Properties

Label 6027.2.a.u.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 4
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: \(4\)
Coefficient field: 4.4.8468.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.31743\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.31743 q^{2} +1.00000 q^{3} -0.264377 q^{4} -0.264377 q^{5} +1.31743 q^{6} -2.98316 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.31743 q^{2} +1.00000 q^{3} -0.264377 q^{4} -0.264377 q^{5} +1.31743 q^{6} -2.98316 q^{8} +1.00000 q^{9} -0.348298 q^{10} +0.401352 q^{11} -0.264377 q^{12} -1.84618 q^{13} -0.264377 q^{15} -3.40135 q^{16} +1.89924 q^{17} +1.31743 q^{18} +6.30059 q^{19} +0.0698950 q^{20} +0.528753 q^{22} -4.48105 q^{23} -2.98316 q^{24} -4.93011 q^{25} -2.43222 q^{26} +1.00000 q^{27} -2.74965 q^{29} -0.348298 q^{30} +5.89924 q^{31} +1.48527 q^{32} +0.401352 q^{33} +2.50211 q^{34} -0.264377 q^{36} -0.497886 q^{37} +8.30059 q^{38} -1.84618 q^{39} +0.788677 q^{40} +1.00000 q^{41} +5.86556 q^{43} -0.106108 q^{44} -0.264377 q^{45} -5.90347 q^{46} +13.1608 q^{47} -3.40135 q^{48} -6.49507 q^{50} +1.89924 q^{51} +0.488088 q^{52} +8.75500 q^{53} +1.31743 q^{54} -0.106108 q^{55} +6.30059 q^{57} -3.62247 q^{58} +2.50211 q^{59} +0.0698950 q^{60} -3.86556 q^{61} +7.77184 q^{62} +8.75945 q^{64} +0.488088 q^{65} +0.528753 q^{66} +1.17319 q^{67} -0.502114 q^{68} -4.48105 q^{69} +15.0292 q^{71} -2.98316 q^{72} +7.37048 q^{73} -0.655930 q^{74} -4.93011 q^{75} -1.66573 q^{76} -2.43222 q^{78} +5.34103 q^{79} +0.899238 q^{80} +1.00000 q^{81} +1.31743 q^{82} -0.106108 q^{83} -0.502114 q^{85} +7.72746 q^{86} -2.74965 q^{87} -1.19730 q^{88} -3.79848 q^{89} -0.348298 q^{90} +1.18468 q^{92} +5.89924 q^{93} +17.3384 q^{94} -1.66573 q^{95} +1.48527 q^{96} -9.72413 q^{97} +0.401352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + O(q^{10}) \) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + 5q^{10} - 5q^{11} + 3q^{12} + 5q^{13} + 3q^{15} - 7q^{16} - 5q^{17} + q^{18} + 6q^{19} + 15q^{20} - 6q^{22} + 3q^{23} + 3q^{24} - 5q^{25} - q^{26} + 4q^{27} + 2q^{29} + 5q^{30} + 11q^{31} - 3q^{32} - 5q^{33} + 16q^{34} + 3q^{36} + 4q^{37} + 14q^{38} + 5q^{39} + 7q^{40} + 4q^{41} - 19q^{43} + 3q^{45} - 23q^{46} + 4q^{47} - 7q^{48} + 12q^{50} - 5q^{51} + 25q^{52} + 9q^{53} + q^{54} + 6q^{57} + 25q^{58} + 16q^{59} + 15q^{60} + 27q^{61} + 20q^{62} - 7q^{64} + 25q^{65} - 6q^{66} - 13q^{67} - 8q^{68} + 3q^{69} + q^{71} + 3q^{72} + 25q^{73} - 21q^{74} - 5q^{75} + 4q^{76} - q^{78} - q^{79} - 9q^{80} + 4q^{81} + q^{82} - 8q^{85} + 16q^{86} + 2q^{87} - 18q^{88} + 10q^{89} + 5q^{90} + 15q^{92} + 11q^{93} - 13q^{94} + 4q^{95} - 3q^{96} - 15q^{97} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31743 0.931564 0.465782 0.884899i \(-0.345773\pi\)
0.465782 + 0.884899i \(0.345773\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.264377 −0.132188
\(5\) −0.264377 −0.118233 −0.0591164 0.998251i \(-0.518828\pi\)
−0.0591164 + 0.998251i \(0.518828\pi\)
\(6\) 1.31743 0.537839
\(7\) 0 0
\(8\) −2.98316 −1.05471
\(9\) 1.00000 0.333333
\(10\) −0.348298 −0.110141
\(11\) 0.401352 0.121012 0.0605061 0.998168i \(-0.480729\pi\)
0.0605061 + 0.998168i \(0.480729\pi\)
\(12\) −0.264377 −0.0763189
\(13\) −1.84618 −0.512039 −0.256020 0.966672i \(-0.582411\pi\)
−0.256020 + 0.966672i \(0.582411\pi\)
\(14\) 0 0
\(15\) −0.264377 −0.0682617
\(16\) −3.40135 −0.850338
\(17\) 1.89924 0.460633 0.230316 0.973116i \(-0.426024\pi\)
0.230316 + 0.973116i \(0.426024\pi\)
\(18\) 1.31743 0.310521
\(19\) 6.30059 1.44545 0.722727 0.691133i \(-0.242888\pi\)
0.722727 + 0.691133i \(0.242888\pi\)
\(20\) 0.0698950 0.0156290
\(21\) 0 0
\(22\) 0.528753 0.112731
\(23\) −4.48105 −0.934362 −0.467181 0.884162i \(-0.654730\pi\)
−0.467181 + 0.884162i \(0.654730\pi\)
\(24\) −2.98316 −0.608935
\(25\) −4.93011 −0.986021
\(26\) −2.43222 −0.476997
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.74965 −0.510597 −0.255299 0.966862i \(-0.582174\pi\)
−0.255299 + 0.966862i \(0.582174\pi\)
\(30\) −0.348298 −0.0635902
\(31\) 5.89924 1.05953 0.529767 0.848143i \(-0.322279\pi\)
0.529767 + 0.848143i \(0.322279\pi\)
\(32\) 1.48527 0.262562
\(33\) 0.401352 0.0698664
\(34\) 2.50211 0.429109
\(35\) 0 0
\(36\) −0.264377 −0.0440628
\(37\) −0.497886 −0.0818520 −0.0409260 0.999162i \(-0.513031\pi\)
−0.0409260 + 0.999162i \(0.513031\pi\)
\(38\) 8.30059 1.34653
\(39\) −1.84618 −0.295626
\(40\) 0.788677 0.124701
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 5.86556 0.894489 0.447244 0.894412i \(-0.352405\pi\)
0.447244 + 0.894412i \(0.352405\pi\)
\(44\) −0.106108 −0.0159964
\(45\) −0.264377 −0.0394109
\(46\) −5.90347 −0.870419
\(47\) 13.1608 1.91970 0.959850 0.280514i \(-0.0905049\pi\)
0.959850 + 0.280514i \(0.0905049\pi\)
\(48\) −3.40135 −0.490943
\(49\) 0 0
\(50\) −6.49507 −0.918542
\(51\) 1.89924 0.265946
\(52\) 0.488088 0.0676856
\(53\) 8.75500 1.20259 0.601296 0.799027i \(-0.294651\pi\)
0.601296 + 0.799027i \(0.294651\pi\)
\(54\) 1.31743 0.179280
\(55\) −0.106108 −0.0143076
\(56\) 0 0
\(57\) 6.30059 0.834533
\(58\) −3.62247 −0.475654
\(59\) 2.50211 0.325747 0.162874 0.986647i \(-0.447924\pi\)
0.162874 + 0.986647i \(0.447924\pi\)
\(60\) 0.0698950 0.00902340
\(61\) −3.86556 −0.494934 −0.247467 0.968896i \(-0.579598\pi\)
−0.247467 + 0.968896i \(0.579598\pi\)
\(62\) 7.77184 0.987024
\(63\) 0 0
\(64\) 8.75945 1.09493
\(65\) 0.488088 0.0605398
\(66\) 0.528753 0.0650850
\(67\) 1.17319 0.143328 0.0716639 0.997429i \(-0.477169\pi\)
0.0716639 + 0.997429i \(0.477169\pi\)
\(68\) −0.502114 −0.0608903
\(69\) −4.48105 −0.539454
\(70\) 0 0
\(71\) 15.0292 1.78363 0.891817 0.452396i \(-0.149431\pi\)
0.891817 + 0.452396i \(0.149431\pi\)
\(72\) −2.98316 −0.351569
\(73\) 7.37048 0.862650 0.431325 0.902197i \(-0.358046\pi\)
0.431325 + 0.902197i \(0.358046\pi\)
\(74\) −0.655930 −0.0762503
\(75\) −4.93011 −0.569279
\(76\) −1.66573 −0.191072
\(77\) 0 0
\(78\) −2.43222 −0.275395
\(79\) 5.34103 0.600913 0.300456 0.953796i \(-0.402861\pi\)
0.300456 + 0.953796i \(0.402861\pi\)
\(80\) 0.899238 0.100538
\(81\) 1.00000 0.111111
\(82\) 1.31743 0.145486
\(83\) −0.106108 −0.0116469 −0.00582343 0.999983i \(-0.501854\pi\)
−0.00582343 + 0.999983i \(0.501854\pi\)
\(84\) 0 0
\(85\) −0.502114 −0.0544619
\(86\) 7.72746 0.833274
\(87\) −2.74965 −0.294793
\(88\) −1.19730 −0.127632
\(89\) −3.79848 −0.402638 −0.201319 0.979526i \(-0.564523\pi\)
−0.201319 + 0.979526i \(0.564523\pi\)
\(90\) −0.348298 −0.0367138
\(91\) 0 0
\(92\) 1.18468 0.123512
\(93\) 5.89924 0.611722
\(94\) 17.3384 1.78832
\(95\) −1.66573 −0.170900
\(96\) 1.48527 0.151590
\(97\) −9.72413 −0.987336 −0.493668 0.869651i \(-0.664344\pi\)
−0.493668 + 0.869651i \(0.664344\pi\)
\(98\) 0 0
\(99\) 0.401352 0.0403374
\(100\) 1.30340 0.130340
\(101\) −0.656155 −0.0652898 −0.0326449 0.999467i \(-0.510393\pi\)
−0.0326449 + 0.999467i \(0.510393\pi\)
\(102\) 2.50211 0.247746
\(103\) 9.80716 0.966328 0.483164 0.875530i \(-0.339488\pi\)
0.483164 + 0.875530i \(0.339488\pi\)
\(104\) 5.50746 0.540051
\(105\) 0 0
\(106\) 11.5341 1.12029
\(107\) −12.6947 −1.22724 −0.613620 0.789601i \(-0.710287\pi\)
−0.613620 + 0.789601i \(0.710287\pi\)
\(108\) −0.264377 −0.0254396
\(109\) −15.6320 −1.49728 −0.748639 0.662978i \(-0.769292\pi\)
−0.748639 + 0.662978i \(0.769292\pi\)
\(110\) −0.139790 −0.0133285
\(111\) −0.497886 −0.0472572
\(112\) 0 0
\(113\) 12.8027 1.20438 0.602189 0.798354i \(-0.294296\pi\)
0.602189 + 0.798354i \(0.294296\pi\)
\(114\) 8.30059 0.777421
\(115\) 1.18468 0.110472
\(116\) 0.726943 0.0674950
\(117\) −1.84618 −0.170680
\(118\) 3.29636 0.303455
\(119\) 0 0
\(120\) 0.788677 0.0719961
\(121\) −10.8389 −0.985356
\(122\) −5.09260 −0.461062
\(123\) 1.00000 0.0901670
\(124\) −1.55962 −0.140058
\(125\) 2.62529 0.234813
\(126\) 0 0
\(127\) 0.889664 0.0789449 0.0394725 0.999221i \(-0.487432\pi\)
0.0394725 + 0.999221i \(0.487432\pi\)
\(128\) 8.56942 0.757437
\(129\) 5.86556 0.516433
\(130\) 0.643022 0.0563967
\(131\) −8.52171 −0.744545 −0.372273 0.928123i \(-0.621421\pi\)
−0.372273 + 0.928123i \(0.621421\pi\)
\(132\) −0.106108 −0.00923552
\(133\) 0 0
\(134\) 1.54559 0.133519
\(135\) −0.264377 −0.0227539
\(136\) −5.66573 −0.485832
\(137\) 0.615489 0.0525848 0.0262924 0.999654i \(-0.491630\pi\)
0.0262924 + 0.999654i \(0.491630\pi\)
\(138\) −5.90347 −0.502536
\(139\) 14.5428 1.23350 0.616751 0.787158i \(-0.288448\pi\)
0.616751 + 0.787158i \(0.288448\pi\)
\(140\) 0 0
\(141\) 13.1608 1.10834
\(142\) 19.7999 1.66157
\(143\) −0.740969 −0.0619630
\(144\) −3.40135 −0.283446
\(145\) 0.726943 0.0603693
\(146\) 9.71010 0.803614
\(147\) 0 0
\(148\) 0.131629 0.0108199
\(149\) 12.3623 1.01276 0.506381 0.862310i \(-0.330983\pi\)
0.506381 + 0.862310i \(0.330983\pi\)
\(150\) −6.49507 −0.530320
\(151\) −1.89389 −0.154123 −0.0770614 0.997026i \(-0.524554\pi\)
−0.0770614 + 0.997026i \(0.524554\pi\)
\(152\) −18.7957 −1.52453
\(153\) 1.89924 0.153544
\(154\) 0 0
\(155\) −1.55962 −0.125272
\(156\) 0.488088 0.0390783
\(157\) 0.238855 0.0190627 0.00953136 0.999955i \(-0.496966\pi\)
0.00953136 + 0.999955i \(0.496966\pi\)
\(158\) 7.03644 0.559789
\(159\) 8.75500 0.694316
\(160\) −0.392671 −0.0310434
\(161\) 0 0
\(162\) 1.31743 0.103507
\(163\) 8.12036 0.636036 0.318018 0.948085i \(-0.396983\pi\)
0.318018 + 0.948085i \(0.396983\pi\)
\(164\) −0.264377 −0.0206443
\(165\) −0.106108 −0.00826050
\(166\) −0.139790 −0.0108498
\(167\) 8.14232 0.630072 0.315036 0.949080i \(-0.397983\pi\)
0.315036 + 0.949080i \(0.397983\pi\)
\(168\) 0 0
\(169\) −9.59161 −0.737816
\(170\) −0.661500 −0.0507348
\(171\) 6.30059 0.481818
\(172\) −1.55072 −0.118241
\(173\) −24.3045 −1.84784 −0.923920 0.382586i \(-0.875033\pi\)
−0.923920 + 0.382586i \(0.875033\pi\)
\(174\) −3.62247 −0.274619
\(175\) 0 0
\(176\) −1.36514 −0.102901
\(177\) 2.50211 0.188070
\(178\) −5.00423 −0.375083
\(179\) 13.2924 0.993523 0.496761 0.867887i \(-0.334522\pi\)
0.496761 + 0.867887i \(0.334522\pi\)
\(180\) 0.0698950 0.00520966
\(181\) 16.4965 1.22617 0.613087 0.790015i \(-0.289927\pi\)
0.613087 + 0.790015i \(0.289927\pi\)
\(182\) 0 0
\(183\) −3.86556 −0.285750
\(184\) 13.3677 0.985478
\(185\) 0.131629 0.00967759
\(186\) 7.77184 0.569859
\(187\) 0.762263 0.0557422
\(188\) −3.47941 −0.253762
\(189\) 0 0
\(190\) −2.19448 −0.159204
\(191\) −8.49366 −0.614580 −0.307290 0.951616i \(-0.599422\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(192\) 8.75945 0.632159
\(193\) 4.08837 0.294288 0.147144 0.989115i \(-0.452992\pi\)
0.147144 + 0.989115i \(0.452992\pi\)
\(194\) −12.8109 −0.919766
\(195\) 0.488088 0.0349527
\(196\) 0 0
\(197\) 9.11034 0.649085 0.324542 0.945871i \(-0.394790\pi\)
0.324542 + 0.945871i \(0.394790\pi\)
\(198\) 0.528753 0.0375769
\(199\) 16.8400 1.19376 0.596879 0.802331i \(-0.296407\pi\)
0.596879 + 0.802331i \(0.296407\pi\)
\(200\) 14.7073 1.03996
\(201\) 1.17319 0.0827503
\(202\) −0.864438 −0.0608217
\(203\) 0 0
\(204\) −0.502114 −0.0351550
\(205\) −0.264377 −0.0184649
\(206\) 12.9202 0.900196
\(207\) −4.48105 −0.311454
\(208\) 6.27952 0.435406
\(209\) 2.52875 0.174918
\(210\) 0 0
\(211\) 13.4560 0.926352 0.463176 0.886266i \(-0.346710\pi\)
0.463176 + 0.886266i \(0.346710\pi\)
\(212\) −2.31462 −0.158968
\(213\) 15.0292 1.02978
\(214\) −16.7244 −1.14325
\(215\) −1.55072 −0.105758
\(216\) −2.98316 −0.202978
\(217\) 0 0
\(218\) −20.5941 −1.39481
\(219\) 7.37048 0.498051
\(220\) 0.0280525 0.00189130
\(221\) −3.50634 −0.235862
\(222\) −0.655930 −0.0440232
\(223\) −3.78445 −0.253425 −0.126713 0.991939i \(-0.540443\pi\)
−0.126713 + 0.991939i \(0.540443\pi\)
\(224\) 0 0
\(225\) −4.93011 −0.328674
\(226\) 16.8667 1.12195
\(227\) 20.1757 1.33911 0.669555 0.742763i \(-0.266485\pi\)
0.669555 + 0.742763i \(0.266485\pi\)
\(228\) −1.66573 −0.110316
\(229\) 19.3384 1.27792 0.638960 0.769240i \(-0.279365\pi\)
0.638960 + 0.769240i \(0.279365\pi\)
\(230\) 1.56074 0.102912
\(231\) 0 0
\(232\) 8.20264 0.538530
\(233\) 9.29636 0.609025 0.304512 0.952508i \(-0.401506\pi\)
0.304512 + 0.952508i \(0.401506\pi\)
\(234\) −2.43222 −0.158999
\(235\) −3.47941 −0.226972
\(236\) −0.661500 −0.0430600
\(237\) 5.34103 0.346937
\(238\) 0 0
\(239\) 13.8265 0.894364 0.447182 0.894443i \(-0.352428\pi\)
0.447182 + 0.894443i \(0.352428\pi\)
\(240\) 0.899238 0.0580456
\(241\) −17.5930 −1.13327 −0.566633 0.823970i \(-0.691754\pi\)
−0.566633 + 0.823970i \(0.691754\pi\)
\(242\) −14.2795 −0.917922
\(243\) 1.00000 0.0641500
\(244\) 1.02196 0.0654244
\(245\) 0 0
\(246\) 1.31743 0.0839963
\(247\) −11.6320 −0.740129
\(248\) −17.5984 −1.11750
\(249\) −0.106108 −0.00672432
\(250\) 3.45863 0.218743
\(251\) 19.2253 1.21349 0.606747 0.794895i \(-0.292474\pi\)
0.606747 + 0.794895i \(0.292474\pi\)
\(252\) 0 0
\(253\) −1.79848 −0.113069
\(254\) 1.17207 0.0735422
\(255\) −0.502114 −0.0314436
\(256\) −6.22928 −0.389330
\(257\) −12.3929 −0.773048 −0.386524 0.922279i \(-0.626324\pi\)
−0.386524 + 0.922279i \(0.626324\pi\)
\(258\) 7.72746 0.481091
\(259\) 0 0
\(260\) −0.129039 −0.00800266
\(261\) −2.74965 −0.170199
\(262\) −11.2268 −0.693592
\(263\) 5.50323 0.339344 0.169672 0.985501i \(-0.445729\pi\)
0.169672 + 0.985501i \(0.445729\pi\)
\(264\) −1.19730 −0.0736885
\(265\) −2.31462 −0.142186
\(266\) 0 0
\(267\) −3.79848 −0.232463
\(268\) −0.310164 −0.0189463
\(269\) 23.9834 1.46229 0.731146 0.682221i \(-0.238986\pi\)
0.731146 + 0.682221i \(0.238986\pi\)
\(270\) −0.348298 −0.0211967
\(271\) −4.44906 −0.270261 −0.135131 0.990828i \(-0.543145\pi\)
−0.135131 + 0.990828i \(0.543145\pi\)
\(272\) −6.45998 −0.391694
\(273\) 0 0
\(274\) 0.810864 0.0489861
\(275\) −1.97871 −0.119321
\(276\) 1.18468 0.0713096
\(277\) −31.7797 −1.90946 −0.954729 0.297477i \(-0.903855\pi\)
−0.954729 + 0.297477i \(0.903855\pi\)
\(278\) 19.1591 1.14909
\(279\) 5.89924 0.353178
\(280\) 0 0
\(281\) 10.6191 0.633485 0.316742 0.948512i \(-0.397411\pi\)
0.316742 + 0.948512i \(0.397411\pi\)
\(282\) 17.3384 1.03249
\(283\) 26.0778 1.55016 0.775081 0.631861i \(-0.217709\pi\)
0.775081 + 0.631861i \(0.217709\pi\)
\(284\) −3.97336 −0.235776
\(285\) −1.66573 −0.0986692
\(286\) −0.976176 −0.0577225
\(287\) 0 0
\(288\) 1.48527 0.0875206
\(289\) −13.3929 −0.787817
\(290\) 0.957697 0.0562379
\(291\) −9.72413 −0.570038
\(292\) −1.94858 −0.114032
\(293\) 4.81695 0.281409 0.140705 0.990052i \(-0.455063\pi\)
0.140705 + 0.990052i \(0.455063\pi\)
\(294\) 0 0
\(295\) −0.661500 −0.0385140
\(296\) 1.48527 0.0863297
\(297\) 0.401352 0.0232888
\(298\) 16.2865 0.943452
\(299\) 8.27283 0.478430
\(300\) 1.30340 0.0752521
\(301\) 0 0
\(302\) −2.49507 −0.143575
\(303\) −0.656155 −0.0376951
\(304\) −21.4305 −1.22912
\(305\) 1.02196 0.0585174
\(306\) 2.50211 0.143036
\(307\) −6.48076 −0.369877 −0.184938 0.982750i \(-0.559209\pi\)
−0.184938 + 0.982750i \(0.559209\pi\)
\(308\) 0 0
\(309\) 9.80716 0.557910
\(310\) −2.05469 −0.116699
\(311\) −26.6495 −1.51115 −0.755577 0.655060i \(-0.772643\pi\)
−0.755577 + 0.655060i \(0.772643\pi\)
\(312\) 5.50746 0.311799
\(313\) 5.80181 0.327938 0.163969 0.986466i \(-0.447570\pi\)
0.163969 + 0.986466i \(0.447570\pi\)
\(314\) 0.314675 0.0177581
\(315\) 0 0
\(316\) −1.41204 −0.0794337
\(317\) 5.92921 0.333018 0.166509 0.986040i \(-0.446751\pi\)
0.166509 + 0.986040i \(0.446751\pi\)
\(318\) 11.5341 0.646800
\(319\) −1.10358 −0.0617884
\(320\) −2.31579 −0.129457
\(321\) −12.6947 −0.708548
\(322\) 0 0
\(323\) 11.9663 0.665824
\(324\) −0.264377 −0.0146876
\(325\) 9.10188 0.504881
\(326\) 10.6980 0.592508
\(327\) −15.6320 −0.864454
\(328\) −2.98316 −0.164717
\(329\) 0 0
\(330\) −0.139790 −0.00769518
\(331\) −32.3045 −1.77562 −0.887809 0.460212i \(-0.847773\pi\)
−0.887809 + 0.460212i \(0.847773\pi\)
\(332\) 0.0280525 0.00153958
\(333\) −0.497886 −0.0272840
\(334\) 10.7269 0.586952
\(335\) −0.310164 −0.0169460
\(336\) 0 0
\(337\) −13.6750 −0.744926 −0.372463 0.928047i \(-0.621487\pi\)
−0.372463 + 0.928047i \(0.621487\pi\)
\(338\) −12.6363 −0.687323
\(339\) 12.8027 0.695347
\(340\) 0.132747 0.00719923
\(341\) 2.36767 0.128217
\(342\) 8.30059 0.448844
\(343\) 0 0
\(344\) −17.4979 −0.943423
\(345\) 1.18468 0.0637812
\(346\) −32.0195 −1.72138
\(347\) −5.98236 −0.321150 −0.160575 0.987024i \(-0.551335\pi\)
−0.160575 + 0.987024i \(0.551335\pi\)
\(348\) 0.726943 0.0389682
\(349\) −3.24984 −0.173960 −0.0869800 0.996210i \(-0.527722\pi\)
−0.0869800 + 0.996210i \(0.527722\pi\)
\(350\) 0 0
\(351\) −1.84618 −0.0985420
\(352\) 0.596117 0.0317731
\(353\) −21.9770 −1.16972 −0.584859 0.811135i \(-0.698850\pi\)
−0.584859 + 0.811135i \(0.698850\pi\)
\(354\) 3.29636 0.175200
\(355\) −3.97336 −0.210884
\(356\) 1.00423 0.0532240
\(357\) 0 0
\(358\) 17.5119 0.925530
\(359\) −35.8970 −1.89457 −0.947286 0.320388i \(-0.896187\pi\)
−0.947286 + 0.320388i \(0.896187\pi\)
\(360\) 0.788677 0.0415669
\(361\) 20.6974 1.08934
\(362\) 21.7330 1.14226
\(363\) −10.8389 −0.568896
\(364\) 0 0
\(365\) −1.94858 −0.101994
\(366\) −5.09260 −0.266195
\(367\) 17.7309 0.925545 0.462772 0.886477i \(-0.346855\pi\)
0.462772 + 0.886477i \(0.346855\pi\)
\(368\) 15.2416 0.794524
\(369\) 1.00000 0.0520579
\(370\) 0.173413 0.00901529
\(371\) 0 0
\(372\) −1.55962 −0.0808626
\(373\) 2.88864 0.149568 0.0747840 0.997200i \(-0.476173\pi\)
0.0747840 + 0.997200i \(0.476173\pi\)
\(374\) 1.00423 0.0519274
\(375\) 2.62529 0.135569
\(376\) −39.2608 −2.02472
\(377\) 5.07636 0.261446
\(378\) 0 0
\(379\) −22.8429 −1.17336 −0.586679 0.809819i \(-0.699565\pi\)
−0.586679 + 0.809819i \(0.699565\pi\)
\(380\) 0.440380 0.0225910
\(381\) 0.889664 0.0455789
\(382\) −11.1898 −0.572520
\(383\) −29.0462 −1.48419 −0.742097 0.670293i \(-0.766168\pi\)
−0.742097 + 0.670293i \(0.766168\pi\)
\(384\) 8.56942 0.437306
\(385\) 0 0
\(386\) 5.38615 0.274148
\(387\) 5.86556 0.298163
\(388\) 2.57083 0.130514
\(389\) 5.68532 0.288257 0.144129 0.989559i \(-0.453962\pi\)
0.144129 + 0.989559i \(0.453962\pi\)
\(390\) 0.643022 0.0325607
\(391\) −8.51057 −0.430398
\(392\) 0 0
\(393\) −8.52171 −0.429863
\(394\) 12.0022 0.604664
\(395\) −1.41204 −0.0710476
\(396\) −0.106108 −0.00533213
\(397\) −34.9153 −1.75235 −0.876174 0.481995i \(-0.839912\pi\)
−0.876174 + 0.481995i \(0.839912\pi\)
\(398\) 22.1856 1.11206
\(399\) 0 0
\(400\) 16.7690 0.838451
\(401\) 0.456327 0.0227879 0.0113939 0.999935i \(-0.496373\pi\)
0.0113939 + 0.999935i \(0.496373\pi\)
\(402\) 1.54559 0.0770872
\(403\) −10.8911 −0.542523
\(404\) 0.173472 0.00863055
\(405\) −0.264377 −0.0131370
\(406\) 0 0
\(407\) −0.199827 −0.00990508
\(408\) −5.66573 −0.280495
\(409\) −19.8922 −0.983606 −0.491803 0.870707i \(-0.663662\pi\)
−0.491803 + 0.870707i \(0.663662\pi\)
\(410\) −0.348298 −0.0172012
\(411\) 0.615489 0.0303598
\(412\) −2.59278 −0.127737
\(413\) 0 0
\(414\) −5.90347 −0.290140
\(415\) 0.0280525 0.00137704
\(416\) −2.74209 −0.134442
\(417\) 14.5428 0.712163
\(418\) 3.33146 0.162947
\(419\) 13.5933 0.664076 0.332038 0.943266i \(-0.392264\pi\)
0.332038 + 0.943266i \(0.392264\pi\)
\(420\) 0 0
\(421\) 25.0224 1.21952 0.609759 0.792587i \(-0.291266\pi\)
0.609759 + 0.792587i \(0.291266\pi\)
\(422\) 17.7274 0.862957
\(423\) 13.1608 0.639900
\(424\) −26.1175 −1.26838
\(425\) −9.36344 −0.454194
\(426\) 19.7999 0.959308
\(427\) 0 0
\(428\) 3.35617 0.162227
\(429\) −0.740969 −0.0357743
\(430\) −2.04296 −0.0985203
\(431\) −15.8532 −0.763620 −0.381810 0.924241i \(-0.624699\pi\)
−0.381810 + 0.924241i \(0.624699\pi\)
\(432\) −3.40135 −0.163648
\(433\) 23.5420 1.13136 0.565678 0.824627i \(-0.308615\pi\)
0.565678 + 0.824627i \(0.308615\pi\)
\(434\) 0 0
\(435\) 0.726943 0.0348542
\(436\) 4.13275 0.197923
\(437\) −28.2332 −1.35058
\(438\) 9.71010 0.463967
\(439\) 31.5310 1.50489 0.752446 0.658654i \(-0.228874\pi\)
0.752446 + 0.658654i \(0.228874\pi\)
\(440\) 0.316537 0.0150903
\(441\) 0 0
\(442\) −4.61936 −0.219721
\(443\) −17.5792 −0.835214 −0.417607 0.908628i \(-0.637131\pi\)
−0.417607 + 0.908628i \(0.637131\pi\)
\(444\) 0.131629 0.00624685
\(445\) 1.00423 0.0476050
\(446\) −4.98575 −0.236082
\(447\) 12.3623 0.584718
\(448\) 0 0
\(449\) −12.3539 −0.583015 −0.291508 0.956569i \(-0.594157\pi\)
−0.291508 + 0.956569i \(0.594157\pi\)
\(450\) −6.49507 −0.306181
\(451\) 0.401352 0.0188989
\(452\) −3.38474 −0.159205
\(453\) −1.89389 −0.0889828
\(454\) 26.5801 1.24747
\(455\) 0 0
\(456\) −18.7957 −0.880187
\(457\) 3.59695 0.168258 0.0841291 0.996455i \(-0.473189\pi\)
0.0841291 + 0.996455i \(0.473189\pi\)
\(458\) 25.4771 1.19046
\(459\) 1.89924 0.0886488
\(460\) −0.313203 −0.0146031
\(461\) 37.1077 1.72828 0.864139 0.503254i \(-0.167864\pi\)
0.864139 + 0.503254i \(0.167864\pi\)
\(462\) 0 0
\(463\) 25.7851 1.19833 0.599167 0.800624i \(-0.295499\pi\)
0.599167 + 0.800624i \(0.295499\pi\)
\(464\) 9.35253 0.434180
\(465\) −1.55962 −0.0723257
\(466\) 12.2473 0.567346
\(467\) −7.64274 −0.353664 −0.176832 0.984241i \(-0.556585\pi\)
−0.176832 + 0.984241i \(0.556585\pi\)
\(468\) 0.488088 0.0225619
\(469\) 0 0
\(470\) −4.58388 −0.211439
\(471\) 0.238855 0.0110059
\(472\) −7.46420 −0.343568
\(473\) 2.35415 0.108244
\(474\) 7.03644 0.323194
\(475\) −31.0626 −1.42525
\(476\) 0 0
\(477\) 8.75500 0.400864
\(478\) 18.2155 0.833157
\(479\) 5.64123 0.257755 0.128877 0.991661i \(-0.458863\pi\)
0.128877 + 0.991661i \(0.458863\pi\)
\(480\) −0.392671 −0.0179229
\(481\) 0.919189 0.0419114
\(482\) −23.1776 −1.05571
\(483\) 0 0
\(484\) 2.86556 0.130253
\(485\) 2.57083 0.116735
\(486\) 1.31743 0.0597599
\(487\) −13.0839 −0.592886 −0.296443 0.955050i \(-0.595801\pi\)
−0.296443 + 0.955050i \(0.595801\pi\)
\(488\) 11.5316 0.522010
\(489\) 8.12036 0.367215
\(490\) 0 0
\(491\) 10.0019 0.451378 0.225689 0.974199i \(-0.427537\pi\)
0.225689 + 0.974199i \(0.427537\pi\)
\(492\) −0.264377 −0.0119190
\(493\) −5.22224 −0.235198
\(494\) −15.3244 −0.689478
\(495\) −0.106108 −0.00476920
\(496\) −20.0654 −0.900962
\(497\) 0 0
\(498\) −0.139790 −0.00626414
\(499\) 19.9798 0.894420 0.447210 0.894429i \(-0.352418\pi\)
0.447210 + 0.894429i \(0.352418\pi\)
\(500\) −0.694065 −0.0310395
\(501\) 8.14232 0.363772
\(502\) 25.3281 1.13045
\(503\) −3.15376 −0.140619 −0.0703095 0.997525i \(-0.522399\pi\)
−0.0703095 + 0.997525i \(0.522399\pi\)
\(504\) 0 0
\(505\) 0.173472 0.00771940
\(506\) −2.36937 −0.105331
\(507\) −9.59161 −0.425978
\(508\) −0.235206 −0.0104356
\(509\) 28.4331 1.26027 0.630136 0.776484i \(-0.282999\pi\)
0.630136 + 0.776484i \(0.282999\pi\)
\(510\) −0.661500 −0.0292917
\(511\) 0 0
\(512\) −25.3455 −1.12012
\(513\) 6.30059 0.278178
\(514\) −16.3268 −0.720143
\(515\) −2.59278 −0.114252
\(516\) −1.55072 −0.0682665
\(517\) 5.28211 0.232307
\(518\) 0 0
\(519\) −24.3045 −1.06685
\(520\) −1.45604 −0.0638517
\(521\) −20.3003 −0.889373 −0.444686 0.895686i \(-0.646685\pi\)
−0.444686 + 0.895686i \(0.646685\pi\)
\(522\) −3.62247 −0.158551
\(523\) 8.46561 0.370175 0.185088 0.982722i \(-0.440743\pi\)
0.185088 + 0.982722i \(0.440743\pi\)
\(524\) 2.25294 0.0984202
\(525\) 0 0
\(526\) 7.25013 0.316121
\(527\) 11.2041 0.488056
\(528\) −1.36514 −0.0594100
\(529\) −2.92024 −0.126967
\(530\) −3.04935 −0.132455
\(531\) 2.50211 0.108582
\(532\) 0 0
\(533\) −1.84618 −0.0799671
\(534\) −5.00423 −0.216554
\(535\) 3.35617 0.145100
\(536\) −3.49981 −0.151169
\(537\) 13.2924 0.573611
\(538\) 31.5964 1.36222
\(539\) 0 0
\(540\) 0.0698950 0.00300780
\(541\) −25.5874 −1.10009 −0.550044 0.835136i \(-0.685389\pi\)
−0.550044 + 0.835136i \(0.685389\pi\)
\(542\) −5.86133 −0.251766
\(543\) 16.4965 0.707932
\(544\) 2.82089 0.120945
\(545\) 4.13275 0.177027
\(546\) 0 0
\(547\) 31.3531 1.34056 0.670282 0.742107i \(-0.266173\pi\)
0.670282 + 0.742107i \(0.266173\pi\)
\(548\) −0.162721 −0.00695109
\(549\) −3.86556 −0.164978
\(550\) −2.60681 −0.111155
\(551\) −17.3244 −0.738045
\(552\) 13.3677 0.568966
\(553\) 0 0
\(554\) −41.8676 −1.77878
\(555\) 0.131629 0.00558736
\(556\) −3.84477 −0.163055
\(557\) 31.0629 1.31618 0.658088 0.752941i \(-0.271366\pi\)
0.658088 + 0.752941i \(0.271366\pi\)
\(558\) 7.77184 0.329008
\(559\) −10.8289 −0.458013
\(560\) 0 0
\(561\) 0.762263 0.0321828
\(562\) 13.9900 0.590132
\(563\) −1.99577 −0.0841118 −0.0420559 0.999115i \(-0.513391\pi\)
−0.0420559 + 0.999115i \(0.513391\pi\)
\(564\) −3.47941 −0.146509
\(565\) −3.38474 −0.142397
\(566\) 34.3557 1.44408
\(567\) 0 0
\(568\) −44.8344 −1.88121
\(569\) −19.3295 −0.810334 −0.405167 0.914243i \(-0.632787\pi\)
−0.405167 + 0.914243i \(0.632787\pi\)
\(570\) −2.19448 −0.0919167
\(571\) −30.3744 −1.27113 −0.635565 0.772047i \(-0.719233\pi\)
−0.635565 + 0.772047i \(0.719233\pi\)
\(572\) 0.195895 0.00819078
\(573\) −8.49366 −0.354828
\(574\) 0 0
\(575\) 22.0920 0.921301
\(576\) 8.75945 0.364977
\(577\) 25.0275 1.04191 0.520954 0.853585i \(-0.325576\pi\)
0.520954 + 0.853585i \(0.325576\pi\)
\(578\) −17.6442 −0.733902
\(579\) 4.08837 0.169907
\(580\) −0.192187 −0.00798012
\(581\) 0 0
\(582\) −12.8109 −0.531027
\(583\) 3.51383 0.145528
\(584\) −21.9873 −0.909842
\(585\) 0.488088 0.0201799
\(586\) 6.34600 0.262151
\(587\) 0.853836 0.0352416 0.0176208 0.999845i \(-0.494391\pi\)
0.0176208 + 0.999845i \(0.494391\pi\)
\(588\) 0 0
\(589\) 37.1687 1.53151
\(590\) −0.871481 −0.0358783
\(591\) 9.11034 0.374749
\(592\) 1.69349 0.0696018
\(593\) −1.16531 −0.0478536 −0.0239268 0.999714i \(-0.507617\pi\)
−0.0239268 + 0.999714i \(0.507617\pi\)
\(594\) 0.528753 0.0216950
\(595\) 0 0
\(596\) −3.26831 −0.133875
\(597\) 16.8400 0.689217
\(598\) 10.8989 0.445688
\(599\) 27.7984 1.13581 0.567906 0.823093i \(-0.307754\pi\)
0.567906 + 0.823093i \(0.307754\pi\)
\(600\) 14.7073 0.600422
\(601\) −33.5231 −1.36743 −0.683717 0.729747i \(-0.739638\pi\)
−0.683717 + 0.729747i \(0.739638\pi\)
\(602\) 0 0
\(603\) 1.17319 0.0477759
\(604\) 0.500701 0.0203732
\(605\) 2.86556 0.116501
\(606\) −0.864438 −0.0351154
\(607\) −26.2691 −1.06623 −0.533116 0.846042i \(-0.678979\pi\)
−0.533116 + 0.846042i \(0.678979\pi\)
\(608\) 9.35810 0.379521
\(609\) 0 0
\(610\) 1.34636 0.0545127
\(611\) −24.2973 −0.982962
\(612\) −0.502114 −0.0202968
\(613\) −41.0477 −1.65790 −0.828951 0.559321i \(-0.811062\pi\)
−0.828951 + 0.559321i \(0.811062\pi\)
\(614\) −8.53795 −0.344564
\(615\) −0.264377 −0.0106607
\(616\) 0 0
\(617\) −20.9335 −0.842750 −0.421375 0.906887i \(-0.638452\pi\)
−0.421375 + 0.906887i \(0.638452\pi\)
\(618\) 12.9202 0.519729
\(619\) −44.6537 −1.79478 −0.897391 0.441236i \(-0.854540\pi\)
−0.897391 + 0.441236i \(0.854540\pi\)
\(620\) 0.412327 0.0165595
\(621\) −4.48105 −0.179818
\(622\) −35.1089 −1.40774
\(623\) 0 0
\(624\) 6.27952 0.251382
\(625\) 23.9565 0.958258
\(626\) 7.64348 0.305495
\(627\) 2.52875 0.100989
\(628\) −0.0631477 −0.00251987
\(629\) −0.945604 −0.0377037
\(630\) 0 0
\(631\) −27.9501 −1.11268 −0.556338 0.830956i \(-0.687794\pi\)
−0.556338 + 0.830956i \(0.687794\pi\)
\(632\) −15.9331 −0.633786
\(633\) 13.4560 0.534830
\(634\) 7.81132 0.310227
\(635\) −0.235206 −0.00933388
\(636\) −2.31462 −0.0917805
\(637\) 0 0
\(638\) −1.45389 −0.0575599
\(639\) 15.0292 0.594545
\(640\) −2.26555 −0.0895539
\(641\) −23.4653 −0.926825 −0.463412 0.886143i \(-0.653375\pi\)
−0.463412 + 0.886143i \(0.653375\pi\)
\(642\) −16.7244 −0.660058
\(643\) 37.8156 1.49130 0.745652 0.666336i \(-0.232138\pi\)
0.745652 + 0.666336i \(0.232138\pi\)
\(644\) 0 0
\(645\) −1.55072 −0.0610594
\(646\) 15.7648 0.620258
\(647\) 21.2285 0.834580 0.417290 0.908773i \(-0.362980\pi\)
0.417290 + 0.908773i \(0.362980\pi\)
\(648\) −2.98316 −0.117190
\(649\) 1.00423 0.0394194
\(650\) 11.9911 0.470329
\(651\) 0 0
\(652\) −2.14683 −0.0840765
\(653\) −32.5672 −1.27445 −0.637227 0.770676i \(-0.719919\pi\)
−0.637227 + 0.770676i \(0.719919\pi\)
\(654\) −20.5941 −0.805294
\(655\) 2.25294 0.0880297
\(656\) −3.40135 −0.132800
\(657\) 7.37048 0.287550
\(658\) 0 0
\(659\) −36.3379 −1.41552 −0.707762 0.706451i \(-0.750295\pi\)
−0.707762 + 0.706451i \(0.750295\pi\)
\(660\) 0.0280525 0.00109194
\(661\) −18.8858 −0.734573 −0.367287 0.930108i \(-0.619713\pi\)
−0.367287 + 0.930108i \(0.619713\pi\)
\(662\) −42.5590 −1.65410
\(663\) −3.50634 −0.136175
\(664\) 0.316537 0.0122840
\(665\) 0 0
\(666\) −0.655930 −0.0254168
\(667\) 12.3213 0.477083
\(668\) −2.15264 −0.0832881
\(669\) −3.78445 −0.146315
\(670\) −0.408619 −0.0157863
\(671\) −1.55145 −0.0598930
\(672\) 0 0
\(673\) 9.43898 0.363846 0.181923 0.983313i \(-0.441768\pi\)
0.181923 + 0.983313i \(0.441768\pi\)
\(674\) −18.0159 −0.693946
\(675\) −4.93011 −0.189760
\(676\) 2.53580 0.0975306
\(677\) −17.4852 −0.672011 −0.336006 0.941860i \(-0.609076\pi\)
−0.336006 + 0.941860i \(0.609076\pi\)
\(678\) 16.8667 0.647761
\(679\) 0 0
\(680\) 1.49789 0.0574413
\(681\) 20.1757 0.773135
\(682\) 3.11924 0.119442
\(683\) −37.9803 −1.45328 −0.726638 0.687021i \(-0.758918\pi\)
−0.726638 + 0.687021i \(0.758918\pi\)
\(684\) −1.66573 −0.0636907
\(685\) −0.162721 −0.00621725
\(686\) 0 0
\(687\) 19.3384 0.737808
\(688\) −19.9508 −0.760618
\(689\) −16.1633 −0.615774
\(690\) 1.56074 0.0594163
\(691\) −8.49462 −0.323151 −0.161575 0.986860i \(-0.551657\pi\)
−0.161575 + 0.986860i \(0.551657\pi\)
\(692\) 6.42555 0.244263
\(693\) 0 0
\(694\) −7.88134 −0.299172
\(695\) −3.84477 −0.145840
\(696\) 8.20264 0.310920
\(697\) 1.89924 0.0719388
\(698\) −4.28144 −0.162055
\(699\) 9.29636 0.351621
\(700\) 0 0
\(701\) 21.9046 0.827325 0.413662 0.910430i \(-0.364249\pi\)
0.413662 + 0.910430i \(0.364249\pi\)
\(702\) −2.43222 −0.0917982
\(703\) −3.13698 −0.118313
\(704\) 3.51562 0.132500
\(705\) −3.47941 −0.131042
\(706\) −28.9532 −1.08967
\(707\) 0 0
\(708\) −0.661500 −0.0248607
\(709\) 18.1981 0.683445 0.341723 0.939801i \(-0.388990\pi\)
0.341723 + 0.939801i \(0.388990\pi\)
\(710\) −5.23463 −0.196452
\(711\) 5.34103 0.200304
\(712\) 11.3315 0.424664
\(713\) −26.4348 −0.989989
\(714\) 0 0
\(715\) 0.195895 0.00732605
\(716\) −3.51421 −0.131332
\(717\) 13.8265 0.516361
\(718\) −47.2918 −1.76492
\(719\) 11.5476 0.430653 0.215327 0.976542i \(-0.430918\pi\)
0.215327 + 0.976542i \(0.430918\pi\)
\(720\) 0.899238 0.0335126
\(721\) 0 0
\(722\) 27.2674 1.01479
\(723\) −17.5930 −0.654291
\(724\) −4.36128 −0.162086
\(725\) 13.5561 0.503459
\(726\) −14.2795 −0.529963
\(727\) −0.769589 −0.0285425 −0.0142712 0.999898i \(-0.504543\pi\)
−0.0142712 + 0.999898i \(0.504543\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.56712 −0.0950135
\(731\) 11.1401 0.412031
\(732\) 1.02196 0.0377728
\(733\) −40.2110 −1.48523 −0.742613 0.669721i \(-0.766414\pi\)
−0.742613 + 0.669721i \(0.766414\pi\)
\(734\) 23.3592 0.862204
\(735\) 0 0
\(736\) −6.65558 −0.245328
\(737\) 0.470861 0.0173444
\(738\) 1.31743 0.0484953
\(739\) −33.7982 −1.24329 −0.621643 0.783300i \(-0.713535\pi\)
−0.621643 + 0.783300i \(0.713535\pi\)
\(740\) −0.0347997 −0.00127926
\(741\) −11.6320 −0.427314
\(742\) 0 0
\(743\) 12.8681 0.472084 0.236042 0.971743i \(-0.424150\pi\)
0.236042 + 0.971743i \(0.424150\pi\)
\(744\) −17.5984 −0.645187
\(745\) −3.26831 −0.119742
\(746\) 3.80558 0.139332
\(747\) −0.106108 −0.00388229
\(748\) −0.201524 −0.00736846
\(749\) 0 0
\(750\) 3.45863 0.126291
\(751\) 35.8029 1.30647 0.653233 0.757157i \(-0.273412\pi\)
0.653233 + 0.757157i \(0.273412\pi\)
\(752\) −44.7645 −1.63239
\(753\) 19.2253 0.700611
\(754\) 6.68775 0.243553
\(755\) 0.500701 0.0182224
\(756\) 0 0
\(757\) 26.8364 0.975385 0.487693 0.873015i \(-0.337839\pi\)
0.487693 + 0.873015i \(0.337839\pi\)
\(758\) −30.0939 −1.09306
\(759\) −1.79848 −0.0652805
\(760\) 4.96913 0.180249
\(761\) 12.8992 0.467597 0.233799 0.972285i \(-0.424884\pi\)
0.233799 + 0.972285i \(0.424884\pi\)
\(762\) 1.17207 0.0424596
\(763\) 0 0
\(764\) 2.24552 0.0812402
\(765\) −0.502114 −0.0181540
\(766\) −38.2664 −1.38262
\(767\) −4.61936 −0.166796
\(768\) −6.22928 −0.224780
\(769\) −6.96424 −0.251137 −0.125568 0.992085i \(-0.540075\pi\)
−0.125568 + 0.992085i \(0.540075\pi\)
\(770\) 0 0
\(771\) −12.3929 −0.446319
\(772\) −1.08087 −0.0389014
\(773\) 6.90488 0.248351 0.124176 0.992260i \(-0.460371\pi\)
0.124176 + 0.992260i \(0.460371\pi\)
\(774\) 7.72746 0.277758
\(775\) −29.0839 −1.04472
\(776\) 29.0086 1.04135
\(777\) 0 0
\(778\) 7.49002 0.268530
\(779\) 6.30059 0.225742
\(780\) −0.129039 −0.00462034
\(781\) 6.03199 0.215841
\(782\) −11.2121 −0.400943
\(783\) −2.74965 −0.0982645
\(784\) 0 0
\(785\) −0.0631477 −0.00225384
\(786\) −11.2268 −0.400445
\(787\) −10.6169 −0.378452 −0.189226 0.981934i \(-0.560598\pi\)
−0.189226 + 0.981934i \(0.560598\pi\)
\(788\) −2.40856 −0.0858014
\(789\) 5.50323 0.195920
\(790\) −1.86027 −0.0661854
\(791\) 0 0
\(792\) −1.19730 −0.0425441
\(793\) 7.13653 0.253425
\(794\) −45.9985 −1.63242
\(795\) −2.31462 −0.0820910
\(796\) −4.45211 −0.157801
\(797\) −21.5437 −0.763116 −0.381558 0.924345i \(-0.624612\pi\)
−0.381558 + 0.924345i \(0.624612\pi\)
\(798\) 0 0
\(799\) 24.9955 0.884277
\(800\) −7.32255 −0.258891
\(801\) −3.79848 −0.134213
\(802\) 0.601179 0.0212284
\(803\) 2.95816 0.104391
\(804\) −0.310164 −0.0109386
\(805\) 0 0
\(806\) −14.3482 −0.505395
\(807\) 23.9834 0.844255
\(808\) 1.95741 0.0688616
\(809\) −8.78913 −0.309009 −0.154505 0.987992i \(-0.549378\pi\)
−0.154505 + 0.987992i \(0.549378\pi\)
\(810\) −0.348298 −0.0122379
\(811\) −24.9708 −0.876842 −0.438421 0.898770i \(-0.644462\pi\)
−0.438421 + 0.898770i \(0.644462\pi\)
\(812\) 0 0
\(813\) −4.44906 −0.156035
\(814\) −0.263259 −0.00922722
\(815\) −2.14683 −0.0752003
\(816\) −6.45998 −0.226144
\(817\) 36.9565 1.29294
\(818\) −26.2066 −0.916292
\(819\) 0 0
\(820\) 0.0698950 0.00244084
\(821\) 44.6324 1.55768 0.778841 0.627221i \(-0.215808\pi\)
0.778841 + 0.627221i \(0.215808\pi\)
\(822\) 0.810864 0.0282821
\(823\) 48.4771 1.68981 0.844903 0.534919i \(-0.179658\pi\)
0.844903 + 0.534919i \(0.179658\pi\)
\(824\) −29.2563 −1.01919
\(825\) −1.97871 −0.0688897
\(826\) 0 0
\(827\) −22.7051 −0.789535 −0.394768 0.918781i \(-0.629175\pi\)
−0.394768 + 0.918781i \(0.629175\pi\)
\(828\) 1.18468 0.0411706
\(829\) 16.2329 0.563793 0.281897 0.959445i \(-0.409036\pi\)
0.281897 + 0.959445i \(0.409036\pi\)
\(830\) 0.0369572 0.00128280
\(831\) −31.7797 −1.10243
\(832\) −16.1716 −0.560648
\(833\) 0 0
\(834\) 19.1591 0.663425
\(835\) −2.15264 −0.0744951
\(836\) −0.668543 −0.0231220
\(837\) 5.89924 0.203907
\(838\) 17.9082 0.618630
\(839\) 6.77718 0.233974 0.116987 0.993133i \(-0.462676\pi\)
0.116987 + 0.993133i \(0.462676\pi\)
\(840\) 0 0
\(841\) −21.4394 −0.739291
\(842\) 32.9653 1.13606
\(843\) 10.6191 0.365743
\(844\) −3.55746 −0.122453
\(845\) 2.53580 0.0872340
\(846\) 17.3384 0.596108
\(847\) 0 0
\(848\) −29.7788 −1.02261
\(849\) 26.0778 0.894987
\(850\) −12.3357 −0.423111
\(851\) 2.23105 0.0764794
\(852\) −3.97336 −0.136125
\(853\) −28.1364 −0.963372 −0.481686 0.876344i \(-0.659975\pi\)
−0.481686 + 0.876344i \(0.659975\pi\)
\(854\) 0 0
\(855\) −1.66573 −0.0569667
\(856\) 37.8702 1.29438
\(857\) 19.5239 0.666922 0.333461 0.942764i \(-0.391783\pi\)
0.333461 + 0.942764i \(0.391783\pi\)
\(858\) −0.976176 −0.0333261
\(859\) 15.2479 0.520252 0.260126 0.965575i \(-0.416236\pi\)
0.260126 + 0.965575i \(0.416236\pi\)
\(860\) 0.409973 0.0139800
\(861\) 0 0
\(862\) −20.8854 −0.711361
\(863\) 30.1625 1.02674 0.513372 0.858166i \(-0.328396\pi\)
0.513372 + 0.858166i \(0.328396\pi\)
\(864\) 1.48527 0.0505300
\(865\) 6.42555 0.218475
\(866\) 31.0149 1.05393
\(867\) −13.3929 −0.454847
\(868\) 0 0
\(869\) 2.14363 0.0727178
\(870\) 0.957697 0.0324690
\(871\) −2.16592 −0.0733894
\(872\) 46.6329 1.57919
\(873\) −9.72413 −0.329112
\(874\) −37.1953 −1.25815
\(875\) 0 0
\(876\) −1.94858 −0.0658365
\(877\) −32.0072 −1.08081 −0.540403 0.841406i \(-0.681728\pi\)
−0.540403 + 0.841406i \(0.681728\pi\)
\(878\) 41.5399 1.40190
\(879\) 4.81695 0.162472
\(880\) 0.360911 0.0121663
\(881\) 1.10922 0.0373705 0.0186853 0.999825i \(-0.494052\pi\)
0.0186853 + 0.999825i \(0.494052\pi\)
\(882\) 0 0
\(883\) −11.6523 −0.392132 −0.196066 0.980591i \(-0.562817\pi\)
−0.196066 + 0.980591i \(0.562817\pi\)
\(884\) 0.926995 0.0311782
\(885\) −0.661500 −0.0222361
\(886\) −23.1594 −0.778055
\(887\) −20.2080 −0.678518 −0.339259 0.940693i \(-0.610176\pi\)
−0.339259 + 0.940693i \(0.610176\pi\)
\(888\) 1.48527 0.0498425
\(889\) 0 0
\(890\) 1.32300 0.0443471
\(891\) 0.401352 0.0134458
\(892\) 1.00052 0.0334999
\(893\) 82.9208 2.77484
\(894\) 16.2865 0.544702
\(895\) −3.51421 −0.117467
\(896\) 0 0
\(897\) 8.27283 0.276222
\(898\) −16.2754 −0.543116
\(899\) −16.2208 −0.540995
\(900\) 1.30340 0.0434468
\(901\) 16.6278 0.553953
\(902\) 0.528753 0.0176056
\(903\) 0 0
\(904\) −38.1925 −1.27026
\(905\) −4.36128 −0.144974
\(906\) −2.49507 −0.0828932
\(907\) 26.3234 0.874054 0.437027 0.899448i \(-0.356031\pi\)
0.437027 + 0.899448i \(0.356031\pi\)
\(908\) −5.33399 −0.177015
\(909\) −0.656155 −0.0217633
\(910\) 0 0
\(911\) −12.3567 −0.409396 −0.204698 0.978825i \(-0.565621\pi\)
−0.204698 + 0.978825i \(0.565621\pi\)
\(912\) −21.4305 −0.709635
\(913\) −0.0425867 −0.00140941
\(914\) 4.73873 0.156743
\(915\) 1.02196 0.0337850
\(916\) −5.11263 −0.168926
\(917\) 0 0
\(918\) 2.50211 0.0825821
\(919\) −52.1119 −1.71901 −0.859507 0.511124i \(-0.829229\pi\)
−0.859507 + 0.511124i \(0.829229\pi\)
\(920\) −3.53410 −0.116516
\(921\) −6.48076 −0.213548
\(922\) 48.8868 1.61000
\(923\) −27.7466 −0.913291
\(924\) 0 0
\(925\) 2.45463 0.0807077
\(926\) 33.9700 1.11632
\(927\) 9.80716 0.322109
\(928\) −4.08398 −0.134063
\(929\) −18.1288 −0.594787 −0.297394 0.954755i \(-0.596117\pi\)
−0.297394 + 0.954755i \(0.596117\pi\)
\(930\) −2.05469 −0.0673760
\(931\) 0 0
\(932\) −2.45774 −0.0805060
\(933\) −26.6495 −0.872465
\(934\) −10.0688 −0.329460
\(935\) −0.201524 −0.00659055
\(936\) 5.50746 0.180017
\(937\) 3.93077 0.128413 0.0642064 0.997937i \(-0.479548\pi\)
0.0642064 + 0.997937i \(0.479548\pi\)
\(938\) 0 0
\(939\) 5.80181 0.189335
\(940\) 0.919874 0.0300030
\(941\) 30.4167 0.991557 0.495778 0.868449i \(-0.334883\pi\)
0.495778 + 0.868449i \(0.334883\pi\)
\(942\) 0.314675 0.0102527
\(943\) −4.48105 −0.145923
\(944\) −8.51057 −0.276995
\(945\) 0 0
\(946\) 3.10143 0.100836
\(947\) 16.0846 0.522679 0.261339 0.965247i \(-0.415836\pi\)
0.261339 + 0.965247i \(0.415836\pi\)
\(948\) −1.41204 −0.0458610
\(949\) −13.6073 −0.441711
\(950\) −40.9228 −1.32771
\(951\) 5.92921 0.192268
\(952\) 0 0
\(953\) 42.7563 1.38501 0.692507 0.721411i \(-0.256506\pi\)
0.692507 + 0.721411i \(0.256506\pi\)
\(954\) 11.5341 0.373430
\(955\) 2.24552 0.0726635
\(956\) −3.65541 −0.118224
\(957\) −1.10358 −0.0356736
\(958\) 7.43194 0.240115
\(959\) 0 0
\(960\) −2.31579 −0.0747419
\(961\) 3.80101 0.122613
\(962\) 1.21097 0.0390432
\(963\) −12.6947 −0.409080
\(964\) 4.65118 0.149804
\(965\) −1.08087 −0.0347944
\(966\) 0 0
\(967\) 54.8388 1.76350 0.881748 0.471720i \(-0.156367\pi\)
0.881748 + 0.471720i \(0.156367\pi\)
\(968\) 32.3342 1.03926
\(969\) 11.9663 0.384414
\(970\) 3.38689 0.108747
\(971\) −26.9195 −0.863888 −0.431944 0.901900i \(-0.642172\pi\)
−0.431944 + 0.901900i \(0.642172\pi\)
\(972\) −0.264377 −0.00847988
\(973\) 0 0
\(974\) −17.2371 −0.552312
\(975\) 9.10188 0.291493
\(976\) 13.1481 0.420861
\(977\) 55.3873 1.77200 0.885998 0.463689i \(-0.153475\pi\)
0.885998 + 0.463689i \(0.153475\pi\)
\(978\) 10.6980 0.342085
\(979\) −1.52453 −0.0487240
\(980\) 0 0
\(981\) −15.6320 −0.499093
\(982\) 13.1768 0.420487
\(983\) 34.7872 1.10954 0.554770 0.832004i \(-0.312806\pi\)
0.554770 + 0.832004i \(0.312806\pi\)
\(984\) −2.98316 −0.0950996
\(985\) −2.40856 −0.0767431
\(986\) −6.87994 −0.219102
\(987\) 0 0
\(988\) 3.07524 0.0978364
\(989\) −26.2838 −0.835777
\(990\) −0.139790 −0.00444282
\(991\) 25.9053 0.822910 0.411455 0.911430i \(-0.365021\pi\)
0.411455 + 0.911430i \(0.365021\pi\)
\(992\) 8.76198 0.278193
\(993\) −32.3045 −1.02515
\(994\) 0 0
\(995\) −4.45211 −0.141141
\(996\) 0.0280525 0.000888877 0
\(997\) −36.1794 −1.14581 −0.572907 0.819620i \(-0.694184\pi\)
−0.572907 + 0.819620i \(0.694184\pi\)
\(998\) 26.3220 0.833210
\(999\) −0.497886 −0.0157524
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 \(a_p\))