Properties

Label 6008.2.a.e.1.19
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 1.19
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.685000 q^{3} +2.14563 q^{5} +4.94928 q^{7} -2.53078 q^{9} +O(q^{10})\) \(q-0.685000 q^{3} +2.14563 q^{5} +4.94928 q^{7} -2.53078 q^{9} +5.84000 q^{11} -0.179952 q^{13} -1.46976 q^{15} +3.12097 q^{17} +1.14439 q^{19} -3.39026 q^{21} -6.64547 q^{23} -0.396256 q^{25} +3.78858 q^{27} +0.232956 q^{29} +7.29442 q^{31} -4.00040 q^{33} +10.6193 q^{35} -5.55468 q^{37} +0.123267 q^{39} +1.51030 q^{41} +2.08398 q^{43} -5.43012 q^{45} +9.61601 q^{47} +17.4954 q^{49} -2.13786 q^{51} +10.2717 q^{53} +12.5305 q^{55} -0.783904 q^{57} -7.92347 q^{59} -0.773842 q^{61} -12.5255 q^{63} -0.386112 q^{65} -7.77866 q^{67} +4.55215 q^{69} +1.12432 q^{71} -10.6802 q^{73} +0.271436 q^{75} +28.9038 q^{77} +3.02508 q^{79} +4.99715 q^{81} +13.8174 q^{83} +6.69646 q^{85} -0.159575 q^{87} -12.5658 q^{89} -0.890634 q^{91} -4.99668 q^{93} +2.45543 q^{95} +6.78459 q^{97} -14.7797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.685000 −0.395485 −0.197742 0.980254i \(-0.563361\pi\)
−0.197742 + 0.980254i \(0.563361\pi\)
\(4\) 0 0
\(5\) 2.14563 0.959557 0.479778 0.877390i \(-0.340717\pi\)
0.479778 + 0.877390i \(0.340717\pi\)
\(6\) 0 0
\(7\) 4.94928 1.87065 0.935326 0.353787i \(-0.115106\pi\)
0.935326 + 0.353787i \(0.115106\pi\)
\(8\) 0 0
\(9\) −2.53078 −0.843592
\(10\) 0 0
\(11\) 5.84000 1.76083 0.880413 0.474208i \(-0.157265\pi\)
0.880413 + 0.474208i \(0.157265\pi\)
\(12\) 0 0
\(13\) −0.179952 −0.0499098 −0.0249549 0.999689i \(-0.507944\pi\)
−0.0249549 + 0.999689i \(0.507944\pi\)
\(14\) 0 0
\(15\) −1.46976 −0.379490
\(16\) 0 0
\(17\) 3.12097 0.756946 0.378473 0.925612i \(-0.376449\pi\)
0.378473 + 0.925612i \(0.376449\pi\)
\(18\) 0 0
\(19\) 1.14439 0.262540 0.131270 0.991347i \(-0.458095\pi\)
0.131270 + 0.991347i \(0.458095\pi\)
\(20\) 0 0
\(21\) −3.39026 −0.739815
\(22\) 0 0
\(23\) −6.64547 −1.38568 −0.692838 0.721093i \(-0.743640\pi\)
−0.692838 + 0.721093i \(0.743640\pi\)
\(24\) 0 0
\(25\) −0.396256 −0.0792513
\(26\) 0 0
\(27\) 3.78858 0.729113
\(28\) 0 0
\(29\) 0.232956 0.0432588 0.0216294 0.999766i \(-0.493115\pi\)
0.0216294 + 0.999766i \(0.493115\pi\)
\(30\) 0 0
\(31\) 7.29442 1.31012 0.655059 0.755578i \(-0.272644\pi\)
0.655059 + 0.755578i \(0.272644\pi\)
\(32\) 0 0
\(33\) −4.00040 −0.696380
\(34\) 0 0
\(35\) 10.6193 1.79500
\(36\) 0 0
\(37\) −5.55468 −0.913184 −0.456592 0.889676i \(-0.650930\pi\)
−0.456592 + 0.889676i \(0.650930\pi\)
\(38\) 0 0
\(39\) 0.123267 0.0197386
\(40\) 0 0
\(41\) 1.51030 0.235868 0.117934 0.993021i \(-0.462373\pi\)
0.117934 + 0.993021i \(0.462373\pi\)
\(42\) 0 0
\(43\) 2.08398 0.317804 0.158902 0.987294i \(-0.449205\pi\)
0.158902 + 0.987294i \(0.449205\pi\)
\(44\) 0 0
\(45\) −5.43012 −0.809474
\(46\) 0 0
\(47\) 9.61601 1.40264 0.701320 0.712847i \(-0.252595\pi\)
0.701320 + 0.712847i \(0.252595\pi\)
\(48\) 0 0
\(49\) 17.4954 2.49934
\(50\) 0 0
\(51\) −2.13786 −0.299361
\(52\) 0 0
\(53\) 10.2717 1.41093 0.705463 0.708747i \(-0.250739\pi\)
0.705463 + 0.708747i \(0.250739\pi\)
\(54\) 0 0
\(55\) 12.5305 1.68961
\(56\) 0 0
\(57\) −0.783904 −0.103831
\(58\) 0 0
\(59\) −7.92347 −1.03155 −0.515774 0.856725i \(-0.672496\pi\)
−0.515774 + 0.856725i \(0.672496\pi\)
\(60\) 0 0
\(61\) −0.773842 −0.0990803 −0.0495401 0.998772i \(-0.515776\pi\)
−0.0495401 + 0.998772i \(0.515776\pi\)
\(62\) 0 0
\(63\) −12.5255 −1.57807
\(64\) 0 0
\(65\) −0.386112 −0.0478913
\(66\) 0 0
\(67\) −7.77866 −0.950314 −0.475157 0.879901i \(-0.657609\pi\)
−0.475157 + 0.879901i \(0.657609\pi\)
\(68\) 0 0
\(69\) 4.55215 0.548014
\(70\) 0 0
\(71\) 1.12432 0.133432 0.0667159 0.997772i \(-0.478748\pi\)
0.0667159 + 0.997772i \(0.478748\pi\)
\(72\) 0 0
\(73\) −10.6802 −1.25003 −0.625013 0.780615i \(-0.714906\pi\)
−0.625013 + 0.780615i \(0.714906\pi\)
\(74\) 0 0
\(75\) 0.271436 0.0313427
\(76\) 0 0
\(77\) 28.9038 3.29389
\(78\) 0 0
\(79\) 3.02508 0.340348 0.170174 0.985414i \(-0.445567\pi\)
0.170174 + 0.985414i \(0.445567\pi\)
\(80\) 0 0
\(81\) 4.99715 0.555239
\(82\) 0 0
\(83\) 13.8174 1.51665 0.758326 0.651875i \(-0.226017\pi\)
0.758326 + 0.651875i \(0.226017\pi\)
\(84\) 0 0
\(85\) 6.69646 0.726333
\(86\) 0 0
\(87\) −0.159575 −0.0171082
\(88\) 0 0
\(89\) −12.5658 −1.33197 −0.665987 0.745963i \(-0.731989\pi\)
−0.665987 + 0.745963i \(0.731989\pi\)
\(90\) 0 0
\(91\) −0.890634 −0.0933639
\(92\) 0 0
\(93\) −4.99668 −0.518132
\(94\) 0 0
\(95\) 2.45543 0.251922
\(96\) 0 0
\(97\) 6.78459 0.688871 0.344436 0.938810i \(-0.388070\pi\)
0.344436 + 0.938810i \(0.388070\pi\)
\(98\) 0 0
\(99\) −14.7797 −1.48542
\(100\) 0 0
\(101\) −2.15273 −0.214204 −0.107102 0.994248i \(-0.534157\pi\)
−0.107102 + 0.994248i \(0.534157\pi\)
\(102\) 0 0
\(103\) 2.33703 0.230274 0.115137 0.993350i \(-0.463269\pi\)
0.115137 + 0.993350i \(0.463269\pi\)
\(104\) 0 0
\(105\) −7.27425 −0.709894
\(106\) 0 0
\(107\) −1.61371 −0.156003 −0.0780014 0.996953i \(-0.524854\pi\)
−0.0780014 + 0.996953i \(0.524854\pi\)
\(108\) 0 0
\(109\) −3.15647 −0.302335 −0.151167 0.988508i \(-0.548303\pi\)
−0.151167 + 0.988508i \(0.548303\pi\)
\(110\) 0 0
\(111\) 3.80496 0.361150
\(112\) 0 0
\(113\) −8.40627 −0.790795 −0.395398 0.918510i \(-0.629393\pi\)
−0.395398 + 0.918510i \(0.629393\pi\)
\(114\) 0 0
\(115\) −14.2587 −1.32963
\(116\) 0 0
\(117\) 0.455419 0.0421035
\(118\) 0 0
\(119\) 15.4466 1.41598
\(120\) 0 0
\(121\) 23.1056 2.10051
\(122\) 0 0
\(123\) −1.03455 −0.0932824
\(124\) 0 0
\(125\) −11.5784 −1.03560
\(126\) 0 0
\(127\) −20.1082 −1.78431 −0.892156 0.451728i \(-0.850808\pi\)
−0.892156 + 0.451728i \(0.850808\pi\)
\(128\) 0 0
\(129\) −1.42753 −0.125687
\(130\) 0 0
\(131\) −19.5208 −1.70554 −0.852769 0.522289i \(-0.825078\pi\)
−0.852769 + 0.522289i \(0.825078\pi\)
\(132\) 0 0
\(133\) 5.66388 0.491121
\(134\) 0 0
\(135\) 8.12891 0.699625
\(136\) 0 0
\(137\) 10.9285 0.933681 0.466840 0.884342i \(-0.345392\pi\)
0.466840 + 0.884342i \(0.345392\pi\)
\(138\) 0 0
\(139\) −8.62610 −0.731657 −0.365828 0.930682i \(-0.619214\pi\)
−0.365828 + 0.930682i \(0.619214\pi\)
\(140\) 0 0
\(141\) −6.58697 −0.554723
\(142\) 0 0
\(143\) −1.05092 −0.0878825
\(144\) 0 0
\(145\) 0.499838 0.0415093
\(146\) 0 0
\(147\) −11.9843 −0.988450
\(148\) 0 0
\(149\) −2.74722 −0.225061 −0.112531 0.993648i \(-0.535896\pi\)
−0.112531 + 0.993648i \(0.535896\pi\)
\(150\) 0 0
\(151\) 17.6361 1.43520 0.717601 0.696455i \(-0.245240\pi\)
0.717601 + 0.696455i \(0.245240\pi\)
\(152\) 0 0
\(153\) −7.89847 −0.638554
\(154\) 0 0
\(155\) 15.6512 1.25713
\(156\) 0 0
\(157\) 18.2560 1.45699 0.728495 0.685051i \(-0.240220\pi\)
0.728495 + 0.685051i \(0.240220\pi\)
\(158\) 0 0
\(159\) −7.03611 −0.558000
\(160\) 0 0
\(161\) −32.8903 −2.59212
\(162\) 0 0
\(163\) −9.78433 −0.766368 −0.383184 0.923672i \(-0.625172\pi\)
−0.383184 + 0.923672i \(0.625172\pi\)
\(164\) 0 0
\(165\) −8.58339 −0.668216
\(166\) 0 0
\(167\) −7.30879 −0.565571 −0.282786 0.959183i \(-0.591259\pi\)
−0.282786 + 0.959183i \(0.591259\pi\)
\(168\) 0 0
\(169\) −12.9676 −0.997509
\(170\) 0 0
\(171\) −2.89618 −0.221477
\(172\) 0 0
\(173\) −2.22954 −0.169508 −0.0847542 0.996402i \(-0.527011\pi\)
−0.0847542 + 0.996402i \(0.527011\pi\)
\(174\) 0 0
\(175\) −1.96118 −0.148252
\(176\) 0 0
\(177\) 5.42758 0.407962
\(178\) 0 0
\(179\) 25.6296 1.91565 0.957825 0.287353i \(-0.0927753\pi\)
0.957825 + 0.287353i \(0.0927753\pi\)
\(180\) 0 0
\(181\) 0.997348 0.0741323 0.0370662 0.999313i \(-0.488199\pi\)
0.0370662 + 0.999313i \(0.488199\pi\)
\(182\) 0 0
\(183\) 0.530081 0.0391847
\(184\) 0 0
\(185\) −11.9183 −0.876252
\(186\) 0 0
\(187\) 18.2265 1.33285
\(188\) 0 0
\(189\) 18.7507 1.36392
\(190\) 0 0
\(191\) −20.3884 −1.47525 −0.737626 0.675210i \(-0.764053\pi\)
−0.737626 + 0.675210i \(0.764053\pi\)
\(192\) 0 0
\(193\) 24.1537 1.73862 0.869312 0.494264i \(-0.164562\pi\)
0.869312 + 0.494264i \(0.164562\pi\)
\(194\) 0 0
\(195\) 0.264487 0.0189403
\(196\) 0 0
\(197\) −22.8243 −1.62617 −0.813083 0.582148i \(-0.802213\pi\)
−0.813083 + 0.582148i \(0.802213\pi\)
\(198\) 0 0
\(199\) −3.18881 −0.226049 −0.113024 0.993592i \(-0.536054\pi\)
−0.113024 + 0.993592i \(0.536054\pi\)
\(200\) 0 0
\(201\) 5.32838 0.375835
\(202\) 0 0
\(203\) 1.15296 0.0809221
\(204\) 0 0
\(205\) 3.24054 0.226329
\(206\) 0 0
\(207\) 16.8182 1.16894
\(208\) 0 0
\(209\) 6.68321 0.462287
\(210\) 0 0
\(211\) −1.22492 −0.0843270 −0.0421635 0.999111i \(-0.513425\pi\)
−0.0421635 + 0.999111i \(0.513425\pi\)
\(212\) 0 0
\(213\) −0.770157 −0.0527703
\(214\) 0 0
\(215\) 4.47146 0.304951
\(216\) 0 0
\(217\) 36.1021 2.45077
\(218\) 0 0
\(219\) 7.31595 0.494366
\(220\) 0 0
\(221\) −0.561626 −0.0377791
\(222\) 0 0
\(223\) −11.9491 −0.800171 −0.400085 0.916478i \(-0.631020\pi\)
−0.400085 + 0.916478i \(0.631020\pi\)
\(224\) 0 0
\(225\) 1.00284 0.0668557
\(226\) 0 0
\(227\) 6.68335 0.443590 0.221795 0.975093i \(-0.428808\pi\)
0.221795 + 0.975093i \(0.428808\pi\)
\(228\) 0 0
\(229\) −3.68476 −0.243496 −0.121748 0.992561i \(-0.538850\pi\)
−0.121748 + 0.992561i \(0.538850\pi\)
\(230\) 0 0
\(231\) −19.7991 −1.30268
\(232\) 0 0
\(233\) 12.3673 0.810209 0.405105 0.914270i \(-0.367235\pi\)
0.405105 + 0.914270i \(0.367235\pi\)
\(234\) 0 0
\(235\) 20.6324 1.34591
\(236\) 0 0
\(237\) −2.07218 −0.134602
\(238\) 0 0
\(239\) −4.19593 −0.271412 −0.135706 0.990749i \(-0.543330\pi\)
−0.135706 + 0.990749i \(0.543330\pi\)
\(240\) 0 0
\(241\) 12.5319 0.807252 0.403626 0.914924i \(-0.367750\pi\)
0.403626 + 0.914924i \(0.367750\pi\)
\(242\) 0 0
\(243\) −14.7888 −0.948701
\(244\) 0 0
\(245\) 37.5386 2.39826
\(246\) 0 0
\(247\) −0.205935 −0.0131033
\(248\) 0 0
\(249\) −9.46489 −0.599813
\(250\) 0 0
\(251\) −3.97786 −0.251080 −0.125540 0.992089i \(-0.540066\pi\)
−0.125540 + 0.992089i \(0.540066\pi\)
\(252\) 0 0
\(253\) −38.8095 −2.43993
\(254\) 0 0
\(255\) −4.58707 −0.287254
\(256\) 0 0
\(257\) 7.02618 0.438281 0.219141 0.975693i \(-0.429675\pi\)
0.219141 + 0.975693i \(0.429675\pi\)
\(258\) 0 0
\(259\) −27.4917 −1.70825
\(260\) 0 0
\(261\) −0.589559 −0.0364928
\(262\) 0 0
\(263\) −14.0263 −0.864899 −0.432449 0.901658i \(-0.642351\pi\)
−0.432449 + 0.901658i \(0.642351\pi\)
\(264\) 0 0
\(265\) 22.0393 1.35386
\(266\) 0 0
\(267\) 8.60759 0.526776
\(268\) 0 0
\(269\) 10.2401 0.624348 0.312174 0.950025i \(-0.398943\pi\)
0.312174 + 0.950025i \(0.398943\pi\)
\(270\) 0 0
\(271\) −22.7598 −1.38256 −0.691279 0.722588i \(-0.742952\pi\)
−0.691279 + 0.722588i \(0.742952\pi\)
\(272\) 0 0
\(273\) 0.610085 0.0369240
\(274\) 0 0
\(275\) −2.31414 −0.139548
\(276\) 0 0
\(277\) 16.9060 1.01578 0.507891 0.861421i \(-0.330425\pi\)
0.507891 + 0.861421i \(0.330425\pi\)
\(278\) 0 0
\(279\) −18.4605 −1.10520
\(280\) 0 0
\(281\) 33.1150 1.97548 0.987738 0.156119i \(-0.0498983\pi\)
0.987738 + 0.156119i \(0.0498983\pi\)
\(282\) 0 0
\(283\) −19.3002 −1.14728 −0.573638 0.819109i \(-0.694468\pi\)
−0.573638 + 0.819109i \(0.694468\pi\)
\(284\) 0 0
\(285\) −1.68197 −0.0996313
\(286\) 0 0
\(287\) 7.47487 0.441228
\(288\) 0 0
\(289\) −7.25954 −0.427032
\(290\) 0 0
\(291\) −4.64745 −0.272438
\(292\) 0 0
\(293\) 9.49110 0.554476 0.277238 0.960801i \(-0.410581\pi\)
0.277238 + 0.960801i \(0.410581\pi\)
\(294\) 0 0
\(295\) −17.0009 −0.989829
\(296\) 0 0
\(297\) 22.1253 1.28384
\(298\) 0 0
\(299\) 1.19587 0.0691588
\(300\) 0 0
\(301\) 10.3142 0.594501
\(302\) 0 0
\(303\) 1.47462 0.0847146
\(304\) 0 0
\(305\) −1.66038 −0.0950731
\(306\) 0 0
\(307\) −22.8314 −1.30305 −0.651527 0.758625i \(-0.725871\pi\)
−0.651527 + 0.758625i \(0.725871\pi\)
\(308\) 0 0
\(309\) −1.60086 −0.0910699
\(310\) 0 0
\(311\) −11.0405 −0.626050 −0.313025 0.949745i \(-0.601342\pi\)
−0.313025 + 0.949745i \(0.601342\pi\)
\(312\) 0 0
\(313\) 1.37876 0.0779323 0.0389662 0.999241i \(-0.487594\pi\)
0.0389662 + 0.999241i \(0.487594\pi\)
\(314\) 0 0
\(315\) −26.8752 −1.51424
\(316\) 0 0
\(317\) 24.0543 1.35103 0.675513 0.737348i \(-0.263922\pi\)
0.675513 + 0.737348i \(0.263922\pi\)
\(318\) 0 0
\(319\) 1.36046 0.0761712
\(320\) 0 0
\(321\) 1.10539 0.0616968
\(322\) 0 0
\(323\) 3.57159 0.198729
\(324\) 0 0
\(325\) 0.0713073 0.00395542
\(326\) 0 0
\(327\) 2.16218 0.119569
\(328\) 0 0
\(329\) 47.5923 2.62385
\(330\) 0 0
\(331\) 16.9664 0.932557 0.466279 0.884638i \(-0.345594\pi\)
0.466279 + 0.884638i \(0.345594\pi\)
\(332\) 0 0
\(333\) 14.0576 0.770354
\(334\) 0 0
\(335\) −16.6902 −0.911880
\(336\) 0 0
\(337\) 9.84136 0.536093 0.268047 0.963406i \(-0.413622\pi\)
0.268047 + 0.963406i \(0.413622\pi\)
\(338\) 0 0
\(339\) 5.75829 0.312748
\(340\) 0 0
\(341\) 42.5994 2.30689
\(342\) 0 0
\(343\) 51.9445 2.80474
\(344\) 0 0
\(345\) 9.76724 0.525850
\(346\) 0 0
\(347\) 2.42800 0.130342 0.0651708 0.997874i \(-0.479241\pi\)
0.0651708 + 0.997874i \(0.479241\pi\)
\(348\) 0 0
\(349\) −19.9933 −1.07022 −0.535108 0.844784i \(-0.679729\pi\)
−0.535108 + 0.844784i \(0.679729\pi\)
\(350\) 0 0
\(351\) −0.681764 −0.0363899
\(352\) 0 0
\(353\) −18.8138 −1.00136 −0.500678 0.865633i \(-0.666916\pi\)
−0.500678 + 0.865633i \(0.666916\pi\)
\(354\) 0 0
\(355\) 2.41237 0.128035
\(356\) 0 0
\(357\) −10.5809 −0.560000
\(358\) 0 0
\(359\) 13.6608 0.720987 0.360494 0.932762i \(-0.382608\pi\)
0.360494 + 0.932762i \(0.382608\pi\)
\(360\) 0 0
\(361\) −17.6904 −0.931073
\(362\) 0 0
\(363\) −15.8273 −0.830719
\(364\) 0 0
\(365\) −22.9158 −1.19947
\(366\) 0 0
\(367\) 8.47228 0.442250 0.221125 0.975246i \(-0.429027\pi\)
0.221125 + 0.975246i \(0.429027\pi\)
\(368\) 0 0
\(369\) −3.82222 −0.198977
\(370\) 0 0
\(371\) 50.8375 2.63935
\(372\) 0 0
\(373\) −0.228118 −0.0118115 −0.00590576 0.999983i \(-0.501880\pi\)
−0.00590576 + 0.999983i \(0.501880\pi\)
\(374\) 0 0
\(375\) 7.93120 0.409565
\(376\) 0 0
\(377\) −0.0419209 −0.00215904
\(378\) 0 0
\(379\) 24.5799 1.26258 0.631292 0.775545i \(-0.282525\pi\)
0.631292 + 0.775545i \(0.282525\pi\)
\(380\) 0 0
\(381\) 13.7741 0.705668
\(382\) 0 0
\(383\) −24.6978 −1.26200 −0.631000 0.775783i \(-0.717355\pi\)
−0.631000 + 0.775783i \(0.717355\pi\)
\(384\) 0 0
\(385\) 62.0169 3.16068
\(386\) 0 0
\(387\) −5.27409 −0.268097
\(388\) 0 0
\(389\) −29.4000 −1.49064 −0.745321 0.666706i \(-0.767704\pi\)
−0.745321 + 0.666706i \(0.767704\pi\)
\(390\) 0 0
\(391\) −20.7403 −1.04888
\(392\) 0 0
\(393\) 13.3717 0.674514
\(394\) 0 0
\(395\) 6.49071 0.326583
\(396\) 0 0
\(397\) 19.2696 0.967116 0.483558 0.875312i \(-0.339344\pi\)
0.483558 + 0.875312i \(0.339344\pi\)
\(398\) 0 0
\(399\) −3.87976 −0.194231
\(400\) 0 0
\(401\) 29.3236 1.46435 0.732176 0.681116i \(-0.238505\pi\)
0.732176 + 0.681116i \(0.238505\pi\)
\(402\) 0 0
\(403\) −1.31265 −0.0653877
\(404\) 0 0
\(405\) 10.7220 0.532783
\(406\) 0 0
\(407\) −32.4393 −1.60796
\(408\) 0 0
\(409\) 13.3658 0.660899 0.330449 0.943824i \(-0.392800\pi\)
0.330449 + 0.943824i \(0.392800\pi\)
\(410\) 0 0
\(411\) −7.48599 −0.369257
\(412\) 0 0
\(413\) −39.2155 −1.92967
\(414\) 0 0
\(415\) 29.6470 1.45531
\(416\) 0 0
\(417\) 5.90888 0.289359
\(418\) 0 0
\(419\) −13.8349 −0.675878 −0.337939 0.941168i \(-0.609730\pi\)
−0.337939 + 0.941168i \(0.609730\pi\)
\(420\) 0 0
\(421\) 24.1254 1.17580 0.587900 0.808934i \(-0.299955\pi\)
0.587900 + 0.808934i \(0.299955\pi\)
\(422\) 0 0
\(423\) −24.3360 −1.18325
\(424\) 0 0
\(425\) −1.23670 −0.0599890
\(426\) 0 0
\(427\) −3.82996 −0.185345
\(428\) 0 0
\(429\) 0.719881 0.0347562
\(430\) 0 0
\(431\) −18.4962 −0.890932 −0.445466 0.895299i \(-0.646962\pi\)
−0.445466 + 0.895299i \(0.646962\pi\)
\(432\) 0 0
\(433\) 9.86211 0.473943 0.236971 0.971517i \(-0.423845\pi\)
0.236971 + 0.971517i \(0.423845\pi\)
\(434\) 0 0
\(435\) −0.342389 −0.0164163
\(436\) 0 0
\(437\) −7.60498 −0.363795
\(438\) 0 0
\(439\) −30.0086 −1.43223 −0.716117 0.697980i \(-0.754082\pi\)
−0.716117 + 0.697980i \(0.754082\pi\)
\(440\) 0 0
\(441\) −44.2768 −2.10842
\(442\) 0 0
\(443\) −4.16482 −0.197877 −0.0989384 0.995094i \(-0.531545\pi\)
−0.0989384 + 0.995094i \(0.531545\pi\)
\(444\) 0 0
\(445\) −26.9616 −1.27810
\(446\) 0 0
\(447\) 1.88185 0.0890083
\(448\) 0 0
\(449\) −1.26226 −0.0595697 −0.0297848 0.999556i \(-0.509482\pi\)
−0.0297848 + 0.999556i \(0.509482\pi\)
\(450\) 0 0
\(451\) 8.82012 0.415323
\(452\) 0 0
\(453\) −12.0807 −0.567601
\(454\) 0 0
\(455\) −1.91098 −0.0895879
\(456\) 0 0
\(457\) −35.2343 −1.64819 −0.824095 0.566452i \(-0.808316\pi\)
−0.824095 + 0.566452i \(0.808316\pi\)
\(458\) 0 0
\(459\) 11.8240 0.551899
\(460\) 0 0
\(461\) 31.8895 1.48524 0.742621 0.669712i \(-0.233582\pi\)
0.742621 + 0.669712i \(0.233582\pi\)
\(462\) 0 0
\(463\) 24.0028 1.11551 0.557753 0.830007i \(-0.311664\pi\)
0.557753 + 0.830007i \(0.311664\pi\)
\(464\) 0 0
\(465\) −10.7210 −0.497177
\(466\) 0 0
\(467\) 3.44249 0.159299 0.0796497 0.996823i \(-0.474620\pi\)
0.0796497 + 0.996823i \(0.474620\pi\)
\(468\) 0 0
\(469\) −38.4988 −1.77771
\(470\) 0 0
\(471\) −12.5054 −0.576218
\(472\) 0 0
\(473\) 12.1705 0.559598
\(474\) 0 0
\(475\) −0.453470 −0.0208066
\(476\) 0 0
\(477\) −25.9953 −1.19025
\(478\) 0 0
\(479\) 19.1306 0.874102 0.437051 0.899437i \(-0.356023\pi\)
0.437051 + 0.899437i \(0.356023\pi\)
\(480\) 0 0
\(481\) 0.999578 0.0455768
\(482\) 0 0
\(483\) 22.5298 1.02514
\(484\) 0 0
\(485\) 14.5573 0.661011
\(486\) 0 0
\(487\) 27.6357 1.25229 0.626147 0.779705i \(-0.284631\pi\)
0.626147 + 0.779705i \(0.284631\pi\)
\(488\) 0 0
\(489\) 6.70227 0.303087
\(490\) 0 0
\(491\) −8.91431 −0.402297 −0.201149 0.979561i \(-0.564467\pi\)
−0.201149 + 0.979561i \(0.564467\pi\)
\(492\) 0 0
\(493\) 0.727048 0.0327446
\(494\) 0 0
\(495\) −31.7119 −1.42534
\(496\) 0 0
\(497\) 5.56456 0.249604
\(498\) 0 0
\(499\) 37.4955 1.67853 0.839265 0.543723i \(-0.182986\pi\)
0.839265 + 0.543723i \(0.182986\pi\)
\(500\) 0 0
\(501\) 5.00652 0.223675
\(502\) 0 0
\(503\) −30.7058 −1.36911 −0.684553 0.728963i \(-0.740003\pi\)
−0.684553 + 0.728963i \(0.740003\pi\)
\(504\) 0 0
\(505\) −4.61896 −0.205541
\(506\) 0 0
\(507\) 8.88282 0.394500
\(508\) 0 0
\(509\) −2.52251 −0.111808 −0.0559042 0.998436i \(-0.517804\pi\)
−0.0559042 + 0.998436i \(0.517804\pi\)
\(510\) 0 0
\(511\) −52.8594 −2.33836
\(512\) 0 0
\(513\) 4.33560 0.191421
\(514\) 0 0
\(515\) 5.01440 0.220961
\(516\) 0 0
\(517\) 56.1575 2.46980
\(518\) 0 0
\(519\) 1.52723 0.0670380
\(520\) 0 0
\(521\) −24.9034 −1.09104 −0.545519 0.838098i \(-0.683667\pi\)
−0.545519 + 0.838098i \(0.683667\pi\)
\(522\) 0 0
\(523\) 0.118779 0.00519382 0.00259691 0.999997i \(-0.499173\pi\)
0.00259691 + 0.999997i \(0.499173\pi\)
\(524\) 0 0
\(525\) 1.34341 0.0586313
\(526\) 0 0
\(527\) 22.7657 0.991689
\(528\) 0 0
\(529\) 21.1623 0.920098
\(530\) 0 0
\(531\) 20.0525 0.870206
\(532\) 0 0
\(533\) −0.271781 −0.0117721
\(534\) 0 0
\(535\) −3.46242 −0.149694
\(536\) 0 0
\(537\) −17.5563 −0.757610
\(538\) 0 0
\(539\) 102.173 4.40090
\(540\) 0 0
\(541\) 13.6990 0.588965 0.294483 0.955657i \(-0.404853\pi\)
0.294483 + 0.955657i \(0.404853\pi\)
\(542\) 0 0
\(543\) −0.683183 −0.0293182
\(544\) 0 0
\(545\) −6.77263 −0.290107
\(546\) 0 0
\(547\) 11.0972 0.474481 0.237241 0.971451i \(-0.423757\pi\)
0.237241 + 0.971451i \(0.423757\pi\)
\(548\) 0 0
\(549\) 1.95842 0.0835833
\(550\) 0 0
\(551\) 0.266591 0.0113572
\(552\) 0 0
\(553\) 14.9720 0.636673
\(554\) 0 0
\(555\) 8.16404 0.346544
\(556\) 0 0
\(557\) 9.91757 0.420221 0.210110 0.977678i \(-0.432618\pi\)
0.210110 + 0.977678i \(0.432618\pi\)
\(558\) 0 0
\(559\) −0.375017 −0.0158615
\(560\) 0 0
\(561\) −12.4851 −0.527122
\(562\) 0 0
\(563\) 40.0932 1.68973 0.844864 0.534982i \(-0.179682\pi\)
0.844864 + 0.534982i \(0.179682\pi\)
\(564\) 0 0
\(565\) −18.0368 −0.758813
\(566\) 0 0
\(567\) 24.7323 1.03866
\(568\) 0 0
\(569\) −9.64889 −0.404503 −0.202251 0.979334i \(-0.564826\pi\)
−0.202251 + 0.979334i \(0.564826\pi\)
\(570\) 0 0
\(571\) −5.11116 −0.213896 −0.106948 0.994265i \(-0.534108\pi\)
−0.106948 + 0.994265i \(0.534108\pi\)
\(572\) 0 0
\(573\) 13.9660 0.583440
\(574\) 0 0
\(575\) 2.63331 0.109817
\(576\) 0 0
\(577\) 13.2909 0.553309 0.276654 0.960969i \(-0.410774\pi\)
0.276654 + 0.960969i \(0.410774\pi\)
\(578\) 0 0
\(579\) −16.5453 −0.687600
\(580\) 0 0
\(581\) 68.3860 2.83713
\(582\) 0 0
\(583\) 59.9867 2.48439
\(584\) 0 0
\(585\) 0.977162 0.0404007
\(586\) 0 0
\(587\) 42.8016 1.76661 0.883305 0.468798i \(-0.155313\pi\)
0.883305 + 0.468798i \(0.155313\pi\)
\(588\) 0 0
\(589\) 8.34763 0.343958
\(590\) 0 0
\(591\) 15.6347 0.643124
\(592\) 0 0
\(593\) −33.1865 −1.36281 −0.681403 0.731909i \(-0.738630\pi\)
−0.681403 + 0.731909i \(0.738630\pi\)
\(594\) 0 0
\(595\) 33.1426 1.35872
\(596\) 0 0
\(597\) 2.18434 0.0893990
\(598\) 0 0
\(599\) 15.0989 0.616924 0.308462 0.951237i \(-0.400186\pi\)
0.308462 + 0.951237i \(0.400186\pi\)
\(600\) 0 0
\(601\) −21.3445 −0.870662 −0.435331 0.900270i \(-0.643369\pi\)
−0.435331 + 0.900270i \(0.643369\pi\)
\(602\) 0 0
\(603\) 19.6860 0.801677
\(604\) 0 0
\(605\) 49.5761 2.01556
\(606\) 0 0
\(607\) 31.1557 1.26457 0.632286 0.774735i \(-0.282117\pi\)
0.632286 + 0.774735i \(0.282117\pi\)
\(608\) 0 0
\(609\) −0.789780 −0.0320035
\(610\) 0 0
\(611\) −1.73042 −0.0700054
\(612\) 0 0
\(613\) 34.8608 1.40802 0.704008 0.710193i \(-0.251392\pi\)
0.704008 + 0.710193i \(0.251392\pi\)
\(614\) 0 0
\(615\) −2.21977 −0.0895097
\(616\) 0 0
\(617\) −32.1336 −1.29365 −0.646825 0.762638i \(-0.723904\pi\)
−0.646825 + 0.762638i \(0.723904\pi\)
\(618\) 0 0
\(619\) 18.2548 0.733723 0.366861 0.930276i \(-0.380432\pi\)
0.366861 + 0.930276i \(0.380432\pi\)
\(620\) 0 0
\(621\) −25.1769 −1.01031
\(622\) 0 0
\(623\) −62.1918 −2.49166
\(624\) 0 0
\(625\) −22.8617 −0.914468
\(626\) 0 0
\(627\) −4.57800 −0.182828
\(628\) 0 0
\(629\) −17.3360 −0.691231
\(630\) 0 0
\(631\) −27.8618 −1.10916 −0.554581 0.832130i \(-0.687122\pi\)
−0.554581 + 0.832130i \(0.687122\pi\)
\(632\) 0 0
\(633\) 0.839070 0.0333500
\(634\) 0 0
\(635\) −43.1448 −1.71215
\(636\) 0 0
\(637\) −3.14833 −0.124741
\(638\) 0 0
\(639\) −2.84539 −0.112562
\(640\) 0 0
\(641\) −30.3218 −1.19764 −0.598820 0.800884i \(-0.704364\pi\)
−0.598820 + 0.800884i \(0.704364\pi\)
\(642\) 0 0
\(643\) −29.6129 −1.16782 −0.583909 0.811819i \(-0.698477\pi\)
−0.583909 + 0.811819i \(0.698477\pi\)
\(644\) 0 0
\(645\) −3.06295 −0.120604
\(646\) 0 0
\(647\) −2.57974 −0.101420 −0.0507100 0.998713i \(-0.516148\pi\)
−0.0507100 + 0.998713i \(0.516148\pi\)
\(648\) 0 0
\(649\) −46.2731 −1.81638
\(650\) 0 0
\(651\) −24.7300 −0.969244
\(652\) 0 0
\(653\) −25.6116 −1.00226 −0.501129 0.865373i \(-0.667082\pi\)
−0.501129 + 0.865373i \(0.667082\pi\)
\(654\) 0 0
\(655\) −41.8844 −1.63656
\(656\) 0 0
\(657\) 27.0292 1.05451
\(658\) 0 0
\(659\) 1.91152 0.0744621 0.0372311 0.999307i \(-0.488146\pi\)
0.0372311 + 0.999307i \(0.488146\pi\)
\(660\) 0 0
\(661\) 29.3213 1.14047 0.570233 0.821483i \(-0.306853\pi\)
0.570233 + 0.821483i \(0.306853\pi\)
\(662\) 0 0
\(663\) 0.384714 0.0149410
\(664\) 0 0
\(665\) 12.1526 0.471258
\(666\) 0 0
\(667\) −1.54810 −0.0599427
\(668\) 0 0
\(669\) 8.18513 0.316455
\(670\) 0 0
\(671\) −4.51923 −0.174463
\(672\) 0 0
\(673\) 32.3544 1.24717 0.623584 0.781756i \(-0.285676\pi\)
0.623584 + 0.781756i \(0.285676\pi\)
\(674\) 0 0
\(675\) −1.50125 −0.0577831
\(676\) 0 0
\(677\) 13.4155 0.515598 0.257799 0.966199i \(-0.417003\pi\)
0.257799 + 0.966199i \(0.417003\pi\)
\(678\) 0 0
\(679\) 33.5788 1.28864
\(680\) 0 0
\(681\) −4.57810 −0.175433
\(682\) 0 0
\(683\) 18.8229 0.720237 0.360118 0.932907i \(-0.382736\pi\)
0.360118 + 0.932907i \(0.382736\pi\)
\(684\) 0 0
\(685\) 23.4485 0.895920
\(686\) 0 0
\(687\) 2.52406 0.0962988
\(688\) 0 0
\(689\) −1.84842 −0.0704190
\(690\) 0 0
\(691\) −21.0021 −0.798959 −0.399479 0.916742i \(-0.630809\pi\)
−0.399479 + 0.916742i \(0.630809\pi\)
\(692\) 0 0
\(693\) −73.1490 −2.77870
\(694\) 0 0
\(695\) −18.5085 −0.702066
\(696\) 0 0
\(697\) 4.71359 0.178540
\(698\) 0 0
\(699\) −8.47161 −0.320426
\(700\) 0 0
\(701\) −8.66385 −0.327229 −0.163615 0.986524i \(-0.552315\pi\)
−0.163615 + 0.986524i \(0.552315\pi\)
\(702\) 0 0
\(703\) −6.35670 −0.239747
\(704\) 0 0
\(705\) −14.1332 −0.532288
\(706\) 0 0
\(707\) −10.6544 −0.400702
\(708\) 0 0
\(709\) 5.20369 0.195429 0.0977144 0.995215i \(-0.468847\pi\)
0.0977144 + 0.995215i \(0.468847\pi\)
\(710\) 0 0
\(711\) −7.65579 −0.287115
\(712\) 0 0
\(713\) −48.4749 −1.81540
\(714\) 0 0
\(715\) −2.25489 −0.0843282
\(716\) 0 0
\(717\) 2.87421 0.107340
\(718\) 0 0
\(719\) 32.4074 1.20859 0.604296 0.796760i \(-0.293454\pi\)
0.604296 + 0.796760i \(0.293454\pi\)
\(720\) 0 0
\(721\) 11.5666 0.430762
\(722\) 0 0
\(723\) −8.58436 −0.319256
\(724\) 0 0
\(725\) −0.0923102 −0.00342832
\(726\) 0 0
\(727\) 9.10375 0.337640 0.168820 0.985647i \(-0.446004\pi\)
0.168820 + 0.985647i \(0.446004\pi\)
\(728\) 0 0
\(729\) −4.86112 −0.180042
\(730\) 0 0
\(731\) 6.50405 0.240561
\(732\) 0 0
\(733\) −5.09445 −0.188168 −0.0940839 0.995564i \(-0.529992\pi\)
−0.0940839 + 0.995564i \(0.529992\pi\)
\(734\) 0 0
\(735\) −25.7140 −0.948474
\(736\) 0 0
\(737\) −45.4274 −1.67334
\(738\) 0 0
\(739\) 33.4122 1.22909 0.614544 0.788883i \(-0.289340\pi\)
0.614544 + 0.788883i \(0.289340\pi\)
\(740\) 0 0
\(741\) 0.141065 0.00518217
\(742\) 0 0
\(743\) −16.9682 −0.622504 −0.311252 0.950327i \(-0.600748\pi\)
−0.311252 + 0.950327i \(0.600748\pi\)
\(744\) 0 0
\(745\) −5.89453 −0.215959
\(746\) 0 0
\(747\) −34.9686 −1.27944
\(748\) 0 0
\(749\) −7.98668 −0.291827
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 2.72483 0.0992985
\(754\) 0 0
\(755\) 37.8405 1.37716
\(756\) 0 0
\(757\) 32.3558 1.17599 0.587995 0.808864i \(-0.299917\pi\)
0.587995 + 0.808864i \(0.299917\pi\)
\(758\) 0 0
\(759\) 26.5845 0.964957
\(760\) 0 0
\(761\) −29.7123 −1.07707 −0.538535 0.842603i \(-0.681022\pi\)
−0.538535 + 0.842603i \(0.681022\pi\)
\(762\) 0 0
\(763\) −15.6222 −0.565563
\(764\) 0 0
\(765\) −16.9472 −0.612728
\(766\) 0 0
\(767\) 1.42585 0.0514844
\(768\) 0 0
\(769\) 0.187541 0.00676290 0.00338145 0.999994i \(-0.498924\pi\)
0.00338145 + 0.999994i \(0.498924\pi\)
\(770\) 0 0
\(771\) −4.81294 −0.173334
\(772\) 0 0
\(773\) −53.6009 −1.92789 −0.963946 0.266099i \(-0.914265\pi\)
−0.963946 + 0.266099i \(0.914265\pi\)
\(774\) 0 0
\(775\) −2.89046 −0.103829
\(776\) 0 0
\(777\) 18.8318 0.675587
\(778\) 0 0
\(779\) 1.72836 0.0619249
\(780\) 0 0
\(781\) 6.56601 0.234950
\(782\) 0 0
\(783\) 0.882572 0.0315405
\(784\) 0 0
\(785\) 39.1708 1.39806
\(786\) 0 0
\(787\) −27.5297 −0.981327 −0.490664 0.871349i \(-0.663246\pi\)
−0.490664 + 0.871349i \(0.663246\pi\)
\(788\) 0 0
\(789\) 9.60801 0.342054
\(790\) 0 0
\(791\) −41.6050 −1.47930
\(792\) 0 0
\(793\) 0.139255 0.00494508
\(794\) 0 0
\(795\) −15.0969 −0.535432
\(796\) 0 0
\(797\) −16.1756 −0.572970 −0.286485 0.958085i \(-0.592487\pi\)
−0.286485 + 0.958085i \(0.592487\pi\)
\(798\) 0 0
\(799\) 30.0113 1.06172
\(800\) 0 0
\(801\) 31.8013 1.12364
\(802\) 0 0
\(803\) −62.3725 −2.20108
\(804\) 0 0
\(805\) −70.5705 −2.48728
\(806\) 0 0
\(807\) −7.01445 −0.246920
\(808\) 0 0
\(809\) 40.8674 1.43682 0.718410 0.695620i \(-0.244870\pi\)
0.718410 + 0.695620i \(0.244870\pi\)
\(810\) 0 0
\(811\) −1.35801 −0.0476863 −0.0238432 0.999716i \(-0.507590\pi\)
−0.0238432 + 0.999716i \(0.507590\pi\)
\(812\) 0 0
\(813\) 15.5904 0.546781
\(814\) 0 0
\(815\) −20.9936 −0.735373
\(816\) 0 0
\(817\) 2.38488 0.0834363
\(818\) 0 0
\(819\) 2.25400 0.0787610
\(820\) 0 0
\(821\) −38.4273 −1.34112 −0.670560 0.741855i \(-0.733946\pi\)
−0.670560 + 0.741855i \(0.733946\pi\)
\(822\) 0 0
\(823\) −37.2785 −1.29945 −0.649723 0.760171i \(-0.725115\pi\)
−0.649723 + 0.760171i \(0.725115\pi\)
\(824\) 0 0
\(825\) 1.58518 0.0551890
\(826\) 0 0
\(827\) 35.6293 1.23895 0.619477 0.785015i \(-0.287345\pi\)
0.619477 + 0.785015i \(0.287345\pi\)
\(828\) 0 0
\(829\) −1.40717 −0.0488730 −0.0244365 0.999701i \(-0.507779\pi\)
−0.0244365 + 0.999701i \(0.507779\pi\)
\(830\) 0 0
\(831\) −11.5806 −0.401727
\(832\) 0 0
\(833\) 54.6025 1.89186
\(834\) 0 0
\(835\) −15.6820 −0.542698
\(836\) 0 0
\(837\) 27.6355 0.955223
\(838\) 0 0
\(839\) 33.1429 1.14422 0.572110 0.820177i \(-0.306125\pi\)
0.572110 + 0.820177i \(0.306125\pi\)
\(840\) 0 0
\(841\) −28.9457 −0.998129
\(842\) 0 0
\(843\) −22.6838 −0.781271
\(844\) 0 0
\(845\) −27.8238 −0.957166
\(846\) 0 0
\(847\) 114.356 3.92932
\(848\) 0 0
\(849\) 13.2206 0.453731
\(850\) 0 0
\(851\) 36.9135 1.26538
\(852\) 0 0
\(853\) −24.1624 −0.827306 −0.413653 0.910435i \(-0.635747\pi\)
−0.413653 + 0.910435i \(0.635747\pi\)
\(854\) 0 0
\(855\) −6.21415 −0.212519
\(856\) 0 0
\(857\) −11.3547 −0.387869 −0.193935 0.981014i \(-0.562125\pi\)
−0.193935 + 0.981014i \(0.562125\pi\)
\(858\) 0 0
\(859\) 3.48115 0.118775 0.0593877 0.998235i \(-0.481085\pi\)
0.0593877 + 0.998235i \(0.481085\pi\)
\(860\) 0 0
\(861\) −5.12029 −0.174499
\(862\) 0 0
\(863\) −31.9669 −1.08816 −0.544082 0.839032i \(-0.683122\pi\)
−0.544082 + 0.839032i \(0.683122\pi\)
\(864\) 0 0
\(865\) −4.78377 −0.162653
\(866\) 0 0
\(867\) 4.97279 0.168885
\(868\) 0 0
\(869\) 17.6665 0.599294
\(870\) 0 0
\(871\) 1.39979 0.0474300
\(872\) 0 0
\(873\) −17.1703 −0.581126
\(874\) 0 0
\(875\) −57.3047 −1.93725
\(876\) 0 0
\(877\) −2.97280 −0.100384 −0.0501922 0.998740i \(-0.515983\pi\)
−0.0501922 + 0.998740i \(0.515983\pi\)
\(878\) 0 0
\(879\) −6.50141 −0.219287
\(880\) 0 0
\(881\) 16.2874 0.548736 0.274368 0.961625i \(-0.411531\pi\)
0.274368 + 0.961625i \(0.411531\pi\)
\(882\) 0 0
\(883\) −52.6411 −1.77151 −0.885757 0.464149i \(-0.846360\pi\)
−0.885757 + 0.464149i \(0.846360\pi\)
\(884\) 0 0
\(885\) 11.6456 0.391462
\(886\) 0 0
\(887\) −7.12621 −0.239275 −0.119637 0.992818i \(-0.538173\pi\)
−0.119637 + 0.992818i \(0.538173\pi\)
\(888\) 0 0
\(889\) −99.5209 −3.33783
\(890\) 0 0
\(891\) 29.1833 0.977679
\(892\) 0 0
\(893\) 11.0044 0.368249
\(894\) 0 0
\(895\) 54.9918 1.83817
\(896\) 0 0
\(897\) −0.819169 −0.0273513
\(898\) 0 0
\(899\) 1.69928 0.0566741
\(900\) 0 0
\(901\) 32.0577 1.06800
\(902\) 0 0
\(903\) −7.06523 −0.235116
\(904\) 0 0
\(905\) 2.13994 0.0711341
\(906\) 0 0
\(907\) −12.9951 −0.431496 −0.215748 0.976449i \(-0.569219\pi\)
−0.215748 + 0.976449i \(0.569219\pi\)
\(908\) 0 0
\(909\) 5.44807 0.180701
\(910\) 0 0
\(911\) −17.0255 −0.564082 −0.282041 0.959402i \(-0.591011\pi\)
−0.282041 + 0.959402i \(0.591011\pi\)
\(912\) 0 0
\(913\) 80.6934 2.67056
\(914\) 0 0
\(915\) 1.13736 0.0376000
\(916\) 0 0
\(917\) −96.6137 −3.19047
\(918\) 0 0
\(919\) −34.2565 −1.13002 −0.565008 0.825085i \(-0.691127\pi\)
−0.565008 + 0.825085i \(0.691127\pi\)
\(920\) 0 0
\(921\) 15.6395 0.515339
\(922\) 0 0
\(923\) −0.202323 −0.00665956
\(924\) 0 0
\(925\) 2.20108 0.0723710
\(926\) 0 0
\(927\) −5.91449 −0.194257
\(928\) 0 0
\(929\) −3.68750 −0.120983 −0.0604915 0.998169i \(-0.519267\pi\)
−0.0604915 + 0.998169i \(0.519267\pi\)
\(930\) 0 0
\(931\) 20.0214 0.656176
\(932\) 0 0
\(933\) 7.56276 0.247594
\(934\) 0 0
\(935\) 39.1073 1.27895
\(936\) 0 0
\(937\) 50.1654 1.63883 0.819417 0.573198i \(-0.194298\pi\)
0.819417 + 0.573198i \(0.194298\pi\)
\(938\) 0 0
\(939\) −0.944453 −0.0308211
\(940\) 0 0
\(941\) −13.0686 −0.426023 −0.213011 0.977050i \(-0.568327\pi\)
−0.213011 + 0.977050i \(0.568327\pi\)
\(942\) 0 0
\(943\) −10.0366 −0.326837
\(944\) 0 0
\(945\) 40.2322 1.30875
\(946\) 0 0
\(947\) −9.54515 −0.310176 −0.155088 0.987901i \(-0.549566\pi\)
−0.155088 + 0.987901i \(0.549566\pi\)
\(948\) 0 0
\(949\) 1.92193 0.0623885
\(950\) 0 0
\(951\) −16.4772 −0.534311
\(952\) 0 0
\(953\) −54.5055 −1.76561 −0.882803 0.469744i \(-0.844346\pi\)
−0.882803 + 0.469744i \(0.844346\pi\)
\(954\) 0 0
\(955\) −43.7460 −1.41559
\(956\) 0 0
\(957\) −0.931916 −0.0301246
\(958\) 0 0
\(959\) 54.0880 1.74659
\(960\) 0 0
\(961\) 22.2086 0.716408
\(962\) 0 0
\(963\) 4.08393 0.131603
\(964\) 0 0
\(965\) 51.8251 1.66831
\(966\) 0 0
\(967\) 4.73060 0.152126 0.0760628 0.997103i \(-0.475765\pi\)
0.0760628 + 0.997103i \(0.475765\pi\)
\(968\) 0 0
\(969\) −2.44654 −0.0785942
\(970\) 0 0
\(971\) 25.9431 0.832553 0.416277 0.909238i \(-0.363335\pi\)
0.416277 + 0.909238i \(0.363335\pi\)
\(972\) 0 0
\(973\) −42.6930 −1.36867
\(974\) 0 0
\(975\) −0.0488455 −0.00156431
\(976\) 0 0
\(977\) −43.4569 −1.39031 −0.695155 0.718859i \(-0.744664\pi\)
−0.695155 + 0.718859i \(0.744664\pi\)
\(978\) 0 0
\(979\) −73.3844 −2.34538
\(980\) 0 0
\(981\) 7.98831 0.255047
\(982\) 0 0
\(983\) −13.7376 −0.438161 −0.219081 0.975707i \(-0.570306\pi\)
−0.219081 + 0.975707i \(0.570306\pi\)
\(984\) 0 0
\(985\) −48.9726 −1.56040
\(986\) 0 0
\(987\) −32.6007 −1.03769
\(988\) 0 0
\(989\) −13.8490 −0.440374
\(990\) 0 0
\(991\) −45.9927 −1.46101 −0.730504 0.682909i \(-0.760715\pi\)
−0.730504 + 0.682909i \(0.760715\pi\)
\(992\) 0 0
\(993\) −11.6220 −0.368812
\(994\) 0 0
\(995\) −6.84203 −0.216907
\(996\) 0 0
\(997\) −23.1200 −0.732219 −0.366109 0.930572i \(-0.619310\pi\)
−0.366109 + 0.930572i \(0.619310\pi\)
\(998\) 0 0
\(999\) −21.0444 −0.665814
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 \(a_p\))