Properties

Label 8002.2.a.d.1.5
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
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: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.04857 q^{3} +1.00000 q^{4} -0.106661 q^{5} -3.04857 q^{6} -0.613952 q^{7} +1.00000 q^{8} +6.29376 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.04857 q^{3} +1.00000 q^{4} -0.106661 q^{5} -3.04857 q^{6} -0.613952 q^{7} +1.00000 q^{8} +6.29376 q^{9} -0.106661 q^{10} +4.91299 q^{11} -3.04857 q^{12} -1.74319 q^{13} -0.613952 q^{14} +0.325162 q^{15} +1.00000 q^{16} +0.753248 q^{17} +6.29376 q^{18} +0.918851 q^{19} -0.106661 q^{20} +1.87168 q^{21} +4.91299 q^{22} -3.35738 q^{23} -3.04857 q^{24} -4.98862 q^{25} -1.74319 q^{26} -10.0413 q^{27} -0.613952 q^{28} +3.52490 q^{29} +0.325162 q^{30} -6.13162 q^{31} +1.00000 q^{32} -14.9776 q^{33} +0.753248 q^{34} +0.0654846 q^{35} +6.29376 q^{36} -1.78363 q^{37} +0.918851 q^{38} +5.31423 q^{39} -0.106661 q^{40} -9.94633 q^{41} +1.87168 q^{42} +5.22747 q^{43} +4.91299 q^{44} -0.671297 q^{45} -3.35738 q^{46} -8.14368 q^{47} -3.04857 q^{48} -6.62306 q^{49} -4.98862 q^{50} -2.29633 q^{51} -1.74319 q^{52} +6.17368 q^{53} -10.0413 q^{54} -0.524023 q^{55} -0.613952 q^{56} -2.80118 q^{57} +3.52490 q^{58} +8.55876 q^{59} +0.325162 q^{60} -3.22483 q^{61} -6.13162 q^{62} -3.86407 q^{63} +1.00000 q^{64} +0.185930 q^{65} -14.9776 q^{66} -4.18508 q^{67} +0.753248 q^{68} +10.2352 q^{69} +0.0654846 q^{70} -0.630097 q^{71} +6.29376 q^{72} -0.360837 q^{73} -1.78363 q^{74} +15.2082 q^{75} +0.918851 q^{76} -3.01634 q^{77} +5.31423 q^{78} +14.1602 q^{79} -0.106661 q^{80} +11.7302 q^{81} -9.94633 q^{82} +4.38774 q^{83} +1.87168 q^{84} -0.0803419 q^{85} +5.22747 q^{86} -10.7459 q^{87} +4.91299 q^{88} +15.2114 q^{89} -0.671297 q^{90} +1.07024 q^{91} -3.35738 q^{92} +18.6927 q^{93} -8.14368 q^{94} -0.0980052 q^{95} -3.04857 q^{96} -2.30536 q^{97} -6.62306 q^{98} +30.9212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q + 69q^{2} - 25q^{3} + 69q^{4} - 33q^{5} - 25q^{6} - 19q^{7} + 69q^{8} + 54q^{9} + O(q^{10}) \) \( 69q + 69q^{2} - 25q^{3} + 69q^{4} - 33q^{5} - 25q^{6} - 19q^{7} + 69q^{8} + 54q^{9} - 33q^{10} - 30q^{11} - 25q^{12} - 58q^{13} - 19q^{14} + 2q^{15} + 69q^{16} - 80q^{17} + 54q^{18} - 40q^{19} - 33q^{20} - 32q^{21} - 30q^{22} - 45q^{23} - 25q^{24} + 42q^{25} - 58q^{26} - 76q^{27} - 19q^{28} - 44q^{29} + 2q^{30} - 12q^{31} + 69q^{32} - 41q^{33} - 80q^{34} - 49q^{35} + 54q^{36} - 47q^{37} - 40q^{38} - 14q^{39} - 33q^{40} - 94q^{41} - 32q^{42} - 10q^{43} - 30q^{44} - 89q^{45} - 45q^{46} - 85q^{47} - 25q^{48} + 32q^{49} + 42q^{50} - 10q^{51} - 58q^{52} - 41q^{53} - 76q^{54} - 27q^{55} - 19q^{56} - 72q^{57} - 44q^{58} - 75q^{59} + 2q^{60} - 98q^{61} - 12q^{62} - 61q^{63} + 69q^{64} - 47q^{65} - 41q^{66} - 22q^{67} - 80q^{68} - 74q^{69} - 49q^{70} - 22q^{71} + 54q^{72} - 129q^{73} - 47q^{74} - 106q^{75} - 40q^{76} - 108q^{77} - 14q^{78} + 21q^{79} - 33q^{80} + 13q^{81} - 94q^{82} - 111q^{83} - 32q^{84} - 67q^{85} - 10q^{86} - 38q^{87} - 30q^{88} - 112q^{89} - 89q^{90} - 55q^{91} - 45q^{92} - 90q^{93} - 85q^{94} - 38q^{95} - 25q^{96} - 98q^{97} + 32q^{98} - 51q^{99} + O(q^{100}) \)

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
\(3\) −3.04857 −1.76009 −0.880046 0.474889i \(-0.842488\pi\)
−0.880046 + 0.474889i \(0.842488\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.106661 −0.0477001 −0.0238500 0.999716i \(-0.507592\pi\)
−0.0238500 + 0.999716i \(0.507592\pi\)
\(6\) −3.04857 −1.24457
\(7\) −0.613952 −0.232052 −0.116026 0.993246i \(-0.537016\pi\)
−0.116026 + 0.993246i \(0.537016\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.29376 2.09792
\(10\) −0.106661 −0.0337291
\(11\) 4.91299 1.48132 0.740662 0.671878i \(-0.234512\pi\)
0.740662 + 0.671878i \(0.234512\pi\)
\(12\) −3.04857 −0.880046
\(13\) −1.74319 −0.483474 −0.241737 0.970342i \(-0.577717\pi\)
−0.241737 + 0.970342i \(0.577717\pi\)
\(14\) −0.613952 −0.164086
\(15\) 0.325162 0.0839565
\(16\) 1.00000 0.250000
\(17\) 0.753248 0.182689 0.0913447 0.995819i \(-0.470883\pi\)
0.0913447 + 0.995819i \(0.470883\pi\)
\(18\) 6.29376 1.48345
\(19\) 0.918851 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(20\) −0.106661 −0.0238500
\(21\) 1.87168 0.408433
\(22\) 4.91299 1.04745
\(23\) −3.35738 −0.700062 −0.350031 0.936738i \(-0.613829\pi\)
−0.350031 + 0.936738i \(0.613829\pi\)
\(24\) −3.04857 −0.622286
\(25\) −4.98862 −0.997725
\(26\) −1.74319 −0.341868
\(27\) −10.0413 −1.93244
\(28\) −0.613952 −0.116026
\(29\) 3.52490 0.654558 0.327279 0.944928i \(-0.393868\pi\)
0.327279 + 0.944928i \(0.393868\pi\)
\(30\) 0.325162 0.0593662
\(31\) −6.13162 −1.10127 −0.550636 0.834746i \(-0.685615\pi\)
−0.550636 + 0.834746i \(0.685615\pi\)
\(32\) 1.00000 0.176777
\(33\) −14.9776 −2.60726
\(34\) 0.753248 0.129181
\(35\) 0.0654846 0.0110689
\(36\) 6.29376 1.04896
\(37\) −1.78363 −0.293227 −0.146613 0.989194i \(-0.546837\pi\)
−0.146613 + 0.989194i \(0.546837\pi\)
\(38\) 0.918851 0.149057
\(39\) 5.31423 0.850958
\(40\) −0.106661 −0.0168645
\(41\) −9.94633 −1.55336 −0.776678 0.629898i \(-0.783097\pi\)
−0.776678 + 0.629898i \(0.783097\pi\)
\(42\) 1.87168 0.288806
\(43\) 5.22747 0.797181 0.398591 0.917129i \(-0.369499\pi\)
0.398591 + 0.917129i \(0.369499\pi\)
\(44\) 4.91299 0.740662
\(45\) −0.671297 −0.100071
\(46\) −3.35738 −0.495018
\(47\) −8.14368 −1.18788 −0.593939 0.804510i \(-0.702428\pi\)
−0.593939 + 0.804510i \(0.702428\pi\)
\(48\) −3.04857 −0.440023
\(49\) −6.62306 −0.946152
\(50\) −4.98862 −0.705498
\(51\) −2.29633 −0.321550
\(52\) −1.74319 −0.241737
\(53\) 6.17368 0.848020 0.424010 0.905658i \(-0.360622\pi\)
0.424010 + 0.905658i \(0.360622\pi\)
\(54\) −10.0413 −1.36644
\(55\) −0.524023 −0.0706593
\(56\) −0.613952 −0.0820428
\(57\) −2.80118 −0.371025
\(58\) 3.52490 0.462842
\(59\) 8.55876 1.11426 0.557128 0.830427i \(-0.311903\pi\)
0.557128 + 0.830427i \(0.311903\pi\)
\(60\) 0.325162 0.0419783
\(61\) −3.22483 −0.412898 −0.206449 0.978457i \(-0.566191\pi\)
−0.206449 + 0.978457i \(0.566191\pi\)
\(62\) −6.13162 −0.778717
\(63\) −3.86407 −0.486827
\(64\) 1.00000 0.125000
\(65\) 0.185930 0.0230617
\(66\) −14.9776 −1.84361
\(67\) −4.18508 −0.511288 −0.255644 0.966771i \(-0.582288\pi\)
−0.255644 + 0.966771i \(0.582288\pi\)
\(68\) 0.753248 0.0913447
\(69\) 10.2352 1.23217
\(70\) 0.0654846 0.00782690
\(71\) −0.630097 −0.0747788 −0.0373894 0.999301i \(-0.511904\pi\)
−0.0373894 + 0.999301i \(0.511904\pi\)
\(72\) 6.29376 0.741727
\(73\) −0.360837 −0.0422328 −0.0211164 0.999777i \(-0.506722\pi\)
−0.0211164 + 0.999777i \(0.506722\pi\)
\(74\) −1.78363 −0.207343
\(75\) 15.2082 1.75609
\(76\) 0.918851 0.105399
\(77\) −3.01634 −0.343744
\(78\) 5.31423 0.601718
\(79\) 14.1602 1.59315 0.796574 0.604541i \(-0.206643\pi\)
0.796574 + 0.604541i \(0.206643\pi\)
\(80\) −0.106661 −0.0119250
\(81\) 11.7302 1.30335
\(82\) −9.94633 −1.09839
\(83\) 4.38774 0.481617 0.240808 0.970573i \(-0.422587\pi\)
0.240808 + 0.970573i \(0.422587\pi\)
\(84\) 1.87168 0.204216
\(85\) −0.0803419 −0.00871430
\(86\) 5.22747 0.563692
\(87\) −10.7459 −1.15208
\(88\) 4.91299 0.523727
\(89\) 15.2114 1.61241 0.806205 0.591637i \(-0.201518\pi\)
0.806205 + 0.591637i \(0.201518\pi\)
\(90\) −0.671297 −0.0707609
\(91\) 1.07024 0.112191
\(92\) −3.35738 −0.350031
\(93\) 18.6927 1.93834
\(94\) −8.14368 −0.839957
\(95\) −0.0980052 −0.0100551
\(96\) −3.04857 −0.311143
\(97\) −2.30536 −0.234074 −0.117037 0.993128i \(-0.537340\pi\)
−0.117037 + 0.993128i \(0.537340\pi\)
\(98\) −6.62306 −0.669030
\(99\) 30.9212 3.10770
\(100\) −4.98862 −0.498862
\(101\) 6.36247 0.633090 0.316545 0.948578i \(-0.397477\pi\)
0.316545 + 0.948578i \(0.397477\pi\)
\(102\) −2.29633 −0.227370
\(103\) −0.453725 −0.0447069 −0.0223534 0.999750i \(-0.507116\pi\)
−0.0223534 + 0.999750i \(0.507116\pi\)
\(104\) −1.74319 −0.170934
\(105\) −0.199634 −0.0194823
\(106\) 6.17368 0.599640
\(107\) −6.75717 −0.653241 −0.326620 0.945156i \(-0.605910\pi\)
−0.326620 + 0.945156i \(0.605910\pi\)
\(108\) −10.0413 −0.966220
\(109\) 8.33265 0.798123 0.399061 0.916924i \(-0.369336\pi\)
0.399061 + 0.916924i \(0.369336\pi\)
\(110\) −0.524023 −0.0499636
\(111\) 5.43751 0.516106
\(112\) −0.613952 −0.0580130
\(113\) −10.8912 −1.02456 −0.512280 0.858819i \(-0.671199\pi\)
−0.512280 + 0.858819i \(0.671199\pi\)
\(114\) −2.80118 −0.262354
\(115\) 0.358100 0.0333930
\(116\) 3.52490 0.327279
\(117\) −10.9712 −1.01429
\(118\) 8.55876 0.787897
\(119\) −0.462458 −0.0423935
\(120\) 0.325162 0.0296831
\(121\) 13.1375 1.19432
\(122\) −3.22483 −0.291963
\(123\) 30.3221 2.73405
\(124\) −6.13162 −0.550636
\(125\) 1.06539 0.0952917
\(126\) −3.86407 −0.344239
\(127\) −14.0274 −1.24473 −0.622365 0.782727i \(-0.713828\pi\)
−0.622365 + 0.782727i \(0.713828\pi\)
\(128\) 1.00000 0.0883883
\(129\) −15.9363 −1.40311
\(130\) 0.185930 0.0163071
\(131\) −8.60225 −0.751582 −0.375791 0.926704i \(-0.622629\pi\)
−0.375791 + 0.926704i \(0.622629\pi\)
\(132\) −14.9776 −1.30363
\(133\) −0.564130 −0.0489163
\(134\) −4.18508 −0.361536
\(135\) 1.07101 0.0921776
\(136\) 0.753248 0.0645905
\(137\) 4.23540 0.361854 0.180927 0.983496i \(-0.442090\pi\)
0.180927 + 0.983496i \(0.442090\pi\)
\(138\) 10.2352 0.871277
\(139\) −17.6617 −1.49804 −0.749022 0.662545i \(-0.769476\pi\)
−0.749022 + 0.662545i \(0.769476\pi\)
\(140\) 0.0654846 0.00553446
\(141\) 24.8266 2.09077
\(142\) −0.630097 −0.0528766
\(143\) −8.56428 −0.716181
\(144\) 6.29376 0.524480
\(145\) −0.375968 −0.0312225
\(146\) −0.360837 −0.0298631
\(147\) 20.1909 1.66531
\(148\) −1.78363 −0.146613
\(149\) 3.34112 0.273715 0.136857 0.990591i \(-0.456300\pi\)
0.136857 + 0.990591i \(0.456300\pi\)
\(150\) 15.2082 1.24174
\(151\) −1.53758 −0.125127 −0.0625633 0.998041i \(-0.519928\pi\)
−0.0625633 + 0.998041i \(0.519928\pi\)
\(152\) 0.918851 0.0745286
\(153\) 4.74076 0.383268
\(154\) −3.01634 −0.243064
\(155\) 0.654003 0.0525308
\(156\) 5.31423 0.425479
\(157\) −15.2523 −1.21726 −0.608631 0.793453i \(-0.708281\pi\)
−0.608631 + 0.793453i \(0.708281\pi\)
\(158\) 14.1602 1.12653
\(159\) −18.8209 −1.49259
\(160\) −0.106661 −0.00843226
\(161\) 2.06127 0.162451
\(162\) 11.7302 0.921608
\(163\) −14.5705 −1.14125 −0.570624 0.821212i \(-0.693298\pi\)
−0.570624 + 0.821212i \(0.693298\pi\)
\(164\) −9.94633 −0.776678
\(165\) 1.59752 0.124367
\(166\) 4.38774 0.340555
\(167\) 5.47291 0.423506 0.211753 0.977323i \(-0.432083\pi\)
0.211753 + 0.977323i \(0.432083\pi\)
\(168\) 1.87168 0.144403
\(169\) −9.96129 −0.766253
\(170\) −0.0803419 −0.00616194
\(171\) 5.78303 0.442239
\(172\) 5.22747 0.398591
\(173\) −19.7961 −1.50507 −0.752535 0.658552i \(-0.771169\pi\)
−0.752535 + 0.658552i \(0.771169\pi\)
\(174\) −10.7459 −0.814645
\(175\) 3.06278 0.231524
\(176\) 4.91299 0.370331
\(177\) −26.0919 −1.96119
\(178\) 15.2114 1.14015
\(179\) −4.91078 −0.367049 −0.183524 0.983015i \(-0.558751\pi\)
−0.183524 + 0.983015i \(0.558751\pi\)
\(180\) −0.671297 −0.0500355
\(181\) −3.08931 −0.229626 −0.114813 0.993387i \(-0.536627\pi\)
−0.114813 + 0.993387i \(0.536627\pi\)
\(182\) 1.07024 0.0793311
\(183\) 9.83113 0.726738
\(184\) −3.35738 −0.247509
\(185\) 0.190243 0.0139869
\(186\) 18.6927 1.37061
\(187\) 3.70070 0.270622
\(188\) −8.14368 −0.593939
\(189\) 6.16485 0.448427
\(190\) −0.0980052 −0.00711004
\(191\) 11.5369 0.834778 0.417389 0.908728i \(-0.362945\pi\)
0.417389 + 0.908728i \(0.362945\pi\)
\(192\) −3.04857 −0.220011
\(193\) −17.7635 −1.27864 −0.639322 0.768939i \(-0.720785\pi\)
−0.639322 + 0.768939i \(0.720785\pi\)
\(194\) −2.30536 −0.165515
\(195\) −0.566819 −0.0405908
\(196\) −6.62306 −0.473076
\(197\) 14.5005 1.03312 0.516559 0.856251i \(-0.327213\pi\)
0.516559 + 0.856251i \(0.327213\pi\)
\(198\) 30.9212 2.19747
\(199\) −4.28047 −0.303435 −0.151717 0.988424i \(-0.548480\pi\)
−0.151717 + 0.988424i \(0.548480\pi\)
\(200\) −4.98862 −0.352749
\(201\) 12.7585 0.899914
\(202\) 6.36247 0.447662
\(203\) −2.16412 −0.151892
\(204\) −2.29633 −0.160775
\(205\) 1.06088 0.0740952
\(206\) −0.453725 −0.0316125
\(207\) −21.1305 −1.46867
\(208\) −1.74319 −0.120868
\(209\) 4.51431 0.312261
\(210\) −0.199634 −0.0137761
\(211\) 5.93973 0.408908 0.204454 0.978876i \(-0.434458\pi\)
0.204454 + 0.978876i \(0.434458\pi\)
\(212\) 6.17368 0.424010
\(213\) 1.92089 0.131618
\(214\) −6.75717 −0.461911
\(215\) −0.557565 −0.0380256
\(216\) −10.0413 −0.683221
\(217\) 3.76452 0.255553
\(218\) 8.33265 0.564358
\(219\) 1.10004 0.0743335
\(220\) −0.524023 −0.0353296
\(221\) −1.31305 −0.0883255
\(222\) 5.43751 0.364942
\(223\) 18.8388 1.26154 0.630770 0.775970i \(-0.282739\pi\)
0.630770 + 0.775970i \(0.282739\pi\)
\(224\) −0.613952 −0.0410214
\(225\) −31.3972 −2.09315
\(226\) −10.8912 −0.724473
\(227\) 15.4741 1.02705 0.513525 0.858074i \(-0.328339\pi\)
0.513525 + 0.858074i \(0.328339\pi\)
\(228\) −2.80118 −0.185513
\(229\) −3.49682 −0.231076 −0.115538 0.993303i \(-0.536859\pi\)
−0.115538 + 0.993303i \(0.536859\pi\)
\(230\) 0.358100 0.0236124
\(231\) 9.19553 0.605021
\(232\) 3.52490 0.231421
\(233\) −25.8327 −1.69236 −0.846179 0.532899i \(-0.821103\pi\)
−0.846179 + 0.532899i \(0.821103\pi\)
\(234\) −10.9712 −0.717211
\(235\) 0.868611 0.0566619
\(236\) 8.55876 0.557128
\(237\) −43.1684 −2.80409
\(238\) −0.462458 −0.0299767
\(239\) 12.5745 0.813380 0.406690 0.913566i \(-0.366683\pi\)
0.406690 + 0.913566i \(0.366683\pi\)
\(240\) 0.325162 0.0209891
\(241\) 6.89941 0.444430 0.222215 0.974998i \(-0.428671\pi\)
0.222215 + 0.974998i \(0.428671\pi\)
\(242\) 13.1375 0.844511
\(243\) −5.63640 −0.361575
\(244\) −3.22483 −0.206449
\(245\) 0.706420 0.0451315
\(246\) 30.3221 1.93326
\(247\) −1.60173 −0.101916
\(248\) −6.13162 −0.389358
\(249\) −13.3763 −0.847689
\(250\) 1.06539 0.0673814
\(251\) 7.65888 0.483424 0.241712 0.970348i \(-0.422291\pi\)
0.241712 + 0.970348i \(0.422291\pi\)
\(252\) −3.86407 −0.243414
\(253\) −16.4948 −1.03702
\(254\) −14.0274 −0.880157
\(255\) 0.244928 0.0153380
\(256\) 1.00000 0.0625000
\(257\) −1.00875 −0.0629243 −0.0314621 0.999505i \(-0.510016\pi\)
−0.0314621 + 0.999505i \(0.510016\pi\)
\(258\) −15.9363 −0.992150
\(259\) 1.09506 0.0680439
\(260\) 0.185930 0.0115309
\(261\) 22.1849 1.37321
\(262\) −8.60225 −0.531449
\(263\) 23.2435 1.43326 0.716628 0.697455i \(-0.245684\pi\)
0.716628 + 0.697455i \(0.245684\pi\)
\(264\) −14.9776 −0.921807
\(265\) −0.658488 −0.0404506
\(266\) −0.564130 −0.0345891
\(267\) −46.3731 −2.83799
\(268\) −4.18508 −0.255644
\(269\) −26.2817 −1.60243 −0.801213 0.598380i \(-0.795811\pi\)
−0.801213 + 0.598380i \(0.795811\pi\)
\(270\) 1.07101 0.0651794
\(271\) −15.6701 −0.951888 −0.475944 0.879475i \(-0.657894\pi\)
−0.475944 + 0.879475i \(0.657894\pi\)
\(272\) 0.753248 0.0456724
\(273\) −3.26268 −0.197467
\(274\) 4.23540 0.255870
\(275\) −24.5091 −1.47795
\(276\) 10.2352 0.616086
\(277\) −11.5647 −0.694856 −0.347428 0.937707i \(-0.612945\pi\)
−0.347428 + 0.937707i \(0.612945\pi\)
\(278\) −17.6617 −1.05928
\(279\) −38.5910 −2.31038
\(280\) 0.0654846 0.00391345
\(281\) −14.1091 −0.841678 −0.420839 0.907135i \(-0.638264\pi\)
−0.420839 + 0.907135i \(0.638264\pi\)
\(282\) 24.8266 1.47840
\(283\) −16.8451 −1.00134 −0.500668 0.865639i \(-0.666912\pi\)
−0.500668 + 0.865639i \(0.666912\pi\)
\(284\) −0.630097 −0.0373894
\(285\) 0.298775 0.0176979
\(286\) −8.56428 −0.506416
\(287\) 6.10657 0.360460
\(288\) 6.29376 0.370863
\(289\) −16.4326 −0.966625
\(290\) −0.375968 −0.0220776
\(291\) 7.02805 0.411992
\(292\) −0.360837 −0.0211164
\(293\) −0.226701 −0.0132440 −0.00662201 0.999978i \(-0.502108\pi\)
−0.00662201 + 0.999978i \(0.502108\pi\)
\(294\) 20.1909 1.17755
\(295\) −0.912882 −0.0531501
\(296\) −1.78363 −0.103671
\(297\) −49.3326 −2.86257
\(298\) 3.34112 0.193546
\(299\) 5.85254 0.338461
\(300\) 15.2082 0.878043
\(301\) −3.20942 −0.184988
\(302\) −1.53758 −0.0884779
\(303\) −19.3964 −1.11430
\(304\) 0.918851 0.0526997
\(305\) 0.343963 0.0196953
\(306\) 4.74076 0.271011
\(307\) −13.6595 −0.779588 −0.389794 0.920902i \(-0.627454\pi\)
−0.389794 + 0.920902i \(0.627454\pi\)
\(308\) −3.01634 −0.171872
\(309\) 1.38321 0.0786882
\(310\) 0.654003 0.0371449
\(311\) −12.3045 −0.697726 −0.348863 0.937174i \(-0.613432\pi\)
−0.348863 + 0.937174i \(0.613432\pi\)
\(312\) 5.31423 0.300859
\(313\) 25.9209 1.46513 0.732567 0.680695i \(-0.238322\pi\)
0.732567 + 0.680695i \(0.238322\pi\)
\(314\) −15.2523 −0.860735
\(315\) 0.412144 0.0232217
\(316\) 14.1602 0.796574
\(317\) −18.2940 −1.02750 −0.513748 0.857941i \(-0.671743\pi\)
−0.513748 + 0.857941i \(0.671743\pi\)
\(318\) −18.8209 −1.05542
\(319\) 17.3178 0.969612
\(320\) −0.106661 −0.00596251
\(321\) 20.5997 1.14976
\(322\) 2.06127 0.114870
\(323\) 0.692122 0.0385107
\(324\) 11.7302 0.651675
\(325\) 8.69611 0.482374
\(326\) −14.5705 −0.806984
\(327\) −25.4026 −1.40477
\(328\) −9.94633 −0.549194
\(329\) 4.99983 0.275650
\(330\) 1.59752 0.0879406
\(331\) 14.0821 0.774024 0.387012 0.922075i \(-0.373507\pi\)
0.387012 + 0.922075i \(0.373507\pi\)
\(332\) 4.38774 0.240808
\(333\) −11.2257 −0.615167
\(334\) 5.47291 0.299464
\(335\) 0.446383 0.0243885
\(336\) 1.87168 0.102108
\(337\) −1.41883 −0.0772888 −0.0386444 0.999253i \(-0.512304\pi\)
−0.0386444 + 0.999253i \(0.512304\pi\)
\(338\) −9.96129 −0.541823
\(339\) 33.2026 1.80332
\(340\) −0.0803419 −0.00435715
\(341\) −30.1246 −1.63134
\(342\) 5.78303 0.312710
\(343\) 8.36391 0.451609
\(344\) 5.22747 0.281846
\(345\) −1.09169 −0.0587747
\(346\) −19.7961 −1.06425
\(347\) 32.7399 1.75757 0.878784 0.477220i \(-0.158355\pi\)
0.878784 + 0.477220i \(0.158355\pi\)
\(348\) −10.7459 −0.576041
\(349\) −22.3611 −1.19696 −0.598482 0.801137i \(-0.704229\pi\)
−0.598482 + 0.801137i \(0.704229\pi\)
\(350\) 3.06278 0.163712
\(351\) 17.5038 0.934284
\(352\) 4.91299 0.261863
\(353\) −29.4548 −1.56772 −0.783860 0.620937i \(-0.786752\pi\)
−0.783860 + 0.620937i \(0.786752\pi\)
\(354\) −26.0919 −1.38677
\(355\) 0.0672066 0.00356696
\(356\) 15.2114 0.806205
\(357\) 1.40984 0.0746164
\(358\) −4.91078 −0.259543
\(359\) 19.3394 1.02070 0.510348 0.859968i \(-0.329517\pi\)
0.510348 + 0.859968i \(0.329517\pi\)
\(360\) −0.671297 −0.0353804
\(361\) −18.1557 −0.955564
\(362\) −3.08931 −0.162370
\(363\) −40.0506 −2.10211
\(364\) 1.07024 0.0560956
\(365\) 0.0384871 0.00201451
\(366\) 9.83113 0.513881
\(367\) −27.7582 −1.44897 −0.724483 0.689293i \(-0.757921\pi\)
−0.724483 + 0.689293i \(0.757921\pi\)
\(368\) −3.35738 −0.175015
\(369\) −62.5998 −3.25882
\(370\) 0.190243 0.00989026
\(371\) −3.79034 −0.196785
\(372\) 18.6927 0.969169
\(373\) −11.2325 −0.581598 −0.290799 0.956784i \(-0.593921\pi\)
−0.290799 + 0.956784i \(0.593921\pi\)
\(374\) 3.70070 0.191359
\(375\) −3.24792 −0.167722
\(376\) −8.14368 −0.419978
\(377\) −6.14457 −0.316462
\(378\) 6.16485 0.317086
\(379\) 24.1984 1.24299 0.621495 0.783418i \(-0.286526\pi\)
0.621495 + 0.783418i \(0.286526\pi\)
\(380\) −0.0980052 −0.00502756
\(381\) 42.7634 2.19084
\(382\) 11.5369 0.590277
\(383\) 20.6939 1.05741 0.528704 0.848806i \(-0.322678\pi\)
0.528704 + 0.848806i \(0.322678\pi\)
\(384\) −3.04857 −0.155572
\(385\) 0.321725 0.0163966
\(386\) −17.7635 −0.904138
\(387\) 32.9004 1.67242
\(388\) −2.30536 −0.117037
\(389\) −25.5726 −1.29658 −0.648290 0.761394i \(-0.724516\pi\)
−0.648290 + 0.761394i \(0.724516\pi\)
\(390\) −0.566819 −0.0287020
\(391\) −2.52894 −0.127894
\(392\) −6.62306 −0.334515
\(393\) 26.2245 1.32285
\(394\) 14.5005 0.730525
\(395\) −1.51034 −0.0759933
\(396\) 30.9212 1.55385
\(397\) −8.57870 −0.430553 −0.215276 0.976553i \(-0.569065\pi\)
−0.215276 + 0.976553i \(0.569065\pi\)
\(398\) −4.28047 −0.214561
\(399\) 1.71979 0.0860972
\(400\) −4.98862 −0.249431
\(401\) 15.1107 0.754591 0.377295 0.926093i \(-0.376854\pi\)
0.377295 + 0.926093i \(0.376854\pi\)
\(402\) 12.7585 0.636335
\(403\) 10.6886 0.532436
\(404\) 6.36247 0.316545
\(405\) −1.25115 −0.0621699
\(406\) −2.16412 −0.107404
\(407\) −8.76296 −0.434364
\(408\) −2.29633 −0.113685
\(409\) 34.2678 1.69443 0.847216 0.531248i \(-0.178277\pi\)
0.847216 + 0.531248i \(0.178277\pi\)
\(410\) 1.06088 0.0523932
\(411\) −12.9119 −0.636897
\(412\) −0.453725 −0.0223534
\(413\) −5.25467 −0.258565
\(414\) −21.1305 −1.03851
\(415\) −0.467999 −0.0229732
\(416\) −1.74319 −0.0854669
\(417\) 53.8428 2.63669
\(418\) 4.51431 0.220802
\(419\) 7.49890 0.366345 0.183173 0.983081i \(-0.441363\pi\)
0.183173 + 0.983081i \(0.441363\pi\)
\(420\) −0.199634 −0.00974115
\(421\) −26.4786 −1.29049 −0.645244 0.763977i \(-0.723244\pi\)
−0.645244 + 0.763977i \(0.723244\pi\)
\(422\) 5.93973 0.289141
\(423\) −51.2544 −2.49207
\(424\) 6.17368 0.299820
\(425\) −3.75767 −0.182274
\(426\) 1.92089 0.0930676
\(427\) 1.97989 0.0958138
\(428\) −6.75717 −0.326620
\(429\) 26.1088 1.26054
\(430\) −0.557565 −0.0268882
\(431\) −18.4406 −0.888253 −0.444126 0.895964i \(-0.646486\pi\)
−0.444126 + 0.895964i \(0.646486\pi\)
\(432\) −10.0413 −0.483110
\(433\) −39.7443 −1.90999 −0.954994 0.296626i \(-0.904138\pi\)
−0.954994 + 0.296626i \(0.904138\pi\)
\(434\) 3.76452 0.180703
\(435\) 1.14616 0.0549544
\(436\) 8.33265 0.399061
\(437\) −3.08493 −0.147572
\(438\) 1.10004 0.0525617
\(439\) −18.3908 −0.877747 −0.438873 0.898549i \(-0.644622\pi\)
−0.438873 + 0.898549i \(0.644622\pi\)
\(440\) −0.524023 −0.0249818
\(441\) −41.6840 −1.98495
\(442\) −1.31305 −0.0624556
\(443\) 40.0120 1.90103 0.950513 0.310685i \(-0.100558\pi\)
0.950513 + 0.310685i \(0.100558\pi\)
\(444\) 5.43751 0.258053
\(445\) −1.62246 −0.0769121
\(446\) 18.8388 0.892044
\(447\) −10.1856 −0.481763
\(448\) −0.613952 −0.0290065
\(449\) −14.8628 −0.701419 −0.350709 0.936484i \(-0.614060\pi\)
−0.350709 + 0.936484i \(0.614060\pi\)
\(450\) −31.3972 −1.48008
\(451\) −48.8662 −2.30102
\(452\) −10.8912 −0.512280
\(453\) 4.68742 0.220234
\(454\) 15.4741 0.726235
\(455\) −0.114152 −0.00535153
\(456\) −2.80118 −0.131177
\(457\) −7.18478 −0.336090 −0.168045 0.985779i \(-0.553745\pi\)
−0.168045 + 0.985779i \(0.553745\pi\)
\(458\) −3.49682 −0.163396
\(459\) −7.56355 −0.353036
\(460\) 0.358100 0.0166965
\(461\) −1.75478 −0.0817284 −0.0408642 0.999165i \(-0.513011\pi\)
−0.0408642 + 0.999165i \(0.513011\pi\)
\(462\) 9.19553 0.427815
\(463\) 32.2241 1.49758 0.748791 0.662806i \(-0.230634\pi\)
0.748791 + 0.662806i \(0.230634\pi\)
\(464\) 3.52490 0.163639
\(465\) −1.99377 −0.0924589
\(466\) −25.8327 −1.19668
\(467\) −32.6604 −1.51134 −0.755671 0.654952i \(-0.772689\pi\)
−0.755671 + 0.654952i \(0.772689\pi\)
\(468\) −10.9712 −0.507145
\(469\) 2.56944 0.118646
\(470\) 0.868611 0.0400660
\(471\) 46.4975 2.14249
\(472\) 8.55876 0.393949
\(473\) 25.6825 1.18088
\(474\) −43.1684 −1.98279
\(475\) −4.58380 −0.210319
\(476\) −0.462458 −0.0211967
\(477\) 38.8557 1.77908
\(478\) 12.5745 0.575146
\(479\) 38.1370 1.74252 0.871261 0.490820i \(-0.163303\pi\)
0.871261 + 0.490820i \(0.163303\pi\)
\(480\) 0.325162 0.0148416
\(481\) 3.10920 0.141767
\(482\) 6.89941 0.314260
\(483\) −6.28392 −0.285928
\(484\) 13.1375 0.597159
\(485\) 0.245891 0.0111654
\(486\) −5.63640 −0.255672
\(487\) −11.4672 −0.519630 −0.259815 0.965658i \(-0.583662\pi\)
−0.259815 + 0.965658i \(0.583662\pi\)
\(488\) −3.22483 −0.145981
\(489\) 44.4191 2.00870
\(490\) 0.706420 0.0319128
\(491\) 4.87300 0.219916 0.109958 0.993936i \(-0.464928\pi\)
0.109958 + 0.993936i \(0.464928\pi\)
\(492\) 30.3221 1.36702
\(493\) 2.65513 0.119581
\(494\) −1.60173 −0.0720653
\(495\) −3.29808 −0.148238
\(496\) −6.13162 −0.275318
\(497\) 0.386850 0.0173526
\(498\) −13.3763 −0.599407
\(499\) 3.32755 0.148962 0.0744808 0.997222i \(-0.476270\pi\)
0.0744808 + 0.997222i \(0.476270\pi\)
\(500\) 1.06539 0.0476458
\(501\) −16.6845 −0.745409
\(502\) 7.65888 0.341833
\(503\) −25.7827 −1.14959 −0.574796 0.818297i \(-0.694919\pi\)
−0.574796 + 0.818297i \(0.694919\pi\)
\(504\) −3.86407 −0.172119
\(505\) −0.678625 −0.0301984
\(506\) −16.4948 −0.733282
\(507\) 30.3677 1.34868
\(508\) −14.0274 −0.622365
\(509\) −31.7711 −1.40823 −0.704114 0.710087i \(-0.748656\pi\)
−0.704114 + 0.710087i \(0.748656\pi\)
\(510\) 0.244928 0.0108456
\(511\) 0.221537 0.00980020
\(512\) 1.00000 0.0441942
\(513\) −9.22641 −0.407356
\(514\) −1.00875 −0.0444942
\(515\) 0.0483947 0.00213252
\(516\) −15.9363 −0.701556
\(517\) −40.0099 −1.75963
\(518\) 1.09506 0.0481143
\(519\) 60.3498 2.64906
\(520\) 0.185930 0.00815356
\(521\) −3.81114 −0.166969 −0.0834845 0.996509i \(-0.526605\pi\)
−0.0834845 + 0.996509i \(0.526605\pi\)
\(522\) 22.1849 0.971007
\(523\) −38.3840 −1.67841 −0.839207 0.543813i \(-0.816980\pi\)
−0.839207 + 0.543813i \(0.816980\pi\)
\(524\) −8.60225 −0.375791
\(525\) −9.33708 −0.407504
\(526\) 23.2435 1.01347
\(527\) −4.61863 −0.201191
\(528\) −14.9776 −0.651816
\(529\) −11.7280 −0.509914
\(530\) −0.658488 −0.0286029
\(531\) 53.8668 2.33762
\(532\) −0.564130 −0.0244582
\(533\) 17.3383 0.751007
\(534\) −46.3731 −2.00676
\(535\) 0.720724 0.0311596
\(536\) −4.18508 −0.180768
\(537\) 14.9708 0.646039
\(538\) −26.2817 −1.13309
\(539\) −32.5391 −1.40156
\(540\) 1.07101 0.0460888
\(541\) −42.5303 −1.82852 −0.914259 0.405130i \(-0.867226\pi\)
−0.914259 + 0.405130i \(0.867226\pi\)
\(542\) −15.6701 −0.673087
\(543\) 9.41796 0.404163
\(544\) 0.753248 0.0322952
\(545\) −0.888766 −0.0380705
\(546\) −3.26268 −0.139630
\(547\) −20.4653 −0.875034 −0.437517 0.899210i \(-0.644142\pi\)
−0.437517 + 0.899210i \(0.644142\pi\)
\(548\) 4.23540 0.180927
\(549\) −20.2963 −0.866227
\(550\) −24.5091 −1.04507
\(551\) 3.23886 0.137980
\(552\) 10.2352 0.435639
\(553\) −8.69370 −0.369694
\(554\) −11.5647 −0.491337
\(555\) −0.579969 −0.0246183
\(556\) −17.6617 −0.749022
\(557\) −10.3026 −0.436536 −0.218268 0.975889i \(-0.570041\pi\)
−0.218268 + 0.975889i \(0.570041\pi\)
\(558\) −38.5910 −1.63369
\(559\) −9.11246 −0.385416
\(560\) 0.0654846 0.00276723
\(561\) −11.2818 −0.476320
\(562\) −14.1091 −0.595156
\(563\) −25.4461 −1.07243 −0.536213 0.844083i \(-0.680145\pi\)
−0.536213 + 0.844083i \(0.680145\pi\)
\(564\) 24.8266 1.04539
\(565\) 1.16166 0.0488716
\(566\) −16.8451 −0.708052
\(567\) −7.20176 −0.302445
\(568\) −0.630097 −0.0264383
\(569\) −33.3982 −1.40013 −0.700063 0.714081i \(-0.746845\pi\)
−0.700063 + 0.714081i \(0.746845\pi\)
\(570\) 0.298775 0.0125143
\(571\) 9.08209 0.380073 0.190037 0.981777i \(-0.439139\pi\)
0.190037 + 0.981777i \(0.439139\pi\)
\(572\) −8.56428 −0.358090
\(573\) −35.1709 −1.46929
\(574\) 6.10657 0.254883
\(575\) 16.7487 0.698469
\(576\) 6.29376 0.262240
\(577\) 28.6130 1.19117 0.595587 0.803291i \(-0.296919\pi\)
0.595587 + 0.803291i \(0.296919\pi\)
\(578\) −16.4326 −0.683507
\(579\) 54.1532 2.25053
\(580\) −0.375968 −0.0156112
\(581\) −2.69386 −0.111760
\(582\) 7.02805 0.291322
\(583\) 30.3312 1.25619
\(584\) −0.360837 −0.0149315
\(585\) 1.17020 0.0483817
\(586\) −0.226701 −0.00936494
\(587\) −8.28498 −0.341958 −0.170979 0.985275i \(-0.554693\pi\)
−0.170979 + 0.985275i \(0.554693\pi\)
\(588\) 20.1909 0.832657
\(589\) −5.63404 −0.232147
\(590\) −0.912882 −0.0375828
\(591\) −44.2058 −1.81838
\(592\) −1.78363 −0.0733067
\(593\) 8.97125 0.368405 0.184203 0.982888i \(-0.441030\pi\)
0.184203 + 0.982888i \(0.441030\pi\)
\(594\) −49.3326 −2.02414
\(595\) 0.0493261 0.00202217
\(596\) 3.34112 0.136857
\(597\) 13.0493 0.534072
\(598\) 5.85254 0.239328
\(599\) −0.162180 −0.00662648 −0.00331324 0.999995i \(-0.501055\pi\)
−0.00331324 + 0.999995i \(0.501055\pi\)
\(600\) 15.2082 0.620870
\(601\) 0.893200 0.0364344 0.0182172 0.999834i \(-0.494201\pi\)
0.0182172 + 0.999834i \(0.494201\pi\)
\(602\) −3.20942 −0.130806
\(603\) −26.3399 −1.07264
\(604\) −1.53758 −0.0625633
\(605\) −1.40125 −0.0569691
\(606\) −19.3964 −0.787926
\(607\) −33.8680 −1.37466 −0.687329 0.726346i \(-0.741217\pi\)
−0.687329 + 0.726346i \(0.741217\pi\)
\(608\) 0.918851 0.0372643
\(609\) 6.59747 0.267343
\(610\) 0.343963 0.0139267
\(611\) 14.1960 0.574308
\(612\) 4.74076 0.191634
\(613\) 3.60845 0.145744 0.0728719 0.997341i \(-0.476784\pi\)
0.0728719 + 0.997341i \(0.476784\pi\)
\(614\) −13.6595 −0.551252
\(615\) −3.23417 −0.130414
\(616\) −3.01634 −0.121532
\(617\) 35.4987 1.42912 0.714562 0.699573i \(-0.246626\pi\)
0.714562 + 0.699573i \(0.246626\pi\)
\(618\) 1.38321 0.0556410
\(619\) 7.22259 0.290300 0.145150 0.989410i \(-0.453633\pi\)
0.145150 + 0.989410i \(0.453633\pi\)
\(620\) 0.654003 0.0262654
\(621\) 33.7123 1.35283
\(622\) −12.3045 −0.493367
\(623\) −9.33910 −0.374163
\(624\) 5.31423 0.212739
\(625\) 24.8295 0.993179
\(626\) 25.9209 1.03601
\(627\) −13.7622 −0.549608
\(628\) −15.2523 −0.608631
\(629\) −1.34351 −0.0535694
\(630\) 0.412144 0.0164202
\(631\) 27.5850 1.09814 0.549071 0.835775i \(-0.314982\pi\)
0.549071 + 0.835775i \(0.314982\pi\)
\(632\) 14.1602 0.563263
\(633\) −18.1077 −0.719715
\(634\) −18.2940 −0.726549
\(635\) 1.49617 0.0593737
\(636\) −18.8209 −0.746296
\(637\) 11.5453 0.457439
\(638\) 17.3178 0.685619
\(639\) −3.96568 −0.156880
\(640\) −0.106661 −0.00421613
\(641\) −0.286667 −0.0113227 −0.00566134 0.999984i \(-0.501802\pi\)
−0.00566134 + 0.999984i \(0.501802\pi\)
\(642\) 20.5997 0.813005
\(643\) −28.1240 −1.10910 −0.554552 0.832149i \(-0.687110\pi\)
−0.554552 + 0.832149i \(0.687110\pi\)
\(644\) 2.06127 0.0812254
\(645\) 1.69977 0.0669286
\(646\) 0.692122 0.0272312
\(647\) −3.07712 −0.120974 −0.0604870 0.998169i \(-0.519265\pi\)
−0.0604870 + 0.998169i \(0.519265\pi\)
\(648\) 11.7302 0.460804
\(649\) 42.0491 1.65057
\(650\) 8.69611 0.341090
\(651\) −11.4764 −0.449796
\(652\) −14.5705 −0.570624
\(653\) −21.4278 −0.838535 −0.419267 0.907863i \(-0.637713\pi\)
−0.419267 + 0.907863i \(0.637713\pi\)
\(654\) −25.4026 −0.993322
\(655\) 0.917522 0.0358505
\(656\) −9.94633 −0.388339
\(657\) −2.27102 −0.0886010
\(658\) 4.99983 0.194914
\(659\) −23.6525 −0.921372 −0.460686 0.887563i \(-0.652397\pi\)
−0.460686 + 0.887563i \(0.652397\pi\)
\(660\) 1.59752 0.0621834
\(661\) −5.78219 −0.224901 −0.112451 0.993657i \(-0.535870\pi\)
−0.112451 + 0.993657i \(0.535870\pi\)
\(662\) 14.0821 0.547317
\(663\) 4.00293 0.155461
\(664\) 4.38774 0.170277
\(665\) 0.0601705 0.00233331
\(666\) −11.2257 −0.434989
\(667\) −11.8344 −0.458231
\(668\) 5.47291 0.211753
\(669\) −57.4314 −2.22043
\(670\) 0.446383 0.0172453
\(671\) −15.8436 −0.611635
\(672\) 1.87168 0.0722014
\(673\) 7.09081 0.273331 0.136665 0.990617i \(-0.456362\pi\)
0.136665 + 0.990617i \(0.456362\pi\)
\(674\) −1.41883 −0.0546514
\(675\) 50.0920 1.92804
\(676\) −9.96129 −0.383127
\(677\) 31.3240 1.20388 0.601940 0.798541i \(-0.294394\pi\)
0.601940 + 0.798541i \(0.294394\pi\)
\(678\) 33.2026 1.27514
\(679\) 1.41538 0.0543174
\(680\) −0.0803419 −0.00308097
\(681\) −47.1738 −1.80770
\(682\) −30.1246 −1.15353
\(683\) 37.9091 1.45055 0.725275 0.688459i \(-0.241713\pi\)
0.725275 + 0.688459i \(0.241713\pi\)
\(684\) 5.78303 0.221120
\(685\) −0.451750 −0.0172605
\(686\) 8.36391 0.319336
\(687\) 10.6603 0.406715
\(688\) 5.22747 0.199295
\(689\) −10.7619 −0.409995
\(690\) −1.09169 −0.0415600
\(691\) −35.8466 −1.36367 −0.681834 0.731507i \(-0.738817\pi\)
−0.681834 + 0.731507i \(0.738817\pi\)
\(692\) −19.7961 −0.752535
\(693\) −18.9841 −0.721148
\(694\) 32.7399 1.24279
\(695\) 1.88381 0.0714568
\(696\) −10.7459 −0.407322
\(697\) −7.49205 −0.283782
\(698\) −22.3611 −0.846381
\(699\) 78.7528 2.97870
\(700\) 3.06278 0.115762
\(701\) −8.39479 −0.317067 −0.158533 0.987354i \(-0.550677\pi\)
−0.158533 + 0.987354i \(0.550677\pi\)
\(702\) 17.5038 0.660639
\(703\) −1.63889 −0.0618119
\(704\) 4.91299 0.185165
\(705\) −2.64802 −0.0997301
\(706\) −29.4548 −1.10855
\(707\) −3.90625 −0.146910
\(708\) −26.0919 −0.980595
\(709\) 40.7039 1.52867 0.764334 0.644821i \(-0.223068\pi\)
0.764334 + 0.644821i \(0.223068\pi\)
\(710\) 0.0672066 0.00252222
\(711\) 89.1210 3.34230
\(712\) 15.2114 0.570073
\(713\) 20.5862 0.770958
\(714\) 1.40984 0.0527618
\(715\) 0.913471 0.0341619
\(716\) −4.91078 −0.183524
\(717\) −38.3344 −1.43162
\(718\) 19.3394 0.721741
\(719\) −17.9616 −0.669854 −0.334927 0.942244i \(-0.608712\pi\)
−0.334927 + 0.942244i \(0.608712\pi\)
\(720\) −0.671297 −0.0250178
\(721\) 0.278566 0.0103743
\(722\) −18.1557 −0.675686
\(723\) −21.0333 −0.782237
\(724\) −3.08931 −0.114813
\(725\) −17.5844 −0.653069
\(726\) −40.0506 −1.48642
\(727\) 32.8911 1.21986 0.609932 0.792454i \(-0.291197\pi\)
0.609932 + 0.792454i \(0.291197\pi\)
\(728\) 1.07024 0.0396655
\(729\) −18.0075 −0.666945
\(730\) 0.0384871 0.00142447
\(731\) 3.93758 0.145637
\(732\) 9.83113 0.363369
\(733\) 9.04047 0.333917 0.166959 0.985964i \(-0.446605\pi\)
0.166959 + 0.985964i \(0.446605\pi\)
\(734\) −27.7582 −1.02457
\(735\) −2.15357 −0.0794356
\(736\) −3.35738 −0.123755
\(737\) −20.5613 −0.757383
\(738\) −62.5998 −2.30433
\(739\) 16.0773 0.591412 0.295706 0.955279i \(-0.404445\pi\)
0.295706 + 0.955279i \(0.404445\pi\)
\(740\) 0.190243 0.00699347
\(741\) 4.88298 0.179381
\(742\) −3.79034 −0.139148
\(743\) 24.2251 0.888734 0.444367 0.895845i \(-0.353429\pi\)
0.444367 + 0.895845i \(0.353429\pi\)
\(744\) 18.6927 0.685306
\(745\) −0.356366 −0.0130562
\(746\) −11.2325 −0.411252
\(747\) 27.6154 1.01039
\(748\) 3.70070 0.135311
\(749\) 4.14858 0.151586
\(750\) −3.24792 −0.118597
\(751\) 9.64049 0.351787 0.175893 0.984409i \(-0.443719\pi\)
0.175893 + 0.984409i \(0.443719\pi\)
\(752\) −8.14368 −0.296970
\(753\) −23.3486 −0.850871
\(754\) −6.14457 −0.223772
\(755\) 0.163999 0.00596855
\(756\) 6.16485 0.224214
\(757\) −8.34692 −0.303374 −0.151687 0.988429i \(-0.548471\pi\)
−0.151687 + 0.988429i \(0.548471\pi\)
\(758\) 24.1984 0.878926
\(759\) 50.2854 1.82525
\(760\) −0.0980052 −0.00355502
\(761\) 11.4700 0.415786 0.207893 0.978152i \(-0.433339\pi\)
0.207893 + 0.978152i \(0.433339\pi\)
\(762\) 42.7634 1.54916
\(763\) −5.11585 −0.185206
\(764\) 11.5369 0.417389
\(765\) −0.505653 −0.0182819
\(766\) 20.6939 0.747701
\(767\) −14.9195 −0.538713
\(768\) −3.04857 −0.110006
\(769\) 0.0609674 0.00219854 0.00109927 0.999999i \(-0.499650\pi\)
0.00109927 + 0.999999i \(0.499650\pi\)
\(770\) 0.321725 0.0115942
\(771\) 3.07525 0.110752
\(772\) −17.7635 −0.639322
\(773\) −7.77696 −0.279718 −0.139859 0.990171i \(-0.544665\pi\)
−0.139859 + 0.990171i \(0.544665\pi\)
\(774\) 32.9004 1.18258
\(775\) 30.5884 1.09877
\(776\) −2.30536 −0.0827577
\(777\) −3.33837 −0.119764
\(778\) −25.5726 −0.916820
\(779\) −9.13919 −0.327445
\(780\) −0.566819 −0.0202954
\(781\) −3.09566 −0.110772
\(782\) −2.52894 −0.0904346
\(783\) −35.3944 −1.26489
\(784\) −6.62306 −0.236538
\(785\) 1.62682 0.0580636
\(786\) 26.2245 0.935398
\(787\) −23.7962 −0.848242 −0.424121 0.905606i \(-0.639417\pi\)
−0.424121 + 0.905606i \(0.639417\pi\)
\(788\) 14.5005 0.516559
\(789\) −70.8594 −2.52266
\(790\) −1.51034 −0.0537354
\(791\) 6.68669 0.237751
\(792\) 30.9212 1.09874
\(793\) 5.62150 0.199625
\(794\) −8.57870 −0.304447
\(795\) 2.00745 0.0711968
\(796\) −4.28047 −0.151717
\(797\) −9.40157 −0.333021 −0.166510 0.986040i \(-0.553250\pi\)
−0.166510 + 0.986040i \(0.553250\pi\)
\(798\) 1.71979 0.0608799
\(799\) −6.13421 −0.217013
\(800\) −4.98862 −0.176374
\(801\) 95.7372 3.38271
\(802\) 15.1107 0.533576
\(803\) −1.77279 −0.0625604
\(804\) 12.7585 0.449957
\(805\) −0.219856 −0.00774892
\(806\) 10.6886 0.376489
\(807\) 80.1216 2.82041
\(808\) 6.36247 0.223831
\(809\) 12.5746 0.442099 0.221049 0.975263i \(-0.429052\pi\)
0.221049 + 0.975263i \(0.429052\pi\)
\(810\) −1.25115 −0.0439608
\(811\) 44.3058 1.55579 0.777894 0.628396i \(-0.216288\pi\)
0.777894 + 0.628396i \(0.216288\pi\)
\(812\) −2.16412 −0.0759458
\(813\) 47.7712 1.67541
\(814\) −8.76296 −0.307142
\(815\) 1.55410 0.0544376
\(816\) −2.29633 −0.0803875
\(817\) 4.80326 0.168045
\(818\) 34.2678 1.19815
\(819\) 6.73580 0.235368
\(820\) 1.06088 0.0370476
\(821\) 22.7577 0.794249 0.397125 0.917765i \(-0.370008\pi\)
0.397125 + 0.917765i \(0.370008\pi\)
\(822\) −12.9119 −0.450354
\(823\) −52.9089 −1.84429 −0.922144 0.386846i \(-0.873564\pi\)
−0.922144 + 0.386846i \(0.873564\pi\)
\(824\) −0.453725 −0.0158063
\(825\) 74.7176 2.60133
\(826\) −5.25467 −0.182833
\(827\) −39.8726 −1.38651 −0.693253 0.720695i \(-0.743823\pi\)
−0.693253 + 0.720695i \(0.743823\pi\)
\(828\) −21.1305 −0.734337
\(829\) 18.1965 0.631990 0.315995 0.948761i \(-0.397662\pi\)
0.315995 + 0.948761i \(0.397662\pi\)
\(830\) −0.467999 −0.0162445
\(831\) 35.2558 1.22301
\(832\) −1.74319 −0.0604342
\(833\) −4.98881 −0.172852
\(834\) 53.8428 1.86442
\(835\) −0.583744 −0.0202013
\(836\) 4.51431 0.156131
\(837\) 61.5692 2.12814
\(838\) 7.49890 0.259045
\(839\) 18.5130 0.639141 0.319570 0.947563i \(-0.396461\pi\)
0.319570 + 0.947563i \(0.396461\pi\)
\(840\) −0.199634 −0.00688803
\(841\) −16.5751 −0.571554
\(842\) −26.4786 −0.912512
\(843\) 43.0125 1.48143
\(844\) 5.93973 0.204454
\(845\) 1.06248 0.0365503
\(846\) −51.2544 −1.76216
\(847\) −8.06580 −0.277144
\(848\) 6.17368 0.212005
\(849\) 51.3534 1.76244
\(850\) −3.75767 −0.128887
\(851\) 5.98832 0.205277
\(852\) 1.92089 0.0658088
\(853\) 27.4700 0.940553 0.470277 0.882519i \(-0.344154\pi\)
0.470277 + 0.882519i \(0.344154\pi\)
\(854\) 1.97989 0.0677506
\(855\) −0.616821 −0.0210948
\(856\) −6.75717 −0.230955
\(857\) 47.0770 1.60812 0.804059 0.594549i \(-0.202669\pi\)
0.804059 + 0.594549i \(0.202669\pi\)
\(858\) 26.1088 0.891339
\(859\) −21.4307 −0.731205 −0.365602 0.930771i \(-0.619137\pi\)
−0.365602 + 0.930771i \(0.619137\pi\)
\(860\) −0.557565 −0.0190128
\(861\) −18.6163 −0.634442
\(862\) −18.4406 −0.628090
\(863\) −8.84649 −0.301138 −0.150569 0.988600i \(-0.548111\pi\)
−0.150569 + 0.988600i \(0.548111\pi\)
\(864\) −10.0413 −0.341610
\(865\) 2.11147 0.0717920
\(866\) −39.7443 −1.35056
\(867\) 50.0959 1.70135
\(868\) 3.76452 0.127776
\(869\) 69.5690 2.35997
\(870\) 1.14616 0.0388586
\(871\) 7.29538 0.247195
\(872\) 8.33265 0.282179
\(873\) −14.5094 −0.491069
\(874\) −3.08493 −0.104349
\(875\) −0.654101 −0.0221126
\(876\) 1.10004 0.0371667
\(877\) 41.9319 1.41594 0.707970 0.706243i \(-0.249611\pi\)
0.707970 + 0.706243i \(0.249611\pi\)
\(878\) −18.3908 −0.620661
\(879\) 0.691114 0.0233107
\(880\) −0.524023 −0.0176648
\(881\) 3.22506 0.108655 0.0543275 0.998523i \(-0.482699\pi\)
0.0543275 + 0.998523i \(0.482699\pi\)
\(882\) −41.6840 −1.40357
\(883\) −14.5819 −0.490720 −0.245360 0.969432i \(-0.578906\pi\)
−0.245360 + 0.969432i \(0.578906\pi\)
\(884\) −1.31305 −0.0441628
\(885\) 2.78298 0.0935490
\(886\) 40.0120 1.34423
\(887\) 9.12280 0.306314 0.153157 0.988202i \(-0.451056\pi\)
0.153157 + 0.988202i \(0.451056\pi\)
\(888\) 5.43751 0.182471
\(889\) 8.61215 0.288842
\(890\) −1.62246 −0.0543851
\(891\) 57.6302 1.93068
\(892\) 18.8388 0.630770
\(893\) −7.48283 −0.250403
\(894\) −10.1856 −0.340658
\(895\) 0.523787 0.0175083
\(896\) −0.613952 −0.0205107
\(897\) −17.8419 −0.595723
\(898\) −14.8628 −0.495978
\(899\) −21.6134 −0.720846
\(900\) −31.3972 −1.04657
\(901\) 4.65031 0.154924
\(902\) −48.8662 −1.62707
\(903\) 9.78412 0.325595
\(904\) −10.8912 −0.362237
\(905\) 0.329507 0.0109532
\(906\) 4.68742 0.155729
\(907\) −31.5625 −1.04802 −0.524008 0.851714i \(-0.675564\pi\)
−0.524008 + 0.851714i \(0.675564\pi\)
\(908\) 15.4741 0.513525
\(909\) 40.0439 1.32817
\(910\) −0.114152 −0.00378410
\(911\) 11.1509 0.369447 0.184723 0.982791i \(-0.440861\pi\)
0.184723 + 0.982791i \(0.440861\pi\)
\(912\) −2.80118 −0.0927563
\(913\) 21.5569 0.713430
\(914\) −7.18478 −0.237651
\(915\) −1.04859 −0.0346655
\(916\) −3.49682 −0.115538
\(917\) 5.28137 0.174406
\(918\) −7.56355 −0.249635
\(919\) −6.67855 −0.220305 −0.110153 0.993915i \(-0.535134\pi\)
−0.110153 + 0.993915i \(0.535134\pi\)
\(920\) 0.358100 0.0118062
\(921\) 41.6419 1.37215
\(922\) −1.75478 −0.0577907
\(923\) 1.09838 0.0361536
\(924\) 9.19553 0.302511
\(925\) 8.89785 0.292560
\(926\) 32.2241 1.05895
\(927\) −2.85564 −0.0937915
\(928\) 3.52490 0.115711
\(929\) 3.01293 0.0988510 0.0494255 0.998778i \(-0.484261\pi\)
0.0494255 + 0.998778i \(0.484261\pi\)
\(930\) −1.99377 −0.0653783
\(931\) −6.08560 −0.199448
\(932\) −25.8327 −0.846179
\(933\) 37.5112 1.22806
\(934\) −32.6604 −1.06868
\(935\) −0.394719 −0.0129087
\(936\) −10.9712 −0.358605
\(937\) −23.5473 −0.769256 −0.384628 0.923072i \(-0.625670\pi\)
−0.384628 + 0.923072i \(0.625670\pi\)
\(938\) 2.56944 0.0838951
\(939\) −79.0215 −2.57877
\(940\) 0.868611 0.0283310
\(941\) 27.4812 0.895861 0.447930 0.894068i \(-0.352161\pi\)
0.447930 + 0.894068i \(0.352161\pi\)
\(942\) 46.4975 1.51497
\(943\) 33.3936 1.08744
\(944\) 8.55876 0.278564
\(945\) −0.657547 −0.0213900
\(946\) 25.6825 0.835011
\(947\) −2.64385 −0.0859136 −0.0429568 0.999077i \(-0.513678\pi\)
−0.0429568 + 0.999077i \(0.513678\pi\)
\(948\) −43.1684 −1.40204
\(949\) 0.629007 0.0204184
\(950\) −4.58380 −0.148718
\(951\) 55.7706 1.80849
\(952\) −0.462458 −0.0149884
\(953\) −48.5720 −1.57340 −0.786701 0.617334i \(-0.788213\pi\)
−0.786701 + 0.617334i \(0.788213\pi\)
\(954\) 38.8557 1.25800
\(955\) −1.23053 −0.0398190
\(956\) 12.5745 0.406690
\(957\) −52.7945 −1.70661
\(958\) 38.1370 1.23215
\(959\) −2.60033 −0.0839691
\(960\) 0.325162 0.0104946
\(961\) 6.59679 0.212800
\(962\) 3.10920 0.100245
\(963\) −42.5280 −1.37045
\(964\) 6.89941 0.222215
\(965\) 1.89467 0.0609914
\(966\) −6.28392 −0.202182
\(967\) 25.1306 0.808147 0.404074 0.914727i \(-0.367594\pi\)
0.404074 + 0.914727i \(0.367594\pi\)
\(968\) 13.1375 0.422255
\(969\) −2.10998 −0.0677824
\(970\) 0.245891 0.00789510
\(971\) −3.99028 −0.128054 −0.0640272 0.997948i \(-0.520394\pi\)
−0.0640272 + 0.997948i \(0.520394\pi\)
\(972\) −5.63640 −0.180788
\(973\) 10.8434 0.347624
\(974\) −11.4672 −0.367434
\(975\) −26.5107 −0.849022
\(976\) −3.22483 −0.103224
\(977\) −33.5520 −1.07342 −0.536712 0.843766i \(-0.680334\pi\)
−0.536712 + 0.843766i \(0.680334\pi\)
\(978\) 44.4191 1.42036
\(979\) 74.7337 2.38850
\(980\) 0.706420 0.0225658
\(981\) 52.4437 1.67440
\(982\) 4.87300 0.155504
\(983\) −27.3889 −0.873571 −0.436786 0.899566i \(-0.643883\pi\)
−0.436786 + 0.899566i \(0.643883\pi\)
\(984\) 30.3221 0.966632
\(985\) −1.54663 −0.0492799
\(986\) 2.65513 0.0845564
\(987\) −15.2423 −0.485169
\(988\) −1.60173 −0.0509578
\(989\) −17.5506 −0.558076
\(990\) −3.29808 −0.104820
\(991\) 23.5918 0.749418 0.374709 0.927142i \(-0.377743\pi\)
0.374709 + 0.927142i \(0.377743\pi\)
\(992\) −6.13162 −0.194679
\(993\) −42.9303 −1.36235
\(994\) 0.386850 0.0122701
\(995\) 0.456558 0.0144739
\(996\) −13.3763 −0.423845
\(997\) −52.7751 −1.67140 −0.835702 0.549184i \(-0.814939\pi\)
−0.835702 + 0.549184i \(0.814939\pi\)
\(998\) 3.32755 0.105332
\(999\) 17.9099 0.566643
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 \(a_p\))