Properties

Label 4026.2.a.bc.1.2
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.88536\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.88536 q^{5}\) \(+1.00000 q^{6}\) \(-2.96592 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.88536 q^{5}\) \(+1.00000 q^{6}\) \(-2.96592 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-2.88536 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+1.99514 q^{13}\) \(-2.96592 q^{14}\) \(-2.88536 q^{15}\) \(+1.00000 q^{16}\) \(+3.32958 q^{17}\) \(+1.00000 q^{18}\) \(-5.75894 q^{19}\) \(-2.88536 q^{20}\) \(-2.96592 q^{21}\) \(+1.00000 q^{22}\) \(+7.24652 q^{23}\) \(+1.00000 q^{24}\) \(+3.32531 q^{25}\) \(+1.99514 q^{26}\) \(+1.00000 q^{27}\) \(-2.96592 q^{28}\) \(-8.65968 q^{29}\) \(-2.88536 q^{30}\) \(+6.36115 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(+3.32958 q^{34}\) \(+8.55776 q^{35}\) \(+1.00000 q^{36}\) \(+0.888652 q^{37}\) \(-5.75894 q^{38}\) \(+1.99514 q^{39}\) \(-2.88536 q^{40}\) \(-8.21059 q^{41}\) \(-2.96592 q^{42}\) \(+8.75258 q^{43}\) \(+1.00000 q^{44}\) \(-2.88536 q^{45}\) \(+7.24652 q^{46}\) \(+7.18416 q^{47}\) \(+1.00000 q^{48}\) \(+1.79670 q^{49}\) \(+3.32531 q^{50}\) \(+3.32958 q^{51}\) \(+1.99514 q^{52}\) \(+11.6265 q^{53}\) \(+1.00000 q^{54}\) \(-2.88536 q^{55}\) \(-2.96592 q^{56}\) \(-5.75894 q^{57}\) \(-8.65968 q^{58}\) \(+4.60591 q^{59}\) \(-2.88536 q^{60}\) \(-1.00000 q^{61}\) \(+6.36115 q^{62}\) \(-2.96592 q^{63}\) \(+1.00000 q^{64}\) \(-5.75669 q^{65}\) \(+1.00000 q^{66}\) \(-0.148761 q^{67}\) \(+3.32958 q^{68}\) \(+7.24652 q^{69}\) \(+8.55776 q^{70}\) \(+10.1133 q^{71}\) \(+1.00000 q^{72}\) \(+13.1127 q^{73}\) \(+0.888652 q^{74}\) \(+3.32531 q^{75}\) \(-5.75894 q^{76}\) \(-2.96592 q^{77}\) \(+1.99514 q^{78}\) \(+0.842774 q^{79}\) \(-2.88536 q^{80}\) \(+1.00000 q^{81}\) \(-8.21059 q^{82}\) \(-2.03186 q^{83}\) \(-2.96592 q^{84}\) \(-9.60705 q^{85}\) \(+8.75258 q^{86}\) \(-8.65968 q^{87}\) \(+1.00000 q^{88}\) \(+4.24660 q^{89}\) \(-2.88536 q^{90}\) \(-5.91742 q^{91}\) \(+7.24652 q^{92}\) \(+6.36115 q^{93}\) \(+7.18416 q^{94}\) \(+16.6166 q^{95}\) \(+1.00000 q^{96}\) \(+15.7876 q^{97}\) \(+1.79670 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −2.88536 −1.29037 −0.645186 0.764025i \(-0.723220\pi\)
−0.645186 + 0.764025i \(0.723220\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.96592 −1.12101 −0.560507 0.828150i \(-0.689394\pi\)
−0.560507 + 0.828150i \(0.689394\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −2.88536 −0.912431
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 1.99514 0.553352 0.276676 0.960963i \(-0.410767\pi\)
0.276676 + 0.960963i \(0.410767\pi\)
\(14\) −2.96592 −0.792676
\(15\) −2.88536 −0.744997
\(16\) 1.00000 0.250000
\(17\) 3.32958 0.807542 0.403771 0.914860i \(-0.367699\pi\)
0.403771 + 0.914860i \(0.367699\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.75894 −1.32119 −0.660595 0.750742i \(-0.729696\pi\)
−0.660595 + 0.750742i \(0.729696\pi\)
\(20\) −2.88536 −0.645186
\(21\) −2.96592 −0.647217
\(22\) 1.00000 0.213201
\(23\) 7.24652 1.51100 0.755502 0.655147i \(-0.227393\pi\)
0.755502 + 0.655147i \(0.227393\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.32531 0.665062
\(26\) 1.99514 0.391279
\(27\) 1.00000 0.192450
\(28\) −2.96592 −0.560507
\(29\) −8.65968 −1.60806 −0.804031 0.594588i \(-0.797315\pi\)
−0.804031 + 0.594588i \(0.797315\pi\)
\(30\) −2.88536 −0.526793
\(31\) 6.36115 1.14250 0.571249 0.820777i \(-0.306459\pi\)
0.571249 + 0.820777i \(0.306459\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 3.32958 0.571018
\(35\) 8.55776 1.44653
\(36\) 1.00000 0.166667
\(37\) 0.888652 0.146094 0.0730468 0.997329i \(-0.476728\pi\)
0.0730468 + 0.997329i \(0.476728\pi\)
\(38\) −5.75894 −0.934223
\(39\) 1.99514 0.319478
\(40\) −2.88536 −0.456216
\(41\) −8.21059 −1.28228 −0.641140 0.767424i \(-0.721538\pi\)
−0.641140 + 0.767424i \(0.721538\pi\)
\(42\) −2.96592 −0.457652
\(43\) 8.75258 1.33476 0.667378 0.744719i \(-0.267417\pi\)
0.667378 + 0.744719i \(0.267417\pi\)
\(44\) 1.00000 0.150756
\(45\) −2.88536 −0.430124
\(46\) 7.24652 1.06844
\(47\) 7.18416 1.04792 0.523958 0.851744i \(-0.324455\pi\)
0.523958 + 0.851744i \(0.324455\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.79670 0.256671
\(50\) 3.32531 0.470270
\(51\) 3.32958 0.466235
\(52\) 1.99514 0.276676
\(53\) 11.6265 1.59703 0.798514 0.601976i \(-0.205620\pi\)
0.798514 + 0.601976i \(0.205620\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.88536 −0.389062
\(56\) −2.96592 −0.396338
\(57\) −5.75894 −0.762790
\(58\) −8.65968 −1.13707
\(59\) 4.60591 0.599638 0.299819 0.953996i \(-0.403074\pi\)
0.299819 + 0.953996i \(0.403074\pi\)
\(60\) −2.88536 −0.372499
\(61\) −1.00000 −0.128037
\(62\) 6.36115 0.807867
\(63\) −2.96592 −0.373671
\(64\) 1.00000 0.125000
\(65\) −5.75669 −0.714030
\(66\) 1.00000 0.123091
\(67\) −0.148761 −0.0181741 −0.00908703 0.999959i \(-0.502893\pi\)
−0.00908703 + 0.999959i \(0.502893\pi\)
\(68\) 3.32958 0.403771
\(69\) 7.24652 0.872378
\(70\) 8.55776 1.02285
\(71\) 10.1133 1.20022 0.600112 0.799916i \(-0.295123\pi\)
0.600112 + 0.799916i \(0.295123\pi\)
\(72\) 1.00000 0.117851
\(73\) 13.1127 1.53472 0.767361 0.641216i \(-0.221570\pi\)
0.767361 + 0.641216i \(0.221570\pi\)
\(74\) 0.888652 0.103304
\(75\) 3.32531 0.383974
\(76\) −5.75894 −0.660595
\(77\) −2.96592 −0.337998
\(78\) 1.99514 0.225905
\(79\) 0.842774 0.0948195 0.0474098 0.998876i \(-0.484903\pi\)
0.0474098 + 0.998876i \(0.484903\pi\)
\(80\) −2.88536 −0.322593
\(81\) 1.00000 0.111111
\(82\) −8.21059 −0.906708
\(83\) −2.03186 −0.223025 −0.111513 0.993763i \(-0.535570\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(84\) −2.96592 −0.323609
\(85\) −9.60705 −1.04203
\(86\) 8.75258 0.943815
\(87\) −8.65968 −0.928415
\(88\) 1.00000 0.106600
\(89\) 4.24660 0.450138 0.225069 0.974343i \(-0.427739\pi\)
0.225069 + 0.974343i \(0.427739\pi\)
\(90\) −2.88536 −0.304144
\(91\) −5.91742 −0.620314
\(92\) 7.24652 0.755502
\(93\) 6.36115 0.659621
\(94\) 7.18416 0.740989
\(95\) 16.6166 1.70483
\(96\) 1.00000 0.102062
\(97\) 15.7876 1.60298 0.801492 0.598006i \(-0.204040\pi\)
0.801492 + 0.598006i \(0.204040\pi\)
\(98\) 1.79670 0.181494
\(99\) 1.00000 0.100504
\(100\) 3.32531 0.332531
\(101\) −3.16276 −0.314706 −0.157353 0.987542i \(-0.550296\pi\)
−0.157353 + 0.987542i \(0.550296\pi\)
\(102\) 3.32958 0.329678
\(103\) 7.25233 0.714593 0.357296 0.933991i \(-0.383699\pi\)
0.357296 + 0.933991i \(0.383699\pi\)
\(104\) 1.99514 0.195639
\(105\) 8.55776 0.835152
\(106\) 11.6265 1.12927
\(107\) −15.9751 −1.54437 −0.772186 0.635397i \(-0.780836\pi\)
−0.772186 + 0.635397i \(0.780836\pi\)
\(108\) 1.00000 0.0962250
\(109\) −7.92043 −0.758640 −0.379320 0.925266i \(-0.623842\pi\)
−0.379320 + 0.925266i \(0.623842\pi\)
\(110\) −2.88536 −0.275108
\(111\) 0.888652 0.0843472
\(112\) −2.96592 −0.280253
\(113\) 9.60725 0.903775 0.451887 0.892075i \(-0.350751\pi\)
0.451887 + 0.892075i \(0.350751\pi\)
\(114\) −5.75894 −0.539374
\(115\) −20.9088 −1.94976
\(116\) −8.65968 −0.804031
\(117\) 1.99514 0.184451
\(118\) 4.60591 0.424008
\(119\) −9.87528 −0.905265
\(120\) −2.88536 −0.263396
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −8.21059 −0.740324
\(124\) 6.36115 0.571249
\(125\) 4.83208 0.432194
\(126\) −2.96592 −0.264225
\(127\) 15.7842 1.40062 0.700310 0.713839i \(-0.253045\pi\)
0.700310 + 0.713839i \(0.253045\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.75258 0.770622
\(130\) −5.75669 −0.504895
\(131\) 7.43708 0.649781 0.324890 0.945752i \(-0.394673\pi\)
0.324890 + 0.945752i \(0.394673\pi\)
\(132\) 1.00000 0.0870388
\(133\) 17.0806 1.48107
\(134\) −0.148761 −0.0128510
\(135\) −2.88536 −0.248332
\(136\) 3.32958 0.285509
\(137\) −18.4993 −1.58050 −0.790251 0.612784i \(-0.790050\pi\)
−0.790251 + 0.612784i \(0.790050\pi\)
\(138\) 7.24652 0.616864
\(139\) 7.48195 0.634611 0.317306 0.948323i \(-0.397222\pi\)
0.317306 + 0.948323i \(0.397222\pi\)
\(140\) 8.55776 0.723263
\(141\) 7.18416 0.605015
\(142\) 10.1133 0.848686
\(143\) 1.99514 0.166842
\(144\) 1.00000 0.0833333
\(145\) 24.9863 2.07500
\(146\) 13.1127 1.08521
\(147\) 1.79670 0.148189
\(148\) 0.888652 0.0730468
\(149\) 24.0818 1.97286 0.986429 0.164186i \(-0.0524998\pi\)
0.986429 + 0.164186i \(0.0524998\pi\)
\(150\) 3.32531 0.271511
\(151\) −17.0023 −1.38363 −0.691815 0.722075i \(-0.743189\pi\)
−0.691815 + 0.722075i \(0.743189\pi\)
\(152\) −5.75894 −0.467111
\(153\) 3.32958 0.269181
\(154\) −2.96592 −0.239001
\(155\) −18.3542 −1.47425
\(156\) 1.99514 0.159739
\(157\) 13.7591 1.09810 0.549049 0.835790i \(-0.314990\pi\)
0.549049 + 0.835790i \(0.314990\pi\)
\(158\) 0.842774 0.0670475
\(159\) 11.6265 0.922045
\(160\) −2.88536 −0.228108
\(161\) −21.4926 −1.69385
\(162\) 1.00000 0.0785674
\(163\) −15.4511 −1.21023 −0.605113 0.796139i \(-0.706872\pi\)
−0.605113 + 0.796139i \(0.706872\pi\)
\(164\) −8.21059 −0.641140
\(165\) −2.88536 −0.224625
\(166\) −2.03186 −0.157703
\(167\) 11.2006 0.866730 0.433365 0.901219i \(-0.357326\pi\)
0.433365 + 0.901219i \(0.357326\pi\)
\(168\) −2.96592 −0.228826
\(169\) −9.01943 −0.693802
\(170\) −9.60705 −0.736827
\(171\) −5.75894 −0.440397
\(172\) 8.75258 0.667378
\(173\) −11.0410 −0.839432 −0.419716 0.907656i \(-0.637870\pi\)
−0.419716 + 0.907656i \(0.637870\pi\)
\(174\) −8.65968 −0.656488
\(175\) −9.86262 −0.745544
\(176\) 1.00000 0.0753778
\(177\) 4.60591 0.346201
\(178\) 4.24660 0.318296
\(179\) −25.0479 −1.87217 −0.936086 0.351772i \(-0.885579\pi\)
−0.936086 + 0.351772i \(0.885579\pi\)
\(180\) −2.88536 −0.215062
\(181\) 7.72044 0.573856 0.286928 0.957952i \(-0.407366\pi\)
0.286928 + 0.957952i \(0.407366\pi\)
\(182\) −5.91742 −0.438629
\(183\) −1.00000 −0.0739221
\(184\) 7.24652 0.534220
\(185\) −2.56408 −0.188515
\(186\) 6.36115 0.466423
\(187\) 3.32958 0.243483
\(188\) 7.18416 0.523958
\(189\) −2.96592 −0.215739
\(190\) 16.6166 1.20550
\(191\) 14.3131 1.03566 0.517830 0.855484i \(-0.326740\pi\)
0.517830 + 0.855484i \(0.326740\pi\)
\(192\) 1.00000 0.0721688
\(193\) 10.8554 0.781390 0.390695 0.920520i \(-0.372235\pi\)
0.390695 + 0.920520i \(0.372235\pi\)
\(194\) 15.7876 1.13348
\(195\) −5.75669 −0.412245
\(196\) 1.79670 0.128335
\(197\) −11.8718 −0.845828 −0.422914 0.906170i \(-0.638993\pi\)
−0.422914 + 0.906170i \(0.638993\pi\)
\(198\) 1.00000 0.0710669
\(199\) 8.01638 0.568266 0.284133 0.958785i \(-0.408294\pi\)
0.284133 + 0.958785i \(0.408294\pi\)
\(200\) 3.32531 0.235135
\(201\) −0.148761 −0.0104928
\(202\) −3.16276 −0.222531
\(203\) 25.6839 1.80266
\(204\) 3.32958 0.233117
\(205\) 23.6905 1.65462
\(206\) 7.25233 0.505293
\(207\) 7.24652 0.503668
\(208\) 1.99514 0.138338
\(209\) −5.75894 −0.398354
\(210\) 8.55776 0.590541
\(211\) −9.63240 −0.663122 −0.331561 0.943434i \(-0.607575\pi\)
−0.331561 + 0.943434i \(0.607575\pi\)
\(212\) 11.6265 0.798514
\(213\) 10.1133 0.692949
\(214\) −15.9751 −1.09204
\(215\) −25.2544 −1.72233
\(216\) 1.00000 0.0680414
\(217\) −18.8667 −1.28075
\(218\) −7.92043 −0.536439
\(219\) 13.1127 0.886072
\(220\) −2.88536 −0.194531
\(221\) 6.64297 0.446855
\(222\) 0.888652 0.0596424
\(223\) 25.1499 1.68416 0.842080 0.539353i \(-0.181331\pi\)
0.842080 + 0.539353i \(0.181331\pi\)
\(224\) −2.96592 −0.198169
\(225\) 3.32531 0.221687
\(226\) 9.60725 0.639065
\(227\) 12.8001 0.849574 0.424787 0.905293i \(-0.360349\pi\)
0.424787 + 0.905293i \(0.360349\pi\)
\(228\) −5.75894 −0.381395
\(229\) 3.78489 0.250112 0.125056 0.992150i \(-0.460089\pi\)
0.125056 + 0.992150i \(0.460089\pi\)
\(230\) −20.9088 −1.37869
\(231\) −2.96592 −0.195143
\(232\) −8.65968 −0.568536
\(233\) 7.44585 0.487794 0.243897 0.969801i \(-0.421574\pi\)
0.243897 + 0.969801i \(0.421574\pi\)
\(234\) 1.99514 0.130426
\(235\) −20.7289 −1.35220
\(236\) 4.60591 0.299819
\(237\) 0.842774 0.0547441
\(238\) −9.87528 −0.640119
\(239\) −18.0695 −1.16882 −0.584411 0.811458i \(-0.698674\pi\)
−0.584411 + 0.811458i \(0.698674\pi\)
\(240\) −2.88536 −0.186249
\(241\) 24.1062 1.55282 0.776409 0.630229i \(-0.217039\pi\)
0.776409 + 0.630229i \(0.217039\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −5.18412 −0.331201
\(246\) −8.21059 −0.523488
\(247\) −11.4899 −0.731083
\(248\) 6.36115 0.403934
\(249\) −2.03186 −0.128764
\(250\) 4.83208 0.305608
\(251\) −24.3202 −1.53508 −0.767538 0.641004i \(-0.778518\pi\)
−0.767538 + 0.641004i \(0.778518\pi\)
\(252\) −2.96592 −0.186836
\(253\) 7.24652 0.455585
\(254\) 15.7842 0.990387
\(255\) −9.60705 −0.601617
\(256\) 1.00000 0.0625000
\(257\) −24.7338 −1.54285 −0.771425 0.636320i \(-0.780456\pi\)
−0.771425 + 0.636320i \(0.780456\pi\)
\(258\) 8.75258 0.544912
\(259\) −2.63567 −0.163773
\(260\) −5.75669 −0.357015
\(261\) −8.65968 −0.536020
\(262\) 7.43708 0.459464
\(263\) −14.5208 −0.895389 −0.447694 0.894187i \(-0.647755\pi\)
−0.447694 + 0.894187i \(0.647755\pi\)
\(264\) 1.00000 0.0615457
\(265\) −33.5468 −2.06076
\(266\) 17.0806 1.04728
\(267\) 4.24660 0.259888
\(268\) −0.148761 −0.00908703
\(269\) 20.0593 1.22304 0.611518 0.791230i \(-0.290559\pi\)
0.611518 + 0.791230i \(0.290559\pi\)
\(270\) −2.88536 −0.175598
\(271\) −20.2969 −1.23295 −0.616475 0.787375i \(-0.711440\pi\)
−0.616475 + 0.787375i \(0.711440\pi\)
\(272\) 3.32958 0.201886
\(273\) −5.91742 −0.358139
\(274\) −18.4993 −1.11758
\(275\) 3.32531 0.200524
\(276\) 7.24652 0.436189
\(277\) 8.52674 0.512322 0.256161 0.966634i \(-0.417542\pi\)
0.256161 + 0.966634i \(0.417542\pi\)
\(278\) 7.48195 0.448738
\(279\) 6.36115 0.380832
\(280\) 8.55776 0.511424
\(281\) −26.5966 −1.58662 −0.793311 0.608816i \(-0.791645\pi\)
−0.793311 + 0.608816i \(0.791645\pi\)
\(282\) 7.18416 0.427810
\(283\) 32.5170 1.93293 0.966467 0.256791i \(-0.0826653\pi\)
0.966467 + 0.256791i \(0.0826653\pi\)
\(284\) 10.1133 0.600112
\(285\) 16.6166 0.984283
\(286\) 1.99514 0.117975
\(287\) 24.3520 1.43745
\(288\) 1.00000 0.0589256
\(289\) −5.91389 −0.347876
\(290\) 24.9863 1.46725
\(291\) 15.7876 0.925483
\(292\) 13.1127 0.767361
\(293\) −33.9091 −1.98099 −0.990497 0.137536i \(-0.956082\pi\)
−0.990497 + 0.137536i \(0.956082\pi\)
\(294\) 1.79670 0.104785
\(295\) −13.2897 −0.773757
\(296\) 0.888652 0.0516519
\(297\) 1.00000 0.0580259
\(298\) 24.0818 1.39502
\(299\) 14.4578 0.836116
\(300\) 3.32531 0.191987
\(301\) −25.9595 −1.49628
\(302\) −17.0023 −0.978374
\(303\) −3.16276 −0.181696
\(304\) −5.75894 −0.330298
\(305\) 2.88536 0.165215
\(306\) 3.32958 0.190339
\(307\) 6.17590 0.352477 0.176239 0.984347i \(-0.443607\pi\)
0.176239 + 0.984347i \(0.443607\pi\)
\(308\) −2.96592 −0.168999
\(309\) 7.25233 0.412570
\(310\) −18.3542 −1.04245
\(311\) −12.4464 −0.705769 −0.352884 0.935667i \(-0.614799\pi\)
−0.352884 + 0.935667i \(0.614799\pi\)
\(312\) 1.99514 0.112952
\(313\) 21.8357 1.23423 0.617113 0.786875i \(-0.288302\pi\)
0.617113 + 0.786875i \(0.288302\pi\)
\(314\) 13.7591 0.776472
\(315\) 8.55776 0.482175
\(316\) 0.842774 0.0474098
\(317\) −19.9615 −1.12115 −0.560574 0.828104i \(-0.689419\pi\)
−0.560574 + 0.828104i \(0.689419\pi\)
\(318\) 11.6265 0.651984
\(319\) −8.65968 −0.484849
\(320\) −2.88536 −0.161297
\(321\) −15.9751 −0.891643
\(322\) −21.4926 −1.19774
\(323\) −19.1748 −1.06692
\(324\) 1.00000 0.0555556
\(325\) 6.63445 0.368013
\(326\) −15.4511 −0.855759
\(327\) −7.92043 −0.438001
\(328\) −8.21059 −0.453354
\(329\) −21.3077 −1.17473
\(330\) −2.88536 −0.158834
\(331\) −33.3076 −1.83075 −0.915377 0.402598i \(-0.868107\pi\)
−0.915377 + 0.402598i \(0.868107\pi\)
\(332\) −2.03186 −0.111513
\(333\) 0.888652 0.0486979
\(334\) 11.2006 0.612871
\(335\) 0.429230 0.0234513
\(336\) −2.96592 −0.161804
\(337\) −12.3478 −0.672626 −0.336313 0.941750i \(-0.609180\pi\)
−0.336313 + 0.941750i \(0.609180\pi\)
\(338\) −9.01943 −0.490592
\(339\) 9.60725 0.521794
\(340\) −9.60705 −0.521015
\(341\) 6.36115 0.344476
\(342\) −5.75894 −0.311408
\(343\) 15.4326 0.833282
\(344\) 8.75258 0.471907
\(345\) −20.9088 −1.12569
\(346\) −11.0410 −0.593568
\(347\) −9.35061 −0.501967 −0.250983 0.967991i \(-0.580754\pi\)
−0.250983 + 0.967991i \(0.580754\pi\)
\(348\) −8.65968 −0.464207
\(349\) −17.6910 −0.946977 −0.473489 0.880800i \(-0.657006\pi\)
−0.473489 + 0.880800i \(0.657006\pi\)
\(350\) −9.86262 −0.527179
\(351\) 1.99514 0.106493
\(352\) 1.00000 0.0533002
\(353\) 0.997385 0.0530855 0.0265427 0.999648i \(-0.491550\pi\)
0.0265427 + 0.999648i \(0.491550\pi\)
\(354\) 4.60591 0.244801
\(355\) −29.1804 −1.54874
\(356\) 4.24660 0.225069
\(357\) −9.87528 −0.522655
\(358\) −25.0479 −1.32383
\(359\) 13.6560 0.720738 0.360369 0.932810i \(-0.382651\pi\)
0.360369 + 0.932810i \(0.382651\pi\)
\(360\) −2.88536 −0.152072
\(361\) 14.1653 0.745545
\(362\) 7.72044 0.405778
\(363\) 1.00000 0.0524864
\(364\) −5.91742 −0.310157
\(365\) −37.8348 −1.98036
\(366\) −1.00000 −0.0522708
\(367\) −25.9368 −1.35389 −0.676946 0.736033i \(-0.736697\pi\)
−0.676946 + 0.736033i \(0.736697\pi\)
\(368\) 7.24652 0.377751
\(369\) −8.21059 −0.427426
\(370\) −2.56408 −0.133300
\(371\) −34.4834 −1.79029
\(372\) 6.36115 0.329811
\(373\) 11.3492 0.587638 0.293819 0.955861i \(-0.405074\pi\)
0.293819 + 0.955861i \(0.405074\pi\)
\(374\) 3.32958 0.172169
\(375\) 4.83208 0.249528
\(376\) 7.18416 0.370495
\(377\) −17.2772 −0.889823
\(378\) −2.96592 −0.152551
\(379\) −15.4499 −0.793607 −0.396803 0.917904i \(-0.629881\pi\)
−0.396803 + 0.917904i \(0.629881\pi\)
\(380\) 16.6166 0.852414
\(381\) 15.7842 0.808648
\(382\) 14.3131 0.732322
\(383\) 10.7110 0.547306 0.273653 0.961828i \(-0.411768\pi\)
0.273653 + 0.961828i \(0.411768\pi\)
\(384\) 1.00000 0.0510310
\(385\) 8.55776 0.436144
\(386\) 10.8554 0.552526
\(387\) 8.75258 0.444919
\(388\) 15.7876 0.801492
\(389\) 11.1350 0.564568 0.282284 0.959331i \(-0.408908\pi\)
0.282284 + 0.959331i \(0.408908\pi\)
\(390\) −5.75669 −0.291501
\(391\) 24.1279 1.22020
\(392\) 1.79670 0.0907469
\(393\) 7.43708 0.375151
\(394\) −11.8718 −0.598091
\(395\) −2.43171 −0.122353
\(396\) 1.00000 0.0502519
\(397\) 6.36784 0.319593 0.159796 0.987150i \(-0.448916\pi\)
0.159796 + 0.987150i \(0.448916\pi\)
\(398\) 8.01638 0.401825
\(399\) 17.0806 0.855097
\(400\) 3.32531 0.166266
\(401\) 11.5521 0.576884 0.288442 0.957497i \(-0.406863\pi\)
0.288442 + 0.957497i \(0.406863\pi\)
\(402\) −0.148761 −0.00741953
\(403\) 12.6914 0.632203
\(404\) −3.16276 −0.157353
\(405\) −2.88536 −0.143375
\(406\) 25.6839 1.27467
\(407\) 0.888652 0.0440489
\(408\) 3.32958 0.164839
\(409\) −25.0051 −1.23642 −0.618211 0.786012i \(-0.712142\pi\)
−0.618211 + 0.786012i \(0.712142\pi\)
\(410\) 23.6905 1.16999
\(411\) −18.4993 −0.912503
\(412\) 7.25233 0.357296
\(413\) −13.6608 −0.672202
\(414\) 7.24652 0.356147
\(415\) 5.86265 0.287786
\(416\) 1.99514 0.0978197
\(417\) 7.48195 0.366393
\(418\) −5.75894 −0.281679
\(419\) −38.6289 −1.88715 −0.943574 0.331163i \(-0.892559\pi\)
−0.943574 + 0.331163i \(0.892559\pi\)
\(420\) 8.55776 0.417576
\(421\) −30.2729 −1.47541 −0.737705 0.675124i \(-0.764090\pi\)
−0.737705 + 0.675124i \(0.764090\pi\)
\(422\) −9.63240 −0.468898
\(423\) 7.18416 0.349306
\(424\) 11.6265 0.564635
\(425\) 11.0719 0.537066
\(426\) 10.1133 0.489989
\(427\) 2.96592 0.143531
\(428\) −15.9751 −0.772186
\(429\) 1.99514 0.0963261
\(430\) −25.2544 −1.21787
\(431\) 15.8946 0.765615 0.382808 0.923828i \(-0.374957\pi\)
0.382808 + 0.923828i \(0.374957\pi\)
\(432\) 1.00000 0.0481125
\(433\) 15.3948 0.739826 0.369913 0.929066i \(-0.379388\pi\)
0.369913 + 0.929066i \(0.379388\pi\)
\(434\) −18.8667 −0.905630
\(435\) 24.9863 1.19800
\(436\) −7.92043 −0.379320
\(437\) −41.7322 −1.99632
\(438\) 13.1127 0.626547
\(439\) 27.8185 1.32770 0.663852 0.747864i \(-0.268920\pi\)
0.663852 + 0.747864i \(0.268920\pi\)
\(440\) −2.88536 −0.137554
\(441\) 1.79670 0.0855570
\(442\) 6.64297 0.315974
\(443\) 25.2358 1.19899 0.599493 0.800380i \(-0.295369\pi\)
0.599493 + 0.800380i \(0.295369\pi\)
\(444\) 0.888652 0.0421736
\(445\) −12.2530 −0.580846
\(446\) 25.1499 1.19088
\(447\) 24.0818 1.13903
\(448\) −2.96592 −0.140127
\(449\) −39.0786 −1.84423 −0.922117 0.386912i \(-0.873542\pi\)
−0.922117 + 0.386912i \(0.873542\pi\)
\(450\) 3.32531 0.156757
\(451\) −8.21059 −0.386622
\(452\) 9.60725 0.451887
\(453\) −17.0023 −0.798839
\(454\) 12.8001 0.600740
\(455\) 17.0739 0.800437
\(456\) −5.75894 −0.269687
\(457\) 34.4683 1.61236 0.806181 0.591669i \(-0.201531\pi\)
0.806181 + 0.591669i \(0.201531\pi\)
\(458\) 3.78489 0.176856
\(459\) 3.32958 0.155412
\(460\) −20.9088 −0.974879
\(461\) 31.0021 1.44391 0.721956 0.691939i \(-0.243244\pi\)
0.721956 + 0.691939i \(0.243244\pi\)
\(462\) −2.96592 −0.137987
\(463\) −18.5190 −0.860649 −0.430325 0.902674i \(-0.641601\pi\)
−0.430325 + 0.902674i \(0.641601\pi\)
\(464\) −8.65968 −0.402015
\(465\) −18.3542 −0.851157
\(466\) 7.44585 0.344922
\(467\) 2.19750 0.101688 0.0508440 0.998707i \(-0.483809\pi\)
0.0508440 + 0.998707i \(0.483809\pi\)
\(468\) 1.99514 0.0922253
\(469\) 0.441214 0.0203734
\(470\) −20.7289 −0.956152
\(471\) 13.7591 0.633987
\(472\) 4.60591 0.212004
\(473\) 8.75258 0.402444
\(474\) 0.842774 0.0387099
\(475\) −19.1503 −0.878674
\(476\) −9.87528 −0.452633
\(477\) 11.6265 0.532343
\(478\) −18.0695 −0.826481
\(479\) −25.6028 −1.16982 −0.584912 0.811097i \(-0.698871\pi\)
−0.584912 + 0.811097i \(0.698871\pi\)
\(480\) −2.88536 −0.131698
\(481\) 1.77298 0.0808411
\(482\) 24.1062 1.09801
\(483\) −21.4926 −0.977947
\(484\) 1.00000 0.0454545
\(485\) −45.5528 −2.06845
\(486\) 1.00000 0.0453609
\(487\) 2.27931 0.103285 0.0516427 0.998666i \(-0.483554\pi\)
0.0516427 + 0.998666i \(0.483554\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −15.4511 −0.698725
\(490\) −5.18412 −0.234195
\(491\) −22.6588 −1.02258 −0.511289 0.859409i \(-0.670832\pi\)
−0.511289 + 0.859409i \(0.670832\pi\)
\(492\) −8.21059 −0.370162
\(493\) −28.8331 −1.29858
\(494\) −11.4899 −0.516954
\(495\) −2.88536 −0.129687
\(496\) 6.36115 0.285624
\(497\) −29.9951 −1.34547
\(498\) −2.03186 −0.0910498
\(499\) 44.3558 1.98564 0.992820 0.119619i \(-0.0381674\pi\)
0.992820 + 0.119619i \(0.0381674\pi\)
\(500\) 4.83208 0.216097
\(501\) 11.2006 0.500407
\(502\) −24.3202 −1.08546
\(503\) −31.2750 −1.39448 −0.697242 0.716836i \(-0.745589\pi\)
−0.697242 + 0.716836i \(0.745589\pi\)
\(504\) −2.96592 −0.132113
\(505\) 9.12569 0.406088
\(506\) 7.24652 0.322147
\(507\) −9.01943 −0.400567
\(508\) 15.7842 0.700310
\(509\) −24.4621 −1.08426 −0.542131 0.840294i \(-0.682382\pi\)
−0.542131 + 0.840294i \(0.682382\pi\)
\(510\) −9.60705 −0.425407
\(511\) −38.8911 −1.72044
\(512\) 1.00000 0.0441942
\(513\) −5.75894 −0.254263
\(514\) −24.7338 −1.09096
\(515\) −20.9256 −0.922091
\(516\) 8.75258 0.385311
\(517\) 7.18416 0.315959
\(518\) −2.63567 −0.115805
\(519\) −11.0410 −0.484646
\(520\) −5.75669 −0.252448
\(521\) 30.7879 1.34884 0.674421 0.738347i \(-0.264393\pi\)
0.674421 + 0.738347i \(0.264393\pi\)
\(522\) −8.65968 −0.379024
\(523\) 34.0818 1.49029 0.745146 0.666901i \(-0.232380\pi\)
0.745146 + 0.666901i \(0.232380\pi\)
\(524\) 7.43708 0.324890
\(525\) −9.86262 −0.430440
\(526\) −14.5208 −0.633136
\(527\) 21.1800 0.922614
\(528\) 1.00000 0.0435194
\(529\) 29.5120 1.28313
\(530\) −33.5468 −1.45718
\(531\) 4.60591 0.199879
\(532\) 17.0806 0.740536
\(533\) −16.3813 −0.709551
\(534\) 4.24660 0.183768
\(535\) 46.0939 1.99281
\(536\) −0.148761 −0.00642550
\(537\) −25.0479 −1.08090
\(538\) 20.0593 0.864817
\(539\) 1.79670 0.0773892
\(540\) −2.88536 −0.124166
\(541\) 4.51198 0.193985 0.0969925 0.995285i \(-0.469078\pi\)
0.0969925 + 0.995285i \(0.469078\pi\)
\(542\) −20.2969 −0.871827
\(543\) 7.72044 0.331316
\(544\) 3.32958 0.142755
\(545\) 22.8533 0.978928
\(546\) −5.91742 −0.253242
\(547\) 19.6521 0.840262 0.420131 0.907463i \(-0.361984\pi\)
0.420131 + 0.907463i \(0.361984\pi\)
\(548\) −18.4993 −0.790251
\(549\) −1.00000 −0.0426790
\(550\) 3.32531 0.141792
\(551\) 49.8705 2.12456
\(552\) 7.24652 0.308432
\(553\) −2.49960 −0.106294
\(554\) 8.52674 0.362267
\(555\) −2.56408 −0.108839
\(556\) 7.48195 0.317306
\(557\) 2.05303 0.0869896 0.0434948 0.999054i \(-0.486151\pi\)
0.0434948 + 0.999054i \(0.486151\pi\)
\(558\) 6.36115 0.269289
\(559\) 17.4626 0.738589
\(560\) 8.55776 0.361631
\(561\) 3.32958 0.140575
\(562\) −26.5966 −1.12191
\(563\) 15.8242 0.666912 0.333456 0.942766i \(-0.391785\pi\)
0.333456 + 0.942766i \(0.391785\pi\)
\(564\) 7.18416 0.302508
\(565\) −27.7204 −1.16621
\(566\) 32.5170 1.36679
\(567\) −2.96592 −0.124557
\(568\) 10.1133 0.424343
\(569\) −1.69727 −0.0711532 −0.0355766 0.999367i \(-0.511327\pi\)
−0.0355766 + 0.999367i \(0.511327\pi\)
\(570\) 16.6166 0.695993
\(571\) −23.2580 −0.973319 −0.486659 0.873592i \(-0.661785\pi\)
−0.486659 + 0.873592i \(0.661785\pi\)
\(572\) 1.99514 0.0834209
\(573\) 14.3131 0.597938
\(574\) 24.3520 1.01643
\(575\) 24.0969 1.00491
\(576\) 1.00000 0.0416667
\(577\) −24.3451 −1.01350 −0.506750 0.862093i \(-0.669153\pi\)
−0.506750 + 0.862093i \(0.669153\pi\)
\(578\) −5.91389 −0.245985
\(579\) 10.8554 0.451136
\(580\) 24.9863 1.03750
\(581\) 6.02634 0.250015
\(582\) 15.7876 0.654415
\(583\) 11.6265 0.481522
\(584\) 13.1127 0.542606
\(585\) −5.75669 −0.238010
\(586\) −33.9091 −1.40077
\(587\) 21.2752 0.878122 0.439061 0.898457i \(-0.355311\pi\)
0.439061 + 0.898457i \(0.355311\pi\)
\(588\) 1.79670 0.0740945
\(589\) −36.6335 −1.50946
\(590\) −13.2897 −0.547129
\(591\) −11.8718 −0.488339
\(592\) 0.888652 0.0365234
\(593\) −8.19254 −0.336427 −0.168214 0.985751i \(-0.553800\pi\)
−0.168214 + 0.985751i \(0.553800\pi\)
\(594\) 1.00000 0.0410305
\(595\) 28.4938 1.16813
\(596\) 24.0818 0.986429
\(597\) 8.01638 0.328088
\(598\) 14.4578 0.591223
\(599\) 27.5630 1.12619 0.563096 0.826391i \(-0.309610\pi\)
0.563096 + 0.826391i \(0.309610\pi\)
\(600\) 3.32531 0.135755
\(601\) 7.77377 0.317099 0.158549 0.987351i \(-0.449318\pi\)
0.158549 + 0.987351i \(0.449318\pi\)
\(602\) −25.9595 −1.05803
\(603\) −0.148761 −0.00605802
\(604\) −17.0023 −0.691815
\(605\) −2.88536 −0.117307
\(606\) −3.16276 −0.128478
\(607\) 15.7812 0.640540 0.320270 0.947326i \(-0.396226\pi\)
0.320270 + 0.947326i \(0.396226\pi\)
\(608\) −5.75894 −0.233556
\(609\) 25.6839 1.04077
\(610\) 2.88536 0.116825
\(611\) 14.3334 0.579866
\(612\) 3.32958 0.134590
\(613\) 18.3830 0.742483 0.371241 0.928536i \(-0.378932\pi\)
0.371241 + 0.928536i \(0.378932\pi\)
\(614\) 6.17590 0.249239
\(615\) 23.6905 0.955294
\(616\) −2.96592 −0.119500
\(617\) 30.3423 1.22153 0.610767 0.791810i \(-0.290861\pi\)
0.610767 + 0.791810i \(0.290861\pi\)
\(618\) 7.25233 0.291731
\(619\) −24.7389 −0.994342 −0.497171 0.867653i \(-0.665628\pi\)
−0.497171 + 0.867653i \(0.665628\pi\)
\(620\) −18.3542 −0.737124
\(621\) 7.24652 0.290793
\(622\) −12.4464 −0.499054
\(623\) −12.5951 −0.504611
\(624\) 1.99514 0.0798694
\(625\) −30.5689 −1.22275
\(626\) 21.8357 0.872729
\(627\) −5.75894 −0.229990
\(628\) 13.7591 0.549049
\(629\) 2.95884 0.117977
\(630\) 8.55776 0.340949
\(631\) 3.17154 0.126257 0.0631286 0.998005i \(-0.479892\pi\)
0.0631286 + 0.998005i \(0.479892\pi\)
\(632\) 0.842774 0.0335238
\(633\) −9.63240 −0.382854
\(634\) −19.9615 −0.792771
\(635\) −45.5431 −1.80732
\(636\) 11.6265 0.461022
\(637\) 3.58466 0.142029
\(638\) −8.65968 −0.342840
\(639\) 10.1133 0.400074
\(640\) −2.88536 −0.114054
\(641\) 14.1212 0.557752 0.278876 0.960327i \(-0.410038\pi\)
0.278876 + 0.960327i \(0.410038\pi\)
\(642\) −15.9751 −0.630487
\(643\) −37.6992 −1.48671 −0.743355 0.668897i \(-0.766767\pi\)
−0.743355 + 0.668897i \(0.766767\pi\)
\(644\) −21.4926 −0.846927
\(645\) −25.2544 −0.994389
\(646\) −19.1748 −0.754424
\(647\) 6.23224 0.245015 0.122507 0.992468i \(-0.460907\pi\)
0.122507 + 0.992468i \(0.460907\pi\)
\(648\) 1.00000 0.0392837
\(649\) 4.60591 0.180798
\(650\) 6.63445 0.260225
\(651\) −18.8667 −0.739444
\(652\) −15.4511 −0.605113
\(653\) 50.1533 1.96265 0.981326 0.192352i \(-0.0616117\pi\)
0.981326 + 0.192352i \(0.0616117\pi\)
\(654\) −7.92043 −0.309713
\(655\) −21.4587 −0.838459
\(656\) −8.21059 −0.320570
\(657\) 13.1127 0.511574
\(658\) −21.3077 −0.830659
\(659\) −11.1019 −0.432469 −0.216234 0.976342i \(-0.569377\pi\)
−0.216234 + 0.976342i \(0.569377\pi\)
\(660\) −2.88536 −0.112313
\(661\) 42.8342 1.66606 0.833028 0.553231i \(-0.186605\pi\)
0.833028 + 0.553231i \(0.186605\pi\)
\(662\) −33.3076 −1.29454
\(663\) 6.64297 0.257992
\(664\) −2.03186 −0.0788514
\(665\) −49.2836 −1.91114
\(666\) 0.888652 0.0344346
\(667\) −62.7525 −2.42979
\(668\) 11.2006 0.433365
\(669\) 25.1499 0.972350
\(670\) 0.429230 0.0165826
\(671\) −1.00000 −0.0386046
\(672\) −2.96592 −0.114413
\(673\) −5.14234 −0.198223 −0.0991113 0.995076i \(-0.531600\pi\)
−0.0991113 + 0.995076i \(0.531600\pi\)
\(674\) −12.3478 −0.475619
\(675\) 3.32531 0.127991
\(676\) −9.01943 −0.346901
\(677\) 16.7004 0.641850 0.320925 0.947105i \(-0.396006\pi\)
0.320925 + 0.947105i \(0.396006\pi\)
\(678\) 9.60725 0.368964
\(679\) −46.8247 −1.79697
\(680\) −9.60705 −0.368413
\(681\) 12.8001 0.490502
\(682\) 6.36115 0.243581
\(683\) −35.9382 −1.37514 −0.687568 0.726120i \(-0.741322\pi\)
−0.687568 + 0.726120i \(0.741322\pi\)
\(684\) −5.75894 −0.220198
\(685\) 53.3771 2.03944
\(686\) 15.4326 0.589219
\(687\) 3.78489 0.144403
\(688\) 8.75258 0.333689
\(689\) 23.1966 0.883718
\(690\) −20.9088 −0.795985
\(691\) −20.4301 −0.777196 −0.388598 0.921407i \(-0.627041\pi\)
−0.388598 + 0.921407i \(0.627041\pi\)
\(692\) −11.0410 −0.419716
\(693\) −2.96592 −0.112666
\(694\) −9.35061 −0.354944
\(695\) −21.5881 −0.818885
\(696\) −8.65968 −0.328244
\(697\) −27.3378 −1.03549
\(698\) −17.6910 −0.669614
\(699\) 7.44585 0.281628
\(700\) −9.86262 −0.372772
\(701\) 1.91477 0.0723200 0.0361600 0.999346i \(-0.488487\pi\)
0.0361600 + 0.999346i \(0.488487\pi\)
\(702\) 1.99514 0.0753016
\(703\) −5.11769 −0.193017
\(704\) 1.00000 0.0376889
\(705\) −20.7289 −0.780695
\(706\) 0.997385 0.0375371
\(707\) 9.38049 0.352790
\(708\) 4.60591 0.173101
\(709\) 44.0106 1.65285 0.826427 0.563044i \(-0.190370\pi\)
0.826427 + 0.563044i \(0.190370\pi\)
\(710\) −29.1804 −1.09512
\(711\) 0.842774 0.0316065
\(712\) 4.24660 0.159148
\(713\) 46.0962 1.72632
\(714\) −9.87528 −0.369573
\(715\) −5.75669 −0.215288
\(716\) −25.0479 −0.936086
\(717\) −18.0695 −0.674819
\(718\) 13.6560 0.509639
\(719\) −1.88569 −0.0703244 −0.0351622 0.999382i \(-0.511195\pi\)
−0.0351622 + 0.999382i \(0.511195\pi\)
\(720\) −2.88536 −0.107531
\(721\) −21.5098 −0.801068
\(722\) 14.1653 0.527180
\(723\) 24.1062 0.896520
\(724\) 7.72044 0.286928
\(725\) −28.7961 −1.06946
\(726\) 1.00000 0.0371135
\(727\) 23.8893 0.886007 0.443003 0.896520i \(-0.353913\pi\)
0.443003 + 0.896520i \(0.353913\pi\)
\(728\) −5.91742 −0.219314
\(729\) 1.00000 0.0370370
\(730\) −37.8348 −1.40033
\(731\) 29.1424 1.07787
\(732\) −1.00000 −0.0369611
\(733\) 8.97824 0.331619 0.165809 0.986158i \(-0.446976\pi\)
0.165809 + 0.986158i \(0.446976\pi\)
\(734\) −25.9368 −0.957346
\(735\) −5.18412 −0.191219
\(736\) 7.24652 0.267110
\(737\) −0.148761 −0.00547968
\(738\) −8.21059 −0.302236
\(739\) −26.9515 −0.991426 −0.495713 0.868487i \(-0.665093\pi\)
−0.495713 + 0.868487i \(0.665093\pi\)
\(740\) −2.56408 −0.0942576
\(741\) −11.4899 −0.422091
\(742\) −34.4834 −1.26593
\(743\) 31.0780 1.14014 0.570070 0.821596i \(-0.306916\pi\)
0.570070 + 0.821596i \(0.306916\pi\)
\(744\) 6.36115 0.233211
\(745\) −69.4847 −2.54572
\(746\) 11.3492 0.415523
\(747\) −2.03186 −0.0743418
\(748\) 3.32958 0.121742
\(749\) 47.3809 1.73126
\(750\) 4.83208 0.176443
\(751\) 24.2425 0.884621 0.442311 0.896862i \(-0.354159\pi\)
0.442311 + 0.896862i \(0.354159\pi\)
\(752\) 7.18416 0.261979
\(753\) −24.3202 −0.886276
\(754\) −17.2772 −0.629200
\(755\) 49.0579 1.78540
\(756\) −2.96592 −0.107870
\(757\) 19.8834 0.722675 0.361337 0.932435i \(-0.382320\pi\)
0.361337 + 0.932435i \(0.382320\pi\)
\(758\) −15.4499 −0.561165
\(759\) 7.24652 0.263032
\(760\) 16.6166 0.602748
\(761\) 0.821022 0.0297620 0.0148810 0.999889i \(-0.495263\pi\)
0.0148810 + 0.999889i \(0.495263\pi\)
\(762\) 15.7842 0.571800
\(763\) 23.4914 0.850445
\(764\) 14.3131 0.517830
\(765\) −9.60705 −0.347343
\(766\) 10.7110 0.387004
\(767\) 9.18942 0.331811
\(768\) 1.00000 0.0360844
\(769\) 13.9751 0.503953 0.251977 0.967733i \(-0.418919\pi\)
0.251977 + 0.967733i \(0.418919\pi\)
\(770\) 8.55776 0.308400
\(771\) −24.7338 −0.890765
\(772\) 10.8554 0.390695
\(773\) −35.8935 −1.29100 −0.645500 0.763760i \(-0.723351\pi\)
−0.645500 + 0.763760i \(0.723351\pi\)
\(774\) 8.75258 0.314605
\(775\) 21.1528 0.759832
\(776\) 15.7876 0.566740
\(777\) −2.63567 −0.0945543
\(778\) 11.1350 0.399210
\(779\) 47.2843 1.69414
\(780\) −5.75669 −0.206123
\(781\) 10.1133 0.361881
\(782\) 24.1279 0.862811
\(783\) −8.65968 −0.309472
\(784\) 1.79670 0.0641677
\(785\) −39.7000 −1.41696
\(786\) 7.43708 0.265272
\(787\) −29.9454 −1.06744 −0.533718 0.845662i \(-0.679206\pi\)
−0.533718 + 0.845662i \(0.679206\pi\)
\(788\) −11.8718 −0.422914
\(789\) −14.5208 −0.516953
\(790\) −2.43171 −0.0865163
\(791\) −28.4944 −1.01314
\(792\) 1.00000 0.0355335
\(793\) −1.99514 −0.0708494
\(794\) 6.36784 0.225986
\(795\) −33.5468 −1.18978
\(796\) 8.01638 0.284133
\(797\) −35.1881 −1.24643 −0.623214 0.782051i \(-0.714173\pi\)
−0.623214 + 0.782051i \(0.714173\pi\)
\(798\) 17.0806 0.604645
\(799\) 23.9202 0.846237
\(800\) 3.32531 0.117568
\(801\) 4.24660 0.150046
\(802\) 11.5521 0.407918
\(803\) 13.1127 0.462736
\(804\) −0.148761 −0.00524640
\(805\) 62.0139 2.18570
\(806\) 12.6914 0.447035
\(807\) 20.0593 0.706120
\(808\) −3.16276 −0.111265
\(809\) 19.4803 0.684889 0.342445 0.939538i \(-0.388745\pi\)
0.342445 + 0.939538i \(0.388745\pi\)
\(810\) −2.88536 −0.101381
\(811\) 9.44906 0.331802 0.165901 0.986142i \(-0.446947\pi\)
0.165901 + 0.986142i \(0.446947\pi\)
\(812\) 25.6839 0.901329
\(813\) −20.2969 −0.711844
\(814\) 0.888652 0.0311473
\(815\) 44.5821 1.56164
\(816\) 3.32958 0.116559
\(817\) −50.4055 −1.76347
\(818\) −25.0051 −0.874282
\(819\) −5.91742 −0.206771
\(820\) 23.6905 0.827309
\(821\) 41.1035 1.43452 0.717261 0.696805i \(-0.245396\pi\)
0.717261 + 0.696805i \(0.245396\pi\)
\(822\) −18.4993 −0.645237
\(823\) 3.00428 0.104723 0.0523613 0.998628i \(-0.483325\pi\)
0.0523613 + 0.998628i \(0.483325\pi\)
\(824\) 7.25233 0.252647
\(825\) 3.32531 0.115773
\(826\) −13.6608 −0.475319
\(827\) −38.8510 −1.35098 −0.675491 0.737368i \(-0.736068\pi\)
−0.675491 + 0.737368i \(0.736068\pi\)
\(828\) 7.24652 0.251834
\(829\) −5.07419 −0.176234 −0.0881170 0.996110i \(-0.528085\pi\)
−0.0881170 + 0.996110i \(0.528085\pi\)
\(830\) 5.86265 0.203495
\(831\) 8.52674 0.295789
\(832\) 1.99514 0.0691689
\(833\) 5.98225 0.207273
\(834\) 7.48195 0.259079
\(835\) −32.3178 −1.11840
\(836\) −5.75894 −0.199177
\(837\) 6.36115 0.219874
\(838\) −38.6289 −1.33441
\(839\) −15.5199 −0.535806 −0.267903 0.963446i \(-0.586331\pi\)
−0.267903 + 0.963446i \(0.586331\pi\)
\(840\) 8.55776 0.295271
\(841\) 45.9900 1.58586
\(842\) −30.2729 −1.04327
\(843\) −26.5966 −0.916037
\(844\) −9.63240 −0.331561
\(845\) 26.0243 0.895263
\(846\) 7.18416 0.246996
\(847\) −2.96592 −0.101910
\(848\) 11.6265 0.399257
\(849\) 32.5170 1.11598
\(850\) 11.0719 0.379763
\(851\) 6.43963 0.220748
\(852\) 10.1133 0.346475
\(853\) 47.1609 1.61476 0.807379 0.590033i \(-0.200885\pi\)
0.807379 + 0.590033i \(0.200885\pi\)
\(854\) 2.96592 0.101492
\(855\) 16.6166 0.568276
\(856\) −15.9751 −0.546018
\(857\) 24.2134 0.827115 0.413557 0.910478i \(-0.364286\pi\)
0.413557 + 0.910478i \(0.364286\pi\)
\(858\) 1.99514 0.0681129
\(859\) −30.9536 −1.05612 −0.528061 0.849206i \(-0.677081\pi\)
−0.528061 + 0.849206i \(0.677081\pi\)
\(860\) −25.2544 −0.861166
\(861\) 24.3520 0.829913
\(862\) 15.8946 0.541372
\(863\) −38.2083 −1.30063 −0.650313 0.759666i \(-0.725362\pi\)
−0.650313 + 0.759666i \(0.725362\pi\)
\(864\) 1.00000 0.0340207
\(865\) 31.8573 1.08318
\(866\) 15.3948 0.523136
\(867\) −5.91389 −0.200846
\(868\) −18.8667 −0.640377
\(869\) 0.842774 0.0285892
\(870\) 24.9863 0.847115
\(871\) −0.296799 −0.0100566
\(872\) −7.92043 −0.268220
\(873\) 15.7876 0.534328
\(874\) −41.7322 −1.41161
\(875\) −14.3316 −0.484496
\(876\) 13.1127 0.443036
\(877\) 42.3533 1.43017 0.715085 0.699037i \(-0.246388\pi\)
0.715085 + 0.699037i \(0.246388\pi\)
\(878\) 27.8185 0.938829
\(879\) −33.9091 −1.14373
\(880\) −2.88536 −0.0972655
\(881\) 6.97035 0.234837 0.117419 0.993083i \(-0.462538\pi\)
0.117419 + 0.993083i \(0.462538\pi\)
\(882\) 1.79670 0.0604979
\(883\) 45.1815 1.52048 0.760239 0.649643i \(-0.225082\pi\)
0.760239 + 0.649643i \(0.225082\pi\)
\(884\) 6.64297 0.223427
\(885\) −13.2897 −0.446729
\(886\) 25.2358 0.847812
\(887\) −14.6704 −0.492585 −0.246292 0.969196i \(-0.579212\pi\)
−0.246292 + 0.969196i \(0.579212\pi\)
\(888\) 0.888652 0.0298212
\(889\) −46.8147 −1.57011
\(890\) −12.2530 −0.410720
\(891\) 1.00000 0.0335013
\(892\) 25.1499 0.842080
\(893\) −41.3731 −1.38450
\(894\) 24.0818 0.805416
\(895\) 72.2724 2.41580
\(896\) −2.96592 −0.0990845
\(897\) 14.4578 0.482732
\(898\) −39.0786 −1.30407
\(899\) −55.0855 −1.83721
\(900\) 3.32531 0.110844
\(901\) 38.7115 1.28967
\(902\) −8.21059 −0.273383
\(903\) −25.9595 −0.863877
\(904\) 9.60725 0.319533
\(905\) −22.2763 −0.740488
\(906\) −17.0023 −0.564864
\(907\) 4.43750 0.147345 0.0736725 0.997282i \(-0.476528\pi\)
0.0736725 + 0.997282i \(0.476528\pi\)
\(908\) 12.8001 0.424787
\(909\) −3.16276 −0.104902
\(910\) 17.0739 0.565994
\(911\) −34.3335 −1.13752 −0.568759 0.822504i \(-0.692576\pi\)
−0.568759 + 0.822504i \(0.692576\pi\)
\(912\) −5.75894 −0.190697
\(913\) −2.03186 −0.0672447
\(914\) 34.4683 1.14011
\(915\) 2.88536 0.0953871
\(916\) 3.78489 0.125056
\(917\) −22.0578 −0.728413
\(918\) 3.32958 0.109893
\(919\) −35.7346 −1.17878 −0.589388 0.807850i \(-0.700631\pi\)
−0.589388 + 0.807850i \(0.700631\pi\)
\(920\) −20.9088 −0.689343
\(921\) 6.17590 0.203503
\(922\) 31.0021 1.02100
\(923\) 20.1773 0.664145
\(924\) −2.96592 −0.0975717
\(925\) 2.95505 0.0971613
\(926\) −18.5190 −0.608571
\(927\) 7.25233 0.238198
\(928\) −8.65968 −0.284268
\(929\) 22.1124 0.725486 0.362743 0.931889i \(-0.381840\pi\)
0.362743 + 0.931889i \(0.381840\pi\)
\(930\) −18.3542 −0.601859
\(931\) −10.3471 −0.339111
\(932\) 7.44585 0.243897
\(933\) −12.4464 −0.407476
\(934\) 2.19750 0.0719043
\(935\) −9.60705 −0.314184
\(936\) 1.99514 0.0652131
\(937\) 16.3301 0.533481 0.266741 0.963768i \(-0.414053\pi\)
0.266741 + 0.963768i \(0.414053\pi\)
\(938\) 0.441214 0.0144061
\(939\) 21.8357 0.712580
\(940\) −20.7289 −0.676102
\(941\) −12.0909 −0.394151 −0.197075 0.980388i \(-0.563144\pi\)
−0.197075 + 0.980388i \(0.563144\pi\)
\(942\) 13.7591 0.448296
\(943\) −59.4982 −1.93753
\(944\) 4.60591 0.149909
\(945\) 8.55776 0.278384
\(946\) 8.75258 0.284571
\(947\) 45.4711 1.47761 0.738806 0.673918i \(-0.235390\pi\)
0.738806 + 0.673918i \(0.235390\pi\)
\(948\) 0.842774 0.0273720
\(949\) 26.1616 0.849240
\(950\) −19.1503 −0.621317
\(951\) −19.9615 −0.647295
\(952\) −9.87528 −0.320060
\(953\) −21.3656 −0.692100 −0.346050 0.938216i \(-0.612477\pi\)
−0.346050 + 0.938216i \(0.612477\pi\)
\(954\) 11.6265 0.376423
\(955\) −41.2985 −1.33639
\(956\) −18.0695 −0.584411
\(957\) −8.65968 −0.279928
\(958\) −25.6028 −0.827190
\(959\) 54.8675 1.77176
\(960\) −2.88536 −0.0931246
\(961\) 9.46429 0.305300
\(962\) 1.77298 0.0571633
\(963\) −15.9751 −0.514790
\(964\) 24.1062 0.776409
\(965\) −31.3218 −1.00828
\(966\) −21.4926 −0.691513
\(967\) −39.2761 −1.26303 −0.631517 0.775362i \(-0.717568\pi\)
−0.631517 + 0.775362i \(0.717568\pi\)
\(968\) 1.00000 0.0321412
\(969\) −19.1748 −0.615985
\(970\) −45.5528 −1.46261
\(971\) 41.0843 1.31846 0.659229 0.751942i \(-0.270883\pi\)
0.659229 + 0.751942i \(0.270883\pi\)
\(972\) 1.00000 0.0320750
\(973\) −22.1909 −0.711408
\(974\) 2.27931 0.0730338
\(975\) 6.63445 0.212473
\(976\) −1.00000 −0.0320092
\(977\) 35.6970 1.14205 0.571023 0.820934i \(-0.306547\pi\)
0.571023 + 0.820934i \(0.306547\pi\)
\(978\) −15.4511 −0.494073
\(979\) 4.24660 0.135722
\(980\) −5.18412 −0.165601
\(981\) −7.92043 −0.252880
\(982\) −22.6588 −0.723072
\(983\) −41.0849 −1.31041 −0.655203 0.755453i \(-0.727417\pi\)
−0.655203 + 0.755453i \(0.727417\pi\)
\(984\) −8.21059 −0.261744
\(985\) 34.2543 1.09143
\(986\) −28.8331 −0.918233
\(987\) −21.3077 −0.678230
\(988\) −11.4899 −0.365541
\(989\) 63.4257 2.01682
\(990\) −2.88536 −0.0917028
\(991\) 25.4687 0.809039 0.404519 0.914529i \(-0.367439\pi\)
0.404519 + 0.914529i \(0.367439\pi\)
\(992\) 6.36115 0.201967
\(993\) −33.3076 −1.05699
\(994\) −29.9951 −0.951388
\(995\) −23.1301 −0.733275
\(996\) −2.03186 −0.0643819
\(997\) 28.4319 0.900448 0.450224 0.892916i \(-0.351344\pi\)
0.450224 + 0.892916i \(0.351344\pi\)
\(998\) 44.3558 1.40406
\(999\) 0.888652 0.0281157
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 \(a_p\))