Properties

Label 8008.2.a.v.1.7
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.674923\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.674923 q^{3} -4.42380 q^{5} -1.00000 q^{7} -2.54448 q^{9} +O(q^{10})\) \(q+0.674923 q^{3} -4.42380 q^{5} -1.00000 q^{7} -2.54448 q^{9} +1.00000 q^{11} -1.00000 q^{13} -2.98573 q^{15} +4.81611 q^{17} -5.29198 q^{19} -0.674923 q^{21} +1.44917 q^{23} +14.5700 q^{25} -3.74210 q^{27} +7.93937 q^{29} +8.10497 q^{31} +0.674923 q^{33} +4.42380 q^{35} -6.99820 q^{37} -0.674923 q^{39} +7.05801 q^{41} -7.92840 q^{43} +11.2563 q^{45} +1.44917 q^{47} +1.00000 q^{49} +3.25050 q^{51} -8.55932 q^{53} -4.42380 q^{55} -3.57168 q^{57} -0.0353024 q^{59} +9.90155 q^{61} +2.54448 q^{63} +4.42380 q^{65} -1.89639 q^{67} +0.978076 q^{69} +9.06086 q^{71} -12.8184 q^{73} +9.83364 q^{75} -1.00000 q^{77} +11.6663 q^{79} +5.10781 q^{81} +9.53027 q^{83} -21.3055 q^{85} +5.35846 q^{87} -3.76222 q^{89} +1.00000 q^{91} +5.47023 q^{93} +23.4107 q^{95} -12.6735 q^{97} -2.54448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) 0.674923 0.389667 0.194833 0.980836i \(-0.437583\pi\)
0.194833 + 0.980836i \(0.437583\pi\)
\(4\) 0 0
\(5\) −4.42380 −1.97838 −0.989192 0.146625i \(-0.953159\pi\)
−0.989192 + 0.146625i \(0.953159\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.54448 −0.848160
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −2.98573 −0.770911
\(16\) 0 0
\(17\) 4.81611 1.16808 0.584039 0.811726i \(-0.301472\pi\)
0.584039 + 0.811726i \(0.301472\pi\)
\(18\) 0 0
\(19\) −5.29198 −1.21406 −0.607032 0.794677i \(-0.707640\pi\)
−0.607032 + 0.794677i \(0.707640\pi\)
\(20\) 0 0
\(21\) −0.674923 −0.147280
\(22\) 0 0
\(23\) 1.44917 0.302172 0.151086 0.988521i \(-0.451723\pi\)
0.151086 + 0.988521i \(0.451723\pi\)
\(24\) 0 0
\(25\) 14.5700 2.91400
\(26\) 0 0
\(27\) −3.74210 −0.720167
\(28\) 0 0
\(29\) 7.93937 1.47430 0.737152 0.675727i \(-0.236170\pi\)
0.737152 + 0.675727i \(0.236170\pi\)
\(30\) 0 0
\(31\) 8.10497 1.45569 0.727847 0.685739i \(-0.240521\pi\)
0.727847 + 0.685739i \(0.240521\pi\)
\(32\) 0 0
\(33\) 0.674923 0.117489
\(34\) 0 0
\(35\) 4.42380 0.747759
\(36\) 0 0
\(37\) −6.99820 −1.15050 −0.575248 0.817979i \(-0.695095\pi\)
−0.575248 + 0.817979i \(0.695095\pi\)
\(38\) 0 0
\(39\) −0.674923 −0.108074
\(40\) 0 0
\(41\) 7.05801 1.10228 0.551138 0.834414i \(-0.314194\pi\)
0.551138 + 0.834414i \(0.314194\pi\)
\(42\) 0 0
\(43\) −7.92840 −1.20907 −0.604535 0.796579i \(-0.706641\pi\)
−0.604535 + 0.796579i \(0.706641\pi\)
\(44\) 0 0
\(45\) 11.2563 1.67799
\(46\) 0 0
\(47\) 1.44917 0.211383 0.105691 0.994399i \(-0.466294\pi\)
0.105691 + 0.994399i \(0.466294\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 3.25050 0.455161
\(52\) 0 0
\(53\) −8.55932 −1.17571 −0.587857 0.808965i \(-0.700028\pi\)
−0.587857 + 0.808965i \(0.700028\pi\)
\(54\) 0 0
\(55\) −4.42380 −0.596505
\(56\) 0 0
\(57\) −3.57168 −0.473081
\(58\) 0 0
\(59\) −0.0353024 −0.00459598 −0.00229799 0.999997i \(-0.500731\pi\)
−0.00229799 + 0.999997i \(0.500731\pi\)
\(60\) 0 0
\(61\) 9.90155 1.26776 0.633882 0.773430i \(-0.281461\pi\)
0.633882 + 0.773430i \(0.281461\pi\)
\(62\) 0 0
\(63\) 2.54448 0.320574
\(64\) 0 0
\(65\) 4.42380 0.548705
\(66\) 0 0
\(67\) −1.89639 −0.231681 −0.115840 0.993268i \(-0.536956\pi\)
−0.115840 + 0.993268i \(0.536956\pi\)
\(68\) 0 0
\(69\) 0.978076 0.117747
\(70\) 0 0
\(71\) 9.06086 1.07533 0.537663 0.843160i \(-0.319307\pi\)
0.537663 + 0.843160i \(0.319307\pi\)
\(72\) 0 0
\(73\) −12.8184 −1.50028 −0.750139 0.661280i \(-0.770014\pi\)
−0.750139 + 0.661280i \(0.770014\pi\)
\(74\) 0 0
\(75\) 9.83364 1.13549
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 11.6663 1.31256 0.656280 0.754518i \(-0.272129\pi\)
0.656280 + 0.754518i \(0.272129\pi\)
\(80\) 0 0
\(81\) 5.10781 0.567535
\(82\) 0 0
\(83\) 9.53027 1.04608 0.523042 0.852307i \(-0.324797\pi\)
0.523042 + 0.852307i \(0.324797\pi\)
\(84\) 0 0
\(85\) −21.3055 −2.31091
\(86\) 0 0
\(87\) 5.35846 0.574487
\(88\) 0 0
\(89\) −3.76222 −0.398795 −0.199397 0.979919i \(-0.563898\pi\)
−0.199397 + 0.979919i \(0.563898\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 5.47023 0.567236
\(94\) 0 0
\(95\) 23.4107 2.40189
\(96\) 0 0
\(97\) −12.6735 −1.28679 −0.643397 0.765532i \(-0.722476\pi\)
−0.643397 + 0.765532i \(0.722476\pi\)
\(98\) 0 0
\(99\) −2.54448 −0.255730
\(100\) 0 0
\(101\) 10.1777 1.01272 0.506360 0.862322i \(-0.330991\pi\)
0.506360 + 0.862322i \(0.330991\pi\)
\(102\) 0 0
\(103\) 9.31106 0.917446 0.458723 0.888579i \(-0.348307\pi\)
0.458723 + 0.888579i \(0.348307\pi\)
\(104\) 0 0
\(105\) 2.98573 0.291377
\(106\) 0 0
\(107\) −11.9527 −1.15551 −0.577756 0.816210i \(-0.696071\pi\)
−0.577756 + 0.816210i \(0.696071\pi\)
\(108\) 0 0
\(109\) −4.51461 −0.432421 −0.216211 0.976347i \(-0.569370\pi\)
−0.216211 + 0.976347i \(0.569370\pi\)
\(110\) 0 0
\(111\) −4.72324 −0.448311
\(112\) 0 0
\(113\) −9.44130 −0.888163 −0.444082 0.895986i \(-0.646470\pi\)
−0.444082 + 0.895986i \(0.646470\pi\)
\(114\) 0 0
\(115\) −6.41083 −0.597813
\(116\) 0 0
\(117\) 2.54448 0.235237
\(118\) 0 0
\(119\) −4.81611 −0.441492
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.76361 0.429521
\(124\) 0 0
\(125\) −42.3359 −3.78664
\(126\) 0 0
\(127\) −10.1471 −0.900412 −0.450206 0.892925i \(-0.648650\pi\)
−0.450206 + 0.892925i \(0.648650\pi\)
\(128\) 0 0
\(129\) −5.35106 −0.471134
\(130\) 0 0
\(131\) −12.4940 −1.09161 −0.545803 0.837914i \(-0.683775\pi\)
−0.545803 + 0.837914i \(0.683775\pi\)
\(132\) 0 0
\(133\) 5.29198 0.458873
\(134\) 0 0
\(135\) 16.5543 1.42477
\(136\) 0 0
\(137\) −11.9240 −1.01873 −0.509367 0.860550i \(-0.670120\pi\)
−0.509367 + 0.860550i \(0.670120\pi\)
\(138\) 0 0
\(139\) −0.714210 −0.0605785 −0.0302893 0.999541i \(-0.509643\pi\)
−0.0302893 + 0.999541i \(0.509643\pi\)
\(140\) 0 0
\(141\) 0.978076 0.0823689
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −35.1222 −2.91674
\(146\) 0 0
\(147\) 0.674923 0.0556667
\(148\) 0 0
\(149\) −3.41829 −0.280038 −0.140019 0.990149i \(-0.544716\pi\)
−0.140019 + 0.990149i \(0.544716\pi\)
\(150\) 0 0
\(151\) 4.15978 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(152\) 0 0
\(153\) −12.2545 −0.990717
\(154\) 0 0
\(155\) −35.8548 −2.87992
\(156\) 0 0
\(157\) 23.1118 1.84452 0.922261 0.386568i \(-0.126340\pi\)
0.922261 + 0.386568i \(0.126340\pi\)
\(158\) 0 0
\(159\) −5.77688 −0.458137
\(160\) 0 0
\(161\) −1.44917 −0.114210
\(162\) 0 0
\(163\) −3.84516 −0.301176 −0.150588 0.988597i \(-0.548117\pi\)
−0.150588 + 0.988597i \(0.548117\pi\)
\(164\) 0 0
\(165\) −2.98573 −0.232438
\(166\) 0 0
\(167\) 5.64659 0.436946 0.218473 0.975843i \(-0.429892\pi\)
0.218473 + 0.975843i \(0.429892\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 13.4653 1.02972
\(172\) 0 0
\(173\) −9.14183 −0.695040 −0.347520 0.937673i \(-0.612976\pi\)
−0.347520 + 0.937673i \(0.612976\pi\)
\(174\) 0 0
\(175\) −14.5700 −1.10139
\(176\) 0 0
\(177\) −0.0238264 −0.00179090
\(178\) 0 0
\(179\) −19.3709 −1.44785 −0.723924 0.689880i \(-0.757663\pi\)
−0.723924 + 0.689880i \(0.757663\pi\)
\(180\) 0 0
\(181\) 1.44636 0.107507 0.0537535 0.998554i \(-0.482881\pi\)
0.0537535 + 0.998554i \(0.482881\pi\)
\(182\) 0 0
\(183\) 6.68278 0.494006
\(184\) 0 0
\(185\) 30.9586 2.27612
\(186\) 0 0
\(187\) 4.81611 0.352189
\(188\) 0 0
\(189\) 3.74210 0.272197
\(190\) 0 0
\(191\) 17.3629 1.25633 0.628166 0.778079i \(-0.283806\pi\)
0.628166 + 0.778079i \(0.283806\pi\)
\(192\) 0 0
\(193\) 15.1736 1.09222 0.546112 0.837712i \(-0.316107\pi\)
0.546112 + 0.837712i \(0.316107\pi\)
\(194\) 0 0
\(195\) 2.98573 0.213812
\(196\) 0 0
\(197\) −24.5498 −1.74910 −0.874552 0.484932i \(-0.838844\pi\)
−0.874552 + 0.484932i \(0.838844\pi\)
\(198\) 0 0
\(199\) 3.34595 0.237188 0.118594 0.992943i \(-0.462161\pi\)
0.118594 + 0.992943i \(0.462161\pi\)
\(200\) 0 0
\(201\) −1.27992 −0.0902783
\(202\) 0 0
\(203\) −7.93937 −0.557234
\(204\) 0 0
\(205\) −31.2233 −2.18073
\(206\) 0 0
\(207\) −3.68737 −0.256290
\(208\) 0 0
\(209\) −5.29198 −0.366054
\(210\) 0 0
\(211\) −14.8500 −1.02232 −0.511158 0.859487i \(-0.670783\pi\)
−0.511158 + 0.859487i \(0.670783\pi\)
\(212\) 0 0
\(213\) 6.11538 0.419019
\(214\) 0 0
\(215\) 35.0737 2.39200
\(216\) 0 0
\(217\) −8.10497 −0.550201
\(218\) 0 0
\(219\) −8.65142 −0.584609
\(220\) 0 0
\(221\) −4.81611 −0.323967
\(222\) 0 0
\(223\) −20.8739 −1.39782 −0.698911 0.715209i \(-0.746331\pi\)
−0.698911 + 0.715209i \(0.746331\pi\)
\(224\) 0 0
\(225\) −37.0731 −2.47154
\(226\) 0 0
\(227\) −11.7135 −0.777455 −0.388728 0.921353i \(-0.627085\pi\)
−0.388728 + 0.921353i \(0.627085\pi\)
\(228\) 0 0
\(229\) 11.1255 0.735196 0.367598 0.929985i \(-0.380180\pi\)
0.367598 + 0.929985i \(0.380180\pi\)
\(230\) 0 0
\(231\) −0.674923 −0.0444067
\(232\) 0 0
\(233\) −2.91286 −0.190828 −0.0954140 0.995438i \(-0.530417\pi\)
−0.0954140 + 0.995438i \(0.530417\pi\)
\(234\) 0 0
\(235\) −6.41083 −0.418196
\(236\) 0 0
\(237\) 7.87384 0.511461
\(238\) 0 0
\(239\) −14.3670 −0.929321 −0.464661 0.885489i \(-0.653824\pi\)
−0.464661 + 0.885489i \(0.653824\pi\)
\(240\) 0 0
\(241\) 14.7627 0.950951 0.475476 0.879729i \(-0.342276\pi\)
0.475476 + 0.879729i \(0.342276\pi\)
\(242\) 0 0
\(243\) 14.6737 0.941316
\(244\) 0 0
\(245\) −4.42380 −0.282626
\(246\) 0 0
\(247\) 5.29198 0.336721
\(248\) 0 0
\(249\) 6.43220 0.407624
\(250\) 0 0
\(251\) 8.98630 0.567210 0.283605 0.958941i \(-0.408469\pi\)
0.283605 + 0.958941i \(0.408469\pi\)
\(252\) 0 0
\(253\) 1.44917 0.0911083
\(254\) 0 0
\(255\) −14.3796 −0.900484
\(256\) 0 0
\(257\) −29.1092 −1.81578 −0.907890 0.419208i \(-0.862308\pi\)
−0.907890 + 0.419208i \(0.862308\pi\)
\(258\) 0 0
\(259\) 6.99820 0.434847
\(260\) 0 0
\(261\) −20.2015 −1.25044
\(262\) 0 0
\(263\) −15.1114 −0.931806 −0.465903 0.884836i \(-0.654270\pi\)
−0.465903 + 0.884836i \(0.654270\pi\)
\(264\) 0 0
\(265\) 37.8647 2.32601
\(266\) 0 0
\(267\) −2.53921 −0.155397
\(268\) 0 0
\(269\) 22.8050 1.39044 0.695222 0.718795i \(-0.255306\pi\)
0.695222 + 0.718795i \(0.255306\pi\)
\(270\) 0 0
\(271\) 18.7533 1.13918 0.569591 0.821928i \(-0.307102\pi\)
0.569591 + 0.821928i \(0.307102\pi\)
\(272\) 0 0
\(273\) 0.674923 0.0408482
\(274\) 0 0
\(275\) 14.5700 0.878605
\(276\) 0 0
\(277\) −3.21177 −0.192977 −0.0964884 0.995334i \(-0.530761\pi\)
−0.0964884 + 0.995334i \(0.530761\pi\)
\(278\) 0 0
\(279\) −20.6229 −1.23466
\(280\) 0 0
\(281\) 7.26096 0.433153 0.216576 0.976266i \(-0.430511\pi\)
0.216576 + 0.976266i \(0.430511\pi\)
\(282\) 0 0
\(283\) 13.4704 0.800733 0.400367 0.916355i \(-0.368883\pi\)
0.400367 + 0.916355i \(0.368883\pi\)
\(284\) 0 0
\(285\) 15.8004 0.935935
\(286\) 0 0
\(287\) −7.05801 −0.416621
\(288\) 0 0
\(289\) 6.19490 0.364406
\(290\) 0 0
\(291\) −8.55361 −0.501421
\(292\) 0 0
\(293\) −18.5449 −1.08341 −0.541703 0.840570i \(-0.682220\pi\)
−0.541703 + 0.840570i \(0.682220\pi\)
\(294\) 0 0
\(295\) 0.156171 0.00909261
\(296\) 0 0
\(297\) −3.74210 −0.217138
\(298\) 0 0
\(299\) −1.44917 −0.0838075
\(300\) 0 0
\(301\) 7.92840 0.456985
\(302\) 0 0
\(303\) 6.86917 0.394624
\(304\) 0 0
\(305\) −43.8025 −2.50812
\(306\) 0 0
\(307\) −21.1261 −1.20573 −0.602864 0.797844i \(-0.705974\pi\)
−0.602864 + 0.797844i \(0.705974\pi\)
\(308\) 0 0
\(309\) 6.28425 0.357498
\(310\) 0 0
\(311\) −2.29335 −0.130044 −0.0650221 0.997884i \(-0.520712\pi\)
−0.0650221 + 0.997884i \(0.520712\pi\)
\(312\) 0 0
\(313\) −6.67680 −0.377395 −0.188697 0.982035i \(-0.560427\pi\)
−0.188697 + 0.982035i \(0.560427\pi\)
\(314\) 0 0
\(315\) −11.2563 −0.634219
\(316\) 0 0
\(317\) −28.1307 −1.57998 −0.789989 0.613121i \(-0.789914\pi\)
−0.789989 + 0.613121i \(0.789914\pi\)
\(318\) 0 0
\(319\) 7.93937 0.444519
\(320\) 0 0
\(321\) −8.06716 −0.450265
\(322\) 0 0
\(323\) −25.4868 −1.41812
\(324\) 0 0
\(325\) −14.5700 −0.808199
\(326\) 0 0
\(327\) −3.04701 −0.168500
\(328\) 0 0
\(329\) −1.44917 −0.0798952
\(330\) 0 0
\(331\) −16.0175 −0.880399 −0.440200 0.897900i \(-0.645092\pi\)
−0.440200 + 0.897900i \(0.645092\pi\)
\(332\) 0 0
\(333\) 17.8068 0.975805
\(334\) 0 0
\(335\) 8.38924 0.458353
\(336\) 0 0
\(337\) 17.2084 0.937403 0.468702 0.883356i \(-0.344722\pi\)
0.468702 + 0.883356i \(0.344722\pi\)
\(338\) 0 0
\(339\) −6.37215 −0.346088
\(340\) 0 0
\(341\) 8.10497 0.438909
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −4.32681 −0.232948
\(346\) 0 0
\(347\) 9.29313 0.498881 0.249441 0.968390i \(-0.419753\pi\)
0.249441 + 0.968390i \(0.419753\pi\)
\(348\) 0 0
\(349\) 23.1239 1.23780 0.618898 0.785472i \(-0.287580\pi\)
0.618898 + 0.785472i \(0.287580\pi\)
\(350\) 0 0
\(351\) 3.74210 0.199738
\(352\) 0 0
\(353\) −13.0249 −0.693245 −0.346623 0.938005i \(-0.612672\pi\)
−0.346623 + 0.938005i \(0.612672\pi\)
\(354\) 0 0
\(355\) −40.0835 −2.12741
\(356\) 0 0
\(357\) −3.25050 −0.172035
\(358\) 0 0
\(359\) 12.2056 0.644189 0.322094 0.946708i \(-0.395613\pi\)
0.322094 + 0.946708i \(0.395613\pi\)
\(360\) 0 0
\(361\) 9.00509 0.473952
\(362\) 0 0
\(363\) 0.674923 0.0354243
\(364\) 0 0
\(365\) 56.7060 2.96813
\(366\) 0 0
\(367\) −16.9347 −0.883983 −0.441991 0.897019i \(-0.645728\pi\)
−0.441991 + 0.897019i \(0.645728\pi\)
\(368\) 0 0
\(369\) −17.9590 −0.934906
\(370\) 0 0
\(371\) 8.55932 0.444378
\(372\) 0 0
\(373\) −3.19837 −0.165605 −0.0828026 0.996566i \(-0.526387\pi\)
−0.0828026 + 0.996566i \(0.526387\pi\)
\(374\) 0 0
\(375\) −28.5735 −1.47553
\(376\) 0 0
\(377\) −7.93937 −0.408898
\(378\) 0 0
\(379\) 16.2298 0.833669 0.416834 0.908982i \(-0.363140\pi\)
0.416834 + 0.908982i \(0.363140\pi\)
\(380\) 0 0
\(381\) −6.84853 −0.350861
\(382\) 0 0
\(383\) −24.4171 −1.24766 −0.623828 0.781562i \(-0.714423\pi\)
−0.623828 + 0.781562i \(0.714423\pi\)
\(384\) 0 0
\(385\) 4.42380 0.225458
\(386\) 0 0
\(387\) 20.1736 1.02548
\(388\) 0 0
\(389\) −20.3401 −1.03129 −0.515643 0.856804i \(-0.672447\pi\)
−0.515643 + 0.856804i \(0.672447\pi\)
\(390\) 0 0
\(391\) 6.97935 0.352961
\(392\) 0 0
\(393\) −8.43248 −0.425362
\(394\) 0 0
\(395\) −51.6093 −2.59675
\(396\) 0 0
\(397\) 29.7422 1.49272 0.746358 0.665544i \(-0.231801\pi\)
0.746358 + 0.665544i \(0.231801\pi\)
\(398\) 0 0
\(399\) 3.57168 0.178808
\(400\) 0 0
\(401\) −27.3109 −1.36384 −0.681921 0.731426i \(-0.738855\pi\)
−0.681921 + 0.731426i \(0.738855\pi\)
\(402\) 0 0
\(403\) −8.10497 −0.403737
\(404\) 0 0
\(405\) −22.5959 −1.12280
\(406\) 0 0
\(407\) −6.99820 −0.346888
\(408\) 0 0
\(409\) 14.1376 0.699058 0.349529 0.936925i \(-0.386342\pi\)
0.349529 + 0.936925i \(0.386342\pi\)
\(410\) 0 0
\(411\) −8.04776 −0.396967
\(412\) 0 0
\(413\) 0.0353024 0.00173712
\(414\) 0 0
\(415\) −42.1600 −2.06955
\(416\) 0 0
\(417\) −0.482037 −0.0236055
\(418\) 0 0
\(419\) −26.0120 −1.27077 −0.635385 0.772195i \(-0.719159\pi\)
−0.635385 + 0.772195i \(0.719159\pi\)
\(420\) 0 0
\(421\) −27.0709 −1.31935 −0.659677 0.751549i \(-0.729307\pi\)
−0.659677 + 0.751549i \(0.729307\pi\)
\(422\) 0 0
\(423\) −3.68737 −0.179286
\(424\) 0 0
\(425\) 70.1708 3.40378
\(426\) 0 0
\(427\) −9.90155 −0.479170
\(428\) 0 0
\(429\) −0.674923 −0.0325856
\(430\) 0 0
\(431\) −17.5232 −0.844061 −0.422030 0.906582i \(-0.638682\pi\)
−0.422030 + 0.906582i \(0.638682\pi\)
\(432\) 0 0
\(433\) −5.55212 −0.266818 −0.133409 0.991061i \(-0.542592\pi\)
−0.133409 + 0.991061i \(0.542592\pi\)
\(434\) 0 0
\(435\) −23.7048 −1.13656
\(436\) 0 0
\(437\) −7.66897 −0.366856
\(438\) 0 0
\(439\) −6.98133 −0.333201 −0.166600 0.986025i \(-0.553279\pi\)
−0.166600 + 0.986025i \(0.553279\pi\)
\(440\) 0 0
\(441\) −2.54448 −0.121166
\(442\) 0 0
\(443\) 37.3655 1.77529 0.887645 0.460528i \(-0.152340\pi\)
0.887645 + 0.460528i \(0.152340\pi\)
\(444\) 0 0
\(445\) 16.6433 0.788969
\(446\) 0 0
\(447\) −2.30709 −0.109121
\(448\) 0 0
\(449\) 7.56395 0.356965 0.178483 0.983943i \(-0.442881\pi\)
0.178483 + 0.983943i \(0.442881\pi\)
\(450\) 0 0
\(451\) 7.05801 0.332349
\(452\) 0 0
\(453\) 2.80753 0.131909
\(454\) 0 0
\(455\) −4.42380 −0.207391
\(456\) 0 0
\(457\) 29.5994 1.38460 0.692301 0.721609i \(-0.256597\pi\)
0.692301 + 0.721609i \(0.256597\pi\)
\(458\) 0 0
\(459\) −18.0223 −0.841211
\(460\) 0 0
\(461\) 38.6887 1.80191 0.900956 0.433911i \(-0.142867\pi\)
0.900956 + 0.433911i \(0.142867\pi\)
\(462\) 0 0
\(463\) −10.4374 −0.485068 −0.242534 0.970143i \(-0.577979\pi\)
−0.242534 + 0.970143i \(0.577979\pi\)
\(464\) 0 0
\(465\) −24.1992 −1.12221
\(466\) 0 0
\(467\) −42.1488 −1.95041 −0.975207 0.221296i \(-0.928971\pi\)
−0.975207 + 0.221296i \(0.928971\pi\)
\(468\) 0 0
\(469\) 1.89639 0.0875671
\(470\) 0 0
\(471\) 15.5987 0.718749
\(472\) 0 0
\(473\) −7.92840 −0.364548
\(474\) 0 0
\(475\) −77.1043 −3.53779
\(476\) 0 0
\(477\) 21.7790 0.997192
\(478\) 0 0
\(479\) −38.5075 −1.75945 −0.879726 0.475481i \(-0.842274\pi\)
−0.879726 + 0.475481i \(0.842274\pi\)
\(480\) 0 0
\(481\) 6.99820 0.319090
\(482\) 0 0
\(483\) −0.978076 −0.0445040
\(484\) 0 0
\(485\) 56.0649 2.54577
\(486\) 0 0
\(487\) −25.6697 −1.16320 −0.581602 0.813474i \(-0.697574\pi\)
−0.581602 + 0.813474i \(0.697574\pi\)
\(488\) 0 0
\(489\) −2.59519 −0.117358
\(490\) 0 0
\(491\) 9.04609 0.408244 0.204122 0.978945i \(-0.434566\pi\)
0.204122 + 0.978945i \(0.434566\pi\)
\(492\) 0 0
\(493\) 38.2368 1.72210
\(494\) 0 0
\(495\) 11.2563 0.505932
\(496\) 0 0
\(497\) −9.06086 −0.406435
\(498\) 0 0
\(499\) 27.9614 1.25172 0.625862 0.779933i \(-0.284747\pi\)
0.625862 + 0.779933i \(0.284747\pi\)
\(500\) 0 0
\(501\) 3.81101 0.170264
\(502\) 0 0
\(503\) 43.6319 1.94545 0.972724 0.231964i \(-0.0745150\pi\)
0.972724 + 0.231964i \(0.0745150\pi\)
\(504\) 0 0
\(505\) −45.0242 −2.00355
\(506\) 0 0
\(507\) 0.674923 0.0299744
\(508\) 0 0
\(509\) −5.18174 −0.229677 −0.114838 0.993384i \(-0.536635\pi\)
−0.114838 + 0.993384i \(0.536635\pi\)
\(510\) 0 0
\(511\) 12.8184 0.567052
\(512\) 0 0
\(513\) 19.8031 0.874329
\(514\) 0 0
\(515\) −41.1903 −1.81506
\(516\) 0 0
\(517\) 1.44917 0.0637343
\(518\) 0 0
\(519\) −6.17003 −0.270834
\(520\) 0 0
\(521\) 8.34229 0.365482 0.182741 0.983161i \(-0.441503\pi\)
0.182741 + 0.983161i \(0.441503\pi\)
\(522\) 0 0
\(523\) −17.9235 −0.783740 −0.391870 0.920021i \(-0.628172\pi\)
−0.391870 + 0.920021i \(0.628172\pi\)
\(524\) 0 0
\(525\) −9.83364 −0.429175
\(526\) 0 0
\(527\) 39.0344 1.70037
\(528\) 0 0
\(529\) −20.8999 −0.908692
\(530\) 0 0
\(531\) 0.0898262 0.00389812
\(532\) 0 0
\(533\) −7.05801 −0.305716
\(534\) 0 0
\(535\) 52.8764 2.28605
\(536\) 0 0
\(537\) −13.0739 −0.564179
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −34.3819 −1.47819 −0.739097 0.673599i \(-0.764747\pi\)
−0.739097 + 0.673599i \(0.764747\pi\)
\(542\) 0 0
\(543\) 0.976180 0.0418919
\(544\) 0 0
\(545\) 19.9717 0.855495
\(546\) 0 0
\(547\) −5.39334 −0.230602 −0.115301 0.993331i \(-0.536783\pi\)
−0.115301 + 0.993331i \(0.536783\pi\)
\(548\) 0 0
\(549\) −25.1943 −1.07527
\(550\) 0 0
\(551\) −42.0150 −1.78990
\(552\) 0 0
\(553\) −11.6663 −0.496101
\(554\) 0 0
\(555\) 20.8947 0.886931
\(556\) 0 0
\(557\) 10.8664 0.460423 0.230211 0.973141i \(-0.426058\pi\)
0.230211 + 0.973141i \(0.426058\pi\)
\(558\) 0 0
\(559\) 7.92840 0.335336
\(560\) 0 0
\(561\) 3.25050 0.137236
\(562\) 0 0
\(563\) 39.8294 1.67861 0.839305 0.543661i \(-0.182962\pi\)
0.839305 + 0.543661i \(0.182962\pi\)
\(564\) 0 0
\(565\) 41.7664 1.75713
\(566\) 0 0
\(567\) −5.10781 −0.214508
\(568\) 0 0
\(569\) 0.623097 0.0261216 0.0130608 0.999915i \(-0.495843\pi\)
0.0130608 + 0.999915i \(0.495843\pi\)
\(570\) 0 0
\(571\) 31.2854 1.30925 0.654627 0.755952i \(-0.272826\pi\)
0.654627 + 0.755952i \(0.272826\pi\)
\(572\) 0 0
\(573\) 11.7186 0.489551
\(574\) 0 0
\(575\) 21.1144 0.880531
\(576\) 0 0
\(577\) −11.9512 −0.497535 −0.248768 0.968563i \(-0.580026\pi\)
−0.248768 + 0.968563i \(0.580026\pi\)
\(578\) 0 0
\(579\) 10.2410 0.425603
\(580\) 0 0
\(581\) −9.53027 −0.395382
\(582\) 0 0
\(583\) −8.55932 −0.354491
\(584\) 0 0
\(585\) −11.2563 −0.465390
\(586\) 0 0
\(587\) 18.5213 0.764454 0.382227 0.924068i \(-0.375157\pi\)
0.382227 + 0.924068i \(0.375157\pi\)
\(588\) 0 0
\(589\) −42.8913 −1.76731
\(590\) 0 0
\(591\) −16.5693 −0.681568
\(592\) 0 0
\(593\) −22.2135 −0.912198 −0.456099 0.889929i \(-0.650754\pi\)
−0.456099 + 0.889929i \(0.650754\pi\)
\(594\) 0 0
\(595\) 21.3055 0.873441
\(596\) 0 0
\(597\) 2.25826 0.0924243
\(598\) 0 0
\(599\) −43.5039 −1.77752 −0.888760 0.458373i \(-0.848432\pi\)
−0.888760 + 0.458373i \(0.848432\pi\)
\(600\) 0 0
\(601\) 28.7556 1.17296 0.586482 0.809962i \(-0.300512\pi\)
0.586482 + 0.809962i \(0.300512\pi\)
\(602\) 0 0
\(603\) 4.82532 0.196502
\(604\) 0 0
\(605\) −4.42380 −0.179853
\(606\) 0 0
\(607\) −23.5911 −0.957533 −0.478766 0.877942i \(-0.658916\pi\)
−0.478766 + 0.877942i \(0.658916\pi\)
\(608\) 0 0
\(609\) −5.35846 −0.217136
\(610\) 0 0
\(611\) −1.44917 −0.0586270
\(612\) 0 0
\(613\) 32.6718 1.31960 0.659801 0.751440i \(-0.270641\pi\)
0.659801 + 0.751440i \(0.270641\pi\)
\(614\) 0 0
\(615\) −21.0733 −0.849757
\(616\) 0 0
\(617\) −13.6524 −0.549626 −0.274813 0.961498i \(-0.588616\pi\)
−0.274813 + 0.961498i \(0.588616\pi\)
\(618\) 0 0
\(619\) −40.7238 −1.63683 −0.818414 0.574628i \(-0.805147\pi\)
−0.818414 + 0.574628i \(0.805147\pi\)
\(620\) 0 0
\(621\) −5.42292 −0.217614
\(622\) 0 0
\(623\) 3.76222 0.150730
\(624\) 0 0
\(625\) 114.435 4.57742
\(626\) 0 0
\(627\) −3.57168 −0.142639
\(628\) 0 0
\(629\) −33.7041 −1.34387
\(630\) 0 0
\(631\) −26.5313 −1.05620 −0.528098 0.849183i \(-0.677095\pi\)
−0.528098 + 0.849183i \(0.677095\pi\)
\(632\) 0 0
\(633\) −10.0226 −0.398363
\(634\) 0 0
\(635\) 44.8889 1.78136
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −23.0552 −0.912049
\(640\) 0 0
\(641\) −38.4309 −1.51793 −0.758965 0.651131i \(-0.774295\pi\)
−0.758965 + 0.651131i \(0.774295\pi\)
\(642\) 0 0
\(643\) 18.0349 0.711227 0.355614 0.934633i \(-0.384272\pi\)
0.355614 + 0.934633i \(0.384272\pi\)
\(644\) 0 0
\(645\) 23.6720 0.932085
\(646\) 0 0
\(647\) 48.5846 1.91006 0.955030 0.296510i \(-0.0958229\pi\)
0.955030 + 0.296510i \(0.0958229\pi\)
\(648\) 0 0
\(649\) −0.0353024 −0.00138574
\(650\) 0 0
\(651\) −5.47023 −0.214395
\(652\) 0 0
\(653\) −5.90005 −0.230887 −0.115443 0.993314i \(-0.536829\pi\)
−0.115443 + 0.993314i \(0.536829\pi\)
\(654\) 0 0
\(655\) 55.2710 2.15961
\(656\) 0 0
\(657\) 32.6161 1.27248
\(658\) 0 0
\(659\) 37.9221 1.47723 0.738617 0.674125i \(-0.235479\pi\)
0.738617 + 0.674125i \(0.235479\pi\)
\(660\) 0 0
\(661\) 34.3083 1.33444 0.667219 0.744862i \(-0.267485\pi\)
0.667219 + 0.744862i \(0.267485\pi\)
\(662\) 0 0
\(663\) −3.25050 −0.126239
\(664\) 0 0
\(665\) −23.4107 −0.907828
\(666\) 0 0
\(667\) 11.5055 0.445493
\(668\) 0 0
\(669\) −14.0883 −0.544685
\(670\) 0 0
\(671\) 9.90155 0.382245
\(672\) 0 0
\(673\) 2.76517 0.106590 0.0532948 0.998579i \(-0.483028\pi\)
0.0532948 + 0.998579i \(0.483028\pi\)
\(674\) 0 0
\(675\) −54.5224 −2.09857
\(676\) 0 0
\(677\) 17.7283 0.681353 0.340677 0.940181i \(-0.389344\pi\)
0.340677 + 0.940181i \(0.389344\pi\)
\(678\) 0 0
\(679\) 12.6735 0.486363
\(680\) 0 0
\(681\) −7.90574 −0.302949
\(682\) 0 0
\(683\) −1.98355 −0.0758985 −0.0379492 0.999280i \(-0.512083\pi\)
−0.0379492 + 0.999280i \(0.512083\pi\)
\(684\) 0 0
\(685\) 52.7493 2.01545
\(686\) 0 0
\(687\) 7.50888 0.286482
\(688\) 0 0
\(689\) 8.55932 0.326084
\(690\) 0 0
\(691\) 39.0568 1.48579 0.742895 0.669408i \(-0.233452\pi\)
0.742895 + 0.669408i \(0.233452\pi\)
\(692\) 0 0
\(693\) 2.54448 0.0966568
\(694\) 0 0
\(695\) 3.15953 0.119848
\(696\) 0 0
\(697\) 33.9922 1.28754
\(698\) 0 0
\(699\) −1.96596 −0.0743593
\(700\) 0 0
\(701\) 8.68915 0.328185 0.164092 0.986445i \(-0.447530\pi\)
0.164092 + 0.986445i \(0.447530\pi\)
\(702\) 0 0
\(703\) 37.0344 1.39678
\(704\) 0 0
\(705\) −4.32681 −0.162957
\(706\) 0 0
\(707\) −10.1777 −0.382772
\(708\) 0 0
\(709\) 9.18636 0.345001 0.172500 0.985009i \(-0.444815\pi\)
0.172500 + 0.985009i \(0.444815\pi\)
\(710\) 0 0
\(711\) −29.6846 −1.11326
\(712\) 0 0
\(713\) 11.7454 0.439871
\(714\) 0 0
\(715\) 4.42380 0.165441
\(716\) 0 0
\(717\) −9.69659 −0.362126
\(718\) 0 0
\(719\) 29.1925 1.08870 0.544349 0.838859i \(-0.316777\pi\)
0.544349 + 0.838859i \(0.316777\pi\)
\(720\) 0 0
\(721\) −9.31106 −0.346762
\(722\) 0 0
\(723\) 9.96371 0.370554
\(724\) 0 0
\(725\) 115.677 4.29613
\(726\) 0 0
\(727\) −45.8196 −1.69935 −0.849677 0.527303i \(-0.823203\pi\)
−0.849677 + 0.527303i \(0.823203\pi\)
\(728\) 0 0
\(729\) −5.41984 −0.200735
\(730\) 0 0
\(731\) −38.1840 −1.41229
\(732\) 0 0
\(733\) −27.7660 −1.02556 −0.512781 0.858519i \(-0.671385\pi\)
−0.512781 + 0.858519i \(0.671385\pi\)
\(734\) 0 0
\(735\) −2.98573 −0.110130
\(736\) 0 0
\(737\) −1.89639 −0.0698543
\(738\) 0 0
\(739\) 5.20611 0.191510 0.0957549 0.995405i \(-0.469473\pi\)
0.0957549 + 0.995405i \(0.469473\pi\)
\(740\) 0 0
\(741\) 3.57168 0.131209
\(742\) 0 0
\(743\) −27.2039 −0.998016 −0.499008 0.866597i \(-0.666302\pi\)
−0.499008 + 0.866597i \(0.666302\pi\)
\(744\) 0 0
\(745\) 15.1219 0.554022
\(746\) 0 0
\(747\) −24.2496 −0.887245
\(748\) 0 0
\(749\) 11.9527 0.436742
\(750\) 0 0
\(751\) −25.6555 −0.936183 −0.468091 0.883680i \(-0.655058\pi\)
−0.468091 + 0.883680i \(0.655058\pi\)
\(752\) 0 0
\(753\) 6.06506 0.221023
\(754\) 0 0
\(755\) −18.4020 −0.669718
\(756\) 0 0
\(757\) 8.79352 0.319606 0.159803 0.987149i \(-0.448914\pi\)
0.159803 + 0.987149i \(0.448914\pi\)
\(758\) 0 0
\(759\) 0.978076 0.0355019
\(760\) 0 0
\(761\) −22.4152 −0.812550 −0.406275 0.913751i \(-0.633173\pi\)
−0.406275 + 0.913751i \(0.633173\pi\)
\(762\) 0 0
\(763\) 4.51461 0.163440
\(764\) 0 0
\(765\) 54.2114 1.96002
\(766\) 0 0
\(767\) 0.0353024 0.00127470
\(768\) 0 0
\(769\) −9.31270 −0.335824 −0.167912 0.985802i \(-0.553703\pi\)
−0.167912 + 0.985802i \(0.553703\pi\)
\(770\) 0 0
\(771\) −19.6464 −0.707550
\(772\) 0 0
\(773\) −35.5241 −1.27771 −0.638857 0.769325i \(-0.720593\pi\)
−0.638857 + 0.769325i \(0.720593\pi\)
\(774\) 0 0
\(775\) 118.090 4.24190
\(776\) 0 0
\(777\) 4.72324 0.169445
\(778\) 0 0
\(779\) −37.3509 −1.33823
\(780\) 0 0
\(781\) 9.06086 0.324223
\(782\) 0 0
\(783\) −29.7099 −1.06174
\(784\) 0 0
\(785\) −102.242 −3.64917
\(786\) 0 0
\(787\) 31.7044 1.13014 0.565070 0.825043i \(-0.308849\pi\)
0.565070 + 0.825043i \(0.308849\pi\)
\(788\) 0 0
\(789\) −10.1990 −0.363094
\(790\) 0 0
\(791\) 9.44130 0.335694
\(792\) 0 0
\(793\) −9.90155 −0.351614
\(794\) 0 0
\(795\) 25.5558 0.906370
\(796\) 0 0
\(797\) 17.6647 0.625716 0.312858 0.949800i \(-0.398714\pi\)
0.312858 + 0.949800i \(0.398714\pi\)
\(798\) 0 0
\(799\) 6.97935 0.246912
\(800\) 0 0
\(801\) 9.57290 0.338242
\(802\) 0 0
\(803\) −12.8184 −0.452351
\(804\) 0 0
\(805\) 6.41083 0.225952
\(806\) 0 0
\(807\) 15.3916 0.541810
\(808\) 0 0
\(809\) −46.9705 −1.65140 −0.825698 0.564113i \(-0.809218\pi\)
−0.825698 + 0.564113i \(0.809218\pi\)
\(810\) 0 0
\(811\) −36.3116 −1.27507 −0.637536 0.770421i \(-0.720046\pi\)
−0.637536 + 0.770421i \(0.720046\pi\)
\(812\) 0 0
\(813\) 12.6570 0.443902
\(814\) 0 0
\(815\) 17.0102 0.595842
\(816\) 0 0
\(817\) 41.9570 1.46789
\(818\) 0 0
\(819\) −2.54448 −0.0889113
\(820\) 0 0
\(821\) −42.5827 −1.48615 −0.743074 0.669209i \(-0.766633\pi\)
−0.743074 + 0.669209i \(0.766633\pi\)
\(822\) 0 0
\(823\) 21.0146 0.732522 0.366261 0.930512i \(-0.380638\pi\)
0.366261 + 0.930512i \(0.380638\pi\)
\(824\) 0 0
\(825\) 9.83364 0.342363
\(826\) 0 0
\(827\) −16.2230 −0.564127 −0.282064 0.959396i \(-0.591019\pi\)
−0.282064 + 0.959396i \(0.591019\pi\)
\(828\) 0 0
\(829\) 15.1367 0.525718 0.262859 0.964834i \(-0.415335\pi\)
0.262859 + 0.964834i \(0.415335\pi\)
\(830\) 0 0
\(831\) −2.16770 −0.0751967
\(832\) 0 0
\(833\) 4.81611 0.166868
\(834\) 0 0
\(835\) −24.9794 −0.864448
\(836\) 0 0
\(837\) −30.3296 −1.04834
\(838\) 0 0
\(839\) −50.1889 −1.73271 −0.866357 0.499425i \(-0.833545\pi\)
−0.866357 + 0.499425i \(0.833545\pi\)
\(840\) 0 0
\(841\) 34.0335 1.17357
\(842\) 0 0
\(843\) 4.90059 0.168785
\(844\) 0 0
\(845\) −4.42380 −0.152183
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 9.09149 0.312019
\(850\) 0 0
\(851\) −10.1416 −0.347648
\(852\) 0 0
\(853\) 6.13538 0.210071 0.105036 0.994468i \(-0.466504\pi\)
0.105036 + 0.994468i \(0.466504\pi\)
\(854\) 0 0
\(855\) −59.5680 −2.03718
\(856\) 0 0
\(857\) −52.2350 −1.78431 −0.892157 0.451725i \(-0.850809\pi\)
−0.892157 + 0.451725i \(0.850809\pi\)
\(858\) 0 0
\(859\) −28.2892 −0.965214 −0.482607 0.875837i \(-0.660310\pi\)
−0.482607 + 0.875837i \(0.660310\pi\)
\(860\) 0 0
\(861\) −4.76361 −0.162344
\(862\) 0 0
\(863\) 31.0049 1.05542 0.527710 0.849425i \(-0.323051\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(864\) 0 0
\(865\) 40.4416 1.37506
\(866\) 0 0
\(867\) 4.18108 0.141997
\(868\) 0 0
\(869\) 11.6663 0.395752
\(870\) 0 0
\(871\) 1.89639 0.0642567
\(872\) 0 0
\(873\) 32.2474 1.09141
\(874\) 0 0
\(875\) 42.3359 1.43121
\(876\) 0 0
\(877\) −17.6466 −0.595884 −0.297942 0.954584i \(-0.596300\pi\)
−0.297942 + 0.954584i \(0.596300\pi\)
\(878\) 0 0
\(879\) −12.5164 −0.422168
\(880\) 0 0
\(881\) 18.2302 0.614192 0.307096 0.951679i \(-0.400643\pi\)
0.307096 + 0.951679i \(0.400643\pi\)
\(882\) 0 0
\(883\) 0.897068 0.0301887 0.0150944 0.999886i \(-0.495195\pi\)
0.0150944 + 0.999886i \(0.495195\pi\)
\(884\) 0 0
\(885\) 0.105403 0.00354309
\(886\) 0 0
\(887\) −40.8563 −1.37182 −0.685910 0.727687i \(-0.740595\pi\)
−0.685910 + 0.727687i \(0.740595\pi\)
\(888\) 0 0
\(889\) 10.1471 0.340324
\(890\) 0 0
\(891\) 5.10781 0.171118
\(892\) 0 0
\(893\) −7.66897 −0.256632
\(894\) 0 0
\(895\) 85.6930 2.86440
\(896\) 0 0
\(897\) −0.978076 −0.0326570
\(898\) 0 0
\(899\) 64.3483 2.14614
\(900\) 0 0
\(901\) −41.2226 −1.37332
\(902\) 0 0
\(903\) 5.35106 0.178072
\(904\) 0 0
\(905\) −6.39840 −0.212690
\(906\) 0 0
\(907\) −17.3319 −0.575497 −0.287749 0.957706i \(-0.592907\pi\)
−0.287749 + 0.957706i \(0.592907\pi\)
\(908\) 0 0
\(909\) −25.8970 −0.858948
\(910\) 0 0
\(911\) −3.89220 −0.128954 −0.0644772 0.997919i \(-0.520538\pi\)
−0.0644772 + 0.997919i \(0.520538\pi\)
\(912\) 0 0
\(913\) 9.53027 0.315406
\(914\) 0 0
\(915\) −29.5633 −0.977333
\(916\) 0 0
\(917\) 12.4940 0.412588
\(918\) 0 0
\(919\) 33.7531 1.11341 0.556706 0.830710i \(-0.312065\pi\)
0.556706 + 0.830710i \(0.312065\pi\)
\(920\) 0 0
\(921\) −14.2585 −0.469832
\(922\) 0 0
\(923\) −9.06086 −0.298242
\(924\) 0 0
\(925\) −101.964 −3.35255
\(926\) 0 0
\(927\) −23.6918 −0.778141
\(928\) 0 0
\(929\) 9.32763 0.306030 0.153015 0.988224i \(-0.451102\pi\)
0.153015 + 0.988224i \(0.451102\pi\)
\(930\) 0 0
\(931\) −5.29198 −0.173438
\(932\) 0 0
\(933\) −1.54784 −0.0506739
\(934\) 0 0
\(935\) −21.3055 −0.696765
\(936\) 0 0
\(937\) 14.0109 0.457716 0.228858 0.973460i \(-0.426501\pi\)
0.228858 + 0.973460i \(0.426501\pi\)
\(938\) 0 0
\(939\) −4.50632 −0.147058
\(940\) 0 0
\(941\) 40.6157 1.32404 0.662018 0.749488i \(-0.269700\pi\)
0.662018 + 0.749488i \(0.269700\pi\)
\(942\) 0 0
\(943\) 10.2282 0.333077
\(944\) 0 0
\(945\) −16.5543 −0.538511
\(946\) 0 0
\(947\) −20.1611 −0.655148 −0.327574 0.944825i \(-0.606231\pi\)
−0.327574 + 0.944825i \(0.606231\pi\)
\(948\) 0 0
\(949\) 12.8184 0.416102
\(950\) 0 0
\(951\) −18.9861 −0.615665
\(952\) 0 0
\(953\) 25.8170 0.836293 0.418147 0.908380i \(-0.362680\pi\)
0.418147 + 0.908380i \(0.362680\pi\)
\(954\) 0 0
\(955\) −76.8098 −2.48551
\(956\) 0 0
\(957\) 5.35846 0.173214
\(958\) 0 0
\(959\) 11.9240 0.385045
\(960\) 0 0
\(961\) 34.6905 1.11905
\(962\) 0 0
\(963\) 30.4134 0.980059
\(964\) 0 0
\(965\) −67.1252 −2.16084
\(966\) 0 0
\(967\) 19.0968 0.614113 0.307056 0.951691i \(-0.400656\pi\)
0.307056 + 0.951691i \(0.400656\pi\)
\(968\) 0 0
\(969\) −17.2016 −0.552595
\(970\) 0 0
\(971\) −7.13725 −0.229045 −0.114523 0.993421i \(-0.536534\pi\)
−0.114523 + 0.993421i \(0.536534\pi\)
\(972\) 0 0
\(973\) 0.714210 0.0228965
\(974\) 0 0
\(975\) −9.83364 −0.314929
\(976\) 0 0
\(977\) 52.8348 1.69033 0.845167 0.534502i \(-0.179501\pi\)
0.845167 + 0.534502i \(0.179501\pi\)
\(978\) 0 0
\(979\) −3.76222 −0.120241
\(980\) 0 0
\(981\) 11.4873 0.366762
\(982\) 0 0
\(983\) −12.9107 −0.411788 −0.205894 0.978574i \(-0.566010\pi\)
−0.205894 + 0.978574i \(0.566010\pi\)
\(984\) 0 0
\(985\) 108.604 3.46040
\(986\) 0 0
\(987\) −0.978076 −0.0311325
\(988\) 0 0
\(989\) −11.4896 −0.365347
\(990\) 0 0
\(991\) 3.28006 0.104194 0.0520972 0.998642i \(-0.483409\pi\)
0.0520972 + 0.998642i \(0.483409\pi\)
\(992\) 0 0
\(993\) −10.8106 −0.343063
\(994\) 0 0
\(995\) −14.8018 −0.469249
\(996\) 0 0
\(997\) 50.7966 1.60875 0.804373 0.594125i \(-0.202501\pi\)
0.804373 + 0.594125i \(0.202501\pi\)
\(998\) 0 0
\(999\) 26.1879 0.828550
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 \(a_p\))