Properties

Label 8024.2.a.y.1.14
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.453475 q^{3} +2.43721 q^{5} +1.57711 q^{7} -2.79436 q^{9} +O(q^{10})\) \(q+0.453475 q^{3} +2.43721 q^{5} +1.57711 q^{7} -2.79436 q^{9} -1.43482 q^{11} -3.06317 q^{13} +1.10521 q^{15} -1.00000 q^{17} +3.99994 q^{19} +0.715178 q^{21} -6.82452 q^{23} +0.939999 q^{25} -2.62760 q^{27} -3.52783 q^{29} +7.83929 q^{31} -0.650656 q^{33} +3.84374 q^{35} -6.03921 q^{37} -1.38907 q^{39} +1.39294 q^{41} +7.98117 q^{43} -6.81045 q^{45} -8.67044 q^{47} -4.51274 q^{49} -0.453475 q^{51} +1.22706 q^{53} -3.49696 q^{55} +1.81387 q^{57} -1.00000 q^{59} +5.68615 q^{61} -4.40700 q^{63} -7.46558 q^{65} -5.05183 q^{67} -3.09475 q^{69} +3.31175 q^{71} +3.07942 q^{73} +0.426266 q^{75} -2.26286 q^{77} -14.6823 q^{79} +7.19153 q^{81} -2.49480 q^{83} -2.43721 q^{85} -1.59978 q^{87} +14.8134 q^{89} -4.83094 q^{91} +3.55492 q^{93} +9.74869 q^{95} -15.8517 q^{97} +4.00941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) 0.453475 0.261814 0.130907 0.991395i \(-0.458211\pi\)
0.130907 + 0.991395i \(0.458211\pi\)
\(4\) 0 0
\(5\) 2.43721 1.08995 0.544977 0.838451i \(-0.316538\pi\)
0.544977 + 0.838451i \(0.316538\pi\)
\(6\) 0 0
\(7\) 1.57711 0.596090 0.298045 0.954552i \(-0.403665\pi\)
0.298045 + 0.954552i \(0.403665\pi\)
\(8\) 0 0
\(9\) −2.79436 −0.931453
\(10\) 0 0
\(11\) −1.43482 −0.432615 −0.216307 0.976325i \(-0.569401\pi\)
−0.216307 + 0.976325i \(0.569401\pi\)
\(12\) 0 0
\(13\) −3.06317 −0.849569 −0.424785 0.905294i \(-0.639650\pi\)
−0.424785 + 0.905294i \(0.639650\pi\)
\(14\) 0 0
\(15\) 1.10521 0.285365
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 3.99994 0.917648 0.458824 0.888527i \(-0.348271\pi\)
0.458824 + 0.888527i \(0.348271\pi\)
\(20\) 0 0
\(21\) 0.715178 0.156065
\(22\) 0 0
\(23\) −6.82452 −1.42301 −0.711505 0.702681i \(-0.751986\pi\)
−0.711505 + 0.702681i \(0.751986\pi\)
\(24\) 0 0
\(25\) 0.939999 0.188000
\(26\) 0 0
\(27\) −2.62760 −0.505682
\(28\) 0 0
\(29\) −3.52783 −0.655101 −0.327550 0.944834i \(-0.606223\pi\)
−0.327550 + 0.944834i \(0.606223\pi\)
\(30\) 0 0
\(31\) 7.83929 1.40798 0.703989 0.710211i \(-0.251400\pi\)
0.703989 + 0.710211i \(0.251400\pi\)
\(32\) 0 0
\(33\) −0.650656 −0.113265
\(34\) 0 0
\(35\) 3.84374 0.649711
\(36\) 0 0
\(37\) −6.03921 −0.992839 −0.496420 0.868083i \(-0.665352\pi\)
−0.496420 + 0.868083i \(0.665352\pi\)
\(38\) 0 0
\(39\) −1.38907 −0.222429
\(40\) 0 0
\(41\) 1.39294 0.217540 0.108770 0.994067i \(-0.465309\pi\)
0.108770 + 0.994067i \(0.465309\pi\)
\(42\) 0 0
\(43\) 7.98117 1.21712 0.608559 0.793509i \(-0.291748\pi\)
0.608559 + 0.793509i \(0.291748\pi\)
\(44\) 0 0
\(45\) −6.81045 −1.01524
\(46\) 0 0
\(47\) −8.67044 −1.26471 −0.632357 0.774677i \(-0.717912\pi\)
−0.632357 + 0.774677i \(0.717912\pi\)
\(48\) 0 0
\(49\) −4.51274 −0.644677
\(50\) 0 0
\(51\) −0.453475 −0.0634992
\(52\) 0 0
\(53\) 1.22706 0.168550 0.0842750 0.996443i \(-0.473143\pi\)
0.0842750 + 0.996443i \(0.473143\pi\)
\(54\) 0 0
\(55\) −3.49696 −0.471530
\(56\) 0 0
\(57\) 1.81387 0.240253
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 5.68615 0.728036 0.364018 0.931392i \(-0.381405\pi\)
0.364018 + 0.931392i \(0.381405\pi\)
\(62\) 0 0
\(63\) −4.40700 −0.555230
\(64\) 0 0
\(65\) −7.46558 −0.925992
\(66\) 0 0
\(67\) −5.05183 −0.617179 −0.308589 0.951195i \(-0.599857\pi\)
−0.308589 + 0.951195i \(0.599857\pi\)
\(68\) 0 0
\(69\) −3.09475 −0.372564
\(70\) 0 0
\(71\) 3.31175 0.393033 0.196516 0.980501i \(-0.437037\pi\)
0.196516 + 0.980501i \(0.437037\pi\)
\(72\) 0 0
\(73\) 3.07942 0.360419 0.180209 0.983628i \(-0.442322\pi\)
0.180209 + 0.983628i \(0.442322\pi\)
\(74\) 0 0
\(75\) 0.426266 0.0492210
\(76\) 0 0
\(77\) −2.26286 −0.257877
\(78\) 0 0
\(79\) −14.6823 −1.65189 −0.825946 0.563749i \(-0.809359\pi\)
−0.825946 + 0.563749i \(0.809359\pi\)
\(80\) 0 0
\(81\) 7.19153 0.799059
\(82\) 0 0
\(83\) −2.49480 −0.273840 −0.136920 0.990582i \(-0.543720\pi\)
−0.136920 + 0.990582i \(0.543720\pi\)
\(84\) 0 0
\(85\) −2.43721 −0.264353
\(86\) 0 0
\(87\) −1.59978 −0.171515
\(88\) 0 0
\(89\) 14.8134 1.57022 0.785109 0.619357i \(-0.212607\pi\)
0.785109 + 0.619357i \(0.212607\pi\)
\(90\) 0 0
\(91\) −4.83094 −0.506420
\(92\) 0 0
\(93\) 3.55492 0.368628
\(94\) 0 0
\(95\) 9.74869 1.00019
\(96\) 0 0
\(97\) −15.8517 −1.60949 −0.804746 0.593620i \(-0.797698\pi\)
−0.804746 + 0.593620i \(0.797698\pi\)
\(98\) 0 0
\(99\) 4.00941 0.402961
\(100\) 0 0
\(101\) −11.4735 −1.14166 −0.570828 0.821070i \(-0.693378\pi\)
−0.570828 + 0.821070i \(0.693378\pi\)
\(102\) 0 0
\(103\) −15.2243 −1.50010 −0.750049 0.661383i \(-0.769970\pi\)
−0.750049 + 0.661383i \(0.769970\pi\)
\(104\) 0 0
\(105\) 1.74304 0.170103
\(106\) 0 0
\(107\) 16.0961 1.55607 0.778035 0.628221i \(-0.216217\pi\)
0.778035 + 0.628221i \(0.216217\pi\)
\(108\) 0 0
\(109\) −6.86840 −0.657873 −0.328937 0.944352i \(-0.606690\pi\)
−0.328937 + 0.944352i \(0.606690\pi\)
\(110\) 0 0
\(111\) −2.73863 −0.259939
\(112\) 0 0
\(113\) 9.61190 0.904211 0.452106 0.891964i \(-0.350673\pi\)
0.452106 + 0.891964i \(0.350673\pi\)
\(114\) 0 0
\(115\) −16.6328 −1.55102
\(116\) 0 0
\(117\) 8.55959 0.791334
\(118\) 0 0
\(119\) −1.57711 −0.144573
\(120\) 0 0
\(121\) −8.94129 −0.812844
\(122\) 0 0
\(123\) 0.631662 0.0569551
\(124\) 0 0
\(125\) −9.89508 −0.885043
\(126\) 0 0
\(127\) −18.6578 −1.65561 −0.827807 0.561013i \(-0.810412\pi\)
−0.827807 + 0.561013i \(0.810412\pi\)
\(128\) 0 0
\(129\) 3.61926 0.318658
\(130\) 0 0
\(131\) −10.6672 −0.931994 −0.465997 0.884786i \(-0.654304\pi\)
−0.465997 + 0.884786i \(0.654304\pi\)
\(132\) 0 0
\(133\) 6.30832 0.547001
\(134\) 0 0
\(135\) −6.40401 −0.551170
\(136\) 0 0
\(137\) −14.8766 −1.27099 −0.635497 0.772103i \(-0.719205\pi\)
−0.635497 + 0.772103i \(0.719205\pi\)
\(138\) 0 0
\(139\) −19.9484 −1.69200 −0.845999 0.533184i \(-0.820995\pi\)
−0.845999 + 0.533184i \(0.820995\pi\)
\(140\) 0 0
\(141\) −3.93183 −0.331120
\(142\) 0 0
\(143\) 4.39509 0.367536
\(144\) 0 0
\(145\) −8.59806 −0.714030
\(146\) 0 0
\(147\) −2.04641 −0.168785
\(148\) 0 0
\(149\) 11.4861 0.940976 0.470488 0.882406i \(-0.344078\pi\)
0.470488 + 0.882406i \(0.344078\pi\)
\(150\) 0 0
\(151\) −0.0206329 −0.00167908 −0.000839542 1.00000i \(-0.500267\pi\)
−0.000839542 1.00000i \(0.500267\pi\)
\(152\) 0 0
\(153\) 2.79436 0.225911
\(154\) 0 0
\(155\) 19.1060 1.53463
\(156\) 0 0
\(157\) 2.61670 0.208835 0.104418 0.994534i \(-0.466702\pi\)
0.104418 + 0.994534i \(0.466702\pi\)
\(158\) 0 0
\(159\) 0.556442 0.0441288
\(160\) 0 0
\(161\) −10.7630 −0.848242
\(162\) 0 0
\(163\) −17.5424 −1.37403 −0.687013 0.726645i \(-0.741079\pi\)
−0.687013 + 0.726645i \(0.741079\pi\)
\(164\) 0 0
\(165\) −1.58579 −0.123453
\(166\) 0 0
\(167\) 18.6026 1.43951 0.719756 0.694227i \(-0.244254\pi\)
0.719756 + 0.694227i \(0.244254\pi\)
\(168\) 0 0
\(169\) −3.61701 −0.278232
\(170\) 0 0
\(171\) −11.1773 −0.854747
\(172\) 0 0
\(173\) 23.9698 1.82239 0.911193 0.411979i \(-0.135162\pi\)
0.911193 + 0.411979i \(0.135162\pi\)
\(174\) 0 0
\(175\) 1.48248 0.112065
\(176\) 0 0
\(177\) −0.453475 −0.0340853
\(178\) 0 0
\(179\) −6.49846 −0.485718 −0.242859 0.970062i \(-0.578085\pi\)
−0.242859 + 0.970062i \(0.578085\pi\)
\(180\) 0 0
\(181\) −10.6417 −0.790989 −0.395494 0.918468i \(-0.629427\pi\)
−0.395494 + 0.918468i \(0.629427\pi\)
\(182\) 0 0
\(183\) 2.57853 0.190610
\(184\) 0 0
\(185\) −14.7188 −1.08215
\(186\) 0 0
\(187\) 1.43482 0.104924
\(188\) 0 0
\(189\) −4.14400 −0.301432
\(190\) 0 0
\(191\) −6.36528 −0.460576 −0.230288 0.973123i \(-0.573967\pi\)
−0.230288 + 0.973123i \(0.573967\pi\)
\(192\) 0 0
\(193\) 17.9200 1.28991 0.644956 0.764220i \(-0.276876\pi\)
0.644956 + 0.764220i \(0.276876\pi\)
\(194\) 0 0
\(195\) −3.38546 −0.242438
\(196\) 0 0
\(197\) −11.9517 −0.851522 −0.425761 0.904836i \(-0.639993\pi\)
−0.425761 + 0.904836i \(0.639993\pi\)
\(198\) 0 0
\(199\) −9.46122 −0.670688 −0.335344 0.942096i \(-0.608853\pi\)
−0.335344 + 0.942096i \(0.608853\pi\)
\(200\) 0 0
\(201\) −2.29088 −0.161586
\(202\) 0 0
\(203\) −5.56375 −0.390499
\(204\) 0 0
\(205\) 3.39488 0.237109
\(206\) 0 0
\(207\) 19.0702 1.32547
\(208\) 0 0
\(209\) −5.73919 −0.396988
\(210\) 0 0
\(211\) −13.2497 −0.912149 −0.456074 0.889942i \(-0.650745\pi\)
−0.456074 + 0.889942i \(0.650745\pi\)
\(212\) 0 0
\(213\) 1.50180 0.102901
\(214\) 0 0
\(215\) 19.4518 1.32660
\(216\) 0 0
\(217\) 12.3634 0.839281
\(218\) 0 0
\(219\) 1.39644 0.0943627
\(220\) 0 0
\(221\) 3.06317 0.206051
\(222\) 0 0
\(223\) 22.8774 1.53199 0.765993 0.642849i \(-0.222248\pi\)
0.765993 + 0.642849i \(0.222248\pi\)
\(224\) 0 0
\(225\) −2.62670 −0.175113
\(226\) 0 0
\(227\) −7.94528 −0.527347 −0.263673 0.964612i \(-0.584934\pi\)
−0.263673 + 0.964612i \(0.584934\pi\)
\(228\) 0 0
\(229\) 14.4559 0.955271 0.477635 0.878558i \(-0.341494\pi\)
0.477635 + 0.878558i \(0.341494\pi\)
\(230\) 0 0
\(231\) −1.02615 −0.0675159
\(232\) 0 0
\(233\) −3.71087 −0.243107 −0.121554 0.992585i \(-0.538788\pi\)
−0.121554 + 0.992585i \(0.538788\pi\)
\(234\) 0 0
\(235\) −21.1317 −1.37848
\(236\) 0 0
\(237\) −6.65808 −0.432489
\(238\) 0 0
\(239\) −15.5117 −1.00337 −0.501685 0.865050i \(-0.667286\pi\)
−0.501685 + 0.865050i \(0.667286\pi\)
\(240\) 0 0
\(241\) −5.60096 −0.360790 −0.180395 0.983594i \(-0.557738\pi\)
−0.180395 + 0.983594i \(0.557738\pi\)
\(242\) 0 0
\(243\) 11.1440 0.714886
\(244\) 0 0
\(245\) −10.9985 −0.702668
\(246\) 0 0
\(247\) −12.2525 −0.779606
\(248\) 0 0
\(249\) −1.13133 −0.0716951
\(250\) 0 0
\(251\) −2.03446 −0.128414 −0.0642069 0.997937i \(-0.520452\pi\)
−0.0642069 + 0.997937i \(0.520452\pi\)
\(252\) 0 0
\(253\) 9.79196 0.615615
\(254\) 0 0
\(255\) −1.10521 −0.0692112
\(256\) 0 0
\(257\) −13.7256 −0.856177 −0.428088 0.903737i \(-0.640813\pi\)
−0.428088 + 0.903737i \(0.640813\pi\)
\(258\) 0 0
\(259\) −9.52447 −0.591822
\(260\) 0 0
\(261\) 9.85802 0.610196
\(262\) 0 0
\(263\) 19.8680 1.22511 0.612557 0.790427i \(-0.290141\pi\)
0.612557 + 0.790427i \(0.290141\pi\)
\(264\) 0 0
\(265\) 2.99061 0.183712
\(266\) 0 0
\(267\) 6.71751 0.411105
\(268\) 0 0
\(269\) −11.6357 −0.709441 −0.354721 0.934972i \(-0.615424\pi\)
−0.354721 + 0.934972i \(0.615424\pi\)
\(270\) 0 0
\(271\) −19.5163 −1.18553 −0.592765 0.805376i \(-0.701964\pi\)
−0.592765 + 0.805376i \(0.701964\pi\)
\(272\) 0 0
\(273\) −2.19071 −0.132588
\(274\) 0 0
\(275\) −1.34873 −0.0813315
\(276\) 0 0
\(277\) 11.3188 0.680079 0.340040 0.940411i \(-0.389560\pi\)
0.340040 + 0.940411i \(0.389560\pi\)
\(278\) 0 0
\(279\) −21.9058 −1.31147
\(280\) 0 0
\(281\) −16.4310 −0.980193 −0.490096 0.871668i \(-0.663038\pi\)
−0.490096 + 0.871668i \(0.663038\pi\)
\(282\) 0 0
\(283\) 17.8720 1.06238 0.531190 0.847253i \(-0.321745\pi\)
0.531190 + 0.847253i \(0.321745\pi\)
\(284\) 0 0
\(285\) 4.42079 0.261865
\(286\) 0 0
\(287\) 2.19681 0.129674
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −7.18833 −0.421387
\(292\) 0 0
\(293\) −0.884128 −0.0516513 −0.0258257 0.999666i \(-0.508221\pi\)
−0.0258257 + 0.999666i \(0.508221\pi\)
\(294\) 0 0
\(295\) −2.43721 −0.141900
\(296\) 0 0
\(297\) 3.77013 0.218765
\(298\) 0 0
\(299\) 20.9046 1.20895
\(300\) 0 0
\(301\) 12.5872 0.725511
\(302\) 0 0
\(303\) −5.20295 −0.298902
\(304\) 0 0
\(305\) 13.8583 0.793526
\(306\) 0 0
\(307\) 24.0731 1.37392 0.686961 0.726694i \(-0.258944\pi\)
0.686961 + 0.726694i \(0.258944\pi\)
\(308\) 0 0
\(309\) −6.90385 −0.392746
\(310\) 0 0
\(311\) −21.7987 −1.23609 −0.618046 0.786142i \(-0.712075\pi\)
−0.618046 + 0.786142i \(0.712075\pi\)
\(312\) 0 0
\(313\) 32.5090 1.83752 0.918758 0.394820i \(-0.129193\pi\)
0.918758 + 0.394820i \(0.129193\pi\)
\(314\) 0 0
\(315\) −10.7408 −0.605175
\(316\) 0 0
\(317\) 13.6868 0.768728 0.384364 0.923182i \(-0.374421\pi\)
0.384364 + 0.923182i \(0.374421\pi\)
\(318\) 0 0
\(319\) 5.06180 0.283406
\(320\) 0 0
\(321\) 7.29919 0.407401
\(322\) 0 0
\(323\) −3.99994 −0.222562
\(324\) 0 0
\(325\) −2.87937 −0.159719
\(326\) 0 0
\(327\) −3.11465 −0.172240
\(328\) 0 0
\(329\) −13.6742 −0.753883
\(330\) 0 0
\(331\) −3.58772 −0.197199 −0.0985994 0.995127i \(-0.531436\pi\)
−0.0985994 + 0.995127i \(0.531436\pi\)
\(332\) 0 0
\(333\) 16.8757 0.924784
\(334\) 0 0
\(335\) −12.3124 −0.672697
\(336\) 0 0
\(337\) 30.1021 1.63977 0.819884 0.572529i \(-0.194038\pi\)
0.819884 + 0.572529i \(0.194038\pi\)
\(338\) 0 0
\(339\) 4.35876 0.236735
\(340\) 0 0
\(341\) −11.2480 −0.609112
\(342\) 0 0
\(343\) −18.1568 −0.980375
\(344\) 0 0
\(345\) −7.54256 −0.406078
\(346\) 0 0
\(347\) −33.0184 −1.77252 −0.886260 0.463187i \(-0.846706\pi\)
−0.886260 + 0.463187i \(0.846706\pi\)
\(348\) 0 0
\(349\) 24.4164 1.30698 0.653490 0.756936i \(-0.273304\pi\)
0.653490 + 0.756936i \(0.273304\pi\)
\(350\) 0 0
\(351\) 8.04877 0.429612
\(352\) 0 0
\(353\) −1.87403 −0.0997445 −0.0498722 0.998756i \(-0.515881\pi\)
−0.0498722 + 0.998756i \(0.515881\pi\)
\(354\) 0 0
\(355\) 8.07144 0.428388
\(356\) 0 0
\(357\) −0.715178 −0.0378512
\(358\) 0 0
\(359\) 2.04466 0.107913 0.0539565 0.998543i \(-0.482817\pi\)
0.0539565 + 0.998543i \(0.482817\pi\)
\(360\) 0 0
\(361\) −3.00051 −0.157922
\(362\) 0 0
\(363\) −4.05465 −0.212814
\(364\) 0 0
\(365\) 7.50519 0.392840
\(366\) 0 0
\(367\) −24.1148 −1.25878 −0.629390 0.777089i \(-0.716695\pi\)
−0.629390 + 0.777089i \(0.716695\pi\)
\(368\) 0 0
\(369\) −3.89237 −0.202629
\(370\) 0 0
\(371\) 1.93521 0.100471
\(372\) 0 0
\(373\) −21.3010 −1.10292 −0.551462 0.834200i \(-0.685930\pi\)
−0.551462 + 0.834200i \(0.685930\pi\)
\(374\) 0 0
\(375\) −4.48717 −0.231717
\(376\) 0 0
\(377\) 10.8063 0.556554
\(378\) 0 0
\(379\) 13.9252 0.715292 0.357646 0.933857i \(-0.383580\pi\)
0.357646 + 0.933857i \(0.383580\pi\)
\(380\) 0 0
\(381\) −8.46086 −0.433463
\(382\) 0 0
\(383\) −2.48053 −0.126749 −0.0633745 0.997990i \(-0.520186\pi\)
−0.0633745 + 0.997990i \(0.520186\pi\)
\(384\) 0 0
\(385\) −5.51508 −0.281074
\(386\) 0 0
\(387\) −22.3023 −1.13369
\(388\) 0 0
\(389\) 27.4212 1.39031 0.695154 0.718861i \(-0.255336\pi\)
0.695154 + 0.718861i \(0.255336\pi\)
\(390\) 0 0
\(391\) 6.82452 0.345131
\(392\) 0 0
\(393\) −4.83729 −0.244009
\(394\) 0 0
\(395\) −35.7840 −1.80049
\(396\) 0 0
\(397\) 5.07589 0.254751 0.127376 0.991855i \(-0.459345\pi\)
0.127376 + 0.991855i \(0.459345\pi\)
\(398\) 0 0
\(399\) 2.86067 0.143212
\(400\) 0 0
\(401\) 17.6730 0.882546 0.441273 0.897373i \(-0.354527\pi\)
0.441273 + 0.897373i \(0.354527\pi\)
\(402\) 0 0
\(403\) −24.0130 −1.19617
\(404\) 0 0
\(405\) 17.5273 0.870938
\(406\) 0 0
\(407\) 8.66518 0.429517
\(408\) 0 0
\(409\) 22.5746 1.11624 0.558121 0.829760i \(-0.311523\pi\)
0.558121 + 0.829760i \(0.311523\pi\)
\(410\) 0 0
\(411\) −6.74617 −0.332764
\(412\) 0 0
\(413\) −1.57711 −0.0776043
\(414\) 0 0
\(415\) −6.08035 −0.298473
\(416\) 0 0
\(417\) −9.04609 −0.442989
\(418\) 0 0
\(419\) 10.3638 0.506304 0.253152 0.967427i \(-0.418533\pi\)
0.253152 + 0.967427i \(0.418533\pi\)
\(420\) 0 0
\(421\) −3.64460 −0.177627 −0.0888136 0.996048i \(-0.528308\pi\)
−0.0888136 + 0.996048i \(0.528308\pi\)
\(422\) 0 0
\(423\) 24.2283 1.17802
\(424\) 0 0
\(425\) −0.939999 −0.0455967
\(426\) 0 0
\(427\) 8.96765 0.433975
\(428\) 0 0
\(429\) 1.99307 0.0962261
\(430\) 0 0
\(431\) 19.3289 0.931043 0.465521 0.885037i \(-0.345867\pi\)
0.465521 + 0.885037i \(0.345867\pi\)
\(432\) 0 0
\(433\) −29.8067 −1.43242 −0.716209 0.697885i \(-0.754124\pi\)
−0.716209 + 0.697885i \(0.754124\pi\)
\(434\) 0 0
\(435\) −3.89901 −0.186943
\(436\) 0 0
\(437\) −27.2976 −1.30582
\(438\) 0 0
\(439\) 28.0908 1.34070 0.670350 0.742045i \(-0.266144\pi\)
0.670350 + 0.742045i \(0.266144\pi\)
\(440\) 0 0
\(441\) 12.6102 0.600487
\(442\) 0 0
\(443\) 2.28491 0.108559 0.0542797 0.998526i \(-0.482714\pi\)
0.0542797 + 0.998526i \(0.482714\pi\)
\(444\) 0 0
\(445\) 36.1034 1.71147
\(446\) 0 0
\(447\) 5.20865 0.246361
\(448\) 0 0
\(449\) 17.1490 0.809312 0.404656 0.914469i \(-0.367391\pi\)
0.404656 + 0.914469i \(0.367391\pi\)
\(450\) 0 0
\(451\) −1.99862 −0.0941111
\(452\) 0 0
\(453\) −0.00935652 −0.000439608 0
\(454\) 0 0
\(455\) −11.7740 −0.551974
\(456\) 0 0
\(457\) 8.30477 0.388481 0.194240 0.980954i \(-0.437776\pi\)
0.194240 + 0.980954i \(0.437776\pi\)
\(458\) 0 0
\(459\) 2.62760 0.122646
\(460\) 0 0
\(461\) 30.1785 1.40555 0.702776 0.711411i \(-0.251944\pi\)
0.702776 + 0.711411i \(0.251944\pi\)
\(462\) 0 0
\(463\) 8.36001 0.388523 0.194261 0.980950i \(-0.437769\pi\)
0.194261 + 0.980950i \(0.437769\pi\)
\(464\) 0 0
\(465\) 8.66410 0.401788
\(466\) 0 0
\(467\) 1.57523 0.0728929 0.0364464 0.999336i \(-0.488396\pi\)
0.0364464 + 0.999336i \(0.488396\pi\)
\(468\) 0 0
\(469\) −7.96726 −0.367894
\(470\) 0 0
\(471\) 1.18661 0.0546760
\(472\) 0 0
\(473\) −11.4516 −0.526543
\(474\) 0 0
\(475\) 3.75994 0.172518
\(476\) 0 0
\(477\) −3.42885 −0.156996
\(478\) 0 0
\(479\) −19.8890 −0.908754 −0.454377 0.890810i \(-0.650138\pi\)
−0.454377 + 0.890810i \(0.650138\pi\)
\(480\) 0 0
\(481\) 18.4991 0.843486
\(482\) 0 0
\(483\) −4.88075 −0.222082
\(484\) 0 0
\(485\) −38.6338 −1.75427
\(486\) 0 0
\(487\) −30.1816 −1.36766 −0.683830 0.729642i \(-0.739687\pi\)
−0.683830 + 0.729642i \(0.739687\pi\)
\(488\) 0 0
\(489\) −7.95504 −0.359739
\(490\) 0 0
\(491\) 13.9373 0.628981 0.314491 0.949261i \(-0.398166\pi\)
0.314491 + 0.949261i \(0.398166\pi\)
\(492\) 0 0
\(493\) 3.52783 0.158885
\(494\) 0 0
\(495\) 9.77177 0.439208
\(496\) 0 0
\(497\) 5.22298 0.234283
\(498\) 0 0
\(499\) −16.7489 −0.749784 −0.374892 0.927068i \(-0.622320\pi\)
−0.374892 + 0.927068i \(0.622320\pi\)
\(500\) 0 0
\(501\) 8.43582 0.376885
\(502\) 0 0
\(503\) 39.9450 1.78106 0.890530 0.454925i \(-0.150334\pi\)
0.890530 + 0.454925i \(0.150334\pi\)
\(504\) 0 0
\(505\) −27.9634 −1.24435
\(506\) 0 0
\(507\) −1.64023 −0.0728450
\(508\) 0 0
\(509\) 14.8624 0.658764 0.329382 0.944197i \(-0.393160\pi\)
0.329382 + 0.944197i \(0.393160\pi\)
\(510\) 0 0
\(511\) 4.85657 0.214842
\(512\) 0 0
\(513\) −10.5102 −0.464038
\(514\) 0 0
\(515\) −37.1049 −1.63504
\(516\) 0 0
\(517\) 12.4405 0.547134
\(518\) 0 0
\(519\) 10.8697 0.477126
\(520\) 0 0
\(521\) −30.2768 −1.32645 −0.663226 0.748419i \(-0.730813\pi\)
−0.663226 + 0.748419i \(0.730813\pi\)
\(522\) 0 0
\(523\) 8.87499 0.388076 0.194038 0.980994i \(-0.437841\pi\)
0.194038 + 0.980994i \(0.437841\pi\)
\(524\) 0 0
\(525\) 0.672267 0.0293401
\(526\) 0 0
\(527\) −7.83929 −0.341485
\(528\) 0 0
\(529\) 23.5740 1.02496
\(530\) 0 0
\(531\) 2.79436 0.121265
\(532\) 0 0
\(533\) −4.26680 −0.184816
\(534\) 0 0
\(535\) 39.2296 1.69605
\(536\) 0 0
\(537\) −2.94689 −0.127168
\(538\) 0 0
\(539\) 6.47497 0.278897
\(540\) 0 0
\(541\) 4.49305 0.193171 0.0965857 0.995325i \(-0.469208\pi\)
0.0965857 + 0.995325i \(0.469208\pi\)
\(542\) 0 0
\(543\) −4.82573 −0.207092
\(544\) 0 0
\(545\) −16.7397 −0.717052
\(546\) 0 0
\(547\) −36.0040 −1.53942 −0.769710 0.638394i \(-0.779599\pi\)
−0.769710 + 0.638394i \(0.779599\pi\)
\(548\) 0 0
\(549\) −15.8891 −0.678132
\(550\) 0 0
\(551\) −14.1111 −0.601152
\(552\) 0 0
\(553\) −23.1556 −0.984676
\(554\) 0 0
\(555\) −6.67462 −0.283322
\(556\) 0 0
\(557\) −12.0897 −0.512259 −0.256129 0.966643i \(-0.582447\pi\)
−0.256129 + 0.966643i \(0.582447\pi\)
\(558\) 0 0
\(559\) −24.4477 −1.03403
\(560\) 0 0
\(561\) 0.650656 0.0274707
\(562\) 0 0
\(563\) 24.8784 1.04850 0.524250 0.851565i \(-0.324346\pi\)
0.524250 + 0.851565i \(0.324346\pi\)
\(564\) 0 0
\(565\) 23.4262 0.985549
\(566\) 0 0
\(567\) 11.3418 0.476311
\(568\) 0 0
\(569\) −4.46486 −0.187177 −0.0935884 0.995611i \(-0.529834\pi\)
−0.0935884 + 0.995611i \(0.529834\pi\)
\(570\) 0 0
\(571\) −9.29575 −0.389015 −0.194508 0.980901i \(-0.562311\pi\)
−0.194508 + 0.980901i \(0.562311\pi\)
\(572\) 0 0
\(573\) −2.88650 −0.120585
\(574\) 0 0
\(575\) −6.41504 −0.267526
\(576\) 0 0
\(577\) 21.7856 0.906948 0.453474 0.891269i \(-0.350184\pi\)
0.453474 + 0.891269i \(0.350184\pi\)
\(578\) 0 0
\(579\) 8.12629 0.337717
\(580\) 0 0
\(581\) −3.93456 −0.163233
\(582\) 0 0
\(583\) −1.76061 −0.0729172
\(584\) 0 0
\(585\) 20.8615 0.862518
\(586\) 0 0
\(587\) 19.8082 0.817574 0.408787 0.912630i \(-0.365952\pi\)
0.408787 + 0.912630i \(0.365952\pi\)
\(588\) 0 0
\(589\) 31.3567 1.29203
\(590\) 0 0
\(591\) −5.41979 −0.222940
\(592\) 0 0
\(593\) 4.36921 0.179422 0.0897111 0.995968i \(-0.471406\pi\)
0.0897111 + 0.995968i \(0.471406\pi\)
\(594\) 0 0
\(595\) −3.84374 −0.157578
\(596\) 0 0
\(597\) −4.29043 −0.175596
\(598\) 0 0
\(599\) −16.4978 −0.674082 −0.337041 0.941490i \(-0.609426\pi\)
−0.337041 + 0.941490i \(0.609426\pi\)
\(600\) 0 0
\(601\) −16.6233 −0.678080 −0.339040 0.940772i \(-0.610102\pi\)
−0.339040 + 0.940772i \(0.610102\pi\)
\(602\) 0 0
\(603\) 14.1166 0.574873
\(604\) 0 0
\(605\) −21.7918 −0.885963
\(606\) 0 0
\(607\) −14.3661 −0.583100 −0.291550 0.956556i \(-0.594171\pi\)
−0.291550 + 0.956556i \(0.594171\pi\)
\(608\) 0 0
\(609\) −2.52302 −0.102238
\(610\) 0 0
\(611\) 26.5590 1.07446
\(612\) 0 0
\(613\) −42.3099 −1.70888 −0.854440 0.519551i \(-0.826099\pi\)
−0.854440 + 0.519551i \(0.826099\pi\)
\(614\) 0 0
\(615\) 1.53949 0.0620784
\(616\) 0 0
\(617\) −1.74462 −0.0702356 −0.0351178 0.999383i \(-0.511181\pi\)
−0.0351178 + 0.999383i \(0.511181\pi\)
\(618\) 0 0
\(619\) −9.61399 −0.386419 −0.193209 0.981158i \(-0.561890\pi\)
−0.193209 + 0.981158i \(0.561890\pi\)
\(620\) 0 0
\(621\) 17.9321 0.719590
\(622\) 0 0
\(623\) 23.3623 0.935991
\(624\) 0 0
\(625\) −28.8164 −1.15266
\(626\) 0 0
\(627\) −2.60258 −0.103937
\(628\) 0 0
\(629\) 6.03921 0.240799
\(630\) 0 0
\(631\) −25.1841 −1.00256 −0.501282 0.865284i \(-0.667138\pi\)
−0.501282 + 0.865284i \(0.667138\pi\)
\(632\) 0 0
\(633\) −6.00842 −0.238813
\(634\) 0 0
\(635\) −45.4731 −1.80454
\(636\) 0 0
\(637\) 13.8233 0.547698
\(638\) 0 0
\(639\) −9.25423 −0.366092
\(640\) 0 0
\(641\) −47.0536 −1.85851 −0.929253 0.369445i \(-0.879548\pi\)
−0.929253 + 0.369445i \(0.879548\pi\)
\(642\) 0 0
\(643\) −1.71605 −0.0676746 −0.0338373 0.999427i \(-0.510773\pi\)
−0.0338373 + 0.999427i \(0.510773\pi\)
\(644\) 0 0
\(645\) 8.82091 0.347323
\(646\) 0 0
\(647\) 5.87748 0.231068 0.115534 0.993304i \(-0.463142\pi\)
0.115534 + 0.993304i \(0.463142\pi\)
\(648\) 0 0
\(649\) 1.43482 0.0563216
\(650\) 0 0
\(651\) 5.60649 0.219736
\(652\) 0 0
\(653\) 15.6602 0.612832 0.306416 0.951898i \(-0.400870\pi\)
0.306416 + 0.951898i \(0.400870\pi\)
\(654\) 0 0
\(655\) −25.9981 −1.01583
\(656\) 0 0
\(657\) −8.60501 −0.335713
\(658\) 0 0
\(659\) 11.3607 0.442549 0.221274 0.975212i \(-0.428978\pi\)
0.221274 + 0.975212i \(0.428978\pi\)
\(660\) 0 0
\(661\) −41.2976 −1.60629 −0.803146 0.595782i \(-0.796842\pi\)
−0.803146 + 0.595782i \(0.796842\pi\)
\(662\) 0 0
\(663\) 1.38907 0.0539470
\(664\) 0 0
\(665\) 15.3747 0.596206
\(666\) 0 0
\(667\) 24.0757 0.932215
\(668\) 0 0
\(669\) 10.3743 0.401095
\(670\) 0 0
\(671\) −8.15860 −0.314959
\(672\) 0 0
\(673\) −26.5471 −1.02331 −0.511657 0.859190i \(-0.670968\pi\)
−0.511657 + 0.859190i \(0.670968\pi\)
\(674\) 0 0
\(675\) −2.46994 −0.0950681
\(676\) 0 0
\(677\) 38.4424 1.47746 0.738731 0.674000i \(-0.235425\pi\)
0.738731 + 0.674000i \(0.235425\pi\)
\(678\) 0 0
\(679\) −24.9997 −0.959401
\(680\) 0 0
\(681\) −3.60299 −0.138067
\(682\) 0 0
\(683\) −30.1923 −1.15528 −0.577638 0.816293i \(-0.696026\pi\)
−0.577638 + 0.816293i \(0.696026\pi\)
\(684\) 0 0
\(685\) −36.2574 −1.38532
\(686\) 0 0
\(687\) 6.55538 0.250103
\(688\) 0 0
\(689\) −3.75870 −0.143195
\(690\) 0 0
\(691\) 8.49880 0.323309 0.161655 0.986847i \(-0.448317\pi\)
0.161655 + 0.986847i \(0.448317\pi\)
\(692\) 0 0
\(693\) 6.32326 0.240201
\(694\) 0 0
\(695\) −48.6184 −1.84420
\(696\) 0 0
\(697\) −1.39294 −0.0527613
\(698\) 0 0
\(699\) −1.68279 −0.0636489
\(700\) 0 0
\(701\) −30.6404 −1.15727 −0.578637 0.815585i \(-0.696415\pi\)
−0.578637 + 0.815585i \(0.696415\pi\)
\(702\) 0 0
\(703\) −24.1564 −0.911077
\(704\) 0 0
\(705\) −9.58270 −0.360905
\(706\) 0 0
\(707\) −18.0949 −0.680530
\(708\) 0 0
\(709\) −29.0445 −1.09079 −0.545395 0.838179i \(-0.683620\pi\)
−0.545395 + 0.838179i \(0.683620\pi\)
\(710\) 0 0
\(711\) 41.0278 1.53866
\(712\) 0 0
\(713\) −53.4994 −2.00357
\(714\) 0 0
\(715\) 10.7118 0.400598
\(716\) 0 0
\(717\) −7.03418 −0.262696
\(718\) 0 0
\(719\) −51.2759 −1.91227 −0.956134 0.292930i \(-0.905370\pi\)
−0.956134 + 0.292930i \(0.905370\pi\)
\(720\) 0 0
\(721\) −24.0104 −0.894193
\(722\) 0 0
\(723\) −2.53990 −0.0944598
\(724\) 0 0
\(725\) −3.31615 −0.123159
\(726\) 0 0
\(727\) 44.4988 1.65037 0.825185 0.564862i \(-0.191071\pi\)
0.825185 + 0.564862i \(0.191071\pi\)
\(728\) 0 0
\(729\) −16.5211 −0.611892
\(730\) 0 0
\(731\) −7.98117 −0.295194
\(732\) 0 0
\(733\) −30.7666 −1.13639 −0.568195 0.822894i \(-0.692358\pi\)
−0.568195 + 0.822894i \(0.692358\pi\)
\(734\) 0 0
\(735\) −4.98755 −0.183968
\(736\) 0 0
\(737\) 7.24847 0.267001
\(738\) 0 0
\(739\) −3.24740 −0.119458 −0.0597288 0.998215i \(-0.519024\pi\)
−0.0597288 + 0.998215i \(0.519024\pi\)
\(740\) 0 0
\(741\) −5.55619 −0.204112
\(742\) 0 0
\(743\) 38.0248 1.39500 0.697498 0.716587i \(-0.254297\pi\)
0.697498 + 0.716587i \(0.254297\pi\)
\(744\) 0 0
\(745\) 27.9940 1.02562
\(746\) 0 0
\(747\) 6.97137 0.255069
\(748\) 0 0
\(749\) 25.3853 0.927558
\(750\) 0 0
\(751\) −20.1695 −0.735996 −0.367998 0.929827i \(-0.619957\pi\)
−0.367998 + 0.929827i \(0.619957\pi\)
\(752\) 0 0
\(753\) −0.922576 −0.0336206
\(754\) 0 0
\(755\) −0.0502868 −0.00183012
\(756\) 0 0
\(757\) 18.1157 0.658425 0.329213 0.944256i \(-0.393217\pi\)
0.329213 + 0.944256i \(0.393217\pi\)
\(758\) 0 0
\(759\) 4.44041 0.161177
\(760\) 0 0
\(761\) 44.8732 1.62665 0.813327 0.581807i \(-0.197654\pi\)
0.813327 + 0.581807i \(0.197654\pi\)
\(762\) 0 0
\(763\) −10.8322 −0.392152
\(764\) 0 0
\(765\) 6.81045 0.246232
\(766\) 0 0
\(767\) 3.06317 0.110605
\(768\) 0 0
\(769\) −21.9293 −0.790790 −0.395395 0.918511i \(-0.629392\pi\)
−0.395395 + 0.918511i \(0.629392\pi\)
\(770\) 0 0
\(771\) −6.22420 −0.224159
\(772\) 0 0
\(773\) 16.1495 0.580858 0.290429 0.956897i \(-0.406202\pi\)
0.290429 + 0.956897i \(0.406202\pi\)
\(774\) 0 0
\(775\) 7.36893 0.264700
\(776\) 0 0
\(777\) −4.31911 −0.154947
\(778\) 0 0
\(779\) 5.57166 0.199625
\(780\) 0 0
\(781\) −4.75177 −0.170032
\(782\) 0 0
\(783\) 9.26971 0.331272
\(784\) 0 0
\(785\) 6.37745 0.227621
\(786\) 0 0
\(787\) 45.3748 1.61744 0.808718 0.588196i \(-0.200162\pi\)
0.808718 + 0.588196i \(0.200162\pi\)
\(788\) 0 0
\(789\) 9.00965 0.320752
\(790\) 0 0
\(791\) 15.1590 0.538991
\(792\) 0 0
\(793\) −17.4176 −0.618517
\(794\) 0 0
\(795\) 1.35617 0.0480983
\(796\) 0 0
\(797\) −44.6951 −1.58318 −0.791592 0.611050i \(-0.790747\pi\)
−0.791592 + 0.611050i \(0.790747\pi\)
\(798\) 0 0
\(799\) 8.67044 0.306738
\(800\) 0 0
\(801\) −41.3940 −1.46259
\(802\) 0 0
\(803\) −4.41841 −0.155922
\(804\) 0 0
\(805\) −26.2317 −0.924545
\(806\) 0 0
\(807\) −5.27650 −0.185742
\(808\) 0 0
\(809\) 8.56691 0.301197 0.150598 0.988595i \(-0.451880\pi\)
0.150598 + 0.988595i \(0.451880\pi\)
\(810\) 0 0
\(811\) −42.1858 −1.48134 −0.740671 0.671868i \(-0.765492\pi\)
−0.740671 + 0.671868i \(0.765492\pi\)
\(812\) 0 0
\(813\) −8.85015 −0.310388
\(814\) 0 0
\(815\) −42.7545 −1.49763
\(816\) 0 0
\(817\) 31.9242 1.11689
\(818\) 0 0
\(819\) 13.4994 0.471706
\(820\) 0 0
\(821\) −22.6151 −0.789273 −0.394636 0.918837i \(-0.629129\pi\)
−0.394636 + 0.918837i \(0.629129\pi\)
\(822\) 0 0
\(823\) 9.32448 0.325031 0.162515 0.986706i \(-0.448039\pi\)
0.162515 + 0.986706i \(0.448039\pi\)
\(824\) 0 0
\(825\) −0.611616 −0.0212937
\(826\) 0 0
\(827\) −29.4618 −1.02449 −0.512244 0.858840i \(-0.671186\pi\)
−0.512244 + 0.858840i \(0.671186\pi\)
\(828\) 0 0
\(829\) 20.7991 0.722381 0.361191 0.932492i \(-0.382370\pi\)
0.361191 + 0.932492i \(0.382370\pi\)
\(830\) 0 0
\(831\) 5.13278 0.178054
\(832\) 0 0
\(833\) 4.51274 0.156357
\(834\) 0 0
\(835\) 45.3385 1.56900
\(836\) 0 0
\(837\) −20.5985 −0.711988
\(838\) 0 0
\(839\) 35.3721 1.22118 0.610590 0.791947i \(-0.290932\pi\)
0.610590 + 0.791947i \(0.290932\pi\)
\(840\) 0 0
\(841\) −16.5544 −0.570843
\(842\) 0 0
\(843\) −7.45106 −0.256628
\(844\) 0 0
\(845\) −8.81543 −0.303260
\(846\) 0 0
\(847\) −14.1014 −0.484528
\(848\) 0 0
\(849\) 8.10451 0.278146
\(850\) 0 0
\(851\) 41.2147 1.41282
\(852\) 0 0
\(853\) 14.3840 0.492498 0.246249 0.969207i \(-0.420802\pi\)
0.246249 + 0.969207i \(0.420802\pi\)
\(854\) 0 0
\(855\) −27.2414 −0.931635
\(856\) 0 0
\(857\) 41.6732 1.42353 0.711765 0.702418i \(-0.247896\pi\)
0.711765 + 0.702418i \(0.247896\pi\)
\(858\) 0 0
\(859\) 44.4605 1.51697 0.758487 0.651688i \(-0.225939\pi\)
0.758487 + 0.651688i \(0.225939\pi\)
\(860\) 0 0
\(861\) 0.996198 0.0339503
\(862\) 0 0
\(863\) −13.1056 −0.446121 −0.223061 0.974805i \(-0.571605\pi\)
−0.223061 + 0.974805i \(0.571605\pi\)
\(864\) 0 0
\(865\) 58.4194 1.98632
\(866\) 0 0
\(867\) 0.453475 0.0154008
\(868\) 0 0
\(869\) 21.0665 0.714633
\(870\) 0 0
\(871\) 15.4746 0.524336
\(872\) 0 0
\(873\) 44.2952 1.49917
\(874\) 0 0
\(875\) −15.6056 −0.527565
\(876\) 0 0
\(877\) 40.6575 1.37291 0.686454 0.727174i \(-0.259166\pi\)
0.686454 + 0.727174i \(0.259166\pi\)
\(878\) 0 0
\(879\) −0.400930 −0.0135230
\(880\) 0 0
\(881\) 18.7742 0.632518 0.316259 0.948673i \(-0.397573\pi\)
0.316259 + 0.948673i \(0.397573\pi\)
\(882\) 0 0
\(883\) −53.0066 −1.78381 −0.891907 0.452219i \(-0.850632\pi\)
−0.891907 + 0.452219i \(0.850632\pi\)
\(884\) 0 0
\(885\) −1.10521 −0.0371514
\(886\) 0 0
\(887\) −29.8268 −1.00148 −0.500742 0.865596i \(-0.666940\pi\)
−0.500742 + 0.865596i \(0.666940\pi\)
\(888\) 0 0
\(889\) −29.4254 −0.986895
\(890\) 0 0
\(891\) −10.3186 −0.345685
\(892\) 0 0
\(893\) −34.6812 −1.16056
\(894\) 0 0
\(895\) −15.8381 −0.529410
\(896\) 0 0
\(897\) 9.47973 0.316519
\(898\) 0 0
\(899\) −27.6556 −0.922367
\(900\) 0 0
\(901\) −1.22706 −0.0408794
\(902\) 0 0
\(903\) 5.70796 0.189949
\(904\) 0 0
\(905\) −25.9360 −0.862142
\(906\) 0 0
\(907\) −13.9145 −0.462025 −0.231012 0.972951i \(-0.574204\pi\)
−0.231012 + 0.972951i \(0.574204\pi\)
\(908\) 0 0
\(909\) 32.0611 1.06340
\(910\) 0 0
\(911\) −34.0797 −1.12911 −0.564556 0.825395i \(-0.690953\pi\)
−0.564556 + 0.825395i \(0.690953\pi\)
\(912\) 0 0
\(913\) 3.57959 0.118467
\(914\) 0 0
\(915\) 6.28441 0.207756
\(916\) 0 0
\(917\) −16.8232 −0.555552
\(918\) 0 0
\(919\) 30.3312 1.00054 0.500268 0.865871i \(-0.333235\pi\)
0.500268 + 0.865871i \(0.333235\pi\)
\(920\) 0 0
\(921\) 10.9165 0.359712
\(922\) 0 0
\(923\) −10.1445 −0.333909
\(924\) 0 0
\(925\) −5.67685 −0.186654
\(926\) 0 0
\(927\) 42.5422 1.39727
\(928\) 0 0
\(929\) 51.9229 1.70354 0.851768 0.523919i \(-0.175531\pi\)
0.851768 + 0.523919i \(0.175531\pi\)
\(930\) 0 0
\(931\) −18.0507 −0.591587
\(932\) 0 0
\(933\) −9.88517 −0.323626
\(934\) 0 0
\(935\) 3.49696 0.114363
\(936\) 0 0
\(937\) 44.2471 1.44549 0.722745 0.691115i \(-0.242880\pi\)
0.722745 + 0.691115i \(0.242880\pi\)
\(938\) 0 0
\(939\) 14.7420 0.481088
\(940\) 0 0
\(941\) 44.5218 1.45137 0.725684 0.688028i \(-0.241524\pi\)
0.725684 + 0.688028i \(0.241524\pi\)
\(942\) 0 0
\(943\) −9.50612 −0.309562
\(944\) 0 0
\(945\) −10.0998 −0.328547
\(946\) 0 0
\(947\) −4.36074 −0.141705 −0.0708524 0.997487i \(-0.522572\pi\)
−0.0708524 + 0.997487i \(0.522572\pi\)
\(948\) 0 0
\(949\) −9.43277 −0.306201
\(950\) 0 0
\(951\) 6.20663 0.201264
\(952\) 0 0
\(953\) 41.1795 1.33393 0.666967 0.745087i \(-0.267592\pi\)
0.666967 + 0.745087i \(0.267592\pi\)
\(954\) 0 0
\(955\) −15.5135 −0.502006
\(956\) 0 0
\(957\) 2.29540 0.0741997
\(958\) 0 0
\(959\) −23.4620 −0.757626
\(960\) 0 0
\(961\) 30.4545 0.982402
\(962\) 0 0
\(963\) −44.9783 −1.44941
\(964\) 0 0
\(965\) 43.6749 1.40594
\(966\) 0 0
\(967\) −28.1059 −0.903826 −0.451913 0.892062i \(-0.649258\pi\)
−0.451913 + 0.892062i \(0.649258\pi\)
\(968\) 0 0
\(969\) −1.81387 −0.0582700
\(970\) 0 0
\(971\) 1.54825 0.0496857 0.0248428 0.999691i \(-0.492091\pi\)
0.0248428 + 0.999691i \(0.492091\pi\)
\(972\) 0 0
\(973\) −31.4607 −1.00858
\(974\) 0 0
\(975\) −1.30572 −0.0418167
\(976\) 0 0
\(977\) 37.7224 1.20685 0.603423 0.797421i \(-0.293803\pi\)
0.603423 + 0.797421i \(0.293803\pi\)
\(978\) 0 0
\(979\) −21.2546 −0.679300
\(980\) 0 0
\(981\) 19.1928 0.612778
\(982\) 0 0
\(983\) 4.83845 0.154323 0.0771614 0.997019i \(-0.475414\pi\)
0.0771614 + 0.997019i \(0.475414\pi\)
\(984\) 0 0
\(985\) −29.1288 −0.928119
\(986\) 0 0
\(987\) −6.20091 −0.197377
\(988\) 0 0
\(989\) −54.4676 −1.73197
\(990\) 0 0
\(991\) 6.16037 0.195691 0.0978454 0.995202i \(-0.468805\pi\)
0.0978454 + 0.995202i \(0.468805\pi\)
\(992\) 0 0
\(993\) −1.62694 −0.0516294
\(994\) 0 0
\(995\) −23.0590 −0.731020
\(996\) 0 0
\(997\) −31.3698 −0.993491 −0.496745 0.867896i \(-0.665472\pi\)
−0.496745 + 0.867896i \(0.665472\pi\)
\(998\) 0 0
\(999\) 15.8686 0.502061
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 \(a_p\))