Properties

Label 6008.2.a.e.1.46
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.46
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00349 q^{3} +3.90143 q^{5} -4.05459 q^{7} +6.02097 q^{9} +O(q^{10})\) \(q+3.00349 q^{3} +3.90143 q^{5} -4.05459 q^{7} +6.02097 q^{9} -1.15784 q^{11} +3.06308 q^{13} +11.7179 q^{15} +2.39254 q^{17} -5.08326 q^{19} -12.1779 q^{21} +5.68251 q^{23} +10.2211 q^{25} +9.07346 q^{27} -6.19683 q^{29} +1.20190 q^{31} -3.47758 q^{33} -15.8187 q^{35} -0.702594 q^{37} +9.19995 q^{39} +3.20524 q^{41} +0.852294 q^{43} +23.4904 q^{45} +9.40596 q^{47} +9.43969 q^{49} +7.18597 q^{51} +2.44430 q^{53} -4.51724 q^{55} -15.2676 q^{57} +8.28158 q^{59} +10.0969 q^{61} -24.4126 q^{63} +11.9504 q^{65} +13.8704 q^{67} +17.0674 q^{69} -0.0237590 q^{71} +1.97219 q^{73} +30.6991 q^{75} +4.69458 q^{77} -11.3522 q^{79} +9.18918 q^{81} -14.2999 q^{83} +9.33431 q^{85} -18.6121 q^{87} -9.64695 q^{89} -12.4195 q^{91} +3.60989 q^{93} -19.8320 q^{95} -4.93677 q^{97} -6.97134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00349 1.73407 0.867034 0.498249i \(-0.166024\pi\)
0.867034 + 0.498249i \(0.166024\pi\)
\(4\) 0 0
\(5\) 3.90143 1.74477 0.872385 0.488819i \(-0.162572\pi\)
0.872385 + 0.488819i \(0.162572\pi\)
\(6\) 0 0
\(7\) −4.05459 −1.53249 −0.766245 0.642548i \(-0.777877\pi\)
−0.766245 + 0.642548i \(0.777877\pi\)
\(8\) 0 0
\(9\) 6.02097 2.00699
\(10\) 0 0
\(11\) −1.15784 −0.349103 −0.174551 0.984648i \(-0.555848\pi\)
−0.174551 + 0.984648i \(0.555848\pi\)
\(12\) 0 0
\(13\) 3.06308 0.849547 0.424773 0.905300i \(-0.360354\pi\)
0.424773 + 0.905300i \(0.360354\pi\)
\(14\) 0 0
\(15\) 11.7179 3.02555
\(16\) 0 0
\(17\) 2.39254 0.580276 0.290138 0.956985i \(-0.406299\pi\)
0.290138 + 0.956985i \(0.406299\pi\)
\(18\) 0 0
\(19\) −5.08326 −1.16618 −0.583090 0.812407i \(-0.698157\pi\)
−0.583090 + 0.812407i \(0.698157\pi\)
\(20\) 0 0
\(21\) −12.1779 −2.65744
\(22\) 0 0
\(23\) 5.68251 1.18489 0.592443 0.805613i \(-0.298164\pi\)
0.592443 + 0.805613i \(0.298164\pi\)
\(24\) 0 0
\(25\) 10.2211 2.04422
\(26\) 0 0
\(27\) 9.07346 1.74619
\(28\) 0 0
\(29\) −6.19683 −1.15072 −0.575361 0.817900i \(-0.695138\pi\)
−0.575361 + 0.817900i \(0.695138\pi\)
\(30\) 0 0
\(31\) 1.20190 0.215867 0.107933 0.994158i \(-0.465577\pi\)
0.107933 + 0.994158i \(0.465577\pi\)
\(32\) 0 0
\(33\) −3.47758 −0.605368
\(34\) 0 0
\(35\) −15.8187 −2.67384
\(36\) 0 0
\(37\) −0.702594 −0.115506 −0.0577529 0.998331i \(-0.518394\pi\)
−0.0577529 + 0.998331i \(0.518394\pi\)
\(38\) 0 0
\(39\) 9.19995 1.47317
\(40\) 0 0
\(41\) 3.20524 0.500575 0.250287 0.968172i \(-0.419475\pi\)
0.250287 + 0.968172i \(0.419475\pi\)
\(42\) 0 0
\(43\) 0.852294 0.129974 0.0649868 0.997886i \(-0.479299\pi\)
0.0649868 + 0.997886i \(0.479299\pi\)
\(44\) 0 0
\(45\) 23.4904 3.50174
\(46\) 0 0
\(47\) 9.40596 1.37200 0.686000 0.727601i \(-0.259365\pi\)
0.686000 + 0.727601i \(0.259365\pi\)
\(48\) 0 0
\(49\) 9.43969 1.34853
\(50\) 0 0
\(51\) 7.18597 1.00624
\(52\) 0 0
\(53\) 2.44430 0.335750 0.167875 0.985808i \(-0.446309\pi\)
0.167875 + 0.985808i \(0.446309\pi\)
\(54\) 0 0
\(55\) −4.51724 −0.609105
\(56\) 0 0
\(57\) −15.2676 −2.02224
\(58\) 0 0
\(59\) 8.28158 1.07817 0.539085 0.842251i \(-0.318770\pi\)
0.539085 + 0.842251i \(0.318770\pi\)
\(60\) 0 0
\(61\) 10.0969 1.29278 0.646389 0.763008i \(-0.276278\pi\)
0.646389 + 0.763008i \(0.276278\pi\)
\(62\) 0 0
\(63\) −24.4126 −3.07569
\(64\) 0 0
\(65\) 11.9504 1.48226
\(66\) 0 0
\(67\) 13.8704 1.69454 0.847271 0.531161i \(-0.178244\pi\)
0.847271 + 0.531161i \(0.178244\pi\)
\(68\) 0 0
\(69\) 17.0674 2.05467
\(70\) 0 0
\(71\) −0.0237590 −0.00281967 −0.00140984 0.999999i \(-0.500449\pi\)
−0.00140984 + 0.999999i \(0.500449\pi\)
\(72\) 0 0
\(73\) 1.97219 0.230828 0.115414 0.993317i \(-0.463181\pi\)
0.115414 + 0.993317i \(0.463181\pi\)
\(74\) 0 0
\(75\) 30.6991 3.54482
\(76\) 0 0
\(77\) 4.69458 0.534997
\(78\) 0 0
\(79\) −11.3522 −1.27722 −0.638610 0.769531i \(-0.720490\pi\)
−0.638610 + 0.769531i \(0.720490\pi\)
\(80\) 0 0
\(81\) 9.18918 1.02102
\(82\) 0 0
\(83\) −14.2999 −1.56962 −0.784808 0.619740i \(-0.787238\pi\)
−0.784808 + 0.619740i \(0.787238\pi\)
\(84\) 0 0
\(85\) 9.33431 1.01245
\(86\) 0 0
\(87\) −18.6121 −1.99543
\(88\) 0 0
\(89\) −9.64695 −1.02257 −0.511287 0.859410i \(-0.670831\pi\)
−0.511287 + 0.859410i \(0.670831\pi\)
\(90\) 0 0
\(91\) −12.4195 −1.30192
\(92\) 0 0
\(93\) 3.60989 0.374328
\(94\) 0 0
\(95\) −19.8320 −2.03472
\(96\) 0 0
\(97\) −4.93677 −0.501253 −0.250626 0.968084i \(-0.580637\pi\)
−0.250626 + 0.968084i \(0.580637\pi\)
\(98\) 0 0
\(99\) −6.97134 −0.700646
\(100\) 0 0
\(101\) 18.7732 1.86800 0.933999 0.357275i \(-0.116294\pi\)
0.933999 + 0.357275i \(0.116294\pi\)
\(102\) 0 0
\(103\) −0.107261 −0.0105688 −0.00528439 0.999986i \(-0.501682\pi\)
−0.00528439 + 0.999986i \(0.501682\pi\)
\(104\) 0 0
\(105\) −47.5113 −4.63663
\(106\) 0 0
\(107\) −16.8588 −1.62980 −0.814899 0.579603i \(-0.803208\pi\)
−0.814899 + 0.579603i \(0.803208\pi\)
\(108\) 0 0
\(109\) −6.81198 −0.652470 −0.326235 0.945289i \(-0.605780\pi\)
−0.326235 + 0.945289i \(0.605780\pi\)
\(110\) 0 0
\(111\) −2.11024 −0.200295
\(112\) 0 0
\(113\) 14.8033 1.39257 0.696287 0.717763i \(-0.254834\pi\)
0.696287 + 0.717763i \(0.254834\pi\)
\(114\) 0 0
\(115\) 22.1699 2.06735
\(116\) 0 0
\(117\) 18.4427 1.70503
\(118\) 0 0
\(119\) −9.70076 −0.889267
\(120\) 0 0
\(121\) −9.65940 −0.878127
\(122\) 0 0
\(123\) 9.62692 0.868030
\(124\) 0 0
\(125\) 20.3698 1.82193
\(126\) 0 0
\(127\) −5.70889 −0.506582 −0.253291 0.967390i \(-0.581513\pi\)
−0.253291 + 0.967390i \(0.581513\pi\)
\(128\) 0 0
\(129\) 2.55986 0.225383
\(130\) 0 0
\(131\) 2.52028 0.220198 0.110099 0.993921i \(-0.464883\pi\)
0.110099 + 0.993921i \(0.464883\pi\)
\(132\) 0 0
\(133\) 20.6105 1.78716
\(134\) 0 0
\(135\) 35.3994 3.04670
\(136\) 0 0
\(137\) 18.5337 1.58344 0.791720 0.610884i \(-0.209186\pi\)
0.791720 + 0.610884i \(0.209186\pi\)
\(138\) 0 0
\(139\) −1.88645 −0.160006 −0.0800032 0.996795i \(-0.525493\pi\)
−0.0800032 + 0.996795i \(0.525493\pi\)
\(140\) 0 0
\(141\) 28.2507 2.37914
\(142\) 0 0
\(143\) −3.54657 −0.296579
\(144\) 0 0
\(145\) −24.1765 −2.00775
\(146\) 0 0
\(147\) 28.3521 2.33844
\(148\) 0 0
\(149\) 14.5348 1.19074 0.595369 0.803452i \(-0.297006\pi\)
0.595369 + 0.803452i \(0.297006\pi\)
\(150\) 0 0
\(151\) 5.11314 0.416102 0.208051 0.978118i \(-0.433288\pi\)
0.208051 + 0.978118i \(0.433288\pi\)
\(152\) 0 0
\(153\) 14.4054 1.16461
\(154\) 0 0
\(155\) 4.68911 0.376638
\(156\) 0 0
\(157\) −19.6197 −1.56582 −0.782911 0.622134i \(-0.786266\pi\)
−0.782911 + 0.622134i \(0.786266\pi\)
\(158\) 0 0
\(159\) 7.34143 0.582213
\(160\) 0 0
\(161\) −23.0402 −1.81583
\(162\) 0 0
\(163\) −15.5788 −1.22023 −0.610113 0.792314i \(-0.708876\pi\)
−0.610113 + 0.792314i \(0.708876\pi\)
\(164\) 0 0
\(165\) −13.5675 −1.05623
\(166\) 0 0
\(167\) −9.61496 −0.744028 −0.372014 0.928227i \(-0.621333\pi\)
−0.372014 + 0.928227i \(0.621333\pi\)
\(168\) 0 0
\(169\) −3.61752 −0.278271
\(170\) 0 0
\(171\) −30.6062 −2.34051
\(172\) 0 0
\(173\) −15.8050 −1.20163 −0.600815 0.799388i \(-0.705157\pi\)
−0.600815 + 0.799388i \(0.705157\pi\)
\(174\) 0 0
\(175\) −41.4424 −3.13275
\(176\) 0 0
\(177\) 24.8737 1.86962
\(178\) 0 0
\(179\) −8.66479 −0.647637 −0.323818 0.946119i \(-0.604967\pi\)
−0.323818 + 0.946119i \(0.604967\pi\)
\(180\) 0 0
\(181\) 15.5265 1.15407 0.577036 0.816719i \(-0.304209\pi\)
0.577036 + 0.816719i \(0.304209\pi\)
\(182\) 0 0
\(183\) 30.3260 2.24177
\(184\) 0 0
\(185\) −2.74112 −0.201531
\(186\) 0 0
\(187\) −2.77019 −0.202576
\(188\) 0 0
\(189\) −36.7892 −2.67602
\(190\) 0 0
\(191\) −11.8356 −0.856397 −0.428198 0.903685i \(-0.640852\pi\)
−0.428198 + 0.903685i \(0.640852\pi\)
\(192\) 0 0
\(193\) −11.3978 −0.820433 −0.410216 0.911988i \(-0.634547\pi\)
−0.410216 + 0.911988i \(0.634547\pi\)
\(194\) 0 0
\(195\) 35.8929 2.57035
\(196\) 0 0
\(197\) 13.5156 0.962948 0.481474 0.876460i \(-0.340102\pi\)
0.481474 + 0.876460i \(0.340102\pi\)
\(198\) 0 0
\(199\) −17.0080 −1.20567 −0.602834 0.797867i \(-0.705962\pi\)
−0.602834 + 0.797867i \(0.705962\pi\)
\(200\) 0 0
\(201\) 41.6597 2.93845
\(202\) 0 0
\(203\) 25.1256 1.76347
\(204\) 0 0
\(205\) 12.5050 0.873388
\(206\) 0 0
\(207\) 34.2142 2.37805
\(208\) 0 0
\(209\) 5.88563 0.407117
\(210\) 0 0
\(211\) 9.71123 0.668549 0.334274 0.942476i \(-0.391509\pi\)
0.334274 + 0.942476i \(0.391509\pi\)
\(212\) 0 0
\(213\) −0.0713600 −0.00488951
\(214\) 0 0
\(215\) 3.32516 0.226774
\(216\) 0 0
\(217\) −4.87319 −0.330814
\(218\) 0 0
\(219\) 5.92347 0.400271
\(220\) 0 0
\(221\) 7.32855 0.492971
\(222\) 0 0
\(223\) 20.4988 1.37270 0.686352 0.727269i \(-0.259211\pi\)
0.686352 + 0.727269i \(0.259211\pi\)
\(224\) 0 0
\(225\) 61.5411 4.10274
\(226\) 0 0
\(227\) 0.250591 0.0166323 0.00831614 0.999965i \(-0.497353\pi\)
0.00831614 + 0.999965i \(0.497353\pi\)
\(228\) 0 0
\(229\) −22.1239 −1.46199 −0.730994 0.682384i \(-0.760943\pi\)
−0.730994 + 0.682384i \(0.760943\pi\)
\(230\) 0 0
\(231\) 14.1001 0.927721
\(232\) 0 0
\(233\) −6.70985 −0.439577 −0.219788 0.975548i \(-0.570537\pi\)
−0.219788 + 0.975548i \(0.570537\pi\)
\(234\) 0 0
\(235\) 36.6967 2.39383
\(236\) 0 0
\(237\) −34.0962 −2.21479
\(238\) 0 0
\(239\) −10.8665 −0.702895 −0.351447 0.936208i \(-0.614310\pi\)
−0.351447 + 0.936208i \(0.614310\pi\)
\(240\) 0 0
\(241\) −1.17637 −0.0757767 −0.0378884 0.999282i \(-0.512063\pi\)
−0.0378884 + 0.999282i \(0.512063\pi\)
\(242\) 0 0
\(243\) 0.379235 0.0243279
\(244\) 0 0
\(245\) 36.8283 2.35287
\(246\) 0 0
\(247\) −15.5705 −0.990725
\(248\) 0 0
\(249\) −42.9496 −2.72182
\(250\) 0 0
\(251\) −19.9124 −1.25686 −0.628431 0.777865i \(-0.716302\pi\)
−0.628431 + 0.777865i \(0.716302\pi\)
\(252\) 0 0
\(253\) −6.57946 −0.413647
\(254\) 0 0
\(255\) 28.0355 1.75565
\(256\) 0 0
\(257\) −14.7530 −0.920264 −0.460132 0.887850i \(-0.652198\pi\)
−0.460132 + 0.887850i \(0.652198\pi\)
\(258\) 0 0
\(259\) 2.84873 0.177011
\(260\) 0 0
\(261\) −37.3109 −2.30949
\(262\) 0 0
\(263\) 23.8677 1.47174 0.735872 0.677120i \(-0.236772\pi\)
0.735872 + 0.677120i \(0.236772\pi\)
\(264\) 0 0
\(265\) 9.53625 0.585807
\(266\) 0 0
\(267\) −28.9745 −1.77321
\(268\) 0 0
\(269\) 8.84139 0.539069 0.269535 0.962991i \(-0.413130\pi\)
0.269535 + 0.962991i \(0.413130\pi\)
\(270\) 0 0
\(271\) 7.77312 0.472184 0.236092 0.971731i \(-0.424133\pi\)
0.236092 + 0.971731i \(0.424133\pi\)
\(272\) 0 0
\(273\) −37.3020 −2.25762
\(274\) 0 0
\(275\) −11.8345 −0.713645
\(276\) 0 0
\(277\) −16.1444 −0.970026 −0.485013 0.874507i \(-0.661185\pi\)
−0.485013 + 0.874507i \(0.661185\pi\)
\(278\) 0 0
\(279\) 7.23658 0.433243
\(280\) 0 0
\(281\) 32.4431 1.93539 0.967697 0.252117i \(-0.0811268\pi\)
0.967697 + 0.252117i \(0.0811268\pi\)
\(282\) 0 0
\(283\) −21.4402 −1.27449 −0.637245 0.770661i \(-0.719926\pi\)
−0.637245 + 0.770661i \(0.719926\pi\)
\(284\) 0 0
\(285\) −59.5652 −3.52834
\(286\) 0 0
\(287\) −12.9959 −0.767126
\(288\) 0 0
\(289\) −11.2758 −0.663280
\(290\) 0 0
\(291\) −14.8275 −0.869206
\(292\) 0 0
\(293\) 14.2796 0.834225 0.417113 0.908855i \(-0.363042\pi\)
0.417113 + 0.908855i \(0.363042\pi\)
\(294\) 0 0
\(295\) 32.3100 1.88116
\(296\) 0 0
\(297\) −10.5057 −0.609600
\(298\) 0 0
\(299\) 17.4060 1.00662
\(300\) 0 0
\(301\) −3.45570 −0.199183
\(302\) 0 0
\(303\) 56.3850 3.23924
\(304\) 0 0
\(305\) 39.3924 2.25560
\(306\) 0 0
\(307\) 8.01951 0.457698 0.228849 0.973462i \(-0.426504\pi\)
0.228849 + 0.973462i \(0.426504\pi\)
\(308\) 0 0
\(309\) −0.322159 −0.0183270
\(310\) 0 0
\(311\) 23.7129 1.34464 0.672318 0.740263i \(-0.265299\pi\)
0.672318 + 0.740263i \(0.265299\pi\)
\(312\) 0 0
\(313\) −27.6785 −1.56448 −0.782242 0.622975i \(-0.785924\pi\)
−0.782242 + 0.622975i \(0.785924\pi\)
\(314\) 0 0
\(315\) −95.2438 −5.36638
\(316\) 0 0
\(317\) −21.0060 −1.17981 −0.589907 0.807471i \(-0.700836\pi\)
−0.589907 + 0.807471i \(0.700836\pi\)
\(318\) 0 0
\(319\) 7.17496 0.401721
\(320\) 0 0
\(321\) −50.6352 −2.82618
\(322\) 0 0
\(323\) −12.1619 −0.676707
\(324\) 0 0
\(325\) 31.3081 1.73666
\(326\) 0 0
\(327\) −20.4597 −1.13143
\(328\) 0 0
\(329\) −38.1373 −2.10258
\(330\) 0 0
\(331\) −5.87277 −0.322796 −0.161398 0.986889i \(-0.551600\pi\)
−0.161398 + 0.986889i \(0.551600\pi\)
\(332\) 0 0
\(333\) −4.23030 −0.231819
\(334\) 0 0
\(335\) 54.1144 2.95659
\(336\) 0 0
\(337\) −25.0951 −1.36702 −0.683508 0.729943i \(-0.739547\pi\)
−0.683508 + 0.729943i \(0.739547\pi\)
\(338\) 0 0
\(339\) 44.4615 2.41482
\(340\) 0 0
\(341\) −1.39161 −0.0753598
\(342\) 0 0
\(343\) −9.89195 −0.534115
\(344\) 0 0
\(345\) 66.5871 3.58493
\(346\) 0 0
\(347\) −28.6888 −1.54010 −0.770048 0.637986i \(-0.779768\pi\)
−0.770048 + 0.637986i \(0.779768\pi\)
\(348\) 0 0
\(349\) −0.227950 −0.0122019 −0.00610093 0.999981i \(-0.501942\pi\)
−0.00610093 + 0.999981i \(0.501942\pi\)
\(350\) 0 0
\(351\) 27.7928 1.48347
\(352\) 0 0
\(353\) 3.91068 0.208144 0.104072 0.994570i \(-0.466813\pi\)
0.104072 + 0.994570i \(0.466813\pi\)
\(354\) 0 0
\(355\) −0.0926939 −0.00491968
\(356\) 0 0
\(357\) −29.1362 −1.54205
\(358\) 0 0
\(359\) 19.2834 1.01774 0.508870 0.860843i \(-0.330063\pi\)
0.508870 + 0.860843i \(0.330063\pi\)
\(360\) 0 0
\(361\) 6.83958 0.359978
\(362\) 0 0
\(363\) −29.0119 −1.52273
\(364\) 0 0
\(365\) 7.69437 0.402742
\(366\) 0 0
\(367\) −27.9097 −1.45687 −0.728437 0.685113i \(-0.759753\pi\)
−0.728437 + 0.685113i \(0.759753\pi\)
\(368\) 0 0
\(369\) 19.2987 1.00465
\(370\) 0 0
\(371\) −9.91062 −0.514534
\(372\) 0 0
\(373\) −4.58737 −0.237525 −0.118762 0.992923i \(-0.537893\pi\)
−0.118762 + 0.992923i \(0.537893\pi\)
\(374\) 0 0
\(375\) 61.1806 3.15935
\(376\) 0 0
\(377\) −18.9814 −0.977592
\(378\) 0 0
\(379\) −2.24248 −0.115189 −0.0575943 0.998340i \(-0.518343\pi\)
−0.0575943 + 0.998340i \(0.518343\pi\)
\(380\) 0 0
\(381\) −17.1466 −0.878447
\(382\) 0 0
\(383\) −34.1039 −1.74263 −0.871315 0.490724i \(-0.836732\pi\)
−0.871315 + 0.490724i \(0.836732\pi\)
\(384\) 0 0
\(385\) 18.3156 0.933447
\(386\) 0 0
\(387\) 5.13164 0.260856
\(388\) 0 0
\(389\) 23.2078 1.17668 0.588342 0.808612i \(-0.299781\pi\)
0.588342 + 0.808612i \(0.299781\pi\)
\(390\) 0 0
\(391\) 13.5956 0.687561
\(392\) 0 0
\(393\) 7.56965 0.381838
\(394\) 0 0
\(395\) −44.2897 −2.22846
\(396\) 0 0
\(397\) 18.2947 0.918182 0.459091 0.888389i \(-0.348175\pi\)
0.459091 + 0.888389i \(0.348175\pi\)
\(398\) 0 0
\(399\) 61.9036 3.09906
\(400\) 0 0
\(401\) −20.1942 −1.00845 −0.504224 0.863573i \(-0.668222\pi\)
−0.504224 + 0.863573i \(0.668222\pi\)
\(402\) 0 0
\(403\) 3.68151 0.183389
\(404\) 0 0
\(405\) 35.8509 1.78144
\(406\) 0 0
\(407\) 0.813494 0.0403234
\(408\) 0 0
\(409\) −6.90809 −0.341583 −0.170791 0.985307i \(-0.554632\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(410\) 0 0
\(411\) 55.6658 2.74579
\(412\) 0 0
\(413\) −33.5784 −1.65229
\(414\) 0 0
\(415\) −55.7899 −2.73862
\(416\) 0 0
\(417\) −5.66594 −0.277462
\(418\) 0 0
\(419\) 32.8613 1.60538 0.802689 0.596397i \(-0.203402\pi\)
0.802689 + 0.596397i \(0.203402\pi\)
\(420\) 0 0
\(421\) 3.32397 0.162000 0.0810002 0.996714i \(-0.474189\pi\)
0.0810002 + 0.996714i \(0.474189\pi\)
\(422\) 0 0
\(423\) 56.6330 2.75359
\(424\) 0 0
\(425\) 24.4544 1.18621
\(426\) 0 0
\(427\) −40.9389 −1.98117
\(428\) 0 0
\(429\) −10.6521 −0.514288
\(430\) 0 0
\(431\) −0.563527 −0.0271442 −0.0135721 0.999908i \(-0.504320\pi\)
−0.0135721 + 0.999908i \(0.504320\pi\)
\(432\) 0 0
\(433\) −34.6983 −1.66749 −0.833746 0.552148i \(-0.813808\pi\)
−0.833746 + 0.552148i \(0.813808\pi\)
\(434\) 0 0
\(435\) −72.6138 −3.48157
\(436\) 0 0
\(437\) −28.8857 −1.38179
\(438\) 0 0
\(439\) −8.95916 −0.427597 −0.213799 0.976878i \(-0.568584\pi\)
−0.213799 + 0.976878i \(0.568584\pi\)
\(440\) 0 0
\(441\) 56.8361 2.70648
\(442\) 0 0
\(443\) −37.2674 −1.77063 −0.885314 0.464993i \(-0.846057\pi\)
−0.885314 + 0.464993i \(0.846057\pi\)
\(444\) 0 0
\(445\) −37.6369 −1.78416
\(446\) 0 0
\(447\) 43.6552 2.06482
\(448\) 0 0
\(449\) 23.1091 1.09058 0.545292 0.838246i \(-0.316419\pi\)
0.545292 + 0.838246i \(0.316419\pi\)
\(450\) 0 0
\(451\) −3.71117 −0.174752
\(452\) 0 0
\(453\) 15.3573 0.721549
\(454\) 0 0
\(455\) −48.4539 −2.27156
\(456\) 0 0
\(457\) −4.86020 −0.227350 −0.113675 0.993518i \(-0.536262\pi\)
−0.113675 + 0.993518i \(0.536262\pi\)
\(458\) 0 0
\(459\) 21.7086 1.01327
\(460\) 0 0
\(461\) 18.9215 0.881261 0.440630 0.897689i \(-0.354755\pi\)
0.440630 + 0.897689i \(0.354755\pi\)
\(462\) 0 0
\(463\) −1.98053 −0.0920429 −0.0460215 0.998940i \(-0.514654\pi\)
−0.0460215 + 0.998940i \(0.514654\pi\)
\(464\) 0 0
\(465\) 14.0837 0.653116
\(466\) 0 0
\(467\) 0.206755 0.00956749 0.00478375 0.999989i \(-0.498477\pi\)
0.00478375 + 0.999989i \(0.498477\pi\)
\(468\) 0 0
\(469\) −56.2389 −2.59687
\(470\) 0 0
\(471\) −58.9276 −2.71524
\(472\) 0 0
\(473\) −0.986823 −0.0453742
\(474\) 0 0
\(475\) −51.9567 −2.38393
\(476\) 0 0
\(477\) 14.7170 0.673847
\(478\) 0 0
\(479\) 11.8039 0.539333 0.269667 0.962954i \(-0.413086\pi\)
0.269667 + 0.962954i \(0.413086\pi\)
\(480\) 0 0
\(481\) −2.15210 −0.0981275
\(482\) 0 0
\(483\) −69.2012 −3.14876
\(484\) 0 0
\(485\) −19.2604 −0.874571
\(486\) 0 0
\(487\) −12.1579 −0.550925 −0.275462 0.961312i \(-0.588831\pi\)
−0.275462 + 0.961312i \(0.588831\pi\)
\(488\) 0 0
\(489\) −46.7909 −2.11596
\(490\) 0 0
\(491\) 14.6769 0.662357 0.331179 0.943568i \(-0.392554\pi\)
0.331179 + 0.943568i \(0.392554\pi\)
\(492\) 0 0
\(493\) −14.8262 −0.667736
\(494\) 0 0
\(495\) −27.1982 −1.22247
\(496\) 0 0
\(497\) 0.0963330 0.00432112
\(498\) 0 0
\(499\) 2.63326 0.117881 0.0589403 0.998262i \(-0.481228\pi\)
0.0589403 + 0.998262i \(0.481228\pi\)
\(500\) 0 0
\(501\) −28.8785 −1.29019
\(502\) 0 0
\(503\) 5.48187 0.244425 0.122212 0.992504i \(-0.461001\pi\)
0.122212 + 0.992504i \(0.461001\pi\)
\(504\) 0 0
\(505\) 73.2421 3.25923
\(506\) 0 0
\(507\) −10.8652 −0.482540
\(508\) 0 0
\(509\) −10.8677 −0.481703 −0.240852 0.970562i \(-0.577427\pi\)
−0.240852 + 0.970562i \(0.577427\pi\)
\(510\) 0 0
\(511\) −7.99644 −0.353742
\(512\) 0 0
\(513\) −46.1228 −2.03637
\(514\) 0 0
\(515\) −0.418472 −0.0184401
\(516\) 0 0
\(517\) −10.8906 −0.478969
\(518\) 0 0
\(519\) −47.4702 −2.08371
\(520\) 0 0
\(521\) −22.7378 −0.996161 −0.498081 0.867131i \(-0.665962\pi\)
−0.498081 + 0.867131i \(0.665962\pi\)
\(522\) 0 0
\(523\) −4.29385 −0.187757 −0.0938784 0.995584i \(-0.529927\pi\)
−0.0938784 + 0.995584i \(0.529927\pi\)
\(524\) 0 0
\(525\) −124.472 −5.43241
\(526\) 0 0
\(527\) 2.87558 0.125262
\(528\) 0 0
\(529\) 9.29093 0.403953
\(530\) 0 0
\(531\) 49.8632 2.16388
\(532\) 0 0
\(533\) 9.81793 0.425262
\(534\) 0 0
\(535\) −65.7732 −2.84362
\(536\) 0 0
\(537\) −26.0246 −1.12305
\(538\) 0 0
\(539\) −10.9297 −0.470775
\(540\) 0 0
\(541\) 3.58128 0.153971 0.0769855 0.997032i \(-0.475470\pi\)
0.0769855 + 0.997032i \(0.475470\pi\)
\(542\) 0 0
\(543\) 46.6336 2.00124
\(544\) 0 0
\(545\) −26.5764 −1.13841
\(546\) 0 0
\(547\) 18.6549 0.797624 0.398812 0.917033i \(-0.369423\pi\)
0.398812 + 0.917033i \(0.369423\pi\)
\(548\) 0 0
\(549\) 60.7933 2.59459
\(550\) 0 0
\(551\) 31.5001 1.34195
\(552\) 0 0
\(553\) 46.0284 1.95733
\(554\) 0 0
\(555\) −8.23293 −0.349468
\(556\) 0 0
\(557\) 15.6996 0.665213 0.332607 0.943066i \(-0.392072\pi\)
0.332607 + 0.943066i \(0.392072\pi\)
\(558\) 0 0
\(559\) 2.61065 0.110419
\(560\) 0 0
\(561\) −8.32024 −0.351281
\(562\) 0 0
\(563\) 30.0469 1.26633 0.633163 0.774018i \(-0.281756\pi\)
0.633163 + 0.774018i \(0.281756\pi\)
\(564\) 0 0
\(565\) 57.7538 2.42972
\(566\) 0 0
\(567\) −37.2583 −1.56470
\(568\) 0 0
\(569\) 42.4359 1.77900 0.889502 0.456931i \(-0.151051\pi\)
0.889502 + 0.456931i \(0.151051\pi\)
\(570\) 0 0
\(571\) −43.0387 −1.80111 −0.900557 0.434738i \(-0.856841\pi\)
−0.900557 + 0.434738i \(0.856841\pi\)
\(572\) 0 0
\(573\) −35.5482 −1.48505
\(574\) 0 0
\(575\) 58.0816 2.42217
\(576\) 0 0
\(577\) 11.4394 0.476226 0.238113 0.971237i \(-0.423471\pi\)
0.238113 + 0.971237i \(0.423471\pi\)
\(578\) 0 0
\(579\) −34.2333 −1.42269
\(580\) 0 0
\(581\) 57.9801 2.40542
\(582\) 0 0
\(583\) −2.83011 −0.117211
\(584\) 0 0
\(585\) 71.9530 2.97489
\(586\) 0 0
\(587\) −41.6737 −1.72006 −0.860029 0.510245i \(-0.829555\pi\)
−0.860029 + 0.510245i \(0.829555\pi\)
\(588\) 0 0
\(589\) −6.10955 −0.251740
\(590\) 0 0
\(591\) 40.5941 1.66982
\(592\) 0 0
\(593\) 26.1597 1.07425 0.537126 0.843502i \(-0.319510\pi\)
0.537126 + 0.843502i \(0.319510\pi\)
\(594\) 0 0
\(595\) −37.8468 −1.55157
\(596\) 0 0
\(597\) −51.0835 −2.09071
\(598\) 0 0
\(599\) −26.5297 −1.08397 −0.541987 0.840387i \(-0.682328\pi\)
−0.541987 + 0.840387i \(0.682328\pi\)
\(600\) 0 0
\(601\) −6.94788 −0.283410 −0.141705 0.989909i \(-0.545258\pi\)
−0.141705 + 0.989909i \(0.545258\pi\)
\(602\) 0 0
\(603\) 83.5134 3.40093
\(604\) 0 0
\(605\) −37.6854 −1.53213
\(606\) 0 0
\(607\) 8.63243 0.350380 0.175190 0.984535i \(-0.443946\pi\)
0.175190 + 0.984535i \(0.443946\pi\)
\(608\) 0 0
\(609\) 75.4645 3.05798
\(610\) 0 0
\(611\) 28.8112 1.16558
\(612\) 0 0
\(613\) −35.9695 −1.45279 −0.726396 0.687276i \(-0.758806\pi\)
−0.726396 + 0.687276i \(0.758806\pi\)
\(614\) 0 0
\(615\) 37.5587 1.51451
\(616\) 0 0
\(617\) −30.0267 −1.20883 −0.604415 0.796670i \(-0.706593\pi\)
−0.604415 + 0.796670i \(0.706593\pi\)
\(618\) 0 0
\(619\) 18.4891 0.743139 0.371569 0.928405i \(-0.378820\pi\)
0.371569 + 0.928405i \(0.378820\pi\)
\(620\) 0 0
\(621\) 51.5601 2.06903
\(622\) 0 0
\(623\) 39.1144 1.56709
\(624\) 0 0
\(625\) 28.3657 1.13463
\(626\) 0 0
\(627\) 17.6774 0.705969
\(628\) 0 0
\(629\) −1.68098 −0.0670252
\(630\) 0 0
\(631\) −5.17204 −0.205896 −0.102948 0.994687i \(-0.532827\pi\)
−0.102948 + 0.994687i \(0.532827\pi\)
\(632\) 0 0
\(633\) 29.1676 1.15931
\(634\) 0 0
\(635\) −22.2728 −0.883869
\(636\) 0 0
\(637\) 28.9146 1.14564
\(638\) 0 0
\(639\) −0.143052 −0.00565906
\(640\) 0 0
\(641\) −16.9314 −0.668750 −0.334375 0.942440i \(-0.608525\pi\)
−0.334375 + 0.942440i \(0.608525\pi\)
\(642\) 0 0
\(643\) 45.4872 1.79384 0.896920 0.442193i \(-0.145799\pi\)
0.896920 + 0.442193i \(0.145799\pi\)
\(644\) 0 0
\(645\) 9.98710 0.393242
\(646\) 0 0
\(647\) 33.7207 1.32570 0.662848 0.748754i \(-0.269348\pi\)
0.662848 + 0.748754i \(0.269348\pi\)
\(648\) 0 0
\(649\) −9.58878 −0.376393
\(650\) 0 0
\(651\) −14.6366 −0.573654
\(652\) 0 0
\(653\) 42.3457 1.65711 0.828557 0.559904i \(-0.189162\pi\)
0.828557 + 0.559904i \(0.189162\pi\)
\(654\) 0 0
\(655\) 9.83270 0.384195
\(656\) 0 0
\(657\) 11.8745 0.463269
\(658\) 0 0
\(659\) −49.8143 −1.94049 −0.970244 0.242129i \(-0.922154\pi\)
−0.970244 + 0.242129i \(0.922154\pi\)
\(660\) 0 0
\(661\) 14.5547 0.566114 0.283057 0.959103i \(-0.408651\pi\)
0.283057 + 0.959103i \(0.408651\pi\)
\(662\) 0 0
\(663\) 22.0112 0.854846
\(664\) 0 0
\(665\) 80.4105 3.11819
\(666\) 0 0
\(667\) −35.2135 −1.36347
\(668\) 0 0
\(669\) 61.5681 2.38036
\(670\) 0 0
\(671\) −11.6907 −0.451313
\(672\) 0 0
\(673\) −24.8922 −0.959523 −0.479761 0.877399i \(-0.659277\pi\)
−0.479761 + 0.877399i \(0.659277\pi\)
\(674\) 0 0
\(675\) 92.7410 3.56960
\(676\) 0 0
\(677\) 30.3177 1.16520 0.582601 0.812758i \(-0.302035\pi\)
0.582601 + 0.812758i \(0.302035\pi\)
\(678\) 0 0
\(679\) 20.0166 0.768165
\(680\) 0 0
\(681\) 0.752647 0.0288415
\(682\) 0 0
\(683\) 20.0088 0.765616 0.382808 0.923828i \(-0.374957\pi\)
0.382808 + 0.923828i \(0.374957\pi\)
\(684\) 0 0
\(685\) 72.3078 2.76274
\(686\) 0 0
\(687\) −66.4490 −2.53519
\(688\) 0 0
\(689\) 7.48709 0.285235
\(690\) 0 0
\(691\) 37.5242 1.42749 0.713744 0.700406i \(-0.246998\pi\)
0.713744 + 0.700406i \(0.246998\pi\)
\(692\) 0 0
\(693\) 28.2659 1.07373
\(694\) 0 0
\(695\) −7.35984 −0.279175
\(696\) 0 0
\(697\) 7.66867 0.290471
\(698\) 0 0
\(699\) −20.1530 −0.762256
\(700\) 0 0
\(701\) −28.8949 −1.09134 −0.545672 0.837999i \(-0.683726\pi\)
−0.545672 + 0.837999i \(0.683726\pi\)
\(702\) 0 0
\(703\) 3.57147 0.134701
\(704\) 0 0
\(705\) 110.218 4.15106
\(706\) 0 0
\(707\) −76.1174 −2.86269
\(708\) 0 0
\(709\) 4.28959 0.161099 0.0805495 0.996751i \(-0.474332\pi\)
0.0805495 + 0.996751i \(0.474332\pi\)
\(710\) 0 0
\(711\) −68.3511 −2.56337
\(712\) 0 0
\(713\) 6.82979 0.255777
\(714\) 0 0
\(715\) −13.8367 −0.517463
\(716\) 0 0
\(717\) −32.6374 −1.21887
\(718\) 0 0
\(719\) −28.0572 −1.04636 −0.523179 0.852223i \(-0.675254\pi\)
−0.523179 + 0.852223i \(0.675254\pi\)
\(720\) 0 0
\(721\) 0.434901 0.0161965
\(722\) 0 0
\(723\) −3.53322 −0.131402
\(724\) 0 0
\(725\) −63.3385 −2.35233
\(726\) 0 0
\(727\) −41.5405 −1.54065 −0.770327 0.637649i \(-0.779907\pi\)
−0.770327 + 0.637649i \(0.779907\pi\)
\(728\) 0 0
\(729\) −26.4285 −0.978833
\(730\) 0 0
\(731\) 2.03915 0.0754206
\(732\) 0 0
\(733\) 51.3178 1.89547 0.947733 0.319065i \(-0.103369\pi\)
0.947733 + 0.319065i \(0.103369\pi\)
\(734\) 0 0
\(735\) 110.613 4.08004
\(736\) 0 0
\(737\) −16.0598 −0.591570
\(738\) 0 0
\(739\) 6.61636 0.243387 0.121693 0.992568i \(-0.461168\pi\)
0.121693 + 0.992568i \(0.461168\pi\)
\(740\) 0 0
\(741\) −46.7658 −1.71798
\(742\) 0 0
\(743\) 46.8632 1.71924 0.859622 0.510930i \(-0.170699\pi\)
0.859622 + 0.510930i \(0.170699\pi\)
\(744\) 0 0
\(745\) 56.7065 2.07757
\(746\) 0 0
\(747\) −86.0991 −3.15020
\(748\) 0 0
\(749\) 68.3554 2.49765
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −59.8069 −2.17948
\(754\) 0 0
\(755\) 19.9486 0.726002
\(756\) 0 0
\(757\) 23.4260 0.851432 0.425716 0.904857i \(-0.360022\pi\)
0.425716 + 0.904857i \(0.360022\pi\)
\(758\) 0 0
\(759\) −19.7614 −0.717292
\(760\) 0 0
\(761\) −25.8260 −0.936191 −0.468096 0.883678i \(-0.655060\pi\)
−0.468096 + 0.883678i \(0.655060\pi\)
\(762\) 0 0
\(763\) 27.6198 0.999904
\(764\) 0 0
\(765\) 56.2016 2.03197
\(766\) 0 0
\(767\) 25.3672 0.915956
\(768\) 0 0
\(769\) −30.5921 −1.10318 −0.551590 0.834116i \(-0.685979\pi\)
−0.551590 + 0.834116i \(0.685979\pi\)
\(770\) 0 0
\(771\) −44.3104 −1.59580
\(772\) 0 0
\(773\) −25.6287 −0.921799 −0.460900 0.887452i \(-0.652473\pi\)
−0.460900 + 0.887452i \(0.652473\pi\)
\(774\) 0 0
\(775\) 12.2847 0.441280
\(776\) 0 0
\(777\) 8.55614 0.306950
\(778\) 0 0
\(779\) −16.2931 −0.583761
\(780\) 0 0
\(781\) 0.0275092 0.000984357 0
\(782\) 0 0
\(783\) −56.2267 −2.00938
\(784\) 0 0
\(785\) −76.5447 −2.73200
\(786\) 0 0
\(787\) 11.9337 0.425392 0.212696 0.977118i \(-0.431776\pi\)
0.212696 + 0.977118i \(0.431776\pi\)
\(788\) 0 0
\(789\) 71.6864 2.55210
\(790\) 0 0
\(791\) −60.0212 −2.13411
\(792\) 0 0
\(793\) 30.9277 1.09828
\(794\) 0 0
\(795\) 28.6420 1.01583
\(796\) 0 0
\(797\) −13.0053 −0.460670 −0.230335 0.973111i \(-0.573982\pi\)
−0.230335 + 0.973111i \(0.573982\pi\)
\(798\) 0 0
\(799\) 22.5041 0.796139
\(800\) 0 0
\(801\) −58.0840 −2.05230
\(802\) 0 0
\(803\) −2.28349 −0.0805827
\(804\) 0 0
\(805\) −89.8898 −3.16820
\(806\) 0 0
\(807\) 26.5551 0.934782
\(808\) 0 0
\(809\) 30.5912 1.07553 0.537765 0.843095i \(-0.319269\pi\)
0.537765 + 0.843095i \(0.319269\pi\)
\(810\) 0 0
\(811\) −9.49311 −0.333348 −0.166674 0.986012i \(-0.553303\pi\)
−0.166674 + 0.986012i \(0.553303\pi\)
\(812\) 0 0
\(813\) 23.3465 0.818798
\(814\) 0 0
\(815\) −60.7796 −2.12902
\(816\) 0 0
\(817\) −4.33244 −0.151573
\(818\) 0 0
\(819\) −74.7777 −2.61295
\(820\) 0 0
\(821\) 45.9272 1.60287 0.801435 0.598081i \(-0.204070\pi\)
0.801435 + 0.598081i \(0.204070\pi\)
\(822\) 0 0
\(823\) −12.7332 −0.443852 −0.221926 0.975064i \(-0.571234\pi\)
−0.221926 + 0.975064i \(0.571234\pi\)
\(824\) 0 0
\(825\) −35.5447 −1.23751
\(826\) 0 0
\(827\) 1.63891 0.0569906 0.0284953 0.999594i \(-0.490928\pi\)
0.0284953 + 0.999594i \(0.490928\pi\)
\(828\) 0 0
\(829\) 0.733575 0.0254781 0.0127391 0.999919i \(-0.495945\pi\)
0.0127391 + 0.999919i \(0.495945\pi\)
\(830\) 0 0
\(831\) −48.4897 −1.68209
\(832\) 0 0
\(833\) 22.5848 0.782518
\(834\) 0 0
\(835\) −37.5120 −1.29816
\(836\) 0 0
\(837\) 10.9054 0.376944
\(838\) 0 0
\(839\) −4.17085 −0.143994 −0.0719968 0.997405i \(-0.522937\pi\)
−0.0719968 + 0.997405i \(0.522937\pi\)
\(840\) 0 0
\(841\) 9.40069 0.324162
\(842\) 0 0
\(843\) 97.4427 3.35610
\(844\) 0 0
\(845\) −14.1135 −0.485518
\(846\) 0 0
\(847\) 39.1649 1.34572
\(848\) 0 0
\(849\) −64.3956 −2.21005
\(850\) 0 0
\(851\) −3.99250 −0.136861
\(852\) 0 0
\(853\) −30.0380 −1.02848 −0.514240 0.857646i \(-0.671926\pi\)
−0.514240 + 0.857646i \(0.671926\pi\)
\(854\) 0 0
\(855\) −119.408 −4.08366
\(856\) 0 0
\(857\) −38.5241 −1.31596 −0.657979 0.753036i \(-0.728588\pi\)
−0.657979 + 0.753036i \(0.728588\pi\)
\(858\) 0 0
\(859\) 47.3399 1.61522 0.807608 0.589720i \(-0.200762\pi\)
0.807608 + 0.589720i \(0.200762\pi\)
\(860\) 0 0
\(861\) −39.0332 −1.33025
\(862\) 0 0
\(863\) −14.2960 −0.486642 −0.243321 0.969946i \(-0.578237\pi\)
−0.243321 + 0.969946i \(0.578237\pi\)
\(864\) 0 0
\(865\) −61.6620 −2.09657
\(866\) 0 0
\(867\) −33.8667 −1.15017
\(868\) 0 0
\(869\) 13.1441 0.445881
\(870\) 0 0
\(871\) 42.4863 1.43959
\(872\) 0 0
\(873\) −29.7241 −1.00601
\(874\) 0 0
\(875\) −82.5912 −2.79209
\(876\) 0 0
\(877\) −0.720461 −0.0243282 −0.0121641 0.999926i \(-0.503872\pi\)
−0.0121641 + 0.999926i \(0.503872\pi\)
\(878\) 0 0
\(879\) 42.8888 1.44660
\(880\) 0 0
\(881\) 44.7151 1.50649 0.753245 0.657740i \(-0.228487\pi\)
0.753245 + 0.657740i \(0.228487\pi\)
\(882\) 0 0
\(883\) −29.3774 −0.988629 −0.494314 0.869283i \(-0.664581\pi\)
−0.494314 + 0.869283i \(0.664581\pi\)
\(884\) 0 0
\(885\) 97.0428 3.26206
\(886\) 0 0
\(887\) 25.2596 0.848133 0.424067 0.905631i \(-0.360602\pi\)
0.424067 + 0.905631i \(0.360602\pi\)
\(888\) 0 0
\(889\) 23.1472 0.776332
\(890\) 0 0
\(891\) −10.6396 −0.356441
\(892\) 0 0
\(893\) −47.8130 −1.60000
\(894\) 0 0
\(895\) −33.8050 −1.12998
\(896\) 0 0
\(897\) 52.2788 1.74554
\(898\) 0 0
\(899\) −7.44794 −0.248403
\(900\) 0 0
\(901\) 5.84808 0.194828
\(902\) 0 0
\(903\) −10.3792 −0.345397
\(904\) 0 0
\(905\) 60.5753 2.01359
\(906\) 0 0
\(907\) 12.3854 0.411252 0.205626 0.978631i \(-0.434077\pi\)
0.205626 + 0.978631i \(0.434077\pi\)
\(908\) 0 0
\(909\) 113.033 3.74906
\(910\) 0 0
\(911\) 12.0835 0.400345 0.200173 0.979761i \(-0.435850\pi\)
0.200173 + 0.979761i \(0.435850\pi\)
\(912\) 0 0
\(913\) 16.5570 0.547957
\(914\) 0 0
\(915\) 118.315 3.91137
\(916\) 0 0
\(917\) −10.2187 −0.337452
\(918\) 0 0
\(919\) −26.0939 −0.860758 −0.430379 0.902648i \(-0.641620\pi\)
−0.430379 + 0.902648i \(0.641620\pi\)
\(920\) 0 0
\(921\) 24.0866 0.793679
\(922\) 0 0
\(923\) −0.0727758 −0.00239544
\(924\) 0 0
\(925\) −7.18130 −0.236120
\(926\) 0 0
\(927\) −0.645817 −0.0212114
\(928\) 0 0
\(929\) 12.5428 0.411517 0.205759 0.978603i \(-0.434034\pi\)
0.205759 + 0.978603i \(0.434034\pi\)
\(930\) 0 0
\(931\) −47.9845 −1.57263
\(932\) 0 0
\(933\) 71.2215 2.33169
\(934\) 0 0
\(935\) −10.8077 −0.353449
\(936\) 0 0
\(937\) 14.8980 0.486697 0.243348 0.969939i \(-0.421754\pi\)
0.243348 + 0.969939i \(0.421754\pi\)
\(938\) 0 0
\(939\) −83.1323 −2.71292
\(940\) 0 0
\(941\) 26.1199 0.851485 0.425743 0.904844i \(-0.360013\pi\)
0.425743 + 0.904844i \(0.360013\pi\)
\(942\) 0 0
\(943\) 18.2138 0.593124
\(944\) 0 0
\(945\) −143.530 −4.66904
\(946\) 0 0
\(947\) −38.9973 −1.26724 −0.633620 0.773644i \(-0.718432\pi\)
−0.633620 + 0.773644i \(0.718432\pi\)
\(948\) 0 0
\(949\) 6.04100 0.196099
\(950\) 0 0
\(951\) −63.0914 −2.04588
\(952\) 0 0
\(953\) 15.9205 0.515715 0.257858 0.966183i \(-0.416983\pi\)
0.257858 + 0.966183i \(0.416983\pi\)
\(954\) 0 0
\(955\) −46.1758 −1.49422
\(956\) 0 0
\(957\) 21.5499 0.696611
\(958\) 0 0
\(959\) −75.1465 −2.42661
\(960\) 0 0
\(961\) −29.5554 −0.953402
\(962\) 0 0
\(963\) −101.506 −3.27099
\(964\) 0 0
\(965\) −44.4677 −1.43147
\(966\) 0 0
\(967\) 36.4744 1.17294 0.586470 0.809971i \(-0.300517\pi\)
0.586470 + 0.809971i \(0.300517\pi\)
\(968\) 0 0
\(969\) −36.5282 −1.17346
\(970\) 0 0
\(971\) 19.2365 0.617328 0.308664 0.951171i \(-0.400118\pi\)
0.308664 + 0.951171i \(0.400118\pi\)
\(972\) 0 0
\(973\) 7.64877 0.245208
\(974\) 0 0
\(975\) 94.0338 3.01149
\(976\) 0 0
\(977\) −2.59668 −0.0830751 −0.0415375 0.999137i \(-0.513226\pi\)
−0.0415375 + 0.999137i \(0.513226\pi\)
\(978\) 0 0
\(979\) 11.1697 0.356984
\(980\) 0 0
\(981\) −41.0148 −1.30950
\(982\) 0 0
\(983\) 14.7358 0.469998 0.234999 0.971996i \(-0.424491\pi\)
0.234999 + 0.971996i \(0.424491\pi\)
\(984\) 0 0
\(985\) 52.7302 1.68012
\(986\) 0 0
\(987\) −114.545 −3.64601
\(988\) 0 0
\(989\) 4.84317 0.154004
\(990\) 0 0
\(991\) 36.8704 1.17123 0.585614 0.810590i \(-0.300854\pi\)
0.585614 + 0.810590i \(0.300854\pi\)
\(992\) 0 0
\(993\) −17.6388 −0.559751
\(994\) 0 0
\(995\) −66.3556 −2.10361
\(996\) 0 0
\(997\) −24.1457 −0.764703 −0.382352 0.924017i \(-0.624886\pi\)
−0.382352 + 0.924017i \(0.624886\pi\)
\(998\) 0 0
\(999\) −6.37496 −0.201695
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 \(a_p\))