Properties

Label 6004.2.a.d.1.7
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 1.7
Root \(2.82169\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.82169 q^{5}\) \(+4.85844 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.82169 q^{5}\) \(+4.85844 q^{7}\) \(-3.00000 q^{9}\) \(+1.69392 q^{11}\) \(+3.33980 q^{13}\) \(-2.21020 q^{17}\) \(+1.00000 q^{19}\) \(+5.35348 q^{23}\) \(+2.96195 q^{25}\) \(-6.61191 q^{29}\) \(+1.16213 q^{31}\) \(+13.7090 q^{35}\) \(+4.72858 q^{37}\) \(-3.45902 q^{41}\) \(-3.96773 q^{43}\) \(-8.46508 q^{45}\) \(+0.312939 q^{47}\) \(+16.6044 q^{49}\) \(+5.80281 q^{53}\) \(+4.77971 q^{55}\) \(+6.38954 q^{59}\) \(+3.99750 q^{61}\) \(-14.5753 q^{63}\) \(+9.42389 q^{65}\) \(-1.03190 q^{67}\) \(+15.9324 q^{71}\) \(-16.0509 q^{73}\) \(+8.22979 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(-1.04666 q^{83}\) \(-6.23651 q^{85}\) \(-16.2736 q^{89}\) \(+16.2262 q^{91}\) \(+2.82169 q^{95}\) \(-6.30683 q^{97}\) \(-5.08175 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.82169 1.26190 0.630950 0.775824i \(-0.282665\pi\)
0.630950 + 0.775824i \(0.282665\pi\)
\(6\) 0 0
\(7\) 4.85844 1.83632 0.918158 0.396214i \(-0.129676\pi\)
0.918158 + 0.396214i \(0.129676\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 1.69392 0.510735 0.255367 0.966844i \(-0.417804\pi\)
0.255367 + 0.966844i \(0.417804\pi\)
\(12\) 0 0
\(13\) 3.33980 0.926294 0.463147 0.886281i \(-0.346720\pi\)
0.463147 + 0.886281i \(0.346720\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.21020 −0.536053 −0.268026 0.963412i \(-0.586371\pi\)
−0.268026 + 0.963412i \(0.586371\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.35348 1.11628 0.558139 0.829747i \(-0.311515\pi\)
0.558139 + 0.829747i \(0.311515\pi\)
\(24\) 0 0
\(25\) 2.96195 0.592390
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.61191 −1.22780 −0.613900 0.789383i \(-0.710400\pi\)
−0.613900 + 0.789383i \(0.710400\pi\)
\(30\) 0 0
\(31\) 1.16213 0.208724 0.104362 0.994539i \(-0.466720\pi\)
0.104362 + 0.994539i \(0.466720\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 13.7090 2.31725
\(36\) 0 0
\(37\) 4.72858 0.777374 0.388687 0.921370i \(-0.372929\pi\)
0.388687 + 0.921370i \(0.372929\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.45902 −0.540209 −0.270104 0.962831i \(-0.587058\pi\)
−0.270104 + 0.962831i \(0.587058\pi\)
\(42\) 0 0
\(43\) −3.96773 −0.605073 −0.302536 0.953138i \(-0.597833\pi\)
−0.302536 + 0.953138i \(0.597833\pi\)
\(44\) 0 0
\(45\) −8.46508 −1.26190
\(46\) 0 0
\(47\) 0.312939 0.0456468 0.0228234 0.999740i \(-0.492734\pi\)
0.0228234 + 0.999740i \(0.492734\pi\)
\(48\) 0 0
\(49\) 16.6044 2.37206
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.80281 0.797077 0.398538 0.917152i \(-0.369518\pi\)
0.398538 + 0.917152i \(0.369518\pi\)
\(54\) 0 0
\(55\) 4.77971 0.644496
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.38954 0.831847 0.415923 0.909400i \(-0.363458\pi\)
0.415923 + 0.909400i \(0.363458\pi\)
\(60\) 0 0
\(61\) 3.99750 0.511828 0.255914 0.966700i \(-0.417624\pi\)
0.255914 + 0.966700i \(0.417624\pi\)
\(62\) 0 0
\(63\) −14.5753 −1.83632
\(64\) 0 0
\(65\) 9.42389 1.16889
\(66\) 0 0
\(67\) −1.03190 −0.126066 −0.0630330 0.998011i \(-0.520077\pi\)
−0.0630330 + 0.998011i \(0.520077\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.9324 1.89083 0.945413 0.325875i \(-0.105659\pi\)
0.945413 + 0.325875i \(0.105659\pi\)
\(72\) 0 0
\(73\) −16.0509 −1.87861 −0.939306 0.343080i \(-0.888530\pi\)
−0.939306 + 0.343080i \(0.888530\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.22979 0.937871
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −1.04666 −0.114885 −0.0574427 0.998349i \(-0.518295\pi\)
−0.0574427 + 0.998349i \(0.518295\pi\)
\(84\) 0 0
\(85\) −6.23651 −0.676445
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −16.2736 −1.72499 −0.862497 0.506063i \(-0.831100\pi\)
−0.862497 + 0.506063i \(0.831100\pi\)
\(90\) 0 0
\(91\) 16.2262 1.70097
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.82169 0.289500
\(96\) 0 0
\(97\) −6.30683 −0.640361 −0.320181 0.947357i \(-0.603744\pi\)
−0.320181 + 0.947357i \(0.603744\pi\)
\(98\) 0 0
\(99\) −5.08175 −0.510735
\(100\) 0 0
\(101\) 10.7068 1.06537 0.532685 0.846313i \(-0.321183\pi\)
0.532685 + 0.846313i \(0.321183\pi\)
\(102\) 0 0
\(103\) −9.74933 −0.960630 −0.480315 0.877096i \(-0.659478\pi\)
−0.480315 + 0.877096i \(0.659478\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.4130 1.68338 0.841690 0.539961i \(-0.181561\pi\)
0.841690 + 0.539961i \(0.181561\pi\)
\(108\) 0 0
\(109\) 3.73579 0.357824 0.178912 0.983865i \(-0.442742\pi\)
0.178912 + 0.983865i \(0.442742\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.2946 1.53287 0.766433 0.642324i \(-0.222030\pi\)
0.766433 + 0.642324i \(0.222030\pi\)
\(114\) 0 0
\(115\) 15.1059 1.40863
\(116\) 0 0
\(117\) −10.0194 −0.926294
\(118\) 0 0
\(119\) −10.7381 −0.984363
\(120\) 0 0
\(121\) −8.13065 −0.739150
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.75075 −0.514362
\(126\) 0 0
\(127\) 11.8975 1.05574 0.527868 0.849327i \(-0.322992\pi\)
0.527868 + 0.849327i \(0.322992\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −21.2357 −1.85537 −0.927687 0.373358i \(-0.878206\pi\)
−0.927687 + 0.373358i \(0.878206\pi\)
\(132\) 0 0
\(133\) 4.85844 0.421280
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.19976 −0.187938 −0.0939692 0.995575i \(-0.529956\pi\)
−0.0939692 + 0.995575i \(0.529956\pi\)
\(138\) 0 0
\(139\) −9.83791 −0.834441 −0.417221 0.908805i \(-0.636996\pi\)
−0.417221 + 0.908805i \(0.636996\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.65734 0.473091
\(144\) 0 0
\(145\) −18.6568 −1.54936
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.64393 0.462369 0.231185 0.972910i \(-0.425740\pi\)
0.231185 + 0.972910i \(0.425740\pi\)
\(150\) 0 0
\(151\) 2.18465 0.177785 0.0888923 0.996041i \(-0.471667\pi\)
0.0888923 + 0.996041i \(0.471667\pi\)
\(152\) 0 0
\(153\) 6.63061 0.536053
\(154\) 0 0
\(155\) 3.27916 0.263389
\(156\) 0 0
\(157\) −6.55976 −0.523526 −0.261763 0.965132i \(-0.584304\pi\)
−0.261763 + 0.965132i \(0.584304\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 26.0096 2.04984
\(162\) 0 0
\(163\) 0.352462 0.0276069 0.0138035 0.999905i \(-0.495606\pi\)
0.0138035 + 0.999905i \(0.495606\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.77728 −0.447059 −0.223530 0.974697i \(-0.571758\pi\)
−0.223530 + 0.974697i \(0.571758\pi\)
\(168\) 0 0
\(169\) −1.84573 −0.141979
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) 11.1712 0.849330 0.424665 0.905350i \(-0.360392\pi\)
0.424665 + 0.905350i \(0.360392\pi\)
\(174\) 0 0
\(175\) 14.3905 1.08782
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.31850 0.322780 0.161390 0.986891i \(-0.448402\pi\)
0.161390 + 0.986891i \(0.448402\pi\)
\(180\) 0 0
\(181\) −2.34931 −0.174622 −0.0873112 0.996181i \(-0.527827\pi\)
−0.0873112 + 0.996181i \(0.527827\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 13.3426 0.980968
\(186\) 0 0
\(187\) −3.74390 −0.273781
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.25296 −0.380091 −0.190045 0.981775i \(-0.560863\pi\)
−0.190045 + 0.981775i \(0.560863\pi\)
\(192\) 0 0
\(193\) 14.7742 1.06347 0.531733 0.846912i \(-0.321541\pi\)
0.531733 + 0.846912i \(0.321541\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.0807586 0.00575381 0.00287690 0.999996i \(-0.499084\pi\)
0.00287690 + 0.999996i \(0.499084\pi\)
\(198\) 0 0
\(199\) −7.68238 −0.544590 −0.272295 0.962214i \(-0.587783\pi\)
−0.272295 + 0.962214i \(0.587783\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −32.1235 −2.25463
\(204\) 0 0
\(205\) −9.76030 −0.681689
\(206\) 0 0
\(207\) −16.0605 −1.11628
\(208\) 0 0
\(209\) 1.69392 0.117171
\(210\) 0 0
\(211\) −17.6243 −1.21331 −0.606653 0.794967i \(-0.707488\pi\)
−0.606653 + 0.794967i \(0.707488\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.1957 −0.763541
\(216\) 0 0
\(217\) 5.64611 0.383283
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7.38164 −0.496543
\(222\) 0 0
\(223\) −9.75731 −0.653398 −0.326699 0.945128i \(-0.605936\pi\)
−0.326699 + 0.945128i \(0.605936\pi\)
\(224\) 0 0
\(225\) −8.88586 −0.592390
\(226\) 0 0
\(227\) 12.4802 0.828341 0.414170 0.910199i \(-0.364072\pi\)
0.414170 + 0.910199i \(0.364072\pi\)
\(228\) 0 0
\(229\) −17.5468 −1.15953 −0.579763 0.814785i \(-0.696855\pi\)
−0.579763 + 0.814785i \(0.696855\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.85189 −0.579906 −0.289953 0.957041i \(-0.593640\pi\)
−0.289953 + 0.957041i \(0.593640\pi\)
\(234\) 0 0
\(235\) 0.883017 0.0576017
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.3177 1.63767 0.818833 0.574031i \(-0.194621\pi\)
0.818833 + 0.574031i \(0.194621\pi\)
\(240\) 0 0
\(241\) −7.86372 −0.506547 −0.253273 0.967395i \(-0.581507\pi\)
−0.253273 + 0.967395i \(0.581507\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 46.8525 2.99330
\(246\) 0 0
\(247\) 3.33980 0.212506
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.2683 −1.15308 −0.576542 0.817068i \(-0.695598\pi\)
−0.576542 + 0.817068i \(0.695598\pi\)
\(252\) 0 0
\(253\) 9.06835 0.570123
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 25.3389 1.58060 0.790300 0.612720i \(-0.209925\pi\)
0.790300 + 0.612720i \(0.209925\pi\)
\(258\) 0 0
\(259\) 22.9735 1.42750
\(260\) 0 0
\(261\) 19.8357 1.22780
\(262\) 0 0
\(263\) −15.9912 −0.986060 −0.493030 0.870012i \(-0.664111\pi\)
−0.493030 + 0.870012i \(0.664111\pi\)
\(264\) 0 0
\(265\) 16.3737 1.00583
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −26.3678 −1.60767 −0.803837 0.594850i \(-0.797211\pi\)
−0.803837 + 0.594850i \(0.797211\pi\)
\(270\) 0 0
\(271\) −15.0837 −0.916267 −0.458134 0.888883i \(-0.651482\pi\)
−0.458134 + 0.888883i \(0.651482\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.01730 0.302554
\(276\) 0 0
\(277\) −32.3249 −1.94222 −0.971108 0.238639i \(-0.923299\pi\)
−0.971108 + 0.238639i \(0.923299\pi\)
\(278\) 0 0
\(279\) −3.48638 −0.208724
\(280\) 0 0
\(281\) 27.9457 1.66710 0.833551 0.552443i \(-0.186304\pi\)
0.833551 + 0.552443i \(0.186304\pi\)
\(282\) 0 0
\(283\) 14.8329 0.881724 0.440862 0.897575i \(-0.354673\pi\)
0.440862 + 0.897575i \(0.354673\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −16.8054 −0.991994
\(288\) 0 0
\(289\) −12.1150 −0.712647
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.757761 −0.0442689 −0.0221344 0.999755i \(-0.507046\pi\)
−0.0221344 + 0.999755i \(0.507046\pi\)
\(294\) 0 0
\(295\) 18.0293 1.04971
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 17.8796 1.03400
\(300\) 0 0
\(301\) −19.2770 −1.11111
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.2797 0.645875
\(306\) 0 0
\(307\) 28.3504 1.61804 0.809022 0.587779i \(-0.199997\pi\)
0.809022 + 0.587779i \(0.199997\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.2091 −1.03254 −0.516272 0.856425i \(-0.672681\pi\)
−0.516272 + 0.856425i \(0.672681\pi\)
\(312\) 0 0
\(313\) −4.19041 −0.236856 −0.118428 0.992963i \(-0.537785\pi\)
−0.118428 + 0.992963i \(0.537785\pi\)
\(314\) 0 0
\(315\) −41.1271 −2.31725
\(316\) 0 0
\(317\) 14.2686 0.801407 0.400704 0.916208i \(-0.368766\pi\)
0.400704 + 0.916208i \(0.368766\pi\)
\(318\) 0 0
\(319\) −11.2000 −0.627081
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.21020 −0.122979
\(324\) 0 0
\(325\) 9.89233 0.548728
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.52039 0.0838220
\(330\) 0 0
\(331\) −1.22901 −0.0675523 −0.0337761 0.999429i \(-0.510753\pi\)
−0.0337761 + 0.999429i \(0.510753\pi\)
\(332\) 0 0
\(333\) −14.1857 −0.777374
\(334\) 0 0
\(335\) −2.91169 −0.159083
\(336\) 0 0
\(337\) 32.8592 1.78995 0.894976 0.446113i \(-0.147192\pi\)
0.894976 + 0.446113i \(0.147192\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.96854 0.106603
\(342\) 0 0
\(343\) 46.6624 2.51953
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.0851 −0.541395 −0.270698 0.962664i \(-0.587254\pi\)
−0.270698 + 0.962664i \(0.587254\pi\)
\(348\) 0 0
\(349\) −11.7912 −0.631170 −0.315585 0.948897i \(-0.602201\pi\)
−0.315585 + 0.948897i \(0.602201\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.6760 1.36660 0.683298 0.730139i \(-0.260545\pi\)
0.683298 + 0.730139i \(0.260545\pi\)
\(354\) 0 0
\(355\) 44.9563 2.38603
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −19.5002 −1.02918 −0.514590 0.857436i \(-0.672056\pi\)
−0.514590 + 0.857436i \(0.672056\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −45.2906 −2.37062
\(366\) 0 0
\(367\) −25.5547 −1.33395 −0.666974 0.745081i \(-0.732411\pi\)
−0.666974 + 0.745081i \(0.732411\pi\)
\(368\) 0 0
\(369\) 10.3771 0.540209
\(370\) 0 0
\(371\) 28.1926 1.46369
\(372\) 0 0
\(373\) 1.53066 0.0792545 0.0396272 0.999215i \(-0.487383\pi\)
0.0396272 + 0.999215i \(0.487383\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.0825 −1.13730
\(378\) 0 0
\(379\) −26.6752 −1.37021 −0.685107 0.728442i \(-0.740245\pi\)
−0.685107 + 0.728442i \(0.740245\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.34435 −0.221986 −0.110993 0.993821i \(-0.535403\pi\)
−0.110993 + 0.993821i \(0.535403\pi\)
\(384\) 0 0
\(385\) 23.2219 1.18350
\(386\) 0 0
\(387\) 11.9032 0.605073
\(388\) 0 0
\(389\) −2.36016 −0.119665 −0.0598325 0.998208i \(-0.519057\pi\)
−0.0598325 + 0.998208i \(0.519057\pi\)
\(390\) 0 0
\(391\) −11.8323 −0.598384
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.82169 0.141975
\(396\) 0 0
\(397\) 34.5939 1.73622 0.868108 0.496375i \(-0.165336\pi\)
0.868108 + 0.496375i \(0.165336\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.0951 −0.853688 −0.426844 0.904325i \(-0.640375\pi\)
−0.426844 + 0.904325i \(0.640375\pi\)
\(402\) 0 0
\(403\) 3.88127 0.193340
\(404\) 0 0
\(405\) 25.3952 1.26190
\(406\) 0 0
\(407\) 8.00982 0.397032
\(408\) 0 0
\(409\) −17.9216 −0.886165 −0.443082 0.896481i \(-0.646115\pi\)
−0.443082 + 0.896481i \(0.646115\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 31.0432 1.52753
\(414\) 0 0
\(415\) −2.95334 −0.144974
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.4187 1.19293 0.596467 0.802638i \(-0.296571\pi\)
0.596467 + 0.802638i \(0.296571\pi\)
\(420\) 0 0
\(421\) 24.5791 1.19791 0.598956 0.800782i \(-0.295583\pi\)
0.598956 + 0.800782i \(0.295583\pi\)
\(422\) 0 0
\(423\) −0.938816 −0.0456468
\(424\) 0 0
\(425\) −6.54651 −0.317552
\(426\) 0 0
\(427\) 19.4216 0.939877
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −31.6064 −1.52243 −0.761213 0.648501i \(-0.775396\pi\)
−0.761213 + 0.648501i \(0.775396\pi\)
\(432\) 0 0
\(433\) −26.0874 −1.25368 −0.626839 0.779149i \(-0.715652\pi\)
−0.626839 + 0.779149i \(0.715652\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.35348 0.256092
\(438\) 0 0
\(439\) 7.85137 0.374725 0.187363 0.982291i \(-0.440006\pi\)
0.187363 + 0.982291i \(0.440006\pi\)
\(440\) 0 0
\(441\) −49.8132 −2.37206
\(442\) 0 0
\(443\) 19.9555 0.948115 0.474057 0.880494i \(-0.342789\pi\)
0.474057 + 0.880494i \(0.342789\pi\)
\(444\) 0 0
\(445\) −45.9190 −2.17677
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 28.2978 1.33545 0.667727 0.744406i \(-0.267267\pi\)
0.667727 + 0.744406i \(0.267267\pi\)
\(450\) 0 0
\(451\) −5.85930 −0.275904
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 45.7854 2.14645
\(456\) 0 0
\(457\) 10.5264 0.492405 0.246203 0.969218i \(-0.420817\pi\)
0.246203 + 0.969218i \(0.420817\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 20.5589 0.957525 0.478763 0.877944i \(-0.341085\pi\)
0.478763 + 0.877944i \(0.341085\pi\)
\(462\) 0 0
\(463\) 17.9097 0.832334 0.416167 0.909288i \(-0.363373\pi\)
0.416167 + 0.909288i \(0.363373\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.500414 0.0231564 0.0115782 0.999933i \(-0.496314\pi\)
0.0115782 + 0.999933i \(0.496314\pi\)
\(468\) 0 0
\(469\) −5.01340 −0.231497
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.72100 −0.309032
\(474\) 0 0
\(475\) 2.96195 0.135904
\(476\) 0 0
\(477\) −17.4084 −0.797077
\(478\) 0 0
\(479\) 9.94940 0.454600 0.227300 0.973825i \(-0.427010\pi\)
0.227300 + 0.973825i \(0.427010\pi\)
\(480\) 0 0
\(481\) 15.7925 0.720077
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.7959 −0.808072
\(486\) 0 0
\(487\) −32.6003 −1.47726 −0.738631 0.674110i \(-0.764528\pi\)
−0.738631 + 0.674110i \(0.764528\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −30.7747 −1.38884 −0.694421 0.719569i \(-0.744340\pi\)
−0.694421 + 0.719569i \(0.744340\pi\)
\(492\) 0 0
\(493\) 14.6137 0.658166
\(494\) 0 0
\(495\) −14.3391 −0.644496
\(496\) 0 0
\(497\) 77.4065 3.47215
\(498\) 0 0
\(499\) 34.9097 1.56277 0.781386 0.624048i \(-0.214513\pi\)
0.781386 + 0.624048i \(0.214513\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −9.90815 −0.441782 −0.220891 0.975298i \(-0.570897\pi\)
−0.220891 + 0.975298i \(0.570897\pi\)
\(504\) 0 0
\(505\) 30.2114 1.34439
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22.7053 1.00639 0.503197 0.864172i \(-0.332157\pi\)
0.503197 + 0.864172i \(0.332157\pi\)
\(510\) 0 0
\(511\) −77.9821 −3.44973
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −27.5096 −1.21222
\(516\) 0 0
\(517\) 0.530092 0.0233134
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.02911 0.307951 0.153975 0.988075i \(-0.450792\pi\)
0.153975 + 0.988075i \(0.450792\pi\)
\(522\) 0 0
\(523\) 24.2642 1.06100 0.530500 0.847685i \(-0.322004\pi\)
0.530500 + 0.847685i \(0.322004\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.56853 −0.111887
\(528\) 0 0
\(529\) 5.65979 0.246078
\(530\) 0 0
\(531\) −19.1686 −0.831847
\(532\) 0 0
\(533\) −11.5525 −0.500392
\(534\) 0 0
\(535\) 49.1342 2.12426
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 28.1265 1.21149
\(540\) 0 0
\(541\) 17.8481 0.767349 0.383674 0.923468i \(-0.374659\pi\)
0.383674 + 0.923468i \(0.374659\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.5413 0.451538
\(546\) 0 0
\(547\) 8.86098 0.378868 0.189434 0.981893i \(-0.439335\pi\)
0.189434 + 0.981893i \(0.439335\pi\)
\(548\) 0 0
\(549\) −11.9925 −0.511828
\(550\) 0 0
\(551\) −6.61191 −0.281677
\(552\) 0 0
\(553\) 4.85844 0.206602
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 45.3172 1.92015 0.960076 0.279741i \(-0.0902485\pi\)
0.960076 + 0.279741i \(0.0902485\pi\)
\(558\) 0 0
\(559\) −13.2514 −0.560475
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.19225 0.134537 0.0672687 0.997735i \(-0.478572\pi\)
0.0672687 + 0.997735i \(0.478572\pi\)
\(564\) 0 0
\(565\) 45.9783 1.93432
\(566\) 0 0
\(567\) 43.7259 1.83632
\(568\) 0 0
\(569\) −7.14434 −0.299506 −0.149753 0.988723i \(-0.547848\pi\)
−0.149753 + 0.988723i \(0.547848\pi\)
\(570\) 0 0
\(571\) 44.1456 1.84744 0.923718 0.383073i \(-0.125134\pi\)
0.923718 + 0.383073i \(0.125134\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 15.8568 0.661273
\(576\) 0 0
\(577\) 12.5902 0.524139 0.262069 0.965049i \(-0.415595\pi\)
0.262069 + 0.965049i \(0.415595\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.08511 −0.210966
\(582\) 0 0
\(583\) 9.82947 0.407095
\(584\) 0 0
\(585\) −28.2717 −1.16889
\(586\) 0 0
\(587\) 22.7855 0.940458 0.470229 0.882545i \(-0.344171\pi\)
0.470229 + 0.882545i \(0.344171\pi\)
\(588\) 0 0
\(589\) 1.16213 0.0478845
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.8252 −0.526668 −0.263334 0.964705i \(-0.584822\pi\)
−0.263334 + 0.964705i \(0.584822\pi\)
\(594\) 0 0
\(595\) −30.2997 −1.24217
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −41.0442 −1.67702 −0.838511 0.544884i \(-0.816574\pi\)
−0.838511 + 0.544884i \(0.816574\pi\)
\(600\) 0 0
\(601\) −2.87696 −0.117354 −0.0586768 0.998277i \(-0.518688\pi\)
−0.0586768 + 0.998277i \(0.518688\pi\)
\(602\) 0 0
\(603\) 3.09569 0.126066
\(604\) 0 0
\(605\) −22.9422 −0.932733
\(606\) 0 0
\(607\) −33.3515 −1.35369 −0.676847 0.736124i \(-0.736654\pi\)
−0.676847 + 0.736124i \(0.736654\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.04515 0.0422824
\(612\) 0 0
\(613\) 24.9191 1.00647 0.503237 0.864149i \(-0.332142\pi\)
0.503237 + 0.864149i \(0.332142\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 46.2527 1.86207 0.931033 0.364936i \(-0.118909\pi\)
0.931033 + 0.364936i \(0.118909\pi\)
\(618\) 0 0
\(619\) −24.7757 −0.995818 −0.497909 0.867229i \(-0.665899\pi\)
−0.497909 + 0.867229i \(0.665899\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −79.0640 −3.16763
\(624\) 0 0
\(625\) −31.0366 −1.24146
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10.4511 −0.416713
\(630\) 0 0
\(631\) 15.7381 0.626526 0.313263 0.949666i \(-0.398578\pi\)
0.313263 + 0.949666i \(0.398578\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 33.5712 1.33223
\(636\) 0 0
\(637\) 55.4554 2.19722
\(638\) 0 0
\(639\) −47.7971 −1.89083
\(640\) 0 0
\(641\) 22.9675 0.907160 0.453580 0.891215i \(-0.350147\pi\)
0.453580 + 0.891215i \(0.350147\pi\)
\(642\) 0 0
\(643\) −45.2197 −1.78329 −0.891646 0.452733i \(-0.850449\pi\)
−0.891646 + 0.452733i \(0.850449\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.6124 0.613788 0.306894 0.951744i \(-0.400710\pi\)
0.306894 + 0.951744i \(0.400710\pi\)
\(648\) 0 0
\(649\) 10.8233 0.424853
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.4940 0.528060 0.264030 0.964514i \(-0.414948\pi\)
0.264030 + 0.964514i \(0.414948\pi\)
\(654\) 0 0
\(655\) −59.9207 −2.34130
\(656\) 0 0
\(657\) 48.1526 1.87861
\(658\) 0 0
\(659\) −21.0964 −0.821799 −0.410900 0.911681i \(-0.634785\pi\)
−0.410900 + 0.911681i \(0.634785\pi\)
\(660\) 0 0
\(661\) −27.6057 −1.07374 −0.536869 0.843666i \(-0.680393\pi\)
−0.536869 + 0.843666i \(0.680393\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.7090 0.531613
\(666\) 0 0
\(667\) −35.3968 −1.37057
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.77143 0.261408
\(672\) 0 0
\(673\) 45.9966 1.77304 0.886519 0.462692i \(-0.153116\pi\)
0.886519 + 0.462692i \(0.153116\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.1259 0.389170 0.194585 0.980886i \(-0.437664\pi\)
0.194585 + 0.980886i \(0.437664\pi\)
\(678\) 0 0
\(679\) −30.6413 −1.17591
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −11.9348 −0.456672 −0.228336 0.973582i \(-0.573329\pi\)
−0.228336 + 0.973582i \(0.573329\pi\)
\(684\) 0 0
\(685\) −6.20705 −0.237159
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 19.3802 0.738328
\(690\) 0 0
\(691\) 29.5500 1.12414 0.562068 0.827091i \(-0.310006\pi\)
0.562068 + 0.827091i \(0.310006\pi\)
\(692\) 0 0
\(693\) −24.6894 −0.937871
\(694\) 0 0
\(695\) −27.7596 −1.05298
\(696\) 0 0
\(697\) 7.64514 0.289580
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.0313 −1.28534 −0.642671 0.766142i \(-0.722174\pi\)
−0.642671 + 0.766142i \(0.722174\pi\)
\(702\) 0 0
\(703\) 4.72858 0.178342
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 52.0185 1.95636
\(708\) 0 0
\(709\) −43.4999 −1.63367 −0.816837 0.576869i \(-0.804274\pi\)
−0.816837 + 0.576869i \(0.804274\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) 6.22142 0.232994
\(714\) 0 0
\(715\) 15.9633 0.596993
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11.5944 −0.432398 −0.216199 0.976349i \(-0.569366\pi\)
−0.216199 + 0.976349i \(0.569366\pi\)
\(720\) 0 0
\(721\) −47.3665 −1.76402
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.5842 −0.727337
\(726\) 0 0
\(727\) 3.51600 0.130401 0.0652006 0.997872i \(-0.479231\pi\)
0.0652006 + 0.997872i \(0.479231\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 8.76948 0.324351
\(732\) 0 0
\(733\) 17.0432 0.629506 0.314753 0.949174i \(-0.398078\pi\)
0.314753 + 0.949174i \(0.398078\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.74794 −0.0643864
\(738\) 0 0
\(739\) −45.0638 −1.65770 −0.828850 0.559471i \(-0.811004\pi\)
−0.828850 + 0.559471i \(0.811004\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19.1124 −0.701167 −0.350583 0.936532i \(-0.614017\pi\)
−0.350583 + 0.936532i \(0.614017\pi\)
\(744\) 0 0
\(745\) 15.9255 0.583463
\(746\) 0 0
\(747\) 3.13997 0.114885
\(748\) 0 0
\(749\) 84.6000 3.09122
\(750\) 0 0
\(751\) 16.9146 0.617224 0.308612 0.951188i \(-0.400136\pi\)
0.308612 + 0.951188i \(0.400136\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.16443 0.224346
\(756\) 0 0
\(757\) −25.6554 −0.932462 −0.466231 0.884663i \(-0.654388\pi\)
−0.466231 + 0.884663i \(0.654388\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 29.3369 1.06346 0.531731 0.846913i \(-0.321542\pi\)
0.531731 + 0.846913i \(0.321542\pi\)
\(762\) 0 0
\(763\) 18.1501 0.657078
\(764\) 0 0
\(765\) 18.7095 0.676445
\(766\) 0 0
\(767\) 21.3398 0.770535
\(768\) 0 0
\(769\) −49.3040 −1.77795 −0.888973 0.457960i \(-0.848580\pi\)
−0.888973 + 0.457960i \(0.848580\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −37.3199 −1.34230 −0.671152 0.741320i \(-0.734200\pi\)
−0.671152 + 0.741320i \(0.734200\pi\)
\(774\) 0 0
\(775\) 3.44216 0.123646
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.45902 −0.123932
\(780\) 0 0
\(781\) 26.9881 0.965711
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −18.5096 −0.660637
\(786\) 0 0
\(787\) 35.4876 1.26500 0.632499 0.774561i \(-0.282029\pi\)
0.632499 + 0.774561i \(0.282029\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 79.1662 2.81483
\(792\) 0 0
\(793\) 13.3509 0.474103
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.24576 −0.256658 −0.128329 0.991732i \(-0.540961\pi\)
−0.128329 + 0.991732i \(0.540961\pi\)
\(798\) 0 0
\(799\) −0.691658 −0.0244691
\(800\) 0 0
\(801\) 48.8207 1.72499
\(802\) 0 0
\(803\) −27.1888 −0.959473
\(804\) 0 0
\(805\) 73.3910 2.58669
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 42.8637 1.50701 0.753504 0.657443i \(-0.228362\pi\)
0.753504 + 0.657443i \(0.228362\pi\)
\(810\) 0 0
\(811\) −52.3293 −1.83753 −0.918765 0.394805i \(-0.870812\pi\)
−0.918765 + 0.394805i \(0.870812\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.994539 0.0348372
\(816\) 0 0
\(817\) −3.96773 −0.138813
\(818\) 0 0
\(819\) −48.6786 −1.70097
\(820\) 0 0
\(821\) −11.2764 −0.393548 −0.196774 0.980449i \(-0.563047\pi\)
−0.196774 + 0.980449i \(0.563047\pi\)
\(822\) 0 0
\(823\) 0.290199 0.0101157 0.00505785 0.999987i \(-0.498390\pi\)
0.00505785 + 0.999987i \(0.498390\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.42289 −0.0494786 −0.0247393 0.999694i \(-0.507876\pi\)
−0.0247393 + 0.999694i \(0.507876\pi\)
\(828\) 0 0
\(829\) −27.7482 −0.963733 −0.481867 0.876245i \(-0.660041\pi\)
−0.481867 + 0.876245i \(0.660041\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −36.6991 −1.27155
\(834\) 0 0
\(835\) −16.3017 −0.564144
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 13.7602 0.475055 0.237527 0.971381i \(-0.423663\pi\)
0.237527 + 0.971381i \(0.423663\pi\)
\(840\) 0 0
\(841\) 14.7174 0.507495
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5.20808 −0.179163
\(846\) 0 0
\(847\) −39.5022 −1.35731
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 25.3144 0.867766
\(852\) 0 0
\(853\) −18.4954 −0.633269 −0.316635 0.948548i \(-0.602553\pi\)
−0.316635 + 0.948548i \(0.602553\pi\)
\(854\) 0 0
\(855\) −8.46508 −0.289500
\(856\) 0 0
\(857\) −19.9754 −0.682348 −0.341174 0.940000i \(-0.610825\pi\)
−0.341174 + 0.940000i \(0.610825\pi\)
\(858\) 0 0
\(859\) −11.7152 −0.399719 −0.199859 0.979825i \(-0.564049\pi\)
−0.199859 + 0.979825i \(0.564049\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.40528 −0.115917 −0.0579586 0.998319i \(-0.518459\pi\)
−0.0579586 + 0.998319i \(0.518459\pi\)
\(864\) 0 0
\(865\) 31.5217 1.07177
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.69392 0.0574622
\(870\) 0 0
\(871\) −3.44633 −0.116774
\(872\) 0 0
\(873\) 18.9205 0.640361
\(874\) 0 0
\(875\) −27.9396 −0.944532
\(876\) 0 0
\(877\) −4.31093 −0.145570 −0.0727848 0.997348i \(-0.523189\pi\)
−0.0727848 + 0.997348i \(0.523189\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 26.5401 0.894158 0.447079 0.894494i \(-0.352464\pi\)
0.447079 + 0.894494i \(0.352464\pi\)
\(882\) 0 0
\(883\) 9.90602 0.333364 0.166682 0.986011i \(-0.446695\pi\)
0.166682 + 0.986011i \(0.446695\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −17.5043 −0.587737 −0.293869 0.955846i \(-0.594943\pi\)
−0.293869 + 0.955846i \(0.594943\pi\)
\(888\) 0 0
\(889\) 57.8034 1.93866
\(890\) 0 0
\(891\) 15.2452 0.510735
\(892\) 0 0
\(893\) 0.312939 0.0104721
\(894\) 0 0
\(895\) 12.1855 0.407315
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.68387 −0.256271
\(900\) 0 0
\(901\) −12.8254 −0.427275
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6.62902 −0.220356
\(906\) 0 0
\(907\) −33.2867 −1.10527 −0.552634 0.833424i \(-0.686377\pi\)
−0.552634 + 0.833424i \(0.686377\pi\)
\(908\) 0 0
\(909\) −32.1205 −1.06537
\(910\) 0 0
\(911\) −22.2695 −0.737822 −0.368911 0.929465i \(-0.620269\pi\)
−0.368911 + 0.929465i \(0.620269\pi\)
\(912\) 0 0
\(913\) −1.77295 −0.0586760
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −103.172 −3.40706
\(918\) 0 0
\(919\) 59.4968 1.96262 0.981309 0.192437i \(-0.0616391\pi\)
0.981309 + 0.192437i \(0.0616391\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 53.2110 1.75146
\(924\) 0 0
\(925\) 14.0058 0.460509
\(926\) 0 0
\(927\) 29.2480 0.960630
\(928\) 0 0
\(929\) −54.6282 −1.79229 −0.896146 0.443759i \(-0.853645\pi\)
−0.896146 + 0.443759i \(0.853645\pi\)
\(930\) 0 0
\(931\) 16.6044 0.544188
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −10.5641 −0.345484
\(936\) 0 0
\(937\) 6.41148 0.209454 0.104727 0.994501i \(-0.466603\pi\)
0.104727 + 0.994501i \(0.466603\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22.5191 −0.734103 −0.367051 0.930201i \(-0.619633\pi\)
−0.367051 + 0.930201i \(0.619633\pi\)
\(942\) 0 0
\(943\) −18.5178 −0.603023
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −60.6625 −1.97127 −0.985634 0.168896i \(-0.945980\pi\)
−0.985634 + 0.168896i \(0.945980\pi\)
\(948\) 0 0
\(949\) −53.6067 −1.74015
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −47.5880 −1.54153 −0.770763 0.637122i \(-0.780125\pi\)
−0.770763 + 0.637122i \(0.780125\pi\)
\(954\) 0 0
\(955\) −14.8222 −0.479636
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −10.6874 −0.345114
\(960\) 0 0
\(961\) −29.6495 −0.956434
\(962\) 0 0
\(963\) −52.2390 −1.68338
\(964\) 0 0
\(965\) 41.6881 1.34199
\(966\) 0 0
\(967\) −34.9569 −1.12414 −0.562069 0.827091i \(-0.689994\pi\)
−0.562069 + 0.827091i \(0.689994\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −17.7678 −0.570196 −0.285098 0.958498i \(-0.592026\pi\)
−0.285098 + 0.958498i \(0.592026\pi\)
\(972\) 0 0
\(973\) −47.7969 −1.53230
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32.7343 −1.04726 −0.523632 0.851945i \(-0.675423\pi\)
−0.523632 + 0.851945i \(0.675423\pi\)
\(978\) 0 0
\(979\) −27.5660 −0.881014
\(980\) 0 0
\(981\) −11.2074 −0.357824
\(982\) 0 0
\(983\) −26.5368 −0.846393 −0.423197 0.906038i \(-0.639092\pi\)
−0.423197 + 0.906038i \(0.639092\pi\)
\(984\) 0 0
\(985\) 0.227876 0.00726073
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −21.2412 −0.675430
\(990\) 0 0
\(991\) 45.3548 1.44074 0.720371 0.693588i \(-0.243971\pi\)
0.720371 + 0.693588i \(0.243971\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −21.6773 −0.687218
\(996\) 0 0
\(997\) 28.1899 0.892783 0.446392 0.894838i \(-0.352709\pi\)
0.446392 + 0.894838i \(0.352709\pi\)
\(998\) 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 \(a_p\))