Properties

Label 6008.2.a.e.1.45
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 1.45
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.93661 q^{3} +3.50463 q^{5} +3.59612 q^{7} +5.62368 q^{9} +O(q^{10})\) \(q+2.93661 q^{3} +3.50463 q^{5} +3.59612 q^{7} +5.62368 q^{9} +2.69390 q^{11} -2.54493 q^{13} +10.2917 q^{15} +2.23138 q^{17} -7.67199 q^{19} +10.5604 q^{21} -1.01256 q^{23} +7.28243 q^{25} +7.70474 q^{27} +5.38015 q^{29} -2.95587 q^{31} +7.91094 q^{33} +12.6031 q^{35} -2.73071 q^{37} -7.47347 q^{39} +3.58852 q^{41} -11.3625 q^{43} +19.7089 q^{45} -1.21067 q^{47} +5.93210 q^{49} +6.55270 q^{51} -11.6872 q^{53} +9.44112 q^{55} -22.5296 q^{57} -3.51792 q^{59} -1.42170 q^{61} +20.2235 q^{63} -8.91905 q^{65} -1.46876 q^{67} -2.97351 q^{69} -8.41321 q^{71} -11.1092 q^{73} +21.3857 q^{75} +9.68759 q^{77} +7.93478 q^{79} +5.75476 q^{81} +10.7358 q^{83} +7.82016 q^{85} +15.7994 q^{87} +14.2270 q^{89} -9.15189 q^{91} -8.68024 q^{93} -26.8875 q^{95} -7.71302 q^{97} +15.1496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.93661 1.69545 0.847727 0.530434i \(-0.177971\pi\)
0.847727 + 0.530434i \(0.177971\pi\)
\(4\) 0 0
\(5\) 3.50463 1.56732 0.783659 0.621191i \(-0.213351\pi\)
0.783659 + 0.621191i \(0.213351\pi\)
\(6\) 0 0
\(7\) 3.59612 1.35921 0.679603 0.733580i \(-0.262152\pi\)
0.679603 + 0.733580i \(0.262152\pi\)
\(8\) 0 0
\(9\) 5.62368 1.87456
\(10\) 0 0
\(11\) 2.69390 0.812241 0.406121 0.913819i \(-0.366881\pi\)
0.406121 + 0.913819i \(0.366881\pi\)
\(12\) 0 0
\(13\) −2.54493 −0.705837 −0.352919 0.935654i \(-0.614811\pi\)
−0.352919 + 0.935654i \(0.614811\pi\)
\(14\) 0 0
\(15\) 10.2917 2.65731
\(16\) 0 0
\(17\) 2.23138 0.541189 0.270595 0.962693i \(-0.412780\pi\)
0.270595 + 0.962693i \(0.412780\pi\)
\(18\) 0 0
\(19\) −7.67199 −1.76007 −0.880037 0.474905i \(-0.842482\pi\)
−0.880037 + 0.474905i \(0.842482\pi\)
\(20\) 0 0
\(21\) 10.5604 2.30447
\(22\) 0 0
\(23\) −1.01256 −0.211134 −0.105567 0.994412i \(-0.533666\pi\)
−0.105567 + 0.994412i \(0.533666\pi\)
\(24\) 0 0
\(25\) 7.28243 1.45649
\(26\) 0 0
\(27\) 7.70474 1.48278
\(28\) 0 0
\(29\) 5.38015 0.999070 0.499535 0.866294i \(-0.333504\pi\)
0.499535 + 0.866294i \(0.333504\pi\)
\(30\) 0 0
\(31\) −2.95587 −0.530890 −0.265445 0.964126i \(-0.585519\pi\)
−0.265445 + 0.964126i \(0.585519\pi\)
\(32\) 0 0
\(33\) 7.91094 1.37712
\(34\) 0 0
\(35\) 12.6031 2.13031
\(36\) 0 0
\(37\) −2.73071 −0.448926 −0.224463 0.974483i \(-0.572063\pi\)
−0.224463 + 0.974483i \(0.572063\pi\)
\(38\) 0 0
\(39\) −7.47347 −1.19671
\(40\) 0 0
\(41\) 3.58852 0.560432 0.280216 0.959937i \(-0.409594\pi\)
0.280216 + 0.959937i \(0.409594\pi\)
\(42\) 0 0
\(43\) −11.3625 −1.73277 −0.866385 0.499377i \(-0.833562\pi\)
−0.866385 + 0.499377i \(0.833562\pi\)
\(44\) 0 0
\(45\) 19.7089 2.93803
\(46\) 0 0
\(47\) −1.21067 −0.176594 −0.0882968 0.996094i \(-0.528142\pi\)
−0.0882968 + 0.996094i \(0.528142\pi\)
\(48\) 0 0
\(49\) 5.93210 0.847443
\(50\) 0 0
\(51\) 6.55270 0.917561
\(52\) 0 0
\(53\) −11.6872 −1.60535 −0.802677 0.596414i \(-0.796592\pi\)
−0.802677 + 0.596414i \(0.796592\pi\)
\(54\) 0 0
\(55\) 9.44112 1.27304
\(56\) 0 0
\(57\) −22.5296 −2.98412
\(58\) 0 0
\(59\) −3.51792 −0.457994 −0.228997 0.973427i \(-0.573545\pi\)
−0.228997 + 0.973427i \(0.573545\pi\)
\(60\) 0 0
\(61\) −1.42170 −0.182030 −0.0910152 0.995850i \(-0.529011\pi\)
−0.0910152 + 0.995850i \(0.529011\pi\)
\(62\) 0 0
\(63\) 20.2235 2.54792
\(64\) 0 0
\(65\) −8.91905 −1.10627
\(66\) 0 0
\(67\) −1.46876 −0.179438 −0.0897188 0.995967i \(-0.528597\pi\)
−0.0897188 + 0.995967i \(0.528597\pi\)
\(68\) 0 0
\(69\) −2.97351 −0.357968
\(70\) 0 0
\(71\) −8.41321 −0.998464 −0.499232 0.866468i \(-0.666384\pi\)
−0.499232 + 0.866468i \(0.666384\pi\)
\(72\) 0 0
\(73\) −11.1092 −1.30023 −0.650114 0.759837i \(-0.725279\pi\)
−0.650114 + 0.759837i \(0.725279\pi\)
\(74\) 0 0
\(75\) 21.3857 2.46941
\(76\) 0 0
\(77\) 9.68759 1.10400
\(78\) 0 0
\(79\) 7.93478 0.892732 0.446366 0.894850i \(-0.352718\pi\)
0.446366 + 0.894850i \(0.352718\pi\)
\(80\) 0 0
\(81\) 5.75476 0.639418
\(82\) 0 0
\(83\) 10.7358 1.17840 0.589201 0.807986i \(-0.299443\pi\)
0.589201 + 0.807986i \(0.299443\pi\)
\(84\) 0 0
\(85\) 7.82016 0.848216
\(86\) 0 0
\(87\) 15.7994 1.69388
\(88\) 0 0
\(89\) 14.2270 1.50806 0.754029 0.656841i \(-0.228108\pi\)
0.754029 + 0.656841i \(0.228108\pi\)
\(90\) 0 0
\(91\) −9.15189 −0.959378
\(92\) 0 0
\(93\) −8.68024 −0.900099
\(94\) 0 0
\(95\) −26.8875 −2.75860
\(96\) 0 0
\(97\) −7.71302 −0.783138 −0.391569 0.920149i \(-0.628068\pi\)
−0.391569 + 0.920149i \(0.628068\pi\)
\(98\) 0 0
\(99\) 15.1496 1.52260
\(100\) 0 0
\(101\) −3.18955 −0.317372 −0.158686 0.987329i \(-0.550726\pi\)
−0.158686 + 0.987329i \(0.550726\pi\)
\(102\) 0 0
\(103\) 14.1045 1.38976 0.694878 0.719128i \(-0.255459\pi\)
0.694878 + 0.719128i \(0.255459\pi\)
\(104\) 0 0
\(105\) 37.0103 3.61184
\(106\) 0 0
\(107\) 15.3289 1.48190 0.740948 0.671562i \(-0.234376\pi\)
0.740948 + 0.671562i \(0.234376\pi\)
\(108\) 0 0
\(109\) −1.80717 −0.173096 −0.0865478 0.996248i \(-0.527584\pi\)
−0.0865478 + 0.996248i \(0.527584\pi\)
\(110\) 0 0
\(111\) −8.01903 −0.761133
\(112\) 0 0
\(113\) 9.98652 0.939453 0.469726 0.882812i \(-0.344353\pi\)
0.469726 + 0.882812i \(0.344353\pi\)
\(114\) 0 0
\(115\) −3.54866 −0.330914
\(116\) 0 0
\(117\) −14.3119 −1.32313
\(118\) 0 0
\(119\) 8.02432 0.735588
\(120\) 0 0
\(121\) −3.74290 −0.340264
\(122\) 0 0
\(123\) 10.5381 0.950186
\(124\) 0 0
\(125\) 7.99909 0.715460
\(126\) 0 0
\(127\) −8.22182 −0.729568 −0.364784 0.931092i \(-0.618857\pi\)
−0.364784 + 0.931092i \(0.618857\pi\)
\(128\) 0 0
\(129\) −33.3673 −2.93783
\(130\) 0 0
\(131\) 2.39359 0.209129 0.104564 0.994518i \(-0.466655\pi\)
0.104564 + 0.994518i \(0.466655\pi\)
\(132\) 0 0
\(133\) −27.5894 −2.39230
\(134\) 0 0
\(135\) 27.0023 2.32398
\(136\) 0 0
\(137\) −1.26489 −0.108067 −0.0540336 0.998539i \(-0.517208\pi\)
−0.0540336 + 0.998539i \(0.517208\pi\)
\(138\) 0 0
\(139\) −13.3386 −1.13137 −0.565684 0.824622i \(-0.691388\pi\)
−0.565684 + 0.824622i \(0.691388\pi\)
\(140\) 0 0
\(141\) −3.55525 −0.299406
\(142\) 0 0
\(143\) −6.85579 −0.573310
\(144\) 0 0
\(145\) 18.8555 1.56586
\(146\) 0 0
\(147\) 17.4203 1.43680
\(148\) 0 0
\(149\) 10.2709 0.841428 0.420714 0.907193i \(-0.361780\pi\)
0.420714 + 0.907193i \(0.361780\pi\)
\(150\) 0 0
\(151\) −19.1035 −1.55462 −0.777310 0.629118i \(-0.783416\pi\)
−0.777310 + 0.629118i \(0.783416\pi\)
\(152\) 0 0
\(153\) 12.5486 1.01449
\(154\) 0 0
\(155\) −10.3592 −0.832074
\(156\) 0 0
\(157\) −11.2678 −0.899268 −0.449634 0.893213i \(-0.648446\pi\)
−0.449634 + 0.893213i \(0.648446\pi\)
\(158\) 0 0
\(159\) −34.3206 −2.72180
\(160\) 0 0
\(161\) −3.64130 −0.286975
\(162\) 0 0
\(163\) −2.86346 −0.224283 −0.112142 0.993692i \(-0.535771\pi\)
−0.112142 + 0.993692i \(0.535771\pi\)
\(164\) 0 0
\(165\) 27.7249 2.15838
\(166\) 0 0
\(167\) −14.8434 −1.14861 −0.574307 0.818640i \(-0.694728\pi\)
−0.574307 + 0.818640i \(0.694728\pi\)
\(168\) 0 0
\(169\) −6.52332 −0.501794
\(170\) 0 0
\(171\) −43.1448 −3.29937
\(172\) 0 0
\(173\) 18.4449 1.40234 0.701171 0.712993i \(-0.252661\pi\)
0.701171 + 0.712993i \(0.252661\pi\)
\(174\) 0 0
\(175\) 26.1885 1.97967
\(176\) 0 0
\(177\) −10.3308 −0.776508
\(178\) 0 0
\(179\) 16.9032 1.26340 0.631701 0.775212i \(-0.282357\pi\)
0.631701 + 0.775212i \(0.282357\pi\)
\(180\) 0 0
\(181\) 14.9920 1.11434 0.557171 0.830397i \(-0.311887\pi\)
0.557171 + 0.830397i \(0.311887\pi\)
\(182\) 0 0
\(183\) −4.17499 −0.308624
\(184\) 0 0
\(185\) −9.57013 −0.703610
\(186\) 0 0
\(187\) 6.01112 0.439576
\(188\) 0 0
\(189\) 27.7072 2.01540
\(190\) 0 0
\(191\) −0.588291 −0.0425673 −0.0212836 0.999773i \(-0.506775\pi\)
−0.0212836 + 0.999773i \(0.506775\pi\)
\(192\) 0 0
\(193\) −5.57048 −0.400972 −0.200486 0.979697i \(-0.564252\pi\)
−0.200486 + 0.979697i \(0.564252\pi\)
\(194\) 0 0
\(195\) −26.1918 −1.87563
\(196\) 0 0
\(197\) 26.2860 1.87280 0.936401 0.350931i \(-0.114135\pi\)
0.936401 + 0.350931i \(0.114135\pi\)
\(198\) 0 0
\(199\) −2.30553 −0.163435 −0.0817175 0.996656i \(-0.526041\pi\)
−0.0817175 + 0.996656i \(0.526041\pi\)
\(200\) 0 0
\(201\) −4.31318 −0.304228
\(202\) 0 0
\(203\) 19.3477 1.35794
\(204\) 0 0
\(205\) 12.5764 0.878376
\(206\) 0 0
\(207\) −5.69434 −0.395784
\(208\) 0 0
\(209\) −20.6676 −1.42960
\(210\) 0 0
\(211\) −13.5911 −0.935651 −0.467825 0.883821i \(-0.654962\pi\)
−0.467825 + 0.883821i \(0.654962\pi\)
\(212\) 0 0
\(213\) −24.7063 −1.69285
\(214\) 0 0
\(215\) −39.8215 −2.71580
\(216\) 0 0
\(217\) −10.6297 −0.721589
\(218\) 0 0
\(219\) −32.6233 −2.20448
\(220\) 0 0
\(221\) −5.67871 −0.381991
\(222\) 0 0
\(223\) −5.85854 −0.392317 −0.196158 0.980572i \(-0.562847\pi\)
−0.196158 + 0.980572i \(0.562847\pi\)
\(224\) 0 0
\(225\) 40.9541 2.73027
\(226\) 0 0
\(227\) 16.9583 1.12556 0.562781 0.826606i \(-0.309731\pi\)
0.562781 + 0.826606i \(0.309731\pi\)
\(228\) 0 0
\(229\) 9.70965 0.641631 0.320816 0.947142i \(-0.396043\pi\)
0.320816 + 0.947142i \(0.396043\pi\)
\(230\) 0 0
\(231\) 28.4487 1.87179
\(232\) 0 0
\(233\) −29.4730 −1.93084 −0.965420 0.260701i \(-0.916046\pi\)
−0.965420 + 0.260701i \(0.916046\pi\)
\(234\) 0 0
\(235\) −4.24293 −0.276779
\(236\) 0 0
\(237\) 23.3014 1.51359
\(238\) 0 0
\(239\) 8.18187 0.529241 0.264621 0.964353i \(-0.414753\pi\)
0.264621 + 0.964353i \(0.414753\pi\)
\(240\) 0 0
\(241\) −19.2420 −1.23948 −0.619742 0.784806i \(-0.712763\pi\)
−0.619742 + 0.784806i \(0.712763\pi\)
\(242\) 0 0
\(243\) −6.21471 −0.398674
\(244\) 0 0
\(245\) 20.7898 1.32821
\(246\) 0 0
\(247\) 19.5247 1.24233
\(248\) 0 0
\(249\) 31.5267 1.99793
\(250\) 0 0
\(251\) −2.42671 −0.153173 −0.0765864 0.997063i \(-0.524402\pi\)
−0.0765864 + 0.997063i \(0.524402\pi\)
\(252\) 0 0
\(253\) −2.72775 −0.171492
\(254\) 0 0
\(255\) 22.9648 1.43811
\(256\) 0 0
\(257\) −15.5109 −0.967544 −0.483772 0.875194i \(-0.660734\pi\)
−0.483772 + 0.875194i \(0.660734\pi\)
\(258\) 0 0
\(259\) −9.81997 −0.610183
\(260\) 0 0
\(261\) 30.2563 1.87282
\(262\) 0 0
\(263\) −1.35072 −0.0832891 −0.0416446 0.999132i \(-0.513260\pi\)
−0.0416446 + 0.999132i \(0.513260\pi\)
\(264\) 0 0
\(265\) −40.9591 −2.51610
\(266\) 0 0
\(267\) 41.7791 2.55684
\(268\) 0 0
\(269\) −5.53476 −0.337460 −0.168730 0.985662i \(-0.553967\pi\)
−0.168730 + 0.985662i \(0.553967\pi\)
\(270\) 0 0
\(271\) −3.07472 −0.186776 −0.0933881 0.995630i \(-0.529770\pi\)
−0.0933881 + 0.995630i \(0.529770\pi\)
\(272\) 0 0
\(273\) −26.8755 −1.62658
\(274\) 0 0
\(275\) 19.6181 1.18302
\(276\) 0 0
\(277\) 0.965160 0.0579908 0.0289954 0.999580i \(-0.490769\pi\)
0.0289954 + 0.999580i \(0.490769\pi\)
\(278\) 0 0
\(279\) −16.6229 −0.995186
\(280\) 0 0
\(281\) 11.1746 0.666623 0.333311 0.942817i \(-0.391834\pi\)
0.333311 + 0.942817i \(0.391834\pi\)
\(282\) 0 0
\(283\) 1.17440 0.0698110 0.0349055 0.999391i \(-0.488887\pi\)
0.0349055 + 0.999391i \(0.488887\pi\)
\(284\) 0 0
\(285\) −78.9580 −4.67707
\(286\) 0 0
\(287\) 12.9047 0.761743
\(288\) 0 0
\(289\) −12.0209 −0.707114
\(290\) 0 0
\(291\) −22.6501 −1.32777
\(292\) 0 0
\(293\) −7.19135 −0.420123 −0.210062 0.977688i \(-0.567366\pi\)
−0.210062 + 0.977688i \(0.567366\pi\)
\(294\) 0 0
\(295\) −12.3290 −0.717823
\(296\) 0 0
\(297\) 20.7558 1.20437
\(298\) 0 0
\(299\) 2.57691 0.149026
\(300\) 0 0
\(301\) −40.8611 −2.35519
\(302\) 0 0
\(303\) −9.36647 −0.538090
\(304\) 0 0
\(305\) −4.98254 −0.285300
\(306\) 0 0
\(307\) −11.3913 −0.650138 −0.325069 0.945690i \(-0.605388\pi\)
−0.325069 + 0.945690i \(0.605388\pi\)
\(308\) 0 0
\(309\) 41.4193 2.35626
\(310\) 0 0
\(311\) −22.8473 −1.29555 −0.647776 0.761831i \(-0.724301\pi\)
−0.647776 + 0.761831i \(0.724301\pi\)
\(312\) 0 0
\(313\) 21.9858 1.24271 0.621356 0.783528i \(-0.286582\pi\)
0.621356 + 0.783528i \(0.286582\pi\)
\(314\) 0 0
\(315\) 70.8757 3.99340
\(316\) 0 0
\(317\) 19.3667 1.08774 0.543871 0.839169i \(-0.316958\pi\)
0.543871 + 0.839169i \(0.316958\pi\)
\(318\) 0 0
\(319\) 14.4936 0.811486
\(320\) 0 0
\(321\) 45.0149 2.51249
\(322\) 0 0
\(323\) −17.1191 −0.952533
\(324\) 0 0
\(325\) −18.5333 −1.02804
\(326\) 0 0
\(327\) −5.30696 −0.293476
\(328\) 0 0
\(329\) −4.35370 −0.240027
\(330\) 0 0
\(331\) 26.0381 1.43118 0.715592 0.698519i \(-0.246157\pi\)
0.715592 + 0.698519i \(0.246157\pi\)
\(332\) 0 0
\(333\) −15.3567 −0.841539
\(334\) 0 0
\(335\) −5.14746 −0.281236
\(336\) 0 0
\(337\) 10.4605 0.569820 0.284910 0.958554i \(-0.408036\pi\)
0.284910 + 0.958554i \(0.408036\pi\)
\(338\) 0 0
\(339\) 29.3265 1.59280
\(340\) 0 0
\(341\) −7.96282 −0.431211
\(342\) 0 0
\(343\) −3.84031 −0.207357
\(344\) 0 0
\(345\) −10.4210 −0.561050
\(346\) 0 0
\(347\) −8.17453 −0.438832 −0.219416 0.975631i \(-0.570415\pi\)
−0.219416 + 0.975631i \(0.570415\pi\)
\(348\) 0 0
\(349\) −6.22532 −0.333234 −0.166617 0.986022i \(-0.553284\pi\)
−0.166617 + 0.986022i \(0.553284\pi\)
\(350\) 0 0
\(351\) −19.6080 −1.04660
\(352\) 0 0
\(353\) 33.8340 1.80080 0.900402 0.435060i \(-0.143273\pi\)
0.900402 + 0.435060i \(0.143273\pi\)
\(354\) 0 0
\(355\) −29.4852 −1.56491
\(356\) 0 0
\(357\) 23.5643 1.24716
\(358\) 0 0
\(359\) 4.15995 0.219554 0.109777 0.993956i \(-0.464986\pi\)
0.109777 + 0.993956i \(0.464986\pi\)
\(360\) 0 0
\(361\) 39.8594 2.09786
\(362\) 0 0
\(363\) −10.9915 −0.576902
\(364\) 0 0
\(365\) −38.9335 −2.03787
\(366\) 0 0
\(367\) 29.0208 1.51488 0.757438 0.652907i \(-0.226451\pi\)
0.757438 + 0.652907i \(0.226451\pi\)
\(368\) 0 0
\(369\) 20.1807 1.05056
\(370\) 0 0
\(371\) −42.0284 −2.18201
\(372\) 0 0
\(373\) 27.5934 1.42873 0.714366 0.699773i \(-0.246715\pi\)
0.714366 + 0.699773i \(0.246715\pi\)
\(374\) 0 0
\(375\) 23.4902 1.21303
\(376\) 0 0
\(377\) −13.6921 −0.705180
\(378\) 0 0
\(379\) 24.1132 1.23861 0.619306 0.785150i \(-0.287414\pi\)
0.619306 + 0.785150i \(0.287414\pi\)
\(380\) 0 0
\(381\) −24.1443 −1.23695
\(382\) 0 0
\(383\) −9.50697 −0.485783 −0.242892 0.970053i \(-0.578096\pi\)
−0.242892 + 0.970053i \(0.578096\pi\)
\(384\) 0 0
\(385\) 33.9514 1.73033
\(386\) 0 0
\(387\) −63.8993 −3.24818
\(388\) 0 0
\(389\) 3.43073 0.173945 0.0869724 0.996211i \(-0.472281\pi\)
0.0869724 + 0.996211i \(0.472281\pi\)
\(390\) 0 0
\(391\) −2.25942 −0.114264
\(392\) 0 0
\(393\) 7.02904 0.354568
\(394\) 0 0
\(395\) 27.8085 1.39920
\(396\) 0 0
\(397\) 38.4129 1.92789 0.963944 0.266105i \(-0.0857367\pi\)
0.963944 + 0.266105i \(0.0857367\pi\)
\(398\) 0 0
\(399\) −81.0193 −4.05604
\(400\) 0 0
\(401\) 5.64454 0.281875 0.140938 0.990018i \(-0.454988\pi\)
0.140938 + 0.990018i \(0.454988\pi\)
\(402\) 0 0
\(403\) 7.52249 0.374722
\(404\) 0 0
\(405\) 20.1683 1.00217
\(406\) 0 0
\(407\) −7.35626 −0.364636
\(408\) 0 0
\(409\) −8.46598 −0.418616 −0.209308 0.977850i \(-0.567121\pi\)
−0.209308 + 0.977850i \(0.567121\pi\)
\(410\) 0 0
\(411\) −3.71450 −0.183223
\(412\) 0 0
\(413\) −12.6509 −0.622509
\(414\) 0 0
\(415\) 37.6249 1.84693
\(416\) 0 0
\(417\) −39.1704 −1.91818
\(418\) 0 0
\(419\) 0.309716 0.0151306 0.00756532 0.999971i \(-0.497592\pi\)
0.00756532 + 0.999971i \(0.497592\pi\)
\(420\) 0 0
\(421\) 18.2903 0.891417 0.445709 0.895178i \(-0.352952\pi\)
0.445709 + 0.895178i \(0.352952\pi\)
\(422\) 0 0
\(423\) −6.80840 −0.331036
\(424\) 0 0
\(425\) 16.2499 0.788235
\(426\) 0 0
\(427\) −5.11262 −0.247417
\(428\) 0 0
\(429\) −20.1328 −0.972020
\(430\) 0 0
\(431\) 35.2770 1.69923 0.849616 0.527402i \(-0.176834\pi\)
0.849616 + 0.527402i \(0.176834\pi\)
\(432\) 0 0
\(433\) −14.6692 −0.704957 −0.352478 0.935820i \(-0.614661\pi\)
−0.352478 + 0.935820i \(0.614661\pi\)
\(434\) 0 0
\(435\) 55.3711 2.65484
\(436\) 0 0
\(437\) 7.76838 0.371612
\(438\) 0 0
\(439\) 12.1285 0.578862 0.289431 0.957199i \(-0.406534\pi\)
0.289431 + 0.957199i \(0.406534\pi\)
\(440\) 0 0
\(441\) 33.3602 1.58858
\(442\) 0 0
\(443\) −15.5872 −0.740568 −0.370284 0.928919i \(-0.620740\pi\)
−0.370284 + 0.928919i \(0.620740\pi\)
\(444\) 0 0
\(445\) 49.8603 2.36361
\(446\) 0 0
\(447\) 30.1618 1.42660
\(448\) 0 0
\(449\) −20.3759 −0.961597 −0.480799 0.876831i \(-0.659653\pi\)
−0.480799 + 0.876831i \(0.659653\pi\)
\(450\) 0 0
\(451\) 9.66710 0.455206
\(452\) 0 0
\(453\) −56.0995 −2.63578
\(454\) 0 0
\(455\) −32.0740 −1.50365
\(456\) 0 0
\(457\) 30.3165 1.41815 0.709073 0.705136i \(-0.249114\pi\)
0.709073 + 0.705136i \(0.249114\pi\)
\(458\) 0 0
\(459\) 17.1922 0.802463
\(460\) 0 0
\(461\) −38.7107 −1.80294 −0.901468 0.432846i \(-0.857509\pi\)
−0.901468 + 0.432846i \(0.857509\pi\)
\(462\) 0 0
\(463\) 8.39874 0.390323 0.195161 0.980771i \(-0.437477\pi\)
0.195161 + 0.980771i \(0.437477\pi\)
\(464\) 0 0
\(465\) −30.4210 −1.41074
\(466\) 0 0
\(467\) 1.32431 0.0612819 0.0306410 0.999530i \(-0.490245\pi\)
0.0306410 + 0.999530i \(0.490245\pi\)
\(468\) 0 0
\(469\) −5.28184 −0.243893
\(470\) 0 0
\(471\) −33.0891 −1.52467
\(472\) 0 0
\(473\) −30.6095 −1.40743
\(474\) 0 0
\(475\) −55.8707 −2.56352
\(476\) 0 0
\(477\) −65.7248 −3.00933
\(478\) 0 0
\(479\) −10.4732 −0.478531 −0.239265 0.970954i \(-0.576907\pi\)
−0.239265 + 0.970954i \(0.576907\pi\)
\(480\) 0 0
\(481\) 6.94947 0.316869
\(482\) 0 0
\(483\) −10.6931 −0.486553
\(484\) 0 0
\(485\) −27.0313 −1.22743
\(486\) 0 0
\(487\) −32.4707 −1.47139 −0.735693 0.677315i \(-0.763144\pi\)
−0.735693 + 0.677315i \(0.763144\pi\)
\(488\) 0 0
\(489\) −8.40886 −0.380262
\(490\) 0 0
\(491\) 13.6299 0.615108 0.307554 0.951531i \(-0.400490\pi\)
0.307554 + 0.951531i \(0.400490\pi\)
\(492\) 0 0
\(493\) 12.0052 0.540686
\(494\) 0 0
\(495\) 53.0939 2.38639
\(496\) 0 0
\(497\) −30.2549 −1.35712
\(498\) 0 0
\(499\) −29.8315 −1.33544 −0.667720 0.744413i \(-0.732730\pi\)
−0.667720 + 0.744413i \(0.732730\pi\)
\(500\) 0 0
\(501\) −43.5891 −1.94742
\(502\) 0 0
\(503\) 19.4135 0.865605 0.432802 0.901489i \(-0.357525\pi\)
0.432802 + 0.901489i \(0.357525\pi\)
\(504\) 0 0
\(505\) −11.1782 −0.497423
\(506\) 0 0
\(507\) −19.1565 −0.850768
\(508\) 0 0
\(509\) 35.7324 1.58381 0.791905 0.610644i \(-0.209089\pi\)
0.791905 + 0.610644i \(0.209089\pi\)
\(510\) 0 0
\(511\) −39.9499 −1.76728
\(512\) 0 0
\(513\) −59.1106 −2.60980
\(514\) 0 0
\(515\) 49.4310 2.17819
\(516\) 0 0
\(517\) −3.26141 −0.143437
\(518\) 0 0
\(519\) 54.1656 2.37760
\(520\) 0 0
\(521\) 27.2806 1.19518 0.597592 0.801800i \(-0.296124\pi\)
0.597592 + 0.801800i \(0.296124\pi\)
\(522\) 0 0
\(523\) −6.84286 −0.299217 −0.149609 0.988745i \(-0.547801\pi\)
−0.149609 + 0.988745i \(0.547801\pi\)
\(524\) 0 0
\(525\) 76.9055 3.35643
\(526\) 0 0
\(527\) −6.59567 −0.287312
\(528\) 0 0
\(529\) −21.9747 −0.955422
\(530\) 0 0
\(531\) −19.7837 −0.858538
\(532\) 0 0
\(533\) −9.13253 −0.395574
\(534\) 0 0
\(535\) 53.7220 2.32260
\(536\) 0 0
\(537\) 49.6380 2.14204
\(538\) 0 0
\(539\) 15.9805 0.688328
\(540\) 0 0
\(541\) 5.60345 0.240911 0.120455 0.992719i \(-0.461564\pi\)
0.120455 + 0.992719i \(0.461564\pi\)
\(542\) 0 0
\(543\) 44.0255 1.88932
\(544\) 0 0
\(545\) −6.33347 −0.271296
\(546\) 0 0
\(547\) −26.4025 −1.12889 −0.564445 0.825471i \(-0.690910\pi\)
−0.564445 + 0.825471i \(0.690910\pi\)
\(548\) 0 0
\(549\) −7.99521 −0.341227
\(550\) 0 0
\(551\) −41.2765 −1.75844
\(552\) 0 0
\(553\) 28.5344 1.21341
\(554\) 0 0
\(555\) −28.1038 −1.19294
\(556\) 0 0
\(557\) −5.85798 −0.248211 −0.124105 0.992269i \(-0.539606\pi\)
−0.124105 + 0.992269i \(0.539606\pi\)
\(558\) 0 0
\(559\) 28.9169 1.22305
\(560\) 0 0
\(561\) 17.6523 0.745281
\(562\) 0 0
\(563\) 15.1862 0.640022 0.320011 0.947414i \(-0.396313\pi\)
0.320011 + 0.947414i \(0.396313\pi\)
\(564\) 0 0
\(565\) 34.9991 1.47242
\(566\) 0 0
\(567\) 20.6948 0.869101
\(568\) 0 0
\(569\) 11.0977 0.465238 0.232619 0.972568i \(-0.425270\pi\)
0.232619 + 0.972568i \(0.425270\pi\)
\(570\) 0 0
\(571\) −41.6029 −1.74103 −0.870515 0.492143i \(-0.836214\pi\)
−0.870515 + 0.492143i \(0.836214\pi\)
\(572\) 0 0
\(573\) −1.72758 −0.0721708
\(574\) 0 0
\(575\) −7.37393 −0.307514
\(576\) 0 0
\(577\) 32.0854 1.33573 0.667867 0.744281i \(-0.267208\pi\)
0.667867 + 0.744281i \(0.267208\pi\)
\(578\) 0 0
\(579\) −16.3583 −0.679829
\(580\) 0 0
\(581\) 38.6071 1.60169
\(582\) 0 0
\(583\) −31.4840 −1.30393
\(584\) 0 0
\(585\) −50.1579 −2.07377
\(586\) 0 0
\(587\) 42.5966 1.75815 0.879074 0.476685i \(-0.158162\pi\)
0.879074 + 0.476685i \(0.158162\pi\)
\(588\) 0 0
\(589\) 22.6774 0.934406
\(590\) 0 0
\(591\) 77.1919 3.17525
\(592\) 0 0
\(593\) −39.7371 −1.63181 −0.815903 0.578189i \(-0.803760\pi\)
−0.815903 + 0.578189i \(0.803760\pi\)
\(594\) 0 0
\(595\) 28.1223 1.15290
\(596\) 0 0
\(597\) −6.77046 −0.277096
\(598\) 0 0
\(599\) 31.5024 1.28715 0.643577 0.765381i \(-0.277450\pi\)
0.643577 + 0.765381i \(0.277450\pi\)
\(600\) 0 0
\(601\) −46.6780 −1.90404 −0.952019 0.306040i \(-0.900996\pi\)
−0.952019 + 0.306040i \(0.900996\pi\)
\(602\) 0 0
\(603\) −8.25984 −0.336367
\(604\) 0 0
\(605\) −13.1175 −0.533302
\(606\) 0 0
\(607\) −4.68374 −0.190107 −0.0950535 0.995472i \(-0.530302\pi\)
−0.0950535 + 0.995472i \(0.530302\pi\)
\(608\) 0 0
\(609\) 56.8166 2.30233
\(610\) 0 0
\(611\) 3.08106 0.124646
\(612\) 0 0
\(613\) 19.2593 0.777874 0.388937 0.921264i \(-0.372842\pi\)
0.388937 + 0.921264i \(0.372842\pi\)
\(614\) 0 0
\(615\) 36.9321 1.48924
\(616\) 0 0
\(617\) 35.6116 1.43367 0.716834 0.697244i \(-0.245591\pi\)
0.716834 + 0.697244i \(0.245591\pi\)
\(618\) 0 0
\(619\) 48.6921 1.95710 0.978550 0.206012i \(-0.0660485\pi\)
0.978550 + 0.206012i \(0.0660485\pi\)
\(620\) 0 0
\(621\) −7.80154 −0.313065
\(622\) 0 0
\(623\) 51.1620 2.04976
\(624\) 0 0
\(625\) −8.37832 −0.335133
\(626\) 0 0
\(627\) −60.6926 −2.42383
\(628\) 0 0
\(629\) −6.09326 −0.242954
\(630\) 0 0
\(631\) −38.5674 −1.53534 −0.767672 0.640843i \(-0.778585\pi\)
−0.767672 + 0.640843i \(0.778585\pi\)
\(632\) 0 0
\(633\) −39.9118 −1.58635
\(634\) 0 0
\(635\) −28.8144 −1.14347
\(636\) 0 0
\(637\) −15.0968 −0.598156
\(638\) 0 0
\(639\) −47.3132 −1.87168
\(640\) 0 0
\(641\) 49.6921 1.96272 0.981360 0.192177i \(-0.0615547\pi\)
0.981360 + 0.192177i \(0.0615547\pi\)
\(642\) 0 0
\(643\) 26.3290 1.03832 0.519158 0.854678i \(-0.326246\pi\)
0.519158 + 0.854678i \(0.326246\pi\)
\(644\) 0 0
\(645\) −116.940 −4.60451
\(646\) 0 0
\(647\) −32.8724 −1.29235 −0.646174 0.763190i \(-0.723632\pi\)
−0.646174 + 0.763190i \(0.723632\pi\)
\(648\) 0 0
\(649\) −9.47693 −0.372002
\(650\) 0 0
\(651\) −31.2152 −1.22342
\(652\) 0 0
\(653\) 47.5574 1.86107 0.930533 0.366208i \(-0.119344\pi\)
0.930533 + 0.366208i \(0.119344\pi\)
\(654\) 0 0
\(655\) 8.38865 0.327772
\(656\) 0 0
\(657\) −62.4744 −2.43736
\(658\) 0 0
\(659\) 29.5009 1.14919 0.574596 0.818437i \(-0.305159\pi\)
0.574596 + 0.818437i \(0.305159\pi\)
\(660\) 0 0
\(661\) 37.1619 1.44543 0.722715 0.691146i \(-0.242894\pi\)
0.722715 + 0.691146i \(0.242894\pi\)
\(662\) 0 0
\(663\) −16.6762 −0.647649
\(664\) 0 0
\(665\) −96.6906 −3.74950
\(666\) 0 0
\(667\) −5.44775 −0.210938
\(668\) 0 0
\(669\) −17.2043 −0.665155
\(670\) 0 0
\(671\) −3.82993 −0.147853
\(672\) 0 0
\(673\) 10.7232 0.413350 0.206675 0.978410i \(-0.433736\pi\)
0.206675 + 0.978410i \(0.433736\pi\)
\(674\) 0 0
\(675\) 56.1092 2.15965
\(676\) 0 0
\(677\) 0.0109611 0.000421268 0 0.000210634 1.00000i \(-0.499933\pi\)
0.000210634 1.00000i \(0.499933\pi\)
\(678\) 0 0
\(679\) −27.7370 −1.06445
\(680\) 0 0
\(681\) 49.7999 1.90834
\(682\) 0 0
\(683\) −35.0223 −1.34009 −0.670045 0.742320i \(-0.733725\pi\)
−0.670045 + 0.742320i \(0.733725\pi\)
\(684\) 0 0
\(685\) −4.43298 −0.169376
\(686\) 0 0
\(687\) 28.5135 1.08786
\(688\) 0 0
\(689\) 29.7430 1.13312
\(690\) 0 0
\(691\) −10.6743 −0.406068 −0.203034 0.979172i \(-0.565080\pi\)
−0.203034 + 0.979172i \(0.565080\pi\)
\(692\) 0 0
\(693\) 54.4800 2.06952
\(694\) 0 0
\(695\) −46.7470 −1.77321
\(696\) 0 0
\(697\) 8.00735 0.303300
\(698\) 0 0
\(699\) −86.5507 −3.27365
\(700\) 0 0
\(701\) −4.72867 −0.178599 −0.0892997 0.996005i \(-0.528463\pi\)
−0.0892997 + 0.996005i \(0.528463\pi\)
\(702\) 0 0
\(703\) 20.9500 0.790143
\(704\) 0 0
\(705\) −12.4598 −0.469265
\(706\) 0 0
\(707\) −11.4700 −0.431375
\(708\) 0 0
\(709\) 9.31840 0.349960 0.174980 0.984572i \(-0.444014\pi\)
0.174980 + 0.984572i \(0.444014\pi\)
\(710\) 0 0
\(711\) 44.6227 1.67348
\(712\) 0 0
\(713\) 2.99301 0.112089
\(714\) 0 0
\(715\) −24.0270 −0.898559
\(716\) 0 0
\(717\) 24.0270 0.897303
\(718\) 0 0
\(719\) 30.7922 1.14836 0.574178 0.818730i \(-0.305322\pi\)
0.574178 + 0.818730i \(0.305322\pi\)
\(720\) 0 0
\(721\) 50.7214 1.88896
\(722\) 0 0
\(723\) −56.5062 −2.10149
\(724\) 0 0
\(725\) 39.1806 1.45513
\(726\) 0 0
\(727\) −9.59936 −0.356021 −0.178010 0.984029i \(-0.556966\pi\)
−0.178010 + 0.984029i \(0.556966\pi\)
\(728\) 0 0
\(729\) −35.5145 −1.31535
\(730\) 0 0
\(731\) −25.3541 −0.937757
\(732\) 0 0
\(733\) −1.09657 −0.0405028 −0.0202514 0.999795i \(-0.506447\pi\)
−0.0202514 + 0.999795i \(0.506447\pi\)
\(734\) 0 0
\(735\) 61.0516 2.25192
\(736\) 0 0
\(737\) −3.95669 −0.145747
\(738\) 0 0
\(739\) −51.7130 −1.90229 −0.951147 0.308738i \(-0.900093\pi\)
−0.951147 + 0.308738i \(0.900093\pi\)
\(740\) 0 0
\(741\) 57.3364 2.10630
\(742\) 0 0
\(743\) 30.2172 1.10856 0.554280 0.832330i \(-0.312994\pi\)
0.554280 + 0.832330i \(0.312994\pi\)
\(744\) 0 0
\(745\) 35.9958 1.31879
\(746\) 0 0
\(747\) 60.3745 2.20899
\(748\) 0 0
\(749\) 55.1244 2.01420
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −7.12632 −0.259697
\(754\) 0 0
\(755\) −66.9507 −2.43658
\(756\) 0 0
\(757\) 8.78653 0.319352 0.159676 0.987169i \(-0.448955\pi\)
0.159676 + 0.987169i \(0.448955\pi\)
\(758\) 0 0
\(759\) −8.01033 −0.290756
\(760\) 0 0
\(761\) 15.5283 0.562900 0.281450 0.959576i \(-0.409185\pi\)
0.281450 + 0.959576i \(0.409185\pi\)
\(762\) 0 0
\(763\) −6.49881 −0.235273
\(764\) 0 0
\(765\) 43.9781 1.59003
\(766\) 0 0
\(767\) 8.95287 0.323269
\(768\) 0 0
\(769\) 19.3925 0.699311 0.349655 0.936878i \(-0.386299\pi\)
0.349655 + 0.936878i \(0.386299\pi\)
\(770\) 0 0
\(771\) −45.5495 −1.64042
\(772\) 0 0
\(773\) −32.4611 −1.16755 −0.583773 0.811917i \(-0.698424\pi\)
−0.583773 + 0.811917i \(0.698424\pi\)
\(774\) 0 0
\(775\) −21.5259 −0.773234
\(776\) 0 0
\(777\) −28.8374 −1.03454
\(778\) 0 0
\(779\) −27.5310 −0.986402
\(780\) 0 0
\(781\) −22.6643 −0.810994
\(782\) 0 0
\(783\) 41.4527 1.48140
\(784\) 0 0
\(785\) −39.4895 −1.40944
\(786\) 0 0
\(787\) −54.2967 −1.93547 −0.967734 0.251974i \(-0.918920\pi\)
−0.967734 + 0.251974i \(0.918920\pi\)
\(788\) 0 0
\(789\) −3.96655 −0.141213
\(790\) 0 0
\(791\) 35.9127 1.27691
\(792\) 0 0
\(793\) 3.61814 0.128484
\(794\) 0 0
\(795\) −120.281 −4.26593
\(796\) 0 0
\(797\) 44.4918 1.57598 0.787990 0.615688i \(-0.211122\pi\)
0.787990 + 0.615688i \(0.211122\pi\)
\(798\) 0 0
\(799\) −2.70146 −0.0955706
\(800\) 0 0
\(801\) 80.0081 2.82695
\(802\) 0 0
\(803\) −29.9269 −1.05610
\(804\) 0 0
\(805\) −12.7614 −0.449781
\(806\) 0 0
\(807\) −16.2534 −0.572148
\(808\) 0 0
\(809\) −25.2194 −0.886665 −0.443333 0.896357i \(-0.646204\pi\)
−0.443333 + 0.896357i \(0.646204\pi\)
\(810\) 0 0
\(811\) −17.9521 −0.630383 −0.315191 0.949028i \(-0.602069\pi\)
−0.315191 + 0.949028i \(0.602069\pi\)
\(812\) 0 0
\(813\) −9.02927 −0.316670
\(814\) 0 0
\(815\) −10.0354 −0.351523
\(816\) 0 0
\(817\) 87.1732 3.04980
\(818\) 0 0
\(819\) −51.4673 −1.79841
\(820\) 0 0
\(821\) 25.8491 0.902139 0.451069 0.892489i \(-0.351043\pi\)
0.451069 + 0.892489i \(0.351043\pi\)
\(822\) 0 0
\(823\) −0.656538 −0.0228855 −0.0114427 0.999935i \(-0.503642\pi\)
−0.0114427 + 0.999935i \(0.503642\pi\)
\(824\) 0 0
\(825\) 57.6109 2.00575
\(826\) 0 0
\(827\) −4.37285 −0.152059 −0.0760295 0.997106i \(-0.524224\pi\)
−0.0760295 + 0.997106i \(0.524224\pi\)
\(828\) 0 0
\(829\) 0.371007 0.0128856 0.00644280 0.999979i \(-0.497949\pi\)
0.00644280 + 0.999979i \(0.497949\pi\)
\(830\) 0 0
\(831\) 2.83430 0.0983207
\(832\) 0 0
\(833\) 13.2368 0.458627
\(834\) 0 0
\(835\) −52.0205 −1.80024
\(836\) 0 0
\(837\) −22.7742 −0.787192
\(838\) 0 0
\(839\) −23.9574 −0.827100 −0.413550 0.910481i \(-0.635711\pi\)
−0.413550 + 0.910481i \(0.635711\pi\)
\(840\) 0 0
\(841\) −0.0539434 −0.00186012
\(842\) 0 0
\(843\) 32.8155 1.13023
\(844\) 0 0
\(845\) −22.8618 −0.786471
\(846\) 0 0
\(847\) −13.4599 −0.462489
\(848\) 0 0
\(849\) 3.44876 0.118361
\(850\) 0 0
\(851\) 2.76502 0.0947836
\(852\) 0 0
\(853\) 33.2099 1.13708 0.568542 0.822654i \(-0.307508\pi\)
0.568542 + 0.822654i \(0.307508\pi\)
\(854\) 0 0
\(855\) −151.207 −5.17116
\(856\) 0 0
\(857\) 10.7486 0.367165 0.183582 0.983004i \(-0.441231\pi\)
0.183582 + 0.983004i \(0.441231\pi\)
\(858\) 0 0
\(859\) 16.2265 0.553643 0.276821 0.960921i \(-0.410719\pi\)
0.276821 + 0.960921i \(0.410719\pi\)
\(860\) 0 0
\(861\) 37.8962 1.29150
\(862\) 0 0
\(863\) 39.4940 1.34439 0.672197 0.740373i \(-0.265351\pi\)
0.672197 + 0.740373i \(0.265351\pi\)
\(864\) 0 0
\(865\) 64.6426 2.19792
\(866\) 0 0
\(867\) −35.3008 −1.19888
\(868\) 0 0
\(869\) 21.3755 0.725114
\(870\) 0 0
\(871\) 3.73789 0.126654
\(872\) 0 0
\(873\) −43.3756 −1.46804
\(874\) 0 0
\(875\) 28.7657 0.972458
\(876\) 0 0
\(877\) −3.12805 −0.105627 −0.0528134 0.998604i \(-0.516819\pi\)
−0.0528134 + 0.998604i \(0.516819\pi\)
\(878\) 0 0
\(879\) −21.1182 −0.712299
\(880\) 0 0
\(881\) −20.1801 −0.679885 −0.339942 0.940446i \(-0.610408\pi\)
−0.339942 + 0.940446i \(0.610408\pi\)
\(882\) 0 0
\(883\) −33.9653 −1.14302 −0.571511 0.820594i \(-0.693643\pi\)
−0.571511 + 0.820594i \(0.693643\pi\)
\(884\) 0 0
\(885\) −36.2055 −1.21704
\(886\) 0 0
\(887\) −20.3478 −0.683212 −0.341606 0.939843i \(-0.610971\pi\)
−0.341606 + 0.939843i \(0.610971\pi\)
\(888\) 0 0
\(889\) −29.5667 −0.991634
\(890\) 0 0
\(891\) 15.5028 0.519362
\(892\) 0 0
\(893\) 9.28821 0.310818
\(894\) 0 0
\(895\) 59.2394 1.98015
\(896\) 0 0
\(897\) 7.56737 0.252667
\(898\) 0 0
\(899\) −15.9030 −0.530396
\(900\) 0 0
\(901\) −26.0785 −0.868800
\(902\) 0 0
\(903\) −119.993 −3.99312
\(904\) 0 0
\(905\) 52.5412 1.74653
\(906\) 0 0
\(907\) −6.23956 −0.207181 −0.103591 0.994620i \(-0.533033\pi\)
−0.103591 + 0.994620i \(0.533033\pi\)
\(908\) 0 0
\(909\) −17.9370 −0.594934
\(910\) 0 0
\(911\) 5.34308 0.177024 0.0885120 0.996075i \(-0.471789\pi\)
0.0885120 + 0.996075i \(0.471789\pi\)
\(912\) 0 0
\(913\) 28.9211 0.957147
\(914\) 0 0
\(915\) −14.6318 −0.483712
\(916\) 0 0
\(917\) 8.60764 0.284249
\(918\) 0 0
\(919\) 9.09577 0.300042 0.150021 0.988683i \(-0.452066\pi\)
0.150021 + 0.988683i \(0.452066\pi\)
\(920\) 0 0
\(921\) −33.4519 −1.10228
\(922\) 0 0
\(923\) 21.4110 0.704753
\(924\) 0 0
\(925\) −19.8862 −0.653855
\(926\) 0 0
\(927\) 79.3191 2.60518
\(928\) 0 0
\(929\) 11.7796 0.386477 0.193238 0.981152i \(-0.438101\pi\)
0.193238 + 0.981152i \(0.438101\pi\)
\(930\) 0 0
\(931\) −45.5110 −1.49156
\(932\) 0 0
\(933\) −67.0936 −2.19655
\(934\) 0 0
\(935\) 21.0667 0.688956
\(936\) 0 0
\(937\) −30.4723 −0.995487 −0.497743 0.867324i \(-0.665838\pi\)
−0.497743 + 0.867324i \(0.665838\pi\)
\(938\) 0 0
\(939\) 64.5638 2.10696
\(940\) 0 0
\(941\) −10.1624 −0.331285 −0.165642 0.986186i \(-0.552970\pi\)
−0.165642 + 0.986186i \(0.552970\pi\)
\(942\) 0 0
\(943\) −3.63360 −0.118326
\(944\) 0 0
\(945\) 97.1034 3.15877
\(946\) 0 0
\(947\) 14.7859 0.480476 0.240238 0.970714i \(-0.422775\pi\)
0.240238 + 0.970714i \(0.422775\pi\)
\(948\) 0 0
\(949\) 28.2720 0.917749
\(950\) 0 0
\(951\) 56.8724 1.84421
\(952\) 0 0
\(953\) −23.8716 −0.773277 −0.386639 0.922231i \(-0.626364\pi\)
−0.386639 + 0.922231i \(0.626364\pi\)
\(954\) 0 0
\(955\) −2.06174 −0.0667164
\(956\) 0 0
\(957\) 42.5620 1.37584
\(958\) 0 0
\(959\) −4.54871 −0.146886
\(960\) 0 0
\(961\) −22.2628 −0.718156
\(962\) 0 0
\(963\) 86.2046 2.77790
\(964\) 0 0
\(965\) −19.5225 −0.628451
\(966\) 0 0
\(967\) −14.7395 −0.473990 −0.236995 0.971511i \(-0.576162\pi\)
−0.236995 + 0.971511i \(0.576162\pi\)
\(968\) 0 0
\(969\) −50.2722 −1.61498
\(970\) 0 0
\(971\) −49.4852 −1.58806 −0.794028 0.607881i \(-0.792020\pi\)
−0.794028 + 0.607881i \(0.792020\pi\)
\(972\) 0 0
\(973\) −47.9674 −1.53776
\(974\) 0 0
\(975\) −54.4251 −1.74300
\(976\) 0 0
\(977\) −50.8293 −1.62617 −0.813087 0.582143i \(-0.802215\pi\)
−0.813087 + 0.582143i \(0.802215\pi\)
\(978\) 0 0
\(979\) 38.3261 1.22491
\(980\) 0 0
\(981\) −10.1630 −0.324478
\(982\) 0 0
\(983\) 27.9347 0.890978 0.445489 0.895287i \(-0.353030\pi\)
0.445489 + 0.895287i \(0.353030\pi\)
\(984\) 0 0
\(985\) 92.1228 2.93528
\(986\) 0 0
\(987\) −12.7851 −0.406955
\(988\) 0 0
\(989\) 11.5053 0.365847
\(990\) 0 0
\(991\) 33.0473 1.04978 0.524891 0.851170i \(-0.324106\pi\)
0.524891 + 0.851170i \(0.324106\pi\)
\(992\) 0 0
\(993\) 76.4637 2.42650
\(994\) 0 0
\(995\) −8.08005 −0.256155
\(996\) 0 0
\(997\) 32.0785 1.01594 0.507968 0.861376i \(-0.330397\pi\)
0.507968 + 0.861376i \(0.330397\pi\)
\(998\) 0 0
\(999\) −21.0394 −0.665657
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 \(a_p\))