Properties

Label 8020.2.a.c.1.18
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.05681 q^{3} -1.00000 q^{5} +3.74444 q^{7} -1.88316 q^{9} +O(q^{10})\) \(q+1.05681 q^{3} -1.00000 q^{5} +3.74444 q^{7} -1.88316 q^{9} -4.91712 q^{11} -1.25004 q^{13} -1.05681 q^{15} +3.28289 q^{17} +2.70701 q^{19} +3.95715 q^{21} +0.0904882 q^{23} +1.00000 q^{25} -5.16056 q^{27} -3.78883 q^{29} -2.75334 q^{31} -5.19645 q^{33} -3.74444 q^{35} +6.68433 q^{37} -1.32105 q^{39} -8.86049 q^{41} +9.41235 q^{43} +1.88316 q^{45} -4.56323 q^{47} +7.02080 q^{49} +3.46938 q^{51} -12.5056 q^{53} +4.91712 q^{55} +2.86079 q^{57} +6.26801 q^{59} +5.05352 q^{61} -7.05136 q^{63} +1.25004 q^{65} +2.00243 q^{67} +0.0956287 q^{69} -3.08275 q^{71} +1.79679 q^{73} +1.05681 q^{75} -18.4118 q^{77} -6.31202 q^{79} +0.195754 q^{81} -14.3011 q^{83} -3.28289 q^{85} -4.00407 q^{87} -6.23627 q^{89} -4.68069 q^{91} -2.90975 q^{93} -2.70701 q^{95} -1.66497 q^{97} +9.25971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + O(q^{10}) \) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + 2q^{11} + 3q^{13} - 3q^{15} - 10q^{17} - 2q^{19} - 12q^{21} - 23q^{23} + 28q^{25} + 9q^{27} - 37q^{29} - 11q^{31} + 2q^{33} + 4q^{35} - 3q^{37} - 19q^{39} - 30q^{41} + 13q^{43} - 17q^{45} - 15q^{47} + 12q^{49} - 8q^{51} - 35q^{53} - 2q^{55} - 22q^{57} - q^{59} - 33q^{61} - 20q^{63} - 3q^{65} + 19q^{67} - 8q^{69} - 31q^{71} + 31q^{73} + 3q^{75} - 42q^{77} - 29q^{79} - 36q^{81} + 14q^{83} + 10q^{85} - 32q^{87} - 32q^{89} - 7q^{91} - 11q^{93} + 2q^{95} + 2q^{97} - 39q^{99} + O(q^{100}) \)

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
\(3\) 1.05681 0.610148 0.305074 0.952329i \(-0.401319\pi\)
0.305074 + 0.952329i \(0.401319\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.74444 1.41526 0.707632 0.706581i \(-0.249764\pi\)
0.707632 + 0.706581i \(0.249764\pi\)
\(8\) 0 0
\(9\) −1.88316 −0.627719
\(10\) 0 0
\(11\) −4.91712 −1.48257 −0.741283 0.671192i \(-0.765783\pi\)
−0.741283 + 0.671192i \(0.765783\pi\)
\(12\) 0 0
\(13\) −1.25004 −0.346698 −0.173349 0.984860i \(-0.555459\pi\)
−0.173349 + 0.984860i \(0.555459\pi\)
\(14\) 0 0
\(15\) −1.05681 −0.272867
\(16\) 0 0
\(17\) 3.28289 0.796218 0.398109 0.917338i \(-0.369667\pi\)
0.398109 + 0.917338i \(0.369667\pi\)
\(18\) 0 0
\(19\) 2.70701 0.621030 0.310515 0.950568i \(-0.399498\pi\)
0.310515 + 0.950568i \(0.399498\pi\)
\(20\) 0 0
\(21\) 3.95715 0.863521
\(22\) 0 0
\(23\) 0.0904882 0.0188681 0.00943405 0.999955i \(-0.496997\pi\)
0.00943405 + 0.999955i \(0.496997\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.16056 −0.993150
\(28\) 0 0
\(29\) −3.78883 −0.703569 −0.351784 0.936081i \(-0.614425\pi\)
−0.351784 + 0.936081i \(0.614425\pi\)
\(30\) 0 0
\(31\) −2.75334 −0.494514 −0.247257 0.968950i \(-0.579529\pi\)
−0.247257 + 0.968950i \(0.579529\pi\)
\(32\) 0 0
\(33\) −5.19645 −0.904586
\(34\) 0 0
\(35\) −3.74444 −0.632925
\(36\) 0 0
\(37\) 6.68433 1.09890 0.549448 0.835528i \(-0.314838\pi\)
0.549448 + 0.835528i \(0.314838\pi\)
\(38\) 0 0
\(39\) −1.32105 −0.211537
\(40\) 0 0
\(41\) −8.86049 −1.38378 −0.691888 0.722005i \(-0.743221\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(42\) 0 0
\(43\) 9.41235 1.43537 0.717685 0.696368i \(-0.245202\pi\)
0.717685 + 0.696368i \(0.245202\pi\)
\(44\) 0 0
\(45\) 1.88316 0.280725
\(46\) 0 0
\(47\) −4.56323 −0.665616 −0.332808 0.942995i \(-0.607996\pi\)
−0.332808 + 0.942995i \(0.607996\pi\)
\(48\) 0 0
\(49\) 7.02080 1.00297
\(50\) 0 0
\(51\) 3.46938 0.485811
\(52\) 0 0
\(53\) −12.5056 −1.71777 −0.858885 0.512168i \(-0.828843\pi\)
−0.858885 + 0.512168i \(0.828843\pi\)
\(54\) 0 0
\(55\) 4.91712 0.663024
\(56\) 0 0
\(57\) 2.86079 0.378921
\(58\) 0 0
\(59\) 6.26801 0.816026 0.408013 0.912976i \(-0.366222\pi\)
0.408013 + 0.912976i \(0.366222\pi\)
\(60\) 0 0
\(61\) 5.05352 0.647037 0.323519 0.946222i \(-0.395134\pi\)
0.323519 + 0.946222i \(0.395134\pi\)
\(62\) 0 0
\(63\) −7.05136 −0.888388
\(64\) 0 0
\(65\) 1.25004 0.155048
\(66\) 0 0
\(67\) 2.00243 0.244635 0.122318 0.992491i \(-0.460967\pi\)
0.122318 + 0.992491i \(0.460967\pi\)
\(68\) 0 0
\(69\) 0.0956287 0.0115123
\(70\) 0 0
\(71\) −3.08275 −0.365855 −0.182927 0.983126i \(-0.558557\pi\)
−0.182927 + 0.983126i \(0.558557\pi\)
\(72\) 0 0
\(73\) 1.79679 0.210299 0.105149 0.994456i \(-0.466468\pi\)
0.105149 + 0.994456i \(0.466468\pi\)
\(74\) 0 0
\(75\) 1.05681 0.122030
\(76\) 0 0
\(77\) −18.4118 −2.09822
\(78\) 0 0
\(79\) −6.31202 −0.710158 −0.355079 0.934836i \(-0.615546\pi\)
−0.355079 + 0.934836i \(0.615546\pi\)
\(80\) 0 0
\(81\) 0.195754 0.0217504
\(82\) 0 0
\(83\) −14.3011 −1.56975 −0.784875 0.619655i \(-0.787273\pi\)
−0.784875 + 0.619655i \(0.787273\pi\)
\(84\) 0 0
\(85\) −3.28289 −0.356080
\(86\) 0 0
\(87\) −4.00407 −0.429281
\(88\) 0 0
\(89\) −6.23627 −0.661043 −0.330522 0.943798i \(-0.607225\pi\)
−0.330522 + 0.943798i \(0.607225\pi\)
\(90\) 0 0
\(91\) −4.68069 −0.490669
\(92\) 0 0
\(93\) −2.90975 −0.301727
\(94\) 0 0
\(95\) −2.70701 −0.277733
\(96\) 0 0
\(97\) −1.66497 −0.169053 −0.0845263 0.996421i \(-0.526938\pi\)
−0.0845263 + 0.996421i \(0.526938\pi\)
\(98\) 0 0
\(99\) 9.25971 0.930636
\(100\) 0 0
\(101\) −6.43910 −0.640715 −0.320357 0.947297i \(-0.603803\pi\)
−0.320357 + 0.947297i \(0.603803\pi\)
\(102\) 0 0
\(103\) −6.37796 −0.628439 −0.314219 0.949350i \(-0.601743\pi\)
−0.314219 + 0.949350i \(0.601743\pi\)
\(104\) 0 0
\(105\) −3.95715 −0.386178
\(106\) 0 0
\(107\) −8.00804 −0.774167 −0.387083 0.922045i \(-0.626517\pi\)
−0.387083 + 0.922045i \(0.626517\pi\)
\(108\) 0 0
\(109\) 11.0073 1.05430 0.527152 0.849771i \(-0.323260\pi\)
0.527152 + 0.849771i \(0.323260\pi\)
\(110\) 0 0
\(111\) 7.06405 0.670490
\(112\) 0 0
\(113\) −5.85815 −0.551089 −0.275544 0.961288i \(-0.588858\pi\)
−0.275544 + 0.961288i \(0.588858\pi\)
\(114\) 0 0
\(115\) −0.0904882 −0.00843807
\(116\) 0 0
\(117\) 2.35402 0.217629
\(118\) 0 0
\(119\) 12.2926 1.12686
\(120\) 0 0
\(121\) 13.1780 1.19800
\(122\) 0 0
\(123\) −9.36383 −0.844308
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.06006 −0.626479 −0.313240 0.949674i \(-0.601414\pi\)
−0.313240 + 0.949674i \(0.601414\pi\)
\(128\) 0 0
\(129\) 9.94705 0.875789
\(130\) 0 0
\(131\) 6.01709 0.525716 0.262858 0.964835i \(-0.415335\pi\)
0.262858 + 0.964835i \(0.415335\pi\)
\(132\) 0 0
\(133\) 10.1362 0.878922
\(134\) 0 0
\(135\) 5.16056 0.444150
\(136\) 0 0
\(137\) −9.93574 −0.848867 −0.424434 0.905459i \(-0.639527\pi\)
−0.424434 + 0.905459i \(0.639527\pi\)
\(138\) 0 0
\(139\) 7.63141 0.647288 0.323644 0.946179i \(-0.395092\pi\)
0.323644 + 0.946179i \(0.395092\pi\)
\(140\) 0 0
\(141\) −4.82246 −0.406124
\(142\) 0 0
\(143\) 6.14658 0.514003
\(144\) 0 0
\(145\) 3.78883 0.314646
\(146\) 0 0
\(147\) 7.41964 0.611961
\(148\) 0 0
\(149\) −5.89207 −0.482697 −0.241349 0.970438i \(-0.577590\pi\)
−0.241349 + 0.970438i \(0.577590\pi\)
\(150\) 0 0
\(151\) −3.05842 −0.248891 −0.124445 0.992226i \(-0.539715\pi\)
−0.124445 + 0.992226i \(0.539715\pi\)
\(152\) 0 0
\(153\) −6.18220 −0.499801
\(154\) 0 0
\(155\) 2.75334 0.221153
\(156\) 0 0
\(157\) −11.7973 −0.941526 −0.470763 0.882260i \(-0.656021\pi\)
−0.470763 + 0.882260i \(0.656021\pi\)
\(158\) 0 0
\(159\) −13.2160 −1.04809
\(160\) 0 0
\(161\) 0.338827 0.0267033
\(162\) 0 0
\(163\) −18.6332 −1.45946 −0.729731 0.683734i \(-0.760355\pi\)
−0.729731 + 0.683734i \(0.760355\pi\)
\(164\) 0 0
\(165\) 5.19645 0.404543
\(166\) 0 0
\(167\) 0.402683 0.0311606 0.0155803 0.999879i \(-0.495040\pi\)
0.0155803 + 0.999879i \(0.495040\pi\)
\(168\) 0 0
\(169\) −11.4374 −0.879800
\(170\) 0 0
\(171\) −5.09772 −0.389833
\(172\) 0 0
\(173\) 13.3812 1.01735 0.508676 0.860958i \(-0.330135\pi\)
0.508676 + 0.860958i \(0.330135\pi\)
\(174\) 0 0
\(175\) 3.74444 0.283053
\(176\) 0 0
\(177\) 6.62409 0.497897
\(178\) 0 0
\(179\) −6.32541 −0.472784 −0.236392 0.971658i \(-0.575965\pi\)
−0.236392 + 0.971658i \(0.575965\pi\)
\(180\) 0 0
\(181\) −4.99761 −0.371469 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(182\) 0 0
\(183\) 5.34060 0.394789
\(184\) 0 0
\(185\) −6.68433 −0.491441
\(186\) 0 0
\(187\) −16.1424 −1.18045
\(188\) 0 0
\(189\) −19.3234 −1.40557
\(190\) 0 0
\(191\) −22.6501 −1.63890 −0.819452 0.573148i \(-0.805722\pi\)
−0.819452 + 0.573148i \(0.805722\pi\)
\(192\) 0 0
\(193\) −4.94284 −0.355793 −0.177897 0.984049i \(-0.556929\pi\)
−0.177897 + 0.984049i \(0.556929\pi\)
\(194\) 0 0
\(195\) 1.32105 0.0946023
\(196\) 0 0
\(197\) 0.473887 0.0337630 0.0168815 0.999857i \(-0.494626\pi\)
0.0168815 + 0.999857i \(0.494626\pi\)
\(198\) 0 0
\(199\) 1.88098 0.133339 0.0666695 0.997775i \(-0.478763\pi\)
0.0666695 + 0.997775i \(0.478763\pi\)
\(200\) 0 0
\(201\) 2.11618 0.149264
\(202\) 0 0
\(203\) −14.1870 −0.995735
\(204\) 0 0
\(205\) 8.86049 0.618843
\(206\) 0 0
\(207\) −0.170404 −0.0118439
\(208\) 0 0
\(209\) −13.3107 −0.920719
\(210\) 0 0
\(211\) −17.5595 −1.20885 −0.604423 0.796663i \(-0.706596\pi\)
−0.604423 + 0.796663i \(0.706596\pi\)
\(212\) 0 0
\(213\) −3.25787 −0.223226
\(214\) 0 0
\(215\) −9.41235 −0.641917
\(216\) 0 0
\(217\) −10.3097 −0.699867
\(218\) 0 0
\(219\) 1.89886 0.128313
\(220\) 0 0
\(221\) −4.10374 −0.276047
\(222\) 0 0
\(223\) −19.6238 −1.31410 −0.657052 0.753845i \(-0.728197\pi\)
−0.657052 + 0.753845i \(0.728197\pi\)
\(224\) 0 0
\(225\) −1.88316 −0.125544
\(226\) 0 0
\(227\) 8.77326 0.582302 0.291151 0.956677i \(-0.405962\pi\)
0.291151 + 0.956677i \(0.405962\pi\)
\(228\) 0 0
\(229\) −0.782931 −0.0517375 −0.0258688 0.999665i \(-0.508235\pi\)
−0.0258688 + 0.999665i \(0.508235\pi\)
\(230\) 0 0
\(231\) −19.4578 −1.28023
\(232\) 0 0
\(233\) 1.17083 0.0767036 0.0383518 0.999264i \(-0.487789\pi\)
0.0383518 + 0.999264i \(0.487789\pi\)
\(234\) 0 0
\(235\) 4.56323 0.297672
\(236\) 0 0
\(237\) −6.67059 −0.433301
\(238\) 0 0
\(239\) 12.5557 0.812160 0.406080 0.913837i \(-0.366895\pi\)
0.406080 + 0.913837i \(0.366895\pi\)
\(240\) 0 0
\(241\) −6.55860 −0.422476 −0.211238 0.977435i \(-0.567750\pi\)
−0.211238 + 0.977435i \(0.567750\pi\)
\(242\) 0 0
\(243\) 15.6885 1.00642
\(244\) 0 0
\(245\) −7.02080 −0.448543
\(246\) 0 0
\(247\) −3.38386 −0.215310
\(248\) 0 0
\(249\) −15.1135 −0.957780
\(250\) 0 0
\(251\) −18.2710 −1.15325 −0.576627 0.817008i \(-0.695631\pi\)
−0.576627 + 0.817008i \(0.695631\pi\)
\(252\) 0 0
\(253\) −0.444941 −0.0279732
\(254\) 0 0
\(255\) −3.46938 −0.217261
\(256\) 0 0
\(257\) 4.25234 0.265254 0.132627 0.991166i \(-0.457659\pi\)
0.132627 + 0.991166i \(0.457659\pi\)
\(258\) 0 0
\(259\) 25.0290 1.55523
\(260\) 0 0
\(261\) 7.13497 0.441644
\(262\) 0 0
\(263\) 5.25857 0.324258 0.162129 0.986770i \(-0.448164\pi\)
0.162129 + 0.986770i \(0.448164\pi\)
\(264\) 0 0
\(265\) 12.5056 0.768211
\(266\) 0 0
\(267\) −6.59054 −0.403334
\(268\) 0 0
\(269\) 19.6671 1.19913 0.599563 0.800327i \(-0.295341\pi\)
0.599563 + 0.800327i \(0.295341\pi\)
\(270\) 0 0
\(271\) −2.94589 −0.178950 −0.0894751 0.995989i \(-0.528519\pi\)
−0.0894751 + 0.995989i \(0.528519\pi\)
\(272\) 0 0
\(273\) −4.94658 −0.299381
\(274\) 0 0
\(275\) −4.91712 −0.296513
\(276\) 0 0
\(277\) 15.3319 0.921207 0.460604 0.887606i \(-0.347633\pi\)
0.460604 + 0.887606i \(0.347633\pi\)
\(278\) 0 0
\(279\) 5.18496 0.310416
\(280\) 0 0
\(281\) 30.8526 1.84051 0.920256 0.391318i \(-0.127981\pi\)
0.920256 + 0.391318i \(0.127981\pi\)
\(282\) 0 0
\(283\) −14.3296 −0.851806 −0.425903 0.904769i \(-0.640044\pi\)
−0.425903 + 0.904769i \(0.640044\pi\)
\(284\) 0 0
\(285\) −2.86079 −0.169458
\(286\) 0 0
\(287\) −33.1775 −1.95841
\(288\) 0 0
\(289\) −6.22263 −0.366037
\(290\) 0 0
\(291\) −1.75956 −0.103147
\(292\) 0 0
\(293\) −0.312539 −0.0182587 −0.00912935 0.999958i \(-0.502906\pi\)
−0.00912935 + 0.999958i \(0.502906\pi\)
\(294\) 0 0
\(295\) −6.26801 −0.364938
\(296\) 0 0
\(297\) 25.3751 1.47241
\(298\) 0 0
\(299\) −0.113114 −0.00654153
\(300\) 0 0
\(301\) 35.2440 2.03143
\(302\) 0 0
\(303\) −6.80490 −0.390931
\(304\) 0 0
\(305\) −5.05352 −0.289364
\(306\) 0 0
\(307\) −28.3896 −1.62028 −0.810141 0.586235i \(-0.800610\pi\)
−0.810141 + 0.586235i \(0.800610\pi\)
\(308\) 0 0
\(309\) −6.74028 −0.383441
\(310\) 0 0
\(311\) 28.6739 1.62595 0.812973 0.582302i \(-0.197848\pi\)
0.812973 + 0.582302i \(0.197848\pi\)
\(312\) 0 0
\(313\) −20.9787 −1.18579 −0.592893 0.805282i \(-0.702014\pi\)
−0.592893 + 0.805282i \(0.702014\pi\)
\(314\) 0 0
\(315\) 7.05136 0.397299
\(316\) 0 0
\(317\) −6.89852 −0.387460 −0.193730 0.981055i \(-0.562059\pi\)
−0.193730 + 0.981055i \(0.562059\pi\)
\(318\) 0 0
\(319\) 18.6301 1.04309
\(320\) 0 0
\(321\) −8.46296 −0.472356
\(322\) 0 0
\(323\) 8.88681 0.494476
\(324\) 0 0
\(325\) −1.25004 −0.0693396
\(326\) 0 0
\(327\) 11.6326 0.643282
\(328\) 0 0
\(329\) −17.0867 −0.942022
\(330\) 0 0
\(331\) −1.06485 −0.0585296 −0.0292648 0.999572i \(-0.509317\pi\)
−0.0292648 + 0.999572i \(0.509317\pi\)
\(332\) 0 0
\(333\) −12.5876 −0.689798
\(334\) 0 0
\(335\) −2.00243 −0.109404
\(336\) 0 0
\(337\) 5.75140 0.313298 0.156649 0.987654i \(-0.449931\pi\)
0.156649 + 0.987654i \(0.449931\pi\)
\(338\) 0 0
\(339\) −6.19094 −0.336246
\(340\) 0 0
\(341\) 13.5385 0.733150
\(342\) 0 0
\(343\) 0.0778875 0.00420553
\(344\) 0 0
\(345\) −0.0956287 −0.00514847
\(346\) 0 0
\(347\) −7.99676 −0.429289 −0.214644 0.976692i \(-0.568859\pi\)
−0.214644 + 0.976692i \(0.568859\pi\)
\(348\) 0 0
\(349\) 13.0355 0.697772 0.348886 0.937165i \(-0.386560\pi\)
0.348886 + 0.937165i \(0.386560\pi\)
\(350\) 0 0
\(351\) 6.45089 0.344323
\(352\) 0 0
\(353\) 28.0474 1.49281 0.746406 0.665491i \(-0.231778\pi\)
0.746406 + 0.665491i \(0.231778\pi\)
\(354\) 0 0
\(355\) 3.08275 0.163615
\(356\) 0 0
\(357\) 12.9909 0.687551
\(358\) 0 0
\(359\) 15.7552 0.831527 0.415763 0.909473i \(-0.363514\pi\)
0.415763 + 0.909473i \(0.363514\pi\)
\(360\) 0 0
\(361\) −11.6721 −0.614321
\(362\) 0 0
\(363\) 13.9267 0.730960
\(364\) 0 0
\(365\) −1.79679 −0.0940484
\(366\) 0 0
\(367\) 2.82759 0.147599 0.0737994 0.997273i \(-0.476488\pi\)
0.0737994 + 0.997273i \(0.476488\pi\)
\(368\) 0 0
\(369\) 16.6857 0.868622
\(370\) 0 0
\(371\) −46.8263 −2.43110
\(372\) 0 0
\(373\) −3.53123 −0.182840 −0.0914200 0.995812i \(-0.529141\pi\)
−0.0914200 + 0.995812i \(0.529141\pi\)
\(374\) 0 0
\(375\) −1.05681 −0.0545733
\(376\) 0 0
\(377\) 4.73618 0.243926
\(378\) 0 0
\(379\) 17.4053 0.894052 0.447026 0.894521i \(-0.352483\pi\)
0.447026 + 0.894521i \(0.352483\pi\)
\(380\) 0 0
\(381\) −7.46113 −0.382245
\(382\) 0 0
\(383\) 15.9950 0.817309 0.408654 0.912689i \(-0.365998\pi\)
0.408654 + 0.912689i \(0.365998\pi\)
\(384\) 0 0
\(385\) 18.4118 0.938354
\(386\) 0 0
\(387\) −17.7249 −0.901009
\(388\) 0 0
\(389\) 25.7786 1.30703 0.653513 0.756916i \(-0.273295\pi\)
0.653513 + 0.756916i \(0.273295\pi\)
\(390\) 0 0
\(391\) 0.297063 0.0150231
\(392\) 0 0
\(393\) 6.35891 0.320764
\(394\) 0 0
\(395\) 6.31202 0.317592
\(396\) 0 0
\(397\) −13.8792 −0.696578 −0.348289 0.937387i \(-0.613237\pi\)
−0.348289 + 0.937387i \(0.613237\pi\)
\(398\) 0 0
\(399\) 10.7120 0.536273
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 3.44177 0.171447
\(404\) 0 0
\(405\) −0.195754 −0.00972708
\(406\) 0 0
\(407\) −32.8676 −1.62919
\(408\) 0 0
\(409\) −28.4614 −1.40733 −0.703663 0.710534i \(-0.748453\pi\)
−0.703663 + 0.710534i \(0.748453\pi\)
\(410\) 0 0
\(411\) −10.5002 −0.517935
\(412\) 0 0
\(413\) 23.4702 1.15489
\(414\) 0 0
\(415\) 14.3011 0.702013
\(416\) 0 0
\(417\) 8.06494 0.394942
\(418\) 0 0
\(419\) −6.10636 −0.298315 −0.149158 0.988813i \(-0.547656\pi\)
−0.149158 + 0.988813i \(0.547656\pi\)
\(420\) 0 0
\(421\) 10.7046 0.521709 0.260855 0.965378i \(-0.415996\pi\)
0.260855 + 0.965378i \(0.415996\pi\)
\(422\) 0 0
\(423\) 8.59328 0.417820
\(424\) 0 0
\(425\) 3.28289 0.159244
\(426\) 0 0
\(427\) 18.9226 0.915729
\(428\) 0 0
\(429\) 6.49576 0.313618
\(430\) 0 0
\(431\) −24.6637 −1.18801 −0.594003 0.804463i \(-0.702453\pi\)
−0.594003 + 0.804463i \(0.702453\pi\)
\(432\) 0 0
\(433\) 22.4493 1.07885 0.539423 0.842035i \(-0.318642\pi\)
0.539423 + 0.842035i \(0.318642\pi\)
\(434\) 0 0
\(435\) 4.00407 0.191980
\(436\) 0 0
\(437\) 0.244952 0.0117177
\(438\) 0 0
\(439\) −8.31761 −0.396978 −0.198489 0.980103i \(-0.563603\pi\)
−0.198489 + 0.980103i \(0.563603\pi\)
\(440\) 0 0
\(441\) −13.2213 −0.629584
\(442\) 0 0
\(443\) −26.5092 −1.25949 −0.629745 0.776802i \(-0.716841\pi\)
−0.629745 + 0.776802i \(0.716841\pi\)
\(444\) 0 0
\(445\) 6.23627 0.295628
\(446\) 0 0
\(447\) −6.22678 −0.294517
\(448\) 0 0
\(449\) −23.3969 −1.10417 −0.552084 0.833788i \(-0.686167\pi\)
−0.552084 + 0.833788i \(0.686167\pi\)
\(450\) 0 0
\(451\) 43.5681 2.05154
\(452\) 0 0
\(453\) −3.23216 −0.151860
\(454\) 0 0
\(455\) 4.68069 0.219434
\(456\) 0 0
\(457\) −9.81149 −0.458962 −0.229481 0.973313i \(-0.573703\pi\)
−0.229481 + 0.973313i \(0.573703\pi\)
\(458\) 0 0
\(459\) −16.9416 −0.790764
\(460\) 0 0
\(461\) 16.3078 0.759529 0.379764 0.925083i \(-0.376005\pi\)
0.379764 + 0.925083i \(0.376005\pi\)
\(462\) 0 0
\(463\) 18.3810 0.854238 0.427119 0.904195i \(-0.359529\pi\)
0.427119 + 0.904195i \(0.359529\pi\)
\(464\) 0 0
\(465\) 2.90975 0.134936
\(466\) 0 0
\(467\) 32.7463 1.51532 0.757660 0.652650i \(-0.226343\pi\)
0.757660 + 0.652650i \(0.226343\pi\)
\(468\) 0 0
\(469\) 7.49795 0.346223
\(470\) 0 0
\(471\) −12.4675 −0.574470
\(472\) 0 0
\(473\) −46.2816 −2.12803
\(474\) 0 0
\(475\) 2.70701 0.124206
\(476\) 0 0
\(477\) 23.5499 1.07828
\(478\) 0 0
\(479\) −17.3004 −0.790474 −0.395237 0.918579i \(-0.629338\pi\)
−0.395237 + 0.918579i \(0.629338\pi\)
\(480\) 0 0
\(481\) −8.35566 −0.380985
\(482\) 0 0
\(483\) 0.358075 0.0162930
\(484\) 0 0
\(485\) 1.66497 0.0756026
\(486\) 0 0
\(487\) −16.5025 −0.747799 −0.373899 0.927469i \(-0.621979\pi\)
−0.373899 + 0.927469i \(0.621979\pi\)
\(488\) 0 0
\(489\) −19.6917 −0.890488
\(490\) 0 0
\(491\) 36.9127 1.66585 0.832924 0.553387i \(-0.186665\pi\)
0.832924 + 0.553387i \(0.186665\pi\)
\(492\) 0 0
\(493\) −12.4383 −0.560194
\(494\) 0 0
\(495\) −9.25971 −0.416193
\(496\) 0 0
\(497\) −11.5431 −0.517781
\(498\) 0 0
\(499\) 4.32181 0.193471 0.0967355 0.995310i \(-0.469160\pi\)
0.0967355 + 0.995310i \(0.469160\pi\)
\(500\) 0 0
\(501\) 0.425559 0.0190126
\(502\) 0 0
\(503\) −19.4831 −0.868708 −0.434354 0.900742i \(-0.643023\pi\)
−0.434354 + 0.900742i \(0.643023\pi\)
\(504\) 0 0
\(505\) 6.43910 0.286536
\(506\) 0 0
\(507\) −12.0871 −0.536809
\(508\) 0 0
\(509\) 4.31667 0.191333 0.0956665 0.995413i \(-0.469502\pi\)
0.0956665 + 0.995413i \(0.469502\pi\)
\(510\) 0 0
\(511\) 6.72797 0.297628
\(512\) 0 0
\(513\) −13.9697 −0.616776
\(514\) 0 0
\(515\) 6.37796 0.281046
\(516\) 0 0
\(517\) 22.4379 0.986820
\(518\) 0 0
\(519\) 14.1413 0.620735
\(520\) 0 0
\(521\) 15.0172 0.657915 0.328957 0.944345i \(-0.393303\pi\)
0.328957 + 0.944345i \(0.393303\pi\)
\(522\) 0 0
\(523\) −11.8035 −0.516130 −0.258065 0.966128i \(-0.583085\pi\)
−0.258065 + 0.966128i \(0.583085\pi\)
\(524\) 0 0
\(525\) 3.95715 0.172704
\(526\) 0 0
\(527\) −9.03890 −0.393741
\(528\) 0 0
\(529\) −22.9918 −0.999644
\(530\) 0 0
\(531\) −11.8037 −0.512235
\(532\) 0 0
\(533\) 11.0759 0.479752
\(534\) 0 0
\(535\) 8.00804 0.346218
\(536\) 0 0
\(537\) −6.68475 −0.288468
\(538\) 0 0
\(539\) −34.5221 −1.48697
\(540\) 0 0
\(541\) −17.0641 −0.733645 −0.366822 0.930291i \(-0.619554\pi\)
−0.366822 + 0.930291i \(0.619554\pi\)
\(542\) 0 0
\(543\) −5.28151 −0.226651
\(544\) 0 0
\(545\) −11.0073 −0.471499
\(546\) 0 0
\(547\) −2.19782 −0.0939719 −0.0469859 0.998896i \(-0.514962\pi\)
−0.0469859 + 0.998896i \(0.514962\pi\)
\(548\) 0 0
\(549\) −9.51658 −0.406158
\(550\) 0 0
\(551\) −10.2564 −0.436938
\(552\) 0 0
\(553\) −23.6350 −1.00506
\(554\) 0 0
\(555\) −7.06405 −0.299852
\(556\) 0 0
\(557\) 2.02193 0.0856720 0.0428360 0.999082i \(-0.486361\pi\)
0.0428360 + 0.999082i \(0.486361\pi\)
\(558\) 0 0
\(559\) −11.7658 −0.497640
\(560\) 0 0
\(561\) −17.0594 −0.720247
\(562\) 0 0
\(563\) 11.0051 0.463809 0.231904 0.972739i \(-0.425504\pi\)
0.231904 + 0.972739i \(0.425504\pi\)
\(564\) 0 0
\(565\) 5.85815 0.246454
\(566\) 0 0
\(567\) 0.732987 0.0307826
\(568\) 0 0
\(569\) 17.3530 0.727476 0.363738 0.931501i \(-0.381500\pi\)
0.363738 + 0.931501i \(0.381500\pi\)
\(570\) 0 0
\(571\) 36.7034 1.53599 0.767995 0.640456i \(-0.221255\pi\)
0.767995 + 0.640456i \(0.221255\pi\)
\(572\) 0 0
\(573\) −23.9368 −0.999975
\(574\) 0 0
\(575\) 0.0904882 0.00377362
\(576\) 0 0
\(577\) −10.7384 −0.447045 −0.223523 0.974699i \(-0.571756\pi\)
−0.223523 + 0.974699i \(0.571756\pi\)
\(578\) 0 0
\(579\) −5.22363 −0.217087
\(580\) 0 0
\(581\) −53.5495 −2.22161
\(582\) 0 0
\(583\) 61.4913 2.54671
\(584\) 0 0
\(585\) −2.35402 −0.0973266
\(586\) 0 0
\(587\) −42.7896 −1.76612 −0.883059 0.469263i \(-0.844520\pi\)
−0.883059 + 0.469263i \(0.844520\pi\)
\(588\) 0 0
\(589\) −7.45330 −0.307108
\(590\) 0 0
\(591\) 0.500807 0.0206005
\(592\) 0 0
\(593\) −6.82762 −0.280377 −0.140188 0.990125i \(-0.544771\pi\)
−0.140188 + 0.990125i \(0.544771\pi\)
\(594\) 0 0
\(595\) −12.2926 −0.503946
\(596\) 0 0
\(597\) 1.98783 0.0813565
\(598\) 0 0
\(599\) 5.48398 0.224069 0.112035 0.993704i \(-0.464263\pi\)
0.112035 + 0.993704i \(0.464263\pi\)
\(600\) 0 0
\(601\) −19.5620 −0.797949 −0.398974 0.916962i \(-0.630634\pi\)
−0.398974 + 0.916962i \(0.630634\pi\)
\(602\) 0 0
\(603\) −3.77088 −0.153562
\(604\) 0 0
\(605\) −13.1780 −0.535764
\(606\) 0 0
\(607\) −43.3479 −1.75944 −0.879718 0.475495i \(-0.842269\pi\)
−0.879718 + 0.475495i \(0.842269\pi\)
\(608\) 0 0
\(609\) −14.9930 −0.607546
\(610\) 0 0
\(611\) 5.70421 0.230768
\(612\) 0 0
\(613\) 0.577104 0.0233090 0.0116545 0.999932i \(-0.496290\pi\)
0.0116545 + 0.999932i \(0.496290\pi\)
\(614\) 0 0
\(615\) 9.36383 0.377586
\(616\) 0 0
\(617\) −27.7804 −1.11840 −0.559199 0.829034i \(-0.688891\pi\)
−0.559199 + 0.829034i \(0.688891\pi\)
\(618\) 0 0
\(619\) 4.85248 0.195038 0.0975188 0.995234i \(-0.468909\pi\)
0.0975188 + 0.995234i \(0.468909\pi\)
\(620\) 0 0
\(621\) −0.466970 −0.0187389
\(622\) 0 0
\(623\) −23.3513 −0.935551
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −14.0668 −0.561775
\(628\) 0 0
\(629\) 21.9439 0.874961
\(630\) 0 0
\(631\) −29.7232 −1.18326 −0.591631 0.806209i \(-0.701516\pi\)
−0.591631 + 0.806209i \(0.701516\pi\)
\(632\) 0 0
\(633\) −18.5570 −0.737575
\(634\) 0 0
\(635\) 7.06006 0.280170
\(636\) 0 0
\(637\) −8.77626 −0.347728
\(638\) 0 0
\(639\) 5.80530 0.229654
\(640\) 0 0
\(641\) −25.1715 −0.994213 −0.497107 0.867690i \(-0.665604\pi\)
−0.497107 + 0.867690i \(0.665604\pi\)
\(642\) 0 0
\(643\) 19.2870 0.760603 0.380302 0.924863i \(-0.375820\pi\)
0.380302 + 0.924863i \(0.375820\pi\)
\(644\) 0 0
\(645\) −9.94705 −0.391665
\(646\) 0 0
\(647\) −3.41305 −0.134181 −0.0670904 0.997747i \(-0.521372\pi\)
−0.0670904 + 0.997747i \(0.521372\pi\)
\(648\) 0 0
\(649\) −30.8206 −1.20981
\(650\) 0 0
\(651\) −10.8954 −0.427023
\(652\) 0 0
\(653\) 22.6264 0.885441 0.442721 0.896660i \(-0.354013\pi\)
0.442721 + 0.896660i \(0.354013\pi\)
\(654\) 0 0
\(655\) −6.01709 −0.235107
\(656\) 0 0
\(657\) −3.38364 −0.132008
\(658\) 0 0
\(659\) 15.0752 0.587248 0.293624 0.955921i \(-0.405139\pi\)
0.293624 + 0.955921i \(0.405139\pi\)
\(660\) 0 0
\(661\) 20.8732 0.811873 0.405936 0.913901i \(-0.366945\pi\)
0.405936 + 0.913901i \(0.366945\pi\)
\(662\) 0 0
\(663\) −4.33686 −0.168430
\(664\) 0 0
\(665\) −10.1362 −0.393066
\(666\) 0 0
\(667\) −0.342845 −0.0132750
\(668\) 0 0
\(669\) −20.7385 −0.801798
\(670\) 0 0
\(671\) −24.8488 −0.959276
\(672\) 0 0
\(673\) 28.3789 1.09392 0.546962 0.837157i \(-0.315784\pi\)
0.546962 + 0.837157i \(0.315784\pi\)
\(674\) 0 0
\(675\) −5.16056 −0.198630
\(676\) 0 0
\(677\) −3.70226 −0.142289 −0.0711447 0.997466i \(-0.522665\pi\)
−0.0711447 + 0.997466i \(0.522665\pi\)
\(678\) 0 0
\(679\) −6.23439 −0.239254
\(680\) 0 0
\(681\) 9.27165 0.355291
\(682\) 0 0
\(683\) 17.0874 0.653833 0.326917 0.945053i \(-0.393990\pi\)
0.326917 + 0.945053i \(0.393990\pi\)
\(684\) 0 0
\(685\) 9.93574 0.379625
\(686\) 0 0
\(687\) −0.827407 −0.0315676
\(688\) 0 0
\(689\) 15.6324 0.595548
\(690\) 0 0
\(691\) 10.6496 0.405132 0.202566 0.979269i \(-0.435072\pi\)
0.202566 + 0.979269i \(0.435072\pi\)
\(692\) 0 0
\(693\) 34.6724 1.31709
\(694\) 0 0
\(695\) −7.63141 −0.289476
\(696\) 0 0
\(697\) −29.0880 −1.10179
\(698\) 0 0
\(699\) 1.23734 0.0468006
\(700\) 0 0
\(701\) −16.2117 −0.612309 −0.306154 0.951982i \(-0.599042\pi\)
−0.306154 + 0.951982i \(0.599042\pi\)
\(702\) 0 0
\(703\) 18.0945 0.682448
\(704\) 0 0
\(705\) 4.82246 0.181624
\(706\) 0 0
\(707\) −24.1108 −0.906780
\(708\) 0 0
\(709\) 1.40278 0.0526827 0.0263413 0.999653i \(-0.491614\pi\)
0.0263413 + 0.999653i \(0.491614\pi\)
\(710\) 0 0
\(711\) 11.8865 0.445780
\(712\) 0 0
\(713\) −0.249145 −0.00933054
\(714\) 0 0
\(715\) −6.14658 −0.229869
\(716\) 0 0
\(717\) 13.2690 0.495538
\(718\) 0 0
\(719\) −33.0603 −1.23294 −0.616470 0.787379i \(-0.711438\pi\)
−0.616470 + 0.787379i \(0.711438\pi\)
\(720\) 0 0
\(721\) −23.8819 −0.889407
\(722\) 0 0
\(723\) −6.93118 −0.257773
\(724\) 0 0
\(725\) −3.78883 −0.140714
\(726\) 0 0
\(727\) −45.8719 −1.70129 −0.850647 0.525737i \(-0.823790\pi\)
−0.850647 + 0.525737i \(0.823790\pi\)
\(728\) 0 0
\(729\) 15.9925 0.592316
\(730\) 0 0
\(731\) 30.8997 1.14287
\(732\) 0 0
\(733\) 47.0247 1.73690 0.868448 0.495780i \(-0.165118\pi\)
0.868448 + 0.495780i \(0.165118\pi\)
\(734\) 0 0
\(735\) −7.41964 −0.273677
\(736\) 0 0
\(737\) −9.84616 −0.362688
\(738\) 0 0
\(739\) 26.5585 0.976969 0.488484 0.872573i \(-0.337550\pi\)
0.488484 + 0.872573i \(0.337550\pi\)
\(740\) 0 0
\(741\) −3.57609 −0.131371
\(742\) 0 0
\(743\) 41.3300 1.51625 0.758125 0.652109i \(-0.226115\pi\)
0.758125 + 0.652109i \(0.226115\pi\)
\(744\) 0 0
\(745\) 5.89207 0.215869
\(746\) 0 0
\(747\) 26.9312 0.985361
\(748\) 0 0
\(749\) −29.9856 −1.09565
\(750\) 0 0
\(751\) 36.3593 1.32677 0.663385 0.748279i \(-0.269119\pi\)
0.663385 + 0.748279i \(0.269119\pi\)
\(752\) 0 0
\(753\) −19.3089 −0.703656
\(754\) 0 0
\(755\) 3.05842 0.111307
\(756\) 0 0
\(757\) −12.6905 −0.461246 −0.230623 0.973043i \(-0.574076\pi\)
−0.230623 + 0.973043i \(0.574076\pi\)
\(758\) 0 0
\(759\) −0.470217 −0.0170678
\(760\) 0 0
\(761\) 42.6066 1.54449 0.772244 0.635326i \(-0.219134\pi\)
0.772244 + 0.635326i \(0.219134\pi\)
\(762\) 0 0
\(763\) 41.2160 1.49212
\(764\) 0 0
\(765\) 6.18220 0.223518
\(766\) 0 0
\(767\) −7.83525 −0.282915
\(768\) 0 0
\(769\) 2.00878 0.0724385 0.0362193 0.999344i \(-0.488469\pi\)
0.0362193 + 0.999344i \(0.488469\pi\)
\(770\) 0 0
\(771\) 4.49390 0.161844
\(772\) 0 0
\(773\) −47.7404 −1.71710 −0.858551 0.512729i \(-0.828635\pi\)
−0.858551 + 0.512729i \(0.828635\pi\)
\(774\) 0 0
\(775\) −2.75334 −0.0989027
\(776\) 0 0
\(777\) 26.4509 0.948920
\(778\) 0 0
\(779\) −23.9854 −0.859367
\(780\) 0 0
\(781\) 15.1582 0.542404
\(782\) 0 0
\(783\) 19.5525 0.698749
\(784\) 0 0
\(785\) 11.7973 0.421063
\(786\) 0 0
\(787\) 29.1783 1.04009 0.520047 0.854138i \(-0.325914\pi\)
0.520047 + 0.854138i \(0.325914\pi\)
\(788\) 0 0
\(789\) 5.55730 0.197845
\(790\) 0 0
\(791\) −21.9355 −0.779936
\(792\) 0 0
\(793\) −6.31709 −0.224327
\(794\) 0 0
\(795\) 13.2160 0.468722
\(796\) 0 0
\(797\) −45.1039 −1.59766 −0.798832 0.601554i \(-0.794548\pi\)
−0.798832 + 0.601554i \(0.794548\pi\)
\(798\) 0 0
\(799\) −14.9806 −0.529975
\(800\) 0 0
\(801\) 11.7439 0.414949
\(802\) 0 0
\(803\) −8.83504 −0.311782
\(804\) 0 0
\(805\) −0.338827 −0.0119421
\(806\) 0 0
\(807\) 20.7844 0.731645
\(808\) 0 0
\(809\) −25.4823 −0.895909 −0.447955 0.894056i \(-0.647847\pi\)
−0.447955 + 0.894056i \(0.647847\pi\)
\(810\) 0 0
\(811\) 7.05225 0.247638 0.123819 0.992305i \(-0.460486\pi\)
0.123819 + 0.992305i \(0.460486\pi\)
\(812\) 0 0
\(813\) −3.11324 −0.109186
\(814\) 0 0
\(815\) 18.6332 0.652691
\(816\) 0 0
\(817\) 25.4793 0.891409
\(818\) 0 0
\(819\) 8.81447 0.308002
\(820\) 0 0
\(821\) −35.1278 −1.22597 −0.612983 0.790096i \(-0.710031\pi\)
−0.612983 + 0.790096i \(0.710031\pi\)
\(822\) 0 0
\(823\) 6.95512 0.242440 0.121220 0.992626i \(-0.461319\pi\)
0.121220 + 0.992626i \(0.461319\pi\)
\(824\) 0 0
\(825\) −5.19645 −0.180917
\(826\) 0 0
\(827\) −34.2821 −1.19211 −0.596054 0.802945i \(-0.703265\pi\)
−0.596054 + 0.802945i \(0.703265\pi\)
\(828\) 0 0
\(829\) −39.4277 −1.36938 −0.684691 0.728834i \(-0.740063\pi\)
−0.684691 + 0.728834i \(0.740063\pi\)
\(830\) 0 0
\(831\) 16.2029 0.562073
\(832\) 0 0
\(833\) 23.0485 0.798584
\(834\) 0 0
\(835\) −0.402683 −0.0139354
\(836\) 0 0
\(837\) 14.2088 0.491126
\(838\) 0 0
\(839\) 11.6032 0.400587 0.200294 0.979736i \(-0.435810\pi\)
0.200294 + 0.979736i \(0.435810\pi\)
\(840\) 0 0
\(841\) −14.6447 −0.504991
\(842\) 0 0
\(843\) 32.6053 1.12298
\(844\) 0 0
\(845\) 11.4374 0.393459
\(846\) 0 0
\(847\) 49.3444 1.69549
\(848\) 0 0
\(849\) −15.1436 −0.519728
\(850\) 0 0
\(851\) 0.604853 0.0207341
\(852\) 0 0
\(853\) −30.6383 −1.04904 −0.524518 0.851400i \(-0.675754\pi\)
−0.524518 + 0.851400i \(0.675754\pi\)
\(854\) 0 0
\(855\) 5.09772 0.174338
\(856\) 0 0
\(857\) −19.8084 −0.676640 −0.338320 0.941031i \(-0.609859\pi\)
−0.338320 + 0.941031i \(0.609859\pi\)
\(858\) 0 0
\(859\) 38.4445 1.31171 0.655854 0.754887i \(-0.272308\pi\)
0.655854 + 0.754887i \(0.272308\pi\)
\(860\) 0 0
\(861\) −35.0623 −1.19492
\(862\) 0 0
\(863\) 37.7715 1.28576 0.642878 0.765969i \(-0.277740\pi\)
0.642878 + 0.765969i \(0.277740\pi\)
\(864\) 0 0
\(865\) −13.3812 −0.454973
\(866\) 0 0
\(867\) −6.57612 −0.223337
\(868\) 0 0
\(869\) 31.0369 1.05286
\(870\) 0 0
\(871\) −2.50311 −0.0848145
\(872\) 0 0
\(873\) 3.13541 0.106118
\(874\) 0 0
\(875\) −3.74444 −0.126585
\(876\) 0 0
\(877\) 20.8955 0.705591 0.352796 0.935700i \(-0.385231\pi\)
0.352796 + 0.935700i \(0.385231\pi\)
\(878\) 0 0
\(879\) −0.330293 −0.0111405
\(880\) 0 0
\(881\) 18.2753 0.615709 0.307855 0.951433i \(-0.400389\pi\)
0.307855 + 0.951433i \(0.400389\pi\)
\(882\) 0 0
\(883\) 51.5596 1.73512 0.867559 0.497334i \(-0.165688\pi\)
0.867559 + 0.497334i \(0.165688\pi\)
\(884\) 0 0
\(885\) −6.62409 −0.222666
\(886\) 0 0
\(887\) −35.8071 −1.20229 −0.601143 0.799142i \(-0.705288\pi\)
−0.601143 + 0.799142i \(0.705288\pi\)
\(888\) 0 0
\(889\) −26.4359 −0.886633
\(890\) 0 0
\(891\) −0.962544 −0.0322464
\(892\) 0 0
\(893\) −12.3527 −0.413368
\(894\) 0 0
\(895\) 6.32541 0.211435
\(896\) 0 0
\(897\) −0.119539 −0.00399131
\(898\) 0 0
\(899\) 10.4319 0.347924
\(900\) 0 0
\(901\) −41.0544 −1.36772
\(902\) 0 0
\(903\) 37.2461 1.23947
\(904\) 0 0
\(905\) 4.99761 0.166126
\(906\) 0 0
\(907\) 27.2510 0.904855 0.452427 0.891801i \(-0.350558\pi\)
0.452427 + 0.891801i \(0.350558\pi\)
\(908\) 0 0
\(909\) 12.1258 0.402189
\(910\) 0 0
\(911\) −41.3107 −1.36869 −0.684343 0.729160i \(-0.739911\pi\)
−0.684343 + 0.729160i \(0.739911\pi\)
\(912\) 0 0
\(913\) 70.3202 2.32726
\(914\) 0 0
\(915\) −5.34060 −0.176555
\(916\) 0 0
\(917\) 22.5306 0.744026
\(918\) 0 0
\(919\) 2.71698 0.0896248 0.0448124 0.998995i \(-0.485731\pi\)
0.0448124 + 0.998995i \(0.485731\pi\)
\(920\) 0 0
\(921\) −30.0024 −0.988613
\(922\) 0 0
\(923\) 3.85355 0.126841
\(924\) 0 0
\(925\) 6.68433 0.219779
\(926\) 0 0
\(927\) 12.0107 0.394483
\(928\) 0 0
\(929\) −10.9603 −0.359596 −0.179798 0.983704i \(-0.557544\pi\)
−0.179798 + 0.983704i \(0.557544\pi\)
\(930\) 0 0
\(931\) 19.0054 0.622876
\(932\) 0 0
\(933\) 30.3028 0.992068
\(934\) 0 0
\(935\) 16.1424 0.527912
\(936\) 0 0
\(937\) 3.00923 0.0983073 0.0491536 0.998791i \(-0.484348\pi\)
0.0491536 + 0.998791i \(0.484348\pi\)
\(938\) 0 0
\(939\) −22.1704 −0.723505
\(940\) 0 0
\(941\) −13.4967 −0.439978 −0.219989 0.975502i \(-0.570602\pi\)
−0.219989 + 0.975502i \(0.570602\pi\)
\(942\) 0 0
\(943\) −0.801770 −0.0261092
\(944\) 0 0
\(945\) 19.3234 0.628590
\(946\) 0 0
\(947\) −44.6148 −1.44979 −0.724893 0.688862i \(-0.758111\pi\)
−0.724893 + 0.688862i \(0.758111\pi\)
\(948\) 0 0
\(949\) −2.24606 −0.0729101
\(950\) 0 0
\(951\) −7.29041 −0.236408
\(952\) 0 0
\(953\) 19.3972 0.628337 0.314168 0.949367i \(-0.398274\pi\)
0.314168 + 0.949367i \(0.398274\pi\)
\(954\) 0 0
\(955\) 22.6501 0.732940
\(956\) 0 0
\(957\) 19.6885 0.636438
\(958\) 0 0
\(959\) −37.2037 −1.20137
\(960\) 0 0
\(961\) −23.4191 −0.755456
\(962\) 0 0
\(963\) 15.0804 0.485959
\(964\) 0 0
\(965\) 4.94284 0.159116
\(966\) 0 0
\(967\) −5.54759 −0.178399 −0.0891993 0.996014i \(-0.528431\pi\)
−0.0891993 + 0.996014i \(0.528431\pi\)
\(968\) 0 0
\(969\) 9.39165 0.301703
\(970\) 0 0
\(971\) 53.0446 1.70228 0.851140 0.524938i \(-0.175912\pi\)
0.851140 + 0.524938i \(0.175912\pi\)
\(972\) 0 0
\(973\) 28.5753 0.916083
\(974\) 0 0
\(975\) −1.32105 −0.0423074
\(976\) 0 0
\(977\) 37.7604 1.20806 0.604032 0.796960i \(-0.293560\pi\)
0.604032 + 0.796960i \(0.293560\pi\)
\(978\) 0 0
\(979\) 30.6645 0.980041
\(980\) 0 0
\(981\) −20.7284 −0.661807
\(982\) 0 0
\(983\) 1.18374 0.0377556 0.0188778 0.999822i \(-0.493991\pi\)
0.0188778 + 0.999822i \(0.493991\pi\)
\(984\) 0 0
\(985\) −0.473887 −0.0150993
\(986\) 0 0
\(987\) −18.0574 −0.574773
\(988\) 0 0
\(989\) 0.851707 0.0270827
\(990\) 0 0
\(991\) −44.3559 −1.40901 −0.704505 0.709699i \(-0.748831\pi\)
−0.704505 + 0.709699i \(0.748831\pi\)
\(992\) 0 0
\(993\) −1.12535 −0.0357118
\(994\) 0 0
\(995\) −1.88098 −0.0596310
\(996\) 0 0
\(997\) 40.8454 1.29359 0.646794 0.762665i \(-0.276110\pi\)
0.646794 + 0.762665i \(0.276110\pi\)
\(998\) 0 0
\(999\) −34.4949 −1.09137
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 \(a_p\))