Properties

Label 6008.2.a.e.1.31
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 1.31
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.823784 q^{3} -1.53384 q^{5} +0.257976 q^{7} -2.32138 q^{9} +O(q^{10})\) \(q+0.823784 q^{3} -1.53384 q^{5} +0.257976 q^{7} -2.32138 q^{9} +1.07385 q^{11} -6.44368 q^{13} -1.26356 q^{15} +3.61157 q^{17} -2.46432 q^{19} +0.212517 q^{21} +6.43274 q^{23} -2.64733 q^{25} -4.38367 q^{27} +6.41256 q^{29} -4.45048 q^{31} +0.884621 q^{33} -0.395695 q^{35} -5.37506 q^{37} -5.30820 q^{39} -1.12753 q^{41} +5.77360 q^{43} +3.56063 q^{45} +10.2174 q^{47} -6.93345 q^{49} +2.97515 q^{51} -3.86551 q^{53} -1.64712 q^{55} -2.03007 q^{57} +12.8763 q^{59} +5.43728 q^{61} -0.598861 q^{63} +9.88360 q^{65} -3.75113 q^{67} +5.29919 q^{69} +1.92554 q^{71} -9.39270 q^{73} -2.18083 q^{75} +0.277028 q^{77} -3.75356 q^{79} +3.35294 q^{81} +7.37289 q^{83} -5.53958 q^{85} +5.28256 q^{87} -2.01587 q^{89} -1.66232 q^{91} -3.66623 q^{93} +3.77988 q^{95} +0.889947 q^{97} -2.49281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 0.823784 0.475612 0.237806 0.971313i \(-0.423572\pi\)
0.237806 + 0.971313i \(0.423572\pi\)
\(4\) 0 0
\(5\) −1.53384 −0.685955 −0.342978 0.939344i \(-0.611436\pi\)
−0.342978 + 0.939344i \(0.611436\pi\)
\(6\) 0 0
\(7\) 0.257976 0.0975059 0.0487530 0.998811i \(-0.484475\pi\)
0.0487530 + 0.998811i \(0.484475\pi\)
\(8\) 0 0
\(9\) −2.32138 −0.773793
\(10\) 0 0
\(11\) 1.07385 0.323778 0.161889 0.986809i \(-0.448241\pi\)
0.161889 + 0.986809i \(0.448241\pi\)
\(12\) 0 0
\(13\) −6.44368 −1.78716 −0.893578 0.448908i \(-0.851813\pi\)
−0.893578 + 0.448908i \(0.851813\pi\)
\(14\) 0 0
\(15\) −1.26356 −0.326249
\(16\) 0 0
\(17\) 3.61157 0.875935 0.437967 0.898991i \(-0.355699\pi\)
0.437967 + 0.898991i \(0.355699\pi\)
\(18\) 0 0
\(19\) −2.46432 −0.565354 −0.282677 0.959215i \(-0.591222\pi\)
−0.282677 + 0.959215i \(0.591222\pi\)
\(20\) 0 0
\(21\) 0.212517 0.0463750
\(22\) 0 0
\(23\) 6.43274 1.34132 0.670659 0.741765i \(-0.266011\pi\)
0.670659 + 0.741765i \(0.266011\pi\)
\(24\) 0 0
\(25\) −2.64733 −0.529465
\(26\) 0 0
\(27\) −4.38367 −0.843637
\(28\) 0 0
\(29\) 6.41256 1.19078 0.595391 0.803436i \(-0.296997\pi\)
0.595391 + 0.803436i \(0.296997\pi\)
\(30\) 0 0
\(31\) −4.45048 −0.799329 −0.399665 0.916661i \(-0.630873\pi\)
−0.399665 + 0.916661i \(0.630873\pi\)
\(32\) 0 0
\(33\) 0.884621 0.153993
\(34\) 0 0
\(35\) −0.395695 −0.0668847
\(36\) 0 0
\(37\) −5.37506 −0.883654 −0.441827 0.897100i \(-0.645670\pi\)
−0.441827 + 0.897100i \(0.645670\pi\)
\(38\) 0 0
\(39\) −5.30820 −0.849993
\(40\) 0 0
\(41\) −1.12753 −0.176091 −0.0880456 0.996116i \(-0.528062\pi\)
−0.0880456 + 0.996116i \(0.528062\pi\)
\(42\) 0 0
\(43\) 5.77360 0.880466 0.440233 0.897883i \(-0.354896\pi\)
0.440233 + 0.897883i \(0.354896\pi\)
\(44\) 0 0
\(45\) 3.56063 0.530788
\(46\) 0 0
\(47\) 10.2174 1.49037 0.745183 0.666860i \(-0.232362\pi\)
0.745183 + 0.666860i \(0.232362\pi\)
\(48\) 0 0
\(49\) −6.93345 −0.990493
\(50\) 0 0
\(51\) 2.97515 0.416605
\(52\) 0 0
\(53\) −3.86551 −0.530968 −0.265484 0.964115i \(-0.585532\pi\)
−0.265484 + 0.964115i \(0.585532\pi\)
\(54\) 0 0
\(55\) −1.64712 −0.222097
\(56\) 0 0
\(57\) −2.03007 −0.268889
\(58\) 0 0
\(59\) 12.8763 1.67635 0.838174 0.545402i \(-0.183623\pi\)
0.838174 + 0.545402i \(0.183623\pi\)
\(60\) 0 0
\(61\) 5.43728 0.696173 0.348086 0.937462i \(-0.386832\pi\)
0.348086 + 0.937462i \(0.386832\pi\)
\(62\) 0 0
\(63\) −0.598861 −0.0754494
\(64\) 0 0
\(65\) 9.88360 1.22591
\(66\) 0 0
\(67\) −3.75113 −0.458274 −0.229137 0.973394i \(-0.573590\pi\)
−0.229137 + 0.973394i \(0.573590\pi\)
\(68\) 0 0
\(69\) 5.29919 0.637947
\(70\) 0 0
\(71\) 1.92554 0.228520 0.114260 0.993451i \(-0.463550\pi\)
0.114260 + 0.993451i \(0.463550\pi\)
\(72\) 0 0
\(73\) −9.39270 −1.09933 −0.549666 0.835384i \(-0.685245\pi\)
−0.549666 + 0.835384i \(0.685245\pi\)
\(74\) 0 0
\(75\) −2.18083 −0.251820
\(76\) 0 0
\(77\) 0.277028 0.0315703
\(78\) 0 0
\(79\) −3.75356 −0.422309 −0.211154 0.977453i \(-0.567722\pi\)
−0.211154 + 0.977453i \(0.567722\pi\)
\(80\) 0 0
\(81\) 3.35294 0.372549
\(82\) 0 0
\(83\) 7.37289 0.809280 0.404640 0.914476i \(-0.367397\pi\)
0.404640 + 0.914476i \(0.367397\pi\)
\(84\) 0 0
\(85\) −5.53958 −0.600852
\(86\) 0 0
\(87\) 5.28256 0.566350
\(88\) 0 0
\(89\) −2.01587 −0.213681 −0.106841 0.994276i \(-0.534073\pi\)
−0.106841 + 0.994276i \(0.534073\pi\)
\(90\) 0 0
\(91\) −1.66232 −0.174258
\(92\) 0 0
\(93\) −3.66623 −0.380171
\(94\) 0 0
\(95\) 3.77988 0.387808
\(96\) 0 0
\(97\) 0.889947 0.0903604 0.0451802 0.998979i \(-0.485614\pi\)
0.0451802 + 0.998979i \(0.485614\pi\)
\(98\) 0 0
\(99\) −2.49281 −0.250537
\(100\) 0 0
\(101\) 3.90622 0.388683 0.194342 0.980934i \(-0.437743\pi\)
0.194342 + 0.980934i \(0.437743\pi\)
\(102\) 0 0
\(103\) 15.5639 1.53355 0.766777 0.641914i \(-0.221859\pi\)
0.766777 + 0.641914i \(0.221859\pi\)
\(104\) 0 0
\(105\) −0.325968 −0.0318112
\(106\) 0 0
\(107\) 12.6240 1.22041 0.610205 0.792244i \(-0.291087\pi\)
0.610205 + 0.792244i \(0.291087\pi\)
\(108\) 0 0
\(109\) 4.46925 0.428076 0.214038 0.976825i \(-0.431338\pi\)
0.214038 + 0.976825i \(0.431338\pi\)
\(110\) 0 0
\(111\) −4.42789 −0.420277
\(112\) 0 0
\(113\) −4.68554 −0.440779 −0.220389 0.975412i \(-0.570733\pi\)
−0.220389 + 0.975412i \(0.570733\pi\)
\(114\) 0 0
\(115\) −9.86681 −0.920085
\(116\) 0 0
\(117\) 14.9582 1.38289
\(118\) 0 0
\(119\) 0.931700 0.0854088
\(120\) 0 0
\(121\) −9.84685 −0.895168
\(122\) 0 0
\(123\) −0.928844 −0.0837511
\(124\) 0 0
\(125\) 11.7298 1.04914
\(126\) 0 0
\(127\) 10.5313 0.934500 0.467250 0.884125i \(-0.345245\pi\)
0.467250 + 0.884125i \(0.345245\pi\)
\(128\) 0 0
\(129\) 4.75620 0.418760
\(130\) 0 0
\(131\) 10.2390 0.894588 0.447294 0.894387i \(-0.352388\pi\)
0.447294 + 0.894387i \(0.352388\pi\)
\(132\) 0 0
\(133\) −0.635737 −0.0551254
\(134\) 0 0
\(135\) 6.72386 0.578698
\(136\) 0 0
\(137\) −11.7184 −1.00117 −0.500587 0.865686i \(-0.666883\pi\)
−0.500587 + 0.865686i \(0.666883\pi\)
\(138\) 0 0
\(139\) 3.10083 0.263009 0.131505 0.991316i \(-0.458019\pi\)
0.131505 + 0.991316i \(0.458019\pi\)
\(140\) 0 0
\(141\) 8.41696 0.708836
\(142\) 0 0
\(143\) −6.91955 −0.578642
\(144\) 0 0
\(145\) −9.83586 −0.816823
\(146\) 0 0
\(147\) −5.71167 −0.471090
\(148\) 0 0
\(149\) 20.6141 1.68877 0.844385 0.535737i \(-0.179966\pi\)
0.844385 + 0.535737i \(0.179966\pi\)
\(150\) 0 0
\(151\) 16.3683 1.33203 0.666015 0.745939i \(-0.267999\pi\)
0.666015 + 0.745939i \(0.267999\pi\)
\(152\) 0 0
\(153\) −8.38383 −0.677792
\(154\) 0 0
\(155\) 6.82633 0.548304
\(156\) 0 0
\(157\) 2.49065 0.198775 0.0993876 0.995049i \(-0.468312\pi\)
0.0993876 + 0.995049i \(0.468312\pi\)
\(158\) 0 0
\(159\) −3.18434 −0.252535
\(160\) 0 0
\(161\) 1.65950 0.130787
\(162\) 0 0
\(163\) 16.7014 1.30816 0.654078 0.756427i \(-0.273057\pi\)
0.654078 + 0.756427i \(0.273057\pi\)
\(164\) 0 0
\(165\) −1.35687 −0.105632
\(166\) 0 0
\(167\) 2.32144 0.179638 0.0898192 0.995958i \(-0.471371\pi\)
0.0898192 + 0.995958i \(0.471371\pi\)
\(168\) 0 0
\(169\) 28.5210 2.19393
\(170\) 0 0
\(171\) 5.72062 0.437467
\(172\) 0 0
\(173\) −10.2380 −0.778384 −0.389192 0.921157i \(-0.627246\pi\)
−0.389192 + 0.921157i \(0.627246\pi\)
\(174\) 0 0
\(175\) −0.682948 −0.0516260
\(176\) 0 0
\(177\) 10.6073 0.797292
\(178\) 0 0
\(179\) −15.2142 −1.13716 −0.568581 0.822627i \(-0.692508\pi\)
−0.568581 + 0.822627i \(0.692508\pi\)
\(180\) 0 0
\(181\) 21.7594 1.61736 0.808682 0.588246i \(-0.200181\pi\)
0.808682 + 0.588246i \(0.200181\pi\)
\(182\) 0 0
\(183\) 4.47915 0.331108
\(184\) 0 0
\(185\) 8.24450 0.606148
\(186\) 0 0
\(187\) 3.87829 0.283608
\(188\) 0 0
\(189\) −1.13088 −0.0822597
\(190\) 0 0
\(191\) −23.6361 −1.71025 −0.855125 0.518422i \(-0.826520\pi\)
−0.855125 + 0.518422i \(0.826520\pi\)
\(192\) 0 0
\(193\) 15.5693 1.12070 0.560352 0.828255i \(-0.310666\pi\)
0.560352 + 0.828255i \(0.310666\pi\)
\(194\) 0 0
\(195\) 8.14195 0.583057
\(196\) 0 0
\(197\) −3.41782 −0.243510 −0.121755 0.992560i \(-0.538852\pi\)
−0.121755 + 0.992560i \(0.538852\pi\)
\(198\) 0 0
\(199\) −1.46278 −0.103694 −0.0518469 0.998655i \(-0.516511\pi\)
−0.0518469 + 0.998655i \(0.516511\pi\)
\(200\) 0 0
\(201\) −3.09012 −0.217961
\(202\) 0 0
\(203\) 1.65429 0.116108
\(204\) 0 0
\(205\) 1.72946 0.120791
\(206\) 0 0
\(207\) −14.9328 −1.03790
\(208\) 0 0
\(209\) −2.64631 −0.183049
\(210\) 0 0
\(211\) −13.0346 −0.897342 −0.448671 0.893697i \(-0.648102\pi\)
−0.448671 + 0.893697i \(0.648102\pi\)
\(212\) 0 0
\(213\) 1.58623 0.108687
\(214\) 0 0
\(215\) −8.85580 −0.603961
\(216\) 0 0
\(217\) −1.14812 −0.0779393
\(218\) 0 0
\(219\) −7.73756 −0.522856
\(220\) 0 0
\(221\) −23.2718 −1.56543
\(222\) 0 0
\(223\) −24.7395 −1.65668 −0.828339 0.560227i \(-0.810714\pi\)
−0.828339 + 0.560227i \(0.810714\pi\)
\(224\) 0 0
\(225\) 6.14545 0.409697
\(226\) 0 0
\(227\) 9.05729 0.601154 0.300577 0.953758i \(-0.402821\pi\)
0.300577 + 0.953758i \(0.402821\pi\)
\(228\) 0 0
\(229\) 15.4397 1.02028 0.510141 0.860091i \(-0.329593\pi\)
0.510141 + 0.860091i \(0.329593\pi\)
\(230\) 0 0
\(231\) 0.228211 0.0150152
\(232\) 0 0
\(233\) 22.5932 1.48013 0.740063 0.672537i \(-0.234795\pi\)
0.740063 + 0.672537i \(0.234795\pi\)
\(234\) 0 0
\(235\) −15.6719 −1.02232
\(236\) 0 0
\(237\) −3.09213 −0.200855
\(238\) 0 0
\(239\) 4.04908 0.261913 0.130957 0.991388i \(-0.458195\pi\)
0.130957 + 0.991388i \(0.458195\pi\)
\(240\) 0 0
\(241\) −15.2685 −0.983534 −0.491767 0.870727i \(-0.663649\pi\)
−0.491767 + 0.870727i \(0.663649\pi\)
\(242\) 0 0
\(243\) 15.9131 1.02083
\(244\) 0 0
\(245\) 10.6348 0.679434
\(246\) 0 0
\(247\) 15.8793 1.01038
\(248\) 0 0
\(249\) 6.07367 0.384903
\(250\) 0 0
\(251\) 1.99522 0.125937 0.0629687 0.998016i \(-0.479943\pi\)
0.0629687 + 0.998016i \(0.479943\pi\)
\(252\) 0 0
\(253\) 6.90780 0.434290
\(254\) 0 0
\(255\) −4.56342 −0.285772
\(256\) 0 0
\(257\) −13.3723 −0.834144 −0.417072 0.908873i \(-0.636944\pi\)
−0.417072 + 0.908873i \(0.636944\pi\)
\(258\) 0 0
\(259\) −1.38664 −0.0861616
\(260\) 0 0
\(261\) −14.8860 −0.921419
\(262\) 0 0
\(263\) −1.82422 −0.112486 −0.0562430 0.998417i \(-0.517912\pi\)
−0.0562430 + 0.998417i \(0.517912\pi\)
\(264\) 0 0
\(265\) 5.92908 0.364220
\(266\) 0 0
\(267\) −1.66064 −0.101629
\(268\) 0 0
\(269\) 23.9092 1.45777 0.728886 0.684635i \(-0.240038\pi\)
0.728886 + 0.684635i \(0.240038\pi\)
\(270\) 0 0
\(271\) −22.3306 −1.35649 −0.678244 0.734837i \(-0.737259\pi\)
−0.678244 + 0.734837i \(0.737259\pi\)
\(272\) 0 0
\(273\) −1.36939 −0.0828793
\(274\) 0 0
\(275\) −2.84283 −0.171429
\(276\) 0 0
\(277\) 7.64305 0.459226 0.229613 0.973282i \(-0.426254\pi\)
0.229613 + 0.973282i \(0.426254\pi\)
\(278\) 0 0
\(279\) 10.3312 0.618515
\(280\) 0 0
\(281\) 16.0867 0.959653 0.479827 0.877363i \(-0.340700\pi\)
0.479827 + 0.877363i \(0.340700\pi\)
\(282\) 0 0
\(283\) −2.06827 −0.122946 −0.0614730 0.998109i \(-0.519580\pi\)
−0.0614730 + 0.998109i \(0.519580\pi\)
\(284\) 0 0
\(285\) 3.11381 0.184446
\(286\) 0 0
\(287\) −0.290877 −0.0171699
\(288\) 0 0
\(289\) −3.95656 −0.232739
\(290\) 0 0
\(291\) 0.733124 0.0429765
\(292\) 0 0
\(293\) 23.2292 1.35706 0.678531 0.734572i \(-0.262617\pi\)
0.678531 + 0.734572i \(0.262617\pi\)
\(294\) 0 0
\(295\) −19.7502 −1.14990
\(296\) 0 0
\(297\) −4.70740 −0.273151
\(298\) 0 0
\(299\) −41.4505 −2.39715
\(300\) 0 0
\(301\) 1.48945 0.0858507
\(302\) 0 0
\(303\) 3.21788 0.184862
\(304\) 0 0
\(305\) −8.33994 −0.477544
\(306\) 0 0
\(307\) −23.5329 −1.34309 −0.671546 0.740962i \(-0.734370\pi\)
−0.671546 + 0.740962i \(0.734370\pi\)
\(308\) 0 0
\(309\) 12.8213 0.729376
\(310\) 0 0
\(311\) 23.3627 1.32478 0.662389 0.749160i \(-0.269543\pi\)
0.662389 + 0.749160i \(0.269543\pi\)
\(312\) 0 0
\(313\) −26.8635 −1.51841 −0.759207 0.650849i \(-0.774413\pi\)
−0.759207 + 0.650849i \(0.774413\pi\)
\(314\) 0 0
\(315\) 0.918559 0.0517550
\(316\) 0 0
\(317\) 18.8629 1.05944 0.529722 0.848171i \(-0.322296\pi\)
0.529722 + 0.848171i \(0.322296\pi\)
\(318\) 0 0
\(319\) 6.88613 0.385549
\(320\) 0 0
\(321\) 10.3995 0.580442
\(322\) 0 0
\(323\) −8.90007 −0.495213
\(324\) 0 0
\(325\) 17.0585 0.946237
\(326\) 0 0
\(327\) 3.68169 0.203598
\(328\) 0 0
\(329\) 2.63586 0.145320
\(330\) 0 0
\(331\) 35.3505 1.94304 0.971520 0.236958i \(-0.0761503\pi\)
0.971520 + 0.236958i \(0.0761503\pi\)
\(332\) 0 0
\(333\) 12.4776 0.683766
\(334\) 0 0
\(335\) 5.75365 0.314355
\(336\) 0 0
\(337\) 3.63805 0.198177 0.0990887 0.995079i \(-0.468407\pi\)
0.0990887 + 0.995079i \(0.468407\pi\)
\(338\) 0 0
\(339\) −3.85988 −0.209640
\(340\) 0 0
\(341\) −4.77915 −0.258805
\(342\) 0 0
\(343\) −3.59450 −0.194085
\(344\) 0 0
\(345\) −8.12812 −0.437603
\(346\) 0 0
\(347\) 4.69117 0.251835 0.125918 0.992041i \(-0.459812\pi\)
0.125918 + 0.992041i \(0.459812\pi\)
\(348\) 0 0
\(349\) 14.5269 0.777609 0.388805 0.921320i \(-0.372888\pi\)
0.388805 + 0.921320i \(0.372888\pi\)
\(350\) 0 0
\(351\) 28.2470 1.50771
\(352\) 0 0
\(353\) −31.7680 −1.69084 −0.845419 0.534104i \(-0.820649\pi\)
−0.845419 + 0.534104i \(0.820649\pi\)
\(354\) 0 0
\(355\) −2.95348 −0.156754
\(356\) 0 0
\(357\) 0.767520 0.0406215
\(358\) 0 0
\(359\) −2.82780 −0.149246 −0.0746229 0.997212i \(-0.523775\pi\)
−0.0746229 + 0.997212i \(0.523775\pi\)
\(360\) 0 0
\(361\) −12.9271 −0.680375
\(362\) 0 0
\(363\) −8.11168 −0.425753
\(364\) 0 0
\(365\) 14.4069 0.754093
\(366\) 0 0
\(367\) 21.7407 1.13486 0.567428 0.823423i \(-0.307938\pi\)
0.567428 + 0.823423i \(0.307938\pi\)
\(368\) 0 0
\(369\) 2.61743 0.136258
\(370\) 0 0
\(371\) −0.997209 −0.0517725
\(372\) 0 0
\(373\) −19.7736 −1.02384 −0.511918 0.859034i \(-0.671065\pi\)
−0.511918 + 0.859034i \(0.671065\pi\)
\(374\) 0 0
\(375\) 9.66282 0.498986
\(376\) 0 0
\(377\) −41.3205 −2.12811
\(378\) 0 0
\(379\) −10.0301 −0.515212 −0.257606 0.966250i \(-0.582934\pi\)
−0.257606 + 0.966250i \(0.582934\pi\)
\(380\) 0 0
\(381\) 8.67550 0.444459
\(382\) 0 0
\(383\) 5.37137 0.274464 0.137232 0.990539i \(-0.456179\pi\)
0.137232 + 0.990539i \(0.456179\pi\)
\(384\) 0 0
\(385\) −0.424918 −0.0216558
\(386\) 0 0
\(387\) −13.4027 −0.681299
\(388\) 0 0
\(389\) −22.9092 −1.16154 −0.580771 0.814067i \(-0.697249\pi\)
−0.580771 + 0.814067i \(0.697249\pi\)
\(390\) 0 0
\(391\) 23.2323 1.17491
\(392\) 0 0
\(393\) 8.43475 0.425477
\(394\) 0 0
\(395\) 5.75738 0.289685
\(396\) 0 0
\(397\) 33.4109 1.67684 0.838421 0.545022i \(-0.183479\pi\)
0.838421 + 0.545022i \(0.183479\pi\)
\(398\) 0 0
\(399\) −0.523710 −0.0262183
\(400\) 0 0
\(401\) 17.1166 0.854761 0.427380 0.904072i \(-0.359437\pi\)
0.427380 + 0.904072i \(0.359437\pi\)
\(402\) 0 0
\(403\) 28.6775 1.42853
\(404\) 0 0
\(405\) −5.14289 −0.255552
\(406\) 0 0
\(407\) −5.77201 −0.286108
\(408\) 0 0
\(409\) 34.3132 1.69668 0.848338 0.529455i \(-0.177603\pi\)
0.848338 + 0.529455i \(0.177603\pi\)
\(410\) 0 0
\(411\) −9.65347 −0.476171
\(412\) 0 0
\(413\) 3.32178 0.163454
\(414\) 0 0
\(415\) −11.3089 −0.555130
\(416\) 0 0
\(417\) 2.55442 0.125090
\(418\) 0 0
\(419\) 10.9327 0.534098 0.267049 0.963683i \(-0.413951\pi\)
0.267049 + 0.963683i \(0.413951\pi\)
\(420\) 0 0
\(421\) 1.85783 0.0905450 0.0452725 0.998975i \(-0.485584\pi\)
0.0452725 + 0.998975i \(0.485584\pi\)
\(422\) 0 0
\(423\) −23.7185 −1.15324
\(424\) 0 0
\(425\) −9.56100 −0.463777
\(426\) 0 0
\(427\) 1.40269 0.0678810
\(428\) 0 0
\(429\) −5.70022 −0.275209
\(430\) 0 0
\(431\) −19.8740 −0.957298 −0.478649 0.878006i \(-0.658873\pi\)
−0.478649 + 0.878006i \(0.658873\pi\)
\(432\) 0 0
\(433\) 20.0400 0.963060 0.481530 0.876430i \(-0.340081\pi\)
0.481530 + 0.876430i \(0.340081\pi\)
\(434\) 0 0
\(435\) −8.10262 −0.388491
\(436\) 0 0
\(437\) −15.8523 −0.758320
\(438\) 0 0
\(439\) 27.9388 1.33345 0.666723 0.745306i \(-0.267697\pi\)
0.666723 + 0.745306i \(0.267697\pi\)
\(440\) 0 0
\(441\) 16.0952 0.766436
\(442\) 0 0
\(443\) −8.10720 −0.385185 −0.192592 0.981279i \(-0.561689\pi\)
−0.192592 + 0.981279i \(0.561689\pi\)
\(444\) 0 0
\(445\) 3.09202 0.146576
\(446\) 0 0
\(447\) 16.9815 0.803199
\(448\) 0 0
\(449\) −10.5796 −0.499282 −0.249641 0.968338i \(-0.580313\pi\)
−0.249641 + 0.968338i \(0.580313\pi\)
\(450\) 0 0
\(451\) −1.21080 −0.0570145
\(452\) 0 0
\(453\) 13.4839 0.633529
\(454\) 0 0
\(455\) 2.54974 0.119533
\(456\) 0 0
\(457\) −6.23297 −0.291566 −0.145783 0.989317i \(-0.546570\pi\)
−0.145783 + 0.989317i \(0.546570\pi\)
\(458\) 0 0
\(459\) −15.8319 −0.738971
\(460\) 0 0
\(461\) −17.7819 −0.828187 −0.414094 0.910234i \(-0.635901\pi\)
−0.414094 + 0.910234i \(0.635901\pi\)
\(462\) 0 0
\(463\) 22.6781 1.05394 0.526970 0.849884i \(-0.323328\pi\)
0.526970 + 0.849884i \(0.323328\pi\)
\(464\) 0 0
\(465\) 5.62342 0.260780
\(466\) 0 0
\(467\) −21.0419 −0.973704 −0.486852 0.873485i \(-0.661855\pi\)
−0.486852 + 0.873485i \(0.661855\pi\)
\(468\) 0 0
\(469\) −0.967704 −0.0446844
\(470\) 0 0
\(471\) 2.05175 0.0945399
\(472\) 0 0
\(473\) 6.19999 0.285076
\(474\) 0 0
\(475\) 6.52386 0.299335
\(476\) 0 0
\(477\) 8.97331 0.410859
\(478\) 0 0
\(479\) 42.1448 1.92564 0.962822 0.270137i \(-0.0870689\pi\)
0.962822 + 0.270137i \(0.0870689\pi\)
\(480\) 0 0
\(481\) 34.6352 1.57923
\(482\) 0 0
\(483\) 1.36707 0.0622037
\(484\) 0 0
\(485\) −1.36504 −0.0619832
\(486\) 0 0
\(487\) −39.9964 −1.81241 −0.906205 0.422838i \(-0.861034\pi\)
−0.906205 + 0.422838i \(0.861034\pi\)
\(488\) 0 0
\(489\) 13.7584 0.622175
\(490\) 0 0
\(491\) −14.7596 −0.666093 −0.333047 0.942910i \(-0.608077\pi\)
−0.333047 + 0.942910i \(0.608077\pi\)
\(492\) 0 0
\(493\) 23.1594 1.04305
\(494\) 0 0
\(495\) 3.82359 0.171857
\(496\) 0 0
\(497\) 0.496745 0.0222820
\(498\) 0 0
\(499\) −30.9064 −1.38356 −0.691780 0.722108i \(-0.743173\pi\)
−0.691780 + 0.722108i \(0.743173\pi\)
\(500\) 0 0
\(501\) 1.91237 0.0854382
\(502\) 0 0
\(503\) −22.3279 −0.995550 −0.497775 0.867306i \(-0.665849\pi\)
−0.497775 + 0.867306i \(0.665849\pi\)
\(504\) 0 0
\(505\) −5.99152 −0.266619
\(506\) 0 0
\(507\) 23.4952 1.04346
\(508\) 0 0
\(509\) −11.9159 −0.528163 −0.264082 0.964500i \(-0.585069\pi\)
−0.264082 + 0.964500i \(0.585069\pi\)
\(510\) 0 0
\(511\) −2.42310 −0.107191
\(512\) 0 0
\(513\) 10.8028 0.476954
\(514\) 0 0
\(515\) −23.8725 −1.05195
\(516\) 0 0
\(517\) 10.9720 0.482548
\(518\) 0 0
\(519\) −8.43394 −0.370209
\(520\) 0 0
\(521\) −5.80323 −0.254244 −0.127122 0.991887i \(-0.540574\pi\)
−0.127122 + 0.991887i \(0.540574\pi\)
\(522\) 0 0
\(523\) 2.65408 0.116055 0.0580275 0.998315i \(-0.481519\pi\)
0.0580275 + 0.998315i \(0.481519\pi\)
\(524\) 0 0
\(525\) −0.562602 −0.0245539
\(526\) 0 0
\(527\) −16.0732 −0.700160
\(528\) 0 0
\(529\) 18.3801 0.799136
\(530\) 0 0
\(531\) −29.8907 −1.29715
\(532\) 0 0
\(533\) 7.26547 0.314702
\(534\) 0 0
\(535\) −19.3633 −0.837147
\(536\) 0 0
\(537\) −12.5332 −0.540848
\(538\) 0 0
\(539\) −7.44549 −0.320700
\(540\) 0 0
\(541\) −37.4325 −1.60935 −0.804675 0.593716i \(-0.797660\pi\)
−0.804675 + 0.593716i \(0.797660\pi\)
\(542\) 0 0
\(543\) 17.9251 0.769238
\(544\) 0 0
\(545\) −6.85512 −0.293641
\(546\) 0 0
\(547\) 11.2642 0.481620 0.240810 0.970572i \(-0.422587\pi\)
0.240810 + 0.970572i \(0.422587\pi\)
\(548\) 0 0
\(549\) −12.6220 −0.538694
\(550\) 0 0
\(551\) −15.8026 −0.673213
\(552\) 0 0
\(553\) −0.968331 −0.0411776
\(554\) 0 0
\(555\) 6.79169 0.288291
\(556\) 0 0
\(557\) 30.3468 1.28583 0.642917 0.765936i \(-0.277724\pi\)
0.642917 + 0.765936i \(0.277724\pi\)
\(558\) 0 0
\(559\) −37.2033 −1.57353
\(560\) 0 0
\(561\) 3.19487 0.134888
\(562\) 0 0
\(563\) −5.47156 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(564\) 0 0
\(565\) 7.18689 0.302355
\(566\) 0 0
\(567\) 0.864980 0.0363258
\(568\) 0 0
\(569\) 36.9163 1.54761 0.773806 0.633423i \(-0.218351\pi\)
0.773806 + 0.633423i \(0.218351\pi\)
\(570\) 0 0
\(571\) 1.66161 0.0695360 0.0347680 0.999395i \(-0.488931\pi\)
0.0347680 + 0.999395i \(0.488931\pi\)
\(572\) 0 0
\(573\) −19.4711 −0.813415
\(574\) 0 0
\(575\) −17.0296 −0.710181
\(576\) 0 0
\(577\) 29.2836 1.21909 0.609546 0.792751i \(-0.291352\pi\)
0.609546 + 0.792751i \(0.291352\pi\)
\(578\) 0 0
\(579\) 12.8258 0.533020
\(580\) 0 0
\(581\) 1.90203 0.0789096
\(582\) 0 0
\(583\) −4.15097 −0.171916
\(584\) 0 0
\(585\) −22.9436 −0.948600
\(586\) 0 0
\(587\) 6.51689 0.268981 0.134490 0.990915i \(-0.457060\pi\)
0.134490 + 0.990915i \(0.457060\pi\)
\(588\) 0 0
\(589\) 10.9674 0.451904
\(590\) 0 0
\(591\) −2.81555 −0.115816
\(592\) 0 0
\(593\) −30.5789 −1.25573 −0.627863 0.778324i \(-0.716070\pi\)
−0.627863 + 0.778324i \(0.716070\pi\)
\(594\) 0 0
\(595\) −1.42908 −0.0585866
\(596\) 0 0
\(597\) −1.20502 −0.0493180
\(598\) 0 0
\(599\) 28.6196 1.16936 0.584682 0.811263i \(-0.301219\pi\)
0.584682 + 0.811263i \(0.301219\pi\)
\(600\) 0 0
\(601\) −9.77277 −0.398640 −0.199320 0.979935i \(-0.563873\pi\)
−0.199320 + 0.979935i \(0.563873\pi\)
\(602\) 0 0
\(603\) 8.70780 0.354609
\(604\) 0 0
\(605\) 15.1035 0.614045
\(606\) 0 0
\(607\) 29.1220 1.18203 0.591013 0.806662i \(-0.298728\pi\)
0.591013 + 0.806662i \(0.298728\pi\)
\(608\) 0 0
\(609\) 1.36278 0.0552225
\(610\) 0 0
\(611\) −65.8379 −2.66352
\(612\) 0 0
\(613\) −30.8416 −1.24568 −0.622839 0.782350i \(-0.714021\pi\)
−0.622839 + 0.782350i \(0.714021\pi\)
\(614\) 0 0
\(615\) 1.42470 0.0574495
\(616\) 0 0
\(617\) 16.1505 0.650195 0.325097 0.945681i \(-0.394603\pi\)
0.325097 + 0.945681i \(0.394603\pi\)
\(618\) 0 0
\(619\) 4.53909 0.182442 0.0912208 0.995831i \(-0.470923\pi\)
0.0912208 + 0.995831i \(0.470923\pi\)
\(620\) 0 0
\(621\) −28.1990 −1.13159
\(622\) 0 0
\(623\) −0.520046 −0.0208352
\(624\) 0 0
\(625\) −4.75504 −0.190202
\(626\) 0 0
\(627\) −2.17999 −0.0870604
\(628\) 0 0
\(629\) −19.4124 −0.774023
\(630\) 0 0
\(631\) 22.0968 0.879659 0.439830 0.898081i \(-0.355039\pi\)
0.439830 + 0.898081i \(0.355039\pi\)
\(632\) 0 0
\(633\) −10.7377 −0.426787
\(634\) 0 0
\(635\) −16.1533 −0.641025
\(636\) 0 0
\(637\) 44.6769 1.77016
\(638\) 0 0
\(639\) −4.46992 −0.176827
\(640\) 0 0
\(641\) −25.0606 −0.989835 −0.494917 0.868940i \(-0.664802\pi\)
−0.494917 + 0.868940i \(0.664802\pi\)
\(642\) 0 0
\(643\) −12.2678 −0.483797 −0.241898 0.970302i \(-0.577770\pi\)
−0.241898 + 0.970302i \(0.577770\pi\)
\(644\) 0 0
\(645\) −7.29527 −0.287251
\(646\) 0 0
\(647\) 38.0505 1.49592 0.747961 0.663743i \(-0.231033\pi\)
0.747961 + 0.663743i \(0.231033\pi\)
\(648\) 0 0
\(649\) 13.8272 0.542765
\(650\) 0 0
\(651\) −0.945802 −0.0370689
\(652\) 0 0
\(653\) −12.7831 −0.500242 −0.250121 0.968215i \(-0.580470\pi\)
−0.250121 + 0.968215i \(0.580470\pi\)
\(654\) 0 0
\(655\) −15.7051 −0.613648
\(656\) 0 0
\(657\) 21.8040 0.850656
\(658\) 0 0
\(659\) −30.5002 −1.18812 −0.594060 0.804421i \(-0.702476\pi\)
−0.594060 + 0.804421i \(0.702476\pi\)
\(660\) 0 0
\(661\) 1.42832 0.0555552 0.0277776 0.999614i \(-0.491157\pi\)
0.0277776 + 0.999614i \(0.491157\pi\)
\(662\) 0 0
\(663\) −19.1709 −0.744538
\(664\) 0 0
\(665\) 0.975120 0.0378135
\(666\) 0 0
\(667\) 41.2503 1.59722
\(668\) 0 0
\(669\) −20.3800 −0.787936
\(670\) 0 0
\(671\) 5.83883 0.225406
\(672\) 0 0
\(673\) −23.6743 −0.912575 −0.456288 0.889832i \(-0.650821\pi\)
−0.456288 + 0.889832i \(0.650821\pi\)
\(674\) 0 0
\(675\) 11.6050 0.446677
\(676\) 0 0
\(677\) 32.8887 1.26401 0.632007 0.774963i \(-0.282231\pi\)
0.632007 + 0.774963i \(0.282231\pi\)
\(678\) 0 0
\(679\) 0.229585 0.00881068
\(680\) 0 0
\(681\) 7.46125 0.285916
\(682\) 0 0
\(683\) −25.2987 −0.968027 −0.484013 0.875061i \(-0.660821\pi\)
−0.484013 + 0.875061i \(0.660821\pi\)
\(684\) 0 0
\(685\) 17.9743 0.686761
\(686\) 0 0
\(687\) 12.7190 0.485259
\(688\) 0 0
\(689\) 24.9081 0.948922
\(690\) 0 0
\(691\) 38.8372 1.47744 0.738718 0.674015i \(-0.235432\pi\)
0.738718 + 0.674015i \(0.235432\pi\)
\(692\) 0 0
\(693\) −0.643087 −0.0244289
\(694\) 0 0
\(695\) −4.75619 −0.180413
\(696\) 0 0
\(697\) −4.07217 −0.154244
\(698\) 0 0
\(699\) 18.6119 0.703966
\(700\) 0 0
\(701\) 1.71520 0.0647824 0.0323912 0.999475i \(-0.489688\pi\)
0.0323912 + 0.999475i \(0.489688\pi\)
\(702\) 0 0
\(703\) 13.2459 0.499577
\(704\) 0 0
\(705\) −12.9103 −0.486230
\(706\) 0 0
\(707\) 1.00771 0.0378989
\(708\) 0 0
\(709\) −35.1255 −1.31917 −0.659583 0.751632i \(-0.729267\pi\)
−0.659583 + 0.751632i \(0.729267\pi\)
\(710\) 0 0
\(711\) 8.71345 0.326780
\(712\) 0 0
\(713\) −28.6288 −1.07216
\(714\) 0 0
\(715\) 10.6135 0.396923
\(716\) 0 0
\(717\) 3.33557 0.124569
\(718\) 0 0
\(719\) −26.1608 −0.975632 −0.487816 0.872946i \(-0.662206\pi\)
−0.487816 + 0.872946i \(0.662206\pi\)
\(720\) 0 0
\(721\) 4.01511 0.149531
\(722\) 0 0
\(723\) −12.5780 −0.467780
\(724\) 0 0
\(725\) −16.9761 −0.630478
\(726\) 0 0
\(727\) −43.2843 −1.60533 −0.802663 0.596433i \(-0.796584\pi\)
−0.802663 + 0.596433i \(0.796584\pi\)
\(728\) 0 0
\(729\) 3.05014 0.112968
\(730\) 0 0
\(731\) 20.8518 0.771231
\(732\) 0 0
\(733\) 22.7171 0.839077 0.419538 0.907738i \(-0.362192\pi\)
0.419538 + 0.907738i \(0.362192\pi\)
\(734\) 0 0
\(735\) 8.76080 0.323147
\(736\) 0 0
\(737\) −4.02816 −0.148379
\(738\) 0 0
\(739\) −12.3423 −0.454018 −0.227009 0.973893i \(-0.572895\pi\)
−0.227009 + 0.973893i \(0.572895\pi\)
\(740\) 0 0
\(741\) 13.0811 0.480547
\(742\) 0 0
\(743\) 15.4100 0.565339 0.282670 0.959217i \(-0.408780\pi\)
0.282670 + 0.959217i \(0.408780\pi\)
\(744\) 0 0
\(745\) −31.6187 −1.15842
\(746\) 0 0
\(747\) −17.1153 −0.626216
\(748\) 0 0
\(749\) 3.25670 0.118997
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 1.64363 0.0598973
\(754\) 0 0
\(755\) −25.1063 −0.913713
\(756\) 0 0
\(757\) −29.1285 −1.05869 −0.529347 0.848405i \(-0.677563\pi\)
−0.529347 + 0.848405i \(0.677563\pi\)
\(758\) 0 0
\(759\) 5.69054 0.206553
\(760\) 0 0
\(761\) −2.20326 −0.0798680 −0.0399340 0.999202i \(-0.512715\pi\)
−0.0399340 + 0.999202i \(0.512715\pi\)
\(762\) 0 0
\(763\) 1.15296 0.0417400
\(764\) 0 0
\(765\) 12.8595 0.464935
\(766\) 0 0
\(767\) −82.9706 −2.99590
\(768\) 0 0
\(769\) −8.54002 −0.307961 −0.153981 0.988074i \(-0.549209\pi\)
−0.153981 + 0.988074i \(0.549209\pi\)
\(770\) 0 0
\(771\) −11.0159 −0.396729
\(772\) 0 0
\(773\) 5.58639 0.200929 0.100464 0.994941i \(-0.467967\pi\)
0.100464 + 0.994941i \(0.467967\pi\)
\(774\) 0 0
\(775\) 11.7819 0.423217
\(776\) 0 0
\(777\) −1.14229 −0.0409795
\(778\) 0 0
\(779\) 2.77860 0.0995538
\(780\) 0 0
\(781\) 2.06775 0.0739897
\(782\) 0 0
\(783\) −28.1105 −1.00459
\(784\) 0 0
\(785\) −3.82026 −0.136351
\(786\) 0 0
\(787\) 48.1750 1.71725 0.858627 0.512602i \(-0.171318\pi\)
0.858627 + 0.512602i \(0.171318\pi\)
\(788\) 0 0
\(789\) −1.50276 −0.0534997
\(790\) 0 0
\(791\) −1.20876 −0.0429785
\(792\) 0 0
\(793\) −35.0361 −1.24417
\(794\) 0 0
\(795\) 4.88428 0.173228
\(796\) 0 0
\(797\) 14.6833 0.520108 0.260054 0.965594i \(-0.416260\pi\)
0.260054 + 0.965594i \(0.416260\pi\)
\(798\) 0 0
\(799\) 36.9010 1.30546
\(800\) 0 0
\(801\) 4.67959 0.165345
\(802\) 0 0
\(803\) −10.0864 −0.355940
\(804\) 0 0
\(805\) −2.54541 −0.0897137
\(806\) 0 0
\(807\) 19.6961 0.693334
\(808\) 0 0
\(809\) 35.0743 1.23315 0.616573 0.787298i \(-0.288521\pi\)
0.616573 + 0.787298i \(0.288521\pi\)
\(810\) 0 0
\(811\) 10.2328 0.359323 0.179662 0.983728i \(-0.442500\pi\)
0.179662 + 0.983728i \(0.442500\pi\)
\(812\) 0 0
\(813\) −18.3956 −0.645162
\(814\) 0 0
\(815\) −25.6174 −0.897337
\(816\) 0 0
\(817\) −14.2280 −0.497775
\(818\) 0 0
\(819\) 3.85887 0.134840
\(820\) 0 0
\(821\) 19.0226 0.663893 0.331946 0.943298i \(-0.392295\pi\)
0.331946 + 0.943298i \(0.392295\pi\)
\(822\) 0 0
\(823\) −23.6733 −0.825199 −0.412599 0.910913i \(-0.635379\pi\)
−0.412599 + 0.910913i \(0.635379\pi\)
\(824\) 0 0
\(825\) −2.34188 −0.0815338
\(826\) 0 0
\(827\) 6.62961 0.230534 0.115267 0.993335i \(-0.463228\pi\)
0.115267 + 0.993335i \(0.463228\pi\)
\(828\) 0 0
\(829\) 38.9608 1.35316 0.676582 0.736368i \(-0.263461\pi\)
0.676582 + 0.736368i \(0.263461\pi\)
\(830\) 0 0
\(831\) 6.29622 0.218414
\(832\) 0 0
\(833\) −25.0406 −0.867607
\(834\) 0 0
\(835\) −3.56072 −0.123224
\(836\) 0 0
\(837\) 19.5094 0.674344
\(838\) 0 0
\(839\) −12.5794 −0.434290 −0.217145 0.976139i \(-0.569675\pi\)
−0.217145 + 0.976139i \(0.569675\pi\)
\(840\) 0 0
\(841\) 12.1209 0.417962
\(842\) 0 0
\(843\) 13.2520 0.456423
\(844\) 0 0
\(845\) −43.7468 −1.50494
\(846\) 0 0
\(847\) −2.54025 −0.0872842
\(848\) 0 0
\(849\) −1.70381 −0.0584746
\(850\) 0 0
\(851\) −34.5764 −1.18526
\(852\) 0 0
\(853\) 57.6697 1.97457 0.987287 0.158946i \(-0.0508096\pi\)
0.987287 + 0.158946i \(0.0508096\pi\)
\(854\) 0 0
\(855\) −8.77454 −0.300083
\(856\) 0 0
\(857\) −47.8245 −1.63365 −0.816827 0.576883i \(-0.804269\pi\)
−0.816827 + 0.576883i \(0.804269\pi\)
\(858\) 0 0
\(859\) −44.5829 −1.52115 −0.760574 0.649251i \(-0.775083\pi\)
−0.760574 + 0.649251i \(0.775083\pi\)
\(860\) 0 0
\(861\) −0.239620 −0.00816623
\(862\) 0 0
\(863\) 3.84737 0.130966 0.0654830 0.997854i \(-0.479141\pi\)
0.0654830 + 0.997854i \(0.479141\pi\)
\(864\) 0 0
\(865\) 15.7035 0.533937
\(866\) 0 0
\(867\) −3.25935 −0.110693
\(868\) 0 0
\(869\) −4.03077 −0.136734
\(870\) 0 0
\(871\) 24.1711 0.819007
\(872\) 0 0
\(873\) −2.06590 −0.0699203
\(874\) 0 0
\(875\) 3.02601 0.102298
\(876\) 0 0
\(877\) −4.56099 −0.154014 −0.0770068 0.997031i \(-0.524536\pi\)
−0.0770068 + 0.997031i \(0.524536\pi\)
\(878\) 0 0
\(879\) 19.1358 0.645435
\(880\) 0 0
\(881\) 25.6292 0.863470 0.431735 0.902001i \(-0.357902\pi\)
0.431735 + 0.902001i \(0.357902\pi\)
\(882\) 0 0
\(883\) 19.0678 0.641681 0.320841 0.947133i \(-0.396035\pi\)
0.320841 + 0.947133i \(0.396035\pi\)
\(884\) 0 0
\(885\) −16.2699 −0.546907
\(886\) 0 0
\(887\) 0.112708 0.00378437 0.00189219 0.999998i \(-0.499398\pi\)
0.00189219 + 0.999998i \(0.499398\pi\)
\(888\) 0 0
\(889\) 2.71682 0.0911193
\(890\) 0 0
\(891\) 3.60056 0.120623
\(892\) 0 0
\(893\) −25.1790 −0.842584
\(894\) 0 0
\(895\) 23.3362 0.780043
\(896\) 0 0
\(897\) −34.1463 −1.14011
\(898\) 0 0
\(899\) −28.5389 −0.951827
\(900\) 0 0
\(901\) −13.9605 −0.465093
\(902\) 0 0
\(903\) 1.22699 0.0408316
\(904\) 0 0
\(905\) −33.3755 −1.10944
\(906\) 0 0
\(907\) −7.52667 −0.249919 −0.124960 0.992162i \(-0.539880\pi\)
−0.124960 + 0.992162i \(0.539880\pi\)
\(908\) 0 0
\(909\) −9.06781 −0.300760
\(910\) 0 0
\(911\) −39.4119 −1.30577 −0.652887 0.757456i \(-0.726442\pi\)
−0.652887 + 0.757456i \(0.726442\pi\)
\(912\) 0 0
\(913\) 7.91739 0.262027
\(914\) 0 0
\(915\) −6.87031 −0.227125
\(916\) 0 0
\(917\) 2.64143 0.0872277
\(918\) 0 0
\(919\) −29.9443 −0.987770 −0.493885 0.869527i \(-0.664424\pi\)
−0.493885 + 0.869527i \(0.664424\pi\)
\(920\) 0 0
\(921\) −19.3860 −0.638791
\(922\) 0 0
\(923\) −12.4076 −0.408401
\(924\) 0 0
\(925\) 14.2295 0.467864
\(926\) 0 0
\(927\) −36.1296 −1.18665
\(928\) 0 0
\(929\) 42.8317 1.40526 0.702632 0.711554i \(-0.252008\pi\)
0.702632 + 0.711554i \(0.252008\pi\)
\(930\) 0 0
\(931\) 17.0862 0.559979
\(932\) 0 0
\(933\) 19.2458 0.630080
\(934\) 0 0
\(935\) −5.94868 −0.194543
\(936\) 0 0
\(937\) 45.8023 1.49630 0.748148 0.663532i \(-0.230943\pi\)
0.748148 + 0.663532i \(0.230943\pi\)
\(938\) 0 0
\(939\) −22.1297 −0.722176
\(940\) 0 0
\(941\) 45.0046 1.46711 0.733554 0.679631i \(-0.237860\pi\)
0.733554 + 0.679631i \(0.237860\pi\)
\(942\) 0 0
\(943\) −7.25313 −0.236194
\(944\) 0 0
\(945\) 1.73460 0.0564265
\(946\) 0 0
\(947\) −2.69868 −0.0876952 −0.0438476 0.999038i \(-0.513962\pi\)
−0.0438476 + 0.999038i \(0.513962\pi\)
\(948\) 0 0
\(949\) 60.5236 1.96468
\(950\) 0 0
\(951\) 15.5389 0.503884
\(952\) 0 0
\(953\) 50.0779 1.62218 0.811091 0.584920i \(-0.198874\pi\)
0.811091 + 0.584920i \(0.198874\pi\)
\(954\) 0 0
\(955\) 36.2541 1.17316
\(956\) 0 0
\(957\) 5.67268 0.183372
\(958\) 0 0
\(959\) −3.02308 −0.0976205
\(960\) 0 0
\(961\) −11.1933 −0.361073
\(962\) 0 0
\(963\) −29.3051 −0.944345
\(964\) 0 0
\(965\) −23.8809 −0.768753
\(966\) 0 0
\(967\) −18.1810 −0.584661 −0.292330 0.956317i \(-0.594431\pi\)
−0.292330 + 0.956317i \(0.594431\pi\)
\(968\) 0 0
\(969\) −7.33173 −0.235529
\(970\) 0 0
\(971\) −27.4217 −0.880003 −0.440002 0.897997i \(-0.645022\pi\)
−0.440002 + 0.897997i \(0.645022\pi\)
\(972\) 0 0
\(973\) 0.799942 0.0256450
\(974\) 0 0
\(975\) 14.0525 0.450042
\(976\) 0 0
\(977\) 51.9065 1.66064 0.830318 0.557290i \(-0.188159\pi\)
0.830318 + 0.557290i \(0.188159\pi\)
\(978\) 0 0
\(979\) −2.16474 −0.0691853
\(980\) 0 0
\(981\) −10.3748 −0.331242
\(982\) 0 0
\(983\) 53.8609 1.71790 0.858948 0.512063i \(-0.171119\pi\)
0.858948 + 0.512063i \(0.171119\pi\)
\(984\) 0 0
\(985\) 5.24240 0.167037
\(986\) 0 0
\(987\) 2.17138 0.0691157
\(988\) 0 0
\(989\) 37.1401 1.18099
\(990\) 0 0
\(991\) −25.5246 −0.810816 −0.405408 0.914136i \(-0.632870\pi\)
−0.405408 + 0.914136i \(0.632870\pi\)
\(992\) 0 0
\(993\) 29.1212 0.924133
\(994\) 0 0
\(995\) 2.24367 0.0711293
\(996\) 0 0
\(997\) −42.3414 −1.34097 −0.670483 0.741925i \(-0.733913\pi\)
−0.670483 + 0.741925i \(0.733913\pi\)
\(998\) 0 0
\(999\) 23.5625 0.745484
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 \(a_p\))