Properties

Label 6008.2.a.e.1.44
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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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 1.44
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.79702 q^{3} -2.61938 q^{5} +0.0133665 q^{7} +4.82334 q^{9} +O(q^{10})\) \(q+2.79702 q^{3} -2.61938 q^{5} +0.0133665 q^{7} +4.82334 q^{9} +0.228502 q^{11} +0.688069 q^{13} -7.32648 q^{15} -1.16498 q^{17} -0.379935 q^{19} +0.0373865 q^{21} +7.37001 q^{23} +1.86117 q^{25} +5.09993 q^{27} -4.16069 q^{29} +5.39262 q^{31} +0.639124 q^{33} -0.0350121 q^{35} +8.04431 q^{37} +1.92455 q^{39} +4.81652 q^{41} -4.53393 q^{43} -12.6342 q^{45} +5.68239 q^{47} -6.99982 q^{49} -3.25848 q^{51} +7.16875 q^{53} -0.598533 q^{55} -1.06269 q^{57} -11.9962 q^{59} +3.14696 q^{61} +0.0644714 q^{63} -1.80232 q^{65} +12.4676 q^{67} +20.6141 q^{69} -11.7784 q^{71} -2.77458 q^{73} +5.20574 q^{75} +0.00305428 q^{77} +13.8738 q^{79} -0.205392 q^{81} +6.29311 q^{83} +3.05153 q^{85} -11.6375 q^{87} +8.77038 q^{89} +0.00919710 q^{91} +15.0833 q^{93} +0.995197 q^{95} -5.10175 q^{97} +1.10214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.79702 1.61486 0.807431 0.589962i \(-0.200857\pi\)
0.807431 + 0.589962i \(0.200857\pi\)
\(4\) 0 0
\(5\) −2.61938 −1.17142 −0.585712 0.810519i \(-0.699185\pi\)
−0.585712 + 0.810519i \(0.699185\pi\)
\(6\) 0 0
\(7\) 0.0133665 0.00505208 0.00252604 0.999997i \(-0.499196\pi\)
0.00252604 + 0.999997i \(0.499196\pi\)
\(8\) 0 0
\(9\) 4.82334 1.60778
\(10\) 0 0
\(11\) 0.228502 0.0688958 0.0344479 0.999406i \(-0.489033\pi\)
0.0344479 + 0.999406i \(0.489033\pi\)
\(12\) 0 0
\(13\) 0.688069 0.190836 0.0954180 0.995437i \(-0.469581\pi\)
0.0954180 + 0.995437i \(0.469581\pi\)
\(14\) 0 0
\(15\) −7.32648 −1.89169
\(16\) 0 0
\(17\) −1.16498 −0.282549 −0.141275 0.989970i \(-0.545120\pi\)
−0.141275 + 0.989970i \(0.545120\pi\)
\(18\) 0 0
\(19\) −0.379935 −0.0871632 −0.0435816 0.999050i \(-0.513877\pi\)
−0.0435816 + 0.999050i \(0.513877\pi\)
\(20\) 0 0
\(21\) 0.0373865 0.00815841
\(22\) 0 0
\(23\) 7.37001 1.53675 0.768376 0.639998i \(-0.221065\pi\)
0.768376 + 0.639998i \(0.221065\pi\)
\(24\) 0 0
\(25\) 1.86117 0.372234
\(26\) 0 0
\(27\) 5.09993 0.981483
\(28\) 0 0
\(29\) −4.16069 −0.772620 −0.386310 0.922369i \(-0.626251\pi\)
−0.386310 + 0.922369i \(0.626251\pi\)
\(30\) 0 0
\(31\) 5.39262 0.968542 0.484271 0.874918i \(-0.339085\pi\)
0.484271 + 0.874918i \(0.339085\pi\)
\(32\) 0 0
\(33\) 0.639124 0.111257
\(34\) 0 0
\(35\) −0.0350121 −0.00591813
\(36\) 0 0
\(37\) 8.04431 1.32248 0.661238 0.750176i \(-0.270031\pi\)
0.661238 + 0.750176i \(0.270031\pi\)
\(38\) 0 0
\(39\) 1.92455 0.308174
\(40\) 0 0
\(41\) 4.81652 0.752214 0.376107 0.926576i \(-0.377263\pi\)
0.376107 + 0.926576i \(0.377263\pi\)
\(42\) 0 0
\(43\) −4.53393 −0.691417 −0.345709 0.938342i \(-0.612361\pi\)
−0.345709 + 0.938342i \(0.612361\pi\)
\(44\) 0 0
\(45\) −12.6342 −1.88339
\(46\) 0 0
\(47\) 5.68239 0.828862 0.414431 0.910081i \(-0.363981\pi\)
0.414431 + 0.910081i \(0.363981\pi\)
\(48\) 0 0
\(49\) −6.99982 −0.999974
\(50\) 0 0
\(51\) −3.25848 −0.456278
\(52\) 0 0
\(53\) 7.16875 0.984703 0.492352 0.870396i \(-0.336137\pi\)
0.492352 + 0.870396i \(0.336137\pi\)
\(54\) 0 0
\(55\) −0.598533 −0.0807062
\(56\) 0 0
\(57\) −1.06269 −0.140757
\(58\) 0 0
\(59\) −11.9962 −1.56178 −0.780888 0.624671i \(-0.785233\pi\)
−0.780888 + 0.624671i \(0.785233\pi\)
\(60\) 0 0
\(61\) 3.14696 0.402927 0.201464 0.979496i \(-0.435430\pi\)
0.201464 + 0.979496i \(0.435430\pi\)
\(62\) 0 0
\(63\) 0.0644714 0.00812263
\(64\) 0 0
\(65\) −1.80232 −0.223550
\(66\) 0 0
\(67\) 12.4676 1.52316 0.761578 0.648074i \(-0.224425\pi\)
0.761578 + 0.648074i \(0.224425\pi\)
\(68\) 0 0
\(69\) 20.6141 2.48164
\(70\) 0 0
\(71\) −11.7784 −1.39784 −0.698918 0.715202i \(-0.746335\pi\)
−0.698918 + 0.715202i \(0.746335\pi\)
\(72\) 0 0
\(73\) −2.77458 −0.324740 −0.162370 0.986730i \(-0.551914\pi\)
−0.162370 + 0.986730i \(0.551914\pi\)
\(74\) 0 0
\(75\) 5.20574 0.601108
\(76\) 0 0
\(77\) 0.00305428 0.000348067 0
\(78\) 0 0
\(79\) 13.8738 1.56092 0.780460 0.625205i \(-0.214985\pi\)
0.780460 + 0.625205i \(0.214985\pi\)
\(80\) 0 0
\(81\) −0.205392 −0.0228213
\(82\) 0 0
\(83\) 6.29311 0.690759 0.345379 0.938463i \(-0.387750\pi\)
0.345379 + 0.938463i \(0.387750\pi\)
\(84\) 0 0
\(85\) 3.05153 0.330985
\(86\) 0 0
\(87\) −11.6375 −1.24768
\(88\) 0 0
\(89\) 8.77038 0.929658 0.464829 0.885400i \(-0.346116\pi\)
0.464829 + 0.885400i \(0.346116\pi\)
\(90\) 0 0
\(91\) 0.00919710 0.000964119 0
\(92\) 0 0
\(93\) 15.0833 1.56406
\(94\) 0 0
\(95\) 0.995197 0.102105
\(96\) 0 0
\(97\) −5.10175 −0.518004 −0.259002 0.965877i \(-0.583394\pi\)
−0.259002 + 0.965877i \(0.583394\pi\)
\(98\) 0 0
\(99\) 1.10214 0.110769
\(100\) 0 0
\(101\) 2.42910 0.241705 0.120852 0.992671i \(-0.461437\pi\)
0.120852 + 0.992671i \(0.461437\pi\)
\(102\) 0 0
\(103\) 7.55877 0.744788 0.372394 0.928075i \(-0.378537\pi\)
0.372394 + 0.928075i \(0.378537\pi\)
\(104\) 0 0
\(105\) −0.0979297 −0.00955696
\(106\) 0 0
\(107\) 11.9024 1.15064 0.575322 0.817927i \(-0.304877\pi\)
0.575322 + 0.817927i \(0.304877\pi\)
\(108\) 0 0
\(109\) 14.6601 1.40418 0.702092 0.712087i \(-0.252250\pi\)
0.702092 + 0.712087i \(0.252250\pi\)
\(110\) 0 0
\(111\) 22.5001 2.13562
\(112\) 0 0
\(113\) −5.64470 −0.531009 −0.265504 0.964110i \(-0.585538\pi\)
−0.265504 + 0.964110i \(0.585538\pi\)
\(114\) 0 0
\(115\) −19.3049 −1.80019
\(116\) 0 0
\(117\) 3.31879 0.306823
\(118\) 0 0
\(119\) −0.0155717 −0.00142746
\(120\) 0 0
\(121\) −10.9478 −0.995253
\(122\) 0 0
\(123\) 13.4719 1.21472
\(124\) 0 0
\(125\) 8.22179 0.735380
\(126\) 0 0
\(127\) 12.0316 1.06763 0.533815 0.845601i \(-0.320758\pi\)
0.533815 + 0.845601i \(0.320758\pi\)
\(128\) 0 0
\(129\) −12.6815 −1.11654
\(130\) 0 0
\(131\) 14.3128 1.25052 0.625259 0.780417i \(-0.284993\pi\)
0.625259 + 0.780417i \(0.284993\pi\)
\(132\) 0 0
\(133\) −0.00507842 −0.000440355 0
\(134\) 0 0
\(135\) −13.3587 −1.14973
\(136\) 0 0
\(137\) −6.20046 −0.529741 −0.264871 0.964284i \(-0.585329\pi\)
−0.264871 + 0.964284i \(0.585329\pi\)
\(138\) 0 0
\(139\) 15.0479 1.27634 0.638172 0.769894i \(-0.279691\pi\)
0.638172 + 0.769894i \(0.279691\pi\)
\(140\) 0 0
\(141\) 15.8938 1.33850
\(142\) 0 0
\(143\) 0.157225 0.0131478
\(144\) 0 0
\(145\) 10.8984 0.905066
\(146\) 0 0
\(147\) −19.5787 −1.61482
\(148\) 0 0
\(149\) 6.36010 0.521040 0.260520 0.965468i \(-0.416106\pi\)
0.260520 + 0.965468i \(0.416106\pi\)
\(150\) 0 0
\(151\) 3.21352 0.261513 0.130756 0.991415i \(-0.458259\pi\)
0.130756 + 0.991415i \(0.458259\pi\)
\(152\) 0 0
\(153\) −5.61910 −0.454277
\(154\) 0 0
\(155\) −14.1253 −1.13457
\(156\) 0 0
\(157\) −9.11889 −0.727767 −0.363883 0.931445i \(-0.618549\pi\)
−0.363883 + 0.931445i \(0.618549\pi\)
\(158\) 0 0
\(159\) 20.0512 1.59016
\(160\) 0 0
\(161\) 0.0985115 0.00776380
\(162\) 0 0
\(163\) 1.60236 0.125507 0.0627533 0.998029i \(-0.480012\pi\)
0.0627533 + 0.998029i \(0.480012\pi\)
\(164\) 0 0
\(165\) −1.67411 −0.130329
\(166\) 0 0
\(167\) −4.18609 −0.323929 −0.161965 0.986797i \(-0.551783\pi\)
−0.161965 + 0.986797i \(0.551783\pi\)
\(168\) 0 0
\(169\) −12.5266 −0.963582
\(170\) 0 0
\(171\) −1.83256 −0.140139
\(172\) 0 0
\(173\) −15.5003 −1.17846 −0.589232 0.807964i \(-0.700569\pi\)
−0.589232 + 0.807964i \(0.700569\pi\)
\(174\) 0 0
\(175\) 0.0248774 0.00188056
\(176\) 0 0
\(177\) −33.5537 −2.52205
\(178\) 0 0
\(179\) 18.0062 1.34585 0.672925 0.739711i \(-0.265038\pi\)
0.672925 + 0.739711i \(0.265038\pi\)
\(180\) 0 0
\(181\) 17.2099 1.27920 0.639600 0.768708i \(-0.279100\pi\)
0.639600 + 0.768708i \(0.279100\pi\)
\(182\) 0 0
\(183\) 8.80213 0.650672
\(184\) 0 0
\(185\) −21.0711 −1.54918
\(186\) 0 0
\(187\) −0.266200 −0.0194664
\(188\) 0 0
\(189\) 0.0681685 0.00495853
\(190\) 0 0
\(191\) 3.53668 0.255905 0.127953 0.991780i \(-0.459159\pi\)
0.127953 + 0.991780i \(0.459159\pi\)
\(192\) 0 0
\(193\) −4.44314 −0.319824 −0.159912 0.987131i \(-0.551121\pi\)
−0.159912 + 0.987131i \(0.551121\pi\)
\(194\) 0 0
\(195\) −5.04112 −0.361002
\(196\) 0 0
\(197\) −21.0182 −1.49749 −0.748744 0.662859i \(-0.769343\pi\)
−0.748744 + 0.662859i \(0.769343\pi\)
\(198\) 0 0
\(199\) −3.41409 −0.242018 −0.121009 0.992651i \(-0.538613\pi\)
−0.121009 + 0.992651i \(0.538613\pi\)
\(200\) 0 0
\(201\) 34.8721 2.45969
\(202\) 0 0
\(203\) −0.0556140 −0.00390334
\(204\) 0 0
\(205\) −12.6163 −0.881161
\(206\) 0 0
\(207\) 35.5481 2.47076
\(208\) 0 0
\(209\) −0.0868158 −0.00600518
\(210\) 0 0
\(211\) 5.66210 0.389795 0.194898 0.980824i \(-0.437563\pi\)
0.194898 + 0.980824i \(0.437563\pi\)
\(212\) 0 0
\(213\) −32.9444 −2.25731
\(214\) 0 0
\(215\) 11.8761 0.809943
\(216\) 0 0
\(217\) 0.0720806 0.00489315
\(218\) 0 0
\(219\) −7.76056 −0.524410
\(220\) 0 0
\(221\) −0.801586 −0.0539205
\(222\) 0 0
\(223\) 18.1060 1.21247 0.606234 0.795287i \(-0.292680\pi\)
0.606234 + 0.795287i \(0.292680\pi\)
\(224\) 0 0
\(225\) 8.97707 0.598472
\(226\) 0 0
\(227\) −17.1140 −1.13589 −0.567946 0.823066i \(-0.692262\pi\)
−0.567946 + 0.823066i \(0.692262\pi\)
\(228\) 0 0
\(229\) −15.7678 −1.04196 −0.520982 0.853567i \(-0.674434\pi\)
−0.520982 + 0.853567i \(0.674434\pi\)
\(230\) 0 0
\(231\) 0.00854288 0.000562080 0
\(232\) 0 0
\(233\) 9.18223 0.601548 0.300774 0.953695i \(-0.402755\pi\)
0.300774 + 0.953695i \(0.402755\pi\)
\(234\) 0 0
\(235\) −14.8844 −0.970949
\(236\) 0 0
\(237\) 38.8053 2.52067
\(238\) 0 0
\(239\) 2.42482 0.156849 0.0784244 0.996920i \(-0.475011\pi\)
0.0784244 + 0.996920i \(0.475011\pi\)
\(240\) 0 0
\(241\) 3.97634 0.256138 0.128069 0.991765i \(-0.459122\pi\)
0.128069 + 0.991765i \(0.459122\pi\)
\(242\) 0 0
\(243\) −15.8743 −1.01834
\(244\) 0 0
\(245\) 18.3352 1.17139
\(246\) 0 0
\(247\) −0.261422 −0.0166339
\(248\) 0 0
\(249\) 17.6020 1.11548
\(250\) 0 0
\(251\) −3.00201 −0.189485 −0.0947425 0.995502i \(-0.530203\pi\)
−0.0947425 + 0.995502i \(0.530203\pi\)
\(252\) 0 0
\(253\) 1.68406 0.105876
\(254\) 0 0
\(255\) 8.53520 0.534495
\(256\) 0 0
\(257\) 15.5002 0.966874 0.483437 0.875379i \(-0.339388\pi\)
0.483437 + 0.875379i \(0.339388\pi\)
\(258\) 0 0
\(259\) 0.107525 0.00668125
\(260\) 0 0
\(261\) −20.0684 −1.24220
\(262\) 0 0
\(263\) −24.5926 −1.51644 −0.758221 0.651998i \(-0.773931\pi\)
−0.758221 + 0.651998i \(0.773931\pi\)
\(264\) 0 0
\(265\) −18.7777 −1.15350
\(266\) 0 0
\(267\) 24.5310 1.50127
\(268\) 0 0
\(269\) 25.5263 1.55637 0.778185 0.628036i \(-0.216141\pi\)
0.778185 + 0.628036i \(0.216141\pi\)
\(270\) 0 0
\(271\) 23.4498 1.42447 0.712237 0.701939i \(-0.247682\pi\)
0.712237 + 0.701939i \(0.247682\pi\)
\(272\) 0 0
\(273\) 0.0257245 0.00155692
\(274\) 0 0
\(275\) 0.425281 0.0256454
\(276\) 0 0
\(277\) 11.9730 0.719386 0.359693 0.933071i \(-0.382881\pi\)
0.359693 + 0.933071i \(0.382881\pi\)
\(278\) 0 0
\(279\) 26.0104 1.55720
\(280\) 0 0
\(281\) −15.1916 −0.906254 −0.453127 0.891446i \(-0.649692\pi\)
−0.453127 + 0.891446i \(0.649692\pi\)
\(282\) 0 0
\(283\) 22.4437 1.33414 0.667070 0.744995i \(-0.267548\pi\)
0.667070 + 0.744995i \(0.267548\pi\)
\(284\) 0 0
\(285\) 2.78359 0.164886
\(286\) 0 0
\(287\) 0.0643802 0.00380024
\(288\) 0 0
\(289\) −15.6428 −0.920166
\(290\) 0 0
\(291\) −14.2697 −0.836505
\(292\) 0 0
\(293\) −26.9534 −1.57463 −0.787317 0.616549i \(-0.788530\pi\)
−0.787317 + 0.616549i \(0.788530\pi\)
\(294\) 0 0
\(295\) 31.4227 1.82950
\(296\) 0 0
\(297\) 1.16534 0.0676201
\(298\) 0 0
\(299\) 5.07108 0.293268
\(300\) 0 0
\(301\) −0.0606029 −0.00349309
\(302\) 0 0
\(303\) 6.79425 0.390320
\(304\) 0 0
\(305\) −8.24311 −0.471999
\(306\) 0 0
\(307\) 4.26500 0.243417 0.121708 0.992566i \(-0.461163\pi\)
0.121708 + 0.992566i \(0.461163\pi\)
\(308\) 0 0
\(309\) 21.1421 1.20273
\(310\) 0 0
\(311\) −12.3339 −0.699389 −0.349695 0.936864i \(-0.613715\pi\)
−0.349695 + 0.936864i \(0.613715\pi\)
\(312\) 0 0
\(313\) −22.9379 −1.29653 −0.648264 0.761416i \(-0.724505\pi\)
−0.648264 + 0.761416i \(0.724505\pi\)
\(314\) 0 0
\(315\) −0.168875 −0.00951505
\(316\) 0 0
\(317\) 34.3786 1.93090 0.965448 0.260595i \(-0.0839188\pi\)
0.965448 + 0.260595i \(0.0839188\pi\)
\(318\) 0 0
\(319\) −0.950724 −0.0532303
\(320\) 0 0
\(321\) 33.2912 1.85813
\(322\) 0 0
\(323\) 0.442617 0.0246279
\(324\) 0 0
\(325\) 1.28062 0.0710358
\(326\) 0 0
\(327\) 41.0047 2.26756
\(328\) 0 0
\(329\) 0.0759540 0.00418748
\(330\) 0 0
\(331\) 7.53098 0.413940 0.206970 0.978347i \(-0.433640\pi\)
0.206970 + 0.978347i \(0.433640\pi\)
\(332\) 0 0
\(333\) 38.8005 2.12625
\(334\) 0 0
\(335\) −32.6573 −1.78426
\(336\) 0 0
\(337\) −20.9185 −1.13950 −0.569751 0.821817i \(-0.692960\pi\)
−0.569751 + 0.821817i \(0.692960\pi\)
\(338\) 0 0
\(339\) −15.7884 −0.857506
\(340\) 0 0
\(341\) 1.23222 0.0667285
\(342\) 0 0
\(343\) −0.187129 −0.0101040
\(344\) 0 0
\(345\) −53.9962 −2.90706
\(346\) 0 0
\(347\) −28.8732 −1.54999 −0.774996 0.631966i \(-0.782248\pi\)
−0.774996 + 0.631966i \(0.782248\pi\)
\(348\) 0 0
\(349\) 18.9850 1.01624 0.508121 0.861286i \(-0.330340\pi\)
0.508121 + 0.861286i \(0.330340\pi\)
\(350\) 0 0
\(351\) 3.50911 0.187302
\(352\) 0 0
\(353\) 30.0690 1.60041 0.800205 0.599727i \(-0.204724\pi\)
0.800205 + 0.599727i \(0.204724\pi\)
\(354\) 0 0
\(355\) 30.8521 1.63746
\(356\) 0 0
\(357\) −0.0435545 −0.00230515
\(358\) 0 0
\(359\) −2.67072 −0.140955 −0.0704775 0.997513i \(-0.522452\pi\)
−0.0704775 + 0.997513i \(0.522452\pi\)
\(360\) 0 0
\(361\) −18.8556 −0.992403
\(362\) 0 0
\(363\) −30.6212 −1.60720
\(364\) 0 0
\(365\) 7.26769 0.380408
\(366\) 0 0
\(367\) −17.7441 −0.926237 −0.463118 0.886296i \(-0.653270\pi\)
−0.463118 + 0.886296i \(0.653270\pi\)
\(368\) 0 0
\(369\) 23.2317 1.20939
\(370\) 0 0
\(371\) 0.0958214 0.00497480
\(372\) 0 0
\(373\) 3.09717 0.160365 0.0801827 0.996780i \(-0.474450\pi\)
0.0801827 + 0.996780i \(0.474450\pi\)
\(374\) 0 0
\(375\) 22.9966 1.18754
\(376\) 0 0
\(377\) −2.86284 −0.147444
\(378\) 0 0
\(379\) 0.477841 0.0245450 0.0122725 0.999925i \(-0.496093\pi\)
0.0122725 + 0.999925i \(0.496093\pi\)
\(380\) 0 0
\(381\) 33.6526 1.72408
\(382\) 0 0
\(383\) −4.35113 −0.222332 −0.111166 0.993802i \(-0.535459\pi\)
−0.111166 + 0.993802i \(0.535459\pi\)
\(384\) 0 0
\(385\) −0.00800032 −0.000407734 0
\(386\) 0 0
\(387\) −21.8687 −1.11165
\(388\) 0 0
\(389\) −19.4169 −0.984475 −0.492237 0.870461i \(-0.663821\pi\)
−0.492237 + 0.870461i \(0.663821\pi\)
\(390\) 0 0
\(391\) −8.58591 −0.434208
\(392\) 0 0
\(393\) 40.0334 2.01942
\(394\) 0 0
\(395\) −36.3407 −1.82850
\(396\) 0 0
\(397\) 0.874016 0.0438656 0.0219328 0.999759i \(-0.493018\pi\)
0.0219328 + 0.999759i \(0.493018\pi\)
\(398\) 0 0
\(399\) −0.0142045 −0.000711113 0
\(400\) 0 0
\(401\) 8.27785 0.413376 0.206688 0.978407i \(-0.433732\pi\)
0.206688 + 0.978407i \(0.433732\pi\)
\(402\) 0 0
\(403\) 3.71049 0.184833
\(404\) 0 0
\(405\) 0.538000 0.0267335
\(406\) 0 0
\(407\) 1.83814 0.0911131
\(408\) 0 0
\(409\) 26.0121 1.28622 0.643109 0.765775i \(-0.277644\pi\)
0.643109 + 0.765775i \(0.277644\pi\)
\(410\) 0 0
\(411\) −17.3428 −0.855460
\(412\) 0 0
\(413\) −0.160348 −0.00789021
\(414\) 0 0
\(415\) −16.4841 −0.809171
\(416\) 0 0
\(417\) 42.0893 2.06112
\(418\) 0 0
\(419\) 1.93898 0.0947253 0.0473626 0.998878i \(-0.484918\pi\)
0.0473626 + 0.998878i \(0.484918\pi\)
\(420\) 0 0
\(421\) 24.9456 1.21577 0.607886 0.794024i \(-0.292018\pi\)
0.607886 + 0.794024i \(0.292018\pi\)
\(422\) 0 0
\(423\) 27.4081 1.33263
\(424\) 0 0
\(425\) −2.16823 −0.105174
\(426\) 0 0
\(427\) 0.0420640 0.00203562
\(428\) 0 0
\(429\) 0.439762 0.0212319
\(430\) 0 0
\(431\) −15.5025 −0.746727 −0.373363 0.927685i \(-0.621796\pi\)
−0.373363 + 0.927685i \(0.621796\pi\)
\(432\) 0 0
\(433\) 20.1305 0.967412 0.483706 0.875231i \(-0.339290\pi\)
0.483706 + 0.875231i \(0.339290\pi\)
\(434\) 0 0
\(435\) 30.4832 1.46156
\(436\) 0 0
\(437\) −2.80013 −0.133948
\(438\) 0 0
\(439\) −24.9259 −1.18965 −0.594824 0.803856i \(-0.702778\pi\)
−0.594824 + 0.803856i \(0.702778\pi\)
\(440\) 0 0
\(441\) −33.7625 −1.60774
\(442\) 0 0
\(443\) −8.52679 −0.405120 −0.202560 0.979270i \(-0.564926\pi\)
−0.202560 + 0.979270i \(0.564926\pi\)
\(444\) 0 0
\(445\) −22.9730 −1.08902
\(446\) 0 0
\(447\) 17.7894 0.841407
\(448\) 0 0
\(449\) 2.52352 0.119092 0.0595460 0.998226i \(-0.481035\pi\)
0.0595460 + 0.998226i \(0.481035\pi\)
\(450\) 0 0
\(451\) 1.10058 0.0518244
\(452\) 0 0
\(453\) 8.98829 0.422307
\(454\) 0 0
\(455\) −0.0240907 −0.00112939
\(456\) 0 0
\(457\) −13.6375 −0.637935 −0.318967 0.947766i \(-0.603336\pi\)
−0.318967 + 0.947766i \(0.603336\pi\)
\(458\) 0 0
\(459\) −5.94132 −0.277317
\(460\) 0 0
\(461\) −17.0818 −0.795580 −0.397790 0.917477i \(-0.630223\pi\)
−0.397790 + 0.917477i \(0.630223\pi\)
\(462\) 0 0
\(463\) 26.4036 1.22708 0.613540 0.789664i \(-0.289745\pi\)
0.613540 + 0.789664i \(0.289745\pi\)
\(464\) 0 0
\(465\) −39.5089 −1.83218
\(466\) 0 0
\(467\) −20.9657 −0.970176 −0.485088 0.874465i \(-0.661212\pi\)
−0.485088 + 0.874465i \(0.661212\pi\)
\(468\) 0 0
\(469\) 0.166648 0.00769510
\(470\) 0 0
\(471\) −25.5058 −1.17524
\(472\) 0 0
\(473\) −1.03601 −0.0476358
\(474\) 0 0
\(475\) −0.707125 −0.0324451
\(476\) 0 0
\(477\) 34.5773 1.58319
\(478\) 0 0
\(479\) −2.05097 −0.0937114 −0.0468557 0.998902i \(-0.514920\pi\)
−0.0468557 + 0.998902i \(0.514920\pi\)
\(480\) 0 0
\(481\) 5.53504 0.252376
\(482\) 0 0
\(483\) 0.275539 0.0125375
\(484\) 0 0
\(485\) 13.3634 0.606802
\(486\) 0 0
\(487\) −34.2267 −1.55096 −0.775480 0.631372i \(-0.782492\pi\)
−0.775480 + 0.631372i \(0.782492\pi\)
\(488\) 0 0
\(489\) 4.48184 0.202676
\(490\) 0 0
\(491\) −22.1369 −0.999026 −0.499513 0.866306i \(-0.666488\pi\)
−0.499513 + 0.866306i \(0.666488\pi\)
\(492\) 0 0
\(493\) 4.84712 0.218303
\(494\) 0 0
\(495\) −2.88693 −0.129758
\(496\) 0 0
\(497\) −0.157436 −0.00706198
\(498\) 0 0
\(499\) 38.1745 1.70892 0.854462 0.519513i \(-0.173887\pi\)
0.854462 + 0.519513i \(0.173887\pi\)
\(500\) 0 0
\(501\) −11.7086 −0.523102
\(502\) 0 0
\(503\) −38.1811 −1.70241 −0.851207 0.524831i \(-0.824129\pi\)
−0.851207 + 0.524831i \(0.824129\pi\)
\(504\) 0 0
\(505\) −6.36275 −0.283139
\(506\) 0 0
\(507\) −35.0371 −1.55605
\(508\) 0 0
\(509\) −2.91801 −0.129338 −0.0646692 0.997907i \(-0.520599\pi\)
−0.0646692 + 0.997907i \(0.520599\pi\)
\(510\) 0 0
\(511\) −0.0370865 −0.00164061
\(512\) 0 0
\(513\) −1.93765 −0.0855491
\(514\) 0 0
\(515\) −19.7993 −0.872462
\(516\) 0 0
\(517\) 1.29844 0.0571052
\(518\) 0 0
\(519\) −43.3546 −1.90306
\(520\) 0 0
\(521\) 8.53808 0.374060 0.187030 0.982354i \(-0.440114\pi\)
0.187030 + 0.982354i \(0.440114\pi\)
\(522\) 0 0
\(523\) −9.70731 −0.424471 −0.212235 0.977219i \(-0.568074\pi\)
−0.212235 + 0.977219i \(0.568074\pi\)
\(524\) 0 0
\(525\) 0.0695828 0.00303684
\(526\) 0 0
\(527\) −6.28229 −0.273661
\(528\) 0 0
\(529\) 31.3170 1.36161
\(530\) 0 0
\(531\) −57.8619 −2.51099
\(532\) 0 0
\(533\) 3.31410 0.143549
\(534\) 0 0
\(535\) −31.1768 −1.34789
\(536\) 0 0
\(537\) 50.3639 2.17336
\(538\) 0 0
\(539\) −1.59947 −0.0688941
\(540\) 0 0
\(541\) −10.0739 −0.433113 −0.216556 0.976270i \(-0.569482\pi\)
−0.216556 + 0.976270i \(0.569482\pi\)
\(542\) 0 0
\(543\) 48.1364 2.06573
\(544\) 0 0
\(545\) −38.4004 −1.64489
\(546\) 0 0
\(547\) −5.00527 −0.214010 −0.107005 0.994258i \(-0.534126\pi\)
−0.107005 + 0.994258i \(0.534126\pi\)
\(548\) 0 0
\(549\) 15.1789 0.647819
\(550\) 0 0
\(551\) 1.58079 0.0673440
\(552\) 0 0
\(553\) 0.185444 0.00788589
\(554\) 0 0
\(555\) −58.9365 −2.50171
\(556\) 0 0
\(557\) −32.3178 −1.36935 −0.684675 0.728849i \(-0.740056\pi\)
−0.684675 + 0.728849i \(0.740056\pi\)
\(558\) 0 0
\(559\) −3.11965 −0.131947
\(560\) 0 0
\(561\) −0.744567 −0.0314356
\(562\) 0 0
\(563\) −6.63057 −0.279445 −0.139723 0.990191i \(-0.544621\pi\)
−0.139723 + 0.990191i \(0.544621\pi\)
\(564\) 0 0
\(565\) 14.7856 0.622036
\(566\) 0 0
\(567\) −0.00274538 −0.000115295 0
\(568\) 0 0
\(569\) −25.4748 −1.06796 −0.533980 0.845497i \(-0.679304\pi\)
−0.533980 + 0.845497i \(0.679304\pi\)
\(570\) 0 0
\(571\) −6.20036 −0.259477 −0.129739 0.991548i \(-0.541414\pi\)
−0.129739 + 0.991548i \(0.541414\pi\)
\(572\) 0 0
\(573\) 9.89217 0.413251
\(574\) 0 0
\(575\) 13.7169 0.572032
\(576\) 0 0
\(577\) −29.1128 −1.21198 −0.605990 0.795472i \(-0.707223\pi\)
−0.605990 + 0.795472i \(0.707223\pi\)
\(578\) 0 0
\(579\) −12.4276 −0.516472
\(580\) 0 0
\(581\) 0.0841171 0.00348977
\(582\) 0 0
\(583\) 1.63807 0.0678419
\(584\) 0 0
\(585\) −8.69319 −0.359419
\(586\) 0 0
\(587\) 10.9788 0.453144 0.226572 0.973994i \(-0.427248\pi\)
0.226572 + 0.973994i \(0.427248\pi\)
\(588\) 0 0
\(589\) −2.04885 −0.0844212
\(590\) 0 0
\(591\) −58.7885 −2.41824
\(592\) 0 0
\(593\) −9.39094 −0.385640 −0.192820 0.981234i \(-0.561763\pi\)
−0.192820 + 0.981234i \(0.561763\pi\)
\(594\) 0 0
\(595\) 0.0407884 0.00167216
\(596\) 0 0
\(597\) −9.54929 −0.390827
\(598\) 0 0
\(599\) −16.6012 −0.678306 −0.339153 0.940731i \(-0.610140\pi\)
−0.339153 + 0.940731i \(0.610140\pi\)
\(600\) 0 0
\(601\) −25.6927 −1.04803 −0.524013 0.851710i \(-0.675566\pi\)
−0.524013 + 0.851710i \(0.675566\pi\)
\(602\) 0 0
\(603\) 60.1353 2.44890
\(604\) 0 0
\(605\) 28.6765 1.16586
\(606\) 0 0
\(607\) −44.3433 −1.79984 −0.899920 0.436056i \(-0.856375\pi\)
−0.899920 + 0.436056i \(0.856375\pi\)
\(608\) 0 0
\(609\) −0.155554 −0.00630335
\(610\) 0 0
\(611\) 3.90988 0.158177
\(612\) 0 0
\(613\) 35.0207 1.41447 0.707237 0.706976i \(-0.249941\pi\)
0.707237 + 0.706976i \(0.249941\pi\)
\(614\) 0 0
\(615\) −35.2881 −1.42295
\(616\) 0 0
\(617\) −20.5618 −0.827786 −0.413893 0.910326i \(-0.635831\pi\)
−0.413893 + 0.910326i \(0.635831\pi\)
\(618\) 0 0
\(619\) −0.416231 −0.0167297 −0.00836486 0.999965i \(-0.502663\pi\)
−0.00836486 + 0.999965i \(0.502663\pi\)
\(620\) 0 0
\(621\) 37.5866 1.50830
\(622\) 0 0
\(623\) 0.117230 0.00469671
\(624\) 0 0
\(625\) −30.8419 −1.23368
\(626\) 0 0
\(627\) −0.242826 −0.00969754
\(628\) 0 0
\(629\) −9.37145 −0.373664
\(630\) 0 0
\(631\) −6.24035 −0.248424 −0.124212 0.992256i \(-0.539640\pi\)
−0.124212 + 0.992256i \(0.539640\pi\)
\(632\) 0 0
\(633\) 15.8370 0.629466
\(634\) 0 0
\(635\) −31.5154 −1.25065
\(636\) 0 0
\(637\) −4.81636 −0.190831
\(638\) 0 0
\(639\) −56.8111 −2.24741
\(640\) 0 0
\(641\) 18.8218 0.743416 0.371708 0.928350i \(-0.378772\pi\)
0.371708 + 0.928350i \(0.378772\pi\)
\(642\) 0 0
\(643\) −6.73031 −0.265418 −0.132709 0.991155i \(-0.542368\pi\)
−0.132709 + 0.991155i \(0.542368\pi\)
\(644\) 0 0
\(645\) 33.2177 1.30795
\(646\) 0 0
\(647\) 28.9280 1.13728 0.568639 0.822587i \(-0.307470\pi\)
0.568639 + 0.822587i \(0.307470\pi\)
\(648\) 0 0
\(649\) −2.74116 −0.107600
\(650\) 0 0
\(651\) 0.201611 0.00790177
\(652\) 0 0
\(653\) −7.42094 −0.290404 −0.145202 0.989402i \(-0.546383\pi\)
−0.145202 + 0.989402i \(0.546383\pi\)
\(654\) 0 0
\(655\) −37.4908 −1.46489
\(656\) 0 0
\(657\) −13.3827 −0.522111
\(658\) 0 0
\(659\) 11.7466 0.457581 0.228790 0.973476i \(-0.426523\pi\)
0.228790 + 0.973476i \(0.426523\pi\)
\(660\) 0 0
\(661\) −12.2584 −0.476798 −0.238399 0.971167i \(-0.576623\pi\)
−0.238399 + 0.971167i \(0.576623\pi\)
\(662\) 0 0
\(663\) −2.24206 −0.0870742
\(664\) 0 0
\(665\) 0.0133023 0.000515843 0
\(666\) 0 0
\(667\) −30.6643 −1.18733
\(668\) 0 0
\(669\) 50.6429 1.95797
\(670\) 0 0
\(671\) 0.719086 0.0277600
\(672\) 0 0
\(673\) 5.91363 0.227954 0.113977 0.993483i \(-0.463641\pi\)
0.113977 + 0.993483i \(0.463641\pi\)
\(674\) 0 0
\(675\) 9.49186 0.365342
\(676\) 0 0
\(677\) −24.0064 −0.922641 −0.461320 0.887234i \(-0.652624\pi\)
−0.461320 + 0.887234i \(0.652624\pi\)
\(678\) 0 0
\(679\) −0.0681927 −0.00261700
\(680\) 0 0
\(681\) −47.8681 −1.83431
\(682\) 0 0
\(683\) −5.59259 −0.213994 −0.106997 0.994259i \(-0.534124\pi\)
−0.106997 + 0.994259i \(0.534124\pi\)
\(684\) 0 0
\(685\) 16.2414 0.620552
\(686\) 0 0
\(687\) −44.1029 −1.68263
\(688\) 0 0
\(689\) 4.93259 0.187917
\(690\) 0 0
\(691\) 0.923589 0.0351350 0.0175675 0.999846i \(-0.494408\pi\)
0.0175675 + 0.999846i \(0.494408\pi\)
\(692\) 0 0
\(693\) 0.0147318 0.000559616 0
\(694\) 0 0
\(695\) −39.4162 −1.49514
\(696\) 0 0
\(697\) −5.61114 −0.212537
\(698\) 0 0
\(699\) 25.6829 0.971417
\(700\) 0 0
\(701\) −7.36440 −0.278150 −0.139075 0.990282i \(-0.544413\pi\)
−0.139075 + 0.990282i \(0.544413\pi\)
\(702\) 0 0
\(703\) −3.05632 −0.115271
\(704\) 0 0
\(705\) −41.6319 −1.56795
\(706\) 0 0
\(707\) 0.0324687 0.00122111
\(708\) 0 0
\(709\) 11.0693 0.415715 0.207857 0.978159i \(-0.433351\pi\)
0.207857 + 0.978159i \(0.433351\pi\)
\(710\) 0 0
\(711\) 66.9179 2.50962
\(712\) 0 0
\(713\) 39.7436 1.48841
\(714\) 0 0
\(715\) −0.411832 −0.0154017
\(716\) 0 0
\(717\) 6.78229 0.253289
\(718\) 0 0
\(719\) −14.3083 −0.533608 −0.266804 0.963751i \(-0.585968\pi\)
−0.266804 + 0.963751i \(0.585968\pi\)
\(720\) 0 0
\(721\) 0.101035 0.00376273
\(722\) 0 0
\(723\) 11.1219 0.413628
\(724\) 0 0
\(725\) −7.74376 −0.287596
\(726\) 0 0
\(727\) 35.7350 1.32534 0.662669 0.748913i \(-0.269424\pi\)
0.662669 + 0.748913i \(0.269424\pi\)
\(728\) 0 0
\(729\) −43.7846 −1.62165
\(730\) 0 0
\(731\) 5.28193 0.195359
\(732\) 0 0
\(733\) −0.467268 −0.0172589 −0.00862947 0.999963i \(-0.502747\pi\)
−0.00862947 + 0.999963i \(0.502747\pi\)
\(734\) 0 0
\(735\) 51.2840 1.89164
\(736\) 0 0
\(737\) 2.84886 0.104939
\(738\) 0 0
\(739\) −30.6771 −1.12847 −0.564237 0.825613i \(-0.690830\pi\)
−0.564237 + 0.825613i \(0.690830\pi\)
\(740\) 0 0
\(741\) −0.731203 −0.0268614
\(742\) 0 0
\(743\) 47.3966 1.73881 0.869406 0.494098i \(-0.164502\pi\)
0.869406 + 0.494098i \(0.164502\pi\)
\(744\) 0 0
\(745\) −16.6595 −0.610358
\(746\) 0 0
\(747\) 30.3538 1.11059
\(748\) 0 0
\(749\) 0.159093 0.00581314
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −8.39668 −0.305992
\(754\) 0 0
\(755\) −8.41744 −0.306342
\(756\) 0 0
\(757\) −39.9824 −1.45318 −0.726592 0.687069i \(-0.758897\pi\)
−0.726592 + 0.687069i \(0.758897\pi\)
\(758\) 0 0
\(759\) 4.71035 0.170975
\(760\) 0 0
\(761\) 43.9031 1.59148 0.795742 0.605635i \(-0.207081\pi\)
0.795742 + 0.605635i \(0.207081\pi\)
\(762\) 0 0
\(763\) 0.195955 0.00709404
\(764\) 0 0
\(765\) 14.7186 0.532151
\(766\) 0 0
\(767\) −8.25423 −0.298043
\(768\) 0 0
\(769\) 40.5042 1.46062 0.730310 0.683116i \(-0.239376\pi\)
0.730310 + 0.683116i \(0.239376\pi\)
\(770\) 0 0
\(771\) 43.3543 1.56137
\(772\) 0 0
\(773\) −30.2429 −1.08776 −0.543880 0.839163i \(-0.683045\pi\)
−0.543880 + 0.839163i \(0.683045\pi\)
\(774\) 0 0
\(775\) 10.0366 0.360525
\(776\) 0 0
\(777\) 0.300749 0.0107893
\(778\) 0 0
\(779\) −1.82997 −0.0655653
\(780\) 0 0
\(781\) −2.69138 −0.0963050
\(782\) 0 0
\(783\) −21.2192 −0.758313
\(784\) 0 0
\(785\) 23.8859 0.852523
\(786\) 0 0
\(787\) 31.4649 1.12160 0.560802 0.827950i \(-0.310493\pi\)
0.560802 + 0.827950i \(0.310493\pi\)
\(788\) 0 0
\(789\) −68.7860 −2.44885
\(790\) 0 0
\(791\) −0.0754501 −0.00268270
\(792\) 0 0
\(793\) 2.16533 0.0768931
\(794\) 0 0
\(795\) −52.5217 −1.86275
\(796\) 0 0
\(797\) −8.94633 −0.316895 −0.158448 0.987367i \(-0.550649\pi\)
−0.158448 + 0.987367i \(0.550649\pi\)
\(798\) 0 0
\(799\) −6.61987 −0.234194
\(800\) 0 0
\(801\) 42.3025 1.49469
\(802\) 0 0
\(803\) −0.633996 −0.0223732
\(804\) 0 0
\(805\) −0.258040 −0.00909470
\(806\) 0 0
\(807\) 71.3978 2.51332
\(808\) 0 0
\(809\) −26.4742 −0.930783 −0.465392 0.885105i \(-0.654087\pi\)
−0.465392 + 0.885105i \(0.654087\pi\)
\(810\) 0 0
\(811\) −18.3607 −0.644732 −0.322366 0.946615i \(-0.604478\pi\)
−0.322366 + 0.946615i \(0.604478\pi\)
\(812\) 0 0
\(813\) 65.5897 2.30033
\(814\) 0 0
\(815\) −4.19720 −0.147021
\(816\) 0 0
\(817\) 1.72260 0.0602661
\(818\) 0 0
\(819\) 0.0443608 0.00155009
\(820\) 0 0
\(821\) 39.0586 1.36316 0.681578 0.731745i \(-0.261294\pi\)
0.681578 + 0.731745i \(0.261294\pi\)
\(822\) 0 0
\(823\) 28.5048 0.993616 0.496808 0.867861i \(-0.334505\pi\)
0.496808 + 0.867861i \(0.334505\pi\)
\(824\) 0 0
\(825\) 1.18952 0.0414138
\(826\) 0 0
\(827\) −46.1765 −1.60571 −0.802856 0.596173i \(-0.796687\pi\)
−0.802856 + 0.596173i \(0.796687\pi\)
\(828\) 0 0
\(829\) 42.8007 1.48653 0.743264 0.668998i \(-0.233277\pi\)
0.743264 + 0.668998i \(0.233277\pi\)
\(830\) 0 0
\(831\) 33.4887 1.16171
\(832\) 0 0
\(833\) 8.15465 0.282542
\(834\) 0 0
\(835\) 10.9650 0.379459
\(836\) 0 0
\(837\) 27.5020 0.950607
\(838\) 0 0
\(839\) −10.7301 −0.370443 −0.185221 0.982697i \(-0.559300\pi\)
−0.185221 + 0.982697i \(0.559300\pi\)
\(840\) 0 0
\(841\) −11.6887 −0.403058
\(842\) 0 0
\(843\) −42.4912 −1.46347
\(844\) 0 0
\(845\) 32.8119 1.12876
\(846\) 0 0
\(847\) −0.146334 −0.00502810
\(848\) 0 0
\(849\) 62.7756 2.15445
\(850\) 0 0
\(851\) 59.2866 2.03232
\(852\) 0 0
\(853\) 32.8526 1.12485 0.562425 0.826848i \(-0.309868\pi\)
0.562425 + 0.826848i \(0.309868\pi\)
\(854\) 0 0
\(855\) 4.80017 0.164163
\(856\) 0 0
\(857\) −16.3586 −0.558800 −0.279400 0.960175i \(-0.590136\pi\)
−0.279400 + 0.960175i \(0.590136\pi\)
\(858\) 0 0
\(859\) 2.23860 0.0763801 0.0381900 0.999270i \(-0.487841\pi\)
0.0381900 + 0.999270i \(0.487841\pi\)
\(860\) 0 0
\(861\) 0.180073 0.00613687
\(862\) 0 0
\(863\) 26.2864 0.894801 0.447400 0.894334i \(-0.352350\pi\)
0.447400 + 0.894334i \(0.352350\pi\)
\(864\) 0 0
\(865\) 40.6011 1.38048
\(866\) 0 0
\(867\) −43.7534 −1.48594
\(868\) 0 0
\(869\) 3.17018 0.107541
\(870\) 0 0
\(871\) 8.57855 0.290673
\(872\) 0 0
\(873\) −24.6075 −0.832837
\(874\) 0 0
\(875\) 0.109897 0.00371520
\(876\) 0 0
\(877\) −18.8001 −0.634835 −0.317417 0.948286i \(-0.602816\pi\)
−0.317417 + 0.948286i \(0.602816\pi\)
\(878\) 0 0
\(879\) −75.3892 −2.54282
\(880\) 0 0
\(881\) −43.8722 −1.47809 −0.739046 0.673655i \(-0.764723\pi\)
−0.739046 + 0.673655i \(0.764723\pi\)
\(882\) 0 0
\(883\) 22.3456 0.751989 0.375994 0.926622i \(-0.377301\pi\)
0.375994 + 0.926622i \(0.377301\pi\)
\(884\) 0 0
\(885\) 87.8901 2.95439
\(886\) 0 0
\(887\) −32.5006 −1.09126 −0.545632 0.838025i \(-0.683711\pi\)
−0.545632 + 0.838025i \(0.683711\pi\)
\(888\) 0 0
\(889\) 0.160821 0.00539375
\(890\) 0 0
\(891\) −0.0469324 −0.00157229
\(892\) 0 0
\(893\) −2.15894 −0.0722463
\(894\) 0 0
\(895\) −47.1653 −1.57656
\(896\) 0 0
\(897\) 14.1839 0.473587
\(898\) 0 0
\(899\) −22.4370 −0.748315
\(900\) 0 0
\(901\) −8.35144 −0.278227
\(902\) 0 0
\(903\) −0.169508 −0.00564087
\(904\) 0 0
\(905\) −45.0793 −1.49849
\(906\) 0 0
\(907\) 26.7498 0.888214 0.444107 0.895974i \(-0.353521\pi\)
0.444107 + 0.895974i \(0.353521\pi\)
\(908\) 0 0
\(909\) 11.7164 0.388608
\(910\) 0 0
\(911\) −29.8806 −0.989988 −0.494994 0.868896i \(-0.664830\pi\)
−0.494994 + 0.868896i \(0.664830\pi\)
\(912\) 0 0
\(913\) 1.43799 0.0475904
\(914\) 0 0
\(915\) −23.0562 −0.762213
\(916\) 0 0
\(917\) 0.191313 0.00631772
\(918\) 0 0
\(919\) 11.7725 0.388338 0.194169 0.980968i \(-0.437799\pi\)
0.194169 + 0.980968i \(0.437799\pi\)
\(920\) 0 0
\(921\) 11.9293 0.393084
\(922\) 0 0
\(923\) −8.10433 −0.266757
\(924\) 0 0
\(925\) 14.9718 0.492271
\(926\) 0 0
\(927\) 36.4585 1.19746
\(928\) 0 0
\(929\) 54.9523 1.80293 0.901464 0.432855i \(-0.142494\pi\)
0.901464 + 0.432855i \(0.142494\pi\)
\(930\) 0 0
\(931\) 2.65948 0.0871609
\(932\) 0 0
\(933\) −34.4981 −1.12942
\(934\) 0 0
\(935\) 0.697279 0.0228035
\(936\) 0 0
\(937\) 12.3117 0.402206 0.201103 0.979570i \(-0.435547\pi\)
0.201103 + 0.979570i \(0.435547\pi\)
\(938\) 0 0
\(939\) −64.1579 −2.09371
\(940\) 0 0
\(941\) 8.73503 0.284754 0.142377 0.989813i \(-0.454526\pi\)
0.142377 + 0.989813i \(0.454526\pi\)
\(942\) 0 0
\(943\) 35.4978 1.15597
\(944\) 0 0
\(945\) −0.178559 −0.00580854
\(946\) 0 0
\(947\) −40.1736 −1.30547 −0.652733 0.757588i \(-0.726378\pi\)
−0.652733 + 0.757588i \(0.726378\pi\)
\(948\) 0 0
\(949\) −1.90910 −0.0619721
\(950\) 0 0
\(951\) 96.1579 3.11813
\(952\) 0 0
\(953\) −16.7400 −0.542261 −0.271130 0.962543i \(-0.587397\pi\)
−0.271130 + 0.962543i \(0.587397\pi\)
\(954\) 0 0
\(955\) −9.26392 −0.299773
\(956\) 0 0
\(957\) −2.65920 −0.0859596
\(958\) 0 0
\(959\) −0.0828788 −0.00267630
\(960\) 0 0
\(961\) −1.91970 −0.0619259
\(962\) 0 0
\(963\) 57.4091 1.84998
\(964\) 0 0
\(965\) 11.6383 0.374650
\(966\) 0 0
\(967\) −32.0724 −1.03138 −0.515689 0.856776i \(-0.672464\pi\)
−0.515689 + 0.856776i \(0.672464\pi\)
\(968\) 0 0
\(969\) 1.23801 0.0397706
\(970\) 0 0
\(971\) 57.0992 1.83240 0.916201 0.400719i \(-0.131240\pi\)
0.916201 + 0.400719i \(0.131240\pi\)
\(972\) 0 0
\(973\) 0.201138 0.00644819
\(974\) 0 0
\(975\) 3.58191 0.114713
\(976\) 0 0
\(977\) 7.17595 0.229579 0.114790 0.993390i \(-0.463381\pi\)
0.114790 + 0.993390i \(0.463381\pi\)
\(978\) 0 0
\(979\) 2.00405 0.0640496
\(980\) 0 0
\(981\) 70.7107 2.25762
\(982\) 0 0
\(983\) −48.5615 −1.54887 −0.774436 0.632652i \(-0.781966\pi\)
−0.774436 + 0.632652i \(0.781966\pi\)
\(984\) 0 0
\(985\) 55.0549 1.75419
\(986\) 0 0
\(987\) 0.212445 0.00676220
\(988\) 0 0
\(989\) −33.4151 −1.06254
\(990\) 0 0
\(991\) −19.8539 −0.630681 −0.315341 0.948979i \(-0.602119\pi\)
−0.315341 + 0.948979i \(0.602119\pi\)
\(992\) 0 0
\(993\) 21.0643 0.668456
\(994\) 0 0
\(995\) 8.94281 0.283506
\(996\) 0 0
\(997\) 4.31953 0.136801 0.0684005 0.997658i \(-0.478210\pi\)
0.0684005 + 0.997658i \(0.478210\pi\)
\(998\) 0 0
\(999\) 41.0254 1.29799
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 \(a_p\))