Properties

Label 8004.2.a.d.1.5
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.58311\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -0.270840 q^{5} +0.409136 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -0.270840 q^{5} +0.409136 q^{7} +1.00000 q^{9} -3.18144 q^{11} +0.382284 q^{13} -0.270840 q^{15} -4.23453 q^{17} +5.44767 q^{19} +0.409136 q^{21} +1.00000 q^{23} -4.92665 q^{25} +1.00000 q^{27} +1.00000 q^{29} +2.08063 q^{31} -3.18144 q^{33} -0.110810 q^{35} -5.55848 q^{37} +0.382284 q^{39} +7.07476 q^{41} -5.46885 q^{43} -0.270840 q^{45} -11.6721 q^{47} -6.83261 q^{49} -4.23453 q^{51} +13.1074 q^{53} +0.861661 q^{55} +5.44767 q^{57} +4.76314 q^{59} -2.32894 q^{61} +0.409136 q^{63} -0.103538 q^{65} +0.562865 q^{67} +1.00000 q^{69} -7.04632 q^{71} -10.9653 q^{73} -4.92665 q^{75} -1.30164 q^{77} -16.6996 q^{79} +1.00000 q^{81} +9.44555 q^{83} +1.14688 q^{85} +1.00000 q^{87} +8.74304 q^{89} +0.156406 q^{91} +2.08063 q^{93} -1.47545 q^{95} -2.87535 q^{97} -3.18144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} - 5q^{11} - 4q^{13} - 5q^{15} - 3q^{17} - 5q^{19} - 4q^{21} + 8q^{23} - 5q^{25} + 8q^{27} + 8q^{29} - 2q^{31} - 5q^{33} - 15q^{35} - 10q^{37} - 4q^{39} - 11q^{41} - 7q^{43} - 5q^{45} - 14q^{47} - 18q^{49} - 3q^{51} - 15q^{53} - 17q^{55} - 5q^{57} + 4q^{59} + q^{61} - 4q^{63} - 5q^{67} + 8q^{69} - q^{71} - 21q^{73} - 5q^{75} - 8q^{79} + 8q^{81} + 3q^{83} + 8q^{87} - 20q^{89} - 7q^{91} - 2q^{93} - 3q^{95} - 7q^{97} - 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −0.270840 −0.121123 −0.0605617 0.998164i \(-0.519289\pi\)
−0.0605617 + 0.998164i \(0.519289\pi\)
\(6\) 0 0
\(7\) 0.409136 0.154639 0.0773195 0.997006i \(-0.475364\pi\)
0.0773195 + 0.997006i \(0.475364\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.18144 −0.959240 −0.479620 0.877476i \(-0.659226\pi\)
−0.479620 + 0.877476i \(0.659226\pi\)
\(12\) 0 0
\(13\) 0.382284 0.106027 0.0530133 0.998594i \(-0.483117\pi\)
0.0530133 + 0.998594i \(0.483117\pi\)
\(14\) 0 0
\(15\) −0.270840 −0.0699306
\(16\) 0 0
\(17\) −4.23453 −1.02702 −0.513512 0.858083i \(-0.671656\pi\)
−0.513512 + 0.858083i \(0.671656\pi\)
\(18\) 0 0
\(19\) 5.44767 1.24978 0.624891 0.780712i \(-0.285144\pi\)
0.624891 + 0.780712i \(0.285144\pi\)
\(20\) 0 0
\(21\) 0.409136 0.0892808
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.92665 −0.985329
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 2.08063 0.373691 0.186846 0.982389i \(-0.440174\pi\)
0.186846 + 0.982389i \(0.440174\pi\)
\(32\) 0 0
\(33\) −3.18144 −0.553818
\(34\) 0 0
\(35\) −0.110810 −0.0187304
\(36\) 0 0
\(37\) −5.55848 −0.913808 −0.456904 0.889516i \(-0.651042\pi\)
−0.456904 + 0.889516i \(0.651042\pi\)
\(38\) 0 0
\(39\) 0.382284 0.0612145
\(40\) 0 0
\(41\) 7.07476 1.10489 0.552446 0.833549i \(-0.313695\pi\)
0.552446 + 0.833549i \(0.313695\pi\)
\(42\) 0 0
\(43\) −5.46885 −0.833992 −0.416996 0.908908i \(-0.636917\pi\)
−0.416996 + 0.908908i \(0.636917\pi\)
\(44\) 0 0
\(45\) −0.270840 −0.0403744
\(46\) 0 0
\(47\) −11.6721 −1.70255 −0.851276 0.524717i \(-0.824171\pi\)
−0.851276 + 0.524717i \(0.824171\pi\)
\(48\) 0 0
\(49\) −6.83261 −0.976087
\(50\) 0 0
\(51\) −4.23453 −0.592952
\(52\) 0 0
\(53\) 13.1074 1.80043 0.900217 0.435441i \(-0.143408\pi\)
0.900217 + 0.435441i \(0.143408\pi\)
\(54\) 0 0
\(55\) 0.861661 0.116186
\(56\) 0 0
\(57\) 5.44767 0.721561
\(58\) 0 0
\(59\) 4.76314 0.620108 0.310054 0.950719i \(-0.399653\pi\)
0.310054 + 0.950719i \(0.399653\pi\)
\(60\) 0 0
\(61\) −2.32894 −0.298190 −0.149095 0.988823i \(-0.547636\pi\)
−0.149095 + 0.988823i \(0.547636\pi\)
\(62\) 0 0
\(63\) 0.409136 0.0515463
\(64\) 0 0
\(65\) −0.103538 −0.0128423
\(66\) 0 0
\(67\) 0.562865 0.0687649 0.0343824 0.999409i \(-0.489054\pi\)
0.0343824 + 0.999409i \(0.489054\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −7.04632 −0.836245 −0.418122 0.908391i \(-0.637312\pi\)
−0.418122 + 0.908391i \(0.637312\pi\)
\(72\) 0 0
\(73\) −10.9653 −1.28340 −0.641698 0.766957i \(-0.721770\pi\)
−0.641698 + 0.766957i \(0.721770\pi\)
\(74\) 0 0
\(75\) −4.92665 −0.568880
\(76\) 0 0
\(77\) −1.30164 −0.148336
\(78\) 0 0
\(79\) −16.6996 −1.87885 −0.939424 0.342758i \(-0.888639\pi\)
−0.939424 + 0.342758i \(0.888639\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.44555 1.03678 0.518392 0.855143i \(-0.326531\pi\)
0.518392 + 0.855143i \(0.326531\pi\)
\(84\) 0 0
\(85\) 1.14688 0.124396
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) 8.74304 0.926760 0.463380 0.886160i \(-0.346637\pi\)
0.463380 + 0.886160i \(0.346637\pi\)
\(90\) 0 0
\(91\) 0.156406 0.0163958
\(92\) 0 0
\(93\) 2.08063 0.215751
\(94\) 0 0
\(95\) −1.47545 −0.151378
\(96\) 0 0
\(97\) −2.87535 −0.291948 −0.145974 0.989288i \(-0.546632\pi\)
−0.145974 + 0.989288i \(0.546632\pi\)
\(98\) 0 0
\(99\) −3.18144 −0.319747
\(100\) 0 0
\(101\) 13.7261 1.36580 0.682900 0.730512i \(-0.260719\pi\)
0.682900 + 0.730512i \(0.260719\pi\)
\(102\) 0 0
\(103\) −12.0130 −1.18367 −0.591837 0.806058i \(-0.701597\pi\)
−0.591837 + 0.806058i \(0.701597\pi\)
\(104\) 0 0
\(105\) −0.110810 −0.0108140
\(106\) 0 0
\(107\) −0.954655 −0.0922900 −0.0461450 0.998935i \(-0.514694\pi\)
−0.0461450 + 0.998935i \(0.514694\pi\)
\(108\) 0 0
\(109\) −9.85059 −0.943516 −0.471758 0.881728i \(-0.656380\pi\)
−0.471758 + 0.881728i \(0.656380\pi\)
\(110\) 0 0
\(111\) −5.55848 −0.527588
\(112\) 0 0
\(113\) 3.54743 0.333714 0.166857 0.985981i \(-0.446638\pi\)
0.166857 + 0.985981i \(0.446638\pi\)
\(114\) 0 0
\(115\) −0.270840 −0.0252560
\(116\) 0 0
\(117\) 0.382284 0.0353422
\(118\) 0 0
\(119\) −1.73250 −0.158818
\(120\) 0 0
\(121\) −0.878442 −0.0798584
\(122\) 0 0
\(123\) 7.07476 0.637910
\(124\) 0 0
\(125\) 2.68853 0.240470
\(126\) 0 0
\(127\) 2.20435 0.195605 0.0978024 0.995206i \(-0.468819\pi\)
0.0978024 + 0.995206i \(0.468819\pi\)
\(128\) 0 0
\(129\) −5.46885 −0.481505
\(130\) 0 0
\(131\) −11.6263 −1.01580 −0.507899 0.861417i \(-0.669578\pi\)
−0.507899 + 0.861417i \(0.669578\pi\)
\(132\) 0 0
\(133\) 2.22884 0.193265
\(134\) 0 0
\(135\) −0.270840 −0.0233102
\(136\) 0 0
\(137\) −8.00999 −0.684340 −0.342170 0.939638i \(-0.611162\pi\)
−0.342170 + 0.939638i \(0.611162\pi\)
\(138\) 0 0
\(139\) −16.7849 −1.42368 −0.711838 0.702343i \(-0.752137\pi\)
−0.711838 + 0.702343i \(0.752137\pi\)
\(140\) 0 0
\(141\) −11.6721 −0.982969
\(142\) 0 0
\(143\) −1.21621 −0.101705
\(144\) 0 0
\(145\) −0.270840 −0.0224920
\(146\) 0 0
\(147\) −6.83261 −0.563544
\(148\) 0 0
\(149\) −16.5791 −1.35821 −0.679107 0.734039i \(-0.737633\pi\)
−0.679107 + 0.734039i \(0.737633\pi\)
\(150\) 0 0
\(151\) 11.8936 0.967888 0.483944 0.875099i \(-0.339204\pi\)
0.483944 + 0.875099i \(0.339204\pi\)
\(152\) 0 0
\(153\) −4.23453 −0.342341
\(154\) 0 0
\(155\) −0.563517 −0.0452628
\(156\) 0 0
\(157\) 8.71347 0.695411 0.347705 0.937604i \(-0.386961\pi\)
0.347705 + 0.937604i \(0.386961\pi\)
\(158\) 0 0
\(159\) 13.1074 1.03948
\(160\) 0 0
\(161\) 0.409136 0.0322444
\(162\) 0 0
\(163\) 15.7742 1.23553 0.617767 0.786362i \(-0.288038\pi\)
0.617767 + 0.786362i \(0.288038\pi\)
\(164\) 0 0
\(165\) 0.861661 0.0670802
\(166\) 0 0
\(167\) −19.0619 −1.47505 −0.737525 0.675320i \(-0.764006\pi\)
−0.737525 + 0.675320i \(0.764006\pi\)
\(168\) 0 0
\(169\) −12.8539 −0.988758
\(170\) 0 0
\(171\) 5.44767 0.416594
\(172\) 0 0
\(173\) 2.35020 0.178682 0.0893410 0.996001i \(-0.471524\pi\)
0.0893410 + 0.996001i \(0.471524\pi\)
\(174\) 0 0
\(175\) −2.01567 −0.152370
\(176\) 0 0
\(177\) 4.76314 0.358019
\(178\) 0 0
\(179\) −6.80243 −0.508437 −0.254219 0.967147i \(-0.581818\pi\)
−0.254219 + 0.967147i \(0.581818\pi\)
\(180\) 0 0
\(181\) −8.35756 −0.621212 −0.310606 0.950539i \(-0.600532\pi\)
−0.310606 + 0.950539i \(0.600532\pi\)
\(182\) 0 0
\(183\) −2.32894 −0.172160
\(184\) 0 0
\(185\) 1.50546 0.110684
\(186\) 0 0
\(187\) 13.4719 0.985162
\(188\) 0 0
\(189\) 0.409136 0.0297603
\(190\) 0 0
\(191\) 16.5128 1.19483 0.597413 0.801934i \(-0.296195\pi\)
0.597413 + 0.801934i \(0.296195\pi\)
\(192\) 0 0
\(193\) −20.6858 −1.48900 −0.744499 0.667623i \(-0.767312\pi\)
−0.744499 + 0.667623i \(0.767312\pi\)
\(194\) 0 0
\(195\) −0.103538 −0.00741450
\(196\) 0 0
\(197\) 6.56222 0.467539 0.233769 0.972292i \(-0.424894\pi\)
0.233769 + 0.972292i \(0.424894\pi\)
\(198\) 0 0
\(199\) 0.673220 0.0477233 0.0238616 0.999715i \(-0.492404\pi\)
0.0238616 + 0.999715i \(0.492404\pi\)
\(200\) 0 0
\(201\) 0.562865 0.0397014
\(202\) 0 0
\(203\) 0.409136 0.0287157
\(204\) 0 0
\(205\) −1.91613 −0.133828
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −17.3314 −1.19884
\(210\) 0 0
\(211\) −24.8206 −1.70872 −0.854359 0.519684i \(-0.826050\pi\)
−0.854359 + 0.519684i \(0.826050\pi\)
\(212\) 0 0
\(213\) −7.04632 −0.482806
\(214\) 0 0
\(215\) 1.48118 0.101016
\(216\) 0 0
\(217\) 0.851259 0.0577872
\(218\) 0 0
\(219\) −10.9653 −0.740969
\(220\) 0 0
\(221\) −1.61879 −0.108892
\(222\) 0 0
\(223\) −27.7648 −1.85927 −0.929633 0.368487i \(-0.879876\pi\)
−0.929633 + 0.368487i \(0.879876\pi\)
\(224\) 0 0
\(225\) −4.92665 −0.328443
\(226\) 0 0
\(227\) −12.5430 −0.832511 −0.416255 0.909248i \(-0.636658\pi\)
−0.416255 + 0.909248i \(0.636658\pi\)
\(228\) 0 0
\(229\) −12.0808 −0.798321 −0.399161 0.916881i \(-0.630698\pi\)
−0.399161 + 0.916881i \(0.630698\pi\)
\(230\) 0 0
\(231\) −1.30164 −0.0856418
\(232\) 0 0
\(233\) 7.64163 0.500620 0.250310 0.968166i \(-0.419468\pi\)
0.250310 + 0.968166i \(0.419468\pi\)
\(234\) 0 0
\(235\) 3.16128 0.206219
\(236\) 0 0
\(237\) −16.6996 −1.08475
\(238\) 0 0
\(239\) 10.0402 0.649445 0.324723 0.945809i \(-0.394729\pi\)
0.324723 + 0.945809i \(0.394729\pi\)
\(240\) 0 0
\(241\) 2.88233 0.185667 0.0928335 0.995682i \(-0.470408\pi\)
0.0928335 + 0.995682i \(0.470408\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.85054 0.118227
\(246\) 0 0
\(247\) 2.08256 0.132510
\(248\) 0 0
\(249\) 9.44555 0.598587
\(250\) 0 0
\(251\) 17.4367 1.10059 0.550297 0.834969i \(-0.314514\pi\)
0.550297 + 0.834969i \(0.314514\pi\)
\(252\) 0 0
\(253\) −3.18144 −0.200015
\(254\) 0 0
\(255\) 1.14688 0.0718204
\(256\) 0 0
\(257\) −23.8712 −1.48904 −0.744522 0.667597i \(-0.767323\pi\)
−0.744522 + 0.667597i \(0.767323\pi\)
\(258\) 0 0
\(259\) −2.27418 −0.141310
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) 13.4132 0.827090 0.413545 0.910484i \(-0.364290\pi\)
0.413545 + 0.910484i \(0.364290\pi\)
\(264\) 0 0
\(265\) −3.55000 −0.218075
\(266\) 0 0
\(267\) 8.74304 0.535065
\(268\) 0 0
\(269\) −1.27424 −0.0776915 −0.0388457 0.999245i \(-0.512368\pi\)
−0.0388457 + 0.999245i \(0.512368\pi\)
\(270\) 0 0
\(271\) 8.32920 0.505963 0.252981 0.967471i \(-0.418589\pi\)
0.252981 + 0.967471i \(0.418589\pi\)
\(272\) 0 0
\(273\) 0.156406 0.00946614
\(274\) 0 0
\(275\) 15.6738 0.945167
\(276\) 0 0
\(277\) 12.4631 0.748834 0.374417 0.927261i \(-0.377843\pi\)
0.374417 + 0.927261i \(0.377843\pi\)
\(278\) 0 0
\(279\) 2.08063 0.124564
\(280\) 0 0
\(281\) 4.79090 0.285801 0.142901 0.989737i \(-0.454357\pi\)
0.142901 + 0.989737i \(0.454357\pi\)
\(282\) 0 0
\(283\) 8.47563 0.503824 0.251912 0.967750i \(-0.418941\pi\)
0.251912 + 0.967750i \(0.418941\pi\)
\(284\) 0 0
\(285\) −1.47545 −0.0873979
\(286\) 0 0
\(287\) 2.89454 0.170859
\(288\) 0 0
\(289\) 0.931210 0.0547770
\(290\) 0 0
\(291\) −2.87535 −0.168556
\(292\) 0 0
\(293\) −25.4167 −1.48486 −0.742431 0.669923i \(-0.766327\pi\)
−0.742431 + 0.669923i \(0.766327\pi\)
\(294\) 0 0
\(295\) −1.29005 −0.0751095
\(296\) 0 0
\(297\) −3.18144 −0.184606
\(298\) 0 0
\(299\) 0.382284 0.0221081
\(300\) 0 0
\(301\) −2.23750 −0.128968
\(302\) 0 0
\(303\) 13.7261 0.788545
\(304\) 0 0
\(305\) 0.630769 0.0361177
\(306\) 0 0
\(307\) 30.3855 1.73419 0.867097 0.498140i \(-0.165983\pi\)
0.867097 + 0.498140i \(0.165983\pi\)
\(308\) 0 0
\(309\) −12.0130 −0.683394
\(310\) 0 0
\(311\) −27.4460 −1.55632 −0.778159 0.628068i \(-0.783846\pi\)
−0.778159 + 0.628068i \(0.783846\pi\)
\(312\) 0 0
\(313\) 13.1030 0.740625 0.370312 0.928907i \(-0.379251\pi\)
0.370312 + 0.928907i \(0.379251\pi\)
\(314\) 0 0
\(315\) −0.110810 −0.00624346
\(316\) 0 0
\(317\) 28.8773 1.62191 0.810956 0.585107i \(-0.198948\pi\)
0.810956 + 0.585107i \(0.198948\pi\)
\(318\) 0 0
\(319\) −3.18144 −0.178126
\(320\) 0 0
\(321\) −0.954655 −0.0532836
\(322\) 0 0
\(323\) −23.0683 −1.28355
\(324\) 0 0
\(325\) −1.88338 −0.104471
\(326\) 0 0
\(327\) −9.85059 −0.544739
\(328\) 0 0
\(329\) −4.77548 −0.263281
\(330\) 0 0
\(331\) 9.77951 0.537531 0.268765 0.963206i \(-0.413384\pi\)
0.268765 + 0.963206i \(0.413384\pi\)
\(332\) 0 0
\(333\) −5.55848 −0.304603
\(334\) 0 0
\(335\) −0.152446 −0.00832903
\(336\) 0 0
\(337\) 32.0122 1.74382 0.871909 0.489668i \(-0.162882\pi\)
0.871909 + 0.489668i \(0.162882\pi\)
\(338\) 0 0
\(339\) 3.54743 0.192670
\(340\) 0 0
\(341\) −6.61939 −0.358460
\(342\) 0 0
\(343\) −5.65942 −0.305580
\(344\) 0 0
\(345\) −0.270840 −0.0145815
\(346\) 0 0
\(347\) −5.80201 −0.311468 −0.155734 0.987799i \(-0.549774\pi\)
−0.155734 + 0.987799i \(0.549774\pi\)
\(348\) 0 0
\(349\) −22.3183 −1.19467 −0.597334 0.801992i \(-0.703773\pi\)
−0.597334 + 0.801992i \(0.703773\pi\)
\(350\) 0 0
\(351\) 0.382284 0.0204048
\(352\) 0 0
\(353\) −7.93967 −0.422586 −0.211293 0.977423i \(-0.567767\pi\)
−0.211293 + 0.977423i \(0.567767\pi\)
\(354\) 0 0
\(355\) 1.90843 0.101289
\(356\) 0 0
\(357\) −1.73250 −0.0916935
\(358\) 0 0
\(359\) −4.91659 −0.259488 −0.129744 0.991548i \(-0.541416\pi\)
−0.129744 + 0.991548i \(0.541416\pi\)
\(360\) 0 0
\(361\) 10.6771 0.561953
\(362\) 0 0
\(363\) −0.878442 −0.0461063
\(364\) 0 0
\(365\) 2.96985 0.155449
\(366\) 0 0
\(367\) −6.68277 −0.348838 −0.174419 0.984672i \(-0.555805\pi\)
−0.174419 + 0.984672i \(0.555805\pi\)
\(368\) 0 0
\(369\) 7.07476 0.368297
\(370\) 0 0
\(371\) 5.36270 0.278417
\(372\) 0 0
\(373\) −12.5263 −0.648587 −0.324293 0.945957i \(-0.605126\pi\)
−0.324293 + 0.945957i \(0.605126\pi\)
\(374\) 0 0
\(375\) 2.68853 0.138835
\(376\) 0 0
\(377\) 0.382284 0.0196886
\(378\) 0 0
\(379\) 14.0180 0.720057 0.360028 0.932941i \(-0.382767\pi\)
0.360028 + 0.932941i \(0.382767\pi\)
\(380\) 0 0
\(381\) 2.20435 0.112933
\(382\) 0 0
\(383\) 24.8668 1.27063 0.635317 0.772252i \(-0.280870\pi\)
0.635317 + 0.772252i \(0.280870\pi\)
\(384\) 0 0
\(385\) 0.352537 0.0179669
\(386\) 0 0
\(387\) −5.46885 −0.277997
\(388\) 0 0
\(389\) −35.5368 −1.80179 −0.900895 0.434037i \(-0.857089\pi\)
−0.900895 + 0.434037i \(0.857089\pi\)
\(390\) 0 0
\(391\) −4.23453 −0.214149
\(392\) 0 0
\(393\) −11.6263 −0.586471
\(394\) 0 0
\(395\) 4.52291 0.227572
\(396\) 0 0
\(397\) 1.45246 0.0728967 0.0364484 0.999336i \(-0.488396\pi\)
0.0364484 + 0.999336i \(0.488396\pi\)
\(398\) 0 0
\(399\) 2.22884 0.111581
\(400\) 0 0
\(401\) −14.4573 −0.721964 −0.360982 0.932573i \(-0.617558\pi\)
−0.360982 + 0.932573i \(0.617558\pi\)
\(402\) 0 0
\(403\) 0.795391 0.0396212
\(404\) 0 0
\(405\) −0.270840 −0.0134581
\(406\) 0 0
\(407\) 17.6840 0.876562
\(408\) 0 0
\(409\) −4.78037 −0.236374 −0.118187 0.992991i \(-0.537708\pi\)
−0.118187 + 0.992991i \(0.537708\pi\)
\(410\) 0 0
\(411\) −8.00999 −0.395104
\(412\) 0 0
\(413\) 1.94877 0.0958928
\(414\) 0 0
\(415\) −2.55823 −0.125579
\(416\) 0 0
\(417\) −16.7849 −0.821960
\(418\) 0 0
\(419\) −38.0916 −1.86090 −0.930448 0.366424i \(-0.880582\pi\)
−0.930448 + 0.366424i \(0.880582\pi\)
\(420\) 0 0
\(421\) −24.7113 −1.20436 −0.602178 0.798362i \(-0.705700\pi\)
−0.602178 + 0.798362i \(0.705700\pi\)
\(422\) 0 0
\(423\) −11.6721 −0.567518
\(424\) 0 0
\(425\) 20.8620 1.01196
\(426\) 0 0
\(427\) −0.952852 −0.0461117
\(428\) 0 0
\(429\) −1.21621 −0.0587194
\(430\) 0 0
\(431\) −0.932560 −0.0449198 −0.0224599 0.999748i \(-0.507150\pi\)
−0.0224599 + 0.999748i \(0.507150\pi\)
\(432\) 0 0
\(433\) −10.5454 −0.506780 −0.253390 0.967364i \(-0.581546\pi\)
−0.253390 + 0.967364i \(0.581546\pi\)
\(434\) 0 0
\(435\) −0.270840 −0.0129858
\(436\) 0 0
\(437\) 5.44767 0.260597
\(438\) 0 0
\(439\) 27.6249 1.31847 0.659233 0.751938i \(-0.270881\pi\)
0.659233 + 0.751938i \(0.270881\pi\)
\(440\) 0 0
\(441\) −6.83261 −0.325362
\(442\) 0 0
\(443\) 29.2217 1.38837 0.694184 0.719798i \(-0.255766\pi\)
0.694184 + 0.719798i \(0.255766\pi\)
\(444\) 0 0
\(445\) −2.36796 −0.112252
\(446\) 0 0
\(447\) −16.5791 −0.784165
\(448\) 0 0
\(449\) −16.7444 −0.790215 −0.395108 0.918635i \(-0.629293\pi\)
−0.395108 + 0.918635i \(0.629293\pi\)
\(450\) 0 0
\(451\) −22.5079 −1.05986
\(452\) 0 0
\(453\) 11.8936 0.558811
\(454\) 0 0
\(455\) −0.0423611 −0.00198592
\(456\) 0 0
\(457\) 4.05973 0.189906 0.0949530 0.995482i \(-0.469730\pi\)
0.0949530 + 0.995482i \(0.469730\pi\)
\(458\) 0 0
\(459\) −4.23453 −0.197651
\(460\) 0 0
\(461\) −32.7229 −1.52406 −0.762028 0.647544i \(-0.775796\pi\)
−0.762028 + 0.647544i \(0.775796\pi\)
\(462\) 0 0
\(463\) −7.16747 −0.333101 −0.166550 0.986033i \(-0.553263\pi\)
−0.166550 + 0.986033i \(0.553263\pi\)
\(464\) 0 0
\(465\) −0.563517 −0.0261325
\(466\) 0 0
\(467\) 15.7373 0.728234 0.364117 0.931353i \(-0.381371\pi\)
0.364117 + 0.931353i \(0.381371\pi\)
\(468\) 0 0
\(469\) 0.230288 0.0106337
\(470\) 0 0
\(471\) 8.71347 0.401496
\(472\) 0 0
\(473\) 17.3988 0.799998
\(474\) 0 0
\(475\) −26.8387 −1.23145
\(476\) 0 0
\(477\) 13.1074 0.600145
\(478\) 0 0
\(479\) −11.3495 −0.518573 −0.259286 0.965800i \(-0.583487\pi\)
−0.259286 + 0.965800i \(0.583487\pi\)
\(480\) 0 0
\(481\) −2.12492 −0.0968880
\(482\) 0 0
\(483\) 0.409136 0.0186163
\(484\) 0 0
\(485\) 0.778760 0.0353617
\(486\) 0 0
\(487\) 2.67846 0.121373 0.0606863 0.998157i \(-0.480671\pi\)
0.0606863 + 0.998157i \(0.480671\pi\)
\(488\) 0 0
\(489\) 15.7742 0.713335
\(490\) 0 0
\(491\) 30.9044 1.39470 0.697349 0.716732i \(-0.254363\pi\)
0.697349 + 0.716732i \(0.254363\pi\)
\(492\) 0 0
\(493\) −4.23453 −0.190713
\(494\) 0 0
\(495\) 0.861661 0.0387288
\(496\) 0 0
\(497\) −2.88291 −0.129316
\(498\) 0 0
\(499\) −23.6171 −1.05725 −0.528623 0.848857i \(-0.677291\pi\)
−0.528623 + 0.848857i \(0.677291\pi\)
\(500\) 0 0
\(501\) −19.0619 −0.851621
\(502\) 0 0
\(503\) 38.8329 1.73147 0.865736 0.500501i \(-0.166851\pi\)
0.865736 + 0.500501i \(0.166851\pi\)
\(504\) 0 0
\(505\) −3.71758 −0.165430
\(506\) 0 0
\(507\) −12.8539 −0.570860
\(508\) 0 0
\(509\) −13.6346 −0.604342 −0.302171 0.953254i \(-0.597711\pi\)
−0.302171 + 0.953254i \(0.597711\pi\)
\(510\) 0 0
\(511\) −4.48632 −0.198463
\(512\) 0 0
\(513\) 5.44767 0.240520
\(514\) 0 0
\(515\) 3.25359 0.143370
\(516\) 0 0
\(517\) 37.1341 1.63316
\(518\) 0 0
\(519\) 2.35020 0.103162
\(520\) 0 0
\(521\) 5.43489 0.238107 0.119053 0.992888i \(-0.462014\pi\)
0.119053 + 0.992888i \(0.462014\pi\)
\(522\) 0 0
\(523\) 23.5508 1.02980 0.514902 0.857249i \(-0.327828\pi\)
0.514902 + 0.857249i \(0.327828\pi\)
\(524\) 0 0
\(525\) −2.01567 −0.0879710
\(526\) 0 0
\(527\) −8.81046 −0.383790
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 4.76314 0.206703
\(532\) 0 0
\(533\) 2.70457 0.117148
\(534\) 0 0
\(535\) 0.258559 0.0111785
\(536\) 0 0
\(537\) −6.80243 −0.293546
\(538\) 0 0
\(539\) 21.7375 0.936302
\(540\) 0 0
\(541\) 18.7530 0.806254 0.403127 0.915144i \(-0.367923\pi\)
0.403127 + 0.915144i \(0.367923\pi\)
\(542\) 0 0
\(543\) −8.35756 −0.358657
\(544\) 0 0
\(545\) 2.66793 0.114282
\(546\) 0 0
\(547\) −16.6602 −0.712338 −0.356169 0.934421i \(-0.615917\pi\)
−0.356169 + 0.934421i \(0.615917\pi\)
\(548\) 0 0
\(549\) −2.32894 −0.0993966
\(550\) 0 0
\(551\) 5.44767 0.232079
\(552\) 0 0
\(553\) −6.83239 −0.290543
\(554\) 0 0
\(555\) 1.50546 0.0639032
\(556\) 0 0
\(557\) 9.73836 0.412627 0.206314 0.978486i \(-0.433853\pi\)
0.206314 + 0.978486i \(0.433853\pi\)
\(558\) 0 0
\(559\) −2.09066 −0.0884253
\(560\) 0 0
\(561\) 13.4719 0.568784
\(562\) 0 0
\(563\) −9.64200 −0.406362 −0.203181 0.979141i \(-0.565128\pi\)
−0.203181 + 0.979141i \(0.565128\pi\)
\(564\) 0 0
\(565\) −0.960786 −0.0404206
\(566\) 0 0
\(567\) 0.409136 0.0171821
\(568\) 0 0
\(569\) 19.0987 0.800659 0.400329 0.916371i \(-0.368896\pi\)
0.400329 + 0.916371i \(0.368896\pi\)
\(570\) 0 0
\(571\) −11.8736 −0.496896 −0.248448 0.968645i \(-0.579920\pi\)
−0.248448 + 0.968645i \(0.579920\pi\)
\(572\) 0 0
\(573\) 16.5128 0.689833
\(574\) 0 0
\(575\) −4.92665 −0.205455
\(576\) 0 0
\(577\) −11.2776 −0.469493 −0.234746 0.972057i \(-0.575426\pi\)
−0.234746 + 0.972057i \(0.575426\pi\)
\(578\) 0 0
\(579\) −20.6858 −0.859674
\(580\) 0 0
\(581\) 3.86452 0.160327
\(582\) 0 0
\(583\) −41.7003 −1.72705
\(584\) 0 0
\(585\) −0.103538 −0.00428076
\(586\) 0 0
\(587\) −0.805937 −0.0332646 −0.0166323 0.999862i \(-0.505294\pi\)
−0.0166323 + 0.999862i \(0.505294\pi\)
\(588\) 0 0
\(589\) 11.3346 0.467032
\(590\) 0 0
\(591\) 6.56222 0.269934
\(592\) 0 0
\(593\) −4.45928 −0.183121 −0.0915603 0.995800i \(-0.529185\pi\)
−0.0915603 + 0.995800i \(0.529185\pi\)
\(594\) 0 0
\(595\) 0.469230 0.0192365
\(596\) 0 0
\(597\) 0.673220 0.0275530
\(598\) 0 0
\(599\) −13.7095 −0.560155 −0.280078 0.959977i \(-0.590360\pi\)
−0.280078 + 0.959977i \(0.590360\pi\)
\(600\) 0 0
\(601\) −2.45512 −0.100146 −0.0500731 0.998746i \(-0.515945\pi\)
−0.0500731 + 0.998746i \(0.515945\pi\)
\(602\) 0 0
\(603\) 0.562865 0.0229216
\(604\) 0 0
\(605\) 0.237917 0.00967271
\(606\) 0 0
\(607\) 2.83771 0.115179 0.0575895 0.998340i \(-0.481659\pi\)
0.0575895 + 0.998340i \(0.481659\pi\)
\(608\) 0 0
\(609\) 0.409136 0.0165790
\(610\) 0 0
\(611\) −4.46207 −0.180516
\(612\) 0 0
\(613\) 30.1424 1.21744 0.608720 0.793385i \(-0.291683\pi\)
0.608720 + 0.793385i \(0.291683\pi\)
\(614\) 0 0
\(615\) −1.91613 −0.0772657
\(616\) 0 0
\(617\) 20.1814 0.812474 0.406237 0.913768i \(-0.366841\pi\)
0.406237 + 0.913768i \(0.366841\pi\)
\(618\) 0 0
\(619\) −34.0792 −1.36976 −0.684880 0.728656i \(-0.740145\pi\)
−0.684880 + 0.728656i \(0.740145\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 3.57709 0.143313
\(624\) 0 0
\(625\) 23.9051 0.956203
\(626\) 0 0
\(627\) −17.3314 −0.692151
\(628\) 0 0
\(629\) 23.5375 0.938503
\(630\) 0 0
\(631\) −0.593809 −0.0236392 −0.0118196 0.999930i \(-0.503762\pi\)
−0.0118196 + 0.999930i \(0.503762\pi\)
\(632\) 0 0
\(633\) −24.8206 −0.986528
\(634\) 0 0
\(635\) −0.597028 −0.0236923
\(636\) 0 0
\(637\) −2.61200 −0.103491
\(638\) 0 0
\(639\) −7.04632 −0.278748
\(640\) 0 0
\(641\) 14.9940 0.592225 0.296113 0.955153i \(-0.404310\pi\)
0.296113 + 0.955153i \(0.404310\pi\)
\(642\) 0 0
\(643\) −47.2413 −1.86302 −0.931508 0.363720i \(-0.881506\pi\)
−0.931508 + 0.363720i \(0.881506\pi\)
\(644\) 0 0
\(645\) 1.48118 0.0583215
\(646\) 0 0
\(647\) −5.46767 −0.214956 −0.107478 0.994207i \(-0.534278\pi\)
−0.107478 + 0.994207i \(0.534278\pi\)
\(648\) 0 0
\(649\) −15.1536 −0.594832
\(650\) 0 0
\(651\) 0.851259 0.0333635
\(652\) 0 0
\(653\) −24.7535 −0.968679 −0.484339 0.874880i \(-0.660940\pi\)
−0.484339 + 0.874880i \(0.660940\pi\)
\(654\) 0 0
\(655\) 3.14888 0.123037
\(656\) 0 0
\(657\) −10.9653 −0.427799
\(658\) 0 0
\(659\) −18.2057 −0.709192 −0.354596 0.935020i \(-0.615382\pi\)
−0.354596 + 0.935020i \(0.615382\pi\)
\(660\) 0 0
\(661\) 46.9906 1.82772 0.913861 0.406028i \(-0.133087\pi\)
0.913861 + 0.406028i \(0.133087\pi\)
\(662\) 0 0
\(663\) −1.61879 −0.0628687
\(664\) 0 0
\(665\) −0.603659 −0.0234089
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) −27.7648 −1.07345
\(670\) 0 0
\(671\) 7.40937 0.286036
\(672\) 0 0
\(673\) −34.6358 −1.33511 −0.667556 0.744559i \(-0.732660\pi\)
−0.667556 + 0.744559i \(0.732660\pi\)
\(674\) 0 0
\(675\) −4.92665 −0.189627
\(676\) 0 0
\(677\) −24.6121 −0.945920 −0.472960 0.881084i \(-0.656815\pi\)
−0.472960 + 0.881084i \(0.656815\pi\)
\(678\) 0 0
\(679\) −1.17641 −0.0451465
\(680\) 0 0
\(681\) −12.5430 −0.480650
\(682\) 0 0
\(683\) −28.3828 −1.08604 −0.543019 0.839720i \(-0.682719\pi\)
−0.543019 + 0.839720i \(0.682719\pi\)
\(684\) 0 0
\(685\) 2.16943 0.0828895
\(686\) 0 0
\(687\) −12.0808 −0.460911
\(688\) 0 0
\(689\) 5.01074 0.190894
\(690\) 0 0
\(691\) 8.08477 0.307559 0.153780 0.988105i \(-0.450855\pi\)
0.153780 + 0.988105i \(0.450855\pi\)
\(692\) 0 0
\(693\) −1.30164 −0.0494453
\(694\) 0 0
\(695\) 4.54602 0.172440
\(696\) 0 0
\(697\) −29.9583 −1.13475
\(698\) 0 0
\(699\) 7.64163 0.289033
\(700\) 0 0
\(701\) −18.1267 −0.684637 −0.342318 0.939584i \(-0.611212\pi\)
−0.342318 + 0.939584i \(0.611212\pi\)
\(702\) 0 0
\(703\) −30.2808 −1.14206
\(704\) 0 0
\(705\) 3.16128 0.119061
\(706\) 0 0
\(707\) 5.61585 0.211206
\(708\) 0 0
\(709\) −14.4856 −0.544018 −0.272009 0.962295i \(-0.587688\pi\)
−0.272009 + 0.962295i \(0.587688\pi\)
\(710\) 0 0
\(711\) −16.6996 −0.626282
\(712\) 0 0
\(713\) 2.08063 0.0779200
\(714\) 0 0
\(715\) 0.329400 0.0123188
\(716\) 0 0
\(717\) 10.0402 0.374957
\(718\) 0 0
\(719\) 19.6488 0.732778 0.366389 0.930462i \(-0.380594\pi\)
0.366389 + 0.930462i \(0.380594\pi\)
\(720\) 0 0
\(721\) −4.91494 −0.183042
\(722\) 0 0
\(723\) 2.88233 0.107195
\(724\) 0 0
\(725\) −4.92665 −0.182971
\(726\) 0 0
\(727\) −14.6587 −0.543659 −0.271830 0.962345i \(-0.587629\pi\)
−0.271830 + 0.962345i \(0.587629\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 23.1580 0.856529
\(732\) 0 0
\(733\) −14.9313 −0.551499 −0.275749 0.961230i \(-0.588926\pi\)
−0.275749 + 0.961230i \(0.588926\pi\)
\(734\) 0 0
\(735\) 1.85054 0.0682583
\(736\) 0 0
\(737\) −1.79072 −0.0659620
\(738\) 0 0
\(739\) −17.8041 −0.654935 −0.327468 0.944862i \(-0.606195\pi\)
−0.327468 + 0.944862i \(0.606195\pi\)
\(740\) 0 0
\(741\) 2.08256 0.0765047
\(742\) 0 0
\(743\) 28.7026 1.05300 0.526498 0.850177i \(-0.323505\pi\)
0.526498 + 0.850177i \(0.323505\pi\)
\(744\) 0 0
\(745\) 4.49029 0.164511
\(746\) 0 0
\(747\) 9.44555 0.345595
\(748\) 0 0
\(749\) −0.390584 −0.0142716
\(750\) 0 0
\(751\) 43.6902 1.59428 0.797139 0.603796i \(-0.206346\pi\)
0.797139 + 0.603796i \(0.206346\pi\)
\(752\) 0 0
\(753\) 17.4367 0.635429
\(754\) 0 0
\(755\) −3.22127 −0.117234
\(756\) 0 0
\(757\) 4.34039 0.157754 0.0788771 0.996884i \(-0.474867\pi\)
0.0788771 + 0.996884i \(0.474867\pi\)
\(758\) 0 0
\(759\) −3.18144 −0.115479
\(760\) 0 0
\(761\) −23.0433 −0.835319 −0.417660 0.908604i \(-0.637150\pi\)
−0.417660 + 0.908604i \(0.637150\pi\)
\(762\) 0 0
\(763\) −4.03023 −0.145904
\(764\) 0 0
\(765\) 1.14688 0.0414655
\(766\) 0 0
\(767\) 1.82087 0.0657479
\(768\) 0 0
\(769\) 17.2849 0.623310 0.311655 0.950195i \(-0.399117\pi\)
0.311655 + 0.950195i \(0.399117\pi\)
\(770\) 0 0
\(771\) −23.8712 −0.859700
\(772\) 0 0
\(773\) 49.4741 1.77946 0.889729 0.456489i \(-0.150893\pi\)
0.889729 + 0.456489i \(0.150893\pi\)
\(774\) 0 0
\(775\) −10.2505 −0.368209
\(776\) 0 0
\(777\) −2.27418 −0.0815856
\(778\) 0 0
\(779\) 38.5410 1.38087
\(780\) 0 0
\(781\) 22.4174 0.802159
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −2.35996 −0.0842305
\(786\) 0 0
\(787\) 22.9575 0.818345 0.409173 0.912457i \(-0.365817\pi\)
0.409173 + 0.912457i \(0.365817\pi\)
\(788\) 0 0
\(789\) 13.4132 0.477521
\(790\) 0 0
\(791\) 1.45138 0.0516052
\(792\) 0 0
\(793\) −0.890316 −0.0316160
\(794\) 0 0
\(795\) −3.55000 −0.125905
\(796\) 0 0
\(797\) 47.6929 1.68937 0.844684 0.535265i \(-0.179788\pi\)
0.844684 + 0.535265i \(0.179788\pi\)
\(798\) 0 0
\(799\) 49.4259 1.74856
\(800\) 0 0
\(801\) 8.74304 0.308920
\(802\) 0 0
\(803\) 34.8856 1.23108
\(804\) 0 0
\(805\) −0.110810 −0.00390556
\(806\) 0 0
\(807\) −1.27424 −0.0448552
\(808\) 0 0
\(809\) −11.4679 −0.403191 −0.201596 0.979469i \(-0.564613\pi\)
−0.201596 + 0.979469i \(0.564613\pi\)
\(810\) 0 0
\(811\) −19.4479 −0.682909 −0.341454 0.939898i \(-0.610919\pi\)
−0.341454 + 0.939898i \(0.610919\pi\)
\(812\) 0 0
\(813\) 8.32920 0.292118
\(814\) 0 0
\(815\) −4.27229 −0.149652
\(816\) 0 0
\(817\) −29.7925 −1.04231
\(818\) 0 0
\(819\) 0.156406 0.00546528
\(820\) 0 0
\(821\) 54.2605 1.89370 0.946852 0.321670i \(-0.104244\pi\)
0.946852 + 0.321670i \(0.104244\pi\)
\(822\) 0 0
\(823\) 12.7804 0.445496 0.222748 0.974876i \(-0.428497\pi\)
0.222748 + 0.974876i \(0.428497\pi\)
\(824\) 0 0
\(825\) 15.6738 0.545693
\(826\) 0 0
\(827\) −9.84339 −0.342288 −0.171144 0.985246i \(-0.554746\pi\)
−0.171144 + 0.985246i \(0.554746\pi\)
\(828\) 0 0
\(829\) −22.9313 −0.796437 −0.398219 0.917291i \(-0.630371\pi\)
−0.398219 + 0.917291i \(0.630371\pi\)
\(830\) 0 0
\(831\) 12.4631 0.432339
\(832\) 0 0
\(833\) 28.9329 1.00246
\(834\) 0 0
\(835\) 5.16271 0.178663
\(836\) 0 0
\(837\) 2.08063 0.0719169
\(838\) 0 0
\(839\) −12.2808 −0.423980 −0.211990 0.977272i \(-0.567994\pi\)
−0.211990 + 0.977272i \(0.567994\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 4.79090 0.165007
\(844\) 0 0
\(845\) 3.48134 0.119762
\(846\) 0 0
\(847\) −0.359403 −0.0123492
\(848\) 0 0
\(849\) 8.47563 0.290883
\(850\) 0 0
\(851\) −5.55848 −0.190542
\(852\) 0 0
\(853\) 20.4262 0.699380 0.349690 0.936865i \(-0.386287\pi\)
0.349690 + 0.936865i \(0.386287\pi\)
\(854\) 0 0
\(855\) −1.47545 −0.0504592
\(856\) 0 0
\(857\) 50.6690 1.73082 0.865410 0.501065i \(-0.167058\pi\)
0.865410 + 0.501065i \(0.167058\pi\)
\(858\) 0 0
\(859\) 20.0628 0.684532 0.342266 0.939603i \(-0.388806\pi\)
0.342266 + 0.939603i \(0.388806\pi\)
\(860\) 0 0
\(861\) 2.89454 0.0986457
\(862\) 0 0
\(863\) −18.6708 −0.635561 −0.317780 0.948164i \(-0.602938\pi\)
−0.317780 + 0.948164i \(0.602938\pi\)
\(864\) 0 0
\(865\) −0.636527 −0.0216426
\(866\) 0 0
\(867\) 0.931210 0.0316255
\(868\) 0 0
\(869\) 53.1286 1.80227
\(870\) 0 0
\(871\) 0.215174 0.00729090
\(872\) 0 0
\(873\) −2.87535 −0.0973159
\(874\) 0 0
\(875\) 1.09998 0.0371860
\(876\) 0 0
\(877\) −41.1010 −1.38788 −0.693941 0.720032i \(-0.744127\pi\)
−0.693941 + 0.720032i \(0.744127\pi\)
\(878\) 0 0
\(879\) −25.4167 −0.857285
\(880\) 0 0
\(881\) −19.2512 −0.648590 −0.324295 0.945956i \(-0.605127\pi\)
−0.324295 + 0.945956i \(0.605127\pi\)
\(882\) 0 0
\(883\) 33.2113 1.11765 0.558825 0.829286i \(-0.311252\pi\)
0.558825 + 0.829286i \(0.311252\pi\)
\(884\) 0 0
\(885\) −1.29005 −0.0433645
\(886\) 0 0
\(887\) −21.2053 −0.712005 −0.356002 0.934485i \(-0.615860\pi\)
−0.356002 + 0.934485i \(0.615860\pi\)
\(888\) 0 0
\(889\) 0.901881 0.0302481
\(890\) 0 0
\(891\) −3.18144 −0.106582
\(892\) 0 0
\(893\) −63.5858 −2.12782
\(894\) 0 0
\(895\) 1.84237 0.0615836
\(896\) 0 0
\(897\) 0.382284 0.0127641
\(898\) 0 0
\(899\) 2.08063 0.0693928
\(900\) 0 0
\(901\) −55.5035 −1.84909
\(902\) 0 0
\(903\) −2.23750 −0.0744595
\(904\) 0 0
\(905\) 2.26356 0.0752433
\(906\) 0 0
\(907\) −12.8168 −0.425575 −0.212788 0.977098i \(-0.568254\pi\)
−0.212788 + 0.977098i \(0.568254\pi\)
\(908\) 0 0
\(909\) 13.7261 0.455266
\(910\) 0 0
\(911\) 16.5644 0.548802 0.274401 0.961615i \(-0.411520\pi\)
0.274401 + 0.961615i \(0.411520\pi\)
\(912\) 0 0
\(913\) −30.0504 −0.994525
\(914\) 0 0
\(915\) 0.630769 0.0208526
\(916\) 0 0
\(917\) −4.75676 −0.157082
\(918\) 0 0
\(919\) 18.7651 0.619005 0.309503 0.950899i \(-0.399837\pi\)
0.309503 + 0.950899i \(0.399837\pi\)
\(920\) 0 0
\(921\) 30.3855 1.00124
\(922\) 0 0
\(923\) −2.69370 −0.0886642
\(924\) 0 0
\(925\) 27.3847 0.900402
\(926\) 0 0
\(927\) −12.0130 −0.394558
\(928\) 0 0
\(929\) −18.0666 −0.592747 −0.296373 0.955072i \(-0.595777\pi\)
−0.296373 + 0.955072i \(0.595777\pi\)
\(930\) 0 0
\(931\) −37.2218 −1.21989
\(932\) 0 0
\(933\) −27.4460 −0.898540
\(934\) 0 0
\(935\) −3.64873 −0.119326
\(936\) 0 0
\(937\) 58.5144 1.91158 0.955792 0.294044i \(-0.0950012\pi\)
0.955792 + 0.294044i \(0.0950012\pi\)
\(938\) 0 0
\(939\) 13.1030 0.427600
\(940\) 0 0
\(941\) −46.9778 −1.53143 −0.765716 0.643178i \(-0.777615\pi\)
−0.765716 + 0.643178i \(0.777615\pi\)
\(942\) 0 0
\(943\) 7.07476 0.230386
\(944\) 0 0
\(945\) −0.110810 −0.00360466
\(946\) 0 0
\(947\) 16.2887 0.529310 0.264655 0.964343i \(-0.414742\pi\)
0.264655 + 0.964343i \(0.414742\pi\)
\(948\) 0 0
\(949\) −4.19188 −0.136074
\(950\) 0 0
\(951\) 28.8773 0.936411
\(952\) 0 0
\(953\) −48.2390 −1.56261 −0.781307 0.624147i \(-0.785447\pi\)
−0.781307 + 0.624147i \(0.785447\pi\)
\(954\) 0 0
\(955\) −4.47233 −0.144721
\(956\) 0 0
\(957\) −3.18144 −0.102841
\(958\) 0 0
\(959\) −3.27718 −0.105826
\(960\) 0 0
\(961\) −26.6710 −0.860355
\(962\) 0 0
\(963\) −0.954655 −0.0307633
\(964\) 0 0
\(965\) 5.60255 0.180352
\(966\) 0 0
\(967\) −13.1024 −0.421345 −0.210672 0.977557i \(-0.567565\pi\)
−0.210672 + 0.977557i \(0.567565\pi\)
\(968\) 0 0
\(969\) −23.0683 −0.741060
\(970\) 0 0
\(971\) 18.6526 0.598592 0.299296 0.954160i \(-0.403248\pi\)
0.299296 + 0.954160i \(0.403248\pi\)
\(972\) 0 0
\(973\) −6.86731 −0.220156
\(974\) 0 0
\(975\) −1.88338 −0.0603164
\(976\) 0 0
\(977\) 25.1509 0.804649 0.402325 0.915497i \(-0.368202\pi\)
0.402325 + 0.915497i \(0.368202\pi\)
\(978\) 0 0
\(979\) −27.8154 −0.888985
\(980\) 0 0
\(981\) −9.85059 −0.314505
\(982\) 0 0
\(983\) 10.4413 0.333025 0.166512 0.986039i \(-0.446749\pi\)
0.166512 + 0.986039i \(0.446749\pi\)
\(984\) 0 0
\(985\) −1.77731 −0.0566299
\(986\) 0 0
\(987\) −4.77548 −0.152005
\(988\) 0 0
\(989\) −5.46885 −0.173899
\(990\) 0 0
\(991\) 46.4100 1.47426 0.737131 0.675750i \(-0.236180\pi\)
0.737131 + 0.675750i \(0.236180\pi\)
\(992\) 0 0
\(993\) 9.77951 0.310343
\(994\) 0 0
\(995\) −0.182335 −0.00578040
\(996\) 0 0
\(997\) −39.3398 −1.24590 −0.622951 0.782261i \(-0.714067\pi\)
−0.622951 + 0.782261i \(0.714067\pi\)
\(998\) 0 0
\(999\) −5.55848 −0.175863
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 \(a_p\))