Properties

Label 4004.2.a.j.1.7
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.497051\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.497051 q^{3} -2.93955 q^{5} -1.00000 q^{7} -2.75294 q^{9} +O(q^{10})\) \(q+0.497051 q^{3} -2.93955 q^{5} -1.00000 q^{7} -2.75294 q^{9} -1.00000 q^{11} -1.00000 q^{13} -1.46111 q^{15} +6.64567 q^{17} -8.43503 q^{19} -0.497051 q^{21} -7.56554 q^{23} +3.64094 q^{25} -2.85951 q^{27} -0.0222906 q^{29} +1.14381 q^{31} -0.497051 q^{33} +2.93955 q^{35} -0.840405 q^{37} -0.497051 q^{39} +4.48124 q^{41} +1.41468 q^{43} +8.09240 q^{45} +6.97254 q^{47} +1.00000 q^{49} +3.30324 q^{51} +11.8143 q^{53} +2.93955 q^{55} -4.19264 q^{57} -0.878482 q^{59} +1.01213 q^{61} +2.75294 q^{63} +2.93955 q^{65} +8.34149 q^{67} -3.76046 q^{69} -13.3351 q^{71} -8.97242 q^{73} +1.80973 q^{75} +1.00000 q^{77} -12.6865 q^{79} +6.83750 q^{81} +2.63360 q^{83} -19.5353 q^{85} -0.0110796 q^{87} -14.9420 q^{89} +1.00000 q^{91} +0.568531 q^{93} +24.7952 q^{95} +19.2853 q^{97} +2.75294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 0.497051 0.286973 0.143486 0.989652i \(-0.454169\pi\)
0.143486 + 0.989652i \(0.454169\pi\)
\(4\) 0 0
\(5\) −2.93955 −1.31461 −0.657303 0.753626i \(-0.728303\pi\)
−0.657303 + 0.753626i \(0.728303\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.75294 −0.917647
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.46111 −0.377256
\(16\) 0 0
\(17\) 6.64567 1.61181 0.805905 0.592044i \(-0.201679\pi\)
0.805905 + 0.592044i \(0.201679\pi\)
\(18\) 0 0
\(19\) −8.43503 −1.93513 −0.967564 0.252625i \(-0.918706\pi\)
−0.967564 + 0.252625i \(0.918706\pi\)
\(20\) 0 0
\(21\) −0.497051 −0.108465
\(22\) 0 0
\(23\) −7.56554 −1.57752 −0.788762 0.614699i \(-0.789278\pi\)
−0.788762 + 0.614699i \(0.789278\pi\)
\(24\) 0 0
\(25\) 3.64094 0.728189
\(26\) 0 0
\(27\) −2.85951 −0.550312
\(28\) 0 0
\(29\) −0.0222906 −0.00413926 −0.00206963 0.999998i \(-0.500659\pi\)
−0.00206963 + 0.999998i \(0.500659\pi\)
\(30\) 0 0
\(31\) 1.14381 0.205434 0.102717 0.994711i \(-0.467246\pi\)
0.102717 + 0.994711i \(0.467246\pi\)
\(32\) 0 0
\(33\) −0.497051 −0.0865255
\(34\) 0 0
\(35\) 2.93955 0.496874
\(36\) 0 0
\(37\) −0.840405 −0.138162 −0.0690809 0.997611i \(-0.522007\pi\)
−0.0690809 + 0.997611i \(0.522007\pi\)
\(38\) 0 0
\(39\) −0.497051 −0.0795919
\(40\) 0 0
\(41\) 4.48124 0.699852 0.349926 0.936777i \(-0.386207\pi\)
0.349926 + 0.936777i \(0.386207\pi\)
\(42\) 0 0
\(43\) 1.41468 0.215737 0.107869 0.994165i \(-0.465597\pi\)
0.107869 + 0.994165i \(0.465597\pi\)
\(44\) 0 0
\(45\) 8.09240 1.20634
\(46\) 0 0
\(47\) 6.97254 1.01705 0.508524 0.861048i \(-0.330191\pi\)
0.508524 + 0.861048i \(0.330191\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 3.30324 0.462546
\(52\) 0 0
\(53\) 11.8143 1.62282 0.811412 0.584475i \(-0.198700\pi\)
0.811412 + 0.584475i \(0.198700\pi\)
\(54\) 0 0
\(55\) 2.93955 0.396369
\(56\) 0 0
\(57\) −4.19264 −0.555329
\(58\) 0 0
\(59\) −0.878482 −0.114369 −0.0571843 0.998364i \(-0.518212\pi\)
−0.0571843 + 0.998364i \(0.518212\pi\)
\(60\) 0 0
\(61\) 1.01213 0.129590 0.0647950 0.997899i \(-0.479361\pi\)
0.0647950 + 0.997899i \(0.479361\pi\)
\(62\) 0 0
\(63\) 2.75294 0.346838
\(64\) 0 0
\(65\) 2.93955 0.364606
\(66\) 0 0
\(67\) 8.34149 1.01907 0.509537 0.860449i \(-0.329817\pi\)
0.509537 + 0.860449i \(0.329817\pi\)
\(68\) 0 0
\(69\) −3.76046 −0.452706
\(70\) 0 0
\(71\) −13.3351 −1.58258 −0.791292 0.611439i \(-0.790591\pi\)
−0.791292 + 0.611439i \(0.790591\pi\)
\(72\) 0 0
\(73\) −8.97242 −1.05014 −0.525071 0.851058i \(-0.675961\pi\)
−0.525071 + 0.851058i \(0.675961\pi\)
\(74\) 0 0
\(75\) 1.80973 0.208970
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −12.6865 −1.42735 −0.713674 0.700478i \(-0.752970\pi\)
−0.713674 + 0.700478i \(0.752970\pi\)
\(80\) 0 0
\(81\) 6.83750 0.759722
\(82\) 0 0
\(83\) 2.63360 0.289076 0.144538 0.989499i \(-0.453830\pi\)
0.144538 + 0.989499i \(0.453830\pi\)
\(84\) 0 0
\(85\) −19.5353 −2.11890
\(86\) 0 0
\(87\) −0.0110796 −0.00118786
\(88\) 0 0
\(89\) −14.9420 −1.58385 −0.791923 0.610621i \(-0.790920\pi\)
−0.791923 + 0.610621i \(0.790920\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0.568531 0.0589539
\(94\) 0 0
\(95\) 24.7952 2.54393
\(96\) 0 0
\(97\) 19.2853 1.95813 0.979064 0.203551i \(-0.0652483\pi\)
0.979064 + 0.203551i \(0.0652483\pi\)
\(98\) 0 0
\(99\) 2.75294 0.276681
\(100\) 0 0
\(101\) −3.05893 −0.304375 −0.152188 0.988352i \(-0.548632\pi\)
−0.152188 + 0.988352i \(0.548632\pi\)
\(102\) 0 0
\(103\) 2.52685 0.248978 0.124489 0.992221i \(-0.460271\pi\)
0.124489 + 0.992221i \(0.460271\pi\)
\(104\) 0 0
\(105\) 1.46111 0.142589
\(106\) 0 0
\(107\) 16.4039 1.58583 0.792913 0.609335i \(-0.208564\pi\)
0.792913 + 0.609335i \(0.208564\pi\)
\(108\) 0 0
\(109\) 15.6346 1.49752 0.748762 0.662839i \(-0.230649\pi\)
0.748762 + 0.662839i \(0.230649\pi\)
\(110\) 0 0
\(111\) −0.417724 −0.0396486
\(112\) 0 0
\(113\) 5.09219 0.479033 0.239516 0.970892i \(-0.423011\pi\)
0.239516 + 0.970892i \(0.423011\pi\)
\(114\) 0 0
\(115\) 22.2393 2.07382
\(116\) 0 0
\(117\) 2.75294 0.254509
\(118\) 0 0
\(119\) −6.64567 −0.609207
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 2.22740 0.200838
\(124\) 0 0
\(125\) 3.99501 0.357325
\(126\) 0 0
\(127\) 7.32853 0.650302 0.325151 0.945662i \(-0.394585\pi\)
0.325151 + 0.945662i \(0.394585\pi\)
\(128\) 0 0
\(129\) 0.703170 0.0619106
\(130\) 0 0
\(131\) 0.588280 0.0513983 0.0256991 0.999670i \(-0.491819\pi\)
0.0256991 + 0.999670i \(0.491819\pi\)
\(132\) 0 0
\(133\) 8.43503 0.731410
\(134\) 0 0
\(135\) 8.40565 0.723443
\(136\) 0 0
\(137\) −18.3928 −1.57141 −0.785703 0.618604i \(-0.787698\pi\)
−0.785703 + 0.618604i \(0.787698\pi\)
\(138\) 0 0
\(139\) 2.14980 0.182344 0.0911719 0.995835i \(-0.470939\pi\)
0.0911719 + 0.995835i \(0.470939\pi\)
\(140\) 0 0
\(141\) 3.46571 0.291865
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 0.0655243 0.00544150
\(146\) 0 0
\(147\) 0.497051 0.0409961
\(148\) 0 0
\(149\) −6.33684 −0.519134 −0.259567 0.965725i \(-0.583580\pi\)
−0.259567 + 0.965725i \(0.583580\pi\)
\(150\) 0 0
\(151\) 7.78880 0.633844 0.316922 0.948452i \(-0.397351\pi\)
0.316922 + 0.948452i \(0.397351\pi\)
\(152\) 0 0
\(153\) −18.2951 −1.47907
\(154\) 0 0
\(155\) −3.36228 −0.270065
\(156\) 0 0
\(157\) 9.41916 0.751731 0.375865 0.926674i \(-0.377346\pi\)
0.375865 + 0.926674i \(0.377346\pi\)
\(158\) 0 0
\(159\) 5.87233 0.465706
\(160\) 0 0
\(161\) 7.56554 0.596248
\(162\) 0 0
\(163\) 22.0204 1.72477 0.862386 0.506251i \(-0.168969\pi\)
0.862386 + 0.506251i \(0.168969\pi\)
\(164\) 0 0
\(165\) 1.46111 0.113747
\(166\) 0 0
\(167\) −19.5196 −1.51047 −0.755236 0.655453i \(-0.772478\pi\)
−0.755236 + 0.655453i \(0.772478\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 23.2211 1.77576
\(172\) 0 0
\(173\) −6.93854 −0.527527 −0.263764 0.964587i \(-0.584964\pi\)
−0.263764 + 0.964587i \(0.584964\pi\)
\(174\) 0 0
\(175\) −3.64094 −0.275229
\(176\) 0 0
\(177\) −0.436651 −0.0328207
\(178\) 0 0
\(179\) 6.01410 0.449515 0.224757 0.974415i \(-0.427841\pi\)
0.224757 + 0.974415i \(0.427841\pi\)
\(180\) 0 0
\(181\) 10.4942 0.780029 0.390014 0.920809i \(-0.372470\pi\)
0.390014 + 0.920809i \(0.372470\pi\)
\(182\) 0 0
\(183\) 0.503081 0.0371888
\(184\) 0 0
\(185\) 2.47041 0.181628
\(186\) 0 0
\(187\) −6.64567 −0.485979
\(188\) 0 0
\(189\) 2.85951 0.207998
\(190\) 0 0
\(191\) 8.16705 0.590947 0.295473 0.955351i \(-0.404523\pi\)
0.295473 + 0.955351i \(0.404523\pi\)
\(192\) 0 0
\(193\) −2.47887 −0.178433 −0.0892164 0.996012i \(-0.528436\pi\)
−0.0892164 + 0.996012i \(0.528436\pi\)
\(194\) 0 0
\(195\) 1.46111 0.104632
\(196\) 0 0
\(197\) 13.2215 0.941992 0.470996 0.882135i \(-0.343895\pi\)
0.470996 + 0.882135i \(0.343895\pi\)
\(198\) 0 0
\(199\) 0.643373 0.0456075 0.0228037 0.999740i \(-0.492741\pi\)
0.0228037 + 0.999740i \(0.492741\pi\)
\(200\) 0 0
\(201\) 4.14614 0.292447
\(202\) 0 0
\(203\) 0.0222906 0.00156449
\(204\) 0 0
\(205\) −13.1728 −0.920030
\(206\) 0 0
\(207\) 20.8275 1.44761
\(208\) 0 0
\(209\) 8.43503 0.583463
\(210\) 0 0
\(211\) 8.75163 0.602487 0.301244 0.953547i \(-0.402598\pi\)
0.301244 + 0.953547i \(0.402598\pi\)
\(212\) 0 0
\(213\) −6.62822 −0.454158
\(214\) 0 0
\(215\) −4.15853 −0.283609
\(216\) 0 0
\(217\) −1.14381 −0.0776468
\(218\) 0 0
\(219\) −4.45975 −0.301362
\(220\) 0 0
\(221\) −6.64567 −0.447036
\(222\) 0 0
\(223\) −1.34705 −0.0902048 −0.0451024 0.998982i \(-0.514361\pi\)
−0.0451024 + 0.998982i \(0.514361\pi\)
\(224\) 0 0
\(225\) −10.0233 −0.668220
\(226\) 0 0
\(227\) −0.959150 −0.0636610 −0.0318305 0.999493i \(-0.510134\pi\)
−0.0318305 + 0.999493i \(0.510134\pi\)
\(228\) 0 0
\(229\) −10.3814 −0.686023 −0.343011 0.939331i \(-0.611447\pi\)
−0.343011 + 0.939331i \(0.611447\pi\)
\(230\) 0 0
\(231\) 0.497051 0.0327036
\(232\) 0 0
\(233\) 6.48083 0.424573 0.212287 0.977207i \(-0.431909\pi\)
0.212287 + 0.977207i \(0.431909\pi\)
\(234\) 0 0
\(235\) −20.4961 −1.33702
\(236\) 0 0
\(237\) −6.30586 −0.409610
\(238\) 0 0
\(239\) −1.47533 −0.0954314 −0.0477157 0.998861i \(-0.515194\pi\)
−0.0477157 + 0.998861i \(0.515194\pi\)
\(240\) 0 0
\(241\) −9.57997 −0.617100 −0.308550 0.951208i \(-0.599844\pi\)
−0.308550 + 0.951208i \(0.599844\pi\)
\(242\) 0 0
\(243\) 11.9771 0.768331
\(244\) 0 0
\(245\) −2.93955 −0.187801
\(246\) 0 0
\(247\) 8.43503 0.536708
\(248\) 0 0
\(249\) 1.30904 0.0829568
\(250\) 0 0
\(251\) 20.8727 1.31747 0.658737 0.752374i \(-0.271091\pi\)
0.658737 + 0.752374i \(0.271091\pi\)
\(252\) 0 0
\(253\) 7.56554 0.475641
\(254\) 0 0
\(255\) −9.71002 −0.608065
\(256\) 0 0
\(257\) 26.6086 1.65980 0.829900 0.557912i \(-0.188397\pi\)
0.829900 + 0.557912i \(0.188397\pi\)
\(258\) 0 0
\(259\) 0.840405 0.0522202
\(260\) 0 0
\(261\) 0.0613647 0.00379838
\(262\) 0 0
\(263\) −5.05996 −0.312011 −0.156005 0.987756i \(-0.549862\pi\)
−0.156005 + 0.987756i \(0.549862\pi\)
\(264\) 0 0
\(265\) −34.7288 −2.13337
\(266\) 0 0
\(267\) −7.42693 −0.454520
\(268\) 0 0
\(269\) −11.6505 −0.710341 −0.355170 0.934802i \(-0.615577\pi\)
−0.355170 + 0.934802i \(0.615577\pi\)
\(270\) 0 0
\(271\) −24.5537 −1.49153 −0.745765 0.666210i \(-0.767916\pi\)
−0.745765 + 0.666210i \(0.767916\pi\)
\(272\) 0 0
\(273\) 0.497051 0.0300829
\(274\) 0 0
\(275\) −3.64094 −0.219557
\(276\) 0 0
\(277\) 8.80267 0.528901 0.264451 0.964399i \(-0.414809\pi\)
0.264451 + 0.964399i \(0.414809\pi\)
\(278\) 0 0
\(279\) −3.14884 −0.188516
\(280\) 0 0
\(281\) 2.58544 0.154234 0.0771172 0.997022i \(-0.475428\pi\)
0.0771172 + 0.997022i \(0.475428\pi\)
\(282\) 0 0
\(283\) −15.0212 −0.892920 −0.446460 0.894804i \(-0.647315\pi\)
−0.446460 + 0.894804i \(0.647315\pi\)
\(284\) 0 0
\(285\) 12.3245 0.730039
\(286\) 0 0
\(287\) −4.48124 −0.264519
\(288\) 0 0
\(289\) 27.1649 1.59793
\(290\) 0 0
\(291\) 9.58579 0.561929
\(292\) 0 0
\(293\) 5.57879 0.325917 0.162958 0.986633i \(-0.447896\pi\)
0.162958 + 0.986633i \(0.447896\pi\)
\(294\) 0 0
\(295\) 2.58234 0.150350
\(296\) 0 0
\(297\) 2.85951 0.165925
\(298\) 0 0
\(299\) 7.56554 0.437526
\(300\) 0 0
\(301\) −1.41468 −0.0815410
\(302\) 0 0
\(303\) −1.52045 −0.0873474
\(304\) 0 0
\(305\) −2.97521 −0.170360
\(306\) 0 0
\(307\) 30.8736 1.76205 0.881024 0.473072i \(-0.156855\pi\)
0.881024 + 0.473072i \(0.156855\pi\)
\(308\) 0 0
\(309\) 1.25597 0.0714498
\(310\) 0 0
\(311\) −17.5943 −0.997683 −0.498842 0.866693i \(-0.666241\pi\)
−0.498842 + 0.866693i \(0.666241\pi\)
\(312\) 0 0
\(313\) 5.67492 0.320765 0.160383 0.987055i \(-0.448727\pi\)
0.160383 + 0.987055i \(0.448727\pi\)
\(314\) 0 0
\(315\) −8.09240 −0.455955
\(316\) 0 0
\(317\) −28.7277 −1.61351 −0.806754 0.590888i \(-0.798778\pi\)
−0.806754 + 0.590888i \(0.798778\pi\)
\(318\) 0 0
\(319\) 0.0222906 0.00124803
\(320\) 0 0
\(321\) 8.15358 0.455089
\(322\) 0 0
\(323\) −56.0564 −3.11906
\(324\) 0 0
\(325\) −3.64094 −0.201963
\(326\) 0 0
\(327\) 7.77120 0.429748
\(328\) 0 0
\(329\) −6.97254 −0.384408
\(330\) 0 0
\(331\) 22.6487 1.24488 0.622442 0.782666i \(-0.286141\pi\)
0.622442 + 0.782666i \(0.286141\pi\)
\(332\) 0 0
\(333\) 2.31359 0.126784
\(334\) 0 0
\(335\) −24.5202 −1.33968
\(336\) 0 0
\(337\) 3.33158 0.181483 0.0907414 0.995874i \(-0.471076\pi\)
0.0907414 + 0.995874i \(0.471076\pi\)
\(338\) 0 0
\(339\) 2.53108 0.137469
\(340\) 0 0
\(341\) −1.14381 −0.0619407
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 11.0541 0.595130
\(346\) 0 0
\(347\) −12.8753 −0.691183 −0.345591 0.938385i \(-0.612322\pi\)
−0.345591 + 0.938385i \(0.612322\pi\)
\(348\) 0 0
\(349\) 7.23667 0.387370 0.193685 0.981064i \(-0.437956\pi\)
0.193685 + 0.981064i \(0.437956\pi\)
\(350\) 0 0
\(351\) 2.85951 0.152629
\(352\) 0 0
\(353\) −31.3422 −1.66817 −0.834087 0.551632i \(-0.814005\pi\)
−0.834087 + 0.551632i \(0.814005\pi\)
\(354\) 0 0
\(355\) 39.1991 2.08047
\(356\) 0 0
\(357\) −3.30324 −0.174826
\(358\) 0 0
\(359\) −8.63676 −0.455831 −0.227915 0.973681i \(-0.573191\pi\)
−0.227915 + 0.973681i \(0.573191\pi\)
\(360\) 0 0
\(361\) 52.1497 2.74472
\(362\) 0 0
\(363\) 0.497051 0.0260884
\(364\) 0 0
\(365\) 26.3748 1.38052
\(366\) 0 0
\(367\) −23.7636 −1.24045 −0.620225 0.784424i \(-0.712959\pi\)
−0.620225 + 0.784424i \(0.712959\pi\)
\(368\) 0 0
\(369\) −12.3366 −0.642217
\(370\) 0 0
\(371\) −11.8143 −0.613369
\(372\) 0 0
\(373\) 30.2981 1.56878 0.784389 0.620269i \(-0.212977\pi\)
0.784389 + 0.620269i \(0.212977\pi\)
\(374\) 0 0
\(375\) 1.98573 0.102542
\(376\) 0 0
\(377\) 0.0222906 0.00114803
\(378\) 0 0
\(379\) −22.8240 −1.17239 −0.586196 0.810170i \(-0.699375\pi\)
−0.586196 + 0.810170i \(0.699375\pi\)
\(380\) 0 0
\(381\) 3.64265 0.186619
\(382\) 0 0
\(383\) −9.44337 −0.482534 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(384\) 0 0
\(385\) −2.93955 −0.149813
\(386\) 0 0
\(387\) −3.89454 −0.197970
\(388\) 0 0
\(389\) −0.167140 −0.00847433 −0.00423716 0.999991i \(-0.501349\pi\)
−0.00423716 + 0.999991i \(0.501349\pi\)
\(390\) 0 0
\(391\) −50.2781 −2.54267
\(392\) 0 0
\(393\) 0.292405 0.0147499
\(394\) 0 0
\(395\) 37.2927 1.87640
\(396\) 0 0
\(397\) −6.43898 −0.323163 −0.161581 0.986859i \(-0.551659\pi\)
−0.161581 + 0.986859i \(0.551659\pi\)
\(398\) 0 0
\(399\) 4.19264 0.209895
\(400\) 0 0
\(401\) 22.4519 1.12119 0.560597 0.828089i \(-0.310572\pi\)
0.560597 + 0.828089i \(0.310572\pi\)
\(402\) 0 0
\(403\) −1.14381 −0.0569771
\(404\) 0 0
\(405\) −20.0992 −0.998735
\(406\) 0 0
\(407\) 0.840405 0.0416573
\(408\) 0 0
\(409\) 31.2869 1.54704 0.773518 0.633774i \(-0.218495\pi\)
0.773518 + 0.633774i \(0.218495\pi\)
\(410\) 0 0
\(411\) −9.14218 −0.450950
\(412\) 0 0
\(413\) 0.878482 0.0432273
\(414\) 0 0
\(415\) −7.74161 −0.380021
\(416\) 0 0
\(417\) 1.06856 0.0523277
\(418\) 0 0
\(419\) 5.99916 0.293078 0.146539 0.989205i \(-0.453187\pi\)
0.146539 + 0.989205i \(0.453187\pi\)
\(420\) 0 0
\(421\) 10.4215 0.507911 0.253956 0.967216i \(-0.418268\pi\)
0.253956 + 0.967216i \(0.418268\pi\)
\(422\) 0 0
\(423\) −19.1950 −0.933292
\(424\) 0 0
\(425\) 24.1965 1.17370
\(426\) 0 0
\(427\) −1.01213 −0.0489804
\(428\) 0 0
\(429\) 0.497051 0.0239979
\(430\) 0 0
\(431\) −18.2146 −0.877367 −0.438684 0.898642i \(-0.644555\pi\)
−0.438684 + 0.898642i \(0.644555\pi\)
\(432\) 0 0
\(433\) −4.08666 −0.196392 −0.0981962 0.995167i \(-0.531307\pi\)
−0.0981962 + 0.995167i \(0.531307\pi\)
\(434\) 0 0
\(435\) 0.0325689 0.00156156
\(436\) 0 0
\(437\) 63.8156 3.05271
\(438\) 0 0
\(439\) −0.274007 −0.0130777 −0.00653883 0.999979i \(-0.502081\pi\)
−0.00653883 + 0.999979i \(0.502081\pi\)
\(440\) 0 0
\(441\) −2.75294 −0.131092
\(442\) 0 0
\(443\) 21.2676 1.01045 0.505226 0.862987i \(-0.331409\pi\)
0.505226 + 0.862987i \(0.331409\pi\)
\(444\) 0 0
\(445\) 43.9227 2.08213
\(446\) 0 0
\(447\) −3.14973 −0.148977
\(448\) 0 0
\(449\) −12.2838 −0.579710 −0.289855 0.957071i \(-0.593607\pi\)
−0.289855 + 0.957071i \(0.593607\pi\)
\(450\) 0 0
\(451\) −4.48124 −0.211013
\(452\) 0 0
\(453\) 3.87143 0.181896
\(454\) 0 0
\(455\) −2.93955 −0.137808
\(456\) 0 0
\(457\) −11.7234 −0.548399 −0.274199 0.961673i \(-0.588413\pi\)
−0.274199 + 0.961673i \(0.588413\pi\)
\(458\) 0 0
\(459\) −19.0033 −0.886999
\(460\) 0 0
\(461\) 3.19309 0.148717 0.0743585 0.997232i \(-0.476309\pi\)
0.0743585 + 0.997232i \(0.476309\pi\)
\(462\) 0 0
\(463\) 19.9860 0.928830 0.464415 0.885618i \(-0.346265\pi\)
0.464415 + 0.885618i \(0.346265\pi\)
\(464\) 0 0
\(465\) −1.67122 −0.0775012
\(466\) 0 0
\(467\) −38.4088 −1.77735 −0.888673 0.458541i \(-0.848372\pi\)
−0.888673 + 0.458541i \(0.848372\pi\)
\(468\) 0 0
\(469\) −8.34149 −0.385174
\(470\) 0 0
\(471\) 4.68180 0.215726
\(472\) 0 0
\(473\) −1.41468 −0.0650472
\(474\) 0 0
\(475\) −30.7115 −1.40914
\(476\) 0 0
\(477\) −32.5241 −1.48918
\(478\) 0 0
\(479\) −40.6119 −1.85561 −0.927803 0.373070i \(-0.878305\pi\)
−0.927803 + 0.373070i \(0.878305\pi\)
\(480\) 0 0
\(481\) 0.840405 0.0383192
\(482\) 0 0
\(483\) 3.76046 0.171107
\(484\) 0 0
\(485\) −56.6902 −2.57417
\(486\) 0 0
\(487\) 29.8727 1.35366 0.676831 0.736139i \(-0.263353\pi\)
0.676831 + 0.736139i \(0.263353\pi\)
\(488\) 0 0
\(489\) 10.9453 0.494962
\(490\) 0 0
\(491\) −5.02149 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(492\) 0 0
\(493\) −0.148136 −0.00667171
\(494\) 0 0
\(495\) −8.09240 −0.363726
\(496\) 0 0
\(497\) 13.3351 0.598160
\(498\) 0 0
\(499\) −31.2389 −1.39844 −0.699222 0.714905i \(-0.746470\pi\)
−0.699222 + 0.714905i \(0.746470\pi\)
\(500\) 0 0
\(501\) −9.70223 −0.433464
\(502\) 0 0
\(503\) 19.6425 0.875818 0.437909 0.899019i \(-0.355719\pi\)
0.437909 + 0.899019i \(0.355719\pi\)
\(504\) 0 0
\(505\) 8.99188 0.400133
\(506\) 0 0
\(507\) 0.497051 0.0220748
\(508\) 0 0
\(509\) −25.1361 −1.11414 −0.557068 0.830467i \(-0.688074\pi\)
−0.557068 + 0.830467i \(0.688074\pi\)
\(510\) 0 0
\(511\) 8.97242 0.396916
\(512\) 0 0
\(513\) 24.1200 1.06492
\(514\) 0 0
\(515\) −7.42779 −0.327308
\(516\) 0 0
\(517\) −6.97254 −0.306652
\(518\) 0 0
\(519\) −3.44881 −0.151386
\(520\) 0 0
\(521\) −11.1585 −0.488862 −0.244431 0.969667i \(-0.578601\pi\)
−0.244431 + 0.969667i \(0.578601\pi\)
\(522\) 0 0
\(523\) −6.91985 −0.302584 −0.151292 0.988489i \(-0.548343\pi\)
−0.151292 + 0.988489i \(0.548343\pi\)
\(524\) 0 0
\(525\) −1.80973 −0.0789833
\(526\) 0 0
\(527\) 7.60137 0.331121
\(528\) 0 0
\(529\) 34.2374 1.48858
\(530\) 0 0
\(531\) 2.41841 0.104950
\(532\) 0 0
\(533\) −4.48124 −0.194104
\(534\) 0 0
\(535\) −48.2201 −2.08474
\(536\) 0 0
\(537\) 2.98931 0.128998
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 39.5333 1.69967 0.849836 0.527048i \(-0.176701\pi\)
0.849836 + 0.527048i \(0.176701\pi\)
\(542\) 0 0
\(543\) 5.21616 0.223847
\(544\) 0 0
\(545\) −45.9587 −1.96865
\(546\) 0 0
\(547\) 44.8339 1.91696 0.958479 0.285162i \(-0.0920474\pi\)
0.958479 + 0.285162i \(0.0920474\pi\)
\(548\) 0 0
\(549\) −2.78634 −0.118918
\(550\) 0 0
\(551\) 0.188022 0.00801001
\(552\) 0 0
\(553\) 12.6865 0.539487
\(554\) 0 0
\(555\) 1.22792 0.0521223
\(556\) 0 0
\(557\) −19.8445 −0.840839 −0.420419 0.907330i \(-0.638117\pi\)
−0.420419 + 0.907330i \(0.638117\pi\)
\(558\) 0 0
\(559\) −1.41468 −0.0598347
\(560\) 0 0
\(561\) −3.30324 −0.139463
\(562\) 0 0
\(563\) −19.3194 −0.814216 −0.407108 0.913380i \(-0.633463\pi\)
−0.407108 + 0.913380i \(0.633463\pi\)
\(564\) 0 0
\(565\) −14.9687 −0.629739
\(566\) 0 0
\(567\) −6.83750 −0.287148
\(568\) 0 0
\(569\) −29.3941 −1.23227 −0.616133 0.787642i \(-0.711302\pi\)
−0.616133 + 0.787642i \(0.711302\pi\)
\(570\) 0 0
\(571\) −19.6340 −0.821659 −0.410829 0.911712i \(-0.634761\pi\)
−0.410829 + 0.911712i \(0.634761\pi\)
\(572\) 0 0
\(573\) 4.05944 0.169585
\(574\) 0 0
\(575\) −27.5457 −1.14874
\(576\) 0 0
\(577\) 4.99071 0.207766 0.103883 0.994590i \(-0.466873\pi\)
0.103883 + 0.994590i \(0.466873\pi\)
\(578\) 0 0
\(579\) −1.23212 −0.0512053
\(580\) 0 0
\(581\) −2.63360 −0.109260
\(582\) 0 0
\(583\) −11.8143 −0.489300
\(584\) 0 0
\(585\) −8.09240 −0.334580
\(586\) 0 0
\(587\) −7.15675 −0.295391 −0.147695 0.989033i \(-0.547186\pi\)
−0.147695 + 0.989033i \(0.547186\pi\)
\(588\) 0 0
\(589\) −9.64806 −0.397541
\(590\) 0 0
\(591\) 6.57176 0.270326
\(592\) 0 0
\(593\) 46.1999 1.89720 0.948601 0.316474i \(-0.102499\pi\)
0.948601 + 0.316474i \(0.102499\pi\)
\(594\) 0 0
\(595\) 19.5353 0.800867
\(596\) 0 0
\(597\) 0.319789 0.0130881
\(598\) 0 0
\(599\) 12.3134 0.503113 0.251556 0.967843i \(-0.419058\pi\)
0.251556 + 0.967843i \(0.419058\pi\)
\(600\) 0 0
\(601\) −4.36559 −0.178076 −0.0890380 0.996028i \(-0.528379\pi\)
−0.0890380 + 0.996028i \(0.528379\pi\)
\(602\) 0 0
\(603\) −22.9636 −0.935151
\(604\) 0 0
\(605\) −2.93955 −0.119510
\(606\) 0 0
\(607\) −7.34490 −0.298120 −0.149060 0.988828i \(-0.547625\pi\)
−0.149060 + 0.988828i \(0.547625\pi\)
\(608\) 0 0
\(609\) 0.0110796 0.000448967 0
\(610\) 0 0
\(611\) −6.97254 −0.282079
\(612\) 0 0
\(613\) 40.0829 1.61893 0.809466 0.587167i \(-0.199757\pi\)
0.809466 + 0.587167i \(0.199757\pi\)
\(614\) 0 0
\(615\) −6.54756 −0.264023
\(616\) 0 0
\(617\) 36.6470 1.47535 0.737677 0.675154i \(-0.235923\pi\)
0.737677 + 0.675154i \(0.235923\pi\)
\(618\) 0 0
\(619\) 2.87216 0.115442 0.0577209 0.998333i \(-0.481617\pi\)
0.0577209 + 0.998333i \(0.481617\pi\)
\(620\) 0 0
\(621\) 21.6337 0.868131
\(622\) 0 0
\(623\) 14.9420 0.598638
\(624\) 0 0
\(625\) −29.9482 −1.19793
\(626\) 0 0
\(627\) 4.19264 0.167438
\(628\) 0 0
\(629\) −5.58505 −0.222691
\(630\) 0 0
\(631\) −18.0530 −0.718678 −0.359339 0.933207i \(-0.616998\pi\)
−0.359339 + 0.933207i \(0.616998\pi\)
\(632\) 0 0
\(633\) 4.35001 0.172897
\(634\) 0 0
\(635\) −21.5426 −0.854891
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 36.7107 1.45225
\(640\) 0 0
\(641\) −21.7333 −0.858412 −0.429206 0.903207i \(-0.641207\pi\)
−0.429206 + 0.903207i \(0.641207\pi\)
\(642\) 0 0
\(643\) −36.3416 −1.43317 −0.716586 0.697499i \(-0.754296\pi\)
−0.716586 + 0.697499i \(0.754296\pi\)
\(644\) 0 0
\(645\) −2.06700 −0.0813881
\(646\) 0 0
\(647\) 45.7454 1.79844 0.899219 0.437499i \(-0.144136\pi\)
0.899219 + 0.437499i \(0.144136\pi\)
\(648\) 0 0
\(649\) 0.878482 0.0344835
\(650\) 0 0
\(651\) −0.568531 −0.0222825
\(652\) 0 0
\(653\) 0.230521 0.00902100 0.00451050 0.999990i \(-0.498564\pi\)
0.00451050 + 0.999990i \(0.498564\pi\)
\(654\) 0 0
\(655\) −1.72928 −0.0675685
\(656\) 0 0
\(657\) 24.7005 0.963659
\(658\) 0 0
\(659\) −19.7196 −0.768167 −0.384083 0.923298i \(-0.625482\pi\)
−0.384083 + 0.923298i \(0.625482\pi\)
\(660\) 0 0
\(661\) −37.0997 −1.44301 −0.721505 0.692409i \(-0.756549\pi\)
−0.721505 + 0.692409i \(0.756549\pi\)
\(662\) 0 0
\(663\) −3.30324 −0.128287
\(664\) 0 0
\(665\) −24.7952 −0.961516
\(666\) 0 0
\(667\) 0.168641 0.00652979
\(668\) 0 0
\(669\) −0.669550 −0.0258863
\(670\) 0 0
\(671\) −1.01213 −0.0390729
\(672\) 0 0
\(673\) 23.2123 0.894768 0.447384 0.894342i \(-0.352356\pi\)
0.447384 + 0.894342i \(0.352356\pi\)
\(674\) 0 0
\(675\) −10.4113 −0.400731
\(676\) 0 0
\(677\) 21.3929 0.822198 0.411099 0.911591i \(-0.365145\pi\)
0.411099 + 0.911591i \(0.365145\pi\)
\(678\) 0 0
\(679\) −19.2853 −0.740103
\(680\) 0 0
\(681\) −0.476747 −0.0182690
\(682\) 0 0
\(683\) 26.8470 1.02727 0.513636 0.858008i \(-0.328298\pi\)
0.513636 + 0.858008i \(0.328298\pi\)
\(684\) 0 0
\(685\) 54.0666 2.06578
\(686\) 0 0
\(687\) −5.16009 −0.196870
\(688\) 0 0
\(689\) −11.8143 −0.450090
\(690\) 0 0
\(691\) 7.08393 0.269485 0.134743 0.990881i \(-0.456979\pi\)
0.134743 + 0.990881i \(0.456979\pi\)
\(692\) 0 0
\(693\) −2.75294 −0.104576
\(694\) 0 0
\(695\) −6.31945 −0.239710
\(696\) 0 0
\(697\) 29.7808 1.12803
\(698\) 0 0
\(699\) 3.22130 0.121841
\(700\) 0 0
\(701\) −34.7313 −1.31178 −0.655892 0.754855i \(-0.727707\pi\)
−0.655892 + 0.754855i \(0.727707\pi\)
\(702\) 0 0
\(703\) 7.08884 0.267361
\(704\) 0 0
\(705\) −10.1876 −0.383688
\(706\) 0 0
\(707\) 3.05893 0.115043
\(708\) 0 0
\(709\) 17.0404 0.639966 0.319983 0.947423i \(-0.396323\pi\)
0.319983 + 0.947423i \(0.396323\pi\)
\(710\) 0 0
\(711\) 34.9253 1.30980
\(712\) 0 0
\(713\) −8.65353 −0.324077
\(714\) 0 0
\(715\) −2.93955 −0.109933
\(716\) 0 0
\(717\) −0.733316 −0.0273862
\(718\) 0 0
\(719\) −3.21732 −0.119986 −0.0599929 0.998199i \(-0.519108\pi\)
−0.0599929 + 0.998199i \(0.519108\pi\)
\(720\) 0 0
\(721\) −2.52685 −0.0941048
\(722\) 0 0
\(723\) −4.76173 −0.177091
\(724\) 0 0
\(725\) −0.0811589 −0.00301416
\(726\) 0 0
\(727\) −9.07075 −0.336416 −0.168208 0.985752i \(-0.553798\pi\)
−0.168208 + 0.985752i \(0.553798\pi\)
\(728\) 0 0
\(729\) −14.5593 −0.539232
\(730\) 0 0
\(731\) 9.40151 0.347727
\(732\) 0 0
\(733\) −30.8602 −1.13985 −0.569923 0.821698i \(-0.693027\pi\)
−0.569923 + 0.821698i \(0.693027\pi\)
\(734\) 0 0
\(735\) −1.46111 −0.0538937
\(736\) 0 0
\(737\) −8.34149 −0.307263
\(738\) 0 0
\(739\) 30.3010 1.11464 0.557320 0.830298i \(-0.311830\pi\)
0.557320 + 0.830298i \(0.311830\pi\)
\(740\) 0 0
\(741\) 4.19264 0.154021
\(742\) 0 0
\(743\) 35.3660 1.29745 0.648726 0.761022i \(-0.275302\pi\)
0.648726 + 0.761022i \(0.275302\pi\)
\(744\) 0 0
\(745\) 18.6275 0.682457
\(746\) 0 0
\(747\) −7.25016 −0.265269
\(748\) 0 0
\(749\) −16.4039 −0.599386
\(750\) 0 0
\(751\) 22.9692 0.838158 0.419079 0.907950i \(-0.362353\pi\)
0.419079 + 0.907950i \(0.362353\pi\)
\(752\) 0 0
\(753\) 10.3748 0.378079
\(754\) 0 0
\(755\) −22.8956 −0.833255
\(756\) 0 0
\(757\) 10.9833 0.399196 0.199598 0.979878i \(-0.436036\pi\)
0.199598 + 0.979878i \(0.436036\pi\)
\(758\) 0 0
\(759\) 3.76046 0.136496
\(760\) 0 0
\(761\) −32.4052 −1.17469 −0.587344 0.809337i \(-0.699827\pi\)
−0.587344 + 0.809337i \(0.699827\pi\)
\(762\) 0 0
\(763\) −15.6346 −0.566011
\(764\) 0 0
\(765\) 53.7794 1.94440
\(766\) 0 0
\(767\) 0.878482 0.0317202
\(768\) 0 0
\(769\) −3.19787 −0.115318 −0.0576590 0.998336i \(-0.518364\pi\)
−0.0576590 + 0.998336i \(0.518364\pi\)
\(770\) 0 0
\(771\) 13.2258 0.476317
\(772\) 0 0
\(773\) −42.5718 −1.53120 −0.765601 0.643315i \(-0.777558\pi\)
−0.765601 + 0.643315i \(0.777558\pi\)
\(774\) 0 0
\(775\) 4.16454 0.149595
\(776\) 0 0
\(777\) 0.417724 0.0149858
\(778\) 0 0
\(779\) −37.7994 −1.35430
\(780\) 0 0
\(781\) 13.3351 0.477167
\(782\) 0 0
\(783\) 0.0637401 0.00227789
\(784\) 0 0
\(785\) −27.6881 −0.988230
\(786\) 0 0
\(787\) −25.4656 −0.907752 −0.453876 0.891065i \(-0.649959\pi\)
−0.453876 + 0.891065i \(0.649959\pi\)
\(788\) 0 0
\(789\) −2.51506 −0.0895385
\(790\) 0 0
\(791\) −5.09219 −0.181057
\(792\) 0 0
\(793\) −1.01213 −0.0359418
\(794\) 0 0
\(795\) −17.2620 −0.612219
\(796\) 0 0
\(797\) 1.19398 0.0422928 0.0211464 0.999776i \(-0.493268\pi\)
0.0211464 + 0.999776i \(0.493268\pi\)
\(798\) 0 0
\(799\) 46.3372 1.63929
\(800\) 0 0
\(801\) 41.1344 1.45341
\(802\) 0 0
\(803\) 8.97242 0.316630
\(804\) 0 0
\(805\) −22.2393 −0.783831
\(806\) 0 0
\(807\) −5.79087 −0.203848
\(808\) 0 0
\(809\) 46.3350 1.62905 0.814526 0.580128i \(-0.196997\pi\)
0.814526 + 0.580128i \(0.196997\pi\)
\(810\) 0 0
\(811\) 6.62835 0.232753 0.116376 0.993205i \(-0.462872\pi\)
0.116376 + 0.993205i \(0.462872\pi\)
\(812\) 0 0
\(813\) −12.2044 −0.428028
\(814\) 0 0
\(815\) −64.7301 −2.26740
\(816\) 0 0
\(817\) −11.9329 −0.417479
\(818\) 0 0
\(819\) −2.75294 −0.0961955
\(820\) 0 0
\(821\) −37.1054 −1.29499 −0.647493 0.762071i \(-0.724183\pi\)
−0.647493 + 0.762071i \(0.724183\pi\)
\(822\) 0 0
\(823\) −18.0648 −0.629701 −0.314850 0.949141i \(-0.601954\pi\)
−0.314850 + 0.949141i \(0.601954\pi\)
\(824\) 0 0
\(825\) −1.80973 −0.0630069
\(826\) 0 0
\(827\) 38.9556 1.35462 0.677310 0.735698i \(-0.263146\pi\)
0.677310 + 0.735698i \(0.263146\pi\)
\(828\) 0 0
\(829\) 25.6819 0.891971 0.445985 0.895040i \(-0.352853\pi\)
0.445985 + 0.895040i \(0.352853\pi\)
\(830\) 0 0
\(831\) 4.37538 0.151780
\(832\) 0 0
\(833\) 6.64567 0.230259
\(834\) 0 0
\(835\) 57.3788 1.98567
\(836\) 0 0
\(837\) −3.27073 −0.113053
\(838\) 0 0
\(839\) 46.6244 1.60965 0.804827 0.593509i \(-0.202258\pi\)
0.804827 + 0.593509i \(0.202258\pi\)
\(840\) 0 0
\(841\) −28.9995 −0.999983
\(842\) 0 0
\(843\) 1.28510 0.0442610
\(844\) 0 0
\(845\) −2.93955 −0.101124
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −7.46632 −0.256243
\(850\) 0 0
\(851\) 6.35812 0.217953
\(852\) 0 0
\(853\) −5.03415 −0.172366 −0.0861830 0.996279i \(-0.527467\pi\)
−0.0861830 + 0.996279i \(0.527467\pi\)
\(854\) 0 0
\(855\) −68.2596 −2.33443
\(856\) 0 0
\(857\) 18.5698 0.634333 0.317166 0.948370i \(-0.397269\pi\)
0.317166 + 0.948370i \(0.397269\pi\)
\(858\) 0 0
\(859\) 29.0060 0.989673 0.494837 0.868986i \(-0.335228\pi\)
0.494837 + 0.868986i \(0.335228\pi\)
\(860\) 0 0
\(861\) −2.22740 −0.0759098
\(862\) 0 0
\(863\) −13.2955 −0.452583 −0.226292 0.974060i \(-0.572660\pi\)
−0.226292 + 0.974060i \(0.572660\pi\)
\(864\) 0 0
\(865\) 20.3962 0.693490
\(866\) 0 0
\(867\) 13.5023 0.458563
\(868\) 0 0
\(869\) 12.6865 0.430362
\(870\) 0 0
\(871\) −8.34149 −0.282640
\(872\) 0 0
\(873\) −53.0914 −1.79687
\(874\) 0 0
\(875\) −3.99501 −0.135056
\(876\) 0 0
\(877\) −24.5596 −0.829320 −0.414660 0.909976i \(-0.636099\pi\)
−0.414660 + 0.909976i \(0.636099\pi\)
\(878\) 0 0
\(879\) 2.77295 0.0935291
\(880\) 0 0
\(881\) −8.92309 −0.300627 −0.150313 0.988638i \(-0.548028\pi\)
−0.150313 + 0.988638i \(0.548028\pi\)
\(882\) 0 0
\(883\) −7.12193 −0.239672 −0.119836 0.992794i \(-0.538237\pi\)
−0.119836 + 0.992794i \(0.538237\pi\)
\(884\) 0 0
\(885\) 1.28356 0.0431462
\(886\) 0 0
\(887\) −32.3572 −1.08645 −0.543224 0.839588i \(-0.682796\pi\)
−0.543224 + 0.839588i \(0.682796\pi\)
\(888\) 0 0
\(889\) −7.32853 −0.245791
\(890\) 0 0
\(891\) −6.83750 −0.229065
\(892\) 0 0
\(893\) −58.8136 −1.96812
\(894\) 0 0
\(895\) −17.6787 −0.590935
\(896\) 0 0
\(897\) 3.76046 0.125558
\(898\) 0 0
\(899\) −0.0254962 −0.000850345 0
\(900\) 0 0
\(901\) 78.5141 2.61568
\(902\) 0 0
\(903\) −0.703170 −0.0234000
\(904\) 0 0
\(905\) −30.8482 −1.02543
\(906\) 0 0
\(907\) −40.6121 −1.34850 −0.674251 0.738502i \(-0.735534\pi\)
−0.674251 + 0.738502i \(0.735534\pi\)
\(908\) 0 0
\(909\) 8.42106 0.279309
\(910\) 0 0
\(911\) −4.77972 −0.158359 −0.0791796 0.996860i \(-0.525230\pi\)
−0.0791796 + 0.996860i \(0.525230\pi\)
\(912\) 0 0
\(913\) −2.63360 −0.0871596
\(914\) 0 0
\(915\) −1.47883 −0.0488886
\(916\) 0 0
\(917\) −0.588280 −0.0194267
\(918\) 0 0
\(919\) 36.2542 1.19591 0.597957 0.801528i \(-0.295979\pi\)
0.597957 + 0.801528i \(0.295979\pi\)
\(920\) 0 0
\(921\) 15.3457 0.505659
\(922\) 0 0
\(923\) 13.3351 0.438930
\(924\) 0 0
\(925\) −3.05987 −0.100608
\(926\) 0 0
\(927\) −6.95626 −0.228474
\(928\) 0 0
\(929\) 21.3237 0.699607 0.349803 0.936823i \(-0.386248\pi\)
0.349803 + 0.936823i \(0.386248\pi\)
\(930\) 0 0
\(931\) −8.43503 −0.276447
\(932\) 0 0
\(933\) −8.74528 −0.286308
\(934\) 0 0
\(935\) 19.5353 0.638871
\(936\) 0 0
\(937\) 21.4550 0.700904 0.350452 0.936581i \(-0.386028\pi\)
0.350452 + 0.936581i \(0.386028\pi\)
\(938\) 0 0
\(939\) 2.82073 0.0920509
\(940\) 0 0
\(941\) 36.4897 1.18953 0.594766 0.803899i \(-0.297245\pi\)
0.594766 + 0.803899i \(0.297245\pi\)
\(942\) 0 0
\(943\) −33.9030 −1.10403
\(944\) 0 0
\(945\) −8.40565 −0.273436
\(946\) 0 0
\(947\) 51.1608 1.66250 0.831251 0.555897i \(-0.187625\pi\)
0.831251 + 0.555897i \(0.187625\pi\)
\(948\) 0 0
\(949\) 8.97242 0.291257
\(950\) 0 0
\(951\) −14.2791 −0.463032
\(952\) 0 0
\(953\) −21.1360 −0.684661 −0.342331 0.939580i \(-0.611216\pi\)
−0.342331 + 0.939580i \(0.611216\pi\)
\(954\) 0 0
\(955\) −24.0074 −0.776862
\(956\) 0 0
\(957\) 0.0110796 0.000358152 0
\(958\) 0 0
\(959\) 18.3928 0.593935
\(960\) 0 0
\(961\) −29.6917 −0.957797
\(962\) 0 0
\(963\) −45.1590 −1.45523
\(964\) 0 0
\(965\) 7.28675 0.234569
\(966\) 0 0
\(967\) −53.5874 −1.72325 −0.861627 0.507542i \(-0.830554\pi\)
−0.861627 + 0.507542i \(0.830554\pi\)
\(968\) 0 0
\(969\) −27.8629 −0.895085
\(970\) 0 0
\(971\) 40.8287 1.31026 0.655128 0.755518i \(-0.272615\pi\)
0.655128 + 0.755518i \(0.272615\pi\)
\(972\) 0 0
\(973\) −2.14980 −0.0689195
\(974\) 0 0
\(975\) −1.80973 −0.0579579
\(976\) 0 0
\(977\) 59.8042 1.91330 0.956652 0.291232i \(-0.0940651\pi\)
0.956652 + 0.291232i \(0.0940651\pi\)
\(978\) 0 0
\(979\) 14.9420 0.477548
\(980\) 0 0
\(981\) −43.0411 −1.37420
\(982\) 0 0
\(983\) −55.4918 −1.76991 −0.884957 0.465673i \(-0.845812\pi\)
−0.884957 + 0.465673i \(0.845812\pi\)
\(984\) 0 0
\(985\) −38.8652 −1.23835
\(986\) 0 0
\(987\) −3.46571 −0.110315
\(988\) 0 0
\(989\) −10.7028 −0.340330
\(990\) 0 0
\(991\) −53.4449 −1.69773 −0.848866 0.528608i \(-0.822714\pi\)
−0.848866 + 0.528608i \(0.822714\pi\)
\(992\) 0 0
\(993\) 11.2576 0.357248
\(994\) 0 0
\(995\) −1.89122 −0.0599559
\(996\) 0 0
\(997\) 44.0110 1.39384 0.696922 0.717147i \(-0.254553\pi\)
0.696922 + 0.717147i \(0.254553\pi\)
\(998\) 0 0
\(999\) 2.40314 0.0760321
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 \(a_p\))