Properties

Label 8008.2.a.u.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.44592\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44592 q^{3} +0.430286 q^{5} -1.00000 q^{7} +2.98251 q^{9} +O(q^{10})\) \(q-2.44592 q^{3} +0.430286 q^{5} -1.00000 q^{7} +2.98251 q^{9} -1.00000 q^{11} -1.00000 q^{13} -1.05244 q^{15} -2.46017 q^{17} +2.25598 q^{19} +2.44592 q^{21} +0.471995 q^{23} -4.81485 q^{25} +0.0427829 q^{27} +3.50972 q^{29} +2.03486 q^{31} +2.44592 q^{33} -0.430286 q^{35} -3.29838 q^{37} +2.44592 q^{39} +4.77742 q^{41} +6.41707 q^{43} +1.28333 q^{45} +4.46079 q^{47} +1.00000 q^{49} +6.01736 q^{51} -14.0776 q^{53} -0.430286 q^{55} -5.51793 q^{57} +2.10449 q^{59} -12.5768 q^{61} -2.98251 q^{63} -0.430286 q^{65} +9.60207 q^{67} -1.15446 q^{69} +3.80453 q^{71} -8.00847 q^{73} +11.7767 q^{75} +1.00000 q^{77} +7.77702 q^{79} -9.05217 q^{81} +16.6675 q^{83} -1.05858 q^{85} -8.58448 q^{87} +4.07691 q^{89} +1.00000 q^{91} -4.97709 q^{93} +0.970714 q^{95} +9.75068 q^{97} -2.98251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) −2.44592 −1.41215 −0.706075 0.708137i \(-0.749536\pi\)
−0.706075 + 0.708137i \(0.749536\pi\)
\(4\) 0 0
\(5\) 0.430286 0.192430 0.0962148 0.995361i \(-0.469326\pi\)
0.0962148 + 0.995361i \(0.469326\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.98251 0.994169
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.05244 −0.271740
\(16\) 0 0
\(17\) −2.46017 −0.596678 −0.298339 0.954460i \(-0.596433\pi\)
−0.298339 + 0.954460i \(0.596433\pi\)
\(18\) 0 0
\(19\) 2.25598 0.517556 0.258778 0.965937i \(-0.416680\pi\)
0.258778 + 0.965937i \(0.416680\pi\)
\(20\) 0 0
\(21\) 2.44592 0.533743
\(22\) 0 0
\(23\) 0.471995 0.0984177 0.0492088 0.998789i \(-0.484330\pi\)
0.0492088 + 0.998789i \(0.484330\pi\)
\(24\) 0 0
\(25\) −4.81485 −0.962971
\(26\) 0 0
\(27\) 0.0427829 0.00823358
\(28\) 0 0
\(29\) 3.50972 0.651739 0.325869 0.945415i \(-0.394343\pi\)
0.325869 + 0.945415i \(0.394343\pi\)
\(30\) 0 0
\(31\) 2.03486 0.365471 0.182735 0.983162i \(-0.441505\pi\)
0.182735 + 0.983162i \(0.441505\pi\)
\(32\) 0 0
\(33\) 2.44592 0.425779
\(34\) 0 0
\(35\) −0.430286 −0.0727316
\(36\) 0 0
\(37\) −3.29838 −0.542251 −0.271126 0.962544i \(-0.587396\pi\)
−0.271126 + 0.962544i \(0.587396\pi\)
\(38\) 0 0
\(39\) 2.44592 0.391660
\(40\) 0 0
\(41\) 4.77742 0.746108 0.373054 0.927810i \(-0.378311\pi\)
0.373054 + 0.927810i \(0.378311\pi\)
\(42\) 0 0
\(43\) 6.41707 0.978593 0.489297 0.872117i \(-0.337254\pi\)
0.489297 + 0.872117i \(0.337254\pi\)
\(44\) 0 0
\(45\) 1.28333 0.191308
\(46\) 0 0
\(47\) 4.46079 0.650673 0.325337 0.945598i \(-0.394522\pi\)
0.325337 + 0.945598i \(0.394522\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 6.01736 0.842600
\(52\) 0 0
\(53\) −14.0776 −1.93371 −0.966854 0.255330i \(-0.917816\pi\)
−0.966854 + 0.255330i \(0.917816\pi\)
\(54\) 0 0
\(55\) −0.430286 −0.0580197
\(56\) 0 0
\(57\) −5.51793 −0.730867
\(58\) 0 0
\(59\) 2.10449 0.273981 0.136991 0.990572i \(-0.456257\pi\)
0.136991 + 0.990572i \(0.456257\pi\)
\(60\) 0 0
\(61\) −12.5768 −1.61029 −0.805144 0.593079i \(-0.797912\pi\)
−0.805144 + 0.593079i \(0.797912\pi\)
\(62\) 0 0
\(63\) −2.98251 −0.375761
\(64\) 0 0
\(65\) −0.430286 −0.0533704
\(66\) 0 0
\(67\) 9.60207 1.17308 0.586540 0.809920i \(-0.300490\pi\)
0.586540 + 0.809920i \(0.300490\pi\)
\(68\) 0 0
\(69\) −1.15446 −0.138981
\(70\) 0 0
\(71\) 3.80453 0.451515 0.225757 0.974184i \(-0.427514\pi\)
0.225757 + 0.974184i \(0.427514\pi\)
\(72\) 0 0
\(73\) −8.00847 −0.937320 −0.468660 0.883379i \(-0.655263\pi\)
−0.468660 + 0.883379i \(0.655263\pi\)
\(74\) 0 0
\(75\) 11.7767 1.35986
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 7.77702 0.874983 0.437491 0.899223i \(-0.355867\pi\)
0.437491 + 0.899223i \(0.355867\pi\)
\(80\) 0 0
\(81\) −9.05217 −1.00580
\(82\) 0 0
\(83\) 16.6675 1.82950 0.914749 0.404022i \(-0.132388\pi\)
0.914749 + 0.404022i \(0.132388\pi\)
\(84\) 0 0
\(85\) −1.05858 −0.114819
\(86\) 0 0
\(87\) −8.58448 −0.920353
\(88\) 0 0
\(89\) 4.07691 0.432152 0.216076 0.976377i \(-0.430674\pi\)
0.216076 + 0.976377i \(0.430674\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −4.97709 −0.516100
\(94\) 0 0
\(95\) 0.970714 0.0995932
\(96\) 0 0
\(97\) 9.75068 0.990032 0.495016 0.868884i \(-0.335162\pi\)
0.495016 + 0.868884i \(0.335162\pi\)
\(98\) 0 0
\(99\) −2.98251 −0.299753
\(100\) 0 0
\(101\) −4.32610 −0.430463 −0.215232 0.976563i \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(102\) 0 0
\(103\) −13.3418 −1.31460 −0.657302 0.753627i \(-0.728303\pi\)
−0.657302 + 0.753627i \(0.728303\pi\)
\(104\) 0 0
\(105\) 1.05244 0.102708
\(106\) 0 0
\(107\) −0.401094 −0.0387752 −0.0193876 0.999812i \(-0.506172\pi\)
−0.0193876 + 0.999812i \(0.506172\pi\)
\(108\) 0 0
\(109\) 10.2616 0.982881 0.491441 0.870911i \(-0.336471\pi\)
0.491441 + 0.870911i \(0.336471\pi\)
\(110\) 0 0
\(111\) 8.06757 0.765740
\(112\) 0 0
\(113\) 14.6946 1.38236 0.691178 0.722685i \(-0.257092\pi\)
0.691178 + 0.722685i \(0.257092\pi\)
\(114\) 0 0
\(115\) 0.203093 0.0189385
\(116\) 0 0
\(117\) −2.98251 −0.275733
\(118\) 0 0
\(119\) 2.46017 0.225523
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −11.6852 −1.05362
\(124\) 0 0
\(125\) −4.22319 −0.377734
\(126\) 0 0
\(127\) −9.61745 −0.853410 −0.426705 0.904391i \(-0.640326\pi\)
−0.426705 + 0.904391i \(0.640326\pi\)
\(128\) 0 0
\(129\) −15.6956 −1.38192
\(130\) 0 0
\(131\) −20.5214 −1.79296 −0.896482 0.443080i \(-0.853886\pi\)
−0.896482 + 0.443080i \(0.853886\pi\)
\(132\) 0 0
\(133\) −2.25598 −0.195618
\(134\) 0 0
\(135\) 0.0184089 0.00158439
\(136\) 0 0
\(137\) −16.6648 −1.42377 −0.711886 0.702295i \(-0.752159\pi\)
−0.711886 + 0.702295i \(0.752159\pi\)
\(138\) 0 0
\(139\) −12.5834 −1.06731 −0.533654 0.845703i \(-0.679182\pi\)
−0.533654 + 0.845703i \(0.679182\pi\)
\(140\) 0 0
\(141\) −10.9107 −0.918848
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.51018 0.125414
\(146\) 0 0
\(147\) −2.44592 −0.201736
\(148\) 0 0
\(149\) −1.08465 −0.0888582 −0.0444291 0.999013i \(-0.514147\pi\)
−0.0444291 + 0.999013i \(0.514147\pi\)
\(150\) 0 0
\(151\) 11.4279 0.929987 0.464994 0.885314i \(-0.346057\pi\)
0.464994 + 0.885314i \(0.346057\pi\)
\(152\) 0 0
\(153\) −7.33747 −0.593199
\(154\) 0 0
\(155\) 0.875570 0.0703275
\(156\) 0 0
\(157\) 15.8207 1.26263 0.631316 0.775526i \(-0.282515\pi\)
0.631316 + 0.775526i \(0.282515\pi\)
\(158\) 0 0
\(159\) 34.4327 2.73069
\(160\) 0 0
\(161\) −0.471995 −0.0371984
\(162\) 0 0
\(163\) −18.4982 −1.44889 −0.724445 0.689333i \(-0.757904\pi\)
−0.724445 + 0.689333i \(0.757904\pi\)
\(164\) 0 0
\(165\) 1.05244 0.0819326
\(166\) 0 0
\(167\) 11.5024 0.890082 0.445041 0.895510i \(-0.353189\pi\)
0.445041 + 0.895510i \(0.353189\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 6.72847 0.514539
\(172\) 0 0
\(173\) 2.45503 0.186652 0.0933261 0.995636i \(-0.470250\pi\)
0.0933261 + 0.995636i \(0.470250\pi\)
\(174\) 0 0
\(175\) 4.81485 0.363969
\(176\) 0 0
\(177\) −5.14740 −0.386903
\(178\) 0 0
\(179\) 24.9468 1.86461 0.932306 0.361671i \(-0.117794\pi\)
0.932306 + 0.361671i \(0.117794\pi\)
\(180\) 0 0
\(181\) 20.4478 1.51987 0.759937 0.649996i \(-0.225230\pi\)
0.759937 + 0.649996i \(0.225230\pi\)
\(182\) 0 0
\(183\) 30.7617 2.27397
\(184\) 0 0
\(185\) −1.41925 −0.104345
\(186\) 0 0
\(187\) 2.46017 0.179905
\(188\) 0 0
\(189\) −0.0427829 −0.00311200
\(190\) 0 0
\(191\) −16.3252 −1.18125 −0.590624 0.806947i \(-0.701118\pi\)
−0.590624 + 0.806947i \(0.701118\pi\)
\(192\) 0 0
\(193\) 5.58042 0.401688 0.200844 0.979623i \(-0.435632\pi\)
0.200844 + 0.979623i \(0.435632\pi\)
\(194\) 0 0
\(195\) 1.05244 0.0753670
\(196\) 0 0
\(197\) −12.8425 −0.914991 −0.457495 0.889212i \(-0.651253\pi\)
−0.457495 + 0.889212i \(0.651253\pi\)
\(198\) 0 0
\(199\) −10.9559 −0.776646 −0.388323 0.921523i \(-0.626946\pi\)
−0.388323 + 0.921523i \(0.626946\pi\)
\(200\) 0 0
\(201\) −23.4859 −1.65657
\(202\) 0 0
\(203\) −3.50972 −0.246334
\(204\) 0 0
\(205\) 2.05566 0.143573
\(206\) 0 0
\(207\) 1.40773 0.0978439
\(208\) 0 0
\(209\) −2.25598 −0.156049
\(210\) 0 0
\(211\) 1.62870 0.112124 0.0560622 0.998427i \(-0.482146\pi\)
0.0560622 + 0.998427i \(0.482146\pi\)
\(212\) 0 0
\(213\) −9.30557 −0.637607
\(214\) 0 0
\(215\) 2.76117 0.188310
\(216\) 0 0
\(217\) −2.03486 −0.138135
\(218\) 0 0
\(219\) 19.5880 1.32364
\(220\) 0 0
\(221\) 2.46017 0.165489
\(222\) 0 0
\(223\) 1.61551 0.108182 0.0540911 0.998536i \(-0.482774\pi\)
0.0540911 + 0.998536i \(0.482774\pi\)
\(224\) 0 0
\(225\) −14.3603 −0.957356
\(226\) 0 0
\(227\) 20.1498 1.33739 0.668693 0.743539i \(-0.266854\pi\)
0.668693 + 0.743539i \(0.266854\pi\)
\(228\) 0 0
\(229\) 22.4708 1.48492 0.742458 0.669893i \(-0.233660\pi\)
0.742458 + 0.669893i \(0.233660\pi\)
\(230\) 0 0
\(231\) −2.44592 −0.160930
\(232\) 0 0
\(233\) −23.3179 −1.52761 −0.763803 0.645450i \(-0.776670\pi\)
−0.763803 + 0.645450i \(0.776670\pi\)
\(234\) 0 0
\(235\) 1.91941 0.125209
\(236\) 0 0
\(237\) −19.0219 −1.23561
\(238\) 0 0
\(239\) −12.2926 −0.795143 −0.397572 0.917571i \(-0.630147\pi\)
−0.397572 + 0.917571i \(0.630147\pi\)
\(240\) 0 0
\(241\) −1.36081 −0.0876576 −0.0438288 0.999039i \(-0.513956\pi\)
−0.0438288 + 0.999039i \(0.513956\pi\)
\(242\) 0 0
\(243\) 22.0125 1.41210
\(244\) 0 0
\(245\) 0.430286 0.0274900
\(246\) 0 0
\(247\) −2.25598 −0.143544
\(248\) 0 0
\(249\) −40.7674 −2.58353
\(250\) 0 0
\(251\) 18.4003 1.16142 0.580710 0.814111i \(-0.302775\pi\)
0.580710 + 0.814111i \(0.302775\pi\)
\(252\) 0 0
\(253\) −0.471995 −0.0296741
\(254\) 0 0
\(255\) 2.58919 0.162141
\(256\) 0 0
\(257\) −9.86941 −0.615637 −0.307819 0.951445i \(-0.599599\pi\)
−0.307819 + 0.951445i \(0.599599\pi\)
\(258\) 0 0
\(259\) 3.29838 0.204952
\(260\) 0 0
\(261\) 10.4678 0.647939
\(262\) 0 0
\(263\) −30.2415 −1.86477 −0.932386 0.361463i \(-0.882277\pi\)
−0.932386 + 0.361463i \(0.882277\pi\)
\(264\) 0 0
\(265\) −6.05739 −0.372103
\(266\) 0 0
\(267\) −9.97179 −0.610264
\(268\) 0 0
\(269\) −8.75389 −0.533734 −0.266867 0.963733i \(-0.585988\pi\)
−0.266867 + 0.963733i \(0.585988\pi\)
\(270\) 0 0
\(271\) 11.6433 0.707278 0.353639 0.935382i \(-0.384944\pi\)
0.353639 + 0.935382i \(0.384944\pi\)
\(272\) 0 0
\(273\) −2.44592 −0.148034
\(274\) 0 0
\(275\) 4.81485 0.290347
\(276\) 0 0
\(277\) −13.7762 −0.827729 −0.413864 0.910339i \(-0.635821\pi\)
−0.413864 + 0.910339i \(0.635821\pi\)
\(278\) 0 0
\(279\) 6.06898 0.363340
\(280\) 0 0
\(281\) 20.0948 1.19875 0.599377 0.800467i \(-0.295415\pi\)
0.599377 + 0.800467i \(0.295415\pi\)
\(282\) 0 0
\(283\) −19.3879 −1.15249 −0.576245 0.817277i \(-0.695483\pi\)
−0.576245 + 0.817277i \(0.695483\pi\)
\(284\) 0 0
\(285\) −2.37429 −0.140641
\(286\) 0 0
\(287\) −4.77742 −0.282002
\(288\) 0 0
\(289\) −10.9476 −0.643975
\(290\) 0 0
\(291\) −23.8494 −1.39807
\(292\) 0 0
\(293\) 22.0144 1.28609 0.643047 0.765827i \(-0.277670\pi\)
0.643047 + 0.765827i \(0.277670\pi\)
\(294\) 0 0
\(295\) 0.905532 0.0527221
\(296\) 0 0
\(297\) −0.0427829 −0.00248252
\(298\) 0 0
\(299\) −0.471995 −0.0272962
\(300\) 0 0
\(301\) −6.41707 −0.369874
\(302\) 0 0
\(303\) 10.5813 0.607879
\(304\) 0 0
\(305\) −5.41160 −0.309867
\(306\) 0 0
\(307\) 2.00157 0.114236 0.0571178 0.998367i \(-0.481809\pi\)
0.0571178 + 0.998367i \(0.481809\pi\)
\(308\) 0 0
\(309\) 32.6329 1.85642
\(310\) 0 0
\(311\) 29.1021 1.65023 0.825115 0.564964i \(-0.191110\pi\)
0.825115 + 0.564964i \(0.191110\pi\)
\(312\) 0 0
\(313\) 17.4016 0.983597 0.491798 0.870709i \(-0.336340\pi\)
0.491798 + 0.870709i \(0.336340\pi\)
\(314\) 0 0
\(315\) −1.28333 −0.0723075
\(316\) 0 0
\(317\) −5.63617 −0.316559 −0.158279 0.987394i \(-0.550595\pi\)
−0.158279 + 0.987394i \(0.550595\pi\)
\(318\) 0 0
\(319\) −3.50972 −0.196507
\(320\) 0 0
\(321\) 0.981042 0.0547564
\(322\) 0 0
\(323\) −5.55008 −0.308815
\(324\) 0 0
\(325\) 4.81485 0.267080
\(326\) 0 0
\(327\) −25.0990 −1.38798
\(328\) 0 0
\(329\) −4.46079 −0.245931
\(330\) 0 0
\(331\) −4.40982 −0.242385 −0.121193 0.992629i \(-0.538672\pi\)
−0.121193 + 0.992629i \(0.538672\pi\)
\(332\) 0 0
\(333\) −9.83746 −0.539089
\(334\) 0 0
\(335\) 4.13164 0.225735
\(336\) 0 0
\(337\) 0.228993 0.0124740 0.00623701 0.999981i \(-0.498015\pi\)
0.00623701 + 0.999981i \(0.498015\pi\)
\(338\) 0 0
\(339\) −35.9419 −1.95210
\(340\) 0 0
\(341\) −2.03486 −0.110194
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −0.496748 −0.0267440
\(346\) 0 0
\(347\) −22.0734 −1.18496 −0.592482 0.805584i \(-0.701852\pi\)
−0.592482 + 0.805584i \(0.701852\pi\)
\(348\) 0 0
\(349\) −37.0083 −1.98101 −0.990505 0.137473i \(-0.956102\pi\)
−0.990505 + 0.137473i \(0.956102\pi\)
\(350\) 0 0
\(351\) −0.0427829 −0.00228358
\(352\) 0 0
\(353\) −33.8429 −1.80128 −0.900638 0.434570i \(-0.856900\pi\)
−0.900638 + 0.434570i \(0.856900\pi\)
\(354\) 0 0
\(355\) 1.63704 0.0868849
\(356\) 0 0
\(357\) −6.01736 −0.318473
\(358\) 0 0
\(359\) −35.9056 −1.89503 −0.947513 0.319718i \(-0.896412\pi\)
−0.947513 + 0.319718i \(0.896412\pi\)
\(360\) 0 0
\(361\) −13.9106 −0.732136
\(362\) 0 0
\(363\) −2.44592 −0.128377
\(364\) 0 0
\(365\) −3.44593 −0.180368
\(366\) 0 0
\(367\) −22.3371 −1.16599 −0.582995 0.812476i \(-0.698119\pi\)
−0.582995 + 0.812476i \(0.698119\pi\)
\(368\) 0 0
\(369\) 14.2487 0.741757
\(370\) 0 0
\(371\) 14.0776 0.730873
\(372\) 0 0
\(373\) −30.0439 −1.55561 −0.777806 0.628504i \(-0.783667\pi\)
−0.777806 + 0.628504i \(0.783667\pi\)
\(374\) 0 0
\(375\) 10.3296 0.533417
\(376\) 0 0
\(377\) −3.50972 −0.180760
\(378\) 0 0
\(379\) 14.4689 0.743219 0.371609 0.928389i \(-0.378806\pi\)
0.371609 + 0.928389i \(0.378806\pi\)
\(380\) 0 0
\(381\) 23.5235 1.20514
\(382\) 0 0
\(383\) −25.4535 −1.30061 −0.650306 0.759672i \(-0.725360\pi\)
−0.650306 + 0.759672i \(0.725360\pi\)
\(384\) 0 0
\(385\) 0.430286 0.0219294
\(386\) 0 0
\(387\) 19.1390 0.972888
\(388\) 0 0
\(389\) 6.42095 0.325555 0.162777 0.986663i \(-0.447955\pi\)
0.162777 + 0.986663i \(0.447955\pi\)
\(390\) 0 0
\(391\) −1.16119 −0.0587237
\(392\) 0 0
\(393\) 50.1937 2.53194
\(394\) 0 0
\(395\) 3.34634 0.168373
\(396\) 0 0
\(397\) −19.1594 −0.961580 −0.480790 0.876836i \(-0.659650\pi\)
−0.480790 + 0.876836i \(0.659650\pi\)
\(398\) 0 0
\(399\) 5.51793 0.276242
\(400\) 0 0
\(401\) −6.39880 −0.319541 −0.159770 0.987154i \(-0.551075\pi\)
−0.159770 + 0.987154i \(0.551075\pi\)
\(402\) 0 0
\(403\) −2.03486 −0.101363
\(404\) 0 0
\(405\) −3.89502 −0.193545
\(406\) 0 0
\(407\) 3.29838 0.163495
\(408\) 0 0
\(409\) 33.3123 1.64719 0.823594 0.567180i \(-0.191966\pi\)
0.823594 + 0.567180i \(0.191966\pi\)
\(410\) 0 0
\(411\) 40.7608 2.01058
\(412\) 0 0
\(413\) −2.10449 −0.103555
\(414\) 0 0
\(415\) 7.17180 0.352050
\(416\) 0 0
\(417\) 30.7779 1.50720
\(418\) 0 0
\(419\) 15.0157 0.733566 0.366783 0.930306i \(-0.380459\pi\)
0.366783 + 0.930306i \(0.380459\pi\)
\(420\) 0 0
\(421\) −39.5704 −1.92854 −0.964271 0.264917i \(-0.914655\pi\)
−0.964271 + 0.264917i \(0.914655\pi\)
\(422\) 0 0
\(423\) 13.3043 0.646879
\(424\) 0 0
\(425\) 11.8453 0.574584
\(426\) 0 0
\(427\) 12.5768 0.608632
\(428\) 0 0
\(429\) −2.44592 −0.118090
\(430\) 0 0
\(431\) −10.0512 −0.484150 −0.242075 0.970258i \(-0.577828\pi\)
−0.242075 + 0.970258i \(0.577828\pi\)
\(432\) 0 0
\(433\) −23.2951 −1.11949 −0.559745 0.828665i \(-0.689101\pi\)
−0.559745 + 0.828665i \(0.689101\pi\)
\(434\) 0 0
\(435\) −3.69378 −0.177103
\(436\) 0 0
\(437\) 1.06481 0.0509367
\(438\) 0 0
\(439\) 31.8872 1.52189 0.760947 0.648814i \(-0.224735\pi\)
0.760947 + 0.648814i \(0.224735\pi\)
\(440\) 0 0
\(441\) 2.98251 0.142024
\(442\) 0 0
\(443\) −29.9351 −1.42226 −0.711130 0.703061i \(-0.751816\pi\)
−0.711130 + 0.703061i \(0.751816\pi\)
\(444\) 0 0
\(445\) 1.75424 0.0831588
\(446\) 0 0
\(447\) 2.65297 0.125481
\(448\) 0 0
\(449\) −37.0024 −1.74625 −0.873125 0.487497i \(-0.837910\pi\)
−0.873125 + 0.487497i \(0.837910\pi\)
\(450\) 0 0
\(451\) −4.77742 −0.224960
\(452\) 0 0
\(453\) −27.9516 −1.31328
\(454\) 0 0
\(455\) 0.430286 0.0201721
\(456\) 0 0
\(457\) 13.3568 0.624803 0.312401 0.949950i \(-0.398867\pi\)
0.312401 + 0.949950i \(0.398867\pi\)
\(458\) 0 0
\(459\) −0.105253 −0.00491280
\(460\) 0 0
\(461\) 11.7343 0.546521 0.273261 0.961940i \(-0.411898\pi\)
0.273261 + 0.961940i \(0.411898\pi\)
\(462\) 0 0
\(463\) −15.9157 −0.739663 −0.369832 0.929099i \(-0.620585\pi\)
−0.369832 + 0.929099i \(0.620585\pi\)
\(464\) 0 0
\(465\) −2.14157 −0.0993130
\(466\) 0 0
\(467\) 28.7261 1.32929 0.664644 0.747160i \(-0.268583\pi\)
0.664644 + 0.747160i \(0.268583\pi\)
\(468\) 0 0
\(469\) −9.60207 −0.443383
\(470\) 0 0
\(471\) −38.6962 −1.78303
\(472\) 0 0
\(473\) −6.41707 −0.295057
\(474\) 0 0
\(475\) −10.8622 −0.498392
\(476\) 0 0
\(477\) −41.9866 −1.92243
\(478\) 0 0
\(479\) −11.8871 −0.543137 −0.271568 0.962419i \(-0.587542\pi\)
−0.271568 + 0.962419i \(0.587542\pi\)
\(480\) 0 0
\(481\) 3.29838 0.150393
\(482\) 0 0
\(483\) 1.15446 0.0525297
\(484\) 0 0
\(485\) 4.19558 0.190511
\(486\) 0 0
\(487\) −30.3669 −1.37605 −0.688027 0.725685i \(-0.741523\pi\)
−0.688027 + 0.725685i \(0.741523\pi\)
\(488\) 0 0
\(489\) 45.2450 2.04605
\(490\) 0 0
\(491\) −6.05583 −0.273296 −0.136648 0.990620i \(-0.543633\pi\)
−0.136648 + 0.990620i \(0.543633\pi\)
\(492\) 0 0
\(493\) −8.63450 −0.388878
\(494\) 0 0
\(495\) −1.28333 −0.0576814
\(496\) 0 0
\(497\) −3.80453 −0.170657
\(498\) 0 0
\(499\) −37.7665 −1.69066 −0.845330 0.534245i \(-0.820596\pi\)
−0.845330 + 0.534245i \(0.820596\pi\)
\(500\) 0 0
\(501\) −28.1339 −1.25693
\(502\) 0 0
\(503\) −40.0601 −1.78619 −0.893096 0.449867i \(-0.851472\pi\)
−0.893096 + 0.449867i \(0.851472\pi\)
\(504\) 0 0
\(505\) −1.86146 −0.0828339
\(506\) 0 0
\(507\) −2.44592 −0.108627
\(508\) 0 0
\(509\) 16.6237 0.736831 0.368415 0.929661i \(-0.379900\pi\)
0.368415 + 0.929661i \(0.379900\pi\)
\(510\) 0 0
\(511\) 8.00847 0.354274
\(512\) 0 0
\(513\) 0.0965173 0.00426134
\(514\) 0 0
\(515\) −5.74078 −0.252969
\(516\) 0 0
\(517\) −4.46079 −0.196185
\(518\) 0 0
\(519\) −6.00479 −0.263581
\(520\) 0 0
\(521\) −28.8994 −1.26611 −0.633053 0.774108i \(-0.718198\pi\)
−0.633053 + 0.774108i \(0.718198\pi\)
\(522\) 0 0
\(523\) 12.0050 0.524940 0.262470 0.964940i \(-0.415463\pi\)
0.262470 + 0.964940i \(0.415463\pi\)
\(524\) 0 0
\(525\) −11.7767 −0.513979
\(526\) 0 0
\(527\) −5.00609 −0.218069
\(528\) 0 0
\(529\) −22.7772 −0.990314
\(530\) 0 0
\(531\) 6.27666 0.272384
\(532\) 0 0
\(533\) −4.77742 −0.206933
\(534\) 0 0
\(535\) −0.172585 −0.00746150
\(536\) 0 0
\(537\) −61.0178 −2.63311
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 37.0483 1.59283 0.796415 0.604750i \(-0.206727\pi\)
0.796415 + 0.604750i \(0.206727\pi\)
\(542\) 0 0
\(543\) −50.0137 −2.14629
\(544\) 0 0
\(545\) 4.41541 0.189135
\(546\) 0 0
\(547\) 10.9024 0.466154 0.233077 0.972458i \(-0.425121\pi\)
0.233077 + 0.972458i \(0.425121\pi\)
\(548\) 0 0
\(549\) −37.5103 −1.60090
\(550\) 0 0
\(551\) 7.91784 0.337311
\(552\) 0 0
\(553\) −7.77702 −0.330712
\(554\) 0 0
\(555\) 3.47136 0.147351
\(556\) 0 0
\(557\) 33.1124 1.40302 0.701508 0.712661i \(-0.252510\pi\)
0.701508 + 0.712661i \(0.252510\pi\)
\(558\) 0 0
\(559\) −6.41707 −0.271413
\(560\) 0 0
\(561\) −6.01736 −0.254053
\(562\) 0 0
\(563\) −34.4266 −1.45091 −0.725455 0.688270i \(-0.758370\pi\)
−0.725455 + 0.688270i \(0.758370\pi\)
\(564\) 0 0
\(565\) 6.32290 0.266006
\(566\) 0 0
\(567\) 9.05217 0.380155
\(568\) 0 0
\(569\) −44.4569 −1.86373 −0.931865 0.362805i \(-0.881819\pi\)
−0.931865 + 0.362805i \(0.881819\pi\)
\(570\) 0 0
\(571\) −2.06974 −0.0866158 −0.0433079 0.999062i \(-0.513790\pi\)
−0.0433079 + 0.999062i \(0.513790\pi\)
\(572\) 0 0
\(573\) 39.9300 1.66810
\(574\) 0 0
\(575\) −2.27259 −0.0947734
\(576\) 0 0
\(577\) −32.1771 −1.33955 −0.669775 0.742564i \(-0.733610\pi\)
−0.669775 + 0.742564i \(0.733610\pi\)
\(578\) 0 0
\(579\) −13.6492 −0.567243
\(580\) 0 0
\(581\) −16.6675 −0.691486
\(582\) 0 0
\(583\) 14.0776 0.583035
\(584\) 0 0
\(585\) −1.28333 −0.0530592
\(586\) 0 0
\(587\) −21.4640 −0.885914 −0.442957 0.896543i \(-0.646070\pi\)
−0.442957 + 0.896543i \(0.646070\pi\)
\(588\) 0 0
\(589\) 4.59059 0.189152
\(590\) 0 0
\(591\) 31.4117 1.29211
\(592\) 0 0
\(593\) −19.9275 −0.818325 −0.409162 0.912462i \(-0.634179\pi\)
−0.409162 + 0.912462i \(0.634179\pi\)
\(594\) 0 0
\(595\) 1.05858 0.0433973
\(596\) 0 0
\(597\) 26.7973 1.09674
\(598\) 0 0
\(599\) 32.8162 1.34083 0.670417 0.741985i \(-0.266115\pi\)
0.670417 + 0.741985i \(0.266115\pi\)
\(600\) 0 0
\(601\) −31.7770 −1.29621 −0.648105 0.761551i \(-0.724438\pi\)
−0.648105 + 0.761551i \(0.724438\pi\)
\(602\) 0 0
\(603\) 28.6383 1.16624
\(604\) 0 0
\(605\) 0.430286 0.0174936
\(606\) 0 0
\(607\) −34.2966 −1.39206 −0.696028 0.718014i \(-0.745051\pi\)
−0.696028 + 0.718014i \(0.745051\pi\)
\(608\) 0 0
\(609\) 8.58448 0.347861
\(610\) 0 0
\(611\) −4.46079 −0.180464
\(612\) 0 0
\(613\) 15.9777 0.645333 0.322666 0.946513i \(-0.395421\pi\)
0.322666 + 0.946513i \(0.395421\pi\)
\(614\) 0 0
\(615\) −5.02796 −0.202747
\(616\) 0 0
\(617\) 2.93761 0.118264 0.0591318 0.998250i \(-0.481167\pi\)
0.0591318 + 0.998250i \(0.481167\pi\)
\(618\) 0 0
\(619\) 29.3199 1.17846 0.589232 0.807964i \(-0.299430\pi\)
0.589232 + 0.807964i \(0.299430\pi\)
\(620\) 0 0
\(621\) 0.0201933 0.000810330 0
\(622\) 0 0
\(623\) −4.07691 −0.163338
\(624\) 0 0
\(625\) 22.2571 0.890284
\(626\) 0 0
\(627\) 5.51793 0.220365
\(628\) 0 0
\(629\) 8.11458 0.323549
\(630\) 0 0
\(631\) −26.5661 −1.05758 −0.528791 0.848752i \(-0.677354\pi\)
−0.528791 + 0.848752i \(0.677354\pi\)
\(632\) 0 0
\(633\) −3.98366 −0.158336
\(634\) 0 0
\(635\) −4.13825 −0.164221
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 11.3470 0.448882
\(640\) 0 0
\(641\) −6.59794 −0.260603 −0.130301 0.991474i \(-0.541595\pi\)
−0.130301 + 0.991474i \(0.541595\pi\)
\(642\) 0 0
\(643\) 42.4949 1.67584 0.837918 0.545795i \(-0.183772\pi\)
0.837918 + 0.545795i \(0.183772\pi\)
\(644\) 0 0
\(645\) −6.75360 −0.265923
\(646\) 0 0
\(647\) −13.1085 −0.515347 −0.257673 0.966232i \(-0.582956\pi\)
−0.257673 + 0.966232i \(0.582956\pi\)
\(648\) 0 0
\(649\) −2.10449 −0.0826084
\(650\) 0 0
\(651\) 4.97709 0.195067
\(652\) 0 0
\(653\) 29.2231 1.14359 0.571794 0.820397i \(-0.306248\pi\)
0.571794 + 0.820397i \(0.306248\pi\)
\(654\) 0 0
\(655\) −8.83007 −0.345019
\(656\) 0 0
\(657\) −23.8853 −0.931855
\(658\) 0 0
\(659\) 12.7328 0.495998 0.247999 0.968760i \(-0.420227\pi\)
0.247999 + 0.968760i \(0.420227\pi\)
\(660\) 0 0
\(661\) 19.2055 0.747007 0.373504 0.927629i \(-0.378156\pi\)
0.373504 + 0.927629i \(0.378156\pi\)
\(662\) 0 0
\(663\) −6.01736 −0.233695
\(664\) 0 0
\(665\) −0.970714 −0.0376427
\(666\) 0 0
\(667\) 1.65657 0.0641426
\(668\) 0 0
\(669\) −3.95139 −0.152770
\(670\) 0 0
\(671\) 12.5768 0.485520
\(672\) 0 0
\(673\) 11.5766 0.446244 0.223122 0.974791i \(-0.428375\pi\)
0.223122 + 0.974791i \(0.428375\pi\)
\(674\) 0 0
\(675\) −0.205994 −0.00792870
\(676\) 0 0
\(677\) 29.9180 1.14984 0.574920 0.818209i \(-0.305033\pi\)
0.574920 + 0.818209i \(0.305033\pi\)
\(678\) 0 0
\(679\) −9.75068 −0.374197
\(680\) 0 0
\(681\) −49.2846 −1.88859
\(682\) 0 0
\(683\) −46.7734 −1.78974 −0.894868 0.446331i \(-0.852730\pi\)
−0.894868 + 0.446331i \(0.852730\pi\)
\(684\) 0 0
\(685\) −7.17064 −0.273976
\(686\) 0 0
\(687\) −54.9618 −2.09692
\(688\) 0 0
\(689\) 14.0776 0.536314
\(690\) 0 0
\(691\) 16.2567 0.618435 0.309218 0.950991i \(-0.399933\pi\)
0.309218 + 0.950991i \(0.399933\pi\)
\(692\) 0 0
\(693\) 2.98251 0.113296
\(694\) 0 0
\(695\) −5.41445 −0.205382
\(696\) 0 0
\(697\) −11.7533 −0.445186
\(698\) 0 0
\(699\) 57.0336 2.15721
\(700\) 0 0
\(701\) −20.7743 −0.784633 −0.392317 0.919830i \(-0.628326\pi\)
−0.392317 + 0.919830i \(0.628326\pi\)
\(702\) 0 0
\(703\) −7.44107 −0.280645
\(704\) 0 0
\(705\) −4.69473 −0.176814
\(706\) 0 0
\(707\) 4.32610 0.162700
\(708\) 0 0
\(709\) 16.3500 0.614038 0.307019 0.951703i \(-0.400668\pi\)
0.307019 + 0.951703i \(0.400668\pi\)
\(710\) 0 0
\(711\) 23.1950 0.869881
\(712\) 0 0
\(713\) 0.960441 0.0359688
\(714\) 0 0
\(715\) 0.430286 0.0160918
\(716\) 0 0
\(717\) 30.0667 1.12286
\(718\) 0 0
\(719\) 31.1224 1.16067 0.580334 0.814379i \(-0.302922\pi\)
0.580334 + 0.814379i \(0.302922\pi\)
\(720\) 0 0
\(721\) 13.3418 0.496874
\(722\) 0 0
\(723\) 3.32843 0.123786
\(724\) 0 0
\(725\) −16.8988 −0.627605
\(726\) 0 0
\(727\) 16.0190 0.594114 0.297057 0.954860i \(-0.403995\pi\)
0.297057 + 0.954860i \(0.403995\pi\)
\(728\) 0 0
\(729\) −26.6842 −0.988305
\(730\) 0 0
\(731\) −15.7871 −0.583905
\(732\) 0 0
\(733\) −29.7086 −1.09731 −0.548657 0.836048i \(-0.684861\pi\)
−0.548657 + 0.836048i \(0.684861\pi\)
\(734\) 0 0
\(735\) −1.05244 −0.0388200
\(736\) 0 0
\(737\) −9.60207 −0.353697
\(738\) 0 0
\(739\) 7.31827 0.269207 0.134603 0.990900i \(-0.457024\pi\)
0.134603 + 0.990900i \(0.457024\pi\)
\(740\) 0 0
\(741\) 5.51793 0.202706
\(742\) 0 0
\(743\) 5.18777 0.190321 0.0951603 0.995462i \(-0.469664\pi\)
0.0951603 + 0.995462i \(0.469664\pi\)
\(744\) 0 0
\(745\) −0.466711 −0.0170990
\(746\) 0 0
\(747\) 49.7110 1.81883
\(748\) 0 0
\(749\) 0.401094 0.0146557
\(750\) 0 0
\(751\) −53.2637 −1.94362 −0.971811 0.235763i \(-0.924241\pi\)
−0.971811 + 0.235763i \(0.924241\pi\)
\(752\) 0 0
\(753\) −45.0057 −1.64010
\(754\) 0 0
\(755\) 4.91725 0.178957
\(756\) 0 0
\(757\) −12.9677 −0.471317 −0.235659 0.971836i \(-0.575725\pi\)
−0.235659 + 0.971836i \(0.575725\pi\)
\(758\) 0 0
\(759\) 1.15446 0.0419042
\(760\) 0 0
\(761\) 20.0232 0.725841 0.362921 0.931820i \(-0.381780\pi\)
0.362921 + 0.931820i \(0.381780\pi\)
\(762\) 0 0
\(763\) −10.2616 −0.371494
\(764\) 0 0
\(765\) −3.15721 −0.114149
\(766\) 0 0
\(767\) −2.10449 −0.0759887
\(768\) 0 0
\(769\) −26.5877 −0.958777 −0.479389 0.877603i \(-0.659142\pi\)
−0.479389 + 0.877603i \(0.659142\pi\)
\(770\) 0 0
\(771\) 24.1398 0.869372
\(772\) 0 0
\(773\) −20.3699 −0.732654 −0.366327 0.930486i \(-0.619385\pi\)
−0.366327 + 0.930486i \(0.619385\pi\)
\(774\) 0 0
\(775\) −9.79754 −0.351938
\(776\) 0 0
\(777\) −8.06757 −0.289423
\(778\) 0 0
\(779\) 10.7777 0.386153
\(780\) 0 0
\(781\) −3.80453 −0.136137
\(782\) 0 0
\(783\) 0.150156 0.00536614
\(784\) 0 0
\(785\) 6.80743 0.242968
\(786\) 0 0
\(787\) −31.0433 −1.10657 −0.553287 0.832991i \(-0.686627\pi\)
−0.553287 + 0.832991i \(0.686627\pi\)
\(788\) 0 0
\(789\) 73.9683 2.63334
\(790\) 0 0
\(791\) −14.6946 −0.522481
\(792\) 0 0
\(793\) 12.5768 0.446614
\(794\) 0 0
\(795\) 14.8159 0.525465
\(796\) 0 0
\(797\) −40.8431 −1.44674 −0.723369 0.690461i \(-0.757408\pi\)
−0.723369 + 0.690461i \(0.757408\pi\)
\(798\) 0 0
\(799\) −10.9743 −0.388242
\(800\) 0 0
\(801\) 12.1594 0.429632
\(802\) 0 0
\(803\) 8.00847 0.282613
\(804\) 0 0
\(805\) −0.203093 −0.00715807
\(806\) 0 0
\(807\) 21.4113 0.753713
\(808\) 0 0
\(809\) −15.3240 −0.538763 −0.269382 0.963034i \(-0.586819\pi\)
−0.269382 + 0.963034i \(0.586819\pi\)
\(810\) 0 0
\(811\) 6.59135 0.231453 0.115727 0.993281i \(-0.463080\pi\)
0.115727 + 0.993281i \(0.463080\pi\)
\(812\) 0 0
\(813\) −28.4784 −0.998782
\(814\) 0 0
\(815\) −7.95951 −0.278809
\(816\) 0 0
\(817\) 14.4767 0.506477
\(818\) 0 0
\(819\) 2.98251 0.104217
\(820\) 0 0
\(821\) −5.27759 −0.184189 −0.0920946 0.995750i \(-0.529356\pi\)
−0.0920946 + 0.995750i \(0.529356\pi\)
\(822\) 0 0
\(823\) 55.7225 1.94236 0.971182 0.238341i \(-0.0766034\pi\)
0.971182 + 0.238341i \(0.0766034\pi\)
\(824\) 0 0
\(825\) −11.7767 −0.410013
\(826\) 0 0
\(827\) −21.4517 −0.745948 −0.372974 0.927842i \(-0.621662\pi\)
−0.372974 + 0.927842i \(0.621662\pi\)
\(828\) 0 0
\(829\) −30.1857 −1.04839 −0.524197 0.851597i \(-0.675634\pi\)
−0.524197 + 0.851597i \(0.675634\pi\)
\(830\) 0 0
\(831\) 33.6953 1.16888
\(832\) 0 0
\(833\) −2.46017 −0.0852398
\(834\) 0 0
\(835\) 4.94932 0.171278
\(836\) 0 0
\(837\) 0.0870571 0.00300913
\(838\) 0 0
\(839\) −43.9728 −1.51811 −0.759055 0.651026i \(-0.774339\pi\)
−0.759055 + 0.651026i \(0.774339\pi\)
\(840\) 0 0
\(841\) −16.6819 −0.575237
\(842\) 0 0
\(843\) −49.1502 −1.69282
\(844\) 0 0
\(845\) 0.430286 0.0148023
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 47.4211 1.62749
\(850\) 0 0
\(851\) −1.55682 −0.0533671
\(852\) 0 0
\(853\) 1.52390 0.0521774 0.0260887 0.999660i \(-0.491695\pi\)
0.0260887 + 0.999660i \(0.491695\pi\)
\(854\) 0 0
\(855\) 2.89516 0.0990125
\(856\) 0 0
\(857\) 42.2986 1.44489 0.722447 0.691426i \(-0.243017\pi\)
0.722447 + 0.691426i \(0.243017\pi\)
\(858\) 0 0
\(859\) 45.4285 1.55000 0.775000 0.631961i \(-0.217750\pi\)
0.775000 + 0.631961i \(0.217750\pi\)
\(860\) 0 0
\(861\) 11.6852 0.398230
\(862\) 0 0
\(863\) 16.2079 0.551723 0.275862 0.961197i \(-0.411037\pi\)
0.275862 + 0.961197i \(0.411037\pi\)
\(864\) 0 0
\(865\) 1.05636 0.0359174
\(866\) 0 0
\(867\) 26.7769 0.909390
\(868\) 0 0
\(869\) −7.77702 −0.263817
\(870\) 0 0
\(871\) −9.60207 −0.325354
\(872\) 0 0
\(873\) 29.0815 0.984259
\(874\) 0 0
\(875\) 4.22319 0.142770
\(876\) 0 0
\(877\) 13.2048 0.445894 0.222947 0.974831i \(-0.428432\pi\)
0.222947 + 0.974831i \(0.428432\pi\)
\(878\) 0 0
\(879\) −53.8454 −1.81616
\(880\) 0 0
\(881\) −36.0770 −1.21546 −0.607732 0.794142i \(-0.707921\pi\)
−0.607732 + 0.794142i \(0.707921\pi\)
\(882\) 0 0
\(883\) 40.5857 1.36582 0.682909 0.730503i \(-0.260714\pi\)
0.682909 + 0.730503i \(0.260714\pi\)
\(884\) 0 0
\(885\) −2.21485 −0.0744515
\(886\) 0 0
\(887\) −17.6532 −0.592738 −0.296369 0.955074i \(-0.595776\pi\)
−0.296369 + 0.955074i \(0.595776\pi\)
\(888\) 0 0
\(889\) 9.61745 0.322559
\(890\) 0 0
\(891\) 9.05217 0.303259
\(892\) 0 0
\(893\) 10.0634 0.336760
\(894\) 0 0
\(895\) 10.7343 0.358807
\(896\) 0 0
\(897\) 1.15446 0.0385463
\(898\) 0 0
\(899\) 7.14177 0.238192
\(900\) 0 0
\(901\) 34.6333 1.15380
\(902\) 0 0
\(903\) 15.6956 0.522317
\(904\) 0 0
\(905\) 8.79841 0.292469
\(906\) 0 0
\(907\) 19.5922 0.650547 0.325274 0.945620i \(-0.394544\pi\)
0.325274 + 0.945620i \(0.394544\pi\)
\(908\) 0 0
\(909\) −12.9026 −0.427953
\(910\) 0 0
\(911\) 44.6191 1.47830 0.739148 0.673543i \(-0.235228\pi\)
0.739148 + 0.673543i \(0.235228\pi\)
\(912\) 0 0
\(913\) −16.6675 −0.551615
\(914\) 0 0
\(915\) 13.2363 0.437579
\(916\) 0 0
\(917\) 20.5214 0.677677
\(918\) 0 0
\(919\) 29.5773 0.975666 0.487833 0.872937i \(-0.337787\pi\)
0.487833 + 0.872937i \(0.337787\pi\)
\(920\) 0 0
\(921\) −4.89567 −0.161318
\(922\) 0 0
\(923\) −3.80453 −0.125228
\(924\) 0 0
\(925\) 15.8812 0.522172
\(926\) 0 0
\(927\) −39.7920 −1.30694
\(928\) 0 0
\(929\) −9.63852 −0.316230 −0.158115 0.987421i \(-0.550542\pi\)
−0.158115 + 0.987421i \(0.550542\pi\)
\(930\) 0 0
\(931\) 2.25598 0.0739366
\(932\) 0 0
\(933\) −71.1814 −2.33037
\(934\) 0 0
\(935\) 1.05858 0.0346191
\(936\) 0 0
\(937\) 17.4870 0.571275 0.285637 0.958338i \(-0.407795\pi\)
0.285637 + 0.958338i \(0.407795\pi\)
\(938\) 0 0
\(939\) −42.5629 −1.38899
\(940\) 0 0
\(941\) 27.9745 0.911941 0.455971 0.889995i \(-0.349292\pi\)
0.455971 + 0.889995i \(0.349292\pi\)
\(942\) 0 0
\(943\) 2.25492 0.0734302
\(944\) 0 0
\(945\) −0.0184089 −0.000598841 0
\(946\) 0 0
\(947\) −55.6986 −1.80996 −0.904981 0.425452i \(-0.860115\pi\)
−0.904981 + 0.425452i \(0.860115\pi\)
\(948\) 0 0
\(949\) 8.00847 0.259966
\(950\) 0 0
\(951\) 13.7856 0.447029
\(952\) 0 0
\(953\) −14.9657 −0.484786 −0.242393 0.970178i \(-0.577932\pi\)
−0.242393 + 0.970178i \(0.577932\pi\)
\(954\) 0 0
\(955\) −7.02449 −0.227307
\(956\) 0 0
\(957\) 8.58448 0.277497
\(958\) 0 0
\(959\) 16.6648 0.538135
\(960\) 0 0
\(961\) −26.8594 −0.866431
\(962\) 0 0
\(963\) −1.19627 −0.0385491
\(964\) 0 0
\(965\) 2.40118 0.0772966
\(966\) 0 0
\(967\) −49.3773 −1.58787 −0.793933 0.608005i \(-0.791970\pi\)
−0.793933 + 0.608005i \(0.791970\pi\)
\(968\) 0 0
\(969\) 13.5750 0.436093
\(970\) 0 0
\(971\) 9.20796 0.295498 0.147749 0.989025i \(-0.452797\pi\)
0.147749 + 0.989025i \(0.452797\pi\)
\(972\) 0 0
\(973\) 12.5834 0.403405
\(974\) 0 0
\(975\) −11.7767 −0.377157
\(976\) 0 0
\(977\) −3.55557 −0.113753 −0.0568764 0.998381i \(-0.518114\pi\)
−0.0568764 + 0.998381i \(0.518114\pi\)
\(978\) 0 0
\(979\) −4.07691 −0.130299
\(980\) 0 0
\(981\) 30.6052 0.977150
\(982\) 0 0
\(983\) −40.8259 −1.30214 −0.651072 0.759016i \(-0.725680\pi\)
−0.651072 + 0.759016i \(0.725680\pi\)
\(984\) 0 0
\(985\) −5.52595 −0.176071
\(986\) 0 0
\(987\) 10.9107 0.347292
\(988\) 0 0
\(989\) 3.02882 0.0963109
\(990\) 0 0
\(991\) 21.5379 0.684174 0.342087 0.939668i \(-0.388866\pi\)
0.342087 + 0.939668i \(0.388866\pi\)
\(992\) 0 0
\(993\) 10.7860 0.342285
\(994\) 0 0
\(995\) −4.71419 −0.149450
\(996\) 0 0
\(997\) −17.3745 −0.550256 −0.275128 0.961408i \(-0.588720\pi\)
−0.275128 + 0.961408i \(0.588720\pi\)
\(998\) 0 0
\(999\) −0.141115 −0.00446467
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 \(a_p\))