Properties

Label 8013.2.a.d.1.2
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75607 q^{2}\) \(+1.00000 q^{3}\) \(+5.59595 q^{4}\) \(+0.110089 q^{5}\) \(-2.75607 q^{6}\) \(+1.43985 q^{7}\) \(-9.91070 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75607 q^{2}\) \(+1.00000 q^{3}\) \(+5.59595 q^{4}\) \(+0.110089 q^{5}\) \(-2.75607 q^{6}\) \(+1.43985 q^{7}\) \(-9.91070 q^{8}\) \(+1.00000 q^{9}\) \(-0.303413 q^{10}\) \(-0.0788383 q^{11}\) \(+5.59595 q^{12}\) \(-1.19203 q^{13}\) \(-3.96832 q^{14}\) \(+0.110089 q^{15}\) \(+16.1227 q^{16}\) \(+0.781615 q^{17}\) \(-2.75607 q^{18}\) \(-2.26675 q^{19}\) \(+0.616051 q^{20}\) \(+1.43985 q^{21}\) \(+0.217284 q^{22}\) \(-5.36820 q^{23}\) \(-9.91070 q^{24}\) \(-4.98788 q^{25}\) \(+3.28531 q^{26}\) \(+1.00000 q^{27}\) \(+8.05730 q^{28}\) \(-0.140154 q^{29}\) \(-0.303413 q^{30}\) \(+6.90226 q^{31}\) \(-24.6140 q^{32}\) \(-0.0788383 q^{33}\) \(-2.15419 q^{34}\) \(+0.158511 q^{35}\) \(+5.59595 q^{36}\) \(+0.903661 q^{37}\) \(+6.24734 q^{38}\) \(-1.19203 q^{39}\) \(-1.09106 q^{40}\) \(-1.92438 q^{41}\) \(-3.96832 q^{42}\) \(-2.72015 q^{43}\) \(-0.441175 q^{44}\) \(+0.110089 q^{45}\) \(+14.7951 q^{46}\) \(-0.0476025 q^{47}\) \(+16.1227 q^{48}\) \(-4.92684 q^{49}\) \(+13.7470 q^{50}\) \(+0.781615 q^{51}\) \(-6.67051 q^{52}\) \(+3.74754 q^{53}\) \(-2.75607 q^{54}\) \(-0.00867922 q^{55}\) \(-14.2699 q^{56}\) \(-2.26675 q^{57}\) \(+0.386276 q^{58}\) \(-11.1497 q^{59}\) \(+0.616051 q^{60}\) \(+6.72295 q^{61}\) \(-19.0231 q^{62}\) \(+1.43985 q^{63}\) \(+35.5927 q^{64}\) \(-0.131229 q^{65}\) \(+0.217284 q^{66}\) \(+9.41624 q^{67}\) \(+4.37388 q^{68}\) \(-5.36820 q^{69}\) \(-0.436868 q^{70}\) \(-2.32642 q^{71}\) \(-9.91070 q^{72}\) \(+15.4500 q^{73}\) \(-2.49056 q^{74}\) \(-4.98788 q^{75}\) \(-12.6846 q^{76}\) \(-0.113515 q^{77}\) \(+3.28531 q^{78}\) \(+7.02174 q^{79}\) \(+1.77493 q^{80}\) \(+1.00000 q^{81}\) \(+5.30373 q^{82}\) \(+14.7129 q^{83}\) \(+8.05730 q^{84}\) \(+0.0860472 q^{85}\) \(+7.49693 q^{86}\) \(-0.140154 q^{87}\) \(+0.781342 q^{88}\) \(-16.0404 q^{89}\) \(-0.303413 q^{90}\) \(-1.71633 q^{91}\) \(-30.0401 q^{92}\) \(+6.90226 q^{93}\) \(+0.131196 q^{94}\) \(-0.249544 q^{95}\) \(-24.6140 q^{96}\) \(-3.16445 q^{97}\) \(+13.5787 q^{98}\) \(-0.0788383 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75607 −1.94884 −0.974419 0.224737i \(-0.927848\pi\)
−0.974419 + 0.224737i \(0.927848\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.59595 2.79797
\(5\) 0.110089 0.0492332 0.0246166 0.999697i \(-0.492163\pi\)
0.0246166 + 0.999697i \(0.492163\pi\)
\(6\) −2.75607 −1.12516
\(7\) 1.43985 0.544211 0.272105 0.962267i \(-0.412280\pi\)
0.272105 + 0.962267i \(0.412280\pi\)
\(8\) −9.91070 −3.50396
\(9\) 1.00000 0.333333
\(10\) −0.303413 −0.0959477
\(11\) −0.0788383 −0.0237706 −0.0118853 0.999929i \(-0.503783\pi\)
−0.0118853 + 0.999929i \(0.503783\pi\)
\(12\) 5.59595 1.61541
\(13\) −1.19203 −0.330608 −0.165304 0.986243i \(-0.552861\pi\)
−0.165304 + 0.986243i \(0.552861\pi\)
\(14\) −3.96832 −1.06058
\(15\) 0.110089 0.0284248
\(16\) 16.1227 4.03068
\(17\) 0.781615 0.189570 0.0947848 0.995498i \(-0.469784\pi\)
0.0947848 + 0.995498i \(0.469784\pi\)
\(18\) −2.75607 −0.649613
\(19\) −2.26675 −0.520029 −0.260015 0.965605i \(-0.583727\pi\)
−0.260015 + 0.965605i \(0.583727\pi\)
\(20\) 0.616051 0.137753
\(21\) 1.43985 0.314200
\(22\) 0.217284 0.0463252
\(23\) −5.36820 −1.11935 −0.559673 0.828714i \(-0.689073\pi\)
−0.559673 + 0.828714i \(0.689073\pi\)
\(24\) −9.91070 −2.02301
\(25\) −4.98788 −0.997576
\(26\) 3.28531 0.644302
\(27\) 1.00000 0.192450
\(28\) 8.05730 1.52269
\(29\) −0.140154 −0.0260260 −0.0130130 0.999915i \(-0.504142\pi\)
−0.0130130 + 0.999915i \(0.504142\pi\)
\(30\) −0.303413 −0.0553954
\(31\) 6.90226 1.23968 0.619841 0.784728i \(-0.287197\pi\)
0.619841 + 0.784728i \(0.287197\pi\)
\(32\) −24.6140 −4.35119
\(33\) −0.0788383 −0.0137240
\(34\) −2.15419 −0.369441
\(35\) 0.158511 0.0267932
\(36\) 5.59595 0.932658
\(37\) 0.903661 0.148561 0.0742805 0.997237i \(-0.476334\pi\)
0.0742805 + 0.997237i \(0.476334\pi\)
\(38\) 6.24734 1.01345
\(39\) −1.19203 −0.190877
\(40\) −1.09106 −0.172511
\(41\) −1.92438 −0.300537 −0.150269 0.988645i \(-0.548014\pi\)
−0.150269 + 0.988645i \(0.548014\pi\)
\(42\) −3.96832 −0.612325
\(43\) −2.72015 −0.414819 −0.207409 0.978254i \(-0.566503\pi\)
−0.207409 + 0.978254i \(0.566503\pi\)
\(44\) −0.441175 −0.0665096
\(45\) 0.110089 0.0164111
\(46\) 14.7951 2.18143
\(47\) −0.0476025 −0.00694354 −0.00347177 0.999994i \(-0.501105\pi\)
−0.00347177 + 0.999994i \(0.501105\pi\)
\(48\) 16.1227 2.32711
\(49\) −4.92684 −0.703835
\(50\) 13.7470 1.94412
\(51\) 0.781615 0.109448
\(52\) −6.67051 −0.925033
\(53\) 3.74754 0.514764 0.257382 0.966310i \(-0.417140\pi\)
0.257382 + 0.966310i \(0.417140\pi\)
\(54\) −2.75607 −0.375054
\(55\) −0.00867922 −0.00117031
\(56\) −14.2699 −1.90689
\(57\) −2.26675 −0.300239
\(58\) 0.386276 0.0507205
\(59\) −11.1497 −1.45157 −0.725784 0.687923i \(-0.758523\pi\)
−0.725784 + 0.687923i \(0.758523\pi\)
\(60\) 0.616051 0.0795319
\(61\) 6.72295 0.860785 0.430393 0.902642i \(-0.358375\pi\)
0.430393 + 0.902642i \(0.358375\pi\)
\(62\) −19.0231 −2.41594
\(63\) 1.43985 0.181404
\(64\) 35.5927 4.44908
\(65\) −0.131229 −0.0162769
\(66\) 0.217284 0.0267458
\(67\) 9.41624 1.15038 0.575188 0.818021i \(-0.304929\pi\)
0.575188 + 0.818021i \(0.304929\pi\)
\(68\) 4.37388 0.530411
\(69\) −5.36820 −0.646255
\(70\) −0.436868 −0.0522157
\(71\) −2.32642 −0.276095 −0.138047 0.990426i \(-0.544083\pi\)
−0.138047 + 0.990426i \(0.544083\pi\)
\(72\) −9.91070 −1.16799
\(73\) 15.4500 1.80829 0.904143 0.427231i \(-0.140511\pi\)
0.904143 + 0.427231i \(0.140511\pi\)
\(74\) −2.49056 −0.289521
\(75\) −4.98788 −0.575951
\(76\) −12.6846 −1.45503
\(77\) −0.113515 −0.0129362
\(78\) 3.28531 0.371988
\(79\) 7.02174 0.790008 0.395004 0.918679i \(-0.370743\pi\)
0.395004 + 0.918679i \(0.370743\pi\)
\(80\) 1.77493 0.198444
\(81\) 1.00000 0.111111
\(82\) 5.30373 0.585699
\(83\) 14.7129 1.61495 0.807474 0.589904i \(-0.200834\pi\)
0.807474 + 0.589904i \(0.200834\pi\)
\(84\) 8.05730 0.879123
\(85\) 0.0860472 0.00933312
\(86\) 7.49693 0.808415
\(87\) −0.140154 −0.0150261
\(88\) 0.781342 0.0832914
\(89\) −16.0404 −1.70028 −0.850138 0.526560i \(-0.823482\pi\)
−0.850138 + 0.526560i \(0.823482\pi\)
\(90\) −0.303413 −0.0319826
\(91\) −1.71633 −0.179920
\(92\) −30.0401 −3.13190
\(93\) 6.90226 0.715731
\(94\) 0.131196 0.0135318
\(95\) −0.249544 −0.0256027
\(96\) −24.6140 −2.51216
\(97\) −3.16445 −0.321302 −0.160651 0.987011i \(-0.551359\pi\)
−0.160651 + 0.987011i \(0.551359\pi\)
\(98\) 13.5787 1.37166
\(99\) −0.0788383 −0.00792355
\(100\) −27.9119 −2.79119
\(101\) 14.7029 1.46299 0.731495 0.681847i \(-0.238823\pi\)
0.731495 + 0.681847i \(0.238823\pi\)
\(102\) −2.15419 −0.213297
\(103\) 7.32325 0.721582 0.360791 0.932647i \(-0.382507\pi\)
0.360791 + 0.932647i \(0.382507\pi\)
\(104\) 11.8138 1.15844
\(105\) 0.158511 0.0154691
\(106\) −10.3285 −1.00319
\(107\) −19.2573 −1.86167 −0.930837 0.365434i \(-0.880921\pi\)
−0.930837 + 0.365434i \(0.880921\pi\)
\(108\) 5.59595 0.538470
\(109\) 2.09641 0.200800 0.100400 0.994947i \(-0.467988\pi\)
0.100400 + 0.994947i \(0.467988\pi\)
\(110\) 0.0239206 0.00228074
\(111\) 0.903661 0.0857717
\(112\) 23.2142 2.19354
\(113\) 13.8910 1.30675 0.653377 0.757032i \(-0.273352\pi\)
0.653377 + 0.757032i \(0.273352\pi\)
\(114\) 6.24734 0.585117
\(115\) −0.590979 −0.0551090
\(116\) −0.784296 −0.0728200
\(117\) −1.19203 −0.110203
\(118\) 30.7294 2.82887
\(119\) 1.12541 0.103166
\(120\) −1.09106 −0.0995995
\(121\) −10.9938 −0.999435
\(122\) −18.5289 −1.67753
\(123\) −1.92438 −0.173515
\(124\) 38.6247 3.46860
\(125\) −1.09955 −0.0983471
\(126\) −3.96832 −0.353526
\(127\) 14.6191 1.29723 0.648616 0.761116i \(-0.275348\pi\)
0.648616 + 0.761116i \(0.275348\pi\)
\(128\) −48.8680 −4.31936
\(129\) −2.72015 −0.239496
\(130\) 0.361676 0.0317211
\(131\) −0.117046 −0.0102263 −0.00511316 0.999987i \(-0.501628\pi\)
−0.00511316 + 0.999987i \(0.501628\pi\)
\(132\) −0.441175 −0.0383993
\(133\) −3.26378 −0.283005
\(134\) −25.9519 −2.24190
\(135\) 0.110089 0.00947494
\(136\) −7.74635 −0.664244
\(137\) 17.2615 1.47475 0.737376 0.675482i \(-0.236065\pi\)
0.737376 + 0.675482i \(0.236065\pi\)
\(138\) 14.7951 1.25945
\(139\) 4.71172 0.399643 0.199821 0.979832i \(-0.435964\pi\)
0.199821 + 0.979832i \(0.435964\pi\)
\(140\) 0.887019 0.0749668
\(141\) −0.0476025 −0.00400885
\(142\) 6.41178 0.538065
\(143\) 0.0939772 0.00785877
\(144\) 16.1227 1.34356
\(145\) −0.0154294 −0.00128134
\(146\) −42.5813 −3.52406
\(147\) −4.92684 −0.406359
\(148\) 5.05684 0.415669
\(149\) −14.3317 −1.17410 −0.587048 0.809552i \(-0.699710\pi\)
−0.587048 + 0.809552i \(0.699710\pi\)
\(150\) 13.7470 1.12244
\(151\) −18.5093 −1.50627 −0.753134 0.657867i \(-0.771459\pi\)
−0.753134 + 0.657867i \(0.771459\pi\)
\(152\) 22.4651 1.82216
\(153\) 0.781615 0.0631899
\(154\) 0.312856 0.0252106
\(155\) 0.759862 0.0610336
\(156\) −6.67051 −0.534068
\(157\) −8.08169 −0.644989 −0.322494 0.946571i \(-0.604521\pi\)
−0.322494 + 0.946571i \(0.604521\pi\)
\(158\) −19.3524 −1.53960
\(159\) 3.74754 0.297199
\(160\) −2.70973 −0.214223
\(161\) −7.72937 −0.609160
\(162\) −2.75607 −0.216538
\(163\) 23.1826 1.81580 0.907902 0.419182i \(-0.137683\pi\)
0.907902 + 0.419182i \(0.137683\pi\)
\(164\) −10.7687 −0.840896
\(165\) −0.00867922 −0.000675676 0
\(166\) −40.5498 −3.14727
\(167\) 6.08845 0.471138 0.235569 0.971858i \(-0.424305\pi\)
0.235569 + 0.971858i \(0.424305\pi\)
\(168\) −14.2699 −1.10094
\(169\) −11.5791 −0.890698
\(170\) −0.237152 −0.0181888
\(171\) −2.26675 −0.173343
\(172\) −15.2218 −1.16065
\(173\) 11.1913 0.850856 0.425428 0.904992i \(-0.360124\pi\)
0.425428 + 0.904992i \(0.360124\pi\)
\(174\) 0.386276 0.0292835
\(175\) −7.18178 −0.542891
\(176\) −1.27109 −0.0958119
\(177\) −11.1497 −0.838063
\(178\) 44.2085 3.31356
\(179\) 2.79118 0.208622 0.104311 0.994545i \(-0.466736\pi\)
0.104311 + 0.994545i \(0.466736\pi\)
\(180\) 0.616051 0.0459178
\(181\) 24.8091 1.84405 0.922023 0.387134i \(-0.126535\pi\)
0.922023 + 0.387134i \(0.126535\pi\)
\(182\) 4.73034 0.350636
\(183\) 6.72295 0.496975
\(184\) 53.2026 3.92214
\(185\) 0.0994830 0.00731414
\(186\) −19.0231 −1.39484
\(187\) −0.0616212 −0.00450619
\(188\) −0.266381 −0.0194278
\(189\) 1.43985 0.104733
\(190\) 0.687763 0.0498956
\(191\) 9.31265 0.673840 0.336920 0.941533i \(-0.390615\pi\)
0.336920 + 0.941533i \(0.390615\pi\)
\(192\) 35.5927 2.56868
\(193\) 5.43914 0.391518 0.195759 0.980652i \(-0.437283\pi\)
0.195759 + 0.980652i \(0.437283\pi\)
\(194\) 8.72147 0.626165
\(195\) −0.131229 −0.00939748
\(196\) −27.5704 −1.96931
\(197\) 13.1030 0.933550 0.466775 0.884376i \(-0.345416\pi\)
0.466775 + 0.884376i \(0.345416\pi\)
\(198\) 0.217284 0.0154417
\(199\) 19.9869 1.41683 0.708415 0.705796i \(-0.249410\pi\)
0.708415 + 0.705796i \(0.249410\pi\)
\(200\) 49.4334 3.49547
\(201\) 9.41624 0.664170
\(202\) −40.5222 −2.85113
\(203\) −0.201801 −0.0141636
\(204\) 4.37388 0.306233
\(205\) −0.211853 −0.0147964
\(206\) −20.1834 −1.40625
\(207\) −5.36820 −0.373115
\(208\) −19.2187 −1.33258
\(209\) 0.178707 0.0123614
\(210\) −0.436868 −0.0301468
\(211\) 18.8138 1.29519 0.647596 0.761984i \(-0.275774\pi\)
0.647596 + 0.761984i \(0.275774\pi\)
\(212\) 20.9710 1.44030
\(213\) −2.32642 −0.159403
\(214\) 53.0746 3.62810
\(215\) −0.299458 −0.0204229
\(216\) −9.91070 −0.674337
\(217\) 9.93818 0.674648
\(218\) −5.77786 −0.391326
\(219\) 15.4500 1.04401
\(220\) −0.0485685 −0.00327448
\(221\) −0.931705 −0.0626733
\(222\) −2.49056 −0.167155
\(223\) 4.35219 0.291444 0.145722 0.989326i \(-0.453449\pi\)
0.145722 + 0.989326i \(0.453449\pi\)
\(224\) −35.4404 −2.36796
\(225\) −4.98788 −0.332525
\(226\) −38.2846 −2.54665
\(227\) −3.16005 −0.209740 −0.104870 0.994486i \(-0.533443\pi\)
−0.104870 + 0.994486i \(0.533443\pi\)
\(228\) −12.6846 −0.840061
\(229\) 9.94671 0.657297 0.328648 0.944452i \(-0.393407\pi\)
0.328648 + 0.944452i \(0.393407\pi\)
\(230\) 1.62878 0.107399
\(231\) −0.113515 −0.00746874
\(232\) 1.38903 0.0911941
\(233\) 21.4661 1.40629 0.703144 0.711048i \(-0.251779\pi\)
0.703144 + 0.711048i \(0.251779\pi\)
\(234\) 3.28531 0.214767
\(235\) −0.00524050 −0.000341853 0
\(236\) −62.3931 −4.06145
\(237\) 7.02174 0.456111
\(238\) −3.10170 −0.201053
\(239\) 7.65270 0.495012 0.247506 0.968886i \(-0.420389\pi\)
0.247506 + 0.968886i \(0.420389\pi\)
\(240\) 1.77493 0.114571
\(241\) 17.1582 1.10526 0.552628 0.833428i \(-0.313625\pi\)
0.552628 + 0.833428i \(0.313625\pi\)
\(242\) 30.2997 1.94774
\(243\) 1.00000 0.0641500
\(244\) 37.6213 2.40845
\(245\) −0.542391 −0.0346521
\(246\) 5.30373 0.338153
\(247\) 2.70203 0.171926
\(248\) −68.4062 −4.34380
\(249\) 14.7129 0.932390
\(250\) 3.03045 0.191663
\(251\) 7.62276 0.481144 0.240572 0.970631i \(-0.422665\pi\)
0.240572 + 0.970631i \(0.422665\pi\)
\(252\) 8.05730 0.507562
\(253\) 0.423219 0.0266076
\(254\) −40.2912 −2.52810
\(255\) 0.0860472 0.00538848
\(256\) 63.4984 3.96865
\(257\) 21.4895 1.34048 0.670241 0.742144i \(-0.266191\pi\)
0.670241 + 0.742144i \(0.266191\pi\)
\(258\) 7.49693 0.466739
\(259\) 1.30113 0.0808484
\(260\) −0.734349 −0.0455424
\(261\) −0.140154 −0.00867533
\(262\) 0.322586 0.0199294
\(263\) −2.73623 −0.168723 −0.0843614 0.996435i \(-0.526885\pi\)
−0.0843614 + 0.996435i \(0.526885\pi\)
\(264\) 0.781342 0.0480883
\(265\) 0.412563 0.0253435
\(266\) 8.99521 0.551532
\(267\) −16.0404 −0.981655
\(268\) 52.6928 3.21872
\(269\) −25.7350 −1.56909 −0.784546 0.620071i \(-0.787104\pi\)
−0.784546 + 0.620071i \(0.787104\pi\)
\(270\) −0.303413 −0.0184651
\(271\) 26.7687 1.62608 0.813042 0.582205i \(-0.197810\pi\)
0.813042 + 0.582205i \(0.197810\pi\)
\(272\) 12.6018 0.764094
\(273\) −1.71633 −0.103877
\(274\) −47.5741 −2.87406
\(275\) 0.393236 0.0237130
\(276\) −30.0401 −1.80820
\(277\) −21.8169 −1.31085 −0.655425 0.755260i \(-0.727510\pi\)
−0.655425 + 0.755260i \(0.727510\pi\)
\(278\) −12.9858 −0.778839
\(279\) 6.90226 0.413227
\(280\) −1.57095 −0.0938825
\(281\) −5.15863 −0.307738 −0.153869 0.988091i \(-0.549173\pi\)
−0.153869 + 0.988091i \(0.549173\pi\)
\(282\) 0.131196 0.00781261
\(283\) −13.2745 −0.789090 −0.394545 0.918877i \(-0.629098\pi\)
−0.394545 + 0.918877i \(0.629098\pi\)
\(284\) −13.0185 −0.772506
\(285\) −0.249544 −0.0147817
\(286\) −0.259008 −0.0153155
\(287\) −2.77081 −0.163556
\(288\) −24.6140 −1.45040
\(289\) −16.3891 −0.964063
\(290\) 0.0425246 0.00249713
\(291\) −3.16445 −0.185504
\(292\) 86.4573 5.05953
\(293\) 25.2928 1.47762 0.738810 0.673914i \(-0.235388\pi\)
0.738810 + 0.673914i \(0.235388\pi\)
\(294\) 13.5787 0.791929
\(295\) −1.22746 −0.0714654
\(296\) −8.95591 −0.520552
\(297\) −0.0788383 −0.00457466
\(298\) 39.4992 2.28812
\(299\) 6.39902 0.370065
\(300\) −27.9119 −1.61150
\(301\) −3.91660 −0.225749
\(302\) 51.0131 2.93547
\(303\) 14.7029 0.844658
\(304\) −36.5463 −2.09607
\(305\) 0.740122 0.0423793
\(306\) −2.15419 −0.123147
\(307\) 8.87263 0.506388 0.253194 0.967416i \(-0.418519\pi\)
0.253194 + 0.967416i \(0.418519\pi\)
\(308\) −0.635224 −0.0361952
\(309\) 7.32325 0.416605
\(310\) −2.09424 −0.118945
\(311\) −12.6628 −0.718043 −0.359022 0.933329i \(-0.616890\pi\)
−0.359022 + 0.933329i \(0.616890\pi\)
\(312\) 11.8138 0.668825
\(313\) 3.64883 0.206244 0.103122 0.994669i \(-0.467117\pi\)
0.103122 + 0.994669i \(0.467117\pi\)
\(314\) 22.2737 1.25698
\(315\) 0.158511 0.00893108
\(316\) 39.2933 2.21042
\(317\) 18.4750 1.03766 0.518829 0.854878i \(-0.326368\pi\)
0.518829 + 0.854878i \(0.326368\pi\)
\(318\) −10.3285 −0.579194
\(319\) 0.0110495 0.000618655 0
\(320\) 3.91836 0.219043
\(321\) −19.2573 −1.07484
\(322\) 21.3027 1.18715
\(323\) −1.77173 −0.0985817
\(324\) 5.59595 0.310886
\(325\) 5.94568 0.329807
\(326\) −63.8931 −3.53871
\(327\) 2.09641 0.115932
\(328\) 19.0719 1.05307
\(329\) −0.0685402 −0.00377875
\(330\) 0.0239206 0.00131678
\(331\) −32.1696 −1.76820 −0.884101 0.467296i \(-0.845228\pi\)
−0.884101 + 0.467296i \(0.845228\pi\)
\(332\) 82.3324 4.51858
\(333\) 0.903661 0.0495203
\(334\) −16.7802 −0.918173
\(335\) 1.03662 0.0566368
\(336\) 23.2142 1.26644
\(337\) −19.3712 −1.05522 −0.527609 0.849487i \(-0.676912\pi\)
−0.527609 + 0.849487i \(0.676912\pi\)
\(338\) 31.9128 1.73583
\(339\) 13.8910 0.754455
\(340\) 0.481515 0.0261138
\(341\) −0.544162 −0.0294680
\(342\) 6.24734 0.337818
\(343\) −17.1728 −0.927245
\(344\) 26.9586 1.45351
\(345\) −0.590979 −0.0318172
\(346\) −30.8439 −1.65818
\(347\) 3.43557 0.184431 0.0922155 0.995739i \(-0.470605\pi\)
0.0922155 + 0.995739i \(0.470605\pi\)
\(348\) −0.784296 −0.0420427
\(349\) 17.0909 0.914857 0.457429 0.889246i \(-0.348771\pi\)
0.457429 + 0.889246i \(0.348771\pi\)
\(350\) 19.7935 1.05801
\(351\) −1.19203 −0.0636256
\(352\) 1.94053 0.103431
\(353\) 28.3332 1.50803 0.754013 0.656859i \(-0.228115\pi\)
0.754013 + 0.656859i \(0.228115\pi\)
\(354\) 30.7294 1.63325
\(355\) −0.256113 −0.0135930
\(356\) −89.7611 −4.75733
\(357\) 1.12541 0.0595628
\(358\) −7.69269 −0.406571
\(359\) 9.50107 0.501447 0.250724 0.968059i \(-0.419331\pi\)
0.250724 + 0.968059i \(0.419331\pi\)
\(360\) −1.09106 −0.0575038
\(361\) −13.8618 −0.729570
\(362\) −68.3758 −3.59375
\(363\) −10.9938 −0.577024
\(364\) −9.60450 −0.503413
\(365\) 1.70087 0.0890277
\(366\) −18.5289 −0.968524
\(367\) −22.7474 −1.18740 −0.593702 0.804685i \(-0.702334\pi\)
−0.593702 + 0.804685i \(0.702334\pi\)
\(368\) −86.5499 −4.51173
\(369\) −1.92438 −0.100179
\(370\) −0.274183 −0.0142541
\(371\) 5.39588 0.280140
\(372\) 38.6247 2.00260
\(373\) 20.8796 1.08111 0.540553 0.841310i \(-0.318215\pi\)
0.540553 + 0.841310i \(0.318215\pi\)
\(374\) 0.169833 0.00878184
\(375\) −1.09955 −0.0567808
\(376\) 0.471774 0.0243299
\(377\) 0.167067 0.00860441
\(378\) −3.96832 −0.204108
\(379\) −26.8200 −1.37765 −0.688826 0.724927i \(-0.741874\pi\)
−0.688826 + 0.724927i \(0.741874\pi\)
\(380\) −1.39644 −0.0716357
\(381\) 14.6191 0.748957
\(382\) −25.6664 −1.31321
\(383\) 27.3799 1.39905 0.699523 0.714610i \(-0.253396\pi\)
0.699523 + 0.714610i \(0.253396\pi\)
\(384\) −48.8680 −2.49378
\(385\) −0.0124967 −0.000636893 0
\(386\) −14.9907 −0.763006
\(387\) −2.72015 −0.138273
\(388\) −17.7081 −0.898994
\(389\) −17.4782 −0.886180 −0.443090 0.896477i \(-0.646118\pi\)
−0.443090 + 0.896477i \(0.646118\pi\)
\(390\) 0.361676 0.0183142
\(391\) −4.19586 −0.212194
\(392\) 48.8285 2.46621
\(393\) −0.117046 −0.00590416
\(394\) −36.1128 −1.81934
\(395\) 0.773016 0.0388946
\(396\) −0.441175 −0.0221699
\(397\) −6.92519 −0.347565 −0.173783 0.984784i \(-0.555599\pi\)
−0.173783 + 0.984784i \(0.555599\pi\)
\(398\) −55.0853 −2.76118
\(399\) −3.26378 −0.163393
\(400\) −80.4182 −4.02091
\(401\) 5.37106 0.268218 0.134109 0.990967i \(-0.457183\pi\)
0.134109 + 0.990967i \(0.457183\pi\)
\(402\) −25.9519 −1.29436
\(403\) −8.22766 −0.409849
\(404\) 82.2765 4.09341
\(405\) 0.110089 0.00547036
\(406\) 0.556177 0.0276026
\(407\) −0.0712431 −0.00353139
\(408\) −7.74635 −0.383502
\(409\) −7.39223 −0.365522 −0.182761 0.983157i \(-0.558503\pi\)
−0.182761 + 0.983157i \(0.558503\pi\)
\(410\) 0.583882 0.0288359
\(411\) 17.2615 0.851449
\(412\) 40.9805 2.01897
\(413\) −16.0538 −0.789958
\(414\) 14.7951 0.727142
\(415\) 1.61972 0.0795091
\(416\) 29.3405 1.43854
\(417\) 4.71172 0.230734
\(418\) −0.492530 −0.0240904
\(419\) 17.6677 0.863124 0.431562 0.902083i \(-0.357963\pi\)
0.431562 + 0.902083i \(0.357963\pi\)
\(420\) 0.887019 0.0432821
\(421\) −2.31305 −0.112731 −0.0563657 0.998410i \(-0.517951\pi\)
−0.0563657 + 0.998410i \(0.517951\pi\)
\(422\) −51.8521 −2.52412
\(423\) −0.0476025 −0.00231451
\(424\) −37.1407 −1.80371
\(425\) −3.89860 −0.189110
\(426\) 6.41178 0.310652
\(427\) 9.68001 0.468449
\(428\) −107.763 −5.20892
\(429\) 0.0939772 0.00453726
\(430\) 0.825329 0.0398009
\(431\) −11.1812 −0.538577 −0.269289 0.963060i \(-0.586789\pi\)
−0.269289 + 0.963060i \(0.586789\pi\)
\(432\) 16.1227 0.775705
\(433\) −32.0607 −1.54074 −0.770369 0.637598i \(-0.779928\pi\)
−0.770369 + 0.637598i \(0.779928\pi\)
\(434\) −27.3904 −1.31478
\(435\) −0.0154294 −0.000739784 0
\(436\) 11.7314 0.561832
\(437\) 12.1684 0.582093
\(438\) −42.5813 −2.03461
\(439\) 27.4159 1.30849 0.654246 0.756282i \(-0.272986\pi\)
0.654246 + 0.756282i \(0.272986\pi\)
\(440\) 0.0860171 0.00410071
\(441\) −4.92684 −0.234612
\(442\) 2.56785 0.122140
\(443\) −20.3313 −0.965971 −0.482985 0.875628i \(-0.660448\pi\)
−0.482985 + 0.875628i \(0.660448\pi\)
\(444\) 5.05684 0.239987
\(445\) −1.76587 −0.0837101
\(446\) −11.9950 −0.567978
\(447\) −14.3317 −0.677865
\(448\) 51.2480 2.42124
\(449\) 26.5362 1.25232 0.626160 0.779694i \(-0.284626\pi\)
0.626160 + 0.779694i \(0.284626\pi\)
\(450\) 13.7470 0.648038
\(451\) 0.151715 0.00714397
\(452\) 77.7333 3.65626
\(453\) −18.5093 −0.869645
\(454\) 8.70932 0.408749
\(455\) −0.188949 −0.00885807
\(456\) 22.4651 1.05203
\(457\) −15.0585 −0.704408 −0.352204 0.935923i \(-0.614568\pi\)
−0.352204 + 0.935923i \(0.614568\pi\)
\(458\) −27.4139 −1.28097
\(459\) 0.781615 0.0364827
\(460\) −3.30708 −0.154194
\(461\) −7.96082 −0.370772 −0.185386 0.982666i \(-0.559354\pi\)
−0.185386 + 0.982666i \(0.559354\pi\)
\(462\) 0.312856 0.0145554
\(463\) −20.1588 −0.936861 −0.468431 0.883500i \(-0.655180\pi\)
−0.468431 + 0.883500i \(0.655180\pi\)
\(464\) −2.25967 −0.104902
\(465\) 0.759862 0.0352377
\(466\) −59.1620 −2.74063
\(467\) −6.00211 −0.277745 −0.138872 0.990310i \(-0.544348\pi\)
−0.138872 + 0.990310i \(0.544348\pi\)
\(468\) −6.67051 −0.308344
\(469\) 13.5579 0.626047
\(470\) 0.0144432 0.000666216 0
\(471\) −8.08169 −0.372384
\(472\) 110.501 5.08623
\(473\) 0.214452 0.00986051
\(474\) −19.3524 −0.888887
\(475\) 11.3063 0.518769
\(476\) 6.29771 0.288655
\(477\) 3.74754 0.171588
\(478\) −21.0914 −0.964699
\(479\) −12.5656 −0.574137 −0.287069 0.957910i \(-0.592681\pi\)
−0.287069 + 0.957910i \(0.592681\pi\)
\(480\) −2.70973 −0.123682
\(481\) −1.07719 −0.0491155
\(482\) −47.2892 −2.15397
\(483\) −7.72937 −0.351699
\(484\) −61.5206 −2.79639
\(485\) −0.348371 −0.0158187
\(486\) −2.75607 −0.125018
\(487\) 2.12392 0.0962441 0.0481221 0.998841i \(-0.484676\pi\)
0.0481221 + 0.998841i \(0.484676\pi\)
\(488\) −66.6291 −3.01616
\(489\) 23.1826 1.04836
\(490\) 1.49487 0.0675313
\(491\) 13.4654 0.607683 0.303842 0.952723i \(-0.401731\pi\)
0.303842 + 0.952723i \(0.401731\pi\)
\(492\) −10.7687 −0.485491
\(493\) −0.109547 −0.00493374
\(494\) −7.44699 −0.335056
\(495\) −0.00867922 −0.000390102 0
\(496\) 111.283 4.99676
\(497\) −3.34968 −0.150254
\(498\) −40.5498 −1.81708
\(499\) 25.7652 1.15341 0.576705 0.816953i \(-0.304338\pi\)
0.576705 + 0.816953i \(0.304338\pi\)
\(500\) −6.15305 −0.275173
\(501\) 6.08845 0.272012
\(502\) −21.0089 −0.937673
\(503\) −18.4764 −0.823820 −0.411910 0.911224i \(-0.635138\pi\)
−0.411910 + 0.911224i \(0.635138\pi\)
\(504\) −14.2699 −0.635631
\(505\) 1.61862 0.0720278
\(506\) −1.16642 −0.0518539
\(507\) −11.5791 −0.514245
\(508\) 81.8075 3.62962
\(509\) −27.5480 −1.22104 −0.610522 0.791999i \(-0.709041\pi\)
−0.610522 + 0.791999i \(0.709041\pi\)
\(510\) −0.237152 −0.0105013
\(511\) 22.2456 0.984088
\(512\) −77.2705 −3.41491
\(513\) −2.26675 −0.100080
\(514\) −59.2268 −2.61238
\(515\) 0.806209 0.0355258
\(516\) −15.2218 −0.670103
\(517\) 0.00375290 0.000165052 0
\(518\) −3.58602 −0.157561
\(519\) 11.1913 0.491242
\(520\) 1.30057 0.0570337
\(521\) −15.0611 −0.659840 −0.329920 0.944009i \(-0.607022\pi\)
−0.329920 + 0.944009i \(0.607022\pi\)
\(522\) 0.386276 0.0169068
\(523\) −29.6345 −1.29583 −0.647914 0.761713i \(-0.724358\pi\)
−0.647914 + 0.761713i \(0.724358\pi\)
\(524\) −0.654980 −0.0286130
\(525\) −7.18178 −0.313439
\(526\) 7.54124 0.328814
\(527\) 5.39491 0.235006
\(528\) −1.27109 −0.0553170
\(529\) 5.81752 0.252936
\(530\) −1.13705 −0.0493904
\(531\) −11.1497 −0.483856
\(532\) −18.2639 −0.791841
\(533\) 2.29391 0.0993601
\(534\) 44.2085 1.91309
\(535\) −2.12002 −0.0916563
\(536\) −93.3215 −4.03087
\(537\) 2.79118 0.120448
\(538\) 70.9276 3.05791
\(539\) 0.388424 0.0167306
\(540\) 0.616051 0.0265106
\(541\) 1.52676 0.0656406 0.0328203 0.999461i \(-0.489551\pi\)
0.0328203 + 0.999461i \(0.489551\pi\)
\(542\) −73.7766 −3.16898
\(543\) 24.8091 1.06466
\(544\) −19.2387 −0.824853
\(545\) 0.230792 0.00988602
\(546\) 4.73034 0.202440
\(547\) −7.58831 −0.324453 −0.162226 0.986754i \(-0.551867\pi\)
−0.162226 + 0.986754i \(0.551867\pi\)
\(548\) 96.5946 4.12632
\(549\) 6.72295 0.286928
\(550\) −1.08379 −0.0462129
\(551\) 0.317695 0.0135343
\(552\) 53.2026 2.26445
\(553\) 10.1102 0.429931
\(554\) 60.1290 2.55464
\(555\) 0.0994830 0.00422282
\(556\) 26.3665 1.11819
\(557\) 15.6551 0.663328 0.331664 0.943398i \(-0.392390\pi\)
0.331664 + 0.943398i \(0.392390\pi\)
\(558\) −19.0231 −0.805313
\(559\) 3.24249 0.137143
\(560\) 2.55563 0.107995
\(561\) −0.0616212 −0.00260165
\(562\) 14.2176 0.599732
\(563\) −6.05473 −0.255177 −0.127588 0.991827i \(-0.540724\pi\)
−0.127588 + 0.991827i \(0.540724\pi\)
\(564\) −0.266381 −0.0112167
\(565\) 1.52924 0.0643358
\(566\) 36.5856 1.53781
\(567\) 1.43985 0.0604678
\(568\) 23.0564 0.967426
\(569\) 9.67767 0.405709 0.202855 0.979209i \(-0.434978\pi\)
0.202855 + 0.979209i \(0.434978\pi\)
\(570\) 0.687763 0.0288072
\(571\) −22.3562 −0.935577 −0.467788 0.883841i \(-0.654949\pi\)
−0.467788 + 0.883841i \(0.654949\pi\)
\(572\) 0.525892 0.0219886
\(573\) 9.31265 0.389042
\(574\) 7.63655 0.318744
\(575\) 26.7759 1.11663
\(576\) 35.5927 1.48303
\(577\) −13.5877 −0.565665 −0.282832 0.959169i \(-0.591274\pi\)
−0.282832 + 0.959169i \(0.591274\pi\)
\(578\) 45.1695 1.87880
\(579\) 5.43914 0.226043
\(580\) −0.0863422 −0.00358517
\(581\) 21.1843 0.878871
\(582\) 8.72147 0.361517
\(583\) −0.295450 −0.0122363
\(584\) −153.120 −6.33616
\(585\) −0.131229 −0.00542564
\(586\) −69.7088 −2.87964
\(587\) −5.20905 −0.215000 −0.107500 0.994205i \(-0.534285\pi\)
−0.107500 + 0.994205i \(0.534285\pi\)
\(588\) −27.5704 −1.13698
\(589\) −15.6457 −0.644671
\(590\) 3.38297 0.139274
\(591\) 13.1030 0.538985
\(592\) 14.5695 0.598802
\(593\) −9.26031 −0.380275 −0.190138 0.981757i \(-0.560893\pi\)
−0.190138 + 0.981757i \(0.560893\pi\)
\(594\) 0.217284 0.00891528
\(595\) 0.123895 0.00507918
\(596\) −80.1993 −3.28509
\(597\) 19.9869 0.818008
\(598\) −17.6362 −0.721197
\(599\) 1.24840 0.0510084 0.0255042 0.999675i \(-0.491881\pi\)
0.0255042 + 0.999675i \(0.491881\pi\)
\(600\) 49.4334 2.01811
\(601\) 4.53374 0.184935 0.0924675 0.995716i \(-0.470525\pi\)
0.0924675 + 0.995716i \(0.470525\pi\)
\(602\) 10.7944 0.439948
\(603\) 9.41624 0.383459
\(604\) −103.577 −4.21450
\(605\) −1.21029 −0.0492054
\(606\) −40.5222 −1.64610
\(607\) 16.1967 0.657403 0.328701 0.944434i \(-0.393389\pi\)
0.328701 + 0.944434i \(0.393389\pi\)
\(608\) 55.7940 2.26274
\(609\) −0.201801 −0.00817737
\(610\) −2.03983 −0.0825903
\(611\) 0.0567434 0.00229559
\(612\) 4.37388 0.176804
\(613\) 2.44721 0.0988417 0.0494209 0.998778i \(-0.484262\pi\)
0.0494209 + 0.998778i \(0.484262\pi\)
\(614\) −24.4536 −0.986869
\(615\) −0.211853 −0.00854272
\(616\) 1.12501 0.0453281
\(617\) −13.6207 −0.548350 −0.274175 0.961680i \(-0.588405\pi\)
−0.274175 + 0.961680i \(0.588405\pi\)
\(618\) −20.1834 −0.811897
\(619\) −11.0613 −0.444590 −0.222295 0.974979i \(-0.571355\pi\)
−0.222295 + 0.974979i \(0.571355\pi\)
\(620\) 4.25214 0.170770
\(621\) −5.36820 −0.215418
\(622\) 34.8997 1.39935
\(623\) −23.0957 −0.925308
\(624\) −19.2187 −0.769363
\(625\) 24.8184 0.992734
\(626\) −10.0565 −0.401937
\(627\) 0.178707 0.00713687
\(628\) −45.2247 −1.80466
\(629\) 0.706315 0.0281626
\(630\) −0.436868 −0.0174052
\(631\) 24.5623 0.977811 0.488906 0.872337i \(-0.337396\pi\)
0.488906 + 0.872337i \(0.337396\pi\)
\(632\) −69.5904 −2.76816
\(633\) 18.8138 0.747780
\(634\) −50.9184 −2.02223
\(635\) 1.60940 0.0638669
\(636\) 20.9710 0.831556
\(637\) 5.87292 0.232694
\(638\) −0.0304533 −0.00120566
\(639\) −2.32642 −0.0920316
\(640\) −5.37982 −0.212656
\(641\) −38.5614 −1.52309 −0.761543 0.648115i \(-0.775558\pi\)
−0.761543 + 0.648115i \(0.775558\pi\)
\(642\) 53.0746 2.09469
\(643\) 33.4818 1.32039 0.660196 0.751094i \(-0.270473\pi\)
0.660196 + 0.751094i \(0.270473\pi\)
\(644\) −43.2532 −1.70441
\(645\) −0.299458 −0.0117912
\(646\) 4.88302 0.192120
\(647\) −26.2525 −1.03209 −0.516046 0.856561i \(-0.672597\pi\)
−0.516046 + 0.856561i \(0.672597\pi\)
\(648\) −9.91070 −0.389329
\(649\) 0.879023 0.0345047
\(650\) −16.3867 −0.642741
\(651\) 9.93818 0.389508
\(652\) 129.729 5.08057
\(653\) 14.1512 0.553781 0.276890 0.960902i \(-0.410696\pi\)
0.276890 + 0.960902i \(0.410696\pi\)
\(654\) −5.77786 −0.225932
\(655\) −0.0128854 −0.000503475 0
\(656\) −31.0262 −1.21137
\(657\) 15.4500 0.602762
\(658\) 0.188902 0.00736417
\(659\) 29.4226 1.14614 0.573072 0.819505i \(-0.305752\pi\)
0.573072 + 0.819505i \(0.305752\pi\)
\(660\) −0.0485685 −0.00189052
\(661\) −30.0095 −1.16724 −0.583618 0.812029i \(-0.698363\pi\)
−0.583618 + 0.812029i \(0.698363\pi\)
\(662\) 88.6619 3.44594
\(663\) −0.931705 −0.0361844
\(664\) −145.815 −5.65871
\(665\) −0.359306 −0.0139333
\(666\) −2.49056 −0.0965071
\(667\) 0.752375 0.0291321
\(668\) 34.0706 1.31823
\(669\) 4.35219 0.168266
\(670\) −2.85701 −0.110376
\(671\) −0.530026 −0.0204614
\(672\) −35.4404 −1.36714
\(673\) 38.7015 1.49183 0.745916 0.666040i \(-0.232012\pi\)
0.745916 + 0.666040i \(0.232012\pi\)
\(674\) 53.3886 2.05645
\(675\) −4.98788 −0.191984
\(676\) −64.7959 −2.49215
\(677\) 17.5453 0.674320 0.337160 0.941447i \(-0.390534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(678\) −38.2846 −1.47031
\(679\) −4.55633 −0.174856
\(680\) −0.852787 −0.0327029
\(681\) −3.16005 −0.121093
\(682\) 1.49975 0.0574284
\(683\) −51.3379 −1.96439 −0.982195 0.187864i \(-0.939844\pi\)
−0.982195 + 0.187864i \(0.939844\pi\)
\(684\) −12.6846 −0.485009
\(685\) 1.90030 0.0726068
\(686\) 47.3296 1.80705
\(687\) 9.94671 0.379491
\(688\) −43.8562 −1.67200
\(689\) −4.46716 −0.170185
\(690\) 1.62878 0.0620066
\(691\) 38.6423 1.47002 0.735010 0.678056i \(-0.237177\pi\)
0.735010 + 0.678056i \(0.237177\pi\)
\(692\) 62.6257 2.38067
\(693\) −0.113515 −0.00431208
\(694\) −9.46868 −0.359426
\(695\) 0.518708 0.0196757
\(696\) 1.38903 0.0526509
\(697\) −1.50412 −0.0569727
\(698\) −47.1039 −1.78291
\(699\) 21.4661 0.811921
\(700\) −40.1888 −1.51900
\(701\) 14.1508 0.534467 0.267233 0.963632i \(-0.413891\pi\)
0.267233 + 0.963632i \(0.413891\pi\)
\(702\) 3.28531 0.123996
\(703\) −2.04838 −0.0772560
\(704\) −2.80607 −0.105758
\(705\) −0.00524050 −0.000197369 0
\(706\) −78.0885 −2.93890
\(707\) 21.1699 0.796175
\(708\) −62.3931 −2.34488
\(709\) −17.2232 −0.646831 −0.323415 0.946257i \(-0.604831\pi\)
−0.323415 + 0.946257i \(0.604831\pi\)
\(710\) 0.705866 0.0264907
\(711\) 7.02174 0.263336
\(712\) 158.971 5.95770
\(713\) −37.0527 −1.38763
\(714\) −3.10170 −0.116078
\(715\) 0.0103458 0.000386913 0
\(716\) 15.6193 0.583720
\(717\) 7.65270 0.285795
\(718\) −26.1857 −0.977240
\(719\) 35.8461 1.33683 0.668417 0.743787i \(-0.266972\pi\)
0.668417 + 0.743787i \(0.266972\pi\)
\(720\) 1.77493 0.0661478
\(721\) 10.5444 0.392692
\(722\) 38.2042 1.42181
\(723\) 17.1582 0.638120
\(724\) 138.830 5.15959
\(725\) 0.699073 0.0259629
\(726\) 30.2997 1.12453
\(727\) 4.64883 0.172415 0.0862077 0.996277i \(-0.472525\pi\)
0.0862077 + 0.996277i \(0.472525\pi\)
\(728\) 17.0100 0.630434
\(729\) 1.00000 0.0370370
\(730\) −4.68773 −0.173501
\(731\) −2.12611 −0.0786370
\(732\) 37.6213 1.39052
\(733\) −12.5447 −0.463349 −0.231674 0.972793i \(-0.574420\pi\)
−0.231674 + 0.972793i \(0.574420\pi\)
\(734\) 62.6935 2.31406
\(735\) −0.542391 −0.0200064
\(736\) 132.133 4.87049
\(737\) −0.742360 −0.0273452
\(738\) 5.30373 0.195233
\(739\) −20.2421 −0.744620 −0.372310 0.928109i \(-0.621434\pi\)
−0.372310 + 0.928109i \(0.621434\pi\)
\(740\) 0.556702 0.0204648
\(741\) 2.70203 0.0992615
\(742\) −14.8715 −0.545948
\(743\) 39.8075 1.46040 0.730198 0.683235i \(-0.239428\pi\)
0.730198 + 0.683235i \(0.239428\pi\)
\(744\) −68.4062 −2.50789
\(745\) −1.57776 −0.0578046
\(746\) −57.5458 −2.10690
\(747\) 14.7129 0.538316
\(748\) −0.344829 −0.0126082
\(749\) −27.7276 −1.01314
\(750\) 3.03045 0.110657
\(751\) 14.8689 0.542573 0.271287 0.962499i \(-0.412551\pi\)
0.271287 + 0.962499i \(0.412551\pi\)
\(752\) −0.767482 −0.0279872
\(753\) 7.62276 0.277789
\(754\) −0.460450 −0.0167686
\(755\) −2.03767 −0.0741585
\(756\) 8.05730 0.293041
\(757\) −22.8113 −0.829092 −0.414546 0.910028i \(-0.636060\pi\)
−0.414546 + 0.910028i \(0.636060\pi\)
\(758\) 73.9180 2.68482
\(759\) 0.423219 0.0153619
\(760\) 2.47316 0.0897109
\(761\) 42.1584 1.52824 0.764121 0.645073i \(-0.223173\pi\)
0.764121 + 0.645073i \(0.223173\pi\)
\(762\) −40.2912 −1.45960
\(763\) 3.01851 0.109277
\(764\) 52.1131 1.88539
\(765\) 0.0860472 0.00311104
\(766\) −75.4610 −2.72652
\(767\) 13.2907 0.479900
\(768\) 63.4984 2.29130
\(769\) 7.39667 0.266731 0.133365 0.991067i \(-0.457422\pi\)
0.133365 + 0.991067i \(0.457422\pi\)
\(770\) 0.0344419 0.00124120
\(771\) 21.4895 0.773927
\(772\) 30.4372 1.09546
\(773\) 5.29348 0.190393 0.0951965 0.995458i \(-0.469652\pi\)
0.0951965 + 0.995458i \(0.469652\pi\)
\(774\) 7.49693 0.269472
\(775\) −34.4276 −1.23668
\(776\) 31.3620 1.12583
\(777\) 1.30113 0.0466779
\(778\) 48.1712 1.72702
\(779\) 4.36209 0.156288
\(780\) −0.734349 −0.0262939
\(781\) 0.183411 0.00656295
\(782\) 11.5641 0.413532
\(783\) −0.140154 −0.00500870
\(784\) −79.4342 −2.83693
\(785\) −0.889704 −0.0317549
\(786\) 0.322586 0.0115063
\(787\) 14.0069 0.499294 0.249647 0.968337i \(-0.419685\pi\)
0.249647 + 0.968337i \(0.419685\pi\)
\(788\) 73.3237 2.61205
\(789\) −2.73623 −0.0974122
\(790\) −2.13049 −0.0757994
\(791\) 20.0009 0.711150
\(792\) 0.781342 0.0277638
\(793\) −8.01392 −0.284583
\(794\) 19.0863 0.677349
\(795\) 0.412563 0.0146321
\(796\) 111.845 3.96425
\(797\) 3.45035 0.122218 0.0611088 0.998131i \(-0.480536\pi\)
0.0611088 + 0.998131i \(0.480536\pi\)
\(798\) 8.99521 0.318427
\(799\) −0.0372068 −0.00131628
\(800\) 122.772 4.34064
\(801\) −16.0404 −0.566759
\(802\) −14.8030 −0.522713
\(803\) −1.21805 −0.0429841
\(804\) 52.6928 1.85833
\(805\) −0.850918 −0.0299909
\(806\) 22.6760 0.798730
\(807\) −25.7350 −0.905916
\(808\) −145.716 −5.12626
\(809\) −15.0161 −0.527937 −0.263969 0.964531i \(-0.585032\pi\)
−0.263969 + 0.964531i \(0.585032\pi\)
\(810\) −0.303413 −0.0106609
\(811\) −52.1260 −1.83039 −0.915195 0.403010i \(-0.867964\pi\)
−0.915195 + 0.403010i \(0.867964\pi\)
\(812\) −1.12926 −0.0396294
\(813\) 26.7687 0.938820
\(814\) 0.196351 0.00688211
\(815\) 2.55215 0.0893979
\(816\) 12.6018 0.441150
\(817\) 6.16591 0.215718
\(818\) 20.3735 0.712344
\(819\) −1.71633 −0.0599735
\(820\) −1.18552 −0.0414000
\(821\) 24.8891 0.868636 0.434318 0.900760i \(-0.356989\pi\)
0.434318 + 0.900760i \(0.356989\pi\)
\(822\) −47.5741 −1.65934
\(823\) 4.90950 0.171134 0.0855671 0.996332i \(-0.472730\pi\)
0.0855671 + 0.996332i \(0.472730\pi\)
\(824\) −72.5786 −2.52839
\(825\) 0.393236 0.0136907
\(826\) 44.2456 1.53950
\(827\) −5.56030 −0.193351 −0.0966753 0.995316i \(-0.530821\pi\)
−0.0966753 + 0.995316i \(0.530821\pi\)
\(828\) −30.0401 −1.04397
\(829\) 2.76310 0.0959665 0.0479833 0.998848i \(-0.484721\pi\)
0.0479833 + 0.998848i \(0.484721\pi\)
\(830\) −4.46408 −0.154950
\(831\) −21.8169 −0.756820
\(832\) −42.4274 −1.47090
\(833\) −3.85090 −0.133426
\(834\) −12.9858 −0.449663
\(835\) 0.670271 0.0231957
\(836\) 1.00004 0.0345869
\(837\) 6.90226 0.238577
\(838\) −48.6935 −1.68209
\(839\) 30.5576 1.05497 0.527483 0.849565i \(-0.323136\pi\)
0.527483 + 0.849565i \(0.323136\pi\)
\(840\) −1.57095 −0.0542031
\(841\) −28.9804 −0.999323
\(842\) 6.37495 0.219695
\(843\) −5.15863 −0.177673
\(844\) 105.281 3.62391
\(845\) −1.27473 −0.0438520
\(846\) 0.131196 0.00451061
\(847\) −15.8294 −0.543903
\(848\) 60.4206 2.07485
\(849\) −13.2745 −0.455581
\(850\) 10.7448 0.368545
\(851\) −4.85103 −0.166291
\(852\) −13.0185 −0.446007
\(853\) −15.7416 −0.538981 −0.269490 0.963003i \(-0.586855\pi\)
−0.269490 + 0.963003i \(0.586855\pi\)
\(854\) −26.6788 −0.912931
\(855\) −0.249544 −0.00853424
\(856\) 190.853 6.52323
\(857\) 15.8132 0.540168 0.270084 0.962837i \(-0.412949\pi\)
0.270084 + 0.962837i \(0.412949\pi\)
\(858\) −0.259008 −0.00884240
\(859\) 19.7235 0.672956 0.336478 0.941691i \(-0.390764\pi\)
0.336478 + 0.941691i \(0.390764\pi\)
\(860\) −1.67575 −0.0571427
\(861\) −2.77081 −0.0944289
\(862\) 30.8161 1.04960
\(863\) 21.0077 0.715110 0.357555 0.933892i \(-0.383610\pi\)
0.357555 + 0.933892i \(0.383610\pi\)
\(864\) −24.6140 −0.837387
\(865\) 1.23203 0.0418904
\(866\) 88.3617 3.00265
\(867\) −16.3891 −0.556602
\(868\) 55.6135 1.88765
\(869\) −0.553582 −0.0187790
\(870\) 0.0425246 0.00144172
\(871\) −11.2244 −0.380324
\(872\) −20.7769 −0.703594
\(873\) −3.16445 −0.107101
\(874\) −33.5370 −1.13440
\(875\) −1.58319 −0.0535216
\(876\) 86.4573 2.92112
\(877\) 55.6593 1.87948 0.939741 0.341887i \(-0.111066\pi\)
0.939741 + 0.341887i \(0.111066\pi\)
\(878\) −75.5604 −2.55004
\(879\) 25.2928 0.853104
\(880\) −0.139933 −0.00471713
\(881\) 42.5623 1.43396 0.716980 0.697094i \(-0.245524\pi\)
0.716980 + 0.697094i \(0.245524\pi\)
\(882\) 13.5787 0.457220
\(883\) 2.58016 0.0868294 0.0434147 0.999057i \(-0.486176\pi\)
0.0434147 + 0.999057i \(0.486176\pi\)
\(884\) −5.21377 −0.175358
\(885\) −1.22746 −0.0412605
\(886\) 56.0347 1.88252
\(887\) −55.0465 −1.84828 −0.924140 0.382054i \(-0.875217\pi\)
−0.924140 + 0.382054i \(0.875217\pi\)
\(888\) −8.95591 −0.300541
\(889\) 21.0492 0.705967
\(890\) 4.86686 0.163138
\(891\) −0.0788383 −0.00264118
\(892\) 24.3546 0.815454
\(893\) 0.107903 0.00361084
\(894\) 39.4992 1.32105
\(895\) 0.307278 0.0102712
\(896\) −70.3624 −2.35064
\(897\) 6.39902 0.213657
\(898\) −73.1357 −2.44057
\(899\) −0.967381 −0.0322639
\(900\) −27.9119 −0.930397
\(901\) 2.92914 0.0975837
\(902\) −0.418137 −0.0139224
\(903\) −3.91660 −0.130336
\(904\) −137.669 −4.57882
\(905\) 2.73121 0.0907884
\(906\) 51.0131 1.69480
\(907\) 37.2310 1.23624 0.618118 0.786085i \(-0.287895\pi\)
0.618118 + 0.786085i \(0.287895\pi\)
\(908\) −17.6834 −0.586846
\(909\) 14.7029 0.487663
\(910\) 0.520758 0.0172630
\(911\) −30.5379 −1.01177 −0.505883 0.862602i \(-0.668833\pi\)
−0.505883 + 0.862602i \(0.668833\pi\)
\(912\) −36.5463 −1.21017
\(913\) −1.15994 −0.0383883
\(914\) 41.5024 1.37278
\(915\) 0.740122 0.0244677
\(916\) 55.6612 1.83910
\(917\) −0.168527 −0.00556527
\(918\) −2.15419 −0.0710989
\(919\) −13.7697 −0.454221 −0.227111 0.973869i \(-0.572928\pi\)
−0.227111 + 0.973869i \(0.572928\pi\)
\(920\) 5.85701 0.193100
\(921\) 8.87263 0.292363
\(922\) 21.9406 0.722576
\(923\) 2.77315 0.0912793
\(924\) −0.635224 −0.0208973
\(925\) −4.50735 −0.148201
\(926\) 55.5593 1.82579
\(927\) 7.32325 0.240527
\(928\) 3.44976 0.113244
\(929\) 11.7525 0.385587 0.192794 0.981239i \(-0.438245\pi\)
0.192794 + 0.981239i \(0.438245\pi\)
\(930\) −2.09424 −0.0686727
\(931\) 11.1679 0.366015
\(932\) 120.123 3.93476
\(933\) −12.6628 −0.414563
\(934\) 16.5423 0.541279
\(935\) −0.00678381 −0.000221854 0
\(936\) 11.8138 0.386146
\(937\) 33.5421 1.09577 0.547887 0.836552i \(-0.315432\pi\)
0.547887 + 0.836552i \(0.315432\pi\)
\(938\) −37.3667 −1.22006
\(939\) 3.64883 0.119075
\(940\) −0.0293256 −0.000956495 0
\(941\) 9.94975 0.324353 0.162176 0.986762i \(-0.448149\pi\)
0.162176 + 0.986762i \(0.448149\pi\)
\(942\) 22.2737 0.725717
\(943\) 10.3304 0.336405
\(944\) −179.764 −5.85080
\(945\) 0.158511 0.00515636
\(946\) −0.591046 −0.0192165
\(947\) 24.5295 0.797102 0.398551 0.917146i \(-0.369513\pi\)
0.398551 + 0.917146i \(0.369513\pi\)
\(948\) 39.2933 1.27619
\(949\) −18.4168 −0.597834
\(950\) −31.1610 −1.01100
\(951\) 18.4750 0.599092
\(952\) −11.1536 −0.361489
\(953\) 41.0257 1.32895 0.664477 0.747309i \(-0.268654\pi\)
0.664477 + 0.747309i \(0.268654\pi\)
\(954\) −10.3285 −0.334398
\(955\) 1.02522 0.0331753
\(956\) 42.8241 1.38503
\(957\) 0.0110495 0.000357180 0
\(958\) 34.6318 1.11890
\(959\) 24.8539 0.802576
\(960\) 3.91836 0.126464
\(961\) 16.6411 0.536811
\(962\) 2.96881 0.0957181
\(963\) −19.2573 −0.620558
\(964\) 96.0163 3.09248
\(965\) 0.598789 0.0192757
\(966\) 21.3027 0.685404
\(967\) 47.5391 1.52875 0.764377 0.644769i \(-0.223047\pi\)
0.764377 + 0.644769i \(0.223047\pi\)
\(968\) 108.956 3.50198
\(969\) −1.77173 −0.0569162
\(970\) 0.960137 0.0308281
\(971\) −7.41369 −0.237917 −0.118958 0.992899i \(-0.537956\pi\)
−0.118958 + 0.992899i \(0.537956\pi\)
\(972\) 5.59595 0.179490
\(973\) 6.78414 0.217490
\(974\) −5.85369 −0.187564
\(975\) 5.94568 0.190414
\(976\) 108.392 3.46955
\(977\) −25.1269 −0.803882 −0.401941 0.915666i \(-0.631664\pi\)
−0.401941 + 0.915666i \(0.631664\pi\)
\(978\) −63.8931 −2.04308
\(979\) 1.26460 0.0404167
\(980\) −3.03519 −0.0969556
\(981\) 2.09641 0.0669333
\(982\) −37.1115 −1.18428
\(983\) 35.6650 1.13754 0.568769 0.822497i \(-0.307420\pi\)
0.568769 + 0.822497i \(0.307420\pi\)
\(984\) 19.0719 0.607991
\(985\) 1.44249 0.0459617
\(986\) 0.301919 0.00961506
\(987\) −0.0685402 −0.00218166
\(988\) 15.1204 0.481044
\(989\) 14.6023 0.464326
\(990\) 0.0239206 0.000760246 0
\(991\) −44.8419 −1.42445 −0.712224 0.701952i \(-0.752312\pi\)
−0.712224 + 0.701952i \(0.752312\pi\)
\(992\) −169.892 −5.39409
\(993\) −32.1696 −1.02087
\(994\) 9.23197 0.292820
\(995\) 2.20033 0.0697552
\(996\) 82.3324 2.60880
\(997\) −17.6539 −0.559105 −0.279552 0.960130i \(-0.590186\pi\)
−0.279552 + 0.960130i \(0.590186\pi\)
\(998\) −71.0109 −2.24781
\(999\) 0.903661 0.0285906
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 \(a_p\))