Properties

Label 6027.2.a.y.1.4
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
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: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
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 1.4
Root \(0.281557\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +2.60041 q^{10} +4.77078 q^{11} +1.48384 q^{12} +1.67717 q^{13} -3.61951 q^{15} +1.16946 q^{16} -4.10812 q^{17} +0.718443 q^{18} -7.21202 q^{19} -5.37077 q^{20} +3.42753 q^{22} +6.09173 q^{23} +2.50294 q^{24} +8.10083 q^{25} +1.20495 q^{26} -1.00000 q^{27} +4.27679 q^{29} -2.60041 q^{30} +9.68962 q^{31} +5.84607 q^{32} -4.77078 q^{33} -2.95145 q^{34} -1.48384 q^{36} -9.29150 q^{37} -5.18143 q^{38} -1.67717 q^{39} -9.05941 q^{40} -1.00000 q^{41} +0.493197 q^{43} -7.07907 q^{44} +3.61951 q^{45} +4.37656 q^{46} +0.929521 q^{47} -1.16946 q^{48} +5.81998 q^{50} +4.10812 q^{51} -2.48865 q^{52} +11.2593 q^{53} -0.718443 q^{54} +17.2679 q^{55} +7.21202 q^{57} +3.07263 q^{58} -0.276180 q^{59} +5.37077 q^{60} -8.28534 q^{61} +6.96144 q^{62} +1.86114 q^{64} +6.07053 q^{65} -3.42753 q^{66} -6.10165 q^{67} +6.09579 q^{68} -6.09173 q^{69} -4.71258 q^{71} -2.50294 q^{72} +9.42904 q^{73} -6.67541 q^{74} -8.10083 q^{75} +10.7015 q^{76} -1.20495 q^{78} +12.3654 q^{79} +4.23288 q^{80} +1.00000 q^{81} -0.718443 q^{82} +8.22541 q^{83} -14.8694 q^{85} +0.354334 q^{86} -4.27679 q^{87} -11.9410 q^{88} -5.51271 q^{89} +2.60041 q^{90} -9.03915 q^{92} -9.68962 q^{93} +0.667807 q^{94} -26.1040 q^{95} -5.84607 q^{96} -4.56102 q^{97} +4.77078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.718443 0.508016 0.254008 0.967202i \(-0.418251\pi\)
0.254008 + 0.967202i \(0.418251\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.48384 −0.741920
\(5\) 3.61951 1.61869 0.809346 0.587332i \(-0.199822\pi\)
0.809346 + 0.587332i \(0.199822\pi\)
\(6\) −0.718443 −0.293303
\(7\) 0 0
\(8\) −2.50294 −0.884923
\(9\) 1.00000 0.333333
\(10\) 2.60041 0.822321
\(11\) 4.77078 1.43844 0.719221 0.694781i \(-0.244499\pi\)
0.719221 + 0.694781i \(0.244499\pi\)
\(12\) 1.48384 0.428348
\(13\) 1.67717 0.465163 0.232582 0.972577i \(-0.425283\pi\)
0.232582 + 0.972577i \(0.425283\pi\)
\(14\) 0 0
\(15\) −3.61951 −0.934553
\(16\) 1.16946 0.292366
\(17\) −4.10812 −0.996364 −0.498182 0.867072i \(-0.665999\pi\)
−0.498182 + 0.867072i \(0.665999\pi\)
\(18\) 0.718443 0.169339
\(19\) −7.21202 −1.65455 −0.827276 0.561796i \(-0.810111\pi\)
−0.827276 + 0.561796i \(0.810111\pi\)
\(20\) −5.37077 −1.20094
\(21\) 0 0
\(22\) 3.42753 0.730751
\(23\) 6.09173 1.27021 0.635106 0.772425i \(-0.280956\pi\)
0.635106 + 0.772425i \(0.280956\pi\)
\(24\) 2.50294 0.510910
\(25\) 8.10083 1.62017
\(26\) 1.20495 0.236310
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.27679 0.794180 0.397090 0.917780i \(-0.370020\pi\)
0.397090 + 0.917780i \(0.370020\pi\)
\(30\) −2.60041 −0.474767
\(31\) 9.68962 1.74031 0.870154 0.492780i \(-0.164019\pi\)
0.870154 + 0.492780i \(0.164019\pi\)
\(32\) 5.84607 1.03345
\(33\) −4.77078 −0.830485
\(34\) −2.95145 −0.506169
\(35\) 0 0
\(36\) −1.48384 −0.247307
\(37\) −9.29150 −1.52751 −0.763756 0.645505i \(-0.776647\pi\)
−0.763756 + 0.645505i \(0.776647\pi\)
\(38\) −5.18143 −0.840538
\(39\) −1.67717 −0.268562
\(40\) −9.05941 −1.43242
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 0.493197 0.0752119 0.0376059 0.999293i \(-0.488027\pi\)
0.0376059 + 0.999293i \(0.488027\pi\)
\(44\) −7.07907 −1.06721
\(45\) 3.61951 0.539564
\(46\) 4.37656 0.645288
\(47\) 0.929521 0.135585 0.0677923 0.997699i \(-0.478404\pi\)
0.0677923 + 0.997699i \(0.478404\pi\)
\(48\) −1.16946 −0.168797
\(49\) 0 0
\(50\) 5.81998 0.823070
\(51\) 4.10812 0.575251
\(52\) −2.48865 −0.345114
\(53\) 11.2593 1.54659 0.773293 0.634049i \(-0.218608\pi\)
0.773293 + 0.634049i \(0.218608\pi\)
\(54\) −0.718443 −0.0977677
\(55\) 17.2679 2.32840
\(56\) 0 0
\(57\) 7.21202 0.955256
\(58\) 3.07263 0.403456
\(59\) −0.276180 −0.0359556 −0.0179778 0.999838i \(-0.505723\pi\)
−0.0179778 + 0.999838i \(0.505723\pi\)
\(60\) 5.37077 0.693364
\(61\) −8.28534 −1.06083 −0.530414 0.847739i \(-0.677964\pi\)
−0.530414 + 0.847739i \(0.677964\pi\)
\(62\) 6.96144 0.884103
\(63\) 0 0
\(64\) 1.86114 0.232643
\(65\) 6.07053 0.752956
\(66\) −3.42753 −0.421900
\(67\) −6.10165 −0.745436 −0.372718 0.927945i \(-0.621574\pi\)
−0.372718 + 0.927945i \(0.621574\pi\)
\(68\) 6.09579 0.739223
\(69\) −6.09173 −0.733358
\(70\) 0 0
\(71\) −4.71258 −0.559281 −0.279640 0.960105i \(-0.590215\pi\)
−0.279640 + 0.960105i \(0.590215\pi\)
\(72\) −2.50294 −0.294974
\(73\) 9.42904 1.10359 0.551793 0.833981i \(-0.313944\pi\)
0.551793 + 0.833981i \(0.313944\pi\)
\(74\) −6.67541 −0.776000
\(75\) −8.10083 −0.935404
\(76\) 10.7015 1.22755
\(77\) 0 0
\(78\) −1.20495 −0.136434
\(79\) 12.3654 1.39122 0.695610 0.718419i \(-0.255134\pi\)
0.695610 + 0.718419i \(0.255134\pi\)
\(80\) 4.23288 0.473250
\(81\) 1.00000 0.111111
\(82\) −0.718443 −0.0793387
\(83\) 8.22541 0.902856 0.451428 0.892308i \(-0.350915\pi\)
0.451428 + 0.892308i \(0.350915\pi\)
\(84\) 0 0
\(85\) −14.8694 −1.61281
\(86\) 0.354334 0.0382088
\(87\) −4.27679 −0.458520
\(88\) −11.9410 −1.27291
\(89\) −5.51271 −0.584346 −0.292173 0.956365i \(-0.594378\pi\)
−0.292173 + 0.956365i \(0.594378\pi\)
\(90\) 2.60041 0.274107
\(91\) 0 0
\(92\) −9.03915 −0.942396
\(93\) −9.68962 −1.00477
\(94\) 0.667807 0.0688791
\(95\) −26.1040 −2.67821
\(96\) −5.84607 −0.596662
\(97\) −4.56102 −0.463102 −0.231551 0.972823i \(-0.574380\pi\)
−0.231551 + 0.972823i \(0.574380\pi\)
\(98\) 0 0
\(99\) 4.77078 0.479481
\(100\) −12.0203 −1.20203
\(101\) 6.54576 0.651327 0.325664 0.945486i \(-0.394412\pi\)
0.325664 + 0.945486i \(0.394412\pi\)
\(102\) 2.95145 0.292237
\(103\) −10.3795 −1.02272 −0.511359 0.859367i \(-0.670858\pi\)
−0.511359 + 0.859367i \(0.670858\pi\)
\(104\) −4.19785 −0.411633
\(105\) 0 0
\(106\) 8.08917 0.785689
\(107\) 0.428154 0.0413912 0.0206956 0.999786i \(-0.493412\pi\)
0.0206956 + 0.999786i \(0.493412\pi\)
\(108\) 1.48384 0.142783
\(109\) 9.21699 0.882827 0.441414 0.897304i \(-0.354477\pi\)
0.441414 + 0.897304i \(0.354477\pi\)
\(110\) 12.4060 1.18286
\(111\) 9.29150 0.881910
\(112\) 0 0
\(113\) 15.1405 1.42430 0.712150 0.702028i \(-0.247722\pi\)
0.712150 + 0.702028i \(0.247722\pi\)
\(114\) 5.18143 0.485285
\(115\) 22.0491 2.05608
\(116\) −6.34607 −0.589218
\(117\) 1.67717 0.155054
\(118\) −0.198419 −0.0182660
\(119\) 0 0
\(120\) 9.05941 0.827007
\(121\) 11.7603 1.06912
\(122\) −5.95254 −0.538917
\(123\) 1.00000 0.0901670
\(124\) −14.3779 −1.29117
\(125\) 11.2235 1.00386
\(126\) 0 0
\(127\) −12.3127 −1.09257 −0.546286 0.837599i \(-0.683959\pi\)
−0.546286 + 0.837599i \(0.683959\pi\)
\(128\) −10.3550 −0.915263
\(129\) −0.493197 −0.0434236
\(130\) 4.36133 0.382514
\(131\) −7.55733 −0.660287 −0.330143 0.943931i \(-0.607097\pi\)
−0.330143 + 0.943931i \(0.607097\pi\)
\(132\) 7.07907 0.616154
\(133\) 0 0
\(134\) −4.38369 −0.378693
\(135\) −3.61951 −0.311518
\(136\) 10.2824 0.881705
\(137\) 3.85038 0.328960 0.164480 0.986380i \(-0.447405\pi\)
0.164480 + 0.986380i \(0.447405\pi\)
\(138\) −4.37656 −0.372557
\(139\) −18.3824 −1.55917 −0.779586 0.626295i \(-0.784570\pi\)
−0.779586 + 0.626295i \(0.784570\pi\)
\(140\) 0 0
\(141\) −0.929521 −0.0782798
\(142\) −3.38572 −0.284123
\(143\) 8.00140 0.669111
\(144\) 1.16946 0.0974552
\(145\) 15.4799 1.28553
\(146\) 6.77423 0.560639
\(147\) 0 0
\(148\) 13.7871 1.13329
\(149\) 10.1266 0.829606 0.414803 0.909911i \(-0.363851\pi\)
0.414803 + 0.909911i \(0.363851\pi\)
\(150\) −5.81998 −0.475200
\(151\) −13.7468 −1.11870 −0.559351 0.828931i \(-0.688950\pi\)
−0.559351 + 0.828931i \(0.688950\pi\)
\(152\) 18.0513 1.46415
\(153\) −4.10812 −0.332121
\(154\) 0 0
\(155\) 35.0717 2.81702
\(156\) 2.48865 0.199252
\(157\) 7.62988 0.608931 0.304466 0.952523i \(-0.401522\pi\)
0.304466 + 0.952523i \(0.401522\pi\)
\(158\) 8.88386 0.706762
\(159\) −11.2593 −0.892921
\(160\) 21.1599 1.67284
\(161\) 0 0
\(162\) 0.718443 0.0564462
\(163\) −6.42437 −0.503196 −0.251598 0.967832i \(-0.580956\pi\)
−0.251598 + 0.967832i \(0.580956\pi\)
\(164\) 1.48384 0.115868
\(165\) −17.2679 −1.34430
\(166\) 5.90948 0.458665
\(167\) 22.3236 1.72745 0.863725 0.503963i \(-0.168125\pi\)
0.863725 + 0.503963i \(0.168125\pi\)
\(168\) 0 0
\(169\) −10.1871 −0.783623
\(170\) −10.6828 −0.819332
\(171\) −7.21202 −0.551517
\(172\) −0.731826 −0.0558012
\(173\) −2.33229 −0.177321 −0.0886605 0.996062i \(-0.528259\pi\)
−0.0886605 + 0.996062i \(0.528259\pi\)
\(174\) −3.07263 −0.232935
\(175\) 0 0
\(176\) 5.57924 0.420551
\(177\) 0.276180 0.0207590
\(178\) −3.96057 −0.296857
\(179\) 18.0617 1.35000 0.674998 0.737820i \(-0.264144\pi\)
0.674998 + 0.737820i \(0.264144\pi\)
\(180\) −5.37077 −0.400314
\(181\) 16.9055 1.25658 0.628289 0.777980i \(-0.283756\pi\)
0.628289 + 0.777980i \(0.283756\pi\)
\(182\) 0 0
\(183\) 8.28534 0.612470
\(184\) −15.2472 −1.12404
\(185\) −33.6306 −2.47257
\(186\) −6.96144 −0.510437
\(187\) −19.5989 −1.43321
\(188\) −1.37926 −0.100593
\(189\) 0 0
\(190\) −18.7542 −1.36057
\(191\) 11.9555 0.865071 0.432535 0.901617i \(-0.357619\pi\)
0.432535 + 0.901617i \(0.357619\pi\)
\(192\) −1.86114 −0.134316
\(193\) −11.2986 −0.813290 −0.406645 0.913586i \(-0.633301\pi\)
−0.406645 + 0.913586i \(0.633301\pi\)
\(194\) −3.27683 −0.235263
\(195\) −6.07053 −0.434719
\(196\) 0 0
\(197\) 15.2853 1.08903 0.544517 0.838750i \(-0.316713\pi\)
0.544517 + 0.838750i \(0.316713\pi\)
\(198\) 3.42753 0.243584
\(199\) 19.9661 1.41536 0.707681 0.706532i \(-0.249741\pi\)
0.707681 + 0.706532i \(0.249741\pi\)
\(200\) −20.2759 −1.43372
\(201\) 6.10165 0.430378
\(202\) 4.70275 0.330884
\(203\) 0 0
\(204\) −6.09579 −0.426790
\(205\) −3.61951 −0.252797
\(206\) −7.45704 −0.519557
\(207\) 6.09173 0.423404
\(208\) 1.96139 0.135998
\(209\) −34.4069 −2.37998
\(210\) 0 0
\(211\) −6.26636 −0.431394 −0.215697 0.976460i \(-0.569202\pi\)
−0.215697 + 0.976460i \(0.569202\pi\)
\(212\) −16.7070 −1.14744
\(213\) 4.71258 0.322901
\(214\) 0.307604 0.0210274
\(215\) 1.78513 0.121745
\(216\) 2.50294 0.170303
\(217\) 0 0
\(218\) 6.62188 0.448490
\(219\) −9.42904 −0.637156
\(220\) −25.6227 −1.72748
\(221\) −6.89001 −0.463472
\(222\) 6.67541 0.448024
\(223\) −24.0197 −1.60848 −0.804239 0.594306i \(-0.797427\pi\)
−0.804239 + 0.594306i \(0.797427\pi\)
\(224\) 0 0
\(225\) 8.10083 0.540056
\(226\) 10.8776 0.723566
\(227\) 17.2170 1.14273 0.571365 0.820696i \(-0.306414\pi\)
0.571365 + 0.820696i \(0.306414\pi\)
\(228\) −10.7015 −0.708724
\(229\) 0.410688 0.0271390 0.0135695 0.999908i \(-0.495681\pi\)
0.0135695 + 0.999908i \(0.495681\pi\)
\(230\) 15.8410 1.04452
\(231\) 0 0
\(232\) −10.7045 −0.702788
\(233\) 20.4805 1.34172 0.670861 0.741583i \(-0.265925\pi\)
0.670861 + 0.741583i \(0.265925\pi\)
\(234\) 1.20495 0.0787700
\(235\) 3.36441 0.219470
\(236\) 0.409807 0.0266762
\(237\) −12.3654 −0.803222
\(238\) 0 0
\(239\) −14.3115 −0.925736 −0.462868 0.886427i \(-0.653180\pi\)
−0.462868 + 0.886427i \(0.653180\pi\)
\(240\) −4.23288 −0.273231
\(241\) −27.0366 −1.74158 −0.870789 0.491658i \(-0.836391\pi\)
−0.870789 + 0.491658i \(0.836391\pi\)
\(242\) 8.44910 0.543129
\(243\) −1.00000 −0.0641500
\(244\) 12.2941 0.787050
\(245\) 0 0
\(246\) 0.718443 0.0458062
\(247\) −12.0958 −0.769637
\(248\) −24.2525 −1.54004
\(249\) −8.22541 −0.521264
\(250\) 8.06343 0.509976
\(251\) −2.15039 −0.135732 −0.0678658 0.997694i \(-0.521619\pi\)
−0.0678658 + 0.997694i \(0.521619\pi\)
\(252\) 0 0
\(253\) 29.0623 1.82713
\(254\) −8.84594 −0.555044
\(255\) 14.8694 0.931155
\(256\) −11.1618 −0.697611
\(257\) 29.1832 1.82040 0.910200 0.414170i \(-0.135928\pi\)
0.910200 + 0.414170i \(0.135928\pi\)
\(258\) −0.354334 −0.0220599
\(259\) 0 0
\(260\) −9.00769 −0.558633
\(261\) 4.27679 0.264727
\(262\) −5.42951 −0.335436
\(263\) 1.29066 0.0795858 0.0397929 0.999208i \(-0.487330\pi\)
0.0397929 + 0.999208i \(0.487330\pi\)
\(264\) 11.9410 0.734915
\(265\) 40.7532 2.50345
\(266\) 0 0
\(267\) 5.51271 0.337372
\(268\) 9.05388 0.553054
\(269\) 23.0819 1.40733 0.703665 0.710531i \(-0.251545\pi\)
0.703665 + 0.710531i \(0.251545\pi\)
\(270\) −2.60041 −0.158256
\(271\) 18.2013 1.10565 0.552826 0.833297i \(-0.313549\pi\)
0.552826 + 0.833297i \(0.313549\pi\)
\(272\) −4.80429 −0.291303
\(273\) 0 0
\(274\) 2.76628 0.167117
\(275\) 38.6473 2.33052
\(276\) 9.03915 0.544093
\(277\) −19.3138 −1.16045 −0.580227 0.814455i \(-0.697036\pi\)
−0.580227 + 0.814455i \(0.697036\pi\)
\(278\) −13.2067 −0.792084
\(279\) 9.68962 0.580102
\(280\) 0 0
\(281\) −10.6700 −0.636517 −0.318258 0.948004i \(-0.603098\pi\)
−0.318258 + 0.948004i \(0.603098\pi\)
\(282\) −0.667807 −0.0397674
\(283\) 19.6343 1.16714 0.583570 0.812063i \(-0.301655\pi\)
0.583570 + 0.812063i \(0.301655\pi\)
\(284\) 6.99272 0.414942
\(285\) 26.1040 1.54627
\(286\) 5.74855 0.339919
\(287\) 0 0
\(288\) 5.84607 0.344483
\(289\) −0.123387 −0.00725803
\(290\) 11.1214 0.653071
\(291\) 4.56102 0.267372
\(292\) −13.9912 −0.818773
\(293\) 6.13638 0.358491 0.179246 0.983804i \(-0.442634\pi\)
0.179246 + 0.983804i \(0.442634\pi\)
\(294\) 0 0
\(295\) −0.999635 −0.0582010
\(296\) 23.2561 1.35173
\(297\) −4.77078 −0.276828
\(298\) 7.27540 0.421453
\(299\) 10.2169 0.590856
\(300\) 12.0203 0.693995
\(301\) 0 0
\(302\) −9.87632 −0.568318
\(303\) −6.54576 −0.376044
\(304\) −8.43419 −0.483734
\(305\) −29.9888 −1.71716
\(306\) −2.95145 −0.168723
\(307\) 9.85765 0.562606 0.281303 0.959619i \(-0.409233\pi\)
0.281303 + 0.959619i \(0.409233\pi\)
\(308\) 0 0
\(309\) 10.3795 0.590467
\(310\) 25.1970 1.43109
\(311\) 20.2723 1.14954 0.574768 0.818316i \(-0.305092\pi\)
0.574768 + 0.818316i \(0.305092\pi\)
\(312\) 4.19785 0.237657
\(313\) 17.9597 1.01514 0.507571 0.861610i \(-0.330544\pi\)
0.507571 + 0.861610i \(0.330544\pi\)
\(314\) 5.48163 0.309346
\(315\) 0 0
\(316\) −18.3483 −1.03217
\(317\) 26.1554 1.46903 0.734516 0.678592i \(-0.237409\pi\)
0.734516 + 0.678592i \(0.237409\pi\)
\(318\) −8.08917 −0.453618
\(319\) 20.4036 1.14238
\(320\) 6.73642 0.376577
\(321\) −0.428154 −0.0238972
\(322\) 0 0
\(323\) 29.6278 1.64854
\(324\) −1.48384 −0.0824356
\(325\) 13.5865 0.753642
\(326\) −4.61554 −0.255631
\(327\) −9.21699 −0.509701
\(328\) 2.50294 0.138202
\(329\) 0 0
\(330\) −12.4060 −0.682926
\(331\) −4.78518 −0.263017 −0.131509 0.991315i \(-0.541982\pi\)
−0.131509 + 0.991315i \(0.541982\pi\)
\(332\) −12.2052 −0.669847
\(333\) −9.29150 −0.509171
\(334\) 16.0382 0.877572
\(335\) −22.0850 −1.20663
\(336\) 0 0
\(337\) 3.08688 0.168153 0.0840767 0.996459i \(-0.473206\pi\)
0.0840767 + 0.996459i \(0.473206\pi\)
\(338\) −7.31885 −0.398093
\(339\) −15.1405 −0.822319
\(340\) 22.0637 1.19657
\(341\) 46.2270 2.50333
\(342\) −5.18143 −0.280179
\(343\) 0 0
\(344\) −1.23444 −0.0665567
\(345\) −22.0491 −1.18708
\(346\) −1.67562 −0.0900818
\(347\) 5.57233 0.299138 0.149569 0.988751i \(-0.452211\pi\)
0.149569 + 0.988751i \(0.452211\pi\)
\(348\) 6.34607 0.340185
\(349\) 7.19830 0.385316 0.192658 0.981266i \(-0.438289\pi\)
0.192658 + 0.981266i \(0.438289\pi\)
\(350\) 0 0
\(351\) −1.67717 −0.0895207
\(352\) 27.8903 1.48656
\(353\) 31.8045 1.69278 0.846392 0.532560i \(-0.178770\pi\)
0.846392 + 0.532560i \(0.178770\pi\)
\(354\) 0.198419 0.0105459
\(355\) −17.0572 −0.905304
\(356\) 8.17998 0.433538
\(357\) 0 0
\(358\) 12.9763 0.685819
\(359\) −11.4920 −0.606523 −0.303261 0.952907i \(-0.598076\pi\)
−0.303261 + 0.952907i \(0.598076\pi\)
\(360\) −9.05941 −0.477473
\(361\) 33.0133 1.73754
\(362\) 12.1456 0.638361
\(363\) −11.7603 −0.617255
\(364\) 0 0
\(365\) 34.1285 1.78637
\(366\) 5.95254 0.311144
\(367\) −36.6507 −1.91315 −0.956574 0.291489i \(-0.905849\pi\)
−0.956574 + 0.291489i \(0.905849\pi\)
\(368\) 7.12404 0.371366
\(369\) −1.00000 −0.0520579
\(370\) −24.1617 −1.25611
\(371\) 0 0
\(372\) 14.3779 0.745457
\(373\) 23.9922 1.24227 0.621134 0.783704i \(-0.286672\pi\)
0.621134 + 0.783704i \(0.286672\pi\)
\(374\) −14.0807 −0.728095
\(375\) −11.2235 −0.579579
\(376\) −2.32653 −0.119982
\(377\) 7.17290 0.369423
\(378\) 0 0
\(379\) 12.8095 0.657978 0.328989 0.944334i \(-0.393292\pi\)
0.328989 + 0.944334i \(0.393292\pi\)
\(380\) 38.7341 1.98702
\(381\) 12.3127 0.630797
\(382\) 8.58935 0.439469
\(383\) −9.99249 −0.510592 −0.255296 0.966863i \(-0.582173\pi\)
−0.255296 + 0.966863i \(0.582173\pi\)
\(384\) 10.3550 0.528427
\(385\) 0 0
\(386\) −8.11739 −0.413164
\(387\) 0.493197 0.0250706
\(388\) 6.76783 0.343585
\(389\) −4.36094 −0.221108 −0.110554 0.993870i \(-0.535263\pi\)
−0.110554 + 0.993870i \(0.535263\pi\)
\(390\) −4.36133 −0.220844
\(391\) −25.0255 −1.26559
\(392\) 0 0
\(393\) 7.55733 0.381217
\(394\) 10.9816 0.553247
\(395\) 44.7568 2.25196
\(396\) −7.07907 −0.355737
\(397\) −1.04587 −0.0524907 −0.0262454 0.999656i \(-0.508355\pi\)
−0.0262454 + 0.999656i \(0.508355\pi\)
\(398\) 14.3445 0.719026
\(399\) 0 0
\(400\) 9.47362 0.473681
\(401\) 34.4257 1.71914 0.859569 0.511020i \(-0.170732\pi\)
0.859569 + 0.511020i \(0.170732\pi\)
\(402\) 4.38369 0.218639
\(403\) 16.2511 0.809527
\(404\) −9.71286 −0.483233
\(405\) 3.61951 0.179855
\(406\) 0 0
\(407\) −44.3276 −2.19724
\(408\) −10.2824 −0.509053
\(409\) 31.0567 1.53566 0.767828 0.640656i \(-0.221338\pi\)
0.767828 + 0.640656i \(0.221338\pi\)
\(410\) −2.60041 −0.128425
\(411\) −3.85038 −0.189925
\(412\) 15.4015 0.758775
\(413\) 0 0
\(414\) 4.37656 0.215096
\(415\) 29.7719 1.46145
\(416\) 9.80485 0.480722
\(417\) 18.3824 0.900188
\(418\) −24.7194 −1.20907
\(419\) −9.64209 −0.471047 −0.235523 0.971869i \(-0.575680\pi\)
−0.235523 + 0.971869i \(0.575680\pi\)
\(420\) 0 0
\(421\) 17.1549 0.836077 0.418039 0.908429i \(-0.362718\pi\)
0.418039 + 0.908429i \(0.362718\pi\)
\(422\) −4.50202 −0.219155
\(423\) 0.929521 0.0451949
\(424\) −28.1814 −1.36861
\(425\) −33.2792 −1.61428
\(426\) 3.38572 0.164039
\(427\) 0 0
\(428\) −0.635311 −0.0307089
\(429\) −8.00140 −0.386311
\(430\) 1.28251 0.0618483
\(431\) −30.7376 −1.48058 −0.740290 0.672287i \(-0.765312\pi\)
−0.740290 + 0.672287i \(0.765312\pi\)
\(432\) −1.16946 −0.0562658
\(433\) 6.14874 0.295490 0.147745 0.989026i \(-0.452799\pi\)
0.147745 + 0.989026i \(0.452799\pi\)
\(434\) 0 0
\(435\) −15.4799 −0.742203
\(436\) −13.6765 −0.654987
\(437\) −43.9337 −2.10163
\(438\) −6.77423 −0.323685
\(439\) −12.8538 −0.613477 −0.306739 0.951794i \(-0.599238\pi\)
−0.306739 + 0.951794i \(0.599238\pi\)
\(440\) −43.2204 −2.06045
\(441\) 0 0
\(442\) −4.95007 −0.235451
\(443\) −14.4939 −0.688625 −0.344312 0.938855i \(-0.611888\pi\)
−0.344312 + 0.938855i \(0.611888\pi\)
\(444\) −13.7871 −0.654307
\(445\) −19.9533 −0.945877
\(446\) −17.2568 −0.817132
\(447\) −10.1266 −0.478973
\(448\) 0 0
\(449\) −24.5899 −1.16047 −0.580236 0.814449i \(-0.697040\pi\)
−0.580236 + 0.814449i \(0.697040\pi\)
\(450\) 5.81998 0.274357
\(451\) −4.77078 −0.224647
\(452\) −22.4661 −1.05672
\(453\) 13.7468 0.645883
\(454\) 12.3694 0.580524
\(455\) 0 0
\(456\) −18.0513 −0.845328
\(457\) −30.5890 −1.43089 −0.715447 0.698667i \(-0.753777\pi\)
−0.715447 + 0.698667i \(0.753777\pi\)
\(458\) 0.295056 0.0137871
\(459\) 4.10812 0.191750
\(460\) −32.7173 −1.52545
\(461\) −2.50315 −0.116583 −0.0582917 0.998300i \(-0.518565\pi\)
−0.0582917 + 0.998300i \(0.518565\pi\)
\(462\) 0 0
\(463\) 3.38170 0.157161 0.0785806 0.996908i \(-0.474961\pi\)
0.0785806 + 0.996908i \(0.474961\pi\)
\(464\) 5.00154 0.232191
\(465\) −35.0717 −1.62641
\(466\) 14.7141 0.681616
\(467\) −20.3032 −0.939522 −0.469761 0.882794i \(-0.655660\pi\)
−0.469761 + 0.882794i \(0.655660\pi\)
\(468\) −2.48865 −0.115038
\(469\) 0 0
\(470\) 2.41713 0.111494
\(471\) −7.62988 −0.351566
\(472\) 0.691262 0.0318179
\(473\) 2.35293 0.108188
\(474\) −8.88386 −0.408049
\(475\) −58.4234 −2.68065
\(476\) 0 0
\(477\) 11.2593 0.515528
\(478\) −10.2820 −0.470289
\(479\) −29.0637 −1.32796 −0.663978 0.747752i \(-0.731133\pi\)
−0.663978 + 0.747752i \(0.731133\pi\)
\(480\) −21.1599 −0.965813
\(481\) −15.5834 −0.710542
\(482\) −19.4242 −0.884749
\(483\) 0 0
\(484\) −17.4504 −0.793200
\(485\) −16.5087 −0.749620
\(486\) −0.718443 −0.0325892
\(487\) 3.58717 0.162550 0.0812752 0.996692i \(-0.474101\pi\)
0.0812752 + 0.996692i \(0.474101\pi\)
\(488\) 20.7377 0.938751
\(489\) 6.42437 0.290520
\(490\) 0 0
\(491\) −12.8947 −0.581929 −0.290964 0.956734i \(-0.593976\pi\)
−0.290964 + 0.956734i \(0.593976\pi\)
\(492\) −1.48384 −0.0668967
\(493\) −17.5695 −0.791293
\(494\) −8.69013 −0.390987
\(495\) 17.2679 0.776132
\(496\) 11.3316 0.508806
\(497\) 0 0
\(498\) −5.90948 −0.264810
\(499\) −29.8308 −1.33541 −0.667705 0.744426i \(-0.732723\pi\)
−0.667705 + 0.744426i \(0.732723\pi\)
\(500\) −16.6539 −0.744784
\(501\) −22.3236 −0.997344
\(502\) −1.54493 −0.0689538
\(503\) 20.0091 0.892163 0.446082 0.894992i \(-0.352819\pi\)
0.446082 + 0.894992i \(0.352819\pi\)
\(504\) 0 0
\(505\) 23.6924 1.05430
\(506\) 20.8796 0.928210
\(507\) 10.1871 0.452425
\(508\) 18.2700 0.810601
\(509\) −16.2303 −0.719394 −0.359697 0.933069i \(-0.617120\pi\)
−0.359697 + 0.933069i \(0.617120\pi\)
\(510\) 10.6828 0.473041
\(511\) 0 0
\(512\) 12.6909 0.560866
\(513\) 7.21202 0.318419
\(514\) 20.9665 0.924791
\(515\) −37.5685 −1.65547
\(516\) 0.731826 0.0322168
\(517\) 4.43454 0.195031
\(518\) 0 0
\(519\) 2.33229 0.102376
\(520\) −15.1942 −0.666308
\(521\) 15.7030 0.687963 0.343981 0.938976i \(-0.388224\pi\)
0.343981 + 0.938976i \(0.388224\pi\)
\(522\) 3.07263 0.134485
\(523\) −2.08067 −0.0909812 −0.0454906 0.998965i \(-0.514485\pi\)
−0.0454906 + 0.998965i \(0.514485\pi\)
\(524\) 11.2139 0.489880
\(525\) 0 0
\(526\) 0.927268 0.0404308
\(527\) −39.8061 −1.73398
\(528\) −5.57924 −0.242805
\(529\) 14.1091 0.613441
\(530\) 29.2788 1.27179
\(531\) −0.276180 −0.0119852
\(532\) 0 0
\(533\) −1.67717 −0.0726463
\(534\) 3.96057 0.171390
\(535\) 1.54970 0.0669996
\(536\) 15.2721 0.659653
\(537\) −18.0617 −0.779421
\(538\) 16.5831 0.714946
\(539\) 0 0
\(540\) 5.37077 0.231121
\(541\) −18.2552 −0.784854 −0.392427 0.919783i \(-0.628364\pi\)
−0.392427 + 0.919783i \(0.628364\pi\)
\(542\) 13.0766 0.561689
\(543\) −16.9055 −0.725485
\(544\) −24.0163 −1.02969
\(545\) 33.3610 1.42903
\(546\) 0 0
\(547\) 5.89322 0.251976 0.125988 0.992032i \(-0.459790\pi\)
0.125988 + 0.992032i \(0.459790\pi\)
\(548\) −5.71335 −0.244062
\(549\) −8.28534 −0.353609
\(550\) 27.7658 1.18394
\(551\) −30.8443 −1.31401
\(552\) 15.2472 0.648965
\(553\) 0 0
\(554\) −13.8759 −0.589529
\(555\) 33.6306 1.42754
\(556\) 27.2765 1.15678
\(557\) 21.6502 0.917350 0.458675 0.888604i \(-0.348324\pi\)
0.458675 + 0.888604i \(0.348324\pi\)
\(558\) 6.96144 0.294701
\(559\) 0.827175 0.0349858
\(560\) 0 0
\(561\) 19.5989 0.827466
\(562\) −7.66576 −0.323361
\(563\) −3.85381 −0.162419 −0.0812093 0.996697i \(-0.525878\pi\)
−0.0812093 + 0.996697i \(0.525878\pi\)
\(564\) 1.37926 0.0580773
\(565\) 54.8012 2.30550
\(566\) 14.1061 0.592926
\(567\) 0 0
\(568\) 11.7953 0.494920
\(569\) 41.0410 1.72053 0.860264 0.509849i \(-0.170299\pi\)
0.860264 + 0.509849i \(0.170299\pi\)
\(570\) 18.7542 0.785527
\(571\) 26.1479 1.09426 0.547128 0.837049i \(-0.315721\pi\)
0.547128 + 0.837049i \(0.315721\pi\)
\(572\) −11.8728 −0.496427
\(573\) −11.9555 −0.499449
\(574\) 0 0
\(575\) 49.3481 2.05796
\(576\) 1.86114 0.0775476
\(577\) −8.41211 −0.350201 −0.175100 0.984551i \(-0.556025\pi\)
−0.175100 + 0.984551i \(0.556025\pi\)
\(578\) −0.0886462 −0.00368719
\(579\) 11.2986 0.469553
\(580\) −22.9697 −0.953763
\(581\) 0 0
\(582\) 3.27683 0.135829
\(583\) 53.7156 2.22467
\(584\) −23.6003 −0.976588
\(585\) 6.07053 0.250985
\(586\) 4.40864 0.182119
\(587\) 15.9572 0.658624 0.329312 0.944221i \(-0.393183\pi\)
0.329312 + 0.944221i \(0.393183\pi\)
\(588\) 0 0
\(589\) −69.8818 −2.87943
\(590\) −0.718181 −0.0295670
\(591\) −15.2853 −0.628755
\(592\) −10.8661 −0.446592
\(593\) −24.8072 −1.01871 −0.509354 0.860557i \(-0.670116\pi\)
−0.509354 + 0.860557i \(0.670116\pi\)
\(594\) −3.42753 −0.140633
\(595\) 0 0
\(596\) −15.0263 −0.615501
\(597\) −19.9661 −0.817160
\(598\) 7.34023 0.300164
\(599\) 28.4289 1.16157 0.580786 0.814056i \(-0.302745\pi\)
0.580786 + 0.814056i \(0.302745\pi\)
\(600\) 20.2759 0.827760
\(601\) 20.8714 0.851362 0.425681 0.904873i \(-0.360035\pi\)
0.425681 + 0.904873i \(0.360035\pi\)
\(602\) 0 0
\(603\) −6.10165 −0.248479
\(604\) 20.3981 0.829988
\(605\) 42.5665 1.73057
\(606\) −4.70275 −0.191036
\(607\) −24.7136 −1.00309 −0.501547 0.865131i \(-0.667235\pi\)
−0.501547 + 0.865131i \(0.667235\pi\)
\(608\) −42.1620 −1.70989
\(609\) 0 0
\(610\) −21.5453 −0.872342
\(611\) 1.55896 0.0630689
\(612\) 6.09579 0.246408
\(613\) 33.3329 1.34630 0.673151 0.739505i \(-0.264941\pi\)
0.673151 + 0.739505i \(0.264941\pi\)
\(614\) 7.08215 0.285813
\(615\) 3.61951 0.145953
\(616\) 0 0
\(617\) −34.5080 −1.38924 −0.694619 0.719378i \(-0.744427\pi\)
−0.694619 + 0.719378i \(0.744427\pi\)
\(618\) 7.45704 0.299966
\(619\) −12.5191 −0.503184 −0.251592 0.967833i \(-0.580954\pi\)
−0.251592 + 0.967833i \(0.580954\pi\)
\(620\) −52.0407 −2.09001
\(621\) −6.09173 −0.244453
\(622\) 14.5645 0.583983
\(623\) 0 0
\(624\) −1.96139 −0.0785183
\(625\) 0.119342 0.00477369
\(626\) 12.9030 0.515708
\(627\) 34.4069 1.37408
\(628\) −11.3215 −0.451778
\(629\) 38.1705 1.52196
\(630\) 0 0
\(631\) 18.1805 0.723756 0.361878 0.932225i \(-0.382136\pi\)
0.361878 + 0.932225i \(0.382136\pi\)
\(632\) −30.9499 −1.23112
\(633\) 6.26636 0.249066
\(634\) 18.7911 0.746291
\(635\) −44.5658 −1.76854
\(636\) 16.7070 0.662476
\(637\) 0 0
\(638\) 14.6588 0.580348
\(639\) −4.71258 −0.186427
\(640\) −37.4801 −1.48153
\(641\) −35.2943 −1.39404 −0.697020 0.717051i \(-0.745491\pi\)
−0.697020 + 0.717051i \(0.745491\pi\)
\(642\) −0.307604 −0.0121402
\(643\) 6.80232 0.268257 0.134129 0.990964i \(-0.457176\pi\)
0.134129 + 0.990964i \(0.457176\pi\)
\(644\) 0 0
\(645\) −1.78513 −0.0702895
\(646\) 21.2859 0.837482
\(647\) 17.8299 0.700965 0.350483 0.936569i \(-0.386018\pi\)
0.350483 + 0.936569i \(0.386018\pi\)
\(648\) −2.50294 −0.0983247
\(649\) −1.31759 −0.0517200
\(650\) 9.76110 0.382862
\(651\) 0 0
\(652\) 9.53274 0.373331
\(653\) −2.93708 −0.114937 −0.0574684 0.998347i \(-0.518303\pi\)
−0.0574684 + 0.998347i \(0.518303\pi\)
\(654\) −6.62188 −0.258936
\(655\) −27.3538 −1.06880
\(656\) −1.16946 −0.0456598
\(657\) 9.42904 0.367862
\(658\) 0 0
\(659\) −40.1383 −1.56357 −0.781783 0.623551i \(-0.785689\pi\)
−0.781783 + 0.623551i \(0.785689\pi\)
\(660\) 25.6227 0.997364
\(661\) −30.1636 −1.17323 −0.586615 0.809866i \(-0.699540\pi\)
−0.586615 + 0.809866i \(0.699540\pi\)
\(662\) −3.43788 −0.133617
\(663\) 6.89001 0.267586
\(664\) −20.5877 −0.798958
\(665\) 0 0
\(666\) −6.67541 −0.258667
\(667\) 26.0530 1.00878
\(668\) −33.1246 −1.28163
\(669\) 24.0197 0.928655
\(670\) −15.8668 −0.612988
\(671\) −39.5275 −1.52594
\(672\) 0 0
\(673\) −36.7315 −1.41589 −0.707947 0.706266i \(-0.750378\pi\)
−0.707947 + 0.706266i \(0.750378\pi\)
\(674\) 2.21775 0.0854245
\(675\) −8.10083 −0.311801
\(676\) 15.1160 0.581386
\(677\) −1.25934 −0.0484003 −0.0242002 0.999707i \(-0.507704\pi\)
−0.0242002 + 0.999707i \(0.507704\pi\)
\(678\) −10.8776 −0.417751
\(679\) 0 0
\(680\) 37.2171 1.42721
\(681\) −17.2170 −0.659755
\(682\) 33.2115 1.27173
\(683\) 35.0039 1.33939 0.669694 0.742637i \(-0.266425\pi\)
0.669694 + 0.742637i \(0.266425\pi\)
\(684\) 10.7015 0.409182
\(685\) 13.9365 0.532486
\(686\) 0 0
\(687\) −0.410688 −0.0156687
\(688\) 0.576776 0.0219894
\(689\) 18.8838 0.719414
\(690\) −15.8410 −0.603056
\(691\) −46.5992 −1.77272 −0.886359 0.462999i \(-0.846773\pi\)
−0.886359 + 0.462999i \(0.846773\pi\)
\(692\) 3.46075 0.131558
\(693\) 0 0
\(694\) 4.00340 0.151967
\(695\) −66.5351 −2.52382
\(696\) 10.7045 0.405755
\(697\) 4.10812 0.155606
\(698\) 5.17156 0.195747
\(699\) −20.4805 −0.774644
\(700\) 0 0
\(701\) 3.08338 0.116457 0.0582287 0.998303i \(-0.481455\pi\)
0.0582287 + 0.998303i \(0.481455\pi\)
\(702\) −1.20495 −0.0454779
\(703\) 67.0105 2.52735
\(704\) 8.87909 0.334643
\(705\) −3.36441 −0.126711
\(706\) 22.8497 0.859961
\(707\) 0 0
\(708\) −0.409807 −0.0154015
\(709\) 11.0616 0.415425 0.207713 0.978190i \(-0.433398\pi\)
0.207713 + 0.978190i \(0.433398\pi\)
\(710\) −12.2546 −0.459909
\(711\) 12.3654 0.463740
\(712\) 13.7980 0.517101
\(713\) 59.0265 2.21056
\(714\) 0 0
\(715\) 28.9611 1.08308
\(716\) −26.8007 −1.00159
\(717\) 14.3115 0.534474
\(718\) −8.25632 −0.308123
\(719\) −29.0002 −1.08152 −0.540762 0.841176i \(-0.681864\pi\)
−0.540762 + 0.841176i \(0.681864\pi\)
\(720\) 4.23288 0.157750
\(721\) 0 0
\(722\) 23.7182 0.882699
\(723\) 27.0366 1.00550
\(724\) −25.0851 −0.932280
\(725\) 34.6456 1.28670
\(726\) −8.44910 −0.313575
\(727\) 29.4341 1.09165 0.545826 0.837899i \(-0.316216\pi\)
0.545826 + 0.837899i \(0.316216\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 24.5194 0.907502
\(731\) −2.02611 −0.0749384
\(732\) −12.2941 −0.454404
\(733\) −22.9658 −0.848261 −0.424130 0.905601i \(-0.639420\pi\)
−0.424130 + 0.905601i \(0.639420\pi\)
\(734\) −26.3314 −0.971909
\(735\) 0 0
\(736\) 35.6127 1.31270
\(737\) −29.1096 −1.07227
\(738\) −0.718443 −0.0264462
\(739\) −8.80545 −0.323914 −0.161957 0.986798i \(-0.551781\pi\)
−0.161957 + 0.986798i \(0.551781\pi\)
\(740\) 49.9025 1.83445
\(741\) 12.0958 0.444350
\(742\) 0 0
\(743\) −7.42487 −0.272392 −0.136196 0.990682i \(-0.543488\pi\)
−0.136196 + 0.990682i \(0.543488\pi\)
\(744\) 24.2525 0.889141
\(745\) 36.6534 1.34288
\(746\) 17.2370 0.631092
\(747\) 8.22541 0.300952
\(748\) 29.0816 1.06333
\(749\) 0 0
\(750\) −8.06343 −0.294435
\(751\) −19.7969 −0.722398 −0.361199 0.932489i \(-0.617633\pi\)
−0.361199 + 0.932489i \(0.617633\pi\)
\(752\) 1.08704 0.0396403
\(753\) 2.15039 0.0783647
\(754\) 5.15332 0.187673
\(755\) −49.7568 −1.81084
\(756\) 0 0
\(757\) −46.0253 −1.67282 −0.836410 0.548104i \(-0.815350\pi\)
−0.836410 + 0.548104i \(0.815350\pi\)
\(758\) 9.20286 0.334263
\(759\) −29.0623 −1.05489
\(760\) 65.3367 2.37001
\(761\) 15.3347 0.555882 0.277941 0.960598i \(-0.410348\pi\)
0.277941 + 0.960598i \(0.410348\pi\)
\(762\) 8.84594 0.320455
\(763\) 0 0
\(764\) −17.7401 −0.641813
\(765\) −14.8694 −0.537603
\(766\) −7.17903 −0.259389
\(767\) −0.463200 −0.0167252
\(768\) 11.1618 0.402766
\(769\) 51.0290 1.84015 0.920076 0.391740i \(-0.128127\pi\)
0.920076 + 0.391740i \(0.128127\pi\)
\(770\) 0 0
\(771\) −29.1832 −1.05101
\(772\) 16.7653 0.603397
\(773\) −19.1501 −0.688782 −0.344391 0.938826i \(-0.611915\pi\)
−0.344391 + 0.938826i \(0.611915\pi\)
\(774\) 0.354334 0.0127363
\(775\) 78.4940 2.81959
\(776\) 11.4160 0.409809
\(777\) 0 0
\(778\) −3.13308 −0.112326
\(779\) 7.21202 0.258398
\(780\) 9.00769 0.322527
\(781\) −22.4827 −0.804494
\(782\) −17.9794 −0.642942
\(783\) −4.27679 −0.152840
\(784\) 0 0
\(785\) 27.6164 0.985672
\(786\) 5.42951 0.193664
\(787\) 3.43549 0.122462 0.0612310 0.998124i \(-0.480497\pi\)
0.0612310 + 0.998124i \(0.480497\pi\)
\(788\) −22.6810 −0.807977
\(789\) −1.29066 −0.0459489
\(790\) 32.1552 1.14403
\(791\) 0 0
\(792\) −11.9410 −0.424304
\(793\) −13.8959 −0.493458
\(794\) −0.751397 −0.0266661
\(795\) −40.7532 −1.44537
\(796\) −29.6266 −1.05009
\(797\) 11.2344 0.397943 0.198971 0.980005i \(-0.436240\pi\)
0.198971 + 0.980005i \(0.436240\pi\)
\(798\) 0 0
\(799\) −3.81858 −0.135092
\(800\) 47.3580 1.67436
\(801\) −5.51271 −0.194782
\(802\) 24.7329 0.873349
\(803\) 44.9838 1.58745
\(804\) −9.05388 −0.319306
\(805\) 0 0
\(806\) 11.6755 0.411252
\(807\) −23.0819 −0.812523
\(808\) −16.3836 −0.576374
\(809\) −1.39828 −0.0491610 −0.0245805 0.999698i \(-0.507825\pi\)
−0.0245805 + 0.999698i \(0.507825\pi\)
\(810\) 2.60041 0.0913690
\(811\) −43.1209 −1.51418 −0.757089 0.653311i \(-0.773379\pi\)
−0.757089 + 0.653311i \(0.773379\pi\)
\(812\) 0 0
\(813\) −18.2013 −0.638349
\(814\) −31.8469 −1.11623
\(815\) −23.2531 −0.814519
\(816\) 4.80429 0.168184
\(817\) −3.55695 −0.124442
\(818\) 22.3125 0.780137
\(819\) 0 0
\(820\) 5.37077 0.187555
\(821\) −40.0686 −1.39840 −0.699202 0.714924i \(-0.746461\pi\)
−0.699202 + 0.714924i \(0.746461\pi\)
\(822\) −2.76628 −0.0964850
\(823\) −29.2972 −1.02124 −0.510619 0.859807i \(-0.670584\pi\)
−0.510619 + 0.859807i \(0.670584\pi\)
\(824\) 25.9791 0.905026
\(825\) −38.6473 −1.34552
\(826\) 0 0
\(827\) 19.6538 0.683429 0.341714 0.939804i \(-0.388992\pi\)
0.341714 + 0.939804i \(0.388992\pi\)
\(828\) −9.03915 −0.314132
\(829\) −45.6356 −1.58499 −0.792495 0.609878i \(-0.791218\pi\)
−0.792495 + 0.609878i \(0.791218\pi\)
\(830\) 21.3894 0.742438
\(831\) 19.3138 0.669988
\(832\) 3.12145 0.108217
\(833\) 0 0
\(834\) 13.2067 0.457310
\(835\) 80.8004 2.79621
\(836\) 51.0544 1.76575
\(837\) −9.68962 −0.334922
\(838\) −6.92729 −0.239299
\(839\) −46.1805 −1.59433 −0.797164 0.603763i \(-0.793667\pi\)
−0.797164 + 0.603763i \(0.793667\pi\)
\(840\) 0 0
\(841\) −10.7091 −0.369278
\(842\) 12.3248 0.424740
\(843\) 10.6700 0.367493
\(844\) 9.29828 0.320060
\(845\) −36.8723 −1.26845
\(846\) 0.667807 0.0229597
\(847\) 0 0
\(848\) 13.1673 0.452168
\(849\) −19.6343 −0.673849
\(850\) −23.9092 −0.820078
\(851\) −56.6013 −1.94027
\(852\) −6.99272 −0.239567
\(853\) 9.33699 0.319693 0.159846 0.987142i \(-0.448900\pi\)
0.159846 + 0.987142i \(0.448900\pi\)
\(854\) 0 0
\(855\) −26.1040 −0.892737
\(856\) −1.07164 −0.0366280
\(857\) 44.6137 1.52397 0.761987 0.647593i \(-0.224224\pi\)
0.761987 + 0.647593i \(0.224224\pi\)
\(858\) −5.74855 −0.196252
\(859\) 14.9917 0.511512 0.255756 0.966741i \(-0.417676\pi\)
0.255756 + 0.966741i \(0.417676\pi\)
\(860\) −2.64885 −0.0903250
\(861\) 0 0
\(862\) −22.0832 −0.752158
\(863\) −55.6314 −1.89371 −0.946857 0.321655i \(-0.895761\pi\)
−0.946857 + 0.321655i \(0.895761\pi\)
\(864\) −5.84607 −0.198887
\(865\) −8.44175 −0.287028
\(866\) 4.41752 0.150113
\(867\) 0.123387 0.00419043
\(868\) 0 0
\(869\) 58.9927 2.00119
\(870\) −11.1214 −0.377051
\(871\) −10.2335 −0.346749
\(872\) −23.0696 −0.781234
\(873\) −4.56102 −0.154367
\(874\) −31.5638 −1.06766
\(875\) 0 0
\(876\) 13.9912 0.472719
\(877\) −21.7454 −0.734291 −0.367145 0.930164i \(-0.619665\pi\)
−0.367145 + 0.930164i \(0.619665\pi\)
\(878\) −9.23470 −0.311656
\(879\) −6.13638 −0.206975
\(880\) 20.1941 0.680743
\(881\) 12.9402 0.435967 0.217984 0.975952i \(-0.430052\pi\)
0.217984 + 0.975952i \(0.430052\pi\)
\(882\) 0 0
\(883\) 32.5785 1.09636 0.548178 0.836362i \(-0.315322\pi\)
0.548178 + 0.836362i \(0.315322\pi\)
\(884\) 10.2237 0.343859
\(885\) 0.999635 0.0336024
\(886\) −10.4130 −0.349832
\(887\) 11.2722 0.378484 0.189242 0.981931i \(-0.439397\pi\)
0.189242 + 0.981931i \(0.439397\pi\)
\(888\) −23.2561 −0.780422
\(889\) 0 0
\(890\) −14.3353 −0.480520
\(891\) 4.77078 0.159827
\(892\) 35.6414 1.19336
\(893\) −6.70373 −0.224332
\(894\) −7.27540 −0.243326
\(895\) 65.3745 2.18523
\(896\) 0 0
\(897\) −10.2169 −0.341131
\(898\) −17.6665 −0.589538
\(899\) 41.4405 1.38212
\(900\) −12.0203 −0.400678
\(901\) −46.2545 −1.54096
\(902\) −3.42753 −0.114124
\(903\) 0 0
\(904\) −37.8958 −1.26039
\(905\) 61.1897 2.03401
\(906\) 9.87632 0.328119
\(907\) 32.1498 1.06752 0.533758 0.845638i \(-0.320780\pi\)
0.533758 + 0.845638i \(0.320780\pi\)
\(908\) −25.5472 −0.847814
\(909\) 6.54576 0.217109
\(910\) 0 0
\(911\) −29.0538 −0.962596 −0.481298 0.876557i \(-0.659835\pi\)
−0.481298 + 0.876557i \(0.659835\pi\)
\(912\) 8.43419 0.279284
\(913\) 39.2416 1.29871
\(914\) −21.9765 −0.726917
\(915\) 29.9888 0.991400
\(916\) −0.609396 −0.0201350
\(917\) 0 0
\(918\) 2.95145 0.0974122
\(919\) −32.7485 −1.08027 −0.540136 0.841578i \(-0.681627\pi\)
−0.540136 + 0.841578i \(0.681627\pi\)
\(920\) −55.1874 −1.81948
\(921\) −9.85765 −0.324821
\(922\) −1.79837 −0.0592262
\(923\) −7.90380 −0.260157
\(924\) 0 0
\(925\) −75.2689 −2.47483
\(926\) 2.42956 0.0798403
\(927\) −10.3795 −0.340906
\(928\) 25.0024 0.820744
\(929\) 2.69655 0.0884709 0.0442354 0.999021i \(-0.485915\pi\)
0.0442354 + 0.999021i \(0.485915\pi\)
\(930\) −25.1970 −0.826241
\(931\) 0 0
\(932\) −30.3898 −0.995451
\(933\) −20.2723 −0.663685
\(934\) −14.5867 −0.477292
\(935\) −70.9383 −2.31993
\(936\) −4.19785 −0.137211
\(937\) 4.00234 0.130751 0.0653753 0.997861i \(-0.479176\pi\)
0.0653753 + 0.997861i \(0.479176\pi\)
\(938\) 0 0
\(939\) −17.9597 −0.586092
\(940\) −4.99224 −0.162829
\(941\) −20.5073 −0.668518 −0.334259 0.942481i \(-0.608486\pi\)
−0.334259 + 0.942481i \(0.608486\pi\)
\(942\) −5.48163 −0.178601
\(943\) −6.09173 −0.198374
\(944\) −0.322982 −0.0105122
\(945\) 0 0
\(946\) 1.69045 0.0549612
\(947\) −37.4551 −1.21713 −0.608564 0.793505i \(-0.708254\pi\)
−0.608564 + 0.793505i \(0.708254\pi\)
\(948\) 18.3483 0.595926
\(949\) 15.8141 0.513347
\(950\) −41.9739 −1.36181
\(951\) −26.1554 −0.848146
\(952\) 0 0
\(953\) −18.1604 −0.588273 −0.294137 0.955763i \(-0.595032\pi\)
−0.294137 + 0.955763i \(0.595032\pi\)
\(954\) 8.08917 0.261896
\(955\) 43.2731 1.40028
\(956\) 21.2360 0.686823
\(957\) −20.4036 −0.659555
\(958\) −20.8806 −0.674622
\(959\) 0 0
\(960\) −6.73642 −0.217417
\(961\) 62.8888 2.02867
\(962\) −11.1958 −0.360967
\(963\) 0.428154 0.0137971
\(964\) 40.1179 1.29211
\(965\) −40.8953 −1.31647
\(966\) 0 0
\(967\) −11.7555 −0.378032 −0.189016 0.981974i \(-0.560530\pi\)
−0.189016 + 0.981974i \(0.560530\pi\)
\(968\) −29.4353 −0.946086
\(969\) −29.6278 −0.951783
\(970\) −11.8605 −0.380819
\(971\) −40.4149 −1.29698 −0.648489 0.761224i \(-0.724599\pi\)
−0.648489 + 0.761224i \(0.724599\pi\)
\(972\) 1.48384 0.0475942
\(973\) 0 0
\(974\) 2.57718 0.0825781
\(975\) −13.5865 −0.435115
\(976\) −9.68939 −0.310150
\(977\) −5.19469 −0.166193 −0.0830965 0.996542i \(-0.526481\pi\)
−0.0830965 + 0.996542i \(0.526481\pi\)
\(978\) 4.61554 0.147589
\(979\) −26.2999 −0.840548
\(980\) 0 0
\(981\) 9.21699 0.294276
\(982\) −9.26409 −0.295629
\(983\) −4.47416 −0.142704 −0.0713518 0.997451i \(-0.522731\pi\)
−0.0713518 + 0.997451i \(0.522731\pi\)
\(984\) −2.50294 −0.0797908
\(985\) 55.3254 1.76281
\(986\) −12.6227 −0.401989
\(987\) 0 0
\(988\) 17.9482 0.571009
\(989\) 3.00442 0.0955351
\(990\) 12.4060 0.394287
\(991\) 40.0982 1.27376 0.636881 0.770963i \(-0.280224\pi\)
0.636881 + 0.770963i \(0.280224\pi\)
\(992\) 56.6462 1.79852
\(993\) 4.78518 0.151853
\(994\) 0 0
\(995\) 72.2676 2.29104
\(996\) 12.2052 0.386736
\(997\) −18.2843 −0.579069 −0.289534 0.957168i \(-0.593500\pi\)
−0.289534 + 0.957168i \(0.593500\pi\)
\(998\) −21.4317 −0.678409
\(999\) 9.29150 0.293970
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 \(a_p\))