Properties

Label 8008.2.a.v.1.4
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 1.4
Root \(1.48564\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.48564 q^{3} -0.395242 q^{5} -1.00000 q^{7} -0.792869 q^{9} +O(q^{10})\) \(q-1.48564 q^{3} -0.395242 q^{5} -1.00000 q^{7} -0.792869 q^{9} +1.00000 q^{11} -1.00000 q^{13} +0.587188 q^{15} -2.74936 q^{17} +5.24077 q^{19} +1.48564 q^{21} -2.01585 q^{23} -4.84378 q^{25} +5.63484 q^{27} +5.19717 q^{29} -8.17745 q^{31} -1.48564 q^{33} +0.395242 q^{35} +3.28617 q^{37} +1.48564 q^{39} +9.42704 q^{41} +6.55917 q^{43} +0.313375 q^{45} -2.01585 q^{47} +1.00000 q^{49} +4.08457 q^{51} -4.08665 q^{53} -0.395242 q^{55} -7.78591 q^{57} +9.11865 q^{59} +9.32901 q^{61} +0.792869 q^{63} +0.395242 q^{65} -8.16464 q^{67} +2.99483 q^{69} -2.19413 q^{71} -9.40454 q^{73} +7.19613 q^{75} -1.00000 q^{77} +5.94436 q^{79} -5.99275 q^{81} -12.9777 q^{83} +1.08666 q^{85} -7.72113 q^{87} +2.69667 q^{89} +1.00000 q^{91} +12.1488 q^{93} -2.07137 q^{95} -9.44684 q^{97} -0.792869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) −1.48564 −0.857736 −0.428868 0.903367i \(-0.641087\pi\)
−0.428868 + 0.903367i \(0.641087\pi\)
\(4\) 0 0
\(5\) −0.395242 −0.176758 −0.0883788 0.996087i \(-0.528169\pi\)
−0.0883788 + 0.996087i \(0.528169\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.792869 −0.264290
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.587188 0.151611
\(16\) 0 0
\(17\) −2.74936 −0.666819 −0.333409 0.942782i \(-0.608199\pi\)
−0.333409 + 0.942782i \(0.608199\pi\)
\(18\) 0 0
\(19\) 5.24077 1.20232 0.601158 0.799130i \(-0.294706\pi\)
0.601158 + 0.799130i \(0.294706\pi\)
\(20\) 0 0
\(21\) 1.48564 0.324194
\(22\) 0 0
\(23\) −2.01585 −0.420334 −0.210167 0.977666i \(-0.567401\pi\)
−0.210167 + 0.977666i \(0.567401\pi\)
\(24\) 0 0
\(25\) −4.84378 −0.968757
\(26\) 0 0
\(27\) 5.63484 1.08443
\(28\) 0 0
\(29\) 5.19717 0.965090 0.482545 0.875871i \(-0.339713\pi\)
0.482545 + 0.875871i \(0.339713\pi\)
\(30\) 0 0
\(31\) −8.17745 −1.46871 −0.734357 0.678764i \(-0.762516\pi\)
−0.734357 + 0.678764i \(0.762516\pi\)
\(32\) 0 0
\(33\) −1.48564 −0.258617
\(34\) 0 0
\(35\) 0.395242 0.0668081
\(36\) 0 0
\(37\) 3.28617 0.540244 0.270122 0.962826i \(-0.412936\pi\)
0.270122 + 0.962826i \(0.412936\pi\)
\(38\) 0 0
\(39\) 1.48564 0.237893
\(40\) 0 0
\(41\) 9.42704 1.47226 0.736128 0.676842i \(-0.236652\pi\)
0.736128 + 0.676842i \(0.236652\pi\)
\(42\) 0 0
\(43\) 6.55917 1.00026 0.500132 0.865949i \(-0.333285\pi\)
0.500132 + 0.865949i \(0.333285\pi\)
\(44\) 0 0
\(45\) 0.313375 0.0467152
\(46\) 0 0
\(47\) −2.01585 −0.294042 −0.147021 0.989133i \(-0.546968\pi\)
−0.147021 + 0.989133i \(0.546968\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.08457 0.571954
\(52\) 0 0
\(53\) −4.08665 −0.561344 −0.280672 0.959804i \(-0.590557\pi\)
−0.280672 + 0.959804i \(0.590557\pi\)
\(54\) 0 0
\(55\) −0.395242 −0.0532944
\(56\) 0 0
\(57\) −7.78591 −1.03127
\(58\) 0 0
\(59\) 9.11865 1.18715 0.593573 0.804780i \(-0.297717\pi\)
0.593573 + 0.804780i \(0.297717\pi\)
\(60\) 0 0
\(61\) 9.32901 1.19446 0.597229 0.802071i \(-0.296268\pi\)
0.597229 + 0.802071i \(0.296268\pi\)
\(62\) 0 0
\(63\) 0.792869 0.0998921
\(64\) 0 0
\(65\) 0.395242 0.0490237
\(66\) 0 0
\(67\) −8.16464 −0.997470 −0.498735 0.866754i \(-0.666202\pi\)
−0.498735 + 0.866754i \(0.666202\pi\)
\(68\) 0 0
\(69\) 2.99483 0.360535
\(70\) 0 0
\(71\) −2.19413 −0.260395 −0.130198 0.991488i \(-0.541561\pi\)
−0.130198 + 0.991488i \(0.541561\pi\)
\(72\) 0 0
\(73\) −9.40454 −1.10072 −0.550359 0.834928i \(-0.685509\pi\)
−0.550359 + 0.834928i \(0.685509\pi\)
\(74\) 0 0
\(75\) 7.19613 0.830937
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 5.94436 0.668793 0.334396 0.942433i \(-0.391468\pi\)
0.334396 + 0.942433i \(0.391468\pi\)
\(80\) 0 0
\(81\) −5.99275 −0.665861
\(82\) 0 0
\(83\) −12.9777 −1.42449 −0.712246 0.701930i \(-0.752322\pi\)
−0.712246 + 0.701930i \(0.752322\pi\)
\(84\) 0 0
\(85\) 1.08666 0.117865
\(86\) 0 0
\(87\) −7.72113 −0.827792
\(88\) 0 0
\(89\) 2.69667 0.285847 0.142923 0.989734i \(-0.454350\pi\)
0.142923 + 0.989734i \(0.454350\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 12.1488 1.25977
\(94\) 0 0
\(95\) −2.07137 −0.212518
\(96\) 0 0
\(97\) −9.44684 −0.959181 −0.479591 0.877492i \(-0.659215\pi\)
−0.479591 + 0.877492i \(0.659215\pi\)
\(98\) 0 0
\(99\) −0.792869 −0.0796864
\(100\) 0 0
\(101\) 4.33953 0.431800 0.215900 0.976416i \(-0.430732\pi\)
0.215900 + 0.976416i \(0.430732\pi\)
\(102\) 0 0
\(103\) −7.30468 −0.719751 −0.359876 0.933000i \(-0.617181\pi\)
−0.359876 + 0.933000i \(0.617181\pi\)
\(104\) 0 0
\(105\) −0.587188 −0.0573037
\(106\) 0 0
\(107\) −12.5263 −1.21096 −0.605481 0.795860i \(-0.707019\pi\)
−0.605481 + 0.795860i \(0.707019\pi\)
\(108\) 0 0
\(109\) 17.8768 1.71229 0.856144 0.516737i \(-0.172853\pi\)
0.856144 + 0.516737i \(0.172853\pi\)
\(110\) 0 0
\(111\) −4.88208 −0.463386
\(112\) 0 0
\(113\) −3.36174 −0.316246 −0.158123 0.987419i \(-0.550544\pi\)
−0.158123 + 0.987419i \(0.550544\pi\)
\(114\) 0 0
\(115\) 0.796748 0.0742971
\(116\) 0 0
\(117\) 0.792869 0.0733008
\(118\) 0 0
\(119\) 2.74936 0.252034
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −14.0052 −1.26281
\(124\) 0 0
\(125\) 3.89068 0.347993
\(126\) 0 0
\(127\) 14.3023 1.26913 0.634563 0.772871i \(-0.281180\pi\)
0.634563 + 0.772871i \(0.281180\pi\)
\(128\) 0 0
\(129\) −9.74457 −0.857961
\(130\) 0 0
\(131\) 14.3233 1.25143 0.625715 0.780051i \(-0.284807\pi\)
0.625715 + 0.780051i \(0.284807\pi\)
\(132\) 0 0
\(133\) −5.24077 −0.454432
\(134\) 0 0
\(135\) −2.22713 −0.191681
\(136\) 0 0
\(137\) 5.01281 0.428273 0.214137 0.976804i \(-0.431306\pi\)
0.214137 + 0.976804i \(0.431306\pi\)
\(138\) 0 0
\(139\) 6.11317 0.518513 0.259256 0.965809i \(-0.416523\pi\)
0.259256 + 0.965809i \(0.416523\pi\)
\(140\) 0 0
\(141\) 2.99483 0.252210
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −2.05414 −0.170587
\(146\) 0 0
\(147\) −1.48564 −0.122534
\(148\) 0 0
\(149\) −3.57652 −0.293000 −0.146500 0.989211i \(-0.546801\pi\)
−0.146500 + 0.989211i \(0.546801\pi\)
\(150\) 0 0
\(151\) 0.966800 0.0786771 0.0393385 0.999226i \(-0.487475\pi\)
0.0393385 + 0.999226i \(0.487475\pi\)
\(152\) 0 0
\(153\) 2.17989 0.176233
\(154\) 0 0
\(155\) 3.23207 0.259606
\(156\) 0 0
\(157\) −8.48916 −0.677509 −0.338754 0.940875i \(-0.610006\pi\)
−0.338754 + 0.940875i \(0.610006\pi\)
\(158\) 0 0
\(159\) 6.07129 0.481485
\(160\) 0 0
\(161\) 2.01585 0.158871
\(162\) 0 0
\(163\) −14.3150 −1.12124 −0.560620 0.828073i \(-0.689437\pi\)
−0.560620 + 0.828073i \(0.689437\pi\)
\(164\) 0 0
\(165\) 0.587188 0.0457125
\(166\) 0 0
\(167\) 10.8926 0.842892 0.421446 0.906854i \(-0.361523\pi\)
0.421446 + 0.906854i \(0.361523\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.15525 −0.317760
\(172\) 0 0
\(173\) 20.8125 1.58234 0.791172 0.611594i \(-0.209471\pi\)
0.791172 + 0.611594i \(0.209471\pi\)
\(174\) 0 0
\(175\) 4.84378 0.366156
\(176\) 0 0
\(177\) −13.5470 −1.01826
\(178\) 0 0
\(179\) −23.2990 −1.74145 −0.870726 0.491769i \(-0.836350\pi\)
−0.870726 + 0.491769i \(0.836350\pi\)
\(180\) 0 0
\(181\) −3.77497 −0.280591 −0.140296 0.990110i \(-0.544805\pi\)
−0.140296 + 0.990110i \(0.544805\pi\)
\(182\) 0 0
\(183\) −13.8596 −1.02453
\(184\) 0 0
\(185\) −1.29883 −0.0954922
\(186\) 0 0
\(187\) −2.74936 −0.201053
\(188\) 0 0
\(189\) −5.63484 −0.409875
\(190\) 0 0
\(191\) 8.41627 0.608980 0.304490 0.952515i \(-0.401514\pi\)
0.304490 + 0.952515i \(0.401514\pi\)
\(192\) 0 0
\(193\) 18.7515 1.34976 0.674880 0.737928i \(-0.264196\pi\)
0.674880 + 0.737928i \(0.264196\pi\)
\(194\) 0 0
\(195\) −0.587188 −0.0420494
\(196\) 0 0
\(197\) −4.89963 −0.349084 −0.174542 0.984650i \(-0.555845\pi\)
−0.174542 + 0.984650i \(0.555845\pi\)
\(198\) 0 0
\(199\) −20.8729 −1.47964 −0.739822 0.672803i \(-0.765090\pi\)
−0.739822 + 0.672803i \(0.765090\pi\)
\(200\) 0 0
\(201\) 12.1297 0.855566
\(202\) 0 0
\(203\) −5.19717 −0.364770
\(204\) 0 0
\(205\) −3.72596 −0.260232
\(206\) 0 0
\(207\) 1.59831 0.111090
\(208\) 0 0
\(209\) 5.24077 0.362512
\(210\) 0 0
\(211\) −25.0853 −1.72694 −0.863470 0.504400i \(-0.831714\pi\)
−0.863470 + 0.504400i \(0.831714\pi\)
\(212\) 0 0
\(213\) 3.25969 0.223350
\(214\) 0 0
\(215\) −2.59246 −0.176804
\(216\) 0 0
\(217\) 8.17745 0.555122
\(218\) 0 0
\(219\) 13.9718 0.944125
\(220\) 0 0
\(221\) 2.74936 0.184942
\(222\) 0 0
\(223\) −19.0089 −1.27293 −0.636464 0.771307i \(-0.719604\pi\)
−0.636464 + 0.771307i \(0.719604\pi\)
\(224\) 0 0
\(225\) 3.84049 0.256033
\(226\) 0 0
\(227\) −6.05764 −0.402060 −0.201030 0.979585i \(-0.564429\pi\)
−0.201030 + 0.979585i \(0.564429\pi\)
\(228\) 0 0
\(229\) 16.9295 1.11874 0.559368 0.828920i \(-0.311044\pi\)
0.559368 + 0.828920i \(0.311044\pi\)
\(230\) 0 0
\(231\) 1.48564 0.0977480
\(232\) 0 0
\(233\) −1.52201 −0.0997099 −0.0498550 0.998756i \(-0.515876\pi\)
−0.0498550 + 0.998756i \(0.515876\pi\)
\(234\) 0 0
\(235\) 0.796748 0.0519741
\(236\) 0 0
\(237\) −8.83118 −0.573647
\(238\) 0 0
\(239\) −17.0413 −1.10231 −0.551156 0.834402i \(-0.685813\pi\)
−0.551156 + 0.834402i \(0.685813\pi\)
\(240\) 0 0
\(241\) 6.41585 0.413281 0.206641 0.978417i \(-0.433747\pi\)
0.206641 + 0.978417i \(0.433747\pi\)
\(242\) 0 0
\(243\) −8.00145 −0.513294
\(244\) 0 0
\(245\) −0.395242 −0.0252511
\(246\) 0 0
\(247\) −5.24077 −0.333462
\(248\) 0 0
\(249\) 19.2803 1.22184
\(250\) 0 0
\(251\) −23.8571 −1.50585 −0.752924 0.658107i \(-0.771357\pi\)
−0.752924 + 0.658107i \(0.771357\pi\)
\(252\) 0 0
\(253\) −2.01585 −0.126735
\(254\) 0 0
\(255\) −1.61439 −0.101097
\(256\) 0 0
\(257\) 15.2849 0.953447 0.476724 0.879053i \(-0.341824\pi\)
0.476724 + 0.879053i \(0.341824\pi\)
\(258\) 0 0
\(259\) −3.28617 −0.204193
\(260\) 0 0
\(261\) −4.12067 −0.255063
\(262\) 0 0
\(263\) −25.5748 −1.57701 −0.788504 0.615029i \(-0.789144\pi\)
−0.788504 + 0.615029i \(0.789144\pi\)
\(264\) 0 0
\(265\) 1.61521 0.0992218
\(266\) 0 0
\(267\) −4.00629 −0.245181
\(268\) 0 0
\(269\) −11.9514 −0.728690 −0.364345 0.931264i \(-0.618707\pi\)
−0.364345 + 0.931264i \(0.618707\pi\)
\(270\) 0 0
\(271\) −20.0837 −1.22000 −0.610000 0.792401i \(-0.708831\pi\)
−0.610000 + 0.792401i \(0.708831\pi\)
\(272\) 0 0
\(273\) −1.48564 −0.0899151
\(274\) 0 0
\(275\) −4.84378 −0.292091
\(276\) 0 0
\(277\) −11.8713 −0.713279 −0.356640 0.934242i \(-0.616078\pi\)
−0.356640 + 0.934242i \(0.616078\pi\)
\(278\) 0 0
\(279\) 6.48365 0.388166
\(280\) 0 0
\(281\) −12.9066 −0.769943 −0.384971 0.922928i \(-0.625789\pi\)
−0.384971 + 0.922928i \(0.625789\pi\)
\(282\) 0 0
\(283\) 5.52500 0.328427 0.164214 0.986425i \(-0.447491\pi\)
0.164214 + 0.986425i \(0.447491\pi\)
\(284\) 0 0
\(285\) 3.07732 0.182284
\(286\) 0 0
\(287\) −9.42704 −0.556461
\(288\) 0 0
\(289\) −9.44099 −0.555353
\(290\) 0 0
\(291\) 14.0346 0.822724
\(292\) 0 0
\(293\) 5.09243 0.297503 0.148751 0.988875i \(-0.452475\pi\)
0.148751 + 0.988875i \(0.452475\pi\)
\(294\) 0 0
\(295\) −3.60407 −0.209837
\(296\) 0 0
\(297\) 5.63484 0.326967
\(298\) 0 0
\(299\) 2.01585 0.116580
\(300\) 0 0
\(301\) −6.55917 −0.378064
\(302\) 0 0
\(303\) −6.44699 −0.370370
\(304\) 0 0
\(305\) −3.68722 −0.211129
\(306\) 0 0
\(307\) 29.9067 1.70686 0.853431 0.521205i \(-0.174517\pi\)
0.853431 + 0.521205i \(0.174517\pi\)
\(308\) 0 0
\(309\) 10.8521 0.617356
\(310\) 0 0
\(311\) 14.2096 0.805755 0.402877 0.915254i \(-0.368010\pi\)
0.402877 + 0.915254i \(0.368010\pi\)
\(312\) 0 0
\(313\) −25.7745 −1.45686 −0.728430 0.685120i \(-0.759750\pi\)
−0.728430 + 0.685120i \(0.759750\pi\)
\(314\) 0 0
\(315\) −0.313375 −0.0176567
\(316\) 0 0
\(317\) −18.9921 −1.06670 −0.533352 0.845893i \(-0.679068\pi\)
−0.533352 + 0.845893i \(0.679068\pi\)
\(318\) 0 0
\(319\) 5.19717 0.290985
\(320\) 0 0
\(321\) 18.6096 1.03869
\(322\) 0 0
\(323\) −14.4088 −0.801727
\(324\) 0 0
\(325\) 4.84378 0.268685
\(326\) 0 0
\(327\) −26.5585 −1.46869
\(328\) 0 0
\(329\) 2.01585 0.111137
\(330\) 0 0
\(331\) −23.1626 −1.27313 −0.636565 0.771223i \(-0.719645\pi\)
−0.636565 + 0.771223i \(0.719645\pi\)
\(332\) 0 0
\(333\) −2.60551 −0.142781
\(334\) 0 0
\(335\) 3.22701 0.176310
\(336\) 0 0
\(337\) 3.46696 0.188857 0.0944287 0.995532i \(-0.469898\pi\)
0.0944287 + 0.995532i \(0.469898\pi\)
\(338\) 0 0
\(339\) 4.99435 0.271256
\(340\) 0 0
\(341\) −8.17745 −0.442834
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.18368 −0.0637273
\(346\) 0 0
\(347\) −16.5966 −0.890954 −0.445477 0.895293i \(-0.646966\pi\)
−0.445477 + 0.895293i \(0.646966\pi\)
\(348\) 0 0
\(349\) 24.3800 1.30503 0.652515 0.757776i \(-0.273714\pi\)
0.652515 + 0.757776i \(0.273714\pi\)
\(350\) 0 0
\(351\) −5.63484 −0.300766
\(352\) 0 0
\(353\) 2.00125 0.106516 0.0532578 0.998581i \(-0.483039\pi\)
0.0532578 + 0.998581i \(0.483039\pi\)
\(354\) 0 0
\(355\) 0.867212 0.0460268
\(356\) 0 0
\(357\) −4.08457 −0.216178
\(358\) 0 0
\(359\) 8.62284 0.455096 0.227548 0.973767i \(-0.426929\pi\)
0.227548 + 0.973767i \(0.426929\pi\)
\(360\) 0 0
\(361\) 8.46568 0.445562
\(362\) 0 0
\(363\) −1.48564 −0.0779760
\(364\) 0 0
\(365\) 3.71707 0.194560
\(366\) 0 0
\(367\) −4.63360 −0.241872 −0.120936 0.992660i \(-0.538590\pi\)
−0.120936 + 0.992660i \(0.538590\pi\)
\(368\) 0 0
\(369\) −7.47441 −0.389102
\(370\) 0 0
\(371\) 4.08665 0.212168
\(372\) 0 0
\(373\) −27.9380 −1.44657 −0.723287 0.690547i \(-0.757370\pi\)
−0.723287 + 0.690547i \(0.757370\pi\)
\(374\) 0 0
\(375\) −5.78015 −0.298486
\(376\) 0 0
\(377\) −5.19717 −0.267668
\(378\) 0 0
\(379\) 12.7993 0.657454 0.328727 0.944425i \(-0.393380\pi\)
0.328727 + 0.944425i \(0.393380\pi\)
\(380\) 0 0
\(381\) −21.2481 −1.08857
\(382\) 0 0
\(383\) 22.8587 1.16803 0.584013 0.811744i \(-0.301482\pi\)
0.584013 + 0.811744i \(0.301482\pi\)
\(384\) 0 0
\(385\) 0.395242 0.0201434
\(386\) 0 0
\(387\) −5.20056 −0.264359
\(388\) 0 0
\(389\) 11.1779 0.566744 0.283372 0.959010i \(-0.408547\pi\)
0.283372 + 0.959010i \(0.408547\pi\)
\(390\) 0 0
\(391\) 5.54231 0.280286
\(392\) 0 0
\(393\) −21.2793 −1.07340
\(394\) 0 0
\(395\) −2.34946 −0.118214
\(396\) 0 0
\(397\) −6.76780 −0.339666 −0.169833 0.985473i \(-0.554323\pi\)
−0.169833 + 0.985473i \(0.554323\pi\)
\(398\) 0 0
\(399\) 7.78591 0.389783
\(400\) 0 0
\(401\) −33.1959 −1.65772 −0.828862 0.559453i \(-0.811011\pi\)
−0.828862 + 0.559453i \(0.811011\pi\)
\(402\) 0 0
\(403\) 8.17745 0.407348
\(404\) 0 0
\(405\) 2.36859 0.117696
\(406\) 0 0
\(407\) 3.28617 0.162890
\(408\) 0 0
\(409\) 38.0191 1.87992 0.939961 0.341282i \(-0.110861\pi\)
0.939961 + 0.341282i \(0.110861\pi\)
\(410\) 0 0
\(411\) −7.44724 −0.367345
\(412\) 0 0
\(413\) −9.11865 −0.448699
\(414\) 0 0
\(415\) 5.12935 0.251790
\(416\) 0 0
\(417\) −9.08199 −0.444747
\(418\) 0 0
\(419\) −34.0207 −1.66202 −0.831011 0.556256i \(-0.812237\pi\)
−0.831011 + 0.556256i \(0.812237\pi\)
\(420\) 0 0
\(421\) 7.64631 0.372658 0.186329 0.982487i \(-0.440341\pi\)
0.186329 + 0.982487i \(0.440341\pi\)
\(422\) 0 0
\(423\) 1.59831 0.0777123
\(424\) 0 0
\(425\) 13.3173 0.645985
\(426\) 0 0
\(427\) −9.32901 −0.451462
\(428\) 0 0
\(429\) 1.48564 0.0717274
\(430\) 0 0
\(431\) 7.67146 0.369521 0.184761 0.982784i \(-0.440849\pi\)
0.184761 + 0.982784i \(0.440849\pi\)
\(432\) 0 0
\(433\) 37.5490 1.80449 0.902245 0.431225i \(-0.141918\pi\)
0.902245 + 0.431225i \(0.141918\pi\)
\(434\) 0 0
\(435\) 3.05171 0.146318
\(436\) 0 0
\(437\) −10.5646 −0.505374
\(438\) 0 0
\(439\) −33.4285 −1.59546 −0.797728 0.603017i \(-0.793965\pi\)
−0.797728 + 0.603017i \(0.793965\pi\)
\(440\) 0 0
\(441\) −0.792869 −0.0377557
\(442\) 0 0
\(443\) 21.2249 1.00842 0.504212 0.863580i \(-0.331783\pi\)
0.504212 + 0.863580i \(0.331783\pi\)
\(444\) 0 0
\(445\) −1.06584 −0.0505256
\(446\) 0 0
\(447\) 5.31343 0.251317
\(448\) 0 0
\(449\) 3.47085 0.163799 0.0818997 0.996641i \(-0.473901\pi\)
0.0818997 + 0.996641i \(0.473901\pi\)
\(450\) 0 0
\(451\) 9.42704 0.443902
\(452\) 0 0
\(453\) −1.43632 −0.0674841
\(454\) 0 0
\(455\) −0.395242 −0.0185292
\(456\) 0 0
\(457\) −3.73156 −0.174555 −0.0872774 0.996184i \(-0.527817\pi\)
−0.0872774 + 0.996184i \(0.527817\pi\)
\(458\) 0 0
\(459\) −15.4922 −0.723116
\(460\) 0 0
\(461\) −24.7886 −1.15452 −0.577261 0.816560i \(-0.695879\pi\)
−0.577261 + 0.816560i \(0.695879\pi\)
\(462\) 0 0
\(463\) 31.9542 1.48504 0.742519 0.669825i \(-0.233631\pi\)
0.742519 + 0.669825i \(0.233631\pi\)
\(464\) 0 0
\(465\) −4.80170 −0.222673
\(466\) 0 0
\(467\) −10.7660 −0.498191 −0.249096 0.968479i \(-0.580133\pi\)
−0.249096 + 0.968479i \(0.580133\pi\)
\(468\) 0 0
\(469\) 8.16464 0.377008
\(470\) 0 0
\(471\) 12.6118 0.581123
\(472\) 0 0
\(473\) 6.55917 0.301591
\(474\) 0 0
\(475\) −25.3852 −1.16475
\(476\) 0 0
\(477\) 3.24018 0.148357
\(478\) 0 0
\(479\) −38.4816 −1.75827 −0.879135 0.476573i \(-0.841879\pi\)
−0.879135 + 0.476573i \(0.841879\pi\)
\(480\) 0 0
\(481\) −3.28617 −0.149837
\(482\) 0 0
\(483\) −2.99483 −0.136269
\(484\) 0 0
\(485\) 3.73379 0.169543
\(486\) 0 0
\(487\) 9.40359 0.426117 0.213059 0.977039i \(-0.431657\pi\)
0.213059 + 0.977039i \(0.431657\pi\)
\(488\) 0 0
\(489\) 21.2670 0.961727
\(490\) 0 0
\(491\) −18.6492 −0.841626 −0.420813 0.907147i \(-0.638255\pi\)
−0.420813 + 0.907147i \(0.638255\pi\)
\(492\) 0 0
\(493\) −14.2889 −0.643540
\(494\) 0 0
\(495\) 0.313375 0.0140852
\(496\) 0 0
\(497\) 2.19413 0.0984202
\(498\) 0 0
\(499\) −15.6231 −0.699387 −0.349694 0.936864i \(-0.613714\pi\)
−0.349694 + 0.936864i \(0.613714\pi\)
\(500\) 0 0
\(501\) −16.1824 −0.722978
\(502\) 0 0
\(503\) −28.6033 −1.27536 −0.637679 0.770302i \(-0.720105\pi\)
−0.637679 + 0.770302i \(0.720105\pi\)
\(504\) 0 0
\(505\) −1.71516 −0.0763238
\(506\) 0 0
\(507\) −1.48564 −0.0659797
\(508\) 0 0
\(509\) −17.0076 −0.753848 −0.376924 0.926244i \(-0.623018\pi\)
−0.376924 + 0.926244i \(0.623018\pi\)
\(510\) 0 0
\(511\) 9.40454 0.416033
\(512\) 0 0
\(513\) 29.5309 1.30382
\(514\) 0 0
\(515\) 2.88711 0.127221
\(516\) 0 0
\(517\) −2.01585 −0.0886570
\(518\) 0 0
\(519\) −30.9199 −1.35723
\(520\) 0 0
\(521\) 6.09237 0.266911 0.133456 0.991055i \(-0.457393\pi\)
0.133456 + 0.991055i \(0.457393\pi\)
\(522\) 0 0
\(523\) 23.1123 1.01063 0.505315 0.862935i \(-0.331376\pi\)
0.505315 + 0.862935i \(0.331376\pi\)
\(524\) 0 0
\(525\) −7.19613 −0.314065
\(526\) 0 0
\(527\) 22.4828 0.979366
\(528\) 0 0
\(529\) −18.9364 −0.823320
\(530\) 0 0
\(531\) −7.22989 −0.313751
\(532\) 0 0
\(533\) −9.42704 −0.408331
\(534\) 0 0
\(535\) 4.95091 0.214047
\(536\) 0 0
\(537\) 34.6140 1.49370
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 7.73491 0.332550 0.166275 0.986079i \(-0.446826\pi\)
0.166275 + 0.986079i \(0.446826\pi\)
\(542\) 0 0
\(543\) 5.60825 0.240673
\(544\) 0 0
\(545\) −7.06567 −0.302660
\(546\) 0 0
\(547\) 9.85752 0.421477 0.210739 0.977542i \(-0.432413\pi\)
0.210739 + 0.977542i \(0.432413\pi\)
\(548\) 0 0
\(549\) −7.39669 −0.315683
\(550\) 0 0
\(551\) 27.2372 1.16034
\(552\) 0 0
\(553\) −5.94436 −0.252780
\(554\) 0 0
\(555\) 1.92960 0.0819070
\(556\) 0 0
\(557\) −25.8727 −1.09626 −0.548130 0.836393i \(-0.684660\pi\)
−0.548130 + 0.836393i \(0.684660\pi\)
\(558\) 0 0
\(559\) −6.55917 −0.277423
\(560\) 0 0
\(561\) 4.08457 0.172451
\(562\) 0 0
\(563\) 0.556102 0.0234369 0.0117185 0.999931i \(-0.496270\pi\)
0.0117185 + 0.999931i \(0.496270\pi\)
\(564\) 0 0
\(565\) 1.32870 0.0558989
\(566\) 0 0
\(567\) 5.99275 0.251672
\(568\) 0 0
\(569\) −30.1810 −1.26525 −0.632626 0.774458i \(-0.718023\pi\)
−0.632626 + 0.774458i \(0.718023\pi\)
\(570\) 0 0
\(571\) −37.8821 −1.58531 −0.792657 0.609667i \(-0.791303\pi\)
−0.792657 + 0.609667i \(0.791303\pi\)
\(572\) 0 0
\(573\) −12.5036 −0.522344
\(574\) 0 0
\(575\) 9.76434 0.407201
\(576\) 0 0
\(577\) −38.2960 −1.59428 −0.797142 0.603792i \(-0.793656\pi\)
−0.797142 + 0.603792i \(0.793656\pi\)
\(578\) 0 0
\(579\) −27.8579 −1.15774
\(580\) 0 0
\(581\) 12.9777 0.538408
\(582\) 0 0
\(583\) −4.08665 −0.169252
\(584\) 0 0
\(585\) −0.313375 −0.0129565
\(586\) 0 0
\(587\) −8.59160 −0.354613 −0.177307 0.984156i \(-0.556738\pi\)
−0.177307 + 0.984156i \(0.556738\pi\)
\(588\) 0 0
\(589\) −42.8562 −1.76586
\(590\) 0 0
\(591\) 7.27910 0.299422
\(592\) 0 0
\(593\) 31.8725 1.30885 0.654424 0.756128i \(-0.272911\pi\)
0.654424 + 0.756128i \(0.272911\pi\)
\(594\) 0 0
\(595\) −1.08666 −0.0445489
\(596\) 0 0
\(597\) 31.0097 1.26914
\(598\) 0 0
\(599\) −0.482125 −0.0196991 −0.00984955 0.999951i \(-0.503135\pi\)
−0.00984955 + 0.999951i \(0.503135\pi\)
\(600\) 0 0
\(601\) −33.1899 −1.35384 −0.676922 0.736055i \(-0.736687\pi\)
−0.676922 + 0.736055i \(0.736687\pi\)
\(602\) 0 0
\(603\) 6.47350 0.263621
\(604\) 0 0
\(605\) −0.395242 −0.0160689
\(606\) 0 0
\(607\) −19.4892 −0.791040 −0.395520 0.918457i \(-0.629436\pi\)
−0.395520 + 0.918457i \(0.629436\pi\)
\(608\) 0 0
\(609\) 7.72113 0.312876
\(610\) 0 0
\(611\) 2.01585 0.0815525
\(612\) 0 0
\(613\) −4.00058 −0.161582 −0.0807910 0.996731i \(-0.525745\pi\)
−0.0807910 + 0.996731i \(0.525745\pi\)
\(614\) 0 0
\(615\) 5.53544 0.223211
\(616\) 0 0
\(617\) −36.3626 −1.46390 −0.731951 0.681357i \(-0.761390\pi\)
−0.731951 + 0.681357i \(0.761390\pi\)
\(618\) 0 0
\(619\) −21.0793 −0.847251 −0.423625 0.905838i \(-0.639243\pi\)
−0.423625 + 0.905838i \(0.639243\pi\)
\(620\) 0 0
\(621\) −11.3590 −0.455821
\(622\) 0 0
\(623\) −2.69667 −0.108040
\(624\) 0 0
\(625\) 22.6812 0.907246
\(626\) 0 0
\(627\) −7.78591 −0.310939
\(628\) 0 0
\(629\) −9.03489 −0.360245
\(630\) 0 0
\(631\) −13.2164 −0.526135 −0.263067 0.964777i \(-0.584734\pi\)
−0.263067 + 0.964777i \(0.584734\pi\)
\(632\) 0 0
\(633\) 37.2677 1.48126
\(634\) 0 0
\(635\) −5.65288 −0.224328
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 1.73966 0.0688198
\(640\) 0 0
\(641\) 9.73131 0.384364 0.192182 0.981359i \(-0.438444\pi\)
0.192182 + 0.981359i \(0.438444\pi\)
\(642\) 0 0
\(643\) 6.29861 0.248393 0.124196 0.992258i \(-0.460365\pi\)
0.124196 + 0.992258i \(0.460365\pi\)
\(644\) 0 0
\(645\) 3.85146 0.151651
\(646\) 0 0
\(647\) 16.6285 0.653735 0.326868 0.945070i \(-0.394007\pi\)
0.326868 + 0.945070i \(0.394007\pi\)
\(648\) 0 0
\(649\) 9.11865 0.357938
\(650\) 0 0
\(651\) −12.1488 −0.476148
\(652\) 0 0
\(653\) −14.7298 −0.576422 −0.288211 0.957567i \(-0.593060\pi\)
−0.288211 + 0.957567i \(0.593060\pi\)
\(654\) 0 0
\(655\) −5.66116 −0.221200
\(656\) 0 0
\(657\) 7.45657 0.290909
\(658\) 0 0
\(659\) −45.9289 −1.78914 −0.894568 0.446932i \(-0.852517\pi\)
−0.894568 + 0.446932i \(0.852517\pi\)
\(660\) 0 0
\(661\) 31.2853 1.21686 0.608428 0.793609i \(-0.291800\pi\)
0.608428 + 0.793609i \(0.291800\pi\)
\(662\) 0 0
\(663\) −4.08457 −0.158632
\(664\) 0 0
\(665\) 2.07137 0.0803244
\(666\) 0 0
\(667\) −10.4767 −0.405660
\(668\) 0 0
\(669\) 28.2404 1.09184
\(670\) 0 0
\(671\) 9.32901 0.360142
\(672\) 0 0
\(673\) −17.9598 −0.692300 −0.346150 0.938179i \(-0.612511\pi\)
−0.346150 + 0.938179i \(0.612511\pi\)
\(674\) 0 0
\(675\) −27.2940 −1.05055
\(676\) 0 0
\(677\) 12.1779 0.468035 0.234018 0.972232i \(-0.424813\pi\)
0.234018 + 0.972232i \(0.424813\pi\)
\(678\) 0 0
\(679\) 9.44684 0.362536
\(680\) 0 0
\(681\) 8.99948 0.344861
\(682\) 0 0
\(683\) −28.0774 −1.07435 −0.537176 0.843470i \(-0.680509\pi\)
−0.537176 + 0.843470i \(0.680509\pi\)
\(684\) 0 0
\(685\) −1.98127 −0.0757005
\(686\) 0 0
\(687\) −25.1512 −0.959579
\(688\) 0 0
\(689\) 4.08665 0.155689
\(690\) 0 0
\(691\) 20.8220 0.792106 0.396053 0.918228i \(-0.370380\pi\)
0.396053 + 0.918228i \(0.370380\pi\)
\(692\) 0 0
\(693\) 0.792869 0.0301186
\(694\) 0 0
\(695\) −2.41618 −0.0916510
\(696\) 0 0
\(697\) −25.9184 −0.981729
\(698\) 0 0
\(699\) 2.26115 0.0855247
\(700\) 0 0
\(701\) 24.6008 0.929161 0.464581 0.885531i \(-0.346205\pi\)
0.464581 + 0.885531i \(0.346205\pi\)
\(702\) 0 0
\(703\) 17.2221 0.649543
\(704\) 0 0
\(705\) −1.18368 −0.0445800
\(706\) 0 0
\(707\) −4.33953 −0.163205
\(708\) 0 0
\(709\) −20.4168 −0.766768 −0.383384 0.923589i \(-0.625241\pi\)
−0.383384 + 0.923589i \(0.625241\pi\)
\(710\) 0 0
\(711\) −4.71310 −0.176755
\(712\) 0 0
\(713\) 16.4845 0.617350
\(714\) 0 0
\(715\) 0.395242 0.0147812
\(716\) 0 0
\(717\) 25.3173 0.945493
\(718\) 0 0
\(719\) 38.5217 1.43662 0.718308 0.695725i \(-0.244917\pi\)
0.718308 + 0.695725i \(0.244917\pi\)
\(720\) 0 0
\(721\) 7.30468 0.272040
\(722\) 0 0
\(723\) −9.53166 −0.354486
\(724\) 0 0
\(725\) −25.1740 −0.934937
\(726\) 0 0
\(727\) 16.0033 0.593528 0.296764 0.954951i \(-0.404092\pi\)
0.296764 + 0.954951i \(0.404092\pi\)
\(728\) 0 0
\(729\) 29.8655 1.10613
\(730\) 0 0
\(731\) −18.0335 −0.666995
\(732\) 0 0
\(733\) 7.77633 0.287225 0.143613 0.989634i \(-0.454128\pi\)
0.143613 + 0.989634i \(0.454128\pi\)
\(734\) 0 0
\(735\) 0.587188 0.0216587
\(736\) 0 0
\(737\) −8.16464 −0.300749
\(738\) 0 0
\(739\) 7.41142 0.272634 0.136317 0.990665i \(-0.456473\pi\)
0.136317 + 0.990665i \(0.456473\pi\)
\(740\) 0 0
\(741\) 7.78591 0.286022
\(742\) 0 0
\(743\) 3.10045 0.113745 0.0568723 0.998381i \(-0.481887\pi\)
0.0568723 + 0.998381i \(0.481887\pi\)
\(744\) 0 0
\(745\) 1.41359 0.0517900
\(746\) 0 0
\(747\) 10.2897 0.376479
\(748\) 0 0
\(749\) 12.5263 0.457701
\(750\) 0 0
\(751\) −31.8867 −1.16356 −0.581780 0.813346i \(-0.697644\pi\)
−0.581780 + 0.813346i \(0.697644\pi\)
\(752\) 0 0
\(753\) 35.4431 1.29162
\(754\) 0 0
\(755\) −0.382120 −0.0139068
\(756\) 0 0
\(757\) −6.97622 −0.253555 −0.126777 0.991931i \(-0.540463\pi\)
−0.126777 + 0.991931i \(0.540463\pi\)
\(758\) 0 0
\(759\) 2.99483 0.108705
\(760\) 0 0
\(761\) −38.6791 −1.40212 −0.701058 0.713104i \(-0.747289\pi\)
−0.701058 + 0.713104i \(0.747289\pi\)
\(762\) 0 0
\(763\) −17.8768 −0.647184
\(764\) 0 0
\(765\) −0.861583 −0.0311506
\(766\) 0 0
\(767\) −9.11865 −0.329255
\(768\) 0 0
\(769\) 11.1344 0.401517 0.200759 0.979641i \(-0.435659\pi\)
0.200759 + 0.979641i \(0.435659\pi\)
\(770\) 0 0
\(771\) −22.7079 −0.817806
\(772\) 0 0
\(773\) −19.1746 −0.689663 −0.344832 0.938665i \(-0.612064\pi\)
−0.344832 + 0.938665i \(0.612064\pi\)
\(774\) 0 0
\(775\) 39.6098 1.42283
\(776\) 0 0
\(777\) 4.88208 0.175144
\(778\) 0 0
\(779\) 49.4050 1.77012
\(780\) 0 0
\(781\) −2.19413 −0.0785122
\(782\) 0 0
\(783\) 29.2852 1.04657
\(784\) 0 0
\(785\) 3.35527 0.119755
\(786\) 0 0
\(787\) 1.33198 0.0474799 0.0237399 0.999718i \(-0.492443\pi\)
0.0237399 + 0.999718i \(0.492443\pi\)
\(788\) 0 0
\(789\) 37.9950 1.35266
\(790\) 0 0
\(791\) 3.36174 0.119530
\(792\) 0 0
\(793\) −9.32901 −0.331283
\(794\) 0 0
\(795\) −2.39963 −0.0851061
\(796\) 0 0
\(797\) −43.3605 −1.53591 −0.767954 0.640505i \(-0.778725\pi\)
−0.767954 + 0.640505i \(0.778725\pi\)
\(798\) 0 0
\(799\) 5.54231 0.196073
\(800\) 0 0
\(801\) −2.13811 −0.0755464
\(802\) 0 0
\(803\) −9.40454 −0.331879
\(804\) 0 0
\(805\) −0.796748 −0.0280817
\(806\) 0 0
\(807\) 17.7555 0.625024
\(808\) 0 0
\(809\) 25.0051 0.879134 0.439567 0.898210i \(-0.355132\pi\)
0.439567 + 0.898210i \(0.355132\pi\)
\(810\) 0 0
\(811\) 24.9268 0.875297 0.437648 0.899146i \(-0.355811\pi\)
0.437648 + 0.899146i \(0.355811\pi\)
\(812\) 0 0
\(813\) 29.8372 1.04644
\(814\) 0 0
\(815\) 5.65790 0.198188
\(816\) 0 0
\(817\) 34.3751 1.20263
\(818\) 0 0
\(819\) −0.792869 −0.0277051
\(820\) 0 0
\(821\) 39.5314 1.37966 0.689828 0.723973i \(-0.257686\pi\)
0.689828 + 0.723973i \(0.257686\pi\)
\(822\) 0 0
\(823\) −53.5703 −1.86734 −0.933671 0.358132i \(-0.883414\pi\)
−0.933671 + 0.358132i \(0.883414\pi\)
\(824\) 0 0
\(825\) 7.19613 0.250537
\(826\) 0 0
\(827\) −50.6925 −1.76275 −0.881376 0.472416i \(-0.843382\pi\)
−0.881376 + 0.472416i \(0.843382\pi\)
\(828\) 0 0
\(829\) 41.3434 1.43592 0.717958 0.696087i \(-0.245077\pi\)
0.717958 + 0.696087i \(0.245077\pi\)
\(830\) 0 0
\(831\) 17.6365 0.611805
\(832\) 0 0
\(833\) −2.74936 −0.0952598
\(834\) 0 0
\(835\) −4.30520 −0.148987
\(836\) 0 0
\(837\) −46.0787 −1.59271
\(838\) 0 0
\(839\) −37.4910 −1.29433 −0.647167 0.762349i \(-0.724046\pi\)
−0.647167 + 0.762349i \(0.724046\pi\)
\(840\) 0 0
\(841\) −1.98946 −0.0686019
\(842\) 0 0
\(843\) 19.1746 0.660407
\(844\) 0 0
\(845\) −0.395242 −0.0135967
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −8.20817 −0.281704
\(850\) 0 0
\(851\) −6.62443 −0.227083
\(852\) 0 0
\(853\) −26.9086 −0.921334 −0.460667 0.887573i \(-0.652390\pi\)
−0.460667 + 0.887573i \(0.652390\pi\)
\(854\) 0 0
\(855\) 1.64233 0.0561664
\(856\) 0 0
\(857\) 2.55222 0.0871822 0.0435911 0.999049i \(-0.486120\pi\)
0.0435911 + 0.999049i \(0.486120\pi\)
\(858\) 0 0
\(859\) −5.76793 −0.196799 −0.0983996 0.995147i \(-0.531372\pi\)
−0.0983996 + 0.995147i \(0.531372\pi\)
\(860\) 0 0
\(861\) 14.0052 0.477296
\(862\) 0 0
\(863\) −37.8214 −1.28745 −0.643727 0.765255i \(-0.722613\pi\)
−0.643727 + 0.765255i \(0.722613\pi\)
\(864\) 0 0
\(865\) −8.22597 −0.279691
\(866\) 0 0
\(867\) 14.0259 0.476346
\(868\) 0 0
\(869\) 5.94436 0.201649
\(870\) 0 0
\(871\) 8.16464 0.276648
\(872\) 0 0
\(873\) 7.49011 0.253502
\(874\) 0 0
\(875\) −3.89068 −0.131529
\(876\) 0 0
\(877\) 0.319206 0.0107788 0.00538941 0.999985i \(-0.498284\pi\)
0.00538941 + 0.999985i \(0.498284\pi\)
\(878\) 0 0
\(879\) −7.56552 −0.255179
\(880\) 0 0
\(881\) −5.06981 −0.170806 −0.0854030 0.996346i \(-0.527218\pi\)
−0.0854030 + 0.996346i \(0.527218\pi\)
\(882\) 0 0
\(883\) −44.7182 −1.50489 −0.752443 0.658657i \(-0.771125\pi\)
−0.752443 + 0.658657i \(0.771125\pi\)
\(884\) 0 0
\(885\) 5.35436 0.179985
\(886\) 0 0
\(887\) 56.8266 1.90805 0.954026 0.299725i \(-0.0968948\pi\)
0.954026 + 0.299725i \(0.0968948\pi\)
\(888\) 0 0
\(889\) −14.3023 −0.479685
\(890\) 0 0
\(891\) −5.99275 −0.200765
\(892\) 0 0
\(893\) −10.5646 −0.353531
\(894\) 0 0
\(895\) 9.20875 0.307815
\(896\) 0 0
\(897\) −2.99483 −0.0999944
\(898\) 0 0
\(899\) −42.4996 −1.41744
\(900\) 0 0
\(901\) 11.2357 0.374315
\(902\) 0 0
\(903\) 9.74457 0.324279
\(904\) 0 0
\(905\) 1.49203 0.0495966
\(906\) 0 0
\(907\) −4.26190 −0.141514 −0.0707570 0.997494i \(-0.522541\pi\)
−0.0707570 + 0.997494i \(0.522541\pi\)
\(908\) 0 0
\(909\) −3.44068 −0.114120
\(910\) 0 0
\(911\) 5.90900 0.195774 0.0978870 0.995198i \(-0.468792\pi\)
0.0978870 + 0.995198i \(0.468792\pi\)
\(912\) 0 0
\(913\) −12.9777 −0.429501
\(914\) 0 0
\(915\) 5.47788 0.181093
\(916\) 0 0
\(917\) −14.3233 −0.472996
\(918\) 0 0
\(919\) 43.4635 1.43373 0.716864 0.697213i \(-0.245577\pi\)
0.716864 + 0.697213i \(0.245577\pi\)
\(920\) 0 0
\(921\) −44.4306 −1.46404
\(922\) 0 0
\(923\) 2.19413 0.0722207
\(924\) 0 0
\(925\) −15.9175 −0.523365
\(926\) 0 0
\(927\) 5.79165 0.190223
\(928\) 0 0
\(929\) −24.9863 −0.819773 −0.409886 0.912137i \(-0.634432\pi\)
−0.409886 + 0.912137i \(0.634432\pi\)
\(930\) 0 0
\(931\) 5.24077 0.171759
\(932\) 0 0
\(933\) −21.1104 −0.691124
\(934\) 0 0
\(935\) 1.08666 0.0355377
\(936\) 0 0
\(937\) −4.23303 −0.138287 −0.0691436 0.997607i \(-0.522027\pi\)
−0.0691436 + 0.997607i \(0.522027\pi\)
\(938\) 0 0
\(939\) 38.2916 1.24960
\(940\) 0 0
\(941\) −4.83900 −0.157747 −0.0788735 0.996885i \(-0.525132\pi\)
−0.0788735 + 0.996885i \(0.525132\pi\)
\(942\) 0 0
\(943\) −19.0035 −0.618839
\(944\) 0 0
\(945\) 2.22713 0.0724484
\(946\) 0 0
\(947\) 34.6261 1.12520 0.562599 0.826730i \(-0.309801\pi\)
0.562599 + 0.826730i \(0.309801\pi\)
\(948\) 0 0
\(949\) 9.40454 0.305284
\(950\) 0 0
\(951\) 28.2155 0.914951
\(952\) 0 0
\(953\) 18.2749 0.591982 0.295991 0.955191i \(-0.404350\pi\)
0.295991 + 0.955191i \(0.404350\pi\)
\(954\) 0 0
\(955\) −3.32646 −0.107642
\(956\) 0 0
\(957\) −7.72113 −0.249589
\(958\) 0 0
\(959\) −5.01281 −0.161872
\(960\) 0 0
\(961\) 35.8707 1.15712
\(962\) 0 0
\(963\) 9.93171 0.320045
\(964\) 0 0
\(965\) −7.41136 −0.238580
\(966\) 0 0
\(967\) −13.5705 −0.436398 −0.218199 0.975904i \(-0.570018\pi\)
−0.218199 + 0.975904i \(0.570018\pi\)
\(968\) 0 0
\(969\) 21.4063 0.687669
\(970\) 0 0
\(971\) 29.5052 0.946867 0.473434 0.880830i \(-0.343014\pi\)
0.473434 + 0.880830i \(0.343014\pi\)
\(972\) 0 0
\(973\) −6.11317 −0.195979
\(974\) 0 0
\(975\) −7.19613 −0.230460
\(976\) 0 0
\(977\) −36.1419 −1.15628 −0.578142 0.815936i \(-0.696222\pi\)
−0.578142 + 0.815936i \(0.696222\pi\)
\(978\) 0 0
\(979\) 2.69667 0.0861860
\(980\) 0 0
\(981\) −14.1740 −0.452540
\(982\) 0 0
\(983\) −13.1017 −0.417879 −0.208939 0.977929i \(-0.567001\pi\)
−0.208939 + 0.977929i \(0.567001\pi\)
\(984\) 0 0
\(985\) 1.93654 0.0617033
\(986\) 0 0
\(987\) −2.99483 −0.0953265
\(988\) 0 0
\(989\) −13.2223 −0.420444
\(990\) 0 0
\(991\) −13.0067 −0.413171 −0.206585 0.978429i \(-0.566235\pi\)
−0.206585 + 0.978429i \(0.566235\pi\)
\(992\) 0 0
\(993\) 34.4113 1.09201
\(994\) 0 0
\(995\) 8.24986 0.261538
\(996\) 0 0
\(997\) −41.2841 −1.30748 −0.653740 0.756719i \(-0.726801\pi\)
−0.653740 + 0.756719i \(0.726801\pi\)
\(998\) 0 0
\(999\) 18.5171 0.585855
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 \(a_p\))