Properties

Label 8002.2.a.e.1.8
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +3.49569 q^{10} -0.518766 q^{11} -2.61328 q^{12} +0.394051 q^{13} +0.478818 q^{14} +9.13523 q^{15} +1.00000 q^{16} -1.63145 q^{17} -3.82924 q^{18} -1.57912 q^{19} -3.49569 q^{20} +1.25129 q^{21} +0.518766 q^{22} -1.44805 q^{23} +2.61328 q^{24} +7.21987 q^{25} -0.394051 q^{26} -2.16703 q^{27} -0.478818 q^{28} +6.68629 q^{29} -9.13523 q^{30} +0.0346656 q^{31} -1.00000 q^{32} +1.35568 q^{33} +1.63145 q^{34} +1.67380 q^{35} +3.82924 q^{36} -0.471003 q^{37} +1.57912 q^{38} -1.02977 q^{39} +3.49569 q^{40} -1.81254 q^{41} -1.25129 q^{42} +0.346409 q^{43} -0.518766 q^{44} -13.3858 q^{45} +1.44805 q^{46} +13.5266 q^{47} -2.61328 q^{48} -6.77073 q^{49} -7.21987 q^{50} +4.26343 q^{51} +0.394051 q^{52} +0.660429 q^{53} +2.16703 q^{54} +1.81344 q^{55} +0.478818 q^{56} +4.12669 q^{57} -6.68629 q^{58} +2.43140 q^{59} +9.13523 q^{60} -6.58531 q^{61} -0.0346656 q^{62} -1.83351 q^{63} +1.00000 q^{64} -1.37748 q^{65} -1.35568 q^{66} -15.0872 q^{67} -1.63145 q^{68} +3.78417 q^{69} -1.67380 q^{70} -3.80058 q^{71} -3.82924 q^{72} -4.71638 q^{73} +0.471003 q^{74} -18.8675 q^{75} -1.57912 q^{76} +0.248394 q^{77} +1.02977 q^{78} -7.31985 q^{79} -3.49569 q^{80} -5.82465 q^{81} +1.81254 q^{82} -1.54698 q^{83} +1.25129 q^{84} +5.70304 q^{85} -0.346409 q^{86} -17.4732 q^{87} +0.518766 q^{88} +15.2625 q^{89} +13.3858 q^{90} -0.188679 q^{91} -1.44805 q^{92} -0.0905911 q^{93} -13.5266 q^{94} +5.52012 q^{95} +2.61328 q^{96} +6.19777 q^{97} +6.77073 q^{98} -1.98648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.61328 −1.50878 −0.754389 0.656427i \(-0.772067\pi\)
−0.754389 + 0.656427i \(0.772067\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.49569 −1.56332 −0.781661 0.623704i \(-0.785627\pi\)
−0.781661 + 0.623704i \(0.785627\pi\)
\(6\) 2.61328 1.06687
\(7\) −0.478818 −0.180976 −0.0904881 0.995898i \(-0.528843\pi\)
−0.0904881 + 0.995898i \(0.528843\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.82924 1.27641
\(10\) 3.49569 1.10544
\(11\) −0.518766 −0.156414 −0.0782068 0.996937i \(-0.524919\pi\)
−0.0782068 + 0.996937i \(0.524919\pi\)
\(12\) −2.61328 −0.754389
\(13\) 0.394051 0.109290 0.0546451 0.998506i \(-0.482597\pi\)
0.0546451 + 0.998506i \(0.482597\pi\)
\(14\) 0.478818 0.127969
\(15\) 9.13523 2.35871
\(16\) 1.00000 0.250000
\(17\) −1.63145 −0.395684 −0.197842 0.980234i \(-0.563393\pi\)
−0.197842 + 0.980234i \(0.563393\pi\)
\(18\) −3.82924 −0.902560
\(19\) −1.57912 −0.362275 −0.181138 0.983458i \(-0.557978\pi\)
−0.181138 + 0.983458i \(0.557978\pi\)
\(20\) −3.49569 −0.781661
\(21\) 1.25129 0.273053
\(22\) 0.518766 0.110601
\(23\) −1.44805 −0.301940 −0.150970 0.988538i \(-0.548240\pi\)
−0.150970 + 0.988538i \(0.548240\pi\)
\(24\) 2.61328 0.533434
\(25\) 7.21987 1.44397
\(26\) −0.394051 −0.0772799
\(27\) −2.16703 −0.417046
\(28\) −0.478818 −0.0904881
\(29\) 6.68629 1.24161 0.620806 0.783964i \(-0.286805\pi\)
0.620806 + 0.783964i \(0.286805\pi\)
\(30\) −9.13523 −1.66786
\(31\) 0.0346656 0.00622613 0.00311307 0.999995i \(-0.499009\pi\)
0.00311307 + 0.999995i \(0.499009\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.35568 0.235994
\(34\) 1.63145 0.279791
\(35\) 1.67380 0.282924
\(36\) 3.82924 0.638206
\(37\) −0.471003 −0.0774323 −0.0387162 0.999250i \(-0.512327\pi\)
−0.0387162 + 0.999250i \(0.512327\pi\)
\(38\) 1.57912 0.256167
\(39\) −1.02977 −0.164895
\(40\) 3.49569 0.552718
\(41\) −1.81254 −0.283071 −0.141536 0.989933i \(-0.545204\pi\)
−0.141536 + 0.989933i \(0.545204\pi\)
\(42\) −1.25129 −0.193078
\(43\) 0.346409 0.0528268 0.0264134 0.999651i \(-0.491591\pi\)
0.0264134 + 0.999651i \(0.491591\pi\)
\(44\) −0.518766 −0.0782068
\(45\) −13.3858 −1.99544
\(46\) 1.44805 0.213504
\(47\) 13.5266 1.97305 0.986526 0.163606i \(-0.0523125\pi\)
0.986526 + 0.163606i \(0.0523125\pi\)
\(48\) −2.61328 −0.377195
\(49\) −6.77073 −0.967248
\(50\) −7.21987 −1.02104
\(51\) 4.26343 0.597000
\(52\) 0.394051 0.0546451
\(53\) 0.660429 0.0907169 0.0453585 0.998971i \(-0.485557\pi\)
0.0453585 + 0.998971i \(0.485557\pi\)
\(54\) 2.16703 0.294896
\(55\) 1.81344 0.244525
\(56\) 0.478818 0.0639847
\(57\) 4.12669 0.546593
\(58\) −6.68629 −0.877953
\(59\) 2.43140 0.316541 0.158271 0.987396i \(-0.449408\pi\)
0.158271 + 0.987396i \(0.449408\pi\)
\(60\) 9.13523 1.17935
\(61\) −6.58531 −0.843163 −0.421581 0.906791i \(-0.638525\pi\)
−0.421581 + 0.906791i \(0.638525\pi\)
\(62\) −0.0346656 −0.00440254
\(63\) −1.83351 −0.231000
\(64\) 1.00000 0.125000
\(65\) −1.37748 −0.170856
\(66\) −1.35568 −0.166873
\(67\) −15.0872 −1.84320 −0.921600 0.388142i \(-0.873117\pi\)
−0.921600 + 0.388142i \(0.873117\pi\)
\(68\) −1.63145 −0.197842
\(69\) 3.78417 0.455561
\(70\) −1.67380 −0.200057
\(71\) −3.80058 −0.451046 −0.225523 0.974238i \(-0.572409\pi\)
−0.225523 + 0.974238i \(0.572409\pi\)
\(72\) −3.82924 −0.451280
\(73\) −4.71638 −0.552011 −0.276005 0.961156i \(-0.589011\pi\)
−0.276005 + 0.961156i \(0.589011\pi\)
\(74\) 0.471003 0.0547529
\(75\) −18.8675 −2.17864
\(76\) −1.57912 −0.181138
\(77\) 0.248394 0.0283071
\(78\) 1.02977 0.116598
\(79\) −7.31985 −0.823548 −0.411774 0.911286i \(-0.635091\pi\)
−0.411774 + 0.911286i \(0.635091\pi\)
\(80\) −3.49569 −0.390830
\(81\) −5.82465 −0.647183
\(82\) 1.81254 0.200162
\(83\) −1.54698 −0.169803 −0.0849017 0.996389i \(-0.527058\pi\)
−0.0849017 + 0.996389i \(0.527058\pi\)
\(84\) 1.25129 0.136526
\(85\) 5.70304 0.618582
\(86\) −0.346409 −0.0373542
\(87\) −17.4732 −1.87332
\(88\) 0.518766 0.0553006
\(89\) 15.2625 1.61782 0.808909 0.587934i \(-0.200059\pi\)
0.808909 + 0.587934i \(0.200059\pi\)
\(90\) 13.3858 1.41099
\(91\) −0.188679 −0.0197789
\(92\) −1.44805 −0.150970
\(93\) −0.0905911 −0.00939386
\(94\) −13.5266 −1.39516
\(95\) 5.52012 0.566352
\(96\) 2.61328 0.266717
\(97\) 6.19777 0.629288 0.314644 0.949210i \(-0.398115\pi\)
0.314644 + 0.949210i \(0.398115\pi\)
\(98\) 6.77073 0.683947
\(99\) −1.98648 −0.199648
\(100\) 7.21987 0.721987
\(101\) −9.37856 −0.933201 −0.466601 0.884468i \(-0.654521\pi\)
−0.466601 + 0.884468i \(0.654521\pi\)
\(102\) −4.26343 −0.422143
\(103\) 15.4375 1.52110 0.760552 0.649277i \(-0.224928\pi\)
0.760552 + 0.649277i \(0.224928\pi\)
\(104\) −0.394051 −0.0386399
\(105\) −4.37411 −0.426869
\(106\) −0.660429 −0.0641465
\(107\) 15.5729 1.50549 0.752744 0.658313i \(-0.228730\pi\)
0.752744 + 0.658313i \(0.228730\pi\)
\(108\) −2.16703 −0.208523
\(109\) −4.04637 −0.387572 −0.193786 0.981044i \(-0.562077\pi\)
−0.193786 + 0.981044i \(0.562077\pi\)
\(110\) −1.81344 −0.172905
\(111\) 1.23086 0.116828
\(112\) −0.478818 −0.0452440
\(113\) 16.3223 1.53547 0.767735 0.640768i \(-0.221384\pi\)
0.767735 + 0.640768i \(0.221384\pi\)
\(114\) −4.12669 −0.386500
\(115\) 5.06195 0.472029
\(116\) 6.68629 0.620806
\(117\) 1.50892 0.139499
\(118\) −2.43140 −0.223828
\(119\) 0.781167 0.0716094
\(120\) −9.13523 −0.833928
\(121\) −10.7309 −0.975535
\(122\) 6.58531 0.596206
\(123\) 4.73668 0.427092
\(124\) 0.0346656 0.00311307
\(125\) −7.75997 −0.694073
\(126\) 1.83351 0.163342
\(127\) −0.835001 −0.0740944 −0.0370472 0.999314i \(-0.511795\pi\)
−0.0370472 + 0.999314i \(0.511795\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.905263 −0.0797039
\(130\) 1.37748 0.120813
\(131\) −16.8384 −1.47118 −0.735589 0.677428i \(-0.763094\pi\)
−0.735589 + 0.677428i \(0.763094\pi\)
\(132\) 1.35568 0.117997
\(133\) 0.756111 0.0655631
\(134\) 15.0872 1.30334
\(135\) 7.57528 0.651977
\(136\) 1.63145 0.139896
\(137\) −20.0997 −1.71723 −0.858615 0.512622i \(-0.828674\pi\)
−0.858615 + 0.512622i \(0.828674\pi\)
\(138\) −3.78417 −0.322130
\(139\) −8.90098 −0.754971 −0.377486 0.926015i \(-0.623211\pi\)
−0.377486 + 0.926015i \(0.623211\pi\)
\(140\) 1.67380 0.141462
\(141\) −35.3487 −2.97690
\(142\) 3.80058 0.318937
\(143\) −0.204420 −0.0170945
\(144\) 3.82924 0.319103
\(145\) −23.3732 −1.94104
\(146\) 4.71638 0.390331
\(147\) 17.6938 1.45936
\(148\) −0.471003 −0.0387162
\(149\) −15.4223 −1.26345 −0.631724 0.775194i \(-0.717652\pi\)
−0.631724 + 0.775194i \(0.717652\pi\)
\(150\) 18.8675 1.54053
\(151\) −23.7803 −1.93521 −0.967607 0.252460i \(-0.918760\pi\)
−0.967607 + 0.252460i \(0.918760\pi\)
\(152\) 1.57912 0.128084
\(153\) −6.24721 −0.505057
\(154\) −0.248394 −0.0200162
\(155\) −0.121180 −0.00973345
\(156\) −1.02977 −0.0824474
\(157\) 7.41881 0.592085 0.296043 0.955175i \(-0.404333\pi\)
0.296043 + 0.955175i \(0.404333\pi\)
\(158\) 7.31985 0.582336
\(159\) −1.72589 −0.136872
\(160\) 3.49569 0.276359
\(161\) 0.693354 0.0546439
\(162\) 5.82465 0.457627
\(163\) −19.8529 −1.55500 −0.777500 0.628883i \(-0.783512\pi\)
−0.777500 + 0.628883i \(0.783512\pi\)
\(164\) −1.81254 −0.141536
\(165\) −4.73904 −0.368934
\(166\) 1.54698 0.120069
\(167\) 2.89092 0.223706 0.111853 0.993725i \(-0.464321\pi\)
0.111853 + 0.993725i \(0.464321\pi\)
\(168\) −1.25129 −0.0965388
\(169\) −12.8447 −0.988056
\(170\) −5.70304 −0.437403
\(171\) −6.04683 −0.462413
\(172\) 0.346409 0.0264134
\(173\) −10.7517 −0.817435 −0.408718 0.912661i \(-0.634024\pi\)
−0.408718 + 0.912661i \(0.634024\pi\)
\(174\) 17.4732 1.32464
\(175\) −3.45700 −0.261325
\(176\) −0.518766 −0.0391034
\(177\) −6.35393 −0.477590
\(178\) −15.2625 −1.14397
\(179\) −1.79236 −0.133967 −0.0669836 0.997754i \(-0.521338\pi\)
−0.0669836 + 0.997754i \(0.521338\pi\)
\(180\) −13.3858 −0.997722
\(181\) −9.37633 −0.696937 −0.348468 0.937320i \(-0.613298\pi\)
−0.348468 + 0.937320i \(0.613298\pi\)
\(182\) 0.188679 0.0139858
\(183\) 17.2093 1.27215
\(184\) 1.44805 0.106752
\(185\) 1.64648 0.121052
\(186\) 0.0905911 0.00664246
\(187\) 0.846339 0.0618905
\(188\) 13.5266 0.986526
\(189\) 1.03761 0.0754753
\(190\) −5.52012 −0.400472
\(191\) −8.09957 −0.586064 −0.293032 0.956103i \(-0.594664\pi\)
−0.293032 + 0.956103i \(0.594664\pi\)
\(192\) −2.61328 −0.188597
\(193\) −15.3567 −1.10540 −0.552700 0.833381i \(-0.686402\pi\)
−0.552700 + 0.833381i \(0.686402\pi\)
\(194\) −6.19777 −0.444974
\(195\) 3.59975 0.257783
\(196\) −6.77073 −0.483624
\(197\) 7.45842 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(198\) 1.98648 0.141173
\(199\) 1.82888 0.129646 0.0648230 0.997897i \(-0.479352\pi\)
0.0648230 + 0.997897i \(0.479352\pi\)
\(200\) −7.21987 −0.510522
\(201\) 39.4272 2.78098
\(202\) 9.37856 0.659873
\(203\) −3.20151 −0.224702
\(204\) 4.26343 0.298500
\(205\) 6.33609 0.442531
\(206\) −15.4375 −1.07558
\(207\) −5.54494 −0.385400
\(208\) 0.394051 0.0273226
\(209\) 0.819193 0.0566648
\(210\) 4.37411 0.301842
\(211\) 12.8834 0.886930 0.443465 0.896292i \(-0.353749\pi\)
0.443465 + 0.896292i \(0.353749\pi\)
\(212\) 0.660429 0.0453585
\(213\) 9.93198 0.680528
\(214\) −15.5729 −1.06454
\(215\) −1.21094 −0.0825853
\(216\) 2.16703 0.147448
\(217\) −0.0165985 −0.00112678
\(218\) 4.04637 0.274055
\(219\) 12.3252 0.832862
\(220\) 1.81344 0.122262
\(221\) −0.642875 −0.0432444
\(222\) −1.23086 −0.0826101
\(223\) −14.3736 −0.962527 −0.481263 0.876576i \(-0.659822\pi\)
−0.481263 + 0.876576i \(0.659822\pi\)
\(224\) 0.478818 0.0319924
\(225\) 27.6466 1.84311
\(226\) −16.3223 −1.08574
\(227\) 25.8048 1.71272 0.856362 0.516376i \(-0.172719\pi\)
0.856362 + 0.516376i \(0.172719\pi\)
\(228\) 4.12669 0.273296
\(229\) −9.81575 −0.648643 −0.324321 0.945947i \(-0.605136\pi\)
−0.324321 + 0.945947i \(0.605136\pi\)
\(230\) −5.06195 −0.333775
\(231\) −0.649124 −0.0427092
\(232\) −6.68629 −0.438976
\(233\) 27.4265 1.79677 0.898384 0.439210i \(-0.144742\pi\)
0.898384 + 0.439210i \(0.144742\pi\)
\(234\) −1.50892 −0.0986410
\(235\) −47.2847 −3.08451
\(236\) 2.43140 0.158271
\(237\) 19.1288 1.24255
\(238\) −0.781167 −0.0506355
\(239\) −11.9191 −0.770985 −0.385493 0.922711i \(-0.625968\pi\)
−0.385493 + 0.922711i \(0.625968\pi\)
\(240\) 9.13523 0.589676
\(241\) −3.75561 −0.241920 −0.120960 0.992657i \(-0.538597\pi\)
−0.120960 + 0.992657i \(0.538597\pi\)
\(242\) 10.7309 0.689807
\(243\) 21.7225 1.39350
\(244\) −6.58531 −0.421581
\(245\) 23.6684 1.51212
\(246\) −4.73668 −0.302000
\(247\) −0.622255 −0.0395931
\(248\) −0.0346656 −0.00220127
\(249\) 4.04270 0.256196
\(250\) 7.75997 0.490784
\(251\) −22.7390 −1.43527 −0.717636 0.696418i \(-0.754776\pi\)
−0.717636 + 0.696418i \(0.754776\pi\)
\(252\) −1.83351 −0.115500
\(253\) 0.751200 0.0472275
\(254\) 0.835001 0.0523926
\(255\) −14.9037 −0.933303
\(256\) 1.00000 0.0625000
\(257\) 15.7572 0.982905 0.491452 0.870904i \(-0.336466\pi\)
0.491452 + 0.870904i \(0.336466\pi\)
\(258\) 0.905263 0.0563592
\(259\) 0.225524 0.0140134
\(260\) −1.37748 −0.0854279
\(261\) 25.6034 1.58481
\(262\) 16.8384 1.04028
\(263\) −3.72559 −0.229730 −0.114865 0.993381i \(-0.536644\pi\)
−0.114865 + 0.993381i \(0.536644\pi\)
\(264\) −1.35568 −0.0834363
\(265\) −2.30866 −0.141820
\(266\) −0.756111 −0.0463601
\(267\) −39.8851 −2.44093
\(268\) −15.0872 −0.921600
\(269\) −11.7094 −0.713934 −0.356967 0.934117i \(-0.616189\pi\)
−0.356967 + 0.934117i \(0.616189\pi\)
\(270\) −7.57528 −0.461017
\(271\) 17.9900 1.09281 0.546407 0.837520i \(-0.315995\pi\)
0.546407 + 0.837520i \(0.315995\pi\)
\(272\) −1.63145 −0.0989211
\(273\) 0.493071 0.0298420
\(274\) 20.0997 1.21426
\(275\) −3.74542 −0.225857
\(276\) 3.78417 0.227780
\(277\) −20.7574 −1.24719 −0.623597 0.781746i \(-0.714329\pi\)
−0.623597 + 0.781746i \(0.714329\pi\)
\(278\) 8.90098 0.533845
\(279\) 0.132743 0.00794712
\(280\) −1.67380 −0.100029
\(281\) 27.2542 1.62585 0.812924 0.582369i \(-0.197874\pi\)
0.812924 + 0.582369i \(0.197874\pi\)
\(282\) 35.3487 2.10498
\(283\) 17.5891 1.04556 0.522782 0.852466i \(-0.324894\pi\)
0.522782 + 0.852466i \(0.324894\pi\)
\(284\) −3.80058 −0.225523
\(285\) −14.4256 −0.854500
\(286\) 0.204420 0.0120876
\(287\) 0.867877 0.0512292
\(288\) −3.82924 −0.225640
\(289\) −14.3384 −0.843434
\(290\) 23.3732 1.37252
\(291\) −16.1965 −0.949457
\(292\) −4.71638 −0.276005
\(293\) −29.2878 −1.71101 −0.855505 0.517794i \(-0.826753\pi\)
−0.855505 + 0.517794i \(0.826753\pi\)
\(294\) −17.6938 −1.03193
\(295\) −8.49942 −0.494855
\(296\) 0.471003 0.0273765
\(297\) 1.12418 0.0652317
\(298\) 15.4223 0.893392
\(299\) −0.570608 −0.0329991
\(300\) −18.8675 −1.08932
\(301\) −0.165867 −0.00956039
\(302\) 23.7803 1.36840
\(303\) 24.5088 1.40799
\(304\) −1.57912 −0.0905688
\(305\) 23.0202 1.31813
\(306\) 6.24721 0.357129
\(307\) 1.91738 0.109431 0.0547154 0.998502i \(-0.482575\pi\)
0.0547154 + 0.998502i \(0.482575\pi\)
\(308\) 0.248394 0.0141536
\(309\) −40.3426 −2.29501
\(310\) 0.121180 0.00688259
\(311\) −2.28986 −0.129846 −0.0649230 0.997890i \(-0.520680\pi\)
−0.0649230 + 0.997890i \(0.520680\pi\)
\(312\) 1.02977 0.0582991
\(313\) 12.8454 0.726067 0.363034 0.931776i \(-0.381741\pi\)
0.363034 + 0.931776i \(0.381741\pi\)
\(314\) −7.41881 −0.418668
\(315\) 6.40938 0.361128
\(316\) −7.31985 −0.411774
\(317\) 2.01283 0.113052 0.0565259 0.998401i \(-0.481998\pi\)
0.0565259 + 0.998401i \(0.481998\pi\)
\(318\) 1.72589 0.0967829
\(319\) −3.46862 −0.194205
\(320\) −3.49569 −0.195415
\(321\) −40.6964 −2.27145
\(322\) −0.693354 −0.0386391
\(323\) 2.57625 0.143347
\(324\) −5.82465 −0.323592
\(325\) 2.84500 0.157812
\(326\) 19.8529 1.09955
\(327\) 10.5743 0.584761
\(328\) 1.81254 0.100081
\(329\) −6.47676 −0.357075
\(330\) 4.73904 0.260876
\(331\) 23.5787 1.29600 0.648001 0.761640i \(-0.275605\pi\)
0.648001 + 0.761640i \(0.275605\pi\)
\(332\) −1.54698 −0.0849017
\(333\) −1.80358 −0.0988356
\(334\) −2.89092 −0.158184
\(335\) 52.7403 2.88151
\(336\) 1.25129 0.0682632
\(337\) −26.4651 −1.44164 −0.720822 0.693120i \(-0.756236\pi\)
−0.720822 + 0.693120i \(0.756236\pi\)
\(338\) 12.8447 0.698661
\(339\) −42.6547 −2.31668
\(340\) 5.70304 0.309291
\(341\) −0.0179833 −0.000973852 0
\(342\) 6.04683 0.326975
\(343\) 6.59367 0.356025
\(344\) −0.346409 −0.0186771
\(345\) −13.2283 −0.712187
\(346\) 10.7517 0.578014
\(347\) −13.2596 −0.711811 −0.355905 0.934522i \(-0.615827\pi\)
−0.355905 + 0.934522i \(0.615827\pi\)
\(348\) −17.4732 −0.936659
\(349\) 13.0888 0.700625 0.350313 0.936633i \(-0.386075\pi\)
0.350313 + 0.936633i \(0.386075\pi\)
\(350\) 3.45700 0.184784
\(351\) −0.853923 −0.0455790
\(352\) 0.518766 0.0276503
\(353\) 13.9656 0.743316 0.371658 0.928370i \(-0.378789\pi\)
0.371658 + 0.928370i \(0.378789\pi\)
\(354\) 6.35393 0.337707
\(355\) 13.2856 0.705129
\(356\) 15.2625 0.808909
\(357\) −2.04141 −0.108043
\(358\) 1.79236 0.0947291
\(359\) 26.5440 1.40094 0.700470 0.713681i \(-0.252974\pi\)
0.700470 + 0.713681i \(0.252974\pi\)
\(360\) 13.3858 0.705496
\(361\) −16.5064 −0.868757
\(362\) 9.37633 0.492809
\(363\) 28.0428 1.47187
\(364\) −0.188679 −0.00988946
\(365\) 16.4870 0.862970
\(366\) −17.2093 −0.899543
\(367\) 16.0040 0.835400 0.417700 0.908585i \(-0.362836\pi\)
0.417700 + 0.908585i \(0.362836\pi\)
\(368\) −1.44805 −0.0754850
\(369\) −6.94065 −0.361316
\(370\) −1.64648 −0.0855964
\(371\) −0.316225 −0.0164176
\(372\) −0.0905911 −0.00469693
\(373\) −28.3811 −1.46952 −0.734759 0.678328i \(-0.762705\pi\)
−0.734759 + 0.678328i \(0.762705\pi\)
\(374\) −0.846339 −0.0437632
\(375\) 20.2790 1.04720
\(376\) −13.5266 −0.697579
\(377\) 2.63474 0.135696
\(378\) −1.03761 −0.0533691
\(379\) 36.9387 1.89741 0.948707 0.316158i \(-0.102393\pi\)
0.948707 + 0.316158i \(0.102393\pi\)
\(380\) 5.52012 0.283176
\(381\) 2.18209 0.111792
\(382\) 8.09957 0.414410
\(383\) 14.6807 0.750147 0.375073 0.926995i \(-0.377618\pi\)
0.375073 + 0.926995i \(0.377618\pi\)
\(384\) 2.61328 0.133358
\(385\) −0.868310 −0.0442532
\(386\) 15.3567 0.781635
\(387\) 1.32648 0.0674288
\(388\) 6.19777 0.314644
\(389\) 8.06683 0.409005 0.204502 0.978866i \(-0.434442\pi\)
0.204502 + 0.978866i \(0.434442\pi\)
\(390\) −3.59975 −0.182280
\(391\) 2.36242 0.119473
\(392\) 6.77073 0.341974
\(393\) 44.0035 2.21968
\(394\) −7.45842 −0.375750
\(395\) 25.5879 1.28747
\(396\) −1.98648 −0.0998242
\(397\) −31.6162 −1.58677 −0.793386 0.608719i \(-0.791684\pi\)
−0.793386 + 0.608719i \(0.791684\pi\)
\(398\) −1.82888 −0.0916735
\(399\) −1.97593 −0.0989203
\(400\) 7.21987 0.360993
\(401\) 2.91703 0.145669 0.0728347 0.997344i \(-0.476795\pi\)
0.0728347 + 0.997344i \(0.476795\pi\)
\(402\) −39.4272 −1.96645
\(403\) 0.0136600 0.000680455 0
\(404\) −9.37856 −0.466601
\(405\) 20.3612 1.01175
\(406\) 3.20151 0.158888
\(407\) 0.244340 0.0121115
\(408\) −4.26343 −0.211071
\(409\) 28.1151 1.39020 0.695102 0.718911i \(-0.255359\pi\)
0.695102 + 0.718911i \(0.255359\pi\)
\(410\) −6.33609 −0.312917
\(411\) 52.5260 2.59092
\(412\) 15.4375 0.760552
\(413\) −1.16420 −0.0572864
\(414\) 5.54494 0.272519
\(415\) 5.40777 0.265457
\(416\) −0.394051 −0.0193200
\(417\) 23.2608 1.13908
\(418\) −0.819193 −0.0400681
\(419\) −34.8537 −1.70271 −0.851356 0.524588i \(-0.824219\pi\)
−0.851356 + 0.524588i \(0.824219\pi\)
\(420\) −4.37411 −0.213435
\(421\) −25.8122 −1.25801 −0.629005 0.777401i \(-0.716537\pi\)
−0.629005 + 0.777401i \(0.716537\pi\)
\(422\) −12.8834 −0.627154
\(423\) 51.7964 2.51843
\(424\) −0.660429 −0.0320733
\(425\) −11.7788 −0.571358
\(426\) −9.93198 −0.481206
\(427\) 3.15317 0.152592
\(428\) 15.5729 0.752744
\(429\) 0.534208 0.0257918
\(430\) 1.21094 0.0583966
\(431\) 16.4844 0.794028 0.397014 0.917813i \(-0.370046\pi\)
0.397014 + 0.917813i \(0.370046\pi\)
\(432\) −2.16703 −0.104261
\(433\) 36.0861 1.73419 0.867094 0.498145i \(-0.165985\pi\)
0.867094 + 0.498145i \(0.165985\pi\)
\(434\) 0.0165985 0.000796755 0
\(435\) 61.0808 2.92860
\(436\) −4.04637 −0.193786
\(437\) 2.28665 0.109385
\(438\) −12.3252 −0.588923
\(439\) 12.2932 0.586721 0.293361 0.956002i \(-0.405226\pi\)
0.293361 + 0.956002i \(0.405226\pi\)
\(440\) −1.81344 −0.0864526
\(441\) −25.9268 −1.23461
\(442\) 0.642875 0.0305784
\(443\) −10.7849 −0.512405 −0.256202 0.966623i \(-0.582471\pi\)
−0.256202 + 0.966623i \(0.582471\pi\)
\(444\) 1.23086 0.0584141
\(445\) −53.3529 −2.52917
\(446\) 14.3736 0.680609
\(447\) 40.3029 1.90626
\(448\) −0.478818 −0.0226220
\(449\) −34.6427 −1.63489 −0.817446 0.576006i \(-0.804611\pi\)
−0.817446 + 0.576006i \(0.804611\pi\)
\(450\) −27.6466 −1.30327
\(451\) 0.940284 0.0442762
\(452\) 16.3223 0.767735
\(453\) 62.1447 2.91981
\(454\) −25.8048 −1.21108
\(455\) 0.659563 0.0309208
\(456\) −4.12669 −0.193250
\(457\) 10.9190 0.510770 0.255385 0.966839i \(-0.417798\pi\)
0.255385 + 0.966839i \(0.417798\pi\)
\(458\) 9.81575 0.458660
\(459\) 3.53540 0.165019
\(460\) 5.06195 0.236015
\(461\) −12.4177 −0.578349 −0.289175 0.957276i \(-0.593381\pi\)
−0.289175 + 0.957276i \(0.593381\pi\)
\(462\) 0.649124 0.0302000
\(463\) −10.9578 −0.509251 −0.254626 0.967040i \(-0.581952\pi\)
−0.254626 + 0.967040i \(0.581952\pi\)
\(464\) 6.68629 0.310403
\(465\) 0.316679 0.0146856
\(466\) −27.4265 −1.27051
\(467\) 1.70410 0.0788561 0.0394281 0.999222i \(-0.487446\pi\)
0.0394281 + 0.999222i \(0.487446\pi\)
\(468\) 1.50892 0.0697497
\(469\) 7.22404 0.333575
\(470\) 47.2847 2.18108
\(471\) −19.3874 −0.893326
\(472\) −2.43140 −0.111914
\(473\) −0.179705 −0.00826283
\(474\) −19.1288 −0.878616
\(475\) −11.4010 −0.523116
\(476\) 0.781167 0.0358047
\(477\) 2.52894 0.115792
\(478\) 11.9191 0.545169
\(479\) −12.8413 −0.586736 −0.293368 0.956000i \(-0.594776\pi\)
−0.293368 + 0.956000i \(0.594776\pi\)
\(480\) −9.13523 −0.416964
\(481\) −0.185599 −0.00846260
\(482\) 3.75561 0.171063
\(483\) −1.81193 −0.0824456
\(484\) −10.7309 −0.487767
\(485\) −21.6655 −0.983780
\(486\) −21.7225 −0.985355
\(487\) 12.2065 0.553127 0.276564 0.960996i \(-0.410804\pi\)
0.276564 + 0.960996i \(0.410804\pi\)
\(488\) 6.58531 0.298103
\(489\) 51.8812 2.34615
\(490\) −23.6684 −1.06923
\(491\) −8.79930 −0.397107 −0.198554 0.980090i \(-0.563624\pi\)
−0.198554 + 0.980090i \(0.563624\pi\)
\(492\) 4.73668 0.213546
\(493\) −10.9083 −0.491287
\(494\) 0.622255 0.0279966
\(495\) 6.94411 0.312115
\(496\) 0.0346656 0.00155653
\(497\) 1.81978 0.0816285
\(498\) −4.04270 −0.181158
\(499\) 23.9035 1.07007 0.535033 0.844831i \(-0.320299\pi\)
0.535033 + 0.844831i \(0.320299\pi\)
\(500\) −7.75997 −0.347036
\(501\) −7.55478 −0.337523
\(502\) 22.7390 1.01489
\(503\) −3.64287 −0.162428 −0.0812138 0.996697i \(-0.525880\pi\)
−0.0812138 + 0.996697i \(0.525880\pi\)
\(504\) 1.83351 0.0816709
\(505\) 32.7845 1.45889
\(506\) −0.751200 −0.0333949
\(507\) 33.5669 1.49076
\(508\) −0.835001 −0.0370472
\(509\) 25.7731 1.14237 0.571186 0.820821i \(-0.306484\pi\)
0.571186 + 0.820821i \(0.306484\pi\)
\(510\) 14.9037 0.659945
\(511\) 2.25829 0.0999008
\(512\) −1.00000 −0.0441942
\(513\) 3.42201 0.151085
\(514\) −15.7572 −0.695019
\(515\) −53.9649 −2.37798
\(516\) −0.905263 −0.0398520
\(517\) −7.01711 −0.308612
\(518\) −0.225524 −0.00990897
\(519\) 28.0972 1.23333
\(520\) 1.37748 0.0604066
\(521\) 10.9232 0.478554 0.239277 0.970951i \(-0.423090\pi\)
0.239277 + 0.970951i \(0.423090\pi\)
\(522\) −25.6034 −1.12063
\(523\) 3.92120 0.171462 0.0857311 0.996318i \(-0.472677\pi\)
0.0857311 + 0.996318i \(0.472677\pi\)
\(524\) −16.8384 −0.735589
\(525\) 9.03411 0.394281
\(526\) 3.72559 0.162444
\(527\) −0.0565552 −0.00246358
\(528\) 1.35568 0.0589984
\(529\) −20.9031 −0.908832
\(530\) 2.30866 0.100282
\(531\) 9.31040 0.404037
\(532\) 0.756111 0.0327816
\(533\) −0.714234 −0.0309369
\(534\) 39.8851 1.72600
\(535\) −54.4381 −2.35356
\(536\) 15.0872 0.651669
\(537\) 4.68394 0.202127
\(538\) 11.7094 0.504828
\(539\) 3.51242 0.151291
\(540\) 7.57528 0.325988
\(541\) 33.3609 1.43430 0.717149 0.696920i \(-0.245447\pi\)
0.717149 + 0.696920i \(0.245447\pi\)
\(542\) −17.9900 −0.772736
\(543\) 24.5030 1.05152
\(544\) 1.63145 0.0699478
\(545\) 14.1449 0.605900
\(546\) −0.493071 −0.0211015
\(547\) −17.5347 −0.749729 −0.374865 0.927080i \(-0.622311\pi\)
−0.374865 + 0.927080i \(0.622311\pi\)
\(548\) −20.0997 −0.858615
\(549\) −25.2167 −1.07622
\(550\) 3.74542 0.159705
\(551\) −10.5585 −0.449805
\(552\) −3.78417 −0.161065
\(553\) 3.50487 0.149042
\(554\) 20.7574 0.881899
\(555\) −4.30272 −0.182640
\(556\) −8.90098 −0.377486
\(557\) 14.0175 0.593940 0.296970 0.954887i \(-0.404024\pi\)
0.296970 + 0.954887i \(0.404024\pi\)
\(558\) −0.132743 −0.00561946
\(559\) 0.136503 0.00577345
\(560\) 1.67380 0.0707310
\(561\) −2.21172 −0.0933790
\(562\) −27.2542 −1.14965
\(563\) −15.2895 −0.644377 −0.322188 0.946676i \(-0.604418\pi\)
−0.322188 + 0.946676i \(0.604418\pi\)
\(564\) −35.3487 −1.48845
\(565\) −57.0576 −2.40043
\(566\) −17.5891 −0.739326
\(567\) 2.78894 0.117125
\(568\) 3.80058 0.159469
\(569\) 21.0722 0.883392 0.441696 0.897165i \(-0.354377\pi\)
0.441696 + 0.897165i \(0.354377\pi\)
\(570\) 14.4256 0.604223
\(571\) −13.4449 −0.562650 −0.281325 0.959613i \(-0.590774\pi\)
−0.281325 + 0.959613i \(0.590774\pi\)
\(572\) −0.204420 −0.00854724
\(573\) 21.1664 0.884241
\(574\) −0.867877 −0.0362245
\(575\) −10.4548 −0.435993
\(576\) 3.82924 0.159552
\(577\) 33.8215 1.40801 0.704004 0.710196i \(-0.251394\pi\)
0.704004 + 0.710196i \(0.251394\pi\)
\(578\) 14.3384 0.596398
\(579\) 40.1314 1.66780
\(580\) −23.3732 −0.970520
\(581\) 0.740723 0.0307304
\(582\) 16.1965 0.671367
\(583\) −0.342608 −0.0141894
\(584\) 4.71638 0.195165
\(585\) −5.27471 −0.218082
\(586\) 29.2878 1.20987
\(587\) −18.8414 −0.777669 −0.388835 0.921308i \(-0.627122\pi\)
−0.388835 + 0.921308i \(0.627122\pi\)
\(588\) 17.6938 0.729681
\(589\) −0.0547412 −0.00225557
\(590\) 8.49942 0.349916
\(591\) −19.4909 −0.801750
\(592\) −0.471003 −0.0193581
\(593\) 7.62865 0.313271 0.156636 0.987656i \(-0.449935\pi\)
0.156636 + 0.987656i \(0.449935\pi\)
\(594\) −1.12418 −0.0461258
\(595\) −2.73072 −0.111949
\(596\) −15.4223 −0.631724
\(597\) −4.77938 −0.195607
\(598\) 0.570608 0.0233339
\(599\) −5.73731 −0.234420 −0.117210 0.993107i \(-0.537395\pi\)
−0.117210 + 0.993107i \(0.537395\pi\)
\(600\) 18.8675 0.770264
\(601\) 27.0126 1.10187 0.550933 0.834550i \(-0.314272\pi\)
0.550933 + 0.834550i \(0.314272\pi\)
\(602\) 0.165867 0.00676022
\(603\) −57.7726 −2.35268
\(604\) −23.7803 −0.967607
\(605\) 37.5119 1.52507
\(606\) −24.5088 −0.995602
\(607\) 10.3655 0.420722 0.210361 0.977624i \(-0.432536\pi\)
0.210361 + 0.977624i \(0.432536\pi\)
\(608\) 1.57912 0.0640418
\(609\) 8.36646 0.339026
\(610\) −23.0202 −0.932062
\(611\) 5.33016 0.215635
\(612\) −6.24721 −0.252528
\(613\) 32.3862 1.30807 0.654034 0.756465i \(-0.273075\pi\)
0.654034 + 0.756465i \(0.273075\pi\)
\(614\) −1.91738 −0.0773792
\(615\) −16.5580 −0.667682
\(616\) −0.248394 −0.0100081
\(617\) 40.2542 1.62057 0.810287 0.586034i \(-0.199311\pi\)
0.810287 + 0.586034i \(0.199311\pi\)
\(618\) 40.3426 1.62282
\(619\) 37.7354 1.51671 0.758357 0.651839i \(-0.226002\pi\)
0.758357 + 0.651839i \(0.226002\pi\)
\(620\) −0.121180 −0.00486672
\(621\) 3.13798 0.125923
\(622\) 2.28986 0.0918149
\(623\) −7.30794 −0.292786
\(624\) −1.02977 −0.0412237
\(625\) −8.97286 −0.358914
\(626\) −12.8454 −0.513407
\(627\) −2.14078 −0.0854946
\(628\) 7.41881 0.296043
\(629\) 0.768417 0.0306388
\(630\) −6.40938 −0.255356
\(631\) −25.7914 −1.02674 −0.513369 0.858168i \(-0.671603\pi\)
−0.513369 + 0.858168i \(0.671603\pi\)
\(632\) 7.31985 0.291168
\(633\) −33.6680 −1.33818
\(634\) −2.01283 −0.0799397
\(635\) 2.91891 0.115833
\(636\) −1.72589 −0.0684359
\(637\) −2.66802 −0.105711
\(638\) 3.46862 0.137324
\(639\) −14.5533 −0.575720
\(640\) 3.49569 0.138179
\(641\) −26.0187 −1.02768 −0.513838 0.857887i \(-0.671777\pi\)
−0.513838 + 0.857887i \(0.671777\pi\)
\(642\) 40.6964 1.60616
\(643\) −0.311293 −0.0122762 −0.00613810 0.999981i \(-0.501954\pi\)
−0.00613810 + 0.999981i \(0.501954\pi\)
\(644\) 0.693354 0.0273220
\(645\) 3.16452 0.124603
\(646\) −2.57625 −0.101361
\(647\) 27.6951 1.08881 0.544403 0.838824i \(-0.316756\pi\)
0.544403 + 0.838824i \(0.316756\pi\)
\(648\) 5.82465 0.228814
\(649\) −1.26133 −0.0495113
\(650\) −2.84500 −0.111590
\(651\) 0.0433766 0.00170006
\(652\) −19.8529 −0.777500
\(653\) −19.7464 −0.772736 −0.386368 0.922345i \(-0.626271\pi\)
−0.386368 + 0.922345i \(0.626271\pi\)
\(654\) −10.5743 −0.413488
\(655\) 58.8619 2.29992
\(656\) −1.81254 −0.0707678
\(657\) −18.0602 −0.704594
\(658\) 6.47676 0.252490
\(659\) 10.9891 0.428075 0.214037 0.976825i \(-0.431339\pi\)
0.214037 + 0.976825i \(0.431339\pi\)
\(660\) −4.73904 −0.184467
\(661\) 39.8747 1.55095 0.775473 0.631381i \(-0.217512\pi\)
0.775473 + 0.631381i \(0.217512\pi\)
\(662\) −23.5787 −0.916412
\(663\) 1.68001 0.0652463
\(664\) 1.54698 0.0600346
\(665\) −2.64313 −0.102496
\(666\) 1.80358 0.0698873
\(667\) −9.68210 −0.374892
\(668\) 2.89092 0.111853
\(669\) 37.5622 1.45224
\(670\) −52.7403 −2.03754
\(671\) 3.41623 0.131882
\(672\) −1.25129 −0.0482694
\(673\) 1.84249 0.0710227 0.0355114 0.999369i \(-0.488694\pi\)
0.0355114 + 0.999369i \(0.488694\pi\)
\(674\) 26.4651 1.01940
\(675\) −15.6457 −0.602203
\(676\) −12.8447 −0.494028
\(677\) 5.72080 0.219868 0.109934 0.993939i \(-0.464936\pi\)
0.109934 + 0.993939i \(0.464936\pi\)
\(678\) 42.6547 1.63814
\(679\) −2.96760 −0.113886
\(680\) −5.70304 −0.218702
\(681\) −67.4352 −2.58412
\(682\) 0.0179833 0.000688618 0
\(683\) −3.41671 −0.130737 −0.0653684 0.997861i \(-0.520822\pi\)
−0.0653684 + 0.997861i \(0.520822\pi\)
\(684\) −6.04683 −0.231206
\(685\) 70.2622 2.68458
\(686\) −6.59367 −0.251748
\(687\) 25.6513 0.978658
\(688\) 0.346409 0.0132067
\(689\) 0.260243 0.00991447
\(690\) 13.2283 0.503593
\(691\) 39.0725 1.48639 0.743194 0.669076i \(-0.233310\pi\)
0.743194 + 0.669076i \(0.233310\pi\)
\(692\) −10.7517 −0.408718
\(693\) 0.951161 0.0361316
\(694\) 13.2596 0.503326
\(695\) 31.1151 1.18026
\(696\) 17.4732 0.662318
\(697\) 2.95707 0.112007
\(698\) −13.0888 −0.495417
\(699\) −71.6731 −2.71093
\(700\) −3.45700 −0.130662
\(701\) 23.3894 0.883404 0.441702 0.897162i \(-0.354375\pi\)
0.441702 + 0.897162i \(0.354375\pi\)
\(702\) 0.853923 0.0322292
\(703\) 0.743770 0.0280518
\(704\) −0.518766 −0.0195517
\(705\) 123.568 4.65385
\(706\) −13.9656 −0.525604
\(707\) 4.49062 0.168887
\(708\) −6.35393 −0.238795
\(709\) 2.90057 0.108933 0.0544665 0.998516i \(-0.482654\pi\)
0.0544665 + 0.998516i \(0.482654\pi\)
\(710\) −13.2856 −0.498602
\(711\) −28.0295 −1.05119
\(712\) −15.2625 −0.571985
\(713\) −0.0501977 −0.00187992
\(714\) 2.04141 0.0763978
\(715\) 0.714591 0.0267242
\(716\) −1.79236 −0.0669836
\(717\) 31.1481 1.16325
\(718\) −26.5440 −0.990615
\(719\) 48.8678 1.82246 0.911231 0.411896i \(-0.135133\pi\)
0.911231 + 0.411896i \(0.135133\pi\)
\(720\) −13.3858 −0.498861
\(721\) −7.39176 −0.275284
\(722\) 16.5064 0.614304
\(723\) 9.81446 0.365004
\(724\) −9.37633 −0.348468
\(725\) 48.2741 1.79286
\(726\) −28.0428 −1.04077
\(727\) −10.0723 −0.373559 −0.186780 0.982402i \(-0.559805\pi\)
−0.186780 + 0.982402i \(0.559805\pi\)
\(728\) 0.188679 0.00699290
\(729\) −39.2932 −1.45530
\(730\) −16.4870 −0.610212
\(731\) −0.565148 −0.0209027
\(732\) 17.2093 0.636073
\(733\) −29.4406 −1.08741 −0.543706 0.839276i \(-0.682979\pi\)
−0.543706 + 0.839276i \(0.682979\pi\)
\(734\) −16.0040 −0.590717
\(735\) −61.8522 −2.28145
\(736\) 1.44805 0.0533759
\(737\) 7.82674 0.288302
\(738\) 6.94065 0.255489
\(739\) 8.37310 0.308009 0.154005 0.988070i \(-0.450783\pi\)
0.154005 + 0.988070i \(0.450783\pi\)
\(740\) 1.64648 0.0605258
\(741\) 1.62613 0.0597373
\(742\) 0.316225 0.0116090
\(743\) −6.24975 −0.229281 −0.114641 0.993407i \(-0.536572\pi\)
−0.114641 + 0.993407i \(0.536572\pi\)
\(744\) 0.0905911 0.00332123
\(745\) 53.9118 1.97517
\(746\) 28.3811 1.03911
\(747\) −5.92376 −0.216739
\(748\) 0.846339 0.0309452
\(749\) −7.45658 −0.272458
\(750\) −20.2790 −0.740484
\(751\) 19.6809 0.718166 0.359083 0.933306i \(-0.383089\pi\)
0.359083 + 0.933306i \(0.383089\pi\)
\(752\) 13.5266 0.493263
\(753\) 59.4234 2.16551
\(754\) −2.63474 −0.0959517
\(755\) 83.1287 3.02536
\(756\) 1.03761 0.0377377
\(757\) −43.2565 −1.57219 −0.786093 0.618109i \(-0.787899\pi\)
−0.786093 + 0.618109i \(0.787899\pi\)
\(758\) −36.9387 −1.34167
\(759\) −1.96310 −0.0712559
\(760\) −5.52012 −0.200236
\(761\) −29.2839 −1.06154 −0.530771 0.847515i \(-0.678098\pi\)
−0.530771 + 0.847515i \(0.678098\pi\)
\(762\) −2.18209 −0.0790489
\(763\) 1.93748 0.0701414
\(764\) −8.09957 −0.293032
\(765\) 21.8383 0.789566
\(766\) −14.6807 −0.530434
\(767\) 0.958096 0.0345948
\(768\) −2.61328 −0.0942987
\(769\) −25.1196 −0.905836 −0.452918 0.891552i \(-0.649617\pi\)
−0.452918 + 0.891552i \(0.649617\pi\)
\(770\) 0.868310 0.0312917
\(771\) −41.1779 −1.48299
\(772\) −15.3567 −0.552700
\(773\) −26.1489 −0.940511 −0.470256 0.882530i \(-0.655838\pi\)
−0.470256 + 0.882530i \(0.655838\pi\)
\(774\) −1.32648 −0.0476794
\(775\) 0.250281 0.00899037
\(776\) −6.19777 −0.222487
\(777\) −0.589359 −0.0211431
\(778\) −8.06683 −0.289210
\(779\) 2.86222 0.102550
\(780\) 3.59975 0.128892
\(781\) 1.97161 0.0705497
\(782\) −2.36242 −0.0844801
\(783\) −14.4894 −0.517809
\(784\) −6.77073 −0.241812
\(785\) −25.9339 −0.925620
\(786\) −44.0035 −1.56955
\(787\) 19.9910 0.712602 0.356301 0.934371i \(-0.384038\pi\)
0.356301 + 0.934371i \(0.384038\pi\)
\(788\) 7.45842 0.265695
\(789\) 9.73602 0.346612
\(790\) −25.5879 −0.910378
\(791\) −7.81539 −0.277883
\(792\) 1.98648 0.0705864
\(793\) −2.59495 −0.0921495
\(794\) 31.6162 1.12202
\(795\) 6.03317 0.213974
\(796\) 1.82888 0.0648230
\(797\) −45.4739 −1.61077 −0.805385 0.592752i \(-0.798041\pi\)
−0.805385 + 0.592752i \(0.798041\pi\)
\(798\) 1.97593 0.0699472
\(799\) −22.0679 −0.780706
\(800\) −7.21987 −0.255261
\(801\) 58.4436 2.06500
\(802\) −2.91703 −0.103004
\(803\) 2.44670 0.0863421
\(804\) 39.4272 1.39049
\(805\) −2.42375 −0.0854260
\(806\) −0.0136600 −0.000481155 0
\(807\) 30.5999 1.07717
\(808\) 9.37856 0.329936
\(809\) 5.29557 0.186182 0.0930912 0.995658i \(-0.470325\pi\)
0.0930912 + 0.995658i \(0.470325\pi\)
\(810\) −20.3612 −0.715419
\(811\) 38.0242 1.33521 0.667605 0.744516i \(-0.267320\pi\)
0.667605 + 0.744516i \(0.267320\pi\)
\(812\) −3.20151 −0.112351
\(813\) −47.0129 −1.64881
\(814\) −0.244340 −0.00856411
\(815\) 69.3997 2.43096
\(816\) 4.26343 0.149250
\(817\) −0.547021 −0.0191378
\(818\) −28.1151 −0.983023
\(819\) −0.722496 −0.0252461
\(820\) 6.33609 0.221266
\(821\) −0.494361 −0.0172533 −0.00862665 0.999963i \(-0.502746\pi\)
−0.00862665 + 0.999963i \(0.502746\pi\)
\(822\) −52.5260 −1.83206
\(823\) −20.8898 −0.728171 −0.364085 0.931366i \(-0.618618\pi\)
−0.364085 + 0.931366i \(0.618618\pi\)
\(824\) −15.4375 −0.537792
\(825\) 9.78783 0.340768
\(826\) 1.16420 0.0405076
\(827\) −41.5104 −1.44346 −0.721728 0.692176i \(-0.756652\pi\)
−0.721728 + 0.692176i \(0.756652\pi\)
\(828\) −5.54494 −0.192700
\(829\) −45.4324 −1.57793 −0.788967 0.614436i \(-0.789384\pi\)
−0.788967 + 0.614436i \(0.789384\pi\)
\(830\) −5.40777 −0.187707
\(831\) 54.2450 1.88174
\(832\) 0.394051 0.0136613
\(833\) 11.0461 0.382725
\(834\) −23.2608 −0.805454
\(835\) −10.1058 −0.349724
\(836\) 0.819193 0.0283324
\(837\) −0.0751216 −0.00259658
\(838\) 34.8537 1.20400
\(839\) 12.5944 0.434806 0.217403 0.976082i \(-0.430241\pi\)
0.217403 + 0.976082i \(0.430241\pi\)
\(840\) 4.37411 0.150921
\(841\) 15.7065 0.541602
\(842\) 25.8122 0.889547
\(843\) −71.2229 −2.45305
\(844\) 12.8834 0.443465
\(845\) 44.9012 1.54465
\(846\) −51.7964 −1.78080
\(847\) 5.13814 0.176548
\(848\) 0.660429 0.0226792
\(849\) −45.9653 −1.57752
\(850\) 11.7788 0.404011
\(851\) 0.682037 0.0233799
\(852\) 9.93198 0.340264
\(853\) 13.0591 0.447135 0.223567 0.974688i \(-0.428230\pi\)
0.223567 + 0.974688i \(0.428230\pi\)
\(854\) −3.15317 −0.107899
\(855\) 21.1379 0.722899
\(856\) −15.5729 −0.532271
\(857\) −39.1314 −1.33670 −0.668352 0.743846i \(-0.733000\pi\)
−0.668352 + 0.743846i \(0.733000\pi\)
\(858\) −0.534208 −0.0182376
\(859\) −38.4392 −1.31153 −0.655763 0.754966i \(-0.727653\pi\)
−0.655763 + 0.754966i \(0.727653\pi\)
\(860\) −1.21094 −0.0412926
\(861\) −2.26801 −0.0772934
\(862\) −16.4844 −0.561463
\(863\) −4.04441 −0.137673 −0.0688367 0.997628i \(-0.521929\pi\)
−0.0688367 + 0.997628i \(0.521929\pi\)
\(864\) 2.16703 0.0737240
\(865\) 37.5846 1.27791
\(866\) −36.0861 −1.22626
\(867\) 37.4702 1.27255
\(868\) −0.0165985 −0.000563391 0
\(869\) 3.79729 0.128814
\(870\) −61.0808 −2.07083
\(871\) −5.94515 −0.201444
\(872\) 4.04637 0.137028
\(873\) 23.7327 0.803232
\(874\) −2.28665 −0.0773471
\(875\) 3.71561 0.125611
\(876\) 12.3252 0.416431
\(877\) 39.3482 1.32870 0.664348 0.747424i \(-0.268709\pi\)
0.664348 + 0.747424i \(0.268709\pi\)
\(878\) −12.2932 −0.414875
\(879\) 76.5372 2.58154
\(880\) 1.81344 0.0611312
\(881\) −28.2778 −0.952703 −0.476351 0.879255i \(-0.658041\pi\)
−0.476351 + 0.879255i \(0.658041\pi\)
\(882\) 25.9268 0.872999
\(883\) 18.9825 0.638813 0.319407 0.947618i \(-0.396516\pi\)
0.319407 + 0.947618i \(0.396516\pi\)
\(884\) −0.642875 −0.0216222
\(885\) 22.2114 0.746627
\(886\) 10.7849 0.362325
\(887\) 16.8953 0.567289 0.283645 0.958929i \(-0.408456\pi\)
0.283645 + 0.958929i \(0.408456\pi\)
\(888\) −1.23086 −0.0413050
\(889\) 0.399813 0.0134093
\(890\) 53.3529 1.78839
\(891\) 3.02163 0.101228
\(892\) −14.3736 −0.481263
\(893\) −21.3601 −0.714787
\(894\) −40.3029 −1.34793
\(895\) 6.26554 0.209434
\(896\) 0.478818 0.0159962
\(897\) 1.49116 0.0497883
\(898\) 34.6427 1.15604
\(899\) 0.231785 0.00773045
\(900\) 27.6466 0.921553
\(901\) −1.07746 −0.0358953
\(902\) −0.940284 −0.0313080
\(903\) 0.433456 0.0144245
\(904\) −16.3223 −0.542871
\(905\) 32.7768 1.08954
\(906\) −62.1447 −2.06462
\(907\) 0.764870 0.0253971 0.0126986 0.999919i \(-0.495958\pi\)
0.0126986 + 0.999919i \(0.495958\pi\)
\(908\) 25.8048 0.856362
\(909\) −35.9127 −1.19115
\(910\) −0.659563 −0.0218643
\(911\) 10.3890 0.344202 0.172101 0.985079i \(-0.444944\pi\)
0.172101 + 0.985079i \(0.444944\pi\)
\(912\) 4.12669 0.136648
\(913\) 0.802521 0.0265596
\(914\) −10.9190 −0.361169
\(915\) −60.1583 −1.98877
\(916\) −9.81575 −0.324321
\(917\) 8.06252 0.266248
\(918\) −3.53540 −0.116686
\(919\) −31.8574 −1.05088 −0.525439 0.850831i \(-0.676099\pi\)
−0.525439 + 0.850831i \(0.676099\pi\)
\(920\) −5.06195 −0.166888
\(921\) −5.01066 −0.165107
\(922\) 12.4177 0.408955
\(923\) −1.49762 −0.0492949
\(924\) −0.649124 −0.0213546
\(925\) −3.40058 −0.111810
\(926\) 10.9578 0.360095
\(927\) 59.1140 1.94156
\(928\) −6.68629 −0.219488
\(929\) 35.6028 1.16809 0.584046 0.811721i \(-0.301469\pi\)
0.584046 + 0.811721i \(0.301469\pi\)
\(930\) −0.316679 −0.0103843
\(931\) 10.6918 0.350410
\(932\) 27.4265 0.898384
\(933\) 5.98404 0.195909
\(934\) −1.70410 −0.0557597
\(935\) −2.95854 −0.0967547
\(936\) −1.50892 −0.0493205
\(937\) −20.9413 −0.684122 −0.342061 0.939678i \(-0.611125\pi\)
−0.342061 + 0.939678i \(0.611125\pi\)
\(938\) −7.22404 −0.235873
\(939\) −33.5688 −1.09547
\(940\) −47.2847 −1.54226
\(941\) −22.3639 −0.729043 −0.364522 0.931195i \(-0.618767\pi\)
−0.364522 + 0.931195i \(0.618767\pi\)
\(942\) 19.3874 0.631677
\(943\) 2.62466 0.0854705
\(944\) 2.43140 0.0791353
\(945\) −3.62718 −0.117992
\(946\) 0.179705 0.00584271
\(947\) 36.8400 1.19714 0.598569 0.801071i \(-0.295736\pi\)
0.598569 + 0.801071i \(0.295736\pi\)
\(948\) 19.1288 0.621275
\(949\) −1.85850 −0.0603294
\(950\) 11.4010 0.369899
\(951\) −5.26009 −0.170570
\(952\) −0.781167 −0.0253178
\(953\) 38.3828 1.24334 0.621671 0.783279i \(-0.286454\pi\)
0.621671 + 0.783279i \(0.286454\pi\)
\(954\) −2.52894 −0.0818775
\(955\) 28.3136 0.916206
\(956\) −11.9191 −0.385493
\(957\) 9.06447 0.293013
\(958\) 12.8413 0.414885
\(959\) 9.62407 0.310777
\(960\) 9.13523 0.294838
\(961\) −30.9988 −0.999961
\(962\) 0.185599 0.00598396
\(963\) 59.6323 1.92163
\(964\) −3.75561 −0.120960
\(965\) 53.6823 1.72809
\(966\) 1.81193 0.0582978
\(967\) 19.3292 0.621586 0.310793 0.950478i \(-0.399405\pi\)
0.310793 + 0.950478i \(0.399405\pi\)
\(968\) 10.7309 0.344904
\(969\) −6.73248 −0.216278
\(970\) 21.6655 0.695637
\(971\) −18.8060 −0.603512 −0.301756 0.953385i \(-0.597573\pi\)
−0.301756 + 0.953385i \(0.597573\pi\)
\(972\) 21.7225 0.696751
\(973\) 4.26195 0.136632
\(974\) −12.2065 −0.391120
\(975\) −7.43478 −0.238104
\(976\) −6.58531 −0.210791
\(977\) −25.7961 −0.825290 −0.412645 0.910892i \(-0.635395\pi\)
−0.412645 + 0.910892i \(0.635395\pi\)
\(978\) −51.8812 −1.65898
\(979\) −7.91764 −0.253049
\(980\) 23.6684 0.756059
\(981\) −15.4945 −0.494702
\(982\) 8.79930 0.280797
\(983\) −32.5300 −1.03755 −0.518773 0.854912i \(-0.673611\pi\)
−0.518773 + 0.854912i \(0.673611\pi\)
\(984\) −4.73668 −0.151000
\(985\) −26.0723 −0.830734
\(986\) 10.9083 0.347392
\(987\) 16.9256 0.538747
\(988\) −0.622255 −0.0197966
\(989\) −0.501618 −0.0159505
\(990\) −6.94411 −0.220698
\(991\) 44.3905 1.41011 0.705055 0.709153i \(-0.250922\pi\)
0.705055 + 0.709153i \(0.250922\pi\)
\(992\) −0.0346656 −0.00110064
\(993\) −61.6177 −1.95538
\(994\) −1.81978 −0.0577200
\(995\) −6.39320 −0.202678
\(996\) 4.04270 0.128098
\(997\) −49.4824 −1.56712 −0.783562 0.621314i \(-0.786599\pi\)
−0.783562 + 0.621314i \(0.786599\pi\)
\(998\) −23.9035 −0.756651
\(999\) 1.02068 0.0322928
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 \(a_p\))