Properties

Label 8042.2.a.c.1.20
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

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: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.75423 q^{3}\) \(+1.00000 q^{4}\) \(-3.88795 q^{5}\) \(+1.75423 q^{6}\) \(+3.77690 q^{7}\) \(-1.00000 q^{8}\) \(+0.0773276 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.75423 q^{3}\) \(+1.00000 q^{4}\) \(-3.88795 q^{5}\) \(+1.75423 q^{6}\) \(+3.77690 q^{7}\) \(-1.00000 q^{8}\) \(+0.0773276 q^{9}\) \(+3.88795 q^{10}\) \(-0.891621 q^{11}\) \(-1.75423 q^{12}\) \(+0.270119 q^{13}\) \(-3.77690 q^{14}\) \(+6.82037 q^{15}\) \(+1.00000 q^{16}\) \(+3.78696 q^{17}\) \(-0.0773276 q^{18}\) \(+6.97343 q^{19}\) \(-3.88795 q^{20}\) \(-6.62556 q^{21}\) \(+0.891621 q^{22}\) \(+1.59417 q^{23}\) \(+1.75423 q^{24}\) \(+10.1162 q^{25}\) \(-0.270119 q^{26}\) \(+5.12704 q^{27}\) \(+3.77690 q^{28}\) \(+5.23837 q^{29}\) \(-6.82037 q^{30}\) \(+5.29808 q^{31}\) \(-1.00000 q^{32}\) \(+1.56411 q^{33}\) \(-3.78696 q^{34}\) \(-14.6844 q^{35}\) \(+0.0773276 q^{36}\) \(+2.71579 q^{37}\) \(-6.97343 q^{38}\) \(-0.473851 q^{39}\) \(+3.88795 q^{40}\) \(-6.00482 q^{41}\) \(+6.62556 q^{42}\) \(+5.68254 q^{43}\) \(-0.891621 q^{44}\) \(-0.300646 q^{45}\) \(-1.59417 q^{46}\) \(-3.50723 q^{47}\) \(-1.75423 q^{48}\) \(+7.26499 q^{49}\) \(-10.1162 q^{50}\) \(-6.64321 q^{51}\) \(+0.270119 q^{52}\) \(+7.83966 q^{53}\) \(-5.12704 q^{54}\) \(+3.46658 q^{55}\) \(-3.77690 q^{56}\) \(-12.2330 q^{57}\) \(-5.23837 q^{58}\) \(+10.0165 q^{59}\) \(+6.82037 q^{60}\) \(+2.93760 q^{61}\) \(-5.29808 q^{62}\) \(+0.292059 q^{63}\) \(+1.00000 q^{64}\) \(-1.05021 q^{65}\) \(-1.56411 q^{66}\) \(+6.65517 q^{67}\) \(+3.78696 q^{68}\) \(-2.79654 q^{69}\) \(+14.6844 q^{70}\) \(-7.44458 q^{71}\) \(-0.0773276 q^{72}\) \(-0.533104 q^{73}\) \(-2.71579 q^{74}\) \(-17.7461 q^{75}\) \(+6.97343 q^{76}\) \(-3.36757 q^{77}\) \(+0.473851 q^{78}\) \(+3.23891 q^{79}\) \(-3.88795 q^{80}\) \(-9.22600 q^{81}\) \(+6.00482 q^{82}\) \(-9.69483 q^{83}\) \(-6.62556 q^{84}\) \(-14.7235 q^{85}\) \(-5.68254 q^{86}\) \(-9.18932 q^{87}\) \(+0.891621 q^{88}\) \(+15.0329 q^{89}\) \(+0.300646 q^{90}\) \(+1.02021 q^{91}\) \(+1.59417 q^{92}\) \(-9.29407 q^{93}\) \(+3.50723 q^{94}\) \(-27.1124 q^{95}\) \(+1.75423 q^{96}\) \(+4.42694 q^{97}\) \(-7.26499 q^{98}\) \(-0.0689469 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.75423 −1.01281 −0.506403 0.862297i \(-0.669025\pi\)
−0.506403 + 0.862297i \(0.669025\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.88795 −1.73875 −0.869373 0.494156i \(-0.835477\pi\)
−0.869373 + 0.494156i \(0.835477\pi\)
\(6\) 1.75423 0.716162
\(7\) 3.77690 1.42753 0.713767 0.700383i \(-0.246987\pi\)
0.713767 + 0.700383i \(0.246987\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.0773276 0.0257759
\(10\) 3.88795 1.22948
\(11\) −0.891621 −0.268834 −0.134417 0.990925i \(-0.542916\pi\)
−0.134417 + 0.990925i \(0.542916\pi\)
\(12\) −1.75423 −0.506403
\(13\) 0.270119 0.0749175 0.0374588 0.999298i \(-0.488074\pi\)
0.0374588 + 0.999298i \(0.488074\pi\)
\(14\) −3.77690 −1.00942
\(15\) 6.82037 1.76101
\(16\) 1.00000 0.250000
\(17\) 3.78696 0.918474 0.459237 0.888314i \(-0.348123\pi\)
0.459237 + 0.888314i \(0.348123\pi\)
\(18\) −0.0773276 −0.0182263
\(19\) 6.97343 1.59982 0.799908 0.600123i \(-0.204882\pi\)
0.799908 + 0.600123i \(0.204882\pi\)
\(20\) −3.88795 −0.869373
\(21\) −6.62556 −1.44582
\(22\) 0.891621 0.190094
\(23\) 1.59417 0.332407 0.166203 0.986091i \(-0.446849\pi\)
0.166203 + 0.986091i \(0.446849\pi\)
\(24\) 1.75423 0.358081
\(25\) 10.1162 2.02324
\(26\) −0.270119 −0.0529747
\(27\) 5.12704 0.986700
\(28\) 3.77690 0.713767
\(29\) 5.23837 0.972741 0.486371 0.873753i \(-0.338320\pi\)
0.486371 + 0.873753i \(0.338320\pi\)
\(30\) −6.82037 −1.24522
\(31\) 5.29808 0.951564 0.475782 0.879563i \(-0.342165\pi\)
0.475782 + 0.879563i \(0.342165\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.56411 0.272277
\(34\) −3.78696 −0.649459
\(35\) −14.6844 −2.48212
\(36\) 0.0773276 0.0128879
\(37\) 2.71579 0.446474 0.223237 0.974764i \(-0.428338\pi\)
0.223237 + 0.974764i \(0.428338\pi\)
\(38\) −6.97343 −1.13124
\(39\) −0.473851 −0.0758769
\(40\) 3.88795 0.614740
\(41\) −6.00482 −0.937796 −0.468898 0.883252i \(-0.655349\pi\)
−0.468898 + 0.883252i \(0.655349\pi\)
\(42\) 6.62556 1.02235
\(43\) 5.68254 0.866579 0.433289 0.901255i \(-0.357353\pi\)
0.433289 + 0.901255i \(0.357353\pi\)
\(44\) −0.891621 −0.134417
\(45\) −0.300646 −0.0448177
\(46\) −1.59417 −0.235047
\(47\) −3.50723 −0.511582 −0.255791 0.966732i \(-0.582336\pi\)
−0.255791 + 0.966732i \(0.582336\pi\)
\(48\) −1.75423 −0.253201
\(49\) 7.26499 1.03786
\(50\) −10.1162 −1.43064
\(51\) −6.64321 −0.930235
\(52\) 0.270119 0.0374588
\(53\) 7.83966 1.07686 0.538430 0.842670i \(-0.319017\pi\)
0.538430 + 0.842670i \(0.319017\pi\)
\(54\) −5.12704 −0.697702
\(55\) 3.46658 0.467434
\(56\) −3.77690 −0.504710
\(57\) −12.2330 −1.62030
\(58\) −5.23837 −0.687832
\(59\) 10.0165 1.30403 0.652017 0.758205i \(-0.273923\pi\)
0.652017 + 0.758205i \(0.273923\pi\)
\(60\) 6.82037 0.880506
\(61\) 2.93760 0.376121 0.188061 0.982157i \(-0.439780\pi\)
0.188061 + 0.982157i \(0.439780\pi\)
\(62\) −5.29808 −0.672857
\(63\) 0.292059 0.0367959
\(64\) 1.00000 0.125000
\(65\) −1.05021 −0.130263
\(66\) −1.56411 −0.192529
\(67\) 6.65517 0.813059 0.406529 0.913638i \(-0.366739\pi\)
0.406529 + 0.913638i \(0.366739\pi\)
\(68\) 3.78696 0.459237
\(69\) −2.79654 −0.336664
\(70\) 14.6844 1.75512
\(71\) −7.44458 −0.883509 −0.441755 0.897136i \(-0.645644\pi\)
−0.441755 + 0.897136i \(0.645644\pi\)
\(72\) −0.0773276 −0.00911314
\(73\) −0.533104 −0.0623951 −0.0311975 0.999513i \(-0.509932\pi\)
−0.0311975 + 0.999513i \(0.509932\pi\)
\(74\) −2.71579 −0.315705
\(75\) −17.7461 −2.04915
\(76\) 6.97343 0.799908
\(77\) −3.36757 −0.383770
\(78\) 0.473851 0.0536531
\(79\) 3.23891 0.364406 0.182203 0.983261i \(-0.441677\pi\)
0.182203 + 0.983261i \(0.441677\pi\)
\(80\) −3.88795 −0.434686
\(81\) −9.22600 −1.02511
\(82\) 6.00482 0.663122
\(83\) −9.69483 −1.06415 −0.532073 0.846698i \(-0.678587\pi\)
−0.532073 + 0.846698i \(0.678587\pi\)
\(84\) −6.62556 −0.722908
\(85\) −14.7235 −1.59699
\(86\) −5.68254 −0.612764
\(87\) −9.18932 −0.985198
\(88\) 0.891621 0.0950471
\(89\) 15.0329 1.59349 0.796743 0.604319i \(-0.206555\pi\)
0.796743 + 0.604319i \(0.206555\pi\)
\(90\) 0.300646 0.0316909
\(91\) 1.02021 0.106947
\(92\) 1.59417 0.166203
\(93\) −9.29407 −0.963750
\(94\) 3.50723 0.361743
\(95\) −27.1124 −2.78167
\(96\) 1.75423 0.179040
\(97\) 4.42694 0.449488 0.224744 0.974418i \(-0.427845\pi\)
0.224744 + 0.974418i \(0.427845\pi\)
\(98\) −7.26499 −0.733875
\(99\) −0.0689469 −0.00692942
\(100\) 10.1162 1.01162
\(101\) 4.94998 0.492541 0.246271 0.969201i \(-0.420795\pi\)
0.246271 + 0.969201i \(0.420795\pi\)
\(102\) 6.64321 0.657776
\(103\) 4.25054 0.418818 0.209409 0.977828i \(-0.432846\pi\)
0.209409 + 0.977828i \(0.432846\pi\)
\(104\) −0.270119 −0.0264873
\(105\) 25.7599 2.51391
\(106\) −7.83966 −0.761456
\(107\) −8.47450 −0.819261 −0.409630 0.912252i \(-0.634342\pi\)
−0.409630 + 0.912252i \(0.634342\pi\)
\(108\) 5.12704 0.493350
\(109\) −4.94777 −0.473910 −0.236955 0.971521i \(-0.576149\pi\)
−0.236955 + 0.971521i \(0.576149\pi\)
\(110\) −3.46658 −0.330526
\(111\) −4.76413 −0.452191
\(112\) 3.77690 0.356884
\(113\) −12.8103 −1.20509 −0.602544 0.798085i \(-0.705846\pi\)
−0.602544 + 0.798085i \(0.705846\pi\)
\(114\) 12.2330 1.14573
\(115\) −6.19805 −0.577971
\(116\) 5.23837 0.486371
\(117\) 0.0208877 0.00193106
\(118\) −10.0165 −0.922091
\(119\) 14.3030 1.31115
\(120\) −6.82037 −0.622612
\(121\) −10.2050 −0.927728
\(122\) −2.93760 −0.265958
\(123\) 10.5338 0.949805
\(124\) 5.29808 0.475782
\(125\) −19.8915 −1.77915
\(126\) −0.292059 −0.0260187
\(127\) 0.461728 0.0409718 0.0204859 0.999790i \(-0.493479\pi\)
0.0204859 + 0.999790i \(0.493479\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.96849 −0.877676
\(130\) 1.05021 0.0921095
\(131\) −6.70343 −0.585681 −0.292840 0.956161i \(-0.594600\pi\)
−0.292840 + 0.956161i \(0.594600\pi\)
\(132\) 1.56411 0.136138
\(133\) 26.3380 2.28379
\(134\) −6.65517 −0.574919
\(135\) −19.9337 −1.71562
\(136\) −3.78696 −0.324729
\(137\) 12.1320 1.03651 0.518254 0.855227i \(-0.326582\pi\)
0.518254 + 0.855227i \(0.326582\pi\)
\(138\) 2.79654 0.238057
\(139\) 17.9890 1.52580 0.762902 0.646514i \(-0.223774\pi\)
0.762902 + 0.646514i \(0.223774\pi\)
\(140\) −14.6844 −1.24106
\(141\) 6.15249 0.518133
\(142\) 7.44458 0.624735
\(143\) −0.240844 −0.0201404
\(144\) 0.0773276 0.00644397
\(145\) −20.3666 −1.69135
\(146\) 0.533104 0.0441200
\(147\) −12.7445 −1.05115
\(148\) 2.71579 0.223237
\(149\) 14.2877 1.17049 0.585245 0.810856i \(-0.300998\pi\)
0.585245 + 0.810856i \(0.300998\pi\)
\(150\) 17.7461 1.44897
\(151\) −15.1888 −1.23605 −0.618023 0.786160i \(-0.712066\pi\)
−0.618023 + 0.786160i \(0.712066\pi\)
\(152\) −6.97343 −0.565620
\(153\) 0.292837 0.0236744
\(154\) 3.36757 0.271366
\(155\) −20.5987 −1.65453
\(156\) −0.473851 −0.0379385
\(157\) 12.2721 0.979423 0.489711 0.871885i \(-0.337102\pi\)
0.489711 + 0.871885i \(0.337102\pi\)
\(158\) −3.23891 −0.257674
\(159\) −13.7526 −1.09065
\(160\) 3.88795 0.307370
\(161\) 6.02101 0.474522
\(162\) 9.22600 0.724863
\(163\) −9.37968 −0.734673 −0.367336 0.930088i \(-0.619730\pi\)
−0.367336 + 0.930088i \(0.619730\pi\)
\(164\) −6.00482 −0.468898
\(165\) −6.08119 −0.473420
\(166\) 9.69483 0.752465
\(167\) −12.3620 −0.956598 −0.478299 0.878197i \(-0.658747\pi\)
−0.478299 + 0.878197i \(0.658747\pi\)
\(168\) 6.62556 0.511173
\(169\) −12.9270 −0.994387
\(170\) 14.7235 1.12924
\(171\) 0.539239 0.0412366
\(172\) 5.68254 0.433289
\(173\) −3.83557 −0.291613 −0.145807 0.989313i \(-0.546578\pi\)
−0.145807 + 0.989313i \(0.546578\pi\)
\(174\) 9.18932 0.696640
\(175\) 38.2078 2.88824
\(176\) −0.891621 −0.0672085
\(177\) −17.5712 −1.32073
\(178\) −15.0329 −1.12676
\(179\) 18.6789 1.39613 0.698065 0.716035i \(-0.254045\pi\)
0.698065 + 0.716035i \(0.254045\pi\)
\(180\) −0.300646 −0.0224088
\(181\) −5.94129 −0.441612 −0.220806 0.975318i \(-0.570869\pi\)
−0.220806 + 0.975318i \(0.570869\pi\)
\(182\) −1.02021 −0.0756232
\(183\) −5.15323 −0.380938
\(184\) −1.59417 −0.117524
\(185\) −10.5589 −0.776304
\(186\) 9.29407 0.681474
\(187\) −3.37654 −0.246917
\(188\) −3.50723 −0.255791
\(189\) 19.3643 1.40855
\(190\) 27.1124 1.96694
\(191\) 12.2179 0.884053 0.442027 0.897002i \(-0.354260\pi\)
0.442027 + 0.897002i \(0.354260\pi\)
\(192\) −1.75423 −0.126601
\(193\) 10.0841 0.725871 0.362935 0.931814i \(-0.381775\pi\)
0.362935 + 0.931814i \(0.381775\pi\)
\(194\) −4.42694 −0.317836
\(195\) 1.84231 0.131931
\(196\) 7.26499 0.518928
\(197\) 12.2085 0.869818 0.434909 0.900474i \(-0.356781\pi\)
0.434909 + 0.900474i \(0.356781\pi\)
\(198\) 0.0689469 0.00489984
\(199\) −21.4321 −1.51928 −0.759640 0.650344i \(-0.774625\pi\)
−0.759640 + 0.650344i \(0.774625\pi\)
\(200\) −10.1162 −0.715322
\(201\) −11.6747 −0.823471
\(202\) −4.94998 −0.348279
\(203\) 19.7848 1.38862
\(204\) −6.64321 −0.465118
\(205\) 23.3465 1.63059
\(206\) −4.25054 −0.296149
\(207\) 0.123273 0.00856807
\(208\) 0.270119 0.0187294
\(209\) −6.21766 −0.430084
\(210\) −25.7599 −1.77760
\(211\) 28.4055 1.95551 0.977756 0.209745i \(-0.0672634\pi\)
0.977756 + 0.209745i \(0.0672634\pi\)
\(212\) 7.83966 0.538430
\(213\) 13.0595 0.894823
\(214\) 8.47450 0.579305
\(215\) −22.0934 −1.50676
\(216\) −5.12704 −0.348851
\(217\) 20.0103 1.35839
\(218\) 4.94777 0.335105
\(219\) 0.935188 0.0631941
\(220\) 3.46658 0.233717
\(221\) 1.02293 0.0688098
\(222\) 4.76413 0.319747
\(223\) −27.9759 −1.87340 −0.936701 0.350130i \(-0.886137\pi\)
−0.936701 + 0.350130i \(0.886137\pi\)
\(224\) −3.77690 −0.252355
\(225\) 0.782260 0.0521507
\(226\) 12.8103 0.852126
\(227\) −19.6923 −1.30703 −0.653513 0.756915i \(-0.726705\pi\)
−0.653513 + 0.756915i \(0.726705\pi\)
\(228\) −12.2330 −0.810151
\(229\) 14.5783 0.963362 0.481681 0.876347i \(-0.340026\pi\)
0.481681 + 0.876347i \(0.340026\pi\)
\(230\) 6.19805 0.408687
\(231\) 5.90749 0.388684
\(232\) −5.23837 −0.343916
\(233\) 12.2580 0.803049 0.401524 0.915848i \(-0.368480\pi\)
0.401524 + 0.915848i \(0.368480\pi\)
\(234\) −0.0208877 −0.00136547
\(235\) 13.6359 0.889511
\(236\) 10.0165 0.652017
\(237\) −5.68179 −0.369072
\(238\) −14.3030 −0.927125
\(239\) −4.81615 −0.311531 −0.155766 0.987794i \(-0.549784\pi\)
−0.155766 + 0.987794i \(0.549784\pi\)
\(240\) 6.82037 0.440253
\(241\) −21.1441 −1.36201 −0.681005 0.732279i \(-0.738457\pi\)
−0.681005 + 0.732279i \(0.738457\pi\)
\(242\) 10.2050 0.656003
\(243\) 0.803413 0.0515390
\(244\) 2.93760 0.188061
\(245\) −28.2459 −1.80457
\(246\) −10.5338 −0.671614
\(247\) 1.88366 0.119854
\(248\) −5.29808 −0.336429
\(249\) 17.0070 1.07777
\(250\) 19.8915 1.25805
\(251\) −10.3012 −0.650205 −0.325102 0.945679i \(-0.605399\pi\)
−0.325102 + 0.945679i \(0.605399\pi\)
\(252\) 0.292059 0.0183980
\(253\) −1.42139 −0.0893622
\(254\) −0.461728 −0.0289714
\(255\) 25.8285 1.61744
\(256\) 1.00000 0.0625000
\(257\) 9.11865 0.568806 0.284403 0.958705i \(-0.408205\pi\)
0.284403 + 0.958705i \(0.408205\pi\)
\(258\) 9.96849 0.620611
\(259\) 10.2573 0.637357
\(260\) −1.05021 −0.0651313
\(261\) 0.405071 0.0250732
\(262\) 6.70343 0.414139
\(263\) 0.0355164 0.00219004 0.00109502 0.999999i \(-0.499651\pi\)
0.00109502 + 0.999999i \(0.499651\pi\)
\(264\) −1.56411 −0.0962643
\(265\) −30.4803 −1.87239
\(266\) −26.3380 −1.61488
\(267\) −26.3712 −1.61389
\(268\) 6.65517 0.406529
\(269\) −1.82249 −0.111119 −0.0555596 0.998455i \(-0.517694\pi\)
−0.0555596 + 0.998455i \(0.517694\pi\)
\(270\) 19.9337 1.21313
\(271\) −16.9264 −1.02821 −0.514104 0.857728i \(-0.671875\pi\)
−0.514104 + 0.857728i \(0.671875\pi\)
\(272\) 3.78696 0.229618
\(273\) −1.78969 −0.108317
\(274\) −12.1320 −0.732921
\(275\) −9.01981 −0.543915
\(276\) −2.79654 −0.168332
\(277\) −22.5995 −1.35787 −0.678937 0.734196i \(-0.737559\pi\)
−0.678937 + 0.734196i \(0.737559\pi\)
\(278\) −17.9890 −1.07891
\(279\) 0.409688 0.0245274
\(280\) 14.6844 0.877562
\(281\) −7.27928 −0.434245 −0.217123 0.976144i \(-0.569667\pi\)
−0.217123 + 0.976144i \(0.569667\pi\)
\(282\) −6.15249 −0.366375
\(283\) −11.9303 −0.709186 −0.354593 0.935021i \(-0.615380\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(284\) −7.44458 −0.441755
\(285\) 47.5614 2.81729
\(286\) 0.240844 0.0142414
\(287\) −22.6796 −1.33874
\(288\) −0.0773276 −0.00455657
\(289\) −2.65891 −0.156406
\(290\) 20.3666 1.19597
\(291\) −7.76588 −0.455244
\(292\) −0.533104 −0.0311975
\(293\) 7.81829 0.456749 0.228375 0.973573i \(-0.426659\pi\)
0.228375 + 0.973573i \(0.426659\pi\)
\(294\) 12.7445 0.743273
\(295\) −38.9436 −2.26738
\(296\) −2.71579 −0.157852
\(297\) −4.57138 −0.265258
\(298\) −14.2877 −0.827662
\(299\) 0.430615 0.0249031
\(300\) −17.7461 −1.02457
\(301\) 21.4624 1.23707
\(302\) 15.1888 0.874016
\(303\) −8.68341 −0.498849
\(304\) 6.97343 0.399954
\(305\) −11.4213 −0.653979
\(306\) −0.292837 −0.0167404
\(307\) 33.1253 1.89056 0.945280 0.326261i \(-0.105789\pi\)
0.945280 + 0.326261i \(0.105789\pi\)
\(308\) −3.36757 −0.191885
\(309\) −7.45644 −0.424182
\(310\) 20.5987 1.16993
\(311\) −17.1099 −0.970214 −0.485107 0.874455i \(-0.661219\pi\)
−0.485107 + 0.874455i \(0.661219\pi\)
\(312\) 0.473851 0.0268265
\(313\) 2.05251 0.116015 0.0580074 0.998316i \(-0.481525\pi\)
0.0580074 + 0.998316i \(0.481525\pi\)
\(314\) −12.2721 −0.692557
\(315\) −1.13551 −0.0639788
\(316\) 3.23891 0.182203
\(317\) 15.0429 0.844892 0.422446 0.906388i \(-0.361172\pi\)
0.422446 + 0.906388i \(0.361172\pi\)
\(318\) 13.7526 0.771207
\(319\) −4.67064 −0.261506
\(320\) −3.88795 −0.217343
\(321\) 14.8662 0.829752
\(322\) −6.02101 −0.335538
\(323\) 26.4081 1.46939
\(324\) −9.22600 −0.512556
\(325\) 2.73257 0.151576
\(326\) 9.37968 0.519492
\(327\) 8.67953 0.479979
\(328\) 6.00482 0.331561
\(329\) −13.2465 −0.730301
\(330\) 6.08119 0.334758
\(331\) −20.6862 −1.13702 −0.568509 0.822677i \(-0.692480\pi\)
−0.568509 + 0.822677i \(0.692480\pi\)
\(332\) −9.69483 −0.532073
\(333\) 0.210006 0.0115082
\(334\) 12.3620 0.676417
\(335\) −25.8750 −1.41370
\(336\) −6.62556 −0.361454
\(337\) −24.8191 −1.35198 −0.675992 0.736909i \(-0.736284\pi\)
−0.675992 + 0.736909i \(0.736284\pi\)
\(338\) 12.9270 0.703138
\(339\) 22.4722 1.22052
\(340\) −14.7235 −0.798496
\(341\) −4.72388 −0.255813
\(342\) −0.539239 −0.0291587
\(343\) 1.00084 0.0540400
\(344\) −5.68254 −0.306382
\(345\) 10.8728 0.585373
\(346\) 3.83557 0.206202
\(347\) 29.5347 1.58551 0.792753 0.609543i \(-0.208647\pi\)
0.792753 + 0.609543i \(0.208647\pi\)
\(348\) −9.18932 −0.492599
\(349\) 8.95922 0.479576 0.239788 0.970825i \(-0.422922\pi\)
0.239788 + 0.970825i \(0.422922\pi\)
\(350\) −38.2078 −2.04230
\(351\) 1.38491 0.0739211
\(352\) 0.891621 0.0475236
\(353\) −4.05140 −0.215634 −0.107817 0.994171i \(-0.534386\pi\)
−0.107817 + 0.994171i \(0.534386\pi\)
\(354\) 17.5712 0.933899
\(355\) 28.9442 1.53620
\(356\) 15.0329 0.796743
\(357\) −25.0908 −1.32794
\(358\) −18.6789 −0.987213
\(359\) 15.6541 0.826193 0.413096 0.910687i \(-0.364447\pi\)
0.413096 + 0.910687i \(0.364447\pi\)
\(360\) 0.300646 0.0158454
\(361\) 29.6288 1.55941
\(362\) 5.94129 0.312267
\(363\) 17.9020 0.939609
\(364\) 1.02021 0.0534737
\(365\) 2.07268 0.108489
\(366\) 5.15323 0.269364
\(367\) 26.1847 1.36683 0.683416 0.730029i \(-0.260494\pi\)
0.683416 + 0.730029i \(0.260494\pi\)
\(368\) 1.59417 0.0831017
\(369\) −0.464338 −0.0241725
\(370\) 10.5589 0.548930
\(371\) 29.6096 1.53726
\(372\) −9.29407 −0.481875
\(373\) −14.0151 −0.725676 −0.362838 0.931852i \(-0.618192\pi\)
−0.362838 + 0.931852i \(0.618192\pi\)
\(374\) 3.37654 0.174597
\(375\) 34.8943 1.80193
\(376\) 3.50723 0.180871
\(377\) 1.41498 0.0728754
\(378\) −19.3643 −0.995994
\(379\) −5.24233 −0.269280 −0.134640 0.990895i \(-0.542988\pi\)
−0.134640 + 0.990895i \(0.542988\pi\)
\(380\) −27.1124 −1.39084
\(381\) −0.809978 −0.0414964
\(382\) −12.2179 −0.625120
\(383\) 9.80693 0.501111 0.250555 0.968102i \(-0.419387\pi\)
0.250555 + 0.968102i \(0.419387\pi\)
\(384\) 1.75423 0.0895202
\(385\) 13.0929 0.667278
\(386\) −10.0841 −0.513268
\(387\) 0.439417 0.0223368
\(388\) 4.42694 0.224744
\(389\) −7.00766 −0.355303 −0.177651 0.984093i \(-0.556850\pi\)
−0.177651 + 0.984093i \(0.556850\pi\)
\(390\) −1.84231 −0.0932891
\(391\) 6.03705 0.305307
\(392\) −7.26499 −0.366937
\(393\) 11.7594 0.593181
\(394\) −12.2085 −0.615054
\(395\) −12.5927 −0.633609
\(396\) −0.0689469 −0.00346471
\(397\) 17.3426 0.870398 0.435199 0.900334i \(-0.356678\pi\)
0.435199 + 0.900334i \(0.356678\pi\)
\(398\) 21.4321 1.07429
\(399\) −46.2029 −2.31304
\(400\) 10.1162 0.505809
\(401\) 27.8421 1.39037 0.695185 0.718831i \(-0.255322\pi\)
0.695185 + 0.718831i \(0.255322\pi\)
\(402\) 11.6747 0.582282
\(403\) 1.43111 0.0712888
\(404\) 4.94998 0.246271
\(405\) 35.8703 1.78241
\(406\) −19.7848 −0.981904
\(407\) −2.42146 −0.120027
\(408\) 6.64321 0.328888
\(409\) 25.1732 1.24473 0.622367 0.782725i \(-0.286171\pi\)
0.622367 + 0.782725i \(0.286171\pi\)
\(410\) −23.3465 −1.15300
\(411\) −21.2823 −1.04978
\(412\) 4.25054 0.209409
\(413\) 37.8312 1.86155
\(414\) −0.123273 −0.00605854
\(415\) 37.6931 1.85028
\(416\) −0.270119 −0.0132437
\(417\) −31.5568 −1.54534
\(418\) 6.21766 0.304116
\(419\) −8.82035 −0.430902 −0.215451 0.976515i \(-0.569122\pi\)
−0.215451 + 0.976515i \(0.569122\pi\)
\(420\) 25.7599 1.25695
\(421\) 10.0679 0.490680 0.245340 0.969437i \(-0.421100\pi\)
0.245340 + 0.969437i \(0.421100\pi\)
\(422\) −28.4055 −1.38276
\(423\) −0.271205 −0.0131865
\(424\) −7.83966 −0.380728
\(425\) 38.3096 1.85829
\(426\) −13.0595 −0.632736
\(427\) 11.0950 0.536926
\(428\) −8.47450 −0.409630
\(429\) 0.422496 0.0203983
\(430\) 22.0934 1.06544
\(431\) −7.32818 −0.352986 −0.176493 0.984302i \(-0.556475\pi\)
−0.176493 + 0.984302i \(0.556475\pi\)
\(432\) 5.12704 0.246675
\(433\) −19.4082 −0.932699 −0.466350 0.884600i \(-0.654431\pi\)
−0.466350 + 0.884600i \(0.654431\pi\)
\(434\) −20.0103 −0.960527
\(435\) 35.7276 1.71301
\(436\) −4.94777 −0.236955
\(437\) 11.1168 0.531790
\(438\) −0.935188 −0.0446850
\(439\) −9.96479 −0.475594 −0.237797 0.971315i \(-0.576425\pi\)
−0.237797 + 0.971315i \(0.576425\pi\)
\(440\) −3.46658 −0.165263
\(441\) 0.561784 0.0267516
\(442\) −1.02293 −0.0486559
\(443\) −10.2194 −0.485538 −0.242769 0.970084i \(-0.578056\pi\)
−0.242769 + 0.970084i \(0.578056\pi\)
\(444\) −4.76413 −0.226096
\(445\) −58.4473 −2.77067
\(446\) 27.9759 1.32470
\(447\) −25.0639 −1.18548
\(448\) 3.77690 0.178442
\(449\) 25.9723 1.22571 0.612855 0.790195i \(-0.290021\pi\)
0.612855 + 0.790195i \(0.290021\pi\)
\(450\) −0.782260 −0.0368761
\(451\) 5.35403 0.252111
\(452\) −12.8103 −0.602544
\(453\) 26.6446 1.25187
\(454\) 19.6923 0.924207
\(455\) −3.96654 −0.185954
\(456\) 12.2330 0.572863
\(457\) −9.99144 −0.467380 −0.233690 0.972311i \(-0.575080\pi\)
−0.233690 + 0.972311i \(0.575080\pi\)
\(458\) −14.5783 −0.681200
\(459\) 19.4159 0.906258
\(460\) −6.19805 −0.288986
\(461\) 31.9429 1.48773 0.743863 0.668332i \(-0.232991\pi\)
0.743863 + 0.668332i \(0.232991\pi\)
\(462\) −5.90749 −0.274841
\(463\) 26.7749 1.24433 0.622167 0.782885i \(-0.286253\pi\)
0.622167 + 0.782885i \(0.286253\pi\)
\(464\) 5.23837 0.243185
\(465\) 36.1349 1.67572
\(466\) −12.2580 −0.567841
\(467\) −31.9630 −1.47907 −0.739535 0.673118i \(-0.764954\pi\)
−0.739535 + 0.673118i \(0.764954\pi\)
\(468\) 0.0208877 0.000965532 0
\(469\) 25.1359 1.16067
\(470\) −13.6359 −0.628979
\(471\) −21.5282 −0.991965
\(472\) −10.0165 −0.461045
\(473\) −5.06667 −0.232966
\(474\) 5.68179 0.260973
\(475\) 70.5446 3.23681
\(476\) 14.3030 0.655576
\(477\) 0.606222 0.0277570
\(478\) 4.81615 0.220286
\(479\) 14.5226 0.663553 0.331777 0.943358i \(-0.392352\pi\)
0.331777 + 0.943358i \(0.392352\pi\)
\(480\) −6.82037 −0.311306
\(481\) 0.733587 0.0334487
\(482\) 21.1441 0.963086
\(483\) −10.5623 −0.480599
\(484\) −10.2050 −0.463864
\(485\) −17.2117 −0.781545
\(486\) −0.803413 −0.0364436
\(487\) −11.8883 −0.538712 −0.269356 0.963041i \(-0.586811\pi\)
−0.269356 + 0.963041i \(0.586811\pi\)
\(488\) −2.93760 −0.132979
\(489\) 16.4541 0.744081
\(490\) 28.2459 1.27602
\(491\) −42.3600 −1.91168 −0.955841 0.293886i \(-0.905052\pi\)
−0.955841 + 0.293886i \(0.905052\pi\)
\(492\) 10.5338 0.474903
\(493\) 19.8375 0.893437
\(494\) −1.88366 −0.0847497
\(495\) 0.268062 0.0120485
\(496\) 5.29808 0.237891
\(497\) −28.1174 −1.26124
\(498\) −17.0070 −0.762101
\(499\) −2.53918 −0.113669 −0.0568347 0.998384i \(-0.518101\pi\)
−0.0568347 + 0.998384i \(0.518101\pi\)
\(500\) −19.8915 −0.889575
\(501\) 21.6858 0.968848
\(502\) 10.3012 0.459764
\(503\) 17.5942 0.784484 0.392242 0.919862i \(-0.371700\pi\)
0.392242 + 0.919862i \(0.371700\pi\)
\(504\) −0.292059 −0.0130093
\(505\) −19.2453 −0.856404
\(506\) 1.42139 0.0631886
\(507\) 22.6770 1.00712
\(508\) 0.461728 0.0204859
\(509\) 3.83278 0.169885 0.0849425 0.996386i \(-0.472929\pi\)
0.0849425 + 0.996386i \(0.472929\pi\)
\(510\) −25.8285 −1.14371
\(511\) −2.01348 −0.0890712
\(512\) −1.00000 −0.0441942
\(513\) 35.7531 1.57854
\(514\) −9.11865 −0.402207
\(515\) −16.5259 −0.728219
\(516\) −9.96849 −0.438838
\(517\) 3.12712 0.137530
\(518\) −10.2573 −0.450679
\(519\) 6.72848 0.295348
\(520\) 1.05021 0.0460548
\(521\) −32.5902 −1.42780 −0.713901 0.700247i \(-0.753073\pi\)
−0.713901 + 0.700247i \(0.753073\pi\)
\(522\) −0.405071 −0.0177295
\(523\) 9.55255 0.417704 0.208852 0.977947i \(-0.433027\pi\)
0.208852 + 0.977947i \(0.433027\pi\)
\(524\) −6.70343 −0.292840
\(525\) −67.0254 −2.92523
\(526\) −0.0355164 −0.00154859
\(527\) 20.0637 0.873986
\(528\) 1.56411 0.0680691
\(529\) −20.4586 −0.889506
\(530\) 30.4803 1.32398
\(531\) 0.774550 0.0336126
\(532\) 26.3380 1.14190
\(533\) −1.62202 −0.0702573
\(534\) 26.3712 1.14119
\(535\) 32.9485 1.42449
\(536\) −6.65517 −0.287460
\(537\) −32.7672 −1.41401
\(538\) 1.82249 0.0785732
\(539\) −6.47762 −0.279011
\(540\) −19.9337 −0.857810
\(541\) 15.0495 0.647027 0.323514 0.946224i \(-0.395136\pi\)
0.323514 + 0.946224i \(0.395136\pi\)
\(542\) 16.9264 0.727053
\(543\) 10.4224 0.447268
\(544\) −3.78696 −0.162365
\(545\) 19.2367 0.824009
\(546\) 1.78969 0.0765916
\(547\) −20.7359 −0.886601 −0.443301 0.896373i \(-0.646193\pi\)
−0.443301 + 0.896373i \(0.646193\pi\)
\(548\) 12.1320 0.518254
\(549\) 0.227158 0.00969485
\(550\) 9.01981 0.384606
\(551\) 36.5294 1.55621
\(552\) 2.79654 0.119029
\(553\) 12.2330 0.520202
\(554\) 22.5995 0.960162
\(555\) 18.5227 0.786245
\(556\) 17.9890 0.762902
\(557\) 20.9110 0.886027 0.443014 0.896515i \(-0.353909\pi\)
0.443014 + 0.896515i \(0.353909\pi\)
\(558\) −0.409688 −0.0173435
\(559\) 1.53496 0.0649219
\(560\) −14.6844 −0.620530
\(561\) 5.92323 0.250079
\(562\) 7.27928 0.307058
\(563\) 18.2332 0.768437 0.384218 0.923242i \(-0.374471\pi\)
0.384218 + 0.923242i \(0.374471\pi\)
\(564\) 6.15249 0.259066
\(565\) 49.8057 2.09534
\(566\) 11.9303 0.501470
\(567\) −34.8457 −1.46338
\(568\) 7.44458 0.312368
\(569\) 40.4829 1.69713 0.848565 0.529092i \(-0.177467\pi\)
0.848565 + 0.529092i \(0.177467\pi\)
\(570\) −47.5614 −1.99213
\(571\) 43.5712 1.82340 0.911698 0.410860i \(-0.134771\pi\)
0.911698 + 0.410860i \(0.134771\pi\)
\(572\) −0.240844 −0.0100702
\(573\) −21.4330 −0.895375
\(574\) 22.6796 0.946629
\(575\) 16.1269 0.672538
\(576\) 0.0773276 0.00322198
\(577\) 16.9182 0.704314 0.352157 0.935941i \(-0.385448\pi\)
0.352157 + 0.935941i \(0.385448\pi\)
\(578\) 2.65891 0.110596
\(579\) −17.6899 −0.735166
\(580\) −20.3666 −0.845675
\(581\) −36.6164 −1.51911
\(582\) 7.76588 0.321906
\(583\) −6.99001 −0.289497
\(584\) 0.533104 0.0220600
\(585\) −0.0812102 −0.00335763
\(586\) −7.81829 −0.322970
\(587\) 40.5944 1.67551 0.837756 0.546045i \(-0.183867\pi\)
0.837756 + 0.546045i \(0.183867\pi\)
\(588\) −12.7445 −0.525573
\(589\) 36.9458 1.52233
\(590\) 38.9436 1.60328
\(591\) −21.4165 −0.880957
\(592\) 2.71579 0.111618
\(593\) 6.74010 0.276783 0.138391 0.990378i \(-0.455807\pi\)
0.138391 + 0.990378i \(0.455807\pi\)
\(594\) 4.57138 0.187566
\(595\) −55.6094 −2.27976
\(596\) 14.2877 0.585245
\(597\) 37.5968 1.53874
\(598\) −0.430615 −0.0176092
\(599\) −25.1112 −1.02602 −0.513008 0.858384i \(-0.671469\pi\)
−0.513008 + 0.858384i \(0.671469\pi\)
\(600\) 17.7461 0.724483
\(601\) 28.4148 1.15906 0.579531 0.814950i \(-0.303236\pi\)
0.579531 + 0.814950i \(0.303236\pi\)
\(602\) −21.4624 −0.874742
\(603\) 0.514628 0.0209573
\(604\) −15.1888 −0.618023
\(605\) 39.6766 1.61308
\(606\) 8.68341 0.352739
\(607\) 0.920037 0.0373431 0.0186716 0.999826i \(-0.494056\pi\)
0.0186716 + 0.999826i \(0.494056\pi\)
\(608\) −6.97343 −0.282810
\(609\) −34.7072 −1.40640
\(610\) 11.4213 0.462433
\(611\) −0.947369 −0.0383264
\(612\) 0.292837 0.0118372
\(613\) 10.5382 0.425636 0.212818 0.977092i \(-0.431736\pi\)
0.212818 + 0.977092i \(0.431736\pi\)
\(614\) −33.1253 −1.33683
\(615\) −40.9551 −1.65147
\(616\) 3.36757 0.135683
\(617\) 17.8182 0.717332 0.358666 0.933466i \(-0.383232\pi\)
0.358666 + 0.933466i \(0.383232\pi\)
\(618\) 7.45644 0.299942
\(619\) 2.87281 0.115468 0.0577340 0.998332i \(-0.481612\pi\)
0.0577340 + 0.998332i \(0.481612\pi\)
\(620\) −20.5987 −0.827264
\(621\) 8.17337 0.327986
\(622\) 17.1099 0.686045
\(623\) 56.7778 2.27476
\(624\) −0.473851 −0.0189692
\(625\) 26.7563 1.07025
\(626\) −2.05251 −0.0820348
\(627\) 10.9072 0.435592
\(628\) 12.2721 0.489711
\(629\) 10.2846 0.410074
\(630\) 1.13551 0.0452398
\(631\) −6.33127 −0.252044 −0.126022 0.992027i \(-0.540221\pi\)
−0.126022 + 0.992027i \(0.540221\pi\)
\(632\) −3.23891 −0.128837
\(633\) −49.8297 −1.98055
\(634\) −15.0429 −0.597429
\(635\) −1.79518 −0.0712395
\(636\) −13.7526 −0.545325
\(637\) 1.96241 0.0777536
\(638\) 4.67064 0.184913
\(639\) −0.575671 −0.0227732
\(640\) 3.88795 0.153685
\(641\) 4.81431 0.190154 0.0950769 0.995470i \(-0.469690\pi\)
0.0950769 + 0.995470i \(0.469690\pi\)
\(642\) −14.8662 −0.586723
\(643\) 19.0899 0.752833 0.376417 0.926451i \(-0.377156\pi\)
0.376417 + 0.926451i \(0.377156\pi\)
\(644\) 6.02101 0.237261
\(645\) 38.7570 1.52606
\(646\) −26.4081 −1.03901
\(647\) −13.3705 −0.525647 −0.262824 0.964844i \(-0.584654\pi\)
−0.262824 + 0.964844i \(0.584654\pi\)
\(648\) 9.22600 0.362432
\(649\) −8.93090 −0.350568
\(650\) −2.73257 −0.107180
\(651\) −35.1028 −1.37579
\(652\) −9.37968 −0.367336
\(653\) 2.41770 0.0946120 0.0473060 0.998880i \(-0.484936\pi\)
0.0473060 + 0.998880i \(0.484936\pi\)
\(654\) −8.67953 −0.339396
\(655\) 26.0626 1.01835
\(656\) −6.00482 −0.234449
\(657\) −0.0412236 −0.00160829
\(658\) 13.2465 0.516400
\(659\) −44.4967 −1.73334 −0.866672 0.498878i \(-0.833745\pi\)
−0.866672 + 0.498878i \(0.833745\pi\)
\(660\) −6.08119 −0.236710
\(661\) −15.4372 −0.600438 −0.300219 0.953870i \(-0.597060\pi\)
−0.300219 + 0.953870i \(0.597060\pi\)
\(662\) 20.6862 0.803994
\(663\) −1.79446 −0.0696909
\(664\) 9.69483 0.376232
\(665\) −102.401 −3.97093
\(666\) −0.210006 −0.00813756
\(667\) 8.35084 0.323346
\(668\) −12.3620 −0.478299
\(669\) 49.0761 1.89739
\(670\) 25.8750 0.999639
\(671\) −2.61923 −0.101114
\(672\) 6.62556 0.255587
\(673\) −35.3144 −1.36127 −0.680635 0.732622i \(-0.738296\pi\)
−0.680635 + 0.732622i \(0.738296\pi\)
\(674\) 24.8191 0.955996
\(675\) 51.8661 1.99633
\(676\) −12.9270 −0.497194
\(677\) −5.70475 −0.219251 −0.109626 0.993973i \(-0.534965\pi\)
−0.109626 + 0.993973i \(0.534965\pi\)
\(678\) −22.4722 −0.863039
\(679\) 16.7201 0.641660
\(680\) 14.7235 0.564622
\(681\) 34.5449 1.32376
\(682\) 4.72388 0.180887
\(683\) 2.39655 0.0917014 0.0458507 0.998948i \(-0.485400\pi\)
0.0458507 + 0.998948i \(0.485400\pi\)
\(684\) 0.539239 0.0206183
\(685\) −47.1687 −1.80222
\(686\) −1.00084 −0.0382121
\(687\) −25.5737 −0.975699
\(688\) 5.68254 0.216645
\(689\) 2.11764 0.0806757
\(690\) −10.8728 −0.413921
\(691\) 9.08309 0.345537 0.172768 0.984962i \(-0.444729\pi\)
0.172768 + 0.984962i \(0.444729\pi\)
\(692\) −3.83557 −0.145807
\(693\) −0.260406 −0.00989199
\(694\) −29.5347 −1.12112
\(695\) −69.9403 −2.65299
\(696\) 9.18932 0.348320
\(697\) −22.7400 −0.861341
\(698\) −8.95922 −0.339111
\(699\) −21.5034 −0.813333
\(700\) 38.2078 1.44412
\(701\) −28.3666 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(702\) −1.38491 −0.0522701
\(703\) 18.9384 0.714275
\(704\) −0.891621 −0.0336042
\(705\) −23.9206 −0.900902
\(706\) 4.05140 0.152477
\(707\) 18.6956 0.703120
\(708\) −17.5712 −0.660366
\(709\) −36.9497 −1.38768 −0.693838 0.720131i \(-0.744082\pi\)
−0.693838 + 0.720131i \(0.744082\pi\)
\(710\) −28.9442 −1.08626
\(711\) 0.250457 0.00939287
\(712\) −15.0329 −0.563382
\(713\) 8.44603 0.316306
\(714\) 25.0908 0.938998
\(715\) 0.936390 0.0350190
\(716\) 18.6789 0.698065
\(717\) 8.44865 0.315521
\(718\) −15.6541 −0.584206
\(719\) −30.3703 −1.13262 −0.566310 0.824192i \(-0.691629\pi\)
−0.566310 + 0.824192i \(0.691629\pi\)
\(720\) −0.300646 −0.0112044
\(721\) 16.0539 0.597878
\(722\) −29.6288 −1.10267
\(723\) 37.0916 1.37945
\(724\) −5.94129 −0.220806
\(725\) 52.9924 1.96809
\(726\) −17.9020 −0.664404
\(727\) 21.1943 0.786054 0.393027 0.919527i \(-0.371428\pi\)
0.393027 + 0.919527i \(0.371428\pi\)
\(728\) −1.02021 −0.0378116
\(729\) 26.2686 0.972912
\(730\) −2.07268 −0.0767135
\(731\) 21.5196 0.795930
\(732\) −5.15323 −0.190469
\(733\) −36.8248 −1.36016 −0.680078 0.733140i \(-0.738054\pi\)
−0.680078 + 0.733140i \(0.738054\pi\)
\(734\) −26.1847 −0.966496
\(735\) 49.5499 1.82768
\(736\) −1.59417 −0.0587618
\(737\) −5.93389 −0.218578
\(738\) 0.464338 0.0170925
\(739\) 8.36301 0.307638 0.153819 0.988099i \(-0.450843\pi\)
0.153819 + 0.988099i \(0.450843\pi\)
\(740\) −10.5589 −0.388152
\(741\) −3.30437 −0.121389
\(742\) −29.6096 −1.08700
\(743\) 43.8790 1.60976 0.804882 0.593435i \(-0.202229\pi\)
0.804882 + 0.593435i \(0.202229\pi\)
\(744\) 9.29407 0.340737
\(745\) −55.5497 −2.03519
\(746\) 14.0151 0.513131
\(747\) −0.749678 −0.0274293
\(748\) −3.37654 −0.123458
\(749\) −32.0073 −1.16952
\(750\) −34.8943 −1.27416
\(751\) 49.2440 1.79694 0.898470 0.439034i \(-0.144679\pi\)
0.898470 + 0.439034i \(0.144679\pi\)
\(752\) −3.50723 −0.127895
\(753\) 18.0707 0.658531
\(754\) −1.41498 −0.0515307
\(755\) 59.0533 2.14917
\(756\) 19.3643 0.704274
\(757\) −3.85726 −0.140195 −0.0700973 0.997540i \(-0.522331\pi\)
−0.0700973 + 0.997540i \(0.522331\pi\)
\(758\) 5.24233 0.190410
\(759\) 2.49345 0.0905066
\(760\) 27.1124 0.983470
\(761\) 17.2533 0.625432 0.312716 0.949847i \(-0.398761\pi\)
0.312716 + 0.949847i \(0.398761\pi\)
\(762\) 0.809978 0.0293424
\(763\) −18.6872 −0.676523
\(764\) 12.2179 0.442027
\(765\) −1.13854 −0.0411639
\(766\) −9.80693 −0.354339
\(767\) 2.70564 0.0976950
\(768\) −1.75423 −0.0633004
\(769\) 17.2644 0.622569 0.311285 0.950317i \(-0.399241\pi\)
0.311285 + 0.950317i \(0.399241\pi\)
\(770\) −13.0929 −0.471837
\(771\) −15.9962 −0.576090
\(772\) 10.0841 0.362935
\(773\) −46.3937 −1.66866 −0.834332 0.551262i \(-0.814146\pi\)
−0.834332 + 0.551262i \(0.814146\pi\)
\(774\) −0.439417 −0.0157945
\(775\) 53.5964 1.92524
\(776\) −4.42694 −0.158918
\(777\) −17.9936 −0.645519
\(778\) 7.00766 0.251237
\(779\) −41.8742 −1.50030
\(780\) 1.84231 0.0659653
\(781\) 6.63774 0.237517
\(782\) −6.03705 −0.215885
\(783\) 26.8574 0.959804
\(784\) 7.26499 0.259464
\(785\) −47.7135 −1.70297
\(786\) −11.7594 −0.419442
\(787\) 25.6917 0.915809 0.457905 0.889001i \(-0.348600\pi\)
0.457905 + 0.889001i \(0.348600\pi\)
\(788\) 12.2085 0.434909
\(789\) −0.0623040 −0.00221808
\(790\) 12.5927 0.448029
\(791\) −48.3831 −1.72031
\(792\) 0.0689469 0.00244992
\(793\) 0.793502 0.0281781
\(794\) −17.3426 −0.615464
\(795\) 53.4694 1.89636
\(796\) −21.4321 −0.759640
\(797\) −17.1929 −0.609003 −0.304502 0.952512i \(-0.598490\pi\)
−0.304502 + 0.952512i \(0.598490\pi\)
\(798\) 46.2029 1.63556
\(799\) −13.2817 −0.469874
\(800\) −10.1162 −0.357661
\(801\) 1.16246 0.0410735
\(802\) −27.8421 −0.983140
\(803\) 0.475327 0.0167739
\(804\) −11.6747 −0.411735
\(805\) −23.4094 −0.825074
\(806\) −1.43111 −0.0504088
\(807\) 3.19707 0.112542
\(808\) −4.94998 −0.174140
\(809\) 16.3961 0.576456 0.288228 0.957562i \(-0.406934\pi\)
0.288228 + 0.957562i \(0.406934\pi\)
\(810\) −35.8703 −1.26035
\(811\) −15.8166 −0.555397 −0.277698 0.960668i \(-0.589572\pi\)
−0.277698 + 0.960668i \(0.589572\pi\)
\(812\) 19.7848 0.694311
\(813\) 29.6929 1.04138
\(814\) 2.42146 0.0848721
\(815\) 36.4678 1.27741
\(816\) −6.64321 −0.232559
\(817\) 39.6268 1.38637
\(818\) −25.1732 −0.880161
\(819\) 0.0788906 0.00275666
\(820\) 23.3465 0.815294
\(821\) 22.8069 0.795968 0.397984 0.917392i \(-0.369710\pi\)
0.397984 + 0.917392i \(0.369710\pi\)
\(822\) 21.2823 0.742307
\(823\) 17.2997 0.603031 0.301516 0.953461i \(-0.402507\pi\)
0.301516 + 0.953461i \(0.402507\pi\)
\(824\) −4.25054 −0.148075
\(825\) 15.8228 0.550880
\(826\) −37.8312 −1.31632
\(827\) −13.5049 −0.469611 −0.234806 0.972042i \(-0.575445\pi\)
−0.234806 + 0.972042i \(0.575445\pi\)
\(828\) 0.123273 0.00428404
\(829\) 0.0781965 0.00271588 0.00135794 0.999999i \(-0.499568\pi\)
0.00135794 + 0.999999i \(0.499568\pi\)
\(830\) −37.6931 −1.30835
\(831\) 39.6448 1.37526
\(832\) 0.270119 0.00936469
\(833\) 27.5122 0.953243
\(834\) 31.5568 1.09272
\(835\) 48.0628 1.66328
\(836\) −6.21766 −0.215042
\(837\) 27.1635 0.938908
\(838\) 8.82035 0.304694
\(839\) 7.63850 0.263710 0.131855 0.991269i \(-0.457907\pi\)
0.131855 + 0.991269i \(0.457907\pi\)
\(840\) −25.7599 −0.888800
\(841\) −1.55945 −0.0537742
\(842\) −10.0679 −0.346963
\(843\) 12.7695 0.439806
\(844\) 28.4055 0.977756
\(845\) 50.2597 1.72899
\(846\) 0.271205 0.00932423
\(847\) −38.5433 −1.32436
\(848\) 7.83966 0.269215
\(849\) 20.9286 0.718267
\(850\) −38.3096 −1.31401
\(851\) 4.32943 0.148411
\(852\) 13.0595 0.447412
\(853\) −19.5560 −0.669586 −0.334793 0.942292i \(-0.608666\pi\)
−0.334793 + 0.942292i \(0.608666\pi\)
\(854\) −11.0950 −0.379664
\(855\) −2.09654 −0.0717000
\(856\) 8.47450 0.289652
\(857\) −23.7702 −0.811974 −0.405987 0.913879i \(-0.633072\pi\)
−0.405987 + 0.913879i \(0.633072\pi\)
\(858\) −0.422496 −0.0144238
\(859\) 11.5432 0.393849 0.196925 0.980419i \(-0.436905\pi\)
0.196925 + 0.980419i \(0.436905\pi\)
\(860\) −22.0934 −0.753380
\(861\) 39.7853 1.35588
\(862\) 7.32818 0.249599
\(863\) 45.2584 1.54061 0.770307 0.637674i \(-0.220103\pi\)
0.770307 + 0.637674i \(0.220103\pi\)
\(864\) −5.12704 −0.174426
\(865\) 14.9125 0.507041
\(866\) 19.4082 0.659518
\(867\) 4.66434 0.158409
\(868\) 20.0103 0.679195
\(869\) −2.88788 −0.0979646
\(870\) −35.7276 −1.21128
\(871\) 1.79769 0.0609123
\(872\) 4.94777 0.167553
\(873\) 0.342325 0.0115859
\(874\) −11.1168 −0.376032
\(875\) −75.1283 −2.53980
\(876\) 0.935188 0.0315971
\(877\) 17.3178 0.584780 0.292390 0.956299i \(-0.405549\pi\)
0.292390 + 0.956299i \(0.405549\pi\)
\(878\) 9.96479 0.336296
\(879\) −13.7151 −0.462598
\(880\) 3.46658 0.116858
\(881\) 35.0018 1.17924 0.589621 0.807680i \(-0.299277\pi\)
0.589621 + 0.807680i \(0.299277\pi\)
\(882\) −0.561784 −0.0189163
\(883\) 41.5003 1.39660 0.698298 0.715807i \(-0.253941\pi\)
0.698298 + 0.715807i \(0.253941\pi\)
\(884\) 1.02293 0.0344049
\(885\) 68.3160 2.29642
\(886\) 10.2194 0.343327
\(887\) 35.5633 1.19410 0.597049 0.802205i \(-0.296340\pi\)
0.597049 + 0.802205i \(0.296340\pi\)
\(888\) 4.76413 0.159874
\(889\) 1.74390 0.0584886
\(890\) 58.4473 1.95916
\(891\) 8.22610 0.275585
\(892\) −27.9759 −0.936701
\(893\) −24.4574 −0.818436
\(894\) 25.0639 0.838261
\(895\) −72.6229 −2.42751
\(896\) −3.77690 −0.126177
\(897\) −0.755398 −0.0252220
\(898\) −25.9723 −0.866708
\(899\) 27.7533 0.925626
\(900\) 0.782260 0.0260753
\(901\) 29.6885 0.989068
\(902\) −5.35403 −0.178270
\(903\) −37.6500 −1.25291
\(904\) 12.8103 0.426063
\(905\) 23.0995 0.767852
\(906\) −26.6446 −0.885209
\(907\) 1.01620 0.0337422 0.0168711 0.999858i \(-0.494630\pi\)
0.0168711 + 0.999858i \(0.494630\pi\)
\(908\) −19.6923 −0.653513
\(909\) 0.382770 0.0126957
\(910\) 3.96654 0.131490
\(911\) −37.6952 −1.24890 −0.624449 0.781066i \(-0.714676\pi\)
−0.624449 + 0.781066i \(0.714676\pi\)
\(912\) −12.2330 −0.405076
\(913\) 8.64412 0.286079
\(914\) 9.99144 0.330488
\(915\) 20.0355 0.662354
\(916\) 14.5783 0.481681
\(917\) −25.3182 −0.836080
\(918\) −19.4159 −0.640821
\(919\) 20.3518 0.671343 0.335672 0.941979i \(-0.391037\pi\)
0.335672 + 0.941979i \(0.391037\pi\)
\(920\) 6.19805 0.204344
\(921\) −58.1094 −1.91477
\(922\) −31.9429 −1.05198
\(923\) −2.01092 −0.0661903
\(924\) 5.90749 0.194342
\(925\) 27.4735 0.903322
\(926\) −26.7749 −0.879877
\(927\) 0.328684 0.0107954
\(928\) −5.23837 −0.171958
\(929\) −44.9593 −1.47507 −0.737533 0.675311i \(-0.764009\pi\)
−0.737533 + 0.675311i \(0.764009\pi\)
\(930\) −36.1349 −1.18491
\(931\) 50.6619 1.66038
\(932\) 12.2580 0.401524
\(933\) 30.0147 0.982639
\(934\) 31.9630 1.04586
\(935\) 13.1278 0.429326
\(936\) −0.0208877 −0.000682734 0
\(937\) 3.61097 0.117965 0.0589827 0.998259i \(-0.481214\pi\)
0.0589827 + 0.998259i \(0.481214\pi\)
\(938\) −25.1359 −0.820717
\(939\) −3.60058 −0.117500
\(940\) 13.6359 0.444755
\(941\) −35.0560 −1.14279 −0.571397 0.820674i \(-0.693598\pi\)
−0.571397 + 0.820674i \(0.693598\pi\)
\(942\) 21.5282 0.701425
\(943\) −9.57269 −0.311730
\(944\) 10.0165 0.326008
\(945\) −75.2877 −2.44911
\(946\) 5.06667 0.164732
\(947\) −16.0441 −0.521364 −0.260682 0.965425i \(-0.583947\pi\)
−0.260682 + 0.965425i \(0.583947\pi\)
\(948\) −5.68179 −0.184536
\(949\) −0.144002 −0.00467449
\(950\) −70.5446 −2.28877
\(951\) −26.3887 −0.855711
\(952\) −14.3030 −0.463563
\(953\) 44.1901 1.43146 0.715729 0.698378i \(-0.246095\pi\)
0.715729 + 0.698378i \(0.246095\pi\)
\(954\) −0.606222 −0.0196272
\(955\) −47.5025 −1.53714
\(956\) −4.81615 −0.155766
\(957\) 8.19339 0.264855
\(958\) −14.5226 −0.469203
\(959\) 45.8214 1.47965
\(960\) 6.82037 0.220127
\(961\) −2.93030 −0.0945258
\(962\) −0.733587 −0.0236518
\(963\) −0.655312 −0.0211171
\(964\) −21.1441 −0.681005
\(965\) −39.2066 −1.26211
\(966\) 10.5623 0.339835
\(967\) −11.4345 −0.367710 −0.183855 0.982953i \(-0.558858\pi\)
−0.183855 + 0.982953i \(0.558858\pi\)
\(968\) 10.2050 0.328002
\(969\) −46.3260 −1.48820
\(970\) 17.2117 0.552636
\(971\) 35.2985 1.13278 0.566391 0.824136i \(-0.308339\pi\)
0.566391 + 0.824136i \(0.308339\pi\)
\(972\) 0.803413 0.0257695
\(973\) 67.9426 2.17814
\(974\) 11.8883 0.380927
\(975\) −4.79357 −0.153517
\(976\) 2.93760 0.0940303
\(977\) −32.2080 −1.03043 −0.515213 0.857062i \(-0.672287\pi\)
−0.515213 + 0.857062i \(0.672287\pi\)
\(978\) −16.4541 −0.526145
\(979\) −13.4037 −0.428383
\(980\) −28.2459 −0.902284
\(981\) −0.382599 −0.0122154
\(982\) 42.3600 1.35176
\(983\) −29.2237 −0.932092 −0.466046 0.884760i \(-0.654322\pi\)
−0.466046 + 0.884760i \(0.654322\pi\)
\(984\) −10.5338 −0.335807
\(985\) −47.4660 −1.51239
\(986\) −19.8375 −0.631756
\(987\) 23.2373 0.739653
\(988\) 1.88366 0.0599271
\(989\) 9.05892 0.288057
\(990\) −0.268062 −0.00851958
\(991\) −24.7241 −0.785386 −0.392693 0.919670i \(-0.628457\pi\)
−0.392693 + 0.919670i \(0.628457\pi\)
\(992\) −5.29808 −0.168214
\(993\) 36.2885 1.15158
\(994\) 28.1174 0.891831
\(995\) 83.3270 2.64164
\(996\) 17.0070 0.538887
\(997\) −53.0189 −1.67912 −0.839562 0.543263i \(-0.817188\pi\)
−0.839562 + 0.543263i \(0.817188\pi\)
\(998\) 2.53918 0.0803764
\(999\) 13.9240 0.440535
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 \(a_p\))