Properties

Label 4015.2.a.h.1.13
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.745458 q^{2}\) \(+3.05905 q^{3}\) \(-1.44429 q^{4}\) \(+1.00000 q^{5}\) \(-2.28039 q^{6}\) \(-3.66055 q^{7}\) \(+2.56757 q^{8}\) \(+6.35779 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.745458 q^{2}\) \(+3.05905 q^{3}\) \(-1.44429 q^{4}\) \(+1.00000 q^{5}\) \(-2.28039 q^{6}\) \(-3.66055 q^{7}\) \(+2.56757 q^{8}\) \(+6.35779 q^{9}\) \(-0.745458 q^{10}\) \(+1.00000 q^{11}\) \(-4.41817 q^{12}\) \(+1.02611 q^{13}\) \(+2.72879 q^{14}\) \(+3.05905 q^{15}\) \(+0.974567 q^{16}\) \(+7.92938 q^{17}\) \(-4.73947 q^{18}\) \(-1.53458 q^{19}\) \(-1.44429 q^{20}\) \(-11.1978 q^{21}\) \(-0.745458 q^{22}\) \(-9.02592 q^{23}\) \(+7.85434 q^{24}\) \(+1.00000 q^{25}\) \(-0.764924 q^{26}\) \(+10.2717 q^{27}\) \(+5.28691 q^{28}\) \(+3.19396 q^{29}\) \(-2.28039 q^{30}\) \(-7.54361 q^{31}\) \(-5.86165 q^{32}\) \(+3.05905 q^{33}\) \(-5.91102 q^{34}\) \(-3.66055 q^{35}\) \(-9.18251 q^{36}\) \(+6.07994 q^{37}\) \(+1.14397 q^{38}\) \(+3.13893 q^{39}\) \(+2.56757 q^{40}\) \(+7.65235 q^{41}\) \(+8.34749 q^{42}\) \(+8.29774 q^{43}\) \(-1.44429 q^{44}\) \(+6.35779 q^{45}\) \(+6.72844 q^{46}\) \(+9.63324 q^{47}\) \(+2.98125 q^{48}\) \(+6.39962 q^{49}\) \(-0.745458 q^{50}\) \(+24.2564 q^{51}\) \(-1.48201 q^{52}\) \(-3.09231 q^{53}\) \(-7.65709 q^{54}\) \(+1.00000 q^{55}\) \(-9.39873 q^{56}\) \(-4.69437 q^{57}\) \(-2.38096 q^{58}\) \(+8.32297 q^{59}\) \(-4.41817 q^{60}\) \(-7.95140 q^{61}\) \(+5.62344 q^{62}\) \(-23.2730 q^{63}\) \(+2.42048 q^{64}\) \(+1.02611 q^{65}\) \(-2.28039 q^{66}\) \(-2.85577 q^{67}\) \(-11.4523 q^{68}\) \(-27.6108 q^{69}\) \(+2.72879 q^{70}\) \(-3.17918 q^{71}\) \(+16.3241 q^{72}\) \(+1.00000 q^{73}\) \(-4.53234 q^{74}\) \(+3.05905 q^{75}\) \(+2.21639 q^{76}\) \(-3.66055 q^{77}\) \(-2.33994 q^{78}\) \(+16.2070 q^{79}\) \(+0.974567 q^{80}\) \(+12.3481 q^{81}\) \(-5.70450 q^{82}\) \(-1.77293 q^{83}\) \(+16.1729 q^{84}\) \(+7.92938 q^{85}\) \(-6.18561 q^{86}\) \(+9.77049 q^{87}\) \(+2.56757 q^{88}\) \(+0.725334 q^{89}\) \(-4.73947 q^{90}\) \(-3.75614 q^{91}\) \(+13.0361 q^{92}\) \(-23.0763 q^{93}\) \(-7.18117 q^{94}\) \(-1.53458 q^{95}\) \(-17.9311 q^{96}\) \(+18.9489 q^{97}\) \(-4.77065 q^{98}\) \(+6.35779 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.745458 −0.527118 −0.263559 0.964643i \(-0.584896\pi\)
−0.263559 + 0.964643i \(0.584896\pi\)
\(3\) 3.05905 1.76614 0.883072 0.469238i \(-0.155471\pi\)
0.883072 + 0.469238i \(0.155471\pi\)
\(4\) −1.44429 −0.722146
\(5\) 1.00000 0.447214
\(6\) −2.28039 −0.930967
\(7\) −3.66055 −1.38356 −0.691779 0.722109i \(-0.743173\pi\)
−0.691779 + 0.722109i \(0.743173\pi\)
\(8\) 2.56757 0.907775
\(9\) 6.35779 2.11926
\(10\) −0.745458 −0.235734
\(11\) 1.00000 0.301511
\(12\) −4.41817 −1.27541
\(13\) 1.02611 0.284593 0.142296 0.989824i \(-0.454551\pi\)
0.142296 + 0.989824i \(0.454551\pi\)
\(14\) 2.72879 0.729298
\(15\) 3.05905 0.789844
\(16\) 0.974567 0.243642
\(17\) 7.92938 1.92316 0.961579 0.274529i \(-0.0885219\pi\)
0.961579 + 0.274529i \(0.0885219\pi\)
\(18\) −4.73947 −1.11710
\(19\) −1.53458 −0.352057 −0.176029 0.984385i \(-0.556325\pi\)
−0.176029 + 0.984385i \(0.556325\pi\)
\(20\) −1.44429 −0.322954
\(21\) −11.1978 −2.44356
\(22\) −0.745458 −0.158932
\(23\) −9.02592 −1.88203 −0.941017 0.338358i \(-0.890129\pi\)
−0.941017 + 0.338358i \(0.890129\pi\)
\(24\) 7.85434 1.60326
\(25\) 1.00000 0.200000
\(26\) −0.764924 −0.150014
\(27\) 10.2717 1.97678
\(28\) 5.28691 0.999131
\(29\) 3.19396 0.593104 0.296552 0.955017i \(-0.404163\pi\)
0.296552 + 0.955017i \(0.404163\pi\)
\(30\) −2.28039 −0.416341
\(31\) −7.54361 −1.35487 −0.677436 0.735582i \(-0.736909\pi\)
−0.677436 + 0.735582i \(0.736909\pi\)
\(32\) −5.86165 −1.03620
\(33\) 3.05905 0.532512
\(34\) −5.91102 −1.01373
\(35\) −3.66055 −0.618746
\(36\) −9.18251 −1.53042
\(37\) 6.07994 0.999535 0.499768 0.866159i \(-0.333419\pi\)
0.499768 + 0.866159i \(0.333419\pi\)
\(38\) 1.14397 0.185576
\(39\) 3.13893 0.502631
\(40\) 2.56757 0.405969
\(41\) 7.65235 1.19510 0.597548 0.801833i \(-0.296142\pi\)
0.597548 + 0.801833i \(0.296142\pi\)
\(42\) 8.34749 1.28805
\(43\) 8.29774 1.26539 0.632696 0.774400i \(-0.281948\pi\)
0.632696 + 0.774400i \(0.281948\pi\)
\(44\) −1.44429 −0.217735
\(45\) 6.35779 0.947764
\(46\) 6.72844 0.992055
\(47\) 9.63324 1.40515 0.702576 0.711609i \(-0.252033\pi\)
0.702576 + 0.711609i \(0.252033\pi\)
\(48\) 2.98125 0.430307
\(49\) 6.39962 0.914232
\(50\) −0.745458 −0.105424
\(51\) 24.2564 3.39657
\(52\) −1.48201 −0.205518
\(53\) −3.09231 −0.424762 −0.212381 0.977187i \(-0.568122\pi\)
−0.212381 + 0.977187i \(0.568122\pi\)
\(54\) −7.65709 −1.04200
\(55\) 1.00000 0.134840
\(56\) −9.39873 −1.25596
\(57\) −4.69437 −0.621784
\(58\) −2.38096 −0.312636
\(59\) 8.32297 1.08356 0.541779 0.840521i \(-0.317751\pi\)
0.541779 + 0.840521i \(0.317751\pi\)
\(60\) −4.41817 −0.570383
\(61\) −7.95140 −1.01807 −0.509036 0.860745i \(-0.669998\pi\)
−0.509036 + 0.860745i \(0.669998\pi\)
\(62\) 5.62344 0.714178
\(63\) −23.2730 −2.93212
\(64\) 2.42048 0.302560
\(65\) 1.02611 0.127274
\(66\) −2.28039 −0.280697
\(67\) −2.85577 −0.348888 −0.174444 0.984667i \(-0.555813\pi\)
−0.174444 + 0.984667i \(0.555813\pi\)
\(68\) −11.4523 −1.38880
\(69\) −27.6108 −3.32394
\(70\) 2.72879 0.326152
\(71\) −3.17918 −0.377300 −0.188650 0.982044i \(-0.560411\pi\)
−0.188650 + 0.982044i \(0.560411\pi\)
\(72\) 16.3241 1.92381
\(73\) 1.00000 0.117041
\(74\) −4.53234 −0.526873
\(75\) 3.05905 0.353229
\(76\) 2.21639 0.254237
\(77\) −3.66055 −0.417158
\(78\) −2.33994 −0.264946
\(79\) 16.2070 1.82343 0.911717 0.410820i \(-0.134757\pi\)
0.911717 + 0.410820i \(0.134757\pi\)
\(80\) 0.974567 0.108960
\(81\) 12.3481 1.37202
\(82\) −5.70450 −0.629957
\(83\) −1.77293 −0.194604 −0.0973021 0.995255i \(-0.531021\pi\)
−0.0973021 + 0.995255i \(0.531021\pi\)
\(84\) 16.1729 1.76461
\(85\) 7.92938 0.860062
\(86\) −6.18561 −0.667012
\(87\) 9.77049 1.04751
\(88\) 2.56757 0.273704
\(89\) 0.725334 0.0768852 0.0384426 0.999261i \(-0.487760\pi\)
0.0384426 + 0.999261i \(0.487760\pi\)
\(90\) −4.73947 −0.499584
\(91\) −3.75614 −0.393750
\(92\) 13.0361 1.35910
\(93\) −23.0763 −2.39290
\(94\) −7.18117 −0.740681
\(95\) −1.53458 −0.157445
\(96\) −17.9311 −1.83008
\(97\) 18.9489 1.92397 0.961983 0.273110i \(-0.0880524\pi\)
0.961983 + 0.273110i \(0.0880524\pi\)
\(98\) −4.77065 −0.481908
\(99\) 6.35779 0.638982
\(100\) −1.44429 −0.144429
\(101\) 2.13994 0.212932 0.106466 0.994316i \(-0.466046\pi\)
0.106466 + 0.994316i \(0.466046\pi\)
\(102\) −18.0821 −1.79040
\(103\) −5.76145 −0.567693 −0.283846 0.958870i \(-0.591611\pi\)
−0.283846 + 0.958870i \(0.591611\pi\)
\(104\) 2.63462 0.258346
\(105\) −11.1978 −1.09279
\(106\) 2.30519 0.223900
\(107\) −17.7209 −1.71314 −0.856571 0.516029i \(-0.827410\pi\)
−0.856571 + 0.516029i \(0.827410\pi\)
\(108\) −14.8353 −1.42753
\(109\) 10.8333 1.03764 0.518821 0.854883i \(-0.326371\pi\)
0.518821 + 0.854883i \(0.326371\pi\)
\(110\) −0.745458 −0.0710766
\(111\) 18.5988 1.76532
\(112\) −3.56745 −0.337093
\(113\) −12.3929 −1.16583 −0.582914 0.812534i \(-0.698087\pi\)
−0.582914 + 0.812534i \(0.698087\pi\)
\(114\) 3.49945 0.327754
\(115\) −9.02592 −0.841672
\(116\) −4.61302 −0.428308
\(117\) 6.52381 0.603127
\(118\) −6.20442 −0.571164
\(119\) −29.0259 −2.66080
\(120\) 7.85434 0.717000
\(121\) 1.00000 0.0909091
\(122\) 5.92744 0.536645
\(123\) 23.4089 2.11071
\(124\) 10.8952 0.978416
\(125\) 1.00000 0.0894427
\(126\) 17.3490 1.54558
\(127\) 16.4683 1.46133 0.730664 0.682737i \(-0.239210\pi\)
0.730664 + 0.682737i \(0.239210\pi\)
\(128\) 9.91893 0.876718
\(129\) 25.3832 2.23487
\(130\) −0.764924 −0.0670883
\(131\) −0.222835 −0.0194692 −0.00973461 0.999953i \(-0.503099\pi\)
−0.00973461 + 0.999953i \(0.503099\pi\)
\(132\) −4.41817 −0.384552
\(133\) 5.61742 0.487092
\(134\) 2.12886 0.183905
\(135\) 10.2717 0.884044
\(136\) 20.3593 1.74579
\(137\) 0.277250 0.0236871 0.0118435 0.999930i \(-0.496230\pi\)
0.0118435 + 0.999930i \(0.496230\pi\)
\(138\) 20.5827 1.75211
\(139\) 7.00548 0.594197 0.297098 0.954847i \(-0.403981\pi\)
0.297098 + 0.954847i \(0.403981\pi\)
\(140\) 5.28691 0.446825
\(141\) 29.4686 2.48170
\(142\) 2.36995 0.198882
\(143\) 1.02611 0.0858079
\(144\) 6.19610 0.516341
\(145\) 3.19396 0.265244
\(146\) −0.745458 −0.0616945
\(147\) 19.5768 1.61467
\(148\) −8.78121 −0.721811
\(149\) −0.618196 −0.0506446 −0.0253223 0.999679i \(-0.508061\pi\)
−0.0253223 + 0.999679i \(0.508061\pi\)
\(150\) −2.28039 −0.186193
\(151\) −8.77873 −0.714403 −0.357201 0.934027i \(-0.616269\pi\)
−0.357201 + 0.934027i \(0.616269\pi\)
\(152\) −3.94016 −0.319589
\(153\) 50.4134 4.07568
\(154\) 2.72879 0.219892
\(155\) −7.54361 −0.605917
\(156\) −4.53354 −0.362974
\(157\) 5.14023 0.410235 0.205118 0.978737i \(-0.434242\pi\)
0.205118 + 0.978737i \(0.434242\pi\)
\(158\) −12.0817 −0.961165
\(159\) −9.45954 −0.750190
\(160\) −5.86165 −0.463404
\(161\) 33.0398 2.60390
\(162\) −9.20502 −0.723215
\(163\) −10.5410 −0.825637 −0.412818 0.910813i \(-0.635456\pi\)
−0.412818 + 0.910813i \(0.635456\pi\)
\(164\) −11.0522 −0.863035
\(165\) 3.05905 0.238147
\(166\) 1.32164 0.102579
\(167\) 0.991594 0.0767319 0.0383659 0.999264i \(-0.487785\pi\)
0.0383659 + 0.999264i \(0.487785\pi\)
\(168\) −28.7512 −2.21820
\(169\) −11.9471 −0.919007
\(170\) −5.91102 −0.453354
\(171\) −9.75656 −0.746103
\(172\) −11.9844 −0.913799
\(173\) −4.27659 −0.325143 −0.162572 0.986697i \(-0.551979\pi\)
−0.162572 + 0.986697i \(0.551979\pi\)
\(174\) −7.28349 −0.552160
\(175\) −3.66055 −0.276712
\(176\) 0.974567 0.0734608
\(177\) 25.4604 1.91372
\(178\) −0.540706 −0.0405276
\(179\) 2.49969 0.186836 0.0934179 0.995627i \(-0.470221\pi\)
0.0934179 + 0.995627i \(0.470221\pi\)
\(180\) −9.18251 −0.684424
\(181\) 3.30917 0.245969 0.122984 0.992409i \(-0.460753\pi\)
0.122984 + 0.992409i \(0.460753\pi\)
\(182\) 2.80004 0.207553
\(183\) −24.3237 −1.79806
\(184\) −23.1747 −1.70846
\(185\) 6.07994 0.447006
\(186\) 17.2024 1.26134
\(187\) 7.92938 0.579854
\(188\) −13.9132 −1.01473
\(189\) −37.5999 −2.73499
\(190\) 1.14397 0.0829920
\(191\) 23.7192 1.71626 0.858132 0.513429i \(-0.171625\pi\)
0.858132 + 0.513429i \(0.171625\pi\)
\(192\) 7.40436 0.534364
\(193\) 9.56799 0.688719 0.344359 0.938838i \(-0.388096\pi\)
0.344359 + 0.938838i \(0.388096\pi\)
\(194\) −14.1256 −1.01416
\(195\) 3.13893 0.224784
\(196\) −9.24293 −0.660209
\(197\) 13.1006 0.933380 0.466690 0.884421i \(-0.345446\pi\)
0.466690 + 0.884421i \(0.345446\pi\)
\(198\) −4.73947 −0.336819
\(199\) −12.6096 −0.893870 −0.446935 0.894566i \(-0.647485\pi\)
−0.446935 + 0.894566i \(0.647485\pi\)
\(200\) 2.56757 0.181555
\(201\) −8.73595 −0.616187
\(202\) −1.59524 −0.112241
\(203\) −11.6917 −0.820593
\(204\) −35.0333 −2.45282
\(205\) 7.65235 0.534463
\(206\) 4.29492 0.299241
\(207\) −57.3849 −3.98853
\(208\) 1.00002 0.0693387
\(209\) −1.53458 −0.106149
\(210\) 8.34749 0.576032
\(211\) 13.6724 0.941245 0.470622 0.882335i \(-0.344029\pi\)
0.470622 + 0.882335i \(0.344029\pi\)
\(212\) 4.46620 0.306740
\(213\) −9.72529 −0.666366
\(214\) 13.2102 0.903029
\(215\) 8.29774 0.565901
\(216\) 26.3733 1.79447
\(217\) 27.6137 1.87454
\(218\) −8.07577 −0.546960
\(219\) 3.05905 0.206712
\(220\) −1.44429 −0.0973742
\(221\) 8.13644 0.547316
\(222\) −13.8646 −0.930534
\(223\) 17.2192 1.15308 0.576541 0.817068i \(-0.304402\pi\)
0.576541 + 0.817068i \(0.304402\pi\)
\(224\) 21.4569 1.43365
\(225\) 6.35779 0.423853
\(226\) 9.23839 0.614529
\(227\) 19.9155 1.32184 0.660918 0.750458i \(-0.270167\pi\)
0.660918 + 0.750458i \(0.270167\pi\)
\(228\) 6.78004 0.449019
\(229\) 2.12024 0.140109 0.0700547 0.997543i \(-0.477683\pi\)
0.0700547 + 0.997543i \(0.477683\pi\)
\(230\) 6.72844 0.443660
\(231\) −11.1978 −0.736762
\(232\) 8.20073 0.538405
\(233\) 19.4593 1.27482 0.637410 0.770525i \(-0.280006\pi\)
0.637410 + 0.770525i \(0.280006\pi\)
\(234\) −4.86323 −0.317919
\(235\) 9.63324 0.628403
\(236\) −12.0208 −0.782488
\(237\) 49.5781 3.22045
\(238\) 21.6376 1.40256
\(239\) 1.35119 0.0874013 0.0437006 0.999045i \(-0.486085\pi\)
0.0437006 + 0.999045i \(0.486085\pi\)
\(240\) 2.98125 0.192439
\(241\) 19.4434 1.25246 0.626228 0.779640i \(-0.284598\pi\)
0.626228 + 0.779640i \(0.284598\pi\)
\(242\) −0.745458 −0.0479198
\(243\) 6.95864 0.446397
\(244\) 11.4842 0.735198
\(245\) 6.39962 0.408857
\(246\) −17.4504 −1.11259
\(247\) −1.57466 −0.100193
\(248\) −19.3688 −1.22992
\(249\) −5.42348 −0.343699
\(250\) −0.745458 −0.0471469
\(251\) 4.96317 0.313273 0.156636 0.987656i \(-0.449935\pi\)
0.156636 + 0.987656i \(0.449935\pi\)
\(252\) 33.6130 2.11742
\(253\) −9.02592 −0.567455
\(254\) −12.2765 −0.770293
\(255\) 24.2564 1.51899
\(256\) −12.2351 −0.764694
\(257\) 6.95937 0.434113 0.217057 0.976159i \(-0.430354\pi\)
0.217057 + 0.976159i \(0.430354\pi\)
\(258\) −18.9221 −1.17804
\(259\) −22.2559 −1.38292
\(260\) −1.48201 −0.0919102
\(261\) 20.3065 1.25694
\(262\) 0.166114 0.0102626
\(263\) −21.5934 −1.33150 −0.665752 0.746173i \(-0.731889\pi\)
−0.665752 + 0.746173i \(0.731889\pi\)
\(264\) 7.85434 0.483401
\(265\) −3.09231 −0.189959
\(266\) −4.18755 −0.256755
\(267\) 2.21883 0.135790
\(268\) 4.12457 0.251948
\(269\) −25.2542 −1.53977 −0.769887 0.638180i \(-0.779688\pi\)
−0.769887 + 0.638180i \(0.779688\pi\)
\(270\) −7.65709 −0.465995
\(271\) −0.0873812 −0.00530803 −0.00265402 0.999996i \(-0.500845\pi\)
−0.00265402 + 0.999996i \(0.500845\pi\)
\(272\) 7.72772 0.468562
\(273\) −11.4902 −0.695420
\(274\) −0.206678 −0.0124859
\(275\) 1.00000 0.0603023
\(276\) 39.8780 2.40037
\(277\) −15.5840 −0.936350 −0.468175 0.883636i \(-0.655088\pi\)
−0.468175 + 0.883636i \(0.655088\pi\)
\(278\) −5.22229 −0.313212
\(279\) −47.9607 −2.87133
\(280\) −9.39873 −0.561682
\(281\) −23.2266 −1.38558 −0.692791 0.721138i \(-0.743619\pi\)
−0.692791 + 0.721138i \(0.743619\pi\)
\(282\) −21.9676 −1.30815
\(283\) −2.22884 −0.132491 −0.0662453 0.997803i \(-0.521102\pi\)
−0.0662453 + 0.997803i \(0.521102\pi\)
\(284\) 4.59167 0.272466
\(285\) −4.69437 −0.278070
\(286\) −0.764924 −0.0452309
\(287\) −28.0118 −1.65348
\(288\) −37.2671 −2.19599
\(289\) 45.8751 2.69854
\(290\) −2.38096 −0.139815
\(291\) 57.9655 3.39800
\(292\) −1.44429 −0.0845208
\(293\) −0.867891 −0.0507027 −0.0253514 0.999679i \(-0.508070\pi\)
−0.0253514 + 0.999679i \(0.508070\pi\)
\(294\) −14.5937 −0.851119
\(295\) 8.32297 0.484582
\(296\) 15.6107 0.907353
\(297\) 10.2717 0.596022
\(298\) 0.460839 0.0266957
\(299\) −9.26162 −0.535613
\(300\) −4.41817 −0.255083
\(301\) −30.3743 −1.75074
\(302\) 6.54417 0.376575
\(303\) 6.54620 0.376069
\(304\) −1.49555 −0.0857759
\(305\) −7.95140 −0.455296
\(306\) −37.5810 −2.14836
\(307\) 21.7728 1.24264 0.621319 0.783558i \(-0.286597\pi\)
0.621319 + 0.783558i \(0.286597\pi\)
\(308\) 5.28691 0.301249
\(309\) −17.6246 −1.00263
\(310\) 5.62344 0.319390
\(311\) −23.3048 −1.32149 −0.660747 0.750609i \(-0.729760\pi\)
−0.660747 + 0.750609i \(0.729760\pi\)
\(312\) 8.05944 0.456276
\(313\) 21.1142 1.19344 0.596722 0.802448i \(-0.296469\pi\)
0.596722 + 0.802448i \(0.296469\pi\)
\(314\) −3.83183 −0.216242
\(315\) −23.2730 −1.31129
\(316\) −23.4077 −1.31679
\(317\) −0.318916 −0.0179121 −0.00895605 0.999960i \(-0.502851\pi\)
−0.00895605 + 0.999960i \(0.502851\pi\)
\(318\) 7.05169 0.395439
\(319\) 3.19396 0.178827
\(320\) 2.42048 0.135309
\(321\) −54.2091 −3.02566
\(322\) −24.6298 −1.37257
\(323\) −12.1683 −0.677062
\(324\) −17.8343 −0.990797
\(325\) 1.02611 0.0569185
\(326\) 7.85789 0.435208
\(327\) 33.1396 1.83263
\(328\) 19.6480 1.08488
\(329\) −35.2629 −1.94411
\(330\) −2.28039 −0.125532
\(331\) −27.0626 −1.48749 −0.743747 0.668462i \(-0.766953\pi\)
−0.743747 + 0.668462i \(0.766953\pi\)
\(332\) 2.56063 0.140533
\(333\) 38.6550 2.11828
\(334\) −0.739192 −0.0404468
\(335\) −2.85577 −0.156028
\(336\) −10.9130 −0.595354
\(337\) 11.4837 0.625555 0.312778 0.949826i \(-0.398741\pi\)
0.312778 + 0.949826i \(0.398741\pi\)
\(338\) 8.90605 0.484425
\(339\) −37.9106 −2.05902
\(340\) −11.4523 −0.621091
\(341\) −7.54361 −0.408509
\(342\) 7.27310 0.393284
\(343\) 2.19770 0.118665
\(344\) 21.3051 1.14869
\(345\) −27.6108 −1.48651
\(346\) 3.18802 0.171389
\(347\) −13.5714 −0.728550 −0.364275 0.931291i \(-0.618683\pi\)
−0.364275 + 0.931291i \(0.618683\pi\)
\(348\) −14.1114 −0.756453
\(349\) 18.2877 0.978917 0.489459 0.872026i \(-0.337194\pi\)
0.489459 + 0.872026i \(0.337194\pi\)
\(350\) 2.72879 0.145860
\(351\) 10.5399 0.562577
\(352\) −5.86165 −0.312427
\(353\) −25.7020 −1.36798 −0.683989 0.729492i \(-0.739757\pi\)
−0.683989 + 0.729492i \(0.739757\pi\)
\(354\) −18.9797 −1.00876
\(355\) −3.17918 −0.168734
\(356\) −1.04759 −0.0555224
\(357\) −88.7917 −4.69936
\(358\) −1.86342 −0.0984846
\(359\) −5.27668 −0.278493 −0.139246 0.990258i \(-0.544468\pi\)
−0.139246 + 0.990258i \(0.544468\pi\)
\(360\) 16.3241 0.860356
\(361\) −16.6451 −0.876056
\(362\) −2.46685 −0.129655
\(363\) 3.05905 0.160559
\(364\) 5.42496 0.284345
\(365\) 1.00000 0.0523424
\(366\) 18.1323 0.947792
\(367\) −21.0497 −1.09879 −0.549393 0.835564i \(-0.685141\pi\)
−0.549393 + 0.835564i \(0.685141\pi\)
\(368\) −8.79637 −0.458542
\(369\) 48.6521 2.53273
\(370\) −4.53234 −0.235625
\(371\) 11.3196 0.587682
\(372\) 33.3289 1.72802
\(373\) 27.2340 1.41012 0.705062 0.709146i \(-0.250919\pi\)
0.705062 + 0.709146i \(0.250919\pi\)
\(374\) −5.91102 −0.305652
\(375\) 3.05905 0.157969
\(376\) 24.7341 1.27556
\(377\) 3.27737 0.168793
\(378\) 28.0291 1.44166
\(379\) −3.29864 −0.169440 −0.0847200 0.996405i \(-0.527000\pi\)
−0.0847200 + 0.996405i \(0.527000\pi\)
\(380\) 2.21639 0.113698
\(381\) 50.3775 2.58092
\(382\) −17.6817 −0.904674
\(383\) −5.14155 −0.262721 −0.131361 0.991335i \(-0.541935\pi\)
−0.131361 + 0.991335i \(0.541935\pi\)
\(384\) 30.3425 1.54841
\(385\) −3.66055 −0.186559
\(386\) −7.13253 −0.363036
\(387\) 52.7553 2.68170
\(388\) −27.3677 −1.38938
\(389\) −5.42794 −0.275207 −0.137604 0.990487i \(-0.543940\pi\)
−0.137604 + 0.990487i \(0.543940\pi\)
\(390\) −2.33994 −0.118488
\(391\) −71.5700 −3.61945
\(392\) 16.4315 0.829917
\(393\) −0.681665 −0.0343854
\(394\) −9.76595 −0.492002
\(395\) 16.2070 0.815464
\(396\) −9.18251 −0.461439
\(397\) −32.9788 −1.65516 −0.827580 0.561348i \(-0.810283\pi\)
−0.827580 + 0.561348i \(0.810283\pi\)
\(398\) 9.39992 0.471175
\(399\) 17.1840 0.860274
\(400\) 0.974567 0.0487284
\(401\) 16.3960 0.818775 0.409388 0.912361i \(-0.365742\pi\)
0.409388 + 0.912361i \(0.365742\pi\)
\(402\) 6.51228 0.324803
\(403\) −7.74060 −0.385587
\(404\) −3.09071 −0.153768
\(405\) 12.3481 0.613584
\(406\) 8.71563 0.432550
\(407\) 6.07994 0.301371
\(408\) 62.2801 3.08332
\(409\) −28.6106 −1.41470 −0.707351 0.706863i \(-0.750110\pi\)
−0.707351 + 0.706863i \(0.750110\pi\)
\(410\) −5.70450 −0.281725
\(411\) 0.848122 0.0418348
\(412\) 8.32123 0.409957
\(413\) −30.4667 −1.49917
\(414\) 42.7780 2.10243
\(415\) −1.77293 −0.0870297
\(416\) −6.01471 −0.294896
\(417\) 21.4301 1.04944
\(418\) 1.14397 0.0559532
\(419\) −30.1719 −1.47400 −0.736998 0.675895i \(-0.763757\pi\)
−0.736998 + 0.675895i \(0.763757\pi\)
\(420\) 16.1729 0.789157
\(421\) −15.5634 −0.758512 −0.379256 0.925292i \(-0.623820\pi\)
−0.379256 + 0.925292i \(0.623820\pi\)
\(422\) −10.1922 −0.496147
\(423\) 61.2461 2.97789
\(424\) −7.93974 −0.385588
\(425\) 7.92938 0.384632
\(426\) 7.24979 0.351254
\(427\) 29.1065 1.40856
\(428\) 25.5941 1.23714
\(429\) 3.13893 0.151549
\(430\) −6.18561 −0.298297
\(431\) −30.5031 −1.46928 −0.734641 0.678456i \(-0.762649\pi\)
−0.734641 + 0.678456i \(0.762649\pi\)
\(432\) 10.0104 0.481627
\(433\) −28.0526 −1.34812 −0.674061 0.738676i \(-0.735451\pi\)
−0.674061 + 0.738676i \(0.735451\pi\)
\(434\) −20.5849 −0.988106
\(435\) 9.77049 0.468459
\(436\) −15.6465 −0.749330
\(437\) 13.8510 0.662584
\(438\) −2.28039 −0.108961
\(439\) −6.29430 −0.300411 −0.150205 0.988655i \(-0.547993\pi\)
−0.150205 + 0.988655i \(0.547993\pi\)
\(440\) 2.56757 0.122404
\(441\) 40.6875 1.93750
\(442\) −6.06537 −0.288500
\(443\) −26.4873 −1.25845 −0.629225 0.777223i \(-0.716627\pi\)
−0.629225 + 0.777223i \(0.716627\pi\)
\(444\) −26.8622 −1.27482
\(445\) 0.725334 0.0343841
\(446\) −12.8362 −0.607810
\(447\) −1.89109 −0.0894457
\(448\) −8.86027 −0.418609
\(449\) 29.1325 1.37485 0.687423 0.726257i \(-0.258742\pi\)
0.687423 + 0.726257i \(0.258742\pi\)
\(450\) −4.73947 −0.223421
\(451\) 7.65235 0.360335
\(452\) 17.8990 0.841898
\(453\) −26.8546 −1.26174
\(454\) −14.8461 −0.696764
\(455\) −3.75614 −0.176090
\(456\) −12.0531 −0.564440
\(457\) 21.4931 1.00541 0.502703 0.864459i \(-0.332339\pi\)
0.502703 + 0.864459i \(0.332339\pi\)
\(458\) −1.58055 −0.0738542
\(459\) 81.4479 3.80166
\(460\) 13.0361 0.607810
\(461\) −7.98018 −0.371674 −0.185837 0.982581i \(-0.559500\pi\)
−0.185837 + 0.982581i \(0.559500\pi\)
\(462\) 8.34749 0.388360
\(463\) 16.0042 0.743779 0.371889 0.928277i \(-0.378710\pi\)
0.371889 + 0.928277i \(0.378710\pi\)
\(464\) 3.11273 0.144505
\(465\) −23.0763 −1.07014
\(466\) −14.5061 −0.671980
\(467\) −32.8843 −1.52170 −0.760851 0.648926i \(-0.775218\pi\)
−0.760851 + 0.648926i \(0.775218\pi\)
\(468\) −9.42230 −0.435546
\(469\) 10.4537 0.482707
\(470\) −7.18117 −0.331243
\(471\) 15.7242 0.724534
\(472\) 21.3699 0.983627
\(473\) 8.29774 0.381530
\(474\) −36.9584 −1.69756
\(475\) −1.53458 −0.0704115
\(476\) 41.9219 1.92149
\(477\) −19.6603 −0.900182
\(478\) −1.00726 −0.0460708
\(479\) 26.6751 1.21882 0.609408 0.792857i \(-0.291407\pi\)
0.609408 + 0.792857i \(0.291407\pi\)
\(480\) −17.9311 −0.818438
\(481\) 6.23870 0.284460
\(482\) −14.4942 −0.660193
\(483\) 101.071 4.59887
\(484\) −1.44429 −0.0656497
\(485\) 18.9489 0.860423
\(486\) −5.18737 −0.235304
\(487\) −27.0336 −1.22501 −0.612504 0.790467i \(-0.709838\pi\)
−0.612504 + 0.790467i \(0.709838\pi\)
\(488\) −20.4158 −0.924181
\(489\) −32.2455 −1.45819
\(490\) −4.77065 −0.215516
\(491\) 32.6940 1.47546 0.737731 0.675095i \(-0.235898\pi\)
0.737731 + 0.675095i \(0.235898\pi\)
\(492\) −33.8094 −1.52424
\(493\) 25.3261 1.14063
\(494\) 1.17384 0.0528135
\(495\) 6.35779 0.285762
\(496\) −7.35175 −0.330103
\(497\) 11.6376 0.522016
\(498\) 4.04298 0.181170
\(499\) 6.50850 0.291361 0.145680 0.989332i \(-0.453463\pi\)
0.145680 + 0.989332i \(0.453463\pi\)
\(500\) −1.44429 −0.0645907
\(501\) 3.03334 0.135520
\(502\) −3.69984 −0.165132
\(503\) 34.5960 1.54256 0.771280 0.636495i \(-0.219617\pi\)
0.771280 + 0.636495i \(0.219617\pi\)
\(504\) −59.7552 −2.66171
\(505\) 2.13994 0.0952263
\(506\) 6.72844 0.299116
\(507\) −36.5468 −1.62310
\(508\) −23.7851 −1.05529
\(509\) 24.2189 1.07348 0.536741 0.843747i \(-0.319655\pi\)
0.536741 + 0.843747i \(0.319655\pi\)
\(510\) −18.0821 −0.800689
\(511\) −3.66055 −0.161933
\(512\) −10.7171 −0.473634
\(513\) −15.7627 −0.695941
\(514\) −5.18791 −0.228829
\(515\) −5.76145 −0.253880
\(516\) −36.6608 −1.61390
\(517\) 9.63324 0.423669
\(518\) 16.5908 0.728960
\(519\) −13.0823 −0.574250
\(520\) 2.63462 0.115536
\(521\) 24.2739 1.06346 0.531730 0.846914i \(-0.321542\pi\)
0.531730 + 0.846914i \(0.321542\pi\)
\(522\) −15.1377 −0.662558
\(523\) −35.7848 −1.56476 −0.782380 0.622802i \(-0.785994\pi\)
−0.782380 + 0.622802i \(0.785994\pi\)
\(524\) 0.321840 0.0140596
\(525\) −11.1978 −0.488712
\(526\) 16.0969 0.701860
\(527\) −59.8161 −2.60563
\(528\) 2.98125 0.129742
\(529\) 58.4673 2.54206
\(530\) 2.30519 0.100131
\(531\) 52.9157 2.29635
\(532\) −8.11319 −0.351752
\(533\) 7.85218 0.340116
\(534\) −1.65405 −0.0715776
\(535\) −17.7209 −0.766141
\(536\) −7.33241 −0.316712
\(537\) 7.64669 0.329979
\(538\) 18.8259 0.811643
\(539\) 6.39962 0.275651
\(540\) −14.8353 −0.638409
\(541\) −4.42411 −0.190207 −0.0951037 0.995467i \(-0.530318\pi\)
−0.0951037 + 0.995467i \(0.530318\pi\)
\(542\) 0.0651390 0.00279796
\(543\) 10.1229 0.434416
\(544\) −46.4792 −1.99278
\(545\) 10.8333 0.464048
\(546\) 8.56547 0.366568
\(547\) −8.59061 −0.367308 −0.183654 0.982991i \(-0.558793\pi\)
−0.183654 + 0.982991i \(0.558793\pi\)
\(548\) −0.400430 −0.0171055
\(549\) −50.5534 −2.15757
\(550\) −0.745458 −0.0317864
\(551\) −4.90140 −0.208807
\(552\) −70.8927 −3.01739
\(553\) −59.3266 −2.52283
\(554\) 11.6172 0.493567
\(555\) 18.5988 0.789477
\(556\) −10.1180 −0.429097
\(557\) −18.6859 −0.791745 −0.395873 0.918305i \(-0.629558\pi\)
−0.395873 + 0.918305i \(0.629558\pi\)
\(558\) 35.7527 1.51353
\(559\) 8.51442 0.360121
\(560\) −3.56745 −0.150752
\(561\) 24.2564 1.02411
\(562\) 17.3144 0.730366
\(563\) −8.39664 −0.353876 −0.176938 0.984222i \(-0.556619\pi\)
−0.176938 + 0.984222i \(0.556619\pi\)
\(564\) −42.5612 −1.79215
\(565\) −12.3929 −0.521374
\(566\) 1.66150 0.0698382
\(567\) −45.2010 −1.89826
\(568\) −8.16279 −0.342503
\(569\) 32.4465 1.36023 0.680113 0.733107i \(-0.261931\pi\)
0.680113 + 0.733107i \(0.261931\pi\)
\(570\) 3.49945 0.146576
\(571\) 10.5141 0.440000 0.220000 0.975500i \(-0.429394\pi\)
0.220000 + 0.975500i \(0.429394\pi\)
\(572\) −1.48201 −0.0619659
\(573\) 72.5584 3.03117
\(574\) 20.8816 0.871582
\(575\) −9.02592 −0.376407
\(576\) 15.3889 0.641204
\(577\) −11.6334 −0.484304 −0.242152 0.970238i \(-0.577853\pi\)
−0.242152 + 0.970238i \(0.577853\pi\)
\(578\) −34.1980 −1.42245
\(579\) 29.2690 1.21638
\(580\) −4.61302 −0.191545
\(581\) 6.48990 0.269246
\(582\) −43.2109 −1.79115
\(583\) −3.09231 −0.128070
\(584\) 2.56757 0.106247
\(585\) 6.52381 0.269727
\(586\) 0.646976 0.0267263
\(587\) 0.883663 0.0364727 0.0182363 0.999834i \(-0.494195\pi\)
0.0182363 + 0.999834i \(0.494195\pi\)
\(588\) −28.2746 −1.16602
\(589\) 11.5763 0.476993
\(590\) −6.20442 −0.255432
\(591\) 40.0754 1.64848
\(592\) 5.92531 0.243529
\(593\) 2.67385 0.109802 0.0549008 0.998492i \(-0.482516\pi\)
0.0549008 + 0.998492i \(0.482516\pi\)
\(594\) −7.65709 −0.314174
\(595\) −29.0259 −1.18995
\(596\) 0.892856 0.0365728
\(597\) −38.5734 −1.57870
\(598\) 6.90414 0.282331
\(599\) −4.46895 −0.182596 −0.0912982 0.995824i \(-0.529102\pi\)
−0.0912982 + 0.995824i \(0.529102\pi\)
\(600\) 7.85434 0.320652
\(601\) −25.3077 −1.03232 −0.516162 0.856491i \(-0.672640\pi\)
−0.516162 + 0.856491i \(0.672640\pi\)
\(602\) 22.6427 0.922849
\(603\) −18.1564 −0.739386
\(604\) 12.6791 0.515903
\(605\) 1.00000 0.0406558
\(606\) −4.87992 −0.198233
\(607\) −26.9252 −1.09286 −0.546431 0.837504i \(-0.684014\pi\)
−0.546431 + 0.837504i \(0.684014\pi\)
\(608\) 8.99518 0.364803
\(609\) −35.7654 −1.44929
\(610\) 5.92744 0.239995
\(611\) 9.88479 0.399896
\(612\) −72.8117 −2.94324
\(613\) 5.84970 0.236267 0.118133 0.992998i \(-0.462309\pi\)
0.118133 + 0.992998i \(0.462309\pi\)
\(614\) −16.2307 −0.655017
\(615\) 23.4089 0.943939
\(616\) −9.39873 −0.378686
\(617\) 25.6742 1.03360 0.516802 0.856105i \(-0.327122\pi\)
0.516802 + 0.856105i \(0.327122\pi\)
\(618\) 13.1384 0.528503
\(619\) 28.5604 1.14794 0.573969 0.818877i \(-0.305403\pi\)
0.573969 + 0.818877i \(0.305403\pi\)
\(620\) 10.8952 0.437561
\(621\) −92.7112 −3.72037
\(622\) 17.3727 0.696583
\(623\) −2.65512 −0.106375
\(624\) 3.05910 0.122462
\(625\) 1.00000 0.0400000
\(626\) −15.7397 −0.629086
\(627\) −4.69437 −0.187475
\(628\) −7.42400 −0.296250
\(629\) 48.2101 1.92226
\(630\) 17.3490 0.691203
\(631\) −13.7548 −0.547570 −0.273785 0.961791i \(-0.588276\pi\)
−0.273785 + 0.961791i \(0.588276\pi\)
\(632\) 41.6128 1.65527
\(633\) 41.8245 1.66237
\(634\) 0.237738 0.00944179
\(635\) 16.4683 0.653526
\(636\) 13.6623 0.541747
\(637\) 6.56674 0.260184
\(638\) −2.38096 −0.0942632
\(639\) −20.2126 −0.799598
\(640\) 9.91893 0.392080
\(641\) −37.3178 −1.47396 −0.736982 0.675912i \(-0.763750\pi\)
−0.736982 + 0.675912i \(0.763750\pi\)
\(642\) 40.4106 1.59488
\(643\) −30.2238 −1.19191 −0.595956 0.803017i \(-0.703227\pi\)
−0.595956 + 0.803017i \(0.703227\pi\)
\(644\) −47.7192 −1.88040
\(645\) 25.3832 0.999462
\(646\) 9.07095 0.356892
\(647\) 0.269979 0.0106140 0.00530699 0.999986i \(-0.498311\pi\)
0.00530699 + 0.999986i \(0.498311\pi\)
\(648\) 31.7048 1.24548
\(649\) 8.32297 0.326705
\(650\) −0.764924 −0.0300028
\(651\) 84.4719 3.31071
\(652\) 15.2243 0.596231
\(653\) −36.8015 −1.44016 −0.720078 0.693893i \(-0.755894\pi\)
−0.720078 + 0.693893i \(0.755894\pi\)
\(654\) −24.7042 −0.966010
\(655\) −0.222835 −0.00870690
\(656\) 7.45773 0.291175
\(657\) 6.35779 0.248041
\(658\) 26.2870 1.02478
\(659\) −11.7704 −0.458510 −0.229255 0.973366i \(-0.573629\pi\)
−0.229255 + 0.973366i \(0.573629\pi\)
\(660\) −4.41817 −0.171977
\(661\) −26.0057 −1.01151 −0.505753 0.862679i \(-0.668785\pi\)
−0.505753 + 0.862679i \(0.668785\pi\)
\(662\) 20.1740 0.784085
\(663\) 24.8898 0.966640
\(664\) −4.55213 −0.176657
\(665\) 5.61742 0.217834
\(666\) −28.8157 −1.11658
\(667\) −28.8284 −1.11624
\(668\) −1.43215 −0.0554117
\(669\) 52.6743 2.03651
\(670\) 2.12886 0.0822449
\(671\) −7.95140 −0.306961
\(672\) 65.6376 2.53203
\(673\) −44.5215 −1.71618 −0.858088 0.513503i \(-0.828348\pi\)
−0.858088 + 0.513503i \(0.828348\pi\)
\(674\) −8.56059 −0.329742
\(675\) 10.2717 0.395356
\(676\) 17.2551 0.663658
\(677\) −38.7167 −1.48801 −0.744003 0.668177i \(-0.767075\pi\)
−0.744003 + 0.668177i \(0.767075\pi\)
\(678\) 28.2607 1.08535
\(679\) −69.3632 −2.66192
\(680\) 20.3593 0.780743
\(681\) 60.9224 2.33455
\(682\) 5.62344 0.215333
\(683\) 32.4364 1.24114 0.620572 0.784149i \(-0.286900\pi\)
0.620572 + 0.784149i \(0.286900\pi\)
\(684\) 14.0913 0.538795
\(685\) 0.277250 0.0105932
\(686\) −1.63830 −0.0625504
\(687\) 6.48592 0.247453
\(688\) 8.08670 0.308303
\(689\) −3.17306 −0.120884
\(690\) 20.5827 0.783568
\(691\) 9.99291 0.380148 0.190074 0.981770i \(-0.439127\pi\)
0.190074 + 0.981770i \(0.439127\pi\)
\(692\) 6.17665 0.234801
\(693\) −23.2730 −0.884069
\(694\) 10.1169 0.384032
\(695\) 7.00548 0.265733
\(696\) 25.0865 0.950900
\(697\) 60.6784 2.29836
\(698\) −13.6327 −0.516005
\(699\) 59.5269 2.25151
\(700\) 5.28691 0.199826
\(701\) −23.9841 −0.905867 −0.452934 0.891544i \(-0.649623\pi\)
−0.452934 + 0.891544i \(0.649623\pi\)
\(702\) −7.85704 −0.296545
\(703\) −9.33017 −0.351894
\(704\) 2.42048 0.0912251
\(705\) 29.4686 1.10985
\(706\) 19.1597 0.721087
\(707\) −7.83337 −0.294604
\(708\) −36.7723 −1.38199
\(709\) 17.0050 0.638637 0.319319 0.947647i \(-0.396546\pi\)
0.319319 + 0.947647i \(0.396546\pi\)
\(710\) 2.36995 0.0889426
\(711\) 103.041 3.86434
\(712\) 1.86235 0.0697945
\(713\) 68.0880 2.54992
\(714\) 66.1905 2.47712
\(715\) 1.02611 0.0383745
\(716\) −3.61029 −0.134923
\(717\) 4.13336 0.154363
\(718\) 3.93354 0.146799
\(719\) 2.46818 0.0920478 0.0460239 0.998940i \(-0.485345\pi\)
0.0460239 + 0.998940i \(0.485345\pi\)
\(720\) 6.19610 0.230915
\(721\) 21.0901 0.785436
\(722\) 12.4082 0.461785
\(723\) 59.4782 2.21202
\(724\) −4.77941 −0.177625
\(725\) 3.19396 0.118621
\(726\) −2.28039 −0.0846333
\(727\) −18.8451 −0.698924 −0.349462 0.936950i \(-0.613636\pi\)
−0.349462 + 0.936950i \(0.613636\pi\)
\(728\) −9.64417 −0.357437
\(729\) −15.7576 −0.583615
\(730\) −0.745458 −0.0275906
\(731\) 65.7959 2.43355
\(732\) 35.1306 1.29846
\(733\) 8.26369 0.305226 0.152613 0.988286i \(-0.451231\pi\)
0.152613 + 0.988286i \(0.451231\pi\)
\(734\) 15.6917 0.579191
\(735\) 19.5768 0.722100
\(736\) 52.9068 1.95017
\(737\) −2.85577 −0.105194
\(738\) −36.2681 −1.33505
\(739\) −38.7957 −1.42712 −0.713562 0.700592i \(-0.752919\pi\)
−0.713562 + 0.700592i \(0.752919\pi\)
\(740\) −8.78121 −0.322804
\(741\) −4.81695 −0.176955
\(742\) −8.43826 −0.309778
\(743\) −12.6764 −0.465052 −0.232526 0.972590i \(-0.574699\pi\)
−0.232526 + 0.972590i \(0.574699\pi\)
\(744\) −59.2501 −2.17221
\(745\) −0.618196 −0.0226490
\(746\) −20.3018 −0.743302
\(747\) −11.2719 −0.412418
\(748\) −11.4523 −0.418739
\(749\) 64.8682 2.37023
\(750\) −2.28039 −0.0832682
\(751\) −29.8876 −1.09061 −0.545307 0.838236i \(-0.683587\pi\)
−0.545307 + 0.838236i \(0.683587\pi\)
\(752\) 9.38824 0.342354
\(753\) 15.1826 0.553285
\(754\) −2.44314 −0.0889738
\(755\) −8.77873 −0.319491
\(756\) 54.3053 1.97506
\(757\) −19.8595 −0.721807 −0.360903 0.932603i \(-0.617532\pi\)
−0.360903 + 0.932603i \(0.617532\pi\)
\(758\) 2.45900 0.0893149
\(759\) −27.6108 −1.00221
\(760\) −3.94016 −0.142924
\(761\) −22.5344 −0.816870 −0.408435 0.912787i \(-0.633925\pi\)
−0.408435 + 0.912787i \(0.633925\pi\)
\(762\) −37.5543 −1.36045
\(763\) −39.6558 −1.43564
\(764\) −34.2575 −1.23939
\(765\) 50.4134 1.82270
\(766\) 3.83281 0.138485
\(767\) 8.54031 0.308373
\(768\) −37.4278 −1.35056
\(769\) −33.6335 −1.21286 −0.606428 0.795139i \(-0.707398\pi\)
−0.606428 + 0.795139i \(0.707398\pi\)
\(770\) 2.72879 0.0983386
\(771\) 21.2891 0.766707
\(772\) −13.8190 −0.497356
\(773\) −3.81775 −0.137315 −0.0686575 0.997640i \(-0.521872\pi\)
−0.0686575 + 0.997640i \(0.521872\pi\)
\(774\) −39.3268 −1.41357
\(775\) −7.54361 −0.270974
\(776\) 48.6526 1.74653
\(777\) −68.0820 −2.44243
\(778\) 4.04630 0.145067
\(779\) −11.7432 −0.420743
\(780\) −4.53354 −0.162327
\(781\) −3.17918 −0.113760
\(782\) 53.3524 1.90788
\(783\) 32.8073 1.17244
\(784\) 6.23686 0.222745
\(785\) 5.14023 0.183463
\(786\) 0.508152 0.0181252
\(787\) −16.4419 −0.586089 −0.293045 0.956099i \(-0.594668\pi\)
−0.293045 + 0.956099i \(0.594668\pi\)
\(788\) −18.9211 −0.674037
\(789\) −66.0552 −2.35163
\(790\) −12.0817 −0.429846
\(791\) 45.3649 1.61299
\(792\) 16.3241 0.580052
\(793\) −8.15904 −0.289736
\(794\) 24.5843 0.872465
\(795\) −9.45954 −0.335495
\(796\) 18.2119 0.645505
\(797\) 38.6822 1.37020 0.685098 0.728451i \(-0.259760\pi\)
0.685098 + 0.728451i \(0.259760\pi\)
\(798\) −12.8099 −0.453466
\(799\) 76.3856 2.70233
\(800\) −5.86165 −0.207241
\(801\) 4.61152 0.162940
\(802\) −12.2225 −0.431591
\(803\) 1.00000 0.0352892
\(804\) 12.6173 0.444977
\(805\) 33.0398 1.16450
\(806\) 5.77029 0.203250
\(807\) −77.2538 −2.71946
\(808\) 5.49447 0.193295
\(809\) 28.5008 1.00203 0.501017 0.865438i \(-0.332960\pi\)
0.501017 + 0.865438i \(0.332960\pi\)
\(810\) −9.20502 −0.323432
\(811\) −13.3390 −0.468396 −0.234198 0.972189i \(-0.575246\pi\)
−0.234198 + 0.972189i \(0.575246\pi\)
\(812\) 16.8862 0.592588
\(813\) −0.267304 −0.00937475
\(814\) −4.53234 −0.158858
\(815\) −10.5410 −0.369236
\(816\) 23.6395 0.827547
\(817\) −12.7336 −0.445491
\(818\) 21.3280 0.745715
\(819\) −23.8807 −0.834461
\(820\) −11.0522 −0.385961
\(821\) 22.4293 0.782787 0.391393 0.920223i \(-0.371993\pi\)
0.391393 + 0.920223i \(0.371993\pi\)
\(822\) −0.632239 −0.0220519
\(823\) −7.55118 −0.263218 −0.131609 0.991302i \(-0.542014\pi\)
−0.131609 + 0.991302i \(0.542014\pi\)
\(824\) −14.7930 −0.515337
\(825\) 3.05905 0.106502
\(826\) 22.7116 0.790238
\(827\) −0.858475 −0.0298521 −0.0149260 0.999889i \(-0.504751\pi\)
−0.0149260 + 0.999889i \(0.504751\pi\)
\(828\) 82.8807 2.88030
\(829\) 46.3599 1.61015 0.805073 0.593175i \(-0.202126\pi\)
0.805073 + 0.593175i \(0.202126\pi\)
\(830\) 1.32164 0.0458749
\(831\) −47.6721 −1.65373
\(832\) 2.48368 0.0861062
\(833\) 50.7451 1.75821
\(834\) −15.9752 −0.553178
\(835\) 0.991594 0.0343155
\(836\) 2.21639 0.0766553
\(837\) −77.4854 −2.67829
\(838\) 22.4919 0.776970
\(839\) 1.05196 0.0363178 0.0181589 0.999835i \(-0.494220\pi\)
0.0181589 + 0.999835i \(0.494220\pi\)
\(840\) −28.7512 −0.992011
\(841\) −18.7986 −0.648228
\(842\) 11.6018 0.399825
\(843\) −71.0513 −2.44714
\(844\) −19.7469 −0.679717
\(845\) −11.9471 −0.410992
\(846\) −45.6564 −1.56970
\(847\) −3.66055 −0.125778
\(848\) −3.01367 −0.103490
\(849\) −6.81813 −0.233998
\(850\) −5.91102 −0.202746
\(851\) −54.8770 −1.88116
\(852\) 14.0462 0.481214
\(853\) −23.3445 −0.799300 −0.399650 0.916668i \(-0.630868\pi\)
−0.399650 + 0.916668i \(0.630868\pi\)
\(854\) −21.6977 −0.742479
\(855\) −9.75656 −0.333667
\(856\) −45.4997 −1.55515
\(857\) −8.85205 −0.302380 −0.151190 0.988505i \(-0.548311\pi\)
−0.151190 + 0.988505i \(0.548311\pi\)
\(858\) −2.33994 −0.0798843
\(859\) −15.5623 −0.530977 −0.265489 0.964114i \(-0.585533\pi\)
−0.265489 + 0.964114i \(0.585533\pi\)
\(860\) −11.9844 −0.408663
\(861\) −85.6896 −2.92029
\(862\) 22.7388 0.774485
\(863\) 28.5694 0.972515 0.486258 0.873816i \(-0.338362\pi\)
0.486258 + 0.873816i \(0.338362\pi\)
\(864\) −60.2088 −2.04835
\(865\) −4.27659 −0.145409
\(866\) 20.9120 0.710619
\(867\) 140.334 4.76600
\(868\) −39.8823 −1.35369
\(869\) 16.2070 0.549786
\(870\) −7.28349 −0.246933
\(871\) −2.93035 −0.0992910
\(872\) 27.8153 0.941946
\(873\) 120.473 4.07739
\(874\) −10.3254 −0.349260
\(875\) −3.66055 −0.123749
\(876\) −4.41817 −0.149276
\(877\) −51.3452 −1.73380 −0.866902 0.498479i \(-0.833892\pi\)
−0.866902 + 0.498479i \(0.833892\pi\)
\(878\) 4.69214 0.158352
\(879\) −2.65492 −0.0895483
\(880\) 0.974567 0.0328527
\(881\) −31.6055 −1.06482 −0.532408 0.846488i \(-0.678713\pi\)
−0.532408 + 0.846488i \(0.678713\pi\)
\(882\) −30.3308 −1.02129
\(883\) −53.5711 −1.80281 −0.901405 0.432977i \(-0.857463\pi\)
−0.901405 + 0.432977i \(0.857463\pi\)
\(884\) −11.7514 −0.395243
\(885\) 25.4604 0.855842
\(886\) 19.7452 0.663352
\(887\) −20.1353 −0.676077 −0.338038 0.941132i \(-0.609763\pi\)
−0.338038 + 0.941132i \(0.609763\pi\)
\(888\) 47.7539 1.60252
\(889\) −60.2832 −2.02183
\(890\) −0.540706 −0.0181245
\(891\) 12.3481 0.413679
\(892\) −24.8695 −0.832693
\(893\) −14.7830 −0.494694
\(894\) 1.40973 0.0471484
\(895\) 2.49969 0.0835555
\(896\) −36.3087 −1.21299
\(897\) −28.3318 −0.945970
\(898\) −21.7170 −0.724707
\(899\) −24.0940 −0.803580
\(900\) −9.18251 −0.306084
\(901\) −24.5201 −0.816884
\(902\) −5.70450 −0.189939
\(903\) −92.9164 −3.09207
\(904\) −31.8197 −1.05831
\(905\) 3.30917 0.110001
\(906\) 20.0189 0.665085
\(907\) 48.1956 1.60031 0.800154 0.599794i \(-0.204751\pi\)
0.800154 + 0.599794i \(0.204751\pi\)
\(908\) −28.7638 −0.954559
\(909\) 13.6053 0.451260
\(910\) 2.80004 0.0928205
\(911\) 2.65861 0.0880838 0.0440419 0.999030i \(-0.485976\pi\)
0.0440419 + 0.999030i \(0.485976\pi\)
\(912\) −4.57498 −0.151493
\(913\) −1.77293 −0.0586754
\(914\) −16.0222 −0.529967
\(915\) −24.3237 −0.804118
\(916\) −3.06225 −0.101179
\(917\) 0.815700 0.0269368
\(918\) −60.7160 −2.00393
\(919\) 34.0241 1.12235 0.561176 0.827696i \(-0.310349\pi\)
0.561176 + 0.827696i \(0.310349\pi\)
\(920\) −23.1747 −0.764048
\(921\) 66.6040 2.19468
\(922\) 5.94889 0.195916
\(923\) −3.26220 −0.107377
\(924\) 16.1729 0.532050
\(925\) 6.07994 0.199907
\(926\) −11.9305 −0.392059
\(927\) −36.6301 −1.20309
\(928\) −18.7219 −0.614576
\(929\) 45.1410 1.48103 0.740514 0.672041i \(-0.234582\pi\)
0.740514 + 0.672041i \(0.234582\pi\)
\(930\) 17.2024 0.564089
\(931\) −9.82075 −0.321862
\(932\) −28.1049 −0.920606
\(933\) −71.2906 −2.33395
\(934\) 24.5138 0.802117
\(935\) 7.92938 0.259319
\(936\) 16.7504 0.547503
\(937\) 23.6534 0.772721 0.386361 0.922348i \(-0.373732\pi\)
0.386361 + 0.922348i \(0.373732\pi\)
\(938\) −7.79279 −0.254444
\(939\) 64.5894 2.10780
\(940\) −13.9132 −0.453799
\(941\) −35.5296 −1.15823 −0.579116 0.815245i \(-0.696602\pi\)
−0.579116 + 0.815245i \(0.696602\pi\)
\(942\) −11.7218 −0.381915
\(943\) −69.0695 −2.24921
\(944\) 8.11130 0.264000
\(945\) −37.5999 −1.22313
\(946\) −6.18561 −0.201112
\(947\) 11.0303 0.358437 0.179219 0.983809i \(-0.442643\pi\)
0.179219 + 0.983809i \(0.442643\pi\)
\(948\) −71.6053 −2.32563
\(949\) 1.02611 0.0333090
\(950\) 1.14397 0.0371152
\(951\) −0.975580 −0.0316353
\(952\) −74.5262 −2.41541
\(953\) −39.0570 −1.26518 −0.632590 0.774487i \(-0.718008\pi\)
−0.632590 + 0.774487i \(0.718008\pi\)
\(954\) 14.6559 0.474503
\(955\) 23.7192 0.767537
\(956\) −1.95151 −0.0631165
\(957\) 9.77049 0.315835
\(958\) −19.8851 −0.642460
\(959\) −1.01489 −0.0327724
\(960\) 7.40436 0.238975
\(961\) 25.9060 0.835678
\(962\) −4.65069 −0.149944
\(963\) −112.666 −3.63060
\(964\) −28.0819 −0.904457
\(965\) 9.56799 0.308004
\(966\) −75.3438 −2.42415
\(967\) −43.6286 −1.40300 −0.701500 0.712669i \(-0.747486\pi\)
−0.701500 + 0.712669i \(0.747486\pi\)
\(968\) 2.56757 0.0825250
\(969\) −37.2234 −1.19579
\(970\) −14.1256 −0.453545
\(971\) −29.7850 −0.955847 −0.477924 0.878401i \(-0.658610\pi\)
−0.477924 + 0.878401i \(0.658610\pi\)
\(972\) −10.0503 −0.322364
\(973\) −25.6439 −0.822106
\(974\) 20.1524 0.645724
\(975\) 3.13893 0.100526
\(976\) −7.74918 −0.248045
\(977\) −42.9978 −1.37562 −0.687810 0.725890i \(-0.741428\pi\)
−0.687810 + 0.725890i \(0.741428\pi\)
\(978\) 24.0377 0.768640
\(979\) 0.725334 0.0231818
\(980\) −9.24293 −0.295255
\(981\) 68.8759 2.19904
\(982\) −24.3720 −0.777742
\(983\) 49.6405 1.58329 0.791643 0.610984i \(-0.209226\pi\)
0.791643 + 0.610984i \(0.209226\pi\)
\(984\) 60.1042 1.91605
\(985\) 13.1006 0.417420
\(986\) −18.8796 −0.601248
\(987\) −107.871 −3.43358
\(988\) 2.27426 0.0723540
\(989\) −74.8947 −2.38151
\(990\) −4.73947 −0.150630
\(991\) 48.0861 1.52751 0.763753 0.645509i \(-0.223355\pi\)
0.763753 + 0.645509i \(0.223355\pi\)
\(992\) 44.2180 1.40392
\(993\) −82.7858 −2.62713
\(994\) −8.67531 −0.275164
\(995\) −12.6096 −0.399751
\(996\) 7.83310 0.248201
\(997\) −37.4483 −1.18600 −0.592999 0.805203i \(-0.702056\pi\)
−0.592999 + 0.805203i \(0.702056\pi\)
\(998\) −4.85181 −0.153581
\(999\) 62.4510 1.97586
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 \(a_p\))