Properties

Label 6013.2.a.e.1.8
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.42826 q^{2}\) \(+1.22129 q^{3}\) \(+3.89645 q^{4}\) \(+0.497994 q^{5}\) \(-2.96562 q^{6}\) \(+1.00000 q^{7}\) \(-4.60506 q^{8}\) \(-1.50844 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.42826 q^{2}\) \(+1.22129 q^{3}\) \(+3.89645 q^{4}\) \(+0.497994 q^{5}\) \(-2.96562 q^{6}\) \(+1.00000 q^{7}\) \(-4.60506 q^{8}\) \(-1.50844 q^{9}\) \(-1.20926 q^{10}\) \(+5.72858 q^{11}\) \(+4.75871 q^{12}\) \(+2.95920 q^{13}\) \(-2.42826 q^{14}\) \(+0.608198 q^{15}\) \(+3.38940 q^{16}\) \(+1.50561 q^{17}\) \(+3.66288 q^{18}\) \(+0.453906 q^{19}\) \(+1.94041 q^{20}\) \(+1.22129 q^{21}\) \(-13.9105 q^{22}\) \(-9.08650 q^{23}\) \(-5.62414 q^{24}\) \(-4.75200 q^{25}\) \(-7.18571 q^{26}\) \(-5.50613 q^{27}\) \(+3.89645 q^{28}\) \(-6.84747 q^{29}\) \(-1.47686 q^{30}\) \(-9.30788 q^{31}\) \(+0.979791 q^{32}\) \(+6.99629 q^{33}\) \(-3.65601 q^{34}\) \(+0.497994 q^{35}\) \(-5.87755 q^{36}\) \(-0.592839 q^{37}\) \(-1.10220 q^{38}\) \(+3.61406 q^{39}\) \(-2.29329 q^{40}\) \(+7.11679 q^{41}\) \(-2.96562 q^{42}\) \(+7.01760 q^{43}\) \(+22.3211 q^{44}\) \(-0.751194 q^{45}\) \(+22.0644 q^{46}\) \(+0.677883 q^{47}\) \(+4.13945 q^{48}\) \(+1.00000 q^{49}\) \(+11.5391 q^{50}\) \(+1.83879 q^{51}\) \(+11.5304 q^{52}\) \(+8.46859 q^{53}\) \(+13.3703 q^{54}\) \(+2.85280 q^{55}\) \(-4.60506 q^{56}\) \(+0.554353 q^{57}\) \(+16.6274 q^{58}\) \(+5.81461 q^{59}\) \(+2.36981 q^{60}\) \(+10.5067 q^{61}\) \(+22.6019 q^{62}\) \(-1.50844 q^{63}\) \(-9.15798 q^{64}\) \(+1.47367 q^{65}\) \(-16.9888 q^{66}\) \(+4.09625 q^{67}\) \(+5.86652 q^{68}\) \(-11.0973 q^{69}\) \(-1.20926 q^{70}\) \(+1.08498 q^{71}\) \(+6.94645 q^{72}\) \(-0.421009 q^{73}\) \(+1.43957 q^{74}\) \(-5.80360 q^{75}\) \(+1.76862 q^{76}\) \(+5.72858 q^{77}\) \(-8.77587 q^{78}\) \(+12.5214 q^{79}\) \(+1.68790 q^{80}\) \(-2.19930 q^{81}\) \(-17.2814 q^{82}\) \(+6.18770 q^{83}\) \(+4.75871 q^{84}\) \(+0.749784 q^{85}\) \(-17.0406 q^{86}\) \(-8.36278 q^{87}\) \(-26.3805 q^{88}\) \(+5.14054 q^{89}\) \(+1.82409 q^{90}\) \(+2.95920 q^{91}\) \(-35.4051 q^{92}\) \(-11.3677 q^{93}\) \(-1.64608 q^{94}\) \(+0.226042 q^{95}\) \(+1.19661 q^{96}\) \(-0.785892 q^{97}\) \(-2.42826 q^{98}\) \(-8.64122 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42826 −1.71704 −0.858519 0.512781i \(-0.828615\pi\)
−0.858519 + 0.512781i \(0.828615\pi\)
\(3\) 1.22129 0.705115 0.352557 0.935790i \(-0.385312\pi\)
0.352557 + 0.935790i \(0.385312\pi\)
\(4\) 3.89645 1.94822
\(5\) 0.497994 0.222710 0.111355 0.993781i \(-0.464481\pi\)
0.111355 + 0.993781i \(0.464481\pi\)
\(6\) −2.96562 −1.21071
\(7\) 1.00000 0.377964
\(8\) −4.60506 −1.62814
\(9\) −1.50844 −0.502813
\(10\) −1.20926 −0.382401
\(11\) 5.72858 1.72723 0.863617 0.504149i \(-0.168194\pi\)
0.863617 + 0.504149i \(0.168194\pi\)
\(12\) 4.75871 1.37372
\(13\) 2.95920 0.820735 0.410367 0.911920i \(-0.365400\pi\)
0.410367 + 0.911920i \(0.365400\pi\)
\(14\) −2.42826 −0.648980
\(15\) 0.608198 0.157036
\(16\) 3.38940 0.847349
\(17\) 1.50561 0.365164 0.182582 0.983191i \(-0.441555\pi\)
0.182582 + 0.983191i \(0.441555\pi\)
\(18\) 3.66288 0.863349
\(19\) 0.453906 0.104133 0.0520666 0.998644i \(-0.483419\pi\)
0.0520666 + 0.998644i \(0.483419\pi\)
\(20\) 1.94041 0.433888
\(21\) 1.22129 0.266508
\(22\) −13.9105 −2.96573
\(23\) −9.08650 −1.89467 −0.947333 0.320249i \(-0.896233\pi\)
−0.947333 + 0.320249i \(0.896233\pi\)
\(24\) −5.62414 −1.14802
\(25\) −4.75200 −0.950400
\(26\) −7.18571 −1.40923
\(27\) −5.50613 −1.05966
\(28\) 3.89645 0.736359
\(29\) −6.84747 −1.27154 −0.635772 0.771877i \(-0.719318\pi\)
−0.635772 + 0.771877i \(0.719318\pi\)
\(30\) −1.47686 −0.269637
\(31\) −9.30788 −1.67174 −0.835872 0.548924i \(-0.815037\pi\)
−0.835872 + 0.548924i \(0.815037\pi\)
\(32\) 0.979791 0.173204
\(33\) 6.99629 1.21790
\(34\) −3.65601 −0.627000
\(35\) 0.497994 0.0841764
\(36\) −5.87755 −0.979592
\(37\) −0.592839 −0.0974621 −0.0487311 0.998812i \(-0.515518\pi\)
−0.0487311 + 0.998812i \(0.515518\pi\)
\(38\) −1.10220 −0.178801
\(39\) 3.61406 0.578712
\(40\) −2.29329 −0.362602
\(41\) 7.11679 1.11146 0.555728 0.831364i \(-0.312440\pi\)
0.555728 + 0.831364i \(0.312440\pi\)
\(42\) −2.96562 −0.457605
\(43\) 7.01760 1.07017 0.535087 0.844797i \(-0.320279\pi\)
0.535087 + 0.844797i \(0.320279\pi\)
\(44\) 22.3211 3.36504
\(45\) −0.751194 −0.111981
\(46\) 22.0644 3.25322
\(47\) 0.677883 0.0988794 0.0494397 0.998777i \(-0.484256\pi\)
0.0494397 + 0.998777i \(0.484256\pi\)
\(48\) 4.13945 0.597478
\(49\) 1.00000 0.142857
\(50\) 11.5391 1.63187
\(51\) 1.83879 0.257482
\(52\) 11.5304 1.59897
\(53\) 8.46859 1.16325 0.581625 0.813457i \(-0.302417\pi\)
0.581625 + 0.813457i \(0.302417\pi\)
\(54\) 13.3703 1.81947
\(55\) 2.85280 0.384672
\(56\) −4.60506 −0.615377
\(57\) 0.554353 0.0734258
\(58\) 16.6274 2.18329
\(59\) 5.81461 0.756998 0.378499 0.925602i \(-0.376440\pi\)
0.378499 + 0.925602i \(0.376440\pi\)
\(60\) 2.36981 0.305941
\(61\) 10.5067 1.34525 0.672623 0.739985i \(-0.265168\pi\)
0.672623 + 0.739985i \(0.265168\pi\)
\(62\) 22.6019 2.87045
\(63\) −1.50844 −0.190045
\(64\) −9.15798 −1.14475
\(65\) 1.47367 0.182786
\(66\) −16.9888 −2.09118
\(67\) 4.09625 0.500436 0.250218 0.968189i \(-0.419498\pi\)
0.250218 + 0.968189i \(0.419498\pi\)
\(68\) 5.86652 0.711420
\(69\) −11.0973 −1.33596
\(70\) −1.20926 −0.144534
\(71\) 1.08498 0.128764 0.0643818 0.997925i \(-0.479492\pi\)
0.0643818 + 0.997925i \(0.479492\pi\)
\(72\) 6.94645 0.818648
\(73\) −0.421009 −0.0492754 −0.0246377 0.999696i \(-0.507843\pi\)
−0.0246377 + 0.999696i \(0.507843\pi\)
\(74\) 1.43957 0.167346
\(75\) −5.80360 −0.670141
\(76\) 1.76862 0.202875
\(77\) 5.72858 0.652833
\(78\) −8.77587 −0.993672
\(79\) 12.5214 1.40877 0.704384 0.709819i \(-0.251223\pi\)
0.704384 + 0.709819i \(0.251223\pi\)
\(80\) 1.68790 0.188713
\(81\) −2.19930 −0.244366
\(82\) −17.2814 −1.90841
\(83\) 6.18770 0.679189 0.339594 0.940572i \(-0.389710\pi\)
0.339594 + 0.940572i \(0.389710\pi\)
\(84\) 4.75871 0.519218
\(85\) 0.749784 0.0813255
\(86\) −17.0406 −1.83753
\(87\) −8.36278 −0.896584
\(88\) −26.3805 −2.81217
\(89\) 5.14054 0.544896 0.272448 0.962171i \(-0.412167\pi\)
0.272448 + 0.962171i \(0.412167\pi\)
\(90\) 1.82409 0.192276
\(91\) 2.95920 0.310209
\(92\) −35.4051 −3.69123
\(93\) −11.3677 −1.17877
\(94\) −1.64608 −0.169780
\(95\) 0.226042 0.0231915
\(96\) 1.19661 0.122129
\(97\) −0.785892 −0.0797953 −0.0398976 0.999204i \(-0.512703\pi\)
−0.0398976 + 0.999204i \(0.512703\pi\)
\(98\) −2.42826 −0.245291
\(99\) −8.64122 −0.868475
\(100\) −18.5159 −1.85159
\(101\) 5.23248 0.520651 0.260326 0.965521i \(-0.416170\pi\)
0.260326 + 0.965521i \(0.416170\pi\)
\(102\) −4.46507 −0.442107
\(103\) 11.0801 1.09176 0.545878 0.837865i \(-0.316196\pi\)
0.545878 + 0.837865i \(0.316196\pi\)
\(104\) −13.6273 −1.33627
\(105\) 0.608198 0.0593540
\(106\) −20.5639 −1.99735
\(107\) 8.55909 0.827438 0.413719 0.910405i \(-0.364230\pi\)
0.413719 + 0.910405i \(0.364230\pi\)
\(108\) −21.4543 −2.06445
\(109\) −12.9658 −1.24190 −0.620948 0.783852i \(-0.713252\pi\)
−0.620948 + 0.783852i \(0.713252\pi\)
\(110\) −6.92734 −0.660496
\(111\) −0.724031 −0.0687220
\(112\) 3.38940 0.320268
\(113\) 2.83237 0.266447 0.133223 0.991086i \(-0.457467\pi\)
0.133223 + 0.991086i \(0.457467\pi\)
\(114\) −1.34611 −0.126075
\(115\) −4.52502 −0.421961
\(116\) −26.6808 −2.47725
\(117\) −4.46378 −0.412676
\(118\) −14.1194 −1.29979
\(119\) 1.50561 0.138019
\(120\) −2.80079 −0.255676
\(121\) 21.8167 1.98333
\(122\) −25.5130 −2.30984
\(123\) 8.69170 0.783704
\(124\) −36.2676 −3.25693
\(125\) −4.85644 −0.434373
\(126\) 3.66288 0.326315
\(127\) 1.60419 0.142349 0.0711744 0.997464i \(-0.477325\pi\)
0.0711744 + 0.997464i \(0.477325\pi\)
\(128\) 20.2784 1.79237
\(129\) 8.57056 0.754596
\(130\) −3.57844 −0.313850
\(131\) 19.9904 1.74657 0.873286 0.487208i \(-0.161984\pi\)
0.873286 + 0.487208i \(0.161984\pi\)
\(132\) 27.2607 2.37274
\(133\) 0.453906 0.0393586
\(134\) −9.94675 −0.859269
\(135\) −2.74202 −0.235996
\(136\) −6.93342 −0.594536
\(137\) 1.40084 0.119682 0.0598410 0.998208i \(-0.480941\pi\)
0.0598410 + 0.998208i \(0.480941\pi\)
\(138\) 26.9471 2.29389
\(139\) 6.34754 0.538391 0.269196 0.963086i \(-0.413242\pi\)
0.269196 + 0.963086i \(0.413242\pi\)
\(140\) 1.94041 0.163994
\(141\) 0.827895 0.0697213
\(142\) −2.63462 −0.221092
\(143\) 16.9520 1.41760
\(144\) −5.11270 −0.426058
\(145\) −3.41000 −0.283185
\(146\) 1.02232 0.0846078
\(147\) 1.22129 0.100731
\(148\) −2.30996 −0.189878
\(149\) 13.8220 1.13234 0.566172 0.824287i \(-0.308424\pi\)
0.566172 + 0.824287i \(0.308424\pi\)
\(150\) 14.0926 1.15066
\(151\) 18.4438 1.50094 0.750469 0.660905i \(-0.229828\pi\)
0.750469 + 0.660905i \(0.229828\pi\)
\(152\) −2.09026 −0.169543
\(153\) −2.27112 −0.183609
\(154\) −13.9105 −1.12094
\(155\) −4.63527 −0.372314
\(156\) 14.0820 1.12746
\(157\) −7.01663 −0.559988 −0.279994 0.960002i \(-0.590332\pi\)
−0.279994 + 0.960002i \(0.590332\pi\)
\(158\) −30.4052 −2.41891
\(159\) 10.3426 0.820225
\(160\) 0.487930 0.0385742
\(161\) −9.08650 −0.716117
\(162\) 5.34046 0.419586
\(163\) −1.75761 −0.137667 −0.0688335 0.997628i \(-0.521928\pi\)
−0.0688335 + 0.997628i \(0.521928\pi\)
\(164\) 27.7302 2.16536
\(165\) 3.48411 0.271238
\(166\) −15.0254 −1.16619
\(167\) −24.1621 −1.86972 −0.934860 0.355016i \(-0.884476\pi\)
−0.934860 + 0.355016i \(0.884476\pi\)
\(168\) −5.62414 −0.433912
\(169\) −4.24312 −0.326394
\(170\) −1.82067 −0.139639
\(171\) −0.684689 −0.0523595
\(172\) 27.3437 2.08494
\(173\) 3.45063 0.262347 0.131173 0.991359i \(-0.458126\pi\)
0.131173 + 0.991359i \(0.458126\pi\)
\(174\) 20.3070 1.53947
\(175\) −4.75200 −0.359218
\(176\) 19.4164 1.46357
\(177\) 7.10135 0.533770
\(178\) −12.4826 −0.935607
\(179\) 21.3532 1.59601 0.798006 0.602649i \(-0.205888\pi\)
0.798006 + 0.602649i \(0.205888\pi\)
\(180\) −2.92698 −0.218165
\(181\) −15.1260 −1.12431 −0.562153 0.827033i \(-0.690027\pi\)
−0.562153 + 0.827033i \(0.690027\pi\)
\(182\) −7.18571 −0.532640
\(183\) 12.8318 0.948553
\(184\) 41.8439 3.08477
\(185\) −0.295230 −0.0217058
\(186\) 27.6036 2.02400
\(187\) 8.62501 0.630723
\(188\) 2.64133 0.192639
\(189\) −5.50613 −0.400512
\(190\) −0.548890 −0.0398207
\(191\) −5.02385 −0.363513 −0.181756 0.983344i \(-0.558178\pi\)
−0.181756 + 0.983344i \(0.558178\pi\)
\(192\) −11.1846 −0.807178
\(193\) 13.3870 0.963617 0.481808 0.876277i \(-0.339980\pi\)
0.481808 + 0.876277i \(0.339980\pi\)
\(194\) 1.90835 0.137012
\(195\) 1.79978 0.128885
\(196\) 3.89645 0.278318
\(197\) 21.6643 1.54352 0.771760 0.635914i \(-0.219377\pi\)
0.771760 + 0.635914i \(0.219377\pi\)
\(198\) 20.9831 1.49121
\(199\) 1.11340 0.0789265 0.0394633 0.999221i \(-0.487435\pi\)
0.0394633 + 0.999221i \(0.487435\pi\)
\(200\) 21.8833 1.54738
\(201\) 5.00273 0.352865
\(202\) −12.7058 −0.893979
\(203\) −6.84747 −0.480598
\(204\) 7.16475 0.501633
\(205\) 3.54412 0.247532
\(206\) −26.9054 −1.87459
\(207\) 13.7064 0.952663
\(208\) 10.0299 0.695449
\(209\) 2.60024 0.179862
\(210\) −1.47686 −0.101913
\(211\) −8.03533 −0.553175 −0.276587 0.960989i \(-0.589204\pi\)
−0.276587 + 0.960989i \(0.589204\pi\)
\(212\) 32.9974 2.26627
\(213\) 1.32508 0.0907931
\(214\) −20.7837 −1.42074
\(215\) 3.49472 0.238338
\(216\) 25.3561 1.72526
\(217\) −9.30788 −0.631860
\(218\) 31.4843 2.13238
\(219\) −0.514176 −0.0347448
\(220\) 11.1158 0.749426
\(221\) 4.45540 0.299703
\(222\) 1.75814 0.117998
\(223\) −24.6009 −1.64740 −0.823700 0.567026i \(-0.808094\pi\)
−0.823700 + 0.567026i \(0.808094\pi\)
\(224\) 0.979791 0.0654650
\(225\) 7.16810 0.477874
\(226\) −6.87773 −0.457500
\(227\) 4.00728 0.265973 0.132986 0.991118i \(-0.457543\pi\)
0.132986 + 0.991118i \(0.457543\pi\)
\(228\) 2.16001 0.143050
\(229\) −25.8729 −1.70973 −0.854864 0.518852i \(-0.826360\pi\)
−0.854864 + 0.518852i \(0.826360\pi\)
\(230\) 10.9879 0.724523
\(231\) 6.99629 0.460322
\(232\) 31.5330 2.07025
\(233\) 11.9375 0.782051 0.391026 0.920380i \(-0.372120\pi\)
0.391026 + 0.920380i \(0.372120\pi\)
\(234\) 10.8392 0.708581
\(235\) 0.337582 0.0220214
\(236\) 22.6563 1.47480
\(237\) 15.2923 0.993344
\(238\) −3.65601 −0.236984
\(239\) −24.3860 −1.57740 −0.788699 0.614779i \(-0.789245\pi\)
−0.788699 + 0.614779i \(0.789245\pi\)
\(240\) 2.06142 0.133064
\(241\) −4.25621 −0.274167 −0.137083 0.990560i \(-0.543773\pi\)
−0.137083 + 0.990560i \(0.543773\pi\)
\(242\) −52.9766 −3.40546
\(243\) 13.8324 0.887350
\(244\) 40.9388 2.62084
\(245\) 0.497994 0.0318157
\(246\) −21.1057 −1.34565
\(247\) 1.34320 0.0854657
\(248\) 42.8634 2.72183
\(249\) 7.55701 0.478906
\(250\) 11.7927 0.745836
\(251\) 11.4512 0.722794 0.361397 0.932412i \(-0.382300\pi\)
0.361397 + 0.932412i \(0.382300\pi\)
\(252\) −5.87755 −0.370251
\(253\) −52.0528 −3.27253
\(254\) −3.89539 −0.244418
\(255\) 0.915708 0.0573438
\(256\) −30.9252 −1.93282
\(257\) −13.3111 −0.830323 −0.415161 0.909748i \(-0.636275\pi\)
−0.415161 + 0.909748i \(0.636275\pi\)
\(258\) −20.8115 −1.29567
\(259\) −0.592839 −0.0368372
\(260\) 5.74206 0.356107
\(261\) 10.3290 0.639349
\(262\) −48.5420 −2.99893
\(263\) 12.5084 0.771302 0.385651 0.922645i \(-0.373977\pi\)
0.385651 + 0.922645i \(0.373977\pi\)
\(264\) −32.2184 −1.98290
\(265\) 4.21731 0.259067
\(266\) −1.10220 −0.0675803
\(267\) 6.27811 0.384214
\(268\) 15.9608 0.974961
\(269\) 16.0722 0.979942 0.489971 0.871739i \(-0.337007\pi\)
0.489971 + 0.871739i \(0.337007\pi\)
\(270\) 6.65834 0.405214
\(271\) 4.42434 0.268760 0.134380 0.990930i \(-0.457096\pi\)
0.134380 + 0.990930i \(0.457096\pi\)
\(272\) 5.10310 0.309421
\(273\) 3.61406 0.218733
\(274\) −3.40161 −0.205499
\(275\) −27.2222 −1.64156
\(276\) −43.2400 −2.60274
\(277\) 14.9616 0.898953 0.449477 0.893292i \(-0.351610\pi\)
0.449477 + 0.893292i \(0.351610\pi\)
\(278\) −15.4135 −0.924439
\(279\) 14.0404 0.840575
\(280\) −2.29329 −0.137051
\(281\) 13.3177 0.794469 0.397235 0.917717i \(-0.369970\pi\)
0.397235 + 0.917717i \(0.369970\pi\)
\(282\) −2.01034 −0.119714
\(283\) 15.4002 0.915446 0.457723 0.889095i \(-0.348665\pi\)
0.457723 + 0.889095i \(0.348665\pi\)
\(284\) 4.22757 0.250860
\(285\) 0.276064 0.0163526
\(286\) −41.1640 −2.43408
\(287\) 7.11679 0.420091
\(288\) −1.47795 −0.0870893
\(289\) −14.7331 −0.866655
\(290\) 8.28037 0.486240
\(291\) −0.959806 −0.0562648
\(292\) −1.64044 −0.0959994
\(293\) 1.99236 0.116395 0.0581974 0.998305i \(-0.481465\pi\)
0.0581974 + 0.998305i \(0.481465\pi\)
\(294\) −2.96562 −0.172959
\(295\) 2.89564 0.168591
\(296\) 2.73006 0.158681
\(297\) −31.5424 −1.83027
\(298\) −33.5635 −1.94428
\(299\) −26.8888 −1.55502
\(300\) −22.6134 −1.30558
\(301\) 7.01760 0.404488
\(302\) −44.7864 −2.57717
\(303\) 6.39040 0.367119
\(304\) 1.53847 0.0882371
\(305\) 5.23228 0.299599
\(306\) 5.51487 0.315264
\(307\) −18.9846 −1.08351 −0.541754 0.840537i \(-0.682240\pi\)
−0.541754 + 0.840537i \(0.682240\pi\)
\(308\) 22.3211 1.27186
\(309\) 13.5321 0.769814
\(310\) 11.2556 0.639277
\(311\) −8.81388 −0.499789 −0.249895 0.968273i \(-0.580396\pi\)
−0.249895 + 0.968273i \(0.580396\pi\)
\(312\) −16.6430 −0.942222
\(313\) 23.4909 1.32779 0.663893 0.747828i \(-0.268903\pi\)
0.663893 + 0.747828i \(0.268903\pi\)
\(314\) 17.0382 0.961521
\(315\) −0.751194 −0.0423250
\(316\) 48.7890 2.74460
\(317\) 27.8797 1.56588 0.782939 0.622099i \(-0.213720\pi\)
0.782939 + 0.622099i \(0.213720\pi\)
\(318\) −25.1146 −1.40836
\(319\) −39.2263 −2.19625
\(320\) −4.56062 −0.254946
\(321\) 10.4532 0.583439
\(322\) 22.0644 1.22960
\(323\) 0.683405 0.0380257
\(324\) −8.56943 −0.476080
\(325\) −14.0621 −0.780027
\(326\) 4.26794 0.236379
\(327\) −15.8350 −0.875679
\(328\) −32.7732 −1.80960
\(329\) 0.677883 0.0373729
\(330\) −8.46033 −0.465726
\(331\) 16.3479 0.898564 0.449282 0.893390i \(-0.351680\pi\)
0.449282 + 0.893390i \(0.351680\pi\)
\(332\) 24.1100 1.32321
\(333\) 0.894261 0.0490052
\(334\) 58.6719 3.21038
\(335\) 2.03991 0.111452
\(336\) 4.13945 0.225826
\(337\) −9.00955 −0.490781 −0.245391 0.969424i \(-0.578916\pi\)
−0.245391 + 0.969424i \(0.578916\pi\)
\(338\) 10.3034 0.560431
\(339\) 3.45916 0.187876
\(340\) 2.92149 0.158440
\(341\) −53.3210 −2.88749
\(342\) 1.66260 0.0899033
\(343\) 1.00000 0.0539949
\(344\) −32.3165 −1.74239
\(345\) −5.52639 −0.297531
\(346\) −8.37903 −0.450459
\(347\) 12.1487 0.652175 0.326088 0.945340i \(-0.394270\pi\)
0.326088 + 0.945340i \(0.394270\pi\)
\(348\) −32.5851 −1.74675
\(349\) 6.44363 0.344920 0.172460 0.985017i \(-0.444828\pi\)
0.172460 + 0.985017i \(0.444828\pi\)
\(350\) 11.5391 0.616791
\(351\) −16.2938 −0.869697
\(352\) 5.61281 0.299164
\(353\) 17.9270 0.954159 0.477080 0.878860i \(-0.341695\pi\)
0.477080 + 0.878860i \(0.341695\pi\)
\(354\) −17.2439 −0.916505
\(355\) 0.540314 0.0286769
\(356\) 20.0298 1.06158
\(357\) 1.83879 0.0973192
\(358\) −51.8511 −2.74041
\(359\) 10.0103 0.528324 0.264162 0.964478i \(-0.414905\pi\)
0.264162 + 0.964478i \(0.414905\pi\)
\(360\) 3.45929 0.182321
\(361\) −18.7940 −0.989156
\(362\) 36.7298 1.93048
\(363\) 26.6446 1.39848
\(364\) 11.5304 0.604356
\(365\) −0.209660 −0.0109741
\(366\) −31.1589 −1.62870
\(367\) 0.955655 0.0498848 0.0249424 0.999689i \(-0.492060\pi\)
0.0249424 + 0.999689i \(0.492060\pi\)
\(368\) −30.7978 −1.60544
\(369\) −10.7352 −0.558854
\(370\) 0.716896 0.0372696
\(371\) 8.46859 0.439667
\(372\) −44.2935 −2.29651
\(373\) 17.1497 0.887976 0.443988 0.896033i \(-0.353563\pi\)
0.443988 + 0.896033i \(0.353563\pi\)
\(374\) −20.9438 −1.08298
\(375\) −5.93114 −0.306283
\(376\) −3.12169 −0.160989
\(377\) −20.2631 −1.04360
\(378\) 13.3703 0.687695
\(379\) −7.78203 −0.399736 −0.199868 0.979823i \(-0.564051\pi\)
−0.199868 + 0.979823i \(0.564051\pi\)
\(380\) 0.880762 0.0451821
\(381\) 1.95919 0.100372
\(382\) 12.1992 0.624166
\(383\) 20.8734 1.06658 0.533291 0.845932i \(-0.320955\pi\)
0.533291 + 0.845932i \(0.320955\pi\)
\(384\) 24.7659 1.26383
\(385\) 2.85280 0.145392
\(386\) −32.5071 −1.65457
\(387\) −10.5856 −0.538097
\(388\) −3.06219 −0.155459
\(389\) −36.0888 −1.82978 −0.914888 0.403709i \(-0.867721\pi\)
−0.914888 + 0.403709i \(0.867721\pi\)
\(390\) −4.37033 −0.221300
\(391\) −13.6807 −0.691864
\(392\) −4.60506 −0.232591
\(393\) 24.4142 1.23153
\(394\) −52.6066 −2.65028
\(395\) 6.23559 0.313747
\(396\) −33.6700 −1.69198
\(397\) 0.765571 0.0384229 0.0192115 0.999815i \(-0.493884\pi\)
0.0192115 + 0.999815i \(0.493884\pi\)
\(398\) −2.70361 −0.135520
\(399\) 0.554353 0.0277524
\(400\) −16.1064 −0.805321
\(401\) 21.9290 1.09508 0.547541 0.836779i \(-0.315564\pi\)
0.547541 + 0.836779i \(0.315564\pi\)
\(402\) −12.1479 −0.605883
\(403\) −27.5439 −1.37206
\(404\) 20.3881 1.01435
\(405\) −1.09524 −0.0544227
\(406\) 16.6274 0.825206
\(407\) −3.39613 −0.168340
\(408\) −8.46775 −0.419216
\(409\) 23.3261 1.15340 0.576701 0.816955i \(-0.304340\pi\)
0.576701 + 0.816955i \(0.304340\pi\)
\(410\) −8.60604 −0.425022
\(411\) 1.71084 0.0843896
\(412\) 43.1731 2.12698
\(413\) 5.81461 0.286118
\(414\) −33.2828 −1.63576
\(415\) 3.08144 0.151262
\(416\) 2.89940 0.142155
\(417\) 7.75222 0.379628
\(418\) −6.31405 −0.308831
\(419\) −27.1176 −1.32478 −0.662391 0.749158i \(-0.730458\pi\)
−0.662391 + 0.749158i \(0.730458\pi\)
\(420\) 2.36981 0.115635
\(421\) −10.9812 −0.535191 −0.267595 0.963531i \(-0.586229\pi\)
−0.267595 + 0.963531i \(0.586229\pi\)
\(422\) 19.5119 0.949823
\(423\) −1.02255 −0.0497178
\(424\) −38.9984 −1.89393
\(425\) −7.15466 −0.347052
\(426\) −3.21764 −0.155895
\(427\) 10.5067 0.508455
\(428\) 33.3500 1.61203
\(429\) 20.7034 0.999571
\(430\) −8.48610 −0.409236
\(431\) −17.9019 −0.862303 −0.431151 0.902280i \(-0.641892\pi\)
−0.431151 + 0.902280i \(0.641892\pi\)
\(432\) −18.6625 −0.897898
\(433\) −14.1833 −0.681607 −0.340804 0.940134i \(-0.610699\pi\)
−0.340804 + 0.940134i \(0.610699\pi\)
\(434\) 22.6019 1.08493
\(435\) −4.16462 −0.199678
\(436\) −50.5204 −2.41949
\(437\) −4.12442 −0.197298
\(438\) 1.24855 0.0596582
\(439\) −1.11313 −0.0531268 −0.0265634 0.999647i \(-0.508456\pi\)
−0.0265634 + 0.999647i \(0.508456\pi\)
\(440\) −13.1373 −0.626297
\(441\) −1.50844 −0.0718304
\(442\) −10.8189 −0.514601
\(443\) −21.4015 −1.01682 −0.508408 0.861117i \(-0.669766\pi\)
−0.508408 + 0.861117i \(0.669766\pi\)
\(444\) −2.82115 −0.133886
\(445\) 2.55996 0.121354
\(446\) 59.7375 2.82865
\(447\) 16.8808 0.798433
\(448\) −9.15798 −0.432674
\(449\) 39.2862 1.85403 0.927015 0.375023i \(-0.122365\pi\)
0.927015 + 0.375023i \(0.122365\pi\)
\(450\) −17.4060 −0.820528
\(451\) 40.7691 1.91974
\(452\) 11.0362 0.519098
\(453\) 22.5254 1.05833
\(454\) −9.73072 −0.456686
\(455\) 1.47367 0.0690865
\(456\) −2.55283 −0.119547
\(457\) 0.0274673 0.00128487 0.000642434 1.00000i \(-0.499796\pi\)
0.000642434 1.00000i \(0.499796\pi\)
\(458\) 62.8261 2.93567
\(459\) −8.29008 −0.386948
\(460\) −17.6315 −0.822073
\(461\) 38.5321 1.79462 0.897309 0.441404i \(-0.145519\pi\)
0.897309 + 0.441404i \(0.145519\pi\)
\(462\) −16.9888 −0.790391
\(463\) 11.6865 0.543118 0.271559 0.962422i \(-0.412461\pi\)
0.271559 + 0.962422i \(0.412461\pi\)
\(464\) −23.2088 −1.07744
\(465\) −5.66103 −0.262524
\(466\) −28.9873 −1.34281
\(467\) 36.3296 1.68113 0.840567 0.541708i \(-0.182222\pi\)
0.840567 + 0.541708i \(0.182222\pi\)
\(468\) −17.3929 −0.803985
\(469\) 4.09625 0.189147
\(470\) −0.819736 −0.0378116
\(471\) −8.56937 −0.394856
\(472\) −26.7766 −1.23249
\(473\) 40.2009 1.84844
\(474\) −37.1338 −1.70561
\(475\) −2.15696 −0.0989682
\(476\) 5.86652 0.268892
\(477\) −12.7744 −0.584897
\(478\) 59.2155 2.70846
\(479\) −28.1663 −1.28695 −0.643477 0.765466i \(-0.722509\pi\)
−0.643477 + 0.765466i \(0.722509\pi\)
\(480\) 0.595906 0.0271993
\(481\) −1.75433 −0.0799906
\(482\) 10.3352 0.470755
\(483\) −11.0973 −0.504945
\(484\) 85.0075 3.86398
\(485\) −0.391370 −0.0177712
\(486\) −33.5887 −1.52361
\(487\) −23.1106 −1.04724 −0.523622 0.851951i \(-0.675419\pi\)
−0.523622 + 0.851951i \(0.675419\pi\)
\(488\) −48.3841 −2.19024
\(489\) −2.14656 −0.0970710
\(490\) −1.20926 −0.0546288
\(491\) −25.9439 −1.17083 −0.585416 0.810733i \(-0.699069\pi\)
−0.585416 + 0.810733i \(0.699069\pi\)
\(492\) 33.8667 1.52683
\(493\) −10.3096 −0.464322
\(494\) −3.26164 −0.146748
\(495\) −4.30328 −0.193418
\(496\) −31.5481 −1.41655
\(497\) 1.08498 0.0486681
\(498\) −18.3504 −0.822300
\(499\) −5.75131 −0.257464 −0.128732 0.991679i \(-0.541091\pi\)
−0.128732 + 0.991679i \(0.541091\pi\)
\(500\) −18.9228 −0.846256
\(501\) −29.5091 −1.31837
\(502\) −27.8065 −1.24107
\(503\) −19.1445 −0.853610 −0.426805 0.904344i \(-0.640361\pi\)
−0.426805 + 0.904344i \(0.640361\pi\)
\(504\) 6.94645 0.309420
\(505\) 2.60575 0.115954
\(506\) 126.398 5.61906
\(507\) −5.18211 −0.230145
\(508\) 6.25064 0.277327
\(509\) −34.0436 −1.50896 −0.754478 0.656326i \(-0.772110\pi\)
−0.754478 + 0.656326i \(0.772110\pi\)
\(510\) −2.22358 −0.0984616
\(511\) −0.421009 −0.0186243
\(512\) 34.5377 1.52636
\(513\) −2.49927 −0.110345
\(514\) 32.3228 1.42570
\(515\) 5.51783 0.243145
\(516\) 33.3947 1.47012
\(517\) 3.88331 0.170788
\(518\) 1.43957 0.0632509
\(519\) 4.21424 0.184985
\(520\) −6.78632 −0.297600
\(521\) −12.6055 −0.552255 −0.276128 0.961121i \(-0.589051\pi\)
−0.276128 + 0.961121i \(0.589051\pi\)
\(522\) −25.0815 −1.09779
\(523\) −29.5711 −1.29306 −0.646528 0.762890i \(-0.723780\pi\)
−0.646528 + 0.762890i \(0.723780\pi\)
\(524\) 77.8916 3.40271
\(525\) −5.80360 −0.253290
\(526\) −30.3737 −1.32436
\(527\) −14.0140 −0.610460
\(528\) 23.7132 1.03198
\(529\) 59.5645 2.58976
\(530\) −10.2407 −0.444828
\(531\) −8.77099 −0.380628
\(532\) 1.76862 0.0766794
\(533\) 21.0600 0.912210
\(534\) −15.2449 −0.659711
\(535\) 4.26237 0.184278
\(536\) −18.8635 −0.814778
\(537\) 26.0785 1.12537
\(538\) −39.0276 −1.68260
\(539\) 5.72858 0.246748
\(540\) −10.6841 −0.459772
\(541\) −15.3463 −0.659790 −0.329895 0.944018i \(-0.607013\pi\)
−0.329895 + 0.944018i \(0.607013\pi\)
\(542\) −10.7435 −0.461471
\(543\) −18.4733 −0.792765
\(544\) 1.47518 0.0632479
\(545\) −6.45688 −0.276582
\(546\) −8.77587 −0.375573
\(547\) 3.68155 0.157412 0.0787059 0.996898i \(-0.474921\pi\)
0.0787059 + 0.996898i \(0.474921\pi\)
\(548\) 5.45831 0.233167
\(549\) −15.8487 −0.676407
\(550\) 66.1027 2.81863
\(551\) −3.10811 −0.132410
\(552\) 51.1037 2.17512
\(553\) 12.5214 0.532465
\(554\) −36.3306 −1.54354
\(555\) −0.360563 −0.0153051
\(556\) 24.7328 1.04891
\(557\) 3.49800 0.148215 0.0741075 0.997250i \(-0.476389\pi\)
0.0741075 + 0.997250i \(0.476389\pi\)
\(558\) −34.0937 −1.44330
\(559\) 20.7665 0.878329
\(560\) 1.68790 0.0713268
\(561\) 10.5337 0.444732
\(562\) −32.3389 −1.36413
\(563\) 26.9566 1.13609 0.568044 0.822998i \(-0.307701\pi\)
0.568044 + 0.822998i \(0.307701\pi\)
\(564\) 3.22585 0.135833
\(565\) 1.41050 0.0593403
\(566\) −37.3957 −1.57186
\(567\) −2.19930 −0.0923617
\(568\) −4.99641 −0.209645
\(569\) 4.39805 0.184376 0.0921880 0.995742i \(-0.470614\pi\)
0.0921880 + 0.995742i \(0.470614\pi\)
\(570\) −0.670356 −0.0280781
\(571\) −35.6256 −1.49089 −0.745443 0.666569i \(-0.767762\pi\)
−0.745443 + 0.666569i \(0.767762\pi\)
\(572\) 66.0527 2.76180
\(573\) −6.13560 −0.256318
\(574\) −17.2814 −0.721312
\(575\) 43.1791 1.80069
\(576\) 13.8142 0.575594
\(577\) 1.98878 0.0827938 0.0413969 0.999143i \(-0.486819\pi\)
0.0413969 + 0.999143i \(0.486819\pi\)
\(578\) 35.7759 1.48808
\(579\) 16.3495 0.679461
\(580\) −13.2869 −0.551708
\(581\) 6.18770 0.256709
\(582\) 2.33066 0.0966089
\(583\) 48.5130 2.00921
\(584\) 1.93877 0.0802270
\(585\) −2.22293 −0.0919070
\(586\) −4.83796 −0.199854
\(587\) 40.2505 1.66131 0.830657 0.556784i \(-0.187965\pi\)
0.830657 + 0.556784i \(0.187965\pi\)
\(588\) 4.75871 0.196246
\(589\) −4.22490 −0.174084
\(590\) −7.03137 −0.289477
\(591\) 26.4585 1.08836
\(592\) −2.00937 −0.0825844
\(593\) −17.9658 −0.737768 −0.368884 0.929475i \(-0.620260\pi\)
−0.368884 + 0.929475i \(0.620260\pi\)
\(594\) 76.5930 3.14265
\(595\) 0.749784 0.0307382
\(596\) 53.8568 2.20606
\(597\) 1.35978 0.0556523
\(598\) 65.2930 2.67003
\(599\) 27.1606 1.10975 0.554875 0.831934i \(-0.312766\pi\)
0.554875 + 0.831934i \(0.312766\pi\)
\(600\) 26.7259 1.09108
\(601\) 0.749272 0.0305634 0.0152817 0.999883i \(-0.495135\pi\)
0.0152817 + 0.999883i \(0.495135\pi\)
\(602\) −17.0406 −0.694521
\(603\) −6.17894 −0.251626
\(604\) 71.8654 2.92416
\(605\) 10.8646 0.441708
\(606\) −15.5176 −0.630358
\(607\) 40.1622 1.63013 0.815066 0.579368i \(-0.196701\pi\)
0.815066 + 0.579368i \(0.196701\pi\)
\(608\) 0.444733 0.0180363
\(609\) −8.36278 −0.338877
\(610\) −12.7053 −0.514424
\(611\) 2.00599 0.0811538
\(612\) −8.84929 −0.357711
\(613\) 24.8473 1.00357 0.501787 0.864991i \(-0.332676\pi\)
0.501787 + 0.864991i \(0.332676\pi\)
\(614\) 46.0996 1.86043
\(615\) 4.32841 0.174538
\(616\) −26.3805 −1.06290
\(617\) 6.00633 0.241806 0.120903 0.992664i \(-0.461421\pi\)
0.120903 + 0.992664i \(0.461421\pi\)
\(618\) −32.8594 −1.32180
\(619\) −15.0809 −0.606151 −0.303076 0.952967i \(-0.598013\pi\)
−0.303076 + 0.952967i \(0.598013\pi\)
\(620\) −18.0611 −0.725350
\(621\) 50.0315 2.00769
\(622\) 21.4024 0.858158
\(623\) 5.14054 0.205951
\(624\) 12.2495 0.490371
\(625\) 21.3415 0.853661
\(626\) −57.0421 −2.27986
\(627\) 3.17566 0.126824
\(628\) −27.3399 −1.09098
\(629\) −0.892583 −0.0355896
\(630\) 1.82409 0.0726736
\(631\) −39.9445 −1.59017 −0.795083 0.606500i \(-0.792573\pi\)
−0.795083 + 0.606500i \(0.792573\pi\)
\(632\) −57.6619 −2.29367
\(633\) −9.81351 −0.390052
\(634\) −67.6991 −2.68867
\(635\) 0.798877 0.0317025
\(636\) 40.2996 1.59798
\(637\) 2.95920 0.117248
\(638\) 95.2517 3.77105
\(639\) −1.63663 −0.0647440
\(640\) 10.0985 0.399179
\(641\) −0.957510 −0.0378194 −0.0189097 0.999821i \(-0.506019\pi\)
−0.0189097 + 0.999821i \(0.506019\pi\)
\(642\) −25.3830 −1.00179
\(643\) −39.3825 −1.55309 −0.776546 0.630060i \(-0.783030\pi\)
−0.776546 + 0.630060i \(0.783030\pi\)
\(644\) −35.4051 −1.39515
\(645\) 4.26809 0.168056
\(646\) −1.65948 −0.0652915
\(647\) 15.0195 0.590476 0.295238 0.955424i \(-0.404601\pi\)
0.295238 + 0.955424i \(0.404601\pi\)
\(648\) 10.1279 0.397861
\(649\) 33.3095 1.30751
\(650\) 34.1465 1.33934
\(651\) −11.3677 −0.445534
\(652\) −6.84844 −0.268206
\(653\) −30.7859 −1.20475 −0.602373 0.798215i \(-0.705778\pi\)
−0.602373 + 0.798215i \(0.705778\pi\)
\(654\) 38.4516 1.50358
\(655\) 9.95512 0.388979
\(656\) 24.1216 0.941791
\(657\) 0.635067 0.0247763
\(658\) −1.64608 −0.0641707
\(659\) −27.9225 −1.08771 −0.543854 0.839180i \(-0.683035\pi\)
−0.543854 + 0.839180i \(0.683035\pi\)
\(660\) 13.5756 0.528431
\(661\) 16.7376 0.651018 0.325509 0.945539i \(-0.394464\pi\)
0.325509 + 0.945539i \(0.394464\pi\)
\(662\) −39.6970 −1.54287
\(663\) 5.44136 0.211325
\(664\) −28.4948 −1.10581
\(665\) 0.226042 0.00876555
\(666\) −2.17150 −0.0841439
\(667\) 62.2196 2.40915
\(668\) −94.1464 −3.64263
\(669\) −30.0450 −1.16161
\(670\) −4.95342 −0.191367
\(671\) 60.1886 2.32355
\(672\) 1.19661 0.0461604
\(673\) −49.6510 −1.91391 −0.956953 0.290243i \(-0.906264\pi\)
−0.956953 + 0.290243i \(0.906264\pi\)
\(674\) 21.8775 0.842691
\(675\) 26.1652 1.00710
\(676\) −16.5331 −0.635888
\(677\) −29.9042 −1.14931 −0.574656 0.818395i \(-0.694864\pi\)
−0.574656 + 0.818395i \(0.694864\pi\)
\(678\) −8.39974 −0.322590
\(679\) −0.785892 −0.0301598
\(680\) −3.45280 −0.132409
\(681\) 4.89407 0.187541
\(682\) 129.477 4.95794
\(683\) −34.9281 −1.33649 −0.668244 0.743942i \(-0.732954\pi\)
−0.668244 + 0.743942i \(0.732954\pi\)
\(684\) −2.66785 −0.102008
\(685\) 0.697611 0.0266544
\(686\) −2.42826 −0.0927114
\(687\) −31.5984 −1.20556
\(688\) 23.7854 0.906811
\(689\) 25.0603 0.954720
\(690\) 13.4195 0.510872
\(691\) −24.4995 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(692\) 13.4452 0.511110
\(693\) −8.64122 −0.328253
\(694\) −29.5002 −1.11981
\(695\) 3.16104 0.119905
\(696\) 38.5111 1.45976
\(697\) 10.7151 0.405863
\(698\) −15.6468 −0.592241
\(699\) 14.5792 0.551436
\(700\) −18.5159 −0.699836
\(701\) 1.18808 0.0448733 0.0224366 0.999748i \(-0.492858\pi\)
0.0224366 + 0.999748i \(0.492858\pi\)
\(702\) 39.5655 1.49330
\(703\) −0.269093 −0.0101490
\(704\) −52.4622 −1.97725
\(705\) 0.412287 0.0155276
\(706\) −43.5315 −1.63833
\(707\) 5.23248 0.196788
\(708\) 27.6700 1.03990
\(709\) −2.46351 −0.0925189 −0.0462595 0.998929i \(-0.514730\pi\)
−0.0462595 + 0.998929i \(0.514730\pi\)
\(710\) −1.31202 −0.0492394
\(711\) −18.8878 −0.708347
\(712\) −23.6725 −0.887164
\(713\) 84.5760 3.16740
\(714\) −4.46507 −0.167101
\(715\) 8.44201 0.315713
\(716\) 83.2015 3.10939
\(717\) −29.7825 −1.11225
\(718\) −24.3076 −0.907153
\(719\) 5.94222 0.221607 0.110804 0.993842i \(-0.464658\pi\)
0.110804 + 0.993842i \(0.464658\pi\)
\(720\) −2.54609 −0.0948873
\(721\) 11.0801 0.412645
\(722\) 45.6366 1.69842
\(723\) −5.19809 −0.193319
\(724\) −58.9376 −2.19040
\(725\) 32.5392 1.20848
\(726\) −64.7000 −2.40124
\(727\) −38.0012 −1.40939 −0.704693 0.709512i \(-0.748915\pi\)
−0.704693 + 0.709512i \(0.748915\pi\)
\(728\) −13.6273 −0.505062
\(729\) 23.4913 0.870050
\(730\) 0.509109 0.0188430
\(731\) 10.5658 0.390789
\(732\) 49.9984 1.84799
\(733\) −26.9069 −0.993829 −0.496914 0.867800i \(-0.665534\pi\)
−0.496914 + 0.867800i \(0.665534\pi\)
\(734\) −2.32058 −0.0856541
\(735\) 0.608198 0.0224337
\(736\) −8.90287 −0.328164
\(737\) 23.4657 0.864370
\(738\) 26.0680 0.959575
\(739\) −3.06661 −0.112807 −0.0564036 0.998408i \(-0.517963\pi\)
−0.0564036 + 0.998408i \(0.517963\pi\)
\(740\) −1.15035 −0.0422877
\(741\) 1.64044 0.0602632
\(742\) −20.5639 −0.754926
\(743\) −17.5491 −0.643812 −0.321906 0.946772i \(-0.604324\pi\)
−0.321906 + 0.946772i \(0.604324\pi\)
\(744\) 52.3488 1.91920
\(745\) 6.88329 0.252184
\(746\) −41.6438 −1.52469
\(747\) −9.33377 −0.341505
\(748\) 33.6069 1.22879
\(749\) 8.55909 0.312742
\(750\) 14.4024 0.525900
\(751\) −33.9202 −1.23776 −0.618882 0.785484i \(-0.712414\pi\)
−0.618882 + 0.785484i \(0.712414\pi\)
\(752\) 2.29761 0.0837854
\(753\) 13.9853 0.509653
\(754\) 49.2040 1.79190
\(755\) 9.18492 0.334274
\(756\) −21.4543 −0.780287
\(757\) 22.5206 0.818526 0.409263 0.912417i \(-0.365786\pi\)
0.409263 + 0.912417i \(0.365786\pi\)
\(758\) 18.8968 0.686363
\(759\) −63.5718 −2.30751
\(760\) −1.04094 −0.0377588
\(761\) 18.3034 0.663498 0.331749 0.943368i \(-0.392361\pi\)
0.331749 + 0.943368i \(0.392361\pi\)
\(762\) −4.75742 −0.172343
\(763\) −12.9658 −0.469393
\(764\) −19.5751 −0.708204
\(765\) −1.13100 −0.0408915
\(766\) −50.6861 −1.83136
\(767\) 17.2066 0.621295
\(768\) −37.7688 −1.36286
\(769\) −13.3791 −0.482463 −0.241232 0.970468i \(-0.577551\pi\)
−0.241232 + 0.970468i \(0.577551\pi\)
\(770\) −6.92734 −0.249644
\(771\) −16.2568 −0.585473
\(772\) 52.1617 1.87734
\(773\) −10.4630 −0.376328 −0.188164 0.982138i \(-0.560254\pi\)
−0.188164 + 0.982138i \(0.560254\pi\)
\(774\) 25.7046 0.923934
\(775\) 44.2310 1.58883
\(776\) 3.61908 0.129918
\(777\) −0.724031 −0.0259745
\(778\) 87.6330 3.14180
\(779\) 3.23035 0.115739
\(780\) 7.01274 0.251096
\(781\) 6.21541 0.222405
\(782\) 33.2203 1.18796
\(783\) 37.7031 1.34740
\(784\) 3.38940 0.121050
\(785\) −3.49424 −0.124715
\(786\) −59.2841 −2.11459
\(787\) −52.9582 −1.88775 −0.943877 0.330296i \(-0.892851\pi\)
−0.943877 + 0.330296i \(0.892851\pi\)
\(788\) 84.4139 3.00712
\(789\) 15.2765 0.543857
\(790\) −15.1416 −0.538715
\(791\) 2.83237 0.100707
\(792\) 39.7934 1.41400
\(793\) 31.0915 1.10409
\(794\) −1.85901 −0.0659737
\(795\) 5.15058 0.182672
\(796\) 4.33829 0.153766
\(797\) −3.04995 −0.108035 −0.0540174 0.998540i \(-0.517203\pi\)
−0.0540174 + 0.998540i \(0.517203\pi\)
\(798\) −1.34611 −0.0476519
\(799\) 1.02063 0.0361072
\(800\) −4.65597 −0.164613
\(801\) −7.75418 −0.273981
\(802\) −53.2494 −1.88030
\(803\) −2.41179 −0.0851101
\(804\) 19.4928 0.687460
\(805\) −4.52502 −0.159486
\(806\) 66.8837 2.35588
\(807\) 19.6290 0.690972
\(808\) −24.0959 −0.847691
\(809\) −49.7930 −1.75063 −0.875314 0.483555i \(-0.839345\pi\)
−0.875314 + 0.483555i \(0.839345\pi\)
\(810\) 2.65952 0.0934459
\(811\) 10.8685 0.381643 0.190822 0.981625i \(-0.438885\pi\)
0.190822 + 0.981625i \(0.438885\pi\)
\(812\) −26.6808 −0.936313
\(813\) 5.40343 0.189506
\(814\) 8.24668 0.289046
\(815\) −0.875281 −0.0306598
\(816\) 6.23240 0.218177
\(817\) 3.18533 0.111441
\(818\) −56.6419 −1.98044
\(819\) −4.46378 −0.155977
\(820\) 13.8095 0.482247
\(821\) 11.9249 0.416181 0.208091 0.978110i \(-0.433275\pi\)
0.208091 + 0.978110i \(0.433275\pi\)
\(822\) −4.15437 −0.144900
\(823\) 18.1062 0.631141 0.315570 0.948902i \(-0.397804\pi\)
0.315570 + 0.948902i \(0.397804\pi\)
\(824\) −51.0246 −1.77753
\(825\) −33.2464 −1.15749
\(826\) −14.1194 −0.491276
\(827\) 2.37024 0.0824215 0.0412107 0.999150i \(-0.486878\pi\)
0.0412107 + 0.999150i \(0.486878\pi\)
\(828\) 53.4064 1.85600
\(829\) −13.1896 −0.458094 −0.229047 0.973415i \(-0.573561\pi\)
−0.229047 + 0.973415i \(0.573561\pi\)
\(830\) −7.48254 −0.259723
\(831\) 18.2725 0.633865
\(832\) −27.1003 −0.939534
\(833\) 1.50561 0.0521663
\(834\) −18.8244 −0.651836
\(835\) −12.0326 −0.416405
\(836\) 10.1317 0.350412
\(837\) 51.2504 1.77147
\(838\) 65.8486 2.27470
\(839\) −2.71925 −0.0938789 −0.0469394 0.998898i \(-0.514947\pi\)
−0.0469394 + 0.998898i \(0.514947\pi\)
\(840\) −2.80079 −0.0966364
\(841\) 17.8879 0.616824
\(842\) 26.6652 0.918944
\(843\) 16.2649 0.560192
\(844\) −31.3092 −1.07771
\(845\) −2.11305 −0.0726911
\(846\) 2.48300 0.0853675
\(847\) 21.8167 0.749630
\(848\) 28.7034 0.985679
\(849\) 18.8082 0.645495
\(850\) 17.3734 0.595901
\(851\) 5.38683 0.184658
\(852\) 5.16311 0.176885
\(853\) 2.98747 0.102289 0.0511445 0.998691i \(-0.483713\pi\)
0.0511445 + 0.998691i \(0.483713\pi\)
\(854\) −25.5130 −0.873038
\(855\) −0.340971 −0.0116610
\(856\) −39.4151 −1.34718
\(857\) −7.87088 −0.268864 −0.134432 0.990923i \(-0.542921\pi\)
−0.134432 + 0.990923i \(0.542921\pi\)
\(858\) −50.2733 −1.71630
\(859\) −1.00000 −0.0341196
\(860\) 13.6170 0.464336
\(861\) 8.69170 0.296212
\(862\) 43.4704 1.48061
\(863\) −19.9621 −0.679518 −0.339759 0.940513i \(-0.610345\pi\)
−0.339759 + 0.940513i \(0.610345\pi\)
\(864\) −5.39486 −0.183537
\(865\) 1.71839 0.0584271
\(866\) 34.4408 1.17035
\(867\) −17.9935 −0.611092
\(868\) −36.2676 −1.23100
\(869\) 71.7300 2.43327
\(870\) 10.1128 0.342855
\(871\) 12.1216 0.410726
\(872\) 59.7082 2.02197
\(873\) 1.18547 0.0401221
\(874\) 10.0152 0.338768
\(875\) −4.85644 −0.164178
\(876\) −2.00346 −0.0676906
\(877\) −2.86759 −0.0968316 −0.0484158 0.998827i \(-0.515417\pi\)
−0.0484158 + 0.998827i \(0.515417\pi\)
\(878\) 2.70297 0.0912208
\(879\) 2.43326 0.0820717
\(880\) 9.66927 0.325951
\(881\) 37.3932 1.25981 0.629904 0.776673i \(-0.283094\pi\)
0.629904 + 0.776673i \(0.283094\pi\)
\(882\) 3.66288 0.123336
\(883\) 12.1701 0.409558 0.204779 0.978808i \(-0.434352\pi\)
0.204779 + 0.978808i \(0.434352\pi\)
\(884\) 17.3602 0.583888
\(885\) 3.53643 0.118876
\(886\) 51.9684 1.74591
\(887\) −34.4318 −1.15611 −0.578054 0.815999i \(-0.696188\pi\)
−0.578054 + 0.815999i \(0.696188\pi\)
\(888\) 3.33421 0.111889
\(889\) 1.60419 0.0538028
\(890\) −6.21624 −0.208369
\(891\) −12.5988 −0.422077
\(892\) −95.8562 −3.20950
\(893\) 0.307695 0.0102966
\(894\) −40.9909 −1.37094
\(895\) 10.6338 0.355447
\(896\) 20.2784 0.677453
\(897\) −32.8391 −1.09647
\(898\) −95.3971 −3.18344
\(899\) 63.7354 2.12570
\(900\) 27.9301 0.931004
\(901\) 12.7504 0.424777
\(902\) −98.9980 −3.29627
\(903\) 8.57056 0.285210
\(904\) −13.0432 −0.433812
\(905\) −7.53265 −0.250394
\(906\) −54.6974 −1.81720
\(907\) 37.4750 1.24434 0.622169 0.782883i \(-0.286252\pi\)
0.622169 + 0.782883i \(0.286252\pi\)
\(908\) 15.6142 0.518174
\(909\) −7.89288 −0.261790
\(910\) −3.57844 −0.118624
\(911\) 10.0246 0.332131 0.166065 0.986115i \(-0.446894\pi\)
0.166065 + 0.986115i \(0.446894\pi\)
\(912\) 1.87892 0.0622173
\(913\) 35.4468 1.17312
\(914\) −0.0666979 −0.00220617
\(915\) 6.39016 0.211252
\(916\) −100.812 −3.33093
\(917\) 19.9904 0.660142
\(918\) 20.1305 0.664405
\(919\) 55.4579 1.82939 0.914694 0.404147i \(-0.132432\pi\)
0.914694 + 0.404147i \(0.132432\pi\)
\(920\) 20.8380 0.687009
\(921\) −23.1858 −0.763998
\(922\) −93.5659 −3.08143
\(923\) 3.21068 0.105681
\(924\) 27.2607 0.896810
\(925\) 2.81717 0.0926280
\(926\) −28.3779 −0.932555
\(927\) −16.7137 −0.548949
\(928\) −6.70909 −0.220237
\(929\) −30.5851 −1.00347 −0.501733 0.865023i \(-0.667304\pi\)
−0.501733 + 0.865023i \(0.667304\pi\)
\(930\) 13.7464 0.450764
\(931\) 0.453906 0.0148762
\(932\) 46.5138 1.52361
\(933\) −10.7643 −0.352409
\(934\) −88.2177 −2.88657
\(935\) 4.29520 0.140468
\(936\) 20.5560 0.671893
\(937\) 54.7656 1.78911 0.894557 0.446953i \(-0.147491\pi\)
0.894557 + 0.446953i \(0.147491\pi\)
\(938\) −9.94675 −0.324773
\(939\) 28.6893 0.936241
\(940\) 1.31537 0.0429026
\(941\) 53.1467 1.73253 0.866266 0.499583i \(-0.166514\pi\)
0.866266 + 0.499583i \(0.166514\pi\)
\(942\) 20.8087 0.677983
\(943\) −64.6667 −2.10584
\(944\) 19.7080 0.641441
\(945\) −2.74202 −0.0891980
\(946\) −97.6183 −3.17384
\(947\) −12.5489 −0.407785 −0.203893 0.978993i \(-0.565359\pi\)
−0.203893 + 0.978993i \(0.565359\pi\)
\(948\) 59.5857 1.93526
\(949\) −1.24585 −0.0404420
\(950\) 5.23766 0.169932
\(951\) 34.0493 1.10412
\(952\) −6.93342 −0.224714
\(953\) 18.1104 0.586653 0.293327 0.956012i \(-0.405238\pi\)
0.293327 + 0.956012i \(0.405238\pi\)
\(954\) 31.0194 1.00429
\(955\) −2.50185 −0.0809578
\(956\) −95.0187 −3.07312
\(957\) −47.9069 −1.54861
\(958\) 68.3952 2.20975
\(959\) 1.40084 0.0452356
\(960\) −5.56986 −0.179766
\(961\) 55.6366 1.79473
\(962\) 4.25997 0.137347
\(963\) −12.9109 −0.416047
\(964\) −16.5841 −0.534138
\(965\) 6.66664 0.214607
\(966\) 26.9471 0.867010
\(967\) 34.0462 1.09485 0.547426 0.836854i \(-0.315608\pi\)
0.547426 + 0.836854i \(0.315608\pi\)
\(968\) −100.467 −3.22914
\(969\) 0.834639 0.0268125
\(970\) 0.950347 0.0305138
\(971\) 15.8962 0.510134 0.255067 0.966923i \(-0.417902\pi\)
0.255067 + 0.966923i \(0.417902\pi\)
\(972\) 53.8972 1.72875
\(973\) 6.34754 0.203493
\(974\) 56.1187 1.79816
\(975\) −17.1740 −0.550009
\(976\) 35.6114 1.13989
\(977\) 19.0161 0.608379 0.304189 0.952612i \(-0.401614\pi\)
0.304189 + 0.952612i \(0.401614\pi\)
\(978\) 5.21242 0.166675
\(979\) 29.4480 0.941162
\(980\) 1.94041 0.0619840
\(981\) 19.5581 0.624441
\(982\) 62.9986 2.01037
\(983\) 33.7935 1.07785 0.538923 0.842355i \(-0.318831\pi\)
0.538923 + 0.842355i \(0.318831\pi\)
\(984\) −40.0258 −1.27598
\(985\) 10.7887 0.343757
\(986\) 25.0344 0.797259
\(987\) 0.827895 0.0263522
\(988\) 5.23370 0.166506
\(989\) −63.7654 −2.02762
\(990\) 10.4495 0.332106
\(991\) 27.8406 0.884384 0.442192 0.896920i \(-0.354201\pi\)
0.442192 + 0.896920i \(0.354201\pi\)
\(992\) −9.11977 −0.289553
\(993\) 19.9656 0.633591
\(994\) −2.63462 −0.0835650
\(995\) 0.554464 0.0175777
\(996\) 29.4455 0.933016
\(997\) −22.5919 −0.715492 −0.357746 0.933819i \(-0.616455\pi\)
−0.357746 + 0.933819i \(0.616455\pi\)
\(998\) 13.9657 0.442075
\(999\) 3.26425 0.103276
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 \(a_p\))