Properties

Label 8008.2.a.y.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.52493\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52493 q^{3} +3.43935 q^{5} +1.00000 q^{7} +3.37528 q^{9} +O(q^{10})\) \(q-2.52493 q^{3} +3.43935 q^{5} +1.00000 q^{7} +3.37528 q^{9} -1.00000 q^{11} -1.00000 q^{13} -8.68412 q^{15} -6.56793 q^{17} +2.74521 q^{19} -2.52493 q^{21} -2.80225 q^{23} +6.82912 q^{25} -0.947546 q^{27} +0.240184 q^{29} +0.281315 q^{31} +2.52493 q^{33} +3.43935 q^{35} +5.95065 q^{37} +2.52493 q^{39} +11.4744 q^{41} -5.59622 q^{43} +11.6088 q^{45} -13.3176 q^{47} +1.00000 q^{49} +16.5836 q^{51} +3.03445 q^{53} -3.43935 q^{55} -6.93147 q^{57} -11.5644 q^{59} -0.183548 q^{61} +3.37528 q^{63} -3.43935 q^{65} +0.658984 q^{67} +7.07550 q^{69} -5.80420 q^{71} -8.78419 q^{73} -17.2431 q^{75} -1.00000 q^{77} -0.408207 q^{79} -7.73334 q^{81} -5.01797 q^{83} -22.5894 q^{85} -0.606448 q^{87} +3.72200 q^{89} -1.00000 q^{91} -0.710301 q^{93} +9.44174 q^{95} +1.91747 q^{97} -3.37528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) −2.52493 −1.45777 −0.728885 0.684636i \(-0.759961\pi\)
−0.728885 + 0.684636i \(0.759961\pi\)
\(4\) 0 0
\(5\) 3.43935 1.53812 0.769062 0.639174i \(-0.220724\pi\)
0.769062 + 0.639174i \(0.220724\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 3.37528 1.12509
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −8.68412 −2.24223
\(16\) 0 0
\(17\) −6.56793 −1.59296 −0.796478 0.604667i \(-0.793306\pi\)
−0.796478 + 0.604667i \(0.793306\pi\)
\(18\) 0 0
\(19\) 2.74521 0.629795 0.314897 0.949126i \(-0.398030\pi\)
0.314897 + 0.949126i \(0.398030\pi\)
\(20\) 0 0
\(21\) −2.52493 −0.550985
\(22\) 0 0
\(23\) −2.80225 −0.584310 −0.292155 0.956371i \(-0.594372\pi\)
−0.292155 + 0.956371i \(0.594372\pi\)
\(24\) 0 0
\(25\) 6.82912 1.36582
\(26\) 0 0
\(27\) −0.947546 −0.182355
\(28\) 0 0
\(29\) 0.240184 0.0446010 0.0223005 0.999751i \(-0.492901\pi\)
0.0223005 + 0.999751i \(0.492901\pi\)
\(30\) 0 0
\(31\) 0.281315 0.0505257 0.0252628 0.999681i \(-0.491958\pi\)
0.0252628 + 0.999681i \(0.491958\pi\)
\(32\) 0 0
\(33\) 2.52493 0.439534
\(34\) 0 0
\(35\) 3.43935 0.581356
\(36\) 0 0
\(37\) 5.95065 0.978281 0.489140 0.872205i \(-0.337311\pi\)
0.489140 + 0.872205i \(0.337311\pi\)
\(38\) 0 0
\(39\) 2.52493 0.404313
\(40\) 0 0
\(41\) 11.4744 1.79200 0.895998 0.444059i \(-0.146462\pi\)
0.895998 + 0.444059i \(0.146462\pi\)
\(42\) 0 0
\(43\) −5.59622 −0.853416 −0.426708 0.904389i \(-0.640327\pi\)
−0.426708 + 0.904389i \(0.640327\pi\)
\(44\) 0 0
\(45\) 11.6088 1.73053
\(46\) 0 0
\(47\) −13.3176 −1.94257 −0.971287 0.237912i \(-0.923537\pi\)
−0.971287 + 0.237912i \(0.923537\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 16.5836 2.32216
\(52\) 0 0
\(53\) 3.03445 0.416813 0.208407 0.978042i \(-0.433172\pi\)
0.208407 + 0.978042i \(0.433172\pi\)
\(54\) 0 0
\(55\) −3.43935 −0.463762
\(56\) 0 0
\(57\) −6.93147 −0.918095
\(58\) 0 0
\(59\) −11.5644 −1.50555 −0.752776 0.658276i \(-0.771286\pi\)
−0.752776 + 0.658276i \(0.771286\pi\)
\(60\) 0 0
\(61\) −0.183548 −0.0235009 −0.0117504 0.999931i \(-0.503740\pi\)
−0.0117504 + 0.999931i \(0.503740\pi\)
\(62\) 0 0
\(63\) 3.37528 0.425245
\(64\) 0 0
\(65\) −3.43935 −0.426599
\(66\) 0 0
\(67\) 0.658984 0.0805077 0.0402538 0.999189i \(-0.487183\pi\)
0.0402538 + 0.999189i \(0.487183\pi\)
\(68\) 0 0
\(69\) 7.07550 0.851790
\(70\) 0 0
\(71\) −5.80420 −0.688832 −0.344416 0.938817i \(-0.611923\pi\)
−0.344416 + 0.938817i \(0.611923\pi\)
\(72\) 0 0
\(73\) −8.78419 −1.02811 −0.514056 0.857757i \(-0.671858\pi\)
−0.514056 + 0.857757i \(0.671858\pi\)
\(74\) 0 0
\(75\) −17.2431 −1.99106
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −0.408207 −0.0459268 −0.0229634 0.999736i \(-0.507310\pi\)
−0.0229634 + 0.999736i \(0.507310\pi\)
\(80\) 0 0
\(81\) −7.73334 −0.859260
\(82\) 0 0
\(83\) −5.01797 −0.550794 −0.275397 0.961331i \(-0.588809\pi\)
−0.275397 + 0.961331i \(0.588809\pi\)
\(84\) 0 0
\(85\) −22.5894 −2.45016
\(86\) 0 0
\(87\) −0.606448 −0.0650180
\(88\) 0 0
\(89\) 3.72200 0.394532 0.197266 0.980350i \(-0.436794\pi\)
0.197266 + 0.980350i \(0.436794\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −0.710301 −0.0736548
\(94\) 0 0
\(95\) 9.44174 0.968702
\(96\) 0 0
\(97\) 1.91747 0.194689 0.0973447 0.995251i \(-0.468965\pi\)
0.0973447 + 0.995251i \(0.468965\pi\)
\(98\) 0 0
\(99\) −3.37528 −0.339228
\(100\) 0 0
\(101\) −0.841815 −0.0837637 −0.0418819 0.999123i \(-0.513335\pi\)
−0.0418819 + 0.999123i \(0.513335\pi\)
\(102\) 0 0
\(103\) 13.4270 1.32301 0.661503 0.749943i \(-0.269919\pi\)
0.661503 + 0.749943i \(0.269919\pi\)
\(104\) 0 0
\(105\) −8.68412 −0.847483
\(106\) 0 0
\(107\) −6.29003 −0.608080 −0.304040 0.952659i \(-0.598336\pi\)
−0.304040 + 0.952659i \(0.598336\pi\)
\(108\) 0 0
\(109\) 1.94525 0.186321 0.0931607 0.995651i \(-0.470303\pi\)
0.0931607 + 0.995651i \(0.470303\pi\)
\(110\) 0 0
\(111\) −15.0250 −1.42611
\(112\) 0 0
\(113\) −17.3415 −1.63135 −0.815674 0.578512i \(-0.803634\pi\)
−0.815674 + 0.578512i \(0.803634\pi\)
\(114\) 0 0
\(115\) −9.63793 −0.898741
\(116\) 0 0
\(117\) −3.37528 −0.312044
\(118\) 0 0
\(119\) −6.56793 −0.602081
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −28.9720 −2.61232
\(124\) 0 0
\(125\) 6.29100 0.562684
\(126\) 0 0
\(127\) −7.69408 −0.682740 −0.341370 0.939929i \(-0.610891\pi\)
−0.341370 + 0.939929i \(0.610891\pi\)
\(128\) 0 0
\(129\) 14.1301 1.24408
\(130\) 0 0
\(131\) −3.11125 −0.271831 −0.135915 0.990720i \(-0.543398\pi\)
−0.135915 + 0.990720i \(0.543398\pi\)
\(132\) 0 0
\(133\) 2.74521 0.238040
\(134\) 0 0
\(135\) −3.25894 −0.280485
\(136\) 0 0
\(137\) −1.81615 −0.155164 −0.0775822 0.996986i \(-0.524720\pi\)
−0.0775822 + 0.996986i \(0.524720\pi\)
\(138\) 0 0
\(139\) −5.63326 −0.477807 −0.238904 0.971043i \(-0.576788\pi\)
−0.238904 + 0.971043i \(0.576788\pi\)
\(140\) 0 0
\(141\) 33.6261 2.83182
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 0.826076 0.0686019
\(146\) 0 0
\(147\) −2.52493 −0.208253
\(148\) 0 0
\(149\) 13.2141 1.08254 0.541271 0.840848i \(-0.317943\pi\)
0.541271 + 0.840848i \(0.317943\pi\)
\(150\) 0 0
\(151\) 13.9976 1.13911 0.569554 0.821954i \(-0.307116\pi\)
0.569554 + 0.821954i \(0.307116\pi\)
\(152\) 0 0
\(153\) −22.1686 −1.79222
\(154\) 0 0
\(155\) 0.967541 0.0777148
\(156\) 0 0
\(157\) −3.59693 −0.287066 −0.143533 0.989645i \(-0.545846\pi\)
−0.143533 + 0.989645i \(0.545846\pi\)
\(158\) 0 0
\(159\) −7.66176 −0.607617
\(160\) 0 0
\(161\) −2.80225 −0.220849
\(162\) 0 0
\(163\) 2.82244 0.221071 0.110535 0.993872i \(-0.464743\pi\)
0.110535 + 0.993872i \(0.464743\pi\)
\(164\) 0 0
\(165\) 8.68412 0.676058
\(166\) 0 0
\(167\) −23.5586 −1.82302 −0.911511 0.411277i \(-0.865083\pi\)
−0.911511 + 0.411277i \(0.865083\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 9.26584 0.708577
\(172\) 0 0
\(173\) 2.55235 0.194052 0.0970259 0.995282i \(-0.469067\pi\)
0.0970259 + 0.995282i \(0.469067\pi\)
\(174\) 0 0
\(175\) 6.82912 0.516233
\(176\) 0 0
\(177\) 29.1992 2.19475
\(178\) 0 0
\(179\) −0.648782 −0.0484923 −0.0242461 0.999706i \(-0.507719\pi\)
−0.0242461 + 0.999706i \(0.507719\pi\)
\(180\) 0 0
\(181\) 14.5072 1.07831 0.539155 0.842207i \(-0.318744\pi\)
0.539155 + 0.842207i \(0.318744\pi\)
\(182\) 0 0
\(183\) 0.463445 0.0342589
\(184\) 0 0
\(185\) 20.4664 1.50472
\(186\) 0 0
\(187\) 6.56793 0.480294
\(188\) 0 0
\(189\) −0.947546 −0.0689238
\(190\) 0 0
\(191\) −15.5571 −1.12567 −0.562837 0.826568i \(-0.690290\pi\)
−0.562837 + 0.826568i \(0.690290\pi\)
\(192\) 0 0
\(193\) 17.9774 1.29404 0.647019 0.762474i \(-0.276015\pi\)
0.647019 + 0.762474i \(0.276015\pi\)
\(194\) 0 0
\(195\) 8.68412 0.621883
\(196\) 0 0
\(197\) −8.43697 −0.601109 −0.300555 0.953765i \(-0.597172\pi\)
−0.300555 + 0.953765i \(0.597172\pi\)
\(198\) 0 0
\(199\) 14.3769 1.01915 0.509575 0.860426i \(-0.329803\pi\)
0.509575 + 0.860426i \(0.329803\pi\)
\(200\) 0 0
\(201\) −1.66389 −0.117362
\(202\) 0 0
\(203\) 0.240184 0.0168576
\(204\) 0 0
\(205\) 39.4644 2.75631
\(206\) 0 0
\(207\) −9.45838 −0.657403
\(208\) 0 0
\(209\) −2.74521 −0.189890
\(210\) 0 0
\(211\) −5.79465 −0.398920 −0.199460 0.979906i \(-0.563919\pi\)
−0.199460 + 0.979906i \(0.563919\pi\)
\(212\) 0 0
\(213\) 14.6552 1.00416
\(214\) 0 0
\(215\) −19.2474 −1.31266
\(216\) 0 0
\(217\) 0.281315 0.0190969
\(218\) 0 0
\(219\) 22.1795 1.49875
\(220\) 0 0
\(221\) 6.56793 0.441807
\(222\) 0 0
\(223\) −23.1268 −1.54868 −0.774342 0.632767i \(-0.781919\pi\)
−0.774342 + 0.632767i \(0.781919\pi\)
\(224\) 0 0
\(225\) 23.0502 1.53668
\(226\) 0 0
\(227\) 11.8937 0.789410 0.394705 0.918808i \(-0.370847\pi\)
0.394705 + 0.918808i \(0.370847\pi\)
\(228\) 0 0
\(229\) −8.61599 −0.569361 −0.284680 0.958622i \(-0.591887\pi\)
−0.284680 + 0.958622i \(0.591887\pi\)
\(230\) 0 0
\(231\) 2.52493 0.166128
\(232\) 0 0
\(233\) −20.5697 −1.34756 −0.673781 0.738931i \(-0.735331\pi\)
−0.673781 + 0.738931i \(0.735331\pi\)
\(234\) 0 0
\(235\) −45.8039 −2.98792
\(236\) 0 0
\(237\) 1.03069 0.0669507
\(238\) 0 0
\(239\) −23.3524 −1.51054 −0.755269 0.655415i \(-0.772494\pi\)
−0.755269 + 0.655415i \(0.772494\pi\)
\(240\) 0 0
\(241\) −0.0162209 −0.00104488 −0.000522440 1.00000i \(-0.500166\pi\)
−0.000522440 1.00000i \(0.500166\pi\)
\(242\) 0 0
\(243\) 22.3688 1.43496
\(244\) 0 0
\(245\) 3.43935 0.219732
\(246\) 0 0
\(247\) −2.74521 −0.174674
\(248\) 0 0
\(249\) 12.6700 0.802931
\(250\) 0 0
\(251\) −15.2276 −0.961160 −0.480580 0.876951i \(-0.659574\pi\)
−0.480580 + 0.876951i \(0.659574\pi\)
\(252\) 0 0
\(253\) 2.80225 0.176176
\(254\) 0 0
\(255\) 57.0367 3.57177
\(256\) 0 0
\(257\) −5.29617 −0.330366 −0.165183 0.986263i \(-0.552822\pi\)
−0.165183 + 0.986263i \(0.552822\pi\)
\(258\) 0 0
\(259\) 5.95065 0.369755
\(260\) 0 0
\(261\) 0.810687 0.0501802
\(262\) 0 0
\(263\) 31.3030 1.93023 0.965113 0.261833i \(-0.0843271\pi\)
0.965113 + 0.261833i \(0.0843271\pi\)
\(264\) 0 0
\(265\) 10.4365 0.641110
\(266\) 0 0
\(267\) −9.39780 −0.575136
\(268\) 0 0
\(269\) 0.990063 0.0603652 0.0301826 0.999544i \(-0.490391\pi\)
0.0301826 + 0.999544i \(0.490391\pi\)
\(270\) 0 0
\(271\) 25.7198 1.56237 0.781183 0.624302i \(-0.214616\pi\)
0.781183 + 0.624302i \(0.214616\pi\)
\(272\) 0 0
\(273\) 2.52493 0.152816
\(274\) 0 0
\(275\) −6.82912 −0.411812
\(276\) 0 0
\(277\) −17.5474 −1.05432 −0.527159 0.849766i \(-0.676743\pi\)
−0.527159 + 0.849766i \(0.676743\pi\)
\(278\) 0 0
\(279\) 0.949516 0.0568460
\(280\) 0 0
\(281\) 5.54813 0.330974 0.165487 0.986212i \(-0.447080\pi\)
0.165487 + 0.986212i \(0.447080\pi\)
\(282\) 0 0
\(283\) −7.14592 −0.424781 −0.212390 0.977185i \(-0.568125\pi\)
−0.212390 + 0.977185i \(0.568125\pi\)
\(284\) 0 0
\(285\) −23.8397 −1.41214
\(286\) 0 0
\(287\) 11.4744 0.677311
\(288\) 0 0
\(289\) 26.1377 1.53751
\(290\) 0 0
\(291\) −4.84147 −0.283812
\(292\) 0 0
\(293\) −16.9967 −0.992956 −0.496478 0.868049i \(-0.665374\pi\)
−0.496478 + 0.868049i \(0.665374\pi\)
\(294\) 0 0
\(295\) −39.7739 −2.31573
\(296\) 0 0
\(297\) 0.947546 0.0549822
\(298\) 0 0
\(299\) 2.80225 0.162059
\(300\) 0 0
\(301\) −5.59622 −0.322561
\(302\) 0 0
\(303\) 2.12552 0.122108
\(304\) 0 0
\(305\) −0.631285 −0.0361473
\(306\) 0 0
\(307\) 20.7792 1.18593 0.592966 0.805228i \(-0.297957\pi\)
0.592966 + 0.805228i \(0.297957\pi\)
\(308\) 0 0
\(309\) −33.9023 −1.92864
\(310\) 0 0
\(311\) 0.483400 0.0274111 0.0137055 0.999906i \(-0.495637\pi\)
0.0137055 + 0.999906i \(0.495637\pi\)
\(312\) 0 0
\(313\) −4.43420 −0.250636 −0.125318 0.992117i \(-0.539995\pi\)
−0.125318 + 0.992117i \(0.539995\pi\)
\(314\) 0 0
\(315\) 11.6088 0.654079
\(316\) 0 0
\(317\) 17.4308 0.979012 0.489506 0.872000i \(-0.337177\pi\)
0.489506 + 0.872000i \(0.337177\pi\)
\(318\) 0 0
\(319\) −0.240184 −0.0134477
\(320\) 0 0
\(321\) 15.8819 0.886441
\(322\) 0 0
\(323\) −18.0303 −1.00323
\(324\) 0 0
\(325\) −6.82912 −0.378812
\(326\) 0 0
\(327\) −4.91163 −0.271614
\(328\) 0 0
\(329\) −13.3176 −0.734224
\(330\) 0 0
\(331\) −30.6243 −1.68327 −0.841633 0.540050i \(-0.818405\pi\)
−0.841633 + 0.540050i \(0.818405\pi\)
\(332\) 0 0
\(333\) 20.0851 1.10066
\(334\) 0 0
\(335\) 2.26648 0.123831
\(336\) 0 0
\(337\) 33.1976 1.80839 0.904195 0.427119i \(-0.140471\pi\)
0.904195 + 0.427119i \(0.140471\pi\)
\(338\) 0 0
\(339\) 43.7860 2.37813
\(340\) 0 0
\(341\) −0.281315 −0.0152341
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 24.3351 1.31016
\(346\) 0 0
\(347\) 2.82249 0.151519 0.0757596 0.997126i \(-0.475862\pi\)
0.0757596 + 0.997126i \(0.475862\pi\)
\(348\) 0 0
\(349\) −33.9939 −1.81965 −0.909826 0.414991i \(-0.863785\pi\)
−0.909826 + 0.414991i \(0.863785\pi\)
\(350\) 0 0
\(351\) 0.947546 0.0505763
\(352\) 0 0
\(353\) 17.9223 0.953909 0.476955 0.878928i \(-0.341741\pi\)
0.476955 + 0.878928i \(0.341741\pi\)
\(354\) 0 0
\(355\) −19.9627 −1.05951
\(356\) 0 0
\(357\) 16.5836 0.877695
\(358\) 0 0
\(359\) 25.1800 1.32895 0.664475 0.747311i \(-0.268655\pi\)
0.664475 + 0.747311i \(0.268655\pi\)
\(360\) 0 0
\(361\) −11.4638 −0.603359
\(362\) 0 0
\(363\) −2.52493 −0.132525
\(364\) 0 0
\(365\) −30.2119 −1.58136
\(366\) 0 0
\(367\) −31.8746 −1.66384 −0.831921 0.554894i \(-0.812759\pi\)
−0.831921 + 0.554894i \(0.812759\pi\)
\(368\) 0 0
\(369\) 38.7292 2.01616
\(370\) 0 0
\(371\) 3.03445 0.157541
\(372\) 0 0
\(373\) −15.2256 −0.788352 −0.394176 0.919035i \(-0.628970\pi\)
−0.394176 + 0.919035i \(0.628970\pi\)
\(374\) 0 0
\(375\) −15.8843 −0.820263
\(376\) 0 0
\(377\) −0.240184 −0.0123701
\(378\) 0 0
\(379\) −10.2654 −0.527298 −0.263649 0.964619i \(-0.584926\pi\)
−0.263649 + 0.964619i \(0.584926\pi\)
\(380\) 0 0
\(381\) 19.4270 0.995277
\(382\) 0 0
\(383\) −12.1745 −0.622087 −0.311043 0.950396i \(-0.600678\pi\)
−0.311043 + 0.950396i \(0.600678\pi\)
\(384\) 0 0
\(385\) −3.43935 −0.175285
\(386\) 0 0
\(387\) −18.8888 −0.960172
\(388\) 0 0
\(389\) 8.85013 0.448720 0.224360 0.974506i \(-0.427971\pi\)
0.224360 + 0.974506i \(0.427971\pi\)
\(390\) 0 0
\(391\) 18.4050 0.930781
\(392\) 0 0
\(393\) 7.85568 0.396267
\(394\) 0 0
\(395\) −1.40397 −0.0706412
\(396\) 0 0
\(397\) −38.2258 −1.91850 −0.959248 0.282565i \(-0.908815\pi\)
−0.959248 + 0.282565i \(0.908815\pi\)
\(398\) 0 0
\(399\) −6.93147 −0.347007
\(400\) 0 0
\(401\) −1.93458 −0.0966083 −0.0483041 0.998833i \(-0.515382\pi\)
−0.0483041 + 0.998833i \(0.515382\pi\)
\(402\) 0 0
\(403\) −0.281315 −0.0140133
\(404\) 0 0
\(405\) −26.5977 −1.32165
\(406\) 0 0
\(407\) −5.95065 −0.294963
\(408\) 0 0
\(409\) −11.0589 −0.546827 −0.273414 0.961897i \(-0.588153\pi\)
−0.273414 + 0.961897i \(0.588153\pi\)
\(410\) 0 0
\(411\) 4.58566 0.226194
\(412\) 0 0
\(413\) −11.5644 −0.569045
\(414\) 0 0
\(415\) −17.2586 −0.847190
\(416\) 0 0
\(417\) 14.2236 0.696533
\(418\) 0 0
\(419\) −28.7518 −1.40462 −0.702310 0.711872i \(-0.747848\pi\)
−0.702310 + 0.711872i \(0.747848\pi\)
\(420\) 0 0
\(421\) −2.95139 −0.143842 −0.0719209 0.997410i \(-0.522913\pi\)
−0.0719209 + 0.997410i \(0.522913\pi\)
\(422\) 0 0
\(423\) −44.9506 −2.18557
\(424\) 0 0
\(425\) −44.8532 −2.17570
\(426\) 0 0
\(427\) −0.183548 −0.00888250
\(428\) 0 0
\(429\) −2.52493 −0.121905
\(430\) 0 0
\(431\) −11.3266 −0.545585 −0.272793 0.962073i \(-0.587947\pi\)
−0.272793 + 0.962073i \(0.587947\pi\)
\(432\) 0 0
\(433\) −32.7738 −1.57501 −0.787504 0.616309i \(-0.788627\pi\)
−0.787504 + 0.616309i \(0.788627\pi\)
\(434\) 0 0
\(435\) −2.08578 −0.100006
\(436\) 0 0
\(437\) −7.69278 −0.367995
\(438\) 0 0
\(439\) 7.05878 0.336897 0.168449 0.985710i \(-0.446124\pi\)
0.168449 + 0.985710i \(0.446124\pi\)
\(440\) 0 0
\(441\) 3.37528 0.160727
\(442\) 0 0
\(443\) −5.75409 −0.273385 −0.136692 0.990614i \(-0.543647\pi\)
−0.136692 + 0.990614i \(0.543647\pi\)
\(444\) 0 0
\(445\) 12.8013 0.606838
\(446\) 0 0
\(447\) −33.3647 −1.57810
\(448\) 0 0
\(449\) −4.18170 −0.197347 −0.0986734 0.995120i \(-0.531460\pi\)
−0.0986734 + 0.995120i \(0.531460\pi\)
\(450\) 0 0
\(451\) −11.4744 −0.540307
\(452\) 0 0
\(453\) −35.3429 −1.66056
\(454\) 0 0
\(455\) −3.43935 −0.161239
\(456\) 0 0
\(457\) −25.5675 −1.19600 −0.597999 0.801497i \(-0.704037\pi\)
−0.597999 + 0.801497i \(0.704037\pi\)
\(458\) 0 0
\(459\) 6.22341 0.290484
\(460\) 0 0
\(461\) −11.5020 −0.535699 −0.267850 0.963461i \(-0.586313\pi\)
−0.267850 + 0.963461i \(0.586313\pi\)
\(462\) 0 0
\(463\) 32.1859 1.49580 0.747902 0.663809i \(-0.231061\pi\)
0.747902 + 0.663809i \(0.231061\pi\)
\(464\) 0 0
\(465\) −2.44297 −0.113290
\(466\) 0 0
\(467\) 34.2239 1.58370 0.791848 0.610719i \(-0.209119\pi\)
0.791848 + 0.610719i \(0.209119\pi\)
\(468\) 0 0
\(469\) 0.658984 0.0304290
\(470\) 0 0
\(471\) 9.08201 0.418477
\(472\) 0 0
\(473\) 5.59622 0.257315
\(474\) 0 0
\(475\) 18.7474 0.860189
\(476\) 0 0
\(477\) 10.2421 0.468953
\(478\) 0 0
\(479\) 14.8111 0.676735 0.338368 0.941014i \(-0.390125\pi\)
0.338368 + 0.941014i \(0.390125\pi\)
\(480\) 0 0
\(481\) −5.95065 −0.271326
\(482\) 0 0
\(483\) 7.07550 0.321946
\(484\) 0 0
\(485\) 6.59484 0.299456
\(486\) 0 0
\(487\) 10.9171 0.494700 0.247350 0.968926i \(-0.420440\pi\)
0.247350 + 0.968926i \(0.420440\pi\)
\(488\) 0 0
\(489\) −7.12648 −0.322270
\(490\) 0 0
\(491\) −32.5095 −1.46713 −0.733566 0.679618i \(-0.762145\pi\)
−0.733566 + 0.679618i \(0.762145\pi\)
\(492\) 0 0
\(493\) −1.57751 −0.0710475
\(494\) 0 0
\(495\) −11.6088 −0.521775
\(496\) 0 0
\(497\) −5.80420 −0.260354
\(498\) 0 0
\(499\) −4.38207 −0.196168 −0.0980842 0.995178i \(-0.531271\pi\)
−0.0980842 + 0.995178i \(0.531271\pi\)
\(500\) 0 0
\(501\) 59.4839 2.65754
\(502\) 0 0
\(503\) −5.31536 −0.237000 −0.118500 0.992954i \(-0.537809\pi\)
−0.118500 + 0.992954i \(0.537809\pi\)
\(504\) 0 0
\(505\) −2.89530 −0.128839
\(506\) 0 0
\(507\) −2.52493 −0.112136
\(508\) 0 0
\(509\) −12.7539 −0.565309 −0.282654 0.959222i \(-0.591215\pi\)
−0.282654 + 0.959222i \(0.591215\pi\)
\(510\) 0 0
\(511\) −8.78419 −0.388590
\(512\) 0 0
\(513\) −2.60121 −0.114846
\(514\) 0 0
\(515\) 46.1803 2.03495
\(516\) 0 0
\(517\) 13.3176 0.585708
\(518\) 0 0
\(519\) −6.44451 −0.282883
\(520\) 0 0
\(521\) −20.7866 −0.910678 −0.455339 0.890318i \(-0.650482\pi\)
−0.455339 + 0.890318i \(0.650482\pi\)
\(522\) 0 0
\(523\) 17.6386 0.771284 0.385642 0.922649i \(-0.373980\pi\)
0.385642 + 0.922649i \(0.373980\pi\)
\(524\) 0 0
\(525\) −17.2431 −0.752549
\(526\) 0 0
\(527\) −1.84766 −0.0804852
\(528\) 0 0
\(529\) −15.1474 −0.658582
\(530\) 0 0
\(531\) −39.0329 −1.69389
\(532\) 0 0
\(533\) −11.4744 −0.497010
\(534\) 0 0
\(535\) −21.6336 −0.935303
\(536\) 0 0
\(537\) 1.63813 0.0706905
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −4.81067 −0.206827 −0.103414 0.994638i \(-0.532976\pi\)
−0.103414 + 0.994638i \(0.532976\pi\)
\(542\) 0 0
\(543\) −36.6296 −1.57193
\(544\) 0 0
\(545\) 6.69040 0.286585
\(546\) 0 0
\(547\) −6.81951 −0.291581 −0.145791 0.989315i \(-0.546573\pi\)
−0.145791 + 0.989315i \(0.546573\pi\)
\(548\) 0 0
\(549\) −0.619524 −0.0264406
\(550\) 0 0
\(551\) 0.659355 0.0280895
\(552\) 0 0
\(553\) −0.408207 −0.0173587
\(554\) 0 0
\(555\) −51.6762 −2.19353
\(556\) 0 0
\(557\) −41.9966 −1.77945 −0.889726 0.456494i \(-0.849105\pi\)
−0.889726 + 0.456494i \(0.849105\pi\)
\(558\) 0 0
\(559\) 5.59622 0.236695
\(560\) 0 0
\(561\) −16.5836 −0.700158
\(562\) 0 0
\(563\) −20.5581 −0.866420 −0.433210 0.901293i \(-0.642619\pi\)
−0.433210 + 0.901293i \(0.642619\pi\)
\(564\) 0 0
\(565\) −59.6434 −2.50921
\(566\) 0 0
\(567\) −7.73334 −0.324770
\(568\) 0 0
\(569\) 35.7553 1.49894 0.749471 0.662037i \(-0.230308\pi\)
0.749471 + 0.662037i \(0.230308\pi\)
\(570\) 0 0
\(571\) 7.24964 0.303388 0.151694 0.988428i \(-0.451527\pi\)
0.151694 + 0.988428i \(0.451527\pi\)
\(572\) 0 0
\(573\) 39.2806 1.64097
\(574\) 0 0
\(575\) −19.1369 −0.798065
\(576\) 0 0
\(577\) 14.7885 0.615652 0.307826 0.951443i \(-0.400399\pi\)
0.307826 + 0.951443i \(0.400399\pi\)
\(578\) 0 0
\(579\) −45.3916 −1.88641
\(580\) 0 0
\(581\) −5.01797 −0.208181
\(582\) 0 0
\(583\) −3.03445 −0.125674
\(584\) 0 0
\(585\) −11.6088 −0.479963
\(586\) 0 0
\(587\) −1.33172 −0.0549658 −0.0274829 0.999622i \(-0.508749\pi\)
−0.0274829 + 0.999622i \(0.508749\pi\)
\(588\) 0 0
\(589\) 0.772269 0.0318208
\(590\) 0 0
\(591\) 21.3028 0.876278
\(592\) 0 0
\(593\) 11.0893 0.455382 0.227691 0.973733i \(-0.426882\pi\)
0.227691 + 0.973733i \(0.426882\pi\)
\(594\) 0 0
\(595\) −22.5894 −0.926075
\(596\) 0 0
\(597\) −36.3006 −1.48569
\(598\) 0 0
\(599\) 23.2983 0.951943 0.475971 0.879461i \(-0.342097\pi\)
0.475971 + 0.879461i \(0.342097\pi\)
\(600\) 0 0
\(601\) −30.9967 −1.26438 −0.632190 0.774813i \(-0.717844\pi\)
−0.632190 + 0.774813i \(0.717844\pi\)
\(602\) 0 0
\(603\) 2.22425 0.0905786
\(604\) 0 0
\(605\) 3.43935 0.139829
\(606\) 0 0
\(607\) −15.8510 −0.643374 −0.321687 0.946846i \(-0.604250\pi\)
−0.321687 + 0.946846i \(0.604250\pi\)
\(608\) 0 0
\(609\) −0.606448 −0.0245745
\(610\) 0 0
\(611\) 13.3176 0.538773
\(612\) 0 0
\(613\) 2.70288 0.109168 0.0545841 0.998509i \(-0.482617\pi\)
0.0545841 + 0.998509i \(0.482617\pi\)
\(614\) 0 0
\(615\) −99.6448 −4.01807
\(616\) 0 0
\(617\) 40.3787 1.62558 0.812792 0.582554i \(-0.197947\pi\)
0.812792 + 0.582554i \(0.197947\pi\)
\(618\) 0 0
\(619\) 1.98989 0.0799806 0.0399903 0.999200i \(-0.487267\pi\)
0.0399903 + 0.999200i \(0.487267\pi\)
\(620\) 0 0
\(621\) 2.65526 0.106552
\(622\) 0 0
\(623\) 3.72200 0.149119
\(624\) 0 0
\(625\) −12.5087 −0.500347
\(626\) 0 0
\(627\) 6.93147 0.276816
\(628\) 0 0
\(629\) −39.0834 −1.55836
\(630\) 0 0
\(631\) −15.4417 −0.614726 −0.307363 0.951592i \(-0.599447\pi\)
−0.307363 + 0.951592i \(0.599447\pi\)
\(632\) 0 0
\(633\) 14.6311 0.581534
\(634\) 0 0
\(635\) −26.4626 −1.05014
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −19.5908 −0.775000
\(640\) 0 0
\(641\) −2.74295 −0.108340 −0.0541700 0.998532i \(-0.517251\pi\)
−0.0541700 + 0.998532i \(0.517251\pi\)
\(642\) 0 0
\(643\) −7.68302 −0.302989 −0.151494 0.988458i \(-0.548409\pi\)
−0.151494 + 0.988458i \(0.548409\pi\)
\(644\) 0 0
\(645\) 48.5983 1.91356
\(646\) 0 0
\(647\) 17.4155 0.684674 0.342337 0.939577i \(-0.388782\pi\)
0.342337 + 0.939577i \(0.388782\pi\)
\(648\) 0 0
\(649\) 11.5644 0.453941
\(650\) 0 0
\(651\) −0.710301 −0.0278389
\(652\) 0 0
\(653\) −20.2655 −0.793052 −0.396526 0.918024i \(-0.629784\pi\)
−0.396526 + 0.918024i \(0.629784\pi\)
\(654\) 0 0
\(655\) −10.7007 −0.418109
\(656\) 0 0
\(657\) −29.6491 −1.15672
\(658\) 0 0
\(659\) 34.4566 1.34224 0.671119 0.741349i \(-0.265814\pi\)
0.671119 + 0.741349i \(0.265814\pi\)
\(660\) 0 0
\(661\) −33.4705 −1.30185 −0.650925 0.759142i \(-0.725619\pi\)
−0.650925 + 0.759142i \(0.725619\pi\)
\(662\) 0 0
\(663\) −16.5836 −0.644052
\(664\) 0 0
\(665\) 9.44174 0.366135
\(666\) 0 0
\(667\) −0.673056 −0.0260608
\(668\) 0 0
\(669\) 58.3936 2.25763
\(670\) 0 0
\(671\) 0.183548 0.00708578
\(672\) 0 0
\(673\) 35.8896 1.38344 0.691721 0.722165i \(-0.256853\pi\)
0.691721 + 0.722165i \(0.256853\pi\)
\(674\) 0 0
\(675\) −6.47091 −0.249065
\(676\) 0 0
\(677\) −30.0190 −1.15372 −0.576862 0.816842i \(-0.695723\pi\)
−0.576862 + 0.816842i \(0.695723\pi\)
\(678\) 0 0
\(679\) 1.91747 0.0735856
\(680\) 0 0
\(681\) −30.0307 −1.15078
\(682\) 0 0
\(683\) −30.4667 −1.16577 −0.582887 0.812553i \(-0.698077\pi\)
−0.582887 + 0.812553i \(0.698077\pi\)
\(684\) 0 0
\(685\) −6.24638 −0.238662
\(686\) 0 0
\(687\) 21.7548 0.829997
\(688\) 0 0
\(689\) −3.03445 −0.115603
\(690\) 0 0
\(691\) 23.9026 0.909296 0.454648 0.890671i \(-0.349765\pi\)
0.454648 + 0.890671i \(0.349765\pi\)
\(692\) 0 0
\(693\) −3.37528 −0.128216
\(694\) 0 0
\(695\) −19.3748 −0.734927
\(696\) 0 0
\(697\) −75.3628 −2.85457
\(698\) 0 0
\(699\) 51.9370 1.96444
\(700\) 0 0
\(701\) 6.97966 0.263618 0.131809 0.991275i \(-0.457921\pi\)
0.131809 + 0.991275i \(0.457921\pi\)
\(702\) 0 0
\(703\) 16.3358 0.616116
\(704\) 0 0
\(705\) 115.652 4.35570
\(706\) 0 0
\(707\) −0.841815 −0.0316597
\(708\) 0 0
\(709\) 35.2603 1.32423 0.662115 0.749402i \(-0.269659\pi\)
0.662115 + 0.749402i \(0.269659\pi\)
\(710\) 0 0
\(711\) −1.37781 −0.0516719
\(712\) 0 0
\(713\) −0.788316 −0.0295227
\(714\) 0 0
\(715\) 3.43935 0.128624
\(716\) 0 0
\(717\) 58.9631 2.20202
\(718\) 0 0
\(719\) −4.35967 −0.162588 −0.0812941 0.996690i \(-0.525905\pi\)
−0.0812941 + 0.996690i \(0.525905\pi\)
\(720\) 0 0
\(721\) 13.4270 0.500049
\(722\) 0 0
\(723\) 0.0409567 0.00152320
\(724\) 0 0
\(725\) 1.64025 0.0609172
\(726\) 0 0
\(727\) −19.6893 −0.730234 −0.365117 0.930962i \(-0.618971\pi\)
−0.365117 + 0.930962i \(0.618971\pi\)
\(728\) 0 0
\(729\) −33.2796 −1.23258
\(730\) 0 0
\(731\) 36.7556 1.35945
\(732\) 0 0
\(733\) −27.6532 −1.02140 −0.510698 0.859760i \(-0.670613\pi\)
−0.510698 + 0.859760i \(0.670613\pi\)
\(734\) 0 0
\(735\) −8.68412 −0.320319
\(736\) 0 0
\(737\) −0.658984 −0.0242740
\(738\) 0 0
\(739\) 53.4502 1.96620 0.983099 0.183077i \(-0.0586056\pi\)
0.983099 + 0.183077i \(0.0586056\pi\)
\(740\) 0 0
\(741\) 6.93147 0.254634
\(742\) 0 0
\(743\) −18.0130 −0.660832 −0.330416 0.943835i \(-0.607189\pi\)
−0.330416 + 0.943835i \(0.607189\pi\)
\(744\) 0 0
\(745\) 45.4480 1.66509
\(746\) 0 0
\(747\) −16.9370 −0.619694
\(748\) 0 0
\(749\) −6.29003 −0.229833
\(750\) 0 0
\(751\) 16.7010 0.609429 0.304715 0.952444i \(-0.401439\pi\)
0.304715 + 0.952444i \(0.401439\pi\)
\(752\) 0 0
\(753\) 38.4487 1.40115
\(754\) 0 0
\(755\) 48.1426 1.75209
\(756\) 0 0
\(757\) −46.5971 −1.69360 −0.846801 0.531910i \(-0.821475\pi\)
−0.846801 + 0.531910i \(0.821475\pi\)
\(758\) 0 0
\(759\) −7.07550 −0.256824
\(760\) 0 0
\(761\) 26.9618 0.977364 0.488682 0.872462i \(-0.337478\pi\)
0.488682 + 0.872462i \(0.337478\pi\)
\(762\) 0 0
\(763\) 1.94525 0.0704228
\(764\) 0 0
\(765\) −76.2454 −2.75666
\(766\) 0 0
\(767\) 11.5644 0.417565
\(768\) 0 0
\(769\) 31.3803 1.13160 0.565801 0.824542i \(-0.308567\pi\)
0.565801 + 0.824542i \(0.308567\pi\)
\(770\) 0 0
\(771\) 13.3725 0.481598
\(772\) 0 0
\(773\) 3.02622 0.108846 0.0544228 0.998518i \(-0.482668\pi\)
0.0544228 + 0.998518i \(0.482668\pi\)
\(774\) 0 0
\(775\) 1.92114 0.0690092
\(776\) 0 0
\(777\) −15.0250 −0.539018
\(778\) 0 0
\(779\) 31.4996 1.12859
\(780\) 0 0
\(781\) 5.80420 0.207691
\(782\) 0 0
\(783\) −0.227585 −0.00813323
\(784\) 0 0
\(785\) −12.3711 −0.441544
\(786\) 0 0
\(787\) −32.3970 −1.15483 −0.577414 0.816452i \(-0.695938\pi\)
−0.577414 + 0.816452i \(0.695938\pi\)
\(788\) 0 0
\(789\) −79.0379 −2.81382
\(790\) 0 0
\(791\) −17.3415 −0.616592
\(792\) 0 0
\(793\) 0.183548 0.00651797
\(794\) 0 0
\(795\) −26.3515 −0.934591
\(796\) 0 0
\(797\) 2.99600 0.106124 0.0530618 0.998591i \(-0.483102\pi\)
0.0530618 + 0.998591i \(0.483102\pi\)
\(798\) 0 0
\(799\) 87.4691 3.09443
\(800\) 0 0
\(801\) 12.5628 0.443884
\(802\) 0 0
\(803\) 8.78419 0.309987
\(804\) 0 0
\(805\) −9.63793 −0.339692
\(806\) 0 0
\(807\) −2.49984 −0.0879986
\(808\) 0 0
\(809\) 2.05449 0.0722320 0.0361160 0.999348i \(-0.488501\pi\)
0.0361160 + 0.999348i \(0.488501\pi\)
\(810\) 0 0
\(811\) −14.9259 −0.524118 −0.262059 0.965052i \(-0.584402\pi\)
−0.262059 + 0.965052i \(0.584402\pi\)
\(812\) 0 0
\(813\) −64.9407 −2.27757
\(814\) 0 0
\(815\) 9.70737 0.340034
\(816\) 0 0
\(817\) −15.3628 −0.537477
\(818\) 0 0
\(819\) −3.37528 −0.117942
\(820\) 0 0
\(821\) 29.4503 1.02782 0.513911 0.857843i \(-0.328196\pi\)
0.513911 + 0.857843i \(0.328196\pi\)
\(822\) 0 0
\(823\) −42.3023 −1.47457 −0.737283 0.675584i \(-0.763892\pi\)
−0.737283 + 0.675584i \(0.763892\pi\)
\(824\) 0 0
\(825\) 17.2431 0.600327
\(826\) 0 0
\(827\) 15.8903 0.552559 0.276279 0.961077i \(-0.410898\pi\)
0.276279 + 0.961077i \(0.410898\pi\)
\(828\) 0 0
\(829\) −45.4270 −1.57774 −0.788872 0.614558i \(-0.789335\pi\)
−0.788872 + 0.614558i \(0.789335\pi\)
\(830\) 0 0
\(831\) 44.3059 1.53695
\(832\) 0 0
\(833\) −6.56793 −0.227565
\(834\) 0 0
\(835\) −81.0263 −2.80403
\(836\) 0 0
\(837\) −0.266559 −0.00921363
\(838\) 0 0
\(839\) −15.1543 −0.523186 −0.261593 0.965178i \(-0.584248\pi\)
−0.261593 + 0.965178i \(0.584248\pi\)
\(840\) 0 0
\(841\) −28.9423 −0.998011
\(842\) 0 0
\(843\) −14.0086 −0.482483
\(844\) 0 0
\(845\) 3.43935 0.118317
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 18.0429 0.619232
\(850\) 0 0
\(851\) −16.6752 −0.571620
\(852\) 0 0
\(853\) 45.4014 1.55452 0.777258 0.629182i \(-0.216610\pi\)
0.777258 + 0.629182i \(0.216610\pi\)
\(854\) 0 0
\(855\) 31.8685 1.08988
\(856\) 0 0
\(857\) −7.01882 −0.239758 −0.119879 0.992788i \(-0.538251\pi\)
−0.119879 + 0.992788i \(0.538251\pi\)
\(858\) 0 0
\(859\) 30.1710 1.02942 0.514711 0.857363i \(-0.327899\pi\)
0.514711 + 0.857363i \(0.327899\pi\)
\(860\) 0 0
\(861\) −28.9720 −0.987363
\(862\) 0 0
\(863\) 41.9524 1.42808 0.714038 0.700107i \(-0.246865\pi\)
0.714038 + 0.700107i \(0.246865\pi\)
\(864\) 0 0
\(865\) 8.77843 0.298476
\(866\) 0 0
\(867\) −65.9958 −2.24133
\(868\) 0 0
\(869\) 0.408207 0.0138475
\(870\) 0 0
\(871\) −0.658984 −0.0223288
\(872\) 0 0
\(873\) 6.47198 0.219043
\(874\) 0 0
\(875\) 6.29100 0.212675
\(876\) 0 0
\(877\) 3.08406 0.104141 0.0520707 0.998643i \(-0.483418\pi\)
0.0520707 + 0.998643i \(0.483418\pi\)
\(878\) 0 0
\(879\) 42.9154 1.44750
\(880\) 0 0
\(881\) −19.7931 −0.666848 −0.333424 0.942777i \(-0.608204\pi\)
−0.333424 + 0.942777i \(0.608204\pi\)
\(882\) 0 0
\(883\) −7.24420 −0.243787 −0.121893 0.992543i \(-0.538897\pi\)
−0.121893 + 0.992543i \(0.538897\pi\)
\(884\) 0 0
\(885\) 100.426 3.37580
\(886\) 0 0
\(887\) −57.8221 −1.94148 −0.970738 0.240139i \(-0.922807\pi\)
−0.970738 + 0.240139i \(0.922807\pi\)
\(888\) 0 0
\(889\) −7.69408 −0.258051
\(890\) 0 0
\(891\) 7.73334 0.259077
\(892\) 0 0
\(893\) −36.5597 −1.22342
\(894\) 0 0
\(895\) −2.23139 −0.0745871
\(896\) 0 0
\(897\) −7.07550 −0.236244
\(898\) 0 0
\(899\) 0.0675673 0.00225350
\(900\) 0 0
\(901\) −19.9300 −0.663965
\(902\) 0 0
\(903\) 14.1301 0.470220
\(904\) 0 0
\(905\) 49.8952 1.65857
\(906\) 0 0
\(907\) 10.5234 0.349423 0.174711 0.984620i \(-0.444101\pi\)
0.174711 + 0.984620i \(0.444101\pi\)
\(908\) 0 0
\(909\) −2.84136 −0.0942419
\(910\) 0 0
\(911\) −0.294005 −0.00974081 −0.00487041 0.999988i \(-0.501550\pi\)
−0.00487041 + 0.999988i \(0.501550\pi\)
\(912\) 0 0
\(913\) 5.01797 0.166071
\(914\) 0 0
\(915\) 1.59395 0.0526944
\(916\) 0 0
\(917\) −3.11125 −0.102742
\(918\) 0 0
\(919\) 37.9983 1.25345 0.626725 0.779241i \(-0.284395\pi\)
0.626725 + 0.779241i \(0.284395\pi\)
\(920\) 0 0
\(921\) −52.4660 −1.72881
\(922\) 0 0
\(923\) 5.80420 0.191048
\(924\) 0 0
\(925\) 40.6377 1.33616
\(926\) 0 0
\(927\) 45.3200 1.48850
\(928\) 0 0
\(929\) −30.6251 −1.00478 −0.502388 0.864642i \(-0.667545\pi\)
−0.502388 + 0.864642i \(0.667545\pi\)
\(930\) 0 0
\(931\) 2.74521 0.0899706
\(932\) 0 0
\(933\) −1.22055 −0.0399591
\(934\) 0 0
\(935\) 22.5894 0.738752
\(936\) 0 0
\(937\) 11.0781 0.361906 0.180953 0.983492i \(-0.442082\pi\)
0.180953 + 0.983492i \(0.442082\pi\)
\(938\) 0 0
\(939\) 11.1960 0.365369
\(940\) 0 0
\(941\) 20.9511 0.682986 0.341493 0.939884i \(-0.389067\pi\)
0.341493 + 0.939884i \(0.389067\pi\)
\(942\) 0 0
\(943\) −32.1541 −1.04708
\(944\) 0 0
\(945\) −3.25894 −0.106013
\(946\) 0 0
\(947\) 52.2717 1.69860 0.849300 0.527910i \(-0.177024\pi\)
0.849300 + 0.527910i \(0.177024\pi\)
\(948\) 0 0
\(949\) 8.78419 0.285147
\(950\) 0 0
\(951\) −44.0116 −1.42717
\(952\) 0 0
\(953\) 29.4013 0.952402 0.476201 0.879336i \(-0.342013\pi\)
0.476201 + 0.879336i \(0.342013\pi\)
\(954\) 0 0
\(955\) −53.5063 −1.73142
\(956\) 0 0
\(957\) 0.606448 0.0196037
\(958\) 0 0
\(959\) −1.81615 −0.0586466
\(960\) 0 0
\(961\) −30.9209 −0.997447
\(962\) 0 0
\(963\) −21.2306 −0.684146
\(964\) 0 0
\(965\) 61.8304 1.99039
\(966\) 0 0
\(967\) −7.32741 −0.235634 −0.117817 0.993035i \(-0.537590\pi\)
−0.117817 + 0.993035i \(0.537590\pi\)
\(968\) 0 0
\(969\) 45.5254 1.46249
\(970\) 0 0
\(971\) −48.1549 −1.54536 −0.772682 0.634793i \(-0.781085\pi\)
−0.772682 + 0.634793i \(0.781085\pi\)
\(972\) 0 0
\(973\) −5.63326 −0.180594
\(974\) 0 0
\(975\) 17.2431 0.552220
\(976\) 0 0
\(977\) 38.6859 1.23767 0.618835 0.785521i \(-0.287605\pi\)
0.618835 + 0.785521i \(0.287605\pi\)
\(978\) 0 0
\(979\) −3.72200 −0.118956
\(980\) 0 0
\(981\) 6.56576 0.209629
\(982\) 0 0
\(983\) −47.0645 −1.50113 −0.750563 0.660799i \(-0.770218\pi\)
−0.750563 + 0.660799i \(0.770218\pi\)
\(984\) 0 0
\(985\) −29.0177 −0.924580
\(986\) 0 0
\(987\) 33.6261 1.07033
\(988\) 0 0
\(989\) 15.6820 0.498660
\(990\) 0 0
\(991\) −26.6427 −0.846335 −0.423167 0.906052i \(-0.639082\pi\)
−0.423167 + 0.906052i \(0.639082\pi\)
\(992\) 0 0
\(993\) 77.3244 2.45381
\(994\) 0 0
\(995\) 49.4471 1.56758
\(996\) 0 0
\(997\) −15.4075 −0.487959 −0.243980 0.969780i \(-0.578453\pi\)
−0.243980 + 0.969780i \(0.578453\pi\)
\(998\) 0 0
\(999\) −5.63852 −0.178395
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 \(a_p\))