Properties

Label 8020.2.a.c.1.12
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 1.12
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.324068 q^{3}\) \(-1.00000 q^{5}\) \(-1.35293 q^{7}\) \(-2.89498 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.324068 q^{3}\) \(-1.00000 q^{5}\) \(-1.35293 q^{7}\) \(-2.89498 q^{9}\) \(-2.28388 q^{11}\) \(-1.54867 q^{13}\) \(+0.324068 q^{15}\) \(+7.82804 q^{17}\) \(+4.53890 q^{19}\) \(+0.438440 q^{21}\) \(+0.446041 q^{23}\) \(+1.00000 q^{25}\) \(+1.91037 q^{27}\) \(+2.54869 q^{29}\) \(-4.39570 q^{31}\) \(+0.740131 q^{33}\) \(+1.35293 q^{35}\) \(-5.52615 q^{37}\) \(+0.501874 q^{39}\) \(+2.55237 q^{41}\) \(-1.78802 q^{43}\) \(+2.89498 q^{45}\) \(-5.32558 q^{47}\) \(-5.16959 q^{49}\) \(-2.53682 q^{51}\) \(+0.0646043 q^{53}\) \(+2.28388 q^{55}\) \(-1.47091 q^{57}\) \(+8.28181 q^{59}\) \(-4.00052 q^{61}\) \(+3.91669 q^{63}\) \(+1.54867 q^{65}\) \(+12.9447 q^{67}\) \(-0.144548 q^{69}\) \(+10.6888 q^{71}\) \(-8.01456 q^{73}\) \(-0.324068 q^{75}\) \(+3.08992 q^{77}\) \(+2.47993 q^{79}\) \(+8.06585 q^{81}\) \(-4.09191 q^{83}\) \(-7.82804 q^{85}\) \(-0.825948 q^{87}\) \(+8.32346 q^{89}\) \(+2.09524 q^{91}\) \(+1.42450 q^{93}\) \(-4.53890 q^{95}\) \(+13.1809 q^{97}\) \(+6.61178 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.324068 −0.187101 −0.0935503 0.995615i \(-0.529822\pi\)
−0.0935503 + 0.995615i \(0.529822\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.35293 −0.511358 −0.255679 0.966762i \(-0.582299\pi\)
−0.255679 + 0.966762i \(0.582299\pi\)
\(8\) 0 0
\(9\) −2.89498 −0.964993
\(10\) 0 0
\(11\) −2.28388 −0.688615 −0.344307 0.938857i \(-0.611886\pi\)
−0.344307 + 0.938857i \(0.611886\pi\)
\(12\) 0 0
\(13\) −1.54867 −0.429524 −0.214762 0.976666i \(-0.568898\pi\)
−0.214762 + 0.976666i \(0.568898\pi\)
\(14\) 0 0
\(15\) 0.324068 0.0836740
\(16\) 0 0
\(17\) 7.82804 1.89858 0.949289 0.314403i \(-0.101804\pi\)
0.949289 + 0.314403i \(0.101804\pi\)
\(18\) 0 0
\(19\) 4.53890 1.04129 0.520647 0.853772i \(-0.325691\pi\)
0.520647 + 0.853772i \(0.325691\pi\)
\(20\) 0 0
\(21\) 0.438440 0.0956754
\(22\) 0 0
\(23\) 0.446041 0.0930060 0.0465030 0.998918i \(-0.485192\pi\)
0.0465030 + 0.998918i \(0.485192\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.91037 0.367652
\(28\) 0 0
\(29\) 2.54869 0.473279 0.236640 0.971597i \(-0.423954\pi\)
0.236640 + 0.971597i \(0.423954\pi\)
\(30\) 0 0
\(31\) −4.39570 −0.789491 −0.394745 0.918791i \(-0.629167\pi\)
−0.394745 + 0.918791i \(0.629167\pi\)
\(32\) 0 0
\(33\) 0.740131 0.128840
\(34\) 0 0
\(35\) 1.35293 0.228686
\(36\) 0 0
\(37\) −5.52615 −0.908494 −0.454247 0.890876i \(-0.650092\pi\)
−0.454247 + 0.890876i \(0.650092\pi\)
\(38\) 0 0
\(39\) 0.501874 0.0803642
\(40\) 0 0
\(41\) 2.55237 0.398613 0.199307 0.979937i \(-0.436131\pi\)
0.199307 + 0.979937i \(0.436131\pi\)
\(42\) 0 0
\(43\) −1.78802 −0.272670 −0.136335 0.990663i \(-0.543532\pi\)
−0.136335 + 0.990663i \(0.543532\pi\)
\(44\) 0 0
\(45\) 2.89498 0.431558
\(46\) 0 0
\(47\) −5.32558 −0.776816 −0.388408 0.921488i \(-0.626975\pi\)
−0.388408 + 0.921488i \(0.626975\pi\)
\(48\) 0 0
\(49\) −5.16959 −0.738513
\(50\) 0 0
\(51\) −2.53682 −0.355225
\(52\) 0 0
\(53\) 0.0646043 0.00887408 0.00443704 0.999990i \(-0.498588\pi\)
0.00443704 + 0.999990i \(0.498588\pi\)
\(54\) 0 0
\(55\) 2.28388 0.307958
\(56\) 0 0
\(57\) −1.47091 −0.194827
\(58\) 0 0
\(59\) 8.28181 1.07820 0.539100 0.842242i \(-0.318765\pi\)
0.539100 + 0.842242i \(0.318765\pi\)
\(60\) 0 0
\(61\) −4.00052 −0.512214 −0.256107 0.966648i \(-0.582440\pi\)
−0.256107 + 0.966648i \(0.582440\pi\)
\(62\) 0 0
\(63\) 3.91669 0.493457
\(64\) 0 0
\(65\) 1.54867 0.192089
\(66\) 0 0
\(67\) 12.9447 1.58145 0.790723 0.612174i \(-0.209705\pi\)
0.790723 + 0.612174i \(0.209705\pi\)
\(68\) 0 0
\(69\) −0.144548 −0.0174015
\(70\) 0 0
\(71\) 10.6888 1.26853 0.634265 0.773116i \(-0.281303\pi\)
0.634265 + 0.773116i \(0.281303\pi\)
\(72\) 0 0
\(73\) −8.01456 −0.938033 −0.469016 0.883189i \(-0.655392\pi\)
−0.469016 + 0.883189i \(0.655392\pi\)
\(74\) 0 0
\(75\) −0.324068 −0.0374201
\(76\) 0 0
\(77\) 3.08992 0.352129
\(78\) 0 0
\(79\) 2.47993 0.279014 0.139507 0.990221i \(-0.455448\pi\)
0.139507 + 0.990221i \(0.455448\pi\)
\(80\) 0 0
\(81\) 8.06585 0.896206
\(82\) 0 0
\(83\) −4.09191 −0.449146 −0.224573 0.974457i \(-0.572099\pi\)
−0.224573 + 0.974457i \(0.572099\pi\)
\(84\) 0 0
\(85\) −7.82804 −0.849070
\(86\) 0 0
\(87\) −0.825948 −0.0885509
\(88\) 0 0
\(89\) 8.32346 0.882285 0.441143 0.897437i \(-0.354573\pi\)
0.441143 + 0.897437i \(0.354573\pi\)
\(90\) 0 0
\(91\) 2.09524 0.219640
\(92\) 0 0
\(93\) 1.42450 0.147714
\(94\) 0 0
\(95\) −4.53890 −0.465681
\(96\) 0 0
\(97\) 13.1809 1.33832 0.669158 0.743120i \(-0.266655\pi\)
0.669158 + 0.743120i \(0.266655\pi\)
\(98\) 0 0
\(99\) 6.61178 0.664509
\(100\) 0 0
\(101\) 5.23850 0.521250 0.260625 0.965440i \(-0.416071\pi\)
0.260625 + 0.965440i \(0.416071\pi\)
\(102\) 0 0
\(103\) 5.76758 0.568297 0.284148 0.958780i \(-0.408289\pi\)
0.284148 + 0.958780i \(0.408289\pi\)
\(104\) 0 0
\(105\) −0.438440 −0.0427873
\(106\) 0 0
\(107\) 1.21818 0.117766 0.0588829 0.998265i \(-0.481246\pi\)
0.0588829 + 0.998265i \(0.481246\pi\)
\(108\) 0 0
\(109\) −10.1815 −0.975210 −0.487605 0.873064i \(-0.662129\pi\)
−0.487605 + 0.873064i \(0.662129\pi\)
\(110\) 0 0
\(111\) 1.79085 0.169980
\(112\) 0 0
\(113\) 4.07269 0.383126 0.191563 0.981480i \(-0.438644\pi\)
0.191563 + 0.981480i \(0.438644\pi\)
\(114\) 0 0
\(115\) −0.446041 −0.0415936
\(116\) 0 0
\(117\) 4.48337 0.414488
\(118\) 0 0
\(119\) −10.5908 −0.970853
\(120\) 0 0
\(121\) −5.78391 −0.525810
\(122\) 0 0
\(123\) −0.827141 −0.0745808
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.7603 −0.954822 −0.477411 0.878680i \(-0.658425\pi\)
−0.477411 + 0.878680i \(0.658425\pi\)
\(128\) 0 0
\(129\) 0.579440 0.0510168
\(130\) 0 0
\(131\) −12.5848 −1.09954 −0.549771 0.835315i \(-0.685285\pi\)
−0.549771 + 0.835315i \(0.685285\pi\)
\(132\) 0 0
\(133\) −6.14079 −0.532474
\(134\) 0 0
\(135\) −1.91037 −0.164419
\(136\) 0 0
\(137\) −12.0756 −1.03169 −0.515843 0.856683i \(-0.672521\pi\)
−0.515843 + 0.856683i \(0.672521\pi\)
\(138\) 0 0
\(139\) 11.0398 0.936387 0.468193 0.883626i \(-0.344905\pi\)
0.468193 + 0.883626i \(0.344905\pi\)
\(140\) 0 0
\(141\) 1.72585 0.145343
\(142\) 0 0
\(143\) 3.53697 0.295776
\(144\) 0 0
\(145\) −2.54869 −0.211657
\(146\) 0 0
\(147\) 1.67530 0.138176
\(148\) 0 0
\(149\) 6.04694 0.495385 0.247692 0.968839i \(-0.420328\pi\)
0.247692 + 0.968839i \(0.420328\pi\)
\(150\) 0 0
\(151\) −5.39115 −0.438725 −0.219363 0.975643i \(-0.570398\pi\)
−0.219363 + 0.975643i \(0.570398\pi\)
\(152\) 0 0
\(153\) −22.6620 −1.83212
\(154\) 0 0
\(155\) 4.39570 0.353071
\(156\) 0 0
\(157\) −20.2708 −1.61779 −0.808894 0.587955i \(-0.799933\pi\)
−0.808894 + 0.587955i \(0.799933\pi\)
\(158\) 0 0
\(159\) −0.0209362 −0.00166035
\(160\) 0 0
\(161\) −0.603461 −0.0475594
\(162\) 0 0
\(163\) 12.0931 0.947202 0.473601 0.880740i \(-0.342954\pi\)
0.473601 + 0.880740i \(0.342954\pi\)
\(164\) 0 0
\(165\) −0.740131 −0.0576191
\(166\) 0 0
\(167\) −3.51510 −0.272007 −0.136003 0.990708i \(-0.543426\pi\)
−0.136003 + 0.990708i \(0.543426\pi\)
\(168\) 0 0
\(169\) −10.6016 −0.815509
\(170\) 0 0
\(171\) −13.1400 −1.00484
\(172\) 0 0
\(173\) −15.6538 −1.19014 −0.595068 0.803675i \(-0.702875\pi\)
−0.595068 + 0.803675i \(0.702875\pi\)
\(174\) 0 0
\(175\) −1.35293 −0.102272
\(176\) 0 0
\(177\) −2.68387 −0.201732
\(178\) 0 0
\(179\) −4.73613 −0.353995 −0.176997 0.984211i \(-0.556638\pi\)
−0.176997 + 0.984211i \(0.556638\pi\)
\(180\) 0 0
\(181\) 2.57853 0.191661 0.0958303 0.995398i \(-0.469449\pi\)
0.0958303 + 0.995398i \(0.469449\pi\)
\(182\) 0 0
\(183\) 1.29644 0.0958356
\(184\) 0 0
\(185\) 5.52615 0.406291
\(186\) 0 0
\(187\) −17.8783 −1.30739
\(188\) 0 0
\(189\) −2.58459 −0.188001
\(190\) 0 0
\(191\) −19.1099 −1.38275 −0.691373 0.722498i \(-0.742994\pi\)
−0.691373 + 0.722498i \(0.742994\pi\)
\(192\) 0 0
\(193\) −2.69558 −0.194032 −0.0970159 0.995283i \(-0.530930\pi\)
−0.0970159 + 0.995283i \(0.530930\pi\)
\(194\) 0 0
\(195\) −0.501874 −0.0359400
\(196\) 0 0
\(197\) −1.74637 −0.124424 −0.0622120 0.998063i \(-0.519815\pi\)
−0.0622120 + 0.998063i \(0.519815\pi\)
\(198\) 0 0
\(199\) −6.19135 −0.438893 −0.219447 0.975624i \(-0.570425\pi\)
−0.219447 + 0.975624i \(0.570425\pi\)
\(200\) 0 0
\(201\) −4.19496 −0.295890
\(202\) 0 0
\(203\) −3.44818 −0.242015
\(204\) 0 0
\(205\) −2.55237 −0.178265
\(206\) 0 0
\(207\) −1.29128 −0.0897502
\(208\) 0 0
\(209\) −10.3663 −0.717050
\(210\) 0 0
\(211\) 4.40624 0.303338 0.151669 0.988431i \(-0.451535\pi\)
0.151669 + 0.988431i \(0.451535\pi\)
\(212\) 0 0
\(213\) −3.46390 −0.237343
\(214\) 0 0
\(215\) 1.78802 0.121942
\(216\) 0 0
\(217\) 5.94705 0.403712
\(218\) 0 0
\(219\) 2.59726 0.175507
\(220\) 0 0
\(221\) −12.1231 −0.815485
\(222\) 0 0
\(223\) −10.0677 −0.674182 −0.337091 0.941472i \(-0.609443\pi\)
−0.337091 + 0.941472i \(0.609443\pi\)
\(224\) 0 0
\(225\) −2.89498 −0.192999
\(226\) 0 0
\(227\) −18.9259 −1.25615 −0.628076 0.778152i \(-0.716157\pi\)
−0.628076 + 0.778152i \(0.716157\pi\)
\(228\) 0 0
\(229\) 5.73467 0.378958 0.189479 0.981885i \(-0.439320\pi\)
0.189479 + 0.981885i \(0.439320\pi\)
\(230\) 0 0
\(231\) −1.00134 −0.0658835
\(232\) 0 0
\(233\) 0.359235 0.0235342 0.0117671 0.999931i \(-0.496254\pi\)
0.0117671 + 0.999931i \(0.496254\pi\)
\(234\) 0 0
\(235\) 5.32558 0.347402
\(236\) 0 0
\(237\) −0.803665 −0.0522037
\(238\) 0 0
\(239\) −13.5999 −0.879701 −0.439851 0.898071i \(-0.644969\pi\)
−0.439851 + 0.898071i \(0.644969\pi\)
\(240\) 0 0
\(241\) −15.0718 −0.970857 −0.485428 0.874276i \(-0.661336\pi\)
−0.485428 + 0.874276i \(0.661336\pi\)
\(242\) 0 0
\(243\) −8.34500 −0.535332
\(244\) 0 0
\(245\) 5.16959 0.330273
\(246\) 0 0
\(247\) −7.02925 −0.447261
\(248\) 0 0
\(249\) 1.32606 0.0840354
\(250\) 0 0
\(251\) −12.8089 −0.808490 −0.404245 0.914651i \(-0.632466\pi\)
−0.404245 + 0.914651i \(0.632466\pi\)
\(252\) 0 0
\(253\) −1.01870 −0.0640453
\(254\) 0 0
\(255\) 2.53682 0.158862
\(256\) 0 0
\(257\) 23.1041 1.44119 0.720597 0.693355i \(-0.243868\pi\)
0.720597 + 0.693355i \(0.243868\pi\)
\(258\) 0 0
\(259\) 7.47648 0.464566
\(260\) 0 0
\(261\) −7.37840 −0.456711
\(262\) 0 0
\(263\) −6.90942 −0.426053 −0.213026 0.977046i \(-0.568332\pi\)
−0.213026 + 0.977046i \(0.568332\pi\)
\(264\) 0 0
\(265\) −0.0646043 −0.00396861
\(266\) 0 0
\(267\) −2.69737 −0.165076
\(268\) 0 0
\(269\) −16.0076 −0.975999 −0.488000 0.872844i \(-0.662273\pi\)
−0.488000 + 0.872844i \(0.662273\pi\)
\(270\) 0 0
\(271\) −12.1477 −0.737921 −0.368961 0.929445i \(-0.620286\pi\)
−0.368961 + 0.929445i \(0.620286\pi\)
\(272\) 0 0
\(273\) −0.678999 −0.0410949
\(274\) 0 0
\(275\) −2.28388 −0.137723
\(276\) 0 0
\(277\) −19.9737 −1.20011 −0.600053 0.799960i \(-0.704854\pi\)
−0.600053 + 0.799960i \(0.704854\pi\)
\(278\) 0 0
\(279\) 12.7255 0.761853
\(280\) 0 0
\(281\) −10.6807 −0.637157 −0.318578 0.947896i \(-0.603205\pi\)
−0.318578 + 0.947896i \(0.603205\pi\)
\(282\) 0 0
\(283\) 0.732385 0.0435358 0.0217679 0.999763i \(-0.493071\pi\)
0.0217679 + 0.999763i \(0.493071\pi\)
\(284\) 0 0
\(285\) 1.47091 0.0871292
\(286\) 0 0
\(287\) −3.45317 −0.203834
\(288\) 0 0
\(289\) 44.2782 2.60460
\(290\) 0 0
\(291\) −4.27150 −0.250400
\(292\) 0 0
\(293\) 24.9233 1.45604 0.728018 0.685559i \(-0.240442\pi\)
0.728018 + 0.685559i \(0.240442\pi\)
\(294\) 0 0
\(295\) −8.28181 −0.482186
\(296\) 0 0
\(297\) −4.36306 −0.253170
\(298\) 0 0
\(299\) −0.690771 −0.0399483
\(300\) 0 0
\(301\) 2.41906 0.139432
\(302\) 0 0
\(303\) −1.69763 −0.0975262
\(304\) 0 0
\(305\) 4.00052 0.229069
\(306\) 0 0
\(307\) −5.62747 −0.321176 −0.160588 0.987021i \(-0.551339\pi\)
−0.160588 + 0.987021i \(0.551339\pi\)
\(308\) 0 0
\(309\) −1.86909 −0.106329
\(310\) 0 0
\(311\) −12.5854 −0.713653 −0.356827 0.934171i \(-0.616141\pi\)
−0.356827 + 0.934171i \(0.616141\pi\)
\(312\) 0 0
\(313\) −7.47883 −0.422728 −0.211364 0.977407i \(-0.567791\pi\)
−0.211364 + 0.977407i \(0.567791\pi\)
\(314\) 0 0
\(315\) −3.91669 −0.220681
\(316\) 0 0
\(317\) −18.4388 −1.03563 −0.517813 0.855494i \(-0.673254\pi\)
−0.517813 + 0.855494i \(0.673254\pi\)
\(318\) 0 0
\(319\) −5.82089 −0.325907
\(320\) 0 0
\(321\) −0.394773 −0.0220341
\(322\) 0 0
\(323\) 35.5307 1.97698
\(324\) 0 0
\(325\) −1.54867 −0.0859048
\(326\) 0 0
\(327\) 3.29950 0.182462
\(328\) 0 0
\(329\) 7.20511 0.397231
\(330\) 0 0
\(331\) 13.9905 0.768988 0.384494 0.923127i \(-0.374376\pi\)
0.384494 + 0.923127i \(0.374376\pi\)
\(332\) 0 0
\(333\) 15.9981 0.876691
\(334\) 0 0
\(335\) −12.9447 −0.707244
\(336\) 0 0
\(337\) −8.52906 −0.464608 −0.232304 0.972643i \(-0.574626\pi\)
−0.232304 + 0.972643i \(0.574626\pi\)
\(338\) 0 0
\(339\) −1.31983 −0.0716831
\(340\) 0 0
\(341\) 10.0392 0.543655
\(342\) 0 0
\(343\) 16.4646 0.889002
\(344\) 0 0
\(345\) 0.144548 0.00778218
\(346\) 0 0
\(347\) −6.21504 −0.333641 −0.166821 0.985987i \(-0.553350\pi\)
−0.166821 + 0.985987i \(0.553350\pi\)
\(348\) 0 0
\(349\) −10.6095 −0.567913 −0.283957 0.958837i \(-0.591647\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(350\) 0 0
\(351\) −2.95854 −0.157915
\(352\) 0 0
\(353\) −16.8299 −0.895763 −0.447881 0.894093i \(-0.647821\pi\)
−0.447881 + 0.894093i \(0.647821\pi\)
\(354\) 0 0
\(355\) −10.6888 −0.567304
\(356\) 0 0
\(357\) 3.43212 0.181647
\(358\) 0 0
\(359\) −26.7261 −1.41055 −0.705275 0.708933i \(-0.749177\pi\)
−0.705275 + 0.708933i \(0.749177\pi\)
\(360\) 0 0
\(361\) 1.60157 0.0842933
\(362\) 0 0
\(363\) 1.87438 0.0983793
\(364\) 0 0
\(365\) 8.01456 0.419501
\(366\) 0 0
\(367\) 23.5577 1.22970 0.614852 0.788643i \(-0.289216\pi\)
0.614852 + 0.788643i \(0.289216\pi\)
\(368\) 0 0
\(369\) −7.38906 −0.384659
\(370\) 0 0
\(371\) −0.0874048 −0.00453783
\(372\) 0 0
\(373\) 31.9026 1.65185 0.825926 0.563778i \(-0.190653\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(374\) 0 0
\(375\) 0.324068 0.0167348
\(376\) 0 0
\(377\) −3.94708 −0.203285
\(378\) 0 0
\(379\) −26.8107 −1.37717 −0.688587 0.725154i \(-0.741769\pi\)
−0.688587 + 0.725154i \(0.741769\pi\)
\(380\) 0 0
\(381\) 3.48707 0.178648
\(382\) 0 0
\(383\) 0.260208 0.0132960 0.00664800 0.999978i \(-0.497884\pi\)
0.00664800 + 0.999978i \(0.497884\pi\)
\(384\) 0 0
\(385\) −3.08992 −0.157477
\(386\) 0 0
\(387\) 5.17628 0.263125
\(388\) 0 0
\(389\) −31.3007 −1.58701 −0.793504 0.608565i \(-0.791746\pi\)
−0.793504 + 0.608565i \(0.791746\pi\)
\(390\) 0 0
\(391\) 3.49163 0.176579
\(392\) 0 0
\(393\) 4.07834 0.205725
\(394\) 0 0
\(395\) −2.47993 −0.124779
\(396\) 0 0
\(397\) −19.6343 −0.985417 −0.492708 0.870195i \(-0.663993\pi\)
−0.492708 + 0.870195i \(0.663993\pi\)
\(398\) 0 0
\(399\) 1.99003 0.0996262
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 6.80749 0.339105
\(404\) 0 0
\(405\) −8.06585 −0.400795
\(406\) 0 0
\(407\) 12.6211 0.625602
\(408\) 0 0
\(409\) −33.1279 −1.63807 −0.819035 0.573744i \(-0.805491\pi\)
−0.819035 + 0.573744i \(0.805491\pi\)
\(410\) 0 0
\(411\) 3.91330 0.193029
\(412\) 0 0
\(413\) −11.2047 −0.551346
\(414\) 0 0
\(415\) 4.09191 0.200864
\(416\) 0 0
\(417\) −3.57766 −0.175199
\(418\) 0 0
\(419\) 29.0081 1.41714 0.708569 0.705642i \(-0.249341\pi\)
0.708569 + 0.705642i \(0.249341\pi\)
\(420\) 0 0
\(421\) 31.5495 1.53763 0.768814 0.639473i \(-0.220847\pi\)
0.768814 + 0.639473i \(0.220847\pi\)
\(422\) 0 0
\(423\) 15.4174 0.749622
\(424\) 0 0
\(425\) 7.82804 0.379716
\(426\) 0 0
\(427\) 5.41241 0.261925
\(428\) 0 0
\(429\) −1.14622 −0.0553400
\(430\) 0 0
\(431\) −19.2499 −0.927234 −0.463617 0.886036i \(-0.653449\pi\)
−0.463617 + 0.886036i \(0.653449\pi\)
\(432\) 0 0
\(433\) −40.7631 −1.95895 −0.979476 0.201562i \(-0.935398\pi\)
−0.979476 + 0.201562i \(0.935398\pi\)
\(434\) 0 0
\(435\) 0.825948 0.0396012
\(436\) 0 0
\(437\) 2.02453 0.0968466
\(438\) 0 0
\(439\) 15.6415 0.746526 0.373263 0.927725i \(-0.378239\pi\)
0.373263 + 0.927725i \(0.378239\pi\)
\(440\) 0 0
\(441\) 14.9659 0.712660
\(442\) 0 0
\(443\) 27.1649 1.29064 0.645322 0.763910i \(-0.276723\pi\)
0.645322 + 0.763910i \(0.276723\pi\)
\(444\) 0 0
\(445\) −8.32346 −0.394570
\(446\) 0 0
\(447\) −1.95962 −0.0926868
\(448\) 0 0
\(449\) −2.87709 −0.135778 −0.0678890 0.997693i \(-0.521626\pi\)
−0.0678890 + 0.997693i \(0.521626\pi\)
\(450\) 0 0
\(451\) −5.82930 −0.274491
\(452\) 0 0
\(453\) 1.74710 0.0820858
\(454\) 0 0
\(455\) −2.09524 −0.0982262
\(456\) 0 0
\(457\) 37.1709 1.73878 0.869390 0.494127i \(-0.164512\pi\)
0.869390 + 0.494127i \(0.164512\pi\)
\(458\) 0 0
\(459\) 14.9545 0.698015
\(460\) 0 0
\(461\) −11.3487 −0.528561 −0.264280 0.964446i \(-0.585134\pi\)
−0.264280 + 0.964446i \(0.585134\pi\)
\(462\) 0 0
\(463\) 38.6067 1.79420 0.897102 0.441823i \(-0.145668\pi\)
0.897102 + 0.441823i \(0.145668\pi\)
\(464\) 0 0
\(465\) −1.42450 −0.0660598
\(466\) 0 0
\(467\) −18.0206 −0.833896 −0.416948 0.908930i \(-0.636900\pi\)
−0.416948 + 0.908930i \(0.636900\pi\)
\(468\) 0 0
\(469\) −17.5132 −0.808685
\(470\) 0 0
\(471\) 6.56912 0.302689
\(472\) 0 0
\(473\) 4.08362 0.187765
\(474\) 0 0
\(475\) 4.53890 0.208259
\(476\) 0 0
\(477\) −0.187028 −0.00856343
\(478\) 0 0
\(479\) 19.6971 0.899982 0.449991 0.893033i \(-0.351427\pi\)
0.449991 + 0.893033i \(0.351427\pi\)
\(480\) 0 0
\(481\) 8.55819 0.390220
\(482\) 0 0
\(483\) 0.195562 0.00889839
\(484\) 0 0
\(485\) −13.1809 −0.598513
\(486\) 0 0
\(487\) 14.6410 0.663445 0.331722 0.943377i \(-0.392370\pi\)
0.331722 + 0.943377i \(0.392370\pi\)
\(488\) 0 0
\(489\) −3.91897 −0.177222
\(490\) 0 0
\(491\) 11.2088 0.505848 0.252924 0.967486i \(-0.418608\pi\)
0.252924 + 0.967486i \(0.418608\pi\)
\(492\) 0 0
\(493\) 19.9512 0.898558
\(494\) 0 0
\(495\) −6.61178 −0.297177
\(496\) 0 0
\(497\) −14.4612 −0.648672
\(498\) 0 0
\(499\) 12.0196 0.538071 0.269036 0.963130i \(-0.413295\pi\)
0.269036 + 0.963130i \(0.413295\pi\)
\(500\) 0 0
\(501\) 1.13913 0.0508926
\(502\) 0 0
\(503\) −6.98878 −0.311614 −0.155807 0.987788i \(-0.549798\pi\)
−0.155807 + 0.987788i \(0.549798\pi\)
\(504\) 0 0
\(505\) −5.23850 −0.233110
\(506\) 0 0
\(507\) 3.43564 0.152582
\(508\) 0 0
\(509\) −33.7782 −1.49719 −0.748595 0.663027i \(-0.769271\pi\)
−0.748595 + 0.663027i \(0.769271\pi\)
\(510\) 0 0
\(511\) 10.8431 0.479670
\(512\) 0 0
\(513\) 8.67098 0.382833
\(514\) 0 0
\(515\) −5.76758 −0.254150
\(516\) 0 0
\(517\) 12.1630 0.534927
\(518\) 0 0
\(519\) 5.07289 0.222675
\(520\) 0 0
\(521\) 9.05093 0.396528 0.198264 0.980149i \(-0.436470\pi\)
0.198264 + 0.980149i \(0.436470\pi\)
\(522\) 0 0
\(523\) 29.7700 1.30175 0.650876 0.759184i \(-0.274402\pi\)
0.650876 + 0.759184i \(0.274402\pi\)
\(524\) 0 0
\(525\) 0.438440 0.0191351
\(526\) 0 0
\(527\) −34.4097 −1.49891
\(528\) 0 0
\(529\) −22.8010 −0.991350
\(530\) 0 0
\(531\) −23.9757 −1.04046
\(532\) 0 0
\(533\) −3.95278 −0.171214
\(534\) 0 0
\(535\) −1.21818 −0.0526665
\(536\) 0 0
\(537\) 1.53483 0.0662326
\(538\) 0 0
\(539\) 11.8067 0.508551
\(540\) 0 0
\(541\) 3.38789 0.145657 0.0728284 0.997344i \(-0.476797\pi\)
0.0728284 + 0.997344i \(0.476797\pi\)
\(542\) 0 0
\(543\) −0.835619 −0.0358598
\(544\) 0 0
\(545\) 10.1815 0.436127
\(546\) 0 0
\(547\) −36.2477 −1.54984 −0.774920 0.632059i \(-0.782210\pi\)
−0.774920 + 0.632059i \(0.782210\pi\)
\(548\) 0 0
\(549\) 11.5814 0.494283
\(550\) 0 0
\(551\) 11.5682 0.492823
\(552\) 0 0
\(553\) −3.35516 −0.142676
\(554\) 0 0
\(555\) −1.79085 −0.0760173
\(556\) 0 0
\(557\) −34.6813 −1.46949 −0.734747 0.678342i \(-0.762699\pi\)
−0.734747 + 0.678342i \(0.762699\pi\)
\(558\) 0 0
\(559\) 2.76905 0.117118
\(560\) 0 0
\(561\) 5.79378 0.244613
\(562\) 0 0
\(563\) 17.7505 0.748096 0.374048 0.927409i \(-0.377970\pi\)
0.374048 + 0.927409i \(0.377970\pi\)
\(564\) 0 0
\(565\) −4.07269 −0.171339
\(566\) 0 0
\(567\) −10.9125 −0.458282
\(568\) 0 0
\(569\) −2.32248 −0.0973634 −0.0486817 0.998814i \(-0.515502\pi\)
−0.0486817 + 0.998814i \(0.515502\pi\)
\(570\) 0 0
\(571\) −29.8713 −1.25007 −0.625037 0.780595i \(-0.714916\pi\)
−0.625037 + 0.780595i \(0.714916\pi\)
\(572\) 0 0
\(573\) 6.19292 0.258713
\(574\) 0 0
\(575\) 0.446041 0.0186012
\(576\) 0 0
\(577\) −41.0344 −1.70828 −0.854142 0.520040i \(-0.825917\pi\)
−0.854142 + 0.520040i \(0.825917\pi\)
\(578\) 0 0
\(579\) 0.873550 0.0363035
\(580\) 0 0
\(581\) 5.53605 0.229674
\(582\) 0 0
\(583\) −0.147548 −0.00611083
\(584\) 0 0
\(585\) −4.48337 −0.185365
\(586\) 0 0
\(587\) −6.28562 −0.259435 −0.129718 0.991551i \(-0.541407\pi\)
−0.129718 + 0.991551i \(0.541407\pi\)
\(588\) 0 0
\(589\) −19.9516 −0.822092
\(590\) 0 0
\(591\) 0.565943 0.0232798
\(592\) 0 0
\(593\) −3.36345 −0.138120 −0.0690601 0.997613i \(-0.522000\pi\)
−0.0690601 + 0.997613i \(0.522000\pi\)
\(594\) 0 0
\(595\) 10.5908 0.434179
\(596\) 0 0
\(597\) 2.00642 0.0821172
\(598\) 0 0
\(599\) −27.4182 −1.12028 −0.560139 0.828399i \(-0.689252\pi\)
−0.560139 + 0.828399i \(0.689252\pi\)
\(600\) 0 0
\(601\) −36.1687 −1.47535 −0.737675 0.675155i \(-0.764077\pi\)
−0.737675 + 0.675155i \(0.764077\pi\)
\(602\) 0 0
\(603\) −37.4746 −1.52609
\(604\) 0 0
\(605\) 5.78391 0.235149
\(606\) 0 0
\(607\) −12.4228 −0.504224 −0.252112 0.967698i \(-0.581125\pi\)
−0.252112 + 0.967698i \(0.581125\pi\)
\(608\) 0 0
\(609\) 1.11745 0.0452812
\(610\) 0 0
\(611\) 8.24757 0.333661
\(612\) 0 0
\(613\) 36.1432 1.45981 0.729905 0.683548i \(-0.239564\pi\)
0.729905 + 0.683548i \(0.239564\pi\)
\(614\) 0 0
\(615\) 0.827141 0.0333535
\(616\) 0 0
\(617\) 30.8006 1.23999 0.619993 0.784607i \(-0.287135\pi\)
0.619993 + 0.784607i \(0.287135\pi\)
\(618\) 0 0
\(619\) 10.0643 0.404518 0.202259 0.979332i \(-0.435172\pi\)
0.202259 + 0.979332i \(0.435172\pi\)
\(620\) 0 0
\(621\) 0.852105 0.0341938
\(622\) 0 0
\(623\) −11.2610 −0.451163
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 3.35938 0.134161
\(628\) 0 0
\(629\) −43.2590 −1.72485
\(630\) 0 0
\(631\) −44.2366 −1.76103 −0.880516 0.474017i \(-0.842804\pi\)
−0.880516 + 0.474017i \(0.842804\pi\)
\(632\) 0 0
\(633\) −1.42792 −0.0567547
\(634\) 0 0
\(635\) 10.7603 0.427009
\(636\) 0 0
\(637\) 8.00599 0.317209
\(638\) 0 0
\(639\) −30.9439 −1.22412
\(640\) 0 0
\(641\) −2.50430 −0.0989139 −0.0494570 0.998776i \(-0.515749\pi\)
−0.0494570 + 0.998776i \(0.515749\pi\)
\(642\) 0 0
\(643\) 22.0101 0.867992 0.433996 0.900915i \(-0.357103\pi\)
0.433996 + 0.900915i \(0.357103\pi\)
\(644\) 0 0
\(645\) −0.579440 −0.0228154
\(646\) 0 0
\(647\) −4.04488 −0.159021 −0.0795103 0.996834i \(-0.525336\pi\)
−0.0795103 + 0.996834i \(0.525336\pi\)
\(648\) 0 0
\(649\) −18.9146 −0.742464
\(650\) 0 0
\(651\) −1.92725 −0.0755348
\(652\) 0 0
\(653\) −17.2195 −0.673851 −0.336925 0.941531i \(-0.609387\pi\)
−0.336925 + 0.941531i \(0.609387\pi\)
\(654\) 0 0
\(655\) 12.5848 0.491730
\(656\) 0 0
\(657\) 23.2020 0.905196
\(658\) 0 0
\(659\) 15.6550 0.609832 0.304916 0.952379i \(-0.401372\pi\)
0.304916 + 0.952379i \(0.401372\pi\)
\(660\) 0 0
\(661\) −31.6730 −1.23194 −0.615968 0.787771i \(-0.711235\pi\)
−0.615968 + 0.787771i \(0.711235\pi\)
\(662\) 0 0
\(663\) 3.92869 0.152578
\(664\) 0 0
\(665\) 6.14079 0.238130
\(666\) 0 0
\(667\) 1.13682 0.0440178
\(668\) 0 0
\(669\) 3.26261 0.126140
\(670\) 0 0
\(671\) 9.13669 0.352718
\(672\) 0 0
\(673\) 18.2786 0.704590 0.352295 0.935889i \(-0.385401\pi\)
0.352295 + 0.935889i \(0.385401\pi\)
\(674\) 0 0
\(675\) 1.91037 0.0735303
\(676\) 0 0
\(677\) −29.5683 −1.13640 −0.568202 0.822889i \(-0.692361\pi\)
−0.568202 + 0.822889i \(0.692361\pi\)
\(678\) 0 0
\(679\) −17.8328 −0.684358
\(680\) 0 0
\(681\) 6.13326 0.235027
\(682\) 0 0
\(683\) −0.237407 −0.00908414 −0.00454207 0.999990i \(-0.501446\pi\)
−0.00454207 + 0.999990i \(0.501446\pi\)
\(684\) 0 0
\(685\) 12.0756 0.461384
\(686\) 0 0
\(687\) −1.85842 −0.0709032
\(688\) 0 0
\(689\) −0.100051 −0.00381163
\(690\) 0 0
\(691\) −3.38838 −0.128900 −0.0644500 0.997921i \(-0.520529\pi\)
−0.0644500 + 0.997921i \(0.520529\pi\)
\(692\) 0 0
\(693\) −8.94524 −0.339802
\(694\) 0 0
\(695\) −11.0398 −0.418765
\(696\) 0 0
\(697\) 19.9801 0.756799
\(698\) 0 0
\(699\) −0.116416 −0.00440327
\(700\) 0 0
\(701\) 21.7522 0.821571 0.410785 0.911732i \(-0.365255\pi\)
0.410785 + 0.911732i \(0.365255\pi\)
\(702\) 0 0
\(703\) −25.0826 −0.946010
\(704\) 0 0
\(705\) −1.72585 −0.0649992
\(706\) 0 0
\(707\) −7.08730 −0.266545
\(708\) 0 0
\(709\) 33.8533 1.27139 0.635693 0.771942i \(-0.280714\pi\)
0.635693 + 0.771942i \(0.280714\pi\)
\(710\) 0 0
\(711\) −7.17935 −0.269247
\(712\) 0 0
\(713\) −1.96066 −0.0734274
\(714\) 0 0
\(715\) −3.53697 −0.132275
\(716\) 0 0
\(717\) 4.40727 0.164593
\(718\) 0 0
\(719\) −5.13757 −0.191599 −0.0957996 0.995401i \(-0.530541\pi\)
−0.0957996 + 0.995401i \(0.530541\pi\)
\(720\) 0 0
\(721\) −7.80311 −0.290603
\(722\) 0 0
\(723\) 4.88427 0.181648
\(724\) 0 0
\(725\) 2.54869 0.0946559
\(726\) 0 0
\(727\) 50.3092 1.86586 0.932932 0.360052i \(-0.117241\pi\)
0.932932 + 0.360052i \(0.117241\pi\)
\(728\) 0 0
\(729\) −21.4932 −0.796045
\(730\) 0 0
\(731\) −13.9967 −0.517686
\(732\) 0 0
\(733\) 8.89863 0.328678 0.164339 0.986404i \(-0.447451\pi\)
0.164339 + 0.986404i \(0.447451\pi\)
\(734\) 0 0
\(735\) −1.67530 −0.0617943
\(736\) 0 0
\(737\) −29.5641 −1.08901
\(738\) 0 0
\(739\) 1.48800 0.0547369 0.0273684 0.999625i \(-0.491287\pi\)
0.0273684 + 0.999625i \(0.491287\pi\)
\(740\) 0 0
\(741\) 2.27795 0.0836828
\(742\) 0 0
\(743\) −1.81572 −0.0666125 −0.0333062 0.999445i \(-0.510604\pi\)
−0.0333062 + 0.999445i \(0.510604\pi\)
\(744\) 0 0
\(745\) −6.04694 −0.221543
\(746\) 0 0
\(747\) 11.8460 0.433423
\(748\) 0 0
\(749\) −1.64811 −0.0602205
\(750\) 0 0
\(751\) −11.4691 −0.418513 −0.209256 0.977861i \(-0.567104\pi\)
−0.209256 + 0.977861i \(0.567104\pi\)
\(752\) 0 0
\(753\) 4.15095 0.151269
\(754\) 0 0
\(755\) 5.39115 0.196204
\(756\) 0 0
\(757\) 28.6945 1.04292 0.521460 0.853276i \(-0.325388\pi\)
0.521460 + 0.853276i \(0.325388\pi\)
\(758\) 0 0
\(759\) 0.330129 0.0119829
\(760\) 0 0
\(761\) −52.5333 −1.90433 −0.952166 0.305582i \(-0.901149\pi\)
−0.952166 + 0.305582i \(0.901149\pi\)
\(762\) 0 0
\(763\) 13.7748 0.498681
\(764\) 0 0
\(765\) 22.6620 0.819347
\(766\) 0 0
\(767\) −12.8258 −0.463113
\(768\) 0 0
\(769\) −19.5173 −0.703813 −0.351907 0.936035i \(-0.614467\pi\)
−0.351907 + 0.936035i \(0.614467\pi\)
\(770\) 0 0
\(771\) −7.48729 −0.269648
\(772\) 0 0
\(773\) −7.80828 −0.280844 −0.140422 0.990092i \(-0.544846\pi\)
−0.140422 + 0.990092i \(0.544846\pi\)
\(774\) 0 0
\(775\) −4.39570 −0.157898
\(776\) 0 0
\(777\) −2.42289 −0.0869205
\(778\) 0 0
\(779\) 11.5849 0.415074
\(780\) 0 0
\(781\) −24.4119 −0.873528
\(782\) 0 0
\(783\) 4.86894 0.174002
\(784\) 0 0
\(785\) 20.2708 0.723497
\(786\) 0 0
\(787\) 30.2113 1.07692 0.538458 0.842652i \(-0.319007\pi\)
0.538458 + 0.842652i \(0.319007\pi\)
\(788\) 0 0
\(789\) 2.23912 0.0797148
\(790\) 0 0
\(791\) −5.51004 −0.195914
\(792\) 0 0
\(793\) 6.19549 0.220008
\(794\) 0 0
\(795\) 0.0209362 0.000742530 0
\(796\) 0 0
\(797\) 10.0463 0.355857 0.177929 0.984043i \(-0.443060\pi\)
0.177929 + 0.984043i \(0.443060\pi\)
\(798\) 0 0
\(799\) −41.6889 −1.47485
\(800\) 0 0
\(801\) −24.0963 −0.851399
\(802\) 0 0
\(803\) 18.3043 0.645943
\(804\) 0 0
\(805\) 0.603461 0.0212692
\(806\) 0 0
\(807\) 5.18754 0.182610
\(808\) 0 0
\(809\) 45.2492 1.59088 0.795439 0.606034i \(-0.207241\pi\)
0.795439 + 0.606034i \(0.207241\pi\)
\(810\) 0 0
\(811\) −2.67838 −0.0940506 −0.0470253 0.998894i \(-0.514974\pi\)
−0.0470253 + 0.998894i \(0.514974\pi\)
\(812\) 0 0
\(813\) 3.93668 0.138065
\(814\) 0 0
\(815\) −12.0931 −0.423601
\(816\) 0 0
\(817\) −8.11563 −0.283930
\(818\) 0 0
\(819\) −6.06567 −0.211952
\(820\) 0 0
\(821\) −0.00264638 −9.23594e−5 0 −4.61797e−5 1.00000i \(-0.500015\pi\)
−4.61797e−5 1.00000i \(0.500015\pi\)
\(822\) 0 0
\(823\) 4.56917 0.159271 0.0796356 0.996824i \(-0.474624\pi\)
0.0796356 + 0.996824i \(0.474624\pi\)
\(824\) 0 0
\(825\) 0.740131 0.0257681
\(826\) 0 0
\(827\) −1.89854 −0.0660188 −0.0330094 0.999455i \(-0.510509\pi\)
−0.0330094 + 0.999455i \(0.510509\pi\)
\(828\) 0 0
\(829\) −6.38272 −0.221681 −0.110840 0.993838i \(-0.535354\pi\)
−0.110840 + 0.993838i \(0.535354\pi\)
\(830\) 0 0
\(831\) 6.47285 0.224541
\(832\) 0 0
\(833\) −40.4678 −1.40213
\(834\) 0 0
\(835\) 3.51510 0.121645
\(836\) 0 0
\(837\) −8.39742 −0.290257
\(838\) 0 0
\(839\) 2.09516 0.0723331 0.0361665 0.999346i \(-0.488485\pi\)
0.0361665 + 0.999346i \(0.488485\pi\)
\(840\) 0 0
\(841\) −22.5042 −0.776007
\(842\) 0 0
\(843\) 3.46127 0.119212
\(844\) 0 0
\(845\) 10.6016 0.364707
\(846\) 0 0
\(847\) 7.82520 0.268877
\(848\) 0 0
\(849\) −0.237342 −0.00814557
\(850\) 0 0
\(851\) −2.46489 −0.0844954
\(852\) 0 0
\(853\) 9.34390 0.319929 0.159965 0.987123i \(-0.448862\pi\)
0.159965 + 0.987123i \(0.448862\pi\)
\(854\) 0 0
\(855\) 13.1400 0.449379
\(856\) 0 0
\(857\) −7.37661 −0.251980 −0.125990 0.992031i \(-0.540211\pi\)
−0.125990 + 0.992031i \(0.540211\pi\)
\(858\) 0 0
\(859\) 50.8509 1.73501 0.867506 0.497428i \(-0.165722\pi\)
0.867506 + 0.497428i \(0.165722\pi\)
\(860\) 0 0
\(861\) 1.11906 0.0381375
\(862\) 0 0
\(863\) 40.3542 1.37367 0.686836 0.726813i \(-0.258999\pi\)
0.686836 + 0.726813i \(0.258999\pi\)
\(864\) 0 0
\(865\) 15.6538 0.532245
\(866\) 0 0
\(867\) −14.3492 −0.487323
\(868\) 0 0
\(869\) −5.66385 −0.192133
\(870\) 0 0
\(871\) −20.0471 −0.679269
\(872\) 0 0
\(873\) −38.1584 −1.29147
\(874\) 0 0
\(875\) 1.35293 0.0457372
\(876\) 0 0
\(877\) −46.1310 −1.55773 −0.778867 0.627189i \(-0.784205\pi\)
−0.778867 + 0.627189i \(0.784205\pi\)
\(878\) 0 0
\(879\) −8.07684 −0.272425
\(880\) 0 0
\(881\) 44.7364 1.50721 0.753605 0.657328i \(-0.228313\pi\)
0.753605 + 0.657328i \(0.228313\pi\)
\(882\) 0 0
\(883\) −1.68377 −0.0566633 −0.0283316 0.999599i \(-0.509019\pi\)
−0.0283316 + 0.999599i \(0.509019\pi\)
\(884\) 0 0
\(885\) 2.68387 0.0902172
\(886\) 0 0
\(887\) 7.16442 0.240558 0.120279 0.992740i \(-0.461621\pi\)
0.120279 + 0.992740i \(0.461621\pi\)
\(888\) 0 0
\(889\) 14.5579 0.488256
\(890\) 0 0
\(891\) −18.4214 −0.617140
\(892\) 0 0
\(893\) −24.1722 −0.808893
\(894\) 0 0
\(895\) 4.73613 0.158311
\(896\) 0 0
\(897\) 0.223857 0.00747435
\(898\) 0 0
\(899\) −11.2033 −0.373650
\(900\) 0 0
\(901\) 0.505725 0.0168482
\(902\) 0 0
\(903\) −0.783939 −0.0260878
\(904\) 0 0
\(905\) −2.57853 −0.0857133
\(906\) 0 0
\(907\) 44.9100 1.49121 0.745605 0.666388i \(-0.232160\pi\)
0.745605 + 0.666388i \(0.232160\pi\)
\(908\) 0 0
\(909\) −15.1654 −0.503003
\(910\) 0 0
\(911\) 13.4452 0.445459 0.222730 0.974880i \(-0.428503\pi\)
0.222730 + 0.974880i \(0.428503\pi\)
\(912\) 0 0
\(913\) 9.34542 0.309288
\(914\) 0 0
\(915\) −1.29644 −0.0428590
\(916\) 0 0
\(917\) 17.0263 0.562259
\(918\) 0 0
\(919\) 39.4959 1.30285 0.651425 0.758713i \(-0.274171\pi\)
0.651425 + 0.758713i \(0.274171\pi\)
\(920\) 0 0
\(921\) 1.82368 0.0600923
\(922\) 0 0
\(923\) −16.5535 −0.544864
\(924\) 0 0
\(925\) −5.52615 −0.181699
\(926\) 0 0
\(927\) −16.6970 −0.548403
\(928\) 0 0
\(929\) −17.2776 −0.566860 −0.283430 0.958993i \(-0.591472\pi\)
−0.283430 + 0.958993i \(0.591472\pi\)
\(930\) 0 0
\(931\) −23.4642 −0.769009
\(932\) 0 0
\(933\) 4.07853 0.133525
\(934\) 0 0
\(935\) 17.8783 0.584682
\(936\) 0 0
\(937\) −15.0352 −0.491179 −0.245590 0.969374i \(-0.578982\pi\)
−0.245590 + 0.969374i \(0.578982\pi\)
\(938\) 0 0
\(939\) 2.42365 0.0790927
\(940\) 0 0
\(941\) 28.8958 0.941977 0.470989 0.882139i \(-0.343897\pi\)
0.470989 + 0.882139i \(0.343897\pi\)
\(942\) 0 0
\(943\) 1.13846 0.0370734
\(944\) 0 0
\(945\) 2.58459 0.0840768
\(946\) 0 0
\(947\) 57.1262 1.85635 0.928176 0.372142i \(-0.121377\pi\)
0.928176 + 0.372142i \(0.121377\pi\)
\(948\) 0 0
\(949\) 12.4119 0.402908
\(950\) 0 0
\(951\) 5.97542 0.193766
\(952\) 0 0
\(953\) −5.55064 −0.179803 −0.0899014 0.995951i \(-0.528655\pi\)
−0.0899014 + 0.995951i \(0.528655\pi\)
\(954\) 0 0
\(955\) 19.1099 0.618383
\(956\) 0 0
\(957\) 1.88636 0.0609774
\(958\) 0 0
\(959\) 16.3374 0.527561
\(960\) 0 0
\(961\) −11.6778 −0.376704
\(962\) 0 0
\(963\) −3.52660 −0.113643
\(964\) 0 0
\(965\) 2.69558 0.0867737
\(966\) 0 0
\(967\) 50.9437 1.63824 0.819119 0.573624i \(-0.194463\pi\)
0.819119 + 0.573624i \(0.194463\pi\)
\(968\) 0 0
\(969\) −11.5143 −0.369894
\(970\) 0 0
\(971\) −39.9308 −1.28144 −0.640719 0.767775i \(-0.721364\pi\)
−0.640719 + 0.767775i \(0.721364\pi\)
\(972\) 0 0
\(973\) −14.9361 −0.478829
\(974\) 0 0
\(975\) 0.501874 0.0160728
\(976\) 0 0
\(977\) −39.7986 −1.27327 −0.636635 0.771165i \(-0.719674\pi\)
−0.636635 + 0.771165i \(0.719674\pi\)
\(978\) 0 0
\(979\) −19.0098 −0.607554
\(980\) 0 0
\(981\) 29.4752 0.941072
\(982\) 0 0
\(983\) −5.22196 −0.166555 −0.0832773 0.996526i \(-0.526539\pi\)
−0.0832773 + 0.996526i \(0.526539\pi\)
\(984\) 0 0
\(985\) 1.74637 0.0556441
\(986\) 0 0
\(987\) −2.33495 −0.0743221
\(988\) 0 0
\(989\) −0.797530 −0.0253600
\(990\) 0 0
\(991\) −45.3443 −1.44041 −0.720204 0.693763i \(-0.755952\pi\)
−0.720204 + 0.693763i \(0.755952\pi\)
\(992\) 0 0
\(993\) −4.53388 −0.143878
\(994\) 0 0
\(995\) 6.19135 0.196279
\(996\) 0 0
\(997\) 47.1591 1.49354 0.746772 0.665080i \(-0.231603\pi\)
0.746772 + 0.665080i \(0.231603\pi\)
\(998\) 0 0
\(999\) −10.5570 −0.334009
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 \(a_p\))