Properties

Label 6036.2.a.g.1.15
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(3.64439\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +2.64439 q^{5} -3.02199 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +2.64439 q^{5} -3.02199 q^{7} +1.00000 q^{9} +0.587142 q^{11} -2.23197 q^{13} +2.64439 q^{15} +1.24552 q^{17} -0.491597 q^{19} -3.02199 q^{21} -0.916648 q^{23} +1.99280 q^{25} +1.00000 q^{27} -5.33298 q^{29} -8.59992 q^{31} +0.587142 q^{33} -7.99132 q^{35} -11.8705 q^{37} -2.23197 q^{39} -2.54414 q^{41} +1.12078 q^{43} +2.64439 q^{45} -2.52693 q^{47} +2.13243 q^{49} +1.24552 q^{51} -0.789358 q^{53} +1.55263 q^{55} -0.491597 q^{57} +9.14016 q^{59} -9.78118 q^{61} -3.02199 q^{63} -5.90220 q^{65} -7.68153 q^{67} -0.916648 q^{69} +3.65743 q^{71} -6.58923 q^{73} +1.99280 q^{75} -1.77434 q^{77} +7.69343 q^{79} +1.00000 q^{81} +11.9522 q^{83} +3.29364 q^{85} -5.33298 q^{87} +3.28897 q^{89} +6.74500 q^{91} -8.59992 q^{93} -1.29997 q^{95} -8.50441 q^{97} +0.587142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} + O(q^{10}) \) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} - 5q^{11} - 14q^{13} - 11q^{15} - 5q^{17} + 3q^{19} - 4q^{21} - 32q^{23} + 2q^{25} + 15q^{27} - 23q^{29} - 13q^{31} - 5q^{33} - 16q^{35} - 10q^{37} - 14q^{39} - 14q^{41} + 4q^{43} - 11q^{45} - 20q^{47} - 9q^{49} - 5q^{51} - 30q^{53} - 10q^{55} + 3q^{57} - 14q^{59} - 38q^{61} - 4q^{63} - 24q^{65} - 8q^{67} - 32q^{69} - 41q^{71} - 19q^{73} + 2q^{75} - 39q^{77} - 27q^{79} + 15q^{81} - 17q^{83} - 6q^{85} - 23q^{87} - 23q^{89} + 4q^{91} - 13q^{93} - 30q^{95} - 18q^{97} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 2.64439 1.18261 0.591303 0.806449i \(-0.298614\pi\)
0.591303 + 0.806449i \(0.298614\pi\)
\(6\) 0 0
\(7\) −3.02199 −1.14221 −0.571103 0.820879i \(-0.693484\pi\)
−0.571103 + 0.820879i \(0.693484\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.587142 0.177030 0.0885150 0.996075i \(-0.471788\pi\)
0.0885150 + 0.996075i \(0.471788\pi\)
\(12\) 0 0
\(13\) −2.23197 −0.619038 −0.309519 0.950893i \(-0.600168\pi\)
−0.309519 + 0.950893i \(0.600168\pi\)
\(14\) 0 0
\(15\) 2.64439 0.682778
\(16\) 0 0
\(17\) 1.24552 0.302083 0.151041 0.988527i \(-0.451737\pi\)
0.151041 + 0.988527i \(0.451737\pi\)
\(18\) 0 0
\(19\) −0.491597 −0.112780 −0.0563900 0.998409i \(-0.517959\pi\)
−0.0563900 + 0.998409i \(0.517959\pi\)
\(20\) 0 0
\(21\) −3.02199 −0.659452
\(22\) 0 0
\(23\) −0.916648 −0.191134 −0.0955671 0.995423i \(-0.530466\pi\)
−0.0955671 + 0.995423i \(0.530466\pi\)
\(24\) 0 0
\(25\) 1.99280 0.398559
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.33298 −0.990309 −0.495155 0.868805i \(-0.664889\pi\)
−0.495155 + 0.868805i \(0.664889\pi\)
\(30\) 0 0
\(31\) −8.59992 −1.54459 −0.772296 0.635263i \(-0.780892\pi\)
−0.772296 + 0.635263i \(0.780892\pi\)
\(32\) 0 0
\(33\) 0.587142 0.102208
\(34\) 0 0
\(35\) −7.99132 −1.35078
\(36\) 0 0
\(37\) −11.8705 −1.95150 −0.975748 0.218895i \(-0.929755\pi\)
−0.975748 + 0.218895i \(0.929755\pi\)
\(38\) 0 0
\(39\) −2.23197 −0.357402
\(40\) 0 0
\(41\) −2.54414 −0.397328 −0.198664 0.980068i \(-0.563660\pi\)
−0.198664 + 0.980068i \(0.563660\pi\)
\(42\) 0 0
\(43\) 1.12078 0.170918 0.0854590 0.996342i \(-0.472764\pi\)
0.0854590 + 0.996342i \(0.472764\pi\)
\(44\) 0 0
\(45\) 2.64439 0.394202
\(46\) 0 0
\(47\) −2.52693 −0.368590 −0.184295 0.982871i \(-0.559000\pi\)
−0.184295 + 0.982871i \(0.559000\pi\)
\(48\) 0 0
\(49\) 2.13243 0.304632
\(50\) 0 0
\(51\) 1.24552 0.174408
\(52\) 0 0
\(53\) −0.789358 −0.108427 −0.0542133 0.998529i \(-0.517265\pi\)
−0.0542133 + 0.998529i \(0.517265\pi\)
\(54\) 0 0
\(55\) 1.55263 0.209357
\(56\) 0 0
\(57\) −0.491597 −0.0651136
\(58\) 0 0
\(59\) 9.14016 1.18995 0.594973 0.803745i \(-0.297163\pi\)
0.594973 + 0.803745i \(0.297163\pi\)
\(60\) 0 0
\(61\) −9.78118 −1.25235 −0.626176 0.779682i \(-0.715381\pi\)
−0.626176 + 0.779682i \(0.715381\pi\)
\(62\) 0 0
\(63\) −3.02199 −0.380735
\(64\) 0 0
\(65\) −5.90220 −0.732078
\(66\) 0 0
\(67\) −7.68153 −0.938449 −0.469224 0.883079i \(-0.655466\pi\)
−0.469224 + 0.883079i \(0.655466\pi\)
\(68\) 0 0
\(69\) −0.916648 −0.110351
\(70\) 0 0
\(71\) 3.65743 0.434057 0.217028 0.976165i \(-0.430364\pi\)
0.217028 + 0.976165i \(0.430364\pi\)
\(72\) 0 0
\(73\) −6.58923 −0.771210 −0.385605 0.922664i \(-0.626007\pi\)
−0.385605 + 0.922664i \(0.626007\pi\)
\(74\) 0 0
\(75\) 1.99280 0.230108
\(76\) 0 0
\(77\) −1.77434 −0.202204
\(78\) 0 0
\(79\) 7.69343 0.865578 0.432789 0.901495i \(-0.357530\pi\)
0.432789 + 0.901495i \(0.357530\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 11.9522 1.31192 0.655962 0.754794i \(-0.272263\pi\)
0.655962 + 0.754794i \(0.272263\pi\)
\(84\) 0 0
\(85\) 3.29364 0.357245
\(86\) 0 0
\(87\) −5.33298 −0.571755
\(88\) 0 0
\(89\) 3.28897 0.348630 0.174315 0.984690i \(-0.444229\pi\)
0.174315 + 0.984690i \(0.444229\pi\)
\(90\) 0 0
\(91\) 6.74500 0.707068
\(92\) 0 0
\(93\) −8.59992 −0.891770
\(94\) 0 0
\(95\) −1.29997 −0.133375
\(96\) 0 0
\(97\) −8.50441 −0.863492 −0.431746 0.901995i \(-0.642102\pi\)
−0.431746 + 0.901995i \(0.642102\pi\)
\(98\) 0 0
\(99\) 0.587142 0.0590100
\(100\) 0 0
\(101\) −6.83549 −0.680157 −0.340079 0.940397i \(-0.610454\pi\)
−0.340079 + 0.940397i \(0.610454\pi\)
\(102\) 0 0
\(103\) −1.17906 −0.116176 −0.0580881 0.998311i \(-0.518500\pi\)
−0.0580881 + 0.998311i \(0.518500\pi\)
\(104\) 0 0
\(105\) −7.99132 −0.779873
\(106\) 0 0
\(107\) 15.7476 1.52238 0.761189 0.648530i \(-0.224616\pi\)
0.761189 + 0.648530i \(0.224616\pi\)
\(108\) 0 0
\(109\) 6.71332 0.643019 0.321510 0.946906i \(-0.395810\pi\)
0.321510 + 0.946906i \(0.395810\pi\)
\(110\) 0 0
\(111\) −11.8705 −1.12670
\(112\) 0 0
\(113\) 10.7161 1.00808 0.504042 0.863679i \(-0.331846\pi\)
0.504042 + 0.863679i \(0.331846\pi\)
\(114\) 0 0
\(115\) −2.42397 −0.226037
\(116\) 0 0
\(117\) −2.23197 −0.206346
\(118\) 0 0
\(119\) −3.76395 −0.345041
\(120\) 0 0
\(121\) −10.6553 −0.968660
\(122\) 0 0
\(123\) −2.54414 −0.229397
\(124\) 0 0
\(125\) −7.95222 −0.711268
\(126\) 0 0
\(127\) 1.93781 0.171953 0.0859766 0.996297i \(-0.472599\pi\)
0.0859766 + 0.996297i \(0.472599\pi\)
\(128\) 0 0
\(129\) 1.12078 0.0986796
\(130\) 0 0
\(131\) −8.74741 −0.764265 −0.382132 0.924108i \(-0.624810\pi\)
−0.382132 + 0.924108i \(0.624810\pi\)
\(132\) 0 0
\(133\) 1.48560 0.128818
\(134\) 0 0
\(135\) 2.64439 0.227593
\(136\) 0 0
\(137\) 13.4646 1.15036 0.575181 0.818026i \(-0.304932\pi\)
0.575181 + 0.818026i \(0.304932\pi\)
\(138\) 0 0
\(139\) −6.12589 −0.519591 −0.259796 0.965664i \(-0.583655\pi\)
−0.259796 + 0.965664i \(0.583655\pi\)
\(140\) 0 0
\(141\) −2.52693 −0.212806
\(142\) 0 0
\(143\) −1.31048 −0.109588
\(144\) 0 0
\(145\) −14.1025 −1.17115
\(146\) 0 0
\(147\) 2.13243 0.175880
\(148\) 0 0
\(149\) 6.53890 0.535687 0.267844 0.963462i \(-0.413689\pi\)
0.267844 + 0.963462i \(0.413689\pi\)
\(150\) 0 0
\(151\) −16.6852 −1.35782 −0.678912 0.734219i \(-0.737548\pi\)
−0.678912 + 0.734219i \(0.737548\pi\)
\(152\) 0 0
\(153\) 1.24552 0.100694
\(154\) 0 0
\(155\) −22.7415 −1.82664
\(156\) 0 0
\(157\) −6.35568 −0.507238 −0.253619 0.967304i \(-0.581621\pi\)
−0.253619 + 0.967304i \(0.581621\pi\)
\(158\) 0 0
\(159\) −0.789358 −0.0626002
\(160\) 0 0
\(161\) 2.77010 0.218315
\(162\) 0 0
\(163\) 12.1987 0.955477 0.477739 0.878502i \(-0.341457\pi\)
0.477739 + 0.878502i \(0.341457\pi\)
\(164\) 0 0
\(165\) 1.55263 0.120872
\(166\) 0 0
\(167\) −14.8626 −1.15011 −0.575053 0.818116i \(-0.695018\pi\)
−0.575053 + 0.818116i \(0.695018\pi\)
\(168\) 0 0
\(169\) −8.01830 −0.616792
\(170\) 0 0
\(171\) −0.491597 −0.0375934
\(172\) 0 0
\(173\) 7.02508 0.534107 0.267054 0.963682i \(-0.413950\pi\)
0.267054 + 0.963682i \(0.413950\pi\)
\(174\) 0 0
\(175\) −6.02221 −0.455236
\(176\) 0 0
\(177\) 9.14016 0.687016
\(178\) 0 0
\(179\) 5.16311 0.385909 0.192955 0.981208i \(-0.438193\pi\)
0.192955 + 0.981208i \(0.438193\pi\)
\(180\) 0 0
\(181\) −1.26496 −0.0940238 −0.0470119 0.998894i \(-0.514970\pi\)
−0.0470119 + 0.998894i \(0.514970\pi\)
\(182\) 0 0
\(183\) −9.78118 −0.723046
\(184\) 0 0
\(185\) −31.3902 −2.30785
\(186\) 0 0
\(187\) 0.731297 0.0534777
\(188\) 0 0
\(189\) −3.02199 −0.219817
\(190\) 0 0
\(191\) 6.03083 0.436376 0.218188 0.975907i \(-0.429985\pi\)
0.218188 + 0.975907i \(0.429985\pi\)
\(192\) 0 0
\(193\) −1.06344 −0.0765480 −0.0382740 0.999267i \(-0.512186\pi\)
−0.0382740 + 0.999267i \(0.512186\pi\)
\(194\) 0 0
\(195\) −5.90220 −0.422666
\(196\) 0 0
\(197\) −22.3630 −1.59330 −0.796649 0.604443i \(-0.793396\pi\)
−0.796649 + 0.604443i \(0.793396\pi\)
\(198\) 0 0
\(199\) −22.8245 −1.61799 −0.808993 0.587818i \(-0.799987\pi\)
−0.808993 + 0.587818i \(0.799987\pi\)
\(200\) 0 0
\(201\) −7.68153 −0.541814
\(202\) 0 0
\(203\) 16.1162 1.13114
\(204\) 0 0
\(205\) −6.72770 −0.469883
\(206\) 0 0
\(207\) −0.916648 −0.0637114
\(208\) 0 0
\(209\) −0.288637 −0.0199654
\(210\) 0 0
\(211\) 12.3297 0.848810 0.424405 0.905472i \(-0.360483\pi\)
0.424405 + 0.905472i \(0.360483\pi\)
\(212\) 0 0
\(213\) 3.65743 0.250603
\(214\) 0 0
\(215\) 2.96379 0.202129
\(216\) 0 0
\(217\) 25.9889 1.76424
\(218\) 0 0
\(219\) −6.58923 −0.445259
\(220\) 0 0
\(221\) −2.77997 −0.187001
\(222\) 0 0
\(223\) 12.5188 0.838318 0.419159 0.907913i \(-0.362325\pi\)
0.419159 + 0.907913i \(0.362325\pi\)
\(224\) 0 0
\(225\) 1.99280 0.132853
\(226\) 0 0
\(227\) 16.9465 1.12478 0.562389 0.826873i \(-0.309882\pi\)
0.562389 + 0.826873i \(0.309882\pi\)
\(228\) 0 0
\(229\) −29.3819 −1.94161 −0.970807 0.239863i \(-0.922897\pi\)
−0.970807 + 0.239863i \(0.922897\pi\)
\(230\) 0 0
\(231\) −1.77434 −0.116743
\(232\) 0 0
\(233\) −28.4814 −1.86588 −0.932939 0.360035i \(-0.882765\pi\)
−0.932939 + 0.360035i \(0.882765\pi\)
\(234\) 0 0
\(235\) −6.68218 −0.435898
\(236\) 0 0
\(237\) 7.69343 0.499742
\(238\) 0 0
\(239\) 22.9104 1.48195 0.740974 0.671533i \(-0.234364\pi\)
0.740974 + 0.671533i \(0.234364\pi\)
\(240\) 0 0
\(241\) −7.46479 −0.480849 −0.240425 0.970668i \(-0.577287\pi\)
−0.240425 + 0.970668i \(0.577287\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 5.63897 0.360260
\(246\) 0 0
\(247\) 1.09723 0.0698151
\(248\) 0 0
\(249\) 11.9522 0.757439
\(250\) 0 0
\(251\) −6.63046 −0.418511 −0.209255 0.977861i \(-0.567104\pi\)
−0.209255 + 0.977861i \(0.567104\pi\)
\(252\) 0 0
\(253\) −0.538202 −0.0338365
\(254\) 0 0
\(255\) 3.29364 0.206256
\(256\) 0 0
\(257\) 2.89579 0.180634 0.0903171 0.995913i \(-0.471212\pi\)
0.0903171 + 0.995913i \(0.471212\pi\)
\(258\) 0 0
\(259\) 35.8725 2.22901
\(260\) 0 0
\(261\) −5.33298 −0.330103
\(262\) 0 0
\(263\) −15.1587 −0.934727 −0.467364 0.884065i \(-0.654796\pi\)
−0.467364 + 0.884065i \(0.654796\pi\)
\(264\) 0 0
\(265\) −2.08737 −0.128226
\(266\) 0 0
\(267\) 3.28897 0.201282
\(268\) 0 0
\(269\) 3.43706 0.209561 0.104781 0.994495i \(-0.466586\pi\)
0.104781 + 0.994495i \(0.466586\pi\)
\(270\) 0 0
\(271\) 27.7359 1.68484 0.842418 0.538824i \(-0.181131\pi\)
0.842418 + 0.538824i \(0.181131\pi\)
\(272\) 0 0
\(273\) 6.74500 0.408226
\(274\) 0 0
\(275\) 1.17005 0.0705569
\(276\) 0 0
\(277\) 20.9720 1.26009 0.630043 0.776561i \(-0.283037\pi\)
0.630043 + 0.776561i \(0.283037\pi\)
\(278\) 0 0
\(279\) −8.59992 −0.514864
\(280\) 0 0
\(281\) 8.05468 0.480502 0.240251 0.970711i \(-0.422770\pi\)
0.240251 + 0.970711i \(0.422770\pi\)
\(282\) 0 0
\(283\) −0.195610 −0.0116278 −0.00581392 0.999983i \(-0.501851\pi\)
−0.00581392 + 0.999983i \(0.501851\pi\)
\(284\) 0 0
\(285\) −1.29997 −0.0770038
\(286\) 0 0
\(287\) 7.68837 0.453830
\(288\) 0 0
\(289\) −15.4487 −0.908746
\(290\) 0 0
\(291\) −8.50441 −0.498538
\(292\) 0 0
\(293\) −2.86744 −0.167518 −0.0837588 0.996486i \(-0.526693\pi\)
−0.0837588 + 0.996486i \(0.526693\pi\)
\(294\) 0 0
\(295\) 24.1701 1.40724
\(296\) 0 0
\(297\) 0.587142 0.0340694
\(298\) 0 0
\(299\) 2.04593 0.118319
\(300\) 0 0
\(301\) −3.38700 −0.195223
\(302\) 0 0
\(303\) −6.83549 −0.392689
\(304\) 0 0
\(305\) −25.8653 −1.48104
\(306\) 0 0
\(307\) 3.76659 0.214971 0.107485 0.994207i \(-0.465720\pi\)
0.107485 + 0.994207i \(0.465720\pi\)
\(308\) 0 0
\(309\) −1.17906 −0.0670744
\(310\) 0 0
\(311\) 27.9652 1.58576 0.792881 0.609377i \(-0.208580\pi\)
0.792881 + 0.609377i \(0.208580\pi\)
\(312\) 0 0
\(313\) 20.9426 1.18374 0.591872 0.806032i \(-0.298389\pi\)
0.591872 + 0.806032i \(0.298389\pi\)
\(314\) 0 0
\(315\) −7.99132 −0.450260
\(316\) 0 0
\(317\) −33.1900 −1.86413 −0.932067 0.362287i \(-0.881996\pi\)
−0.932067 + 0.362287i \(0.881996\pi\)
\(318\) 0 0
\(319\) −3.13121 −0.175314
\(320\) 0 0
\(321\) 15.7476 0.878945
\(322\) 0 0
\(323\) −0.612294 −0.0340689
\(324\) 0 0
\(325\) −4.44787 −0.246723
\(326\) 0 0
\(327\) 6.71332 0.371247
\(328\) 0 0
\(329\) 7.63636 0.421006
\(330\) 0 0
\(331\) −17.6285 −0.968950 −0.484475 0.874805i \(-0.660989\pi\)
−0.484475 + 0.874805i \(0.660989\pi\)
\(332\) 0 0
\(333\) −11.8705 −0.650499
\(334\) 0 0
\(335\) −20.3130 −1.10982
\(336\) 0 0
\(337\) −4.53441 −0.247005 −0.123502 0.992344i \(-0.539413\pi\)
−0.123502 + 0.992344i \(0.539413\pi\)
\(338\) 0 0
\(339\) 10.7161 0.582017
\(340\) 0 0
\(341\) −5.04937 −0.273439
\(342\) 0 0
\(343\) 14.7098 0.794252
\(344\) 0 0
\(345\) −2.42397 −0.130502
\(346\) 0 0
\(347\) 2.66210 0.142909 0.0714545 0.997444i \(-0.477236\pi\)
0.0714545 + 0.997444i \(0.477236\pi\)
\(348\) 0 0
\(349\) 17.5601 0.939968 0.469984 0.882675i \(-0.344260\pi\)
0.469984 + 0.882675i \(0.344260\pi\)
\(350\) 0 0
\(351\) −2.23197 −0.119134
\(352\) 0 0
\(353\) 0.525759 0.0279833 0.0139917 0.999902i \(-0.495546\pi\)
0.0139917 + 0.999902i \(0.495546\pi\)
\(354\) 0 0
\(355\) 9.67166 0.513319
\(356\) 0 0
\(357\) −3.76395 −0.199209
\(358\) 0 0
\(359\) −10.8769 −0.574061 −0.287031 0.957921i \(-0.592668\pi\)
−0.287031 + 0.957921i \(0.592668\pi\)
\(360\) 0 0
\(361\) −18.7583 −0.987281
\(362\) 0 0
\(363\) −10.6553 −0.559256
\(364\) 0 0
\(365\) −17.4245 −0.912039
\(366\) 0 0
\(367\) −21.9209 −1.14426 −0.572132 0.820162i \(-0.693883\pi\)
−0.572132 + 0.820162i \(0.693883\pi\)
\(368\) 0 0
\(369\) −2.54414 −0.132443
\(370\) 0 0
\(371\) 2.38543 0.123845
\(372\) 0 0
\(373\) 5.77269 0.298899 0.149449 0.988769i \(-0.452250\pi\)
0.149449 + 0.988769i \(0.452250\pi\)
\(374\) 0 0
\(375\) −7.95222 −0.410651
\(376\) 0 0
\(377\) 11.9031 0.613039
\(378\) 0 0
\(379\) −25.4249 −1.30599 −0.652994 0.757363i \(-0.726487\pi\)
−0.652994 + 0.757363i \(0.726487\pi\)
\(380\) 0 0
\(381\) 1.93781 0.0992772
\(382\) 0 0
\(383\) −29.6411 −1.51459 −0.757294 0.653074i \(-0.773479\pi\)
−0.757294 + 0.653074i \(0.773479\pi\)
\(384\) 0 0
\(385\) −4.69204 −0.239128
\(386\) 0 0
\(387\) 1.12078 0.0569727
\(388\) 0 0
\(389\) −1.17069 −0.0593563 −0.0296781 0.999560i \(-0.509448\pi\)
−0.0296781 + 0.999560i \(0.509448\pi\)
\(390\) 0 0
\(391\) −1.14170 −0.0577384
\(392\) 0 0
\(393\) −8.74741 −0.441248
\(394\) 0 0
\(395\) 20.3444 1.02364
\(396\) 0 0
\(397\) −7.52841 −0.377840 −0.188920 0.981992i \(-0.560499\pi\)
−0.188920 + 0.981992i \(0.560499\pi\)
\(398\) 0 0
\(399\) 1.48560 0.0743731
\(400\) 0 0
\(401\) 10.8561 0.542128 0.271064 0.962561i \(-0.412625\pi\)
0.271064 + 0.962561i \(0.412625\pi\)
\(402\) 0 0
\(403\) 19.1948 0.956160
\(404\) 0 0
\(405\) 2.64439 0.131401
\(406\) 0 0
\(407\) −6.96966 −0.345473
\(408\) 0 0
\(409\) −18.0532 −0.892675 −0.446337 0.894865i \(-0.647272\pi\)
−0.446337 + 0.894865i \(0.647272\pi\)
\(410\) 0 0
\(411\) 13.4646 0.664162
\(412\) 0 0
\(413\) −27.6215 −1.35916
\(414\) 0 0
\(415\) 31.6063 1.55149
\(416\) 0 0
\(417\) −6.12589 −0.299986
\(418\) 0 0
\(419\) 0.721252 0.0352355 0.0176177 0.999845i \(-0.494392\pi\)
0.0176177 + 0.999845i \(0.494392\pi\)
\(420\) 0 0
\(421\) 4.65373 0.226809 0.113404 0.993549i \(-0.463824\pi\)
0.113404 + 0.993549i \(0.463824\pi\)
\(422\) 0 0
\(423\) −2.52693 −0.122863
\(424\) 0 0
\(425\) 2.48207 0.120398
\(426\) 0 0
\(427\) 29.5586 1.43044
\(428\) 0 0
\(429\) −1.31048 −0.0632708
\(430\) 0 0
\(431\) 18.5254 0.892335 0.446167 0.894949i \(-0.352789\pi\)
0.446167 + 0.894949i \(0.352789\pi\)
\(432\) 0 0
\(433\) 12.2153 0.587028 0.293514 0.955955i \(-0.405175\pi\)
0.293514 + 0.955955i \(0.405175\pi\)
\(434\) 0 0
\(435\) −14.1025 −0.676162
\(436\) 0 0
\(437\) 0.450621 0.0215561
\(438\) 0 0
\(439\) 5.86727 0.280029 0.140015 0.990149i \(-0.455285\pi\)
0.140015 + 0.990149i \(0.455285\pi\)
\(440\) 0 0
\(441\) 2.13243 0.101544
\(442\) 0 0
\(443\) −26.1190 −1.24095 −0.620476 0.784225i \(-0.713061\pi\)
−0.620476 + 0.784225i \(0.713061\pi\)
\(444\) 0 0
\(445\) 8.69732 0.412292
\(446\) 0 0
\(447\) 6.53890 0.309279
\(448\) 0 0
\(449\) 33.6711 1.58904 0.794518 0.607241i \(-0.207724\pi\)
0.794518 + 0.607241i \(0.207724\pi\)
\(450\) 0 0
\(451\) −1.49377 −0.0703389
\(452\) 0 0
\(453\) −16.6852 −0.783940
\(454\) 0 0
\(455\) 17.8364 0.836184
\(456\) 0 0
\(457\) 19.7672 0.924670 0.462335 0.886705i \(-0.347012\pi\)
0.462335 + 0.886705i \(0.347012\pi\)
\(458\) 0 0
\(459\) 1.24552 0.0581359
\(460\) 0 0
\(461\) 24.9988 1.16431 0.582155 0.813078i \(-0.302210\pi\)
0.582155 + 0.813078i \(0.302210\pi\)
\(462\) 0 0
\(463\) 22.9788 1.06791 0.533957 0.845512i \(-0.320705\pi\)
0.533957 + 0.845512i \(0.320705\pi\)
\(464\) 0 0
\(465\) −22.7415 −1.05461
\(466\) 0 0
\(467\) 13.4653 0.623098 0.311549 0.950230i \(-0.399152\pi\)
0.311549 + 0.950230i \(0.399152\pi\)
\(468\) 0 0
\(469\) 23.2135 1.07190
\(470\) 0 0
\(471\) −6.35568 −0.292854
\(472\) 0 0
\(473\) 0.658060 0.0302576
\(474\) 0 0
\(475\) −0.979653 −0.0449495
\(476\) 0 0
\(477\) −0.789358 −0.0361422
\(478\) 0 0
\(479\) −4.43406 −0.202598 −0.101299 0.994856i \(-0.532300\pi\)
−0.101299 + 0.994856i \(0.532300\pi\)
\(480\) 0 0
\(481\) 26.4946 1.20805
\(482\) 0 0
\(483\) 2.77010 0.126044
\(484\) 0 0
\(485\) −22.4890 −1.02117
\(486\) 0 0
\(487\) −16.2455 −0.736152 −0.368076 0.929796i \(-0.619983\pi\)
−0.368076 + 0.929796i \(0.619983\pi\)
\(488\) 0 0
\(489\) 12.1987 0.551645
\(490\) 0 0
\(491\) −37.2553 −1.68131 −0.840655 0.541571i \(-0.817830\pi\)
−0.840655 + 0.541571i \(0.817830\pi\)
\(492\) 0 0
\(493\) −6.64233 −0.299156
\(494\) 0 0
\(495\) 1.55263 0.0697856
\(496\) 0 0
\(497\) −11.0527 −0.495782
\(498\) 0 0
\(499\) 18.9636 0.848928 0.424464 0.905445i \(-0.360463\pi\)
0.424464 + 0.905445i \(0.360463\pi\)
\(500\) 0 0
\(501\) −14.8626 −0.664014
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −18.0757 −0.804359
\(506\) 0 0
\(507\) −8.01830 −0.356105
\(508\) 0 0
\(509\) 3.26730 0.144820 0.0724102 0.997375i \(-0.476931\pi\)
0.0724102 + 0.997375i \(0.476931\pi\)
\(510\) 0 0
\(511\) 19.9126 0.880881
\(512\) 0 0
\(513\) −0.491597 −0.0217045
\(514\) 0 0
\(515\) −3.11789 −0.137391
\(516\) 0 0
\(517\) −1.48367 −0.0652515
\(518\) 0 0
\(519\) 7.02508 0.308367
\(520\) 0 0
\(521\) −25.5062 −1.11745 −0.558723 0.829355i \(-0.688708\pi\)
−0.558723 + 0.829355i \(0.688708\pi\)
\(522\) 0 0
\(523\) 15.3011 0.669072 0.334536 0.942383i \(-0.391420\pi\)
0.334536 + 0.942383i \(0.391420\pi\)
\(524\) 0 0
\(525\) −6.02221 −0.262831
\(526\) 0 0
\(527\) −10.7114 −0.466595
\(528\) 0 0
\(529\) −22.1598 −0.963468
\(530\) 0 0
\(531\) 9.14016 0.396649
\(532\) 0 0
\(533\) 5.67845 0.245961
\(534\) 0 0
\(535\) 41.6428 1.80037
\(536\) 0 0
\(537\) 5.16311 0.222805
\(538\) 0 0
\(539\) 1.25204 0.0539291
\(540\) 0 0
\(541\) 33.0023 1.41888 0.709441 0.704765i \(-0.248948\pi\)
0.709441 + 0.704765i \(0.248948\pi\)
\(542\) 0 0
\(543\) −1.26496 −0.0542847
\(544\) 0 0
\(545\) 17.7526 0.760439
\(546\) 0 0
\(547\) −6.64394 −0.284074 −0.142037 0.989861i \(-0.545365\pi\)
−0.142037 + 0.989861i \(0.545365\pi\)
\(548\) 0 0
\(549\) −9.78118 −0.417451
\(550\) 0 0
\(551\) 2.62168 0.111687
\(552\) 0 0
\(553\) −23.2495 −0.988668
\(554\) 0 0
\(555\) −31.3902 −1.33244
\(556\) 0 0
\(557\) 29.2945 1.24125 0.620624 0.784108i \(-0.286879\pi\)
0.620624 + 0.784108i \(0.286879\pi\)
\(558\) 0 0
\(559\) −2.50156 −0.105805
\(560\) 0 0
\(561\) 0.731297 0.0308754
\(562\) 0 0
\(563\) −23.1598 −0.976071 −0.488035 0.872824i \(-0.662286\pi\)
−0.488035 + 0.872824i \(0.662286\pi\)
\(564\) 0 0
\(565\) 28.3375 1.19217
\(566\) 0 0
\(567\) −3.02199 −0.126912
\(568\) 0 0
\(569\) −3.99492 −0.167476 −0.0837379 0.996488i \(-0.526686\pi\)
−0.0837379 + 0.996488i \(0.526686\pi\)
\(570\) 0 0
\(571\) −8.99135 −0.376276 −0.188138 0.982143i \(-0.560245\pi\)
−0.188138 + 0.982143i \(0.560245\pi\)
\(572\) 0 0
\(573\) 6.03083 0.251942
\(574\) 0 0
\(575\) −1.82669 −0.0761783
\(576\) 0 0
\(577\) −0.478841 −0.0199344 −0.00996722 0.999950i \(-0.503173\pi\)
−0.00996722 + 0.999950i \(0.503173\pi\)
\(578\) 0 0
\(579\) −1.06344 −0.0441950
\(580\) 0 0
\(581\) −36.1194 −1.49849
\(582\) 0 0
\(583\) −0.463465 −0.0191948
\(584\) 0 0
\(585\) −5.90220 −0.244026
\(586\) 0 0
\(587\) −27.1571 −1.12089 −0.560447 0.828191i \(-0.689371\pi\)
−0.560447 + 0.828191i \(0.689371\pi\)
\(588\) 0 0
\(589\) 4.22770 0.174199
\(590\) 0 0
\(591\) −22.3630 −0.919891
\(592\) 0 0
\(593\) 31.2986 1.28528 0.642640 0.766169i \(-0.277839\pi\)
0.642640 + 0.766169i \(0.277839\pi\)
\(594\) 0 0
\(595\) −9.95335 −0.408047
\(596\) 0 0
\(597\) −22.8245 −0.934145
\(598\) 0 0
\(599\) −41.2958 −1.68730 −0.843651 0.536892i \(-0.819598\pi\)
−0.843651 + 0.536892i \(0.819598\pi\)
\(600\) 0 0
\(601\) −10.7160 −0.437115 −0.218558 0.975824i \(-0.570135\pi\)
−0.218558 + 0.975824i \(0.570135\pi\)
\(602\) 0 0
\(603\) −7.68153 −0.312816
\(604\) 0 0
\(605\) −28.1767 −1.14554
\(606\) 0 0
\(607\) 23.5255 0.954871 0.477436 0.878667i \(-0.341566\pi\)
0.477436 + 0.878667i \(0.341566\pi\)
\(608\) 0 0
\(609\) 16.1162 0.653062
\(610\) 0 0
\(611\) 5.64004 0.228171
\(612\) 0 0
\(613\) 22.0125 0.889075 0.444538 0.895760i \(-0.353368\pi\)
0.444538 + 0.895760i \(0.353368\pi\)
\(614\) 0 0
\(615\) −6.72770 −0.271287
\(616\) 0 0
\(617\) 30.2743 1.21880 0.609400 0.792863i \(-0.291411\pi\)
0.609400 + 0.792863i \(0.291411\pi\)
\(618\) 0 0
\(619\) −2.65262 −0.106618 −0.0533089 0.998578i \(-0.516977\pi\)
−0.0533089 + 0.998578i \(0.516977\pi\)
\(620\) 0 0
\(621\) −0.916648 −0.0367838
\(622\) 0 0
\(623\) −9.93924 −0.398207
\(624\) 0 0
\(625\) −30.9927 −1.23971
\(626\) 0 0
\(627\) −0.288637 −0.0115271
\(628\) 0 0
\(629\) −14.7849 −0.589514
\(630\) 0 0
\(631\) 12.7539 0.507724 0.253862 0.967240i \(-0.418299\pi\)
0.253862 + 0.967240i \(0.418299\pi\)
\(632\) 0 0
\(633\) 12.3297 0.490061
\(634\) 0 0
\(635\) 5.12433 0.203353
\(636\) 0 0
\(637\) −4.75952 −0.188579
\(638\) 0 0
\(639\) 3.65743 0.144686
\(640\) 0 0
\(641\) −12.8796 −0.508715 −0.254358 0.967110i \(-0.581864\pi\)
−0.254358 + 0.967110i \(0.581864\pi\)
\(642\) 0 0
\(643\) −28.0870 −1.10764 −0.553822 0.832635i \(-0.686831\pi\)
−0.553822 + 0.832635i \(0.686831\pi\)
\(644\) 0 0
\(645\) 2.96379 0.116699
\(646\) 0 0
\(647\) 1.25841 0.0494731 0.0247365 0.999694i \(-0.492125\pi\)
0.0247365 + 0.999694i \(0.492125\pi\)
\(648\) 0 0
\(649\) 5.36657 0.210656
\(650\) 0 0
\(651\) 25.9889 1.01858
\(652\) 0 0
\(653\) −45.8218 −1.79315 −0.896574 0.442895i \(-0.853952\pi\)
−0.896574 + 0.442895i \(0.853952\pi\)
\(654\) 0 0
\(655\) −23.1316 −0.903825
\(656\) 0 0
\(657\) −6.58923 −0.257070
\(658\) 0 0
\(659\) −6.42765 −0.250386 −0.125193 0.992132i \(-0.539955\pi\)
−0.125193 + 0.992132i \(0.539955\pi\)
\(660\) 0 0
\(661\) 4.50232 0.175120 0.0875600 0.996159i \(-0.472093\pi\)
0.0875600 + 0.996159i \(0.472093\pi\)
\(662\) 0 0
\(663\) −2.77997 −0.107965
\(664\) 0 0
\(665\) 3.92851 0.152341
\(666\) 0 0
\(667\) 4.88846 0.189282
\(668\) 0 0
\(669\) 12.5188 0.484003
\(670\) 0 0
\(671\) −5.74294 −0.221704
\(672\) 0 0
\(673\) 43.8991 1.69219 0.846094 0.533034i \(-0.178948\pi\)
0.846094 + 0.533034i \(0.178948\pi\)
\(674\) 0 0
\(675\) 1.99280 0.0767028
\(676\) 0 0
\(677\) −9.04130 −0.347486 −0.173743 0.984791i \(-0.555586\pi\)
−0.173743 + 0.984791i \(0.555586\pi\)
\(678\) 0 0
\(679\) 25.7003 0.986285
\(680\) 0 0
\(681\) 16.9465 0.649391
\(682\) 0 0
\(683\) 33.2015 1.27042 0.635210 0.772340i \(-0.280914\pi\)
0.635210 + 0.772340i \(0.280914\pi\)
\(684\) 0 0
\(685\) 35.6057 1.36043
\(686\) 0 0
\(687\) −29.3819 −1.12099
\(688\) 0 0
\(689\) 1.76183 0.0671202
\(690\) 0 0
\(691\) −12.2706 −0.466796 −0.233398 0.972381i \(-0.574984\pi\)
−0.233398 + 0.972381i \(0.574984\pi\)
\(692\) 0 0
\(693\) −1.77434 −0.0674015
\(694\) 0 0
\(695\) −16.1992 −0.614472
\(696\) 0 0
\(697\) −3.16878 −0.120026
\(698\) 0 0
\(699\) −28.4814 −1.07726
\(700\) 0 0
\(701\) −16.5272 −0.624224 −0.312112 0.950045i \(-0.601036\pi\)
−0.312112 + 0.950045i \(0.601036\pi\)
\(702\) 0 0
\(703\) 5.83550 0.220090
\(704\) 0 0
\(705\) −6.68218 −0.251666
\(706\) 0 0
\(707\) 20.6568 0.776879
\(708\) 0 0
\(709\) −17.5665 −0.659722 −0.329861 0.944029i \(-0.607002\pi\)
−0.329861 + 0.944029i \(0.607002\pi\)
\(710\) 0 0
\(711\) 7.69343 0.288526
\(712\) 0 0
\(713\) 7.88310 0.295224
\(714\) 0 0
\(715\) −3.46543 −0.129600
\(716\) 0 0
\(717\) 22.9104 0.855604
\(718\) 0 0
\(719\) 31.4665 1.17350 0.586751 0.809767i \(-0.300407\pi\)
0.586751 + 0.809767i \(0.300407\pi\)
\(720\) 0 0
\(721\) 3.56311 0.132697
\(722\) 0 0
\(723\) −7.46479 −0.277618
\(724\) 0 0
\(725\) −10.6275 −0.394697
\(726\) 0 0
\(727\) 17.8165 0.660778 0.330389 0.943845i \(-0.392820\pi\)
0.330389 + 0.943845i \(0.392820\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.39596 0.0516314
\(732\) 0 0
\(733\) −19.1822 −0.708509 −0.354255 0.935149i \(-0.615265\pi\)
−0.354255 + 0.935149i \(0.615265\pi\)
\(734\) 0 0
\(735\) 5.63897 0.207996
\(736\) 0 0
\(737\) −4.51015 −0.166133
\(738\) 0 0
\(739\) 14.5735 0.536097 0.268048 0.963405i \(-0.413621\pi\)
0.268048 + 0.963405i \(0.413621\pi\)
\(740\) 0 0
\(741\) 1.09723 0.0403078
\(742\) 0 0
\(743\) −7.55964 −0.277336 −0.138668 0.990339i \(-0.544282\pi\)
−0.138668 + 0.990339i \(0.544282\pi\)
\(744\) 0 0
\(745\) 17.2914 0.633508
\(746\) 0 0
\(747\) 11.9522 0.437308
\(748\) 0 0
\(749\) −47.5891 −1.73887
\(750\) 0 0
\(751\) −4.47286 −0.163217 −0.0816084 0.996664i \(-0.526006\pi\)
−0.0816084 + 0.996664i \(0.526006\pi\)
\(752\) 0 0
\(753\) −6.63046 −0.241627
\(754\) 0 0
\(755\) −44.1222 −1.60577
\(756\) 0 0
\(757\) −37.9865 −1.38064 −0.690322 0.723503i \(-0.742531\pi\)
−0.690322 + 0.723503i \(0.742531\pi\)
\(758\) 0 0
\(759\) −0.538202 −0.0195355
\(760\) 0 0
\(761\) −11.9130 −0.431848 −0.215924 0.976410i \(-0.569276\pi\)
−0.215924 + 0.976410i \(0.569276\pi\)
\(762\) 0 0
\(763\) −20.2876 −0.734460
\(764\) 0 0
\(765\) 3.29364 0.119082
\(766\) 0 0
\(767\) −20.4006 −0.736622
\(768\) 0 0
\(769\) −13.7398 −0.495468 −0.247734 0.968828i \(-0.579686\pi\)
−0.247734 + 0.968828i \(0.579686\pi\)
\(770\) 0 0
\(771\) 2.89579 0.104289
\(772\) 0 0
\(773\) −30.1541 −1.08457 −0.542285 0.840195i \(-0.682441\pi\)
−0.542285 + 0.840195i \(0.682441\pi\)
\(774\) 0 0
\(775\) −17.1379 −0.615611
\(776\) 0 0
\(777\) 35.8725 1.28692
\(778\) 0 0
\(779\) 1.25069 0.0448107
\(780\) 0 0
\(781\) 2.14743 0.0768410
\(782\) 0 0
\(783\) −5.33298 −0.190585
\(784\) 0 0
\(785\) −16.8069 −0.599863
\(786\) 0 0
\(787\) −53.6781 −1.91342 −0.956709 0.291047i \(-0.905996\pi\)
−0.956709 + 0.291047i \(0.905996\pi\)
\(788\) 0 0
\(789\) −15.1587 −0.539665
\(790\) 0 0
\(791\) −32.3839 −1.15144
\(792\) 0 0
\(793\) 21.8313 0.775253
\(794\) 0 0
\(795\) −2.08737 −0.0740314
\(796\) 0 0
\(797\) 28.5773 1.01226 0.506130 0.862457i \(-0.331076\pi\)
0.506130 + 0.862457i \(0.331076\pi\)
\(798\) 0 0
\(799\) −3.14734 −0.111345
\(800\) 0 0
\(801\) 3.28897 0.116210
\(802\) 0 0
\(803\) −3.86881 −0.136527
\(804\) 0 0
\(805\) 7.32523 0.258180
\(806\) 0 0
\(807\) 3.43706 0.120990
\(808\) 0 0
\(809\) 32.2686 1.13450 0.567251 0.823545i \(-0.308007\pi\)
0.567251 + 0.823545i \(0.308007\pi\)
\(810\) 0 0
\(811\) −37.5741 −1.31940 −0.659702 0.751528i \(-0.729317\pi\)
−0.659702 + 0.751528i \(0.729317\pi\)
\(812\) 0 0
\(813\) 27.7359 0.972741
\(814\) 0 0
\(815\) 32.2582 1.12995
\(816\) 0 0
\(817\) −0.550974 −0.0192762
\(818\) 0 0
\(819\) 6.74500 0.235689
\(820\) 0 0
\(821\) 10.9386 0.381761 0.190881 0.981613i \(-0.438866\pi\)
0.190881 + 0.981613i \(0.438866\pi\)
\(822\) 0 0
\(823\) 46.8692 1.63376 0.816878 0.576810i \(-0.195703\pi\)
0.816878 + 0.576810i \(0.195703\pi\)
\(824\) 0 0
\(825\) 1.17005 0.0407360
\(826\) 0 0
\(827\) 30.3247 1.05449 0.527247 0.849712i \(-0.323224\pi\)
0.527247 + 0.849712i \(0.323224\pi\)
\(828\) 0 0
\(829\) 31.7701 1.10342 0.551711 0.834035i \(-0.313975\pi\)
0.551711 + 0.834035i \(0.313975\pi\)
\(830\) 0 0
\(831\) 20.9720 0.727511
\(832\) 0 0
\(833\) 2.65598 0.0920243
\(834\) 0 0
\(835\) −39.3026 −1.36012
\(836\) 0 0
\(837\) −8.59992 −0.297257
\(838\) 0 0
\(839\) −34.8586 −1.20345 −0.601726 0.798702i \(-0.705520\pi\)
−0.601726 + 0.798702i \(0.705520\pi\)
\(840\) 0 0
\(841\) −0.559339 −0.0192876
\(842\) 0 0
\(843\) 8.05468 0.277418
\(844\) 0 0
\(845\) −21.2035 −0.729423
\(846\) 0 0
\(847\) 32.2001 1.10641
\(848\) 0 0
\(849\) −0.195610 −0.00671333
\(850\) 0 0
\(851\) 10.8811 0.372998
\(852\) 0 0
\(853\) 25.0784 0.858667 0.429333 0.903146i \(-0.358749\pi\)
0.429333 + 0.903146i \(0.358749\pi\)
\(854\) 0 0
\(855\) −1.29997 −0.0444582
\(856\) 0 0
\(857\) 25.7574 0.879855 0.439927 0.898033i \(-0.355004\pi\)
0.439927 + 0.898033i \(0.355004\pi\)
\(858\) 0 0
\(859\) −18.3344 −0.625561 −0.312780 0.949826i \(-0.601260\pi\)
−0.312780 + 0.949826i \(0.601260\pi\)
\(860\) 0 0
\(861\) 7.68837 0.262019
\(862\) 0 0
\(863\) 35.0214 1.19214 0.596072 0.802931i \(-0.296727\pi\)
0.596072 + 0.802931i \(0.296727\pi\)
\(864\) 0 0
\(865\) 18.5771 0.631639
\(866\) 0 0
\(867\) −15.4487 −0.524665
\(868\) 0 0
\(869\) 4.51713 0.153233
\(870\) 0 0
\(871\) 17.1450 0.580935
\(872\) 0 0
\(873\) −8.50441 −0.287831
\(874\) 0 0
\(875\) 24.0315 0.812414
\(876\) 0 0
\(877\) −0.348285 −0.0117607 −0.00588037 0.999983i \(-0.501872\pi\)
−0.00588037 + 0.999983i \(0.501872\pi\)
\(878\) 0 0
\(879\) −2.86744 −0.0967163
\(880\) 0 0
\(881\) −1.76588 −0.0594940 −0.0297470 0.999557i \(-0.509470\pi\)
−0.0297470 + 0.999557i \(0.509470\pi\)
\(882\) 0 0
\(883\) 8.89614 0.299379 0.149690 0.988733i \(-0.452173\pi\)
0.149690 + 0.988733i \(0.452173\pi\)
\(884\) 0 0
\(885\) 24.1701 0.812470
\(886\) 0 0
\(887\) −0.453290 −0.0152200 −0.00760999 0.999971i \(-0.502422\pi\)
−0.00760999 + 0.999971i \(0.502422\pi\)
\(888\) 0 0
\(889\) −5.85605 −0.196406
\(890\) 0 0
\(891\) 0.587142 0.0196700
\(892\) 0 0
\(893\) 1.24223 0.0415697
\(894\) 0 0
\(895\) 13.6533 0.456379
\(896\) 0 0
\(897\) 2.04593 0.0683117
\(898\) 0 0
\(899\) 45.8632 1.52962
\(900\) 0 0
\(901\) −0.983161 −0.0327538
\(902\) 0 0
\(903\) −3.38700 −0.112712
\(904\) 0 0
\(905\) −3.34505 −0.111193
\(906\) 0 0
\(907\) 27.0906 0.899530 0.449765 0.893147i \(-0.351508\pi\)
0.449765 + 0.893147i \(0.351508\pi\)
\(908\) 0 0
\(909\) −6.83549 −0.226719
\(910\) 0 0
\(911\) −7.48478 −0.247982 −0.123991 0.992283i \(-0.539569\pi\)
−0.123991 + 0.992283i \(0.539569\pi\)
\(912\) 0 0
\(913\) 7.01763 0.232250
\(914\) 0 0
\(915\) −25.8653 −0.855079
\(916\) 0 0
\(917\) 26.4346 0.872947
\(918\) 0 0
\(919\) −1.29744 −0.0427984 −0.0213992 0.999771i \(-0.506812\pi\)
−0.0213992 + 0.999771i \(0.506812\pi\)
\(920\) 0 0
\(921\) 3.76659 0.124113
\(922\) 0 0
\(923\) −8.16328 −0.268697
\(924\) 0 0
\(925\) −23.6555 −0.777787
\(926\) 0 0
\(927\) −1.17906 −0.0387254
\(928\) 0 0
\(929\) −46.7480 −1.53375 −0.766875 0.641796i \(-0.778190\pi\)
−0.766875 + 0.641796i \(0.778190\pi\)
\(930\) 0 0
\(931\) −1.04829 −0.0343565
\(932\) 0 0
\(933\) 27.9652 0.915540
\(934\) 0 0
\(935\) 1.93383 0.0632431
\(936\) 0 0
\(937\) −27.8406 −0.909514 −0.454757 0.890616i \(-0.650274\pi\)
−0.454757 + 0.890616i \(0.650274\pi\)
\(938\) 0 0
\(939\) 20.9426 0.683435
\(940\) 0 0
\(941\) −40.3568 −1.31560 −0.657798 0.753195i \(-0.728512\pi\)
−0.657798 + 0.753195i \(0.728512\pi\)
\(942\) 0 0
\(943\) 2.33208 0.0759430
\(944\) 0 0
\(945\) −7.99132 −0.259958
\(946\) 0 0
\(947\) −5.07179 −0.164811 −0.0824055 0.996599i \(-0.526260\pi\)
−0.0824055 + 0.996599i \(0.526260\pi\)
\(948\) 0 0
\(949\) 14.7070 0.477408
\(950\) 0 0
\(951\) −33.1900 −1.07626
\(952\) 0 0
\(953\) −7.29876 −0.236430 −0.118215 0.992988i \(-0.537717\pi\)
−0.118215 + 0.992988i \(0.537717\pi\)
\(954\) 0 0
\(955\) 15.9479 0.516061
\(956\) 0 0
\(957\) −3.13121 −0.101218
\(958\) 0 0
\(959\) −40.6900 −1.31395
\(960\) 0 0
\(961\) 42.9587 1.38576
\(962\) 0 0
\(963\) 15.7476 0.507459
\(964\) 0 0
\(965\) −2.81214 −0.0905261
\(966\) 0 0
\(967\) 41.1589 1.32358 0.661791 0.749688i \(-0.269797\pi\)
0.661791 + 0.749688i \(0.269797\pi\)
\(968\) 0 0
\(969\) −0.612294 −0.0196697
\(970\) 0 0
\(971\) 29.1881 0.936691 0.468345 0.883545i \(-0.344850\pi\)
0.468345 + 0.883545i \(0.344850\pi\)
\(972\) 0 0
\(973\) 18.5124 0.593479
\(974\) 0 0
\(975\) −4.44787 −0.142446
\(976\) 0 0
\(977\) 10.4025 0.332806 0.166403 0.986058i \(-0.446785\pi\)
0.166403 + 0.986058i \(0.446785\pi\)
\(978\) 0 0
\(979\) 1.93109 0.0617180
\(980\) 0 0
\(981\) 6.71332 0.214340
\(982\) 0 0
\(983\) 5.76886 0.183998 0.0919990 0.995759i \(-0.470674\pi\)
0.0919990 + 0.995759i \(0.470674\pi\)
\(984\) 0 0
\(985\) −59.1365 −1.88424
\(986\) 0 0
\(987\) 7.63636 0.243068
\(988\) 0 0
\(989\) −1.02736 −0.0326683
\(990\) 0 0
\(991\) 4.47663 0.142205 0.0711025 0.997469i \(-0.477348\pi\)
0.0711025 + 0.997469i \(0.477348\pi\)
\(992\) 0 0
\(993\) −17.6285 −0.559423
\(994\) 0 0
\(995\) −60.3569 −1.91344
\(996\) 0 0
\(997\) 43.3463 1.37279 0.686396 0.727228i \(-0.259192\pi\)
0.686396 + 0.727228i \(0.259192\pi\)
\(998\) 0 0
\(999\) −11.8705 −0.375566
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 \(a_p\))