Properties

Label 8015.2.a.l.1.31
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.31
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +O(q^{10})\) \(q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +0.0447957 q^{10} +1.58257 q^{11} +4.76992 q^{12} +4.30209 q^{13} +0.0447957 q^{14} +2.38735 q^{15} +3.98796 q^{16} -0.131751 q^{17} -0.120924 q^{18} +5.31805 q^{19} +1.99799 q^{20} +2.38735 q^{21} -0.0708926 q^{22} +4.65052 q^{23} -0.427558 q^{24} +1.00000 q^{25} -0.192715 q^{26} +0.717497 q^{27} +1.99799 q^{28} +3.43161 q^{29} -0.106943 q^{30} +7.13841 q^{31} -0.536830 q^{32} -3.77817 q^{33} +0.00590190 q^{34} +1.00000 q^{35} -5.39350 q^{36} +11.3215 q^{37} -0.238226 q^{38} -10.2706 q^{39} -0.179093 q^{40} -2.91849 q^{41} -0.106943 q^{42} -8.72221 q^{43} -3.16197 q^{44} -2.69946 q^{45} -0.208323 q^{46} +5.61847 q^{47} -9.52068 q^{48} +1.00000 q^{49} -0.0447957 q^{50} +0.314537 q^{51} -8.59555 q^{52} +11.2601 q^{53} -0.0321408 q^{54} -1.58257 q^{55} -0.179093 q^{56} -12.6961 q^{57} -0.153721 q^{58} +12.4882 q^{59} -4.76992 q^{60} -6.94914 q^{61} -0.319770 q^{62} -2.69946 q^{63} -7.95188 q^{64} -4.30209 q^{65} +0.169246 q^{66} +11.4949 q^{67} +0.263239 q^{68} -11.1024 q^{69} -0.0447957 q^{70} +1.19614 q^{71} +0.483454 q^{72} +13.0473 q^{73} -0.507153 q^{74} -2.38735 q^{75} -10.6254 q^{76} -1.58257 q^{77} +0.460079 q^{78} +10.1506 q^{79} -3.98796 q^{80} -9.81130 q^{81} +0.130736 q^{82} -15.3767 q^{83} -4.76992 q^{84} +0.131751 q^{85} +0.390718 q^{86} -8.19246 q^{87} +0.283428 q^{88} +0.726485 q^{89} +0.120924 q^{90} -4.30209 q^{91} -9.29171 q^{92} -17.0419 q^{93} -0.251684 q^{94} -5.31805 q^{95} +1.28160 q^{96} +9.26771 q^{97} -0.0447957 q^{98} +4.27210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0447957 −0.0316754 −0.0158377 0.999875i \(-0.505042\pi\)
−0.0158377 + 0.999875i \(0.505042\pi\)
\(3\) −2.38735 −1.37834 −0.689170 0.724600i \(-0.742025\pi\)
−0.689170 + 0.724600i \(0.742025\pi\)
\(4\) −1.99799 −0.998997
\(5\) −1.00000 −0.447214
\(6\) 0.106943 0.0436594
\(7\) −1.00000 −0.377964
\(8\) 0.179093 0.0633189
\(9\) 2.69946 0.899820
\(10\) 0.0447957 0.0141656
\(11\) 1.58257 0.477164 0.238582 0.971122i \(-0.423317\pi\)
0.238582 + 0.971122i \(0.423317\pi\)
\(12\) 4.76992 1.37696
\(13\) 4.30209 1.19319 0.596593 0.802544i \(-0.296521\pi\)
0.596593 + 0.802544i \(0.296521\pi\)
\(14\) 0.0447957 0.0119722
\(15\) 2.38735 0.616412
\(16\) 3.98796 0.996991
\(17\) −0.131751 −0.0319544 −0.0159772 0.999872i \(-0.505086\pi\)
−0.0159772 + 0.999872i \(0.505086\pi\)
\(18\) −0.120924 −0.0285021
\(19\) 5.31805 1.22004 0.610022 0.792385i \(-0.291161\pi\)
0.610022 + 0.792385i \(0.291161\pi\)
\(20\) 1.99799 0.446765
\(21\) 2.38735 0.520963
\(22\) −0.0708926 −0.0151143
\(23\) 4.65052 0.969700 0.484850 0.874597i \(-0.338874\pi\)
0.484850 + 0.874597i \(0.338874\pi\)
\(24\) −0.427558 −0.0872750
\(25\) 1.00000 0.200000
\(26\) −0.192715 −0.0377946
\(27\) 0.717497 0.138082
\(28\) 1.99799 0.377585
\(29\) 3.43161 0.637233 0.318617 0.947884i \(-0.396782\pi\)
0.318617 + 0.947884i \(0.396782\pi\)
\(30\) −0.106943 −0.0195251
\(31\) 7.13841 1.28210 0.641048 0.767501i \(-0.278500\pi\)
0.641048 + 0.767501i \(0.278500\pi\)
\(32\) −0.536830 −0.0948990
\(33\) −3.77817 −0.657694
\(34\) 0.00590190 0.00101217
\(35\) 1.00000 0.169031
\(36\) −5.39350 −0.898917
\(37\) 11.3215 1.86124 0.930618 0.365991i \(-0.119270\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(38\) −0.238226 −0.0386453
\(39\) −10.2706 −1.64461
\(40\) −0.179093 −0.0283171
\(41\) −2.91849 −0.455792 −0.227896 0.973685i \(-0.573185\pi\)
−0.227896 + 0.973685i \(0.573185\pi\)
\(42\) −0.106943 −0.0165017
\(43\) −8.72221 −1.33012 −0.665062 0.746788i \(-0.731595\pi\)
−0.665062 + 0.746788i \(0.731595\pi\)
\(44\) −3.16197 −0.476685
\(45\) −2.69946 −0.402412
\(46\) −0.208323 −0.0307156
\(47\) 5.61847 0.819538 0.409769 0.912189i \(-0.365609\pi\)
0.409769 + 0.912189i \(0.365609\pi\)
\(48\) −9.52068 −1.37419
\(49\) 1.00000 0.142857
\(50\) −0.0447957 −0.00633507
\(51\) 0.314537 0.0440440
\(52\) −8.59555 −1.19199
\(53\) 11.2601 1.54669 0.773344 0.633986i \(-0.218582\pi\)
0.773344 + 0.633986i \(0.218582\pi\)
\(54\) −0.0321408 −0.00437381
\(55\) −1.58257 −0.213394
\(56\) −0.179093 −0.0239323
\(57\) −12.6961 −1.68163
\(58\) −0.153721 −0.0201846
\(59\) 12.4882 1.62583 0.812915 0.582383i \(-0.197879\pi\)
0.812915 + 0.582383i \(0.197879\pi\)
\(60\) −4.76992 −0.615794
\(61\) −6.94914 −0.889747 −0.444873 0.895593i \(-0.646751\pi\)
−0.444873 + 0.895593i \(0.646751\pi\)
\(62\) −0.319770 −0.0406109
\(63\) −2.69946 −0.340100
\(64\) −7.95188 −0.993985
\(65\) −4.30209 −0.533609
\(66\) 0.169246 0.0208327
\(67\) 11.4949 1.40432 0.702162 0.712017i \(-0.252218\pi\)
0.702162 + 0.712017i \(0.252218\pi\)
\(68\) 0.263239 0.0319224
\(69\) −11.1024 −1.33658
\(70\) −0.0447957 −0.00535411
\(71\) 1.19614 0.141956 0.0709780 0.997478i \(-0.477388\pi\)
0.0709780 + 0.997478i \(0.477388\pi\)
\(72\) 0.483454 0.0569756
\(73\) 13.0473 1.52708 0.763538 0.645763i \(-0.223461\pi\)
0.763538 + 0.645763i \(0.223461\pi\)
\(74\) −0.507153 −0.0589553
\(75\) −2.38735 −0.275668
\(76\) −10.6254 −1.21882
\(77\) −1.58257 −0.180351
\(78\) 0.460079 0.0520937
\(79\) 10.1506 1.14204 0.571018 0.820937i \(-0.306548\pi\)
0.571018 + 0.820937i \(0.306548\pi\)
\(80\) −3.98796 −0.445868
\(81\) −9.81130 −1.09014
\(82\) 0.130736 0.0144374
\(83\) −15.3767 −1.68781 −0.843905 0.536493i \(-0.819749\pi\)
−0.843905 + 0.536493i \(0.819749\pi\)
\(84\) −4.76992 −0.520441
\(85\) 0.131751 0.0142905
\(86\) 0.390718 0.0421322
\(87\) −8.19246 −0.878324
\(88\) 0.283428 0.0302135
\(89\) 0.726485 0.0770073 0.0385036 0.999258i \(-0.487741\pi\)
0.0385036 + 0.999258i \(0.487741\pi\)
\(90\) 0.120924 0.0127465
\(91\) −4.30209 −0.450982
\(92\) −9.29171 −0.968727
\(93\) −17.0419 −1.76716
\(94\) −0.251684 −0.0259592
\(95\) −5.31805 −0.545620
\(96\) 1.28160 0.130803
\(97\) 9.26771 0.940993 0.470497 0.882402i \(-0.344075\pi\)
0.470497 + 0.882402i \(0.344075\pi\)
\(98\) −0.0447957 −0.00452505
\(99\) 4.27210 0.429362
\(100\) −1.99799 −0.199799
\(101\) 0.448686 0.0446459 0.0223230 0.999751i \(-0.492894\pi\)
0.0223230 + 0.999751i \(0.492894\pi\)
\(102\) −0.0140899 −0.00139511
\(103\) −8.83920 −0.870952 −0.435476 0.900200i \(-0.643420\pi\)
−0.435476 + 0.900200i \(0.643420\pi\)
\(104\) 0.770474 0.0755512
\(105\) −2.38735 −0.232982
\(106\) −0.504403 −0.0489919
\(107\) −13.6818 −1.32267 −0.661333 0.750092i \(-0.730009\pi\)
−0.661333 + 0.750092i \(0.730009\pi\)
\(108\) −1.43355 −0.137944
\(109\) −8.47924 −0.812164 −0.406082 0.913837i \(-0.633105\pi\)
−0.406082 + 0.913837i \(0.633105\pi\)
\(110\) 0.0708926 0.00675934
\(111\) −27.0283 −2.56542
\(112\) −3.98796 −0.376827
\(113\) 0.442889 0.0416635 0.0208318 0.999783i \(-0.493369\pi\)
0.0208318 + 0.999783i \(0.493369\pi\)
\(114\) 0.568729 0.0532664
\(115\) −4.65052 −0.433663
\(116\) −6.85633 −0.636594
\(117\) 11.6133 1.07365
\(118\) −0.559419 −0.0514987
\(119\) 0.131751 0.0120776
\(120\) 0.427558 0.0390306
\(121\) −8.49546 −0.772314
\(122\) 0.311292 0.0281830
\(123\) 6.96748 0.628236
\(124\) −14.2625 −1.28081
\(125\) −1.00000 −0.0894427
\(126\) 0.120924 0.0107728
\(127\) 10.8071 0.958972 0.479486 0.877549i \(-0.340823\pi\)
0.479486 + 0.877549i \(0.340823\pi\)
\(128\) 1.42987 0.126384
\(129\) 20.8230 1.83336
\(130\) 0.192715 0.0169022
\(131\) 12.2219 1.06783 0.533917 0.845537i \(-0.320719\pi\)
0.533917 + 0.845537i \(0.320719\pi\)
\(132\) 7.54875 0.657034
\(133\) −5.31805 −0.461133
\(134\) −0.514922 −0.0444825
\(135\) −0.717497 −0.0617523
\(136\) −0.0235958 −0.00202332
\(137\) −12.2241 −1.04438 −0.522188 0.852831i \(-0.674884\pi\)
−0.522188 + 0.852831i \(0.674884\pi\)
\(138\) 0.497342 0.0423365
\(139\) 4.55663 0.386489 0.193244 0.981151i \(-0.438099\pi\)
0.193244 + 0.981151i \(0.438099\pi\)
\(140\) −1.99799 −0.168861
\(141\) −13.4133 −1.12960
\(142\) −0.0535821 −0.00449651
\(143\) 6.80838 0.569345
\(144\) 10.7653 0.897112
\(145\) −3.43161 −0.284979
\(146\) −0.584465 −0.0483706
\(147\) −2.38735 −0.196906
\(148\) −22.6202 −1.85937
\(149\) −17.5863 −1.44072 −0.720362 0.693598i \(-0.756024\pi\)
−0.720362 + 0.693598i \(0.756024\pi\)
\(150\) 0.106943 0.00873188
\(151\) −9.59414 −0.780760 −0.390380 0.920654i \(-0.627656\pi\)
−0.390380 + 0.920654i \(0.627656\pi\)
\(152\) 0.952425 0.0772518
\(153\) −0.355658 −0.0287532
\(154\) 0.0708926 0.00571269
\(155\) −7.13841 −0.573371
\(156\) 20.5206 1.64296
\(157\) 20.3023 1.62030 0.810151 0.586221i \(-0.199385\pi\)
0.810151 + 0.586221i \(0.199385\pi\)
\(158\) −0.454705 −0.0361744
\(159\) −26.8818 −2.13186
\(160\) 0.536830 0.0424401
\(161\) −4.65052 −0.366512
\(162\) 0.439504 0.0345307
\(163\) 9.14773 0.716506 0.358253 0.933625i \(-0.383373\pi\)
0.358253 + 0.933625i \(0.383373\pi\)
\(164\) 5.83113 0.455335
\(165\) 3.77817 0.294130
\(166\) 0.688809 0.0534620
\(167\) −2.19873 −0.170143 −0.0850713 0.996375i \(-0.527112\pi\)
−0.0850713 + 0.996375i \(0.527112\pi\)
\(168\) 0.427558 0.0329868
\(169\) 5.50798 0.423691
\(170\) −0.00590190 −0.000452655 0
\(171\) 14.3558 1.09782
\(172\) 17.4269 1.32879
\(173\) −2.87001 −0.218203 −0.109101 0.994031i \(-0.534797\pi\)
−0.109101 + 0.994031i \(0.534797\pi\)
\(174\) 0.366987 0.0278212
\(175\) −1.00000 −0.0755929
\(176\) 6.31125 0.475728
\(177\) −29.8138 −2.24094
\(178\) −0.0325434 −0.00243923
\(179\) 17.4808 1.30657 0.653287 0.757110i \(-0.273389\pi\)
0.653287 + 0.757110i \(0.273389\pi\)
\(180\) 5.39350 0.402008
\(181\) 17.6474 1.31172 0.655860 0.754883i \(-0.272306\pi\)
0.655860 + 0.754883i \(0.272306\pi\)
\(182\) 0.192715 0.0142850
\(183\) 16.5901 1.22637
\(184\) 0.832875 0.0614004
\(185\) −11.3215 −0.832370
\(186\) 0.763405 0.0559756
\(187\) −0.208506 −0.0152475
\(188\) −11.2257 −0.818716
\(189\) −0.717497 −0.0521902
\(190\) 0.238226 0.0172827
\(191\) 17.5339 1.26871 0.634356 0.773041i \(-0.281265\pi\)
0.634356 + 0.773041i \(0.281265\pi\)
\(192\) 18.9840 1.37005
\(193\) 12.5294 0.901883 0.450941 0.892554i \(-0.351088\pi\)
0.450941 + 0.892554i \(0.351088\pi\)
\(194\) −0.415154 −0.0298063
\(195\) 10.2706 0.735494
\(196\) −1.99799 −0.142714
\(197\) 27.7307 1.97573 0.987864 0.155318i \(-0.0496403\pi\)
0.987864 + 0.155318i \(0.0496403\pi\)
\(198\) −0.191372 −0.0136002
\(199\) −19.8798 −1.40924 −0.704622 0.709583i \(-0.748883\pi\)
−0.704622 + 0.709583i \(0.748883\pi\)
\(200\) 0.179093 0.0126638
\(201\) −27.4424 −1.93563
\(202\) −0.0200992 −0.00141418
\(203\) −3.43161 −0.240852
\(204\) −0.628444 −0.0439998
\(205\) 2.91849 0.203836
\(206\) 0.395958 0.0275877
\(207\) 12.5539 0.872556
\(208\) 17.1566 1.18959
\(209\) 8.41620 0.582161
\(210\) 0.106943 0.00737978
\(211\) −9.49510 −0.653670 −0.326835 0.945081i \(-0.605982\pi\)
−0.326835 + 0.945081i \(0.605982\pi\)
\(212\) −22.4975 −1.54514
\(213\) −2.85562 −0.195664
\(214\) 0.612885 0.0418959
\(215\) 8.72221 0.594850
\(216\) 0.128499 0.00874322
\(217\) −7.13841 −0.484587
\(218\) 0.379834 0.0257256
\(219\) −31.1486 −2.10483
\(220\) 3.16197 0.213180
\(221\) −0.566807 −0.0381275
\(222\) 1.21075 0.0812605
\(223\) −8.30400 −0.556077 −0.278038 0.960570i \(-0.589684\pi\)
−0.278038 + 0.960570i \(0.589684\pi\)
\(224\) 0.536830 0.0358684
\(225\) 2.69946 0.179964
\(226\) −0.0198395 −0.00131971
\(227\) 4.06216 0.269615 0.134808 0.990872i \(-0.456958\pi\)
0.134808 + 0.990872i \(0.456958\pi\)
\(228\) 25.3666 1.67995
\(229\) 1.00000 0.0660819
\(230\) 0.208323 0.0137364
\(231\) 3.77817 0.248585
\(232\) 0.614577 0.0403489
\(233\) 17.0263 1.11543 0.557715 0.830033i \(-0.311678\pi\)
0.557715 + 0.830033i \(0.311678\pi\)
\(234\) −0.520227 −0.0340083
\(235\) −5.61847 −0.366509
\(236\) −24.9514 −1.62420
\(237\) −24.2332 −1.57411
\(238\) −0.00590190 −0.000382563 0
\(239\) −14.7844 −0.956320 −0.478160 0.878273i \(-0.658696\pi\)
−0.478160 + 0.878273i \(0.658696\pi\)
\(240\) 9.52068 0.614557
\(241\) 29.4672 1.89815 0.949073 0.315056i \(-0.102023\pi\)
0.949073 + 0.315056i \(0.102023\pi\)
\(242\) 0.380560 0.0244633
\(243\) 21.2705 1.36451
\(244\) 13.8843 0.888854
\(245\) −1.00000 −0.0638877
\(246\) −0.312113 −0.0198996
\(247\) 22.8787 1.45574
\(248\) 1.27844 0.0811810
\(249\) 36.7096 2.32637
\(250\) 0.0447957 0.00283313
\(251\) −21.2218 −1.33951 −0.669755 0.742582i \(-0.733601\pi\)
−0.669755 + 0.742582i \(0.733601\pi\)
\(252\) 5.39350 0.339759
\(253\) 7.35979 0.462706
\(254\) −0.484110 −0.0303758
\(255\) −0.314537 −0.0196971
\(256\) 15.8397 0.989982
\(257\) −16.4599 −1.02674 −0.513370 0.858167i \(-0.671603\pi\)
−0.513370 + 0.858167i \(0.671603\pi\)
\(258\) −0.932781 −0.0580724
\(259\) −11.3215 −0.703481
\(260\) 8.59555 0.533073
\(261\) 9.26348 0.573395
\(262\) −0.547490 −0.0338240
\(263\) −20.6340 −1.27235 −0.636173 0.771546i \(-0.719484\pi\)
−0.636173 + 0.771546i \(0.719484\pi\)
\(264\) −0.676643 −0.0416445
\(265\) −11.2601 −0.691700
\(266\) 0.238226 0.0146066
\(267\) −1.73438 −0.106142
\(268\) −22.9667 −1.40291
\(269\) −2.14376 −0.130707 −0.0653536 0.997862i \(-0.520818\pi\)
−0.0653536 + 0.997862i \(0.520818\pi\)
\(270\) 0.0321408 0.00195603
\(271\) −15.7274 −0.955369 −0.477685 0.878531i \(-0.658524\pi\)
−0.477685 + 0.878531i \(0.658524\pi\)
\(272\) −0.525420 −0.0318583
\(273\) 10.2706 0.621606
\(274\) 0.547587 0.0330810
\(275\) 1.58257 0.0954328
\(276\) 22.1826 1.33524
\(277\) 17.2915 1.03894 0.519471 0.854488i \(-0.326129\pi\)
0.519471 + 0.854488i \(0.326129\pi\)
\(278\) −0.204118 −0.0122422
\(279\) 19.2699 1.15366
\(280\) 0.179093 0.0107029
\(281\) −5.11865 −0.305353 −0.152677 0.988276i \(-0.548789\pi\)
−0.152677 + 0.988276i \(0.548789\pi\)
\(282\) 0.600858 0.0357806
\(283\) −18.9392 −1.12582 −0.562909 0.826519i \(-0.690318\pi\)
−0.562909 + 0.826519i \(0.690318\pi\)
\(284\) −2.38989 −0.141814
\(285\) 12.6961 0.752050
\(286\) −0.304986 −0.0180342
\(287\) 2.91849 0.172273
\(288\) −1.44915 −0.0853920
\(289\) −16.9826 −0.998979
\(290\) 0.153721 0.00902682
\(291\) −22.1253 −1.29701
\(292\) −26.0685 −1.52554
\(293\) −8.58792 −0.501712 −0.250856 0.968024i \(-0.580712\pi\)
−0.250856 + 0.968024i \(0.580712\pi\)
\(294\) 0.106943 0.00623706
\(295\) −12.4882 −0.727093
\(296\) 2.02759 0.117852
\(297\) 1.13549 0.0658879
\(298\) 0.787790 0.0456355
\(299\) 20.0070 1.15703
\(300\) 4.76992 0.275391
\(301\) 8.72221 0.502740
\(302\) 0.429777 0.0247309
\(303\) −1.07117 −0.0615372
\(304\) 21.2082 1.21637
\(305\) 6.94914 0.397907
\(306\) 0.0159319 0.000910768 0
\(307\) 34.2547 1.95502 0.977510 0.210889i \(-0.0676358\pi\)
0.977510 + 0.210889i \(0.0676358\pi\)
\(308\) 3.16197 0.180170
\(309\) 21.1023 1.20047
\(310\) 0.319770 0.0181617
\(311\) 10.3773 0.588441 0.294221 0.955738i \(-0.404940\pi\)
0.294221 + 0.955738i \(0.404940\pi\)
\(312\) −1.83939 −0.104135
\(313\) 26.6713 1.50755 0.753775 0.657133i \(-0.228231\pi\)
0.753775 + 0.657133i \(0.228231\pi\)
\(314\) −0.909457 −0.0513236
\(315\) 2.69946 0.152097
\(316\) −20.2809 −1.14089
\(317\) −9.62408 −0.540542 −0.270271 0.962784i \(-0.587113\pi\)
−0.270271 + 0.962784i \(0.587113\pi\)
\(318\) 1.20419 0.0675275
\(319\) 5.43077 0.304065
\(320\) 7.95188 0.444524
\(321\) 32.6632 1.82308
\(322\) 0.208323 0.0116094
\(323\) −0.700660 −0.0389858
\(324\) 19.6029 1.08905
\(325\) 4.30209 0.238637
\(326\) −0.409779 −0.0226956
\(327\) 20.2430 1.11944
\(328\) −0.522682 −0.0288603
\(329\) −5.61847 −0.309756
\(330\) −0.169246 −0.00931667
\(331\) −19.0463 −1.04688 −0.523439 0.852063i \(-0.675351\pi\)
−0.523439 + 0.852063i \(0.675351\pi\)
\(332\) 30.7225 1.68612
\(333\) 30.5618 1.67478
\(334\) 0.0984936 0.00538933
\(335\) −11.4949 −0.628033
\(336\) 9.52068 0.519396
\(337\) −10.6270 −0.578888 −0.289444 0.957195i \(-0.593470\pi\)
−0.289444 + 0.957195i \(0.593470\pi\)
\(338\) −0.246734 −0.0134206
\(339\) −1.05733 −0.0574265
\(340\) −0.263239 −0.0142761
\(341\) 11.2971 0.611770
\(342\) −0.643081 −0.0347738
\(343\) −1.00000 −0.0539949
\(344\) −1.56209 −0.0842221
\(345\) 11.1024 0.597735
\(346\) 0.128564 0.00691164
\(347\) 35.3660 1.89854 0.949272 0.314455i \(-0.101822\pi\)
0.949272 + 0.314455i \(0.101822\pi\)
\(348\) 16.3685 0.877443
\(349\) 28.5450 1.52798 0.763988 0.645230i \(-0.223238\pi\)
0.763988 + 0.645230i \(0.223238\pi\)
\(350\) 0.0447957 0.00239443
\(351\) 3.08674 0.164758
\(352\) −0.849573 −0.0452824
\(353\) −20.8107 −1.10764 −0.553821 0.832635i \(-0.686831\pi\)
−0.553821 + 0.832635i \(0.686831\pi\)
\(354\) 1.33553 0.0709827
\(355\) −1.19614 −0.0634847
\(356\) −1.45151 −0.0769300
\(357\) −0.314537 −0.0166471
\(358\) −0.783064 −0.0413862
\(359\) 16.1956 0.854769 0.427384 0.904070i \(-0.359435\pi\)
0.427384 + 0.904070i \(0.359435\pi\)
\(360\) −0.483454 −0.0254803
\(361\) 9.28161 0.488506
\(362\) −0.790527 −0.0415492
\(363\) 20.2817 1.06451
\(364\) 8.59555 0.450529
\(365\) −13.0473 −0.682929
\(366\) −0.743164 −0.0388458
\(367\) 0.475455 0.0248185 0.0124093 0.999923i \(-0.496050\pi\)
0.0124093 + 0.999923i \(0.496050\pi\)
\(368\) 18.5461 0.966783
\(369\) −7.87836 −0.410131
\(370\) 0.507153 0.0263656
\(371\) −11.2601 −0.584593
\(372\) 34.0496 1.76539
\(373\) −25.8090 −1.33634 −0.668170 0.744009i \(-0.732922\pi\)
−0.668170 + 0.744009i \(0.732922\pi\)
\(374\) 0.00934020 0.000482970 0
\(375\) 2.38735 0.123282
\(376\) 1.00623 0.0518923
\(377\) 14.7631 0.760337
\(378\) 0.0321408 0.00165314
\(379\) −30.8518 −1.58475 −0.792376 0.610033i \(-0.791156\pi\)
−0.792376 + 0.610033i \(0.791156\pi\)
\(380\) 10.6254 0.545073
\(381\) −25.8003 −1.32179
\(382\) −0.785446 −0.0401869
\(383\) −11.8981 −0.607967 −0.303983 0.952677i \(-0.598317\pi\)
−0.303983 + 0.952677i \(0.598317\pi\)
\(384\) −3.41360 −0.174200
\(385\) 1.58257 0.0806555
\(386\) −0.561262 −0.0285675
\(387\) −23.5453 −1.19687
\(388\) −18.5168 −0.940049
\(389\) −30.5690 −1.54991 −0.774955 0.632016i \(-0.782228\pi\)
−0.774955 + 0.632016i \(0.782228\pi\)
\(390\) −0.460079 −0.0232970
\(391\) −0.612713 −0.0309862
\(392\) 0.179093 0.00904556
\(393\) −29.1781 −1.47184
\(394\) −1.24222 −0.0625819
\(395\) −10.1506 −0.510734
\(396\) −8.53562 −0.428931
\(397\) 11.6761 0.586007 0.293003 0.956111i \(-0.405345\pi\)
0.293003 + 0.956111i \(0.405345\pi\)
\(398\) 0.890531 0.0446383
\(399\) 12.6961 0.635598
\(400\) 3.98796 0.199398
\(401\) 5.16742 0.258049 0.129024 0.991641i \(-0.458815\pi\)
0.129024 + 0.991641i \(0.458815\pi\)
\(402\) 1.22930 0.0613119
\(403\) 30.7101 1.52978
\(404\) −0.896471 −0.0446011
\(405\) 9.81130 0.487527
\(406\) 0.153721 0.00762906
\(407\) 17.9171 0.888115
\(408\) 0.0563314 0.00278882
\(409\) 31.6378 1.56439 0.782194 0.623035i \(-0.214101\pi\)
0.782194 + 0.623035i \(0.214101\pi\)
\(410\) −0.130736 −0.00645659
\(411\) 29.1833 1.43950
\(412\) 17.6607 0.870078
\(413\) −12.4882 −0.614506
\(414\) −0.562360 −0.0276385
\(415\) 15.3767 0.754811
\(416\) −2.30949 −0.113232
\(417\) −10.8783 −0.532712
\(418\) −0.377010 −0.0184402
\(419\) −10.2940 −0.502896 −0.251448 0.967871i \(-0.580907\pi\)
−0.251448 + 0.967871i \(0.580907\pi\)
\(420\) 4.76992 0.232748
\(421\) 27.6143 1.34584 0.672920 0.739715i \(-0.265040\pi\)
0.672920 + 0.739715i \(0.265040\pi\)
\(422\) 0.425340 0.0207052
\(423\) 15.1668 0.737437
\(424\) 2.01660 0.0979347
\(425\) −0.131751 −0.00639088
\(426\) 0.127919 0.00619771
\(427\) 6.94914 0.336293
\(428\) 27.3361 1.32134
\(429\) −16.2540 −0.784751
\(430\) −0.390718 −0.0188421
\(431\) −14.4263 −0.694893 −0.347446 0.937700i \(-0.612951\pi\)
−0.347446 + 0.937700i \(0.612951\pi\)
\(432\) 2.86135 0.137667
\(433\) −24.4376 −1.17439 −0.587197 0.809444i \(-0.699769\pi\)
−0.587197 + 0.809444i \(0.699769\pi\)
\(434\) 0.319770 0.0153495
\(435\) 8.19246 0.392798
\(436\) 16.9415 0.811349
\(437\) 24.7317 1.18308
\(438\) 1.39532 0.0666712
\(439\) −4.21055 −0.200958 −0.100479 0.994939i \(-0.532038\pi\)
−0.100479 + 0.994939i \(0.532038\pi\)
\(440\) −0.283428 −0.0135119
\(441\) 2.69946 0.128546
\(442\) 0.0253905 0.00120770
\(443\) 5.39441 0.256296 0.128148 0.991755i \(-0.459097\pi\)
0.128148 + 0.991755i \(0.459097\pi\)
\(444\) 54.0024 2.56284
\(445\) −0.726485 −0.0344387
\(446\) 0.371984 0.0176139
\(447\) 41.9847 1.98581
\(448\) 7.95188 0.375691
\(449\) −8.52527 −0.402332 −0.201166 0.979557i \(-0.564473\pi\)
−0.201166 + 0.979557i \(0.564473\pi\)
\(450\) −0.120924 −0.00570042
\(451\) −4.61873 −0.217488
\(452\) −0.884890 −0.0416217
\(453\) 22.9046 1.07615
\(454\) −0.181967 −0.00854016
\(455\) 4.30209 0.201685
\(456\) −2.27377 −0.106479
\(457\) −17.1537 −0.802414 −0.401207 0.915987i \(-0.631409\pi\)
−0.401207 + 0.915987i \(0.631409\pi\)
\(458\) −0.0447957 −0.00209317
\(459\) −0.0945312 −0.00441234
\(460\) 9.29171 0.433228
\(461\) 2.81101 0.130922 0.0654608 0.997855i \(-0.479148\pi\)
0.0654608 + 0.997855i \(0.479148\pi\)
\(462\) −0.169246 −0.00787402
\(463\) 3.37771 0.156975 0.0784877 0.996915i \(-0.474991\pi\)
0.0784877 + 0.996915i \(0.474991\pi\)
\(464\) 13.6851 0.635316
\(465\) 17.0419 0.790300
\(466\) −0.762705 −0.0353316
\(467\) 19.7102 0.912077 0.456039 0.889960i \(-0.349268\pi\)
0.456039 + 0.889960i \(0.349268\pi\)
\(468\) −23.2033 −1.07257
\(469\) −11.4949 −0.530785
\(470\) 0.251684 0.0116093
\(471\) −48.4688 −2.23333
\(472\) 2.23655 0.102946
\(473\) −13.8035 −0.634688
\(474\) 1.08554 0.0498606
\(475\) 5.31805 0.244009
\(476\) −0.263239 −0.0120655
\(477\) 30.3961 1.39174
\(478\) 0.662276 0.0302918
\(479\) −17.7879 −0.812751 −0.406375 0.913706i \(-0.633207\pi\)
−0.406375 + 0.913706i \(0.633207\pi\)
\(480\) −1.28160 −0.0584969
\(481\) 48.7059 2.22080
\(482\) −1.32000 −0.0601245
\(483\) 11.1024 0.505178
\(484\) 16.9739 0.771539
\(485\) −9.26771 −0.420825
\(486\) −0.952830 −0.0432212
\(487\) 3.07983 0.139561 0.0697803 0.997562i \(-0.477770\pi\)
0.0697803 + 0.997562i \(0.477770\pi\)
\(488\) −1.24454 −0.0563378
\(489\) −21.8389 −0.987588
\(490\) 0.0447957 0.00202366
\(491\) −25.1134 −1.13335 −0.566675 0.823941i \(-0.691771\pi\)
−0.566675 + 0.823941i \(0.691771\pi\)
\(492\) −13.9210 −0.627606
\(493\) −0.452119 −0.0203624
\(494\) −1.02487 −0.0461110
\(495\) −4.27210 −0.192016
\(496\) 28.4677 1.27824
\(497\) −1.19614 −0.0536543
\(498\) −1.64443 −0.0736887
\(499\) 30.4339 1.36241 0.681204 0.732094i \(-0.261457\pi\)
0.681204 + 0.732094i \(0.261457\pi\)
\(500\) 1.99799 0.0893530
\(501\) 5.24914 0.234514
\(502\) 0.950647 0.0424294
\(503\) −14.8887 −0.663854 −0.331927 0.943305i \(-0.607699\pi\)
−0.331927 + 0.943305i \(0.607699\pi\)
\(504\) −0.483454 −0.0215348
\(505\) −0.448686 −0.0199663
\(506\) −0.329687 −0.0146564
\(507\) −13.1495 −0.583990
\(508\) −21.5925 −0.958010
\(509\) 29.0596 1.28804 0.644022 0.765007i \(-0.277264\pi\)
0.644022 + 0.765007i \(0.277264\pi\)
\(510\) 0.0140899 0.000623912 0
\(511\) −13.0473 −0.577180
\(512\) −3.56929 −0.157742
\(513\) 3.81568 0.168466
\(514\) 0.737333 0.0325224
\(515\) 8.83920 0.389502
\(516\) −41.6042 −1.83152
\(517\) 8.89165 0.391054
\(518\) 0.507153 0.0222830
\(519\) 6.85172 0.300757
\(520\) −0.770474 −0.0337875
\(521\) 38.4920 1.68637 0.843183 0.537627i \(-0.180679\pi\)
0.843183 + 0.537627i \(0.180679\pi\)
\(522\) −0.414964 −0.0181625
\(523\) −15.6306 −0.683478 −0.341739 0.939795i \(-0.611016\pi\)
−0.341739 + 0.939795i \(0.611016\pi\)
\(524\) −24.4193 −1.06676
\(525\) 2.38735 0.104193
\(526\) 0.924315 0.0403020
\(527\) −0.940496 −0.0409686
\(528\) −15.0672 −0.655715
\(529\) −1.37267 −0.0596813
\(530\) 0.504403 0.0219099
\(531\) 33.7115 1.46295
\(532\) 10.6254 0.460670
\(533\) −12.5556 −0.543844
\(534\) 0.0776927 0.00336209
\(535\) 13.6818 0.591514
\(536\) 2.05865 0.0889203
\(537\) −41.7328 −1.80090
\(538\) 0.0960312 0.00414020
\(539\) 1.58257 0.0681663
\(540\) 1.43355 0.0616903
\(541\) −23.4221 −1.00699 −0.503497 0.863997i \(-0.667954\pi\)
−0.503497 + 0.863997i \(0.667954\pi\)
\(542\) 0.704519 0.0302617
\(543\) −42.1306 −1.80800
\(544\) 0.0707281 0.00303244
\(545\) 8.47924 0.363211
\(546\) −0.460079 −0.0196896
\(547\) −15.1112 −0.646108 −0.323054 0.946381i \(-0.604710\pi\)
−0.323054 + 0.946381i \(0.604710\pi\)
\(548\) 24.4237 1.04333
\(549\) −18.7589 −0.800612
\(550\) −0.0708926 −0.00302287
\(551\) 18.2494 0.777452
\(552\) −1.98837 −0.0846306
\(553\) −10.1506 −0.431649
\(554\) −0.774583 −0.0329089
\(555\) 27.0283 1.14729
\(556\) −9.10412 −0.386101
\(557\) 34.0106 1.44107 0.720537 0.693417i \(-0.243895\pi\)
0.720537 + 0.693417i \(0.243895\pi\)
\(558\) −0.863207 −0.0365425
\(559\) −37.5237 −1.58708
\(560\) 3.98796 0.168522
\(561\) 0.497779 0.0210162
\(562\) 0.229294 0.00967217
\(563\) −6.52356 −0.274935 −0.137468 0.990506i \(-0.543896\pi\)
−0.137468 + 0.990506i \(0.543896\pi\)
\(564\) 26.7997 1.12847
\(565\) −0.442889 −0.0186325
\(566\) 0.848395 0.0356607
\(567\) 9.81130 0.412036
\(568\) 0.214221 0.00898850
\(569\) −14.7350 −0.617724 −0.308862 0.951107i \(-0.599948\pi\)
−0.308862 + 0.951107i \(0.599948\pi\)
\(570\) −0.568729 −0.0238214
\(571\) −28.2587 −1.18259 −0.591296 0.806455i \(-0.701383\pi\)
−0.591296 + 0.806455i \(0.701383\pi\)
\(572\) −13.6031 −0.568774
\(573\) −41.8597 −1.74872
\(574\) −0.130736 −0.00545682
\(575\) 4.65052 0.193940
\(576\) −21.4658 −0.894407
\(577\) −8.82553 −0.367412 −0.183706 0.982981i \(-0.558809\pi\)
−0.183706 + 0.982981i \(0.558809\pi\)
\(578\) 0.760750 0.0316430
\(579\) −29.9120 −1.24310
\(580\) 6.85633 0.284693
\(581\) 15.3767 0.637932
\(582\) 0.991119 0.0410832
\(583\) 17.8199 0.738025
\(584\) 2.33669 0.0966928
\(585\) −11.6133 −0.480152
\(586\) 0.384702 0.0158919
\(587\) 28.4393 1.17382 0.586909 0.809653i \(-0.300345\pi\)
0.586909 + 0.809653i \(0.300345\pi\)
\(588\) 4.76992 0.196708
\(589\) 37.9624 1.56421
\(590\) 0.559419 0.0230309
\(591\) −66.2029 −2.72323
\(592\) 45.1496 1.85564
\(593\) 27.0401 1.11041 0.555203 0.831715i \(-0.312641\pi\)
0.555203 + 0.831715i \(0.312641\pi\)
\(594\) −0.0508652 −0.00208702
\(595\) −0.131751 −0.00540128
\(596\) 35.1373 1.43928
\(597\) 47.4602 1.94242
\(598\) −0.896226 −0.0366494
\(599\) −22.2615 −0.909580 −0.454790 0.890599i \(-0.650286\pi\)
−0.454790 + 0.890599i \(0.650286\pi\)
\(600\) −0.427558 −0.0174550
\(601\) −15.6646 −0.638974 −0.319487 0.947591i \(-0.603511\pi\)
−0.319487 + 0.947591i \(0.603511\pi\)
\(602\) −0.390718 −0.0159245
\(603\) 31.0300 1.26364
\(604\) 19.1690 0.779977
\(605\) 8.49546 0.345389
\(606\) 0.0479839 0.00194921
\(607\) −12.0908 −0.490752 −0.245376 0.969428i \(-0.578911\pi\)
−0.245376 + 0.969428i \(0.578911\pi\)
\(608\) −2.85488 −0.115781
\(609\) 8.19246 0.331975
\(610\) −0.311292 −0.0126038
\(611\) 24.1712 0.977861
\(612\) 0.710602 0.0287244
\(613\) −6.44146 −0.260168 −0.130084 0.991503i \(-0.541525\pi\)
−0.130084 + 0.991503i \(0.541525\pi\)
\(614\) −1.53446 −0.0619260
\(615\) −6.96748 −0.280956
\(616\) −0.283428 −0.0114196
\(617\) −7.58935 −0.305536 −0.152768 0.988262i \(-0.548819\pi\)
−0.152768 + 0.988262i \(0.548819\pi\)
\(618\) −0.945293 −0.0380253
\(619\) 32.3591 1.30062 0.650310 0.759669i \(-0.274639\pi\)
0.650310 + 0.759669i \(0.274639\pi\)
\(620\) 14.2625 0.572796
\(621\) 3.33673 0.133898
\(622\) −0.464858 −0.0186391
\(623\) −0.726485 −0.0291060
\(624\) −40.9588 −1.63967
\(625\) 1.00000 0.0400000
\(626\) −1.19476 −0.0477522
\(627\) −20.0925 −0.802415
\(628\) −40.5639 −1.61868
\(629\) −1.49162 −0.0594747
\(630\) −0.120924 −0.00481774
\(631\) −10.0271 −0.399172 −0.199586 0.979880i \(-0.563960\pi\)
−0.199586 + 0.979880i \(0.563960\pi\)
\(632\) 1.81791 0.0723126
\(633\) 22.6682 0.900979
\(634\) 0.431118 0.0171219
\(635\) −10.8071 −0.428865
\(636\) 53.7096 2.12972
\(637\) 4.30209 0.170455
\(638\) −0.243275 −0.00963136
\(639\) 3.22894 0.127735
\(640\) −1.42987 −0.0565206
\(641\) 8.01352 0.316515 0.158257 0.987398i \(-0.449412\pi\)
0.158257 + 0.987398i \(0.449412\pi\)
\(642\) −1.46317 −0.0577468
\(643\) −27.2831 −1.07594 −0.537971 0.842963i \(-0.680809\pi\)
−0.537971 + 0.842963i \(0.680809\pi\)
\(644\) 9.29171 0.366145
\(645\) −20.8230 −0.819905
\(646\) 0.0313866 0.00123489
\(647\) 26.0778 1.02523 0.512613 0.858620i \(-0.328678\pi\)
0.512613 + 0.858620i \(0.328678\pi\)
\(648\) −1.75713 −0.0690268
\(649\) 19.7636 0.775788
\(650\) −0.192715 −0.00755891
\(651\) 17.0419 0.667925
\(652\) −18.2771 −0.715787
\(653\) 9.61095 0.376105 0.188053 0.982159i \(-0.439782\pi\)
0.188053 + 0.982159i \(0.439782\pi\)
\(654\) −0.906798 −0.0354586
\(655\) −12.2219 −0.477550
\(656\) −11.6388 −0.454421
\(657\) 35.2208 1.37409
\(658\) 0.251684 0.00981164
\(659\) −46.6714 −1.81806 −0.909030 0.416732i \(-0.863175\pi\)
−0.909030 + 0.416732i \(0.863175\pi\)
\(660\) −7.54875 −0.293835
\(661\) −49.0933 −1.90951 −0.954753 0.297400i \(-0.903881\pi\)
−0.954753 + 0.297400i \(0.903881\pi\)
\(662\) 0.853192 0.0331603
\(663\) 1.35317 0.0525527
\(664\) −2.75385 −0.106870
\(665\) 5.31805 0.206225
\(666\) −1.36904 −0.0530492
\(667\) 15.9588 0.617925
\(668\) 4.39304 0.169972
\(669\) 19.8246 0.766463
\(670\) 0.514922 0.0198932
\(671\) −10.9975 −0.424555
\(672\) −1.28160 −0.0494389
\(673\) −29.7534 −1.14691 −0.573456 0.819237i \(-0.694397\pi\)
−0.573456 + 0.819237i \(0.694397\pi\)
\(674\) 0.476043 0.0183365
\(675\) 0.717497 0.0276165
\(676\) −11.0049 −0.423266
\(677\) 37.8497 1.45468 0.727340 0.686277i \(-0.240756\pi\)
0.727340 + 0.686277i \(0.240756\pi\)
\(678\) 0.0473640 0.00181900
\(679\) −9.26771 −0.355662
\(680\) 0.0235958 0.000904856 0
\(681\) −9.69782 −0.371621
\(682\) −0.506060 −0.0193780
\(683\) −21.3425 −0.816648 −0.408324 0.912837i \(-0.633887\pi\)
−0.408324 + 0.912837i \(0.633887\pi\)
\(684\) −28.6829 −1.09672
\(685\) 12.2241 0.467059
\(686\) 0.0447957 0.00171031
\(687\) −2.38735 −0.0910832
\(688\) −34.7839 −1.32612
\(689\) 48.4418 1.84549
\(690\) −0.497342 −0.0189335
\(691\) −15.5758 −0.592531 −0.296265 0.955106i \(-0.595741\pi\)
−0.296265 + 0.955106i \(0.595741\pi\)
\(692\) 5.73425 0.217984
\(693\) −4.27210 −0.162283
\(694\) −1.58424 −0.0601371
\(695\) −4.55663 −0.172843
\(696\) −1.46721 −0.0556145
\(697\) 0.384516 0.0145646
\(698\) −1.27869 −0.0483992
\(699\) −40.6478 −1.53744
\(700\) 1.99799 0.0755171
\(701\) −19.5113 −0.736931 −0.368466 0.929641i \(-0.620117\pi\)
−0.368466 + 0.929641i \(0.620117\pi\)
\(702\) −0.138273 −0.00521876
\(703\) 60.2080 2.27079
\(704\) −12.5844 −0.474294
\(705\) 13.4133 0.505173
\(706\) 0.932231 0.0350850
\(707\) −0.448686 −0.0168746
\(708\) 59.5678 2.23870
\(709\) 22.2566 0.835864 0.417932 0.908478i \(-0.362755\pi\)
0.417932 + 0.908478i \(0.362755\pi\)
\(710\) 0.0535821 0.00201090
\(711\) 27.4013 1.02763
\(712\) 0.130108 0.00487602
\(713\) 33.1973 1.24325
\(714\) 0.0140899 0.000527302 0
\(715\) −6.80838 −0.254619
\(716\) −34.9265 −1.30526
\(717\) 35.2955 1.31813
\(718\) −0.725491 −0.0270751
\(719\) 43.4834 1.62166 0.810829 0.585283i \(-0.199017\pi\)
0.810829 + 0.585283i \(0.199017\pi\)
\(720\) −10.7653 −0.401201
\(721\) 8.83920 0.329189
\(722\) −0.415776 −0.0154736
\(723\) −70.3485 −2.61629
\(724\) −35.2594 −1.31040
\(725\) 3.43161 0.127447
\(726\) −0.908532 −0.0337188
\(727\) 33.7653 1.25228 0.626142 0.779709i \(-0.284633\pi\)
0.626142 + 0.779709i \(0.284633\pi\)
\(728\) −0.770474 −0.0285557
\(729\) −21.3464 −0.790609
\(730\) 0.584465 0.0216320
\(731\) 1.14916 0.0425034
\(732\) −33.1468 −1.22514
\(733\) −26.0884 −0.963596 −0.481798 0.876282i \(-0.660016\pi\)
−0.481798 + 0.876282i \(0.660016\pi\)
\(734\) −0.0212983 −0.000786136 0
\(735\) 2.38735 0.0880589
\(736\) −2.49654 −0.0920236
\(737\) 18.1915 0.670093
\(738\) 0.352917 0.0129910
\(739\) 7.60255 0.279664 0.139832 0.990175i \(-0.455344\pi\)
0.139832 + 0.990175i \(0.455344\pi\)
\(740\) 22.6202 0.831535
\(741\) −54.6196 −2.00650
\(742\) 0.504403 0.0185172
\(743\) −16.1009 −0.590685 −0.295343 0.955391i \(-0.595434\pi\)
−0.295343 + 0.955391i \(0.595434\pi\)
\(744\) −3.05209 −0.111895
\(745\) 17.5863 0.644312
\(746\) 1.15613 0.0423290
\(747\) −41.5087 −1.51872
\(748\) 0.416595 0.0152322
\(749\) 13.6818 0.499921
\(750\) −0.106943 −0.00390501
\(751\) −44.1925 −1.61261 −0.806304 0.591501i \(-0.798535\pi\)
−0.806304 + 0.591501i \(0.798535\pi\)
\(752\) 22.4063 0.817072
\(753\) 50.6640 1.84630
\(754\) −0.661323 −0.0240840
\(755\) 9.59414 0.349167
\(756\) 1.43355 0.0521378
\(757\) 6.38567 0.232091 0.116046 0.993244i \(-0.462978\pi\)
0.116046 + 0.993244i \(0.462978\pi\)
\(758\) 1.38203 0.0501976
\(759\) −17.5704 −0.637766
\(760\) −0.952425 −0.0345481
\(761\) −7.46314 −0.270539 −0.135269 0.990809i \(-0.543190\pi\)
−0.135269 + 0.990809i \(0.543190\pi\)
\(762\) 1.15574 0.0418681
\(763\) 8.47924 0.306969
\(764\) −35.0327 −1.26744
\(765\) 0.355658 0.0128588
\(766\) 0.532986 0.0192576
\(767\) 53.7255 1.93992
\(768\) −37.8150 −1.36453
\(769\) 6.07455 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(770\) −0.0708926 −0.00255479
\(771\) 39.2956 1.41520
\(772\) −25.0336 −0.900978
\(773\) −7.70400 −0.277093 −0.138547 0.990356i \(-0.544243\pi\)
−0.138547 + 0.990356i \(0.544243\pi\)
\(774\) 1.05473 0.0379114
\(775\) 7.13841 0.256419
\(776\) 1.65978 0.0595827
\(777\) 27.0283 0.969636
\(778\) 1.36936 0.0490940
\(779\) −15.5207 −0.556086
\(780\) −20.5206 −0.734756
\(781\) 1.89299 0.0677363
\(782\) 0.0274469 0.000981499 0
\(783\) 2.46217 0.0879906
\(784\) 3.98796 0.142427
\(785\) −20.3023 −0.724621
\(786\) 1.30705 0.0466210
\(787\) −18.0338 −0.642837 −0.321418 0.946937i \(-0.604160\pi\)
−0.321418 + 0.946937i \(0.604160\pi\)
\(788\) −55.4057 −1.97375
\(789\) 49.2606 1.75373
\(790\) 0.454705 0.0161777
\(791\) −0.442889 −0.0157473
\(792\) 0.765102 0.0271867
\(793\) −29.8958 −1.06163
\(794\) −0.523039 −0.0185620
\(795\) 26.8818 0.953398
\(796\) 39.7198 1.40783
\(797\) 38.2591 1.35521 0.677603 0.735428i \(-0.263019\pi\)
0.677603 + 0.735428i \(0.263019\pi\)
\(798\) −0.568729 −0.0201328
\(799\) −0.740242 −0.0261879
\(800\) −0.536830 −0.0189798
\(801\) 1.96112 0.0692927
\(802\) −0.231478 −0.00817379
\(803\) 20.6484 0.728665
\(804\) 54.8297 1.93369
\(805\) 4.65052 0.163909
\(806\) −1.37568 −0.0484563
\(807\) 5.11791 0.180159
\(808\) 0.0803565 0.00282693
\(809\) −22.3576 −0.786052 −0.393026 0.919527i \(-0.628572\pi\)
−0.393026 + 0.919527i \(0.628572\pi\)
\(810\) −0.439504 −0.0154426
\(811\) −51.1104 −1.79473 −0.897365 0.441290i \(-0.854521\pi\)
−0.897365 + 0.441290i \(0.854521\pi\)
\(812\) 6.85633 0.240610
\(813\) 37.5468 1.31682
\(814\) −0.802607 −0.0281314
\(815\) −9.14773 −0.320431
\(816\) 1.25436 0.0439115
\(817\) −46.3851 −1.62281
\(818\) −1.41724 −0.0495525
\(819\) −11.6133 −0.405802
\(820\) −5.83113 −0.203632
\(821\) −29.2457 −1.02068 −0.510341 0.859972i \(-0.670481\pi\)
−0.510341 + 0.859972i \(0.670481\pi\)
\(822\) −1.30728 −0.0455968
\(823\) 56.2610 1.96114 0.980568 0.196180i \(-0.0628535\pi\)
0.980568 + 0.196180i \(0.0628535\pi\)
\(824\) −1.58304 −0.0551478
\(825\) −3.77817 −0.131539
\(826\) 0.559419 0.0194647
\(827\) −42.4840 −1.47731 −0.738656 0.674082i \(-0.764539\pi\)
−0.738656 + 0.674082i \(0.764539\pi\)
\(828\) −25.0826 −0.871680
\(829\) 10.1327 0.351925 0.175962 0.984397i \(-0.443696\pi\)
0.175962 + 0.984397i \(0.443696\pi\)
\(830\) −0.688809 −0.0239089
\(831\) −41.2808 −1.43202
\(832\) −34.2097 −1.18601
\(833\) −0.131751 −0.00456492
\(834\) 0.487301 0.0168739
\(835\) 2.19873 0.0760901
\(836\) −16.8155 −0.581577
\(837\) 5.12179 0.177035
\(838\) 0.461128 0.0159294
\(839\) 17.9616 0.620105 0.310052 0.950720i \(-0.399653\pi\)
0.310052 + 0.950720i \(0.399653\pi\)
\(840\) −0.427558 −0.0147522
\(841\) −17.2241 −0.593934
\(842\) −1.23700 −0.0426299
\(843\) 12.2200 0.420880
\(844\) 18.9712 0.653014
\(845\) −5.50798 −0.189480
\(846\) −0.679409 −0.0233586
\(847\) 8.49546 0.291907
\(848\) 44.9047 1.54203
\(849\) 45.2146 1.55176
\(850\) 0.00590190 0.000202434 0
\(851\) 52.6507 1.80484
\(852\) 5.70550 0.195467
\(853\) 30.4095 1.04120 0.520601 0.853800i \(-0.325708\pi\)
0.520601 + 0.853800i \(0.325708\pi\)
\(854\) −0.311292 −0.0106522
\(855\) −14.3558 −0.490960
\(856\) −2.45031 −0.0837498
\(857\) −3.29365 −0.112509 −0.0562545 0.998416i \(-0.517916\pi\)
−0.0562545 + 0.998416i \(0.517916\pi\)
\(858\) 0.728110 0.0248573
\(859\) −49.7394 −1.69709 −0.848543 0.529127i \(-0.822520\pi\)
−0.848543 + 0.529127i \(0.822520\pi\)
\(860\) −17.4269 −0.594253
\(861\) −6.96748 −0.237451
\(862\) 0.646238 0.0220110
\(863\) 18.8970 0.643262 0.321631 0.946865i \(-0.395769\pi\)
0.321631 + 0.946865i \(0.395769\pi\)
\(864\) −0.385173 −0.0131039
\(865\) 2.87001 0.0975831
\(866\) 1.09470 0.0371994
\(867\) 40.5436 1.37693
\(868\) 14.2625 0.484101
\(869\) 16.0642 0.544939
\(870\) −0.366987 −0.0124420
\(871\) 49.4520 1.67562
\(872\) −1.51857 −0.0514254
\(873\) 25.0178 0.846725
\(874\) −1.10787 −0.0374744
\(875\) 1.00000 0.0338062
\(876\) 62.2347 2.10272
\(877\) 29.7300 1.00391 0.501955 0.864893i \(-0.332614\pi\)
0.501955 + 0.864893i \(0.332614\pi\)
\(878\) 0.188614 0.00636543
\(879\) 20.5024 0.691529
\(880\) −6.31125 −0.212752
\(881\) 0.647171 0.0218038 0.0109019 0.999941i \(-0.496530\pi\)
0.0109019 + 0.999941i \(0.496530\pi\)
\(882\) −0.120924 −0.00407173
\(883\) −32.2563 −1.08551 −0.542755 0.839891i \(-0.682619\pi\)
−0.542755 + 0.839891i \(0.682619\pi\)
\(884\) 1.13248 0.0380893
\(885\) 29.8138 1.00218
\(886\) −0.241646 −0.00811827
\(887\) −20.7771 −0.697627 −0.348813 0.937192i \(-0.613415\pi\)
−0.348813 + 0.937192i \(0.613415\pi\)
\(888\) −4.84058 −0.162439
\(889\) −10.8071 −0.362457
\(890\) 0.0325434 0.00109086
\(891\) −15.5271 −0.520178
\(892\) 16.5913 0.555519
\(893\) 29.8793 0.999872
\(894\) −1.88073 −0.0629012
\(895\) −17.4808 −0.584318
\(896\) −1.42987 −0.0477686
\(897\) −47.7637 −1.59478
\(898\) 0.381895 0.0127440
\(899\) 24.4962 0.816995
\(900\) −5.39350 −0.179783
\(901\) −1.48353 −0.0494235
\(902\) 0.206899 0.00688900
\(903\) −20.8230 −0.692946
\(904\) 0.0793184 0.00263809
\(905\) −17.6474 −0.586619
\(906\) −1.02603 −0.0340875
\(907\) −11.1973 −0.371799 −0.185899 0.982569i \(-0.559520\pi\)
−0.185899 + 0.982569i \(0.559520\pi\)
\(908\) −8.11617 −0.269345
\(909\) 1.21121 0.0401733
\(910\) −0.192715 −0.00638845
\(911\) 12.4711 0.413186 0.206593 0.978427i \(-0.433762\pi\)
0.206593 + 0.978427i \(0.433762\pi\)
\(912\) −50.6314 −1.67657
\(913\) −24.3347 −0.805362
\(914\) 0.768410 0.0254167
\(915\) −16.5901 −0.548451
\(916\) −1.99799 −0.0660156
\(917\) −12.2219 −0.403604
\(918\) 0.00423459 0.000139762 0
\(919\) 9.46365 0.312177 0.156089 0.987743i \(-0.450111\pi\)
0.156089 + 0.987743i \(0.450111\pi\)
\(920\) −0.832875 −0.0274591
\(921\) −81.7781 −2.69468
\(922\) −0.125921 −0.00414699
\(923\) 5.14591 0.169380
\(924\) −7.54875 −0.248336
\(925\) 11.3215 0.372247
\(926\) −0.151307 −0.00497225
\(927\) −23.8611 −0.783700
\(928\) −1.84219 −0.0604728
\(929\) −45.1942 −1.48277 −0.741386 0.671079i \(-0.765831\pi\)
−0.741386 + 0.671079i \(0.765831\pi\)
\(930\) −0.763405 −0.0250330
\(931\) 5.31805 0.174292
\(932\) −34.0184 −1.11431
\(933\) −24.7742 −0.811072
\(934\) −0.882930 −0.0288904
\(935\) 0.208506 0.00681889
\(936\) 2.07986 0.0679825
\(937\) −4.10157 −0.133992 −0.0669962 0.997753i \(-0.521342\pi\)
−0.0669962 + 0.997753i \(0.521342\pi\)
\(938\) 0.514922 0.0168128
\(939\) −63.6738 −2.07792
\(940\) 11.2257 0.366141
\(941\) −13.1563 −0.428884 −0.214442 0.976737i \(-0.568793\pi\)
−0.214442 + 0.976737i \(0.568793\pi\)
\(942\) 2.17120 0.0707414
\(943\) −13.5725 −0.441982
\(944\) 49.8026 1.62094
\(945\) 0.717497 0.0233402
\(946\) 0.618340 0.0201040
\(947\) 9.70373 0.315329 0.157664 0.987493i \(-0.449604\pi\)
0.157664 + 0.987493i \(0.449604\pi\)
\(948\) 48.4177 1.57254
\(949\) 56.1308 1.82208
\(950\) −0.238226 −0.00772906
\(951\) 22.9761 0.745051
\(952\) 0.0235958 0.000764743 0
\(953\) −6.73093 −0.218036 −0.109018 0.994040i \(-0.534771\pi\)
−0.109018 + 0.994040i \(0.534771\pi\)
\(954\) −1.36161 −0.0440839
\(955\) −17.5339 −0.567385
\(956\) 29.5390 0.955361
\(957\) −12.9652 −0.419105
\(958\) 0.796823 0.0257442
\(959\) 12.2241 0.394737
\(960\) −18.9840 −0.612704
\(961\) 19.9569 0.643771
\(962\) −2.18182 −0.0703446
\(963\) −36.9334 −1.19016
\(964\) −58.8752 −1.89624
\(965\) −12.5294 −0.403334
\(966\) −0.497342 −0.0160017
\(967\) 10.8231 0.348048 0.174024 0.984741i \(-0.444323\pi\)
0.174024 + 0.984741i \(0.444323\pi\)
\(968\) −1.52148 −0.0489021
\(969\) 1.67272 0.0537356
\(970\) 0.415154 0.0133298
\(971\) −19.0539 −0.611468 −0.305734 0.952117i \(-0.598902\pi\)
−0.305734 + 0.952117i \(0.598902\pi\)
\(972\) −42.4984 −1.36314
\(973\) −4.55663 −0.146079
\(974\) −0.137963 −0.00442063
\(975\) −10.2706 −0.328923
\(976\) −27.7129 −0.887070
\(977\) −62.3826 −1.99580 −0.997898 0.0648026i \(-0.979358\pi\)
−0.997898 + 0.0648026i \(0.979358\pi\)
\(978\) 0.978288 0.0312822
\(979\) 1.14972 0.0367451
\(980\) 1.99799 0.0638236
\(981\) −22.8894 −0.730802
\(982\) 1.12497 0.0358993
\(983\) −14.7685 −0.471042 −0.235521 0.971869i \(-0.575680\pi\)
−0.235521 + 0.971869i \(0.575680\pi\)
\(984\) 1.24783 0.0397793
\(985\) −27.7307 −0.883573
\(986\) 0.0202530 0.000644987 0
\(987\) 13.4133 0.426950
\(988\) −45.7115 −1.45428
\(989\) −40.5628 −1.28982
\(990\) 0.191372 0.00608219
\(991\) −6.92792 −0.220073 −0.110036 0.993928i \(-0.535097\pi\)
−0.110036 + 0.993928i \(0.535097\pi\)
\(992\) −3.83211 −0.121670
\(993\) 45.4702 1.44295
\(994\) 0.0535821 0.00169952
\(995\) 19.8798 0.630233
\(996\) −73.3455 −2.32404
\(997\) −20.7116 −0.655942 −0.327971 0.944688i \(-0.606365\pi\)
−0.327971 + 0.944688i \(0.606365\pi\)
\(998\) −1.36331 −0.0431548
\(999\) 8.12311 0.257004
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 \(a_p\))