Properties

Label 8015.2.a.l.1.47
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.47
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.71867 q^{2} +2.98867 q^{3} +0.953829 q^{4} -1.00000 q^{5} +5.13655 q^{6} -1.00000 q^{7} -1.79802 q^{8} +5.93217 q^{9} +O(q^{10})\) \(q+1.71867 q^{2} +2.98867 q^{3} +0.953829 q^{4} -1.00000 q^{5} +5.13655 q^{6} -1.00000 q^{7} -1.79802 q^{8} +5.93217 q^{9} -1.71867 q^{10} -2.58842 q^{11} +2.85068 q^{12} +2.49362 q^{13} -1.71867 q^{14} -2.98867 q^{15} -4.99787 q^{16} -1.60527 q^{17} +10.1955 q^{18} +4.99210 q^{19} -0.953829 q^{20} -2.98867 q^{21} -4.44865 q^{22} +6.92222 q^{23} -5.37371 q^{24} +1.00000 q^{25} +4.28570 q^{26} +8.76331 q^{27} -0.953829 q^{28} +10.2434 q^{29} -5.13655 q^{30} +8.48682 q^{31} -4.99364 q^{32} -7.73596 q^{33} -2.75893 q^{34} +1.00000 q^{35} +5.65828 q^{36} -7.50564 q^{37} +8.57978 q^{38} +7.45261 q^{39} +1.79802 q^{40} +0.0621418 q^{41} -5.13655 q^{42} -4.94818 q^{43} -2.46892 q^{44} -5.93217 q^{45} +11.8970 q^{46} +2.50251 q^{47} -14.9370 q^{48} +1.00000 q^{49} +1.71867 q^{50} -4.79762 q^{51} +2.37848 q^{52} +10.4911 q^{53} +15.0612 q^{54} +2.58842 q^{55} +1.79802 q^{56} +14.9198 q^{57} +17.6051 q^{58} -10.9191 q^{59} -2.85068 q^{60} +2.59765 q^{61} +14.5861 q^{62} -5.93217 q^{63} +1.41331 q^{64} -2.49362 q^{65} -13.2956 q^{66} -2.10858 q^{67} -1.53115 q^{68} +20.6882 q^{69} +1.71867 q^{70} +13.1283 q^{71} -10.6662 q^{72} +12.0683 q^{73} -12.8997 q^{74} +2.98867 q^{75} +4.76161 q^{76} +2.58842 q^{77} +12.8086 q^{78} -14.0565 q^{79} +4.99787 q^{80} +8.39415 q^{81} +0.106801 q^{82} +6.55734 q^{83} -2.85068 q^{84} +1.60527 q^{85} -8.50429 q^{86} +30.6143 q^{87} +4.65405 q^{88} -0.754527 q^{89} -10.1955 q^{90} -2.49362 q^{91} +6.60261 q^{92} +25.3644 q^{93} +4.30099 q^{94} -4.99210 q^{95} -14.9244 q^{96} -14.2332 q^{97} +1.71867 q^{98} -15.3550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.71867 1.21528 0.607642 0.794211i \(-0.292116\pi\)
0.607642 + 0.794211i \(0.292116\pi\)
\(3\) 2.98867 1.72551 0.862756 0.505621i \(-0.168736\pi\)
0.862756 + 0.505621i \(0.168736\pi\)
\(4\) 0.953829 0.476915
\(5\) −1.00000 −0.447214
\(6\) 5.13655 2.09699
\(7\) −1.00000 −0.377964
\(8\) −1.79802 −0.635697
\(9\) 5.93217 1.97739
\(10\) −1.71867 −0.543491
\(11\) −2.58842 −0.780439 −0.390220 0.920722i \(-0.627601\pi\)
−0.390220 + 0.920722i \(0.627601\pi\)
\(12\) 2.85068 0.822922
\(13\) 2.49362 0.691605 0.345802 0.938307i \(-0.387607\pi\)
0.345802 + 0.938307i \(0.387607\pi\)
\(14\) −1.71867 −0.459334
\(15\) −2.98867 −0.771672
\(16\) −4.99787 −1.24947
\(17\) −1.60527 −0.389335 −0.194667 0.980869i \(-0.562363\pi\)
−0.194667 + 0.980869i \(0.562363\pi\)
\(18\) 10.1955 2.40309
\(19\) 4.99210 1.14527 0.572633 0.819812i \(-0.305922\pi\)
0.572633 + 0.819812i \(0.305922\pi\)
\(20\) −0.953829 −0.213283
\(21\) −2.98867 −0.652182
\(22\) −4.44865 −0.948455
\(23\) 6.92222 1.44338 0.721691 0.692215i \(-0.243365\pi\)
0.721691 + 0.692215i \(0.243365\pi\)
\(24\) −5.37371 −1.09690
\(25\) 1.00000 0.200000
\(26\) 4.28570 0.840496
\(27\) 8.76331 1.68650
\(28\) −0.953829 −0.180257
\(29\) 10.2434 1.90216 0.951079 0.308949i \(-0.0999772\pi\)
0.951079 + 0.308949i \(0.0999772\pi\)
\(30\) −5.13655 −0.937801
\(31\) 8.48682 1.52428 0.762139 0.647413i \(-0.224149\pi\)
0.762139 + 0.647413i \(0.224149\pi\)
\(32\) −4.99364 −0.882760
\(33\) −7.73596 −1.34666
\(34\) −2.75893 −0.473152
\(35\) 1.00000 0.169031
\(36\) 5.65828 0.943046
\(37\) −7.50564 −1.23392 −0.616960 0.786995i \(-0.711636\pi\)
−0.616960 + 0.786995i \(0.711636\pi\)
\(38\) 8.57978 1.39182
\(39\) 7.45261 1.19337
\(40\) 1.79802 0.284292
\(41\) 0.0621418 0.00970492 0.00485246 0.999988i \(-0.498455\pi\)
0.00485246 + 0.999988i \(0.498455\pi\)
\(42\) −5.13655 −0.792586
\(43\) −4.94818 −0.754590 −0.377295 0.926093i \(-0.623146\pi\)
−0.377295 + 0.926093i \(0.623146\pi\)
\(44\) −2.46892 −0.372203
\(45\) −5.93217 −0.884316
\(46\) 11.8970 1.75412
\(47\) 2.50251 0.365028 0.182514 0.983203i \(-0.441576\pi\)
0.182514 + 0.983203i \(0.441576\pi\)
\(48\) −14.9370 −2.15597
\(49\) 1.00000 0.142857
\(50\) 1.71867 0.243057
\(51\) −4.79762 −0.671802
\(52\) 2.37848 0.329836
\(53\) 10.4911 1.44107 0.720534 0.693419i \(-0.243897\pi\)
0.720534 + 0.693419i \(0.243897\pi\)
\(54\) 15.0612 2.04958
\(55\) 2.58842 0.349023
\(56\) 1.79802 0.240271
\(57\) 14.9198 1.97617
\(58\) 17.6051 2.31166
\(59\) −10.9191 −1.42154 −0.710770 0.703424i \(-0.751653\pi\)
−0.710770 + 0.703424i \(0.751653\pi\)
\(60\) −2.85068 −0.368022
\(61\) 2.59765 0.332594 0.166297 0.986076i \(-0.446819\pi\)
0.166297 + 0.986076i \(0.446819\pi\)
\(62\) 14.5861 1.85243
\(63\) −5.93217 −0.747383
\(64\) 1.41331 0.176663
\(65\) −2.49362 −0.309295
\(66\) −13.2956 −1.63657
\(67\) −2.10858 −0.257604 −0.128802 0.991670i \(-0.541113\pi\)
−0.128802 + 0.991670i \(0.541113\pi\)
\(68\) −1.53115 −0.185679
\(69\) 20.6882 2.49057
\(70\) 1.71867 0.205420
\(71\) 13.1283 1.55805 0.779023 0.626995i \(-0.215715\pi\)
0.779023 + 0.626995i \(0.215715\pi\)
\(72\) −10.6662 −1.25702
\(73\) 12.0683 1.41249 0.706244 0.707969i \(-0.250388\pi\)
0.706244 + 0.707969i \(0.250388\pi\)
\(74\) −12.8997 −1.49956
\(75\) 2.98867 0.345102
\(76\) 4.76161 0.546194
\(77\) 2.58842 0.294978
\(78\) 12.8086 1.45029
\(79\) −14.0565 −1.58148 −0.790741 0.612151i \(-0.790304\pi\)
−0.790741 + 0.612151i \(0.790304\pi\)
\(80\) 4.99787 0.558779
\(81\) 8.39415 0.932684
\(82\) 0.106801 0.0117942
\(83\) 6.55734 0.719761 0.359881 0.932998i \(-0.382817\pi\)
0.359881 + 0.932998i \(0.382817\pi\)
\(84\) −2.85068 −0.311035
\(85\) 1.60527 0.174116
\(86\) −8.50429 −0.917041
\(87\) 30.6143 3.28219
\(88\) 4.65405 0.496123
\(89\) −0.754527 −0.0799797 −0.0399898 0.999200i \(-0.512733\pi\)
−0.0399898 + 0.999200i \(0.512733\pi\)
\(90\) −10.1955 −1.07469
\(91\) −2.49362 −0.261402
\(92\) 6.60261 0.688370
\(93\) 25.3644 2.63016
\(94\) 4.30099 0.443613
\(95\) −4.99210 −0.512179
\(96\) −14.9244 −1.52321
\(97\) −14.2332 −1.44517 −0.722583 0.691284i \(-0.757045\pi\)
−0.722583 + 0.691284i \(0.757045\pi\)
\(98\) 1.71867 0.173612
\(99\) −15.3550 −1.54323
\(100\) 0.953829 0.0953829
\(101\) −2.88454 −0.287023 −0.143511 0.989649i \(-0.545839\pi\)
−0.143511 + 0.989649i \(0.545839\pi\)
\(102\) −8.24554 −0.816430
\(103\) −9.54503 −0.940500 −0.470250 0.882533i \(-0.655836\pi\)
−0.470250 + 0.882533i \(0.655836\pi\)
\(104\) −4.48358 −0.439651
\(105\) 2.98867 0.291665
\(106\) 18.0308 1.75131
\(107\) −13.8210 −1.33613 −0.668063 0.744105i \(-0.732876\pi\)
−0.668063 + 0.744105i \(0.732876\pi\)
\(108\) 8.35870 0.804316
\(109\) 17.3847 1.66515 0.832575 0.553912i \(-0.186866\pi\)
0.832575 + 0.553912i \(0.186866\pi\)
\(110\) 4.44865 0.424162
\(111\) −22.4319 −2.12914
\(112\) 4.99787 0.472254
\(113\) 15.5005 1.45816 0.729082 0.684426i \(-0.239947\pi\)
0.729082 + 0.684426i \(0.239947\pi\)
\(114\) 25.6422 2.40161
\(115\) −6.92222 −0.645500
\(116\) 9.77048 0.907167
\(117\) 14.7926 1.36757
\(118\) −18.7663 −1.72757
\(119\) 1.60527 0.147155
\(120\) 5.37371 0.490550
\(121\) −4.30006 −0.390914
\(122\) 4.46450 0.404197
\(123\) 0.185722 0.0167460
\(124\) 8.09498 0.726951
\(125\) −1.00000 −0.0894427
\(126\) −10.1955 −0.908283
\(127\) −6.28392 −0.557608 −0.278804 0.960348i \(-0.589938\pi\)
−0.278804 + 0.960348i \(0.589938\pi\)
\(128\) 12.4163 1.09746
\(129\) −14.7885 −1.30205
\(130\) −4.28570 −0.375881
\(131\) 10.4308 0.911344 0.455672 0.890148i \(-0.349399\pi\)
0.455672 + 0.890148i \(0.349399\pi\)
\(132\) −7.37878 −0.642241
\(133\) −4.99210 −0.432870
\(134\) −3.62395 −0.313061
\(135\) −8.76331 −0.754225
\(136\) 2.88631 0.247499
\(137\) −4.31594 −0.368736 −0.184368 0.982857i \(-0.559024\pi\)
−0.184368 + 0.982857i \(0.559024\pi\)
\(138\) 35.5563 3.02675
\(139\) 10.4798 0.888887 0.444443 0.895807i \(-0.353401\pi\)
0.444443 + 0.895807i \(0.353401\pi\)
\(140\) 0.953829 0.0806133
\(141\) 7.47918 0.629860
\(142\) 22.5633 1.89347
\(143\) −6.45454 −0.539756
\(144\) −29.6482 −2.47068
\(145\) −10.2434 −0.850671
\(146\) 20.7414 1.71657
\(147\) 2.98867 0.246502
\(148\) −7.15910 −0.588474
\(149\) 16.7860 1.37516 0.687581 0.726108i \(-0.258673\pi\)
0.687581 + 0.726108i \(0.258673\pi\)
\(150\) 5.13655 0.419397
\(151\) 5.26242 0.428250 0.214125 0.976806i \(-0.431310\pi\)
0.214125 + 0.976806i \(0.431310\pi\)
\(152\) −8.97591 −0.728043
\(153\) −9.52273 −0.769867
\(154\) 4.44865 0.358482
\(155\) −8.48682 −0.681678
\(156\) 7.10851 0.569136
\(157\) 8.32402 0.664329 0.332165 0.943221i \(-0.392221\pi\)
0.332165 + 0.943221i \(0.392221\pi\)
\(158\) −24.1585 −1.92195
\(159\) 31.3546 2.48658
\(160\) 4.99364 0.394782
\(161\) −6.92222 −0.545547
\(162\) 14.4268 1.13348
\(163\) 19.9541 1.56292 0.781462 0.623953i \(-0.214474\pi\)
0.781462 + 0.623953i \(0.214474\pi\)
\(164\) 0.0592727 0.00462842
\(165\) 7.73596 0.602244
\(166\) 11.2699 0.874714
\(167\) −4.07611 −0.315419 −0.157709 0.987486i \(-0.550411\pi\)
−0.157709 + 0.987486i \(0.550411\pi\)
\(168\) 5.37371 0.414590
\(169\) −6.78188 −0.521683
\(170\) 2.75893 0.211600
\(171\) 29.6140 2.26464
\(172\) −4.71972 −0.359875
\(173\) 23.9651 1.82203 0.911016 0.412371i \(-0.135299\pi\)
0.911016 + 0.412371i \(0.135299\pi\)
\(174\) 52.6159 3.98880
\(175\) −1.00000 −0.0755929
\(176\) 12.9366 0.975133
\(177\) −32.6335 −2.45288
\(178\) −1.29678 −0.0971980
\(179\) 2.12699 0.158979 0.0794894 0.996836i \(-0.474671\pi\)
0.0794894 + 0.996836i \(0.474671\pi\)
\(180\) −5.65828 −0.421743
\(181\) −25.3090 −1.88120 −0.940600 0.339517i \(-0.889736\pi\)
−0.940600 + 0.339517i \(0.889736\pi\)
\(182\) −4.28570 −0.317678
\(183\) 7.76352 0.573896
\(184\) −12.4463 −0.917554
\(185\) 7.50564 0.551825
\(186\) 43.5930 3.19639
\(187\) 4.15512 0.303852
\(188\) 2.38696 0.174087
\(189\) −8.76331 −0.637437
\(190\) −8.57978 −0.622443
\(191\) −18.7581 −1.35729 −0.678644 0.734468i \(-0.737432\pi\)
−0.678644 + 0.734468i \(0.737432\pi\)
\(192\) 4.22392 0.304835
\(193\) −1.09742 −0.0789943 −0.0394971 0.999220i \(-0.512576\pi\)
−0.0394971 + 0.999220i \(0.512576\pi\)
\(194\) −24.4622 −1.75629
\(195\) −7.45261 −0.533692
\(196\) 0.953829 0.0681307
\(197\) 12.6261 0.899574 0.449787 0.893136i \(-0.351500\pi\)
0.449787 + 0.893136i \(0.351500\pi\)
\(198\) −26.3902 −1.87547
\(199\) −3.79252 −0.268845 −0.134422 0.990924i \(-0.542918\pi\)
−0.134422 + 0.990924i \(0.542918\pi\)
\(200\) −1.79802 −0.127139
\(201\) −6.30185 −0.444498
\(202\) −4.95758 −0.348814
\(203\) −10.2434 −0.718948
\(204\) −4.57611 −0.320392
\(205\) −0.0621418 −0.00434017
\(206\) −16.4048 −1.14297
\(207\) 41.0638 2.85413
\(208\) −12.4628 −0.864137
\(209\) −12.9217 −0.893811
\(210\) 5.13655 0.354455
\(211\) 18.1869 1.25204 0.626019 0.779808i \(-0.284683\pi\)
0.626019 + 0.779808i \(0.284683\pi\)
\(212\) 10.0068 0.687267
\(213\) 39.2363 2.68843
\(214\) −23.7537 −1.62377
\(215\) 4.94818 0.337463
\(216\) −15.7566 −1.07210
\(217\) −8.48682 −0.576123
\(218\) 29.8785 2.02363
\(219\) 36.0682 2.43726
\(220\) 2.46892 0.166454
\(221\) −4.00292 −0.269266
\(222\) −38.5531 −2.58751
\(223\) −11.3104 −0.757399 −0.378699 0.925520i \(-0.623629\pi\)
−0.378699 + 0.925520i \(0.623629\pi\)
\(224\) 4.99364 0.333652
\(225\) 5.93217 0.395478
\(226\) 26.6402 1.77208
\(227\) 2.46590 0.163668 0.0818338 0.996646i \(-0.473922\pi\)
0.0818338 + 0.996646i \(0.473922\pi\)
\(228\) 14.2309 0.942465
\(229\) 1.00000 0.0660819
\(230\) −11.8970 −0.784466
\(231\) 7.73596 0.508989
\(232\) −18.4179 −1.20920
\(233\) 15.4443 1.01179 0.505894 0.862595i \(-0.331163\pi\)
0.505894 + 0.862595i \(0.331163\pi\)
\(234\) 25.4235 1.66199
\(235\) −2.50251 −0.163246
\(236\) −10.4149 −0.677953
\(237\) −42.0104 −2.72887
\(238\) 2.75893 0.178835
\(239\) 4.73569 0.306326 0.153163 0.988201i \(-0.451054\pi\)
0.153163 + 0.988201i \(0.451054\pi\)
\(240\) 14.9370 0.964179
\(241\) −0.223275 −0.0143824 −0.00719120 0.999974i \(-0.502289\pi\)
−0.00719120 + 0.999974i \(0.502289\pi\)
\(242\) −7.39038 −0.475072
\(243\) −1.20253 −0.0771426
\(244\) 2.47771 0.158619
\(245\) −1.00000 −0.0638877
\(246\) 0.319194 0.0203511
\(247\) 12.4484 0.792072
\(248\) −15.2595 −0.968980
\(249\) 19.5977 1.24196
\(250\) −1.71867 −0.108698
\(251\) 6.73357 0.425019 0.212510 0.977159i \(-0.431836\pi\)
0.212510 + 0.977159i \(0.431836\pi\)
\(252\) −5.65828 −0.356438
\(253\) −17.9176 −1.12647
\(254\) −10.8000 −0.677652
\(255\) 4.79762 0.300439
\(256\) 18.5129 1.15706
\(257\) −7.76249 −0.484211 −0.242105 0.970250i \(-0.577838\pi\)
−0.242105 + 0.970250i \(0.577838\pi\)
\(258\) −25.4166 −1.58237
\(259\) 7.50564 0.466378
\(260\) −2.37848 −0.147507
\(261\) 60.7658 3.76131
\(262\) 17.9271 1.10754
\(263\) −26.6773 −1.64500 −0.822498 0.568769i \(-0.807420\pi\)
−0.822498 + 0.568769i \(0.807420\pi\)
\(264\) 13.9094 0.856066
\(265\) −10.4911 −0.644466
\(266\) −8.57978 −0.526060
\(267\) −2.25503 −0.138006
\(268\) −2.01122 −0.122855
\(269\) −22.1004 −1.34749 −0.673743 0.738965i \(-0.735315\pi\)
−0.673743 + 0.738965i \(0.735315\pi\)
\(270\) −15.0612 −0.916598
\(271\) −15.1357 −0.919427 −0.459714 0.888067i \(-0.652048\pi\)
−0.459714 + 0.888067i \(0.652048\pi\)
\(272\) 8.02292 0.486461
\(273\) −7.45261 −0.451052
\(274\) −7.41768 −0.448119
\(275\) −2.58842 −0.156088
\(276\) 19.7331 1.18779
\(277\) −27.1869 −1.63350 −0.816752 0.576989i \(-0.804228\pi\)
−0.816752 + 0.576989i \(0.804228\pi\)
\(278\) 18.0114 1.08025
\(279\) 50.3453 3.01409
\(280\) −1.79802 −0.107452
\(281\) −31.3042 −1.86745 −0.933725 0.357991i \(-0.883462\pi\)
−0.933725 + 0.357991i \(0.883462\pi\)
\(282\) 12.8542 0.765459
\(283\) 8.05205 0.478645 0.239322 0.970940i \(-0.423075\pi\)
0.239322 + 0.970940i \(0.423075\pi\)
\(284\) 12.5222 0.743055
\(285\) −14.9198 −0.883771
\(286\) −11.0932 −0.655956
\(287\) −0.0621418 −0.00366812
\(288\) −29.6232 −1.74556
\(289\) −14.4231 −0.848418
\(290\) −17.6051 −1.03381
\(291\) −42.5385 −2.49365
\(292\) 11.5111 0.673636
\(293\) −29.2879 −1.71102 −0.855508 0.517790i \(-0.826755\pi\)
−0.855508 + 0.517790i \(0.826755\pi\)
\(294\) 5.13655 0.299569
\(295\) 10.9191 0.635732
\(296\) 13.4953 0.784399
\(297\) −22.6832 −1.31621
\(298\) 28.8496 1.67121
\(299\) 17.2613 0.998249
\(300\) 2.85068 0.164584
\(301\) 4.94818 0.285208
\(302\) 9.04436 0.520445
\(303\) −8.62096 −0.495261
\(304\) −24.9499 −1.43097
\(305\) −2.59765 −0.148741
\(306\) −16.3664 −0.935607
\(307\) −13.6449 −0.778758 −0.389379 0.921078i \(-0.627310\pi\)
−0.389379 + 0.921078i \(0.627310\pi\)
\(308\) 2.46892 0.140679
\(309\) −28.5270 −1.62284
\(310\) −14.5861 −0.828432
\(311\) −21.2834 −1.20687 −0.603434 0.797413i \(-0.706201\pi\)
−0.603434 + 0.797413i \(0.706201\pi\)
\(312\) −13.4000 −0.758623
\(313\) −6.96416 −0.393637 −0.196819 0.980440i \(-0.563061\pi\)
−0.196819 + 0.980440i \(0.563061\pi\)
\(314\) 14.3063 0.807349
\(315\) 5.93217 0.334240
\(316\) −13.4075 −0.754232
\(317\) 15.3647 0.862970 0.431485 0.902120i \(-0.357990\pi\)
0.431485 + 0.902120i \(0.357990\pi\)
\(318\) 53.8882 3.02190
\(319\) −26.5144 −1.48452
\(320\) −1.41331 −0.0790063
\(321\) −41.3064 −2.30550
\(322\) −11.8970 −0.662994
\(323\) −8.01366 −0.445892
\(324\) 8.00659 0.444810
\(325\) 2.49362 0.138321
\(326\) 34.2945 1.89940
\(327\) 51.9572 2.87324
\(328\) −0.111732 −0.00616939
\(329\) −2.50251 −0.137968
\(330\) 13.2956 0.731897
\(331\) −6.25879 −0.344014 −0.172007 0.985096i \(-0.555025\pi\)
−0.172007 + 0.985096i \(0.555025\pi\)
\(332\) 6.25458 0.343265
\(333\) −44.5247 −2.43994
\(334\) −7.00549 −0.383323
\(335\) 2.10858 0.115204
\(336\) 14.9370 0.814880
\(337\) 6.33726 0.345213 0.172606 0.984991i \(-0.444781\pi\)
0.172606 + 0.984991i \(0.444781\pi\)
\(338\) −11.6558 −0.633993
\(339\) 46.3259 2.51608
\(340\) 1.53115 0.0830384
\(341\) −21.9675 −1.18961
\(342\) 50.8967 2.75218
\(343\) −1.00000 −0.0539949
\(344\) 8.89694 0.479691
\(345\) −20.6882 −1.11382
\(346\) 41.1881 2.21429
\(347\) 29.2180 1.56850 0.784252 0.620443i \(-0.213047\pi\)
0.784252 + 0.620443i \(0.213047\pi\)
\(348\) 29.2008 1.56533
\(349\) 14.8977 0.797458 0.398729 0.917069i \(-0.369451\pi\)
0.398729 + 0.917069i \(0.369451\pi\)
\(350\) −1.71867 −0.0918668
\(351\) 21.8523 1.16639
\(352\) 12.9257 0.688941
\(353\) 5.29554 0.281853 0.140927 0.990020i \(-0.454992\pi\)
0.140927 + 0.990020i \(0.454992\pi\)
\(354\) −56.0862 −2.98095
\(355\) −13.1283 −0.696780
\(356\) −0.719690 −0.0381435
\(357\) 4.79762 0.253917
\(358\) 3.65560 0.193204
\(359\) −36.4601 −1.92429 −0.962145 0.272538i \(-0.912137\pi\)
−0.962145 + 0.272538i \(0.912137\pi\)
\(360\) 10.6662 0.562157
\(361\) 5.92107 0.311636
\(362\) −43.4978 −2.28619
\(363\) −12.8515 −0.674527
\(364\) −2.37848 −0.124666
\(365\) −12.0683 −0.631683
\(366\) 13.3429 0.697446
\(367\) 12.0061 0.626714 0.313357 0.949635i \(-0.398546\pi\)
0.313357 + 0.949635i \(0.398546\pi\)
\(368\) −34.5963 −1.80346
\(369\) 0.368636 0.0191904
\(370\) 12.8997 0.670624
\(371\) −10.4911 −0.544673
\(372\) 24.1933 1.25436
\(373\) −0.947578 −0.0490637 −0.0245319 0.999699i \(-0.507810\pi\)
−0.0245319 + 0.999699i \(0.507810\pi\)
\(374\) 7.14128 0.369267
\(375\) −2.98867 −0.154334
\(376\) −4.49957 −0.232047
\(377\) 25.5432 1.31554
\(378\) −15.0612 −0.774667
\(379\) 12.0547 0.619208 0.309604 0.950866i \(-0.399804\pi\)
0.309604 + 0.950866i \(0.399804\pi\)
\(380\) −4.76161 −0.244266
\(381\) −18.7806 −0.962159
\(382\) −32.2390 −1.64949
\(383\) −9.57640 −0.489331 −0.244666 0.969608i \(-0.578678\pi\)
−0.244666 + 0.969608i \(0.578678\pi\)
\(384\) 37.1083 1.89367
\(385\) −2.58842 −0.131918
\(386\) −1.88611 −0.0960005
\(387\) −29.3535 −1.49212
\(388\) −13.5761 −0.689221
\(389\) −13.1398 −0.666217 −0.333108 0.942889i \(-0.608097\pi\)
−0.333108 + 0.942889i \(0.608097\pi\)
\(390\) −12.8086 −0.648587
\(391\) −11.1120 −0.561959
\(392\) −1.79802 −0.0908139
\(393\) 31.1743 1.57253
\(394\) 21.7002 1.09324
\(395\) 14.0565 0.707260
\(396\) −14.6460 −0.735991
\(397\) 25.8115 1.29544 0.647722 0.761877i \(-0.275722\pi\)
0.647722 + 0.761877i \(0.275722\pi\)
\(398\) −6.51809 −0.326722
\(399\) −14.9198 −0.746922
\(400\) −4.99787 −0.249893
\(401\) −0.267879 −0.0133772 −0.00668862 0.999978i \(-0.502129\pi\)
−0.00668862 + 0.999978i \(0.502129\pi\)
\(402\) −10.8308 −0.540191
\(403\) 21.1629 1.05420
\(404\) −2.75136 −0.136885
\(405\) −8.39415 −0.417109
\(406\) −17.6051 −0.873726
\(407\) 19.4278 0.962999
\(408\) 8.62624 0.427062
\(409\) 6.83566 0.338002 0.169001 0.985616i \(-0.445946\pi\)
0.169001 + 0.985616i \(0.445946\pi\)
\(410\) −0.106801 −0.00527454
\(411\) −12.8989 −0.636258
\(412\) −9.10433 −0.448538
\(413\) 10.9191 0.537292
\(414\) 70.5751 3.46858
\(415\) −6.55734 −0.321887
\(416\) −12.4522 −0.610521
\(417\) 31.3208 1.53378
\(418\) −22.2081 −1.08623
\(419\) −29.1855 −1.42580 −0.712901 0.701264i \(-0.752619\pi\)
−0.712901 + 0.701264i \(0.752619\pi\)
\(420\) 2.85068 0.139099
\(421\) 8.75521 0.426703 0.213351 0.976976i \(-0.431562\pi\)
0.213351 + 0.976976i \(0.431562\pi\)
\(422\) 31.2573 1.52158
\(423\) 14.8453 0.721803
\(424\) −18.8633 −0.916083
\(425\) −1.60527 −0.0778669
\(426\) 67.4343 3.26720
\(427\) −2.59765 −0.125709
\(428\) −13.1829 −0.637218
\(429\) −19.2905 −0.931355
\(430\) 8.50429 0.410113
\(431\) −12.8117 −0.617119 −0.308560 0.951205i \(-0.599847\pi\)
−0.308560 + 0.951205i \(0.599847\pi\)
\(432\) −43.7979 −2.10723
\(433\) −28.9383 −1.39068 −0.695342 0.718679i \(-0.744747\pi\)
−0.695342 + 0.718679i \(0.744747\pi\)
\(434\) −14.5861 −0.700153
\(435\) −30.6143 −1.46784
\(436\) 16.5820 0.794135
\(437\) 34.5564 1.65306
\(438\) 61.9894 2.96197
\(439\) −17.4275 −0.831771 −0.415885 0.909417i \(-0.636528\pi\)
−0.415885 + 0.909417i \(0.636528\pi\)
\(440\) −4.65405 −0.221873
\(441\) 5.93217 0.282484
\(442\) −6.87971 −0.327234
\(443\) −31.1315 −1.47910 −0.739552 0.673100i \(-0.764962\pi\)
−0.739552 + 0.673100i \(0.764962\pi\)
\(444\) −21.3962 −1.01542
\(445\) 0.754527 0.0357680
\(446\) −19.4388 −0.920454
\(447\) 50.1678 2.37286
\(448\) −1.41331 −0.0667725
\(449\) −8.20023 −0.386993 −0.193496 0.981101i \(-0.561983\pi\)
−0.193496 + 0.981101i \(0.561983\pi\)
\(450\) 10.1955 0.480618
\(451\) −0.160849 −0.00757410
\(452\) 14.7848 0.695420
\(453\) 15.7277 0.738950
\(454\) 4.23807 0.198903
\(455\) 2.49362 0.116903
\(456\) −26.8261 −1.25625
\(457\) 8.96593 0.419408 0.209704 0.977765i \(-0.432750\pi\)
0.209704 + 0.977765i \(0.432750\pi\)
\(458\) 1.71867 0.0803082
\(459\) −14.0675 −0.656613
\(460\) −6.60261 −0.307848
\(461\) −27.8648 −1.29779 −0.648896 0.760877i \(-0.724769\pi\)
−0.648896 + 0.760877i \(0.724769\pi\)
\(462\) 13.2956 0.618566
\(463\) 10.9177 0.507386 0.253693 0.967285i \(-0.418355\pi\)
0.253693 + 0.967285i \(0.418355\pi\)
\(464\) −51.1953 −2.37668
\(465\) −25.3644 −1.17624
\(466\) 26.5436 1.22961
\(467\) 16.6236 0.769250 0.384625 0.923073i \(-0.374331\pi\)
0.384625 + 0.923073i \(0.374331\pi\)
\(468\) 14.1096 0.652215
\(469\) 2.10858 0.0973650
\(470\) −4.30099 −0.198390
\(471\) 24.8778 1.14631
\(472\) 19.6327 0.903669
\(473\) 12.8080 0.588912
\(474\) −72.2020 −3.31635
\(475\) 4.99210 0.229053
\(476\) 1.53115 0.0701802
\(477\) 62.2353 2.84956
\(478\) 8.13908 0.372273
\(479\) −2.33393 −0.106640 −0.0533200 0.998577i \(-0.516980\pi\)
−0.0533200 + 0.998577i \(0.516980\pi\)
\(480\) 14.9244 0.681201
\(481\) −18.7162 −0.853384
\(482\) −0.383736 −0.0174787
\(483\) −20.6882 −0.941348
\(484\) −4.10152 −0.186433
\(485\) 14.2332 0.646298
\(486\) −2.06676 −0.0937502
\(487\) 6.53717 0.296228 0.148114 0.988970i \(-0.452680\pi\)
0.148114 + 0.988970i \(0.452680\pi\)
\(488\) −4.67063 −0.211429
\(489\) 59.6363 2.69684
\(490\) −1.71867 −0.0776416
\(491\) −23.9084 −1.07897 −0.539486 0.841995i \(-0.681381\pi\)
−0.539486 + 0.841995i \(0.681381\pi\)
\(492\) 0.177147 0.00798639
\(493\) −16.4435 −0.740576
\(494\) 21.3947 0.962592
\(495\) 15.3550 0.690155
\(496\) −42.4160 −1.90454
\(497\) −13.1283 −0.588886
\(498\) 33.6821 1.50933
\(499\) 26.4920 1.18594 0.592972 0.805223i \(-0.297955\pi\)
0.592972 + 0.805223i \(0.297955\pi\)
\(500\) −0.953829 −0.0426565
\(501\) −12.1822 −0.544259
\(502\) 11.5728 0.516519
\(503\) 11.1418 0.496788 0.248394 0.968659i \(-0.420097\pi\)
0.248394 + 0.968659i \(0.420097\pi\)
\(504\) 10.6662 0.475110
\(505\) 2.88454 0.128361
\(506\) −30.7945 −1.36898
\(507\) −20.2688 −0.900170
\(508\) −5.99379 −0.265931
\(509\) −33.1254 −1.46826 −0.734129 0.679010i \(-0.762409\pi\)
−0.734129 + 0.679010i \(0.762409\pi\)
\(510\) 8.24554 0.365118
\(511\) −12.0683 −0.533870
\(512\) 6.98500 0.308697
\(513\) 43.7473 1.93149
\(514\) −13.3412 −0.588453
\(515\) 9.54503 0.420604
\(516\) −14.1057 −0.620969
\(517\) −6.47755 −0.284882
\(518\) 12.8997 0.566781
\(519\) 71.6238 3.14394
\(520\) 4.48358 0.196618
\(521\) −2.66617 −0.116807 −0.0584035 0.998293i \(-0.518601\pi\)
−0.0584035 + 0.998293i \(0.518601\pi\)
\(522\) 104.436 4.57106
\(523\) 36.4560 1.59411 0.797055 0.603907i \(-0.206390\pi\)
0.797055 + 0.603907i \(0.206390\pi\)
\(524\) 9.94921 0.434633
\(525\) −2.98867 −0.130436
\(526\) −45.8496 −1.99914
\(527\) −13.6236 −0.593455
\(528\) 38.6633 1.68260
\(529\) 24.9171 1.08335
\(530\) −18.0308 −0.783209
\(531\) −64.7737 −2.81094
\(532\) −4.76161 −0.206442
\(533\) 0.154958 0.00671197
\(534\) −3.87566 −0.167716
\(535\) 13.8210 0.597534
\(536\) 3.79127 0.163758
\(537\) 6.35688 0.274320
\(538\) −37.9834 −1.63758
\(539\) −2.58842 −0.111491
\(540\) −8.35870 −0.359701
\(541\) 1.85396 0.0797080 0.0398540 0.999206i \(-0.487311\pi\)
0.0398540 + 0.999206i \(0.487311\pi\)
\(542\) −26.0133 −1.11737
\(543\) −75.6402 −3.24603
\(544\) 8.01614 0.343689
\(545\) −17.3847 −0.744678
\(546\) −12.8086 −0.548156
\(547\) 3.47960 0.148777 0.0743884 0.997229i \(-0.476300\pi\)
0.0743884 + 0.997229i \(0.476300\pi\)
\(548\) −4.11667 −0.175855
\(549\) 15.4097 0.657669
\(550\) −4.44865 −0.189691
\(551\) 51.1362 2.17848
\(552\) −37.1979 −1.58325
\(553\) 14.0565 0.597744
\(554\) −46.7254 −1.98517
\(555\) 22.4319 0.952181
\(556\) 9.99596 0.423923
\(557\) −3.77795 −0.160077 −0.0800384 0.996792i \(-0.525504\pi\)
−0.0800384 + 0.996792i \(0.525504\pi\)
\(558\) 86.5270 3.66298
\(559\) −12.3389 −0.521878
\(560\) −4.99787 −0.211198
\(561\) 12.4183 0.524301
\(562\) −53.8015 −2.26948
\(563\) −26.5422 −1.11862 −0.559310 0.828958i \(-0.688934\pi\)
−0.559310 + 0.828958i \(0.688934\pi\)
\(564\) 7.13386 0.300390
\(565\) −15.5005 −0.652111
\(566\) 13.8388 0.581689
\(567\) −8.39415 −0.352521
\(568\) −23.6051 −0.990446
\(569\) −15.3193 −0.642220 −0.321110 0.947042i \(-0.604056\pi\)
−0.321110 + 0.947042i \(0.604056\pi\)
\(570\) −25.6422 −1.07403
\(571\) −24.2824 −1.01619 −0.508094 0.861302i \(-0.669650\pi\)
−0.508094 + 0.861302i \(0.669650\pi\)
\(572\) −6.15653 −0.257417
\(573\) −56.0618 −2.34202
\(574\) −0.106801 −0.00445780
\(575\) 6.92222 0.288676
\(576\) 8.38399 0.349333
\(577\) 37.3321 1.55415 0.777077 0.629405i \(-0.216702\pi\)
0.777077 + 0.629405i \(0.216702\pi\)
\(578\) −24.7886 −1.03107
\(579\) −3.27984 −0.136306
\(580\) −9.77048 −0.405697
\(581\) −6.55734 −0.272044
\(582\) −73.1097 −3.03049
\(583\) −27.1555 −1.12467
\(584\) −21.6991 −0.897914
\(585\) −14.7926 −0.611597
\(586\) −50.3362 −2.07937
\(587\) −38.0015 −1.56849 −0.784245 0.620451i \(-0.786949\pi\)
−0.784245 + 0.620451i \(0.786949\pi\)
\(588\) 2.85068 0.117560
\(589\) 42.3671 1.74571
\(590\) 18.7663 0.772595
\(591\) 37.7354 1.55223
\(592\) 37.5122 1.54174
\(593\) −24.7386 −1.01589 −0.507945 0.861389i \(-0.669595\pi\)
−0.507945 + 0.861389i \(0.669595\pi\)
\(594\) −38.9849 −1.59957
\(595\) −1.60527 −0.0658096
\(596\) 16.0110 0.655835
\(597\) −11.3346 −0.463894
\(598\) 29.6666 1.21316
\(599\) −22.1218 −0.903872 −0.451936 0.892050i \(-0.649266\pi\)
−0.451936 + 0.892050i \(0.649266\pi\)
\(600\) −5.37371 −0.219381
\(601\) −1.07752 −0.0439532 −0.0219766 0.999758i \(-0.506996\pi\)
−0.0219766 + 0.999758i \(0.506996\pi\)
\(602\) 8.50429 0.346609
\(603\) −12.5084 −0.509383
\(604\) 5.01945 0.204238
\(605\) 4.30006 0.174822
\(606\) −14.8166 −0.601883
\(607\) 20.5327 0.833395 0.416697 0.909045i \(-0.363188\pi\)
0.416697 + 0.909045i \(0.363188\pi\)
\(608\) −24.9288 −1.01100
\(609\) −30.6143 −1.24055
\(610\) −4.46450 −0.180762
\(611\) 6.24029 0.252455
\(612\) −9.08306 −0.367161
\(613\) 19.6185 0.792383 0.396191 0.918168i \(-0.370332\pi\)
0.396191 + 0.918168i \(0.370332\pi\)
\(614\) −23.4512 −0.946412
\(615\) −0.185722 −0.00748902
\(616\) −4.65405 −0.187517
\(617\) 15.1976 0.611831 0.305915 0.952059i \(-0.401038\pi\)
0.305915 + 0.952059i \(0.401038\pi\)
\(618\) −49.0285 −1.97221
\(619\) 16.2629 0.653662 0.326831 0.945083i \(-0.394019\pi\)
0.326831 + 0.945083i \(0.394019\pi\)
\(620\) −8.09498 −0.325102
\(621\) 60.6615 2.43426
\(622\) −36.5791 −1.46669
\(623\) 0.754527 0.0302295
\(624\) −37.2471 −1.49108
\(625\) 1.00000 0.0400000
\(626\) −11.9691 −0.478381
\(627\) −38.6187 −1.54228
\(628\) 7.93969 0.316828
\(629\) 12.0486 0.480408
\(630\) 10.1955 0.406197
\(631\) −0.867869 −0.0345493 −0.0172747 0.999851i \(-0.505499\pi\)
−0.0172747 + 0.999851i \(0.505499\pi\)
\(632\) 25.2739 1.00534
\(633\) 54.3547 2.16040
\(634\) 26.4069 1.04875
\(635\) 6.28392 0.249370
\(636\) 29.9069 1.18589
\(637\) 2.49362 0.0988007
\(638\) −45.5694 −1.80411
\(639\) 77.8795 3.08087
\(640\) −12.4163 −0.490797
\(641\) 31.3984 1.24016 0.620082 0.784537i \(-0.287100\pi\)
0.620082 + 0.784537i \(0.287100\pi\)
\(642\) −70.9922 −2.80184
\(643\) 6.49828 0.256267 0.128134 0.991757i \(-0.459101\pi\)
0.128134 + 0.991757i \(0.459101\pi\)
\(644\) −6.60261 −0.260179
\(645\) 14.7885 0.582296
\(646\) −13.7728 −0.541885
\(647\) 16.3970 0.644633 0.322316 0.946632i \(-0.395538\pi\)
0.322316 + 0.946632i \(0.395538\pi\)
\(648\) −15.0929 −0.592904
\(649\) 28.2632 1.10943
\(650\) 4.28570 0.168099
\(651\) −25.3644 −0.994107
\(652\) 19.0328 0.745381
\(653\) −7.00912 −0.274288 −0.137144 0.990551i \(-0.543792\pi\)
−0.137144 + 0.990551i \(0.543792\pi\)
\(654\) 89.2972 3.49180
\(655\) −10.4308 −0.407565
\(656\) −0.310577 −0.0121260
\(657\) 71.5912 2.79304
\(658\) −4.30099 −0.167670
\(659\) −8.28207 −0.322624 −0.161312 0.986903i \(-0.551572\pi\)
−0.161312 + 0.986903i \(0.551572\pi\)
\(660\) 7.37878 0.287219
\(661\) 29.9745 1.16587 0.582937 0.812517i \(-0.301903\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(662\) −10.7568 −0.418075
\(663\) −11.9634 −0.464621
\(664\) −11.7902 −0.457550
\(665\) 4.99210 0.193585
\(666\) −76.5234 −2.96522
\(667\) 70.9072 2.74554
\(668\) −3.88791 −0.150428
\(669\) −33.8030 −1.30690
\(670\) 3.62395 0.140005
\(671\) −6.72381 −0.259570
\(672\) 14.9244 0.575720
\(673\) −26.1184 −1.00679 −0.503395 0.864057i \(-0.667916\pi\)
−0.503395 + 0.864057i \(0.667916\pi\)
\(674\) 10.8917 0.419531
\(675\) 8.76331 0.337300
\(676\) −6.46875 −0.248798
\(677\) −32.4814 −1.24836 −0.624180 0.781280i \(-0.714567\pi\)
−0.624180 + 0.781280i \(0.714567\pi\)
\(678\) 79.6190 3.05775
\(679\) 14.2332 0.546222
\(680\) −2.88631 −0.110685
\(681\) 7.36978 0.282410
\(682\) −37.7549 −1.44571
\(683\) −31.6652 −1.21163 −0.605817 0.795604i \(-0.707154\pi\)
−0.605817 + 0.795604i \(0.707154\pi\)
\(684\) 28.2467 1.08004
\(685\) 4.31594 0.164904
\(686\) −1.71867 −0.0656192
\(687\) 2.98867 0.114025
\(688\) 24.7303 0.942836
\(689\) 26.1609 0.996650
\(690\) −35.5563 −1.35360
\(691\) −40.1525 −1.52747 −0.763736 0.645529i \(-0.776637\pi\)
−0.763736 + 0.645529i \(0.776637\pi\)
\(692\) 22.8586 0.868954
\(693\) 15.3550 0.583288
\(694\) 50.2161 1.90618
\(695\) −10.4798 −0.397522
\(696\) −55.0452 −2.08648
\(697\) −0.0997543 −0.00377846
\(698\) 25.6043 0.969138
\(699\) 46.1579 1.74585
\(700\) −0.953829 −0.0360514
\(701\) −36.3265 −1.37203 −0.686016 0.727586i \(-0.740642\pi\)
−0.686016 + 0.727586i \(0.740642\pi\)
\(702\) 37.5570 1.41750
\(703\) −37.4689 −1.41317
\(704\) −3.65824 −0.137875
\(705\) −7.47918 −0.281682
\(706\) 9.10129 0.342532
\(707\) 2.88454 0.108484
\(708\) −31.1268 −1.16982
\(709\) −25.7268 −0.966189 −0.483094 0.875568i \(-0.660487\pi\)
−0.483094 + 0.875568i \(0.660487\pi\)
\(710\) −22.5633 −0.846785
\(711\) −83.3857 −3.12721
\(712\) 1.35666 0.0508429
\(713\) 58.7476 2.20012
\(714\) 8.24554 0.308581
\(715\) 6.45454 0.241386
\(716\) 2.02879 0.0758193
\(717\) 14.1534 0.528569
\(718\) −62.6629 −2.33856
\(719\) 30.1001 1.12254 0.561272 0.827632i \(-0.310312\pi\)
0.561272 + 0.827632i \(0.310312\pi\)
\(720\) 29.6482 1.10492
\(721\) 9.54503 0.355475
\(722\) 10.1764 0.378726
\(723\) −0.667296 −0.0248170
\(724\) −24.1404 −0.897172
\(725\) 10.2434 0.380431
\(726\) −22.0874 −0.819742
\(727\) 7.97316 0.295708 0.147854 0.989009i \(-0.452763\pi\)
0.147854 + 0.989009i \(0.452763\pi\)
\(728\) 4.48358 0.166173
\(729\) −28.7764 −1.06579
\(730\) −20.7414 −0.767675
\(731\) 7.94316 0.293788
\(732\) 7.40507 0.273699
\(733\) 25.5651 0.944267 0.472134 0.881527i \(-0.343484\pi\)
0.472134 + 0.881527i \(0.343484\pi\)
\(734\) 20.6345 0.761635
\(735\) −2.98867 −0.110239
\(736\) −34.5671 −1.27416
\(737\) 5.45789 0.201044
\(738\) 0.633564 0.0233218
\(739\) 35.6717 1.31220 0.656102 0.754672i \(-0.272204\pi\)
0.656102 + 0.754672i \(0.272204\pi\)
\(740\) 7.15910 0.263174
\(741\) 37.2042 1.36673
\(742\) −18.0308 −0.661932
\(743\) −37.9824 −1.39344 −0.696719 0.717344i \(-0.745358\pi\)
−0.696719 + 0.717344i \(0.745358\pi\)
\(744\) −45.6057 −1.67199
\(745\) −16.7860 −0.614991
\(746\) −1.62857 −0.0596263
\(747\) 38.8993 1.42325
\(748\) 3.96327 0.144912
\(749\) 13.8210 0.505008
\(750\) −5.13655 −0.187560
\(751\) 10.7851 0.393553 0.196776 0.980448i \(-0.436953\pi\)
0.196776 + 0.980448i \(0.436953\pi\)
\(752\) −12.5072 −0.456091
\(753\) 20.1244 0.733376
\(754\) 43.9003 1.59876
\(755\) −5.26242 −0.191519
\(756\) −8.35870 −0.304003
\(757\) −11.0028 −0.399903 −0.199951 0.979806i \(-0.564078\pi\)
−0.199951 + 0.979806i \(0.564078\pi\)
\(758\) 20.7180 0.752513
\(759\) −53.5500 −1.94374
\(760\) 8.97591 0.325591
\(761\) 36.8820 1.33697 0.668486 0.743724i \(-0.266942\pi\)
0.668486 + 0.743724i \(0.266942\pi\)
\(762\) −32.2777 −1.16930
\(763\) −17.3847 −0.629368
\(764\) −17.8920 −0.647310
\(765\) 9.52273 0.344295
\(766\) −16.4587 −0.594676
\(767\) −27.2279 −0.983144
\(768\) 55.3291 1.99652
\(769\) 26.1789 0.944036 0.472018 0.881589i \(-0.343526\pi\)
0.472018 + 0.881589i \(0.343526\pi\)
\(770\) −4.44865 −0.160318
\(771\) −23.1995 −0.835511
\(772\) −1.04675 −0.0376735
\(773\) 37.3901 1.34483 0.672415 0.740175i \(-0.265257\pi\)
0.672415 + 0.740175i \(0.265257\pi\)
\(774\) −50.4489 −1.81335
\(775\) 8.48682 0.304856
\(776\) 25.5917 0.918688
\(777\) 22.4319 0.804740
\(778\) −22.5831 −0.809642
\(779\) 0.310218 0.0111147
\(780\) −7.10851 −0.254526
\(781\) −33.9817 −1.21596
\(782\) −19.0979 −0.682939
\(783\) 89.7663 3.20799
\(784\) −4.99787 −0.178495
\(785\) −8.32402 −0.297097
\(786\) 53.5783 1.91108
\(787\) −13.0730 −0.466004 −0.233002 0.972476i \(-0.574855\pi\)
−0.233002 + 0.972476i \(0.574855\pi\)
\(788\) 12.0432 0.429020
\(789\) −79.7299 −2.83846
\(790\) 24.1585 0.859522
\(791\) −15.5005 −0.551134
\(792\) 27.6086 0.981029
\(793\) 6.47753 0.230024
\(794\) 44.3616 1.57433
\(795\) −31.3546 −1.11203
\(796\) −3.61742 −0.128216
\(797\) −28.4984 −1.00947 −0.504733 0.863275i \(-0.668409\pi\)
−0.504733 + 0.863275i \(0.668409\pi\)
\(798\) −25.6422 −0.907723
\(799\) −4.01719 −0.142118
\(800\) −4.99364 −0.176552
\(801\) −4.47598 −0.158151
\(802\) −0.460396 −0.0162572
\(803\) −31.2379 −1.10236
\(804\) −6.01088 −0.211988
\(805\) 6.92222 0.243976
\(806\) 36.3720 1.28115
\(807\) −66.0510 −2.32510
\(808\) 5.18648 0.182460
\(809\) 4.98266 0.175181 0.0875906 0.996157i \(-0.472083\pi\)
0.0875906 + 0.996157i \(0.472083\pi\)
\(810\) −14.4268 −0.506906
\(811\) 43.1869 1.51650 0.758248 0.651966i \(-0.226055\pi\)
0.758248 + 0.651966i \(0.226055\pi\)
\(812\) −9.77048 −0.342877
\(813\) −45.2356 −1.58648
\(814\) 33.3900 1.17032
\(815\) −19.9541 −0.698961
\(816\) 23.9779 0.839394
\(817\) −24.7018 −0.864207
\(818\) 11.7482 0.410768
\(819\) −14.7926 −0.516894
\(820\) −0.0592727 −0.00206989
\(821\) −49.5240 −1.72840 −0.864200 0.503149i \(-0.832175\pi\)
−0.864200 + 0.503149i \(0.832175\pi\)
\(822\) −22.1690 −0.773234
\(823\) 11.9212 0.415548 0.207774 0.978177i \(-0.433378\pi\)
0.207774 + 0.978177i \(0.433378\pi\)
\(824\) 17.1622 0.597873
\(825\) −7.73596 −0.269331
\(826\) 18.7663 0.652962
\(827\) 3.74076 0.130079 0.0650395 0.997883i \(-0.479283\pi\)
0.0650395 + 0.997883i \(0.479283\pi\)
\(828\) 39.1678 1.36118
\(829\) −29.5750 −1.02718 −0.513591 0.858035i \(-0.671685\pi\)
−0.513591 + 0.858035i \(0.671685\pi\)
\(830\) −11.2699 −0.391184
\(831\) −81.2529 −2.81863
\(832\) 3.52425 0.122181
\(833\) −1.60527 −0.0556192
\(834\) 53.8301 1.86398
\(835\) 4.07611 0.141060
\(836\) −12.3251 −0.426272
\(837\) 74.3727 2.57070
\(838\) −50.1602 −1.73275
\(839\) 36.2034 1.24988 0.624939 0.780673i \(-0.285124\pi\)
0.624939 + 0.780673i \(0.285124\pi\)
\(840\) −5.37371 −0.185410
\(841\) 75.9279 2.61820
\(842\) 15.0473 0.518565
\(843\) −93.5579 −3.22231
\(844\) 17.3472 0.597115
\(845\) 6.78188 0.233304
\(846\) 25.5142 0.877196
\(847\) 4.30006 0.147752
\(848\) −52.4333 −1.80057
\(849\) 24.0650 0.825907
\(850\) −2.75893 −0.0946304
\(851\) −51.9556 −1.78102
\(852\) 37.4247 1.28215
\(853\) 33.0461 1.13148 0.565738 0.824585i \(-0.308591\pi\)
0.565738 + 0.824585i \(0.308591\pi\)
\(854\) −4.46450 −0.152772
\(855\) −29.6140 −1.01278
\(856\) 24.8505 0.849371
\(857\) −22.4301 −0.766198 −0.383099 0.923707i \(-0.625143\pi\)
−0.383099 + 0.923707i \(0.625143\pi\)
\(858\) −33.1540 −1.13186
\(859\) −46.5415 −1.58798 −0.793988 0.607933i \(-0.791999\pi\)
−0.793988 + 0.607933i \(0.791999\pi\)
\(860\) 4.71972 0.160941
\(861\) −0.185722 −0.00632938
\(862\) −22.0191 −0.749975
\(863\) −51.4066 −1.74990 −0.874950 0.484213i \(-0.839106\pi\)
−0.874950 + 0.484213i \(0.839106\pi\)
\(864\) −43.7608 −1.48877
\(865\) −23.9651 −0.814838
\(866\) −49.7354 −1.69008
\(867\) −43.1060 −1.46396
\(868\) −8.09498 −0.274762
\(869\) 36.3842 1.23425
\(870\) −52.6159 −1.78384
\(871\) −5.25798 −0.178160
\(872\) −31.2581 −1.05853
\(873\) −84.4340 −2.85766
\(874\) 59.3911 2.00893
\(875\) 1.00000 0.0338062
\(876\) 34.4029 1.16237
\(877\) 41.6264 1.40562 0.702812 0.711375i \(-0.251927\pi\)
0.702812 + 0.711375i \(0.251927\pi\)
\(878\) −29.9522 −1.01084
\(879\) −87.5319 −2.95238
\(880\) −12.9366 −0.436093
\(881\) 5.40727 0.182175 0.0910877 0.995843i \(-0.470966\pi\)
0.0910877 + 0.995843i \(0.470966\pi\)
\(882\) 10.1955 0.343299
\(883\) 50.3899 1.69576 0.847878 0.530192i \(-0.177880\pi\)
0.847878 + 0.530192i \(0.177880\pi\)
\(884\) −3.81810 −0.128417
\(885\) 32.6335 1.09696
\(886\) −53.5048 −1.79753
\(887\) −16.2276 −0.544870 −0.272435 0.962174i \(-0.587829\pi\)
−0.272435 + 0.962174i \(0.587829\pi\)
\(888\) 40.3331 1.35349
\(889\) 6.28392 0.210756
\(890\) 1.29678 0.0434683
\(891\) −21.7276 −0.727903
\(892\) −10.7882 −0.361215
\(893\) 12.4928 0.418055
\(894\) 86.2220 2.88370
\(895\) −2.12699 −0.0710974
\(896\) −12.4163 −0.414799
\(897\) 51.5885 1.72249
\(898\) −14.0935 −0.470306
\(899\) 86.9342 2.89942
\(900\) 5.65828 0.188609
\(901\) −16.8411 −0.561058
\(902\) −0.276447 −0.00920469
\(903\) 14.7885 0.492130
\(904\) −27.8703 −0.926951
\(905\) 25.3090 0.841298
\(906\) 27.0307 0.898033
\(907\) −54.3644 −1.80514 −0.902570 0.430543i \(-0.858322\pi\)
−0.902570 + 0.430543i \(0.858322\pi\)
\(908\) 2.35205 0.0780555
\(909\) −17.1116 −0.567556
\(910\) 4.28570 0.142070
\(911\) 43.6526 1.44628 0.723138 0.690704i \(-0.242699\pi\)
0.723138 + 0.690704i \(0.242699\pi\)
\(912\) −74.5670 −2.46916
\(913\) −16.9732 −0.561730
\(914\) 15.4095 0.509700
\(915\) −7.76352 −0.256654
\(916\) 0.953829 0.0315154
\(917\) −10.4308 −0.344456
\(918\) −24.1773 −0.797971
\(919\) 48.9151 1.61356 0.806779 0.590853i \(-0.201209\pi\)
0.806779 + 0.590853i \(0.201209\pi\)
\(920\) 12.4463 0.410343
\(921\) −40.7803 −1.34376
\(922\) −47.8904 −1.57719
\(923\) 32.7370 1.07755
\(924\) 7.37878 0.242744
\(925\) −7.50564 −0.246784
\(926\) 18.7638 0.616618
\(927\) −56.6228 −1.85974
\(928\) −51.1520 −1.67915
\(929\) 6.69369 0.219613 0.109806 0.993953i \(-0.464977\pi\)
0.109806 + 0.993953i \(0.464977\pi\)
\(930\) −43.5930 −1.42947
\(931\) 4.99210 0.163610
\(932\) 14.7312 0.482537
\(933\) −63.6090 −2.08247
\(934\) 28.5706 0.934857
\(935\) −4.15512 −0.135887
\(936\) −26.5974 −0.869362
\(937\) 36.3051 1.18604 0.593018 0.805189i \(-0.297936\pi\)
0.593018 + 0.805189i \(0.297936\pi\)
\(938\) 3.62395 0.118326
\(939\) −20.8136 −0.679226
\(940\) −2.38696 −0.0778542
\(941\) −45.3421 −1.47811 −0.739055 0.673645i \(-0.764728\pi\)
−0.739055 + 0.673645i \(0.764728\pi\)
\(942\) 42.7567 1.39309
\(943\) 0.430159 0.0140079
\(944\) 54.5720 1.77617
\(945\) 8.76331 0.285070
\(946\) 22.0127 0.715695
\(947\) −42.6472 −1.38585 −0.692923 0.721011i \(-0.743678\pi\)
−0.692923 + 0.721011i \(0.743678\pi\)
\(948\) −40.0707 −1.30144
\(949\) 30.0937 0.976883
\(950\) 8.57978 0.278365
\(951\) 45.9202 1.48906
\(952\) −2.88631 −0.0935458
\(953\) −2.52634 −0.0818360 −0.0409180 0.999163i \(-0.513028\pi\)
−0.0409180 + 0.999163i \(0.513028\pi\)
\(954\) 106.962 3.46302
\(955\) 18.7581 0.606997
\(956\) 4.51703 0.146091
\(957\) −79.2428 −2.56155
\(958\) −4.01126 −0.129598
\(959\) 4.31594 0.139369
\(960\) −4.22392 −0.136326
\(961\) 41.0262 1.32343
\(962\) −32.1669 −1.03710
\(963\) −81.9885 −2.64204
\(964\) −0.212966 −0.00685918
\(965\) 1.09742 0.0353273
\(966\) −35.5563 −1.14400
\(967\) −8.86804 −0.285177 −0.142588 0.989782i \(-0.545543\pi\)
−0.142588 + 0.989782i \(0.545543\pi\)
\(968\) 7.73160 0.248503
\(969\) −23.9502 −0.769392
\(970\) 24.4622 0.785436
\(971\) 36.2224 1.16243 0.581216 0.813749i \(-0.302577\pi\)
0.581216 + 0.813749i \(0.302577\pi\)
\(972\) −1.14701 −0.0367904
\(973\) −10.4798 −0.335968
\(974\) 11.2352 0.360001
\(975\) 7.45261 0.238674
\(976\) −12.9827 −0.415566
\(977\) 48.0417 1.53699 0.768495 0.639856i \(-0.221006\pi\)
0.768495 + 0.639856i \(0.221006\pi\)
\(978\) 102.495 3.27743
\(979\) 1.95304 0.0624193
\(980\) −0.953829 −0.0304690
\(981\) 103.129 3.29265
\(982\) −41.0907 −1.31126
\(983\) 5.54888 0.176982 0.0884910 0.996077i \(-0.471796\pi\)
0.0884910 + 0.996077i \(0.471796\pi\)
\(984\) −0.333932 −0.0106454
\(985\) −12.6261 −0.402302
\(986\) −28.2609 −0.900010
\(987\) −7.47918 −0.238065
\(988\) 11.8736 0.377751
\(989\) −34.2524 −1.08916
\(990\) 26.3902 0.838734
\(991\) 15.1140 0.480111 0.240055 0.970759i \(-0.422834\pi\)
0.240055 + 0.970759i \(0.422834\pi\)
\(992\) −42.3802 −1.34557
\(993\) −18.7055 −0.593601
\(994\) −22.5633 −0.715664
\(995\) 3.79252 0.120231
\(996\) 18.6929 0.592307
\(997\) 11.3090 0.358161 0.179080 0.983834i \(-0.442688\pi\)
0.179080 + 0.983834i \(0.442688\pi\)
\(998\) 45.5310 1.44126
\(999\) −65.7742 −2.08100
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 \(a_p\))