Properties

Label 6008.2.a.e.1.40
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 1.40
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.15655 q^{3} +1.11683 q^{5} -1.03539 q^{7} +1.65070 q^{9} +O(q^{10})\) \(q+2.15655 q^{3} +1.11683 q^{5} -1.03539 q^{7} +1.65070 q^{9} +2.85069 q^{11} +3.74207 q^{13} +2.40850 q^{15} +5.19567 q^{17} +1.79315 q^{19} -2.23286 q^{21} +6.06395 q^{23} -3.75269 q^{25} -2.90984 q^{27} +0.462966 q^{29} +1.21315 q^{31} +6.14765 q^{33} -1.15635 q^{35} -7.34179 q^{37} +8.06994 q^{39} +6.52229 q^{41} +2.05942 q^{43} +1.84355 q^{45} -5.41764 q^{47} -5.92797 q^{49} +11.2047 q^{51} +2.63975 q^{53} +3.18374 q^{55} +3.86702 q^{57} -1.09961 q^{59} +14.7487 q^{61} -1.70911 q^{63} +4.17926 q^{65} -13.2027 q^{67} +13.0772 q^{69} -2.35417 q^{71} -6.45396 q^{73} -8.09284 q^{75} -2.95157 q^{77} +0.844569 q^{79} -11.2273 q^{81} +13.6825 q^{83} +5.80269 q^{85} +0.998407 q^{87} +0.307688 q^{89} -3.87449 q^{91} +2.61622 q^{93} +2.00265 q^{95} -5.44127 q^{97} +4.70562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.15655 1.24508 0.622542 0.782587i \(-0.286100\pi\)
0.622542 + 0.782587i \(0.286100\pi\)
\(4\) 0 0
\(5\) 1.11683 0.499463 0.249731 0.968315i \(-0.419658\pi\)
0.249731 + 0.968315i \(0.419658\pi\)
\(6\) 0 0
\(7\) −1.03539 −0.391340 −0.195670 0.980670i \(-0.562688\pi\)
−0.195670 + 0.980670i \(0.562688\pi\)
\(8\) 0 0
\(9\) 1.65070 0.550232
\(10\) 0 0
\(11\) 2.85069 0.859515 0.429758 0.902944i \(-0.358599\pi\)
0.429758 + 0.902944i \(0.358599\pi\)
\(12\) 0 0
\(13\) 3.74207 1.03786 0.518931 0.854816i \(-0.326330\pi\)
0.518931 + 0.854816i \(0.326330\pi\)
\(14\) 0 0
\(15\) 2.40850 0.621872
\(16\) 0 0
\(17\) 5.19567 1.26013 0.630067 0.776540i \(-0.283027\pi\)
0.630067 + 0.776540i \(0.283027\pi\)
\(18\) 0 0
\(19\) 1.79315 0.411377 0.205689 0.978617i \(-0.434057\pi\)
0.205689 + 0.978617i \(0.434057\pi\)
\(20\) 0 0
\(21\) −2.23286 −0.487251
\(22\) 0 0
\(23\) 6.06395 1.26442 0.632211 0.774796i \(-0.282148\pi\)
0.632211 + 0.774796i \(0.282148\pi\)
\(24\) 0 0
\(25\) −3.75269 −0.750537
\(26\) 0 0
\(27\) −2.90984 −0.559998
\(28\) 0 0
\(29\) 0.462966 0.0859706 0.0429853 0.999076i \(-0.486313\pi\)
0.0429853 + 0.999076i \(0.486313\pi\)
\(30\) 0 0
\(31\) 1.21315 0.217888 0.108944 0.994048i \(-0.465253\pi\)
0.108944 + 0.994048i \(0.465253\pi\)
\(32\) 0 0
\(33\) 6.14765 1.07017
\(34\) 0 0
\(35\) −1.15635 −0.195460
\(36\) 0 0
\(37\) −7.34179 −1.20698 −0.603492 0.797369i \(-0.706224\pi\)
−0.603492 + 0.797369i \(0.706224\pi\)
\(38\) 0 0
\(39\) 8.06994 1.29223
\(40\) 0 0
\(41\) 6.52229 1.01861 0.509305 0.860586i \(-0.329902\pi\)
0.509305 + 0.860586i \(0.329902\pi\)
\(42\) 0 0
\(43\) 2.05942 0.314059 0.157029 0.987594i \(-0.449808\pi\)
0.157029 + 0.987594i \(0.449808\pi\)
\(44\) 0 0
\(45\) 1.84355 0.274820
\(46\) 0 0
\(47\) −5.41764 −0.790245 −0.395122 0.918629i \(-0.629298\pi\)
−0.395122 + 0.918629i \(0.629298\pi\)
\(48\) 0 0
\(49\) −5.92797 −0.846853
\(50\) 0 0
\(51\) 11.2047 1.56897
\(52\) 0 0
\(53\) 2.63975 0.362597 0.181299 0.983428i \(-0.441970\pi\)
0.181299 + 0.983428i \(0.441970\pi\)
\(54\) 0 0
\(55\) 3.18374 0.429296
\(56\) 0 0
\(57\) 3.86702 0.512199
\(58\) 0 0
\(59\) −1.09961 −0.143157 −0.0715787 0.997435i \(-0.522804\pi\)
−0.0715787 + 0.997435i \(0.522804\pi\)
\(60\) 0 0
\(61\) 14.7487 1.88837 0.944187 0.329411i \(-0.106850\pi\)
0.944187 + 0.329411i \(0.106850\pi\)
\(62\) 0 0
\(63\) −1.70911 −0.215328
\(64\) 0 0
\(65\) 4.17926 0.518373
\(66\) 0 0
\(67\) −13.2027 −1.61297 −0.806483 0.591257i \(-0.798632\pi\)
−0.806483 + 0.591257i \(0.798632\pi\)
\(68\) 0 0
\(69\) 13.0772 1.57431
\(70\) 0 0
\(71\) −2.35417 −0.279389 −0.139694 0.990195i \(-0.544612\pi\)
−0.139694 + 0.990195i \(0.544612\pi\)
\(72\) 0 0
\(73\) −6.45396 −0.755378 −0.377689 0.925932i \(-0.623281\pi\)
−0.377689 + 0.925932i \(0.623281\pi\)
\(74\) 0 0
\(75\) −8.09284 −0.934481
\(76\) 0 0
\(77\) −2.95157 −0.336363
\(78\) 0 0
\(79\) 0.844569 0.0950214 0.0475107 0.998871i \(-0.484871\pi\)
0.0475107 + 0.998871i \(0.484871\pi\)
\(80\) 0 0
\(81\) −11.2273 −1.24748
\(82\) 0 0
\(83\) 13.6825 1.50185 0.750925 0.660388i \(-0.229608\pi\)
0.750925 + 0.660388i \(0.229608\pi\)
\(84\) 0 0
\(85\) 5.80269 0.629390
\(86\) 0 0
\(87\) 0.998407 0.107040
\(88\) 0 0
\(89\) 0.307688 0.0326149 0.0163074 0.999867i \(-0.494809\pi\)
0.0163074 + 0.999867i \(0.494809\pi\)
\(90\) 0 0
\(91\) −3.87449 −0.406157
\(92\) 0 0
\(93\) 2.61622 0.271289
\(94\) 0 0
\(95\) 2.00265 0.205467
\(96\) 0 0
\(97\) −5.44127 −0.552478 −0.276239 0.961089i \(-0.589088\pi\)
−0.276239 + 0.961089i \(0.589088\pi\)
\(98\) 0 0
\(99\) 4.70562 0.472933
\(100\) 0 0
\(101\) −7.01883 −0.698400 −0.349200 0.937048i \(-0.613547\pi\)
−0.349200 + 0.937048i \(0.613547\pi\)
\(102\) 0 0
\(103\) −5.77002 −0.568536 −0.284268 0.958745i \(-0.591751\pi\)
−0.284268 + 0.958745i \(0.591751\pi\)
\(104\) 0 0
\(105\) −2.49373 −0.243363
\(106\) 0 0
\(107\) 0.369862 0.0357559 0.0178779 0.999840i \(-0.494309\pi\)
0.0178779 + 0.999840i \(0.494309\pi\)
\(108\) 0 0
\(109\) 15.5269 1.48720 0.743602 0.668623i \(-0.233116\pi\)
0.743602 + 0.668623i \(0.233116\pi\)
\(110\) 0 0
\(111\) −15.8329 −1.50279
\(112\) 0 0
\(113\) 8.41022 0.791167 0.395583 0.918430i \(-0.370542\pi\)
0.395583 + 0.918430i \(0.370542\pi\)
\(114\) 0 0
\(115\) 6.77242 0.631531
\(116\) 0 0
\(117\) 6.17702 0.571065
\(118\) 0 0
\(119\) −5.37953 −0.493141
\(120\) 0 0
\(121\) −2.87357 −0.261233
\(122\) 0 0
\(123\) 14.0656 1.26825
\(124\) 0 0
\(125\) −9.77528 −0.874328
\(126\) 0 0
\(127\) −10.5742 −0.938311 −0.469156 0.883116i \(-0.655442\pi\)
−0.469156 + 0.883116i \(0.655442\pi\)
\(128\) 0 0
\(129\) 4.44124 0.391029
\(130\) 0 0
\(131\) 5.63867 0.492653 0.246326 0.969187i \(-0.420776\pi\)
0.246326 + 0.969187i \(0.420776\pi\)
\(132\) 0 0
\(133\) −1.85661 −0.160988
\(134\) 0 0
\(135\) −3.24980 −0.279698
\(136\) 0 0
\(137\) 12.8379 1.09682 0.548408 0.836211i \(-0.315234\pi\)
0.548408 + 0.836211i \(0.315234\pi\)
\(138\) 0 0
\(139\) −8.80162 −0.746544 −0.373272 0.927722i \(-0.621764\pi\)
−0.373272 + 0.927722i \(0.621764\pi\)
\(140\) 0 0
\(141\) −11.6834 −0.983920
\(142\) 0 0
\(143\) 10.6675 0.892059
\(144\) 0 0
\(145\) 0.517055 0.0429391
\(146\) 0 0
\(147\) −12.7840 −1.05440
\(148\) 0 0
\(149\) −0.134806 −0.0110438 −0.00552188 0.999985i \(-0.501758\pi\)
−0.00552188 + 0.999985i \(0.501758\pi\)
\(150\) 0 0
\(151\) 0.150825 0.0122740 0.00613699 0.999981i \(-0.498047\pi\)
0.00613699 + 0.999981i \(0.498047\pi\)
\(152\) 0 0
\(153\) 8.57647 0.693367
\(154\) 0 0
\(155\) 1.35489 0.108827
\(156\) 0 0
\(157\) 21.8541 1.74415 0.872075 0.489371i \(-0.162774\pi\)
0.872075 + 0.489371i \(0.162774\pi\)
\(158\) 0 0
\(159\) 5.69274 0.451464
\(160\) 0 0
\(161\) −6.27854 −0.494819
\(162\) 0 0
\(163\) 12.6530 0.991062 0.495531 0.868590i \(-0.334974\pi\)
0.495531 + 0.868590i \(0.334974\pi\)
\(164\) 0 0
\(165\) 6.86589 0.534509
\(166\) 0 0
\(167\) 22.3537 1.72978 0.864890 0.501962i \(-0.167388\pi\)
0.864890 + 0.501962i \(0.167388\pi\)
\(168\) 0 0
\(169\) 1.00306 0.0771586
\(170\) 0 0
\(171\) 2.95995 0.226353
\(172\) 0 0
\(173\) 20.5153 1.55975 0.779875 0.625935i \(-0.215283\pi\)
0.779875 + 0.625935i \(0.215283\pi\)
\(174\) 0 0
\(175\) 3.88549 0.293715
\(176\) 0 0
\(177\) −2.37137 −0.178243
\(178\) 0 0
\(179\) −14.2623 −1.06601 −0.533005 0.846112i \(-0.678937\pi\)
−0.533005 + 0.846112i \(0.678937\pi\)
\(180\) 0 0
\(181\) −22.2037 −1.65039 −0.825194 0.564849i \(-0.808934\pi\)
−0.825194 + 0.564849i \(0.808934\pi\)
\(182\) 0 0
\(183\) 31.8062 2.35118
\(184\) 0 0
\(185\) −8.19955 −0.602843
\(186\) 0 0
\(187\) 14.8112 1.08311
\(188\) 0 0
\(189\) 3.01281 0.219150
\(190\) 0 0
\(191\) 17.0531 1.23392 0.616959 0.786995i \(-0.288365\pi\)
0.616959 + 0.786995i \(0.288365\pi\)
\(192\) 0 0
\(193\) 1.05421 0.0758835 0.0379417 0.999280i \(-0.487920\pi\)
0.0379417 + 0.999280i \(0.487920\pi\)
\(194\) 0 0
\(195\) 9.01277 0.645418
\(196\) 0 0
\(197\) 2.78465 0.198398 0.0991991 0.995068i \(-0.468372\pi\)
0.0991991 + 0.995068i \(0.468372\pi\)
\(198\) 0 0
\(199\) 7.43942 0.527367 0.263683 0.964609i \(-0.415063\pi\)
0.263683 + 0.964609i \(0.415063\pi\)
\(200\) 0 0
\(201\) −28.4722 −2.00828
\(202\) 0 0
\(203\) −0.479349 −0.0336437
\(204\) 0 0
\(205\) 7.28430 0.508758
\(206\) 0 0
\(207\) 10.0097 0.695725
\(208\) 0 0
\(209\) 5.11172 0.353585
\(210\) 0 0
\(211\) −13.4294 −0.924517 −0.462259 0.886745i \(-0.652961\pi\)
−0.462259 + 0.886745i \(0.652961\pi\)
\(212\) 0 0
\(213\) −5.07688 −0.347862
\(214\) 0 0
\(215\) 2.30003 0.156860
\(216\) 0 0
\(217\) −1.25608 −0.0852684
\(218\) 0 0
\(219\) −13.9183 −0.940509
\(220\) 0 0
\(221\) 19.4425 1.30785
\(222\) 0 0
\(223\) 5.26025 0.352252 0.176126 0.984368i \(-0.443643\pi\)
0.176126 + 0.984368i \(0.443643\pi\)
\(224\) 0 0
\(225\) −6.19454 −0.412970
\(226\) 0 0
\(227\) −12.4816 −0.828430 −0.414215 0.910179i \(-0.635944\pi\)
−0.414215 + 0.910179i \(0.635944\pi\)
\(228\) 0 0
\(229\) 3.73617 0.246893 0.123447 0.992351i \(-0.460605\pi\)
0.123447 + 0.992351i \(0.460605\pi\)
\(230\) 0 0
\(231\) −6.36520 −0.418799
\(232\) 0 0
\(233\) 6.63095 0.434408 0.217204 0.976126i \(-0.430306\pi\)
0.217204 + 0.976126i \(0.430306\pi\)
\(234\) 0 0
\(235\) −6.05060 −0.394698
\(236\) 0 0
\(237\) 1.82135 0.118310
\(238\) 0 0
\(239\) 15.1290 0.978617 0.489308 0.872111i \(-0.337249\pi\)
0.489308 + 0.872111i \(0.337249\pi\)
\(240\) 0 0
\(241\) 6.26415 0.403509 0.201755 0.979436i \(-0.435336\pi\)
0.201755 + 0.979436i \(0.435336\pi\)
\(242\) 0 0
\(243\) −15.4827 −0.993214
\(244\) 0 0
\(245\) −6.62055 −0.422971
\(246\) 0 0
\(247\) 6.71009 0.426953
\(248\) 0 0
\(249\) 29.5070 1.86993
\(250\) 0 0
\(251\) 6.24782 0.394359 0.197180 0.980367i \(-0.436822\pi\)
0.197180 + 0.980367i \(0.436822\pi\)
\(252\) 0 0
\(253\) 17.2864 1.08679
\(254\) 0 0
\(255\) 12.5138 0.783643
\(256\) 0 0
\(257\) 1.51441 0.0944666 0.0472333 0.998884i \(-0.484960\pi\)
0.0472333 + 0.998884i \(0.484960\pi\)
\(258\) 0 0
\(259\) 7.60160 0.472341
\(260\) 0 0
\(261\) 0.764216 0.0473038
\(262\) 0 0
\(263\) −10.6885 −0.659082 −0.329541 0.944141i \(-0.606894\pi\)
−0.329541 + 0.944141i \(0.606894\pi\)
\(264\) 0 0
\(265\) 2.94816 0.181104
\(266\) 0 0
\(267\) 0.663544 0.0406082
\(268\) 0 0
\(269\) −15.0899 −0.920047 −0.460024 0.887907i \(-0.652159\pi\)
−0.460024 + 0.887907i \(0.652159\pi\)
\(270\) 0 0
\(271\) 3.21500 0.195297 0.0976486 0.995221i \(-0.468868\pi\)
0.0976486 + 0.995221i \(0.468868\pi\)
\(272\) 0 0
\(273\) −8.35552 −0.505699
\(274\) 0 0
\(275\) −10.6977 −0.645098
\(276\) 0 0
\(277\) 12.5164 0.752036 0.376018 0.926612i \(-0.377293\pi\)
0.376018 + 0.926612i \(0.377293\pi\)
\(278\) 0 0
\(279\) 2.00254 0.119889
\(280\) 0 0
\(281\) 12.8585 0.767072 0.383536 0.923526i \(-0.374706\pi\)
0.383536 + 0.923526i \(0.374706\pi\)
\(282\) 0 0
\(283\) −8.81621 −0.524070 −0.262035 0.965058i \(-0.584394\pi\)
−0.262035 + 0.965058i \(0.584394\pi\)
\(284\) 0 0
\(285\) 4.31881 0.255824
\(286\) 0 0
\(287\) −6.75310 −0.398623
\(288\) 0 0
\(289\) 9.99497 0.587940
\(290\) 0 0
\(291\) −11.7344 −0.687881
\(292\) 0 0
\(293\) −14.6682 −0.856924 −0.428462 0.903560i \(-0.640944\pi\)
−0.428462 + 0.903560i \(0.640944\pi\)
\(294\) 0 0
\(295\) −1.22808 −0.0715017
\(296\) 0 0
\(297\) −8.29504 −0.481327
\(298\) 0 0
\(299\) 22.6917 1.31230
\(300\) 0 0
\(301\) −2.13230 −0.122904
\(302\) 0 0
\(303\) −15.1364 −0.869566
\(304\) 0 0
\(305\) 16.4718 0.943172
\(306\) 0 0
\(307\) −9.04718 −0.516350 −0.258175 0.966098i \(-0.583121\pi\)
−0.258175 + 0.966098i \(0.583121\pi\)
\(308\) 0 0
\(309\) −12.4433 −0.707875
\(310\) 0 0
\(311\) 8.12467 0.460708 0.230354 0.973107i \(-0.426012\pi\)
0.230354 + 0.973107i \(0.426012\pi\)
\(312\) 0 0
\(313\) 7.65731 0.432817 0.216408 0.976303i \(-0.430566\pi\)
0.216408 + 0.976303i \(0.430566\pi\)
\(314\) 0 0
\(315\) −1.90879 −0.107548
\(316\) 0 0
\(317\) −25.2787 −1.41979 −0.709897 0.704306i \(-0.751258\pi\)
−0.709897 + 0.704306i \(0.751258\pi\)
\(318\) 0 0
\(319\) 1.31977 0.0738930
\(320\) 0 0
\(321\) 0.797624 0.0445190
\(322\) 0 0
\(323\) 9.31662 0.518391
\(324\) 0 0
\(325\) −14.0428 −0.778954
\(326\) 0 0
\(327\) 33.4844 1.85169
\(328\) 0 0
\(329\) 5.60936 0.309254
\(330\) 0 0
\(331\) −20.0214 −1.10047 −0.550237 0.835009i \(-0.685463\pi\)
−0.550237 + 0.835009i \(0.685463\pi\)
\(332\) 0 0
\(333\) −12.1191 −0.664121
\(334\) 0 0
\(335\) −14.7452 −0.805616
\(336\) 0 0
\(337\) 16.0377 0.873632 0.436816 0.899551i \(-0.356106\pi\)
0.436816 + 0.899551i \(0.356106\pi\)
\(338\) 0 0
\(339\) 18.1370 0.985068
\(340\) 0 0
\(341\) 3.45832 0.187278
\(342\) 0 0
\(343\) 13.3855 0.722747
\(344\) 0 0
\(345\) 14.6050 0.786309
\(346\) 0 0
\(347\) −21.2603 −1.14131 −0.570656 0.821189i \(-0.693311\pi\)
−0.570656 + 0.821189i \(0.693311\pi\)
\(348\) 0 0
\(349\) −17.9375 −0.960171 −0.480085 0.877222i \(-0.659394\pi\)
−0.480085 + 0.877222i \(0.659394\pi\)
\(350\) 0 0
\(351\) −10.8888 −0.581201
\(352\) 0 0
\(353\) 4.12954 0.219793 0.109897 0.993943i \(-0.464948\pi\)
0.109897 + 0.993943i \(0.464948\pi\)
\(354\) 0 0
\(355\) −2.62922 −0.139544
\(356\) 0 0
\(357\) −11.6012 −0.614002
\(358\) 0 0
\(359\) 6.46751 0.341342 0.170671 0.985328i \(-0.445406\pi\)
0.170671 + 0.985328i \(0.445406\pi\)
\(360\) 0 0
\(361\) −15.7846 −0.830769
\(362\) 0 0
\(363\) −6.19698 −0.325257
\(364\) 0 0
\(365\) −7.20799 −0.377283
\(366\) 0 0
\(367\) −12.6490 −0.660270 −0.330135 0.943934i \(-0.607094\pi\)
−0.330135 + 0.943934i \(0.607094\pi\)
\(368\) 0 0
\(369\) 10.7663 0.560472
\(370\) 0 0
\(371\) −2.73316 −0.141899
\(372\) 0 0
\(373\) 22.3923 1.15943 0.579714 0.814820i \(-0.303164\pi\)
0.579714 + 0.814820i \(0.303164\pi\)
\(374\) 0 0
\(375\) −21.0809 −1.08861
\(376\) 0 0
\(377\) 1.73245 0.0892256
\(378\) 0 0
\(379\) −10.4196 −0.535217 −0.267608 0.963528i \(-0.586233\pi\)
−0.267608 + 0.963528i \(0.586233\pi\)
\(380\) 0 0
\(381\) −22.8038 −1.16828
\(382\) 0 0
\(383\) −13.5146 −0.690563 −0.345281 0.938499i \(-0.612216\pi\)
−0.345281 + 0.938499i \(0.612216\pi\)
\(384\) 0 0
\(385\) −3.29641 −0.168001
\(386\) 0 0
\(387\) 3.39948 0.172805
\(388\) 0 0
\(389\) −16.3967 −0.831345 −0.415673 0.909514i \(-0.636454\pi\)
−0.415673 + 0.909514i \(0.636454\pi\)
\(390\) 0 0
\(391\) 31.5063 1.59334
\(392\) 0 0
\(393\) 12.1601 0.613394
\(394\) 0 0
\(395\) 0.943242 0.0474597
\(396\) 0 0
\(397\) −7.08382 −0.355527 −0.177763 0.984073i \(-0.556886\pi\)
−0.177763 + 0.984073i \(0.556886\pi\)
\(398\) 0 0
\(399\) −4.00386 −0.200444
\(400\) 0 0
\(401\) 11.3630 0.567440 0.283720 0.958907i \(-0.408431\pi\)
0.283720 + 0.958907i \(0.408431\pi\)
\(402\) 0 0
\(403\) 4.53969 0.226138
\(404\) 0 0
\(405\) −12.5390 −0.623068
\(406\) 0 0
\(407\) −20.9292 −1.03742
\(408\) 0 0
\(409\) −32.2956 −1.59691 −0.798457 0.602052i \(-0.794350\pi\)
−0.798457 + 0.602052i \(0.794350\pi\)
\(410\) 0 0
\(411\) 27.6855 1.36563
\(412\) 0 0
\(413\) 1.13853 0.0560232
\(414\) 0 0
\(415\) 15.2811 0.750117
\(416\) 0 0
\(417\) −18.9811 −0.929509
\(418\) 0 0
\(419\) −12.7646 −0.623593 −0.311797 0.950149i \(-0.600931\pi\)
−0.311797 + 0.950149i \(0.600931\pi\)
\(420\) 0 0
\(421\) 12.7387 0.620845 0.310422 0.950599i \(-0.399530\pi\)
0.310422 + 0.950599i \(0.399530\pi\)
\(422\) 0 0
\(423\) −8.94288 −0.434818
\(424\) 0 0
\(425\) −19.4977 −0.945778
\(426\) 0 0
\(427\) −15.2706 −0.738996
\(428\) 0 0
\(429\) 23.0049 1.11069
\(430\) 0 0
\(431\) −14.0208 −0.675360 −0.337680 0.941261i \(-0.609642\pi\)
−0.337680 + 0.941261i \(0.609642\pi\)
\(432\) 0 0
\(433\) −15.1063 −0.725963 −0.362982 0.931796i \(-0.618241\pi\)
−0.362982 + 0.931796i \(0.618241\pi\)
\(434\) 0 0
\(435\) 1.11505 0.0534627
\(436\) 0 0
\(437\) 10.8736 0.520154
\(438\) 0 0
\(439\) 2.57545 0.122919 0.0614597 0.998110i \(-0.480424\pi\)
0.0614597 + 0.998110i \(0.480424\pi\)
\(440\) 0 0
\(441\) −9.78528 −0.465966
\(442\) 0 0
\(443\) −4.14957 −0.197152 −0.0985760 0.995130i \(-0.531429\pi\)
−0.0985760 + 0.995130i \(0.531429\pi\)
\(444\) 0 0
\(445\) 0.343636 0.0162899
\(446\) 0 0
\(447\) −0.290716 −0.0137504
\(448\) 0 0
\(449\) 11.7581 0.554900 0.277450 0.960740i \(-0.410511\pi\)
0.277450 + 0.960740i \(0.410511\pi\)
\(450\) 0 0
\(451\) 18.5930 0.875511
\(452\) 0 0
\(453\) 0.325262 0.0152821
\(454\) 0 0
\(455\) −4.32716 −0.202860
\(456\) 0 0
\(457\) 5.84962 0.273634 0.136817 0.990596i \(-0.456313\pi\)
0.136817 + 0.990596i \(0.456313\pi\)
\(458\) 0 0
\(459\) −15.1186 −0.705674
\(460\) 0 0
\(461\) −21.1899 −0.986913 −0.493457 0.869770i \(-0.664267\pi\)
−0.493457 + 0.869770i \(0.664267\pi\)
\(462\) 0 0
\(463\) −18.2654 −0.848864 −0.424432 0.905460i \(-0.639526\pi\)
−0.424432 + 0.905460i \(0.639526\pi\)
\(464\) 0 0
\(465\) 2.92188 0.135499
\(466\) 0 0
\(467\) −31.3091 −1.44881 −0.724407 0.689373i \(-0.757886\pi\)
−0.724407 + 0.689373i \(0.757886\pi\)
\(468\) 0 0
\(469\) 13.6699 0.631218
\(470\) 0 0
\(471\) 47.1295 2.17161
\(472\) 0 0
\(473\) 5.87077 0.269938
\(474\) 0 0
\(475\) −6.72914 −0.308754
\(476\) 0 0
\(477\) 4.35742 0.199513
\(478\) 0 0
\(479\) 15.9830 0.730281 0.365141 0.930952i \(-0.381021\pi\)
0.365141 + 0.930952i \(0.381021\pi\)
\(480\) 0 0
\(481\) −27.4735 −1.25268
\(482\) 0 0
\(483\) −13.5400 −0.616090
\(484\) 0 0
\(485\) −6.07699 −0.275942
\(486\) 0 0
\(487\) 9.82136 0.445048 0.222524 0.974927i \(-0.428570\pi\)
0.222524 + 0.974927i \(0.428570\pi\)
\(488\) 0 0
\(489\) 27.2869 1.23395
\(490\) 0 0
\(491\) −9.55488 −0.431206 −0.215603 0.976481i \(-0.569172\pi\)
−0.215603 + 0.976481i \(0.569172\pi\)
\(492\) 0 0
\(493\) 2.40542 0.108334
\(494\) 0 0
\(495\) 5.25539 0.236212
\(496\) 0 0
\(497\) 2.43748 0.109336
\(498\) 0 0
\(499\) −9.73479 −0.435789 −0.217895 0.975972i \(-0.569919\pi\)
−0.217895 + 0.975972i \(0.569919\pi\)
\(500\) 0 0
\(501\) 48.2068 2.15372
\(502\) 0 0
\(503\) −37.0775 −1.65320 −0.826602 0.562787i \(-0.809729\pi\)
−0.826602 + 0.562787i \(0.809729\pi\)
\(504\) 0 0
\(505\) −7.83886 −0.348825
\(506\) 0 0
\(507\) 2.16315 0.0960689
\(508\) 0 0
\(509\) 35.9330 1.59270 0.796351 0.604834i \(-0.206761\pi\)
0.796351 + 0.604834i \(0.206761\pi\)
\(510\) 0 0
\(511\) 6.68235 0.295610
\(512\) 0 0
\(513\) −5.21778 −0.230371
\(514\) 0 0
\(515\) −6.44414 −0.283963
\(516\) 0 0
\(517\) −15.4440 −0.679227
\(518\) 0 0
\(519\) 44.2422 1.94202
\(520\) 0 0
\(521\) 38.8629 1.70261 0.851307 0.524668i \(-0.175810\pi\)
0.851307 + 0.524668i \(0.175810\pi\)
\(522\) 0 0
\(523\) 12.7790 0.558786 0.279393 0.960177i \(-0.409867\pi\)
0.279393 + 0.960177i \(0.409867\pi\)
\(524\) 0 0
\(525\) 8.37924 0.365700
\(526\) 0 0
\(527\) 6.30313 0.274569
\(528\) 0 0
\(529\) 13.7715 0.598762
\(530\) 0 0
\(531\) −1.81513 −0.0787698
\(532\) 0 0
\(533\) 24.4068 1.05718
\(534\) 0 0
\(535\) 0.413073 0.0178587
\(536\) 0 0
\(537\) −30.7572 −1.32727
\(538\) 0 0
\(539\) −16.8988 −0.727883
\(540\) 0 0
\(541\) −14.9793 −0.644011 −0.322006 0.946738i \(-0.604357\pi\)
−0.322006 + 0.946738i \(0.604357\pi\)
\(542\) 0 0
\(543\) −47.8833 −2.05487
\(544\) 0 0
\(545\) 17.3409 0.742802
\(546\) 0 0
\(547\) −19.8845 −0.850201 −0.425101 0.905146i \(-0.639761\pi\)
−0.425101 + 0.905146i \(0.639761\pi\)
\(548\) 0 0
\(549\) 24.3456 1.03904
\(550\) 0 0
\(551\) 0.830168 0.0353663
\(552\) 0 0
\(553\) −0.874457 −0.0371857
\(554\) 0 0
\(555\) −17.6827 −0.750589
\(556\) 0 0
\(557\) 26.3583 1.11684 0.558418 0.829560i \(-0.311409\pi\)
0.558418 + 0.829560i \(0.311409\pi\)
\(558\) 0 0
\(559\) 7.70649 0.325950
\(560\) 0 0
\(561\) 31.9411 1.34856
\(562\) 0 0
\(563\) −30.5426 −1.28722 −0.643609 0.765354i \(-0.722564\pi\)
−0.643609 + 0.765354i \(0.722564\pi\)
\(564\) 0 0
\(565\) 9.39280 0.395158
\(566\) 0 0
\(567\) 11.6246 0.488187
\(568\) 0 0
\(569\) 11.5650 0.484830 0.242415 0.970173i \(-0.422060\pi\)
0.242415 + 0.970173i \(0.422060\pi\)
\(570\) 0 0
\(571\) −33.9047 −1.41887 −0.709433 0.704773i \(-0.751049\pi\)
−0.709433 + 0.704773i \(0.751049\pi\)
\(572\) 0 0
\(573\) 36.7758 1.53633
\(574\) 0 0
\(575\) −22.7561 −0.948995
\(576\) 0 0
\(577\) −45.5815 −1.89758 −0.948791 0.315904i \(-0.897692\pi\)
−0.948791 + 0.315904i \(0.897692\pi\)
\(578\) 0 0
\(579\) 2.27345 0.0944812
\(580\) 0 0
\(581\) −14.1667 −0.587734
\(582\) 0 0
\(583\) 7.52510 0.311658
\(584\) 0 0
\(585\) 6.89869 0.285226
\(586\) 0 0
\(587\) −47.1595 −1.94648 −0.973241 0.229787i \(-0.926197\pi\)
−0.973241 + 0.229787i \(0.926197\pi\)
\(588\) 0 0
\(589\) 2.17536 0.0896343
\(590\) 0 0
\(591\) 6.00523 0.247022
\(592\) 0 0
\(593\) −13.5334 −0.555752 −0.277876 0.960617i \(-0.589630\pi\)
−0.277876 + 0.960617i \(0.589630\pi\)
\(594\) 0 0
\(595\) −6.00804 −0.246305
\(596\) 0 0
\(597\) 16.0435 0.656615
\(598\) 0 0
\(599\) −26.6936 −1.09067 −0.545336 0.838217i \(-0.683598\pi\)
−0.545336 + 0.838217i \(0.683598\pi\)
\(600\) 0 0
\(601\) 16.4173 0.669677 0.334838 0.942276i \(-0.391318\pi\)
0.334838 + 0.942276i \(0.391318\pi\)
\(602\) 0 0
\(603\) −21.7936 −0.887506
\(604\) 0 0
\(605\) −3.20929 −0.130476
\(606\) 0 0
\(607\) −5.17188 −0.209920 −0.104960 0.994476i \(-0.533471\pi\)
−0.104960 + 0.994476i \(0.533471\pi\)
\(608\) 0 0
\(609\) −1.03374 −0.0418892
\(610\) 0 0
\(611\) −20.2732 −0.820165
\(612\) 0 0
\(613\) 47.5270 1.91960 0.959799 0.280689i \(-0.0905630\pi\)
0.959799 + 0.280689i \(0.0905630\pi\)
\(614\) 0 0
\(615\) 15.7089 0.633446
\(616\) 0 0
\(617\) −46.9899 −1.89174 −0.945870 0.324545i \(-0.894789\pi\)
−0.945870 + 0.324545i \(0.894789\pi\)
\(618\) 0 0
\(619\) 17.3290 0.696512 0.348256 0.937399i \(-0.386774\pi\)
0.348256 + 0.937399i \(0.386774\pi\)
\(620\) 0 0
\(621\) −17.6451 −0.708074
\(622\) 0 0
\(623\) −0.318576 −0.0127635
\(624\) 0 0
\(625\) 7.84608 0.313843
\(626\) 0 0
\(627\) 11.0237 0.440243
\(628\) 0 0
\(629\) −38.1455 −1.52096
\(630\) 0 0
\(631\) 29.5377 1.17588 0.587939 0.808905i \(-0.299940\pi\)
0.587939 + 0.808905i \(0.299940\pi\)
\(632\) 0 0
\(633\) −28.9611 −1.15110
\(634\) 0 0
\(635\) −11.8096 −0.468651
\(636\) 0 0
\(637\) −22.1829 −0.878917
\(638\) 0 0
\(639\) −3.88602 −0.153729
\(640\) 0 0
\(641\) 23.6635 0.934650 0.467325 0.884086i \(-0.345218\pi\)
0.467325 + 0.884086i \(0.345218\pi\)
\(642\) 0 0
\(643\) 25.1262 0.990880 0.495440 0.868642i \(-0.335007\pi\)
0.495440 + 0.868642i \(0.335007\pi\)
\(644\) 0 0
\(645\) 4.96011 0.195304
\(646\) 0 0
\(647\) −25.1637 −0.989288 −0.494644 0.869096i \(-0.664702\pi\)
−0.494644 + 0.869096i \(0.664702\pi\)
\(648\) 0 0
\(649\) −3.13465 −0.123046
\(650\) 0 0
\(651\) −2.70880 −0.106166
\(652\) 0 0
\(653\) −25.9591 −1.01586 −0.507929 0.861399i \(-0.669589\pi\)
−0.507929 + 0.861399i \(0.669589\pi\)
\(654\) 0 0
\(655\) 6.29745 0.246062
\(656\) 0 0
\(657\) −10.6535 −0.415633
\(658\) 0 0
\(659\) −5.37016 −0.209192 −0.104596 0.994515i \(-0.533355\pi\)
−0.104596 + 0.994515i \(0.533355\pi\)
\(660\) 0 0
\(661\) 16.7159 0.650174 0.325087 0.945684i \(-0.394606\pi\)
0.325087 + 0.945684i \(0.394606\pi\)
\(662\) 0 0
\(663\) 41.9288 1.62838
\(664\) 0 0
\(665\) −2.07352 −0.0804076
\(666\) 0 0
\(667\) 2.80740 0.108703
\(668\) 0 0
\(669\) 11.3440 0.438583
\(670\) 0 0
\(671\) 42.0439 1.62309
\(672\) 0 0
\(673\) −31.5558 −1.21639 −0.608193 0.793790i \(-0.708105\pi\)
−0.608193 + 0.793790i \(0.708105\pi\)
\(674\) 0 0
\(675\) 10.9197 0.420300
\(676\) 0 0
\(677\) 15.4499 0.593788 0.296894 0.954911i \(-0.404049\pi\)
0.296894 + 0.954911i \(0.404049\pi\)
\(678\) 0 0
\(679\) 5.63383 0.216207
\(680\) 0 0
\(681\) −26.9171 −1.03146
\(682\) 0 0
\(683\) 42.1816 1.61404 0.807018 0.590527i \(-0.201080\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(684\) 0 0
\(685\) 14.3378 0.547818
\(686\) 0 0
\(687\) 8.05724 0.307403
\(688\) 0 0
\(689\) 9.87811 0.376326
\(690\) 0 0
\(691\) −35.8621 −1.36426 −0.682130 0.731231i \(-0.738946\pi\)
−0.682130 + 0.731231i \(0.738946\pi\)
\(692\) 0 0
\(693\) −4.87215 −0.185078
\(694\) 0 0
\(695\) −9.82993 −0.372871
\(696\) 0 0
\(697\) 33.8877 1.28359
\(698\) 0 0
\(699\) 14.3000 0.540874
\(700\) 0 0
\(701\) 27.2216 1.02815 0.514073 0.857747i \(-0.328136\pi\)
0.514073 + 0.857747i \(0.328136\pi\)
\(702\) 0 0
\(703\) −13.1649 −0.496525
\(704\) 0 0
\(705\) −13.0484 −0.491431
\(706\) 0 0
\(707\) 7.26722 0.273312
\(708\) 0 0
\(709\) −31.7905 −1.19392 −0.596958 0.802272i \(-0.703624\pi\)
−0.596958 + 0.802272i \(0.703624\pi\)
\(710\) 0 0
\(711\) 1.39413 0.0522838
\(712\) 0 0
\(713\) 7.35649 0.275503
\(714\) 0 0
\(715\) 11.9138 0.445550
\(716\) 0 0
\(717\) 32.6265 1.21846
\(718\) 0 0
\(719\) −15.8452 −0.590926 −0.295463 0.955354i \(-0.595474\pi\)
−0.295463 + 0.955354i \(0.595474\pi\)
\(720\) 0 0
\(721\) 5.97420 0.222491
\(722\) 0 0
\(723\) 13.5089 0.502402
\(724\) 0 0
\(725\) −1.73736 −0.0645241
\(726\) 0 0
\(727\) 15.6071 0.578837 0.289418 0.957203i \(-0.406538\pi\)
0.289418 + 0.957203i \(0.406538\pi\)
\(728\) 0 0
\(729\) 0.292759 0.0108429
\(730\) 0 0
\(731\) 10.7001 0.395756
\(732\) 0 0
\(733\) −16.5963 −0.612999 −0.306499 0.951871i \(-0.599158\pi\)
−0.306499 + 0.951871i \(0.599158\pi\)
\(734\) 0 0
\(735\) −14.2775 −0.526635
\(736\) 0 0
\(737\) −37.6368 −1.38637
\(738\) 0 0
\(739\) −14.8369 −0.545785 −0.272892 0.962045i \(-0.587980\pi\)
−0.272892 + 0.962045i \(0.587980\pi\)
\(740\) 0 0
\(741\) 14.4706 0.531592
\(742\) 0 0
\(743\) −30.2839 −1.11101 −0.555504 0.831514i \(-0.687475\pi\)
−0.555504 + 0.831514i \(0.687475\pi\)
\(744\) 0 0
\(745\) −0.150556 −0.00551595
\(746\) 0 0
\(747\) 22.5856 0.826366
\(748\) 0 0
\(749\) −0.382950 −0.0139927
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 13.4737 0.491010
\(754\) 0 0
\(755\) 0.168446 0.00613040
\(756\) 0 0
\(757\) 7.95776 0.289230 0.144615 0.989488i \(-0.453806\pi\)
0.144615 + 0.989488i \(0.453806\pi\)
\(758\) 0 0
\(759\) 37.2790 1.35314
\(760\) 0 0
\(761\) −5.15733 −0.186953 −0.0934765 0.995621i \(-0.529798\pi\)
−0.0934765 + 0.995621i \(0.529798\pi\)
\(762\) 0 0
\(763\) −16.0763 −0.582002
\(764\) 0 0
\(765\) 9.57848 0.346311
\(766\) 0 0
\(767\) −4.11482 −0.148578
\(768\) 0 0
\(769\) −30.1482 −1.08717 −0.543586 0.839353i \(-0.682934\pi\)
−0.543586 + 0.839353i \(0.682934\pi\)
\(770\) 0 0
\(771\) 3.26591 0.117619
\(772\) 0 0
\(773\) 44.6084 1.60445 0.802227 0.597019i \(-0.203648\pi\)
0.802227 + 0.597019i \(0.203648\pi\)
\(774\) 0 0
\(775\) −4.55257 −0.163533
\(776\) 0 0
\(777\) 16.3932 0.588103
\(778\) 0 0
\(779\) 11.6955 0.419033
\(780\) 0 0
\(781\) −6.71101 −0.240139
\(782\) 0 0
\(783\) −1.34715 −0.0481434
\(784\) 0 0
\(785\) 24.4074 0.871138
\(786\) 0 0
\(787\) −37.8061 −1.34764 −0.673821 0.738895i \(-0.735348\pi\)
−0.673821 + 0.738895i \(0.735348\pi\)
\(788\) 0 0
\(789\) −23.0503 −0.820612
\(790\) 0 0
\(791\) −8.70784 −0.309615
\(792\) 0 0
\(793\) 55.1905 1.95987
\(794\) 0 0
\(795\) 6.35784 0.225489
\(796\) 0 0
\(797\) 12.5860 0.445819 0.222910 0.974839i \(-0.428445\pi\)
0.222910 + 0.974839i \(0.428445\pi\)
\(798\) 0 0
\(799\) −28.1483 −0.995815
\(800\) 0 0
\(801\) 0.507899 0.0179457
\(802\) 0 0
\(803\) −18.3982 −0.649259
\(804\) 0 0
\(805\) −7.01208 −0.247143
\(806\) 0 0
\(807\) −32.5421 −1.14554
\(808\) 0 0
\(809\) 27.8387 0.978757 0.489378 0.872072i \(-0.337224\pi\)
0.489378 + 0.872072i \(0.337224\pi\)
\(810\) 0 0
\(811\) 47.6031 1.67157 0.835786 0.549056i \(-0.185013\pi\)
0.835786 + 0.549056i \(0.185013\pi\)
\(812\) 0 0
\(813\) 6.93329 0.243161
\(814\) 0 0
\(815\) 14.1313 0.494998
\(816\) 0 0
\(817\) 3.69285 0.129197
\(818\) 0 0
\(819\) −6.39561 −0.223481
\(820\) 0 0
\(821\) 21.0081 0.733186 0.366593 0.930381i \(-0.380524\pi\)
0.366593 + 0.930381i \(0.380524\pi\)
\(822\) 0 0
\(823\) 16.9903 0.592245 0.296122 0.955150i \(-0.404306\pi\)
0.296122 + 0.955150i \(0.404306\pi\)
\(824\) 0 0
\(825\) −23.0702 −0.803201
\(826\) 0 0
\(827\) −0.312392 −0.0108629 −0.00543146 0.999985i \(-0.501729\pi\)
−0.00543146 + 0.999985i \(0.501729\pi\)
\(828\) 0 0
\(829\) −4.03882 −0.140274 −0.0701370 0.997537i \(-0.522344\pi\)
−0.0701370 + 0.997537i \(0.522344\pi\)
\(830\) 0 0
\(831\) 26.9921 0.936347
\(832\) 0 0
\(833\) −30.7998 −1.06715
\(834\) 0 0
\(835\) 24.9653 0.863960
\(836\) 0 0
\(837\) −3.53007 −0.122017
\(838\) 0 0
\(839\) −47.1610 −1.62818 −0.814090 0.580739i \(-0.802764\pi\)
−0.814090 + 0.580739i \(0.802764\pi\)
\(840\) 0 0
\(841\) −28.7857 −0.992609
\(842\) 0 0
\(843\) 27.7299 0.955069
\(844\) 0 0
\(845\) 1.12025 0.0385378
\(846\) 0 0
\(847\) 2.97526 0.102231
\(848\) 0 0
\(849\) −19.0126 −0.652510
\(850\) 0 0
\(851\) −44.5203 −1.52614
\(852\) 0 0
\(853\) −36.4086 −1.24661 −0.623304 0.781980i \(-0.714210\pi\)
−0.623304 + 0.781980i \(0.714210\pi\)
\(854\) 0 0
\(855\) 3.30577 0.113055
\(856\) 0 0
\(857\) 23.3770 0.798544 0.399272 0.916832i \(-0.369263\pi\)
0.399272 + 0.916832i \(0.369263\pi\)
\(858\) 0 0
\(859\) −23.3953 −0.798238 −0.399119 0.916899i \(-0.630684\pi\)
−0.399119 + 0.916899i \(0.630684\pi\)
\(860\) 0 0
\(861\) −14.5634 −0.496319
\(862\) 0 0
\(863\) 9.88486 0.336485 0.168242 0.985746i \(-0.446191\pi\)
0.168242 + 0.985746i \(0.446191\pi\)
\(864\) 0 0
\(865\) 22.9122 0.779037
\(866\) 0 0
\(867\) 21.5546 0.732034
\(868\) 0 0
\(869\) 2.40760 0.0816724
\(870\) 0 0
\(871\) −49.4054 −1.67404
\(872\) 0 0
\(873\) −8.98189 −0.303991
\(874\) 0 0
\(875\) 10.1212 0.342159
\(876\) 0 0
\(877\) 36.0742 1.21814 0.609069 0.793117i \(-0.291543\pi\)
0.609069 + 0.793117i \(0.291543\pi\)
\(878\) 0 0
\(879\) −31.6326 −1.06694
\(880\) 0 0
\(881\) 27.2176 0.916985 0.458493 0.888698i \(-0.348390\pi\)
0.458493 + 0.888698i \(0.348390\pi\)
\(882\) 0 0
\(883\) 8.59263 0.289165 0.144583 0.989493i \(-0.453816\pi\)
0.144583 + 0.989493i \(0.453816\pi\)
\(884\) 0 0
\(885\) −2.64842 −0.0890256
\(886\) 0 0
\(887\) −15.5178 −0.521036 −0.260518 0.965469i \(-0.583893\pi\)
−0.260518 + 0.965469i \(0.583893\pi\)
\(888\) 0 0
\(889\) 10.9484 0.367199
\(890\) 0 0
\(891\) −32.0055 −1.07223
\(892\) 0 0
\(893\) −9.71466 −0.325089
\(894\) 0 0
\(895\) −15.9285 −0.532432
\(896\) 0 0
\(897\) 48.9358 1.63392
\(898\) 0 0
\(899\) 0.561647 0.0187320
\(900\) 0 0
\(901\) 13.7153 0.456921
\(902\) 0 0
\(903\) −4.59840 −0.153025
\(904\) 0 0
\(905\) −24.7978 −0.824307
\(906\) 0 0
\(907\) −24.3134 −0.807313 −0.403657 0.914911i \(-0.632261\pi\)
−0.403657 + 0.914911i \(0.632261\pi\)
\(908\) 0 0
\(909\) −11.5860 −0.384282
\(910\) 0 0
\(911\) 15.3373 0.508148 0.254074 0.967185i \(-0.418229\pi\)
0.254074 + 0.967185i \(0.418229\pi\)
\(912\) 0 0
\(913\) 39.0046 1.29086
\(914\) 0 0
\(915\) 35.5222 1.17433
\(916\) 0 0
\(917\) −5.83821 −0.192795
\(918\) 0 0
\(919\) −25.2258 −0.832121 −0.416061 0.909337i \(-0.636590\pi\)
−0.416061 + 0.909337i \(0.636590\pi\)
\(920\) 0 0
\(921\) −19.5107 −0.642898
\(922\) 0 0
\(923\) −8.80947 −0.289967
\(924\) 0 0
\(925\) 27.5514 0.905886
\(926\) 0 0
\(927\) −9.52454 −0.312827
\(928\) 0 0
\(929\) −27.5440 −0.903689 −0.451845 0.892097i \(-0.649234\pi\)
−0.451845 + 0.892097i \(0.649234\pi\)
\(930\) 0 0
\(931\) −10.6298 −0.348376
\(932\) 0 0
\(933\) 17.5212 0.573620
\(934\) 0 0
\(935\) 16.5417 0.540970
\(936\) 0 0
\(937\) 33.9734 1.10986 0.554931 0.831897i \(-0.312745\pi\)
0.554931 + 0.831897i \(0.312745\pi\)
\(938\) 0 0
\(939\) 16.5133 0.538893
\(940\) 0 0
\(941\) 32.6469 1.06426 0.532129 0.846663i \(-0.321392\pi\)
0.532129 + 0.846663i \(0.321392\pi\)
\(942\) 0 0
\(943\) 39.5508 1.28795
\(944\) 0 0
\(945\) 3.36480 0.109457
\(946\) 0 0
\(947\) −60.1595 −1.95492 −0.977461 0.211118i \(-0.932290\pi\)
−0.977461 + 0.211118i \(0.932290\pi\)
\(948\) 0 0
\(949\) −24.1511 −0.783979
\(950\) 0 0
\(951\) −54.5147 −1.76776
\(952\) 0 0
\(953\) 19.5815 0.634307 0.317154 0.948374i \(-0.397273\pi\)
0.317154 + 0.948374i \(0.397273\pi\)
\(954\) 0 0
\(955\) 19.0454 0.616296
\(956\) 0 0
\(957\) 2.84615 0.0920029
\(958\) 0 0
\(959\) −13.2922 −0.429228
\(960\) 0 0
\(961\) −29.5283 −0.952525
\(962\) 0 0
\(963\) 0.610529 0.0196740
\(964\) 0 0
\(965\) 1.17737 0.0379009
\(966\) 0 0
\(967\) 25.5911 0.822954 0.411477 0.911420i \(-0.365013\pi\)
0.411477 + 0.911420i \(0.365013\pi\)
\(968\) 0 0
\(969\) 20.0917 0.645440
\(970\) 0 0
\(971\) 29.3292 0.941220 0.470610 0.882341i \(-0.344034\pi\)
0.470610 + 0.882341i \(0.344034\pi\)
\(972\) 0 0
\(973\) 9.11309 0.292152
\(974\) 0 0
\(975\) −30.2840 −0.969863
\(976\) 0 0
\(977\) −27.0385 −0.865038 −0.432519 0.901625i \(-0.642375\pi\)
−0.432519 + 0.901625i \(0.642375\pi\)
\(978\) 0 0
\(979\) 0.877123 0.0280330
\(980\) 0 0
\(981\) 25.6301 0.818307
\(982\) 0 0
\(983\) 11.4927 0.366561 0.183281 0.983061i \(-0.441328\pi\)
0.183281 + 0.983061i \(0.441328\pi\)
\(984\) 0 0
\(985\) 3.10999 0.0990924
\(986\) 0 0
\(987\) 12.0969 0.385047
\(988\) 0 0
\(989\) 12.4882 0.397102
\(990\) 0 0
\(991\) −50.0434 −1.58968 −0.794841 0.606818i \(-0.792446\pi\)
−0.794841 + 0.606818i \(0.792446\pi\)
\(992\) 0 0
\(993\) −43.1770 −1.37018
\(994\) 0 0
\(995\) 8.30858 0.263400
\(996\) 0 0
\(997\) 52.7736 1.67136 0.835678 0.549219i \(-0.185075\pi\)
0.835678 + 0.549219i \(0.185075\pi\)
\(998\) 0 0
\(999\) 21.3634 0.675909
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 \(a_p\))