Newspace parameters
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1767625.1 |
Defining polynomial: | \(x^{6} - 7 x^{4} - x^{3} + 11 x^{2} + x - 1\) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.39213\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.899709 | 0.636190 | 0.318095 | − | 0.948059i | \(-0.396957\pi\) | ||||
0.318095 | + | 0.948059i | \(0.396957\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.19052 | −0.595262 | ||||||||
\(5\) | −1.67380 | −0.748547 | −0.374273 | − | 0.927318i | \(-0.622108\pi\) | ||||
−0.374273 | + | 0.927318i | \(0.622108\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.75765 | −0.664330 | −0.332165 | − | 0.943221i | \(-0.607779\pi\) | ||||
−0.332165 | + | 0.943221i | \(0.607779\pi\) | |||||||
\(8\) | −2.87054 | −1.01489 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50593 | −0.476218 | ||||||||
\(11\) | 5.08858 | 1.53427 | 0.767133 | − | 0.641488i | \(-0.221683\pi\) | ||||
0.767133 | + | 0.641488i | \(0.221683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.43675 | 1.78523 | 0.892617 | − | 0.450816i | \(-0.148867\pi\) | ||||
0.892617 | + | 0.450816i | \(0.148867\pi\) | |||||||
\(14\) | −1.58137 | −0.422640 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.201602 | −0.0504005 | ||||||||
\(17\) | 2.24001 | 0.543283 | 0.271641 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271641 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.96067 | −0.908641 | −0.454320 | − | 0.890838i | \(-0.650118\pi\) | ||||
−0.454320 | + | 0.890838i | \(0.650118\pi\) | |||||||
\(20\) | 1.99270 | 0.445582 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.57824 | 0.976085 | ||||||||
\(23\) | −7.71459 | −1.60860 | −0.804301 | − | 0.594222i | \(-0.797460\pi\) | ||||
−0.804301 | + | 0.594222i | \(0.797460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.19839 | −0.439678 | ||||||||
\(26\) | 5.79120 | 1.13575 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.09253 | 0.395451 | ||||||||
\(29\) | −0.101311 | −0.0188129 | −0.00940644 | − | 0.999956i | \(-0.502994\pi\) | ||||
−0.00940644 | + | 0.999956i | \(0.502994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.63283 | −0.832080 | −0.416040 | − | 0.909346i | \(-0.636582\pi\) | ||||
−0.416040 | + | 0.909346i | \(0.636582\pi\) | |||||||
\(32\) | 5.55970 | 0.982826 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.01536 | 0.345631 | ||||||||
\(35\) | 2.94196 | 0.497282 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.78041 | −1.27909 | −0.639546 | − | 0.768753i | \(-0.720878\pi\) | ||||
−0.639546 | + | 0.768753i | \(0.720878\pi\) | |||||||
\(38\) | −3.56345 | −0.578068 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.80472 | 0.759692 | ||||||||
\(41\) | −1.42586 | −0.222682 | −0.111341 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111341 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.65358 | −0.557166 | −0.278583 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278583 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(44\) | −6.05808 | −0.913291 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.94088 | −1.02338 | ||||||||
\(47\) | 7.73754 | 1.12864 | 0.564318 | − | 0.825558i | \(-0.309139\pi\) | ||||
0.564318 | + | 0.825558i | \(0.309139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.91066 | −0.558665 | ||||||||
\(50\) | −1.97791 | −0.279719 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.66311 | −1.06268 | ||||||||
\(53\) | −1.61074 | −0.221252 | −0.110626 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110626 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.51728 | −1.14847 | ||||||||
\(56\) | 5.04542 | 0.674222 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0911499 | −0.0119686 | ||||||||
\(59\) | 2.46261 | 0.320604 | 0.160302 | − | 0.987068i | \(-0.448753\pi\) | ||||
0.160302 | + | 0.987068i | \(0.448753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.77088 | −0.610849 | −0.305424 | − | 0.952216i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952216i | \(0.598798\pi\) | |||||||
\(62\) | −4.16819 | −0.529361 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.40531 | 0.675664 | ||||||||
\(65\) | −10.7738 | −1.33633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.42357 | −0.418255 | −0.209128 | − | 0.977888i | \(-0.567062\pi\) | ||||
−0.209128 | + | 0.977888i | \(0.567062\pi\) | |||||||
\(68\) | −2.66679 | −0.323396 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.64691 | 0.316366 | ||||||||
\(71\) | 13.1223 | 1.55733 | 0.778665 | − | 0.627440i | \(-0.215897\pi\) | ||||
0.778665 | + | 0.627440i | \(0.215897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4582 | −1.69220 | −0.846100 | − | 0.533025i | \(-0.821055\pi\) | ||||
−0.846100 | + | 0.533025i | \(0.821055\pi\) | |||||||
\(74\) | −7.00010 | −0.813745 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.71528 | 0.540880 | ||||||||
\(77\) | −8.94396 | −1.01926 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0644 | −1.46986 | −0.734930 | − | 0.678143i | \(-0.762785\pi\) | ||||
−0.734930 | + | 0.678143i | \(0.762785\pi\) | |||||||
\(80\) | 0.337442 | 0.0377271 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.28286 | −0.141668 | ||||||||
\(83\) | 0.423954 | 0.0465350 | 0.0232675 | − | 0.999729i | \(-0.492593\pi\) | ||||
0.0232675 | + | 0.999729i | \(0.492593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.74933 | −0.406672 | ||||||||
\(86\) | −3.28716 | −0.354463 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14.6070 | −1.55711 | ||||||||
\(89\) | −17.1426 | −1.81711 | −0.908556 | − | 0.417763i | \(-0.862814\pi\) | ||||
−0.908556 | + | 0.417763i | \(0.862814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3136 | −1.18598 | ||||||||
\(92\) | 9.18440 | 0.957540 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.96153 | 0.718027 | ||||||||
\(95\) | 6.62938 | 0.680160 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.06424 | 0.615730 | 0.307865 | − | 0.951430i | \(-0.400386\pi\) | ||||
0.307865 | + | 0.951430i | \(0.400386\pi\) | |||||||
\(98\) | −3.51845 | −0.355417 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.61724 | 0.261724 | ||||||||
\(101\) | −10.1166 | −1.00664 | −0.503320 | − | 0.864100i | \(-0.667888\pi\) | ||||
−0.503320 | + | 0.864100i | \(0.667888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.53914 | 0.250189 | 0.125094 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125094 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(104\) | −18.4770 | −1.81182 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.44919 | −0.140758 | ||||||||
\(107\) | −9.82497 | −0.949816 | −0.474908 | − | 0.880035i | \(-0.657519\pi\) | ||||
−0.474908 | + | 0.880035i | \(0.657519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1110 | −1.44738 | −0.723688 | − | 0.690127i | \(-0.757555\pi\) | ||||
−0.723688 | + | 0.690127i | \(0.757555\pi\) | |||||||
\(110\) | −7.66307 | −0.730645 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.354346 | 0.0334826 | ||||||||
\(113\) | −2.58916 | −0.243568 | −0.121784 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121784 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9127 | 1.20411 | ||||||||
\(116\) | 0.120613 | 0.0111986 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.21563 | 0.203965 | ||||||||
\(119\) | −3.93716 | −0.360919 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8937 | 1.35397 | ||||||||
\(122\) | −4.29240 | −0.388616 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.51549 | 0.495306 | ||||||||
\(125\) | 12.0487 | 1.07767 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.24277 | 0.642692 | 0.321346 | − | 0.946962i | \(-0.395865\pi\) | ||||
0.321346 | + | 0.946962i | \(0.395865\pi\) | |||||||
\(128\) | −6.25619 | −0.552975 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.69332 | −0.850160 | ||||||||
\(131\) | −2.14842 | −0.187709 | −0.0938543 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938543 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.96149 | 0.603637 | ||||||||
\(134\) | −3.08021 | −0.266090 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.43005 | −0.551372 | ||||||||
\(137\) | −6.53872 | −0.558640 | −0.279320 | − | 0.960198i | \(-0.590109\pi\) | ||||
−0.279320 | + | 0.960198i | \(0.590109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.78192 | 0.829691 | 0.414846 | − | 0.909892i | \(-0.363836\pi\) | ||||
0.414846 | + | 0.909892i | \(0.363836\pi\) | |||||||
\(140\) | −3.50248 | −0.296013 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.8062 | 0.990758 | ||||||||
\(143\) | 32.7540 | 2.73902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.169574 | 0.0140823 | ||||||||
\(146\) | −13.0081 | −1.07656 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.26277 | 0.761395 | ||||||||
\(149\) | 12.0860 | 0.990120 | 0.495060 | − | 0.868859i | \(-0.335146\pi\) | ||||
0.495060 | + | 0.868859i | \(0.335146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6923 | 1.03288 | 0.516442 | − | 0.856322i | \(-0.327256\pi\) | ||||
0.516442 | + | 0.856322i | \(0.327256\pi\) | |||||||
\(152\) | 11.3693 | 0.922170 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.04696 | −0.648442 | ||||||||
\(155\) | 7.75443 | 0.622851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.3326 | −1.62272 | −0.811359 | − | 0.584548i | \(-0.801272\pi\) | ||||
−0.811359 | + | 0.584548i | \(0.801272\pi\) | |||||||
\(158\) | −11.7542 | −0.935110 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.30583 | −0.735691 | ||||||||
\(161\) | 13.5596 | 1.06864 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3750 | −1.12593 | −0.562967 | − | 0.826480i | \(-0.690340\pi\) | ||||
−0.562967 | + | 0.826480i | \(0.690340\pi\) | |||||||
\(164\) | 1.69752 | 0.132554 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.381435 | 0.0296051 | ||||||||
\(167\) | 18.7294 | 1.44933 | 0.724663 | − | 0.689103i | \(-0.241995\pi\) | ||||
0.724663 | + | 0.689103i | \(0.241995\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.4318 | 2.18706 | ||||||||
\(170\) | −3.37331 | −0.258721 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.34968 | 0.331660 | ||||||||
\(173\) | 11.7428 | 0.892786 | 0.446393 | − | 0.894837i | \(-0.352708\pi\) | ||||
0.446393 | + | 0.894837i | \(0.352708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.86401 | 0.292091 | ||||||||
\(176\) | −1.02587 | −0.0773278 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.4233 | −1.15603 | ||||||||
\(179\) | −24.5193 | −1.83266 | −0.916328 | − | 0.400429i | \(-0.868861\pi\) | ||||
−0.916328 | + | 0.400429i | \(0.868861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.13689 | 0.158833 | 0.0794167 | − | 0.996842i | \(-0.474694\pi\) | ||||
0.0794167 | + | 0.996842i | \(0.474694\pi\) | |||||||
\(182\) | −10.1789 | −0.754512 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 22.1450 | 1.63255 | ||||||||
\(185\) | 13.0229 | 0.957460 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3985 | 0.833540 | ||||||||
\(188\) | −9.21173 | −0.671834 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.96451 | 0.432711 | ||||||||
\(191\) | −11.6936 | −0.846118 | −0.423059 | − | 0.906102i | \(-0.639044\pi\) | ||||
−0.423059 | + | 0.906102i | \(0.639044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.15548 | 0.155155 | 0.0775774 | − | 0.996986i | \(-0.475282\pi\) | ||||
0.0775774 | + | 0.996986i | \(0.475282\pi\) | |||||||
\(194\) | 5.45605 | 0.391721 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.65573 | 0.332552 | ||||||||
\(197\) | −6.46675 | −0.460737 | −0.230368 | − | 0.973104i | \(-0.573993\pi\) | ||||
−0.230368 | + | 0.973104i | \(0.573993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.8975 | 1.55228 | 0.776138 | − | 0.630563i | \(-0.217176\pi\) | ||||
0.776138 | + | 0.630563i | \(0.217176\pi\) | |||||||
\(200\) | 6.31057 | 0.446225 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.10200 | −0.640415 | ||||||||
\(203\) | 0.178069 | 0.0124980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.38661 | 0.166688 | ||||||||
\(206\) | 2.28449 | 0.159168 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.29766 | −0.0899767 | ||||||||
\(209\) | −20.1542 | −1.39410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2465 | 0.774243 | 0.387122 | − | 0.922029i | \(-0.373469\pi\) | ||||
0.387122 | + | 0.922029i | \(0.373469\pi\) | |||||||
\(212\) | 1.91762 | 0.131703 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.83961 | −0.604263 | ||||||||
\(215\) | 6.11537 | 0.417065 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.14290 | 0.552776 | ||||||||
\(218\) | −13.5955 | −0.920806 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.1400 | 0.683641 | ||||||||
\(221\) | 14.4184 | 0.969887 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8849 | −1.33159 | −0.665797 | − | 0.746133i | \(-0.731908\pi\) | ||||
−0.665797 | + | 0.746133i | \(0.731908\pi\) | |||||||
\(224\) | −9.77202 | −0.652921 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.32949 | −0.154955 | ||||||||
\(227\) | 6.20415 | 0.411784 | 0.205892 | − | 0.978575i | \(-0.433990\pi\) | ||||
0.205892 | + | 0.978575i | \(0.433990\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.29386 | −0.415910 | −0.207955 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207955 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(230\) | 11.6177 | 0.766045 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.290816 | 0.0190930 | ||||||||
\(233\) | 1.37434 | 0.0900362 | 0.0450181 | − | 0.998986i | \(-0.485665\pi\) | ||||
0.0450181 | + | 0.998986i | \(0.485665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9511 | −0.844836 | ||||||||
\(236\) | −2.93179 | −0.190843 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.54230 | −0.229613 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6512 | −1.07260 | −0.536299 | − | 0.844028i | \(-0.680178\pi\) | ||||
−0.536299 | + | 0.844028i | \(0.680178\pi\) | |||||||
\(242\) | 13.4000 | 0.861383 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.67985 | 0.363615 | ||||||||
\(245\) | 6.54566 | 0.418187 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4939 | −1.62214 | ||||||||
\(248\) | 13.2987 | 0.844470 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.8403 | 0.685600 | ||||||||
\(251\) | −8.70369 | −0.549372 | −0.274686 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274686 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.2563 | −2.46802 | ||||||||
\(254\) | 6.51638 | 0.408874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.4394 | −1.02746 | ||||||||
\(257\) | 17.8087 | 1.11087 | 0.555437 | − | 0.831559i | \(-0.312551\pi\) | ||||
0.555437 | + | 0.831559i | \(0.312551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6753 | 0.849739 | ||||||||
\(260\) | 12.8265 | 0.795467 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.93295 | −0.119418 | ||||||||
\(263\) | −21.2660 | −1.31132 | −0.655658 | − | 0.755058i | \(-0.727609\pi\) | ||||
−0.655658 | + | 0.755058i | \(0.727609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.69605 | 0.165617 | ||||||||
\(266\) | 6.26331 | 0.384028 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.07584 | 0.248971 | ||||||||
\(269\) | 17.1887 | 1.04801 | 0.524005 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524005 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1030 | 1.16043 | 0.580213 | − | 0.814465i | \(-0.302969\pi\) | ||||
0.580213 | + | 0.814465i | \(0.302969\pi\) | |||||||
\(272\) | −0.451591 | −0.0273817 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.88294 | −0.355401 | ||||||||
\(275\) | −11.1867 | −0.674583 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3315 | 1.16152 | 0.580760 | − | 0.814075i | \(-0.302755\pi\) | ||||
0.580760 | + | 0.814075i | \(0.302755\pi\) | |||||||
\(278\) | 8.80087 | 0.527841 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.44502 | −0.504687 | ||||||||
\(281\) | 4.05588 | 0.241954 | 0.120977 | − | 0.992655i | \(-0.461397\pi\) | ||||
0.120977 | + | 0.992655i | \(0.461397\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8007 | −0.642035 | −0.321018 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321018 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(284\) | −15.6224 | −0.927020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.4690 | 1.74254 | ||||||||
\(287\) | 2.50617 | 0.147934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9823 | −0.704844 | ||||||||
\(290\) | 0.152567 | 0.00895903 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.2128 | 1.00730 | ||||||||
\(293\) | −5.01609 | −0.293043 | −0.146522 | − | 0.989207i | \(-0.546808\pi\) | ||||
−0.146522 | + | 0.989207i | \(0.546808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.12191 | −0.239987 | ||||||||
\(296\) | 22.3340 | 1.29814 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.8738 | 0.629904 | ||||||||
\(299\) | −49.6569 | −2.87173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.42173 | 0.370142 | ||||||||
\(302\) | 11.4194 | 0.657110 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.798480 | 0.0457959 | ||||||||
\(305\) | 7.98550 | 0.457249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.70591 | −0.553945 | −0.276973 | − | 0.960878i | \(-0.589331\pi\) | ||||
−0.276973 | + | 0.960878i | \(0.589331\pi\) | |||||||
\(308\) | 10.6480 | 0.606727 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.97673 | 0.396251 | ||||||||
\(311\) | 10.3411 | 0.586389 | 0.293195 | − | 0.956053i | \(-0.405282\pi\) | ||||
0.293195 | + | 0.956053i | \(0.405282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8987 | −1.35084 | −0.675418 | − | 0.737435i | \(-0.736037\pi\) | ||||
−0.675418 | + | 0.737435i | \(0.736037\pi\) | |||||||
\(314\) | −18.2934 | −1.03236 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5535 | 0.874952 | ||||||||
\(317\) | 1.48619 | 0.0834729 | 0.0417365 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417365 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.515527 | −0.0288640 | ||||||||
\(320\) | −9.04742 | −0.505766 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.1997 | 0.679860 | ||||||||
\(323\) | −8.87196 | −0.493649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1505 | −0.784928 | ||||||||
\(326\) | −12.9333 | −0.716307 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.09299 | 0.225998 | ||||||||
\(329\) | −13.5999 | −0.749787 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6038 | −0.967593 | −0.483797 | − | 0.875180i | \(-0.660743\pi\) | ||||
−0.483797 | + | 0.875180i | \(0.660743\pi\) | |||||||
\(332\) | −0.504728 | −0.0277006 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.8510 | 0.922047 | ||||||||
\(335\) | 5.73037 | 0.313083 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9294 | 1.03115 | 0.515576 | − | 0.856844i | \(-0.327578\pi\) | ||||
0.515576 | + | 0.856844i | \(0.327578\pi\) | |||||||
\(338\) | 25.5803 | 1.39139 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.46368 | 0.242077 | ||||||||
\(341\) | −23.5745 | −1.27663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1771 | 1.03547 | ||||||||
\(344\) | 10.4878 | 0.565462 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5651 | 0.567982 | ||||||||
\(347\) | 1.63077 | 0.0875444 | 0.0437722 | − | 0.999042i | \(-0.486062\pi\) | ||||
0.0437722 | + | 0.999042i | \(0.486062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00213 | 0.428344 | 0.214172 | − | 0.976796i | \(-0.431295\pi\) | ||||
0.214172 | + | 0.976796i | \(0.431295\pi\) | |||||||
\(350\) | 3.47648 | 0.185826 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.2910 | 1.50792 | ||||||||
\(353\) | −9.60124 | −0.511022 | −0.255511 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255511 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.9641 | −1.16573 | ||||||||
\(356\) | 20.4087 | 1.08166 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.0602 | −1.16592 | ||||||||
\(359\) | 31.4338 | 1.65901 | 0.829506 | − | 0.558498i | \(-0.188622\pi\) | ||||
0.829506 | + | 0.558498i | \(0.188622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.31307 | −0.174372 | ||||||||
\(362\) | 1.92257 | 0.101048 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.4691 | 0.705972 | ||||||||
\(365\) | 24.2001 | 1.26669 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.76744 | −0.509856 | −0.254928 | − | 0.966960i | \(-0.582052\pi\) | ||||
−0.254928 | + | 0.966960i | \(0.582052\pi\) | |||||||
\(368\) | 1.55528 | 0.0810744 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.7168 | 0.609126 | ||||||||
\(371\) | 2.83111 | 0.146984 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4876 | 0.957252 | 0.478626 | − | 0.878019i | \(-0.341135\pi\) | ||||
0.478626 | + | 0.878019i | \(0.341135\pi\) | |||||||
\(374\) | 10.2553 | 0.530290 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.2109 | −1.14544 | ||||||||
\(377\) | −0.652111 | −0.0335854 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.80626 | −0.0927813 | −0.0463907 | − | 0.998923i | \(-0.514772\pi\) | ||||
−0.0463907 | + | 0.998923i | \(0.514772\pi\) | |||||||
\(380\) | −7.89244 | −0.404874 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5208 | −0.538292 | ||||||||
\(383\) | 25.2177 | 1.28856 | 0.644281 | − | 0.764789i | \(-0.277157\pi\) | ||||
0.644281 | + | 0.764789i | \(0.277157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.9704 | 0.762963 | ||||||||
\(386\) | 1.93930 | 0.0987079 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.21962 | −0.366521 | ||||||||
\(389\) | −29.1698 | −1.47897 | −0.739485 | − | 0.673173i | \(-0.764931\pi\) | ||||
−0.739485 | + | 0.673173i | \(0.764931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.2808 | −0.873926 | ||||||||
\(392\) | 11.2257 | 0.566984 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.81819 | −0.293116 | ||||||||
\(395\) | 21.8672 | 1.10026 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.3463 | 1.87435 | 0.937177 | − | 0.348853i | \(-0.113429\pi\) | ||||
0.937177 | + | 0.348853i | \(0.113429\pi\) | |||||||
\(398\) | 19.7014 | 0.987542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.443200 | 0.0221600 | ||||||||
\(401\) | −5.50916 | −0.275114 | −0.137557 | − | 0.990494i | \(-0.543925\pi\) | ||||
−0.137557 | + | 0.990494i | \(0.543925\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.8204 | −1.48546 | ||||||||
\(404\) | 12.0441 | 0.599215 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.160210 | 0.00795108 | ||||||||
\(407\) | −39.5913 | −1.96247 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.2723 | −1.39797 | −0.698987 | − | 0.715134i | \(-0.746366\pi\) | ||||
−0.698987 | + | 0.715134i | \(0.746366\pi\) | |||||||
\(410\) | 2.14725 | 0.106045 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.02291 | −0.148928 | ||||||||
\(413\) | −4.32840 | −0.212987 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.709615 | −0.0348337 | ||||||||
\(416\) | 35.7864 | 1.75457 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.1329 | −0.886910 | ||||||||
\(419\) | −12.0357 | −0.587983 | −0.293992 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293992 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9983 | −1.46203 | −0.731015 | − | 0.682362i | \(-0.760953\pi\) | ||||
−0.731015 | + | 0.682362i | \(0.760953\pi\) | |||||||
\(422\) | 10.1186 | 0.492566 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.62368 | 0.224546 | ||||||||
\(425\) | −4.92442 | −0.238869 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.38555 | 0.405805 | ||||||||
\(428\) | 11.6969 | 0.565390 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.50205 | 0.265332 | ||||||||
\(431\) | 17.8098 | 0.857870 | 0.428935 | − | 0.903335i | \(-0.358889\pi\) | ||||
0.428935 | + | 0.903335i | \(0.358889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2488 | 0.973094 | 0.486547 | − | 0.873654i | \(-0.338256\pi\) | ||||
0.486547 | + | 0.873654i | \(0.338256\pi\) | |||||||
\(434\) | 7.32623 | 0.351670 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.9901 | 0.861568 | ||||||||
\(437\) | 30.5550 | 1.46164 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.7608 | −1.65904 | −0.829521 | − | 0.558475i | \(-0.811387\pi\) | ||||
−0.829521 | + | 0.558475i | \(0.811387\pi\) | |||||||
\(440\) | 24.4492 | 1.16557 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9724 | 0.617032 | ||||||||
\(443\) | 25.7595 | 1.22387 | 0.611935 | − | 0.790908i | \(-0.290392\pi\) | ||||
0.611935 | + | 0.790908i | \(0.290392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.6933 | 1.36019 | ||||||||
\(446\) | −17.8907 | −0.847147 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.50066 | −0.448864 | ||||||||
\(449\) | 30.2122 | 1.42580 | 0.712901 | − | 0.701265i | \(-0.247381\pi\) | ||||
0.712901 | + | 0.701265i | \(0.247381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.25561 | −0.341653 | ||||||||
\(452\) | 3.08246 | 0.144987 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.58193 | 0.261973 | ||||||||
\(455\) | 18.9367 | 0.887765 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.33578 | 0.0624850 | 0.0312425 | − | 0.999512i | \(-0.490054\pi\) | ||||
0.0312425 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(458\) | −5.66264 | −0.264598 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.3729 | −0.716764 | ||||||||
\(461\) | −16.6243 | −0.774272 | −0.387136 | − | 0.922023i | \(-0.626536\pi\) | ||||
−0.387136 | + | 0.922023i | \(0.626536\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4246 | 1.36748 | 0.683739 | − | 0.729726i | \(-0.260353\pi\) | ||||
0.683739 | + | 0.729726i | \(0.260353\pi\) | |||||||
\(464\) | 0.0204244 | 0.000948179 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.23651 | 0.0572801 | ||||||||
\(467\) | 2.53660 | 0.117380 | 0.0586899 | − | 0.998276i | \(-0.481308\pi\) | ||||
0.0586899 | + | 0.998276i | \(0.481308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.01744 | 0.277859 | ||||||||
\(470\) | −11.6522 | −0.537476 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.06901 | −0.325378 | ||||||||
\(473\) | −18.5916 | −0.854841 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.70710 | 0.399509 | ||||||||
\(476\) | 4.68729 | 0.214842 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.899709 | 0.0411517 | ||||||||
\(479\) | −38.6620 | −1.76651 | −0.883255 | − | 0.468893i | \(-0.844653\pi\) | ||||
−0.883255 | + | 0.468893i | \(0.844653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50.0806 | −2.28348 | ||||||||
\(482\) | −14.9812 | −0.682376 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.7313 | −0.805968 | ||||||||
\(485\) | −10.1503 | −0.460903 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.29522 | 0.421207 | 0.210603 | − | 0.977572i | \(-0.432457\pi\) | ||||
0.210603 | + | 0.977572i | \(0.432457\pi\) | |||||||
\(488\) | 13.6950 | 0.619944 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.88919 | 0.266046 | ||||||||
\(491\) | −11.3475 | −0.512105 | −0.256052 | − | 0.966663i | \(-0.582422\pi\) | ||||
−0.256052 | + | 0.966663i | \(0.582422\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.226937 | −0.0102207 | ||||||||
\(494\) | −22.9371 | −1.03199 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.933987 | 0.0419372 | ||||||||
\(497\) | −23.0644 | −1.03458 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8745 | 1.11353 | 0.556767 | − | 0.830669i | \(-0.312042\pi\) | ||||
0.556767 | + | 0.830669i | \(0.312042\pi\) | |||||||
\(500\) | −14.3442 | −0.641494 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.83078 | −0.349505 | ||||||||
\(503\) | −13.2786 | −0.592064 | −0.296032 | − | 0.955178i | \(-0.595663\pi\) | ||||
−0.296032 | + | 0.955178i | \(0.595663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.9332 | 0.753517 | ||||||||
\(506\) | −35.3192 | −1.57013 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.62270 | −0.382570 | ||||||||
\(509\) | −33.4053 | −1.48067 | −0.740333 | − | 0.672241i | \(-0.765332\pi\) | ||||
−0.740333 | + | 0.672241i | \(0.765332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.4124 | 1.12418 | ||||||||
\(512\) | −2.27826 | −0.100686 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.0226 | 0.706727 | ||||||||
\(515\) | −4.25001 | −0.187278 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.3731 | 1.73163 | ||||||||
\(518\) | 12.3037 | 0.540596 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 30.9268 | 1.35623 | ||||||||
\(521\) | −33.4430 | −1.46516 | −0.732582 | − | 0.680678i | \(-0.761685\pi\) | ||||
−0.732582 | + | 0.680678i | \(0.761685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7941 | −1.12790 | −0.563948 | − | 0.825810i | \(-0.690718\pi\) | ||||
−0.563948 | + | 0.825810i | \(0.690718\pi\) | |||||||
\(524\) | 2.55775 | 0.111736 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1332 | −0.834246 | ||||||||
\(527\) | −10.3776 | −0.452055 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.5148 | 1.58760 | ||||||||
\(530\) | 2.42566 | 0.105364 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.28782 | −0.359323 | ||||||||
\(533\) | −9.17791 | −0.397540 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.4451 | 0.710982 | ||||||||
\(536\) | 9.82749 | 0.424483 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.4648 | 0.666734 | ||||||||
\(539\) | −19.8997 | −0.857141 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.49430 | 0.193225 | 0.0966126 | − | 0.995322i | \(-0.469199\pi\) | ||||
0.0966126 | + | 0.995322i | \(0.469199\pi\) | |||||||
\(542\) | 17.1871 | 0.738251 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.4538 | 0.533952 | ||||||||
\(545\) | 25.2929 | 1.08343 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.5160 | −1.04823 | −0.524114 | − | 0.851648i | \(-0.675603\pi\) | ||||
−0.524114 | + | 0.851648i | \(0.675603\pi\) | |||||||
\(548\) | 7.78450 | 0.332537 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.0648 | −0.429163 | ||||||||
\(551\) | 0.401258 | 0.0170942 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.9627 | 0.976472 | ||||||||
\(554\) | 17.3928 | 0.738947 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.6456 | −0.493884 | ||||||||
\(557\) | −25.5502 | −1.08260 | −0.541299 | − | 0.840830i | \(-0.682067\pi\) | ||||
−0.541299 | + | 0.840830i | \(0.682067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.5172 | −0.994672 | ||||||||
\(560\) | −0.593105 | −0.0250633 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.64911 | 0.153929 | ||||||||
\(563\) | 13.4776 | 0.568011 | 0.284006 | − | 0.958823i | \(-0.408337\pi\) | ||||
0.284006 | + | 0.958823i | \(0.408337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.33374 | 0.182322 | ||||||||
\(566\) | −9.71749 | −0.408456 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.6681 | −1.58052 | ||||||||
\(569\) | 6.39428 | 0.268062 | 0.134031 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134031 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9506 | −0.751210 | −0.375605 | − | 0.926780i | \(-0.622565\pi\) | ||||
−0.375605 | + | 0.926780i | \(0.622565\pi\) | |||||||
\(572\) | −38.9944 | −1.63044 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.25482 | 0.0941144 | ||||||||
\(575\) | 16.9597 | 0.707267 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1291 | −1.54571 | −0.772853 | − | 0.634585i | \(-0.781171\pi\) | ||||
−0.772853 | + | 0.634585i | \(0.781171\pi\) | |||||||
\(578\) | −10.7806 | −0.448415 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.201882 | −0.00838268 | ||||||||
\(581\) | −0.745165 | −0.0309146 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.19636 | −0.339459 | ||||||||
\(584\) | 41.5027 | 1.71740 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.51302 | −0.186431 | ||||||||
\(587\) | 36.6232 | 1.51160 | 0.755800 | − | 0.654803i | \(-0.227248\pi\) | ||||
0.755800 | + | 0.654803i | \(0.227248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.3491 | 0.756062 | ||||||||
\(590\) | −3.70852 | −0.152677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.56855 | 0.0644669 | ||||||||
\(593\) | −38.1568 | −1.56691 | −0.783456 | − | 0.621447i | \(-0.786545\pi\) | ||||
−0.783456 | + | 0.621447i | \(0.786545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.59003 | 0.270165 | ||||||||
\(596\) | −14.3886 | −0.589381 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −44.6767 | −1.82697 | ||||||||
\(599\) | −48.4161 | −1.97823 | −0.989115 | − | 0.147148i | \(-0.952991\pi\) | ||||
−0.989115 | + | 0.147148i | \(0.952991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2469 | 0.907472 | 0.453736 | − | 0.891136i | \(-0.350091\pi\) | ||||
0.453736 | + | 0.891136i | \(0.350091\pi\) | |||||||
\(602\) | 5.77768 | 0.235481 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.1105 | −0.614837 | ||||||||
\(605\) | −24.9291 | −1.01351 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.3888 | 1.63933 | 0.819665 | − | 0.572842i | \(-0.194159\pi\) | ||||
0.819665 | + | 0.572842i | \(0.194159\pi\) | |||||||
\(608\) | −22.0202 | −0.893035 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.18463 | 0.290897 | ||||||||
\(611\) | 49.8046 | 2.01488 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.3156 | −0.658979 | −0.329490 | − | 0.944159i | \(-0.606877\pi\) | ||||
−0.329490 | + | 0.944159i | \(0.606877\pi\) | |||||||
\(614\) | −8.73249 | −0.352415 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.6740 | 1.03444 | ||||||||
\(617\) | −5.46752 | −0.220114 | −0.110057 | − | 0.993925i | \(-0.535103\pi\) | ||||
−0.110057 | + | 0.993925i | \(0.535103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.6271 | 1.75352 | 0.876761 | − | 0.480926i | \(-0.159700\pi\) | ||||
0.876761 | + | 0.480926i | \(0.159700\pi\) | |||||||
\(620\) | −9.23184 | −0.370760 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.30397 | 0.373055 | ||||||||
\(623\) | 30.1307 | 1.20716 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.17513 | −0.367005 | ||||||||
\(626\) | −21.5019 | −0.859389 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.2065 | 0.965943 | ||||||||
\(629\) | −17.4282 | −0.694908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7573 | 1.02538 | 0.512692 | − | 0.858573i | \(-0.328648\pi\) | ||||
0.512692 | + | 0.858573i | \(0.328648\pi\) | |||||||
\(632\) | 37.5019 | 1.49175 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.33714 | 0.0531046 | ||||||||
\(635\) | −12.1230 | −0.481085 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.1719 | −0.997349 | ||||||||
\(638\) | −0.463824 | −0.0183630 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.4716 | 0.413927 | ||||||||
\(641\) | −2.85693 | −0.112842 | −0.0564210 | − | 0.998407i | \(-0.517969\pi\) | ||||
−0.0564210 | + | 0.998407i | \(0.517969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7053 | 0.422176 | 0.211088 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211088 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(644\) | −16.1430 | −0.636123 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.98217 | −0.314054 | ||||||||
\(647\) | −10.9862 | −0.431913 | −0.215956 | − | 0.976403i | \(-0.569287\pi\) | ||||
−0.215956 | + | 0.976403i | \(0.569287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.5312 | 0.491892 | ||||||||
\(650\) | −12.7313 | −0.499363 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.1137 | 0.670226 | ||||||||
\(653\) | 41.1768 | 1.61137 | 0.805687 | − | 0.592342i | \(-0.201797\pi\) | ||||
0.805687 | + | 0.592342i | \(0.201797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.59603 | 0.140509 | ||||||||
\(656\) | 0.287456 | 0.0112233 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2359 | −0.477007 | ||||||||
\(659\) | −1.39962 | −0.0545216 | −0.0272608 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272608 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.9112 | 1.04673 | 0.523363 | − | 0.852110i | \(-0.324677\pi\) | ||||
0.523363 | + | 0.852110i | \(0.324677\pi\) | |||||||
\(662\) | −15.8383 | −0.615573 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.21698 | −0.0472280 | ||||||||
\(665\) | −11.6521 | −0.451851 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.781569 | 0.0302625 | ||||||||
\(668\) | −22.2978 | −0.862729 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.15566 | 0.199181 | ||||||||
\(671\) | −24.2770 | −0.937204 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4943 | 1.36821 | 0.684103 | − | 0.729386i | \(-0.260194\pi\) | ||||
0.684103 | + | 0.729386i | \(0.260194\pi\) | |||||||
\(674\) | 17.0310 | 0.656009 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.8487 | −1.30187 | ||||||||
\(677\) | −7.66192 | −0.294471 | −0.147236 | − | 0.989101i | \(-0.547038\pi\) | ||||
−0.147236 | + | 0.989101i | \(0.547038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6588 | −0.409048 | ||||||||
\(680\) | 10.7626 | 0.412728 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.2102 | −0.812180 | ||||||||
\(683\) | 11.5533 | 0.442074 | 0.221037 | − | 0.975265i | \(-0.429056\pi\) | ||||
0.221037 | + | 0.975265i | \(0.429056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.9445 | 0.418168 | ||||||||
\(686\) | 17.2538 | 0.658755 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.736569 | 0.0280814 | ||||||||
\(689\) | −10.3679 | −0.394986 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.48943 | 0.360995 | 0.180498 | − | 0.983575i | \(-0.442229\pi\) | ||||
0.180498 | + | 0.983575i | \(0.442229\pi\) | |||||||
\(692\) | −13.9801 | −0.531442 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.46722 | 0.0556949 | ||||||||
\(695\) | −16.3730 | −0.621063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.19395 | −0.120979 | ||||||||
\(698\) | 7.19959 | 0.272508 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.60019 | −0.173871 | ||||||||
\(701\) | 33.6461 | 1.27079 | 0.635397 | − | 0.772186i | \(-0.280836\pi\) | ||||
0.635397 | + | 0.772186i | \(0.280836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.8157 | 1.16223 | ||||||||
\(704\) | 27.5054 | 1.03665 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.63831 | −0.325107 | ||||||||
\(707\) | 17.7815 | 0.668742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7519 | −1.04224 | −0.521122 | − | 0.853482i | \(-0.674486\pi\) | ||||
−0.521122 | + | 0.853482i | \(0.674486\pi\) | |||||||
\(710\) | −19.7613 | −0.741629 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49.2085 | 1.84417 | ||||||||
\(713\) | 35.7403 | 1.33849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.8236 | −2.05029 | ||||||||
\(716\) | 29.1908 | 1.09091 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.2812 | 1.05545 | ||||||||
\(719\) | 28.9767 | 1.08065 | 0.540324 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540324 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.46292 | −0.166208 | ||||||||
\(722\) | −2.98080 | −0.110934 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.54402 | −0.0945476 | ||||||||
\(725\) | 0.222720 | 0.00827161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.6229 | −0.653599 | −0.326799 | − | 0.945094i | \(-0.605970\pi\) | ||||
−0.326799 | + | 0.945094i | \(0.605970\pi\) | |||||||
\(728\) | 32.4761 | 1.20364 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.7730 | 0.805855 | ||||||||
\(731\) | −8.18407 | −0.302699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.2978 | 0.380359 | 0.190180 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190180 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(734\) | −8.78785 | −0.324366 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.8908 | −1.58098 | ||||||||
\(737\) | −17.4211 | −0.641714 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2229 | 0.486411 | 0.243206 | − | 0.969975i | \(-0.421801\pi\) | ||||
0.243206 | + | 0.969975i | \(0.421801\pi\) | |||||||
\(740\) | −15.5040 | −0.569940 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.54718 | 0.0935098 | ||||||||
\(743\) | −7.80394 | −0.286299 | −0.143149 | − | 0.989701i | \(-0.545723\pi\) | ||||
−0.143149 | + | 0.989701i | \(0.545723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.2295 | −0.741151 | ||||||||
\(746\) | 16.6335 | 0.608994 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.5702 | −0.496175 | ||||||||
\(749\) | 17.2689 | 0.630991 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.3886 | 1.83871 | 0.919353 | − | 0.393435i | \(-0.128713\pi\) | ||||
0.919353 | + | 0.393435i | \(0.128713\pi\) | |||||||
\(752\) | −1.55990 | −0.0568838 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.586710 | −0.0213667 | ||||||||
\(755\) | −21.2444 | −0.773162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.6796 | −1.69660 | −0.848299 | − | 0.529517i | \(-0.822373\pi\) | ||||
−0.848299 | + | 0.529517i | \(0.822373\pi\) | |||||||
\(758\) | −1.62511 | −0.0590265 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.0299 | −0.690287 | ||||||||
\(761\) | −24.2370 | −0.878591 | −0.439296 | − | 0.898343i | \(-0.644772\pi\) | ||||
−0.439296 | + | 0.898343i | \(0.644772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.5600 | 0.961536 | ||||||||
\(764\) | 13.9215 | 0.503662 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.6886 | 0.819771 | ||||||||
\(767\) | 15.8512 | 0.572353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.9656 | 0.864222 | 0.432111 | − | 0.901820i | \(-0.357769\pi\) | ||||
0.432111 | + | 0.901820i | \(0.357769\pi\) | |||||||
\(770\) | 13.4690 | 0.485389 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.56615 | −0.0923578 | ||||||||
\(773\) | −1.40235 | −0.0504391 | −0.0252195 | − | 0.999682i | \(-0.508028\pi\) | ||||
−0.0252195 | + | 0.999682i | \(0.508028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1848 | 0.365847 | ||||||||
\(776\) | −17.4076 | −0.624898 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.2444 | −0.940906 | ||||||||
\(779\) | 5.64737 | 0.202338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.7739 | 2.38936 | ||||||||
\(782\) | −15.5477 | −0.555983 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.788396 | 0.0281570 | ||||||||
\(785\) | 34.0327 | 1.21468 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5141 | −0.802540 | −0.401270 | − | 0.915960i | \(-0.631431\pi\) | ||||
−0.401270 | + | 0.915960i | \(0.631431\pi\) | |||||||
\(788\) | 7.69882 | 0.274259 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19.6741 | 0.699974 | ||||||||
\(791\) | 4.55085 | 0.161809 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7090 | −1.09051 | ||||||||
\(794\) | 33.6007 | 1.19245 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.0696 | −0.924011 | ||||||||
\(797\) | 35.7937 | 1.26788 | 0.633939 | − | 0.773383i | \(-0.281437\pi\) | ||||
0.633939 | + | 0.773383i | \(0.281437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.3322 | 0.613168 | ||||||||
\(800\) | −12.2224 | −0.432127 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.95664 | −0.175025 | ||||||||
\(803\) | −73.5715 | −2.59628 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.6960 | −0.799929 | ||||||||
\(806\) | −26.8296 | −0.945033 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 29.0402 | 1.02163 | ||||||||
\(809\) | 22.3480 | 0.785712 | 0.392856 | − | 0.919600i | \(-0.371487\pi\) | ||||
0.392856 | + | 0.919600i | \(0.371487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.5070 | 0.439182 | 0.219591 | − | 0.975592i | \(-0.429528\pi\) | ||||
0.219591 | + | 0.975592i | \(0.429528\pi\) | |||||||
\(812\) | −0.211995 | −0.00743957 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.6206 | −1.24850 | ||||||||
\(815\) | 24.0608 | 0.842813 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.4706 | 0.506264 | ||||||||
\(818\) | −25.4368 | −0.889377 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.84131 | −0.0992230 | ||||||||
\(821\) | 38.7711 | 1.35312 | 0.676560 | − | 0.736387i | \(-0.263470\pi\) | ||||
0.676560 | + | 0.736387i | \(0.263470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.3284 | 1.78920 | 0.894598 | − | 0.446872i | \(-0.147462\pi\) | ||||
0.894598 | + | 0.446872i | \(0.147462\pi\) | |||||||
\(824\) | −7.28871 | −0.253914 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.89430 | −0.135500 | ||||||||
\(827\) | 15.0423 | 0.523072 | 0.261536 | − | 0.965194i | \(-0.415771\pi\) | ||||
0.261536 | + | 0.965194i | \(0.415771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.9052 | −0.864992 | −0.432496 | − | 0.901636i | \(-0.642367\pi\) | ||||
−0.432496 | + | 0.901636i | \(0.642367\pi\) | |||||||
\(830\) | −0.638447 | −0.0221608 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 34.7927 | 1.20622 | ||||||||
\(833\) | −8.75992 | −0.303513 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.3493 | −1.08489 | ||||||||
\(836\) | 23.9941 | 0.829853 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.8286 | −0.374069 | ||||||||
\(839\) | −14.5488 | −0.502279 | −0.251139 | − | 0.967951i | \(-0.580805\pi\) | ||||
−0.251139 | + | 0.967951i | \(0.580805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9897 | −0.999646 | ||||||||
\(842\) | −26.9898 | −0.930129 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3893 | −0.460878 | ||||||||
\(845\) | −47.5892 | −1.63712 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.1779 | −0.899484 | ||||||||
\(848\) | 0.324727 | 0.0111512 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.43054 | −0.151966 | ||||||||
\(851\) | 60.0226 | 2.05755 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.7550 | −1.15575 | −0.577875 | − | 0.816125i | \(-0.696118\pi\) | ||||
−0.577875 | + | 0.816125i | \(0.696118\pi\) | |||||||
\(854\) | 7.54455 | 0.258169 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.2030 | 0.963959 | ||||||||
\(857\) | −47.0497 | −1.60719 | −0.803593 | − | 0.595179i | \(-0.797081\pi\) | ||||
−0.803593 | + | 0.595179i | \(0.797081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.7888 | −1.63053 | −0.815267 | − | 0.579085i | \(-0.803410\pi\) | ||||
−0.815267 | + | 0.579085i | \(0.803410\pi\) | |||||||
\(860\) | −7.28050 | −0.248263 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0237 | 0.545768 | ||||||||
\(863\) | −30.8008 | −1.04847 | −0.524236 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524236 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.6551 | −0.668292 | ||||||||
\(866\) | 18.2180 | 0.619072 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.69432 | −0.329047 | ||||||||
\(869\) | −66.4793 | −2.25516 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0366 | −0.746683 | ||||||||
\(872\) | 43.3769 | 1.46893 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.4906 | 0.929882 | ||||||||
\(875\) | −21.1774 | −0.715926 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.0660 | −1.45424 | −0.727118 | − | 0.686512i | \(-0.759141\pi\) | ||||
−0.727118 | + | 0.686512i | \(0.759141\pi\) | |||||||
\(878\) | −31.2746 | −1.05547 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.71710 | 0.0578834 | ||||||||
\(881\) | −30.2543 | −1.01929 | −0.509647 | − | 0.860384i | \(-0.670224\pi\) | ||||
−0.509647 | + | 0.860384i | \(0.670224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4773 | 1.12660 | 0.563300 | − | 0.826252i | \(-0.309531\pi\) | ||||
0.563300 | + | 0.826252i | \(0.309531\pi\) | |||||||
\(884\) | −17.1655 | −0.577337 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1760 | 0.778613 | ||||||||
\(887\) | 34.7429 | 1.16655 | 0.583277 | − | 0.812274i | \(-0.301770\pi\) | ||||
0.583277 | + | 0.812274i | \(0.301770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7303 | −0.426960 | ||||||||
\(890\) | 25.8156 | 0.865341 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.6735 | 0.792648 | ||||||||
\(893\) | −30.6458 | −1.02552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.0404 | 1.37183 | ||||||||
\(896\) | 10.9962 | 0.367358 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.1822 | 0.907081 | ||||||||
\(899\) | 0.469354 | 0.0156538 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.60807 | −0.120202 | ||||||||
\(902\) | −6.52794 | −0.217356 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.43230 | 0.247194 | ||||||||
\(905\) | −3.57672 | −0.118894 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9277 | −0.628484 | −0.314242 | − | 0.949343i | \(-0.601750\pi\) | ||||
−0.314242 | + | 0.949343i | \(0.601750\pi\) | |||||||
\(908\) | −7.38620 | −0.245120 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.0375 | 0.564787 | ||||||||
\(911\) | 53.6024 | 1.77593 | 0.887964 | − | 0.459914i | \(-0.152120\pi\) | ||||
0.887964 | + | 0.459914i | \(0.152120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.15733 | 0.0713971 | ||||||||
\(914\) | 1.20181 | 0.0397524 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.49300 | 0.247576 | ||||||||
\(917\) | 3.77618 | 0.124701 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1249 | −1.25762 | −0.628812 | − | 0.777558i | \(-0.716458\pi\) | ||||
−0.628812 | + | 0.777558i | \(0.716458\pi\) | |||||||
\(920\) | −37.0664 | −1.22204 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.9571 | −0.492584 | ||||||||
\(923\) | 84.4650 | 2.78020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1044 | 0.562388 | ||||||||
\(926\) | 26.4736 | 0.869976 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.563256 | −0.0184898 | ||||||||
\(929\) | −23.1631 | −0.759957 | −0.379978 | − | 0.924995i | \(-0.624069\pi\) | ||||
−0.379978 | + | 0.924995i | \(0.624069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4888 | 0.507626 | ||||||||
\(932\) | −1.63619 | −0.0535952 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.28220 | 0.0746758 | ||||||||
\(935\) | −19.0788 | −0.623944 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.99000 | 0.130348 | 0.0651738 | − | 0.997874i | \(-0.479240\pi\) | ||||
0.0651738 | + | 0.997874i | \(0.479240\pi\) | |||||||
\(938\) | 5.41394 | 0.176771 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.4186 | 0.502899 | ||||||||
\(941\) | −15.0860 | −0.491790 | −0.245895 | − | 0.969296i | \(-0.579082\pi\) | ||||
−0.245895 | + | 0.969296i | \(0.579082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9999 | 0.358207 | ||||||||
\(944\) | −0.496466 | −0.0161586 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.7270 | −0.543841 | ||||||||
\(947\) | 55.4188 | 1.80087 | 0.900435 | − | 0.434991i | \(-0.143248\pi\) | ||||
0.900435 | + | 0.434991i | \(0.143248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −93.0636 | −3.02097 | ||||||||
\(950\) | 7.83385 | 0.254164 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.3018 | 0.366293 | ||||||||
\(953\) | 46.8160 | 1.51652 | 0.758259 | − | 0.651953i | \(-0.226050\pi\) | ||||
0.758259 | + | 0.651953i | \(0.226050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5727 | 0.633359 | ||||||||
\(956\) | −1.19052 | −0.0385043 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.7845 | −1.12384 | ||||||||
\(959\) | 11.4928 | 0.371122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.53693 | −0.307643 | ||||||||
\(962\) | −45.0579 | −1.45273 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.8237 | 0.638477 | ||||||||
\(965\) | −3.60784 | −0.116141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6031 | −1.04844 | −0.524222 | − | 0.851582i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851582i | \(0.675644\pi\) | |||||||
\(968\) | −42.7530 | −1.37413 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.13233 | −0.293222 | ||||||||
\(971\) | 22.8194 | 0.732310 | 0.366155 | − | 0.930554i | \(-0.380674\pi\) | ||||
0.366155 | + | 0.930554i | \(0.380674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1932 | −0.551189 | ||||||||
\(974\) | 8.36299 | 0.267967 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.961819 | 0.0307871 | ||||||||
\(977\) | 13.1827 | 0.421751 | 0.210875 | − | 0.977513i | \(-0.432369\pi\) | ||||
0.210875 | + | 0.977513i | \(0.432369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −87.2315 | −2.78793 | ||||||||
\(980\) | −7.79277 | −0.248931 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2094 | −0.325796 | ||||||||
\(983\) | 26.5649 | 0.847290 | 0.423645 | − | 0.905828i | \(-0.360750\pi\) | ||||
0.423645 | + | 0.905828i | \(0.360750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.8240 | 0.344883 | ||||||||
\(986\) | −0.204177 | −0.00650232 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.3511 | 0.965597 | ||||||||
\(989\) | 28.1859 | 0.896259 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8250 | 0.947423 | 0.473711 | − | 0.880680i | \(-0.342914\pi\) | ||||
0.473711 | + | 0.880680i | \(0.342914\pi\) | |||||||
\(992\) | −25.7571 | −0.817790 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.7513 | −0.658191 | ||||||||
\(995\) | −36.6521 | −1.16195 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.3442 | 0.675976 | 0.337988 | − | 0.941150i | \(-0.390254\pi\) | ||||
0.337988 | + | 0.941150i | \(0.390254\pi\) | |||||||
\(998\) | 22.3798 | 0.708419 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.2.a.e.1.4 | 6 | ||
3.2 | odd | 2 | 717.2.a.d.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.d.1.3 | ✓ | 6 | 3.2 | odd | 2 | ||
2151.2.a.e.1.4 | 6 | 1.1 | even | 1 | trivial |