Properties

Label 8018.2.a.f.1.16
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 1.16
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} -2.52015 q^{10} +5.01379 q^{11} -0.860547 q^{12} -0.222564 q^{13} +0.0296623 q^{14} -2.16871 q^{15} +1.00000 q^{16} +3.18383 q^{17} +2.25946 q^{18} -1.00000 q^{19} +2.52015 q^{20} +0.0255258 q^{21} -5.01379 q^{22} +5.25526 q^{23} +0.860547 q^{24} +1.35115 q^{25} +0.222564 q^{26} +4.52601 q^{27} -0.0296623 q^{28} -9.76733 q^{29} +2.16871 q^{30} -1.46739 q^{31} -1.00000 q^{32} -4.31461 q^{33} -3.18383 q^{34} -0.0747534 q^{35} -2.25946 q^{36} -8.01581 q^{37} +1.00000 q^{38} +0.191526 q^{39} -2.52015 q^{40} -11.7770 q^{41} -0.0255258 q^{42} +1.24837 q^{43} +5.01379 q^{44} -5.69417 q^{45} -5.25526 q^{46} -6.14331 q^{47} -0.860547 q^{48} -6.99912 q^{49} -1.35115 q^{50} -2.73984 q^{51} -0.222564 q^{52} -1.12509 q^{53} -4.52601 q^{54} +12.6355 q^{55} +0.0296623 q^{56} +0.860547 q^{57} +9.76733 q^{58} -8.52613 q^{59} -2.16871 q^{60} +3.33339 q^{61} +1.46739 q^{62} +0.0670207 q^{63} +1.00000 q^{64} -0.560893 q^{65} +4.31461 q^{66} +0.833415 q^{67} +3.18383 q^{68} -4.52240 q^{69} +0.0747534 q^{70} +5.44844 q^{71} +2.25946 q^{72} -0.905671 q^{73} +8.01581 q^{74} -1.16273 q^{75} -1.00000 q^{76} -0.148721 q^{77} -0.191526 q^{78} -6.25659 q^{79} +2.52015 q^{80} +2.88353 q^{81} +11.7770 q^{82} -10.6237 q^{83} +0.0255258 q^{84} +8.02373 q^{85} -1.24837 q^{86} +8.40525 q^{87} -5.01379 q^{88} -12.0829 q^{89} +5.69417 q^{90} +0.00660175 q^{91} +5.25526 q^{92} +1.26276 q^{93} +6.14331 q^{94} -2.52015 q^{95} +0.860547 q^{96} -9.41167 q^{97} +6.99912 q^{98} -11.3285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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
\(3\) −0.860547 −0.496837 −0.248419 0.968653i \(-0.579911\pi\)
−0.248419 + 0.968653i \(0.579911\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.52015 1.12704 0.563522 0.826101i \(-0.309446\pi\)
0.563522 + 0.826101i \(0.309446\pi\)
\(6\) 0.860547 0.351317
\(7\) −0.0296623 −0.0112113 −0.00560565 0.999984i \(-0.501784\pi\)
−0.00560565 + 0.999984i \(0.501784\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.25946 −0.753153
\(10\) −2.52015 −0.796941
\(11\) 5.01379 1.51172 0.755858 0.654736i \(-0.227220\pi\)
0.755858 + 0.654736i \(0.227220\pi\)
\(12\) −0.860547 −0.248419
\(13\) −0.222564 −0.0617280 −0.0308640 0.999524i \(-0.509826\pi\)
−0.0308640 + 0.999524i \(0.509826\pi\)
\(14\) 0.0296623 0.00792758
\(15\) −2.16871 −0.559958
\(16\) 1.00000 0.250000
\(17\) 3.18383 0.772193 0.386096 0.922458i \(-0.373823\pi\)
0.386096 + 0.922458i \(0.373823\pi\)
\(18\) 2.25946 0.532559
\(19\) −1.00000 −0.229416
\(20\) 2.52015 0.563522
\(21\) 0.0255258 0.00557019
\(22\) −5.01379 −1.06894
\(23\) 5.25526 1.09580 0.547899 0.836545i \(-0.315428\pi\)
0.547899 + 0.836545i \(0.315428\pi\)
\(24\) 0.860547 0.175659
\(25\) 1.35115 0.270230
\(26\) 0.222564 0.0436483
\(27\) 4.52601 0.871032
\(28\) −0.0296623 −0.00560565
\(29\) −9.76733 −1.81375 −0.906874 0.421402i \(-0.861538\pi\)
−0.906874 + 0.421402i \(0.861538\pi\)
\(30\) 2.16871 0.395950
\(31\) −1.46739 −0.263550 −0.131775 0.991280i \(-0.542068\pi\)
−0.131775 + 0.991280i \(0.542068\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.31461 −0.751077
\(34\) −3.18383 −0.546023
\(35\) −0.0747534 −0.0126356
\(36\) −2.25946 −0.376576
\(37\) −8.01581 −1.31779 −0.658895 0.752235i \(-0.728976\pi\)
−0.658895 + 0.752235i \(0.728976\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.191526 0.0306688
\(40\) −2.52015 −0.398470
\(41\) −11.7770 −1.83926 −0.919631 0.392784i \(-0.871512\pi\)
−0.919631 + 0.392784i \(0.871512\pi\)
\(42\) −0.0255258 −0.00393872
\(43\) 1.24837 0.190375 0.0951874 0.995459i \(-0.469655\pi\)
0.0951874 + 0.995459i \(0.469655\pi\)
\(44\) 5.01379 0.755858
\(45\) −5.69417 −0.848837
\(46\) −5.25526 −0.774846
\(47\) −6.14331 −0.896094 −0.448047 0.894010i \(-0.647880\pi\)
−0.448047 + 0.894010i \(0.647880\pi\)
\(48\) −0.860547 −0.124209
\(49\) −6.99912 −0.999874
\(50\) −1.35115 −0.191081
\(51\) −2.73984 −0.383654
\(52\) −0.222564 −0.0308640
\(53\) −1.12509 −0.154543 −0.0772716 0.997010i \(-0.524621\pi\)
−0.0772716 + 0.997010i \(0.524621\pi\)
\(54\) −4.52601 −0.615912
\(55\) 12.6355 1.70377
\(56\) 0.0296623 0.00396379
\(57\) 0.860547 0.113982
\(58\) 9.76733 1.28251
\(59\) −8.52613 −1.11001 −0.555004 0.831848i \(-0.687283\pi\)
−0.555004 + 0.831848i \(0.687283\pi\)
\(60\) −2.16871 −0.279979
\(61\) 3.33339 0.426797 0.213398 0.976965i \(-0.431547\pi\)
0.213398 + 0.976965i \(0.431547\pi\)
\(62\) 1.46739 0.186358
\(63\) 0.0670207 0.00844382
\(64\) 1.00000 0.125000
\(65\) −0.560893 −0.0695702
\(66\) 4.31461 0.531092
\(67\) 0.833415 0.101818 0.0509089 0.998703i \(-0.483788\pi\)
0.0509089 + 0.998703i \(0.483788\pi\)
\(68\) 3.18383 0.386096
\(69\) −4.52240 −0.544433
\(70\) 0.0747534 0.00893474
\(71\) 5.44844 0.646611 0.323305 0.946295i \(-0.395206\pi\)
0.323305 + 0.946295i \(0.395206\pi\)
\(72\) 2.25946 0.266280
\(73\) −0.905671 −0.106001 −0.0530004 0.998594i \(-0.516878\pi\)
−0.0530004 + 0.998594i \(0.516878\pi\)
\(74\) 8.01581 0.931818
\(75\) −1.16273 −0.134260
\(76\) −1.00000 −0.114708
\(77\) −0.148721 −0.0169483
\(78\) −0.191526 −0.0216861
\(79\) −6.25659 −0.703922 −0.351961 0.936015i \(-0.614485\pi\)
−0.351961 + 0.936015i \(0.614485\pi\)
\(80\) 2.52015 0.281761
\(81\) 2.88353 0.320392
\(82\) 11.7770 1.30055
\(83\) −10.6237 −1.16610 −0.583051 0.812436i \(-0.698141\pi\)
−0.583051 + 0.812436i \(0.698141\pi\)
\(84\) 0.0255258 0.00278510
\(85\) 8.02373 0.870295
\(86\) −1.24837 −0.134615
\(87\) 8.40525 0.901137
\(88\) −5.01379 −0.534472
\(89\) −12.0829 −1.28079 −0.640395 0.768046i \(-0.721229\pi\)
−0.640395 + 0.768046i \(0.721229\pi\)
\(90\) 5.69417 0.600218
\(91\) 0.00660175 0.000692051 0
\(92\) 5.25526 0.547899
\(93\) 1.26276 0.130942
\(94\) 6.14331 0.633634
\(95\) −2.52015 −0.258562
\(96\) 0.860547 0.0878293
\(97\) −9.41167 −0.955611 −0.477805 0.878466i \(-0.658568\pi\)
−0.477805 + 0.878466i \(0.658568\pi\)
\(98\) 6.99912 0.707018
\(99\) −11.3285 −1.13855
\(100\) 1.35115 0.135115
\(101\) 17.5243 1.74373 0.871867 0.489743i \(-0.162910\pi\)
0.871867 + 0.489743i \(0.162910\pi\)
\(102\) 2.73984 0.271284
\(103\) −3.53667 −0.348478 −0.174239 0.984703i \(-0.555747\pi\)
−0.174239 + 0.984703i \(0.555747\pi\)
\(104\) 0.222564 0.0218241
\(105\) 0.0643289 0.00627785
\(106\) 1.12509 0.109278
\(107\) −6.29343 −0.608409 −0.304205 0.952607i \(-0.598391\pi\)
−0.304205 + 0.952607i \(0.598391\pi\)
\(108\) 4.52601 0.435516
\(109\) 13.2389 1.26806 0.634029 0.773309i \(-0.281400\pi\)
0.634029 + 0.773309i \(0.281400\pi\)
\(110\) −12.6355 −1.20475
\(111\) 6.89798 0.654727
\(112\) −0.0296623 −0.00280282
\(113\) 9.17526 0.863136 0.431568 0.902081i \(-0.357961\pi\)
0.431568 + 0.902081i \(0.357961\pi\)
\(114\) −0.860547 −0.0805976
\(115\) 13.2440 1.23501
\(116\) −9.76733 −0.906874
\(117\) 0.502873 0.0464906
\(118\) 8.52613 0.784894
\(119\) −0.0944398 −0.00865728
\(120\) 2.16871 0.197975
\(121\) 14.1381 1.28529
\(122\) −3.33339 −0.301791
\(123\) 10.1347 0.913813
\(124\) −1.46739 −0.131775
\(125\) −9.19565 −0.822484
\(126\) −0.0670207 −0.00597068
\(127\) −4.76962 −0.423235 −0.211617 0.977353i \(-0.567873\pi\)
−0.211617 + 0.977353i \(0.567873\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.07428 −0.0945853
\(130\) 0.560893 0.0491936
\(131\) −18.0524 −1.57725 −0.788624 0.614876i \(-0.789206\pi\)
−0.788624 + 0.614876i \(0.789206\pi\)
\(132\) −4.31461 −0.375538
\(133\) 0.0296623 0.00257205
\(134\) −0.833415 −0.0719961
\(135\) 11.4062 0.981692
\(136\) −3.18383 −0.273011
\(137\) −6.30139 −0.538364 −0.269182 0.963089i \(-0.586753\pi\)
−0.269182 + 0.963089i \(0.586753\pi\)
\(138\) 4.52240 0.384972
\(139\) −3.04750 −0.258486 −0.129243 0.991613i \(-0.541255\pi\)
−0.129243 + 0.991613i \(0.541255\pi\)
\(140\) −0.0747534 −0.00631782
\(141\) 5.28661 0.445213
\(142\) −5.44844 −0.457223
\(143\) −1.11589 −0.0933152
\(144\) −2.25946 −0.188288
\(145\) −24.6151 −2.04417
\(146\) 0.905671 0.0749538
\(147\) 6.02307 0.496775
\(148\) −8.01581 −0.658895
\(149\) −11.5581 −0.946873 −0.473437 0.880828i \(-0.656987\pi\)
−0.473437 + 0.880828i \(0.656987\pi\)
\(150\) 1.16273 0.0949363
\(151\) 13.7023 1.11508 0.557539 0.830151i \(-0.311746\pi\)
0.557539 + 0.830151i \(0.311746\pi\)
\(152\) 1.00000 0.0811107
\(153\) −7.19373 −0.581579
\(154\) 0.148721 0.0119843
\(155\) −3.69803 −0.297033
\(156\) 0.191526 0.0153344
\(157\) 4.98953 0.398208 0.199104 0.979978i \(-0.436197\pi\)
0.199104 + 0.979978i \(0.436197\pi\)
\(158\) 6.25659 0.497748
\(159\) 0.968194 0.0767828
\(160\) −2.52015 −0.199235
\(161\) −0.155883 −0.0122853
\(162\) −2.88353 −0.226551
\(163\) 2.90353 0.227422 0.113711 0.993514i \(-0.463726\pi\)
0.113711 + 0.993514i \(0.463726\pi\)
\(164\) −11.7770 −0.919631
\(165\) −10.8735 −0.846497
\(166\) 10.6237 0.824558
\(167\) 21.2988 1.64815 0.824074 0.566482i \(-0.191696\pi\)
0.824074 + 0.566482i \(0.191696\pi\)
\(168\) −0.0255258 −0.00196936
\(169\) −12.9505 −0.996190
\(170\) −8.02373 −0.615392
\(171\) 2.25946 0.172785
\(172\) 1.24837 0.0951874
\(173\) −19.3813 −1.47353 −0.736765 0.676149i \(-0.763647\pi\)
−0.736765 + 0.676149i \(0.763647\pi\)
\(174\) −8.40525 −0.637200
\(175\) −0.0400782 −0.00302963
\(176\) 5.01379 0.377929
\(177\) 7.33714 0.551493
\(178\) 12.0829 0.905655
\(179\) −18.9865 −1.41912 −0.709561 0.704644i \(-0.751107\pi\)
−0.709561 + 0.704644i \(0.751107\pi\)
\(180\) −5.69417 −0.424418
\(181\) 5.40224 0.401545 0.200773 0.979638i \(-0.435655\pi\)
0.200773 + 0.979638i \(0.435655\pi\)
\(182\) −0.00660175 −0.000489354 0
\(183\) −2.86854 −0.212049
\(184\) −5.25526 −0.387423
\(185\) −20.2010 −1.48521
\(186\) −1.26276 −0.0925897
\(187\) 15.9631 1.16734
\(188\) −6.14331 −0.448047
\(189\) −0.134252 −0.00976539
\(190\) 2.52015 0.182831
\(191\) −7.31657 −0.529408 −0.264704 0.964330i \(-0.585274\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(192\) −0.860547 −0.0621047
\(193\) −4.18426 −0.301190 −0.150595 0.988596i \(-0.548119\pi\)
−0.150595 + 0.988596i \(0.548119\pi\)
\(194\) 9.41167 0.675719
\(195\) 0.482675 0.0345651
\(196\) −6.99912 −0.499937
\(197\) −1.52396 −0.108577 −0.0542887 0.998525i \(-0.517289\pi\)
−0.0542887 + 0.998525i \(0.517289\pi\)
\(198\) 11.3285 0.805079
\(199\) 22.3056 1.58120 0.790600 0.612333i \(-0.209769\pi\)
0.790600 + 0.612333i \(0.209769\pi\)
\(200\) −1.35115 −0.0955406
\(201\) −0.717193 −0.0505869
\(202\) −17.5243 −1.23301
\(203\) 0.289721 0.0203345
\(204\) −2.73984 −0.191827
\(205\) −29.6798 −2.07293
\(206\) 3.53667 0.246411
\(207\) −11.8740 −0.825303
\(208\) −0.222564 −0.0154320
\(209\) −5.01379 −0.346811
\(210\) −0.0643289 −0.00443911
\(211\) −1.00000 −0.0688428
\(212\) −1.12509 −0.0772716
\(213\) −4.68864 −0.321260
\(214\) 6.29343 0.430210
\(215\) 3.14608 0.214561
\(216\) −4.52601 −0.307956
\(217\) 0.0435261 0.00295474
\(218\) −13.2389 −0.896652
\(219\) 0.779372 0.0526651
\(220\) 12.6355 0.851886
\(221\) −0.708605 −0.0476659
\(222\) −6.89798 −0.462962
\(223\) −29.0976 −1.94852 −0.974258 0.225434i \(-0.927620\pi\)
−0.974258 + 0.225434i \(0.927620\pi\)
\(224\) 0.0296623 0.00198190
\(225\) −3.05286 −0.203524
\(226\) −9.17526 −0.610329
\(227\) 23.2960 1.54621 0.773105 0.634278i \(-0.218703\pi\)
0.773105 + 0.634278i \(0.218703\pi\)
\(228\) 0.860547 0.0569911
\(229\) 15.4214 1.01908 0.509539 0.860448i \(-0.329816\pi\)
0.509539 + 0.860448i \(0.329816\pi\)
\(230\) −13.2440 −0.873286
\(231\) 0.127981 0.00842055
\(232\) 9.76733 0.641257
\(233\) −3.14863 −0.206274 −0.103137 0.994667i \(-0.532888\pi\)
−0.103137 + 0.994667i \(0.532888\pi\)
\(234\) −0.502873 −0.0328738
\(235\) −15.4821 −1.00994
\(236\) −8.52613 −0.555004
\(237\) 5.38409 0.349735
\(238\) 0.0944398 0.00612162
\(239\) −12.7965 −0.827737 −0.413868 0.910337i \(-0.635823\pi\)
−0.413868 + 0.910337i \(0.635823\pi\)
\(240\) −2.16871 −0.139989
\(241\) 0.450062 0.0289911 0.0144955 0.999895i \(-0.495386\pi\)
0.0144955 + 0.999895i \(0.495386\pi\)
\(242\) −14.1381 −0.908834
\(243\) −16.0594 −1.03021
\(244\) 3.33339 0.213398
\(245\) −17.6388 −1.12690
\(246\) −10.1347 −0.646164
\(247\) 0.222564 0.0141614
\(248\) 1.46739 0.0931791
\(249\) 9.14219 0.579363
\(250\) 9.19565 0.581584
\(251\) 26.7435 1.68804 0.844019 0.536314i \(-0.180184\pi\)
0.844019 + 0.536314i \(0.180184\pi\)
\(252\) 0.0670207 0.00422191
\(253\) 26.3488 1.65654
\(254\) 4.76962 0.299272
\(255\) −6.90480 −0.432395
\(256\) 1.00000 0.0625000
\(257\) 21.3320 1.33066 0.665328 0.746551i \(-0.268292\pi\)
0.665328 + 0.746551i \(0.268292\pi\)
\(258\) 1.07428 0.0668819
\(259\) 0.237767 0.0147741
\(260\) −0.560893 −0.0347851
\(261\) 22.0689 1.36603
\(262\) 18.0524 1.11528
\(263\) 1.59249 0.0981972 0.0490986 0.998794i \(-0.484365\pi\)
0.0490986 + 0.998794i \(0.484365\pi\)
\(264\) 4.31461 0.265546
\(265\) −2.83540 −0.174177
\(266\) −0.0296623 −0.00181871
\(267\) 10.3979 0.636344
\(268\) 0.833415 0.0509089
\(269\) 30.5204 1.86086 0.930430 0.366470i \(-0.119434\pi\)
0.930430 + 0.366470i \(0.119434\pi\)
\(270\) −11.4062 −0.694161
\(271\) −0.0288858 −0.00175469 −0.000877345 1.00000i \(-0.500279\pi\)
−0.000877345 1.00000i \(0.500279\pi\)
\(272\) 3.18383 0.193048
\(273\) −0.00568112 −0.000343837 0
\(274\) 6.30139 0.380681
\(275\) 6.77438 0.408511
\(276\) −4.52240 −0.272217
\(277\) 2.62360 0.157637 0.0788185 0.996889i \(-0.474885\pi\)
0.0788185 + 0.996889i \(0.474885\pi\)
\(278\) 3.04750 0.182777
\(279\) 3.31550 0.198494
\(280\) 0.0747534 0.00446737
\(281\) −7.68302 −0.458330 −0.229165 0.973388i \(-0.573600\pi\)
−0.229165 + 0.973388i \(0.573600\pi\)
\(282\) −5.28661 −0.314813
\(283\) −6.15859 −0.366090 −0.183045 0.983105i \(-0.558595\pi\)
−0.183045 + 0.983105i \(0.558595\pi\)
\(284\) 5.44844 0.323305
\(285\) 2.16871 0.128463
\(286\) 1.11589 0.0659838
\(287\) 0.349333 0.0206205
\(288\) 2.25946 0.133140
\(289\) −6.86322 −0.403719
\(290\) 24.6151 1.44545
\(291\) 8.09919 0.474783
\(292\) −0.905671 −0.0530004
\(293\) 14.5946 0.852625 0.426313 0.904576i \(-0.359812\pi\)
0.426313 + 0.904576i \(0.359812\pi\)
\(294\) −6.02307 −0.351273
\(295\) −21.4871 −1.25103
\(296\) 8.01581 0.465909
\(297\) 22.6925 1.31675
\(298\) 11.5581 0.669541
\(299\) −1.16963 −0.0676414
\(300\) −1.16273 −0.0671301
\(301\) −0.0370296 −0.00213435
\(302\) −13.7023 −0.788479
\(303\) −15.0805 −0.866352
\(304\) −1.00000 −0.0573539
\(305\) 8.40064 0.481019
\(306\) 7.19373 0.411238
\(307\) −32.4099 −1.84973 −0.924865 0.380296i \(-0.875822\pi\)
−0.924865 + 0.380296i \(0.875822\pi\)
\(308\) −0.148721 −0.00847415
\(309\) 3.04347 0.173137
\(310\) 3.69803 0.210034
\(311\) −20.5365 −1.16452 −0.582258 0.813004i \(-0.697831\pi\)
−0.582258 + 0.813004i \(0.697831\pi\)
\(312\) −0.191526 −0.0108431
\(313\) 21.1913 1.19780 0.598902 0.800822i \(-0.295604\pi\)
0.598902 + 0.800822i \(0.295604\pi\)
\(314\) −4.98953 −0.281576
\(315\) 0.168902 0.00951656
\(316\) −6.25659 −0.351961
\(317\) 24.0002 1.34799 0.673993 0.738738i \(-0.264578\pi\)
0.673993 + 0.738738i \(0.264578\pi\)
\(318\) −0.968194 −0.0542936
\(319\) −48.9714 −2.74187
\(320\) 2.52015 0.140881
\(321\) 5.41580 0.302280
\(322\) 0.155883 0.00868703
\(323\) −3.18383 −0.177153
\(324\) 2.88353 0.160196
\(325\) −0.300716 −0.0166807
\(326\) −2.90353 −0.160812
\(327\) −11.3927 −0.630018
\(328\) 11.7770 0.650277
\(329\) 0.182225 0.0100464
\(330\) 10.8735 0.598564
\(331\) 3.63684 0.199899 0.0999494 0.994993i \(-0.468132\pi\)
0.0999494 + 0.994993i \(0.468132\pi\)
\(332\) −10.6237 −0.583051
\(333\) 18.1114 0.992497
\(334\) −21.2988 −1.16542
\(335\) 2.10033 0.114753
\(336\) 0.0255258 0.00139255
\(337\) 20.0352 1.09139 0.545693 0.837985i \(-0.316267\pi\)
0.545693 + 0.837985i \(0.316267\pi\)
\(338\) 12.9505 0.704412
\(339\) −7.89574 −0.428838
\(340\) 8.02373 0.435148
\(341\) −7.35717 −0.398413
\(342\) −2.25946 −0.122178
\(343\) 0.415246 0.0224212
\(344\) −1.24837 −0.0673077
\(345\) −11.3971 −0.613600
\(346\) 19.3813 1.04194
\(347\) −7.42937 −0.398830 −0.199415 0.979915i \(-0.563904\pi\)
−0.199415 + 0.979915i \(0.563904\pi\)
\(348\) 8.40525 0.450569
\(349\) 24.7756 1.32621 0.663104 0.748527i \(-0.269239\pi\)
0.663104 + 0.748527i \(0.269239\pi\)
\(350\) 0.0400782 0.00214227
\(351\) −1.00733 −0.0537671
\(352\) −5.01379 −0.267236
\(353\) −1.77080 −0.0942504 −0.0471252 0.998889i \(-0.515006\pi\)
−0.0471252 + 0.998889i \(0.515006\pi\)
\(354\) −7.33714 −0.389964
\(355\) 13.7309 0.728759
\(356\) −12.0829 −0.640395
\(357\) 0.0812699 0.00430126
\(358\) 18.9865 1.00347
\(359\) −35.7298 −1.88575 −0.942873 0.333151i \(-0.891888\pi\)
−0.942873 + 0.333151i \(0.891888\pi\)
\(360\) 5.69417 0.300109
\(361\) 1.00000 0.0526316
\(362\) −5.40224 −0.283935
\(363\) −12.1665 −0.638578
\(364\) 0.00660175 0.000346026 0
\(365\) −2.28242 −0.119468
\(366\) 2.86854 0.149941
\(367\) 0.959187 0.0500691 0.0250346 0.999687i \(-0.492030\pi\)
0.0250346 + 0.999687i \(0.492030\pi\)
\(368\) 5.25526 0.273949
\(369\) 26.6097 1.38524
\(370\) 20.2010 1.05020
\(371\) 0.0333728 0.00173263
\(372\) 1.26276 0.0654708
\(373\) −20.1033 −1.04091 −0.520456 0.853889i \(-0.674238\pi\)
−0.520456 + 0.853889i \(0.674238\pi\)
\(374\) −15.9631 −0.825431
\(375\) 7.91329 0.408641
\(376\) 6.14331 0.316817
\(377\) 2.17385 0.111959
\(378\) 0.134252 0.00690518
\(379\) 0.895330 0.0459900 0.0229950 0.999736i \(-0.492680\pi\)
0.0229950 + 0.999736i \(0.492680\pi\)
\(380\) −2.52015 −0.129281
\(381\) 4.10448 0.210279
\(382\) 7.31657 0.374348
\(383\) −5.71870 −0.292212 −0.146106 0.989269i \(-0.546674\pi\)
−0.146106 + 0.989269i \(0.546674\pi\)
\(384\) 0.860547 0.0439146
\(385\) −0.374798 −0.0191015
\(386\) 4.18426 0.212973
\(387\) −2.82064 −0.143381
\(388\) −9.41167 −0.477805
\(389\) −24.0148 −1.21760 −0.608800 0.793323i \(-0.708349\pi\)
−0.608800 + 0.793323i \(0.708349\pi\)
\(390\) −0.482675 −0.0244412
\(391\) 16.7319 0.846167
\(392\) 6.99912 0.353509
\(393\) 15.5350 0.783636
\(394\) 1.52396 0.0767758
\(395\) −15.7675 −0.793351
\(396\) −11.3285 −0.569277
\(397\) −12.1982 −0.612209 −0.306105 0.951998i \(-0.599026\pi\)
−0.306105 + 0.951998i \(0.599026\pi\)
\(398\) −22.3056 −1.11808
\(399\) −0.0255258 −0.00127789
\(400\) 1.35115 0.0675574
\(401\) −6.57122 −0.328151 −0.164075 0.986448i \(-0.552464\pi\)
−0.164075 + 0.986448i \(0.552464\pi\)
\(402\) 0.717193 0.0357704
\(403\) 0.326587 0.0162684
\(404\) 17.5243 0.871867
\(405\) 7.26691 0.361096
\(406\) −0.289721 −0.0143786
\(407\) −40.1896 −1.99212
\(408\) 2.73984 0.135642
\(409\) 19.8248 0.980272 0.490136 0.871646i \(-0.336947\pi\)
0.490136 + 0.871646i \(0.336947\pi\)
\(410\) 29.6798 1.46578
\(411\) 5.42265 0.267479
\(412\) −3.53667 −0.174239
\(413\) 0.252905 0.0124446
\(414\) 11.8740 0.583577
\(415\) −26.7733 −1.31425
\(416\) 0.222564 0.0109121
\(417\) 2.62252 0.128425
\(418\) 5.01379 0.245233
\(419\) −18.9986 −0.928142 −0.464071 0.885798i \(-0.653612\pi\)
−0.464071 + 0.885798i \(0.653612\pi\)
\(420\) 0.0643289 0.00313893
\(421\) −20.7075 −1.00922 −0.504610 0.863347i \(-0.668364\pi\)
−0.504610 + 0.863347i \(0.668364\pi\)
\(422\) 1.00000 0.0486792
\(423\) 13.8806 0.674896
\(424\) 1.12509 0.0546392
\(425\) 4.30183 0.208669
\(426\) 4.68864 0.227165
\(427\) −0.0988760 −0.00478495
\(428\) −6.29343 −0.304205
\(429\) 0.960274 0.0463625
\(430\) −3.14608 −0.151718
\(431\) 4.31233 0.207718 0.103859 0.994592i \(-0.466881\pi\)
0.103859 + 0.994592i \(0.466881\pi\)
\(432\) 4.52601 0.217758
\(433\) −19.5928 −0.941572 −0.470786 0.882248i \(-0.656030\pi\)
−0.470786 + 0.882248i \(0.656030\pi\)
\(434\) −0.0435261 −0.00208932
\(435\) 21.1825 1.01562
\(436\) 13.2389 0.634029
\(437\) −5.25526 −0.251393
\(438\) −0.779372 −0.0372399
\(439\) 15.0337 0.717520 0.358760 0.933430i \(-0.383200\pi\)
0.358760 + 0.933430i \(0.383200\pi\)
\(440\) −12.6355 −0.602374
\(441\) 15.8142 0.753058
\(442\) 0.708605 0.0337049
\(443\) −21.1704 −1.00584 −0.502918 0.864334i \(-0.667740\pi\)
−0.502918 + 0.864334i \(0.667740\pi\)
\(444\) 6.89798 0.327364
\(445\) −30.4508 −1.44351
\(446\) 29.0976 1.37781
\(447\) 9.94626 0.470442
\(448\) −0.0296623 −0.00140141
\(449\) 40.7663 1.92388 0.961941 0.273258i \(-0.0881013\pi\)
0.961941 + 0.273258i \(0.0881013\pi\)
\(450\) 3.05286 0.143913
\(451\) −59.0476 −2.78044
\(452\) 9.17526 0.431568
\(453\) −11.7915 −0.554012
\(454\) −23.2960 −1.09334
\(455\) 0.0166374 0.000779973 0
\(456\) −0.860547 −0.0402988
\(457\) 8.18021 0.382654 0.191327 0.981526i \(-0.438721\pi\)
0.191327 + 0.981526i \(0.438721\pi\)
\(458\) −15.4214 −0.720596
\(459\) 14.4101 0.672604
\(460\) 13.2440 0.617507
\(461\) −9.09547 −0.423618 −0.211809 0.977311i \(-0.567936\pi\)
−0.211809 + 0.977311i \(0.567936\pi\)
\(462\) −0.127981 −0.00595422
\(463\) −4.16675 −0.193646 −0.0968228 0.995302i \(-0.530868\pi\)
−0.0968228 + 0.995302i \(0.530868\pi\)
\(464\) −9.76733 −0.453437
\(465\) 3.18233 0.147577
\(466\) 3.14863 0.145857
\(467\) 16.1212 0.746001 0.373000 0.927831i \(-0.378329\pi\)
0.373000 + 0.927831i \(0.378329\pi\)
\(468\) 0.502873 0.0232453
\(469\) −0.0247210 −0.00114151
\(470\) 15.4821 0.714134
\(471\) −4.29373 −0.197845
\(472\) 8.52613 0.392447
\(473\) 6.25908 0.287793
\(474\) −5.38409 −0.247300
\(475\) −1.35115 −0.0619950
\(476\) −0.0944398 −0.00432864
\(477\) 2.54210 0.116395
\(478\) 12.7965 0.585298
\(479\) 20.4401 0.933933 0.466966 0.884275i \(-0.345347\pi\)
0.466966 + 0.884275i \(0.345347\pi\)
\(480\) 2.16871 0.0989875
\(481\) 1.78403 0.0813446
\(482\) −0.450062 −0.0204998
\(483\) 0.134145 0.00610380
\(484\) 14.1381 0.642643
\(485\) −23.7188 −1.07702
\(486\) 16.0594 0.728471
\(487\) 7.56813 0.342945 0.171472 0.985189i \(-0.445148\pi\)
0.171472 + 0.985189i \(0.445148\pi\)
\(488\) −3.33339 −0.150895
\(489\) −2.49863 −0.112992
\(490\) 17.6388 0.796841
\(491\) 3.59508 0.162244 0.0811219 0.996704i \(-0.474150\pi\)
0.0811219 + 0.996704i \(0.474150\pi\)
\(492\) 10.1347 0.456907
\(493\) −31.0975 −1.40056
\(494\) −0.222564 −0.0100136
\(495\) −28.5494 −1.28320
\(496\) −1.46739 −0.0658876
\(497\) −0.161613 −0.00724935
\(498\) −9.14219 −0.409671
\(499\) −4.44310 −0.198901 −0.0994503 0.995043i \(-0.531708\pi\)
−0.0994503 + 0.995043i \(0.531708\pi\)
\(500\) −9.19565 −0.411242
\(501\) −18.3286 −0.818861
\(502\) −26.7435 −1.19362
\(503\) 15.2203 0.678640 0.339320 0.940671i \(-0.389803\pi\)
0.339320 + 0.940671i \(0.389803\pi\)
\(504\) −0.0670207 −0.00298534
\(505\) 44.1638 1.96527
\(506\) −26.3488 −1.17135
\(507\) 11.1445 0.494944
\(508\) −4.76962 −0.211617
\(509\) −0.520118 −0.0230538 −0.0115269 0.999934i \(-0.503669\pi\)
−0.0115269 + 0.999934i \(0.503669\pi\)
\(510\) 6.90480 0.305750
\(511\) 0.0268643 0.00118841
\(512\) −1.00000 −0.0441942
\(513\) −4.52601 −0.199828
\(514\) −21.3320 −0.940916
\(515\) −8.91293 −0.392751
\(516\) −1.07428 −0.0472927
\(517\) −30.8013 −1.35464
\(518\) −0.237767 −0.0104469
\(519\) 16.6785 0.732104
\(520\) 0.560893 0.0245968
\(521\) 11.1839 0.489976 0.244988 0.969526i \(-0.421216\pi\)
0.244988 + 0.969526i \(0.421216\pi\)
\(522\) −22.0689 −0.965928
\(523\) 12.5800 0.550086 0.275043 0.961432i \(-0.411308\pi\)
0.275043 + 0.961432i \(0.411308\pi\)
\(524\) −18.0524 −0.788624
\(525\) 0.0344892 0.00150523
\(526\) −1.59249 −0.0694359
\(527\) −4.67191 −0.203512
\(528\) −4.31461 −0.187769
\(529\) 4.61777 0.200773
\(530\) 2.83540 0.123162
\(531\) 19.2644 0.836005
\(532\) 0.0296623 0.00128602
\(533\) 2.62113 0.113534
\(534\) −10.3979 −0.449963
\(535\) −15.8604 −0.685704
\(536\) −0.833415 −0.0359981
\(537\) 16.3388 0.705072
\(538\) −30.5204 −1.31583
\(539\) −35.0922 −1.51153
\(540\) 11.4062 0.490846
\(541\) −2.39105 −0.102799 −0.0513997 0.998678i \(-0.516368\pi\)
−0.0513997 + 0.998678i \(0.516368\pi\)
\(542\) 0.0288858 0.00124075
\(543\) −4.64888 −0.199503
\(544\) −3.18383 −0.136506
\(545\) 33.3640 1.42916
\(546\) 0.00568112 0.000243129 0
\(547\) −42.2702 −1.80735 −0.903673 0.428224i \(-0.859139\pi\)
−0.903673 + 0.428224i \(0.859139\pi\)
\(548\) −6.30139 −0.269182
\(549\) −7.53166 −0.321443
\(550\) −6.77438 −0.288861
\(551\) 9.76733 0.416102
\(552\) 4.52240 0.192486
\(553\) 0.185585 0.00789187
\(554\) −2.62360 −0.111466
\(555\) 17.3839 0.737907
\(556\) −3.04750 −0.129243
\(557\) −23.8100 −1.00886 −0.504431 0.863452i \(-0.668298\pi\)
−0.504431 + 0.863452i \(0.668298\pi\)
\(558\) −3.31550 −0.140356
\(559\) −0.277842 −0.0117515
\(560\) −0.0747534 −0.00315891
\(561\) −13.7370 −0.579976
\(562\) 7.68302 0.324089
\(563\) −3.06108 −0.129009 −0.0645046 0.997917i \(-0.520547\pi\)
−0.0645046 + 0.997917i \(0.520547\pi\)
\(564\) 5.28661 0.222606
\(565\) 23.1230 0.972792
\(566\) 6.15859 0.258865
\(567\) −0.0855320 −0.00359201
\(568\) −5.44844 −0.228611
\(569\) 9.86924 0.413740 0.206870 0.978368i \(-0.433672\pi\)
0.206870 + 0.978368i \(0.433672\pi\)
\(570\) −2.16871 −0.0908372
\(571\) 30.6161 1.28124 0.640621 0.767857i \(-0.278677\pi\)
0.640621 + 0.767857i \(0.278677\pi\)
\(572\) −1.11589 −0.0466576
\(573\) 6.29625 0.263030
\(574\) −0.349333 −0.0145809
\(575\) 7.10064 0.296117
\(576\) −2.25946 −0.0941441
\(577\) −19.3481 −0.805473 −0.402737 0.915316i \(-0.631941\pi\)
−0.402737 + 0.915316i \(0.631941\pi\)
\(578\) 6.86322 0.285472
\(579\) 3.60075 0.149642
\(580\) −24.6151 −1.02209
\(581\) 0.315123 0.0130735
\(582\) −8.09919 −0.335722
\(583\) −5.64097 −0.233625
\(584\) 0.905671 0.0374769
\(585\) 1.26731 0.0523970
\(586\) −14.5946 −0.602897
\(587\) 8.82453 0.364227 0.182114 0.983277i \(-0.441706\pi\)
0.182114 + 0.983277i \(0.441706\pi\)
\(588\) 6.02307 0.248387
\(589\) 1.46739 0.0604626
\(590\) 21.4871 0.884610
\(591\) 1.31144 0.0539453
\(592\) −8.01581 −0.329448
\(593\) −25.6885 −1.05490 −0.527449 0.849586i \(-0.676852\pi\)
−0.527449 + 0.849586i \(0.676852\pi\)
\(594\) −22.6925 −0.931085
\(595\) −0.238002 −0.00975714
\(596\) −11.5581 −0.473437
\(597\) −19.1950 −0.785599
\(598\) 1.16963 0.0478297
\(599\) 28.7061 1.17290 0.586451 0.809985i \(-0.300525\pi\)
0.586451 + 0.809985i \(0.300525\pi\)
\(600\) 1.16273 0.0474682
\(601\) −2.31156 −0.0942904 −0.0471452 0.998888i \(-0.515012\pi\)
−0.0471452 + 0.998888i \(0.515012\pi\)
\(602\) 0.0370296 0.00150921
\(603\) −1.88307 −0.0766844
\(604\) 13.7023 0.557539
\(605\) 35.6302 1.44857
\(606\) 15.0805 0.612603
\(607\) −28.6107 −1.16127 −0.580637 0.814163i \(-0.697196\pi\)
−0.580637 + 0.814163i \(0.697196\pi\)
\(608\) 1.00000 0.0405554
\(609\) −0.249319 −0.0101029
\(610\) −8.40064 −0.340132
\(611\) 1.36728 0.0553141
\(612\) −7.19373 −0.290789
\(613\) −7.31330 −0.295381 −0.147691 0.989034i \(-0.547184\pi\)
−0.147691 + 0.989034i \(0.547184\pi\)
\(614\) 32.4099 1.30796
\(615\) 25.5409 1.02991
\(616\) 0.148721 0.00599213
\(617\) 1.53020 0.0616034 0.0308017 0.999526i \(-0.490194\pi\)
0.0308017 + 0.999526i \(0.490194\pi\)
\(618\) −3.04347 −0.122426
\(619\) −0.281979 −0.0113337 −0.00566685 0.999984i \(-0.501804\pi\)
−0.00566685 + 0.999984i \(0.501804\pi\)
\(620\) −3.69803 −0.148517
\(621\) 23.7854 0.954474
\(622\) 20.5365 0.823437
\(623\) 0.358408 0.0143593
\(624\) 0.191526 0.00766719
\(625\) −29.9301 −1.19721
\(626\) −21.1913 −0.846976
\(627\) 4.31461 0.172309
\(628\) 4.98953 0.199104
\(629\) −25.5210 −1.01759
\(630\) −0.168902 −0.00672922
\(631\) 30.5588 1.21653 0.608264 0.793735i \(-0.291866\pi\)
0.608264 + 0.793735i \(0.291866\pi\)
\(632\) 6.25659 0.248874
\(633\) 0.860547 0.0342037
\(634\) −24.0002 −0.953170
\(635\) −12.0201 −0.477005
\(636\) 0.968194 0.0383914
\(637\) 1.55775 0.0617203
\(638\) 48.9714 1.93880
\(639\) −12.3105 −0.486997
\(640\) −2.52015 −0.0996176
\(641\) −12.1246 −0.478892 −0.239446 0.970910i \(-0.576966\pi\)
−0.239446 + 0.970910i \(0.576966\pi\)
\(642\) −5.41580 −0.213745
\(643\) −19.1273 −0.754307 −0.377154 0.926151i \(-0.623097\pi\)
−0.377154 + 0.926151i \(0.623097\pi\)
\(644\) −0.155883 −0.00614266
\(645\) −2.70735 −0.106602
\(646\) 3.18383 0.125266
\(647\) −29.1395 −1.14559 −0.572796 0.819698i \(-0.694141\pi\)
−0.572796 + 0.819698i \(0.694141\pi\)
\(648\) −2.88353 −0.113276
\(649\) −42.7483 −1.67802
\(650\) 0.300716 0.0117951
\(651\) −0.0374562 −0.00146803
\(652\) 2.90353 0.113711
\(653\) 1.81037 0.0708451 0.0354225 0.999372i \(-0.488722\pi\)
0.0354225 + 0.999372i \(0.488722\pi\)
\(654\) 11.3927 0.445490
\(655\) −45.4948 −1.77763
\(656\) −11.7770 −0.459815
\(657\) 2.04632 0.0798347
\(658\) −0.182225 −0.00710386
\(659\) −4.06468 −0.158337 −0.0791687 0.996861i \(-0.525227\pi\)
−0.0791687 + 0.996861i \(0.525227\pi\)
\(660\) −10.8735 −0.423249
\(661\) 45.5246 1.77070 0.885352 0.464922i \(-0.153918\pi\)
0.885352 + 0.464922i \(0.153918\pi\)
\(662\) −3.63684 −0.141350
\(663\) 0.609788 0.0236822
\(664\) 10.6237 0.412279
\(665\) 0.0747534 0.00289881
\(666\) −18.1114 −0.701802
\(667\) −51.3299 −1.98750
\(668\) 21.2988 0.824074
\(669\) 25.0398 0.968096
\(670\) −2.10033 −0.0811428
\(671\) 16.7129 0.645196
\(672\) −0.0255258 −0.000984680 0
\(673\) 23.7554 0.915704 0.457852 0.889028i \(-0.348619\pi\)
0.457852 + 0.889028i \(0.348619\pi\)
\(674\) −20.0352 −0.771726
\(675\) 6.11532 0.235379
\(676\) −12.9505 −0.498095
\(677\) −12.2946 −0.472521 −0.236261 0.971690i \(-0.575922\pi\)
−0.236261 + 0.971690i \(0.575922\pi\)
\(678\) 7.89574 0.303234
\(679\) 0.279172 0.0107136
\(680\) −8.02373 −0.307696
\(681\) −20.0473 −0.768215
\(682\) 7.35717 0.281721
\(683\) −1.56366 −0.0598318 −0.0299159 0.999552i \(-0.509524\pi\)
−0.0299159 + 0.999552i \(0.509524\pi\)
\(684\) 2.25946 0.0863925
\(685\) −15.8804 −0.606760
\(686\) −0.415246 −0.0158542
\(687\) −13.2709 −0.506316
\(688\) 1.24837 0.0475937
\(689\) 0.250404 0.00953964
\(690\) 11.3971 0.433881
\(691\) −37.5952 −1.43019 −0.715094 0.699029i \(-0.753616\pi\)
−0.715094 + 0.699029i \(0.753616\pi\)
\(692\) −19.3813 −0.736765
\(693\) 0.336028 0.0127647
\(694\) 7.42937 0.282015
\(695\) −7.68016 −0.291325
\(696\) −8.40525 −0.318600
\(697\) −37.4960 −1.42026
\(698\) −24.7756 −0.937771
\(699\) 2.70954 0.102484
\(700\) −0.0400782 −0.00151481
\(701\) 24.9060 0.940686 0.470343 0.882484i \(-0.344130\pi\)
0.470343 + 0.882484i \(0.344130\pi\)
\(702\) 1.00733 0.0380190
\(703\) 8.01581 0.302322
\(704\) 5.01379 0.188965
\(705\) 13.3230 0.501775
\(706\) 1.77080 0.0666451
\(707\) −0.519811 −0.0195495
\(708\) 7.33714 0.275746
\(709\) −27.7247 −1.04122 −0.520612 0.853793i \(-0.674296\pi\)
−0.520612 + 0.853793i \(0.674296\pi\)
\(710\) −13.7309 −0.515311
\(711\) 14.1365 0.530161
\(712\) 12.0829 0.452827
\(713\) −7.71150 −0.288798
\(714\) −0.0812699 −0.00304145
\(715\) −2.81220 −0.105170
\(716\) −18.9865 −0.709561
\(717\) 11.0120 0.411251
\(718\) 35.7298 1.33342
\(719\) −15.4129 −0.574805 −0.287402 0.957810i \(-0.592792\pi\)
−0.287402 + 0.957810i \(0.592792\pi\)
\(720\) −5.69417 −0.212209
\(721\) 0.104906 0.00390689
\(722\) −1.00000 −0.0372161
\(723\) −0.387300 −0.0144038
\(724\) 5.40224 0.200773
\(725\) −13.1971 −0.490129
\(726\) 12.1665 0.451543
\(727\) −23.7326 −0.880194 −0.440097 0.897950i \(-0.645056\pi\)
−0.440097 + 0.897950i \(0.645056\pi\)
\(728\) −0.00660175 −0.000244677 0
\(729\) 5.16934 0.191457
\(730\) 2.28242 0.0844763
\(731\) 3.97460 0.147006
\(732\) −2.86854 −0.106024
\(733\) −41.4373 −1.53052 −0.765261 0.643720i \(-0.777390\pi\)
−0.765261 + 0.643720i \(0.777390\pi\)
\(734\) −0.959187 −0.0354042
\(735\) 15.1790 0.559887
\(736\) −5.25526 −0.193711
\(737\) 4.17857 0.153920
\(738\) −26.6097 −0.979516
\(739\) 7.16667 0.263630 0.131815 0.991274i \(-0.457919\pi\)
0.131815 + 0.991274i \(0.457919\pi\)
\(740\) −20.2010 −0.742604
\(741\) −0.191526 −0.00703590
\(742\) −0.0333728 −0.00122515
\(743\) 10.2019 0.374273 0.187136 0.982334i \(-0.440079\pi\)
0.187136 + 0.982334i \(0.440079\pi\)
\(744\) −1.26276 −0.0462949
\(745\) −29.1280 −1.06717
\(746\) 20.1033 0.736036
\(747\) 24.0038 0.878253
\(748\) 15.9631 0.583668
\(749\) 0.186678 0.00682106
\(750\) −7.91329 −0.288953
\(751\) −29.8760 −1.09019 −0.545095 0.838374i \(-0.683506\pi\)
−0.545095 + 0.838374i \(0.683506\pi\)
\(752\) −6.14331 −0.224023
\(753\) −23.0141 −0.838680
\(754\) −2.17385 −0.0791670
\(755\) 34.5318 1.25674
\(756\) −0.134252 −0.00488270
\(757\) 10.1738 0.369773 0.184887 0.982760i \(-0.440808\pi\)
0.184887 + 0.982760i \(0.440808\pi\)
\(758\) −0.895330 −0.0325198
\(759\) −22.6744 −0.823028
\(760\) 2.52015 0.0914154
\(761\) 7.25106 0.262851 0.131425 0.991326i \(-0.458045\pi\)
0.131425 + 0.991326i \(0.458045\pi\)
\(762\) −4.10448 −0.148690
\(763\) −0.392697 −0.0142166
\(764\) −7.31657 −0.264704
\(765\) −18.1293 −0.655465
\(766\) 5.71870 0.206625
\(767\) 1.89761 0.0685185
\(768\) −0.860547 −0.0310523
\(769\) −16.1672 −0.583004 −0.291502 0.956570i \(-0.594155\pi\)
−0.291502 + 0.956570i \(0.594155\pi\)
\(770\) 0.374798 0.0135068
\(771\) −18.3572 −0.661119
\(772\) −4.18426 −0.150595
\(773\) 12.1919 0.438510 0.219255 0.975668i \(-0.429637\pi\)
0.219255 + 0.975668i \(0.429637\pi\)
\(774\) 2.82064 0.101386
\(775\) −1.98266 −0.0712191
\(776\) 9.41167 0.337859
\(777\) −0.204610 −0.00734034
\(778\) 24.0148 0.860974
\(779\) 11.7770 0.421955
\(780\) 0.482675 0.0172825
\(781\) 27.3174 0.977492
\(782\) −16.7319 −0.598330
\(783\) −44.2071 −1.57983
\(784\) −6.99912 −0.249969
\(785\) 12.5744 0.448798
\(786\) −15.5350 −0.554114
\(787\) −2.85992 −0.101945 −0.0509726 0.998700i \(-0.516232\pi\)
−0.0509726 + 0.998700i \(0.516232\pi\)
\(788\) −1.52396 −0.0542887
\(789\) −1.37041 −0.0487880
\(790\) 15.7675 0.560984
\(791\) −0.272159 −0.00967687
\(792\) 11.3285 0.402539
\(793\) −0.741891 −0.0263453
\(794\) 12.1982 0.432897
\(795\) 2.43999 0.0865376
\(796\) 22.3056 0.790600
\(797\) −16.2058 −0.574038 −0.287019 0.957925i \(-0.592664\pi\)
−0.287019 + 0.957925i \(0.592664\pi\)
\(798\) 0.0255258 0.000903604 0
\(799\) −19.5593 −0.691957
\(800\) −1.35115 −0.0477703
\(801\) 27.3009 0.964630
\(802\) 6.57122 0.232038
\(803\) −4.54085 −0.160243
\(804\) −0.717193 −0.0252935
\(805\) −0.392849 −0.0138461
\(806\) −0.326587 −0.0115035
\(807\) −26.2642 −0.924544
\(808\) −17.5243 −0.616503
\(809\) −3.65111 −0.128366 −0.0641831 0.997938i \(-0.520444\pi\)
−0.0641831 + 0.997938i \(0.520444\pi\)
\(810\) −7.26691 −0.255333
\(811\) 11.2751 0.395922 0.197961 0.980210i \(-0.436568\pi\)
0.197961 + 0.980210i \(0.436568\pi\)
\(812\) 0.289721 0.0101672
\(813\) 0.0248576 0.000871795 0
\(814\) 40.1896 1.40864
\(815\) 7.31734 0.256315
\(816\) −2.73984 −0.0959135
\(817\) −1.24837 −0.0436750
\(818\) −19.8248 −0.693157
\(819\) −0.0149164 −0.000521220 0
\(820\) −29.6798 −1.03646
\(821\) 45.2771 1.58018 0.790091 0.612990i \(-0.210033\pi\)
0.790091 + 0.612990i \(0.210033\pi\)
\(822\) −5.42265 −0.189136
\(823\) 3.63808 0.126816 0.0634078 0.997988i \(-0.479803\pi\)
0.0634078 + 0.997988i \(0.479803\pi\)
\(824\) 3.53667 0.123206
\(825\) −5.82968 −0.202963
\(826\) −0.252905 −0.00879968
\(827\) 7.14954 0.248614 0.124307 0.992244i \(-0.460329\pi\)
0.124307 + 0.992244i \(0.460329\pi\)
\(828\) −11.8740 −0.412652
\(829\) −37.8847 −1.31579 −0.657895 0.753110i \(-0.728553\pi\)
−0.657895 + 0.753110i \(0.728553\pi\)
\(830\) 26.7733 0.929314
\(831\) −2.25773 −0.0783199
\(832\) −0.222564 −0.00771600
\(833\) −22.2840 −0.772095
\(834\) −2.62252 −0.0908105
\(835\) 53.6760 1.85754
\(836\) −5.01379 −0.173406
\(837\) −6.64141 −0.229561
\(838\) 18.9986 0.656296
\(839\) −45.9912 −1.58779 −0.793896 0.608053i \(-0.791951\pi\)
−0.793896 + 0.608053i \(0.791951\pi\)
\(840\) −0.0643289 −0.00221956
\(841\) 66.4007 2.28968
\(842\) 20.7075 0.713626
\(843\) 6.61160 0.227716
\(844\) −1.00000 −0.0344214
\(845\) −32.6371 −1.12275
\(846\) −13.8806 −0.477223
\(847\) −0.419370 −0.0144097
\(848\) −1.12509 −0.0386358
\(849\) 5.29976 0.181887
\(850\) −4.30183 −0.147552
\(851\) −42.1251 −1.44403
\(852\) −4.68864 −0.160630
\(853\) −55.7213 −1.90786 −0.953930 0.300028i \(-0.903004\pi\)
−0.953930 + 0.300028i \(0.903004\pi\)
\(854\) 0.0988760 0.00338347
\(855\) 5.69417 0.194737
\(856\) 6.29343 0.215105
\(857\) 30.2926 1.03478 0.517388 0.855751i \(-0.326905\pi\)
0.517388 + 0.855751i \(0.326905\pi\)
\(858\) −0.960274 −0.0327832
\(859\) −6.49878 −0.221736 −0.110868 0.993835i \(-0.535363\pi\)
−0.110868 + 0.993835i \(0.535363\pi\)
\(860\) 3.14608 0.107281
\(861\) −0.300618 −0.0102450
\(862\) −4.31233 −0.146879
\(863\) −12.5898 −0.428563 −0.214282 0.976772i \(-0.568741\pi\)
−0.214282 + 0.976772i \(0.568741\pi\)
\(864\) −4.52601 −0.153978
\(865\) −48.8436 −1.66073
\(866\) 19.5928 0.665792
\(867\) 5.90612 0.200582
\(868\) 0.0435261 0.00147737
\(869\) −31.3693 −1.06413
\(870\) −21.1825 −0.718153
\(871\) −0.185488 −0.00628502
\(872\) −13.2389 −0.448326
\(873\) 21.2653 0.719721
\(874\) 5.25526 0.177762
\(875\) 0.272764 0.00922111
\(876\) 0.779372 0.0263326
\(877\) 15.4915 0.523109 0.261555 0.965189i \(-0.415765\pi\)
0.261555 + 0.965189i \(0.415765\pi\)
\(878\) −15.0337 −0.507364
\(879\) −12.5593 −0.423616
\(880\) 12.6355 0.425943
\(881\) 25.8977 0.872517 0.436258 0.899821i \(-0.356303\pi\)
0.436258 + 0.899821i \(0.356303\pi\)
\(882\) −15.8142 −0.532492
\(883\) 3.91482 0.131744 0.0658721 0.997828i \(-0.479017\pi\)
0.0658721 + 0.997828i \(0.479017\pi\)
\(884\) −0.708605 −0.0238330
\(885\) 18.4907 0.621557
\(886\) 21.1704 0.711233
\(887\) −28.8607 −0.969047 −0.484524 0.874778i \(-0.661007\pi\)
−0.484524 + 0.874778i \(0.661007\pi\)
\(888\) −6.89798 −0.231481
\(889\) 0.141478 0.00474501
\(890\) 30.4508 1.02071
\(891\) 14.4574 0.484341
\(892\) −29.0976 −0.974258
\(893\) 6.14331 0.205578
\(894\) −9.94626 −0.332653
\(895\) −47.8489 −1.59941
\(896\) 0.0296623 0.000990948 0
\(897\) 1.00652 0.0336068
\(898\) −40.7663 −1.36039
\(899\) 14.3324 0.478014
\(900\) −3.05286 −0.101762
\(901\) −3.58210 −0.119337
\(902\) 59.0476 1.96607
\(903\) 0.0318657 0.00106042
\(904\) −9.17526 −0.305165
\(905\) 13.6144 0.452559
\(906\) 11.7915 0.391746
\(907\) −12.8810 −0.427705 −0.213853 0.976866i \(-0.568601\pi\)
−0.213853 + 0.976866i \(0.568601\pi\)
\(908\) 23.2960 0.773105
\(909\) −39.5954 −1.31330
\(910\) −0.0166374 −0.000551524 0
\(911\) 0.560899 0.0185834 0.00929171 0.999957i \(-0.497042\pi\)
0.00929171 + 0.999957i \(0.497042\pi\)
\(912\) 0.860547 0.0284956
\(913\) −53.2650 −1.76281
\(914\) −8.18021 −0.270577
\(915\) −7.22915 −0.238988
\(916\) 15.4214 0.509539
\(917\) 0.535477 0.0176830
\(918\) −14.4101 −0.475603
\(919\) −1.10702 −0.0365172 −0.0182586 0.999833i \(-0.505812\pi\)
−0.0182586 + 0.999833i \(0.505812\pi\)
\(920\) −13.2440 −0.436643
\(921\) 27.8902 0.919014
\(922\) 9.09547 0.299543
\(923\) −1.21262 −0.0399140
\(924\) 0.127981 0.00421027
\(925\) −10.8305 −0.356106
\(926\) 4.16675 0.136928
\(927\) 7.99096 0.262457
\(928\) 9.76733 0.320628
\(929\) 18.9780 0.622646 0.311323 0.950304i \(-0.399228\pi\)
0.311323 + 0.950304i \(0.399228\pi\)
\(930\) −3.18233 −0.104353
\(931\) 6.99912 0.229387
\(932\) −3.14863 −0.103137
\(933\) 17.6726 0.578575
\(934\) −16.1212 −0.527502
\(935\) 40.2293 1.31564
\(936\) −0.502873 −0.0164369
\(937\) −48.9810 −1.60014 −0.800071 0.599906i \(-0.795205\pi\)
−0.800071 + 0.599906i \(0.795205\pi\)
\(938\) 0.0247210 0.000807170 0
\(939\) −18.2361 −0.595114
\(940\) −15.4821 −0.504969
\(941\) 40.8895 1.33296 0.666479 0.745524i \(-0.267801\pi\)
0.666479 + 0.745524i \(0.267801\pi\)
\(942\) 4.29373 0.139897
\(943\) −61.8913 −2.01546
\(944\) −8.52613 −0.277502
\(945\) −0.338335 −0.0110060
\(946\) −6.25908 −0.203500
\(947\) 14.6355 0.475591 0.237796 0.971315i \(-0.423575\pi\)
0.237796 + 0.971315i \(0.423575\pi\)
\(948\) 5.38409 0.174867
\(949\) 0.201569 0.00654321
\(950\) 1.35115 0.0438371
\(951\) −20.6533 −0.669730
\(952\) 0.0944398 0.00306081
\(953\) −5.02387 −0.162739 −0.0813696 0.996684i \(-0.525929\pi\)
−0.0813696 + 0.996684i \(0.525929\pi\)
\(954\) −2.54210 −0.0823034
\(955\) −18.4388 −0.596667
\(956\) −12.7965 −0.413868
\(957\) 42.1422 1.36226
\(958\) −20.4401 −0.660390
\(959\) 0.186914 0.00603576
\(960\) −2.16871 −0.0699947
\(961\) −28.8468 −0.930541
\(962\) −1.78403 −0.0575193
\(963\) 14.2198 0.458225
\(964\) 0.450062 0.0144955
\(965\) −10.5450 −0.339454
\(966\) −0.134145 −0.00431604
\(967\) −1.83231 −0.0589230 −0.0294615 0.999566i \(-0.509379\pi\)
−0.0294615 + 0.999566i \(0.509379\pi\)
\(968\) −14.1381 −0.454417
\(969\) 2.73984 0.0880163
\(970\) 23.7188 0.761565
\(971\) 2.42613 0.0778581 0.0389291 0.999242i \(-0.487605\pi\)
0.0389291 + 0.999242i \(0.487605\pi\)
\(972\) −16.0594 −0.515107
\(973\) 0.0903960 0.00289796
\(974\) −7.56813 −0.242499
\(975\) 0.258781 0.00828762
\(976\) 3.33339 0.106699
\(977\) 32.7403 1.04745 0.523727 0.851886i \(-0.324541\pi\)
0.523727 + 0.851886i \(0.324541\pi\)
\(978\) 2.49863 0.0798973
\(979\) −60.5814 −1.93619
\(980\) −17.6388 −0.563452
\(981\) −29.9128 −0.955041
\(982\) −3.59508 −0.114724
\(983\) 39.5703 1.26210 0.631048 0.775744i \(-0.282625\pi\)
0.631048 + 0.775744i \(0.282625\pi\)
\(984\) −10.1347 −0.323082
\(985\) −3.84060 −0.122372
\(986\) 31.0975 0.990347
\(987\) −0.156813 −0.00499141
\(988\) 0.222564 0.00708069
\(989\) 6.56052 0.208612
\(990\) 28.5494 0.907360
\(991\) −50.9884 −1.61970 −0.809849 0.586638i \(-0.800451\pi\)
−0.809849 + 0.586638i \(0.800451\pi\)
\(992\) 1.46739 0.0465896
\(993\) −3.12967 −0.0993172
\(994\) 0.161613 0.00512606
\(995\) 56.2134 1.78208
\(996\) 9.14219 0.289681
\(997\) −30.8110 −0.975795 −0.487898 0.872901i \(-0.662236\pi\)
−0.487898 + 0.872901i \(0.662236\pi\)
\(998\) 4.44310 0.140644
\(999\) −36.2796 −1.14784
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 \(a_p\))