Properties

Label 6003.2.a.t.1.13
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.183492 q^{2} -1.96633 q^{4} +0.926834 q^{5} -0.385808 q^{7} -0.727789 q^{8} +O(q^{10})\) \(q+0.183492 q^{2} -1.96633 q^{4} +0.926834 q^{5} -0.385808 q^{7} -0.727789 q^{8} +0.170066 q^{10} +0.749819 q^{11} +2.20193 q^{13} -0.0707926 q^{14} +3.79912 q^{16} -1.34638 q^{17} -3.59030 q^{19} -1.82246 q^{20} +0.137586 q^{22} +1.00000 q^{23} -4.14098 q^{25} +0.404037 q^{26} +0.758626 q^{28} +1.00000 q^{29} -1.24496 q^{31} +2.15269 q^{32} -0.247049 q^{34} -0.357580 q^{35} +3.97019 q^{37} -0.658790 q^{38} -0.674540 q^{40} -9.73001 q^{41} +4.45412 q^{43} -1.47439 q^{44} +0.183492 q^{46} -0.400723 q^{47} -6.85115 q^{49} -0.759836 q^{50} -4.32973 q^{52} -1.84679 q^{53} +0.694958 q^{55} +0.280787 q^{56} +0.183492 q^{58} -0.0802578 q^{59} +3.33682 q^{61} -0.228440 q^{62} -7.20324 q^{64} +2.04083 q^{65} +9.55846 q^{67} +2.64743 q^{68} -0.0656130 q^{70} +14.2456 q^{71} +7.66525 q^{73} +0.728497 q^{74} +7.05971 q^{76} -0.289286 q^{77} -12.3660 q^{79} +3.52115 q^{80} -1.78538 q^{82} -16.2698 q^{83} -1.24787 q^{85} +0.817295 q^{86} -0.545710 q^{88} -2.45409 q^{89} -0.849523 q^{91} -1.96633 q^{92} -0.0735294 q^{94} -3.32761 q^{95} -0.126390 q^{97} -1.25713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.183492 0.129748 0.0648741 0.997893i \(-0.479335\pi\)
0.0648741 + 0.997893i \(0.479335\pi\)
\(3\) 0 0
\(4\) −1.96633 −0.983165
\(5\) 0.926834 0.414493 0.207246 0.978289i \(-0.433550\pi\)
0.207246 + 0.978289i \(0.433550\pi\)
\(6\) 0 0
\(7\) −0.385808 −0.145822 −0.0729108 0.997338i \(-0.523229\pi\)
−0.0729108 + 0.997338i \(0.523229\pi\)
\(8\) −0.727789 −0.257312
\(9\) 0 0
\(10\) 0.170066 0.0537797
\(11\) 0.749819 0.226079 0.113039 0.993590i \(-0.463941\pi\)
0.113039 + 0.993590i \(0.463941\pi\)
\(12\) 0 0
\(13\) 2.20193 0.610706 0.305353 0.952239i \(-0.401225\pi\)
0.305353 + 0.952239i \(0.401225\pi\)
\(14\) −0.0707926 −0.0189201
\(15\) 0 0
\(16\) 3.79912 0.949780
\(17\) −1.34638 −0.326545 −0.163272 0.986581i \(-0.552205\pi\)
−0.163272 + 0.986581i \(0.552205\pi\)
\(18\) 0 0
\(19\) −3.59030 −0.823671 −0.411835 0.911258i \(-0.635112\pi\)
−0.411835 + 0.911258i \(0.635112\pi\)
\(20\) −1.82246 −0.407515
\(21\) 0 0
\(22\) 0.137586 0.0293334
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.14098 −0.828196
\(26\) 0.404037 0.0792381
\(27\) 0 0
\(28\) 0.758626 0.143367
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −1.24496 −0.223602 −0.111801 0.993731i \(-0.535662\pi\)
−0.111801 + 0.993731i \(0.535662\pi\)
\(32\) 2.15269 0.380545
\(33\) 0 0
\(34\) −0.247049 −0.0423686
\(35\) −0.357580 −0.0604420
\(36\) 0 0
\(37\) 3.97019 0.652695 0.326348 0.945250i \(-0.394182\pi\)
0.326348 + 0.945250i \(0.394182\pi\)
\(38\) −0.658790 −0.106870
\(39\) 0 0
\(40\) −0.674540 −0.106654
\(41\) −9.73001 −1.51957 −0.759786 0.650173i \(-0.774696\pi\)
−0.759786 + 0.650173i \(0.774696\pi\)
\(42\) 0 0
\(43\) 4.45412 0.679247 0.339623 0.940561i \(-0.389700\pi\)
0.339623 + 0.940561i \(0.389700\pi\)
\(44\) −1.47439 −0.222273
\(45\) 0 0
\(46\) 0.183492 0.0270544
\(47\) −0.400723 −0.0584515 −0.0292257 0.999573i \(-0.509304\pi\)
−0.0292257 + 0.999573i \(0.509304\pi\)
\(48\) 0 0
\(49\) −6.85115 −0.978736
\(50\) −0.759836 −0.107457
\(51\) 0 0
\(52\) −4.32973 −0.600425
\(53\) −1.84679 −0.253676 −0.126838 0.991923i \(-0.540483\pi\)
−0.126838 + 0.991923i \(0.540483\pi\)
\(54\) 0 0
\(55\) 0.694958 0.0937081
\(56\) 0.280787 0.0375217
\(57\) 0 0
\(58\) 0.183492 0.0240937
\(59\) −0.0802578 −0.0104487 −0.00522434 0.999986i \(-0.501663\pi\)
−0.00522434 + 0.999986i \(0.501663\pi\)
\(60\) 0 0
\(61\) 3.33682 0.427237 0.213618 0.976917i \(-0.431475\pi\)
0.213618 + 0.976917i \(0.431475\pi\)
\(62\) −0.228440 −0.0290120
\(63\) 0 0
\(64\) −7.20324 −0.900405
\(65\) 2.04083 0.253133
\(66\) 0 0
\(67\) 9.55846 1.16775 0.583876 0.811843i \(-0.301535\pi\)
0.583876 + 0.811843i \(0.301535\pi\)
\(68\) 2.64743 0.321048
\(69\) 0 0
\(70\) −0.0656130 −0.00784225
\(71\) 14.2456 1.69064 0.845321 0.534259i \(-0.179409\pi\)
0.845321 + 0.534259i \(0.179409\pi\)
\(72\) 0 0
\(73\) 7.66525 0.897150 0.448575 0.893745i \(-0.351932\pi\)
0.448575 + 0.893745i \(0.351932\pi\)
\(74\) 0.728497 0.0846861
\(75\) 0 0
\(76\) 7.05971 0.809805
\(77\) −0.289286 −0.0329672
\(78\) 0 0
\(79\) −12.3660 −1.39128 −0.695641 0.718390i \(-0.744879\pi\)
−0.695641 + 0.718390i \(0.744879\pi\)
\(80\) 3.52115 0.393677
\(81\) 0 0
\(82\) −1.78538 −0.197162
\(83\) −16.2698 −1.78584 −0.892920 0.450215i \(-0.851347\pi\)
−0.892920 + 0.450215i \(0.851347\pi\)
\(84\) 0 0
\(85\) −1.24787 −0.135350
\(86\) 0.817295 0.0881311
\(87\) 0 0
\(88\) −0.545710 −0.0581729
\(89\) −2.45409 −0.260133 −0.130066 0.991505i \(-0.541519\pi\)
−0.130066 + 0.991505i \(0.541519\pi\)
\(90\) 0 0
\(91\) −0.849523 −0.0890542
\(92\) −1.96633 −0.205004
\(93\) 0 0
\(94\) −0.0735294 −0.00758398
\(95\) −3.32761 −0.341406
\(96\) 0 0
\(97\) −0.126390 −0.0128329 −0.00641646 0.999979i \(-0.502042\pi\)
−0.00641646 + 0.999979i \(0.502042\pi\)
\(98\) −1.25713 −0.126989
\(99\) 0 0
\(100\) 8.14253 0.814253
\(101\) 13.4109 1.33444 0.667219 0.744862i \(-0.267485\pi\)
0.667219 + 0.744862i \(0.267485\pi\)
\(102\) 0 0
\(103\) 10.7952 1.06368 0.531839 0.846845i \(-0.321501\pi\)
0.531839 + 0.846845i \(0.321501\pi\)
\(104\) −1.60254 −0.157142
\(105\) 0 0
\(106\) −0.338871 −0.0329140
\(107\) −16.7814 −1.62232 −0.811161 0.584823i \(-0.801164\pi\)
−0.811161 + 0.584823i \(0.801164\pi\)
\(108\) 0 0
\(109\) −12.4718 −1.19458 −0.597292 0.802024i \(-0.703757\pi\)
−0.597292 + 0.802024i \(0.703757\pi\)
\(110\) 0.127519 0.0121585
\(111\) 0 0
\(112\) −1.46573 −0.138498
\(113\) 14.9119 1.40279 0.701397 0.712770i \(-0.252560\pi\)
0.701397 + 0.712770i \(0.252560\pi\)
\(114\) 0 0
\(115\) 0.926834 0.0864277
\(116\) −1.96633 −0.182569
\(117\) 0 0
\(118\) −0.0147266 −0.00135570
\(119\) 0.519443 0.0476173
\(120\) 0 0
\(121\) −10.4378 −0.948888
\(122\) 0.612280 0.0554332
\(123\) 0 0
\(124\) 2.44801 0.219838
\(125\) −8.47217 −0.757774
\(126\) 0 0
\(127\) −10.5731 −0.938214 −0.469107 0.883141i \(-0.655424\pi\)
−0.469107 + 0.883141i \(0.655424\pi\)
\(128\) −5.62711 −0.497371
\(129\) 0 0
\(130\) 0.374475 0.0328436
\(131\) −13.0008 −1.13588 −0.567941 0.823069i \(-0.692260\pi\)
−0.567941 + 0.823069i \(0.692260\pi\)
\(132\) 0 0
\(133\) 1.38517 0.120109
\(134\) 1.75390 0.151514
\(135\) 0 0
\(136\) 0.979880 0.0840240
\(137\) 0.664712 0.0567902 0.0283951 0.999597i \(-0.490960\pi\)
0.0283951 + 0.999597i \(0.490960\pi\)
\(138\) 0 0
\(139\) 2.31036 0.195962 0.0979810 0.995188i \(-0.468762\pi\)
0.0979810 + 0.995188i \(0.468762\pi\)
\(140\) 0.703120 0.0594245
\(141\) 0 0
\(142\) 2.61395 0.219358
\(143\) 1.65105 0.138068
\(144\) 0 0
\(145\) 0.926834 0.0769694
\(146\) 1.40651 0.116404
\(147\) 0 0
\(148\) −7.80671 −0.641707
\(149\) −9.64076 −0.789801 −0.394901 0.918724i \(-0.629221\pi\)
−0.394901 + 0.918724i \(0.629221\pi\)
\(150\) 0 0
\(151\) 13.3668 1.08778 0.543889 0.839157i \(-0.316951\pi\)
0.543889 + 0.839157i \(0.316951\pi\)
\(152\) 2.61298 0.211941
\(153\) 0 0
\(154\) −0.0530816 −0.00427744
\(155\) −1.15387 −0.0926814
\(156\) 0 0
\(157\) 7.62314 0.608393 0.304197 0.952609i \(-0.401612\pi\)
0.304197 + 0.952609i \(0.401612\pi\)
\(158\) −2.26906 −0.180516
\(159\) 0 0
\(160\) 1.99518 0.157733
\(161\) −0.385808 −0.0304059
\(162\) 0 0
\(163\) −13.0638 −1.02324 −0.511619 0.859212i \(-0.670954\pi\)
−0.511619 + 0.859212i \(0.670954\pi\)
\(164\) 19.1324 1.49399
\(165\) 0 0
\(166\) −2.98537 −0.231710
\(167\) −9.82954 −0.760632 −0.380316 0.924857i \(-0.624185\pi\)
−0.380316 + 0.924857i \(0.624185\pi\)
\(168\) 0 0
\(169\) −8.15149 −0.627038
\(170\) −0.228974 −0.0175615
\(171\) 0 0
\(172\) −8.75827 −0.667812
\(173\) −0.210024 −0.0159678 −0.00798390 0.999968i \(-0.502541\pi\)
−0.00798390 + 0.999968i \(0.502541\pi\)
\(174\) 0 0
\(175\) 1.59762 0.120769
\(176\) 2.84865 0.214725
\(177\) 0 0
\(178\) −0.450305 −0.0337518
\(179\) 12.3911 0.926155 0.463078 0.886318i \(-0.346745\pi\)
0.463078 + 0.886318i \(0.346745\pi\)
\(180\) 0 0
\(181\) −11.5594 −0.859202 −0.429601 0.903019i \(-0.641346\pi\)
−0.429601 + 0.903019i \(0.641346\pi\)
\(182\) −0.155880 −0.0115546
\(183\) 0 0
\(184\) −0.727789 −0.0536533
\(185\) 3.67971 0.270537
\(186\) 0 0
\(187\) −1.00954 −0.0738249
\(188\) 0.787954 0.0574675
\(189\) 0 0
\(190\) −0.610589 −0.0442968
\(191\) 6.13869 0.444180 0.222090 0.975026i \(-0.428712\pi\)
0.222090 + 0.975026i \(0.428712\pi\)
\(192\) 0 0
\(193\) −17.8749 −1.28667 −0.643333 0.765586i \(-0.722449\pi\)
−0.643333 + 0.765586i \(0.722449\pi\)
\(194\) −0.0231915 −0.00166505
\(195\) 0 0
\(196\) 13.4716 0.962259
\(197\) 12.6179 0.898986 0.449493 0.893284i \(-0.351605\pi\)
0.449493 + 0.893284i \(0.351605\pi\)
\(198\) 0 0
\(199\) −26.6935 −1.89225 −0.946126 0.323800i \(-0.895040\pi\)
−0.946126 + 0.323800i \(0.895040\pi\)
\(200\) 3.01376 0.213105
\(201\) 0 0
\(202\) 2.46080 0.173141
\(203\) −0.385808 −0.0270784
\(204\) 0 0
\(205\) −9.01811 −0.629852
\(206\) 1.98082 0.138010
\(207\) 0 0
\(208\) 8.36540 0.580036
\(209\) −2.69207 −0.186215
\(210\) 0 0
\(211\) −14.2682 −0.982266 −0.491133 0.871084i \(-0.663417\pi\)
−0.491133 + 0.871084i \(0.663417\pi\)
\(212\) 3.63140 0.249405
\(213\) 0 0
\(214\) −3.07926 −0.210494
\(215\) 4.12823 0.281543
\(216\) 0 0
\(217\) 0.480316 0.0326060
\(218\) −2.28848 −0.154995
\(219\) 0 0
\(220\) −1.36652 −0.0921306
\(221\) −2.96464 −0.199423
\(222\) 0 0
\(223\) −7.94405 −0.531973 −0.265986 0.963977i \(-0.585698\pi\)
−0.265986 + 0.963977i \(0.585698\pi\)
\(224\) −0.830523 −0.0554916
\(225\) 0 0
\(226\) 2.73621 0.182010
\(227\) 10.5170 0.698038 0.349019 0.937116i \(-0.386515\pi\)
0.349019 + 0.937116i \(0.386515\pi\)
\(228\) 0 0
\(229\) −27.2804 −1.80274 −0.901368 0.433053i \(-0.857436\pi\)
−0.901368 + 0.433053i \(0.857436\pi\)
\(230\) 0.170066 0.0112139
\(231\) 0 0
\(232\) −0.727789 −0.0477817
\(233\) 21.6476 1.41818 0.709092 0.705116i \(-0.249105\pi\)
0.709092 + 0.705116i \(0.249105\pi\)
\(234\) 0 0
\(235\) −0.371404 −0.0242277
\(236\) 0.157813 0.0102728
\(237\) 0 0
\(238\) 0.0953136 0.00617826
\(239\) −0.517454 −0.0334713 −0.0167356 0.999860i \(-0.505327\pi\)
−0.0167356 + 0.999860i \(0.505327\pi\)
\(240\) 0 0
\(241\) −26.4992 −1.70696 −0.853481 0.521124i \(-0.825513\pi\)
−0.853481 + 0.521124i \(0.825513\pi\)
\(242\) −1.91525 −0.123117
\(243\) 0 0
\(244\) −6.56130 −0.420044
\(245\) −6.34988 −0.405679
\(246\) 0 0
\(247\) −7.90560 −0.503021
\(248\) 0.906070 0.0575355
\(249\) 0 0
\(250\) −1.55457 −0.0983199
\(251\) −26.2662 −1.65791 −0.828955 0.559315i \(-0.811064\pi\)
−0.828955 + 0.559315i \(0.811064\pi\)
\(252\) 0 0
\(253\) 0.749819 0.0471407
\(254\) −1.94008 −0.121732
\(255\) 0 0
\(256\) 13.3739 0.835872
\(257\) −10.5961 −0.660965 −0.330483 0.943812i \(-0.607212\pi\)
−0.330483 + 0.943812i \(0.607212\pi\)
\(258\) 0 0
\(259\) −1.53173 −0.0951771
\(260\) −4.01294 −0.248872
\(261\) 0 0
\(262\) −2.38553 −0.147379
\(263\) 2.52748 0.155851 0.0779256 0.996959i \(-0.475170\pi\)
0.0779256 + 0.996959i \(0.475170\pi\)
\(264\) 0 0
\(265\) −1.71167 −0.105147
\(266\) 0.254166 0.0155839
\(267\) 0 0
\(268\) −18.7951 −1.14809
\(269\) −9.80921 −0.598078 −0.299039 0.954241i \(-0.596666\pi\)
−0.299039 + 0.954241i \(0.596666\pi\)
\(270\) 0 0
\(271\) −7.40116 −0.449588 −0.224794 0.974406i \(-0.572171\pi\)
−0.224794 + 0.974406i \(0.572171\pi\)
\(272\) −5.11505 −0.310146
\(273\) 0 0
\(274\) 0.121969 0.00736843
\(275\) −3.10498 −0.187238
\(276\) 0 0
\(277\) −19.8615 −1.19336 −0.596681 0.802479i \(-0.703514\pi\)
−0.596681 + 0.802479i \(0.703514\pi\)
\(278\) 0.423932 0.0254257
\(279\) 0 0
\(280\) 0.260243 0.0155525
\(281\) −0.951509 −0.0567623 −0.0283811 0.999597i \(-0.509035\pi\)
−0.0283811 + 0.999597i \(0.509035\pi\)
\(282\) 0 0
\(283\) −2.52964 −0.150371 −0.0751857 0.997170i \(-0.523955\pi\)
−0.0751857 + 0.997170i \(0.523955\pi\)
\(284\) −28.0116 −1.66218
\(285\) 0 0
\(286\) 0.302954 0.0179141
\(287\) 3.75391 0.221587
\(288\) 0 0
\(289\) −15.1873 −0.893369
\(290\) 0.170066 0.00998665
\(291\) 0 0
\(292\) −15.0724 −0.882047
\(293\) 24.6757 1.44157 0.720784 0.693159i \(-0.243782\pi\)
0.720784 + 0.693159i \(0.243782\pi\)
\(294\) 0 0
\(295\) −0.0743857 −0.00433090
\(296\) −2.88946 −0.167946
\(297\) 0 0
\(298\) −1.76900 −0.102475
\(299\) 2.20193 0.127341
\(300\) 0 0
\(301\) −1.71843 −0.0990489
\(302\) 2.45270 0.141137
\(303\) 0 0
\(304\) −13.6400 −0.782306
\(305\) 3.09268 0.177086
\(306\) 0 0
\(307\) −7.53667 −0.430140 −0.215070 0.976599i \(-0.568998\pi\)
−0.215070 + 0.976599i \(0.568998\pi\)
\(308\) 0.568832 0.0324122
\(309\) 0 0
\(310\) −0.211726 −0.0120252
\(311\) −29.6639 −1.68209 −0.841043 0.540968i \(-0.818058\pi\)
−0.841043 + 0.540968i \(0.818058\pi\)
\(312\) 0 0
\(313\) 3.52220 0.199087 0.0995433 0.995033i \(-0.468262\pi\)
0.0995433 + 0.995033i \(0.468262\pi\)
\(314\) 1.39878 0.0789380
\(315\) 0 0
\(316\) 24.3156 1.36786
\(317\) 11.3919 0.639834 0.319917 0.947446i \(-0.396345\pi\)
0.319917 + 0.947446i \(0.396345\pi\)
\(318\) 0 0
\(319\) 0.749819 0.0419818
\(320\) −6.67621 −0.373211
\(321\) 0 0
\(322\) −0.0707926 −0.00394512
\(323\) 4.83390 0.268965
\(324\) 0 0
\(325\) −9.11816 −0.505784
\(326\) −2.39711 −0.132763
\(327\) 0 0
\(328\) 7.08140 0.391005
\(329\) 0.154602 0.00852349
\(330\) 0 0
\(331\) −2.32690 −0.127898 −0.0639490 0.997953i \(-0.520370\pi\)
−0.0639490 + 0.997953i \(0.520370\pi\)
\(332\) 31.9918 1.75578
\(333\) 0 0
\(334\) −1.80364 −0.0986907
\(335\) 8.85911 0.484025
\(336\) 0 0
\(337\) 7.86996 0.428704 0.214352 0.976756i \(-0.431236\pi\)
0.214352 + 0.976756i \(0.431236\pi\)
\(338\) −1.49573 −0.0813571
\(339\) 0 0
\(340\) 2.45372 0.133072
\(341\) −0.933497 −0.0505517
\(342\) 0 0
\(343\) 5.34388 0.288543
\(344\) −3.24166 −0.174779
\(345\) 0 0
\(346\) −0.0385376 −0.00207179
\(347\) 4.33984 0.232975 0.116487 0.993192i \(-0.462837\pi\)
0.116487 + 0.993192i \(0.462837\pi\)
\(348\) 0 0
\(349\) 3.80390 0.203618 0.101809 0.994804i \(-0.467537\pi\)
0.101809 + 0.994804i \(0.467537\pi\)
\(350\) 0.293150 0.0156696
\(351\) 0 0
\(352\) 1.61412 0.0860331
\(353\) −35.7730 −1.90400 −0.952002 0.306093i \(-0.900978\pi\)
−0.952002 + 0.306093i \(0.900978\pi\)
\(354\) 0 0
\(355\) 13.2033 0.700759
\(356\) 4.82555 0.255754
\(357\) 0 0
\(358\) 2.27367 0.120167
\(359\) 31.8517 1.68107 0.840534 0.541759i \(-0.182241\pi\)
0.840534 + 0.541759i \(0.182241\pi\)
\(360\) 0 0
\(361\) −6.10976 −0.321566
\(362\) −2.12105 −0.111480
\(363\) 0 0
\(364\) 1.67044 0.0875550
\(365\) 7.10442 0.371862
\(366\) 0 0
\(367\) −9.65204 −0.503832 −0.251916 0.967749i \(-0.581061\pi\)
−0.251916 + 0.967749i \(0.581061\pi\)
\(368\) 3.79912 0.198043
\(369\) 0 0
\(370\) 0.675196 0.0351018
\(371\) 0.712505 0.0369914
\(372\) 0 0
\(373\) 33.8951 1.75502 0.877511 0.479556i \(-0.159202\pi\)
0.877511 + 0.479556i \(0.159202\pi\)
\(374\) −0.185242 −0.00957866
\(375\) 0 0
\(376\) 0.291642 0.0150403
\(377\) 2.20193 0.113405
\(378\) 0 0
\(379\) 10.2771 0.527898 0.263949 0.964537i \(-0.414975\pi\)
0.263949 + 0.964537i \(0.414975\pi\)
\(380\) 6.54318 0.335658
\(381\) 0 0
\(382\) 1.12640 0.0576316
\(383\) −6.26703 −0.320230 −0.160115 0.987098i \(-0.551187\pi\)
−0.160115 + 0.987098i \(0.551187\pi\)
\(384\) 0 0
\(385\) −0.268120 −0.0136647
\(386\) −3.27991 −0.166943
\(387\) 0 0
\(388\) 0.248524 0.0126169
\(389\) 1.50479 0.0762960 0.0381480 0.999272i \(-0.487854\pi\)
0.0381480 + 0.999272i \(0.487854\pi\)
\(390\) 0 0
\(391\) −1.34638 −0.0680893
\(392\) 4.98619 0.251841
\(393\) 0 0
\(394\) 2.31527 0.116642
\(395\) −11.4612 −0.576676
\(396\) 0 0
\(397\) 18.0745 0.907131 0.453566 0.891223i \(-0.350152\pi\)
0.453566 + 0.891223i \(0.350152\pi\)
\(398\) −4.89804 −0.245516
\(399\) 0 0
\(400\) −15.7321 −0.786603
\(401\) −16.4662 −0.822282 −0.411141 0.911572i \(-0.634870\pi\)
−0.411141 + 0.911572i \(0.634870\pi\)
\(402\) 0 0
\(403\) −2.74132 −0.136555
\(404\) −26.3703 −1.31197
\(405\) 0 0
\(406\) −0.0707926 −0.00351338
\(407\) 2.97692 0.147561
\(408\) 0 0
\(409\) −33.6007 −1.66145 −0.830724 0.556685i \(-0.812073\pi\)
−0.830724 + 0.556685i \(0.812073\pi\)
\(410\) −1.65475 −0.0817222
\(411\) 0 0
\(412\) −21.2268 −1.04577
\(413\) 0.0309641 0.00152364
\(414\) 0 0
\(415\) −15.0794 −0.740218
\(416\) 4.74007 0.232401
\(417\) 0 0
\(418\) −0.493974 −0.0241610
\(419\) 37.4551 1.82980 0.914902 0.403677i \(-0.132268\pi\)
0.914902 + 0.403677i \(0.132268\pi\)
\(420\) 0 0
\(421\) −27.1254 −1.32201 −0.661005 0.750382i \(-0.729870\pi\)
−0.661005 + 0.750382i \(0.729870\pi\)
\(422\) −2.61811 −0.127447
\(423\) 0 0
\(424\) 1.34407 0.0652739
\(425\) 5.57532 0.270443
\(426\) 0 0
\(427\) −1.28737 −0.0623003
\(428\) 32.9978 1.59501
\(429\) 0 0
\(430\) 0.757497 0.0365297
\(431\) 32.4650 1.56378 0.781892 0.623413i \(-0.214255\pi\)
0.781892 + 0.623413i \(0.214255\pi\)
\(432\) 0 0
\(433\) −39.8665 −1.91586 −0.957932 0.286997i \(-0.907343\pi\)
−0.957932 + 0.286997i \(0.907343\pi\)
\(434\) 0.0881341 0.00423057
\(435\) 0 0
\(436\) 24.5237 1.17447
\(437\) −3.59030 −0.171747
\(438\) 0 0
\(439\) 25.2011 1.20278 0.601391 0.798955i \(-0.294613\pi\)
0.601391 + 0.798955i \(0.294613\pi\)
\(440\) −0.505783 −0.0241123
\(441\) 0 0
\(442\) −0.543986 −0.0258748
\(443\) −21.7528 −1.03351 −0.516754 0.856134i \(-0.672860\pi\)
−0.516754 + 0.856134i \(0.672860\pi\)
\(444\) 0 0
\(445\) −2.27453 −0.107823
\(446\) −1.45767 −0.0690225
\(447\) 0 0
\(448\) 2.77906 0.131298
\(449\) −34.1849 −1.61328 −0.806641 0.591041i \(-0.798717\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(450\) 0 0
\(451\) −7.29575 −0.343543
\(452\) −29.3218 −1.37918
\(453\) 0 0
\(454\) 1.92978 0.0905692
\(455\) −0.787367 −0.0369123
\(456\) 0 0
\(457\) −34.3663 −1.60759 −0.803793 0.594909i \(-0.797188\pi\)
−0.803793 + 0.594909i \(0.797188\pi\)
\(458\) −5.00572 −0.233902
\(459\) 0 0
\(460\) −1.82246 −0.0849728
\(461\) 12.5371 0.583912 0.291956 0.956432i \(-0.405694\pi\)
0.291956 + 0.956432i \(0.405694\pi\)
\(462\) 0 0
\(463\) −3.04685 −0.141599 −0.0707996 0.997491i \(-0.522555\pi\)
−0.0707996 + 0.997491i \(0.522555\pi\)
\(464\) 3.79912 0.176370
\(465\) 0 0
\(466\) 3.97216 0.184007
\(467\) −9.69440 −0.448603 −0.224302 0.974520i \(-0.572010\pi\)
−0.224302 + 0.974520i \(0.572010\pi\)
\(468\) 0 0
\(469\) −3.68773 −0.170284
\(470\) −0.0681496 −0.00314351
\(471\) 0 0
\(472\) 0.0584108 0.00268857
\(473\) 3.33978 0.153563
\(474\) 0 0
\(475\) 14.8673 0.682161
\(476\) −1.02140 −0.0468157
\(477\) 0 0
\(478\) −0.0949485 −0.00434284
\(479\) 33.2429 1.51891 0.759453 0.650562i \(-0.225467\pi\)
0.759453 + 0.650562i \(0.225467\pi\)
\(480\) 0 0
\(481\) 8.74209 0.398605
\(482\) −4.86238 −0.221475
\(483\) 0 0
\(484\) 20.5241 0.932914
\(485\) −0.117142 −0.00531916
\(486\) 0 0
\(487\) −20.1894 −0.914868 −0.457434 0.889244i \(-0.651231\pi\)
−0.457434 + 0.889244i \(0.651231\pi\)
\(488\) −2.42850 −0.109933
\(489\) 0 0
\(490\) −1.16515 −0.0526362
\(491\) 29.1577 1.31587 0.657935 0.753075i \(-0.271430\pi\)
0.657935 + 0.753075i \(0.271430\pi\)
\(492\) 0 0
\(493\) −1.34638 −0.0606378
\(494\) −1.45061 −0.0652661
\(495\) 0 0
\(496\) −4.72976 −0.212372
\(497\) −5.49606 −0.246532
\(498\) 0 0
\(499\) 12.6666 0.567035 0.283517 0.958967i \(-0.408499\pi\)
0.283517 + 0.958967i \(0.408499\pi\)
\(500\) 16.6591 0.745017
\(501\) 0 0
\(502\) −4.81964 −0.215111
\(503\) 16.7240 0.745688 0.372844 0.927894i \(-0.378383\pi\)
0.372844 + 0.927894i \(0.378383\pi\)
\(504\) 0 0
\(505\) 12.4297 0.553115
\(506\) 0.137586 0.00611643
\(507\) 0 0
\(508\) 20.7903 0.922419
\(509\) 20.1057 0.891168 0.445584 0.895240i \(-0.352996\pi\)
0.445584 + 0.895240i \(0.352996\pi\)
\(510\) 0 0
\(511\) −2.95731 −0.130824
\(512\) 13.7082 0.605823
\(513\) 0 0
\(514\) −1.94429 −0.0857591
\(515\) 10.0053 0.440887
\(516\) 0 0
\(517\) −0.300470 −0.0132147
\(518\) −0.281060 −0.0123491
\(519\) 0 0
\(520\) −1.48529 −0.0651344
\(521\) −35.8407 −1.57021 −0.785104 0.619363i \(-0.787391\pi\)
−0.785104 + 0.619363i \(0.787391\pi\)
\(522\) 0 0
\(523\) −34.1618 −1.49379 −0.746895 0.664942i \(-0.768456\pi\)
−0.746895 + 0.664942i \(0.768456\pi\)
\(524\) 25.5638 1.11676
\(525\) 0 0
\(526\) 0.463772 0.0202214
\(527\) 1.67619 0.0730160
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −0.314077 −0.0136426
\(531\) 0 0
\(532\) −2.72369 −0.118087
\(533\) −21.4248 −0.928012
\(534\) 0 0
\(535\) −15.5536 −0.672441
\(536\) −6.95655 −0.300477
\(537\) 0 0
\(538\) −1.79991 −0.0775996
\(539\) −5.13713 −0.221272
\(540\) 0 0
\(541\) 38.2085 1.64271 0.821357 0.570415i \(-0.193218\pi\)
0.821357 + 0.570415i \(0.193218\pi\)
\(542\) −1.35805 −0.0583333
\(543\) 0 0
\(544\) −2.89833 −0.124265
\(545\) −11.5593 −0.495147
\(546\) 0 0
\(547\) 25.1716 1.07626 0.538131 0.842861i \(-0.319131\pi\)
0.538131 + 0.842861i \(0.319131\pi\)
\(548\) −1.30704 −0.0558341
\(549\) 0 0
\(550\) −0.569739 −0.0242938
\(551\) −3.59030 −0.152952
\(552\) 0 0
\(553\) 4.77089 0.202879
\(554\) −3.64442 −0.154837
\(555\) 0 0
\(556\) −4.54293 −0.192663
\(557\) 12.9380 0.548202 0.274101 0.961701i \(-0.411620\pi\)
0.274101 + 0.961701i \(0.411620\pi\)
\(558\) 0 0
\(559\) 9.80768 0.414820
\(560\) −1.35849 −0.0574066
\(561\) 0 0
\(562\) −0.174594 −0.00736481
\(563\) −33.6052 −1.41629 −0.708145 0.706067i \(-0.750468\pi\)
−0.708145 + 0.706067i \(0.750468\pi\)
\(564\) 0 0
\(565\) 13.8209 0.581448
\(566\) −0.464168 −0.0195104
\(567\) 0 0
\(568\) −10.3678 −0.435023
\(569\) −7.99893 −0.335333 −0.167666 0.985844i \(-0.553623\pi\)
−0.167666 + 0.985844i \(0.553623\pi\)
\(570\) 0 0
\(571\) 19.1730 0.802367 0.401183 0.915998i \(-0.368599\pi\)
0.401183 + 0.915998i \(0.368599\pi\)
\(572\) −3.24651 −0.135744
\(573\) 0 0
\(574\) 0.688812 0.0287505
\(575\) −4.14098 −0.172691
\(576\) 0 0
\(577\) −24.9987 −1.04071 −0.520354 0.853951i \(-0.674200\pi\)
−0.520354 + 0.853951i \(0.674200\pi\)
\(578\) −2.78674 −0.115913
\(579\) 0 0
\(580\) −1.82246 −0.0756736
\(581\) 6.27701 0.260414
\(582\) 0 0
\(583\) −1.38476 −0.0573508
\(584\) −5.57869 −0.230848
\(585\) 0 0
\(586\) 4.52779 0.187041
\(587\) 23.0785 0.952551 0.476275 0.879296i \(-0.341987\pi\)
0.476275 + 0.879296i \(0.341987\pi\)
\(588\) 0 0
\(589\) 4.46979 0.184174
\(590\) −0.0136492 −0.000561927 0
\(591\) 0 0
\(592\) 15.0832 0.619916
\(593\) −14.9820 −0.615236 −0.307618 0.951510i \(-0.599532\pi\)
−0.307618 + 0.951510i \(0.599532\pi\)
\(594\) 0 0
\(595\) 0.481438 0.0197370
\(596\) 18.9569 0.776505
\(597\) 0 0
\(598\) 0.404037 0.0165223
\(599\) −32.0926 −1.31127 −0.655633 0.755080i \(-0.727598\pi\)
−0.655633 + 0.755080i \(0.727598\pi\)
\(600\) 0 0
\(601\) −24.2848 −0.990598 −0.495299 0.868723i \(-0.664941\pi\)
−0.495299 + 0.868723i \(0.664941\pi\)
\(602\) −0.315319 −0.0128514
\(603\) 0 0
\(604\) −26.2836 −1.06947
\(605\) −9.67408 −0.393307
\(606\) 0 0
\(607\) 45.9454 1.86486 0.932432 0.361345i \(-0.117682\pi\)
0.932432 + 0.361345i \(0.117682\pi\)
\(608\) −7.72878 −0.313444
\(609\) 0 0
\(610\) 0.567482 0.0229767
\(611\) −0.882366 −0.0356967
\(612\) 0 0
\(613\) −28.4632 −1.14962 −0.574810 0.818287i \(-0.694924\pi\)
−0.574810 + 0.818287i \(0.694924\pi\)
\(614\) −1.38292 −0.0558100
\(615\) 0 0
\(616\) 0.210539 0.00848287
\(617\) −17.7981 −0.716524 −0.358262 0.933621i \(-0.616631\pi\)
−0.358262 + 0.933621i \(0.616631\pi\)
\(618\) 0 0
\(619\) −37.3427 −1.50093 −0.750465 0.660910i \(-0.770170\pi\)
−0.750465 + 0.660910i \(0.770170\pi\)
\(620\) 2.26890 0.0911211
\(621\) 0 0
\(622\) −5.44309 −0.218248
\(623\) 0.946806 0.0379330
\(624\) 0 0
\(625\) 12.8526 0.514104
\(626\) 0.646295 0.0258311
\(627\) 0 0
\(628\) −14.9896 −0.598151
\(629\) −5.34538 −0.213134
\(630\) 0 0
\(631\) −2.33993 −0.0931513 −0.0465756 0.998915i \(-0.514831\pi\)
−0.0465756 + 0.998915i \(0.514831\pi\)
\(632\) 8.99983 0.357994
\(633\) 0 0
\(634\) 2.09032 0.0830174
\(635\) −9.79954 −0.388883
\(636\) 0 0
\(637\) −15.0858 −0.597720
\(638\) 0.137586 0.00544707
\(639\) 0 0
\(640\) −5.21539 −0.206157
\(641\) 26.9889 1.06600 0.532998 0.846116i \(-0.321065\pi\)
0.532998 + 0.846116i \(0.321065\pi\)
\(642\) 0 0
\(643\) 25.0301 0.987090 0.493545 0.869720i \(-0.335701\pi\)
0.493545 + 0.869720i \(0.335701\pi\)
\(644\) 0.758626 0.0298940
\(645\) 0 0
\(646\) 0.886981 0.0348978
\(647\) −28.4657 −1.11910 −0.559550 0.828796i \(-0.689026\pi\)
−0.559550 + 0.828796i \(0.689026\pi\)
\(648\) 0 0
\(649\) −0.0601788 −0.00236223
\(650\) −1.67311 −0.0656247
\(651\) 0 0
\(652\) 25.6878 1.00601
\(653\) −5.11404 −0.200128 −0.100064 0.994981i \(-0.531905\pi\)
−0.100064 + 0.994981i \(0.531905\pi\)
\(654\) 0 0
\(655\) −12.0496 −0.470815
\(656\) −36.9655 −1.44326
\(657\) 0 0
\(658\) 0.0283682 0.00110591
\(659\) 13.4130 0.522496 0.261248 0.965272i \(-0.415866\pi\)
0.261248 + 0.965272i \(0.415866\pi\)
\(660\) 0 0
\(661\) −6.72595 −0.261609 −0.130805 0.991408i \(-0.541756\pi\)
−0.130805 + 0.991408i \(0.541756\pi\)
\(662\) −0.426967 −0.0165946
\(663\) 0 0
\(664\) 11.8410 0.459519
\(665\) 1.28382 0.0497843
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 19.3281 0.747827
\(669\) 0 0
\(670\) 1.62557 0.0628014
\(671\) 2.50201 0.0965892
\(672\) 0 0
\(673\) 9.11955 0.351533 0.175766 0.984432i \(-0.443760\pi\)
0.175766 + 0.984432i \(0.443760\pi\)
\(674\) 1.44407 0.0556236
\(675\) 0 0
\(676\) 16.0285 0.616482
\(677\) −24.5508 −0.943564 −0.471782 0.881715i \(-0.656389\pi\)
−0.471782 + 0.881715i \(0.656389\pi\)
\(678\) 0 0
\(679\) 0.0487621 0.00187132
\(680\) 0.908186 0.0348273
\(681\) 0 0
\(682\) −0.171289 −0.00655899
\(683\) 43.5434 1.66614 0.833071 0.553166i \(-0.186580\pi\)
0.833071 + 0.553166i \(0.186580\pi\)
\(684\) 0 0
\(685\) 0.616078 0.0235391
\(686\) 0.980559 0.0374379
\(687\) 0 0
\(688\) 16.9217 0.645135
\(689\) −4.06651 −0.154922
\(690\) 0 0
\(691\) 14.7682 0.561807 0.280904 0.959736i \(-0.409366\pi\)
0.280904 + 0.959736i \(0.409366\pi\)
\(692\) 0.412976 0.0156990
\(693\) 0 0
\(694\) 0.796326 0.0302281
\(695\) 2.14132 0.0812248
\(696\) 0 0
\(697\) 13.1003 0.496208
\(698\) 0.697984 0.0264191
\(699\) 0 0
\(700\) −3.14145 −0.118736
\(701\) 35.2124 1.32995 0.664977 0.746864i \(-0.268441\pi\)
0.664977 + 0.746864i \(0.268441\pi\)
\(702\) 0 0
\(703\) −14.2542 −0.537606
\(704\) −5.40112 −0.203563
\(705\) 0 0
\(706\) −6.56405 −0.247041
\(707\) −5.17404 −0.194590
\(708\) 0 0
\(709\) −29.0997 −1.09286 −0.546432 0.837504i \(-0.684014\pi\)
−0.546432 + 0.837504i \(0.684014\pi\)
\(710\) 2.42270 0.0909223
\(711\) 0 0
\(712\) 1.78606 0.0669354
\(713\) −1.24496 −0.0466242
\(714\) 0 0
\(715\) 1.53025 0.0572281
\(716\) −24.3650 −0.910564
\(717\) 0 0
\(718\) 5.84452 0.218116
\(719\) −20.7747 −0.774766 −0.387383 0.921919i \(-0.626621\pi\)
−0.387383 + 0.921919i \(0.626621\pi\)
\(720\) 0 0
\(721\) −4.16485 −0.155107
\(722\) −1.12109 −0.0417227
\(723\) 0 0
\(724\) 22.7296 0.844738
\(725\) −4.14098 −0.153792
\(726\) 0 0
\(727\) −1.69278 −0.0627817 −0.0313908 0.999507i \(-0.509994\pi\)
−0.0313908 + 0.999507i \(0.509994\pi\)
\(728\) 0.618274 0.0229147
\(729\) 0 0
\(730\) 1.30360 0.0482485
\(731\) −5.99693 −0.221805
\(732\) 0 0
\(733\) 30.7492 1.13575 0.567874 0.823116i \(-0.307766\pi\)
0.567874 + 0.823116i \(0.307766\pi\)
\(734\) −1.77107 −0.0653714
\(735\) 0 0
\(736\) 2.15269 0.0793490
\(737\) 7.16712 0.264004
\(738\) 0 0
\(739\) −21.8356 −0.803237 −0.401619 0.915807i \(-0.631552\pi\)
−0.401619 + 0.915807i \(0.631552\pi\)
\(740\) −7.23552 −0.265983
\(741\) 0 0
\(742\) 0.130739 0.00479958
\(743\) −25.3649 −0.930548 −0.465274 0.885167i \(-0.654044\pi\)
−0.465274 + 0.885167i \(0.654044\pi\)
\(744\) 0 0
\(745\) −8.93538 −0.327367
\(746\) 6.21948 0.227711
\(747\) 0 0
\(748\) 1.98509 0.0725821
\(749\) 6.47441 0.236570
\(750\) 0 0
\(751\) 39.4256 1.43866 0.719330 0.694669i \(-0.244449\pi\)
0.719330 + 0.694669i \(0.244449\pi\)
\(752\) −1.52239 −0.0555160
\(753\) 0 0
\(754\) 0.404037 0.0147141
\(755\) 12.3888 0.450876
\(756\) 0 0
\(757\) −6.47394 −0.235299 −0.117650 0.993055i \(-0.537536\pi\)
−0.117650 + 0.993055i \(0.537536\pi\)
\(758\) 1.88576 0.0684939
\(759\) 0 0
\(760\) 2.42180 0.0878479
\(761\) 53.9004 1.95389 0.976945 0.213492i \(-0.0684838\pi\)
0.976945 + 0.213492i \(0.0684838\pi\)
\(762\) 0 0
\(763\) 4.81173 0.174196
\(764\) −12.0707 −0.436702
\(765\) 0 0
\(766\) −1.14995 −0.0415493
\(767\) −0.176722 −0.00638107
\(768\) 0 0
\(769\) 11.0960 0.400133 0.200066 0.979782i \(-0.435884\pi\)
0.200066 + 0.979782i \(0.435884\pi\)
\(770\) −0.0491979 −0.00177297
\(771\) 0 0
\(772\) 35.1480 1.26501
\(773\) 41.9688 1.50951 0.754756 0.656005i \(-0.227755\pi\)
0.754756 + 0.656005i \(0.227755\pi\)
\(774\) 0 0
\(775\) 5.15536 0.185186
\(776\) 0.0919850 0.00330207
\(777\) 0 0
\(778\) 0.276117 0.00989928
\(779\) 34.9336 1.25163
\(780\) 0 0
\(781\) 10.6816 0.382219
\(782\) −0.247049 −0.00883447
\(783\) 0 0
\(784\) −26.0283 −0.929583
\(785\) 7.06539 0.252175
\(786\) 0 0
\(787\) −7.36397 −0.262497 −0.131249 0.991349i \(-0.541899\pi\)
−0.131249 + 0.991349i \(0.541899\pi\)
\(788\) −24.8109 −0.883852
\(789\) 0 0
\(790\) −2.10304 −0.0748228
\(791\) −5.75313 −0.204558
\(792\) 0 0
\(793\) 7.34746 0.260916
\(794\) 3.31652 0.117699
\(795\) 0 0
\(796\) 52.4882 1.86040
\(797\) 35.5482 1.25918 0.629590 0.776927i \(-0.283223\pi\)
0.629590 + 0.776927i \(0.283223\pi\)
\(798\) 0 0
\(799\) 0.539525 0.0190870
\(800\) −8.91422 −0.315165
\(801\) 0 0
\(802\) −3.02141 −0.106690
\(803\) 5.74755 0.202827
\(804\) 0 0
\(805\) −0.357580 −0.0126030
\(806\) −0.503010 −0.0177178
\(807\) 0 0
\(808\) −9.76033 −0.343367
\(809\) −24.8265 −0.872852 −0.436426 0.899740i \(-0.643756\pi\)
−0.436426 + 0.899740i \(0.643756\pi\)
\(810\) 0 0
\(811\) 4.46243 0.156697 0.0783486 0.996926i \(-0.475035\pi\)
0.0783486 + 0.996926i \(0.475035\pi\)
\(812\) 0.758626 0.0266225
\(813\) 0 0
\(814\) 0.546241 0.0191457
\(815\) −12.1080 −0.424125
\(816\) 0 0
\(817\) −15.9916 −0.559476
\(818\) −6.16545 −0.215570
\(819\) 0 0
\(820\) 17.7326 0.619249
\(821\) −32.1527 −1.12214 −0.561069 0.827769i \(-0.689610\pi\)
−0.561069 + 0.827769i \(0.689610\pi\)
\(822\) 0 0
\(823\) 36.9464 1.28787 0.643936 0.765079i \(-0.277300\pi\)
0.643936 + 0.765079i \(0.277300\pi\)
\(824\) −7.85660 −0.273697
\(825\) 0 0
\(826\) 0.00568166 0.000197690 0
\(827\) −17.9151 −0.622969 −0.311485 0.950251i \(-0.600826\pi\)
−0.311485 + 0.950251i \(0.600826\pi\)
\(828\) 0 0
\(829\) −0.432599 −0.0150248 −0.00751239 0.999972i \(-0.502391\pi\)
−0.00751239 + 0.999972i \(0.502391\pi\)
\(830\) −2.76694 −0.0960420
\(831\) 0 0
\(832\) −15.8610 −0.549883
\(833\) 9.22424 0.319601
\(834\) 0 0
\(835\) −9.11035 −0.315277
\(836\) 5.29351 0.183080
\(837\) 0 0
\(838\) 6.87271 0.237414
\(839\) −31.6009 −1.09098 −0.545492 0.838116i \(-0.683657\pi\)
−0.545492 + 0.838116i \(0.683657\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −4.97728 −0.171528
\(843\) 0 0
\(844\) 28.0561 0.965730
\(845\) −7.55508 −0.259903
\(846\) 0 0
\(847\) 4.02697 0.138368
\(848\) −7.01617 −0.240936
\(849\) 0 0
\(850\) 1.02303 0.0350895
\(851\) 3.97019 0.136096
\(852\) 0 0
\(853\) −36.6916 −1.25630 −0.628148 0.778094i \(-0.716187\pi\)
−0.628148 + 0.778094i \(0.716187\pi\)
\(854\) −0.236222 −0.00808336
\(855\) 0 0
\(856\) 12.2133 0.417444
\(857\) 14.6234 0.499527 0.249763 0.968307i \(-0.419647\pi\)
0.249763 + 0.968307i \(0.419647\pi\)
\(858\) 0 0
\(859\) 17.8847 0.610219 0.305110 0.952317i \(-0.401307\pi\)
0.305110 + 0.952317i \(0.401307\pi\)
\(860\) −8.11747 −0.276803
\(861\) 0 0
\(862\) 5.95706 0.202898
\(863\) −5.51718 −0.187807 −0.0939034 0.995581i \(-0.529934\pi\)
−0.0939034 + 0.995581i \(0.529934\pi\)
\(864\) 0 0
\(865\) −0.194657 −0.00661854
\(866\) −7.31518 −0.248580
\(867\) 0 0
\(868\) −0.944460 −0.0320571
\(869\) −9.27225 −0.314540
\(870\) 0 0
\(871\) 21.0471 0.713154
\(872\) 9.07686 0.307381
\(873\) 0 0
\(874\) −0.658790 −0.0222839
\(875\) 3.26863 0.110500
\(876\) 0 0
\(877\) 7.12677 0.240654 0.120327 0.992734i \(-0.461606\pi\)
0.120327 + 0.992734i \(0.461606\pi\)
\(878\) 4.62419 0.156059
\(879\) 0 0
\(880\) 2.64023 0.0890021
\(881\) 20.5458 0.692206 0.346103 0.938197i \(-0.387505\pi\)
0.346103 + 0.938197i \(0.387505\pi\)
\(882\) 0 0
\(883\) 49.5380 1.66709 0.833543 0.552455i \(-0.186309\pi\)
0.833543 + 0.552455i \(0.186309\pi\)
\(884\) 5.82945 0.196066
\(885\) 0 0
\(886\) −3.99147 −0.134096
\(887\) −40.4280 −1.35744 −0.678720 0.734397i \(-0.737465\pi\)
−0.678720 + 0.734397i \(0.737465\pi\)
\(888\) 0 0
\(889\) 4.07920 0.136812
\(890\) −0.417358 −0.0139899
\(891\) 0 0
\(892\) 15.6206 0.523017
\(893\) 1.43872 0.0481448
\(894\) 0 0
\(895\) 11.4845 0.383885
\(896\) 2.17098 0.0725274
\(897\) 0 0
\(898\) −6.27264 −0.209321
\(899\) −1.24496 −0.0415218
\(900\) 0 0
\(901\) 2.48648 0.0828366
\(902\) −1.33871 −0.0445742
\(903\) 0 0
\(904\) −10.8527 −0.360956
\(905\) −10.7136 −0.356133
\(906\) 0 0
\(907\) −31.7948 −1.05573 −0.527864 0.849329i \(-0.677007\pi\)
−0.527864 + 0.849329i \(0.677007\pi\)
\(908\) −20.6799 −0.686287
\(909\) 0 0
\(910\) −0.144475 −0.00478931
\(911\) 51.3127 1.70007 0.850034 0.526729i \(-0.176582\pi\)
0.850034 + 0.526729i \(0.176582\pi\)
\(912\) 0 0
\(913\) −12.1994 −0.403741
\(914\) −6.30593 −0.208582
\(915\) 0 0
\(916\) 53.6422 1.77239
\(917\) 5.01580 0.165636
\(918\) 0 0
\(919\) −41.3474 −1.36393 −0.681963 0.731387i \(-0.738874\pi\)
−0.681963 + 0.731387i \(0.738874\pi\)
\(920\) −0.674540 −0.0222389
\(921\) 0 0
\(922\) 2.30046 0.0757616
\(923\) 31.3679 1.03249
\(924\) 0 0
\(925\) −16.4405 −0.540559
\(926\) −0.559072 −0.0183723
\(927\) 0 0
\(928\) 2.15269 0.0706654
\(929\) 0.914960 0.0300189 0.0150094 0.999887i \(-0.495222\pi\)
0.0150094 + 0.999887i \(0.495222\pi\)
\(930\) 0 0
\(931\) 24.5977 0.806156
\(932\) −42.5664 −1.39431
\(933\) 0 0
\(934\) −1.77884 −0.0582055
\(935\) −0.935677 −0.0305999
\(936\) 0 0
\(937\) 48.1226 1.57210 0.786048 0.618165i \(-0.212124\pi\)
0.786048 + 0.618165i \(0.212124\pi\)
\(938\) −0.676668 −0.0220940
\(939\) 0 0
\(940\) 0.730303 0.0238199
\(941\) 14.3235 0.466934 0.233467 0.972365i \(-0.424993\pi\)
0.233467 + 0.972365i \(0.424993\pi\)
\(942\) 0 0
\(943\) −9.73001 −0.316853
\(944\) −0.304909 −0.00992394
\(945\) 0 0
\(946\) 0.612823 0.0199246
\(947\) −11.7482 −0.381767 −0.190883 0.981613i \(-0.561135\pi\)
−0.190883 + 0.981613i \(0.561135\pi\)
\(948\) 0 0
\(949\) 16.8784 0.547895
\(950\) 2.72804 0.0885092
\(951\) 0 0
\(952\) −0.378045 −0.0122525
\(953\) −49.0159 −1.58778 −0.793890 0.608061i \(-0.791947\pi\)
−0.793890 + 0.608061i \(0.791947\pi\)
\(954\) 0 0
\(955\) 5.68955 0.184109
\(956\) 1.01748 0.0329078
\(957\) 0 0
\(958\) 6.09980 0.197075
\(959\) −0.256451 −0.00828124
\(960\) 0 0
\(961\) −29.4501 −0.950002
\(962\) 1.60410 0.0517183
\(963\) 0 0
\(964\) 52.1062 1.67823
\(965\) −16.5671 −0.533314
\(966\) 0 0
\(967\) 44.3688 1.42681 0.713403 0.700754i \(-0.247153\pi\)
0.713403 + 0.700754i \(0.247153\pi\)
\(968\) 7.59650 0.244161
\(969\) 0 0
\(970\) −0.0214946 −0.000690152 0
\(971\) 59.4564 1.90805 0.954024 0.299731i \(-0.0968969\pi\)
0.954024 + 0.299731i \(0.0968969\pi\)
\(972\) 0 0
\(973\) −0.891354 −0.0285755
\(974\) −3.70458 −0.118703
\(975\) 0 0
\(976\) 12.6770 0.405780
\(977\) 20.5068 0.656069 0.328035 0.944666i \(-0.393614\pi\)
0.328035 + 0.944666i \(0.393614\pi\)
\(978\) 0 0
\(979\) −1.84012 −0.0588106
\(980\) 12.4860 0.398850
\(981\) 0 0
\(982\) 5.35020 0.170732
\(983\) −36.1826 −1.15405 −0.577023 0.816728i \(-0.695786\pi\)
−0.577023 + 0.816728i \(0.695786\pi\)
\(984\) 0 0
\(985\) 11.6947 0.372623
\(986\) −0.247049 −0.00786766
\(987\) 0 0
\(988\) 15.5450 0.494553
\(989\) 4.45412 0.141633
\(990\) 0 0
\(991\) 39.6822 1.26055 0.630274 0.776373i \(-0.282943\pi\)
0.630274 + 0.776373i \(0.282943\pi\)
\(992\) −2.68001 −0.0850905
\(993\) 0 0
\(994\) −1.00848 −0.0319871
\(995\) −24.7404 −0.784325
\(996\) 0 0
\(997\) 32.3711 1.02520 0.512601 0.858627i \(-0.328682\pi\)
0.512601 + 0.858627i \(0.328682\pi\)
\(998\) 2.32422 0.0735718
\(999\) 0 0
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 \(a_p\))