Properties

Label 6027.2.a.bk.1.6
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.766034\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.766034 q^{2} +1.00000 q^{3} -1.41319 q^{4} +0.561773 q^{5} -0.766034 q^{6} +2.61462 q^{8} +1.00000 q^{9} -0.430337 q^{10} -3.11111 q^{11} -1.41319 q^{12} +5.92656 q^{13} +0.561773 q^{15} +0.823497 q^{16} +3.15286 q^{17} -0.766034 q^{18} -0.142324 q^{19} -0.793894 q^{20} +2.38321 q^{22} -4.62821 q^{23} +2.61462 q^{24} -4.68441 q^{25} -4.53994 q^{26} +1.00000 q^{27} -8.30868 q^{29} -0.430337 q^{30} -0.336298 q^{31} -5.86007 q^{32} -3.11111 q^{33} -2.41520 q^{34} -1.41319 q^{36} -9.44997 q^{37} +0.109025 q^{38} +5.92656 q^{39} +1.46882 q^{40} -1.00000 q^{41} +9.28869 q^{43} +4.39659 q^{44} +0.561773 q^{45} +3.54537 q^{46} -7.35790 q^{47} +0.823497 q^{48} +3.58842 q^{50} +3.15286 q^{51} -8.37537 q^{52} -8.42111 q^{53} -0.766034 q^{54} -1.74774 q^{55} -0.142324 q^{57} +6.36473 q^{58} +0.911205 q^{59} -0.793894 q^{60} -3.48407 q^{61} +0.257615 q^{62} +2.84201 q^{64} +3.32938 q^{65} +2.38321 q^{66} -0.537448 q^{67} -4.45560 q^{68} -4.62821 q^{69} -0.835931 q^{71} +2.61462 q^{72} +8.54657 q^{73} +7.23899 q^{74} -4.68441 q^{75} +0.201131 q^{76} -4.53994 q^{78} -10.4527 q^{79} +0.462619 q^{80} +1.00000 q^{81} +0.766034 q^{82} -5.99692 q^{83} +1.77119 q^{85} -7.11545 q^{86} -8.30868 q^{87} -8.13436 q^{88} +18.7260 q^{89} -0.430337 q^{90} +6.54056 q^{92} -0.336298 q^{93} +5.63640 q^{94} -0.0799537 q^{95} -5.86007 q^{96} +10.9913 q^{97} -3.11111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766034 −0.541668 −0.270834 0.962626i \(-0.587299\pi\)
−0.270834 + 0.962626i \(0.587299\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.41319 −0.706596
\(5\) 0.561773 0.251233 0.125616 0.992079i \(-0.459909\pi\)
0.125616 + 0.992079i \(0.459909\pi\)
\(6\) −0.766034 −0.312732
\(7\) 0 0
\(8\) 2.61462 0.924408
\(9\) 1.00000 0.333333
\(10\) −0.430337 −0.136085
\(11\) −3.11111 −0.938034 −0.469017 0.883189i \(-0.655392\pi\)
−0.469017 + 0.883189i \(0.655392\pi\)
\(12\) −1.41319 −0.407953
\(13\) 5.92656 1.64373 0.821866 0.569681i \(-0.192933\pi\)
0.821866 + 0.569681i \(0.192933\pi\)
\(14\) 0 0
\(15\) 0.561773 0.145049
\(16\) 0.823497 0.205874
\(17\) 3.15286 0.764681 0.382341 0.924021i \(-0.375118\pi\)
0.382341 + 0.924021i \(0.375118\pi\)
\(18\) −0.766034 −0.180556
\(19\) −0.142324 −0.0326513 −0.0163256 0.999867i \(-0.505197\pi\)
−0.0163256 + 0.999867i \(0.505197\pi\)
\(20\) −0.793894 −0.177520
\(21\) 0 0
\(22\) 2.38321 0.508102
\(23\) −4.62821 −0.965049 −0.482525 0.875882i \(-0.660280\pi\)
−0.482525 + 0.875882i \(0.660280\pi\)
\(24\) 2.61462 0.533707
\(25\) −4.68441 −0.936882
\(26\) −4.53994 −0.890356
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.30868 −1.54288 −0.771442 0.636300i \(-0.780464\pi\)
−0.771442 + 0.636300i \(0.780464\pi\)
\(30\) −0.430337 −0.0785685
\(31\) −0.336298 −0.0604008 −0.0302004 0.999544i \(-0.509615\pi\)
−0.0302004 + 0.999544i \(0.509615\pi\)
\(32\) −5.86007 −1.03592
\(33\) −3.11111 −0.541574
\(34\) −2.41520 −0.414203
\(35\) 0 0
\(36\) −1.41319 −0.235532
\(37\) −9.44997 −1.55356 −0.776782 0.629769i \(-0.783150\pi\)
−0.776782 + 0.629769i \(0.783150\pi\)
\(38\) 0.109025 0.0176861
\(39\) 5.92656 0.949009
\(40\) 1.46882 0.232242
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 9.28869 1.41651 0.708256 0.705956i \(-0.249482\pi\)
0.708256 + 0.705956i \(0.249482\pi\)
\(44\) 4.39659 0.662811
\(45\) 0.561773 0.0837442
\(46\) 3.54537 0.522736
\(47\) −7.35790 −1.07326 −0.536630 0.843818i \(-0.680303\pi\)
−0.536630 + 0.843818i \(0.680303\pi\)
\(48\) 0.823497 0.118862
\(49\) 0 0
\(50\) 3.58842 0.507479
\(51\) 3.15286 0.441489
\(52\) −8.37537 −1.16145
\(53\) −8.42111 −1.15673 −0.578364 0.815779i \(-0.696309\pi\)
−0.578364 + 0.815779i \(0.696309\pi\)
\(54\) −0.766034 −0.104244
\(55\) −1.74774 −0.235665
\(56\) 0 0
\(57\) −0.142324 −0.0188512
\(58\) 6.36473 0.835730
\(59\) 0.911205 0.118629 0.0593144 0.998239i \(-0.481109\pi\)
0.0593144 + 0.998239i \(0.481109\pi\)
\(60\) −0.793894 −0.102491
\(61\) −3.48407 −0.446090 −0.223045 0.974808i \(-0.571600\pi\)
−0.223045 + 0.974808i \(0.571600\pi\)
\(62\) 0.257615 0.0327172
\(63\) 0 0
\(64\) 2.84201 0.355252
\(65\) 3.32938 0.412959
\(66\) 2.38321 0.293353
\(67\) −0.537448 −0.0656597 −0.0328298 0.999461i \(-0.510452\pi\)
−0.0328298 + 0.999461i \(0.510452\pi\)
\(68\) −4.45560 −0.540321
\(69\) −4.62821 −0.557172
\(70\) 0 0
\(71\) −0.835931 −0.0992067 −0.0496034 0.998769i \(-0.515796\pi\)
−0.0496034 + 0.998769i \(0.515796\pi\)
\(72\) 2.61462 0.308136
\(73\) 8.54657 1.00030 0.500150 0.865939i \(-0.333278\pi\)
0.500150 + 0.865939i \(0.333278\pi\)
\(74\) 7.23899 0.841516
\(75\) −4.68441 −0.540909
\(76\) 0.201131 0.0230713
\(77\) 0 0
\(78\) −4.53994 −0.514047
\(79\) −10.4527 −1.17602 −0.588010 0.808854i \(-0.700088\pi\)
−0.588010 + 0.808854i \(0.700088\pi\)
\(80\) 0.462619 0.0517224
\(81\) 1.00000 0.111111
\(82\) 0.766034 0.0845943
\(83\) −5.99692 −0.658248 −0.329124 0.944287i \(-0.606753\pi\)
−0.329124 + 0.944287i \(0.606753\pi\)
\(84\) 0 0
\(85\) 1.77119 0.192113
\(86\) −7.11545 −0.767279
\(87\) −8.30868 −0.890784
\(88\) −8.13436 −0.867126
\(89\) 18.7260 1.98495 0.992474 0.122457i \(-0.0390774\pi\)
0.992474 + 0.122457i \(0.0390774\pi\)
\(90\) −0.430337 −0.0453615
\(91\) 0 0
\(92\) 6.54056 0.681900
\(93\) −0.336298 −0.0348724
\(94\) 5.63640 0.581350
\(95\) −0.0799537 −0.00820307
\(96\) −5.86007 −0.598091
\(97\) 10.9913 1.11599 0.557996 0.829843i \(-0.311570\pi\)
0.557996 + 0.829843i \(0.311570\pi\)
\(98\) 0 0
\(99\) −3.11111 −0.312678
\(100\) 6.61997 0.661997
\(101\) 0.288673 0.0287241 0.0143620 0.999897i \(-0.495428\pi\)
0.0143620 + 0.999897i \(0.495428\pi\)
\(102\) −2.41520 −0.239140
\(103\) 15.6537 1.54241 0.771205 0.636587i \(-0.219655\pi\)
0.771205 + 0.636587i \(0.219655\pi\)
\(104\) 15.4957 1.51948
\(105\) 0 0
\(106\) 6.45086 0.626562
\(107\) 11.0431 1.06758 0.533790 0.845617i \(-0.320767\pi\)
0.533790 + 0.845617i \(0.320767\pi\)
\(108\) −1.41319 −0.135984
\(109\) −16.4108 −1.57187 −0.785934 0.618311i \(-0.787817\pi\)
−0.785934 + 0.618311i \(0.787817\pi\)
\(110\) 1.33883 0.127652
\(111\) −9.44997 −0.896951
\(112\) 0 0
\(113\) 8.10161 0.762136 0.381068 0.924547i \(-0.375556\pi\)
0.381068 + 0.924547i \(0.375556\pi\)
\(114\) 0.109025 0.0102111
\(115\) −2.60001 −0.242452
\(116\) 11.7418 1.09020
\(117\) 5.92656 0.547910
\(118\) −0.698014 −0.0642574
\(119\) 0 0
\(120\) 1.46882 0.134085
\(121\) −1.32102 −0.120093
\(122\) 2.66892 0.241632
\(123\) −1.00000 −0.0901670
\(124\) 0.475253 0.0426790
\(125\) −5.44045 −0.486608
\(126\) 0 0
\(127\) −13.5484 −1.20223 −0.601113 0.799164i \(-0.705276\pi\)
−0.601113 + 0.799164i \(0.705276\pi\)
\(128\) 9.54306 0.843495
\(129\) 9.28869 0.817824
\(130\) −2.55042 −0.223687
\(131\) 17.4438 1.52407 0.762037 0.647533i \(-0.224199\pi\)
0.762037 + 0.647533i \(0.224199\pi\)
\(132\) 4.39659 0.382674
\(133\) 0 0
\(134\) 0.411703 0.0355657
\(135\) 0.561773 0.0483498
\(136\) 8.24354 0.706877
\(137\) −20.2741 −1.73214 −0.866069 0.499925i \(-0.833361\pi\)
−0.866069 + 0.499925i \(0.833361\pi\)
\(138\) 3.54537 0.301802
\(139\) −9.45159 −0.801674 −0.400837 0.916149i \(-0.631281\pi\)
−0.400837 + 0.916149i \(0.631281\pi\)
\(140\) 0 0
\(141\) −7.35790 −0.619647
\(142\) 0.640351 0.0537371
\(143\) −18.4381 −1.54188
\(144\) 0.823497 0.0686248
\(145\) −4.66760 −0.387623
\(146\) −6.54696 −0.541830
\(147\) 0 0
\(148\) 13.3546 1.09774
\(149\) −19.7136 −1.61500 −0.807501 0.589866i \(-0.799181\pi\)
−0.807501 + 0.589866i \(0.799181\pi\)
\(150\) 3.58842 0.292993
\(151\) 19.6751 1.60114 0.800570 0.599240i \(-0.204530\pi\)
0.800570 + 0.599240i \(0.204530\pi\)
\(152\) −0.372122 −0.0301831
\(153\) 3.15286 0.254894
\(154\) 0 0
\(155\) −0.188923 −0.0151747
\(156\) −8.37537 −0.670566
\(157\) −16.7932 −1.34025 −0.670123 0.742250i \(-0.733759\pi\)
−0.670123 + 0.742250i \(0.733759\pi\)
\(158\) 8.00712 0.637012
\(159\) −8.42111 −0.667838
\(160\) −3.29203 −0.260258
\(161\) 0 0
\(162\) −0.766034 −0.0601853
\(163\) −2.83566 −0.222106 −0.111053 0.993814i \(-0.535422\pi\)
−0.111053 + 0.993814i \(0.535422\pi\)
\(164\) 1.41319 0.110352
\(165\) −1.74774 −0.136061
\(166\) 4.59384 0.356551
\(167\) 6.23667 0.482608 0.241304 0.970450i \(-0.422425\pi\)
0.241304 + 0.970450i \(0.422425\pi\)
\(168\) 0 0
\(169\) 22.1241 1.70185
\(170\) −1.35679 −0.104061
\(171\) −0.142324 −0.0108838
\(172\) −13.1267 −1.00090
\(173\) −24.1412 −1.83542 −0.917709 0.397252i \(-0.869964\pi\)
−0.917709 + 0.397252i \(0.869964\pi\)
\(174\) 6.36473 0.482509
\(175\) 0 0
\(176\) −2.56199 −0.193117
\(177\) 0.911205 0.0684903
\(178\) −14.3447 −1.07518
\(179\) −14.3311 −1.07116 −0.535580 0.844485i \(-0.679907\pi\)
−0.535580 + 0.844485i \(0.679907\pi\)
\(180\) −0.793894 −0.0591734
\(181\) −7.16449 −0.532532 −0.266266 0.963900i \(-0.585790\pi\)
−0.266266 + 0.963900i \(0.585790\pi\)
\(182\) 0 0
\(183\) −3.48407 −0.257550
\(184\) −12.1010 −0.892099
\(185\) −5.30874 −0.390306
\(186\) 0.257615 0.0188893
\(187\) −9.80888 −0.717297
\(188\) 10.3981 0.758361
\(189\) 0 0
\(190\) 0.0612472 0.00444334
\(191\) −17.8171 −1.28920 −0.644601 0.764519i \(-0.722976\pi\)
−0.644601 + 0.764519i \(0.722976\pi\)
\(192\) 2.84201 0.205105
\(193\) 17.8976 1.28830 0.644150 0.764899i \(-0.277211\pi\)
0.644150 + 0.764899i \(0.277211\pi\)
\(194\) −8.41967 −0.604497
\(195\) 3.32938 0.238422
\(196\) 0 0
\(197\) −1.27454 −0.0908069 −0.0454034 0.998969i \(-0.514457\pi\)
−0.0454034 + 0.998969i \(0.514457\pi\)
\(198\) 2.38321 0.169367
\(199\) −26.9626 −1.91133 −0.955666 0.294454i \(-0.904862\pi\)
−0.955666 + 0.294454i \(0.904862\pi\)
\(200\) −12.2480 −0.866061
\(201\) −0.537448 −0.0379086
\(202\) −0.221134 −0.0155589
\(203\) 0 0
\(204\) −4.45560 −0.311954
\(205\) −0.561773 −0.0392360
\(206\) −11.9913 −0.835473
\(207\) −4.62821 −0.321683
\(208\) 4.88050 0.338402
\(209\) 0.442784 0.0306280
\(210\) 0 0
\(211\) −8.25353 −0.568196 −0.284098 0.958795i \(-0.591694\pi\)
−0.284098 + 0.958795i \(0.591694\pi\)
\(212\) 11.9006 0.817340
\(213\) −0.835931 −0.0572770
\(214\) −8.45942 −0.578274
\(215\) 5.21814 0.355874
\(216\) 2.61462 0.177902
\(217\) 0 0
\(218\) 12.5712 0.851430
\(219\) 8.54657 0.577524
\(220\) 2.46989 0.166520
\(221\) 18.6856 1.25693
\(222\) 7.23899 0.485849
\(223\) 9.94467 0.665944 0.332972 0.942937i \(-0.391948\pi\)
0.332972 + 0.942937i \(0.391948\pi\)
\(224\) 0 0
\(225\) −4.68441 −0.312294
\(226\) −6.20611 −0.412824
\(227\) −8.59955 −0.570772 −0.285386 0.958413i \(-0.592122\pi\)
−0.285386 + 0.958413i \(0.592122\pi\)
\(228\) 0.201131 0.0133202
\(229\) −7.01808 −0.463768 −0.231884 0.972743i \(-0.574489\pi\)
−0.231884 + 0.972743i \(0.574489\pi\)
\(230\) 1.99169 0.131328
\(231\) 0 0
\(232\) −21.7240 −1.42625
\(233\) 0.664006 0.0435005 0.0217502 0.999763i \(-0.493076\pi\)
0.0217502 + 0.999763i \(0.493076\pi\)
\(234\) −4.53994 −0.296785
\(235\) −4.13347 −0.269638
\(236\) −1.28771 −0.0838226
\(237\) −10.4527 −0.678975
\(238\) 0 0
\(239\) 3.89087 0.251679 0.125840 0.992051i \(-0.459837\pi\)
0.125840 + 0.992051i \(0.459837\pi\)
\(240\) 0.462619 0.0298619
\(241\) −1.93117 −0.124398 −0.0621989 0.998064i \(-0.519811\pi\)
−0.0621989 + 0.998064i \(0.519811\pi\)
\(242\) 1.01195 0.0650505
\(243\) 1.00000 0.0641500
\(244\) 4.92366 0.315205
\(245\) 0 0
\(246\) 0.766034 0.0488405
\(247\) −0.843490 −0.0536700
\(248\) −0.879290 −0.0558350
\(249\) −5.99692 −0.380039
\(250\) 4.16756 0.263580
\(251\) 19.7811 1.24857 0.624285 0.781197i \(-0.285390\pi\)
0.624285 + 0.781197i \(0.285390\pi\)
\(252\) 0 0
\(253\) 14.3989 0.905249
\(254\) 10.3785 0.651207
\(255\) 1.77119 0.110916
\(256\) −12.9943 −0.812146
\(257\) −10.8991 −0.679866 −0.339933 0.940450i \(-0.610404\pi\)
−0.339933 + 0.940450i \(0.610404\pi\)
\(258\) −7.11545 −0.442989
\(259\) 0 0
\(260\) −4.70506 −0.291795
\(261\) −8.30868 −0.514294
\(262\) −13.3626 −0.825542
\(263\) −12.8647 −0.793268 −0.396634 0.917977i \(-0.629822\pi\)
−0.396634 + 0.917977i \(0.629822\pi\)
\(264\) −8.13436 −0.500635
\(265\) −4.73076 −0.290608
\(266\) 0 0
\(267\) 18.7260 1.14601
\(268\) 0.759517 0.0463949
\(269\) 1.49766 0.0913140 0.0456570 0.998957i \(-0.485462\pi\)
0.0456570 + 0.998957i \(0.485462\pi\)
\(270\) −0.430337 −0.0261895
\(271\) −16.3381 −0.992466 −0.496233 0.868189i \(-0.665284\pi\)
−0.496233 + 0.868189i \(0.665284\pi\)
\(272\) 2.59637 0.157428
\(273\) 0 0
\(274\) 15.5307 0.938243
\(275\) 14.5737 0.878827
\(276\) 6.54056 0.393695
\(277\) 0.682460 0.0410051 0.0205025 0.999790i \(-0.493473\pi\)
0.0205025 + 0.999790i \(0.493473\pi\)
\(278\) 7.24024 0.434241
\(279\) −0.336298 −0.0201336
\(280\) 0 0
\(281\) −18.5463 −1.10638 −0.553190 0.833055i \(-0.686590\pi\)
−0.553190 + 0.833055i \(0.686590\pi\)
\(282\) 5.63640 0.335643
\(283\) −6.11849 −0.363707 −0.181853 0.983326i \(-0.558210\pi\)
−0.181853 + 0.983326i \(0.558210\pi\)
\(284\) 1.18133 0.0700991
\(285\) −0.0799537 −0.00473605
\(286\) 14.1242 0.835184
\(287\) 0 0
\(288\) −5.86007 −0.345308
\(289\) −7.05946 −0.415263
\(290\) 3.57554 0.209963
\(291\) 10.9913 0.644319
\(292\) −12.0779 −0.706808
\(293\) −24.0482 −1.40491 −0.702456 0.711727i \(-0.747913\pi\)
−0.702456 + 0.711727i \(0.747913\pi\)
\(294\) 0 0
\(295\) 0.511891 0.0298034
\(296\) −24.7081 −1.43613
\(297\) −3.11111 −0.180525
\(298\) 15.1013 0.874795
\(299\) −27.4294 −1.58628
\(300\) 6.61997 0.382204
\(301\) 0 0
\(302\) −15.0718 −0.867286
\(303\) 0.288673 0.0165839
\(304\) −0.117203 −0.00672206
\(305\) −1.95726 −0.112072
\(306\) −2.41520 −0.138068
\(307\) 24.2257 1.38263 0.691317 0.722551i \(-0.257031\pi\)
0.691317 + 0.722551i \(0.257031\pi\)
\(308\) 0 0
\(309\) 15.6537 0.890510
\(310\) 0.144721 0.00821962
\(311\) 17.6804 1.00257 0.501283 0.865284i \(-0.332862\pi\)
0.501283 + 0.865284i \(0.332862\pi\)
\(312\) 15.4957 0.877271
\(313\) 22.0256 1.24496 0.622480 0.782635i \(-0.286125\pi\)
0.622480 + 0.782635i \(0.286125\pi\)
\(314\) 12.8642 0.725968
\(315\) 0 0
\(316\) 14.7717 0.830971
\(317\) 3.06800 0.172316 0.0861579 0.996281i \(-0.472541\pi\)
0.0861579 + 0.996281i \(0.472541\pi\)
\(318\) 6.45086 0.361746
\(319\) 25.8492 1.44728
\(320\) 1.59657 0.0892509
\(321\) 11.0431 0.616368
\(322\) 0 0
\(323\) −0.448727 −0.0249678
\(324\) −1.41319 −0.0785107
\(325\) −27.7624 −1.53998
\(326\) 2.17221 0.120308
\(327\) −16.4108 −0.907518
\(328\) −2.61462 −0.144368
\(329\) 0 0
\(330\) 1.33883 0.0736999
\(331\) −25.9353 −1.42553 −0.712765 0.701403i \(-0.752558\pi\)
−0.712765 + 0.701403i \(0.752558\pi\)
\(332\) 8.47480 0.465115
\(333\) −9.44997 −0.517855
\(334\) −4.77750 −0.261413
\(335\) −0.301924 −0.0164959
\(336\) 0 0
\(337\) 23.2651 1.26733 0.633666 0.773606i \(-0.281549\pi\)
0.633666 + 0.773606i \(0.281549\pi\)
\(338\) −16.9478 −0.921839
\(339\) 8.10161 0.440019
\(340\) −2.50304 −0.135746
\(341\) 1.04626 0.0566580
\(342\) 0.109025 0.00589538
\(343\) 0 0
\(344\) 24.2864 1.30943
\(345\) −2.60001 −0.139980
\(346\) 18.4929 0.994187
\(347\) −3.95967 −0.212566 −0.106283 0.994336i \(-0.533895\pi\)
−0.106283 + 0.994336i \(0.533895\pi\)
\(348\) 11.7418 0.629425
\(349\) −21.7095 −1.16209 −0.581043 0.813873i \(-0.697355\pi\)
−0.581043 + 0.813873i \(0.697355\pi\)
\(350\) 0 0
\(351\) 5.92656 0.316336
\(352\) 18.2313 0.971731
\(353\) 4.27161 0.227355 0.113677 0.993518i \(-0.463737\pi\)
0.113677 + 0.993518i \(0.463737\pi\)
\(354\) −0.698014 −0.0370990
\(355\) −0.469604 −0.0249240
\(356\) −26.4634 −1.40256
\(357\) 0 0
\(358\) 10.9781 0.580212
\(359\) −2.51480 −0.132726 −0.0663631 0.997796i \(-0.521140\pi\)
−0.0663631 + 0.997796i \(0.521140\pi\)
\(360\) 1.46882 0.0774138
\(361\) −18.9797 −0.998934
\(362\) 5.48824 0.288455
\(363\) −1.32102 −0.0693358
\(364\) 0 0
\(365\) 4.80124 0.251308
\(366\) 2.66892 0.139506
\(367\) 7.53136 0.393134 0.196567 0.980490i \(-0.437021\pi\)
0.196567 + 0.980490i \(0.437021\pi\)
\(368\) −3.81132 −0.198679
\(369\) −1.00000 −0.0520579
\(370\) 4.06667 0.211416
\(371\) 0 0
\(372\) 0.475253 0.0246407
\(373\) 30.3545 1.57170 0.785849 0.618419i \(-0.212226\pi\)
0.785849 + 0.618419i \(0.212226\pi\)
\(374\) 7.51394 0.388536
\(375\) −5.44045 −0.280943
\(376\) −19.2381 −0.992130
\(377\) −49.2419 −2.53609
\(378\) 0 0
\(379\) 13.9206 0.715054 0.357527 0.933903i \(-0.383620\pi\)
0.357527 + 0.933903i \(0.383620\pi\)
\(380\) 0.112990 0.00579626
\(381\) −13.5484 −0.694106
\(382\) 13.6485 0.698319
\(383\) −12.3726 −0.632209 −0.316104 0.948724i \(-0.602375\pi\)
−0.316104 + 0.948724i \(0.602375\pi\)
\(384\) 9.54306 0.486992
\(385\) 0 0
\(386\) −13.7102 −0.697831
\(387\) 9.28869 0.472171
\(388\) −15.5328 −0.788556
\(389\) −21.3306 −1.08151 −0.540753 0.841182i \(-0.681860\pi\)
−0.540753 + 0.841182i \(0.681860\pi\)
\(390\) −2.55042 −0.129146
\(391\) −14.5921 −0.737955
\(392\) 0 0
\(393\) 17.4438 0.879925
\(394\) 0.976337 0.0491871
\(395\) −5.87205 −0.295455
\(396\) 4.39659 0.220937
\(397\) −32.1083 −1.61147 −0.805736 0.592275i \(-0.798230\pi\)
−0.805736 + 0.592275i \(0.798230\pi\)
\(398\) 20.6543 1.03531
\(399\) 0 0
\(400\) −3.85760 −0.192880
\(401\) 11.0839 0.553503 0.276751 0.960942i \(-0.410742\pi\)
0.276751 + 0.960942i \(0.410742\pi\)
\(402\) 0.411703 0.0205339
\(403\) −1.99309 −0.0992827
\(404\) −0.407951 −0.0202963
\(405\) 0.561773 0.0279147
\(406\) 0 0
\(407\) 29.3998 1.45730
\(408\) 8.24354 0.408116
\(409\) −14.2017 −0.702229 −0.351114 0.936333i \(-0.614197\pi\)
−0.351114 + 0.936333i \(0.614197\pi\)
\(410\) 0.430337 0.0212529
\(411\) −20.2741 −1.00005
\(412\) −22.1217 −1.08986
\(413\) 0 0
\(414\) 3.54537 0.174245
\(415\) −3.36891 −0.165373
\(416\) −34.7300 −1.70278
\(417\) −9.45159 −0.462846
\(418\) −0.339187 −0.0165902
\(419\) −17.9651 −0.877654 −0.438827 0.898572i \(-0.644606\pi\)
−0.438827 + 0.898572i \(0.644606\pi\)
\(420\) 0 0
\(421\) 15.4655 0.753741 0.376871 0.926266i \(-0.377000\pi\)
0.376871 + 0.926266i \(0.377000\pi\)
\(422\) 6.32248 0.307774
\(423\) −7.35790 −0.357753
\(424\) −22.0180 −1.06929
\(425\) −14.7693 −0.716416
\(426\) 0.640351 0.0310251
\(427\) 0 0
\(428\) −15.6061 −0.754348
\(429\) −18.4381 −0.890202
\(430\) −3.99727 −0.192766
\(431\) 10.7203 0.516378 0.258189 0.966094i \(-0.416874\pi\)
0.258189 + 0.966094i \(0.416874\pi\)
\(432\) 0.823497 0.0396205
\(433\) 17.0262 0.818228 0.409114 0.912483i \(-0.365838\pi\)
0.409114 + 0.912483i \(0.365838\pi\)
\(434\) 0 0
\(435\) −4.66760 −0.223794
\(436\) 23.1916 1.11068
\(437\) 0.658705 0.0315101
\(438\) −6.54696 −0.312826
\(439\) −9.07115 −0.432942 −0.216471 0.976289i \(-0.569455\pi\)
−0.216471 + 0.976289i \(0.569455\pi\)
\(440\) −4.56967 −0.217850
\(441\) 0 0
\(442\) −14.3138 −0.680839
\(443\) 19.4595 0.924548 0.462274 0.886737i \(-0.347034\pi\)
0.462274 + 0.886737i \(0.347034\pi\)
\(444\) 13.3546 0.633782
\(445\) 10.5197 0.498684
\(446\) −7.61795 −0.360721
\(447\) −19.7136 −0.932422
\(448\) 0 0
\(449\) −26.9820 −1.27336 −0.636680 0.771129i \(-0.719693\pi\)
−0.636680 + 0.771129i \(0.719693\pi\)
\(450\) 3.58842 0.169160
\(451\) 3.11111 0.146496
\(452\) −11.4491 −0.538522
\(453\) 19.6751 0.924418
\(454\) 6.58755 0.309169
\(455\) 0 0
\(456\) −0.372122 −0.0174262
\(457\) −5.46329 −0.255562 −0.127781 0.991802i \(-0.540785\pi\)
−0.127781 + 0.991802i \(0.540785\pi\)
\(458\) 5.37609 0.251208
\(459\) 3.15286 0.147163
\(460\) 3.67431 0.171316
\(461\) −37.0737 −1.72669 −0.863347 0.504610i \(-0.831636\pi\)
−0.863347 + 0.504610i \(0.831636\pi\)
\(462\) 0 0
\(463\) 24.7212 1.14889 0.574446 0.818542i \(-0.305217\pi\)
0.574446 + 0.818542i \(0.305217\pi\)
\(464\) −6.84218 −0.317640
\(465\) −0.188923 −0.00876110
\(466\) −0.508651 −0.0235628
\(467\) 14.3275 0.662999 0.331499 0.943455i \(-0.392446\pi\)
0.331499 + 0.943455i \(0.392446\pi\)
\(468\) −8.37537 −0.387151
\(469\) 0 0
\(470\) 3.16638 0.146054
\(471\) −16.7932 −0.773792
\(472\) 2.38245 0.109661
\(473\) −28.8981 −1.32874
\(474\) 8.00712 0.367779
\(475\) 0.666703 0.0305904
\(476\) 0 0
\(477\) −8.42111 −0.385576
\(478\) −2.98054 −0.136327
\(479\) 27.6827 1.26485 0.632427 0.774620i \(-0.282059\pi\)
0.632427 + 0.774620i \(0.282059\pi\)
\(480\) −3.29203 −0.150260
\(481\) −56.0058 −2.55364
\(482\) 1.47934 0.0673823
\(483\) 0 0
\(484\) 1.86686 0.0848573
\(485\) 6.17459 0.280374
\(486\) −0.766034 −0.0347480
\(487\) 9.78574 0.443434 0.221717 0.975111i \(-0.428834\pi\)
0.221717 + 0.975111i \(0.428834\pi\)
\(488\) −9.10952 −0.412369
\(489\) −2.83566 −0.128233
\(490\) 0 0
\(491\) −23.0245 −1.03908 −0.519541 0.854445i \(-0.673897\pi\)
−0.519541 + 0.854445i \(0.673897\pi\)
\(492\) 1.41319 0.0637116
\(493\) −26.1961 −1.17981
\(494\) 0.646141 0.0290713
\(495\) −1.74774 −0.0785549
\(496\) −0.276940 −0.0124350
\(497\) 0 0
\(498\) 4.59384 0.205855
\(499\) 26.0648 1.16682 0.583410 0.812178i \(-0.301718\pi\)
0.583410 + 0.812178i \(0.301718\pi\)
\(500\) 7.68840 0.343835
\(501\) 6.23667 0.278634
\(502\) −15.1530 −0.676310
\(503\) 5.13546 0.228979 0.114489 0.993424i \(-0.463477\pi\)
0.114489 + 0.993424i \(0.463477\pi\)
\(504\) 0 0
\(505\) 0.162169 0.00721643
\(506\) −11.0300 −0.490344
\(507\) 22.1241 0.982565
\(508\) 19.1465 0.849488
\(509\) 24.5525 1.08827 0.544135 0.838997i \(-0.316858\pi\)
0.544135 + 0.838997i \(0.316858\pi\)
\(510\) −1.35679 −0.0600799
\(511\) 0 0
\(512\) −9.13201 −0.403582
\(513\) −0.142324 −0.00628374
\(514\) 8.34906 0.368261
\(515\) 8.79386 0.387504
\(516\) −13.1267 −0.577871
\(517\) 22.8912 1.00675
\(518\) 0 0
\(519\) −24.1412 −1.05968
\(520\) 8.70507 0.381743
\(521\) 1.40704 0.0616437 0.0308219 0.999525i \(-0.490188\pi\)
0.0308219 + 0.999525i \(0.490188\pi\)
\(522\) 6.36473 0.278577
\(523\) 4.67309 0.204340 0.102170 0.994767i \(-0.467421\pi\)
0.102170 + 0.994767i \(0.467421\pi\)
\(524\) −24.6515 −1.07691
\(525\) 0 0
\(526\) 9.85476 0.429688
\(527\) −1.06030 −0.0461874
\(528\) −2.56199 −0.111496
\(529\) −1.57963 −0.0686795
\(530\) 3.62392 0.157413
\(531\) 0.911205 0.0395429
\(532\) 0 0
\(533\) −5.92656 −0.256708
\(534\) −14.3447 −0.620757
\(535\) 6.20374 0.268211
\(536\) −1.40522 −0.0606963
\(537\) −14.3311 −0.618434
\(538\) −1.14726 −0.0494619
\(539\) 0 0
\(540\) −0.793894 −0.0341638
\(541\) 34.9134 1.50105 0.750523 0.660844i \(-0.229802\pi\)
0.750523 + 0.660844i \(0.229802\pi\)
\(542\) 12.5155 0.537587
\(543\) −7.16449 −0.307458
\(544\) −18.4760 −0.792151
\(545\) −9.21914 −0.394904
\(546\) 0 0
\(547\) 12.6091 0.539128 0.269564 0.962982i \(-0.413120\pi\)
0.269564 + 0.962982i \(0.413120\pi\)
\(548\) 28.6513 1.22392
\(549\) −3.48407 −0.148697
\(550\) −11.1639 −0.476032
\(551\) 1.18252 0.0503771
\(552\) −12.1010 −0.515054
\(553\) 0 0
\(554\) −0.522788 −0.0222111
\(555\) −5.30874 −0.225343
\(556\) 13.3569 0.566460
\(557\) 11.4906 0.486872 0.243436 0.969917i \(-0.421725\pi\)
0.243436 + 0.969917i \(0.421725\pi\)
\(558\) 0.257615 0.0109057
\(559\) 55.0500 2.32837
\(560\) 0 0
\(561\) −9.80888 −0.414131
\(562\) 14.2071 0.599290
\(563\) −7.94311 −0.334762 −0.167381 0.985892i \(-0.553531\pi\)
−0.167381 + 0.985892i \(0.553531\pi\)
\(564\) 10.3981 0.437840
\(565\) 4.55127 0.191473
\(566\) 4.68697 0.197008
\(567\) 0 0
\(568\) −2.18564 −0.0917075
\(569\) −20.4591 −0.857688 −0.428844 0.903379i \(-0.641079\pi\)
−0.428844 + 0.903379i \(0.641079\pi\)
\(570\) 0.0612472 0.00256536
\(571\) 24.9522 1.04422 0.522108 0.852879i \(-0.325146\pi\)
0.522108 + 0.852879i \(0.325146\pi\)
\(572\) 26.0566 1.08948
\(573\) −17.8171 −0.744321
\(574\) 0 0
\(575\) 21.6805 0.904138
\(576\) 2.84201 0.118417
\(577\) 5.42180 0.225712 0.112856 0.993611i \(-0.464000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(578\) 5.40779 0.224934
\(579\) 17.8976 0.743801
\(580\) 6.59621 0.273893
\(581\) 0 0
\(582\) −8.41967 −0.349007
\(583\) 26.1990 1.08505
\(584\) 22.3460 0.924686
\(585\) 3.32938 0.137653
\(586\) 18.4217 0.760995
\(587\) −3.53886 −0.146064 −0.0730322 0.997330i \(-0.523268\pi\)
−0.0730322 + 0.997330i \(0.523268\pi\)
\(588\) 0 0
\(589\) 0.0478631 0.00197217
\(590\) −0.392126 −0.0161436
\(591\) −1.27454 −0.0524274
\(592\) −7.78202 −0.319839
\(593\) −6.19628 −0.254451 −0.127225 0.991874i \(-0.540607\pi\)
−0.127225 + 0.991874i \(0.540607\pi\)
\(594\) 2.38321 0.0977844
\(595\) 0 0
\(596\) 27.8591 1.14115
\(597\) −26.9626 −1.10351
\(598\) 21.0118 0.859238
\(599\) 0.570423 0.0233068 0.0116534 0.999932i \(-0.496291\pi\)
0.0116534 + 0.999932i \(0.496291\pi\)
\(600\) −12.2480 −0.500021
\(601\) −6.47851 −0.264264 −0.132132 0.991232i \(-0.542182\pi\)
−0.132132 + 0.991232i \(0.542182\pi\)
\(602\) 0 0
\(603\) −0.537448 −0.0218866
\(604\) −27.8047 −1.13136
\(605\) −0.742116 −0.0301713
\(606\) −0.221134 −0.00898294
\(607\) 6.62026 0.268708 0.134354 0.990933i \(-0.457104\pi\)
0.134354 + 0.990933i \(0.457104\pi\)
\(608\) 0.834026 0.0338242
\(609\) 0 0
\(610\) 1.49933 0.0607059
\(611\) −43.6070 −1.76415
\(612\) −4.45560 −0.180107
\(613\) 14.0034 0.565592 0.282796 0.959180i \(-0.408738\pi\)
0.282796 + 0.959180i \(0.408738\pi\)
\(614\) −18.5577 −0.748928
\(615\) −0.561773 −0.0226529
\(616\) 0 0
\(617\) −37.3456 −1.50348 −0.751739 0.659460i \(-0.770785\pi\)
−0.751739 + 0.659460i \(0.770785\pi\)
\(618\) −11.9913 −0.482361
\(619\) −24.8145 −0.997377 −0.498689 0.866781i \(-0.666185\pi\)
−0.498689 + 0.866781i \(0.666185\pi\)
\(620\) 0.266985 0.0107224
\(621\) −4.62821 −0.185724
\(622\) −13.5438 −0.543057
\(623\) 0 0
\(624\) 4.88050 0.195377
\(625\) 20.3658 0.814630
\(626\) −16.8724 −0.674355
\(627\) 0.442784 0.0176831
\(628\) 23.7321 0.947013
\(629\) −29.7944 −1.18798
\(630\) 0 0
\(631\) −41.0974 −1.63606 −0.818031 0.575173i \(-0.804935\pi\)
−0.818031 + 0.575173i \(0.804935\pi\)
\(632\) −27.3298 −1.08712
\(633\) −8.25353 −0.328048
\(634\) −2.35019 −0.0933379
\(635\) −7.61113 −0.302039
\(636\) 11.9006 0.471891
\(637\) 0 0
\(638\) −19.8013 −0.783943
\(639\) −0.835931 −0.0330689
\(640\) 5.36104 0.211914
\(641\) 3.33905 0.131884 0.0659422 0.997823i \(-0.478995\pi\)
0.0659422 + 0.997823i \(0.478995\pi\)
\(642\) −8.45942 −0.333867
\(643\) 27.6056 1.08866 0.544330 0.838871i \(-0.316784\pi\)
0.544330 + 0.838871i \(0.316784\pi\)
\(644\) 0 0
\(645\) 5.21814 0.205464
\(646\) 0.343740 0.0135243
\(647\) 27.3768 1.07629 0.538147 0.842851i \(-0.319124\pi\)
0.538147 + 0.842851i \(0.319124\pi\)
\(648\) 2.61462 0.102712
\(649\) −2.83485 −0.111278
\(650\) 21.2670 0.834159
\(651\) 0 0
\(652\) 4.00733 0.156939
\(653\) −50.3901 −1.97192 −0.985959 0.166985i \(-0.946597\pi\)
−0.985959 + 0.166985i \(0.946597\pi\)
\(654\) 12.5712 0.491573
\(655\) 9.79948 0.382897
\(656\) −0.823497 −0.0321522
\(657\) 8.54657 0.333433
\(658\) 0 0
\(659\) 1.97744 0.0770303 0.0385152 0.999258i \(-0.487737\pi\)
0.0385152 + 0.999258i \(0.487737\pi\)
\(660\) 2.46989 0.0961403
\(661\) −34.6552 −1.34793 −0.673965 0.738763i \(-0.735410\pi\)
−0.673965 + 0.738763i \(0.735410\pi\)
\(662\) 19.8673 0.772164
\(663\) 18.6856 0.725689
\(664\) −15.6797 −0.608489
\(665\) 0 0
\(666\) 7.23899 0.280505
\(667\) 38.4544 1.48896
\(668\) −8.81361 −0.341009
\(669\) 9.94467 0.384483
\(670\) 0.231284 0.00893527
\(671\) 10.8393 0.418447
\(672\) 0 0
\(673\) −9.37694 −0.361455 −0.180727 0.983533i \(-0.557845\pi\)
−0.180727 + 0.983533i \(0.557845\pi\)
\(674\) −17.8219 −0.686473
\(675\) −4.68441 −0.180303
\(676\) −31.2656 −1.20252
\(677\) −9.75240 −0.374815 −0.187408 0.982282i \(-0.560009\pi\)
−0.187408 + 0.982282i \(0.560009\pi\)
\(678\) −6.20611 −0.238344
\(679\) 0 0
\(680\) 4.63100 0.177591
\(681\) −8.59955 −0.329536
\(682\) −0.801468 −0.0306898
\(683\) 15.3801 0.588502 0.294251 0.955728i \(-0.404930\pi\)
0.294251 + 0.955728i \(0.404930\pi\)
\(684\) 0.201131 0.00769043
\(685\) −11.3895 −0.435170
\(686\) 0 0
\(687\) −7.01808 −0.267757
\(688\) 7.64921 0.291623
\(689\) −49.9082 −1.90135
\(690\) 1.99169 0.0758225
\(691\) 33.8947 1.28942 0.644708 0.764429i \(-0.276979\pi\)
0.644708 + 0.764429i \(0.276979\pi\)
\(692\) 34.1161 1.29690
\(693\) 0 0
\(694\) 3.03324 0.115140
\(695\) −5.30965 −0.201407
\(696\) −21.7240 −0.823448
\(697\) −3.15286 −0.119423
\(698\) 16.6302 0.629464
\(699\) 0.664006 0.0251150
\(700\) 0 0
\(701\) −31.8433 −1.20271 −0.601353 0.798984i \(-0.705371\pi\)
−0.601353 + 0.798984i \(0.705371\pi\)
\(702\) −4.53994 −0.171349
\(703\) 1.34495 0.0507259
\(704\) −8.84181 −0.333238
\(705\) −4.13347 −0.155676
\(706\) −3.27220 −0.123151
\(707\) 0 0
\(708\) −1.28771 −0.0483950
\(709\) 11.2444 0.422292 0.211146 0.977455i \(-0.432280\pi\)
0.211146 + 0.977455i \(0.432280\pi\)
\(710\) 0.359732 0.0135005
\(711\) −10.4527 −0.392007
\(712\) 48.9613 1.83490
\(713\) 1.55646 0.0582898
\(714\) 0 0
\(715\) −10.3581 −0.387370
\(716\) 20.2527 0.756877
\(717\) 3.89087 0.145307
\(718\) 1.92642 0.0718935
\(719\) −32.1389 −1.19858 −0.599289 0.800532i \(-0.704550\pi\)
−0.599289 + 0.800532i \(0.704550\pi\)
\(720\) 0.462619 0.0172408
\(721\) 0 0
\(722\) 14.5391 0.541090
\(723\) −1.93117 −0.0718211
\(724\) 10.1248 0.376285
\(725\) 38.9213 1.44550
\(726\) 1.01195 0.0375569
\(727\) 20.1797 0.748425 0.374212 0.927343i \(-0.377913\pi\)
0.374212 + 0.927343i \(0.377913\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.67791 −0.136126
\(731\) 29.2860 1.08318
\(732\) 4.92366 0.181984
\(733\) −49.0009 −1.80989 −0.904944 0.425530i \(-0.860088\pi\)
−0.904944 + 0.425530i \(0.860088\pi\)
\(734\) −5.76928 −0.212948
\(735\) 0 0
\(736\) 27.1217 0.999717
\(737\) 1.67206 0.0615910
\(738\) 0.766034 0.0281981
\(739\) −18.4871 −0.680060 −0.340030 0.940415i \(-0.610437\pi\)
−0.340030 + 0.940415i \(0.610437\pi\)
\(740\) 7.50227 0.275789
\(741\) −0.843490 −0.0309864
\(742\) 0 0
\(743\) −0.0512035 −0.00187847 −0.000939237 1.00000i \(-0.500299\pi\)
−0.000939237 1.00000i \(0.500299\pi\)
\(744\) −0.879290 −0.0322364
\(745\) −11.0746 −0.405742
\(746\) −23.2526 −0.851338
\(747\) −5.99692 −0.219416
\(748\) 13.8618 0.506839
\(749\) 0 0
\(750\) 4.16756 0.152178
\(751\) −22.4662 −0.819802 −0.409901 0.912130i \(-0.634437\pi\)
−0.409901 + 0.912130i \(0.634437\pi\)
\(752\) −6.05921 −0.220957
\(753\) 19.7811 0.720862
\(754\) 37.7209 1.37372
\(755\) 11.0530 0.402259
\(756\) 0 0
\(757\) 9.36483 0.340370 0.170185 0.985412i \(-0.445563\pi\)
0.170185 + 0.985412i \(0.445563\pi\)
\(758\) −10.6637 −0.387322
\(759\) 14.3989 0.522646
\(760\) −0.209049 −0.00758299
\(761\) −8.28605 −0.300369 −0.150185 0.988658i \(-0.547987\pi\)
−0.150185 + 0.988658i \(0.547987\pi\)
\(762\) 10.3785 0.375975
\(763\) 0 0
\(764\) 25.1790 0.910945
\(765\) 1.77119 0.0640377
\(766\) 9.47781 0.342447
\(767\) 5.40031 0.194994
\(768\) −12.9943 −0.468893
\(769\) −8.71914 −0.314420 −0.157210 0.987565i \(-0.550250\pi\)
−0.157210 + 0.987565i \(0.550250\pi\)
\(770\) 0 0
\(771\) −10.8991 −0.392521
\(772\) −25.2928 −0.910308
\(773\) 39.2093 1.41026 0.705130 0.709078i \(-0.250889\pi\)
0.705130 + 0.709078i \(0.250889\pi\)
\(774\) −7.11545 −0.255760
\(775\) 1.57536 0.0565885
\(776\) 28.7380 1.03163
\(777\) 0 0
\(778\) 16.3400 0.585816
\(779\) 0.142324 0.00509928
\(780\) −4.70506 −0.168468
\(781\) 2.60067 0.0930592
\(782\) 11.1781 0.399726
\(783\) −8.30868 −0.296928
\(784\) 0 0
\(785\) −9.43400 −0.336714
\(786\) −13.3626 −0.476627
\(787\) 29.7849 1.06172 0.530858 0.847461i \(-0.321870\pi\)
0.530858 + 0.847461i \(0.321870\pi\)
\(788\) 1.80116 0.0641638
\(789\) −12.8647 −0.457994
\(790\) 4.49819 0.160038
\(791\) 0 0
\(792\) −8.13436 −0.289042
\(793\) −20.6485 −0.733251
\(794\) 24.5961 0.872882
\(795\) −4.73076 −0.167783
\(796\) 38.1034 1.35054
\(797\) −10.9573 −0.388127 −0.194063 0.980989i \(-0.562167\pi\)
−0.194063 + 0.980989i \(0.562167\pi\)
\(798\) 0 0
\(799\) −23.1984 −0.820702
\(800\) 27.4510 0.970538
\(801\) 18.7260 0.661649
\(802\) −8.49063 −0.299814
\(803\) −26.5893 −0.938315
\(804\) 0.759517 0.0267861
\(805\) 0 0
\(806\) 1.52677 0.0537782
\(807\) 1.49766 0.0527202
\(808\) 0.754771 0.0265528
\(809\) −35.3162 −1.24165 −0.620826 0.783949i \(-0.713203\pi\)
−0.620826 + 0.783949i \(0.713203\pi\)
\(810\) −0.430337 −0.0151205
\(811\) 16.1352 0.566582 0.283291 0.959034i \(-0.408574\pi\)
0.283291 + 0.959034i \(0.408574\pi\)
\(812\) 0 0
\(813\) −16.3381 −0.573000
\(814\) −22.5213 −0.789370
\(815\) −1.59300 −0.0558003
\(816\) 2.59637 0.0908912
\(817\) −1.32200 −0.0462510
\(818\) 10.8790 0.380374
\(819\) 0 0
\(820\) 0.793894 0.0277240
\(821\) 5.76072 0.201050 0.100525 0.994935i \(-0.467948\pi\)
0.100525 + 0.994935i \(0.467948\pi\)
\(822\) 15.5307 0.541695
\(823\) 49.8189 1.73658 0.868290 0.496057i \(-0.165219\pi\)
0.868290 + 0.496057i \(0.165219\pi\)
\(824\) 40.9286 1.42582
\(825\) 14.5737 0.507391
\(826\) 0 0
\(827\) −56.4094 −1.96155 −0.980773 0.195151i \(-0.937480\pi\)
−0.980773 + 0.195151i \(0.937480\pi\)
\(828\) 6.54056 0.227300
\(829\) −18.1146 −0.629144 −0.314572 0.949234i \(-0.601861\pi\)
−0.314572 + 0.949234i \(0.601861\pi\)
\(830\) 2.58070 0.0895774
\(831\) 0.682460 0.0236743
\(832\) 16.8434 0.583939
\(833\) 0 0
\(834\) 7.24024 0.250709
\(835\) 3.50360 0.121247
\(836\) −0.625739 −0.0216416
\(837\) −0.336298 −0.0116241
\(838\) 13.7619 0.475397
\(839\) −7.52465 −0.259780 −0.129890 0.991528i \(-0.541462\pi\)
−0.129890 + 0.991528i \(0.541462\pi\)
\(840\) 0 0
\(841\) 40.0342 1.38049
\(842\) −11.8471 −0.408277
\(843\) −18.5463 −0.638768
\(844\) 11.6638 0.401485
\(845\) 12.4287 0.427561
\(846\) 5.63640 0.193783
\(847\) 0 0
\(848\) −6.93476 −0.238141
\(849\) −6.11849 −0.209986
\(850\) 11.3138 0.388059
\(851\) 43.7365 1.49927
\(852\) 1.18133 0.0404717
\(853\) 2.09284 0.0716576 0.0358288 0.999358i \(-0.488593\pi\)
0.0358288 + 0.999358i \(0.488593\pi\)
\(854\) 0 0
\(855\) −0.0799537 −0.00273436
\(856\) 28.8736 0.986880
\(857\) −29.6948 −1.01436 −0.507178 0.861841i \(-0.669311\pi\)
−0.507178 + 0.861841i \(0.669311\pi\)
\(858\) 14.1242 0.482194
\(859\) 55.8092 1.90419 0.952093 0.305809i \(-0.0989268\pi\)
0.952093 + 0.305809i \(0.0989268\pi\)
\(860\) −7.37424 −0.251459
\(861\) 0 0
\(862\) −8.21210 −0.279705
\(863\) −33.0298 −1.12435 −0.562173 0.827020i \(-0.690035\pi\)
−0.562173 + 0.827020i \(0.690035\pi\)
\(864\) −5.86007 −0.199364
\(865\) −13.5619 −0.461117
\(866\) −13.0427 −0.443207
\(867\) −7.05946 −0.239752
\(868\) 0 0
\(869\) 32.5194 1.10315
\(870\) 3.57554 0.121222
\(871\) −3.18521 −0.107927
\(872\) −42.9079 −1.45305
\(873\) 10.9913 0.371998
\(874\) −0.504590 −0.0170680
\(875\) 0 0
\(876\) −12.0779 −0.408076
\(877\) 35.0276 1.18280 0.591398 0.806380i \(-0.298576\pi\)
0.591398 + 0.806380i \(0.298576\pi\)
\(878\) 6.94881 0.234511
\(879\) −24.0482 −0.811126
\(880\) −1.43926 −0.0485173
\(881\) −9.28557 −0.312839 −0.156419 0.987691i \(-0.549995\pi\)
−0.156419 + 0.987691i \(0.549995\pi\)
\(882\) 0 0
\(883\) −14.6176 −0.491920 −0.245960 0.969280i \(-0.579103\pi\)
−0.245960 + 0.969280i \(0.579103\pi\)
\(884\) −26.4064 −0.888142
\(885\) 0.511891 0.0172070
\(886\) −14.9066 −0.500798
\(887\) 4.58271 0.153872 0.0769361 0.997036i \(-0.475486\pi\)
0.0769361 + 0.997036i \(0.475486\pi\)
\(888\) −24.7081 −0.829149
\(889\) 0 0
\(890\) −8.05848 −0.270121
\(891\) −3.11111 −0.104226
\(892\) −14.0537 −0.470554
\(893\) 1.04720 0.0350433
\(894\) 15.1013 0.505063
\(895\) −8.05085 −0.269110
\(896\) 0 0
\(897\) −27.4294 −0.915840
\(898\) 20.6691 0.689737
\(899\) 2.79419 0.0931914
\(900\) 6.61997 0.220666
\(901\) −26.5506 −0.884529
\(902\) −2.38321 −0.0793523
\(903\) 0 0
\(904\) 21.1826 0.704524
\(905\) −4.02482 −0.133790
\(906\) −15.0718 −0.500728
\(907\) 50.5590 1.67879 0.839393 0.543525i \(-0.182911\pi\)
0.839393 + 0.543525i \(0.182911\pi\)
\(908\) 12.1528 0.403306
\(909\) 0.288673 0.00957469
\(910\) 0 0
\(911\) −0.442249 −0.0146524 −0.00732618 0.999973i \(-0.502332\pi\)
−0.00732618 + 0.999973i \(0.502332\pi\)
\(912\) −0.117203 −0.00388098
\(913\) 18.6571 0.617458
\(914\) 4.18506 0.138430
\(915\) −1.95726 −0.0647050
\(916\) 9.91790 0.327697
\(917\) 0 0
\(918\) −2.41520 −0.0797134
\(919\) −18.0403 −0.595095 −0.297547 0.954707i \(-0.596169\pi\)
−0.297547 + 0.954707i \(0.596169\pi\)
\(920\) −6.79803 −0.224125
\(921\) 24.2257 0.798264
\(922\) 28.3997 0.935295
\(923\) −4.95419 −0.163069
\(924\) 0 0
\(925\) 44.2675 1.45551
\(926\) −18.9373 −0.622318
\(927\) 15.6537 0.514136
\(928\) 48.6894 1.59831
\(929\) 38.6217 1.26714 0.633569 0.773687i \(-0.281589\pi\)
0.633569 + 0.773687i \(0.281589\pi\)
\(930\) 0.144721 0.00474560
\(931\) 0 0
\(932\) −0.938368 −0.0307373
\(933\) 17.6804 0.578831
\(934\) −10.9754 −0.359125
\(935\) −5.51037 −0.180208
\(936\) 15.4957 0.506493
\(937\) −5.99551 −0.195865 −0.0979324 0.995193i \(-0.531223\pi\)
−0.0979324 + 0.995193i \(0.531223\pi\)
\(938\) 0 0
\(939\) 22.0256 0.718778
\(940\) 5.84139 0.190525
\(941\) −28.1503 −0.917674 −0.458837 0.888520i \(-0.651734\pi\)
−0.458837 + 0.888520i \(0.651734\pi\)
\(942\) 12.8642 0.419138
\(943\) 4.62821 0.150715
\(944\) 0.750375 0.0244226
\(945\) 0 0
\(946\) 22.1369 0.719733
\(947\) −26.4200 −0.858534 −0.429267 0.903178i \(-0.641228\pi\)
−0.429267 + 0.903178i \(0.641228\pi\)
\(948\) 14.7717 0.479761
\(949\) 50.6517 1.64423
\(950\) −0.510717 −0.0165698
\(951\) 3.06800 0.0994866
\(952\) 0 0
\(953\) 19.0038 0.615592 0.307796 0.951452i \(-0.400409\pi\)
0.307796 + 0.951452i \(0.400409\pi\)
\(954\) 6.45086 0.208854
\(955\) −10.0092 −0.323890
\(956\) −5.49855 −0.177836
\(957\) 25.8492 0.835585
\(958\) −21.2059 −0.685130
\(959\) 0 0
\(960\) 1.59657 0.0515290
\(961\) −30.8869 −0.996352
\(962\) 42.9023 1.38323
\(963\) 11.0431 0.355860
\(964\) 2.72912 0.0878991
\(965\) 10.0544 0.323663
\(966\) 0 0
\(967\) −38.9197 −1.25157 −0.625787 0.779994i \(-0.715222\pi\)
−0.625787 + 0.779994i \(0.715222\pi\)
\(968\) −3.45398 −0.111015
\(969\) −0.448727 −0.0144152
\(970\) −4.72995 −0.151869
\(971\) −48.6690 −1.56186 −0.780931 0.624617i \(-0.785255\pi\)
−0.780931 + 0.624617i \(0.785255\pi\)
\(972\) −1.41319 −0.0453282
\(973\) 0 0
\(974\) −7.49620 −0.240194
\(975\) −27.7624 −0.889109
\(976\) −2.86912 −0.0918384
\(977\) 19.6134 0.627490 0.313745 0.949507i \(-0.398416\pi\)
0.313745 + 0.949507i \(0.398416\pi\)
\(978\) 2.17221 0.0694596
\(979\) −58.2584 −1.86195
\(980\) 0 0
\(981\) −16.4108 −0.523956
\(982\) 17.6376 0.562838
\(983\) 3.19009 0.101748 0.0508741 0.998705i \(-0.483799\pi\)
0.0508741 + 0.998705i \(0.483799\pi\)
\(984\) −2.61462 −0.0833511
\(985\) −0.716000 −0.0228137
\(986\) 20.0671 0.639067
\(987\) 0 0
\(988\) 1.19201 0.0379230
\(989\) −42.9901 −1.36700
\(990\) 1.33883 0.0425507
\(991\) 58.7305 1.86564 0.932819 0.360346i \(-0.117342\pi\)
0.932819 + 0.360346i \(0.117342\pi\)
\(992\) 1.97073 0.0625706
\(993\) −25.9353 −0.823030
\(994\) 0 0
\(995\) −15.1469 −0.480189
\(996\) 8.47480 0.268534
\(997\) 46.2376 1.46436 0.732179 0.681112i \(-0.238503\pi\)
0.732179 + 0.681112i \(0.238503\pi\)
\(998\) −19.9665 −0.632029
\(999\) −9.44997 −0.298984
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 \(a_p\))