Properties

Label 8004.2.a.j.1.13
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(2.96949\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.96949 q^{5}\) \(-3.61534 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.96949 q^{5}\) \(-3.61534 q^{7}\) \(+1.00000 q^{9}\) \(-1.51788 q^{11}\) \(+0.595774 q^{13}\) \(+2.96949 q^{15}\) \(+0.748243 q^{17}\) \(-3.13742 q^{19}\) \(-3.61534 q^{21}\) \(+1.00000 q^{23}\) \(+3.81787 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+1.50532 q^{31}\) \(-1.51788 q^{33}\) \(-10.7357 q^{35}\) \(+3.65707 q^{37}\) \(+0.595774 q^{39}\) \(-0.901553 q^{41}\) \(-7.23898 q^{43}\) \(+2.96949 q^{45}\) \(+6.53719 q^{47}\) \(+6.07071 q^{49}\) \(+0.748243 q^{51}\) \(+11.1195 q^{53}\) \(-4.50733 q^{55}\) \(-3.13742 q^{57}\) \(+14.9523 q^{59}\) \(+4.00415 q^{61}\) \(-3.61534 q^{63}\) \(+1.76915 q^{65}\) \(+7.19360 q^{67}\) \(+1.00000 q^{69}\) \(+7.23527 q^{71}\) \(+8.91700 q^{73}\) \(+3.81787 q^{75}\) \(+5.48765 q^{77}\) \(+8.63438 q^{79}\) \(+1.00000 q^{81}\) \(-7.09135 q^{83}\) \(+2.22190 q^{85}\) \(-1.00000 q^{87}\) \(+14.5972 q^{89}\) \(-2.15393 q^{91}\) \(+1.50532 q^{93}\) \(-9.31653 q^{95}\) \(-7.05569 q^{97}\) \(-1.51788 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.96949 1.32800 0.663998 0.747734i \(-0.268858\pi\)
0.663998 + 0.747734i \(0.268858\pi\)
\(6\) 0 0
\(7\) −3.61534 −1.36647 −0.683236 0.730198i \(-0.739428\pi\)
−0.683236 + 0.730198i \(0.739428\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.51788 −0.457658 −0.228829 0.973467i \(-0.573490\pi\)
−0.228829 + 0.973467i \(0.573490\pi\)
\(12\) 0 0
\(13\) 0.595774 0.165238 0.0826191 0.996581i \(-0.473672\pi\)
0.0826191 + 0.996581i \(0.473672\pi\)
\(14\) 0 0
\(15\) 2.96949 0.766719
\(16\) 0 0
\(17\) 0.748243 0.181476 0.0907378 0.995875i \(-0.471077\pi\)
0.0907378 + 0.995875i \(0.471077\pi\)
\(18\) 0 0
\(19\) −3.13742 −0.719773 −0.359886 0.932996i \(-0.617185\pi\)
−0.359886 + 0.932996i \(0.617185\pi\)
\(20\) 0 0
\(21\) −3.61534 −0.788933
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 3.81787 0.763574
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 1.50532 0.270363 0.135182 0.990821i \(-0.456838\pi\)
0.135182 + 0.990821i \(0.456838\pi\)
\(32\) 0 0
\(33\) −1.51788 −0.264229
\(34\) 0 0
\(35\) −10.7357 −1.81467
\(36\) 0 0
\(37\) 3.65707 0.601218 0.300609 0.953747i \(-0.402810\pi\)
0.300609 + 0.953747i \(0.402810\pi\)
\(38\) 0 0
\(39\) 0.595774 0.0954003
\(40\) 0 0
\(41\) −0.901553 −0.140799 −0.0703995 0.997519i \(-0.522427\pi\)
−0.0703995 + 0.997519i \(0.522427\pi\)
\(42\) 0 0
\(43\) −7.23898 −1.10393 −0.551967 0.833866i \(-0.686123\pi\)
−0.551967 + 0.833866i \(0.686123\pi\)
\(44\) 0 0
\(45\) 2.96949 0.442665
\(46\) 0 0
\(47\) 6.53719 0.953547 0.476774 0.879026i \(-0.341806\pi\)
0.476774 + 0.879026i \(0.341806\pi\)
\(48\) 0 0
\(49\) 6.07071 0.867244
\(50\) 0 0
\(51\) 0.748243 0.104775
\(52\) 0 0
\(53\) 11.1195 1.52738 0.763688 0.645585i \(-0.223386\pi\)
0.763688 + 0.645585i \(0.223386\pi\)
\(54\) 0 0
\(55\) −4.50733 −0.607768
\(56\) 0 0
\(57\) −3.13742 −0.415561
\(58\) 0 0
\(59\) 14.9523 1.94662 0.973310 0.229495i \(-0.0737073\pi\)
0.973310 + 0.229495i \(0.0737073\pi\)
\(60\) 0 0
\(61\) 4.00415 0.512679 0.256340 0.966587i \(-0.417483\pi\)
0.256340 + 0.966587i \(0.417483\pi\)
\(62\) 0 0
\(63\) −3.61534 −0.455490
\(64\) 0 0
\(65\) 1.76915 0.219436
\(66\) 0 0
\(67\) 7.19360 0.878838 0.439419 0.898282i \(-0.355184\pi\)
0.439419 + 0.898282i \(0.355184\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 7.23527 0.858668 0.429334 0.903146i \(-0.358748\pi\)
0.429334 + 0.903146i \(0.358748\pi\)
\(72\) 0 0
\(73\) 8.91700 1.04366 0.521828 0.853051i \(-0.325250\pi\)
0.521828 + 0.853051i \(0.325250\pi\)
\(74\) 0 0
\(75\) 3.81787 0.440850
\(76\) 0 0
\(77\) 5.48765 0.625376
\(78\) 0 0
\(79\) 8.63438 0.971444 0.485722 0.874113i \(-0.338557\pi\)
0.485722 + 0.874113i \(0.338557\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.09135 −0.778377 −0.389188 0.921158i \(-0.627244\pi\)
−0.389188 + 0.921158i \(0.627244\pi\)
\(84\) 0 0
\(85\) 2.22190 0.240999
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 14.5972 1.54730 0.773650 0.633613i \(-0.218429\pi\)
0.773650 + 0.633613i \(0.218429\pi\)
\(90\) 0 0
\(91\) −2.15393 −0.225793
\(92\) 0 0
\(93\) 1.50532 0.156094
\(94\) 0 0
\(95\) −9.31653 −0.955856
\(96\) 0 0
\(97\) −7.05569 −0.716397 −0.358199 0.933645i \(-0.616609\pi\)
−0.358199 + 0.933645i \(0.616609\pi\)
\(98\) 0 0
\(99\) −1.51788 −0.152553
\(100\) 0 0
\(101\) 0.489092 0.0486665 0.0243332 0.999704i \(-0.492254\pi\)
0.0243332 + 0.999704i \(0.492254\pi\)
\(102\) 0 0
\(103\) −7.56907 −0.745802 −0.372901 0.927871i \(-0.621637\pi\)
−0.372901 + 0.927871i \(0.621637\pi\)
\(104\) 0 0
\(105\) −10.7357 −1.04770
\(106\) 0 0
\(107\) −15.9910 −1.54591 −0.772956 0.634460i \(-0.781223\pi\)
−0.772956 + 0.634460i \(0.781223\pi\)
\(108\) 0 0
\(109\) −5.98769 −0.573516 −0.286758 0.958003i \(-0.592578\pi\)
−0.286758 + 0.958003i \(0.592578\pi\)
\(110\) 0 0
\(111\) 3.65707 0.347114
\(112\) 0 0
\(113\) 19.5955 1.84339 0.921696 0.387912i \(-0.126804\pi\)
0.921696 + 0.387912i \(0.126804\pi\)
\(114\) 0 0
\(115\) 2.96949 0.276906
\(116\) 0 0
\(117\) 0.595774 0.0550794
\(118\) 0 0
\(119\) −2.70516 −0.247981
\(120\) 0 0
\(121\) −8.69604 −0.790549
\(122\) 0 0
\(123\) −0.901553 −0.0812903
\(124\) 0 0
\(125\) −3.51032 −0.313973
\(126\) 0 0
\(127\) −0.522271 −0.0463440 −0.0231720 0.999731i \(-0.507377\pi\)
−0.0231720 + 0.999731i \(0.507377\pi\)
\(128\) 0 0
\(129\) −7.23898 −0.637357
\(130\) 0 0
\(131\) 2.62958 0.229747 0.114874 0.993380i \(-0.463354\pi\)
0.114874 + 0.993380i \(0.463354\pi\)
\(132\) 0 0
\(133\) 11.3428 0.983549
\(134\) 0 0
\(135\) 2.96949 0.255573
\(136\) 0 0
\(137\) −6.98816 −0.597039 −0.298519 0.954404i \(-0.596493\pi\)
−0.298519 + 0.954404i \(0.596493\pi\)
\(138\) 0 0
\(139\) 13.6556 1.15825 0.579125 0.815239i \(-0.303394\pi\)
0.579125 + 0.815239i \(0.303394\pi\)
\(140\) 0 0
\(141\) 6.53719 0.550531
\(142\) 0 0
\(143\) −0.904314 −0.0756225
\(144\) 0 0
\(145\) −2.96949 −0.246603
\(146\) 0 0
\(147\) 6.07071 0.500704
\(148\) 0 0
\(149\) 22.8048 1.86824 0.934122 0.356953i \(-0.116184\pi\)
0.934122 + 0.356953i \(0.116184\pi\)
\(150\) 0 0
\(151\) 10.8986 0.886915 0.443458 0.896295i \(-0.353752\pi\)
0.443458 + 0.896295i \(0.353752\pi\)
\(152\) 0 0
\(153\) 0.748243 0.0604919
\(154\) 0 0
\(155\) 4.47003 0.359042
\(156\) 0 0
\(157\) −11.3841 −0.908553 −0.454277 0.890861i \(-0.650102\pi\)
−0.454277 + 0.890861i \(0.650102\pi\)
\(158\) 0 0
\(159\) 11.1195 0.881831
\(160\) 0 0
\(161\) −3.61534 −0.284929
\(162\) 0 0
\(163\) 9.05790 0.709469 0.354735 0.934967i \(-0.384571\pi\)
0.354735 + 0.934967i \(0.384571\pi\)
\(164\) 0 0
\(165\) −4.50733 −0.350895
\(166\) 0 0
\(167\) −0.683362 −0.0528802 −0.0264401 0.999650i \(-0.508417\pi\)
−0.0264401 + 0.999650i \(0.508417\pi\)
\(168\) 0 0
\(169\) −12.6451 −0.972696
\(170\) 0 0
\(171\) −3.13742 −0.239924
\(172\) 0 0
\(173\) 18.5209 1.40812 0.704058 0.710142i \(-0.251369\pi\)
0.704058 + 0.710142i \(0.251369\pi\)
\(174\) 0 0
\(175\) −13.8029 −1.04340
\(176\) 0 0
\(177\) 14.9523 1.12388
\(178\) 0 0
\(179\) 15.3322 1.14598 0.572990 0.819562i \(-0.305783\pi\)
0.572990 + 0.819562i \(0.305783\pi\)
\(180\) 0 0
\(181\) 17.8648 1.32788 0.663940 0.747786i \(-0.268883\pi\)
0.663940 + 0.747786i \(0.268883\pi\)
\(182\) 0 0
\(183\) 4.00415 0.295996
\(184\) 0 0
\(185\) 10.8596 0.798416
\(186\) 0 0
\(187\) −1.13574 −0.0830537
\(188\) 0 0
\(189\) −3.61534 −0.262978
\(190\) 0 0
\(191\) 11.9148 0.862127 0.431063 0.902322i \(-0.358139\pi\)
0.431063 + 0.902322i \(0.358139\pi\)
\(192\) 0 0
\(193\) 2.56622 0.184721 0.0923603 0.995726i \(-0.470559\pi\)
0.0923603 + 0.995726i \(0.470559\pi\)
\(194\) 0 0
\(195\) 1.76915 0.126691
\(196\) 0 0
\(197\) 24.1492 1.72056 0.860280 0.509823i \(-0.170289\pi\)
0.860280 + 0.509823i \(0.170289\pi\)
\(198\) 0 0
\(199\) −18.0349 −1.27846 −0.639231 0.769015i \(-0.720747\pi\)
−0.639231 + 0.769015i \(0.720747\pi\)
\(200\) 0 0
\(201\) 7.19360 0.507397
\(202\) 0 0
\(203\) 3.61534 0.253747
\(204\) 0 0
\(205\) −2.67715 −0.186981
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 4.76222 0.329410
\(210\) 0 0
\(211\) −24.7157 −1.70150 −0.850751 0.525569i \(-0.823852\pi\)
−0.850751 + 0.525569i \(0.823852\pi\)
\(212\) 0 0
\(213\) 7.23527 0.495752
\(214\) 0 0
\(215\) −21.4961 −1.46602
\(216\) 0 0
\(217\) −5.44225 −0.369444
\(218\) 0 0
\(219\) 8.91700 0.602555
\(220\) 0 0
\(221\) 0.445784 0.0299867
\(222\) 0 0
\(223\) −18.6236 −1.24713 −0.623563 0.781773i \(-0.714315\pi\)
−0.623563 + 0.781773i \(0.714315\pi\)
\(224\) 0 0
\(225\) 3.81787 0.254525
\(226\) 0 0
\(227\) −19.2355 −1.27671 −0.638354 0.769743i \(-0.720384\pi\)
−0.638354 + 0.769743i \(0.720384\pi\)
\(228\) 0 0
\(229\) 19.3237 1.27694 0.638472 0.769645i \(-0.279567\pi\)
0.638472 + 0.769645i \(0.279567\pi\)
\(230\) 0 0
\(231\) 5.48765 0.361061
\(232\) 0 0
\(233\) 6.70768 0.439435 0.219718 0.975564i \(-0.429486\pi\)
0.219718 + 0.975564i \(0.429486\pi\)
\(234\) 0 0
\(235\) 19.4121 1.26631
\(236\) 0 0
\(237\) 8.63438 0.560863
\(238\) 0 0
\(239\) −8.25440 −0.533933 −0.266966 0.963706i \(-0.586021\pi\)
−0.266966 + 0.963706i \(0.586021\pi\)
\(240\) 0 0
\(241\) 2.59131 0.166921 0.0834604 0.996511i \(-0.473403\pi\)
0.0834604 + 0.996511i \(0.473403\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 18.0269 1.15170
\(246\) 0 0
\(247\) −1.86919 −0.118934
\(248\) 0 0
\(249\) −7.09135 −0.449396
\(250\) 0 0
\(251\) 13.2452 0.836028 0.418014 0.908441i \(-0.362726\pi\)
0.418014 + 0.908441i \(0.362726\pi\)
\(252\) 0 0
\(253\) −1.51788 −0.0954282
\(254\) 0 0
\(255\) 2.22190 0.139141
\(256\) 0 0
\(257\) 18.4842 1.15301 0.576505 0.817094i \(-0.304416\pi\)
0.576505 + 0.817094i \(0.304416\pi\)
\(258\) 0 0
\(259\) −13.2216 −0.821548
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −17.5161 −1.08009 −0.540044 0.841637i \(-0.681592\pi\)
−0.540044 + 0.841637i \(0.681592\pi\)
\(264\) 0 0
\(265\) 33.0192 2.02835
\(266\) 0 0
\(267\) 14.5972 0.893334
\(268\) 0 0
\(269\) −12.9857 −0.791754 −0.395877 0.918303i \(-0.629559\pi\)
−0.395877 + 0.918303i \(0.629559\pi\)
\(270\) 0 0
\(271\) −3.97009 −0.241166 −0.120583 0.992703i \(-0.538476\pi\)
−0.120583 + 0.992703i \(0.538476\pi\)
\(272\) 0 0
\(273\) −2.15393 −0.130362
\(274\) 0 0
\(275\) −5.79507 −0.349456
\(276\) 0 0
\(277\) −23.8848 −1.43510 −0.717549 0.696508i \(-0.754736\pi\)
−0.717549 + 0.696508i \(0.754736\pi\)
\(278\) 0 0
\(279\) 1.50532 0.0901211
\(280\) 0 0
\(281\) −26.7422 −1.59531 −0.797654 0.603115i \(-0.793926\pi\)
−0.797654 + 0.603115i \(0.793926\pi\)
\(282\) 0 0
\(283\) 16.1073 0.957480 0.478740 0.877957i \(-0.341094\pi\)
0.478740 + 0.877957i \(0.341094\pi\)
\(284\) 0 0
\(285\) −9.31653 −0.551863
\(286\) 0 0
\(287\) 3.25943 0.192398
\(288\) 0 0
\(289\) −16.4401 −0.967067
\(290\) 0 0
\(291\) −7.05569 −0.413612
\(292\) 0 0
\(293\) −16.4362 −0.960215 −0.480107 0.877210i \(-0.659402\pi\)
−0.480107 + 0.877210i \(0.659402\pi\)
\(294\) 0 0
\(295\) 44.4006 2.58510
\(296\) 0 0
\(297\) −1.51788 −0.0880763
\(298\) 0 0
\(299\) 0.595774 0.0344545
\(300\) 0 0
\(301\) 26.1714 1.50849
\(302\) 0 0
\(303\) 0.489092 0.0280976
\(304\) 0 0
\(305\) 11.8903 0.680836
\(306\) 0 0
\(307\) −11.2107 −0.639827 −0.319914 0.947447i \(-0.603654\pi\)
−0.319914 + 0.947447i \(0.603654\pi\)
\(308\) 0 0
\(309\) −7.56907 −0.430589
\(310\) 0 0
\(311\) 25.7748 1.46156 0.730779 0.682614i \(-0.239157\pi\)
0.730779 + 0.682614i \(0.239157\pi\)
\(312\) 0 0
\(313\) 14.0344 0.793272 0.396636 0.917976i \(-0.370178\pi\)
0.396636 + 0.917976i \(0.370178\pi\)
\(314\) 0 0
\(315\) −10.7357 −0.604890
\(316\) 0 0
\(317\) 23.8531 1.33972 0.669862 0.742485i \(-0.266353\pi\)
0.669862 + 0.742485i \(0.266353\pi\)
\(318\) 0 0
\(319\) 1.51788 0.0849849
\(320\) 0 0
\(321\) −15.9910 −0.892533
\(322\) 0 0
\(323\) −2.34755 −0.130621
\(324\) 0 0
\(325\) 2.27459 0.126172
\(326\) 0 0
\(327\) −5.98769 −0.331120
\(328\) 0 0
\(329\) −23.6342 −1.30299
\(330\) 0 0
\(331\) −18.1473 −0.997463 −0.498732 0.866756i \(-0.666201\pi\)
−0.498732 + 0.866756i \(0.666201\pi\)
\(332\) 0 0
\(333\) 3.65707 0.200406
\(334\) 0 0
\(335\) 21.3613 1.16709
\(336\) 0 0
\(337\) 10.9981 0.599107 0.299554 0.954079i \(-0.403162\pi\)
0.299554 + 0.954079i \(0.403162\pi\)
\(338\) 0 0
\(339\) 19.5955 1.06428
\(340\) 0 0
\(341\) −2.28489 −0.123734
\(342\) 0 0
\(343\) 3.35971 0.181407
\(344\) 0 0
\(345\) 2.96949 0.159872
\(346\) 0 0
\(347\) −13.9639 −0.749621 −0.374810 0.927101i \(-0.622292\pi\)
−0.374810 + 0.927101i \(0.622292\pi\)
\(348\) 0 0
\(349\) −32.6420 −1.74729 −0.873643 0.486568i \(-0.838249\pi\)
−0.873643 + 0.486568i \(0.838249\pi\)
\(350\) 0 0
\(351\) 0.595774 0.0318001
\(352\) 0 0
\(353\) 9.20185 0.489765 0.244883 0.969553i \(-0.421251\pi\)
0.244883 + 0.969553i \(0.421251\pi\)
\(354\) 0 0
\(355\) 21.4851 1.14031
\(356\) 0 0
\(357\) −2.70516 −0.143172
\(358\) 0 0
\(359\) 19.7939 1.04468 0.522340 0.852737i \(-0.325059\pi\)
0.522340 + 0.852737i \(0.325059\pi\)
\(360\) 0 0
\(361\) −9.15662 −0.481927
\(362\) 0 0
\(363\) −8.69604 −0.456424
\(364\) 0 0
\(365\) 26.4789 1.38597
\(366\) 0 0
\(367\) −37.4361 −1.95415 −0.977074 0.212900i \(-0.931709\pi\)
−0.977074 + 0.212900i \(0.931709\pi\)
\(368\) 0 0
\(369\) −0.901553 −0.0469330
\(370\) 0 0
\(371\) −40.2007 −2.08712
\(372\) 0 0
\(373\) 5.28532 0.273664 0.136832 0.990594i \(-0.456308\pi\)
0.136832 + 0.990594i \(0.456308\pi\)
\(374\) 0 0
\(375\) −3.51032 −0.181272
\(376\) 0 0
\(377\) −0.595774 −0.0306839
\(378\) 0 0
\(379\) −8.48940 −0.436071 −0.218036 0.975941i \(-0.569965\pi\)
−0.218036 + 0.975941i \(0.569965\pi\)
\(380\) 0 0
\(381\) −0.522271 −0.0267567
\(382\) 0 0
\(383\) −30.8141 −1.57453 −0.787263 0.616618i \(-0.788502\pi\)
−0.787263 + 0.616618i \(0.788502\pi\)
\(384\) 0 0
\(385\) 16.2955 0.830497
\(386\) 0 0
\(387\) −7.23898 −0.367978
\(388\) 0 0
\(389\) −25.1893 −1.27715 −0.638573 0.769561i \(-0.720475\pi\)
−0.638573 + 0.769561i \(0.720475\pi\)
\(390\) 0 0
\(391\) 0.748243 0.0378403
\(392\) 0 0
\(393\) 2.62958 0.132645
\(394\) 0 0
\(395\) 25.6397 1.29007
\(396\) 0 0
\(397\) 3.19320 0.160262 0.0801311 0.996784i \(-0.474466\pi\)
0.0801311 + 0.996784i \(0.474466\pi\)
\(398\) 0 0
\(399\) 11.3428 0.567852
\(400\) 0 0
\(401\) 21.8365 1.09047 0.545233 0.838285i \(-0.316441\pi\)
0.545233 + 0.838285i \(0.316441\pi\)
\(402\) 0 0
\(403\) 0.896831 0.0446743
\(404\) 0 0
\(405\) 2.96949 0.147555
\(406\) 0 0
\(407\) −5.55099 −0.275152
\(408\) 0 0
\(409\) 27.4123 1.35545 0.677726 0.735315i \(-0.262966\pi\)
0.677726 + 0.735315i \(0.262966\pi\)
\(410\) 0 0
\(411\) −6.98816 −0.344700
\(412\) 0 0
\(413\) −54.0576 −2.66000
\(414\) 0 0
\(415\) −21.0577 −1.03368
\(416\) 0 0
\(417\) 13.6556 0.668716
\(418\) 0 0
\(419\) −35.6782 −1.74299 −0.871497 0.490400i \(-0.836851\pi\)
−0.871497 + 0.490400i \(0.836851\pi\)
\(420\) 0 0
\(421\) 35.1282 1.71205 0.856023 0.516939i \(-0.172928\pi\)
0.856023 + 0.516939i \(0.172928\pi\)
\(422\) 0 0
\(423\) 6.53719 0.317849
\(424\) 0 0
\(425\) 2.85670 0.138570
\(426\) 0 0
\(427\) −14.4764 −0.700562
\(428\) 0 0
\(429\) −0.904314 −0.0436607
\(430\) 0 0
\(431\) −31.1086 −1.49845 −0.749224 0.662317i \(-0.769573\pi\)
−0.749224 + 0.662317i \(0.769573\pi\)
\(432\) 0 0
\(433\) 26.3963 1.26852 0.634262 0.773118i \(-0.281304\pi\)
0.634262 + 0.773118i \(0.281304\pi\)
\(434\) 0 0
\(435\) −2.96949 −0.142376
\(436\) 0 0
\(437\) −3.13742 −0.150083
\(438\) 0 0
\(439\) 10.4597 0.499212 0.249606 0.968347i \(-0.419699\pi\)
0.249606 + 0.968347i \(0.419699\pi\)
\(440\) 0 0
\(441\) 6.07071 0.289081
\(442\) 0 0
\(443\) 10.5558 0.501521 0.250760 0.968049i \(-0.419319\pi\)
0.250760 + 0.968049i \(0.419319\pi\)
\(444\) 0 0
\(445\) 43.3462 2.05481
\(446\) 0 0
\(447\) 22.8048 1.07863
\(448\) 0 0
\(449\) −20.8975 −0.986212 −0.493106 0.869969i \(-0.664139\pi\)
−0.493106 + 0.869969i \(0.664139\pi\)
\(450\) 0 0
\(451\) 1.36845 0.0644378
\(452\) 0 0
\(453\) 10.8986 0.512061
\(454\) 0 0
\(455\) −6.39607 −0.299852
\(456\) 0 0
\(457\) 31.4248 1.46999 0.734996 0.678071i \(-0.237184\pi\)
0.734996 + 0.678071i \(0.237184\pi\)
\(458\) 0 0
\(459\) 0.748243 0.0349250
\(460\) 0 0
\(461\) 33.5817 1.56406 0.782028 0.623243i \(-0.214185\pi\)
0.782028 + 0.623243i \(0.214185\pi\)
\(462\) 0 0
\(463\) −7.03132 −0.326773 −0.163387 0.986562i \(-0.552242\pi\)
−0.163387 + 0.986562i \(0.552242\pi\)
\(464\) 0 0
\(465\) 4.47003 0.207293
\(466\) 0 0
\(467\) 28.1474 1.30250 0.651252 0.758861i \(-0.274244\pi\)
0.651252 + 0.758861i \(0.274244\pi\)
\(468\) 0 0
\(469\) −26.0073 −1.20091
\(470\) 0 0
\(471\) −11.3841 −0.524554
\(472\) 0 0
\(473\) 10.9879 0.505224
\(474\) 0 0
\(475\) −11.9783 −0.549600
\(476\) 0 0
\(477\) 11.1195 0.509126
\(478\) 0 0
\(479\) −0.674384 −0.0308134 −0.0154067 0.999881i \(-0.504904\pi\)
−0.0154067 + 0.999881i \(0.504904\pi\)
\(480\) 0 0
\(481\) 2.17879 0.0993442
\(482\) 0 0
\(483\) −3.61534 −0.164504
\(484\) 0 0
\(485\) −20.9518 −0.951373
\(486\) 0 0
\(487\) 3.35339 0.151957 0.0759783 0.997109i \(-0.475792\pi\)
0.0759783 + 0.997109i \(0.475792\pi\)
\(488\) 0 0
\(489\) 9.05790 0.409612
\(490\) 0 0
\(491\) −8.13220 −0.367001 −0.183501 0.983020i \(-0.558743\pi\)
−0.183501 + 0.983020i \(0.558743\pi\)
\(492\) 0 0
\(493\) −0.748243 −0.0336992
\(494\) 0 0
\(495\) −4.50733 −0.202589
\(496\) 0 0
\(497\) −26.1580 −1.17335
\(498\) 0 0
\(499\) 20.1591 0.902447 0.451224 0.892411i \(-0.350988\pi\)
0.451224 + 0.892411i \(0.350988\pi\)
\(500\) 0 0
\(501\) −0.683362 −0.0305304
\(502\) 0 0
\(503\) −7.03823 −0.313819 −0.156910 0.987613i \(-0.550153\pi\)
−0.156910 + 0.987613i \(0.550153\pi\)
\(504\) 0 0
\(505\) 1.45235 0.0646289
\(506\) 0 0
\(507\) −12.6451 −0.561587
\(508\) 0 0
\(509\) 1.35598 0.0601029 0.0300514 0.999548i \(-0.490433\pi\)
0.0300514 + 0.999548i \(0.490433\pi\)
\(510\) 0 0
\(511\) −32.2380 −1.42613
\(512\) 0 0
\(513\) −3.13742 −0.138520
\(514\) 0 0
\(515\) −22.4763 −0.990423
\(516\) 0 0
\(517\) −9.92266 −0.436398
\(518\) 0 0
\(519\) 18.5209 0.812977
\(520\) 0 0
\(521\) −38.3386 −1.67964 −0.839821 0.542863i \(-0.817340\pi\)
−0.839821 + 0.542863i \(0.817340\pi\)
\(522\) 0 0
\(523\) 41.8322 1.82919 0.914597 0.404367i \(-0.132508\pi\)
0.914597 + 0.404367i \(0.132508\pi\)
\(524\) 0 0
\(525\) −13.8029 −0.602409
\(526\) 0 0
\(527\) 1.12635 0.0490644
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 14.9523 0.648873
\(532\) 0 0
\(533\) −0.537123 −0.0232654
\(534\) 0 0
\(535\) −47.4852 −2.05297
\(536\) 0 0
\(537\) 15.3322 0.661632
\(538\) 0 0
\(539\) −9.21460 −0.396901
\(540\) 0 0
\(541\) −1.04015 −0.0447197 −0.0223599 0.999750i \(-0.507118\pi\)
−0.0223599 + 0.999750i \(0.507118\pi\)
\(542\) 0 0
\(543\) 17.8648 0.766652
\(544\) 0 0
\(545\) −17.7804 −0.761628
\(546\) 0 0
\(547\) 14.0370 0.600178 0.300089 0.953911i \(-0.402984\pi\)
0.300089 + 0.953911i \(0.402984\pi\)
\(548\) 0 0
\(549\) 4.00415 0.170893
\(550\) 0 0
\(551\) 3.13742 0.133658
\(552\) 0 0
\(553\) −31.2163 −1.32745
\(554\) 0 0
\(555\) 10.8596 0.460966
\(556\) 0 0
\(557\) 5.83425 0.247205 0.123603 0.992332i \(-0.460555\pi\)
0.123603 + 0.992332i \(0.460555\pi\)
\(558\) 0 0
\(559\) −4.31280 −0.182412
\(560\) 0 0
\(561\) −1.13574 −0.0479511
\(562\) 0 0
\(563\) −1.56991 −0.0661639 −0.0330820 0.999453i \(-0.510532\pi\)
−0.0330820 + 0.999453i \(0.510532\pi\)
\(564\) 0 0
\(565\) 58.1887 2.44802
\(566\) 0 0
\(567\) −3.61534 −0.151830
\(568\) 0 0
\(569\) −3.71444 −0.155717 −0.0778587 0.996964i \(-0.524808\pi\)
−0.0778587 + 0.996964i \(0.524808\pi\)
\(570\) 0 0
\(571\) −17.2059 −0.720044 −0.360022 0.932944i \(-0.617231\pi\)
−0.360022 + 0.932944i \(0.617231\pi\)
\(572\) 0 0
\(573\) 11.9148 0.497749
\(574\) 0 0
\(575\) 3.81787 0.159216
\(576\) 0 0
\(577\) −14.4600 −0.601979 −0.300990 0.953627i \(-0.597317\pi\)
−0.300990 + 0.953627i \(0.597317\pi\)
\(578\) 0 0
\(579\) 2.56622 0.106649
\(580\) 0 0
\(581\) 25.6377 1.06363
\(582\) 0 0
\(583\) −16.8780 −0.699016
\(584\) 0 0
\(585\) 1.76915 0.0731452
\(586\) 0 0
\(587\) −12.2038 −0.503704 −0.251852 0.967766i \(-0.581040\pi\)
−0.251852 + 0.967766i \(0.581040\pi\)
\(588\) 0 0
\(589\) −4.72281 −0.194600
\(590\) 0 0
\(591\) 24.1492 0.993365
\(592\) 0 0
\(593\) 4.93531 0.202669 0.101334 0.994852i \(-0.467689\pi\)
0.101334 + 0.994852i \(0.467689\pi\)
\(594\) 0 0
\(595\) −8.03294 −0.329318
\(596\) 0 0
\(597\) −18.0349 −0.738121
\(598\) 0 0
\(599\) −7.75551 −0.316881 −0.158441 0.987368i \(-0.550647\pi\)
−0.158441 + 0.987368i \(0.550647\pi\)
\(600\) 0 0
\(601\) 2.38433 0.0972589 0.0486295 0.998817i \(-0.484515\pi\)
0.0486295 + 0.998817i \(0.484515\pi\)
\(602\) 0 0
\(603\) 7.19360 0.292946
\(604\) 0 0
\(605\) −25.8228 −1.04985
\(606\) 0 0
\(607\) 37.4722 1.52095 0.760475 0.649367i \(-0.224966\pi\)
0.760475 + 0.649367i \(0.224966\pi\)
\(608\) 0 0
\(609\) 3.61534 0.146501
\(610\) 0 0
\(611\) 3.89469 0.157562
\(612\) 0 0
\(613\) −36.0966 −1.45793 −0.728965 0.684551i \(-0.759998\pi\)
−0.728965 + 0.684551i \(0.759998\pi\)
\(614\) 0 0
\(615\) −2.67715 −0.107953
\(616\) 0 0
\(617\) 19.7814 0.796370 0.398185 0.917305i \(-0.369640\pi\)
0.398185 + 0.917305i \(0.369640\pi\)
\(618\) 0 0
\(619\) 3.42660 0.137727 0.0688633 0.997626i \(-0.478063\pi\)
0.0688633 + 0.997626i \(0.478063\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −52.7739 −2.11434
\(624\) 0 0
\(625\) −29.5132 −1.18053
\(626\) 0 0
\(627\) 4.76222 0.190185
\(628\) 0 0
\(629\) 2.73638 0.109107
\(630\) 0 0
\(631\) −6.82247 −0.271598 −0.135799 0.990736i \(-0.543360\pi\)
−0.135799 + 0.990736i \(0.543360\pi\)
\(632\) 0 0
\(633\) −24.7157 −0.982363
\(634\) 0 0
\(635\) −1.55088 −0.0615447
\(636\) 0 0
\(637\) 3.61677 0.143302
\(638\) 0 0
\(639\) 7.23527 0.286223
\(640\) 0 0
\(641\) −47.5579 −1.87842 −0.939212 0.343337i \(-0.888443\pi\)
−0.939212 + 0.343337i \(0.888443\pi\)
\(642\) 0 0
\(643\) −4.07286 −0.160618 −0.0803090 0.996770i \(-0.525591\pi\)
−0.0803090 + 0.996770i \(0.525591\pi\)
\(644\) 0 0
\(645\) −21.4961 −0.846407
\(646\) 0 0
\(647\) 6.44068 0.253209 0.126605 0.991953i \(-0.459592\pi\)
0.126605 + 0.991953i \(0.459592\pi\)
\(648\) 0 0
\(649\) −22.6957 −0.890886
\(650\) 0 0
\(651\) −5.44225 −0.213298
\(652\) 0 0
\(653\) 19.4753 0.762128 0.381064 0.924549i \(-0.375558\pi\)
0.381064 + 0.924549i \(0.375558\pi\)
\(654\) 0 0
\(655\) 7.80851 0.305104
\(656\) 0 0
\(657\) 8.91700 0.347885
\(658\) 0 0
\(659\) −2.19761 −0.0856068 −0.0428034 0.999084i \(-0.513629\pi\)
−0.0428034 + 0.999084i \(0.513629\pi\)
\(660\) 0 0
\(661\) −49.2488 −1.91556 −0.957778 0.287509i \(-0.907173\pi\)
−0.957778 + 0.287509i \(0.907173\pi\)
\(662\) 0 0
\(663\) 0.445784 0.0173128
\(664\) 0 0
\(665\) 33.6824 1.30615
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −18.6236 −0.720028
\(670\) 0 0
\(671\) −6.07782 −0.234632
\(672\) 0 0
\(673\) 10.9216 0.420999 0.210499 0.977594i \(-0.432491\pi\)
0.210499 + 0.977594i \(0.432491\pi\)
\(674\) 0 0
\(675\) 3.81787 0.146950
\(676\) 0 0
\(677\) −38.2241 −1.46907 −0.734535 0.678571i \(-0.762600\pi\)
−0.734535 + 0.678571i \(0.762600\pi\)
\(678\) 0 0
\(679\) 25.5088 0.978936
\(680\) 0 0
\(681\) −19.2355 −0.737108
\(682\) 0 0
\(683\) 5.44797 0.208461 0.104230 0.994553i \(-0.466762\pi\)
0.104230 + 0.994553i \(0.466762\pi\)
\(684\) 0 0
\(685\) −20.7513 −0.792865
\(686\) 0 0
\(687\) 19.3237 0.737244
\(688\) 0 0
\(689\) 6.62470 0.252381
\(690\) 0 0
\(691\) −37.7948 −1.43778 −0.718890 0.695123i \(-0.755350\pi\)
−0.718890 + 0.695123i \(0.755350\pi\)
\(692\) 0 0
\(693\) 5.48765 0.208459
\(694\) 0 0
\(695\) 40.5501 1.53815
\(696\) 0 0
\(697\) −0.674581 −0.0255516
\(698\) 0 0
\(699\) 6.70768 0.253708
\(700\) 0 0
\(701\) 26.7296 1.00956 0.504782 0.863247i \(-0.331573\pi\)
0.504782 + 0.863247i \(0.331573\pi\)
\(702\) 0 0
\(703\) −11.4737 −0.432741
\(704\) 0 0
\(705\) 19.4121 0.731103
\(706\) 0 0
\(707\) −1.76824 −0.0665013
\(708\) 0 0
\(709\) −11.5893 −0.435244 −0.217622 0.976033i \(-0.569830\pi\)
−0.217622 + 0.976033i \(0.569830\pi\)
\(710\) 0 0
\(711\) 8.63438 0.323815
\(712\) 0 0
\(713\) 1.50532 0.0563747
\(714\) 0 0
\(715\) −2.68535 −0.100426
\(716\) 0 0
\(717\) −8.25440 −0.308266
\(718\) 0 0
\(719\) 26.3213 0.981618 0.490809 0.871267i \(-0.336701\pi\)
0.490809 + 0.871267i \(0.336701\pi\)
\(720\) 0 0
\(721\) 27.3648 1.01912
\(722\) 0 0
\(723\) 2.59131 0.0963718
\(724\) 0 0
\(725\) −3.81787 −0.141792
\(726\) 0 0
\(727\) 26.5364 0.984179 0.492090 0.870545i \(-0.336233\pi\)
0.492090 + 0.870545i \(0.336233\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.41652 −0.200337
\(732\) 0 0
\(733\) −33.8396 −1.24989 −0.624946 0.780668i \(-0.714879\pi\)
−0.624946 + 0.780668i \(0.714879\pi\)
\(734\) 0 0
\(735\) 18.0269 0.664932
\(736\) 0 0
\(737\) −10.9190 −0.402207
\(738\) 0 0
\(739\) 9.65004 0.354983 0.177491 0.984122i \(-0.443202\pi\)
0.177491 + 0.984122i \(0.443202\pi\)
\(740\) 0 0
\(741\) −1.86919 −0.0686665
\(742\) 0 0
\(743\) −33.3923 −1.22505 −0.612523 0.790453i \(-0.709845\pi\)
−0.612523 + 0.790453i \(0.709845\pi\)
\(744\) 0 0
\(745\) 67.7187 2.48102
\(746\) 0 0
\(747\) −7.09135 −0.259459
\(748\) 0 0
\(749\) 57.8131 2.11244
\(750\) 0 0
\(751\) −13.0629 −0.476673 −0.238336 0.971183i \(-0.576602\pi\)
−0.238336 + 0.971183i \(0.576602\pi\)
\(752\) 0 0
\(753\) 13.2452 0.482681
\(754\) 0 0
\(755\) 32.3633 1.17782
\(756\) 0 0
\(757\) 12.7202 0.462323 0.231162 0.972915i \(-0.425747\pi\)
0.231162 + 0.972915i \(0.425747\pi\)
\(758\) 0 0
\(759\) −1.51788 −0.0550955
\(760\) 0 0
\(761\) 8.96963 0.325149 0.162574 0.986696i \(-0.448020\pi\)
0.162574 + 0.986696i \(0.448020\pi\)
\(762\) 0 0
\(763\) 21.6475 0.783694
\(764\) 0 0
\(765\) 2.22190 0.0803330
\(766\) 0 0
\(767\) 8.90818 0.321656
\(768\) 0 0
\(769\) 46.1450 1.66403 0.832015 0.554753i \(-0.187187\pi\)
0.832015 + 0.554753i \(0.187187\pi\)
\(770\) 0 0
\(771\) 18.4842 0.665690
\(772\) 0 0
\(773\) −12.9246 −0.464866 −0.232433 0.972612i \(-0.574669\pi\)
−0.232433 + 0.972612i \(0.574669\pi\)
\(774\) 0 0
\(775\) 5.74712 0.206443
\(776\) 0 0
\(777\) −13.2216 −0.474321
\(778\) 0 0
\(779\) 2.82855 0.101343
\(780\) 0 0
\(781\) −10.9823 −0.392976
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −33.8051 −1.20656
\(786\) 0 0
\(787\) 34.2016 1.21916 0.609578 0.792726i \(-0.291339\pi\)
0.609578 + 0.792726i \(0.291339\pi\)
\(788\) 0 0
\(789\) −17.5161 −0.623589
\(790\) 0 0
\(791\) −70.8446 −2.51894
\(792\) 0 0
\(793\) 2.38557 0.0847142
\(794\) 0 0
\(795\) 33.0192 1.17107
\(796\) 0 0
\(797\) −2.29771 −0.0813892 −0.0406946 0.999172i \(-0.512957\pi\)
−0.0406946 + 0.999172i \(0.512957\pi\)
\(798\) 0 0
\(799\) 4.89141 0.173046
\(800\) 0 0
\(801\) 14.5972 0.515767
\(802\) 0 0
\(803\) −13.5349 −0.477637
\(804\) 0 0
\(805\) −10.7357 −0.378385
\(806\) 0 0
\(807\) −12.9857 −0.457120
\(808\) 0 0
\(809\) 25.8336 0.908263 0.454131 0.890935i \(-0.349950\pi\)
0.454131 + 0.890935i \(0.349950\pi\)
\(810\) 0 0
\(811\) 47.3390 1.66230 0.831148 0.556051i \(-0.187684\pi\)
0.831148 + 0.556051i \(0.187684\pi\)
\(812\) 0 0
\(813\) −3.97009 −0.139237
\(814\) 0 0
\(815\) 26.8973 0.942173
\(816\) 0 0
\(817\) 22.7117 0.794582
\(818\) 0 0
\(819\) −2.15393 −0.0752644
\(820\) 0 0
\(821\) −26.8013 −0.935370 −0.467685 0.883895i \(-0.654912\pi\)
−0.467685 + 0.883895i \(0.654912\pi\)
\(822\) 0 0
\(823\) 39.6268 1.38130 0.690651 0.723188i \(-0.257324\pi\)
0.690651 + 0.723188i \(0.257324\pi\)
\(824\) 0 0
\(825\) −5.79507 −0.201758
\(826\) 0 0
\(827\) 11.2693 0.391873 0.195936 0.980617i \(-0.437225\pi\)
0.195936 + 0.980617i \(0.437225\pi\)
\(828\) 0 0
\(829\) −16.4640 −0.571818 −0.285909 0.958257i \(-0.592295\pi\)
−0.285909 + 0.958257i \(0.592295\pi\)
\(830\) 0 0
\(831\) −23.8848 −0.828555
\(832\) 0 0
\(833\) 4.54237 0.157384
\(834\) 0 0
\(835\) −2.02924 −0.0702246
\(836\) 0 0
\(837\) 1.50532 0.0520315
\(838\) 0 0
\(839\) −9.94977 −0.343504 −0.171752 0.985140i \(-0.554943\pi\)
−0.171752 + 0.985140i \(0.554943\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −26.7422 −0.921051
\(844\) 0 0
\(845\) −37.5494 −1.29174
\(846\) 0 0
\(847\) 31.4392 1.08026
\(848\) 0 0
\(849\) 16.1073 0.552801
\(850\) 0 0
\(851\) 3.65707 0.125363
\(852\) 0 0
\(853\) −26.2812 −0.899850 −0.449925 0.893066i \(-0.648549\pi\)
−0.449925 + 0.893066i \(0.648549\pi\)
\(854\) 0 0
\(855\) −9.31653 −0.318619
\(856\) 0 0
\(857\) −28.6513 −0.978708 −0.489354 0.872085i \(-0.662767\pi\)
−0.489354 + 0.872085i \(0.662767\pi\)
\(858\) 0 0
\(859\) 32.0376 1.09311 0.546555 0.837423i \(-0.315939\pi\)
0.546555 + 0.837423i \(0.315939\pi\)
\(860\) 0 0
\(861\) 3.25943 0.111081
\(862\) 0 0
\(863\) 2.20860 0.0751816 0.0375908 0.999293i \(-0.488032\pi\)
0.0375908 + 0.999293i \(0.488032\pi\)
\(864\) 0 0
\(865\) 54.9976 1.86997
\(866\) 0 0
\(867\) −16.4401 −0.558336
\(868\) 0 0
\(869\) −13.1059 −0.444589
\(870\) 0 0
\(871\) 4.28576 0.145218
\(872\) 0 0
\(873\) −7.05569 −0.238799
\(874\) 0 0
\(875\) 12.6910 0.429035
\(876\) 0 0
\(877\) 4.99989 0.168834 0.0844172 0.996430i \(-0.473097\pi\)
0.0844172 + 0.996430i \(0.473097\pi\)
\(878\) 0 0
\(879\) −16.4362 −0.554380
\(880\) 0 0
\(881\) −16.5006 −0.555921 −0.277960 0.960593i \(-0.589658\pi\)
−0.277960 + 0.960593i \(0.589658\pi\)
\(882\) 0 0
\(883\) 5.44352 0.183189 0.0915944 0.995796i \(-0.470804\pi\)
0.0915944 + 0.995796i \(0.470804\pi\)
\(884\) 0 0
\(885\) 44.4006 1.49251
\(886\) 0 0
\(887\) −28.3234 −0.951007 −0.475503 0.879714i \(-0.657734\pi\)
−0.475503 + 0.879714i \(0.657734\pi\)
\(888\) 0 0
\(889\) 1.88819 0.0633278
\(890\) 0 0
\(891\) −1.51788 −0.0508509
\(892\) 0 0
\(893\) −20.5099 −0.686337
\(894\) 0 0
\(895\) 45.5288 1.52186
\(896\) 0 0
\(897\) 0.595774 0.0198923
\(898\) 0 0
\(899\) −1.50532 −0.0502052
\(900\) 0 0
\(901\) 8.32007 0.277182
\(902\) 0 0
\(903\) 26.1714 0.870930
\(904\) 0 0
\(905\) 53.0493 1.76342
\(906\) 0 0
\(907\) 56.7963 1.88589 0.942945 0.332947i \(-0.108043\pi\)
0.942945 + 0.332947i \(0.108043\pi\)
\(908\) 0 0
\(909\) 0.489092 0.0162222
\(910\) 0 0
\(911\) −5.50129 −0.182266 −0.0911329 0.995839i \(-0.529049\pi\)
−0.0911329 + 0.995839i \(0.529049\pi\)
\(912\) 0 0
\(913\) 10.7638 0.356230
\(914\) 0 0
\(915\) 11.8903 0.393081
\(916\) 0 0
\(917\) −9.50683 −0.313943
\(918\) 0 0
\(919\) −13.7290 −0.452878 −0.226439 0.974025i \(-0.572708\pi\)
−0.226439 + 0.974025i \(0.572708\pi\)
\(920\) 0 0
\(921\) −11.2107 −0.369404
\(922\) 0 0
\(923\) 4.31059 0.141885
\(924\) 0 0
\(925\) 13.9622 0.459075
\(926\) 0 0
\(927\) −7.56907 −0.248601
\(928\) 0 0
\(929\) 49.5234 1.62481 0.812406 0.583093i \(-0.198158\pi\)
0.812406 + 0.583093i \(0.198158\pi\)
\(930\) 0 0
\(931\) −19.0463 −0.624219
\(932\) 0 0
\(933\) 25.7748 0.843831
\(934\) 0 0
\(935\) −3.37258 −0.110295
\(936\) 0 0
\(937\) −11.2506 −0.367541 −0.183771 0.982969i \(-0.558830\pi\)
−0.183771 + 0.982969i \(0.558830\pi\)
\(938\) 0 0
\(939\) 14.0344 0.457996
\(940\) 0 0
\(941\) −26.2221 −0.854816 −0.427408 0.904059i \(-0.640573\pi\)
−0.427408 + 0.904059i \(0.640573\pi\)
\(942\) 0 0
\(943\) −0.901553 −0.0293586
\(944\) 0 0
\(945\) −10.7357 −0.349233
\(946\) 0 0
\(947\) −17.2120 −0.559315 −0.279657 0.960100i \(-0.590221\pi\)
−0.279657 + 0.960100i \(0.590221\pi\)
\(948\) 0 0
\(949\) 5.31252 0.172452
\(950\) 0 0
\(951\) 23.8531 0.773490
\(952\) 0 0
\(953\) −9.18539 −0.297544 −0.148772 0.988872i \(-0.547532\pi\)
−0.148772 + 0.988872i \(0.547532\pi\)
\(954\) 0 0
\(955\) 35.3810 1.14490
\(956\) 0 0
\(957\) 1.51788 0.0490661
\(958\) 0 0
\(959\) 25.2646 0.815836
\(960\) 0 0
\(961\) −28.7340 −0.926904
\(962\) 0 0
\(963\) −15.9910 −0.515304
\(964\) 0 0
\(965\) 7.62037 0.245308
\(966\) 0 0
\(967\) 1.33968 0.0430813 0.0215407 0.999768i \(-0.493143\pi\)
0.0215407 + 0.999768i \(0.493143\pi\)
\(968\) 0 0
\(969\) −2.34755 −0.0754142
\(970\) 0 0
\(971\) −22.3694 −0.717868 −0.358934 0.933363i \(-0.616860\pi\)
−0.358934 + 0.933363i \(0.616860\pi\)
\(972\) 0 0
\(973\) −49.3696 −1.58272
\(974\) 0 0
\(975\) 2.27459 0.0728452
\(976\) 0 0
\(977\) 16.4507 0.526303 0.263151 0.964755i \(-0.415238\pi\)
0.263151 + 0.964755i \(0.415238\pi\)
\(978\) 0 0
\(979\) −22.1568 −0.708134
\(980\) 0 0
\(981\) −5.98769 −0.191172
\(982\) 0 0
\(983\) −4.90684 −0.156504 −0.0782519 0.996934i \(-0.524934\pi\)
−0.0782519 + 0.996934i \(0.524934\pi\)
\(984\) 0 0
\(985\) 71.7108 2.28490
\(986\) 0 0
\(987\) −23.6342 −0.752284
\(988\) 0 0
\(989\) −7.23898 −0.230186
\(990\) 0 0
\(991\) 34.4570 1.09456 0.547282 0.836948i \(-0.315663\pi\)
0.547282 + 0.836948i \(0.315663\pi\)
\(992\) 0 0
\(993\) −18.1473 −0.575886
\(994\) 0 0
\(995\) −53.5546 −1.69779
\(996\) 0 0
\(997\) 41.1311 1.30264 0.651318 0.758805i \(-0.274217\pi\)
0.651318 + 0.758805i \(0.274217\pi\)
\(998\) 0 0
\(999\) 3.65707 0.115705
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 \(a_p\))