Properties

Label 6026.2.a.h.1.20
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +1.62268 q^{10} +0.118061 q^{11} +2.29919 q^{12} +4.81440 q^{13} +0.601158 q^{14} -3.73086 q^{15} +1.00000 q^{16} -3.51146 q^{17} -2.28626 q^{18} -2.74780 q^{19} -1.62268 q^{20} -1.38218 q^{21} -0.118061 q^{22} -1.00000 q^{23} -2.29919 q^{24} -2.36690 q^{25} -4.81440 q^{26} -1.64101 q^{27} -0.601158 q^{28} +5.80808 q^{29} +3.73086 q^{30} -6.64833 q^{31} -1.00000 q^{32} +0.271445 q^{33} +3.51146 q^{34} +0.975490 q^{35} +2.28626 q^{36} -4.44857 q^{37} +2.74780 q^{38} +11.0692 q^{39} +1.62268 q^{40} +8.02457 q^{41} +1.38218 q^{42} +11.2206 q^{43} +0.118061 q^{44} -3.70988 q^{45} +1.00000 q^{46} +0.815901 q^{47} +2.29919 q^{48} -6.63861 q^{49} +2.36690 q^{50} -8.07350 q^{51} +4.81440 q^{52} -7.82807 q^{53} +1.64101 q^{54} -0.191576 q^{55} +0.601158 q^{56} -6.31772 q^{57} -5.80808 q^{58} -10.7632 q^{59} -3.73086 q^{60} -3.23578 q^{61} +6.64833 q^{62} -1.37441 q^{63} +1.00000 q^{64} -7.81225 q^{65} -0.271445 q^{66} -8.38187 q^{67} -3.51146 q^{68} -2.29919 q^{69} -0.975490 q^{70} +3.85349 q^{71} -2.28626 q^{72} +6.09743 q^{73} +4.44857 q^{74} -5.44194 q^{75} -2.74780 q^{76} -0.0709734 q^{77} -11.0692 q^{78} -15.8125 q^{79} -1.62268 q^{80} -10.6318 q^{81} -8.02457 q^{82} -0.448185 q^{83} -1.38218 q^{84} +5.69798 q^{85} -11.2206 q^{86} +13.3539 q^{87} -0.118061 q^{88} +10.4150 q^{89} +3.70988 q^{90} -2.89421 q^{91} -1.00000 q^{92} -15.2858 q^{93} -0.815901 q^{94} +4.45882 q^{95} -2.29919 q^{96} -4.65467 q^{97} +6.63861 q^{98} +0.269919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} + 7q^{14} - 6q^{15} + 24q^{16} + 5q^{17} - 27q^{18} - 20q^{19} - q^{20} + 4q^{22} - 24q^{23} + q^{24} + q^{25} + 5q^{26} - q^{27} - 7q^{28} - 6q^{29} + 6q^{30} - 23q^{31} - 24q^{32} - 6q^{33} - 5q^{34} + 5q^{35} + 27q^{36} - 6q^{37} + 20q^{38} - 39q^{39} + q^{40} - q^{41} - 44q^{43} - 4q^{44} - 13q^{45} + 24q^{46} + 32q^{47} - q^{48} - 13q^{49} - q^{50} - 44q^{51} - 5q^{52} + 21q^{53} + q^{54} - 13q^{55} + 7q^{56} + 10q^{57} + 6q^{58} - 24q^{59} - 6q^{60} - 40q^{61} + 23q^{62} - 54q^{63} + 24q^{64} - 29q^{65} + 6q^{66} - 17q^{67} + 5q^{68} + q^{69} - 5q^{70} + 4q^{71} - 27q^{72} - 16q^{73} + 6q^{74} - 36q^{75} - 20q^{76} + 24q^{77} + 39q^{78} - 53q^{79} - q^{80} + 24q^{81} + q^{82} - 9q^{83} - 37q^{85} + 44q^{86} + 7q^{87} + 4q^{88} - 46q^{89} + 13q^{90} - 44q^{91} - 24q^{92} + 23q^{93} - 32q^{94} + 28q^{95} + q^{96} - 20q^{97} + 13q^{98} - 78q^{99} + O(q^{100}) \)

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
\(3\) 2.29919 1.32744 0.663718 0.747983i \(-0.268977\pi\)
0.663718 + 0.747983i \(0.268977\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.62268 −0.725686 −0.362843 0.931850i \(-0.618194\pi\)
−0.362843 + 0.931850i \(0.618194\pi\)
\(6\) −2.29919 −0.938639
\(7\) −0.601158 −0.227216 −0.113608 0.993526i \(-0.536241\pi\)
−0.113608 + 0.993526i \(0.536241\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.28626 0.762088
\(10\) 1.62268 0.513138
\(11\) 0.118061 0.0355968 0.0177984 0.999842i \(-0.494334\pi\)
0.0177984 + 0.999842i \(0.494334\pi\)
\(12\) 2.29919 0.663718
\(13\) 4.81440 1.33527 0.667637 0.744487i \(-0.267306\pi\)
0.667637 + 0.744487i \(0.267306\pi\)
\(14\) 0.601158 0.160666
\(15\) −3.73086 −0.963303
\(16\) 1.00000 0.250000
\(17\) −3.51146 −0.851653 −0.425827 0.904805i \(-0.640017\pi\)
−0.425827 + 0.904805i \(0.640017\pi\)
\(18\) −2.28626 −0.538878
\(19\) −2.74780 −0.630389 −0.315195 0.949027i \(-0.602070\pi\)
−0.315195 + 0.949027i \(0.602070\pi\)
\(20\) −1.62268 −0.362843
\(21\) −1.38218 −0.301615
\(22\) −0.118061 −0.0251707
\(23\) −1.00000 −0.208514
\(24\) −2.29919 −0.469320
\(25\) −2.36690 −0.473379
\(26\) −4.81440 −0.944181
\(27\) −1.64101 −0.315813
\(28\) −0.601158 −0.113608
\(29\) 5.80808 1.07853 0.539267 0.842135i \(-0.318701\pi\)
0.539267 + 0.842135i \(0.318701\pi\)
\(30\) 3.73086 0.681158
\(31\) −6.64833 −1.19408 −0.597038 0.802213i \(-0.703656\pi\)
−0.597038 + 0.802213i \(0.703656\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.271445 0.0472525
\(34\) 3.51146 0.602210
\(35\) 0.975490 0.164888
\(36\) 2.28626 0.381044
\(37\) −4.44857 −0.731341 −0.365670 0.930744i \(-0.619160\pi\)
−0.365670 + 0.930744i \(0.619160\pi\)
\(38\) 2.74780 0.445753
\(39\) 11.0692 1.77249
\(40\) 1.62268 0.256569
\(41\) 8.02457 1.25323 0.626613 0.779330i \(-0.284441\pi\)
0.626613 + 0.779330i \(0.284441\pi\)
\(42\) 1.38218 0.213274
\(43\) 11.2206 1.71112 0.855562 0.517701i \(-0.173212\pi\)
0.855562 + 0.517701i \(0.173212\pi\)
\(44\) 0.118061 0.0177984
\(45\) −3.70988 −0.553037
\(46\) 1.00000 0.147442
\(47\) 0.815901 0.119011 0.0595057 0.998228i \(-0.481048\pi\)
0.0595057 + 0.998228i \(0.481048\pi\)
\(48\) 2.29919 0.331859
\(49\) −6.63861 −0.948373
\(50\) 2.36690 0.334730
\(51\) −8.07350 −1.13052
\(52\) 4.81440 0.667637
\(53\) −7.82807 −1.07527 −0.537634 0.843178i \(-0.680682\pi\)
−0.537634 + 0.843178i \(0.680682\pi\)
\(54\) 1.64101 0.223313
\(55\) −0.191576 −0.0258321
\(56\) 0.601158 0.0803331
\(57\) −6.31772 −0.836802
\(58\) −5.80808 −0.762638
\(59\) −10.7632 −1.40125 −0.700626 0.713528i \(-0.747096\pi\)
−0.700626 + 0.713528i \(0.747096\pi\)
\(60\) −3.73086 −0.481651
\(61\) −3.23578 −0.414300 −0.207150 0.978309i \(-0.566419\pi\)
−0.207150 + 0.978309i \(0.566419\pi\)
\(62\) 6.64833 0.844339
\(63\) −1.37441 −0.173159
\(64\) 1.00000 0.125000
\(65\) −7.81225 −0.968990
\(66\) −0.271445 −0.0334126
\(67\) −8.38187 −1.02401 −0.512004 0.858983i \(-0.671097\pi\)
−0.512004 + 0.858983i \(0.671097\pi\)
\(68\) −3.51146 −0.425827
\(69\) −2.29919 −0.276790
\(70\) −0.975490 −0.116593
\(71\) 3.85349 0.457325 0.228662 0.973506i \(-0.426565\pi\)
0.228662 + 0.973506i \(0.426565\pi\)
\(72\) −2.28626 −0.269439
\(73\) 6.09743 0.713650 0.356825 0.934171i \(-0.383859\pi\)
0.356825 + 0.934171i \(0.383859\pi\)
\(74\) 4.44857 0.517136
\(75\) −5.44194 −0.628381
\(76\) −2.74780 −0.315195
\(77\) −0.0709734 −0.00808817
\(78\) −11.0692 −1.25334
\(79\) −15.8125 −1.77905 −0.889523 0.456890i \(-0.848963\pi\)
−0.889523 + 0.456890i \(0.848963\pi\)
\(80\) −1.62268 −0.181422
\(81\) −10.6318 −1.18131
\(82\) −8.02457 −0.886165
\(83\) −0.448185 −0.0491947 −0.0245973 0.999697i \(-0.507830\pi\)
−0.0245973 + 0.999697i \(0.507830\pi\)
\(84\) −1.38218 −0.150808
\(85\) 5.69798 0.618033
\(86\) −11.2206 −1.20995
\(87\) 13.3539 1.43168
\(88\) −0.118061 −0.0125854
\(89\) 10.4150 1.10399 0.551995 0.833847i \(-0.313867\pi\)
0.551995 + 0.833847i \(0.313867\pi\)
\(90\) 3.70988 0.391056
\(91\) −2.89421 −0.303396
\(92\) −1.00000 −0.104257
\(93\) −15.2858 −1.58506
\(94\) −0.815901 −0.0841537
\(95\) 4.45882 0.457465
\(96\) −2.29919 −0.234660
\(97\) −4.65467 −0.472610 −0.236305 0.971679i \(-0.575936\pi\)
−0.236305 + 0.971679i \(0.575936\pi\)
\(98\) 6.63861 0.670601
\(99\) 0.269919 0.0271279
\(100\) −2.36690 −0.236690
\(101\) 10.3386 1.02873 0.514363 0.857573i \(-0.328029\pi\)
0.514363 + 0.857573i \(0.328029\pi\)
\(102\) 8.07350 0.799395
\(103\) −13.5478 −1.33490 −0.667451 0.744654i \(-0.732615\pi\)
−0.667451 + 0.744654i \(0.732615\pi\)
\(104\) −4.81440 −0.472090
\(105\) 2.24283 0.218878
\(106\) 7.82807 0.760330
\(107\) 5.10264 0.493291 0.246645 0.969106i \(-0.420672\pi\)
0.246645 + 0.969106i \(0.420672\pi\)
\(108\) −1.64101 −0.157906
\(109\) −6.01964 −0.576577 −0.288288 0.957544i \(-0.593086\pi\)
−0.288288 + 0.957544i \(0.593086\pi\)
\(110\) 0.191576 0.0182661
\(111\) −10.2281 −0.970808
\(112\) −0.601158 −0.0568041
\(113\) 6.58382 0.619354 0.309677 0.950842i \(-0.399779\pi\)
0.309677 + 0.950842i \(0.399779\pi\)
\(114\) 6.31772 0.591708
\(115\) 1.62268 0.151316
\(116\) 5.80808 0.539267
\(117\) 11.0070 1.01760
\(118\) 10.7632 0.990835
\(119\) 2.11094 0.193510
\(120\) 3.73086 0.340579
\(121\) −10.9861 −0.998733
\(122\) 3.23578 0.292954
\(123\) 18.4500 1.66358
\(124\) −6.64833 −0.597038
\(125\) 11.9541 1.06921
\(126\) 1.37441 0.122442
\(127\) −6.72267 −0.596540 −0.298270 0.954481i \(-0.596410\pi\)
−0.298270 + 0.954481i \(0.596410\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 25.7982 2.27141
\(130\) 7.81225 0.685179
\(131\) −1.00000 −0.0873704
\(132\) 0.271445 0.0236262
\(133\) 1.65186 0.143235
\(134\) 8.38187 0.724083
\(135\) 2.66284 0.229181
\(136\) 3.51146 0.301105
\(137\) −14.5852 −1.24609 −0.623047 0.782185i \(-0.714105\pi\)
−0.623047 + 0.782185i \(0.714105\pi\)
\(138\) 2.29919 0.195720
\(139\) 6.91226 0.586290 0.293145 0.956068i \(-0.405298\pi\)
0.293145 + 0.956068i \(0.405298\pi\)
\(140\) 0.975490 0.0824439
\(141\) 1.87591 0.157980
\(142\) −3.85349 −0.323377
\(143\) 0.568393 0.0475314
\(144\) 2.28626 0.190522
\(145\) −9.42468 −0.782677
\(146\) −6.09743 −0.504627
\(147\) −15.2634 −1.25890
\(148\) −4.44857 −0.365670
\(149\) 1.01745 0.0833528 0.0416764 0.999131i \(-0.486730\pi\)
0.0416764 + 0.999131i \(0.486730\pi\)
\(150\) 5.44194 0.444332
\(151\) 1.34391 0.109365 0.0546827 0.998504i \(-0.482585\pi\)
0.0546827 + 0.998504i \(0.482585\pi\)
\(152\) 2.74780 0.222876
\(153\) −8.02812 −0.649035
\(154\) 0.0709734 0.00571920
\(155\) 10.7881 0.866525
\(156\) 11.0692 0.886246
\(157\) −7.69200 −0.613888 −0.306944 0.951728i \(-0.599306\pi\)
−0.306944 + 0.951728i \(0.599306\pi\)
\(158\) 15.8125 1.25798
\(159\) −17.9982 −1.42735
\(160\) 1.62268 0.128284
\(161\) 0.601158 0.0473779
\(162\) 10.6318 0.835312
\(163\) −9.79436 −0.767154 −0.383577 0.923509i \(-0.625308\pi\)
−0.383577 + 0.923509i \(0.625308\pi\)
\(164\) 8.02457 0.626613
\(165\) −0.440469 −0.0342905
\(166\) 0.448185 0.0347859
\(167\) −16.0930 −1.24531 −0.622657 0.782495i \(-0.713947\pi\)
−0.622657 + 0.782495i \(0.713947\pi\)
\(168\) 1.38218 0.106637
\(169\) 10.1784 0.782955
\(170\) −5.69798 −0.437015
\(171\) −6.28220 −0.480412
\(172\) 11.2206 0.855562
\(173\) 9.80576 0.745518 0.372759 0.927928i \(-0.378412\pi\)
0.372759 + 0.927928i \(0.378412\pi\)
\(174\) −13.3539 −1.01235
\(175\) 1.42288 0.107560
\(176\) 0.118061 0.00889920
\(177\) −24.7467 −1.86007
\(178\) −10.4150 −0.780639
\(179\) −5.16756 −0.386242 −0.193121 0.981175i \(-0.561861\pi\)
−0.193121 + 0.981175i \(0.561861\pi\)
\(180\) −3.70988 −0.276518
\(181\) 8.10081 0.602129 0.301064 0.953604i \(-0.402658\pi\)
0.301064 + 0.953604i \(0.402658\pi\)
\(182\) 2.89421 0.214533
\(183\) −7.43968 −0.549957
\(184\) 1.00000 0.0737210
\(185\) 7.21863 0.530724
\(186\) 15.2858 1.12081
\(187\) −0.414567 −0.0303161
\(188\) 0.815901 0.0595057
\(189\) 0.986508 0.0717579
\(190\) −4.45882 −0.323477
\(191\) 8.70768 0.630066 0.315033 0.949081i \(-0.397984\pi\)
0.315033 + 0.949081i \(0.397984\pi\)
\(192\) 2.29919 0.165930
\(193\) 23.1241 1.66451 0.832256 0.554391i \(-0.187049\pi\)
0.832256 + 0.554391i \(0.187049\pi\)
\(194\) 4.65467 0.334186
\(195\) −17.9618 −1.28627
\(196\) −6.63861 −0.474186
\(197\) −6.73646 −0.479953 −0.239977 0.970779i \(-0.577140\pi\)
−0.239977 + 0.970779i \(0.577140\pi\)
\(198\) −0.269919 −0.0191823
\(199\) −1.93685 −0.137300 −0.0686500 0.997641i \(-0.521869\pi\)
−0.0686500 + 0.997641i \(0.521869\pi\)
\(200\) 2.36690 0.167365
\(201\) −19.2715 −1.35931
\(202\) −10.3386 −0.727419
\(203\) −3.49157 −0.245060
\(204\) −8.07350 −0.565258
\(205\) −13.0213 −0.909449
\(206\) 13.5478 0.943918
\(207\) −2.28626 −0.158906
\(208\) 4.81440 0.333818
\(209\) −0.324409 −0.0224398
\(210\) −2.24283 −0.154770
\(211\) −12.6938 −0.873879 −0.436940 0.899491i \(-0.643938\pi\)
−0.436940 + 0.899491i \(0.643938\pi\)
\(212\) −7.82807 −0.537634
\(213\) 8.85989 0.607070
\(214\) −5.10264 −0.348809
\(215\) −18.2075 −1.24174
\(216\) 1.64101 0.111657
\(217\) 3.99670 0.271314
\(218\) 6.01964 0.407701
\(219\) 14.0191 0.947326
\(220\) −0.191576 −0.0129161
\(221\) −16.9055 −1.13719
\(222\) 10.2281 0.686465
\(223\) −10.5092 −0.703749 −0.351874 0.936047i \(-0.614456\pi\)
−0.351874 + 0.936047i \(0.614456\pi\)
\(224\) 0.601158 0.0401666
\(225\) −5.41135 −0.360757
\(226\) −6.58382 −0.437949
\(227\) −22.9375 −1.52242 −0.761208 0.648507i \(-0.775394\pi\)
−0.761208 + 0.648507i \(0.775394\pi\)
\(228\) −6.31772 −0.418401
\(229\) −24.6843 −1.63118 −0.815591 0.578629i \(-0.803588\pi\)
−0.815591 + 0.578629i \(0.803588\pi\)
\(230\) −1.62268 −0.106997
\(231\) −0.163181 −0.0107365
\(232\) −5.80808 −0.381319
\(233\) −2.94955 −0.193231 −0.0966157 0.995322i \(-0.530802\pi\)
−0.0966157 + 0.995322i \(0.530802\pi\)
\(234\) −11.0070 −0.719549
\(235\) −1.32395 −0.0863649
\(236\) −10.7632 −0.700626
\(237\) −36.3559 −2.36157
\(238\) −2.11094 −0.136832
\(239\) 8.98230 0.581016 0.290508 0.956872i \(-0.406176\pi\)
0.290508 + 0.956872i \(0.406176\pi\)
\(240\) −3.73086 −0.240826
\(241\) −12.4279 −0.800551 −0.400276 0.916395i \(-0.631086\pi\)
−0.400276 + 0.916395i \(0.631086\pi\)
\(242\) 10.9861 0.706211
\(243\) −19.5214 −1.25230
\(244\) −3.23578 −0.207150
\(245\) 10.7724 0.688221
\(246\) −18.4500 −1.17633
\(247\) −13.2290 −0.841742
\(248\) 6.64833 0.422170
\(249\) −1.03046 −0.0653028
\(250\) −11.9541 −0.756047
\(251\) −9.30722 −0.587466 −0.293733 0.955887i \(-0.594898\pi\)
−0.293733 + 0.955887i \(0.594898\pi\)
\(252\) −1.37441 −0.0865795
\(253\) −0.118061 −0.00742244
\(254\) 6.72267 0.421818
\(255\) 13.1007 0.820400
\(256\) 1.00000 0.0625000
\(257\) 17.1110 1.06736 0.533678 0.845688i \(-0.320809\pi\)
0.533678 + 0.845688i \(0.320809\pi\)
\(258\) −25.7982 −1.60613
\(259\) 2.67430 0.166173
\(260\) −7.81225 −0.484495
\(261\) 13.2788 0.821937
\(262\) 1.00000 0.0617802
\(263\) 1.75797 0.108401 0.0542006 0.998530i \(-0.482739\pi\)
0.0542006 + 0.998530i \(0.482739\pi\)
\(264\) −0.271445 −0.0167063
\(265\) 12.7025 0.780308
\(266\) −1.65186 −0.101282
\(267\) 23.9461 1.46548
\(268\) −8.38187 −0.512004
\(269\) −8.81830 −0.537661 −0.268830 0.963188i \(-0.586637\pi\)
−0.268830 + 0.963188i \(0.586637\pi\)
\(270\) −2.66284 −0.162056
\(271\) −11.4333 −0.694521 −0.347260 0.937769i \(-0.612888\pi\)
−0.347260 + 0.937769i \(0.612888\pi\)
\(272\) −3.51146 −0.212913
\(273\) −6.65434 −0.402739
\(274\) 14.5852 0.881121
\(275\) −0.279439 −0.0168508
\(276\) −2.29919 −0.138395
\(277\) 12.0380 0.723294 0.361647 0.932315i \(-0.382215\pi\)
0.361647 + 0.932315i \(0.382215\pi\)
\(278\) −6.91226 −0.414570
\(279\) −15.1999 −0.909991
\(280\) −0.975490 −0.0582967
\(281\) −13.2570 −0.790847 −0.395423 0.918499i \(-0.629402\pi\)
−0.395423 + 0.918499i \(0.629402\pi\)
\(282\) −1.87591 −0.111709
\(283\) −1.40466 −0.0834981 −0.0417491 0.999128i \(-0.513293\pi\)
−0.0417491 + 0.999128i \(0.513293\pi\)
\(284\) 3.85349 0.228662
\(285\) 10.2517 0.607256
\(286\) −0.568393 −0.0336098
\(287\) −4.82403 −0.284754
\(288\) −2.28626 −0.134719
\(289\) −4.66968 −0.274687
\(290\) 9.42468 0.553436
\(291\) −10.7020 −0.627360
\(292\) 6.09743 0.356825
\(293\) 1.08531 0.0634044 0.0317022 0.999497i \(-0.489907\pi\)
0.0317022 + 0.999497i \(0.489907\pi\)
\(294\) 15.2634 0.890180
\(295\) 17.4653 1.01687
\(296\) 4.44857 0.258568
\(297\) −0.193740 −0.0112419
\(298\) −1.01745 −0.0589394
\(299\) −4.81440 −0.278424
\(300\) −5.44194 −0.314191
\(301\) −6.74535 −0.388795
\(302\) −1.34391 −0.0773331
\(303\) 23.7703 1.36557
\(304\) −2.74780 −0.157597
\(305\) 5.25066 0.300652
\(306\) 8.02812 0.458937
\(307\) −12.1620 −0.694125 −0.347062 0.937842i \(-0.612821\pi\)
−0.347062 + 0.937842i \(0.612821\pi\)
\(308\) −0.0709734 −0.00404409
\(309\) −31.1489 −1.77200
\(310\) −10.7881 −0.612726
\(311\) −3.42649 −0.194298 −0.0971491 0.995270i \(-0.530972\pi\)
−0.0971491 + 0.995270i \(0.530972\pi\)
\(312\) −11.0692 −0.626670
\(313\) −6.15710 −0.348020 −0.174010 0.984744i \(-0.555672\pi\)
−0.174010 + 0.984744i \(0.555672\pi\)
\(314\) 7.69200 0.434084
\(315\) 2.23023 0.125659
\(316\) −15.8125 −0.889523
\(317\) 34.2244 1.92223 0.961117 0.276141i \(-0.0890556\pi\)
0.961117 + 0.276141i \(0.0890556\pi\)
\(318\) 17.9982 1.00929
\(319\) 0.685709 0.0383923
\(320\) −1.62268 −0.0907108
\(321\) 11.7319 0.654812
\(322\) −0.601158 −0.0335012
\(323\) 9.64879 0.536873
\(324\) −10.6318 −0.590655
\(325\) −11.3952 −0.632091
\(326\) 9.79436 0.542459
\(327\) −13.8403 −0.765369
\(328\) −8.02457 −0.443082
\(329\) −0.490485 −0.0270413
\(330\) 0.440469 0.0242470
\(331\) 21.3451 1.17323 0.586617 0.809865i \(-0.300459\pi\)
0.586617 + 0.809865i \(0.300459\pi\)
\(332\) −0.448185 −0.0245973
\(333\) −10.1706 −0.557346
\(334\) 16.0930 0.880570
\(335\) 13.6011 0.743109
\(336\) −1.38218 −0.0754039
\(337\) −5.03354 −0.274194 −0.137097 0.990558i \(-0.543777\pi\)
−0.137097 + 0.990558i \(0.543777\pi\)
\(338\) −10.1784 −0.553633
\(339\) 15.1374 0.822153
\(340\) 5.69798 0.309016
\(341\) −0.784910 −0.0425053
\(342\) 6.28220 0.339703
\(343\) 8.19896 0.442702
\(344\) −11.2206 −0.604973
\(345\) 3.73086 0.200863
\(346\) −9.80576 −0.527161
\(347\) −12.8733 −0.691075 −0.345537 0.938405i \(-0.612303\pi\)
−0.345537 + 0.938405i \(0.612303\pi\)
\(348\) 13.3539 0.715842
\(349\) 20.6690 1.10639 0.553194 0.833052i \(-0.313409\pi\)
0.553194 + 0.833052i \(0.313409\pi\)
\(350\) −1.42288 −0.0760561
\(351\) −7.90048 −0.421697
\(352\) −0.118061 −0.00629268
\(353\) −11.5217 −0.613240 −0.306620 0.951832i \(-0.599198\pi\)
−0.306620 + 0.951832i \(0.599198\pi\)
\(354\) 24.7467 1.31527
\(355\) −6.25299 −0.331874
\(356\) 10.4150 0.551995
\(357\) 4.85345 0.256872
\(358\) 5.16756 0.273114
\(359\) 6.80640 0.359228 0.179614 0.983737i \(-0.442515\pi\)
0.179614 + 0.983737i \(0.442515\pi\)
\(360\) 3.70988 0.195528
\(361\) −11.4496 −0.602609
\(362\) −8.10081 −0.425769
\(363\) −25.2590 −1.32575
\(364\) −2.89421 −0.151698
\(365\) −9.89421 −0.517886
\(366\) 7.43968 0.388878
\(367\) −0.533112 −0.0278282 −0.0139141 0.999903i \(-0.504429\pi\)
−0.0139141 + 0.999903i \(0.504429\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 18.3463 0.955069
\(370\) −7.21863 −0.375279
\(371\) 4.70591 0.244319
\(372\) −15.2858 −0.792530
\(373\) 13.4325 0.695508 0.347754 0.937586i \(-0.386944\pi\)
0.347754 + 0.937586i \(0.386944\pi\)
\(374\) 0.414567 0.0214367
\(375\) 27.4848 1.41931
\(376\) −0.815901 −0.0420769
\(377\) 27.9624 1.44014
\(378\) −0.986508 −0.0507405
\(379\) 0.744775 0.0382565 0.0191283 0.999817i \(-0.493911\pi\)
0.0191283 + 0.999817i \(0.493911\pi\)
\(380\) 4.45882 0.228732
\(381\) −15.4567 −0.791870
\(382\) −8.70768 −0.445524
\(383\) −21.5517 −1.10124 −0.550621 0.834755i \(-0.685609\pi\)
−0.550621 + 0.834755i \(0.685609\pi\)
\(384\) −2.29919 −0.117330
\(385\) 0.115167 0.00586948
\(386\) −23.1241 −1.17699
\(387\) 25.6532 1.30403
\(388\) −4.65467 −0.236305
\(389\) 13.6072 0.689914 0.344957 0.938619i \(-0.387894\pi\)
0.344957 + 0.938619i \(0.387894\pi\)
\(390\) 17.9618 0.909532
\(391\) 3.51146 0.177582
\(392\) 6.63861 0.335300
\(393\) −2.29919 −0.115979
\(394\) 6.73646 0.339378
\(395\) 25.6587 1.29103
\(396\) 0.269919 0.0135639
\(397\) −22.8790 −1.14826 −0.574132 0.818763i \(-0.694660\pi\)
−0.574132 + 0.818763i \(0.694660\pi\)
\(398\) 1.93685 0.0970857
\(399\) 3.79795 0.190135
\(400\) −2.36690 −0.118345
\(401\) −22.9781 −1.14747 −0.573736 0.819041i \(-0.694506\pi\)
−0.573736 + 0.819041i \(0.694506\pi\)
\(402\) 19.2715 0.961175
\(403\) −32.0077 −1.59442
\(404\) 10.3386 0.514363
\(405\) 17.2520 0.857260
\(406\) 3.49157 0.173284
\(407\) −0.525204 −0.0260334
\(408\) 8.07350 0.399698
\(409\) −31.4559 −1.55539 −0.777697 0.628639i \(-0.783612\pi\)
−0.777697 + 0.628639i \(0.783612\pi\)
\(410\) 13.0213 0.643078
\(411\) −33.5340 −1.65411
\(412\) −13.5478 −0.667451
\(413\) 6.47040 0.318388
\(414\) 2.28626 0.112364
\(415\) 0.727263 0.0356999
\(416\) −4.81440 −0.236045
\(417\) 15.8926 0.778263
\(418\) 0.324409 0.0158674
\(419\) −0.850397 −0.0415446 −0.0207723 0.999784i \(-0.506613\pi\)
−0.0207723 + 0.999784i \(0.506613\pi\)
\(420\) 2.24283 0.109439
\(421\) −1.80229 −0.0878385 −0.0439192 0.999035i \(-0.513984\pi\)
−0.0439192 + 0.999035i \(0.513984\pi\)
\(422\) 12.6938 0.617926
\(423\) 1.86536 0.0906971
\(424\) 7.82807 0.380165
\(425\) 8.31125 0.403155
\(426\) −8.85989 −0.429263
\(427\) 1.94522 0.0941357
\(428\) 5.10264 0.246645
\(429\) 1.30684 0.0630950
\(430\) 18.2075 0.878042
\(431\) 11.5367 0.555702 0.277851 0.960624i \(-0.410378\pi\)
0.277851 + 0.960624i \(0.410378\pi\)
\(432\) −1.64101 −0.0789532
\(433\) 11.4637 0.550912 0.275456 0.961314i \(-0.411171\pi\)
0.275456 + 0.961314i \(0.411171\pi\)
\(434\) −3.99670 −0.191848
\(435\) −21.6691 −1.03895
\(436\) −6.01964 −0.288288
\(437\) 2.74780 0.131445
\(438\) −14.0191 −0.669860
\(439\) 17.4847 0.834501 0.417250 0.908792i \(-0.362994\pi\)
0.417250 + 0.908792i \(0.362994\pi\)
\(440\) 0.191576 0.00913303
\(441\) −15.1776 −0.722744
\(442\) 16.9055 0.804115
\(443\) 23.7018 1.12611 0.563054 0.826420i \(-0.309626\pi\)
0.563054 + 0.826420i \(0.309626\pi\)
\(444\) −10.2281 −0.485404
\(445\) −16.9003 −0.801151
\(446\) 10.5092 0.497626
\(447\) 2.33931 0.110646
\(448\) −0.601158 −0.0284021
\(449\) −22.3938 −1.05683 −0.528414 0.848987i \(-0.677213\pi\)
−0.528414 + 0.848987i \(0.677213\pi\)
\(450\) 5.41135 0.255094
\(451\) 0.947390 0.0446108
\(452\) 6.58382 0.309677
\(453\) 3.08989 0.145176
\(454\) 22.9375 1.07651
\(455\) 4.69639 0.220170
\(456\) 6.31772 0.295854
\(457\) −20.5209 −0.959925 −0.479963 0.877289i \(-0.659350\pi\)
−0.479963 + 0.877289i \(0.659350\pi\)
\(458\) 24.6843 1.15342
\(459\) 5.76234 0.268963
\(460\) 1.62268 0.0756580
\(461\) −23.4636 −1.09281 −0.546405 0.837521i \(-0.684004\pi\)
−0.546405 + 0.837521i \(0.684004\pi\)
\(462\) 0.163181 0.00759188
\(463\) −10.0337 −0.466306 −0.233153 0.972440i \(-0.574904\pi\)
−0.233153 + 0.972440i \(0.574904\pi\)
\(464\) 5.80808 0.269633
\(465\) 24.8040 1.15026
\(466\) 2.94955 0.136635
\(467\) −3.18900 −0.147569 −0.0737847 0.997274i \(-0.523508\pi\)
−0.0737847 + 0.997274i \(0.523508\pi\)
\(468\) 11.0070 0.508798
\(469\) 5.03883 0.232672
\(470\) 1.32395 0.0610692
\(471\) −17.6853 −0.814898
\(472\) 10.7632 0.495418
\(473\) 1.32472 0.0609105
\(474\) 36.3559 1.66988
\(475\) 6.50377 0.298413
\(476\) 2.11094 0.0967548
\(477\) −17.8970 −0.819449
\(478\) −8.98230 −0.410841
\(479\) 13.7447 0.628010 0.314005 0.949421i \(-0.398329\pi\)
0.314005 + 0.949421i \(0.398329\pi\)
\(480\) 3.73086 0.170289
\(481\) −21.4172 −0.976540
\(482\) 12.4279 0.566075
\(483\) 1.38218 0.0628912
\(484\) −10.9861 −0.499366
\(485\) 7.55306 0.342967
\(486\) 19.5214 0.885511
\(487\) −34.9908 −1.58558 −0.792792 0.609492i \(-0.791373\pi\)
−0.792792 + 0.609492i \(0.791373\pi\)
\(488\) 3.23578 0.146477
\(489\) −22.5191 −1.01835
\(490\) −10.7724 −0.486646
\(491\) 18.4775 0.833876 0.416938 0.908935i \(-0.363103\pi\)
0.416938 + 0.908935i \(0.363103\pi\)
\(492\) 18.4500 0.831789
\(493\) −20.3948 −0.918536
\(494\) 13.2290 0.595202
\(495\) −0.437993 −0.0196863
\(496\) −6.64833 −0.298519
\(497\) −2.31655 −0.103912
\(498\) 1.03046 0.0461761
\(499\) 17.1021 0.765594 0.382797 0.923832i \(-0.374961\pi\)
0.382797 + 0.923832i \(0.374961\pi\)
\(500\) 11.9541 0.534606
\(501\) −37.0008 −1.65308
\(502\) 9.30722 0.415401
\(503\) −7.78887 −0.347289 −0.173644 0.984808i \(-0.555554\pi\)
−0.173644 + 0.984808i \(0.555554\pi\)
\(504\) 1.37441 0.0612209
\(505\) −16.7762 −0.746532
\(506\) 0.118061 0.00524846
\(507\) 23.4021 1.03932
\(508\) −6.72267 −0.298270
\(509\) 19.0632 0.844960 0.422480 0.906372i \(-0.361160\pi\)
0.422480 + 0.906372i \(0.361160\pi\)
\(510\) −13.1007 −0.580110
\(511\) −3.66552 −0.162153
\(512\) −1.00000 −0.0441942
\(513\) 4.50918 0.199085
\(514\) −17.1110 −0.754735
\(515\) 21.9838 0.968720
\(516\) 25.7982 1.13570
\(517\) 0.0963262 0.00423642
\(518\) −2.67430 −0.117502
\(519\) 22.5453 0.989628
\(520\) 7.81225 0.342590
\(521\) −7.54190 −0.330417 −0.165208 0.986259i \(-0.552830\pi\)
−0.165208 + 0.986259i \(0.552830\pi\)
\(522\) −13.2788 −0.581198
\(523\) 17.7776 0.777360 0.388680 0.921373i \(-0.372931\pi\)
0.388680 + 0.921373i \(0.372931\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 3.27147 0.142778
\(526\) −1.75797 −0.0766512
\(527\) 23.3453 1.01694
\(528\) 0.271445 0.0118131
\(529\) 1.00000 0.0434783
\(530\) −12.7025 −0.551761
\(531\) −24.6076 −1.06788
\(532\) 1.65186 0.0716174
\(533\) 38.6334 1.67340
\(534\) −23.9461 −1.03625
\(535\) −8.27997 −0.357974
\(536\) 8.38187 0.362042
\(537\) −11.8812 −0.512711
\(538\) 8.81830 0.380184
\(539\) −0.783762 −0.0337590
\(540\) 2.66284 0.114591
\(541\) 29.2667 1.25828 0.629138 0.777294i \(-0.283408\pi\)
0.629138 + 0.777294i \(0.283408\pi\)
\(542\) 11.4333 0.491100
\(543\) 18.6253 0.799288
\(544\) 3.51146 0.150552
\(545\) 9.76797 0.418414
\(546\) 6.65434 0.284780
\(547\) −26.9384 −1.15180 −0.575902 0.817519i \(-0.695349\pi\)
−0.575902 + 0.817519i \(0.695349\pi\)
\(548\) −14.5852 −0.623047
\(549\) −7.39786 −0.315733
\(550\) 0.279439 0.0119153
\(551\) −15.9595 −0.679896
\(552\) 2.29919 0.0978599
\(553\) 9.50582 0.404229
\(554\) −12.0380 −0.511446
\(555\) 16.5970 0.704502
\(556\) 6.91226 0.293145
\(557\) 43.7703 1.85461 0.927304 0.374310i \(-0.122120\pi\)
0.927304 + 0.374310i \(0.122120\pi\)
\(558\) 15.1999 0.643461
\(559\) 54.0204 2.28482
\(560\) 0.975490 0.0412220
\(561\) −0.953166 −0.0402427
\(562\) 13.2570 0.559213
\(563\) 9.44853 0.398208 0.199104 0.979978i \(-0.436197\pi\)
0.199104 + 0.979978i \(0.436197\pi\)
\(564\) 1.87591 0.0789900
\(565\) −10.6835 −0.449457
\(566\) 1.40466 0.0590421
\(567\) 6.39139 0.268413
\(568\) −3.85349 −0.161689
\(569\) −34.3904 −1.44172 −0.720859 0.693081i \(-0.756253\pi\)
−0.720859 + 0.693081i \(0.756253\pi\)
\(570\) −10.2517 −0.429395
\(571\) 38.8193 1.62454 0.812268 0.583284i \(-0.198233\pi\)
0.812268 + 0.583284i \(0.198233\pi\)
\(572\) 0.568393 0.0237657
\(573\) 20.0206 0.836372
\(574\) 4.82403 0.201351
\(575\) 2.36690 0.0987064
\(576\) 2.28626 0.0952610
\(577\) −0.193257 −0.00804541 −0.00402270 0.999992i \(-0.501280\pi\)
−0.00402270 + 0.999992i \(0.501280\pi\)
\(578\) 4.66968 0.194233
\(579\) 53.1667 2.20953
\(580\) −9.42468 −0.391338
\(581\) 0.269430 0.0111778
\(582\) 10.7020 0.443611
\(583\) −0.924192 −0.0382761
\(584\) −6.09743 −0.252314
\(585\) −17.8609 −0.738456
\(586\) −1.08531 −0.0448337
\(587\) 0.471622 0.0194659 0.00973296 0.999953i \(-0.496902\pi\)
0.00973296 + 0.999953i \(0.496902\pi\)
\(588\) −15.2634 −0.629452
\(589\) 18.2683 0.752733
\(590\) −17.4653 −0.719036
\(591\) −15.4884 −0.637107
\(592\) −4.44857 −0.182835
\(593\) 0.443621 0.0182173 0.00910867 0.999959i \(-0.497101\pi\)
0.00910867 + 0.999959i \(0.497101\pi\)
\(594\) 0.193740 0.00794924
\(595\) −3.42539 −0.140427
\(596\) 1.01745 0.0416764
\(597\) −4.45319 −0.182257
\(598\) 4.81440 0.196875
\(599\) 5.57915 0.227958 0.113979 0.993483i \(-0.463640\pi\)
0.113979 + 0.993483i \(0.463640\pi\)
\(600\) 5.44194 0.222166
\(601\) 35.2000 1.43584 0.717920 0.696126i \(-0.245094\pi\)
0.717920 + 0.696126i \(0.245094\pi\)
\(602\) 6.74535 0.274920
\(603\) −19.1632 −0.780385
\(604\) 1.34391 0.0546827
\(605\) 17.8269 0.724767
\(606\) −23.7703 −0.965602
\(607\) 31.8953 1.29459 0.647294 0.762240i \(-0.275901\pi\)
0.647294 + 0.762240i \(0.275901\pi\)
\(608\) 2.74780 0.111438
\(609\) −8.02779 −0.325302
\(610\) −5.25066 −0.212593
\(611\) 3.92807 0.158913
\(612\) −8.02812 −0.324517
\(613\) 10.8474 0.438124 0.219062 0.975711i \(-0.429700\pi\)
0.219062 + 0.975711i \(0.429700\pi\)
\(614\) 12.1620 0.490820
\(615\) −29.9385 −1.20724
\(616\) 0.0709734 0.00285960
\(617\) −42.3653 −1.70556 −0.852782 0.522267i \(-0.825087\pi\)
−0.852782 + 0.522267i \(0.825087\pi\)
\(618\) 31.1489 1.25299
\(619\) −21.7581 −0.874533 −0.437266 0.899332i \(-0.644053\pi\)
−0.437266 + 0.899332i \(0.644053\pi\)
\(620\) 10.7881 0.433262
\(621\) 1.64101 0.0658516
\(622\) 3.42649 0.137390
\(623\) −6.26108 −0.250845
\(624\) 11.0692 0.443123
\(625\) −7.56332 −0.302533
\(626\) 6.15710 0.246087
\(627\) −0.745877 −0.0297875
\(628\) −7.69200 −0.306944
\(629\) 15.6210 0.622849
\(630\) −2.23023 −0.0888544
\(631\) −5.17826 −0.206143 −0.103072 0.994674i \(-0.532867\pi\)
−0.103072 + 0.994674i \(0.532867\pi\)
\(632\) 15.8125 0.628988
\(633\) −29.1855 −1.16002
\(634\) −34.2244 −1.35922
\(635\) 10.9088 0.432901
\(636\) −17.9982 −0.713676
\(637\) −31.9609 −1.26634
\(638\) −0.685709 −0.0271475
\(639\) 8.81009 0.348522
\(640\) 1.62268 0.0641422
\(641\) −4.36173 −0.172278 −0.0861390 0.996283i \(-0.527453\pi\)
−0.0861390 + 0.996283i \(0.527453\pi\)
\(642\) −11.7319 −0.463022
\(643\) −13.7337 −0.541604 −0.270802 0.962635i \(-0.587289\pi\)
−0.270802 + 0.962635i \(0.587289\pi\)
\(644\) 0.601158 0.0236889
\(645\) −41.8624 −1.64833
\(646\) −9.64879 −0.379626
\(647\) 21.3908 0.840959 0.420479 0.907302i \(-0.361862\pi\)
0.420479 + 0.907302i \(0.361862\pi\)
\(648\) 10.6318 0.417656
\(649\) −1.27072 −0.0498801
\(650\) 11.3952 0.446956
\(651\) 9.18916 0.360152
\(652\) −9.79436 −0.383577
\(653\) −5.04152 −0.197290 −0.0986449 0.995123i \(-0.531451\pi\)
−0.0986449 + 0.995123i \(0.531451\pi\)
\(654\) 13.8403 0.541198
\(655\) 1.62268 0.0634035
\(656\) 8.02457 0.313307
\(657\) 13.9403 0.543865
\(658\) 0.490485 0.0191211
\(659\) −15.6129 −0.608191 −0.304096 0.952641i \(-0.598354\pi\)
−0.304096 + 0.952641i \(0.598354\pi\)
\(660\) −0.440469 −0.0171452
\(661\) −16.7470 −0.651381 −0.325691 0.945476i \(-0.605597\pi\)
−0.325691 + 0.945476i \(0.605597\pi\)
\(662\) −21.3451 −0.829602
\(663\) −38.8690 −1.50955
\(664\) 0.448185 0.0173930
\(665\) −2.68045 −0.103944
\(666\) 10.1706 0.394103
\(667\) −5.80808 −0.224890
\(668\) −16.0930 −0.622657
\(669\) −24.1627 −0.934182
\(670\) −13.6011 −0.525457
\(671\) −0.382021 −0.0147477
\(672\) 1.38218 0.0533186
\(673\) 22.0691 0.850703 0.425351 0.905028i \(-0.360150\pi\)
0.425351 + 0.905028i \(0.360150\pi\)
\(674\) 5.03354 0.193885
\(675\) 3.88411 0.149499
\(676\) 10.1784 0.391478
\(677\) 0.176272 0.00677467 0.00338733 0.999994i \(-0.498922\pi\)
0.00338733 + 0.999994i \(0.498922\pi\)
\(678\) −15.1374 −0.581350
\(679\) 2.79819 0.107385
\(680\) −5.69798 −0.218508
\(681\) −52.7377 −2.02091
\(682\) 0.784910 0.0300558
\(683\) 46.4105 1.77585 0.887925 0.459988i \(-0.152146\pi\)
0.887925 + 0.459988i \(0.152146\pi\)
\(684\) −6.28220 −0.240206
\(685\) 23.6671 0.904273
\(686\) −8.19896 −0.313038
\(687\) −56.7538 −2.16529
\(688\) 11.2206 0.427781
\(689\) −37.6875 −1.43578
\(690\) −3.73086 −0.142031
\(691\) −1.42767 −0.0543111 −0.0271555 0.999631i \(-0.508645\pi\)
−0.0271555 + 0.999631i \(0.508645\pi\)
\(692\) 9.80576 0.372759
\(693\) −0.162264 −0.00616390
\(694\) 12.8733 0.488664
\(695\) −11.2164 −0.425463
\(696\) −13.3539 −0.506177
\(697\) −28.1779 −1.06731
\(698\) −20.6690 −0.782335
\(699\) −6.78157 −0.256502
\(700\) 1.42288 0.0537798
\(701\) 26.3563 0.995464 0.497732 0.867331i \(-0.334166\pi\)
0.497732 + 0.867331i \(0.334166\pi\)
\(702\) 7.90048 0.298185
\(703\) 12.2238 0.461029
\(704\) 0.118061 0.00444960
\(705\) −3.04401 −0.114644
\(706\) 11.5217 0.433626
\(707\) −6.21511 −0.233743
\(708\) −24.7467 −0.930037
\(709\) −37.5284 −1.40941 −0.704703 0.709502i \(-0.748920\pi\)
−0.704703 + 0.709502i \(0.748920\pi\)
\(710\) 6.25299 0.234671
\(711\) −36.1516 −1.35579
\(712\) −10.4150 −0.390320
\(713\) 6.64833 0.248982
\(714\) −4.85345 −0.181636
\(715\) −0.922323 −0.0344929
\(716\) −5.16756 −0.193121
\(717\) 20.6520 0.771263
\(718\) −6.80640 −0.254013
\(719\) 31.6776 1.18138 0.590688 0.806900i \(-0.298856\pi\)
0.590688 + 0.806900i \(0.298856\pi\)
\(720\) −3.70988 −0.138259
\(721\) 8.14436 0.303312
\(722\) 11.4496 0.426109
\(723\) −28.5741 −1.06268
\(724\) 8.10081 0.301064
\(725\) −13.7471 −0.510555
\(726\) 25.2590 0.937450
\(727\) 2.69450 0.0999335 0.0499668 0.998751i \(-0.484088\pi\)
0.0499668 + 0.998751i \(0.484088\pi\)
\(728\) 2.89421 0.107267
\(729\) −12.9881 −0.481040
\(730\) 9.89421 0.366201
\(731\) −39.4006 −1.45728
\(732\) −7.43968 −0.274978
\(733\) 29.8995 1.10436 0.552182 0.833724i \(-0.313796\pi\)
0.552182 + 0.833724i \(0.313796\pi\)
\(734\) 0.533112 0.0196775
\(735\) 24.7677 0.913570
\(736\) 1.00000 0.0368605
\(737\) −0.989574 −0.0364514
\(738\) −18.3463 −0.675336
\(739\) −8.16117 −0.300214 −0.150107 0.988670i \(-0.547962\pi\)
−0.150107 + 0.988670i \(0.547962\pi\)
\(740\) 7.21863 0.265362
\(741\) −30.4160 −1.11736
\(742\) −4.70591 −0.172759
\(743\) 18.9856 0.696515 0.348258 0.937399i \(-0.386773\pi\)
0.348258 + 0.937399i \(0.386773\pi\)
\(744\) 15.2858 0.560403
\(745\) −1.65100 −0.0604880
\(746\) −13.4325 −0.491798
\(747\) −1.02467 −0.0374907
\(748\) −0.414567 −0.0151581
\(749\) −3.06749 −0.112084
\(750\) −27.4848 −1.00360
\(751\) 29.1539 1.06384 0.531920 0.846794i \(-0.321471\pi\)
0.531920 + 0.846794i \(0.321471\pi\)
\(752\) 0.815901 0.0297528
\(753\) −21.3990 −0.779824
\(754\) −27.9624 −1.01833
\(755\) −2.18073 −0.0793651
\(756\) 0.986508 0.0358789
\(757\) −3.75880 −0.136616 −0.0683080 0.997664i \(-0.521760\pi\)
−0.0683080 + 0.997664i \(0.521760\pi\)
\(758\) −0.744775 −0.0270514
\(759\) −0.271445 −0.00985282
\(760\) −4.45882 −0.161738
\(761\) −31.4160 −1.13883 −0.569415 0.822051i \(-0.692830\pi\)
−0.569415 + 0.822051i \(0.692830\pi\)
\(762\) 15.4567 0.559936
\(763\) 3.61875 0.131008
\(764\) 8.70768 0.315033
\(765\) 13.0271 0.470996
\(766\) 21.5517 0.778695
\(767\) −51.8184 −1.87106
\(768\) 2.29919 0.0829648
\(769\) 22.3818 0.807108 0.403554 0.914956i \(-0.367775\pi\)
0.403554 + 0.914956i \(0.367775\pi\)
\(770\) −0.115167 −0.00415035
\(771\) 39.3414 1.41685
\(772\) 23.1241 0.832256
\(773\) 32.6438 1.17411 0.587057 0.809545i \(-0.300286\pi\)
0.587057 + 0.809545i \(0.300286\pi\)
\(774\) −25.6532 −0.922086
\(775\) 15.7359 0.565251
\(776\) 4.65467 0.167093
\(777\) 6.14871 0.220584
\(778\) −13.6072 −0.487843
\(779\) −22.0499 −0.790021
\(780\) −17.9618 −0.643136
\(781\) 0.454947 0.0162793
\(782\) −3.51146 −0.125569
\(783\) −9.53113 −0.340615
\(784\) −6.63861 −0.237093
\(785\) 12.4817 0.445490
\(786\) 2.29919 0.0820093
\(787\) −14.3986 −0.513255 −0.256628 0.966510i \(-0.582611\pi\)
−0.256628 + 0.966510i \(0.582611\pi\)
\(788\) −6.73646 −0.239977
\(789\) 4.04191 0.143896
\(790\) −25.6587 −0.912896
\(791\) −3.95792 −0.140727
\(792\) −0.269919 −0.00959116
\(793\) −15.5784 −0.553204
\(794\) 22.8790 0.811945
\(795\) 29.2054 1.03581
\(796\) −1.93685 −0.0686500
\(797\) 5.18362 0.183613 0.0918066 0.995777i \(-0.470736\pi\)
0.0918066 + 0.995777i \(0.470736\pi\)
\(798\) −3.79795 −0.134446
\(799\) −2.86500 −0.101356
\(800\) 2.36690 0.0836824
\(801\) 23.8115 0.841338
\(802\) 22.9781 0.811385
\(803\) 0.719870 0.0254037
\(804\) −19.2715 −0.679653
\(805\) −0.975490 −0.0343815
\(806\) 32.0077 1.12742
\(807\) −20.2749 −0.713711
\(808\) −10.3386 −0.363709
\(809\) −50.2302 −1.76600 −0.882999 0.469374i \(-0.844480\pi\)
−0.882999 + 0.469374i \(0.844480\pi\)
\(810\) −17.2520 −0.606175
\(811\) 18.1535 0.637455 0.318728 0.947846i \(-0.396744\pi\)
0.318728 + 0.947846i \(0.396744\pi\)
\(812\) −3.49157 −0.122530
\(813\) −26.2872 −0.921933
\(814\) 0.525204 0.0184084
\(815\) 15.8932 0.556713
\(816\) −8.07350 −0.282629
\(817\) −30.8320 −1.07867
\(818\) 31.4559 1.09983
\(819\) −6.61694 −0.231215
\(820\) −13.0213 −0.454725
\(821\) −18.4093 −0.642488 −0.321244 0.946996i \(-0.604101\pi\)
−0.321244 + 0.946996i \(0.604101\pi\)
\(822\) 33.5340 1.16963
\(823\) −37.5643 −1.30941 −0.654704 0.755885i \(-0.727207\pi\)
−0.654704 + 0.755885i \(0.727207\pi\)
\(824\) 13.5478 0.471959
\(825\) −0.642482 −0.0223683
\(826\) −6.47040 −0.225134
\(827\) −45.9054 −1.59629 −0.798143 0.602468i \(-0.794184\pi\)
−0.798143 + 0.602468i \(0.794184\pi\)
\(828\) −2.28626 −0.0794532
\(829\) 49.2869 1.71181 0.855903 0.517137i \(-0.173002\pi\)
0.855903 + 0.517137i \(0.173002\pi\)
\(830\) −0.727263 −0.0252437
\(831\) 27.6776 0.960126
\(832\) 4.81440 0.166909
\(833\) 23.3112 0.807684
\(834\) −15.8926 −0.550315
\(835\) 26.1139 0.903708
\(836\) −0.324409 −0.0112199
\(837\) 10.9100 0.377105
\(838\) 0.850397 0.0293765
\(839\) −8.05676 −0.278150 −0.139075 0.990282i \(-0.544413\pi\)
−0.139075 + 0.990282i \(0.544413\pi\)
\(840\) −2.24283 −0.0773851
\(841\) 4.73379 0.163234
\(842\) 1.80229 0.0621112
\(843\) −30.4804 −1.04980
\(844\) −12.6938 −0.436940
\(845\) −16.5164 −0.568180
\(846\) −1.86536 −0.0641326
\(847\) 6.60436 0.226929
\(848\) −7.82807 −0.268817
\(849\) −3.22957 −0.110838
\(850\) −8.31125 −0.285074
\(851\) 4.44857 0.152495
\(852\) 8.85989 0.303535
\(853\) 13.2386 0.453280 0.226640 0.973979i \(-0.427226\pi\)
0.226640 + 0.973979i \(0.427226\pi\)
\(854\) −1.94522 −0.0665640
\(855\) 10.1940 0.348629
\(856\) −5.10264 −0.174405
\(857\) −5.97496 −0.204101 −0.102050 0.994779i \(-0.532540\pi\)
−0.102050 + 0.994779i \(0.532540\pi\)
\(858\) −1.30684 −0.0446149
\(859\) 27.5217 0.939029 0.469515 0.882925i \(-0.344429\pi\)
0.469515 + 0.882925i \(0.344429\pi\)
\(860\) −18.2075 −0.620869
\(861\) −11.0914 −0.377992
\(862\) −11.5367 −0.392940
\(863\) −25.5864 −0.870972 −0.435486 0.900195i \(-0.643424\pi\)
−0.435486 + 0.900195i \(0.643424\pi\)
\(864\) 1.64101 0.0558284
\(865\) −15.9117 −0.541012
\(866\) −11.4637 −0.389554
\(867\) −10.7365 −0.364630
\(868\) 3.99670 0.135657
\(869\) −1.86684 −0.0633283
\(870\) 21.6691 0.734651
\(871\) −40.3537 −1.36733
\(872\) 6.01964 0.203851
\(873\) −10.6418 −0.360171
\(874\) −2.74780 −0.0929458
\(875\) −7.18633 −0.242942
\(876\) 14.0191 0.473663
\(877\) −51.0839 −1.72498 −0.862490 0.506075i \(-0.831096\pi\)
−0.862490 + 0.506075i \(0.831096\pi\)
\(878\) −17.4847 −0.590081
\(879\) 2.49533 0.0841653
\(880\) −0.191576 −0.00645803
\(881\) 2.49391 0.0840219 0.0420110 0.999117i \(-0.486624\pi\)
0.0420110 + 0.999117i \(0.486624\pi\)
\(882\) 15.1776 0.511057
\(883\) 37.1651 1.25070 0.625352 0.780343i \(-0.284955\pi\)
0.625352 + 0.780343i \(0.284955\pi\)
\(884\) −16.9055 −0.568595
\(885\) 40.1560 1.34983
\(886\) −23.7018 −0.796278
\(887\) −22.3446 −0.750258 −0.375129 0.926973i \(-0.622402\pi\)
−0.375129 + 0.926973i \(0.622402\pi\)
\(888\) 10.2281 0.343233
\(889\) 4.04139 0.135544
\(890\) 16.9003 0.566499
\(891\) −1.25520 −0.0420508
\(892\) −10.5092 −0.351874
\(893\) −2.24193 −0.0750235
\(894\) −2.33931 −0.0782383
\(895\) 8.38532 0.280290
\(896\) 0.601158 0.0200833
\(897\) −11.0692 −0.369590
\(898\) 22.3938 0.747290
\(899\) −38.6141 −1.28785
\(900\) −5.41135 −0.180378
\(901\) 27.4879 0.915756
\(902\) −0.947390 −0.0315446
\(903\) −15.5088 −0.516101
\(904\) −6.58382 −0.218975
\(905\) −13.1451 −0.436957
\(906\) −3.08989 −0.102655
\(907\) −29.9119 −0.993209 −0.496605 0.867977i \(-0.665420\pi\)
−0.496605 + 0.867977i \(0.665420\pi\)
\(908\) −22.9375 −0.761208
\(909\) 23.6367 0.783979
\(910\) −4.69639 −0.155684
\(911\) −15.7724 −0.522561 −0.261281 0.965263i \(-0.584145\pi\)
−0.261281 + 0.965263i \(0.584145\pi\)
\(912\) −6.31772 −0.209200
\(913\) −0.0529133 −0.00175117
\(914\) 20.5209 0.678770
\(915\) 12.0722 0.399096
\(916\) −24.6843 −0.815591
\(917\) 0.601158 0.0198520
\(918\) −5.76234 −0.190186
\(919\) −31.4918 −1.03882 −0.519409 0.854526i \(-0.673848\pi\)
−0.519409 + 0.854526i \(0.673848\pi\)
\(920\) −1.62268 −0.0534983
\(921\) −27.9628 −0.921406
\(922\) 23.4636 0.772733
\(923\) 18.5522 0.610654
\(924\) −0.163181 −0.00536827
\(925\) 10.5293 0.346202
\(926\) 10.0337 0.329728
\(927\) −30.9738 −1.01731
\(928\) −5.80808 −0.190660
\(929\) 17.8498 0.585633 0.292816 0.956169i \(-0.405408\pi\)
0.292816 + 0.956169i \(0.405408\pi\)
\(930\) −24.8040 −0.813354
\(931\) 18.2416 0.597844
\(932\) −2.94955 −0.0966157
\(933\) −7.87814 −0.257919
\(934\) 3.18900 0.104347
\(935\) 0.672711 0.0220000
\(936\) −11.0070 −0.359775
\(937\) 16.6891 0.545210 0.272605 0.962126i \(-0.412115\pi\)
0.272605 + 0.962126i \(0.412115\pi\)
\(938\) −5.03883 −0.164524
\(939\) −14.1563 −0.461974
\(940\) −1.32395 −0.0431825
\(941\) 47.7185 1.55558 0.777789 0.628525i \(-0.216341\pi\)
0.777789 + 0.628525i \(0.216341\pi\)
\(942\) 17.6853 0.576220
\(943\) −8.02457 −0.261316
\(944\) −10.7632 −0.350313
\(945\) −1.60079 −0.0520737
\(946\) −1.32472 −0.0430702
\(947\) 3.53327 0.114816 0.0574079 0.998351i \(-0.481716\pi\)
0.0574079 + 0.998351i \(0.481716\pi\)
\(948\) −36.3559 −1.18079
\(949\) 29.3555 0.952919
\(950\) −6.50377 −0.211010
\(951\) 78.6883 2.55164
\(952\) −2.11094 −0.0684160
\(953\) 0.182648 0.00591654 0.00295827 0.999996i \(-0.499058\pi\)
0.00295827 + 0.999996i \(0.499058\pi\)
\(954\) 17.8970 0.579438
\(955\) −14.1298 −0.457230
\(956\) 8.98230 0.290508
\(957\) 1.57657 0.0509634
\(958\) −13.7447 −0.444070
\(959\) 8.76798 0.283133
\(960\) −3.73086 −0.120413
\(961\) 13.2004 0.425818
\(962\) 21.4172 0.690518
\(963\) 11.6660 0.375931
\(964\) −12.4279 −0.400276
\(965\) −37.5232 −1.20791
\(966\) −1.38218 −0.0444708
\(967\) 27.8245 0.894774 0.447387 0.894340i \(-0.352355\pi\)
0.447387 + 0.894340i \(0.352355\pi\)
\(968\) 10.9861 0.353105
\(969\) 22.1844 0.712665
\(970\) −7.55306 −0.242514
\(971\) −16.9958 −0.545423 −0.272711 0.962096i \(-0.587920\pi\)
−0.272711 + 0.962096i \(0.587920\pi\)
\(972\) −19.5214 −0.626151
\(973\) −4.15536 −0.133215
\(974\) 34.9908 1.12118
\(975\) −26.1997 −0.839061
\(976\) −3.23578 −0.103575
\(977\) −23.5314 −0.752838 −0.376419 0.926450i \(-0.622845\pi\)
−0.376419 + 0.926450i \(0.622845\pi\)
\(978\) 22.5191 0.720081
\(979\) 1.22961 0.0392985
\(980\) 10.7724 0.344111
\(981\) −13.7625 −0.439402
\(982\) −18.4775 −0.589639
\(983\) −25.4980 −0.813259 −0.406630 0.913593i \(-0.633296\pi\)
−0.406630 + 0.913593i \(0.633296\pi\)
\(984\) −18.4500 −0.588164
\(985\) 10.9311 0.348295
\(986\) 20.3948 0.649503
\(987\) −1.12772 −0.0358957
\(988\) −13.2290 −0.420871
\(989\) −11.2206 −0.356794
\(990\) 0.437993 0.0139203
\(991\) 42.9548 1.36450 0.682252 0.731117i \(-0.261001\pi\)
0.682252 + 0.731117i \(0.261001\pi\)
\(992\) 6.64833 0.211085
\(993\) 49.0764 1.55739
\(994\) 2.31655 0.0734766
\(995\) 3.14290 0.0996367
\(996\) −1.03046 −0.0326514
\(997\) −21.4965 −0.680802 −0.340401 0.940280i \(-0.610563\pi\)
−0.340401 + 0.940280i \(0.610563\pi\)
\(998\) −17.1021 −0.541357
\(999\) 7.30016 0.230967
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 \(a_p\))