Properties

Label 8008.2.a.u.1.8
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.76763\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.76763 q^{3} +0.187208 q^{5} -1.00000 q^{7} +0.124526 q^{9} +O(q^{10})\) \(q+1.76763 q^{3} +0.187208 q^{5} -1.00000 q^{7} +0.124526 q^{9} -1.00000 q^{11} -1.00000 q^{13} +0.330915 q^{15} +4.32648 q^{17} -5.79897 q^{19} -1.76763 q^{21} +5.19778 q^{23} -4.96495 q^{25} -5.08278 q^{27} +1.25596 q^{29} +6.52310 q^{31} -1.76763 q^{33} -0.187208 q^{35} -5.96866 q^{37} -1.76763 q^{39} +5.23412 q^{41} -3.99762 q^{43} +0.0233124 q^{45} -5.21957 q^{47} +1.00000 q^{49} +7.64763 q^{51} -1.33361 q^{53} -0.187208 q^{55} -10.2504 q^{57} +7.28024 q^{59} -3.40345 q^{61} -0.124526 q^{63} -0.187208 q^{65} -2.43127 q^{67} +9.18776 q^{69} -2.65660 q^{71} -12.4341 q^{73} -8.77621 q^{75} +1.00000 q^{77} +3.58710 q^{79} -9.35807 q^{81} -9.04444 q^{83} +0.809952 q^{85} +2.22008 q^{87} -12.7021 q^{89} +1.00000 q^{91} +11.5304 q^{93} -1.08561 q^{95} -4.31505 q^{97} -0.124526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 1.76763 1.02054 0.510272 0.860013i \(-0.329545\pi\)
0.510272 + 0.860013i \(0.329545\pi\)
\(4\) 0 0
\(5\) 0.187208 0.0837220 0.0418610 0.999123i \(-0.486671\pi\)
0.0418610 + 0.999123i \(0.486671\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0.124526 0.0415088
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.330915 0.0854420
\(16\) 0 0
\(17\) 4.32648 1.04933 0.524663 0.851310i \(-0.324191\pi\)
0.524663 + 0.851310i \(0.324191\pi\)
\(18\) 0 0
\(19\) −5.79897 −1.33037 −0.665187 0.746677i \(-0.731648\pi\)
−0.665187 + 0.746677i \(0.731648\pi\)
\(20\) 0 0
\(21\) −1.76763 −0.385729
\(22\) 0 0
\(23\) 5.19778 1.08381 0.541906 0.840439i \(-0.317703\pi\)
0.541906 + 0.840439i \(0.317703\pi\)
\(24\) 0 0
\(25\) −4.96495 −0.992991
\(26\) 0 0
\(27\) −5.08278 −0.978182
\(28\) 0 0
\(29\) 1.25596 0.233226 0.116613 0.993177i \(-0.462796\pi\)
0.116613 + 0.993177i \(0.462796\pi\)
\(30\) 0 0
\(31\) 6.52310 1.17158 0.585792 0.810462i \(-0.300784\pi\)
0.585792 + 0.810462i \(0.300784\pi\)
\(32\) 0 0
\(33\) −1.76763 −0.307705
\(34\) 0 0
\(35\) −0.187208 −0.0316440
\(36\) 0 0
\(37\) −5.96866 −0.981241 −0.490621 0.871373i \(-0.663230\pi\)
−0.490621 + 0.871373i \(0.663230\pi\)
\(38\) 0 0
\(39\) −1.76763 −0.283048
\(40\) 0 0
\(41\) 5.23412 0.817432 0.408716 0.912662i \(-0.365977\pi\)
0.408716 + 0.912662i \(0.365977\pi\)
\(42\) 0 0
\(43\) −3.99762 −0.609631 −0.304815 0.952411i \(-0.598595\pi\)
−0.304815 + 0.952411i \(0.598595\pi\)
\(44\) 0 0
\(45\) 0.0233124 0.00347520
\(46\) 0 0
\(47\) −5.21957 −0.761352 −0.380676 0.924708i \(-0.624309\pi\)
−0.380676 + 0.924708i \(0.624309\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 7.64763 1.07088
\(52\) 0 0
\(53\) −1.33361 −0.183186 −0.0915930 0.995797i \(-0.529196\pi\)
−0.0915930 + 0.995797i \(0.529196\pi\)
\(54\) 0 0
\(55\) −0.187208 −0.0252431
\(56\) 0 0
\(57\) −10.2504 −1.35770
\(58\) 0 0
\(59\) 7.28024 0.947806 0.473903 0.880577i \(-0.342845\pi\)
0.473903 + 0.880577i \(0.342845\pi\)
\(60\) 0 0
\(61\) −3.40345 −0.435767 −0.217884 0.975975i \(-0.569915\pi\)
−0.217884 + 0.975975i \(0.569915\pi\)
\(62\) 0 0
\(63\) −0.124526 −0.0156889
\(64\) 0 0
\(65\) −0.187208 −0.0232203
\(66\) 0 0
\(67\) −2.43127 −0.297027 −0.148514 0.988910i \(-0.547449\pi\)
−0.148514 + 0.988910i \(0.547449\pi\)
\(68\) 0 0
\(69\) 9.18776 1.10608
\(70\) 0 0
\(71\) −2.65660 −0.315281 −0.157640 0.987497i \(-0.550389\pi\)
−0.157640 + 0.987497i \(0.550389\pi\)
\(72\) 0 0
\(73\) −12.4341 −1.45530 −0.727649 0.685950i \(-0.759387\pi\)
−0.727649 + 0.685950i \(0.759387\pi\)
\(74\) 0 0
\(75\) −8.77621 −1.01339
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 3.58710 0.403580 0.201790 0.979429i \(-0.435324\pi\)
0.201790 + 0.979429i \(0.435324\pi\)
\(80\) 0 0
\(81\) −9.35807 −1.03979
\(82\) 0 0
\(83\) −9.04444 −0.992756 −0.496378 0.868107i \(-0.665337\pi\)
−0.496378 + 0.868107i \(0.665337\pi\)
\(84\) 0 0
\(85\) 0.809952 0.0878516
\(86\) 0 0
\(87\) 2.22008 0.238018
\(88\) 0 0
\(89\) −12.7021 −1.34642 −0.673210 0.739451i \(-0.735085\pi\)
−0.673210 + 0.739451i \(0.735085\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 11.5304 1.19565
\(94\) 0 0
\(95\) −1.08561 −0.111382
\(96\) 0 0
\(97\) −4.31505 −0.438127 −0.219064 0.975711i \(-0.570300\pi\)
−0.219064 + 0.975711i \(0.570300\pi\)
\(98\) 0 0
\(99\) −0.124526 −0.0125154
\(100\) 0 0
\(101\) 2.48362 0.247129 0.123564 0.992337i \(-0.460567\pi\)
0.123564 + 0.992337i \(0.460567\pi\)
\(102\) 0 0
\(103\) −14.0267 −1.38209 −0.691047 0.722810i \(-0.742850\pi\)
−0.691047 + 0.722810i \(0.742850\pi\)
\(104\) 0 0
\(105\) −0.330915 −0.0322940
\(106\) 0 0
\(107\) 12.9847 1.25528 0.627638 0.778505i \(-0.284022\pi\)
0.627638 + 0.778505i \(0.284022\pi\)
\(108\) 0 0
\(109\) 3.60242 0.345049 0.172524 0.985005i \(-0.444808\pi\)
0.172524 + 0.985005i \(0.444808\pi\)
\(110\) 0 0
\(111\) −10.5504 −1.00140
\(112\) 0 0
\(113\) −16.7312 −1.57394 −0.786970 0.616991i \(-0.788351\pi\)
−0.786970 + 0.616991i \(0.788351\pi\)
\(114\) 0 0
\(115\) 0.973066 0.0907389
\(116\) 0 0
\(117\) −0.124526 −0.0115125
\(118\) 0 0
\(119\) −4.32648 −0.396608
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 9.25200 0.834224
\(124\) 0 0
\(125\) −1.86552 −0.166857
\(126\) 0 0
\(127\) −13.1367 −1.16570 −0.582848 0.812582i \(-0.698062\pi\)
−0.582848 + 0.812582i \(0.698062\pi\)
\(128\) 0 0
\(129\) −7.06632 −0.622155
\(130\) 0 0
\(131\) 6.10959 0.533798 0.266899 0.963725i \(-0.414001\pi\)
0.266899 + 0.963725i \(0.414001\pi\)
\(132\) 0 0
\(133\) 5.79897 0.502834
\(134\) 0 0
\(135\) −0.951538 −0.0818954
\(136\) 0 0
\(137\) 13.6249 1.16405 0.582025 0.813171i \(-0.302260\pi\)
0.582025 + 0.813171i \(0.302260\pi\)
\(138\) 0 0
\(139\) 1.19652 0.101488 0.0507439 0.998712i \(-0.483841\pi\)
0.0507439 + 0.998712i \(0.483841\pi\)
\(140\) 0 0
\(141\) −9.22628 −0.776993
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 0.235126 0.0195262
\(146\) 0 0
\(147\) 1.76763 0.145792
\(148\) 0 0
\(149\) −8.15546 −0.668121 −0.334061 0.942552i \(-0.608419\pi\)
−0.334061 + 0.942552i \(0.608419\pi\)
\(150\) 0 0
\(151\) −12.2259 −0.994934 −0.497467 0.867483i \(-0.665736\pi\)
−0.497467 + 0.867483i \(0.665736\pi\)
\(152\) 0 0
\(153\) 0.538761 0.0435562
\(154\) 0 0
\(155\) 1.22118 0.0980873
\(156\) 0 0
\(157\) −20.2040 −1.61246 −0.806228 0.591605i \(-0.798494\pi\)
−0.806228 + 0.591605i \(0.798494\pi\)
\(158\) 0 0
\(159\) −2.35734 −0.186949
\(160\) 0 0
\(161\) −5.19778 −0.409642
\(162\) 0 0
\(163\) −16.7786 −1.31420 −0.657099 0.753804i \(-0.728217\pi\)
−0.657099 + 0.753804i \(0.728217\pi\)
\(164\) 0 0
\(165\) −0.330915 −0.0257617
\(166\) 0 0
\(167\) 1.21006 0.0936376 0.0468188 0.998903i \(-0.485092\pi\)
0.0468188 + 0.998903i \(0.485092\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −0.722124 −0.0552222
\(172\) 0 0
\(173\) 13.2712 1.00899 0.504494 0.863415i \(-0.331679\pi\)
0.504494 + 0.863415i \(0.331679\pi\)
\(174\) 0 0
\(175\) 4.96495 0.375315
\(176\) 0 0
\(177\) 12.8688 0.967277
\(178\) 0 0
\(179\) 18.5205 1.38429 0.692144 0.721759i \(-0.256666\pi\)
0.692144 + 0.721759i \(0.256666\pi\)
\(180\) 0 0
\(181\) 14.9939 1.11449 0.557244 0.830348i \(-0.311859\pi\)
0.557244 + 0.830348i \(0.311859\pi\)
\(182\) 0 0
\(183\) −6.01605 −0.444719
\(184\) 0 0
\(185\) −1.11738 −0.0821515
\(186\) 0 0
\(187\) −4.32648 −0.316383
\(188\) 0 0
\(189\) 5.08278 0.369718
\(190\) 0 0
\(191\) −8.49034 −0.614339 −0.307170 0.951655i \(-0.599382\pi\)
−0.307170 + 0.951655i \(0.599382\pi\)
\(192\) 0 0
\(193\) −10.9141 −0.785611 −0.392805 0.919622i \(-0.628495\pi\)
−0.392805 + 0.919622i \(0.628495\pi\)
\(194\) 0 0
\(195\) −0.330915 −0.0236973
\(196\) 0 0
\(197\) −19.8771 −1.41619 −0.708094 0.706119i \(-0.750445\pi\)
−0.708094 + 0.706119i \(0.750445\pi\)
\(198\) 0 0
\(199\) −26.7949 −1.89944 −0.949720 0.313100i \(-0.898633\pi\)
−0.949720 + 0.313100i \(0.898633\pi\)
\(200\) 0 0
\(201\) −4.29760 −0.303129
\(202\) 0 0
\(203\) −1.25596 −0.0881513
\(204\) 0 0
\(205\) 0.979869 0.0684370
\(206\) 0 0
\(207\) 0.647260 0.0449877
\(208\) 0 0
\(209\) 5.79897 0.401123
\(210\) 0 0
\(211\) 11.3739 0.783015 0.391507 0.920175i \(-0.371954\pi\)
0.391507 + 0.920175i \(0.371954\pi\)
\(212\) 0 0
\(213\) −4.69590 −0.321758
\(214\) 0 0
\(215\) −0.748387 −0.0510395
\(216\) 0 0
\(217\) −6.52310 −0.442817
\(218\) 0 0
\(219\) −21.9789 −1.48519
\(220\) 0 0
\(221\) −4.32648 −0.291030
\(222\) 0 0
\(223\) −23.3245 −1.56193 −0.780963 0.624578i \(-0.785271\pi\)
−0.780963 + 0.624578i \(0.785271\pi\)
\(224\) 0 0
\(225\) −0.618268 −0.0412178
\(226\) 0 0
\(227\) 8.19009 0.543596 0.271798 0.962354i \(-0.412382\pi\)
0.271798 + 0.962354i \(0.412382\pi\)
\(228\) 0 0
\(229\) −16.2055 −1.07089 −0.535446 0.844569i \(-0.679857\pi\)
−0.535446 + 0.844569i \(0.679857\pi\)
\(230\) 0 0
\(231\) 1.76763 0.116302
\(232\) 0 0
\(233\) −18.0871 −1.18492 −0.592462 0.805598i \(-0.701844\pi\)
−0.592462 + 0.805598i \(0.701844\pi\)
\(234\) 0 0
\(235\) −0.977146 −0.0637419
\(236\) 0 0
\(237\) 6.34068 0.411871
\(238\) 0 0
\(239\) 11.8444 0.766152 0.383076 0.923717i \(-0.374865\pi\)
0.383076 + 0.923717i \(0.374865\pi\)
\(240\) 0 0
\(241\) 20.7427 1.33615 0.668077 0.744092i \(-0.267118\pi\)
0.668077 + 0.744092i \(0.267118\pi\)
\(242\) 0 0
\(243\) −1.29329 −0.0829647
\(244\) 0 0
\(245\) 0.187208 0.0119603
\(246\) 0 0
\(247\) 5.79897 0.368979
\(248\) 0 0
\(249\) −15.9872 −1.01315
\(250\) 0 0
\(251\) 9.39562 0.593046 0.296523 0.955026i \(-0.404173\pi\)
0.296523 + 0.955026i \(0.404173\pi\)
\(252\) 0 0
\(253\) −5.19778 −0.326781
\(254\) 0 0
\(255\) 1.43170 0.0896564
\(256\) 0 0
\(257\) −7.86272 −0.490463 −0.245232 0.969465i \(-0.578864\pi\)
−0.245232 + 0.969465i \(0.578864\pi\)
\(258\) 0 0
\(259\) 5.96866 0.370874
\(260\) 0 0
\(261\) 0.156400 0.00968094
\(262\) 0 0
\(263\) −0.230621 −0.0142207 −0.00711036 0.999975i \(-0.502263\pi\)
−0.00711036 + 0.999975i \(0.502263\pi\)
\(264\) 0 0
\(265\) −0.249663 −0.0153367
\(266\) 0 0
\(267\) −22.4526 −1.37408
\(268\) 0 0
\(269\) 17.4203 1.06214 0.531069 0.847329i \(-0.321791\pi\)
0.531069 + 0.847329i \(0.321791\pi\)
\(270\) 0 0
\(271\) −16.7770 −1.01913 −0.509564 0.860433i \(-0.670193\pi\)
−0.509564 + 0.860433i \(0.670193\pi\)
\(272\) 0 0
\(273\) 1.76763 0.106982
\(274\) 0 0
\(275\) 4.96495 0.299398
\(276\) 0 0
\(277\) 3.16058 0.189901 0.0949504 0.995482i \(-0.469731\pi\)
0.0949504 + 0.995482i \(0.469731\pi\)
\(278\) 0 0
\(279\) 0.812298 0.0486310
\(280\) 0 0
\(281\) 11.2627 0.671877 0.335938 0.941884i \(-0.390947\pi\)
0.335938 + 0.941884i \(0.390947\pi\)
\(282\) 0 0
\(283\) 16.4640 0.978682 0.489341 0.872092i \(-0.337237\pi\)
0.489341 + 0.872092i \(0.337237\pi\)
\(284\) 0 0
\(285\) −1.91897 −0.113670
\(286\) 0 0
\(287\) −5.23412 −0.308960
\(288\) 0 0
\(289\) 1.71842 0.101083
\(290\) 0 0
\(291\) −7.62743 −0.447128
\(292\) 0 0
\(293\) −10.3742 −0.606068 −0.303034 0.952980i \(-0.598000\pi\)
−0.303034 + 0.952980i \(0.598000\pi\)
\(294\) 0 0
\(295\) 1.36292 0.0793523
\(296\) 0 0
\(297\) 5.08278 0.294933
\(298\) 0 0
\(299\) −5.19778 −0.300595
\(300\) 0 0
\(301\) 3.99762 0.230419
\(302\) 0 0
\(303\) 4.39012 0.252206
\(304\) 0 0
\(305\) −0.637154 −0.0364833
\(306\) 0 0
\(307\) 8.28375 0.472778 0.236389 0.971658i \(-0.424036\pi\)
0.236389 + 0.971658i \(0.424036\pi\)
\(308\) 0 0
\(309\) −24.7941 −1.41049
\(310\) 0 0
\(311\) −5.90180 −0.334660 −0.167330 0.985901i \(-0.553515\pi\)
−0.167330 + 0.985901i \(0.553515\pi\)
\(312\) 0 0
\(313\) −9.92094 −0.560765 −0.280382 0.959888i \(-0.590461\pi\)
−0.280382 + 0.959888i \(0.590461\pi\)
\(314\) 0 0
\(315\) −0.0233124 −0.00131350
\(316\) 0 0
\(317\) −6.69036 −0.375768 −0.187884 0.982191i \(-0.560163\pi\)
−0.187884 + 0.982191i \(0.560163\pi\)
\(318\) 0 0
\(319\) −1.25596 −0.0703204
\(320\) 0 0
\(321\) 22.9521 1.28106
\(322\) 0 0
\(323\) −25.0891 −1.39599
\(324\) 0 0
\(325\) 4.96495 0.275406
\(326\) 0 0
\(327\) 6.36775 0.352137
\(328\) 0 0
\(329\) 5.21957 0.287764
\(330\) 0 0
\(331\) 18.8852 1.03803 0.519013 0.854766i \(-0.326299\pi\)
0.519013 + 0.854766i \(0.326299\pi\)
\(332\) 0 0
\(333\) −0.743256 −0.0407302
\(334\) 0 0
\(335\) −0.455154 −0.0248677
\(336\) 0 0
\(337\) −11.3932 −0.620627 −0.310313 0.950634i \(-0.600434\pi\)
−0.310313 + 0.950634i \(0.600434\pi\)
\(338\) 0 0
\(339\) −29.5746 −1.60627
\(340\) 0 0
\(341\) −6.52310 −0.353246
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 1.72002 0.0926030
\(346\) 0 0
\(347\) −15.6924 −0.842411 −0.421205 0.906965i \(-0.638393\pi\)
−0.421205 + 0.906965i \(0.638393\pi\)
\(348\) 0 0
\(349\) −14.1132 −0.755465 −0.377732 0.925915i \(-0.623296\pi\)
−0.377732 + 0.925915i \(0.623296\pi\)
\(350\) 0 0
\(351\) 5.08278 0.271299
\(352\) 0 0
\(353\) 18.8716 1.00443 0.502217 0.864741i \(-0.332518\pi\)
0.502217 + 0.864741i \(0.332518\pi\)
\(354\) 0 0
\(355\) −0.497338 −0.0263959
\(356\) 0 0
\(357\) −7.64763 −0.404755
\(358\) 0 0
\(359\) 4.09500 0.216126 0.108063 0.994144i \(-0.465535\pi\)
0.108063 + 0.994144i \(0.465535\pi\)
\(360\) 0 0
\(361\) 14.6280 0.769895
\(362\) 0 0
\(363\) 1.76763 0.0927767
\(364\) 0 0
\(365\) −2.32776 −0.121840
\(366\) 0 0
\(367\) 10.8091 0.564230 0.282115 0.959381i \(-0.408964\pi\)
0.282115 + 0.959381i \(0.408964\pi\)
\(368\) 0 0
\(369\) 0.651786 0.0339306
\(370\) 0 0
\(371\) 1.33361 0.0692378
\(372\) 0 0
\(373\) 20.5928 1.06625 0.533127 0.846035i \(-0.321017\pi\)
0.533127 + 0.846035i \(0.321017\pi\)
\(374\) 0 0
\(375\) −3.29756 −0.170285
\(376\) 0 0
\(377\) −1.25596 −0.0646853
\(378\) 0 0
\(379\) −31.8324 −1.63512 −0.817560 0.575843i \(-0.804674\pi\)
−0.817560 + 0.575843i \(0.804674\pi\)
\(380\) 0 0
\(381\) −23.2209 −1.18964
\(382\) 0 0
\(383\) 1.47019 0.0751232 0.0375616 0.999294i \(-0.488041\pi\)
0.0375616 + 0.999294i \(0.488041\pi\)
\(384\) 0 0
\(385\) 0.187208 0.00954101
\(386\) 0 0
\(387\) −0.497809 −0.0253050
\(388\) 0 0
\(389\) −1.97538 −0.100156 −0.0500780 0.998745i \(-0.515947\pi\)
−0.0500780 + 0.998745i \(0.515947\pi\)
\(390\) 0 0
\(391\) 22.4881 1.13727
\(392\) 0 0
\(393\) 10.7995 0.544764
\(394\) 0 0
\(395\) 0.671535 0.0337886
\(396\) 0 0
\(397\) 27.8123 1.39586 0.697929 0.716166i \(-0.254105\pi\)
0.697929 + 0.716166i \(0.254105\pi\)
\(398\) 0 0
\(399\) 10.2504 0.513164
\(400\) 0 0
\(401\) 7.71223 0.385130 0.192565 0.981284i \(-0.438319\pi\)
0.192565 + 0.981284i \(0.438319\pi\)
\(402\) 0 0
\(403\) −6.52310 −0.324939
\(404\) 0 0
\(405\) −1.75191 −0.0870530
\(406\) 0 0
\(407\) 5.96866 0.295855
\(408\) 0 0
\(409\) −30.7736 −1.52166 −0.760828 0.648953i \(-0.775207\pi\)
−0.760828 + 0.648953i \(0.775207\pi\)
\(410\) 0 0
\(411\) 24.0838 1.18796
\(412\) 0 0
\(413\) −7.28024 −0.358237
\(414\) 0 0
\(415\) −1.69319 −0.0831155
\(416\) 0 0
\(417\) 2.11501 0.103573
\(418\) 0 0
\(419\) −22.0196 −1.07573 −0.537865 0.843031i \(-0.680769\pi\)
−0.537865 + 0.843031i \(0.680769\pi\)
\(420\) 0 0
\(421\) −8.39136 −0.408970 −0.204485 0.978870i \(-0.565552\pi\)
−0.204485 + 0.978870i \(0.565552\pi\)
\(422\) 0 0
\(423\) −0.649974 −0.0316028
\(424\) 0 0
\(425\) −21.4808 −1.04197
\(426\) 0 0
\(427\) 3.40345 0.164704
\(428\) 0 0
\(429\) 1.76763 0.0853421
\(430\) 0 0
\(431\) 2.60175 0.125322 0.0626610 0.998035i \(-0.480041\pi\)
0.0626610 + 0.998035i \(0.480041\pi\)
\(432\) 0 0
\(433\) 6.06670 0.291547 0.145773 0.989318i \(-0.453433\pi\)
0.145773 + 0.989318i \(0.453433\pi\)
\(434\) 0 0
\(435\) 0.415617 0.0199273
\(436\) 0 0
\(437\) −30.1417 −1.44187
\(438\) 0 0
\(439\) 31.5583 1.50619 0.753097 0.657910i \(-0.228559\pi\)
0.753097 + 0.657910i \(0.228559\pi\)
\(440\) 0 0
\(441\) 0.124526 0.00592983
\(442\) 0 0
\(443\) −7.90800 −0.375720 −0.187860 0.982196i \(-0.560155\pi\)
−0.187860 + 0.982196i \(0.560155\pi\)
\(444\) 0 0
\(445\) −2.37794 −0.112725
\(446\) 0 0
\(447\) −14.4159 −0.681847
\(448\) 0 0
\(449\) 35.2243 1.66234 0.831170 0.556019i \(-0.187672\pi\)
0.831170 + 0.556019i \(0.187672\pi\)
\(450\) 0 0
\(451\) −5.23412 −0.246465
\(452\) 0 0
\(453\) −21.6110 −1.01537
\(454\) 0 0
\(455\) 0.187208 0.00877645
\(456\) 0 0
\(457\) −15.2350 −0.712662 −0.356331 0.934360i \(-0.615972\pi\)
−0.356331 + 0.934360i \(0.615972\pi\)
\(458\) 0 0
\(459\) −21.9905 −1.02643
\(460\) 0 0
\(461\) −10.0347 −0.467362 −0.233681 0.972313i \(-0.575077\pi\)
−0.233681 + 0.972313i \(0.575077\pi\)
\(462\) 0 0
\(463\) 12.1534 0.564819 0.282409 0.959294i \(-0.408866\pi\)
0.282409 + 0.959294i \(0.408866\pi\)
\(464\) 0 0
\(465\) 2.15859 0.100102
\(466\) 0 0
\(467\) 14.4572 0.669001 0.334501 0.942396i \(-0.391432\pi\)
0.334501 + 0.942396i \(0.391432\pi\)
\(468\) 0 0
\(469\) 2.43127 0.112266
\(470\) 0 0
\(471\) −35.7133 −1.64558
\(472\) 0 0
\(473\) 3.99762 0.183811
\(474\) 0 0
\(475\) 28.7916 1.32105
\(476\) 0 0
\(477\) −0.166070 −0.00760383
\(478\) 0 0
\(479\) 11.5569 0.528049 0.264024 0.964516i \(-0.414950\pi\)
0.264024 + 0.964516i \(0.414950\pi\)
\(480\) 0 0
\(481\) 5.96866 0.272147
\(482\) 0 0
\(483\) −9.18776 −0.418058
\(484\) 0 0
\(485\) −0.807813 −0.0366809
\(486\) 0 0
\(487\) 15.0710 0.682932 0.341466 0.939894i \(-0.389077\pi\)
0.341466 + 0.939894i \(0.389077\pi\)
\(488\) 0 0
\(489\) −29.6583 −1.34120
\(490\) 0 0
\(491\) 42.9728 1.93933 0.969667 0.244430i \(-0.0786009\pi\)
0.969667 + 0.244430i \(0.0786009\pi\)
\(492\) 0 0
\(493\) 5.43389 0.244730
\(494\) 0 0
\(495\) −0.0233124 −0.00104781
\(496\) 0 0
\(497\) 2.65660 0.119165
\(498\) 0 0
\(499\) 5.91705 0.264884 0.132442 0.991191i \(-0.457718\pi\)
0.132442 + 0.991191i \(0.457718\pi\)
\(500\) 0 0
\(501\) 2.13895 0.0955612
\(502\) 0 0
\(503\) −43.6034 −1.94418 −0.972090 0.234607i \(-0.924620\pi\)
−0.972090 + 0.234607i \(0.924620\pi\)
\(504\) 0 0
\(505\) 0.464953 0.0206901
\(506\) 0 0
\(507\) 1.76763 0.0785033
\(508\) 0 0
\(509\) −12.5945 −0.558242 −0.279121 0.960256i \(-0.590043\pi\)
−0.279121 + 0.960256i \(0.590043\pi\)
\(510\) 0 0
\(511\) 12.4341 0.550051
\(512\) 0 0
\(513\) 29.4749 1.30135
\(514\) 0 0
\(515\) −2.62592 −0.115712
\(516\) 0 0
\(517\) 5.21957 0.229556
\(518\) 0 0
\(519\) 23.4585 1.02972
\(520\) 0 0
\(521\) 4.89362 0.214393 0.107197 0.994238i \(-0.465813\pi\)
0.107197 + 0.994238i \(0.465813\pi\)
\(522\) 0 0
\(523\) 10.0064 0.437551 0.218775 0.975775i \(-0.429794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(524\) 0 0
\(525\) 8.77621 0.383025
\(526\) 0 0
\(527\) 28.2221 1.22937
\(528\) 0 0
\(529\) 4.01688 0.174647
\(530\) 0 0
\(531\) 0.906582 0.0393423
\(532\) 0 0
\(533\) −5.23412 −0.226715
\(534\) 0 0
\(535\) 2.43084 0.105094
\(536\) 0 0
\(537\) 32.7375 1.41273
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −5.34680 −0.229877 −0.114938 0.993373i \(-0.536667\pi\)
−0.114938 + 0.993373i \(0.536667\pi\)
\(542\) 0 0
\(543\) 26.5037 1.13738
\(544\) 0 0
\(545\) 0.674402 0.0288882
\(546\) 0 0
\(547\) 30.1478 1.28903 0.644513 0.764593i \(-0.277060\pi\)
0.644513 + 0.764593i \(0.277060\pi\)
\(548\) 0 0
\(549\) −0.423819 −0.0180882
\(550\) 0 0
\(551\) −7.28328 −0.310278
\(552\) 0 0
\(553\) −3.58710 −0.152539
\(554\) 0 0
\(555\) −1.97512 −0.0838392
\(556\) 0 0
\(557\) 11.8352 0.501474 0.250737 0.968055i \(-0.419327\pi\)
0.250737 + 0.968055i \(0.419327\pi\)
\(558\) 0 0
\(559\) 3.99762 0.169081
\(560\) 0 0
\(561\) −7.64763 −0.322883
\(562\) 0 0
\(563\) −6.17425 −0.260214 −0.130107 0.991500i \(-0.541532\pi\)
−0.130107 + 0.991500i \(0.541532\pi\)
\(564\) 0 0
\(565\) −3.13222 −0.131773
\(566\) 0 0
\(567\) 9.35807 0.393002
\(568\) 0 0
\(569\) 17.9554 0.752730 0.376365 0.926472i \(-0.377174\pi\)
0.376365 + 0.926472i \(0.377174\pi\)
\(570\) 0 0
\(571\) 25.5500 1.06923 0.534617 0.845094i \(-0.320456\pi\)
0.534617 + 0.845094i \(0.320456\pi\)
\(572\) 0 0
\(573\) −15.0078 −0.626960
\(574\) 0 0
\(575\) −25.8067 −1.07621
\(576\) 0 0
\(577\) −36.6591 −1.52614 −0.763069 0.646317i \(-0.776308\pi\)
−0.763069 + 0.646317i \(0.776308\pi\)
\(578\) 0 0
\(579\) −19.2920 −0.801750
\(580\) 0 0
\(581\) 9.04444 0.375226
\(582\) 0 0
\(583\) 1.33361 0.0552326
\(584\) 0 0
\(585\) −0.0233124 −0.000963847 0
\(586\) 0 0
\(587\) 42.7022 1.76251 0.881254 0.472643i \(-0.156700\pi\)
0.881254 + 0.472643i \(0.156700\pi\)
\(588\) 0 0
\(589\) −37.8272 −1.55864
\(590\) 0 0
\(591\) −35.1355 −1.44528
\(592\) 0 0
\(593\) −4.02047 −0.165101 −0.0825504 0.996587i \(-0.526307\pi\)
−0.0825504 + 0.996587i \(0.526307\pi\)
\(594\) 0 0
\(595\) −0.809952 −0.0332048
\(596\) 0 0
\(597\) −47.3636 −1.93846
\(598\) 0 0
\(599\) −8.16880 −0.333768 −0.166884 0.985977i \(-0.553371\pi\)
−0.166884 + 0.985977i \(0.553371\pi\)
\(600\) 0 0
\(601\) −13.7887 −0.562452 −0.281226 0.959642i \(-0.590741\pi\)
−0.281226 + 0.959642i \(0.590741\pi\)
\(602\) 0 0
\(603\) −0.302757 −0.0123292
\(604\) 0 0
\(605\) 0.187208 0.00761109
\(606\) 0 0
\(607\) 38.7177 1.57150 0.785752 0.618541i \(-0.212276\pi\)
0.785752 + 0.618541i \(0.212276\pi\)
\(608\) 0 0
\(609\) −2.22008 −0.0899622
\(610\) 0 0
\(611\) 5.21957 0.211161
\(612\) 0 0
\(613\) 29.7798 1.20280 0.601398 0.798949i \(-0.294610\pi\)
0.601398 + 0.798949i \(0.294610\pi\)
\(614\) 0 0
\(615\) 1.73205 0.0698430
\(616\) 0 0
\(617\) −32.1833 −1.29565 −0.647826 0.761788i \(-0.724322\pi\)
−0.647826 + 0.761788i \(0.724322\pi\)
\(618\) 0 0
\(619\) 33.9357 1.36399 0.681996 0.731356i \(-0.261112\pi\)
0.681996 + 0.731356i \(0.261112\pi\)
\(620\) 0 0
\(621\) −26.4192 −1.06016
\(622\) 0 0
\(623\) 12.7021 0.508899
\(624\) 0 0
\(625\) 24.4755 0.979021
\(626\) 0 0
\(627\) 10.2504 0.409363
\(628\) 0 0
\(629\) −25.8233 −1.02964
\(630\) 0 0
\(631\) −37.7604 −1.50322 −0.751610 0.659608i \(-0.770722\pi\)
−0.751610 + 0.659608i \(0.770722\pi\)
\(632\) 0 0
\(633\) 20.1050 0.799101
\(634\) 0 0
\(635\) −2.45930 −0.0975944
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −0.330817 −0.0130869
\(640\) 0 0
\(641\) 17.9804 0.710184 0.355092 0.934831i \(-0.384450\pi\)
0.355092 + 0.934831i \(0.384450\pi\)
\(642\) 0 0
\(643\) −26.5417 −1.04670 −0.523351 0.852117i \(-0.675318\pi\)
−0.523351 + 0.852117i \(0.675318\pi\)
\(644\) 0 0
\(645\) −1.32287 −0.0520881
\(646\) 0 0
\(647\) −43.3705 −1.70507 −0.852534 0.522671i \(-0.824936\pi\)
−0.852534 + 0.522671i \(0.824936\pi\)
\(648\) 0 0
\(649\) −7.28024 −0.285774
\(650\) 0 0
\(651\) −11.5304 −0.451914
\(652\) 0 0
\(653\) −14.5353 −0.568812 −0.284406 0.958704i \(-0.591796\pi\)
−0.284406 + 0.958704i \(0.591796\pi\)
\(654\) 0 0
\(655\) 1.14377 0.0446906
\(656\) 0 0
\(657\) −1.54837 −0.0604076
\(658\) 0 0
\(659\) 44.7224 1.74214 0.871069 0.491161i \(-0.163427\pi\)
0.871069 + 0.491161i \(0.163427\pi\)
\(660\) 0 0
\(661\) −18.4491 −0.717589 −0.358794 0.933417i \(-0.616812\pi\)
−0.358794 + 0.933417i \(0.616812\pi\)
\(662\) 0 0
\(663\) −7.64763 −0.297009
\(664\) 0 0
\(665\) 1.08561 0.0420983
\(666\) 0 0
\(667\) 6.52821 0.252773
\(668\) 0 0
\(669\) −41.2292 −1.59401
\(670\) 0 0
\(671\) 3.40345 0.131389
\(672\) 0 0
\(673\) 43.8438 1.69005 0.845026 0.534725i \(-0.179585\pi\)
0.845026 + 0.534725i \(0.179585\pi\)
\(674\) 0 0
\(675\) 25.2358 0.971325
\(676\) 0 0
\(677\) −22.1603 −0.851690 −0.425845 0.904796i \(-0.640023\pi\)
−0.425845 + 0.904796i \(0.640023\pi\)
\(678\) 0 0
\(679\) 4.31505 0.165596
\(680\) 0 0
\(681\) 14.4771 0.554763
\(682\) 0 0
\(683\) 32.2063 1.23234 0.616170 0.787613i \(-0.288683\pi\)
0.616170 + 0.787613i \(0.288683\pi\)
\(684\) 0 0
\(685\) 2.55069 0.0974567
\(686\) 0 0
\(687\) −28.6455 −1.09289
\(688\) 0 0
\(689\) 1.33361 0.0508066
\(690\) 0 0
\(691\) −1.70081 −0.0647020 −0.0323510 0.999477i \(-0.510299\pi\)
−0.0323510 + 0.999477i \(0.510299\pi\)
\(692\) 0 0
\(693\) 0.124526 0.00473037
\(694\) 0 0
\(695\) 0.223999 0.00849676
\(696\) 0 0
\(697\) 22.6453 0.857751
\(698\) 0 0
\(699\) −31.9713 −1.20927
\(700\) 0 0
\(701\) 8.11443 0.306478 0.153239 0.988189i \(-0.451030\pi\)
0.153239 + 0.988189i \(0.451030\pi\)
\(702\) 0 0
\(703\) 34.6120 1.30542
\(704\) 0 0
\(705\) −1.72723 −0.0650514
\(706\) 0 0
\(707\) −2.48362 −0.0934060
\(708\) 0 0
\(709\) −41.6051 −1.56251 −0.781256 0.624211i \(-0.785421\pi\)
−0.781256 + 0.624211i \(0.785421\pi\)
\(710\) 0 0
\(711\) 0.446689 0.0167521
\(712\) 0 0
\(713\) 33.9056 1.26978
\(714\) 0 0
\(715\) 0.187208 0.00700119
\(716\) 0 0
\(717\) 20.9366 0.781891
\(718\) 0 0
\(719\) 18.5432 0.691545 0.345773 0.938318i \(-0.387617\pi\)
0.345773 + 0.938318i \(0.387617\pi\)
\(720\) 0 0
\(721\) 14.0267 0.522383
\(722\) 0 0
\(723\) 36.6655 1.36360
\(724\) 0 0
\(725\) −6.23579 −0.231592
\(726\) 0 0
\(727\) 32.6335 1.21031 0.605155 0.796107i \(-0.293111\pi\)
0.605155 + 0.796107i \(0.293111\pi\)
\(728\) 0 0
\(729\) 25.7882 0.955117
\(730\) 0 0
\(731\) −17.2956 −0.639701
\(732\) 0 0
\(733\) 4.50958 0.166565 0.0832826 0.996526i \(-0.473460\pi\)
0.0832826 + 0.996526i \(0.473460\pi\)
\(734\) 0 0
\(735\) 0.330915 0.0122060
\(736\) 0 0
\(737\) 2.43127 0.0895570
\(738\) 0 0
\(739\) 18.1237 0.666690 0.333345 0.942805i \(-0.391823\pi\)
0.333345 + 0.942805i \(0.391823\pi\)
\(740\) 0 0
\(741\) 10.2504 0.376559
\(742\) 0 0
\(743\) −44.2109 −1.62194 −0.810971 0.585087i \(-0.801061\pi\)
−0.810971 + 0.585087i \(0.801061\pi\)
\(744\) 0 0
\(745\) −1.52677 −0.0559365
\(746\) 0 0
\(747\) −1.12627 −0.0412081
\(748\) 0 0
\(749\) −12.9847 −0.474450
\(750\) 0 0
\(751\) −21.1389 −0.771369 −0.385684 0.922631i \(-0.626035\pi\)
−0.385684 + 0.922631i \(0.626035\pi\)
\(752\) 0 0
\(753\) 16.6080 0.605229
\(754\) 0 0
\(755\) −2.28880 −0.0832979
\(756\) 0 0
\(757\) 25.2934 0.919305 0.459653 0.888099i \(-0.347974\pi\)
0.459653 + 0.888099i \(0.347974\pi\)
\(758\) 0 0
\(759\) −9.18776 −0.333495
\(760\) 0 0
\(761\) −18.7837 −0.680910 −0.340455 0.940261i \(-0.610581\pi\)
−0.340455 + 0.940261i \(0.610581\pi\)
\(762\) 0 0
\(763\) −3.60242 −0.130416
\(764\) 0 0
\(765\) 0.100860 0.00364662
\(766\) 0 0
\(767\) −7.28024 −0.262874
\(768\) 0 0
\(769\) −44.0937 −1.59006 −0.795030 0.606570i \(-0.792545\pi\)
−0.795030 + 0.606570i \(0.792545\pi\)
\(770\) 0 0
\(771\) −13.8984 −0.500539
\(772\) 0 0
\(773\) −28.7377 −1.03362 −0.516811 0.856100i \(-0.672881\pi\)
−0.516811 + 0.856100i \(0.672881\pi\)
\(774\) 0 0
\(775\) −32.3869 −1.16337
\(776\) 0 0
\(777\) 10.5504 0.378493
\(778\) 0 0
\(779\) −30.3525 −1.08749
\(780\) 0 0
\(781\) 2.65660 0.0950607
\(782\) 0 0
\(783\) −6.38378 −0.228138
\(784\) 0 0
\(785\) −3.78236 −0.134998
\(786\) 0 0
\(787\) 20.0356 0.714193 0.357097 0.934067i \(-0.383767\pi\)
0.357097 + 0.934067i \(0.383767\pi\)
\(788\) 0 0
\(789\) −0.407654 −0.0145129
\(790\) 0 0
\(791\) 16.7312 0.594893
\(792\) 0 0
\(793\) 3.40345 0.120860
\(794\) 0 0
\(795\) −0.441313 −0.0156518
\(796\) 0 0
\(797\) 12.4961 0.442633 0.221317 0.975202i \(-0.428965\pi\)
0.221317 + 0.975202i \(0.428965\pi\)
\(798\) 0 0
\(799\) −22.5823 −0.798906
\(800\) 0 0
\(801\) −1.58175 −0.0558883
\(802\) 0 0
\(803\) 12.4341 0.438789
\(804\) 0 0
\(805\) −0.973066 −0.0342961
\(806\) 0 0
\(807\) 30.7928 1.08396
\(808\) 0 0
\(809\) −14.5390 −0.511162 −0.255581 0.966788i \(-0.582267\pi\)
−0.255581 + 0.966788i \(0.582267\pi\)
\(810\) 0 0
\(811\) 33.8243 1.18773 0.593866 0.804564i \(-0.297601\pi\)
0.593866 + 0.804564i \(0.297601\pi\)
\(812\) 0 0
\(813\) −29.6555 −1.04006
\(814\) 0 0
\(815\) −3.14108 −0.110027
\(816\) 0 0
\(817\) 23.1820 0.811037
\(818\) 0 0
\(819\) 0.124526 0.00435130
\(820\) 0 0
\(821\) −13.6665 −0.476966 −0.238483 0.971147i \(-0.576650\pi\)
−0.238483 + 0.971147i \(0.576650\pi\)
\(822\) 0 0
\(823\) −3.95988 −0.138033 −0.0690163 0.997616i \(-0.521986\pi\)
−0.0690163 + 0.997616i \(0.521986\pi\)
\(824\) 0 0
\(825\) 8.77621 0.305549
\(826\) 0 0
\(827\) −45.6515 −1.58746 −0.793728 0.608272i \(-0.791863\pi\)
−0.793728 + 0.608272i \(0.791863\pi\)
\(828\) 0 0
\(829\) −43.4499 −1.50908 −0.754538 0.656257i \(-0.772139\pi\)
−0.754538 + 0.656257i \(0.772139\pi\)
\(830\) 0 0
\(831\) 5.58674 0.193802
\(832\) 0 0
\(833\) 4.32648 0.149904
\(834\) 0 0
\(835\) 0.226534 0.00783953
\(836\) 0 0
\(837\) −33.1555 −1.14602
\(838\) 0 0
\(839\) 17.2572 0.595785 0.297893 0.954599i \(-0.403716\pi\)
0.297893 + 0.954599i \(0.403716\pi\)
\(840\) 0 0
\(841\) −27.4226 −0.945605
\(842\) 0 0
\(843\) 19.9083 0.685680
\(844\) 0 0
\(845\) 0.187208 0.00644016
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 29.1023 0.998788
\(850\) 0 0
\(851\) −31.0238 −1.06348
\(852\) 0 0
\(853\) 2.52750 0.0865401 0.0432700 0.999063i \(-0.486222\pi\)
0.0432700 + 0.999063i \(0.486222\pi\)
\(854\) 0 0
\(855\) −0.135188 −0.00462332
\(856\) 0 0
\(857\) 38.7291 1.32296 0.661480 0.749963i \(-0.269929\pi\)
0.661480 + 0.749963i \(0.269929\pi\)
\(858\) 0 0
\(859\) −5.04338 −0.172078 −0.0860390 0.996292i \(-0.527421\pi\)
−0.0860390 + 0.996292i \(0.527421\pi\)
\(860\) 0 0
\(861\) −9.25200 −0.315307
\(862\) 0 0
\(863\) −27.5510 −0.937846 −0.468923 0.883239i \(-0.655358\pi\)
−0.468923 + 0.883239i \(0.655358\pi\)
\(864\) 0 0
\(865\) 2.48447 0.0844745
\(866\) 0 0
\(867\) 3.03753 0.103160
\(868\) 0 0
\(869\) −3.58710 −0.121684
\(870\) 0 0
\(871\) 2.43127 0.0823805
\(872\) 0 0
\(873\) −0.537338 −0.0181861
\(874\) 0 0
\(875\) 1.86552 0.0630661
\(876\) 0 0
\(877\) 24.3947 0.823751 0.411876 0.911240i \(-0.364874\pi\)
0.411876 + 0.911240i \(0.364874\pi\)
\(878\) 0 0
\(879\) −18.3378 −0.618518
\(880\) 0 0
\(881\) 19.5933 0.660117 0.330058 0.943961i \(-0.392932\pi\)
0.330058 + 0.943961i \(0.392932\pi\)
\(882\) 0 0
\(883\) −52.4809 −1.76612 −0.883061 0.469258i \(-0.844521\pi\)
−0.883061 + 0.469258i \(0.844521\pi\)
\(884\) 0 0
\(885\) 2.40914 0.0809824
\(886\) 0 0
\(887\) −7.77851 −0.261177 −0.130588 0.991437i \(-0.541687\pi\)
−0.130588 + 0.991437i \(0.541687\pi\)
\(888\) 0 0
\(889\) 13.1367 0.440591
\(890\) 0 0
\(891\) 9.35807 0.313507
\(892\) 0 0
\(893\) 30.2681 1.01288
\(894\) 0 0
\(895\) 3.46719 0.115895
\(896\) 0 0
\(897\) −9.18776 −0.306770
\(898\) 0 0
\(899\) 8.19277 0.273244
\(900\) 0 0
\(901\) −5.76985 −0.192222
\(902\) 0 0
\(903\) 7.06632 0.235152
\(904\) 0 0
\(905\) 2.80698 0.0933073
\(906\) 0 0
\(907\) 24.8514 0.825178 0.412589 0.910917i \(-0.364625\pi\)
0.412589 + 0.910917i \(0.364625\pi\)
\(908\) 0 0
\(909\) 0.309276 0.0102580
\(910\) 0 0
\(911\) 14.1481 0.468748 0.234374 0.972147i \(-0.424696\pi\)
0.234374 + 0.972147i \(0.424696\pi\)
\(912\) 0 0
\(913\) 9.04444 0.299327
\(914\) 0 0
\(915\) −1.12625 −0.0372328
\(916\) 0 0
\(917\) −6.10959 −0.201756
\(918\) 0 0
\(919\) 34.8296 1.14892 0.574462 0.818532i \(-0.305211\pi\)
0.574462 + 0.818532i \(0.305211\pi\)
\(920\) 0 0
\(921\) 14.6426 0.482491
\(922\) 0 0
\(923\) 2.65660 0.0874431
\(924\) 0 0
\(925\) 29.6341 0.974364
\(926\) 0 0
\(927\) −1.74670 −0.0573691
\(928\) 0 0
\(929\) −39.7577 −1.30441 −0.652204 0.758043i \(-0.726156\pi\)
−0.652204 + 0.758043i \(0.726156\pi\)
\(930\) 0 0
\(931\) −5.79897 −0.190053
\(932\) 0 0
\(933\) −10.4322 −0.341535
\(934\) 0 0
\(935\) −0.809952 −0.0264883
\(936\) 0 0
\(937\) 7.61195 0.248672 0.124336 0.992240i \(-0.460320\pi\)
0.124336 + 0.992240i \(0.460320\pi\)
\(938\) 0 0
\(939\) −17.5366 −0.572285
\(940\) 0 0
\(941\) −20.6401 −0.672849 −0.336424 0.941710i \(-0.609218\pi\)
−0.336424 + 0.941710i \(0.609218\pi\)
\(942\) 0 0
\(943\) 27.2058 0.885942
\(944\) 0 0
\(945\) 0.951538 0.0309535
\(946\) 0 0
\(947\) 41.8689 1.36056 0.680278 0.732954i \(-0.261859\pi\)
0.680278 + 0.732954i \(0.261859\pi\)
\(948\) 0 0
\(949\) 12.4341 0.403627
\(950\) 0 0
\(951\) −11.8261 −0.383488
\(952\) 0 0
\(953\) 8.13721 0.263590 0.131795 0.991277i \(-0.457926\pi\)
0.131795 + 0.991277i \(0.457926\pi\)
\(954\) 0 0
\(955\) −1.58946 −0.0514337
\(956\) 0 0
\(957\) −2.22008 −0.0717650
\(958\) 0 0
\(959\) −13.6249 −0.439970
\(960\) 0 0
\(961\) 11.5508 0.372607
\(962\) 0 0
\(963\) 1.61693 0.0521050
\(964\) 0 0
\(965\) −2.04320 −0.0657729
\(966\) 0 0
\(967\) 48.5726 1.56199 0.780995 0.624538i \(-0.214713\pi\)
0.780995 + 0.624538i \(0.214713\pi\)
\(968\) 0 0
\(969\) −44.3483 −1.42467
\(970\) 0 0
\(971\) 29.5249 0.947500 0.473750 0.880659i \(-0.342900\pi\)
0.473750 + 0.880659i \(0.342900\pi\)
\(972\) 0 0
\(973\) −1.19652 −0.0383588
\(974\) 0 0
\(975\) 8.77621 0.281064
\(976\) 0 0
\(977\) −8.68546 −0.277873 −0.138936 0.990301i \(-0.544368\pi\)
−0.138936 + 0.990301i \(0.544368\pi\)
\(978\) 0 0
\(979\) 12.7021 0.405961
\(980\) 0 0
\(981\) 0.448596 0.0143226
\(982\) 0 0
\(983\) −16.3899 −0.522756 −0.261378 0.965237i \(-0.584177\pi\)
−0.261378 + 0.965237i \(0.584177\pi\)
\(984\) 0 0
\(985\) −3.72116 −0.118566
\(986\) 0 0
\(987\) 9.22628 0.293676
\(988\) 0 0
\(989\) −20.7787 −0.660725
\(990\) 0 0
\(991\) −37.3457 −1.18633 −0.593163 0.805083i \(-0.702121\pi\)
−0.593163 + 0.805083i \(0.702121\pi\)
\(992\) 0 0
\(993\) 33.3822 1.05935
\(994\) 0 0
\(995\) −5.01622 −0.159025
\(996\) 0 0
\(997\) 12.5699 0.398092 0.199046 0.979990i \(-0.436216\pi\)
0.199046 + 0.979990i \(0.436216\pi\)
\(998\) 0 0
\(999\) 30.3374 0.959833
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 \(a_p\))