 0.861415i \(0.669579\pi\)
\(810\) 0 0
\(811\) −11.2287 −0.394294 −0.197147 0.980374i \(-0.563168\pi\)
−0.197147 + 0.980374i \(0.563168\pi\)
\(812\) 0 0
\(813\) 28.2844 0.991977
\(814\) 0 0
\(815\) −35.4071 −1.24026
\(816\) 0 0
\(817\) 6.26370 0.219139
\(818\) 0 0
\(819\) −13.8620 −0.484378
\(820\) 0 0
\(821\) 31.1064 1.08562 0.542811 0.839855i \(-0.317360\pi\)
0.542811 + 0.839855i \(0.317360\pi\)
\(822\) 0 0
\(823\) −14.8374 −0.517198 −0.258599 0.965985i \(-0.583261\pi\)
−0.258599 + 0.965985i \(0.583261\pi\)
\(824\) 0 0
\(825\) 7.47010 0.260075
\(826\) 0 0
\(827\) 28.1314 0.978224 0.489112 0.872221i \(-0.337321\pi\)
0.489112 + 0.872221i \(0.337321\pi\)
\(828\) 0 0
\(829\) 29.6051 1.02823 0.514113 0.857722i \(-0.328121\pi\)
0.514113 + 0.857722i \(0.328121\pi\)
\(830\) 0 0
\(831\) 11.3786 0.394720
\(832\) 0 0
\(833\) 51.1734 1.77305
\(834\) 0 0
\(835\) 30.9315 1.07043
\(836\) 0 0
\(837\) −5.41813 −0.187278
\(838\) 0 0
\(839\) 37.4631 1.29337 0.646684 0.762758i \(-0.276155\pi\)
0.646684 + 0.762758i \(0.276155\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 8.08816 0.278571
\(844\) 0 0
\(845\) 8.98107 0.308958
\(846\) 0 0
\(847\) −64.7852 −2.22605
\(848\) 0 0
\(849\) 7.42987 0.254993
\(850\) 0 0
\(851\) −6.81511 −0.233619
\(852\) 0 0
\(853\) −8.37850 −0.286874 −0.143437 0.989659i \(-0.545815\pi\)
−0.143437 + 0.989659i \(0.545815\pi\)
\(854\) 0 0
\(855\) 3.63939 0.124464
\(856\) 0 0
\(857\) −52.4602 −1.79201 −0.896003 0.444047i \(-0.853542\pi\)
−0.896003 + 0.444047i \(0.853542\pi\)
\(858\) 0 0
\(859\) 0.570326 0.0194593 0.00972964 0.999953i \(-0.496903\pi\)
0.00972964 + 0.999953i \(0.496903\pi\)
\(860\) 0 0
\(861\) −49.3220 −1.68089
\(862\) 0 0
\(863\) 21.9161 0.746034 0.373017 0.927825i \(-0.378323\pi\)
0.373017 + 0.927825i \(0.378323\pi\)
\(864\) 0 0
\(865\) −44.5630 −1.51519
\(866\) 0 0
\(867\) −7.33551 −0.249127
\(868\) 0 0
\(869\) −51.3447 −1.74175
\(870\) 0 0
\(871\) −11.8576 −0.401780
\(872\) 0 0
\(873\) 6.06388 0.205231
\(874\) 0 0
\(875\) −58.9088 −1.99148
\(876\) 0 0
\(877\) 39.4269 1.33135 0.665676 0.746241i \(-0.268143\pi\)
0.665676 + 0.746241i \(0.268143\pi\)
\(878\) 0 0
\(879\) −11.1144 −0.374881
\(880\) 0 0
\(881\) −10.7692 −0.362824 −0.181412 0.983407i \(-0.558067\pi\)
−0.181412 + 0.983407i \(0.558067\pi\)
\(882\) 0 0
\(883\) −6.56188 −0.220825 −0.110412 0.993886i \(-0.535217\pi\)
−0.110412 + 0.993886i \(0.535217\pi\)
\(884\) 0 0
\(885\) −2.57417 −0.0865298
\(886\) 0 0
\(887\) −27.2217 −0.914016 −0.457008 0.889463i \(-0.651079\pi\)
−0.457008 + 0.889463i \(0.651079\pi\)
\(888\) 0 0
\(889\) 19.6306 0.658390
\(890\) 0 0
\(891\) −4.93713 −0.165400
\(892\) 0 0
\(893\) 24.0352 0.804306
\(894\) 0 0
\(895\) −22.8363 −0.763333
\(896\) 0 0
\(897\) 2.86190 0.0955559
\(898\) 0 0
\(899\) 5.41813 0.180705
\(900\) 0 0
\(901\) −41.8520 −1.39429
\(902\) 0 0
\(903\) 15.5668 0.518030
\(904\) 0 0
\(905\) −21.7408 −0.722689
\(906\) 0 0
\(907\) −12.2816 −0.407804 −0.203902 0.978991i \(-0.565362\pi\)
−0.203902 + 0.978991i \(0.565362\pi\)
\(908\) 0 0
\(909\) 7.91628 0.262566
\(910\) 0 0
\(911\) −32.9611 −1.09205 −0.546025 0.837769i \(-0.683860\pi\)
−0.546025 + 0.837769i \(0.683860\pi\)
\(912\) 0 0
\(913\) −67.7682 −2.24280
\(914\) 0 0
\(915\) 10.1701 0.336213
\(916\) 0 0
\(917\) −17.8922 −0.590854
\(918\) 0 0
\(919\) −48.3611 −1.59528 −0.797642 0.603131i \(-0.793920\pi\)
−0.797642 + 0.603131i \(0.793920\pi\)
\(920\) 0 0
\(921\) 6.59206 0.217216
\(922\) 0 0
\(923\) −29.4149 −0.968204
\(924\) 0 0
\(925\) 10.3116 0.339042
\(926\) 0 0
\(927\) 9.03978 0.296905
\(928\) 0 0
\(929\) 44.4504 1.45837 0.729185 0.684316i \(-0.239899\pi\)
0.729185 + 0.684316i \(0.239899\pi\)
\(930\) 0 0
\(931\) −32.0819 −1.05144
\(932\) 0 0
\(933\) 1.87943 0.0615297
\(934\) 0 0
\(935\) 28.6608 0.937307
\(936\) 0 0
\(937\) 21.4331 0.700190 0.350095 0.936714i \(-0.386149\pi\)
0.350095 + 0.936714i \(0.386149\pi\)
\(938\) 0 0
\(939\) 25.4792 0.831483
\(940\) 0 0
\(941\) 15.6533 0.510282 0.255141 0.966904i \(-0.417878\pi\)
0.255141 + 0.966904i \(0.417878\pi\)
\(942\) 0 0
\(943\) 10.1828 0.331598
\(944\) 0 0
\(945\) 9.04474 0.294225
\(946\) 0 0
\(947\) 14.8996 0.484173 0.242087 0.970255i \(-0.422168\pi\)
0.242087 + 0.970255i \(0.422168\pi\)
\(948\) 0 0
\(949\) −14.0380 −0.455694
\(950\) 0 0
\(951\) −12.0671 −0.391302
\(952\) 0 0
\(953\) 43.3059 1.40281 0.701407 0.712761i \(-0.252555\pi\)
0.701407 + 0.712761i \(0.252555\pi\)
\(954\) 0 0
\(955\) 42.7794 1.38431
\(956\) 0 0
\(957\) 4.93713 0.159595
\(958\) 0 0
\(959\) 71.9184 2.32237
\(960\) 0 0
\(961\) −1.64382 −0.0530265
\(962\) 0 0
\(963\) −9.79071 −0.315501
\(964\) 0 0
\(965\) −35.5972 −1.14591
\(966\) 0 0
\(967\) −32.8380 −1.05600 −0.527999 0.849245i \(-0.677057\pi\)
−0.527999 + 0.849245i \(0.677057\pi\)
\(968\) 0 0
\(969\) −6.05891 −0.194640
\(970\) 0 0
\(971\) −33.2710 −1.06772 −0.533859 0.845574i \(-0.679259\pi\)
−0.533859 + 0.845574i \(0.679259\pi\)
\(972\) 0 0
\(973\) 3.64973 0.117005
\(974\) 0 0
\(975\) −4.33017 −0.138676
\(976\) 0 0
\(977\) 53.8741 1.72359 0.861793 0.507260i \(-0.169342\pi\)
0.861793 + 0.507260i \(0.169342\pi\)
\(978\) 0 0
\(979\) 9.34631 0.298709
\(980\) 0 0
\(981\) 14.4248 0.460548
\(982\) 0 0
\(983\) −27.9078 −0.890120 −0.445060 0.895501i \(-0.646818\pi\)
−0.445060 + 0.895501i \(0.646818\pi\)
\(984\) 0 0
\(985\) 23.2970 0.742303
\(986\) 0 0
\(987\) 59.7330 1.90132
\(988\) 0 0
\(989\) −3.21385 −0.102195
\(990\) 0 0
\(991\) 4.94439 0.157064 0.0785318 0.996912i \(-0.474977\pi\)
0.0785318 + 0.996912i \(0.474977\pi\)
\(992\) 0 0
\(993\) −34.5193 −1.09544
\(994\) 0 0
\(995\) 38.3239 1.21495
\(996\) 0 0
\(997\) 3.56994 0.113061 0.0565306 0.998401i \(-0.481996\pi\)
0.0565306 + 0.998401i \(0.481996\pi\)
\(998\) 0 0
\(999\) −6.81511 −0.215620
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 \(a_p\))