Properties

Label 6008.2.a.e.1.32
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.32
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.13231 q^{3} -1.95898 q^{5} -2.91195 q^{7} -1.71788 q^{9} +O(q^{10})\) \(q+1.13231 q^{3} -1.95898 q^{5} -2.91195 q^{7} -1.71788 q^{9} +0.469326 q^{11} -0.568218 q^{13} -2.21816 q^{15} +0.0179401 q^{17} -5.38988 q^{19} -3.29722 q^{21} +1.38567 q^{23} -1.16241 q^{25} -5.34209 q^{27} -1.74404 q^{29} +2.46772 q^{31} +0.531420 q^{33} +5.70443 q^{35} +4.93171 q^{37} -0.643397 q^{39} -0.996312 q^{41} +3.10157 q^{43} +3.36529 q^{45} -11.0080 q^{47} +1.47944 q^{49} +0.0203137 q^{51} +8.32113 q^{53} -0.919398 q^{55} -6.10299 q^{57} +8.95620 q^{59} -5.75029 q^{61} +5.00239 q^{63} +1.11313 q^{65} -4.44499 q^{67} +1.56900 q^{69} +12.6689 q^{71} +6.04979 q^{73} -1.31621 q^{75} -1.36665 q^{77} +6.75973 q^{79} -0.895225 q^{81} +6.31454 q^{83} -0.0351442 q^{85} -1.97479 q^{87} +11.8411 q^{89} +1.65462 q^{91} +2.79422 q^{93} +10.5586 q^{95} -18.4646 q^{97} -0.806247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 1.13231 0.653737 0.326869 0.945070i \(-0.394007\pi\)
0.326869 + 0.945070i \(0.394007\pi\)
\(4\) 0 0
\(5\) −1.95898 −0.876081 −0.438040 0.898955i \(-0.644327\pi\)
−0.438040 + 0.898955i \(0.644327\pi\)
\(6\) 0 0
\(7\) −2.91195 −1.10061 −0.550306 0.834963i \(-0.685489\pi\)
−0.550306 + 0.834963i \(0.685489\pi\)
\(8\) 0 0
\(9\) −1.71788 −0.572628
\(10\) 0 0
\(11\) 0.469326 0.141507 0.0707535 0.997494i \(-0.477460\pi\)
0.0707535 + 0.997494i \(0.477460\pi\)
\(12\) 0 0
\(13\) −0.568218 −0.157595 −0.0787977 0.996891i \(-0.525108\pi\)
−0.0787977 + 0.996891i \(0.525108\pi\)
\(14\) 0 0
\(15\) −2.21816 −0.572726
\(16\) 0 0
\(17\) 0.0179401 0.00435111 0.00217556 0.999998i \(-0.499307\pi\)
0.00217556 + 0.999998i \(0.499307\pi\)
\(18\) 0 0
\(19\) −5.38988 −1.23652 −0.618262 0.785972i \(-0.712163\pi\)
−0.618262 + 0.785972i \(0.712163\pi\)
\(20\) 0 0
\(21\) −3.29722 −0.719511
\(22\) 0 0
\(23\) 1.38567 0.288932 0.144466 0.989510i \(-0.453854\pi\)
0.144466 + 0.989510i \(0.453854\pi\)
\(24\) 0 0
\(25\) −1.16241 −0.232483
\(26\) 0 0
\(27\) −5.34209 −1.02809
\(28\) 0 0
\(29\) −1.74404 −0.323861 −0.161930 0.986802i \(-0.551772\pi\)
−0.161930 + 0.986802i \(0.551772\pi\)
\(30\) 0 0
\(31\) 2.46772 0.443216 0.221608 0.975136i \(-0.428869\pi\)
0.221608 + 0.975136i \(0.428869\pi\)
\(32\) 0 0
\(33\) 0.531420 0.0925084
\(34\) 0 0
\(35\) 5.70443 0.964225
\(36\) 0 0
\(37\) 4.93171 0.810767 0.405384 0.914147i \(-0.367138\pi\)
0.405384 + 0.914147i \(0.367138\pi\)
\(38\) 0 0
\(39\) −0.643397 −0.103026
\(40\) 0 0
\(41\) −0.996312 −0.155598 −0.0777989 0.996969i \(-0.524789\pi\)
−0.0777989 + 0.996969i \(0.524789\pi\)
\(42\) 0 0
\(43\) 3.10157 0.472986 0.236493 0.971633i \(-0.424002\pi\)
0.236493 + 0.971633i \(0.424002\pi\)
\(44\) 0 0
\(45\) 3.36529 0.501668
\(46\) 0 0
\(47\) −11.0080 −1.60569 −0.802844 0.596189i \(-0.796681\pi\)
−0.802844 + 0.596189i \(0.796681\pi\)
\(48\) 0 0
\(49\) 1.47944 0.211348
\(50\) 0 0
\(51\) 0.0203137 0.00284448
\(52\) 0 0
\(53\) 8.32113 1.14300 0.571498 0.820604i \(-0.306363\pi\)
0.571498 + 0.820604i \(0.306363\pi\)
\(54\) 0 0
\(55\) −0.919398 −0.123972
\(56\) 0 0
\(57\) −6.10299 −0.808361
\(58\) 0 0
\(59\) 8.95620 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(60\) 0 0
\(61\) −5.75029 −0.736249 −0.368124 0.929777i \(-0.620000\pi\)
−0.368124 + 0.929777i \(0.620000\pi\)
\(62\) 0 0
\(63\) 5.00239 0.630242
\(64\) 0 0
\(65\) 1.11313 0.138066
\(66\) 0 0
\(67\) −4.44499 −0.543042 −0.271521 0.962433i \(-0.587527\pi\)
−0.271521 + 0.962433i \(0.587527\pi\)
\(68\) 0 0
\(69\) 1.56900 0.188885
\(70\) 0 0
\(71\) 12.6689 1.50352 0.751758 0.659439i \(-0.229206\pi\)
0.751758 + 0.659439i \(0.229206\pi\)
\(72\) 0 0
\(73\) 6.04979 0.708075 0.354037 0.935231i \(-0.384809\pi\)
0.354037 + 0.935231i \(0.384809\pi\)
\(74\) 0 0
\(75\) −1.31621 −0.151983
\(76\) 0 0
\(77\) −1.36665 −0.155744
\(78\) 0 0
\(79\) 6.75973 0.760529 0.380264 0.924878i \(-0.375833\pi\)
0.380264 + 0.924878i \(0.375833\pi\)
\(80\) 0 0
\(81\) −0.895225 −0.0994695
\(82\) 0 0
\(83\) 6.31454 0.693111 0.346555 0.938030i \(-0.387351\pi\)
0.346555 + 0.938030i \(0.387351\pi\)
\(84\) 0 0
\(85\) −0.0351442 −0.00381192
\(86\) 0 0
\(87\) −1.97479 −0.211720
\(88\) 0 0
\(89\) 11.8411 1.25515 0.627576 0.778555i \(-0.284047\pi\)
0.627576 + 0.778555i \(0.284047\pi\)
\(90\) 0 0
\(91\) 1.65462 0.173452
\(92\) 0 0
\(93\) 2.79422 0.289747
\(94\) 0 0
\(95\) 10.5586 1.08329
\(96\) 0 0
\(97\) −18.4646 −1.87480 −0.937400 0.348256i \(-0.886774\pi\)
−0.937400 + 0.348256i \(0.886774\pi\)
\(98\) 0 0
\(99\) −0.806247 −0.0810309
\(100\) 0 0
\(101\) −3.76171 −0.374304 −0.187152 0.982331i \(-0.559926\pi\)
−0.187152 + 0.982331i \(0.559926\pi\)
\(102\) 0 0
\(103\) 10.7020 1.05450 0.527249 0.849711i \(-0.323223\pi\)
0.527249 + 0.849711i \(0.323223\pi\)
\(104\) 0 0
\(105\) 6.45916 0.630350
\(106\) 0 0
\(107\) −17.6815 −1.70934 −0.854670 0.519172i \(-0.826240\pi\)
−0.854670 + 0.519172i \(0.826240\pi\)
\(108\) 0 0
\(109\) 4.46330 0.427506 0.213753 0.976888i \(-0.431431\pi\)
0.213753 + 0.976888i \(0.431431\pi\)
\(110\) 0 0
\(111\) 5.58420 0.530029
\(112\) 0 0
\(113\) 15.5439 1.46225 0.731123 0.682246i \(-0.238997\pi\)
0.731123 + 0.682246i \(0.238997\pi\)
\(114\) 0 0
\(115\) −2.71449 −0.253128
\(116\) 0 0
\(117\) 0.976133 0.0902435
\(118\) 0 0
\(119\) −0.0522406 −0.00478889
\(120\) 0 0
\(121\) −10.7797 −0.979976
\(122\) 0 0
\(123\) −1.12813 −0.101720
\(124\) 0 0
\(125\) 12.0720 1.07975
\(126\) 0 0
\(127\) 7.76363 0.688910 0.344455 0.938803i \(-0.388064\pi\)
0.344455 + 0.938803i \(0.388064\pi\)
\(128\) 0 0
\(129\) 3.51193 0.309208
\(130\) 0 0
\(131\) −16.5290 −1.44414 −0.722072 0.691818i \(-0.756810\pi\)
−0.722072 + 0.691818i \(0.756810\pi\)
\(132\) 0 0
\(133\) 15.6950 1.36093
\(134\) 0 0
\(135\) 10.4650 0.900685
\(136\) 0 0
\(137\) 15.8147 1.35114 0.675570 0.737296i \(-0.263897\pi\)
0.675570 + 0.737296i \(0.263897\pi\)
\(138\) 0 0
\(139\) 18.6914 1.58539 0.792694 0.609620i \(-0.208678\pi\)
0.792694 + 0.609620i \(0.208678\pi\)
\(140\) 0 0
\(141\) −12.4645 −1.04970
\(142\) 0 0
\(143\) −0.266679 −0.0223009
\(144\) 0 0
\(145\) 3.41654 0.283728
\(146\) 0 0
\(147\) 1.67518 0.138166
\(148\) 0 0
\(149\) −20.9147 −1.71340 −0.856699 0.515817i \(-0.827489\pi\)
−0.856699 + 0.515817i \(0.827489\pi\)
\(150\) 0 0
\(151\) −3.69325 −0.300552 −0.150276 0.988644i \(-0.548016\pi\)
−0.150276 + 0.988644i \(0.548016\pi\)
\(152\) 0 0
\(153\) −0.0308190 −0.00249157
\(154\) 0 0
\(155\) −4.83421 −0.388293
\(156\) 0 0
\(157\) 9.73140 0.776650 0.388325 0.921522i \(-0.373054\pi\)
0.388325 + 0.921522i \(0.373054\pi\)
\(158\) 0 0
\(159\) 9.42207 0.747219
\(160\) 0 0
\(161\) −4.03499 −0.318002
\(162\) 0 0
\(163\) −5.38709 −0.421949 −0.210975 0.977492i \(-0.567664\pi\)
−0.210975 + 0.977492i \(0.567664\pi\)
\(164\) 0 0
\(165\) −1.04104 −0.0810448
\(166\) 0 0
\(167\) −17.6929 −1.36912 −0.684558 0.728958i \(-0.740005\pi\)
−0.684558 + 0.728958i \(0.740005\pi\)
\(168\) 0 0
\(169\) −12.6771 −0.975164
\(170\) 0 0
\(171\) 9.25919 0.708068
\(172\) 0 0
\(173\) 4.07975 0.310178 0.155089 0.987901i \(-0.450434\pi\)
0.155089 + 0.987901i \(0.450434\pi\)
\(174\) 0 0
\(175\) 3.38489 0.255874
\(176\) 0 0
\(177\) 10.1412 0.762256
\(178\) 0 0
\(179\) 6.90974 0.516458 0.258229 0.966084i \(-0.416861\pi\)
0.258229 + 0.966084i \(0.416861\pi\)
\(180\) 0 0
\(181\) 12.3699 0.919451 0.459726 0.888061i \(-0.347948\pi\)
0.459726 + 0.888061i \(0.347948\pi\)
\(182\) 0 0
\(183\) −6.51108 −0.481313
\(184\) 0 0
\(185\) −9.66109 −0.710298
\(186\) 0 0
\(187\) 0.00841975 0.000615713 0
\(188\) 0 0
\(189\) 15.5559 1.13152
\(190\) 0 0
\(191\) −17.5379 −1.26900 −0.634498 0.772925i \(-0.718793\pi\)
−0.634498 + 0.772925i \(0.718793\pi\)
\(192\) 0 0
\(193\) −2.32863 −0.167619 −0.0838094 0.996482i \(-0.526709\pi\)
−0.0838094 + 0.996482i \(0.526709\pi\)
\(194\) 0 0
\(195\) 1.26040 0.0902590
\(196\) 0 0
\(197\) 17.7413 1.26401 0.632006 0.774963i \(-0.282232\pi\)
0.632006 + 0.774963i \(0.282232\pi\)
\(198\) 0 0
\(199\) 21.4707 1.52202 0.761008 0.648742i \(-0.224705\pi\)
0.761008 + 0.648742i \(0.224705\pi\)
\(200\) 0 0
\(201\) −5.03309 −0.355007
\(202\) 0 0
\(203\) 5.07857 0.356445
\(204\) 0 0
\(205\) 1.95175 0.136316
\(206\) 0 0
\(207\) −2.38042 −0.165450
\(208\) 0 0
\(209\) −2.52961 −0.174977
\(210\) 0 0
\(211\) 13.8591 0.954101 0.477051 0.878876i \(-0.341706\pi\)
0.477051 + 0.878876i \(0.341706\pi\)
\(212\) 0 0
\(213\) 14.3450 0.982904
\(214\) 0 0
\(215\) −6.07591 −0.414374
\(216\) 0 0
\(217\) −7.18588 −0.487810
\(218\) 0 0
\(219\) 6.85021 0.462895
\(220\) 0 0
\(221\) −0.0101939 −0.000685715 0
\(222\) 0 0
\(223\) 12.7958 0.856869 0.428434 0.903573i \(-0.359065\pi\)
0.428434 + 0.903573i \(0.359065\pi\)
\(224\) 0 0
\(225\) 1.99689 0.133126
\(226\) 0 0
\(227\) 22.2017 1.47358 0.736790 0.676122i \(-0.236341\pi\)
0.736790 + 0.676122i \(0.236341\pi\)
\(228\) 0 0
\(229\) 8.81439 0.582471 0.291236 0.956651i \(-0.405934\pi\)
0.291236 + 0.956651i \(0.405934\pi\)
\(230\) 0 0
\(231\) −1.54747 −0.101816
\(232\) 0 0
\(233\) −9.85676 −0.645738 −0.322869 0.946444i \(-0.604647\pi\)
−0.322869 + 0.946444i \(0.604647\pi\)
\(234\) 0 0
\(235\) 21.5645 1.40671
\(236\) 0 0
\(237\) 7.65408 0.497186
\(238\) 0 0
\(239\) −6.93235 −0.448417 −0.224208 0.974541i \(-0.571980\pi\)
−0.224208 + 0.974541i \(0.571980\pi\)
\(240\) 0 0
\(241\) −3.67040 −0.236432 −0.118216 0.992988i \(-0.537717\pi\)
−0.118216 + 0.992988i \(0.537717\pi\)
\(242\) 0 0
\(243\) 15.0126 0.963058
\(244\) 0 0
\(245\) −2.89819 −0.185158
\(246\) 0 0
\(247\) 3.06263 0.194870
\(248\) 0 0
\(249\) 7.14999 0.453112
\(250\) 0 0
\(251\) 14.9684 0.944797 0.472398 0.881385i \(-0.343388\pi\)
0.472398 + 0.881385i \(0.343388\pi\)
\(252\) 0 0
\(253\) 0.650330 0.0408859
\(254\) 0 0
\(255\) −0.0397940 −0.00249200
\(256\) 0 0
\(257\) 25.4360 1.58665 0.793327 0.608795i \(-0.208347\pi\)
0.793327 + 0.608795i \(0.208347\pi\)
\(258\) 0 0
\(259\) −14.3609 −0.892341
\(260\) 0 0
\(261\) 2.99606 0.185452
\(262\) 0 0
\(263\) 7.93251 0.489140 0.244570 0.969632i \(-0.421353\pi\)
0.244570 + 0.969632i \(0.421353\pi\)
\(264\) 0 0
\(265\) −16.3009 −1.00136
\(266\) 0 0
\(267\) 13.4077 0.820539
\(268\) 0 0
\(269\) 22.5590 1.37545 0.687724 0.725973i \(-0.258610\pi\)
0.687724 + 0.725973i \(0.258610\pi\)
\(270\) 0 0
\(271\) 12.6823 0.770394 0.385197 0.922834i \(-0.374133\pi\)
0.385197 + 0.922834i \(0.374133\pi\)
\(272\) 0 0
\(273\) 1.87354 0.113392
\(274\) 0 0
\(275\) −0.545551 −0.0328980
\(276\) 0 0
\(277\) −17.8844 −1.07457 −0.537283 0.843402i \(-0.680549\pi\)
−0.537283 + 0.843402i \(0.680549\pi\)
\(278\) 0 0
\(279\) −4.23926 −0.253798
\(280\) 0 0
\(281\) 17.1988 1.02600 0.512998 0.858390i \(-0.328535\pi\)
0.512998 + 0.858390i \(0.328535\pi\)
\(282\) 0 0
\(283\) −29.5331 −1.75556 −0.877779 0.479065i \(-0.840976\pi\)
−0.877779 + 0.479065i \(0.840976\pi\)
\(284\) 0 0
\(285\) 11.9556 0.708189
\(286\) 0 0
\(287\) 2.90121 0.171253
\(288\) 0 0
\(289\) −16.9997 −0.999981
\(290\) 0 0
\(291\) −20.9076 −1.22563
\(292\) 0 0
\(293\) −3.33697 −0.194948 −0.0974741 0.995238i \(-0.531076\pi\)
−0.0974741 + 0.995238i \(0.531076\pi\)
\(294\) 0 0
\(295\) −17.5450 −1.02151
\(296\) 0 0
\(297\) −2.50718 −0.145481
\(298\) 0 0
\(299\) −0.787362 −0.0455343
\(300\) 0 0
\(301\) −9.03162 −0.520574
\(302\) 0 0
\(303\) −4.25940 −0.244696
\(304\) 0 0
\(305\) 11.2647 0.645013
\(306\) 0 0
\(307\) −5.03491 −0.287357 −0.143679 0.989624i \(-0.545893\pi\)
−0.143679 + 0.989624i \(0.545893\pi\)
\(308\) 0 0
\(309\) 12.1179 0.689365
\(310\) 0 0
\(311\) 27.4509 1.55660 0.778299 0.627894i \(-0.216083\pi\)
0.778299 + 0.627894i \(0.216083\pi\)
\(312\) 0 0
\(313\) 9.37875 0.530118 0.265059 0.964232i \(-0.414609\pi\)
0.265059 + 0.964232i \(0.414609\pi\)
\(314\) 0 0
\(315\) −9.79955 −0.552142
\(316\) 0 0
\(317\) 26.6467 1.49663 0.748314 0.663344i \(-0.230864\pi\)
0.748314 + 0.663344i \(0.230864\pi\)
\(318\) 0 0
\(319\) −0.818525 −0.0458286
\(320\) 0 0
\(321\) −20.0209 −1.11746
\(322\) 0 0
\(323\) −0.0966949 −0.00538025
\(324\) 0 0
\(325\) 0.660505 0.0366382
\(326\) 0 0
\(327\) 5.05382 0.279477
\(328\) 0 0
\(329\) 32.0549 1.76724
\(330\) 0 0
\(331\) −18.8732 −1.03737 −0.518683 0.854967i \(-0.673577\pi\)
−0.518683 + 0.854967i \(0.673577\pi\)
\(332\) 0 0
\(333\) −8.47210 −0.464268
\(334\) 0 0
\(335\) 8.70763 0.475748
\(336\) 0 0
\(337\) 21.3875 1.16505 0.582525 0.812813i \(-0.302065\pi\)
0.582525 + 0.812813i \(0.302065\pi\)
\(338\) 0 0
\(339\) 17.6004 0.955924
\(340\) 0 0
\(341\) 1.15817 0.0627182
\(342\) 0 0
\(343\) 16.0756 0.868000
\(344\) 0 0
\(345\) −3.07363 −0.165479
\(346\) 0 0
\(347\) −36.4844 −1.95859 −0.979293 0.202448i \(-0.935110\pi\)
−0.979293 + 0.202448i \(0.935110\pi\)
\(348\) 0 0
\(349\) 15.6910 0.839918 0.419959 0.907543i \(-0.362045\pi\)
0.419959 + 0.907543i \(0.362045\pi\)
\(350\) 0 0
\(351\) 3.03547 0.162021
\(352\) 0 0
\(353\) −25.7321 −1.36958 −0.684791 0.728739i \(-0.740107\pi\)
−0.684791 + 0.728739i \(0.740107\pi\)
\(354\) 0 0
\(355\) −24.8180 −1.31720
\(356\) 0 0
\(357\) −0.0591523 −0.00313067
\(358\) 0 0
\(359\) −10.5835 −0.558576 −0.279288 0.960207i \(-0.590098\pi\)
−0.279288 + 0.960207i \(0.590098\pi\)
\(360\) 0 0
\(361\) 10.0508 0.528990
\(362\) 0 0
\(363\) −12.2060 −0.640646
\(364\) 0 0
\(365\) −11.8514 −0.620330
\(366\) 0 0
\(367\) −1.48021 −0.0772662 −0.0386331 0.999253i \(-0.512300\pi\)
−0.0386331 + 0.999253i \(0.512300\pi\)
\(368\) 0 0
\(369\) 1.71155 0.0890997
\(370\) 0 0
\(371\) −24.2307 −1.25800
\(372\) 0 0
\(373\) −25.4166 −1.31602 −0.658012 0.753008i \(-0.728602\pi\)
−0.658012 + 0.753008i \(0.728602\pi\)
\(374\) 0 0
\(375\) 13.6692 0.705875
\(376\) 0 0
\(377\) 0.990998 0.0510390
\(378\) 0 0
\(379\) 1.01737 0.0522587 0.0261294 0.999659i \(-0.491682\pi\)
0.0261294 + 0.999659i \(0.491682\pi\)
\(380\) 0 0
\(381\) 8.79080 0.450366
\(382\) 0 0
\(383\) −3.49480 −0.178576 −0.0892879 0.996006i \(-0.528459\pi\)
−0.0892879 + 0.996006i \(0.528459\pi\)
\(384\) 0 0
\(385\) 2.67724 0.136445
\(386\) 0 0
\(387\) −5.32814 −0.270845
\(388\) 0 0
\(389\) 7.20197 0.365155 0.182577 0.983192i \(-0.441556\pi\)
0.182577 + 0.983192i \(0.441556\pi\)
\(390\) 0 0
\(391\) 0.0248590 0.00125717
\(392\) 0 0
\(393\) −18.7159 −0.944090
\(394\) 0 0
\(395\) −13.2421 −0.666285
\(396\) 0 0
\(397\) 2.13497 0.107151 0.0535755 0.998564i \(-0.482938\pi\)
0.0535755 + 0.998564i \(0.482938\pi\)
\(398\) 0 0
\(399\) 17.7716 0.889692
\(400\) 0 0
\(401\) −26.8772 −1.34218 −0.671092 0.741374i \(-0.734174\pi\)
−0.671092 + 0.741374i \(0.734174\pi\)
\(402\) 0 0
\(403\) −1.40221 −0.0698489
\(404\) 0 0
\(405\) 1.75372 0.0871433
\(406\) 0 0
\(407\) 2.31458 0.114729
\(408\) 0 0
\(409\) 8.97024 0.443550 0.221775 0.975098i \(-0.428815\pi\)
0.221775 + 0.975098i \(0.428815\pi\)
\(410\) 0 0
\(411\) 17.9071 0.883291
\(412\) 0 0
\(413\) −26.0800 −1.28331
\(414\) 0 0
\(415\) −12.3700 −0.607221
\(416\) 0 0
\(417\) 21.1644 1.03643
\(418\) 0 0
\(419\) −27.5235 −1.34461 −0.672305 0.740274i \(-0.734696\pi\)
−0.672305 + 0.740274i \(0.734696\pi\)
\(420\) 0 0
\(421\) 37.3857 1.82207 0.911034 0.412332i \(-0.135286\pi\)
0.911034 + 0.412332i \(0.135286\pi\)
\(422\) 0 0
\(423\) 18.9105 0.919462
\(424\) 0 0
\(425\) −0.0208538 −0.00101156
\(426\) 0 0
\(427\) 16.7445 0.810325
\(428\) 0 0
\(429\) −0.301963 −0.0145789
\(430\) 0 0
\(431\) −30.9766 −1.49209 −0.746044 0.665897i \(-0.768049\pi\)
−0.746044 + 0.665897i \(0.768049\pi\)
\(432\) 0 0
\(433\) −8.12538 −0.390481 −0.195240 0.980755i \(-0.562549\pi\)
−0.195240 + 0.980755i \(0.562549\pi\)
\(434\) 0 0
\(435\) 3.86857 0.185484
\(436\) 0 0
\(437\) −7.46859 −0.357271
\(438\) 0 0
\(439\) −2.18958 −0.104503 −0.0522515 0.998634i \(-0.516640\pi\)
−0.0522515 + 0.998634i \(0.516640\pi\)
\(440\) 0 0
\(441\) −2.54150 −0.121024
\(442\) 0 0
\(443\) −27.4515 −1.30426 −0.652130 0.758107i \(-0.726124\pi\)
−0.652130 + 0.758107i \(0.726124\pi\)
\(444\) 0 0
\(445\) −23.1964 −1.09961
\(446\) 0 0
\(447\) −23.6818 −1.12011
\(448\) 0 0
\(449\) 16.3971 0.773829 0.386914 0.922116i \(-0.373541\pi\)
0.386914 + 0.922116i \(0.373541\pi\)
\(450\) 0 0
\(451\) −0.467595 −0.0220182
\(452\) 0 0
\(453\) −4.18188 −0.196482
\(454\) 0 0
\(455\) −3.24136 −0.151957
\(456\) 0 0
\(457\) 22.3609 1.04600 0.523000 0.852333i \(-0.324813\pi\)
0.523000 + 0.852333i \(0.324813\pi\)
\(458\) 0 0
\(459\) −0.0958375 −0.00447331
\(460\) 0 0
\(461\) 31.6429 1.47375 0.736877 0.676026i \(-0.236300\pi\)
0.736877 + 0.676026i \(0.236300\pi\)
\(462\) 0 0
\(463\) −15.2255 −0.707589 −0.353794 0.935323i \(-0.615109\pi\)
−0.353794 + 0.935323i \(0.615109\pi\)
\(464\) 0 0
\(465\) −5.47381 −0.253842
\(466\) 0 0
\(467\) −34.4941 −1.59619 −0.798097 0.602529i \(-0.794160\pi\)
−0.798097 + 0.602529i \(0.794160\pi\)
\(468\) 0 0
\(469\) 12.9436 0.597679
\(470\) 0 0
\(471\) 11.0189 0.507725
\(472\) 0 0
\(473\) 1.45565 0.0669308
\(474\) 0 0
\(475\) 6.26527 0.287470
\(476\) 0 0
\(477\) −14.2947 −0.654511
\(478\) 0 0
\(479\) 5.80105 0.265057 0.132528 0.991179i \(-0.457690\pi\)
0.132528 + 0.991179i \(0.457690\pi\)
\(480\) 0 0
\(481\) −2.80229 −0.127773
\(482\) 0 0
\(483\) −4.56885 −0.207890
\(484\) 0 0
\(485\) 36.1718 1.64247
\(486\) 0 0
\(487\) 16.1178 0.730367 0.365183 0.930936i \(-0.381006\pi\)
0.365183 + 0.930936i \(0.381006\pi\)
\(488\) 0 0
\(489\) −6.09983 −0.275844
\(490\) 0 0
\(491\) 17.9645 0.810727 0.405363 0.914156i \(-0.367145\pi\)
0.405363 + 0.914156i \(0.367145\pi\)
\(492\) 0 0
\(493\) −0.0312883 −0.00140915
\(494\) 0 0
\(495\) 1.57942 0.0709896
\(496\) 0 0
\(497\) −36.8910 −1.65479
\(498\) 0 0
\(499\) −24.2804 −1.08694 −0.543469 0.839429i \(-0.682890\pi\)
−0.543469 + 0.839429i \(0.682890\pi\)
\(500\) 0 0
\(501\) −20.0338 −0.895042
\(502\) 0 0
\(503\) 25.4654 1.13545 0.567724 0.823219i \(-0.307824\pi\)
0.567724 + 0.823219i \(0.307824\pi\)
\(504\) 0 0
\(505\) 7.36909 0.327920
\(506\) 0 0
\(507\) −14.3544 −0.637501
\(508\) 0 0
\(509\) 39.7761 1.76304 0.881522 0.472143i \(-0.156519\pi\)
0.881522 + 0.472143i \(0.156519\pi\)
\(510\) 0 0
\(511\) −17.6167 −0.779316
\(512\) 0 0
\(513\) 28.7932 1.27125
\(514\) 0 0
\(515\) −20.9649 −0.923826
\(516\) 0 0
\(517\) −5.16636 −0.227216
\(518\) 0 0
\(519\) 4.61952 0.202775
\(520\) 0 0
\(521\) −15.2119 −0.666445 −0.333222 0.942848i \(-0.608136\pi\)
−0.333222 + 0.942848i \(0.608136\pi\)
\(522\) 0 0
\(523\) 0.0967773 0.00423178 0.00211589 0.999998i \(-0.499326\pi\)
0.00211589 + 0.999998i \(0.499326\pi\)
\(524\) 0 0
\(525\) 3.83273 0.167274
\(526\) 0 0
\(527\) 0.0442712 0.00192848
\(528\) 0 0
\(529\) −21.0799 −0.916518
\(530\) 0 0
\(531\) −15.3857 −0.667683
\(532\) 0 0
\(533\) 0.566123 0.0245215
\(534\) 0 0
\(535\) 34.6377 1.49752
\(536\) 0 0
\(537\) 7.82393 0.337628
\(538\) 0 0
\(539\) 0.694339 0.0299073
\(540\) 0 0
\(541\) −3.15797 −0.135772 −0.0678858 0.997693i \(-0.521625\pi\)
−0.0678858 + 0.997693i \(0.521625\pi\)
\(542\) 0 0
\(543\) 14.0066 0.601079
\(544\) 0 0
\(545\) −8.74349 −0.374530
\(546\) 0 0
\(547\) −17.3725 −0.742795 −0.371397 0.928474i \(-0.621121\pi\)
−0.371397 + 0.928474i \(0.621121\pi\)
\(548\) 0 0
\(549\) 9.87832 0.421597
\(550\) 0 0
\(551\) 9.40019 0.400462
\(552\) 0 0
\(553\) −19.6840 −0.837048
\(554\) 0 0
\(555\) −10.9393 −0.464348
\(556\) 0 0
\(557\) −7.75560 −0.328615 −0.164308 0.986409i \(-0.552539\pi\)
−0.164308 + 0.986409i \(0.552539\pi\)
\(558\) 0 0
\(559\) −1.76237 −0.0745404
\(560\) 0 0
\(561\) 0.00953373 0.000402514 0
\(562\) 0 0
\(563\) −12.2764 −0.517389 −0.258695 0.965959i \(-0.583292\pi\)
−0.258695 + 0.965959i \(0.583292\pi\)
\(564\) 0 0
\(565\) −30.4501 −1.28105
\(566\) 0 0
\(567\) 2.60685 0.109477
\(568\) 0 0
\(569\) −38.0739 −1.59614 −0.798071 0.602564i \(-0.794146\pi\)
−0.798071 + 0.602564i \(0.794146\pi\)
\(570\) 0 0
\(571\) −1.65542 −0.0692770 −0.0346385 0.999400i \(-0.511028\pi\)
−0.0346385 + 0.999400i \(0.511028\pi\)
\(572\) 0 0
\(573\) −19.8582 −0.829589
\(574\) 0 0
\(575\) −1.61072 −0.0671717
\(576\) 0 0
\(577\) 45.2771 1.88491 0.942454 0.334335i \(-0.108512\pi\)
0.942454 + 0.334335i \(0.108512\pi\)
\(578\) 0 0
\(579\) −2.63673 −0.109579
\(580\) 0 0
\(581\) −18.3876 −0.762846
\(582\) 0 0
\(583\) 3.90532 0.161742
\(584\) 0 0
\(585\) −1.91222 −0.0790606
\(586\) 0 0
\(587\) 31.1122 1.28414 0.642070 0.766646i \(-0.278076\pi\)
0.642070 + 0.766646i \(0.278076\pi\)
\(588\) 0 0
\(589\) −13.3007 −0.548047
\(590\) 0 0
\(591\) 20.0885 0.826332
\(592\) 0 0
\(593\) 6.75378 0.277345 0.138672 0.990338i \(-0.455717\pi\)
0.138672 + 0.990338i \(0.455717\pi\)
\(594\) 0 0
\(595\) 0.102338 0.00419545
\(596\) 0 0
\(597\) 24.3114 0.994998
\(598\) 0 0
\(599\) −5.60991 −0.229215 −0.114607 0.993411i \(-0.536561\pi\)
−0.114607 + 0.993411i \(0.536561\pi\)
\(600\) 0 0
\(601\) 1.02510 0.0418148 0.0209074 0.999781i \(-0.493344\pi\)
0.0209074 + 0.999781i \(0.493344\pi\)
\(602\) 0 0
\(603\) 7.63597 0.310961
\(604\) 0 0
\(605\) 21.1172 0.858538
\(606\) 0 0
\(607\) 10.8697 0.441189 0.220594 0.975366i \(-0.429200\pi\)
0.220594 + 0.975366i \(0.429200\pi\)
\(608\) 0 0
\(609\) 5.75049 0.233022
\(610\) 0 0
\(611\) 6.25497 0.253049
\(612\) 0 0
\(613\) 38.3844 1.55033 0.775167 0.631757i \(-0.217666\pi\)
0.775167 + 0.631757i \(0.217666\pi\)
\(614\) 0 0
\(615\) 2.20998 0.0891150
\(616\) 0 0
\(617\) −12.9640 −0.521912 −0.260956 0.965351i \(-0.584038\pi\)
−0.260956 + 0.965351i \(0.584038\pi\)
\(618\) 0 0
\(619\) −30.1697 −1.21262 −0.606312 0.795227i \(-0.707352\pi\)
−0.606312 + 0.795227i \(0.707352\pi\)
\(620\) 0 0
\(621\) −7.40236 −0.297047
\(622\) 0 0
\(623\) −34.4806 −1.38144
\(624\) 0 0
\(625\) −17.8367 −0.713469
\(626\) 0 0
\(627\) −2.86429 −0.114389
\(628\) 0 0
\(629\) 0.0884753 0.00352774
\(630\) 0 0
\(631\) 0.931962 0.0371008 0.0185504 0.999828i \(-0.494095\pi\)
0.0185504 + 0.999828i \(0.494095\pi\)
\(632\) 0 0
\(633\) 15.6928 0.623731
\(634\) 0 0
\(635\) −15.2088 −0.603541
\(636\) 0 0
\(637\) −0.840644 −0.0333075
\(638\) 0 0
\(639\) −21.7636 −0.860955
\(640\) 0 0
\(641\) −1.62066 −0.0640121 −0.0320061 0.999488i \(-0.510190\pi\)
−0.0320061 + 0.999488i \(0.510190\pi\)
\(642\) 0 0
\(643\) 38.8892 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(644\) 0 0
\(645\) −6.87979 −0.270891
\(646\) 0 0
\(647\) −35.2419 −1.38550 −0.692750 0.721178i \(-0.743601\pi\)
−0.692750 + 0.721178i \(0.743601\pi\)
\(648\) 0 0
\(649\) 4.20337 0.164997
\(650\) 0 0
\(651\) −8.13662 −0.318899
\(652\) 0 0
\(653\) −37.6976 −1.47522 −0.737611 0.675226i \(-0.764046\pi\)
−0.737611 + 0.675226i \(0.764046\pi\)
\(654\) 0 0
\(655\) 32.3799 1.26519
\(656\) 0 0
\(657\) −10.3928 −0.405463
\(658\) 0 0
\(659\) −27.5799 −1.07436 −0.537180 0.843467i \(-0.680511\pi\)
−0.537180 + 0.843467i \(0.680511\pi\)
\(660\) 0 0
\(661\) 8.39217 0.326418 0.163209 0.986592i \(-0.447816\pi\)
0.163209 + 0.986592i \(0.447816\pi\)
\(662\) 0 0
\(663\) −0.0115426 −0.000448277 0
\(664\) 0 0
\(665\) −30.7462 −1.19229
\(666\) 0 0
\(667\) −2.41667 −0.0935737
\(668\) 0 0
\(669\) 14.4887 0.560167
\(670\) 0 0
\(671\) −2.69876 −0.104184
\(672\) 0 0
\(673\) 34.5373 1.33131 0.665657 0.746258i \(-0.268151\pi\)
0.665657 + 0.746258i \(0.268151\pi\)
\(674\) 0 0
\(675\) 6.20972 0.239012
\(676\) 0 0
\(677\) 1.83654 0.0705838 0.0352919 0.999377i \(-0.488764\pi\)
0.0352919 + 0.999377i \(0.488764\pi\)
\(678\) 0 0
\(679\) 53.7680 2.06343
\(680\) 0 0
\(681\) 25.1391 0.963333
\(682\) 0 0
\(683\) −41.0721 −1.57158 −0.785791 0.618492i \(-0.787744\pi\)
−0.785791 + 0.618492i \(0.787744\pi\)
\(684\) 0 0
\(685\) −30.9806 −1.18371
\(686\) 0 0
\(687\) 9.98058 0.380783
\(688\) 0 0
\(689\) −4.72822 −0.180131
\(690\) 0 0
\(691\) 1.76631 0.0671938 0.0335969 0.999435i \(-0.489304\pi\)
0.0335969 + 0.999435i \(0.489304\pi\)
\(692\) 0 0
\(693\) 2.34775 0.0891836
\(694\) 0 0
\(695\) −36.6161 −1.38893
\(696\) 0 0
\(697\) −0.0178739 −0.000677024 0
\(698\) 0 0
\(699\) −11.1609 −0.422143
\(700\) 0 0
\(701\) 14.9748 0.565589 0.282794 0.959181i \(-0.408739\pi\)
0.282794 + 0.959181i \(0.408739\pi\)
\(702\) 0 0
\(703\) −26.5813 −1.00253
\(704\) 0 0
\(705\) 24.4176 0.919620
\(706\) 0 0
\(707\) 10.9539 0.411964
\(708\) 0 0
\(709\) 23.0808 0.866819 0.433410 0.901197i \(-0.357310\pi\)
0.433410 + 0.901197i \(0.357310\pi\)
\(710\) 0 0
\(711\) −11.6124 −0.435500
\(712\) 0 0
\(713\) 3.41945 0.128059
\(714\) 0 0
\(715\) 0.522419 0.0195373
\(716\) 0 0
\(717\) −7.84954 −0.293147
\(718\) 0 0
\(719\) −46.1537 −1.72124 −0.860620 0.509247i \(-0.829924\pi\)
−0.860620 + 0.509247i \(0.829924\pi\)
\(720\) 0 0
\(721\) −31.1636 −1.16059
\(722\) 0 0
\(723\) −4.15602 −0.154564
\(724\) 0 0
\(725\) 2.02730 0.0752921
\(726\) 0 0
\(727\) −37.1770 −1.37882 −0.689410 0.724371i \(-0.742130\pi\)
−0.689410 + 0.724371i \(0.742130\pi\)
\(728\) 0 0
\(729\) 19.6845 0.729056
\(730\) 0 0
\(731\) 0.0556425 0.00205801
\(732\) 0 0
\(733\) −11.1429 −0.411571 −0.205786 0.978597i \(-0.565975\pi\)
−0.205786 + 0.978597i \(0.565975\pi\)
\(734\) 0 0
\(735\) −3.28163 −0.121045
\(736\) 0 0
\(737\) −2.08615 −0.0768442
\(738\) 0 0
\(739\) 44.9738 1.65439 0.827194 0.561916i \(-0.189936\pi\)
0.827194 + 0.561916i \(0.189936\pi\)
\(740\) 0 0
\(741\) 3.46783 0.127394
\(742\) 0 0
\(743\) 33.4684 1.22784 0.613919 0.789369i \(-0.289592\pi\)
0.613919 + 0.789369i \(0.289592\pi\)
\(744\) 0 0
\(745\) 40.9714 1.50107
\(746\) 0 0
\(747\) −10.8476 −0.396894
\(748\) 0 0
\(749\) 51.4877 1.88132
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 16.9488 0.617649
\(754\) 0 0
\(755\) 7.23498 0.263308
\(756\) 0 0
\(757\) 52.1947 1.89705 0.948525 0.316703i \(-0.102576\pi\)
0.948525 + 0.316703i \(0.102576\pi\)
\(758\) 0 0
\(759\) 0.736372 0.0267286
\(760\) 0 0
\(761\) 34.1943 1.23954 0.619772 0.784782i \(-0.287225\pi\)
0.619772 + 0.784782i \(0.287225\pi\)
\(762\) 0 0
\(763\) −12.9969 −0.470519
\(764\) 0 0
\(765\) 0.0603737 0.00218281
\(766\) 0 0
\(767\) −5.08908 −0.183756
\(768\) 0 0
\(769\) 0.0184882 0.000666700 0 0.000333350 1.00000i \(-0.499894\pi\)
0.000333350 1.00000i \(0.499894\pi\)
\(770\) 0 0
\(771\) 28.8013 1.03726
\(772\) 0 0
\(773\) −27.6351 −0.993965 −0.496982 0.867761i \(-0.665559\pi\)
−0.496982 + 0.867761i \(0.665559\pi\)
\(774\) 0 0
\(775\) −2.86852 −0.103040
\(776\) 0 0
\(777\) −16.2609 −0.583356
\(778\) 0 0
\(779\) 5.37000 0.192400
\(780\) 0 0
\(781\) 5.94582 0.212758
\(782\) 0 0
\(783\) 9.31684 0.332957
\(784\) 0 0
\(785\) −19.0636 −0.680408
\(786\) 0 0
\(787\) −38.6144 −1.37645 −0.688227 0.725495i \(-0.741611\pi\)
−0.688227 + 0.725495i \(0.741611\pi\)
\(788\) 0 0
\(789\) 8.98203 0.319769
\(790\) 0 0
\(791\) −45.2630 −1.60937
\(792\) 0 0
\(793\) 3.26742 0.116029
\(794\) 0 0
\(795\) −18.4576 −0.654624
\(796\) 0 0
\(797\) 6.59449 0.233589 0.116794 0.993156i \(-0.462738\pi\)
0.116794 + 0.993156i \(0.462738\pi\)
\(798\) 0 0
\(799\) −0.197485 −0.00698653
\(800\) 0 0
\(801\) −20.3416 −0.718735
\(802\) 0 0
\(803\) 2.83932 0.100198
\(804\) 0 0
\(805\) 7.90445 0.278595
\(806\) 0 0
\(807\) 25.5437 0.899181
\(808\) 0 0
\(809\) 50.1555 1.76337 0.881686 0.471836i \(-0.156409\pi\)
0.881686 + 0.471836i \(0.156409\pi\)
\(810\) 0 0
\(811\) −23.5456 −0.826798 −0.413399 0.910550i \(-0.635658\pi\)
−0.413399 + 0.910550i \(0.635658\pi\)
\(812\) 0 0
\(813\) 14.3602 0.503635
\(814\) 0 0
\(815\) 10.5532 0.369662
\(816\) 0 0
\(817\) −16.7171 −0.584858
\(818\) 0 0
\(819\) −2.84245 −0.0993232
\(820\) 0 0
\(821\) −30.7543 −1.07333 −0.536667 0.843794i \(-0.680317\pi\)
−0.536667 + 0.843794i \(0.680317\pi\)
\(822\) 0 0
\(823\) 25.9832 0.905717 0.452859 0.891582i \(-0.350404\pi\)
0.452859 + 0.891582i \(0.350404\pi\)
\(824\) 0 0
\(825\) −0.617730 −0.0215066
\(826\) 0 0
\(827\) −0.456809 −0.0158848 −0.00794241 0.999968i \(-0.502528\pi\)
−0.00794241 + 0.999968i \(0.502528\pi\)
\(828\) 0 0
\(829\) 45.6445 1.58530 0.792650 0.609677i \(-0.208701\pi\)
0.792650 + 0.609677i \(0.208701\pi\)
\(830\) 0 0
\(831\) −20.2506 −0.702484
\(832\) 0 0
\(833\) 0.0265413 0.000919601 0
\(834\) 0 0
\(835\) 34.6599 1.19946
\(836\) 0 0
\(837\) −13.1828 −0.455664
\(838\) 0 0
\(839\) 3.50708 0.121078 0.0605389 0.998166i \(-0.480718\pi\)
0.0605389 + 0.998166i \(0.480718\pi\)
\(840\) 0 0
\(841\) −25.9583 −0.895114
\(842\) 0 0
\(843\) 19.4743 0.670731
\(844\) 0 0
\(845\) 24.8342 0.854322
\(846\) 0 0
\(847\) 31.3900 1.07857
\(848\) 0 0
\(849\) −33.4405 −1.14767
\(850\) 0 0
\(851\) 6.83371 0.234257
\(852\) 0 0
\(853\) 51.4488 1.76157 0.880786 0.473515i \(-0.157015\pi\)
0.880786 + 0.473515i \(0.157015\pi\)
\(854\) 0 0
\(855\) −18.1385 −0.620324
\(856\) 0 0
\(857\) −5.92601 −0.202429 −0.101214 0.994865i \(-0.532273\pi\)
−0.101214 + 0.994865i \(0.532273\pi\)
\(858\) 0 0
\(859\) 54.2744 1.85182 0.925909 0.377746i \(-0.123301\pi\)
0.925909 + 0.377746i \(0.123301\pi\)
\(860\) 0 0
\(861\) 3.28506 0.111954
\(862\) 0 0
\(863\) −32.4021 −1.10298 −0.551490 0.834182i \(-0.685940\pi\)
−0.551490 + 0.834182i \(0.685940\pi\)
\(864\) 0 0
\(865\) −7.99213 −0.271741
\(866\) 0 0
\(867\) −19.2488 −0.653725
\(868\) 0 0
\(869\) 3.17251 0.107620
\(870\) 0 0
\(871\) 2.52572 0.0855809
\(872\) 0 0
\(873\) 31.7201 1.07356
\(874\) 0 0
\(875\) −35.1531 −1.18839
\(876\) 0 0
\(877\) −22.2435 −0.751110 −0.375555 0.926800i \(-0.622548\pi\)
−0.375555 + 0.926800i \(0.622548\pi\)
\(878\) 0 0
\(879\) −3.77848 −0.127445
\(880\) 0 0
\(881\) 1.03750 0.0349543 0.0174771 0.999847i \(-0.494437\pi\)
0.0174771 + 0.999847i \(0.494437\pi\)
\(882\) 0 0
\(883\) −12.5611 −0.422715 −0.211357 0.977409i \(-0.567788\pi\)
−0.211357 + 0.977409i \(0.567788\pi\)
\(884\) 0 0
\(885\) −19.8663 −0.667798
\(886\) 0 0
\(887\) −6.95005 −0.233360 −0.116680 0.993170i \(-0.537225\pi\)
−0.116680 + 0.993170i \(0.537225\pi\)
\(888\) 0 0
\(889\) −22.6073 −0.758224
\(890\) 0 0
\(891\) −0.420152 −0.0140756
\(892\) 0 0
\(893\) 59.3320 1.98547
\(894\) 0 0
\(895\) −13.5360 −0.452459
\(896\) 0 0
\(897\) −0.891535 −0.0297675
\(898\) 0 0
\(899\) −4.30382 −0.143540
\(900\) 0 0
\(901\) 0.149282 0.00497330
\(902\) 0 0
\(903\) −10.2266 −0.340319
\(904\) 0 0
\(905\) −24.2324 −0.805513
\(906\) 0 0
\(907\) −29.4503 −0.977882 −0.488941 0.872317i \(-0.662617\pi\)
−0.488941 + 0.872317i \(0.662617\pi\)
\(908\) 0 0
\(909\) 6.46217 0.214337
\(910\) 0 0
\(911\) 2.88626 0.0956260 0.0478130 0.998856i \(-0.484775\pi\)
0.0478130 + 0.998856i \(0.484775\pi\)
\(912\) 0 0
\(913\) 2.96358 0.0980800
\(914\) 0 0
\(915\) 12.7551 0.421669
\(916\) 0 0
\(917\) 48.1315 1.58944
\(918\) 0 0
\(919\) 19.5777 0.645809 0.322905 0.946431i \(-0.395341\pi\)
0.322905 + 0.946431i \(0.395341\pi\)
\(920\) 0 0
\(921\) −5.70106 −0.187856
\(922\) 0 0
\(923\) −7.19868 −0.236947
\(924\) 0 0
\(925\) −5.73268 −0.188490
\(926\) 0 0
\(927\) −18.3848 −0.603835
\(928\) 0 0
\(929\) −60.5576 −1.98683 −0.993414 0.114577i \(-0.963449\pi\)
−0.993414 + 0.114577i \(0.963449\pi\)
\(930\) 0 0
\(931\) −7.97400 −0.261337
\(932\) 0 0
\(933\) 31.0828 1.01761
\(934\) 0 0
\(935\) −0.0164941 −0.000539414 0
\(936\) 0 0
\(937\) −15.3177 −0.500407 −0.250203 0.968193i \(-0.580497\pi\)
−0.250203 + 0.968193i \(0.580497\pi\)
\(938\) 0 0
\(939\) 10.6196 0.346558
\(940\) 0 0
\(941\) −16.6993 −0.544383 −0.272192 0.962243i \(-0.587748\pi\)
−0.272192 + 0.962243i \(0.587748\pi\)
\(942\) 0 0
\(943\) −1.38056 −0.0449572
\(944\) 0 0
\(945\) −30.4736 −0.991306
\(946\) 0 0
\(947\) 46.3409 1.50588 0.752938 0.658091i \(-0.228636\pi\)
0.752938 + 0.658091i \(0.228636\pi\)
\(948\) 0 0
\(949\) −3.43760 −0.111589
\(950\) 0 0
\(951\) 30.1722 0.978401
\(952\) 0 0
\(953\) 49.0506 1.58891 0.794453 0.607326i \(-0.207758\pi\)
0.794453 + 0.607326i \(0.207758\pi\)
\(954\) 0 0
\(955\) 34.3563 1.11174
\(956\) 0 0
\(957\) −0.926820 −0.0299598
\(958\) 0 0
\(959\) −46.0516 −1.48708
\(960\) 0 0
\(961\) −24.9103 −0.803559
\(962\) 0 0
\(963\) 30.3748 0.978815
\(964\) 0 0
\(965\) 4.56174 0.146848
\(966\) 0 0
\(967\) −10.8296 −0.348255 −0.174128 0.984723i \(-0.555711\pi\)
−0.174128 + 0.984723i \(0.555711\pi\)
\(968\) 0 0
\(969\) −0.109488 −0.00351727
\(970\) 0 0
\(971\) 6.42742 0.206266 0.103133 0.994668i \(-0.467113\pi\)
0.103133 + 0.994668i \(0.467113\pi\)
\(972\) 0 0
\(973\) −54.4285 −1.74490
\(974\) 0 0
\(975\) 0.747894 0.0239518
\(976\) 0 0
\(977\) 22.7256 0.727055 0.363527 0.931584i \(-0.381572\pi\)
0.363527 + 0.931584i \(0.381572\pi\)
\(978\) 0 0
\(979\) 5.55732 0.177613
\(980\) 0 0
\(981\) −7.66742 −0.244802
\(982\) 0 0
\(983\) −0.861312 −0.0274716 −0.0137358 0.999906i \(-0.504372\pi\)
−0.0137358 + 0.999906i \(0.504372\pi\)
\(984\) 0 0
\(985\) −34.7547 −1.10738
\(986\) 0 0
\(987\) 36.2959 1.15531
\(988\) 0 0
\(989\) 4.29775 0.136661
\(990\) 0 0
\(991\) 0.928715 0.0295016 0.0147508 0.999891i \(-0.495305\pi\)
0.0147508 + 0.999891i \(0.495305\pi\)
\(992\) 0 0
\(993\) −21.3703 −0.678164
\(994\) 0 0
\(995\) −42.0605 −1.33341
\(996\) 0 0
\(997\) 27.5025 0.871013 0.435507 0.900186i \(-0.356569\pi\)
0.435507 + 0.900186i \(0.356569\pi\)
\(998\) 0 0
\(999\) −26.3456 −0.833538
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 \(a_p\))