Properties

Label 6027.2.a.bn.1.21
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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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: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} -5.88785 q^{10} +4.46600 q^{11} -4.19062 q^{12} +5.01637 q^{13} +2.36641 q^{15} +5.18004 q^{16} -4.88608 q^{17} +2.48810 q^{18} +3.64438 q^{19} -9.91672 q^{20} +11.1118 q^{22} -2.22001 q^{23} -5.45047 q^{24} +0.599893 q^{25} +12.4812 q^{26} -1.00000 q^{27} +2.88239 q^{29} +5.88785 q^{30} -1.18084 q^{31} +1.98751 q^{32} -4.46600 q^{33} -12.1570 q^{34} +4.19062 q^{36} -0.748295 q^{37} +9.06756 q^{38} -5.01637 q^{39} -12.8980 q^{40} +1.00000 q^{41} +6.98238 q^{43} +18.7153 q^{44} -2.36641 q^{45} -5.52359 q^{46} +7.64313 q^{47} -5.18004 q^{48} +1.49259 q^{50} +4.88608 q^{51} +21.0217 q^{52} +10.3267 q^{53} -2.48810 q^{54} -10.5684 q^{55} -3.64438 q^{57} +7.17166 q^{58} -8.70177 q^{59} +9.91672 q^{60} -8.35367 q^{61} -2.93804 q^{62} -5.41498 q^{64} -11.8708 q^{65} -11.1118 q^{66} -0.0922892 q^{67} -20.4757 q^{68} +2.22001 q^{69} +3.08552 q^{71} +5.45047 q^{72} +9.88365 q^{73} -1.86183 q^{74} -0.599893 q^{75} +15.2722 q^{76} -12.4812 q^{78} +7.87830 q^{79} -12.2581 q^{80} +1.00000 q^{81} +2.48810 q^{82} +6.26355 q^{83} +11.5625 q^{85} +17.3728 q^{86} -2.88239 q^{87} +24.3418 q^{88} +10.3142 q^{89} -5.88785 q^{90} -9.30321 q^{92} +1.18084 q^{93} +19.0168 q^{94} -8.62409 q^{95} -1.98751 q^{96} +4.64324 q^{97} +4.46600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.48810 1.75935 0.879675 0.475576i \(-0.157760\pi\)
0.879675 + 0.475576i \(0.157760\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.19062 2.09531
\(5\) −2.36641 −1.05829 −0.529145 0.848531i \(-0.677487\pi\)
−0.529145 + 0.848531i \(0.677487\pi\)
\(6\) −2.48810 −1.01576
\(7\) 0 0
\(8\) 5.45047 1.92703
\(9\) 1.00000 0.333333
\(10\) −5.88785 −1.86190
\(11\) 4.46600 1.34655 0.673275 0.739392i \(-0.264887\pi\)
0.673275 + 0.739392i \(0.264887\pi\)
\(12\) −4.19062 −1.20973
\(13\) 5.01637 1.39129 0.695645 0.718385i \(-0.255118\pi\)
0.695645 + 0.718385i \(0.255118\pi\)
\(14\) 0 0
\(15\) 2.36641 0.611004
\(16\) 5.18004 1.29501
\(17\) −4.88608 −1.18505 −0.592524 0.805552i \(-0.701869\pi\)
−0.592524 + 0.805552i \(0.701869\pi\)
\(18\) 2.48810 0.586450
\(19\) 3.64438 0.836078 0.418039 0.908429i \(-0.362718\pi\)
0.418039 + 0.908429i \(0.362718\pi\)
\(20\) −9.91672 −2.21745
\(21\) 0 0
\(22\) 11.1118 2.36905
\(23\) −2.22001 −0.462904 −0.231452 0.972846i \(-0.574348\pi\)
−0.231452 + 0.972846i \(0.574348\pi\)
\(24\) −5.45047 −1.11257
\(25\) 0.599893 0.119979
\(26\) 12.4812 2.44777
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.88239 0.535246 0.267623 0.963524i \(-0.413762\pi\)
0.267623 + 0.963524i \(0.413762\pi\)
\(30\) 5.88785 1.07497
\(31\) −1.18084 −0.212085 −0.106043 0.994362i \(-0.533818\pi\)
−0.106043 + 0.994362i \(0.533818\pi\)
\(32\) 1.98751 0.351345
\(33\) −4.46600 −0.777431
\(34\) −12.1570 −2.08491
\(35\) 0 0
\(36\) 4.19062 0.698436
\(37\) −0.748295 −0.123019 −0.0615095 0.998107i \(-0.519591\pi\)
−0.0615095 + 0.998107i \(0.519591\pi\)
\(38\) 9.06756 1.47095
\(39\) −5.01637 −0.803262
\(40\) −12.8980 −2.03936
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 6.98238 1.06480 0.532402 0.846492i \(-0.321290\pi\)
0.532402 + 0.846492i \(0.321290\pi\)
\(44\) 18.7153 2.82144
\(45\) −2.36641 −0.352763
\(46\) −5.52359 −0.814409
\(47\) 7.64313 1.11486 0.557432 0.830222i \(-0.311787\pi\)
0.557432 + 0.830222i \(0.311787\pi\)
\(48\) −5.18004 −0.747675
\(49\) 0 0
\(50\) 1.49259 0.211084
\(51\) 4.88608 0.684188
\(52\) 21.0217 2.91518
\(53\) 10.3267 1.41848 0.709238 0.704969i \(-0.249039\pi\)
0.709238 + 0.704969i \(0.249039\pi\)
\(54\) −2.48810 −0.338587
\(55\) −10.5684 −1.42504
\(56\) 0 0
\(57\) −3.64438 −0.482710
\(58\) 7.17166 0.941685
\(59\) −8.70177 −1.13287 −0.566437 0.824105i \(-0.691679\pi\)
−0.566437 + 0.824105i \(0.691679\pi\)
\(60\) 9.91672 1.28024
\(61\) −8.35367 −1.06958 −0.534789 0.844986i \(-0.679609\pi\)
−0.534789 + 0.844986i \(0.679609\pi\)
\(62\) −2.93804 −0.373132
\(63\) 0 0
\(64\) −5.41498 −0.676872
\(65\) −11.8708 −1.47239
\(66\) −11.1118 −1.36777
\(67\) −0.0922892 −0.0112749 −0.00563746 0.999984i \(-0.501794\pi\)
−0.00563746 + 0.999984i \(0.501794\pi\)
\(68\) −20.4757 −2.48304
\(69\) 2.22001 0.267258
\(70\) 0 0
\(71\) 3.08552 0.366184 0.183092 0.983096i \(-0.441389\pi\)
0.183092 + 0.983096i \(0.441389\pi\)
\(72\) 5.45047 0.642344
\(73\) 9.88365 1.15679 0.578397 0.815755i \(-0.303678\pi\)
0.578397 + 0.815755i \(0.303678\pi\)
\(74\) −1.86183 −0.216433
\(75\) −0.599893 −0.0692696
\(76\) 15.2722 1.75184
\(77\) 0 0
\(78\) −12.4812 −1.41322
\(79\) 7.87830 0.886378 0.443189 0.896428i \(-0.353847\pi\)
0.443189 + 0.896428i \(0.353847\pi\)
\(80\) −12.2581 −1.37050
\(81\) 1.00000 0.111111
\(82\) 2.48810 0.274764
\(83\) 6.26355 0.687514 0.343757 0.939059i \(-0.388300\pi\)
0.343757 + 0.939059i \(0.388300\pi\)
\(84\) 0 0
\(85\) 11.5625 1.25413
\(86\) 17.3728 1.87336
\(87\) −2.88239 −0.309024
\(88\) 24.3418 2.59484
\(89\) 10.3142 1.09330 0.546652 0.837360i \(-0.315902\pi\)
0.546652 + 0.837360i \(0.315902\pi\)
\(90\) −5.88785 −0.620634
\(91\) 0 0
\(92\) −9.30321 −0.969926
\(93\) 1.18084 0.122447
\(94\) 19.0168 1.96144
\(95\) −8.62409 −0.884813
\(96\) −1.98751 −0.202849
\(97\) 4.64324 0.471449 0.235725 0.971820i \(-0.424254\pi\)
0.235725 + 0.971820i \(0.424254\pi\)
\(98\) 0 0
\(99\) 4.46600 0.448850
\(100\) 2.51392 0.251392
\(101\) 13.8197 1.37511 0.687555 0.726133i \(-0.258684\pi\)
0.687555 + 0.726133i \(0.258684\pi\)
\(102\) 12.1570 1.20373
\(103\) 13.0191 1.28281 0.641403 0.767204i \(-0.278353\pi\)
0.641403 + 0.767204i \(0.278353\pi\)
\(104\) 27.3416 2.68106
\(105\) 0 0
\(106\) 25.6937 2.49560
\(107\) −19.9762 −1.93117 −0.965586 0.260083i \(-0.916250\pi\)
−0.965586 + 0.260083i \(0.916250\pi\)
\(108\) −4.19062 −0.403242
\(109\) 4.41695 0.423067 0.211533 0.977371i \(-0.432154\pi\)
0.211533 + 0.977371i \(0.432154\pi\)
\(110\) −26.2952 −2.50714
\(111\) 0.748295 0.0710250
\(112\) 0 0
\(113\) −14.4815 −1.36230 −0.681151 0.732143i \(-0.738520\pi\)
−0.681151 + 0.732143i \(0.738520\pi\)
\(114\) −9.06756 −0.849255
\(115\) 5.25345 0.489887
\(116\) 12.0790 1.12151
\(117\) 5.01637 0.463764
\(118\) −21.6508 −1.99312
\(119\) 0 0
\(120\) 12.8980 1.17742
\(121\) 8.94517 0.813197
\(122\) −20.7847 −1.88176
\(123\) −1.00000 −0.0901670
\(124\) −4.94845 −0.444384
\(125\) 10.4125 0.931318
\(126\) 0 0
\(127\) 17.9357 1.59154 0.795769 0.605600i \(-0.207067\pi\)
0.795769 + 0.605600i \(0.207067\pi\)
\(128\) −17.4480 −1.54220
\(129\) −6.98238 −0.614765
\(130\) −29.5356 −2.59045
\(131\) −1.81416 −0.158504 −0.0792518 0.996855i \(-0.525253\pi\)
−0.0792518 + 0.996855i \(0.525253\pi\)
\(132\) −18.7153 −1.62896
\(133\) 0 0
\(134\) −0.229624 −0.0198365
\(135\) 2.36641 0.203668
\(136\) −26.6314 −2.28363
\(137\) 10.3191 0.881623 0.440811 0.897600i \(-0.354691\pi\)
0.440811 + 0.897600i \(0.354691\pi\)
\(138\) 5.52359 0.470199
\(139\) 12.1318 1.02901 0.514504 0.857488i \(-0.327976\pi\)
0.514504 + 0.857488i \(0.327976\pi\)
\(140\) 0 0
\(141\) −7.64313 −0.643667
\(142\) 7.67708 0.644246
\(143\) 22.4031 1.87344
\(144\) 5.18004 0.431670
\(145\) −6.82091 −0.566446
\(146\) 24.5915 2.03520
\(147\) 0 0
\(148\) −3.13582 −0.257763
\(149\) −16.8170 −1.37771 −0.688853 0.724901i \(-0.741886\pi\)
−0.688853 + 0.724901i \(0.741886\pi\)
\(150\) −1.49259 −0.121869
\(151\) −16.1017 −1.31034 −0.655168 0.755483i \(-0.727402\pi\)
−0.655168 + 0.755483i \(0.727402\pi\)
\(152\) 19.8636 1.61115
\(153\) −4.88608 −0.395016
\(154\) 0 0
\(155\) 2.79435 0.224448
\(156\) −21.0217 −1.68308
\(157\) −7.43656 −0.593502 −0.296751 0.954955i \(-0.595903\pi\)
−0.296751 + 0.954955i \(0.595903\pi\)
\(158\) 19.6020 1.55945
\(159\) −10.3267 −0.818958
\(160\) −4.70326 −0.371825
\(161\) 0 0
\(162\) 2.48810 0.195483
\(163\) 19.1144 1.49715 0.748576 0.663049i \(-0.230738\pi\)
0.748576 + 0.663049i \(0.230738\pi\)
\(164\) 4.19062 0.327232
\(165\) 10.5684 0.822748
\(166\) 15.5843 1.20958
\(167\) 3.05717 0.236571 0.118285 0.992980i \(-0.462260\pi\)
0.118285 + 0.992980i \(0.462260\pi\)
\(168\) 0 0
\(169\) 12.1640 0.935690
\(170\) 28.7685 2.20645
\(171\) 3.64438 0.278693
\(172\) 29.2605 2.23109
\(173\) −12.6063 −0.958439 −0.479219 0.877695i \(-0.659080\pi\)
−0.479219 + 0.877695i \(0.659080\pi\)
\(174\) −7.17166 −0.543682
\(175\) 0 0
\(176\) 23.1341 1.74380
\(177\) 8.70177 0.654065
\(178\) 25.6627 1.92350
\(179\) −6.53673 −0.488578 −0.244289 0.969702i \(-0.578555\pi\)
−0.244289 + 0.969702i \(0.578555\pi\)
\(180\) −9.91672 −0.739148
\(181\) −1.75566 −0.130497 −0.0652487 0.997869i \(-0.520784\pi\)
−0.0652487 + 0.997869i \(0.520784\pi\)
\(182\) 0 0
\(183\) 8.35367 0.617521
\(184\) −12.1001 −0.892030
\(185\) 1.77077 0.130190
\(186\) 2.93804 0.215428
\(187\) −21.8212 −1.59573
\(188\) 32.0294 2.33599
\(189\) 0 0
\(190\) −21.4576 −1.55669
\(191\) 3.79254 0.274418 0.137209 0.990542i \(-0.456187\pi\)
0.137209 + 0.990542i \(0.456187\pi\)
\(192\) 5.41498 0.390792
\(193\) −0.179574 −0.0129260 −0.00646302 0.999979i \(-0.502057\pi\)
−0.00646302 + 0.999979i \(0.502057\pi\)
\(194\) 11.5528 0.829444
\(195\) 11.8708 0.850085
\(196\) 0 0
\(197\) −13.2115 −0.941280 −0.470640 0.882325i \(-0.655977\pi\)
−0.470640 + 0.882325i \(0.655977\pi\)
\(198\) 11.1118 0.789684
\(199\) −5.46727 −0.387564 −0.193782 0.981045i \(-0.562075\pi\)
−0.193782 + 0.981045i \(0.562075\pi\)
\(200\) 3.26969 0.231202
\(201\) 0.0922892 0.00650958
\(202\) 34.3847 2.41930
\(203\) 0 0
\(204\) 20.4757 1.43359
\(205\) −2.36641 −0.165277
\(206\) 32.3926 2.25690
\(207\) −2.22001 −0.154301
\(208\) 25.9850 1.80174
\(209\) 16.2758 1.12582
\(210\) 0 0
\(211\) 12.8035 0.881430 0.440715 0.897647i \(-0.354725\pi\)
0.440715 + 0.897647i \(0.354725\pi\)
\(212\) 43.2751 2.97215
\(213\) −3.08552 −0.211417
\(214\) −49.7027 −3.39761
\(215\) −16.5232 −1.12687
\(216\) −5.45047 −0.370857
\(217\) 0 0
\(218\) 10.9898 0.744322
\(219\) −9.88365 −0.667875
\(220\) −44.2881 −2.98590
\(221\) −24.5104 −1.64875
\(222\) 1.86183 0.124958
\(223\) 1.61990 0.108477 0.0542383 0.998528i \(-0.482727\pi\)
0.0542383 + 0.998528i \(0.482727\pi\)
\(224\) 0 0
\(225\) 0.599893 0.0399928
\(226\) −36.0313 −2.39676
\(227\) 7.09352 0.470813 0.235407 0.971897i \(-0.424358\pi\)
0.235407 + 0.971897i \(0.424358\pi\)
\(228\) −15.2722 −1.01143
\(229\) −10.2801 −0.679326 −0.339663 0.940547i \(-0.610313\pi\)
−0.339663 + 0.940547i \(0.610313\pi\)
\(230\) 13.0711 0.861882
\(231\) 0 0
\(232\) 15.7104 1.03144
\(233\) 26.2441 1.71931 0.859656 0.510874i \(-0.170678\pi\)
0.859656 + 0.510874i \(0.170678\pi\)
\(234\) 12.4812 0.815922
\(235\) −18.0868 −1.17985
\(236\) −36.4658 −2.37372
\(237\) −7.87830 −0.511750
\(238\) 0 0
\(239\) 9.99590 0.646581 0.323290 0.946300i \(-0.395211\pi\)
0.323290 + 0.946300i \(0.395211\pi\)
\(240\) 12.2581 0.791257
\(241\) 2.67886 0.172560 0.0862801 0.996271i \(-0.472502\pi\)
0.0862801 + 0.996271i \(0.472502\pi\)
\(242\) 22.2564 1.43070
\(243\) −1.00000 −0.0641500
\(244\) −35.0071 −2.24110
\(245\) 0 0
\(246\) −2.48810 −0.158635
\(247\) 18.2815 1.16323
\(248\) −6.43613 −0.408695
\(249\) −6.26355 −0.396936
\(250\) 25.9072 1.63851
\(251\) 23.4644 1.48106 0.740529 0.672024i \(-0.234575\pi\)
0.740529 + 0.672024i \(0.234575\pi\)
\(252\) 0 0
\(253\) −9.91456 −0.623323
\(254\) 44.6258 2.80007
\(255\) −11.5625 −0.724070
\(256\) −32.5823 −2.03639
\(257\) −20.6351 −1.28718 −0.643590 0.765370i \(-0.722556\pi\)
−0.643590 + 0.765370i \(0.722556\pi\)
\(258\) −17.3728 −1.08159
\(259\) 0 0
\(260\) −49.7459 −3.08511
\(261\) 2.88239 0.178415
\(262\) −4.51380 −0.278863
\(263\) 10.4139 0.642152 0.321076 0.947054i \(-0.395956\pi\)
0.321076 + 0.947054i \(0.395956\pi\)
\(264\) −24.3418 −1.49813
\(265\) −24.4371 −1.50116
\(266\) 0 0
\(267\) −10.3142 −0.631219
\(268\) −0.386749 −0.0236244
\(269\) −18.0405 −1.09995 −0.549973 0.835182i \(-0.685362\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(270\) 5.88785 0.358323
\(271\) 30.1360 1.83063 0.915315 0.402739i \(-0.131942\pi\)
0.915315 + 0.402739i \(0.131942\pi\)
\(272\) −25.3101 −1.53465
\(273\) 0 0
\(274\) 25.6750 1.55108
\(275\) 2.67912 0.161557
\(276\) 9.30321 0.559987
\(277\) −15.2878 −0.918558 −0.459279 0.888292i \(-0.651892\pi\)
−0.459279 + 0.888292i \(0.651892\pi\)
\(278\) 30.1851 1.81038
\(279\) −1.18084 −0.0706950
\(280\) 0 0
\(281\) 4.02679 0.240218 0.120109 0.992761i \(-0.461676\pi\)
0.120109 + 0.992761i \(0.461676\pi\)
\(282\) −19.0168 −1.13244
\(283\) −18.0462 −1.07274 −0.536368 0.843984i \(-0.680204\pi\)
−0.536368 + 0.843984i \(0.680204\pi\)
\(284\) 12.9303 0.767269
\(285\) 8.62409 0.510847
\(286\) 55.7411 3.29604
\(287\) 0 0
\(288\) 1.98751 0.117115
\(289\) 6.87380 0.404341
\(290\) −16.9711 −0.996576
\(291\) −4.64324 −0.272191
\(292\) 41.4186 2.42384
\(293\) −5.56871 −0.325327 −0.162664 0.986682i \(-0.552009\pi\)
−0.162664 + 0.986682i \(0.552009\pi\)
\(294\) 0 0
\(295\) 20.5920 1.19891
\(296\) −4.07856 −0.237061
\(297\) −4.46600 −0.259144
\(298\) −41.8424 −2.42387
\(299\) −11.1364 −0.644034
\(300\) −2.51392 −0.145141
\(301\) 0 0
\(302\) −40.0625 −2.30534
\(303\) −13.8197 −0.793920
\(304\) 18.8780 1.08273
\(305\) 19.7682 1.13192
\(306\) −12.1570 −0.694972
\(307\) 20.3285 1.16021 0.580106 0.814541i \(-0.303011\pi\)
0.580106 + 0.814541i \(0.303011\pi\)
\(308\) 0 0
\(309\) −13.0191 −0.740628
\(310\) 6.95261 0.394882
\(311\) 24.9893 1.41701 0.708505 0.705705i \(-0.249370\pi\)
0.708505 + 0.705705i \(0.249370\pi\)
\(312\) −27.3416 −1.54791
\(313\) 19.0197 1.07506 0.537529 0.843245i \(-0.319358\pi\)
0.537529 + 0.843245i \(0.319358\pi\)
\(314\) −18.5029 −1.04418
\(315\) 0 0
\(316\) 33.0149 1.85724
\(317\) −26.7130 −1.50035 −0.750177 0.661237i \(-0.770032\pi\)
−0.750177 + 0.661237i \(0.770032\pi\)
\(318\) −25.6937 −1.44083
\(319\) 12.8728 0.720736
\(320\) 12.8140 0.716327
\(321\) 19.9762 1.11496
\(322\) 0 0
\(323\) −17.8067 −0.990793
\(324\) 4.19062 0.232812
\(325\) 3.00928 0.166925
\(326\) 47.5583 2.63401
\(327\) −4.41695 −0.244258
\(328\) 5.45047 0.300952
\(329\) 0 0
\(330\) 26.2952 1.44750
\(331\) −28.7281 −1.57904 −0.789519 0.613726i \(-0.789670\pi\)
−0.789519 + 0.613726i \(0.789670\pi\)
\(332\) 26.2481 1.44055
\(333\) −0.748295 −0.0410063
\(334\) 7.60652 0.416210
\(335\) 0.218394 0.0119321
\(336\) 0 0
\(337\) 5.39749 0.294020 0.147010 0.989135i \(-0.453035\pi\)
0.147010 + 0.989135i \(0.453035\pi\)
\(338\) 30.2651 1.64621
\(339\) 14.4815 0.786525
\(340\) 48.4539 2.62778
\(341\) −5.27363 −0.285583
\(342\) 9.06756 0.490317
\(343\) 0 0
\(344\) 38.0573 2.05191
\(345\) −5.25345 −0.282836
\(346\) −31.3657 −1.68623
\(347\) −11.2384 −0.603308 −0.301654 0.953418i \(-0.597539\pi\)
−0.301654 + 0.953418i \(0.597539\pi\)
\(348\) −12.0790 −0.647502
\(349\) 32.7910 1.75526 0.877631 0.479337i \(-0.159123\pi\)
0.877631 + 0.479337i \(0.159123\pi\)
\(350\) 0 0
\(351\) −5.01637 −0.267754
\(352\) 8.87622 0.473104
\(353\) −37.0316 −1.97099 −0.985496 0.169699i \(-0.945720\pi\)
−0.985496 + 0.169699i \(0.945720\pi\)
\(354\) 21.6508 1.15073
\(355\) −7.30161 −0.387529
\(356\) 43.2229 2.29081
\(357\) 0 0
\(358\) −16.2640 −0.859579
\(359\) −28.8297 −1.52157 −0.760786 0.649003i \(-0.775186\pi\)
−0.760786 + 0.649003i \(0.775186\pi\)
\(360\) −12.8980 −0.679786
\(361\) −5.71851 −0.300974
\(362\) −4.36826 −0.229590
\(363\) −8.94517 −0.469499
\(364\) 0 0
\(365\) −23.3888 −1.22422
\(366\) 20.7847 1.08644
\(367\) −30.4855 −1.59133 −0.795664 0.605738i \(-0.792878\pi\)
−0.795664 + 0.605738i \(0.792878\pi\)
\(368\) −11.4997 −0.599465
\(369\) 1.00000 0.0520579
\(370\) 4.40585 0.229049
\(371\) 0 0
\(372\) 4.94845 0.256565
\(373\) 11.0618 0.572758 0.286379 0.958116i \(-0.407548\pi\)
0.286379 + 0.958116i \(0.407548\pi\)
\(374\) −54.2933 −2.80744
\(375\) −10.4125 −0.537697
\(376\) 41.6586 2.14838
\(377\) 14.4591 0.744683
\(378\) 0 0
\(379\) 18.5413 0.952404 0.476202 0.879336i \(-0.342013\pi\)
0.476202 + 0.879336i \(0.342013\pi\)
\(380\) −36.1403 −1.85396
\(381\) −17.9357 −0.918875
\(382\) 9.43620 0.482798
\(383\) −25.7669 −1.31663 −0.658313 0.752745i \(-0.728729\pi\)
−0.658313 + 0.752745i \(0.728729\pi\)
\(384\) 17.4480 0.890389
\(385\) 0 0
\(386\) −0.446798 −0.0227414
\(387\) 6.98238 0.354935
\(388\) 19.4580 0.987832
\(389\) 8.98025 0.455317 0.227658 0.973741i \(-0.426893\pi\)
0.227658 + 0.973741i \(0.426893\pi\)
\(390\) 29.5356 1.49560
\(391\) 10.8471 0.548564
\(392\) 0 0
\(393\) 1.81416 0.0915121
\(394\) −32.8715 −1.65604
\(395\) −18.6433 −0.938045
\(396\) 18.7153 0.940479
\(397\) −29.8142 −1.49633 −0.748165 0.663513i \(-0.769065\pi\)
−0.748165 + 0.663513i \(0.769065\pi\)
\(398\) −13.6031 −0.681861
\(399\) 0 0
\(400\) 3.10747 0.155373
\(401\) 30.6347 1.52983 0.764913 0.644134i \(-0.222782\pi\)
0.764913 + 0.644134i \(0.222782\pi\)
\(402\) 0.229624 0.0114526
\(403\) −5.92353 −0.295072
\(404\) 57.9130 2.88128
\(405\) −2.36641 −0.117588
\(406\) 0 0
\(407\) −3.34189 −0.165651
\(408\) 26.6314 1.31845
\(409\) −9.88842 −0.488951 −0.244475 0.969656i \(-0.578616\pi\)
−0.244475 + 0.969656i \(0.578616\pi\)
\(410\) −5.88785 −0.290780
\(411\) −10.3191 −0.509005
\(412\) 54.5579 2.68787
\(413\) 0 0
\(414\) −5.52359 −0.271470
\(415\) −14.8221 −0.727589
\(416\) 9.97008 0.488823
\(417\) −12.1318 −0.594098
\(418\) 40.4957 1.98071
\(419\) 7.68415 0.375395 0.187698 0.982227i \(-0.439897\pi\)
0.187698 + 0.982227i \(0.439897\pi\)
\(420\) 0 0
\(421\) −5.53541 −0.269780 −0.134890 0.990861i \(-0.543068\pi\)
−0.134890 + 0.990861i \(0.543068\pi\)
\(422\) 31.8563 1.55074
\(423\) 7.64313 0.371622
\(424\) 56.2851 2.73345
\(425\) −2.93112 −0.142180
\(426\) −7.67708 −0.371956
\(427\) 0 0
\(428\) −83.7126 −4.04640
\(429\) −22.4031 −1.08163
\(430\) −41.1112 −1.98256
\(431\) −34.5461 −1.66403 −0.832014 0.554755i \(-0.812812\pi\)
−0.832014 + 0.554755i \(0.812812\pi\)
\(432\) −5.18004 −0.249225
\(433\) 1.93996 0.0932284 0.0466142 0.998913i \(-0.485157\pi\)
0.0466142 + 0.998913i \(0.485157\pi\)
\(434\) 0 0
\(435\) 6.82091 0.327038
\(436\) 18.5097 0.886455
\(437\) −8.09055 −0.387023
\(438\) −24.5915 −1.17503
\(439\) −36.9625 −1.76412 −0.882062 0.471134i \(-0.843845\pi\)
−0.882062 + 0.471134i \(0.843845\pi\)
\(440\) −57.6026 −2.74610
\(441\) 0 0
\(442\) −60.9842 −2.90072
\(443\) −28.9153 −1.37381 −0.686903 0.726749i \(-0.741030\pi\)
−0.686903 + 0.726749i \(0.741030\pi\)
\(444\) 3.13582 0.148819
\(445\) −24.4076 −1.15703
\(446\) 4.03047 0.190848
\(447\) 16.8170 0.795419
\(448\) 0 0
\(449\) −8.04865 −0.379839 −0.189920 0.981800i \(-0.560823\pi\)
−0.189920 + 0.981800i \(0.560823\pi\)
\(450\) 1.49259 0.0703614
\(451\) 4.46600 0.210296
\(452\) −60.6863 −2.85444
\(453\) 16.1017 0.756523
\(454\) 17.6493 0.828325
\(455\) 0 0
\(456\) −19.8636 −0.930196
\(457\) 4.73364 0.221430 0.110715 0.993852i \(-0.464686\pi\)
0.110715 + 0.993852i \(0.464686\pi\)
\(458\) −25.5778 −1.19517
\(459\) 4.88608 0.228063
\(460\) 22.0152 1.02646
\(461\) −36.8719 −1.71730 −0.858648 0.512567i \(-0.828695\pi\)
−0.858648 + 0.512567i \(0.828695\pi\)
\(462\) 0 0
\(463\) 11.4447 0.531880 0.265940 0.963990i \(-0.414318\pi\)
0.265940 + 0.963990i \(0.414318\pi\)
\(464\) 14.9309 0.693150
\(465\) −2.79435 −0.129585
\(466\) 65.2979 3.02487
\(467\) −9.31809 −0.431190 −0.215595 0.976483i \(-0.569169\pi\)
−0.215595 + 0.976483i \(0.569169\pi\)
\(468\) 21.0217 0.971728
\(469\) 0 0
\(470\) −45.0016 −2.07577
\(471\) 7.43656 0.342658
\(472\) −47.4287 −2.18308
\(473\) 31.1833 1.43381
\(474\) −19.6020 −0.900348
\(475\) 2.18624 0.100311
\(476\) 0 0
\(477\) 10.3267 0.472826
\(478\) 24.8707 1.13756
\(479\) −39.5784 −1.80838 −0.904191 0.427128i \(-0.859525\pi\)
−0.904191 + 0.427128i \(0.859525\pi\)
\(480\) 4.70326 0.214673
\(481\) −3.75372 −0.171155
\(482\) 6.66525 0.303594
\(483\) 0 0
\(484\) 37.4858 1.70390
\(485\) −10.9878 −0.498930
\(486\) −2.48810 −0.112862
\(487\) 25.9347 1.17521 0.587607 0.809147i \(-0.300070\pi\)
0.587607 + 0.809147i \(0.300070\pi\)
\(488\) −45.5314 −2.06111
\(489\) −19.1144 −0.864381
\(490\) 0 0
\(491\) −11.5856 −0.522851 −0.261426 0.965224i \(-0.584193\pi\)
−0.261426 + 0.965224i \(0.584193\pi\)
\(492\) −4.19062 −0.188928
\(493\) −14.0836 −0.634293
\(494\) 45.4862 2.04652
\(495\) −10.5684 −0.475014
\(496\) −6.11680 −0.274653
\(497\) 0 0
\(498\) −15.5843 −0.698349
\(499\) 22.5754 1.01061 0.505306 0.862940i \(-0.331380\pi\)
0.505306 + 0.862940i \(0.331380\pi\)
\(500\) 43.6346 1.95140
\(501\) −3.05717 −0.136584
\(502\) 58.3816 2.60570
\(503\) −23.5474 −1.04993 −0.524963 0.851125i \(-0.675921\pi\)
−0.524963 + 0.851125i \(0.675921\pi\)
\(504\) 0 0
\(505\) −32.7030 −1.45527
\(506\) −24.6684 −1.09664
\(507\) −12.1640 −0.540221
\(508\) 75.1618 3.33476
\(509\) −27.1606 −1.20387 −0.601937 0.798543i \(-0.705604\pi\)
−0.601937 + 0.798543i \(0.705604\pi\)
\(510\) −28.7685 −1.27389
\(511\) 0 0
\(512\) −46.1719 −2.04053
\(513\) −3.64438 −0.160903
\(514\) −51.3420 −2.26460
\(515\) −30.8084 −1.35758
\(516\) −29.2605 −1.28812
\(517\) 34.1342 1.50122
\(518\) 0 0
\(519\) 12.6063 0.553355
\(520\) −64.7013 −2.83734
\(521\) 19.8395 0.869183 0.434592 0.900628i \(-0.356893\pi\)
0.434592 + 0.900628i \(0.356893\pi\)
\(522\) 7.17166 0.313895
\(523\) 3.17412 0.138795 0.0693974 0.997589i \(-0.477892\pi\)
0.0693974 + 0.997589i \(0.477892\pi\)
\(524\) −7.60244 −0.332114
\(525\) 0 0
\(526\) 25.9109 1.12977
\(527\) 5.76968 0.251331
\(528\) −23.1341 −1.00678
\(529\) −18.0716 −0.785720
\(530\) −60.8019 −2.64106
\(531\) −8.70177 −0.377625
\(532\) 0 0
\(533\) 5.01637 0.217283
\(534\) −25.6627 −1.11054
\(535\) 47.2719 2.04374
\(536\) −0.503019 −0.0217271
\(537\) 6.53673 0.282081
\(538\) −44.8864 −1.93519
\(539\) 0 0
\(540\) 9.91672 0.426748
\(541\) −25.4484 −1.09411 −0.547057 0.837096i \(-0.684252\pi\)
−0.547057 + 0.837096i \(0.684252\pi\)
\(542\) 74.9812 3.22072
\(543\) 1.75566 0.0753427
\(544\) −9.71113 −0.416361
\(545\) −10.4523 −0.447727
\(546\) 0 0
\(547\) −41.5789 −1.77779 −0.888893 0.458116i \(-0.848525\pi\)
−0.888893 + 0.458116i \(0.848525\pi\)
\(548\) 43.2435 1.84727
\(549\) −8.35367 −0.356526
\(550\) 6.66591 0.284235
\(551\) 10.5045 0.447507
\(552\) 12.1001 0.515014
\(553\) 0 0
\(554\) −38.0376 −1.61606
\(555\) −1.77077 −0.0751651
\(556\) 50.8398 2.15609
\(557\) 40.8397 1.73043 0.865217 0.501398i \(-0.167181\pi\)
0.865217 + 0.501398i \(0.167181\pi\)
\(558\) −2.93804 −0.124377
\(559\) 35.0262 1.48145
\(560\) 0 0
\(561\) 21.8212 0.921294
\(562\) 10.0190 0.422627
\(563\) −7.56052 −0.318638 −0.159319 0.987227i \(-0.550930\pi\)
−0.159319 + 0.987227i \(0.550930\pi\)
\(564\) −32.0294 −1.34868
\(565\) 34.2691 1.44171
\(566\) −44.9007 −1.88732
\(567\) 0 0
\(568\) 16.8175 0.705649
\(569\) −20.8842 −0.875513 −0.437756 0.899094i \(-0.644227\pi\)
−0.437756 + 0.899094i \(0.644227\pi\)
\(570\) 21.4576 0.898758
\(571\) −29.6774 −1.24196 −0.620980 0.783827i \(-0.713265\pi\)
−0.620980 + 0.783827i \(0.713265\pi\)
\(572\) 93.8829 3.92544
\(573\) −3.79254 −0.158436
\(574\) 0 0
\(575\) −1.33177 −0.0555385
\(576\) −5.41498 −0.225624
\(577\) 0.394080 0.0164057 0.00820287 0.999966i \(-0.497389\pi\)
0.00820287 + 0.999966i \(0.497389\pi\)
\(578\) 17.1027 0.711377
\(579\) 0.179574 0.00746285
\(580\) −28.5838 −1.18688
\(581\) 0 0
\(582\) −11.5528 −0.478879
\(583\) 46.1189 1.91005
\(584\) 53.8705 2.22918
\(585\) −11.8708 −0.490797
\(586\) −13.8555 −0.572364
\(587\) 12.0519 0.497435 0.248717 0.968576i \(-0.419991\pi\)
0.248717 + 0.968576i \(0.419991\pi\)
\(588\) 0 0
\(589\) −4.30343 −0.177320
\(590\) 51.2348 2.10930
\(591\) 13.2115 0.543448
\(592\) −3.87620 −0.159311
\(593\) 34.1529 1.40249 0.701246 0.712919i \(-0.252627\pi\)
0.701246 + 0.712919i \(0.252627\pi\)
\(594\) −11.1118 −0.455924
\(595\) 0 0
\(596\) −70.4738 −2.88672
\(597\) 5.46727 0.223760
\(598\) −27.7084 −1.13308
\(599\) −2.14962 −0.0878312 −0.0439156 0.999035i \(-0.513983\pi\)
−0.0439156 + 0.999035i \(0.513983\pi\)
\(600\) −3.26969 −0.133485
\(601\) 15.3782 0.627291 0.313646 0.949540i \(-0.398450\pi\)
0.313646 + 0.949540i \(0.398450\pi\)
\(602\) 0 0
\(603\) −0.0922892 −0.00375831
\(604\) −67.4760 −2.74556
\(605\) −21.1679 −0.860598
\(606\) −34.3847 −1.39678
\(607\) −31.2239 −1.26734 −0.633669 0.773604i \(-0.718452\pi\)
−0.633669 + 0.773604i \(0.718452\pi\)
\(608\) 7.24323 0.293752
\(609\) 0 0
\(610\) 49.1852 1.99145
\(611\) 38.3408 1.55110
\(612\) −20.4757 −0.827681
\(613\) 32.6293 1.31789 0.658943 0.752193i \(-0.271004\pi\)
0.658943 + 0.752193i \(0.271004\pi\)
\(614\) 50.5794 2.04122
\(615\) 2.36641 0.0954228
\(616\) 0 0
\(617\) −33.6100 −1.35309 −0.676544 0.736402i \(-0.736523\pi\)
−0.676544 + 0.736402i \(0.736523\pi\)
\(618\) −32.3926 −1.30302
\(619\) 24.9576 1.00313 0.501566 0.865119i \(-0.332757\pi\)
0.501566 + 0.865119i \(0.332757\pi\)
\(620\) 11.7101 0.470287
\(621\) 2.22001 0.0890859
\(622\) 62.1757 2.49302
\(623\) 0 0
\(624\) −25.9850 −1.04023
\(625\) −27.6396 −1.10558
\(626\) 47.3229 1.89140
\(627\) −16.2758 −0.649993
\(628\) −31.1638 −1.24357
\(629\) 3.65623 0.145783
\(630\) 0 0
\(631\) −25.2251 −1.00420 −0.502099 0.864810i \(-0.667439\pi\)
−0.502099 + 0.864810i \(0.667439\pi\)
\(632\) 42.9404 1.70808
\(633\) −12.8035 −0.508894
\(634\) −66.4646 −2.63965
\(635\) −42.4433 −1.68431
\(636\) −43.2751 −1.71597
\(637\) 0 0
\(638\) 32.0286 1.26803
\(639\) 3.08552 0.122061
\(640\) 41.2891 1.63209
\(641\) 0.428767 0.0169353 0.00846764 0.999964i \(-0.497305\pi\)
0.00846764 + 0.999964i \(0.497305\pi\)
\(642\) 49.7027 1.96161
\(643\) −35.6986 −1.40781 −0.703907 0.710292i \(-0.748563\pi\)
−0.703907 + 0.710292i \(0.748563\pi\)
\(644\) 0 0
\(645\) 16.5232 0.650600
\(646\) −44.3048 −1.74315
\(647\) 1.15325 0.0453389 0.0226695 0.999743i \(-0.492783\pi\)
0.0226695 + 0.999743i \(0.492783\pi\)
\(648\) 5.45047 0.214115
\(649\) −38.8621 −1.52547
\(650\) 7.48738 0.293679
\(651\) 0 0
\(652\) 80.1010 3.13700
\(653\) −10.8046 −0.422815 −0.211408 0.977398i \(-0.567805\pi\)
−0.211408 + 0.977398i \(0.567805\pi\)
\(654\) −10.9898 −0.429734
\(655\) 4.29304 0.167743
\(656\) 5.18004 0.202247
\(657\) 9.88365 0.385598
\(658\) 0 0
\(659\) −21.9857 −0.856441 −0.428220 0.903674i \(-0.640859\pi\)
−0.428220 + 0.903674i \(0.640859\pi\)
\(660\) 44.2881 1.72391
\(661\) 12.5178 0.486885 0.243443 0.969915i \(-0.421723\pi\)
0.243443 + 0.969915i \(0.421723\pi\)
\(662\) −71.4782 −2.77808
\(663\) 24.5104 0.951905
\(664\) 34.1393 1.32486
\(665\) 0 0
\(666\) −1.86183 −0.0721444
\(667\) −6.39893 −0.247767
\(668\) 12.8114 0.495689
\(669\) −1.61990 −0.0626290
\(670\) 0.543385 0.0209928
\(671\) −37.3075 −1.44024
\(672\) 0 0
\(673\) −31.4333 −1.21166 −0.605832 0.795593i \(-0.707160\pi\)
−0.605832 + 0.795593i \(0.707160\pi\)
\(674\) 13.4295 0.517284
\(675\) −0.599893 −0.0230899
\(676\) 50.9746 1.96056
\(677\) 35.2655 1.35536 0.677682 0.735355i \(-0.262985\pi\)
0.677682 + 0.735355i \(0.262985\pi\)
\(678\) 36.0313 1.38377
\(679\) 0 0
\(680\) 63.0208 2.41674
\(681\) −7.09352 −0.271824
\(682\) −13.1213 −0.502441
\(683\) 9.57717 0.366460 0.183230 0.983070i \(-0.441345\pi\)
0.183230 + 0.983070i \(0.441345\pi\)
\(684\) 15.2722 0.583947
\(685\) −24.4193 −0.933013
\(686\) 0 0
\(687\) 10.2801 0.392209
\(688\) 36.1691 1.37893
\(689\) 51.8024 1.97351
\(690\) −13.0711 −0.497608
\(691\) −37.0205 −1.40832 −0.704162 0.710039i \(-0.748677\pi\)
−0.704162 + 0.710039i \(0.748677\pi\)
\(692\) −52.8282 −2.00823
\(693\) 0 0
\(694\) −27.9622 −1.06143
\(695\) −28.7089 −1.08899
\(696\) −15.7104 −0.595500
\(697\) −4.88608 −0.185074
\(698\) 81.5871 3.08812
\(699\) −26.2441 −0.992645
\(700\) 0 0
\(701\) −23.3692 −0.882641 −0.441320 0.897350i \(-0.645490\pi\)
−0.441320 + 0.897350i \(0.645490\pi\)
\(702\) −12.4812 −0.471073
\(703\) −2.72707 −0.102853
\(704\) −24.1833 −0.911442
\(705\) 18.0868 0.681187
\(706\) −92.1381 −3.46766
\(707\) 0 0
\(708\) 36.4658 1.37047
\(709\) −14.6548 −0.550371 −0.275185 0.961391i \(-0.588739\pi\)
−0.275185 + 0.961391i \(0.588739\pi\)
\(710\) −18.1671 −0.681799
\(711\) 7.87830 0.295459
\(712\) 56.2173 2.10683
\(713\) 2.62148 0.0981750
\(714\) 0 0
\(715\) −53.0149 −1.98265
\(716\) −27.3929 −1.02372
\(717\) −9.99590 −0.373304
\(718\) −71.7309 −2.67697
\(719\) −30.4680 −1.13626 −0.568132 0.822937i \(-0.692334\pi\)
−0.568132 + 0.822937i \(0.692334\pi\)
\(720\) −12.2581 −0.456833
\(721\) 0 0
\(722\) −14.2282 −0.529519
\(723\) −2.67886 −0.0996277
\(724\) −7.35731 −0.273432
\(725\) 1.72912 0.0642180
\(726\) −22.2564 −0.826013
\(727\) 15.9546 0.591723 0.295861 0.955231i \(-0.404393\pi\)
0.295861 + 0.955231i \(0.404393\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −58.1935 −2.15384
\(731\) −34.1165 −1.26184
\(732\) 35.0071 1.29390
\(733\) −0.380394 −0.0140502 −0.00702509 0.999975i \(-0.502236\pi\)
−0.00702509 + 0.999975i \(0.502236\pi\)
\(734\) −75.8507 −2.79970
\(735\) 0 0
\(736\) −4.41229 −0.162639
\(737\) −0.412163 −0.0151822
\(738\) 2.48810 0.0915881
\(739\) 2.04392 0.0751868 0.0375934 0.999293i \(-0.488031\pi\)
0.0375934 + 0.999293i \(0.488031\pi\)
\(740\) 7.42063 0.272788
\(741\) −18.2815 −0.671589
\(742\) 0 0
\(743\) 10.1113 0.370948 0.185474 0.982649i \(-0.440618\pi\)
0.185474 + 0.982649i \(0.440618\pi\)
\(744\) 6.43613 0.235960
\(745\) 39.7960 1.45801
\(746\) 27.5228 1.00768
\(747\) 6.26355 0.229171
\(748\) −91.4445 −3.34354
\(749\) 0 0
\(750\) −25.9072 −0.945996
\(751\) 35.9620 1.31227 0.656136 0.754643i \(-0.272190\pi\)
0.656136 + 0.754643i \(0.272190\pi\)
\(752\) 39.5917 1.44376
\(753\) −23.4644 −0.855090
\(754\) 35.9757 1.31016
\(755\) 38.1032 1.38672
\(756\) 0 0
\(757\) 6.05727 0.220155 0.110078 0.993923i \(-0.464890\pi\)
0.110078 + 0.993923i \(0.464890\pi\)
\(758\) 46.1326 1.67561
\(759\) 9.91456 0.359876
\(760\) −47.0053 −1.70506
\(761\) −51.1971 −1.85589 −0.927947 0.372712i \(-0.878428\pi\)
−0.927947 + 0.372712i \(0.878428\pi\)
\(762\) −44.6258 −1.61662
\(763\) 0 0
\(764\) 15.8931 0.574991
\(765\) 11.5625 0.418042
\(766\) −64.1104 −2.31640
\(767\) −43.6513 −1.57616
\(768\) 32.5823 1.17571
\(769\) −24.5528 −0.885396 −0.442698 0.896671i \(-0.645979\pi\)
−0.442698 + 0.896671i \(0.645979\pi\)
\(770\) 0 0
\(771\) 20.6351 0.743154
\(772\) −0.752527 −0.0270840
\(773\) 51.3061 1.84535 0.922676 0.385577i \(-0.125998\pi\)
0.922676 + 0.385577i \(0.125998\pi\)
\(774\) 17.3728 0.624454
\(775\) −0.708377 −0.0254457
\(776\) 25.3078 0.908497
\(777\) 0 0
\(778\) 22.3437 0.801061
\(779\) 3.64438 0.130573
\(780\) 49.7459 1.78119
\(781\) 13.7800 0.493086
\(782\) 26.9887 0.965115
\(783\) −2.88239 −0.103008
\(784\) 0 0
\(785\) 17.5979 0.628097
\(786\) 4.51380 0.161002
\(787\) −8.42945 −0.300478 −0.150239 0.988650i \(-0.548004\pi\)
−0.150239 + 0.988650i \(0.548004\pi\)
\(788\) −55.3643 −1.97227
\(789\) −10.4139 −0.370746
\(790\) −46.3862 −1.65035
\(791\) 0 0
\(792\) 24.3418 0.864948
\(793\) −41.9051 −1.48809
\(794\) −74.1805 −2.63257
\(795\) 24.4371 0.866695
\(796\) −22.9112 −0.812067
\(797\) 43.9602 1.55715 0.778575 0.627551i \(-0.215943\pi\)
0.778575 + 0.627551i \(0.215943\pi\)
\(798\) 0 0
\(799\) −37.3449 −1.32117
\(800\) 1.19229 0.0421539
\(801\) 10.3142 0.364435
\(802\) 76.2222 2.69150
\(803\) 44.1404 1.55768
\(804\) 0.386749 0.0136396
\(805\) 0 0
\(806\) −14.7383 −0.519135
\(807\) 18.0405 0.635054
\(808\) 75.3237 2.64988
\(809\) 41.9373 1.47444 0.737218 0.675655i \(-0.236139\pi\)
0.737218 + 0.675655i \(0.236139\pi\)
\(810\) −5.88785 −0.206878
\(811\) 1.50049 0.0526892 0.0263446 0.999653i \(-0.491613\pi\)
0.0263446 + 0.999653i \(0.491613\pi\)
\(812\) 0 0
\(813\) −30.1360 −1.05691
\(814\) −8.31493 −0.291438
\(815\) −45.2324 −1.58442
\(816\) 25.3101 0.886031
\(817\) 25.4464 0.890259
\(818\) −24.6033 −0.860235
\(819\) 0 0
\(820\) −9.91672 −0.346307
\(821\) 46.6313 1.62744 0.813722 0.581255i \(-0.197438\pi\)
0.813722 + 0.581255i \(0.197438\pi\)
\(822\) −25.6750 −0.895518
\(823\) 12.4390 0.433595 0.216797 0.976217i \(-0.430439\pi\)
0.216797 + 0.976217i \(0.430439\pi\)
\(824\) 70.9599 2.47201
\(825\) −2.67912 −0.0932750
\(826\) 0 0
\(827\) 25.6272 0.891147 0.445573 0.895245i \(-0.353000\pi\)
0.445573 + 0.895245i \(0.353000\pi\)
\(828\) −9.30321 −0.323309
\(829\) 8.98335 0.312005 0.156002 0.987757i \(-0.450139\pi\)
0.156002 + 0.987757i \(0.450139\pi\)
\(830\) −36.8788 −1.28008
\(831\) 15.2878 0.530329
\(832\) −27.1635 −0.941726
\(833\) 0 0
\(834\) −30.1851 −1.04523
\(835\) −7.23451 −0.250360
\(836\) 68.2056 2.35894
\(837\) 1.18084 0.0408158
\(838\) 19.1189 0.660451
\(839\) −14.9267 −0.515326 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(840\) 0 0
\(841\) −20.6918 −0.713512
\(842\) −13.7726 −0.474636
\(843\) −4.02679 −0.138690
\(844\) 53.6546 1.84687
\(845\) −28.7849 −0.990232
\(846\) 19.0168 0.653812
\(847\) 0 0
\(848\) 53.4926 1.83694
\(849\) 18.0462 0.619345
\(850\) −7.29292 −0.250145
\(851\) 1.66122 0.0569459
\(852\) −12.9303 −0.442983
\(853\) −29.3002 −1.00322 −0.501610 0.865094i \(-0.667259\pi\)
−0.501610 + 0.865094i \(0.667259\pi\)
\(854\) 0 0
\(855\) −8.62409 −0.294938
\(856\) −108.880 −3.72143
\(857\) −0.206054 −0.00703868 −0.00351934 0.999994i \(-0.501120\pi\)
−0.00351934 + 0.999994i \(0.501120\pi\)
\(858\) −55.7411 −1.90297
\(859\) 10.3195 0.352096 0.176048 0.984382i \(-0.443669\pi\)
0.176048 + 0.984382i \(0.443669\pi\)
\(860\) −69.2423 −2.36114
\(861\) 0 0
\(862\) −85.9540 −2.92761
\(863\) 2.67563 0.0910796 0.0455398 0.998963i \(-0.485499\pi\)
0.0455398 + 0.998963i \(0.485499\pi\)
\(864\) −1.98751 −0.0676164
\(865\) 29.8317 1.01431
\(866\) 4.82680 0.164021
\(867\) −6.87380 −0.233446
\(868\) 0 0
\(869\) 35.1845 1.19355
\(870\) 16.9711 0.575373
\(871\) −0.462957 −0.0156867
\(872\) 24.0744 0.815263
\(873\) 4.64324 0.157150
\(874\) −20.1301 −0.680909
\(875\) 0 0
\(876\) −41.4186 −1.39941
\(877\) 28.0493 0.947158 0.473579 0.880751i \(-0.342962\pi\)
0.473579 + 0.880751i \(0.342962\pi\)
\(878\) −91.9662 −3.10371
\(879\) 5.56871 0.187828
\(880\) −54.7447 −1.84544
\(881\) −2.95290 −0.0994856 −0.0497428 0.998762i \(-0.515840\pi\)
−0.0497428 + 0.998762i \(0.515840\pi\)
\(882\) 0 0
\(883\) 12.2203 0.411246 0.205623 0.978631i \(-0.434078\pi\)
0.205623 + 0.978631i \(0.434078\pi\)
\(884\) −102.714 −3.45464
\(885\) −20.5920 −0.692191
\(886\) −71.9440 −2.41700
\(887\) −10.3073 −0.346084 −0.173042 0.984914i \(-0.555360\pi\)
−0.173042 + 0.984914i \(0.555360\pi\)
\(888\) 4.07856 0.136867
\(889\) 0 0
\(890\) −60.7285 −2.03563
\(891\) 4.46600 0.149617
\(892\) 6.78838 0.227292
\(893\) 27.8544 0.932113
\(894\) 41.8424 1.39942
\(895\) 15.4686 0.517057
\(896\) 0 0
\(897\) 11.1364 0.371833
\(898\) −20.0258 −0.668270
\(899\) −3.40364 −0.113518
\(900\) 2.51392 0.0837974
\(901\) −50.4569 −1.68096
\(902\) 11.1118 0.369984
\(903\) 0 0
\(904\) −78.9308 −2.62520
\(905\) 4.15462 0.138104
\(906\) 40.0625 1.33099
\(907\) 29.2512 0.971269 0.485635 0.874162i \(-0.338589\pi\)
0.485635 + 0.874162i \(0.338589\pi\)
\(908\) 29.7262 0.986499
\(909\) 13.8197 0.458370
\(910\) 0 0
\(911\) 14.2520 0.472190 0.236095 0.971730i \(-0.424132\pi\)
0.236095 + 0.971730i \(0.424132\pi\)
\(912\) −18.8780 −0.625114
\(913\) 27.9730 0.925772
\(914\) 11.7777 0.389573
\(915\) −19.7682 −0.653517
\(916\) −43.0799 −1.42340
\(917\) 0 0
\(918\) 12.1570 0.401242
\(919\) 21.2445 0.700791 0.350395 0.936602i \(-0.386047\pi\)
0.350395 + 0.936602i \(0.386047\pi\)
\(920\) 28.6337 0.944027
\(921\) −20.3285 −0.669848
\(922\) −91.7408 −3.02132
\(923\) 15.4781 0.509469
\(924\) 0 0
\(925\) −0.448897 −0.0147596
\(926\) 28.4755 0.935763
\(927\) 13.0191 0.427602
\(928\) 5.72877 0.188056
\(929\) −32.1903 −1.05613 −0.528064 0.849204i \(-0.677082\pi\)
−0.528064 + 0.849204i \(0.677082\pi\)
\(930\) −6.95261 −0.227985
\(931\) 0 0
\(932\) 109.979 3.60249
\(933\) −24.9893 −0.818112
\(934\) −23.1843 −0.758613
\(935\) 51.6380 1.68874
\(936\) 27.3416 0.893687
\(937\) 30.2630 0.988649 0.494324 0.869278i \(-0.335415\pi\)
0.494324 + 0.869278i \(0.335415\pi\)
\(938\) 0 0
\(939\) −19.0197 −0.620685
\(940\) −75.7947 −2.47215
\(941\) 21.1631 0.689897 0.344948 0.938622i \(-0.387896\pi\)
0.344948 + 0.938622i \(0.387896\pi\)
\(942\) 18.5029 0.602856
\(943\) −2.22001 −0.0722934
\(944\) −45.0756 −1.46708
\(945\) 0 0
\(946\) 77.5871 2.52257
\(947\) 49.3799 1.60463 0.802316 0.596900i \(-0.203601\pi\)
0.802316 + 0.596900i \(0.203601\pi\)
\(948\) −33.0149 −1.07228
\(949\) 49.5801 1.60944
\(950\) 5.43956 0.176483
\(951\) 26.7130 0.866230
\(952\) 0 0
\(953\) 42.6273 1.38083 0.690417 0.723412i \(-0.257427\pi\)
0.690417 + 0.723412i \(0.257427\pi\)
\(954\) 25.6937 0.831865
\(955\) −8.97470 −0.290414
\(956\) 41.8890 1.35479
\(957\) −12.8728 −0.416117
\(958\) −98.4748 −3.18158
\(959\) 0 0
\(960\) −12.8140 −0.413572
\(961\) −29.6056 −0.955020
\(962\) −9.33962 −0.301122
\(963\) −19.9762 −0.643724
\(964\) 11.2261 0.361567
\(965\) 0.424946 0.0136795
\(966\) 0 0
\(967\) 40.3526 1.29765 0.648826 0.760937i \(-0.275260\pi\)
0.648826 + 0.760937i \(0.275260\pi\)
\(968\) 48.7553 1.56706
\(969\) 17.8067 0.572035
\(970\) −27.3387 −0.877792
\(971\) 58.4250 1.87495 0.937474 0.348057i \(-0.113158\pi\)
0.937474 + 0.348057i \(0.113158\pi\)
\(972\) −4.19062 −0.134414
\(973\) 0 0
\(974\) 64.5280 2.06761
\(975\) −3.00928 −0.0963742
\(976\) −43.2724 −1.38512
\(977\) −0.829520 −0.0265387 −0.0132694 0.999912i \(-0.504224\pi\)
−0.0132694 + 0.999912i \(0.504224\pi\)
\(978\) −47.5583 −1.52075
\(979\) 46.0633 1.47219
\(980\) 0 0
\(981\) 4.41695 0.141022
\(982\) −28.8261 −0.919877
\(983\) 2.32545 0.0741703 0.0370852 0.999312i \(-0.488193\pi\)
0.0370852 + 0.999312i \(0.488193\pi\)
\(984\) −5.45047 −0.173755
\(985\) 31.2638 0.996148
\(986\) −35.0413 −1.11594
\(987\) 0 0
\(988\) 76.6110 2.43732
\(989\) −15.5010 −0.492902
\(990\) −26.2952 −0.835715
\(991\) −16.1129 −0.511843 −0.255921 0.966698i \(-0.582379\pi\)
−0.255921 + 0.966698i \(0.582379\pi\)
\(992\) −2.34693 −0.0745151
\(993\) 28.7281 0.911659
\(994\) 0 0
\(995\) 12.9378 0.410156
\(996\) −26.2481 −0.831704
\(997\) 0.484528 0.0153452 0.00767258 0.999971i \(-0.497558\pi\)
0.00767258 + 0.999971i \(0.497558\pi\)
\(998\) 56.1697 1.77802
\(999\) 0.748295 0.0236750
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 \(a_p\))