Properties

Label 4008.2.a.l.1.10
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.93317\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.93317 q^{5}\) \(+1.35675 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.93317 q^{5}\) \(+1.35675 q^{7}\) \(+1.00000 q^{9}\) \(-0.0643015 q^{11}\) \(-2.07209 q^{13}\) \(+2.93317 q^{15}\) \(-1.73736 q^{17}\) \(+7.35449 q^{19}\) \(+1.35675 q^{21}\) \(-0.641526 q^{23}\) \(+3.60351 q^{25}\) \(+1.00000 q^{27}\) \(+3.65476 q^{29}\) \(-3.92456 q^{31}\) \(-0.0643015 q^{33}\) \(+3.97960 q^{35}\) \(+8.28523 q^{37}\) \(-2.07209 q^{39}\) \(+1.55401 q^{41}\) \(-2.77619 q^{43}\) \(+2.93317 q^{45}\) \(-4.51709 q^{47}\) \(-5.15922 q^{49}\) \(-1.73736 q^{51}\) \(-1.55065 q^{53}\) \(-0.188608 q^{55}\) \(+7.35449 q^{57}\) \(+11.0736 q^{59}\) \(+13.4007 q^{61}\) \(+1.35675 q^{63}\) \(-6.07781 q^{65}\) \(+4.50770 q^{67}\) \(-0.641526 q^{69}\) \(+10.2267 q^{71}\) \(-6.16638 q^{73}\) \(+3.60351 q^{75}\) \(-0.0872414 q^{77}\) \(+2.51122 q^{79}\) \(+1.00000 q^{81}\) \(+1.74485 q^{83}\) \(-5.09598 q^{85}\) \(+3.65476 q^{87}\) \(-17.4735 q^{89}\) \(-2.81132 q^{91}\) \(-3.92456 q^{93}\) \(+21.5720 q^{95}\) \(+17.6851 q^{97}\) \(-0.0643015 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.93317 1.31175 0.655877 0.754867i \(-0.272299\pi\)
0.655877 + 0.754867i \(0.272299\pi\)
\(6\) 0 0
\(7\) 1.35675 0.512805 0.256402 0.966570i \(-0.417463\pi\)
0.256402 + 0.966570i \(0.417463\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.0643015 −0.0193876 −0.00969382 0.999953i \(-0.503086\pi\)
−0.00969382 + 0.999953i \(0.503086\pi\)
\(12\) 0 0
\(13\) −2.07209 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(14\) 0 0
\(15\) 2.93317 0.757342
\(16\) 0 0
\(17\) −1.73736 −0.421372 −0.210686 0.977554i \(-0.567570\pi\)
−0.210686 + 0.977554i \(0.567570\pi\)
\(18\) 0 0
\(19\) 7.35449 1.68724 0.843618 0.536943i \(-0.180421\pi\)
0.843618 + 0.536943i \(0.180421\pi\)
\(20\) 0 0
\(21\) 1.35675 0.296068
\(22\) 0 0
\(23\) −0.641526 −0.133767 −0.0668837 0.997761i \(-0.521306\pi\)
−0.0668837 + 0.997761i \(0.521306\pi\)
\(24\) 0 0
\(25\) 3.60351 0.720701
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.65476 0.678672 0.339336 0.940665i \(-0.389798\pi\)
0.339336 + 0.940665i \(0.389798\pi\)
\(30\) 0 0
\(31\) −3.92456 −0.704871 −0.352436 0.935836i \(-0.614646\pi\)
−0.352436 + 0.935836i \(0.614646\pi\)
\(32\) 0 0
\(33\) −0.0643015 −0.0111935
\(34\) 0 0
\(35\) 3.97960 0.672674
\(36\) 0 0
\(37\) 8.28523 1.36208 0.681041 0.732245i \(-0.261527\pi\)
0.681041 + 0.732245i \(0.261527\pi\)
\(38\) 0 0
\(39\) −2.07209 −0.331801
\(40\) 0 0
\(41\) 1.55401 0.242696 0.121348 0.992610i \(-0.461278\pi\)
0.121348 + 0.992610i \(0.461278\pi\)
\(42\) 0 0
\(43\) −2.77619 −0.423364 −0.211682 0.977339i \(-0.567894\pi\)
−0.211682 + 0.977339i \(0.567894\pi\)
\(44\) 0 0
\(45\) 2.93317 0.437252
\(46\) 0 0
\(47\) −4.51709 −0.658886 −0.329443 0.944176i \(-0.606861\pi\)
−0.329443 + 0.944176i \(0.606861\pi\)
\(48\) 0 0
\(49\) −5.15922 −0.737031
\(50\) 0 0
\(51\) −1.73736 −0.243279
\(52\) 0 0
\(53\) −1.55065 −0.212998 −0.106499 0.994313i \(-0.533964\pi\)
−0.106499 + 0.994313i \(0.533964\pi\)
\(54\) 0 0
\(55\) −0.188608 −0.0254318
\(56\) 0 0
\(57\) 7.35449 0.974127
\(58\) 0 0
\(59\) 11.0736 1.44165 0.720827 0.693115i \(-0.243762\pi\)
0.720827 + 0.693115i \(0.243762\pi\)
\(60\) 0 0
\(61\) 13.4007 1.71578 0.857892 0.513830i \(-0.171774\pi\)
0.857892 + 0.513830i \(0.171774\pi\)
\(62\) 0 0
\(63\) 1.35675 0.170935
\(64\) 0 0
\(65\) −6.07781 −0.753860
\(66\) 0 0
\(67\) 4.50770 0.550703 0.275352 0.961344i \(-0.411206\pi\)
0.275352 + 0.961344i \(0.411206\pi\)
\(68\) 0 0
\(69\) −0.641526 −0.0772307
\(70\) 0 0
\(71\) 10.2267 1.21369 0.606843 0.794822i \(-0.292436\pi\)
0.606843 + 0.794822i \(0.292436\pi\)
\(72\) 0 0
\(73\) −6.16638 −0.721720 −0.360860 0.932620i \(-0.617517\pi\)
−0.360860 + 0.932620i \(0.617517\pi\)
\(74\) 0 0
\(75\) 3.60351 0.416097
\(76\) 0 0
\(77\) −0.0872414 −0.00994208
\(78\) 0 0
\(79\) 2.51122 0.282534 0.141267 0.989972i \(-0.454882\pi\)
0.141267 + 0.989972i \(0.454882\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 1.74485 0.191523 0.0957613 0.995404i \(-0.469471\pi\)
0.0957613 + 0.995404i \(0.469471\pi\)
\(84\) 0 0
\(85\) −5.09598 −0.552736
\(86\) 0 0
\(87\) 3.65476 0.391831
\(88\) 0 0
\(89\) −17.4735 −1.85219 −0.926095 0.377291i \(-0.876856\pi\)
−0.926095 + 0.377291i \(0.876856\pi\)
\(90\) 0 0
\(91\) −2.81132 −0.294707
\(92\) 0 0
\(93\) −3.92456 −0.406958
\(94\) 0 0
\(95\) 21.5720 2.21324
\(96\) 0 0
\(97\) 17.6851 1.79565 0.897824 0.440354i \(-0.145147\pi\)
0.897824 + 0.440354i \(0.145147\pi\)
\(98\) 0 0
\(99\) −0.0643015 −0.00646255
\(100\) 0 0
\(101\) 10.0244 0.997464 0.498732 0.866756i \(-0.333799\pi\)
0.498732 + 0.866756i \(0.333799\pi\)
\(102\) 0 0
\(103\) 6.08730 0.599800 0.299900 0.953971i \(-0.403047\pi\)
0.299900 + 0.953971i \(0.403047\pi\)
\(104\) 0 0
\(105\) 3.97960 0.388369
\(106\) 0 0
\(107\) 12.5950 1.21760 0.608801 0.793323i \(-0.291651\pi\)
0.608801 + 0.793323i \(0.291651\pi\)
\(108\) 0 0
\(109\) −17.0536 −1.63343 −0.816717 0.577038i \(-0.804208\pi\)
−0.816717 + 0.577038i \(0.804208\pi\)
\(110\) 0 0
\(111\) 8.28523 0.786399
\(112\) 0 0
\(113\) −11.3676 −1.06937 −0.534686 0.845051i \(-0.679570\pi\)
−0.534686 + 0.845051i \(0.679570\pi\)
\(114\) 0 0
\(115\) −1.88171 −0.175470
\(116\) 0 0
\(117\) −2.07209 −0.191565
\(118\) 0 0
\(119\) −2.35717 −0.216081
\(120\) 0 0
\(121\) −10.9959 −0.999624
\(122\) 0 0
\(123\) 1.55401 0.140120
\(124\) 0 0
\(125\) −4.09616 −0.366372
\(126\) 0 0
\(127\) 4.85124 0.430478 0.215239 0.976561i \(-0.430947\pi\)
0.215239 + 0.976561i \(0.430947\pi\)
\(128\) 0 0
\(129\) −2.77619 −0.244430
\(130\) 0 0
\(131\) −13.1490 −1.14884 −0.574419 0.818562i \(-0.694772\pi\)
−0.574419 + 0.818562i \(0.694772\pi\)
\(132\) 0 0
\(133\) 9.97824 0.865223
\(134\) 0 0
\(135\) 2.93317 0.252447
\(136\) 0 0
\(137\) 9.39248 0.802454 0.401227 0.915979i \(-0.368584\pi\)
0.401227 + 0.915979i \(0.368584\pi\)
\(138\) 0 0
\(139\) −6.71091 −0.569212 −0.284606 0.958645i \(-0.591863\pi\)
−0.284606 + 0.958645i \(0.591863\pi\)
\(140\) 0 0
\(141\) −4.51709 −0.380408
\(142\) 0 0
\(143\) 0.133239 0.0111420
\(144\) 0 0
\(145\) 10.7200 0.890251
\(146\) 0 0
\(147\) −5.15922 −0.425525
\(148\) 0 0
\(149\) −6.09023 −0.498931 −0.249466 0.968384i \(-0.580255\pi\)
−0.249466 + 0.968384i \(0.580255\pi\)
\(150\) 0 0
\(151\) −13.3009 −1.08241 −0.541206 0.840890i \(-0.682032\pi\)
−0.541206 + 0.840890i \(0.682032\pi\)
\(152\) 0 0
\(153\) −1.73736 −0.140457
\(154\) 0 0
\(155\) −11.5114 −0.924618
\(156\) 0 0
\(157\) −21.4309 −1.71037 −0.855186 0.518322i \(-0.826557\pi\)
−0.855186 + 0.518322i \(0.826557\pi\)
\(158\) 0 0
\(159\) −1.55065 −0.122974
\(160\) 0 0
\(161\) −0.870393 −0.0685966
\(162\) 0 0
\(163\) 16.4013 1.28465 0.642324 0.766433i \(-0.277970\pi\)
0.642324 + 0.766433i \(0.277970\pi\)
\(164\) 0 0
\(165\) −0.188608 −0.0146831
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −8.70642 −0.669725
\(170\) 0 0
\(171\) 7.35449 0.562412
\(172\) 0 0
\(173\) −7.77119 −0.590833 −0.295416 0.955369i \(-0.595458\pi\)
−0.295416 + 0.955369i \(0.595458\pi\)
\(174\) 0 0
\(175\) 4.88907 0.369579
\(176\) 0 0
\(177\) 11.0736 0.832339
\(178\) 0 0
\(179\) 20.5631 1.53696 0.768479 0.639875i \(-0.221014\pi\)
0.768479 + 0.639875i \(0.221014\pi\)
\(180\) 0 0
\(181\) −6.27861 −0.466686 −0.233343 0.972395i \(-0.574966\pi\)
−0.233343 + 0.972395i \(0.574966\pi\)
\(182\) 0 0
\(183\) 13.4007 0.990608
\(184\) 0 0
\(185\) 24.3020 1.78672
\(186\) 0 0
\(187\) 0.111715 0.00816940
\(188\) 0 0
\(189\) 1.35675 0.0986894
\(190\) 0 0
\(191\) −10.4618 −0.756991 −0.378495 0.925603i \(-0.623558\pi\)
−0.378495 + 0.925603i \(0.623558\pi\)
\(192\) 0 0
\(193\) 3.93031 0.282910 0.141455 0.989945i \(-0.454822\pi\)
0.141455 + 0.989945i \(0.454822\pi\)
\(194\) 0 0
\(195\) −6.07781 −0.435241
\(196\) 0 0
\(197\) −9.96631 −0.710070 −0.355035 0.934853i \(-0.615531\pi\)
−0.355035 + 0.934853i \(0.615531\pi\)
\(198\) 0 0
\(199\) −23.2537 −1.64841 −0.824205 0.566291i \(-0.808378\pi\)
−0.824205 + 0.566291i \(0.808378\pi\)
\(200\) 0 0
\(201\) 4.50770 0.317949
\(202\) 0 0
\(203\) 4.95861 0.348026
\(204\) 0 0
\(205\) 4.55818 0.318357
\(206\) 0 0
\(207\) −0.641526 −0.0445892
\(208\) 0 0
\(209\) −0.472905 −0.0327115
\(210\) 0 0
\(211\) −1.84912 −0.127298 −0.0636492 0.997972i \(-0.520274\pi\)
−0.0636492 + 0.997972i \(0.520274\pi\)
\(212\) 0 0
\(213\) 10.2267 0.700722
\(214\) 0 0
\(215\) −8.14303 −0.555350
\(216\) 0 0
\(217\) −5.32466 −0.361462
\(218\) 0 0
\(219\) −6.16638 −0.416685
\(220\) 0 0
\(221\) 3.59997 0.242160
\(222\) 0 0
\(223\) 19.7420 1.32202 0.661010 0.750377i \(-0.270128\pi\)
0.661010 + 0.750377i \(0.270128\pi\)
\(224\) 0 0
\(225\) 3.60351 0.240234
\(226\) 0 0
\(227\) −4.07103 −0.270204 −0.135102 0.990832i \(-0.543136\pi\)
−0.135102 + 0.990832i \(0.543136\pi\)
\(228\) 0 0
\(229\) 16.3832 1.08263 0.541315 0.840820i \(-0.317926\pi\)
0.541315 + 0.840820i \(0.317926\pi\)
\(230\) 0 0
\(231\) −0.0872414 −0.00574006
\(232\) 0 0
\(233\) −14.9192 −0.977392 −0.488696 0.872454i \(-0.662527\pi\)
−0.488696 + 0.872454i \(0.662527\pi\)
\(234\) 0 0
\(235\) −13.2494 −0.864297
\(236\) 0 0
\(237\) 2.51122 0.163121
\(238\) 0 0
\(239\) −10.0543 −0.650362 −0.325181 0.945652i \(-0.605425\pi\)
−0.325181 + 0.945652i \(0.605425\pi\)
\(240\) 0 0
\(241\) 17.4465 1.12383 0.561915 0.827195i \(-0.310065\pi\)
0.561915 + 0.827195i \(0.310065\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −15.1329 −0.966804
\(246\) 0 0
\(247\) −15.2392 −0.969648
\(248\) 0 0
\(249\) 1.74485 0.110576
\(250\) 0 0
\(251\) −9.90197 −0.625007 −0.312504 0.949917i \(-0.601168\pi\)
−0.312504 + 0.949917i \(0.601168\pi\)
\(252\) 0 0
\(253\) 0.0412511 0.00259344
\(254\) 0 0
\(255\) −5.09598 −0.319123
\(256\) 0 0
\(257\) −19.8372 −1.23741 −0.618704 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(258\) 0 0
\(259\) 11.2410 0.698483
\(260\) 0 0
\(261\) 3.65476 0.226224
\(262\) 0 0
\(263\) 10.8242 0.667447 0.333723 0.942671i \(-0.391695\pi\)
0.333723 + 0.942671i \(0.391695\pi\)
\(264\) 0 0
\(265\) −4.54832 −0.279401
\(266\) 0 0
\(267\) −17.4735 −1.06936
\(268\) 0 0
\(269\) −8.67721 −0.529059 −0.264530 0.964378i \(-0.585217\pi\)
−0.264530 + 0.964378i \(0.585217\pi\)
\(270\) 0 0
\(271\) 18.8503 1.14507 0.572536 0.819879i \(-0.305960\pi\)
0.572536 + 0.819879i \(0.305960\pi\)
\(272\) 0 0
\(273\) −2.81132 −0.170149
\(274\) 0 0
\(275\) −0.231711 −0.0139727
\(276\) 0 0
\(277\) 5.13118 0.308303 0.154151 0.988047i \(-0.450736\pi\)
0.154151 + 0.988047i \(0.450736\pi\)
\(278\) 0 0
\(279\) −3.92456 −0.234957
\(280\) 0 0
\(281\) −17.8779 −1.06650 −0.533252 0.845956i \(-0.679030\pi\)
−0.533252 + 0.845956i \(0.679030\pi\)
\(282\) 0 0
\(283\) 13.0771 0.777351 0.388676 0.921375i \(-0.372933\pi\)
0.388676 + 0.921375i \(0.372933\pi\)
\(284\) 0 0
\(285\) 21.5720 1.27782
\(286\) 0 0
\(287\) 2.10841 0.124456
\(288\) 0 0
\(289\) −13.9816 −0.822446
\(290\) 0 0
\(291\) 17.6851 1.03672
\(292\) 0 0
\(293\) 16.1704 0.944682 0.472341 0.881416i \(-0.343409\pi\)
0.472341 + 0.881416i \(0.343409\pi\)
\(294\) 0 0
\(295\) 32.4806 1.89110
\(296\) 0 0
\(297\) −0.0643015 −0.00373115
\(298\) 0 0
\(299\) 1.32930 0.0768756
\(300\) 0 0
\(301\) −3.76660 −0.217103
\(302\) 0 0
\(303\) 10.0244 0.575886
\(304\) 0 0
\(305\) 39.3066 2.25069
\(306\) 0 0
\(307\) 12.5563 0.716623 0.358312 0.933602i \(-0.383353\pi\)
0.358312 + 0.933602i \(0.383353\pi\)
\(308\) 0 0
\(309\) 6.08730 0.346295
\(310\) 0 0
\(311\) −2.18454 −0.123874 −0.0619368 0.998080i \(-0.519728\pi\)
−0.0619368 + 0.998080i \(0.519728\pi\)
\(312\) 0 0
\(313\) 29.7286 1.68036 0.840179 0.542310i \(-0.182450\pi\)
0.840179 + 0.542310i \(0.182450\pi\)
\(314\) 0 0
\(315\) 3.97960 0.224225
\(316\) 0 0
\(317\) 24.6910 1.38678 0.693392 0.720561i \(-0.256116\pi\)
0.693392 + 0.720561i \(0.256116\pi\)
\(318\) 0 0
\(319\) −0.235007 −0.0131578
\(320\) 0 0
\(321\) 12.5950 0.702983
\(322\) 0 0
\(323\) −12.7774 −0.710954
\(324\) 0 0
\(325\) −7.46680 −0.414184
\(326\) 0 0
\(327\) −17.0536 −0.943064
\(328\) 0 0
\(329\) −6.12859 −0.337880
\(330\) 0 0
\(331\) 25.3306 1.39230 0.696148 0.717899i \(-0.254896\pi\)
0.696148 + 0.717899i \(0.254896\pi\)
\(332\) 0 0
\(333\) 8.28523 0.454028
\(334\) 0 0
\(335\) 13.2219 0.722387
\(336\) 0 0
\(337\) 1.00882 0.0549542 0.0274771 0.999622i \(-0.491253\pi\)
0.0274771 + 0.999622i \(0.491253\pi\)
\(338\) 0 0
\(339\) −11.3676 −0.617402
\(340\) 0 0
\(341\) 0.252355 0.0136658
\(342\) 0 0
\(343\) −16.4971 −0.890758
\(344\) 0 0
\(345\) −1.88171 −0.101308
\(346\) 0 0
\(347\) −5.37742 −0.288675 −0.144337 0.989529i \(-0.546105\pi\)
−0.144337 + 0.989529i \(0.546105\pi\)
\(348\) 0 0
\(349\) −34.8774 −1.86694 −0.933471 0.358653i \(-0.883236\pi\)
−0.933471 + 0.358653i \(0.883236\pi\)
\(350\) 0 0
\(351\) −2.07209 −0.110600
\(352\) 0 0
\(353\) −36.1276 −1.92288 −0.961438 0.275020i \(-0.911315\pi\)
−0.961438 + 0.275020i \(0.911315\pi\)
\(354\) 0 0
\(355\) 29.9967 1.59206
\(356\) 0 0
\(357\) −2.35717 −0.124755
\(358\) 0 0
\(359\) −23.1328 −1.22090 −0.610451 0.792054i \(-0.709012\pi\)
−0.610451 + 0.792054i \(0.709012\pi\)
\(360\) 0 0
\(361\) 35.0886 1.84677
\(362\) 0 0
\(363\) −10.9959 −0.577133
\(364\) 0 0
\(365\) −18.0871 −0.946720
\(366\) 0 0
\(367\) 8.93252 0.466274 0.233137 0.972444i \(-0.425101\pi\)
0.233137 + 0.972444i \(0.425101\pi\)
\(368\) 0 0
\(369\) 1.55401 0.0808986
\(370\) 0 0
\(371\) −2.10385 −0.109226
\(372\) 0 0
\(373\) 16.2017 0.838891 0.419445 0.907781i \(-0.362225\pi\)
0.419445 + 0.907781i \(0.362225\pi\)
\(374\) 0 0
\(375\) −4.09616 −0.211525
\(376\) 0 0
\(377\) −7.57301 −0.390030
\(378\) 0 0
\(379\) −2.95663 −0.151872 −0.0759361 0.997113i \(-0.524194\pi\)
−0.0759361 + 0.997113i \(0.524194\pi\)
\(380\) 0 0
\(381\) 4.85124 0.248536
\(382\) 0 0
\(383\) 10.0666 0.514381 0.257191 0.966361i \(-0.417203\pi\)
0.257191 + 0.966361i \(0.417203\pi\)
\(384\) 0 0
\(385\) −0.255894 −0.0130416
\(386\) 0 0
\(387\) −2.77619 −0.141121
\(388\) 0 0
\(389\) 13.7618 0.697749 0.348874 0.937170i \(-0.386564\pi\)
0.348874 + 0.937170i \(0.386564\pi\)
\(390\) 0 0
\(391\) 1.11456 0.0563658
\(392\) 0 0
\(393\) −13.1490 −0.663281
\(394\) 0 0
\(395\) 7.36584 0.370615
\(396\) 0 0
\(397\) −29.8647 −1.49887 −0.749433 0.662081i \(-0.769674\pi\)
−0.749433 + 0.662081i \(0.769674\pi\)
\(398\) 0 0
\(399\) 9.97824 0.499537
\(400\) 0 0
\(401\) −25.3485 −1.26584 −0.632922 0.774215i \(-0.718145\pi\)
−0.632922 + 0.774215i \(0.718145\pi\)
\(402\) 0 0
\(403\) 8.13205 0.405086
\(404\) 0 0
\(405\) 2.93317 0.145751
\(406\) 0 0
\(407\) −0.532753 −0.0264076
\(408\) 0 0
\(409\) 11.5335 0.570293 0.285147 0.958484i \(-0.407958\pi\)
0.285147 + 0.958484i \(0.407958\pi\)
\(410\) 0 0
\(411\) 9.39248 0.463297
\(412\) 0 0
\(413\) 15.0241 0.739287
\(414\) 0 0
\(415\) 5.11796 0.251231
\(416\) 0 0
\(417\) −6.71091 −0.328635
\(418\) 0 0
\(419\) 30.1036 1.47066 0.735328 0.677711i \(-0.237028\pi\)
0.735328 + 0.677711i \(0.237028\pi\)
\(420\) 0 0
\(421\) 2.97021 0.144759 0.0723795 0.997377i \(-0.476941\pi\)
0.0723795 + 0.997377i \(0.476941\pi\)
\(422\) 0 0
\(423\) −4.51709 −0.219629
\(424\) 0 0
\(425\) −6.26059 −0.303683
\(426\) 0 0
\(427\) 18.1815 0.879862
\(428\) 0 0
\(429\) 0.133239 0.00643283
\(430\) 0 0
\(431\) −0.290617 −0.0139985 −0.00699927 0.999976i \(-0.502228\pi\)
−0.00699927 + 0.999976i \(0.502228\pi\)
\(432\) 0 0
\(433\) −8.66027 −0.416186 −0.208093 0.978109i \(-0.566726\pi\)
−0.208093 + 0.978109i \(0.566726\pi\)
\(434\) 0 0
\(435\) 10.7200 0.513987
\(436\) 0 0
\(437\) −4.71810 −0.225697
\(438\) 0 0
\(439\) 36.4829 1.74123 0.870616 0.491963i \(-0.163721\pi\)
0.870616 + 0.491963i \(0.163721\pi\)
\(440\) 0 0
\(441\) −5.15922 −0.245677
\(442\) 0 0
\(443\) −38.6330 −1.83551 −0.917754 0.397149i \(-0.870000\pi\)
−0.917754 + 0.397149i \(0.870000\pi\)
\(444\) 0 0
\(445\) −51.2529 −2.42962
\(446\) 0 0
\(447\) −6.09023 −0.288058
\(448\) 0 0
\(449\) −26.1961 −1.23627 −0.618136 0.786071i \(-0.712112\pi\)
−0.618136 + 0.786071i \(0.712112\pi\)
\(450\) 0 0
\(451\) −0.0999253 −0.00470530
\(452\) 0 0
\(453\) −13.3009 −0.624931
\(454\) 0 0
\(455\) −8.24610 −0.386583
\(456\) 0 0
\(457\) 5.98759 0.280088 0.140044 0.990145i \(-0.455276\pi\)
0.140044 + 0.990145i \(0.455276\pi\)
\(458\) 0 0
\(459\) −1.73736 −0.0810930
\(460\) 0 0
\(461\) −33.6863 −1.56893 −0.784464 0.620174i \(-0.787062\pi\)
−0.784464 + 0.620174i \(0.787062\pi\)
\(462\) 0 0
\(463\) −15.4825 −0.719532 −0.359766 0.933043i \(-0.617143\pi\)
−0.359766 + 0.933043i \(0.617143\pi\)
\(464\) 0 0
\(465\) −11.5114 −0.533829
\(466\) 0 0
\(467\) −4.98854 −0.230842 −0.115421 0.993317i \(-0.536822\pi\)
−0.115421 + 0.993317i \(0.536822\pi\)
\(468\) 0 0
\(469\) 6.11584 0.282403
\(470\) 0 0
\(471\) −21.4309 −0.987483
\(472\) 0 0
\(473\) 0.178513 0.00820804
\(474\) 0 0
\(475\) 26.5020 1.21599
\(476\) 0 0
\(477\) −1.55065 −0.0709993
\(478\) 0 0
\(479\) 15.2655 0.697499 0.348749 0.937216i \(-0.386606\pi\)
0.348749 + 0.937216i \(0.386606\pi\)
\(480\) 0 0
\(481\) −17.1678 −0.782783
\(482\) 0 0
\(483\) −0.870393 −0.0396043
\(484\) 0 0
\(485\) 51.8734 2.35545
\(486\) 0 0
\(487\) 29.7295 1.34717 0.673587 0.739108i \(-0.264753\pi\)
0.673587 + 0.739108i \(0.264753\pi\)
\(488\) 0 0
\(489\) 16.4013 0.741692
\(490\) 0 0
\(491\) −37.9213 −1.71136 −0.855682 0.517502i \(-0.826862\pi\)
−0.855682 + 0.517502i \(0.826862\pi\)
\(492\) 0 0
\(493\) −6.34963 −0.285973
\(494\) 0 0
\(495\) −0.188608 −0.00847728
\(496\) 0 0
\(497\) 13.8751 0.622384
\(498\) 0 0
\(499\) 1.26368 0.0565699 0.0282850 0.999600i \(-0.490995\pi\)
0.0282850 + 0.999600i \(0.490995\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 11.1166 0.495665 0.247833 0.968803i \(-0.420282\pi\)
0.247833 + 0.968803i \(0.420282\pi\)
\(504\) 0 0
\(505\) 29.4033 1.30843
\(506\) 0 0
\(507\) −8.70642 −0.386666
\(508\) 0 0
\(509\) 36.4271 1.61460 0.807301 0.590140i \(-0.200927\pi\)
0.807301 + 0.590140i \(0.200927\pi\)
\(510\) 0 0
\(511\) −8.36626 −0.370102
\(512\) 0 0
\(513\) 7.35449 0.324709
\(514\) 0 0
\(515\) 17.8551 0.786790
\(516\) 0 0
\(517\) 0.290456 0.0127742
\(518\) 0 0
\(519\) −7.77119 −0.341118
\(520\) 0 0
\(521\) −28.0491 −1.22885 −0.614427 0.788974i \(-0.710613\pi\)
−0.614427 + 0.788974i \(0.710613\pi\)
\(522\) 0 0
\(523\) −35.4652 −1.55078 −0.775392 0.631481i \(-0.782447\pi\)
−0.775392 + 0.631481i \(0.782447\pi\)
\(524\) 0 0
\(525\) 4.88907 0.213377
\(526\) 0 0
\(527\) 6.81837 0.297013
\(528\) 0 0
\(529\) −22.5884 −0.982106
\(530\) 0 0
\(531\) 11.0736 0.480551
\(532\) 0 0
\(533\) −3.22006 −0.139476
\(534\) 0 0
\(535\) 36.9432 1.59720
\(536\) 0 0
\(537\) 20.5631 0.887363
\(538\) 0 0
\(539\) 0.331746 0.0142893
\(540\) 0 0
\(541\) 7.84741 0.337387 0.168693 0.985669i \(-0.446045\pi\)
0.168693 + 0.985669i \(0.446045\pi\)
\(542\) 0 0
\(543\) −6.27861 −0.269441
\(544\) 0 0
\(545\) −50.0210 −2.14267
\(546\) 0 0
\(547\) −26.0303 −1.11297 −0.556487 0.830856i \(-0.687851\pi\)
−0.556487 + 0.830856i \(0.687851\pi\)
\(548\) 0 0
\(549\) 13.4007 0.571928
\(550\) 0 0
\(551\) 26.8789 1.14508
\(552\) 0 0
\(553\) 3.40711 0.144885
\(554\) 0 0
\(555\) 24.3020 1.03156
\(556\) 0 0
\(557\) 23.5772 0.998999 0.499499 0.866314i \(-0.333517\pi\)
0.499499 + 0.866314i \(0.333517\pi\)
\(558\) 0 0
\(559\) 5.75252 0.243306
\(560\) 0 0
\(561\) 0.111715 0.00471661
\(562\) 0 0
\(563\) 1.45924 0.0614997 0.0307498 0.999527i \(-0.490210\pi\)
0.0307498 + 0.999527i \(0.490210\pi\)
\(564\) 0 0
\(565\) −33.3431 −1.40275
\(566\) 0 0
\(567\) 1.35675 0.0569783
\(568\) 0 0
\(569\) −18.4501 −0.773470 −0.386735 0.922191i \(-0.626397\pi\)
−0.386735 + 0.922191i \(0.626397\pi\)
\(570\) 0 0
\(571\) 27.0806 1.13329 0.566644 0.823963i \(-0.308242\pi\)
0.566644 + 0.823963i \(0.308242\pi\)
\(572\) 0 0
\(573\) −10.4618 −0.437049
\(574\) 0 0
\(575\) −2.31174 −0.0964063
\(576\) 0 0
\(577\) 11.7436 0.488894 0.244447 0.969663i \(-0.421394\pi\)
0.244447 + 0.969663i \(0.421394\pi\)
\(578\) 0 0
\(579\) 3.93031 0.163338
\(580\) 0 0
\(581\) 2.36734 0.0982138
\(582\) 0 0
\(583\) 0.0997091 0.00412953
\(584\) 0 0
\(585\) −6.07781 −0.251287
\(586\) 0 0
\(587\) −17.5381 −0.723874 −0.361937 0.932203i \(-0.617884\pi\)
−0.361937 + 0.932203i \(0.617884\pi\)
\(588\) 0 0
\(589\) −28.8631 −1.18928
\(590\) 0 0
\(591\) −9.96631 −0.409959
\(592\) 0 0
\(593\) −22.8036 −0.936433 −0.468216 0.883614i \(-0.655103\pi\)
−0.468216 + 0.883614i \(0.655103\pi\)
\(594\) 0 0
\(595\) −6.91399 −0.283446
\(596\) 0 0
\(597\) −23.2537 −0.951710
\(598\) 0 0
\(599\) −21.3655 −0.872971 −0.436485 0.899711i \(-0.643777\pi\)
−0.436485 + 0.899711i \(0.643777\pi\)
\(600\) 0 0
\(601\) −2.09186 −0.0853288 −0.0426644 0.999089i \(-0.513585\pi\)
−0.0426644 + 0.999089i \(0.513585\pi\)
\(602\) 0 0
\(603\) 4.50770 0.183568
\(604\) 0 0
\(605\) −32.2528 −1.31126
\(606\) 0 0
\(607\) 0.887942 0.0360405 0.0180202 0.999838i \(-0.494264\pi\)
0.0180202 + 0.999838i \(0.494264\pi\)
\(608\) 0 0
\(609\) 4.95861 0.200933
\(610\) 0 0
\(611\) 9.35984 0.378659
\(612\) 0 0
\(613\) 31.2654 1.26280 0.631399 0.775458i \(-0.282481\pi\)
0.631399 + 0.775458i \(0.282481\pi\)
\(614\) 0 0
\(615\) 4.55818 0.183804
\(616\) 0 0
\(617\) 19.7468 0.794975 0.397488 0.917608i \(-0.369882\pi\)
0.397488 + 0.917608i \(0.369882\pi\)
\(618\) 0 0
\(619\) −1.73668 −0.0698032 −0.0349016 0.999391i \(-0.511112\pi\)
−0.0349016 + 0.999391i \(0.511112\pi\)
\(620\) 0 0
\(621\) −0.641526 −0.0257436
\(622\) 0 0
\(623\) −23.7073 −0.949812
\(624\) 0 0
\(625\) −30.0323 −1.20129
\(626\) 0 0
\(627\) −0.472905 −0.0188860
\(628\) 0 0
\(629\) −14.3944 −0.573943
\(630\) 0 0
\(631\) −3.51023 −0.139740 −0.0698700 0.997556i \(-0.522258\pi\)
−0.0698700 + 0.997556i \(0.522258\pi\)
\(632\) 0 0
\(633\) −1.84912 −0.0734958
\(634\) 0 0
\(635\) 14.2295 0.564681
\(636\) 0 0
\(637\) 10.6904 0.423569
\(638\) 0 0
\(639\) 10.2267 0.404562
\(640\) 0 0
\(641\) −27.8251 −1.09902 −0.549512 0.835486i \(-0.685186\pi\)
−0.549512 + 0.835486i \(0.685186\pi\)
\(642\) 0 0
\(643\) −13.8299 −0.545399 −0.272700 0.962099i \(-0.587916\pi\)
−0.272700 + 0.962099i \(0.587916\pi\)
\(644\) 0 0
\(645\) −8.14303 −0.320632
\(646\) 0 0
\(647\) −16.6414 −0.654241 −0.327120 0.944983i \(-0.606078\pi\)
−0.327120 + 0.944983i \(0.606078\pi\)
\(648\) 0 0
\(649\) −0.712046 −0.0279503
\(650\) 0 0
\(651\) −5.32466 −0.208690
\(652\) 0 0
\(653\) 26.1625 1.02382 0.511909 0.859040i \(-0.328938\pi\)
0.511909 + 0.859040i \(0.328938\pi\)
\(654\) 0 0
\(655\) −38.5684 −1.50699
\(656\) 0 0
\(657\) −6.16638 −0.240573
\(658\) 0 0
\(659\) −41.9458 −1.63398 −0.816989 0.576653i \(-0.804358\pi\)
−0.816989 + 0.576653i \(0.804358\pi\)
\(660\) 0 0
\(661\) −25.6903 −0.999236 −0.499618 0.866246i \(-0.666526\pi\)
−0.499618 + 0.866246i \(0.666526\pi\)
\(662\) 0 0
\(663\) 3.59997 0.139811
\(664\) 0 0
\(665\) 29.2679 1.13496
\(666\) 0 0
\(667\) −2.34462 −0.0907842
\(668\) 0 0
\(669\) 19.7420 0.763269
\(670\) 0 0
\(671\) −0.861686 −0.0332650
\(672\) 0 0
\(673\) −0.468458 −0.0180577 −0.00902887 0.999959i \(-0.502874\pi\)
−0.00902887 + 0.999959i \(0.502874\pi\)
\(674\) 0 0
\(675\) 3.60351 0.138699
\(676\) 0 0
\(677\) 5.12748 0.197065 0.0985325 0.995134i \(-0.468585\pi\)
0.0985325 + 0.995134i \(0.468585\pi\)
\(678\) 0 0
\(679\) 23.9943 0.920817
\(680\) 0 0
\(681\) −4.07103 −0.156002
\(682\) 0 0
\(683\) −1.24490 −0.0476349 −0.0238174 0.999716i \(-0.507582\pi\)
−0.0238174 + 0.999716i \(0.507582\pi\)
\(684\) 0 0
\(685\) 27.5498 1.05262
\(686\) 0 0
\(687\) 16.3832 0.625057
\(688\) 0 0
\(689\) 3.21309 0.122409
\(690\) 0 0
\(691\) −12.8788 −0.489934 −0.244967 0.969531i \(-0.578777\pi\)
−0.244967 + 0.969531i \(0.578777\pi\)
\(692\) 0 0
\(693\) −0.0872414 −0.00331403
\(694\) 0 0
\(695\) −19.6843 −0.746666
\(696\) 0 0
\(697\) −2.69988 −0.102265
\(698\) 0 0
\(699\) −14.9192 −0.564298
\(700\) 0 0
\(701\) −12.0111 −0.453654 −0.226827 0.973935i \(-0.572835\pi\)
−0.226827 + 0.973935i \(0.572835\pi\)
\(702\) 0 0
\(703\) 60.9337 2.29816
\(704\) 0 0
\(705\) −13.2494 −0.499002
\(706\) 0 0
\(707\) 13.6006 0.511505
\(708\) 0 0
\(709\) 0.333173 0.0125126 0.00625628 0.999980i \(-0.498009\pi\)
0.00625628 + 0.999980i \(0.498009\pi\)
\(710\) 0 0
\(711\) 2.51122 0.0941780
\(712\) 0 0
\(713\) 2.51771 0.0942889
\(714\) 0 0
\(715\) 0.390813 0.0146156
\(716\) 0 0
\(717\) −10.0543 −0.375486
\(718\) 0 0
\(719\) −4.69923 −0.175252 −0.0876258 0.996153i \(-0.527928\pi\)
−0.0876258 + 0.996153i \(0.527928\pi\)
\(720\) 0 0
\(721\) 8.25898 0.307580
\(722\) 0 0
\(723\) 17.4465 0.648843
\(724\) 0 0
\(725\) 13.1699 0.489119
\(726\) 0 0
\(727\) 16.9255 0.627733 0.313866 0.949467i \(-0.398376\pi\)
0.313866 + 0.949467i \(0.398376\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.82323 0.178394
\(732\) 0 0
\(733\) 20.7928 0.767998 0.383999 0.923333i \(-0.374547\pi\)
0.383999 + 0.923333i \(0.374547\pi\)
\(734\) 0 0
\(735\) −15.1329 −0.558185
\(736\) 0 0
\(737\) −0.289852 −0.0106768
\(738\) 0 0
\(739\) 38.1583 1.40368 0.701838 0.712336i \(-0.252363\pi\)
0.701838 + 0.712336i \(0.252363\pi\)
\(740\) 0 0
\(741\) −15.2392 −0.559826
\(742\) 0 0
\(743\) 1.00712 0.0369476 0.0184738 0.999829i \(-0.494119\pi\)
0.0184738 + 0.999829i \(0.494119\pi\)
\(744\) 0 0
\(745\) −17.8637 −0.654475
\(746\) 0 0
\(747\) 1.74485 0.0638409
\(748\) 0 0
\(749\) 17.0883 0.624392
\(750\) 0 0
\(751\) −10.4846 −0.382589 −0.191295 0.981533i \(-0.561269\pi\)
−0.191295 + 0.981533i \(0.561269\pi\)
\(752\) 0 0
\(753\) −9.90197 −0.360848
\(754\) 0 0
\(755\) −39.0139 −1.41986
\(756\) 0 0
\(757\) 22.4109 0.814537 0.407269 0.913308i \(-0.366481\pi\)
0.407269 + 0.913308i \(0.366481\pi\)
\(758\) 0 0
\(759\) 0.0412511 0.00149732
\(760\) 0 0
\(761\) 2.38127 0.0863211 0.0431606 0.999068i \(-0.486257\pi\)
0.0431606 + 0.999068i \(0.486257\pi\)
\(762\) 0 0
\(763\) −23.1375 −0.837633
\(764\) 0 0
\(765\) −5.09598 −0.184245
\(766\) 0 0
\(767\) −22.9454 −0.828512
\(768\) 0 0
\(769\) 6.71515 0.242154 0.121077 0.992643i \(-0.461365\pi\)
0.121077 + 0.992643i \(0.461365\pi\)
\(770\) 0 0
\(771\) −19.8372 −0.714418
\(772\) 0 0
\(773\) −18.7417 −0.674091 −0.337046 0.941488i \(-0.609428\pi\)
−0.337046 + 0.941488i \(0.609428\pi\)
\(774\) 0 0
\(775\) −14.1422 −0.508002
\(776\) 0 0
\(777\) 11.2410 0.403269
\(778\) 0 0
\(779\) 11.4290 0.409485
\(780\) 0 0
\(781\) −0.657593 −0.0235305
\(782\) 0 0
\(783\) 3.65476 0.130610
\(784\) 0 0
\(785\) −62.8605 −2.24359
\(786\) 0 0
\(787\) −7.60078 −0.270939 −0.135469 0.990782i \(-0.543254\pi\)
−0.135469 + 0.990782i \(0.543254\pi\)
\(788\) 0 0
\(789\) 10.8242 0.385351
\(790\) 0 0
\(791\) −15.4230 −0.548379
\(792\) 0 0
\(793\) −27.7675 −0.986054
\(794\) 0 0
\(795\) −4.54832 −0.161312
\(796\) 0 0
\(797\) 20.3082 0.719352 0.359676 0.933077i \(-0.382887\pi\)
0.359676 + 0.933077i \(0.382887\pi\)
\(798\) 0 0
\(799\) 7.84782 0.277636
\(800\) 0 0
\(801\) −17.4735 −0.617397
\(802\) 0 0
\(803\) 0.396508 0.0139925
\(804\) 0 0
\(805\) −2.55301 −0.0899819
\(806\) 0 0
\(807\) −8.67721 −0.305452
\(808\) 0 0
\(809\) −4.84896 −0.170480 −0.0852402 0.996360i \(-0.527166\pi\)
−0.0852402 + 0.996360i \(0.527166\pi\)
\(810\) 0 0
\(811\) −0.215265 −0.00755897 −0.00377948 0.999993i \(-0.501203\pi\)
−0.00377948 + 0.999993i \(0.501203\pi\)
\(812\) 0 0
\(813\) 18.8503 0.661108
\(814\) 0 0
\(815\) 48.1078 1.68514
\(816\) 0 0
\(817\) −20.4174 −0.714316
\(818\) 0 0
\(819\) −2.81132 −0.0982356
\(820\) 0 0
\(821\) −22.6835 −0.791659 −0.395829 0.918324i \(-0.629543\pi\)
−0.395829 + 0.918324i \(0.629543\pi\)
\(822\) 0 0
\(823\) 9.75812 0.340147 0.170073 0.985431i \(-0.445600\pi\)
0.170073 + 0.985431i \(0.445600\pi\)
\(824\) 0 0
\(825\) −0.231711 −0.00806714
\(826\) 0 0
\(827\) −29.6125 −1.02973 −0.514863 0.857272i \(-0.672157\pi\)
−0.514863 + 0.857272i \(0.672157\pi\)
\(828\) 0 0
\(829\) −43.3806 −1.50667 −0.753336 0.657636i \(-0.771557\pi\)
−0.753336 + 0.657636i \(0.771557\pi\)
\(830\) 0 0
\(831\) 5.13118 0.177999
\(832\) 0 0
\(833\) 8.96342 0.310564
\(834\) 0 0
\(835\) 2.93317 0.101507
\(836\) 0 0
\(837\) −3.92456 −0.135653
\(838\) 0 0
\(839\) −39.6211 −1.36787 −0.683936 0.729542i \(-0.739733\pi\)
−0.683936 + 0.729542i \(0.739733\pi\)
\(840\) 0 0
\(841\) −15.6427 −0.539405
\(842\) 0 0
\(843\) −17.8779 −0.615746
\(844\) 0 0
\(845\) −25.5375 −0.878515
\(846\) 0 0
\(847\) −14.9187 −0.512612
\(848\) 0 0
\(849\) 13.0771 0.448804
\(850\) 0 0
\(851\) −5.31519 −0.182202
\(852\) 0 0
\(853\) −34.6643 −1.18688 −0.593442 0.804877i \(-0.702231\pi\)
−0.593442 + 0.804877i \(0.702231\pi\)
\(854\) 0 0
\(855\) 21.5720 0.737747
\(856\) 0 0
\(857\) 19.6878 0.672522 0.336261 0.941769i \(-0.390838\pi\)
0.336261 + 0.941769i \(0.390838\pi\)
\(858\) 0 0
\(859\) 11.1405 0.380108 0.190054 0.981774i \(-0.439134\pi\)
0.190054 + 0.981774i \(0.439134\pi\)
\(860\) 0 0
\(861\) 2.10841 0.0718545
\(862\) 0 0
\(863\) −28.5360 −0.971377 −0.485688 0.874132i \(-0.661431\pi\)
−0.485688 + 0.874132i \(0.661431\pi\)
\(864\) 0 0
\(865\) −22.7943 −0.775028
\(866\) 0 0
\(867\) −13.9816 −0.474839
\(868\) 0 0
\(869\) −0.161475 −0.00547767
\(870\) 0 0
\(871\) −9.34038 −0.316487
\(872\) 0 0
\(873\) 17.6851 0.598549
\(874\) 0 0
\(875\) −5.55748 −0.187877
\(876\) 0 0
\(877\) 33.5568 1.13313 0.566566 0.824016i \(-0.308272\pi\)
0.566566 + 0.824016i \(0.308272\pi\)
\(878\) 0 0
\(879\) 16.1704 0.545413
\(880\) 0 0
\(881\) −34.9200 −1.17648 −0.588242 0.808685i \(-0.700180\pi\)
−0.588242 + 0.808685i \(0.700180\pi\)
\(882\) 0 0
\(883\) −3.89129 −0.130952 −0.0654761 0.997854i \(-0.520857\pi\)
−0.0654761 + 0.997854i \(0.520857\pi\)
\(884\) 0 0
\(885\) 32.4806 1.09182
\(886\) 0 0
\(887\) 18.7256 0.628745 0.314372 0.949300i \(-0.398206\pi\)
0.314372 + 0.949300i \(0.398206\pi\)
\(888\) 0 0
\(889\) 6.58194 0.220751
\(890\) 0 0
\(891\) −0.0643015 −0.00215418
\(892\) 0 0
\(893\) −33.2209 −1.11170
\(894\) 0 0
\(895\) 60.3151 2.01611
\(896\) 0 0
\(897\) 1.32930 0.0443841
\(898\) 0 0
\(899\) −14.3433 −0.478376
\(900\) 0 0
\(901\) 2.69403 0.0897513
\(902\) 0 0
\(903\) −3.76660 −0.125345
\(904\) 0 0
\(905\) −18.4163 −0.612177
\(906\) 0 0
\(907\) 4.23006 0.140457 0.0702285 0.997531i \(-0.477627\pi\)
0.0702285 + 0.997531i \(0.477627\pi\)
\(908\) 0 0
\(909\) 10.0244 0.332488
\(910\) 0 0
\(911\) −32.4195 −1.07411 −0.537053 0.843549i \(-0.680462\pi\)
−0.537053 + 0.843549i \(0.680462\pi\)
\(912\) 0 0
\(913\) −0.112197 −0.00371317
\(914\) 0 0
\(915\) 39.3066 1.29944
\(916\) 0 0
\(917\) −17.8400 −0.589129
\(918\) 0 0
\(919\) 7.50842 0.247680 0.123840 0.992302i \(-0.460479\pi\)
0.123840 + 0.992302i \(0.460479\pi\)
\(920\) 0 0
\(921\) 12.5563 0.413743
\(922\) 0 0
\(923\) −21.1907 −0.697500
\(924\) 0 0
\(925\) 29.8559 0.981655
\(926\) 0 0
\(927\) 6.08730 0.199933
\(928\) 0 0
\(929\) 14.6459 0.480516 0.240258 0.970709i \(-0.422768\pi\)
0.240258 + 0.970709i \(0.422768\pi\)
\(930\) 0 0
\(931\) −37.9434 −1.24355
\(932\) 0 0
\(933\) −2.18454 −0.0715185
\(934\) 0 0
\(935\) 0.327679 0.0107163
\(936\) 0 0
\(937\) −33.5660 −1.09655 −0.548277 0.836297i \(-0.684716\pi\)
−0.548277 + 0.836297i \(0.684716\pi\)
\(938\) 0 0
\(939\) 29.7286 0.970155
\(940\) 0 0
\(941\) −9.09313 −0.296428 −0.148214 0.988955i \(-0.547352\pi\)
−0.148214 + 0.988955i \(0.547352\pi\)
\(942\) 0 0
\(943\) −0.996939 −0.0324648
\(944\) 0 0
\(945\) 3.97960 0.129456
\(946\) 0 0
\(947\) −33.3348 −1.08323 −0.541617 0.840625i \(-0.682188\pi\)
−0.541617 + 0.840625i \(0.682188\pi\)
\(948\) 0 0
\(949\) 12.7773 0.414769
\(950\) 0 0
\(951\) 24.6910 0.800660
\(952\) 0 0
\(953\) −26.3126 −0.852349 −0.426174 0.904641i \(-0.640139\pi\)
−0.426174 + 0.904641i \(0.640139\pi\)
\(954\) 0 0
\(955\) −30.6863 −0.992987
\(956\) 0 0
\(957\) −0.235007 −0.00759669
\(958\) 0 0
\(959\) 12.7433 0.411502
\(960\) 0 0
\(961\) −15.5978 −0.503156
\(962\) 0 0
\(963\) 12.5950 0.405867
\(964\) 0 0
\(965\) 11.5283 0.371109
\(966\) 0 0
\(967\) 55.3925 1.78130 0.890651 0.454687i \(-0.150249\pi\)
0.890651 + 0.454687i \(0.150249\pi\)
\(968\) 0 0
\(969\) −12.7774 −0.410469
\(970\) 0 0
\(971\) −16.9200 −0.542990 −0.271495 0.962440i \(-0.587518\pi\)
−0.271495 + 0.962440i \(0.587518\pi\)
\(972\) 0 0
\(973\) −9.10505 −0.291895
\(974\) 0 0
\(975\) −7.46680 −0.239129
\(976\) 0 0
\(977\) −5.54245 −0.177319 −0.0886594 0.996062i \(-0.528258\pi\)
−0.0886594 + 0.996062i \(0.528258\pi\)
\(978\) 0 0
\(979\) 1.12357 0.0359096
\(980\) 0 0
\(981\) −17.0536 −0.544478
\(982\) 0 0
\(983\) 20.9074 0.666842 0.333421 0.942778i \(-0.391797\pi\)
0.333421 + 0.942778i \(0.391797\pi\)
\(984\) 0 0
\(985\) −29.2329 −0.931438
\(986\) 0 0
\(987\) −6.12859 −0.195075
\(988\) 0 0
\(989\) 1.78100 0.0566324
\(990\) 0 0
\(991\) 45.9402 1.45934 0.729669 0.683800i \(-0.239674\pi\)
0.729669 + 0.683800i \(0.239674\pi\)
\(992\) 0 0
\(993\) 25.3306 0.803842
\(994\) 0 0
\(995\) −68.2071 −2.16231
\(996\) 0 0
\(997\) −29.5386 −0.935498 −0.467749 0.883861i \(-0.654935\pi\)
−0.467749 + 0.883861i \(0.654935\pi\)
\(998\) 0 0
\(999\) 8.28523 0.262133
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 \(a_p\))