Properties

Label 6008.2.a.e.1.2
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 1.2
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.97826 q^{3} -0.794149 q^{5} -3.63896 q^{7} +5.87005 q^{9} +O(q^{10})\) \(q-2.97826 q^{3} -0.794149 q^{5} -3.63896 q^{7} +5.87005 q^{9} -0.674085 q^{11} -1.02843 q^{13} +2.36518 q^{15} +3.65416 q^{17} +3.51928 q^{19} +10.8378 q^{21} +4.04783 q^{23} -4.36933 q^{25} -8.54776 q^{27} +2.95252 q^{29} -3.73972 q^{31} +2.00760 q^{33} +2.88987 q^{35} +3.30857 q^{37} +3.06292 q^{39} -12.0974 q^{41} -1.05637 q^{43} -4.66169 q^{45} -6.46297 q^{47} +6.24201 q^{49} -10.8831 q^{51} +2.27933 q^{53} +0.535324 q^{55} -10.4813 q^{57} -14.8230 q^{59} -6.97730 q^{61} -21.3609 q^{63} +0.816724 q^{65} -12.8224 q^{67} -12.0555 q^{69} -3.34117 q^{71} +13.2862 q^{73} +13.0130 q^{75} +2.45297 q^{77} -15.7620 q^{79} +7.84734 q^{81} +8.63077 q^{83} -2.90195 q^{85} -8.79338 q^{87} +8.61968 q^{89} +3.74240 q^{91} +11.1379 q^{93} -2.79483 q^{95} +13.8912 q^{97} -3.95691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.97826 −1.71950 −0.859750 0.510714i \(-0.829381\pi\)
−0.859750 + 0.510714i \(0.829381\pi\)
\(4\) 0 0
\(5\) −0.794149 −0.355154 −0.177577 0.984107i \(-0.556826\pi\)
−0.177577 + 0.984107i \(0.556826\pi\)
\(6\) 0 0
\(7\) −3.63896 −1.37540 −0.687698 0.725997i \(-0.741379\pi\)
−0.687698 + 0.725997i \(0.741379\pi\)
\(8\) 0 0
\(9\) 5.87005 1.95668
\(10\) 0 0
\(11\) −0.674085 −0.203244 −0.101622 0.994823i \(-0.532403\pi\)
−0.101622 + 0.994823i \(0.532403\pi\)
\(12\) 0 0
\(13\) −1.02843 −0.285234 −0.142617 0.989778i \(-0.545552\pi\)
−0.142617 + 0.989778i \(0.545552\pi\)
\(14\) 0 0
\(15\) 2.36518 0.610688
\(16\) 0 0
\(17\) 3.65416 0.886264 0.443132 0.896456i \(-0.353867\pi\)
0.443132 + 0.896456i \(0.353867\pi\)
\(18\) 0 0
\(19\) 3.51928 0.807378 0.403689 0.914896i \(-0.367728\pi\)
0.403689 + 0.914896i \(0.367728\pi\)
\(20\) 0 0
\(21\) 10.8378 2.36500
\(22\) 0 0
\(23\) 4.04783 0.844031 0.422015 0.906589i \(-0.361323\pi\)
0.422015 + 0.906589i \(0.361323\pi\)
\(24\) 0 0
\(25\) −4.36933 −0.873866
\(26\) 0 0
\(27\) −8.54776 −1.64502
\(28\) 0 0
\(29\) 2.95252 0.548269 0.274135 0.961691i \(-0.411609\pi\)
0.274135 + 0.961691i \(0.411609\pi\)
\(30\) 0 0
\(31\) −3.73972 −0.671673 −0.335837 0.941920i \(-0.609019\pi\)
−0.335837 + 0.941920i \(0.609019\pi\)
\(32\) 0 0
\(33\) 2.00760 0.349479
\(34\) 0 0
\(35\) 2.88987 0.488478
\(36\) 0 0
\(37\) 3.30857 0.543926 0.271963 0.962308i \(-0.412327\pi\)
0.271963 + 0.962308i \(0.412327\pi\)
\(38\) 0 0
\(39\) 3.06292 0.490460
\(40\) 0 0
\(41\) −12.0974 −1.88929 −0.944646 0.328090i \(-0.893595\pi\)
−0.944646 + 0.328090i \(0.893595\pi\)
\(42\) 0 0
\(43\) −1.05637 −0.161095 −0.0805475 0.996751i \(-0.525667\pi\)
−0.0805475 + 0.996751i \(0.525667\pi\)
\(44\) 0 0
\(45\) −4.66169 −0.694924
\(46\) 0 0
\(47\) −6.46297 −0.942721 −0.471361 0.881941i \(-0.656237\pi\)
−0.471361 + 0.881941i \(0.656237\pi\)
\(48\) 0 0
\(49\) 6.24201 0.891715
\(50\) 0 0
\(51\) −10.8831 −1.52393
\(52\) 0 0
\(53\) 2.27933 0.313090 0.156545 0.987671i \(-0.449964\pi\)
0.156545 + 0.987671i \(0.449964\pi\)
\(54\) 0 0
\(55\) 0.535324 0.0721831
\(56\) 0 0
\(57\) −10.4813 −1.38829
\(58\) 0 0
\(59\) −14.8230 −1.92979 −0.964896 0.262633i \(-0.915409\pi\)
−0.964896 + 0.262633i \(0.915409\pi\)
\(60\) 0 0
\(61\) −6.97730 −0.893351 −0.446676 0.894696i \(-0.647392\pi\)
−0.446676 + 0.894696i \(0.647392\pi\)
\(62\) 0 0
\(63\) −21.3609 −2.69121
\(64\) 0 0
\(65\) 0.816724 0.101302
\(66\) 0 0
\(67\) −12.8224 −1.56650 −0.783250 0.621707i \(-0.786440\pi\)
−0.783250 + 0.621707i \(0.786440\pi\)
\(68\) 0 0
\(69\) −12.0555 −1.45131
\(70\) 0 0
\(71\) −3.34117 −0.396523 −0.198262 0.980149i \(-0.563530\pi\)
−0.198262 + 0.980149i \(0.563530\pi\)
\(72\) 0 0
\(73\) 13.2862 1.55503 0.777516 0.628863i \(-0.216479\pi\)
0.777516 + 0.628863i \(0.216479\pi\)
\(74\) 0 0
\(75\) 13.0130 1.50261
\(76\) 0 0
\(77\) 2.45297 0.279541
\(78\) 0 0
\(79\) −15.7620 −1.77336 −0.886679 0.462385i \(-0.846994\pi\)
−0.886679 + 0.462385i \(0.846994\pi\)
\(80\) 0 0
\(81\) 7.84734 0.871926
\(82\) 0 0
\(83\) 8.63077 0.947350 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(84\) 0 0
\(85\) −2.90195 −0.314760
\(86\) 0 0
\(87\) −8.79338 −0.942749
\(88\) 0 0
\(89\) 8.61968 0.913684 0.456842 0.889548i \(-0.348980\pi\)
0.456842 + 0.889548i \(0.348980\pi\)
\(90\) 0 0
\(91\) 3.74240 0.392310
\(92\) 0 0
\(93\) 11.1379 1.15494
\(94\) 0 0
\(95\) −2.79483 −0.286744
\(96\) 0 0
\(97\) 13.8912 1.41044 0.705219 0.708989i \(-0.250849\pi\)
0.705219 + 0.708989i \(0.250849\pi\)
\(98\) 0 0
\(99\) −3.95691 −0.397685
\(100\) 0 0
\(101\) 18.3869 1.82957 0.914784 0.403943i \(-0.132361\pi\)
0.914784 + 0.403943i \(0.132361\pi\)
\(102\) 0 0
\(103\) 2.57401 0.253624 0.126812 0.991927i \(-0.459525\pi\)
0.126812 + 0.991927i \(0.459525\pi\)
\(104\) 0 0
\(105\) −8.60680 −0.839938
\(106\) 0 0
\(107\) 1.04842 0.101355 0.0506774 0.998715i \(-0.483862\pi\)
0.0506774 + 0.998715i \(0.483862\pi\)
\(108\) 0 0
\(109\) −0.281841 −0.0269955 −0.0134977 0.999909i \(-0.504297\pi\)
−0.0134977 + 0.999909i \(0.504297\pi\)
\(110\) 0 0
\(111\) −9.85380 −0.935281
\(112\) 0 0
\(113\) −0.371691 −0.0349658 −0.0174829 0.999847i \(-0.505565\pi\)
−0.0174829 + 0.999847i \(0.505565\pi\)
\(114\) 0 0
\(115\) −3.21458 −0.299761
\(116\) 0 0
\(117\) −6.03691 −0.558113
\(118\) 0 0
\(119\) −13.2973 −1.21896
\(120\) 0 0
\(121\) −10.5456 −0.958692
\(122\) 0 0
\(123\) 36.0292 3.24864
\(124\) 0 0
\(125\) 7.44064 0.665511
\(126\) 0 0
\(127\) −4.08332 −0.362336 −0.181168 0.983452i \(-0.557988\pi\)
−0.181168 + 0.983452i \(0.557988\pi\)
\(128\) 0 0
\(129\) 3.14615 0.277003
\(130\) 0 0
\(131\) −16.6139 −1.45156 −0.725782 0.687924i \(-0.758522\pi\)
−0.725782 + 0.687924i \(0.758522\pi\)
\(132\) 0 0
\(133\) −12.8065 −1.11046
\(134\) 0 0
\(135\) 6.78820 0.584235
\(136\) 0 0
\(137\) −22.5413 −1.92584 −0.962918 0.269794i \(-0.913044\pi\)
−0.962918 + 0.269794i \(0.913044\pi\)
\(138\) 0 0
\(139\) 18.3102 1.55305 0.776526 0.630086i \(-0.216980\pi\)
0.776526 + 0.630086i \(0.216980\pi\)
\(140\) 0 0
\(141\) 19.2484 1.62101
\(142\) 0 0
\(143\) 0.693247 0.0579722
\(144\) 0 0
\(145\) −2.34474 −0.194720
\(146\) 0 0
\(147\) −18.5903 −1.53330
\(148\) 0 0
\(149\) 13.7808 1.12897 0.564486 0.825443i \(-0.309075\pi\)
0.564486 + 0.825443i \(0.309075\pi\)
\(150\) 0 0
\(151\) −11.7703 −0.957856 −0.478928 0.877854i \(-0.658975\pi\)
−0.478928 + 0.877854i \(0.658975\pi\)
\(152\) 0 0
\(153\) 21.4501 1.73414
\(154\) 0 0
\(155\) 2.96989 0.238548
\(156\) 0 0
\(157\) −19.0243 −1.51830 −0.759150 0.650915i \(-0.774385\pi\)
−0.759150 + 0.650915i \(0.774385\pi\)
\(158\) 0 0
\(159\) −6.78845 −0.538359
\(160\) 0 0
\(161\) −14.7299 −1.16088
\(162\) 0 0
\(163\) −10.1480 −0.794854 −0.397427 0.917634i \(-0.630097\pi\)
−0.397427 + 0.917634i \(0.630097\pi\)
\(164\) 0 0
\(165\) −1.59434 −0.124119
\(166\) 0 0
\(167\) 13.5569 1.04907 0.524534 0.851390i \(-0.324240\pi\)
0.524534 + 0.851390i \(0.324240\pi\)
\(168\) 0 0
\(169\) −11.9423 −0.918642
\(170\) 0 0
\(171\) 20.6583 1.57978
\(172\) 0 0
\(173\) 19.4368 1.47775 0.738875 0.673843i \(-0.235357\pi\)
0.738875 + 0.673843i \(0.235357\pi\)
\(174\) 0 0
\(175\) 15.8998 1.20191
\(176\) 0 0
\(177\) 44.1468 3.31828
\(178\) 0 0
\(179\) −11.3997 −0.852051 −0.426025 0.904711i \(-0.640087\pi\)
−0.426025 + 0.904711i \(0.640087\pi\)
\(180\) 0 0
\(181\) −23.5225 −1.74842 −0.874208 0.485552i \(-0.838619\pi\)
−0.874208 + 0.485552i \(0.838619\pi\)
\(182\) 0 0
\(183\) 20.7802 1.53612
\(184\) 0 0
\(185\) −2.62750 −0.193178
\(186\) 0 0
\(187\) −2.46322 −0.180128
\(188\) 0 0
\(189\) 31.1049 2.26255
\(190\) 0 0
\(191\) −8.92852 −0.646045 −0.323022 0.946391i \(-0.604699\pi\)
−0.323022 + 0.946391i \(0.604699\pi\)
\(192\) 0 0
\(193\) 2.02084 0.145463 0.0727315 0.997352i \(-0.476828\pi\)
0.0727315 + 0.997352i \(0.476828\pi\)
\(194\) 0 0
\(195\) −2.43242 −0.174189
\(196\) 0 0
\(197\) 9.92643 0.707229 0.353615 0.935391i \(-0.384952\pi\)
0.353615 + 0.935391i \(0.384952\pi\)
\(198\) 0 0
\(199\) −17.7531 −1.25849 −0.629244 0.777208i \(-0.716635\pi\)
−0.629244 + 0.777208i \(0.716635\pi\)
\(200\) 0 0
\(201\) 38.1883 2.69360
\(202\) 0 0
\(203\) −10.7441 −0.754087
\(204\) 0 0
\(205\) 9.60712 0.670990
\(206\) 0 0
\(207\) 23.7610 1.65150
\(208\) 0 0
\(209\) −2.37229 −0.164095
\(210\) 0 0
\(211\) 25.3158 1.74281 0.871406 0.490563i \(-0.163209\pi\)
0.871406 + 0.490563i \(0.163209\pi\)
\(212\) 0 0
\(213\) 9.95087 0.681822
\(214\) 0 0
\(215\) 0.838916 0.0572136
\(216\) 0 0
\(217\) 13.6087 0.923817
\(218\) 0 0
\(219\) −39.5698 −2.67388
\(220\) 0 0
\(221\) −3.75804 −0.252793
\(222\) 0 0
\(223\) 18.7341 1.25453 0.627265 0.778806i \(-0.284174\pi\)
0.627265 + 0.778806i \(0.284174\pi\)
\(224\) 0 0
\(225\) −25.6482 −1.70988
\(226\) 0 0
\(227\) 11.4194 0.757932 0.378966 0.925411i \(-0.376280\pi\)
0.378966 + 0.925411i \(0.376280\pi\)
\(228\) 0 0
\(229\) 1.67879 0.110938 0.0554689 0.998460i \(-0.482335\pi\)
0.0554689 + 0.998460i \(0.482335\pi\)
\(230\) 0 0
\(231\) −7.30558 −0.480672
\(232\) 0 0
\(233\) 1.11739 0.0732026 0.0366013 0.999330i \(-0.488347\pi\)
0.0366013 + 0.999330i \(0.488347\pi\)
\(234\) 0 0
\(235\) 5.13256 0.334811
\(236\) 0 0
\(237\) 46.9433 3.04929
\(238\) 0 0
\(239\) 27.3842 1.77134 0.885669 0.464318i \(-0.153700\pi\)
0.885669 + 0.464318i \(0.153700\pi\)
\(240\) 0 0
\(241\) −1.17894 −0.0759423 −0.0379712 0.999279i \(-0.512090\pi\)
−0.0379712 + 0.999279i \(0.512090\pi\)
\(242\) 0 0
\(243\) 2.27186 0.145740
\(244\) 0 0
\(245\) −4.95708 −0.316696
\(246\) 0 0
\(247\) −3.61932 −0.230292
\(248\) 0 0
\(249\) −25.7047 −1.62897
\(250\) 0 0
\(251\) 24.8123 1.56614 0.783068 0.621936i \(-0.213653\pi\)
0.783068 + 0.621936i \(0.213653\pi\)
\(252\) 0 0
\(253\) −2.72858 −0.171544
\(254\) 0 0
\(255\) 8.64277 0.541231
\(256\) 0 0
\(257\) −3.30502 −0.206162 −0.103081 0.994673i \(-0.532870\pi\)
−0.103081 + 0.994673i \(0.532870\pi\)
\(258\) 0 0
\(259\) −12.0397 −0.748114
\(260\) 0 0
\(261\) 17.3314 1.07279
\(262\) 0 0
\(263\) −12.1592 −0.749769 −0.374884 0.927072i \(-0.622318\pi\)
−0.374884 + 0.927072i \(0.622318\pi\)
\(264\) 0 0
\(265\) −1.81013 −0.111195
\(266\) 0 0
\(267\) −25.6717 −1.57108
\(268\) 0 0
\(269\) 13.2356 0.806988 0.403494 0.914982i \(-0.367796\pi\)
0.403494 + 0.914982i \(0.367796\pi\)
\(270\) 0 0
\(271\) −3.84027 −0.233280 −0.116640 0.993174i \(-0.537212\pi\)
−0.116640 + 0.993174i \(0.537212\pi\)
\(272\) 0 0
\(273\) −11.1458 −0.674577
\(274\) 0 0
\(275\) 2.94530 0.177608
\(276\) 0 0
\(277\) −6.44068 −0.386983 −0.193491 0.981102i \(-0.561981\pi\)
−0.193491 + 0.981102i \(0.561981\pi\)
\(278\) 0 0
\(279\) −21.9523 −1.31425
\(280\) 0 0
\(281\) −17.4304 −1.03981 −0.519904 0.854224i \(-0.674032\pi\)
−0.519904 + 0.854224i \(0.674032\pi\)
\(282\) 0 0
\(283\) 2.81014 0.167045 0.0835227 0.996506i \(-0.473383\pi\)
0.0835227 + 0.996506i \(0.473383\pi\)
\(284\) 0 0
\(285\) 8.32374 0.493056
\(286\) 0 0
\(287\) 44.0218 2.59853
\(288\) 0 0
\(289\) −3.64710 −0.214535
\(290\) 0 0
\(291\) −41.3717 −2.42525
\(292\) 0 0
\(293\) 24.3123 1.42034 0.710168 0.704032i \(-0.248619\pi\)
0.710168 + 0.704032i \(0.248619\pi\)
\(294\) 0 0
\(295\) 11.7717 0.685374
\(296\) 0 0
\(297\) 5.76192 0.334340
\(298\) 0 0
\(299\) −4.16289 −0.240746
\(300\) 0 0
\(301\) 3.84409 0.221570
\(302\) 0 0
\(303\) −54.7611 −3.14594
\(304\) 0 0
\(305\) 5.54101 0.317277
\(306\) 0 0
\(307\) 9.76945 0.557572 0.278786 0.960353i \(-0.410068\pi\)
0.278786 + 0.960353i \(0.410068\pi\)
\(308\) 0 0
\(309\) −7.66607 −0.436107
\(310\) 0 0
\(311\) 8.77584 0.497632 0.248816 0.968551i \(-0.419959\pi\)
0.248816 + 0.968551i \(0.419959\pi\)
\(312\) 0 0
\(313\) −21.1371 −1.19474 −0.597369 0.801967i \(-0.703787\pi\)
−0.597369 + 0.801967i \(0.703787\pi\)
\(314\) 0 0
\(315\) 16.9637 0.955796
\(316\) 0 0
\(317\) −3.01533 −0.169358 −0.0846788 0.996408i \(-0.526986\pi\)
−0.0846788 + 0.996408i \(0.526986\pi\)
\(318\) 0 0
\(319\) −1.99025 −0.111433
\(320\) 0 0
\(321\) −3.12248 −0.174280
\(322\) 0 0
\(323\) 12.8600 0.715550
\(324\) 0 0
\(325\) 4.49353 0.249256
\(326\) 0 0
\(327\) 0.839396 0.0464187
\(328\) 0 0
\(329\) 23.5185 1.29662
\(330\) 0 0
\(331\) 10.6238 0.583938 0.291969 0.956428i \(-0.405690\pi\)
0.291969 + 0.956428i \(0.405690\pi\)
\(332\) 0 0
\(333\) 19.4215 1.06429
\(334\) 0 0
\(335\) 10.1829 0.556349
\(336\) 0 0
\(337\) 24.9753 1.36049 0.680246 0.732984i \(-0.261873\pi\)
0.680246 + 0.732984i \(0.261873\pi\)
\(338\) 0 0
\(339\) 1.10699 0.0601237
\(340\) 0 0
\(341\) 2.52089 0.136514
\(342\) 0 0
\(343\) 2.75831 0.148935
\(344\) 0 0
\(345\) 9.57386 0.515439
\(346\) 0 0
\(347\) 4.78427 0.256833 0.128417 0.991720i \(-0.459011\pi\)
0.128417 + 0.991720i \(0.459011\pi\)
\(348\) 0 0
\(349\) 17.1674 0.918949 0.459474 0.888191i \(-0.348038\pi\)
0.459474 + 0.888191i \(0.348038\pi\)
\(350\) 0 0
\(351\) 8.79074 0.469215
\(352\) 0 0
\(353\) −34.5313 −1.83792 −0.918958 0.394356i \(-0.870968\pi\)
−0.918958 + 0.394356i \(0.870968\pi\)
\(354\) 0 0
\(355\) 2.65338 0.140827
\(356\) 0 0
\(357\) 39.6030 2.09601
\(358\) 0 0
\(359\) 23.1325 1.22089 0.610444 0.792059i \(-0.290991\pi\)
0.610444 + 0.792059i \(0.290991\pi\)
\(360\) 0 0
\(361\) −6.61468 −0.348141
\(362\) 0 0
\(363\) 31.4076 1.64847
\(364\) 0 0
\(365\) −10.5512 −0.552276
\(366\) 0 0
\(367\) 11.5508 0.602949 0.301474 0.953474i \(-0.402521\pi\)
0.301474 + 0.953474i \(0.402521\pi\)
\(368\) 0 0
\(369\) −71.0122 −3.69675
\(370\) 0 0
\(371\) −8.29439 −0.430623
\(372\) 0 0
\(373\) 36.2752 1.87826 0.939130 0.343563i \(-0.111634\pi\)
0.939130 + 0.343563i \(0.111634\pi\)
\(374\) 0 0
\(375\) −22.1602 −1.14435
\(376\) 0 0
\(377\) −3.03645 −0.156385
\(378\) 0 0
\(379\) −29.6449 −1.52275 −0.761377 0.648309i \(-0.775477\pi\)
−0.761377 + 0.648309i \(0.775477\pi\)
\(380\) 0 0
\(381\) 12.1612 0.623037
\(382\) 0 0
\(383\) −17.8011 −0.909596 −0.454798 0.890595i \(-0.650289\pi\)
−0.454798 + 0.890595i \(0.650289\pi\)
\(384\) 0 0
\(385\) −1.94802 −0.0992803
\(386\) 0 0
\(387\) −6.20095 −0.315212
\(388\) 0 0
\(389\) −36.2806 −1.83950 −0.919751 0.392503i \(-0.871609\pi\)
−0.919751 + 0.392503i \(0.871609\pi\)
\(390\) 0 0
\(391\) 14.7914 0.748034
\(392\) 0 0
\(393\) 49.4806 2.49597
\(394\) 0 0
\(395\) 12.5173 0.629816
\(396\) 0 0
\(397\) 28.7250 1.44167 0.720833 0.693109i \(-0.243759\pi\)
0.720833 + 0.693109i \(0.243759\pi\)
\(398\) 0 0
\(399\) 38.1411 1.90944
\(400\) 0 0
\(401\) 0.316301 0.0157953 0.00789766 0.999969i \(-0.497486\pi\)
0.00789766 + 0.999969i \(0.497486\pi\)
\(402\) 0 0
\(403\) 3.84603 0.191584
\(404\) 0 0
\(405\) −6.23195 −0.309668
\(406\) 0 0
\(407\) −2.23026 −0.110550
\(408\) 0 0
\(409\) 15.0906 0.746180 0.373090 0.927795i \(-0.378298\pi\)
0.373090 + 0.927795i \(0.378298\pi\)
\(410\) 0 0
\(411\) 67.1340 3.31148
\(412\) 0 0
\(413\) 53.9403 2.65423
\(414\) 0 0
\(415\) −6.85412 −0.336455
\(416\) 0 0
\(417\) −54.5326 −2.67047
\(418\) 0 0
\(419\) 6.77733 0.331094 0.165547 0.986202i \(-0.447061\pi\)
0.165547 + 0.986202i \(0.447061\pi\)
\(420\) 0 0
\(421\) 9.18722 0.447758 0.223879 0.974617i \(-0.428128\pi\)
0.223879 + 0.974617i \(0.428128\pi\)
\(422\) 0 0
\(423\) −37.9380 −1.84461
\(424\) 0 0
\(425\) −15.9662 −0.774476
\(426\) 0 0
\(427\) 25.3901 1.22871
\(428\) 0 0
\(429\) −2.06467 −0.0996833
\(430\) 0 0
\(431\) −7.70399 −0.371088 −0.185544 0.982636i \(-0.559405\pi\)
−0.185544 + 0.982636i \(0.559405\pi\)
\(432\) 0 0
\(433\) −24.8136 −1.19247 −0.596234 0.802811i \(-0.703337\pi\)
−0.596234 + 0.802811i \(0.703337\pi\)
\(434\) 0 0
\(435\) 6.98325 0.334821
\(436\) 0 0
\(437\) 14.2454 0.681452
\(438\) 0 0
\(439\) 21.4745 1.02492 0.512461 0.858710i \(-0.328734\pi\)
0.512461 + 0.858710i \(0.328734\pi\)
\(440\) 0 0
\(441\) 36.6409 1.74480
\(442\) 0 0
\(443\) −7.32253 −0.347904 −0.173952 0.984754i \(-0.555654\pi\)
−0.173952 + 0.984754i \(0.555654\pi\)
\(444\) 0 0
\(445\) −6.84531 −0.324499
\(446\) 0 0
\(447\) −41.0430 −1.94127
\(448\) 0 0
\(449\) −3.94124 −0.185999 −0.0929994 0.995666i \(-0.529645\pi\)
−0.0929994 + 0.995666i \(0.529645\pi\)
\(450\) 0 0
\(451\) 8.15466 0.383988
\(452\) 0 0
\(453\) 35.0551 1.64703
\(454\) 0 0
\(455\) −2.97202 −0.139331
\(456\) 0 0
\(457\) −37.2086 −1.74054 −0.870272 0.492571i \(-0.836057\pi\)
−0.870272 + 0.492571i \(0.836057\pi\)
\(458\) 0 0
\(459\) −31.2349 −1.45792
\(460\) 0 0
\(461\) −14.0239 −0.653159 −0.326579 0.945170i \(-0.605896\pi\)
−0.326579 + 0.945170i \(0.605896\pi\)
\(462\) 0 0
\(463\) 35.6643 1.65746 0.828730 0.559649i \(-0.189064\pi\)
0.828730 + 0.559649i \(0.189064\pi\)
\(464\) 0 0
\(465\) −8.84512 −0.410183
\(466\) 0 0
\(467\) 4.20947 0.194791 0.0973956 0.995246i \(-0.468949\pi\)
0.0973956 + 0.995246i \(0.468949\pi\)
\(468\) 0 0
\(469\) 46.6600 2.15456
\(470\) 0 0
\(471\) 56.6592 2.61072
\(472\) 0 0
\(473\) 0.712084 0.0327417
\(474\) 0 0
\(475\) −15.3769 −0.705540
\(476\) 0 0
\(477\) 13.3798 0.612619
\(478\) 0 0
\(479\) 17.6113 0.804682 0.402341 0.915490i \(-0.368197\pi\)
0.402341 + 0.915490i \(0.368197\pi\)
\(480\) 0 0
\(481\) −3.40262 −0.155146
\(482\) 0 0
\(483\) 43.8694 1.99613
\(484\) 0 0
\(485\) −11.0317 −0.500923
\(486\) 0 0
\(487\) 19.3114 0.875081 0.437541 0.899199i \(-0.355850\pi\)
0.437541 + 0.899199i \(0.355850\pi\)
\(488\) 0 0
\(489\) 30.2235 1.36675
\(490\) 0 0
\(491\) 13.5411 0.611099 0.305550 0.952176i \(-0.401160\pi\)
0.305550 + 0.952176i \(0.401160\pi\)
\(492\) 0 0
\(493\) 10.7890 0.485911
\(494\) 0 0
\(495\) 3.14238 0.141239
\(496\) 0 0
\(497\) 12.1584 0.545377
\(498\) 0 0
\(499\) 16.7939 0.751796 0.375898 0.926661i \(-0.377334\pi\)
0.375898 + 0.926661i \(0.377334\pi\)
\(500\) 0 0
\(501\) −40.3761 −1.80387
\(502\) 0 0
\(503\) −9.61359 −0.428649 −0.214324 0.976763i \(-0.568755\pi\)
−0.214324 + 0.976763i \(0.568755\pi\)
\(504\) 0 0
\(505\) −14.6020 −0.649779
\(506\) 0 0
\(507\) 35.5674 1.57960
\(508\) 0 0
\(509\) −22.1395 −0.981315 −0.490657 0.871353i \(-0.663243\pi\)
−0.490657 + 0.871353i \(0.663243\pi\)
\(510\) 0 0
\(511\) −48.3479 −2.13879
\(512\) 0 0
\(513\) −30.0820 −1.32815
\(514\) 0 0
\(515\) −2.04415 −0.0900758
\(516\) 0 0
\(517\) 4.35659 0.191603
\(518\) 0 0
\(519\) −57.8878 −2.54099
\(520\) 0 0
\(521\) 23.9418 1.04891 0.524456 0.851438i \(-0.324269\pi\)
0.524456 + 0.851438i \(0.324269\pi\)
\(522\) 0 0
\(523\) 25.7322 1.12519 0.562595 0.826733i \(-0.309803\pi\)
0.562595 + 0.826733i \(0.309803\pi\)
\(524\) 0 0
\(525\) −47.3538 −2.06669
\(526\) 0 0
\(527\) −13.6655 −0.595280
\(528\) 0 0
\(529\) −6.61508 −0.287612
\(530\) 0 0
\(531\) −87.0118 −3.77599
\(532\) 0 0
\(533\) 12.4413 0.538891
\(534\) 0 0
\(535\) −0.832603 −0.0359966
\(536\) 0 0
\(537\) 33.9512 1.46510
\(538\) 0 0
\(539\) −4.20764 −0.181236
\(540\) 0 0
\(541\) −33.0623 −1.42146 −0.710730 0.703465i \(-0.751635\pi\)
−0.710730 + 0.703465i \(0.751635\pi\)
\(542\) 0 0
\(543\) 70.0563 3.00640
\(544\) 0 0
\(545\) 0.223824 0.00958755
\(546\) 0 0
\(547\) 34.2049 1.46250 0.731249 0.682111i \(-0.238938\pi\)
0.731249 + 0.682111i \(0.238938\pi\)
\(548\) 0 0
\(549\) −40.9571 −1.74801
\(550\) 0 0
\(551\) 10.3907 0.442660
\(552\) 0 0
\(553\) 57.3571 2.43907
\(554\) 0 0
\(555\) 7.82538 0.332169
\(556\) 0 0
\(557\) 29.8896 1.26646 0.633231 0.773963i \(-0.281728\pi\)
0.633231 + 0.773963i \(0.281728\pi\)
\(558\) 0 0
\(559\) 1.08640 0.0459498
\(560\) 0 0
\(561\) 7.33610 0.309731
\(562\) 0 0
\(563\) 17.6079 0.742087 0.371043 0.928616i \(-0.379000\pi\)
0.371043 + 0.928616i \(0.379000\pi\)
\(564\) 0 0
\(565\) 0.295178 0.0124182
\(566\) 0 0
\(567\) −28.5561 −1.19924
\(568\) 0 0
\(569\) 25.6068 1.07349 0.536746 0.843744i \(-0.319653\pi\)
0.536746 + 0.843744i \(0.319653\pi\)
\(570\) 0 0
\(571\) −3.81141 −0.159503 −0.0797514 0.996815i \(-0.525413\pi\)
−0.0797514 + 0.996815i \(0.525413\pi\)
\(572\) 0 0
\(573\) 26.5915 1.11087
\(574\) 0 0
\(575\) −17.6863 −0.737569
\(576\) 0 0
\(577\) 22.1253 0.921088 0.460544 0.887637i \(-0.347654\pi\)
0.460544 + 0.887637i \(0.347654\pi\)
\(578\) 0 0
\(579\) −6.01858 −0.250124
\(580\) 0 0
\(581\) −31.4070 −1.30298
\(582\) 0 0
\(583\) −1.53646 −0.0636338
\(584\) 0 0
\(585\) 4.79421 0.198216
\(586\) 0 0
\(587\) −27.1289 −1.11973 −0.559865 0.828584i \(-0.689147\pi\)
−0.559865 + 0.828584i \(0.689147\pi\)
\(588\) 0 0
\(589\) −13.1611 −0.542294
\(590\) 0 0
\(591\) −29.5635 −1.21608
\(592\) 0 0
\(593\) 11.7915 0.484220 0.242110 0.970249i \(-0.422160\pi\)
0.242110 + 0.970249i \(0.422160\pi\)
\(594\) 0 0
\(595\) 10.5601 0.432920
\(596\) 0 0
\(597\) 52.8735 2.16397
\(598\) 0 0
\(599\) 2.26400 0.0925045 0.0462523 0.998930i \(-0.485272\pi\)
0.0462523 + 0.998930i \(0.485272\pi\)
\(600\) 0 0
\(601\) −6.81460 −0.277973 −0.138987 0.990294i \(-0.544385\pi\)
−0.138987 + 0.990294i \(0.544385\pi\)
\(602\) 0 0
\(603\) −75.2679 −3.06514
\(604\) 0 0
\(605\) 8.37478 0.340483
\(606\) 0 0
\(607\) −10.9269 −0.443509 −0.221754 0.975103i \(-0.571178\pi\)
−0.221754 + 0.975103i \(0.571178\pi\)
\(608\) 0 0
\(609\) 31.9987 1.29665
\(610\) 0 0
\(611\) 6.64669 0.268896
\(612\) 0 0
\(613\) 36.4841 1.47358 0.736790 0.676122i \(-0.236341\pi\)
0.736790 + 0.676122i \(0.236341\pi\)
\(614\) 0 0
\(615\) −28.6125 −1.15377
\(616\) 0 0
\(617\) −26.5517 −1.06893 −0.534465 0.845190i \(-0.679487\pi\)
−0.534465 + 0.845190i \(0.679487\pi\)
\(618\) 0 0
\(619\) −29.2059 −1.17388 −0.586942 0.809629i \(-0.699668\pi\)
−0.586942 + 0.809629i \(0.699668\pi\)
\(620\) 0 0
\(621\) −34.5999 −1.38845
\(622\) 0 0
\(623\) −31.3666 −1.25668
\(624\) 0 0
\(625\) 15.9377 0.637506
\(626\) 0 0
\(627\) 7.06531 0.282161
\(628\) 0 0
\(629\) 12.0901 0.482062
\(630\) 0 0
\(631\) 20.2857 0.807560 0.403780 0.914856i \(-0.367696\pi\)
0.403780 + 0.914856i \(0.367696\pi\)
\(632\) 0 0
\(633\) −75.3971 −2.99677
\(634\) 0 0
\(635\) 3.24276 0.128685
\(636\) 0 0
\(637\) −6.41944 −0.254348
\(638\) 0 0
\(639\) −19.6128 −0.775871
\(640\) 0 0
\(641\) 2.84368 0.112318 0.0561592 0.998422i \(-0.482115\pi\)
0.0561592 + 0.998422i \(0.482115\pi\)
\(642\) 0 0
\(643\) 18.3771 0.724722 0.362361 0.932038i \(-0.381971\pi\)
0.362361 + 0.932038i \(0.381971\pi\)
\(644\) 0 0
\(645\) −2.49851 −0.0983788
\(646\) 0 0
\(647\) −49.8807 −1.96101 −0.980507 0.196483i \(-0.937048\pi\)
−0.980507 + 0.196483i \(0.937048\pi\)
\(648\) 0 0
\(649\) 9.99197 0.392219
\(650\) 0 0
\(651\) −40.5302 −1.58850
\(652\) 0 0
\(653\) −8.82773 −0.345456 −0.172728 0.984970i \(-0.555258\pi\)
−0.172728 + 0.984970i \(0.555258\pi\)
\(654\) 0 0
\(655\) 13.1939 0.515529
\(656\) 0 0
\(657\) 77.9906 3.04270
\(658\) 0 0
\(659\) −18.0733 −0.704037 −0.352018 0.935993i \(-0.614505\pi\)
−0.352018 + 0.935993i \(0.614505\pi\)
\(660\) 0 0
\(661\) 16.5209 0.642589 0.321294 0.946979i \(-0.395882\pi\)
0.321294 + 0.946979i \(0.395882\pi\)
\(662\) 0 0
\(663\) 11.1924 0.434677
\(664\) 0 0
\(665\) 10.1703 0.394386
\(666\) 0 0
\(667\) 11.9513 0.462756
\(668\) 0 0
\(669\) −55.7952 −2.15717
\(670\) 0 0
\(671\) 4.70329 0.181569
\(672\) 0 0
\(673\) 9.45602 0.364503 0.182251 0.983252i \(-0.441662\pi\)
0.182251 + 0.983252i \(0.441662\pi\)
\(674\) 0 0
\(675\) 37.3480 1.43752
\(676\) 0 0
\(677\) −43.1767 −1.65941 −0.829707 0.558199i \(-0.811493\pi\)
−0.829707 + 0.558199i \(0.811493\pi\)
\(678\) 0 0
\(679\) −50.5495 −1.93991
\(680\) 0 0
\(681\) −34.0100 −1.30327
\(682\) 0 0
\(683\) −38.7228 −1.48169 −0.740843 0.671679i \(-0.765574\pi\)
−0.740843 + 0.671679i \(0.765574\pi\)
\(684\) 0 0
\(685\) 17.9012 0.683969
\(686\) 0 0
\(687\) −4.99988 −0.190757
\(688\) 0 0
\(689\) −2.34412 −0.0893040
\(690\) 0 0
\(691\) 26.4221 1.00514 0.502572 0.864535i \(-0.332387\pi\)
0.502572 + 0.864535i \(0.332387\pi\)
\(692\) 0 0
\(693\) 14.3990 0.546974
\(694\) 0 0
\(695\) −14.5410 −0.551573
\(696\) 0 0
\(697\) −44.2058 −1.67441
\(698\) 0 0
\(699\) −3.32788 −0.125872
\(700\) 0 0
\(701\) 9.17771 0.346637 0.173319 0.984866i \(-0.444551\pi\)
0.173319 + 0.984866i \(0.444551\pi\)
\(702\) 0 0
\(703\) 11.6438 0.439154
\(704\) 0 0
\(705\) −15.2861 −0.575709
\(706\) 0 0
\(707\) −66.9093 −2.51638
\(708\) 0 0
\(709\) 23.1965 0.871164 0.435582 0.900149i \(-0.356543\pi\)
0.435582 + 0.900149i \(0.356543\pi\)
\(710\) 0 0
\(711\) −92.5235 −3.46990
\(712\) 0 0
\(713\) −15.1377 −0.566913
\(714\) 0 0
\(715\) −0.550541 −0.0205891
\(716\) 0 0
\(717\) −81.5574 −3.04582
\(718\) 0 0
\(719\) 0.742779 0.0277010 0.0138505 0.999904i \(-0.495591\pi\)
0.0138505 + 0.999904i \(0.495591\pi\)
\(720\) 0 0
\(721\) −9.36670 −0.348834
\(722\) 0 0
\(723\) 3.51120 0.130583
\(724\) 0 0
\(725\) −12.9005 −0.479113
\(726\) 0 0
\(727\) 17.7406 0.657963 0.328981 0.944336i \(-0.393295\pi\)
0.328981 + 0.944336i \(0.393295\pi\)
\(728\) 0 0
\(729\) −30.3082 −1.12253
\(730\) 0 0
\(731\) −3.86015 −0.142773
\(732\) 0 0
\(733\) −22.3181 −0.824339 −0.412170 0.911107i \(-0.635229\pi\)
−0.412170 + 0.911107i \(0.635229\pi\)
\(734\) 0 0
\(735\) 14.7635 0.544560
\(736\) 0 0
\(737\) 8.64336 0.318382
\(738\) 0 0
\(739\) −20.2234 −0.743931 −0.371965 0.928247i \(-0.621316\pi\)
−0.371965 + 0.928247i \(0.621316\pi\)
\(740\) 0 0
\(741\) 10.7793 0.395987
\(742\) 0 0
\(743\) 15.6864 0.575478 0.287739 0.957709i \(-0.407096\pi\)
0.287739 + 0.957709i \(0.407096\pi\)
\(744\) 0 0
\(745\) −10.9440 −0.400959
\(746\) 0 0
\(747\) 50.6630 1.85366
\(748\) 0 0
\(749\) −3.81516 −0.139403
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −73.8975 −2.69297
\(754\) 0 0
\(755\) 9.34740 0.340187
\(756\) 0 0
\(757\) 44.3594 1.61227 0.806135 0.591731i \(-0.201555\pi\)
0.806135 + 0.591731i \(0.201555\pi\)
\(758\) 0 0
\(759\) 8.12643 0.294971
\(760\) 0 0
\(761\) 23.1134 0.837859 0.418930 0.908019i \(-0.362405\pi\)
0.418930 + 0.908019i \(0.362405\pi\)
\(762\) 0 0
\(763\) 1.02561 0.0371295
\(764\) 0 0
\(765\) −17.0346 −0.615887
\(766\) 0 0
\(767\) 15.2444 0.550442
\(768\) 0 0
\(769\) −4.01909 −0.144932 −0.0724661 0.997371i \(-0.523087\pi\)
−0.0724661 + 0.997371i \(0.523087\pi\)
\(770\) 0 0
\(771\) 9.84323 0.354495
\(772\) 0 0
\(773\) 14.8793 0.535170 0.267585 0.963534i \(-0.413774\pi\)
0.267585 + 0.963534i \(0.413774\pi\)
\(774\) 0 0
\(775\) 16.3401 0.586952
\(776\) 0 0
\(777\) 35.8575 1.28638
\(778\) 0 0
\(779\) −42.5740 −1.52537
\(780\) 0 0
\(781\) 2.25223 0.0805911
\(782\) 0 0
\(783\) −25.2374 −0.901912
\(784\) 0 0
\(785\) 15.1081 0.539231
\(786\) 0 0
\(787\) 12.3080 0.438733 0.219366 0.975643i \(-0.429601\pi\)
0.219366 + 0.975643i \(0.429601\pi\)
\(788\) 0 0
\(789\) 36.2133 1.28923
\(790\) 0 0
\(791\) 1.35257 0.0480918
\(792\) 0 0
\(793\) 7.17563 0.254814
\(794\) 0 0
\(795\) 5.39104 0.191201
\(796\) 0 0
\(797\) −6.52092 −0.230983 −0.115491 0.993308i \(-0.536844\pi\)
−0.115491 + 0.993308i \(0.536844\pi\)
\(798\) 0 0
\(799\) −23.6167 −0.835500
\(800\) 0 0
\(801\) 50.5980 1.78779
\(802\) 0 0
\(803\) −8.95603 −0.316051
\(804\) 0 0
\(805\) 11.6977 0.412290
\(806\) 0 0
\(807\) −39.4191 −1.38762
\(808\) 0 0
\(809\) −20.0644 −0.705426 −0.352713 0.935732i \(-0.614741\pi\)
−0.352713 + 0.935732i \(0.614741\pi\)
\(810\) 0 0
\(811\) 17.2658 0.606284 0.303142 0.952945i \(-0.401964\pi\)
0.303142 + 0.952945i \(0.401964\pi\)
\(812\) 0 0
\(813\) 11.4373 0.401125
\(814\) 0 0
\(815\) 8.05904 0.282296
\(816\) 0 0
\(817\) −3.71766 −0.130065
\(818\) 0 0
\(819\) 21.9681 0.767626
\(820\) 0 0
\(821\) 35.5425 1.24044 0.620221 0.784428i \(-0.287043\pi\)
0.620221 + 0.784428i \(0.287043\pi\)
\(822\) 0 0
\(823\) 40.3182 1.40540 0.702702 0.711484i \(-0.251977\pi\)
0.702702 + 0.711484i \(0.251977\pi\)
\(824\) 0 0
\(825\) −8.77187 −0.305397
\(826\) 0 0
\(827\) 26.1404 0.908990 0.454495 0.890749i \(-0.349820\pi\)
0.454495 + 0.890749i \(0.349820\pi\)
\(828\) 0 0
\(829\) 51.5006 1.78869 0.894344 0.447379i \(-0.147643\pi\)
0.894344 + 0.447379i \(0.147643\pi\)
\(830\) 0 0
\(831\) 19.1820 0.665417
\(832\) 0 0
\(833\) 22.8093 0.790295
\(834\) 0 0
\(835\) −10.7662 −0.372581
\(836\) 0 0
\(837\) 31.9662 1.10491
\(838\) 0 0
\(839\) 5.30819 0.183259 0.0916295 0.995793i \(-0.470792\pi\)
0.0916295 + 0.995793i \(0.470792\pi\)
\(840\) 0 0
\(841\) −20.2826 −0.699401
\(842\) 0 0
\(843\) 51.9122 1.78795
\(844\) 0 0
\(845\) 9.48400 0.326259
\(846\) 0 0
\(847\) 38.3750 1.31858
\(848\) 0 0
\(849\) −8.36933 −0.287235
\(850\) 0 0
\(851\) 13.3925 0.459090
\(852\) 0 0
\(853\) −28.7449 −0.984205 −0.492103 0.870537i \(-0.663772\pi\)
−0.492103 + 0.870537i \(0.663772\pi\)
\(854\) 0 0
\(855\) −16.4058 −0.561066
\(856\) 0 0
\(857\) 46.0432 1.57280 0.786402 0.617714i \(-0.211941\pi\)
0.786402 + 0.617714i \(0.211941\pi\)
\(858\) 0 0
\(859\) −12.4321 −0.424177 −0.212089 0.977250i \(-0.568027\pi\)
−0.212089 + 0.977250i \(0.568027\pi\)
\(860\) 0 0
\(861\) −131.109 −4.46817
\(862\) 0 0
\(863\) 2.84583 0.0968732 0.0484366 0.998826i \(-0.484576\pi\)
0.0484366 + 0.998826i \(0.484576\pi\)
\(864\) 0 0
\(865\) −15.4357 −0.524829
\(866\) 0 0
\(867\) 10.8620 0.368894
\(868\) 0 0
\(869\) 10.6249 0.360425
\(870\) 0 0
\(871\) 13.1868 0.446819
\(872\) 0 0
\(873\) 81.5421 2.75978
\(874\) 0 0
\(875\) −27.0762 −0.915342
\(876\) 0 0
\(877\) 9.77392 0.330042 0.165021 0.986290i \(-0.447231\pi\)
0.165021 + 0.986290i \(0.447231\pi\)
\(878\) 0 0
\(879\) −72.4083 −2.44227
\(880\) 0 0
\(881\) 35.7683 1.20507 0.602533 0.798094i \(-0.294158\pi\)
0.602533 + 0.798094i \(0.294158\pi\)
\(882\) 0 0
\(883\) −15.5981 −0.524919 −0.262460 0.964943i \(-0.584534\pi\)
−0.262460 + 0.964943i \(0.584534\pi\)
\(884\) 0 0
\(885\) −35.0592 −1.17850
\(886\) 0 0
\(887\) 25.9717 0.872045 0.436022 0.899936i \(-0.356387\pi\)
0.436022 + 0.899936i \(0.356387\pi\)
\(888\) 0 0
\(889\) 14.8590 0.498355
\(890\) 0 0
\(891\) −5.28977 −0.177214
\(892\) 0 0
\(893\) −22.7450 −0.761132
\(894\) 0 0
\(895\) 9.05303 0.302609
\(896\) 0 0
\(897\) 12.3982 0.413964
\(898\) 0 0
\(899\) −11.0416 −0.368258
\(900\) 0 0
\(901\) 8.32905 0.277481
\(902\) 0 0
\(903\) −11.4487 −0.380989
\(904\) 0 0
\(905\) 18.6804 0.620957
\(906\) 0 0
\(907\) 43.0763 1.43033 0.715163 0.698958i \(-0.246353\pi\)
0.715163 + 0.698958i \(0.246353\pi\)
\(908\) 0 0
\(909\) 107.932 3.57989
\(910\) 0 0
\(911\) −15.4292 −0.511193 −0.255596 0.966784i \(-0.582272\pi\)
−0.255596 + 0.966784i \(0.582272\pi\)
\(912\) 0 0
\(913\) −5.81787 −0.192543
\(914\) 0 0
\(915\) −16.5026 −0.545559
\(916\) 0 0
\(917\) 60.4573 1.99648
\(918\) 0 0
\(919\) 28.8801 0.952667 0.476333 0.879265i \(-0.341966\pi\)
0.476333 + 0.879265i \(0.341966\pi\)
\(920\) 0 0
\(921\) −29.0960 −0.958745
\(922\) 0 0
\(923\) 3.43614 0.113102
\(924\) 0 0
\(925\) −14.4562 −0.475318
\(926\) 0 0
\(927\) 15.1096 0.496263
\(928\) 0 0
\(929\) −14.7303 −0.483286 −0.241643 0.970365i \(-0.577686\pi\)
−0.241643 + 0.970365i \(0.577686\pi\)
\(930\) 0 0
\(931\) 21.9674 0.719951
\(932\) 0 0
\(933\) −26.1368 −0.855679
\(934\) 0 0
\(935\) 1.95616 0.0639733
\(936\) 0 0
\(937\) −25.5827 −0.835751 −0.417876 0.908504i \(-0.637225\pi\)
−0.417876 + 0.908504i \(0.637225\pi\)
\(938\) 0 0
\(939\) 62.9518 2.05435
\(940\) 0 0
\(941\) −17.8800 −0.582872 −0.291436 0.956590i \(-0.594133\pi\)
−0.291436 + 0.956590i \(0.594133\pi\)
\(942\) 0 0
\(943\) −48.9681 −1.59462
\(944\) 0 0
\(945\) −24.7020 −0.803555
\(946\) 0 0
\(947\) 27.0473 0.878921 0.439460 0.898262i \(-0.355170\pi\)
0.439460 + 0.898262i \(0.355170\pi\)
\(948\) 0 0
\(949\) −13.6639 −0.443548
\(950\) 0 0
\(951\) 8.98044 0.291211
\(952\) 0 0
\(953\) −56.3147 −1.82421 −0.912106 0.409955i \(-0.865544\pi\)
−0.912106 + 0.409955i \(0.865544\pi\)
\(954\) 0 0
\(955\) 7.09057 0.229446
\(956\) 0 0
\(957\) 5.92749 0.191608
\(958\) 0 0
\(959\) 82.0269 2.64879
\(960\) 0 0
\(961\) −17.0145 −0.548855
\(962\) 0 0
\(963\) 6.15429 0.198319
\(964\) 0 0
\(965\) −1.60484 −0.0516618
\(966\) 0 0
\(967\) −43.4123 −1.39605 −0.698023 0.716075i \(-0.745937\pi\)
−0.698023 + 0.716075i \(0.745937\pi\)
\(968\) 0 0
\(969\) −38.3005 −1.23039
\(970\) 0 0
\(971\) 24.6853 0.792188 0.396094 0.918210i \(-0.370365\pi\)
0.396094 + 0.918210i \(0.370365\pi\)
\(972\) 0 0
\(973\) −66.6300 −2.13606
\(974\) 0 0
\(975\) −13.3829 −0.428596
\(976\) 0 0
\(977\) 6.17037 0.197408 0.0987039 0.995117i \(-0.468530\pi\)
0.0987039 + 0.995117i \(0.468530\pi\)
\(978\) 0 0
\(979\) −5.81040 −0.185701
\(980\) 0 0
\(981\) −1.65442 −0.0528216
\(982\) 0 0
\(983\) 4.85529 0.154860 0.0774298 0.996998i \(-0.475329\pi\)
0.0774298 + 0.996998i \(0.475329\pi\)
\(984\) 0 0
\(985\) −7.88307 −0.251175
\(986\) 0 0
\(987\) −70.0442 −2.22953
\(988\) 0 0
\(989\) −4.27601 −0.135969
\(990\) 0 0
\(991\) −10.7139 −0.340339 −0.170169 0.985415i \(-0.554431\pi\)
−0.170169 + 0.985415i \(0.554431\pi\)
\(992\) 0 0
\(993\) −31.6405 −1.00408
\(994\) 0 0
\(995\) 14.0986 0.446957
\(996\) 0 0
\(997\) −36.1490 −1.14485 −0.572425 0.819957i \(-0.693997\pi\)
−0.572425 + 0.819957i \(0.693997\pi\)
\(998\) 0 0
\(999\) −28.2809 −0.894768
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 \(a_p\))