Properties

Label 8008.2.a.n.1.7
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.15169\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.15169 q^{3} -3.19313 q^{5} -1.00000 q^{7} -1.67362 q^{9} +O(q^{10})\) \(q+1.15169 q^{3} -3.19313 q^{5} -1.00000 q^{7} -1.67362 q^{9} +1.00000 q^{11} -1.00000 q^{13} -3.67749 q^{15} -5.49259 q^{17} -5.11526 q^{19} -1.15169 q^{21} +1.48841 q^{23} +5.19610 q^{25} -5.38254 q^{27} -2.51163 q^{29} -7.49076 q^{31} +1.15169 q^{33} +3.19313 q^{35} +4.43821 q^{37} -1.15169 q^{39} +0.657467 q^{41} +6.68846 q^{43} +5.34408 q^{45} +2.89407 q^{47} +1.00000 q^{49} -6.32575 q^{51} -3.25916 q^{53} -3.19313 q^{55} -5.89118 q^{57} +3.56070 q^{59} -10.9451 q^{61} +1.67362 q^{63} +3.19313 q^{65} -7.93486 q^{67} +1.71418 q^{69} +6.97464 q^{71} -5.60557 q^{73} +5.98428 q^{75} -1.00000 q^{77} +8.60100 q^{79} -1.17816 q^{81} +14.3251 q^{83} +17.5386 q^{85} -2.89261 q^{87} -9.04126 q^{89} +1.00000 q^{91} -8.62701 q^{93} +16.3337 q^{95} +7.78347 q^{97} -1.67362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) 1.15169 0.664927 0.332463 0.943116i \(-0.392120\pi\)
0.332463 + 0.943116i \(0.392120\pi\)
\(4\) 0 0
\(5\) −3.19313 −1.42801 −0.714006 0.700139i \(-0.753121\pi\)
−0.714006 + 0.700139i \(0.753121\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.67362 −0.557872
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.67749 −0.949524
\(16\) 0 0
\(17\) −5.49259 −1.33215 −0.666074 0.745885i \(-0.732027\pi\)
−0.666074 + 0.745885i \(0.732027\pi\)
\(18\) 0 0
\(19\) −5.11526 −1.17352 −0.586761 0.809760i \(-0.699597\pi\)
−0.586761 + 0.809760i \(0.699597\pi\)
\(20\) 0 0
\(21\) −1.15169 −0.251319
\(22\) 0 0
\(23\) 1.48841 0.310355 0.155177 0.987887i \(-0.450405\pi\)
0.155177 + 0.987887i \(0.450405\pi\)
\(24\) 0 0
\(25\) 5.19610 1.03922
\(26\) 0 0
\(27\) −5.38254 −1.03587
\(28\) 0 0
\(29\) −2.51163 −0.466397 −0.233199 0.972429i \(-0.574919\pi\)
−0.233199 + 0.972429i \(0.574919\pi\)
\(30\) 0 0
\(31\) −7.49076 −1.34538 −0.672690 0.739924i \(-0.734861\pi\)
−0.672690 + 0.739924i \(0.734861\pi\)
\(32\) 0 0
\(33\) 1.15169 0.200483
\(34\) 0 0
\(35\) 3.19313 0.539738
\(36\) 0 0
\(37\) 4.43821 0.729637 0.364819 0.931079i \(-0.381131\pi\)
0.364819 + 0.931079i \(0.381131\pi\)
\(38\) 0 0
\(39\) −1.15169 −0.184418
\(40\) 0 0
\(41\) 0.657467 0.102679 0.0513395 0.998681i \(-0.483651\pi\)
0.0513395 + 0.998681i \(0.483651\pi\)
\(42\) 0 0
\(43\) 6.68846 1.01998 0.509990 0.860180i \(-0.329649\pi\)
0.509990 + 0.860180i \(0.329649\pi\)
\(44\) 0 0
\(45\) 5.34408 0.796648
\(46\) 0 0
\(47\) 2.89407 0.422144 0.211072 0.977471i \(-0.432305\pi\)
0.211072 + 0.977471i \(0.432305\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −6.32575 −0.885782
\(52\) 0 0
\(53\) −3.25916 −0.447680 −0.223840 0.974626i \(-0.571859\pi\)
−0.223840 + 0.974626i \(0.571859\pi\)
\(54\) 0 0
\(55\) −3.19313 −0.430562
\(56\) 0 0
\(57\) −5.89118 −0.780306
\(58\) 0 0
\(59\) 3.56070 0.463564 0.231782 0.972768i \(-0.425544\pi\)
0.231782 + 0.972768i \(0.425544\pi\)
\(60\) 0 0
\(61\) −10.9451 −1.40137 −0.700686 0.713470i \(-0.747122\pi\)
−0.700686 + 0.713470i \(0.747122\pi\)
\(62\) 0 0
\(63\) 1.67362 0.210856
\(64\) 0 0
\(65\) 3.19313 0.396059
\(66\) 0 0
\(67\) −7.93486 −0.969398 −0.484699 0.874681i \(-0.661071\pi\)
−0.484699 + 0.874681i \(0.661071\pi\)
\(68\) 0 0
\(69\) 1.71418 0.206363
\(70\) 0 0
\(71\) 6.97464 0.827738 0.413869 0.910337i \(-0.364177\pi\)
0.413869 + 0.910337i \(0.364177\pi\)
\(72\) 0 0
\(73\) −5.60557 −0.656082 −0.328041 0.944663i \(-0.606388\pi\)
−0.328041 + 0.944663i \(0.606388\pi\)
\(74\) 0 0
\(75\) 5.98428 0.691006
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 8.60100 0.967688 0.483844 0.875154i \(-0.339240\pi\)
0.483844 + 0.875154i \(0.339240\pi\)
\(80\) 0 0
\(81\) −1.17816 −0.130907
\(82\) 0 0
\(83\) 14.3251 1.57239 0.786195 0.617979i \(-0.212048\pi\)
0.786195 + 0.617979i \(0.212048\pi\)
\(84\) 0 0
\(85\) 17.5386 1.90233
\(86\) 0 0
\(87\) −2.89261 −0.310120
\(88\) 0 0
\(89\) −9.04126 −0.958372 −0.479186 0.877713i \(-0.659068\pi\)
−0.479186 + 0.877713i \(0.659068\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −8.62701 −0.894580
\(94\) 0 0
\(95\) 16.3337 1.67580
\(96\) 0 0
\(97\) 7.78347 0.790292 0.395146 0.918618i \(-0.370694\pi\)
0.395146 + 0.918618i \(0.370694\pi\)
\(98\) 0 0
\(99\) −1.67362 −0.168205
\(100\) 0 0
\(101\) −6.81145 −0.677765 −0.338883 0.940829i \(-0.610049\pi\)
−0.338883 + 0.940829i \(0.610049\pi\)
\(102\) 0 0
\(103\) 10.6098 1.04541 0.522706 0.852513i \(-0.324922\pi\)
0.522706 + 0.852513i \(0.324922\pi\)
\(104\) 0 0
\(105\) 3.67749 0.358886
\(106\) 0 0
\(107\) 2.52753 0.244345 0.122173 0.992509i \(-0.461014\pi\)
0.122173 + 0.992509i \(0.461014\pi\)
\(108\) 0 0
\(109\) 14.0056 1.34149 0.670747 0.741686i \(-0.265974\pi\)
0.670747 + 0.741686i \(0.265974\pi\)
\(110\) 0 0
\(111\) 5.11143 0.485156
\(112\) 0 0
\(113\) −18.0938 −1.70212 −0.851061 0.525067i \(-0.824040\pi\)
−0.851061 + 0.525067i \(0.824040\pi\)
\(114\) 0 0
\(115\) −4.75269 −0.443191
\(116\) 0 0
\(117\) 1.67362 0.154726
\(118\) 0 0
\(119\) 5.49259 0.503505
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.757196 0.0682741
\(124\) 0 0
\(125\) −0.626178 −0.0560070
\(126\) 0 0
\(127\) 7.09235 0.629345 0.314672 0.949200i \(-0.398105\pi\)
0.314672 + 0.949200i \(0.398105\pi\)
\(128\) 0 0
\(129\) 7.70301 0.678212
\(130\) 0 0
\(131\) 4.79039 0.418539 0.209269 0.977858i \(-0.432891\pi\)
0.209269 + 0.977858i \(0.432891\pi\)
\(132\) 0 0
\(133\) 5.11526 0.443550
\(134\) 0 0
\(135\) 17.1872 1.47924
\(136\) 0 0
\(137\) −10.9050 −0.931679 −0.465839 0.884869i \(-0.654248\pi\)
−0.465839 + 0.884869i \(0.654248\pi\)
\(138\) 0 0
\(139\) −13.8452 −1.17433 −0.587167 0.809466i \(-0.699757\pi\)
−0.587167 + 0.809466i \(0.699757\pi\)
\(140\) 0 0
\(141\) 3.33307 0.280695
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 8.01996 0.666021
\(146\) 0 0
\(147\) 1.15169 0.0949896
\(148\) 0 0
\(149\) 9.87354 0.808872 0.404436 0.914566i \(-0.367468\pi\)
0.404436 + 0.914566i \(0.367468\pi\)
\(150\) 0 0
\(151\) 16.8258 1.36926 0.684630 0.728890i \(-0.259964\pi\)
0.684630 + 0.728890i \(0.259964\pi\)
\(152\) 0 0
\(153\) 9.19249 0.743169
\(154\) 0 0
\(155\) 23.9190 1.92122
\(156\) 0 0
\(157\) −7.91635 −0.631793 −0.315897 0.948794i \(-0.602305\pi\)
−0.315897 + 0.948794i \(0.602305\pi\)
\(158\) 0 0
\(159\) −3.75353 −0.297674
\(160\) 0 0
\(161\) −1.48841 −0.117303
\(162\) 0 0
\(163\) −4.55660 −0.356901 −0.178450 0.983949i \(-0.557108\pi\)
−0.178450 + 0.983949i \(0.557108\pi\)
\(164\) 0 0
\(165\) −3.67749 −0.286292
\(166\) 0 0
\(167\) −14.5899 −1.12900 −0.564501 0.825433i \(-0.690931\pi\)
−0.564501 + 0.825433i \(0.690931\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 8.56099 0.654675
\(172\) 0 0
\(173\) 5.73367 0.435923 0.217961 0.975957i \(-0.430059\pi\)
0.217961 + 0.975957i \(0.430059\pi\)
\(174\) 0 0
\(175\) −5.19610 −0.392788
\(176\) 0 0
\(177\) 4.10082 0.308236
\(178\) 0 0
\(179\) 6.30899 0.471556 0.235778 0.971807i \(-0.424236\pi\)
0.235778 + 0.971807i \(0.424236\pi\)
\(180\) 0 0
\(181\) −9.20399 −0.684128 −0.342064 0.939677i \(-0.611126\pi\)
−0.342064 + 0.939677i \(0.611126\pi\)
\(182\) 0 0
\(183\) −12.6053 −0.931809
\(184\) 0 0
\(185\) −14.1718 −1.04193
\(186\) 0 0
\(187\) −5.49259 −0.401658
\(188\) 0 0
\(189\) 5.38254 0.391523
\(190\) 0 0
\(191\) 17.2186 1.24589 0.622946 0.782265i \(-0.285935\pi\)
0.622946 + 0.782265i \(0.285935\pi\)
\(192\) 0 0
\(193\) −18.2319 −1.31236 −0.656179 0.754605i \(-0.727829\pi\)
−0.656179 + 0.754605i \(0.727829\pi\)
\(194\) 0 0
\(195\) 3.67749 0.263351
\(196\) 0 0
\(197\) 23.6356 1.68397 0.841983 0.539504i \(-0.181388\pi\)
0.841983 + 0.539504i \(0.181388\pi\)
\(198\) 0 0
\(199\) −23.6424 −1.67597 −0.837983 0.545696i \(-0.816265\pi\)
−0.837983 + 0.545696i \(0.816265\pi\)
\(200\) 0 0
\(201\) −9.13848 −0.644579
\(202\) 0 0
\(203\) 2.51163 0.176282
\(204\) 0 0
\(205\) −2.09938 −0.146627
\(206\) 0 0
\(207\) −2.49103 −0.173138
\(208\) 0 0
\(209\) −5.11526 −0.353830
\(210\) 0 0
\(211\) −3.74551 −0.257852 −0.128926 0.991654i \(-0.541153\pi\)
−0.128926 + 0.991654i \(0.541153\pi\)
\(212\) 0 0
\(213\) 8.03261 0.550385
\(214\) 0 0
\(215\) −21.3571 −1.45654
\(216\) 0 0
\(217\) 7.49076 0.508506
\(218\) 0 0
\(219\) −6.45586 −0.436247
\(220\) 0 0
\(221\) 5.49259 0.369472
\(222\) 0 0
\(223\) 22.3938 1.49960 0.749801 0.661664i \(-0.230149\pi\)
0.749801 + 0.661664i \(0.230149\pi\)
\(224\) 0 0
\(225\) −8.69628 −0.579752
\(226\) 0 0
\(227\) −25.7624 −1.70991 −0.854956 0.518701i \(-0.826416\pi\)
−0.854956 + 0.518701i \(0.826416\pi\)
\(228\) 0 0
\(229\) 0.0318014 0.00210149 0.00105075 0.999999i \(-0.499666\pi\)
0.00105075 + 0.999999i \(0.499666\pi\)
\(230\) 0 0
\(231\) −1.15169 −0.0757755
\(232\) 0 0
\(233\) 5.22987 0.342620 0.171310 0.985217i \(-0.445200\pi\)
0.171310 + 0.985217i \(0.445200\pi\)
\(234\) 0 0
\(235\) −9.24116 −0.602827
\(236\) 0 0
\(237\) 9.90566 0.643442
\(238\) 0 0
\(239\) 15.9016 1.02859 0.514296 0.857613i \(-0.328053\pi\)
0.514296 + 0.857613i \(0.328053\pi\)
\(240\) 0 0
\(241\) 20.6146 1.32790 0.663952 0.747776i \(-0.268878\pi\)
0.663952 + 0.747776i \(0.268878\pi\)
\(242\) 0 0
\(243\) 14.7908 0.948828
\(244\) 0 0
\(245\) −3.19313 −0.204002
\(246\) 0 0
\(247\) 5.11526 0.325476
\(248\) 0 0
\(249\) 16.4981 1.04552
\(250\) 0 0
\(251\) 16.2958 1.02858 0.514292 0.857615i \(-0.328055\pi\)
0.514292 + 0.857615i \(0.328055\pi\)
\(252\) 0 0
\(253\) 1.48841 0.0935755
\(254\) 0 0
\(255\) 20.1990 1.26491
\(256\) 0 0
\(257\) −8.81802 −0.550053 −0.275026 0.961437i \(-0.588687\pi\)
−0.275026 + 0.961437i \(0.588687\pi\)
\(258\) 0 0
\(259\) −4.43821 −0.275777
\(260\) 0 0
\(261\) 4.20350 0.260190
\(262\) 0 0
\(263\) 5.91886 0.364972 0.182486 0.983208i \(-0.441586\pi\)
0.182486 + 0.983208i \(0.441586\pi\)
\(264\) 0 0
\(265\) 10.4069 0.639293
\(266\) 0 0
\(267\) −10.4127 −0.637247
\(268\) 0 0
\(269\) −3.12063 −0.190268 −0.0951341 0.995464i \(-0.530328\pi\)
−0.0951341 + 0.995464i \(0.530328\pi\)
\(270\) 0 0
\(271\) −7.75129 −0.470858 −0.235429 0.971892i \(-0.575649\pi\)
−0.235429 + 0.971892i \(0.575649\pi\)
\(272\) 0 0
\(273\) 1.15169 0.0697033
\(274\) 0 0
\(275\) 5.19610 0.313337
\(276\) 0 0
\(277\) −11.0217 −0.662227 −0.331113 0.943591i \(-0.607424\pi\)
−0.331113 + 0.943591i \(0.607424\pi\)
\(278\) 0 0
\(279\) 12.5367 0.750550
\(280\) 0 0
\(281\) 14.8628 0.886643 0.443321 0.896363i \(-0.353800\pi\)
0.443321 + 0.896363i \(0.353800\pi\)
\(282\) 0 0
\(283\) 11.6996 0.695467 0.347734 0.937593i \(-0.386951\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(284\) 0 0
\(285\) 18.8113 1.11429
\(286\) 0 0
\(287\) −0.657467 −0.0388090
\(288\) 0 0
\(289\) 13.1685 0.774621
\(290\) 0 0
\(291\) 8.96412 0.525486
\(292\) 0 0
\(293\) 3.94767 0.230625 0.115313 0.993329i \(-0.463213\pi\)
0.115313 + 0.993329i \(0.463213\pi\)
\(294\) 0 0
\(295\) −11.3698 −0.661975
\(296\) 0 0
\(297\) −5.38254 −0.312327
\(298\) 0 0
\(299\) −1.48841 −0.0860770
\(300\) 0 0
\(301\) −6.68846 −0.385516
\(302\) 0 0
\(303\) −7.84467 −0.450664
\(304\) 0 0
\(305\) 34.9490 2.00118
\(306\) 0 0
\(307\) 16.6040 0.947638 0.473819 0.880622i \(-0.342875\pi\)
0.473819 + 0.880622i \(0.342875\pi\)
\(308\) 0 0
\(309\) 12.2192 0.695123
\(310\) 0 0
\(311\) 0.516275 0.0292753 0.0146376 0.999893i \(-0.495341\pi\)
0.0146376 + 0.999893i \(0.495341\pi\)
\(312\) 0 0
\(313\) 22.5348 1.27374 0.636870 0.770971i \(-0.280229\pi\)
0.636870 + 0.770971i \(0.280229\pi\)
\(314\) 0 0
\(315\) −5.34408 −0.301105
\(316\) 0 0
\(317\) −6.65100 −0.373558 −0.186779 0.982402i \(-0.559805\pi\)
−0.186779 + 0.982402i \(0.559805\pi\)
\(318\) 0 0
\(319\) −2.51163 −0.140624
\(320\) 0 0
\(321\) 2.91092 0.162472
\(322\) 0 0
\(323\) 28.0960 1.56331
\(324\) 0 0
\(325\) −5.19610 −0.288228
\(326\) 0 0
\(327\) 16.1301 0.891995
\(328\) 0 0
\(329\) −2.89407 −0.159555
\(330\) 0 0
\(331\) −33.3581 −1.83353 −0.916764 0.399429i \(-0.869208\pi\)
−0.916764 + 0.399429i \(0.869208\pi\)
\(332\) 0 0
\(333\) −7.42786 −0.407044
\(334\) 0 0
\(335\) 25.3371 1.38431
\(336\) 0 0
\(337\) −16.0788 −0.875868 −0.437934 0.899007i \(-0.644290\pi\)
−0.437934 + 0.899007i \(0.644290\pi\)
\(338\) 0 0
\(339\) −20.8384 −1.13179
\(340\) 0 0
\(341\) −7.49076 −0.405647
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −5.47361 −0.294690
\(346\) 0 0
\(347\) −23.6214 −1.26806 −0.634031 0.773308i \(-0.718601\pi\)
−0.634031 + 0.773308i \(0.718601\pi\)
\(348\) 0 0
\(349\) 7.41847 0.397102 0.198551 0.980091i \(-0.436377\pi\)
0.198551 + 0.980091i \(0.436377\pi\)
\(350\) 0 0
\(351\) 5.38254 0.287299
\(352\) 0 0
\(353\) 23.8417 1.26897 0.634483 0.772937i \(-0.281213\pi\)
0.634483 + 0.772937i \(0.281213\pi\)
\(354\) 0 0
\(355\) −22.2710 −1.18202
\(356\) 0 0
\(357\) 6.32575 0.334794
\(358\) 0 0
\(359\) 27.6605 1.45986 0.729931 0.683520i \(-0.239552\pi\)
0.729931 + 0.683520i \(0.239552\pi\)
\(360\) 0 0
\(361\) 7.16592 0.377154
\(362\) 0 0
\(363\) 1.15169 0.0604479
\(364\) 0 0
\(365\) 17.8993 0.936893
\(366\) 0 0
\(367\) −3.24550 −0.169414 −0.0847068 0.996406i \(-0.526995\pi\)
−0.0847068 + 0.996406i \(0.526995\pi\)
\(368\) 0 0
\(369\) −1.10035 −0.0572818
\(370\) 0 0
\(371\) 3.25916 0.169207
\(372\) 0 0
\(373\) −17.4106 −0.901484 −0.450742 0.892654i \(-0.648841\pi\)
−0.450742 + 0.892654i \(0.648841\pi\)
\(374\) 0 0
\(375\) −0.721161 −0.0372406
\(376\) 0 0
\(377\) 2.51163 0.129355
\(378\) 0 0
\(379\) 18.9886 0.975378 0.487689 0.873017i \(-0.337840\pi\)
0.487689 + 0.873017i \(0.337840\pi\)
\(380\) 0 0
\(381\) 8.16817 0.418468
\(382\) 0 0
\(383\) −6.84355 −0.349689 −0.174844 0.984596i \(-0.555942\pi\)
−0.174844 + 0.984596i \(0.555942\pi\)
\(384\) 0 0
\(385\) 3.19313 0.162737
\(386\) 0 0
\(387\) −11.1939 −0.569018
\(388\) 0 0
\(389\) 27.6909 1.40399 0.701993 0.712183i \(-0.252294\pi\)
0.701993 + 0.712183i \(0.252294\pi\)
\(390\) 0 0
\(391\) −8.17523 −0.413439
\(392\) 0 0
\(393\) 5.51703 0.278298
\(394\) 0 0
\(395\) −27.4641 −1.38187
\(396\) 0 0
\(397\) 4.04314 0.202919 0.101460 0.994840i \(-0.467649\pi\)
0.101460 + 0.994840i \(0.467649\pi\)
\(398\) 0 0
\(399\) 5.89118 0.294928
\(400\) 0 0
\(401\) −13.7722 −0.687750 −0.343875 0.939015i \(-0.611740\pi\)
−0.343875 + 0.939015i \(0.611740\pi\)
\(402\) 0 0
\(403\) 7.49076 0.373141
\(404\) 0 0
\(405\) 3.76202 0.186936
\(406\) 0 0
\(407\) 4.43821 0.219994
\(408\) 0 0
\(409\) 9.64938 0.477131 0.238566 0.971126i \(-0.423323\pi\)
0.238566 + 0.971126i \(0.423323\pi\)
\(410\) 0 0
\(411\) −12.5592 −0.619498
\(412\) 0 0
\(413\) −3.56070 −0.175211
\(414\) 0 0
\(415\) −45.7421 −2.24539
\(416\) 0 0
\(417\) −15.9453 −0.780847
\(418\) 0 0
\(419\) 34.4696 1.68395 0.841976 0.539515i \(-0.181392\pi\)
0.841976 + 0.539515i \(0.181392\pi\)
\(420\) 0 0
\(421\) 13.6190 0.663751 0.331875 0.943323i \(-0.392319\pi\)
0.331875 + 0.943323i \(0.392319\pi\)
\(422\) 0 0
\(423\) −4.84357 −0.235502
\(424\) 0 0
\(425\) −28.5401 −1.38440
\(426\) 0 0
\(427\) 10.9451 0.529668
\(428\) 0 0
\(429\) −1.15169 −0.0556040
\(430\) 0 0
\(431\) −7.89910 −0.380486 −0.190243 0.981737i \(-0.560928\pi\)
−0.190243 + 0.981737i \(0.560928\pi\)
\(432\) 0 0
\(433\) −18.1358 −0.871551 −0.435775 0.900056i \(-0.643526\pi\)
−0.435775 + 0.900056i \(0.643526\pi\)
\(434\) 0 0
\(435\) 9.23649 0.442856
\(436\) 0 0
\(437\) −7.61361 −0.364208
\(438\) 0 0
\(439\) 3.17686 0.151623 0.0758116 0.997122i \(-0.475845\pi\)
0.0758116 + 0.997122i \(0.475845\pi\)
\(440\) 0 0
\(441\) −1.67362 −0.0796960
\(442\) 0 0
\(443\) −8.62724 −0.409893 −0.204946 0.978773i \(-0.565702\pi\)
−0.204946 + 0.978773i \(0.565702\pi\)
\(444\) 0 0
\(445\) 28.8700 1.36857
\(446\) 0 0
\(447\) 11.3712 0.537841
\(448\) 0 0
\(449\) 40.5356 1.91299 0.956495 0.291747i \(-0.0942366\pi\)
0.956495 + 0.291747i \(0.0942366\pi\)
\(450\) 0 0
\(451\) 0.657467 0.0309589
\(452\) 0 0
\(453\) 19.3780 0.910458
\(454\) 0 0
\(455\) −3.19313 −0.149696
\(456\) 0 0
\(457\) −33.7129 −1.57702 −0.788512 0.615020i \(-0.789148\pi\)
−0.788512 + 0.615020i \(0.789148\pi\)
\(458\) 0 0
\(459\) 29.5641 1.37993
\(460\) 0 0
\(461\) 0.915513 0.0426397 0.0213199 0.999773i \(-0.493213\pi\)
0.0213199 + 0.999773i \(0.493213\pi\)
\(462\) 0 0
\(463\) 1.71416 0.0796639 0.0398319 0.999206i \(-0.487318\pi\)
0.0398319 + 0.999206i \(0.487318\pi\)
\(464\) 0 0
\(465\) 27.5472 1.27747
\(466\) 0 0
\(467\) 29.8740 1.38240 0.691201 0.722662i \(-0.257082\pi\)
0.691201 + 0.722662i \(0.257082\pi\)
\(468\) 0 0
\(469\) 7.93486 0.366398
\(470\) 0 0
\(471\) −9.11715 −0.420096
\(472\) 0 0
\(473\) 6.68846 0.307536
\(474\) 0 0
\(475\) −26.5794 −1.21955
\(476\) 0 0
\(477\) 5.45458 0.249748
\(478\) 0 0
\(479\) 5.95888 0.272268 0.136134 0.990690i \(-0.456532\pi\)
0.136134 + 0.990690i \(0.456532\pi\)
\(480\) 0 0
\(481\) −4.43821 −0.202365
\(482\) 0 0
\(483\) −1.71418 −0.0779980
\(484\) 0 0
\(485\) −24.8537 −1.12855
\(486\) 0 0
\(487\) 14.6419 0.663487 0.331743 0.943370i \(-0.392363\pi\)
0.331743 + 0.943370i \(0.392363\pi\)
\(488\) 0 0
\(489\) −5.24778 −0.237313
\(490\) 0 0
\(491\) 5.47310 0.246997 0.123499 0.992345i \(-0.460589\pi\)
0.123499 + 0.992345i \(0.460589\pi\)
\(492\) 0 0
\(493\) 13.7953 0.621311
\(494\) 0 0
\(495\) 5.34408 0.240199
\(496\) 0 0
\(497\) −6.97464 −0.312855
\(498\) 0 0
\(499\) −12.1550 −0.544131 −0.272066 0.962279i \(-0.587707\pi\)
−0.272066 + 0.962279i \(0.587707\pi\)
\(500\) 0 0
\(501\) −16.8030 −0.750704
\(502\) 0 0
\(503\) −21.7857 −0.971375 −0.485687 0.874133i \(-0.661431\pi\)
−0.485687 + 0.874133i \(0.661431\pi\)
\(504\) 0 0
\(505\) 21.7499 0.967857
\(506\) 0 0
\(507\) 1.15169 0.0511482
\(508\) 0 0
\(509\) 31.0660 1.37697 0.688487 0.725249i \(-0.258275\pi\)
0.688487 + 0.725249i \(0.258275\pi\)
\(510\) 0 0
\(511\) 5.60557 0.247976
\(512\) 0 0
\(513\) 27.5331 1.21562
\(514\) 0 0
\(515\) −33.8784 −1.49286
\(516\) 0 0
\(517\) 2.89407 0.127281
\(518\) 0 0
\(519\) 6.60340 0.289857
\(520\) 0 0
\(521\) 4.80836 0.210658 0.105329 0.994437i \(-0.466410\pi\)
0.105329 + 0.994437i \(0.466410\pi\)
\(522\) 0 0
\(523\) 22.1847 0.970069 0.485035 0.874495i \(-0.338807\pi\)
0.485035 + 0.874495i \(0.338807\pi\)
\(524\) 0 0
\(525\) −5.98428 −0.261176
\(526\) 0 0
\(527\) 41.1437 1.79225
\(528\) 0 0
\(529\) −20.7846 −0.903680
\(530\) 0 0
\(531\) −5.95925 −0.258610
\(532\) 0 0
\(533\) −0.657467 −0.0284781
\(534\) 0 0
\(535\) −8.07074 −0.348928
\(536\) 0 0
\(537\) 7.26598 0.313550
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −9.47073 −0.407179 −0.203589 0.979056i \(-0.565261\pi\)
−0.203589 + 0.979056i \(0.565261\pi\)
\(542\) 0 0
\(543\) −10.6001 −0.454895
\(544\) 0 0
\(545\) −44.7218 −1.91567
\(546\) 0 0
\(547\) 23.9926 1.02585 0.512925 0.858433i \(-0.328562\pi\)
0.512925 + 0.858433i \(0.328562\pi\)
\(548\) 0 0
\(549\) 18.3178 0.781786
\(550\) 0 0
\(551\) 12.8476 0.547328
\(552\) 0 0
\(553\) −8.60100 −0.365752
\(554\) 0 0
\(555\) −16.3215 −0.692808
\(556\) 0 0
\(557\) 31.9648 1.35439 0.677197 0.735802i \(-0.263195\pi\)
0.677197 + 0.735802i \(0.263195\pi\)
\(558\) 0 0
\(559\) −6.68846 −0.282892
\(560\) 0 0
\(561\) −6.32575 −0.267073
\(562\) 0 0
\(563\) −34.2755 −1.44454 −0.722270 0.691612i \(-0.756901\pi\)
−0.722270 + 0.691612i \(0.756901\pi\)
\(564\) 0 0
\(565\) 57.7759 2.43065
\(566\) 0 0
\(567\) 1.17816 0.0494780
\(568\) 0 0
\(569\) 3.97784 0.166760 0.0833798 0.996518i \(-0.473429\pi\)
0.0833798 + 0.996518i \(0.473429\pi\)
\(570\) 0 0
\(571\) −15.1454 −0.633816 −0.316908 0.948456i \(-0.602645\pi\)
−0.316908 + 0.948456i \(0.602645\pi\)
\(572\) 0 0
\(573\) 19.8304 0.828428
\(574\) 0 0
\(575\) 7.73393 0.322527
\(576\) 0 0
\(577\) 32.2893 1.34422 0.672110 0.740451i \(-0.265388\pi\)
0.672110 + 0.740451i \(0.265388\pi\)
\(578\) 0 0
\(579\) −20.9974 −0.872623
\(580\) 0 0
\(581\) −14.3251 −0.594307
\(582\) 0 0
\(583\) −3.25916 −0.134981
\(584\) 0 0
\(585\) −5.34408 −0.220951
\(586\) 0 0
\(587\) 12.6327 0.521406 0.260703 0.965419i \(-0.416046\pi\)
0.260703 + 0.965419i \(0.416046\pi\)
\(588\) 0 0
\(589\) 38.3172 1.57883
\(590\) 0 0
\(591\) 27.2208 1.11971
\(592\) 0 0
\(593\) 5.03913 0.206932 0.103466 0.994633i \(-0.467007\pi\)
0.103466 + 0.994633i \(0.467007\pi\)
\(594\) 0 0
\(595\) −17.5386 −0.719011
\(596\) 0 0
\(597\) −27.2287 −1.11440
\(598\) 0 0
\(599\) 6.73471 0.275173 0.137586 0.990490i \(-0.456066\pi\)
0.137586 + 0.990490i \(0.456066\pi\)
\(600\) 0 0
\(601\) 30.5674 1.24687 0.623436 0.781875i \(-0.285736\pi\)
0.623436 + 0.781875i \(0.285736\pi\)
\(602\) 0 0
\(603\) 13.2799 0.540800
\(604\) 0 0
\(605\) −3.19313 −0.129819
\(606\) 0 0
\(607\) 10.8667 0.441067 0.220533 0.975379i \(-0.429220\pi\)
0.220533 + 0.975379i \(0.429220\pi\)
\(608\) 0 0
\(609\) 2.89261 0.117214
\(610\) 0 0
\(611\) −2.89407 −0.117082
\(612\) 0 0
\(613\) −18.4609 −0.745629 −0.372814 0.927906i \(-0.621607\pi\)
−0.372814 + 0.927906i \(0.621607\pi\)
\(614\) 0 0
\(615\) −2.41783 −0.0974963
\(616\) 0 0
\(617\) −14.3895 −0.579301 −0.289651 0.957132i \(-0.593539\pi\)
−0.289651 + 0.957132i \(0.593539\pi\)
\(618\) 0 0
\(619\) −32.0020 −1.28627 −0.643135 0.765753i \(-0.722367\pi\)
−0.643135 + 0.765753i \(0.722367\pi\)
\(620\) 0 0
\(621\) −8.01143 −0.321488
\(622\) 0 0
\(623\) 9.04126 0.362230
\(624\) 0 0
\(625\) −23.9810 −0.959242
\(626\) 0 0
\(627\) −5.89118 −0.235271
\(628\) 0 0
\(629\) −24.3773 −0.971986
\(630\) 0 0
\(631\) 3.86188 0.153739 0.0768694 0.997041i \(-0.475508\pi\)
0.0768694 + 0.997041i \(0.475508\pi\)
\(632\) 0 0
\(633\) −4.31366 −0.171453
\(634\) 0 0
\(635\) −22.6468 −0.898712
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −11.6729 −0.461772
\(640\) 0 0
\(641\) −41.6474 −1.64498 −0.822488 0.568783i \(-0.807414\pi\)
−0.822488 + 0.568783i \(0.807414\pi\)
\(642\) 0 0
\(643\) −33.8908 −1.33652 −0.668261 0.743927i \(-0.732961\pi\)
−0.668261 + 0.743927i \(0.732961\pi\)
\(644\) 0 0
\(645\) −24.5967 −0.968496
\(646\) 0 0
\(647\) −31.6688 −1.24503 −0.622515 0.782608i \(-0.713889\pi\)
−0.622515 + 0.782608i \(0.713889\pi\)
\(648\) 0 0
\(649\) 3.56070 0.139770
\(650\) 0 0
\(651\) 8.62701 0.338119
\(652\) 0 0
\(653\) −34.0158 −1.33114 −0.665572 0.746334i \(-0.731812\pi\)
−0.665572 + 0.746334i \(0.731812\pi\)
\(654\) 0 0
\(655\) −15.2964 −0.597678
\(656\) 0 0
\(657\) 9.38157 0.366010
\(658\) 0 0
\(659\) −7.03109 −0.273892 −0.136946 0.990578i \(-0.543729\pi\)
−0.136946 + 0.990578i \(0.543729\pi\)
\(660\) 0 0
\(661\) 17.1479 0.666975 0.333487 0.942755i \(-0.391775\pi\)
0.333487 + 0.942755i \(0.391775\pi\)
\(662\) 0 0
\(663\) 6.32575 0.245672
\(664\) 0 0
\(665\) −16.3337 −0.633394
\(666\) 0 0
\(667\) −3.73833 −0.144749
\(668\) 0 0
\(669\) 25.7907 0.997125
\(670\) 0 0
\(671\) −10.9451 −0.422529
\(672\) 0 0
\(673\) 1.45446 0.0560655 0.0280327 0.999607i \(-0.491076\pi\)
0.0280327 + 0.999607i \(0.491076\pi\)
\(674\) 0 0
\(675\) −27.9682 −1.07650
\(676\) 0 0
\(677\) −4.48851 −0.172507 −0.0862537 0.996273i \(-0.527490\pi\)
−0.0862537 + 0.996273i \(0.527490\pi\)
\(678\) 0 0
\(679\) −7.78347 −0.298702
\(680\) 0 0
\(681\) −29.6702 −1.13697
\(682\) 0 0
\(683\) −14.5046 −0.555005 −0.277502 0.960725i \(-0.589507\pi\)
−0.277502 + 0.960725i \(0.589507\pi\)
\(684\) 0 0
\(685\) 34.8212 1.33045
\(686\) 0 0
\(687\) 0.0366252 0.00139734
\(688\) 0 0
\(689\) 3.25916 0.124164
\(690\) 0 0
\(691\) −24.3588 −0.926652 −0.463326 0.886188i \(-0.653344\pi\)
−0.463326 + 0.886188i \(0.653344\pi\)
\(692\) 0 0
\(693\) 1.67362 0.0635754
\(694\) 0 0
\(695\) 44.2096 1.67696
\(696\) 0 0
\(697\) −3.61120 −0.136784
\(698\) 0 0
\(699\) 6.02317 0.227817
\(700\) 0 0
\(701\) 0.580261 0.0219162 0.0109581 0.999940i \(-0.496512\pi\)
0.0109581 + 0.999940i \(0.496512\pi\)
\(702\) 0 0
\(703\) −22.7026 −0.856245
\(704\) 0 0
\(705\) −10.6429 −0.400836
\(706\) 0 0
\(707\) 6.81145 0.256171
\(708\) 0 0
\(709\) −18.3983 −0.690961 −0.345481 0.938426i \(-0.612284\pi\)
−0.345481 + 0.938426i \(0.612284\pi\)
\(710\) 0 0
\(711\) −14.3948 −0.539846
\(712\) 0 0
\(713\) −11.1493 −0.417545
\(714\) 0 0
\(715\) 3.19313 0.119416
\(716\) 0 0
\(717\) 18.3137 0.683938
\(718\) 0 0
\(719\) 4.22821 0.157685 0.0788427 0.996887i \(-0.474878\pi\)
0.0788427 + 0.996887i \(0.474878\pi\)
\(720\) 0 0
\(721\) −10.6098 −0.395129
\(722\) 0 0
\(723\) 23.7416 0.882959
\(724\) 0 0
\(725\) −13.0507 −0.484690
\(726\) 0 0
\(727\) 18.0197 0.668313 0.334156 0.942518i \(-0.391549\pi\)
0.334156 + 0.942518i \(0.391549\pi\)
\(728\) 0 0
\(729\) 20.5688 0.761808
\(730\) 0 0
\(731\) −36.7370 −1.35877
\(732\) 0 0
\(733\) 48.5080 1.79169 0.895843 0.444371i \(-0.146573\pi\)
0.895843 + 0.444371i \(0.146573\pi\)
\(734\) 0 0
\(735\) −3.67749 −0.135646
\(736\) 0 0
\(737\) −7.93486 −0.292284
\(738\) 0 0
\(739\) −37.3878 −1.37533 −0.687667 0.726027i \(-0.741365\pi\)
−0.687667 + 0.726027i \(0.741365\pi\)
\(740\) 0 0
\(741\) 5.89118 0.216418
\(742\) 0 0
\(743\) 0.0895219 0.00328424 0.00164212 0.999999i \(-0.499477\pi\)
0.00164212 + 0.999999i \(0.499477\pi\)
\(744\) 0 0
\(745\) −31.5275 −1.15508
\(746\) 0 0
\(747\) −23.9748 −0.877192
\(748\) 0 0
\(749\) −2.52753 −0.0923539
\(750\) 0 0
\(751\) −30.3163 −1.10626 −0.553129 0.833095i \(-0.686566\pi\)
−0.553129 + 0.833095i \(0.686566\pi\)
\(752\) 0 0
\(753\) 18.7677 0.683933
\(754\) 0 0
\(755\) −53.7269 −1.95532
\(756\) 0 0
\(757\) −23.0525 −0.837858 −0.418929 0.908019i \(-0.637594\pi\)
−0.418929 + 0.908019i \(0.637594\pi\)
\(758\) 0 0
\(759\) 1.71418 0.0622209
\(760\) 0 0
\(761\) 0.337876 0.0122480 0.00612400 0.999981i \(-0.498051\pi\)
0.00612400 + 0.999981i \(0.498051\pi\)
\(762\) 0 0
\(763\) −14.0056 −0.507037
\(764\) 0 0
\(765\) −29.3528 −1.06125
\(766\) 0 0
\(767\) −3.56070 −0.128570
\(768\) 0 0
\(769\) 2.15926 0.0778650 0.0389325 0.999242i \(-0.487604\pi\)
0.0389325 + 0.999242i \(0.487604\pi\)
\(770\) 0 0
\(771\) −10.1556 −0.365745
\(772\) 0 0
\(773\) 38.9587 1.40125 0.700623 0.713532i \(-0.252905\pi\)
0.700623 + 0.713532i \(0.252905\pi\)
\(774\) 0 0
\(775\) −38.9228 −1.39815
\(776\) 0 0
\(777\) −5.11143 −0.183372
\(778\) 0 0
\(779\) −3.36312 −0.120496
\(780\) 0 0
\(781\) 6.97464 0.249572
\(782\) 0 0
\(783\) 13.5189 0.483128
\(784\) 0 0
\(785\) 25.2779 0.902209
\(786\) 0 0
\(787\) −16.4751 −0.587274 −0.293637 0.955917i \(-0.594866\pi\)
−0.293637 + 0.955917i \(0.594866\pi\)
\(788\) 0 0
\(789\) 6.81667 0.242680
\(790\) 0 0
\(791\) 18.0938 0.643341
\(792\) 0 0
\(793\) 10.9451 0.388670
\(794\) 0 0
\(795\) 11.9855 0.425083
\(796\) 0 0
\(797\) −11.6125 −0.411337 −0.205668 0.978622i \(-0.565937\pi\)
−0.205668 + 0.978622i \(0.565937\pi\)
\(798\) 0 0
\(799\) −15.8959 −0.562358
\(800\) 0 0
\(801\) 15.1316 0.534649
\(802\) 0 0
\(803\) −5.60557 −0.197816
\(804\) 0 0
\(805\) 4.75269 0.167510
\(806\) 0 0
\(807\) −3.59399 −0.126514
\(808\) 0 0
\(809\) 28.2585 0.993516 0.496758 0.867889i \(-0.334524\pi\)
0.496758 + 0.867889i \(0.334524\pi\)
\(810\) 0 0
\(811\) −42.8226 −1.50371 −0.751853 0.659331i \(-0.770840\pi\)
−0.751853 + 0.659331i \(0.770840\pi\)
\(812\) 0 0
\(813\) −8.92707 −0.313086
\(814\) 0 0
\(815\) 14.5498 0.509659
\(816\) 0 0
\(817\) −34.2132 −1.19697
\(818\) 0 0
\(819\) −1.67362 −0.0584809
\(820\) 0 0
\(821\) −54.7578 −1.91106 −0.955530 0.294892i \(-0.904716\pi\)
−0.955530 + 0.294892i \(0.904716\pi\)
\(822\) 0 0
\(823\) −15.8240 −0.551591 −0.275796 0.961216i \(-0.588941\pi\)
−0.275796 + 0.961216i \(0.588941\pi\)
\(824\) 0 0
\(825\) 5.98428 0.208346
\(826\) 0 0
\(827\) 25.6261 0.891107 0.445553 0.895255i \(-0.353007\pi\)
0.445553 + 0.895255i \(0.353007\pi\)
\(828\) 0 0
\(829\) −46.2982 −1.60800 −0.804002 0.594626i \(-0.797300\pi\)
−0.804002 + 0.594626i \(0.797300\pi\)
\(830\) 0 0
\(831\) −12.6935 −0.440332
\(832\) 0 0
\(833\) −5.49259 −0.190307
\(834\) 0 0
\(835\) 46.5875 1.61223
\(836\) 0 0
\(837\) 40.3194 1.39364
\(838\) 0 0
\(839\) −9.83308 −0.339476 −0.169738 0.985489i \(-0.554292\pi\)
−0.169738 + 0.985489i \(0.554292\pi\)
\(840\) 0 0
\(841\) −22.6917 −0.782473
\(842\) 0 0
\(843\) 17.1173 0.589553
\(844\) 0 0
\(845\) −3.19313 −0.109847
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 13.4742 0.462435
\(850\) 0 0
\(851\) 6.60588 0.226447
\(852\) 0 0
\(853\) −30.7939 −1.05436 −0.527182 0.849753i \(-0.676751\pi\)
−0.527182 + 0.849753i \(0.676751\pi\)
\(854\) 0 0
\(855\) −27.3364 −0.934885
\(856\) 0 0
\(857\) 48.2402 1.64785 0.823927 0.566696i \(-0.191779\pi\)
0.823927 + 0.566696i \(0.191779\pi\)
\(858\) 0 0
\(859\) −40.9383 −1.39680 −0.698398 0.715709i \(-0.746104\pi\)
−0.698398 + 0.715709i \(0.746104\pi\)
\(860\) 0 0
\(861\) −0.757196 −0.0258052
\(862\) 0 0
\(863\) 12.0303 0.409516 0.204758 0.978813i \(-0.434359\pi\)
0.204758 + 0.978813i \(0.434359\pi\)
\(864\) 0 0
\(865\) −18.3084 −0.622503
\(866\) 0 0
\(867\) 15.1661 0.515066
\(868\) 0 0
\(869\) 8.60100 0.291769
\(870\) 0 0
\(871\) 7.93486 0.268863
\(872\) 0 0
\(873\) −13.0265 −0.440882
\(874\) 0 0
\(875\) 0.626178 0.0211687
\(876\) 0 0
\(877\) 21.5528 0.727785 0.363892 0.931441i \(-0.381448\pi\)
0.363892 + 0.931441i \(0.381448\pi\)
\(878\) 0 0
\(879\) 4.54648 0.153349
\(880\) 0 0
\(881\) 43.1277 1.45301 0.726505 0.687161i \(-0.241143\pi\)
0.726505 + 0.687161i \(0.241143\pi\)
\(882\) 0 0
\(883\) 13.3391 0.448897 0.224449 0.974486i \(-0.427942\pi\)
0.224449 + 0.974486i \(0.427942\pi\)
\(884\) 0 0
\(885\) −13.0945 −0.440165
\(886\) 0 0
\(887\) −8.25494 −0.277174 −0.138587 0.990350i \(-0.544256\pi\)
−0.138587 + 0.990350i \(0.544256\pi\)
\(888\) 0 0
\(889\) −7.09235 −0.237870
\(890\) 0 0
\(891\) −1.17816 −0.0394698
\(892\) 0 0
\(893\) −14.8039 −0.495395
\(894\) 0 0
\(895\) −20.1454 −0.673388
\(896\) 0 0
\(897\) −1.71418 −0.0572349
\(898\) 0 0
\(899\) 18.8140 0.627482
\(900\) 0 0
\(901\) 17.9012 0.596376
\(902\) 0 0
\(903\) −7.70301 −0.256340
\(904\) 0 0
\(905\) 29.3896 0.976943
\(906\) 0 0
\(907\) −47.1844 −1.56673 −0.783366 0.621561i \(-0.786499\pi\)
−0.783366 + 0.621561i \(0.786499\pi\)
\(908\) 0 0
\(909\) 11.3998 0.378106
\(910\) 0 0
\(911\) 20.4782 0.678474 0.339237 0.940701i \(-0.389831\pi\)
0.339237 + 0.940701i \(0.389831\pi\)
\(912\) 0 0
\(913\) 14.3251 0.474093
\(914\) 0 0
\(915\) 40.2504 1.33064
\(916\) 0 0
\(917\) −4.79039 −0.158193
\(918\) 0 0
\(919\) −1.84653 −0.0609115 −0.0304558 0.999536i \(-0.509696\pi\)
−0.0304558 + 0.999536i \(0.509696\pi\)
\(920\) 0 0
\(921\) 19.1226 0.630110
\(922\) 0 0
\(923\) −6.97464 −0.229573
\(924\) 0 0
\(925\) 23.0614 0.758254
\(926\) 0 0
\(927\) −17.7567 −0.583207
\(928\) 0 0
\(929\) −4.88976 −0.160428 −0.0802140 0.996778i \(-0.525560\pi\)
−0.0802140 + 0.996778i \(0.525560\pi\)
\(930\) 0 0
\(931\) −5.11526 −0.167646
\(932\) 0 0
\(933\) 0.594587 0.0194659
\(934\) 0 0
\(935\) 17.5386 0.573573
\(936\) 0 0
\(937\) 13.7300 0.448539 0.224269 0.974527i \(-0.428000\pi\)
0.224269 + 0.974527i \(0.428000\pi\)
\(938\) 0 0
\(939\) 25.9530 0.846944
\(940\) 0 0
\(941\) 8.82281 0.287616 0.143808 0.989606i \(-0.454065\pi\)
0.143808 + 0.989606i \(0.454065\pi\)
\(942\) 0 0
\(943\) 0.978580 0.0318670
\(944\) 0 0
\(945\) −17.1872 −0.559099
\(946\) 0 0
\(947\) −24.5390 −0.797410 −0.398705 0.917079i \(-0.630540\pi\)
−0.398705 + 0.917079i \(0.630540\pi\)
\(948\) 0 0
\(949\) 5.60557 0.181964
\(950\) 0 0
\(951\) −7.65988 −0.248389
\(952\) 0 0
\(953\) 24.4194 0.791023 0.395511 0.918461i \(-0.370567\pi\)
0.395511 + 0.918461i \(0.370567\pi\)
\(954\) 0 0
\(955\) −54.9812 −1.77915
\(956\) 0 0
\(957\) −2.89261 −0.0935048
\(958\) 0 0
\(959\) 10.9050 0.352141
\(960\) 0 0
\(961\) 25.1115 0.810048
\(962\) 0 0
\(963\) −4.23011 −0.136313
\(964\) 0 0
\(965\) 58.2168 1.87407
\(966\) 0 0
\(967\) 34.2066 1.10001 0.550005 0.835161i \(-0.314626\pi\)
0.550005 + 0.835161i \(0.314626\pi\)
\(968\) 0 0
\(969\) 32.3579 1.03948
\(970\) 0 0
\(971\) −41.5267 −1.33266 −0.666328 0.745659i \(-0.732135\pi\)
−0.666328 + 0.745659i \(0.732135\pi\)
\(972\) 0 0
\(973\) 13.8452 0.443857
\(974\) 0 0
\(975\) −5.98428 −0.191650
\(976\) 0 0
\(977\) −8.08981 −0.258816 −0.129408 0.991591i \(-0.541308\pi\)
−0.129408 + 0.991591i \(0.541308\pi\)
\(978\) 0 0
\(979\) −9.04126 −0.288960
\(980\) 0 0
\(981\) −23.4400 −0.748382
\(982\) 0 0
\(983\) 8.93745 0.285060 0.142530 0.989790i \(-0.454476\pi\)
0.142530 + 0.989790i \(0.454476\pi\)
\(984\) 0 0
\(985\) −75.4716 −2.40472
\(986\) 0 0
\(987\) −3.33307 −0.106093
\(988\) 0 0
\(989\) 9.95516 0.316556
\(990\) 0 0
\(991\) 27.8666 0.885210 0.442605 0.896717i \(-0.354054\pi\)
0.442605 + 0.896717i \(0.354054\pi\)
\(992\) 0 0
\(993\) −38.4181 −1.21916
\(994\) 0 0
\(995\) 75.4934 2.39330
\(996\) 0 0
\(997\) −23.7592 −0.752461 −0.376231 0.926526i \(-0.622780\pi\)
−0.376231 + 0.926526i \(0.622780\pi\)
\(998\) 0 0
\(999\) −23.8889 −0.755810
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 \(a_p\))