Properties

Label 8008.2.a.v.1.10
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-2.29224\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.29224 q^{3} +0.279184 q^{5} -1.00000 q^{7} +2.25438 q^{9} +O(q^{10})\) \(q+2.29224 q^{3} +0.279184 q^{5} -1.00000 q^{7} +2.25438 q^{9} +1.00000 q^{11} -1.00000 q^{13} +0.639958 q^{15} +2.22354 q^{17} -8.55315 q^{19} -2.29224 q^{21} -3.73720 q^{23} -4.92206 q^{25} -1.70914 q^{27} +8.08689 q^{29} -8.68510 q^{31} +2.29224 q^{33} -0.279184 q^{35} +7.36294 q^{37} -2.29224 q^{39} -0.628104 q^{41} -2.32914 q^{43} +0.629387 q^{45} -3.73720 q^{47} +1.00000 q^{49} +5.09689 q^{51} +6.34813 q^{53} +0.279184 q^{55} -19.6059 q^{57} +5.45723 q^{59} +0.113940 q^{61} -2.25438 q^{63} -0.279184 q^{65} -2.41610 q^{67} -8.56656 q^{69} -13.8194 q^{71} -7.30849 q^{73} -11.2826 q^{75} -1.00000 q^{77} -12.8219 q^{79} -10.6809 q^{81} +7.64233 q^{83} +0.620776 q^{85} +18.5371 q^{87} +8.78585 q^{89} +1.00000 q^{91} -19.9084 q^{93} -2.38790 q^{95} -9.03350 q^{97} +2.25438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) 2.29224 1.32343 0.661714 0.749757i \(-0.269829\pi\)
0.661714 + 0.749757i \(0.269829\pi\)
\(4\) 0 0
\(5\) 0.279184 0.124855 0.0624274 0.998050i \(-0.480116\pi\)
0.0624274 + 0.998050i \(0.480116\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.25438 0.751460
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.639958 0.165236
\(16\) 0 0
\(17\) 2.22354 0.539287 0.269644 0.962960i \(-0.413094\pi\)
0.269644 + 0.962960i \(0.413094\pi\)
\(18\) 0 0
\(19\) −8.55315 −1.96223 −0.981114 0.193431i \(-0.938038\pi\)
−0.981114 + 0.193431i \(0.938038\pi\)
\(20\) 0 0
\(21\) −2.29224 −0.500209
\(22\) 0 0
\(23\) −3.73720 −0.779259 −0.389630 0.920972i \(-0.627397\pi\)
−0.389630 + 0.920972i \(0.627397\pi\)
\(24\) 0 0
\(25\) −4.92206 −0.984411
\(26\) 0 0
\(27\) −1.70914 −0.328924
\(28\) 0 0
\(29\) 8.08689 1.50170 0.750849 0.660474i \(-0.229644\pi\)
0.750849 + 0.660474i \(0.229644\pi\)
\(30\) 0 0
\(31\) −8.68510 −1.55989 −0.779945 0.625848i \(-0.784753\pi\)
−0.779945 + 0.625848i \(0.784753\pi\)
\(32\) 0 0
\(33\) 2.29224 0.399028
\(34\) 0 0
\(35\) −0.279184 −0.0471907
\(36\) 0 0
\(37\) 7.36294 1.21046 0.605230 0.796051i \(-0.293081\pi\)
0.605230 + 0.796051i \(0.293081\pi\)
\(38\) 0 0
\(39\) −2.29224 −0.367053
\(40\) 0 0
\(41\) −0.628104 −0.0980934 −0.0490467 0.998796i \(-0.515618\pi\)
−0.0490467 + 0.998796i \(0.515618\pi\)
\(42\) 0 0
\(43\) −2.32914 −0.355191 −0.177596 0.984104i \(-0.556832\pi\)
−0.177596 + 0.984104i \(0.556832\pi\)
\(44\) 0 0
\(45\) 0.629387 0.0938235
\(46\) 0 0
\(47\) −3.73720 −0.545126 −0.272563 0.962138i \(-0.587871\pi\)
−0.272563 + 0.962138i \(0.587871\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 5.09689 0.713707
\(52\) 0 0
\(53\) 6.34813 0.871983 0.435991 0.899951i \(-0.356398\pi\)
0.435991 + 0.899951i \(0.356398\pi\)
\(54\) 0 0
\(55\) 0.279184 0.0376452
\(56\) 0 0
\(57\) −19.6059 −2.59687
\(58\) 0 0
\(59\) 5.45723 0.710471 0.355235 0.934777i \(-0.384401\pi\)
0.355235 + 0.934777i \(0.384401\pi\)
\(60\) 0 0
\(61\) 0.113940 0.0145886 0.00729429 0.999973i \(-0.497678\pi\)
0.00729429 + 0.999973i \(0.497678\pi\)
\(62\) 0 0
\(63\) −2.25438 −0.284025
\(64\) 0 0
\(65\) −0.279184 −0.0346285
\(66\) 0 0
\(67\) −2.41610 −0.295174 −0.147587 0.989049i \(-0.547151\pi\)
−0.147587 + 0.989049i \(0.547151\pi\)
\(68\) 0 0
\(69\) −8.56656 −1.03129
\(70\) 0 0
\(71\) −13.8194 −1.64006 −0.820031 0.572319i \(-0.806044\pi\)
−0.820031 + 0.572319i \(0.806044\pi\)
\(72\) 0 0
\(73\) −7.30849 −0.855395 −0.427697 0.903922i \(-0.640675\pi\)
−0.427697 + 0.903922i \(0.640675\pi\)
\(74\) 0 0
\(75\) −11.2826 −1.30280
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −12.8219 −1.44257 −0.721287 0.692636i \(-0.756449\pi\)
−0.721287 + 0.692636i \(0.756449\pi\)
\(80\) 0 0
\(81\) −10.6809 −1.18677
\(82\) 0 0
\(83\) 7.64233 0.838855 0.419427 0.907789i \(-0.362231\pi\)
0.419427 + 0.907789i \(0.362231\pi\)
\(84\) 0 0
\(85\) 0.620776 0.0673326
\(86\) 0 0
\(87\) 18.5371 1.98739
\(88\) 0 0
\(89\) 8.78585 0.931299 0.465649 0.884969i \(-0.345821\pi\)
0.465649 + 0.884969i \(0.345821\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −19.9084 −2.06440
\(94\) 0 0
\(95\) −2.38790 −0.244994
\(96\) 0 0
\(97\) −9.03350 −0.917213 −0.458606 0.888640i \(-0.651651\pi\)
−0.458606 + 0.888640i \(0.651651\pi\)
\(98\) 0 0
\(99\) 2.25438 0.226574
\(100\) 0 0
\(101\) 1.56739 0.155962 0.0779808 0.996955i \(-0.475153\pi\)
0.0779808 + 0.996955i \(0.475153\pi\)
\(102\) 0 0
\(103\) −5.72438 −0.564040 −0.282020 0.959409i \(-0.591004\pi\)
−0.282020 + 0.959409i \(0.591004\pi\)
\(104\) 0 0
\(105\) −0.639958 −0.0624535
\(106\) 0 0
\(107\) −0.400752 −0.0387421 −0.0193711 0.999812i \(-0.506166\pi\)
−0.0193711 + 0.999812i \(0.506166\pi\)
\(108\) 0 0
\(109\) −20.3077 −1.94512 −0.972561 0.232649i \(-0.925261\pi\)
−0.972561 + 0.232649i \(0.925261\pi\)
\(110\) 0 0
\(111\) 16.8776 1.60195
\(112\) 0 0
\(113\) −12.1185 −1.14001 −0.570007 0.821640i \(-0.693059\pi\)
−0.570007 + 0.821640i \(0.693059\pi\)
\(114\) 0 0
\(115\) −1.04337 −0.0972943
\(116\) 0 0
\(117\) −2.25438 −0.208418
\(118\) 0 0
\(119\) −2.22354 −0.203831
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −1.43977 −0.129819
\(124\) 0 0
\(125\) −2.77008 −0.247763
\(126\) 0 0
\(127\) −11.2734 −1.00035 −0.500174 0.865925i \(-0.666731\pi\)
−0.500174 + 0.865925i \(0.666731\pi\)
\(128\) 0 0
\(129\) −5.33896 −0.470070
\(130\) 0 0
\(131\) 0.756782 0.0661204 0.0330602 0.999453i \(-0.489475\pi\)
0.0330602 + 0.999453i \(0.489475\pi\)
\(132\) 0 0
\(133\) 8.55315 0.741652
\(134\) 0 0
\(135\) −0.477165 −0.0410678
\(136\) 0 0
\(137\) −7.77046 −0.663875 −0.331938 0.943301i \(-0.607702\pi\)
−0.331938 + 0.943301i \(0.607702\pi\)
\(138\) 0 0
\(139\) −13.7690 −1.16787 −0.583936 0.811800i \(-0.698488\pi\)
−0.583936 + 0.811800i \(0.698488\pi\)
\(140\) 0 0
\(141\) −8.56656 −0.721435
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 2.25773 0.187494
\(146\) 0 0
\(147\) 2.29224 0.189061
\(148\) 0 0
\(149\) 6.78265 0.555656 0.277828 0.960631i \(-0.410385\pi\)
0.277828 + 0.960631i \(0.410385\pi\)
\(150\) 0 0
\(151\) −15.5829 −1.26812 −0.634060 0.773284i \(-0.718613\pi\)
−0.634060 + 0.773284i \(0.718613\pi\)
\(152\) 0 0
\(153\) 5.01270 0.405253
\(154\) 0 0
\(155\) −2.42474 −0.194760
\(156\) 0 0
\(157\) 1.46924 0.117258 0.0586290 0.998280i \(-0.481327\pi\)
0.0586290 + 0.998280i \(0.481327\pi\)
\(158\) 0 0
\(159\) 14.5515 1.15401
\(160\) 0 0
\(161\) 3.73720 0.294532
\(162\) 0 0
\(163\) 11.7669 0.921657 0.460828 0.887489i \(-0.347552\pi\)
0.460828 + 0.887489i \(0.347552\pi\)
\(164\) 0 0
\(165\) 0.639958 0.0498206
\(166\) 0 0
\(167\) 10.7199 0.829530 0.414765 0.909929i \(-0.363864\pi\)
0.414765 + 0.909929i \(0.363864\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −19.2821 −1.47454
\(172\) 0 0
\(173\) 4.17187 0.317181 0.158591 0.987344i \(-0.449305\pi\)
0.158591 + 0.987344i \(0.449305\pi\)
\(174\) 0 0
\(175\) 4.92206 0.372072
\(176\) 0 0
\(177\) 12.5093 0.940256
\(178\) 0 0
\(179\) 15.5429 1.16173 0.580867 0.813999i \(-0.302714\pi\)
0.580867 + 0.813999i \(0.302714\pi\)
\(180\) 0 0
\(181\) 22.9274 1.70418 0.852089 0.523398i \(-0.175336\pi\)
0.852089 + 0.523398i \(0.175336\pi\)
\(182\) 0 0
\(183\) 0.261179 0.0193069
\(184\) 0 0
\(185\) 2.05561 0.151132
\(186\) 0 0
\(187\) 2.22354 0.162601
\(188\) 0 0
\(189\) 1.70914 0.124322
\(190\) 0 0
\(191\) 6.07976 0.439916 0.219958 0.975509i \(-0.429408\pi\)
0.219958 + 0.975509i \(0.429408\pi\)
\(192\) 0 0
\(193\) 0.753290 0.0542230 0.0271115 0.999632i \(-0.491369\pi\)
0.0271115 + 0.999632i \(0.491369\pi\)
\(194\) 0 0
\(195\) −0.639958 −0.0458283
\(196\) 0 0
\(197\) 4.08285 0.290891 0.145446 0.989366i \(-0.453538\pi\)
0.145446 + 0.989366i \(0.453538\pi\)
\(198\) 0 0
\(199\) 25.1545 1.78316 0.891579 0.452865i \(-0.149598\pi\)
0.891579 + 0.452865i \(0.149598\pi\)
\(200\) 0 0
\(201\) −5.53830 −0.390641
\(202\) 0 0
\(203\) −8.08689 −0.567589
\(204\) 0 0
\(205\) −0.175357 −0.0122474
\(206\) 0 0
\(207\) −8.42506 −0.585582
\(208\) 0 0
\(209\) −8.55315 −0.591634
\(210\) 0 0
\(211\) −4.72132 −0.325029 −0.162515 0.986706i \(-0.551960\pi\)
−0.162515 + 0.986706i \(0.551960\pi\)
\(212\) 0 0
\(213\) −31.6775 −2.17050
\(214\) 0 0
\(215\) −0.650260 −0.0443473
\(216\) 0 0
\(217\) 8.68510 0.589583
\(218\) 0 0
\(219\) −16.7528 −1.13205
\(220\) 0 0
\(221\) −2.22354 −0.149571
\(222\) 0 0
\(223\) 14.7656 0.988775 0.494387 0.869242i \(-0.335392\pi\)
0.494387 + 0.869242i \(0.335392\pi\)
\(224\) 0 0
\(225\) −11.0962 −0.739746
\(226\) 0 0
\(227\) −12.4810 −0.828396 −0.414198 0.910187i \(-0.635938\pi\)
−0.414198 + 0.910187i \(0.635938\pi\)
\(228\) 0 0
\(229\) −19.4633 −1.28617 −0.643086 0.765794i \(-0.722346\pi\)
−0.643086 + 0.765794i \(0.722346\pi\)
\(230\) 0 0
\(231\) −2.29224 −0.150819
\(232\) 0 0
\(233\) 1.30972 0.0858029 0.0429014 0.999079i \(-0.486340\pi\)
0.0429014 + 0.999079i \(0.486340\pi\)
\(234\) 0 0
\(235\) −1.04337 −0.0680617
\(236\) 0 0
\(237\) −29.3909 −1.90914
\(238\) 0 0
\(239\) −17.2472 −1.11563 −0.557816 0.829965i \(-0.688360\pi\)
−0.557816 + 0.829965i \(0.688360\pi\)
\(240\) 0 0
\(241\) −2.50501 −0.161362 −0.0806810 0.996740i \(-0.525710\pi\)
−0.0806810 + 0.996740i \(0.525710\pi\)
\(242\) 0 0
\(243\) −19.3558 −1.24168
\(244\) 0 0
\(245\) 0.279184 0.0178364
\(246\) 0 0
\(247\) 8.55315 0.544224
\(248\) 0 0
\(249\) 17.5181 1.11016
\(250\) 0 0
\(251\) −1.65297 −0.104334 −0.0521672 0.998638i \(-0.516613\pi\)
−0.0521672 + 0.998638i \(0.516613\pi\)
\(252\) 0 0
\(253\) −3.73720 −0.234956
\(254\) 0 0
\(255\) 1.42297 0.0891098
\(256\) 0 0
\(257\) 18.1451 1.13186 0.565930 0.824453i \(-0.308517\pi\)
0.565930 + 0.824453i \(0.308517\pi\)
\(258\) 0 0
\(259\) −7.36294 −0.457511
\(260\) 0 0
\(261\) 18.2309 1.12847
\(262\) 0 0
\(263\) 10.8985 0.672032 0.336016 0.941856i \(-0.390920\pi\)
0.336016 + 0.941856i \(0.390920\pi\)
\(264\) 0 0
\(265\) 1.77230 0.108871
\(266\) 0 0
\(267\) 20.1393 1.23251
\(268\) 0 0
\(269\) 21.4420 1.30734 0.653672 0.756778i \(-0.273228\pi\)
0.653672 + 0.756778i \(0.273228\pi\)
\(270\) 0 0
\(271\) −18.8573 −1.14550 −0.572750 0.819730i \(-0.694123\pi\)
−0.572750 + 0.819730i \(0.694123\pi\)
\(272\) 0 0
\(273\) 2.29224 0.138733
\(274\) 0 0
\(275\) −4.92206 −0.296811
\(276\) 0 0
\(277\) 0.187651 0.0112749 0.00563743 0.999984i \(-0.498206\pi\)
0.00563743 + 0.999984i \(0.498206\pi\)
\(278\) 0 0
\(279\) −19.5795 −1.17220
\(280\) 0 0
\(281\) −31.4355 −1.87529 −0.937643 0.347600i \(-0.886997\pi\)
−0.937643 + 0.347600i \(0.886997\pi\)
\(282\) 0 0
\(283\) −1.92359 −0.114345 −0.0571727 0.998364i \(-0.518209\pi\)
−0.0571727 + 0.998364i \(0.518209\pi\)
\(284\) 0 0
\(285\) −5.47366 −0.324231
\(286\) 0 0
\(287\) 0.628104 0.0370758
\(288\) 0 0
\(289\) −12.0559 −0.709170
\(290\) 0 0
\(291\) −20.7070 −1.21386
\(292\) 0 0
\(293\) 15.2224 0.889304 0.444652 0.895703i \(-0.353327\pi\)
0.444652 + 0.895703i \(0.353327\pi\)
\(294\) 0 0
\(295\) 1.52357 0.0887057
\(296\) 0 0
\(297\) −1.70914 −0.0991744
\(298\) 0 0
\(299\) 3.73720 0.216128
\(300\) 0 0
\(301\) 2.32914 0.134250
\(302\) 0 0
\(303\) 3.59285 0.206404
\(304\) 0 0
\(305\) 0.0318104 0.00182146
\(306\) 0 0
\(307\) −29.0297 −1.65681 −0.828405 0.560130i \(-0.810751\pi\)
−0.828405 + 0.560130i \(0.810751\pi\)
\(308\) 0 0
\(309\) −13.1217 −0.746466
\(310\) 0 0
\(311\) 18.8919 1.07126 0.535631 0.844452i \(-0.320074\pi\)
0.535631 + 0.844452i \(0.320074\pi\)
\(312\) 0 0
\(313\) −11.8187 −0.668032 −0.334016 0.942567i \(-0.608404\pi\)
−0.334016 + 0.942567i \(0.608404\pi\)
\(314\) 0 0
\(315\) −0.629387 −0.0354619
\(316\) 0 0
\(317\) 29.8309 1.67547 0.837735 0.546076i \(-0.183879\pi\)
0.837735 + 0.546076i \(0.183879\pi\)
\(318\) 0 0
\(319\) 8.08689 0.452779
\(320\) 0 0
\(321\) −0.918621 −0.0512724
\(322\) 0 0
\(323\) −19.0183 −1.05820
\(324\) 0 0
\(325\) 4.92206 0.273027
\(326\) 0 0
\(327\) −46.5501 −2.57423
\(328\) 0 0
\(329\) 3.73720 0.206038
\(330\) 0 0
\(331\) 0.536178 0.0294710 0.0147355 0.999891i \(-0.495309\pi\)
0.0147355 + 0.999891i \(0.495309\pi\)
\(332\) 0 0
\(333\) 16.5989 0.909612
\(334\) 0 0
\(335\) −0.674537 −0.0368539
\(336\) 0 0
\(337\) −19.4470 −1.05935 −0.529674 0.848201i \(-0.677686\pi\)
−0.529674 + 0.848201i \(0.677686\pi\)
\(338\) 0 0
\(339\) −27.7786 −1.50873
\(340\) 0 0
\(341\) −8.68510 −0.470325
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −2.39165 −0.128762
\(346\) 0 0
\(347\) 12.8081 0.687575 0.343787 0.939048i \(-0.388290\pi\)
0.343787 + 0.939048i \(0.388290\pi\)
\(348\) 0 0
\(349\) −7.93120 −0.424547 −0.212274 0.977210i \(-0.568087\pi\)
−0.212274 + 0.977210i \(0.568087\pi\)
\(350\) 0 0
\(351\) 1.70914 0.0912272
\(352\) 0 0
\(353\) −3.31648 −0.176518 −0.0882591 0.996098i \(-0.528130\pi\)
−0.0882591 + 0.996098i \(0.528130\pi\)
\(354\) 0 0
\(355\) −3.85816 −0.204770
\(356\) 0 0
\(357\) −5.09689 −0.269756
\(358\) 0 0
\(359\) 36.7085 1.93740 0.968700 0.248235i \(-0.0798506\pi\)
0.968700 + 0.248235i \(0.0798506\pi\)
\(360\) 0 0
\(361\) 54.1564 2.85034
\(362\) 0 0
\(363\) 2.29224 0.120312
\(364\) 0 0
\(365\) −2.04041 −0.106800
\(366\) 0 0
\(367\) 17.2739 0.901688 0.450844 0.892603i \(-0.351123\pi\)
0.450844 + 0.892603i \(0.351123\pi\)
\(368\) 0 0
\(369\) −1.41599 −0.0737133
\(370\) 0 0
\(371\) −6.34813 −0.329578
\(372\) 0 0
\(373\) −32.9384 −1.70549 −0.852744 0.522329i \(-0.825063\pi\)
−0.852744 + 0.522329i \(0.825063\pi\)
\(374\) 0 0
\(375\) −6.34970 −0.327897
\(376\) 0 0
\(377\) −8.08689 −0.416496
\(378\) 0 0
\(379\) −14.5118 −0.745423 −0.372711 0.927947i \(-0.621572\pi\)
−0.372711 + 0.927947i \(0.621572\pi\)
\(380\) 0 0
\(381\) −25.8413 −1.32389
\(382\) 0 0
\(383\) 23.6646 1.20920 0.604602 0.796527i \(-0.293332\pi\)
0.604602 + 0.796527i \(0.293332\pi\)
\(384\) 0 0
\(385\) −0.279184 −0.0142285
\(386\) 0 0
\(387\) −5.25078 −0.266912
\(388\) 0 0
\(389\) 5.96694 0.302536 0.151268 0.988493i \(-0.451664\pi\)
0.151268 + 0.988493i \(0.451664\pi\)
\(390\) 0 0
\(391\) −8.30980 −0.420244
\(392\) 0 0
\(393\) 1.73473 0.0875055
\(394\) 0 0
\(395\) −3.57966 −0.180112
\(396\) 0 0
\(397\) 13.3533 0.670182 0.335091 0.942186i \(-0.391233\pi\)
0.335091 + 0.942186i \(0.391233\pi\)
\(398\) 0 0
\(399\) 19.6059 0.981523
\(400\) 0 0
\(401\) −20.7917 −1.03829 −0.519145 0.854686i \(-0.673750\pi\)
−0.519145 + 0.854686i \(0.673750\pi\)
\(402\) 0 0
\(403\) 8.68510 0.432636
\(404\) 0 0
\(405\) −2.98194 −0.148174
\(406\) 0 0
\(407\) 7.36294 0.364967
\(408\) 0 0
\(409\) 6.18004 0.305583 0.152792 0.988258i \(-0.451174\pi\)
0.152792 + 0.988258i \(0.451174\pi\)
\(410\) 0 0
\(411\) −17.8118 −0.878591
\(412\) 0 0
\(413\) −5.45723 −0.268533
\(414\) 0 0
\(415\) 2.13362 0.104735
\(416\) 0 0
\(417\) −31.5619 −1.54559
\(418\) 0 0
\(419\) −16.8424 −0.822807 −0.411403 0.911453i \(-0.634961\pi\)
−0.411403 + 0.911453i \(0.634961\pi\)
\(420\) 0 0
\(421\) 32.5332 1.58557 0.792785 0.609502i \(-0.208631\pi\)
0.792785 + 0.609502i \(0.208631\pi\)
\(422\) 0 0
\(423\) −8.42506 −0.409641
\(424\) 0 0
\(425\) −10.9444 −0.530880
\(426\) 0 0
\(427\) −0.113940 −0.00551397
\(428\) 0 0
\(429\) −2.29224 −0.110671
\(430\) 0 0
\(431\) −5.41035 −0.260607 −0.130304 0.991474i \(-0.541595\pi\)
−0.130304 + 0.991474i \(0.541595\pi\)
\(432\) 0 0
\(433\) −31.0387 −1.49163 −0.745813 0.666155i \(-0.767939\pi\)
−0.745813 + 0.666155i \(0.767939\pi\)
\(434\) 0 0
\(435\) 5.17527 0.248135
\(436\) 0 0
\(437\) 31.9648 1.52908
\(438\) 0 0
\(439\) −10.1812 −0.485924 −0.242962 0.970036i \(-0.578119\pi\)
−0.242962 + 0.970036i \(0.578119\pi\)
\(440\) 0 0
\(441\) 2.25438 0.107351
\(442\) 0 0
\(443\) −27.3171 −1.29788 −0.648938 0.760841i \(-0.724786\pi\)
−0.648938 + 0.760841i \(0.724786\pi\)
\(444\) 0 0
\(445\) 2.45287 0.116277
\(446\) 0 0
\(447\) 15.5475 0.735371
\(448\) 0 0
\(449\) −30.9671 −1.46143 −0.730713 0.682684i \(-0.760812\pi\)
−0.730713 + 0.682684i \(0.760812\pi\)
\(450\) 0 0
\(451\) −0.628104 −0.0295763
\(452\) 0 0
\(453\) −35.7198 −1.67826
\(454\) 0 0
\(455\) 0.279184 0.0130883
\(456\) 0 0
\(457\) −2.91169 −0.136203 −0.0681015 0.997678i \(-0.521694\pi\)
−0.0681015 + 0.997678i \(0.521694\pi\)
\(458\) 0 0
\(459\) −3.80034 −0.177385
\(460\) 0 0
\(461\) −31.8908 −1.48530 −0.742652 0.669677i \(-0.766433\pi\)
−0.742652 + 0.669677i \(0.766433\pi\)
\(462\) 0 0
\(463\) 10.4282 0.484641 0.242320 0.970196i \(-0.422091\pi\)
0.242320 + 0.970196i \(0.422091\pi\)
\(464\) 0 0
\(465\) −5.55810 −0.257751
\(466\) 0 0
\(467\) 14.1950 0.656866 0.328433 0.944527i \(-0.393480\pi\)
0.328433 + 0.944527i \(0.393480\pi\)
\(468\) 0 0
\(469\) 2.41610 0.111565
\(470\) 0 0
\(471\) 3.36785 0.155182
\(472\) 0 0
\(473\) −2.32914 −0.107094
\(474\) 0 0
\(475\) 42.0991 1.93164
\(476\) 0 0
\(477\) 14.3111 0.655260
\(478\) 0 0
\(479\) 30.8316 1.40873 0.704365 0.709838i \(-0.251232\pi\)
0.704365 + 0.709838i \(0.251232\pi\)
\(480\) 0 0
\(481\) −7.36294 −0.335721
\(482\) 0 0
\(483\) 8.56656 0.389792
\(484\) 0 0
\(485\) −2.52201 −0.114518
\(486\) 0 0
\(487\) −22.2542 −1.00843 −0.504217 0.863577i \(-0.668219\pi\)
−0.504217 + 0.863577i \(0.668219\pi\)
\(488\) 0 0
\(489\) 26.9727 1.21975
\(490\) 0 0
\(491\) 3.96661 0.179010 0.0895052 0.995986i \(-0.471471\pi\)
0.0895052 + 0.995986i \(0.471471\pi\)
\(492\) 0 0
\(493\) 17.9815 0.809847
\(494\) 0 0
\(495\) 0.629387 0.0282888
\(496\) 0 0
\(497\) 13.8194 0.619885
\(498\) 0 0
\(499\) −28.3583 −1.26949 −0.634745 0.772722i \(-0.718895\pi\)
−0.634745 + 0.772722i \(0.718895\pi\)
\(500\) 0 0
\(501\) 24.5726 1.09782
\(502\) 0 0
\(503\) −4.75558 −0.212041 −0.106020 0.994364i \(-0.533811\pi\)
−0.106020 + 0.994364i \(0.533811\pi\)
\(504\) 0 0
\(505\) 0.437591 0.0194726
\(506\) 0 0
\(507\) 2.29224 0.101802
\(508\) 0 0
\(509\) −0.591914 −0.0262361 −0.0131181 0.999914i \(-0.504176\pi\)
−0.0131181 + 0.999914i \(0.504176\pi\)
\(510\) 0 0
\(511\) 7.30849 0.323309
\(512\) 0 0
\(513\) 14.6185 0.645424
\(514\) 0 0
\(515\) −1.59815 −0.0704231
\(516\) 0 0
\(517\) −3.73720 −0.164362
\(518\) 0 0
\(519\) 9.56294 0.419767
\(520\) 0 0
\(521\) 13.9905 0.612935 0.306468 0.951881i \(-0.400853\pi\)
0.306468 + 0.951881i \(0.400853\pi\)
\(522\) 0 0
\(523\) 12.1696 0.532138 0.266069 0.963954i \(-0.414275\pi\)
0.266069 + 0.963954i \(0.414275\pi\)
\(524\) 0 0
\(525\) 11.2826 0.492411
\(526\) 0 0
\(527\) −19.3116 −0.841229
\(528\) 0 0
\(529\) −9.03336 −0.392755
\(530\) 0 0
\(531\) 12.3027 0.533890
\(532\) 0 0
\(533\) 0.628104 0.0272062
\(534\) 0 0
\(535\) −0.111883 −0.00483714
\(536\) 0 0
\(537\) 35.6282 1.53747
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −0.354874 −0.0152572 −0.00762860 0.999971i \(-0.502428\pi\)
−0.00762860 + 0.999971i \(0.502428\pi\)
\(542\) 0 0
\(543\) 52.5551 2.25535
\(544\) 0 0
\(545\) −5.66958 −0.242858
\(546\) 0 0
\(547\) 27.8547 1.19098 0.595490 0.803363i \(-0.296958\pi\)
0.595490 + 0.803363i \(0.296958\pi\)
\(548\) 0 0
\(549\) 0.256865 0.0109627
\(550\) 0 0
\(551\) −69.1684 −2.94667
\(552\) 0 0
\(553\) 12.8219 0.545242
\(554\) 0 0
\(555\) 4.71197 0.200012
\(556\) 0 0
\(557\) −17.3136 −0.733602 −0.366801 0.930299i \(-0.619547\pi\)
−0.366801 + 0.930299i \(0.619547\pi\)
\(558\) 0 0
\(559\) 2.32914 0.0985123
\(560\) 0 0
\(561\) 5.09689 0.215191
\(562\) 0 0
\(563\) −5.13413 −0.216378 −0.108189 0.994130i \(-0.534505\pi\)
−0.108189 + 0.994130i \(0.534505\pi\)
\(564\) 0 0
\(565\) −3.38329 −0.142336
\(566\) 0 0
\(567\) 10.6809 0.448556
\(568\) 0 0
\(569\) −26.8307 −1.12480 −0.562401 0.826864i \(-0.690122\pi\)
−0.562401 + 0.826864i \(0.690122\pi\)
\(570\) 0 0
\(571\) −6.71293 −0.280927 −0.140464 0.990086i \(-0.544859\pi\)
−0.140464 + 0.990086i \(0.544859\pi\)
\(572\) 0 0
\(573\) 13.9363 0.582196
\(574\) 0 0
\(575\) 18.3947 0.767112
\(576\) 0 0
\(577\) 22.7930 0.948887 0.474443 0.880286i \(-0.342649\pi\)
0.474443 + 0.880286i \(0.342649\pi\)
\(578\) 0 0
\(579\) 1.72672 0.0717602
\(580\) 0 0
\(581\) −7.64233 −0.317057
\(582\) 0 0
\(583\) 6.34813 0.262913
\(584\) 0 0
\(585\) −0.629387 −0.0260219
\(586\) 0 0
\(587\) 12.8844 0.531795 0.265897 0.964001i \(-0.414332\pi\)
0.265897 + 0.964001i \(0.414332\pi\)
\(588\) 0 0
\(589\) 74.2850 3.06086
\(590\) 0 0
\(591\) 9.35889 0.384973
\(592\) 0 0
\(593\) −6.84093 −0.280923 −0.140462 0.990086i \(-0.544859\pi\)
−0.140462 + 0.990086i \(0.544859\pi\)
\(594\) 0 0
\(595\) −0.620776 −0.0254493
\(596\) 0 0
\(597\) 57.6603 2.35988
\(598\) 0 0
\(599\) 10.7168 0.437878 0.218939 0.975739i \(-0.429740\pi\)
0.218939 + 0.975739i \(0.429740\pi\)
\(600\) 0 0
\(601\) 15.4963 0.632108 0.316054 0.948741i \(-0.397642\pi\)
0.316054 + 0.948741i \(0.397642\pi\)
\(602\) 0 0
\(603\) −5.44681 −0.221811
\(604\) 0 0
\(605\) 0.279184 0.0113504
\(606\) 0 0
\(607\) −39.5904 −1.60693 −0.803463 0.595355i \(-0.797011\pi\)
−0.803463 + 0.595355i \(0.797011\pi\)
\(608\) 0 0
\(609\) −18.5371 −0.751162
\(610\) 0 0
\(611\) 3.73720 0.151191
\(612\) 0 0
\(613\) 5.56507 0.224771 0.112386 0.993665i \(-0.464151\pi\)
0.112386 + 0.993665i \(0.464151\pi\)
\(614\) 0 0
\(615\) −0.401960 −0.0162086
\(616\) 0 0
\(617\) −21.8623 −0.880141 −0.440071 0.897963i \(-0.645047\pi\)
−0.440071 + 0.897963i \(0.645047\pi\)
\(618\) 0 0
\(619\) −16.6118 −0.667685 −0.333842 0.942629i \(-0.608345\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(620\) 0 0
\(621\) 6.38740 0.256317
\(622\) 0 0
\(623\) −8.78585 −0.351998
\(624\) 0 0
\(625\) 23.8369 0.953477
\(626\) 0 0
\(627\) −19.6059 −0.782985
\(628\) 0 0
\(629\) 16.3718 0.652785
\(630\) 0 0
\(631\) 3.57830 0.142450 0.0712249 0.997460i \(-0.477309\pi\)
0.0712249 + 0.997460i \(0.477309\pi\)
\(632\) 0 0
\(633\) −10.8224 −0.430153
\(634\) 0 0
\(635\) −3.14734 −0.124898
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −31.1542 −1.23244
\(640\) 0 0
\(641\) −31.0054 −1.22464 −0.612319 0.790611i \(-0.709763\pi\)
−0.612319 + 0.790611i \(0.709763\pi\)
\(642\) 0 0
\(643\) 27.6660 1.09104 0.545520 0.838098i \(-0.316332\pi\)
0.545520 + 0.838098i \(0.316332\pi\)
\(644\) 0 0
\(645\) −1.49055 −0.0586905
\(646\) 0 0
\(647\) −3.56435 −0.140129 −0.0700645 0.997542i \(-0.522321\pi\)
−0.0700645 + 0.997542i \(0.522321\pi\)
\(648\) 0 0
\(649\) 5.45723 0.214215
\(650\) 0 0
\(651\) 19.9084 0.780271
\(652\) 0 0
\(653\) 23.2536 0.909983 0.454991 0.890496i \(-0.349642\pi\)
0.454991 + 0.890496i \(0.349642\pi\)
\(654\) 0 0
\(655\) 0.211281 0.00825545
\(656\) 0 0
\(657\) −16.4761 −0.642795
\(658\) 0 0
\(659\) −17.8541 −0.695498 −0.347749 0.937588i \(-0.613054\pi\)
−0.347749 + 0.937588i \(0.613054\pi\)
\(660\) 0 0
\(661\) 43.8439 1.70533 0.852666 0.522457i \(-0.174984\pi\)
0.852666 + 0.522457i \(0.174984\pi\)
\(662\) 0 0
\(663\) −5.09689 −0.197947
\(664\) 0 0
\(665\) 2.38790 0.0925989
\(666\) 0 0
\(667\) −30.2223 −1.17021
\(668\) 0 0
\(669\) 33.8462 1.30857
\(670\) 0 0
\(671\) 0.113940 0.00439862
\(672\) 0 0
\(673\) −19.5097 −0.752046 −0.376023 0.926610i \(-0.622709\pi\)
−0.376023 + 0.926610i \(0.622709\pi\)
\(674\) 0 0
\(675\) 8.41249 0.323797
\(676\) 0 0
\(677\) 35.4639 1.36299 0.681494 0.731824i \(-0.261331\pi\)
0.681494 + 0.731824i \(0.261331\pi\)
\(678\) 0 0
\(679\) 9.03350 0.346674
\(680\) 0 0
\(681\) −28.6096 −1.09632
\(682\) 0 0
\(683\) 18.7385 0.717007 0.358504 0.933528i \(-0.383287\pi\)
0.358504 + 0.933528i \(0.383287\pi\)
\(684\) 0 0
\(685\) −2.16939 −0.0828881
\(686\) 0 0
\(687\) −44.6146 −1.70215
\(688\) 0 0
\(689\) −6.34813 −0.241844
\(690\) 0 0
\(691\) −31.2763 −1.18981 −0.594904 0.803797i \(-0.702810\pi\)
−0.594904 + 0.803797i \(0.702810\pi\)
\(692\) 0 0
\(693\) −2.25438 −0.0856368
\(694\) 0 0
\(695\) −3.84409 −0.145815
\(696\) 0 0
\(697\) −1.39661 −0.0529005
\(698\) 0 0
\(699\) 3.00221 0.113554
\(700\) 0 0
\(701\) −1.79838 −0.0679239 −0.0339620 0.999423i \(-0.510813\pi\)
−0.0339620 + 0.999423i \(0.510813\pi\)
\(702\) 0 0
\(703\) −62.9763 −2.37520
\(704\) 0 0
\(705\) −2.39165 −0.0900747
\(706\) 0 0
\(707\) −1.56739 −0.0589479
\(708\) 0 0
\(709\) −5.22509 −0.196232 −0.0981162 0.995175i \(-0.531282\pi\)
−0.0981162 + 0.995175i \(0.531282\pi\)
\(710\) 0 0
\(711\) −28.9054 −1.08404
\(712\) 0 0
\(713\) 32.4579 1.21556
\(714\) 0 0
\(715\) −0.279184 −0.0104409
\(716\) 0 0
\(717\) −39.5349 −1.47646
\(718\) 0 0
\(719\) −28.8074 −1.07433 −0.537167 0.843476i \(-0.680505\pi\)
−0.537167 + 0.843476i \(0.680505\pi\)
\(720\) 0 0
\(721\) 5.72438 0.213187
\(722\) 0 0
\(723\) −5.74210 −0.213551
\(724\) 0 0
\(725\) −39.8041 −1.47829
\(726\) 0 0
\(727\) 12.5656 0.466033 0.233016 0.972473i \(-0.425140\pi\)
0.233016 + 0.972473i \(0.425140\pi\)
\(728\) 0 0
\(729\) −12.3255 −0.456501
\(730\) 0 0
\(731\) −5.17894 −0.191550
\(732\) 0 0
\(733\) 26.1826 0.967075 0.483538 0.875324i \(-0.339352\pi\)
0.483538 + 0.875324i \(0.339352\pi\)
\(734\) 0 0
\(735\) 0.639958 0.0236052
\(736\) 0 0
\(737\) −2.41610 −0.0889983
\(738\) 0 0
\(739\) 43.0901 1.58509 0.792547 0.609811i \(-0.208755\pi\)
0.792547 + 0.609811i \(0.208755\pi\)
\(740\) 0 0
\(741\) 19.6059 0.720241
\(742\) 0 0
\(743\) 16.2792 0.597226 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(744\) 0 0
\(745\) 1.89361 0.0693764
\(746\) 0 0
\(747\) 17.2287 0.630366
\(748\) 0 0
\(749\) 0.400752 0.0146431
\(750\) 0 0
\(751\) 28.8174 1.05156 0.525780 0.850621i \(-0.323773\pi\)
0.525780 + 0.850621i \(0.323773\pi\)
\(752\) 0 0
\(753\) −3.78901 −0.138079
\(754\) 0 0
\(755\) −4.35050 −0.158331
\(756\) 0 0
\(757\) −22.0739 −0.802290 −0.401145 0.916015i \(-0.631388\pi\)
−0.401145 + 0.916015i \(0.631388\pi\)
\(758\) 0 0
\(759\) −8.56656 −0.310947
\(760\) 0 0
\(761\) 16.4069 0.594748 0.297374 0.954761i \(-0.403889\pi\)
0.297374 + 0.954761i \(0.403889\pi\)
\(762\) 0 0
\(763\) 20.3077 0.735187
\(764\) 0 0
\(765\) 1.39947 0.0505978
\(766\) 0 0
\(767\) −5.45723 −0.197049
\(768\) 0 0
\(769\) −23.4283 −0.844846 −0.422423 0.906399i \(-0.638820\pi\)
−0.422423 + 0.906399i \(0.638820\pi\)
\(770\) 0 0
\(771\) 41.5930 1.49793
\(772\) 0 0
\(773\) 13.7376 0.494106 0.247053 0.969002i \(-0.420538\pi\)
0.247053 + 0.969002i \(0.420538\pi\)
\(774\) 0 0
\(775\) 42.7486 1.53557
\(776\) 0 0
\(777\) −16.8776 −0.605482
\(778\) 0 0
\(779\) 5.37227 0.192482
\(780\) 0 0
\(781\) −13.8194 −0.494497
\(782\) 0 0
\(783\) −13.8216 −0.493945
\(784\) 0 0
\(785\) 0.410188 0.0146402
\(786\) 0 0
\(787\) −39.8352 −1.41997 −0.709986 0.704215i \(-0.751299\pi\)
−0.709986 + 0.704215i \(0.751299\pi\)
\(788\) 0 0
\(789\) 24.9821 0.889386
\(790\) 0 0
\(791\) 12.1185 0.430885
\(792\) 0 0
\(793\) −0.113940 −0.00404614
\(794\) 0 0
\(795\) 4.06253 0.144083
\(796\) 0 0
\(797\) 23.7805 0.842349 0.421174 0.906980i \(-0.361618\pi\)
0.421174 + 0.906980i \(0.361618\pi\)
\(798\) 0 0
\(799\) −8.30980 −0.293979
\(800\) 0 0
\(801\) 19.8067 0.699834
\(802\) 0 0
\(803\) −7.30849 −0.257911
\(804\) 0 0
\(805\) 1.04337 0.0367738
\(806\) 0 0
\(807\) 49.1504 1.73017
\(808\) 0 0
\(809\) −24.7253 −0.869294 −0.434647 0.900601i \(-0.643127\pi\)
−0.434647 + 0.900601i \(0.643127\pi\)
\(810\) 0 0
\(811\) 29.7470 1.04456 0.522280 0.852774i \(-0.325082\pi\)
0.522280 + 0.852774i \(0.325082\pi\)
\(812\) 0 0
\(813\) −43.2255 −1.51599
\(814\) 0 0
\(815\) 3.28514 0.115073
\(816\) 0 0
\(817\) 19.9215 0.696966
\(818\) 0 0
\(819\) 2.25438 0.0787744
\(820\) 0 0
\(821\) 18.2476 0.636847 0.318423 0.947949i \(-0.396847\pi\)
0.318423 + 0.947949i \(0.396847\pi\)
\(822\) 0 0
\(823\) 41.8020 1.45713 0.728563 0.684979i \(-0.240189\pi\)
0.728563 + 0.684979i \(0.240189\pi\)
\(824\) 0 0
\(825\) −11.2826 −0.392808
\(826\) 0 0
\(827\) −34.0851 −1.18526 −0.592628 0.805477i \(-0.701909\pi\)
−0.592628 + 0.805477i \(0.701909\pi\)
\(828\) 0 0
\(829\) 31.9074 1.10819 0.554095 0.832454i \(-0.313064\pi\)
0.554095 + 0.832454i \(0.313064\pi\)
\(830\) 0 0
\(831\) 0.430142 0.0149215
\(832\) 0 0
\(833\) 2.22354 0.0770410
\(834\) 0 0
\(835\) 2.99282 0.103571
\(836\) 0 0
\(837\) 14.8441 0.513086
\(838\) 0 0
\(839\) −32.9192 −1.13650 −0.568248 0.822857i \(-0.692379\pi\)
−0.568248 + 0.822857i \(0.692379\pi\)
\(840\) 0 0
\(841\) 36.3979 1.25510
\(842\) 0 0
\(843\) −72.0579 −2.48180
\(844\) 0 0
\(845\) 0.279184 0.00960422
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −4.40933 −0.151328
\(850\) 0 0
\(851\) −27.5167 −0.943262
\(852\) 0 0
\(853\) −37.3653 −1.27936 −0.639681 0.768640i \(-0.720934\pi\)
−0.639681 + 0.768640i \(0.720934\pi\)
\(854\) 0 0
\(855\) −5.38324 −0.184103
\(856\) 0 0
\(857\) 10.1339 0.346169 0.173085 0.984907i \(-0.444627\pi\)
0.173085 + 0.984907i \(0.444627\pi\)
\(858\) 0 0
\(859\) −18.7270 −0.638958 −0.319479 0.947593i \(-0.603508\pi\)
−0.319479 + 0.947593i \(0.603508\pi\)
\(860\) 0 0
\(861\) 1.43977 0.0490671
\(862\) 0 0
\(863\) 3.82969 0.130364 0.0651821 0.997873i \(-0.479237\pi\)
0.0651821 + 0.997873i \(0.479237\pi\)
\(864\) 0 0
\(865\) 1.16472 0.0396016
\(866\) 0 0
\(867\) −27.6350 −0.938534
\(868\) 0 0
\(869\) −12.8219 −0.434952
\(870\) 0 0
\(871\) 2.41610 0.0818665
\(872\) 0 0
\(873\) −20.3649 −0.689249
\(874\) 0 0
\(875\) 2.77008 0.0936458
\(876\) 0 0
\(877\) 28.2904 0.955300 0.477650 0.878550i \(-0.341489\pi\)
0.477650 + 0.878550i \(0.341489\pi\)
\(878\) 0 0
\(879\) 34.8935 1.17693
\(880\) 0 0
\(881\) 38.8110 1.30757 0.653787 0.756678i \(-0.273179\pi\)
0.653787 + 0.756678i \(0.273179\pi\)
\(882\) 0 0
\(883\) 15.9988 0.538402 0.269201 0.963084i \(-0.413240\pi\)
0.269201 + 0.963084i \(0.413240\pi\)
\(884\) 0 0
\(885\) 3.49240 0.117396
\(886\) 0 0
\(887\) 10.4734 0.351663 0.175832 0.984420i \(-0.443739\pi\)
0.175832 + 0.984420i \(0.443739\pi\)
\(888\) 0 0
\(889\) 11.2734 0.378096
\(890\) 0 0
\(891\) −10.6809 −0.357824
\(892\) 0 0
\(893\) 31.9648 1.06966
\(894\) 0 0
\(895\) 4.33934 0.145048
\(896\) 0 0
\(897\) 8.56656 0.286029
\(898\) 0 0
\(899\) −70.2355 −2.34248
\(900\) 0 0
\(901\) 14.1153 0.470249
\(902\) 0 0
\(903\) 5.33896 0.177670
\(904\) 0 0
\(905\) 6.40095 0.212775
\(906\) 0 0
\(907\) 1.14389 0.0379823 0.0189912 0.999820i \(-0.493955\pi\)
0.0189912 + 0.999820i \(0.493955\pi\)
\(908\) 0 0
\(909\) 3.53350 0.117199
\(910\) 0 0
\(911\) −40.1015 −1.32862 −0.664312 0.747456i \(-0.731275\pi\)
−0.664312 + 0.747456i \(0.731275\pi\)
\(912\) 0 0
\(913\) 7.64233 0.252924
\(914\) 0 0
\(915\) 0.0729171 0.00241056
\(916\) 0 0
\(917\) −0.756782 −0.0249911
\(918\) 0 0
\(919\) 35.0200 1.15520 0.577601 0.816319i \(-0.303989\pi\)
0.577601 + 0.816319i \(0.303989\pi\)
\(920\) 0 0
\(921\) −66.5430 −2.19267
\(922\) 0 0
\(923\) 13.8194 0.454872
\(924\) 0 0
\(925\) −36.2408 −1.19159
\(926\) 0 0
\(927\) −12.9049 −0.423853
\(928\) 0 0
\(929\) −28.5737 −0.937471 −0.468736 0.883338i \(-0.655290\pi\)
−0.468736 + 0.883338i \(0.655290\pi\)
\(930\) 0 0
\(931\) −8.55315 −0.280318
\(932\) 0 0
\(933\) 43.3049 1.41774
\(934\) 0 0
\(935\) 0.620776 0.0203015
\(936\) 0 0
\(937\) 0.618145 0.0201939 0.0100970 0.999949i \(-0.496786\pi\)
0.0100970 + 0.999949i \(0.496786\pi\)
\(938\) 0 0
\(939\) −27.0913 −0.884091
\(940\) 0 0
\(941\) −1.65313 −0.0538905 −0.0269453 0.999637i \(-0.508578\pi\)
−0.0269453 + 0.999637i \(0.508578\pi\)
\(942\) 0 0
\(943\) 2.34735 0.0764402
\(944\) 0 0
\(945\) 0.477165 0.0155222
\(946\) 0 0
\(947\) 25.0407 0.813713 0.406857 0.913492i \(-0.366625\pi\)
0.406857 + 0.913492i \(0.366625\pi\)
\(948\) 0 0
\(949\) 7.30849 0.237244
\(950\) 0 0
\(951\) 68.3797 2.21736
\(952\) 0 0
\(953\) −46.9384 −1.52048 −0.760242 0.649640i \(-0.774920\pi\)
−0.760242 + 0.649640i \(0.774920\pi\)
\(954\) 0 0
\(955\) 1.69737 0.0549256
\(956\) 0 0
\(957\) 18.5371 0.599220
\(958\) 0 0
\(959\) 7.77046 0.250921
\(960\) 0 0
\(961\) 44.4310 1.43326
\(962\) 0 0
\(963\) −0.903447 −0.0291132
\(964\) 0 0
\(965\) 0.210307 0.00677001
\(966\) 0 0
\(967\) −19.5619 −0.629067 −0.314534 0.949246i \(-0.601848\pi\)
−0.314534 + 0.949246i \(0.601848\pi\)
\(968\) 0 0
\(969\) −43.5945 −1.40046
\(970\) 0 0
\(971\) 20.3428 0.652832 0.326416 0.945226i \(-0.394159\pi\)
0.326416 + 0.945226i \(0.394159\pi\)
\(972\) 0 0
\(973\) 13.7690 0.441414
\(974\) 0 0
\(975\) 11.2826 0.361331
\(976\) 0 0
\(977\) 23.5135 0.752264 0.376132 0.926566i \(-0.377254\pi\)
0.376132 + 0.926566i \(0.377254\pi\)
\(978\) 0 0
\(979\) 8.78585 0.280797
\(980\) 0 0
\(981\) −45.7812 −1.46168
\(982\) 0 0
\(983\) −48.2794 −1.53987 −0.769936 0.638121i \(-0.779712\pi\)
−0.769936 + 0.638121i \(0.779712\pi\)
\(984\) 0 0
\(985\) 1.13987 0.0363192
\(986\) 0 0
\(987\) 8.56656 0.272677
\(988\) 0 0
\(989\) 8.70447 0.276786
\(990\) 0 0
\(991\) −15.5806 −0.494933 −0.247467 0.968896i \(-0.579598\pi\)
−0.247467 + 0.968896i \(0.579598\pi\)
\(992\) 0 0
\(993\) 1.22905 0.0390027
\(994\) 0 0
\(995\) 7.02275 0.222636
\(996\) 0 0
\(997\) −3.57523 −0.113229 −0.0566144 0.998396i \(-0.518031\pi\)
−0.0566144 + 0.998396i \(0.518031\pi\)
\(998\) 0 0
\(999\) −12.5843 −0.398150
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 \(a_p\))