Properties

Label 8008.2.a.n.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.63046\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.63046 q^{3} -1.01052 q^{5} -1.00000 q^{7} -0.341611 q^{9} +O(q^{10})\) \(q-1.63046 q^{3} -1.01052 q^{5} -1.00000 q^{7} -0.341611 q^{9} +1.00000 q^{11} -1.00000 q^{13} +1.64761 q^{15} +6.58995 q^{17} -7.83065 q^{19} +1.63046 q^{21} -8.66793 q^{23} -3.97885 q^{25} +5.44835 q^{27} -2.21969 q^{29} +2.76878 q^{31} -1.63046 q^{33} +1.01052 q^{35} +0.284567 q^{37} +1.63046 q^{39} -4.59265 q^{41} +7.84302 q^{43} +0.345205 q^{45} -7.89216 q^{47} +1.00000 q^{49} -10.7446 q^{51} -2.84986 q^{53} -1.01052 q^{55} +12.7675 q^{57} -0.589884 q^{59} +9.66169 q^{61} +0.341611 q^{63} +1.01052 q^{65} -12.3522 q^{67} +14.1327 q^{69} +7.88928 q^{71} -6.45328 q^{73} +6.48734 q^{75} -1.00000 q^{77} -5.04021 q^{79} -7.85847 q^{81} +0.656668 q^{83} -6.65929 q^{85} +3.61910 q^{87} +8.01216 q^{89} +1.00000 q^{91} -4.51437 q^{93} +7.91304 q^{95} -5.20331 q^{97} -0.341611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.63046 −0.941345 −0.470672 0.882308i \(-0.655989\pi\)
−0.470672 + 0.882308i \(0.655989\pi\)
\(4\) 0 0
\(5\) −1.01052 −0.451919 −0.225959 0.974137i \(-0.572552\pi\)
−0.225959 + 0.974137i \(0.572552\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.341611 −0.113870
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.64761 0.425411
\(16\) 0 0
\(17\) 6.58995 1.59830 0.799149 0.601133i \(-0.205284\pi\)
0.799149 + 0.601133i \(0.205284\pi\)
\(18\) 0 0
\(19\) −7.83065 −1.79647 −0.898237 0.439511i \(-0.855152\pi\)
−0.898237 + 0.439511i \(0.855152\pi\)
\(20\) 0 0
\(21\) 1.63046 0.355795
\(22\) 0 0
\(23\) −8.66793 −1.80739 −0.903695 0.428178i \(-0.859156\pi\)
−0.903695 + 0.428178i \(0.859156\pi\)
\(24\) 0 0
\(25\) −3.97885 −0.795769
\(26\) 0 0
\(27\) 5.44835 1.04854
\(28\) 0 0
\(29\) −2.21969 −0.412185 −0.206093 0.978532i \(-0.566075\pi\)
−0.206093 + 0.978532i \(0.566075\pi\)
\(30\) 0 0
\(31\) 2.76878 0.497287 0.248644 0.968595i \(-0.420015\pi\)
0.248644 + 0.968595i \(0.420015\pi\)
\(32\) 0 0
\(33\) −1.63046 −0.283826
\(34\) 0 0
\(35\) 1.01052 0.170809
\(36\) 0 0
\(37\) 0.284567 0.0467825 0.0233912 0.999726i \(-0.492554\pi\)
0.0233912 + 0.999726i \(0.492554\pi\)
\(38\) 0 0
\(39\) 1.63046 0.261082
\(40\) 0 0
\(41\) −4.59265 −0.717251 −0.358626 0.933481i \(-0.616755\pi\)
−0.358626 + 0.933481i \(0.616755\pi\)
\(42\) 0 0
\(43\) 7.84302 1.19605 0.598025 0.801477i \(-0.295952\pi\)
0.598025 + 0.801477i \(0.295952\pi\)
\(44\) 0 0
\(45\) 0.345205 0.0514602
\(46\) 0 0
\(47\) −7.89216 −1.15119 −0.575595 0.817735i \(-0.695229\pi\)
−0.575595 + 0.817735i \(0.695229\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −10.7446 −1.50455
\(52\) 0 0
\(53\) −2.84986 −0.391458 −0.195729 0.980658i \(-0.562707\pi\)
−0.195729 + 0.980658i \(0.562707\pi\)
\(54\) 0 0
\(55\) −1.01052 −0.136259
\(56\) 0 0
\(57\) 12.7675 1.69110
\(58\) 0 0
\(59\) −0.589884 −0.0767964 −0.0383982 0.999263i \(-0.512226\pi\)
−0.0383982 + 0.999263i \(0.512226\pi\)
\(60\) 0 0
\(61\) 9.66169 1.23705 0.618526 0.785764i \(-0.287730\pi\)
0.618526 + 0.785764i \(0.287730\pi\)
\(62\) 0 0
\(63\) 0.341611 0.0430390
\(64\) 0 0
\(65\) 1.01052 0.125340
\(66\) 0 0
\(67\) −12.3522 −1.50906 −0.754531 0.656265i \(-0.772135\pi\)
−0.754531 + 0.656265i \(0.772135\pi\)
\(68\) 0 0
\(69\) 14.1327 1.70138
\(70\) 0 0
\(71\) 7.88928 0.936285 0.468143 0.883653i \(-0.344923\pi\)
0.468143 + 0.883653i \(0.344923\pi\)
\(72\) 0 0
\(73\) −6.45328 −0.755300 −0.377650 0.925948i \(-0.623268\pi\)
−0.377650 + 0.925948i \(0.623268\pi\)
\(74\) 0 0
\(75\) 6.48734 0.749093
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −5.04021 −0.567068 −0.283534 0.958962i \(-0.591507\pi\)
−0.283534 + 0.958962i \(0.591507\pi\)
\(80\) 0 0
\(81\) −7.85847 −0.873163
\(82\) 0 0
\(83\) 0.656668 0.0720787 0.0360393 0.999350i \(-0.488526\pi\)
0.0360393 + 0.999350i \(0.488526\pi\)
\(84\) 0 0
\(85\) −6.65929 −0.722301
\(86\) 0 0
\(87\) 3.61910 0.388008
\(88\) 0 0
\(89\) 8.01216 0.849287 0.424644 0.905361i \(-0.360399\pi\)
0.424644 + 0.905361i \(0.360399\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −4.51437 −0.468119
\(94\) 0 0
\(95\) 7.91304 0.811861
\(96\) 0 0
\(97\) −5.20331 −0.528316 −0.264158 0.964479i \(-0.585094\pi\)
−0.264158 + 0.964479i \(0.585094\pi\)
\(98\) 0 0
\(99\) −0.341611 −0.0343332
\(100\) 0 0
\(101\) −17.1239 −1.70389 −0.851946 0.523629i \(-0.824578\pi\)
−0.851946 + 0.523629i \(0.824578\pi\)
\(102\) 0 0
\(103\) −1.80920 −0.178265 −0.0891327 0.996020i \(-0.528410\pi\)
−0.0891327 + 0.996020i \(0.528410\pi\)
\(104\) 0 0
\(105\) −1.64761 −0.160790
\(106\) 0 0
\(107\) −13.2852 −1.28433 −0.642163 0.766568i \(-0.721963\pi\)
−0.642163 + 0.766568i \(0.721963\pi\)
\(108\) 0 0
\(109\) 9.09072 0.870733 0.435366 0.900253i \(-0.356619\pi\)
0.435366 + 0.900253i \(0.356619\pi\)
\(110\) 0 0
\(111\) −0.463973 −0.0440384
\(112\) 0 0
\(113\) 7.24578 0.681625 0.340813 0.940131i \(-0.389298\pi\)
0.340813 + 0.940131i \(0.389298\pi\)
\(114\) 0 0
\(115\) 8.75913 0.816793
\(116\) 0 0
\(117\) 0.341611 0.0315820
\(118\) 0 0
\(119\) −6.58995 −0.604100
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 7.48812 0.675181
\(124\) 0 0
\(125\) 9.07332 0.811542
\(126\) 0 0
\(127\) 2.01023 0.178380 0.0891898 0.996015i \(-0.471572\pi\)
0.0891898 + 0.996015i \(0.471572\pi\)
\(128\) 0 0
\(129\) −12.7877 −1.12590
\(130\) 0 0
\(131\) −21.3014 −1.86111 −0.930555 0.366153i \(-0.880675\pi\)
−0.930555 + 0.366153i \(0.880675\pi\)
\(132\) 0 0
\(133\) 7.83065 0.679003
\(134\) 0 0
\(135\) −5.50568 −0.473853
\(136\) 0 0
\(137\) 7.36515 0.629248 0.314624 0.949216i \(-0.398122\pi\)
0.314624 + 0.949216i \(0.398122\pi\)
\(138\) 0 0
\(139\) −12.2761 −1.04125 −0.520625 0.853786i \(-0.674301\pi\)
−0.520625 + 0.853786i \(0.674301\pi\)
\(140\) 0 0
\(141\) 12.8678 1.08367
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 2.24304 0.186274
\(146\) 0 0
\(147\) −1.63046 −0.134478
\(148\) 0 0
\(149\) 4.60344 0.377128 0.188564 0.982061i \(-0.439617\pi\)
0.188564 + 0.982061i \(0.439617\pi\)
\(150\) 0 0
\(151\) −6.58994 −0.536282 −0.268141 0.963380i \(-0.586409\pi\)
−0.268141 + 0.963380i \(0.586409\pi\)
\(152\) 0 0
\(153\) −2.25120 −0.181999
\(154\) 0 0
\(155\) −2.79791 −0.224734
\(156\) 0 0
\(157\) −8.01450 −0.639627 −0.319813 0.947481i \(-0.603620\pi\)
−0.319813 + 0.947481i \(0.603620\pi\)
\(158\) 0 0
\(159\) 4.64657 0.368497
\(160\) 0 0
\(161\) 8.66793 0.683129
\(162\) 0 0
\(163\) −2.94606 −0.230753 −0.115377 0.993322i \(-0.536807\pi\)
−0.115377 + 0.993322i \(0.536807\pi\)
\(164\) 0 0
\(165\) 1.64761 0.128266
\(166\) 0 0
\(167\) 16.6083 1.28519 0.642595 0.766206i \(-0.277858\pi\)
0.642595 + 0.766206i \(0.277858\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.67504 0.204565
\(172\) 0 0
\(173\) −10.5360 −0.801037 −0.400519 0.916289i \(-0.631170\pi\)
−0.400519 + 0.916289i \(0.631170\pi\)
\(174\) 0 0
\(175\) 3.97885 0.300773
\(176\) 0 0
\(177\) 0.961781 0.0722919
\(178\) 0 0
\(179\) −12.8996 −0.964161 −0.482081 0.876127i \(-0.660119\pi\)
−0.482081 + 0.876127i \(0.660119\pi\)
\(180\) 0 0
\(181\) 10.6910 0.794654 0.397327 0.917677i \(-0.369938\pi\)
0.397327 + 0.917677i \(0.369938\pi\)
\(182\) 0 0
\(183\) −15.7530 −1.16449
\(184\) 0 0
\(185\) −0.287561 −0.0211419
\(186\) 0 0
\(187\) 6.58995 0.481905
\(188\) 0 0
\(189\) −5.44835 −0.396309
\(190\) 0 0
\(191\) 19.3122 1.39738 0.698691 0.715424i \(-0.253766\pi\)
0.698691 + 0.715424i \(0.253766\pi\)
\(192\) 0 0
\(193\) 4.58395 0.329960 0.164980 0.986297i \(-0.447244\pi\)
0.164980 + 0.986297i \(0.447244\pi\)
\(194\) 0 0
\(195\) −1.64761 −0.117988
\(196\) 0 0
\(197\) 7.61572 0.542598 0.271299 0.962495i \(-0.412547\pi\)
0.271299 + 0.962495i \(0.412547\pi\)
\(198\) 0 0
\(199\) −15.2375 −1.08016 −0.540078 0.841615i \(-0.681605\pi\)
−0.540078 + 0.841615i \(0.681605\pi\)
\(200\) 0 0
\(201\) 20.1397 1.42055
\(202\) 0 0
\(203\) 2.21969 0.155791
\(204\) 0 0
\(205\) 4.64097 0.324139
\(206\) 0 0
\(207\) 2.96106 0.205808
\(208\) 0 0
\(209\) −7.83065 −0.541657
\(210\) 0 0
\(211\) 19.1955 1.32147 0.660735 0.750619i \(-0.270245\pi\)
0.660735 + 0.750619i \(0.270245\pi\)
\(212\) 0 0
\(213\) −12.8631 −0.881367
\(214\) 0 0
\(215\) −7.92554 −0.540518
\(216\) 0 0
\(217\) −2.76878 −0.187957
\(218\) 0 0
\(219\) 10.5218 0.710997
\(220\) 0 0
\(221\) −6.58995 −0.443288
\(222\) 0 0
\(223\) 16.2546 1.08849 0.544243 0.838928i \(-0.316817\pi\)
0.544243 + 0.838928i \(0.316817\pi\)
\(224\) 0 0
\(225\) 1.35922 0.0906146
\(226\) 0 0
\(227\) 0.803763 0.0533476 0.0266738 0.999644i \(-0.491508\pi\)
0.0266738 + 0.999644i \(0.491508\pi\)
\(228\) 0 0
\(229\) −2.58268 −0.170669 −0.0853343 0.996352i \(-0.527196\pi\)
−0.0853343 + 0.996352i \(0.527196\pi\)
\(230\) 0 0
\(231\) 1.63046 0.107276
\(232\) 0 0
\(233\) −19.7321 −1.29269 −0.646345 0.763045i \(-0.723703\pi\)
−0.646345 + 0.763045i \(0.723703\pi\)
\(234\) 0 0
\(235\) 7.97519 0.520244
\(236\) 0 0
\(237\) 8.21785 0.533807
\(238\) 0 0
\(239\) 21.5124 1.39152 0.695761 0.718273i \(-0.255067\pi\)
0.695761 + 0.718273i \(0.255067\pi\)
\(240\) 0 0
\(241\) −26.5112 −1.70774 −0.853869 0.520489i \(-0.825750\pi\)
−0.853869 + 0.520489i \(0.825750\pi\)
\(242\) 0 0
\(243\) −3.53217 −0.226589
\(244\) 0 0
\(245\) −1.01052 −0.0645598
\(246\) 0 0
\(247\) 7.83065 0.498252
\(248\) 0 0
\(249\) −1.07067 −0.0678509
\(250\) 0 0
\(251\) −10.9124 −0.688784 −0.344392 0.938826i \(-0.611915\pi\)
−0.344392 + 0.938826i \(0.611915\pi\)
\(252\) 0 0
\(253\) −8.66793 −0.544948
\(254\) 0 0
\(255\) 10.8577 0.679934
\(256\) 0 0
\(257\) 3.63887 0.226986 0.113493 0.993539i \(-0.463796\pi\)
0.113493 + 0.993539i \(0.463796\pi\)
\(258\) 0 0
\(259\) −0.284567 −0.0176821
\(260\) 0 0
\(261\) 0.758270 0.0469357
\(262\) 0 0
\(263\) −0.397875 −0.0245340 −0.0122670 0.999925i \(-0.503905\pi\)
−0.0122670 + 0.999925i \(0.503905\pi\)
\(264\) 0 0
\(265\) 2.87984 0.176907
\(266\) 0 0
\(267\) −13.0635 −0.799472
\(268\) 0 0
\(269\) −1.15149 −0.0702074 −0.0351037 0.999384i \(-0.511176\pi\)
−0.0351037 + 0.999384i \(0.511176\pi\)
\(270\) 0 0
\(271\) −6.23525 −0.378764 −0.189382 0.981903i \(-0.560649\pi\)
−0.189382 + 0.981903i \(0.560649\pi\)
\(272\) 0 0
\(273\) −1.63046 −0.0986797
\(274\) 0 0
\(275\) −3.97885 −0.239933
\(276\) 0 0
\(277\) 20.4736 1.23014 0.615069 0.788473i \(-0.289128\pi\)
0.615069 + 0.788473i \(0.289128\pi\)
\(278\) 0 0
\(279\) −0.945846 −0.0566263
\(280\) 0 0
\(281\) 25.7896 1.53848 0.769239 0.638961i \(-0.220635\pi\)
0.769239 + 0.638961i \(0.220635\pi\)
\(282\) 0 0
\(283\) 23.0846 1.37223 0.686117 0.727491i \(-0.259314\pi\)
0.686117 + 0.727491i \(0.259314\pi\)
\(284\) 0 0
\(285\) −12.9019 −0.764241
\(286\) 0 0
\(287\) 4.59265 0.271096
\(288\) 0 0
\(289\) 26.4275 1.55456
\(290\) 0 0
\(291\) 8.48378 0.497328
\(292\) 0 0
\(293\) −4.53701 −0.265055 −0.132528 0.991179i \(-0.542309\pi\)
−0.132528 + 0.991179i \(0.542309\pi\)
\(294\) 0 0
\(295\) 0.596091 0.0347057
\(296\) 0 0
\(297\) 5.44835 0.316145
\(298\) 0 0
\(299\) 8.66793 0.501280
\(300\) 0 0
\(301\) −7.84302 −0.452064
\(302\) 0 0
\(303\) 27.9198 1.60395
\(304\) 0 0
\(305\) −9.76334 −0.559047
\(306\) 0 0
\(307\) −0.000320838 0 −1.83112e−5 0 −9.15559e−6 1.00000i \(-0.500003\pi\)
−9.15559e−6 1.00000i \(0.500003\pi\)
\(308\) 0 0
\(309\) 2.94982 0.167809
\(310\) 0 0
\(311\) 28.6272 1.62330 0.811650 0.584144i \(-0.198570\pi\)
0.811650 + 0.584144i \(0.198570\pi\)
\(312\) 0 0
\(313\) 14.8475 0.839228 0.419614 0.907703i \(-0.362165\pi\)
0.419614 + 0.907703i \(0.362165\pi\)
\(314\) 0 0
\(315\) −0.345205 −0.0194501
\(316\) 0 0
\(317\) 14.7789 0.830065 0.415032 0.909807i \(-0.363770\pi\)
0.415032 + 0.909807i \(0.363770\pi\)
\(318\) 0 0
\(319\) −2.21969 −0.124279
\(320\) 0 0
\(321\) 21.6609 1.20899
\(322\) 0 0
\(323\) −51.6036 −2.87130
\(324\) 0 0
\(325\) 3.97885 0.220707
\(326\) 0 0
\(327\) −14.8220 −0.819660
\(328\) 0 0
\(329\) 7.89216 0.435109
\(330\) 0 0
\(331\) 5.78522 0.317985 0.158992 0.987280i \(-0.449176\pi\)
0.158992 + 0.987280i \(0.449176\pi\)
\(332\) 0 0
\(333\) −0.0972111 −0.00532714
\(334\) 0 0
\(335\) 12.4822 0.681973
\(336\) 0 0
\(337\) 33.4910 1.82437 0.912185 0.409779i \(-0.134394\pi\)
0.912185 + 0.409779i \(0.134394\pi\)
\(338\) 0 0
\(339\) −11.8139 −0.641644
\(340\) 0 0
\(341\) 2.76878 0.149938
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −14.2814 −0.768884
\(346\) 0 0
\(347\) 7.69418 0.413045 0.206523 0.978442i \(-0.433785\pi\)
0.206523 + 0.978442i \(0.433785\pi\)
\(348\) 0 0
\(349\) 12.3304 0.660031 0.330016 0.943975i \(-0.392946\pi\)
0.330016 + 0.943975i \(0.392946\pi\)
\(350\) 0 0
\(351\) −5.44835 −0.290812
\(352\) 0 0
\(353\) 21.2893 1.13311 0.566557 0.824022i \(-0.308275\pi\)
0.566557 + 0.824022i \(0.308275\pi\)
\(354\) 0 0
\(355\) −7.97229 −0.423125
\(356\) 0 0
\(357\) 10.7446 0.568666
\(358\) 0 0
\(359\) 5.94504 0.313767 0.156884 0.987617i \(-0.449855\pi\)
0.156884 + 0.987617i \(0.449855\pi\)
\(360\) 0 0
\(361\) 42.3191 2.22732
\(362\) 0 0
\(363\) −1.63046 −0.0855768
\(364\) 0 0
\(365\) 6.52118 0.341334
\(366\) 0 0
\(367\) 27.6703 1.44438 0.722189 0.691696i \(-0.243136\pi\)
0.722189 + 0.691696i \(0.243136\pi\)
\(368\) 0 0
\(369\) 1.56890 0.0816737
\(370\) 0 0
\(371\) 2.84986 0.147957
\(372\) 0 0
\(373\) 6.21110 0.321598 0.160799 0.986987i \(-0.448593\pi\)
0.160799 + 0.986987i \(0.448593\pi\)
\(374\) 0 0
\(375\) −14.7936 −0.763941
\(376\) 0 0
\(377\) 2.21969 0.114320
\(378\) 0 0
\(379\) 14.0374 0.721054 0.360527 0.932749i \(-0.382597\pi\)
0.360527 + 0.932749i \(0.382597\pi\)
\(380\) 0 0
\(381\) −3.27760 −0.167917
\(382\) 0 0
\(383\) 1.22522 0.0626056 0.0313028 0.999510i \(-0.490034\pi\)
0.0313028 + 0.999510i \(0.490034\pi\)
\(384\) 0 0
\(385\) 1.01052 0.0515009
\(386\) 0 0
\(387\) −2.67927 −0.136195
\(388\) 0 0
\(389\) 36.5223 1.85176 0.925878 0.377823i \(-0.123327\pi\)
0.925878 + 0.377823i \(0.123327\pi\)
\(390\) 0 0
\(391\) −57.1213 −2.88875
\(392\) 0 0
\(393\) 34.7310 1.75195
\(394\) 0 0
\(395\) 5.09324 0.256269
\(396\) 0 0
\(397\) 24.3305 1.22111 0.610557 0.791972i \(-0.290946\pi\)
0.610557 + 0.791972i \(0.290946\pi\)
\(398\) 0 0
\(399\) −12.7675 −0.639176
\(400\) 0 0
\(401\) 23.6117 1.17911 0.589556 0.807728i \(-0.299303\pi\)
0.589556 + 0.807728i \(0.299303\pi\)
\(402\) 0 0
\(403\) −2.76878 −0.137923
\(404\) 0 0
\(405\) 7.94115 0.394599
\(406\) 0 0
\(407\) 0.284567 0.0141054
\(408\) 0 0
\(409\) 26.8639 1.32833 0.664167 0.747584i \(-0.268786\pi\)
0.664167 + 0.747584i \(0.268786\pi\)
\(410\) 0 0
\(411\) −12.0086 −0.592339
\(412\) 0 0
\(413\) 0.589884 0.0290263
\(414\) 0 0
\(415\) −0.663577 −0.0325737
\(416\) 0 0
\(417\) 20.0157 0.980174
\(418\) 0 0
\(419\) −31.1713 −1.52282 −0.761408 0.648273i \(-0.775492\pi\)
−0.761408 + 0.648273i \(0.775492\pi\)
\(420\) 0 0
\(421\) −34.8244 −1.69724 −0.848619 0.529005i \(-0.822565\pi\)
−0.848619 + 0.529005i \(0.822565\pi\)
\(422\) 0 0
\(423\) 2.69605 0.131086
\(424\) 0 0
\(425\) −26.2204 −1.27188
\(426\) 0 0
\(427\) −9.66169 −0.467562
\(428\) 0 0
\(429\) 1.63046 0.0787192
\(430\) 0 0
\(431\) −25.8570 −1.24549 −0.622743 0.782426i \(-0.713982\pi\)
−0.622743 + 0.782426i \(0.713982\pi\)
\(432\) 0 0
\(433\) −21.2777 −1.02254 −0.511270 0.859420i \(-0.670825\pi\)
−0.511270 + 0.859420i \(0.670825\pi\)
\(434\) 0 0
\(435\) −3.65718 −0.175348
\(436\) 0 0
\(437\) 67.8756 3.24693
\(438\) 0 0
\(439\) 10.2258 0.488050 0.244025 0.969769i \(-0.421532\pi\)
0.244025 + 0.969769i \(0.421532\pi\)
\(440\) 0 0
\(441\) −0.341611 −0.0162672
\(442\) 0 0
\(443\) −31.8349 −1.51252 −0.756260 0.654271i \(-0.772976\pi\)
−0.756260 + 0.654271i \(0.772976\pi\)
\(444\) 0 0
\(445\) −8.09646 −0.383809
\(446\) 0 0
\(447\) −7.50570 −0.355008
\(448\) 0 0
\(449\) −26.2503 −1.23883 −0.619414 0.785064i \(-0.712630\pi\)
−0.619414 + 0.785064i \(0.712630\pi\)
\(450\) 0 0
\(451\) −4.59265 −0.216259
\(452\) 0 0
\(453\) 10.7446 0.504826
\(454\) 0 0
\(455\) −1.01052 −0.0473740
\(456\) 0 0
\(457\) 16.3481 0.764731 0.382365 0.924011i \(-0.375110\pi\)
0.382365 + 0.924011i \(0.375110\pi\)
\(458\) 0 0
\(459\) 35.9044 1.67587
\(460\) 0 0
\(461\) −5.04145 −0.234804 −0.117402 0.993084i \(-0.537457\pi\)
−0.117402 + 0.993084i \(0.537457\pi\)
\(462\) 0 0
\(463\) −18.6612 −0.867261 −0.433631 0.901091i \(-0.642768\pi\)
−0.433631 + 0.901091i \(0.642768\pi\)
\(464\) 0 0
\(465\) 4.56187 0.211552
\(466\) 0 0
\(467\) −38.7103 −1.79130 −0.895650 0.444759i \(-0.853289\pi\)
−0.895650 + 0.444759i \(0.853289\pi\)
\(468\) 0 0
\(469\) 12.3522 0.570372
\(470\) 0 0
\(471\) 13.0673 0.602109
\(472\) 0 0
\(473\) 7.84302 0.360623
\(474\) 0 0
\(475\) 31.1570 1.42958
\(476\) 0 0
\(477\) 0.973543 0.0445755
\(478\) 0 0
\(479\) −15.1138 −0.690569 −0.345285 0.938498i \(-0.612218\pi\)
−0.345285 + 0.938498i \(0.612218\pi\)
\(480\) 0 0
\(481\) −0.284567 −0.0129751
\(482\) 0 0
\(483\) −14.1327 −0.643060
\(484\) 0 0
\(485\) 5.25806 0.238756
\(486\) 0 0
\(487\) 16.2720 0.737355 0.368677 0.929557i \(-0.379811\pi\)
0.368677 + 0.929557i \(0.379811\pi\)
\(488\) 0 0
\(489\) 4.80342 0.217218
\(490\) 0 0
\(491\) 13.1257 0.592353 0.296176 0.955133i \(-0.404288\pi\)
0.296176 + 0.955133i \(0.404288\pi\)
\(492\) 0 0
\(493\) −14.6276 −0.658795
\(494\) 0 0
\(495\) 0.345205 0.0155158
\(496\) 0 0
\(497\) −7.88928 −0.353883
\(498\) 0 0
\(499\) 11.0920 0.496545 0.248272 0.968690i \(-0.420137\pi\)
0.248272 + 0.968690i \(0.420137\pi\)
\(500\) 0 0
\(501\) −27.0791 −1.20981
\(502\) 0 0
\(503\) −21.9485 −0.978637 −0.489318 0.872105i \(-0.662754\pi\)
−0.489318 + 0.872105i \(0.662754\pi\)
\(504\) 0 0
\(505\) 17.3041 0.770021
\(506\) 0 0
\(507\) −1.63046 −0.0724111
\(508\) 0 0
\(509\) −5.91381 −0.262125 −0.131062 0.991374i \(-0.541839\pi\)
−0.131062 + 0.991374i \(0.541839\pi\)
\(510\) 0 0
\(511\) 6.45328 0.285476
\(512\) 0 0
\(513\) −42.6641 −1.88367
\(514\) 0 0
\(515\) 1.82823 0.0805615
\(516\) 0 0
\(517\) −7.89216 −0.347097
\(518\) 0 0
\(519\) 17.1785 0.754052
\(520\) 0 0
\(521\) −4.93775 −0.216327 −0.108163 0.994133i \(-0.534497\pi\)
−0.108163 + 0.994133i \(0.534497\pi\)
\(522\) 0 0
\(523\) −36.6654 −1.60327 −0.801634 0.597815i \(-0.796036\pi\)
−0.801634 + 0.597815i \(0.796036\pi\)
\(524\) 0 0
\(525\) −6.48734 −0.283131
\(526\) 0 0
\(527\) 18.2461 0.794813
\(528\) 0 0
\(529\) 52.1331 2.26666
\(530\) 0 0
\(531\) 0.201511 0.00874484
\(532\) 0 0
\(533\) 4.59265 0.198930
\(534\) 0 0
\(535\) 13.4250 0.580411
\(536\) 0 0
\(537\) 21.0322 0.907608
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −30.0850 −1.29346 −0.646728 0.762720i \(-0.723863\pi\)
−0.646728 + 0.762720i \(0.723863\pi\)
\(542\) 0 0
\(543\) −17.4312 −0.748043
\(544\) 0 0
\(545\) −9.18636 −0.393501
\(546\) 0 0
\(547\) −39.3319 −1.68171 −0.840856 0.541259i \(-0.817948\pi\)
−0.840856 + 0.541259i \(0.817948\pi\)
\(548\) 0 0
\(549\) −3.30054 −0.140864
\(550\) 0 0
\(551\) 17.3816 0.740480
\(552\) 0 0
\(553\) 5.04021 0.214332
\(554\) 0 0
\(555\) 0.468855 0.0199018
\(556\) 0 0
\(557\) 29.6195 1.25502 0.627510 0.778608i \(-0.284074\pi\)
0.627510 + 0.778608i \(0.284074\pi\)
\(558\) 0 0
\(559\) −7.84302 −0.331725
\(560\) 0 0
\(561\) −10.7446 −0.453639
\(562\) 0 0
\(563\) −3.21060 −0.135311 −0.0676553 0.997709i \(-0.521552\pi\)
−0.0676553 + 0.997709i \(0.521552\pi\)
\(564\) 0 0
\(565\) −7.32201 −0.308039
\(566\) 0 0
\(567\) 7.85847 0.330025
\(568\) 0 0
\(569\) 3.26920 0.137052 0.0685260 0.997649i \(-0.478170\pi\)
0.0685260 + 0.997649i \(0.478170\pi\)
\(570\) 0 0
\(571\) 1.13830 0.0476366 0.0238183 0.999716i \(-0.492418\pi\)
0.0238183 + 0.999716i \(0.492418\pi\)
\(572\) 0 0
\(573\) −31.4877 −1.31542
\(574\) 0 0
\(575\) 34.4884 1.43826
\(576\) 0 0
\(577\) 26.2995 1.09486 0.547432 0.836850i \(-0.315605\pi\)
0.547432 + 0.836850i \(0.315605\pi\)
\(578\) 0 0
\(579\) −7.47394 −0.310606
\(580\) 0 0
\(581\) −0.656668 −0.0272432
\(582\) 0 0
\(583\) −2.84986 −0.118029
\(584\) 0 0
\(585\) −0.345205 −0.0142725
\(586\) 0 0
\(587\) 19.5354 0.806312 0.403156 0.915131i \(-0.367913\pi\)
0.403156 + 0.915131i \(0.367913\pi\)
\(588\) 0 0
\(589\) −21.6813 −0.893364
\(590\) 0 0
\(591\) −12.4171 −0.510772
\(592\) 0 0
\(593\) −21.0247 −0.863383 −0.431691 0.902021i \(-0.642083\pi\)
−0.431691 + 0.902021i \(0.642083\pi\)
\(594\) 0 0
\(595\) 6.65929 0.273004
\(596\) 0 0
\(597\) 24.8441 1.01680
\(598\) 0 0
\(599\) −21.8012 −0.890774 −0.445387 0.895338i \(-0.646934\pi\)
−0.445387 + 0.895338i \(0.646934\pi\)
\(600\) 0 0
\(601\) 3.26827 0.133316 0.0666578 0.997776i \(-0.478766\pi\)
0.0666578 + 0.997776i \(0.478766\pi\)
\(602\) 0 0
\(603\) 4.21965 0.171837
\(604\) 0 0
\(605\) −1.01052 −0.0410835
\(606\) 0 0
\(607\) 19.3996 0.787406 0.393703 0.919238i \(-0.371194\pi\)
0.393703 + 0.919238i \(0.371194\pi\)
\(608\) 0 0
\(609\) −3.61910 −0.146653
\(610\) 0 0
\(611\) 7.89216 0.319283
\(612\) 0 0
\(613\) 16.4441 0.664170 0.332085 0.943250i \(-0.392248\pi\)
0.332085 + 0.943250i \(0.392248\pi\)
\(614\) 0 0
\(615\) −7.56690 −0.305127
\(616\) 0 0
\(617\) 45.2914 1.82336 0.911682 0.410897i \(-0.134784\pi\)
0.911682 + 0.410897i \(0.134784\pi\)
\(618\) 0 0
\(619\) 0.475651 0.0191180 0.00955902 0.999954i \(-0.496957\pi\)
0.00955902 + 0.999954i \(0.496957\pi\)
\(620\) 0 0
\(621\) −47.2260 −1.89511
\(622\) 0 0
\(623\) −8.01216 −0.321000
\(624\) 0 0
\(625\) 10.7255 0.429018
\(626\) 0 0
\(627\) 12.7675 0.509886
\(628\) 0 0
\(629\) 1.87528 0.0747723
\(630\) 0 0
\(631\) 33.2454 1.32348 0.661739 0.749734i \(-0.269819\pi\)
0.661739 + 0.749734i \(0.269819\pi\)
\(632\) 0 0
\(633\) −31.2974 −1.24396
\(634\) 0 0
\(635\) −2.03139 −0.0806131
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −2.69507 −0.106615
\(640\) 0 0
\(641\) 20.8933 0.825235 0.412617 0.910904i \(-0.364615\pi\)
0.412617 + 0.910904i \(0.364615\pi\)
\(642\) 0 0
\(643\) −36.4939 −1.43918 −0.719589 0.694400i \(-0.755670\pi\)
−0.719589 + 0.694400i \(0.755670\pi\)
\(644\) 0 0
\(645\) 12.9223 0.508813
\(646\) 0 0
\(647\) −10.5107 −0.413220 −0.206610 0.978423i \(-0.566243\pi\)
−0.206610 + 0.978423i \(0.566243\pi\)
\(648\) 0 0
\(649\) −0.589884 −0.0231550
\(650\) 0 0
\(651\) 4.51437 0.176932
\(652\) 0 0
\(653\) 31.9060 1.24858 0.624289 0.781193i \(-0.285389\pi\)
0.624289 + 0.781193i \(0.285389\pi\)
\(654\) 0 0
\(655\) 21.5255 0.841070
\(656\) 0 0
\(657\) 2.20451 0.0860063
\(658\) 0 0
\(659\) 16.5782 0.645793 0.322897 0.946434i \(-0.395343\pi\)
0.322897 + 0.946434i \(0.395343\pi\)
\(660\) 0 0
\(661\) 44.3900 1.72657 0.863285 0.504717i \(-0.168403\pi\)
0.863285 + 0.504717i \(0.168403\pi\)
\(662\) 0 0
\(663\) 10.7446 0.417287
\(664\) 0 0
\(665\) −7.91304 −0.306854
\(666\) 0 0
\(667\) 19.2401 0.744979
\(668\) 0 0
\(669\) −26.5024 −1.02464
\(670\) 0 0
\(671\) 9.66169 0.372985
\(672\) 0 0
\(673\) 20.2672 0.781244 0.390622 0.920551i \(-0.372260\pi\)
0.390622 + 0.920551i \(0.372260\pi\)
\(674\) 0 0
\(675\) −21.6782 −0.834393
\(676\) 0 0
\(677\) −23.1083 −0.888123 −0.444062 0.895996i \(-0.646463\pi\)
−0.444062 + 0.895996i \(0.646463\pi\)
\(678\) 0 0
\(679\) 5.20331 0.199685
\(680\) 0 0
\(681\) −1.31050 −0.0502185
\(682\) 0 0
\(683\) 25.1819 0.963560 0.481780 0.876292i \(-0.339990\pi\)
0.481780 + 0.876292i \(0.339990\pi\)
\(684\) 0 0
\(685\) −7.44264 −0.284369
\(686\) 0 0
\(687\) 4.21095 0.160658
\(688\) 0 0
\(689\) 2.84986 0.108571
\(690\) 0 0
\(691\) −19.0893 −0.726193 −0.363096 0.931752i \(-0.618280\pi\)
−0.363096 + 0.931752i \(0.618280\pi\)
\(692\) 0 0
\(693\) 0.341611 0.0129767
\(694\) 0 0
\(695\) 12.4053 0.470560
\(696\) 0 0
\(697\) −30.2653 −1.14638
\(698\) 0 0
\(699\) 32.1723 1.21687
\(700\) 0 0
\(701\) 25.5784 0.966081 0.483041 0.875598i \(-0.339532\pi\)
0.483041 + 0.875598i \(0.339532\pi\)
\(702\) 0 0
\(703\) −2.22834 −0.0840435
\(704\) 0 0
\(705\) −13.0032 −0.489729
\(706\) 0 0
\(707\) 17.1239 0.644011
\(708\) 0 0
\(709\) 32.0595 1.20402 0.602010 0.798488i \(-0.294367\pi\)
0.602010 + 0.798488i \(0.294367\pi\)
\(710\) 0 0
\(711\) 1.72179 0.0645723
\(712\) 0 0
\(713\) −23.9996 −0.898792
\(714\) 0 0
\(715\) 1.01052 0.0377914
\(716\) 0 0
\(717\) −35.0750 −1.30990
\(718\) 0 0
\(719\) −10.1162 −0.377270 −0.188635 0.982047i \(-0.560406\pi\)
−0.188635 + 0.982047i \(0.560406\pi\)
\(720\) 0 0
\(721\) 1.80920 0.0673780
\(722\) 0 0
\(723\) 43.2254 1.60757
\(724\) 0 0
\(725\) 8.83179 0.328005
\(726\) 0 0
\(727\) 7.51842 0.278843 0.139421 0.990233i \(-0.455476\pi\)
0.139421 + 0.990233i \(0.455476\pi\)
\(728\) 0 0
\(729\) 29.3344 1.08646
\(730\) 0 0
\(731\) 51.6851 1.91164
\(732\) 0 0
\(733\) −30.7775 −1.13679 −0.568396 0.822755i \(-0.692436\pi\)
−0.568396 + 0.822755i \(0.692436\pi\)
\(734\) 0 0
\(735\) 1.64761 0.0607731
\(736\) 0 0
\(737\) −12.3522 −0.454999
\(738\) 0 0
\(739\) −20.2601 −0.745279 −0.372639 0.927976i \(-0.621547\pi\)
−0.372639 + 0.927976i \(0.621547\pi\)
\(740\) 0 0
\(741\) −12.7675 −0.469027
\(742\) 0 0
\(743\) 29.4311 1.07972 0.539861 0.841754i \(-0.318477\pi\)
0.539861 + 0.841754i \(0.318477\pi\)
\(744\) 0 0
\(745\) −4.65187 −0.170431
\(746\) 0 0
\(747\) −0.224325 −0.00820763
\(748\) 0 0
\(749\) 13.2852 0.485430
\(750\) 0 0
\(751\) −29.5755 −1.07923 −0.539614 0.841913i \(-0.681430\pi\)
−0.539614 + 0.841913i \(0.681430\pi\)
\(752\) 0 0
\(753\) 17.7922 0.648384
\(754\) 0 0
\(755\) 6.65927 0.242356
\(756\) 0 0
\(757\) −39.4525 −1.43392 −0.716962 0.697112i \(-0.754468\pi\)
−0.716962 + 0.697112i \(0.754468\pi\)
\(758\) 0 0
\(759\) 14.1327 0.512984
\(760\) 0 0
\(761\) 1.93230 0.0700457 0.0350229 0.999387i \(-0.488850\pi\)
0.0350229 + 0.999387i \(0.488850\pi\)
\(762\) 0 0
\(763\) −9.09072 −0.329106
\(764\) 0 0
\(765\) 2.27489 0.0822487
\(766\) 0 0
\(767\) 0.589884 0.0212995
\(768\) 0 0
\(769\) 2.12957 0.0767941 0.0383971 0.999263i \(-0.487775\pi\)
0.0383971 + 0.999263i \(0.487775\pi\)
\(770\) 0 0
\(771\) −5.93302 −0.213672
\(772\) 0 0
\(773\) −9.86935 −0.354976 −0.177488 0.984123i \(-0.556797\pi\)
−0.177488 + 0.984123i \(0.556797\pi\)
\(774\) 0 0
\(775\) −11.0165 −0.395726
\(776\) 0 0
\(777\) 0.463973 0.0166450
\(778\) 0 0
\(779\) 35.9634 1.28852
\(780\) 0 0
\(781\) 7.88928 0.282301
\(782\) 0 0
\(783\) −12.0936 −0.432191
\(784\) 0 0
\(785\) 8.09882 0.289059
\(786\) 0 0
\(787\) 37.2890 1.32921 0.664605 0.747195i \(-0.268600\pi\)
0.664605 + 0.747195i \(0.268600\pi\)
\(788\) 0 0
\(789\) 0.648717 0.0230949
\(790\) 0 0
\(791\) −7.24578 −0.257630
\(792\) 0 0
\(793\) −9.66169 −0.343097
\(794\) 0 0
\(795\) −4.69546 −0.166531
\(796\) 0 0
\(797\) 13.0966 0.463906 0.231953 0.972727i \(-0.425488\pi\)
0.231953 + 0.972727i \(0.425488\pi\)
\(798\) 0 0
\(799\) −52.0089 −1.83994
\(800\) 0 0
\(801\) −2.73704 −0.0967087
\(802\) 0 0
\(803\) −6.45328 −0.227731
\(804\) 0 0
\(805\) −8.75913 −0.308719
\(806\) 0 0
\(807\) 1.87745 0.0660894
\(808\) 0 0
\(809\) 13.6573 0.480164 0.240082 0.970753i \(-0.422826\pi\)
0.240082 + 0.970753i \(0.422826\pi\)
\(810\) 0 0
\(811\) −43.9546 −1.54345 −0.771727 0.635954i \(-0.780607\pi\)
−0.771727 + 0.635954i \(0.780607\pi\)
\(812\) 0 0
\(813\) 10.1663 0.356548
\(814\) 0 0
\(815\) 2.97705 0.104282
\(816\) 0 0
\(817\) −61.4160 −2.14867
\(818\) 0 0
\(819\) −0.341611 −0.0119369
\(820\) 0 0
\(821\) 28.3000 0.987677 0.493839 0.869554i \(-0.335593\pi\)
0.493839 + 0.869554i \(0.335593\pi\)
\(822\) 0 0
\(823\) −20.7854 −0.724533 −0.362267 0.932075i \(-0.617997\pi\)
−0.362267 + 0.932075i \(0.617997\pi\)
\(824\) 0 0
\(825\) 6.48734 0.225860
\(826\) 0 0
\(827\) −5.06281 −0.176051 −0.0880256 0.996118i \(-0.528056\pi\)
−0.0880256 + 0.996118i \(0.528056\pi\)
\(828\) 0 0
\(829\) 12.5852 0.437101 0.218550 0.975826i \(-0.429867\pi\)
0.218550 + 0.975826i \(0.429867\pi\)
\(830\) 0 0
\(831\) −33.3813 −1.15798
\(832\) 0 0
\(833\) 6.58995 0.228328
\(834\) 0 0
\(835\) −16.7830 −0.580801
\(836\) 0 0
\(837\) 15.0853 0.521424
\(838\) 0 0
\(839\) 40.9133 1.41248 0.706241 0.707971i \(-0.250389\pi\)
0.706241 + 0.707971i \(0.250389\pi\)
\(840\) 0 0
\(841\) −24.0730 −0.830103
\(842\) 0 0
\(843\) −42.0488 −1.44824
\(844\) 0 0
\(845\) −1.01052 −0.0347630
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −37.6384 −1.29175
\(850\) 0 0
\(851\) −2.46660 −0.0845541
\(852\) 0 0
\(853\) 31.2619 1.07039 0.535193 0.844730i \(-0.320239\pi\)
0.535193 + 0.844730i \(0.320239\pi\)
\(854\) 0 0
\(855\) −2.70318 −0.0924469
\(856\) 0 0
\(857\) 13.2176 0.451504 0.225752 0.974185i \(-0.427516\pi\)
0.225752 + 0.974185i \(0.427516\pi\)
\(858\) 0 0
\(859\) 49.7823 1.69855 0.849275 0.527951i \(-0.177040\pi\)
0.849275 + 0.527951i \(0.177040\pi\)
\(860\) 0 0
\(861\) −7.48812 −0.255194
\(862\) 0 0
\(863\) 37.9512 1.29187 0.645936 0.763391i \(-0.276467\pi\)
0.645936 + 0.763391i \(0.276467\pi\)
\(864\) 0 0
\(865\) 10.6469 0.362004
\(866\) 0 0
\(867\) −43.0888 −1.46337
\(868\) 0 0
\(869\) −5.04021 −0.170978
\(870\) 0 0
\(871\) 12.3522 0.418538
\(872\) 0 0
\(873\) 1.77751 0.0601596
\(874\) 0 0
\(875\) −9.07332 −0.306734
\(876\) 0 0
\(877\) 13.6688 0.461562 0.230781 0.973006i \(-0.425872\pi\)
0.230781 + 0.973006i \(0.425872\pi\)
\(878\) 0 0
\(879\) 7.39740 0.249508
\(880\) 0 0
\(881\) 31.8133 1.07182 0.535909 0.844276i \(-0.319969\pi\)
0.535909 + 0.844276i \(0.319969\pi\)
\(882\) 0 0
\(883\) −50.8122 −1.70997 −0.854984 0.518655i \(-0.826433\pi\)
−0.854984 + 0.518655i \(0.826433\pi\)
\(884\) 0 0
\(885\) −0.971900 −0.0326701
\(886\) 0 0
\(887\) 22.1064 0.742261 0.371131 0.928581i \(-0.378970\pi\)
0.371131 + 0.928581i \(0.378970\pi\)
\(888\) 0 0
\(889\) −2.01023 −0.0674211
\(890\) 0 0
\(891\) −7.85847 −0.263269
\(892\) 0 0
\(893\) 61.8007 2.06808
\(894\) 0 0
\(895\) 13.0353 0.435723
\(896\) 0 0
\(897\) −14.1327 −0.471877
\(898\) 0 0
\(899\) −6.14582 −0.204975
\(900\) 0 0
\(901\) −18.7804 −0.625666
\(902\) 0 0
\(903\) 12.7877 0.425548
\(904\) 0 0
\(905\) −10.8035 −0.359119
\(906\) 0 0
\(907\) 15.0408 0.499421 0.249710 0.968321i \(-0.419665\pi\)
0.249710 + 0.968321i \(0.419665\pi\)
\(908\) 0 0
\(909\) 5.84972 0.194023
\(910\) 0 0
\(911\) 30.7148 1.01763 0.508814 0.860877i \(-0.330084\pi\)
0.508814 + 0.860877i \(0.330084\pi\)
\(912\) 0 0
\(913\) 0.656668 0.0217325
\(914\) 0 0
\(915\) 15.9187 0.526256
\(916\) 0 0
\(917\) 21.3014 0.703433
\(918\) 0 0
\(919\) 14.3866 0.474572 0.237286 0.971440i \(-0.423742\pi\)
0.237286 + 0.971440i \(0.423742\pi\)
\(920\) 0 0
\(921\) 0.000523112 0 1.72371e−5 0
\(922\) 0 0
\(923\) −7.88928 −0.259679
\(924\) 0 0
\(925\) −1.13225 −0.0372280
\(926\) 0 0
\(927\) 0.618042 0.0202992
\(928\) 0 0
\(929\) −7.30951 −0.239817 −0.119909 0.992785i \(-0.538260\pi\)
−0.119909 + 0.992785i \(0.538260\pi\)
\(930\) 0 0
\(931\) −7.83065 −0.256639
\(932\) 0 0
\(933\) −46.6754 −1.52808
\(934\) 0 0
\(935\) −6.65929 −0.217782
\(936\) 0 0
\(937\) 17.7813 0.580891 0.290445 0.956892i \(-0.406197\pi\)
0.290445 + 0.956892i \(0.406197\pi\)
\(938\) 0 0
\(939\) −24.2081 −0.790003
\(940\) 0 0
\(941\) −25.8804 −0.843676 −0.421838 0.906671i \(-0.638615\pi\)
−0.421838 + 0.906671i \(0.638615\pi\)
\(942\) 0 0
\(943\) 39.8088 1.29635
\(944\) 0 0
\(945\) 5.50568 0.179100
\(946\) 0 0
\(947\) 59.1048 1.92065 0.960323 0.278890i \(-0.0899663\pi\)
0.960323 + 0.278890i \(0.0899663\pi\)
\(948\) 0 0
\(949\) 6.45328 0.209482
\(950\) 0 0
\(951\) −24.0963 −0.781377
\(952\) 0 0
\(953\) −34.2136 −1.10829 −0.554144 0.832421i \(-0.686954\pi\)
−0.554144 + 0.832421i \(0.686954\pi\)
\(954\) 0 0
\(955\) −19.5154 −0.631503
\(956\) 0 0
\(957\) 3.61910 0.116989
\(958\) 0 0
\(959\) −7.36515 −0.237833
\(960\) 0 0
\(961\) −23.3339 −0.752705
\(962\) 0 0
\(963\) 4.53837 0.146247
\(964\) 0 0
\(965\) −4.63218 −0.149115
\(966\) 0 0
\(967\) −36.3189 −1.16794 −0.583968 0.811777i \(-0.698501\pi\)
−0.583968 + 0.811777i \(0.698501\pi\)
\(968\) 0 0
\(969\) 84.1374 2.70288
\(970\) 0 0
\(971\) 31.3112 1.00482 0.502412 0.864628i \(-0.332446\pi\)
0.502412 + 0.864628i \(0.332446\pi\)
\(972\) 0 0
\(973\) 12.2761 0.393555
\(974\) 0 0
\(975\) −6.48734 −0.207761
\(976\) 0 0
\(977\) −47.7753 −1.52847 −0.764234 0.644940i \(-0.776883\pi\)
−0.764234 + 0.644940i \(0.776883\pi\)
\(978\) 0 0
\(979\) 8.01216 0.256070
\(980\) 0 0
\(981\) −3.10549 −0.0991507
\(982\) 0 0
\(983\) 18.6736 0.595595 0.297797 0.954629i \(-0.403748\pi\)
0.297797 + 0.954629i \(0.403748\pi\)
\(984\) 0 0
\(985\) −7.69585 −0.245210
\(986\) 0 0
\(987\) −12.8678 −0.409587
\(988\) 0 0
\(989\) −67.9828 −2.16173
\(990\) 0 0
\(991\) −12.2744 −0.389910 −0.194955 0.980812i \(-0.562456\pi\)
−0.194955 + 0.980812i \(0.562456\pi\)
\(992\) 0 0
\(993\) −9.43255 −0.299333
\(994\) 0 0
\(995\) 15.3978 0.488143
\(996\) 0 0
\(997\) −12.2115 −0.386743 −0.193372 0.981126i \(-0.561942\pi\)
−0.193372 + 0.981126i \(0.561942\pi\)
\(998\) 0 0
\(999\) 1.55042 0.0490531
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 \(a_p\))