Properties

Label 6008.2.a.e.1.30
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 1.30
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.765267 q^{3} +3.23588 q^{5} -3.39376 q^{7} -2.41437 q^{9} +O(q^{10})\) \(q+0.765267 q^{3} +3.23588 q^{5} -3.39376 q^{7} -2.41437 q^{9} -5.84859 q^{11} -4.58513 q^{13} +2.47631 q^{15} +2.17872 q^{17} +0.556540 q^{19} -2.59714 q^{21} +6.51662 q^{23} +5.47091 q^{25} -4.14344 q^{27} +8.72546 q^{29} +3.80343 q^{31} -4.47574 q^{33} -10.9818 q^{35} +8.20409 q^{37} -3.50885 q^{39} +4.82551 q^{41} +11.5830 q^{43} -7.81259 q^{45} -5.50981 q^{47} +4.51764 q^{49} +1.66730 q^{51} -13.2072 q^{53} -18.9253 q^{55} +0.425901 q^{57} -13.9115 q^{59} -3.42295 q^{61} +8.19379 q^{63} -14.8369 q^{65} +6.71360 q^{67} +4.98695 q^{69} +4.59076 q^{71} +6.05739 q^{73} +4.18671 q^{75} +19.8487 q^{77} -7.64089 q^{79} +4.07226 q^{81} +13.5018 q^{83} +7.05007 q^{85} +6.67731 q^{87} +10.9998 q^{89} +15.5608 q^{91} +2.91064 q^{93} +1.80089 q^{95} -1.70386 q^{97} +14.1206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 0.765267 0.441827 0.220914 0.975293i \(-0.429096\pi\)
0.220914 + 0.975293i \(0.429096\pi\)
\(4\) 0 0
\(5\) 3.23588 1.44713 0.723564 0.690257i \(-0.242502\pi\)
0.723564 + 0.690257i \(0.242502\pi\)
\(6\) 0 0
\(7\) −3.39376 −1.28272 −0.641361 0.767239i \(-0.721630\pi\)
−0.641361 + 0.767239i \(0.721630\pi\)
\(8\) 0 0
\(9\) −2.41437 −0.804789
\(10\) 0 0
\(11\) −5.84859 −1.76342 −0.881709 0.471794i \(-0.843606\pi\)
−0.881709 + 0.471794i \(0.843606\pi\)
\(12\) 0 0
\(13\) −4.58513 −1.27169 −0.635843 0.771819i \(-0.719347\pi\)
−0.635843 + 0.771819i \(0.719347\pi\)
\(14\) 0 0
\(15\) 2.47631 0.639381
\(16\) 0 0
\(17\) 2.17872 0.528417 0.264209 0.964466i \(-0.414889\pi\)
0.264209 + 0.964466i \(0.414889\pi\)
\(18\) 0 0
\(19\) 0.556540 0.127679 0.0638395 0.997960i \(-0.479665\pi\)
0.0638395 + 0.997960i \(0.479665\pi\)
\(20\) 0 0
\(21\) −2.59714 −0.566742
\(22\) 0 0
\(23\) 6.51662 1.35881 0.679404 0.733764i \(-0.262238\pi\)
0.679404 + 0.733764i \(0.262238\pi\)
\(24\) 0 0
\(25\) 5.47091 1.09418
\(26\) 0 0
\(27\) −4.14344 −0.797405
\(28\) 0 0
\(29\) 8.72546 1.62028 0.810138 0.586239i \(-0.199392\pi\)
0.810138 + 0.586239i \(0.199392\pi\)
\(30\) 0 0
\(31\) 3.80343 0.683116 0.341558 0.939861i \(-0.389045\pi\)
0.341558 + 0.939861i \(0.389045\pi\)
\(32\) 0 0
\(33\) −4.47574 −0.779126
\(34\) 0 0
\(35\) −10.9818 −1.85626
\(36\) 0 0
\(37\) 8.20409 1.34874 0.674372 0.738392i \(-0.264415\pi\)
0.674372 + 0.738392i \(0.264415\pi\)
\(38\) 0 0
\(39\) −3.50885 −0.561865
\(40\) 0 0
\(41\) 4.82551 0.753619 0.376809 0.926291i \(-0.377021\pi\)
0.376809 + 0.926291i \(0.377021\pi\)
\(42\) 0 0
\(43\) 11.5830 1.76640 0.883199 0.468998i \(-0.155385\pi\)
0.883199 + 0.468998i \(0.155385\pi\)
\(44\) 0 0
\(45\) −7.81259 −1.16463
\(46\) 0 0
\(47\) −5.50981 −0.803689 −0.401844 0.915708i \(-0.631631\pi\)
−0.401844 + 0.915708i \(0.631631\pi\)
\(48\) 0 0
\(49\) 4.51764 0.645377
\(50\) 0 0
\(51\) 1.66730 0.233469
\(52\) 0 0
\(53\) −13.2072 −1.81415 −0.907077 0.420965i \(-0.861691\pi\)
−0.907077 + 0.420965i \(0.861691\pi\)
\(54\) 0 0
\(55\) −18.9253 −2.55189
\(56\) 0 0
\(57\) 0.425901 0.0564120
\(58\) 0 0
\(59\) −13.9115 −1.81112 −0.905558 0.424222i \(-0.860548\pi\)
−0.905558 + 0.424222i \(0.860548\pi\)
\(60\) 0 0
\(61\) −3.42295 −0.438264 −0.219132 0.975695i \(-0.570322\pi\)
−0.219132 + 0.975695i \(0.570322\pi\)
\(62\) 0 0
\(63\) 8.19379 1.03232
\(64\) 0 0
\(65\) −14.8369 −1.84029
\(66\) 0 0
\(67\) 6.71360 0.820197 0.410098 0.912041i \(-0.365494\pi\)
0.410098 + 0.912041i \(0.365494\pi\)
\(68\) 0 0
\(69\) 4.98695 0.600359
\(70\) 0 0
\(71\) 4.59076 0.544823 0.272411 0.962181i \(-0.412179\pi\)
0.272411 + 0.962181i \(0.412179\pi\)
\(72\) 0 0
\(73\) 6.05739 0.708963 0.354482 0.935063i \(-0.384657\pi\)
0.354482 + 0.935063i \(0.384657\pi\)
\(74\) 0 0
\(75\) 4.18671 0.483439
\(76\) 0 0
\(77\) 19.8487 2.26197
\(78\) 0 0
\(79\) −7.64089 −0.859668 −0.429834 0.902908i \(-0.641428\pi\)
−0.429834 + 0.902908i \(0.641428\pi\)
\(80\) 0 0
\(81\) 4.07226 0.452473
\(82\) 0 0
\(83\) 13.5018 1.48202 0.741008 0.671497i \(-0.234348\pi\)
0.741008 + 0.671497i \(0.234348\pi\)
\(84\) 0 0
\(85\) 7.05007 0.764688
\(86\) 0 0
\(87\) 6.67731 0.715882
\(88\) 0 0
\(89\) 10.9998 1.16598 0.582991 0.812479i \(-0.301882\pi\)
0.582991 + 0.812479i \(0.301882\pi\)
\(90\) 0 0
\(91\) 15.5608 1.63122
\(92\) 0 0
\(93\) 2.91064 0.301819
\(94\) 0 0
\(95\) 1.80089 0.184768
\(96\) 0 0
\(97\) −1.70386 −0.173001 −0.0865005 0.996252i \(-0.527568\pi\)
−0.0865005 + 0.996252i \(0.527568\pi\)
\(98\) 0 0
\(99\) 14.1206 1.41918
\(100\) 0 0
\(101\) 16.0381 1.59585 0.797927 0.602754i \(-0.205930\pi\)
0.797927 + 0.602754i \(0.205930\pi\)
\(102\) 0 0
\(103\) −14.6823 −1.44669 −0.723345 0.690486i \(-0.757397\pi\)
−0.723345 + 0.690486i \(0.757397\pi\)
\(104\) 0 0
\(105\) −8.40402 −0.820148
\(106\) 0 0
\(107\) 13.4319 1.29851 0.649254 0.760572i \(-0.275081\pi\)
0.649254 + 0.760572i \(0.275081\pi\)
\(108\) 0 0
\(109\) 12.4824 1.19560 0.597799 0.801646i \(-0.296042\pi\)
0.597799 + 0.801646i \(0.296042\pi\)
\(110\) 0 0
\(111\) 6.27832 0.595912
\(112\) 0 0
\(113\) 6.66217 0.626725 0.313362 0.949634i \(-0.398545\pi\)
0.313362 + 0.949634i \(0.398545\pi\)
\(114\) 0 0
\(115\) 21.0870 1.96637
\(116\) 0 0
\(117\) 11.0702 1.02344
\(118\) 0 0
\(119\) −7.39406 −0.677813
\(120\) 0 0
\(121\) 23.2060 2.10964
\(122\) 0 0
\(123\) 3.69281 0.332969
\(124\) 0 0
\(125\) 1.52381 0.136294
\(126\) 0 0
\(127\) −15.6062 −1.38482 −0.692412 0.721503i \(-0.743452\pi\)
−0.692412 + 0.721503i \(0.743452\pi\)
\(128\) 0 0
\(129\) 8.86413 0.780443
\(130\) 0 0
\(131\) −7.53692 −0.658504 −0.329252 0.944242i \(-0.606797\pi\)
−0.329252 + 0.944242i \(0.606797\pi\)
\(132\) 0 0
\(133\) −1.88876 −0.163777
\(134\) 0 0
\(135\) −13.4077 −1.15395
\(136\) 0 0
\(137\) 5.17007 0.441708 0.220854 0.975307i \(-0.429115\pi\)
0.220854 + 0.975307i \(0.429115\pi\)
\(138\) 0 0
\(139\) −4.77033 −0.404614 −0.202307 0.979322i \(-0.564844\pi\)
−0.202307 + 0.979322i \(0.564844\pi\)
\(140\) 0 0
\(141\) −4.21648 −0.355092
\(142\) 0 0
\(143\) 26.8165 2.24251
\(144\) 0 0
\(145\) 28.2345 2.34475
\(146\) 0 0
\(147\) 3.45720 0.285145
\(148\) 0 0
\(149\) 12.9819 1.06352 0.531759 0.846896i \(-0.321531\pi\)
0.531759 + 0.846896i \(0.321531\pi\)
\(150\) 0 0
\(151\) −19.2409 −1.56580 −0.782902 0.622145i \(-0.786261\pi\)
−0.782902 + 0.622145i \(0.786261\pi\)
\(152\) 0 0
\(153\) −5.26023 −0.425264
\(154\) 0 0
\(155\) 12.3074 0.988557
\(156\) 0 0
\(157\) 5.20359 0.415292 0.207646 0.978204i \(-0.433420\pi\)
0.207646 + 0.978204i \(0.433420\pi\)
\(158\) 0 0
\(159\) −10.1071 −0.801543
\(160\) 0 0
\(161\) −22.1159 −1.74297
\(162\) 0 0
\(163\) −11.6864 −0.915348 −0.457674 0.889120i \(-0.651317\pi\)
−0.457674 + 0.889120i \(0.651317\pi\)
\(164\) 0 0
\(165\) −14.4829 −1.12750
\(166\) 0 0
\(167\) 10.8175 0.837082 0.418541 0.908198i \(-0.362542\pi\)
0.418541 + 0.908198i \(0.362542\pi\)
\(168\) 0 0
\(169\) 8.02338 0.617183
\(170\) 0 0
\(171\) −1.34369 −0.102755
\(172\) 0 0
\(173\) −15.3019 −1.16338 −0.581690 0.813410i \(-0.697608\pi\)
−0.581690 + 0.813410i \(0.697608\pi\)
\(174\) 0 0
\(175\) −18.5670 −1.40353
\(176\) 0 0
\(177\) −10.6460 −0.800201
\(178\) 0 0
\(179\) 15.4080 1.15165 0.575823 0.817574i \(-0.304682\pi\)
0.575823 + 0.817574i \(0.304682\pi\)
\(180\) 0 0
\(181\) 13.7078 1.01889 0.509445 0.860503i \(-0.329851\pi\)
0.509445 + 0.860503i \(0.329851\pi\)
\(182\) 0 0
\(183\) −2.61947 −0.193637
\(184\) 0 0
\(185\) 26.5474 1.95181
\(186\) 0 0
\(187\) −12.7424 −0.931820
\(188\) 0 0
\(189\) 14.0619 1.02285
\(190\) 0 0
\(191\) 14.0063 1.01346 0.506729 0.862105i \(-0.330854\pi\)
0.506729 + 0.862105i \(0.330854\pi\)
\(192\) 0 0
\(193\) 7.81914 0.562834 0.281417 0.959586i \(-0.409196\pi\)
0.281417 + 0.959586i \(0.409196\pi\)
\(194\) 0 0
\(195\) −11.3542 −0.813091
\(196\) 0 0
\(197\) 1.11344 0.0793291 0.0396645 0.999213i \(-0.487371\pi\)
0.0396645 + 0.999213i \(0.487371\pi\)
\(198\) 0 0
\(199\) 16.2889 1.15469 0.577346 0.816500i \(-0.304089\pi\)
0.577346 + 0.816500i \(0.304089\pi\)
\(200\) 0 0
\(201\) 5.13770 0.362385
\(202\) 0 0
\(203\) −29.6121 −2.07837
\(204\) 0 0
\(205\) 15.6148 1.09058
\(206\) 0 0
\(207\) −15.7335 −1.09355
\(208\) 0 0
\(209\) −3.25497 −0.225151
\(210\) 0 0
\(211\) −17.0068 −1.17080 −0.585398 0.810746i \(-0.699062\pi\)
−0.585398 + 0.810746i \(0.699062\pi\)
\(212\) 0 0
\(213\) 3.51316 0.240718
\(214\) 0 0
\(215\) 37.4813 2.55621
\(216\) 0 0
\(217\) −12.9079 −0.876248
\(218\) 0 0
\(219\) 4.63552 0.313239
\(220\) 0 0
\(221\) −9.98970 −0.671980
\(222\) 0 0
\(223\) 15.2058 1.01826 0.509129 0.860690i \(-0.329968\pi\)
0.509129 + 0.860690i \(0.329968\pi\)
\(224\) 0 0
\(225\) −13.2088 −0.880585
\(226\) 0 0
\(227\) −2.74299 −0.182059 −0.0910294 0.995848i \(-0.529016\pi\)
−0.0910294 + 0.995848i \(0.529016\pi\)
\(228\) 0 0
\(229\) 20.0154 1.32266 0.661328 0.750097i \(-0.269993\pi\)
0.661328 + 0.750097i \(0.269993\pi\)
\(230\) 0 0
\(231\) 15.1896 0.999402
\(232\) 0 0
\(233\) 7.83957 0.513588 0.256794 0.966466i \(-0.417334\pi\)
0.256794 + 0.966466i \(0.417334\pi\)
\(234\) 0 0
\(235\) −17.8291 −1.16304
\(236\) 0 0
\(237\) −5.84733 −0.379825
\(238\) 0 0
\(239\) −7.51519 −0.486117 −0.243058 0.970012i \(-0.578151\pi\)
−0.243058 + 0.970012i \(0.578151\pi\)
\(240\) 0 0
\(241\) 0.466774 0.0300676 0.0150338 0.999887i \(-0.495214\pi\)
0.0150338 + 0.999887i \(0.495214\pi\)
\(242\) 0 0
\(243\) 15.5467 0.997320
\(244\) 0 0
\(245\) 14.6185 0.933943
\(246\) 0 0
\(247\) −2.55180 −0.162367
\(248\) 0 0
\(249\) 10.3325 0.654795
\(250\) 0 0
\(251\) 5.42805 0.342615 0.171308 0.985218i \(-0.445201\pi\)
0.171308 + 0.985218i \(0.445201\pi\)
\(252\) 0 0
\(253\) −38.1130 −2.39615
\(254\) 0 0
\(255\) 5.39519 0.337860
\(256\) 0 0
\(257\) 0.702942 0.0438483 0.0219242 0.999760i \(-0.493021\pi\)
0.0219242 + 0.999760i \(0.493021\pi\)
\(258\) 0 0
\(259\) −27.8427 −1.73006
\(260\) 0 0
\(261\) −21.0664 −1.30398
\(262\) 0 0
\(263\) 17.8308 1.09949 0.549746 0.835332i \(-0.314724\pi\)
0.549746 + 0.835332i \(0.314724\pi\)
\(264\) 0 0
\(265\) −42.7370 −2.62531
\(266\) 0 0
\(267\) 8.41783 0.515163
\(268\) 0 0
\(269\) 20.1950 1.23131 0.615656 0.788015i \(-0.288891\pi\)
0.615656 + 0.788015i \(0.288891\pi\)
\(270\) 0 0
\(271\) 3.30293 0.200639 0.100319 0.994955i \(-0.468014\pi\)
0.100319 + 0.994955i \(0.468014\pi\)
\(272\) 0 0
\(273\) 11.9082 0.720717
\(274\) 0 0
\(275\) −31.9971 −1.92950
\(276\) 0 0
\(277\) −6.75489 −0.405862 −0.202931 0.979193i \(-0.565047\pi\)
−0.202931 + 0.979193i \(0.565047\pi\)
\(278\) 0 0
\(279\) −9.18287 −0.549764
\(280\) 0 0
\(281\) 5.46524 0.326029 0.163015 0.986624i \(-0.447878\pi\)
0.163015 + 0.986624i \(0.447878\pi\)
\(282\) 0 0
\(283\) 7.41340 0.440681 0.220340 0.975423i \(-0.429283\pi\)
0.220340 + 0.975423i \(0.429283\pi\)
\(284\) 0 0
\(285\) 1.37817 0.0816355
\(286\) 0 0
\(287\) −16.3767 −0.966683
\(288\) 0 0
\(289\) −12.2532 −0.720775
\(290\) 0 0
\(291\) −1.30391 −0.0764366
\(292\) 0 0
\(293\) −9.17003 −0.535719 −0.267859 0.963458i \(-0.586316\pi\)
−0.267859 + 0.963458i \(0.586316\pi\)
\(294\) 0 0
\(295\) −45.0158 −2.62092
\(296\) 0 0
\(297\) 24.2333 1.40616
\(298\) 0 0
\(299\) −29.8795 −1.72798
\(300\) 0 0
\(301\) −39.3101 −2.26580
\(302\) 0 0
\(303\) 12.2735 0.705092
\(304\) 0 0
\(305\) −11.0762 −0.634224
\(306\) 0 0
\(307\) 4.74332 0.270715 0.135358 0.990797i \(-0.456782\pi\)
0.135358 + 0.990797i \(0.456782\pi\)
\(308\) 0 0
\(309\) −11.2359 −0.639188
\(310\) 0 0
\(311\) −0.965760 −0.0547632 −0.0273816 0.999625i \(-0.508717\pi\)
−0.0273816 + 0.999625i \(0.508717\pi\)
\(312\) 0 0
\(313\) 29.2758 1.65477 0.827384 0.561637i \(-0.189828\pi\)
0.827384 + 0.561637i \(0.189828\pi\)
\(314\) 0 0
\(315\) 26.5141 1.49390
\(316\) 0 0
\(317\) 2.84503 0.159793 0.0798965 0.996803i \(-0.474541\pi\)
0.0798965 + 0.996803i \(0.474541\pi\)
\(318\) 0 0
\(319\) −51.0316 −2.85722
\(320\) 0 0
\(321\) 10.2790 0.573716
\(322\) 0 0
\(323\) 1.21254 0.0674677
\(324\) 0 0
\(325\) −25.0848 −1.39145
\(326\) 0 0
\(327\) 9.55238 0.528248
\(328\) 0 0
\(329\) 18.6990 1.03091
\(330\) 0 0
\(331\) 21.0952 1.15950 0.579749 0.814795i \(-0.303151\pi\)
0.579749 + 0.814795i \(0.303151\pi\)
\(332\) 0 0
\(333\) −19.8077 −1.08545
\(334\) 0 0
\(335\) 21.7244 1.18693
\(336\) 0 0
\(337\) −22.7765 −1.24072 −0.620359 0.784318i \(-0.713013\pi\)
−0.620359 + 0.784318i \(0.713013\pi\)
\(338\) 0 0
\(339\) 5.09834 0.276904
\(340\) 0 0
\(341\) −22.2447 −1.20462
\(342\) 0 0
\(343\) 8.42455 0.454883
\(344\) 0 0
\(345\) 16.1372 0.868796
\(346\) 0 0
\(347\) −28.8258 −1.54745 −0.773726 0.633520i \(-0.781609\pi\)
−0.773726 + 0.633520i \(0.781609\pi\)
\(348\) 0 0
\(349\) −25.0085 −1.33868 −0.669338 0.742958i \(-0.733422\pi\)
−0.669338 + 0.742958i \(0.733422\pi\)
\(350\) 0 0
\(351\) 18.9982 1.01405
\(352\) 0 0
\(353\) −27.9977 −1.49017 −0.745084 0.666970i \(-0.767591\pi\)
−0.745084 + 0.666970i \(0.767591\pi\)
\(354\) 0 0
\(355\) 14.8551 0.788429
\(356\) 0 0
\(357\) −5.65843 −0.299476
\(358\) 0 0
\(359\) 3.91910 0.206842 0.103421 0.994638i \(-0.467021\pi\)
0.103421 + 0.994638i \(0.467021\pi\)
\(360\) 0 0
\(361\) −18.6903 −0.983698
\(362\) 0 0
\(363\) 17.7588 0.932097
\(364\) 0 0
\(365\) 19.6010 1.02596
\(366\) 0 0
\(367\) 18.8814 0.985603 0.492801 0.870142i \(-0.335973\pi\)
0.492801 + 0.870142i \(0.335973\pi\)
\(368\) 0 0
\(369\) −11.6506 −0.606504
\(370\) 0 0
\(371\) 44.8223 2.32706
\(372\) 0 0
\(373\) −15.1045 −0.782079 −0.391040 0.920374i \(-0.627884\pi\)
−0.391040 + 0.920374i \(0.627884\pi\)
\(374\) 0 0
\(375\) 1.16612 0.0602182
\(376\) 0 0
\(377\) −40.0073 −2.06048
\(378\) 0 0
\(379\) 17.7674 0.912648 0.456324 0.889814i \(-0.349166\pi\)
0.456324 + 0.889814i \(0.349166\pi\)
\(380\) 0 0
\(381\) −11.9429 −0.611853
\(382\) 0 0
\(383\) 36.4408 1.86204 0.931019 0.364971i \(-0.118921\pi\)
0.931019 + 0.364971i \(0.118921\pi\)
\(384\) 0 0
\(385\) 64.2281 3.27337
\(386\) 0 0
\(387\) −27.9657 −1.42158
\(388\) 0 0
\(389\) 12.8959 0.653846 0.326923 0.945051i \(-0.393988\pi\)
0.326923 + 0.945051i \(0.393988\pi\)
\(390\) 0 0
\(391\) 14.1979 0.718018
\(392\) 0 0
\(393\) −5.76776 −0.290945
\(394\) 0 0
\(395\) −24.7250 −1.24405
\(396\) 0 0
\(397\) −0.598243 −0.0300250 −0.0150125 0.999887i \(-0.504779\pi\)
−0.0150125 + 0.999887i \(0.504779\pi\)
\(398\) 0 0
\(399\) −1.44541 −0.0723610
\(400\) 0 0
\(401\) 31.5859 1.57733 0.788663 0.614825i \(-0.210773\pi\)
0.788663 + 0.614825i \(0.210773\pi\)
\(402\) 0 0
\(403\) −17.4392 −0.868709
\(404\) 0 0
\(405\) 13.1773 0.654787
\(406\) 0 0
\(407\) −47.9824 −2.37840
\(408\) 0 0
\(409\) −38.1064 −1.88424 −0.942120 0.335276i \(-0.891170\pi\)
−0.942120 + 0.335276i \(0.891170\pi\)
\(410\) 0 0
\(411\) 3.95648 0.195159
\(412\) 0 0
\(413\) 47.2122 2.32316
\(414\) 0 0
\(415\) 43.6902 2.14467
\(416\) 0 0
\(417\) −3.65057 −0.178769
\(418\) 0 0
\(419\) −30.7909 −1.50424 −0.752118 0.659028i \(-0.770968\pi\)
−0.752118 + 0.659028i \(0.770968\pi\)
\(420\) 0 0
\(421\) 24.0309 1.17120 0.585598 0.810602i \(-0.300860\pi\)
0.585598 + 0.810602i \(0.300860\pi\)
\(422\) 0 0
\(423\) 13.3027 0.646800
\(424\) 0 0
\(425\) 11.9196 0.578185
\(426\) 0 0
\(427\) 11.6167 0.562171
\(428\) 0 0
\(429\) 20.5218 0.990803
\(430\) 0 0
\(431\) 4.84457 0.233355 0.116677 0.993170i \(-0.462776\pi\)
0.116677 + 0.993170i \(0.462776\pi\)
\(432\) 0 0
\(433\) 12.0471 0.578945 0.289472 0.957186i \(-0.406520\pi\)
0.289472 + 0.957186i \(0.406520\pi\)
\(434\) 0 0
\(435\) 21.6070 1.03597
\(436\) 0 0
\(437\) 3.62675 0.173491
\(438\) 0 0
\(439\) −18.8132 −0.897904 −0.448952 0.893556i \(-0.648203\pi\)
−0.448952 + 0.893556i \(0.648203\pi\)
\(440\) 0 0
\(441\) −10.9072 −0.519392
\(442\) 0 0
\(443\) 8.62168 0.409628 0.204814 0.978801i \(-0.434341\pi\)
0.204814 + 0.978801i \(0.434341\pi\)
\(444\) 0 0
\(445\) 35.5942 1.68733
\(446\) 0 0
\(447\) 9.93462 0.469892
\(448\) 0 0
\(449\) 4.93292 0.232799 0.116399 0.993202i \(-0.462865\pi\)
0.116399 + 0.993202i \(0.462865\pi\)
\(450\) 0 0
\(451\) −28.2225 −1.32894
\(452\) 0 0
\(453\) −14.7244 −0.691815
\(454\) 0 0
\(455\) 50.3530 2.36058
\(456\) 0 0
\(457\) 15.3039 0.715886 0.357943 0.933744i \(-0.383478\pi\)
0.357943 + 0.933744i \(0.383478\pi\)
\(458\) 0 0
\(459\) −9.02739 −0.421362
\(460\) 0 0
\(461\) 0.668936 0.0311554 0.0155777 0.999879i \(-0.495041\pi\)
0.0155777 + 0.999879i \(0.495041\pi\)
\(462\) 0 0
\(463\) −29.1923 −1.35668 −0.678340 0.734748i \(-0.737300\pi\)
−0.678340 + 0.734748i \(0.737300\pi\)
\(464\) 0 0
\(465\) 9.41848 0.436771
\(466\) 0 0
\(467\) 0.0530828 0.00245638 0.00122819 0.999999i \(-0.499609\pi\)
0.00122819 + 0.999999i \(0.499609\pi\)
\(468\) 0 0
\(469\) −22.7844 −1.05208
\(470\) 0 0
\(471\) 3.98214 0.183487
\(472\) 0 0
\(473\) −67.7445 −3.11490
\(474\) 0 0
\(475\) 3.04478 0.139704
\(476\) 0 0
\(477\) 31.8871 1.46001
\(478\) 0 0
\(479\) 30.0569 1.37333 0.686667 0.726973i \(-0.259073\pi\)
0.686667 + 0.726973i \(0.259073\pi\)
\(480\) 0 0
\(481\) −37.6168 −1.71518
\(482\) 0 0
\(483\) −16.9245 −0.770094
\(484\) 0 0
\(485\) −5.51349 −0.250355
\(486\) 0 0
\(487\) −33.7655 −1.53006 −0.765031 0.643994i \(-0.777276\pi\)
−0.765031 + 0.643994i \(0.777276\pi\)
\(488\) 0 0
\(489\) −8.94320 −0.404426
\(490\) 0 0
\(491\) −36.1428 −1.63110 −0.815551 0.578685i \(-0.803566\pi\)
−0.815551 + 0.578685i \(0.803566\pi\)
\(492\) 0 0
\(493\) 19.0103 0.856182
\(494\) 0 0
\(495\) 45.6927 2.05373
\(496\) 0 0
\(497\) −15.5799 −0.698856
\(498\) 0 0
\(499\) −37.0888 −1.66032 −0.830161 0.557524i \(-0.811751\pi\)
−0.830161 + 0.557524i \(0.811751\pi\)
\(500\) 0 0
\(501\) 8.27827 0.369846
\(502\) 0 0
\(503\) −11.5443 −0.514734 −0.257367 0.966314i \(-0.582855\pi\)
−0.257367 + 0.966314i \(0.582855\pi\)
\(504\) 0 0
\(505\) 51.8974 2.30941
\(506\) 0 0
\(507\) 6.14003 0.272688
\(508\) 0 0
\(509\) −23.0395 −1.02121 −0.510605 0.859815i \(-0.670579\pi\)
−0.510605 + 0.859815i \(0.670579\pi\)
\(510\) 0 0
\(511\) −20.5573 −0.909403
\(512\) 0 0
\(513\) −2.30599 −0.101812
\(514\) 0 0
\(515\) −47.5102 −2.09355
\(516\) 0 0
\(517\) 32.2247 1.41724
\(518\) 0 0
\(519\) −11.7100 −0.514013
\(520\) 0 0
\(521\) −5.09378 −0.223163 −0.111581 0.993755i \(-0.535592\pi\)
−0.111581 + 0.993755i \(0.535592\pi\)
\(522\) 0 0
\(523\) 29.5181 1.29074 0.645368 0.763872i \(-0.276704\pi\)
0.645368 + 0.763872i \(0.276704\pi\)
\(524\) 0 0
\(525\) −14.2087 −0.620119
\(526\) 0 0
\(527\) 8.28661 0.360970
\(528\) 0 0
\(529\) 19.4663 0.846361
\(530\) 0 0
\(531\) 33.5873 1.45757
\(532\) 0 0
\(533\) −22.1256 −0.958365
\(534\) 0 0
\(535\) 43.4639 1.87911
\(536\) 0 0
\(537\) 11.7912 0.508829
\(538\) 0 0
\(539\) −26.4218 −1.13807
\(540\) 0 0
\(541\) −2.22210 −0.0955357 −0.0477679 0.998858i \(-0.515211\pi\)
−0.0477679 + 0.998858i \(0.515211\pi\)
\(542\) 0 0
\(543\) 10.4901 0.450173
\(544\) 0 0
\(545\) 40.3916 1.73018
\(546\) 0 0
\(547\) −9.36339 −0.400350 −0.200175 0.979760i \(-0.564151\pi\)
−0.200175 + 0.979760i \(0.564151\pi\)
\(548\) 0 0
\(549\) 8.26425 0.352710
\(550\) 0 0
\(551\) 4.85606 0.206875
\(552\) 0 0
\(553\) 25.9314 1.10272
\(554\) 0 0
\(555\) 20.3159 0.862361
\(556\) 0 0
\(557\) −26.4523 −1.12082 −0.560410 0.828215i \(-0.689356\pi\)
−0.560410 + 0.828215i \(0.689356\pi\)
\(558\) 0 0
\(559\) −53.1097 −2.24630
\(560\) 0 0
\(561\) −9.75138 −0.411703
\(562\) 0 0
\(563\) 14.8805 0.627139 0.313569 0.949565i \(-0.398475\pi\)
0.313569 + 0.949565i \(0.398475\pi\)
\(564\) 0 0
\(565\) 21.5580 0.906951
\(566\) 0 0
\(567\) −13.8203 −0.580398
\(568\) 0 0
\(569\) −27.6969 −1.16111 −0.580557 0.814220i \(-0.697165\pi\)
−0.580557 + 0.814220i \(0.697165\pi\)
\(570\) 0 0
\(571\) −8.16086 −0.341521 −0.170761 0.985313i \(-0.554622\pi\)
−0.170761 + 0.985313i \(0.554622\pi\)
\(572\) 0 0
\(573\) 10.7185 0.447774
\(574\) 0 0
\(575\) 35.6518 1.48678
\(576\) 0 0
\(577\) −33.2338 −1.38354 −0.691770 0.722118i \(-0.743169\pi\)
−0.691770 + 0.722118i \(0.743169\pi\)
\(578\) 0 0
\(579\) 5.98373 0.248676
\(580\) 0 0
\(581\) −45.8219 −1.90101
\(582\) 0 0
\(583\) 77.2438 3.19911
\(584\) 0 0
\(585\) 35.8217 1.48105
\(586\) 0 0
\(587\) 11.0593 0.456464 0.228232 0.973607i \(-0.426705\pi\)
0.228232 + 0.973607i \(0.426705\pi\)
\(588\) 0 0
\(589\) 2.11676 0.0872195
\(590\) 0 0
\(591\) 0.852077 0.0350498
\(592\) 0 0
\(593\) 13.8183 0.567449 0.283724 0.958906i \(-0.408430\pi\)
0.283724 + 0.958906i \(0.408430\pi\)
\(594\) 0 0
\(595\) −23.9263 −0.980882
\(596\) 0 0
\(597\) 12.4654 0.510174
\(598\) 0 0
\(599\) 38.4999 1.57306 0.786532 0.617550i \(-0.211875\pi\)
0.786532 + 0.617550i \(0.211875\pi\)
\(600\) 0 0
\(601\) 37.4916 1.52932 0.764658 0.644436i \(-0.222908\pi\)
0.764658 + 0.644436i \(0.222908\pi\)
\(602\) 0 0
\(603\) −16.2091 −0.660085
\(604\) 0 0
\(605\) 75.0919 3.05292
\(606\) 0 0
\(607\) −3.68230 −0.149460 −0.0747300 0.997204i \(-0.523809\pi\)
−0.0747300 + 0.997204i \(0.523809\pi\)
\(608\) 0 0
\(609\) −22.6612 −0.918278
\(610\) 0 0
\(611\) 25.2632 1.02204
\(612\) 0 0
\(613\) −14.7869 −0.597236 −0.298618 0.954373i \(-0.596526\pi\)
−0.298618 + 0.954373i \(0.596526\pi\)
\(614\) 0 0
\(615\) 11.9495 0.481849
\(616\) 0 0
\(617\) 36.9347 1.48694 0.743468 0.668771i \(-0.233179\pi\)
0.743468 + 0.668771i \(0.233179\pi\)
\(618\) 0 0
\(619\) 14.3869 0.578258 0.289129 0.957290i \(-0.406634\pi\)
0.289129 + 0.957290i \(0.406634\pi\)
\(620\) 0 0
\(621\) −27.0012 −1.08352
\(622\) 0 0
\(623\) −37.3309 −1.49563
\(624\) 0 0
\(625\) −22.4237 −0.896948
\(626\) 0 0
\(627\) −2.49092 −0.0994779
\(628\) 0 0
\(629\) 17.8744 0.712699
\(630\) 0 0
\(631\) −16.0583 −0.639269 −0.319634 0.947541i \(-0.603560\pi\)
−0.319634 + 0.947541i \(0.603560\pi\)
\(632\) 0 0
\(633\) −13.0148 −0.517290
\(634\) 0 0
\(635\) −50.4997 −2.00402
\(636\) 0 0
\(637\) −20.7139 −0.820716
\(638\) 0 0
\(639\) −11.0838 −0.438467
\(640\) 0 0
\(641\) −11.3742 −0.449256 −0.224628 0.974445i \(-0.572117\pi\)
−0.224628 + 0.974445i \(0.572117\pi\)
\(642\) 0 0
\(643\) −25.9574 −1.02366 −0.511829 0.859087i \(-0.671032\pi\)
−0.511829 + 0.859087i \(0.671032\pi\)
\(644\) 0 0
\(645\) 28.6832 1.12940
\(646\) 0 0
\(647\) −41.5169 −1.63220 −0.816098 0.577913i \(-0.803867\pi\)
−0.816098 + 0.577913i \(0.803867\pi\)
\(648\) 0 0
\(649\) 81.3624 3.19375
\(650\) 0 0
\(651\) −9.87803 −0.387150
\(652\) 0 0
\(653\) 3.62532 0.141870 0.0709349 0.997481i \(-0.477402\pi\)
0.0709349 + 0.997481i \(0.477402\pi\)
\(654\) 0 0
\(655\) −24.3886 −0.952940
\(656\) 0 0
\(657\) −14.6247 −0.570566
\(658\) 0 0
\(659\) 0.914082 0.0356076 0.0178038 0.999841i \(-0.494333\pi\)
0.0178038 + 0.999841i \(0.494333\pi\)
\(660\) 0 0
\(661\) 0.630739 0.0245329 0.0122664 0.999925i \(-0.496095\pi\)
0.0122664 + 0.999925i \(0.496095\pi\)
\(662\) 0 0
\(663\) −7.64479 −0.296899
\(664\) 0 0
\(665\) −6.11181 −0.237006
\(666\) 0 0
\(667\) 56.8605 2.20165
\(668\) 0 0
\(669\) 11.6365 0.449894
\(670\) 0 0
\(671\) 20.0194 0.772842
\(672\) 0 0
\(673\) 18.3996 0.709254 0.354627 0.935008i \(-0.384608\pi\)
0.354627 + 0.935008i \(0.384608\pi\)
\(674\) 0 0
\(675\) −22.6684 −0.872506
\(676\) 0 0
\(677\) 0.413243 0.0158822 0.00794110 0.999968i \(-0.497472\pi\)
0.00794110 + 0.999968i \(0.497472\pi\)
\(678\) 0 0
\(679\) 5.78251 0.221912
\(680\) 0 0
\(681\) −2.09912 −0.0804386
\(682\) 0 0
\(683\) 37.6549 1.44083 0.720413 0.693545i \(-0.243952\pi\)
0.720413 + 0.693545i \(0.243952\pi\)
\(684\) 0 0
\(685\) 16.7297 0.639209
\(686\) 0 0
\(687\) 15.3171 0.584385
\(688\) 0 0
\(689\) 60.5568 2.30703
\(690\) 0 0
\(691\) −21.3359 −0.811655 −0.405827 0.913950i \(-0.633017\pi\)
−0.405827 + 0.913950i \(0.633017\pi\)
\(692\) 0 0
\(693\) −47.9221 −1.82041
\(694\) 0 0
\(695\) −15.4362 −0.585528
\(696\) 0 0
\(697\) 10.5134 0.398225
\(698\) 0 0
\(699\) 5.99937 0.226917
\(700\) 0 0
\(701\) 6.62865 0.250361 0.125180 0.992134i \(-0.460049\pi\)
0.125180 + 0.992134i \(0.460049\pi\)
\(702\) 0 0
\(703\) 4.56590 0.172206
\(704\) 0 0
\(705\) −13.6440 −0.513863
\(706\) 0 0
\(707\) −54.4296 −2.04704
\(708\) 0 0
\(709\) 44.6143 1.67552 0.837762 0.546036i \(-0.183864\pi\)
0.837762 + 0.546036i \(0.183864\pi\)
\(710\) 0 0
\(711\) 18.4479 0.691851
\(712\) 0 0
\(713\) 24.7855 0.928224
\(714\) 0 0
\(715\) 86.7750 3.24520
\(716\) 0 0
\(717\) −5.75113 −0.214780
\(718\) 0 0
\(719\) −4.79209 −0.178715 −0.0893573 0.996000i \(-0.528481\pi\)
−0.0893573 + 0.996000i \(0.528481\pi\)
\(720\) 0 0
\(721\) 49.8283 1.85570
\(722\) 0 0
\(723\) 0.357207 0.0132847
\(724\) 0 0
\(725\) 47.7362 1.77288
\(726\) 0 0
\(727\) 40.2422 1.49250 0.746250 0.665666i \(-0.231852\pi\)
0.746250 + 0.665666i \(0.231852\pi\)
\(728\) 0 0
\(729\) −0.319416 −0.0118302
\(730\) 0 0
\(731\) 25.2362 0.933395
\(732\) 0 0
\(733\) −5.87345 −0.216941 −0.108470 0.994100i \(-0.534595\pi\)
−0.108470 + 0.994100i \(0.534595\pi\)
\(734\) 0 0
\(735\) 11.1871 0.412642
\(736\) 0 0
\(737\) −39.2651 −1.44635
\(738\) 0 0
\(739\) −7.33495 −0.269820 −0.134910 0.990858i \(-0.543075\pi\)
−0.134910 + 0.990858i \(0.543075\pi\)
\(740\) 0 0
\(741\) −1.95281 −0.0717383
\(742\) 0 0
\(743\) 13.9483 0.511712 0.255856 0.966715i \(-0.417643\pi\)
0.255856 + 0.966715i \(0.417643\pi\)
\(744\) 0 0
\(745\) 42.0079 1.53905
\(746\) 0 0
\(747\) −32.5983 −1.19271
\(748\) 0 0
\(749\) −45.5846 −1.66563
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 4.15391 0.151377
\(754\) 0 0
\(755\) −62.2613 −2.26592
\(756\) 0 0
\(757\) 26.3916 0.959220 0.479610 0.877482i \(-0.340778\pi\)
0.479610 + 0.877482i \(0.340778\pi\)
\(758\) 0 0
\(759\) −29.1667 −1.05868
\(760\) 0 0
\(761\) −24.5870 −0.891278 −0.445639 0.895213i \(-0.647024\pi\)
−0.445639 + 0.895213i \(0.647024\pi\)
\(762\) 0 0
\(763\) −42.3624 −1.53362
\(764\) 0 0
\(765\) −17.0215 −0.615412
\(766\) 0 0
\(767\) 63.7858 2.30317
\(768\) 0 0
\(769\) −31.1447 −1.12311 −0.561553 0.827441i \(-0.689796\pi\)
−0.561553 + 0.827441i \(0.689796\pi\)
\(770\) 0 0
\(771\) 0.537939 0.0193734
\(772\) 0 0
\(773\) −26.6561 −0.958755 −0.479377 0.877609i \(-0.659137\pi\)
−0.479377 + 0.877609i \(0.659137\pi\)
\(774\) 0 0
\(775\) 20.8082 0.747453
\(776\) 0 0
\(777\) −21.3071 −0.764389
\(778\) 0 0
\(779\) 2.68559 0.0962212
\(780\) 0 0
\(781\) −26.8495 −0.960750
\(782\) 0 0
\(783\) −36.1534 −1.29202
\(784\) 0 0
\(785\) 16.8382 0.600981
\(786\) 0 0
\(787\) −7.15777 −0.255147 −0.127574 0.991829i \(-0.540719\pi\)
−0.127574 + 0.991829i \(0.540719\pi\)
\(788\) 0 0
\(789\) 13.6453 0.485786
\(790\) 0 0
\(791\) −22.6099 −0.803914
\(792\) 0 0
\(793\) 15.6946 0.557333
\(794\) 0 0
\(795\) −32.7052 −1.15994
\(796\) 0 0
\(797\) −16.2400 −0.575249 −0.287624 0.957743i \(-0.592865\pi\)
−0.287624 + 0.957743i \(0.592865\pi\)
\(798\) 0 0
\(799\) −12.0043 −0.424683
\(800\) 0 0
\(801\) −26.5577 −0.938369
\(802\) 0 0
\(803\) −35.4272 −1.25020
\(804\) 0 0
\(805\) −71.5642 −2.52231
\(806\) 0 0
\(807\) 15.4546 0.544027
\(808\) 0 0
\(809\) −36.5517 −1.28509 −0.642545 0.766248i \(-0.722121\pi\)
−0.642545 + 0.766248i \(0.722121\pi\)
\(810\) 0 0
\(811\) 0.908184 0.0318907 0.0159453 0.999873i \(-0.494924\pi\)
0.0159453 + 0.999873i \(0.494924\pi\)
\(812\) 0 0
\(813\) 2.52762 0.0886476
\(814\) 0 0
\(815\) −37.8157 −1.32463
\(816\) 0 0
\(817\) 6.44642 0.225532
\(818\) 0 0
\(819\) −37.5696 −1.31279
\(820\) 0 0
\(821\) −45.4633 −1.58668 −0.793340 0.608778i \(-0.791660\pi\)
−0.793340 + 0.608778i \(0.791660\pi\)
\(822\) 0 0
\(823\) −23.2278 −0.809670 −0.404835 0.914390i \(-0.632671\pi\)
−0.404835 + 0.914390i \(0.632671\pi\)
\(824\) 0 0
\(825\) −24.4864 −0.852505
\(826\) 0 0
\(827\) −2.11683 −0.0736093 −0.0368046 0.999322i \(-0.511718\pi\)
−0.0368046 + 0.999322i \(0.511718\pi\)
\(828\) 0 0
\(829\) −5.08046 −0.176452 −0.0882259 0.996100i \(-0.528120\pi\)
−0.0882259 + 0.996100i \(0.528120\pi\)
\(830\) 0 0
\(831\) −5.16930 −0.179321
\(832\) 0 0
\(833\) 9.84267 0.341028
\(834\) 0 0
\(835\) 35.0041 1.21137
\(836\) 0 0
\(837\) −15.7593 −0.544720
\(838\) 0 0
\(839\) 37.1831 1.28370 0.641852 0.766828i \(-0.278166\pi\)
0.641852 + 0.766828i \(0.278166\pi\)
\(840\) 0 0
\(841\) 47.1336 1.62530
\(842\) 0 0
\(843\) 4.18237 0.144049
\(844\) 0 0
\(845\) 25.9627 0.893143
\(846\) 0 0
\(847\) −78.7558 −2.70608
\(848\) 0 0
\(849\) 5.67323 0.194705
\(850\) 0 0
\(851\) 53.4629 1.83268
\(852\) 0 0
\(853\) 29.2192 1.00044 0.500222 0.865897i \(-0.333252\pi\)
0.500222 + 0.865897i \(0.333252\pi\)
\(854\) 0 0
\(855\) −4.34802 −0.148699
\(856\) 0 0
\(857\) 30.3067 1.03526 0.517628 0.855606i \(-0.326815\pi\)
0.517628 + 0.855606i \(0.326815\pi\)
\(858\) 0 0
\(859\) 17.2880 0.589860 0.294930 0.955519i \(-0.404704\pi\)
0.294930 + 0.955519i \(0.404704\pi\)
\(860\) 0 0
\(861\) −12.5325 −0.427107
\(862\) 0 0
\(863\) −17.0801 −0.581415 −0.290707 0.956812i \(-0.593891\pi\)
−0.290707 + 0.956812i \(0.593891\pi\)
\(864\) 0 0
\(865\) −49.5150 −1.68356
\(866\) 0 0
\(867\) −9.37696 −0.318458
\(868\) 0 0
\(869\) 44.6885 1.51595
\(870\) 0 0
\(871\) −30.7827 −1.04303
\(872\) 0 0
\(873\) 4.11375 0.139229
\(874\) 0 0
\(875\) −5.17145 −0.174827
\(876\) 0 0
\(877\) −37.7052 −1.27321 −0.636607 0.771188i \(-0.719663\pi\)
−0.636607 + 0.771188i \(0.719663\pi\)
\(878\) 0 0
\(879\) −7.01752 −0.236695
\(880\) 0 0
\(881\) −2.79242 −0.0940790 −0.0470395 0.998893i \(-0.514979\pi\)
−0.0470395 + 0.998893i \(0.514979\pi\)
\(882\) 0 0
\(883\) −4.90793 −0.165165 −0.0825825 0.996584i \(-0.526317\pi\)
−0.0825825 + 0.996584i \(0.526317\pi\)
\(884\) 0 0
\(885\) −34.4491 −1.15799
\(886\) 0 0
\(887\) 1.70211 0.0571512 0.0285756 0.999592i \(-0.490903\pi\)
0.0285756 + 0.999592i \(0.490903\pi\)
\(888\) 0 0
\(889\) 52.9637 1.77634
\(890\) 0 0
\(891\) −23.8170 −0.797899
\(892\) 0 0
\(893\) −3.06643 −0.102614
\(894\) 0 0
\(895\) 49.8583 1.66658
\(896\) 0 0
\(897\) −22.8658 −0.763467
\(898\) 0 0
\(899\) 33.1867 1.10684
\(900\) 0 0
\(901\) −28.7749 −0.958630
\(902\) 0 0
\(903\) −30.0828 −1.00109
\(904\) 0 0
\(905\) 44.3566 1.47446
\(906\) 0 0
\(907\) 19.7176 0.654712 0.327356 0.944901i \(-0.393842\pi\)
0.327356 + 0.944901i \(0.393842\pi\)
\(908\) 0 0
\(909\) −38.7219 −1.28432
\(910\) 0 0
\(911\) −20.6859 −0.685354 −0.342677 0.939453i \(-0.611334\pi\)
−0.342677 + 0.939453i \(0.611334\pi\)
\(912\) 0 0
\(913\) −78.9665 −2.61341
\(914\) 0 0
\(915\) −8.47629 −0.280217
\(916\) 0 0
\(917\) 25.5785 0.844678
\(918\) 0 0
\(919\) −7.46112 −0.246120 −0.123060 0.992399i \(-0.539271\pi\)
−0.123060 + 0.992399i \(0.539271\pi\)
\(920\) 0 0
\(921\) 3.62991 0.119609
\(922\) 0 0
\(923\) −21.0492 −0.692843
\(924\) 0 0
\(925\) 44.8838 1.47577
\(926\) 0 0
\(927\) 35.4485 1.16428
\(928\) 0 0
\(929\) 31.3116 1.02730 0.513651 0.857999i \(-0.328293\pi\)
0.513651 + 0.857999i \(0.328293\pi\)
\(930\) 0 0
\(931\) 2.51424 0.0824010
\(932\) 0 0
\(933\) −0.739064 −0.0241959
\(934\) 0 0
\(935\) −41.2330 −1.34846
\(936\) 0 0
\(937\) −19.6845 −0.643063 −0.321532 0.946899i \(-0.604198\pi\)
−0.321532 + 0.946899i \(0.604198\pi\)
\(938\) 0 0
\(939\) 22.4038 0.731122
\(940\) 0 0
\(941\) 57.1933 1.86445 0.932224 0.361881i \(-0.117865\pi\)
0.932224 + 0.361881i \(0.117865\pi\)
\(942\) 0 0
\(943\) 31.4460 1.02402
\(944\) 0 0
\(945\) 45.5024 1.48019
\(946\) 0 0
\(947\) −6.14626 −0.199727 −0.0998634 0.995001i \(-0.531841\pi\)
−0.0998634 + 0.995001i \(0.531841\pi\)
\(948\) 0 0
\(949\) −27.7739 −0.901578
\(950\) 0 0
\(951\) 2.17721 0.0706009
\(952\) 0 0
\(953\) 45.8124 1.48401 0.742005 0.670395i \(-0.233875\pi\)
0.742005 + 0.670395i \(0.233875\pi\)
\(954\) 0 0
\(955\) 45.3226 1.46661
\(956\) 0 0
\(957\) −39.0528 −1.26240
\(958\) 0 0
\(959\) −17.5460 −0.566589
\(960\) 0 0
\(961\) −16.5339 −0.533352
\(962\) 0 0
\(963\) −32.4295 −1.04502
\(964\) 0 0
\(965\) 25.3018 0.814494
\(966\) 0 0
\(967\) 17.1965 0.553004 0.276502 0.961013i \(-0.410825\pi\)
0.276502 + 0.961013i \(0.410825\pi\)
\(968\) 0 0
\(969\) 0.927920 0.0298091
\(970\) 0 0
\(971\) 37.9153 1.21676 0.608379 0.793646i \(-0.291820\pi\)
0.608379 + 0.793646i \(0.291820\pi\)
\(972\) 0 0
\(973\) 16.1894 0.519007
\(974\) 0 0
\(975\) −19.1966 −0.614783
\(976\) 0 0
\(977\) −41.0385 −1.31294 −0.656469 0.754353i \(-0.727951\pi\)
−0.656469 + 0.754353i \(0.727951\pi\)
\(978\) 0 0
\(979\) −64.3336 −2.05611
\(980\) 0 0
\(981\) −30.1371 −0.962204
\(982\) 0 0
\(983\) −19.6445 −0.626563 −0.313281 0.949660i \(-0.601428\pi\)
−0.313281 + 0.949660i \(0.601428\pi\)
\(984\) 0 0
\(985\) 3.60295 0.114799
\(986\) 0 0
\(987\) 14.3097 0.455484
\(988\) 0 0
\(989\) 75.4823 2.40020
\(990\) 0 0
\(991\) 2.19516 0.0697316 0.0348658 0.999392i \(-0.488900\pi\)
0.0348658 + 0.999392i \(0.488900\pi\)
\(992\) 0 0
\(993\) 16.1435 0.512298
\(994\) 0 0
\(995\) 52.7090 1.67099
\(996\) 0 0
\(997\) 8.00820 0.253622 0.126811 0.991927i \(-0.459526\pi\)
0.126811 + 0.991927i \(0.459526\pi\)
\(998\) 0 0
\(999\) −33.9931 −1.07549
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 \(a_p\))