Properties

Label 8018.2.a.d.1.20
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +2.51574 q^{10} -0.0753521 q^{11} +0.846820 q^{12} -5.73702 q^{13} -3.73115 q^{14} +2.13038 q^{15} +1.00000 q^{16} +3.44373 q^{17} -2.28290 q^{18} +1.00000 q^{19} +2.51574 q^{20} -3.15962 q^{21} -0.0753521 q^{22} +6.79036 q^{23} +0.846820 q^{24} +1.32895 q^{25} -5.73702 q^{26} -4.47366 q^{27} -3.73115 q^{28} +1.05848 q^{29} +2.13038 q^{30} -3.37751 q^{31} +1.00000 q^{32} -0.0638097 q^{33} +3.44373 q^{34} -9.38662 q^{35} -2.28290 q^{36} +0.0136820 q^{37} +1.00000 q^{38} -4.85823 q^{39} +2.51574 q^{40} -5.23820 q^{41} -3.15962 q^{42} -8.50526 q^{43} -0.0753521 q^{44} -5.74317 q^{45} +6.79036 q^{46} -6.20848 q^{47} +0.846820 q^{48} +6.92151 q^{49} +1.32895 q^{50} +2.91622 q^{51} -5.73702 q^{52} +3.31645 q^{53} -4.47366 q^{54} -0.189566 q^{55} -3.73115 q^{56} +0.846820 q^{57} +1.05848 q^{58} +8.85589 q^{59} +2.13038 q^{60} -1.05386 q^{61} -3.37751 q^{62} +8.51784 q^{63} +1.00000 q^{64} -14.4329 q^{65} -0.0638097 q^{66} -14.4792 q^{67} +3.44373 q^{68} +5.75021 q^{69} -9.38662 q^{70} -10.5764 q^{71} -2.28290 q^{72} -10.5869 q^{73} +0.0136820 q^{74} +1.12539 q^{75} +1.00000 q^{76} +0.281150 q^{77} -4.85823 q^{78} +9.08302 q^{79} +2.51574 q^{80} +3.06030 q^{81} -5.23820 q^{82} +0.661023 q^{83} -3.15962 q^{84} +8.66354 q^{85} -8.50526 q^{86} +0.896345 q^{87} -0.0753521 q^{88} -4.15153 q^{89} -5.74317 q^{90} +21.4057 q^{91} +6.79036 q^{92} -2.86015 q^{93} -6.20848 q^{94} +2.51574 q^{95} +0.846820 q^{96} -0.682779 q^{97} +6.92151 q^{98} +0.172021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.846820 0.488912 0.244456 0.969660i \(-0.421391\pi\)
0.244456 + 0.969660i \(0.421391\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.51574 1.12507 0.562537 0.826772i \(-0.309825\pi\)
0.562537 + 0.826772i \(0.309825\pi\)
\(6\) 0.846820 0.345713
\(7\) −3.73115 −1.41024 −0.705122 0.709086i \(-0.749108\pi\)
−0.705122 + 0.709086i \(0.749108\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.28290 −0.760965
\(10\) 2.51574 0.795547
\(11\) −0.0753521 −0.0227195 −0.0113598 0.999935i \(-0.503616\pi\)
−0.0113598 + 0.999935i \(0.503616\pi\)
\(12\) 0.846820 0.244456
\(13\) −5.73702 −1.59116 −0.795582 0.605846i \(-0.792835\pi\)
−0.795582 + 0.605846i \(0.792835\pi\)
\(14\) −3.73115 −0.997193
\(15\) 2.13038 0.550062
\(16\) 1.00000 0.250000
\(17\) 3.44373 0.835228 0.417614 0.908625i \(-0.362866\pi\)
0.417614 + 0.908625i \(0.362866\pi\)
\(18\) −2.28290 −0.538084
\(19\) 1.00000 0.229416
\(20\) 2.51574 0.562537
\(21\) −3.15962 −0.689485
\(22\) −0.0753521 −0.0160651
\(23\) 6.79036 1.41589 0.707944 0.706269i \(-0.249623\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(24\) 0.846820 0.172856
\(25\) 1.32895 0.265791
\(26\) −5.73702 −1.12512
\(27\) −4.47366 −0.860957
\(28\) −3.73115 −0.705122
\(29\) 1.05848 0.196555 0.0982777 0.995159i \(-0.468667\pi\)
0.0982777 + 0.995159i \(0.468667\pi\)
\(30\) 2.13038 0.388952
\(31\) −3.37751 −0.606619 −0.303310 0.952892i \(-0.598092\pi\)
−0.303310 + 0.952892i \(0.598092\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.0638097 −0.0111078
\(34\) 3.44373 0.590595
\(35\) −9.38662 −1.58663
\(36\) −2.28290 −0.380483
\(37\) 0.0136820 0.00224930 0.00112465 0.999999i \(-0.499642\pi\)
0.00112465 + 0.999999i \(0.499642\pi\)
\(38\) 1.00000 0.162221
\(39\) −4.85823 −0.777939
\(40\) 2.51574 0.397774
\(41\) −5.23820 −0.818069 −0.409034 0.912519i \(-0.634134\pi\)
−0.409034 + 0.912519i \(0.634134\pi\)
\(42\) −3.15962 −0.487539
\(43\) −8.50526 −1.29704 −0.648520 0.761198i \(-0.724612\pi\)
−0.648520 + 0.761198i \(0.724612\pi\)
\(44\) −0.0753521 −0.0113598
\(45\) −5.74317 −0.856142
\(46\) 6.79036 1.00118
\(47\) −6.20848 −0.905600 −0.452800 0.891612i \(-0.649575\pi\)
−0.452800 + 0.891612i \(0.649575\pi\)
\(48\) 0.846820 0.122228
\(49\) 6.92151 0.988788
\(50\) 1.32895 0.187943
\(51\) 2.91622 0.408353
\(52\) −5.73702 −0.795582
\(53\) 3.31645 0.455550 0.227775 0.973714i \(-0.426855\pi\)
0.227775 + 0.973714i \(0.426855\pi\)
\(54\) −4.47366 −0.608788
\(55\) −0.189566 −0.0255611
\(56\) −3.73115 −0.498596
\(57\) 0.846820 0.112164
\(58\) 1.05848 0.138986
\(59\) 8.85589 1.15294 0.576469 0.817119i \(-0.304430\pi\)
0.576469 + 0.817119i \(0.304430\pi\)
\(60\) 2.13038 0.275031
\(61\) −1.05386 −0.134933 −0.0674665 0.997722i \(-0.521492\pi\)
−0.0674665 + 0.997722i \(0.521492\pi\)
\(62\) −3.37751 −0.428944
\(63\) 8.51784 1.07315
\(64\) 1.00000 0.125000
\(65\) −14.4329 −1.79018
\(66\) −0.0638097 −0.00785443
\(67\) −14.4792 −1.76891 −0.884455 0.466625i \(-0.845470\pi\)
−0.884455 + 0.466625i \(0.845470\pi\)
\(68\) 3.44373 0.417614
\(69\) 5.75021 0.692244
\(70\) −9.38662 −1.12192
\(71\) −10.5764 −1.25518 −0.627592 0.778542i \(-0.715960\pi\)
−0.627592 + 0.778542i \(0.715960\pi\)
\(72\) −2.28290 −0.269042
\(73\) −10.5869 −1.23910 −0.619550 0.784957i \(-0.712685\pi\)
−0.619550 + 0.784957i \(0.712685\pi\)
\(74\) 0.0136820 0.00159050
\(75\) 1.12539 0.129948
\(76\) 1.00000 0.114708
\(77\) 0.281150 0.0320400
\(78\) −4.85823 −0.550086
\(79\) 9.08302 1.02192 0.510960 0.859604i \(-0.329290\pi\)
0.510960 + 0.859604i \(0.329290\pi\)
\(80\) 2.51574 0.281268
\(81\) 3.06030 0.340033
\(82\) −5.23820 −0.578462
\(83\) 0.661023 0.0725567 0.0362784 0.999342i \(-0.488450\pi\)
0.0362784 + 0.999342i \(0.488450\pi\)
\(84\) −3.15962 −0.344742
\(85\) 8.66354 0.939693
\(86\) −8.50526 −0.917145
\(87\) 0.896345 0.0960983
\(88\) −0.0753521 −0.00803256
\(89\) −4.15153 −0.440061 −0.220030 0.975493i \(-0.570616\pi\)
−0.220030 + 0.975493i \(0.570616\pi\)
\(90\) −5.74317 −0.605384
\(91\) 21.4057 2.24393
\(92\) 6.79036 0.707944
\(93\) −2.86015 −0.296583
\(94\) −6.20848 −0.640356
\(95\) 2.51574 0.258110
\(96\) 0.846820 0.0864282
\(97\) −0.682779 −0.0693257 −0.0346628 0.999399i \(-0.511036\pi\)
−0.0346628 + 0.999399i \(0.511036\pi\)
\(98\) 6.92151 0.699178
\(99\) 0.172021 0.0172888
\(100\) 1.32895 0.132895
\(101\) −6.09314 −0.606290 −0.303145 0.952944i \(-0.598037\pi\)
−0.303145 + 0.952944i \(0.598037\pi\)
\(102\) 2.91622 0.288749
\(103\) −16.5270 −1.62846 −0.814228 0.580545i \(-0.802840\pi\)
−0.814228 + 0.580545i \(0.802840\pi\)
\(104\) −5.73702 −0.562561
\(105\) −7.94878 −0.775721
\(106\) 3.31645 0.322122
\(107\) 9.14029 0.883625 0.441813 0.897107i \(-0.354336\pi\)
0.441813 + 0.897107i \(0.354336\pi\)
\(108\) −4.47366 −0.430478
\(109\) 4.48298 0.429392 0.214696 0.976681i \(-0.431124\pi\)
0.214696 + 0.976681i \(0.431124\pi\)
\(110\) −0.189566 −0.0180744
\(111\) 0.0115862 0.00109971
\(112\) −3.73115 −0.352561
\(113\) −19.2161 −1.80770 −0.903850 0.427849i \(-0.859271\pi\)
−0.903850 + 0.427849i \(0.859271\pi\)
\(114\) 0.846820 0.0793120
\(115\) 17.0828 1.59298
\(116\) 1.05848 0.0982777
\(117\) 13.0970 1.21082
\(118\) 8.85589 0.815250
\(119\) −12.8491 −1.17787
\(120\) 2.13038 0.194476
\(121\) −10.9943 −0.999484
\(122\) −1.05386 −0.0954121
\(123\) −4.43581 −0.399964
\(124\) −3.37751 −0.303310
\(125\) −9.23540 −0.826039
\(126\) 8.51784 0.758829
\(127\) −13.1175 −1.16399 −0.581995 0.813192i \(-0.697728\pi\)
−0.581995 + 0.813192i \(0.697728\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.20242 −0.634138
\(130\) −14.4329 −1.26585
\(131\) 13.7876 1.20463 0.602316 0.798258i \(-0.294245\pi\)
0.602316 + 0.798258i \(0.294245\pi\)
\(132\) −0.0638097 −0.00555392
\(133\) −3.73115 −0.323532
\(134\) −14.4792 −1.25081
\(135\) −11.2546 −0.968640
\(136\) 3.44373 0.295298
\(137\) −3.46483 −0.296020 −0.148010 0.988986i \(-0.547287\pi\)
−0.148010 + 0.988986i \(0.547287\pi\)
\(138\) 5.75021 0.489491
\(139\) −4.06379 −0.344686 −0.172343 0.985037i \(-0.555134\pi\)
−0.172343 + 0.985037i \(0.555134\pi\)
\(140\) −9.38662 −0.793314
\(141\) −5.25747 −0.442759
\(142\) −10.5764 −0.887550
\(143\) 0.432297 0.0361505
\(144\) −2.28290 −0.190241
\(145\) 2.66287 0.221139
\(146\) −10.5869 −0.876176
\(147\) 5.86128 0.483430
\(148\) 0.0136820 0.00112465
\(149\) 3.68372 0.301782 0.150891 0.988550i \(-0.451786\pi\)
0.150891 + 0.988550i \(0.451786\pi\)
\(150\) 1.12539 0.0918873
\(151\) 7.08380 0.576472 0.288236 0.957559i \(-0.406931\pi\)
0.288236 + 0.957559i \(0.406931\pi\)
\(152\) 1.00000 0.0811107
\(153\) −7.86168 −0.635579
\(154\) 0.281150 0.0226557
\(155\) −8.49695 −0.682491
\(156\) −4.85823 −0.388969
\(157\) −1.84050 −0.146888 −0.0734439 0.997299i \(-0.523399\pi\)
−0.0734439 + 0.997299i \(0.523399\pi\)
\(158\) 9.08302 0.722607
\(159\) 2.80844 0.222724
\(160\) 2.51574 0.198887
\(161\) −25.3359 −1.99675
\(162\) 3.06030 0.240440
\(163\) −9.61863 −0.753390 −0.376695 0.926337i \(-0.622939\pi\)
−0.376695 + 0.926337i \(0.622939\pi\)
\(164\) −5.23820 −0.409034
\(165\) −0.160529 −0.0124971
\(166\) 0.661023 0.0513053
\(167\) 10.5078 0.813120 0.406560 0.913624i \(-0.366728\pi\)
0.406560 + 0.913624i \(0.366728\pi\)
\(168\) −3.15962 −0.243770
\(169\) 19.9134 1.53180
\(170\) 8.66354 0.664463
\(171\) −2.28290 −0.174577
\(172\) −8.50526 −0.648520
\(173\) −10.9446 −0.832099 −0.416049 0.909342i \(-0.636586\pi\)
−0.416049 + 0.909342i \(0.636586\pi\)
\(174\) 0.896345 0.0679517
\(175\) −4.95853 −0.374830
\(176\) −0.0753521 −0.00567988
\(177\) 7.49934 0.563685
\(178\) −4.15153 −0.311170
\(179\) 6.23538 0.466054 0.233027 0.972470i \(-0.425137\pi\)
0.233027 + 0.972470i \(0.425137\pi\)
\(180\) −5.74317 −0.428071
\(181\) 9.18136 0.682445 0.341223 0.939982i \(-0.389159\pi\)
0.341223 + 0.939982i \(0.389159\pi\)
\(182\) 21.4057 1.58670
\(183\) −0.892431 −0.0659704
\(184\) 6.79036 0.500592
\(185\) 0.0344203 0.00253063
\(186\) −2.86015 −0.209716
\(187\) −0.259492 −0.0189760
\(188\) −6.20848 −0.452800
\(189\) 16.6919 1.21416
\(190\) 2.51574 0.182511
\(191\) −4.66074 −0.337239 −0.168619 0.985681i \(-0.553931\pi\)
−0.168619 + 0.985681i \(0.553931\pi\)
\(192\) 0.846820 0.0611140
\(193\) 2.69972 0.194330 0.0971650 0.995268i \(-0.469023\pi\)
0.0971650 + 0.995268i \(0.469023\pi\)
\(194\) −0.682779 −0.0490207
\(195\) −12.2220 −0.875238
\(196\) 6.92151 0.494394
\(197\) −17.6195 −1.25534 −0.627668 0.778481i \(-0.715990\pi\)
−0.627668 + 0.778481i \(0.715990\pi\)
\(198\) 0.172021 0.0122250
\(199\) 11.3966 0.807887 0.403943 0.914784i \(-0.367639\pi\)
0.403943 + 0.914784i \(0.367639\pi\)
\(200\) 1.32895 0.0939713
\(201\) −12.2612 −0.864841
\(202\) −6.09314 −0.428712
\(203\) −3.94936 −0.277191
\(204\) 2.91622 0.204176
\(205\) −13.1779 −0.920388
\(206\) −16.5270 −1.15149
\(207\) −15.5017 −1.07744
\(208\) −5.73702 −0.397791
\(209\) −0.0753521 −0.00521221
\(210\) −7.94878 −0.548518
\(211\) −1.00000 −0.0688428
\(212\) 3.31645 0.227775
\(213\) −8.95629 −0.613675
\(214\) 9.14029 0.624817
\(215\) −21.3970 −1.45927
\(216\) −4.47366 −0.304394
\(217\) 12.6020 0.855481
\(218\) 4.48298 0.303626
\(219\) −8.96518 −0.605811
\(220\) −0.189566 −0.0127806
\(221\) −19.7568 −1.32898
\(222\) 0.0115862 0.000777614 0
\(223\) −22.9125 −1.53434 −0.767169 0.641446i \(-0.778335\pi\)
−0.767169 + 0.641446i \(0.778335\pi\)
\(224\) −3.73115 −0.249298
\(225\) −3.03386 −0.202258
\(226\) −19.2161 −1.27824
\(227\) −14.4216 −0.957196 −0.478598 0.878034i \(-0.658855\pi\)
−0.478598 + 0.878034i \(0.658855\pi\)
\(228\) 0.846820 0.0560820
\(229\) −23.6041 −1.55980 −0.779902 0.625901i \(-0.784731\pi\)
−0.779902 + 0.625901i \(0.784731\pi\)
\(230\) 17.0828 1.12641
\(231\) 0.238084 0.0156648
\(232\) 1.05848 0.0694928
\(233\) −25.4543 −1.66757 −0.833784 0.552090i \(-0.813830\pi\)
−0.833784 + 0.552090i \(0.813830\pi\)
\(234\) 13.0970 0.856179
\(235\) −15.6189 −1.01887
\(236\) 8.85589 0.576469
\(237\) 7.69169 0.499629
\(238\) −12.8491 −0.832883
\(239\) −8.55439 −0.553338 −0.276669 0.960965i \(-0.589230\pi\)
−0.276669 + 0.960965i \(0.589230\pi\)
\(240\) 2.13038 0.137515
\(241\) 25.2877 1.62893 0.814463 0.580215i \(-0.197031\pi\)
0.814463 + 0.580215i \(0.197031\pi\)
\(242\) −10.9943 −0.706742
\(243\) 16.0125 1.02720
\(244\) −1.05386 −0.0674665
\(245\) 17.4127 1.11246
\(246\) −4.43581 −0.282817
\(247\) −5.73702 −0.365038
\(248\) −3.37751 −0.214472
\(249\) 0.559768 0.0354738
\(250\) −9.23540 −0.584098
\(251\) 13.8372 0.873394 0.436697 0.899609i \(-0.356148\pi\)
0.436697 + 0.899609i \(0.356148\pi\)
\(252\) 8.51784 0.536573
\(253\) −0.511668 −0.0321683
\(254\) −13.1175 −0.823066
\(255\) 7.33646 0.459427
\(256\) 1.00000 0.0625000
\(257\) 1.16464 0.0726482 0.0363241 0.999340i \(-0.488435\pi\)
0.0363241 + 0.999340i \(0.488435\pi\)
\(258\) −7.20242 −0.448403
\(259\) −0.0510496 −0.00317207
\(260\) −14.4329 −0.895088
\(261\) −2.41641 −0.149572
\(262\) 13.7876 0.851804
\(263\) 17.2266 1.06224 0.531120 0.847297i \(-0.321771\pi\)
0.531120 + 0.847297i \(0.321771\pi\)
\(264\) −0.0638097 −0.00392721
\(265\) 8.34333 0.512527
\(266\) −3.73115 −0.228772
\(267\) −3.51560 −0.215151
\(268\) −14.4792 −0.884455
\(269\) −5.59641 −0.341219 −0.170610 0.985339i \(-0.554574\pi\)
−0.170610 + 0.985339i \(0.554574\pi\)
\(270\) −11.2546 −0.684932
\(271\) −6.36372 −0.386568 −0.193284 0.981143i \(-0.561914\pi\)
−0.193284 + 0.981143i \(0.561914\pi\)
\(272\) 3.44373 0.208807
\(273\) 18.1268 1.09708
\(274\) −3.46483 −0.209318
\(275\) −0.100139 −0.00603864
\(276\) 5.75021 0.346122
\(277\) 23.2939 1.39959 0.699797 0.714342i \(-0.253274\pi\)
0.699797 + 0.714342i \(0.253274\pi\)
\(278\) −4.06379 −0.243730
\(279\) 7.71051 0.461616
\(280\) −9.38662 −0.560958
\(281\) 30.9071 1.84376 0.921880 0.387475i \(-0.126653\pi\)
0.921880 + 0.387475i \(0.126653\pi\)
\(282\) −5.25747 −0.313078
\(283\) 7.88482 0.468704 0.234352 0.972152i \(-0.424703\pi\)
0.234352 + 0.972152i \(0.424703\pi\)
\(284\) −10.5764 −0.627592
\(285\) 2.13038 0.126193
\(286\) 0.432297 0.0255622
\(287\) 19.5445 1.15368
\(288\) −2.28290 −0.134521
\(289\) −5.14071 −0.302394
\(290\) 2.66287 0.156369
\(291\) −0.578191 −0.0338942
\(292\) −10.5869 −0.619550
\(293\) −26.7684 −1.56382 −0.781912 0.623389i \(-0.785755\pi\)
−0.781912 + 0.623389i \(0.785755\pi\)
\(294\) 5.86128 0.341837
\(295\) 22.2791 1.29714
\(296\) 0.0136820 0.000795249 0
\(297\) 0.337100 0.0195605
\(298\) 3.68372 0.213392
\(299\) −38.9564 −2.25291
\(300\) 1.12539 0.0649741
\(301\) 31.7344 1.82914
\(302\) 7.08380 0.407627
\(303\) −5.15979 −0.296422
\(304\) 1.00000 0.0573539
\(305\) −2.65124 −0.151810
\(306\) −7.86168 −0.449422
\(307\) 21.6088 1.23328 0.616638 0.787247i \(-0.288494\pi\)
0.616638 + 0.787247i \(0.288494\pi\)
\(308\) 0.281150 0.0160200
\(309\) −13.9954 −0.796172
\(310\) −8.49695 −0.482594
\(311\) 4.23255 0.240006 0.120003 0.992774i \(-0.461710\pi\)
0.120003 + 0.992774i \(0.461710\pi\)
\(312\) −4.85823 −0.275043
\(313\) 21.2458 1.20088 0.600442 0.799668i \(-0.294991\pi\)
0.600442 + 0.799668i \(0.294991\pi\)
\(314\) −1.84050 −0.103865
\(315\) 21.4287 1.20737
\(316\) 9.08302 0.510960
\(317\) 24.3234 1.36614 0.683070 0.730353i \(-0.260644\pi\)
0.683070 + 0.730353i \(0.260644\pi\)
\(318\) 2.80844 0.157489
\(319\) −0.0797589 −0.00446564
\(320\) 2.51574 0.140634
\(321\) 7.74018 0.432015
\(322\) −25.3359 −1.41191
\(323\) 3.44373 0.191614
\(324\) 3.06030 0.170017
\(325\) −7.62424 −0.422917
\(326\) −9.61863 −0.532727
\(327\) 3.79628 0.209935
\(328\) −5.23820 −0.289231
\(329\) 23.1648 1.27712
\(330\) −0.160529 −0.00883681
\(331\) 9.82654 0.540115 0.270058 0.962844i \(-0.412957\pi\)
0.270058 + 0.962844i \(0.412957\pi\)
\(332\) 0.661023 0.0362784
\(333\) −0.0312345 −0.00171164
\(334\) 10.5078 0.574962
\(335\) −36.4258 −1.99015
\(336\) −3.15962 −0.172371
\(337\) 16.0274 0.873070 0.436535 0.899687i \(-0.356206\pi\)
0.436535 + 0.899687i \(0.356206\pi\)
\(338\) 19.9134 1.08315
\(339\) −16.2726 −0.883806
\(340\) 8.66354 0.469846
\(341\) 0.254503 0.0137821
\(342\) −2.28290 −0.123445
\(343\) 0.292848 0.0158123
\(344\) −8.50526 −0.458573
\(345\) 14.4661 0.778826
\(346\) −10.9446 −0.588383
\(347\) 3.93856 0.211433 0.105717 0.994396i \(-0.466286\pi\)
0.105717 + 0.994396i \(0.466286\pi\)
\(348\) 0.896345 0.0480491
\(349\) 1.23767 0.0662512 0.0331256 0.999451i \(-0.489454\pi\)
0.0331256 + 0.999451i \(0.489454\pi\)
\(350\) −4.95853 −0.265045
\(351\) 25.6655 1.36992
\(352\) −0.0753521 −0.00401628
\(353\) 5.65440 0.300953 0.150477 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(354\) 7.49934 0.398586
\(355\) −26.6074 −1.41218
\(356\) −4.15153 −0.220030
\(357\) −10.8809 −0.575877
\(358\) 6.23538 0.329550
\(359\) 9.74840 0.514501 0.257250 0.966345i \(-0.417184\pi\)
0.257250 + 0.966345i \(0.417184\pi\)
\(360\) −5.74317 −0.302692
\(361\) 1.00000 0.0526316
\(362\) 9.18136 0.482562
\(363\) −9.31021 −0.488660
\(364\) 21.4057 1.12196
\(365\) −26.6339 −1.39408
\(366\) −0.892431 −0.0466481
\(367\) −8.60189 −0.449015 −0.224507 0.974472i \(-0.572077\pi\)
−0.224507 + 0.974472i \(0.572077\pi\)
\(368\) 6.79036 0.353972
\(369\) 11.9583 0.622522
\(370\) 0.0344203 0.00178943
\(371\) −12.3742 −0.642436
\(372\) −2.86015 −0.148292
\(373\) 6.05625 0.313581 0.156790 0.987632i \(-0.449885\pi\)
0.156790 + 0.987632i \(0.449885\pi\)
\(374\) −0.259492 −0.0134180
\(375\) −7.82072 −0.403860
\(376\) −6.20848 −0.320178
\(377\) −6.07254 −0.312752
\(378\) 16.6919 0.858540
\(379\) 20.3044 1.04296 0.521482 0.853262i \(-0.325379\pi\)
0.521482 + 0.853262i \(0.325379\pi\)
\(380\) 2.51574 0.129055
\(381\) −11.1082 −0.569089
\(382\) −4.66074 −0.238464
\(383\) 31.1049 1.58939 0.794694 0.607011i \(-0.207632\pi\)
0.794694 + 0.607011i \(0.207632\pi\)
\(384\) 0.846820 0.0432141
\(385\) 0.707301 0.0360474
\(386\) 2.69972 0.137412
\(387\) 19.4166 0.987002
\(388\) −0.682779 −0.0346628
\(389\) −7.23787 −0.366974 −0.183487 0.983022i \(-0.558739\pi\)
−0.183487 + 0.983022i \(0.558739\pi\)
\(390\) −12.2220 −0.618887
\(391\) 23.3842 1.18259
\(392\) 6.92151 0.349589
\(393\) 11.6757 0.588959
\(394\) −17.6195 −0.887657
\(395\) 22.8505 1.14974
\(396\) 0.172021 0.00864438
\(397\) 22.1359 1.11097 0.555483 0.831528i \(-0.312533\pi\)
0.555483 + 0.831528i \(0.312533\pi\)
\(398\) 11.3966 0.571262
\(399\) −3.15962 −0.158179
\(400\) 1.32895 0.0664477
\(401\) 13.9938 0.698816 0.349408 0.936971i \(-0.386383\pi\)
0.349408 + 0.936971i \(0.386383\pi\)
\(402\) −12.2612 −0.611535
\(403\) 19.3769 0.965230
\(404\) −6.09314 −0.303145
\(405\) 7.69892 0.382562
\(406\) −3.94936 −0.196004
\(407\) −0.00103097 −5.11031e−5 0
\(408\) 2.91622 0.144375
\(409\) 25.7319 1.27236 0.636180 0.771540i \(-0.280513\pi\)
0.636180 + 0.771540i \(0.280513\pi\)
\(410\) −13.1779 −0.650812
\(411\) −2.93408 −0.144728
\(412\) −16.5270 −0.814228
\(413\) −33.0427 −1.62592
\(414\) −15.5017 −0.761866
\(415\) 1.66296 0.0816316
\(416\) −5.73702 −0.281281
\(417\) −3.44130 −0.168521
\(418\) −0.0753521 −0.00368559
\(419\) 1.36340 0.0666064 0.0333032 0.999445i \(-0.489397\pi\)
0.0333032 + 0.999445i \(0.489397\pi\)
\(420\) −7.94878 −0.387861
\(421\) −2.18984 −0.106726 −0.0533632 0.998575i \(-0.516994\pi\)
−0.0533632 + 0.998575i \(0.516994\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 14.1733 0.689130
\(424\) 3.31645 0.161061
\(425\) 4.57656 0.221996
\(426\) −8.95629 −0.433934
\(427\) 3.93212 0.190288
\(428\) 9.14029 0.441813
\(429\) 0.366077 0.0176744
\(430\) −21.3970 −1.03186
\(431\) 8.48009 0.408471 0.204236 0.978922i \(-0.434529\pi\)
0.204236 + 0.978922i \(0.434529\pi\)
\(432\) −4.47366 −0.215239
\(433\) −10.4229 −0.500893 −0.250446 0.968130i \(-0.580577\pi\)
−0.250446 + 0.968130i \(0.580577\pi\)
\(434\) 12.6020 0.604916
\(435\) 2.25497 0.108118
\(436\) 4.48298 0.214696
\(437\) 6.79036 0.324827
\(438\) −8.96518 −0.428373
\(439\) −12.6496 −0.603733 −0.301866 0.953350i \(-0.597610\pi\)
−0.301866 + 0.953350i \(0.597610\pi\)
\(440\) −0.189566 −0.00903722
\(441\) −15.8011 −0.752433
\(442\) −19.7568 −0.939734
\(443\) −35.3294 −1.67855 −0.839276 0.543705i \(-0.817021\pi\)
−0.839276 + 0.543705i \(0.817021\pi\)
\(444\) 0.0115862 0.000549856 0
\(445\) −10.4442 −0.495101
\(446\) −22.9125 −1.08494
\(447\) 3.11945 0.147545
\(448\) −3.73115 −0.176280
\(449\) −9.46560 −0.446710 −0.223355 0.974737i \(-0.571701\pi\)
−0.223355 + 0.974737i \(0.571701\pi\)
\(450\) −3.03386 −0.143018
\(451\) 0.394709 0.0185861
\(452\) −19.2161 −0.903850
\(453\) 5.99871 0.281844
\(454\) −14.4216 −0.676840
\(455\) 53.8512 2.52459
\(456\) 0.846820 0.0396560
\(457\) −32.0612 −1.49976 −0.749879 0.661575i \(-0.769889\pi\)
−0.749879 + 0.661575i \(0.769889\pi\)
\(458\) −23.6041 −1.10295
\(459\) −15.4061 −0.719095
\(460\) 17.0828 0.796489
\(461\) 27.2979 1.27139 0.635696 0.771940i \(-0.280713\pi\)
0.635696 + 0.771940i \(0.280713\pi\)
\(462\) 0.238084 0.0110767
\(463\) 32.4611 1.50859 0.754297 0.656533i \(-0.227978\pi\)
0.754297 + 0.656533i \(0.227978\pi\)
\(464\) 1.05848 0.0491388
\(465\) −7.19539 −0.333678
\(466\) −25.4543 −1.17915
\(467\) −31.2049 −1.44399 −0.721996 0.691897i \(-0.756775\pi\)
−0.721996 + 0.691897i \(0.756775\pi\)
\(468\) 13.0970 0.605410
\(469\) 54.0240 2.49459
\(470\) −15.6189 −0.720448
\(471\) −1.55857 −0.0718152
\(472\) 8.85589 0.407625
\(473\) 0.640889 0.0294681
\(474\) 7.69169 0.353291
\(475\) 1.32895 0.0609766
\(476\) −12.8491 −0.588937
\(477\) −7.57111 −0.346657
\(478\) −8.55439 −0.391269
\(479\) −22.2905 −1.01848 −0.509240 0.860625i \(-0.670073\pi\)
−0.509240 + 0.860625i \(0.670073\pi\)
\(480\) 2.13038 0.0972381
\(481\) −0.0784939 −0.00357901
\(482\) 25.2877 1.15183
\(483\) −21.4549 −0.976233
\(484\) −10.9943 −0.499742
\(485\) −1.71770 −0.0779965
\(486\) 16.0125 0.726342
\(487\) 4.50007 0.203918 0.101959 0.994789i \(-0.467489\pi\)
0.101959 + 0.994789i \(0.467489\pi\)
\(488\) −1.05386 −0.0477060
\(489\) −8.14525 −0.368341
\(490\) 17.4127 0.786627
\(491\) −39.6320 −1.78857 −0.894284 0.447499i \(-0.852315\pi\)
−0.894284 + 0.447499i \(0.852315\pi\)
\(492\) −4.43581 −0.199982
\(493\) 3.64513 0.164169
\(494\) −5.73702 −0.258121
\(495\) 0.432760 0.0194511
\(496\) −3.37751 −0.151655
\(497\) 39.4621 1.77012
\(498\) 0.559768 0.0250838
\(499\) 17.7075 0.792696 0.396348 0.918100i \(-0.370277\pi\)
0.396348 + 0.918100i \(0.370277\pi\)
\(500\) −9.23540 −0.413020
\(501\) 8.89823 0.397544
\(502\) 13.8372 0.617583
\(503\) 40.0337 1.78501 0.892507 0.451034i \(-0.148945\pi\)
0.892507 + 0.451034i \(0.148945\pi\)
\(504\) 8.51784 0.379415
\(505\) −15.3288 −0.682121
\(506\) −0.511668 −0.0227464
\(507\) 16.8631 0.748916
\(508\) −13.1175 −0.581995
\(509\) 9.74155 0.431786 0.215893 0.976417i \(-0.430734\pi\)
0.215893 + 0.976417i \(0.430734\pi\)
\(510\) 7.33646 0.324864
\(511\) 39.5013 1.74743
\(512\) 1.00000 0.0441942
\(513\) −4.47366 −0.197517
\(514\) 1.16464 0.0513700
\(515\) −41.5777 −1.83213
\(516\) −7.20242 −0.317069
\(517\) 0.467822 0.0205748
\(518\) −0.0510496 −0.00224299
\(519\) −9.26807 −0.406823
\(520\) −14.4329 −0.632923
\(521\) −16.2677 −0.712700 −0.356350 0.934353i \(-0.615979\pi\)
−0.356350 + 0.934353i \(0.615979\pi\)
\(522\) −2.41641 −0.105763
\(523\) 34.1150 1.49174 0.745872 0.666090i \(-0.232033\pi\)
0.745872 + 0.666090i \(0.232033\pi\)
\(524\) 13.7876 0.602316
\(525\) −4.19899 −0.183259
\(526\) 17.2266 0.751117
\(527\) −11.6312 −0.506665
\(528\) −0.0638097 −0.00277696
\(529\) 23.1090 1.00474
\(530\) 8.34333 0.362411
\(531\) −20.2171 −0.877346
\(532\) −3.73115 −0.161766
\(533\) 30.0516 1.30168
\(534\) −3.51560 −0.152135
\(535\) 22.9946 0.994143
\(536\) −14.4792 −0.625404
\(537\) 5.28024 0.227859
\(538\) −5.59641 −0.241278
\(539\) −0.521550 −0.0224648
\(540\) −11.2546 −0.484320
\(541\) −14.8874 −0.640059 −0.320029 0.947408i \(-0.603693\pi\)
−0.320029 + 0.947408i \(0.603693\pi\)
\(542\) −6.36372 −0.273345
\(543\) 7.77496 0.333656
\(544\) 3.44373 0.147649
\(545\) 11.2780 0.483097
\(546\) 18.1268 0.775755
\(547\) −33.1241 −1.41628 −0.708142 0.706070i \(-0.750467\pi\)
−0.708142 + 0.706070i \(0.750467\pi\)
\(548\) −3.46483 −0.148010
\(549\) 2.40585 0.102679
\(550\) −0.100139 −0.00426996
\(551\) 1.05848 0.0450929
\(552\) 5.75021 0.244745
\(553\) −33.8902 −1.44116
\(554\) 23.2939 0.989662
\(555\) 0.0291478 0.00123726
\(556\) −4.06379 −0.172343
\(557\) −19.4433 −0.823839 −0.411920 0.911220i \(-0.635142\pi\)
−0.411920 + 0.911220i \(0.635142\pi\)
\(558\) 7.71051 0.326412
\(559\) 48.7948 2.06380
\(560\) −9.38662 −0.396657
\(561\) −0.219743 −0.00927758
\(562\) 30.9071 1.30374
\(563\) 27.6601 1.16573 0.582867 0.812568i \(-0.301931\pi\)
0.582867 + 0.812568i \(0.301931\pi\)
\(564\) −5.25747 −0.221379
\(565\) −48.3428 −2.03380
\(566\) 7.88482 0.331424
\(567\) −11.4184 −0.479530
\(568\) −10.5764 −0.443775
\(569\) −25.2610 −1.05900 −0.529499 0.848311i \(-0.677620\pi\)
−0.529499 + 0.848311i \(0.677620\pi\)
\(570\) 2.13038 0.0892318
\(571\) −2.57697 −0.107843 −0.0539213 0.998545i \(-0.517172\pi\)
−0.0539213 + 0.998545i \(0.517172\pi\)
\(572\) 0.432297 0.0180752
\(573\) −3.94681 −0.164880
\(574\) 19.5445 0.815772
\(575\) 9.02408 0.376330
\(576\) −2.28290 −0.0951206
\(577\) 12.0125 0.500087 0.250043 0.968235i \(-0.419555\pi\)
0.250043 + 0.968235i \(0.419555\pi\)
\(578\) −5.14071 −0.213825
\(579\) 2.28618 0.0950102
\(580\) 2.66287 0.110570
\(581\) −2.46638 −0.102323
\(582\) −0.578191 −0.0239668
\(583\) −0.249902 −0.0103499
\(584\) −10.5869 −0.438088
\(585\) 32.9487 1.36226
\(586\) −26.7684 −1.10579
\(587\) −20.3688 −0.840710 −0.420355 0.907360i \(-0.638095\pi\)
−0.420355 + 0.907360i \(0.638095\pi\)
\(588\) 5.86128 0.241715
\(589\) −3.37751 −0.139168
\(590\) 22.2791 0.917217
\(591\) −14.9205 −0.613749
\(592\) 0.0136820 0.000562326 0
\(593\) 17.1310 0.703486 0.351743 0.936097i \(-0.385589\pi\)
0.351743 + 0.936097i \(0.385589\pi\)
\(594\) 0.337100 0.0138314
\(595\) −32.3250 −1.32520
\(596\) 3.68372 0.150891
\(597\) 9.65091 0.394985
\(598\) −38.9564 −1.59305
\(599\) 5.99149 0.244806 0.122403 0.992481i \(-0.460940\pi\)
0.122403 + 0.992481i \(0.460940\pi\)
\(600\) 1.12539 0.0459437
\(601\) 28.3842 1.15782 0.578908 0.815393i \(-0.303479\pi\)
0.578908 + 0.815393i \(0.303479\pi\)
\(602\) 31.7344 1.29340
\(603\) 33.0544 1.34608
\(604\) 7.08380 0.288236
\(605\) −27.6589 −1.12449
\(606\) −5.15979 −0.209602
\(607\) 36.1322 1.46656 0.733281 0.679926i \(-0.237988\pi\)
0.733281 + 0.679926i \(0.237988\pi\)
\(608\) 1.00000 0.0405554
\(609\) −3.34440 −0.135522
\(610\) −2.65124 −0.107346
\(611\) 35.6182 1.44096
\(612\) −7.86168 −0.317790
\(613\) −19.6460 −0.793496 −0.396748 0.917928i \(-0.629861\pi\)
−0.396748 + 0.917928i \(0.629861\pi\)
\(614\) 21.6088 0.872058
\(615\) −11.1594 −0.449988
\(616\) 0.281150 0.0113279
\(617\) −25.6886 −1.03419 −0.517093 0.855929i \(-0.672986\pi\)
−0.517093 + 0.855929i \(0.672986\pi\)
\(618\) −13.9954 −0.562978
\(619\) 40.6099 1.63225 0.816124 0.577876i \(-0.196118\pi\)
0.816124 + 0.577876i \(0.196118\pi\)
\(620\) −8.49695 −0.341246
\(621\) −30.3778 −1.21902
\(622\) 4.23255 0.169710
\(623\) 15.4900 0.620593
\(624\) −4.85823 −0.194485
\(625\) −29.8787 −1.19515
\(626\) 21.2458 0.849153
\(627\) −0.0638097 −0.00254831
\(628\) −1.84050 −0.0734439
\(629\) 0.0471171 0.00187868
\(630\) 21.4287 0.853739
\(631\) −30.5871 −1.21766 −0.608828 0.793303i \(-0.708360\pi\)
−0.608828 + 0.793303i \(0.708360\pi\)
\(632\) 9.08302 0.361303
\(633\) −0.846820 −0.0336581
\(634\) 24.3234 0.966007
\(635\) −33.0003 −1.30958
\(636\) 2.80844 0.111362
\(637\) −39.7089 −1.57332
\(638\) −0.0797589 −0.00315769
\(639\) 24.1448 0.955152
\(640\) 2.51574 0.0994434
\(641\) −16.0251 −0.632954 −0.316477 0.948600i \(-0.602500\pi\)
−0.316477 + 0.948600i \(0.602500\pi\)
\(642\) 7.74018 0.305481
\(643\) 4.93100 0.194460 0.0972299 0.995262i \(-0.469002\pi\)
0.0972299 + 0.995262i \(0.469002\pi\)
\(644\) −25.3359 −0.998374
\(645\) −18.1194 −0.713452
\(646\) 3.44373 0.135492
\(647\) 25.6515 1.00847 0.504233 0.863568i \(-0.331775\pi\)
0.504233 + 0.863568i \(0.331775\pi\)
\(648\) 3.06030 0.120220
\(649\) −0.667309 −0.0261942
\(650\) −7.62424 −0.299047
\(651\) 10.6716 0.418255
\(652\) −9.61863 −0.376695
\(653\) −27.2836 −1.06769 −0.533844 0.845583i \(-0.679253\pi\)
−0.533844 + 0.845583i \(0.679253\pi\)
\(654\) 3.79628 0.148446
\(655\) 34.6862 1.35530
\(656\) −5.23820 −0.204517
\(657\) 24.1687 0.942912
\(658\) 23.1648 0.903058
\(659\) −41.1158 −1.60164 −0.800821 0.598904i \(-0.795603\pi\)
−0.800821 + 0.598904i \(0.795603\pi\)
\(660\) −0.160529 −0.00624857
\(661\) 18.2616 0.710294 0.355147 0.934811i \(-0.384431\pi\)
0.355147 + 0.934811i \(0.384431\pi\)
\(662\) 9.82654 0.381919
\(663\) −16.7304 −0.649756
\(664\) 0.661023 0.0256527
\(665\) −9.38662 −0.363997
\(666\) −0.0312345 −0.00121031
\(667\) 7.18748 0.278300
\(668\) 10.5078 0.406560
\(669\) −19.4028 −0.750156
\(670\) −36.4258 −1.40725
\(671\) 0.0794106 0.00306561
\(672\) −3.15962 −0.121885
\(673\) −5.97396 −0.230279 −0.115140 0.993349i \(-0.536732\pi\)
−0.115140 + 0.993349i \(0.536732\pi\)
\(674\) 16.0274 0.617353
\(675\) −5.94529 −0.228834
\(676\) 19.9134 0.765901
\(677\) 9.51990 0.365880 0.182940 0.983124i \(-0.441439\pi\)
0.182940 + 0.983124i \(0.441439\pi\)
\(678\) −16.2726 −0.624945
\(679\) 2.54755 0.0977661
\(680\) 8.66354 0.332232
\(681\) −12.2125 −0.467984
\(682\) 0.254503 0.00974541
\(683\) 32.9274 1.25993 0.629966 0.776623i \(-0.283069\pi\)
0.629966 + 0.776623i \(0.283069\pi\)
\(684\) −2.28290 −0.0872887
\(685\) −8.71660 −0.333044
\(686\) 0.292848 0.0111810
\(687\) −19.9885 −0.762607
\(688\) −8.50526 −0.324260
\(689\) −19.0266 −0.724854
\(690\) 14.4661 0.550713
\(691\) −34.0226 −1.29428 −0.647140 0.762371i \(-0.724035\pi\)
−0.647140 + 0.762371i \(0.724035\pi\)
\(692\) −10.9446 −0.416049
\(693\) −0.641837 −0.0243814
\(694\) 3.93856 0.149506
\(695\) −10.2234 −0.387797
\(696\) 0.896345 0.0339759
\(697\) −18.0389 −0.683274
\(698\) 1.23767 0.0468467
\(699\) −21.5552 −0.815294
\(700\) −4.95853 −0.187415
\(701\) −25.5674 −0.965668 −0.482834 0.875712i \(-0.660392\pi\)
−0.482834 + 0.875712i \(0.660392\pi\)
\(702\) 25.6655 0.968682
\(703\) 0.0136820 0.000516026 0
\(704\) −0.0753521 −0.00283994
\(705\) −13.2264 −0.498136
\(706\) 5.65440 0.212806
\(707\) 22.7344 0.855016
\(708\) 7.49934 0.281843
\(709\) 10.2425 0.384663 0.192332 0.981330i \(-0.438395\pi\)
0.192332 + 0.981330i \(0.438395\pi\)
\(710\) −26.6074 −0.998559
\(711\) −20.7356 −0.777646
\(712\) −4.15153 −0.155585
\(713\) −22.9345 −0.858905
\(714\) −10.8809 −0.407207
\(715\) 1.08755 0.0406719
\(716\) 6.23538 0.233027
\(717\) −7.24403 −0.270533
\(718\) 9.74840 0.363807
\(719\) −18.3629 −0.684820 −0.342410 0.939551i \(-0.611243\pi\)
−0.342410 + 0.939551i \(0.611243\pi\)
\(720\) −5.74317 −0.214035
\(721\) 61.6649 2.29652
\(722\) 1.00000 0.0372161
\(723\) 21.4142 0.796402
\(724\) 9.18136 0.341223
\(725\) 1.40668 0.0522426
\(726\) −9.31021 −0.345534
\(727\) 13.9659 0.517967 0.258983 0.965882i \(-0.416613\pi\)
0.258983 + 0.965882i \(0.416613\pi\)
\(728\) 21.4057 0.793349
\(729\) 4.37882 0.162179
\(730\) −26.6339 −0.985763
\(731\) −29.2898 −1.08332
\(732\) −0.892431 −0.0329852
\(733\) −11.4936 −0.424526 −0.212263 0.977213i \(-0.568083\pi\)
−0.212263 + 0.977213i \(0.568083\pi\)
\(734\) −8.60189 −0.317502
\(735\) 14.7455 0.543894
\(736\) 6.79036 0.250296
\(737\) 1.09103 0.0401888
\(738\) 11.9583 0.440189
\(739\) −8.84645 −0.325422 −0.162711 0.986674i \(-0.552024\pi\)
−0.162711 + 0.986674i \(0.552024\pi\)
\(740\) 0.0344203 0.00126532
\(741\) −4.85823 −0.178471
\(742\) −12.3742 −0.454271
\(743\) 19.4815 0.714708 0.357354 0.933969i \(-0.383679\pi\)
0.357354 + 0.933969i \(0.383679\pi\)
\(744\) −2.86015 −0.104858
\(745\) 9.26729 0.339527
\(746\) 6.05625 0.221735
\(747\) −1.50905 −0.0552131
\(748\) −0.259492 −0.00948798
\(749\) −34.1038 −1.24613
\(750\) −7.82072 −0.285572
\(751\) −37.7993 −1.37932 −0.689658 0.724135i \(-0.742239\pi\)
−0.689658 + 0.724135i \(0.742239\pi\)
\(752\) −6.20848 −0.226400
\(753\) 11.7176 0.427013
\(754\) −6.07254 −0.221149
\(755\) 17.8210 0.648573
\(756\) 16.6919 0.607079
\(757\) −21.6737 −0.787745 −0.393873 0.919165i \(-0.628865\pi\)
−0.393873 + 0.919165i \(0.628865\pi\)
\(758\) 20.3044 0.737487
\(759\) −0.433291 −0.0157275
\(760\) 2.51574 0.0912555
\(761\) 3.87589 0.140501 0.0702505 0.997529i \(-0.477620\pi\)
0.0702505 + 0.997529i \(0.477620\pi\)
\(762\) −11.1082 −0.402407
\(763\) −16.7267 −0.605547
\(764\) −4.66074 −0.168619
\(765\) −19.7780 −0.715074
\(766\) 31.1049 1.12387
\(767\) −50.8064 −1.83451
\(768\) 0.846820 0.0305570
\(769\) −49.1946 −1.77400 −0.887002 0.461766i \(-0.847216\pi\)
−0.887002 + 0.461766i \(0.847216\pi\)
\(770\) 0.707301 0.0254894
\(771\) 0.986240 0.0355186
\(772\) 2.69972 0.0971650
\(773\) 30.8200 1.10852 0.554260 0.832344i \(-0.313001\pi\)
0.554260 + 0.832344i \(0.313001\pi\)
\(774\) 19.4166 0.697916
\(775\) −4.48856 −0.161234
\(776\) −0.682779 −0.0245103
\(777\) −0.0432298 −0.00155086
\(778\) −7.23787 −0.259490
\(779\) −5.23820 −0.187678
\(780\) −12.2220 −0.437619
\(781\) 0.796952 0.0285172
\(782\) 23.3842 0.836217
\(783\) −4.73530 −0.169226
\(784\) 6.92151 0.247197
\(785\) −4.63022 −0.165260
\(786\) 11.6757 0.416457
\(787\) −20.2589 −0.722153 −0.361077 0.932536i \(-0.617591\pi\)
−0.361077 + 0.932536i \(0.617591\pi\)
\(788\) −17.6195 −0.627668
\(789\) 14.5879 0.519342
\(790\) 22.8505 0.812986
\(791\) 71.6983 2.54930
\(792\) 0.172021 0.00611250
\(793\) 6.04602 0.214701
\(794\) 22.1359 0.785572
\(795\) 7.06530 0.250580
\(796\) 11.3966 0.403943
\(797\) 42.7498 1.51428 0.757139 0.653254i \(-0.226597\pi\)
0.757139 + 0.653254i \(0.226597\pi\)
\(798\) −3.15962 −0.111849
\(799\) −21.3803 −0.756382
\(800\) 1.32895 0.0469856
\(801\) 9.47750 0.334871
\(802\) 13.9938 0.494138
\(803\) 0.797744 0.0281518
\(804\) −12.2612 −0.432421
\(805\) −63.7385 −2.24649
\(806\) 19.3769 0.682521
\(807\) −4.73915 −0.166826
\(808\) −6.09314 −0.214356
\(809\) −21.8005 −0.766465 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(810\) 7.69892 0.270512
\(811\) 39.8101 1.39792 0.698962 0.715159i \(-0.253646\pi\)
0.698962 + 0.715159i \(0.253646\pi\)
\(812\) −3.94936 −0.138595
\(813\) −5.38892 −0.188998
\(814\) −0.00103097 −3.61354e−5 0
\(815\) −24.1980 −0.847619
\(816\) 2.91622 0.102088
\(817\) −8.50526 −0.297561
\(818\) 25.7319 0.899695
\(819\) −48.8670 −1.70755
\(820\) −13.1779 −0.460194
\(821\) 34.0338 1.18779 0.593895 0.804543i \(-0.297590\pi\)
0.593895 + 0.804543i \(0.297590\pi\)
\(822\) −2.93408 −0.102338
\(823\) 36.5418 1.27377 0.636883 0.770960i \(-0.280223\pi\)
0.636883 + 0.770960i \(0.280223\pi\)
\(824\) −16.5270 −0.575746
\(825\) −0.0848001 −0.00295236
\(826\) −33.0427 −1.14970
\(827\) 50.5007 1.75608 0.878041 0.478585i \(-0.158850\pi\)
0.878041 + 0.478585i \(0.158850\pi\)
\(828\) −15.5017 −0.538721
\(829\) −5.06039 −0.175755 −0.0878773 0.996131i \(-0.528008\pi\)
−0.0878773 + 0.996131i \(0.528008\pi\)
\(830\) 1.66296 0.0577223
\(831\) 19.7257 0.684278
\(832\) −5.73702 −0.198895
\(833\) 23.8358 0.825863
\(834\) −3.44130 −0.119162
\(835\) 26.4350 0.914819
\(836\) −0.0753521 −0.00260611
\(837\) 15.1099 0.522273
\(838\) 1.36340 0.0470978
\(839\) −12.8972 −0.445261 −0.222630 0.974903i \(-0.571464\pi\)
−0.222630 + 0.974903i \(0.571464\pi\)
\(840\) −7.94878 −0.274259
\(841\) −27.8796 −0.961366
\(842\) −2.18984 −0.0754670
\(843\) 26.1727 0.901437
\(844\) −1.00000 −0.0344214
\(845\) 50.0970 1.72339
\(846\) 14.1733 0.487288
\(847\) 41.0215 1.40952
\(848\) 3.31645 0.113887
\(849\) 6.67703 0.229155
\(850\) 4.57656 0.156975
\(851\) 0.0929056 0.00318476
\(852\) −8.95629 −0.306837
\(853\) 13.0874 0.448103 0.224052 0.974577i \(-0.428072\pi\)
0.224052 + 0.974577i \(0.428072\pi\)
\(854\) 3.93212 0.134554
\(855\) −5.74317 −0.196412
\(856\) 9.14029 0.312409
\(857\) −3.57872 −0.122247 −0.0611234 0.998130i \(-0.519468\pi\)
−0.0611234 + 0.998130i \(0.519468\pi\)
\(858\) 0.366077 0.0124977
\(859\) 35.9009 1.22492 0.612461 0.790501i \(-0.290180\pi\)
0.612461 + 0.790501i \(0.290180\pi\)
\(860\) −21.3970 −0.729633
\(861\) 16.5507 0.564046
\(862\) 8.48009 0.288833
\(863\) 51.2372 1.74414 0.872068 0.489385i \(-0.162779\pi\)
0.872068 + 0.489385i \(0.162779\pi\)
\(864\) −4.47366 −0.152197
\(865\) −27.5337 −0.936172
\(866\) −10.4229 −0.354185
\(867\) −4.35325 −0.147844
\(868\) 12.6020 0.427740
\(869\) −0.684425 −0.0232175
\(870\) 2.25497 0.0764507
\(871\) 83.0672 2.81463
\(872\) 4.48298 0.151813
\(873\) 1.55871 0.0527544
\(874\) 6.79036 0.229687
\(875\) 34.4587 1.16492
\(876\) −8.96518 −0.302906
\(877\) 2.74250 0.0926076 0.0463038 0.998927i \(-0.485256\pi\)
0.0463038 + 0.998927i \(0.485256\pi\)
\(878\) −12.6496 −0.426904
\(879\) −22.6680 −0.764572
\(880\) −0.189566 −0.00639028
\(881\) −28.3894 −0.956462 −0.478231 0.878234i \(-0.658722\pi\)
−0.478231 + 0.878234i \(0.658722\pi\)
\(882\) −15.8011 −0.532050
\(883\) 43.2360 1.45501 0.727504 0.686103i \(-0.240680\pi\)
0.727504 + 0.686103i \(0.240680\pi\)
\(884\) −19.7568 −0.664492
\(885\) 18.8664 0.634187
\(886\) −35.3294 −1.18692
\(887\) −51.4742 −1.72834 −0.864168 0.503204i \(-0.832154\pi\)
−0.864168 + 0.503204i \(0.832154\pi\)
\(888\) 0.0115862 0.000388807 0
\(889\) 48.9434 1.64151
\(890\) −10.4442 −0.350089
\(891\) −0.230600 −0.00772539
\(892\) −22.9125 −0.767169
\(893\) −6.20848 −0.207759
\(894\) 3.11945 0.104330
\(895\) 15.6866 0.524345
\(896\) −3.73115 −0.124649
\(897\) −32.9891 −1.10147
\(898\) −9.46560 −0.315871
\(899\) −3.57504 −0.119234
\(900\) −3.03386 −0.101129
\(901\) 11.4210 0.380488
\(902\) 0.394709 0.0131424
\(903\) 26.8734 0.894289
\(904\) −19.2161 −0.639118
\(905\) 23.0979 0.767801
\(906\) 5.99871 0.199294
\(907\) 2.28392 0.0758365 0.0379182 0.999281i \(-0.487927\pi\)
0.0379182 + 0.999281i \(0.487927\pi\)
\(908\) −14.4216 −0.478598
\(909\) 13.9100 0.461365
\(910\) 53.8512 1.78515
\(911\) −45.5629 −1.50956 −0.754782 0.655975i \(-0.772258\pi\)
−0.754782 + 0.655975i \(0.772258\pi\)
\(912\) 0.846820 0.0280410
\(913\) −0.0498095 −0.00164845
\(914\) −32.0612 −1.06049
\(915\) −2.24512 −0.0742215
\(916\) −23.6041 −0.779902
\(917\) −51.4438 −1.69883
\(918\) −15.4061 −0.508477
\(919\) −48.0167 −1.58392 −0.791962 0.610571i \(-0.790940\pi\)
−0.791962 + 0.610571i \(0.790940\pi\)
\(920\) 17.0828 0.563203
\(921\) 18.2987 0.602964
\(922\) 27.2979 0.899009
\(923\) 60.6769 1.99720
\(924\) 0.238084 0.00783238
\(925\) 0.0181827 0.000597845 0
\(926\) 32.4611 1.06674
\(927\) 37.7295 1.23920
\(928\) 1.05848 0.0347464
\(929\) −42.4245 −1.39190 −0.695951 0.718089i \(-0.745017\pi\)
−0.695951 + 0.718089i \(0.745017\pi\)
\(930\) −7.19539 −0.235946
\(931\) 6.92151 0.226843
\(932\) −25.4543 −0.833784
\(933\) 3.58421 0.117342
\(934\) −31.2049 −1.02106
\(935\) −0.652816 −0.0213494
\(936\) 13.0970 0.428090
\(937\) −49.6572 −1.62223 −0.811115 0.584886i \(-0.801139\pi\)
−0.811115 + 0.584886i \(0.801139\pi\)
\(938\) 54.0240 1.76394
\(939\) 17.9914 0.587126
\(940\) −15.6189 −0.509433
\(941\) −45.4562 −1.48183 −0.740915 0.671599i \(-0.765608\pi\)
−0.740915 + 0.671599i \(0.765608\pi\)
\(942\) −1.55857 −0.0507810
\(943\) −35.5692 −1.15829
\(944\) 8.85589 0.288235
\(945\) 41.9926 1.36602
\(946\) 0.640889 0.0208371
\(947\) −16.2142 −0.526892 −0.263446 0.964674i \(-0.584859\pi\)
−0.263446 + 0.964674i \(0.584859\pi\)
\(948\) 7.69169 0.249814
\(949\) 60.7372 1.97161
\(950\) 1.32895 0.0431170
\(951\) 20.5976 0.667922
\(952\) −12.8491 −0.416442
\(953\) −32.2726 −1.04541 −0.522706 0.852513i \(-0.675078\pi\)
−0.522706 + 0.852513i \(0.675078\pi\)
\(954\) −7.57111 −0.245124
\(955\) −11.7252 −0.379419
\(956\) −8.55439 −0.276669
\(957\) −0.0675415 −0.00218331
\(958\) −22.2905 −0.720174
\(959\) 12.9278 0.417460
\(960\) 2.13038 0.0687577
\(961\) −19.5924 −0.632013
\(962\) −0.0784939 −0.00253074
\(963\) −20.8663 −0.672408
\(964\) 25.2877 0.814463
\(965\) 6.79179 0.218636
\(966\) −21.4549 −0.690301
\(967\) 17.3653 0.558431 0.279216 0.960228i \(-0.409926\pi\)
0.279216 + 0.960228i \(0.409926\pi\)
\(968\) −10.9943 −0.353371
\(969\) 2.91622 0.0936826
\(970\) −1.71770 −0.0551519
\(971\) −3.71071 −0.119082 −0.0595412 0.998226i \(-0.518964\pi\)
−0.0595412 + 0.998226i \(0.518964\pi\)
\(972\) 16.0125 0.513602
\(973\) 15.1626 0.486091
\(974\) 4.50007 0.144192
\(975\) −6.45636 −0.206769
\(976\) −1.05386 −0.0337333
\(977\) −30.3366 −0.970554 −0.485277 0.874360i \(-0.661281\pi\)
−0.485277 + 0.874360i \(0.661281\pi\)
\(978\) −8.14525 −0.260456
\(979\) 0.312826 0.00999797
\(980\) 17.4127 0.556229
\(981\) −10.2342 −0.326752
\(982\) −39.6320 −1.26471
\(983\) 0.696013 0.0221994 0.0110997 0.999938i \(-0.496467\pi\)
0.0110997 + 0.999938i \(0.496467\pi\)
\(984\) −4.43581 −0.141408
\(985\) −44.3261 −1.41235
\(986\) 3.64513 0.116085
\(987\) 19.6164 0.624397
\(988\) −5.73702 −0.182519
\(989\) −57.7538 −1.83646
\(990\) 0.432760 0.0137540
\(991\) 8.15308 0.258991 0.129496 0.991580i \(-0.458664\pi\)
0.129496 + 0.991580i \(0.458664\pi\)
\(992\) −3.37751 −0.107236
\(993\) 8.32131 0.264069
\(994\) 39.4621 1.25166
\(995\) 28.6710 0.908932
\(996\) 0.559768 0.0177369
\(997\) −22.6110 −0.716098 −0.358049 0.933703i \(-0.616558\pi\)
−0.358049 + 0.933703i \(0.616558\pi\)
\(998\) 17.7075 0.560521
\(999\) −0.0612086 −0.00193655
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 \(a_p\))