Properties

Label 6004.2.a.d.1.8
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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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: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(3.98766\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.98766 q^{5}\) \(+0.872374 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.98766 q^{5}\) \(+0.872374 q^{7}\) \(-3.00000 q^{9}\) \(-2.27985 q^{11}\) \(-2.48344 q^{13}\) \(+5.54683 q^{17}\) \(+1.00000 q^{19}\) \(-1.94254 q^{23}\) \(+10.9014 q^{25}\) \(+6.64516 q^{29}\) \(+5.65034 q^{31}\) \(+3.47873 q^{35}\) \(-6.90214 q^{37}\) \(-2.55402 q^{41}\) \(+3.83331 q^{43}\) \(-11.9630 q^{45}\) \(-3.63462 q^{47}\) \(-6.23896 q^{49}\) \(+7.39374 q^{53}\) \(-9.09127 q^{55}\) \(+2.04855 q^{59}\) \(+8.17891 q^{61}\) \(-2.61712 q^{63}\) \(-9.90312 q^{65}\) \(+5.55917 q^{67}\) \(-1.39664 q^{71}\) \(+2.85774 q^{73}\) \(-1.98888 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(-0.801980 q^{83}\) \(+22.1189 q^{85}\) \(+8.75832 q^{89}\) \(-2.16649 q^{91}\) \(+3.98766 q^{95}\) \(+0.744519 q^{97}\) \(+6.83956 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 3.98766 1.78333 0.891667 0.452691i \(-0.149536\pi\)
0.891667 + 0.452691i \(0.149536\pi\)
\(6\) 0 0
\(7\) 0.872374 0.329726 0.164863 0.986316i \(-0.447282\pi\)
0.164863 + 0.986316i \(0.447282\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −2.27985 −0.687402 −0.343701 0.939079i \(-0.611681\pi\)
−0.343701 + 0.939079i \(0.611681\pi\)
\(12\) 0 0
\(13\) −2.48344 −0.688783 −0.344392 0.938826i \(-0.611915\pi\)
−0.344392 + 0.938826i \(0.611915\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.54683 1.34530 0.672652 0.739959i \(-0.265155\pi\)
0.672652 + 0.739959i \(0.265155\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.94254 −0.405047 −0.202524 0.979277i \(-0.564914\pi\)
−0.202524 + 0.979277i \(0.564914\pi\)
\(24\) 0 0
\(25\) 10.9014 2.18028
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.64516 1.23398 0.616988 0.786973i \(-0.288353\pi\)
0.616988 + 0.786973i \(0.288353\pi\)
\(30\) 0 0
\(31\) 5.65034 1.01483 0.507416 0.861701i \(-0.330601\pi\)
0.507416 + 0.861701i \(0.330601\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.47873 0.588012
\(36\) 0 0
\(37\) −6.90214 −1.13470 −0.567352 0.823475i \(-0.692032\pi\)
−0.567352 + 0.823475i \(0.692032\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.55402 −0.398871 −0.199435 0.979911i \(-0.563911\pi\)
−0.199435 + 0.979911i \(0.563911\pi\)
\(42\) 0 0
\(43\) 3.83331 0.584574 0.292287 0.956331i \(-0.405584\pi\)
0.292287 + 0.956331i \(0.405584\pi\)
\(44\) 0 0
\(45\) −11.9630 −1.78333
\(46\) 0 0
\(47\) −3.63462 −0.530164 −0.265082 0.964226i \(-0.585399\pi\)
−0.265082 + 0.964226i \(0.585399\pi\)
\(48\) 0 0
\(49\) −6.23896 −0.891281
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.39374 1.01561 0.507804 0.861472i \(-0.330457\pi\)
0.507804 + 0.861472i \(0.330457\pi\)
\(54\) 0 0
\(55\) −9.09127 −1.22587
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.04855 0.266699 0.133349 0.991069i \(-0.457427\pi\)
0.133349 + 0.991069i \(0.457427\pi\)
\(60\) 0 0
\(61\) 8.17891 1.04720 0.523601 0.851964i \(-0.324588\pi\)
0.523601 + 0.851964i \(0.324588\pi\)
\(62\) 0 0
\(63\) −2.61712 −0.329726
\(64\) 0 0
\(65\) −9.90312 −1.22833
\(66\) 0 0
\(67\) 5.55917 0.679161 0.339581 0.940577i \(-0.389715\pi\)
0.339581 + 0.940577i \(0.389715\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.39664 −0.165751 −0.0828753 0.996560i \(-0.526410\pi\)
−0.0828753 + 0.996560i \(0.526410\pi\)
\(72\) 0 0
\(73\) 2.85774 0.334473 0.167237 0.985917i \(-0.446516\pi\)
0.167237 + 0.985917i \(0.446516\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.98888 −0.226654
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −0.801980 −0.0880287 −0.0440144 0.999031i \(-0.514015\pi\)
−0.0440144 + 0.999031i \(0.514015\pi\)
\(84\) 0 0
\(85\) 22.1189 2.39913
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.75832 0.928381 0.464190 0.885736i \(-0.346345\pi\)
0.464190 + 0.885736i \(0.346345\pi\)
\(90\) 0 0
\(91\) −2.16649 −0.227110
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.98766 0.409125
\(96\) 0 0
\(97\) 0.744519 0.0755945 0.0377972 0.999285i \(-0.487966\pi\)
0.0377972 + 0.999285i \(0.487966\pi\)
\(98\) 0 0
\(99\) 6.83956 0.687402
\(100\) 0 0
\(101\) 11.5768 1.15193 0.575966 0.817474i \(-0.304626\pi\)
0.575966 + 0.817474i \(0.304626\pi\)
\(102\) 0 0
\(103\) 7.53366 0.742314 0.371157 0.928570i \(-0.378961\pi\)
0.371157 + 0.928570i \(0.378961\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.14032 0.206913 0.103456 0.994634i \(-0.467010\pi\)
0.103456 + 0.994634i \(0.467010\pi\)
\(108\) 0 0
\(109\) 14.4799 1.38692 0.693460 0.720495i \(-0.256085\pi\)
0.693460 + 0.720495i \(0.256085\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.04557 0.756864 0.378432 0.925629i \(-0.376463\pi\)
0.378432 + 0.925629i \(0.376463\pi\)
\(114\) 0 0
\(115\) −7.74618 −0.722335
\(116\) 0 0
\(117\) 7.45033 0.688783
\(118\) 0 0
\(119\) 4.83891 0.443582
\(120\) 0 0
\(121\) −5.80227 −0.527479
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 23.5328 2.10484
\(126\) 0 0
\(127\) 6.66732 0.591629 0.295815 0.955245i \(-0.404409\pi\)
0.295815 + 0.955245i \(0.404409\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.7110 −1.02320 −0.511598 0.859225i \(-0.670946\pi\)
−0.511598 + 0.859225i \(0.670946\pi\)
\(132\) 0 0
\(133\) 0.872374 0.0756444
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.2910 1.64814 0.824071 0.566486i \(-0.191698\pi\)
0.824071 + 0.566486i \(0.191698\pi\)
\(138\) 0 0
\(139\) −8.11435 −0.688250 −0.344125 0.938924i \(-0.611824\pi\)
−0.344125 + 0.938924i \(0.611824\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.66189 0.473471
\(144\) 0 0
\(145\) 26.4986 2.20059
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.2057 −0.918004 −0.459002 0.888435i \(-0.651793\pi\)
−0.459002 + 0.888435i \(0.651793\pi\)
\(150\) 0 0
\(151\) 7.82671 0.636929 0.318464 0.947935i \(-0.396833\pi\)
0.318464 + 0.947935i \(0.396833\pi\)
\(152\) 0 0
\(153\) −16.6405 −1.34530
\(154\) 0 0
\(155\) 22.5316 1.80978
\(156\) 0 0
\(157\) 8.77306 0.700166 0.350083 0.936719i \(-0.386153\pi\)
0.350083 + 0.936719i \(0.386153\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.69462 −0.133555
\(162\) 0 0
\(163\) −16.0618 −1.25806 −0.629030 0.777381i \(-0.716548\pi\)
−0.629030 + 0.777381i \(0.716548\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.5889 −1.59321 −0.796607 0.604498i \(-0.793374\pi\)
−0.796607 + 0.604498i \(0.793374\pi\)
\(168\) 0 0
\(169\) −6.83251 −0.525577
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) −8.94682 −0.680214 −0.340107 0.940387i \(-0.610463\pi\)
−0.340107 + 0.940387i \(0.610463\pi\)
\(174\) 0 0
\(175\) 9.51011 0.718897
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.47553 −0.484004 −0.242002 0.970276i \(-0.577804\pi\)
−0.242002 + 0.970276i \(0.577804\pi\)
\(180\) 0 0
\(181\) 5.64865 0.419861 0.209930 0.977716i \(-0.432676\pi\)
0.209930 + 0.977716i \(0.432676\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −27.5234 −2.02356
\(186\) 0 0
\(187\) −12.6460 −0.924764
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.5415 1.26926 0.634628 0.772818i \(-0.281153\pi\)
0.634628 + 0.772818i \(0.281153\pi\)
\(192\) 0 0
\(193\) 12.2859 0.884359 0.442179 0.896927i \(-0.354206\pi\)
0.442179 + 0.896927i \(0.354206\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.2090 −0.869855 −0.434928 0.900465i \(-0.643226\pi\)
−0.434928 + 0.900465i \(0.643226\pi\)
\(198\) 0 0
\(199\) 0.321349 0.0227799 0.0113899 0.999935i \(-0.496374\pi\)
0.0113899 + 0.999935i \(0.496374\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.79707 0.406874
\(204\) 0 0
\(205\) −10.1845 −0.711320
\(206\) 0 0
\(207\) 5.82762 0.405047
\(208\) 0 0
\(209\) −2.27985 −0.157701
\(210\) 0 0
\(211\) 10.9444 0.753442 0.376721 0.926327i \(-0.377052\pi\)
0.376721 + 0.926327i \(0.377052\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 15.2859 1.04249
\(216\) 0 0
\(217\) 4.92921 0.334617
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −13.7752 −0.926623
\(222\) 0 0
\(223\) −12.9386 −0.866430 −0.433215 0.901291i \(-0.642621\pi\)
−0.433215 + 0.901291i \(0.642621\pi\)
\(224\) 0 0
\(225\) −32.7042 −2.18028
\(226\) 0 0
\(227\) −11.8651 −0.787516 −0.393758 0.919214i \(-0.628825\pi\)
−0.393758 + 0.919214i \(0.628825\pi\)
\(228\) 0 0
\(229\) 4.23471 0.279837 0.139919 0.990163i \(-0.455316\pi\)
0.139919 + 0.990163i \(0.455316\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.179775 0.0117774 0.00588871 0.999983i \(-0.498126\pi\)
0.00588871 + 0.999983i \(0.498126\pi\)
\(234\) 0 0
\(235\) −14.4936 −0.945460
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.22256 0.273135 0.136567 0.990631i \(-0.456393\pi\)
0.136567 + 0.990631i \(0.456393\pi\)
\(240\) 0 0
\(241\) 12.5055 0.805553 0.402776 0.915298i \(-0.368045\pi\)
0.402776 + 0.915298i \(0.368045\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −24.8789 −1.58945
\(246\) 0 0
\(247\) −2.48344 −0.158018
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.7232 −0.803082 −0.401541 0.915841i \(-0.631525\pi\)
−0.401541 + 0.915841i \(0.631525\pi\)
\(252\) 0 0
\(253\) 4.42870 0.278430
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.0193 0.624988 0.312494 0.949920i \(-0.398836\pi\)
0.312494 + 0.949920i \(0.398836\pi\)
\(258\) 0 0
\(259\) −6.02124 −0.374142
\(260\) 0 0
\(261\) −19.9355 −1.23398
\(262\) 0 0
\(263\) 14.8454 0.915409 0.457705 0.889104i \(-0.348672\pi\)
0.457705 + 0.889104i \(0.348672\pi\)
\(264\) 0 0
\(265\) 29.4837 1.81117
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.3622 1.11956 0.559781 0.828641i \(-0.310885\pi\)
0.559781 + 0.828641i \(0.310885\pi\)
\(270\) 0 0
\(271\) −19.0513 −1.15729 −0.578643 0.815581i \(-0.696417\pi\)
−0.578643 + 0.815581i \(0.696417\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −24.8536 −1.49873
\(276\) 0 0
\(277\) 1.79884 0.108082 0.0540408 0.998539i \(-0.482790\pi\)
0.0540408 + 0.998539i \(0.482790\pi\)
\(278\) 0 0
\(279\) −16.9510 −1.01483
\(280\) 0 0
\(281\) −10.8457 −0.646999 −0.323499 0.946228i \(-0.604859\pi\)
−0.323499 + 0.946228i \(0.604859\pi\)
\(282\) 0 0
\(283\) −9.02051 −0.536213 −0.268107 0.963389i \(-0.586398\pi\)
−0.268107 + 0.963389i \(0.586398\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.22806 −0.131518
\(288\) 0 0
\(289\) 13.7673 0.809843
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.13503 −0.416833 −0.208416 0.978040i \(-0.566831\pi\)
−0.208416 + 0.978040i \(0.566831\pi\)
\(294\) 0 0
\(295\) 8.16893 0.475613
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.82419 0.278990
\(300\) 0 0
\(301\) 3.34408 0.192750
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 32.6147 1.86751
\(306\) 0 0
\(307\) 26.8103 1.53014 0.765072 0.643945i \(-0.222703\pi\)
0.765072 + 0.643945i \(0.222703\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 31.0212 1.75905 0.879526 0.475851i \(-0.157860\pi\)
0.879526 + 0.475851i \(0.157860\pi\)
\(312\) 0 0
\(313\) 10.3000 0.582192 0.291096 0.956694i \(-0.405980\pi\)
0.291096 + 0.956694i \(0.405980\pi\)
\(314\) 0 0
\(315\) −10.4362 −0.588012
\(316\) 0 0
\(317\) −22.6423 −1.27172 −0.635860 0.771804i \(-0.719354\pi\)
−0.635860 + 0.771804i \(0.719354\pi\)
\(318\) 0 0
\(319\) −15.1500 −0.848237
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.54683 0.308634
\(324\) 0 0
\(325\) −27.0730 −1.50174
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.17075 −0.174809
\(330\) 0 0
\(331\) 27.7124 1.52321 0.761605 0.648041i \(-0.224412\pi\)
0.761605 + 0.648041i \(0.224412\pi\)
\(332\) 0 0
\(333\) 20.7064 1.13470
\(334\) 0 0
\(335\) 22.1681 1.21117
\(336\) 0 0
\(337\) −2.90426 −0.158205 −0.0791026 0.996866i \(-0.525205\pi\)
−0.0791026 + 0.996866i \(0.525205\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.8820 −0.697597
\(342\) 0 0
\(343\) −11.5493 −0.623605
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 24.0824 1.29281 0.646406 0.762993i \(-0.276271\pi\)
0.646406 + 0.762993i \(0.276271\pi\)
\(348\) 0 0
\(349\) −23.1267 −1.23794 −0.618971 0.785414i \(-0.712450\pi\)
−0.618971 + 0.785414i \(0.712450\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.06998 −0.323072 −0.161536 0.986867i \(-0.551645\pi\)
−0.161536 + 0.986867i \(0.551645\pi\)
\(354\) 0 0
\(355\) −5.56932 −0.295589
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.3493 −1.49622 −0.748110 0.663575i \(-0.769038\pi\)
−0.748110 + 0.663575i \(0.769038\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.3957 0.596477
\(366\) 0 0
\(367\) −25.1135 −1.31091 −0.655457 0.755232i \(-0.727524\pi\)
−0.655457 + 0.755232i \(0.727524\pi\)
\(368\) 0 0
\(369\) 7.66205 0.398871
\(370\) 0 0
\(371\) 6.45011 0.334873
\(372\) 0 0
\(373\) 1.06942 0.0553726 0.0276863 0.999617i \(-0.491186\pi\)
0.0276863 + 0.999617i \(0.491186\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.5029 −0.849942
\(378\) 0 0
\(379\) 21.6068 1.10987 0.554933 0.831895i \(-0.312744\pi\)
0.554933 + 0.831895i \(0.312744\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.3609 −0.631614 −0.315807 0.948823i \(-0.602275\pi\)
−0.315807 + 0.948823i \(0.602275\pi\)
\(384\) 0 0
\(385\) −7.93099 −0.404201
\(386\) 0 0
\(387\) −11.4999 −0.584574
\(388\) 0 0
\(389\) −2.82206 −0.143084 −0.0715422 0.997438i \(-0.522792\pi\)
−0.0715422 + 0.997438i \(0.522792\pi\)
\(390\) 0 0
\(391\) −10.7749 −0.544912
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.98766 0.200641
\(396\) 0 0
\(397\) 15.8720 0.796590 0.398295 0.917257i \(-0.369602\pi\)
0.398295 + 0.917257i \(0.369602\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.49385 −0.224412 −0.112206 0.993685i \(-0.535792\pi\)
−0.112206 + 0.993685i \(0.535792\pi\)
\(402\) 0 0
\(403\) −14.0323 −0.698999
\(404\) 0 0
\(405\) 35.8889 1.78333
\(406\) 0 0
\(407\) 15.7359 0.779998
\(408\) 0 0
\(409\) 3.09478 0.153027 0.0765134 0.997069i \(-0.475621\pi\)
0.0765134 + 0.997069i \(0.475621\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.78710 0.0879377
\(414\) 0 0
\(415\) −3.19802 −0.156985
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14.3679 −0.701917 −0.350958 0.936391i \(-0.614144\pi\)
−0.350958 + 0.936391i \(0.614144\pi\)
\(420\) 0 0
\(421\) −11.5319 −0.562031 −0.281016 0.959703i \(-0.590671\pi\)
−0.281016 + 0.959703i \(0.590671\pi\)
\(422\) 0 0
\(423\) 10.9039 0.530164
\(424\) 0 0
\(425\) 60.4683 2.93314
\(426\) 0 0
\(427\) 7.13506 0.345290
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.4239 −0.694775 −0.347387 0.937722i \(-0.612931\pi\)
−0.347387 + 0.937722i \(0.612931\pi\)
\(432\) 0 0
\(433\) −0.445323 −0.0214008 −0.0107004 0.999943i \(-0.503406\pi\)
−0.0107004 + 0.999943i \(0.503406\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.94254 −0.0929243
\(438\) 0 0
\(439\) −38.1363 −1.82015 −0.910073 0.414448i \(-0.863975\pi\)
−0.910073 + 0.414448i \(0.863975\pi\)
\(440\) 0 0
\(441\) 18.7169 0.891281
\(442\) 0 0
\(443\) −15.4816 −0.735554 −0.367777 0.929914i \(-0.619881\pi\)
−0.367777 + 0.929914i \(0.619881\pi\)
\(444\) 0 0
\(445\) 34.9252 1.65561
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.87322 0.135596 0.0677978 0.997699i \(-0.478403\pi\)
0.0677978 + 0.997699i \(0.478403\pi\)
\(450\) 0 0
\(451\) 5.82279 0.274184
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.63923 −0.405013
\(456\) 0 0
\(457\) −12.7373 −0.595824 −0.297912 0.954593i \(-0.596290\pi\)
−0.297912 + 0.954593i \(0.596290\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 25.2623 1.17658 0.588290 0.808650i \(-0.299801\pi\)
0.588290 + 0.808650i \(0.299801\pi\)
\(462\) 0 0
\(463\) −2.98300 −0.138632 −0.0693158 0.997595i \(-0.522082\pi\)
−0.0693158 + 0.997595i \(0.522082\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −26.1982 −1.21231 −0.606155 0.795347i \(-0.707289\pi\)
−0.606155 + 0.795347i \(0.707289\pi\)
\(468\) 0 0
\(469\) 4.84968 0.223937
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8.73939 −0.401837
\(474\) 0 0
\(475\) 10.9014 0.500191
\(476\) 0 0
\(477\) −22.1812 −1.01561
\(478\) 0 0
\(479\) −0.146462 −0.00669200 −0.00334600 0.999994i \(-0.501065\pi\)
−0.00334600 + 0.999994i \(0.501065\pi\)
\(480\) 0 0
\(481\) 17.1411 0.781565
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.96889 0.134810
\(486\) 0 0
\(487\) 21.1050 0.956361 0.478181 0.878262i \(-0.341296\pi\)
0.478181 + 0.878262i \(0.341296\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −13.6210 −0.614706 −0.307353 0.951596i \(-0.599443\pi\)
−0.307353 + 0.951596i \(0.599443\pi\)
\(492\) 0 0
\(493\) 36.8596 1.66007
\(494\) 0 0
\(495\) 27.2738 1.22587
\(496\) 0 0
\(497\) −1.21839 −0.0546523
\(498\) 0 0
\(499\) −30.0285 −1.34426 −0.672130 0.740434i \(-0.734620\pi\)
−0.672130 + 0.740434i \(0.734620\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.6193 −1.00854 −0.504272 0.863545i \(-0.668239\pi\)
−0.504272 + 0.863545i \(0.668239\pi\)
\(504\) 0 0
\(505\) 46.1642 2.05428
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.93587 −0.174454 −0.0872271 0.996188i \(-0.527801\pi\)
−0.0872271 + 0.996188i \(0.527801\pi\)
\(510\) 0 0
\(511\) 2.49302 0.110285
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 30.0417 1.32379
\(516\) 0 0
\(517\) 8.28641 0.364436
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 36.4829 1.59835 0.799173 0.601101i \(-0.205271\pi\)
0.799173 + 0.601101i \(0.205271\pi\)
\(522\) 0 0
\(523\) 14.0284 0.613420 0.306710 0.951803i \(-0.400772\pi\)
0.306710 + 0.951803i \(0.400772\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 31.3415 1.36526
\(528\) 0 0
\(529\) −19.2265 −0.835937
\(530\) 0 0
\(531\) −6.14566 −0.266699
\(532\) 0 0
\(533\) 6.34276 0.274735
\(534\) 0 0
\(535\) 8.53487 0.368995
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.2239 0.612668
\(540\) 0 0
\(541\) 20.6015 0.885726 0.442863 0.896589i \(-0.353963\pi\)
0.442863 + 0.896589i \(0.353963\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 57.7408 2.47334
\(546\) 0 0
\(547\) 10.4113 0.445156 0.222578 0.974915i \(-0.428553\pi\)
0.222578 + 0.974915i \(0.428553\pi\)
\(548\) 0 0
\(549\) −24.5367 −1.04720
\(550\) 0 0
\(551\) 6.64516 0.283093
\(552\) 0 0
\(553\) 0.872374 0.0370971
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11.3290 −0.480024 −0.240012 0.970770i \(-0.577151\pi\)
−0.240012 + 0.970770i \(0.577151\pi\)
\(558\) 0 0
\(559\) −9.51981 −0.402645
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.0048 1.05383 0.526914 0.849919i \(-0.323349\pi\)
0.526914 + 0.849919i \(0.323349\pi\)
\(564\) 0 0
\(565\) 32.0830 1.34974
\(566\) 0 0
\(567\) 7.85137 0.329726
\(568\) 0 0
\(569\) 21.0875 0.884033 0.442017 0.897007i \(-0.354263\pi\)
0.442017 + 0.897007i \(0.354263\pi\)
\(570\) 0 0
\(571\) 7.55987 0.316371 0.158185 0.987409i \(-0.449436\pi\)
0.158185 + 0.987409i \(0.449436\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −21.1764 −0.883118
\(576\) 0 0
\(577\) 10.2474 0.426604 0.213302 0.976986i \(-0.431578\pi\)
0.213302 + 0.976986i \(0.431578\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.699626 −0.0290254
\(582\) 0 0
\(583\) −16.8566 −0.698131
\(584\) 0 0
\(585\) 29.7094 1.22833
\(586\) 0 0
\(587\) −25.8692 −1.06773 −0.533867 0.845568i \(-0.679262\pi\)
−0.533867 + 0.845568i \(0.679262\pi\)
\(588\) 0 0
\(589\) 5.65034 0.232818
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.5603 0.680052 0.340026 0.940416i \(-0.389564\pi\)
0.340026 + 0.940416i \(0.389564\pi\)
\(594\) 0 0
\(595\) 19.2959 0.791055
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −45.5143 −1.85966 −0.929832 0.367984i \(-0.880048\pi\)
−0.929832 + 0.367984i \(0.880048\pi\)
\(600\) 0 0
\(601\) 3.71450 0.151518 0.0757588 0.997126i \(-0.475862\pi\)
0.0757588 + 0.997126i \(0.475862\pi\)
\(602\) 0 0
\(603\) −16.6775 −0.679161
\(604\) 0 0
\(605\) −23.1375 −0.940672
\(606\) 0 0
\(607\) −13.2147 −0.536366 −0.268183 0.963368i \(-0.586423\pi\)
−0.268183 + 0.963368i \(0.586423\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.02638 0.365168
\(612\) 0 0
\(613\) 17.5702 0.709652 0.354826 0.934932i \(-0.384540\pi\)
0.354826 + 0.934932i \(0.384540\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.46378 0.139447 0.0697233 0.997566i \(-0.477788\pi\)
0.0697233 + 0.997566i \(0.477788\pi\)
\(618\) 0 0
\(619\) 10.0396 0.403527 0.201764 0.979434i \(-0.435333\pi\)
0.201764 + 0.979434i \(0.435333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.64053 0.306112
\(624\) 0 0
\(625\) 39.3337 1.57335
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −38.2850 −1.52652
\(630\) 0 0
\(631\) −20.4222 −0.812997 −0.406498 0.913651i \(-0.633250\pi\)
−0.406498 + 0.913651i \(0.633250\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 26.5870 1.05507
\(636\) 0 0
\(637\) 15.4941 0.613899
\(638\) 0 0
\(639\) 4.18992 0.165751
\(640\) 0 0
\(641\) 4.93322 0.194850 0.0974251 0.995243i \(-0.468939\pi\)
0.0974251 + 0.995243i \(0.468939\pi\)
\(642\) 0 0
\(643\) 31.8777 1.25713 0.628566 0.777756i \(-0.283642\pi\)
0.628566 + 0.777756i \(0.283642\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.12314 0.0834694 0.0417347 0.999129i \(-0.486712\pi\)
0.0417347 + 0.999129i \(0.486712\pi\)
\(648\) 0 0
\(649\) −4.67040 −0.183329
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 30.5999 1.19747 0.598734 0.800948i \(-0.295671\pi\)
0.598734 + 0.800948i \(0.295671\pi\)
\(654\) 0 0
\(655\) −46.6995 −1.82470
\(656\) 0 0
\(657\) −8.57322 −0.334473
\(658\) 0 0
\(659\) 22.9880 0.895486 0.447743 0.894162i \(-0.352228\pi\)
0.447743 + 0.894162i \(0.352228\pi\)
\(660\) 0 0
\(661\) 15.9218 0.619287 0.309644 0.950853i \(-0.399790\pi\)
0.309644 + 0.950853i \(0.399790\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.47873 0.134899
\(666\) 0 0
\(667\) −12.9085 −0.499819
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.6467 −0.719848
\(672\) 0 0
\(673\) −10.7354 −0.413820 −0.206910 0.978360i \(-0.566341\pi\)
−0.206910 + 0.978360i \(0.566341\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −49.5312 −1.90364 −0.951820 0.306657i \(-0.900789\pi\)
−0.951820 + 0.306657i \(0.900789\pi\)
\(678\) 0 0
\(679\) 0.649499 0.0249255
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.67031 −0.216968 −0.108484 0.994098i \(-0.534600\pi\)
−0.108484 + 0.994098i \(0.534600\pi\)
\(684\) 0 0
\(685\) 76.9260 2.93919
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.3619 −0.699534
\(690\) 0 0
\(691\) −8.95821 −0.340786 −0.170393 0.985376i \(-0.554504\pi\)
−0.170393 + 0.985376i \(0.554504\pi\)
\(692\) 0 0
\(693\) 5.96665 0.226654
\(694\) 0 0
\(695\) −32.3573 −1.22738
\(696\) 0 0
\(697\) −14.1667 −0.536602
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −17.2560 −0.651752 −0.325876 0.945413i \(-0.605659\pi\)
−0.325876 + 0.945413i \(0.605659\pi\)
\(702\) 0 0
\(703\) −6.90214 −0.260319
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.0993 0.379822
\(708\) 0 0
\(709\) −10.4533 −0.392583 −0.196291 0.980546i \(-0.562890\pi\)
−0.196291 + 0.980546i \(0.562890\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −10.9760 −0.411055
\(714\) 0 0
\(715\) 22.5777 0.844357
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −39.8893 −1.48762 −0.743809 0.668392i \(-0.766983\pi\)
−0.743809 + 0.668392i \(0.766983\pi\)
\(720\) 0 0
\(721\) 6.57217 0.244760
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 72.4416 2.69041
\(726\) 0 0
\(727\) 24.0286 0.891170 0.445585 0.895240i \(-0.352996\pi\)
0.445585 + 0.895240i \(0.352996\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 21.2627 0.786430
\(732\) 0 0
\(733\) 6.99852 0.258496 0.129248 0.991612i \(-0.458744\pi\)
0.129248 + 0.991612i \(0.458744\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.6741 −0.466856
\(738\) 0 0
\(739\) −4.23781 −0.155890 −0.0779452 0.996958i \(-0.524836\pi\)
−0.0779452 + 0.996958i \(0.524836\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.34362 0.196038 0.0980192 0.995185i \(-0.468749\pi\)
0.0980192 + 0.995185i \(0.468749\pi\)
\(744\) 0 0
\(745\) −44.6844 −1.63711
\(746\) 0 0
\(747\) 2.40594 0.0880287
\(748\) 0 0
\(749\) 1.86716 0.0682246
\(750\) 0 0
\(751\) −48.2579 −1.76095 −0.880477 0.474089i \(-0.842778\pi\)
−0.880477 + 0.474089i \(0.842778\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 31.2102 1.13586
\(756\) 0 0
\(757\) 10.7924 0.392256 0.196128 0.980578i \(-0.437163\pi\)
0.196128 + 0.980578i \(0.437163\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −48.2148 −1.74779 −0.873893 0.486119i \(-0.838412\pi\)
−0.873893 + 0.486119i \(0.838412\pi\)
\(762\) 0 0
\(763\) 12.6319 0.457304
\(764\) 0 0
\(765\) −66.3566 −2.39913
\(766\) 0 0
\(767\) −5.08747 −0.183698
\(768\) 0 0
\(769\) 26.5293 0.956671 0.478336 0.878177i \(-0.341240\pi\)
0.478336 + 0.878177i \(0.341240\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19.0436 0.684950 0.342475 0.939527i \(-0.388735\pi\)
0.342475 + 0.939527i \(0.388735\pi\)
\(774\) 0 0
\(775\) 61.5967 2.21262
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.55402 −0.0915072
\(780\) 0 0
\(781\) 3.18413 0.113937
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 34.9839 1.24863
\(786\) 0 0
\(787\) 2.84495 0.101412 0.0507058 0.998714i \(-0.483853\pi\)
0.0507058 + 0.998714i \(0.483853\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.01875 0.249558
\(792\) 0 0
\(793\) −20.3119 −0.721295
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.83860 −0.100548 −0.0502741 0.998735i \(-0.516009\pi\)
−0.0502741 + 0.998735i \(0.516009\pi\)
\(798\) 0 0
\(799\) −20.1606 −0.713232
\(800\) 0 0
\(801\) −26.2750 −0.928381
\(802\) 0 0
\(803\) −6.51523 −0.229917
\(804\) 0 0
\(805\) −6.75757 −0.238173
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −40.7219 −1.43171 −0.715853 0.698251i \(-0.753962\pi\)
−0.715853 + 0.698251i \(0.753962\pi\)
\(810\) 0 0
\(811\) 6.88322 0.241703 0.120851 0.992671i \(-0.461438\pi\)
0.120851 + 0.992671i \(0.461438\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −64.0491 −2.24354
\(816\) 0 0
\(817\) 3.83331 0.134111
\(818\) 0 0
\(819\) 6.49948 0.227110
\(820\) 0 0
\(821\) 20.0312 0.699093 0.349546 0.936919i \(-0.386336\pi\)
0.349546 + 0.936919i \(0.386336\pi\)
\(822\) 0 0
\(823\) 7.22063 0.251695 0.125848 0.992050i \(-0.459835\pi\)
0.125848 + 0.992050i \(0.459835\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.92971 −0.136649 −0.0683247 0.997663i \(-0.521765\pi\)
−0.0683247 + 0.997663i \(0.521765\pi\)
\(828\) 0 0
\(829\) −34.6915 −1.20488 −0.602442 0.798163i \(-0.705806\pi\)
−0.602442 + 0.798163i \(0.705806\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −34.6065 −1.19904
\(834\) 0 0
\(835\) −82.1013 −2.84123
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 46.9673 1.62149 0.810745 0.585400i \(-0.199062\pi\)
0.810745 + 0.585400i \(0.199062\pi\)
\(840\) 0 0
\(841\) 15.1582 0.522695
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −27.2457 −0.937280
\(846\) 0 0
\(847\) −5.06175 −0.173924
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 13.4077 0.459609
\(852\) 0 0
\(853\) −29.1513 −0.998120 −0.499060 0.866567i \(-0.666321\pi\)
−0.499060 + 0.866567i \(0.666321\pi\)
\(854\) 0 0
\(855\) −11.9630 −0.409125
\(856\) 0 0
\(857\) −54.9357 −1.87657 −0.938284 0.345867i \(-0.887585\pi\)
−0.938284 + 0.345867i \(0.887585\pi\)
\(858\) 0 0
\(859\) −15.8361 −0.540322 −0.270161 0.962815i \(-0.587077\pi\)
−0.270161 + 0.962815i \(0.587077\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 41.3913 1.40898 0.704489 0.709715i \(-0.251176\pi\)
0.704489 + 0.709715i \(0.251176\pi\)
\(864\) 0 0
\(865\) −35.6769 −1.21305
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.27985 −0.0773387
\(870\) 0 0
\(871\) −13.8059 −0.467795
\(872\) 0 0
\(873\) −2.23356 −0.0755945
\(874\) 0 0
\(875\) 20.5294 0.694021
\(876\) 0 0
\(877\) 28.2513 0.953980 0.476990 0.878909i \(-0.341728\pi\)
0.476990 + 0.878909i \(0.341728\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7.20945 −0.242893 −0.121446 0.992598i \(-0.538753\pi\)
−0.121446 + 0.992598i \(0.538753\pi\)
\(882\) 0 0
\(883\) −34.8519 −1.17286 −0.586429 0.810001i \(-0.699467\pi\)
−0.586429 + 0.810001i \(0.699467\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14.5025 0.486947 0.243473 0.969908i \(-0.421713\pi\)
0.243473 + 0.969908i \(0.421713\pi\)
\(888\) 0 0
\(889\) 5.81640 0.195076
\(890\) 0 0
\(891\) −20.5187 −0.687402
\(892\) 0 0
\(893\) −3.63462 −0.121628
\(894\) 0 0
\(895\) −25.8222 −0.863141
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 37.5474 1.25228
\(900\) 0 0
\(901\) 41.0118 1.36630
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 22.5249 0.748752
\(906\) 0 0
\(907\) −16.5530 −0.549634 −0.274817 0.961497i \(-0.588617\pi\)
−0.274817 + 0.961497i \(0.588617\pi\)
\(908\) 0 0
\(909\) −34.7303 −1.15193
\(910\) 0 0
\(911\) 33.4685 1.10886 0.554431 0.832230i \(-0.312936\pi\)
0.554431 + 0.832230i \(0.312936\pi\)
\(912\) 0 0
\(913\) 1.82840 0.0605111
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10.2164 −0.337375
\(918\) 0 0
\(919\) −48.1504 −1.58833 −0.794167 0.607699i \(-0.792093\pi\)
−0.794167 + 0.607699i \(0.792093\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 3.46847 0.114166
\(924\) 0 0
\(925\) −75.2430 −2.47398
\(926\) 0 0
\(927\) −22.6010 −0.742314
\(928\) 0 0
\(929\) 31.9599 1.04857 0.524285 0.851543i \(-0.324333\pi\)
0.524285 + 0.851543i \(0.324333\pi\)
\(930\) 0 0
\(931\) −6.23896 −0.204474
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −50.4278 −1.64916
\(936\) 0 0
\(937\) 29.0852 0.950172 0.475086 0.879939i \(-0.342417\pi\)
0.475086 + 0.879939i \(0.342417\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −33.3042 −1.08569 −0.542843 0.839834i \(-0.682652\pi\)
−0.542843 + 0.839834i \(0.682652\pi\)
\(942\) 0 0
\(943\) 4.96128 0.161562
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.83837 0.0597391 0.0298695 0.999554i \(-0.490491\pi\)
0.0298695 + 0.999554i \(0.490491\pi\)
\(948\) 0 0
\(949\) −7.09703 −0.230379
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −14.3031 −0.463323 −0.231661 0.972797i \(-0.574416\pi\)
−0.231661 + 0.972797i \(0.574416\pi\)
\(954\) 0 0
\(955\) 69.9494 2.26351
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16.8290 0.543436
\(960\) 0 0
\(961\) 0.926384 0.0298834
\(962\) 0 0
\(963\) −6.42096 −0.206913
\(964\) 0 0
\(965\) 48.9920 1.57711
\(966\) 0 0
\(967\) −44.2581 −1.42325 −0.711623 0.702562i \(-0.752040\pi\)
−0.711623 + 0.702562i \(0.752040\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 5.60977 0.180026 0.0900131 0.995941i \(-0.471309\pi\)
0.0900131 + 0.995941i \(0.471309\pi\)
\(972\) 0 0
\(973\) −7.07875 −0.226934
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −15.7298 −0.503241 −0.251620 0.967826i \(-0.580963\pi\)
−0.251620 + 0.967826i \(0.580963\pi\)
\(978\) 0 0
\(979\) −19.9677 −0.638170
\(980\) 0 0
\(981\) −43.4396 −1.38692
\(982\) 0 0
\(983\) 23.2066 0.740177 0.370088 0.928997i \(-0.379327\pi\)
0.370088 + 0.928997i \(0.379327\pi\)
\(984\) 0 0
\(985\) −48.6853 −1.55124
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.44636 −0.236780
\(990\) 0 0
\(991\) −39.6636 −1.25996 −0.629978 0.776613i \(-0.716936\pi\)
−0.629978 + 0.776613i \(0.716936\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.28143 0.0406241
\(996\) 0 0
\(997\) −16.3777 −0.518688 −0.259344 0.965785i \(-0.583506\pi\)
−0.259344 + 0.965785i \(0.583506\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))