Properties

Label 8004.2.a.j.1.15
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 1.15
Root \(4.08902\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +4.08902 q^{5} +2.57555 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +4.08902 q^{5} +2.57555 q^{7} +1.00000 q^{9} +4.61172 q^{11} -4.79639 q^{13} +4.08902 q^{15} -1.83258 q^{17} +4.89968 q^{19} +2.57555 q^{21} +1.00000 q^{23} +11.7201 q^{25} +1.00000 q^{27} -1.00000 q^{29} +8.03980 q^{31} +4.61172 q^{33} +10.5315 q^{35} -8.43013 q^{37} -4.79639 q^{39} +8.64925 q^{41} -7.46071 q^{43} +4.08902 q^{45} -5.52609 q^{47} -0.366553 q^{49} -1.83258 q^{51} -7.81069 q^{53} +18.8574 q^{55} +4.89968 q^{57} +7.57493 q^{59} -10.4358 q^{61} +2.57555 q^{63} -19.6125 q^{65} +8.30407 q^{67} +1.00000 q^{69} -0.0870476 q^{71} +9.17475 q^{73} +11.7201 q^{75} +11.8777 q^{77} -8.38478 q^{79} +1.00000 q^{81} -9.19932 q^{83} -7.49346 q^{85} -1.00000 q^{87} -11.9049 q^{89} -12.3533 q^{91} +8.03980 q^{93} +20.0349 q^{95} +6.00162 q^{97} +4.61172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + 5q^{11} + 6q^{13} + 3q^{15} + 3q^{17} + 11q^{19} + 4q^{21} + 16q^{23} + 27q^{25} + 16q^{27} - 16q^{29} + 14q^{31} + 5q^{33} + 11q^{35} + 4q^{37} + 6q^{39} + 11q^{41} + 23q^{43} + 3q^{45} - 2q^{47} + 34q^{49} + 3q^{51} + 19q^{53} + 31q^{55} + 11q^{57} + 32q^{59} + 19q^{61} + 4q^{63} + 6q^{65} + 33q^{67} + 16q^{69} - 5q^{71} + 23q^{73} + 27q^{75} + 42q^{77} + 24q^{79} + 16q^{81} + 7q^{83} - 16q^{87} - 2q^{89} + 25q^{91} + 14q^{93} + 7q^{95} + 33q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 4.08902 1.82866 0.914332 0.404965i \(-0.132716\pi\)
0.914332 + 0.404965i \(0.132716\pi\)
\(6\) 0 0
\(7\) 2.57555 0.973466 0.486733 0.873551i \(-0.338189\pi\)
0.486733 + 0.873551i \(0.338189\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.61172 1.39049 0.695243 0.718775i \(-0.255297\pi\)
0.695243 + 0.718775i \(0.255297\pi\)
\(12\) 0 0
\(13\) −4.79639 −1.33028 −0.665140 0.746719i \(-0.731628\pi\)
−0.665140 + 0.746719i \(0.731628\pi\)
\(14\) 0 0
\(15\) 4.08902 1.05578
\(16\) 0 0
\(17\) −1.83258 −0.444466 −0.222233 0.974994i \(-0.571335\pi\)
−0.222233 + 0.974994i \(0.571335\pi\)
\(18\) 0 0
\(19\) 4.89968 1.12406 0.562032 0.827116i \(-0.310020\pi\)
0.562032 + 0.827116i \(0.310020\pi\)
\(20\) 0 0
\(21\) 2.57555 0.562031
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.7201 2.34401
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 8.03980 1.44399 0.721996 0.691898i \(-0.243225\pi\)
0.721996 + 0.691898i \(0.243225\pi\)
\(32\) 0 0
\(33\) 4.61172 0.802797
\(34\) 0 0
\(35\) 10.5315 1.78014
\(36\) 0 0
\(37\) −8.43013 −1.38591 −0.692953 0.720983i \(-0.743691\pi\)
−0.692953 + 0.720983i \(0.743691\pi\)
\(38\) 0 0
\(39\) −4.79639 −0.768037
\(40\) 0 0
\(41\) 8.64925 1.35079 0.675393 0.737458i \(-0.263974\pi\)
0.675393 + 0.737458i \(0.263974\pi\)
\(42\) 0 0
\(43\) −7.46071 −1.13775 −0.568874 0.822425i \(-0.692621\pi\)
−0.568874 + 0.822425i \(0.692621\pi\)
\(44\) 0 0
\(45\) 4.08902 0.609555
\(46\) 0 0
\(47\) −5.52609 −0.806063 −0.403032 0.915186i \(-0.632044\pi\)
−0.403032 + 0.915186i \(0.632044\pi\)
\(48\) 0 0
\(49\) −0.366553 −0.0523647
\(50\) 0 0
\(51\) −1.83258 −0.256613
\(52\) 0 0
\(53\) −7.81069 −1.07288 −0.536441 0.843938i \(-0.680231\pi\)
−0.536441 + 0.843938i \(0.680231\pi\)
\(54\) 0 0
\(55\) 18.8574 2.54273
\(56\) 0 0
\(57\) 4.89968 0.648978
\(58\) 0 0
\(59\) 7.57493 0.986172 0.493086 0.869981i \(-0.335869\pi\)
0.493086 + 0.869981i \(0.335869\pi\)
\(60\) 0 0
\(61\) −10.4358 −1.33616 −0.668082 0.744088i \(-0.732885\pi\)
−0.668082 + 0.744088i \(0.732885\pi\)
\(62\) 0 0
\(63\) 2.57555 0.324489
\(64\) 0 0
\(65\) −19.6125 −2.43263
\(66\) 0 0
\(67\) 8.30407 1.01450 0.507252 0.861798i \(-0.330661\pi\)
0.507252 + 0.861798i \(0.330661\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −0.0870476 −0.0103306 −0.00516532 0.999987i \(-0.501644\pi\)
−0.00516532 + 0.999987i \(0.501644\pi\)
\(72\) 0 0
\(73\) 9.17475 1.07382 0.536912 0.843639i \(-0.319591\pi\)
0.536912 + 0.843639i \(0.319591\pi\)
\(74\) 0 0
\(75\) 11.7201 1.35332
\(76\) 0 0
\(77\) 11.8777 1.35359
\(78\) 0 0
\(79\) −8.38478 −0.943361 −0.471680 0.881770i \(-0.656352\pi\)
−0.471680 + 0.881770i \(0.656352\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −9.19932 −1.00976 −0.504878 0.863191i \(-0.668463\pi\)
−0.504878 + 0.863191i \(0.668463\pi\)
\(84\) 0 0
\(85\) −7.49346 −0.812780
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −11.9049 −1.26191 −0.630957 0.775818i \(-0.717337\pi\)
−0.630957 + 0.775818i \(0.717337\pi\)
\(90\) 0 0
\(91\) −12.3533 −1.29498
\(92\) 0 0
\(93\) 8.03980 0.833689
\(94\) 0 0
\(95\) 20.0349 2.05553
\(96\) 0 0
\(97\) 6.00162 0.609372 0.304686 0.952453i \(-0.401448\pi\)
0.304686 + 0.952453i \(0.401448\pi\)
\(98\) 0 0
\(99\) 4.61172 0.463495
\(100\) 0 0
\(101\) 14.2557 1.41849 0.709246 0.704961i \(-0.249036\pi\)
0.709246 + 0.704961i \(0.249036\pi\)
\(102\) 0 0
\(103\) −15.9300 −1.56963 −0.784817 0.619727i \(-0.787243\pi\)
−0.784817 + 0.619727i \(0.787243\pi\)
\(104\) 0 0
\(105\) 10.5315 1.02777
\(106\) 0 0
\(107\) 13.6477 1.31937 0.659686 0.751542i \(-0.270689\pi\)
0.659686 + 0.751542i \(0.270689\pi\)
\(108\) 0 0
\(109\) −10.7879 −1.03329 −0.516646 0.856199i \(-0.672820\pi\)
−0.516646 + 0.856199i \(0.672820\pi\)
\(110\) 0 0
\(111\) −8.43013 −0.800153
\(112\) 0 0
\(113\) 14.8279 1.39490 0.697448 0.716635i \(-0.254319\pi\)
0.697448 + 0.716635i \(0.254319\pi\)
\(114\) 0 0
\(115\) 4.08902 0.381303
\(116\) 0 0
\(117\) −4.79639 −0.443426
\(118\) 0 0
\(119\) −4.71990 −0.432673
\(120\) 0 0
\(121\) 10.2679 0.933450
\(122\) 0 0
\(123\) 8.64925 0.779876
\(124\) 0 0
\(125\) 27.4785 2.45775
\(126\) 0 0
\(127\) −6.83178 −0.606223 −0.303111 0.952955i \(-0.598025\pi\)
−0.303111 + 0.952955i \(0.598025\pi\)
\(128\) 0 0
\(129\) −7.46071 −0.656879
\(130\) 0 0
\(131\) 13.1242 1.14667 0.573335 0.819321i \(-0.305649\pi\)
0.573335 + 0.819321i \(0.305649\pi\)
\(132\) 0 0
\(133\) 12.6194 1.09424
\(134\) 0 0
\(135\) 4.08902 0.351927
\(136\) 0 0
\(137\) −16.4552 −1.40587 −0.702933 0.711256i \(-0.748127\pi\)
−0.702933 + 0.711256i \(0.748127\pi\)
\(138\) 0 0
\(139\) 17.7348 1.50425 0.752123 0.659023i \(-0.229030\pi\)
0.752123 + 0.659023i \(0.229030\pi\)
\(140\) 0 0
\(141\) −5.52609 −0.465381
\(142\) 0 0
\(143\) −22.1196 −1.84973
\(144\) 0 0
\(145\) −4.08902 −0.339574
\(146\) 0 0
\(147\) −0.366553 −0.0302328
\(148\) 0 0
\(149\) −13.4929 −1.10538 −0.552689 0.833388i \(-0.686398\pi\)
−0.552689 + 0.833388i \(0.686398\pi\)
\(150\) 0 0
\(151\) −6.07542 −0.494410 −0.247205 0.968963i \(-0.579512\pi\)
−0.247205 + 0.968963i \(0.579512\pi\)
\(152\) 0 0
\(153\) −1.83258 −0.148155
\(154\) 0 0
\(155\) 32.8749 2.64057
\(156\) 0 0
\(157\) −7.80818 −0.623161 −0.311580 0.950220i \(-0.600858\pi\)
−0.311580 + 0.950220i \(0.600858\pi\)
\(158\) 0 0
\(159\) −7.81069 −0.619428
\(160\) 0 0
\(161\) 2.57555 0.202982
\(162\) 0 0
\(163\) −9.01307 −0.705958 −0.352979 0.935631i \(-0.614831\pi\)
−0.352979 + 0.935631i \(0.614831\pi\)
\(164\) 0 0
\(165\) 18.8574 1.46805
\(166\) 0 0
\(167\) 16.9939 1.31503 0.657513 0.753443i \(-0.271609\pi\)
0.657513 + 0.753443i \(0.271609\pi\)
\(168\) 0 0
\(169\) 10.0054 0.769643
\(170\) 0 0
\(171\) 4.89968 0.374688
\(172\) 0 0
\(173\) 20.5627 1.56335 0.781676 0.623685i \(-0.214365\pi\)
0.781676 + 0.623685i \(0.214365\pi\)
\(174\) 0 0
\(175\) 30.1856 2.28182
\(176\) 0 0
\(177\) 7.57493 0.569367
\(178\) 0 0
\(179\) 5.34572 0.399558 0.199779 0.979841i \(-0.435978\pi\)
0.199779 + 0.979841i \(0.435978\pi\)
\(180\) 0 0
\(181\) −5.46362 −0.406108 −0.203054 0.979168i \(-0.565087\pi\)
−0.203054 + 0.979168i \(0.565087\pi\)
\(182\) 0 0
\(183\) −10.4358 −0.771435
\(184\) 0 0
\(185\) −34.4710 −2.53436
\(186\) 0 0
\(187\) −8.45135 −0.618024
\(188\) 0 0
\(189\) 2.57555 0.187344
\(190\) 0 0
\(191\) −8.74290 −0.632614 −0.316307 0.948657i \(-0.602443\pi\)
−0.316307 + 0.948657i \(0.602443\pi\)
\(192\) 0 0
\(193\) −21.2254 −1.52784 −0.763920 0.645312i \(-0.776728\pi\)
−0.763920 + 0.645312i \(0.776728\pi\)
\(194\) 0 0
\(195\) −19.6125 −1.40448
\(196\) 0 0
\(197\) −19.3805 −1.38080 −0.690400 0.723428i \(-0.742565\pi\)
−0.690400 + 0.723428i \(0.742565\pi\)
\(198\) 0 0
\(199\) 21.6802 1.53687 0.768435 0.639928i \(-0.221036\pi\)
0.768435 + 0.639928i \(0.221036\pi\)
\(200\) 0 0
\(201\) 8.30407 0.585724
\(202\) 0 0
\(203\) −2.57555 −0.180768
\(204\) 0 0
\(205\) 35.3669 2.47013
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 22.5959 1.56299
\(210\) 0 0
\(211\) 25.2974 1.74155 0.870774 0.491684i \(-0.163619\pi\)
0.870774 + 0.491684i \(0.163619\pi\)
\(212\) 0 0
\(213\) −0.0870476 −0.00596440
\(214\) 0 0
\(215\) −30.5070 −2.08056
\(216\) 0 0
\(217\) 20.7069 1.40568
\(218\) 0 0
\(219\) 9.17475 0.619972
\(220\) 0 0
\(221\) 8.78978 0.591264
\(222\) 0 0
\(223\) −22.4964 −1.50647 −0.753234 0.657753i \(-0.771507\pi\)
−0.753234 + 0.657753i \(0.771507\pi\)
\(224\) 0 0
\(225\) 11.7201 0.781338
\(226\) 0 0
\(227\) 0.0204943 0.00136026 0.000680128 1.00000i \(-0.499784\pi\)
0.000680128 1.00000i \(0.499784\pi\)
\(228\) 0 0
\(229\) −14.9723 −0.989399 −0.494700 0.869064i \(-0.664722\pi\)
−0.494700 + 0.869064i \(0.664722\pi\)
\(230\) 0 0
\(231\) 11.8777 0.781495
\(232\) 0 0
\(233\) −7.81673 −0.512091 −0.256045 0.966665i \(-0.582420\pi\)
−0.256045 + 0.966665i \(0.582420\pi\)
\(234\) 0 0
\(235\) −22.5963 −1.47402
\(236\) 0 0
\(237\) −8.38478 −0.544650
\(238\) 0 0
\(239\) −8.24516 −0.533335 −0.266668 0.963789i \(-0.585923\pi\)
−0.266668 + 0.963789i \(0.585923\pi\)
\(240\) 0 0
\(241\) 2.39246 0.154112 0.0770560 0.997027i \(-0.475448\pi\)
0.0770560 + 0.997027i \(0.475448\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −1.49884 −0.0957575
\(246\) 0 0
\(247\) −23.5008 −1.49532
\(248\) 0 0
\(249\) −9.19932 −0.582983
\(250\) 0 0
\(251\) 5.14853 0.324972 0.162486 0.986711i \(-0.448049\pi\)
0.162486 + 0.986711i \(0.448049\pi\)
\(252\) 0 0
\(253\) 4.61172 0.289936
\(254\) 0 0
\(255\) −7.49346 −0.469258
\(256\) 0 0
\(257\) 19.8047 1.23538 0.617690 0.786421i \(-0.288068\pi\)
0.617690 + 0.786421i \(0.288068\pi\)
\(258\) 0 0
\(259\) −21.7122 −1.34913
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −29.0507 −1.79135 −0.895673 0.444714i \(-0.853305\pi\)
−0.895673 + 0.444714i \(0.853305\pi\)
\(264\) 0 0
\(265\) −31.9381 −1.96194
\(266\) 0 0
\(267\) −11.9049 −0.728566
\(268\) 0 0
\(269\) −8.83872 −0.538906 −0.269453 0.963013i \(-0.586843\pi\)
−0.269453 + 0.963013i \(0.586843\pi\)
\(270\) 0 0
\(271\) −10.4526 −0.634951 −0.317476 0.948266i \(-0.602835\pi\)
−0.317476 + 0.948266i \(0.602835\pi\)
\(272\) 0 0
\(273\) −12.3533 −0.747658
\(274\) 0 0
\(275\) 54.0496 3.25932
\(276\) 0 0
\(277\) −11.7721 −0.707317 −0.353658 0.935375i \(-0.615062\pi\)
−0.353658 + 0.935375i \(0.615062\pi\)
\(278\) 0 0
\(279\) 8.03980 0.481330
\(280\) 0 0
\(281\) −30.2251 −1.80308 −0.901539 0.432698i \(-0.857562\pi\)
−0.901539 + 0.432698i \(0.857562\pi\)
\(282\) 0 0
\(283\) −18.5425 −1.10224 −0.551118 0.834427i \(-0.685799\pi\)
−0.551118 + 0.834427i \(0.685799\pi\)
\(284\) 0 0
\(285\) 20.0349 1.18676
\(286\) 0 0
\(287\) 22.2765 1.31494
\(288\) 0 0
\(289\) −13.6416 −0.802450
\(290\) 0 0
\(291\) 6.00162 0.351821
\(292\) 0 0
\(293\) 12.1800 0.711563 0.355781 0.934569i \(-0.384215\pi\)
0.355781 + 0.934569i \(0.384215\pi\)
\(294\) 0 0
\(295\) 30.9740 1.80338
\(296\) 0 0
\(297\) 4.61172 0.267599
\(298\) 0 0
\(299\) −4.79639 −0.277382
\(300\) 0 0
\(301\) −19.2154 −1.10756
\(302\) 0 0
\(303\) 14.2557 0.818966
\(304\) 0 0
\(305\) −42.6721 −2.44340
\(306\) 0 0
\(307\) 23.3621 1.33335 0.666673 0.745351i \(-0.267718\pi\)
0.666673 + 0.745351i \(0.267718\pi\)
\(308\) 0 0
\(309\) −15.9300 −0.906229
\(310\) 0 0
\(311\) −4.26341 −0.241756 −0.120878 0.992667i \(-0.538571\pi\)
−0.120878 + 0.992667i \(0.538571\pi\)
\(312\) 0 0
\(313\) 8.27089 0.467498 0.233749 0.972297i \(-0.424901\pi\)
0.233749 + 0.972297i \(0.424901\pi\)
\(314\) 0 0
\(315\) 10.5315 0.593381
\(316\) 0 0
\(317\) −33.9633 −1.90757 −0.953783 0.300495i \(-0.902848\pi\)
−0.953783 + 0.300495i \(0.902848\pi\)
\(318\) 0 0
\(319\) −4.61172 −0.258207
\(320\) 0 0
\(321\) 13.6477 0.761739
\(322\) 0 0
\(323\) −8.97906 −0.499608
\(324\) 0 0
\(325\) −56.2140 −3.11819
\(326\) 0 0
\(327\) −10.7879 −0.596572
\(328\) 0 0
\(329\) −14.2327 −0.784675
\(330\) 0 0
\(331\) −21.1396 −1.16194 −0.580969 0.813926i \(-0.697326\pi\)
−0.580969 + 0.813926i \(0.697326\pi\)
\(332\) 0 0
\(333\) −8.43013 −0.461968
\(334\) 0 0
\(335\) 33.9555 1.85519
\(336\) 0 0
\(337\) 15.1873 0.827303 0.413651 0.910435i \(-0.364253\pi\)
0.413651 + 0.910435i \(0.364253\pi\)
\(338\) 0 0
\(339\) 14.8279 0.805344
\(340\) 0 0
\(341\) 37.0773 2.00785
\(342\) 0 0
\(343\) −18.9729 −1.02444
\(344\) 0 0
\(345\) 4.08902 0.220145
\(346\) 0 0
\(347\) −19.3836 −1.04056 −0.520282 0.853994i \(-0.674173\pi\)
−0.520282 + 0.853994i \(0.674173\pi\)
\(348\) 0 0
\(349\) 34.6528 1.85492 0.927461 0.373920i \(-0.121987\pi\)
0.927461 + 0.373920i \(0.121987\pi\)
\(350\) 0 0
\(351\) −4.79639 −0.256012
\(352\) 0 0
\(353\) 7.36647 0.392078 0.196039 0.980596i \(-0.437192\pi\)
0.196039 + 0.980596i \(0.437192\pi\)
\(354\) 0 0
\(355\) −0.355939 −0.0188913
\(356\) 0 0
\(357\) −4.71990 −0.249804
\(358\) 0 0
\(359\) 12.8569 0.678559 0.339280 0.940686i \(-0.389817\pi\)
0.339280 + 0.940686i \(0.389817\pi\)
\(360\) 0 0
\(361\) 5.00684 0.263518
\(362\) 0 0
\(363\) 10.2679 0.538927
\(364\) 0 0
\(365\) 37.5157 1.96366
\(366\) 0 0
\(367\) −8.53494 −0.445520 −0.222760 0.974873i \(-0.571507\pi\)
−0.222760 + 0.974873i \(0.571507\pi\)
\(368\) 0 0
\(369\) 8.64925 0.450262
\(370\) 0 0
\(371\) −20.1168 −1.04441
\(372\) 0 0
\(373\) −3.58762 −0.185760 −0.0928799 0.995677i \(-0.529607\pi\)
−0.0928799 + 0.995677i \(0.529607\pi\)
\(374\) 0 0
\(375\) 27.4785 1.41898
\(376\) 0 0
\(377\) 4.79639 0.247027
\(378\) 0 0
\(379\) 1.08870 0.0559229 0.0279614 0.999609i \(-0.491098\pi\)
0.0279614 + 0.999609i \(0.491098\pi\)
\(380\) 0 0
\(381\) −6.83178 −0.350003
\(382\) 0 0
\(383\) −2.77293 −0.141690 −0.0708450 0.997487i \(-0.522570\pi\)
−0.0708450 + 0.997487i \(0.522570\pi\)
\(384\) 0 0
\(385\) 48.5681 2.47526
\(386\) 0 0
\(387\) −7.46071 −0.379249
\(388\) 0 0
\(389\) 13.3371 0.676216 0.338108 0.941107i \(-0.390213\pi\)
0.338108 + 0.941107i \(0.390213\pi\)
\(390\) 0 0
\(391\) −1.83258 −0.0926776
\(392\) 0 0
\(393\) 13.1242 0.662030
\(394\) 0 0
\(395\) −34.2855 −1.72509
\(396\) 0 0
\(397\) 31.3261 1.57221 0.786107 0.618090i \(-0.212093\pi\)
0.786107 + 0.618090i \(0.212093\pi\)
\(398\) 0 0
\(399\) 12.6194 0.631758
\(400\) 0 0
\(401\) 35.8572 1.79063 0.895313 0.445438i \(-0.146952\pi\)
0.895313 + 0.445438i \(0.146952\pi\)
\(402\) 0 0
\(403\) −38.5620 −1.92091
\(404\) 0 0
\(405\) 4.08902 0.203185
\(406\) 0 0
\(407\) −38.8774 −1.92708
\(408\) 0 0
\(409\) 33.1034 1.63686 0.818430 0.574607i \(-0.194845\pi\)
0.818430 + 0.574607i \(0.194845\pi\)
\(410\) 0 0
\(411\) −16.4552 −0.811677
\(412\) 0 0
\(413\) 19.5096 0.960004
\(414\) 0 0
\(415\) −37.6162 −1.84651
\(416\) 0 0
\(417\) 17.7348 0.868477
\(418\) 0 0
\(419\) −27.2056 −1.32908 −0.664540 0.747253i \(-0.731373\pi\)
−0.664540 + 0.747253i \(0.731373\pi\)
\(420\) 0 0
\(421\) 6.97246 0.339817 0.169908 0.985460i \(-0.445653\pi\)
0.169908 + 0.985460i \(0.445653\pi\)
\(422\) 0 0
\(423\) −5.52609 −0.268688
\(424\) 0 0
\(425\) −21.4780 −1.04183
\(426\) 0 0
\(427\) −26.8778 −1.30071
\(428\) 0 0
\(429\) −22.1196 −1.06794
\(430\) 0 0
\(431\) −14.5307 −0.699921 −0.349960 0.936764i \(-0.613805\pi\)
−0.349960 + 0.936764i \(0.613805\pi\)
\(432\) 0 0
\(433\) 36.5362 1.75582 0.877909 0.478828i \(-0.158938\pi\)
0.877909 + 0.478828i \(0.158938\pi\)
\(434\) 0 0
\(435\) −4.08902 −0.196053
\(436\) 0 0
\(437\) 4.89968 0.234383
\(438\) 0 0
\(439\) −12.4792 −0.595600 −0.297800 0.954628i \(-0.596253\pi\)
−0.297800 + 0.954628i \(0.596253\pi\)
\(440\) 0 0
\(441\) −0.366553 −0.0174549
\(442\) 0 0
\(443\) 28.1712 1.33845 0.669226 0.743059i \(-0.266626\pi\)
0.669226 + 0.743059i \(0.266626\pi\)
\(444\) 0 0
\(445\) −48.6792 −2.30762
\(446\) 0 0
\(447\) −13.4929 −0.638190
\(448\) 0 0
\(449\) 20.9088 0.986749 0.493374 0.869817i \(-0.335763\pi\)
0.493374 + 0.869817i \(0.335763\pi\)
\(450\) 0 0
\(451\) 39.8879 1.87825
\(452\) 0 0
\(453\) −6.07542 −0.285448
\(454\) 0 0
\(455\) −50.5130 −2.36809
\(456\) 0 0
\(457\) −22.1453 −1.03591 −0.517956 0.855407i \(-0.673307\pi\)
−0.517956 + 0.855407i \(0.673307\pi\)
\(458\) 0 0
\(459\) −1.83258 −0.0855376
\(460\) 0 0
\(461\) 24.7242 1.15152 0.575760 0.817619i \(-0.304706\pi\)
0.575760 + 0.817619i \(0.304706\pi\)
\(462\) 0 0
\(463\) 1.91742 0.0891101 0.0445550 0.999007i \(-0.485813\pi\)
0.0445550 + 0.999007i \(0.485813\pi\)
\(464\) 0 0
\(465\) 32.8749 1.52454
\(466\) 0 0
\(467\) −5.84323 −0.270393 −0.135196 0.990819i \(-0.543167\pi\)
−0.135196 + 0.990819i \(0.543167\pi\)
\(468\) 0 0
\(469\) 21.3875 0.987584
\(470\) 0 0
\(471\) −7.80818 −0.359782
\(472\) 0 0
\(473\) −34.4067 −1.58202
\(474\) 0 0
\(475\) 57.4245 2.63482
\(476\) 0 0
\(477\) −7.81069 −0.357627
\(478\) 0 0
\(479\) 18.8889 0.863057 0.431529 0.902099i \(-0.357974\pi\)
0.431529 + 0.902099i \(0.357974\pi\)
\(480\) 0 0
\(481\) 40.4342 1.84364
\(482\) 0 0
\(483\) 2.57555 0.117191
\(484\) 0 0
\(485\) 24.5407 1.11434
\(486\) 0 0
\(487\) 17.8317 0.808030 0.404015 0.914752i \(-0.367614\pi\)
0.404015 + 0.914752i \(0.367614\pi\)
\(488\) 0 0
\(489\) −9.01307 −0.407585
\(490\) 0 0
\(491\) 20.8005 0.938712 0.469356 0.883009i \(-0.344486\pi\)
0.469356 + 0.883009i \(0.344486\pi\)
\(492\) 0 0
\(493\) 1.83258 0.0825353
\(494\) 0 0
\(495\) 18.8574 0.847577
\(496\) 0 0
\(497\) −0.224195 −0.0100565
\(498\) 0 0
\(499\) −14.3965 −0.644478 −0.322239 0.946658i \(-0.604435\pi\)
−0.322239 + 0.946658i \(0.604435\pi\)
\(500\) 0 0
\(501\) 16.9939 0.759231
\(502\) 0 0
\(503\) −32.9726 −1.47018 −0.735089 0.677971i \(-0.762859\pi\)
−0.735089 + 0.677971i \(0.762859\pi\)
\(504\) 0 0
\(505\) 58.2917 2.59394
\(506\) 0 0
\(507\) 10.0054 0.444354
\(508\) 0 0
\(509\) −14.8224 −0.656991 −0.328496 0.944506i \(-0.606542\pi\)
−0.328496 + 0.944506i \(0.606542\pi\)
\(510\) 0 0
\(511\) 23.6300 1.04533
\(512\) 0 0
\(513\) 4.89968 0.216326
\(514\) 0 0
\(515\) −65.1382 −2.87033
\(516\) 0 0
\(517\) −25.4848 −1.12082
\(518\) 0 0
\(519\) 20.5627 0.902601
\(520\) 0 0
\(521\) 36.0062 1.57746 0.788730 0.614740i \(-0.210739\pi\)
0.788730 + 0.614740i \(0.210739\pi\)
\(522\) 0 0
\(523\) −2.29678 −0.100431 −0.0502157 0.998738i \(-0.515991\pi\)
−0.0502157 + 0.998738i \(0.515991\pi\)
\(524\) 0 0
\(525\) 30.1856 1.31741
\(526\) 0 0
\(527\) −14.7336 −0.641805
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 7.57493 0.328724
\(532\) 0 0
\(533\) −41.4852 −1.79692
\(534\) 0 0
\(535\) 55.8056 2.41269
\(536\) 0 0
\(537\) 5.34572 0.230685
\(538\) 0 0
\(539\) −1.69044 −0.0728124
\(540\) 0 0
\(541\) 37.7612 1.62348 0.811741 0.584018i \(-0.198520\pi\)
0.811741 + 0.584018i \(0.198520\pi\)
\(542\) 0 0
\(543\) −5.46362 −0.234466
\(544\) 0 0
\(545\) −44.1119 −1.88955
\(546\) 0 0
\(547\) −0.134339 −0.00574390 −0.00287195 0.999996i \(-0.500914\pi\)
−0.00287195 + 0.999996i \(0.500914\pi\)
\(548\) 0 0
\(549\) −10.4358 −0.445388
\(550\) 0 0
\(551\) −4.89968 −0.208733
\(552\) 0 0
\(553\) −21.5954 −0.918329
\(554\) 0 0
\(555\) −34.4710 −1.46321
\(556\) 0 0
\(557\) −18.8767 −0.799833 −0.399917 0.916552i \(-0.630961\pi\)
−0.399917 + 0.916552i \(0.630961\pi\)
\(558\) 0 0
\(559\) 35.7845 1.51352
\(560\) 0 0
\(561\) −8.45135 −0.356816
\(562\) 0 0
\(563\) −43.1815 −1.81988 −0.909941 0.414737i \(-0.863874\pi\)
−0.909941 + 0.414737i \(0.863874\pi\)
\(564\) 0 0
\(565\) 60.6317 2.55080
\(566\) 0 0
\(567\) 2.57555 0.108163
\(568\) 0 0
\(569\) −34.4190 −1.44292 −0.721459 0.692457i \(-0.756528\pi\)
−0.721459 + 0.692457i \(0.756528\pi\)
\(570\) 0 0
\(571\) −7.69661 −0.322093 −0.161047 0.986947i \(-0.551487\pi\)
−0.161047 + 0.986947i \(0.551487\pi\)
\(572\) 0 0
\(573\) −8.74290 −0.365240
\(574\) 0 0
\(575\) 11.7201 0.488760
\(576\) 0 0
\(577\) 18.7060 0.778740 0.389370 0.921082i \(-0.372693\pi\)
0.389370 + 0.921082i \(0.372693\pi\)
\(578\) 0 0
\(579\) −21.2254 −0.882098
\(580\) 0 0
\(581\) −23.6933 −0.982963
\(582\) 0 0
\(583\) −36.0207 −1.49183
\(584\) 0 0
\(585\) −19.6125 −0.810878
\(586\) 0 0
\(587\) 10.1984 0.420934 0.210467 0.977601i \(-0.432502\pi\)
0.210467 + 0.977601i \(0.432502\pi\)
\(588\) 0 0
\(589\) 39.3924 1.62314
\(590\) 0 0
\(591\) −19.3805 −0.797205
\(592\) 0 0
\(593\) −27.5308 −1.13055 −0.565277 0.824901i \(-0.691231\pi\)
−0.565277 + 0.824901i \(0.691231\pi\)
\(594\) 0 0
\(595\) −19.2998 −0.791213
\(596\) 0 0
\(597\) 21.6802 0.887312
\(598\) 0 0
\(599\) −6.81479 −0.278445 −0.139222 0.990261i \(-0.544460\pi\)
−0.139222 + 0.990261i \(0.544460\pi\)
\(600\) 0 0
\(601\) 8.18356 0.333814 0.166907 0.985973i \(-0.446622\pi\)
0.166907 + 0.985973i \(0.446622\pi\)
\(602\) 0 0
\(603\) 8.30407 0.338168
\(604\) 0 0
\(605\) 41.9858 1.70697
\(606\) 0 0
\(607\) −13.2929 −0.539543 −0.269771 0.962924i \(-0.586948\pi\)
−0.269771 + 0.962924i \(0.586948\pi\)
\(608\) 0 0
\(609\) −2.57555 −0.104366
\(610\) 0 0
\(611\) 26.5053 1.07229
\(612\) 0 0
\(613\) −2.91465 −0.117722 −0.0588608 0.998266i \(-0.518747\pi\)
−0.0588608 + 0.998266i \(0.518747\pi\)
\(614\) 0 0
\(615\) 35.3669 1.42613
\(616\) 0 0
\(617\) −48.6323 −1.95786 −0.978931 0.204190i \(-0.934544\pi\)
−0.978931 + 0.204190i \(0.934544\pi\)
\(618\) 0 0
\(619\) −6.13839 −0.246723 −0.123361 0.992362i \(-0.539367\pi\)
−0.123361 + 0.992362i \(0.539367\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −30.6616 −1.22843
\(624\) 0 0
\(625\) 53.7596 2.15038
\(626\) 0 0
\(627\) 22.5959 0.902395
\(628\) 0 0
\(629\) 15.4489 0.615988
\(630\) 0 0
\(631\) −3.23694 −0.128860 −0.0644302 0.997922i \(-0.520523\pi\)
−0.0644302 + 0.997922i \(0.520523\pi\)
\(632\) 0 0
\(633\) 25.2974 1.00548
\(634\) 0 0
\(635\) −27.9353 −1.10858
\(636\) 0 0
\(637\) 1.75813 0.0696597
\(638\) 0 0
\(639\) −0.0870476 −0.00344355
\(640\) 0 0
\(641\) 32.5722 1.28652 0.643262 0.765646i \(-0.277581\pi\)
0.643262 + 0.765646i \(0.277581\pi\)
\(642\) 0 0
\(643\) −3.35815 −0.132433 −0.0662163 0.997805i \(-0.521093\pi\)
−0.0662163 + 0.997805i \(0.521093\pi\)
\(644\) 0 0
\(645\) −30.5070 −1.20121
\(646\) 0 0
\(647\) 25.7591 1.01270 0.506348 0.862329i \(-0.330995\pi\)
0.506348 + 0.862329i \(0.330995\pi\)
\(648\) 0 0
\(649\) 34.9334 1.37126
\(650\) 0 0
\(651\) 20.7069 0.811567
\(652\) 0 0
\(653\) −13.9565 −0.546162 −0.273081 0.961991i \(-0.588043\pi\)
−0.273081 + 0.961991i \(0.588043\pi\)
\(654\) 0 0
\(655\) 53.6652 2.09687
\(656\) 0 0
\(657\) 9.17475 0.357941
\(658\) 0 0
\(659\) −40.1400 −1.56363 −0.781815 0.623510i \(-0.785706\pi\)
−0.781815 + 0.623510i \(0.785706\pi\)
\(660\) 0 0
\(661\) 19.1524 0.744944 0.372472 0.928043i \(-0.378510\pi\)
0.372472 + 0.928043i \(0.378510\pi\)
\(662\) 0 0
\(663\) 8.78978 0.341367
\(664\) 0 0
\(665\) 51.6008 2.00099
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −22.4964 −0.869760
\(670\) 0 0
\(671\) −48.1269 −1.85792
\(672\) 0 0
\(673\) 21.5637 0.831221 0.415610 0.909543i \(-0.363568\pi\)
0.415610 + 0.909543i \(0.363568\pi\)
\(674\) 0 0
\(675\) 11.7201 0.451105
\(676\) 0 0
\(677\) −4.25248 −0.163436 −0.0817180 0.996655i \(-0.526041\pi\)
−0.0817180 + 0.996655i \(0.526041\pi\)
\(678\) 0 0
\(679\) 15.4575 0.593203
\(680\) 0 0
\(681\) 0.0204943 0.000785344 0
\(682\) 0 0
\(683\) 21.3257 0.816006 0.408003 0.912981i \(-0.366225\pi\)
0.408003 + 0.912981i \(0.366225\pi\)
\(684\) 0 0
\(685\) −67.2858 −2.57086
\(686\) 0 0
\(687\) −14.9723 −0.571230
\(688\) 0 0
\(689\) 37.4631 1.42723
\(690\) 0 0
\(691\) −5.87470 −0.223484 −0.111742 0.993737i \(-0.535643\pi\)
−0.111742 + 0.993737i \(0.535643\pi\)
\(692\) 0 0
\(693\) 11.8777 0.451197
\(694\) 0 0
\(695\) 72.5179 2.75076
\(696\) 0 0
\(697\) −15.8504 −0.600378
\(698\) 0 0
\(699\) −7.81673 −0.295656
\(700\) 0 0
\(701\) −18.4384 −0.696410 −0.348205 0.937419i \(-0.613209\pi\)
−0.348205 + 0.937419i \(0.613209\pi\)
\(702\) 0 0
\(703\) −41.3049 −1.55785
\(704\) 0 0
\(705\) −22.5963 −0.851025
\(706\) 0 0
\(707\) 36.7161 1.38085
\(708\) 0 0
\(709\) 44.5791 1.67421 0.837103 0.547046i \(-0.184248\pi\)
0.837103 + 0.547046i \(0.184248\pi\)
\(710\) 0 0
\(711\) −8.38478 −0.314454
\(712\) 0 0
\(713\) 8.03980 0.301093
\(714\) 0 0
\(715\) −90.4474 −3.38254
\(716\) 0 0
\(717\) −8.24516 −0.307921
\(718\) 0 0
\(719\) 20.6171 0.768888 0.384444 0.923148i \(-0.374393\pi\)
0.384444 + 0.923148i \(0.374393\pi\)
\(720\) 0 0
\(721\) −41.0286 −1.52798
\(722\) 0 0
\(723\) 2.39246 0.0889766
\(724\) 0 0
\(725\) −11.7201 −0.435272
\(726\) 0 0
\(727\) 17.2029 0.638021 0.319010 0.947751i \(-0.396650\pi\)
0.319010 + 0.947751i \(0.396650\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 13.6724 0.505691
\(732\) 0 0
\(733\) −27.3497 −1.01018 −0.505092 0.863065i \(-0.668541\pi\)
−0.505092 + 0.863065i \(0.668541\pi\)
\(734\) 0 0
\(735\) −1.49884 −0.0552856
\(736\) 0 0
\(737\) 38.2960 1.41065
\(738\) 0 0
\(739\) 5.64790 0.207761 0.103881 0.994590i \(-0.466874\pi\)
0.103881 + 0.994590i \(0.466874\pi\)
\(740\) 0 0
\(741\) −23.5008 −0.863322
\(742\) 0 0
\(743\) 33.4297 1.22642 0.613208 0.789922i \(-0.289879\pi\)
0.613208 + 0.789922i \(0.289879\pi\)
\(744\) 0 0
\(745\) −55.1725 −2.02136
\(746\) 0 0
\(747\) −9.19932 −0.336586
\(748\) 0 0
\(749\) 35.1503 1.28436
\(750\) 0 0
\(751\) −5.76461 −0.210354 −0.105177 0.994454i \(-0.533541\pi\)
−0.105177 + 0.994454i \(0.533541\pi\)
\(752\) 0 0
\(753\) 5.14853 0.187623
\(754\) 0 0
\(755\) −24.8425 −0.904111
\(756\) 0 0
\(757\) 35.7253 1.29846 0.649229 0.760593i \(-0.275092\pi\)
0.649229 + 0.760593i \(0.275092\pi\)
\(758\) 0 0
\(759\) 4.61172 0.167395
\(760\) 0 0
\(761\) −43.5930 −1.58025 −0.790123 0.612948i \(-0.789983\pi\)
−0.790123 + 0.612948i \(0.789983\pi\)
\(762\) 0 0
\(763\) −27.7847 −1.00588
\(764\) 0 0
\(765\) −7.49346 −0.270927
\(766\) 0 0
\(767\) −36.3323 −1.31188
\(768\) 0 0
\(769\) 2.90207 0.104651 0.0523257 0.998630i \(-0.483337\pi\)
0.0523257 + 0.998630i \(0.483337\pi\)
\(770\) 0 0
\(771\) 19.8047 0.713248
\(772\) 0 0
\(773\) −18.6284 −0.670016 −0.335008 0.942215i \(-0.608739\pi\)
−0.335008 + 0.942215i \(0.608739\pi\)
\(774\) 0 0
\(775\) 94.2270 3.38473
\(776\) 0 0
\(777\) −21.7122 −0.778921
\(778\) 0 0
\(779\) 42.3785 1.51837
\(780\) 0 0
\(781\) −0.401439 −0.0143646
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −31.9278 −1.13955
\(786\) 0 0
\(787\) −17.0913 −0.609239 −0.304619 0.952474i \(-0.598529\pi\)
−0.304619 + 0.952474i \(0.598529\pi\)
\(788\) 0 0
\(789\) −29.0507 −1.03423
\(790\) 0 0
\(791\) 38.1901 1.35788
\(792\) 0 0
\(793\) 50.0541 1.77747
\(794\) 0 0
\(795\) −31.9381 −1.13273
\(796\) 0 0
\(797\) 14.4626 0.512291 0.256146 0.966638i \(-0.417547\pi\)
0.256146 + 0.966638i \(0.417547\pi\)
\(798\) 0 0
\(799\) 10.1270 0.358268
\(800\) 0 0
\(801\) −11.9049 −0.420638
\(802\) 0 0
\(803\) 42.3114 1.49314
\(804\) 0 0
\(805\) 10.5315 0.371185
\(806\) 0 0
\(807\) −8.83872 −0.311138
\(808\) 0 0
\(809\) 11.8020 0.414937 0.207468 0.978242i \(-0.433478\pi\)
0.207468 + 0.978242i \(0.433478\pi\)
\(810\) 0 0
\(811\) −14.9607 −0.525342 −0.262671 0.964885i \(-0.584603\pi\)
−0.262671 + 0.964885i \(0.584603\pi\)
\(812\) 0 0
\(813\) −10.4526 −0.366589
\(814\) 0 0
\(815\) −36.8546 −1.29096
\(816\) 0 0
\(817\) −36.5551 −1.27890
\(818\) 0 0
\(819\) −12.3533 −0.431660
\(820\) 0 0
\(821\) −1.87938 −0.0655908 −0.0327954 0.999462i \(-0.510441\pi\)
−0.0327954 + 0.999462i \(0.510441\pi\)
\(822\) 0 0
\(823\) 37.3394 1.30157 0.650785 0.759262i \(-0.274440\pi\)
0.650785 + 0.759262i \(0.274440\pi\)
\(824\) 0 0
\(825\) 54.0496 1.88177
\(826\) 0 0
\(827\) −5.86439 −0.203925 −0.101962 0.994788i \(-0.532512\pi\)
−0.101962 + 0.994788i \(0.532512\pi\)
\(828\) 0 0
\(829\) 51.8217 1.79984 0.899920 0.436054i \(-0.143624\pi\)
0.899920 + 0.436054i \(0.143624\pi\)
\(830\) 0 0
\(831\) −11.7721 −0.408370
\(832\) 0 0
\(833\) 0.671738 0.0232744
\(834\) 0 0
\(835\) 69.4883 2.40474
\(836\) 0 0
\(837\) 8.03980 0.277896
\(838\) 0 0
\(839\) −43.0640 −1.48674 −0.743368 0.668883i \(-0.766773\pi\)
−0.743368 + 0.668883i \(0.766773\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −30.2251 −1.04101
\(844\) 0 0
\(845\) 40.9121 1.40742
\(846\) 0 0
\(847\) 26.4456 0.908681
\(848\) 0 0
\(849\) −18.5425 −0.636376
\(850\) 0 0
\(851\) −8.43013 −0.288981
\(852\) 0 0
\(853\) −5.44120 −0.186303 −0.0931515 0.995652i \(-0.529694\pi\)
−0.0931515 + 0.995652i \(0.529694\pi\)
\(854\) 0 0
\(855\) 20.0349 0.685178
\(856\) 0 0
\(857\) 2.25114 0.0768974 0.0384487 0.999261i \(-0.487758\pi\)
0.0384487 + 0.999261i \(0.487758\pi\)
\(858\) 0 0
\(859\) −22.2512 −0.759203 −0.379601 0.925150i \(-0.623939\pi\)
−0.379601 + 0.925150i \(0.623939\pi\)
\(860\) 0 0
\(861\) 22.2765 0.759183
\(862\) 0 0
\(863\) 14.2820 0.486164 0.243082 0.970006i \(-0.421842\pi\)
0.243082 + 0.970006i \(0.421842\pi\)
\(864\) 0 0
\(865\) 84.0812 2.85884
\(866\) 0 0
\(867\) −13.6416 −0.463295
\(868\) 0 0
\(869\) −38.6682 −1.31173
\(870\) 0 0
\(871\) −39.8295 −1.34957
\(872\) 0 0
\(873\) 6.00162 0.203124
\(874\) 0 0
\(875\) 70.7721 2.39253
\(876\) 0 0
\(877\) −1.50627 −0.0508631 −0.0254315 0.999677i \(-0.508096\pi\)
−0.0254315 + 0.999677i \(0.508096\pi\)
\(878\) 0 0
\(879\) 12.1800 0.410821
\(880\) 0 0
\(881\) −1.41483 −0.0476669 −0.0238335 0.999716i \(-0.507587\pi\)
−0.0238335 + 0.999716i \(0.507587\pi\)
\(882\) 0 0
\(883\) 31.0284 1.04419 0.522095 0.852888i \(-0.325151\pi\)
0.522095 + 0.852888i \(0.325151\pi\)
\(884\) 0 0
\(885\) 30.9740 1.04118
\(886\) 0 0
\(887\) 53.7505 1.80477 0.902383 0.430935i \(-0.141816\pi\)
0.902383 + 0.430935i \(0.141816\pi\)
\(888\) 0 0
\(889\) −17.5956 −0.590137
\(890\) 0 0
\(891\) 4.61172 0.154498
\(892\) 0 0
\(893\) −27.0761 −0.906066
\(894\) 0 0
\(895\) 21.8587 0.730657
\(896\) 0 0
\(897\) −4.79639 −0.160147
\(898\) 0 0
\(899\) −8.03980 −0.268142
\(900\) 0 0
\(901\) 14.3137 0.476859
\(902\) 0 0
\(903\) −19.2154 −0.639449
\(904\) 0 0
\(905\) −22.3408 −0.742635
\(906\) 0 0
\(907\) −43.5740 −1.44685 −0.723426 0.690402i \(-0.757434\pi\)
−0.723426 + 0.690402i \(0.757434\pi\)
\(908\) 0 0
\(909\) 14.2557 0.472830
\(910\) 0 0
\(911\) −26.4435 −0.876114 −0.438057 0.898947i \(-0.644333\pi\)
−0.438057 + 0.898947i \(0.644333\pi\)
\(912\) 0 0
\(913\) −42.4247 −1.40405
\(914\) 0 0
\(915\) −42.6721 −1.41070
\(916\) 0 0
\(917\) 33.8021 1.11624
\(918\) 0 0
\(919\) −54.2766 −1.79042 −0.895209 0.445646i \(-0.852974\pi\)
−0.895209 + 0.445646i \(0.852974\pi\)
\(920\) 0 0
\(921\) 23.3621 0.769807
\(922\) 0 0
\(923\) 0.417514 0.0137426
\(924\) 0 0
\(925\) −98.8017 −3.24858
\(926\) 0 0
\(927\) −15.9300 −0.523211
\(928\) 0 0
\(929\) −32.9093 −1.07972 −0.539859 0.841755i \(-0.681522\pi\)
−0.539859 + 0.841755i \(0.681522\pi\)
\(930\) 0 0
\(931\) −1.79599 −0.0588613
\(932\) 0 0
\(933\) −4.26341 −0.139578
\(934\) 0 0
\(935\) −34.5577 −1.13016
\(936\) 0 0
\(937\) −52.6248 −1.71918 −0.859589 0.510986i \(-0.829281\pi\)
−0.859589 + 0.510986i \(0.829281\pi\)
\(938\) 0 0
\(939\) 8.27089 0.269910
\(940\) 0 0
\(941\) 31.9101 1.04024 0.520121 0.854093i \(-0.325887\pi\)
0.520121 + 0.854093i \(0.325887\pi\)
\(942\) 0 0
\(943\) 8.64925 0.281658
\(944\) 0 0
\(945\) 10.5315 0.342588
\(946\) 0 0
\(947\) 37.9610 1.23357 0.616783 0.787134i \(-0.288436\pi\)
0.616783 + 0.787134i \(0.288436\pi\)
\(948\) 0 0
\(949\) −44.0057 −1.42848
\(950\) 0 0
\(951\) −33.9633 −1.10133
\(952\) 0 0
\(953\) 2.24358 0.0726765 0.0363383 0.999340i \(-0.488431\pi\)
0.0363383 + 0.999340i \(0.488431\pi\)
\(954\) 0 0
\(955\) −35.7499 −1.15684
\(956\) 0 0
\(957\) −4.61172 −0.149076
\(958\) 0 0
\(959\) −42.3813 −1.36856
\(960\) 0 0
\(961\) 33.6384 1.08511
\(962\) 0 0
\(963\) 13.6477 0.439790
\(964\) 0 0
\(965\) −86.7911 −2.79390
\(966\) 0 0
\(967\) −1.55361 −0.0499608 −0.0249804 0.999688i \(-0.507952\pi\)
−0.0249804 + 0.999688i \(0.507952\pi\)
\(968\) 0 0
\(969\) −8.97906 −0.288449
\(970\) 0 0
\(971\) −42.2327 −1.35531 −0.677655 0.735380i \(-0.737004\pi\)
−0.677655 + 0.735380i \(0.737004\pi\)
\(972\) 0 0
\(973\) 45.6768 1.46433
\(974\) 0 0
\(975\) −56.2140 −1.80029
\(976\) 0 0
\(977\) −13.1262 −0.419946 −0.209973 0.977707i \(-0.567338\pi\)
−0.209973 + 0.977707i \(0.567338\pi\)
\(978\) 0 0
\(979\) −54.9019 −1.75467
\(980\) 0 0
\(981\) −10.7879 −0.344431
\(982\) 0 0
\(983\) 44.3672 1.41510 0.707548 0.706666i \(-0.249801\pi\)
0.707548 + 0.706666i \(0.249801\pi\)
\(984\) 0 0
\(985\) −79.2470 −2.52502
\(986\) 0 0
\(987\) −14.2327 −0.453032
\(988\) 0 0
\(989\) −7.46071 −0.237237
\(990\) 0 0
\(991\) −12.8996 −0.409770 −0.204885 0.978786i \(-0.565682\pi\)
−0.204885 + 0.978786i \(0.565682\pi\)
\(992\) 0 0
\(993\) −21.1396 −0.670845
\(994\) 0 0
\(995\) 88.6508 2.81042
\(996\) 0 0
\(997\) 35.7713 1.13289 0.566445 0.824100i \(-0.308319\pi\)
0.566445 + 0.824100i \(0.308319\pi\)
\(998\) 0 0
\(999\) −8.43013 −0.266718
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 \(a_p\))