Properties

Label 4014.2.a.q.1.3
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 1
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.10273.1
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 1.3
Root \(0.673533\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-0.326467 q^{5}\) \(-1.59754 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-0.326467 q^{5}\) \(-1.59754 q^{7}\) \(+1.00000 q^{8}\) \(-0.326467 q^{10}\) \(+2.21989 q^{11}\) \(+2.49096 q^{13}\) \(-1.59754 q^{14}\) \(+1.00000 q^{16}\) \(-6.46037 q^{17}\) \(-7.66776 q^{19}\) \(-0.326467 q^{20}\) \(+2.21989 q^{22}\) \(-2.91402 q^{23}\) \(-4.89342 q^{25}\) \(+2.49096 q^{26}\) \(-1.59754 q^{28}\) \(+4.18930 q^{29}\) \(+5.66776 q^{31}\) \(+1.00000 q^{32}\) \(-6.46037 q^{34}\) \(+0.521543 q^{35}\) \(-2.05540 q^{37}\) \(-7.66776 q^{38}\) \(-0.326467 q^{40}\) \(-12.2901 q^{41}\) \(-8.89342 q^{43}\) \(+2.21989 q^{44}\) \(-2.91402 q^{46}\) \(+8.26530 q^{47}\) \(-4.44787 q^{49}\) \(-4.89342 q^{50}\) \(+2.49096 q^{52}\) \(+6.20990 q^{53}\) \(-0.724719 q^{55}\) \(-1.59754 q^{56}\) \(+4.18930 q^{58}\) \(+0.283381 q^{59}\) \(-2.94460 q^{61}\) \(+5.66776 q^{62}\) \(+1.00000 q^{64}\) \(-0.813215 q^{65}\) \(-5.67353 q^{67}\) \(-6.46037 q^{68}\) \(+0.521543 q^{70}\) \(-4.12141 q^{71}\) \(+7.69257 q^{73}\) \(-2.05540 q^{74}\) \(-7.66776 q^{76}\) \(-3.54635 q^{77}\) \(-0.116565 q^{79}\) \(-0.326467 q^{80}\) \(-12.2901 q^{82}\) \(+7.08850 q^{83}\) \(+2.10910 q^{85}\) \(-8.89342 q^{86}\) \(+2.21989 q^{88}\) \(-0.513252 q^{89}\) \(-3.97940 q^{91}\) \(-2.91402 q^{92}\) \(+8.26530 q^{94}\) \(+2.50327 q^{95}\) \(-6.38186 q^{97}\) \(-4.44787 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 5q^{28} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut -\mathstrut 3q^{73} \) \(\mathstrut -\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 7q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −0.326467 −0.146000 −0.0730002 0.997332i \(-0.523257\pi\)
−0.0730002 + 0.997332i \(0.523257\pi\)
\(6\) 0 0
\(7\) −1.59754 −0.603813 −0.301906 0.953338i \(-0.597623\pi\)
−0.301906 + 0.953338i \(0.597623\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.326467 −0.103238
\(11\) 2.21989 0.669321 0.334660 0.942339i \(-0.391378\pi\)
0.334660 + 0.942339i \(0.391378\pi\)
\(12\) 0 0
\(13\) 2.49096 0.690867 0.345434 0.938443i \(-0.387732\pi\)
0.345434 + 0.938443i \(0.387732\pi\)
\(14\) −1.59754 −0.426960
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.46037 −1.56687 −0.783435 0.621473i \(-0.786534\pi\)
−0.783435 + 0.621473i \(0.786534\pi\)
\(18\) 0 0
\(19\) −7.66776 −1.75910 −0.879552 0.475802i \(-0.842158\pi\)
−0.879552 + 0.475802i \(0.842158\pi\)
\(20\) −0.326467 −0.0730002
\(21\) 0 0
\(22\) 2.21989 0.473281
\(23\) −2.91402 −0.607615 −0.303808 0.952733i \(-0.598258\pi\)
−0.303808 + 0.952733i \(0.598258\pi\)
\(24\) 0 0
\(25\) −4.89342 −0.978684
\(26\) 2.49096 0.488517
\(27\) 0 0
\(28\) −1.59754 −0.301906
\(29\) 4.18930 0.777934 0.388967 0.921252i \(-0.372832\pi\)
0.388967 + 0.921252i \(0.372832\pi\)
\(30\) 0 0
\(31\) 5.66776 1.01796 0.508980 0.860779i \(-0.330023\pi\)
0.508980 + 0.860779i \(0.330023\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −6.46037 −1.10794
\(35\) 0.521543 0.0881568
\(36\) 0 0
\(37\) −2.05540 −0.337905 −0.168952 0.985624i \(-0.554038\pi\)
−0.168952 + 0.985624i \(0.554038\pi\)
\(38\) −7.66776 −1.24387
\(39\) 0 0
\(40\) −0.326467 −0.0516189
\(41\) −12.2901 −1.91939 −0.959696 0.281040i \(-0.909321\pi\)
−0.959696 + 0.281040i \(0.909321\pi\)
\(42\) 0 0
\(43\) −8.89342 −1.35623 −0.678117 0.734954i \(-0.737204\pi\)
−0.678117 + 0.734954i \(0.737204\pi\)
\(44\) 2.21989 0.334660
\(45\) 0 0
\(46\) −2.91402 −0.429649
\(47\) 8.26530 1.20562 0.602809 0.797886i \(-0.294048\pi\)
0.602809 + 0.797886i \(0.294048\pi\)
\(48\) 0 0
\(49\) −4.44787 −0.635410
\(50\) −4.89342 −0.692034
\(51\) 0 0
\(52\) 2.49096 0.345434
\(53\) 6.20990 0.852996 0.426498 0.904489i \(-0.359747\pi\)
0.426498 + 0.904489i \(0.359747\pi\)
\(54\) 0 0
\(55\) −0.724719 −0.0977211
\(56\) −1.59754 −0.213480
\(57\) 0 0
\(58\) 4.18930 0.550082
\(59\) 0.283381 0.0368930 0.0184465 0.999830i \(-0.494128\pi\)
0.0184465 + 0.999830i \(0.494128\pi\)
\(60\) 0 0
\(61\) −2.94460 −0.377018 −0.188509 0.982071i \(-0.560365\pi\)
−0.188509 + 0.982071i \(0.560365\pi\)
\(62\) 5.66776 0.719806
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.813215 −0.100867
\(66\) 0 0
\(67\) −5.67353 −0.693132 −0.346566 0.938026i \(-0.612652\pi\)
−0.346566 + 0.938026i \(0.612652\pi\)
\(68\) −6.46037 −0.783435
\(69\) 0 0
\(70\) 0.521543 0.0623363
\(71\) −4.12141 −0.489121 −0.244560 0.969634i \(-0.578644\pi\)
−0.244560 + 0.969634i \(0.578644\pi\)
\(72\) 0 0
\(73\) 7.69257 0.900347 0.450173 0.892941i \(-0.351362\pi\)
0.450173 + 0.892941i \(0.351362\pi\)
\(74\) −2.05540 −0.238935
\(75\) 0 0
\(76\) −7.66776 −0.879552
\(77\) −3.54635 −0.404144
\(78\) 0 0
\(79\) −0.116565 −0.0131146 −0.00655732 0.999979i \(-0.502087\pi\)
−0.00655732 + 0.999979i \(0.502087\pi\)
\(80\) −0.326467 −0.0365001
\(81\) 0 0
\(82\) −12.2901 −1.35722
\(83\) 7.08850 0.778063 0.389032 0.921224i \(-0.372810\pi\)
0.389032 + 0.921224i \(0.372810\pi\)
\(84\) 0 0
\(85\) 2.10910 0.228764
\(86\) −8.89342 −0.959002
\(87\) 0 0
\(88\) 2.21989 0.236641
\(89\) −0.513252 −0.0544046 −0.0272023 0.999630i \(-0.508660\pi\)
−0.0272023 + 0.999630i \(0.508660\pi\)
\(90\) 0 0
\(91\) −3.97940 −0.417154
\(92\) −2.91402 −0.303808
\(93\) 0 0
\(94\) 8.26530 0.852500
\(95\) 2.50327 0.256830
\(96\) 0 0
\(97\) −6.38186 −0.647980 −0.323990 0.946061i \(-0.605024\pi\)
−0.323990 + 0.946061i \(0.605024\pi\)
\(98\) −4.44787 −0.449303
\(99\) 0 0
\(100\) −4.89342 −0.489342
\(101\) 12.2801 1.22192 0.610959 0.791662i \(-0.290784\pi\)
0.610959 + 0.791662i \(0.290784\pi\)
\(102\) 0 0
\(103\) −19.4504 −1.91650 −0.958252 0.285926i \(-0.907699\pi\)
−0.958252 + 0.285926i \(0.907699\pi\)
\(104\) 2.49096 0.244258
\(105\) 0 0
\(106\) 6.20990 0.603159
\(107\) 6.16028 0.595537 0.297768 0.954638i \(-0.403758\pi\)
0.297768 + 0.954638i \(0.403758\pi\)
\(108\) 0 0
\(109\) −9.68026 −0.927201 −0.463600 0.886044i \(-0.653443\pi\)
−0.463600 + 0.886044i \(0.653443\pi\)
\(110\) −0.724719 −0.0690992
\(111\) 0 0
\(112\) −1.59754 −0.150953
\(113\) −3.79915 −0.357394 −0.178697 0.983904i \(-0.557188\pi\)
−0.178697 + 0.983904i \(0.557188\pi\)
\(114\) 0 0
\(115\) 0.951330 0.0887120
\(116\) 4.18930 0.388967
\(117\) 0 0
\(118\) 0.283381 0.0260873
\(119\) 10.3207 0.946096
\(120\) 0 0
\(121\) −6.07211 −0.552010
\(122\) −2.94460 −0.266592
\(123\) 0 0
\(124\) 5.66776 0.508980
\(125\) 3.22987 0.288888
\(126\) 0 0
\(127\) −17.9861 −1.59601 −0.798005 0.602650i \(-0.794111\pi\)
−0.798005 + 0.602650i \(0.794111\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −0.813215 −0.0713236
\(131\) −7.32898 −0.640336 −0.320168 0.947361i \(-0.603739\pi\)
−0.320168 + 0.947361i \(0.603739\pi\)
\(132\) 0 0
\(133\) 12.2495 1.06217
\(134\) −5.67353 −0.490119
\(135\) 0 0
\(136\) −6.46037 −0.553972
\(137\) 8.66776 0.740537 0.370268 0.928925i \(-0.379266\pi\)
0.370268 + 0.928925i \(0.379266\pi\)
\(138\) 0 0
\(139\) 5.85706 0.496789 0.248395 0.968659i \(-0.420097\pi\)
0.248395 + 0.968659i \(0.420097\pi\)
\(140\) 0.521543 0.0440784
\(141\) 0 0
\(142\) −4.12141 −0.345861
\(143\) 5.52964 0.462412
\(144\) 0 0
\(145\) −1.36767 −0.113579
\(146\) 7.69257 0.636641
\(147\) 0 0
\(148\) −2.05540 −0.168952
\(149\) 15.7586 1.29099 0.645497 0.763763i \(-0.276650\pi\)
0.645497 + 0.763763i \(0.276650\pi\)
\(150\) 0 0
\(151\) −7.78263 −0.633341 −0.316671 0.948536i \(-0.602565\pi\)
−0.316671 + 0.948536i \(0.602565\pi\)
\(152\) −7.66776 −0.621937
\(153\) 0 0
\(154\) −3.54635 −0.285773
\(155\) −1.85033 −0.148622
\(156\) 0 0
\(157\) 3.52575 0.281386 0.140693 0.990053i \(-0.455067\pi\)
0.140693 + 0.990053i \(0.455067\pi\)
\(158\) −0.116565 −0.00927345
\(159\) 0 0
\(160\) −0.326467 −0.0258095
\(161\) 4.65526 0.366886
\(162\) 0 0
\(163\) 0.0621204 0.00486564 0.00243282 0.999997i \(-0.499226\pi\)
0.00243282 + 0.999997i \(0.499226\pi\)
\(164\) −12.2901 −0.959696
\(165\) 0 0
\(166\) 7.08850 0.550174
\(167\) −2.08850 −0.161613 −0.0808063 0.996730i \(-0.525750\pi\)
−0.0808063 + 0.996730i \(0.525750\pi\)
\(168\) 0 0
\(169\) −6.79513 −0.522702
\(170\) 2.10910 0.161760
\(171\) 0 0
\(172\) −8.89342 −0.678117
\(173\) 14.2597 1.08415 0.542073 0.840331i \(-0.317640\pi\)
0.542073 + 0.840331i \(0.317640\pi\)
\(174\) 0 0
\(175\) 7.81742 0.590942
\(176\) 2.21989 0.167330
\(177\) 0 0
\(178\) −0.513252 −0.0384699
\(179\) −24.5192 −1.83265 −0.916327 0.400431i \(-0.868860\pi\)
−0.916327 + 0.400431i \(0.868860\pi\)
\(180\) 0 0
\(181\) −18.2125 −1.35373 −0.676864 0.736108i \(-0.736661\pi\)
−0.676864 + 0.736108i \(0.736661\pi\)
\(182\) −3.97940 −0.294973
\(183\) 0 0
\(184\) −2.91402 −0.214824
\(185\) 0.671018 0.0493342
\(186\) 0 0
\(187\) −14.3413 −1.04874
\(188\) 8.26530 0.602809
\(189\) 0 0
\(190\) 2.50327 0.181606
\(191\) −21.0644 −1.52417 −0.762085 0.647477i \(-0.775824\pi\)
−0.762085 + 0.647477i \(0.775824\pi\)
\(192\) 0 0
\(193\) −27.0985 −1.95059 −0.975296 0.220901i \(-0.929100\pi\)
−0.975296 + 0.220901i \(0.929100\pi\)
\(194\) −6.38186 −0.458191
\(195\) 0 0
\(196\) −4.44787 −0.317705
\(197\) −17.7547 −1.26497 −0.632485 0.774573i \(-0.717965\pi\)
−0.632485 + 0.774573i \(0.717965\pi\)
\(198\) 0 0
\(199\) 20.2190 1.43328 0.716642 0.697442i \(-0.245678\pi\)
0.716642 + 0.697442i \(0.245678\pi\)
\(200\) −4.89342 −0.346017
\(201\) 0 0
\(202\) 12.2801 0.864026
\(203\) −6.69257 −0.469726
\(204\) 0 0
\(205\) 4.01231 0.280232
\(206\) −19.4504 −1.35517
\(207\) 0 0
\(208\) 2.49096 0.172717
\(209\) −17.0216 −1.17741
\(210\) 0 0
\(211\) −11.3049 −0.778264 −0.389132 0.921182i \(-0.627225\pi\)
−0.389132 + 0.921182i \(0.627225\pi\)
\(212\) 6.20990 0.426498
\(213\) 0 0
\(214\) 6.16028 0.421108
\(215\) 2.90340 0.198011
\(216\) 0 0
\(217\) −9.05446 −0.614657
\(218\) −9.68026 −0.655630
\(219\) 0 0
\(220\) −0.724719 −0.0488605
\(221\) −16.0925 −1.08250
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) −1.59754 −0.106740
\(225\) 0 0
\(226\) −3.79915 −0.252716
\(227\) −18.8653 −1.25214 −0.626069 0.779768i \(-0.715337\pi\)
−0.626069 + 0.779768i \(0.715337\pi\)
\(228\) 0 0
\(229\) 25.1506 1.66200 0.831000 0.556273i \(-0.187769\pi\)
0.831000 + 0.556273i \(0.187769\pi\)
\(230\) 0.951330 0.0627289
\(231\) 0 0
\(232\) 4.18930 0.275041
\(233\) 2.13736 0.140023 0.0700115 0.997546i \(-0.477696\pi\)
0.0700115 + 0.997546i \(0.477696\pi\)
\(234\) 0 0
\(235\) −2.69834 −0.176021
\(236\) 0.283381 0.0184465
\(237\) 0 0
\(238\) 10.3207 0.668991
\(239\) −0.112547 −0.00728005 −0.00364003 0.999993i \(-0.501159\pi\)
−0.00364003 + 0.999993i \(0.501159\pi\)
\(240\) 0 0
\(241\) 13.8957 0.895104 0.447552 0.894258i \(-0.352296\pi\)
0.447552 + 0.894258i \(0.352296\pi\)
\(242\) −6.07211 −0.390330
\(243\) 0 0
\(244\) −2.94460 −0.188509
\(245\) 1.45208 0.0927701
\(246\) 0 0
\(247\) −19.1001 −1.21531
\(248\) 5.66776 0.359903
\(249\) 0 0
\(250\) 3.22987 0.204275
\(251\) −1.18698 −0.0749213 −0.0374607 0.999298i \(-0.511927\pi\)
−0.0374607 + 0.999298i \(0.511927\pi\)
\(252\) 0 0
\(253\) −6.46879 −0.406689
\(254\) −17.9861 −1.12855
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 9.49749 0.592437 0.296219 0.955120i \(-0.404274\pi\)
0.296219 + 0.955120i \(0.404274\pi\)
\(258\) 0 0
\(259\) 3.28357 0.204031
\(260\) −0.813215 −0.0504334
\(261\) 0 0
\(262\) −7.32898 −0.452786
\(263\) 20.2440 1.24830 0.624148 0.781306i \(-0.285446\pi\)
0.624148 + 0.781306i \(0.285446\pi\)
\(264\) 0 0
\(265\) −2.02733 −0.124538
\(266\) 12.2495 0.751067
\(267\) 0 0
\(268\) −5.67353 −0.346566
\(269\) 9.55885 0.582814 0.291407 0.956599i \(-0.405877\pi\)
0.291407 + 0.956599i \(0.405877\pi\)
\(270\) 0 0
\(271\) 24.0547 1.46122 0.730608 0.682797i \(-0.239237\pi\)
0.730608 + 0.682797i \(0.239237\pi\)
\(272\) −6.46037 −0.391718
\(273\) 0 0
\(274\) 8.66776 0.523638
\(275\) −10.8628 −0.655054
\(276\) 0 0
\(277\) 30.8702 1.85481 0.927405 0.374059i \(-0.122034\pi\)
0.927405 + 0.374059i \(0.122034\pi\)
\(278\) 5.85706 0.351283
\(279\) 0 0
\(280\) 0.521543 0.0311681
\(281\) −6.78665 −0.404857 −0.202429 0.979297i \(-0.564883\pi\)
−0.202429 + 0.979297i \(0.564883\pi\)
\(282\) 0 0
\(283\) 12.2466 0.727984 0.363992 0.931402i \(-0.381414\pi\)
0.363992 + 0.931402i \(0.381414\pi\)
\(284\) −4.12141 −0.244560
\(285\) 0 0
\(286\) 5.52964 0.326975
\(287\) 19.6339 1.15895
\(288\) 0 0
\(289\) 24.7364 1.45508
\(290\) −1.36767 −0.0803122
\(291\) 0 0
\(292\) 7.69257 0.450173
\(293\) 10.7176 0.626127 0.313064 0.949732i \(-0.398645\pi\)
0.313064 + 0.949732i \(0.398645\pi\)
\(294\) 0 0
\(295\) −0.0925144 −0.00538640
\(296\) −2.05540 −0.119467
\(297\) 0 0
\(298\) 15.7586 0.912870
\(299\) −7.25870 −0.419781
\(300\) 0 0
\(301\) 14.2076 0.818911
\(302\) −7.78263 −0.447840
\(303\) 0 0
\(304\) −7.66776 −0.439776
\(305\) 0.961315 0.0550447
\(306\) 0 0
\(307\) 6.39669 0.365078 0.182539 0.983199i \(-0.441568\pi\)
0.182539 + 0.983199i \(0.441568\pi\)
\(308\) −3.54635 −0.202072
\(309\) 0 0
\(310\) −1.85033 −0.105092
\(311\) 6.95535 0.394402 0.197201 0.980363i \(-0.436815\pi\)
0.197201 + 0.980363i \(0.436815\pi\)
\(312\) 0 0
\(313\) 6.45365 0.364782 0.182391 0.983226i \(-0.441616\pi\)
0.182391 + 0.983226i \(0.441616\pi\)
\(314\) 3.52575 0.198970
\(315\) 0 0
\(316\) −0.116565 −0.00655732
\(317\) −5.56695 −0.312671 −0.156336 0.987704i \(-0.549968\pi\)
−0.156336 + 0.987704i \(0.549968\pi\)
\(318\) 0 0
\(319\) 9.29977 0.520687
\(320\) −0.326467 −0.0182500
\(321\) 0 0
\(322\) 4.65526 0.259427
\(323\) 49.5366 2.75629
\(324\) 0 0
\(325\) −12.1893 −0.676141
\(326\) 0.0621204 0.00344053
\(327\) 0 0
\(328\) −12.2901 −0.678608
\(329\) −13.2041 −0.727967
\(330\) 0 0
\(331\) −24.9131 −1.36935 −0.684673 0.728850i \(-0.740055\pi\)
−0.684673 + 0.728850i \(0.740055\pi\)
\(332\) 7.08850 0.389032
\(333\) 0 0
\(334\) −2.08850 −0.114277
\(335\) 1.85222 0.101198
\(336\) 0 0
\(337\) 12.2978 0.669902 0.334951 0.942236i \(-0.391280\pi\)
0.334951 + 0.942236i \(0.391280\pi\)
\(338\) −6.79513 −0.369606
\(339\) 0 0
\(340\) 2.10910 0.114382
\(341\) 12.5818 0.681341
\(342\) 0 0
\(343\) 18.2884 0.987481
\(344\) −8.89342 −0.479501
\(345\) 0 0
\(346\) 14.2597 0.766607
\(347\) 2.80103 0.150367 0.0751837 0.997170i \(-0.476046\pi\)
0.0751837 + 0.997170i \(0.476046\pi\)
\(348\) 0 0
\(349\) 13.6847 0.732523 0.366262 0.930512i \(-0.380638\pi\)
0.366262 + 0.930512i \(0.380638\pi\)
\(350\) 7.81742 0.417859
\(351\) 0 0
\(352\) 2.21989 0.118320
\(353\) −19.7430 −1.05081 −0.525407 0.850851i \(-0.676087\pi\)
−0.525407 + 0.850851i \(0.676087\pi\)
\(354\) 0 0
\(355\) 1.34550 0.0714118
\(356\) −0.513252 −0.0272023
\(357\) 0 0
\(358\) −24.5192 −1.29588
\(359\) −9.56526 −0.504835 −0.252418 0.967618i \(-0.581226\pi\)
−0.252418 + 0.967618i \(0.581226\pi\)
\(360\) 0 0
\(361\) 39.7945 2.09445
\(362\) −18.2125 −0.957230
\(363\) 0 0
\(364\) −3.97940 −0.208577
\(365\) −2.51137 −0.131451
\(366\) 0 0
\(367\) −24.7755 −1.29327 −0.646635 0.762800i \(-0.723824\pi\)
−0.646635 + 0.762800i \(0.723824\pi\)
\(368\) −2.91402 −0.151904
\(369\) 0 0
\(370\) 0.671018 0.0348846
\(371\) −9.92055 −0.515049
\(372\) 0 0
\(373\) 35.7002 1.84849 0.924244 0.381802i \(-0.124696\pi\)
0.924244 + 0.381802i \(0.124696\pi\)
\(374\) −14.3413 −0.741571
\(375\) 0 0
\(376\) 8.26530 0.426250
\(377\) 10.4354 0.537449
\(378\) 0 0
\(379\) −14.3802 −0.738660 −0.369330 0.929298i \(-0.620413\pi\)
−0.369330 + 0.929298i \(0.620413\pi\)
\(380\) 2.50327 0.128415
\(381\) 0 0
\(382\) −21.0644 −1.07775
\(383\) 30.9671 1.58235 0.791173 0.611593i \(-0.209471\pi\)
0.791173 + 0.611593i \(0.209471\pi\)
\(384\) 0 0
\(385\) 1.15777 0.0590052
\(386\) −27.0985 −1.37928
\(387\) 0 0
\(388\) −6.38186 −0.323990
\(389\) −8.50767 −0.431356 −0.215678 0.976465i \(-0.569196\pi\)
−0.215678 + 0.976465i \(0.569196\pi\)
\(390\) 0 0
\(391\) 18.8257 0.952054
\(392\) −4.44787 −0.224651
\(393\) 0 0
\(394\) −17.7547 −0.894468
\(395\) 0.0380547 0.00191474
\(396\) 0 0
\(397\) −14.2651 −0.715945 −0.357973 0.933732i \(-0.616532\pi\)
−0.357973 + 0.933732i \(0.616532\pi\)
\(398\) 20.2190 1.01348
\(399\) 0 0
\(400\) −4.89342 −0.244671
\(401\) −31.5109 −1.57358 −0.786791 0.617220i \(-0.788259\pi\)
−0.786791 + 0.617220i \(0.788259\pi\)
\(402\) 0 0
\(403\) 14.1181 0.703275
\(404\) 12.2801 0.610959
\(405\) 0 0
\(406\) −6.69257 −0.332147
\(407\) −4.56274 −0.226167
\(408\) 0 0
\(409\) −9.16293 −0.453078 −0.226539 0.974002i \(-0.572741\pi\)
−0.226539 + 0.974002i \(0.572741\pi\)
\(410\) 4.01231 0.198154
\(411\) 0 0
\(412\) −19.4504 −0.958252
\(413\) −0.452712 −0.0222765
\(414\) 0 0
\(415\) −2.31416 −0.113598
\(416\) 2.49096 0.122129
\(417\) 0 0
\(418\) −17.0216 −0.832551
\(419\) 29.4201 1.43727 0.718634 0.695389i \(-0.244768\pi\)
0.718634 + 0.695389i \(0.244768\pi\)
\(420\) 0 0
\(421\) 28.8396 1.40556 0.702778 0.711409i \(-0.251943\pi\)
0.702778 + 0.711409i \(0.251943\pi\)
\(422\) −11.3049 −0.550315
\(423\) 0 0
\(424\) 6.20990 0.301579
\(425\) 31.6133 1.53347
\(426\) 0 0
\(427\) 4.70412 0.227648
\(428\) 6.16028 0.297768
\(429\) 0 0
\(430\) 2.90340 0.140015
\(431\) −29.9517 −1.44272 −0.721360 0.692560i \(-0.756483\pi\)
−0.721360 + 0.692560i \(0.756483\pi\)
\(432\) 0 0
\(433\) −11.1833 −0.537437 −0.268718 0.963219i \(-0.586600\pi\)
−0.268718 + 0.963219i \(0.586600\pi\)
\(434\) −9.05446 −0.434628
\(435\) 0 0
\(436\) −9.68026 −0.463600
\(437\) 22.3440 1.06886
\(438\) 0 0
\(439\) −30.8644 −1.47308 −0.736539 0.676395i \(-0.763541\pi\)
−0.736539 + 0.676395i \(0.763541\pi\)
\(440\) −0.724719 −0.0345496
\(441\) 0 0
\(442\) −16.0925 −0.765443
\(443\) 35.8542 1.70349 0.851743 0.523960i \(-0.175546\pi\)
0.851743 + 0.523960i \(0.175546\pi\)
\(444\) 0 0
\(445\) 0.167560 0.00794309
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) −1.59754 −0.0754766
\(449\) 15.7066 0.741242 0.370621 0.928784i \(-0.379145\pi\)
0.370621 + 0.928784i \(0.379145\pi\)
\(450\) 0 0
\(451\) −27.2826 −1.28469
\(452\) −3.79915 −0.178697
\(453\) 0 0
\(454\) −18.8653 −0.885395
\(455\) 1.29914 0.0609047
\(456\) 0 0
\(457\) −29.0459 −1.35871 −0.679355 0.733809i \(-0.737741\pi\)
−0.679355 + 0.733809i \(0.737741\pi\)
\(458\) 25.1506 1.17521
\(459\) 0 0
\(460\) 0.951330 0.0443560
\(461\) −21.5743 −1.00482 −0.502408 0.864631i \(-0.667552\pi\)
−0.502408 + 0.864631i \(0.667552\pi\)
\(462\) 0 0
\(463\) 24.3686 1.13251 0.566253 0.824232i \(-0.308393\pi\)
0.566253 + 0.824232i \(0.308393\pi\)
\(464\) 4.18930 0.194483
\(465\) 0 0
\(466\) 2.13736 0.0990111
\(467\) 32.4960 1.50374 0.751868 0.659314i \(-0.229153\pi\)
0.751868 + 0.659314i \(0.229153\pi\)
\(468\) 0 0
\(469\) 9.06369 0.418522
\(470\) −2.69834 −0.124465
\(471\) 0 0
\(472\) 0.283381 0.0130437
\(473\) −19.7424 −0.907756
\(474\) 0 0
\(475\) 37.5216 1.72161
\(476\) 10.3207 0.473048
\(477\) 0 0
\(478\) −0.112547 −0.00514778
\(479\) −34.9175 −1.59542 −0.797710 0.603041i \(-0.793956\pi\)
−0.797710 + 0.603041i \(0.793956\pi\)
\(480\) 0 0
\(481\) −5.11990 −0.233447
\(482\) 13.8957 0.632934
\(483\) 0 0
\(484\) −6.07211 −0.276005
\(485\) 2.08346 0.0946053
\(486\) 0 0
\(487\) −6.46037 −0.292747 −0.146374 0.989229i \(-0.546760\pi\)
−0.146374 + 0.989229i \(0.546760\pi\)
\(488\) −2.94460 −0.133296
\(489\) 0 0
\(490\) 1.45208 0.0655984
\(491\) 0.708520 0.0319750 0.0159875 0.999872i \(-0.494911\pi\)
0.0159875 + 0.999872i \(0.494911\pi\)
\(492\) 0 0
\(493\) −27.0644 −1.21892
\(494\) −19.1001 −0.859352
\(495\) 0 0
\(496\) 5.66776 0.254490
\(497\) 6.58410 0.295337
\(498\) 0 0
\(499\) 20.2230 0.905304 0.452652 0.891687i \(-0.350478\pi\)
0.452652 + 0.891687i \(0.350478\pi\)
\(500\) 3.22987 0.144444
\(501\) 0 0
\(502\) −1.18698 −0.0529774
\(503\) 36.3380 1.62023 0.810116 0.586269i \(-0.199404\pi\)
0.810116 + 0.586269i \(0.199404\pi\)
\(504\) 0 0
\(505\) −4.00905 −0.178400
\(506\) −6.46879 −0.287573
\(507\) 0 0
\(508\) −17.9861 −0.798005
\(509\) −4.16857 −0.184769 −0.0923844 0.995723i \(-0.529449\pi\)
−0.0923844 + 0.995723i \(0.529449\pi\)
\(510\) 0 0
\(511\) −12.2892 −0.543641
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 9.49749 0.418916
\(515\) 6.34990 0.279810
\(516\) 0 0
\(517\) 18.3480 0.806945
\(518\) 3.28357 0.144272
\(519\) 0 0
\(520\) −0.813215 −0.0356618
\(521\) 16.3684 0.717114 0.358557 0.933508i \(-0.383269\pi\)
0.358557 + 0.933508i \(0.383269\pi\)
\(522\) 0 0
\(523\) 31.9673 1.39783 0.698916 0.715204i \(-0.253666\pi\)
0.698916 + 0.715204i \(0.253666\pi\)
\(524\) −7.32898 −0.320168
\(525\) 0 0
\(526\) 20.2440 0.882678
\(527\) −36.6158 −1.59501
\(528\) 0 0
\(529\) −14.5085 −0.630804
\(530\) −2.02733 −0.0880614
\(531\) 0 0
\(532\) 12.2495 0.531085
\(533\) −30.6141 −1.32605
\(534\) 0 0
\(535\) −2.01113 −0.0869486
\(536\) −5.67353 −0.245059
\(537\) 0 0
\(538\) 9.55885 0.412111
\(539\) −9.87377 −0.425293
\(540\) 0 0
\(541\) 31.0977 1.33700 0.668498 0.743714i \(-0.266937\pi\)
0.668498 + 0.743714i \(0.266937\pi\)
\(542\) 24.0547 1.03324
\(543\) 0 0
\(544\) −6.46037 −0.276986
\(545\) 3.16028 0.135372
\(546\) 0 0
\(547\) −21.5025 −0.919381 −0.459691 0.888079i \(-0.652040\pi\)
−0.459691 + 0.888079i \(0.652040\pi\)
\(548\) 8.66776 0.370268
\(549\) 0 0
\(550\) −10.8628 −0.463193
\(551\) −32.1225 −1.36847
\(552\) 0 0
\(553\) 0.186218 0.00791879
\(554\) 30.8702 1.31155
\(555\) 0 0
\(556\) 5.85706 0.248395
\(557\) −0.144826 −0.00613649 −0.00306824 0.999995i \(-0.500977\pi\)
−0.00306824 + 0.999995i \(0.500977\pi\)
\(558\) 0 0
\(559\) −22.1531 −0.936978
\(560\) 0.521543 0.0220392
\(561\) 0 0
\(562\) −6.78665 −0.286277
\(563\) −26.8290 −1.13071 −0.565354 0.824849i \(-0.691260\pi\)
−0.565354 + 0.824849i \(0.691260\pi\)
\(564\) 0 0
\(565\) 1.24030 0.0521796
\(566\) 12.2466 0.514762
\(567\) 0 0
\(568\) −4.12141 −0.172930
\(569\) 25.5083 1.06936 0.534682 0.845054i \(-0.320431\pi\)
0.534682 + 0.845054i \(0.320431\pi\)
\(570\) 0 0
\(571\) 1.66059 0.0694937 0.0347468 0.999396i \(-0.488938\pi\)
0.0347468 + 0.999396i \(0.488938\pi\)
\(572\) 5.52964 0.231206
\(573\) 0 0
\(574\) 19.6339 0.819504
\(575\) 14.2595 0.594663
\(576\) 0 0
\(577\) −9.53888 −0.397109 −0.198554 0.980090i \(-0.563625\pi\)
−0.198554 + 0.980090i \(0.563625\pi\)
\(578\) 24.7364 1.02890
\(579\) 0 0
\(580\) −1.36767 −0.0567893
\(581\) −11.3241 −0.469805
\(582\) 0 0
\(583\) 13.7853 0.570928
\(584\) 7.69257 0.318321
\(585\) 0 0
\(586\) 10.7176 0.442739
\(587\) −13.8126 −0.570107 −0.285053 0.958512i \(-0.592011\pi\)
−0.285053 + 0.958512i \(0.592011\pi\)
\(588\) 0 0
\(589\) −43.4590 −1.79070
\(590\) −0.0925144 −0.00380876
\(591\) 0 0
\(592\) −2.05540 −0.0844762
\(593\) 9.72780 0.399473 0.199736 0.979850i \(-0.435991\pi\)
0.199736 + 0.979850i \(0.435991\pi\)
\(594\) 0 0
\(595\) −3.36936 −0.138130
\(596\) 15.7586 0.645497
\(597\) 0 0
\(598\) −7.25870 −0.296830
\(599\) −36.0854 −1.47441 −0.737204 0.675670i \(-0.763854\pi\)
−0.737204 + 0.675670i \(0.763854\pi\)
\(600\) 0 0
\(601\) 11.5725 0.472054 0.236027 0.971747i \(-0.424155\pi\)
0.236027 + 0.971747i \(0.424155\pi\)
\(602\) 14.2076 0.579058
\(603\) 0 0
\(604\) −7.78263 −0.316671
\(605\) 1.98234 0.0805936
\(606\) 0 0
\(607\) 13.4321 0.545193 0.272596 0.962129i \(-0.412118\pi\)
0.272596 + 0.962129i \(0.412118\pi\)
\(608\) −7.66776 −0.310969
\(609\) 0 0
\(610\) 0.961315 0.0389225
\(611\) 20.5885 0.832922
\(612\) 0 0
\(613\) −11.7622 −0.475072 −0.237536 0.971379i \(-0.576340\pi\)
−0.237536 + 0.971379i \(0.576340\pi\)
\(614\) 6.39669 0.258149
\(615\) 0 0
\(616\) −3.54635 −0.142887
\(617\) 42.4730 1.70990 0.854950 0.518711i \(-0.173588\pi\)
0.854950 + 0.518711i \(0.173588\pi\)
\(618\) 0 0
\(619\) −43.7701 −1.75927 −0.879635 0.475649i \(-0.842213\pi\)
−0.879635 + 0.475649i \(0.842213\pi\)
\(620\) −1.85033 −0.0743112
\(621\) 0 0
\(622\) 6.95535 0.278884
\(623\) 0.819940 0.0328502
\(624\) 0 0
\(625\) 23.4127 0.936506
\(626\) 6.45365 0.257940
\(627\) 0 0
\(628\) 3.52575 0.140693
\(629\) 13.2786 0.529453
\(630\) 0 0
\(631\) −38.5593 −1.53502 −0.767511 0.641036i \(-0.778505\pi\)
−0.767511 + 0.641036i \(0.778505\pi\)
\(632\) −0.116565 −0.00463673
\(633\) 0 0
\(634\) −5.56695 −0.221092
\(635\) 5.87187 0.233018
\(636\) 0 0
\(637\) −11.0795 −0.438984
\(638\) 9.29977 0.368181
\(639\) 0 0
\(640\) −0.326467 −0.0129047
\(641\) −47.9344 −1.89330 −0.946648 0.322268i \(-0.895555\pi\)
−0.946648 + 0.322268i \(0.895555\pi\)
\(642\) 0 0
\(643\) −33.1025 −1.30544 −0.652718 0.757601i \(-0.726371\pi\)
−0.652718 + 0.757601i \(0.726371\pi\)
\(644\) 4.65526 0.183443
\(645\) 0 0
\(646\) 49.5366 1.94899
\(647\) −21.7062 −0.853359 −0.426680 0.904403i \(-0.640317\pi\)
−0.426680 + 0.904403i \(0.640317\pi\)
\(648\) 0 0
\(649\) 0.629073 0.0246933
\(650\) −12.1893 −0.478104
\(651\) 0 0
\(652\) 0.0621204 0.00243282
\(653\) 32.0324 1.25352 0.626761 0.779211i \(-0.284380\pi\)
0.626761 + 0.779211i \(0.284380\pi\)
\(654\) 0 0
\(655\) 2.39267 0.0934893
\(656\) −12.2901 −0.479848
\(657\) 0 0
\(658\) −13.2041 −0.514750
\(659\) 21.7155 0.845915 0.422958 0.906149i \(-0.360992\pi\)
0.422958 + 0.906149i \(0.360992\pi\)
\(660\) 0 0
\(661\) 17.2593 0.671310 0.335655 0.941985i \(-0.391042\pi\)
0.335655 + 0.941985i \(0.391042\pi\)
\(662\) −24.9131 −0.968275
\(663\) 0 0
\(664\) 7.08850 0.275087
\(665\) −3.99906 −0.155077
\(666\) 0 0
\(667\) −12.2077 −0.472684
\(668\) −2.08850 −0.0808063
\(669\) 0 0
\(670\) 1.85222 0.0715575
\(671\) −6.53669 −0.252346
\(672\) 0 0
\(673\) 22.1687 0.854541 0.427270 0.904124i \(-0.359475\pi\)
0.427270 + 0.904124i \(0.359475\pi\)
\(674\) 12.2978 0.473692
\(675\) 0 0
\(676\) −6.79513 −0.261351
\(677\) −4.75877 −0.182894 −0.0914472 0.995810i \(-0.529149\pi\)
−0.0914472 + 0.995810i \(0.529149\pi\)
\(678\) 0 0
\(679\) 10.1953 0.391258
\(680\) 2.10910 0.0808801
\(681\) 0 0
\(682\) 12.5818 0.481781
\(683\) −18.3973 −0.703954 −0.351977 0.936009i \(-0.614490\pi\)
−0.351977 + 0.936009i \(0.614490\pi\)
\(684\) 0 0
\(685\) −2.82973 −0.108119
\(686\) 18.2884 0.698255
\(687\) 0 0
\(688\) −8.89342 −0.339058
\(689\) 15.4686 0.589307
\(690\) 0 0
\(691\) 28.6842 1.09120 0.545598 0.838047i \(-0.316302\pi\)
0.545598 + 0.838047i \(0.316302\pi\)
\(692\) 14.2597 0.542073
\(693\) 0 0
\(694\) 2.80103 0.106326
\(695\) −1.91213 −0.0725314
\(696\) 0 0
\(697\) 79.3987 3.00744
\(698\) 13.6847 0.517972
\(699\) 0 0
\(700\) 7.81742 0.295471
\(701\) 49.5192 1.87032 0.935158 0.354231i \(-0.115257\pi\)
0.935158 + 0.354231i \(0.115257\pi\)
\(702\) 0 0
\(703\) 15.7603 0.594410
\(704\) 2.21989 0.0836651
\(705\) 0 0
\(706\) −19.7430 −0.743038
\(707\) −19.6180 −0.737809
\(708\) 0 0
\(709\) −11.5396 −0.433380 −0.216690 0.976240i \(-0.569526\pi\)
−0.216690 + 0.976240i \(0.569526\pi\)
\(710\) 1.34550 0.0504958
\(711\) 0 0
\(712\) −0.513252 −0.0192349
\(713\) −16.5160 −0.618528
\(714\) 0 0
\(715\) −1.80524 −0.0675123
\(716\) −24.5192 −0.916327
\(717\) 0 0
\(718\) −9.56526 −0.356972
\(719\) 4.75550 0.177350 0.0886750 0.996061i \(-0.471737\pi\)
0.0886750 + 0.996061i \(0.471737\pi\)
\(720\) 0 0
\(721\) 31.0727 1.15721
\(722\) 39.7945 1.48100
\(723\) 0 0
\(724\) −18.2125 −0.676864
\(725\) −20.5000 −0.761351
\(726\) 0 0
\(727\) 11.4025 0.422894 0.211447 0.977389i \(-0.432182\pi\)
0.211447 + 0.977389i \(0.432182\pi\)
\(728\) −3.97940 −0.147486
\(729\) 0 0
\(730\) −2.51137 −0.0929499
\(731\) 57.4548 2.12504
\(732\) 0 0
\(733\) 4.38123 0.161824 0.0809122 0.996721i \(-0.474217\pi\)
0.0809122 + 0.996721i \(0.474217\pi\)
\(734\) −24.7755 −0.914480
\(735\) 0 0
\(736\) −2.91402 −0.107412
\(737\) −12.5946 −0.463928
\(738\) 0 0
\(739\) 19.2143 0.706810 0.353405 0.935471i \(-0.385024\pi\)
0.353405 + 0.935471i \(0.385024\pi\)
\(740\) 0.671018 0.0246671
\(741\) 0 0
\(742\) −9.92055 −0.364195
\(743\) −11.5536 −0.423862 −0.211931 0.977285i \(-0.567975\pi\)
−0.211931 + 0.977285i \(0.567975\pi\)
\(744\) 0 0
\(745\) −5.14465 −0.188485
\(746\) 35.7002 1.30708
\(747\) 0 0
\(748\) −14.3413 −0.524370
\(749\) −9.84128 −0.359593
\(750\) 0 0
\(751\) −28.3814 −1.03565 −0.517827 0.855486i \(-0.673259\pi\)
−0.517827 + 0.855486i \(0.673259\pi\)
\(752\) 8.26530 0.301404
\(753\) 0 0
\(754\) 10.4354 0.380034
\(755\) 2.54077 0.0924680
\(756\) 0 0
\(757\) −2.52311 −0.0917039 −0.0458520 0.998948i \(-0.514600\pi\)
−0.0458520 + 0.998948i \(0.514600\pi\)
\(758\) −14.3802 −0.522311
\(759\) 0 0
\(760\) 2.50327 0.0908030
\(761\) 38.2137 1.38525 0.692623 0.721300i \(-0.256455\pi\)
0.692623 + 0.721300i \(0.256455\pi\)
\(762\) 0 0
\(763\) 15.4646 0.559855
\(764\) −21.0644 −0.762085
\(765\) 0 0
\(766\) 30.9671 1.11889
\(767\) 0.705890 0.0254882
\(768\) 0 0
\(769\) −18.2995 −0.659898 −0.329949 0.943999i \(-0.607032\pi\)
−0.329949 + 0.943999i \(0.607032\pi\)
\(770\) 1.15777 0.0417230
\(771\) 0 0
\(772\) −27.0985 −0.975296
\(773\) 14.7714 0.531290 0.265645 0.964071i \(-0.414415\pi\)
0.265645 + 0.964071i \(0.414415\pi\)
\(774\) 0 0
\(775\) −27.7347 −0.996260
\(776\) −6.38186 −0.229095
\(777\) 0 0
\(778\) −8.50767 −0.305015
\(779\) 94.2376 3.37641
\(780\) 0 0
\(781\) −9.14905 −0.327379
\(782\) 18.8257 0.673204
\(783\) 0 0
\(784\) −4.44787 −0.158853
\(785\) −1.15104 −0.0410824
\(786\) 0 0
\(787\) −3.28144 −0.116971 −0.0584853 0.998288i \(-0.518627\pi\)
−0.0584853 + 0.998288i \(0.518627\pi\)
\(788\) −17.7547 −0.632485
\(789\) 0 0
\(790\) 0.0380547 0.00135393
\(791\) 6.06928 0.215799
\(792\) 0 0
\(793\) −7.33489 −0.260469
\(794\) −14.2651 −0.506250
\(795\) 0 0
\(796\) 20.2190 0.716642
\(797\) −15.6573 −0.554612 −0.277306 0.960782i \(-0.589442\pi\)
−0.277306 + 0.960782i \(0.589442\pi\)
\(798\) 0 0
\(799\) −53.3969 −1.88905
\(800\) −4.89342 −0.173009
\(801\) 0 0
\(802\) −31.5109 −1.11269
\(803\) 17.0766 0.602621
\(804\) 0 0
\(805\) −1.51979 −0.0535654
\(806\) 14.1181 0.497290
\(807\) 0 0
\(808\) 12.2801 0.432013
\(809\) 31.0320 1.09103 0.545513 0.838102i \(-0.316335\pi\)
0.545513 + 0.838102i \(0.316335\pi\)
\(810\) 0 0
\(811\) 22.1470 0.777688 0.388844 0.921304i \(-0.372875\pi\)
0.388844 + 0.921304i \(0.372875\pi\)
\(812\) −6.69257 −0.234863
\(813\) 0 0
\(814\) −4.56274 −0.159924
\(815\) −0.0202802 −0.000710385 0
\(816\) 0 0
\(817\) 68.1926 2.38576
\(818\) −9.16293 −0.320374
\(819\) 0 0
\(820\) 4.01231 0.140116
\(821\) 7.24105 0.252715 0.126357 0.991985i \(-0.459671\pi\)
0.126357 + 0.991985i \(0.459671\pi\)
\(822\) 0 0
\(823\) 12.0581 0.420319 0.210160 0.977667i \(-0.432602\pi\)
0.210160 + 0.977667i \(0.432602\pi\)
\(824\) −19.4504 −0.677586
\(825\) 0 0
\(826\) −0.452712 −0.0157519
\(827\) −28.5104 −0.991403 −0.495701 0.868493i \(-0.665089\pi\)
−0.495701 + 0.868493i \(0.665089\pi\)
\(828\) 0 0
\(829\) 9.20256 0.319618 0.159809 0.987148i \(-0.448912\pi\)
0.159809 + 0.987148i \(0.448912\pi\)
\(830\) −2.31416 −0.0803256
\(831\) 0 0
\(832\) 2.49096 0.0863584
\(833\) 28.7349 0.995606
\(834\) 0 0
\(835\) 0.681824 0.0235955
\(836\) −17.0216 −0.588703
\(837\) 0 0
\(838\) 29.4201 1.01630
\(839\) 16.9775 0.586129 0.293064 0.956093i \(-0.405325\pi\)
0.293064 + 0.956093i \(0.405325\pi\)
\(840\) 0 0
\(841\) −11.4498 −0.394819
\(842\) 28.8396 0.993878
\(843\) 0 0
\(844\) −11.3049 −0.389132
\(845\) 2.21838 0.0763147
\(846\) 0 0
\(847\) 9.70042 0.333310
\(848\) 6.20990 0.213249
\(849\) 0 0
\(850\) 31.6133 1.08433
\(851\) 5.98946 0.205316
\(852\) 0 0
\(853\) 26.0908 0.893333 0.446666 0.894701i \(-0.352611\pi\)
0.446666 + 0.894701i \(0.352611\pi\)
\(854\) 4.70412 0.160972
\(855\) 0 0
\(856\) 6.16028 0.210554
\(857\) 14.7870 0.505115 0.252558 0.967582i \(-0.418728\pi\)
0.252558 + 0.967582i \(0.418728\pi\)
\(858\) 0 0
\(859\) 25.5670 0.872334 0.436167 0.899866i \(-0.356336\pi\)
0.436167 + 0.899866i \(0.356336\pi\)
\(860\) 2.90340 0.0990053
\(861\) 0 0
\(862\) −29.9517 −1.02016
\(863\) −44.4272 −1.51232 −0.756159 0.654388i \(-0.772926\pi\)
−0.756159 + 0.654388i \(0.772926\pi\)
\(864\) 0 0
\(865\) −4.65532 −0.158286
\(866\) −11.1833 −0.380025
\(867\) 0 0
\(868\) −9.05446 −0.307328
\(869\) −0.258762 −0.00877790
\(870\) 0 0
\(871\) −14.1325 −0.478863
\(872\) −9.68026 −0.327815
\(873\) 0 0
\(874\) 22.3440 0.755797
\(875\) −5.15984 −0.174435
\(876\) 0 0
\(877\) −11.9340 −0.402983 −0.201491 0.979490i \(-0.564579\pi\)
−0.201491 + 0.979490i \(0.564579\pi\)
\(878\) −30.8644 −1.04162
\(879\) 0 0
\(880\) −0.724719 −0.0244303
\(881\) −34.8986 −1.17576 −0.587882 0.808947i \(-0.700038\pi\)
−0.587882 + 0.808947i \(0.700038\pi\)
\(882\) 0 0
\(883\) −37.8330 −1.27318 −0.636591 0.771202i \(-0.719656\pi\)
−0.636591 + 0.771202i \(0.719656\pi\)
\(884\) −16.0925 −0.541250
\(885\) 0 0
\(886\) 35.8542 1.20455
\(887\) 41.1789 1.38265 0.691326 0.722543i \(-0.257027\pi\)
0.691326 + 0.722543i \(0.257027\pi\)
\(888\) 0 0
\(889\) 28.7335 0.963691
\(890\) 0.167560 0.00561661
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −63.3763 −2.12081
\(894\) 0 0
\(895\) 8.00471 0.267568
\(896\) −1.59754 −0.0533700
\(897\) 0 0
\(898\) 15.7066 0.524137
\(899\) 23.7439 0.791905
\(900\) 0 0
\(901\) −40.1183 −1.33653
\(902\) −27.2826 −0.908412
\(903\) 0 0
\(904\) −3.79915 −0.126358
\(905\) 5.94579 0.197645
\(906\) 0 0
\(907\) −53.0797 −1.76248 −0.881241 0.472668i \(-0.843291\pi\)
−0.881241 + 0.472668i \(0.843291\pi\)
\(908\) −18.8653 −0.626069
\(909\) 0 0
\(910\) 1.29914 0.0430661
\(911\) −40.1408 −1.32992 −0.664961 0.746878i \(-0.731552\pi\)
−0.664961 + 0.746878i \(0.731552\pi\)
\(912\) 0 0
\(913\) 15.7357 0.520774
\(914\) −29.0459 −0.960754
\(915\) 0 0
\(916\) 25.1506 0.831000
\(917\) 11.7083 0.386643
\(918\) 0 0
\(919\) −23.1072 −0.762237 −0.381118 0.924526i \(-0.624461\pi\)
−0.381118 + 0.924526i \(0.624461\pi\)
\(920\) 0.951330 0.0313644
\(921\) 0 0
\(922\) −21.5743 −0.710512
\(923\) −10.2662 −0.337918
\(924\) 0 0
\(925\) 10.0579 0.330702
\(926\) 24.3686 0.800802
\(927\) 0 0
\(928\) 4.18930 0.137521
\(929\) 1.79556 0.0589105 0.0294553 0.999566i \(-0.490623\pi\)
0.0294553 + 0.999566i \(0.490623\pi\)
\(930\) 0 0
\(931\) 34.1052 1.11775
\(932\) 2.13736 0.0700115
\(933\) 0 0
\(934\) 32.4960 1.06330
\(935\) 4.68195 0.153116
\(936\) 0 0
\(937\) −9.00535 −0.294192 −0.147096 0.989122i \(-0.546993\pi\)
−0.147096 + 0.989122i \(0.546993\pi\)
\(938\) 9.06369 0.295940
\(939\) 0 0
\(940\) −2.69834 −0.0880103
\(941\) 13.2698 0.432584 0.216292 0.976329i \(-0.430604\pi\)
0.216292 + 0.976329i \(0.430604\pi\)
\(942\) 0 0
\(943\) 35.8136 1.16625
\(944\) 0.283381 0.00922326
\(945\) 0 0
\(946\) −19.7424 −0.641880
\(947\) −38.7970 −1.26073 −0.630366 0.776298i \(-0.717095\pi\)
−0.630366 + 0.776298i \(0.717095\pi\)
\(948\) 0 0
\(949\) 19.1619 0.622020
\(950\) 37.5216 1.21736
\(951\) 0 0
\(952\) 10.3207 0.334496
\(953\) −57.9423 −1.87694 −0.938468 0.345367i \(-0.887754\pi\)
−0.938468 + 0.345367i \(0.887754\pi\)
\(954\) 0 0
\(955\) 6.87684 0.222529
\(956\) −0.112547 −0.00364003
\(957\) 0 0
\(958\) −34.9175 −1.12813
\(959\) −13.8471 −0.447145
\(960\) 0 0
\(961\) 1.12348 0.0362414
\(962\) −5.11990 −0.165072
\(963\) 0 0
\(964\) 13.8957 0.447552
\(965\) 8.84675 0.284787
\(966\) 0 0
\(967\) 35.0066 1.12574 0.562868 0.826547i \(-0.309698\pi\)
0.562868 + 0.826547i \(0.309698\pi\)
\(968\) −6.07211 −0.195165
\(969\) 0 0
\(970\) 2.08346 0.0668960
\(971\) −31.1405 −0.999345 −0.499672 0.866214i \(-0.666546\pi\)
−0.499672 + 0.866214i \(0.666546\pi\)
\(972\) 0 0
\(973\) −9.35688 −0.299968
\(974\) −6.46037 −0.207004
\(975\) 0 0
\(976\) −2.94460 −0.0942545
\(977\) 9.44587 0.302200 0.151100 0.988518i \(-0.451718\pi\)
0.151100 + 0.988518i \(0.451718\pi\)
\(978\) 0 0
\(979\) −1.13936 −0.0364141
\(980\) 1.45208 0.0463850
\(981\) 0 0
\(982\) 0.708520 0.0226098
\(983\) 20.5690 0.656051 0.328025 0.944669i \(-0.393617\pi\)
0.328025 + 0.944669i \(0.393617\pi\)
\(984\) 0 0
\(985\) 5.79631 0.184686
\(986\) −27.0644 −0.861908
\(987\) 0 0
\(988\) −19.1001 −0.607654
\(989\) 25.9156 0.824068
\(990\) 0 0
\(991\) −7.89877 −0.250913 −0.125456 0.992099i \(-0.540040\pi\)
−0.125456 + 0.992099i \(0.540040\pi\)
\(992\) 5.66776 0.179951
\(993\) 0 0
\(994\) 6.58410 0.208835
\(995\) −6.60081 −0.209260
\(996\) 0 0
\(997\) 6.14766 0.194698 0.0973492 0.995250i \(-0.468964\pi\)
0.0973492 + 0.995250i \(0.468964\pi\)
\(998\) 20.2230 0.640147
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))