Properties

Label 6036.2.a.i.1.20
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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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 1.20
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+2.53458 q^{5}\) \(+3.60576 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+2.53458 q^{5}\) \(+3.60576 q^{7}\) \(+1.00000 q^{9}\) \(+4.66613 q^{11}\) \(-2.60384 q^{13}\) \(-2.53458 q^{15}\) \(+2.74474 q^{17}\) \(+0.716395 q^{19}\) \(-3.60576 q^{21}\) \(+7.76678 q^{23}\) \(+1.42411 q^{25}\) \(-1.00000 q^{27}\) \(+8.07933 q^{29}\) \(-4.58770 q^{31}\) \(-4.66613 q^{33}\) \(+9.13909 q^{35}\) \(-10.4330 q^{37}\) \(+2.60384 q^{39}\) \(+10.0989 q^{41}\) \(-1.83235 q^{43}\) \(+2.53458 q^{45}\) \(+2.79183 q^{47}\) \(+6.00147 q^{49}\) \(-2.74474 q^{51}\) \(-10.2851 q^{53}\) \(+11.8267 q^{55}\) \(-0.716395 q^{57}\) \(+5.44275 q^{59}\) \(+8.24320 q^{61}\) \(+3.60576 q^{63}\) \(-6.59965 q^{65}\) \(-1.77928 q^{67}\) \(-7.76678 q^{69}\) \(+0.897417 q^{71}\) \(+0.515081 q^{73}\) \(-1.42411 q^{75}\) \(+16.8249 q^{77}\) \(+6.23609 q^{79}\) \(+1.00000 q^{81}\) \(-7.92540 q^{83}\) \(+6.95678 q^{85}\) \(-8.07933 q^{87}\) \(+3.24000 q^{89}\) \(-9.38882 q^{91}\) \(+4.58770 q^{93}\) \(+1.81576 q^{95}\) \(-0.898636 q^{97}\) \(+4.66613 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.53458 1.13350 0.566750 0.823890i \(-0.308201\pi\)
0.566750 + 0.823890i \(0.308201\pi\)
\(6\) 0 0
\(7\) 3.60576 1.36285 0.681424 0.731889i \(-0.261361\pi\)
0.681424 + 0.731889i \(0.261361\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.66613 1.40689 0.703446 0.710749i \(-0.251644\pi\)
0.703446 + 0.710749i \(0.251644\pi\)
\(12\) 0 0
\(13\) −2.60384 −0.722176 −0.361088 0.932532i \(-0.617595\pi\)
−0.361088 + 0.932532i \(0.617595\pi\)
\(14\) 0 0
\(15\) −2.53458 −0.654426
\(16\) 0 0
\(17\) 2.74474 0.665698 0.332849 0.942980i \(-0.391990\pi\)
0.332849 + 0.942980i \(0.391990\pi\)
\(18\) 0 0
\(19\) 0.716395 0.164352 0.0821762 0.996618i \(-0.473813\pi\)
0.0821762 + 0.996618i \(0.473813\pi\)
\(20\) 0 0
\(21\) −3.60576 −0.786840
\(22\) 0 0
\(23\) 7.76678 1.61948 0.809742 0.586786i \(-0.199607\pi\)
0.809742 + 0.586786i \(0.199607\pi\)
\(24\) 0 0
\(25\) 1.42411 0.284822
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.07933 1.50029 0.750147 0.661271i \(-0.229983\pi\)
0.750147 + 0.661271i \(0.229983\pi\)
\(30\) 0 0
\(31\) −4.58770 −0.823976 −0.411988 0.911189i \(-0.635165\pi\)
−0.411988 + 0.911189i \(0.635165\pi\)
\(32\) 0 0
\(33\) −4.66613 −0.812269
\(34\) 0 0
\(35\) 9.13909 1.54479
\(36\) 0 0
\(37\) −10.4330 −1.71517 −0.857586 0.514341i \(-0.828037\pi\)
−0.857586 + 0.514341i \(0.828037\pi\)
\(38\) 0 0
\(39\) 2.60384 0.416948
\(40\) 0 0
\(41\) 10.0989 1.57718 0.788591 0.614918i \(-0.210811\pi\)
0.788591 + 0.614918i \(0.210811\pi\)
\(42\) 0 0
\(43\) −1.83235 −0.279431 −0.139715 0.990192i \(-0.544619\pi\)
−0.139715 + 0.990192i \(0.544619\pi\)
\(44\) 0 0
\(45\) 2.53458 0.377833
\(46\) 0 0
\(47\) 2.79183 0.407230 0.203615 0.979051i \(-0.434731\pi\)
0.203615 + 0.979051i \(0.434731\pi\)
\(48\) 0 0
\(49\) 6.00147 0.857353
\(50\) 0 0
\(51\) −2.74474 −0.384341
\(52\) 0 0
\(53\) −10.2851 −1.41277 −0.706386 0.707827i \(-0.749676\pi\)
−0.706386 + 0.707827i \(0.749676\pi\)
\(54\) 0 0
\(55\) 11.8267 1.59471
\(56\) 0 0
\(57\) −0.716395 −0.0948889
\(58\) 0 0
\(59\) 5.44275 0.708586 0.354293 0.935134i \(-0.384722\pi\)
0.354293 + 0.935134i \(0.384722\pi\)
\(60\) 0 0
\(61\) 8.24320 1.05543 0.527717 0.849421i \(-0.323048\pi\)
0.527717 + 0.849421i \(0.323048\pi\)
\(62\) 0 0
\(63\) 3.60576 0.454282
\(64\) 0 0
\(65\) −6.59965 −0.818586
\(66\) 0 0
\(67\) −1.77928 −0.217373 −0.108687 0.994076i \(-0.534664\pi\)
−0.108687 + 0.994076i \(0.534664\pi\)
\(68\) 0 0
\(69\) −7.76678 −0.935010
\(70\) 0 0
\(71\) 0.897417 0.106504 0.0532519 0.998581i \(-0.483041\pi\)
0.0532519 + 0.998581i \(0.483041\pi\)
\(72\) 0 0
\(73\) 0.515081 0.0602857 0.0301428 0.999546i \(-0.490404\pi\)
0.0301428 + 0.999546i \(0.490404\pi\)
\(74\) 0 0
\(75\) −1.42411 −0.164442
\(76\) 0 0
\(77\) 16.8249 1.91738
\(78\) 0 0
\(79\) 6.23609 0.701615 0.350807 0.936448i \(-0.385907\pi\)
0.350807 + 0.936448i \(0.385907\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.92540 −0.869925 −0.434963 0.900448i \(-0.643238\pi\)
−0.434963 + 0.900448i \(0.643238\pi\)
\(84\) 0 0
\(85\) 6.95678 0.754568
\(86\) 0 0
\(87\) −8.07933 −0.866195
\(88\) 0 0
\(89\) 3.24000 0.343439 0.171720 0.985146i \(-0.445068\pi\)
0.171720 + 0.985146i \(0.445068\pi\)
\(90\) 0 0
\(91\) −9.38882 −0.984215
\(92\) 0 0
\(93\) 4.58770 0.475723
\(94\) 0 0
\(95\) 1.81576 0.186293
\(96\) 0 0
\(97\) −0.898636 −0.0912426 −0.0456213 0.998959i \(-0.514527\pi\)
−0.0456213 + 0.998959i \(0.514527\pi\)
\(98\) 0 0
\(99\) 4.66613 0.468964
\(100\) 0 0
\(101\) −1.73787 −0.172924 −0.0864621 0.996255i \(-0.527556\pi\)
−0.0864621 + 0.996255i \(0.527556\pi\)
\(102\) 0 0
\(103\) −8.02139 −0.790371 −0.395185 0.918601i \(-0.629320\pi\)
−0.395185 + 0.918601i \(0.629320\pi\)
\(104\) 0 0
\(105\) −9.13909 −0.891883
\(106\) 0 0
\(107\) −8.60577 −0.831951 −0.415976 0.909376i \(-0.636560\pi\)
−0.415976 + 0.909376i \(0.636560\pi\)
\(108\) 0 0
\(109\) 2.78090 0.266362 0.133181 0.991092i \(-0.457481\pi\)
0.133181 + 0.991092i \(0.457481\pi\)
\(110\) 0 0
\(111\) 10.4330 0.990255
\(112\) 0 0
\(113\) −10.0371 −0.944212 −0.472106 0.881542i \(-0.656506\pi\)
−0.472106 + 0.881542i \(0.656506\pi\)
\(114\) 0 0
\(115\) 19.6855 1.83569
\(116\) 0 0
\(117\) −2.60384 −0.240725
\(118\) 0 0
\(119\) 9.89687 0.907245
\(120\) 0 0
\(121\) 10.7728 0.979345
\(122\) 0 0
\(123\) −10.0989 −0.910586
\(124\) 0 0
\(125\) −9.06339 −0.810654
\(126\) 0 0
\(127\) −5.09845 −0.452415 −0.226207 0.974079i \(-0.572633\pi\)
−0.226207 + 0.974079i \(0.572633\pi\)
\(128\) 0 0
\(129\) 1.83235 0.161329
\(130\) 0 0
\(131\) −12.0250 −1.05063 −0.525315 0.850908i \(-0.676052\pi\)
−0.525315 + 0.850908i \(0.676052\pi\)
\(132\) 0 0
\(133\) 2.58315 0.223987
\(134\) 0 0
\(135\) −2.53458 −0.218142
\(136\) 0 0
\(137\) 11.7745 1.00596 0.502980 0.864298i \(-0.332237\pi\)
0.502980 + 0.864298i \(0.332237\pi\)
\(138\) 0 0
\(139\) 1.29925 0.110201 0.0551005 0.998481i \(-0.482452\pi\)
0.0551005 + 0.998481i \(0.482452\pi\)
\(140\) 0 0
\(141\) −2.79183 −0.235114
\(142\) 0 0
\(143\) −12.1499 −1.01602
\(144\) 0 0
\(145\) 20.4777 1.70058
\(146\) 0 0
\(147\) −6.00147 −0.494993
\(148\) 0 0
\(149\) 2.16907 0.177697 0.0888487 0.996045i \(-0.471681\pi\)
0.0888487 + 0.996045i \(0.471681\pi\)
\(150\) 0 0
\(151\) 2.72560 0.221806 0.110903 0.993831i \(-0.464626\pi\)
0.110903 + 0.993831i \(0.464626\pi\)
\(152\) 0 0
\(153\) 2.74474 0.221899
\(154\) 0 0
\(155\) −11.6279 −0.933976
\(156\) 0 0
\(157\) −6.40827 −0.511436 −0.255718 0.966751i \(-0.582312\pi\)
−0.255718 + 0.966751i \(0.582312\pi\)
\(158\) 0 0
\(159\) 10.2851 0.815664
\(160\) 0 0
\(161\) 28.0051 2.20711
\(162\) 0 0
\(163\) 8.87797 0.695376 0.347688 0.937610i \(-0.386967\pi\)
0.347688 + 0.937610i \(0.386967\pi\)
\(164\) 0 0
\(165\) −11.8267 −0.920707
\(166\) 0 0
\(167\) −20.3375 −1.57376 −0.786881 0.617105i \(-0.788305\pi\)
−0.786881 + 0.617105i \(0.788305\pi\)
\(168\) 0 0
\(169\) −6.22001 −0.478462
\(170\) 0 0
\(171\) 0.716395 0.0547841
\(172\) 0 0
\(173\) −22.7571 −1.73019 −0.865094 0.501610i \(-0.832741\pi\)
−0.865094 + 0.501610i \(0.832741\pi\)
\(174\) 0 0
\(175\) 5.13499 0.388169
\(176\) 0 0
\(177\) −5.44275 −0.409102
\(178\) 0 0
\(179\) −22.2626 −1.66398 −0.831992 0.554787i \(-0.812800\pi\)
−0.831992 + 0.554787i \(0.812800\pi\)
\(180\) 0 0
\(181\) 14.1664 1.05298 0.526491 0.850181i \(-0.323508\pi\)
0.526491 + 0.850181i \(0.323508\pi\)
\(182\) 0 0
\(183\) −8.24320 −0.609355
\(184\) 0 0
\(185\) −26.4433 −1.94415
\(186\) 0 0
\(187\) 12.8073 0.936565
\(188\) 0 0
\(189\) −3.60576 −0.262280
\(190\) 0 0
\(191\) 8.82642 0.638657 0.319329 0.947644i \(-0.396543\pi\)
0.319329 + 0.947644i \(0.396543\pi\)
\(192\) 0 0
\(193\) −11.3649 −0.818065 −0.409033 0.912520i \(-0.634134\pi\)
−0.409033 + 0.912520i \(0.634134\pi\)
\(194\) 0 0
\(195\) 6.59965 0.472611
\(196\) 0 0
\(197\) 11.8414 0.843664 0.421832 0.906674i \(-0.361387\pi\)
0.421832 + 0.906674i \(0.361387\pi\)
\(198\) 0 0
\(199\) 0.591504 0.0419306 0.0209653 0.999780i \(-0.493326\pi\)
0.0209653 + 0.999780i \(0.493326\pi\)
\(200\) 0 0
\(201\) 1.77928 0.125500
\(202\) 0 0
\(203\) 29.1321 2.04467
\(204\) 0 0
\(205\) 25.5965 1.78774
\(206\) 0 0
\(207\) 7.76678 0.539828
\(208\) 0 0
\(209\) 3.34280 0.231226
\(210\) 0 0
\(211\) −27.5368 −1.89571 −0.947857 0.318695i \(-0.896755\pi\)
−0.947857 + 0.318695i \(0.896755\pi\)
\(212\) 0 0
\(213\) −0.897417 −0.0614900
\(214\) 0 0
\(215\) −4.64424 −0.316734
\(216\) 0 0
\(217\) −16.5421 −1.12295
\(218\) 0 0
\(219\) −0.515081 −0.0348059
\(220\) 0 0
\(221\) −7.14687 −0.480751
\(222\) 0 0
\(223\) −7.63357 −0.511182 −0.255591 0.966785i \(-0.582270\pi\)
−0.255591 + 0.966785i \(0.582270\pi\)
\(224\) 0 0
\(225\) 1.42411 0.0949407
\(226\) 0 0
\(227\) 14.4554 0.959442 0.479721 0.877421i \(-0.340738\pi\)
0.479721 + 0.877421i \(0.340738\pi\)
\(228\) 0 0
\(229\) 0.542149 0.0358262 0.0179131 0.999840i \(-0.494298\pi\)
0.0179131 + 0.999840i \(0.494298\pi\)
\(230\) 0 0
\(231\) −16.8249 −1.10700
\(232\) 0 0
\(233\) −26.2667 −1.72079 −0.860393 0.509631i \(-0.829782\pi\)
−0.860393 + 0.509631i \(0.829782\pi\)
\(234\) 0 0
\(235\) 7.07611 0.461595
\(236\) 0 0
\(237\) −6.23609 −0.405077
\(238\) 0 0
\(239\) 7.55778 0.488872 0.244436 0.969665i \(-0.421397\pi\)
0.244436 + 0.969665i \(0.421397\pi\)
\(240\) 0 0
\(241\) 15.2058 0.979495 0.489747 0.871864i \(-0.337089\pi\)
0.489747 + 0.871864i \(0.337089\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 15.2112 0.971810
\(246\) 0 0
\(247\) −1.86538 −0.118691
\(248\) 0 0
\(249\) 7.92540 0.502252
\(250\) 0 0
\(251\) −13.4480 −0.848831 −0.424415 0.905468i \(-0.639520\pi\)
−0.424415 + 0.905468i \(0.639520\pi\)
\(252\) 0 0
\(253\) 36.2408 2.27844
\(254\) 0 0
\(255\) −6.95678 −0.435650
\(256\) 0 0
\(257\) 15.3341 0.956513 0.478256 0.878220i \(-0.341269\pi\)
0.478256 + 0.878220i \(0.341269\pi\)
\(258\) 0 0
\(259\) −37.6188 −2.33752
\(260\) 0 0
\(261\) 8.07933 0.500098
\(262\) 0 0
\(263\) 6.84467 0.422060 0.211030 0.977480i \(-0.432318\pi\)
0.211030 + 0.977480i \(0.432318\pi\)
\(264\) 0 0
\(265\) −26.0685 −1.60138
\(266\) 0 0
\(267\) −3.24000 −0.198285
\(268\) 0 0
\(269\) −25.6870 −1.56617 −0.783083 0.621918i \(-0.786354\pi\)
−0.783083 + 0.621918i \(0.786354\pi\)
\(270\) 0 0
\(271\) −22.0183 −1.33752 −0.668758 0.743480i \(-0.733174\pi\)
−0.668758 + 0.743480i \(0.733174\pi\)
\(272\) 0 0
\(273\) 9.38882 0.568237
\(274\) 0 0
\(275\) 6.64508 0.400714
\(276\) 0 0
\(277\) 25.7727 1.54853 0.774264 0.632862i \(-0.218120\pi\)
0.774264 + 0.632862i \(0.218120\pi\)
\(278\) 0 0
\(279\) −4.58770 −0.274659
\(280\) 0 0
\(281\) 5.79858 0.345914 0.172957 0.984929i \(-0.444668\pi\)
0.172957 + 0.984929i \(0.444668\pi\)
\(282\) 0 0
\(283\) −0.919794 −0.0546761 −0.0273380 0.999626i \(-0.508703\pi\)
−0.0273380 + 0.999626i \(0.508703\pi\)
\(284\) 0 0
\(285\) −1.81576 −0.107557
\(286\) 0 0
\(287\) 36.4141 2.14946
\(288\) 0 0
\(289\) −9.46639 −0.556846
\(290\) 0 0
\(291\) 0.898636 0.0526789
\(292\) 0 0
\(293\) 13.7089 0.800883 0.400442 0.916322i \(-0.368857\pi\)
0.400442 + 0.916322i \(0.368857\pi\)
\(294\) 0 0
\(295\) 13.7951 0.803182
\(296\) 0 0
\(297\) −4.66613 −0.270756
\(298\) 0 0
\(299\) −20.2235 −1.16955
\(300\) 0 0
\(301\) −6.60700 −0.380821
\(302\) 0 0
\(303\) 1.73787 0.0998379
\(304\) 0 0
\(305\) 20.8931 1.19633
\(306\) 0 0
\(307\) −11.9361 −0.681232 −0.340616 0.940203i \(-0.610636\pi\)
−0.340616 + 0.940203i \(0.610636\pi\)
\(308\) 0 0
\(309\) 8.02139 0.456321
\(310\) 0 0
\(311\) −8.91744 −0.505662 −0.252831 0.967510i \(-0.581362\pi\)
−0.252831 + 0.967510i \(0.581362\pi\)
\(312\) 0 0
\(313\) −13.0506 −0.737661 −0.368831 0.929497i \(-0.620242\pi\)
−0.368831 + 0.929497i \(0.620242\pi\)
\(314\) 0 0
\(315\) 9.13909 0.514929
\(316\) 0 0
\(317\) 22.5539 1.26675 0.633377 0.773844i \(-0.281668\pi\)
0.633377 + 0.773844i \(0.281668\pi\)
\(318\) 0 0
\(319\) 37.6992 2.11075
\(320\) 0 0
\(321\) 8.60577 0.480327
\(322\) 0 0
\(323\) 1.96632 0.109409
\(324\) 0 0
\(325\) −3.70816 −0.205692
\(326\) 0 0
\(327\) −2.78090 −0.153784
\(328\) 0 0
\(329\) 10.0666 0.554992
\(330\) 0 0
\(331\) 4.18703 0.230140 0.115070 0.993357i \(-0.463291\pi\)
0.115070 + 0.993357i \(0.463291\pi\)
\(332\) 0 0
\(333\) −10.4330 −0.571724
\(334\) 0 0
\(335\) −4.50972 −0.246392
\(336\) 0 0
\(337\) 21.6046 1.17688 0.588439 0.808542i \(-0.299743\pi\)
0.588439 + 0.808542i \(0.299743\pi\)
\(338\) 0 0
\(339\) 10.0371 0.545141
\(340\) 0 0
\(341\) −21.4068 −1.15924
\(342\) 0 0
\(343\) −3.60044 −0.194406
\(344\) 0 0
\(345\) −19.6855 −1.05983
\(346\) 0 0
\(347\) 19.5054 1.04711 0.523553 0.851993i \(-0.324606\pi\)
0.523553 + 0.851993i \(0.324606\pi\)
\(348\) 0 0
\(349\) 34.9855 1.87273 0.936365 0.351027i \(-0.114168\pi\)
0.936365 + 0.351027i \(0.114168\pi\)
\(350\) 0 0
\(351\) 2.60384 0.138983
\(352\) 0 0
\(353\) 27.9902 1.48977 0.744883 0.667195i \(-0.232505\pi\)
0.744883 + 0.667195i \(0.232505\pi\)
\(354\) 0 0
\(355\) 2.27458 0.120722
\(356\) 0 0
\(357\) −9.89687 −0.523798
\(358\) 0 0
\(359\) 34.0080 1.79487 0.897436 0.441145i \(-0.145428\pi\)
0.897436 + 0.441145i \(0.145428\pi\)
\(360\) 0 0
\(361\) −18.4868 −0.972988
\(362\) 0 0
\(363\) −10.7728 −0.565425
\(364\) 0 0
\(365\) 1.30552 0.0683338
\(366\) 0 0
\(367\) 0.261922 0.0136722 0.00683612 0.999977i \(-0.497824\pi\)
0.00683612 + 0.999977i \(0.497824\pi\)
\(368\) 0 0
\(369\) 10.0989 0.525727
\(370\) 0 0
\(371\) −37.0857 −1.92539
\(372\) 0 0
\(373\) 4.57946 0.237115 0.118558 0.992947i \(-0.462173\pi\)
0.118558 + 0.992947i \(0.462173\pi\)
\(374\) 0 0
\(375\) 9.06339 0.468031
\(376\) 0 0
\(377\) −21.0373 −1.08348
\(378\) 0 0
\(379\) −10.7251 −0.550913 −0.275456 0.961314i \(-0.588829\pi\)
−0.275456 + 0.961314i \(0.588829\pi\)
\(380\) 0 0
\(381\) 5.09845 0.261202
\(382\) 0 0
\(383\) 32.9032 1.68128 0.840638 0.541598i \(-0.182180\pi\)
0.840638 + 0.541598i \(0.182180\pi\)
\(384\) 0 0
\(385\) 42.6442 2.17335
\(386\) 0 0
\(387\) −1.83235 −0.0931435
\(388\) 0 0
\(389\) −11.6460 −0.590477 −0.295239 0.955424i \(-0.595399\pi\)
−0.295239 + 0.955424i \(0.595399\pi\)
\(390\) 0 0
\(391\) 21.3178 1.07809
\(392\) 0 0
\(393\) 12.0250 0.606581
\(394\) 0 0
\(395\) 15.8059 0.795280
\(396\) 0 0
\(397\) 27.5160 1.38099 0.690493 0.723339i \(-0.257394\pi\)
0.690493 + 0.723339i \(0.257394\pi\)
\(398\) 0 0
\(399\) −2.58315 −0.129319
\(400\) 0 0
\(401\) 34.8087 1.73826 0.869132 0.494580i \(-0.164678\pi\)
0.869132 + 0.494580i \(0.164678\pi\)
\(402\) 0 0
\(403\) 11.9457 0.595055
\(404\) 0 0
\(405\) 2.53458 0.125944
\(406\) 0 0
\(407\) −48.6817 −2.41306
\(408\) 0 0
\(409\) 36.7083 1.81511 0.907554 0.419935i \(-0.137947\pi\)
0.907554 + 0.419935i \(0.137947\pi\)
\(410\) 0 0
\(411\) −11.7745 −0.580792
\(412\) 0 0
\(413\) 19.6252 0.965695
\(414\) 0 0
\(415\) −20.0876 −0.986060
\(416\) 0 0
\(417\) −1.29925 −0.0636246
\(418\) 0 0
\(419\) 32.0237 1.56446 0.782230 0.622989i \(-0.214082\pi\)
0.782230 + 0.622989i \(0.214082\pi\)
\(420\) 0 0
\(421\) −9.64139 −0.469893 −0.234946 0.972008i \(-0.575491\pi\)
−0.234946 + 0.972008i \(0.575491\pi\)
\(422\) 0 0
\(423\) 2.79183 0.135743
\(424\) 0 0
\(425\) 3.90881 0.189605
\(426\) 0 0
\(427\) 29.7230 1.43839
\(428\) 0 0
\(429\) 12.1499 0.586601
\(430\) 0 0
\(431\) 9.65654 0.465139 0.232570 0.972580i \(-0.425287\pi\)
0.232570 + 0.972580i \(0.425287\pi\)
\(432\) 0 0
\(433\) 24.5946 1.18194 0.590970 0.806694i \(-0.298745\pi\)
0.590970 + 0.806694i \(0.298745\pi\)
\(434\) 0 0
\(435\) −20.4777 −0.981832
\(436\) 0 0
\(437\) 5.56408 0.266166
\(438\) 0 0
\(439\) −26.7881 −1.27853 −0.639264 0.768988i \(-0.720761\pi\)
−0.639264 + 0.768988i \(0.720761\pi\)
\(440\) 0 0
\(441\) 6.00147 0.285784
\(442\) 0 0
\(443\) −39.4079 −1.87232 −0.936162 0.351568i \(-0.885649\pi\)
−0.936162 + 0.351568i \(0.885649\pi\)
\(444\) 0 0
\(445\) 8.21205 0.389288
\(446\) 0 0
\(447\) −2.16907 −0.102594
\(448\) 0 0
\(449\) −2.09208 −0.0987312 −0.0493656 0.998781i \(-0.515720\pi\)
−0.0493656 + 0.998781i \(0.515720\pi\)
\(450\) 0 0
\(451\) 47.1228 2.21892
\(452\) 0 0
\(453\) −2.72560 −0.128060
\(454\) 0 0
\(455\) −23.7967 −1.11561
\(456\) 0 0
\(457\) −18.4503 −0.863069 −0.431535 0.902096i \(-0.642028\pi\)
−0.431535 + 0.902096i \(0.642028\pi\)
\(458\) 0 0
\(459\) −2.74474 −0.128114
\(460\) 0 0
\(461\) 22.0069 1.02496 0.512482 0.858698i \(-0.328726\pi\)
0.512482 + 0.858698i \(0.328726\pi\)
\(462\) 0 0
\(463\) 21.7884 1.01259 0.506297 0.862359i \(-0.331014\pi\)
0.506297 + 0.862359i \(0.331014\pi\)
\(464\) 0 0
\(465\) 11.6279 0.539231
\(466\) 0 0
\(467\) −39.9361 −1.84802 −0.924011 0.382365i \(-0.875110\pi\)
−0.924011 + 0.382365i \(0.875110\pi\)
\(468\) 0 0
\(469\) −6.41564 −0.296247
\(470\) 0 0
\(471\) 6.40827 0.295278
\(472\) 0 0
\(473\) −8.54998 −0.393129
\(474\) 0 0
\(475\) 1.02023 0.0468112
\(476\) 0 0
\(477\) −10.2851 −0.470924
\(478\) 0 0
\(479\) −23.9302 −1.09340 −0.546701 0.837328i \(-0.684116\pi\)
−0.546701 + 0.837328i \(0.684116\pi\)
\(480\) 0 0
\(481\) 27.1658 1.23866
\(482\) 0 0
\(483\) −28.0051 −1.27428
\(484\) 0 0
\(485\) −2.27767 −0.103423
\(486\) 0 0
\(487\) −33.2562 −1.50698 −0.753491 0.657458i \(-0.771632\pi\)
−0.753491 + 0.657458i \(0.771632\pi\)
\(488\) 0 0
\(489\) −8.87797 −0.401475
\(490\) 0 0
\(491\) −36.3830 −1.64194 −0.820970 0.570971i \(-0.806567\pi\)
−0.820970 + 0.570971i \(0.806567\pi\)
\(492\) 0 0
\(493\) 22.1757 0.998742
\(494\) 0 0
\(495\) 11.8267 0.531571
\(496\) 0 0
\(497\) 3.23586 0.145148
\(498\) 0 0
\(499\) −6.52720 −0.292198 −0.146099 0.989270i \(-0.546672\pi\)
−0.146099 + 0.989270i \(0.546672\pi\)
\(500\) 0 0
\(501\) 20.3375 0.908611
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −4.40477 −0.196010
\(506\) 0 0
\(507\) 6.22001 0.276240
\(508\) 0 0
\(509\) 21.7241 0.962905 0.481452 0.876472i \(-0.340109\pi\)
0.481452 + 0.876472i \(0.340109\pi\)
\(510\) 0 0
\(511\) 1.85726 0.0821601
\(512\) 0 0
\(513\) −0.716395 −0.0316296
\(514\) 0 0
\(515\) −20.3309 −0.895885
\(516\) 0 0
\(517\) 13.0270 0.572928
\(518\) 0 0
\(519\) 22.7571 0.998924
\(520\) 0 0
\(521\) −4.03880 −0.176943 −0.0884716 0.996079i \(-0.528198\pi\)
−0.0884716 + 0.996079i \(0.528198\pi\)
\(522\) 0 0
\(523\) 35.9547 1.57219 0.786094 0.618107i \(-0.212100\pi\)
0.786094 + 0.618107i \(0.212100\pi\)
\(524\) 0 0
\(525\) −5.13499 −0.224109
\(526\) 0 0
\(527\) −12.5921 −0.548519
\(528\) 0 0
\(529\) 37.3228 1.62273
\(530\) 0 0
\(531\) 5.44275 0.236195
\(532\) 0 0
\(533\) −26.2959 −1.13900
\(534\) 0 0
\(535\) −21.8120 −0.943017
\(536\) 0 0
\(537\) 22.2626 0.960702
\(538\) 0 0
\(539\) 28.0037 1.20620
\(540\) 0 0
\(541\) 19.5129 0.838924 0.419462 0.907773i \(-0.362219\pi\)
0.419462 + 0.907773i \(0.362219\pi\)
\(542\) 0 0
\(543\) −14.1664 −0.607939
\(544\) 0 0
\(545\) 7.04843 0.301922
\(546\) 0 0
\(547\) 6.92271 0.295994 0.147997 0.988988i \(-0.452717\pi\)
0.147997 + 0.988988i \(0.452717\pi\)
\(548\) 0 0
\(549\) 8.24320 0.351811
\(550\) 0 0
\(551\) 5.78799 0.246577
\(552\) 0 0
\(553\) 22.4858 0.956194
\(554\) 0 0
\(555\) 26.4433 1.12245
\(556\) 0 0
\(557\) −31.5605 −1.33726 −0.668631 0.743594i \(-0.733120\pi\)
−0.668631 + 0.743594i \(0.733120\pi\)
\(558\) 0 0
\(559\) 4.77115 0.201798
\(560\) 0 0
\(561\) −12.8073 −0.540726
\(562\) 0 0
\(563\) 10.2354 0.431371 0.215686 0.976463i \(-0.430801\pi\)
0.215686 + 0.976463i \(0.430801\pi\)
\(564\) 0 0
\(565\) −25.4399 −1.07026
\(566\) 0 0
\(567\) 3.60576 0.151427
\(568\) 0 0
\(569\) 4.06701 0.170498 0.0852489 0.996360i \(-0.472831\pi\)
0.0852489 + 0.996360i \(0.472831\pi\)
\(570\) 0 0
\(571\) 22.5816 0.945008 0.472504 0.881328i \(-0.343350\pi\)
0.472504 + 0.881328i \(0.343350\pi\)
\(572\) 0 0
\(573\) −8.82642 −0.368729
\(574\) 0 0
\(575\) 11.0607 0.461265
\(576\) 0 0
\(577\) −28.4583 −1.18474 −0.592368 0.805667i \(-0.701807\pi\)
−0.592368 + 0.805667i \(0.701807\pi\)
\(578\) 0 0
\(579\) 11.3649 0.472310
\(580\) 0 0
\(581\) −28.5770 −1.18558
\(582\) 0 0
\(583\) −47.9918 −1.98762
\(584\) 0 0
\(585\) −6.59965 −0.272862
\(586\) 0 0
\(587\) 36.0094 1.48627 0.743133 0.669143i \(-0.233339\pi\)
0.743133 + 0.669143i \(0.233339\pi\)
\(588\) 0 0
\(589\) −3.28661 −0.135422
\(590\) 0 0
\(591\) −11.8414 −0.487090
\(592\) 0 0
\(593\) −6.77699 −0.278297 −0.139149 0.990271i \(-0.544437\pi\)
−0.139149 + 0.990271i \(0.544437\pi\)
\(594\) 0 0
\(595\) 25.0844 1.02836
\(596\) 0 0
\(597\) −0.591504 −0.0242086
\(598\) 0 0
\(599\) −19.4825 −0.796035 −0.398017 0.917378i \(-0.630302\pi\)
−0.398017 + 0.917378i \(0.630302\pi\)
\(600\) 0 0
\(601\) 8.85452 0.361183 0.180592 0.983558i \(-0.442199\pi\)
0.180592 + 0.983558i \(0.442199\pi\)
\(602\) 0 0
\(603\) −1.77928 −0.0724577
\(604\) 0 0
\(605\) 27.3045 1.11009
\(606\) 0 0
\(607\) 0.631788 0.0256435 0.0128217 0.999918i \(-0.495919\pi\)
0.0128217 + 0.999918i \(0.495919\pi\)
\(608\) 0 0
\(609\) −29.1321 −1.18049
\(610\) 0 0
\(611\) −7.26947 −0.294091
\(612\) 0 0
\(613\) −26.5371 −1.07182 −0.535911 0.844275i \(-0.680032\pi\)
−0.535911 + 0.844275i \(0.680032\pi\)
\(614\) 0 0
\(615\) −25.5965 −1.03215
\(616\) 0 0
\(617\) 13.5304 0.544713 0.272356 0.962196i \(-0.412197\pi\)
0.272356 + 0.962196i \(0.412197\pi\)
\(618\) 0 0
\(619\) 2.03673 0.0818632 0.0409316 0.999162i \(-0.486967\pi\)
0.0409316 + 0.999162i \(0.486967\pi\)
\(620\) 0 0
\(621\) −7.76678 −0.311670
\(622\) 0 0
\(623\) 11.6827 0.468056
\(624\) 0 0
\(625\) −30.0925 −1.20370
\(626\) 0 0
\(627\) −3.34280 −0.133498
\(628\) 0 0
\(629\) −28.6358 −1.14179
\(630\) 0 0
\(631\) −47.9419 −1.90854 −0.954269 0.298948i \(-0.903364\pi\)
−0.954269 + 0.298948i \(0.903364\pi\)
\(632\) 0 0
\(633\) 27.5368 1.09449
\(634\) 0 0
\(635\) −12.9225 −0.512812
\(636\) 0 0
\(637\) −15.6269 −0.619160
\(638\) 0 0
\(639\) 0.897417 0.0355013
\(640\) 0 0
\(641\) −13.6629 −0.539654 −0.269827 0.962909i \(-0.586966\pi\)
−0.269827 + 0.962909i \(0.586966\pi\)
\(642\) 0 0
\(643\) −33.0345 −1.30275 −0.651377 0.758754i \(-0.725809\pi\)
−0.651377 + 0.758754i \(0.725809\pi\)
\(644\) 0 0
\(645\) 4.64424 0.182867
\(646\) 0 0
\(647\) −2.85739 −0.112335 −0.0561677 0.998421i \(-0.517888\pi\)
−0.0561677 + 0.998421i \(0.517888\pi\)
\(648\) 0 0
\(649\) 25.3966 0.996904
\(650\) 0 0
\(651\) 16.5421 0.648337
\(652\) 0 0
\(653\) 2.37650 0.0929997 0.0464998 0.998918i \(-0.485193\pi\)
0.0464998 + 0.998918i \(0.485193\pi\)
\(654\) 0 0
\(655\) −30.4784 −1.19089
\(656\) 0 0
\(657\) 0.515081 0.0200952
\(658\) 0 0
\(659\) 31.9662 1.24523 0.622613 0.782530i \(-0.286071\pi\)
0.622613 + 0.782530i \(0.286071\pi\)
\(660\) 0 0
\(661\) −27.7011 −1.07745 −0.538725 0.842482i \(-0.681094\pi\)
−0.538725 + 0.842482i \(0.681094\pi\)
\(662\) 0 0
\(663\) 7.14687 0.277562
\(664\) 0 0
\(665\) 6.54720 0.253889
\(666\) 0 0
\(667\) 62.7503 2.42970
\(668\) 0 0
\(669\) 7.63357 0.295131
\(670\) 0 0
\(671\) 38.4638 1.48488
\(672\) 0 0
\(673\) −4.83451 −0.186357 −0.0931784 0.995649i \(-0.529703\pi\)
−0.0931784 + 0.995649i \(0.529703\pi\)
\(674\) 0 0
\(675\) −1.42411 −0.0548140
\(676\) 0 0
\(677\) 25.4646 0.978683 0.489341 0.872092i \(-0.337237\pi\)
0.489341 + 0.872092i \(0.337237\pi\)
\(678\) 0 0
\(679\) −3.24026 −0.124350
\(680\) 0 0
\(681\) −14.4554 −0.553934
\(682\) 0 0
\(683\) 19.3731 0.741291 0.370646 0.928774i \(-0.379136\pi\)
0.370646 + 0.928774i \(0.379136\pi\)
\(684\) 0 0
\(685\) 29.8434 1.14026
\(686\) 0 0
\(687\) −0.542149 −0.0206843
\(688\) 0 0
\(689\) 26.7809 1.02027
\(690\) 0 0
\(691\) −28.3147 −1.07714 −0.538571 0.842580i \(-0.681036\pi\)
−0.538571 + 0.842580i \(0.681036\pi\)
\(692\) 0 0
\(693\) 16.8249 0.639126
\(694\) 0 0
\(695\) 3.29306 0.124913
\(696\) 0 0
\(697\) 27.7189 1.04993
\(698\) 0 0
\(699\) 26.2667 0.993496
\(700\) 0 0
\(701\) −2.49563 −0.0942588 −0.0471294 0.998889i \(-0.515007\pi\)
−0.0471294 + 0.998889i \(0.515007\pi\)
\(702\) 0 0
\(703\) −7.47414 −0.281893
\(704\) 0 0
\(705\) −7.07611 −0.266502
\(706\) 0 0
\(707\) −6.26632 −0.235669
\(708\) 0 0
\(709\) 23.1400 0.869041 0.434520 0.900662i \(-0.356918\pi\)
0.434520 + 0.900662i \(0.356918\pi\)
\(710\) 0 0
\(711\) 6.23609 0.233872
\(712\) 0 0
\(713\) −35.6317 −1.33442
\(714\) 0 0
\(715\) −30.7949 −1.15166
\(716\) 0 0
\(717\) −7.55778 −0.282251
\(718\) 0 0
\(719\) −18.3342 −0.683752 −0.341876 0.939745i \(-0.611062\pi\)
−0.341876 + 0.939745i \(0.611062\pi\)
\(720\) 0 0
\(721\) −28.9232 −1.07715
\(722\) 0 0
\(723\) −15.2058 −0.565512
\(724\) 0 0
\(725\) 11.5058 0.427317
\(726\) 0 0
\(727\) 41.8186 1.55096 0.775482 0.631369i \(-0.217507\pi\)
0.775482 + 0.631369i \(0.217507\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.02933 −0.186016
\(732\) 0 0
\(733\) 10.1949 0.376558 0.188279 0.982116i \(-0.439709\pi\)
0.188279 + 0.982116i \(0.439709\pi\)
\(734\) 0 0
\(735\) −15.2112 −0.561075
\(736\) 0 0
\(737\) −8.30234 −0.305821
\(738\) 0 0
\(739\) −42.8021 −1.57450 −0.787251 0.616633i \(-0.788496\pi\)
−0.787251 + 0.616633i \(0.788496\pi\)
\(740\) 0 0
\(741\) 1.86538 0.0685264
\(742\) 0 0
\(743\) 8.80981 0.323200 0.161600 0.986856i \(-0.448334\pi\)
0.161600 + 0.986856i \(0.448334\pi\)
\(744\) 0 0
\(745\) 5.49770 0.201420
\(746\) 0 0
\(747\) −7.92540 −0.289975
\(748\) 0 0
\(749\) −31.0303 −1.13382
\(750\) 0 0
\(751\) 1.00494 0.0366708 0.0183354 0.999832i \(-0.494163\pi\)
0.0183354 + 0.999832i \(0.494163\pi\)
\(752\) 0 0
\(753\) 13.4480 0.490073
\(754\) 0 0
\(755\) 6.90826 0.251417
\(756\) 0 0
\(757\) −14.7193 −0.534982 −0.267491 0.963560i \(-0.586195\pi\)
−0.267491 + 0.963560i \(0.586195\pi\)
\(758\) 0 0
\(759\) −36.2408 −1.31546
\(760\) 0 0
\(761\) 12.0817 0.437961 0.218980 0.975729i \(-0.429727\pi\)
0.218980 + 0.975729i \(0.429727\pi\)
\(762\) 0 0
\(763\) 10.0273 0.363011
\(764\) 0 0
\(765\) 6.95678 0.251523
\(766\) 0 0
\(767\) −14.1721 −0.511724
\(768\) 0 0
\(769\) 45.9933 1.65856 0.829281 0.558832i \(-0.188750\pi\)
0.829281 + 0.558832i \(0.188750\pi\)
\(770\) 0 0
\(771\) −15.3341 −0.552243
\(772\) 0 0
\(773\) 4.51290 0.162318 0.0811589 0.996701i \(-0.474138\pi\)
0.0811589 + 0.996701i \(0.474138\pi\)
\(774\) 0 0
\(775\) −6.53339 −0.234686
\(776\) 0 0
\(777\) 37.6188 1.34957
\(778\) 0 0
\(779\) 7.23480 0.259214
\(780\) 0 0
\(781\) 4.18746 0.149839
\(782\) 0 0
\(783\) −8.07933 −0.288732
\(784\) 0 0
\(785\) −16.2423 −0.579712
\(786\) 0 0
\(787\) −18.8514 −0.671980 −0.335990 0.941865i \(-0.609071\pi\)
−0.335990 + 0.941865i \(0.609071\pi\)
\(788\) 0 0
\(789\) −6.84467 −0.243677
\(790\) 0 0
\(791\) −36.1914 −1.28682
\(792\) 0 0
\(793\) −21.4640 −0.762208
\(794\) 0 0
\(795\) 26.0685 0.924555
\(796\) 0 0
\(797\) −27.0011 −0.956430 −0.478215 0.878243i \(-0.658716\pi\)
−0.478215 + 0.878243i \(0.658716\pi\)
\(798\) 0 0
\(799\) 7.66284 0.271092
\(800\) 0 0
\(801\) 3.24000 0.114480
\(802\) 0 0
\(803\) 2.40344 0.0848154
\(804\) 0 0
\(805\) 70.9812 2.50176
\(806\) 0 0
\(807\) 25.6870 0.904226
\(808\) 0 0
\(809\) 18.5046 0.650588 0.325294 0.945613i \(-0.394537\pi\)
0.325294 + 0.945613i \(0.394537\pi\)
\(810\) 0 0
\(811\) 1.32514 0.0465320 0.0232660 0.999729i \(-0.492594\pi\)
0.0232660 + 0.999729i \(0.492594\pi\)
\(812\) 0 0
\(813\) 22.0183 0.772215
\(814\) 0 0
\(815\) 22.5019 0.788208
\(816\) 0 0
\(817\) −1.31269 −0.0459251
\(818\) 0 0
\(819\) −9.38882 −0.328072
\(820\) 0 0
\(821\) 1.13965 0.0397739 0.0198870 0.999802i \(-0.493669\pi\)
0.0198870 + 0.999802i \(0.493669\pi\)
\(822\) 0 0
\(823\) −29.2285 −1.01884 −0.509421 0.860518i \(-0.670140\pi\)
−0.509421 + 0.860518i \(0.670140\pi\)
\(824\) 0 0
\(825\) −6.64508 −0.231352
\(826\) 0 0
\(827\) −16.8206 −0.584908 −0.292454 0.956280i \(-0.594472\pi\)
−0.292454 + 0.956280i \(0.594472\pi\)
\(828\) 0 0
\(829\) −44.4361 −1.54333 −0.771665 0.636029i \(-0.780576\pi\)
−0.771665 + 0.636029i \(0.780576\pi\)
\(830\) 0 0
\(831\) −25.7727 −0.894044
\(832\) 0 0
\(833\) 16.4725 0.570738
\(834\) 0 0
\(835\) −51.5470 −1.78386
\(836\) 0 0
\(837\) 4.58770 0.158574
\(838\) 0 0
\(839\) 48.4989 1.67437 0.837184 0.546922i \(-0.184201\pi\)
0.837184 + 0.546922i \(0.184201\pi\)
\(840\) 0 0
\(841\) 36.2755 1.25088
\(842\) 0 0
\(843\) −5.79858 −0.199714
\(844\) 0 0
\(845\) −15.7651 −0.542337
\(846\) 0 0
\(847\) 38.8441 1.33470
\(848\) 0 0
\(849\) 0.919794 0.0315672
\(850\) 0 0
\(851\) −81.0306 −2.77769
\(852\) 0 0
\(853\) 25.3564 0.868185 0.434093 0.900868i \(-0.357069\pi\)
0.434093 + 0.900868i \(0.357069\pi\)
\(854\) 0 0
\(855\) 1.81576 0.0620978
\(856\) 0 0
\(857\) 8.99949 0.307417 0.153708 0.988116i \(-0.450878\pi\)
0.153708 + 0.988116i \(0.450878\pi\)
\(858\) 0 0
\(859\) −22.1970 −0.757352 −0.378676 0.925529i \(-0.623620\pi\)
−0.378676 + 0.925529i \(0.623620\pi\)
\(860\) 0 0
\(861\) −36.4141 −1.24099
\(862\) 0 0
\(863\) −35.0196 −1.19208 −0.596040 0.802955i \(-0.703260\pi\)
−0.596040 + 0.802955i \(0.703260\pi\)
\(864\) 0 0
\(865\) −57.6797 −1.96117
\(866\) 0 0
\(867\) 9.46639 0.321495
\(868\) 0 0
\(869\) 29.0984 0.987096
\(870\) 0 0
\(871\) 4.63295 0.156982
\(872\) 0 0
\(873\) −0.898636 −0.0304142
\(874\) 0 0
\(875\) −32.6804 −1.10480
\(876\) 0 0
\(877\) 4.60081 0.155358 0.0776791 0.996978i \(-0.475249\pi\)
0.0776791 + 0.996978i \(0.475249\pi\)
\(878\) 0 0
\(879\) −13.7089 −0.462390
\(880\) 0 0
\(881\) 31.5850 1.06412 0.532062 0.846705i \(-0.321417\pi\)
0.532062 + 0.846705i \(0.321417\pi\)
\(882\) 0 0
\(883\) 0.793183 0.0266927 0.0133464 0.999911i \(-0.495752\pi\)
0.0133464 + 0.999911i \(0.495752\pi\)
\(884\) 0 0
\(885\) −13.7951 −0.463717
\(886\) 0 0
\(887\) −12.4746 −0.418858 −0.209429 0.977824i \(-0.567160\pi\)
−0.209429 + 0.977824i \(0.567160\pi\)
\(888\) 0 0
\(889\) −18.3838 −0.616572
\(890\) 0 0
\(891\) 4.66613 0.156321
\(892\) 0 0
\(893\) 2.00005 0.0669291
\(894\) 0 0
\(895\) −56.4264 −1.88613
\(896\) 0 0
\(897\) 20.2235 0.675242
\(898\) 0 0
\(899\) −37.0656 −1.23621
\(900\) 0 0
\(901\) −28.2300 −0.940479
\(902\) 0 0
\(903\) 6.60700 0.219867
\(904\) 0 0
\(905\) 35.9059 1.19355
\(906\) 0 0
\(907\) −12.4391 −0.413035 −0.206518 0.978443i \(-0.566213\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(908\) 0 0
\(909\) −1.73787 −0.0576414
\(910\) 0 0
\(911\) −60.0276 −1.98880 −0.994402 0.105660i \(-0.966305\pi\)
−0.994402 + 0.105660i \(0.966305\pi\)
\(912\) 0 0
\(913\) −36.9810 −1.22389
\(914\) 0 0
\(915\) −20.8931 −0.690703
\(916\) 0 0
\(917\) −43.3592 −1.43185
\(918\) 0 0
\(919\) 23.5259 0.776046 0.388023 0.921650i \(-0.373158\pi\)
0.388023 + 0.921650i \(0.373158\pi\)
\(920\) 0 0
\(921\) 11.9361 0.393309
\(922\) 0 0
\(923\) −2.33673 −0.0769144
\(924\) 0 0
\(925\) −14.8577 −0.488519
\(926\) 0 0
\(927\) −8.02139 −0.263457
\(928\) 0 0
\(929\) 57.0540 1.87188 0.935940 0.352159i \(-0.114552\pi\)
0.935940 + 0.352159i \(0.114552\pi\)
\(930\) 0 0
\(931\) 4.29943 0.140908
\(932\) 0 0
\(933\) 8.91744 0.291944
\(934\) 0 0
\(935\) 32.4612 1.06160
\(936\) 0 0
\(937\) −23.1246 −0.755449 −0.377725 0.925918i \(-0.623293\pi\)
−0.377725 + 0.925918i \(0.623293\pi\)
\(938\) 0 0
\(939\) 13.0506 0.425889
\(940\) 0 0
\(941\) −48.1987 −1.57123 −0.785617 0.618713i \(-0.787654\pi\)
−0.785617 + 0.618713i \(0.787654\pi\)
\(942\) 0 0
\(943\) 78.4358 2.55422
\(944\) 0 0
\(945\) −9.13909 −0.297294
\(946\) 0 0
\(947\) −2.36134 −0.0767332 −0.0383666 0.999264i \(-0.512215\pi\)
−0.0383666 + 0.999264i \(0.512215\pi\)
\(948\) 0 0
\(949\) −1.34119 −0.0435368
\(950\) 0 0
\(951\) −22.5539 −0.731360
\(952\) 0 0
\(953\) 12.2459 0.396683 0.198341 0.980133i \(-0.436445\pi\)
0.198341 + 0.980133i \(0.436445\pi\)
\(954\) 0 0
\(955\) 22.3713 0.723918
\(956\) 0 0
\(957\) −37.6992 −1.21864
\(958\) 0 0
\(959\) 42.4558 1.37097
\(960\) 0 0
\(961\) −9.95299 −0.321064
\(962\) 0 0
\(963\) −8.60577 −0.277317
\(964\) 0 0
\(965\) −28.8053 −0.927277
\(966\) 0 0
\(967\) 12.5200 0.402618 0.201309 0.979528i \(-0.435481\pi\)
0.201309 + 0.979528i \(0.435481\pi\)
\(968\) 0 0
\(969\) −1.96632 −0.0631673
\(970\) 0 0
\(971\) −23.8316 −0.764793 −0.382396 0.923998i \(-0.624901\pi\)
−0.382396 + 0.923998i \(0.624901\pi\)
\(972\) 0 0
\(973\) 4.68478 0.150187
\(974\) 0 0
\(975\) 3.70816 0.118756
\(976\) 0 0
\(977\) −30.7902 −0.985064 −0.492532 0.870294i \(-0.663929\pi\)
−0.492532 + 0.870294i \(0.663929\pi\)
\(978\) 0 0
\(979\) 15.1183 0.483182
\(980\) 0 0
\(981\) 2.78090 0.0887874
\(982\) 0 0
\(983\) −35.3799 −1.12844 −0.564221 0.825624i \(-0.690823\pi\)
−0.564221 + 0.825624i \(0.690823\pi\)
\(984\) 0 0
\(985\) 30.0130 0.956293
\(986\) 0 0
\(987\) −10.0666 −0.320425
\(988\) 0 0
\(989\) −14.2314 −0.452534
\(990\) 0 0
\(991\) 27.5363 0.874719 0.437360 0.899287i \(-0.355914\pi\)
0.437360 + 0.899287i \(0.355914\pi\)
\(992\) 0 0
\(993\) −4.18703 −0.132871
\(994\) 0 0
\(995\) 1.49921 0.0475283
\(996\) 0 0
\(997\) −34.2241 −1.08389 −0.541944 0.840415i \(-0.682312\pi\)
−0.541944 + 0.840415i \(0.682312\pi\)
\(998\) 0 0
\(999\) 10.4330 0.330085
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 \(a_p\))