Properties

Label 6047.2.a.a.1.8
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65451 q^{2} -2.99510 q^{3} +5.04641 q^{4} -2.08040 q^{5} +7.95052 q^{6} -1.11556 q^{7} -8.08670 q^{8} +5.97065 q^{9} +O(q^{10})\) \(q-2.65451 q^{2} -2.99510 q^{3} +5.04641 q^{4} -2.08040 q^{5} +7.95052 q^{6} -1.11556 q^{7} -8.08670 q^{8} +5.97065 q^{9} +5.52243 q^{10} +3.38425 q^{11} -15.1145 q^{12} -3.23622 q^{13} +2.96127 q^{14} +6.23101 q^{15} +11.3734 q^{16} +4.29870 q^{17} -15.8491 q^{18} +0.715567 q^{19} -10.4985 q^{20} +3.34123 q^{21} -8.98352 q^{22} +0.981717 q^{23} +24.2205 q^{24} -0.671946 q^{25} +8.59058 q^{26} -8.89739 q^{27} -5.62959 q^{28} -2.22960 q^{29} -16.5402 q^{30} +0.355075 q^{31} -14.0173 q^{32} -10.1362 q^{33} -11.4109 q^{34} +2.32082 q^{35} +30.1303 q^{36} +11.1937 q^{37} -1.89948 q^{38} +9.69283 q^{39} +16.8236 q^{40} -1.13870 q^{41} -8.86932 q^{42} -6.13987 q^{43} +17.0783 q^{44} -12.4213 q^{45} -2.60597 q^{46} -2.54799 q^{47} -34.0645 q^{48} -5.75552 q^{49} +1.78369 q^{50} -12.8750 q^{51} -16.3313 q^{52} -12.6824 q^{53} +23.6182 q^{54} -7.04059 q^{55} +9.02124 q^{56} -2.14320 q^{57} +5.91850 q^{58} +12.1366 q^{59} +31.4442 q^{60} +7.65047 q^{61} -0.942549 q^{62} -6.66064 q^{63} +14.4624 q^{64} +6.73263 q^{65} +26.9066 q^{66} -9.28979 q^{67} +21.6930 q^{68} -2.94034 q^{69} -6.16063 q^{70} -3.24012 q^{71} -48.2828 q^{72} -4.55854 q^{73} -29.7138 q^{74} +2.01255 q^{75} +3.61104 q^{76} -3.77535 q^{77} -25.7297 q^{78} -2.45178 q^{79} -23.6612 q^{80} +8.73667 q^{81} +3.02268 q^{82} +7.49212 q^{83} +16.8612 q^{84} -8.94300 q^{85} +16.2983 q^{86} +6.67790 q^{87} -27.3675 q^{88} +11.6238 q^{89} +32.9725 q^{90} +3.61022 q^{91} +4.95414 q^{92} -1.06349 q^{93} +6.76364 q^{94} -1.48866 q^{95} +41.9834 q^{96} -10.6560 q^{97} +15.2781 q^{98} +20.2062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65451 −1.87702 −0.938510 0.345253i \(-0.887793\pi\)
−0.938510 + 0.345253i \(0.887793\pi\)
\(3\) −2.99510 −1.72922 −0.864612 0.502440i \(-0.832436\pi\)
−0.864612 + 0.502440i \(0.832436\pi\)
\(4\) 5.04641 2.52320
\(5\) −2.08040 −0.930382 −0.465191 0.885210i \(-0.654014\pi\)
−0.465191 + 0.885210i \(0.654014\pi\)
\(6\) 7.95052 3.24579
\(7\) −1.11556 −0.421644 −0.210822 0.977524i \(-0.567614\pi\)
−0.210822 + 0.977524i \(0.567614\pi\)
\(8\) −8.08670 −2.85908
\(9\) 5.97065 1.99022
\(10\) 5.52243 1.74635
\(11\) 3.38425 1.02039 0.510195 0.860059i \(-0.329573\pi\)
0.510195 + 0.860059i \(0.329573\pi\)
\(12\) −15.1145 −4.36318
\(13\) −3.23622 −0.897567 −0.448784 0.893640i \(-0.648143\pi\)
−0.448784 + 0.893640i \(0.648143\pi\)
\(14\) 2.96127 0.791434
\(15\) 6.23101 1.60884
\(16\) 11.3734 2.84335
\(17\) 4.29870 1.04259 0.521293 0.853378i \(-0.325450\pi\)
0.521293 + 0.853378i \(0.325450\pi\)
\(18\) −15.8491 −3.73567
\(19\) 0.715567 0.164162 0.0820811 0.996626i \(-0.473843\pi\)
0.0820811 + 0.996626i \(0.473843\pi\)
\(20\) −10.4985 −2.34754
\(21\) 3.34123 0.729117
\(22\) −8.98352 −1.91529
\(23\) 0.981717 0.204702 0.102351 0.994748i \(-0.467363\pi\)
0.102351 + 0.994748i \(0.467363\pi\)
\(24\) 24.2205 4.94399
\(25\) −0.671946 −0.134389
\(26\) 8.59058 1.68475
\(27\) −8.89739 −1.71230
\(28\) −5.62959 −1.06389
\(29\) −2.22960 −0.414027 −0.207014 0.978338i \(-0.566374\pi\)
−0.207014 + 0.978338i \(0.566374\pi\)
\(30\) −16.5402 −3.01982
\(31\) 0.355075 0.0637734 0.0318867 0.999491i \(-0.489848\pi\)
0.0318867 + 0.999491i \(0.489848\pi\)
\(32\) −14.0173 −2.47794
\(33\) −10.1362 −1.76448
\(34\) −11.4109 −1.95696
\(35\) 2.32082 0.392290
\(36\) 30.1303 5.02172
\(37\) 11.1937 1.84024 0.920118 0.391641i \(-0.128092\pi\)
0.920118 + 0.391641i \(0.128092\pi\)
\(38\) −1.89948 −0.308136
\(39\) 9.69283 1.55209
\(40\) 16.8236 2.66004
\(41\) −1.13870 −0.177834 −0.0889172 0.996039i \(-0.528341\pi\)
−0.0889172 + 0.996039i \(0.528341\pi\)
\(42\) −8.86932 −1.36857
\(43\) −6.13987 −0.936321 −0.468160 0.883643i \(-0.655083\pi\)
−0.468160 + 0.883643i \(0.655083\pi\)
\(44\) 17.0783 2.57465
\(45\) −12.4213 −1.85166
\(46\) −2.60597 −0.384230
\(47\) −2.54799 −0.371662 −0.185831 0.982582i \(-0.559498\pi\)
−0.185831 + 0.982582i \(0.559498\pi\)
\(48\) −34.0645 −4.91679
\(49\) −5.75552 −0.822216
\(50\) 1.78369 0.252251
\(51\) −12.8750 −1.80287
\(52\) −16.3313 −2.26474
\(53\) −12.6824 −1.74206 −0.871028 0.491233i \(-0.836546\pi\)
−0.871028 + 0.491233i \(0.836546\pi\)
\(54\) 23.6182 3.21403
\(55\) −7.04059 −0.949353
\(56\) 9.02124 1.20551
\(57\) −2.14320 −0.283873
\(58\) 5.91850 0.777137
\(59\) 12.1366 1.58005 0.790027 0.613072i \(-0.210067\pi\)
0.790027 + 0.613072i \(0.210067\pi\)
\(60\) 31.4442 4.05943
\(61\) 7.65047 0.979543 0.489771 0.871851i \(-0.337080\pi\)
0.489771 + 0.871851i \(0.337080\pi\)
\(62\) −0.942549 −0.119704
\(63\) −6.66064 −0.839162
\(64\) 14.4624 1.80779
\(65\) 6.73263 0.835080
\(66\) 26.9066 3.31197
\(67\) −9.28979 −1.13493 −0.567464 0.823398i \(-0.692076\pi\)
−0.567464 + 0.823398i \(0.692076\pi\)
\(68\) 21.6930 2.63066
\(69\) −2.94034 −0.353976
\(70\) −6.16063 −0.736336
\(71\) −3.24012 −0.384531 −0.192266 0.981343i \(-0.561584\pi\)
−0.192266 + 0.981343i \(0.561584\pi\)
\(72\) −48.2828 −5.69019
\(73\) −4.55854 −0.533537 −0.266769 0.963761i \(-0.585956\pi\)
−0.266769 + 0.963761i \(0.585956\pi\)
\(74\) −29.7138 −3.45416
\(75\) 2.01255 0.232389
\(76\) 3.61104 0.414215
\(77\) −3.77535 −0.430241
\(78\) −25.7297 −2.91331
\(79\) −2.45178 −0.275847 −0.137924 0.990443i \(-0.544043\pi\)
−0.137924 + 0.990443i \(0.544043\pi\)
\(80\) −23.6612 −2.64540
\(81\) 8.73667 0.970742
\(82\) 3.02268 0.333799
\(83\) 7.49212 0.822367 0.411184 0.911553i \(-0.365115\pi\)
0.411184 + 0.911553i \(0.365115\pi\)
\(84\) 16.8612 1.83971
\(85\) −8.94300 −0.970004
\(86\) 16.2983 1.75749
\(87\) 6.67790 0.715946
\(88\) −27.3675 −2.91738
\(89\) 11.6238 1.23212 0.616059 0.787700i \(-0.288728\pi\)
0.616059 + 0.787700i \(0.288728\pi\)
\(90\) 32.9725 3.47560
\(91\) 3.61022 0.378454
\(92\) 4.95414 0.516505
\(93\) −1.06349 −0.110278
\(94\) 6.76364 0.697617
\(95\) −1.48866 −0.152734
\(96\) 41.9834 4.28491
\(97\) −10.6560 −1.08196 −0.540979 0.841036i \(-0.681946\pi\)
−0.540979 + 0.841036i \(0.681946\pi\)
\(98\) 15.2781 1.54332
\(99\) 20.2062 2.03080
\(100\) −3.39091 −0.339091
\(101\) 4.79542 0.477162 0.238581 0.971123i \(-0.423318\pi\)
0.238581 + 0.971123i \(0.423318\pi\)
\(102\) 34.1769 3.38402
\(103\) −15.0541 −1.48332 −0.741662 0.670774i \(-0.765962\pi\)
−0.741662 + 0.670774i \(0.765962\pi\)
\(104\) 26.1704 2.56622
\(105\) −6.95109 −0.678357
\(106\) 33.6654 3.26987
\(107\) 4.83698 0.467609 0.233804 0.972284i \(-0.424882\pi\)
0.233804 + 0.972284i \(0.424882\pi\)
\(108\) −44.8998 −4.32049
\(109\) −10.7199 −1.02678 −0.513390 0.858156i \(-0.671610\pi\)
−0.513390 + 0.858156i \(0.671610\pi\)
\(110\) 18.6893 1.78195
\(111\) −33.5264 −3.18218
\(112\) −12.6878 −1.19888
\(113\) −7.17112 −0.674602 −0.337301 0.941397i \(-0.609514\pi\)
−0.337301 + 0.941397i \(0.609514\pi\)
\(114\) 5.68913 0.532836
\(115\) −2.04236 −0.190451
\(116\) −11.2515 −1.04467
\(117\) −19.3223 −1.78635
\(118\) −32.2167 −2.96579
\(119\) −4.79547 −0.439600
\(120\) −50.3883 −4.59980
\(121\) 0.453170 0.0411973
\(122\) −20.3082 −1.83862
\(123\) 3.41051 0.307516
\(124\) 1.79185 0.160913
\(125\) 11.7999 1.05542
\(126\) 17.6807 1.57512
\(127\) 17.7855 1.57821 0.789106 0.614258i \(-0.210544\pi\)
0.789106 + 0.614258i \(0.210544\pi\)
\(128\) −10.3557 −0.915325
\(129\) 18.3895 1.61911
\(130\) −17.8718 −1.56746
\(131\) −3.25337 −0.284248 −0.142124 0.989849i \(-0.545393\pi\)
−0.142124 + 0.989849i \(0.545393\pi\)
\(132\) −51.1513 −4.45215
\(133\) −0.798261 −0.0692180
\(134\) 24.6598 2.13028
\(135\) 18.5101 1.59310
\(136\) −34.7623 −2.98084
\(137\) 10.0179 0.855884 0.427942 0.903806i \(-0.359239\pi\)
0.427942 + 0.903806i \(0.359239\pi\)
\(138\) 7.80516 0.664420
\(139\) −12.9376 −1.09735 −0.548676 0.836035i \(-0.684868\pi\)
−0.548676 + 0.836035i \(0.684868\pi\)
\(140\) 11.7118 0.989827
\(141\) 7.63148 0.642687
\(142\) 8.60092 0.721773
\(143\) −10.9522 −0.915869
\(144\) 67.9065 5.65888
\(145\) 4.63846 0.385203
\(146\) 12.1007 1.00146
\(147\) 17.2384 1.42180
\(148\) 56.4880 4.64329
\(149\) 18.6786 1.53021 0.765105 0.643906i \(-0.222687\pi\)
0.765105 + 0.643906i \(0.222687\pi\)
\(150\) −5.34232 −0.436199
\(151\) −14.4072 −1.17244 −0.586221 0.810151i \(-0.699385\pi\)
−0.586221 + 0.810151i \(0.699385\pi\)
\(152\) −5.78657 −0.469353
\(153\) 25.6660 2.07497
\(154\) 10.0217 0.807572
\(155\) −0.738697 −0.0593336
\(156\) 48.9139 3.91625
\(157\) 16.7766 1.33892 0.669458 0.742850i \(-0.266526\pi\)
0.669458 + 0.742850i \(0.266526\pi\)
\(158\) 6.50828 0.517771
\(159\) 37.9850 3.01241
\(160\) 29.1617 2.30543
\(161\) −1.09517 −0.0863114
\(162\) −23.1916 −1.82210
\(163\) 4.31063 0.337635 0.168817 0.985647i \(-0.446005\pi\)
0.168817 + 0.985647i \(0.446005\pi\)
\(164\) −5.74632 −0.448712
\(165\) 21.0873 1.64164
\(166\) −19.8879 −1.54360
\(167\) −14.3337 −1.10917 −0.554587 0.832126i \(-0.687124\pi\)
−0.554587 + 0.832126i \(0.687124\pi\)
\(168\) −27.0196 −2.08460
\(169\) −2.52685 −0.194373
\(170\) 23.7392 1.82072
\(171\) 4.27239 0.326718
\(172\) −30.9843 −2.36253
\(173\) −7.50239 −0.570396 −0.285198 0.958469i \(-0.592059\pi\)
−0.285198 + 0.958469i \(0.592059\pi\)
\(174\) −17.7265 −1.34384
\(175\) 0.749600 0.0566644
\(176\) 38.4905 2.90133
\(177\) −36.3504 −2.73227
\(178\) −30.8554 −2.31271
\(179\) −2.38194 −0.178035 −0.0890173 0.996030i \(-0.528373\pi\)
−0.0890173 + 0.996030i \(0.528373\pi\)
\(180\) −62.6830 −4.67211
\(181\) −2.47823 −0.184205 −0.0921026 0.995750i \(-0.529359\pi\)
−0.0921026 + 0.995750i \(0.529359\pi\)
\(182\) −9.58335 −0.710365
\(183\) −22.9140 −1.69385
\(184\) −7.93886 −0.585260
\(185\) −23.2874 −1.71212
\(186\) 2.82303 0.206995
\(187\) 14.5479 1.06385
\(188\) −12.8582 −0.937778
\(189\) 9.92562 0.721982
\(190\) 3.95167 0.286684
\(191\) −1.92863 −0.139551 −0.0697754 0.997563i \(-0.522228\pi\)
−0.0697754 + 0.997563i \(0.522228\pi\)
\(192\) −43.3162 −3.12608
\(193\) 10.2727 0.739447 0.369723 0.929142i \(-0.379452\pi\)
0.369723 + 0.929142i \(0.379452\pi\)
\(194\) 28.2866 2.03086
\(195\) −20.1649 −1.44404
\(196\) −29.0447 −2.07462
\(197\) 22.7684 1.62218 0.811090 0.584922i \(-0.198875\pi\)
0.811090 + 0.584922i \(0.198875\pi\)
\(198\) −53.6374 −3.81185
\(199\) 20.5648 1.45780 0.728900 0.684621i \(-0.240032\pi\)
0.728900 + 0.684621i \(0.240032\pi\)
\(200\) 5.43383 0.384230
\(201\) 27.8239 1.96255
\(202\) −12.7295 −0.895643
\(203\) 2.48727 0.174572
\(204\) −64.9727 −4.54900
\(205\) 2.36894 0.165454
\(206\) 39.9612 2.78423
\(207\) 5.86149 0.407401
\(208\) −36.8069 −2.55210
\(209\) 2.42166 0.167510
\(210\) 18.4517 1.27329
\(211\) −11.0025 −0.757446 −0.378723 0.925510i \(-0.623637\pi\)
−0.378723 + 0.925510i \(0.623637\pi\)
\(212\) −64.0003 −4.39556
\(213\) 9.70449 0.664941
\(214\) −12.8398 −0.877711
\(215\) 12.7734 0.871136
\(216\) 71.9506 4.89562
\(217\) −0.396109 −0.0268897
\(218\) 28.4560 1.92728
\(219\) 13.6533 0.922605
\(220\) −35.5297 −2.39541
\(221\) −13.9115 −0.935792
\(222\) 88.9959 5.97302
\(223\) 22.3094 1.49395 0.746973 0.664854i \(-0.231506\pi\)
0.746973 + 0.664854i \(0.231506\pi\)
\(224\) 15.6373 1.04481
\(225\) −4.01195 −0.267464
\(226\) 19.0358 1.26624
\(227\) −5.76706 −0.382773 −0.191387 0.981515i \(-0.561298\pi\)
−0.191387 + 0.981515i \(0.561298\pi\)
\(228\) −10.8154 −0.716270
\(229\) −10.0640 −0.665048 −0.332524 0.943095i \(-0.607900\pi\)
−0.332524 + 0.943095i \(0.607900\pi\)
\(230\) 5.42146 0.357481
\(231\) 11.3076 0.743984
\(232\) 18.0301 1.18374
\(233\) −8.36503 −0.548011 −0.274006 0.961728i \(-0.588349\pi\)
−0.274006 + 0.961728i \(0.588349\pi\)
\(234\) 51.2913 3.35302
\(235\) 5.30082 0.345788
\(236\) 61.2463 3.98679
\(237\) 7.34335 0.477002
\(238\) 12.7296 0.825138
\(239\) 11.2520 0.727832 0.363916 0.931432i \(-0.381440\pi\)
0.363916 + 0.931432i \(0.381440\pi\)
\(240\) 70.8677 4.57449
\(241\) −7.91275 −0.509705 −0.254853 0.966980i \(-0.582027\pi\)
−0.254853 + 0.966980i \(0.582027\pi\)
\(242\) −1.20294 −0.0773281
\(243\) 0.524932 0.0336744
\(244\) 38.6074 2.47158
\(245\) 11.9738 0.764975
\(246\) −9.05323 −0.577213
\(247\) −2.31573 −0.147347
\(248\) −2.87139 −0.182333
\(249\) −22.4397 −1.42206
\(250\) −31.3229 −1.98104
\(251\) 5.57587 0.351946 0.175973 0.984395i \(-0.443693\pi\)
0.175973 + 0.984395i \(0.443693\pi\)
\(252\) −33.6123 −2.11738
\(253\) 3.32238 0.208876
\(254\) −47.2118 −2.96233
\(255\) 26.7852 1.67735
\(256\) −1.43539 −0.0897121
\(257\) 25.4249 1.58596 0.792979 0.609248i \(-0.208529\pi\)
0.792979 + 0.609248i \(0.208529\pi\)
\(258\) −48.8151 −3.03910
\(259\) −12.4873 −0.775924
\(260\) 33.9756 2.10708
\(261\) −13.3122 −0.824003
\(262\) 8.63608 0.533539
\(263\) 15.9468 0.983324 0.491662 0.870786i \(-0.336390\pi\)
0.491662 + 0.870786i \(0.336390\pi\)
\(264\) 81.9684 5.04480
\(265\) 26.3844 1.62078
\(266\) 2.11899 0.129924
\(267\) −34.8144 −2.13061
\(268\) −46.8801 −2.86366
\(269\) 14.3454 0.874657 0.437329 0.899302i \(-0.355925\pi\)
0.437329 + 0.899302i \(0.355925\pi\)
\(270\) −49.1352 −2.99027
\(271\) 17.8005 1.08130 0.540651 0.841247i \(-0.318178\pi\)
0.540651 + 0.841247i \(0.318178\pi\)
\(272\) 48.8908 2.96444
\(273\) −10.8130 −0.654431
\(274\) −26.5925 −1.60651
\(275\) −2.27404 −0.137130
\(276\) −14.8382 −0.893153
\(277\) 1.67238 0.100484 0.0502419 0.998737i \(-0.484001\pi\)
0.0502419 + 0.998737i \(0.484001\pi\)
\(278\) 34.3429 2.05975
\(279\) 2.12003 0.126923
\(280\) −18.7678 −1.12159
\(281\) −10.7527 −0.641453 −0.320727 0.947172i \(-0.603927\pi\)
−0.320727 + 0.947172i \(0.603927\pi\)
\(282\) −20.2578 −1.20634
\(283\) 24.5654 1.46026 0.730130 0.683308i \(-0.239459\pi\)
0.730130 + 0.683308i \(0.239459\pi\)
\(284\) −16.3510 −0.970251
\(285\) 4.45870 0.264111
\(286\) 29.0727 1.71910
\(287\) 1.27029 0.0749828
\(288\) −83.6926 −4.93164
\(289\) 1.47878 0.0869873
\(290\) −12.3128 −0.723034
\(291\) 31.9160 1.87095
\(292\) −23.0043 −1.34622
\(293\) −3.89252 −0.227403 −0.113702 0.993515i \(-0.536271\pi\)
−0.113702 + 0.993515i \(0.536271\pi\)
\(294\) −45.7594 −2.66874
\(295\) −25.2490 −1.47005
\(296\) −90.5203 −5.26139
\(297\) −30.1110 −1.74722
\(298\) −49.5824 −2.87223
\(299\) −3.17706 −0.183734
\(300\) 10.1561 0.586365
\(301\) 6.84942 0.394794
\(302\) 38.2440 2.20070
\(303\) −14.3628 −0.825120
\(304\) 8.13842 0.466770
\(305\) −15.9160 −0.911349
\(306\) −68.1305 −3.89476
\(307\) 6.84135 0.390457 0.195228 0.980758i \(-0.437455\pi\)
0.195228 + 0.980758i \(0.437455\pi\)
\(308\) −19.0520 −1.08559
\(309\) 45.0886 2.56500
\(310\) 1.96088 0.111370
\(311\) 26.9202 1.52650 0.763252 0.646101i \(-0.223602\pi\)
0.763252 + 0.646101i \(0.223602\pi\)
\(312\) −78.3830 −4.43756
\(313\) −9.98612 −0.564449 −0.282224 0.959348i \(-0.591072\pi\)
−0.282224 + 0.959348i \(0.591072\pi\)
\(314\) −44.5335 −2.51317
\(315\) 13.8568 0.780741
\(316\) −12.3727 −0.696019
\(317\) 17.0621 0.958302 0.479151 0.877732i \(-0.340945\pi\)
0.479151 + 0.877732i \(0.340945\pi\)
\(318\) −100.831 −5.65434
\(319\) −7.54555 −0.422469
\(320\) −30.0874 −1.68194
\(321\) −14.4873 −0.808600
\(322\) 2.90713 0.162008
\(323\) 3.07600 0.171153
\(324\) 44.0888 2.44938
\(325\) 2.17457 0.120623
\(326\) −11.4426 −0.633747
\(327\) 32.1072 1.77553
\(328\) 9.20830 0.508443
\(329\) 2.84244 0.156709
\(330\) −55.9764 −3.08140
\(331\) 12.4753 0.685707 0.342853 0.939389i \(-0.388607\pi\)
0.342853 + 0.939389i \(0.388607\pi\)
\(332\) 37.8083 2.07500
\(333\) 66.8337 3.66247
\(334\) 38.0488 2.08194
\(335\) 19.3265 1.05592
\(336\) 38.0012 2.07313
\(337\) −4.17402 −0.227374 −0.113687 0.993517i \(-0.536266\pi\)
−0.113687 + 0.993517i \(0.536266\pi\)
\(338\) 6.70755 0.364843
\(339\) 21.4782 1.16654
\(340\) −45.1300 −2.44752
\(341\) 1.20166 0.0650738
\(342\) −11.3411 −0.613256
\(343\) 14.2296 0.768326
\(344\) 49.6513 2.67702
\(345\) 6.11709 0.329333
\(346\) 19.9152 1.07065
\(347\) −1.54513 −0.0829468 −0.0414734 0.999140i \(-0.513205\pi\)
−0.0414734 + 0.999140i \(0.513205\pi\)
\(348\) 33.6994 1.80648
\(349\) 15.9650 0.854589 0.427295 0.904112i \(-0.359467\pi\)
0.427295 + 0.904112i \(0.359467\pi\)
\(350\) −1.98982 −0.106360
\(351\) 28.7940 1.53691
\(352\) −47.4383 −2.52847
\(353\) −20.0161 −1.06535 −0.532675 0.846320i \(-0.678813\pi\)
−0.532675 + 0.846320i \(0.678813\pi\)
\(354\) 96.4925 5.12852
\(355\) 6.74074 0.357761
\(356\) 58.6583 3.10888
\(357\) 14.3629 0.760167
\(358\) 6.32288 0.334174
\(359\) 3.06598 0.161816 0.0809080 0.996722i \(-0.474218\pi\)
0.0809080 + 0.996722i \(0.474218\pi\)
\(360\) 100.447 5.29405
\(361\) −18.4880 −0.973051
\(362\) 6.57847 0.345757
\(363\) −1.35729 −0.0712394
\(364\) 18.2186 0.954915
\(365\) 9.48358 0.496393
\(366\) 60.8253 3.17939
\(367\) 19.9579 1.04179 0.520897 0.853620i \(-0.325598\pi\)
0.520897 + 0.853620i \(0.325598\pi\)
\(368\) 11.1655 0.582040
\(369\) −6.79875 −0.353929
\(370\) 61.8165 3.21369
\(371\) 14.1480 0.734527
\(372\) −5.36679 −0.278255
\(373\) −31.2790 −1.61956 −0.809781 0.586732i \(-0.800414\pi\)
−0.809781 + 0.586732i \(0.800414\pi\)
\(374\) −38.6174 −1.99686
\(375\) −35.3419 −1.82505
\(376\) 20.6048 1.06261
\(377\) 7.21550 0.371617
\(378\) −26.3476 −1.35518
\(379\) 21.2304 1.09053 0.545267 0.838262i \(-0.316428\pi\)
0.545267 + 0.838262i \(0.316428\pi\)
\(380\) −7.51240 −0.385378
\(381\) −53.2695 −2.72908
\(382\) 5.11956 0.261939
\(383\) −7.97632 −0.407571 −0.203785 0.979016i \(-0.565324\pi\)
−0.203785 + 0.979016i \(0.565324\pi\)
\(384\) 31.0164 1.58280
\(385\) 7.85424 0.400289
\(386\) −27.2690 −1.38796
\(387\) −36.6590 −1.86348
\(388\) −53.7747 −2.73000
\(389\) −13.0994 −0.664168 −0.332084 0.943250i \(-0.607752\pi\)
−0.332084 + 0.943250i \(0.607752\pi\)
\(390\) 53.5279 2.71049
\(391\) 4.22010 0.213420
\(392\) 46.5431 2.35078
\(393\) 9.74417 0.491528
\(394\) −60.4388 −3.04486
\(395\) 5.10069 0.256643
\(396\) 101.969 5.12411
\(397\) −7.38795 −0.370790 −0.185395 0.982664i \(-0.559357\pi\)
−0.185395 + 0.982664i \(0.559357\pi\)
\(398\) −54.5894 −2.73632
\(399\) 2.39087 0.119693
\(400\) −7.64231 −0.382116
\(401\) −8.17292 −0.408136 −0.204068 0.978957i \(-0.565416\pi\)
−0.204068 + 0.978957i \(0.565416\pi\)
\(402\) −73.8587 −3.68374
\(403\) −1.14910 −0.0572409
\(404\) 24.1996 1.20398
\(405\) −18.1758 −0.903161
\(406\) −6.60247 −0.327675
\(407\) 37.8824 1.87776
\(408\) 104.117 5.15454
\(409\) −21.3014 −1.05329 −0.526643 0.850087i \(-0.676549\pi\)
−0.526643 + 0.850087i \(0.676549\pi\)
\(410\) −6.28837 −0.310560
\(411\) −30.0045 −1.48001
\(412\) −75.9691 −3.74273
\(413\) −13.5392 −0.666220
\(414\) −15.5594 −0.764700
\(415\) −15.5866 −0.765116
\(416\) 45.3633 2.22412
\(417\) 38.7494 1.89757
\(418\) −6.42831 −0.314419
\(419\) −12.8051 −0.625572 −0.312786 0.949824i \(-0.601262\pi\)
−0.312786 + 0.949824i \(0.601262\pi\)
\(420\) −35.0780 −1.71163
\(421\) −33.8202 −1.64830 −0.824148 0.566374i \(-0.808346\pi\)
−0.824148 + 0.566374i \(0.808346\pi\)
\(422\) 29.2063 1.42174
\(423\) −15.2131 −0.739687
\(424\) 102.558 4.98068
\(425\) −2.88849 −0.140112
\(426\) −25.7606 −1.24811
\(427\) −8.53460 −0.413018
\(428\) 24.4094 1.17987
\(429\) 32.8030 1.58374
\(430\) −33.9070 −1.63514
\(431\) 1.97569 0.0951655 0.0475827 0.998867i \(-0.484848\pi\)
0.0475827 + 0.998867i \(0.484848\pi\)
\(432\) −101.194 −4.86868
\(433\) 30.4554 1.46359 0.731797 0.681523i \(-0.238682\pi\)
0.731797 + 0.681523i \(0.238682\pi\)
\(434\) 1.05147 0.0504724
\(435\) −13.8927 −0.666103
\(436\) −54.0969 −2.59077
\(437\) 0.702484 0.0336044
\(438\) −36.2428 −1.73175
\(439\) 36.2092 1.72817 0.864084 0.503347i \(-0.167898\pi\)
0.864084 + 0.503347i \(0.167898\pi\)
\(440\) 56.9352 2.71428
\(441\) −34.3641 −1.63639
\(442\) 36.9283 1.75650
\(443\) −22.2613 −1.05767 −0.528834 0.848725i \(-0.677371\pi\)
−0.528834 + 0.848725i \(0.677371\pi\)
\(444\) −169.188 −8.02929
\(445\) −24.1821 −1.14634
\(446\) −59.2204 −2.80417
\(447\) −55.9443 −2.64607
\(448\) −16.1337 −0.762245
\(449\) 26.3429 1.24320 0.621599 0.783336i \(-0.286483\pi\)
0.621599 + 0.783336i \(0.286483\pi\)
\(450\) 10.6498 0.502034
\(451\) −3.85364 −0.181461
\(452\) −36.1884 −1.70216
\(453\) 43.1511 2.02741
\(454\) 15.3087 0.718473
\(455\) −7.51069 −0.352106
\(456\) 17.3314 0.811617
\(457\) −41.1676 −1.92574 −0.962870 0.269967i \(-0.912987\pi\)
−0.962870 + 0.269967i \(0.912987\pi\)
\(458\) 26.7149 1.24831
\(459\) −38.2472 −1.78523
\(460\) −10.3066 −0.480547
\(461\) −2.21473 −0.103150 −0.0515752 0.998669i \(-0.516424\pi\)
−0.0515752 + 0.998669i \(0.516424\pi\)
\(462\) −30.0160 −1.39647
\(463\) −13.0498 −0.606476 −0.303238 0.952915i \(-0.598068\pi\)
−0.303238 + 0.952915i \(0.598068\pi\)
\(464\) −25.3582 −1.17722
\(465\) 2.21248 0.102601
\(466\) 22.2050 1.02863
\(467\) 11.2239 0.519379 0.259689 0.965692i \(-0.416380\pi\)
0.259689 + 0.965692i \(0.416380\pi\)
\(468\) −97.5084 −4.50733
\(469\) 10.3634 0.478536
\(470\) −14.0711 −0.649050
\(471\) −50.2476 −2.31529
\(472\) −98.1452 −4.51750
\(473\) −20.7789 −0.955413
\(474\) −19.4930 −0.895342
\(475\) −0.480822 −0.0220616
\(476\) −24.1999 −1.10920
\(477\) −75.7219 −3.46707
\(478\) −29.8685 −1.36616
\(479\) −18.5816 −0.849016 −0.424508 0.905424i \(-0.639553\pi\)
−0.424508 + 0.905424i \(0.639553\pi\)
\(480\) −87.3422 −3.98661
\(481\) −36.2254 −1.65174
\(482\) 21.0045 0.956727
\(483\) 3.28014 0.149252
\(484\) 2.28688 0.103949
\(485\) 22.1688 1.00663
\(486\) −1.39343 −0.0632075
\(487\) −36.3379 −1.64663 −0.823313 0.567587i \(-0.807877\pi\)
−0.823313 + 0.567587i \(0.807877\pi\)
\(488\) −61.8671 −2.80059
\(489\) −12.9108 −0.583846
\(490\) −31.7844 −1.43587
\(491\) 24.6739 1.11352 0.556759 0.830674i \(-0.312045\pi\)
0.556759 + 0.830674i \(0.312045\pi\)
\(492\) 17.2108 0.775924
\(493\) −9.58439 −0.431659
\(494\) 6.14713 0.276572
\(495\) −42.0369 −1.88942
\(496\) 4.03841 0.181330
\(497\) 3.61456 0.162135
\(498\) 59.5663 2.66923
\(499\) 12.0686 0.540266 0.270133 0.962823i \(-0.412932\pi\)
0.270133 + 0.962823i \(0.412932\pi\)
\(500\) 59.5471 2.66303
\(501\) 42.9308 1.91801
\(502\) −14.8012 −0.660610
\(503\) −35.0987 −1.56497 −0.782487 0.622666i \(-0.786049\pi\)
−0.782487 + 0.622666i \(0.786049\pi\)
\(504\) 53.8626 2.39923
\(505\) −9.97638 −0.443943
\(506\) −8.81928 −0.392065
\(507\) 7.56819 0.336115
\(508\) 89.7530 3.98215
\(509\) −23.0318 −1.02087 −0.510433 0.859917i \(-0.670515\pi\)
−0.510433 + 0.859917i \(0.670515\pi\)
\(510\) −71.1015 −3.14843
\(511\) 5.08535 0.224963
\(512\) 24.5217 1.08372
\(513\) −6.36668 −0.281096
\(514\) −67.4904 −2.97688
\(515\) 31.3185 1.38006
\(516\) 92.8011 4.08534
\(517\) −8.62303 −0.379240
\(518\) 33.1477 1.45643
\(519\) 22.4704 0.986343
\(520\) −54.4448 −2.38756
\(521\) −20.0094 −0.876626 −0.438313 0.898822i \(-0.644424\pi\)
−0.438313 + 0.898822i \(0.644424\pi\)
\(522\) 35.3373 1.54667
\(523\) −19.1158 −0.835875 −0.417937 0.908476i \(-0.637247\pi\)
−0.417937 + 0.908476i \(0.637247\pi\)
\(524\) −16.4178 −0.717215
\(525\) −2.24513 −0.0979855
\(526\) −42.3310 −1.84572
\(527\) 1.52636 0.0664893
\(528\) −115.283 −5.01704
\(529\) −22.0362 −0.958097
\(530\) −70.0374 −3.04223
\(531\) 72.4635 3.14465
\(532\) −4.02835 −0.174651
\(533\) 3.68508 0.159618
\(534\) 92.4151 3.99919
\(535\) −10.0628 −0.435055
\(536\) 75.1238 3.24485
\(537\) 7.13416 0.307862
\(538\) −38.0801 −1.64175
\(539\) −19.4781 −0.838982
\(540\) 93.4095 4.01971
\(541\) −12.8024 −0.550417 −0.275208 0.961385i \(-0.588747\pi\)
−0.275208 + 0.961385i \(0.588747\pi\)
\(542\) −47.2515 −2.02963
\(543\) 7.42255 0.318532
\(544\) −60.2563 −2.58347
\(545\) 22.3016 0.955297
\(546\) 28.7031 1.22838
\(547\) −14.9095 −0.637486 −0.318743 0.947841i \(-0.603261\pi\)
−0.318743 + 0.947841i \(0.603261\pi\)
\(548\) 50.5542 2.15957
\(549\) 45.6783 1.94950
\(550\) 6.03645 0.257395
\(551\) −1.59543 −0.0679676
\(552\) 23.7777 1.01205
\(553\) 2.73512 0.116309
\(554\) −4.43936 −0.188610
\(555\) 69.7481 2.96064
\(556\) −65.2883 −2.76884
\(557\) −18.1673 −0.769774 −0.384887 0.922964i \(-0.625760\pi\)
−0.384887 + 0.922964i \(0.625760\pi\)
\(558\) −5.62763 −0.238236
\(559\) 19.8700 0.840411
\(560\) 26.3956 1.11542
\(561\) −43.5724 −1.83963
\(562\) 28.5432 1.20402
\(563\) 34.3825 1.44905 0.724524 0.689249i \(-0.242060\pi\)
0.724524 + 0.689249i \(0.242060\pi\)
\(564\) 38.5115 1.62163
\(565\) 14.9188 0.627637
\(566\) −65.2090 −2.74094
\(567\) −9.74633 −0.409307
\(568\) 26.2019 1.09941
\(569\) 2.33082 0.0977129 0.0488565 0.998806i \(-0.484442\pi\)
0.0488565 + 0.998806i \(0.484442\pi\)
\(570\) −11.8356 −0.495741
\(571\) 34.3236 1.43640 0.718200 0.695837i \(-0.244966\pi\)
0.718200 + 0.695837i \(0.244966\pi\)
\(572\) −55.2693 −2.31092
\(573\) 5.77645 0.241314
\(574\) −3.37199 −0.140744
\(575\) −0.659661 −0.0275098
\(576\) 86.3496 3.59790
\(577\) −22.6331 −0.942228 −0.471114 0.882072i \(-0.656148\pi\)
−0.471114 + 0.882072i \(0.656148\pi\)
\(578\) −3.92544 −0.163277
\(579\) −30.7679 −1.27867
\(580\) 23.4076 0.971946
\(581\) −8.35795 −0.346746
\(582\) −84.7212 −3.51180
\(583\) −42.9203 −1.77758
\(584\) 36.8636 1.52543
\(585\) 40.1982 1.66199
\(586\) 10.3327 0.426841
\(587\) 12.2595 0.506003 0.253001 0.967466i \(-0.418582\pi\)
0.253001 + 0.967466i \(0.418582\pi\)
\(588\) 86.9918 3.58748
\(589\) 0.254080 0.0104692
\(590\) 67.0236 2.75932
\(591\) −68.1936 −2.80511
\(592\) 127.311 5.23243
\(593\) 2.68708 0.110345 0.0551726 0.998477i \(-0.482429\pi\)
0.0551726 + 0.998477i \(0.482429\pi\)
\(594\) 79.9299 3.27956
\(595\) 9.97649 0.408996
\(596\) 94.2597 3.86103
\(597\) −61.5937 −2.52086
\(598\) 8.43352 0.344872
\(599\) 12.6420 0.516537 0.258268 0.966073i \(-0.416848\pi\)
0.258268 + 0.966073i \(0.416848\pi\)
\(600\) −16.2749 −0.664419
\(601\) 4.33060 0.176649 0.0883244 0.996092i \(-0.471849\pi\)
0.0883244 + 0.996092i \(0.471849\pi\)
\(602\) −18.1818 −0.741036
\(603\) −55.4661 −2.25875
\(604\) −72.7046 −2.95831
\(605\) −0.942774 −0.0383292
\(606\) 38.1261 1.54877
\(607\) 0.468327 0.0190088 0.00950441 0.999955i \(-0.496975\pi\)
0.00950441 + 0.999955i \(0.496975\pi\)
\(608\) −10.0303 −0.406784
\(609\) −7.44963 −0.301874
\(610\) 42.2492 1.71062
\(611\) 8.24585 0.333591
\(612\) 129.521 5.23558
\(613\) −13.2115 −0.533609 −0.266805 0.963751i \(-0.585968\pi\)
−0.266805 + 0.963751i \(0.585968\pi\)
\(614\) −18.1604 −0.732895
\(615\) −7.09522 −0.286107
\(616\) 30.5302 1.23010
\(617\) −12.5231 −0.504163 −0.252081 0.967706i \(-0.581115\pi\)
−0.252081 + 0.967706i \(0.581115\pi\)
\(618\) −119.688 −4.81456
\(619\) −21.8618 −0.878701 −0.439351 0.898316i \(-0.644791\pi\)
−0.439351 + 0.898316i \(0.644791\pi\)
\(620\) −3.72777 −0.149711
\(621\) −8.73472 −0.350512
\(622\) −71.4598 −2.86528
\(623\) −12.9671 −0.519515
\(624\) 110.240 4.41315
\(625\) −21.1888 −0.847550
\(626\) 26.5082 1.05948
\(627\) −7.25312 −0.289662
\(628\) 84.6614 3.37836
\(629\) 48.1184 1.91861
\(630\) −36.7829 −1.46547
\(631\) −30.6788 −1.22130 −0.610652 0.791899i \(-0.709093\pi\)
−0.610652 + 0.791899i \(0.709093\pi\)
\(632\) 19.8269 0.788670
\(633\) 32.9537 1.30979
\(634\) −45.2914 −1.79875
\(635\) −37.0010 −1.46834
\(636\) 191.688 7.60091
\(637\) 18.6261 0.737994
\(638\) 20.0297 0.792983
\(639\) −19.3456 −0.765300
\(640\) 21.5440 0.851601
\(641\) 28.0285 1.10706 0.553529 0.832830i \(-0.313281\pi\)
0.553529 + 0.832830i \(0.313281\pi\)
\(642\) 38.4565 1.51776
\(643\) 39.3726 1.55270 0.776352 0.630300i \(-0.217068\pi\)
0.776352 + 0.630300i \(0.217068\pi\)
\(644\) −5.52667 −0.217781
\(645\) −38.2575 −1.50639
\(646\) −8.16527 −0.321258
\(647\) 2.07740 0.0816710 0.0408355 0.999166i \(-0.486998\pi\)
0.0408355 + 0.999166i \(0.486998\pi\)
\(648\) −70.6509 −2.77543
\(649\) 41.0734 1.61227
\(650\) −5.77241 −0.226412
\(651\) 1.18639 0.0464982
\(652\) 21.7532 0.851921
\(653\) −10.1212 −0.396074 −0.198037 0.980195i \(-0.563457\pi\)
−0.198037 + 0.980195i \(0.563457\pi\)
\(654\) −85.2287 −3.33271
\(655\) 6.76830 0.264459
\(656\) −12.9508 −0.505645
\(657\) −27.2175 −1.06185
\(658\) −7.54528 −0.294146
\(659\) −14.1521 −0.551286 −0.275643 0.961260i \(-0.588891\pi\)
−0.275643 + 0.961260i \(0.588891\pi\)
\(660\) 106.415 4.14220
\(661\) −36.0369 −1.40167 −0.700836 0.713323i \(-0.747189\pi\)
−0.700836 + 0.713323i \(0.747189\pi\)
\(662\) −33.1159 −1.28708
\(663\) 41.6665 1.61819
\(664\) −60.5866 −2.35122
\(665\) 1.66070 0.0643992
\(666\) −177.411 −6.87452
\(667\) −2.18884 −0.0847522
\(668\) −72.3335 −2.79867
\(669\) −66.8189 −2.58337
\(670\) −51.3022 −1.98198
\(671\) 25.8911 0.999516
\(672\) −46.8352 −1.80671
\(673\) 22.0857 0.851340 0.425670 0.904878i \(-0.360038\pi\)
0.425670 + 0.904878i \(0.360038\pi\)
\(674\) 11.0800 0.426785
\(675\) 5.97857 0.230115
\(676\) −12.7515 −0.490443
\(677\) 14.4705 0.556146 0.278073 0.960560i \(-0.410304\pi\)
0.278073 + 0.960560i \(0.410304\pi\)
\(678\) −57.0141 −2.18961
\(679\) 11.8875 0.456201
\(680\) 72.3194 2.77332
\(681\) 17.2730 0.661901
\(682\) −3.18983 −0.122145
\(683\) −0.0799145 −0.00305784 −0.00152892 0.999999i \(-0.500487\pi\)
−0.00152892 + 0.999999i \(0.500487\pi\)
\(684\) 21.5602 0.824376
\(685\) −20.8411 −0.796299
\(686\) −37.7726 −1.44216
\(687\) 30.1427 1.15002
\(688\) −69.8311 −2.66229
\(689\) 41.0430 1.56361
\(690\) −16.2378 −0.618164
\(691\) 6.46607 0.245981 0.122990 0.992408i \(-0.460752\pi\)
0.122990 + 0.992408i \(0.460752\pi\)
\(692\) −37.8601 −1.43923
\(693\) −22.5413 −0.856273
\(694\) 4.10155 0.155693
\(695\) 26.9153 1.02096
\(696\) −54.0022 −2.04695
\(697\) −4.89491 −0.185408
\(698\) −42.3793 −1.60408
\(699\) 25.0541 0.947634
\(700\) 3.78278 0.142976
\(701\) 8.66524 0.327282 0.163641 0.986520i \(-0.447676\pi\)
0.163641 + 0.986520i \(0.447676\pi\)
\(702\) −76.4337 −2.88481
\(703\) 8.00985 0.302097
\(704\) 48.9443 1.84466
\(705\) −15.8765 −0.597944
\(706\) 53.1329 1.99968
\(707\) −5.34960 −0.201192
\(708\) −183.439 −6.89406
\(709\) −3.77392 −0.141733 −0.0708663 0.997486i \(-0.522576\pi\)
−0.0708663 + 0.997486i \(0.522576\pi\)
\(710\) −17.8933 −0.671525
\(711\) −14.6387 −0.548996
\(712\) −93.9980 −3.52273
\(713\) 0.348583 0.0130545
\(714\) −38.1265 −1.42685
\(715\) 22.7849 0.852108
\(716\) −12.0202 −0.449217
\(717\) −33.7009 −1.25858
\(718\) −8.13866 −0.303732
\(719\) −25.8889 −0.965492 −0.482746 0.875761i \(-0.660360\pi\)
−0.482746 + 0.875761i \(0.660360\pi\)
\(720\) −141.273 −5.26492
\(721\) 16.7938 0.625435
\(722\) 49.0764 1.82644
\(723\) 23.6995 0.881394
\(724\) −12.5061 −0.464787
\(725\) 1.49817 0.0556408
\(726\) 3.60294 0.133718
\(727\) −32.9660 −1.22264 −0.611320 0.791383i \(-0.709361\pi\)
−0.611320 + 0.791383i \(0.709361\pi\)
\(728\) −29.1948 −1.08203
\(729\) −27.7822 −1.02897
\(730\) −25.1742 −0.931740
\(731\) −26.3934 −0.976196
\(732\) −115.633 −4.27392
\(733\) 2.09021 0.0772037 0.0386018 0.999255i \(-0.487710\pi\)
0.0386018 + 0.999255i \(0.487710\pi\)
\(734\) −52.9784 −1.95547
\(735\) −35.8627 −1.32281
\(736\) −13.7611 −0.507240
\(737\) −31.4390 −1.15807
\(738\) 18.0473 0.664331
\(739\) −7.31887 −0.269229 −0.134614 0.990898i \(-0.542980\pi\)
−0.134614 + 0.990898i \(0.542980\pi\)
\(740\) −117.518 −4.32003
\(741\) 6.93586 0.254795
\(742\) −37.5559 −1.37872
\(743\) −27.8176 −1.02053 −0.510264 0.860018i \(-0.670452\pi\)
−0.510264 + 0.860018i \(0.670452\pi\)
\(744\) 8.60010 0.315295
\(745\) −38.8589 −1.42368
\(746\) 83.0302 3.03995
\(747\) 44.7328 1.63669
\(748\) 73.4145 2.68430
\(749\) −5.39597 −0.197164
\(750\) 93.8154 3.42565
\(751\) −10.1157 −0.369127 −0.184563 0.982821i \(-0.559087\pi\)
−0.184563 + 0.982821i \(0.559087\pi\)
\(752\) −28.9792 −1.05676
\(753\) −16.7003 −0.608594
\(754\) −19.1536 −0.697533
\(755\) 29.9727 1.09082
\(756\) 50.0887 1.82171
\(757\) 50.1035 1.82104 0.910522 0.413461i \(-0.135680\pi\)
0.910522 + 0.413461i \(0.135680\pi\)
\(758\) −56.3564 −2.04695
\(759\) −9.95087 −0.361194
\(760\) 12.0384 0.436678
\(761\) −23.9710 −0.868947 −0.434473 0.900685i \(-0.643066\pi\)
−0.434473 + 0.900685i \(0.643066\pi\)
\(762\) 141.404 5.12254
\(763\) 11.9587 0.432935
\(764\) −9.73265 −0.352115
\(765\) −53.3955 −1.93052
\(766\) 21.1732 0.765018
\(767\) −39.2768 −1.41820
\(768\) 4.29915 0.155132
\(769\) −41.4527 −1.49482 −0.747412 0.664361i \(-0.768704\pi\)
−0.747412 + 0.664361i \(0.768704\pi\)
\(770\) −20.8491 −0.751350
\(771\) −76.1501 −2.74248
\(772\) 51.8403 1.86577
\(773\) −41.1687 −1.48073 −0.740367 0.672203i \(-0.765348\pi\)
−0.740367 + 0.672203i \(0.765348\pi\)
\(774\) 97.3115 3.49779
\(775\) −0.238591 −0.00857046
\(776\) 86.1723 3.09341
\(777\) 37.4008 1.34175
\(778\) 34.7726 1.24666
\(779\) −0.814813 −0.0291937
\(780\) −101.760 −3.64361
\(781\) −10.9654 −0.392372
\(782\) −11.2023 −0.400593
\(783\) 19.8377 0.708940
\(784\) −65.4598 −2.33785
\(785\) −34.9019 −1.24570
\(786\) −25.8660 −0.922608
\(787\) 15.5666 0.554891 0.277445 0.960741i \(-0.410512\pi\)
0.277445 + 0.960741i \(0.410512\pi\)
\(788\) 114.898 4.09309
\(789\) −47.7624 −1.70039
\(790\) −13.5398 −0.481725
\(791\) 7.99984 0.284442
\(792\) −163.401 −5.80621
\(793\) −24.7586 −0.879205
\(794\) 19.6113 0.695981
\(795\) −79.0239 −2.80269
\(796\) 103.778 3.67832
\(797\) 21.4327 0.759185 0.379592 0.925154i \(-0.376064\pi\)
0.379592 + 0.925154i \(0.376064\pi\)
\(798\) −6.34659 −0.224667
\(799\) −10.9530 −0.387490
\(800\) 9.41891 0.333009
\(801\) 69.4015 2.45218
\(802\) 21.6951 0.766080
\(803\) −15.4273 −0.544417
\(804\) 140.411 4.95190
\(805\) 2.27839 0.0803026
\(806\) 3.05030 0.107442
\(807\) −42.9661 −1.51248
\(808\) −38.7791 −1.36425
\(809\) −7.93616 −0.279020 −0.139510 0.990221i \(-0.544553\pi\)
−0.139510 + 0.990221i \(0.544553\pi\)
\(810\) 48.2477 1.69525
\(811\) 19.6150 0.688774 0.344387 0.938828i \(-0.388087\pi\)
0.344387 + 0.938828i \(0.388087\pi\)
\(812\) 12.5518 0.440480
\(813\) −53.3143 −1.86981
\(814\) −100.559 −3.52459
\(815\) −8.96783 −0.314129
\(816\) −146.433 −5.12618
\(817\) −4.39348 −0.153709
\(818\) 56.5446 1.97704
\(819\) 21.5553 0.753204
\(820\) 11.9546 0.417474
\(821\) 26.2538 0.916263 0.458132 0.888884i \(-0.348519\pi\)
0.458132 + 0.888884i \(0.348519\pi\)
\(822\) 79.6472 2.77802
\(823\) −27.3948 −0.954921 −0.477461 0.878653i \(-0.658443\pi\)
−0.477461 + 0.878653i \(0.658443\pi\)
\(824\) 121.738 4.24095
\(825\) 6.81098 0.237128
\(826\) 35.9399 1.25051
\(827\) 18.4701 0.642267 0.321134 0.947034i \(-0.395936\pi\)
0.321134 + 0.947034i \(0.395936\pi\)
\(828\) 29.5794 1.02796
\(829\) 25.6304 0.890180 0.445090 0.895486i \(-0.353172\pi\)
0.445090 + 0.895486i \(0.353172\pi\)
\(830\) 41.3747 1.43614
\(831\) −5.00897 −0.173759
\(832\) −46.8034 −1.62262
\(833\) −24.7412 −0.857232
\(834\) −102.861 −3.56177
\(835\) 29.8197 1.03195
\(836\) 12.2207 0.422661
\(837\) −3.15924 −0.109199
\(838\) 33.9913 1.17421
\(839\) −20.4166 −0.704858 −0.352429 0.935838i \(-0.614644\pi\)
−0.352429 + 0.935838i \(0.614644\pi\)
\(840\) 56.2114 1.93948
\(841\) −24.0289 −0.828582
\(842\) 89.7760 3.09388
\(843\) 32.2055 1.10922
\(844\) −55.5233 −1.91119
\(845\) 5.25686 0.180841
\(846\) 40.3833 1.38841
\(847\) −0.505541 −0.0173706
\(848\) −144.242 −4.95327
\(849\) −73.5759 −2.52512
\(850\) 7.66752 0.262994
\(851\) 10.9891 0.376700
\(852\) 48.9728 1.67778
\(853\) 5.62072 0.192450 0.0962249 0.995360i \(-0.469323\pi\)
0.0962249 + 0.995360i \(0.469323\pi\)
\(854\) 22.6551 0.775243
\(855\) −8.88828 −0.303973
\(856\) −39.1153 −1.33693
\(857\) −18.7527 −0.640581 −0.320290 0.947319i \(-0.603781\pi\)
−0.320290 + 0.947319i \(0.603781\pi\)
\(858\) −87.0757 −2.97272
\(859\) −6.75647 −0.230528 −0.115264 0.993335i \(-0.536771\pi\)
−0.115264 + 0.993335i \(0.536771\pi\)
\(860\) 64.4596 2.19805
\(861\) −3.80465 −0.129662
\(862\) −5.24447 −0.178627
\(863\) 4.92266 0.167569 0.0837847 0.996484i \(-0.473299\pi\)
0.0837847 + 0.996484i \(0.473299\pi\)
\(864\) 124.718 4.24299
\(865\) 15.6080 0.530687
\(866\) −80.8441 −2.74719
\(867\) −4.42911 −0.150421
\(868\) −1.99893 −0.0678480
\(869\) −8.29746 −0.281472
\(870\) 36.8782 1.25029
\(871\) 30.0639 1.01867
\(872\) 86.6886 2.93565
\(873\) −63.6235 −2.15333
\(874\) −1.86475 −0.0630761
\(875\) −13.1636 −0.445009
\(876\) 68.9002 2.32792
\(877\) 33.4684 1.13015 0.565074 0.825040i \(-0.308848\pi\)
0.565074 + 0.825040i \(0.308848\pi\)
\(878\) −96.1174 −3.24381
\(879\) 11.6585 0.393232
\(880\) −80.0754 −2.69934
\(881\) −13.2892 −0.447723 −0.223862 0.974621i \(-0.571866\pi\)
−0.223862 + 0.974621i \(0.571866\pi\)
\(882\) 91.2198 3.07153
\(883\) −5.26124 −0.177055 −0.0885274 0.996074i \(-0.528216\pi\)
−0.0885274 + 0.996074i \(0.528216\pi\)
\(884\) −70.2033 −2.36119
\(885\) 75.6234 2.54205
\(886\) 59.0929 1.98526
\(887\) −31.6616 −1.06309 −0.531547 0.847029i \(-0.678389\pi\)
−0.531547 + 0.847029i \(0.678389\pi\)
\(888\) 271.118 9.09811
\(889\) −19.8409 −0.665443
\(890\) 64.1915 2.15170
\(891\) 29.5671 0.990536
\(892\) 112.582 3.76953
\(893\) −1.82325 −0.0610128
\(894\) 148.505 4.96673
\(895\) 4.95538 0.165640
\(896\) 11.5525 0.385941
\(897\) 9.51561 0.317717
\(898\) −69.9274 −2.33351
\(899\) −0.791677 −0.0264039
\(900\) −20.2459 −0.674865
\(901\) −54.5176 −1.81624
\(902\) 10.2295 0.340605
\(903\) −20.5147 −0.682687
\(904\) 57.9907 1.92874
\(905\) 5.15570 0.171381
\(906\) −114.545 −3.80550
\(907\) 7.43424 0.246850 0.123425 0.992354i \(-0.460612\pi\)
0.123425 + 0.992354i \(0.460612\pi\)
\(908\) −29.1029 −0.965815
\(909\) 28.6318 0.949655
\(910\) 19.9372 0.660911
\(911\) −9.25748 −0.306714 −0.153357 0.988171i \(-0.549008\pi\)
−0.153357 + 0.988171i \(0.549008\pi\)
\(912\) −24.3754 −0.807151
\(913\) 25.3552 0.839136
\(914\) 109.280 3.61465
\(915\) 47.6701 1.57593
\(916\) −50.7870 −1.67805
\(917\) 3.62934 0.119851
\(918\) 101.527 3.35090
\(919\) −2.32860 −0.0768134 −0.0384067 0.999262i \(-0.512228\pi\)
−0.0384067 + 0.999262i \(0.512228\pi\)
\(920\) 16.5160 0.544516
\(921\) −20.4906 −0.675187
\(922\) 5.87903 0.193615
\(923\) 10.4858 0.345143
\(924\) 57.0626 1.87722
\(925\) −7.52158 −0.247308
\(926\) 34.6408 1.13837
\(927\) −89.8827 −2.95213
\(928\) 31.2531 1.02593
\(929\) −1.00084 −0.0328366 −0.0164183 0.999865i \(-0.505226\pi\)
−0.0164183 + 0.999865i \(0.505226\pi\)
\(930\) −5.87303 −0.192584
\(931\) −4.11845 −0.134977
\(932\) −42.2133 −1.38274
\(933\) −80.6287 −2.63967
\(934\) −29.7938 −0.974884
\(935\) −30.2654 −0.989783
\(936\) 156.254 5.10732
\(937\) 23.7432 0.775658 0.387829 0.921731i \(-0.373225\pi\)
0.387829 + 0.921731i \(0.373225\pi\)
\(938\) −27.5096 −0.898221
\(939\) 29.9095 0.976059
\(940\) 26.7501 0.872492
\(941\) 3.67235 0.119715 0.0598576 0.998207i \(-0.480935\pi\)
0.0598576 + 0.998207i \(0.480935\pi\)
\(942\) 133.383 4.34584
\(943\) −1.11788 −0.0364031
\(944\) 138.035 4.49264
\(945\) −20.6492 −0.671719
\(946\) 55.1576 1.79333
\(947\) 43.5506 1.41520 0.707602 0.706611i \(-0.249777\pi\)
0.707602 + 0.706611i \(0.249777\pi\)
\(948\) 37.0575 1.20357
\(949\) 14.7525 0.478885
\(950\) 1.27635 0.0414101
\(951\) −51.1027 −1.65712
\(952\) 38.7796 1.25685
\(953\) −14.9357 −0.483815 −0.241907 0.970299i \(-0.577773\pi\)
−0.241907 + 0.970299i \(0.577773\pi\)
\(954\) 201.004 6.50775
\(955\) 4.01232 0.129836
\(956\) 56.7822 1.83647
\(957\) 22.5997 0.730544
\(958\) 49.3251 1.59362
\(959\) −11.1756 −0.360878
\(960\) 90.1150 2.90845
\(961\) −30.8739 −0.995933
\(962\) 96.1605 3.10034
\(963\) 28.8799 0.930642
\(964\) −39.9310 −1.28609
\(965\) −21.3713 −0.687968
\(966\) −8.70717 −0.280148
\(967\) −2.72744 −0.0877084 −0.0438542 0.999038i \(-0.513964\pi\)
−0.0438542 + 0.999038i \(0.513964\pi\)
\(968\) −3.66465 −0.117786
\(969\) −9.21295 −0.295962
\(970\) −58.8473 −1.88947
\(971\) −24.2522 −0.778289 −0.389145 0.921177i \(-0.627229\pi\)
−0.389145 + 0.921177i \(0.627229\pi\)
\(972\) 2.64902 0.0849673
\(973\) 14.4327 0.462692
\(974\) 96.4591 3.09075
\(975\) −6.51306 −0.208585
\(976\) 87.0119 2.78518
\(977\) −18.6446 −0.596493 −0.298246 0.954489i \(-0.596402\pi\)
−0.298246 + 0.954489i \(0.596402\pi\)
\(978\) 34.2718 1.09589
\(979\) 39.3378 1.25724
\(980\) 60.4244 1.93019
\(981\) −64.0047 −2.04351
\(982\) −65.4970 −2.09009
\(983\) 47.0685 1.50125 0.750626 0.660727i \(-0.229752\pi\)
0.750626 + 0.660727i \(0.229752\pi\)
\(984\) −27.5798 −0.879212
\(985\) −47.3673 −1.50925
\(986\) 25.4418 0.810233
\(987\) −8.51341 −0.270985
\(988\) −11.6861 −0.371785
\(989\) −6.02761 −0.191667
\(990\) 111.587 3.54647
\(991\) −10.6374 −0.337907 −0.168953 0.985624i \(-0.554039\pi\)
−0.168953 + 0.985624i \(0.554039\pi\)
\(992\) −4.97721 −0.158027
\(993\) −37.3649 −1.18574
\(994\) −9.59488 −0.304331
\(995\) −42.7829 −1.35631
\(996\) −113.240 −3.58814
\(997\) 13.9469 0.441704 0.220852 0.975307i \(-0.429116\pi\)
0.220852 + 0.975307i \(0.429116\pi\)
\(998\) −32.0362 −1.01409
\(999\) −99.5949 −3.15104
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 \(a_p\))