Properties

Label 8042.2.a.a.1.13
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.16681 q^{3}\) \(+1.00000 q^{4}\) \(-2.63325 q^{5}\) \(-2.16681 q^{6}\) \(-3.58663 q^{7}\) \(+1.00000 q^{8}\) \(+1.69508 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.16681 q^{3}\) \(+1.00000 q^{4}\) \(-2.63325 q^{5}\) \(-2.16681 q^{6}\) \(-3.58663 q^{7}\) \(+1.00000 q^{8}\) \(+1.69508 q^{9}\) \(-2.63325 q^{10}\) \(-2.72032 q^{11}\) \(-2.16681 q^{12}\) \(-3.55957 q^{13}\) \(-3.58663 q^{14}\) \(+5.70576 q^{15}\) \(+1.00000 q^{16}\) \(+5.45332 q^{17}\) \(+1.69508 q^{18}\) \(+0.879136 q^{19}\) \(-2.63325 q^{20}\) \(+7.77156 q^{21}\) \(-2.72032 q^{22}\) \(+8.64820 q^{23}\) \(-2.16681 q^{24}\) \(+1.93400 q^{25}\) \(-3.55957 q^{26}\) \(+2.82751 q^{27}\) \(-3.58663 q^{28}\) \(-4.56127 q^{29}\) \(+5.70576 q^{30}\) \(-8.85929 q^{31}\) \(+1.00000 q^{32}\) \(+5.89442 q^{33}\) \(+5.45332 q^{34}\) \(+9.44449 q^{35}\) \(+1.69508 q^{36}\) \(+7.07454 q^{37}\) \(+0.879136 q^{38}\) \(+7.71294 q^{39}\) \(-2.63325 q^{40}\) \(-4.17143 q^{41}\) \(+7.77156 q^{42}\) \(+11.3694 q^{43}\) \(-2.72032 q^{44}\) \(-4.46358 q^{45}\) \(+8.64820 q^{46}\) \(+12.6680 q^{47}\) \(-2.16681 q^{48}\) \(+5.86390 q^{49}\) \(+1.93400 q^{50}\) \(-11.8163 q^{51}\) \(-3.55957 q^{52}\) \(-6.00130 q^{53}\) \(+2.82751 q^{54}\) \(+7.16328 q^{55}\) \(-3.58663 q^{56}\) \(-1.90492 q^{57}\) \(-4.56127 q^{58}\) \(+1.97871 q^{59}\) \(+5.70576 q^{60}\) \(+10.4498 q^{61}\) \(-8.85929 q^{62}\) \(-6.07964 q^{63}\) \(+1.00000 q^{64}\) \(+9.37325 q^{65}\) \(+5.89442 q^{66}\) \(-12.7025 q^{67}\) \(+5.45332 q^{68}\) \(-18.7390 q^{69}\) \(+9.44449 q^{70}\) \(-13.1015 q^{71}\) \(+1.69508 q^{72}\) \(+16.9049 q^{73}\) \(+7.07454 q^{74}\) \(-4.19063 q^{75}\) \(+0.879136 q^{76}\) \(+9.75677 q^{77}\) \(+7.71294 q^{78}\) \(+2.73471 q^{79}\) \(-2.63325 q^{80}\) \(-11.2119 q^{81}\) \(-4.17143 q^{82}\) \(+2.17661 q^{83}\) \(+7.77156 q^{84}\) \(-14.3599 q^{85}\) \(+11.3694 q^{86}\) \(+9.88343 q^{87}\) \(-2.72032 q^{88}\) \(-15.5102 q^{89}\) \(-4.46358 q^{90}\) \(+12.7669 q^{91}\) \(+8.64820 q^{92}\) \(+19.1964 q^{93}\) \(+12.6680 q^{94}\) \(-2.31499 q^{95}\) \(-2.16681 q^{96}\) \(+0.589255 q^{97}\) \(+5.86390 q^{98}\) \(-4.61117 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.16681 −1.25101 −0.625505 0.780220i \(-0.715107\pi\)
−0.625505 + 0.780220i \(0.715107\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.63325 −1.17763 −0.588813 0.808270i \(-0.700404\pi\)
−0.588813 + 0.808270i \(0.700404\pi\)
\(6\) −2.16681 −0.884598
\(7\) −3.58663 −1.35562 −0.677809 0.735238i \(-0.737070\pi\)
−0.677809 + 0.735238i \(0.737070\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.69508 0.565028
\(10\) −2.63325 −0.832707
\(11\) −2.72032 −0.820207 −0.410103 0.912039i \(-0.634507\pi\)
−0.410103 + 0.912039i \(0.634507\pi\)
\(12\) −2.16681 −0.625505
\(13\) −3.55957 −0.987248 −0.493624 0.869675i \(-0.664328\pi\)
−0.493624 + 0.869675i \(0.664328\pi\)
\(14\) −3.58663 −0.958567
\(15\) 5.70576 1.47322
\(16\) 1.00000 0.250000
\(17\) 5.45332 1.32262 0.661312 0.750111i \(-0.270000\pi\)
0.661312 + 0.750111i \(0.270000\pi\)
\(18\) 1.69508 0.399535
\(19\) 0.879136 0.201688 0.100844 0.994902i \(-0.467846\pi\)
0.100844 + 0.994902i \(0.467846\pi\)
\(20\) −2.63325 −0.588813
\(21\) 7.77156 1.69589
\(22\) −2.72032 −0.579974
\(23\) 8.64820 1.80327 0.901637 0.432493i \(-0.142366\pi\)
0.901637 + 0.432493i \(0.142366\pi\)
\(24\) −2.16681 −0.442299
\(25\) 1.93400 0.386801
\(26\) −3.55957 −0.698090
\(27\) 2.82751 0.544155
\(28\) −3.58663 −0.677809
\(29\) −4.56127 −0.847007 −0.423504 0.905894i \(-0.639200\pi\)
−0.423504 + 0.905894i \(0.639200\pi\)
\(30\) 5.70576 1.04173
\(31\) −8.85929 −1.59118 −0.795588 0.605838i \(-0.792838\pi\)
−0.795588 + 0.605838i \(0.792838\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.89442 1.02609
\(34\) 5.45332 0.935236
\(35\) 9.44449 1.59641
\(36\) 1.69508 0.282514
\(37\) 7.07454 1.16305 0.581523 0.813530i \(-0.302457\pi\)
0.581523 + 0.813530i \(0.302457\pi\)
\(38\) 0.879136 0.142615
\(39\) 7.71294 1.23506
\(40\) −2.63325 −0.416353
\(41\) −4.17143 −0.651467 −0.325734 0.945462i \(-0.605611\pi\)
−0.325734 + 0.945462i \(0.605611\pi\)
\(42\) 7.77156 1.19918
\(43\) 11.3694 1.73382 0.866910 0.498465i \(-0.166103\pi\)
0.866910 + 0.498465i \(0.166103\pi\)
\(44\) −2.72032 −0.410103
\(45\) −4.46358 −0.665391
\(46\) 8.64820 1.27511
\(47\) 12.6680 1.84782 0.923910 0.382610i \(-0.124975\pi\)
0.923910 + 0.382610i \(0.124975\pi\)
\(48\) −2.16681 −0.312753
\(49\) 5.86390 0.837700
\(50\) 1.93400 0.273510
\(51\) −11.8163 −1.65462
\(52\) −3.55957 −0.493624
\(53\) −6.00130 −0.824342 −0.412171 0.911106i \(-0.635229\pi\)
−0.412171 + 0.911106i \(0.635229\pi\)
\(54\) 2.82751 0.384776
\(55\) 7.16328 0.965896
\(56\) −3.58663 −0.479283
\(57\) −1.90492 −0.252313
\(58\) −4.56127 −0.598924
\(59\) 1.97871 0.257606 0.128803 0.991670i \(-0.458887\pi\)
0.128803 + 0.991670i \(0.458887\pi\)
\(60\) 5.70576 0.736611
\(61\) 10.4498 1.33796 0.668979 0.743281i \(-0.266731\pi\)
0.668979 + 0.743281i \(0.266731\pi\)
\(62\) −8.85929 −1.12513
\(63\) −6.07964 −0.765962
\(64\) 1.00000 0.125000
\(65\) 9.37325 1.16261
\(66\) 5.89442 0.725553
\(67\) −12.7025 −1.55185 −0.775927 0.630823i \(-0.782717\pi\)
−0.775927 + 0.630823i \(0.782717\pi\)
\(68\) 5.45332 0.661312
\(69\) −18.7390 −2.25592
\(70\) 9.44449 1.12883
\(71\) −13.1015 −1.55486 −0.777430 0.628970i \(-0.783477\pi\)
−0.777430 + 0.628970i \(0.783477\pi\)
\(72\) 1.69508 0.199768
\(73\) 16.9049 1.97857 0.989283 0.146014i \(-0.0466443\pi\)
0.989283 + 0.146014i \(0.0466443\pi\)
\(74\) 7.07454 0.822398
\(75\) −4.19063 −0.483892
\(76\) 0.879136 0.100844
\(77\) 9.75677 1.11189
\(78\) 7.71294 0.873318
\(79\) 2.73471 0.307679 0.153840 0.988096i \(-0.450836\pi\)
0.153840 + 0.988096i \(0.450836\pi\)
\(80\) −2.63325 −0.294406
\(81\) −11.2119 −1.24577
\(82\) −4.17143 −0.460657
\(83\) 2.17661 0.238914 0.119457 0.992839i \(-0.461885\pi\)
0.119457 + 0.992839i \(0.461885\pi\)
\(84\) 7.77156 0.847946
\(85\) −14.3599 −1.55756
\(86\) 11.3694 1.22600
\(87\) 9.88343 1.05961
\(88\) −2.72032 −0.289987
\(89\) −15.5102 −1.64408 −0.822039 0.569431i \(-0.807163\pi\)
−0.822039 + 0.569431i \(0.807163\pi\)
\(90\) −4.46358 −0.470503
\(91\) 12.7669 1.33833
\(92\) 8.64820 0.901637
\(93\) 19.1964 1.99058
\(94\) 12.6680 1.30661
\(95\) −2.31499 −0.237512
\(96\) −2.16681 −0.221150
\(97\) 0.589255 0.0598298 0.0299149 0.999552i \(-0.490476\pi\)
0.0299149 + 0.999552i \(0.490476\pi\)
\(98\) 5.86390 0.592344
\(99\) −4.61117 −0.463440
\(100\) 1.93400 0.193400
\(101\) 8.04875 0.800881 0.400440 0.916323i \(-0.368857\pi\)
0.400440 + 0.916323i \(0.368857\pi\)
\(102\) −11.8163 −1.16999
\(103\) −13.3113 −1.31161 −0.655803 0.754932i \(-0.727670\pi\)
−0.655803 + 0.754932i \(0.727670\pi\)
\(104\) −3.55957 −0.349045
\(105\) −20.4645 −1.99713
\(106\) −6.00130 −0.582898
\(107\) −1.22465 −0.118392 −0.0591958 0.998246i \(-0.518854\pi\)
−0.0591958 + 0.998246i \(0.518854\pi\)
\(108\) 2.82751 0.272077
\(109\) 13.1327 1.25789 0.628945 0.777450i \(-0.283487\pi\)
0.628945 + 0.777450i \(0.283487\pi\)
\(110\) 7.16328 0.682992
\(111\) −15.3292 −1.45498
\(112\) −3.58663 −0.338905
\(113\) 4.94615 0.465295 0.232647 0.972561i \(-0.425261\pi\)
0.232647 + 0.972561i \(0.425261\pi\)
\(114\) −1.90492 −0.178413
\(115\) −22.7729 −2.12358
\(116\) −4.56127 −0.423504
\(117\) −6.03378 −0.557823
\(118\) 1.97871 0.182155
\(119\) −19.5590 −1.79297
\(120\) 5.70576 0.520863
\(121\) −3.59987 −0.327261
\(122\) 10.4498 0.946080
\(123\) 9.03870 0.814992
\(124\) −8.85929 −0.795588
\(125\) 8.07353 0.722119
\(126\) −6.07964 −0.541617
\(127\) −1.61198 −0.143040 −0.0715202 0.997439i \(-0.522785\pi\)
−0.0715202 + 0.997439i \(0.522785\pi\)
\(128\) 1.00000 0.0883883
\(129\) −24.6354 −2.16903
\(130\) 9.37325 0.822088
\(131\) 14.6187 1.27724 0.638622 0.769521i \(-0.279505\pi\)
0.638622 + 0.769521i \(0.279505\pi\)
\(132\) 5.89442 0.513044
\(133\) −3.15314 −0.273411
\(134\) −12.7025 −1.09733
\(135\) −7.44554 −0.640810
\(136\) 5.45332 0.467618
\(137\) −12.8442 −1.09736 −0.548678 0.836034i \(-0.684869\pi\)
−0.548678 + 0.836034i \(0.684869\pi\)
\(138\) −18.7390 −1.59517
\(139\) 18.5575 1.57403 0.787014 0.616935i \(-0.211626\pi\)
0.787014 + 0.616935i \(0.211626\pi\)
\(140\) 9.44449 0.798205
\(141\) −27.4492 −2.31164
\(142\) −13.1015 −1.09945
\(143\) 9.68318 0.809748
\(144\) 1.69508 0.141257
\(145\) 12.0110 0.997457
\(146\) 16.9049 1.39906
\(147\) −12.7060 −1.04797
\(148\) 7.07454 0.581523
\(149\) −19.4969 −1.59725 −0.798624 0.601830i \(-0.794439\pi\)
−0.798624 + 0.601830i \(0.794439\pi\)
\(150\) −4.19063 −0.342163
\(151\) −12.6917 −1.03284 −0.516419 0.856336i \(-0.672735\pi\)
−0.516419 + 0.856336i \(0.672735\pi\)
\(152\) 0.879136 0.0713074
\(153\) 9.24383 0.747319
\(154\) 9.75677 0.786223
\(155\) 23.3287 1.87381
\(156\) 7.71294 0.617529
\(157\) −8.38080 −0.668861 −0.334430 0.942420i \(-0.608544\pi\)
−0.334430 + 0.942420i \(0.608544\pi\)
\(158\) 2.73471 0.217562
\(159\) 13.0037 1.03126
\(160\) −2.63325 −0.208177
\(161\) −31.0179 −2.44455
\(162\) −11.2119 −0.880893
\(163\) −16.7291 −1.31033 −0.655163 0.755488i \(-0.727400\pi\)
−0.655163 + 0.755488i \(0.727400\pi\)
\(164\) −4.17143 −0.325734
\(165\) −15.5215 −1.20835
\(166\) 2.17661 0.168938
\(167\) −13.3770 −1.03514 −0.517571 0.855640i \(-0.673164\pi\)
−0.517571 + 0.855640i \(0.673164\pi\)
\(168\) 7.77156 0.599589
\(169\) −0.329429 −0.0253407
\(170\) −14.3599 −1.10136
\(171\) 1.49021 0.113959
\(172\) 11.3694 0.866910
\(173\) 14.9931 1.13991 0.569953 0.821677i \(-0.306961\pi\)
0.569953 + 0.821677i \(0.306961\pi\)
\(174\) 9.88343 0.749261
\(175\) −6.93656 −0.524354
\(176\) −2.72032 −0.205052
\(177\) −4.28749 −0.322267
\(178\) −15.5102 −1.16254
\(179\) 12.2441 0.915166 0.457583 0.889167i \(-0.348715\pi\)
0.457583 + 0.889167i \(0.348715\pi\)
\(180\) −4.46358 −0.332696
\(181\) 7.19185 0.534566 0.267283 0.963618i \(-0.413874\pi\)
0.267283 + 0.963618i \(0.413874\pi\)
\(182\) 12.7669 0.946343
\(183\) −22.6428 −1.67380
\(184\) 8.64820 0.637554
\(185\) −18.6290 −1.36963
\(186\) 19.1964 1.40755
\(187\) −14.8348 −1.08483
\(188\) 12.6680 0.923910
\(189\) −10.1412 −0.737666
\(190\) −2.31499 −0.167947
\(191\) 11.1634 0.807753 0.403876 0.914814i \(-0.367663\pi\)
0.403876 + 0.914814i \(0.367663\pi\)
\(192\) −2.16681 −0.156376
\(193\) −0.336046 −0.0241891 −0.0120946 0.999927i \(-0.503850\pi\)
−0.0120946 + 0.999927i \(0.503850\pi\)
\(194\) 0.589255 0.0423061
\(195\) −20.3101 −1.45444
\(196\) 5.86390 0.418850
\(197\) −9.84975 −0.701766 −0.350883 0.936419i \(-0.614118\pi\)
−0.350883 + 0.936419i \(0.614118\pi\)
\(198\) −4.61117 −0.327701
\(199\) −7.70799 −0.546405 −0.273203 0.961957i \(-0.588083\pi\)
−0.273203 + 0.961957i \(0.588083\pi\)
\(200\) 1.93400 0.136755
\(201\) 27.5239 1.94139
\(202\) 8.04875 0.566308
\(203\) 16.3596 1.14822
\(204\) −11.8163 −0.827308
\(205\) 10.9844 0.767184
\(206\) −13.3113 −0.927446
\(207\) 14.6594 1.01890
\(208\) −3.55957 −0.246812
\(209\) −2.39153 −0.165426
\(210\) −20.4645 −1.41218
\(211\) 9.70765 0.668302 0.334151 0.942520i \(-0.391550\pi\)
0.334151 + 0.942520i \(0.391550\pi\)
\(212\) −6.00130 −0.412171
\(213\) 28.3885 1.94515
\(214\) −1.22465 −0.0837156
\(215\) −29.9385 −2.04179
\(216\) 2.82751 0.192388
\(217\) 31.7750 2.15703
\(218\) 13.1327 0.889462
\(219\) −36.6297 −2.47521
\(220\) 7.16328 0.482948
\(221\) −19.4115 −1.30576
\(222\) −15.3292 −1.02883
\(223\) 21.4091 1.43366 0.716831 0.697247i \(-0.245592\pi\)
0.716831 + 0.697247i \(0.245592\pi\)
\(224\) −3.58663 −0.239642
\(225\) 3.27830 0.218553
\(226\) 4.94615 0.329013
\(227\) 9.09940 0.603949 0.301974 0.953316i \(-0.402354\pi\)
0.301974 + 0.953316i \(0.402354\pi\)
\(228\) −1.90492 −0.126157
\(229\) 18.3060 1.20970 0.604848 0.796341i \(-0.293234\pi\)
0.604848 + 0.796341i \(0.293234\pi\)
\(230\) −22.7729 −1.50160
\(231\) −21.1411 −1.39098
\(232\) −4.56127 −0.299462
\(233\) −14.2533 −0.933766 −0.466883 0.884319i \(-0.654623\pi\)
−0.466883 + 0.884319i \(0.654623\pi\)
\(234\) −6.03378 −0.394440
\(235\) −33.3580 −2.17604
\(236\) 1.97871 0.128803
\(237\) −5.92561 −0.384910
\(238\) −19.5590 −1.26782
\(239\) 13.6487 0.882858 0.441429 0.897296i \(-0.354472\pi\)
0.441429 + 0.897296i \(0.354472\pi\)
\(240\) 5.70576 0.368305
\(241\) −11.2223 −0.722890 −0.361445 0.932393i \(-0.617716\pi\)
−0.361445 + 0.932393i \(0.617716\pi\)
\(242\) −3.59987 −0.231408
\(243\) 15.8117 1.01432
\(244\) 10.4498 0.668979
\(245\) −15.4411 −0.986497
\(246\) 9.03870 0.576287
\(247\) −3.12935 −0.199116
\(248\) −8.85929 −0.562566
\(249\) −4.71631 −0.298884
\(250\) 8.07353 0.510615
\(251\) −0.508330 −0.0320855 −0.0160427 0.999871i \(-0.505107\pi\)
−0.0160427 + 0.999871i \(0.505107\pi\)
\(252\) −6.07964 −0.382981
\(253\) −23.5259 −1.47906
\(254\) −1.61198 −0.101145
\(255\) 31.1153 1.94852
\(256\) 1.00000 0.0625000
\(257\) −14.1431 −0.882221 −0.441110 0.897453i \(-0.645415\pi\)
−0.441110 + 0.897453i \(0.645415\pi\)
\(258\) −24.6354 −1.53373
\(259\) −25.3737 −1.57665
\(260\) 9.37325 0.581304
\(261\) −7.73174 −0.478583
\(262\) 14.6187 0.903148
\(263\) −23.3660 −1.44081 −0.720405 0.693553i \(-0.756044\pi\)
−0.720405 + 0.693553i \(0.756044\pi\)
\(264\) 5.89442 0.362777
\(265\) 15.8029 0.970766
\(266\) −3.15314 −0.193331
\(267\) 33.6077 2.05676
\(268\) −12.7025 −0.775927
\(269\) −20.8768 −1.27288 −0.636439 0.771327i \(-0.719593\pi\)
−0.636439 + 0.771327i \(0.719593\pi\)
\(270\) −7.44554 −0.453121
\(271\) 9.58159 0.582040 0.291020 0.956717i \(-0.406005\pi\)
0.291020 + 0.956717i \(0.406005\pi\)
\(272\) 5.45332 0.330656
\(273\) −27.6634 −1.67427
\(274\) −12.8442 −0.775948
\(275\) −5.26111 −0.317257
\(276\) −18.7390 −1.12796
\(277\) −25.4950 −1.53185 −0.765923 0.642933i \(-0.777717\pi\)
−0.765923 + 0.642933i \(0.777717\pi\)
\(278\) 18.5575 1.11301
\(279\) −15.0172 −0.899059
\(280\) 9.44449 0.564416
\(281\) −12.9909 −0.774974 −0.387487 0.921875i \(-0.626657\pi\)
−0.387487 + 0.921875i \(0.626657\pi\)
\(282\) −27.4492 −1.63458
\(283\) −28.8328 −1.71393 −0.856967 0.515371i \(-0.827654\pi\)
−0.856967 + 0.515371i \(0.827654\pi\)
\(284\) −13.1015 −0.777430
\(285\) 5.01614 0.297131
\(286\) 9.68318 0.572578
\(287\) 14.9614 0.883141
\(288\) 1.69508 0.0998838
\(289\) 12.7387 0.749334
\(290\) 12.0110 0.705308
\(291\) −1.27681 −0.0748477
\(292\) 16.9049 0.989283
\(293\) 4.93012 0.288021 0.144010 0.989576i \(-0.454000\pi\)
0.144010 + 0.989576i \(0.454000\pi\)
\(294\) −12.7060 −0.741028
\(295\) −5.21043 −0.303363
\(296\) 7.07454 0.411199
\(297\) −7.69173 −0.446319
\(298\) −19.4969 −1.12943
\(299\) −30.7839 −1.78028
\(300\) −4.19063 −0.241946
\(301\) −40.7779 −2.35040
\(302\) −12.6917 −0.730327
\(303\) −17.4402 −1.00191
\(304\) 0.879136 0.0504219
\(305\) −27.5169 −1.57561
\(306\) 9.24383 0.528435
\(307\) 17.8898 1.02103 0.510513 0.859870i \(-0.329456\pi\)
0.510513 + 0.859870i \(0.329456\pi\)
\(308\) 9.75677 0.555944
\(309\) 28.8432 1.64083
\(310\) 23.3287 1.32498
\(311\) −20.9486 −1.18789 −0.593944 0.804506i \(-0.702430\pi\)
−0.593944 + 0.804506i \(0.702430\pi\)
\(312\) 7.71294 0.436659
\(313\) 3.40369 0.192388 0.0961940 0.995363i \(-0.469333\pi\)
0.0961940 + 0.995363i \(0.469333\pi\)
\(314\) −8.38080 −0.472956
\(315\) 16.0092 0.902016
\(316\) 2.73471 0.153840
\(317\) 5.01900 0.281895 0.140948 0.990017i \(-0.454985\pi\)
0.140948 + 0.990017i \(0.454985\pi\)
\(318\) 13.0037 0.729212
\(319\) 12.4081 0.694721
\(320\) −2.63325 −0.147203
\(321\) 2.65360 0.148109
\(322\) −31.0179 −1.72856
\(323\) 4.79421 0.266757
\(324\) −11.2119 −0.622886
\(325\) −6.88423 −0.381869
\(326\) −16.7291 −0.926540
\(327\) −28.4562 −1.57363
\(328\) −4.17143 −0.230328
\(329\) −45.4355 −2.50494
\(330\) −15.5215 −0.854430
\(331\) −1.55646 −0.0855508 −0.0427754 0.999085i \(-0.513620\pi\)
−0.0427754 + 0.999085i \(0.513620\pi\)
\(332\) 2.17661 0.119457
\(333\) 11.9919 0.657154
\(334\) −13.3770 −0.731956
\(335\) 33.4488 1.82750
\(336\) 7.77156 0.423973
\(337\) 20.5517 1.11952 0.559760 0.828655i \(-0.310893\pi\)
0.559760 + 0.828655i \(0.310893\pi\)
\(338\) −0.329429 −0.0179186
\(339\) −10.7174 −0.582089
\(340\) −14.3599 −0.778778
\(341\) 24.1001 1.30509
\(342\) 1.49021 0.0805813
\(343\) 4.07476 0.220016
\(344\) 11.3694 0.612998
\(345\) 49.3446 2.65662
\(346\) 14.9931 0.806035
\(347\) 28.3800 1.52352 0.761759 0.647861i \(-0.224336\pi\)
0.761759 + 0.647861i \(0.224336\pi\)
\(348\) 9.88343 0.529807
\(349\) 18.7188 1.00199 0.500997 0.865449i \(-0.332967\pi\)
0.500997 + 0.865449i \(0.332967\pi\)
\(350\) −6.93656 −0.370774
\(351\) −10.0647 −0.537216
\(352\) −2.72032 −0.144993
\(353\) −23.9757 −1.27610 −0.638048 0.769996i \(-0.720258\pi\)
−0.638048 + 0.769996i \(0.720258\pi\)
\(354\) −4.28749 −0.227877
\(355\) 34.4995 1.83104
\(356\) −15.5102 −0.822039
\(357\) 42.3808 2.24303
\(358\) 12.2441 0.647120
\(359\) 9.36182 0.494098 0.247049 0.969003i \(-0.420539\pi\)
0.247049 + 0.969003i \(0.420539\pi\)
\(360\) −4.46358 −0.235251
\(361\) −18.2271 −0.959322
\(362\) 7.19185 0.377995
\(363\) 7.80025 0.409407
\(364\) 12.7669 0.669166
\(365\) −44.5147 −2.33001
\(366\) −22.6428 −1.18356
\(367\) −1.58772 −0.0828782 −0.0414391 0.999141i \(-0.513194\pi\)
−0.0414391 + 0.999141i \(0.513194\pi\)
\(368\) 8.64820 0.450819
\(369\) −7.07091 −0.368097
\(370\) −18.6290 −0.968477
\(371\) 21.5244 1.11749
\(372\) 19.1964 0.995289
\(373\) −35.4264 −1.83431 −0.917155 0.398532i \(-0.869520\pi\)
−0.917155 + 0.398532i \(0.869520\pi\)
\(374\) −14.8348 −0.767087
\(375\) −17.4938 −0.903378
\(376\) 12.6680 0.653303
\(377\) 16.2362 0.836206
\(378\) −10.1412 −0.521609
\(379\) 34.8392 1.78957 0.894786 0.446495i \(-0.147328\pi\)
0.894786 + 0.446495i \(0.147328\pi\)
\(380\) −2.31499 −0.118756
\(381\) 3.49287 0.178945
\(382\) 11.1634 0.571167
\(383\) 8.15572 0.416738 0.208369 0.978050i \(-0.433185\pi\)
0.208369 + 0.978050i \(0.433185\pi\)
\(384\) −2.16681 −0.110575
\(385\) −25.6920 −1.30939
\(386\) −0.336046 −0.0171043
\(387\) 19.2721 0.979656
\(388\) 0.589255 0.0299149
\(389\) −17.5055 −0.887566 −0.443783 0.896134i \(-0.646364\pi\)
−0.443783 + 0.896134i \(0.646364\pi\)
\(390\) −20.3101 −1.02844
\(391\) 47.1614 2.38505
\(392\) 5.86390 0.296172
\(393\) −31.6761 −1.59785
\(394\) −9.84975 −0.496223
\(395\) −7.20118 −0.362331
\(396\) −4.61117 −0.231720
\(397\) 6.73925 0.338233 0.169117 0.985596i \(-0.445909\pi\)
0.169117 + 0.985596i \(0.445909\pi\)
\(398\) −7.70799 −0.386367
\(399\) 6.83226 0.342041
\(400\) 1.93400 0.0967002
\(401\) 29.9563 1.49595 0.747973 0.663729i \(-0.231027\pi\)
0.747973 + 0.663729i \(0.231027\pi\)
\(402\) 27.5239 1.37277
\(403\) 31.5353 1.57089
\(404\) 8.04875 0.400440
\(405\) 29.5238 1.46705
\(406\) 16.3596 0.811913
\(407\) −19.2450 −0.953939
\(408\) −11.8163 −0.584995
\(409\) 0.596412 0.0294907 0.0147453 0.999891i \(-0.495306\pi\)
0.0147453 + 0.999891i \(0.495306\pi\)
\(410\) 10.9844 0.542481
\(411\) 27.8311 1.37280
\(412\) −13.3113 −0.655803
\(413\) −7.09688 −0.349215
\(414\) 14.6594 0.720472
\(415\) −5.73156 −0.281351
\(416\) −3.55957 −0.174523
\(417\) −40.2107 −1.96913
\(418\) −2.39153 −0.116974
\(419\) −21.1500 −1.03324 −0.516622 0.856213i \(-0.672811\pi\)
−0.516622 + 0.856213i \(0.672811\pi\)
\(420\) −20.4645 −0.998563
\(421\) −10.2422 −0.499174 −0.249587 0.968352i \(-0.580295\pi\)
−0.249587 + 0.968352i \(0.580295\pi\)
\(422\) 9.70765 0.472561
\(423\) 21.4733 1.04407
\(424\) −6.00130 −0.291449
\(425\) 10.5467 0.511592
\(426\) 28.3885 1.37543
\(427\) −37.4795 −1.81376
\(428\) −1.22465 −0.0591958
\(429\) −20.9816 −1.01300
\(430\) −29.9385 −1.44376
\(431\) −19.1207 −0.921010 −0.460505 0.887657i \(-0.652332\pi\)
−0.460505 + 0.887657i \(0.652332\pi\)
\(432\) 2.82751 0.136039
\(433\) −21.6741 −1.04159 −0.520796 0.853681i \(-0.674365\pi\)
−0.520796 + 0.853681i \(0.674365\pi\)
\(434\) 31.7750 1.52525
\(435\) −26.0255 −1.24783
\(436\) 13.1327 0.628945
\(437\) 7.60295 0.363698
\(438\) −36.6297 −1.75024
\(439\) 12.3347 0.588703 0.294352 0.955697i \(-0.404896\pi\)
0.294352 + 0.955697i \(0.404896\pi\)
\(440\) 7.16328 0.341496
\(441\) 9.93981 0.473324
\(442\) −19.4115 −0.923311
\(443\) 21.1311 1.00397 0.501984 0.864877i \(-0.332604\pi\)
0.501984 + 0.864877i \(0.332604\pi\)
\(444\) −15.3292 −0.727492
\(445\) 40.8422 1.93611
\(446\) 21.4091 1.01375
\(447\) 42.2462 1.99818
\(448\) −3.58663 −0.169452
\(449\) −24.7970 −1.17024 −0.585121 0.810946i \(-0.698953\pi\)
−0.585121 + 0.810946i \(0.698953\pi\)
\(450\) 3.27830 0.154541
\(451\) 11.3476 0.534338
\(452\) 4.94615 0.232647
\(453\) 27.5006 1.29209
\(454\) 9.09940 0.427056
\(455\) −33.6184 −1.57605
\(456\) −1.90492 −0.0892063
\(457\) −2.26738 −0.106064 −0.0530318 0.998593i \(-0.516888\pi\)
−0.0530318 + 0.998593i \(0.516888\pi\)
\(458\) 18.3060 0.855384
\(459\) 15.4193 0.719712
\(460\) −22.7729 −1.06179
\(461\) 14.5354 0.676980 0.338490 0.940970i \(-0.390084\pi\)
0.338490 + 0.940970i \(0.390084\pi\)
\(462\) −21.1411 −0.983573
\(463\) 9.21637 0.428321 0.214161 0.976798i \(-0.431298\pi\)
0.214161 + 0.976798i \(0.431298\pi\)
\(464\) −4.56127 −0.211752
\(465\) −50.5490 −2.34416
\(466\) −14.2533 −0.660272
\(467\) 42.0625 1.94642 0.973211 0.229915i \(-0.0738448\pi\)
0.973211 + 0.229915i \(0.0738448\pi\)
\(468\) −6.03378 −0.278911
\(469\) 45.5590 2.10372
\(470\) −33.3580 −1.53869
\(471\) 18.1596 0.836752
\(472\) 1.97871 0.0910773
\(473\) −30.9284 −1.42209
\(474\) −5.92561 −0.272172
\(475\) 1.70025 0.0780130
\(476\) −19.5590 −0.896486
\(477\) −10.1727 −0.465776
\(478\) 13.6487 0.624275
\(479\) 10.9050 0.498260 0.249130 0.968470i \(-0.419855\pi\)
0.249130 + 0.968470i \(0.419855\pi\)
\(480\) 5.70576 0.260431
\(481\) −25.1823 −1.14822
\(482\) −11.2223 −0.511160
\(483\) 67.2100 3.05816
\(484\) −3.59987 −0.163630
\(485\) −1.55166 −0.0704571
\(486\) 15.8117 0.717232
\(487\) −20.4181 −0.925233 −0.462617 0.886558i \(-0.653089\pi\)
−0.462617 + 0.886558i \(0.653089\pi\)
\(488\) 10.4498 0.473040
\(489\) 36.2489 1.63923
\(490\) −15.4411 −0.697559
\(491\) 15.7205 0.709455 0.354728 0.934970i \(-0.384574\pi\)
0.354728 + 0.934970i \(0.384574\pi\)
\(492\) 9.03870 0.407496
\(493\) −24.8741 −1.12027
\(494\) −3.12935 −0.140796
\(495\) 12.1424 0.545758
\(496\) −8.85929 −0.397794
\(497\) 46.9901 2.10780
\(498\) −4.71631 −0.211343
\(499\) 5.41477 0.242399 0.121199 0.992628i \(-0.461326\pi\)
0.121199 + 0.992628i \(0.461326\pi\)
\(500\) 8.07353 0.361059
\(501\) 28.9854 1.29497
\(502\) −0.508330 −0.0226879
\(503\) 7.93633 0.353863 0.176932 0.984223i \(-0.443383\pi\)
0.176932 + 0.984223i \(0.443383\pi\)
\(504\) −6.07964 −0.270808
\(505\) −21.1944 −0.943137
\(506\) −23.5259 −1.04585
\(507\) 0.713811 0.0317014
\(508\) −1.61198 −0.0715202
\(509\) −12.2169 −0.541505 −0.270752 0.962649i \(-0.587272\pi\)
−0.270752 + 0.962649i \(0.587272\pi\)
\(510\) 31.1153 1.37781
\(511\) −60.6315 −2.68218
\(512\) 1.00000 0.0441942
\(513\) 2.48577 0.109749
\(514\) −14.1431 −0.623824
\(515\) 35.0521 1.54458
\(516\) −24.6354 −1.08451
\(517\) −34.4610 −1.51559
\(518\) −25.3737 −1.11486
\(519\) −32.4873 −1.42603
\(520\) 9.37325 0.411044
\(521\) 18.9290 0.829294 0.414647 0.909982i \(-0.363905\pi\)
0.414647 + 0.909982i \(0.363905\pi\)
\(522\) −7.73174 −0.338409
\(523\) 30.5655 1.33653 0.668267 0.743921i \(-0.267036\pi\)
0.668267 + 0.743921i \(0.267036\pi\)
\(524\) 14.6187 0.638622
\(525\) 15.0302 0.655973
\(526\) −23.3660 −1.01881
\(527\) −48.3125 −2.10453
\(528\) 5.89442 0.256522
\(529\) 51.7914 2.25180
\(530\) 15.8029 0.686435
\(531\) 3.35407 0.145554
\(532\) −3.15314 −0.136706
\(533\) 14.8485 0.643160
\(534\) 33.6077 1.45435
\(535\) 3.22482 0.139421
\(536\) −12.7025 −0.548663
\(537\) −26.5307 −1.14488
\(538\) −20.8768 −0.900061
\(539\) −15.9517 −0.687088
\(540\) −7.44554 −0.320405
\(541\) 15.6498 0.672836 0.336418 0.941713i \(-0.390785\pi\)
0.336418 + 0.941713i \(0.390785\pi\)
\(542\) 9.58159 0.411565
\(543\) −15.5834 −0.668748
\(544\) 5.45332 0.233809
\(545\) −34.5818 −1.48132
\(546\) −27.6634 −1.18389
\(547\) −18.7379 −0.801175 −0.400587 0.916259i \(-0.631194\pi\)
−0.400587 + 0.916259i \(0.631194\pi\)
\(548\) −12.8442 −0.548678
\(549\) 17.7133 0.755984
\(550\) −5.26111 −0.224334
\(551\) −4.00998 −0.170831
\(552\) −18.7390 −0.797587
\(553\) −9.80840 −0.417096
\(554\) −25.4950 −1.08318
\(555\) 40.3656 1.71343
\(556\) 18.5575 0.787014
\(557\) −17.0652 −0.723077 −0.361538 0.932357i \(-0.617748\pi\)
−0.361538 + 0.932357i \(0.617748\pi\)
\(558\) −15.0172 −0.635731
\(559\) −40.4703 −1.71171
\(560\) 9.44449 0.399102
\(561\) 32.1442 1.35713
\(562\) −12.9909 −0.547990
\(563\) 24.5523 1.03476 0.517378 0.855757i \(-0.326908\pi\)
0.517378 + 0.855757i \(0.326908\pi\)
\(564\) −27.4492 −1.15582
\(565\) −13.0245 −0.547943
\(566\) −28.8328 −1.21193
\(567\) 40.2131 1.68879
\(568\) −13.1015 −0.549726
\(569\) 10.8278 0.453926 0.226963 0.973903i \(-0.427120\pi\)
0.226963 + 0.973903i \(0.427120\pi\)
\(570\) 5.01614 0.210103
\(571\) −6.25324 −0.261690 −0.130845 0.991403i \(-0.541769\pi\)
−0.130845 + 0.991403i \(0.541769\pi\)
\(572\) 9.68318 0.404874
\(573\) −24.1889 −1.01051
\(574\) 14.9614 0.624475
\(575\) 16.7257 0.697508
\(576\) 1.69508 0.0706285
\(577\) −35.0404 −1.45875 −0.729376 0.684113i \(-0.760190\pi\)
−0.729376 + 0.684113i \(0.760190\pi\)
\(578\) 12.7387 0.529859
\(579\) 0.728149 0.0302608
\(580\) 12.0110 0.498728
\(581\) −7.80669 −0.323876
\(582\) −1.27681 −0.0529253
\(583\) 16.3254 0.676131
\(584\) 16.9049 0.699528
\(585\) 15.8884 0.656906
\(586\) 4.93012 0.203661
\(587\) −7.32743 −0.302435 −0.151218 0.988500i \(-0.548319\pi\)
−0.151218 + 0.988500i \(0.548319\pi\)
\(588\) −12.7060 −0.523986
\(589\) −7.78853 −0.320921
\(590\) −5.21043 −0.214510
\(591\) 21.3426 0.877916
\(592\) 7.07454 0.290762
\(593\) −17.6775 −0.725930 −0.362965 0.931803i \(-0.618236\pi\)
−0.362965 + 0.931803i \(0.618236\pi\)
\(594\) −7.69173 −0.315596
\(595\) 51.5038 2.11145
\(596\) −19.4969 −0.798624
\(597\) 16.7018 0.683559
\(598\) −30.7839 −1.25885
\(599\) −29.0133 −1.18545 −0.592725 0.805405i \(-0.701948\pi\)
−0.592725 + 0.805405i \(0.701948\pi\)
\(600\) −4.19063 −0.171082
\(601\) −25.8170 −1.05310 −0.526548 0.850145i \(-0.676514\pi\)
−0.526548 + 0.850145i \(0.676514\pi\)
\(602\) −40.7779 −1.66198
\(603\) −21.5317 −0.876840
\(604\) −12.6917 −0.516419
\(605\) 9.47935 0.385390
\(606\) −17.4402 −0.708458
\(607\) −10.4459 −0.423984 −0.211992 0.977271i \(-0.567995\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(608\) 0.879136 0.0356537
\(609\) −35.4482 −1.43643
\(610\) −27.5169 −1.11413
\(611\) −45.0927 −1.82426
\(612\) 9.24383 0.373660
\(613\) 7.85116 0.317105 0.158553 0.987351i \(-0.449317\pi\)
0.158553 + 0.987351i \(0.449317\pi\)
\(614\) 17.8898 0.721974
\(615\) −23.8012 −0.959756
\(616\) 9.75677 0.393111
\(617\) −16.4732 −0.663187 −0.331594 0.943422i \(-0.607586\pi\)
−0.331594 + 0.943422i \(0.607586\pi\)
\(618\) 28.8432 1.16024
\(619\) −25.8124 −1.03749 −0.518744 0.854930i \(-0.673600\pi\)
−0.518744 + 0.854930i \(0.673600\pi\)
\(620\) 23.3287 0.936904
\(621\) 24.4529 0.981261
\(622\) −20.9486 −0.839964
\(623\) 55.6293 2.22874
\(624\) 7.71294 0.308765
\(625\) −30.9296 −1.23719
\(626\) 3.40369 0.136039
\(627\) 5.18200 0.206949
\(628\) −8.38080 −0.334430
\(629\) 38.5797 1.53827
\(630\) 16.0092 0.637822
\(631\) 7.97799 0.317599 0.158799 0.987311i \(-0.449238\pi\)
0.158799 + 0.987311i \(0.449238\pi\)
\(632\) 2.73471 0.108781
\(633\) −21.0347 −0.836053
\(634\) 5.01900 0.199330
\(635\) 4.24476 0.168448
\(636\) 13.0037 0.515630
\(637\) −20.8730 −0.827018
\(638\) 12.4081 0.491242
\(639\) −22.2081 −0.878539
\(640\) −2.63325 −0.104088
\(641\) 39.8863 1.57542 0.787708 0.616049i \(-0.211268\pi\)
0.787708 + 0.616049i \(0.211268\pi\)
\(642\) 2.65360 0.104729
\(643\) 15.7579 0.621431 0.310715 0.950503i \(-0.399431\pi\)
0.310715 + 0.950503i \(0.399431\pi\)
\(644\) −31.0179 −1.22228
\(645\) 64.8712 2.55430
\(646\) 4.79421 0.188626
\(647\) −18.6199 −0.732024 −0.366012 0.930610i \(-0.619277\pi\)
−0.366012 + 0.930610i \(0.619277\pi\)
\(648\) −11.2119 −0.440447
\(649\) −5.38271 −0.211290
\(650\) −6.88423 −0.270022
\(651\) −68.8505 −2.69846
\(652\) −16.7291 −0.655163
\(653\) −8.43123 −0.329939 −0.164970 0.986299i \(-0.552753\pi\)
−0.164970 + 0.986299i \(0.552753\pi\)
\(654\) −28.4562 −1.11273
\(655\) −38.4948 −1.50411
\(656\) −4.17143 −0.162867
\(657\) 28.6552 1.11794
\(658\) −45.4355 −1.77126
\(659\) −11.9357 −0.464950 −0.232475 0.972602i \(-0.574682\pi\)
−0.232475 + 0.972602i \(0.574682\pi\)
\(660\) −15.5215 −0.604173
\(661\) −37.2554 −1.44907 −0.724533 0.689240i \(-0.757944\pi\)
−0.724533 + 0.689240i \(0.757944\pi\)
\(662\) −1.55646 −0.0604936
\(663\) 42.0611 1.63352
\(664\) 2.17661 0.0844689
\(665\) 8.30299 0.321976
\(666\) 11.9919 0.464678
\(667\) −39.4468 −1.52739
\(668\) −13.3770 −0.517571
\(669\) −46.3896 −1.79353
\(670\) 33.4488 1.29224
\(671\) −28.4268 −1.09740
\(672\) 7.77156 0.299794
\(673\) −16.8939 −0.651214 −0.325607 0.945505i \(-0.605569\pi\)
−0.325607 + 0.945505i \(0.605569\pi\)
\(674\) 20.5517 0.791621
\(675\) 5.46842 0.210480
\(676\) −0.329429 −0.0126703
\(677\) 12.6099 0.484636 0.242318 0.970197i \(-0.422092\pi\)
0.242318 + 0.970197i \(0.422092\pi\)
\(678\) −10.7174 −0.411599
\(679\) −2.11344 −0.0811064
\(680\) −14.3599 −0.550679
\(681\) −19.7167 −0.755546
\(682\) 24.1001 0.922840
\(683\) 19.1663 0.733379 0.366690 0.930343i \(-0.380491\pi\)
0.366690 + 0.930343i \(0.380491\pi\)
\(684\) 1.49021 0.0569796
\(685\) 33.8221 1.29227
\(686\) 4.07476 0.155575
\(687\) −39.6657 −1.51334
\(688\) 11.3694 0.433455
\(689\) 21.3621 0.813830
\(690\) 49.3446 1.87852
\(691\) 16.3248 0.621023 0.310512 0.950570i \(-0.399500\pi\)
0.310512 + 0.950570i \(0.399500\pi\)
\(692\) 14.9931 0.569953
\(693\) 16.5385 0.628247
\(694\) 28.3800 1.07729
\(695\) −48.8666 −1.85362
\(696\) 9.88343 0.374630
\(697\) −22.7481 −0.861646
\(698\) 18.7188 0.708517
\(699\) 30.8843 1.16815
\(700\) −6.93656 −0.262177
\(701\) 10.4526 0.394789 0.197395 0.980324i \(-0.436752\pi\)
0.197395 + 0.980324i \(0.436752\pi\)
\(702\) −10.0647 −0.379869
\(703\) 6.21948 0.234572
\(704\) −2.72032 −0.102526
\(705\) 72.2807 2.72225
\(706\) −23.9757 −0.902337
\(707\) −28.8679 −1.08569
\(708\) −4.28749 −0.161134
\(709\) −48.7109 −1.82938 −0.914688 0.404160i \(-0.867564\pi\)
−0.914688 + 0.404160i \(0.867564\pi\)
\(710\) 34.4995 1.29474
\(711\) 4.63557 0.173847
\(712\) −15.5102 −0.581269
\(713\) −76.6170 −2.86933
\(714\) 42.3808 1.58606
\(715\) −25.4982 −0.953579
\(716\) 12.2441 0.457583
\(717\) −29.5741 −1.10447
\(718\) 9.36182 0.349380
\(719\) −28.5575 −1.06501 −0.532507 0.846426i \(-0.678750\pi\)
−0.532507 + 0.846426i \(0.678750\pi\)
\(720\) −4.46358 −0.166348
\(721\) 47.7429 1.77804
\(722\) −18.2271 −0.678343
\(723\) 24.3166 0.904343
\(724\) 7.19185 0.267283
\(725\) −8.82152 −0.327623
\(726\) 7.80025 0.289494
\(727\) −23.3547 −0.866176 −0.433088 0.901352i \(-0.642576\pi\)
−0.433088 + 0.901352i \(0.642576\pi\)
\(728\) 12.7669 0.473172
\(729\) −0.625106 −0.0231521
\(730\) −44.5147 −1.64756
\(731\) 62.0010 2.29319
\(732\) −22.6428 −0.836900
\(733\) 12.0568 0.445327 0.222663 0.974895i \(-0.428525\pi\)
0.222663 + 0.974895i \(0.428525\pi\)
\(734\) −1.58772 −0.0586037
\(735\) 33.4580 1.23412
\(736\) 8.64820 0.318777
\(737\) 34.5548 1.27284
\(738\) −7.07091 −0.260284
\(739\) 22.1837 0.816039 0.408020 0.912973i \(-0.366219\pi\)
0.408020 + 0.912973i \(0.366219\pi\)
\(740\) −18.6290 −0.684817
\(741\) 6.78072 0.249096
\(742\) 21.5244 0.790187
\(743\) −9.10897 −0.334176 −0.167088 0.985942i \(-0.553436\pi\)
−0.167088 + 0.985942i \(0.553436\pi\)
\(744\) 19.1964 0.703776
\(745\) 51.3402 1.88096
\(746\) −35.4264 −1.29705
\(747\) 3.68954 0.134993
\(748\) −14.8348 −0.542413
\(749\) 4.39238 0.160494
\(750\) −17.4938 −0.638785
\(751\) −28.8867 −1.05409 −0.527046 0.849837i \(-0.676700\pi\)
−0.527046 + 0.849837i \(0.676700\pi\)
\(752\) 12.6680 0.461955
\(753\) 1.10146 0.0401393
\(754\) 16.2362 0.591287
\(755\) 33.4205 1.21630
\(756\) −10.1412 −0.368833
\(757\) 3.88043 0.141037 0.0705184 0.997510i \(-0.477535\pi\)
0.0705184 + 0.997510i \(0.477535\pi\)
\(758\) 34.8392 1.26542
\(759\) 50.9762 1.85032
\(760\) −2.31499 −0.0839733
\(761\) −27.8279 −1.00876 −0.504381 0.863481i \(-0.668279\pi\)
−0.504381 + 0.863481i \(0.668279\pi\)
\(762\) 3.49287 0.126533
\(763\) −47.1023 −1.70522
\(764\) 11.1634 0.403876
\(765\) −24.3413 −0.880062
\(766\) 8.15572 0.294678
\(767\) −7.04335 −0.254321
\(768\) −2.16681 −0.0781882
\(769\) −16.5287 −0.596039 −0.298020 0.954560i \(-0.596326\pi\)
−0.298020 + 0.954560i \(0.596326\pi\)
\(770\) −25.6920 −0.925876
\(771\) 30.6454 1.10367
\(772\) −0.336046 −0.0120946
\(773\) −39.3899 −1.41675 −0.708377 0.705834i \(-0.750572\pi\)
−0.708377 + 0.705834i \(0.750572\pi\)
\(774\) 19.2721 0.692722
\(775\) −17.1339 −0.615468
\(776\) 0.589255 0.0211530
\(777\) 54.9802 1.97240
\(778\) −17.5055 −0.627604
\(779\) −3.66725 −0.131393
\(780\) −20.3101 −0.727218
\(781\) 35.6402 1.27531
\(782\) 47.1614 1.68649
\(783\) −12.8970 −0.460903
\(784\) 5.86390 0.209425
\(785\) 22.0687 0.787667
\(786\) −31.6761 −1.12985
\(787\) 12.1422 0.432823 0.216411 0.976302i \(-0.430565\pi\)
0.216411 + 0.976302i \(0.430565\pi\)
\(788\) −9.84975 −0.350883
\(789\) 50.6298 1.80247
\(790\) −7.20118 −0.256207
\(791\) −17.7400 −0.630762
\(792\) −4.61117 −0.163851
\(793\) −37.1968 −1.32090
\(794\) 6.73925 0.239167
\(795\) −34.2420 −1.21444
\(796\) −7.70799 −0.273203
\(797\) −17.0440 −0.603729 −0.301864 0.953351i \(-0.597609\pi\)
−0.301864 + 0.953351i \(0.597609\pi\)
\(798\) 6.83226 0.241859
\(799\) 69.0827 2.44397
\(800\) 1.93400 0.0683774
\(801\) −26.2911 −0.928950
\(802\) 29.9563 1.05779
\(803\) −45.9866 −1.62283
\(804\) 27.5239 0.970693
\(805\) 81.6778 2.87877
\(806\) 31.5353 1.11078
\(807\) 45.2361 1.59238
\(808\) 8.04875 0.283154
\(809\) 30.6461 1.07746 0.538729 0.842479i \(-0.318905\pi\)
0.538729 + 0.842479i \(0.318905\pi\)
\(810\) 29.5238 1.03736
\(811\) −8.13804 −0.285765 −0.142883 0.989740i \(-0.545637\pi\)
−0.142883 + 0.989740i \(0.545637\pi\)
\(812\) 16.3596 0.574109
\(813\) −20.7615 −0.728139
\(814\) −19.2450 −0.674537
\(815\) 44.0519 1.54307
\(816\) −11.8163 −0.413654
\(817\) 9.99526 0.349690
\(818\) 0.596412 0.0208530
\(819\) 21.6409 0.756195
\(820\) 10.9844 0.383592
\(821\) 32.9040 1.14836 0.574178 0.818730i \(-0.305322\pi\)
0.574178 + 0.818730i \(0.305322\pi\)
\(822\) 27.8311 0.970720
\(823\) −20.7529 −0.723401 −0.361701 0.932294i \(-0.617804\pi\)
−0.361701 + 0.932294i \(0.617804\pi\)
\(824\) −13.3113 −0.463723
\(825\) 11.3998 0.396892
\(826\) −7.09688 −0.246932
\(827\) −29.5029 −1.02592 −0.512958 0.858414i \(-0.671450\pi\)
−0.512958 + 0.858414i \(0.671450\pi\)
\(828\) 14.6594 0.509450
\(829\) −49.4402 −1.71713 −0.858564 0.512706i \(-0.828643\pi\)
−0.858564 + 0.512706i \(0.828643\pi\)
\(830\) −5.73156 −0.198945
\(831\) 55.2429 1.91636
\(832\) −3.55957 −0.123406
\(833\) 31.9777 1.10796
\(834\) −40.2107 −1.39238
\(835\) 35.2249 1.21901
\(836\) −2.39153 −0.0827128
\(837\) −25.0498 −0.865846
\(838\) −21.1500 −0.730614
\(839\) −16.6412 −0.574517 −0.287258 0.957853i \(-0.592744\pi\)
−0.287258 + 0.957853i \(0.592744\pi\)
\(840\) −20.4645 −0.706091
\(841\) −8.19479 −0.282579
\(842\) −10.2422 −0.352969
\(843\) 28.1490 0.969501
\(844\) 9.70765 0.334151
\(845\) 0.867468 0.0298418
\(846\) 21.4733 0.738269
\(847\) 12.9114 0.443641
\(848\) −6.00130 −0.206086
\(849\) 62.4754 2.14415
\(850\) 10.5467 0.361750
\(851\) 61.1820 2.09729
\(852\) 28.3885 0.972573
\(853\) 48.5817 1.66341 0.831704 0.555220i \(-0.187366\pi\)
0.831704 + 0.555220i \(0.187366\pi\)
\(854\) −37.4795 −1.28252
\(855\) −3.92409 −0.134201
\(856\) −1.22465 −0.0418578
\(857\) 23.1136 0.789545 0.394772 0.918779i \(-0.370823\pi\)
0.394772 + 0.918779i \(0.370823\pi\)
\(858\) −20.9816 −0.716301
\(859\) −55.2570 −1.88534 −0.942672 0.333720i \(-0.891696\pi\)
−0.942672 + 0.333720i \(0.891696\pi\)
\(860\) −29.9385 −1.02089
\(861\) −32.4185 −1.10482
\(862\) −19.1207 −0.651253
\(863\) −49.1212 −1.67211 −0.836053 0.548649i \(-0.815142\pi\)
−0.836053 + 0.548649i \(0.815142\pi\)
\(864\) 2.82751 0.0961939
\(865\) −39.4806 −1.34238
\(866\) −21.6741 −0.736517
\(867\) −27.6023 −0.937425
\(868\) 31.7750 1.07851
\(869\) −7.43929 −0.252361
\(870\) −26.0255 −0.882348
\(871\) 45.2154 1.53206
\(872\) 13.1327 0.444731
\(873\) 0.998837 0.0338055
\(874\) 7.60295 0.257174
\(875\) −28.9568 −0.978917
\(876\) −36.6297 −1.23760
\(877\) −54.6943 −1.84689 −0.923447 0.383726i \(-0.874641\pi\)
−0.923447 + 0.383726i \(0.874641\pi\)
\(878\) 12.3347 0.416276
\(879\) −10.6827 −0.360317
\(880\) 7.16328 0.241474
\(881\) −11.4378 −0.385350 −0.192675 0.981263i \(-0.561716\pi\)
−0.192675 + 0.981263i \(0.561716\pi\)
\(882\) 9.93981 0.334691
\(883\) −5.37084 −0.180743 −0.0903715 0.995908i \(-0.528805\pi\)
−0.0903715 + 0.995908i \(0.528805\pi\)
\(884\) −19.4115 −0.652879
\(885\) 11.2900 0.379510
\(886\) 21.1311 0.709912
\(887\) 38.9985 1.30944 0.654721 0.755871i \(-0.272786\pi\)
0.654721 + 0.755871i \(0.272786\pi\)
\(888\) −15.3292 −0.514415
\(889\) 5.78159 0.193908
\(890\) 40.8422 1.36903
\(891\) 30.5001 1.02179
\(892\) 21.4091 0.716831
\(893\) 11.1369 0.372683
\(894\) 42.2462 1.41292
\(895\) −32.2417 −1.07772
\(896\) −3.58663 −0.119821
\(897\) 66.7030 2.22715
\(898\) −24.7970 −0.827485
\(899\) 40.4097 1.34774
\(900\) 3.27830 0.109277
\(901\) −32.7270 −1.09029
\(902\) 11.3476 0.377834
\(903\) 88.3581 2.94037
\(904\) 4.94615 0.164507
\(905\) −18.9379 −0.629519
\(906\) 27.5006 0.913647
\(907\) −14.1298 −0.469172 −0.234586 0.972095i \(-0.575373\pi\)
−0.234586 + 0.972095i \(0.575373\pi\)
\(908\) 9.09940 0.301974
\(909\) 13.6433 0.452520
\(910\) −33.6184 −1.11444
\(911\) −3.68240 −0.122003 −0.0610017 0.998138i \(-0.519430\pi\)
−0.0610017 + 0.998138i \(0.519430\pi\)
\(912\) −1.90492 −0.0630784
\(913\) −5.92107 −0.195959
\(914\) −2.26738 −0.0749984
\(915\) 59.6240 1.97111
\(916\) 18.3060 0.604848
\(917\) −52.4319 −1.73146
\(918\) 15.4193 0.508913
\(919\) −33.3049 −1.09863 −0.549313 0.835617i \(-0.685111\pi\)
−0.549313 + 0.835617i \(0.685111\pi\)
\(920\) −22.7729 −0.750800
\(921\) −38.7639 −1.27731
\(922\) 14.5354 0.478697
\(923\) 46.6357 1.53503
\(924\) −21.1411 −0.695491
\(925\) 13.6822 0.449868
\(926\) 9.21637 0.302869
\(927\) −22.5638 −0.741094
\(928\) −4.56127 −0.149731
\(929\) −41.9157 −1.37521 −0.687605 0.726085i \(-0.741338\pi\)
−0.687605 + 0.726085i \(0.741338\pi\)
\(930\) −50.5490 −1.65757
\(931\) 5.15517 0.168954
\(932\) −14.2533 −0.466883
\(933\) 45.3918 1.48606
\(934\) 42.0625 1.37633
\(935\) 39.0636 1.27752
\(936\) −6.03378 −0.197220
\(937\) −20.6823 −0.675662 −0.337831 0.941207i \(-0.609693\pi\)
−0.337831 + 0.941207i \(0.609693\pi\)
\(938\) 45.5590 1.48755
\(939\) −7.37517 −0.240680
\(940\) −33.3580 −1.08802
\(941\) −41.4672 −1.35179 −0.675896 0.736997i \(-0.736243\pi\)
−0.675896 + 0.736997i \(0.736243\pi\)
\(942\) 18.1596 0.591673
\(943\) −36.0753 −1.17477
\(944\) 1.97871 0.0644014
\(945\) 26.7044 0.868694
\(946\) −30.9284 −1.00557
\(947\) −0.553610 −0.0179899 −0.00899495 0.999960i \(-0.502863\pi\)
−0.00899495 + 0.999960i \(0.502863\pi\)
\(948\) −5.92561 −0.192455
\(949\) −60.1741 −1.95334
\(950\) 1.70025 0.0551635
\(951\) −10.8752 −0.352654
\(952\) −19.5590 −0.633912
\(953\) 47.4110 1.53579 0.767897 0.640573i \(-0.221303\pi\)
0.767897 + 0.640573i \(0.221303\pi\)
\(954\) −10.1727 −0.329354
\(955\) −29.3959 −0.951230
\(956\) 13.6487 0.441429
\(957\) −26.8861 −0.869103
\(958\) 10.9050 0.352323
\(959\) 46.0675 1.48760
\(960\) 5.70576 0.184153
\(961\) 47.4871 1.53184
\(962\) −25.1823 −0.811911
\(963\) −2.07589 −0.0668946
\(964\) −11.2223 −0.361445
\(965\) 0.884893 0.0284857
\(966\) 67.2100 2.16245
\(967\) 40.1457 1.29100 0.645500 0.763760i \(-0.276649\pi\)
0.645500 + 0.763760i \(0.276649\pi\)
\(968\) −3.59987 −0.115704
\(969\) −10.3882 −0.333716
\(970\) −1.55166 −0.0498207
\(971\) 33.9983 1.09106 0.545528 0.838092i \(-0.316329\pi\)
0.545528 + 0.838092i \(0.316329\pi\)
\(972\) 15.8117 0.507159
\(973\) −66.5589 −2.13378
\(974\) −20.4181 −0.654239
\(975\) 14.9169 0.477722
\(976\) 10.4498 0.334490
\(977\) 6.00161 0.192008 0.0960042 0.995381i \(-0.469394\pi\)
0.0960042 + 0.995381i \(0.469394\pi\)
\(978\) 36.2489 1.15911
\(979\) 42.1927 1.34848
\(980\) −15.4411 −0.493249
\(981\) 22.2611 0.710742
\(982\) 15.7205 0.501661
\(983\) 36.9547 1.17867 0.589336 0.807888i \(-0.299390\pi\)
0.589336 + 0.807888i \(0.299390\pi\)
\(984\) 9.03870 0.288143
\(985\) 25.9369 0.826417
\(986\) −24.8741 −0.792152
\(987\) 98.4502 3.13370
\(988\) −3.12935 −0.0995579
\(989\) 98.3250 3.12655
\(990\) 12.1424 0.385909
\(991\) −0.448183 −0.0142370 −0.00711850 0.999975i \(-0.502266\pi\)
−0.00711850 + 0.999975i \(0.502266\pi\)
\(992\) −8.85929 −0.281283
\(993\) 3.37256 0.107025
\(994\) 46.9901 1.49044
\(995\) 20.2971 0.643460
\(996\) −4.71631 −0.149442
\(997\) −5.43259 −0.172052 −0.0860259 0.996293i \(-0.527417\pi\)
−0.0860259 + 0.996293i \(0.527417\pi\)
\(998\) 5.41477 0.171402
\(999\) 20.0033 0.632878
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 \(a_p\))