Properties

Label 6008.2.a.e.1.20
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 1.20
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.684026 q^{3} -2.03205 q^{5} -0.0739397 q^{7} -2.53211 q^{9} +O(q^{10})\) \(q-0.684026 q^{3} -2.03205 q^{5} -0.0739397 q^{7} -2.53211 q^{9} -6.59782 q^{11} -2.19215 q^{13} +1.38998 q^{15} -2.82314 q^{17} +3.57602 q^{19} +0.0505766 q^{21} -3.59900 q^{23} -0.870764 q^{25} +3.78411 q^{27} -0.888227 q^{29} -3.39569 q^{31} +4.51308 q^{33} +0.150249 q^{35} -1.90012 q^{37} +1.49949 q^{39} -5.01384 q^{41} -8.72563 q^{43} +5.14538 q^{45} -7.66472 q^{47} -6.99453 q^{49} +1.93110 q^{51} -7.04401 q^{53} +13.4071 q^{55} -2.44609 q^{57} -1.37245 q^{59} +0.987178 q^{61} +0.187223 q^{63} +4.45457 q^{65} -0.134803 q^{67} +2.46181 q^{69} +3.40620 q^{71} +10.5929 q^{73} +0.595625 q^{75} +0.487841 q^{77} -13.9690 q^{79} +5.00790 q^{81} -0.111240 q^{83} +5.73676 q^{85} +0.607570 q^{87} -0.114945 q^{89} +0.162087 q^{91} +2.32274 q^{93} -7.26666 q^{95} -14.8142 q^{97} +16.7064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.684026 −0.394922 −0.197461 0.980311i \(-0.563270\pi\)
−0.197461 + 0.980311i \(0.563270\pi\)
\(4\) 0 0
\(5\) −2.03205 −0.908761 −0.454381 0.890808i \(-0.650139\pi\)
−0.454381 + 0.890808i \(0.650139\pi\)
\(6\) 0 0
\(7\) −0.0739397 −0.0279466 −0.0139733 0.999902i \(-0.504448\pi\)
−0.0139733 + 0.999902i \(0.504448\pi\)
\(8\) 0 0
\(9\) −2.53211 −0.844036
\(10\) 0 0
\(11\) −6.59782 −1.98932 −0.994659 0.103212i \(-0.967088\pi\)
−0.994659 + 0.103212i \(0.967088\pi\)
\(12\) 0 0
\(13\) −2.19215 −0.607994 −0.303997 0.952673i \(-0.598321\pi\)
−0.303997 + 0.952673i \(0.598321\pi\)
\(14\) 0 0
\(15\) 1.38998 0.358890
\(16\) 0 0
\(17\) −2.82314 −0.684711 −0.342356 0.939570i \(-0.611225\pi\)
−0.342356 + 0.939570i \(0.611225\pi\)
\(18\) 0 0
\(19\) 3.57602 0.820395 0.410197 0.911997i \(-0.365460\pi\)
0.410197 + 0.911997i \(0.365460\pi\)
\(20\) 0 0
\(21\) 0.0505766 0.0110367
\(22\) 0 0
\(23\) −3.59900 −0.750444 −0.375222 0.926935i \(-0.622434\pi\)
−0.375222 + 0.926935i \(0.622434\pi\)
\(24\) 0 0
\(25\) −0.870764 −0.174153
\(26\) 0 0
\(27\) 3.78411 0.728251
\(28\) 0 0
\(29\) −0.888227 −0.164940 −0.0824698 0.996594i \(-0.526281\pi\)
−0.0824698 + 0.996594i \(0.526281\pi\)
\(30\) 0 0
\(31\) −3.39569 −0.609883 −0.304942 0.952371i \(-0.598637\pi\)
−0.304942 + 0.952371i \(0.598637\pi\)
\(32\) 0 0
\(33\) 4.51308 0.785627
\(34\) 0 0
\(35\) 0.150249 0.0253968
\(36\) 0 0
\(37\) −1.90012 −0.312378 −0.156189 0.987727i \(-0.549921\pi\)
−0.156189 + 0.987727i \(0.549921\pi\)
\(38\) 0 0
\(39\) 1.49949 0.240111
\(40\) 0 0
\(41\) −5.01384 −0.783031 −0.391515 0.920172i \(-0.628049\pi\)
−0.391515 + 0.920172i \(0.628049\pi\)
\(42\) 0 0
\(43\) −8.72563 −1.33065 −0.665323 0.746555i \(-0.731706\pi\)
−0.665323 + 0.746555i \(0.731706\pi\)
\(44\) 0 0
\(45\) 5.14538 0.767028
\(46\) 0 0
\(47\) −7.66472 −1.11801 −0.559007 0.829163i \(-0.688818\pi\)
−0.559007 + 0.829163i \(0.688818\pi\)
\(48\) 0 0
\(49\) −6.99453 −0.999219
\(50\) 0 0
\(51\) 1.93110 0.270408
\(52\) 0 0
\(53\) −7.04401 −0.967570 −0.483785 0.875187i \(-0.660738\pi\)
−0.483785 + 0.875187i \(0.660738\pi\)
\(54\) 0 0
\(55\) 13.4071 1.80782
\(56\) 0 0
\(57\) −2.44609 −0.323992
\(58\) 0 0
\(59\) −1.37245 −0.178677 −0.0893387 0.996001i \(-0.528475\pi\)
−0.0893387 + 0.996001i \(0.528475\pi\)
\(60\) 0 0
\(61\) 0.987178 0.126395 0.0631976 0.998001i \(-0.479870\pi\)
0.0631976 + 0.998001i \(0.479870\pi\)
\(62\) 0 0
\(63\) 0.187223 0.0235879
\(64\) 0 0
\(65\) 4.45457 0.552522
\(66\) 0 0
\(67\) −0.134803 −0.0164687 −0.00823437 0.999966i \(-0.502621\pi\)
−0.00823437 + 0.999966i \(0.502621\pi\)
\(68\) 0 0
\(69\) 2.46181 0.296367
\(70\) 0 0
\(71\) 3.40620 0.404241 0.202121 0.979361i \(-0.435217\pi\)
0.202121 + 0.979361i \(0.435217\pi\)
\(72\) 0 0
\(73\) 10.5929 1.23980 0.619901 0.784680i \(-0.287173\pi\)
0.619901 + 0.784680i \(0.287173\pi\)
\(74\) 0 0
\(75\) 0.595625 0.0687768
\(76\) 0 0
\(77\) 0.487841 0.0555946
\(78\) 0 0
\(79\) −13.9690 −1.57163 −0.785816 0.618460i \(-0.787757\pi\)
−0.785816 + 0.618460i \(0.787757\pi\)
\(80\) 0 0
\(81\) 5.00790 0.556433
\(82\) 0 0
\(83\) −0.111240 −0.0122102 −0.00610510 0.999981i \(-0.501943\pi\)
−0.00610510 + 0.999981i \(0.501943\pi\)
\(84\) 0 0
\(85\) 5.73676 0.622239
\(86\) 0 0
\(87\) 0.607570 0.0651384
\(88\) 0 0
\(89\) −0.114945 −0.0121841 −0.00609206 0.999981i \(-0.501939\pi\)
−0.00609206 + 0.999981i \(0.501939\pi\)
\(90\) 0 0
\(91\) 0.162087 0.0169914
\(92\) 0 0
\(93\) 2.32274 0.240857
\(94\) 0 0
\(95\) −7.26666 −0.745543
\(96\) 0 0
\(97\) −14.8142 −1.50416 −0.752078 0.659074i \(-0.770948\pi\)
−0.752078 + 0.659074i \(0.770948\pi\)
\(98\) 0 0
\(99\) 16.7064 1.67906
\(100\) 0 0
\(101\) −9.10734 −0.906214 −0.453107 0.891456i \(-0.649685\pi\)
−0.453107 + 0.891456i \(0.649685\pi\)
\(102\) 0 0
\(103\) −4.35467 −0.429078 −0.214539 0.976715i \(-0.568825\pi\)
−0.214539 + 0.976715i \(0.568825\pi\)
\(104\) 0 0
\(105\) −0.102774 −0.0100298
\(106\) 0 0
\(107\) 12.0099 1.16104 0.580520 0.814246i \(-0.302849\pi\)
0.580520 + 0.814246i \(0.302849\pi\)
\(108\) 0 0
\(109\) 6.48899 0.621533 0.310766 0.950486i \(-0.399414\pi\)
0.310766 + 0.950486i \(0.399414\pi\)
\(110\) 0 0
\(111\) 1.29973 0.123365
\(112\) 0 0
\(113\) 3.15578 0.296870 0.148435 0.988922i \(-0.452576\pi\)
0.148435 + 0.988922i \(0.452576\pi\)
\(114\) 0 0
\(115\) 7.31336 0.681975
\(116\) 0 0
\(117\) 5.55077 0.513169
\(118\) 0 0
\(119\) 0.208742 0.0191353
\(120\) 0 0
\(121\) 32.5313 2.95739
\(122\) 0 0
\(123\) 3.42960 0.309236
\(124\) 0 0
\(125\) 11.9297 1.06702
\(126\) 0 0
\(127\) 20.5968 1.82767 0.913834 0.406087i \(-0.133107\pi\)
0.913834 + 0.406087i \(0.133107\pi\)
\(128\) 0 0
\(129\) 5.96856 0.525502
\(130\) 0 0
\(131\) −9.61578 −0.840134 −0.420067 0.907493i \(-0.637994\pi\)
−0.420067 + 0.907493i \(0.637994\pi\)
\(132\) 0 0
\(133\) −0.264410 −0.0229272
\(134\) 0 0
\(135\) −7.68950 −0.661807
\(136\) 0 0
\(137\) −13.9773 −1.19416 −0.597080 0.802182i \(-0.703673\pi\)
−0.597080 + 0.802182i \(0.703673\pi\)
\(138\) 0 0
\(139\) −10.4785 −0.888778 −0.444389 0.895834i \(-0.646579\pi\)
−0.444389 + 0.895834i \(0.646579\pi\)
\(140\) 0 0
\(141\) 5.24287 0.441529
\(142\) 0 0
\(143\) 14.4634 1.20949
\(144\) 0 0
\(145\) 1.80492 0.149891
\(146\) 0 0
\(147\) 4.78444 0.394614
\(148\) 0 0
\(149\) 10.2924 0.843186 0.421593 0.906785i \(-0.361471\pi\)
0.421593 + 0.906785i \(0.361471\pi\)
\(150\) 0 0
\(151\) 11.1865 0.910348 0.455174 0.890403i \(-0.349577\pi\)
0.455174 + 0.890403i \(0.349577\pi\)
\(152\) 0 0
\(153\) 7.14849 0.577921
\(154\) 0 0
\(155\) 6.90021 0.554238
\(156\) 0 0
\(157\) 24.2198 1.93295 0.966476 0.256756i \(-0.0826537\pi\)
0.966476 + 0.256756i \(0.0826537\pi\)
\(158\) 0 0
\(159\) 4.81829 0.382115
\(160\) 0 0
\(161\) 0.266109 0.0209723
\(162\) 0 0
\(163\) 5.13680 0.402345 0.201172 0.979556i \(-0.435525\pi\)
0.201172 + 0.979556i \(0.435525\pi\)
\(164\) 0 0
\(165\) −9.17082 −0.713947
\(166\) 0 0
\(167\) −21.0597 −1.62965 −0.814823 0.579709i \(-0.803166\pi\)
−0.814823 + 0.579709i \(0.803166\pi\)
\(168\) 0 0
\(169\) −8.19446 −0.630343
\(170\) 0 0
\(171\) −9.05487 −0.692443
\(172\) 0 0
\(173\) −1.32914 −0.101052 −0.0505262 0.998723i \(-0.516090\pi\)
−0.0505262 + 0.998723i \(0.516090\pi\)
\(174\) 0 0
\(175\) 0.0643840 0.00486697
\(176\) 0 0
\(177\) 0.938789 0.0705637
\(178\) 0 0
\(179\) 2.45619 0.183585 0.0917923 0.995778i \(-0.470740\pi\)
0.0917923 + 0.995778i \(0.470740\pi\)
\(180\) 0 0
\(181\) −1.46195 −0.108666 −0.0543329 0.998523i \(-0.517303\pi\)
−0.0543329 + 0.998523i \(0.517303\pi\)
\(182\) 0 0
\(183\) −0.675255 −0.0499163
\(184\) 0 0
\(185\) 3.86114 0.283877
\(186\) 0 0
\(187\) 18.6266 1.36211
\(188\) 0 0
\(189\) −0.279795 −0.0203521
\(190\) 0 0
\(191\) −16.9734 −1.22815 −0.614077 0.789246i \(-0.710471\pi\)
−0.614077 + 0.789246i \(0.710471\pi\)
\(192\) 0 0
\(193\) 13.0514 0.939460 0.469730 0.882810i \(-0.344351\pi\)
0.469730 + 0.882810i \(0.344351\pi\)
\(194\) 0 0
\(195\) −3.04704 −0.218203
\(196\) 0 0
\(197\) −10.7913 −0.768846 −0.384423 0.923157i \(-0.625600\pi\)
−0.384423 + 0.923157i \(0.625600\pi\)
\(198\) 0 0
\(199\) −13.1948 −0.935356 −0.467678 0.883899i \(-0.654909\pi\)
−0.467678 + 0.883899i \(0.654909\pi\)
\(200\) 0 0
\(201\) 0.0922084 0.00650388
\(202\) 0 0
\(203\) 0.0656752 0.00460950
\(204\) 0 0
\(205\) 10.1884 0.711588
\(206\) 0 0
\(207\) 9.11307 0.633402
\(208\) 0 0
\(209\) −23.5939 −1.63203
\(210\) 0 0
\(211\) −5.40060 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(212\) 0 0
\(213\) −2.32993 −0.159644
\(214\) 0 0
\(215\) 17.7309 1.20924
\(216\) 0 0
\(217\) 0.251076 0.0170441
\(218\) 0 0
\(219\) −7.24580 −0.489625
\(220\) 0 0
\(221\) 6.18875 0.416301
\(222\) 0 0
\(223\) −11.8012 −0.790267 −0.395133 0.918624i \(-0.629302\pi\)
−0.395133 + 0.918624i \(0.629302\pi\)
\(224\) 0 0
\(225\) 2.20487 0.146991
\(226\) 0 0
\(227\) −4.74047 −0.314636 −0.157318 0.987548i \(-0.550285\pi\)
−0.157318 + 0.987548i \(0.550285\pi\)
\(228\) 0 0
\(229\) −8.72948 −0.576860 −0.288430 0.957501i \(-0.593133\pi\)
−0.288430 + 0.957501i \(0.593133\pi\)
\(230\) 0 0
\(231\) −0.333696 −0.0219556
\(232\) 0 0
\(233\) 12.1653 0.796978 0.398489 0.917173i \(-0.369535\pi\)
0.398489 + 0.917173i \(0.369535\pi\)
\(234\) 0 0
\(235\) 15.5751 1.01601
\(236\) 0 0
\(237\) 9.55514 0.620673
\(238\) 0 0
\(239\) −19.0737 −1.23377 −0.616886 0.787053i \(-0.711606\pi\)
−0.616886 + 0.787053i \(0.711606\pi\)
\(240\) 0 0
\(241\) 22.1823 1.42889 0.714445 0.699692i \(-0.246679\pi\)
0.714445 + 0.699692i \(0.246679\pi\)
\(242\) 0 0
\(243\) −14.7778 −0.947999
\(244\) 0 0
\(245\) 14.2133 0.908052
\(246\) 0 0
\(247\) −7.83918 −0.498795
\(248\) 0 0
\(249\) 0.0760912 0.00482208
\(250\) 0 0
\(251\) 9.02726 0.569795 0.284898 0.958558i \(-0.408040\pi\)
0.284898 + 0.958558i \(0.408040\pi\)
\(252\) 0 0
\(253\) 23.7456 1.49287
\(254\) 0 0
\(255\) −3.92409 −0.245736
\(256\) 0 0
\(257\) 21.5454 1.34396 0.671982 0.740567i \(-0.265443\pi\)
0.671982 + 0.740567i \(0.265443\pi\)
\(258\) 0 0
\(259\) 0.140494 0.00872988
\(260\) 0 0
\(261\) 2.24909 0.139215
\(262\) 0 0
\(263\) −4.45476 −0.274692 −0.137346 0.990523i \(-0.543857\pi\)
−0.137346 + 0.990523i \(0.543857\pi\)
\(264\) 0 0
\(265\) 14.3138 0.879290
\(266\) 0 0
\(267\) 0.0786252 0.00481179
\(268\) 0 0
\(269\) 8.86029 0.540221 0.270111 0.962829i \(-0.412940\pi\)
0.270111 + 0.962829i \(0.412940\pi\)
\(270\) 0 0
\(271\) 15.2266 0.924950 0.462475 0.886632i \(-0.346961\pi\)
0.462475 + 0.886632i \(0.346961\pi\)
\(272\) 0 0
\(273\) −0.110872 −0.00671027
\(274\) 0 0
\(275\) 5.74515 0.346445
\(276\) 0 0
\(277\) −7.58816 −0.455928 −0.227964 0.973670i \(-0.573207\pi\)
−0.227964 + 0.973670i \(0.573207\pi\)
\(278\) 0 0
\(279\) 8.59824 0.514763
\(280\) 0 0
\(281\) −27.6883 −1.65174 −0.825871 0.563859i \(-0.809316\pi\)
−0.825871 + 0.563859i \(0.809316\pi\)
\(282\) 0 0
\(283\) −2.19348 −0.130389 −0.0651945 0.997873i \(-0.520767\pi\)
−0.0651945 + 0.997873i \(0.520767\pi\)
\(284\) 0 0
\(285\) 4.97058 0.294432
\(286\) 0 0
\(287\) 0.370722 0.0218830
\(288\) 0 0
\(289\) −9.02990 −0.531170
\(290\) 0 0
\(291\) 10.1333 0.594025
\(292\) 0 0
\(293\) −24.3560 −1.42289 −0.711445 0.702742i \(-0.751959\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(294\) 0 0
\(295\) 2.78888 0.162375
\(296\) 0 0
\(297\) −24.9669 −1.44872
\(298\) 0 0
\(299\) 7.88957 0.456266
\(300\) 0 0
\(301\) 0.645170 0.0371870
\(302\) 0 0
\(303\) 6.22966 0.357884
\(304\) 0 0
\(305\) −2.00600 −0.114863
\(306\) 0 0
\(307\) −10.7080 −0.611137 −0.305569 0.952170i \(-0.598847\pi\)
−0.305569 + 0.952170i \(0.598847\pi\)
\(308\) 0 0
\(309\) 2.97871 0.169453
\(310\) 0 0
\(311\) 14.4226 0.817832 0.408916 0.912572i \(-0.365907\pi\)
0.408916 + 0.912572i \(0.365907\pi\)
\(312\) 0 0
\(313\) 4.86957 0.275244 0.137622 0.990485i \(-0.456054\pi\)
0.137622 + 0.990485i \(0.456054\pi\)
\(314\) 0 0
\(315\) −0.380447 −0.0214358
\(316\) 0 0
\(317\) 13.9059 0.781032 0.390516 0.920596i \(-0.372297\pi\)
0.390516 + 0.920596i \(0.372297\pi\)
\(318\) 0 0
\(319\) 5.86037 0.328118
\(320\) 0 0
\(321\) −8.21508 −0.458521
\(322\) 0 0
\(323\) −10.0956 −0.561734
\(324\) 0 0
\(325\) 1.90885 0.105884
\(326\) 0 0
\(327\) −4.43864 −0.245457
\(328\) 0 0
\(329\) 0.566727 0.0312447
\(330\) 0 0
\(331\) 3.63288 0.199681 0.0998405 0.995003i \(-0.468167\pi\)
0.0998405 + 0.995003i \(0.468167\pi\)
\(332\) 0 0
\(333\) 4.81131 0.263658
\(334\) 0 0
\(335\) 0.273926 0.0149662
\(336\) 0 0
\(337\) −17.6872 −0.963485 −0.481742 0.876313i \(-0.659996\pi\)
−0.481742 + 0.876313i \(0.659996\pi\)
\(338\) 0 0
\(339\) −2.15863 −0.117241
\(340\) 0 0
\(341\) 22.4041 1.21325
\(342\) 0 0
\(343\) 1.03475 0.0558713
\(344\) 0 0
\(345\) −5.00253 −0.269327
\(346\) 0 0
\(347\) 27.7350 1.48889 0.744447 0.667682i \(-0.232713\pi\)
0.744447 + 0.667682i \(0.232713\pi\)
\(348\) 0 0
\(349\) 18.1023 0.968994 0.484497 0.874793i \(-0.339003\pi\)
0.484497 + 0.874793i \(0.339003\pi\)
\(350\) 0 0
\(351\) −8.29534 −0.442773
\(352\) 0 0
\(353\) −26.5805 −1.41474 −0.707368 0.706845i \(-0.750118\pi\)
−0.707368 + 0.706845i \(0.750118\pi\)
\(354\) 0 0
\(355\) −6.92157 −0.367359
\(356\) 0 0
\(357\) −0.142785 −0.00755697
\(358\) 0 0
\(359\) 6.79611 0.358685 0.179343 0.983787i \(-0.442603\pi\)
0.179343 + 0.983787i \(0.442603\pi\)
\(360\) 0 0
\(361\) −6.21209 −0.326952
\(362\) 0 0
\(363\) −22.2522 −1.16794
\(364\) 0 0
\(365\) −21.5253 −1.12668
\(366\) 0 0
\(367\) −27.8948 −1.45610 −0.728048 0.685526i \(-0.759572\pi\)
−0.728048 + 0.685526i \(0.759572\pi\)
\(368\) 0 0
\(369\) 12.6956 0.660906
\(370\) 0 0
\(371\) 0.520832 0.0270403
\(372\) 0 0
\(373\) 34.0340 1.76222 0.881108 0.472916i \(-0.156799\pi\)
0.881108 + 0.472916i \(0.156799\pi\)
\(374\) 0 0
\(375\) −8.16022 −0.421392
\(376\) 0 0
\(377\) 1.94713 0.100282
\(378\) 0 0
\(379\) 19.5596 1.00471 0.502353 0.864662i \(-0.332468\pi\)
0.502353 + 0.864662i \(0.332468\pi\)
\(380\) 0 0
\(381\) −14.0887 −0.721787
\(382\) 0 0
\(383\) −32.7659 −1.67426 −0.837131 0.547003i \(-0.815769\pi\)
−0.837131 + 0.547003i \(0.815769\pi\)
\(384\) 0 0
\(385\) −0.991318 −0.0505223
\(386\) 0 0
\(387\) 22.0943 1.12311
\(388\) 0 0
\(389\) 0.197018 0.00998919 0.00499459 0.999988i \(-0.498410\pi\)
0.00499459 + 0.999988i \(0.498410\pi\)
\(390\) 0 0
\(391\) 10.1605 0.513838
\(392\) 0 0
\(393\) 6.57744 0.331788
\(394\) 0 0
\(395\) 28.3857 1.42824
\(396\) 0 0
\(397\) 4.33378 0.217506 0.108753 0.994069i \(-0.465314\pi\)
0.108753 + 0.994069i \(0.465314\pi\)
\(398\) 0 0
\(399\) 0.180863 0.00905448
\(400\) 0 0
\(401\) 24.6346 1.23020 0.615098 0.788451i \(-0.289117\pi\)
0.615098 + 0.788451i \(0.289117\pi\)
\(402\) 0 0
\(403\) 7.44387 0.370805
\(404\) 0 0
\(405\) −10.1763 −0.505665
\(406\) 0 0
\(407\) 12.5367 0.621419
\(408\) 0 0
\(409\) 14.7034 0.727035 0.363518 0.931587i \(-0.381576\pi\)
0.363518 + 0.931587i \(0.381576\pi\)
\(410\) 0 0
\(411\) 9.56082 0.471601
\(412\) 0 0
\(413\) 0.101478 0.00499342
\(414\) 0 0
\(415\) 0.226046 0.0110962
\(416\) 0 0
\(417\) 7.16759 0.350998
\(418\) 0 0
\(419\) −16.7968 −0.820578 −0.410289 0.911955i \(-0.634572\pi\)
−0.410289 + 0.911955i \(0.634572\pi\)
\(420\) 0 0
\(421\) 27.7889 1.35435 0.677174 0.735823i \(-0.263204\pi\)
0.677174 + 0.735823i \(0.263204\pi\)
\(422\) 0 0
\(423\) 19.4079 0.943645
\(424\) 0 0
\(425\) 2.45829 0.119244
\(426\) 0 0
\(427\) −0.0729916 −0.00353231
\(428\) 0 0
\(429\) −9.89337 −0.477656
\(430\) 0 0
\(431\) −34.2474 −1.64964 −0.824818 0.565398i \(-0.808723\pi\)
−0.824818 + 0.565398i \(0.808723\pi\)
\(432\) 0 0
\(433\) 8.03722 0.386244 0.193122 0.981175i \(-0.438139\pi\)
0.193122 + 0.981175i \(0.438139\pi\)
\(434\) 0 0
\(435\) −1.23461 −0.0591952
\(436\) 0 0
\(437\) −12.8701 −0.615661
\(438\) 0 0
\(439\) −9.23717 −0.440866 −0.220433 0.975402i \(-0.570747\pi\)
−0.220433 + 0.975402i \(0.570747\pi\)
\(440\) 0 0
\(441\) 17.7109 0.843377
\(442\) 0 0
\(443\) −37.8221 −1.79698 −0.898490 0.438994i \(-0.855335\pi\)
−0.898490 + 0.438994i \(0.855335\pi\)
\(444\) 0 0
\(445\) 0.233574 0.0110725
\(446\) 0 0
\(447\) −7.04026 −0.332993
\(448\) 0 0
\(449\) −3.04929 −0.143905 −0.0719524 0.997408i \(-0.522923\pi\)
−0.0719524 + 0.997408i \(0.522923\pi\)
\(450\) 0 0
\(451\) 33.0805 1.55770
\(452\) 0 0
\(453\) −7.65188 −0.359517
\(454\) 0 0
\(455\) −0.329370 −0.0154411
\(456\) 0 0
\(457\) −0.581707 −0.0272111 −0.0136056 0.999907i \(-0.504331\pi\)
−0.0136056 + 0.999907i \(0.504331\pi\)
\(458\) 0 0
\(459\) −10.6830 −0.498642
\(460\) 0 0
\(461\) 10.1282 0.471718 0.235859 0.971787i \(-0.424210\pi\)
0.235859 + 0.971787i \(0.424210\pi\)
\(462\) 0 0
\(463\) −8.72104 −0.405301 −0.202651 0.979251i \(-0.564956\pi\)
−0.202651 + 0.979251i \(0.564956\pi\)
\(464\) 0 0
\(465\) −4.71992 −0.218881
\(466\) 0 0
\(467\) −16.2772 −0.753217 −0.376609 0.926372i \(-0.622910\pi\)
−0.376609 + 0.926372i \(0.622910\pi\)
\(468\) 0 0
\(469\) 0.00996725 0.000460245 0
\(470\) 0 0
\(471\) −16.5670 −0.763366
\(472\) 0 0
\(473\) 57.5702 2.64708
\(474\) 0 0
\(475\) −3.11387 −0.142874
\(476\) 0 0
\(477\) 17.8362 0.816664
\(478\) 0 0
\(479\) −15.6527 −0.715192 −0.357596 0.933876i \(-0.616404\pi\)
−0.357596 + 0.933876i \(0.616404\pi\)
\(480\) 0 0
\(481\) 4.16535 0.189924
\(482\) 0 0
\(483\) −0.182026 −0.00828245
\(484\) 0 0
\(485\) 30.1033 1.36692
\(486\) 0 0
\(487\) −34.0089 −1.54109 −0.770546 0.637385i \(-0.780016\pi\)
−0.770546 + 0.637385i \(0.780016\pi\)
\(488\) 0 0
\(489\) −3.51370 −0.158895
\(490\) 0 0
\(491\) 13.9859 0.631175 0.315588 0.948896i \(-0.397798\pi\)
0.315588 + 0.948896i \(0.397798\pi\)
\(492\) 0 0
\(493\) 2.50759 0.112936
\(494\) 0 0
\(495\) −33.9483 −1.52586
\(496\) 0 0
\(497\) −0.251853 −0.0112972
\(498\) 0 0
\(499\) 23.0930 1.03379 0.516893 0.856050i \(-0.327088\pi\)
0.516893 + 0.856050i \(0.327088\pi\)
\(500\) 0 0
\(501\) 14.4054 0.643584
\(502\) 0 0
\(503\) −5.22159 −0.232819 −0.116410 0.993201i \(-0.537139\pi\)
−0.116410 + 0.993201i \(0.537139\pi\)
\(504\) 0 0
\(505\) 18.5066 0.823533
\(506\) 0 0
\(507\) 5.60522 0.248937
\(508\) 0 0
\(509\) 22.9495 1.01722 0.508609 0.860998i \(-0.330160\pi\)
0.508609 + 0.860998i \(0.330160\pi\)
\(510\) 0 0
\(511\) −0.783233 −0.0346482
\(512\) 0 0
\(513\) 13.5320 0.597454
\(514\) 0 0
\(515\) 8.84891 0.389930
\(516\) 0 0
\(517\) 50.5705 2.22409
\(518\) 0 0
\(519\) 0.909165 0.0399079
\(520\) 0 0
\(521\) 13.5137 0.592046 0.296023 0.955181i \(-0.404339\pi\)
0.296023 + 0.955181i \(0.404339\pi\)
\(522\) 0 0
\(523\) 7.79860 0.341009 0.170504 0.985357i \(-0.445460\pi\)
0.170504 + 0.985357i \(0.445460\pi\)
\(524\) 0 0
\(525\) −0.0440403 −0.00192208
\(526\) 0 0
\(527\) 9.58649 0.417594
\(528\) 0 0
\(529\) −10.0472 −0.436834
\(530\) 0 0
\(531\) 3.47518 0.150810
\(532\) 0 0
\(533\) 10.9911 0.476078
\(534\) 0 0
\(535\) −24.4047 −1.05511
\(536\) 0 0
\(537\) −1.68010 −0.0725017
\(538\) 0 0
\(539\) 46.1487 1.98777
\(540\) 0 0
\(541\) 8.47910 0.364545 0.182272 0.983248i \(-0.441655\pi\)
0.182272 + 0.983248i \(0.441655\pi\)
\(542\) 0 0
\(543\) 1.00001 0.0429146
\(544\) 0 0
\(545\) −13.1860 −0.564825
\(546\) 0 0
\(547\) 11.0793 0.473717 0.236858 0.971544i \(-0.423882\pi\)
0.236858 + 0.971544i \(0.423882\pi\)
\(548\) 0 0
\(549\) −2.49964 −0.106682
\(550\) 0 0
\(551\) −3.17632 −0.135316
\(552\) 0 0
\(553\) 1.03286 0.0439217
\(554\) 0 0
\(555\) −2.64112 −0.112109
\(556\) 0 0
\(557\) 28.9480 1.22657 0.613283 0.789863i \(-0.289848\pi\)
0.613283 + 0.789863i \(0.289848\pi\)
\(558\) 0 0
\(559\) 19.1279 0.809025
\(560\) 0 0
\(561\) −12.7410 −0.537928
\(562\) 0 0
\(563\) −31.2581 −1.31737 −0.658685 0.752418i \(-0.728887\pi\)
−0.658685 + 0.752418i \(0.728887\pi\)
\(564\) 0 0
\(565\) −6.41270 −0.269784
\(566\) 0 0
\(567\) −0.370283 −0.0155504
\(568\) 0 0
\(569\) 2.75797 0.115620 0.0578100 0.998328i \(-0.481588\pi\)
0.0578100 + 0.998328i \(0.481588\pi\)
\(570\) 0 0
\(571\) 34.2703 1.43417 0.717084 0.696986i \(-0.245476\pi\)
0.717084 + 0.696986i \(0.245476\pi\)
\(572\) 0 0
\(573\) 11.6103 0.485025
\(574\) 0 0
\(575\) 3.13388 0.130692
\(576\) 0 0
\(577\) −46.3408 −1.92919 −0.964597 0.263728i \(-0.915048\pi\)
−0.964597 + 0.263728i \(0.915048\pi\)
\(578\) 0 0
\(579\) −8.92749 −0.371014
\(580\) 0 0
\(581\) 0.00822506 0.000341233 0
\(582\) 0 0
\(583\) 46.4752 1.92480
\(584\) 0 0
\(585\) −11.2795 −0.466348
\(586\) 0 0
\(587\) −10.5190 −0.434166 −0.217083 0.976153i \(-0.569654\pi\)
−0.217083 + 0.976153i \(0.569654\pi\)
\(588\) 0 0
\(589\) −12.1430 −0.500345
\(590\) 0 0
\(591\) 7.38151 0.303635
\(592\) 0 0
\(593\) −15.6067 −0.640890 −0.320445 0.947267i \(-0.603832\pi\)
−0.320445 + 0.947267i \(0.603832\pi\)
\(594\) 0 0
\(595\) −0.424174 −0.0173895
\(596\) 0 0
\(597\) 9.02560 0.369393
\(598\) 0 0
\(599\) −13.7620 −0.562300 −0.281150 0.959664i \(-0.590716\pi\)
−0.281150 + 0.959664i \(0.590716\pi\)
\(600\) 0 0
\(601\) 31.2077 1.27299 0.636493 0.771282i \(-0.280384\pi\)
0.636493 + 0.771282i \(0.280384\pi\)
\(602\) 0 0
\(603\) 0.341335 0.0139002
\(604\) 0 0
\(605\) −66.1053 −2.68756
\(606\) 0 0
\(607\) 3.52856 0.143220 0.0716100 0.997433i \(-0.477186\pi\)
0.0716100 + 0.997433i \(0.477186\pi\)
\(608\) 0 0
\(609\) −0.0449235 −0.00182039
\(610\) 0 0
\(611\) 16.8023 0.679746
\(612\) 0 0
\(613\) 0.995724 0.0402169 0.0201085 0.999798i \(-0.493599\pi\)
0.0201085 + 0.999798i \(0.493599\pi\)
\(614\) 0 0
\(615\) −6.96912 −0.281022
\(616\) 0 0
\(617\) −10.7787 −0.433936 −0.216968 0.976179i \(-0.569617\pi\)
−0.216968 + 0.976179i \(0.569617\pi\)
\(618\) 0 0
\(619\) −41.8494 −1.68207 −0.841034 0.540982i \(-0.818053\pi\)
−0.841034 + 0.540982i \(0.818053\pi\)
\(620\) 0 0
\(621\) −13.6190 −0.546512
\(622\) 0 0
\(623\) 0.00849898 0.000340505 0
\(624\) 0 0
\(625\) −19.8880 −0.795518
\(626\) 0 0
\(627\) 16.1389 0.644524
\(628\) 0 0
\(629\) 5.36430 0.213888
\(630\) 0 0
\(631\) −24.5218 −0.976196 −0.488098 0.872789i \(-0.662309\pi\)
−0.488098 + 0.872789i \(0.662309\pi\)
\(632\) 0 0
\(633\) 3.69415 0.146829
\(634\) 0 0
\(635\) −41.8537 −1.66091
\(636\) 0 0
\(637\) 15.3331 0.607519
\(638\) 0 0
\(639\) −8.62486 −0.341194
\(640\) 0 0
\(641\) −23.0254 −0.909447 −0.454724 0.890633i \(-0.650262\pi\)
−0.454724 + 0.890633i \(0.650262\pi\)
\(642\) 0 0
\(643\) −11.5967 −0.457327 −0.228664 0.973505i \(-0.573436\pi\)
−0.228664 + 0.973505i \(0.573436\pi\)
\(644\) 0 0
\(645\) −12.1284 −0.477556
\(646\) 0 0
\(647\) 5.54198 0.217878 0.108939 0.994048i \(-0.465255\pi\)
0.108939 + 0.994048i \(0.465255\pi\)
\(648\) 0 0
\(649\) 9.05516 0.355446
\(650\) 0 0
\(651\) −0.171742 −0.00673111
\(652\) 0 0
\(653\) −3.89284 −0.152339 −0.0761693 0.997095i \(-0.524269\pi\)
−0.0761693 + 0.997095i \(0.524269\pi\)
\(654\) 0 0
\(655\) 19.5398 0.763482
\(656\) 0 0
\(657\) −26.8223 −1.04644
\(658\) 0 0
\(659\) −17.9274 −0.698353 −0.349177 0.937057i \(-0.613539\pi\)
−0.349177 + 0.937057i \(0.613539\pi\)
\(660\) 0 0
\(661\) 5.52221 0.214789 0.107395 0.994216i \(-0.465749\pi\)
0.107395 + 0.994216i \(0.465749\pi\)
\(662\) 0 0
\(663\) −4.23327 −0.164406
\(664\) 0 0
\(665\) 0.537294 0.0208354
\(666\) 0 0
\(667\) 3.19673 0.123778
\(668\) 0 0
\(669\) 8.07233 0.312094
\(670\) 0 0
\(671\) −6.51323 −0.251440
\(672\) 0 0
\(673\) 32.1520 1.23937 0.619684 0.784852i \(-0.287261\pi\)
0.619684 + 0.784852i \(0.287261\pi\)
\(674\) 0 0
\(675\) −3.29506 −0.126827
\(676\) 0 0
\(677\) 38.6060 1.48375 0.741874 0.670539i \(-0.233937\pi\)
0.741874 + 0.670539i \(0.233937\pi\)
\(678\) 0 0
\(679\) 1.09536 0.0420360
\(680\) 0 0
\(681\) 3.24260 0.124257
\(682\) 0 0
\(683\) −20.8357 −0.797257 −0.398628 0.917113i \(-0.630514\pi\)
−0.398628 + 0.917113i \(0.630514\pi\)
\(684\) 0 0
\(685\) 28.4026 1.08521
\(686\) 0 0
\(687\) 5.97119 0.227815
\(688\) 0 0
\(689\) 15.4416 0.588277
\(690\) 0 0
\(691\) −39.6858 −1.50972 −0.754860 0.655886i \(-0.772295\pi\)
−0.754860 + 0.655886i \(0.772295\pi\)
\(692\) 0 0
\(693\) −1.23527 −0.0469239
\(694\) 0 0
\(695\) 21.2929 0.807687
\(696\) 0 0
\(697\) 14.1548 0.536150
\(698\) 0 0
\(699\) −8.32141 −0.314745
\(700\) 0 0
\(701\) −21.7469 −0.821368 −0.410684 0.911778i \(-0.634710\pi\)
−0.410684 + 0.911778i \(0.634710\pi\)
\(702\) 0 0
\(703\) −6.79486 −0.256273
\(704\) 0 0
\(705\) −10.6538 −0.401245
\(706\) 0 0
\(707\) 0.673394 0.0253256
\(708\) 0 0
\(709\) −10.9993 −0.413086 −0.206543 0.978437i \(-0.566221\pi\)
−0.206543 + 0.978437i \(0.566221\pi\)
\(710\) 0 0
\(711\) 35.3710 1.32651
\(712\) 0 0
\(713\) 12.2211 0.457683
\(714\) 0 0
\(715\) −29.3905 −1.09914
\(716\) 0 0
\(717\) 13.0469 0.487244
\(718\) 0 0
\(719\) −9.63747 −0.359417 −0.179709 0.983720i \(-0.557515\pi\)
−0.179709 + 0.983720i \(0.557515\pi\)
\(720\) 0 0
\(721\) 0.321983 0.0119913
\(722\) 0 0
\(723\) −15.1733 −0.564300
\(724\) 0 0
\(725\) 0.773436 0.0287247
\(726\) 0 0
\(727\) 3.59365 0.133281 0.0666406 0.997777i \(-0.478772\pi\)
0.0666406 + 0.997777i \(0.478772\pi\)
\(728\) 0 0
\(729\) −4.91527 −0.182047
\(730\) 0 0
\(731\) 24.6337 0.911109
\(732\) 0 0
\(733\) 6.58136 0.243088 0.121544 0.992586i \(-0.461215\pi\)
0.121544 + 0.992586i \(0.461215\pi\)
\(734\) 0 0
\(735\) −9.72223 −0.358610
\(736\) 0 0
\(737\) 0.889403 0.0327616
\(738\) 0 0
\(739\) −43.6462 −1.60555 −0.802775 0.596282i \(-0.796644\pi\)
−0.802775 + 0.596282i \(0.796644\pi\)
\(740\) 0 0
\(741\) 5.36220 0.196986
\(742\) 0 0
\(743\) 9.15433 0.335840 0.167920 0.985801i \(-0.446295\pi\)
0.167920 + 0.985801i \(0.446295\pi\)
\(744\) 0 0
\(745\) −20.9147 −0.766255
\(746\) 0 0
\(747\) 0.281672 0.0103058
\(748\) 0 0
\(749\) −0.888008 −0.0324471
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −6.17488 −0.225025
\(754\) 0 0
\(755\) −22.7316 −0.827289
\(756\) 0 0
\(757\) −44.0111 −1.59961 −0.799806 0.600259i \(-0.795064\pi\)
−0.799806 + 0.600259i \(0.795064\pi\)
\(758\) 0 0
\(759\) −16.2426 −0.589569
\(760\) 0 0
\(761\) 23.6173 0.856125 0.428062 0.903749i \(-0.359196\pi\)
0.428062 + 0.903749i \(0.359196\pi\)
\(762\) 0 0
\(763\) −0.479794 −0.0173697
\(764\) 0 0
\(765\) −14.5261 −0.525192
\(766\) 0 0
\(767\) 3.00862 0.108635
\(768\) 0 0
\(769\) −25.8416 −0.931873 −0.465937 0.884818i \(-0.654283\pi\)
−0.465937 + 0.884818i \(0.654283\pi\)
\(770\) 0 0
\(771\) −14.7376 −0.530762
\(772\) 0 0
\(773\) 44.6722 1.60675 0.803374 0.595474i \(-0.203036\pi\)
0.803374 + 0.595474i \(0.203036\pi\)
\(774\) 0 0
\(775\) 2.95684 0.106213
\(776\) 0 0
\(777\) −0.0961016 −0.00344763
\(778\) 0 0
\(779\) −17.9296 −0.642395
\(780\) 0 0
\(781\) −22.4735 −0.804165
\(782\) 0 0
\(783\) −3.36114 −0.120118
\(784\) 0 0
\(785\) −49.2159 −1.75659
\(786\) 0 0
\(787\) −10.8667 −0.387357 −0.193679 0.981065i \(-0.562042\pi\)
−0.193679 + 0.981065i \(0.562042\pi\)
\(788\) 0 0
\(789\) 3.04717 0.108482
\(790\) 0 0
\(791\) −0.233337 −0.00829651
\(792\) 0 0
\(793\) −2.16405 −0.0768476
\(794\) 0 0
\(795\) −9.79101 −0.347251
\(796\) 0 0
\(797\) 30.0713 1.06518 0.532590 0.846373i \(-0.321219\pi\)
0.532590 + 0.846373i \(0.321219\pi\)
\(798\) 0 0
\(799\) 21.6386 0.765517
\(800\) 0 0
\(801\) 0.291053 0.0102838
\(802\) 0 0
\(803\) −69.8899 −2.46636
\(804\) 0 0
\(805\) −0.540748 −0.0190589
\(806\) 0 0
\(807\) −6.06067 −0.213346
\(808\) 0 0
\(809\) −18.8383 −0.662321 −0.331160 0.943574i \(-0.607440\pi\)
−0.331160 + 0.943574i \(0.607440\pi\)
\(810\) 0 0
\(811\) −4.65017 −0.163290 −0.0816448 0.996661i \(-0.526017\pi\)
−0.0816448 + 0.996661i \(0.526017\pi\)
\(812\) 0 0
\(813\) −10.4154 −0.365284
\(814\) 0 0
\(815\) −10.4382 −0.365636
\(816\) 0 0
\(817\) −31.2030 −1.09166
\(818\) 0 0
\(819\) −0.410422 −0.0143413
\(820\) 0 0
\(821\) −20.4667 −0.714292 −0.357146 0.934049i \(-0.616250\pi\)
−0.357146 + 0.934049i \(0.616250\pi\)
\(822\) 0 0
\(823\) −44.7395 −1.55952 −0.779760 0.626079i \(-0.784659\pi\)
−0.779760 + 0.626079i \(0.784659\pi\)
\(824\) 0 0
\(825\) −3.92983 −0.136819
\(826\) 0 0
\(827\) −32.4135 −1.12713 −0.563564 0.826072i \(-0.690570\pi\)
−0.563564 + 0.826072i \(0.690570\pi\)
\(828\) 0 0
\(829\) 19.9565 0.693119 0.346559 0.938028i \(-0.387350\pi\)
0.346559 + 0.938028i \(0.387350\pi\)
\(830\) 0 0
\(831\) 5.19049 0.180056
\(832\) 0 0
\(833\) 19.7465 0.684177
\(834\) 0 0
\(835\) 42.7944 1.48096
\(836\) 0 0
\(837\) −12.8496 −0.444148
\(838\) 0 0
\(839\) −17.1453 −0.591922 −0.295961 0.955200i \(-0.595640\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(840\) 0 0
\(841\) −28.2111 −0.972795
\(842\) 0 0
\(843\) 18.9395 0.652310
\(844\) 0 0
\(845\) 16.6516 0.572831
\(846\) 0 0
\(847\) −2.40535 −0.0826489
\(848\) 0 0
\(849\) 1.50040 0.0514935
\(850\) 0 0
\(851\) 6.83853 0.234422
\(852\) 0 0
\(853\) −1.20277 −0.0411821 −0.0205911 0.999788i \(-0.506555\pi\)
−0.0205911 + 0.999788i \(0.506555\pi\)
\(854\) 0 0
\(855\) 18.4000 0.629266
\(856\) 0 0
\(857\) −12.9389 −0.441986 −0.220993 0.975275i \(-0.570930\pi\)
−0.220993 + 0.975275i \(0.570930\pi\)
\(858\) 0 0
\(859\) −17.9312 −0.611805 −0.305903 0.952063i \(-0.598958\pi\)
−0.305903 + 0.952063i \(0.598958\pi\)
\(860\) 0 0
\(861\) −0.253583 −0.00864210
\(862\) 0 0
\(863\) 41.2906 1.40555 0.702774 0.711413i \(-0.251945\pi\)
0.702774 + 0.711413i \(0.251945\pi\)
\(864\) 0 0
\(865\) 2.70088 0.0918326
\(866\) 0 0
\(867\) 6.17668 0.209771
\(868\) 0 0
\(869\) 92.1648 3.12648
\(870\) 0 0
\(871\) 0.295508 0.0100129
\(872\) 0 0
\(873\) 37.5112 1.26956
\(874\) 0 0
\(875\) −0.882078 −0.0298197
\(876\) 0 0
\(877\) −34.1316 −1.15254 −0.576271 0.817259i \(-0.695493\pi\)
−0.576271 + 0.817259i \(0.695493\pi\)
\(878\) 0 0
\(879\) 16.6601 0.561931
\(880\) 0 0
\(881\) −33.9088 −1.14242 −0.571208 0.820805i \(-0.693525\pi\)
−0.571208 + 0.820805i \(0.693525\pi\)
\(882\) 0 0
\(883\) −4.13156 −0.139038 −0.0695190 0.997581i \(-0.522146\pi\)
−0.0695190 + 0.997581i \(0.522146\pi\)
\(884\) 0 0
\(885\) −1.90767 −0.0641256
\(886\) 0 0
\(887\) 52.9804 1.77891 0.889453 0.457026i \(-0.151086\pi\)
0.889453 + 0.457026i \(0.151086\pi\)
\(888\) 0 0
\(889\) −1.52292 −0.0510771
\(890\) 0 0
\(891\) −33.0412 −1.10692
\(892\) 0 0
\(893\) −27.4092 −0.917214
\(894\) 0 0
\(895\) −4.99112 −0.166835
\(896\) 0 0
\(897\) −5.39667 −0.180190
\(898\) 0 0
\(899\) 3.01614 0.100594
\(900\) 0 0
\(901\) 19.8862 0.662506
\(902\) 0 0
\(903\) −0.441313 −0.0146860
\(904\) 0 0
\(905\) 2.97076 0.0987513
\(906\) 0 0
\(907\) 29.5783 0.982130 0.491065 0.871123i \(-0.336608\pi\)
0.491065 + 0.871123i \(0.336608\pi\)
\(908\) 0 0
\(909\) 23.0608 0.764878
\(910\) 0 0
\(911\) 39.3813 1.30476 0.652381 0.757891i \(-0.273770\pi\)
0.652381 + 0.757891i \(0.273770\pi\)
\(912\) 0 0
\(913\) 0.733943 0.0242900
\(914\) 0 0
\(915\) 1.37215 0.0453620
\(916\) 0 0
\(917\) 0.710987 0.0234789
\(918\) 0 0
\(919\) 4.83998 0.159656 0.0798282 0.996809i \(-0.474563\pi\)
0.0798282 + 0.996809i \(0.474563\pi\)
\(920\) 0 0
\(921\) 7.32454 0.241352
\(922\) 0 0
\(923\) −7.46691 −0.245776
\(924\) 0 0
\(925\) 1.65455 0.0544014
\(926\) 0 0
\(927\) 11.0265 0.362158
\(928\) 0 0
\(929\) −30.7096 −1.00755 −0.503775 0.863835i \(-0.668056\pi\)
−0.503775 + 0.863835i \(0.668056\pi\)
\(930\) 0 0
\(931\) −25.0126 −0.819754
\(932\) 0 0
\(933\) −9.86545 −0.322980
\(934\) 0 0
\(935\) −37.8501 −1.23783
\(936\) 0 0
\(937\) −48.5000 −1.58443 −0.792213 0.610245i \(-0.791071\pi\)
−0.792213 + 0.610245i \(0.791071\pi\)
\(938\) 0 0
\(939\) −3.33091 −0.108700
\(940\) 0 0
\(941\) −42.2803 −1.37830 −0.689150 0.724619i \(-0.742016\pi\)
−0.689150 + 0.724619i \(0.742016\pi\)
\(942\) 0 0
\(943\) 18.0448 0.587621
\(944\) 0 0
\(945\) 0.568559 0.0184952
\(946\) 0 0
\(947\) 7.93645 0.257900 0.128950 0.991651i \(-0.458839\pi\)
0.128950 + 0.991651i \(0.458839\pi\)
\(948\) 0 0
\(949\) −23.2212 −0.753792
\(950\) 0 0
\(951\) −9.51198 −0.308447
\(952\) 0 0
\(953\) −50.2558 −1.62795 −0.813973 0.580903i \(-0.802700\pi\)
−0.813973 + 0.580903i \(0.802700\pi\)
\(954\) 0 0
\(955\) 34.4909 1.11610
\(956\) 0 0
\(957\) −4.00864 −0.129581
\(958\) 0 0
\(959\) 1.03348 0.0333727
\(960\) 0 0
\(961\) −19.4693 −0.628043
\(962\) 0 0
\(963\) −30.4104 −0.979960
\(964\) 0 0
\(965\) −26.5211 −0.853745
\(966\) 0 0
\(967\) 45.7638 1.47166 0.735832 0.677164i \(-0.236791\pi\)
0.735832 + 0.677164i \(0.236791\pi\)
\(968\) 0 0
\(969\) 6.90565 0.221841
\(970\) 0 0
\(971\) −59.5742 −1.91183 −0.955914 0.293647i \(-0.905131\pi\)
−0.955914 + 0.293647i \(0.905131\pi\)
\(972\) 0 0
\(973\) 0.774779 0.0248383
\(974\) 0 0
\(975\) −1.30570 −0.0418159
\(976\) 0 0
\(977\) −35.2079 −1.12640 −0.563200 0.826321i \(-0.690430\pi\)
−0.563200 + 0.826321i \(0.690430\pi\)
\(978\) 0 0
\(979\) 0.758386 0.0242381
\(980\) 0 0
\(981\) −16.4308 −0.524596
\(982\) 0 0
\(983\) 21.7034 0.692231 0.346115 0.938192i \(-0.387501\pi\)
0.346115 + 0.938192i \(0.387501\pi\)
\(984\) 0 0
\(985\) 21.9284 0.698698
\(986\) 0 0
\(987\) −0.387656 −0.0123392
\(988\) 0 0
\(989\) 31.4036 0.998576
\(990\) 0 0
\(991\) −40.2004 −1.27701 −0.638504 0.769619i \(-0.720446\pi\)
−0.638504 + 0.769619i \(0.720446\pi\)
\(992\) 0 0
\(993\) −2.48498 −0.0788585
\(994\) 0 0
\(995\) 26.8126 0.850016
\(996\) 0 0
\(997\) −32.0912 −1.01634 −0.508169 0.861257i \(-0.669678\pi\)
−0.508169 + 0.861257i \(0.669678\pi\)
\(998\) 0 0
\(999\) −7.19025 −0.227489
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 \(a_p\))