Properties

Label 8008.2.a.y.1.7
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.528665\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.528665 q^{3} +0.933973 q^{5} +1.00000 q^{7} -2.72051 q^{9} +O(q^{10})\) \(q-0.528665 q^{3} +0.933973 q^{5} +1.00000 q^{7} -2.72051 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.493759 q^{15} +0.372048 q^{17} -3.48213 q^{19} -0.528665 q^{21} -4.94271 q^{23} -4.12769 q^{25} +3.02424 q^{27} +9.77261 q^{29} +8.42408 q^{31} +0.528665 q^{33} +0.933973 q^{35} -2.32225 q^{37} +0.528665 q^{39} +8.25828 q^{41} +1.29298 q^{43} -2.54089 q^{45} +10.0753 q^{47} +1.00000 q^{49} -0.196689 q^{51} +1.68137 q^{53} -0.933973 q^{55} +1.84088 q^{57} +13.7033 q^{59} -6.52555 q^{61} -2.72051 q^{63} -0.933973 q^{65} -14.1966 q^{67} +2.61304 q^{69} -9.57695 q^{71} -3.18018 q^{73} +2.18217 q^{75} -1.00000 q^{77} -17.5913 q^{79} +6.56273 q^{81} -2.45504 q^{83} +0.347483 q^{85} -5.16644 q^{87} -10.5225 q^{89} -1.00000 q^{91} -4.45352 q^{93} -3.25221 q^{95} -6.79736 q^{97} +2.72051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) −0.528665 −0.305225 −0.152612 0.988286i \(-0.548769\pi\)
−0.152612 + 0.988286i \(0.548769\pi\)
\(4\) 0 0
\(5\) 0.933973 0.417685 0.208843 0.977949i \(-0.433030\pi\)
0.208843 + 0.977949i \(0.433030\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.72051 −0.906838
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.493759 −0.127488
\(16\) 0 0
\(17\) 0.372048 0.0902349 0.0451175 0.998982i \(-0.485634\pi\)
0.0451175 + 0.998982i \(0.485634\pi\)
\(18\) 0 0
\(19\) −3.48213 −0.798855 −0.399427 0.916765i \(-0.630791\pi\)
−0.399427 + 0.916765i \(0.630791\pi\)
\(20\) 0 0
\(21\) −0.528665 −0.115364
\(22\) 0 0
\(23\) −4.94271 −1.03063 −0.515314 0.857002i \(-0.672325\pi\)
−0.515314 + 0.857002i \(0.672325\pi\)
\(24\) 0 0
\(25\) −4.12769 −0.825539
\(26\) 0 0
\(27\) 3.02424 0.582014
\(28\) 0 0
\(29\) 9.77261 1.81473 0.907364 0.420346i \(-0.138091\pi\)
0.907364 + 0.420346i \(0.138091\pi\)
\(30\) 0 0
\(31\) 8.42408 1.51301 0.756505 0.653988i \(-0.226905\pi\)
0.756505 + 0.653988i \(0.226905\pi\)
\(32\) 0 0
\(33\) 0.528665 0.0920288
\(34\) 0 0
\(35\) 0.933973 0.157870
\(36\) 0 0
\(37\) −2.32225 −0.381776 −0.190888 0.981612i \(-0.561137\pi\)
−0.190888 + 0.981612i \(0.561137\pi\)
\(38\) 0 0
\(39\) 0.528665 0.0846541
\(40\) 0 0
\(41\) 8.25828 1.28973 0.644864 0.764298i \(-0.276914\pi\)
0.644864 + 0.764298i \(0.276914\pi\)
\(42\) 0 0
\(43\) 1.29298 0.197178 0.0985890 0.995128i \(-0.468567\pi\)
0.0985890 + 0.995128i \(0.468567\pi\)
\(44\) 0 0
\(45\) −2.54089 −0.378773
\(46\) 0 0
\(47\) 10.0753 1.46964 0.734819 0.678263i \(-0.237267\pi\)
0.734819 + 0.678263i \(0.237267\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −0.196689 −0.0275419
\(52\) 0 0
\(53\) 1.68137 0.230954 0.115477 0.993310i \(-0.463160\pi\)
0.115477 + 0.993310i \(0.463160\pi\)
\(54\) 0 0
\(55\) −0.933973 −0.125937
\(56\) 0 0
\(57\) 1.84088 0.243830
\(58\) 0 0
\(59\) 13.7033 1.78401 0.892007 0.452022i \(-0.149297\pi\)
0.892007 + 0.452022i \(0.149297\pi\)
\(60\) 0 0
\(61\) −6.52555 −0.835511 −0.417755 0.908560i \(-0.637183\pi\)
−0.417755 + 0.908560i \(0.637183\pi\)
\(62\) 0 0
\(63\) −2.72051 −0.342752
\(64\) 0 0
\(65\) −0.933973 −0.115845
\(66\) 0 0
\(67\) −14.1966 −1.73439 −0.867194 0.497970i \(-0.834079\pi\)
−0.867194 + 0.497970i \(0.834079\pi\)
\(68\) 0 0
\(69\) 2.61304 0.314573
\(70\) 0 0
\(71\) −9.57695 −1.13658 −0.568288 0.822830i \(-0.692394\pi\)
−0.568288 + 0.822830i \(0.692394\pi\)
\(72\) 0 0
\(73\) −3.18018 −0.372212 −0.186106 0.982530i \(-0.559587\pi\)
−0.186106 + 0.982530i \(0.559587\pi\)
\(74\) 0 0
\(75\) 2.18217 0.251975
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −17.5913 −1.97918 −0.989590 0.143917i \(-0.954030\pi\)
−0.989590 + 0.143917i \(0.954030\pi\)
\(80\) 0 0
\(81\) 6.56273 0.729193
\(82\) 0 0
\(83\) −2.45504 −0.269476 −0.134738 0.990881i \(-0.543019\pi\)
−0.134738 + 0.990881i \(0.543019\pi\)
\(84\) 0 0
\(85\) 0.347483 0.0376898
\(86\) 0 0
\(87\) −5.16644 −0.553900
\(88\) 0 0
\(89\) −10.5225 −1.11538 −0.557690 0.830049i \(-0.688312\pi\)
−0.557690 + 0.830049i \(0.688312\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −4.45352 −0.461808
\(94\) 0 0
\(95\) −3.25221 −0.333670
\(96\) 0 0
\(97\) −6.79736 −0.690167 −0.345083 0.938572i \(-0.612149\pi\)
−0.345083 + 0.938572i \(0.612149\pi\)
\(98\) 0 0
\(99\) 2.72051 0.273422
\(100\) 0 0
\(101\) 6.58580 0.655311 0.327656 0.944797i \(-0.393741\pi\)
0.327656 + 0.944797i \(0.393741\pi\)
\(102\) 0 0
\(103\) −14.4920 −1.42794 −0.713968 0.700178i \(-0.753104\pi\)
−0.713968 + 0.700178i \(0.753104\pi\)
\(104\) 0 0
\(105\) −0.493759 −0.0481859
\(106\) 0 0
\(107\) −14.5657 −1.40811 −0.704057 0.710143i \(-0.748630\pi\)
−0.704057 + 0.710143i \(0.748630\pi\)
\(108\) 0 0
\(109\) −13.6628 −1.30866 −0.654331 0.756208i \(-0.727050\pi\)
−0.654331 + 0.756208i \(0.727050\pi\)
\(110\) 0 0
\(111\) 1.22769 0.116527
\(112\) 0 0
\(113\) 9.72536 0.914885 0.457443 0.889239i \(-0.348766\pi\)
0.457443 + 0.889239i \(0.348766\pi\)
\(114\) 0 0
\(115\) −4.61636 −0.430478
\(116\) 0 0
\(117\) 2.72051 0.251512
\(118\) 0 0
\(119\) 0.372048 0.0341056
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −4.36586 −0.393657
\(124\) 0 0
\(125\) −8.52502 −0.762501
\(126\) 0 0
\(127\) −5.48189 −0.486439 −0.243219 0.969971i \(-0.578204\pi\)
−0.243219 + 0.969971i \(0.578204\pi\)
\(128\) 0 0
\(129\) −0.683555 −0.0601836
\(130\) 0 0
\(131\) 0.957619 0.0836675 0.0418338 0.999125i \(-0.486680\pi\)
0.0418338 + 0.999125i \(0.486680\pi\)
\(132\) 0 0
\(133\) −3.48213 −0.301939
\(134\) 0 0
\(135\) 2.82455 0.243099
\(136\) 0 0
\(137\) 0.243329 0.0207890 0.0103945 0.999946i \(-0.496691\pi\)
0.0103945 + 0.999946i \(0.496691\pi\)
\(138\) 0 0
\(139\) 4.71861 0.400227 0.200114 0.979773i \(-0.435869\pi\)
0.200114 + 0.979773i \(0.435869\pi\)
\(140\) 0 0
\(141\) −5.32648 −0.448570
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 9.12735 0.757985
\(146\) 0 0
\(147\) −0.528665 −0.0436036
\(148\) 0 0
\(149\) 6.74561 0.552622 0.276311 0.961068i \(-0.410888\pi\)
0.276311 + 0.961068i \(0.410888\pi\)
\(150\) 0 0
\(151\) 18.4337 1.50011 0.750055 0.661375i \(-0.230027\pi\)
0.750055 + 0.661375i \(0.230027\pi\)
\(152\) 0 0
\(153\) −1.01216 −0.0818285
\(154\) 0 0
\(155\) 7.86786 0.631962
\(156\) 0 0
\(157\) −16.8281 −1.34303 −0.671514 0.740992i \(-0.734356\pi\)
−0.671514 + 0.740992i \(0.734356\pi\)
\(158\) 0 0
\(159\) −0.888883 −0.0704930
\(160\) 0 0
\(161\) −4.94271 −0.389540
\(162\) 0 0
\(163\) 20.5879 1.61257 0.806286 0.591526i \(-0.201474\pi\)
0.806286 + 0.591526i \(0.201474\pi\)
\(164\) 0 0
\(165\) 0.493759 0.0384391
\(166\) 0 0
\(167\) −21.9427 −1.69798 −0.848988 0.528412i \(-0.822788\pi\)
−0.848988 + 0.528412i \(0.822788\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 9.47317 0.724432
\(172\) 0 0
\(173\) −21.7997 −1.65740 −0.828699 0.559695i \(-0.810918\pi\)
−0.828699 + 0.559695i \(0.810918\pi\)
\(174\) 0 0
\(175\) −4.12769 −0.312024
\(176\) 0 0
\(177\) −7.24444 −0.544525
\(178\) 0 0
\(179\) −21.1571 −1.58136 −0.790678 0.612232i \(-0.790272\pi\)
−0.790678 + 0.612232i \(0.790272\pi\)
\(180\) 0 0
\(181\) 8.29825 0.616804 0.308402 0.951256i \(-0.400206\pi\)
0.308402 + 0.951256i \(0.400206\pi\)
\(182\) 0 0
\(183\) 3.44983 0.255019
\(184\) 0 0
\(185\) −2.16892 −0.159462
\(186\) 0 0
\(187\) −0.372048 −0.0272069
\(188\) 0 0
\(189\) 3.02424 0.219981
\(190\) 0 0
\(191\) −22.0851 −1.59802 −0.799010 0.601318i \(-0.794643\pi\)
−0.799010 + 0.601318i \(0.794643\pi\)
\(192\) 0 0
\(193\) 0.950189 0.0683961 0.0341981 0.999415i \(-0.489112\pi\)
0.0341981 + 0.999415i \(0.489112\pi\)
\(194\) 0 0
\(195\) 0.493759 0.0353588
\(196\) 0 0
\(197\) −8.17415 −0.582384 −0.291192 0.956665i \(-0.594052\pi\)
−0.291192 + 0.956665i \(0.594052\pi\)
\(198\) 0 0
\(199\) 23.1537 1.64132 0.820661 0.571415i \(-0.193605\pi\)
0.820661 + 0.571415i \(0.193605\pi\)
\(200\) 0 0
\(201\) 7.50523 0.529378
\(202\) 0 0
\(203\) 9.77261 0.685903
\(204\) 0 0
\(205\) 7.71301 0.538700
\(206\) 0 0
\(207\) 13.4467 0.934612
\(208\) 0 0
\(209\) 3.48213 0.240864
\(210\) 0 0
\(211\) −14.8345 −1.02125 −0.510626 0.859803i \(-0.670586\pi\)
−0.510626 + 0.859803i \(0.670586\pi\)
\(212\) 0 0
\(213\) 5.06300 0.346911
\(214\) 0 0
\(215\) 1.20761 0.0823584
\(216\) 0 0
\(217\) 8.42408 0.571864
\(218\) 0 0
\(219\) 1.68125 0.113608
\(220\) 0 0
\(221\) −0.372048 −0.0250267
\(222\) 0 0
\(223\) −9.33295 −0.624980 −0.312490 0.949921i \(-0.601163\pi\)
−0.312490 + 0.949921i \(0.601163\pi\)
\(224\) 0 0
\(225\) 11.2294 0.748630
\(226\) 0 0
\(227\) −23.2598 −1.54381 −0.771903 0.635740i \(-0.780695\pi\)
−0.771903 + 0.635740i \(0.780695\pi\)
\(228\) 0 0
\(229\) 7.74296 0.511669 0.255834 0.966721i \(-0.417650\pi\)
0.255834 + 0.966721i \(0.417650\pi\)
\(230\) 0 0
\(231\) 0.528665 0.0347836
\(232\) 0 0
\(233\) 21.7728 1.42638 0.713191 0.700969i \(-0.247249\pi\)
0.713191 + 0.700969i \(0.247249\pi\)
\(234\) 0 0
\(235\) 9.41009 0.613846
\(236\) 0 0
\(237\) 9.29992 0.604095
\(238\) 0 0
\(239\) 4.83967 0.313052 0.156526 0.987674i \(-0.449971\pi\)
0.156526 + 0.987674i \(0.449971\pi\)
\(240\) 0 0
\(241\) 2.09112 0.134701 0.0673505 0.997729i \(-0.478545\pi\)
0.0673505 + 0.997729i \(0.478545\pi\)
\(242\) 0 0
\(243\) −12.5422 −0.804582
\(244\) 0 0
\(245\) 0.933973 0.0596693
\(246\) 0 0
\(247\) 3.48213 0.221562
\(248\) 0 0
\(249\) 1.29790 0.0822508
\(250\) 0 0
\(251\) −8.95974 −0.565534 −0.282767 0.959189i \(-0.591252\pi\)
−0.282767 + 0.959189i \(0.591252\pi\)
\(252\) 0 0
\(253\) 4.94271 0.310746
\(254\) 0 0
\(255\) −0.183702 −0.0115039
\(256\) 0 0
\(257\) −23.7700 −1.48273 −0.741367 0.671100i \(-0.765822\pi\)
−0.741367 + 0.671100i \(0.765822\pi\)
\(258\) 0 0
\(259\) −2.32225 −0.144298
\(260\) 0 0
\(261\) −26.5865 −1.64566
\(262\) 0 0
\(263\) −19.2435 −1.18660 −0.593302 0.804980i \(-0.702176\pi\)
−0.593302 + 0.804980i \(0.702176\pi\)
\(264\) 0 0
\(265\) 1.57036 0.0964662
\(266\) 0 0
\(267\) 5.56286 0.340442
\(268\) 0 0
\(269\) 0.525897 0.0320645 0.0160322 0.999871i \(-0.494897\pi\)
0.0160322 + 0.999871i \(0.494897\pi\)
\(270\) 0 0
\(271\) −21.6902 −1.31759 −0.658793 0.752324i \(-0.728933\pi\)
−0.658793 + 0.752324i \(0.728933\pi\)
\(272\) 0 0
\(273\) 0.528665 0.0319963
\(274\) 0 0
\(275\) 4.12769 0.248909
\(276\) 0 0
\(277\) −6.69386 −0.402195 −0.201097 0.979571i \(-0.564451\pi\)
−0.201097 + 0.979571i \(0.564451\pi\)
\(278\) 0 0
\(279\) −22.9178 −1.37205
\(280\) 0 0
\(281\) 1.55903 0.0930040 0.0465020 0.998918i \(-0.485193\pi\)
0.0465020 + 0.998918i \(0.485193\pi\)
\(282\) 0 0
\(283\) 14.3182 0.851126 0.425563 0.904929i \(-0.360076\pi\)
0.425563 + 0.904929i \(0.360076\pi\)
\(284\) 0 0
\(285\) 1.71933 0.101844
\(286\) 0 0
\(287\) 8.25828 0.487471
\(288\) 0 0
\(289\) −16.8616 −0.991858
\(290\) 0 0
\(291\) 3.59352 0.210656
\(292\) 0 0
\(293\) 8.51062 0.497196 0.248598 0.968607i \(-0.420030\pi\)
0.248598 + 0.968607i \(0.420030\pi\)
\(294\) 0 0
\(295\) 12.7985 0.745156
\(296\) 0 0
\(297\) −3.02424 −0.175484
\(298\) 0 0
\(299\) 4.94271 0.285845
\(300\) 0 0
\(301\) 1.29298 0.0745263
\(302\) 0 0
\(303\) −3.48168 −0.200017
\(304\) 0 0
\(305\) −6.09468 −0.348981
\(306\) 0 0
\(307\) −14.1322 −0.806567 −0.403283 0.915075i \(-0.632131\pi\)
−0.403283 + 0.915075i \(0.632131\pi\)
\(308\) 0 0
\(309\) 7.66140 0.435842
\(310\) 0 0
\(311\) −9.41608 −0.533937 −0.266968 0.963705i \(-0.586022\pi\)
−0.266968 + 0.963705i \(0.586022\pi\)
\(312\) 0 0
\(313\) 20.9266 1.18284 0.591421 0.806363i \(-0.298567\pi\)
0.591421 + 0.806363i \(0.298567\pi\)
\(314\) 0 0
\(315\) −2.54089 −0.143163
\(316\) 0 0
\(317\) 28.0936 1.57789 0.788946 0.614463i \(-0.210627\pi\)
0.788946 + 0.614463i \(0.210627\pi\)
\(318\) 0 0
\(319\) −9.77261 −0.547161
\(320\) 0 0
\(321\) 7.70035 0.429792
\(322\) 0 0
\(323\) −1.29552 −0.0720846
\(324\) 0 0
\(325\) 4.12769 0.228963
\(326\) 0 0
\(327\) 7.22306 0.399436
\(328\) 0 0
\(329\) 10.0753 0.555471
\(330\) 0 0
\(331\) 9.69656 0.532971 0.266486 0.963839i \(-0.414138\pi\)
0.266486 + 0.963839i \(0.414138\pi\)
\(332\) 0 0
\(333\) 6.31771 0.346209
\(334\) 0 0
\(335\) −13.2592 −0.724428
\(336\) 0 0
\(337\) −9.12736 −0.497199 −0.248599 0.968606i \(-0.579970\pi\)
−0.248599 + 0.968606i \(0.579970\pi\)
\(338\) 0 0
\(339\) −5.14146 −0.279246
\(340\) 0 0
\(341\) −8.42408 −0.456190
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 2.44051 0.131393
\(346\) 0 0
\(347\) −12.8688 −0.690833 −0.345416 0.938450i \(-0.612262\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(348\) 0 0
\(349\) 21.9680 1.17592 0.587960 0.808890i \(-0.299931\pi\)
0.587960 + 0.808890i \(0.299931\pi\)
\(350\) 0 0
\(351\) −3.02424 −0.161422
\(352\) 0 0
\(353\) 16.6928 0.888466 0.444233 0.895911i \(-0.353476\pi\)
0.444233 + 0.895911i \(0.353476\pi\)
\(354\) 0 0
\(355\) −8.94461 −0.474731
\(356\) 0 0
\(357\) −0.196689 −0.0104099
\(358\) 0 0
\(359\) −27.2966 −1.44066 −0.720330 0.693632i \(-0.756010\pi\)
−0.720330 + 0.693632i \(0.756010\pi\)
\(360\) 0 0
\(361\) −6.87480 −0.361831
\(362\) 0 0
\(363\) −0.528665 −0.0277477
\(364\) 0 0
\(365\) −2.97020 −0.155468
\(366\) 0 0
\(367\) −15.0514 −0.785675 −0.392838 0.919608i \(-0.628507\pi\)
−0.392838 + 0.919608i \(0.628507\pi\)
\(368\) 0 0
\(369\) −22.4668 −1.16957
\(370\) 0 0
\(371\) 1.68137 0.0872925
\(372\) 0 0
\(373\) −13.2726 −0.687231 −0.343616 0.939110i \(-0.611652\pi\)
−0.343616 + 0.939110i \(0.611652\pi\)
\(374\) 0 0
\(375\) 4.50688 0.232734
\(376\) 0 0
\(377\) −9.77261 −0.503315
\(378\) 0 0
\(379\) −13.1865 −0.677347 −0.338674 0.940904i \(-0.609978\pi\)
−0.338674 + 0.940904i \(0.609978\pi\)
\(380\) 0 0
\(381\) 2.89808 0.148473
\(382\) 0 0
\(383\) 0.569479 0.0290990 0.0145495 0.999894i \(-0.495369\pi\)
0.0145495 + 0.999894i \(0.495369\pi\)
\(384\) 0 0
\(385\) −0.933973 −0.0475997
\(386\) 0 0
\(387\) −3.51758 −0.178808
\(388\) 0 0
\(389\) 9.68298 0.490946 0.245473 0.969403i \(-0.421057\pi\)
0.245473 + 0.969403i \(0.421057\pi\)
\(390\) 0 0
\(391\) −1.83893 −0.0929986
\(392\) 0 0
\(393\) −0.506260 −0.0255374
\(394\) 0 0
\(395\) −16.4298 −0.826674
\(396\) 0 0
\(397\) −14.6845 −0.736992 −0.368496 0.929629i \(-0.620127\pi\)
−0.368496 + 0.929629i \(0.620127\pi\)
\(398\) 0 0
\(399\) 1.84088 0.0921592
\(400\) 0 0
\(401\) 21.6342 1.08036 0.540180 0.841549i \(-0.318356\pi\)
0.540180 + 0.841549i \(0.318356\pi\)
\(402\) 0 0
\(403\) −8.42408 −0.419634
\(404\) 0 0
\(405\) 6.12941 0.304573
\(406\) 0 0
\(407\) 2.32225 0.115110
\(408\) 0 0
\(409\) 10.7570 0.531900 0.265950 0.963987i \(-0.414314\pi\)
0.265950 + 0.963987i \(0.414314\pi\)
\(410\) 0 0
\(411\) −0.128640 −0.00634533
\(412\) 0 0
\(413\) 13.7033 0.674294
\(414\) 0 0
\(415\) −2.29294 −0.112556
\(416\) 0 0
\(417\) −2.49456 −0.122159
\(418\) 0 0
\(419\) −2.90107 −0.141726 −0.0708632 0.997486i \(-0.522575\pi\)
−0.0708632 + 0.997486i \(0.522575\pi\)
\(420\) 0 0
\(421\) −37.8475 −1.84457 −0.922286 0.386508i \(-0.873681\pi\)
−0.922286 + 0.386508i \(0.873681\pi\)
\(422\) 0 0
\(423\) −27.4101 −1.33272
\(424\) 0 0
\(425\) −1.53570 −0.0744925
\(426\) 0 0
\(427\) −6.52555 −0.315793
\(428\) 0 0
\(429\) −0.528665 −0.0255242
\(430\) 0 0
\(431\) −23.1454 −1.11487 −0.557437 0.830219i \(-0.688215\pi\)
−0.557437 + 0.830219i \(0.688215\pi\)
\(432\) 0 0
\(433\) 5.68155 0.273038 0.136519 0.990637i \(-0.456409\pi\)
0.136519 + 0.990637i \(0.456409\pi\)
\(434\) 0 0
\(435\) −4.82531 −0.231356
\(436\) 0 0
\(437\) 17.2112 0.823321
\(438\) 0 0
\(439\) 22.7782 1.08714 0.543571 0.839363i \(-0.317072\pi\)
0.543571 + 0.839363i \(0.317072\pi\)
\(440\) 0 0
\(441\) −2.72051 −0.129548
\(442\) 0 0
\(443\) −2.60012 −0.123535 −0.0617676 0.998091i \(-0.519674\pi\)
−0.0617676 + 0.998091i \(0.519674\pi\)
\(444\) 0 0
\(445\) −9.82770 −0.465878
\(446\) 0 0
\(447\) −3.56617 −0.168674
\(448\) 0 0
\(449\) −19.5119 −0.920825 −0.460413 0.887705i \(-0.652299\pi\)
−0.460413 + 0.887705i \(0.652299\pi\)
\(450\) 0 0
\(451\) −8.25828 −0.388867
\(452\) 0 0
\(453\) −9.74523 −0.457871
\(454\) 0 0
\(455\) −0.933973 −0.0437853
\(456\) 0 0
\(457\) 23.6042 1.10416 0.552079 0.833792i \(-0.313835\pi\)
0.552079 + 0.833792i \(0.313835\pi\)
\(458\) 0 0
\(459\) 1.12516 0.0525180
\(460\) 0 0
\(461\) 1.54946 0.0721656 0.0360828 0.999349i \(-0.488512\pi\)
0.0360828 + 0.999349i \(0.488512\pi\)
\(462\) 0 0
\(463\) 18.7272 0.870325 0.435163 0.900352i \(-0.356691\pi\)
0.435163 + 0.900352i \(0.356691\pi\)
\(464\) 0 0
\(465\) −4.15946 −0.192891
\(466\) 0 0
\(467\) −6.95315 −0.321753 −0.160877 0.986975i \(-0.551432\pi\)
−0.160877 + 0.986975i \(0.551432\pi\)
\(468\) 0 0
\(469\) −14.1966 −0.655537
\(470\) 0 0
\(471\) 8.89642 0.409925
\(472\) 0 0
\(473\) −1.29298 −0.0594514
\(474\) 0 0
\(475\) 14.3732 0.659486
\(476\) 0 0
\(477\) −4.57420 −0.209438
\(478\) 0 0
\(479\) −0.436792 −0.0199575 −0.00997877 0.999950i \(-0.503176\pi\)
−0.00997877 + 0.999950i \(0.503176\pi\)
\(480\) 0 0
\(481\) 2.32225 0.105886
\(482\) 0 0
\(483\) 2.61304 0.118897
\(484\) 0 0
\(485\) −6.34855 −0.288273
\(486\) 0 0
\(487\) 19.0384 0.862710 0.431355 0.902182i \(-0.358036\pi\)
0.431355 + 0.902182i \(0.358036\pi\)
\(488\) 0 0
\(489\) −10.8841 −0.492197
\(490\) 0 0
\(491\) −8.83175 −0.398571 −0.199286 0.979941i \(-0.563862\pi\)
−0.199286 + 0.979941i \(0.563862\pi\)
\(492\) 0 0
\(493\) 3.63588 0.163752
\(494\) 0 0
\(495\) 2.54089 0.114204
\(496\) 0 0
\(497\) −9.57695 −0.429585
\(498\) 0 0
\(499\) 6.14601 0.275133 0.137567 0.990493i \(-0.456072\pi\)
0.137567 + 0.990493i \(0.456072\pi\)
\(500\) 0 0
\(501\) 11.6003 0.518265
\(502\) 0 0
\(503\) −5.98619 −0.266911 −0.133455 0.991055i \(-0.542607\pi\)
−0.133455 + 0.991055i \(0.542607\pi\)
\(504\) 0 0
\(505\) 6.15095 0.273714
\(506\) 0 0
\(507\) −0.528665 −0.0234788
\(508\) 0 0
\(509\) 29.5736 1.31083 0.655413 0.755271i \(-0.272495\pi\)
0.655413 + 0.755271i \(0.272495\pi\)
\(510\) 0 0
\(511\) −3.18018 −0.140683
\(512\) 0 0
\(513\) −10.5308 −0.464945
\(514\) 0 0
\(515\) −13.5351 −0.596428
\(516\) 0 0
\(517\) −10.0753 −0.443113
\(518\) 0 0
\(519\) 11.5247 0.505879
\(520\) 0 0
\(521\) 36.2021 1.58604 0.793022 0.609194i \(-0.208507\pi\)
0.793022 + 0.609194i \(0.208507\pi\)
\(522\) 0 0
\(523\) 8.45323 0.369634 0.184817 0.982773i \(-0.440831\pi\)
0.184817 + 0.982773i \(0.440831\pi\)
\(524\) 0 0
\(525\) 2.18217 0.0952376
\(526\) 0 0
\(527\) 3.13417 0.136526
\(528\) 0 0
\(529\) 1.43042 0.0621922
\(530\) 0 0
\(531\) −37.2799 −1.61781
\(532\) 0 0
\(533\) −8.25828 −0.357706
\(534\) 0 0
\(535\) −13.6039 −0.588149
\(536\) 0 0
\(537\) 11.1850 0.482669
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 40.8656 1.75695 0.878475 0.477788i \(-0.158561\pi\)
0.878475 + 0.477788i \(0.158561\pi\)
\(542\) 0 0
\(543\) −4.38699 −0.188264
\(544\) 0 0
\(545\) −12.7607 −0.546609
\(546\) 0 0
\(547\) −26.0400 −1.11339 −0.556694 0.830718i \(-0.687930\pi\)
−0.556694 + 0.830718i \(0.687930\pi\)
\(548\) 0 0
\(549\) 17.7528 0.757673
\(550\) 0 0
\(551\) −34.0295 −1.44970
\(552\) 0 0
\(553\) −17.5913 −0.748060
\(554\) 0 0
\(555\) 1.14663 0.0486718
\(556\) 0 0
\(557\) −6.33403 −0.268381 −0.134191 0.990956i \(-0.542843\pi\)
−0.134191 + 0.990956i \(0.542843\pi\)
\(558\) 0 0
\(559\) −1.29298 −0.0546873
\(560\) 0 0
\(561\) 0.196689 0.00830421
\(562\) 0 0
\(563\) 28.4713 1.19992 0.599961 0.800030i \(-0.295183\pi\)
0.599961 + 0.800030i \(0.295183\pi\)
\(564\) 0 0
\(565\) 9.08322 0.382134
\(566\) 0 0
\(567\) 6.56273 0.275609
\(568\) 0 0
\(569\) 11.9445 0.500739 0.250370 0.968150i \(-0.419448\pi\)
0.250370 + 0.968150i \(0.419448\pi\)
\(570\) 0 0
\(571\) 13.2488 0.554445 0.277222 0.960806i \(-0.410586\pi\)
0.277222 + 0.960806i \(0.410586\pi\)
\(572\) 0 0
\(573\) 11.6756 0.487755
\(574\) 0 0
\(575\) 20.4020 0.850823
\(576\) 0 0
\(577\) −4.14213 −0.172439 −0.0862195 0.996276i \(-0.527479\pi\)
−0.0862195 + 0.996276i \(0.527479\pi\)
\(578\) 0 0
\(579\) −0.502332 −0.0208762
\(580\) 0 0
\(581\) −2.45504 −0.101852
\(582\) 0 0
\(583\) −1.68137 −0.0696353
\(584\) 0 0
\(585\) 2.54089 0.105053
\(586\) 0 0
\(587\) −17.4677 −0.720969 −0.360484 0.932765i \(-0.617389\pi\)
−0.360484 + 0.932765i \(0.617389\pi\)
\(588\) 0 0
\(589\) −29.3337 −1.20868
\(590\) 0 0
\(591\) 4.32139 0.177758
\(592\) 0 0
\(593\) −29.2995 −1.20319 −0.601593 0.798803i \(-0.705467\pi\)
−0.601593 + 0.798803i \(0.705467\pi\)
\(594\) 0 0
\(595\) 0.347483 0.0142454
\(596\) 0 0
\(597\) −12.2406 −0.500972
\(598\) 0 0
\(599\) 17.9878 0.734960 0.367480 0.930031i \(-0.380221\pi\)
0.367480 + 0.930031i \(0.380221\pi\)
\(600\) 0 0
\(601\) 14.2872 0.582786 0.291393 0.956603i \(-0.405881\pi\)
0.291393 + 0.956603i \(0.405881\pi\)
\(602\) 0 0
\(603\) 38.6220 1.57281
\(604\) 0 0
\(605\) 0.933973 0.0379714
\(606\) 0 0
\(607\) 29.7899 1.20913 0.604567 0.796555i \(-0.293346\pi\)
0.604567 + 0.796555i \(0.293346\pi\)
\(608\) 0 0
\(609\) −5.16644 −0.209355
\(610\) 0 0
\(611\) −10.0753 −0.407604
\(612\) 0 0
\(613\) 21.0152 0.848797 0.424399 0.905475i \(-0.360485\pi\)
0.424399 + 0.905475i \(0.360485\pi\)
\(614\) 0 0
\(615\) −4.07760 −0.164425
\(616\) 0 0
\(617\) −3.66609 −0.147591 −0.0737956 0.997273i \(-0.523511\pi\)
−0.0737956 + 0.997273i \(0.523511\pi\)
\(618\) 0 0
\(619\) 25.1426 1.01057 0.505284 0.862953i \(-0.331388\pi\)
0.505284 + 0.862953i \(0.331388\pi\)
\(620\) 0 0
\(621\) −14.9479 −0.599840
\(622\) 0 0
\(623\) −10.5225 −0.421574
\(624\) 0 0
\(625\) 12.6763 0.507054
\(626\) 0 0
\(627\) −1.84088 −0.0735176
\(628\) 0 0
\(629\) −0.863989 −0.0344495
\(630\) 0 0
\(631\) −25.5222 −1.01602 −0.508010 0.861351i \(-0.669619\pi\)
−0.508010 + 0.861351i \(0.669619\pi\)
\(632\) 0 0
\(633\) 7.84250 0.311712
\(634\) 0 0
\(635\) −5.11993 −0.203178
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 26.0542 1.03069
\(640\) 0 0
\(641\) 28.9750 1.14444 0.572221 0.820099i \(-0.306082\pi\)
0.572221 + 0.820099i \(0.306082\pi\)
\(642\) 0 0
\(643\) −33.5369 −1.32257 −0.661283 0.750137i \(-0.729988\pi\)
−0.661283 + 0.750137i \(0.729988\pi\)
\(644\) 0 0
\(645\) −0.638421 −0.0251378
\(646\) 0 0
\(647\) −40.8038 −1.60416 −0.802082 0.597214i \(-0.796274\pi\)
−0.802082 + 0.597214i \(0.796274\pi\)
\(648\) 0 0
\(649\) −13.7033 −0.537900
\(650\) 0 0
\(651\) −4.45352 −0.174547
\(652\) 0 0
\(653\) 14.3615 0.562010 0.281005 0.959706i \(-0.409332\pi\)
0.281005 + 0.959706i \(0.409332\pi\)
\(654\) 0 0
\(655\) 0.894390 0.0349467
\(656\) 0 0
\(657\) 8.65173 0.337536
\(658\) 0 0
\(659\) −5.65171 −0.220159 −0.110080 0.993923i \(-0.535111\pi\)
−0.110080 + 0.993923i \(0.535111\pi\)
\(660\) 0 0
\(661\) 27.1044 1.05424 0.527120 0.849791i \(-0.323272\pi\)
0.527120 + 0.849791i \(0.323272\pi\)
\(662\) 0 0
\(663\) 0.196689 0.00763876
\(664\) 0 0
\(665\) −3.25221 −0.126115
\(666\) 0 0
\(667\) −48.3032 −1.87031
\(668\) 0 0
\(669\) 4.93400 0.190760
\(670\) 0 0
\(671\) 6.52555 0.251916
\(672\) 0 0
\(673\) 35.3336 1.36201 0.681005 0.732279i \(-0.261543\pi\)
0.681005 + 0.732279i \(0.261543\pi\)
\(674\) 0 0
\(675\) −12.4831 −0.480476
\(676\) 0 0
\(677\) 9.97653 0.383429 0.191715 0.981451i \(-0.438595\pi\)
0.191715 + 0.981451i \(0.438595\pi\)
\(678\) 0 0
\(679\) −6.79736 −0.260859
\(680\) 0 0
\(681\) 12.2966 0.471208
\(682\) 0 0
\(683\) −51.3730 −1.96573 −0.982866 0.184322i \(-0.940991\pi\)
−0.982866 + 0.184322i \(0.940991\pi\)
\(684\) 0 0
\(685\) 0.227263 0.00868327
\(686\) 0 0
\(687\) −4.09343 −0.156174
\(688\) 0 0
\(689\) −1.68137 −0.0640552
\(690\) 0 0
\(691\) −24.3730 −0.927193 −0.463596 0.886046i \(-0.653441\pi\)
−0.463596 + 0.886046i \(0.653441\pi\)
\(692\) 0 0
\(693\) 2.72051 0.103344
\(694\) 0 0
\(695\) 4.40705 0.167169
\(696\) 0 0
\(697\) 3.07248 0.116378
\(698\) 0 0
\(699\) −11.5105 −0.435367
\(700\) 0 0
\(701\) −21.4248 −0.809204 −0.404602 0.914493i \(-0.632590\pi\)
−0.404602 + 0.914493i \(0.632590\pi\)
\(702\) 0 0
\(703\) 8.08637 0.304983
\(704\) 0 0
\(705\) −4.97478 −0.187361
\(706\) 0 0
\(707\) 6.58580 0.247684
\(708\) 0 0
\(709\) −39.5345 −1.48475 −0.742374 0.669985i \(-0.766300\pi\)
−0.742374 + 0.669985i \(0.766300\pi\)
\(710\) 0 0
\(711\) 47.8575 1.79479
\(712\) 0 0
\(713\) −41.6378 −1.55935
\(714\) 0 0
\(715\) 0.933973 0.0349286
\(716\) 0 0
\(717\) −2.55856 −0.0955512
\(718\) 0 0
\(719\) −42.5602 −1.58723 −0.793614 0.608422i \(-0.791803\pi\)
−0.793614 + 0.608422i \(0.791803\pi\)
\(720\) 0 0
\(721\) −14.4920 −0.539709
\(722\) 0 0
\(723\) −1.10550 −0.0411141
\(724\) 0 0
\(725\) −40.3384 −1.49813
\(726\) 0 0
\(727\) 15.0575 0.558453 0.279226 0.960225i \(-0.409922\pi\)
0.279226 + 0.960225i \(0.409922\pi\)
\(728\) 0 0
\(729\) −13.0576 −0.483614
\(730\) 0 0
\(731\) 0.481052 0.0177923
\(732\) 0 0
\(733\) −23.2906 −0.860257 −0.430129 0.902768i \(-0.641532\pi\)
−0.430129 + 0.902768i \(0.641532\pi\)
\(734\) 0 0
\(735\) −0.493759 −0.0182126
\(736\) 0 0
\(737\) 14.1966 0.522938
\(738\) 0 0
\(739\) −35.9234 −1.32146 −0.660732 0.750622i \(-0.729754\pi\)
−0.660732 + 0.750622i \(0.729754\pi\)
\(740\) 0 0
\(741\) −1.84088 −0.0676264
\(742\) 0 0
\(743\) 22.4649 0.824157 0.412079 0.911148i \(-0.364803\pi\)
0.412079 + 0.911148i \(0.364803\pi\)
\(744\) 0 0
\(745\) 6.30021 0.230822
\(746\) 0 0
\(747\) 6.67898 0.244371
\(748\) 0 0
\(749\) −14.5657 −0.532217
\(750\) 0 0
\(751\) −19.1213 −0.697746 −0.348873 0.937170i \(-0.613436\pi\)
−0.348873 + 0.937170i \(0.613436\pi\)
\(752\) 0 0
\(753\) 4.73670 0.172615
\(754\) 0 0
\(755\) 17.2165 0.626574
\(756\) 0 0
\(757\) −36.6307 −1.33136 −0.665682 0.746235i \(-0.731859\pi\)
−0.665682 + 0.746235i \(0.731859\pi\)
\(758\) 0 0
\(759\) −2.61304 −0.0948473
\(760\) 0 0
\(761\) −9.79570 −0.355094 −0.177547 0.984112i \(-0.556816\pi\)
−0.177547 + 0.984112i \(0.556816\pi\)
\(762\) 0 0
\(763\) −13.6628 −0.494628
\(764\) 0 0
\(765\) −0.945332 −0.0341785
\(766\) 0 0
\(767\) −13.7033 −0.494796
\(768\) 0 0
\(769\) −21.1550 −0.762868 −0.381434 0.924396i \(-0.624570\pi\)
−0.381434 + 0.924396i \(0.624570\pi\)
\(770\) 0 0
\(771\) 12.5664 0.452567
\(772\) 0 0
\(773\) −3.22490 −0.115992 −0.0579958 0.998317i \(-0.518471\pi\)
−0.0579958 + 0.998317i \(0.518471\pi\)
\(774\) 0 0
\(775\) −34.7721 −1.24905
\(776\) 0 0
\(777\) 1.22769 0.0440432
\(778\) 0 0
\(779\) −28.7564 −1.03030
\(780\) 0 0
\(781\) 9.57695 0.342690
\(782\) 0 0
\(783\) 29.5547 1.05620
\(784\) 0 0
\(785\) −15.7170 −0.560963
\(786\) 0 0
\(787\) 1.35097 0.0481568 0.0240784 0.999710i \(-0.492335\pi\)
0.0240784 + 0.999710i \(0.492335\pi\)
\(788\) 0 0
\(789\) 10.1734 0.362181
\(790\) 0 0
\(791\) 9.72536 0.345794
\(792\) 0 0
\(793\) 6.52555 0.231729
\(794\) 0 0
\(795\) −0.830192 −0.0294439
\(796\) 0 0
\(797\) −56.0012 −1.98366 −0.991832 0.127552i \(-0.959288\pi\)
−0.991832 + 0.127552i \(0.959288\pi\)
\(798\) 0 0
\(799\) 3.74851 0.132613
\(800\) 0 0
\(801\) 28.6265 1.01147
\(802\) 0 0
\(803\) 3.18018 0.112226
\(804\) 0 0
\(805\) −4.61636 −0.162705
\(806\) 0 0
\(807\) −0.278023 −0.00978688
\(808\) 0 0
\(809\) −15.3551 −0.539858 −0.269929 0.962880i \(-0.587000\pi\)
−0.269929 + 0.962880i \(0.587000\pi\)
\(810\) 0 0
\(811\) 4.51841 0.158663 0.0793313 0.996848i \(-0.474721\pi\)
0.0793313 + 0.996848i \(0.474721\pi\)
\(812\) 0 0
\(813\) 11.4669 0.402160
\(814\) 0 0
\(815\) 19.2286 0.673547
\(816\) 0 0
\(817\) −4.50233 −0.157517
\(818\) 0 0
\(819\) 2.72051 0.0950624
\(820\) 0 0
\(821\) −11.6419 −0.406306 −0.203153 0.979147i \(-0.565119\pi\)
−0.203153 + 0.979147i \(0.565119\pi\)
\(822\) 0 0
\(823\) 15.9212 0.554979 0.277489 0.960729i \(-0.410498\pi\)
0.277489 + 0.960729i \(0.410498\pi\)
\(824\) 0 0
\(825\) −2.18217 −0.0759733
\(826\) 0 0
\(827\) 8.89577 0.309336 0.154668 0.987966i \(-0.450569\pi\)
0.154668 + 0.987966i \(0.450569\pi\)
\(828\) 0 0
\(829\) −44.7425 −1.55397 −0.776986 0.629517i \(-0.783253\pi\)
−0.776986 + 0.629517i \(0.783253\pi\)
\(830\) 0 0
\(831\) 3.53881 0.122760
\(832\) 0 0
\(833\) 0.372048 0.0128907
\(834\) 0 0
\(835\) −20.4939 −0.709220
\(836\) 0 0
\(837\) 25.4764 0.880594
\(838\) 0 0
\(839\) 19.1279 0.660369 0.330185 0.943916i \(-0.392889\pi\)
0.330185 + 0.943916i \(0.392889\pi\)
\(840\) 0 0
\(841\) 66.5039 2.29324
\(842\) 0 0
\(843\) −0.824205 −0.0283871
\(844\) 0 0
\(845\) 0.933973 0.0321296
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −7.56951 −0.259785
\(850\) 0 0
\(851\) 11.4782 0.393468
\(852\) 0 0
\(853\) 1.64029 0.0561624 0.0280812 0.999606i \(-0.491060\pi\)
0.0280812 + 0.999606i \(0.491060\pi\)
\(854\) 0 0
\(855\) 8.84768 0.302584
\(856\) 0 0
\(857\) −15.1131 −0.516255 −0.258127 0.966111i \(-0.583105\pi\)
−0.258127 + 0.966111i \(0.583105\pi\)
\(858\) 0 0
\(859\) −9.23148 −0.314974 −0.157487 0.987521i \(-0.550339\pi\)
−0.157487 + 0.987521i \(0.550339\pi\)
\(860\) 0 0
\(861\) −4.36586 −0.148788
\(862\) 0 0
\(863\) 30.5560 1.04014 0.520068 0.854125i \(-0.325906\pi\)
0.520068 + 0.854125i \(0.325906\pi\)
\(864\) 0 0
\(865\) −20.3603 −0.692270
\(866\) 0 0
\(867\) 8.91413 0.302740
\(868\) 0 0
\(869\) 17.5913 0.596745
\(870\) 0 0
\(871\) 14.1966 0.481033
\(872\) 0 0
\(873\) 18.4923 0.625869
\(874\) 0 0
\(875\) −8.52502 −0.288198
\(876\) 0 0
\(877\) −50.5110 −1.70564 −0.852818 0.522208i \(-0.825109\pi\)
−0.852818 + 0.522208i \(0.825109\pi\)
\(878\) 0 0
\(879\) −4.49927 −0.151757
\(880\) 0 0
\(881\) −16.7308 −0.563674 −0.281837 0.959462i \(-0.590944\pi\)
−0.281837 + 0.959462i \(0.590944\pi\)
\(882\) 0 0
\(883\) −5.82152 −0.195910 −0.0979549 0.995191i \(-0.531230\pi\)
−0.0979549 + 0.995191i \(0.531230\pi\)
\(884\) 0 0
\(885\) −6.76611 −0.227440
\(886\) 0 0
\(887\) −12.2498 −0.411308 −0.205654 0.978625i \(-0.565932\pi\)
−0.205654 + 0.978625i \(0.565932\pi\)
\(888\) 0 0
\(889\) −5.48189 −0.183857
\(890\) 0 0
\(891\) −6.56273 −0.219860
\(892\) 0 0
\(893\) −35.0836 −1.17403
\(894\) 0 0
\(895\) −19.7602 −0.660509
\(896\) 0 0
\(897\) −2.61304 −0.0872469
\(898\) 0 0
\(899\) 82.3253 2.74570
\(900\) 0 0
\(901\) 0.625552 0.0208401
\(902\) 0 0
\(903\) −0.683555 −0.0227473
\(904\) 0 0
\(905\) 7.75033 0.257630
\(906\) 0 0
\(907\) −33.3906 −1.10872 −0.554359 0.832278i \(-0.687036\pi\)
−0.554359 + 0.832278i \(0.687036\pi\)
\(908\) 0 0
\(909\) −17.9167 −0.594261
\(910\) 0 0
\(911\) −32.2936 −1.06993 −0.534967 0.844873i \(-0.679676\pi\)
−0.534967 + 0.844873i \(0.679676\pi\)
\(912\) 0 0
\(913\) 2.45504 0.0812501
\(914\) 0 0
\(915\) 3.22205 0.106518
\(916\) 0 0
\(917\) 0.957619 0.0316234
\(918\) 0 0
\(919\) −56.0214 −1.84798 −0.923988 0.382422i \(-0.875090\pi\)
−0.923988 + 0.382422i \(0.875090\pi\)
\(920\) 0 0
\(921\) 7.47119 0.246184
\(922\) 0 0
\(923\) 9.57695 0.315229
\(924\) 0 0
\(925\) 9.58554 0.315171
\(926\) 0 0
\(927\) 39.4256 1.29491
\(928\) 0 0
\(929\) −10.4649 −0.343342 −0.171671 0.985154i \(-0.554917\pi\)
−0.171671 + 0.985154i \(0.554917\pi\)
\(930\) 0 0
\(931\) −3.48213 −0.114122
\(932\) 0 0
\(933\) 4.97795 0.162971
\(934\) 0 0
\(935\) −0.347483 −0.0113639
\(936\) 0 0
\(937\) 23.9879 0.783649 0.391824 0.920040i \(-0.371844\pi\)
0.391824 + 0.920040i \(0.371844\pi\)
\(938\) 0 0
\(939\) −11.0632 −0.361033
\(940\) 0 0
\(941\) −9.65798 −0.314841 −0.157421 0.987532i \(-0.550318\pi\)
−0.157421 + 0.987532i \(0.550318\pi\)
\(942\) 0 0
\(943\) −40.8183 −1.32923
\(944\) 0 0
\(945\) 2.82455 0.0918827
\(946\) 0 0
\(947\) 25.0206 0.813060 0.406530 0.913637i \(-0.366739\pi\)
0.406530 + 0.913637i \(0.366739\pi\)
\(948\) 0 0
\(949\) 3.18018 0.103233
\(950\) 0 0
\(951\) −14.8521 −0.481612
\(952\) 0 0
\(953\) 8.74580 0.283304 0.141652 0.989917i \(-0.454759\pi\)
0.141652 + 0.989917i \(0.454759\pi\)
\(954\) 0 0
\(955\) −20.6269 −0.667469
\(956\) 0 0
\(957\) 5.16644 0.167007
\(958\) 0 0
\(959\) 0.243329 0.00785752
\(960\) 0 0
\(961\) 39.9652 1.28920
\(962\) 0 0
\(963\) 39.6261 1.27693
\(964\) 0 0
\(965\) 0.887451 0.0285681
\(966\) 0 0
\(967\) 48.2746 1.55241 0.776203 0.630482i \(-0.217143\pi\)
0.776203 + 0.630482i \(0.217143\pi\)
\(968\) 0 0
\(969\) 0.684895 0.0220020
\(970\) 0 0
\(971\) −58.9239 −1.89096 −0.945479 0.325682i \(-0.894406\pi\)
−0.945479 + 0.325682i \(0.894406\pi\)
\(972\) 0 0
\(973\) 4.71861 0.151272
\(974\) 0 0
\(975\) −2.18217 −0.0698853
\(976\) 0 0
\(977\) 26.7961 0.857284 0.428642 0.903475i \(-0.358992\pi\)
0.428642 + 0.903475i \(0.358992\pi\)
\(978\) 0 0
\(979\) 10.5225 0.336300
\(980\) 0 0
\(981\) 37.1699 1.18674
\(982\) 0 0
\(983\) 25.6014 0.816557 0.408279 0.912857i \(-0.366129\pi\)
0.408279 + 0.912857i \(0.366129\pi\)
\(984\) 0 0
\(985\) −7.63444 −0.243253
\(986\) 0 0
\(987\) −5.32648 −0.169544
\(988\) 0 0
\(989\) −6.39084 −0.203217
\(990\) 0 0
\(991\) 37.0898 1.17820 0.589098 0.808061i \(-0.299483\pi\)
0.589098 + 0.808061i \(0.299483\pi\)
\(992\) 0 0
\(993\) −5.12623 −0.162676
\(994\) 0 0
\(995\) 21.6249 0.685556
\(996\) 0 0
\(997\) −1.24256 −0.0393524 −0.0196762 0.999806i \(-0.506264\pi\)
−0.0196762 + 0.999806i \(0.506264\pi\)
\(998\) 0 0
\(999\) −7.02303 −0.222199
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 \(a_p\))