Properties

Label 6004.2.a.g.1.22
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.56278 q^{3} -2.37537 q^{5} +2.65817 q^{7} -0.557733 q^{9} +O(q^{10})\) \(q+1.56278 q^{3} -2.37537 q^{5} +2.65817 q^{7} -0.557733 q^{9} -2.81237 q^{11} +2.78992 q^{13} -3.71217 q^{15} -7.35621 q^{17} +1.00000 q^{19} +4.15412 q^{21} +5.90957 q^{23} +0.642390 q^{25} -5.55994 q^{27} +2.21464 q^{29} +1.03131 q^{31} -4.39511 q^{33} -6.31413 q^{35} +4.56380 q^{37} +4.36002 q^{39} +2.65150 q^{41} +6.23613 q^{43} +1.32482 q^{45} +0.283410 q^{47} +0.0658470 q^{49} -11.4961 q^{51} -8.74189 q^{53} +6.68043 q^{55} +1.56278 q^{57} -10.5307 q^{59} +2.64975 q^{61} -1.48255 q^{63} -6.62710 q^{65} -12.4441 q^{67} +9.23533 q^{69} +0.602756 q^{71} -4.37373 q^{73} +1.00391 q^{75} -7.47576 q^{77} -1.00000 q^{79} -7.01573 q^{81} -2.88505 q^{83} +17.4737 q^{85} +3.46098 q^{87} -17.4000 q^{89} +7.41607 q^{91} +1.61170 q^{93} -2.37537 q^{95} -10.5573 q^{97} +1.56855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 1.56278 0.902269 0.451134 0.892456i \(-0.351020\pi\)
0.451134 + 0.892456i \(0.351020\pi\)
\(4\) 0 0
\(5\) −2.37537 −1.06230 −0.531149 0.847278i \(-0.678240\pi\)
−0.531149 + 0.847278i \(0.678240\pi\)
\(6\) 0 0
\(7\) 2.65817 1.00469 0.502346 0.864667i \(-0.332470\pi\)
0.502346 + 0.864667i \(0.332470\pi\)
\(8\) 0 0
\(9\) −0.557733 −0.185911
\(10\) 0 0
\(11\) −2.81237 −0.847963 −0.423981 0.905671i \(-0.639368\pi\)
−0.423981 + 0.905671i \(0.639368\pi\)
\(12\) 0 0
\(13\) 2.78992 0.773785 0.386892 0.922125i \(-0.373548\pi\)
0.386892 + 0.922125i \(0.373548\pi\)
\(14\) 0 0
\(15\) −3.71217 −0.958479
\(16\) 0 0
\(17\) −7.35621 −1.78414 −0.892071 0.451895i \(-0.850748\pi\)
−0.892071 + 0.451895i \(0.850748\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 4.15412 0.906503
\(22\) 0 0
\(23\) 5.90957 1.23223 0.616115 0.787656i \(-0.288706\pi\)
0.616115 + 0.787656i \(0.288706\pi\)
\(24\) 0 0
\(25\) 0.642390 0.128478
\(26\) 0 0
\(27\) −5.55994 −1.07001
\(28\) 0 0
\(29\) 2.21464 0.411248 0.205624 0.978631i \(-0.434078\pi\)
0.205624 + 0.978631i \(0.434078\pi\)
\(30\) 0 0
\(31\) 1.03131 0.185228 0.0926142 0.995702i \(-0.470478\pi\)
0.0926142 + 0.995702i \(0.470478\pi\)
\(32\) 0 0
\(33\) −4.39511 −0.765090
\(34\) 0 0
\(35\) −6.31413 −1.06728
\(36\) 0 0
\(37\) 4.56380 0.750283 0.375142 0.926967i \(-0.377594\pi\)
0.375142 + 0.926967i \(0.377594\pi\)
\(38\) 0 0
\(39\) 4.36002 0.698162
\(40\) 0 0
\(41\) 2.65150 0.414095 0.207048 0.978331i \(-0.433615\pi\)
0.207048 + 0.978331i \(0.433615\pi\)
\(42\) 0 0
\(43\) 6.23613 0.951001 0.475500 0.879715i \(-0.342267\pi\)
0.475500 + 0.879715i \(0.342267\pi\)
\(44\) 0 0
\(45\) 1.32482 0.197493
\(46\) 0 0
\(47\) 0.283410 0.0413395 0.0206698 0.999786i \(-0.493420\pi\)
0.0206698 + 0.999786i \(0.493420\pi\)
\(48\) 0 0
\(49\) 0.0658470 0.00940672
\(50\) 0 0
\(51\) −11.4961 −1.60978
\(52\) 0 0
\(53\) −8.74189 −1.20079 −0.600395 0.799703i \(-0.704990\pi\)
−0.600395 + 0.799703i \(0.704990\pi\)
\(54\) 0 0
\(55\) 6.68043 0.900789
\(56\) 0 0
\(57\) 1.56278 0.206995
\(58\) 0 0
\(59\) −10.5307 −1.37098 −0.685491 0.728081i \(-0.740413\pi\)
−0.685491 + 0.728081i \(0.740413\pi\)
\(60\) 0 0
\(61\) 2.64975 0.339266 0.169633 0.985507i \(-0.445742\pi\)
0.169633 + 0.985507i \(0.445742\pi\)
\(62\) 0 0
\(63\) −1.48255 −0.186783
\(64\) 0 0
\(65\) −6.62710 −0.821990
\(66\) 0 0
\(67\) −12.4441 −1.52028 −0.760142 0.649757i \(-0.774871\pi\)
−0.760142 + 0.649757i \(0.774871\pi\)
\(68\) 0 0
\(69\) 9.23533 1.11180
\(70\) 0 0
\(71\) 0.602756 0.0715339 0.0357670 0.999360i \(-0.488613\pi\)
0.0357670 + 0.999360i \(0.488613\pi\)
\(72\) 0 0
\(73\) −4.37373 −0.511907 −0.255953 0.966689i \(-0.582389\pi\)
−0.255953 + 0.966689i \(0.582389\pi\)
\(74\) 0 0
\(75\) 1.00391 0.115922
\(76\) 0 0
\(77\) −7.47576 −0.851942
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −7.01573 −0.779526
\(82\) 0 0
\(83\) −2.88505 −0.316676 −0.158338 0.987385i \(-0.550614\pi\)
−0.158338 + 0.987385i \(0.550614\pi\)
\(84\) 0 0
\(85\) 17.4737 1.89529
\(86\) 0 0
\(87\) 3.46098 0.371056
\(88\) 0 0
\(89\) −17.4000 −1.84439 −0.922196 0.386723i \(-0.873607\pi\)
−0.922196 + 0.386723i \(0.873607\pi\)
\(90\) 0 0
\(91\) 7.41607 0.777416
\(92\) 0 0
\(93\) 1.61170 0.167126
\(94\) 0 0
\(95\) −2.37537 −0.243708
\(96\) 0 0
\(97\) −10.5573 −1.07193 −0.535965 0.844240i \(-0.680052\pi\)
−0.535965 + 0.844240i \(0.680052\pi\)
\(98\) 0 0
\(99\) 1.56855 0.157646
\(100\) 0 0
\(101\) −2.75201 −0.273835 −0.136917 0.990582i \(-0.543720\pi\)
−0.136917 + 0.990582i \(0.543720\pi\)
\(102\) 0 0
\(103\) −5.66925 −0.558608 −0.279304 0.960203i \(-0.590104\pi\)
−0.279304 + 0.960203i \(0.590104\pi\)
\(104\) 0 0
\(105\) −9.86757 −0.962976
\(106\) 0 0
\(107\) −14.3653 −1.38875 −0.694375 0.719613i \(-0.744319\pi\)
−0.694375 + 0.719613i \(0.744319\pi\)
\(108\) 0 0
\(109\) −0.523715 −0.0501628 −0.0250814 0.999685i \(-0.507984\pi\)
−0.0250814 + 0.999685i \(0.507984\pi\)
\(110\) 0 0
\(111\) 7.13219 0.676957
\(112\) 0 0
\(113\) −2.92082 −0.274767 −0.137384 0.990518i \(-0.543869\pi\)
−0.137384 + 0.990518i \(0.543869\pi\)
\(114\) 0 0
\(115\) −14.0374 −1.30900
\(116\) 0 0
\(117\) −1.55603 −0.143855
\(118\) 0 0
\(119\) −19.5540 −1.79251
\(120\) 0 0
\(121\) −3.09055 −0.280959
\(122\) 0 0
\(123\) 4.14370 0.373625
\(124\) 0 0
\(125\) 10.3509 0.925817
\(126\) 0 0
\(127\) 4.42976 0.393078 0.196539 0.980496i \(-0.437030\pi\)
0.196539 + 0.980496i \(0.437030\pi\)
\(128\) 0 0
\(129\) 9.74567 0.858058
\(130\) 0 0
\(131\) −9.70591 −0.848009 −0.424005 0.905660i \(-0.639376\pi\)
−0.424005 + 0.905660i \(0.639376\pi\)
\(132\) 0 0
\(133\) 2.65817 0.230492
\(134\) 0 0
\(135\) 13.2069 1.13667
\(136\) 0 0
\(137\) 18.0611 1.54307 0.771533 0.636189i \(-0.219490\pi\)
0.771533 + 0.636189i \(0.219490\pi\)
\(138\) 0 0
\(139\) −0.330382 −0.0280226 −0.0140113 0.999902i \(-0.504460\pi\)
−0.0140113 + 0.999902i \(0.504460\pi\)
\(140\) 0 0
\(141\) 0.442906 0.0372994
\(142\) 0 0
\(143\) −7.84630 −0.656141
\(144\) 0 0
\(145\) −5.26058 −0.436868
\(146\) 0 0
\(147\) 0.102904 0.00848739
\(148\) 0 0
\(149\) −19.6987 −1.61378 −0.806890 0.590702i \(-0.798851\pi\)
−0.806890 + 0.590702i \(0.798851\pi\)
\(150\) 0 0
\(151\) −14.0623 −1.14437 −0.572186 0.820124i \(-0.693905\pi\)
−0.572186 + 0.820124i \(0.693905\pi\)
\(152\) 0 0
\(153\) 4.10280 0.331692
\(154\) 0 0
\(155\) −2.44974 −0.196768
\(156\) 0 0
\(157\) 6.60714 0.527307 0.263653 0.964617i \(-0.415072\pi\)
0.263653 + 0.964617i \(0.415072\pi\)
\(158\) 0 0
\(159\) −13.6616 −1.08344
\(160\) 0 0
\(161\) 15.7086 1.23801
\(162\) 0 0
\(163\) −15.5967 −1.22163 −0.610815 0.791773i \(-0.709158\pi\)
−0.610815 + 0.791773i \(0.709158\pi\)
\(164\) 0 0
\(165\) 10.4400 0.812754
\(166\) 0 0
\(167\) 6.06399 0.469246 0.234623 0.972086i \(-0.424615\pi\)
0.234623 + 0.972086i \(0.424615\pi\)
\(168\) 0 0
\(169\) −5.21634 −0.401257
\(170\) 0 0
\(171\) −0.557733 −0.0426509
\(172\) 0 0
\(173\) 23.5265 1.78869 0.894344 0.447380i \(-0.147643\pi\)
0.894344 + 0.447380i \(0.147643\pi\)
\(174\) 0 0
\(175\) 1.70758 0.129081
\(176\) 0 0
\(177\) −16.4571 −1.23700
\(178\) 0 0
\(179\) −9.87404 −0.738021 −0.369010 0.929425i \(-0.620303\pi\)
−0.369010 + 0.929425i \(0.620303\pi\)
\(180\) 0 0
\(181\) 11.4674 0.852363 0.426181 0.904638i \(-0.359859\pi\)
0.426181 + 0.904638i \(0.359859\pi\)
\(182\) 0 0
\(183\) 4.14097 0.306109
\(184\) 0 0
\(185\) −10.8407 −0.797025
\(186\) 0 0
\(187\) 20.6884 1.51289
\(188\) 0 0
\(189\) −14.7792 −1.07503
\(190\) 0 0
\(191\) 2.72793 0.197386 0.0986932 0.995118i \(-0.468534\pi\)
0.0986932 + 0.995118i \(0.468534\pi\)
\(192\) 0 0
\(193\) 5.72730 0.412260 0.206130 0.978525i \(-0.433913\pi\)
0.206130 + 0.978525i \(0.433913\pi\)
\(194\) 0 0
\(195\) −10.3567 −0.741656
\(196\) 0 0
\(197\) 9.81881 0.699561 0.349781 0.936832i \(-0.386256\pi\)
0.349781 + 0.936832i \(0.386256\pi\)
\(198\) 0 0
\(199\) −5.27929 −0.374239 −0.187120 0.982337i \(-0.559915\pi\)
−0.187120 + 0.982337i \(0.559915\pi\)
\(200\) 0 0
\(201\) −19.4473 −1.37170
\(202\) 0 0
\(203\) 5.88687 0.413177
\(204\) 0 0
\(205\) −6.29830 −0.439893
\(206\) 0 0
\(207\) −3.29596 −0.229085
\(208\) 0 0
\(209\) −2.81237 −0.194536
\(210\) 0 0
\(211\) 18.3437 1.26283 0.631415 0.775445i \(-0.282475\pi\)
0.631415 + 0.775445i \(0.282475\pi\)
\(212\) 0 0
\(213\) 0.941972 0.0645428
\(214\) 0 0
\(215\) −14.8131 −1.01025
\(216\) 0 0
\(217\) 2.74139 0.186098
\(218\) 0 0
\(219\) −6.83516 −0.461878
\(220\) 0 0
\(221\) −20.5232 −1.38054
\(222\) 0 0
\(223\) −20.1720 −1.35081 −0.675407 0.737445i \(-0.736032\pi\)
−0.675407 + 0.737445i \(0.736032\pi\)
\(224\) 0 0
\(225\) −0.358282 −0.0238855
\(226\) 0 0
\(227\) 12.4056 0.823391 0.411695 0.911322i \(-0.364937\pi\)
0.411695 + 0.911322i \(0.364937\pi\)
\(228\) 0 0
\(229\) −13.6254 −0.900389 −0.450195 0.892930i \(-0.648645\pi\)
−0.450195 + 0.892930i \(0.648645\pi\)
\(230\) 0 0
\(231\) −11.6829 −0.768680
\(232\) 0 0
\(233\) −1.35532 −0.0887900 −0.0443950 0.999014i \(-0.514136\pi\)
−0.0443950 + 0.999014i \(0.514136\pi\)
\(234\) 0 0
\(235\) −0.673203 −0.0439149
\(236\) 0 0
\(237\) −1.56278 −0.101513
\(238\) 0 0
\(239\) −17.3282 −1.12087 −0.560434 0.828199i \(-0.689366\pi\)
−0.560434 + 0.828199i \(0.689366\pi\)
\(240\) 0 0
\(241\) 23.3441 1.50373 0.751864 0.659318i \(-0.229155\pi\)
0.751864 + 0.659318i \(0.229155\pi\)
\(242\) 0 0
\(243\) 5.71580 0.366669
\(244\) 0 0
\(245\) −0.156411 −0.00999275
\(246\) 0 0
\(247\) 2.78992 0.177518
\(248\) 0 0
\(249\) −4.50869 −0.285727
\(250\) 0 0
\(251\) 23.7545 1.49937 0.749686 0.661794i \(-0.230205\pi\)
0.749686 + 0.661794i \(0.230205\pi\)
\(252\) 0 0
\(253\) −16.6199 −1.04489
\(254\) 0 0
\(255\) 27.3075 1.71006
\(256\) 0 0
\(257\) −17.6146 −1.09877 −0.549385 0.835570i \(-0.685138\pi\)
−0.549385 + 0.835570i \(0.685138\pi\)
\(258\) 0 0
\(259\) 12.1313 0.753804
\(260\) 0 0
\(261\) −1.23518 −0.0764555
\(262\) 0 0
\(263\) −7.39406 −0.455937 −0.227969 0.973668i \(-0.573208\pi\)
−0.227969 + 0.973668i \(0.573208\pi\)
\(264\) 0 0
\(265\) 20.7652 1.27560
\(266\) 0 0
\(267\) −27.1922 −1.66414
\(268\) 0 0
\(269\) −23.5474 −1.43571 −0.717855 0.696193i \(-0.754876\pi\)
−0.717855 + 0.696193i \(0.754876\pi\)
\(270\) 0 0
\(271\) 28.8464 1.75229 0.876147 0.482044i \(-0.160105\pi\)
0.876147 + 0.482044i \(0.160105\pi\)
\(272\) 0 0
\(273\) 11.5897 0.701438
\(274\) 0 0
\(275\) −1.80664 −0.108945
\(276\) 0 0
\(277\) 16.6207 0.998639 0.499320 0.866418i \(-0.333583\pi\)
0.499320 + 0.866418i \(0.333583\pi\)
\(278\) 0 0
\(279\) −0.575195 −0.0344360
\(280\) 0 0
\(281\) −8.39482 −0.500793 −0.250397 0.968143i \(-0.580561\pi\)
−0.250397 + 0.968143i \(0.580561\pi\)
\(282\) 0 0
\(283\) −22.6926 −1.34893 −0.674467 0.738305i \(-0.735627\pi\)
−0.674467 + 0.738305i \(0.735627\pi\)
\(284\) 0 0
\(285\) −3.71217 −0.219890
\(286\) 0 0
\(287\) 7.04813 0.416038
\(288\) 0 0
\(289\) 37.1138 2.18316
\(290\) 0 0
\(291\) −16.4987 −0.967169
\(292\) 0 0
\(293\) 29.5373 1.72559 0.862795 0.505554i \(-0.168712\pi\)
0.862795 + 0.505554i \(0.168712\pi\)
\(294\) 0 0
\(295\) 25.0144 1.45639
\(296\) 0 0
\(297\) 15.6366 0.907329
\(298\) 0 0
\(299\) 16.4872 0.953481
\(300\) 0 0
\(301\) 16.5767 0.955463
\(302\) 0 0
\(303\) −4.30077 −0.247073
\(304\) 0 0
\(305\) −6.29415 −0.360402
\(306\) 0 0
\(307\) −31.4187 −1.79316 −0.896579 0.442883i \(-0.853956\pi\)
−0.896579 + 0.442883i \(0.853956\pi\)
\(308\) 0 0
\(309\) −8.85977 −0.504014
\(310\) 0 0
\(311\) −13.9990 −0.793811 −0.396906 0.917859i \(-0.629916\pi\)
−0.396906 + 0.917859i \(0.629916\pi\)
\(312\) 0 0
\(313\) −17.8802 −1.01065 −0.505324 0.862930i \(-0.668627\pi\)
−0.505324 + 0.862930i \(0.668627\pi\)
\(314\) 0 0
\(315\) 3.52160 0.198420
\(316\) 0 0
\(317\) −33.4054 −1.87623 −0.938117 0.346318i \(-0.887432\pi\)
−0.938117 + 0.346318i \(0.887432\pi\)
\(318\) 0 0
\(319\) −6.22839 −0.348723
\(320\) 0 0
\(321\) −22.4498 −1.25303
\(322\) 0 0
\(323\) −7.35621 −0.409310
\(324\) 0 0
\(325\) 1.79222 0.0994143
\(326\) 0 0
\(327\) −0.818448 −0.0452603
\(328\) 0 0
\(329\) 0.753350 0.0415335
\(330\) 0 0
\(331\) 15.4450 0.848936 0.424468 0.905443i \(-0.360461\pi\)
0.424468 + 0.905443i \(0.360461\pi\)
\(332\) 0 0
\(333\) −2.54538 −0.139486
\(334\) 0 0
\(335\) 29.5593 1.61500
\(336\) 0 0
\(337\) 21.9521 1.19581 0.597904 0.801567i \(-0.296000\pi\)
0.597904 + 0.801567i \(0.296000\pi\)
\(338\) 0 0
\(339\) −4.56458 −0.247914
\(340\) 0 0
\(341\) −2.90042 −0.157067
\(342\) 0 0
\(343\) −18.4321 −0.995241
\(344\) 0 0
\(345\) −21.9373 −1.18107
\(346\) 0 0
\(347\) −35.1377 −1.88629 −0.943146 0.332377i \(-0.892149\pi\)
−0.943146 + 0.332377i \(0.892149\pi\)
\(348\) 0 0
\(349\) 4.90555 0.262588 0.131294 0.991343i \(-0.458087\pi\)
0.131294 + 0.991343i \(0.458087\pi\)
\(350\) 0 0
\(351\) −15.5118 −0.827958
\(352\) 0 0
\(353\) 15.3524 0.817127 0.408564 0.912730i \(-0.366030\pi\)
0.408564 + 0.912730i \(0.366030\pi\)
\(354\) 0 0
\(355\) −1.43177 −0.0759904
\(356\) 0 0
\(357\) −30.5585 −1.61733
\(358\) 0 0
\(359\) −32.8499 −1.73375 −0.866876 0.498523i \(-0.833876\pi\)
−0.866876 + 0.498523i \(0.833876\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −4.82984 −0.253501
\(364\) 0 0
\(365\) 10.3892 0.543798
\(366\) 0 0
\(367\) −23.4768 −1.22548 −0.612740 0.790285i \(-0.709933\pi\)
−0.612740 + 0.790285i \(0.709933\pi\)
\(368\) 0 0
\(369\) −1.47883 −0.0769849
\(370\) 0 0
\(371\) −23.2374 −1.20643
\(372\) 0 0
\(373\) 17.5148 0.906883 0.453442 0.891286i \(-0.350196\pi\)
0.453442 + 0.891286i \(0.350196\pi\)
\(374\) 0 0
\(375\) 16.1762 0.835335
\(376\) 0 0
\(377\) 6.17866 0.318217
\(378\) 0 0
\(379\) 21.3936 1.09892 0.549458 0.835521i \(-0.314834\pi\)
0.549458 + 0.835521i \(0.314834\pi\)
\(380\) 0 0
\(381\) 6.92272 0.354662
\(382\) 0 0
\(383\) 12.0971 0.618131 0.309065 0.951041i \(-0.399984\pi\)
0.309065 + 0.951041i \(0.399984\pi\)
\(384\) 0 0
\(385\) 17.7577 0.905016
\(386\) 0 0
\(387\) −3.47810 −0.176802
\(388\) 0 0
\(389\) −29.1021 −1.47553 −0.737767 0.675055i \(-0.764120\pi\)
−0.737767 + 0.675055i \(0.764120\pi\)
\(390\) 0 0
\(391\) −43.4720 −2.19847
\(392\) 0 0
\(393\) −15.1682 −0.765132
\(394\) 0 0
\(395\) 2.37537 0.119518
\(396\) 0 0
\(397\) 21.4051 1.07429 0.537145 0.843490i \(-0.319503\pi\)
0.537145 + 0.843490i \(0.319503\pi\)
\(398\) 0 0
\(399\) 4.15412 0.207966
\(400\) 0 0
\(401\) −16.0342 −0.800711 −0.400355 0.916360i \(-0.631113\pi\)
−0.400355 + 0.916360i \(0.631113\pi\)
\(402\) 0 0
\(403\) 2.87727 0.143327
\(404\) 0 0
\(405\) 16.6650 0.828089
\(406\) 0 0
\(407\) −12.8351 −0.636212
\(408\) 0 0
\(409\) 9.84131 0.486621 0.243311 0.969948i \(-0.421767\pi\)
0.243311 + 0.969948i \(0.421767\pi\)
\(410\) 0 0
\(411\) 28.2255 1.39226
\(412\) 0 0
\(413\) −27.9924 −1.37742
\(414\) 0 0
\(415\) 6.85307 0.336404
\(416\) 0 0
\(417\) −0.516312 −0.0252839
\(418\) 0 0
\(419\) −8.50107 −0.415304 −0.207652 0.978203i \(-0.566582\pi\)
−0.207652 + 0.978203i \(0.566582\pi\)
\(420\) 0 0
\(421\) −15.3125 −0.746285 −0.373143 0.927774i \(-0.621720\pi\)
−0.373143 + 0.927774i \(0.621720\pi\)
\(422\) 0 0
\(423\) −0.158067 −0.00768548
\(424\) 0 0
\(425\) −4.72555 −0.229223
\(426\) 0 0
\(427\) 7.04348 0.340858
\(428\) 0 0
\(429\) −12.2620 −0.592015
\(430\) 0 0
\(431\) 34.0627 1.64074 0.820371 0.571831i \(-0.193767\pi\)
0.820371 + 0.571831i \(0.193767\pi\)
\(432\) 0 0
\(433\) 3.44618 0.165613 0.0828063 0.996566i \(-0.473612\pi\)
0.0828063 + 0.996566i \(0.473612\pi\)
\(434\) 0 0
\(435\) −8.22111 −0.394172
\(436\) 0 0
\(437\) 5.90957 0.282693
\(438\) 0 0
\(439\) −12.0948 −0.577252 −0.288626 0.957442i \(-0.593198\pi\)
−0.288626 + 0.957442i \(0.593198\pi\)
\(440\) 0 0
\(441\) −0.0367251 −0.00174881
\(442\) 0 0
\(443\) −19.9393 −0.947345 −0.473672 0.880701i \(-0.657072\pi\)
−0.473672 + 0.880701i \(0.657072\pi\)
\(444\) 0 0
\(445\) 41.3314 1.95929
\(446\) 0 0
\(447\) −30.7846 −1.45606
\(448\) 0 0
\(449\) −0.0515726 −0.00243386 −0.00121693 0.999999i \(-0.500387\pi\)
−0.00121693 + 0.999999i \(0.500387\pi\)
\(450\) 0 0
\(451\) −7.45702 −0.351137
\(452\) 0 0
\(453\) −21.9762 −1.03253
\(454\) 0 0
\(455\) −17.6159 −0.825848
\(456\) 0 0
\(457\) −17.3459 −0.811405 −0.405702 0.914005i \(-0.632973\pi\)
−0.405702 + 0.914005i \(0.632973\pi\)
\(458\) 0 0
\(459\) 40.9000 1.90905
\(460\) 0 0
\(461\) −9.08283 −0.423030 −0.211515 0.977375i \(-0.567840\pi\)
−0.211515 + 0.977375i \(0.567840\pi\)
\(462\) 0 0
\(463\) −2.23886 −0.104049 −0.0520243 0.998646i \(-0.516567\pi\)
−0.0520243 + 0.998646i \(0.516567\pi\)
\(464\) 0 0
\(465\) −3.82839 −0.177537
\(466\) 0 0
\(467\) −40.7948 −1.88776 −0.943879 0.330292i \(-0.892853\pi\)
−0.943879 + 0.330292i \(0.892853\pi\)
\(468\) 0 0
\(469\) −33.0784 −1.52742
\(470\) 0 0
\(471\) 10.3255 0.475772
\(472\) 0 0
\(473\) −17.5383 −0.806413
\(474\) 0 0
\(475\) 0.642390 0.0294749
\(476\) 0 0
\(477\) 4.87564 0.223240
\(478\) 0 0
\(479\) 23.9061 1.09230 0.546148 0.837688i \(-0.316093\pi\)
0.546148 + 0.837688i \(0.316093\pi\)
\(480\) 0 0
\(481\) 12.7326 0.580558
\(482\) 0 0
\(483\) 24.5490 1.11702
\(484\) 0 0
\(485\) 25.0775 1.13871
\(486\) 0 0
\(487\) −9.03173 −0.409267 −0.204633 0.978839i \(-0.565600\pi\)
−0.204633 + 0.978839i \(0.565600\pi\)
\(488\) 0 0
\(489\) −24.3742 −1.10224
\(490\) 0 0
\(491\) 6.96464 0.314310 0.157155 0.987574i \(-0.449768\pi\)
0.157155 + 0.987574i \(0.449768\pi\)
\(492\) 0 0
\(493\) −16.2913 −0.733724
\(494\) 0 0
\(495\) −3.72590 −0.167467
\(496\) 0 0
\(497\) 1.60222 0.0718696
\(498\) 0 0
\(499\) 4.05697 0.181615 0.0908075 0.995868i \(-0.471055\pi\)
0.0908075 + 0.995868i \(0.471055\pi\)
\(500\) 0 0
\(501\) 9.47665 0.423386
\(502\) 0 0
\(503\) 24.9372 1.11190 0.555948 0.831217i \(-0.312355\pi\)
0.555948 + 0.831217i \(0.312355\pi\)
\(504\) 0 0
\(505\) 6.53704 0.290894
\(506\) 0 0
\(507\) −8.15197 −0.362042
\(508\) 0 0
\(509\) 2.36751 0.104938 0.0524690 0.998623i \(-0.483291\pi\)
0.0524690 + 0.998623i \(0.483291\pi\)
\(510\) 0 0
\(511\) −11.6261 −0.514309
\(512\) 0 0
\(513\) −5.55994 −0.245477
\(514\) 0 0
\(515\) 13.4666 0.593408
\(516\) 0 0
\(517\) −0.797054 −0.0350544
\(518\) 0 0
\(519\) 36.7667 1.61388
\(520\) 0 0
\(521\) 36.6137 1.60407 0.802037 0.597274i \(-0.203749\pi\)
0.802037 + 0.597274i \(0.203749\pi\)
\(522\) 0 0
\(523\) −9.84827 −0.430635 −0.215317 0.976544i \(-0.569079\pi\)
−0.215317 + 0.976544i \(0.569079\pi\)
\(524\) 0 0
\(525\) 2.66856 0.116466
\(526\) 0 0
\(527\) −7.58652 −0.330474
\(528\) 0 0
\(529\) 11.9230 0.518391
\(530\) 0 0
\(531\) 5.87333 0.254881
\(532\) 0 0
\(533\) 7.39748 0.320421
\(534\) 0 0
\(535\) 34.1230 1.47527
\(536\) 0 0
\(537\) −15.4309 −0.665893
\(538\) 0 0
\(539\) −0.185187 −0.00797655
\(540\) 0 0
\(541\) 10.8869 0.468064 0.234032 0.972229i \(-0.424808\pi\)
0.234032 + 0.972229i \(0.424808\pi\)
\(542\) 0 0
\(543\) 17.9209 0.769060
\(544\) 0 0
\(545\) 1.24402 0.0532878
\(546\) 0 0
\(547\) 27.0875 1.15818 0.579088 0.815265i \(-0.303409\pi\)
0.579088 + 0.815265i \(0.303409\pi\)
\(548\) 0 0
\(549\) −1.47786 −0.0630733
\(550\) 0 0
\(551\) 2.21464 0.0943467
\(552\) 0 0
\(553\) −2.65817 −0.113037
\(554\) 0 0
\(555\) −16.9416 −0.719131
\(556\) 0 0
\(557\) 30.8838 1.30859 0.654294 0.756240i \(-0.272966\pi\)
0.654294 + 0.756240i \(0.272966\pi\)
\(558\) 0 0
\(559\) 17.3983 0.735870
\(560\) 0 0
\(561\) 32.3313 1.36503
\(562\) 0 0
\(563\) −0.864093 −0.0364172 −0.0182086 0.999834i \(-0.505796\pi\)
−0.0182086 + 0.999834i \(0.505796\pi\)
\(564\) 0 0
\(565\) 6.93802 0.291885
\(566\) 0 0
\(567\) −18.6490 −0.783184
\(568\) 0 0
\(569\) −8.20239 −0.343862 −0.171931 0.985109i \(-0.555001\pi\)
−0.171931 + 0.985109i \(0.555001\pi\)
\(570\) 0 0
\(571\) 22.4774 0.940652 0.470326 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(572\) 0 0
\(573\) 4.26315 0.178096
\(574\) 0 0
\(575\) 3.79625 0.158314
\(576\) 0 0
\(577\) −24.5620 −1.02253 −0.511264 0.859423i \(-0.670823\pi\)
−0.511264 + 0.859423i \(0.670823\pi\)
\(578\) 0 0
\(579\) 8.95049 0.371970
\(580\) 0 0
\(581\) −7.66895 −0.318162
\(582\) 0 0
\(583\) 24.5855 1.01823
\(584\) 0 0
\(585\) 3.69615 0.152817
\(586\) 0 0
\(587\) 13.3448 0.550801 0.275400 0.961330i \(-0.411190\pi\)
0.275400 + 0.961330i \(0.411190\pi\)
\(588\) 0 0
\(589\) 1.03131 0.0424943
\(590\) 0 0
\(591\) 15.3446 0.631192
\(592\) 0 0
\(593\) 38.9410 1.59911 0.799557 0.600591i \(-0.205068\pi\)
0.799557 + 0.600591i \(0.205068\pi\)
\(594\) 0 0
\(595\) 46.4481 1.90418
\(596\) 0 0
\(597\) −8.25035 −0.337664
\(598\) 0 0
\(599\) 4.09820 0.167448 0.0837239 0.996489i \(-0.473319\pi\)
0.0837239 + 0.996489i \(0.473319\pi\)
\(600\) 0 0
\(601\) 12.7060 0.518288 0.259144 0.965839i \(-0.416560\pi\)
0.259144 + 0.965839i \(0.416560\pi\)
\(602\) 0 0
\(603\) 6.94047 0.282638
\(604\) 0 0
\(605\) 7.34121 0.298463
\(606\) 0 0
\(607\) 13.5034 0.548088 0.274044 0.961717i \(-0.411639\pi\)
0.274044 + 0.961717i \(0.411639\pi\)
\(608\) 0 0
\(609\) 9.19986 0.372797
\(610\) 0 0
\(611\) 0.790690 0.0319879
\(612\) 0 0
\(613\) 24.6511 0.995648 0.497824 0.867278i \(-0.334133\pi\)
0.497824 + 0.867278i \(0.334133\pi\)
\(614\) 0 0
\(615\) −9.84283 −0.396901
\(616\) 0 0
\(617\) −22.2078 −0.894052 −0.447026 0.894521i \(-0.647517\pi\)
−0.447026 + 0.894521i \(0.647517\pi\)
\(618\) 0 0
\(619\) 13.8966 0.558553 0.279276 0.960211i \(-0.409905\pi\)
0.279276 + 0.960211i \(0.409905\pi\)
\(620\) 0 0
\(621\) −32.8568 −1.31850
\(622\) 0 0
\(623\) −46.2520 −1.85305
\(624\) 0 0
\(625\) −27.7993 −1.11197
\(626\) 0 0
\(627\) −4.39511 −0.175524
\(628\) 0 0
\(629\) −33.5722 −1.33861
\(630\) 0 0
\(631\) −14.5999 −0.581212 −0.290606 0.956843i \(-0.593857\pi\)
−0.290606 + 0.956843i \(0.593857\pi\)
\(632\) 0 0
\(633\) 28.6670 1.13941
\(634\) 0 0
\(635\) −10.5223 −0.417566
\(636\) 0 0
\(637\) 0.183708 0.00727878
\(638\) 0 0
\(639\) −0.336177 −0.0132990
\(640\) 0 0
\(641\) 32.8320 1.29679 0.648394 0.761305i \(-0.275441\pi\)
0.648394 + 0.761305i \(0.275441\pi\)
\(642\) 0 0
\(643\) −14.4574 −0.570143 −0.285071 0.958506i \(-0.592017\pi\)
−0.285071 + 0.958506i \(0.592017\pi\)
\(644\) 0 0
\(645\) −23.1496 −0.911514
\(646\) 0 0
\(647\) 38.1091 1.49822 0.749111 0.662444i \(-0.230481\pi\)
0.749111 + 0.662444i \(0.230481\pi\)
\(648\) 0 0
\(649\) 29.6163 1.16254
\(650\) 0 0
\(651\) 4.28417 0.167910
\(652\) 0 0
\(653\) −27.2350 −1.06579 −0.532895 0.846182i \(-0.678896\pi\)
−0.532895 + 0.846182i \(0.678896\pi\)
\(654\) 0 0
\(655\) 23.0551 0.900839
\(656\) 0 0
\(657\) 2.43938 0.0951692
\(658\) 0 0
\(659\) 31.0547 1.20972 0.604859 0.796333i \(-0.293230\pi\)
0.604859 + 0.796333i \(0.293230\pi\)
\(660\) 0 0
\(661\) 33.2533 1.29341 0.646703 0.762742i \(-0.276148\pi\)
0.646703 + 0.762742i \(0.276148\pi\)
\(662\) 0 0
\(663\) −32.0732 −1.24562
\(664\) 0 0
\(665\) −6.31413 −0.244852
\(666\) 0 0
\(667\) 13.0875 0.506752
\(668\) 0 0
\(669\) −31.5242 −1.21880
\(670\) 0 0
\(671\) −7.45210 −0.287685
\(672\) 0 0
\(673\) −36.2614 −1.39777 −0.698886 0.715233i \(-0.746321\pi\)
−0.698886 + 0.715233i \(0.746321\pi\)
\(674\) 0 0
\(675\) −3.57165 −0.137473
\(676\) 0 0
\(677\) 40.8989 1.57187 0.785937 0.618307i \(-0.212181\pi\)
0.785937 + 0.618307i \(0.212181\pi\)
\(678\) 0 0
\(679\) −28.0630 −1.07696
\(680\) 0 0
\(681\) 19.3872 0.742920
\(682\) 0 0
\(683\) −13.2518 −0.507065 −0.253533 0.967327i \(-0.581592\pi\)
−0.253533 + 0.967327i \(0.581592\pi\)
\(684\) 0 0
\(685\) −42.9019 −1.63920
\(686\) 0 0
\(687\) −21.2934 −0.812393
\(688\) 0 0
\(689\) −24.3892 −0.929154
\(690\) 0 0
\(691\) 10.9408 0.416207 0.208104 0.978107i \(-0.433271\pi\)
0.208104 + 0.978107i \(0.433271\pi\)
\(692\) 0 0
\(693\) 4.16948 0.158385
\(694\) 0 0
\(695\) 0.784779 0.0297684
\(696\) 0 0
\(697\) −19.5050 −0.738805
\(698\) 0 0
\(699\) −2.11806 −0.0801125
\(700\) 0 0
\(701\) −15.2890 −0.577456 −0.288728 0.957411i \(-0.593232\pi\)
−0.288728 + 0.957411i \(0.593232\pi\)
\(702\) 0 0
\(703\) 4.56380 0.172127
\(704\) 0 0
\(705\) −1.05207 −0.0396231
\(706\) 0 0
\(707\) −7.31529 −0.275120
\(708\) 0 0
\(709\) −14.8840 −0.558980 −0.279490 0.960149i \(-0.590165\pi\)
−0.279490 + 0.960149i \(0.590165\pi\)
\(710\) 0 0
\(711\) 0.557733 0.0209166
\(712\) 0 0
\(713\) 6.09459 0.228244
\(714\) 0 0
\(715\) 18.6379 0.697017
\(716\) 0 0
\(717\) −27.0801 −1.01132
\(718\) 0 0
\(719\) 50.5214 1.88413 0.942065 0.335430i \(-0.108882\pi\)
0.942065 + 0.335430i \(0.108882\pi\)
\(720\) 0 0
\(721\) −15.0698 −0.561229
\(722\) 0 0
\(723\) 36.4816 1.35677
\(724\) 0 0
\(725\) 1.42266 0.0528363
\(726\) 0 0
\(727\) 25.2650 0.937026 0.468513 0.883457i \(-0.344790\pi\)
0.468513 + 0.883457i \(0.344790\pi\)
\(728\) 0 0
\(729\) 29.9797 1.11036
\(730\) 0 0
\(731\) −45.8743 −1.69672
\(732\) 0 0
\(733\) 49.0305 1.81098 0.905491 0.424364i \(-0.139502\pi\)
0.905491 + 0.424364i \(0.139502\pi\)
\(734\) 0 0
\(735\) −0.244436 −0.00901614
\(736\) 0 0
\(737\) 34.9973 1.28914
\(738\) 0 0
\(739\) −23.6030 −0.868251 −0.434126 0.900852i \(-0.642943\pi\)
−0.434126 + 0.900852i \(0.642943\pi\)
\(740\) 0 0
\(741\) 4.36002 0.160169
\(742\) 0 0
\(743\) −28.0798 −1.03015 −0.515074 0.857146i \(-0.672235\pi\)
−0.515074 + 0.857146i \(0.672235\pi\)
\(744\) 0 0
\(745\) 46.7917 1.71432
\(746\) 0 0
\(747\) 1.60909 0.0588735
\(748\) 0 0
\(749\) −38.1855 −1.39527
\(750\) 0 0
\(751\) 24.5568 0.896092 0.448046 0.894011i \(-0.352120\pi\)
0.448046 + 0.894011i \(0.352120\pi\)
\(752\) 0 0
\(753\) 37.1230 1.35284
\(754\) 0 0
\(755\) 33.4032 1.21567
\(756\) 0 0
\(757\) −3.33164 −0.121090 −0.0605452 0.998165i \(-0.519284\pi\)
−0.0605452 + 0.998165i \(0.519284\pi\)
\(758\) 0 0
\(759\) −25.9732 −0.942767
\(760\) 0 0
\(761\) −36.9530 −1.33954 −0.669772 0.742567i \(-0.733608\pi\)
−0.669772 + 0.742567i \(0.733608\pi\)
\(762\) 0 0
\(763\) −1.39212 −0.0503981
\(764\) 0 0
\(765\) −9.74568 −0.352356
\(766\) 0 0
\(767\) −29.3799 −1.06085
\(768\) 0 0
\(769\) −39.3221 −1.41799 −0.708995 0.705213i \(-0.750851\pi\)
−0.708995 + 0.705213i \(0.750851\pi\)
\(770\) 0 0
\(771\) −27.5277 −0.991385
\(772\) 0 0
\(773\) −36.9053 −1.32739 −0.663695 0.748003i \(-0.731013\pi\)
−0.663695 + 0.748003i \(0.731013\pi\)
\(774\) 0 0
\(775\) 0.662502 0.0237978
\(776\) 0 0
\(777\) 18.9585 0.680134
\(778\) 0 0
\(779\) 2.65150 0.0949999
\(780\) 0 0
\(781\) −1.69517 −0.0606581
\(782\) 0 0
\(783\) −12.3132 −0.440039
\(784\) 0 0
\(785\) −15.6944 −0.560157
\(786\) 0 0
\(787\) −35.7524 −1.27444 −0.637219 0.770683i \(-0.719915\pi\)
−0.637219 + 0.770683i \(0.719915\pi\)
\(788\) 0 0
\(789\) −11.5553 −0.411378
\(790\) 0 0
\(791\) −7.76402 −0.276057
\(792\) 0 0
\(793\) 7.39260 0.262519
\(794\) 0 0
\(795\) 32.4514 1.15093
\(796\) 0 0
\(797\) −24.8500 −0.880231 −0.440115 0.897941i \(-0.645062\pi\)
−0.440115 + 0.897941i \(0.645062\pi\)
\(798\) 0 0
\(799\) −2.08482 −0.0737556
\(800\) 0 0
\(801\) 9.70454 0.342893
\(802\) 0 0
\(803\) 12.3006 0.434078
\(804\) 0 0
\(805\) −37.3138 −1.31514
\(806\) 0 0
\(807\) −36.7993 −1.29540
\(808\) 0 0
\(809\) −22.9418 −0.806589 −0.403295 0.915070i \(-0.632135\pi\)
−0.403295 + 0.915070i \(0.632135\pi\)
\(810\) 0 0
\(811\) −7.06552 −0.248104 −0.124052 0.992276i \(-0.539589\pi\)
−0.124052 + 0.992276i \(0.539589\pi\)
\(812\) 0 0
\(813\) 45.0805 1.58104
\(814\) 0 0
\(815\) 37.0480 1.29774
\(816\) 0 0
\(817\) 6.23613 0.218175
\(818\) 0 0
\(819\) −4.13619 −0.144530
\(820\) 0 0
\(821\) 54.7782 1.91177 0.955887 0.293735i \(-0.0948982\pi\)
0.955887 + 0.293735i \(0.0948982\pi\)
\(822\) 0 0
\(823\) −40.8241 −1.42304 −0.711518 0.702667i \(-0.751992\pi\)
−0.711518 + 0.702667i \(0.751992\pi\)
\(824\) 0 0
\(825\) −2.82337 −0.0982972
\(826\) 0 0
\(827\) 16.2035 0.563451 0.281726 0.959495i \(-0.409093\pi\)
0.281726 + 0.959495i \(0.409093\pi\)
\(828\) 0 0
\(829\) −33.9941 −1.18066 −0.590332 0.807160i \(-0.701003\pi\)
−0.590332 + 0.807160i \(0.701003\pi\)
\(830\) 0 0
\(831\) 25.9744 0.901041
\(832\) 0 0
\(833\) −0.484384 −0.0167829
\(834\) 0 0
\(835\) −14.4042 −0.498479
\(836\) 0 0
\(837\) −5.73401 −0.198196
\(838\) 0 0
\(839\) 25.8596 0.892771 0.446386 0.894841i \(-0.352711\pi\)
0.446386 + 0.894841i \(0.352711\pi\)
\(840\) 0 0
\(841\) −24.0954 −0.830875
\(842\) 0 0
\(843\) −13.1192 −0.451850
\(844\) 0 0
\(845\) 12.3907 0.426255
\(846\) 0 0
\(847\) −8.21520 −0.282278
\(848\) 0 0
\(849\) −35.4634 −1.21710
\(850\) 0 0
\(851\) 26.9701 0.924522
\(852\) 0 0
\(853\) 20.9860 0.718547 0.359273 0.933232i \(-0.383025\pi\)
0.359273 + 0.933232i \(0.383025\pi\)
\(854\) 0 0
\(855\) 1.32482 0.0453080
\(856\) 0 0
\(857\) −25.1394 −0.858745 −0.429372 0.903128i \(-0.641265\pi\)
−0.429372 + 0.903128i \(0.641265\pi\)
\(858\) 0 0
\(859\) 38.0207 1.29725 0.648626 0.761108i \(-0.275344\pi\)
0.648626 + 0.761108i \(0.275344\pi\)
\(860\) 0 0
\(861\) 11.0147 0.375378
\(862\) 0 0
\(863\) 13.1640 0.448106 0.224053 0.974577i \(-0.428071\pi\)
0.224053 + 0.974577i \(0.428071\pi\)
\(864\) 0 0
\(865\) −55.8842 −1.90012
\(866\) 0 0
\(867\) 58.0005 1.96980
\(868\) 0 0
\(869\) 2.81237 0.0954032
\(870\) 0 0
\(871\) −34.7179 −1.17637
\(872\) 0 0
\(873\) 5.88815 0.199284
\(874\) 0 0
\(875\) 27.5145 0.930161
\(876\) 0 0
\(877\) 16.4665 0.556035 0.278018 0.960576i \(-0.410323\pi\)
0.278018 + 0.960576i \(0.410323\pi\)
\(878\) 0 0
\(879\) 46.1602 1.55695
\(880\) 0 0
\(881\) 9.27474 0.312474 0.156237 0.987720i \(-0.450064\pi\)
0.156237 + 0.987720i \(0.450064\pi\)
\(882\) 0 0
\(883\) 54.7385 1.84210 0.921048 0.389449i \(-0.127335\pi\)
0.921048 + 0.389449i \(0.127335\pi\)
\(884\) 0 0
\(885\) 39.0918 1.31406
\(886\) 0 0
\(887\) −11.9704 −0.401926 −0.200963 0.979599i \(-0.564407\pi\)
−0.200963 + 0.979599i \(0.564407\pi\)
\(888\) 0 0
\(889\) 11.7750 0.394922
\(890\) 0 0
\(891\) 19.7309 0.661009
\(892\) 0 0
\(893\) 0.283410 0.00948394
\(894\) 0 0
\(895\) 23.4545 0.783998
\(896\) 0 0
\(897\) 25.7658 0.860296
\(898\) 0 0
\(899\) 2.28397 0.0761748
\(900\) 0 0
\(901\) 64.3071 2.14238
\(902\) 0 0
\(903\) 25.9056 0.862085
\(904\) 0 0
\(905\) −27.2393 −0.905464
\(906\) 0 0
\(907\) 12.9993 0.431636 0.215818 0.976434i \(-0.430758\pi\)
0.215818 + 0.976434i \(0.430758\pi\)
\(908\) 0 0
\(909\) 1.53489 0.0509090
\(910\) 0 0
\(911\) −23.2411 −0.770014 −0.385007 0.922914i \(-0.625801\pi\)
−0.385007 + 0.922914i \(0.625801\pi\)
\(912\) 0 0
\(913\) 8.11385 0.268529
\(914\) 0 0
\(915\) −9.83634 −0.325179
\(916\) 0 0
\(917\) −25.7999 −0.851988
\(918\) 0 0
\(919\) −47.3640 −1.56239 −0.781197 0.624284i \(-0.785391\pi\)
−0.781197 + 0.624284i \(0.785391\pi\)
\(920\) 0 0
\(921\) −49.1003 −1.61791
\(922\) 0 0
\(923\) 1.68164 0.0553519
\(924\) 0 0
\(925\) 2.93174 0.0963949
\(926\) 0 0
\(927\) 3.16193 0.103851
\(928\) 0 0
\(929\) 58.9374 1.93367 0.966837 0.255393i \(-0.0822047\pi\)
0.966837 + 0.255393i \(0.0822047\pi\)
\(930\) 0 0
\(931\) 0.0658470 0.00215805
\(932\) 0 0
\(933\) −21.8773 −0.716231
\(934\) 0 0
\(935\) −49.1426 −1.60714
\(936\) 0 0
\(937\) −23.6257 −0.771820 −0.385910 0.922537i \(-0.626112\pi\)
−0.385910 + 0.922537i \(0.626112\pi\)
\(938\) 0 0
\(939\) −27.9427 −0.911876
\(940\) 0 0
\(941\) −49.6290 −1.61786 −0.808930 0.587906i \(-0.799953\pi\)
−0.808930 + 0.587906i \(0.799953\pi\)
\(942\) 0 0
\(943\) 15.6692 0.510261
\(944\) 0 0
\(945\) 35.1062 1.14200
\(946\) 0 0
\(947\) 36.6499 1.19096 0.595481 0.803370i \(-0.296962\pi\)
0.595481 + 0.803370i \(0.296962\pi\)
\(948\) 0 0
\(949\) −12.2024 −0.396106
\(950\) 0 0
\(951\) −52.2051 −1.69287
\(952\) 0 0
\(953\) −35.4904 −1.14965 −0.574823 0.818278i \(-0.694929\pi\)
−0.574823 + 0.818278i \(0.694929\pi\)
\(954\) 0 0
\(955\) −6.47986 −0.209683
\(956\) 0 0
\(957\) −9.73357 −0.314642
\(958\) 0 0
\(959\) 48.0095 1.55031
\(960\) 0 0
\(961\) −29.9364 −0.965690
\(962\) 0 0
\(963\) 8.01203 0.258184
\(964\) 0 0
\(965\) −13.6045 −0.437944
\(966\) 0 0
\(967\) −4.87977 −0.156923 −0.0784614 0.996917i \(-0.525001\pi\)
−0.0784614 + 0.996917i \(0.525001\pi\)
\(968\) 0 0
\(969\) −11.4961 −0.369308
\(970\) 0 0
\(971\) 27.5433 0.883908 0.441954 0.897038i \(-0.354285\pi\)
0.441954 + 0.897038i \(0.354285\pi\)
\(972\) 0 0
\(973\) −0.878210 −0.0281541
\(974\) 0 0
\(975\) 2.80083 0.0896984
\(976\) 0 0
\(977\) −18.9025 −0.604746 −0.302373 0.953190i \(-0.597779\pi\)
−0.302373 + 0.953190i \(0.597779\pi\)
\(978\) 0 0
\(979\) 48.9352 1.56398
\(980\) 0 0
\(981\) 0.292093 0.00932581
\(982\) 0 0
\(983\) 23.0231 0.734323 0.367161 0.930157i \(-0.380330\pi\)
0.367161 + 0.930157i \(0.380330\pi\)
\(984\) 0 0
\(985\) −23.3233 −0.743143
\(986\) 0 0
\(987\) 1.17732 0.0374744
\(988\) 0 0
\(989\) 36.8528 1.17185
\(990\) 0 0
\(991\) 10.7418 0.341224 0.170612 0.985338i \(-0.445426\pi\)
0.170612 + 0.985338i \(0.445426\pi\)
\(992\) 0 0
\(993\) 24.1371 0.765968
\(994\) 0 0
\(995\) 12.5403 0.397554
\(996\) 0 0
\(997\) 39.6665 1.25625 0.628126 0.778112i \(-0.283822\pi\)
0.628126 + 0.778112i \(0.283822\pi\)
\(998\) 0 0
\(999\) −25.3744 −0.802811
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 \(a_p\))