Properties

Label 8002.2.a.e.1.19
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.65847 q^{3} +1.00000 q^{4} -0.802626 q^{5} +1.65847 q^{6} -0.0977002 q^{7} -1.00000 q^{8} -0.249472 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.65847 q^{3} +1.00000 q^{4} -0.802626 q^{5} +1.65847 q^{6} -0.0977002 q^{7} -1.00000 q^{8} -0.249472 q^{9} +0.802626 q^{10} -4.28508 q^{11} -1.65847 q^{12} -5.88772 q^{13} +0.0977002 q^{14} +1.33113 q^{15} +1.00000 q^{16} +4.10249 q^{17} +0.249472 q^{18} +4.88102 q^{19} -0.802626 q^{20} +0.162033 q^{21} +4.28508 q^{22} -7.15578 q^{23} +1.65847 q^{24} -4.35579 q^{25} +5.88772 q^{26} +5.38916 q^{27} -0.0977002 q^{28} +6.43182 q^{29} -1.33113 q^{30} -4.30233 q^{31} -1.00000 q^{32} +7.10668 q^{33} -4.10249 q^{34} +0.0784167 q^{35} -0.249472 q^{36} -0.738173 q^{37} -4.88102 q^{38} +9.76462 q^{39} +0.802626 q^{40} -9.15637 q^{41} -0.162033 q^{42} -3.11395 q^{43} -4.28508 q^{44} +0.200233 q^{45} +7.15578 q^{46} +7.49518 q^{47} -1.65847 q^{48} -6.99045 q^{49} +4.35579 q^{50} -6.80386 q^{51} -5.88772 q^{52} -8.00141 q^{53} -5.38916 q^{54} +3.43932 q^{55} +0.0977002 q^{56} -8.09504 q^{57} -6.43182 q^{58} -8.80842 q^{59} +1.33113 q^{60} -2.70949 q^{61} +4.30233 q^{62} +0.0243734 q^{63} +1.00000 q^{64} +4.72564 q^{65} -7.10668 q^{66} -10.2707 q^{67} +4.10249 q^{68} +11.8677 q^{69} -0.0784167 q^{70} -10.3343 q^{71} +0.249472 q^{72} +0.0428290 q^{73} +0.738173 q^{74} +7.22396 q^{75} +4.88102 q^{76} +0.418653 q^{77} -9.76462 q^{78} +3.97141 q^{79} -0.802626 q^{80} -8.18935 q^{81} +9.15637 q^{82} +6.86346 q^{83} +0.162033 q^{84} -3.29276 q^{85} +3.11395 q^{86} -10.6670 q^{87} +4.28508 q^{88} -5.35914 q^{89} -0.200233 q^{90} +0.575231 q^{91} -7.15578 q^{92} +7.13529 q^{93} -7.49518 q^{94} -3.91764 q^{95} +1.65847 q^{96} -4.07812 q^{97} +6.99045 q^{98} +1.06901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −1.65847 −0.957519 −0.478760 0.877946i \(-0.658913\pi\)
−0.478760 + 0.877946i \(0.658913\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.802626 −0.358945 −0.179473 0.983763i \(-0.557439\pi\)
−0.179473 + 0.983763i \(0.557439\pi\)
\(6\) 1.65847 0.677068
\(7\) −0.0977002 −0.0369272 −0.0184636 0.999830i \(-0.505877\pi\)
−0.0184636 + 0.999830i \(0.505877\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.249472 −0.0831572
\(10\) 0.802626 0.253813
\(11\) −4.28508 −1.29200 −0.646000 0.763338i \(-0.723559\pi\)
−0.646000 + 0.763338i \(0.723559\pi\)
\(12\) −1.65847 −0.478760
\(13\) −5.88772 −1.63296 −0.816480 0.577374i \(-0.804078\pi\)
−0.816480 + 0.577374i \(0.804078\pi\)
\(14\) 0.0977002 0.0261115
\(15\) 1.33113 0.343697
\(16\) 1.00000 0.250000
\(17\) 4.10249 0.994999 0.497500 0.867464i \(-0.334252\pi\)
0.497500 + 0.867464i \(0.334252\pi\)
\(18\) 0.249472 0.0588011
\(19\) 4.88102 1.11978 0.559892 0.828566i \(-0.310843\pi\)
0.559892 + 0.828566i \(0.310843\pi\)
\(20\) −0.802626 −0.179473
\(21\) 0.162033 0.0353585
\(22\) 4.28508 0.913582
\(23\) −7.15578 −1.49208 −0.746042 0.665899i \(-0.768048\pi\)
−0.746042 + 0.665899i \(0.768048\pi\)
\(24\) 1.65847 0.338534
\(25\) −4.35579 −0.871158
\(26\) 5.88772 1.15468
\(27\) 5.38916 1.03714
\(28\) −0.0977002 −0.0184636
\(29\) 6.43182 1.19436 0.597179 0.802108i \(-0.296288\pi\)
0.597179 + 0.802108i \(0.296288\pi\)
\(30\) −1.33113 −0.243031
\(31\) −4.30233 −0.772721 −0.386360 0.922348i \(-0.626268\pi\)
−0.386360 + 0.922348i \(0.626268\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.10668 1.23711
\(34\) −4.10249 −0.703571
\(35\) 0.0784167 0.0132548
\(36\) −0.249472 −0.0415786
\(37\) −0.738173 −0.121355 −0.0606775 0.998157i \(-0.519326\pi\)
−0.0606775 + 0.998157i \(0.519326\pi\)
\(38\) −4.88102 −0.791806
\(39\) 9.76462 1.56359
\(40\) 0.802626 0.126906
\(41\) −9.15637 −1.42999 −0.714993 0.699132i \(-0.753570\pi\)
−0.714993 + 0.699132i \(0.753570\pi\)
\(42\) −0.162033 −0.0250022
\(43\) −3.11395 −0.474873 −0.237437 0.971403i \(-0.576307\pi\)
−0.237437 + 0.971403i \(0.576307\pi\)
\(44\) −4.28508 −0.646000
\(45\) 0.200233 0.0298489
\(46\) 7.15578 1.05506
\(47\) 7.49518 1.09328 0.546642 0.837366i \(-0.315906\pi\)
0.546642 + 0.837366i \(0.315906\pi\)
\(48\) −1.65847 −0.239380
\(49\) −6.99045 −0.998636
\(50\) 4.35579 0.616002
\(51\) −6.80386 −0.952731
\(52\) −5.88772 −0.816480
\(53\) −8.00141 −1.09908 −0.549539 0.835468i \(-0.685197\pi\)
−0.549539 + 0.835468i \(0.685197\pi\)
\(54\) −5.38916 −0.733371
\(55\) 3.43932 0.463757
\(56\) 0.0977002 0.0130557
\(57\) −8.09504 −1.07221
\(58\) −6.43182 −0.844539
\(59\) −8.80842 −1.14676 −0.573379 0.819290i \(-0.694368\pi\)
−0.573379 + 0.819290i \(0.694368\pi\)
\(60\) 1.33113 0.171849
\(61\) −2.70949 −0.346915 −0.173458 0.984841i \(-0.555494\pi\)
−0.173458 + 0.984841i \(0.555494\pi\)
\(62\) 4.30233 0.546396
\(63\) 0.0243734 0.00307076
\(64\) 1.00000 0.125000
\(65\) 4.72564 0.586143
\(66\) −7.10668 −0.874772
\(67\) −10.2707 −1.25476 −0.627380 0.778713i \(-0.715873\pi\)
−0.627380 + 0.778713i \(0.715873\pi\)
\(68\) 4.10249 0.497500
\(69\) 11.8677 1.42870
\(70\) −0.0784167 −0.00937259
\(71\) −10.3343 −1.22646 −0.613229 0.789905i \(-0.710130\pi\)
−0.613229 + 0.789905i \(0.710130\pi\)
\(72\) 0.249472 0.0294005
\(73\) 0.0428290 0.00501276 0.00250638 0.999997i \(-0.499202\pi\)
0.00250638 + 0.999997i \(0.499202\pi\)
\(74\) 0.738173 0.0858109
\(75\) 7.22396 0.834151
\(76\) 4.88102 0.559892
\(77\) 0.418653 0.0477099
\(78\) −9.76462 −1.10563
\(79\) 3.97141 0.446818 0.223409 0.974725i \(-0.428281\pi\)
0.223409 + 0.974725i \(0.428281\pi\)
\(80\) −0.802626 −0.0897363
\(81\) −8.18935 −0.909928
\(82\) 9.15637 1.01115
\(83\) 6.86346 0.753362 0.376681 0.926343i \(-0.377065\pi\)
0.376681 + 0.926343i \(0.377065\pi\)
\(84\) 0.162033 0.0176792
\(85\) −3.29276 −0.357150
\(86\) 3.11395 0.335786
\(87\) −10.6670 −1.14362
\(88\) 4.28508 0.456791
\(89\) −5.35914 −0.568067 −0.284034 0.958814i \(-0.591673\pi\)
−0.284034 + 0.958814i \(0.591673\pi\)
\(90\) −0.200233 −0.0211064
\(91\) 0.575231 0.0603006
\(92\) −7.15578 −0.746042
\(93\) 7.13529 0.739895
\(94\) −7.49518 −0.773069
\(95\) −3.91764 −0.401941
\(96\) 1.65847 0.169267
\(97\) −4.07812 −0.414071 −0.207035 0.978333i \(-0.566381\pi\)
−0.207035 + 0.978333i \(0.566381\pi\)
\(98\) 6.99045 0.706143
\(99\) 1.06901 0.107439
\(100\) −4.35579 −0.435579
\(101\) −5.49159 −0.546434 −0.273217 0.961952i \(-0.588088\pi\)
−0.273217 + 0.961952i \(0.588088\pi\)
\(102\) 6.80386 0.673682
\(103\) −17.9063 −1.76436 −0.882180 0.470913i \(-0.843925\pi\)
−0.882180 + 0.470913i \(0.843925\pi\)
\(104\) 5.88772 0.577339
\(105\) −0.130052 −0.0126918
\(106\) 8.00141 0.777166
\(107\) −11.2606 −1.08860 −0.544301 0.838890i \(-0.683205\pi\)
−0.544301 + 0.838890i \(0.683205\pi\)
\(108\) 5.38916 0.518572
\(109\) −6.84529 −0.655660 −0.327830 0.944737i \(-0.606317\pi\)
−0.327830 + 0.944737i \(0.606317\pi\)
\(110\) −3.43932 −0.327926
\(111\) 1.22424 0.116200
\(112\) −0.0977002 −0.00923180
\(113\) 10.7483 1.01112 0.505558 0.862792i \(-0.331286\pi\)
0.505558 + 0.862792i \(0.331286\pi\)
\(114\) 8.09504 0.758170
\(115\) 5.74342 0.535577
\(116\) 6.43182 0.597179
\(117\) 1.46882 0.135792
\(118\) 8.80842 0.810881
\(119\) −0.400814 −0.0367425
\(120\) −1.33113 −0.121515
\(121\) 7.36190 0.669263
\(122\) 2.70949 0.245306
\(123\) 15.1856 1.36924
\(124\) −4.30233 −0.386360
\(125\) 7.50920 0.671644
\(126\) −0.0243734 −0.00217136
\(127\) −7.85976 −0.697441 −0.348721 0.937227i \(-0.613384\pi\)
−0.348721 + 0.937227i \(0.613384\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.16440 0.454700
\(130\) −4.72564 −0.414466
\(131\) −20.3039 −1.77396 −0.886981 0.461806i \(-0.847202\pi\)
−0.886981 + 0.461806i \(0.847202\pi\)
\(132\) 7.10668 0.618557
\(133\) −0.476877 −0.0413505
\(134\) 10.2707 0.887250
\(135\) −4.32548 −0.372278
\(136\) −4.10249 −0.351785
\(137\) 11.7342 1.00252 0.501262 0.865296i \(-0.332869\pi\)
0.501262 + 0.865296i \(0.332869\pi\)
\(138\) −11.8677 −1.01024
\(139\) 3.26959 0.277323 0.138661 0.990340i \(-0.455720\pi\)
0.138661 + 0.990340i \(0.455720\pi\)
\(140\) 0.0784167 0.00662742
\(141\) −12.4305 −1.04684
\(142\) 10.3343 0.867237
\(143\) 25.2293 2.10978
\(144\) −0.249472 −0.0207893
\(145\) −5.16235 −0.428710
\(146\) −0.0428290 −0.00354455
\(147\) 11.5935 0.956213
\(148\) −0.738173 −0.0606775
\(149\) 4.82312 0.395126 0.197563 0.980290i \(-0.436697\pi\)
0.197563 + 0.980290i \(0.436697\pi\)
\(150\) −7.22396 −0.589834
\(151\) 12.8253 1.04371 0.521854 0.853035i \(-0.325241\pi\)
0.521854 + 0.853035i \(0.325241\pi\)
\(152\) −4.88102 −0.395903
\(153\) −1.02345 −0.0827414
\(154\) −0.418653 −0.0337360
\(155\) 3.45316 0.277365
\(156\) 9.76462 0.781795
\(157\) −0.792102 −0.0632166 −0.0316083 0.999500i \(-0.510063\pi\)
−0.0316083 + 0.999500i \(0.510063\pi\)
\(158\) −3.97141 −0.315948
\(159\) 13.2701 1.05239
\(160\) 0.802626 0.0634532
\(161\) 0.699121 0.0550985
\(162\) 8.18935 0.643416
\(163\) 11.2416 0.880513 0.440256 0.897872i \(-0.354888\pi\)
0.440256 + 0.897872i \(0.354888\pi\)
\(164\) −9.15637 −0.714993
\(165\) −5.70401 −0.444056
\(166\) −6.86346 −0.532708
\(167\) −11.1276 −0.861082 −0.430541 0.902571i \(-0.641677\pi\)
−0.430541 + 0.902571i \(0.641677\pi\)
\(168\) −0.162033 −0.0125011
\(169\) 21.6653 1.66656
\(170\) 3.29276 0.252543
\(171\) −1.21768 −0.0931181
\(172\) −3.11395 −0.237437
\(173\) −3.93491 −0.299166 −0.149583 0.988749i \(-0.547793\pi\)
−0.149583 + 0.988749i \(0.547793\pi\)
\(174\) 10.6670 0.808662
\(175\) 0.425562 0.0321694
\(176\) −4.28508 −0.323000
\(177\) 14.6085 1.09804
\(178\) 5.35914 0.401684
\(179\) −9.10842 −0.680795 −0.340398 0.940282i \(-0.610562\pi\)
−0.340398 + 0.940282i \(0.610562\pi\)
\(180\) 0.200233 0.0149245
\(181\) −9.30241 −0.691443 −0.345721 0.938337i \(-0.612366\pi\)
−0.345721 + 0.938337i \(0.612366\pi\)
\(182\) −0.575231 −0.0426390
\(183\) 4.49362 0.332178
\(184\) 7.15578 0.527531
\(185\) 0.592477 0.0435598
\(186\) −7.13529 −0.523185
\(187\) −17.5795 −1.28554
\(188\) 7.49518 0.546642
\(189\) −0.526522 −0.0382988
\(190\) 3.91764 0.284215
\(191\) 13.3414 0.965349 0.482674 0.875800i \(-0.339665\pi\)
0.482674 + 0.875800i \(0.339665\pi\)
\(192\) −1.65847 −0.119690
\(193\) 4.90829 0.353307 0.176653 0.984273i \(-0.443473\pi\)
0.176653 + 0.984273i \(0.443473\pi\)
\(194\) 4.07812 0.292792
\(195\) −7.83734 −0.561244
\(196\) −6.99045 −0.499318
\(197\) 1.64123 0.116933 0.0584663 0.998289i \(-0.481379\pi\)
0.0584663 + 0.998289i \(0.481379\pi\)
\(198\) −1.06901 −0.0759710
\(199\) −4.52532 −0.320791 −0.160396 0.987053i \(-0.551277\pi\)
−0.160396 + 0.987053i \(0.551277\pi\)
\(200\) 4.35579 0.308001
\(201\) 17.0336 1.20146
\(202\) 5.49159 0.386387
\(203\) −0.628390 −0.0441043
\(204\) −6.80386 −0.476365
\(205\) 7.34915 0.513287
\(206\) 17.9063 1.24759
\(207\) 1.78517 0.124078
\(208\) −5.88772 −0.408240
\(209\) −20.9156 −1.44676
\(210\) 0.130052 0.00897444
\(211\) −0.227580 −0.0156672 −0.00783361 0.999969i \(-0.502494\pi\)
−0.00783361 + 0.999969i \(0.502494\pi\)
\(212\) −8.00141 −0.549539
\(213\) 17.1392 1.17436
\(214\) 11.2606 0.769758
\(215\) 2.49934 0.170454
\(216\) −5.38916 −0.366686
\(217\) 0.420338 0.0285344
\(218\) 6.84529 0.463622
\(219\) −0.0710307 −0.00479981
\(220\) 3.43932 0.231879
\(221\) −24.1543 −1.62479
\(222\) −1.22424 −0.0821656
\(223\) 13.0588 0.874483 0.437241 0.899344i \(-0.355956\pi\)
0.437241 + 0.899344i \(0.355956\pi\)
\(224\) 0.0977002 0.00652787
\(225\) 1.08665 0.0724431
\(226\) −10.7483 −0.714968
\(227\) 12.3681 0.820898 0.410449 0.911884i \(-0.365372\pi\)
0.410449 + 0.911884i \(0.365372\pi\)
\(228\) −8.09504 −0.536107
\(229\) −27.7355 −1.83281 −0.916406 0.400251i \(-0.868923\pi\)
−0.916406 + 0.400251i \(0.868923\pi\)
\(230\) −5.74342 −0.378710
\(231\) −0.694324 −0.0456832
\(232\) −6.43182 −0.422270
\(233\) 16.0290 1.05010 0.525048 0.851073i \(-0.324047\pi\)
0.525048 + 0.851073i \(0.324047\pi\)
\(234\) −1.46882 −0.0960198
\(235\) −6.01583 −0.392429
\(236\) −8.80842 −0.573379
\(237\) −6.58646 −0.427837
\(238\) 0.400814 0.0259809
\(239\) 19.1279 1.23728 0.618640 0.785674i \(-0.287684\pi\)
0.618640 + 0.785674i \(0.287684\pi\)
\(240\) 1.33113 0.0859243
\(241\) −26.5054 −1.70737 −0.853683 0.520794i \(-0.825636\pi\)
−0.853683 + 0.520794i \(0.825636\pi\)
\(242\) −7.36190 −0.473241
\(243\) −2.58567 −0.165871
\(244\) −2.70949 −0.173458
\(245\) 5.61072 0.358456
\(246\) −15.1856 −0.968198
\(247\) −28.7381 −1.82856
\(248\) 4.30233 0.273198
\(249\) −11.3828 −0.721359
\(250\) −7.50920 −0.474924
\(251\) 10.3539 0.653535 0.326767 0.945105i \(-0.394041\pi\)
0.326767 + 0.945105i \(0.394041\pi\)
\(252\) 0.0243734 0.00153538
\(253\) 30.6631 1.92777
\(254\) 7.85976 0.493165
\(255\) 5.46096 0.341978
\(256\) 1.00000 0.0625000
\(257\) 1.73524 0.108242 0.0541208 0.998534i \(-0.482764\pi\)
0.0541208 + 0.998534i \(0.482764\pi\)
\(258\) −5.16440 −0.321521
\(259\) 0.0721197 0.00448130
\(260\) 4.72564 0.293072
\(261\) −1.60456 −0.0993196
\(262\) 20.3039 1.25438
\(263\) 8.81690 0.543673 0.271837 0.962343i \(-0.412369\pi\)
0.271837 + 0.962343i \(0.412369\pi\)
\(264\) −7.10668 −0.437386
\(265\) 6.42214 0.394509
\(266\) 0.476877 0.0292392
\(267\) 8.88798 0.543935
\(268\) −10.2707 −0.627380
\(269\) 3.26925 0.199330 0.0996649 0.995021i \(-0.468223\pi\)
0.0996649 + 0.995021i \(0.468223\pi\)
\(270\) 4.32548 0.263240
\(271\) −23.0568 −1.40060 −0.700301 0.713848i \(-0.746951\pi\)
−0.700301 + 0.713848i \(0.746951\pi\)
\(272\) 4.10249 0.248750
\(273\) −0.954005 −0.0577390
\(274\) −11.7342 −0.708891
\(275\) 18.6649 1.12554
\(276\) 11.8677 0.714349
\(277\) −20.6326 −1.23969 −0.619846 0.784723i \(-0.712805\pi\)
−0.619846 + 0.784723i \(0.712805\pi\)
\(278\) −3.26959 −0.196097
\(279\) 1.07331 0.0642573
\(280\) −0.0784167 −0.00468630
\(281\) −28.5470 −1.70297 −0.851486 0.524377i \(-0.824298\pi\)
−0.851486 + 0.524377i \(0.824298\pi\)
\(282\) 12.4305 0.740228
\(283\) 12.6676 0.753012 0.376506 0.926414i \(-0.377126\pi\)
0.376506 + 0.926414i \(0.377126\pi\)
\(284\) −10.3343 −0.613229
\(285\) 6.49729 0.384866
\(286\) −25.2293 −1.49184
\(287\) 0.894579 0.0528053
\(288\) 0.249472 0.0147003
\(289\) −0.169596 −0.00997623
\(290\) 5.16235 0.303143
\(291\) 6.76345 0.396480
\(292\) 0.0428290 0.00250638
\(293\) −16.3219 −0.953533 −0.476767 0.879030i \(-0.658191\pi\)
−0.476767 + 0.879030i \(0.658191\pi\)
\(294\) −11.5935 −0.676145
\(295\) 7.06987 0.411624
\(296\) 0.738173 0.0429055
\(297\) −23.0930 −1.33999
\(298\) −4.82312 −0.279396
\(299\) 42.1312 2.43651
\(300\) 7.22396 0.417075
\(301\) 0.304234 0.0175357
\(302\) −12.8253 −0.738013
\(303\) 9.10765 0.523221
\(304\) 4.88102 0.279946
\(305\) 2.17471 0.124524
\(306\) 1.02345 0.0585070
\(307\) 11.0823 0.632502 0.316251 0.948676i \(-0.397576\pi\)
0.316251 + 0.948676i \(0.397576\pi\)
\(308\) 0.418653 0.0238550
\(309\) 29.6971 1.68941
\(310\) −3.45316 −0.196126
\(311\) 29.0299 1.64614 0.823068 0.567943i \(-0.192260\pi\)
0.823068 + 0.567943i \(0.192260\pi\)
\(312\) −9.76462 −0.552813
\(313\) −6.07292 −0.343262 −0.171631 0.985161i \(-0.554904\pi\)
−0.171631 + 0.985161i \(0.554904\pi\)
\(314\) 0.792102 0.0447009
\(315\) −0.0195628 −0.00110224
\(316\) 3.97141 0.223409
\(317\) −9.81771 −0.551417 −0.275709 0.961241i \(-0.588912\pi\)
−0.275709 + 0.961241i \(0.588912\pi\)
\(318\) −13.2701 −0.744151
\(319\) −27.5608 −1.54311
\(320\) −0.802626 −0.0448682
\(321\) 18.6754 1.04236
\(322\) −0.699121 −0.0389605
\(323\) 20.0243 1.11418
\(324\) −8.18935 −0.454964
\(325\) 25.6457 1.42257
\(326\) −11.2416 −0.622617
\(327\) 11.3527 0.627807
\(328\) 9.15637 0.505576
\(329\) −0.732281 −0.0403719
\(330\) 5.70401 0.313995
\(331\) −31.5144 −1.73219 −0.866094 0.499882i \(-0.833377\pi\)
−0.866094 + 0.499882i \(0.833377\pi\)
\(332\) 6.86346 0.376681
\(333\) 0.184153 0.0100915
\(334\) 11.1276 0.608877
\(335\) 8.24350 0.450391
\(336\) 0.162033 0.00883962
\(337\) 2.34590 0.127790 0.0638948 0.997957i \(-0.479648\pi\)
0.0638948 + 0.997957i \(0.479648\pi\)
\(338\) −21.6653 −1.17843
\(339\) −17.8258 −0.968164
\(340\) −3.29276 −0.178575
\(341\) 18.4358 0.998355
\(342\) 1.21768 0.0658444
\(343\) 1.36687 0.0738040
\(344\) 3.11395 0.167893
\(345\) −9.52530 −0.512825
\(346\) 3.93491 0.211542
\(347\) −16.3252 −0.876380 −0.438190 0.898882i \(-0.644380\pi\)
−0.438190 + 0.898882i \(0.644380\pi\)
\(348\) −10.6670 −0.571811
\(349\) 33.6684 1.80223 0.901114 0.433581i \(-0.142750\pi\)
0.901114 + 0.433581i \(0.142750\pi\)
\(350\) −0.425562 −0.0227472
\(351\) −31.7299 −1.69361
\(352\) 4.28508 0.228395
\(353\) −12.2203 −0.650419 −0.325209 0.945642i \(-0.605435\pi\)
−0.325209 + 0.945642i \(0.605435\pi\)
\(354\) −14.6085 −0.776434
\(355\) 8.29460 0.440232
\(356\) −5.35914 −0.284034
\(357\) 0.664738 0.0351817
\(358\) 9.10842 0.481395
\(359\) −0.786973 −0.0415348 −0.0207674 0.999784i \(-0.506611\pi\)
−0.0207674 + 0.999784i \(0.506611\pi\)
\(360\) −0.200233 −0.0105532
\(361\) 4.82438 0.253915
\(362\) 9.30241 0.488924
\(363\) −12.2095 −0.640833
\(364\) 0.575231 0.0301503
\(365\) −0.0343757 −0.00179931
\(366\) −4.49362 −0.234885
\(367\) 15.6163 0.815164 0.407582 0.913169i \(-0.366372\pi\)
0.407582 + 0.913169i \(0.366372\pi\)
\(368\) −7.15578 −0.373021
\(369\) 2.28426 0.118914
\(370\) −0.592477 −0.0308014
\(371\) 0.781739 0.0405859
\(372\) 7.13529 0.369947
\(373\) 2.46615 0.127692 0.0638461 0.997960i \(-0.479663\pi\)
0.0638461 + 0.997960i \(0.479663\pi\)
\(374\) 17.5795 0.909013
\(375\) −12.4538 −0.643112
\(376\) −7.49518 −0.386535
\(377\) −37.8688 −1.95034
\(378\) 0.526522 0.0270813
\(379\) −2.86090 −0.146954 −0.0734772 0.997297i \(-0.523410\pi\)
−0.0734772 + 0.997297i \(0.523410\pi\)
\(380\) −3.91764 −0.200971
\(381\) 13.0352 0.667813
\(382\) −13.3414 −0.682605
\(383\) 27.7756 1.41927 0.709634 0.704570i \(-0.248860\pi\)
0.709634 + 0.704570i \(0.248860\pi\)
\(384\) 1.65847 0.0846335
\(385\) −0.336022 −0.0171253
\(386\) −4.90829 −0.249826
\(387\) 0.776843 0.0394891
\(388\) −4.07812 −0.207035
\(389\) −19.4925 −0.988311 −0.494156 0.869374i \(-0.664523\pi\)
−0.494156 + 0.869374i \(0.664523\pi\)
\(390\) 7.83734 0.396859
\(391\) −29.3565 −1.48462
\(392\) 6.99045 0.353071
\(393\) 33.6735 1.69860
\(394\) −1.64123 −0.0826838
\(395\) −3.18755 −0.160383
\(396\) 1.06901 0.0537196
\(397\) −5.27141 −0.264564 −0.132282 0.991212i \(-0.542231\pi\)
−0.132282 + 0.991212i \(0.542231\pi\)
\(398\) 4.52532 0.226834
\(399\) 0.790887 0.0395939
\(400\) −4.35579 −0.217790
\(401\) 17.5397 0.875889 0.437944 0.899002i \(-0.355707\pi\)
0.437944 + 0.899002i \(0.355707\pi\)
\(402\) −17.0336 −0.849559
\(403\) 25.3309 1.26182
\(404\) −5.49159 −0.273217
\(405\) 6.57299 0.326614
\(406\) 0.628390 0.0311865
\(407\) 3.16313 0.156791
\(408\) 6.80386 0.336841
\(409\) −19.6791 −0.973067 −0.486533 0.873662i \(-0.661739\pi\)
−0.486533 + 0.873662i \(0.661739\pi\)
\(410\) −7.34915 −0.362948
\(411\) −19.4609 −0.959935
\(412\) −17.9063 −0.882180
\(413\) 0.860584 0.0423466
\(414\) −1.78517 −0.0877361
\(415\) −5.50879 −0.270416
\(416\) 5.88772 0.288669
\(417\) −5.42252 −0.265542
\(418\) 20.9156 1.02301
\(419\) 39.5113 1.93025 0.965126 0.261786i \(-0.0843116\pi\)
0.965126 + 0.261786i \(0.0843116\pi\)
\(420\) −0.130052 −0.00634588
\(421\) −6.83947 −0.333335 −0.166668 0.986013i \(-0.553301\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(422\) 0.227580 0.0110784
\(423\) −1.86984 −0.0909146
\(424\) 8.00141 0.388583
\(425\) −17.8696 −0.866802
\(426\) −17.1392 −0.830396
\(427\) 0.264718 0.0128106
\(428\) −11.2606 −0.544301
\(429\) −41.8422 −2.02016
\(430\) −2.49934 −0.120529
\(431\) −15.8031 −0.761210 −0.380605 0.924738i \(-0.624284\pi\)
−0.380605 + 0.924738i \(0.624284\pi\)
\(432\) 5.38916 0.259286
\(433\) −22.3223 −1.07274 −0.536370 0.843983i \(-0.680205\pi\)
−0.536370 + 0.843983i \(0.680205\pi\)
\(434\) −0.420338 −0.0201769
\(435\) 8.56160 0.410498
\(436\) −6.84529 −0.327830
\(437\) −34.9275 −1.67081
\(438\) 0.0710307 0.00339398
\(439\) −7.48827 −0.357396 −0.178698 0.983904i \(-0.557188\pi\)
−0.178698 + 0.983904i \(0.557188\pi\)
\(440\) −3.43932 −0.163963
\(441\) 1.74392 0.0830439
\(442\) 24.1543 1.14890
\(443\) −8.30280 −0.394478 −0.197239 0.980355i \(-0.563197\pi\)
−0.197239 + 0.980355i \(0.563197\pi\)
\(444\) 1.22424 0.0580998
\(445\) 4.30138 0.203905
\(446\) −13.0588 −0.618353
\(447\) −7.99901 −0.378340
\(448\) −0.0977002 −0.00461590
\(449\) 22.7332 1.07285 0.536423 0.843949i \(-0.319775\pi\)
0.536423 + 0.843949i \(0.319775\pi\)
\(450\) −1.08665 −0.0512250
\(451\) 39.2358 1.84754
\(452\) 10.7483 0.505558
\(453\) −21.2704 −0.999371
\(454\) −12.3681 −0.580462
\(455\) −0.461696 −0.0216446
\(456\) 8.09504 0.379085
\(457\) 15.6497 0.732064 0.366032 0.930602i \(-0.380716\pi\)
0.366032 + 0.930602i \(0.380716\pi\)
\(458\) 27.7355 1.29599
\(459\) 22.1089 1.03196
\(460\) 5.74342 0.267788
\(461\) −21.2303 −0.988792 −0.494396 0.869237i \(-0.664611\pi\)
−0.494396 + 0.869237i \(0.664611\pi\)
\(462\) 0.694324 0.0323029
\(463\) 26.7309 1.24229 0.621145 0.783696i \(-0.286668\pi\)
0.621145 + 0.783696i \(0.286668\pi\)
\(464\) 6.43182 0.298590
\(465\) −5.72697 −0.265582
\(466\) −16.0290 −0.742530
\(467\) 9.39671 0.434828 0.217414 0.976079i \(-0.430238\pi\)
0.217414 + 0.976079i \(0.430238\pi\)
\(468\) 1.46882 0.0678962
\(469\) 1.00345 0.0463348
\(470\) 6.01583 0.277490
\(471\) 1.31368 0.0605311
\(472\) 8.80842 0.405440
\(473\) 13.3435 0.613536
\(474\) 6.58646 0.302526
\(475\) −21.2607 −0.975509
\(476\) −0.400814 −0.0183713
\(477\) 1.99613 0.0913963
\(478\) −19.1279 −0.874890
\(479\) −10.0603 −0.459667 −0.229833 0.973230i \(-0.573818\pi\)
−0.229833 + 0.973230i \(0.573818\pi\)
\(480\) −1.33113 −0.0607576
\(481\) 4.34616 0.198168
\(482\) 26.5054 1.20729
\(483\) −1.15947 −0.0527578
\(484\) 7.36190 0.334632
\(485\) 3.27321 0.148629
\(486\) 2.58567 0.117288
\(487\) −11.1698 −0.506150 −0.253075 0.967447i \(-0.581442\pi\)
−0.253075 + 0.967447i \(0.581442\pi\)
\(488\) 2.70949 0.122653
\(489\) −18.6439 −0.843108
\(490\) −5.61072 −0.253467
\(491\) 16.0088 0.722467 0.361233 0.932475i \(-0.382356\pi\)
0.361233 + 0.932475i \(0.382356\pi\)
\(492\) 15.1856 0.684619
\(493\) 26.3865 1.18839
\(494\) 28.7381 1.29299
\(495\) −0.858012 −0.0385648
\(496\) −4.30233 −0.193180
\(497\) 1.00967 0.0452897
\(498\) 11.3828 0.510078
\(499\) 7.49915 0.335708 0.167854 0.985812i \(-0.446316\pi\)
0.167854 + 0.985812i \(0.446316\pi\)
\(500\) 7.50920 0.335822
\(501\) 18.4549 0.824503
\(502\) −10.3539 −0.462119
\(503\) 8.50531 0.379233 0.189616 0.981858i \(-0.439276\pi\)
0.189616 + 0.981858i \(0.439276\pi\)
\(504\) −0.0243734 −0.00108568
\(505\) 4.40770 0.196140
\(506\) −30.6631 −1.36314
\(507\) −35.9312 −1.59576
\(508\) −7.85976 −0.348721
\(509\) −14.9416 −0.662273 −0.331137 0.943583i \(-0.607432\pi\)
−0.331137 + 0.943583i \(0.607432\pi\)
\(510\) −5.46096 −0.241815
\(511\) −0.00418440 −0.000185107 0
\(512\) −1.00000 −0.0441942
\(513\) 26.3046 1.16138
\(514\) −1.73524 −0.0765383
\(515\) 14.3721 0.633309
\(516\) 5.16440 0.227350
\(517\) −32.1174 −1.41252
\(518\) −0.0721197 −0.00316876
\(519\) 6.52594 0.286457
\(520\) −4.72564 −0.207233
\(521\) 18.1638 0.795768 0.397884 0.917436i \(-0.369745\pi\)
0.397884 + 0.917436i \(0.369745\pi\)
\(522\) 1.60456 0.0702296
\(523\) −3.89656 −0.170385 −0.0851924 0.996365i \(-0.527150\pi\)
−0.0851924 + 0.996365i \(0.527150\pi\)
\(524\) −20.3039 −0.886981
\(525\) −0.705782 −0.0308028
\(526\) −8.81690 −0.384435
\(527\) −17.6502 −0.768857
\(528\) 7.10668 0.309279
\(529\) 28.2052 1.22631
\(530\) −6.42214 −0.278960
\(531\) 2.19745 0.0953613
\(532\) −0.476877 −0.0206752
\(533\) 53.9102 2.33511
\(534\) −8.88798 −0.384620
\(535\) 9.03805 0.390749
\(536\) 10.2707 0.443625
\(537\) 15.1061 0.651875
\(538\) −3.26925 −0.140947
\(539\) 29.9546 1.29024
\(540\) −4.32548 −0.186139
\(541\) 29.6054 1.27283 0.636417 0.771345i \(-0.280416\pi\)
0.636417 + 0.771345i \(0.280416\pi\)
\(542\) 23.0568 0.990375
\(543\) 15.4278 0.662070
\(544\) −4.10249 −0.175893
\(545\) 5.49421 0.235346
\(546\) 0.954005 0.0408276
\(547\) 27.6682 1.18301 0.591503 0.806303i \(-0.298535\pi\)
0.591503 + 0.806303i \(0.298535\pi\)
\(548\) 11.7342 0.501262
\(549\) 0.675942 0.0288485
\(550\) −18.6649 −0.795874
\(551\) 31.3939 1.33742
\(552\) −11.8677 −0.505121
\(553\) −0.388007 −0.0164997
\(554\) 20.6326 0.876595
\(555\) −0.982607 −0.0417093
\(556\) 3.26959 0.138661
\(557\) 30.9459 1.31122 0.655610 0.755100i \(-0.272412\pi\)
0.655610 + 0.755100i \(0.272412\pi\)
\(558\) −1.07331 −0.0454368
\(559\) 18.3341 0.775449
\(560\) 0.0784167 0.00331371
\(561\) 29.1551 1.23093
\(562\) 28.5470 1.20418
\(563\) 28.5625 1.20377 0.601883 0.798584i \(-0.294417\pi\)
0.601883 + 0.798584i \(0.294417\pi\)
\(564\) −12.4305 −0.523420
\(565\) −8.62688 −0.362936
\(566\) −12.6676 −0.532460
\(567\) 0.800101 0.0336011
\(568\) 10.3343 0.433619
\(569\) 41.8278 1.75351 0.876757 0.480934i \(-0.159702\pi\)
0.876757 + 0.480934i \(0.159702\pi\)
\(570\) −6.49729 −0.272142
\(571\) −30.5524 −1.27858 −0.639289 0.768967i \(-0.720771\pi\)
−0.639289 + 0.768967i \(0.720771\pi\)
\(572\) 25.2293 1.05489
\(573\) −22.1263 −0.924340
\(574\) −0.894579 −0.0373390
\(575\) 31.1691 1.29984
\(576\) −0.249472 −0.0103947
\(577\) −15.9307 −0.663203 −0.331602 0.943419i \(-0.607589\pi\)
−0.331602 + 0.943419i \(0.607589\pi\)
\(578\) 0.169596 0.00705426
\(579\) −8.14026 −0.338298
\(580\) −5.16235 −0.214355
\(581\) −0.670561 −0.0278196
\(582\) −6.76345 −0.280354
\(583\) 34.2867 1.42001
\(584\) −0.0428290 −0.00177228
\(585\) −1.17891 −0.0487421
\(586\) 16.3219 0.674250
\(587\) 6.09090 0.251398 0.125699 0.992068i \(-0.459883\pi\)
0.125699 + 0.992068i \(0.459883\pi\)
\(588\) 11.5935 0.478107
\(589\) −20.9998 −0.865280
\(590\) −7.06987 −0.291062
\(591\) −2.72193 −0.111965
\(592\) −0.738173 −0.0303387
\(593\) −42.0285 −1.72590 −0.862952 0.505285i \(-0.831387\pi\)
−0.862952 + 0.505285i \(0.831387\pi\)
\(594\) 23.0930 0.947516
\(595\) 0.321704 0.0131886
\(596\) 4.82312 0.197563
\(597\) 7.50512 0.307164
\(598\) −42.1312 −1.72287
\(599\) 15.7289 0.642666 0.321333 0.946966i \(-0.395869\pi\)
0.321333 + 0.946966i \(0.395869\pi\)
\(600\) −7.22396 −0.294917
\(601\) −41.2478 −1.68253 −0.841266 0.540621i \(-0.818189\pi\)
−0.841266 + 0.540621i \(0.818189\pi\)
\(602\) −0.304234 −0.0123996
\(603\) 2.56224 0.104342
\(604\) 12.8253 0.521854
\(605\) −5.90885 −0.240229
\(606\) −9.10765 −0.369973
\(607\) −5.31367 −0.215675 −0.107838 0.994169i \(-0.534393\pi\)
−0.107838 + 0.994169i \(0.534393\pi\)
\(608\) −4.88102 −0.197952
\(609\) 1.04217 0.0422307
\(610\) −2.17471 −0.0880515
\(611\) −44.1295 −1.78529
\(612\) −1.02345 −0.0413707
\(613\) −7.97335 −0.322041 −0.161020 0.986951i \(-0.551478\pi\)
−0.161020 + 0.986951i \(0.551478\pi\)
\(614\) −11.0823 −0.447246
\(615\) −12.1883 −0.491482
\(616\) −0.418653 −0.0168680
\(617\) −4.90797 −0.197587 −0.0987937 0.995108i \(-0.531498\pi\)
−0.0987937 + 0.995108i \(0.531498\pi\)
\(618\) −29.6971 −1.19459
\(619\) −21.0560 −0.846311 −0.423155 0.906057i \(-0.639078\pi\)
−0.423155 + 0.906057i \(0.639078\pi\)
\(620\) 3.45316 0.138682
\(621\) −38.5636 −1.54751
\(622\) −29.0299 −1.16399
\(623\) 0.523589 0.0209771
\(624\) 9.76462 0.390898
\(625\) 15.7519 0.630075
\(626\) 6.07292 0.242723
\(627\) 34.6879 1.38530
\(628\) −0.792102 −0.0316083
\(629\) −3.02835 −0.120748
\(630\) 0.0195628 0.000779399 0
\(631\) 30.3314 1.20747 0.603737 0.797184i \(-0.293678\pi\)
0.603737 + 0.797184i \(0.293678\pi\)
\(632\) −3.97141 −0.157974
\(633\) 0.377434 0.0150017
\(634\) 9.81771 0.389911
\(635\) 6.30845 0.250343
\(636\) 13.2701 0.526194
\(637\) 41.1578 1.63073
\(638\) 27.5608 1.09114
\(639\) 2.57812 0.101989
\(640\) 0.802626 0.0317266
\(641\) 45.8922 1.81263 0.906317 0.422599i \(-0.138882\pi\)
0.906317 + 0.422599i \(0.138882\pi\)
\(642\) −18.6754 −0.737058
\(643\) −11.0864 −0.437204 −0.218602 0.975814i \(-0.570150\pi\)
−0.218602 + 0.975814i \(0.570150\pi\)
\(644\) 0.699121 0.0275492
\(645\) −4.14508 −0.163212
\(646\) −20.0243 −0.787847
\(647\) 33.8818 1.33203 0.666015 0.745938i \(-0.267999\pi\)
0.666015 + 0.745938i \(0.267999\pi\)
\(648\) 8.18935 0.321708
\(649\) 37.7448 1.48161
\(650\) −25.6457 −1.00591
\(651\) −0.697119 −0.0273222
\(652\) 11.2416 0.440256
\(653\) 7.10147 0.277902 0.138951 0.990299i \(-0.455627\pi\)
0.138951 + 0.990299i \(0.455627\pi\)
\(654\) −11.3527 −0.443927
\(655\) 16.2965 0.636755
\(656\) −9.15637 −0.357496
\(657\) −0.0106846 −0.000416847 0
\(658\) 0.732281 0.0285473
\(659\) 12.3793 0.482228 0.241114 0.970497i \(-0.422487\pi\)
0.241114 + 0.970497i \(0.422487\pi\)
\(660\) −5.70401 −0.222028
\(661\) 36.6294 1.42472 0.712359 0.701815i \(-0.247627\pi\)
0.712359 + 0.701815i \(0.247627\pi\)
\(662\) 31.5144 1.22484
\(663\) 40.0592 1.55577
\(664\) −6.86346 −0.266354
\(665\) 0.382754 0.0148426
\(666\) −0.184153 −0.00713580
\(667\) −46.0247 −1.78208
\(668\) −11.1276 −0.430541
\(669\) −21.6577 −0.837334
\(670\) −8.24350 −0.318474
\(671\) 11.6104 0.448214
\(672\) −0.162033 −0.00625056
\(673\) 43.8692 1.69103 0.845517 0.533948i \(-0.179292\pi\)
0.845517 + 0.533948i \(0.179292\pi\)
\(674\) −2.34590 −0.0903609
\(675\) −23.4740 −0.903516
\(676\) 21.6653 0.833279
\(677\) −0.191652 −0.00736577 −0.00368288 0.999993i \(-0.501172\pi\)
−0.00368288 + 0.999993i \(0.501172\pi\)
\(678\) 17.8258 0.684595
\(679\) 0.398433 0.0152905
\(680\) 3.29276 0.126272
\(681\) −20.5121 −0.786025
\(682\) −18.4358 −0.705944
\(683\) 23.0823 0.883221 0.441611 0.897207i \(-0.354407\pi\)
0.441611 + 0.897207i \(0.354407\pi\)
\(684\) −1.21768 −0.0465591
\(685\) −9.41820 −0.359851
\(686\) −1.36687 −0.0521873
\(687\) 45.9985 1.75495
\(688\) −3.11395 −0.118718
\(689\) 47.1101 1.79475
\(690\) 9.52530 0.362622
\(691\) −14.5510 −0.553544 −0.276772 0.960936i \(-0.589265\pi\)
−0.276772 + 0.960936i \(0.589265\pi\)
\(692\) −3.93491 −0.149583
\(693\) −0.104442 −0.00396743
\(694\) 16.3252 0.619694
\(695\) −2.62426 −0.0995438
\(696\) 10.6670 0.404331
\(697\) −37.5639 −1.42283
\(698\) −33.6684 −1.27437
\(699\) −26.5837 −1.00549
\(700\) 0.425562 0.0160847
\(701\) −4.85468 −0.183359 −0.0916794 0.995789i \(-0.529224\pi\)
−0.0916794 + 0.995789i \(0.529224\pi\)
\(702\) 31.7299 1.19757
\(703\) −3.60304 −0.135891
\(704\) −4.28508 −0.161500
\(705\) 9.97708 0.375759
\(706\) 12.2203 0.459915
\(707\) 0.536530 0.0201783
\(708\) 14.6085 0.549022
\(709\) 51.6131 1.93837 0.969186 0.246330i \(-0.0792248\pi\)
0.969186 + 0.246330i \(0.0792248\pi\)
\(710\) −8.29460 −0.311291
\(711\) −0.990754 −0.0371562
\(712\) 5.35914 0.200842
\(713\) 30.7865 1.15296
\(714\) −0.664738 −0.0248772
\(715\) −20.2497 −0.757297
\(716\) −9.10842 −0.340398
\(717\) −31.7231 −1.18472
\(718\) 0.786973 0.0293696
\(719\) 22.4510 0.837280 0.418640 0.908152i \(-0.362507\pi\)
0.418640 + 0.908152i \(0.362507\pi\)
\(720\) 0.200233 0.00746223
\(721\) 1.74945 0.0651529
\(722\) −4.82438 −0.179545
\(723\) 43.9585 1.63483
\(724\) −9.30241 −0.345721
\(725\) −28.0157 −1.04048
\(726\) 12.2095 0.453137
\(727\) 29.2295 1.08406 0.542031 0.840359i \(-0.317656\pi\)
0.542031 + 0.840359i \(0.317656\pi\)
\(728\) −0.575231 −0.0213195
\(729\) 28.8563 1.06875
\(730\) 0.0343757 0.00127230
\(731\) −12.7749 −0.472498
\(732\) 4.49362 0.166089
\(733\) 49.8269 1.84040 0.920200 0.391450i \(-0.128026\pi\)
0.920200 + 0.391450i \(0.128026\pi\)
\(734\) −15.6163 −0.576408
\(735\) −9.30522 −0.343228
\(736\) 7.15578 0.263766
\(737\) 44.0106 1.62115
\(738\) −2.28426 −0.0840846
\(739\) −53.0377 −1.95102 −0.975511 0.219949i \(-0.929411\pi\)
−0.975511 + 0.219949i \(0.929411\pi\)
\(740\) 0.592477 0.0217799
\(741\) 47.6613 1.75088
\(742\) −0.781739 −0.0286986
\(743\) −14.1535 −0.519240 −0.259620 0.965711i \(-0.583597\pi\)
−0.259620 + 0.965711i \(0.583597\pi\)
\(744\) −7.13529 −0.261592
\(745\) −3.87116 −0.141828
\(746\) −2.46615 −0.0902921
\(747\) −1.71224 −0.0626475
\(748\) −17.5795 −0.642769
\(749\) 1.10016 0.0401990
\(750\) 12.4538 0.454749
\(751\) −38.0657 −1.38904 −0.694519 0.719474i \(-0.744383\pi\)
−0.694519 + 0.719474i \(0.744383\pi\)
\(752\) 7.49518 0.273321
\(753\) −17.1717 −0.625772
\(754\) 37.8688 1.37910
\(755\) −10.2939 −0.374634
\(756\) −0.526522 −0.0191494
\(757\) 0.760696 0.0276480 0.0138240 0.999904i \(-0.495600\pi\)
0.0138240 + 0.999904i \(0.495600\pi\)
\(758\) 2.86090 0.103912
\(759\) −50.8539 −1.84588
\(760\) 3.91764 0.142108
\(761\) 47.3777 1.71744 0.858720 0.512446i \(-0.171260\pi\)
0.858720 + 0.512446i \(0.171260\pi\)
\(762\) −13.0352 −0.472215
\(763\) 0.668786 0.0242117
\(764\) 13.3414 0.482674
\(765\) 0.821452 0.0296996
\(766\) −27.7756 −1.00357
\(767\) 51.8615 1.87261
\(768\) −1.65847 −0.0598449
\(769\) −31.3581 −1.13080 −0.565401 0.824816i \(-0.691279\pi\)
−0.565401 + 0.824816i \(0.691279\pi\)
\(770\) 0.336022 0.0121094
\(771\) −2.87785 −0.103643
\(772\) 4.90829 0.176653
\(773\) 12.3595 0.444540 0.222270 0.974985i \(-0.428653\pi\)
0.222270 + 0.974985i \(0.428653\pi\)
\(774\) −0.776843 −0.0279230
\(775\) 18.7400 0.673162
\(776\) 4.07812 0.146396
\(777\) −0.119608 −0.00429093
\(778\) 19.4925 0.698841
\(779\) −44.6925 −1.60127
\(780\) −7.83734 −0.280622
\(781\) 44.2834 1.58458
\(782\) 29.3565 1.04979
\(783\) 34.6621 1.23872
\(784\) −6.99045 −0.249659
\(785\) 0.635762 0.0226913
\(786\) −33.6735 −1.20109
\(787\) −52.5595 −1.87354 −0.936771 0.349942i \(-0.886201\pi\)
−0.936771 + 0.349942i \(0.886201\pi\)
\(788\) 1.64123 0.0584663
\(789\) −14.6226 −0.520577
\(790\) 3.18755 0.113408
\(791\) −1.05011 −0.0373377
\(792\) −1.06901 −0.0379855
\(793\) 15.9527 0.566499
\(794\) 5.27141 0.187075
\(795\) −10.6509 −0.377750
\(796\) −4.52532 −0.160396
\(797\) −22.6091 −0.800856 −0.400428 0.916328i \(-0.631139\pi\)
−0.400428 + 0.916328i \(0.631139\pi\)
\(798\) −0.790887 −0.0279971
\(799\) 30.7489 1.08782
\(800\) 4.35579 0.154000
\(801\) 1.33695 0.0472389
\(802\) −17.5397 −0.619347
\(803\) −0.183526 −0.00647648
\(804\) 17.0336 0.600729
\(805\) −0.561133 −0.0197773
\(806\) −25.3309 −0.892243
\(807\) −5.42196 −0.190862
\(808\) 5.49159 0.193194
\(809\) −39.0578 −1.37320 −0.686599 0.727036i \(-0.740897\pi\)
−0.686599 + 0.727036i \(0.740897\pi\)
\(810\) −6.57299 −0.230951
\(811\) 21.7603 0.764109 0.382054 0.924140i \(-0.375217\pi\)
0.382054 + 0.924140i \(0.375217\pi\)
\(812\) −0.628390 −0.0220522
\(813\) 38.2391 1.34110
\(814\) −3.16313 −0.110868
\(815\) −9.02283 −0.316056
\(816\) −6.80386 −0.238183
\(817\) −15.1993 −0.531755
\(818\) 19.6791 0.688062
\(819\) −0.143504 −0.00501444
\(820\) 7.34915 0.256643
\(821\) −45.5228 −1.58876 −0.794379 0.607423i \(-0.792203\pi\)
−0.794379 + 0.607423i \(0.792203\pi\)
\(822\) 19.4609 0.678777
\(823\) −17.6042 −0.613643 −0.306822 0.951767i \(-0.599266\pi\)
−0.306822 + 0.951767i \(0.599266\pi\)
\(824\) 17.9063 0.623795
\(825\) −30.9552 −1.07772
\(826\) −0.860584 −0.0299436
\(827\) 50.3123 1.74953 0.874765 0.484547i \(-0.161015\pi\)
0.874765 + 0.484547i \(0.161015\pi\)
\(828\) 1.78517 0.0620388
\(829\) 47.1262 1.63676 0.818381 0.574676i \(-0.194872\pi\)
0.818381 + 0.574676i \(0.194872\pi\)
\(830\) 5.50879 0.191213
\(831\) 34.2186 1.18703
\(832\) −5.88772 −0.204120
\(833\) −28.6783 −0.993643
\(834\) 5.42252 0.187767
\(835\) 8.93133 0.309082
\(836\) −20.9156 −0.723380
\(837\) −23.1859 −0.801423
\(838\) −39.5113 −1.36489
\(839\) 9.19789 0.317546 0.158773 0.987315i \(-0.449246\pi\)
0.158773 + 0.987315i \(0.449246\pi\)
\(840\) 0.130052 0.00448722
\(841\) 12.3683 0.426493
\(842\) 6.83947 0.235704
\(843\) 47.3444 1.63063
\(844\) −0.227580 −0.00783361
\(845\) −17.3891 −0.598203
\(846\) 1.86984 0.0642863
\(847\) −0.719259 −0.0247140
\(848\) −8.00141 −0.274770
\(849\) −21.0089 −0.721023
\(850\) 17.8696 0.612921
\(851\) 5.28221 0.181072
\(852\) 17.1392 0.587179
\(853\) −21.1509 −0.724193 −0.362097 0.932141i \(-0.617939\pi\)
−0.362097 + 0.932141i \(0.617939\pi\)
\(854\) −0.264718 −0.00905847
\(855\) 0.977340 0.0334243
\(856\) 11.2606 0.384879
\(857\) 17.7553 0.606511 0.303255 0.952909i \(-0.401926\pi\)
0.303255 + 0.952909i \(0.401926\pi\)
\(858\) 41.8422 1.42847
\(859\) −47.0523 −1.60540 −0.802702 0.596381i \(-0.796605\pi\)
−0.802702 + 0.596381i \(0.796605\pi\)
\(860\) 2.49934 0.0852268
\(861\) −1.48363 −0.0505621
\(862\) 15.8031 0.538257
\(863\) −4.78579 −0.162910 −0.0814551 0.996677i \(-0.525957\pi\)
−0.0814551 + 0.996677i \(0.525957\pi\)
\(864\) −5.38916 −0.183343
\(865\) 3.15826 0.107384
\(866\) 22.3223 0.758542
\(867\) 0.281270 0.00955243
\(868\) 0.420338 0.0142672
\(869\) −17.0178 −0.577289
\(870\) −8.56160 −0.290266
\(871\) 60.4708 2.04897
\(872\) 6.84529 0.231811
\(873\) 1.01738 0.0344330
\(874\) 34.9275 1.18144
\(875\) −0.733651 −0.0248019
\(876\) −0.0710307 −0.00239991
\(877\) −20.8922 −0.705480 −0.352740 0.935721i \(-0.614750\pi\)
−0.352740 + 0.935721i \(0.614750\pi\)
\(878\) 7.48827 0.252717
\(879\) 27.0693 0.913026
\(880\) 3.43932 0.115939
\(881\) −47.5976 −1.60360 −0.801802 0.597590i \(-0.796125\pi\)
−0.801802 + 0.597590i \(0.796125\pi\)
\(882\) −1.74392 −0.0587209
\(883\) −35.4578 −1.19325 −0.596625 0.802520i \(-0.703492\pi\)
−0.596625 + 0.802520i \(0.703492\pi\)
\(884\) −24.1543 −0.812397
\(885\) −11.7252 −0.394138
\(886\) 8.30280 0.278938
\(887\) 37.9632 1.27468 0.637340 0.770582i \(-0.280035\pi\)
0.637340 + 0.770582i \(0.280035\pi\)
\(888\) −1.22424 −0.0410828
\(889\) 0.767900 0.0257546
\(890\) −4.30138 −0.144183
\(891\) 35.0920 1.17563
\(892\) 13.0588 0.437241
\(893\) 36.5842 1.22424
\(894\) 7.99901 0.267527
\(895\) 7.31066 0.244368
\(896\) 0.0977002 0.00326393
\(897\) −69.8735 −2.33301
\(898\) −22.7332 −0.758616
\(899\) −27.6718 −0.922906
\(900\) 1.08665 0.0362216
\(901\) −32.8257 −1.09358
\(902\) −39.2358 −1.30641
\(903\) −0.504563 −0.0167908
\(904\) −10.7483 −0.357484
\(905\) 7.46636 0.248190
\(906\) 21.2704 0.706662
\(907\) 21.0148 0.697786 0.348893 0.937163i \(-0.386558\pi\)
0.348893 + 0.937163i \(0.386558\pi\)
\(908\) 12.3681 0.410449
\(909\) 1.37000 0.0454399
\(910\) 0.461696 0.0153051
\(911\) −31.4707 −1.04267 −0.521335 0.853352i \(-0.674566\pi\)
−0.521335 + 0.853352i \(0.674566\pi\)
\(912\) −8.09504 −0.268053
\(913\) −29.4104 −0.973344
\(914\) −15.6497 −0.517647
\(915\) −3.60670 −0.119234
\(916\) −27.7355 −0.916406
\(917\) 1.98370 0.0655074
\(918\) −22.1089 −0.729704
\(919\) 32.3594 1.06744 0.533719 0.845662i \(-0.320794\pi\)
0.533719 + 0.845662i \(0.320794\pi\)
\(920\) −5.74342 −0.189355
\(921\) −18.3797 −0.605632
\(922\) 21.2303 0.699181
\(923\) 60.8456 2.00276
\(924\) −0.694324 −0.0228416
\(925\) 3.21533 0.105719
\(926\) −26.7309 −0.878432
\(927\) 4.46711 0.146719
\(928\) −6.43182 −0.211135
\(929\) 20.2891 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(930\) 5.72697 0.187795
\(931\) −34.1206 −1.11826
\(932\) 16.0290 0.525048
\(933\) −48.1453 −1.57621
\(934\) −9.39671 −0.307470
\(935\) 14.1098 0.461438
\(936\) −1.46882 −0.0480099
\(937\) −25.6601 −0.838280 −0.419140 0.907922i \(-0.637668\pi\)
−0.419140 + 0.907922i \(0.637668\pi\)
\(938\) −1.00345 −0.0327636
\(939\) 10.0718 0.328680
\(940\) −6.01583 −0.196215
\(941\) −25.2864 −0.824313 −0.412157 0.911113i \(-0.635224\pi\)
−0.412157 + 0.911113i \(0.635224\pi\)
\(942\) −1.31368 −0.0428019
\(943\) 65.5210 2.13366
\(944\) −8.80842 −0.286690
\(945\) 0.422600 0.0137472
\(946\) −13.3435 −0.433835
\(947\) −9.96278 −0.323747 −0.161873 0.986812i \(-0.551754\pi\)
−0.161873 + 0.986812i \(0.551754\pi\)
\(948\) −6.58646 −0.213918
\(949\) −0.252165 −0.00818563
\(950\) 21.2607 0.689789
\(951\) 16.2824 0.527993
\(952\) 0.400814 0.0129904
\(953\) −45.2388 −1.46543 −0.732715 0.680536i \(-0.761747\pi\)
−0.732715 + 0.680536i \(0.761747\pi\)
\(954\) −1.99613 −0.0646270
\(955\) −10.7081 −0.346508
\(956\) 19.1279 0.618640
\(957\) 45.7089 1.47756
\(958\) 10.0603 0.325033
\(959\) −1.14644 −0.0370204
\(960\) 1.33113 0.0429621
\(961\) −12.4900 −0.402903
\(962\) −4.34616 −0.140126
\(963\) 2.80920 0.0905252
\(964\) −26.5054 −0.853683
\(965\) −3.93952 −0.126818
\(966\) 1.15947 0.0373054
\(967\) 45.5246 1.46397 0.731987 0.681319i \(-0.238593\pi\)
0.731987 + 0.681319i \(0.238593\pi\)
\(968\) −7.36190 −0.236620
\(969\) −33.2098 −1.06685
\(970\) −3.27321 −0.105096
\(971\) −12.0528 −0.386792 −0.193396 0.981121i \(-0.561950\pi\)
−0.193396 + 0.981121i \(0.561950\pi\)
\(972\) −2.58567 −0.0829353
\(973\) −0.319440 −0.0102408
\(974\) 11.1698 0.357902
\(975\) −42.5326 −1.36213
\(976\) −2.70949 −0.0867288
\(977\) 40.3367 1.29049 0.645243 0.763977i \(-0.276756\pi\)
0.645243 + 0.763977i \(0.276756\pi\)
\(978\) 18.6439 0.596167
\(979\) 22.9643 0.733943
\(980\) 5.61072 0.179228
\(981\) 1.70771 0.0545229
\(982\) −16.0088 −0.510861
\(983\) 0.920216 0.0293503 0.0146752 0.999892i \(-0.495329\pi\)
0.0146752 + 0.999892i \(0.495329\pi\)
\(984\) −15.1856 −0.484099
\(985\) −1.31729 −0.0419724
\(986\) −26.3865 −0.840316
\(987\) 1.21447 0.0386569
\(988\) −28.7381 −0.914281
\(989\) 22.2828 0.708550
\(990\) 0.858012 0.0272694
\(991\) 28.7618 0.913650 0.456825 0.889557i \(-0.348987\pi\)
0.456825 + 0.889557i \(0.348987\pi\)
\(992\) 4.30233 0.136599
\(993\) 52.2657 1.65860
\(994\) −1.00967 −0.0320246
\(995\) 3.63214 0.115147
\(996\) −11.3828 −0.360679
\(997\) −46.0569 −1.45864 −0.729318 0.684175i \(-0.760163\pi\)
−0.729318 + 0.684175i \(0.760163\pi\)
\(998\) −7.49915 −0.237381
\(999\) −3.97813 −0.125863
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 \(a_p\))