Properties

Label 6036.2.a.i.1.18
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+1.90366 q^{5}\) \(-3.61918 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+1.90366 q^{5}\) \(-3.61918 q^{7}\) \(+1.00000 q^{9}\) \(+5.57755 q^{11}\) \(+5.61913 q^{13}\) \(-1.90366 q^{15}\) \(+6.17169 q^{17}\) \(-0.419270 q^{19}\) \(+3.61918 q^{21}\) \(+3.21783 q^{23}\) \(-1.37606 q^{25}\) \(-1.00000 q^{27}\) \(+3.62615 q^{29}\) \(+5.39266 q^{31}\) \(-5.57755 q^{33}\) \(-6.88970 q^{35}\) \(-2.73595 q^{37}\) \(-5.61913 q^{39}\) \(-2.39155 q^{41}\) \(+2.76555 q^{43}\) \(+1.90366 q^{45}\) \(+0.129160 q^{47}\) \(+6.09845 q^{49}\) \(-6.17169 q^{51}\) \(+8.82207 q^{53}\) \(+10.6178 q^{55}\) \(+0.419270 q^{57}\) \(-0.0305566 q^{59}\) \(-3.48688 q^{61}\) \(-3.61918 q^{63}\) \(+10.6969 q^{65}\) \(-11.2996 q^{67}\) \(-3.21783 q^{69}\) \(+3.48404 q^{71}\) \(-7.80164 q^{73}\) \(+1.37606 q^{75}\) \(-20.1862 q^{77}\) \(-14.5184 q^{79}\) \(+1.00000 q^{81}\) \(+5.10465 q^{83}\) \(+11.7488 q^{85}\) \(-3.62615 q^{87}\) \(+11.8290 q^{89}\) \(-20.3366 q^{91}\) \(-5.39266 q^{93}\) \(-0.798150 q^{95}\) \(-11.7288 q^{97}\) \(+5.57755 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.90366 0.851345 0.425672 0.904877i \(-0.360038\pi\)
0.425672 + 0.904877i \(0.360038\pi\)
\(6\) 0 0
\(7\) −3.61918 −1.36792 −0.683960 0.729519i \(-0.739744\pi\)
−0.683960 + 0.729519i \(0.739744\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.57755 1.68170 0.840848 0.541272i \(-0.182057\pi\)
0.840848 + 0.541272i \(0.182057\pi\)
\(12\) 0 0
\(13\) 5.61913 1.55847 0.779234 0.626734i \(-0.215609\pi\)
0.779234 + 0.626734i \(0.215609\pi\)
\(14\) 0 0
\(15\) −1.90366 −0.491524
\(16\) 0 0
\(17\) 6.17169 1.49685 0.748427 0.663217i \(-0.230809\pi\)
0.748427 + 0.663217i \(0.230809\pi\)
\(18\) 0 0
\(19\) −0.419270 −0.0961872 −0.0480936 0.998843i \(-0.515315\pi\)
−0.0480936 + 0.998843i \(0.515315\pi\)
\(20\) 0 0
\(21\) 3.61918 0.789770
\(22\) 0 0
\(23\) 3.21783 0.670964 0.335482 0.942047i \(-0.391101\pi\)
0.335482 + 0.942047i \(0.391101\pi\)
\(24\) 0 0
\(25\) −1.37606 −0.275212
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.62615 0.673360 0.336680 0.941619i \(-0.390696\pi\)
0.336680 + 0.941619i \(0.390696\pi\)
\(30\) 0 0
\(31\) 5.39266 0.968550 0.484275 0.874916i \(-0.339083\pi\)
0.484275 + 0.874916i \(0.339083\pi\)
\(32\) 0 0
\(33\) −5.57755 −0.970927
\(34\) 0 0
\(35\) −6.88970 −1.16457
\(36\) 0 0
\(37\) −2.73595 −0.449787 −0.224894 0.974383i \(-0.572203\pi\)
−0.224894 + 0.974383i \(0.572203\pi\)
\(38\) 0 0
\(39\) −5.61913 −0.899781
\(40\) 0 0
\(41\) −2.39155 −0.373497 −0.186749 0.982408i \(-0.559795\pi\)
−0.186749 + 0.982408i \(0.559795\pi\)
\(42\) 0 0
\(43\) 2.76555 0.421743 0.210872 0.977514i \(-0.432370\pi\)
0.210872 + 0.977514i \(0.432370\pi\)
\(44\) 0 0
\(45\) 1.90366 0.283782
\(46\) 0 0
\(47\) 0.129160 0.0188399 0.00941994 0.999956i \(-0.497001\pi\)
0.00941994 + 0.999956i \(0.497001\pi\)
\(48\) 0 0
\(49\) 6.09845 0.871208
\(50\) 0 0
\(51\) −6.17169 −0.864209
\(52\) 0 0
\(53\) 8.82207 1.21180 0.605902 0.795539i \(-0.292812\pi\)
0.605902 + 0.795539i \(0.292812\pi\)
\(54\) 0 0
\(55\) 10.6178 1.43170
\(56\) 0 0
\(57\) 0.419270 0.0555337
\(58\) 0 0
\(59\) −0.0305566 −0.00397813 −0.00198906 0.999998i \(-0.500633\pi\)
−0.00198906 + 0.999998i \(0.500633\pi\)
\(60\) 0 0
\(61\) −3.48688 −0.446450 −0.223225 0.974767i \(-0.571658\pi\)
−0.223225 + 0.974767i \(0.571658\pi\)
\(62\) 0 0
\(63\) −3.61918 −0.455974
\(64\) 0 0
\(65\) 10.6969 1.32679
\(66\) 0 0
\(67\) −11.2996 −1.38046 −0.690232 0.723588i \(-0.742492\pi\)
−0.690232 + 0.723588i \(0.742492\pi\)
\(68\) 0 0
\(69\) −3.21783 −0.387381
\(70\) 0 0
\(71\) 3.48404 0.413480 0.206740 0.978396i \(-0.433715\pi\)
0.206740 + 0.978396i \(0.433715\pi\)
\(72\) 0 0
\(73\) −7.80164 −0.913113 −0.456556 0.889694i \(-0.650917\pi\)
−0.456556 + 0.889694i \(0.650917\pi\)
\(74\) 0 0
\(75\) 1.37606 0.158894
\(76\) 0 0
\(77\) −20.1862 −2.30043
\(78\) 0 0
\(79\) −14.5184 −1.63344 −0.816722 0.577032i \(-0.804211\pi\)
−0.816722 + 0.577032i \(0.804211\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.10465 0.560308 0.280154 0.959955i \(-0.409614\pi\)
0.280154 + 0.959955i \(0.409614\pi\)
\(84\) 0 0
\(85\) 11.7488 1.27434
\(86\) 0 0
\(87\) −3.62615 −0.388764
\(88\) 0 0
\(89\) 11.8290 1.25387 0.626936 0.779070i \(-0.284309\pi\)
0.626936 + 0.779070i \(0.284309\pi\)
\(90\) 0 0
\(91\) −20.3366 −2.13186
\(92\) 0 0
\(93\) −5.39266 −0.559193
\(94\) 0 0
\(95\) −0.798150 −0.0818884
\(96\) 0 0
\(97\) −11.7288 −1.19088 −0.595441 0.803399i \(-0.703023\pi\)
−0.595441 + 0.803399i \(0.703023\pi\)
\(98\) 0 0
\(99\) 5.57755 0.560565
\(100\) 0 0
\(101\) 18.1101 1.80202 0.901012 0.433794i \(-0.142825\pi\)
0.901012 + 0.433794i \(0.142825\pi\)
\(102\) 0 0
\(103\) −13.1885 −1.29950 −0.649750 0.760148i \(-0.725126\pi\)
−0.649750 + 0.760148i \(0.725126\pi\)
\(104\) 0 0
\(105\) 6.88970 0.672366
\(106\) 0 0
\(107\) 0.332326 0.0321272 0.0160636 0.999871i \(-0.494887\pi\)
0.0160636 + 0.999871i \(0.494887\pi\)
\(108\) 0 0
\(109\) −17.5340 −1.67946 −0.839728 0.543007i \(-0.817286\pi\)
−0.839728 + 0.543007i \(0.817286\pi\)
\(110\) 0 0
\(111\) 2.73595 0.259685
\(112\) 0 0
\(113\) 4.03768 0.379833 0.189916 0.981800i \(-0.439178\pi\)
0.189916 + 0.981800i \(0.439178\pi\)
\(114\) 0 0
\(115\) 6.12567 0.571222
\(116\) 0 0
\(117\) 5.61913 0.519489
\(118\) 0 0
\(119\) −22.3364 −2.04758
\(120\) 0 0
\(121\) 20.1091 1.82810
\(122\) 0 0
\(123\) 2.39155 0.215639
\(124\) 0 0
\(125\) −12.1379 −1.08565
\(126\) 0 0
\(127\) −6.02421 −0.534562 −0.267281 0.963619i \(-0.586125\pi\)
−0.267281 + 0.963619i \(0.586125\pi\)
\(128\) 0 0
\(129\) −2.76555 −0.243493
\(130\) 0 0
\(131\) −9.22093 −0.805636 −0.402818 0.915280i \(-0.631969\pi\)
−0.402818 + 0.915280i \(0.631969\pi\)
\(132\) 0 0
\(133\) 1.51741 0.131576
\(134\) 0 0
\(135\) −1.90366 −0.163841
\(136\) 0 0
\(137\) 14.9935 1.28098 0.640491 0.767966i \(-0.278731\pi\)
0.640491 + 0.767966i \(0.278731\pi\)
\(138\) 0 0
\(139\) −11.1669 −0.947161 −0.473580 0.880751i \(-0.657039\pi\)
−0.473580 + 0.880751i \(0.657039\pi\)
\(140\) 0 0
\(141\) −0.129160 −0.0108772
\(142\) 0 0
\(143\) 31.3410 2.62087
\(144\) 0 0
\(145\) 6.90298 0.573261
\(146\) 0 0
\(147\) −6.09845 −0.502992
\(148\) 0 0
\(149\) 19.6013 1.60580 0.802900 0.596114i \(-0.203289\pi\)
0.802900 + 0.596114i \(0.203289\pi\)
\(150\) 0 0
\(151\) −3.73694 −0.304108 −0.152054 0.988372i \(-0.548589\pi\)
−0.152054 + 0.988372i \(0.548589\pi\)
\(152\) 0 0
\(153\) 6.17169 0.498951
\(154\) 0 0
\(155\) 10.2658 0.824570
\(156\) 0 0
\(157\) 24.8232 1.98111 0.990553 0.137131i \(-0.0437882\pi\)
0.990553 + 0.137131i \(0.0437882\pi\)
\(158\) 0 0
\(159\) −8.82207 −0.699635
\(160\) 0 0
\(161\) −11.6459 −0.917826
\(162\) 0 0
\(163\) 19.1568 1.50048 0.750239 0.661167i \(-0.229939\pi\)
0.750239 + 0.661167i \(0.229939\pi\)
\(164\) 0 0
\(165\) −10.6178 −0.826594
\(166\) 0 0
\(167\) −16.2557 −1.25790 −0.628951 0.777445i \(-0.716516\pi\)
−0.628951 + 0.777445i \(0.716516\pi\)
\(168\) 0 0
\(169\) 18.5747 1.42882
\(170\) 0 0
\(171\) −0.419270 −0.0320624
\(172\) 0 0
\(173\) 13.3360 1.01392 0.506958 0.861971i \(-0.330770\pi\)
0.506958 + 0.861971i \(0.330770\pi\)
\(174\) 0 0
\(175\) 4.98021 0.376469
\(176\) 0 0
\(177\) 0.0305566 0.00229677
\(178\) 0 0
\(179\) 24.0711 1.79916 0.899579 0.436757i \(-0.143873\pi\)
0.899579 + 0.436757i \(0.143873\pi\)
\(180\) 0 0
\(181\) 6.94634 0.516318 0.258159 0.966102i \(-0.416884\pi\)
0.258159 + 0.966102i \(0.416884\pi\)
\(182\) 0 0
\(183\) 3.48688 0.257758
\(184\) 0 0
\(185\) −5.20833 −0.382924
\(186\) 0 0
\(187\) 34.4229 2.51725
\(188\) 0 0
\(189\) 3.61918 0.263257
\(190\) 0 0
\(191\) −12.5873 −0.910784 −0.455392 0.890291i \(-0.650501\pi\)
−0.455392 + 0.890291i \(0.650501\pi\)
\(192\) 0 0
\(193\) −5.10938 −0.367781 −0.183890 0.982947i \(-0.558869\pi\)
−0.183890 + 0.982947i \(0.558869\pi\)
\(194\) 0 0
\(195\) −10.6969 −0.766024
\(196\) 0 0
\(197\) −2.47196 −0.176120 −0.0880599 0.996115i \(-0.528067\pi\)
−0.0880599 + 0.996115i \(0.528067\pi\)
\(198\) 0 0
\(199\) 25.0861 1.77830 0.889152 0.457612i \(-0.151295\pi\)
0.889152 + 0.457612i \(0.151295\pi\)
\(200\) 0 0
\(201\) 11.2996 0.797011
\(202\) 0 0
\(203\) −13.1237 −0.921103
\(204\) 0 0
\(205\) −4.55271 −0.317975
\(206\) 0 0
\(207\) 3.21783 0.223655
\(208\) 0 0
\(209\) −2.33850 −0.161758
\(210\) 0 0
\(211\) 15.0915 1.03894 0.519471 0.854488i \(-0.326129\pi\)
0.519471 + 0.854488i \(0.326129\pi\)
\(212\) 0 0
\(213\) −3.48404 −0.238723
\(214\) 0 0
\(215\) 5.26469 0.359049
\(216\) 0 0
\(217\) −19.5170 −1.32490
\(218\) 0 0
\(219\) 7.80164 0.527186
\(220\) 0 0
\(221\) 34.6795 2.33280
\(222\) 0 0
\(223\) −27.7017 −1.85504 −0.927522 0.373768i \(-0.878066\pi\)
−0.927522 + 0.373768i \(0.878066\pi\)
\(224\) 0 0
\(225\) −1.37606 −0.0917374
\(226\) 0 0
\(227\) −14.0651 −0.933536 −0.466768 0.884380i \(-0.654582\pi\)
−0.466768 + 0.884380i \(0.654582\pi\)
\(228\) 0 0
\(229\) −10.9817 −0.725690 −0.362845 0.931850i \(-0.618195\pi\)
−0.362845 + 0.931850i \(0.618195\pi\)
\(230\) 0 0
\(231\) 20.1862 1.32815
\(232\) 0 0
\(233\) −16.3683 −1.07232 −0.536162 0.844115i \(-0.680127\pi\)
−0.536162 + 0.844115i \(0.680127\pi\)
\(234\) 0 0
\(235\) 0.245877 0.0160392
\(236\) 0 0
\(237\) 14.5184 0.943069
\(238\) 0 0
\(239\) −27.8170 −1.79933 −0.899665 0.436581i \(-0.856189\pi\)
−0.899665 + 0.436581i \(0.856189\pi\)
\(240\) 0 0
\(241\) 10.8561 0.699302 0.349651 0.936880i \(-0.386300\pi\)
0.349651 + 0.936880i \(0.386300\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 11.6094 0.741698
\(246\) 0 0
\(247\) −2.35594 −0.149905
\(248\) 0 0
\(249\) −5.10465 −0.323494
\(250\) 0 0
\(251\) −4.31403 −0.272299 −0.136150 0.990688i \(-0.543473\pi\)
−0.136150 + 0.990688i \(0.543473\pi\)
\(252\) 0 0
\(253\) 17.9476 1.12836
\(254\) 0 0
\(255\) −11.7488 −0.735740
\(256\) 0 0
\(257\) −26.7299 −1.66737 −0.833683 0.552244i \(-0.813772\pi\)
−0.833683 + 0.552244i \(0.813772\pi\)
\(258\) 0 0
\(259\) 9.90189 0.615273
\(260\) 0 0
\(261\) 3.62615 0.224453
\(262\) 0 0
\(263\) −7.27645 −0.448685 −0.224342 0.974510i \(-0.572023\pi\)
−0.224342 + 0.974510i \(0.572023\pi\)
\(264\) 0 0
\(265\) 16.7943 1.03166
\(266\) 0 0
\(267\) −11.8290 −0.723924
\(268\) 0 0
\(269\) 6.84338 0.417248 0.208624 0.977996i \(-0.433101\pi\)
0.208624 + 0.977996i \(0.433101\pi\)
\(270\) 0 0
\(271\) −24.3794 −1.48094 −0.740471 0.672089i \(-0.765397\pi\)
−0.740471 + 0.672089i \(0.765397\pi\)
\(272\) 0 0
\(273\) 20.3366 1.23083
\(274\) 0 0
\(275\) −7.67505 −0.462823
\(276\) 0 0
\(277\) −6.73872 −0.404891 −0.202445 0.979294i \(-0.564889\pi\)
−0.202445 + 0.979294i \(0.564889\pi\)
\(278\) 0 0
\(279\) 5.39266 0.322850
\(280\) 0 0
\(281\) 14.6602 0.874552 0.437276 0.899327i \(-0.355943\pi\)
0.437276 + 0.899327i \(0.355943\pi\)
\(282\) 0 0
\(283\) 10.3854 0.617346 0.308673 0.951168i \(-0.400115\pi\)
0.308673 + 0.951168i \(0.400115\pi\)
\(284\) 0 0
\(285\) 0.798150 0.0472783
\(286\) 0 0
\(287\) 8.65545 0.510915
\(288\) 0 0
\(289\) 21.0897 1.24057
\(290\) 0 0
\(291\) 11.7288 0.687556
\(292\) 0 0
\(293\) 16.0050 0.935020 0.467510 0.883988i \(-0.345151\pi\)
0.467510 + 0.883988i \(0.345151\pi\)
\(294\) 0 0
\(295\) −0.0581695 −0.00338676
\(296\) 0 0
\(297\) −5.57755 −0.323642
\(298\) 0 0
\(299\) 18.0814 1.04568
\(300\) 0 0
\(301\) −10.0090 −0.576911
\(302\) 0 0
\(303\) −18.1101 −1.04040
\(304\) 0 0
\(305\) −6.63786 −0.380082
\(306\) 0 0
\(307\) 15.5437 0.887126 0.443563 0.896243i \(-0.353714\pi\)
0.443563 + 0.896243i \(0.353714\pi\)
\(308\) 0 0
\(309\) 13.1885 0.750266
\(310\) 0 0
\(311\) 5.59429 0.317223 0.158611 0.987341i \(-0.449298\pi\)
0.158611 + 0.987341i \(0.449298\pi\)
\(312\) 0 0
\(313\) 24.5636 1.38841 0.694207 0.719775i \(-0.255755\pi\)
0.694207 + 0.719775i \(0.255755\pi\)
\(314\) 0 0
\(315\) −6.88970 −0.388191
\(316\) 0 0
\(317\) −3.67825 −0.206591 −0.103295 0.994651i \(-0.532939\pi\)
−0.103295 + 0.994651i \(0.532939\pi\)
\(318\) 0 0
\(319\) 20.2251 1.13239
\(320\) 0 0
\(321\) −0.332326 −0.0185486
\(322\) 0 0
\(323\) −2.58760 −0.143978
\(324\) 0 0
\(325\) −7.73227 −0.428909
\(326\) 0 0
\(327\) 17.5340 0.969634
\(328\) 0 0
\(329\) −0.467452 −0.0257715
\(330\) 0 0
\(331\) 25.4670 1.39979 0.699896 0.714245i \(-0.253230\pi\)
0.699896 + 0.714245i \(0.253230\pi\)
\(332\) 0 0
\(333\) −2.73595 −0.149929
\(334\) 0 0
\(335\) −21.5106 −1.17525
\(336\) 0 0
\(337\) −27.7981 −1.51426 −0.757130 0.653264i \(-0.773399\pi\)
−0.757130 + 0.653264i \(0.773399\pi\)
\(338\) 0 0
\(339\) −4.03768 −0.219296
\(340\) 0 0
\(341\) 30.0778 1.62881
\(342\) 0 0
\(343\) 3.26286 0.176178
\(344\) 0 0
\(345\) −6.12567 −0.329795
\(346\) 0 0
\(347\) 12.8933 0.692147 0.346073 0.938207i \(-0.387515\pi\)
0.346073 + 0.938207i \(0.387515\pi\)
\(348\) 0 0
\(349\) 25.7314 1.37737 0.688684 0.725061i \(-0.258189\pi\)
0.688684 + 0.725061i \(0.258189\pi\)
\(350\) 0 0
\(351\) −5.61913 −0.299927
\(352\) 0 0
\(353\) −9.39146 −0.499857 −0.249929 0.968264i \(-0.580407\pi\)
−0.249929 + 0.968264i \(0.580407\pi\)
\(354\) 0 0
\(355\) 6.63245 0.352014
\(356\) 0 0
\(357\) 22.3364 1.18217
\(358\) 0 0
\(359\) 32.7278 1.72731 0.863653 0.504086i \(-0.168171\pi\)
0.863653 + 0.504086i \(0.168171\pi\)
\(360\) 0 0
\(361\) −18.8242 −0.990748
\(362\) 0 0
\(363\) −20.1091 −1.05545
\(364\) 0 0
\(365\) −14.8517 −0.777374
\(366\) 0 0
\(367\) 10.5432 0.550353 0.275176 0.961394i \(-0.411264\pi\)
0.275176 + 0.961394i \(0.411264\pi\)
\(368\) 0 0
\(369\) −2.39155 −0.124499
\(370\) 0 0
\(371\) −31.9286 −1.65765
\(372\) 0 0
\(373\) −15.5545 −0.805382 −0.402691 0.915336i \(-0.631925\pi\)
−0.402691 + 0.915336i \(0.631925\pi\)
\(374\) 0 0
\(375\) 12.1379 0.626798
\(376\) 0 0
\(377\) 20.3758 1.04941
\(378\) 0 0
\(379\) −2.27475 −0.116846 −0.0584231 0.998292i \(-0.518607\pi\)
−0.0584231 + 0.998292i \(0.518607\pi\)
\(380\) 0 0
\(381\) 6.02421 0.308630
\(382\) 0 0
\(383\) −3.50779 −0.179240 −0.0896199 0.995976i \(-0.528565\pi\)
−0.0896199 + 0.995976i \(0.528565\pi\)
\(384\) 0 0
\(385\) −38.4277 −1.95846
\(386\) 0 0
\(387\) 2.76555 0.140581
\(388\) 0 0
\(389\) 31.3820 1.59113 0.795565 0.605868i \(-0.207174\pi\)
0.795565 + 0.605868i \(0.207174\pi\)
\(390\) 0 0
\(391\) 19.8594 1.00434
\(392\) 0 0
\(393\) 9.22093 0.465134
\(394\) 0 0
\(395\) −27.6381 −1.39062
\(396\) 0 0
\(397\) −19.6125 −0.984325 −0.492163 0.870503i \(-0.663793\pi\)
−0.492163 + 0.870503i \(0.663793\pi\)
\(398\) 0 0
\(399\) −1.51741 −0.0759657
\(400\) 0 0
\(401\) 7.08248 0.353682 0.176841 0.984239i \(-0.443412\pi\)
0.176841 + 0.984239i \(0.443412\pi\)
\(402\) 0 0
\(403\) 30.3021 1.50945
\(404\) 0 0
\(405\) 1.90366 0.0945939
\(406\) 0 0
\(407\) −15.2599 −0.756405
\(408\) 0 0
\(409\) −16.5777 −0.819714 −0.409857 0.912150i \(-0.634421\pi\)
−0.409857 + 0.912150i \(0.634421\pi\)
\(410\) 0 0
\(411\) −14.9935 −0.739575
\(412\) 0 0
\(413\) 0.110590 0.00544176
\(414\) 0 0
\(415\) 9.71755 0.477016
\(416\) 0 0
\(417\) 11.1669 0.546844
\(418\) 0 0
\(419\) −36.5142 −1.78384 −0.891918 0.452196i \(-0.850641\pi\)
−0.891918 + 0.452196i \(0.850641\pi\)
\(420\) 0 0
\(421\) −19.7421 −0.962172 −0.481086 0.876673i \(-0.659758\pi\)
−0.481086 + 0.876673i \(0.659758\pi\)
\(422\) 0 0
\(423\) 0.129160 0.00627996
\(424\) 0 0
\(425\) −8.49262 −0.411952
\(426\) 0 0
\(427\) 12.6197 0.610708
\(428\) 0 0
\(429\) −31.3410 −1.51316
\(430\) 0 0
\(431\) 3.77006 0.181597 0.0907986 0.995869i \(-0.471058\pi\)
0.0907986 + 0.995869i \(0.471058\pi\)
\(432\) 0 0
\(433\) 11.6330 0.559045 0.279522 0.960139i \(-0.409824\pi\)
0.279522 + 0.960139i \(0.409824\pi\)
\(434\) 0 0
\(435\) −6.90298 −0.330972
\(436\) 0 0
\(437\) −1.34914 −0.0645382
\(438\) 0 0
\(439\) 36.0749 1.72176 0.860880 0.508809i \(-0.169914\pi\)
0.860880 + 0.508809i \(0.169914\pi\)
\(440\) 0 0
\(441\) 6.09845 0.290403
\(442\) 0 0
\(443\) 28.7802 1.36739 0.683694 0.729769i \(-0.260373\pi\)
0.683694 + 0.729769i \(0.260373\pi\)
\(444\) 0 0
\(445\) 22.5185 1.06748
\(446\) 0 0
\(447\) −19.6013 −0.927109
\(448\) 0 0
\(449\) −13.3412 −0.629609 −0.314805 0.949157i \(-0.601939\pi\)
−0.314805 + 0.949157i \(0.601939\pi\)
\(450\) 0 0
\(451\) −13.3390 −0.628109
\(452\) 0 0
\(453\) 3.73694 0.175577
\(454\) 0 0
\(455\) −38.7142 −1.81495
\(456\) 0 0
\(457\) −30.3061 −1.41766 −0.708830 0.705379i \(-0.750777\pi\)
−0.708830 + 0.705379i \(0.750777\pi\)
\(458\) 0 0
\(459\) −6.17169 −0.288070
\(460\) 0 0
\(461\) 9.62387 0.448228 0.224114 0.974563i \(-0.428051\pi\)
0.224114 + 0.974563i \(0.428051\pi\)
\(462\) 0 0
\(463\) 1.99653 0.0927867 0.0463934 0.998923i \(-0.485227\pi\)
0.0463934 + 0.998923i \(0.485227\pi\)
\(464\) 0 0
\(465\) −10.2658 −0.476066
\(466\) 0 0
\(467\) 0.964828 0.0446469 0.0223235 0.999751i \(-0.492894\pi\)
0.0223235 + 0.999751i \(0.492894\pi\)
\(468\) 0 0
\(469\) 40.8952 1.88837
\(470\) 0 0
\(471\) −24.8232 −1.14379
\(472\) 0 0
\(473\) 15.4250 0.709243
\(474\) 0 0
\(475\) 0.576941 0.0264719
\(476\) 0 0
\(477\) 8.82207 0.403935
\(478\) 0 0
\(479\) −20.4762 −0.935581 −0.467790 0.883839i \(-0.654950\pi\)
−0.467790 + 0.883839i \(0.654950\pi\)
\(480\) 0 0
\(481\) −15.3737 −0.700979
\(482\) 0 0
\(483\) 11.6459 0.529907
\(484\) 0 0
\(485\) −22.3277 −1.01385
\(486\) 0 0
\(487\) −13.3594 −0.605370 −0.302685 0.953091i \(-0.597883\pi\)
−0.302685 + 0.953091i \(0.597883\pi\)
\(488\) 0 0
\(489\) −19.1568 −0.866301
\(490\) 0 0
\(491\) 1.02733 0.0463629 0.0231815 0.999731i \(-0.492620\pi\)
0.0231815 + 0.999731i \(0.492620\pi\)
\(492\) 0 0
\(493\) 22.3795 1.00792
\(494\) 0 0
\(495\) 10.6178 0.477234
\(496\) 0 0
\(497\) −12.6094 −0.565608
\(498\) 0 0
\(499\) −38.8368 −1.73858 −0.869288 0.494307i \(-0.835422\pi\)
−0.869288 + 0.494307i \(0.835422\pi\)
\(500\) 0 0
\(501\) 16.2557 0.726250
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 34.4756 1.53414
\(506\) 0 0
\(507\) −18.5747 −0.824930
\(508\) 0 0
\(509\) −12.4332 −0.551093 −0.275547 0.961288i \(-0.588859\pi\)
−0.275547 + 0.961288i \(0.588859\pi\)
\(510\) 0 0
\(511\) 28.2355 1.24907
\(512\) 0 0
\(513\) 0.419270 0.0185112
\(514\) 0 0
\(515\) −25.1064 −1.10632
\(516\) 0 0
\(517\) 0.720395 0.0316830
\(518\) 0 0
\(519\) −13.3360 −0.585385
\(520\) 0 0
\(521\) 0.694905 0.0304444 0.0152222 0.999884i \(-0.495154\pi\)
0.0152222 + 0.999884i \(0.495154\pi\)
\(522\) 0 0
\(523\) −11.4278 −0.499703 −0.249852 0.968284i \(-0.580382\pi\)
−0.249852 + 0.968284i \(0.580382\pi\)
\(524\) 0 0
\(525\) −4.98021 −0.217354
\(526\) 0 0
\(527\) 33.2818 1.44978
\(528\) 0 0
\(529\) −12.6456 −0.549807
\(530\) 0 0
\(531\) −0.0305566 −0.00132604
\(532\) 0 0
\(533\) −13.4384 −0.582084
\(534\) 0 0
\(535\) 0.632638 0.0273513
\(536\) 0 0
\(537\) −24.0711 −1.03874
\(538\) 0 0
\(539\) 34.0144 1.46511
\(540\) 0 0
\(541\) 26.3541 1.13305 0.566526 0.824044i \(-0.308287\pi\)
0.566526 + 0.824044i \(0.308287\pi\)
\(542\) 0 0
\(543\) −6.94634 −0.298096
\(544\) 0 0
\(545\) −33.3789 −1.42980
\(546\) 0 0
\(547\) 6.56641 0.280759 0.140380 0.990098i \(-0.455168\pi\)
0.140380 + 0.990098i \(0.455168\pi\)
\(548\) 0 0
\(549\) −3.48688 −0.148817
\(550\) 0 0
\(551\) −1.52034 −0.0647686
\(552\) 0 0
\(553\) 52.5446 2.23442
\(554\) 0 0
\(555\) 5.20833 0.221081
\(556\) 0 0
\(557\) 33.8341 1.43360 0.716799 0.697280i \(-0.245607\pi\)
0.716799 + 0.697280i \(0.245607\pi\)
\(558\) 0 0
\(559\) 15.5400 0.657273
\(560\) 0 0
\(561\) −34.4229 −1.45334
\(562\) 0 0
\(563\) −0.556859 −0.0234688 −0.0117344 0.999931i \(-0.503735\pi\)
−0.0117344 + 0.999931i \(0.503735\pi\)
\(564\) 0 0
\(565\) 7.68638 0.323368
\(566\) 0 0
\(567\) −3.61918 −0.151991
\(568\) 0 0
\(569\) 21.0750 0.883509 0.441754 0.897136i \(-0.354356\pi\)
0.441754 + 0.897136i \(0.354356\pi\)
\(570\) 0 0
\(571\) 3.38512 0.141663 0.0708314 0.997488i \(-0.477435\pi\)
0.0708314 + 0.997488i \(0.477435\pi\)
\(572\) 0 0
\(573\) 12.5873 0.525841
\(574\) 0 0
\(575\) −4.42793 −0.184658
\(576\) 0 0
\(577\) −12.4257 −0.517289 −0.258645 0.965973i \(-0.583276\pi\)
−0.258645 + 0.965973i \(0.583276\pi\)
\(578\) 0 0
\(579\) 5.10938 0.212338
\(580\) 0 0
\(581\) −18.4746 −0.766458
\(582\) 0 0
\(583\) 49.2055 2.03789
\(584\) 0 0
\(585\) 10.6969 0.442264
\(586\) 0 0
\(587\) 20.9155 0.863274 0.431637 0.902047i \(-0.357936\pi\)
0.431637 + 0.902047i \(0.357936\pi\)
\(588\) 0 0
\(589\) −2.26098 −0.0931621
\(590\) 0 0
\(591\) 2.47196 0.101683
\(592\) 0 0
\(593\) 8.03087 0.329788 0.164894 0.986311i \(-0.447272\pi\)
0.164894 + 0.986311i \(0.447272\pi\)
\(594\) 0 0
\(595\) −42.5211 −1.74319
\(596\) 0 0
\(597\) −25.0861 −1.02670
\(598\) 0 0
\(599\) 13.4615 0.550024 0.275012 0.961441i \(-0.411318\pi\)
0.275012 + 0.961441i \(0.411318\pi\)
\(600\) 0 0
\(601\) −25.1994 −1.02790 −0.513952 0.857819i \(-0.671819\pi\)
−0.513952 + 0.857819i \(0.671819\pi\)
\(602\) 0 0
\(603\) −11.2996 −0.460155
\(604\) 0 0
\(605\) 38.2810 1.55634
\(606\) 0 0
\(607\) 9.94928 0.403829 0.201914 0.979403i \(-0.435284\pi\)
0.201914 + 0.979403i \(0.435284\pi\)
\(608\) 0 0
\(609\) 13.1237 0.531799
\(610\) 0 0
\(611\) 0.725766 0.0293613
\(612\) 0 0
\(613\) 42.0466 1.69825 0.849123 0.528195i \(-0.177131\pi\)
0.849123 + 0.528195i \(0.177131\pi\)
\(614\) 0 0
\(615\) 4.55271 0.183583
\(616\) 0 0
\(617\) −2.69200 −0.108376 −0.0541880 0.998531i \(-0.517257\pi\)
−0.0541880 + 0.998531i \(0.517257\pi\)
\(618\) 0 0
\(619\) −7.98069 −0.320771 −0.160386 0.987054i \(-0.551274\pi\)
−0.160386 + 0.987054i \(0.551274\pi\)
\(620\) 0 0
\(621\) −3.21783 −0.129127
\(622\) 0 0
\(623\) −42.8113 −1.71520
\(624\) 0 0
\(625\) −16.2262 −0.649046
\(626\) 0 0
\(627\) 2.33850 0.0933908
\(628\) 0 0
\(629\) −16.8854 −0.673266
\(630\) 0 0
\(631\) 9.56812 0.380901 0.190450 0.981697i \(-0.439005\pi\)
0.190450 + 0.981697i \(0.439005\pi\)
\(632\) 0 0
\(633\) −15.0915 −0.599834
\(634\) 0 0
\(635\) −11.4681 −0.455097
\(636\) 0 0
\(637\) 34.2680 1.35775
\(638\) 0 0
\(639\) 3.48404 0.137827
\(640\) 0 0
\(641\) 22.5848 0.892045 0.446023 0.895022i \(-0.352840\pi\)
0.446023 + 0.895022i \(0.352840\pi\)
\(642\) 0 0
\(643\) 19.5119 0.769473 0.384736 0.923026i \(-0.374292\pi\)
0.384736 + 0.923026i \(0.374292\pi\)
\(644\) 0 0
\(645\) −5.26469 −0.207297
\(646\) 0 0
\(647\) 10.9375 0.429996 0.214998 0.976614i \(-0.431025\pi\)
0.214998 + 0.976614i \(0.431025\pi\)
\(648\) 0 0
\(649\) −0.170431 −0.00669000
\(650\) 0 0
\(651\) 19.5170 0.764932
\(652\) 0 0
\(653\) −10.6523 −0.416858 −0.208429 0.978037i \(-0.566835\pi\)
−0.208429 + 0.978037i \(0.566835\pi\)
\(654\) 0 0
\(655\) −17.5535 −0.685874
\(656\) 0 0
\(657\) −7.80164 −0.304371
\(658\) 0 0
\(659\) −17.2770 −0.673017 −0.336509 0.941680i \(-0.609246\pi\)
−0.336509 + 0.941680i \(0.609246\pi\)
\(660\) 0 0
\(661\) −42.7456 −1.66261 −0.831306 0.555815i \(-0.812406\pi\)
−0.831306 + 0.555815i \(0.812406\pi\)
\(662\) 0 0
\(663\) −34.6795 −1.34684
\(664\) 0 0
\(665\) 2.88865 0.112017
\(666\) 0 0
\(667\) 11.6683 0.451800
\(668\) 0 0
\(669\) 27.7017 1.07101
\(670\) 0 0
\(671\) −19.4483 −0.750792
\(672\) 0 0
\(673\) 2.48147 0.0956535 0.0478268 0.998856i \(-0.484770\pi\)
0.0478268 + 0.998856i \(0.484770\pi\)
\(674\) 0 0
\(675\) 1.37606 0.0529646
\(676\) 0 0
\(677\) 19.1210 0.734882 0.367441 0.930047i \(-0.380234\pi\)
0.367441 + 0.930047i \(0.380234\pi\)
\(678\) 0 0
\(679\) 42.4487 1.62903
\(680\) 0 0
\(681\) 14.0651 0.538977
\(682\) 0 0
\(683\) −44.5689 −1.70538 −0.852690 0.522417i \(-0.825030\pi\)
−0.852690 + 0.522417i \(0.825030\pi\)
\(684\) 0 0
\(685\) 28.5426 1.09056
\(686\) 0 0
\(687\) 10.9817 0.418977
\(688\) 0 0
\(689\) 49.5724 1.88856
\(690\) 0 0
\(691\) 25.0227 0.951908 0.475954 0.879470i \(-0.342103\pi\)
0.475954 + 0.879470i \(0.342103\pi\)
\(692\) 0 0
\(693\) −20.1862 −0.766809
\(694\) 0 0
\(695\) −21.2580 −0.806360
\(696\) 0 0
\(697\) −14.7599 −0.559071
\(698\) 0 0
\(699\) 16.3683 0.619107
\(700\) 0 0
\(701\) 25.2592 0.954028 0.477014 0.878896i \(-0.341719\pi\)
0.477014 + 0.878896i \(0.341719\pi\)
\(702\) 0 0
\(703\) 1.14710 0.0432638
\(704\) 0 0
\(705\) −0.245877 −0.00926026
\(706\) 0 0
\(707\) −65.5438 −2.46503
\(708\) 0 0
\(709\) 9.60807 0.360839 0.180419 0.983590i \(-0.442255\pi\)
0.180419 + 0.983590i \(0.442255\pi\)
\(710\) 0 0
\(711\) −14.5184 −0.544481
\(712\) 0 0
\(713\) 17.3527 0.649863
\(714\) 0 0
\(715\) 59.6628 2.23126
\(716\) 0 0
\(717\) 27.8170 1.03884
\(718\) 0 0
\(719\) −18.8898 −0.704472 −0.352236 0.935911i \(-0.614579\pi\)
−0.352236 + 0.935911i \(0.614579\pi\)
\(720\) 0 0
\(721\) 47.7315 1.77761
\(722\) 0 0
\(723\) −10.8561 −0.403742
\(724\) 0 0
\(725\) −4.98981 −0.185317
\(726\) 0 0
\(727\) 1.60379 0.0594811 0.0297406 0.999558i \(-0.490532\pi\)
0.0297406 + 0.999558i \(0.490532\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 17.0681 0.631288
\(732\) 0 0
\(733\) 38.2841 1.41405 0.707027 0.707186i \(-0.250036\pi\)
0.707027 + 0.707186i \(0.250036\pi\)
\(734\) 0 0
\(735\) −11.6094 −0.428220
\(736\) 0 0
\(737\) −63.0240 −2.32152
\(738\) 0 0
\(739\) −11.0649 −0.407028 −0.203514 0.979072i \(-0.565236\pi\)
−0.203514 + 0.979072i \(0.565236\pi\)
\(740\) 0 0
\(741\) 2.35594 0.0865474
\(742\) 0 0
\(743\) −12.2036 −0.447706 −0.223853 0.974623i \(-0.571864\pi\)
−0.223853 + 0.974623i \(0.571864\pi\)
\(744\) 0 0
\(745\) 37.3143 1.36709
\(746\) 0 0
\(747\) 5.10465 0.186769
\(748\) 0 0
\(749\) −1.20275 −0.0439475
\(750\) 0 0
\(751\) 20.0871 0.732987 0.366493 0.930421i \(-0.380558\pi\)
0.366493 + 0.930421i \(0.380558\pi\)
\(752\) 0 0
\(753\) 4.31403 0.157212
\(754\) 0 0
\(755\) −7.11388 −0.258901
\(756\) 0 0
\(757\) −0.813516 −0.0295677 −0.0147839 0.999891i \(-0.504706\pi\)
−0.0147839 + 0.999891i \(0.504706\pi\)
\(758\) 0 0
\(759\) −17.9476 −0.651457
\(760\) 0 0
\(761\) −40.9585 −1.48474 −0.742372 0.669988i \(-0.766299\pi\)
−0.742372 + 0.669988i \(0.766299\pi\)
\(762\) 0 0
\(763\) 63.4588 2.29736
\(764\) 0 0
\(765\) 11.7488 0.424780
\(766\) 0 0
\(767\) −0.171701 −0.00619978
\(768\) 0 0
\(769\) 23.5116 0.847852 0.423926 0.905697i \(-0.360652\pi\)
0.423926 + 0.905697i \(0.360652\pi\)
\(770\) 0 0
\(771\) 26.7299 0.962654
\(772\) 0 0
\(773\) −7.38215 −0.265517 −0.132759 0.991148i \(-0.542384\pi\)
−0.132759 + 0.991148i \(0.542384\pi\)
\(774\) 0 0
\(775\) −7.42063 −0.266557
\(776\) 0 0
\(777\) −9.90189 −0.355228
\(778\) 0 0
\(779\) 1.00271 0.0359257
\(780\) 0 0
\(781\) 19.4324 0.695347
\(782\) 0 0
\(783\) −3.62615 −0.129588
\(784\) 0 0
\(785\) 47.2550 1.68660
\(786\) 0 0
\(787\) −42.1085 −1.50101 −0.750503 0.660867i \(-0.770189\pi\)
−0.750503 + 0.660867i \(0.770189\pi\)
\(788\) 0 0
\(789\) 7.27645 0.259048
\(790\) 0 0
\(791\) −14.6131 −0.519581
\(792\) 0 0
\(793\) −19.5933 −0.695777
\(794\) 0 0
\(795\) −16.7943 −0.595631
\(796\) 0 0
\(797\) −43.0432 −1.52467 −0.762335 0.647183i \(-0.775947\pi\)
−0.762335 + 0.647183i \(0.775947\pi\)
\(798\) 0 0
\(799\) 0.797134 0.0282006
\(800\) 0 0
\(801\) 11.8290 0.417958
\(802\) 0 0
\(803\) −43.5141 −1.53558
\(804\) 0 0
\(805\) −22.1699 −0.781386
\(806\) 0 0
\(807\) −6.84338 −0.240898
\(808\) 0 0
\(809\) −14.2585 −0.501301 −0.250650 0.968078i \(-0.580644\pi\)
−0.250650 + 0.968078i \(0.580644\pi\)
\(810\) 0 0
\(811\) 12.1148 0.425407 0.212704 0.977117i \(-0.431773\pi\)
0.212704 + 0.977117i \(0.431773\pi\)
\(812\) 0 0
\(813\) 24.3794 0.855022
\(814\) 0 0
\(815\) 36.4681 1.27742
\(816\) 0 0
\(817\) −1.15951 −0.0405663
\(818\) 0 0
\(819\) −20.3366 −0.710620
\(820\) 0 0
\(821\) −50.6102 −1.76631 −0.883155 0.469082i \(-0.844585\pi\)
−0.883155 + 0.469082i \(0.844585\pi\)
\(822\) 0 0
\(823\) 32.3566 1.12788 0.563939 0.825816i \(-0.309285\pi\)
0.563939 + 0.825816i \(0.309285\pi\)
\(824\) 0 0
\(825\) 7.67505 0.267211
\(826\) 0 0
\(827\) 11.8726 0.412849 0.206425 0.978462i \(-0.433817\pi\)
0.206425 + 0.978462i \(0.433817\pi\)
\(828\) 0 0
\(829\) 16.3237 0.566947 0.283473 0.958980i \(-0.408513\pi\)
0.283473 + 0.958980i \(0.408513\pi\)
\(830\) 0 0
\(831\) 6.73872 0.233764
\(832\) 0 0
\(833\) 37.6377 1.30407
\(834\) 0 0
\(835\) −30.9454 −1.07091
\(836\) 0 0
\(837\) −5.39266 −0.186398
\(838\) 0 0
\(839\) 48.5929 1.67761 0.838807 0.544428i \(-0.183253\pi\)
0.838807 + 0.544428i \(0.183253\pi\)
\(840\) 0 0
\(841\) −15.8510 −0.546587
\(842\) 0 0
\(843\) −14.6602 −0.504923
\(844\) 0 0
\(845\) 35.3599 1.21642
\(846\) 0 0
\(847\) −72.7784 −2.50070
\(848\) 0 0
\(849\) −10.3854 −0.356425
\(850\) 0 0
\(851\) −8.80382 −0.301791
\(852\) 0 0
\(853\) −29.7272 −1.01784 −0.508920 0.860814i \(-0.669955\pi\)
−0.508920 + 0.860814i \(0.669955\pi\)
\(854\) 0 0
\(855\) −0.798150 −0.0272961
\(856\) 0 0
\(857\) −6.14166 −0.209795 −0.104897 0.994483i \(-0.533451\pi\)
−0.104897 + 0.994483i \(0.533451\pi\)
\(858\) 0 0
\(859\) −19.2930 −0.658269 −0.329135 0.944283i \(-0.606757\pi\)
−0.329135 + 0.944283i \(0.606757\pi\)
\(860\) 0 0
\(861\) −8.65545 −0.294977
\(862\) 0 0
\(863\) 21.5629 0.734009 0.367004 0.930219i \(-0.380383\pi\)
0.367004 + 0.930219i \(0.380383\pi\)
\(864\) 0 0
\(865\) 25.3873 0.863193
\(866\) 0 0
\(867\) −21.0897 −0.716244
\(868\) 0 0
\(869\) −80.9769 −2.74695
\(870\) 0 0
\(871\) −63.4939 −2.15141
\(872\) 0 0
\(873\) −11.7288 −0.396961
\(874\) 0 0
\(875\) 43.9292 1.48508
\(876\) 0 0
\(877\) −43.7559 −1.47753 −0.738766 0.673962i \(-0.764591\pi\)
−0.738766 + 0.673962i \(0.764591\pi\)
\(878\) 0 0
\(879\) −16.0050 −0.539834
\(880\) 0 0
\(881\) 37.3214 1.25739 0.628696 0.777651i \(-0.283589\pi\)
0.628696 + 0.777651i \(0.283589\pi\)
\(882\) 0 0
\(883\) −3.04779 −0.102566 −0.0512831 0.998684i \(-0.516331\pi\)
−0.0512831 + 0.998684i \(0.516331\pi\)
\(884\) 0 0
\(885\) 0.0581695 0.00195535
\(886\) 0 0
\(887\) 10.4385 0.350490 0.175245 0.984525i \(-0.443928\pi\)
0.175245 + 0.984525i \(0.443928\pi\)
\(888\) 0 0
\(889\) 21.8027 0.731239
\(890\) 0 0
\(891\) 5.57755 0.186855
\(892\) 0 0
\(893\) −0.0541528 −0.00181216
\(894\) 0 0
\(895\) 45.8233 1.53170
\(896\) 0 0
\(897\) −18.0814 −0.603721
\(898\) 0 0
\(899\) 19.5546 0.652183
\(900\) 0 0
\(901\) 54.4470 1.81389
\(902\) 0 0
\(903\) 10.0090 0.333080
\(904\) 0 0
\(905\) 13.2235 0.439564
\(906\) 0 0
\(907\) −45.4241 −1.50828 −0.754141 0.656713i \(-0.771946\pi\)
−0.754141 + 0.656713i \(0.771946\pi\)
\(908\) 0 0
\(909\) 18.1101 0.600675
\(910\) 0 0
\(911\) 23.1594 0.767305 0.383652 0.923478i \(-0.374666\pi\)
0.383652 + 0.923478i \(0.374666\pi\)
\(912\) 0 0
\(913\) 28.4715 0.942268
\(914\) 0 0
\(915\) 6.63786 0.219441
\(916\) 0 0
\(917\) 33.3722 1.10205
\(918\) 0 0
\(919\) 1.92326 0.0634425 0.0317213 0.999497i \(-0.489901\pi\)
0.0317213 + 0.999497i \(0.489901\pi\)
\(920\) 0 0
\(921\) −15.5437 −0.512182
\(922\) 0 0
\(923\) 19.5773 0.644395
\(924\) 0 0
\(925\) 3.76483 0.123787
\(926\) 0 0
\(927\) −13.1885 −0.433167
\(928\) 0 0
\(929\) −32.2206 −1.05712 −0.528561 0.848895i \(-0.677268\pi\)
−0.528561 + 0.848895i \(0.677268\pi\)
\(930\) 0 0
\(931\) −2.55690 −0.0837990
\(932\) 0 0
\(933\) −5.59429 −0.183149
\(934\) 0 0
\(935\) 65.5297 2.14305
\(936\) 0 0
\(937\) −6.72064 −0.219554 −0.109777 0.993956i \(-0.535014\pi\)
−0.109777 + 0.993956i \(0.535014\pi\)
\(938\) 0 0
\(939\) −24.5636 −0.801602
\(940\) 0 0
\(941\) 52.5431 1.71286 0.856428 0.516266i \(-0.172678\pi\)
0.856428 + 0.516266i \(0.172678\pi\)
\(942\) 0 0
\(943\) −7.69561 −0.250603
\(944\) 0 0
\(945\) 6.88970 0.224122
\(946\) 0 0
\(947\) −9.59653 −0.311845 −0.155923 0.987769i \(-0.549835\pi\)
−0.155923 + 0.987769i \(0.549835\pi\)
\(948\) 0 0
\(949\) −43.8385 −1.42306
\(950\) 0 0
\(951\) 3.67825 0.119275
\(952\) 0 0
\(953\) 21.5868 0.699264 0.349632 0.936887i \(-0.386307\pi\)
0.349632 + 0.936887i \(0.386307\pi\)
\(954\) 0 0
\(955\) −23.9620 −0.775391
\(956\) 0 0
\(957\) −20.2251 −0.653783
\(958\) 0 0
\(959\) −54.2642 −1.75228
\(960\) 0 0
\(961\) −1.91921 −0.0619100
\(962\) 0 0
\(963\) 0.332326 0.0107091
\(964\) 0 0
\(965\) −9.72654 −0.313108
\(966\) 0 0
\(967\) 34.0890 1.09623 0.548114 0.836404i \(-0.315346\pi\)
0.548114 + 0.836404i \(0.315346\pi\)
\(968\) 0 0
\(969\) 2.58760 0.0831258
\(970\) 0 0
\(971\) −10.3510 −0.332179 −0.166089 0.986111i \(-0.553114\pi\)
−0.166089 + 0.986111i \(0.553114\pi\)
\(972\) 0 0
\(973\) 40.4149 1.29564
\(974\) 0 0
\(975\) 7.73227 0.247631
\(976\) 0 0
\(977\) −57.8074 −1.84942 −0.924711 0.380670i \(-0.875693\pi\)
−0.924711 + 0.380670i \(0.875693\pi\)
\(978\) 0 0
\(979\) 65.9769 2.10863
\(980\) 0 0
\(981\) −17.5340 −0.559819
\(982\) 0 0
\(983\) −61.7179 −1.96849 −0.984247 0.176797i \(-0.943426\pi\)
−0.984247 + 0.176797i \(0.943426\pi\)
\(984\) 0 0
\(985\) −4.70578 −0.149939
\(986\) 0 0
\(987\) 0.467452 0.0148792
\(988\) 0 0
\(989\) 8.89909 0.282974
\(990\) 0 0
\(991\) 25.5848 0.812727 0.406364 0.913711i \(-0.366797\pi\)
0.406364 + 0.913711i \(0.366797\pi\)
\(992\) 0 0
\(993\) −25.4670 −0.808170
\(994\) 0 0
\(995\) 47.7554 1.51395
\(996\) 0 0
\(997\) −21.9572 −0.695391 −0.347695 0.937608i \(-0.613036\pi\)
−0.347695 + 0.937608i \(0.613036\pi\)
\(998\) 0 0
\(999\) 2.73595 0.0865616
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 \(a_p\))