Properties

Label 8018.2.a.f.1.2
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.17050 q^{3}\) \(+1.00000 q^{4}\) \(+4.15425 q^{5}\) \(+3.17050 q^{6}\) \(+1.45443 q^{7}\) \(-1.00000 q^{8}\) \(+7.05209 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.17050 q^{3}\) \(+1.00000 q^{4}\) \(+4.15425 q^{5}\) \(+3.17050 q^{6}\) \(+1.45443 q^{7}\) \(-1.00000 q^{8}\) \(+7.05209 q^{9}\) \(-4.15425 q^{10}\) \(-3.03789 q^{11}\) \(-3.17050 q^{12}\) \(+3.91980 q^{13}\) \(-1.45443 q^{14}\) \(-13.1711 q^{15}\) \(+1.00000 q^{16}\) \(-0.0576653 q^{17}\) \(-7.05209 q^{18}\) \(-1.00000 q^{19}\) \(+4.15425 q^{20}\) \(-4.61128 q^{21}\) \(+3.03789 q^{22}\) \(+0.939084 q^{23}\) \(+3.17050 q^{24}\) \(+12.2578 q^{25}\) \(-3.91980 q^{26}\) \(-12.8472 q^{27}\) \(+1.45443 q^{28}\) \(-9.74846 q^{29}\) \(+13.1711 q^{30}\) \(+3.98084 q^{31}\) \(-1.00000 q^{32}\) \(+9.63163 q^{33}\) \(+0.0576653 q^{34}\) \(+6.04207 q^{35}\) \(+7.05209 q^{36}\) \(-10.1478 q^{37}\) \(+1.00000 q^{38}\) \(-12.4277 q^{39}\) \(-4.15425 q^{40}\) \(+6.40788 q^{41}\) \(+4.61128 q^{42}\) \(-0.156989 q^{43}\) \(-3.03789 q^{44}\) \(+29.2962 q^{45}\) \(-0.939084 q^{46}\) \(-3.44285 q^{47}\) \(-3.17050 q^{48}\) \(-4.88463 q^{49}\) \(-12.2578 q^{50}\) \(+0.182828 q^{51}\) \(+3.91980 q^{52}\) \(+8.72651 q^{53}\) \(+12.8472 q^{54}\) \(-12.6201 q^{55}\) \(-1.45443 q^{56}\) \(+3.17050 q^{57}\) \(+9.74846 q^{58}\) \(-6.77204 q^{59}\) \(-13.1711 q^{60}\) \(+0.287029 q^{61}\) \(-3.98084 q^{62}\) \(+10.2568 q^{63}\) \(+1.00000 q^{64}\) \(+16.2838 q^{65}\) \(-9.63163 q^{66}\) \(-0.311296 q^{67}\) \(-0.0576653 q^{68}\) \(-2.97737 q^{69}\) \(-6.04207 q^{70}\) \(-4.31993 q^{71}\) \(-7.05209 q^{72}\) \(-12.8177 q^{73}\) \(+10.1478 q^{74}\) \(-38.8634 q^{75}\) \(-1.00000 q^{76}\) \(-4.41839 q^{77}\) \(+12.4277 q^{78}\) \(-12.9034 q^{79}\) \(+4.15425 q^{80}\) \(+19.5758 q^{81}\) \(-6.40788 q^{82}\) \(-3.11104 q^{83}\) \(-4.61128 q^{84}\) \(-0.239556 q^{85}\) \(+0.156989 q^{86}\) \(+30.9075 q^{87}\) \(+3.03789 q^{88}\) \(-9.56741 q^{89}\) \(-29.2962 q^{90}\) \(+5.70108 q^{91}\) \(+0.939084 q^{92}\) \(-12.6213 q^{93}\) \(+3.44285 q^{94}\) \(-4.15425 q^{95}\) \(+3.17050 q^{96}\) \(-18.1356 q^{97}\) \(+4.88463 q^{98}\) \(-21.4235 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.17050 −1.83049 −0.915246 0.402896i \(-0.868004\pi\)
−0.915246 + 0.402896i \(0.868004\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.15425 1.85784 0.928919 0.370284i \(-0.120740\pi\)
0.928919 + 0.370284i \(0.120740\pi\)
\(6\) 3.17050 1.29435
\(7\) 1.45443 0.549723 0.274862 0.961484i \(-0.411368\pi\)
0.274862 + 0.961484i \(0.411368\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.05209 2.35070
\(10\) −4.15425 −1.31369
\(11\) −3.03789 −0.915957 −0.457979 0.888963i \(-0.651426\pi\)
−0.457979 + 0.888963i \(0.651426\pi\)
\(12\) −3.17050 −0.915246
\(13\) 3.91980 1.08716 0.543579 0.839358i \(-0.317069\pi\)
0.543579 + 0.839358i \(0.317069\pi\)
\(14\) −1.45443 −0.388713
\(15\) −13.1711 −3.40075
\(16\) 1.00000 0.250000
\(17\) −0.0576653 −0.0139859 −0.00699294 0.999976i \(-0.502226\pi\)
−0.00699294 + 0.999976i \(0.502226\pi\)
\(18\) −7.05209 −1.66219
\(19\) −1.00000 −0.229416
\(20\) 4.15425 0.928919
\(21\) −4.61128 −1.00626
\(22\) 3.03789 0.647679
\(23\) 0.939084 0.195813 0.0979063 0.995196i \(-0.468785\pi\)
0.0979063 + 0.995196i \(0.468785\pi\)
\(24\) 3.17050 0.647176
\(25\) 12.2578 2.45156
\(26\) −3.91980 −0.768736
\(27\) −12.8472 −2.47244
\(28\) 1.45443 0.274862
\(29\) −9.74846 −1.81024 −0.905122 0.425152i \(-0.860221\pi\)
−0.905122 + 0.425152i \(0.860221\pi\)
\(30\) 13.1711 2.40470
\(31\) 3.98084 0.714981 0.357490 0.933917i \(-0.383633\pi\)
0.357490 + 0.933917i \(0.383633\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.63163 1.67665
\(34\) 0.0576653 0.00988951
\(35\) 6.04207 1.02130
\(36\) 7.05209 1.17535
\(37\) −10.1478 −1.66829 −0.834145 0.551545i \(-0.814038\pi\)
−0.834145 + 0.551545i \(0.814038\pi\)
\(38\) 1.00000 0.162221
\(39\) −12.4277 −1.99003
\(40\) −4.15425 −0.656845
\(41\) 6.40788 1.00074 0.500372 0.865811i \(-0.333197\pi\)
0.500372 + 0.865811i \(0.333197\pi\)
\(42\) 4.61128 0.711536
\(43\) −0.156989 −0.0239406 −0.0119703 0.999928i \(-0.503810\pi\)
−0.0119703 + 0.999928i \(0.503810\pi\)
\(44\) −3.03789 −0.457979
\(45\) 29.2962 4.36721
\(46\) −0.939084 −0.138460
\(47\) −3.44285 −0.502191 −0.251095 0.967962i \(-0.580791\pi\)
−0.251095 + 0.967962i \(0.580791\pi\)
\(48\) −3.17050 −0.457623
\(49\) −4.88463 −0.697805
\(50\) −12.2578 −1.73351
\(51\) 0.182828 0.0256010
\(52\) 3.91980 0.543579
\(53\) 8.72651 1.19868 0.599339 0.800495i \(-0.295430\pi\)
0.599339 + 0.800495i \(0.295430\pi\)
\(54\) 12.8472 1.74828
\(55\) −12.6201 −1.70170
\(56\) −1.45443 −0.194356
\(57\) 3.17050 0.419943
\(58\) 9.74846 1.28004
\(59\) −6.77204 −0.881644 −0.440822 0.897595i \(-0.645313\pi\)
−0.440822 + 0.897595i \(0.645313\pi\)
\(60\) −13.1711 −1.70038
\(61\) 0.287029 0.0367503 0.0183751 0.999831i \(-0.494151\pi\)
0.0183751 + 0.999831i \(0.494151\pi\)
\(62\) −3.98084 −0.505568
\(63\) 10.2568 1.29223
\(64\) 1.00000 0.125000
\(65\) 16.2838 2.01976
\(66\) −9.63163 −1.18557
\(67\) −0.311296 −0.0380309 −0.0190155 0.999819i \(-0.506053\pi\)
−0.0190155 + 0.999819i \(0.506053\pi\)
\(68\) −0.0576653 −0.00699294
\(69\) −2.97737 −0.358433
\(70\) −6.04207 −0.722165
\(71\) −4.31993 −0.512681 −0.256341 0.966587i \(-0.582517\pi\)
−0.256341 + 0.966587i \(0.582517\pi\)
\(72\) −7.05209 −0.831097
\(73\) −12.8177 −1.50020 −0.750099 0.661325i \(-0.769994\pi\)
−0.750099 + 0.661325i \(0.769994\pi\)
\(74\) 10.1478 1.17966
\(75\) −38.8634 −4.48756
\(76\) −1.00000 −0.114708
\(77\) −4.41839 −0.503523
\(78\) 12.4277 1.40717
\(79\) −12.9034 −1.45174 −0.725872 0.687830i \(-0.758564\pi\)
−0.725872 + 0.687830i \(0.758564\pi\)
\(80\) 4.15425 0.464459
\(81\) 19.5758 2.17508
\(82\) −6.40788 −0.707632
\(83\) −3.11104 −0.341481 −0.170741 0.985316i \(-0.554616\pi\)
−0.170741 + 0.985316i \(0.554616\pi\)
\(84\) −4.61128 −0.503132
\(85\) −0.239556 −0.0259835
\(86\) 0.156989 0.0169285
\(87\) 30.9075 3.31364
\(88\) 3.03789 0.323840
\(89\) −9.56741 −1.01414 −0.507072 0.861904i \(-0.669272\pi\)
−0.507072 + 0.861904i \(0.669272\pi\)
\(90\) −29.2962 −3.08809
\(91\) 5.70108 0.597635
\(92\) 0.939084 0.0979063
\(93\) −12.6213 −1.30877
\(94\) 3.44285 0.355102
\(95\) −4.15425 −0.426217
\(96\) 3.17050 0.323588
\(97\) −18.1356 −1.84140 −0.920698 0.390276i \(-0.872380\pi\)
−0.920698 + 0.390276i \(0.872380\pi\)
\(98\) 4.88463 0.493422
\(99\) −21.4235 −2.15314
\(100\) 12.2578 1.22578
\(101\) −7.67850 −0.764039 −0.382019 0.924154i \(-0.624771\pi\)
−0.382019 + 0.924154i \(0.624771\pi\)
\(102\) −0.182828 −0.0181027
\(103\) −13.1794 −1.29861 −0.649304 0.760529i \(-0.724940\pi\)
−0.649304 + 0.760529i \(0.724940\pi\)
\(104\) −3.91980 −0.384368
\(105\) −19.1564 −1.86947
\(106\) −8.72651 −0.847594
\(107\) −14.2013 −1.37289 −0.686445 0.727182i \(-0.740830\pi\)
−0.686445 + 0.727182i \(0.740830\pi\)
\(108\) −12.8472 −1.23622
\(109\) −0.357816 −0.0342726 −0.0171363 0.999853i \(-0.505455\pi\)
−0.0171363 + 0.999853i \(0.505455\pi\)
\(110\) 12.6201 1.20328
\(111\) 32.1737 3.05379
\(112\) 1.45443 0.137431
\(113\) −6.97326 −0.655989 −0.327995 0.944680i \(-0.606373\pi\)
−0.327995 + 0.944680i \(0.606373\pi\)
\(114\) −3.17050 −0.296945
\(115\) 3.90119 0.363788
\(116\) −9.74846 −0.905122
\(117\) 27.6428 2.55558
\(118\) 6.77204 0.623416
\(119\) −0.0838701 −0.00768836
\(120\) 13.1711 1.20235
\(121\) −1.77125 −0.161023
\(122\) −0.287029 −0.0259864
\(123\) −20.3162 −1.83185
\(124\) 3.98084 0.357490
\(125\) 30.1507 2.69676
\(126\) −10.2568 −0.913747
\(127\) −8.53078 −0.756985 −0.378492 0.925604i \(-0.623557\pi\)
−0.378492 + 0.925604i \(0.623557\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.497733 0.0438230
\(130\) −16.2838 −1.42819
\(131\) 10.4714 0.914889 0.457445 0.889238i \(-0.348765\pi\)
0.457445 + 0.889238i \(0.348765\pi\)
\(132\) 9.63163 0.838326
\(133\) −1.45443 −0.126115
\(134\) 0.311296 0.0268919
\(135\) −53.3704 −4.59339
\(136\) 0.0576653 0.00494476
\(137\) 2.96722 0.253507 0.126753 0.991934i \(-0.459544\pi\)
0.126753 + 0.991934i \(0.459544\pi\)
\(138\) 2.97737 0.253451
\(139\) −13.6710 −1.15956 −0.579781 0.814772i \(-0.696862\pi\)
−0.579781 + 0.814772i \(0.696862\pi\)
\(140\) 6.04207 0.510648
\(141\) 10.9156 0.919256
\(142\) 4.31993 0.362520
\(143\) −11.9079 −0.995789
\(144\) 7.05209 0.587675
\(145\) −40.4975 −3.36314
\(146\) 12.8177 1.06080
\(147\) 15.4867 1.27733
\(148\) −10.1478 −0.834145
\(149\) 23.5793 1.93169 0.965847 0.259114i \(-0.0834305\pi\)
0.965847 + 0.259114i \(0.0834305\pi\)
\(150\) 38.8634 3.17318
\(151\) −10.2850 −0.836983 −0.418492 0.908221i \(-0.637441\pi\)
−0.418492 + 0.908221i \(0.637441\pi\)
\(152\) 1.00000 0.0811107
\(153\) −0.406661 −0.0328766
\(154\) 4.41839 0.356044
\(155\) 16.5374 1.32832
\(156\) −12.4277 −0.995016
\(157\) 12.3626 0.986643 0.493321 0.869847i \(-0.335783\pi\)
0.493321 + 0.869847i \(0.335783\pi\)
\(158\) 12.9034 1.02654
\(159\) −27.6674 −2.19417
\(160\) −4.15425 −0.328422
\(161\) 1.36583 0.107643
\(162\) −19.5758 −1.53802
\(163\) −6.34732 −0.497160 −0.248580 0.968611i \(-0.579964\pi\)
−0.248580 + 0.968611i \(0.579964\pi\)
\(164\) 6.40788 0.500372
\(165\) 40.0122 3.11495
\(166\) 3.11104 0.241464
\(167\) −10.5337 −0.815122 −0.407561 0.913178i \(-0.633621\pi\)
−0.407561 + 0.913178i \(0.633621\pi\)
\(168\) 4.61128 0.355768
\(169\) 2.36484 0.181911
\(170\) 0.239556 0.0183731
\(171\) −7.05209 −0.539287
\(172\) −0.156989 −0.0119703
\(173\) 8.42256 0.640355 0.320178 0.947358i \(-0.396257\pi\)
0.320178 + 0.947358i \(0.396257\pi\)
\(174\) −30.9075 −2.34309
\(175\) 17.8281 1.34768
\(176\) −3.03789 −0.228989
\(177\) 21.4708 1.61384
\(178\) 9.56741 0.717107
\(179\) 7.95295 0.594431 0.297216 0.954810i \(-0.403942\pi\)
0.297216 + 0.954810i \(0.403942\pi\)
\(180\) 29.2962 2.18361
\(181\) 14.8269 1.10208 0.551038 0.834480i \(-0.314232\pi\)
0.551038 + 0.834480i \(0.314232\pi\)
\(182\) −5.70108 −0.422592
\(183\) −0.910026 −0.0672710
\(184\) −0.939084 −0.0692302
\(185\) −42.1566 −3.09941
\(186\) 12.6213 0.925437
\(187\) 0.175180 0.0128105
\(188\) −3.44285 −0.251095
\(189\) −18.6853 −1.35916
\(190\) 4.15425 0.301381
\(191\) −9.97021 −0.721419 −0.360710 0.932678i \(-0.617465\pi\)
−0.360710 + 0.932678i \(0.617465\pi\)
\(192\) −3.17050 −0.228811
\(193\) 1.78617 0.128572 0.0642858 0.997932i \(-0.479523\pi\)
0.0642858 + 0.997932i \(0.479523\pi\)
\(194\) 18.1356 1.30206
\(195\) −51.6280 −3.69716
\(196\) −4.88463 −0.348902
\(197\) −13.7517 −0.979765 −0.489883 0.871788i \(-0.662960\pi\)
−0.489883 + 0.871788i \(0.662960\pi\)
\(198\) 21.4235 1.52250
\(199\) −19.8784 −1.40914 −0.704571 0.709634i \(-0.748860\pi\)
−0.704571 + 0.709634i \(0.748860\pi\)
\(200\) −12.2578 −0.866757
\(201\) 0.986967 0.0696153
\(202\) 7.67850 0.540257
\(203\) −14.1785 −0.995133
\(204\) 0.182828 0.0128005
\(205\) 26.6200 1.85922
\(206\) 13.1794 0.918255
\(207\) 6.62251 0.460296
\(208\) 3.91980 0.271789
\(209\) 3.03789 0.210135
\(210\) 19.1564 1.32192
\(211\) −1.00000 −0.0688428
\(212\) 8.72651 0.599339
\(213\) 13.6964 0.938458
\(214\) 14.2013 0.970780
\(215\) −0.652171 −0.0444777
\(216\) 12.8472 0.874140
\(217\) 5.78986 0.393041
\(218\) 0.357816 0.0242344
\(219\) 40.6386 2.74610
\(220\) −12.6201 −0.850850
\(221\) −0.226036 −0.0152049
\(222\) −32.1737 −2.15936
\(223\) 4.38025 0.293323 0.146662 0.989187i \(-0.453147\pi\)
0.146662 + 0.989187i \(0.453147\pi\)
\(224\) −1.45443 −0.0971782
\(225\) 86.4431 5.76288
\(226\) 6.97326 0.463854
\(227\) 19.0575 1.26489 0.632445 0.774605i \(-0.282051\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(228\) 3.17050 0.209972
\(229\) −11.0057 −0.727275 −0.363638 0.931540i \(-0.618465\pi\)
−0.363638 + 0.931540i \(0.618465\pi\)
\(230\) −3.90119 −0.257237
\(231\) 14.0085 0.921694
\(232\) 9.74846 0.640018
\(233\) 20.5312 1.34504 0.672522 0.740077i \(-0.265211\pi\)
0.672522 + 0.740077i \(0.265211\pi\)
\(234\) −27.6428 −1.80707
\(235\) −14.3024 −0.932989
\(236\) −6.77204 −0.440822
\(237\) 40.9102 2.65741
\(238\) 0.0838701 0.00543649
\(239\) 7.63091 0.493603 0.246801 0.969066i \(-0.420621\pi\)
0.246801 + 0.969066i \(0.420621\pi\)
\(240\) −13.1711 −0.850189
\(241\) 7.91820 0.510056 0.255028 0.966934i \(-0.417915\pi\)
0.255028 + 0.966934i \(0.417915\pi\)
\(242\) 1.77125 0.113860
\(243\) −23.5235 −1.50903
\(244\) 0.287029 0.0183751
\(245\) −20.2920 −1.29641
\(246\) 20.3162 1.29531
\(247\) −3.91980 −0.249411
\(248\) −3.98084 −0.252784
\(249\) 9.86357 0.625078
\(250\) −30.1507 −1.90690
\(251\) 16.9552 1.07020 0.535102 0.844787i \(-0.320273\pi\)
0.535102 + 0.844787i \(0.320273\pi\)
\(252\) 10.2568 0.646116
\(253\) −2.85283 −0.179356
\(254\) 8.53078 0.535269
\(255\) 0.759513 0.0475625
\(256\) 1.00000 0.0625000
\(257\) −6.24300 −0.389428 −0.194714 0.980860i \(-0.562378\pi\)
−0.194714 + 0.980860i \(0.562378\pi\)
\(258\) −0.497733 −0.0309875
\(259\) −14.7593 −0.917097
\(260\) 16.2838 1.00988
\(261\) −68.7471 −4.25534
\(262\) −10.4714 −0.646924
\(263\) −12.6080 −0.777442 −0.388721 0.921356i \(-0.627083\pi\)
−0.388721 + 0.921356i \(0.627083\pi\)
\(264\) −9.63163 −0.592786
\(265\) 36.2521 2.22695
\(266\) 1.45443 0.0891769
\(267\) 30.3335 1.85638
\(268\) −0.311296 −0.0190155
\(269\) 29.0252 1.76970 0.884850 0.465876i \(-0.154261\pi\)
0.884850 + 0.465876i \(0.154261\pi\)
\(270\) 53.3704 3.24802
\(271\) −7.49327 −0.455184 −0.227592 0.973757i \(-0.573085\pi\)
−0.227592 + 0.973757i \(0.573085\pi\)
\(272\) −0.0576653 −0.00349647
\(273\) −18.0753 −1.09397
\(274\) −2.96722 −0.179256
\(275\) −37.2378 −2.24552
\(276\) −2.97737 −0.179217
\(277\) −6.01689 −0.361520 −0.180760 0.983527i \(-0.557856\pi\)
−0.180760 + 0.983527i \(0.557856\pi\)
\(278\) 13.6710 0.819934
\(279\) 28.0733 1.68070
\(280\) −6.04207 −0.361083
\(281\) 14.4898 0.864389 0.432194 0.901781i \(-0.357739\pi\)
0.432194 + 0.901781i \(0.357739\pi\)
\(282\) −10.9156 −0.650012
\(283\) −2.63201 −0.156457 −0.0782284 0.996935i \(-0.524926\pi\)
−0.0782284 + 0.996935i \(0.524926\pi\)
\(284\) −4.31993 −0.256341
\(285\) 13.1711 0.780187
\(286\) 11.9079 0.704129
\(287\) 9.31982 0.550132
\(288\) −7.05209 −0.415549
\(289\) −16.9967 −0.999804
\(290\) 40.4975 2.37810
\(291\) 57.4991 3.37066
\(292\) −12.8177 −0.750099
\(293\) −24.2872 −1.41888 −0.709438 0.704768i \(-0.751051\pi\)
−0.709438 + 0.704768i \(0.751051\pi\)
\(294\) −15.4867 −0.903205
\(295\) −28.1327 −1.63795
\(296\) 10.1478 0.589830
\(297\) 39.0283 2.26465
\(298\) −23.5793 −1.36591
\(299\) 3.68102 0.212879
\(300\) −38.8634 −2.24378
\(301\) −0.228329 −0.0131607
\(302\) 10.2850 0.591837
\(303\) 24.3447 1.39857
\(304\) −1.00000 −0.0573539
\(305\) 1.19239 0.0682760
\(306\) 0.406661 0.0232473
\(307\) 8.75471 0.499658 0.249829 0.968290i \(-0.419626\pi\)
0.249829 + 0.968290i \(0.419626\pi\)
\(308\) −4.41839 −0.251761
\(309\) 41.7855 2.37709
\(310\) −16.5374 −0.939262
\(311\) 15.4390 0.875466 0.437733 0.899105i \(-0.355782\pi\)
0.437733 + 0.899105i \(0.355782\pi\)
\(312\) 12.4277 0.703583
\(313\) −0.386613 −0.0218526 −0.0109263 0.999940i \(-0.503478\pi\)
−0.0109263 + 0.999940i \(0.503478\pi\)
\(314\) −12.3626 −0.697662
\(315\) 42.6092 2.40076
\(316\) −12.9034 −0.725872
\(317\) −13.7997 −0.775068 −0.387534 0.921855i \(-0.626673\pi\)
−0.387534 + 0.921855i \(0.626673\pi\)
\(318\) 27.6674 1.55151
\(319\) 29.6147 1.65811
\(320\) 4.15425 0.232230
\(321\) 45.0252 2.51306
\(322\) −1.36583 −0.0761149
\(323\) 0.0576653 0.00320858
\(324\) 19.5758 1.08754
\(325\) 48.0481 2.66523
\(326\) 6.34732 0.351545
\(327\) 1.13446 0.0627356
\(328\) −6.40788 −0.353816
\(329\) −5.00738 −0.276066
\(330\) −40.0122 −2.20260
\(331\) 19.8794 1.09267 0.546334 0.837567i \(-0.316023\pi\)
0.546334 + 0.837567i \(0.316023\pi\)
\(332\) −3.11104 −0.170741
\(333\) −71.5633 −3.92165
\(334\) 10.5337 0.576379
\(335\) −1.29320 −0.0706552
\(336\) −4.61128 −0.251566
\(337\) −12.9732 −0.706693 −0.353346 0.935493i \(-0.614956\pi\)
−0.353346 + 0.935493i \(0.614956\pi\)
\(338\) −2.36484 −0.128631
\(339\) 22.1087 1.20078
\(340\) −0.239556 −0.0129917
\(341\) −12.0933 −0.654892
\(342\) 7.05209 0.381334
\(343\) −17.2854 −0.933322
\(344\) 0.156989 0.00846427
\(345\) −12.3687 −0.665911
\(346\) −8.42256 −0.452799
\(347\) 27.7440 1.48937 0.744687 0.667414i \(-0.232599\pi\)
0.744687 + 0.667414i \(0.232599\pi\)
\(348\) 30.9075 1.65682
\(349\) 6.35553 0.340204 0.170102 0.985426i \(-0.445590\pi\)
0.170102 + 0.985426i \(0.445590\pi\)
\(350\) −17.8281 −0.952953
\(351\) −50.3584 −2.68793
\(352\) 3.03789 0.161920
\(353\) 7.68243 0.408894 0.204447 0.978878i \(-0.434460\pi\)
0.204447 + 0.978878i \(0.434460\pi\)
\(354\) −21.4708 −1.14116
\(355\) −17.9461 −0.952478
\(356\) −9.56741 −0.507072
\(357\) 0.265911 0.0140735
\(358\) −7.95295 −0.420326
\(359\) 9.93902 0.524561 0.262281 0.964992i \(-0.415525\pi\)
0.262281 + 0.964992i \(0.415525\pi\)
\(360\) −29.2962 −1.54404
\(361\) 1.00000 0.0526316
\(362\) −14.8269 −0.779285
\(363\) 5.61575 0.294750
\(364\) 5.70108 0.298818
\(365\) −53.2479 −2.78712
\(366\) 0.910026 0.0475678
\(367\) 4.61257 0.240774 0.120387 0.992727i \(-0.461586\pi\)
0.120387 + 0.992727i \(0.461586\pi\)
\(368\) 0.939084 0.0489532
\(369\) 45.1890 2.35245
\(370\) 42.1566 2.19161
\(371\) 12.6921 0.658941
\(372\) −12.6213 −0.654383
\(373\) 16.1022 0.833743 0.416871 0.908965i \(-0.363127\pi\)
0.416871 + 0.908965i \(0.363127\pi\)
\(374\) −0.175180 −0.00905837
\(375\) −95.5929 −4.93640
\(376\) 3.44285 0.177551
\(377\) −38.2120 −1.96802
\(378\) 18.6853 0.961070
\(379\) 29.8705 1.53434 0.767171 0.641442i \(-0.221664\pi\)
0.767171 + 0.641442i \(0.221664\pi\)
\(380\) −4.15425 −0.213109
\(381\) 27.0469 1.38565
\(382\) 9.97021 0.510120
\(383\) −23.5745 −1.20460 −0.602301 0.798269i \(-0.705749\pi\)
−0.602301 + 0.798269i \(0.705749\pi\)
\(384\) 3.17050 0.161794
\(385\) −18.3551 −0.935463
\(386\) −1.78617 −0.0909138
\(387\) −1.10710 −0.0562770
\(388\) −18.1356 −0.920698
\(389\) −19.8553 −1.00671 −0.503353 0.864081i \(-0.667900\pi\)
−0.503353 + 0.864081i \(0.667900\pi\)
\(390\) 51.6280 2.61428
\(391\) −0.0541525 −0.00273861
\(392\) 4.88463 0.246711
\(393\) −33.1996 −1.67470
\(394\) 13.7517 0.692799
\(395\) −53.6039 −2.69710
\(396\) −21.4235 −1.07657
\(397\) −13.7957 −0.692388 −0.346194 0.938163i \(-0.612526\pi\)
−0.346194 + 0.938163i \(0.612526\pi\)
\(398\) 19.8784 0.996413
\(399\) 4.61128 0.230853
\(400\) 12.2578 0.612890
\(401\) 14.5213 0.725159 0.362579 0.931953i \(-0.381896\pi\)
0.362579 + 0.931953i \(0.381896\pi\)
\(402\) −0.986967 −0.0492254
\(403\) 15.6041 0.777296
\(404\) −7.67850 −0.382019
\(405\) 81.3226 4.04095
\(406\) 14.1785 0.703665
\(407\) 30.8279 1.52808
\(408\) −0.182828 −0.00905133
\(409\) 11.8236 0.584637 0.292319 0.956321i \(-0.405573\pi\)
0.292319 + 0.956321i \(0.405573\pi\)
\(410\) −26.6200 −1.31467
\(411\) −9.40759 −0.464042
\(412\) −13.1794 −0.649304
\(413\) −9.84946 −0.484660
\(414\) −6.62251 −0.325479
\(415\) −12.9240 −0.634416
\(416\) −3.91980 −0.192184
\(417\) 43.3441 2.12257
\(418\) −3.03789 −0.148588
\(419\) −33.1411 −1.61905 −0.809525 0.587085i \(-0.800276\pi\)
−0.809525 + 0.587085i \(0.800276\pi\)
\(420\) −19.1564 −0.934737
\(421\) 19.8284 0.966377 0.483188 0.875516i \(-0.339479\pi\)
0.483188 + 0.875516i \(0.339479\pi\)
\(422\) 1.00000 0.0486792
\(423\) −24.2793 −1.18050
\(424\) −8.72651 −0.423797
\(425\) −0.706849 −0.0342872
\(426\) −13.6964 −0.663590
\(427\) 0.417463 0.0202025
\(428\) −14.2013 −0.686445
\(429\) 37.7541 1.82278
\(430\) 0.652171 0.0314505
\(431\) 8.59521 0.414017 0.207008 0.978339i \(-0.433627\pi\)
0.207008 + 0.978339i \(0.433627\pi\)
\(432\) −12.8472 −0.618110
\(433\) 32.5387 1.56371 0.781854 0.623461i \(-0.214274\pi\)
0.781854 + 0.623461i \(0.214274\pi\)
\(434\) −5.78986 −0.277922
\(435\) 128.398 6.15620
\(436\) −0.357816 −0.0171363
\(437\) −0.939084 −0.0449225
\(438\) −40.6386 −1.94179
\(439\) −29.6704 −1.41609 −0.708045 0.706167i \(-0.750423\pi\)
−0.708045 + 0.706167i \(0.750423\pi\)
\(440\) 12.6201 0.601642
\(441\) −34.4469 −1.64033
\(442\) 0.226036 0.0107515
\(443\) 24.8856 1.18235 0.591176 0.806543i \(-0.298664\pi\)
0.591176 + 0.806543i \(0.298664\pi\)
\(444\) 32.1737 1.52690
\(445\) −39.7454 −1.88411
\(446\) −4.38025 −0.207411
\(447\) −74.7583 −3.53595
\(448\) 1.45443 0.0687154
\(449\) 9.84769 0.464741 0.232371 0.972627i \(-0.425352\pi\)
0.232371 + 0.972627i \(0.425352\pi\)
\(450\) −86.4431 −4.07497
\(451\) −19.4664 −0.916638
\(452\) −6.97326 −0.327995
\(453\) 32.6087 1.53209
\(454\) −19.0575 −0.894412
\(455\) 23.6837 1.11031
\(456\) −3.17050 −0.148472
\(457\) 0.777880 0.0363877 0.0181939 0.999834i \(-0.494208\pi\)
0.0181939 + 0.999834i \(0.494208\pi\)
\(458\) 11.0057 0.514261
\(459\) 0.740836 0.0345793
\(460\) 3.90119 0.181894
\(461\) 19.4510 0.905922 0.452961 0.891530i \(-0.350368\pi\)
0.452961 + 0.891530i \(0.350368\pi\)
\(462\) −14.0085 −0.651736
\(463\) −27.1820 −1.26325 −0.631626 0.775273i \(-0.717612\pi\)
−0.631626 + 0.775273i \(0.717612\pi\)
\(464\) −9.74846 −0.452561
\(465\) −52.4320 −2.43147
\(466\) −20.5312 −0.951090
\(467\) −24.0989 −1.11517 −0.557583 0.830121i \(-0.688271\pi\)
−0.557583 + 0.830121i \(0.688271\pi\)
\(468\) 27.6428 1.27779
\(469\) −0.452759 −0.0209065
\(470\) 14.3024 0.659723
\(471\) −39.1957 −1.80604
\(472\) 6.77204 0.311708
\(473\) 0.476914 0.0219285
\(474\) −40.9102 −1.87907
\(475\) −12.2578 −0.562426
\(476\) −0.0838701 −0.00384418
\(477\) 61.5402 2.81773
\(478\) −7.63091 −0.349030
\(479\) −21.9273 −1.00188 −0.500942 0.865481i \(-0.667013\pi\)
−0.500942 + 0.865481i \(0.667013\pi\)
\(480\) 13.1711 0.601174
\(481\) −39.7774 −1.81369
\(482\) −7.91820 −0.360664
\(483\) −4.33038 −0.197039
\(484\) −1.77125 −0.0805113
\(485\) −75.3400 −3.42101
\(486\) 23.5235 1.06705
\(487\) −21.2962 −0.965021 −0.482511 0.875890i \(-0.660275\pi\)
−0.482511 + 0.875890i \(0.660275\pi\)
\(488\) −0.287029 −0.0129932
\(489\) 20.1242 0.910048
\(490\) 20.2920 0.916698
\(491\) 25.6131 1.15590 0.577952 0.816071i \(-0.303852\pi\)
0.577952 + 0.816071i \(0.303852\pi\)
\(492\) −20.3162 −0.915926
\(493\) 0.562148 0.0253179
\(494\) 3.91980 0.176360
\(495\) −88.9984 −4.00018
\(496\) 3.98084 0.178745
\(497\) −6.28304 −0.281833
\(498\) −9.86357 −0.441997
\(499\) 18.2866 0.818619 0.409309 0.912396i \(-0.365770\pi\)
0.409309 + 0.912396i \(0.365770\pi\)
\(500\) 30.1507 1.34838
\(501\) 33.3971 1.49207
\(502\) −16.9552 −0.756749
\(503\) −6.95013 −0.309891 −0.154945 0.987923i \(-0.549520\pi\)
−0.154945 + 0.987923i \(0.549520\pi\)
\(504\) −10.2568 −0.456873
\(505\) −31.8984 −1.41946
\(506\) 2.85283 0.126824
\(507\) −7.49775 −0.332987
\(508\) −8.53078 −0.378492
\(509\) −20.8092 −0.922353 −0.461176 0.887308i \(-0.652572\pi\)
−0.461176 + 0.887308i \(0.652572\pi\)
\(510\) −0.759513 −0.0336318
\(511\) −18.6425 −0.824694
\(512\) −1.00000 −0.0441942
\(513\) 12.8472 0.567217
\(514\) 6.24300 0.275367
\(515\) −54.7507 −2.41260
\(516\) 0.497733 0.0219115
\(517\) 10.4590 0.459985
\(518\) 14.7593 0.648486
\(519\) −26.7037 −1.17216
\(520\) −16.2838 −0.714093
\(521\) 3.50225 0.153437 0.0767183 0.997053i \(-0.475556\pi\)
0.0767183 + 0.997053i \(0.475556\pi\)
\(522\) 68.7471 3.00898
\(523\) −21.4134 −0.936342 −0.468171 0.883638i \(-0.655087\pi\)
−0.468171 + 0.883638i \(0.655087\pi\)
\(524\) 10.4714 0.457445
\(525\) −56.5241 −2.46691
\(526\) 12.6080 0.549734
\(527\) −0.229556 −0.00999963
\(528\) 9.63163 0.419163
\(529\) −22.1181 −0.961657
\(530\) −36.2521 −1.57469
\(531\) −47.7570 −2.07248
\(532\) −1.45443 −0.0630576
\(533\) 25.1176 1.08797
\(534\) −30.3335 −1.31266
\(535\) −58.9957 −2.55061
\(536\) 0.311296 0.0134460
\(537\) −25.2148 −1.08810
\(538\) −29.0252 −1.25137
\(539\) 14.8390 0.639159
\(540\) −53.3704 −2.29670
\(541\) −9.83922 −0.423021 −0.211511 0.977376i \(-0.567838\pi\)
−0.211511 + 0.977376i \(0.567838\pi\)
\(542\) 7.49327 0.321864
\(543\) −47.0088 −2.01734
\(544\) 0.0576653 0.00247238
\(545\) −1.48646 −0.0636728
\(546\) 18.0753 0.773551
\(547\) 37.8317 1.61757 0.808784 0.588106i \(-0.200126\pi\)
0.808784 + 0.588106i \(0.200126\pi\)
\(548\) 2.96722 0.126753
\(549\) 2.02415 0.0863888
\(550\) 37.2378 1.58782
\(551\) 9.74846 0.415298
\(552\) 2.97737 0.126725
\(553\) −18.7671 −0.798057
\(554\) 6.01689 0.255633
\(555\) 133.658 5.67345
\(556\) −13.6710 −0.579781
\(557\) 34.4159 1.45825 0.729123 0.684382i \(-0.239928\pi\)
0.729123 + 0.684382i \(0.239928\pi\)
\(558\) −28.0733 −1.18844
\(559\) −0.615365 −0.0260272
\(560\) 6.04207 0.255324
\(561\) −0.555410 −0.0234494
\(562\) −14.4898 −0.611215
\(563\) −22.0278 −0.928360 −0.464180 0.885741i \(-0.653651\pi\)
−0.464180 + 0.885741i \(0.653651\pi\)
\(564\) 10.9156 0.459628
\(565\) −28.9687 −1.21872
\(566\) 2.63201 0.110632
\(567\) 28.4716 1.19569
\(568\) 4.31993 0.181260
\(569\) 4.21399 0.176660 0.0883299 0.996091i \(-0.471847\pi\)
0.0883299 + 0.996091i \(0.471847\pi\)
\(570\) −13.1711 −0.551675
\(571\) 17.3831 0.727460 0.363730 0.931505i \(-0.381503\pi\)
0.363730 + 0.931505i \(0.381503\pi\)
\(572\) −11.9079 −0.497895
\(573\) 31.6106 1.32055
\(574\) −9.31982 −0.389002
\(575\) 11.5111 0.480046
\(576\) 7.05209 0.293837
\(577\) −4.62484 −0.192534 −0.0962672 0.995356i \(-0.530690\pi\)
−0.0962672 + 0.995356i \(0.530690\pi\)
\(578\) 16.9967 0.706968
\(579\) −5.66307 −0.235349
\(580\) −40.4975 −1.68157
\(581\) −4.52479 −0.187720
\(582\) −57.4991 −2.38342
\(583\) −26.5102 −1.09794
\(584\) 12.8177 0.530400
\(585\) 114.835 4.74785
\(586\) 24.2872 1.00330
\(587\) −42.3463 −1.74782 −0.873909 0.486090i \(-0.838423\pi\)
−0.873909 + 0.486090i \(0.838423\pi\)
\(588\) 15.4867 0.638663
\(589\) −3.98084 −0.164028
\(590\) 28.1327 1.15821
\(591\) 43.5997 1.79345
\(592\) −10.1478 −0.417073
\(593\) 2.60427 0.106944 0.0534722 0.998569i \(-0.482971\pi\)
0.0534722 + 0.998569i \(0.482971\pi\)
\(594\) −39.0283 −1.60135
\(595\) −0.348417 −0.0142837
\(596\) 23.5793 0.965847
\(597\) 63.0245 2.57942
\(598\) −3.68102 −0.150528
\(599\) −30.3389 −1.23961 −0.619806 0.784755i \(-0.712789\pi\)
−0.619806 + 0.784755i \(0.712789\pi\)
\(600\) 38.8634 1.58659
\(601\) 1.18657 0.0484014 0.0242007 0.999707i \(-0.492296\pi\)
0.0242007 + 0.999707i \(0.492296\pi\)
\(602\) 0.228329 0.00930600
\(603\) −2.19529 −0.0893992
\(604\) −10.2850 −0.418492
\(605\) −7.35821 −0.299154
\(606\) −24.3447 −0.988936
\(607\) 14.9293 0.605961 0.302980 0.952997i \(-0.402018\pi\)
0.302980 + 0.952997i \(0.402018\pi\)
\(608\) 1.00000 0.0405554
\(609\) 44.9529 1.82158
\(610\) −1.19239 −0.0482784
\(611\) −13.4953 −0.545960
\(612\) −0.406661 −0.0164383
\(613\) −2.75792 −0.111391 −0.0556957 0.998448i \(-0.517738\pi\)
−0.0556957 + 0.998448i \(0.517738\pi\)
\(614\) −8.75471 −0.353311
\(615\) −84.3987 −3.40328
\(616\) 4.41839 0.178022
\(617\) −44.1691 −1.77818 −0.889090 0.457733i \(-0.848662\pi\)
−0.889090 + 0.457733i \(0.848662\pi\)
\(618\) −41.7855 −1.68086
\(619\) 44.7128 1.79716 0.898580 0.438810i \(-0.144600\pi\)
0.898580 + 0.438810i \(0.144600\pi\)
\(620\) 16.5374 0.664159
\(621\) −12.0646 −0.484135
\(622\) −15.4390 −0.619048
\(623\) −13.9151 −0.557498
\(624\) −12.4277 −0.497508
\(625\) 63.9646 2.55858
\(626\) 0.386613 0.0154521
\(627\) −9.63163 −0.384650
\(628\) 12.3626 0.493321
\(629\) 0.585176 0.0233325
\(630\) −42.6092 −1.69759
\(631\) −37.2117 −1.48137 −0.740687 0.671851i \(-0.765500\pi\)
−0.740687 + 0.671851i \(0.765500\pi\)
\(632\) 12.9034 0.513269
\(633\) 3.17050 0.126016
\(634\) 13.7997 0.548056
\(635\) −35.4390 −1.40635
\(636\) −27.6674 −1.09709
\(637\) −19.1468 −0.758623
\(638\) −29.6147 −1.17246
\(639\) −30.4645 −1.20516
\(640\) −4.15425 −0.164211
\(641\) −28.2909 −1.11742 −0.558711 0.829362i \(-0.688704\pi\)
−0.558711 + 0.829362i \(0.688704\pi\)
\(642\) −45.0252 −1.77700
\(643\) 19.9394 0.786334 0.393167 0.919467i \(-0.371380\pi\)
0.393167 + 0.919467i \(0.371380\pi\)
\(644\) 1.36583 0.0538214
\(645\) 2.06771 0.0814160
\(646\) −0.0576653 −0.00226881
\(647\) 10.1935 0.400747 0.200374 0.979720i \(-0.435784\pi\)
0.200374 + 0.979720i \(0.435784\pi\)
\(648\) −19.5758 −0.769008
\(649\) 20.5727 0.807548
\(650\) −48.0481 −1.88460
\(651\) −18.3568 −0.719459
\(652\) −6.34732 −0.248580
\(653\) 30.1532 1.17998 0.589992 0.807409i \(-0.299131\pi\)
0.589992 + 0.807409i \(0.299131\pi\)
\(654\) −1.13446 −0.0443608
\(655\) 43.5008 1.69972
\(656\) 6.40788 0.250186
\(657\) −90.3916 −3.52651
\(658\) 5.00738 0.195208
\(659\) 48.1829 1.87694 0.938470 0.345361i \(-0.112244\pi\)
0.938470 + 0.345361i \(0.112244\pi\)
\(660\) 40.0122 1.55747
\(661\) −27.8493 −1.08321 −0.541606 0.840633i \(-0.682183\pi\)
−0.541606 + 0.840633i \(0.682183\pi\)
\(662\) −19.8794 −0.772634
\(663\) 0.716649 0.0278323
\(664\) 3.11104 0.120732
\(665\) −6.04207 −0.234301
\(666\) 71.5633 2.77302
\(667\) −9.15463 −0.354469
\(668\) −10.5337 −0.407561
\(669\) −13.8876 −0.536926
\(670\) 1.29320 0.0499608
\(671\) −0.871961 −0.0336617
\(672\) 4.61128 0.177884
\(673\) −9.17870 −0.353813 −0.176906 0.984228i \(-0.556609\pi\)
−0.176906 + 0.984228i \(0.556609\pi\)
\(674\) 12.9732 0.499707
\(675\) −157.478 −6.06134
\(676\) 2.36484 0.0909555
\(677\) −24.6506 −0.947398 −0.473699 0.880687i \(-0.657082\pi\)
−0.473699 + 0.880687i \(0.657082\pi\)
\(678\) −22.1087 −0.849081
\(679\) −26.3770 −1.01226
\(680\) 0.239556 0.00918655
\(681\) −60.4218 −2.31537
\(682\) 12.0933 0.463078
\(683\) 25.3240 0.968996 0.484498 0.874792i \(-0.339002\pi\)
0.484498 + 0.874792i \(0.339002\pi\)
\(684\) −7.05209 −0.269644
\(685\) 12.3266 0.470975
\(686\) 17.2854 0.659959
\(687\) 34.8935 1.33127
\(688\) −0.156989 −0.00598514
\(689\) 34.2062 1.30315
\(690\) 12.3687 0.470870
\(691\) −17.2389 −0.655799 −0.327900 0.944713i \(-0.606341\pi\)
−0.327900 + 0.944713i \(0.606341\pi\)
\(692\) 8.42256 0.320178
\(693\) −31.1589 −1.18363
\(694\) −27.7440 −1.05315
\(695\) −56.7929 −2.15428
\(696\) −30.9075 −1.17155
\(697\) −0.369512 −0.0139963
\(698\) −6.35553 −0.240560
\(699\) −65.0943 −2.46209
\(700\) 17.8281 0.673839
\(701\) −4.73529 −0.178850 −0.0894248 0.995994i \(-0.528503\pi\)
−0.0894248 + 0.995994i \(0.528503\pi\)
\(702\) 50.3584 1.90066
\(703\) 10.1478 0.382732
\(704\) −3.03789 −0.114495
\(705\) 45.3460 1.70783
\(706\) −7.68243 −0.289132
\(707\) −11.1678 −0.420010
\(708\) 21.4708 0.806921
\(709\) 20.3422 0.763969 0.381984 0.924169i \(-0.375241\pi\)
0.381984 + 0.924169i \(0.375241\pi\)
\(710\) 17.9461 0.673504
\(711\) −90.9959 −3.41261
\(712\) 9.56741 0.358554
\(713\) 3.73835 0.140002
\(714\) −0.265911 −0.00995145
\(715\) −49.4684 −1.85001
\(716\) 7.95295 0.297216
\(717\) −24.1938 −0.903535
\(718\) −9.93902 −0.370921
\(719\) 34.9210 1.30233 0.651167 0.758935i \(-0.274280\pi\)
0.651167 + 0.758935i \(0.274280\pi\)
\(720\) 29.2962 1.09180
\(721\) −19.1686 −0.713875
\(722\) −1.00000 −0.0372161
\(723\) −25.1047 −0.933653
\(724\) 14.8269 0.551038
\(725\) −119.495 −4.43792
\(726\) −5.61575 −0.208420
\(727\) 37.0004 1.37227 0.686134 0.727475i \(-0.259306\pi\)
0.686134 + 0.727475i \(0.259306\pi\)
\(728\) −5.70108 −0.211296
\(729\) 15.8539 0.587183
\(730\) 53.2479 1.97079
\(731\) 0.00905280 0.000334830 0
\(732\) −0.910026 −0.0336355
\(733\) 5.92531 0.218856 0.109428 0.993995i \(-0.465098\pi\)
0.109428 + 0.993995i \(0.465098\pi\)
\(734\) −4.61257 −0.170253
\(735\) 64.3358 2.37306
\(736\) −0.939084 −0.0346151
\(737\) 0.945683 0.0348347
\(738\) −45.1890 −1.66343
\(739\) −5.80209 −0.213433 −0.106717 0.994289i \(-0.534034\pi\)
−0.106717 + 0.994289i \(0.534034\pi\)
\(740\) −42.1566 −1.54971
\(741\) 12.4277 0.456545
\(742\) −12.6921 −0.465942
\(743\) −30.1097 −1.10462 −0.552309 0.833640i \(-0.686253\pi\)
−0.552309 + 0.833640i \(0.686253\pi\)
\(744\) 12.6213 0.462719
\(745\) 97.9544 3.58877
\(746\) −16.1022 −0.589545
\(747\) −21.9394 −0.802719
\(748\) 0.175180 0.00640523
\(749\) −20.6548 −0.754709
\(750\) 95.5929 3.49056
\(751\) 35.8092 1.30670 0.653348 0.757058i \(-0.273364\pi\)
0.653348 + 0.757058i \(0.273364\pi\)
\(752\) −3.44285 −0.125548
\(753\) −53.7566 −1.95900
\(754\) 38.2120 1.39160
\(755\) −42.7266 −1.55498
\(756\) −18.6853 −0.679579
\(757\) −51.7008 −1.87910 −0.939549 0.342413i \(-0.888756\pi\)
−0.939549 + 0.342413i \(0.888756\pi\)
\(758\) −29.8705 −1.08494
\(759\) 9.04491 0.328310
\(760\) 4.15425 0.150691
\(761\) 6.50864 0.235938 0.117969 0.993017i \(-0.462362\pi\)
0.117969 + 0.993017i \(0.462362\pi\)
\(762\) −27.0469 −0.979805
\(763\) −0.520419 −0.0188404
\(764\) −9.97021 −0.360710
\(765\) −1.68937 −0.0610793
\(766\) 23.5745 0.851782
\(767\) −26.5450 −0.958486
\(768\) −3.17050 −0.114406
\(769\) 43.9051 1.58326 0.791630 0.611001i \(-0.209233\pi\)
0.791630 + 0.611001i \(0.209233\pi\)
\(770\) 18.3551 0.661472
\(771\) 19.7935 0.712844
\(772\) 1.78617 0.0642858
\(773\) 2.09840 0.0754742 0.0377371 0.999288i \(-0.487985\pi\)
0.0377371 + 0.999288i \(0.487985\pi\)
\(774\) 1.10710 0.0397939
\(775\) 48.7964 1.75282
\(776\) 18.1356 0.651032
\(777\) 46.7944 1.67874
\(778\) 19.8553 0.711848
\(779\) −6.40788 −0.229586
\(780\) −51.6280 −1.84858
\(781\) 13.1235 0.469594
\(782\) 0.0541525 0.00193649
\(783\) 125.240 4.47572
\(784\) −4.88463 −0.174451
\(785\) 51.3573 1.83302
\(786\) 33.1996 1.18419
\(787\) −33.1316 −1.18101 −0.590507 0.807033i \(-0.701072\pi\)
−0.590507 + 0.807033i \(0.701072\pi\)
\(788\) −13.7517 −0.489883
\(789\) 39.9737 1.42310
\(790\) 53.6039 1.90714
\(791\) −10.1421 −0.360612
\(792\) 21.4235 0.761249
\(793\) 1.12510 0.0399533
\(794\) 13.7957 0.489592
\(795\) −114.937 −4.07641
\(796\) −19.8784 −0.704571
\(797\) −33.8646 −1.19955 −0.599773 0.800170i \(-0.704742\pi\)
−0.599773 + 0.800170i \(0.704742\pi\)
\(798\) −4.61128 −0.163237
\(799\) 0.198533 0.00702358
\(800\) −12.2578 −0.433379
\(801\) −67.4703 −2.38394
\(802\) −14.5213 −0.512765
\(803\) 38.9387 1.37412
\(804\) 0.986967 0.0348076
\(805\) 5.67401 0.199983
\(806\) −15.6041 −0.549632
\(807\) −92.0246 −3.23942
\(808\) 7.67850 0.270129
\(809\) −20.2397 −0.711589 −0.355794 0.934564i \(-0.615790\pi\)
−0.355794 + 0.934564i \(0.615790\pi\)
\(810\) −81.3226 −2.85738
\(811\) 10.4968 0.368593 0.184297 0.982871i \(-0.440999\pi\)
0.184297 + 0.982871i \(0.440999\pi\)
\(812\) −14.1785 −0.497566
\(813\) 23.7575 0.833210
\(814\) −30.8279 −1.08052
\(815\) −26.3684 −0.923643
\(816\) 0.182828 0.00640026
\(817\) 0.156989 0.00549234
\(818\) −11.8236 −0.413401
\(819\) 40.2045 1.40486
\(820\) 26.6200 0.929609
\(821\) 52.5147 1.83277 0.916387 0.400293i \(-0.131092\pi\)
0.916387 + 0.400293i \(0.131092\pi\)
\(822\) 9.40759 0.328127
\(823\) −33.5956 −1.17107 −0.585534 0.810648i \(-0.699115\pi\)
−0.585534 + 0.810648i \(0.699115\pi\)
\(824\) 13.1794 0.459127
\(825\) 118.063 4.11041
\(826\) 9.84946 0.342706
\(827\) 3.54004 0.123099 0.0615497 0.998104i \(-0.480396\pi\)
0.0615497 + 0.998104i \(0.480396\pi\)
\(828\) 6.62251 0.230148
\(829\) 33.7704 1.17289 0.586447 0.809988i \(-0.300526\pi\)
0.586447 + 0.809988i \(0.300526\pi\)
\(830\) 12.9240 0.448600
\(831\) 19.0766 0.661759
\(832\) 3.91980 0.135895
\(833\) 0.281674 0.00975941
\(834\) −43.3441 −1.50088
\(835\) −43.7596 −1.51436
\(836\) 3.03789 0.105067
\(837\) −51.1426 −1.76775
\(838\) 33.1411 1.14484
\(839\) 45.3293 1.56494 0.782471 0.622687i \(-0.213959\pi\)
0.782471 + 0.622687i \(0.213959\pi\)
\(840\) 19.1564 0.660959
\(841\) 66.0325 2.27698
\(842\) −19.8284 −0.683332
\(843\) −45.9399 −1.58226
\(844\) −1.00000 −0.0344214
\(845\) 9.82415 0.337961
\(846\) 24.2793 0.834739
\(847\) −2.57616 −0.0885178
\(848\) 8.72651 0.299670
\(849\) 8.34480 0.286393
\(850\) 0.706849 0.0242447
\(851\) −9.52965 −0.326672
\(852\) 13.6964 0.469229
\(853\) −6.92761 −0.237197 −0.118598 0.992942i \(-0.537840\pi\)
−0.118598 + 0.992942i \(0.537840\pi\)
\(854\) −0.417463 −0.0142853
\(855\) −29.2962 −1.00191
\(856\) 14.2013 0.485390
\(857\) −41.2487 −1.40903 −0.704515 0.709689i \(-0.748836\pi\)
−0.704515 + 0.709689i \(0.748836\pi\)
\(858\) −37.7541 −1.28890
\(859\) 45.2548 1.54407 0.772037 0.635578i \(-0.219238\pi\)
0.772037 + 0.635578i \(0.219238\pi\)
\(860\) −0.652171 −0.0222388
\(861\) −29.5485 −1.00701
\(862\) −8.59521 −0.292754
\(863\) 49.3379 1.67948 0.839741 0.542987i \(-0.182707\pi\)
0.839741 + 0.542987i \(0.182707\pi\)
\(864\) 12.8472 0.437070
\(865\) 34.9894 1.18968
\(866\) −32.5387 −1.10571
\(867\) 53.8880 1.83013
\(868\) 5.78986 0.196521
\(869\) 39.1990 1.32974
\(870\) −128.398 −4.35309
\(871\) −1.22022 −0.0413456
\(872\) 0.357816 0.0121172
\(873\) −127.894 −4.32857
\(874\) 0.939084 0.0317650
\(875\) 43.8521 1.48247
\(876\) 40.6386 1.37305
\(877\) −32.3710 −1.09309 −0.546545 0.837430i \(-0.684057\pi\)
−0.546545 + 0.837430i \(0.684057\pi\)
\(878\) 29.6704 1.00133
\(879\) 77.0028 2.59724
\(880\) −12.6201 −0.425425
\(881\) −39.5537 −1.33260 −0.666299 0.745685i \(-0.732123\pi\)
−0.666299 + 0.745685i \(0.732123\pi\)
\(882\) 34.4469 1.15989
\(883\) 39.4514 1.32765 0.663823 0.747890i \(-0.268933\pi\)
0.663823 + 0.747890i \(0.268933\pi\)
\(884\) −0.226036 −0.00760243
\(885\) 89.1949 2.99826
\(886\) −24.8856 −0.836049
\(887\) 8.24868 0.276964 0.138482 0.990365i \(-0.455778\pi\)
0.138482 + 0.990365i \(0.455778\pi\)
\(888\) −32.1737 −1.07968
\(889\) −12.4074 −0.416132
\(890\) 39.7454 1.33227
\(891\) −59.4689 −1.99228
\(892\) 4.38025 0.146662
\(893\) 3.44285 0.115210
\(894\) 74.7583 2.50029
\(895\) 33.0385 1.10436
\(896\) −1.45443 −0.0485891
\(897\) −11.6707 −0.389673
\(898\) −9.84769 −0.328622
\(899\) −38.8071 −1.29429
\(900\) 86.4431 2.88144
\(901\) −0.503217 −0.0167646
\(902\) 19.4664 0.648161
\(903\) 0.723919 0.0240905
\(904\) 6.97326 0.231927
\(905\) 61.5947 2.04748
\(906\) −32.6087 −1.08335
\(907\) 0.955559 0.0317288 0.0158644 0.999874i \(-0.494950\pi\)
0.0158644 + 0.999874i \(0.494950\pi\)
\(908\) 19.0575 0.632445
\(909\) −54.1495 −1.79602
\(910\) −23.6837 −0.785107
\(911\) 48.9747 1.62260 0.811302 0.584628i \(-0.198759\pi\)
0.811302 + 0.584628i \(0.198759\pi\)
\(912\) 3.17050 0.104986
\(913\) 9.45099 0.312782
\(914\) −0.777880 −0.0257300
\(915\) −3.78047 −0.124979
\(916\) −11.0057 −0.363638
\(917\) 15.2299 0.502936
\(918\) −0.740836 −0.0244512
\(919\) 30.8314 1.01704 0.508518 0.861051i \(-0.330194\pi\)
0.508518 + 0.861051i \(0.330194\pi\)
\(920\) −3.90119 −0.128618
\(921\) −27.7568 −0.914619
\(922\) −19.4510 −0.640584
\(923\) −16.9333 −0.557365
\(924\) 14.0085 0.460847
\(925\) −124.390 −4.08991
\(926\) 27.1820 0.893255
\(927\) −92.9426 −3.05264
\(928\) 9.74846 0.320009
\(929\) 9.70941 0.318555 0.159278 0.987234i \(-0.449083\pi\)
0.159278 + 0.987234i \(0.449083\pi\)
\(930\) 52.4320 1.71931
\(931\) 4.88463 0.160087
\(932\) 20.5312 0.672522
\(933\) −48.9494 −1.60253
\(934\) 24.0989 0.788541
\(935\) 0.727744 0.0237998
\(936\) −27.6428 −0.903533
\(937\) −8.70932 −0.284521 −0.142260 0.989829i \(-0.545437\pi\)
−0.142260 + 0.989829i \(0.545437\pi\)
\(938\) 0.452759 0.0147831
\(939\) 1.22576 0.0400010
\(940\) −14.3024 −0.466494
\(941\) −33.6765 −1.09782 −0.548911 0.835881i \(-0.684957\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(942\) 39.1957 1.27706
\(943\) 6.01754 0.195958
\(944\) −6.77204 −0.220411
\(945\) −77.6235 −2.52509
\(946\) −0.476914 −0.0155058
\(947\) −33.7792 −1.09768 −0.548838 0.835929i \(-0.684930\pi\)
−0.548838 + 0.835929i \(0.684930\pi\)
\(948\) 40.9102 1.32870
\(949\) −50.2428 −1.63095
\(950\) 12.2578 0.397695
\(951\) 43.7520 1.41875
\(952\) 0.0838701 0.00271825
\(953\) 3.70589 0.120045 0.0600227 0.998197i \(-0.480883\pi\)
0.0600227 + 0.998197i \(0.480883\pi\)
\(954\) −61.5402 −1.99244
\(955\) −41.4188 −1.34028
\(956\) 7.63091 0.246801
\(957\) −93.8936 −3.03515
\(958\) 21.9273 0.708439
\(959\) 4.31562 0.139359
\(960\) −13.1711 −0.425094
\(961\) −15.1529 −0.488803
\(962\) 39.7774 1.28248
\(963\) −100.149 −3.22725
\(964\) 7.91820 0.255028
\(965\) 7.42021 0.238865
\(966\) 4.33038 0.139328
\(967\) 21.3235 0.685716 0.342858 0.939387i \(-0.388605\pi\)
0.342858 + 0.939387i \(0.388605\pi\)
\(968\) 1.77125 0.0569301
\(969\) −0.182828 −0.00587328
\(970\) 75.3400 2.41902
\(971\) 25.9844 0.833877 0.416939 0.908935i \(-0.363103\pi\)
0.416939 + 0.908935i \(0.363103\pi\)
\(972\) −23.5235 −0.754515
\(973\) −19.8836 −0.637438
\(974\) 21.2962 0.682373
\(975\) −152.337 −4.87868
\(976\) 0.287029 0.00918757
\(977\) −3.60541 −0.115347 −0.0576737 0.998335i \(-0.518368\pi\)
−0.0576737 + 0.998335i \(0.518368\pi\)
\(978\) −20.1242 −0.643501
\(979\) 29.0647 0.928912
\(980\) −20.2920 −0.648204
\(981\) −2.52335 −0.0805645
\(982\) −25.6131 −0.817348
\(983\) −23.2306 −0.740941 −0.370470 0.928844i \(-0.620803\pi\)
−0.370470 + 0.928844i \(0.620803\pi\)
\(984\) 20.3162 0.647657
\(985\) −57.1279 −1.82024
\(986\) −0.562148 −0.0179024
\(987\) 15.8759 0.505336
\(988\) −3.91980 −0.124705
\(989\) −0.147426 −0.00468786
\(990\) 88.9984 2.82856
\(991\) −0.555456 −0.0176446 −0.00882232 0.999961i \(-0.502808\pi\)
−0.00882232 + 0.999961i \(0.502808\pi\)
\(992\) −3.98084 −0.126392
\(993\) −63.0276 −2.00012
\(994\) 6.28304 0.199286
\(995\) −82.5798 −2.61795
\(996\) 9.86357 0.312539
\(997\) −42.7170 −1.35286 −0.676431 0.736506i \(-0.736474\pi\)
−0.676431 + 0.736506i \(0.736474\pi\)
\(998\) −18.2866 −0.578851
\(999\) 130.371 4.12475
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 \(a_p\))