Properties

Label 8007.2.a.f.1.10
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.95217 q^{2} -1.00000 q^{3} +1.81095 q^{4} -1.54543 q^{5} +1.95217 q^{6} +2.71405 q^{7} +0.369057 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.95217 q^{2} -1.00000 q^{3} +1.81095 q^{4} -1.54543 q^{5} +1.95217 q^{6} +2.71405 q^{7} +0.369057 q^{8} +1.00000 q^{9} +3.01694 q^{10} -1.66349 q^{11} -1.81095 q^{12} -3.33253 q^{13} -5.29827 q^{14} +1.54543 q^{15} -4.34236 q^{16} -1.00000 q^{17} -1.95217 q^{18} -1.70792 q^{19} -2.79870 q^{20} -2.71405 q^{21} +3.24741 q^{22} +4.45104 q^{23} -0.369057 q^{24} -2.61164 q^{25} +6.50564 q^{26} -1.00000 q^{27} +4.91501 q^{28} +3.74714 q^{29} -3.01694 q^{30} +1.92264 q^{31} +7.73889 q^{32} +1.66349 q^{33} +1.95217 q^{34} -4.19437 q^{35} +1.81095 q^{36} -5.87260 q^{37} +3.33415 q^{38} +3.33253 q^{39} -0.570351 q^{40} +9.83995 q^{41} +5.29827 q^{42} +9.63183 q^{43} -3.01250 q^{44} -1.54543 q^{45} -8.68917 q^{46} -10.5456 q^{47} +4.34236 q^{48} +0.366058 q^{49} +5.09836 q^{50} +1.00000 q^{51} -6.03504 q^{52} +6.79511 q^{53} +1.95217 q^{54} +2.57081 q^{55} +1.00164 q^{56} +1.70792 q^{57} -7.31503 q^{58} -2.46360 q^{59} +2.79870 q^{60} -2.56603 q^{61} -3.75331 q^{62} +2.71405 q^{63} -6.42288 q^{64} +5.15019 q^{65} -3.24741 q^{66} -0.665522 q^{67} -1.81095 q^{68} -4.45104 q^{69} +8.18811 q^{70} +7.81224 q^{71} +0.369057 q^{72} -0.675902 q^{73} +11.4643 q^{74} +2.61164 q^{75} -3.09296 q^{76} -4.51480 q^{77} -6.50564 q^{78} -10.8817 q^{79} +6.71082 q^{80} +1.00000 q^{81} -19.2092 q^{82} +6.98396 q^{83} -4.91501 q^{84} +1.54543 q^{85} -18.8029 q^{86} -3.74714 q^{87} -0.613923 q^{88} -14.6407 q^{89} +3.01694 q^{90} -9.04464 q^{91} +8.06061 q^{92} -1.92264 q^{93} +20.5868 q^{94} +2.63948 q^{95} -7.73889 q^{96} -5.15236 q^{97} -0.714606 q^{98} -1.66349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95217 −1.38039 −0.690195 0.723624i \(-0.742475\pi\)
−0.690195 + 0.723624i \(0.742475\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.81095 0.905475
\(5\) −1.54543 −0.691138 −0.345569 0.938393i \(-0.612314\pi\)
−0.345569 + 0.938393i \(0.612314\pi\)
\(6\) 1.95217 0.796968
\(7\) 2.71405 1.02581 0.512907 0.858444i \(-0.328569\pi\)
0.512907 + 0.858444i \(0.328569\pi\)
\(8\) 0.369057 0.130481
\(9\) 1.00000 0.333333
\(10\) 3.01694 0.954039
\(11\) −1.66349 −0.501562 −0.250781 0.968044i \(-0.580687\pi\)
−0.250781 + 0.968044i \(0.580687\pi\)
\(12\) −1.81095 −0.522776
\(13\) −3.33253 −0.924277 −0.462138 0.886808i \(-0.652918\pi\)
−0.462138 + 0.886808i \(0.652918\pi\)
\(14\) −5.29827 −1.41602
\(15\) 1.54543 0.399029
\(16\) −4.34236 −1.08559
\(17\) −1.00000 −0.242536
\(18\) −1.95217 −0.460130
\(19\) −1.70792 −0.391825 −0.195912 0.980621i \(-0.562767\pi\)
−0.195912 + 0.980621i \(0.562767\pi\)
\(20\) −2.79870 −0.625808
\(21\) −2.71405 −0.592254
\(22\) 3.24741 0.692351
\(23\) 4.45104 0.928106 0.464053 0.885807i \(-0.346395\pi\)
0.464053 + 0.885807i \(0.346395\pi\)
\(24\) −0.369057 −0.0753334
\(25\) −2.61164 −0.522329
\(26\) 6.50564 1.27586
\(27\) −1.00000 −0.192450
\(28\) 4.91501 0.928849
\(29\) 3.74714 0.695826 0.347913 0.937527i \(-0.386891\pi\)
0.347913 + 0.937527i \(0.386891\pi\)
\(30\) −3.01694 −0.550815
\(31\) 1.92264 0.345316 0.172658 0.984982i \(-0.444764\pi\)
0.172658 + 0.984982i \(0.444764\pi\)
\(32\) 7.73889 1.36806
\(33\) 1.66349 0.289577
\(34\) 1.95217 0.334794
\(35\) −4.19437 −0.708979
\(36\) 1.81095 0.301825
\(37\) −5.87260 −0.965450 −0.482725 0.875772i \(-0.660353\pi\)
−0.482725 + 0.875772i \(0.660353\pi\)
\(38\) 3.33415 0.540870
\(39\) 3.33253 0.533631
\(40\) −0.570351 −0.0901805
\(41\) 9.83995 1.53674 0.768371 0.640005i \(-0.221068\pi\)
0.768371 + 0.640005i \(0.221068\pi\)
\(42\) 5.29827 0.817541
\(43\) 9.63183 1.46884 0.734420 0.678695i \(-0.237454\pi\)
0.734420 + 0.678695i \(0.237454\pi\)
\(44\) −3.01250 −0.454152
\(45\) −1.54543 −0.230379
\(46\) −8.68917 −1.28115
\(47\) −10.5456 −1.53824 −0.769120 0.639104i \(-0.779305\pi\)
−0.769120 + 0.639104i \(0.779305\pi\)
\(48\) 4.34236 0.626766
\(49\) 0.366058 0.0522940
\(50\) 5.09836 0.721017
\(51\) 1.00000 0.140028
\(52\) −6.03504 −0.836909
\(53\) 6.79511 0.933380 0.466690 0.884421i \(-0.345446\pi\)
0.466690 + 0.884421i \(0.345446\pi\)
\(54\) 1.95217 0.265656
\(55\) 2.57081 0.346648
\(56\) 1.00164 0.133849
\(57\) 1.70792 0.226220
\(58\) −7.31503 −0.960510
\(59\) −2.46360 −0.320733 −0.160367 0.987058i \(-0.551268\pi\)
−0.160367 + 0.987058i \(0.551268\pi\)
\(60\) 2.79870 0.361310
\(61\) −2.56603 −0.328546 −0.164273 0.986415i \(-0.552528\pi\)
−0.164273 + 0.986415i \(0.552528\pi\)
\(62\) −3.75331 −0.476670
\(63\) 2.71405 0.341938
\(64\) −6.42288 −0.802860
\(65\) 5.15019 0.638802
\(66\) −3.24741 −0.399729
\(67\) −0.665522 −0.0813064 −0.0406532 0.999173i \(-0.512944\pi\)
−0.0406532 + 0.999173i \(0.512944\pi\)
\(68\) −1.81095 −0.219610
\(69\) −4.45104 −0.535842
\(70\) 8.18811 0.978667
\(71\) 7.81224 0.927142 0.463571 0.886060i \(-0.346568\pi\)
0.463571 + 0.886060i \(0.346568\pi\)
\(72\) 0.369057 0.0434937
\(73\) −0.675902 −0.0791084 −0.0395542 0.999217i \(-0.512594\pi\)
−0.0395542 + 0.999217i \(0.512594\pi\)
\(74\) 11.4643 1.33270
\(75\) 2.61164 0.301567
\(76\) −3.09296 −0.354787
\(77\) −4.51480 −0.514509
\(78\) −6.50564 −0.736619
\(79\) −10.8817 −1.22429 −0.612145 0.790745i \(-0.709693\pi\)
−0.612145 + 0.790745i \(0.709693\pi\)
\(80\) 6.71082 0.750292
\(81\) 1.00000 0.111111
\(82\) −19.2092 −2.12130
\(83\) 6.98396 0.766589 0.383295 0.923626i \(-0.374789\pi\)
0.383295 + 0.923626i \(0.374789\pi\)
\(84\) −4.91501 −0.536271
\(85\) 1.54543 0.167626
\(86\) −18.8029 −2.02757
\(87\) −3.74714 −0.401735
\(88\) −0.613923 −0.0654444
\(89\) −14.6407 −1.55191 −0.775953 0.630790i \(-0.782731\pi\)
−0.775953 + 0.630790i \(0.782731\pi\)
\(90\) 3.01694 0.318013
\(91\) −9.04464 −0.948136
\(92\) 8.06061 0.840377
\(93\) −1.92264 −0.199368
\(94\) 20.5868 2.12337
\(95\) 2.63948 0.270805
\(96\) −7.73889 −0.789847
\(97\) −5.15236 −0.523143 −0.261572 0.965184i \(-0.584241\pi\)
−0.261572 + 0.965184i \(0.584241\pi\)
\(98\) −0.714606 −0.0721861
\(99\) −1.66349 −0.167187
\(100\) −4.72955 −0.472955
\(101\) 3.60312 0.358524 0.179262 0.983801i \(-0.442629\pi\)
0.179262 + 0.983801i \(0.442629\pi\)
\(102\) −1.95217 −0.193293
\(103\) −7.76429 −0.765038 −0.382519 0.923948i \(-0.624943\pi\)
−0.382519 + 0.923948i \(0.624943\pi\)
\(104\) −1.22989 −0.120601
\(105\) 4.19437 0.409329
\(106\) −13.2652 −1.28843
\(107\) −1.52459 −0.147387 −0.0736936 0.997281i \(-0.523479\pi\)
−0.0736936 + 0.997281i \(0.523479\pi\)
\(108\) −1.81095 −0.174259
\(109\) 17.7535 1.70048 0.850240 0.526395i \(-0.176457\pi\)
0.850240 + 0.526395i \(0.176457\pi\)
\(110\) −5.01865 −0.478510
\(111\) 5.87260 0.557403
\(112\) −11.7854 −1.11361
\(113\) 11.2796 1.06109 0.530546 0.847656i \(-0.321987\pi\)
0.530546 + 0.847656i \(0.321987\pi\)
\(114\) −3.33415 −0.312272
\(115\) −6.87878 −0.641449
\(116\) 6.78588 0.630053
\(117\) −3.33253 −0.308092
\(118\) 4.80935 0.442737
\(119\) −2.71405 −0.248796
\(120\) 0.570351 0.0520657
\(121\) −8.23279 −0.748436
\(122\) 5.00931 0.453521
\(123\) −9.83995 −0.887238
\(124\) 3.48180 0.312675
\(125\) 11.7633 1.05214
\(126\) −5.29827 −0.472008
\(127\) −11.9313 −1.05873 −0.529365 0.848394i \(-0.677570\pi\)
−0.529365 + 0.848394i \(0.677570\pi\)
\(128\) −2.93926 −0.259797
\(129\) −9.63183 −0.848035
\(130\) −10.0540 −0.881796
\(131\) 5.31341 0.464235 0.232117 0.972688i \(-0.425435\pi\)
0.232117 + 0.972688i \(0.425435\pi\)
\(132\) 3.01250 0.262205
\(133\) −4.63539 −0.401939
\(134\) 1.29921 0.112235
\(135\) 1.54543 0.133010
\(136\) −0.369057 −0.0316463
\(137\) −1.06335 −0.0908478 −0.0454239 0.998968i \(-0.514464\pi\)
−0.0454239 + 0.998968i \(0.514464\pi\)
\(138\) 8.68917 0.739671
\(139\) 7.23319 0.613511 0.306755 0.951788i \(-0.400757\pi\)
0.306755 + 0.951788i \(0.400757\pi\)
\(140\) −7.59580 −0.641963
\(141\) 10.5456 0.888103
\(142\) −15.2508 −1.27982
\(143\) 5.54363 0.463582
\(144\) −4.34236 −0.361863
\(145\) −5.79094 −0.480911
\(146\) 1.31947 0.109200
\(147\) −0.366058 −0.0301920
\(148\) −10.6350 −0.874190
\(149\) −7.73303 −0.633515 −0.316757 0.948507i \(-0.602594\pi\)
−0.316757 + 0.948507i \(0.602594\pi\)
\(150\) −5.09836 −0.416279
\(151\) −7.07748 −0.575957 −0.287979 0.957637i \(-0.592983\pi\)
−0.287979 + 0.957637i \(0.592983\pi\)
\(152\) −0.630320 −0.0511257
\(153\) −1.00000 −0.0808452
\(154\) 8.81363 0.710223
\(155\) −2.97130 −0.238661
\(156\) 6.03504 0.483190
\(157\) −1.00000 −0.0798087
\(158\) 21.2429 1.69000
\(159\) −6.79511 −0.538887
\(160\) −11.9599 −0.945515
\(161\) 12.0803 0.952064
\(162\) −1.95217 −0.153377
\(163\) 9.55015 0.748025 0.374013 0.927424i \(-0.377982\pi\)
0.374013 + 0.927424i \(0.377982\pi\)
\(164\) 17.8197 1.39148
\(165\) −2.57081 −0.200137
\(166\) −13.6338 −1.05819
\(167\) −3.05876 −0.236694 −0.118347 0.992972i \(-0.537759\pi\)
−0.118347 + 0.992972i \(0.537759\pi\)
\(168\) −1.00164 −0.0772780
\(169\) −1.89427 −0.145713
\(170\) −3.01694 −0.231389
\(171\) −1.70792 −0.130608
\(172\) 17.4428 1.33000
\(173\) 11.2098 0.852263 0.426132 0.904661i \(-0.359876\pi\)
0.426132 + 0.904661i \(0.359876\pi\)
\(174\) 7.31503 0.554551
\(175\) −7.08812 −0.535812
\(176\) 7.22348 0.544490
\(177\) 2.46360 0.185175
\(178\) 28.5810 2.14224
\(179\) −6.52567 −0.487751 −0.243876 0.969807i \(-0.578419\pi\)
−0.243876 + 0.969807i \(0.578419\pi\)
\(180\) −2.79870 −0.208603
\(181\) −16.0327 −1.19170 −0.595850 0.803096i \(-0.703185\pi\)
−0.595850 + 0.803096i \(0.703185\pi\)
\(182\) 17.6566 1.30880
\(183\) 2.56603 0.189686
\(184\) 1.64269 0.121100
\(185\) 9.07570 0.667259
\(186\) 3.75331 0.275206
\(187\) 1.66349 0.121647
\(188\) −19.0976 −1.39284
\(189\) −2.71405 −0.197418
\(190\) −5.15270 −0.373816
\(191\) 7.93274 0.573993 0.286997 0.957932i \(-0.407343\pi\)
0.286997 + 0.957932i \(0.407343\pi\)
\(192\) 6.42288 0.463531
\(193\) −15.9809 −1.15033 −0.575165 0.818037i \(-0.695062\pi\)
−0.575165 + 0.818037i \(0.695062\pi\)
\(194\) 10.0583 0.722141
\(195\) −5.15019 −0.368813
\(196\) 0.662913 0.0473509
\(197\) 15.2616 1.08735 0.543673 0.839297i \(-0.317033\pi\)
0.543673 + 0.839297i \(0.317033\pi\)
\(198\) 3.24741 0.230784
\(199\) 3.88864 0.275659 0.137829 0.990456i \(-0.455987\pi\)
0.137829 + 0.990456i \(0.455987\pi\)
\(200\) −0.963844 −0.0681541
\(201\) 0.665522 0.0469423
\(202\) −7.03389 −0.494903
\(203\) 10.1699 0.713788
\(204\) 1.81095 0.126792
\(205\) −15.2070 −1.06210
\(206\) 15.1572 1.05605
\(207\) 4.45104 0.309369
\(208\) 14.4710 1.00339
\(209\) 2.84112 0.196524
\(210\) −8.18811 −0.565034
\(211\) −1.53521 −0.105688 −0.0528440 0.998603i \(-0.516829\pi\)
−0.0528440 + 0.998603i \(0.516829\pi\)
\(212\) 12.3056 0.845152
\(213\) −7.81224 −0.535286
\(214\) 2.97624 0.203452
\(215\) −14.8853 −1.01517
\(216\) −0.369057 −0.0251111
\(217\) 5.21813 0.354230
\(218\) −34.6578 −2.34732
\(219\) 0.675902 0.0456733
\(220\) 4.65561 0.313881
\(221\) 3.33253 0.224170
\(222\) −11.4643 −0.769433
\(223\) 27.1444 1.81772 0.908861 0.417100i \(-0.136954\pi\)
0.908861 + 0.417100i \(0.136954\pi\)
\(224\) 21.0037 1.40337
\(225\) −2.61164 −0.174110
\(226\) −22.0196 −1.46472
\(227\) −13.4640 −0.893639 −0.446820 0.894624i \(-0.647443\pi\)
−0.446820 + 0.894624i \(0.647443\pi\)
\(228\) 3.09296 0.204837
\(229\) 15.0396 0.993847 0.496924 0.867794i \(-0.334463\pi\)
0.496924 + 0.867794i \(0.334463\pi\)
\(230\) 13.4285 0.885450
\(231\) 4.51480 0.297052
\(232\) 1.38290 0.0907922
\(233\) 2.03797 0.133512 0.0667560 0.997769i \(-0.478735\pi\)
0.0667560 + 0.997769i \(0.478735\pi\)
\(234\) 6.50564 0.425287
\(235\) 16.2976 1.06314
\(236\) −4.46145 −0.290416
\(237\) 10.8817 0.706844
\(238\) 5.29827 0.343436
\(239\) 6.32134 0.408893 0.204447 0.978878i \(-0.434461\pi\)
0.204447 + 0.978878i \(0.434461\pi\)
\(240\) −6.71082 −0.433181
\(241\) 19.6807 1.26774 0.633872 0.773438i \(-0.281465\pi\)
0.633872 + 0.773438i \(0.281465\pi\)
\(242\) 16.0718 1.03313
\(243\) −1.00000 −0.0641500
\(244\) −4.64694 −0.297490
\(245\) −0.565718 −0.0361424
\(246\) 19.2092 1.22473
\(247\) 5.69170 0.362154
\(248\) 0.709562 0.0450572
\(249\) −6.98396 −0.442591
\(250\) −22.9638 −1.45236
\(251\) 8.45666 0.533779 0.266890 0.963727i \(-0.414004\pi\)
0.266890 + 0.963727i \(0.414004\pi\)
\(252\) 4.91501 0.309616
\(253\) −7.40427 −0.465503
\(254\) 23.2918 1.46146
\(255\) −1.54543 −0.0967786
\(256\) 18.5837 1.16148
\(257\) 17.3131 1.07996 0.539980 0.841678i \(-0.318432\pi\)
0.539980 + 0.841678i \(0.318432\pi\)
\(258\) 18.8029 1.17062
\(259\) −15.9385 −0.990371
\(260\) 9.32674 0.578420
\(261\) 3.74714 0.231942
\(262\) −10.3727 −0.640824
\(263\) −16.8482 −1.03891 −0.519453 0.854499i \(-0.673864\pi\)
−0.519453 + 0.854499i \(0.673864\pi\)
\(264\) 0.613923 0.0377843
\(265\) −10.5014 −0.645094
\(266\) 9.04904 0.554832
\(267\) 14.6407 0.895994
\(268\) −1.20523 −0.0736209
\(269\) 25.0166 1.52529 0.762643 0.646819i \(-0.223901\pi\)
0.762643 + 0.646819i \(0.223901\pi\)
\(270\) −3.01694 −0.183605
\(271\) −21.0634 −1.27951 −0.639755 0.768579i \(-0.720964\pi\)
−0.639755 + 0.768579i \(0.720964\pi\)
\(272\) 4.34236 0.263294
\(273\) 9.04464 0.547406
\(274\) 2.07583 0.125405
\(275\) 4.34445 0.261980
\(276\) −8.06061 −0.485192
\(277\) −6.68856 −0.401877 −0.200938 0.979604i \(-0.564399\pi\)
−0.200938 + 0.979604i \(0.564399\pi\)
\(278\) −14.1204 −0.846884
\(279\) 1.92264 0.115105
\(280\) −1.54796 −0.0925084
\(281\) 7.88656 0.470473 0.235236 0.971938i \(-0.424414\pi\)
0.235236 + 0.971938i \(0.424414\pi\)
\(282\) −20.5868 −1.22593
\(283\) 16.0102 0.951709 0.475854 0.879524i \(-0.342139\pi\)
0.475854 + 0.879524i \(0.342139\pi\)
\(284\) 14.1476 0.839504
\(285\) −2.63948 −0.156349
\(286\) −10.8221 −0.639923
\(287\) 26.7061 1.57641
\(288\) 7.73889 0.456019
\(289\) 1.00000 0.0588235
\(290\) 11.3049 0.663845
\(291\) 5.15236 0.302037
\(292\) −1.22403 −0.0716307
\(293\) 6.74299 0.393930 0.196965 0.980411i \(-0.436892\pi\)
0.196965 + 0.980411i \(0.436892\pi\)
\(294\) 0.714606 0.0416767
\(295\) 3.80732 0.221671
\(296\) −2.16732 −0.125973
\(297\) 1.66349 0.0965256
\(298\) 15.0962 0.874497
\(299\) −14.8332 −0.857827
\(300\) 4.72955 0.273061
\(301\) 26.1413 1.50676
\(302\) 13.8164 0.795045
\(303\) −3.60312 −0.206994
\(304\) 7.41642 0.425361
\(305\) 3.96562 0.227070
\(306\) 1.95217 0.111598
\(307\) 14.1528 0.807741 0.403871 0.914816i \(-0.367665\pi\)
0.403871 + 0.914816i \(0.367665\pi\)
\(308\) −8.17607 −0.465875
\(309\) 7.76429 0.441695
\(310\) 5.80048 0.329445
\(311\) −23.8230 −1.35088 −0.675439 0.737416i \(-0.736046\pi\)
−0.675439 + 0.737416i \(0.736046\pi\)
\(312\) 1.22989 0.0696289
\(313\) 23.4770 1.32700 0.663500 0.748176i \(-0.269070\pi\)
0.663500 + 0.748176i \(0.269070\pi\)
\(314\) 1.95217 0.110167
\(315\) −4.19437 −0.236326
\(316\) −19.7063 −1.10856
\(317\) −7.50828 −0.421707 −0.210854 0.977518i \(-0.567624\pi\)
−0.210854 + 0.977518i \(0.567624\pi\)
\(318\) 13.2652 0.743874
\(319\) −6.23333 −0.348999
\(320\) 9.92612 0.554887
\(321\) 1.52459 0.0850940
\(322\) −23.5828 −1.31422
\(323\) 1.70792 0.0950314
\(324\) 1.81095 0.100608
\(325\) 8.70337 0.482776
\(326\) −18.6435 −1.03257
\(327\) −17.7535 −0.981772
\(328\) 3.63150 0.200516
\(329\) −28.6214 −1.57795
\(330\) 5.01865 0.276268
\(331\) −12.7493 −0.700766 −0.350383 0.936607i \(-0.613949\pi\)
−0.350383 + 0.936607i \(0.613949\pi\)
\(332\) 12.6476 0.694128
\(333\) −5.87260 −0.321817
\(334\) 5.97120 0.326729
\(335\) 1.02852 0.0561939
\(336\) 11.7854 0.642945
\(337\) −27.5519 −1.50085 −0.750424 0.660957i \(-0.770151\pi\)
−0.750424 + 0.660957i \(0.770151\pi\)
\(338\) 3.69792 0.201140
\(339\) −11.2796 −0.612621
\(340\) 2.79870 0.151781
\(341\) −3.19829 −0.173197
\(342\) 3.33415 0.180290
\(343\) −18.0048 −0.972170
\(344\) 3.55469 0.191656
\(345\) 6.87878 0.370341
\(346\) −21.8833 −1.17646
\(347\) −0.626200 −0.0336162 −0.0168081 0.999859i \(-0.505350\pi\)
−0.0168081 + 0.999859i \(0.505350\pi\)
\(348\) −6.78588 −0.363761
\(349\) 1.35194 0.0723676 0.0361838 0.999345i \(-0.488480\pi\)
0.0361838 + 0.999345i \(0.488480\pi\)
\(350\) 13.8372 0.739629
\(351\) 3.33253 0.177877
\(352\) −12.8736 −0.686164
\(353\) 4.31869 0.229861 0.114930 0.993374i \(-0.463335\pi\)
0.114930 + 0.993374i \(0.463335\pi\)
\(354\) −4.80935 −0.255614
\(355\) −12.0733 −0.640783
\(356\) −26.5135 −1.40521
\(357\) 2.71405 0.143643
\(358\) 12.7392 0.673287
\(359\) −31.3311 −1.65359 −0.826797 0.562501i \(-0.809839\pi\)
−0.826797 + 0.562501i \(0.809839\pi\)
\(360\) −0.570351 −0.0300602
\(361\) −16.0830 −0.846474
\(362\) 31.2985 1.64501
\(363\) 8.23279 0.432110
\(364\) −16.3794 −0.858513
\(365\) 1.04456 0.0546748
\(366\) −5.00931 −0.261841
\(367\) 9.60967 0.501621 0.250810 0.968036i \(-0.419303\pi\)
0.250810 + 0.968036i \(0.419303\pi\)
\(368\) −19.3280 −1.00754
\(369\) 9.83995 0.512247
\(370\) −17.7173 −0.921077
\(371\) 18.4423 0.957474
\(372\) −3.48180 −0.180523
\(373\) −19.2296 −0.995670 −0.497835 0.867272i \(-0.665871\pi\)
−0.497835 + 0.867272i \(0.665871\pi\)
\(374\) −3.24741 −0.167920
\(375\) −11.7633 −0.607453
\(376\) −3.89194 −0.200711
\(377\) −12.4874 −0.643135
\(378\) 5.29827 0.272514
\(379\) −16.7160 −0.858641 −0.429321 0.903152i \(-0.641247\pi\)
−0.429321 + 0.903152i \(0.641247\pi\)
\(380\) 4.77996 0.245207
\(381\) 11.9313 0.611258
\(382\) −15.4860 −0.792334
\(383\) 1.92098 0.0981573 0.0490787 0.998795i \(-0.484371\pi\)
0.0490787 + 0.998795i \(0.484371\pi\)
\(384\) 2.93926 0.149994
\(385\) 6.97731 0.355597
\(386\) 31.1974 1.58790
\(387\) 9.63183 0.489613
\(388\) −9.33067 −0.473693
\(389\) 9.07602 0.460173 0.230086 0.973170i \(-0.426099\pi\)
0.230086 + 0.973170i \(0.426099\pi\)
\(390\) 10.0540 0.509105
\(391\) −4.45104 −0.225099
\(392\) 0.135096 0.00682339
\(393\) −5.31341 −0.268026
\(394\) −29.7932 −1.50096
\(395\) 16.8170 0.846153
\(396\) −3.01250 −0.151384
\(397\) 2.08037 0.104411 0.0522054 0.998636i \(-0.483375\pi\)
0.0522054 + 0.998636i \(0.483375\pi\)
\(398\) −7.59128 −0.380516
\(399\) 4.63539 0.232060
\(400\) 11.3407 0.567035
\(401\) −16.8535 −0.841624 −0.420812 0.907148i \(-0.638255\pi\)
−0.420812 + 0.907148i \(0.638255\pi\)
\(402\) −1.29921 −0.0647986
\(403\) −6.40724 −0.319167
\(404\) 6.52507 0.324635
\(405\) −1.54543 −0.0767931
\(406\) −19.8533 −0.985305
\(407\) 9.76902 0.484233
\(408\) 0.369057 0.0182710
\(409\) −6.18163 −0.305662 −0.152831 0.988252i \(-0.548839\pi\)
−0.152831 + 0.988252i \(0.548839\pi\)
\(410\) 29.6865 1.46611
\(411\) 1.06335 0.0524510
\(412\) −14.0607 −0.692723
\(413\) −6.68632 −0.329012
\(414\) −8.68917 −0.427049
\(415\) −10.7932 −0.529819
\(416\) −25.7901 −1.26446
\(417\) −7.23319 −0.354211
\(418\) −5.54633 −0.271280
\(419\) −4.07372 −0.199014 −0.0995071 0.995037i \(-0.531727\pi\)
−0.0995071 + 0.995037i \(0.531727\pi\)
\(420\) 7.59580 0.370637
\(421\) 6.42731 0.313248 0.156624 0.987658i \(-0.449939\pi\)
0.156624 + 0.987658i \(0.449939\pi\)
\(422\) 2.99698 0.145891
\(423\) −10.5456 −0.512747
\(424\) 2.50778 0.121789
\(425\) 2.61164 0.126683
\(426\) 15.2508 0.738903
\(427\) −6.96432 −0.337027
\(428\) −2.76095 −0.133455
\(429\) −5.54363 −0.267649
\(430\) 29.0586 1.40133
\(431\) −2.22474 −0.107162 −0.0535809 0.998564i \(-0.517063\pi\)
−0.0535809 + 0.998564i \(0.517063\pi\)
\(432\) 4.34236 0.208922
\(433\) −20.5414 −0.987154 −0.493577 0.869702i \(-0.664311\pi\)
−0.493577 + 0.869702i \(0.664311\pi\)
\(434\) −10.1867 −0.488975
\(435\) 5.79094 0.277654
\(436\) 32.1508 1.53974
\(437\) −7.60204 −0.363655
\(438\) −1.31947 −0.0630469
\(439\) 20.1019 0.959413 0.479707 0.877429i \(-0.340743\pi\)
0.479707 + 0.877429i \(0.340743\pi\)
\(440\) 0.948775 0.0452311
\(441\) 0.366058 0.0174313
\(442\) −6.50564 −0.309442
\(443\) −28.5176 −1.35491 −0.677456 0.735563i \(-0.736918\pi\)
−0.677456 + 0.735563i \(0.736918\pi\)
\(444\) 10.6350 0.504714
\(445\) 22.6261 1.07258
\(446\) −52.9903 −2.50916
\(447\) 7.73303 0.365760
\(448\) −17.4320 −0.823585
\(449\) −24.0773 −1.13628 −0.568140 0.822932i \(-0.692337\pi\)
−0.568140 + 0.822932i \(0.692337\pi\)
\(450\) 5.09836 0.240339
\(451\) −16.3687 −0.770771
\(452\) 20.4267 0.960792
\(453\) 7.07748 0.332529
\(454\) 26.2840 1.23357
\(455\) 13.9779 0.655292
\(456\) 0.630320 0.0295175
\(457\) −11.2347 −0.525537 −0.262769 0.964859i \(-0.584636\pi\)
−0.262769 + 0.964859i \(0.584636\pi\)
\(458\) −29.3599 −1.37190
\(459\) 1.00000 0.0466760
\(460\) −12.4571 −0.580816
\(461\) −12.9338 −0.602388 −0.301194 0.953563i \(-0.597385\pi\)
−0.301194 + 0.953563i \(0.597385\pi\)
\(462\) −8.81363 −0.410047
\(463\) 27.6207 1.28364 0.641821 0.766854i \(-0.278179\pi\)
0.641821 + 0.766854i \(0.278179\pi\)
\(464\) −16.2714 −0.755381
\(465\) 2.97130 0.137791
\(466\) −3.97846 −0.184299
\(467\) 3.07968 0.142510 0.0712552 0.997458i \(-0.477300\pi\)
0.0712552 + 0.997458i \(0.477300\pi\)
\(468\) −6.03504 −0.278970
\(469\) −1.80626 −0.0834052
\(470\) −31.8155 −1.46754
\(471\) 1.00000 0.0460776
\(472\) −0.909207 −0.0418496
\(473\) −16.0225 −0.736714
\(474\) −21.2429 −0.975721
\(475\) 4.46049 0.204661
\(476\) −4.91501 −0.225279
\(477\) 6.79511 0.311127
\(478\) −12.3403 −0.564432
\(479\) 8.31883 0.380097 0.190049 0.981775i \(-0.439135\pi\)
0.190049 + 0.981775i \(0.439135\pi\)
\(480\) 11.9599 0.545893
\(481\) 19.5706 0.892342
\(482\) −38.4199 −1.74998
\(483\) −12.0803 −0.549674
\(484\) −14.9092 −0.677690
\(485\) 7.96262 0.361564
\(486\) 1.95217 0.0885520
\(487\) −20.3721 −0.923148 −0.461574 0.887102i \(-0.652715\pi\)
−0.461574 + 0.887102i \(0.652715\pi\)
\(488\) −0.947009 −0.0428691
\(489\) −9.55015 −0.431873
\(490\) 1.10437 0.0498906
\(491\) −37.1512 −1.67661 −0.838304 0.545202i \(-0.816453\pi\)
−0.838304 + 0.545202i \(0.816453\pi\)
\(492\) −17.8197 −0.803372
\(493\) −3.74714 −0.168762
\(494\) −11.1111 −0.499914
\(495\) 2.57081 0.115549
\(496\) −8.34878 −0.374871
\(497\) 21.2028 0.951076
\(498\) 13.6338 0.610947
\(499\) −19.4192 −0.869321 −0.434660 0.900594i \(-0.643132\pi\)
−0.434660 + 0.900594i \(0.643132\pi\)
\(500\) 21.3027 0.952685
\(501\) 3.05876 0.136655
\(502\) −16.5088 −0.736824
\(503\) −34.1719 −1.52365 −0.761826 0.647782i \(-0.775697\pi\)
−0.761826 + 0.647782i \(0.775697\pi\)
\(504\) 1.00164 0.0446165
\(505\) −5.56838 −0.247790
\(506\) 14.4544 0.642575
\(507\) 1.89427 0.0841273
\(508\) −21.6070 −0.958654
\(509\) 37.3515 1.65557 0.827787 0.561042i \(-0.189599\pi\)
0.827787 + 0.561042i \(0.189599\pi\)
\(510\) 3.01694 0.133592
\(511\) −1.83443 −0.0811505
\(512\) −30.3999 −1.34350
\(513\) 1.70792 0.0754067
\(514\) −33.7980 −1.49077
\(515\) 11.9992 0.528747
\(516\) −17.4428 −0.767875
\(517\) 17.5426 0.771522
\(518\) 31.1146 1.36710
\(519\) −11.2098 −0.492055
\(520\) 1.90071 0.0833517
\(521\) 26.3522 1.15451 0.577255 0.816564i \(-0.304124\pi\)
0.577255 + 0.816564i \(0.304124\pi\)
\(522\) −7.31503 −0.320170
\(523\) 11.7830 0.515234 0.257617 0.966247i \(-0.417063\pi\)
0.257617 + 0.966247i \(0.417063\pi\)
\(524\) 9.62232 0.420353
\(525\) 7.08812 0.309351
\(526\) 32.8905 1.43409
\(527\) −1.92264 −0.0837514
\(528\) −7.22348 −0.314362
\(529\) −3.18824 −0.138619
\(530\) 20.5004 0.890481
\(531\) −2.46360 −0.106911
\(532\) −8.39445 −0.363946
\(533\) −32.7919 −1.42037
\(534\) −28.5810 −1.23682
\(535\) 2.35614 0.101865
\(536\) −0.245615 −0.0106090
\(537\) 6.52567 0.281603
\(538\) −48.8365 −2.10549
\(539\) −0.608935 −0.0262287
\(540\) 2.79870 0.120437
\(541\) 12.4065 0.533396 0.266698 0.963780i \(-0.414067\pi\)
0.266698 + 0.963780i \(0.414067\pi\)
\(542\) 41.1192 1.76622
\(543\) 16.0327 0.688028
\(544\) −7.73889 −0.331802
\(545\) −27.4369 −1.17527
\(546\) −17.6566 −0.755634
\(547\) −5.39383 −0.230623 −0.115312 0.993329i \(-0.536787\pi\)
−0.115312 + 0.993329i \(0.536787\pi\)
\(548\) −1.92567 −0.0822604
\(549\) −2.56603 −0.109515
\(550\) −8.48108 −0.361634
\(551\) −6.39982 −0.272642
\(552\) −1.64269 −0.0699173
\(553\) −29.5335 −1.25589
\(554\) 13.0572 0.554746
\(555\) −9.07570 −0.385242
\(556\) 13.0989 0.555519
\(557\) −41.1180 −1.74223 −0.871113 0.491082i \(-0.836602\pi\)
−0.871113 + 0.491082i \(0.836602\pi\)
\(558\) −3.75331 −0.158890
\(559\) −32.0983 −1.35761
\(560\) 18.2135 0.769660
\(561\) −1.66349 −0.0702327
\(562\) −15.3959 −0.649436
\(563\) 7.89306 0.332653 0.166327 0.986071i \(-0.446809\pi\)
0.166327 + 0.986071i \(0.446809\pi\)
\(564\) 19.0976 0.804155
\(565\) −17.4318 −0.733360
\(566\) −31.2546 −1.31373
\(567\) 2.71405 0.113979
\(568\) 2.88316 0.120975
\(569\) 26.4835 1.11025 0.555123 0.831768i \(-0.312671\pi\)
0.555123 + 0.831768i \(0.312671\pi\)
\(570\) 5.15270 0.215823
\(571\) 14.2875 0.597914 0.298957 0.954267i \(-0.403361\pi\)
0.298957 + 0.954267i \(0.403361\pi\)
\(572\) 10.0392 0.419762
\(573\) −7.93274 −0.331395
\(574\) −52.1347 −2.17606
\(575\) −11.6245 −0.484776
\(576\) −6.42288 −0.267620
\(577\) −2.69439 −0.112169 −0.0560845 0.998426i \(-0.517862\pi\)
−0.0560845 + 0.998426i \(0.517862\pi\)
\(578\) −1.95217 −0.0811994
\(579\) 15.9809 0.664144
\(580\) −10.4871 −0.435453
\(581\) 18.9548 0.786378
\(582\) −10.0583 −0.416928
\(583\) −11.3036 −0.468148
\(584\) −0.249446 −0.0103222
\(585\) 5.15019 0.212934
\(586\) −13.1634 −0.543776
\(587\) −1.73660 −0.0716770 −0.0358385 0.999358i \(-0.511410\pi\)
−0.0358385 + 0.999358i \(0.511410\pi\)
\(588\) −0.662913 −0.0273381
\(589\) −3.28372 −0.135303
\(590\) −7.43252 −0.305992
\(591\) −15.2616 −0.627779
\(592\) 25.5009 1.04808
\(593\) −15.5298 −0.637731 −0.318866 0.947800i \(-0.603302\pi\)
−0.318866 + 0.947800i \(0.603302\pi\)
\(594\) −3.24741 −0.133243
\(595\) 4.19437 0.171953
\(596\) −14.0041 −0.573632
\(597\) −3.88864 −0.159152
\(598\) 28.9569 1.18414
\(599\) −13.7690 −0.562585 −0.281292 0.959622i \(-0.590763\pi\)
−0.281292 + 0.959622i \(0.590763\pi\)
\(600\) 0.963844 0.0393488
\(601\) −39.8338 −1.62485 −0.812427 0.583063i \(-0.801854\pi\)
−0.812427 + 0.583063i \(0.801854\pi\)
\(602\) −51.0321 −2.07991
\(603\) −0.665522 −0.0271021
\(604\) −12.8170 −0.521515
\(605\) 12.7232 0.517272
\(606\) 7.03389 0.285732
\(607\) 38.5513 1.56475 0.782374 0.622808i \(-0.214008\pi\)
0.782374 + 0.622808i \(0.214008\pi\)
\(608\) −13.2174 −0.536038
\(609\) −10.1699 −0.412105
\(610\) −7.74154 −0.313446
\(611\) 35.1436 1.42176
\(612\) −1.81095 −0.0732033
\(613\) −39.4073 −1.59165 −0.795823 0.605529i \(-0.792962\pi\)
−0.795823 + 0.605529i \(0.792962\pi\)
\(614\) −27.6285 −1.11500
\(615\) 15.2070 0.613204
\(616\) −1.66622 −0.0671337
\(617\) 2.65413 0.106851 0.0534256 0.998572i \(-0.482986\pi\)
0.0534256 + 0.998572i \(0.482986\pi\)
\(618\) −15.1572 −0.609711
\(619\) 24.8745 0.999790 0.499895 0.866086i \(-0.333372\pi\)
0.499895 + 0.866086i \(0.333372\pi\)
\(620\) −5.38088 −0.216101
\(621\) −4.45104 −0.178614
\(622\) 46.5064 1.86474
\(623\) −39.7354 −1.59197
\(624\) −14.4710 −0.579305
\(625\) −5.12111 −0.204844
\(626\) −45.8310 −1.83178
\(627\) −2.84112 −0.113463
\(628\) −1.81095 −0.0722648
\(629\) 5.87260 0.234156
\(630\) 8.18811 0.326222
\(631\) −7.56205 −0.301040 −0.150520 0.988607i \(-0.548095\pi\)
−0.150520 + 0.988607i \(0.548095\pi\)
\(632\) −4.01597 −0.159747
\(633\) 1.53521 0.0610190
\(634\) 14.6574 0.582120
\(635\) 18.4390 0.731729
\(636\) −12.3056 −0.487949
\(637\) −1.21990 −0.0483341
\(638\) 12.1685 0.481755
\(639\) 7.81224 0.309047
\(640\) 4.54243 0.179555
\(641\) 36.1517 1.42790 0.713952 0.700194i \(-0.246903\pi\)
0.713952 + 0.700194i \(0.246903\pi\)
\(642\) −2.97624 −0.117463
\(643\) −2.49062 −0.0982204 −0.0491102 0.998793i \(-0.515639\pi\)
−0.0491102 + 0.998793i \(0.515639\pi\)
\(644\) 21.8769 0.862070
\(645\) 14.8853 0.586109
\(646\) −3.33415 −0.131180
\(647\) −37.2881 −1.46595 −0.732973 0.680258i \(-0.761868\pi\)
−0.732973 + 0.680258i \(0.761868\pi\)
\(648\) 0.369057 0.0144979
\(649\) 4.09818 0.160867
\(650\) −16.9904 −0.666419
\(651\) −5.21813 −0.204515
\(652\) 17.2948 0.677318
\(653\) 2.43001 0.0950938 0.0475469 0.998869i \(-0.484860\pi\)
0.0475469 + 0.998869i \(0.484860\pi\)
\(654\) 34.6578 1.35523
\(655\) −8.21150 −0.320850
\(656\) −42.7286 −1.66827
\(657\) −0.675902 −0.0263695
\(658\) 55.8737 2.17818
\(659\) 10.8257 0.421709 0.210854 0.977518i \(-0.432375\pi\)
0.210854 + 0.977518i \(0.432375\pi\)
\(660\) −4.65561 −0.181219
\(661\) 34.0870 1.32583 0.662915 0.748695i \(-0.269319\pi\)
0.662915 + 0.748695i \(0.269319\pi\)
\(662\) 24.8888 0.967330
\(663\) −3.33253 −0.129425
\(664\) 2.57748 0.100025
\(665\) 7.16367 0.277795
\(666\) 11.4643 0.444232
\(667\) 16.6787 0.645800
\(668\) −5.53925 −0.214320
\(669\) −27.1444 −1.04946
\(670\) −2.00784 −0.0775695
\(671\) 4.26856 0.164786
\(672\) −21.0037 −0.810236
\(673\) −43.8131 −1.68887 −0.844435 0.535659i \(-0.820063\pi\)
−0.844435 + 0.535659i \(0.820063\pi\)
\(674\) 53.7859 2.07175
\(675\) 2.61164 0.100522
\(676\) −3.43042 −0.131939
\(677\) −0.850008 −0.0326684 −0.0163342 0.999867i \(-0.505200\pi\)
−0.0163342 + 0.999867i \(0.505200\pi\)
\(678\) 22.0196 0.845656
\(679\) −13.9838 −0.536647
\(680\) 0.570351 0.0218720
\(681\) 13.4640 0.515943
\(682\) 6.24360 0.239080
\(683\) −10.6395 −0.407111 −0.203555 0.979063i \(-0.565250\pi\)
−0.203555 + 0.979063i \(0.565250\pi\)
\(684\) −3.09296 −0.118262
\(685\) 1.64333 0.0627884
\(686\) 35.1484 1.34197
\(687\) −15.0396 −0.573798
\(688\) −41.8249 −1.59456
\(689\) −22.6449 −0.862701
\(690\) −13.4285 −0.511215
\(691\) 32.0689 1.21996 0.609980 0.792417i \(-0.291177\pi\)
0.609980 + 0.792417i \(0.291177\pi\)
\(692\) 20.3003 0.771703
\(693\) −4.51480 −0.171503
\(694\) 1.22245 0.0464034
\(695\) −11.1784 −0.424021
\(696\) −1.38290 −0.0524189
\(697\) −9.83995 −0.372715
\(698\) −2.63921 −0.0998954
\(699\) −2.03797 −0.0770832
\(700\) −12.8362 −0.485164
\(701\) −22.3341 −0.843549 −0.421775 0.906701i \(-0.638593\pi\)
−0.421775 + 0.906701i \(0.638593\pi\)
\(702\) −6.50564 −0.245540
\(703\) 10.0300 0.378287
\(704\) 10.6844 0.402684
\(705\) −16.2976 −0.613802
\(706\) −8.43081 −0.317298
\(707\) 9.77905 0.367779
\(708\) 4.46145 0.167672
\(709\) 28.1113 1.05574 0.527871 0.849324i \(-0.322990\pi\)
0.527871 + 0.849324i \(0.322990\pi\)
\(710\) 23.5690 0.884530
\(711\) −10.8817 −0.408097
\(712\) −5.40323 −0.202495
\(713\) 8.55774 0.320490
\(714\) −5.29827 −0.198283
\(715\) −8.56730 −0.320399
\(716\) −11.8177 −0.441647
\(717\) −6.32134 −0.236075
\(718\) 61.1635 2.28260
\(719\) −0.241688 −0.00901344 −0.00450672 0.999990i \(-0.501435\pi\)
−0.00450672 + 0.999990i \(0.501435\pi\)
\(720\) 6.71082 0.250097
\(721\) −21.0727 −0.784787
\(722\) 31.3967 1.16846
\(723\) −19.6807 −0.731932
\(724\) −29.0344 −1.07905
\(725\) −9.78618 −0.363450
\(726\) −16.0718 −0.596480
\(727\) 6.09188 0.225935 0.112968 0.993599i \(-0.463964\pi\)
0.112968 + 0.993599i \(0.463964\pi\)
\(728\) −3.33798 −0.123714
\(729\) 1.00000 0.0370370
\(730\) −2.03916 −0.0754725
\(731\) −9.63183 −0.356246
\(732\) 4.64694 0.171756
\(733\) −41.6050 −1.53672 −0.768358 0.640021i \(-0.778926\pi\)
−0.768358 + 0.640021i \(0.778926\pi\)
\(734\) −18.7597 −0.692432
\(735\) 0.565718 0.0208668
\(736\) 34.4461 1.26970
\(737\) 1.10709 0.0407802
\(738\) −19.2092 −0.707101
\(739\) −22.9344 −0.843654 −0.421827 0.906676i \(-0.638611\pi\)
−0.421827 + 0.906676i \(0.638611\pi\)
\(740\) 16.4356 0.604186
\(741\) −5.69170 −0.209090
\(742\) −36.0023 −1.32169
\(743\) 10.7945 0.396013 0.198007 0.980201i \(-0.436553\pi\)
0.198007 + 0.980201i \(0.436553\pi\)
\(744\) −0.709562 −0.0260138
\(745\) 11.9509 0.437846
\(746\) 37.5393 1.37441
\(747\) 6.98396 0.255530
\(748\) 3.01250 0.110148
\(749\) −4.13780 −0.151192
\(750\) 22.9638 0.838521
\(751\) −46.0539 −1.68053 −0.840266 0.542174i \(-0.817601\pi\)
−0.840266 + 0.542174i \(0.817601\pi\)
\(752\) 45.7930 1.66990
\(753\) −8.45666 −0.308178
\(754\) 24.3775 0.887777
\(755\) 10.9378 0.398066
\(756\) −4.91501 −0.178757
\(757\) −23.1462 −0.841263 −0.420632 0.907232i \(-0.638192\pi\)
−0.420632 + 0.907232i \(0.638192\pi\)
\(758\) 32.6323 1.18526
\(759\) 7.40427 0.268758
\(760\) 0.974117 0.0353349
\(761\) 43.4767 1.57603 0.788015 0.615656i \(-0.211109\pi\)
0.788015 + 0.615656i \(0.211109\pi\)
\(762\) −23.2918 −0.843775
\(763\) 48.1839 1.74438
\(764\) 14.3658 0.519737
\(765\) 1.54543 0.0558752
\(766\) −3.75006 −0.135495
\(767\) 8.21000 0.296446
\(768\) −18.5837 −0.670581
\(769\) 16.1839 0.583606 0.291803 0.956478i \(-0.405745\pi\)
0.291803 + 0.956478i \(0.405745\pi\)
\(770\) −13.6209 −0.490862
\(771\) −17.3131 −0.623515
\(772\) −28.9406 −1.04160
\(773\) 6.69933 0.240958 0.120479 0.992716i \(-0.461557\pi\)
0.120479 + 0.992716i \(0.461557\pi\)
\(774\) −18.8029 −0.675857
\(775\) −5.02124 −0.180368
\(776\) −1.90151 −0.0682603
\(777\) 15.9385 0.571791
\(778\) −17.7179 −0.635217
\(779\) −16.8059 −0.602133
\(780\) −9.32674 −0.333951
\(781\) −12.9956 −0.465019
\(782\) 8.68917 0.310724
\(783\) −3.74714 −0.133912
\(784\) −1.58956 −0.0567699
\(785\) 1.54543 0.0551588
\(786\) 10.3727 0.369980
\(787\) −20.2089 −0.720371 −0.360186 0.932881i \(-0.617287\pi\)
−0.360186 + 0.932881i \(0.617287\pi\)
\(788\) 27.6380 0.984565
\(789\) 16.8482 0.599813
\(790\) −32.8295 −1.16802
\(791\) 30.6133 1.08848
\(792\) −0.613923 −0.0218148
\(793\) 8.55135 0.303667
\(794\) −4.06122 −0.144127
\(795\) 10.5014 0.372445
\(796\) 7.04214 0.249602
\(797\) −16.4067 −0.581157 −0.290578 0.956851i \(-0.593848\pi\)
−0.290578 + 0.956851i \(0.593848\pi\)
\(798\) −9.04904 −0.320333
\(799\) 10.5456 0.373078
\(800\) −20.2112 −0.714575
\(801\) −14.6407 −0.517302
\(802\) 32.9008 1.16177
\(803\) 1.12436 0.0396777
\(804\) 1.20523 0.0425051
\(805\) −18.6693 −0.658008
\(806\) 12.5080 0.440575
\(807\) −25.0166 −0.880625
\(808\) 1.32976 0.0467806
\(809\) −43.4183 −1.52650 −0.763252 0.646100i \(-0.776399\pi\)
−0.763252 + 0.646100i \(0.776399\pi\)
\(810\) 3.01694 0.106004
\(811\) −0.755165 −0.0265174 −0.0132587 0.999912i \(-0.504221\pi\)
−0.0132587 + 0.999912i \(0.504221\pi\)
\(812\) 18.4172 0.646317
\(813\) 21.0634 0.738725
\(814\) −19.0708 −0.668429
\(815\) −14.7591 −0.516989
\(816\) −4.34236 −0.152013
\(817\) −16.4504 −0.575528
\(818\) 12.0676 0.421933
\(819\) −9.04464 −0.316045
\(820\) −27.5391 −0.961705
\(821\) 11.0595 0.385978 0.192989 0.981201i \(-0.438182\pi\)
0.192989 + 0.981201i \(0.438182\pi\)
\(822\) −2.07583 −0.0724028
\(823\) 9.57611 0.333802 0.166901 0.985974i \(-0.446624\pi\)
0.166901 + 0.985974i \(0.446624\pi\)
\(824\) −2.86546 −0.0998231
\(825\) −4.34445 −0.151254
\(826\) 13.0528 0.454165
\(827\) −46.2868 −1.60955 −0.804775 0.593580i \(-0.797714\pi\)
−0.804775 + 0.593580i \(0.797714\pi\)
\(828\) 8.06061 0.280126
\(829\) 7.26483 0.252318 0.126159 0.992010i \(-0.459735\pi\)
0.126159 + 0.992010i \(0.459735\pi\)
\(830\) 21.0702 0.731356
\(831\) 6.68856 0.232024
\(832\) 21.4044 0.742064
\(833\) −0.366058 −0.0126832
\(834\) 14.1204 0.488949
\(835\) 4.72710 0.163588
\(836\) 5.14512 0.177948
\(837\) −1.92264 −0.0664561
\(838\) 7.95258 0.274717
\(839\) 28.5198 0.984615 0.492307 0.870421i \(-0.336154\pi\)
0.492307 + 0.870421i \(0.336154\pi\)
\(840\) 1.54796 0.0534097
\(841\) −14.9590 −0.515827
\(842\) −12.5472 −0.432404
\(843\) −7.88656 −0.271628
\(844\) −2.78019 −0.0956979
\(845\) 2.92746 0.100708
\(846\) 20.5868 0.707790
\(847\) −22.3442 −0.767756
\(848\) −29.5068 −1.01327
\(849\) −16.0102 −0.549469
\(850\) −5.09836 −0.174872
\(851\) −26.1392 −0.896040
\(852\) −14.1476 −0.484688
\(853\) −10.6566 −0.364875 −0.182438 0.983217i \(-0.558399\pi\)
−0.182438 + 0.983217i \(0.558399\pi\)
\(854\) 13.5955 0.465228
\(855\) 2.63948 0.0902682
\(856\) −0.562658 −0.0192313
\(857\) 26.3234 0.899191 0.449595 0.893232i \(-0.351568\pi\)
0.449595 + 0.893232i \(0.351568\pi\)
\(858\) 10.8221 0.369460
\(859\) 10.7569 0.367019 0.183510 0.983018i \(-0.441254\pi\)
0.183510 + 0.983018i \(0.441254\pi\)
\(860\) −26.9566 −0.919212
\(861\) −26.7061 −0.910141
\(862\) 4.34305 0.147925
\(863\) −31.8093 −1.08280 −0.541400 0.840765i \(-0.682105\pi\)
−0.541400 + 0.840765i \(0.682105\pi\)
\(864\) −7.73889 −0.263282
\(865\) −17.3239 −0.589031
\(866\) 40.1001 1.36266
\(867\) −1.00000 −0.0339618
\(868\) 9.44977 0.320746
\(869\) 18.1017 0.614057
\(870\) −11.3049 −0.383271
\(871\) 2.21787 0.0751496
\(872\) 6.55206 0.221881
\(873\) −5.15236 −0.174381
\(874\) 14.8404 0.501985
\(875\) 31.9261 1.07930
\(876\) 1.22403 0.0413560
\(877\) −6.13856 −0.207284 −0.103642 0.994615i \(-0.533050\pi\)
−0.103642 + 0.994615i \(0.533050\pi\)
\(878\) −39.2423 −1.32436
\(879\) −6.74299 −0.227435
\(880\) −11.1634 −0.376318
\(881\) 18.3041 0.616681 0.308341 0.951276i \(-0.400226\pi\)
0.308341 + 0.951276i \(0.400226\pi\)
\(882\) −0.714606 −0.0240620
\(883\) −40.6662 −1.36853 −0.684264 0.729234i \(-0.739876\pi\)
−0.684264 + 0.729234i \(0.739876\pi\)
\(884\) 6.03504 0.202980
\(885\) −3.80732 −0.127982
\(886\) 55.6711 1.87031
\(887\) −17.2872 −0.580446 −0.290223 0.956959i \(-0.593730\pi\)
−0.290223 + 0.956959i \(0.593730\pi\)
\(888\) 2.16732 0.0727305
\(889\) −32.3821 −1.08606
\(890\) −44.1699 −1.48058
\(891\) −1.66349 −0.0557291
\(892\) 49.1571 1.64590
\(893\) 18.0111 0.602720
\(894\) −15.0962 −0.504891
\(895\) 10.0850 0.337103
\(896\) −7.97730 −0.266503
\(897\) 14.8332 0.495267
\(898\) 47.0029 1.56851
\(899\) 7.20438 0.240280
\(900\) −4.72955 −0.157652
\(901\) −6.79511 −0.226378
\(902\) 31.9544 1.06396
\(903\) −26.1413 −0.869926
\(904\) 4.16279 0.138452
\(905\) 24.7774 0.823629
\(906\) −13.8164 −0.459020
\(907\) −21.0323 −0.698366 −0.349183 0.937055i \(-0.613541\pi\)
−0.349183 + 0.937055i \(0.613541\pi\)
\(908\) −24.3827 −0.809168
\(909\) 3.60312 0.119508
\(910\) −27.2871 −0.904559
\(911\) −20.2208 −0.669943 −0.334972 0.942228i \(-0.608727\pi\)
−0.334972 + 0.942228i \(0.608727\pi\)
\(912\) −7.41642 −0.245582
\(913\) −11.6178 −0.384492
\(914\) 21.9320 0.725446
\(915\) −3.96562 −0.131099
\(916\) 27.2360 0.899904
\(917\) 14.4208 0.476218
\(918\) −1.95217 −0.0644311
\(919\) −26.6764 −0.879973 −0.439986 0.898005i \(-0.645017\pi\)
−0.439986 + 0.898005i \(0.645017\pi\)
\(920\) −2.53866 −0.0836971
\(921\) −14.1528 −0.466350
\(922\) 25.2489 0.831530
\(923\) −26.0345 −0.856936
\(924\) 8.17607 0.268973
\(925\) 15.3371 0.504282
\(926\) −53.9202 −1.77193
\(927\) −7.76429 −0.255013
\(928\) 28.9987 0.951928
\(929\) −52.4701 −1.72149 −0.860743 0.509039i \(-0.830001\pi\)
−0.860743 + 0.509039i \(0.830001\pi\)
\(930\) −5.80048 −0.190205
\(931\) −0.625199 −0.0204901
\(932\) 3.69067 0.120892
\(933\) 23.8230 0.779929
\(934\) −6.01204 −0.196720
\(935\) −2.57081 −0.0840746
\(936\) −1.22989 −0.0402002
\(937\) −35.8643 −1.17164 −0.585818 0.810442i \(-0.699227\pi\)
−0.585818 + 0.810442i \(0.699227\pi\)
\(938\) 3.52611 0.115132
\(939\) −23.4770 −0.766144
\(940\) 29.5141 0.962643
\(941\) 19.5134 0.636118 0.318059 0.948071i \(-0.396969\pi\)
0.318059 + 0.948071i \(0.396969\pi\)
\(942\) −1.95217 −0.0636050
\(943\) 43.7980 1.42626
\(944\) 10.6978 0.348185
\(945\) 4.19437 0.136443
\(946\) 31.2785 1.01695
\(947\) 5.00962 0.162791 0.0813953 0.996682i \(-0.474062\pi\)
0.0813953 + 0.996682i \(0.474062\pi\)
\(948\) 19.7063 0.640030
\(949\) 2.25246 0.0731180
\(950\) −8.70761 −0.282512
\(951\) 7.50828 0.243473
\(952\) −1.00164 −0.0324633
\(953\) 34.9866 1.13333 0.566664 0.823949i \(-0.308234\pi\)
0.566664 + 0.823949i \(0.308234\pi\)
\(954\) −13.2652 −0.429476
\(955\) −12.2595 −0.396708
\(956\) 11.4476 0.370243
\(957\) 6.23333 0.201495
\(958\) −16.2397 −0.524682
\(959\) −2.88597 −0.0931930
\(960\) −9.92612 −0.320364
\(961\) −27.3035 −0.880757
\(962\) −38.2050 −1.23178
\(963\) −1.52459 −0.0491291
\(964\) 35.6407 1.14791
\(965\) 24.6974 0.795037
\(966\) 23.5828 0.758765
\(967\) −3.22322 −0.103652 −0.0518258 0.998656i \(-0.516504\pi\)
−0.0518258 + 0.998656i \(0.516504\pi\)
\(968\) −3.03837 −0.0976568
\(969\) −1.70792 −0.0548664
\(970\) −15.5444 −0.499099
\(971\) 3.45258 0.110799 0.0553993 0.998464i \(-0.482357\pi\)
0.0553993 + 0.998464i \(0.482357\pi\)
\(972\) −1.81095 −0.0580863
\(973\) 19.6312 0.629348
\(974\) 39.7697 1.27430
\(975\) −8.70337 −0.278731
\(976\) 11.1426 0.356666
\(977\) −25.3516 −0.811068 −0.405534 0.914080i \(-0.632914\pi\)
−0.405534 + 0.914080i \(0.632914\pi\)
\(978\) 18.6435 0.596152
\(979\) 24.3546 0.778377
\(980\) −1.02449 −0.0327260
\(981\) 17.7535 0.566827
\(982\) 72.5252 2.31437
\(983\) −37.4593 −1.19477 −0.597383 0.801956i \(-0.703793\pi\)
−0.597383 + 0.801956i \(0.703793\pi\)
\(984\) −3.63150 −0.115768
\(985\) −23.5858 −0.751506
\(986\) 7.31503 0.232958
\(987\) 28.6214 0.911029
\(988\) 10.3074 0.327922
\(989\) 42.8717 1.36324
\(990\) −5.01865 −0.159503
\(991\) −22.2469 −0.706696 −0.353348 0.935492i \(-0.614957\pi\)
−0.353348 + 0.935492i \(0.614957\pi\)
\(992\) 14.8791 0.472411
\(993\) 12.7493 0.404587
\(994\) −41.3914 −1.31285
\(995\) −6.00963 −0.190518
\(996\) −12.6476 −0.400755
\(997\) 13.5803 0.430091 0.215045 0.976604i \(-0.431010\pi\)
0.215045 + 0.976604i \(0.431010\pi\)
\(998\) 37.9094 1.20000
\(999\) 5.87260 0.185801
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 \(a_p\))