Properties

Label 8043.2.a.t.1.6
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +4.36349 q^{10} -4.89366 q^{11} -3.54201 q^{12} +4.60003 q^{13} -2.35415 q^{14} +1.85354 q^{15} +1.46181 q^{16} -1.22303 q^{17} -2.35415 q^{18} -2.61498 q^{19} -6.56524 q^{20} -1.00000 q^{21} +11.5204 q^{22} -1.19009 q^{23} +3.63012 q^{24} -1.56441 q^{25} -10.8292 q^{26} -1.00000 q^{27} +3.54201 q^{28} +3.14129 q^{29} -4.36349 q^{30} +4.94813 q^{31} +3.81891 q^{32} +4.89366 q^{33} +2.87920 q^{34} -1.85354 q^{35} +3.54201 q^{36} +4.92663 q^{37} +6.15604 q^{38} -4.60003 q^{39} +6.72855 q^{40} +7.78435 q^{41} +2.35415 q^{42} -9.42641 q^{43} -17.3334 q^{44} -1.85354 q^{45} +2.80164 q^{46} -10.0129 q^{47} -1.46181 q^{48} +1.00000 q^{49} +3.68285 q^{50} +1.22303 q^{51} +16.2934 q^{52} -10.1192 q^{53} +2.35415 q^{54} +9.07056 q^{55} -3.63012 q^{56} +2.61498 q^{57} -7.39505 q^{58} -8.79243 q^{59} +6.56524 q^{60} -6.61793 q^{61} -11.6486 q^{62} +1.00000 q^{63} -11.9139 q^{64} -8.52632 q^{65} -11.5204 q^{66} +8.06470 q^{67} -4.33199 q^{68} +1.19009 q^{69} +4.36349 q^{70} -4.14638 q^{71} -3.63012 q^{72} +7.78221 q^{73} -11.5980 q^{74} +1.56441 q^{75} -9.26227 q^{76} -4.89366 q^{77} +10.8292 q^{78} +1.22109 q^{79} -2.70952 q^{80} +1.00000 q^{81} -18.3255 q^{82} +7.07122 q^{83} -3.54201 q^{84} +2.26693 q^{85} +22.1912 q^{86} -3.14129 q^{87} +17.7645 q^{88} +10.1317 q^{89} +4.36349 q^{90} +4.60003 q^{91} -4.21530 q^{92} -4.94813 q^{93} +23.5719 q^{94} +4.84695 q^{95} -3.81891 q^{96} -10.3978 q^{97} -2.35415 q^{98} -4.89366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35415 −1.66463 −0.832317 0.554300i \(-0.812986\pi\)
−0.832317 + 0.554300i \(0.812986\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.54201 1.77100
\(5\) −1.85354 −0.828926 −0.414463 0.910066i \(-0.636031\pi\)
−0.414463 + 0.910066i \(0.636031\pi\)
\(6\) 2.35415 0.961077
\(7\) 1.00000 0.377964
\(8\) −3.63012 −1.28344
\(9\) 1.00000 0.333333
\(10\) 4.36349 1.37986
\(11\) −4.89366 −1.47549 −0.737746 0.675078i \(-0.764110\pi\)
−0.737746 + 0.675078i \(0.764110\pi\)
\(12\) −3.54201 −1.02249
\(13\) 4.60003 1.27582 0.637910 0.770111i \(-0.279799\pi\)
0.637910 + 0.770111i \(0.279799\pi\)
\(14\) −2.35415 −0.629172
\(15\) 1.85354 0.478581
\(16\) 1.46181 0.365453
\(17\) −1.22303 −0.296629 −0.148314 0.988940i \(-0.547385\pi\)
−0.148314 + 0.988940i \(0.547385\pi\)
\(18\) −2.35415 −0.554878
\(19\) −2.61498 −0.599916 −0.299958 0.953952i \(-0.596973\pi\)
−0.299958 + 0.953952i \(0.596973\pi\)
\(20\) −6.56524 −1.46803
\(21\) −1.00000 −0.218218
\(22\) 11.5204 2.45615
\(23\) −1.19009 −0.248150 −0.124075 0.992273i \(-0.539596\pi\)
−0.124075 + 0.992273i \(0.539596\pi\)
\(24\) 3.63012 0.740995
\(25\) −1.56441 −0.312882
\(26\) −10.8292 −2.12377
\(27\) −1.00000 −0.192450
\(28\) 3.54201 0.669377
\(29\) 3.14129 0.583322 0.291661 0.956522i \(-0.405792\pi\)
0.291661 + 0.956522i \(0.405792\pi\)
\(30\) −4.36349 −0.796661
\(31\) 4.94813 0.888711 0.444356 0.895851i \(-0.353433\pi\)
0.444356 + 0.895851i \(0.353433\pi\)
\(32\) 3.81891 0.675095
\(33\) 4.89366 0.851876
\(34\) 2.87920 0.493778
\(35\) −1.85354 −0.313305
\(36\) 3.54201 0.590335
\(37\) 4.92663 0.809932 0.404966 0.914332i \(-0.367283\pi\)
0.404966 + 0.914332i \(0.367283\pi\)
\(38\) 6.15604 0.998641
\(39\) −4.60003 −0.736595
\(40\) 6.72855 1.06388
\(41\) 7.78435 1.21571 0.607856 0.794047i \(-0.292030\pi\)
0.607856 + 0.794047i \(0.292030\pi\)
\(42\) 2.35415 0.363253
\(43\) −9.42641 −1.43751 −0.718757 0.695261i \(-0.755289\pi\)
−0.718757 + 0.695261i \(0.755289\pi\)
\(44\) −17.3334 −2.61310
\(45\) −1.85354 −0.276309
\(46\) 2.80164 0.413079
\(47\) −10.0129 −1.46054 −0.730269 0.683160i \(-0.760605\pi\)
−0.730269 + 0.683160i \(0.760605\pi\)
\(48\) −1.46181 −0.210994
\(49\) 1.00000 0.142857
\(50\) 3.68285 0.520833
\(51\) 1.22303 0.171259
\(52\) 16.2934 2.25948
\(53\) −10.1192 −1.38998 −0.694989 0.719021i \(-0.744591\pi\)
−0.694989 + 0.719021i \(0.744591\pi\)
\(54\) 2.35415 0.320359
\(55\) 9.07056 1.22307
\(56\) −3.63012 −0.485095
\(57\) 2.61498 0.346362
\(58\) −7.39505 −0.971018
\(59\) −8.79243 −1.14468 −0.572339 0.820017i \(-0.693964\pi\)
−0.572339 + 0.820017i \(0.693964\pi\)
\(60\) 6.56524 0.847569
\(61\) −6.61793 −0.847339 −0.423669 0.905817i \(-0.639258\pi\)
−0.423669 + 0.905817i \(0.639258\pi\)
\(62\) −11.6486 −1.47938
\(63\) 1.00000 0.125988
\(64\) −11.9139 −1.48924
\(65\) −8.52632 −1.05756
\(66\) −11.5204 −1.41806
\(67\) 8.06470 0.985260 0.492630 0.870239i \(-0.336036\pi\)
0.492630 + 0.870239i \(0.336036\pi\)
\(68\) −4.33199 −0.525331
\(69\) 1.19009 0.143270
\(70\) 4.36349 0.521537
\(71\) −4.14638 −0.492085 −0.246042 0.969259i \(-0.579130\pi\)
−0.246042 + 0.969259i \(0.579130\pi\)
\(72\) −3.63012 −0.427813
\(73\) 7.78221 0.910839 0.455419 0.890277i \(-0.349489\pi\)
0.455419 + 0.890277i \(0.349489\pi\)
\(74\) −11.5980 −1.34824
\(75\) 1.56441 0.180642
\(76\) −9.26227 −1.06245
\(77\) −4.89366 −0.557684
\(78\) 10.8292 1.22616
\(79\) 1.22109 0.137383 0.0686914 0.997638i \(-0.478118\pi\)
0.0686914 + 0.997638i \(0.478118\pi\)
\(80\) −2.70952 −0.302933
\(81\) 1.00000 0.111111
\(82\) −18.3255 −2.02371
\(83\) 7.07122 0.776167 0.388084 0.921624i \(-0.373137\pi\)
0.388084 + 0.921624i \(0.373137\pi\)
\(84\) −3.54201 −0.386465
\(85\) 2.26693 0.245883
\(86\) 22.1912 2.39293
\(87\) −3.14129 −0.336781
\(88\) 17.7645 1.89371
\(89\) 10.1317 1.07395 0.536977 0.843597i \(-0.319566\pi\)
0.536977 + 0.843597i \(0.319566\pi\)
\(90\) 4.36349 0.459953
\(91\) 4.60003 0.482215
\(92\) −4.21530 −0.439475
\(93\) −4.94813 −0.513098
\(94\) 23.5719 2.43126
\(95\) 4.84695 0.497286
\(96\) −3.81891 −0.389766
\(97\) −10.3978 −1.05574 −0.527871 0.849325i \(-0.677009\pi\)
−0.527871 + 0.849325i \(0.677009\pi\)
\(98\) −2.35415 −0.237805
\(99\) −4.89366 −0.491831
\(100\) −5.54115 −0.554115
\(101\) 16.3808 1.62995 0.814975 0.579496i \(-0.196751\pi\)
0.814975 + 0.579496i \(0.196751\pi\)
\(102\) −2.87920 −0.285083
\(103\) 3.30738 0.325885 0.162943 0.986636i \(-0.447901\pi\)
0.162943 + 0.986636i \(0.447901\pi\)
\(104\) −16.6987 −1.63744
\(105\) 1.85354 0.180887
\(106\) 23.8221 2.31380
\(107\) −7.82407 −0.756382 −0.378191 0.925728i \(-0.623454\pi\)
−0.378191 + 0.925728i \(0.623454\pi\)
\(108\) −3.54201 −0.340830
\(109\) 17.0627 1.63431 0.817157 0.576416i \(-0.195549\pi\)
0.817157 + 0.576416i \(0.195549\pi\)
\(110\) −21.3534 −2.03597
\(111\) −4.92663 −0.467615
\(112\) 1.46181 0.138128
\(113\) −1.97723 −0.186002 −0.0930012 0.995666i \(-0.529646\pi\)
−0.0930012 + 0.995666i \(0.529646\pi\)
\(114\) −6.15604 −0.576566
\(115\) 2.20587 0.205698
\(116\) 11.1265 1.03307
\(117\) 4.60003 0.425273
\(118\) 20.6987 1.90547
\(119\) −1.22303 −0.112115
\(120\) −6.72855 −0.614230
\(121\) 12.9479 1.17708
\(122\) 15.5796 1.41051
\(123\) −7.78435 −0.701892
\(124\) 17.5263 1.57391
\(125\) 12.1674 1.08828
\(126\) −2.35415 −0.209724
\(127\) −10.9174 −0.968764 −0.484382 0.874857i \(-0.660956\pi\)
−0.484382 + 0.874857i \(0.660956\pi\)
\(128\) 20.4093 1.80394
\(129\) 9.42641 0.829949
\(130\) 20.0722 1.76045
\(131\) −18.4955 −1.61596 −0.807978 0.589213i \(-0.799438\pi\)
−0.807978 + 0.589213i \(0.799438\pi\)
\(132\) 17.3334 1.50868
\(133\) −2.61498 −0.226747
\(134\) −18.9855 −1.64010
\(135\) 1.85354 0.159527
\(136\) 4.43975 0.380705
\(137\) −17.6056 −1.50415 −0.752073 0.659080i \(-0.770946\pi\)
−0.752073 + 0.659080i \(0.770946\pi\)
\(138\) −2.80164 −0.238492
\(139\) 3.45178 0.292776 0.146388 0.989227i \(-0.453235\pi\)
0.146388 + 0.989227i \(0.453235\pi\)
\(140\) −6.56524 −0.554864
\(141\) 10.0129 0.843242
\(142\) 9.76119 0.819141
\(143\) −22.5110 −1.88246
\(144\) 1.46181 0.121818
\(145\) −5.82249 −0.483531
\(146\) −18.3205 −1.51621
\(147\) −1.00000 −0.0824786
\(148\) 17.4502 1.43439
\(149\) −8.98603 −0.736164 −0.368082 0.929793i \(-0.619985\pi\)
−0.368082 + 0.929793i \(0.619985\pi\)
\(150\) −3.68285 −0.300703
\(151\) −21.2363 −1.72818 −0.864091 0.503336i \(-0.832106\pi\)
−0.864091 + 0.503336i \(0.832106\pi\)
\(152\) 9.49267 0.769957
\(153\) −1.22303 −0.0988763
\(154\) 11.5204 0.928339
\(155\) −9.17154 −0.736676
\(156\) −16.2934 −1.30451
\(157\) 23.5031 1.87575 0.937874 0.346976i \(-0.112791\pi\)
0.937874 + 0.346976i \(0.112791\pi\)
\(158\) −2.87461 −0.228692
\(159\) 10.1192 0.802504
\(160\) −7.07849 −0.559604
\(161\) −1.19009 −0.0937920
\(162\) −2.35415 −0.184959
\(163\) −9.13294 −0.715347 −0.357673 0.933847i \(-0.616430\pi\)
−0.357673 + 0.933847i \(0.616430\pi\)
\(164\) 27.5723 2.15303
\(165\) −9.07056 −0.706142
\(166\) −16.6467 −1.29203
\(167\) 12.3621 0.956608 0.478304 0.878194i \(-0.341252\pi\)
0.478304 + 0.878194i \(0.341252\pi\)
\(168\) 3.63012 0.280070
\(169\) 8.16031 0.627716
\(170\) −5.33669 −0.409306
\(171\) −2.61498 −0.199972
\(172\) −33.3884 −2.54584
\(173\) −2.75338 −0.209336 −0.104668 0.994507i \(-0.533378\pi\)
−0.104668 + 0.994507i \(0.533378\pi\)
\(174\) 7.39505 0.560617
\(175\) −1.56441 −0.118258
\(176\) −7.15360 −0.539223
\(177\) 8.79243 0.660880
\(178\) −23.8514 −1.78774
\(179\) 9.71086 0.725824 0.362912 0.931823i \(-0.381783\pi\)
0.362912 + 0.931823i \(0.381783\pi\)
\(180\) −6.56524 −0.489344
\(181\) −18.5594 −1.37951 −0.689754 0.724044i \(-0.742281\pi\)
−0.689754 + 0.724044i \(0.742281\pi\)
\(182\) −10.8292 −0.802710
\(183\) 6.61793 0.489211
\(184\) 4.32016 0.318486
\(185\) −9.13167 −0.671374
\(186\) 11.6486 0.854119
\(187\) 5.98510 0.437674
\(188\) −35.4659 −2.58662
\(189\) −1.00000 −0.0727393
\(190\) −11.4104 −0.827800
\(191\) 2.05200 0.148477 0.0742386 0.997241i \(-0.476347\pi\)
0.0742386 + 0.997241i \(0.476347\pi\)
\(192\) 11.9139 0.859812
\(193\) 2.11366 0.152144 0.0760722 0.997102i \(-0.475762\pi\)
0.0760722 + 0.997102i \(0.475762\pi\)
\(194\) 24.4781 1.75742
\(195\) 8.52632 0.610583
\(196\) 3.54201 0.253001
\(197\) 18.0674 1.28725 0.643623 0.765342i \(-0.277430\pi\)
0.643623 + 0.765342i \(0.277430\pi\)
\(198\) 11.5204 0.818718
\(199\) −20.2945 −1.43864 −0.719321 0.694678i \(-0.755547\pi\)
−0.719321 + 0.694678i \(0.755547\pi\)
\(200\) 5.67898 0.401565
\(201\) −8.06470 −0.568840
\(202\) −38.5628 −2.71327
\(203\) 3.14129 0.220475
\(204\) 4.33199 0.303300
\(205\) −14.4286 −1.00774
\(206\) −7.78605 −0.542480
\(207\) −1.19009 −0.0827168
\(208\) 6.72438 0.466252
\(209\) 12.7968 0.885172
\(210\) −4.36349 −0.301110
\(211\) 11.1772 0.769470 0.384735 0.923027i \(-0.374293\pi\)
0.384735 + 0.923027i \(0.374293\pi\)
\(212\) −35.8423 −2.46166
\(213\) 4.14638 0.284105
\(214\) 18.4190 1.25910
\(215\) 17.4722 1.19159
\(216\) 3.63012 0.246998
\(217\) 4.94813 0.335901
\(218\) −40.1682 −2.72053
\(219\) −7.78221 −0.525873
\(220\) 32.1280 2.16607
\(221\) −5.62599 −0.378445
\(222\) 11.5980 0.778407
\(223\) 3.42614 0.229431 0.114716 0.993398i \(-0.463404\pi\)
0.114716 + 0.993398i \(0.463404\pi\)
\(224\) 3.81891 0.255162
\(225\) −1.56441 −0.104294
\(226\) 4.65470 0.309626
\(227\) −6.56401 −0.435669 −0.217834 0.975986i \(-0.569899\pi\)
−0.217834 + 0.975986i \(0.569899\pi\)
\(228\) 9.26227 0.613409
\(229\) 15.2317 1.00654 0.503268 0.864130i \(-0.332131\pi\)
0.503268 + 0.864130i \(0.332131\pi\)
\(230\) −5.19294 −0.342412
\(231\) 4.89366 0.321979
\(232\) −11.4032 −0.748659
\(233\) −16.4911 −1.08037 −0.540185 0.841546i \(-0.681646\pi\)
−0.540185 + 0.841546i \(0.681646\pi\)
\(234\) −10.8292 −0.707924
\(235\) 18.5593 1.21068
\(236\) −31.1429 −2.02723
\(237\) −1.22109 −0.0793180
\(238\) 2.87920 0.186631
\(239\) 11.2169 0.725561 0.362780 0.931875i \(-0.381828\pi\)
0.362780 + 0.931875i \(0.381828\pi\)
\(240\) 2.70952 0.174899
\(241\) −15.9218 −1.02561 −0.512805 0.858505i \(-0.671394\pi\)
−0.512805 + 0.858505i \(0.671394\pi\)
\(242\) −30.4812 −1.95940
\(243\) −1.00000 −0.0641500
\(244\) −23.4408 −1.50064
\(245\) −1.85354 −0.118418
\(246\) 18.3255 1.16839
\(247\) −12.0290 −0.765385
\(248\) −17.9623 −1.14061
\(249\) −7.07122 −0.448120
\(250\) −28.6438 −1.81159
\(251\) 26.2970 1.65985 0.829925 0.557875i \(-0.188383\pi\)
0.829925 + 0.557875i \(0.188383\pi\)
\(252\) 3.54201 0.223126
\(253\) 5.82388 0.366144
\(254\) 25.7012 1.61264
\(255\) −2.26693 −0.141961
\(256\) −24.2186 −1.51366
\(257\) −20.9871 −1.30914 −0.654571 0.756000i \(-0.727151\pi\)
−0.654571 + 0.756000i \(0.727151\pi\)
\(258\) −22.1912 −1.38156
\(259\) 4.92663 0.306126
\(260\) −30.2003 −1.87294
\(261\) 3.14129 0.194441
\(262\) 43.5410 2.68997
\(263\) 9.81052 0.604942 0.302471 0.953159i \(-0.402188\pi\)
0.302471 + 0.953159i \(0.402188\pi\)
\(264\) −17.7645 −1.09333
\(265\) 18.7563 1.15219
\(266\) 6.15604 0.377451
\(267\) −10.1317 −0.620048
\(268\) 28.5652 1.74490
\(269\) −18.6174 −1.13513 −0.567563 0.823330i \(-0.692114\pi\)
−0.567563 + 0.823330i \(0.692114\pi\)
\(270\) −4.36349 −0.265554
\(271\) −7.90843 −0.480403 −0.240202 0.970723i \(-0.577214\pi\)
−0.240202 + 0.970723i \(0.577214\pi\)
\(272\) −1.78784 −0.108404
\(273\) −4.60003 −0.278407
\(274\) 41.4461 2.50385
\(275\) 7.65567 0.461654
\(276\) 4.21530 0.253731
\(277\) 10.3134 0.619671 0.309836 0.950790i \(-0.399726\pi\)
0.309836 + 0.950790i \(0.399726\pi\)
\(278\) −8.12599 −0.487365
\(279\) 4.94813 0.296237
\(280\) 6.72855 0.402108
\(281\) 18.2638 1.08953 0.544765 0.838589i \(-0.316619\pi\)
0.544765 + 0.838589i \(0.316619\pi\)
\(282\) −23.5719 −1.40369
\(283\) 10.3572 0.615671 0.307836 0.951440i \(-0.400395\pi\)
0.307836 + 0.951440i \(0.400395\pi\)
\(284\) −14.6865 −0.871485
\(285\) −4.84695 −0.287108
\(286\) 52.9942 3.13361
\(287\) 7.78435 0.459496
\(288\) 3.81891 0.225032
\(289\) −15.5042 −0.912011
\(290\) 13.7070 0.804902
\(291\) 10.3978 0.609532
\(292\) 27.5647 1.61310
\(293\) −28.6888 −1.67602 −0.838008 0.545657i \(-0.816280\pi\)
−0.838008 + 0.545657i \(0.816280\pi\)
\(294\) 2.35415 0.137297
\(295\) 16.2971 0.948853
\(296\) −17.8842 −1.03950
\(297\) 4.89366 0.283959
\(298\) 21.1544 1.22544
\(299\) −5.47444 −0.316595
\(300\) 5.54115 0.319918
\(301\) −9.42641 −0.543329
\(302\) 49.9933 2.87679
\(303\) −16.3808 −0.941052
\(304\) −3.82260 −0.219241
\(305\) 12.2666 0.702381
\(306\) 2.87920 0.164593
\(307\) 1.95046 0.111318 0.0556592 0.998450i \(-0.482274\pi\)
0.0556592 + 0.998450i \(0.482274\pi\)
\(308\) −17.3334 −0.987661
\(309\) −3.30738 −0.188150
\(310\) 21.5912 1.22630
\(311\) −21.1800 −1.20101 −0.600505 0.799621i \(-0.705034\pi\)
−0.600505 + 0.799621i \(0.705034\pi\)
\(312\) 16.6987 0.945376
\(313\) −12.8187 −0.724555 −0.362278 0.932070i \(-0.618001\pi\)
−0.362278 + 0.932070i \(0.618001\pi\)
\(314\) −55.3297 −3.12243
\(315\) −1.85354 −0.104435
\(316\) 4.32510 0.243306
\(317\) 4.36874 0.245373 0.122686 0.992445i \(-0.460849\pi\)
0.122686 + 0.992445i \(0.460849\pi\)
\(318\) −23.8221 −1.33587
\(319\) −15.3724 −0.860688
\(320\) 22.0829 1.23447
\(321\) 7.82407 0.436697
\(322\) 2.80164 0.156129
\(323\) 3.19820 0.177953
\(324\) 3.54201 0.196778
\(325\) −7.19633 −0.399180
\(326\) 21.5003 1.19079
\(327\) −17.0627 −0.943571
\(328\) −28.2581 −1.56029
\(329\) −10.0129 −0.552031
\(330\) 21.3534 1.17547
\(331\) −21.3008 −1.17080 −0.585400 0.810745i \(-0.699063\pi\)
−0.585400 + 0.810745i \(0.699063\pi\)
\(332\) 25.0463 1.37460
\(333\) 4.92663 0.269977
\(334\) −29.1022 −1.59240
\(335\) −14.9482 −0.816707
\(336\) −1.46181 −0.0797484
\(337\) 13.2733 0.723044 0.361522 0.932364i \(-0.382257\pi\)
0.361522 + 0.932364i \(0.382257\pi\)
\(338\) −19.2106 −1.04492
\(339\) 1.97723 0.107389
\(340\) 8.02950 0.435461
\(341\) −24.2145 −1.31129
\(342\) 6.15604 0.332880
\(343\) 1.00000 0.0539949
\(344\) 34.2190 1.84496
\(345\) −2.20587 −0.118760
\(346\) 6.48187 0.348468
\(347\) 28.8843 1.55059 0.775295 0.631599i \(-0.217601\pi\)
0.775295 + 0.631599i \(0.217601\pi\)
\(348\) −11.1265 −0.596441
\(349\) −15.8185 −0.846746 −0.423373 0.905955i \(-0.639154\pi\)
−0.423373 + 0.905955i \(0.639154\pi\)
\(350\) 3.68285 0.196856
\(351\) −4.60003 −0.245532
\(352\) −18.6885 −0.996098
\(353\) −4.09048 −0.217714 −0.108857 0.994057i \(-0.534719\pi\)
−0.108857 + 0.994057i \(0.534719\pi\)
\(354\) −20.6987 −1.10012
\(355\) 7.68546 0.407902
\(356\) 35.8865 1.90198
\(357\) 1.22303 0.0647297
\(358\) −22.8608 −1.20823
\(359\) 0.184855 0.00975628 0.00487814 0.999988i \(-0.498447\pi\)
0.00487814 + 0.999988i \(0.498447\pi\)
\(360\) 6.72855 0.354626
\(361\) −12.1619 −0.640100
\(362\) 43.6915 2.29637
\(363\) −12.9479 −0.679587
\(364\) 16.2934 0.854004
\(365\) −14.4246 −0.755018
\(366\) −15.5796 −0.814357
\(367\) −35.7770 −1.86754 −0.933772 0.357869i \(-0.883503\pi\)
−0.933772 + 0.357869i \(0.883503\pi\)
\(368\) −1.73968 −0.0906873
\(369\) 7.78435 0.405237
\(370\) 21.4973 1.11759
\(371\) −10.1192 −0.525362
\(372\) −17.5263 −0.908698
\(373\) 29.1089 1.50720 0.753600 0.657333i \(-0.228316\pi\)
0.753600 + 0.657333i \(0.228316\pi\)
\(374\) −14.0898 −0.728566
\(375\) −12.1674 −0.628320
\(376\) 36.3482 1.87451
\(377\) 14.4500 0.744214
\(378\) 2.35415 0.121084
\(379\) −16.4447 −0.844707 −0.422353 0.906431i \(-0.638796\pi\)
−0.422353 + 0.906431i \(0.638796\pi\)
\(380\) 17.1679 0.880697
\(381\) 10.9174 0.559316
\(382\) −4.83070 −0.247160
\(383\) −1.00000 −0.0510976
\(384\) −20.4093 −1.04151
\(385\) 9.07056 0.462279
\(386\) −4.97586 −0.253265
\(387\) −9.42641 −0.479172
\(388\) −36.8293 −1.86972
\(389\) −1.58700 −0.0804643 −0.0402322 0.999190i \(-0.512810\pi\)
−0.0402322 + 0.999190i \(0.512810\pi\)
\(390\) −20.0722 −1.01640
\(391\) 1.45552 0.0736086
\(392\) −3.63012 −0.183349
\(393\) 18.4955 0.932972
\(394\) −42.5332 −2.14279
\(395\) −2.26332 −0.113880
\(396\) −17.3334 −0.871035
\(397\) 39.6043 1.98768 0.993841 0.110818i \(-0.0353470\pi\)
0.993841 + 0.110818i \(0.0353470\pi\)
\(398\) 47.7764 2.39481
\(399\) 2.61498 0.130913
\(400\) −2.28687 −0.114343
\(401\) −3.21257 −0.160428 −0.0802141 0.996778i \(-0.525560\pi\)
−0.0802141 + 0.996778i \(0.525560\pi\)
\(402\) 18.9855 0.946910
\(403\) 22.7616 1.13384
\(404\) 58.0209 2.88665
\(405\) −1.85354 −0.0921029
\(406\) −7.39505 −0.367010
\(407\) −24.1092 −1.19505
\(408\) −4.43975 −0.219800
\(409\) −6.10980 −0.302110 −0.151055 0.988525i \(-0.548267\pi\)
−0.151055 + 0.988525i \(0.548267\pi\)
\(410\) 33.9670 1.67751
\(411\) 17.6056 0.868419
\(412\) 11.7148 0.577144
\(413\) −8.79243 −0.432647
\(414\) 2.80164 0.137693
\(415\) −13.1068 −0.643385
\(416\) 17.5671 0.861300
\(417\) −3.45178 −0.169034
\(418\) −30.1255 −1.47349
\(419\) 6.65302 0.325022 0.162511 0.986707i \(-0.448041\pi\)
0.162511 + 0.986707i \(0.448041\pi\)
\(420\) 6.56524 0.320351
\(421\) −15.2817 −0.744784 −0.372392 0.928075i \(-0.621462\pi\)
−0.372392 + 0.928075i \(0.621462\pi\)
\(422\) −26.3128 −1.28089
\(423\) −10.0129 −0.486846
\(424\) 36.7338 1.78395
\(425\) 1.91332 0.0928097
\(426\) −9.76119 −0.472931
\(427\) −6.61793 −0.320264
\(428\) −27.7129 −1.33956
\(429\) 22.5110 1.08684
\(430\) −41.1321 −1.98357
\(431\) −10.5743 −0.509345 −0.254673 0.967027i \(-0.581968\pi\)
−0.254673 + 0.967027i \(0.581968\pi\)
\(432\) −1.46181 −0.0703314
\(433\) 26.5598 1.27638 0.638192 0.769877i \(-0.279683\pi\)
0.638192 + 0.769877i \(0.279683\pi\)
\(434\) −11.6486 −0.559152
\(435\) 5.82249 0.279167
\(436\) 60.4363 2.89438
\(437\) 3.11205 0.148869
\(438\) 18.3205 0.875386
\(439\) −1.21182 −0.0578369 −0.0289184 0.999582i \(-0.509206\pi\)
−0.0289184 + 0.999582i \(0.509206\pi\)
\(440\) −32.9272 −1.56974
\(441\) 1.00000 0.0476190
\(442\) 13.2444 0.629972
\(443\) 9.53937 0.453229 0.226615 0.973984i \(-0.427234\pi\)
0.226615 + 0.973984i \(0.427234\pi\)
\(444\) −17.4502 −0.828148
\(445\) −18.7794 −0.890229
\(446\) −8.06564 −0.381919
\(447\) 8.98603 0.425024
\(448\) −11.9139 −0.562879
\(449\) 16.3208 0.770224 0.385112 0.922870i \(-0.374163\pi\)
0.385112 + 0.922870i \(0.374163\pi\)
\(450\) 3.68285 0.173611
\(451\) −38.0940 −1.79377
\(452\) −7.00338 −0.329411
\(453\) 21.2363 0.997766
\(454\) 15.4526 0.725229
\(455\) −8.52632 −0.399720
\(456\) −9.49267 −0.444535
\(457\) −13.3906 −0.626384 −0.313192 0.949690i \(-0.601398\pi\)
−0.313192 + 0.949690i \(0.601398\pi\)
\(458\) −35.8576 −1.67551
\(459\) 1.22303 0.0570863
\(460\) 7.81321 0.364293
\(461\) 22.5156 1.04865 0.524327 0.851517i \(-0.324317\pi\)
0.524327 + 0.851517i \(0.324317\pi\)
\(462\) −11.5204 −0.535977
\(463\) −10.9731 −0.509963 −0.254981 0.966946i \(-0.582069\pi\)
−0.254981 + 0.966946i \(0.582069\pi\)
\(464\) 4.59197 0.213177
\(465\) 9.17154 0.425320
\(466\) 38.8226 1.79842
\(467\) 8.77488 0.406053 0.203027 0.979173i \(-0.434922\pi\)
0.203027 + 0.979173i \(0.434922\pi\)
\(468\) 16.2934 0.753161
\(469\) 8.06470 0.372393
\(470\) −43.6914 −2.01533
\(471\) −23.5031 −1.08296
\(472\) 31.9176 1.46913
\(473\) 46.1296 2.12104
\(474\) 2.87461 0.132035
\(475\) 4.09089 0.187703
\(476\) −4.33199 −0.198557
\(477\) −10.1192 −0.463326
\(478\) −26.4062 −1.20779
\(479\) −25.5503 −1.16742 −0.583711 0.811962i \(-0.698400\pi\)
−0.583711 + 0.811962i \(0.698400\pi\)
\(480\) 7.07849 0.323087
\(481\) 22.6626 1.03333
\(482\) 37.4822 1.70727
\(483\) 1.19009 0.0541509
\(484\) 45.8615 2.08461
\(485\) 19.2728 0.875131
\(486\) 2.35415 0.106786
\(487\) −11.6535 −0.528069 −0.264035 0.964513i \(-0.585053\pi\)
−0.264035 + 0.964513i \(0.585053\pi\)
\(488\) 24.0238 1.08751
\(489\) 9.13294 0.413006
\(490\) 4.36349 0.197123
\(491\) 9.35777 0.422310 0.211155 0.977453i \(-0.432277\pi\)
0.211155 + 0.977453i \(0.432277\pi\)
\(492\) −27.5723 −1.24305
\(493\) −3.84190 −0.173030
\(494\) 28.3180 1.27409
\(495\) 9.07056 0.407691
\(496\) 7.23324 0.324782
\(497\) −4.14638 −0.185991
\(498\) 16.6467 0.745956
\(499\) −19.1838 −0.858783 −0.429392 0.903118i \(-0.641272\pi\)
−0.429392 + 0.903118i \(0.641272\pi\)
\(500\) 43.0969 1.92735
\(501\) −12.3621 −0.552298
\(502\) −61.9069 −2.76304
\(503\) 0.363491 0.0162073 0.00810363 0.999967i \(-0.497421\pi\)
0.00810363 + 0.999967i \(0.497421\pi\)
\(504\) −3.63012 −0.161698
\(505\) −30.3624 −1.35111
\(506\) −13.7103 −0.609496
\(507\) −8.16031 −0.362412
\(508\) −38.6696 −1.71569
\(509\) −22.5669 −1.00026 −0.500130 0.865951i \(-0.666714\pi\)
−0.500130 + 0.865951i \(0.666714\pi\)
\(510\) 5.33669 0.236313
\(511\) 7.78221 0.344265
\(512\) 16.1956 0.715752
\(513\) 2.61498 0.115454
\(514\) 49.4068 2.17924
\(515\) −6.13034 −0.270135
\(516\) 33.3884 1.46984
\(517\) 48.9999 2.15501
\(518\) −11.5980 −0.509587
\(519\) 2.75338 0.120860
\(520\) 30.9516 1.35732
\(521\) 20.1970 0.884846 0.442423 0.896806i \(-0.354119\pi\)
0.442423 + 0.896806i \(0.354119\pi\)
\(522\) −7.39505 −0.323673
\(523\) 20.7367 0.906752 0.453376 0.891319i \(-0.350220\pi\)
0.453376 + 0.891319i \(0.350220\pi\)
\(524\) −65.5111 −2.86186
\(525\) 1.56441 0.0682763
\(526\) −23.0954 −1.00701
\(527\) −6.05173 −0.263617
\(528\) 7.15360 0.311321
\(529\) −21.5837 −0.938421
\(530\) −44.1550 −1.91797
\(531\) −8.79243 −0.381559
\(532\) −9.26227 −0.401570
\(533\) 35.8083 1.55103
\(534\) 23.8514 1.03215
\(535\) 14.5022 0.626984
\(536\) −29.2758 −1.26452
\(537\) −9.71086 −0.419055
\(538\) 43.8282 1.88957
\(539\) −4.89366 −0.210785
\(540\) 6.56524 0.282523
\(541\) 28.4854 1.22468 0.612341 0.790594i \(-0.290228\pi\)
0.612341 + 0.790594i \(0.290228\pi\)
\(542\) 18.6176 0.799695
\(543\) 18.5594 0.796459
\(544\) −4.67066 −0.200253
\(545\) −31.6264 −1.35472
\(546\) 10.8292 0.463445
\(547\) −12.0685 −0.516012 −0.258006 0.966143i \(-0.583065\pi\)
−0.258006 + 0.966143i \(0.583065\pi\)
\(548\) −62.3591 −2.66385
\(549\) −6.61793 −0.282446
\(550\) −18.0226 −0.768485
\(551\) −8.21439 −0.349945
\(552\) −4.32016 −0.183878
\(553\) 1.22109 0.0519258
\(554\) −24.2792 −1.03153
\(555\) 9.13167 0.387618
\(556\) 12.2262 0.518508
\(557\) 26.4991 1.12280 0.561401 0.827544i \(-0.310263\pi\)
0.561401 + 0.827544i \(0.310263\pi\)
\(558\) −11.6486 −0.493126
\(559\) −43.3618 −1.83401
\(560\) −2.70952 −0.114498
\(561\) −5.98510 −0.252691
\(562\) −42.9958 −1.81367
\(563\) 10.1578 0.428100 0.214050 0.976823i \(-0.431334\pi\)
0.214050 + 0.976823i \(0.431334\pi\)
\(564\) 35.4659 1.49339
\(565\) 3.66487 0.154182
\(566\) −24.3824 −1.02487
\(567\) 1.00000 0.0419961
\(568\) 15.0519 0.631562
\(569\) −24.7666 −1.03827 −0.519134 0.854693i \(-0.673745\pi\)
−0.519134 + 0.854693i \(0.673745\pi\)
\(570\) 11.4104 0.477930
\(571\) 12.4559 0.521262 0.260631 0.965438i \(-0.416069\pi\)
0.260631 + 0.965438i \(0.416069\pi\)
\(572\) −79.7341 −3.33385
\(573\) −2.05200 −0.0857234
\(574\) −18.3255 −0.764892
\(575\) 1.86178 0.0776417
\(576\) −11.9139 −0.496413
\(577\) −18.5600 −0.772661 −0.386331 0.922360i \(-0.626258\pi\)
−0.386331 + 0.922360i \(0.626258\pi\)
\(578\) 36.4992 1.51816
\(579\) −2.11366 −0.0878406
\(580\) −20.6233 −0.856336
\(581\) 7.07122 0.293364
\(582\) −24.4781 −1.01465
\(583\) 49.5198 2.05090
\(584\) −28.2503 −1.16901
\(585\) −8.52632 −0.352520
\(586\) 67.5376 2.78995
\(587\) 10.2136 0.421561 0.210780 0.977533i \(-0.432399\pi\)
0.210780 + 0.977533i \(0.432399\pi\)
\(588\) −3.54201 −0.146070
\(589\) −12.9392 −0.533152
\(590\) −38.3657 −1.57949
\(591\) −18.0674 −0.743192
\(592\) 7.20180 0.295992
\(593\) −21.0053 −0.862586 −0.431293 0.902212i \(-0.641942\pi\)
−0.431293 + 0.902212i \(0.641942\pi\)
\(594\) −11.5204 −0.472687
\(595\) 2.26693 0.0929352
\(596\) −31.8286 −1.30375
\(597\) 20.2945 0.830601
\(598\) 12.8876 0.527015
\(599\) −25.1037 −1.02571 −0.512854 0.858476i \(-0.671412\pi\)
−0.512854 + 0.858476i \(0.671412\pi\)
\(600\) −5.67898 −0.231844
\(601\) 25.3801 1.03528 0.517638 0.855600i \(-0.326811\pi\)
0.517638 + 0.855600i \(0.326811\pi\)
\(602\) 22.1912 0.904444
\(603\) 8.06470 0.328420
\(604\) −75.2190 −3.06062
\(605\) −23.9993 −0.975711
\(606\) 38.5628 1.56651
\(607\) 36.0789 1.46440 0.732199 0.681091i \(-0.238494\pi\)
0.732199 + 0.681091i \(0.238494\pi\)
\(608\) −9.98637 −0.405001
\(609\) −3.14129 −0.127291
\(610\) −28.8773 −1.16921
\(611\) −46.0599 −1.86338
\(612\) −4.33199 −0.175110
\(613\) 13.6296 0.550494 0.275247 0.961374i \(-0.411240\pi\)
0.275247 + 0.961374i \(0.411240\pi\)
\(614\) −4.59166 −0.185304
\(615\) 14.4286 0.581816
\(616\) 17.7645 0.715754
\(617\) 48.8545 1.96681 0.983404 0.181429i \(-0.0580722\pi\)
0.983404 + 0.181429i \(0.0580722\pi\)
\(618\) 7.78605 0.313201
\(619\) −12.7279 −0.511576 −0.255788 0.966733i \(-0.582335\pi\)
−0.255788 + 0.966733i \(0.582335\pi\)
\(620\) −32.4857 −1.30466
\(621\) 1.19009 0.0477566
\(622\) 49.8609 1.99924
\(623\) 10.1317 0.405917
\(624\) −6.72438 −0.269191
\(625\) −14.7306 −0.589224
\(626\) 30.1771 1.20612
\(627\) −12.7968 −0.511055
\(628\) 83.2480 3.32196
\(629\) −6.02542 −0.240249
\(630\) 4.36349 0.173846
\(631\) 15.6795 0.624191 0.312095 0.950051i \(-0.398969\pi\)
0.312095 + 0.950051i \(0.398969\pi\)
\(632\) −4.43268 −0.176323
\(633\) −11.1772 −0.444254
\(634\) −10.2847 −0.408456
\(635\) 20.2358 0.803034
\(636\) 35.8423 1.42124
\(637\) 4.60003 0.182260
\(638\) 36.1888 1.43273
\(639\) −4.14638 −0.164028
\(640\) −37.8293 −1.49533
\(641\) 38.5578 1.52294 0.761470 0.648200i \(-0.224478\pi\)
0.761470 + 0.648200i \(0.224478\pi\)
\(642\) −18.4190 −0.726941
\(643\) −12.1674 −0.479834 −0.239917 0.970793i \(-0.577120\pi\)
−0.239917 + 0.970793i \(0.577120\pi\)
\(644\) −4.21530 −0.166106
\(645\) −17.4722 −0.687967
\(646\) −7.52903 −0.296226
\(647\) 30.9802 1.21796 0.608978 0.793187i \(-0.291580\pi\)
0.608978 + 0.793187i \(0.291580\pi\)
\(648\) −3.63012 −0.142604
\(649\) 43.0271 1.68896
\(650\) 16.9412 0.664489
\(651\) −4.94813 −0.193933
\(652\) −32.3489 −1.26688
\(653\) 29.5979 1.15825 0.579127 0.815237i \(-0.303393\pi\)
0.579127 + 0.815237i \(0.303393\pi\)
\(654\) 40.1682 1.57070
\(655\) 34.2820 1.33951
\(656\) 11.3793 0.444285
\(657\) 7.78221 0.303613
\(658\) 23.5719 0.918930
\(659\) 34.0802 1.32758 0.663788 0.747920i \(-0.268948\pi\)
0.663788 + 0.747920i \(0.268948\pi\)
\(660\) −32.1280 −1.25058
\(661\) 21.6834 0.843388 0.421694 0.906738i \(-0.361436\pi\)
0.421694 + 0.906738i \(0.361436\pi\)
\(662\) 50.1453 1.94895
\(663\) 5.62599 0.218495
\(664\) −25.6694 −0.996164
\(665\) 4.84695 0.187957
\(666\) −11.5980 −0.449413
\(667\) −3.73841 −0.144752
\(668\) 43.7867 1.69416
\(669\) −3.42614 −0.132462
\(670\) 35.1903 1.35952
\(671\) 32.3859 1.25024
\(672\) −3.81891 −0.147318
\(673\) 43.4986 1.67675 0.838373 0.545097i \(-0.183507\pi\)
0.838373 + 0.545097i \(0.183507\pi\)
\(674\) −31.2474 −1.20360
\(675\) 1.56441 0.0602141
\(676\) 28.9039 1.11169
\(677\) 42.2892 1.62531 0.812654 0.582747i \(-0.198022\pi\)
0.812654 + 0.582747i \(0.198022\pi\)
\(678\) −4.65470 −0.178763
\(679\) −10.3978 −0.399033
\(680\) −8.22923 −0.315577
\(681\) 6.56401 0.251533
\(682\) 57.0044 2.18281
\(683\) −45.2459 −1.73128 −0.865642 0.500663i \(-0.833090\pi\)
−0.865642 + 0.500663i \(0.833090\pi\)
\(684\) −9.26227 −0.354152
\(685\) 32.6326 1.24683
\(686\) −2.35415 −0.0898818
\(687\) −15.2317 −0.581124
\(688\) −13.7796 −0.525344
\(689\) −46.5486 −1.77336
\(690\) 5.19294 0.197692
\(691\) 49.2823 1.87479 0.937393 0.348273i \(-0.113232\pi\)
0.937393 + 0.348273i \(0.113232\pi\)
\(692\) −9.75251 −0.370735
\(693\) −4.89366 −0.185895
\(694\) −67.9979 −2.58117
\(695\) −6.39799 −0.242690
\(696\) 11.4032 0.432239
\(697\) −9.52052 −0.360615
\(698\) 37.2391 1.40952
\(699\) 16.4911 0.623752
\(700\) −5.54115 −0.209436
\(701\) −8.56365 −0.323445 −0.161722 0.986836i \(-0.551705\pi\)
−0.161722 + 0.986836i \(0.551705\pi\)
\(702\) 10.8292 0.408720
\(703\) −12.8830 −0.485892
\(704\) 58.3026 2.19736
\(705\) −18.5593 −0.698985
\(706\) 9.62960 0.362415
\(707\) 16.3808 0.616063
\(708\) 31.1429 1.17042
\(709\) −48.8916 −1.83616 −0.918081 0.396393i \(-0.870262\pi\)
−0.918081 + 0.396393i \(0.870262\pi\)
\(710\) −18.0927 −0.679007
\(711\) 1.22109 0.0457943
\(712\) −36.7792 −1.37836
\(713\) −5.88871 −0.220534
\(714\) −2.87920 −0.107751
\(715\) 41.7249 1.56042
\(716\) 34.3960 1.28544
\(717\) −11.2169 −0.418903
\(718\) −0.435176 −0.0162406
\(719\) −0.993109 −0.0370367 −0.0185184 0.999829i \(-0.505895\pi\)
−0.0185184 + 0.999829i \(0.505895\pi\)
\(720\) −2.70952 −0.100978
\(721\) 3.30738 0.123173
\(722\) 28.6309 1.06553
\(723\) 15.9218 0.592136
\(724\) −65.7375 −2.44311
\(725\) −4.91425 −0.182511
\(726\) 30.4812 1.13126
\(727\) 23.9986 0.890058 0.445029 0.895516i \(-0.353193\pi\)
0.445029 + 0.895516i \(0.353193\pi\)
\(728\) −16.6987 −0.618894
\(729\) 1.00000 0.0370370
\(730\) 33.9576 1.25683
\(731\) 11.5288 0.426408
\(732\) 23.4408 0.866395
\(733\) 22.4447 0.829012 0.414506 0.910047i \(-0.363954\pi\)
0.414506 + 0.910047i \(0.363954\pi\)
\(734\) 84.2243 3.10878
\(735\) 1.85354 0.0683687
\(736\) −4.54484 −0.167525
\(737\) −39.4659 −1.45374
\(738\) −18.3255 −0.674572
\(739\) 47.7930 1.75809 0.879046 0.476737i \(-0.158180\pi\)
0.879046 + 0.476737i \(0.158180\pi\)
\(740\) −32.3445 −1.18901
\(741\) 12.0290 0.441895
\(742\) 23.8221 0.874535
\(743\) 28.0421 1.02876 0.514382 0.857561i \(-0.328021\pi\)
0.514382 + 0.857561i \(0.328021\pi\)
\(744\) 17.9623 0.658530
\(745\) 16.6559 0.610225
\(746\) −68.5266 −2.50894
\(747\) 7.07122 0.258722
\(748\) 21.1993 0.775122
\(749\) −7.82407 −0.285885
\(750\) 28.6438 1.04592
\(751\) −28.9560 −1.05662 −0.528309 0.849052i \(-0.677174\pi\)
−0.528309 + 0.849052i \(0.677174\pi\)
\(752\) −14.6370 −0.533758
\(753\) −26.2970 −0.958315
\(754\) −34.0175 −1.23884
\(755\) 39.3621 1.43254
\(756\) −3.54201 −0.128822
\(757\) 16.7150 0.607518 0.303759 0.952749i \(-0.401758\pi\)
0.303759 + 0.952749i \(0.401758\pi\)
\(758\) 38.7132 1.40613
\(759\) −5.82388 −0.211393
\(760\) −17.5950 −0.638237
\(761\) −39.8124 −1.44320 −0.721599 0.692311i \(-0.756593\pi\)
−0.721599 + 0.692311i \(0.756593\pi\)
\(762\) −25.7012 −0.931056
\(763\) 17.0627 0.617712
\(764\) 7.26819 0.262954
\(765\) 2.26693 0.0819611
\(766\) 2.35415 0.0850588
\(767\) −40.4455 −1.46040
\(768\) 24.2186 0.873914
\(769\) 26.5906 0.958881 0.479441 0.877574i \(-0.340840\pi\)
0.479441 + 0.877574i \(0.340840\pi\)
\(770\) −21.3534 −0.769525
\(771\) 20.9871 0.755834
\(772\) 7.48660 0.269449
\(773\) 36.2738 1.30468 0.652339 0.757927i \(-0.273788\pi\)
0.652339 + 0.757927i \(0.273788\pi\)
\(774\) 22.1912 0.797645
\(775\) −7.74090 −0.278061
\(776\) 37.7454 1.35498
\(777\) −4.92663 −0.176742
\(778\) 3.73604 0.133944
\(779\) −20.3559 −0.729326
\(780\) 30.2003 1.08134
\(781\) 20.2910 0.726068
\(782\) −3.42650 −0.122531
\(783\) −3.14129 −0.112260
\(784\) 1.46181 0.0522076
\(785\) −43.5637 −1.55486
\(786\) −43.5410 −1.55306
\(787\) 24.8943 0.887385 0.443692 0.896179i \(-0.353668\pi\)
0.443692 + 0.896179i \(0.353668\pi\)
\(788\) 63.9948 2.27972
\(789\) −9.81052 −0.349264
\(790\) 5.32820 0.189569
\(791\) −1.97723 −0.0703023
\(792\) 17.7645 0.631236
\(793\) −30.4427 −1.08105
\(794\) −93.2343 −3.30876
\(795\) −18.7563 −0.665216
\(796\) −71.8835 −2.54784
\(797\) −3.18869 −0.112949 −0.0564747 0.998404i \(-0.517986\pi\)
−0.0564747 + 0.998404i \(0.517986\pi\)
\(798\) −6.15604 −0.217921
\(799\) 12.2462 0.433238
\(800\) −5.97434 −0.211225
\(801\) 10.1317 0.357985
\(802\) 7.56287 0.267054
\(803\) −38.0835 −1.34394
\(804\) −28.5652 −1.00742
\(805\) 2.20587 0.0777467
\(806\) −53.5841 −1.88742
\(807\) 18.6174 0.655365
\(808\) −59.4642 −2.09194
\(809\) 53.2753 1.87306 0.936529 0.350589i \(-0.114019\pi\)
0.936529 + 0.350589i \(0.114019\pi\)
\(810\) 4.36349 0.153318
\(811\) 35.7884 1.25670 0.628351 0.777930i \(-0.283730\pi\)
0.628351 + 0.777930i \(0.283730\pi\)
\(812\) 11.1265 0.390462
\(813\) 7.90843 0.277361
\(814\) 56.7566 1.98932
\(815\) 16.9282 0.592970
\(816\) 1.78784 0.0625870
\(817\) 24.6498 0.862389
\(818\) 14.3834 0.502903
\(819\) 4.60003 0.160738
\(820\) −51.1061 −1.78470
\(821\) 14.0268 0.489540 0.244770 0.969581i \(-0.421288\pi\)
0.244770 + 0.969581i \(0.421288\pi\)
\(822\) −41.4461 −1.44560
\(823\) 32.5594 1.13495 0.567475 0.823391i \(-0.307921\pi\)
0.567475 + 0.823391i \(0.307921\pi\)
\(824\) −12.0062 −0.418254
\(825\) −7.65567 −0.266536
\(826\) 20.6987 0.720199
\(827\) −32.5828 −1.13301 −0.566507 0.824057i \(-0.691705\pi\)
−0.566507 + 0.824057i \(0.691705\pi\)
\(828\) −4.21530 −0.146492
\(829\) −21.0641 −0.731585 −0.365793 0.930696i \(-0.619202\pi\)
−0.365793 + 0.930696i \(0.619202\pi\)
\(830\) 30.8552 1.07100
\(831\) −10.3134 −0.357767
\(832\) −54.8044 −1.90000
\(833\) −1.22303 −0.0423756
\(834\) 8.12599 0.281380
\(835\) −22.9136 −0.792957
\(836\) 45.3263 1.56764
\(837\) −4.94813 −0.171033
\(838\) −15.6622 −0.541042
\(839\) 31.6584 1.09297 0.546485 0.837469i \(-0.315966\pi\)
0.546485 + 0.837469i \(0.315966\pi\)
\(840\) −6.72855 −0.232157
\(841\) −19.1323 −0.659735
\(842\) 35.9754 1.23979
\(843\) −18.2638 −0.629040
\(844\) 39.5897 1.36274
\(845\) −15.1254 −0.520330
\(846\) 23.5719 0.810420
\(847\) 12.9479 0.444894
\(848\) −14.7923 −0.507971
\(849\) −10.3572 −0.355458
\(850\) −4.50424 −0.154494
\(851\) −5.86312 −0.200985
\(852\) 14.6865 0.503152
\(853\) −15.9443 −0.545924 −0.272962 0.962025i \(-0.588003\pi\)
−0.272962 + 0.962025i \(0.588003\pi\)
\(854\) 15.5796 0.533122
\(855\) 4.84695 0.165762
\(856\) 28.4023 0.970771
\(857\) −22.9826 −0.785072 −0.392536 0.919737i \(-0.628402\pi\)
−0.392536 + 0.919737i \(0.628402\pi\)
\(858\) −52.9942 −1.80919
\(859\) −7.19134 −0.245365 −0.122683 0.992446i \(-0.539150\pi\)
−0.122683 + 0.992446i \(0.539150\pi\)
\(860\) 61.8867 2.11032
\(861\) −7.78435 −0.265290
\(862\) 24.8934 0.847873
\(863\) −16.8748 −0.574424 −0.287212 0.957867i \(-0.592728\pi\)
−0.287212 + 0.957867i \(0.592728\pi\)
\(864\) −3.81891 −0.129922
\(865\) 5.10349 0.173524
\(866\) −62.5257 −2.12471
\(867\) 15.5042 0.526550
\(868\) 17.5263 0.594883
\(869\) −5.97557 −0.202707
\(870\) −13.7070 −0.464710
\(871\) 37.0979 1.25701
\(872\) −61.9397 −2.09754
\(873\) −10.3978 −0.351914
\(874\) −7.32622 −0.247813
\(875\) 12.1674 0.411332
\(876\) −27.5647 −0.931323
\(877\) −7.00838 −0.236656 −0.118328 0.992975i \(-0.537753\pi\)
−0.118328 + 0.992975i \(0.537753\pi\)
\(878\) 2.85279 0.0962772
\(879\) 28.6888 0.967649
\(880\) 13.2595 0.446976
\(881\) −12.9394 −0.435938 −0.217969 0.975956i \(-0.569943\pi\)
−0.217969 + 0.975956i \(0.569943\pi\)
\(882\) −2.35415 −0.0792683
\(883\) 37.9016 1.27549 0.637744 0.770248i \(-0.279868\pi\)
0.637744 + 0.770248i \(0.279868\pi\)
\(884\) −19.9273 −0.670228
\(885\) −16.2971 −0.547821
\(886\) −22.4571 −0.754461
\(887\) −16.3022 −0.547375 −0.273688 0.961819i \(-0.588243\pi\)
−0.273688 + 0.961819i \(0.588243\pi\)
\(888\) 17.8842 0.600155
\(889\) −10.9174 −0.366158
\(890\) 44.2095 1.48191
\(891\) −4.89366 −0.163944
\(892\) 12.1354 0.406324
\(893\) 26.1836 0.876201
\(894\) −21.1544 −0.707510
\(895\) −17.9994 −0.601654
\(896\) 20.4093 0.681826
\(897\) 5.47444 0.182786
\(898\) −38.4215 −1.28214
\(899\) 15.5435 0.518405
\(900\) −5.54115 −0.184705
\(901\) 12.3761 0.412307
\(902\) 89.6788 2.98598
\(903\) 9.42641 0.313691
\(904\) 7.17759 0.238723
\(905\) 34.4004 1.14351
\(906\) −49.9933 −1.66092
\(907\) 58.4566 1.94102 0.970510 0.241059i \(-0.0774949\pi\)
0.970510 + 0.241059i \(0.0774949\pi\)
\(908\) −23.2498 −0.771571
\(909\) 16.3808 0.543317
\(910\) 20.0722 0.665388
\(911\) 40.9171 1.35565 0.677823 0.735225i \(-0.262924\pi\)
0.677823 + 0.735225i \(0.262924\pi\)
\(912\) 3.82260 0.126579
\(913\) −34.6041 −1.14523
\(914\) 31.5233 1.04270
\(915\) −12.2666 −0.405520
\(916\) 53.9507 1.78258
\(917\) −18.4955 −0.610774
\(918\) −2.87920 −0.0950277
\(919\) 52.0962 1.71850 0.859248 0.511559i \(-0.170932\pi\)
0.859248 + 0.511559i \(0.170932\pi\)
\(920\) −8.00756 −0.264002
\(921\) −1.95046 −0.0642697
\(922\) −53.0050 −1.74563
\(923\) −19.0735 −0.627812
\(924\) 17.3334 0.570226
\(925\) −7.70725 −0.253413
\(926\) 25.8323 0.848901
\(927\) 3.30738 0.108628
\(928\) 11.9963 0.393798
\(929\) 38.2945 1.25640 0.628201 0.778051i \(-0.283791\pi\)
0.628201 + 0.778051i \(0.283791\pi\)
\(930\) −21.5912 −0.708002
\(931\) −2.61498 −0.0857024
\(932\) −58.4118 −1.91334
\(933\) 21.1800 0.693403
\(934\) −20.6574 −0.675930
\(935\) −11.0936 −0.362799
\(936\) −16.6987 −0.545813
\(937\) −1.38476 −0.0452380 −0.0226190 0.999744i \(-0.507200\pi\)
−0.0226190 + 0.999744i \(0.507200\pi\)
\(938\) −18.9855 −0.619898
\(939\) 12.8187 0.418322
\(940\) 65.7374 2.14412
\(941\) 3.25997 0.106272 0.0531360 0.998587i \(-0.483078\pi\)
0.0531360 + 0.998587i \(0.483078\pi\)
\(942\) 55.3297 1.80274
\(943\) −9.26406 −0.301679
\(944\) −12.8529 −0.418326
\(945\) 1.85354 0.0602955
\(946\) −108.596 −3.53076
\(947\) 36.0830 1.17254 0.586271 0.810115i \(-0.300596\pi\)
0.586271 + 0.810115i \(0.300596\pi\)
\(948\) −4.32510 −0.140473
\(949\) 35.7984 1.16207
\(950\) −9.63055 −0.312456
\(951\) −4.36874 −0.141666
\(952\) 4.43975 0.143893
\(953\) 28.6766 0.928926 0.464463 0.885593i \(-0.346247\pi\)
0.464463 + 0.885593i \(0.346247\pi\)
\(954\) 23.8221 0.771267
\(955\) −3.80345 −0.123077
\(956\) 39.7304 1.28497
\(957\) 15.3724 0.496918
\(958\) 60.1491 1.94333
\(959\) −17.6056 −0.568514
\(960\) −22.0829 −0.712721
\(961\) −6.51597 −0.210193
\(962\) −53.3512 −1.72011
\(963\) −7.82407 −0.252127
\(964\) −56.3950 −1.81636
\(965\) −3.91774 −0.126116
\(966\) −2.80164 −0.0901413
\(967\) −44.5008 −1.43105 −0.715524 0.698588i \(-0.753812\pi\)
−0.715524 + 0.698588i \(0.753812\pi\)
\(968\) −47.0023 −1.51071
\(969\) −3.19820 −0.102741
\(970\) −45.3709 −1.45677
\(971\) 12.7056 0.407742 0.203871 0.978998i \(-0.434648\pi\)
0.203871 + 0.978998i \(0.434648\pi\)
\(972\) −3.54201 −0.113610
\(973\) 3.45178 0.110659
\(974\) 27.4340 0.879042
\(975\) 7.19633 0.230467
\(976\) −9.67416 −0.309662
\(977\) 8.47552 0.271156 0.135578 0.990767i \(-0.456711\pi\)
0.135578 + 0.990767i \(0.456711\pi\)
\(978\) −21.5003 −0.687503
\(979\) −49.5809 −1.58461
\(980\) −6.56524 −0.209719
\(981\) 17.0627 0.544771
\(982\) −22.0296 −0.702992
\(983\) −42.9901 −1.37117 −0.685586 0.727992i \(-0.740454\pi\)
−0.685586 + 0.727992i \(0.740454\pi\)
\(984\) 28.2581 0.900836
\(985\) −33.4885 −1.06703
\(986\) 9.04439 0.288032
\(987\) 10.0129 0.318715
\(988\) −42.6067 −1.35550
\(989\) 11.2183 0.356720
\(990\) −21.3534 −0.678657
\(991\) −11.4870 −0.364895 −0.182448 0.983216i \(-0.558402\pi\)
−0.182448 + 0.983216i \(0.558402\pi\)
\(992\) 18.8965 0.599964
\(993\) 21.3008 0.675962
\(994\) 9.76119 0.309606
\(995\) 37.6167 1.19253
\(996\) −25.0463 −0.793623
\(997\) 41.3523 1.30964 0.654820 0.755785i \(-0.272745\pi\)
0.654820 + 0.755785i \(0.272745\pi\)
\(998\) 45.1614 1.42956
\(999\) −4.92663 −0.155872
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 \(a_p\))