Properties

Label 6026.2.a.i.1.14
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.180068 q^{3}\) \(+1.00000 q^{4}\) \(-3.11636 q^{5}\) \(-0.180068 q^{6}\) \(+2.83625 q^{7}\) \(-1.00000 q^{8}\) \(-2.96758 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.180068 q^{3}\) \(+1.00000 q^{4}\) \(-3.11636 q^{5}\) \(-0.180068 q^{6}\) \(+2.83625 q^{7}\) \(-1.00000 q^{8}\) \(-2.96758 q^{9}\) \(+3.11636 q^{10}\) \(+1.84231 q^{11}\) \(+0.180068 q^{12}\) \(-3.19934 q^{13}\) \(-2.83625 q^{14}\) \(-0.561156 q^{15}\) \(+1.00000 q^{16}\) \(+5.26163 q^{17}\) \(+2.96758 q^{18}\) \(-2.30746 q^{19}\) \(-3.11636 q^{20}\) \(+0.510718 q^{21}\) \(-1.84231 q^{22}\) \(+1.00000 q^{23}\) \(-0.180068 q^{24}\) \(+4.71170 q^{25}\) \(+3.19934 q^{26}\) \(-1.07457 q^{27}\) \(+2.83625 q^{28}\) \(-4.19619 q^{29}\) \(+0.561156 q^{30}\) \(+0.161014 q^{31}\) \(-1.00000 q^{32}\) \(+0.331740 q^{33}\) \(-5.26163 q^{34}\) \(-8.83879 q^{35}\) \(-2.96758 q^{36}\) \(+3.37004 q^{37}\) \(+2.30746 q^{38}\) \(-0.576099 q^{39}\) \(+3.11636 q^{40}\) \(+7.27050 q^{41}\) \(-0.510718 q^{42}\) \(-4.10314 q^{43}\) \(+1.84231 q^{44}\) \(+9.24803 q^{45}\) \(-1.00000 q^{46}\) \(+8.67972 q^{47}\) \(+0.180068 q^{48}\) \(+1.04433 q^{49}\) \(-4.71170 q^{50}\) \(+0.947450 q^{51}\) \(-3.19934 q^{52}\) \(-5.41261 q^{53}\) \(+1.07457 q^{54}\) \(-5.74129 q^{55}\) \(-2.83625 q^{56}\) \(-0.415500 q^{57}\) \(+4.19619 q^{58}\) \(-11.3258 q^{59}\) \(-0.561156 q^{60}\) \(+4.07919 q^{61}\) \(-0.161014 q^{62}\) \(-8.41680 q^{63}\) \(+1.00000 q^{64}\) \(+9.97030 q^{65}\) \(-0.331740 q^{66}\) \(-8.82256 q^{67}\) \(+5.26163 q^{68}\) \(+0.180068 q^{69}\) \(+8.83879 q^{70}\) \(+3.83844 q^{71}\) \(+2.96758 q^{72}\) \(-3.38686 q^{73}\) \(-3.37004 q^{74}\) \(+0.848425 q^{75}\) \(-2.30746 q^{76}\) \(+5.22525 q^{77}\) \(+0.576099 q^{78}\) \(+15.0426 q^{79}\) \(-3.11636 q^{80}\) \(+8.70923 q^{81}\) \(-7.27050 q^{82}\) \(+14.6578 q^{83}\) \(+0.510718 q^{84}\) \(-16.3971 q^{85}\) \(+4.10314 q^{86}\) \(-0.755599 q^{87}\) \(-1.84231 q^{88}\) \(+4.17165 q^{89}\) \(-9.24803 q^{90}\) \(-9.07414 q^{91}\) \(+1.00000 q^{92}\) \(+0.0289934 q^{93}\) \(-8.67972 q^{94}\) \(+7.19088 q^{95}\) \(-0.180068 q^{96}\) \(-0.272963 q^{97}\) \(-1.04433 q^{98}\) \(-5.46718 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.180068 0.103962 0.0519811 0.998648i \(-0.483446\pi\)
0.0519811 + 0.998648i \(0.483446\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.11636 −1.39368 −0.696839 0.717227i \(-0.745411\pi\)
−0.696839 + 0.717227i \(0.745411\pi\)
\(6\) −0.180068 −0.0735124
\(7\) 2.83625 1.07200 0.536001 0.844217i \(-0.319934\pi\)
0.536001 + 0.844217i \(0.319934\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.96758 −0.989192
\(10\) 3.11636 0.985479
\(11\) 1.84231 0.555476 0.277738 0.960657i \(-0.410415\pi\)
0.277738 + 0.960657i \(0.410415\pi\)
\(12\) 0.180068 0.0519811
\(13\) −3.19934 −0.887338 −0.443669 0.896191i \(-0.646323\pi\)
−0.443669 + 0.896191i \(0.646323\pi\)
\(14\) −2.83625 −0.758021
\(15\) −0.561156 −0.144890
\(16\) 1.00000 0.250000
\(17\) 5.26163 1.27613 0.638066 0.769982i \(-0.279735\pi\)
0.638066 + 0.769982i \(0.279735\pi\)
\(18\) 2.96758 0.699464
\(19\) −2.30746 −0.529368 −0.264684 0.964335i \(-0.585268\pi\)
−0.264684 + 0.964335i \(0.585268\pi\)
\(20\) −3.11636 −0.696839
\(21\) 0.510718 0.111448
\(22\) −1.84231 −0.392781
\(23\) 1.00000 0.208514
\(24\) −0.180068 −0.0367562
\(25\) 4.71170 0.942340
\(26\) 3.19934 0.627443
\(27\) −1.07457 −0.206801
\(28\) 2.83625 0.536001
\(29\) −4.19619 −0.779213 −0.389606 0.920981i \(-0.627389\pi\)
−0.389606 + 0.920981i \(0.627389\pi\)
\(30\) 0.561156 0.102453
\(31\) 0.161014 0.0289189 0.0144595 0.999895i \(-0.495397\pi\)
0.0144595 + 0.999895i \(0.495397\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.331740 0.0577486
\(34\) −5.26163 −0.902362
\(35\) −8.83879 −1.49403
\(36\) −2.96758 −0.494596
\(37\) 3.37004 0.554032 0.277016 0.960865i \(-0.410655\pi\)
0.277016 + 0.960865i \(0.410655\pi\)
\(38\) 2.30746 0.374320
\(39\) −0.576099 −0.0922496
\(40\) 3.11636 0.492740
\(41\) 7.27050 1.13546 0.567730 0.823215i \(-0.307822\pi\)
0.567730 + 0.823215i \(0.307822\pi\)
\(42\) −0.510718 −0.0788055
\(43\) −4.10314 −0.625724 −0.312862 0.949799i \(-0.601288\pi\)
−0.312862 + 0.949799i \(0.601288\pi\)
\(44\) 1.84231 0.277738
\(45\) 9.24803 1.37862
\(46\) −1.00000 −0.147442
\(47\) 8.67972 1.26607 0.633033 0.774125i \(-0.281810\pi\)
0.633033 + 0.774125i \(0.281810\pi\)
\(48\) 0.180068 0.0259906
\(49\) 1.04433 0.149190
\(50\) −4.71170 −0.666335
\(51\) 0.947450 0.132670
\(52\) −3.19934 −0.443669
\(53\) −5.41261 −0.743479 −0.371740 0.928337i \(-0.621239\pi\)
−0.371740 + 0.928337i \(0.621239\pi\)
\(54\) 1.07457 0.146230
\(55\) −5.74129 −0.774155
\(56\) −2.83625 −0.379010
\(57\) −0.415500 −0.0550343
\(58\) 4.19619 0.550987
\(59\) −11.3258 −1.47449 −0.737245 0.675626i \(-0.763874\pi\)
−0.737245 + 0.675626i \(0.763874\pi\)
\(60\) −0.561156 −0.0724450
\(61\) 4.07919 0.522287 0.261143 0.965300i \(-0.415900\pi\)
0.261143 + 0.965300i \(0.415900\pi\)
\(62\) −0.161014 −0.0204488
\(63\) −8.41680 −1.06042
\(64\) 1.00000 0.125000
\(65\) 9.97030 1.23666
\(66\) −0.331740 −0.0408344
\(67\) −8.82256 −1.07785 −0.538924 0.842355i \(-0.681169\pi\)
−0.538924 + 0.842355i \(0.681169\pi\)
\(68\) 5.26163 0.638066
\(69\) 0.180068 0.0216776
\(70\) 8.83879 1.05644
\(71\) 3.83844 0.455539 0.227769 0.973715i \(-0.426857\pi\)
0.227769 + 0.973715i \(0.426857\pi\)
\(72\) 2.96758 0.349732
\(73\) −3.38686 −0.396402 −0.198201 0.980161i \(-0.563510\pi\)
−0.198201 + 0.980161i \(0.563510\pi\)
\(74\) −3.37004 −0.391759
\(75\) 0.848425 0.0979677
\(76\) −2.30746 −0.264684
\(77\) 5.22525 0.595472
\(78\) 0.576099 0.0652303
\(79\) 15.0426 1.69242 0.846210 0.532849i \(-0.178879\pi\)
0.846210 + 0.532849i \(0.178879\pi\)
\(80\) −3.11636 −0.348420
\(81\) 8.70923 0.967692
\(82\) −7.27050 −0.802892
\(83\) 14.6578 1.60891 0.804453 0.594016i \(-0.202458\pi\)
0.804453 + 0.594016i \(0.202458\pi\)
\(84\) 0.510718 0.0557239
\(85\) −16.3971 −1.77852
\(86\) 4.10314 0.442453
\(87\) −0.755599 −0.0810087
\(88\) −1.84231 −0.196391
\(89\) 4.17165 0.442194 0.221097 0.975252i \(-0.429036\pi\)
0.221097 + 0.975252i \(0.429036\pi\)
\(90\) −9.24803 −0.974828
\(91\) −9.07414 −0.951229
\(92\) 1.00000 0.104257
\(93\) 0.0289934 0.00300648
\(94\) −8.67972 −0.895244
\(95\) 7.19088 0.737769
\(96\) −0.180068 −0.0183781
\(97\) −0.272963 −0.0277152 −0.0138576 0.999904i \(-0.504411\pi\)
−0.0138576 + 0.999904i \(0.504411\pi\)
\(98\) −1.04433 −0.105494
\(99\) −5.46718 −0.549473
\(100\) 4.71170 0.471170
\(101\) −1.72561 −0.171704 −0.0858521 0.996308i \(-0.527361\pi\)
−0.0858521 + 0.996308i \(0.527361\pi\)
\(102\) −0.947450 −0.0938115
\(103\) −15.7235 −1.54929 −0.774643 0.632399i \(-0.782070\pi\)
−0.774643 + 0.632399i \(0.782070\pi\)
\(104\) 3.19934 0.313721
\(105\) −1.59158 −0.155322
\(106\) 5.41261 0.525719
\(107\) 8.87665 0.858138 0.429069 0.903272i \(-0.358842\pi\)
0.429069 + 0.903272i \(0.358842\pi\)
\(108\) −1.07457 −0.103400
\(109\) −12.2645 −1.17472 −0.587361 0.809325i \(-0.699833\pi\)
−0.587361 + 0.809325i \(0.699833\pi\)
\(110\) 5.74129 0.547410
\(111\) 0.606836 0.0575984
\(112\) 2.83625 0.268001
\(113\) −15.2526 −1.43485 −0.717424 0.696637i \(-0.754679\pi\)
−0.717424 + 0.696637i \(0.754679\pi\)
\(114\) 0.415500 0.0389151
\(115\) −3.11636 −0.290602
\(116\) −4.19619 −0.389606
\(117\) 9.49429 0.877747
\(118\) 11.3258 1.04262
\(119\) 14.9233 1.36802
\(120\) 0.561156 0.0512263
\(121\) −7.60591 −0.691446
\(122\) −4.07919 −0.369312
\(123\) 1.30918 0.118045
\(124\) 0.161014 0.0144595
\(125\) 0.898453 0.0803601
\(126\) 8.41680 0.749828
\(127\) −3.70620 −0.328872 −0.164436 0.986388i \(-0.552580\pi\)
−0.164436 + 0.986388i \(0.552580\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.738844 −0.0650516
\(130\) −9.97030 −0.874453
\(131\) 1.00000 0.0873704
\(132\) 0.331740 0.0288743
\(133\) −6.54454 −0.567484
\(134\) 8.82256 0.762153
\(135\) 3.34874 0.288214
\(136\) −5.26163 −0.451181
\(137\) 6.34452 0.542049 0.271025 0.962572i \(-0.412638\pi\)
0.271025 + 0.962572i \(0.412638\pi\)
\(138\) −0.180068 −0.0153284
\(139\) −0.627932 −0.0532605 −0.0266302 0.999645i \(-0.508478\pi\)
−0.0266302 + 0.999645i \(0.508478\pi\)
\(140\) −8.83879 −0.747014
\(141\) 1.56294 0.131623
\(142\) −3.83844 −0.322115
\(143\) −5.89417 −0.492895
\(144\) −2.96758 −0.247298
\(145\) 13.0768 1.08597
\(146\) 3.38686 0.280299
\(147\) 0.188051 0.0155102
\(148\) 3.37004 0.277016
\(149\) −7.01246 −0.574483 −0.287242 0.957858i \(-0.592738\pi\)
−0.287242 + 0.957858i \(0.592738\pi\)
\(150\) −0.848425 −0.0692736
\(151\) 10.1219 0.823708 0.411854 0.911250i \(-0.364881\pi\)
0.411854 + 0.911250i \(0.364881\pi\)
\(152\) 2.30746 0.187160
\(153\) −15.6143 −1.26234
\(154\) −5.22525 −0.421062
\(155\) −0.501777 −0.0403037
\(156\) −0.576099 −0.0461248
\(157\) −18.1972 −1.45230 −0.726148 0.687538i \(-0.758691\pi\)
−0.726148 + 0.687538i \(0.758691\pi\)
\(158\) −15.0426 −1.19672
\(159\) −0.974637 −0.0772938
\(160\) 3.11636 0.246370
\(161\) 2.83625 0.223528
\(162\) −8.70923 −0.684262
\(163\) 1.13547 0.0889369 0.0444684 0.999011i \(-0.485841\pi\)
0.0444684 + 0.999011i \(0.485841\pi\)
\(164\) 7.27050 0.567730
\(165\) −1.03382 −0.0804829
\(166\) −14.6578 −1.13767
\(167\) 9.90036 0.766113 0.383056 0.923725i \(-0.374871\pi\)
0.383056 + 0.923725i \(0.374871\pi\)
\(168\) −0.510718 −0.0394028
\(169\) −2.76421 −0.212632
\(170\) 16.3971 1.25760
\(171\) 6.84756 0.523646
\(172\) −4.10314 −0.312862
\(173\) −20.3169 −1.54466 −0.772331 0.635220i \(-0.780909\pi\)
−0.772331 + 0.635220i \(0.780909\pi\)
\(174\) 0.755599 0.0572818
\(175\) 13.3636 1.01019
\(176\) 1.84231 0.138869
\(177\) −2.03941 −0.153291
\(178\) −4.17165 −0.312678
\(179\) 11.1814 0.835734 0.417867 0.908508i \(-0.362778\pi\)
0.417867 + 0.908508i \(0.362778\pi\)
\(180\) 9.24803 0.689308
\(181\) −2.66605 −0.198166 −0.0990828 0.995079i \(-0.531591\pi\)
−0.0990828 + 0.995079i \(0.531591\pi\)
\(182\) 9.07414 0.672620
\(183\) 0.734531 0.0542981
\(184\) −1.00000 −0.0737210
\(185\) −10.5023 −0.772142
\(186\) −0.0289934 −0.00212590
\(187\) 9.69353 0.708861
\(188\) 8.67972 0.633033
\(189\) −3.04775 −0.221691
\(190\) −7.19088 −0.521681
\(191\) 1.79571 0.129933 0.0649665 0.997887i \(-0.479306\pi\)
0.0649665 + 0.997887i \(0.479306\pi\)
\(192\) 0.180068 0.0129953
\(193\) −7.22308 −0.519929 −0.259964 0.965618i \(-0.583711\pi\)
−0.259964 + 0.965618i \(0.583711\pi\)
\(194\) 0.272963 0.0195976
\(195\) 1.79533 0.128566
\(196\) 1.04433 0.0745952
\(197\) 15.2774 1.08847 0.544233 0.838934i \(-0.316821\pi\)
0.544233 + 0.838934i \(0.316821\pi\)
\(198\) 5.46718 0.388536
\(199\) −4.82621 −0.342121 −0.171060 0.985261i \(-0.554719\pi\)
−0.171060 + 0.985261i \(0.554719\pi\)
\(200\) −4.71170 −0.333167
\(201\) −1.58866 −0.112055
\(202\) 1.72561 0.121413
\(203\) −11.9015 −0.835319
\(204\) 0.947450 0.0663348
\(205\) −22.6575 −1.58247
\(206\) 15.7235 1.09551
\(207\) −2.96758 −0.206261
\(208\) −3.19934 −0.221834
\(209\) −4.25105 −0.294051
\(210\) 1.59158 0.109830
\(211\) 15.1183 1.04078 0.520392 0.853928i \(-0.325786\pi\)
0.520392 + 0.853928i \(0.325786\pi\)
\(212\) −5.41261 −0.371740
\(213\) 0.691180 0.0473588
\(214\) −8.87665 −0.606795
\(215\) 12.7869 0.872058
\(216\) 1.07457 0.0731151
\(217\) 0.456676 0.0310012
\(218\) 12.2645 0.830654
\(219\) −0.609865 −0.0412108
\(220\) −5.74129 −0.387078
\(221\) −16.8337 −1.13236
\(222\) −0.606836 −0.0407282
\(223\) 6.41023 0.429261 0.214631 0.976695i \(-0.431145\pi\)
0.214631 + 0.976695i \(0.431145\pi\)
\(224\) −2.83625 −0.189505
\(225\) −13.9823 −0.932155
\(226\) 15.2526 1.01459
\(227\) −24.4650 −1.62380 −0.811898 0.583799i \(-0.801566\pi\)
−0.811898 + 0.583799i \(0.801566\pi\)
\(228\) −0.415500 −0.0275171
\(229\) −28.7523 −1.90001 −0.950003 0.312242i \(-0.898920\pi\)
−0.950003 + 0.312242i \(0.898920\pi\)
\(230\) 3.11636 0.205487
\(231\) 0.940899 0.0619066
\(232\) 4.19619 0.275493
\(233\) −15.9419 −1.04439 −0.522195 0.852826i \(-0.674887\pi\)
−0.522195 + 0.852826i \(0.674887\pi\)
\(234\) −9.49429 −0.620661
\(235\) −27.0491 −1.76449
\(236\) −11.3258 −0.737245
\(237\) 2.70868 0.175948
\(238\) −14.9233 −0.967335
\(239\) −11.9789 −0.774852 −0.387426 0.921901i \(-0.626636\pi\)
−0.387426 + 0.921901i \(0.626636\pi\)
\(240\) −0.561156 −0.0362225
\(241\) −7.44765 −0.479745 −0.239873 0.970804i \(-0.577106\pi\)
−0.239873 + 0.970804i \(0.577106\pi\)
\(242\) 7.60591 0.488926
\(243\) 4.79196 0.307404
\(244\) 4.07919 0.261143
\(245\) −3.25452 −0.207923
\(246\) −1.30918 −0.0834705
\(247\) 7.38236 0.469728
\(248\) −0.161014 −0.0102244
\(249\) 2.63941 0.167266
\(250\) −0.898453 −0.0568232
\(251\) −8.65134 −0.546068 −0.273034 0.962004i \(-0.588027\pi\)
−0.273034 + 0.962004i \(0.588027\pi\)
\(252\) −8.41680 −0.530208
\(253\) 1.84231 0.115825
\(254\) 3.70620 0.232548
\(255\) −2.95260 −0.184899
\(256\) 1.00000 0.0625000
\(257\) 3.12698 0.195056 0.0975279 0.995233i \(-0.468906\pi\)
0.0975279 + 0.995233i \(0.468906\pi\)
\(258\) 0.738844 0.0459984
\(259\) 9.55829 0.593924
\(260\) 9.97030 0.618332
\(261\) 12.4525 0.770791
\(262\) −1.00000 −0.0617802
\(263\) 4.74709 0.292718 0.146359 0.989232i \(-0.453244\pi\)
0.146359 + 0.989232i \(0.453244\pi\)
\(264\) −0.331740 −0.0204172
\(265\) 16.8676 1.03617
\(266\) 6.54454 0.401272
\(267\) 0.751179 0.0459714
\(268\) −8.82256 −0.538924
\(269\) 14.5561 0.887504 0.443752 0.896150i \(-0.353647\pi\)
0.443752 + 0.896150i \(0.353647\pi\)
\(270\) −3.34874 −0.203798
\(271\) 9.44993 0.574042 0.287021 0.957924i \(-0.407335\pi\)
0.287021 + 0.957924i \(0.407335\pi\)
\(272\) 5.26163 0.319033
\(273\) −1.63396 −0.0988919
\(274\) −6.34452 −0.383287
\(275\) 8.68039 0.523447
\(276\) 0.180068 0.0108388
\(277\) −11.7380 −0.705265 −0.352633 0.935762i \(-0.614713\pi\)
−0.352633 + 0.935762i \(0.614713\pi\)
\(278\) 0.627932 0.0376608
\(279\) −0.477821 −0.0286064
\(280\) 8.83879 0.528218
\(281\) 5.06304 0.302036 0.151018 0.988531i \(-0.451745\pi\)
0.151018 + 0.988531i \(0.451745\pi\)
\(282\) −1.56294 −0.0930716
\(283\) 3.36418 0.199980 0.0999898 0.994988i \(-0.468119\pi\)
0.0999898 + 0.994988i \(0.468119\pi\)
\(284\) 3.83844 0.227769
\(285\) 1.29485 0.0767001
\(286\) 5.89417 0.348529
\(287\) 20.6210 1.21722
\(288\) 2.96758 0.174866
\(289\) 10.6847 0.628513
\(290\) −13.0768 −0.767898
\(291\) −0.0491518 −0.00288133
\(292\) −3.38686 −0.198201
\(293\) −24.6029 −1.43732 −0.718659 0.695363i \(-0.755244\pi\)
−0.718659 + 0.695363i \(0.755244\pi\)
\(294\) −0.188051 −0.0109673
\(295\) 35.2952 2.05496
\(296\) −3.37004 −0.195880
\(297\) −1.97968 −0.114873
\(298\) 7.01246 0.406221
\(299\) −3.19934 −0.185023
\(300\) 0.848425 0.0489839
\(301\) −11.6376 −0.670778
\(302\) −10.1219 −0.582449
\(303\) −0.310726 −0.0178508
\(304\) −2.30746 −0.132342
\(305\) −12.7122 −0.727900
\(306\) 15.6143 0.892609
\(307\) −22.2355 −1.26905 −0.634524 0.772903i \(-0.718804\pi\)
−0.634524 + 0.772903i \(0.718804\pi\)
\(308\) 5.22525 0.297736
\(309\) −2.83130 −0.161067
\(310\) 0.501777 0.0284990
\(311\) −21.8598 −1.23956 −0.619778 0.784777i \(-0.712777\pi\)
−0.619778 + 0.784777i \(0.712777\pi\)
\(312\) 0.576099 0.0326152
\(313\) 1.35107 0.0763670 0.0381835 0.999271i \(-0.487843\pi\)
0.0381835 + 0.999271i \(0.487843\pi\)
\(314\) 18.1972 1.02693
\(315\) 26.2298 1.47788
\(316\) 15.0426 0.846210
\(317\) 13.8256 0.776525 0.388262 0.921549i \(-0.373075\pi\)
0.388262 + 0.921549i \(0.373075\pi\)
\(318\) 0.974637 0.0546549
\(319\) −7.73067 −0.432834
\(320\) −3.11636 −0.174210
\(321\) 1.59840 0.0892139
\(322\) −2.83625 −0.158058
\(323\) −12.1410 −0.675543
\(324\) 8.70923 0.483846
\(325\) −15.0743 −0.836174
\(326\) −1.13547 −0.0628879
\(327\) −2.20843 −0.122127
\(328\) −7.27050 −0.401446
\(329\) 24.6179 1.35723
\(330\) 1.03382 0.0569100
\(331\) 0.802881 0.0441303 0.0220652 0.999757i \(-0.492976\pi\)
0.0220652 + 0.999757i \(0.492976\pi\)
\(332\) 14.6578 0.804453
\(333\) −10.0009 −0.548044
\(334\) −9.90036 −0.541724
\(335\) 27.4943 1.50217
\(336\) 0.510718 0.0278620
\(337\) −20.0302 −1.09111 −0.545557 0.838074i \(-0.683682\pi\)
−0.545557 + 0.838074i \(0.683682\pi\)
\(338\) 2.76421 0.150353
\(339\) −2.74651 −0.149170
\(340\) −16.3971 −0.889259
\(341\) 0.296637 0.0160638
\(342\) −6.84756 −0.370274
\(343\) −16.8918 −0.912070
\(344\) 4.10314 0.221227
\(345\) −0.561156 −0.0302116
\(346\) 20.3169 1.09224
\(347\) 0.578901 0.0310770 0.0155385 0.999879i \(-0.495054\pi\)
0.0155385 + 0.999879i \(0.495054\pi\)
\(348\) −0.755599 −0.0405044
\(349\) −25.7649 −1.37916 −0.689581 0.724209i \(-0.742205\pi\)
−0.689581 + 0.724209i \(0.742205\pi\)
\(350\) −13.3636 −0.714313
\(351\) 3.43791 0.183502
\(352\) −1.84231 −0.0981953
\(353\) −17.6860 −0.941332 −0.470666 0.882312i \(-0.655986\pi\)
−0.470666 + 0.882312i \(0.655986\pi\)
\(354\) 2.03941 0.108393
\(355\) −11.9620 −0.634875
\(356\) 4.17165 0.221097
\(357\) 2.68721 0.142222
\(358\) −11.1814 −0.590953
\(359\) 11.8894 0.627497 0.313749 0.949506i \(-0.398415\pi\)
0.313749 + 0.949506i \(0.398415\pi\)
\(360\) −9.24803 −0.487414
\(361\) −13.6756 −0.719770
\(362\) 2.66605 0.140124
\(363\) −1.36958 −0.0718843
\(364\) −9.07414 −0.475614
\(365\) 10.5547 0.552457
\(366\) −0.734531 −0.0383945
\(367\) 7.26661 0.379314 0.189657 0.981850i \(-0.439262\pi\)
0.189657 + 0.981850i \(0.439262\pi\)
\(368\) 1.00000 0.0521286
\(369\) −21.5757 −1.12319
\(370\) 10.5023 0.545987
\(371\) −15.3515 −0.797012
\(372\) 0.0289934 0.00150324
\(373\) −13.5275 −0.700430 −0.350215 0.936669i \(-0.613891\pi\)
−0.350215 + 0.936669i \(0.613891\pi\)
\(374\) −9.69353 −0.501241
\(375\) 0.161783 0.00835442
\(376\) −8.67972 −0.447622
\(377\) 13.4250 0.691425
\(378\) 3.04775 0.156759
\(379\) 12.8909 0.662162 0.331081 0.943602i \(-0.392587\pi\)
0.331081 + 0.943602i \(0.392587\pi\)
\(380\) 7.19088 0.368884
\(381\) −0.667368 −0.0341903
\(382\) −1.79571 −0.0918766
\(383\) −8.96319 −0.457998 −0.228999 0.973427i \(-0.573545\pi\)
−0.228999 + 0.973427i \(0.573545\pi\)
\(384\) −0.180068 −0.00918905
\(385\) −16.2838 −0.829897
\(386\) 7.22308 0.367645
\(387\) 12.1764 0.618961
\(388\) −0.272963 −0.0138576
\(389\) −28.0289 −1.42112 −0.710560 0.703636i \(-0.751558\pi\)
−0.710560 + 0.703636i \(0.751558\pi\)
\(390\) −1.79533 −0.0909101
\(391\) 5.26163 0.266092
\(392\) −1.04433 −0.0527468
\(393\) 0.180068 0.00908322
\(394\) −15.2774 −0.769662
\(395\) −46.8780 −2.35869
\(396\) −5.46718 −0.274736
\(397\) 20.6532 1.03656 0.518278 0.855212i \(-0.326573\pi\)
0.518278 + 0.855212i \(0.326573\pi\)
\(398\) 4.82621 0.241916
\(399\) −1.17846 −0.0589969
\(400\) 4.71170 0.235585
\(401\) −21.1495 −1.05615 −0.528077 0.849197i \(-0.677087\pi\)
−0.528077 + 0.849197i \(0.677087\pi\)
\(402\) 1.58866 0.0792351
\(403\) −0.515139 −0.0256609
\(404\) −1.72561 −0.0858521
\(405\) −27.1411 −1.34865
\(406\) 11.9015 0.590659
\(407\) 6.20865 0.307751
\(408\) −0.947450 −0.0469058
\(409\) 7.40738 0.366271 0.183136 0.983088i \(-0.441375\pi\)
0.183136 + 0.983088i \(0.441375\pi\)
\(410\) 22.6575 1.11897
\(411\) 1.14244 0.0563526
\(412\) −15.7235 −0.774643
\(413\) −32.1228 −1.58066
\(414\) 2.96758 0.145848
\(415\) −45.6791 −2.24230
\(416\) 3.19934 0.156861
\(417\) −0.113070 −0.00553708
\(418\) 4.25105 0.207926
\(419\) −31.3233 −1.53024 −0.765122 0.643885i \(-0.777321\pi\)
−0.765122 + 0.643885i \(0.777321\pi\)
\(420\) −1.59158 −0.0776612
\(421\) −25.1680 −1.22661 −0.613305 0.789846i \(-0.710161\pi\)
−0.613305 + 0.789846i \(0.710161\pi\)
\(422\) −15.1183 −0.735945
\(423\) −25.7577 −1.25238
\(424\) 5.41261 0.262860
\(425\) 24.7912 1.20255
\(426\) −0.691180 −0.0334878
\(427\) 11.5696 0.559893
\(428\) 8.87665 0.429069
\(429\) −1.06135 −0.0512425
\(430\) −12.7869 −0.616638
\(431\) 20.4496 0.985021 0.492511 0.870306i \(-0.336079\pi\)
0.492511 + 0.870306i \(0.336079\pi\)
\(432\) −1.07457 −0.0517002
\(433\) 13.6040 0.653765 0.326882 0.945065i \(-0.394002\pi\)
0.326882 + 0.945065i \(0.394002\pi\)
\(434\) −0.456676 −0.0219212
\(435\) 2.35472 0.112900
\(436\) −12.2645 −0.587361
\(437\) −2.30746 −0.110381
\(438\) 0.609865 0.0291405
\(439\) −9.19695 −0.438947 −0.219473 0.975619i \(-0.570434\pi\)
−0.219473 + 0.975619i \(0.570434\pi\)
\(440\) 5.74129 0.273705
\(441\) −3.09914 −0.147578
\(442\) 16.8337 0.800700
\(443\) −9.54765 −0.453622 −0.226811 0.973939i \(-0.572830\pi\)
−0.226811 + 0.973939i \(0.572830\pi\)
\(444\) 0.606836 0.0287992
\(445\) −13.0004 −0.616276
\(446\) −6.41023 −0.303533
\(447\) −1.26272 −0.0597245
\(448\) 2.83625 0.134000
\(449\) 2.94871 0.139158 0.0695792 0.997576i \(-0.477834\pi\)
0.0695792 + 0.997576i \(0.477834\pi\)
\(450\) 13.9823 0.659133
\(451\) 13.3945 0.630722
\(452\) −15.2526 −0.717424
\(453\) 1.82263 0.0856345
\(454\) 24.4650 1.14820
\(455\) 28.2783 1.32571
\(456\) 0.415500 0.0194575
\(457\) −27.5060 −1.28668 −0.643338 0.765582i \(-0.722451\pi\)
−0.643338 + 0.765582i \(0.722451\pi\)
\(458\) 28.7523 1.34351
\(459\) −5.65398 −0.263905
\(460\) −3.11636 −0.145301
\(461\) 37.7226 1.75692 0.878459 0.477818i \(-0.158572\pi\)
0.878459 + 0.477818i \(0.158572\pi\)
\(462\) −0.940899 −0.0437746
\(463\) −4.23431 −0.196785 −0.0983925 0.995148i \(-0.531370\pi\)
−0.0983925 + 0.995148i \(0.531370\pi\)
\(464\) −4.19619 −0.194803
\(465\) −0.0903540 −0.00419006
\(466\) 15.9419 0.738495
\(467\) −18.2718 −0.845519 −0.422759 0.906242i \(-0.638938\pi\)
−0.422759 + 0.906242i \(0.638938\pi\)
\(468\) 9.49429 0.438874
\(469\) −25.0230 −1.15546
\(470\) 27.0491 1.24768
\(471\) −3.27674 −0.150984
\(472\) 11.3258 0.521311
\(473\) −7.55925 −0.347575
\(474\) −2.70868 −0.124414
\(475\) −10.8721 −0.498844
\(476\) 14.9233 0.684009
\(477\) 16.0623 0.735444
\(478\) 11.9789 0.547903
\(479\) −7.83957 −0.358199 −0.179100 0.983831i \(-0.557318\pi\)
−0.179100 + 0.983831i \(0.557318\pi\)
\(480\) 0.561156 0.0256132
\(481\) −10.7819 −0.491613
\(482\) 7.44765 0.339231
\(483\) 0.510718 0.0232385
\(484\) −7.60591 −0.345723
\(485\) 0.850650 0.0386260
\(486\) −4.79196 −0.217368
\(487\) −2.46633 −0.111760 −0.0558801 0.998437i \(-0.517796\pi\)
−0.0558801 + 0.998437i \(0.517796\pi\)
\(488\) −4.07919 −0.184656
\(489\) 0.204462 0.00924608
\(490\) 3.25452 0.147024
\(491\) 10.0832 0.455050 0.227525 0.973772i \(-0.426937\pi\)
0.227525 + 0.973772i \(0.426937\pi\)
\(492\) 1.30918 0.0590225
\(493\) −22.0788 −0.994379
\(494\) −7.38236 −0.332148
\(495\) 17.0377 0.765788
\(496\) 0.161014 0.00722974
\(497\) 10.8868 0.488339
\(498\) −2.63941 −0.118275
\(499\) −26.8782 −1.20323 −0.601616 0.798785i \(-0.705476\pi\)
−0.601616 + 0.798785i \(0.705476\pi\)
\(500\) 0.898453 0.0401801
\(501\) 1.78274 0.0796468
\(502\) 8.65134 0.386128
\(503\) 14.1835 0.632412 0.316206 0.948691i \(-0.397591\pi\)
0.316206 + 0.948691i \(0.397591\pi\)
\(504\) 8.41680 0.374914
\(505\) 5.37761 0.239301
\(506\) −1.84231 −0.0819005
\(507\) −0.497746 −0.0221057
\(508\) −3.70620 −0.164436
\(509\) 26.0094 1.15285 0.576423 0.817151i \(-0.304448\pi\)
0.576423 + 0.817151i \(0.304448\pi\)
\(510\) 2.95260 0.130743
\(511\) −9.60600 −0.424944
\(512\) −1.00000 −0.0441942
\(513\) 2.47953 0.109474
\(514\) −3.12698 −0.137925
\(515\) 49.0002 2.15921
\(516\) −0.738844 −0.0325258
\(517\) 15.9907 0.703270
\(518\) −9.55829 −0.419967
\(519\) −3.65841 −0.160586
\(520\) −9.97030 −0.437227
\(521\) −6.54328 −0.286666 −0.143333 0.989675i \(-0.545782\pi\)
−0.143333 + 0.989675i \(0.545782\pi\)
\(522\) −12.4525 −0.545032
\(523\) 0.573062 0.0250583 0.0125291 0.999922i \(-0.496012\pi\)
0.0125291 + 0.999922i \(0.496012\pi\)
\(524\) 1.00000 0.0436852
\(525\) 2.40635 0.105022
\(526\) −4.74709 −0.206983
\(527\) 0.847195 0.0369044
\(528\) 0.331740 0.0144371
\(529\) 1.00000 0.0434783
\(530\) −16.8676 −0.732684
\(531\) 33.6101 1.45855
\(532\) −6.54454 −0.283742
\(533\) −23.2608 −1.00754
\(534\) −0.751179 −0.0325067
\(535\) −27.6628 −1.19597
\(536\) 8.82256 0.381077
\(537\) 2.01340 0.0868847
\(538\) −14.5561 −0.627560
\(539\) 1.92398 0.0828717
\(540\) 3.34874 0.144107
\(541\) 19.7449 0.848898 0.424449 0.905452i \(-0.360468\pi\)
0.424449 + 0.905452i \(0.360468\pi\)
\(542\) −9.44993 −0.405909
\(543\) −0.480069 −0.0206017
\(544\) −5.26163 −0.225590
\(545\) 38.2204 1.63718
\(546\) 1.63396 0.0699271
\(547\) 3.22818 0.138027 0.0690134 0.997616i \(-0.478015\pi\)
0.0690134 + 0.997616i \(0.478015\pi\)
\(548\) 6.34452 0.271025
\(549\) −12.1053 −0.516642
\(550\) −8.68039 −0.370133
\(551\) 9.68255 0.412490
\(552\) −0.180068 −0.00766420
\(553\) 42.6645 1.81428
\(554\) 11.7380 0.498698
\(555\) −1.89112 −0.0802736
\(556\) −0.627932 −0.0266302
\(557\) 21.9754 0.931127 0.465563 0.885014i \(-0.345852\pi\)
0.465563 + 0.885014i \(0.345852\pi\)
\(558\) 0.477821 0.0202278
\(559\) 13.1274 0.555228
\(560\) −8.83879 −0.373507
\(561\) 1.74549 0.0736948
\(562\) −5.06304 −0.213572
\(563\) 36.7629 1.54937 0.774685 0.632347i \(-0.217908\pi\)
0.774685 + 0.632347i \(0.217908\pi\)
\(564\) 1.56294 0.0658116
\(565\) 47.5327 1.99972
\(566\) −3.36418 −0.141407
\(567\) 24.7016 1.03737
\(568\) −3.83844 −0.161057
\(569\) 23.2653 0.975332 0.487666 0.873030i \(-0.337848\pi\)
0.487666 + 0.873030i \(0.337848\pi\)
\(570\) −1.29485 −0.0542351
\(571\) −24.4745 −1.02423 −0.512113 0.858918i \(-0.671137\pi\)
−0.512113 + 0.858918i \(0.671137\pi\)
\(572\) −5.89417 −0.246448
\(573\) 0.323350 0.0135081
\(574\) −20.6210 −0.860703
\(575\) 4.71170 0.196491
\(576\) −2.96758 −0.123649
\(577\) −34.8341 −1.45016 −0.725082 0.688662i \(-0.758198\pi\)
−0.725082 + 0.688662i \(0.758198\pi\)
\(578\) −10.6847 −0.444426
\(579\) −1.30065 −0.0540530
\(580\) 13.0768 0.542986
\(581\) 41.5733 1.72475
\(582\) 0.0491518 0.00203741
\(583\) −9.97169 −0.412985
\(584\) 3.38686 0.140149
\(585\) −29.5876 −1.22330
\(586\) 24.6029 1.01634
\(587\) −40.8390 −1.68561 −0.842804 0.538221i \(-0.819097\pi\)
−0.842804 + 0.538221i \(0.819097\pi\)
\(588\) 0.188051 0.00775508
\(589\) −0.371533 −0.0153088
\(590\) −35.2952 −1.45308
\(591\) 2.75096 0.113159
\(592\) 3.37004 0.138508
\(593\) −13.2205 −0.542901 −0.271451 0.962452i \(-0.587503\pi\)
−0.271451 + 0.962452i \(0.587503\pi\)
\(594\) 1.97968 0.0812274
\(595\) −46.5064 −1.90658
\(596\) −7.01246 −0.287242
\(597\) −0.869045 −0.0355676
\(598\) 3.19934 0.130831
\(599\) −2.11524 −0.0864263 −0.0432131 0.999066i \(-0.513759\pi\)
−0.0432131 + 0.999066i \(0.513759\pi\)
\(600\) −0.848425 −0.0346368
\(601\) −20.1091 −0.820269 −0.410135 0.912025i \(-0.634518\pi\)
−0.410135 + 0.912025i \(0.634518\pi\)
\(602\) 11.6376 0.474311
\(603\) 26.1816 1.06620
\(604\) 10.1219 0.411854
\(605\) 23.7027 0.963653
\(606\) 0.310726 0.0126224
\(607\) −31.9652 −1.29743 −0.648715 0.761032i \(-0.724693\pi\)
−0.648715 + 0.761032i \(0.724693\pi\)
\(608\) 2.30746 0.0935799
\(609\) −2.14307 −0.0868416
\(610\) 12.7122 0.514703
\(611\) −27.7694 −1.12343
\(612\) −15.6143 −0.631170
\(613\) 23.0258 0.930003 0.465001 0.885310i \(-0.346054\pi\)
0.465001 + 0.885310i \(0.346054\pi\)
\(614\) 22.2355 0.897353
\(615\) −4.07988 −0.164517
\(616\) −5.22525 −0.210531
\(617\) −23.0805 −0.929185 −0.464593 0.885524i \(-0.653799\pi\)
−0.464593 + 0.885524i \(0.653799\pi\)
\(618\) 2.83130 0.113892
\(619\) −48.1720 −1.93619 −0.968097 0.250575i \(-0.919380\pi\)
−0.968097 + 0.250575i \(0.919380\pi\)
\(620\) −0.501777 −0.0201519
\(621\) −1.07457 −0.0431210
\(622\) 21.8598 0.876499
\(623\) 11.8318 0.474033
\(624\) −0.576099 −0.0230624
\(625\) −26.3584 −1.05434
\(626\) −1.35107 −0.0539996
\(627\) −0.765478 −0.0305702
\(628\) −18.1972 −0.726148
\(629\) 17.7319 0.707018
\(630\) −26.2298 −1.04502
\(631\) 27.8966 1.11055 0.555273 0.831668i \(-0.312614\pi\)
0.555273 + 0.831668i \(0.312614\pi\)
\(632\) −15.0426 −0.598361
\(633\) 2.72231 0.108202
\(634\) −13.8256 −0.549086
\(635\) 11.5499 0.458342
\(636\) −0.974637 −0.0386469
\(637\) −3.34118 −0.132382
\(638\) 7.73067 0.306060
\(639\) −11.3909 −0.450615
\(640\) 3.11636 0.123185
\(641\) 0.194820 0.00769494 0.00384747 0.999993i \(-0.498775\pi\)
0.00384747 + 0.999993i \(0.498775\pi\)
\(642\) −1.59840 −0.0630838
\(643\) −13.8637 −0.546732 −0.273366 0.961910i \(-0.588137\pi\)
−0.273366 + 0.961910i \(0.588137\pi\)
\(644\) 2.83625 0.111764
\(645\) 2.30250 0.0906610
\(646\) 12.1410 0.477681
\(647\) 16.3051 0.641019 0.320510 0.947245i \(-0.396146\pi\)
0.320510 + 0.947245i \(0.396146\pi\)
\(648\) −8.70923 −0.342131
\(649\) −20.8655 −0.819044
\(650\) 15.0743 0.591264
\(651\) 0.0822327 0.00322295
\(652\) 1.13547 0.0444684
\(653\) −28.9898 −1.13446 −0.567229 0.823560i \(-0.691985\pi\)
−0.567229 + 0.823560i \(0.691985\pi\)
\(654\) 2.20843 0.0863566
\(655\) −3.11636 −0.121766
\(656\) 7.27050 0.283865
\(657\) 10.0508 0.392118
\(658\) −24.6179 −0.959705
\(659\) 11.8918 0.463239 0.231619 0.972806i \(-0.425598\pi\)
0.231619 + 0.972806i \(0.425598\pi\)
\(660\) −1.03382 −0.0402415
\(661\) −16.8772 −0.656448 −0.328224 0.944600i \(-0.606450\pi\)
−0.328224 + 0.944600i \(0.606450\pi\)
\(662\) −0.802881 −0.0312049
\(663\) −3.03122 −0.117723
\(664\) −14.6578 −0.568834
\(665\) 20.3952 0.790890
\(666\) 10.0009 0.387525
\(667\) −4.19619 −0.162477
\(668\) 9.90036 0.383056
\(669\) 1.15428 0.0446269
\(670\) −27.4943 −1.06220
\(671\) 7.51512 0.290118
\(672\) −0.510718 −0.0197014
\(673\) 7.74456 0.298531 0.149266 0.988797i \(-0.452309\pi\)
0.149266 + 0.988797i \(0.452309\pi\)
\(674\) 20.0302 0.771535
\(675\) −5.06304 −0.194877
\(676\) −2.76421 −0.106316
\(677\) −7.87180 −0.302538 −0.151269 0.988493i \(-0.548336\pi\)
−0.151269 + 0.988493i \(0.548336\pi\)
\(678\) 2.74651 0.105479
\(679\) −0.774192 −0.0297108
\(680\) 16.3971 0.628801
\(681\) −4.40535 −0.168813
\(682\) −0.296637 −0.0113588
\(683\) 47.6935 1.82494 0.912470 0.409144i \(-0.134173\pi\)
0.912470 + 0.409144i \(0.134173\pi\)
\(684\) 6.84756 0.261823
\(685\) −19.7718 −0.755442
\(686\) 16.8918 0.644931
\(687\) −5.17736 −0.197529
\(688\) −4.10314 −0.156431
\(689\) 17.3168 0.659717
\(690\) 0.561156 0.0213629
\(691\) 14.8643 0.565463 0.282732 0.959199i \(-0.408759\pi\)
0.282732 + 0.959199i \(0.408759\pi\)
\(692\) −20.3169 −0.772331
\(693\) −15.5063 −0.589036
\(694\) −0.578901 −0.0219748
\(695\) 1.95686 0.0742280
\(696\) 0.755599 0.0286409
\(697\) 38.2547 1.44900
\(698\) 25.7649 0.975215
\(699\) −2.87063 −0.108577
\(700\) 13.3636 0.505095
\(701\) −13.4474 −0.507900 −0.253950 0.967217i \(-0.581730\pi\)
−0.253950 + 0.967217i \(0.581730\pi\)
\(702\) −3.43791 −0.129756
\(703\) −7.77624 −0.293287
\(704\) 1.84231 0.0694345
\(705\) −4.87068 −0.183440
\(706\) 17.6860 0.665622
\(707\) −4.89426 −0.184068
\(708\) −2.03941 −0.0766456
\(709\) −36.2297 −1.36063 −0.680317 0.732918i \(-0.738158\pi\)
−0.680317 + 0.732918i \(0.738158\pi\)
\(710\) 11.9620 0.448924
\(711\) −44.6399 −1.67413
\(712\) −4.17165 −0.156339
\(713\) 0.161014 0.00603002
\(714\) −2.68721 −0.100566
\(715\) 18.3683 0.686937
\(716\) 11.1814 0.417867
\(717\) −2.15702 −0.0805553
\(718\) −11.8894 −0.443708
\(719\) −26.6363 −0.993367 −0.496684 0.867932i \(-0.665449\pi\)
−0.496684 + 0.867932i \(0.665449\pi\)
\(720\) 9.24803 0.344654
\(721\) −44.5959 −1.66084
\(722\) 13.6756 0.508954
\(723\) −1.34108 −0.0498754
\(724\) −2.66605 −0.0990828
\(725\) −19.7712 −0.734283
\(726\) 1.36958 0.0508299
\(727\) 45.2769 1.67923 0.839614 0.543184i \(-0.182781\pi\)
0.839614 + 0.543184i \(0.182781\pi\)
\(728\) 9.07414 0.336310
\(729\) −25.2648 −0.935734
\(730\) −10.5547 −0.390646
\(731\) −21.5892 −0.798506
\(732\) 0.734531 0.0271490
\(733\) −15.3558 −0.567181 −0.283591 0.958945i \(-0.591526\pi\)
−0.283591 + 0.958945i \(0.591526\pi\)
\(734\) −7.26661 −0.268215
\(735\) −0.586034 −0.0216162
\(736\) −1.00000 −0.0368605
\(737\) −16.2539 −0.598719
\(738\) 21.5757 0.794214
\(739\) −21.0246 −0.773403 −0.386702 0.922205i \(-0.626386\pi\)
−0.386702 + 0.922205i \(0.626386\pi\)
\(740\) −10.5023 −0.386071
\(741\) 1.32933 0.0488340
\(742\) 15.3515 0.563573
\(743\) 30.6421 1.12415 0.562076 0.827086i \(-0.310003\pi\)
0.562076 + 0.827086i \(0.310003\pi\)
\(744\) −0.0289934 −0.00106295
\(745\) 21.8533 0.800645
\(746\) 13.5275 0.495278
\(747\) −43.4982 −1.59152
\(748\) 9.69353 0.354431
\(749\) 25.1764 0.919926
\(750\) −0.161783 −0.00590746
\(751\) 14.1536 0.516472 0.258236 0.966082i \(-0.416859\pi\)
0.258236 + 0.966082i \(0.416859\pi\)
\(752\) 8.67972 0.316517
\(753\) −1.55783 −0.0567704
\(754\) −13.4250 −0.488911
\(755\) −31.5435 −1.14798
\(756\) −3.04775 −0.110846
\(757\) 12.2832 0.446439 0.223220 0.974768i \(-0.428343\pi\)
0.223220 + 0.974768i \(0.428343\pi\)
\(758\) −12.8909 −0.468219
\(759\) 0.331740 0.0120414
\(760\) −7.19088 −0.260841
\(761\) −33.1950 −1.20332 −0.601659 0.798753i \(-0.705493\pi\)
−0.601659 + 0.798753i \(0.705493\pi\)
\(762\) 0.667368 0.0241762
\(763\) −34.7851 −1.25931
\(764\) 1.79571 0.0649665
\(765\) 48.6597 1.75930
\(766\) 8.96319 0.323853
\(767\) 36.2350 1.30837
\(768\) 0.180068 0.00649764
\(769\) −5.22214 −0.188315 −0.0941577 0.995557i \(-0.530016\pi\)
−0.0941577 + 0.995557i \(0.530016\pi\)
\(770\) 16.2838 0.586826
\(771\) 0.563069 0.0202784
\(772\) −7.22308 −0.259964
\(773\) −3.16545 −0.113853 −0.0569267 0.998378i \(-0.518130\pi\)
−0.0569267 + 0.998378i \(0.518130\pi\)
\(774\) −12.1764 −0.437671
\(775\) 0.758649 0.0272515
\(776\) 0.272963 0.00979879
\(777\) 1.72114 0.0617456
\(778\) 28.0289 1.00488
\(779\) −16.7764 −0.601076
\(780\) 1.79533 0.0642832
\(781\) 7.07158 0.253041
\(782\) −5.26163 −0.188155
\(783\) 4.50909 0.161142
\(784\) 1.04433 0.0372976
\(785\) 56.7091 2.02403
\(786\) −0.180068 −0.00642281
\(787\) 30.8609 1.10007 0.550036 0.835141i \(-0.314614\pi\)
0.550036 + 0.835141i \(0.314614\pi\)
\(788\) 15.2774 0.544233
\(789\) 0.854799 0.0304317
\(790\) 46.8780 1.66785
\(791\) −43.2604 −1.53816
\(792\) 5.46718 0.194268
\(793\) −13.0507 −0.463445
\(794\) −20.6532 −0.732955
\(795\) 3.03732 0.107723
\(796\) −4.82621 −0.171060
\(797\) −40.8799 −1.44804 −0.724020 0.689779i \(-0.757708\pi\)
−0.724020 + 0.689779i \(0.757708\pi\)
\(798\) 1.17846 0.0417171
\(799\) 45.6694 1.61567
\(800\) −4.71170 −0.166584
\(801\) −12.3797 −0.437414
\(802\) 21.1495 0.746814
\(803\) −6.23964 −0.220192
\(804\) −1.58866 −0.0560277
\(805\) −8.83879 −0.311526
\(806\) 0.515139 0.0181450
\(807\) 2.62109 0.0922668
\(808\) 1.72561 0.0607066
\(809\) −40.7854 −1.43394 −0.716969 0.697106i \(-0.754471\pi\)
−0.716969 + 0.697106i \(0.754471\pi\)
\(810\) 27.1411 0.953641
\(811\) −29.2687 −1.02776 −0.513882 0.857861i \(-0.671793\pi\)
−0.513882 + 0.857861i \(0.671793\pi\)
\(812\) −11.9015 −0.417659
\(813\) 1.70163 0.0596787
\(814\) −6.20865 −0.217613
\(815\) −3.53853 −0.123949
\(816\) 0.947450 0.0331674
\(817\) 9.46785 0.331238
\(818\) −7.40738 −0.258993
\(819\) 26.9282 0.940948
\(820\) −22.6575 −0.791234
\(821\) −22.0476 −0.769468 −0.384734 0.923028i \(-0.625707\pi\)
−0.384734 + 0.923028i \(0.625707\pi\)
\(822\) −1.14244 −0.0398473
\(823\) 13.1850 0.459600 0.229800 0.973238i \(-0.426193\pi\)
0.229800 + 0.973238i \(0.426193\pi\)
\(824\) 15.7235 0.547755
\(825\) 1.56306 0.0544187
\(826\) 32.1228 1.11769
\(827\) 21.4821 0.747006 0.373503 0.927629i \(-0.378156\pi\)
0.373503 + 0.927629i \(0.378156\pi\)
\(828\) −2.96758 −0.103130
\(829\) 34.7655 1.20746 0.603728 0.797190i \(-0.293681\pi\)
0.603728 + 0.797190i \(0.293681\pi\)
\(830\) 45.6791 1.58554
\(831\) −2.11363 −0.0733210
\(832\) −3.19934 −0.110917
\(833\) 5.49489 0.190387
\(834\) 0.113070 0.00391531
\(835\) −30.8531 −1.06772
\(836\) −4.25105 −0.147026
\(837\) −0.173020 −0.00598046
\(838\) 31.3233 1.08205
\(839\) 32.3696 1.11752 0.558761 0.829329i \(-0.311277\pi\)
0.558761 + 0.829329i \(0.311277\pi\)
\(840\) 1.59158 0.0549148
\(841\) −11.3920 −0.392827
\(842\) 25.1680 0.867345
\(843\) 0.911692 0.0314003
\(844\) 15.1183 0.520392
\(845\) 8.61428 0.296340
\(846\) 25.7577 0.885568
\(847\) −21.5723 −0.741232
\(848\) −5.41261 −0.185870
\(849\) 0.605780 0.0207903
\(850\) −24.7912 −0.850331
\(851\) 3.37004 0.115524
\(852\) 0.691180 0.0236794
\(853\) 1.09492 0.0374893 0.0187447 0.999824i \(-0.494033\pi\)
0.0187447 + 0.999824i \(0.494033\pi\)
\(854\) −11.5696 −0.395904
\(855\) −21.3395 −0.729795
\(856\) −8.87665 −0.303398
\(857\) −15.3754 −0.525214 −0.262607 0.964903i \(-0.584582\pi\)
−0.262607 + 0.964903i \(0.584582\pi\)
\(858\) 1.06135 0.0362339
\(859\) 39.1222 1.33483 0.667416 0.744685i \(-0.267401\pi\)
0.667416 + 0.744685i \(0.267401\pi\)
\(860\) 12.7869 0.436029
\(861\) 3.71317 0.126545
\(862\) −20.4496 −0.696515
\(863\) −9.41233 −0.320399 −0.160200 0.987085i \(-0.551214\pi\)
−0.160200 + 0.987085i \(0.551214\pi\)
\(864\) 1.07457 0.0365576
\(865\) 63.3146 2.15276
\(866\) −13.6040 −0.462281
\(867\) 1.92398 0.0653417
\(868\) 0.456676 0.0155006
\(869\) 27.7130 0.940099
\(870\) −2.35472 −0.0798324
\(871\) 28.2264 0.956415
\(872\) 12.2645 0.415327
\(873\) 0.810038 0.0274156
\(874\) 2.30746 0.0780510
\(875\) 2.54824 0.0861463
\(876\) −0.609865 −0.0206054
\(877\) 44.3929 1.49904 0.749520 0.661982i \(-0.230284\pi\)
0.749520 + 0.661982i \(0.230284\pi\)
\(878\) 9.19695 0.310382
\(879\) −4.43020 −0.149427
\(880\) −5.74129 −0.193539
\(881\) 39.9281 1.34521 0.672605 0.740001i \(-0.265175\pi\)
0.672605 + 0.740001i \(0.265175\pi\)
\(882\) 3.09914 0.104353
\(883\) −13.9955 −0.470988 −0.235494 0.971876i \(-0.575671\pi\)
−0.235494 + 0.971876i \(0.575671\pi\)
\(884\) −16.8337 −0.566180
\(885\) 6.35553 0.213639
\(886\) 9.54765 0.320759
\(887\) −11.9828 −0.402345 −0.201172 0.979556i \(-0.564475\pi\)
−0.201172 + 0.979556i \(0.564475\pi\)
\(888\) −0.606836 −0.0203641
\(889\) −10.5117 −0.352552
\(890\) 13.0004 0.435773
\(891\) 16.0451 0.537530
\(892\) 6.41023 0.214631
\(893\) −20.0281 −0.670215
\(894\) 1.26272 0.0422316
\(895\) −34.8451 −1.16474
\(896\) −2.83625 −0.0947526
\(897\) −0.576099 −0.0192354
\(898\) −2.94871 −0.0983999
\(899\) −0.675645 −0.0225340
\(900\) −13.9823 −0.466077
\(901\) −28.4791 −0.948778
\(902\) −13.3945 −0.445988
\(903\) −2.09555 −0.0697355
\(904\) 15.2526 0.507295
\(905\) 8.30836 0.276179
\(906\) −1.82263 −0.0605527
\(907\) −48.0125 −1.59423 −0.797114 0.603828i \(-0.793641\pi\)
−0.797114 + 0.603828i \(0.793641\pi\)
\(908\) −24.4650 −0.811898
\(909\) 5.12087 0.169848
\(910\) −28.2783 −0.937416
\(911\) 0.727120 0.0240906 0.0120453 0.999927i \(-0.496166\pi\)
0.0120453 + 0.999927i \(0.496166\pi\)
\(912\) −0.415500 −0.0137586
\(913\) 27.0042 0.893710
\(914\) 27.5060 0.909817
\(915\) −2.28906 −0.0756741
\(916\) −28.7523 −0.950003
\(917\) 2.83625 0.0936613
\(918\) 5.65398 0.186609
\(919\) −32.2213 −1.06288 −0.531441 0.847095i \(-0.678349\pi\)
−0.531441 + 0.847095i \(0.678349\pi\)
\(920\) 3.11636 0.102743
\(921\) −4.00390 −0.131933
\(922\) −37.7226 −1.24233
\(923\) −12.2805 −0.404217
\(924\) 0.940899 0.0309533
\(925\) 15.8786 0.522086
\(926\) 4.23431 0.139148
\(927\) 46.6608 1.53254
\(928\) 4.19619 0.137747
\(929\) −34.0838 −1.11825 −0.559126 0.829083i \(-0.688863\pi\)
−0.559126 + 0.829083i \(0.688863\pi\)
\(930\) 0.0903540 0.00296282
\(931\) −2.40976 −0.0789766
\(932\) −15.9419 −0.522195
\(933\) −3.93625 −0.128867
\(934\) 18.2718 0.597872
\(935\) −30.2085 −0.987925
\(936\) −9.49429 −0.310331
\(937\) 8.24127 0.269231 0.134615 0.990898i \(-0.457020\pi\)
0.134615 + 0.990898i \(0.457020\pi\)
\(938\) 25.0230 0.817031
\(939\) 0.243284 0.00793928
\(940\) −27.0491 −0.882245
\(941\) −2.75065 −0.0896685 −0.0448343 0.998994i \(-0.514276\pi\)
−0.0448343 + 0.998994i \(0.514276\pi\)
\(942\) 3.27674 0.106762
\(943\) 7.27050 0.236760
\(944\) −11.3258 −0.368622
\(945\) 9.49788 0.308966
\(946\) 7.55925 0.245772
\(947\) −33.4469 −1.08688 −0.543439 0.839449i \(-0.682878\pi\)
−0.543439 + 0.839449i \(0.682878\pi\)
\(948\) 2.70868 0.0879739
\(949\) 10.8357 0.351743
\(950\) 10.8721 0.352736
\(951\) 2.48955 0.0807293
\(952\) −14.9233 −0.483667
\(953\) 38.8227 1.25759 0.628795 0.777571i \(-0.283549\pi\)
0.628795 + 0.777571i \(0.283549\pi\)
\(954\) −16.0623 −0.520037
\(955\) −5.59608 −0.181085
\(956\) −11.9789 −0.387426
\(957\) −1.39204 −0.0449984
\(958\) 7.83957 0.253285
\(959\) 17.9947 0.581078
\(960\) −0.561156 −0.0181112
\(961\) −30.9741 −0.999164
\(962\) 10.7819 0.347623
\(963\) −26.3421 −0.848863
\(964\) −7.44765 −0.239873
\(965\) 22.5097 0.724614
\(966\) −0.510718 −0.0164321
\(967\) 20.7530 0.667371 0.333686 0.942684i \(-0.391708\pi\)
0.333686 + 0.942684i \(0.391708\pi\)
\(968\) 7.60591 0.244463
\(969\) −2.18620 −0.0702310
\(970\) −0.850650 −0.0273127
\(971\) 47.8740 1.53635 0.768175 0.640240i \(-0.221165\pi\)
0.768175 + 0.640240i \(0.221165\pi\)
\(972\) 4.79196 0.153702
\(973\) −1.78097 −0.0570954
\(974\) 2.46633 0.0790265
\(975\) −2.71440 −0.0869305
\(976\) 4.07919 0.130572
\(977\) 1.85090 0.0592155 0.0296077 0.999562i \(-0.490574\pi\)
0.0296077 + 0.999562i \(0.490574\pi\)
\(978\) −0.204462 −0.00653796
\(979\) 7.68545 0.245628
\(980\) −3.25452 −0.103962
\(981\) 36.3957 1.16202
\(982\) −10.0832 −0.321769
\(983\) −32.3375 −1.03141 −0.515703 0.856767i \(-0.672469\pi\)
−0.515703 + 0.856767i \(0.672469\pi\)
\(984\) −1.30918 −0.0417352
\(985\) −47.6097 −1.51697
\(986\) 22.0788 0.703132
\(987\) 4.43289 0.141100
\(988\) 7.38236 0.234864
\(989\) −4.10314 −0.130472
\(990\) −17.0377 −0.541494
\(991\) −35.5786 −1.13019 −0.565096 0.825025i \(-0.691161\pi\)
−0.565096 + 0.825025i \(0.691161\pi\)
\(992\) −0.161014 −0.00511220
\(993\) 0.144573 0.00458789
\(994\) −10.8868 −0.345308
\(995\) 15.0402 0.476806
\(996\) 2.63941 0.0836328
\(997\) 11.6446 0.368790 0.184395 0.982852i \(-0.440968\pi\)
0.184395 + 0.982852i \(0.440968\pi\)
\(998\) 26.8782 0.850814
\(999\) −3.62134 −0.114574
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 \(a_p\))