Properties

Label 8041.2.a.i.1.13
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 1.13
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.93837 q^{2} -3.28485 q^{3} +1.75726 q^{4} -1.73342 q^{5} +6.36724 q^{6} +2.63625 q^{7} +0.470510 q^{8} +7.79024 q^{9} +O(q^{10})\) \(q-1.93837 q^{2} -3.28485 q^{3} +1.75726 q^{4} -1.73342 q^{5} +6.36724 q^{6} +2.63625 q^{7} +0.470510 q^{8} +7.79024 q^{9} +3.36000 q^{10} +1.00000 q^{11} -5.77235 q^{12} +2.10897 q^{13} -5.11001 q^{14} +5.69402 q^{15} -4.42655 q^{16} -1.00000 q^{17} -15.1003 q^{18} -7.62951 q^{19} -3.04607 q^{20} -8.65968 q^{21} -1.93837 q^{22} -0.362529 q^{23} -1.54555 q^{24} -1.99526 q^{25} -4.08795 q^{26} -15.7352 q^{27} +4.63258 q^{28} -1.80328 q^{29} -11.0371 q^{30} -3.50784 q^{31} +7.63926 q^{32} -3.28485 q^{33} +1.93837 q^{34} -4.56972 q^{35} +13.6895 q^{36} +10.7945 q^{37} +14.7888 q^{38} -6.92765 q^{39} -0.815589 q^{40} -8.51539 q^{41} +16.7856 q^{42} -1.00000 q^{43} +1.75726 q^{44} -13.5037 q^{45} +0.702714 q^{46} +6.48736 q^{47} +14.5406 q^{48} -0.0502022 q^{49} +3.86755 q^{50} +3.28485 q^{51} +3.70602 q^{52} -14.3090 q^{53} +30.5006 q^{54} -1.73342 q^{55} +1.24038 q^{56} +25.0618 q^{57} +3.49542 q^{58} +1.58726 q^{59} +10.0059 q^{60} -12.3456 q^{61} +6.79949 q^{62} +20.5370 q^{63} -5.95458 q^{64} -3.65572 q^{65} +6.36724 q^{66} -7.42453 q^{67} -1.75726 q^{68} +1.19085 q^{69} +8.85778 q^{70} +14.1196 q^{71} +3.66538 q^{72} -4.56933 q^{73} -20.9237 q^{74} +6.55415 q^{75} -13.4071 q^{76} +2.63625 q^{77} +13.4283 q^{78} -4.74964 q^{79} +7.67306 q^{80} +28.3171 q^{81} +16.5059 q^{82} -5.79051 q^{83} -15.2173 q^{84} +1.73342 q^{85} +1.93837 q^{86} +5.92351 q^{87} +0.470510 q^{88} +15.7617 q^{89} +26.1752 q^{90} +5.55976 q^{91} -0.637059 q^{92} +11.5227 q^{93} -12.5749 q^{94} +13.2251 q^{95} -25.0938 q^{96} -7.02794 q^{97} +0.0973102 q^{98} +7.79024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93837 −1.37063 −0.685316 0.728246i \(-0.740336\pi\)
−0.685316 + 0.728246i \(0.740336\pi\)
\(3\) −3.28485 −1.89651 −0.948255 0.317511i \(-0.897153\pi\)
−0.948255 + 0.317511i \(0.897153\pi\)
\(4\) 1.75726 0.878632
\(5\) −1.73342 −0.775208 −0.387604 0.921826i \(-0.626697\pi\)
−0.387604 + 0.921826i \(0.626697\pi\)
\(6\) 6.36724 2.59942
\(7\) 2.63625 0.996408 0.498204 0.867060i \(-0.333993\pi\)
0.498204 + 0.867060i \(0.333993\pi\)
\(8\) 0.470510 0.166350
\(9\) 7.79024 2.59675
\(10\) 3.36000 1.06252
\(11\) 1.00000 0.301511
\(12\) −5.77235 −1.66633
\(13\) 2.10897 0.584923 0.292461 0.956277i \(-0.405526\pi\)
0.292461 + 0.956277i \(0.405526\pi\)
\(14\) −5.11001 −1.36571
\(15\) 5.69402 1.47019
\(16\) −4.42655 −1.10664
\(17\) −1.00000 −0.242536
\(18\) −15.1003 −3.55918
\(19\) −7.62951 −1.75033 −0.875164 0.483826i \(-0.839247\pi\)
−0.875164 + 0.483826i \(0.839247\pi\)
\(20\) −3.04607 −0.681123
\(21\) −8.65968 −1.88970
\(22\) −1.93837 −0.413261
\(23\) −0.362529 −0.0755925 −0.0377962 0.999285i \(-0.512034\pi\)
−0.0377962 + 0.999285i \(0.512034\pi\)
\(24\) −1.54555 −0.315485
\(25\) −1.99526 −0.399053
\(26\) −4.08795 −0.801714
\(27\) −15.7352 −3.02824
\(28\) 4.63258 0.875476
\(29\) −1.80328 −0.334861 −0.167431 0.985884i \(-0.553547\pi\)
−0.167431 + 0.985884i \(0.553547\pi\)
\(30\) −11.0371 −2.01509
\(31\) −3.50784 −0.630027 −0.315014 0.949087i \(-0.602009\pi\)
−0.315014 + 0.949087i \(0.602009\pi\)
\(32\) 7.63926 1.35044
\(33\) −3.28485 −0.571819
\(34\) 1.93837 0.332427
\(35\) −4.56972 −0.772423
\(36\) 13.6895 2.28159
\(37\) 10.7945 1.77461 0.887303 0.461186i \(-0.152576\pi\)
0.887303 + 0.461186i \(0.152576\pi\)
\(38\) 14.7888 2.39906
\(39\) −6.92765 −1.10931
\(40\) −0.815589 −0.128956
\(41\) −8.51539 −1.32988 −0.664940 0.746897i \(-0.731543\pi\)
−0.664940 + 0.746897i \(0.731543\pi\)
\(42\) 16.7856 2.59008
\(43\) −1.00000 −0.152499
\(44\) 1.75726 0.264918
\(45\) −13.5037 −2.01302
\(46\) 0.702714 0.103609
\(47\) 6.48736 0.946278 0.473139 0.880988i \(-0.343121\pi\)
0.473139 + 0.880988i \(0.343121\pi\)
\(48\) 14.5406 2.09875
\(49\) −0.0502022 −0.00717174
\(50\) 3.86755 0.546955
\(51\) 3.28485 0.459971
\(52\) 3.70602 0.513932
\(53\) −14.3090 −1.96549 −0.982744 0.184970i \(-0.940781\pi\)
−0.982744 + 0.184970i \(0.940781\pi\)
\(54\) 30.5006 4.15061
\(55\) −1.73342 −0.233734
\(56\) 1.24038 0.165753
\(57\) 25.0618 3.31951
\(58\) 3.49542 0.458971
\(59\) 1.58726 0.206643 0.103322 0.994648i \(-0.467053\pi\)
0.103322 + 0.994648i \(0.467053\pi\)
\(60\) 10.0059 1.29176
\(61\) −12.3456 −1.58069 −0.790344 0.612664i \(-0.790098\pi\)
−0.790344 + 0.612664i \(0.790098\pi\)
\(62\) 6.79949 0.863536
\(63\) 20.5370 2.58742
\(64\) −5.95458 −0.744323
\(65\) −3.65572 −0.453437
\(66\) 6.36724 0.783753
\(67\) −7.42453 −0.907051 −0.453526 0.891243i \(-0.649834\pi\)
−0.453526 + 0.891243i \(0.649834\pi\)
\(68\) −1.75726 −0.213100
\(69\) 1.19085 0.143362
\(70\) 8.85778 1.05871
\(71\) 14.1196 1.67569 0.837845 0.545908i \(-0.183815\pi\)
0.837845 + 0.545908i \(0.183815\pi\)
\(72\) 3.66538 0.431969
\(73\) −4.56933 −0.534799 −0.267400 0.963586i \(-0.586164\pi\)
−0.267400 + 0.963586i \(0.586164\pi\)
\(74\) −20.9237 −2.43233
\(75\) 6.55415 0.756808
\(76\) −13.4071 −1.53790
\(77\) 2.63625 0.300428
\(78\) 13.4283 1.52046
\(79\) −4.74964 −0.534376 −0.267188 0.963644i \(-0.586094\pi\)
−0.267188 + 0.963644i \(0.586094\pi\)
\(80\) 7.67306 0.857874
\(81\) 28.3171 3.14635
\(82\) 16.5059 1.82278
\(83\) −5.79051 −0.635591 −0.317795 0.948159i \(-0.602943\pi\)
−0.317795 + 0.948159i \(0.602943\pi\)
\(84\) −15.2173 −1.66035
\(85\) 1.73342 0.188015
\(86\) 1.93837 0.209019
\(87\) 5.92351 0.635067
\(88\) 0.470510 0.0501565
\(89\) 15.7617 1.67073 0.835367 0.549692i \(-0.185255\pi\)
0.835367 + 0.549692i \(0.185255\pi\)
\(90\) 26.1752 2.75911
\(91\) 5.55976 0.582821
\(92\) −0.637059 −0.0664180
\(93\) 11.5227 1.19485
\(94\) −12.5749 −1.29700
\(95\) 13.2251 1.35687
\(96\) −25.0938 −2.56113
\(97\) −7.02794 −0.713579 −0.356789 0.934185i \(-0.616129\pi\)
−0.356789 + 0.934185i \(0.616129\pi\)
\(98\) 0.0973102 0.00982981
\(99\) 7.79024 0.782949
\(100\) −3.50621 −0.350621
\(101\) 9.07212 0.902710 0.451355 0.892345i \(-0.350941\pi\)
0.451355 + 0.892345i \(0.350941\pi\)
\(102\) −6.36724 −0.630451
\(103\) 10.5510 1.03962 0.519810 0.854282i \(-0.326003\pi\)
0.519810 + 0.854282i \(0.326003\pi\)
\(104\) 0.992290 0.0973020
\(105\) 15.0108 1.46491
\(106\) 27.7360 2.69396
\(107\) 0.926153 0.0895346 0.0447673 0.998997i \(-0.485745\pi\)
0.0447673 + 0.998997i \(0.485745\pi\)
\(108\) −27.6509 −2.66071
\(109\) 20.0743 1.92277 0.961385 0.275206i \(-0.0887461\pi\)
0.961385 + 0.275206i \(0.0887461\pi\)
\(110\) 3.36000 0.320363
\(111\) −35.4584 −3.36556
\(112\) −11.6695 −1.10266
\(113\) −2.16933 −0.204074 −0.102037 0.994781i \(-0.532536\pi\)
−0.102037 + 0.994781i \(0.532536\pi\)
\(114\) −48.5789 −4.54983
\(115\) 0.628414 0.0585999
\(116\) −3.16884 −0.294220
\(117\) 16.4294 1.51890
\(118\) −3.07669 −0.283232
\(119\) −2.63625 −0.241664
\(120\) 2.67909 0.244566
\(121\) 1.00000 0.0909091
\(122\) 23.9302 2.16654
\(123\) 27.9718 2.52213
\(124\) −6.16421 −0.553563
\(125\) 12.1257 1.08456
\(126\) −39.8082 −3.54640
\(127\) −18.9399 −1.68064 −0.840321 0.542089i \(-0.817634\pi\)
−0.840321 + 0.542089i \(0.817634\pi\)
\(128\) −3.73635 −0.330250
\(129\) 3.28485 0.289215
\(130\) 7.08613 0.621495
\(131\) −2.15337 −0.188141 −0.0940704 0.995566i \(-0.529988\pi\)
−0.0940704 + 0.995566i \(0.529988\pi\)
\(132\) −5.77235 −0.502419
\(133\) −20.1133 −1.74404
\(134\) 14.3915 1.24323
\(135\) 27.2757 2.34752
\(136\) −0.470510 −0.0403459
\(137\) −5.92940 −0.506583 −0.253291 0.967390i \(-0.581513\pi\)
−0.253291 + 0.967390i \(0.581513\pi\)
\(138\) −2.30831 −0.196496
\(139\) −13.4992 −1.14499 −0.572495 0.819908i \(-0.694025\pi\)
−0.572495 + 0.819908i \(0.694025\pi\)
\(140\) −8.03020 −0.678676
\(141\) −21.3100 −1.79462
\(142\) −27.3690 −2.29676
\(143\) 2.10897 0.176361
\(144\) −34.4839 −2.87366
\(145\) 3.12584 0.259587
\(146\) 8.85703 0.733013
\(147\) 0.164907 0.0136013
\(148\) 18.9688 1.55923
\(149\) −19.2090 −1.57366 −0.786830 0.617170i \(-0.788279\pi\)
−0.786830 + 0.617170i \(0.788279\pi\)
\(150\) −12.7043 −1.03730
\(151\) 10.1344 0.824727 0.412364 0.911019i \(-0.364703\pi\)
0.412364 + 0.911019i \(0.364703\pi\)
\(152\) −3.58976 −0.291168
\(153\) −7.79024 −0.629804
\(154\) −5.11001 −0.411777
\(155\) 6.08056 0.488402
\(156\) −12.1737 −0.974677
\(157\) −4.01938 −0.320782 −0.160391 0.987054i \(-0.551275\pi\)
−0.160391 + 0.987054i \(0.551275\pi\)
\(158\) 9.20654 0.732433
\(159\) 47.0028 3.72757
\(160\) −13.2420 −1.04687
\(161\) −0.955715 −0.0753209
\(162\) −54.8890 −4.31248
\(163\) 17.6005 1.37858 0.689289 0.724487i \(-0.257923\pi\)
0.689289 + 0.724487i \(0.257923\pi\)
\(164\) −14.9638 −1.16848
\(165\) 5.69402 0.443278
\(166\) 11.2241 0.871161
\(167\) −12.1450 −0.939808 −0.469904 0.882718i \(-0.655711\pi\)
−0.469904 + 0.882718i \(0.655711\pi\)
\(168\) −4.07446 −0.314351
\(169\) −8.55225 −0.657866
\(170\) −3.36000 −0.257700
\(171\) −59.4357 −4.54516
\(172\) −1.75726 −0.133990
\(173\) −3.68542 −0.280197 −0.140099 0.990138i \(-0.544742\pi\)
−0.140099 + 0.990138i \(0.544742\pi\)
\(174\) −11.4819 −0.870443
\(175\) −5.26001 −0.397619
\(176\) −4.42655 −0.333664
\(177\) −5.21390 −0.391901
\(178\) −30.5519 −2.28996
\(179\) 14.6315 1.09361 0.546805 0.837260i \(-0.315844\pi\)
0.546805 + 0.837260i \(0.315844\pi\)
\(180\) −23.7296 −1.76870
\(181\) −25.7946 −1.91730 −0.958649 0.284590i \(-0.908142\pi\)
−0.958649 + 0.284590i \(0.908142\pi\)
\(182\) −10.7769 −0.798834
\(183\) 40.5533 2.99779
\(184\) −0.170573 −0.0125748
\(185\) −18.7114 −1.37569
\(186\) −22.3353 −1.63770
\(187\) −1.00000 −0.0731272
\(188\) 11.4000 0.831431
\(189\) −41.4819 −3.01737
\(190\) −25.6351 −1.85977
\(191\) 17.0102 1.23082 0.615409 0.788208i \(-0.288991\pi\)
0.615409 + 0.788208i \(0.288991\pi\)
\(192\) 19.5599 1.41161
\(193\) −3.59857 −0.259031 −0.129515 0.991577i \(-0.541342\pi\)
−0.129515 + 0.991577i \(0.541342\pi\)
\(194\) 13.6227 0.978054
\(195\) 12.0085 0.859946
\(196\) −0.0882185 −0.00630132
\(197\) −21.3078 −1.51812 −0.759058 0.651023i \(-0.774340\pi\)
−0.759058 + 0.651023i \(0.774340\pi\)
\(198\) −15.1003 −1.07313
\(199\) 20.7318 1.46964 0.734819 0.678263i \(-0.237267\pi\)
0.734819 + 0.678263i \(0.237267\pi\)
\(200\) −0.938791 −0.0663826
\(201\) 24.3885 1.72023
\(202\) −17.5851 −1.23728
\(203\) −4.75390 −0.333658
\(204\) 5.77235 0.404145
\(205\) 14.7607 1.03093
\(206\) −20.4517 −1.42494
\(207\) −2.82419 −0.196295
\(208\) −9.33545 −0.647297
\(209\) −7.62951 −0.527744
\(210\) −29.0965 −2.00785
\(211\) −20.8729 −1.43695 −0.718475 0.695553i \(-0.755159\pi\)
−0.718475 + 0.695553i \(0.755159\pi\)
\(212\) −25.1447 −1.72694
\(213\) −46.3808 −3.17796
\(214\) −1.79522 −0.122719
\(215\) 1.73342 0.118218
\(216\) −7.40357 −0.503749
\(217\) −9.24754 −0.627764
\(218\) −38.9114 −2.63541
\(219\) 15.0096 1.01425
\(220\) −3.04607 −0.205366
\(221\) −2.10897 −0.141865
\(222\) 68.7313 4.61294
\(223\) −21.1868 −1.41878 −0.709388 0.704818i \(-0.751028\pi\)
−0.709388 + 0.704818i \(0.751028\pi\)
\(224\) 20.1390 1.34559
\(225\) −15.5436 −1.03624
\(226\) 4.20497 0.279710
\(227\) 25.5971 1.69894 0.849471 0.527635i \(-0.176921\pi\)
0.849471 + 0.527635i \(0.176921\pi\)
\(228\) 44.0402 2.91663
\(229\) 8.52123 0.563098 0.281549 0.959547i \(-0.409152\pi\)
0.281549 + 0.959547i \(0.409152\pi\)
\(230\) −1.21810 −0.0803189
\(231\) −8.65968 −0.569765
\(232\) −0.848461 −0.0557042
\(233\) −4.36722 −0.286106 −0.143053 0.989715i \(-0.545692\pi\)
−0.143053 + 0.989715i \(0.545692\pi\)
\(234\) −31.8461 −2.08185
\(235\) −11.2453 −0.733562
\(236\) 2.78923 0.181563
\(237\) 15.6019 1.01345
\(238\) 5.11001 0.331233
\(239\) 16.7372 1.08264 0.541320 0.840817i \(-0.317925\pi\)
0.541320 + 0.840817i \(0.317925\pi\)
\(240\) −25.2048 −1.62697
\(241\) −4.75528 −0.306314 −0.153157 0.988202i \(-0.548944\pi\)
−0.153157 + 0.988202i \(0.548944\pi\)
\(242\) −1.93837 −0.124603
\(243\) −45.8118 −2.93883
\(244\) −21.6944 −1.38884
\(245\) 0.0870213 0.00555959
\(246\) −54.2195 −3.45691
\(247\) −16.0904 −1.02381
\(248\) −1.65047 −0.104805
\(249\) 19.0209 1.20540
\(250\) −23.5041 −1.48653
\(251\) −4.41879 −0.278912 −0.139456 0.990228i \(-0.544535\pi\)
−0.139456 + 0.990228i \(0.544535\pi\)
\(252\) 36.0889 2.27339
\(253\) −0.362529 −0.0227920
\(254\) 36.7124 2.30354
\(255\) −5.69402 −0.356573
\(256\) 19.1516 1.19697
\(257\) −0.986666 −0.0615466 −0.0307733 0.999526i \(-0.509797\pi\)
−0.0307733 + 0.999526i \(0.509797\pi\)
\(258\) −6.36724 −0.396407
\(259\) 28.4570 1.76823
\(260\) −6.42407 −0.398404
\(261\) −14.0480 −0.869549
\(262\) 4.17402 0.257872
\(263\) 25.6101 1.57919 0.789594 0.613630i \(-0.210291\pi\)
0.789594 + 0.613630i \(0.210291\pi\)
\(264\) −1.54555 −0.0951222
\(265\) 24.8034 1.52366
\(266\) 38.9869 2.39044
\(267\) −51.7748 −3.16856
\(268\) −13.0469 −0.796964
\(269\) 8.59937 0.524313 0.262156 0.965025i \(-0.415566\pi\)
0.262156 + 0.965025i \(0.415566\pi\)
\(270\) −52.8703 −3.21758
\(271\) 10.2081 0.620100 0.310050 0.950720i \(-0.399654\pi\)
0.310050 + 0.950720i \(0.399654\pi\)
\(272\) 4.42655 0.268399
\(273\) −18.2630 −1.10533
\(274\) 11.4933 0.694339
\(275\) −1.99526 −0.120319
\(276\) 2.09264 0.125962
\(277\) 2.46814 0.148296 0.0741480 0.997247i \(-0.476376\pi\)
0.0741480 + 0.997247i \(0.476376\pi\)
\(278\) 26.1665 1.56936
\(279\) −27.3269 −1.63602
\(280\) −2.15009 −0.128493
\(281\) 19.1564 1.14278 0.571388 0.820680i \(-0.306405\pi\)
0.571388 + 0.820680i \(0.306405\pi\)
\(282\) 41.3066 2.45977
\(283\) 17.9968 1.06980 0.534901 0.844915i \(-0.320349\pi\)
0.534901 + 0.844915i \(0.320349\pi\)
\(284\) 24.8119 1.47232
\(285\) −43.4425 −2.57331
\(286\) −4.08795 −0.241726
\(287\) −22.4487 −1.32510
\(288\) 59.5116 3.50676
\(289\) 1.00000 0.0588235
\(290\) −6.05902 −0.355798
\(291\) 23.0857 1.35331
\(292\) −8.02952 −0.469892
\(293\) 1.62157 0.0947334 0.0473667 0.998878i \(-0.484917\pi\)
0.0473667 + 0.998878i \(0.484917\pi\)
\(294\) −0.319649 −0.0186423
\(295\) −2.75138 −0.160191
\(296\) 5.07892 0.295206
\(297\) −15.7352 −0.913050
\(298\) 37.2340 2.15691
\(299\) −0.764562 −0.0442158
\(300\) 11.5174 0.664956
\(301\) −2.63625 −0.151951
\(302\) −19.6442 −1.13040
\(303\) −29.8006 −1.71200
\(304\) 33.7724 1.93698
\(305\) 21.4000 1.22536
\(306\) 15.1003 0.863229
\(307\) −1.29565 −0.0739464 −0.0369732 0.999316i \(-0.511772\pi\)
−0.0369732 + 0.999316i \(0.511772\pi\)
\(308\) 4.63258 0.263966
\(309\) −34.6584 −1.97165
\(310\) −11.7863 −0.669420
\(311\) 17.2252 0.976752 0.488376 0.872633i \(-0.337589\pi\)
0.488376 + 0.872633i \(0.337589\pi\)
\(312\) −3.25952 −0.184534
\(313\) −0.933560 −0.0527679 −0.0263840 0.999652i \(-0.508399\pi\)
−0.0263840 + 0.999652i \(0.508399\pi\)
\(314\) 7.79104 0.439674
\(315\) −35.5992 −2.00579
\(316\) −8.34637 −0.469520
\(317\) −6.56153 −0.368532 −0.184266 0.982876i \(-0.558991\pi\)
−0.184266 + 0.982876i \(0.558991\pi\)
\(318\) −91.1087 −5.10912
\(319\) −1.80328 −0.100964
\(320\) 10.3218 0.577005
\(321\) −3.04227 −0.169803
\(322\) 1.85253 0.103237
\(323\) 7.62951 0.424517
\(324\) 49.7607 2.76448
\(325\) −4.20795 −0.233415
\(326\) −34.1162 −1.88952
\(327\) −65.9411 −3.64655
\(328\) −4.00657 −0.221226
\(329\) 17.1023 0.942879
\(330\) −11.0371 −0.607572
\(331\) −21.1745 −1.16385 −0.581927 0.813241i \(-0.697701\pi\)
−0.581927 + 0.813241i \(0.697701\pi\)
\(332\) −10.1755 −0.558451
\(333\) 84.0918 4.60820
\(334\) 23.5414 1.28813
\(335\) 12.8698 0.703153
\(336\) 38.3325 2.09121
\(337\) 7.47086 0.406964 0.203482 0.979079i \(-0.434774\pi\)
0.203482 + 0.979079i \(0.434774\pi\)
\(338\) 16.5774 0.901692
\(339\) 7.12594 0.387028
\(340\) 3.04607 0.165197
\(341\) −3.50784 −0.189960
\(342\) 115.208 6.22974
\(343\) −18.5861 −1.00355
\(344\) −0.470510 −0.0253682
\(345\) −2.06424 −0.111135
\(346\) 7.14369 0.384047
\(347\) 2.89115 0.155205 0.0776026 0.996984i \(-0.475273\pi\)
0.0776026 + 0.996984i \(0.475273\pi\)
\(348\) 10.4092 0.557990
\(349\) −30.4560 −1.63027 −0.815137 0.579268i \(-0.803338\pi\)
−0.815137 + 0.579268i \(0.803338\pi\)
\(350\) 10.1958 0.544990
\(351\) −33.1851 −1.77129
\(352\) 7.63926 0.407174
\(353\) −33.4799 −1.78196 −0.890978 0.454047i \(-0.849980\pi\)
−0.890978 + 0.454047i \(0.849980\pi\)
\(354\) 10.1065 0.537152
\(355\) −24.4752 −1.29901
\(356\) 27.6974 1.46796
\(357\) 8.65968 0.458319
\(358\) −28.3612 −1.49894
\(359\) 12.3324 0.650878 0.325439 0.945563i \(-0.394488\pi\)
0.325439 + 0.945563i \(0.394488\pi\)
\(360\) −6.35364 −0.334866
\(361\) 39.2094 2.06365
\(362\) 49.9994 2.62791
\(363\) −3.28485 −0.172410
\(364\) 9.76997 0.512086
\(365\) 7.92055 0.414581
\(366\) −78.6072 −4.10886
\(367\) −0.325187 −0.0169746 −0.00848732 0.999964i \(-0.502702\pi\)
−0.00848732 + 0.999964i \(0.502702\pi\)
\(368\) 1.60475 0.0836535
\(369\) −66.3369 −3.45336
\(370\) 36.2695 1.88556
\(371\) −37.7220 −1.95843
\(372\) 20.2485 1.04984
\(373\) −12.6901 −0.657069 −0.328535 0.944492i \(-0.606555\pi\)
−0.328535 + 0.944492i \(0.606555\pi\)
\(374\) 1.93837 0.100231
\(375\) −39.8311 −2.05687
\(376\) 3.05236 0.157414
\(377\) −3.80306 −0.195868
\(378\) 80.4072 4.13570
\(379\) 3.66547 0.188283 0.0941414 0.995559i \(-0.469989\pi\)
0.0941414 + 0.995559i \(0.469989\pi\)
\(380\) 23.2400 1.19219
\(381\) 62.2146 3.18735
\(382\) −32.9721 −1.68700
\(383\) −29.2462 −1.49441 −0.747206 0.664592i \(-0.768605\pi\)
−0.747206 + 0.664592i \(0.768605\pi\)
\(384\) 12.2734 0.626322
\(385\) −4.56972 −0.232894
\(386\) 6.97535 0.355036
\(387\) −7.79024 −0.396000
\(388\) −12.3499 −0.626974
\(389\) 27.5697 1.39784 0.698920 0.715200i \(-0.253664\pi\)
0.698920 + 0.715200i \(0.253664\pi\)
\(390\) −23.2769 −1.17867
\(391\) 0.362529 0.0183339
\(392\) −0.0236206 −0.00119302
\(393\) 7.07350 0.356811
\(394\) 41.3023 2.08078
\(395\) 8.23311 0.414253
\(396\) 13.6895 0.687924
\(397\) 14.7001 0.737775 0.368888 0.929474i \(-0.379739\pi\)
0.368888 + 0.929474i \(0.379739\pi\)
\(398\) −40.1858 −2.01433
\(399\) 66.0691 3.30759
\(400\) 8.83214 0.441607
\(401\) 22.7800 1.13758 0.568789 0.822483i \(-0.307412\pi\)
0.568789 + 0.822483i \(0.307412\pi\)
\(402\) −47.2738 −2.35780
\(403\) −7.39793 −0.368517
\(404\) 15.9421 0.793150
\(405\) −49.0854 −2.43907
\(406\) 9.21479 0.457323
\(407\) 10.7945 0.535064
\(408\) 1.54555 0.0765163
\(409\) 32.7770 1.62072 0.810359 0.585933i \(-0.199272\pi\)
0.810359 + 0.585933i \(0.199272\pi\)
\(410\) −28.6117 −1.41303
\(411\) 19.4772 0.960739
\(412\) 18.5409 0.913443
\(413\) 4.18440 0.205901
\(414\) 5.47431 0.269048
\(415\) 10.0374 0.492715
\(416\) 16.1110 0.789904
\(417\) 44.3430 2.17149
\(418\) 14.7888 0.723343
\(419\) −5.25119 −0.256537 −0.128269 0.991739i \(-0.540942\pi\)
−0.128269 + 0.991739i \(0.540942\pi\)
\(420\) 26.3780 1.28711
\(421\) 13.2186 0.644238 0.322119 0.946699i \(-0.395605\pi\)
0.322119 + 0.946699i \(0.395605\pi\)
\(422\) 40.4593 1.96953
\(423\) 50.5381 2.45724
\(424\) −6.73251 −0.326959
\(425\) 1.99526 0.0967846
\(426\) 89.9031 4.35582
\(427\) −32.5459 −1.57501
\(428\) 1.62750 0.0786680
\(429\) −6.92765 −0.334470
\(430\) −3.36000 −0.162033
\(431\) −20.0108 −0.963885 −0.481942 0.876203i \(-0.660069\pi\)
−0.481942 + 0.876203i \(0.660069\pi\)
\(432\) 69.6527 3.35117
\(433\) −16.8124 −0.807954 −0.403977 0.914769i \(-0.632372\pi\)
−0.403977 + 0.914769i \(0.632372\pi\)
\(434\) 17.9251 0.860434
\(435\) −10.2679 −0.492309
\(436\) 35.2759 1.68941
\(437\) 2.76592 0.132312
\(438\) −29.0940 −1.39017
\(439\) 8.70931 0.415673 0.207836 0.978164i \(-0.433358\pi\)
0.207836 + 0.978164i \(0.433358\pi\)
\(440\) −0.815589 −0.0388817
\(441\) −0.391087 −0.0186232
\(442\) 4.08795 0.194444
\(443\) −18.7428 −0.890498 −0.445249 0.895407i \(-0.646885\pi\)
−0.445249 + 0.895407i \(0.646885\pi\)
\(444\) −62.3097 −2.95709
\(445\) −27.3216 −1.29517
\(446\) 41.0679 1.94462
\(447\) 63.0986 2.98446
\(448\) −15.6977 −0.741649
\(449\) 17.0722 0.805686 0.402843 0.915269i \(-0.368022\pi\)
0.402843 + 0.915269i \(0.368022\pi\)
\(450\) 30.1292 1.42030
\(451\) −8.51539 −0.400974
\(452\) −3.81210 −0.179306
\(453\) −33.2900 −1.56410
\(454\) −49.6166 −2.32862
\(455\) −9.63739 −0.451808
\(456\) 11.7918 0.552202
\(457\) 4.76009 0.222668 0.111334 0.993783i \(-0.464488\pi\)
0.111334 + 0.993783i \(0.464488\pi\)
\(458\) −16.5173 −0.771801
\(459\) 15.7352 0.734457
\(460\) 1.10429 0.0514878
\(461\) −14.2643 −0.664354 −0.332177 0.943217i \(-0.607783\pi\)
−0.332177 + 0.943217i \(0.607783\pi\)
\(462\) 16.7856 0.780938
\(463\) −13.8442 −0.643396 −0.321698 0.946842i \(-0.604254\pi\)
−0.321698 + 0.946842i \(0.604254\pi\)
\(464\) 7.98232 0.370570
\(465\) −19.9737 −0.926259
\(466\) 8.46528 0.392146
\(467\) 0.602905 0.0278991 0.0139496 0.999903i \(-0.495560\pi\)
0.0139496 + 0.999903i \(0.495560\pi\)
\(468\) 28.8708 1.33455
\(469\) −19.5729 −0.903793
\(470\) 21.7975 1.00544
\(471\) 13.2031 0.608365
\(472\) 0.746820 0.0343752
\(473\) −1.00000 −0.0459800
\(474\) −30.2421 −1.38907
\(475\) 15.2229 0.698474
\(476\) −4.63258 −0.212334
\(477\) −111.470 −5.10387
\(478\) −32.4428 −1.48390
\(479\) −4.75380 −0.217207 −0.108603 0.994085i \(-0.534638\pi\)
−0.108603 + 0.994085i \(0.534638\pi\)
\(480\) 43.4980 1.98541
\(481\) 22.7653 1.03801
\(482\) 9.21747 0.419844
\(483\) 3.13938 0.142847
\(484\) 1.75726 0.0798757
\(485\) 12.1823 0.553172
\(486\) 88.8001 4.02805
\(487\) −14.2195 −0.644348 −0.322174 0.946680i \(-0.604414\pi\)
−0.322174 + 0.946680i \(0.604414\pi\)
\(488\) −5.80870 −0.262948
\(489\) −57.8150 −2.61448
\(490\) −0.168679 −0.00762015
\(491\) 7.54747 0.340613 0.170306 0.985391i \(-0.445524\pi\)
0.170306 + 0.985391i \(0.445524\pi\)
\(492\) 49.1538 2.21602
\(493\) 1.80328 0.0812157
\(494\) 31.1891 1.40326
\(495\) −13.5037 −0.606948
\(496\) 15.5276 0.697212
\(497\) 37.2228 1.66967
\(498\) −36.8696 −1.65216
\(499\) −0.417796 −0.0187031 −0.00935155 0.999956i \(-0.502977\pi\)
−0.00935155 + 0.999956i \(0.502977\pi\)
\(500\) 21.3081 0.952927
\(501\) 39.8945 1.78235
\(502\) 8.56524 0.382285
\(503\) 32.1190 1.43212 0.716058 0.698041i \(-0.245945\pi\)
0.716058 + 0.698041i \(0.245945\pi\)
\(504\) 9.66285 0.430418
\(505\) −15.7258 −0.699788
\(506\) 0.702714 0.0312394
\(507\) 28.0929 1.24765
\(508\) −33.2824 −1.47667
\(509\) 5.98032 0.265073 0.132536 0.991178i \(-0.457688\pi\)
0.132536 + 0.991178i \(0.457688\pi\)
\(510\) 11.0371 0.488731
\(511\) −12.0459 −0.532878
\(512\) −29.6501 −1.31036
\(513\) 120.052 5.30042
\(514\) 1.91252 0.0843577
\(515\) −18.2893 −0.805921
\(516\) 5.77235 0.254114
\(517\) 6.48736 0.285314
\(518\) −55.1601 −2.42360
\(519\) 12.1060 0.531396
\(520\) −1.72005 −0.0754293
\(521\) 7.49057 0.328168 0.164084 0.986446i \(-0.447533\pi\)
0.164084 + 0.986446i \(0.447533\pi\)
\(522\) 27.2302 1.19183
\(523\) −30.6647 −1.34087 −0.670437 0.741966i \(-0.733893\pi\)
−0.670437 + 0.741966i \(0.733893\pi\)
\(524\) −3.78404 −0.165307
\(525\) 17.2783 0.754089
\(526\) −49.6418 −2.16448
\(527\) 3.50784 0.152804
\(528\) 14.5406 0.632796
\(529\) −22.8686 −0.994286
\(530\) −48.0781 −2.08838
\(531\) 12.3651 0.536600
\(532\) −35.3443 −1.53237
\(533\) −17.9587 −0.777877
\(534\) 100.358 4.34293
\(535\) −1.60541 −0.0694079
\(536\) −3.49331 −0.150888
\(537\) −48.0623 −2.07404
\(538\) −16.6687 −0.718640
\(539\) −0.0502022 −0.00216236
\(540\) 47.9306 2.06261
\(541\) 34.5039 1.48344 0.741720 0.670710i \(-0.234010\pi\)
0.741720 + 0.670710i \(0.234010\pi\)
\(542\) −19.7871 −0.849929
\(543\) 84.7314 3.63617
\(544\) −7.63926 −0.327530
\(545\) −34.7972 −1.49055
\(546\) 35.4004 1.51500
\(547\) −37.0653 −1.58480 −0.792399 0.610004i \(-0.791168\pi\)
−0.792399 + 0.610004i \(0.791168\pi\)
\(548\) −10.4195 −0.445100
\(549\) −96.1749 −4.10464
\(550\) 3.86755 0.164913
\(551\) 13.7582 0.586117
\(552\) 0.560308 0.0238483
\(553\) −12.5212 −0.532457
\(554\) −4.78415 −0.203259
\(555\) 61.4641 2.60901
\(556\) −23.7217 −1.00603
\(557\) −12.7907 −0.541958 −0.270979 0.962585i \(-0.587347\pi\)
−0.270979 + 0.962585i \(0.587347\pi\)
\(558\) 52.9696 2.24238
\(559\) −2.10897 −0.0891999
\(560\) 20.2281 0.854792
\(561\) 3.28485 0.138686
\(562\) −37.1322 −1.56633
\(563\) −8.43124 −0.355334 −0.177667 0.984091i \(-0.556855\pi\)
−0.177667 + 0.984091i \(0.556855\pi\)
\(564\) −37.4473 −1.57682
\(565\) 3.76036 0.158200
\(566\) −34.8845 −1.46630
\(567\) 74.6509 3.13504
\(568\) 6.64342 0.278752
\(569\) −22.0010 −0.922328 −0.461164 0.887315i \(-0.652568\pi\)
−0.461164 + 0.887315i \(0.652568\pi\)
\(570\) 84.2075 3.52707
\(571\) 38.8605 1.62626 0.813130 0.582081i \(-0.197762\pi\)
0.813130 + 0.582081i \(0.197762\pi\)
\(572\) 3.70602 0.154956
\(573\) −55.8761 −2.33426
\(574\) 43.5137 1.81623
\(575\) 0.723341 0.0301654
\(576\) −46.3876 −1.93282
\(577\) 3.80886 0.158565 0.0792826 0.996852i \(-0.474737\pi\)
0.0792826 + 0.996852i \(0.474737\pi\)
\(578\) −1.93837 −0.0806254
\(579\) 11.8208 0.491254
\(580\) 5.49293 0.228081
\(581\) −15.2652 −0.633308
\(582\) −44.7486 −1.85489
\(583\) −14.3090 −0.592617
\(584\) −2.14991 −0.0889640
\(585\) −28.4790 −1.17746
\(586\) −3.14321 −0.129845
\(587\) 12.8549 0.530577 0.265289 0.964169i \(-0.414533\pi\)
0.265289 + 0.964169i \(0.414533\pi\)
\(588\) 0.289784 0.0119505
\(589\) 26.7631 1.10276
\(590\) 5.33318 0.219564
\(591\) 69.9928 2.87912
\(592\) −47.7824 −1.96385
\(593\) −10.9993 −0.451687 −0.225843 0.974164i \(-0.572514\pi\)
−0.225843 + 0.974164i \(0.572514\pi\)
\(594\) 30.5006 1.25146
\(595\) 4.56972 0.187340
\(596\) −33.7552 −1.38267
\(597\) −68.1008 −2.78718
\(598\) 1.48200 0.0606035
\(599\) 31.4069 1.28325 0.641625 0.767018i \(-0.278260\pi\)
0.641625 + 0.767018i \(0.278260\pi\)
\(600\) 3.08379 0.125895
\(601\) −7.52642 −0.307009 −0.153504 0.988148i \(-0.549056\pi\)
−0.153504 + 0.988148i \(0.549056\pi\)
\(602\) 5.11001 0.208269
\(603\) −57.8389 −2.35538
\(604\) 17.8089 0.724632
\(605\) −1.73342 −0.0704734
\(606\) 57.7644 2.34652
\(607\) 29.2571 1.18751 0.593754 0.804646i \(-0.297645\pi\)
0.593754 + 0.804646i \(0.297645\pi\)
\(608\) −58.2838 −2.36372
\(609\) 15.6158 0.632786
\(610\) −41.4811 −1.67952
\(611\) 13.6816 0.553499
\(612\) −13.6895 −0.553366
\(613\) −27.8085 −1.12318 −0.561588 0.827417i \(-0.689809\pi\)
−0.561588 + 0.827417i \(0.689809\pi\)
\(614\) 2.51144 0.101353
\(615\) −48.4867 −1.95517
\(616\) 1.24038 0.0499763
\(617\) −0.753517 −0.0303355 −0.0151677 0.999885i \(-0.504828\pi\)
−0.0151677 + 0.999885i \(0.504828\pi\)
\(618\) 67.1807 2.70240
\(619\) −28.6224 −1.15043 −0.575215 0.818002i \(-0.695082\pi\)
−0.575215 + 0.818002i \(0.695082\pi\)
\(620\) 10.6852 0.429126
\(621\) 5.70447 0.228912
\(622\) −33.3888 −1.33877
\(623\) 41.5517 1.66473
\(624\) 30.6656 1.22761
\(625\) −11.0426 −0.441704
\(626\) 1.80958 0.0723254
\(627\) 25.0618 1.00087
\(628\) −7.06312 −0.281849
\(629\) −10.7945 −0.430405
\(630\) 69.0043 2.74920
\(631\) −30.9091 −1.23047 −0.615235 0.788343i \(-0.710939\pi\)
−0.615235 + 0.788343i \(0.710939\pi\)
\(632\) −2.23475 −0.0888936
\(633\) 68.5643 2.72519
\(634\) 12.7187 0.505122
\(635\) 32.8307 1.30285
\(636\) 82.5964 3.27516
\(637\) −0.105875 −0.00419491
\(638\) 3.49542 0.138385
\(639\) 109.995 4.35134
\(640\) 6.47666 0.256012
\(641\) 38.3146 1.51334 0.756668 0.653800i \(-0.226826\pi\)
0.756668 + 0.653800i \(0.226826\pi\)
\(642\) 5.89704 0.232738
\(643\) 29.0357 1.14506 0.572528 0.819885i \(-0.305963\pi\)
0.572528 + 0.819885i \(0.305963\pi\)
\(644\) −1.67945 −0.0661794
\(645\) −5.69402 −0.224202
\(646\) −14.7888 −0.581857
\(647\) −35.4898 −1.39525 −0.697624 0.716464i \(-0.745759\pi\)
−0.697624 + 0.716464i \(0.745759\pi\)
\(648\) 13.3235 0.523395
\(649\) 1.58726 0.0623053
\(650\) 8.15655 0.319926
\(651\) 30.3768 1.19056
\(652\) 30.9287 1.21126
\(653\) 33.4577 1.30930 0.654651 0.755931i \(-0.272815\pi\)
0.654651 + 0.755931i \(0.272815\pi\)
\(654\) 127.818 4.99808
\(655\) 3.73269 0.145848
\(656\) 37.6938 1.47169
\(657\) −35.5962 −1.38874
\(658\) −33.1505 −1.29234
\(659\) 41.4542 1.61483 0.807413 0.589986i \(-0.200867\pi\)
0.807413 + 0.589986i \(0.200867\pi\)
\(660\) 10.0059 0.389479
\(661\) −35.7494 −1.39049 −0.695245 0.718773i \(-0.744704\pi\)
−0.695245 + 0.718773i \(0.744704\pi\)
\(662\) 41.0439 1.59522
\(663\) 6.92765 0.269047
\(664\) −2.72449 −0.105731
\(665\) 34.8647 1.35199
\(666\) −163.001 −6.31615
\(667\) 0.653742 0.0253130
\(668\) −21.3420 −0.825746
\(669\) 69.5956 2.69072
\(670\) −24.9464 −0.963764
\(671\) −12.3456 −0.476595
\(672\) −66.1535 −2.55193
\(673\) 24.6497 0.950177 0.475089 0.879938i \(-0.342416\pi\)
0.475089 + 0.879938i \(0.342416\pi\)
\(674\) −14.4813 −0.557798
\(675\) 31.3959 1.20843
\(676\) −15.0286 −0.578022
\(677\) 48.9934 1.88297 0.941485 0.337056i \(-0.109431\pi\)
0.941485 + 0.337056i \(0.109431\pi\)
\(678\) −13.8127 −0.530473
\(679\) −18.5274 −0.711015
\(680\) 0.815589 0.0312764
\(681\) −84.0828 −3.22206
\(682\) 6.79949 0.260366
\(683\) 7.64087 0.292370 0.146185 0.989257i \(-0.453301\pi\)
0.146185 + 0.989257i \(0.453301\pi\)
\(684\) −104.444 −3.99353
\(685\) 10.2781 0.392707
\(686\) 36.0266 1.37550
\(687\) −27.9909 −1.06792
\(688\) 4.42655 0.168761
\(689\) −30.1772 −1.14966
\(690\) 4.00126 0.152325
\(691\) −23.7285 −0.902675 −0.451337 0.892353i \(-0.649053\pi\)
−0.451337 + 0.892353i \(0.649053\pi\)
\(692\) −6.47625 −0.246190
\(693\) 20.5370 0.780136
\(694\) −5.60411 −0.212729
\(695\) 23.3998 0.887606
\(696\) 2.78707 0.105644
\(697\) 8.51539 0.322543
\(698\) 59.0350 2.23451
\(699\) 14.3457 0.542603
\(700\) −9.24323 −0.349361
\(701\) −2.88945 −0.109133 −0.0545664 0.998510i \(-0.517378\pi\)
−0.0545664 + 0.998510i \(0.517378\pi\)
\(702\) 64.3249 2.42779
\(703\) −82.3568 −3.10615
\(704\) −5.95458 −0.224422
\(705\) 36.9391 1.39121
\(706\) 64.8963 2.44240
\(707\) 23.9163 0.899467
\(708\) −9.16221 −0.344337
\(709\) −44.2952 −1.66354 −0.831771 0.555119i \(-0.812673\pi\)
−0.831771 + 0.555119i \(0.812673\pi\)
\(710\) 47.4419 1.78046
\(711\) −37.0008 −1.38764
\(712\) 7.41602 0.277927
\(713\) 1.27169 0.0476253
\(714\) −16.7856 −0.628186
\(715\) −3.65572 −0.136716
\(716\) 25.7114 0.960881
\(717\) −54.9792 −2.05324
\(718\) −23.9047 −0.892114
\(719\) −46.5819 −1.73721 −0.868605 0.495504i \(-0.834983\pi\)
−0.868605 + 0.495504i \(0.834983\pi\)
\(720\) 59.7750 2.22768
\(721\) 27.8150 1.03588
\(722\) −76.0021 −2.82851
\(723\) 15.6204 0.580928
\(724\) −45.3280 −1.68460
\(725\) 3.59803 0.133627
\(726\) 6.36724 0.236311
\(727\) 27.5183 1.02060 0.510299 0.859997i \(-0.329535\pi\)
0.510299 + 0.859997i \(0.329535\pi\)
\(728\) 2.61592 0.0969525
\(729\) 65.5336 2.42717
\(730\) −15.3529 −0.568237
\(731\) 1.00000 0.0369863
\(732\) 71.2629 2.63395
\(733\) 2.42830 0.0896913 0.0448456 0.998994i \(-0.485720\pi\)
0.0448456 + 0.998994i \(0.485720\pi\)
\(734\) 0.630332 0.0232660
\(735\) −0.285852 −0.0105438
\(736\) −2.76945 −0.102083
\(737\) −7.42453 −0.273486
\(738\) 128.585 4.73329
\(739\) −4.45515 −0.163885 −0.0819427 0.996637i \(-0.526112\pi\)
−0.0819427 + 0.996637i \(0.526112\pi\)
\(740\) −32.8809 −1.20872
\(741\) 52.8545 1.94166
\(742\) 73.1190 2.68428
\(743\) 43.2479 1.58661 0.793306 0.608823i \(-0.208358\pi\)
0.793306 + 0.608823i \(0.208358\pi\)
\(744\) 5.42156 0.198764
\(745\) 33.2972 1.21991
\(746\) 24.5981 0.900600
\(747\) −45.1094 −1.65047
\(748\) −1.75726 −0.0642520
\(749\) 2.44157 0.0892129
\(750\) 77.2074 2.81921
\(751\) 4.57822 0.167062 0.0835308 0.996505i \(-0.473380\pi\)
0.0835308 + 0.996505i \(0.473380\pi\)
\(752\) −28.7166 −1.04719
\(753\) 14.5151 0.528958
\(754\) 7.37173 0.268463
\(755\) −17.5672 −0.639335
\(756\) −72.8947 −2.65116
\(757\) 5.63988 0.204985 0.102492 0.994734i \(-0.467318\pi\)
0.102492 + 0.994734i \(0.467318\pi\)
\(758\) −7.10503 −0.258066
\(759\) 1.19085 0.0432252
\(760\) 6.22254 0.225715
\(761\) −42.5977 −1.54416 −0.772082 0.635523i \(-0.780785\pi\)
−0.772082 + 0.635523i \(0.780785\pi\)
\(762\) −120.595 −4.36869
\(763\) 52.9208 1.91586
\(764\) 29.8915 1.08144
\(765\) 13.5037 0.488229
\(766\) 56.6899 2.04829
\(767\) 3.34748 0.120870
\(768\) −62.9101 −2.27007
\(769\) 40.0796 1.44531 0.722653 0.691211i \(-0.242923\pi\)
0.722653 + 0.691211i \(0.242923\pi\)
\(770\) 8.85778 0.319212
\(771\) 3.24105 0.116724
\(772\) −6.32364 −0.227593
\(773\) −23.9124 −0.860071 −0.430035 0.902812i \(-0.641499\pi\)
−0.430035 + 0.902812i \(0.641499\pi\)
\(774\) 15.1003 0.542771
\(775\) 6.99908 0.251414
\(776\) −3.30671 −0.118704
\(777\) −93.4770 −3.35347
\(778\) −53.4402 −1.91592
\(779\) 64.9682 2.32773
\(780\) 21.1021 0.755577
\(781\) 14.1196 0.505240
\(782\) −0.702714 −0.0251290
\(783\) 28.3750 1.01404
\(784\) 0.222222 0.00793651
\(785\) 6.96727 0.248672
\(786\) −13.7110 −0.489056
\(787\) 22.1403 0.789215 0.394607 0.918850i \(-0.370881\pi\)
0.394607 + 0.918850i \(0.370881\pi\)
\(788\) −37.4434 −1.33387
\(789\) −84.1254 −2.99494
\(790\) −15.9588 −0.567788
\(791\) −5.71890 −0.203341
\(792\) 3.66538 0.130244
\(793\) −26.0364 −0.924580
\(794\) −28.4941 −1.01122
\(795\) −81.4755 −2.88964
\(796\) 36.4313 1.29127
\(797\) −22.4021 −0.793523 −0.396762 0.917922i \(-0.629866\pi\)
−0.396762 + 0.917922i \(0.629866\pi\)
\(798\) −128.066 −4.53349
\(799\) −6.48736 −0.229506
\(800\) −15.2423 −0.538898
\(801\) 122.787 4.33847
\(802\) −44.1560 −1.55920
\(803\) −4.56933 −0.161248
\(804\) 42.8570 1.51145
\(805\) 1.65665 0.0583894
\(806\) 14.3399 0.505102
\(807\) −28.2476 −0.994364
\(808\) 4.26852 0.150166
\(809\) −32.8106 −1.15356 −0.576780 0.816900i \(-0.695691\pi\)
−0.576780 + 0.816900i \(0.695691\pi\)
\(810\) 95.1454 3.34307
\(811\) −48.3551 −1.69798 −0.848988 0.528412i \(-0.822788\pi\)
−0.848988 + 0.528412i \(0.822788\pi\)
\(812\) −8.35386 −0.293163
\(813\) −33.5322 −1.17602
\(814\) −20.9237 −0.733376
\(815\) −30.5090 −1.06868
\(816\) −14.5406 −0.509021
\(817\) 7.62951 0.266923
\(818\) −63.5339 −2.22141
\(819\) 43.3119 1.51344
\(820\) 25.9385 0.905811
\(821\) 2.45472 0.0856703 0.0428351 0.999082i \(-0.486361\pi\)
0.0428351 + 0.999082i \(0.486361\pi\)
\(822\) −37.7539 −1.31682
\(823\) 41.4164 1.44368 0.721842 0.692057i \(-0.243296\pi\)
0.721842 + 0.692057i \(0.243296\pi\)
\(824\) 4.96434 0.172941
\(825\) 6.55415 0.228186
\(826\) −8.11090 −0.282214
\(827\) 23.0951 0.803096 0.401548 0.915838i \(-0.368472\pi\)
0.401548 + 0.915838i \(0.368472\pi\)
\(828\) −4.96284 −0.172471
\(829\) 28.2170 0.980016 0.490008 0.871718i \(-0.336994\pi\)
0.490008 + 0.871718i \(0.336994\pi\)
\(830\) −19.4561 −0.675331
\(831\) −8.10746 −0.281245
\(832\) −12.5580 −0.435371
\(833\) 0.0502022 0.00173940
\(834\) −85.9530 −2.97631
\(835\) 21.0523 0.728546
\(836\) −13.4071 −0.463693
\(837\) 55.1967 1.90788
\(838\) 10.1787 0.351618
\(839\) 19.1594 0.661456 0.330728 0.943726i \(-0.392706\pi\)
0.330728 + 0.943726i \(0.392706\pi\)
\(840\) 7.06274 0.243688
\(841\) −25.7482 −0.887868
\(842\) −25.6226 −0.883013
\(843\) −62.9260 −2.16729
\(844\) −36.6792 −1.26255
\(845\) 14.8246 0.509982
\(846\) −97.9613 −3.36798
\(847\) 2.63625 0.0905825
\(848\) 63.3394 2.17508
\(849\) −59.1169 −2.02889
\(850\) −3.86755 −0.132656
\(851\) −3.91332 −0.134147
\(852\) −81.5034 −2.79226
\(853\) −48.2807 −1.65310 −0.826550 0.562863i \(-0.809700\pi\)
−0.826550 + 0.562863i \(0.809700\pi\)
\(854\) 63.0860 2.15876
\(855\) 103.027 3.52344
\(856\) 0.435764 0.0148941
\(857\) 47.9734 1.63874 0.819371 0.573264i \(-0.194323\pi\)
0.819371 + 0.573264i \(0.194323\pi\)
\(858\) 13.4283 0.458435
\(859\) −7.57082 −0.258313 −0.129157 0.991624i \(-0.541227\pi\)
−0.129157 + 0.991624i \(0.541227\pi\)
\(860\) 3.04607 0.103870
\(861\) 73.7405 2.51307
\(862\) 38.7882 1.32113
\(863\) 16.9193 0.575939 0.287969 0.957640i \(-0.407020\pi\)
0.287969 + 0.957640i \(0.407020\pi\)
\(864\) −120.205 −4.08947
\(865\) 6.38836 0.217211
\(866\) 32.5887 1.10741
\(867\) −3.28485 −0.111559
\(868\) −16.2504 −0.551574
\(869\) −4.74964 −0.161120
\(870\) 19.9030 0.674774
\(871\) −15.6581 −0.530555
\(872\) 9.44516 0.319853
\(873\) −54.7493 −1.85298
\(874\) −5.36136 −0.181351
\(875\) 31.9664 1.08066
\(876\) 26.3758 0.891155
\(877\) −21.9229 −0.740282 −0.370141 0.928976i \(-0.620691\pi\)
−0.370141 + 0.928976i \(0.620691\pi\)
\(878\) −16.8818 −0.569734
\(879\) −5.32663 −0.179663
\(880\) 7.67306 0.258659
\(881\) −12.1434 −0.409121 −0.204561 0.978854i \(-0.565577\pi\)
−0.204561 + 0.978854i \(0.565577\pi\)
\(882\) 0.758070 0.0255255
\(883\) 46.8397 1.57628 0.788140 0.615496i \(-0.211044\pi\)
0.788140 + 0.615496i \(0.211044\pi\)
\(884\) −3.70602 −0.124647
\(885\) 9.03787 0.303805
\(886\) 36.3305 1.22055
\(887\) 22.5429 0.756918 0.378459 0.925618i \(-0.376454\pi\)
0.378459 + 0.925618i \(0.376454\pi\)
\(888\) −16.6835 −0.559861
\(889\) −49.9302 −1.67460
\(890\) 52.9592 1.77520
\(891\) 28.3171 0.948659
\(892\) −37.2309 −1.24658
\(893\) −49.4953 −1.65630
\(894\) −122.308 −4.09060
\(895\) −25.3625 −0.847774
\(896\) −9.84995 −0.329064
\(897\) 2.51147 0.0838556
\(898\) −33.0921 −1.10430
\(899\) 6.32563 0.210972
\(900\) −27.3142 −0.910474
\(901\) 14.3090 0.476701
\(902\) 16.5059 0.549588
\(903\) 8.65968 0.288176
\(904\) −1.02069 −0.0339477
\(905\) 44.7128 1.48630
\(906\) 64.5283 2.14381
\(907\) −20.6351 −0.685179 −0.342589 0.939485i \(-0.611304\pi\)
−0.342589 + 0.939485i \(0.611304\pi\)
\(908\) 44.9810 1.49275
\(909\) 70.6740 2.34411
\(910\) 18.6808 0.619262
\(911\) 8.35217 0.276720 0.138360 0.990382i \(-0.455817\pi\)
0.138360 + 0.990382i \(0.455817\pi\)
\(912\) −110.937 −3.67350
\(913\) −5.79051 −0.191638
\(914\) −9.22680 −0.305195
\(915\) −70.2958 −2.32391
\(916\) 14.9741 0.494757
\(917\) −5.67681 −0.187465
\(918\) −30.5006 −1.00667
\(919\) 35.8513 1.18263 0.591313 0.806442i \(-0.298610\pi\)
0.591313 + 0.806442i \(0.298610\pi\)
\(920\) 0.295675 0.00974810
\(921\) 4.25600 0.140240
\(922\) 27.6494 0.910586
\(923\) 29.7778 0.980149
\(924\) −15.2173 −0.500614
\(925\) −21.5379 −0.708162
\(926\) 26.8352 0.881859
\(927\) 82.1947 2.69963
\(928\) −13.7757 −0.452211
\(929\) 43.6799 1.43309 0.716546 0.697540i \(-0.245722\pi\)
0.716546 + 0.697540i \(0.245722\pi\)
\(930\) 38.7164 1.26956
\(931\) 0.383018 0.0125529
\(932\) −7.67437 −0.251382
\(933\) −56.5823 −1.85242
\(934\) −1.16865 −0.0382394
\(935\) 1.73342 0.0566888
\(936\) 7.73018 0.252669
\(937\) 58.7575 1.91952 0.959762 0.280814i \(-0.0906045\pi\)
0.959762 + 0.280814i \(0.0906045\pi\)
\(938\) 37.9395 1.23877
\(939\) 3.06660 0.100075
\(940\) −19.7610 −0.644531
\(941\) −39.1228 −1.27537 −0.637684 0.770298i \(-0.720107\pi\)
−0.637684 + 0.770298i \(0.720107\pi\)
\(942\) −25.5924 −0.833845
\(943\) 3.08707 0.100529
\(944\) −7.02607 −0.228679
\(945\) 71.9055 2.33909
\(946\) 1.93837 0.0630217
\(947\) −18.6990 −0.607637 −0.303818 0.952730i \(-0.598262\pi\)
−0.303818 + 0.952730i \(0.598262\pi\)
\(948\) 27.4166 0.890449
\(949\) −9.63657 −0.312816
\(950\) −29.5075 −0.957351
\(951\) 21.5537 0.698925
\(952\) −1.24038 −0.0402009
\(953\) −39.2364 −1.27099 −0.635495 0.772105i \(-0.719204\pi\)
−0.635495 + 0.772105i \(0.719204\pi\)
\(954\) 216.070 6.99553
\(955\) −29.4859 −0.954140
\(956\) 29.4117 0.951242
\(957\) 5.92351 0.191480
\(958\) 9.21461 0.297710
\(959\) −15.6314 −0.504763
\(960\) −33.9055 −1.09429
\(961\) −18.6950 −0.603065
\(962\) −44.1275 −1.42273
\(963\) 7.21495 0.232499
\(964\) −8.35628 −0.269138
\(965\) 6.23782 0.200803
\(966\) −6.08527 −0.195790
\(967\) −23.8704 −0.767621 −0.383811 0.923412i \(-0.625388\pi\)
−0.383811 + 0.923412i \(0.625388\pi\)
\(968\) 0.470510 0.0151227
\(969\) −25.0618 −0.805100
\(970\) −23.6139 −0.758195
\(971\) 15.7806 0.506423 0.253212 0.967411i \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(972\) −80.5035 −2.58215
\(973\) −35.5873 −1.14088
\(974\) 27.5626 0.883164
\(975\) 13.8225 0.442674
\(976\) 54.6482 1.74925
\(977\) 40.9037 1.30863 0.654313 0.756224i \(-0.272958\pi\)
0.654313 + 0.756224i \(0.272958\pi\)
\(978\) 112.067 3.58350
\(979\) 15.7617 0.503745
\(980\) 0.152919 0.00488483
\(981\) 156.384 4.99295
\(982\) −14.6298 −0.466855
\(983\) −30.9473 −0.987066 −0.493533 0.869727i \(-0.664295\pi\)
−0.493533 + 0.869727i \(0.664295\pi\)
\(984\) 13.1610 0.419557
\(985\) 36.9353 1.17686
\(986\) −3.49542 −0.111317
\(987\) −56.1784 −1.78818
\(988\) −28.2751 −0.899550
\(989\) 0.362529 0.0115277
\(990\) 26.1752 0.831902
\(991\) −2.23823 −0.0710998 −0.0355499 0.999368i \(-0.511318\pi\)
−0.0355499 + 0.999368i \(0.511318\pi\)
\(992\) −26.7973 −0.850816
\(993\) 69.5550 2.20726
\(994\) −72.1514 −2.28850
\(995\) −35.9368 −1.13927
\(996\) 33.4248 1.05911
\(997\) −46.5959 −1.47571 −0.737853 0.674962i \(-0.764160\pi\)
−0.737853 + 0.674962i \(0.764160\pi\)
\(998\) 0.809841 0.0256351
\(999\) −169.854 −5.37394
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 \(a_p\))