Properties

Label 8041.2.a.i.1.14
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} +O(q^{10})\) \(q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} -6.60584 q^{10} +1.00000 q^{11} -1.76742 q^{12} -3.64938 q^{13} +7.27994 q^{14} -3.49462 q^{15} -4.46726 q^{16} -1.00000 q^{17} +3.77789 q^{18} -5.82980 q^{19} +5.91697 q^{20} +3.85123 q^{21} -1.93129 q^{22} +6.80071 q^{23} -0.532970 q^{24} +6.69929 q^{25} +7.04803 q^{26} +5.06365 q^{27} -6.52077 q^{28} +8.99508 q^{29} +6.74914 q^{30} +8.93511 q^{31} +7.58427 q^{32} -1.02169 q^{33} +1.93129 q^{34} -12.8932 q^{35} -3.38392 q^{36} +5.86524 q^{37} +11.2591 q^{38} +3.72854 q^{39} +1.78428 q^{40} -12.1917 q^{41} -7.43785 q^{42} -1.00000 q^{43} +1.72989 q^{44} -6.69084 q^{45} -13.1342 q^{46} -8.53866 q^{47} +4.56416 q^{48} +7.20884 q^{49} -12.9383 q^{50} +1.02169 q^{51} -6.31304 q^{52} -1.76229 q^{53} -9.77940 q^{54} +3.42042 q^{55} -1.96636 q^{56} +5.95626 q^{57} -17.3721 q^{58} -8.40601 q^{59} -6.04532 q^{60} -13.7622 q^{61} -17.2563 q^{62} +7.37361 q^{63} -5.71294 q^{64} -12.4824 q^{65} +1.97319 q^{66} +10.2727 q^{67} -1.72989 q^{68} -6.94823 q^{69} +24.9005 q^{70} +6.02117 q^{71} -1.02043 q^{72} -9.17547 q^{73} -11.3275 q^{74} -6.84462 q^{75} -10.0849 q^{76} -3.76946 q^{77} -7.20091 q^{78} -6.50847 q^{79} -15.2799 q^{80} +0.694938 q^{81} +23.5458 q^{82} +13.6004 q^{83} +6.66222 q^{84} -3.42042 q^{85} +1.93129 q^{86} -9.19021 q^{87} +0.521655 q^{88} -6.66144 q^{89} +12.9220 q^{90} +13.7562 q^{91} +11.7645 q^{92} -9.12893 q^{93} +16.4907 q^{94} -19.9404 q^{95} -7.74879 q^{96} +2.21727 q^{97} -13.9224 q^{98} -1.95614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93129 −1.36563 −0.682815 0.730591i \(-0.739245\pi\)
−0.682815 + 0.730591i \(0.739245\pi\)
\(3\) −1.02169 −0.589874 −0.294937 0.955517i \(-0.595299\pi\)
−0.294937 + 0.955517i \(0.595299\pi\)
\(4\) 1.72989 0.864947
\(5\) 3.42042 1.52966 0.764830 0.644232i \(-0.222823\pi\)
0.764830 + 0.644232i \(0.222823\pi\)
\(6\) 1.97319 0.805550
\(7\) −3.76946 −1.42472 −0.712361 0.701813i \(-0.752374\pi\)
−0.712361 + 0.701813i \(0.752374\pi\)
\(8\) 0.521655 0.184433
\(9\) −1.95614 −0.652048
\(10\) −6.60584 −2.08895
\(11\) 1.00000 0.301511
\(12\) −1.76742 −0.510210
\(13\) −3.64938 −1.01216 −0.506078 0.862488i \(-0.668905\pi\)
−0.506078 + 0.862488i \(0.668905\pi\)
\(14\) 7.27994 1.94564
\(15\) −3.49462 −0.902307
\(16\) −4.46726 −1.11681
\(17\) −1.00000 −0.242536
\(18\) 3.77789 0.890457
\(19\) −5.82980 −1.33745 −0.668724 0.743511i \(-0.733159\pi\)
−0.668724 + 0.743511i \(0.733159\pi\)
\(20\) 5.91697 1.32307
\(21\) 3.85123 0.840407
\(22\) −1.93129 −0.411753
\(23\) 6.80071 1.41805 0.709023 0.705185i \(-0.249136\pi\)
0.709023 + 0.705185i \(0.249136\pi\)
\(24\) −0.532970 −0.108792
\(25\) 6.69929 1.33986
\(26\) 7.04803 1.38223
\(27\) 5.06365 0.974501
\(28\) −6.52077 −1.23231
\(29\) 8.99508 1.67035 0.835173 0.549988i \(-0.185368\pi\)
0.835173 + 0.549988i \(0.185368\pi\)
\(30\) 6.74914 1.23222
\(31\) 8.93511 1.60479 0.802396 0.596792i \(-0.203558\pi\)
0.802396 + 0.596792i \(0.203558\pi\)
\(32\) 7.58427 1.34072
\(33\) −1.02169 −0.177854
\(34\) 1.93129 0.331214
\(35\) −12.8932 −2.17934
\(36\) −3.38392 −0.563987
\(37\) 5.86524 0.964240 0.482120 0.876105i \(-0.339867\pi\)
0.482120 + 0.876105i \(0.339867\pi\)
\(38\) 11.2591 1.82646
\(39\) 3.72854 0.597045
\(40\) 1.78428 0.282119
\(41\) −12.1917 −1.90403 −0.952016 0.306049i \(-0.900993\pi\)
−0.952016 + 0.306049i \(0.900993\pi\)
\(42\) −7.43785 −1.14769
\(43\) −1.00000 −0.152499
\(44\) 1.72989 0.260791
\(45\) −6.69084 −0.997412
\(46\) −13.1342 −1.93653
\(47\) −8.53866 −1.24549 −0.622746 0.782424i \(-0.713983\pi\)
−0.622746 + 0.782424i \(0.713983\pi\)
\(48\) 4.56416 0.658780
\(49\) 7.20884 1.02983
\(50\) −12.9383 −1.82975
\(51\) 1.02169 0.143066
\(52\) −6.31304 −0.875461
\(53\) −1.76229 −0.242070 −0.121035 0.992648i \(-0.538621\pi\)
−0.121035 + 0.992648i \(0.538621\pi\)
\(54\) −9.77940 −1.33081
\(55\) 3.42042 0.461210
\(56\) −1.96636 −0.262765
\(57\) 5.95626 0.788926
\(58\) −17.3721 −2.28107
\(59\) −8.40601 −1.09437 −0.547184 0.837012i \(-0.684300\pi\)
−0.547184 + 0.837012i \(0.684300\pi\)
\(60\) −6.04532 −0.780447
\(61\) −13.7622 −1.76207 −0.881033 0.473054i \(-0.843152\pi\)
−0.881033 + 0.473054i \(0.843152\pi\)
\(62\) −17.2563 −2.19155
\(63\) 7.37361 0.928988
\(64\) −5.71294 −0.714118
\(65\) −12.4824 −1.54825
\(66\) 1.97319 0.242883
\(67\) 10.2727 1.25501 0.627505 0.778613i \(-0.284076\pi\)
0.627505 + 0.778613i \(0.284076\pi\)
\(68\) −1.72989 −0.209780
\(69\) −6.94823 −0.836469
\(70\) 24.9005 2.97617
\(71\) 6.02117 0.714582 0.357291 0.933993i \(-0.383700\pi\)
0.357291 + 0.933993i \(0.383700\pi\)
\(72\) −1.02043 −0.120259
\(73\) −9.17547 −1.07391 −0.536954 0.843612i \(-0.680425\pi\)
−0.536954 + 0.843612i \(0.680425\pi\)
\(74\) −11.3275 −1.31680
\(75\) −6.84462 −0.790348
\(76\) −10.0849 −1.15682
\(77\) −3.76946 −0.429570
\(78\) −7.20091 −0.815343
\(79\) −6.50847 −0.732260 −0.366130 0.930564i \(-0.619317\pi\)
−0.366130 + 0.930564i \(0.619317\pi\)
\(80\) −15.2799 −1.70835
\(81\) 0.694938 0.0772153
\(82\) 23.5458 2.60020
\(83\) 13.6004 1.49284 0.746419 0.665477i \(-0.231772\pi\)
0.746419 + 0.665477i \(0.231772\pi\)
\(84\) 6.66222 0.726907
\(85\) −3.42042 −0.370997
\(86\) 1.93129 0.208257
\(87\) −9.19021 −0.985294
\(88\) 0.521655 0.0556086
\(89\) −6.66144 −0.706112 −0.353056 0.935602i \(-0.614857\pi\)
−0.353056 + 0.935602i \(0.614857\pi\)
\(90\) 12.9220 1.36210
\(91\) 13.7562 1.44204
\(92\) 11.7645 1.22653
\(93\) −9.12893 −0.946626
\(94\) 16.4907 1.70088
\(95\) −19.9404 −2.04584
\(96\) −7.74879 −0.790858
\(97\) 2.21727 0.225130 0.112565 0.993644i \(-0.464093\pi\)
0.112565 + 0.993644i \(0.464093\pi\)
\(98\) −13.9224 −1.40637
\(99\) −1.95614 −0.196600
\(100\) 11.5891 1.15891
\(101\) 5.24444 0.521841 0.260920 0.965360i \(-0.415974\pi\)
0.260920 + 0.965360i \(0.415974\pi\)
\(102\) −1.97319 −0.195375
\(103\) −9.95886 −0.981276 −0.490638 0.871364i \(-0.663236\pi\)
−0.490638 + 0.871364i \(0.663236\pi\)
\(104\) −1.90372 −0.186675
\(105\) 13.1728 1.28554
\(106\) 3.40351 0.330578
\(107\) −7.62475 −0.737113 −0.368556 0.929605i \(-0.620148\pi\)
−0.368556 + 0.929605i \(0.620148\pi\)
\(108\) 8.75958 0.842891
\(109\) 7.18893 0.688575 0.344287 0.938864i \(-0.388121\pi\)
0.344287 + 0.938864i \(0.388121\pi\)
\(110\) −6.60584 −0.629842
\(111\) −5.99247 −0.568780
\(112\) 16.8391 1.59115
\(113\) −15.6487 −1.47211 −0.736053 0.676923i \(-0.763313\pi\)
−0.736053 + 0.676923i \(0.763313\pi\)
\(114\) −11.5033 −1.07738
\(115\) 23.2613 2.16913
\(116\) 15.5605 1.44476
\(117\) 7.13872 0.659975
\(118\) 16.2345 1.49450
\(119\) 3.76946 0.345546
\(120\) −1.82298 −0.166415
\(121\) 1.00000 0.0909091
\(122\) 26.5788 2.40633
\(123\) 12.4562 1.12314
\(124\) 15.4568 1.38806
\(125\) 5.81230 0.519868
\(126\) −14.2406 −1.26865
\(127\) −10.1601 −0.901564 −0.450782 0.892634i \(-0.648855\pi\)
−0.450782 + 0.892634i \(0.648855\pi\)
\(128\) −4.13518 −0.365502
\(129\) 1.02169 0.0899550
\(130\) 24.1072 2.11434
\(131\) 8.02982 0.701568 0.350784 0.936456i \(-0.385915\pi\)
0.350784 + 0.936456i \(0.385915\pi\)
\(132\) −1.76742 −0.153834
\(133\) 21.9752 1.90549
\(134\) −19.8396 −1.71388
\(135\) 17.3198 1.49065
\(136\) −0.521655 −0.0447315
\(137\) −11.7124 −1.00065 −0.500327 0.865836i \(-0.666787\pi\)
−0.500327 + 0.865836i \(0.666787\pi\)
\(138\) 13.4191 1.14231
\(139\) 5.23493 0.444021 0.222010 0.975044i \(-0.428738\pi\)
0.222010 + 0.975044i \(0.428738\pi\)
\(140\) −22.3038 −1.88501
\(141\) 8.72388 0.734683
\(142\) −11.6287 −0.975855
\(143\) −3.64938 −0.305177
\(144\) 8.73860 0.728217
\(145\) 30.7670 2.55506
\(146\) 17.7205 1.46656
\(147\) −7.36521 −0.607473
\(148\) 10.1462 0.834016
\(149\) −0.961166 −0.0787418 −0.0393709 0.999225i \(-0.512535\pi\)
−0.0393709 + 0.999225i \(0.512535\pi\)
\(150\) 13.2190 1.07932
\(151\) −17.0146 −1.38463 −0.692315 0.721595i \(-0.743409\pi\)
−0.692315 + 0.721595i \(0.743409\pi\)
\(152\) −3.04114 −0.246669
\(153\) 1.95614 0.158145
\(154\) 7.27994 0.586634
\(155\) 30.5618 2.45479
\(156\) 6.44999 0.516412
\(157\) 22.4675 1.79311 0.896553 0.442937i \(-0.146064\pi\)
0.896553 + 0.442937i \(0.146064\pi\)
\(158\) 12.5698 0.999997
\(159\) 1.80052 0.142791
\(160\) 25.9414 2.05085
\(161\) −25.6350 −2.02032
\(162\) −1.34213 −0.105448
\(163\) −13.4178 −1.05096 −0.525481 0.850805i \(-0.676115\pi\)
−0.525481 + 0.850805i \(0.676115\pi\)
\(164\) −21.0904 −1.64689
\(165\) −3.49462 −0.272056
\(166\) −26.2664 −2.03866
\(167\) −7.54783 −0.584068 −0.292034 0.956408i \(-0.594332\pi\)
−0.292034 + 0.956408i \(0.594332\pi\)
\(168\) 2.00901 0.154999
\(169\) 0.317983 0.0244602
\(170\) 6.60584 0.506645
\(171\) 11.4039 0.872081
\(172\) −1.72989 −0.131903
\(173\) 8.09816 0.615692 0.307846 0.951436i \(-0.400392\pi\)
0.307846 + 0.951436i \(0.400392\pi\)
\(174\) 17.7490 1.34555
\(175\) −25.2527 −1.90893
\(176\) −4.46726 −0.336732
\(177\) 8.58835 0.645540
\(178\) 12.8652 0.964287
\(179\) −2.36120 −0.176484 −0.0882422 0.996099i \(-0.528125\pi\)
−0.0882422 + 0.996099i \(0.528125\pi\)
\(180\) −11.5744 −0.862708
\(181\) 15.5183 1.15346 0.576732 0.816933i \(-0.304328\pi\)
0.576732 + 0.816933i \(0.304328\pi\)
\(182\) −26.5673 −1.96930
\(183\) 14.0607 1.03940
\(184\) 3.54762 0.261534
\(185\) 20.0616 1.47496
\(186\) 17.6306 1.29274
\(187\) −1.00000 −0.0731272
\(188\) −14.7710 −1.07728
\(189\) −19.0873 −1.38839
\(190\) 38.5107 2.79386
\(191\) 17.0247 1.23187 0.615934 0.787798i \(-0.288779\pi\)
0.615934 + 0.787798i \(0.288779\pi\)
\(192\) 5.83687 0.421240
\(193\) 18.9266 1.36237 0.681185 0.732111i \(-0.261465\pi\)
0.681185 + 0.732111i \(0.261465\pi\)
\(194\) −4.28220 −0.307444
\(195\) 12.7532 0.913276
\(196\) 12.4705 0.890752
\(197\) −15.9397 −1.13566 −0.567828 0.823147i \(-0.692216\pi\)
−0.567828 + 0.823147i \(0.692216\pi\)
\(198\) 3.77789 0.268483
\(199\) 9.77181 0.692705 0.346353 0.938104i \(-0.387420\pi\)
0.346353 + 0.938104i \(0.387420\pi\)
\(200\) 3.49472 0.247114
\(201\) −10.4955 −0.740298
\(202\) −10.1285 −0.712642
\(203\) −33.9066 −2.37978
\(204\) 1.76742 0.123744
\(205\) −41.7009 −2.91252
\(206\) 19.2335 1.34006
\(207\) −13.3032 −0.924635
\(208\) 16.3027 1.13039
\(209\) −5.82980 −0.403256
\(210\) −25.4406 −1.75557
\(211\) 22.1858 1.52733 0.763667 0.645610i \(-0.223397\pi\)
0.763667 + 0.645610i \(0.223397\pi\)
\(212\) −3.04858 −0.209377
\(213\) −6.15179 −0.421513
\(214\) 14.7256 1.00662
\(215\) −3.42042 −0.233271
\(216\) 2.64148 0.179730
\(217\) −33.6805 −2.28638
\(218\) −13.8839 −0.940338
\(219\) 9.37451 0.633470
\(220\) 5.91697 0.398922
\(221\) 3.64938 0.245484
\(222\) 11.5732 0.776744
\(223\) −21.8547 −1.46350 −0.731750 0.681573i \(-0.761296\pi\)
−0.731750 + 0.681573i \(0.761296\pi\)
\(224\) −28.5886 −1.91016
\(225\) −13.1048 −0.873653
\(226\) 30.2222 2.01035
\(227\) 5.06855 0.336411 0.168206 0.985752i \(-0.446203\pi\)
0.168206 + 0.985752i \(0.446203\pi\)
\(228\) 10.3037 0.682379
\(229\) 0.194465 0.0128506 0.00642531 0.999979i \(-0.497955\pi\)
0.00642531 + 0.999979i \(0.497955\pi\)
\(230\) −44.9244 −2.96223
\(231\) 3.85123 0.253392
\(232\) 4.69233 0.308066
\(233\) −23.3548 −1.53002 −0.765011 0.644018i \(-0.777266\pi\)
−0.765011 + 0.644018i \(0.777266\pi\)
\(234\) −13.7870 −0.901282
\(235\) −29.2058 −1.90518
\(236\) −14.5415 −0.946571
\(237\) 6.64965 0.431941
\(238\) −7.27994 −0.471888
\(239\) 13.9058 0.899492 0.449746 0.893157i \(-0.351515\pi\)
0.449746 + 0.893157i \(0.351515\pi\)
\(240\) 15.6114 1.00771
\(241\) 19.5543 1.25960 0.629800 0.776757i \(-0.283137\pi\)
0.629800 + 0.776757i \(0.283137\pi\)
\(242\) −1.93129 −0.124148
\(243\) −15.9010 −1.02005
\(244\) −23.8071 −1.52409
\(245\) 24.6573 1.57530
\(246\) −24.0566 −1.53379
\(247\) 21.2752 1.35371
\(248\) 4.66104 0.295976
\(249\) −13.8954 −0.880586
\(250\) −11.2253 −0.709948
\(251\) −11.3731 −0.717865 −0.358932 0.933364i \(-0.616859\pi\)
−0.358932 + 0.933364i \(0.616859\pi\)
\(252\) 12.7556 0.803525
\(253\) 6.80071 0.427557
\(254\) 19.6222 1.23120
\(255\) 3.49462 0.218842
\(256\) 19.4121 1.21326
\(257\) 13.8509 0.863995 0.431998 0.901875i \(-0.357809\pi\)
0.431998 + 0.901875i \(0.357809\pi\)
\(258\) −1.97319 −0.122845
\(259\) −22.1088 −1.37377
\(260\) −21.5933 −1.33916
\(261\) −17.5957 −1.08915
\(262\) −15.5079 −0.958083
\(263\) 0.255501 0.0157549 0.00787743 0.999969i \(-0.497493\pi\)
0.00787743 + 0.999969i \(0.497493\pi\)
\(264\) −0.532970 −0.0328021
\(265\) −6.02779 −0.370284
\(266\) −42.4406 −2.60220
\(267\) 6.80594 0.416517
\(268\) 17.7707 1.08552
\(269\) −12.2374 −0.746129 −0.373065 0.927805i \(-0.621693\pi\)
−0.373065 + 0.927805i \(0.621693\pi\)
\(270\) −33.4497 −2.03568
\(271\) 18.3874 1.11696 0.558478 0.829519i \(-0.311385\pi\)
0.558478 + 0.829519i \(0.311385\pi\)
\(272\) 4.46726 0.270867
\(273\) −14.0546 −0.850623
\(274\) 22.6200 1.36652
\(275\) 6.69929 0.403983
\(276\) −12.0197 −0.723501
\(277\) 14.1613 0.850872 0.425436 0.904988i \(-0.360121\pi\)
0.425436 + 0.904988i \(0.360121\pi\)
\(278\) −10.1102 −0.606369
\(279\) −17.4784 −1.04640
\(280\) −6.72577 −0.401942
\(281\) 0.898035 0.0535723 0.0267861 0.999641i \(-0.491473\pi\)
0.0267861 + 0.999641i \(0.491473\pi\)
\(282\) −16.8484 −1.00331
\(283\) −2.41574 −0.143601 −0.0718003 0.997419i \(-0.522874\pi\)
−0.0718003 + 0.997419i \(0.522874\pi\)
\(284\) 10.4160 0.618075
\(285\) 20.3729 1.20679
\(286\) 7.04803 0.416758
\(287\) 45.9563 2.71272
\(288\) −14.8359 −0.874216
\(289\) 1.00000 0.0588235
\(290\) −59.4201 −3.48927
\(291\) −2.26537 −0.132798
\(292\) −15.8726 −0.928873
\(293\) 8.41438 0.491573 0.245787 0.969324i \(-0.420954\pi\)
0.245787 + 0.969324i \(0.420954\pi\)
\(294\) 14.2244 0.829583
\(295\) −28.7521 −1.67401
\(296\) 3.05963 0.177837
\(297\) 5.06365 0.293823
\(298\) 1.85629 0.107532
\(299\) −24.8184 −1.43528
\(300\) −11.8405 −0.683609
\(301\) 3.76946 0.217268
\(302\) 32.8602 1.89089
\(303\) −5.35820 −0.307821
\(304\) 26.0432 1.49368
\(305\) −47.0725 −2.69536
\(306\) −3.77789 −0.215968
\(307\) 24.0642 1.37342 0.686708 0.726933i \(-0.259055\pi\)
0.686708 + 0.726933i \(0.259055\pi\)
\(308\) −6.52077 −0.371555
\(309\) 10.1749 0.578829
\(310\) −59.0239 −3.35233
\(311\) 31.5879 1.79119 0.895593 0.444875i \(-0.146752\pi\)
0.895593 + 0.444875i \(0.146752\pi\)
\(312\) 1.94501 0.110115
\(313\) −13.9224 −0.786943 −0.393472 0.919337i \(-0.628726\pi\)
−0.393472 + 0.919337i \(0.628726\pi\)
\(314\) −43.3914 −2.44872
\(315\) 25.2209 1.42104
\(316\) −11.2590 −0.633366
\(317\) −6.38616 −0.358682 −0.179341 0.983787i \(-0.557397\pi\)
−0.179341 + 0.983787i \(0.557397\pi\)
\(318\) −3.47734 −0.194999
\(319\) 8.99508 0.503628
\(320\) −19.5407 −1.09236
\(321\) 7.79015 0.434804
\(322\) 49.5087 2.75901
\(323\) 5.82980 0.324379
\(324\) 1.20217 0.0667872
\(325\) −24.4483 −1.35615
\(326\) 25.9137 1.43523
\(327\) −7.34487 −0.406172
\(328\) −6.35988 −0.351166
\(329\) 32.1861 1.77448
\(330\) 6.74914 0.371528
\(331\) 22.9611 1.26205 0.631027 0.775761i \(-0.282634\pi\)
0.631027 + 0.775761i \(0.282634\pi\)
\(332\) 23.5272 1.29122
\(333\) −11.4733 −0.628731
\(334\) 14.5771 0.797622
\(335\) 35.1370 1.91974
\(336\) −17.2044 −0.938578
\(337\) 13.3485 0.727141 0.363570 0.931567i \(-0.381558\pi\)
0.363570 + 0.931567i \(0.381558\pi\)
\(338\) −0.614118 −0.0334036
\(339\) 15.9882 0.868358
\(340\) −5.91697 −0.320893
\(341\) 8.93511 0.483863
\(342\) −22.0243 −1.19094
\(343\) −0.787207 −0.0425052
\(344\) −0.521655 −0.0281257
\(345\) −23.7659 −1.27951
\(346\) −15.6399 −0.840807
\(347\) 1.90774 0.102413 0.0512065 0.998688i \(-0.483693\pi\)
0.0512065 + 0.998688i \(0.483693\pi\)
\(348\) −15.8981 −0.852227
\(349\) −1.79108 −0.0958746 −0.0479373 0.998850i \(-0.515265\pi\)
−0.0479373 + 0.998850i \(0.515265\pi\)
\(350\) 48.7704 2.60689
\(351\) −18.4792 −0.986347
\(352\) 7.58427 0.404243
\(353\) −4.88142 −0.259812 −0.129906 0.991526i \(-0.541468\pi\)
−0.129906 + 0.991526i \(0.541468\pi\)
\(354\) −16.5866 −0.881569
\(355\) 20.5950 1.09307
\(356\) −11.5236 −0.610749
\(357\) −3.85123 −0.203829
\(358\) 4.56017 0.241013
\(359\) 31.9392 1.68568 0.842842 0.538161i \(-0.180881\pi\)
0.842842 + 0.538161i \(0.180881\pi\)
\(360\) −3.49031 −0.183955
\(361\) 14.9866 0.788767
\(362\) −29.9704 −1.57521
\(363\) −1.02169 −0.0536249
\(364\) 23.7968 1.24729
\(365\) −31.3840 −1.64271
\(366\) −27.1554 −1.41943
\(367\) 3.54576 0.185087 0.0925435 0.995709i \(-0.470500\pi\)
0.0925435 + 0.995709i \(0.470500\pi\)
\(368\) −30.3805 −1.58369
\(369\) 23.8488 1.24152
\(370\) −38.7449 −2.01425
\(371\) 6.64290 0.344882
\(372\) −15.7921 −0.818781
\(373\) −9.40947 −0.487204 −0.243602 0.969875i \(-0.578329\pi\)
−0.243602 + 0.969875i \(0.578329\pi\)
\(374\) 1.93129 0.0998648
\(375\) −5.93838 −0.306657
\(376\) −4.45423 −0.229709
\(377\) −32.8265 −1.69065
\(378\) 36.8631 1.89603
\(379\) −4.19081 −0.215267 −0.107634 0.994191i \(-0.534327\pi\)
−0.107634 + 0.994191i \(0.534327\pi\)
\(380\) −34.4947 −1.76954
\(381\) 10.3805 0.531809
\(382\) −32.8798 −1.68228
\(383\) 1.80572 0.0922680 0.0461340 0.998935i \(-0.485310\pi\)
0.0461340 + 0.998935i \(0.485310\pi\)
\(384\) 4.22488 0.215600
\(385\) −12.8932 −0.657096
\(386\) −36.5529 −1.86049
\(387\) 1.95614 0.0994364
\(388\) 3.83565 0.194725
\(389\) 6.60879 0.335079 0.167539 0.985865i \(-0.446418\pi\)
0.167539 + 0.985865i \(0.446418\pi\)
\(390\) −24.6302 −1.24720
\(391\) −6.80071 −0.343927
\(392\) 3.76052 0.189935
\(393\) −8.20400 −0.413837
\(394\) 30.7842 1.55089
\(395\) −22.2617 −1.12011
\(396\) −3.38392 −0.170049
\(397\) −31.2363 −1.56770 −0.783851 0.620948i \(-0.786748\pi\)
−0.783851 + 0.620948i \(0.786748\pi\)
\(398\) −18.8722 −0.945980
\(399\) −22.4519 −1.12400
\(400\) −29.9275 −1.49637
\(401\) 17.7698 0.887381 0.443690 0.896180i \(-0.353669\pi\)
0.443690 + 0.896180i \(0.353669\pi\)
\(402\) 20.2700 1.01097
\(403\) −32.6076 −1.62430
\(404\) 9.07232 0.451365
\(405\) 2.37698 0.118113
\(406\) 65.4836 3.24990
\(407\) 5.86524 0.290729
\(408\) 0.532970 0.0263860
\(409\) 17.4893 0.864793 0.432396 0.901684i \(-0.357668\pi\)
0.432396 + 0.901684i \(0.357668\pi\)
\(410\) 80.5367 3.97743
\(411\) 11.9664 0.590260
\(412\) −17.2278 −0.848751
\(413\) 31.6861 1.55917
\(414\) 25.6923 1.26271
\(415\) 46.5191 2.28353
\(416\) −27.6779 −1.35702
\(417\) −5.34849 −0.261917
\(418\) 11.2591 0.550698
\(419\) 20.4807 1.00055 0.500274 0.865867i \(-0.333233\pi\)
0.500274 + 0.865867i \(0.333233\pi\)
\(420\) 22.7876 1.11192
\(421\) 9.21966 0.449339 0.224669 0.974435i \(-0.427870\pi\)
0.224669 + 0.974435i \(0.427870\pi\)
\(422\) −42.8473 −2.08578
\(423\) 16.7029 0.812121
\(424\) −0.919309 −0.0446456
\(425\) −6.69929 −0.324963
\(426\) 11.8809 0.575632
\(427\) 51.8760 2.51046
\(428\) −13.1900 −0.637563
\(429\) 3.72854 0.180016
\(430\) 6.60584 0.318562
\(431\) −12.7939 −0.616261 −0.308130 0.951344i \(-0.599703\pi\)
−0.308130 + 0.951344i \(0.599703\pi\)
\(432\) −22.6206 −1.08834
\(433\) −32.6914 −1.57105 −0.785524 0.618831i \(-0.787607\pi\)
−0.785524 + 0.618831i \(0.787607\pi\)
\(434\) 65.0470 3.12236
\(435\) −31.4344 −1.50716
\(436\) 12.4361 0.595580
\(437\) −39.6468 −1.89656
\(438\) −18.1049 −0.865086
\(439\) −37.1147 −1.77139 −0.885695 0.464267i \(-0.846318\pi\)
−0.885695 + 0.464267i \(0.846318\pi\)
\(440\) 1.78428 0.0850622
\(441\) −14.1015 −0.671502
\(442\) −7.04803 −0.335240
\(443\) 5.41595 0.257319 0.128660 0.991689i \(-0.458933\pi\)
0.128660 + 0.991689i \(0.458933\pi\)
\(444\) −10.3663 −0.491965
\(445\) −22.7850 −1.08011
\(446\) 42.2079 1.99860
\(447\) 0.982016 0.0464478
\(448\) 21.5347 1.01742
\(449\) −0.222969 −0.0105226 −0.00526129 0.999986i \(-0.501675\pi\)
−0.00526129 + 0.999986i \(0.501675\pi\)
\(450\) 25.3092 1.19309
\(451\) −12.1917 −0.574087
\(452\) −27.0706 −1.27329
\(453\) 17.3837 0.816758
\(454\) −9.78885 −0.459413
\(455\) 47.0520 2.20583
\(456\) 3.10711 0.145504
\(457\) 20.6408 0.965537 0.482769 0.875748i \(-0.339631\pi\)
0.482769 + 0.875748i \(0.339631\pi\)
\(458\) −0.375569 −0.0175492
\(459\) −5.06365 −0.236351
\(460\) 40.2396 1.87618
\(461\) 4.38320 0.204146 0.102073 0.994777i \(-0.467452\pi\)
0.102073 + 0.994777i \(0.467452\pi\)
\(462\) −7.43785 −0.346040
\(463\) 18.8999 0.878351 0.439176 0.898401i \(-0.355271\pi\)
0.439176 + 0.898401i \(0.355271\pi\)
\(464\) −40.1833 −1.86546
\(465\) −31.2248 −1.44802
\(466\) 45.1049 2.08944
\(467\) 34.8619 1.61322 0.806609 0.591085i \(-0.201300\pi\)
0.806609 + 0.591085i \(0.201300\pi\)
\(468\) 12.3492 0.570843
\(469\) −38.7225 −1.78804
\(470\) 56.4050 2.60177
\(471\) −22.9549 −1.05771
\(472\) −4.38503 −0.201837
\(473\) −1.00000 −0.0459800
\(474\) −12.8424 −0.589872
\(475\) −39.0555 −1.79199
\(476\) 6.52077 0.298879
\(477\) 3.44730 0.157841
\(478\) −26.8562 −1.22837
\(479\) 19.7107 0.900607 0.450304 0.892876i \(-0.351316\pi\)
0.450304 + 0.892876i \(0.351316\pi\)
\(480\) −26.5041 −1.20974
\(481\) −21.4045 −0.975962
\(482\) −37.7650 −1.72015
\(483\) 26.1911 1.19174
\(484\) 1.72989 0.0786315
\(485\) 7.58401 0.344372
\(486\) 30.7095 1.39301
\(487\) −22.3747 −1.01389 −0.506947 0.861977i \(-0.669226\pi\)
−0.506947 + 0.861977i \(0.669226\pi\)
\(488\) −7.17910 −0.324983
\(489\) 13.7089 0.619936
\(490\) −47.6204 −2.15127
\(491\) 33.7975 1.52526 0.762630 0.646835i \(-0.223908\pi\)
0.762630 + 0.646835i \(0.223908\pi\)
\(492\) 21.5479 0.971456
\(493\) −8.99508 −0.405118
\(494\) −41.0886 −1.84866
\(495\) −6.69084 −0.300731
\(496\) −39.9154 −1.79225
\(497\) −22.6966 −1.01808
\(498\) 26.8361 1.20256
\(499\) 24.7803 1.10932 0.554659 0.832078i \(-0.312849\pi\)
0.554659 + 0.832078i \(0.312849\pi\)
\(500\) 10.0547 0.449658
\(501\) 7.71156 0.344527
\(502\) 21.9648 0.980338
\(503\) 24.6990 1.10127 0.550636 0.834745i \(-0.314385\pi\)
0.550636 + 0.834745i \(0.314385\pi\)
\(504\) 3.84648 0.171336
\(505\) 17.9382 0.798239
\(506\) −13.1342 −0.583885
\(507\) −0.324881 −0.0144285
\(508\) −17.5759 −0.779805
\(509\) 2.71097 0.120161 0.0600807 0.998194i \(-0.480864\pi\)
0.0600807 + 0.998194i \(0.480864\pi\)
\(510\) −6.74914 −0.298857
\(511\) 34.5866 1.53002
\(512\) −29.2201 −1.29136
\(513\) −29.5201 −1.30334
\(514\) −26.7501 −1.17990
\(515\) −34.0635 −1.50102
\(516\) 1.76742 0.0778063
\(517\) −8.53866 −0.375530
\(518\) 42.6986 1.87607
\(519\) −8.27383 −0.363181
\(520\) −6.51151 −0.285549
\(521\) −27.3984 −1.20035 −0.600174 0.799870i \(-0.704902\pi\)
−0.600174 + 0.799870i \(0.704902\pi\)
\(522\) 33.9824 1.48737
\(523\) 3.46716 0.151608 0.0758042 0.997123i \(-0.475848\pi\)
0.0758042 + 0.997123i \(0.475848\pi\)
\(524\) 13.8907 0.606819
\(525\) 25.8005 1.12603
\(526\) −0.493447 −0.0215153
\(527\) −8.93511 −0.389219
\(528\) 4.56416 0.198630
\(529\) 23.2497 1.01086
\(530\) 11.6414 0.505672
\(531\) 16.4434 0.713581
\(532\) 38.0148 1.64815
\(533\) 44.4923 1.92718
\(534\) −13.1443 −0.568808
\(535\) −26.0799 −1.12753
\(536\) 5.35880 0.231465
\(537\) 2.41242 0.104104
\(538\) 23.6341 1.01894
\(539\) 7.20884 0.310507
\(540\) 29.9615 1.28934
\(541\) 26.8951 1.15631 0.578156 0.815926i \(-0.303773\pi\)
0.578156 + 0.815926i \(0.303773\pi\)
\(542\) −35.5115 −1.52535
\(543\) −15.8549 −0.680399
\(544\) −7.58427 −0.325173
\(545\) 24.5892 1.05328
\(546\) 27.1436 1.16164
\(547\) −9.20692 −0.393660 −0.196830 0.980438i \(-0.563065\pi\)
−0.196830 + 0.980438i \(0.563065\pi\)
\(548\) −20.2611 −0.865513
\(549\) 26.9208 1.14895
\(550\) −12.9383 −0.551691
\(551\) −52.4395 −2.23400
\(552\) −3.62458 −0.154272
\(553\) 24.5334 1.04327
\(554\) −27.3497 −1.16198
\(555\) −20.4968 −0.870040
\(556\) 9.05587 0.384055
\(557\) −42.2262 −1.78918 −0.894591 0.446886i \(-0.852533\pi\)
−0.894591 + 0.446886i \(0.852533\pi\)
\(558\) 33.7558 1.42900
\(559\) 3.64938 0.154352
\(560\) 57.5970 2.43392
\(561\) 1.02169 0.0431359
\(562\) −1.73437 −0.0731599
\(563\) 41.5016 1.74908 0.874541 0.484952i \(-0.161163\pi\)
0.874541 + 0.484952i \(0.161163\pi\)
\(564\) 15.0914 0.635462
\(565\) −53.5252 −2.25182
\(566\) 4.66549 0.196105
\(567\) −2.61954 −0.110010
\(568\) 3.14097 0.131792
\(569\) 5.80289 0.243270 0.121635 0.992575i \(-0.461186\pi\)
0.121635 + 0.992575i \(0.461186\pi\)
\(570\) −39.3461 −1.64803
\(571\) −9.85080 −0.412243 −0.206121 0.978526i \(-0.566084\pi\)
−0.206121 + 0.978526i \(0.566084\pi\)
\(572\) −6.31304 −0.263962
\(573\) −17.3941 −0.726647
\(574\) −88.7551 −3.70457
\(575\) 45.5600 1.89998
\(576\) 11.1753 0.465639
\(577\) −18.3695 −0.764732 −0.382366 0.924011i \(-0.624891\pi\)
−0.382366 + 0.924011i \(0.624891\pi\)
\(578\) −1.93129 −0.0803312
\(579\) −19.3372 −0.803627
\(580\) 53.2236 2.20999
\(581\) −51.2662 −2.12688
\(582\) 4.37509 0.181353
\(583\) −1.76229 −0.0729868
\(584\) −4.78642 −0.198064
\(585\) 24.4174 1.00954
\(586\) −16.2506 −0.671308
\(587\) 3.33679 0.137724 0.0688621 0.997626i \(-0.478063\pi\)
0.0688621 + 0.997626i \(0.478063\pi\)
\(588\) −12.7410 −0.525431
\(589\) −52.0899 −2.14633
\(590\) 55.5287 2.28608
\(591\) 16.2855 0.669895
\(592\) −26.2015 −1.07688
\(593\) 26.1905 1.07551 0.537757 0.843100i \(-0.319272\pi\)
0.537757 + 0.843100i \(0.319272\pi\)
\(594\) −9.77940 −0.401254
\(595\) 12.8932 0.528568
\(596\) −1.66272 −0.0681075
\(597\) −9.98379 −0.408609
\(598\) 47.9316 1.96007
\(599\) 20.4406 0.835182 0.417591 0.908635i \(-0.362874\pi\)
0.417591 + 0.908635i \(0.362874\pi\)
\(600\) −3.57052 −0.145766
\(601\) 0.260039 0.0106072 0.00530360 0.999986i \(-0.498312\pi\)
0.00530360 + 0.999986i \(0.498312\pi\)
\(602\) −7.27994 −0.296708
\(603\) −20.0949 −0.818327
\(604\) −29.4335 −1.19763
\(605\) 3.42042 0.139060
\(606\) 10.3483 0.420369
\(607\) 4.00843 0.162697 0.0813485 0.996686i \(-0.474077\pi\)
0.0813485 + 0.996686i \(0.474077\pi\)
\(608\) −44.2148 −1.79315
\(609\) 34.6421 1.40377
\(610\) 90.9108 3.68087
\(611\) 31.1608 1.26063
\(612\) 3.38392 0.136787
\(613\) 39.2250 1.58428 0.792141 0.610338i \(-0.208966\pi\)
0.792141 + 0.610338i \(0.208966\pi\)
\(614\) −46.4750 −1.87558
\(615\) 42.6055 1.71802
\(616\) −1.96636 −0.0792268
\(617\) −17.2989 −0.696428 −0.348214 0.937415i \(-0.613212\pi\)
−0.348214 + 0.937415i \(0.613212\pi\)
\(618\) −19.6507 −0.790467
\(619\) −25.2206 −1.01370 −0.506850 0.862034i \(-0.669190\pi\)
−0.506850 + 0.862034i \(0.669190\pi\)
\(620\) 52.8687 2.12326
\(621\) 34.4365 1.38189
\(622\) −61.0055 −2.44610
\(623\) 25.1101 1.00601
\(624\) −16.6564 −0.666788
\(625\) −13.6159 −0.544638
\(626\) 26.8883 1.07467
\(627\) 5.95626 0.237870
\(628\) 38.8665 1.55094
\(629\) −5.86524 −0.233863
\(630\) −48.7089 −1.94061
\(631\) 31.7362 1.26340 0.631699 0.775214i \(-0.282358\pi\)
0.631699 + 0.775214i \(0.282358\pi\)
\(632\) −3.39517 −0.135053
\(633\) −22.6671 −0.900936
\(634\) 12.3335 0.489827
\(635\) −34.7519 −1.37909
\(636\) 3.11471 0.123506
\(637\) −26.3078 −1.04235
\(638\) −17.3721 −0.687770
\(639\) −11.7783 −0.465942
\(640\) −14.1441 −0.559093
\(641\) 6.15248 0.243008 0.121504 0.992591i \(-0.461228\pi\)
0.121504 + 0.992591i \(0.461228\pi\)
\(642\) −15.0451 −0.593781
\(643\) 12.4271 0.490077 0.245039 0.969513i \(-0.421199\pi\)
0.245039 + 0.969513i \(0.421199\pi\)
\(644\) −44.3459 −1.74747
\(645\) 3.49462 0.137601
\(646\) −11.2591 −0.442982
\(647\) −34.7380 −1.36569 −0.682845 0.730563i \(-0.739258\pi\)
−0.682845 + 0.730563i \(0.739258\pi\)
\(648\) 0.362518 0.0142410
\(649\) −8.40601 −0.329965
\(650\) 47.2168 1.85199
\(651\) 34.4111 1.34868
\(652\) −23.2114 −0.909027
\(653\) −17.7273 −0.693722 −0.346861 0.937917i \(-0.612752\pi\)
−0.346861 + 0.937917i \(0.612752\pi\)
\(654\) 14.1851 0.554681
\(655\) 27.4654 1.07316
\(656\) 54.4637 2.12645
\(657\) 17.9485 0.700240
\(658\) −62.1609 −2.42328
\(659\) 33.4208 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(660\) −6.04532 −0.235314
\(661\) 36.1367 1.40556 0.702778 0.711409i \(-0.251943\pi\)
0.702778 + 0.711409i \(0.251943\pi\)
\(662\) −44.3445 −1.72350
\(663\) −3.72854 −0.144805
\(664\) 7.09471 0.275328
\(665\) 75.1645 2.91475
\(666\) 22.1582 0.858614
\(667\) 61.1730 2.36863
\(668\) −13.0569 −0.505188
\(669\) 22.3288 0.863281
\(670\) −67.8598 −2.62165
\(671\) −13.7622 −0.531283
\(672\) 29.2088 1.12675
\(673\) −7.49134 −0.288770 −0.144385 0.989522i \(-0.546120\pi\)
−0.144385 + 0.989522i \(0.546120\pi\)
\(674\) −25.7799 −0.993006
\(675\) 33.9229 1.30569
\(676\) 0.550077 0.0211568
\(677\) −24.2124 −0.930559 −0.465279 0.885164i \(-0.654046\pi\)
−0.465279 + 0.885164i \(0.654046\pi\)
\(678\) −30.8778 −1.18586
\(679\) −8.35792 −0.320748
\(680\) −1.78428 −0.0684240
\(681\) −5.17849 −0.198440
\(682\) −17.2563 −0.660778
\(683\) 18.4436 0.705724 0.352862 0.935675i \(-0.385208\pi\)
0.352862 + 0.935675i \(0.385208\pi\)
\(684\) 19.7276 0.754303
\(685\) −40.0612 −1.53066
\(686\) 1.52033 0.0580464
\(687\) −0.198683 −0.00758025
\(688\) 4.46726 0.170313
\(689\) 6.43128 0.245012
\(690\) 45.8989 1.74734
\(691\) 42.2587 1.60760 0.803799 0.594902i \(-0.202809\pi\)
0.803799 + 0.594902i \(0.202809\pi\)
\(692\) 14.0090 0.532540
\(693\) 7.37361 0.280100
\(694\) −3.68441 −0.139858
\(695\) 17.9057 0.679201
\(696\) −4.79411 −0.181720
\(697\) 12.1917 0.461795
\(698\) 3.45911 0.130929
\(699\) 23.8614 0.902520
\(700\) −43.6845 −1.65112
\(701\) 15.2137 0.574613 0.287306 0.957839i \(-0.407240\pi\)
0.287306 + 0.957839i \(0.407240\pi\)
\(702\) 35.6888 1.34699
\(703\) −34.1932 −1.28962
\(704\) −5.71294 −0.215315
\(705\) 29.8394 1.12382
\(706\) 9.42746 0.354807
\(707\) −19.7687 −0.743479
\(708\) 14.8569 0.558358
\(709\) 16.0512 0.602814 0.301407 0.953496i \(-0.402544\pi\)
0.301407 + 0.953496i \(0.402544\pi\)
\(710\) −39.7749 −1.49273
\(711\) 12.7315 0.477469
\(712\) −3.47497 −0.130230
\(713\) 60.7651 2.27567
\(714\) 7.43785 0.278355
\(715\) −12.4824 −0.466816
\(716\) −4.08463 −0.152650
\(717\) −14.2075 −0.530587
\(718\) −61.6839 −2.30202
\(719\) −10.4185 −0.388543 −0.194271 0.980948i \(-0.562234\pi\)
−0.194271 + 0.980948i \(0.562234\pi\)
\(720\) 29.8897 1.11392
\(721\) 37.5395 1.39805
\(722\) −28.9435 −1.07716
\(723\) −19.9784 −0.743006
\(724\) 26.8450 0.997686
\(725\) 60.2607 2.23803
\(726\) 1.97319 0.0732319
\(727\) 17.2552 0.639960 0.319980 0.947424i \(-0.396324\pi\)
0.319980 + 0.947424i \(0.396324\pi\)
\(728\) 7.17598 0.265960
\(729\) 14.1611 0.524485
\(730\) 60.6117 2.24334
\(731\) 1.00000 0.0369863
\(732\) 24.3235 0.899024
\(733\) −46.1287 −1.70380 −0.851901 0.523703i \(-0.824550\pi\)
−0.851901 + 0.523703i \(0.824550\pi\)
\(734\) −6.84790 −0.252761
\(735\) −25.1921 −0.929226
\(736\) 51.5784 1.90121
\(737\) 10.2727 0.378400
\(738\) −46.0591 −1.69546
\(739\) 17.2437 0.634319 0.317159 0.948372i \(-0.397271\pi\)
0.317159 + 0.948372i \(0.397271\pi\)
\(740\) 34.7045 1.27576
\(741\) −21.7367 −0.798517
\(742\) −12.8294 −0.470982
\(743\) −21.1967 −0.777633 −0.388816 0.921315i \(-0.627116\pi\)
−0.388816 + 0.921315i \(0.627116\pi\)
\(744\) −4.76215 −0.174589
\(745\) −3.28759 −0.120448
\(746\) 18.1724 0.665340
\(747\) −26.6043 −0.973402
\(748\) −1.72989 −0.0632512
\(749\) 28.7412 1.05018
\(750\) 11.4688 0.418780
\(751\) 43.5191 1.58804 0.794018 0.607894i \(-0.207986\pi\)
0.794018 + 0.607894i \(0.207986\pi\)
\(752\) 38.1444 1.39098
\(753\) 11.6198 0.423450
\(754\) 63.3976 2.30880
\(755\) −58.1972 −2.11801
\(756\) −33.0189 −1.20089
\(757\) −27.8734 −1.01308 −0.506538 0.862217i \(-0.669075\pi\)
−0.506538 + 0.862217i \(0.669075\pi\)
\(758\) 8.09368 0.293976
\(759\) −6.94823 −0.252205
\(760\) −10.4020 −0.377320
\(761\) −47.8990 −1.73634 −0.868169 0.496269i \(-0.834703\pi\)
−0.868169 + 0.496269i \(0.834703\pi\)
\(762\) −20.0478 −0.726255
\(763\) −27.0984 −0.981028
\(764\) 29.4510 1.06550
\(765\) 6.69084 0.241908
\(766\) −3.48737 −0.126004
\(767\) 30.6767 1.10767
\(768\) −19.8332 −0.715669
\(769\) −34.7810 −1.25423 −0.627117 0.778925i \(-0.715765\pi\)
−0.627117 + 0.778925i \(0.715765\pi\)
\(770\) 24.9005 0.897350
\(771\) −14.1514 −0.509649
\(772\) 32.7411 1.17838
\(773\) 27.7518 0.998161 0.499081 0.866556i \(-0.333671\pi\)
0.499081 + 0.866556i \(0.333671\pi\)
\(774\) −3.77789 −0.135793
\(775\) 59.8589 2.15020
\(776\) 1.15665 0.0415213
\(777\) 22.5884 0.810354
\(778\) −12.7635 −0.457594
\(779\) 71.0755 2.54654
\(780\) 22.0617 0.789935
\(781\) 6.02117 0.215455
\(782\) 13.1342 0.469677
\(783\) 45.5480 1.62775
\(784\) −32.2037 −1.15013
\(785\) 76.8485 2.74284
\(786\) 15.8443 0.565149
\(787\) 30.5023 1.08729 0.543645 0.839315i \(-0.317044\pi\)
0.543645 + 0.839315i \(0.317044\pi\)
\(788\) −27.5740 −0.982282
\(789\) −0.261043 −0.00929339
\(790\) 42.9939 1.52965
\(791\) 58.9872 2.09734
\(792\) −1.02043 −0.0362595
\(793\) 50.2234 1.78349
\(794\) 60.3264 2.14090
\(795\) 6.15855 0.218421
\(796\) 16.9042 0.599153
\(797\) −25.7925 −0.913619 −0.456809 0.889565i \(-0.651008\pi\)
−0.456809 + 0.889565i \(0.651008\pi\)
\(798\) 43.3612 1.53497
\(799\) 8.53866 0.302076
\(800\) 50.8093 1.79638
\(801\) 13.0307 0.460419
\(802\) −34.3187 −1.21183
\(803\) −9.17547 −0.323795
\(804\) −18.1562 −0.640318
\(805\) −87.6826 −3.09041
\(806\) 62.9749 2.21819
\(807\) 12.5029 0.440122
\(808\) 2.73578 0.0962446
\(809\) 0.926092 0.0325596 0.0162798 0.999867i \(-0.494818\pi\)
0.0162798 + 0.999867i \(0.494818\pi\)
\(810\) −4.59065 −0.161299
\(811\) −13.0943 −0.459803 −0.229901 0.973214i \(-0.573840\pi\)
−0.229901 + 0.973214i \(0.573840\pi\)
\(812\) −58.6549 −2.05838
\(813\) −18.7863 −0.658864
\(814\) −11.3275 −0.397029
\(815\) −45.8945 −1.60762
\(816\) −4.56416 −0.159778
\(817\) 5.82980 0.203959
\(818\) −33.7771 −1.18099
\(819\) −26.9091 −0.940281
\(820\) −72.1382 −2.51917
\(821\) −9.87585 −0.344669 −0.172335 0.985038i \(-0.555131\pi\)
−0.172335 + 0.985038i \(0.555131\pi\)
\(822\) −23.1107 −0.806077
\(823\) −52.9875 −1.84703 −0.923515 0.383563i \(-0.874697\pi\)
−0.923515 + 0.383563i \(0.874697\pi\)
\(824\) −5.19508 −0.180979
\(825\) −6.84462 −0.238299
\(826\) −61.1952 −2.12925
\(827\) 49.3467 1.71595 0.857976 0.513690i \(-0.171722\pi\)
0.857976 + 0.513690i \(0.171722\pi\)
\(828\) −23.0131 −0.799760
\(829\) −46.7956 −1.62528 −0.812639 0.582767i \(-0.801970\pi\)
−0.812639 + 0.582767i \(0.801970\pi\)
\(830\) −89.8420 −3.11846
\(831\) −14.4685 −0.501908
\(832\) 20.8487 0.722799
\(833\) −7.20884 −0.249771
\(834\) 10.3295 0.357681
\(835\) −25.8168 −0.893426
\(836\) −10.0849 −0.348795
\(837\) 45.2443 1.56387
\(838\) −39.5543 −1.36638
\(839\) −29.9248 −1.03312 −0.516560 0.856251i \(-0.672788\pi\)
−0.516560 + 0.856251i \(0.672788\pi\)
\(840\) 6.87167 0.237095
\(841\) 51.9115 1.79005
\(842\) −17.8059 −0.613631
\(843\) −0.917515 −0.0316009
\(844\) 38.3791 1.32106
\(845\) 1.08764 0.0374158
\(846\) −32.2581 −1.10906
\(847\) −3.76946 −0.129520
\(848\) 7.87262 0.270347
\(849\) 2.46814 0.0847063
\(850\) 12.9383 0.443780
\(851\) 39.8878 1.36734
\(852\) −10.6419 −0.364587
\(853\) 29.3458 1.00478 0.502390 0.864641i \(-0.332454\pi\)
0.502390 + 0.864641i \(0.332454\pi\)
\(854\) −100.188 −3.42836
\(855\) 39.0063 1.33399
\(856\) −3.97749 −0.135948
\(857\) 14.8651 0.507781 0.253891 0.967233i \(-0.418290\pi\)
0.253891 + 0.967233i \(0.418290\pi\)
\(858\) −7.20091 −0.245835
\(859\) 51.4083 1.75403 0.877014 0.480465i \(-0.159532\pi\)
0.877014 + 0.480465i \(0.159532\pi\)
\(860\) −5.91697 −0.201767
\(861\) −46.9532 −1.60016
\(862\) 24.7088 0.841585
\(863\) 43.4321 1.47845 0.739223 0.673460i \(-0.235193\pi\)
0.739223 + 0.673460i \(0.235193\pi\)
\(864\) 38.4041 1.30654
\(865\) 27.6991 0.941799
\(866\) 63.1367 2.14547
\(867\) −1.02169 −0.0346985
\(868\) −58.2637 −1.97760
\(869\) −6.50847 −0.220785
\(870\) 60.7090 2.05823
\(871\) −37.4890 −1.27027
\(872\) 3.75014 0.126996
\(873\) −4.33731 −0.146796
\(874\) 76.5696 2.59000
\(875\) −21.9092 −0.740668
\(876\) 16.2169 0.547918
\(877\) 46.8935 1.58348 0.791740 0.610858i \(-0.209175\pi\)
0.791740 + 0.610858i \(0.209175\pi\)
\(878\) 71.6795 2.41906
\(879\) −8.59691 −0.289967
\(880\) −15.2799 −0.515085
\(881\) 17.0668 0.574995 0.287497 0.957781i \(-0.407177\pi\)
0.287497 + 0.957781i \(0.407177\pi\)
\(882\) 27.2342 0.917023
\(883\) 38.2164 1.28608 0.643042 0.765831i \(-0.277672\pi\)
0.643042 + 0.765831i \(0.277672\pi\)
\(884\) 6.31304 0.212331
\(885\) 29.3758 0.987457
\(886\) −10.4598 −0.351403
\(887\) −40.9640 −1.37544 −0.687718 0.725978i \(-0.741387\pi\)
−0.687718 + 0.725978i \(0.741387\pi\)
\(888\) −3.12600 −0.104902
\(889\) 38.2981 1.28448
\(890\) 44.0044 1.47503
\(891\) 0.694938 0.0232813
\(892\) −37.8063 −1.26585
\(893\) 49.7787 1.66578
\(894\) −1.89656 −0.0634305
\(895\) −8.07631 −0.269961
\(896\) 15.5874 0.520738
\(897\) 25.3568 0.846637
\(898\) 0.430619 0.0143699
\(899\) 80.3720 2.68056
\(900\) −22.6699 −0.755663
\(901\) 1.76229 0.0587105
\(902\) 23.5458 0.783991
\(903\) −3.85123 −0.128161
\(904\) −8.16322 −0.271505
\(905\) 53.0791 1.76441
\(906\) −33.5731 −1.11539
\(907\) 39.9965 1.32806 0.664031 0.747705i \(-0.268844\pi\)
0.664031 + 0.747705i \(0.268844\pi\)
\(908\) 8.76805 0.290978
\(909\) −10.2589 −0.340266
\(910\) −90.8713 −3.01235
\(911\) 36.0926 1.19580 0.597900 0.801571i \(-0.296002\pi\)
0.597900 + 0.801571i \(0.296002\pi\)
\(912\) −26.6081 −0.881084
\(913\) 13.6004 0.450107
\(914\) −39.8635 −1.31857
\(915\) 48.0936 1.58993
\(916\) 0.336404 0.0111151
\(917\) −30.2681 −0.999540
\(918\) 9.77940 0.322768
\(919\) −0.880867 −0.0290571 −0.0145286 0.999894i \(-0.504625\pi\)
−0.0145286 + 0.999894i \(0.504625\pi\)
\(920\) 12.1344 0.400058
\(921\) −24.5862 −0.810143
\(922\) −8.46525 −0.278788
\(923\) −21.9736 −0.723268
\(924\) 6.66222 0.219171
\(925\) 39.2930 1.29195
\(926\) −36.5012 −1.19950
\(927\) 19.4810 0.639839
\(928\) 68.2212 2.23947
\(929\) 56.0330 1.83838 0.919191 0.393812i \(-0.128844\pi\)
0.919191 + 0.393812i \(0.128844\pi\)
\(930\) 60.3042 1.97745
\(931\) −42.0261 −1.37735
\(932\) −40.4013 −1.32339
\(933\) −32.2731 −1.05657
\(934\) −67.3286 −2.20306
\(935\) −3.42042 −0.111860
\(936\) 3.72394 0.121721
\(937\) −43.1219 −1.40873 −0.704366 0.709837i \(-0.748768\pi\)
−0.704366 + 0.709837i \(0.748768\pi\)
\(938\) 74.7846 2.44180
\(939\) 14.2245 0.464198
\(940\) −50.5230 −1.64788
\(941\) 38.1153 1.24252 0.621261 0.783603i \(-0.286621\pi\)
0.621261 + 0.783603i \(0.286621\pi\)
\(942\) 44.3327 1.44444
\(943\) −82.9126 −2.70000
\(944\) 37.5518 1.22221
\(945\) −65.2865 −2.12377
\(946\) 1.93129 0.0627918
\(947\) −10.7696 −0.349966 −0.174983 0.984571i \(-0.555987\pi\)
−0.174983 + 0.984571i \(0.555987\pi\)
\(948\) 11.5032 0.373606
\(949\) 33.4848 1.08696
\(950\) 75.4277 2.44720
\(951\) 6.52469 0.211577
\(952\) 1.96636 0.0637300
\(953\) 42.2032 1.36710 0.683548 0.729906i \(-0.260436\pi\)
0.683548 + 0.729906i \(0.260436\pi\)
\(954\) −6.65775 −0.215553
\(955\) 58.2318 1.88434
\(956\) 24.0556 0.778013
\(957\) −9.19021 −0.297077
\(958\) −38.0672 −1.22990
\(959\) 44.1493 1.42565
\(960\) 19.9646 0.644353
\(961\) 48.8361 1.57536
\(962\) 41.3384 1.33280
\(963\) 14.9151 0.480633
\(964\) 33.8268 1.08949
\(965\) 64.7371 2.08396
\(966\) −50.5827 −1.62747
\(967\) −57.7994 −1.85870 −0.929351 0.369197i \(-0.879633\pi\)
−0.929351 + 0.369197i \(0.879633\pi\)
\(968\) 0.521655 0.0167666
\(969\) −5.95626 −0.191343
\(970\) −14.6469 −0.470285
\(971\) −58.9849 −1.89292 −0.946458 0.322827i \(-0.895367\pi\)
−0.946458 + 0.322827i \(0.895367\pi\)
\(972\) −27.5070 −0.882287
\(973\) −19.7329 −0.632607
\(974\) 43.2121 1.38460
\(975\) 24.9786 0.799956
\(976\) 61.4792 1.96790
\(977\) −9.45071 −0.302355 −0.151178 0.988507i \(-0.548307\pi\)
−0.151178 + 0.988507i \(0.548307\pi\)
\(978\) −26.4758 −0.846604
\(979\) −6.66144 −0.212901
\(980\) 42.6545 1.36255
\(981\) −14.0626 −0.448984
\(982\) −65.2729 −2.08294
\(983\) 28.3445 0.904049 0.452024 0.892006i \(-0.350702\pi\)
0.452024 + 0.892006i \(0.350702\pi\)
\(984\) 6.49784 0.207144
\(985\) −54.5205 −1.73717
\(986\) 17.3721 0.553242
\(987\) −32.8843 −1.04672
\(988\) 36.8038 1.17088
\(989\) −6.80071 −0.216250
\(990\) 12.9220 0.410687
\(991\) −29.5356 −0.938231 −0.469115 0.883137i \(-0.655427\pi\)
−0.469115 + 0.883137i \(0.655427\pi\)
\(992\) 67.7663 2.15158
\(993\) −23.4591 −0.744453
\(994\) 43.8338 1.39032
\(995\) 33.4237 1.05960
\(996\) −24.0376 −0.761660
\(997\) 37.8583 1.19898 0.599492 0.800381i \(-0.295369\pi\)
0.599492 + 0.800381i \(0.295369\pi\)
\(998\) −47.8580 −1.51492
\(999\) 29.6996 0.939653
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 \(a_p\))