Properties

Label 8041.2.a.i.1.18
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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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 1.18
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} +O(q^{10})\) \(q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} -4.40747 q^{10} +1.00000 q^{11} +2.74675 q^{12} +2.82188 q^{13} +5.11310 q^{14} +7.75599 q^{15} -4.99266 q^{16} -1.00000 q^{17} -10.2851 q^{18} -4.52884 q^{19} +2.36060 q^{20} -8.99771 q^{21} -1.70714 q^{22} +8.03274 q^{23} +5.56781 q^{24} +1.66562 q^{25} -4.81735 q^{26} +9.08665 q^{27} -2.73853 q^{28} -1.93883 q^{29} -13.2406 q^{30} -4.01354 q^{31} +4.81639 q^{32} +3.00412 q^{33} +1.70714 q^{34} -7.73277 q^{35} +5.50859 q^{36} +3.59747 q^{37} +7.73136 q^{38} +8.47727 q^{39} +4.78506 q^{40} -3.41107 q^{41} +15.3604 q^{42} -1.00000 q^{43} +0.914329 q^{44} +15.5546 q^{45} -13.7130 q^{46} +5.66303 q^{47} -14.9985 q^{48} +1.97077 q^{49} -2.84345 q^{50} -3.00412 q^{51} +2.58013 q^{52} -3.29387 q^{53} -15.5122 q^{54} +2.58179 q^{55} -5.55114 q^{56} -13.6052 q^{57} +3.30986 q^{58} +3.03259 q^{59} +7.09153 q^{60} +7.35064 q^{61} +6.85167 q^{62} -18.0448 q^{63} +1.76307 q^{64} +7.28549 q^{65} -5.12845 q^{66} +12.8738 q^{67} -0.914329 q^{68} +24.1313 q^{69} +13.2009 q^{70} -1.74265 q^{71} +11.1662 q^{72} +9.72601 q^{73} -6.14138 q^{74} +5.00372 q^{75} -4.14085 q^{76} -2.99512 q^{77} -14.4719 q^{78} +10.1543 q^{79} -12.8900 q^{80} +9.22319 q^{81} +5.82318 q^{82} -0.743214 q^{83} -8.22687 q^{84} -2.58179 q^{85} +1.70714 q^{86} -5.82449 q^{87} +1.85339 q^{88} +2.14243 q^{89} -26.5538 q^{90} -8.45189 q^{91} +7.34457 q^{92} -12.0571 q^{93} -9.66759 q^{94} -11.6925 q^{95} +14.4690 q^{96} +7.44229 q^{97} -3.36438 q^{98} +6.02473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70714 −1.20713 −0.603565 0.797314i \(-0.706254\pi\)
−0.603565 + 0.797314i \(0.706254\pi\)
\(3\) 3.00412 1.73443 0.867214 0.497935i \(-0.165908\pi\)
0.867214 + 0.497935i \(0.165908\pi\)
\(4\) 0.914329 0.457165
\(5\) 2.58179 1.15461 0.577305 0.816529i \(-0.304104\pi\)
0.577305 + 0.816529i \(0.304104\pi\)
\(6\) −5.12845 −2.09368
\(7\) −2.99512 −1.13205 −0.566025 0.824388i \(-0.691520\pi\)
−0.566025 + 0.824388i \(0.691520\pi\)
\(8\) 1.85339 0.655273
\(9\) 6.02473 2.00824
\(10\) −4.40747 −1.39377
\(11\) 1.00000 0.301511
\(12\) 2.74675 0.792920
\(13\) 2.82188 0.782649 0.391325 0.920253i \(-0.372017\pi\)
0.391325 + 0.920253i \(0.372017\pi\)
\(14\) 5.11310 1.36653
\(15\) 7.75599 2.00259
\(16\) −4.99266 −1.24817
\(17\) −1.00000 −0.242536
\(18\) −10.2851 −2.42421
\(19\) −4.52884 −1.03899 −0.519493 0.854475i \(-0.673879\pi\)
−0.519493 + 0.854475i \(0.673879\pi\)
\(20\) 2.36060 0.527847
\(21\) −8.99771 −1.96346
\(22\) −1.70714 −0.363964
\(23\) 8.03274 1.67494 0.837471 0.546482i \(-0.184033\pi\)
0.837471 + 0.546482i \(0.184033\pi\)
\(24\) 5.56781 1.13652
\(25\) 1.66562 0.333124
\(26\) −4.81735 −0.944760
\(27\) 9.08665 1.74873
\(28\) −2.73853 −0.517534
\(29\) −1.93883 −0.360032 −0.180016 0.983664i \(-0.557615\pi\)
−0.180016 + 0.983664i \(0.557615\pi\)
\(30\) −13.2406 −2.41739
\(31\) −4.01354 −0.720852 −0.360426 0.932788i \(-0.617369\pi\)
−0.360426 + 0.932788i \(0.617369\pi\)
\(32\) 4.81639 0.851425
\(33\) 3.00412 0.522950
\(34\) 1.70714 0.292772
\(35\) −7.73277 −1.30708
\(36\) 5.50859 0.918098
\(37\) 3.59747 0.591420 0.295710 0.955278i \(-0.404444\pi\)
0.295710 + 0.955278i \(0.404444\pi\)
\(38\) 7.73136 1.25419
\(39\) 8.47727 1.35745
\(40\) 4.78506 0.756585
\(41\) −3.41107 −0.532720 −0.266360 0.963874i \(-0.585821\pi\)
−0.266360 + 0.963874i \(0.585821\pi\)
\(42\) 15.3604 2.37015
\(43\) −1.00000 −0.152499
\(44\) 0.914329 0.137840
\(45\) 15.5546 2.31874
\(46\) −13.7130 −2.02187
\(47\) 5.66303 0.826038 0.413019 0.910722i \(-0.364474\pi\)
0.413019 + 0.910722i \(0.364474\pi\)
\(48\) −14.9985 −2.16485
\(49\) 1.97077 0.281538
\(50\) −2.84345 −0.402124
\(51\) −3.00412 −0.420661
\(52\) 2.58013 0.357800
\(53\) −3.29387 −0.452448 −0.226224 0.974075i \(-0.572638\pi\)
−0.226224 + 0.974075i \(0.572638\pi\)
\(54\) −15.5122 −2.11094
\(55\) 2.58179 0.348128
\(56\) −5.55114 −0.741802
\(57\) −13.6052 −1.80205
\(58\) 3.30986 0.434606
\(59\) 3.03259 0.394809 0.197405 0.980322i \(-0.436749\pi\)
0.197405 + 0.980322i \(0.436749\pi\)
\(60\) 7.09153 0.915513
\(61\) 7.35064 0.941153 0.470576 0.882359i \(-0.344046\pi\)
0.470576 + 0.882359i \(0.344046\pi\)
\(62\) 6.85167 0.870163
\(63\) −18.0448 −2.27343
\(64\) 1.76307 0.220383
\(65\) 7.28549 0.903654
\(66\) −5.12845 −0.631269
\(67\) 12.8738 1.57279 0.786393 0.617726i \(-0.211946\pi\)
0.786393 + 0.617726i \(0.211946\pi\)
\(68\) −0.914329 −0.110879
\(69\) 24.1313 2.90507
\(70\) 13.2009 1.57781
\(71\) −1.74265 −0.206814 −0.103407 0.994639i \(-0.532974\pi\)
−0.103407 + 0.994639i \(0.532974\pi\)
\(72\) 11.1662 1.31595
\(73\) 9.72601 1.13834 0.569172 0.822219i \(-0.307264\pi\)
0.569172 + 0.822219i \(0.307264\pi\)
\(74\) −6.14138 −0.713921
\(75\) 5.00372 0.577780
\(76\) −4.14085 −0.474988
\(77\) −2.99512 −0.341326
\(78\) −14.4719 −1.63862
\(79\) 10.1543 1.14245 0.571224 0.820794i \(-0.306469\pi\)
0.571224 + 0.820794i \(0.306469\pi\)
\(80\) −12.8900 −1.44114
\(81\) 9.22319 1.02480
\(82\) 5.82318 0.643063
\(83\) −0.743214 −0.0815784 −0.0407892 0.999168i \(-0.512987\pi\)
−0.0407892 + 0.999168i \(0.512987\pi\)
\(84\) −8.22687 −0.897625
\(85\) −2.58179 −0.280034
\(86\) 1.70714 0.184086
\(87\) −5.82449 −0.624451
\(88\) 1.85339 0.197572
\(89\) 2.14243 0.227097 0.113549 0.993532i \(-0.463778\pi\)
0.113549 + 0.993532i \(0.463778\pi\)
\(90\) −26.5538 −2.79902
\(91\) −8.45189 −0.885998
\(92\) 7.34457 0.765724
\(93\) −12.0571 −1.25027
\(94\) −9.66759 −0.997136
\(95\) −11.6925 −1.19962
\(96\) 14.4690 1.47674
\(97\) 7.44229 0.755650 0.377825 0.925877i \(-0.376672\pi\)
0.377825 + 0.925877i \(0.376672\pi\)
\(98\) −3.36438 −0.339854
\(99\) 6.02473 0.605508
\(100\) 1.52293 0.152293
\(101\) −9.81951 −0.977078 −0.488539 0.872542i \(-0.662470\pi\)
−0.488539 + 0.872542i \(0.662470\pi\)
\(102\) 5.12845 0.507793
\(103\) 8.89443 0.876394 0.438197 0.898879i \(-0.355617\pi\)
0.438197 + 0.898879i \(0.355617\pi\)
\(104\) 5.23005 0.512849
\(105\) −23.2302 −2.26703
\(106\) 5.62311 0.546164
\(107\) 19.4655 1.88180 0.940900 0.338685i \(-0.109982\pi\)
0.940900 + 0.338685i \(0.109982\pi\)
\(108\) 8.30819 0.799456
\(109\) 9.31212 0.891940 0.445970 0.895048i \(-0.352859\pi\)
0.445970 + 0.895048i \(0.352859\pi\)
\(110\) −4.40747 −0.420236
\(111\) 10.8072 1.02578
\(112\) 14.9536 1.41299
\(113\) 12.0389 1.13253 0.566263 0.824224i \(-0.308389\pi\)
0.566263 + 0.824224i \(0.308389\pi\)
\(114\) 23.2259 2.17531
\(115\) 20.7388 1.93390
\(116\) −1.77273 −0.164594
\(117\) 17.0011 1.57175
\(118\) −5.17705 −0.476586
\(119\) 2.99512 0.274563
\(120\) 14.3749 1.31224
\(121\) 1.00000 0.0909091
\(122\) −12.5486 −1.13609
\(123\) −10.2473 −0.923965
\(124\) −3.66969 −0.329548
\(125\) −8.60866 −0.769982
\(126\) 30.8050 2.74433
\(127\) −15.4638 −1.37219 −0.686096 0.727511i \(-0.740677\pi\)
−0.686096 + 0.727511i \(0.740677\pi\)
\(128\) −12.6426 −1.11746
\(129\) −3.00412 −0.264498
\(130\) −12.4374 −1.09083
\(131\) 3.00229 0.262312 0.131156 0.991362i \(-0.458131\pi\)
0.131156 + 0.991362i \(0.458131\pi\)
\(132\) 2.74675 0.239074
\(133\) 13.5644 1.17619
\(134\) −21.9774 −1.89856
\(135\) 23.4598 2.01910
\(136\) −1.85339 −0.158927
\(137\) −5.04309 −0.430860 −0.215430 0.976519i \(-0.569115\pi\)
−0.215430 + 0.976519i \(0.569115\pi\)
\(138\) −41.1955 −3.50680
\(139\) 6.41950 0.544495 0.272248 0.962227i \(-0.412233\pi\)
0.272248 + 0.962227i \(0.412233\pi\)
\(140\) −7.07030 −0.597549
\(141\) 17.0124 1.43270
\(142\) 2.97495 0.249652
\(143\) 2.82188 0.235978
\(144\) −30.0794 −2.50662
\(145\) −5.00565 −0.415697
\(146\) −16.6037 −1.37413
\(147\) 5.92043 0.488308
\(148\) 3.28927 0.270376
\(149\) 3.09057 0.253189 0.126595 0.991955i \(-0.459595\pi\)
0.126595 + 0.991955i \(0.459595\pi\)
\(150\) −8.54206 −0.697456
\(151\) 1.88358 0.153283 0.0766417 0.997059i \(-0.475580\pi\)
0.0766417 + 0.997059i \(0.475580\pi\)
\(152\) −8.39371 −0.680820
\(153\) −6.02473 −0.487071
\(154\) 5.11310 0.412025
\(155\) −10.3621 −0.832303
\(156\) 7.75101 0.620578
\(157\) 13.8893 1.10849 0.554245 0.832354i \(-0.313007\pi\)
0.554245 + 0.832354i \(0.313007\pi\)
\(158\) −17.3348 −1.37908
\(159\) −9.89519 −0.784739
\(160\) 12.4349 0.983064
\(161\) −24.0591 −1.89612
\(162\) −15.7453 −1.23707
\(163\) 17.6830 1.38504 0.692522 0.721397i \(-0.256500\pi\)
0.692522 + 0.721397i \(0.256500\pi\)
\(164\) −3.11884 −0.243541
\(165\) 7.75599 0.603803
\(166\) 1.26877 0.0984757
\(167\) −6.84736 −0.529865 −0.264932 0.964267i \(-0.585350\pi\)
−0.264932 + 0.964267i \(0.585350\pi\)
\(168\) −16.6763 −1.28660
\(169\) −5.03699 −0.387460
\(170\) 4.40747 0.338038
\(171\) −27.2850 −2.08654
\(172\) −0.914329 −0.0697170
\(173\) 1.26214 0.0959585 0.0479792 0.998848i \(-0.484722\pi\)
0.0479792 + 0.998848i \(0.484722\pi\)
\(174\) 9.94322 0.753794
\(175\) −4.98874 −0.377113
\(176\) −4.99266 −0.376336
\(177\) 9.11025 0.684769
\(178\) −3.65743 −0.274136
\(179\) 8.56192 0.639948 0.319974 0.947426i \(-0.396326\pi\)
0.319974 + 0.947426i \(0.396326\pi\)
\(180\) 14.2220 1.06005
\(181\) −17.1931 −1.27795 −0.638977 0.769226i \(-0.720642\pi\)
−0.638977 + 0.769226i \(0.720642\pi\)
\(182\) 14.4286 1.06952
\(183\) 22.0822 1.63236
\(184\) 14.8878 1.09754
\(185\) 9.28789 0.682859
\(186\) 20.5832 1.50924
\(187\) −1.00000 −0.0731272
\(188\) 5.17788 0.377635
\(189\) −27.2157 −1.97965
\(190\) 19.9607 1.44810
\(191\) −17.3556 −1.25581 −0.627905 0.778290i \(-0.716087\pi\)
−0.627905 + 0.778290i \(0.716087\pi\)
\(192\) 5.29646 0.382239
\(193\) −6.21215 −0.447161 −0.223580 0.974686i \(-0.571774\pi\)
−0.223580 + 0.974686i \(0.571774\pi\)
\(194\) −12.7050 −0.912168
\(195\) 21.8865 1.56732
\(196\) 1.80193 0.128709
\(197\) 2.56523 0.182765 0.0913824 0.995816i \(-0.470871\pi\)
0.0913824 + 0.995816i \(0.470871\pi\)
\(198\) −10.2851 −0.730928
\(199\) −14.6875 −1.04117 −0.520586 0.853809i \(-0.674286\pi\)
−0.520586 + 0.853809i \(0.674286\pi\)
\(200\) 3.08705 0.218287
\(201\) 38.6745 2.72789
\(202\) 16.7633 1.17946
\(203\) 5.80705 0.407575
\(204\) −2.74675 −0.192311
\(205\) −8.80666 −0.615084
\(206\) −15.1840 −1.05792
\(207\) 48.3951 3.36369
\(208\) −14.0887 −0.976875
\(209\) −4.52884 −0.313266
\(210\) 39.6572 2.73660
\(211\) −16.3647 −1.12659 −0.563296 0.826255i \(-0.690467\pi\)
−0.563296 + 0.826255i \(0.690467\pi\)
\(212\) −3.01169 −0.206843
\(213\) −5.23512 −0.358705
\(214\) −33.2303 −2.27158
\(215\) −2.58179 −0.176076
\(216\) 16.8411 1.14589
\(217\) 12.0210 0.816041
\(218\) −15.8971 −1.07669
\(219\) 29.2181 1.97438
\(220\) 2.36060 0.159152
\(221\) −2.82188 −0.189820
\(222\) −18.4494 −1.23825
\(223\) 2.55653 0.171198 0.0855990 0.996330i \(-0.472720\pi\)
0.0855990 + 0.996330i \(0.472720\pi\)
\(224\) −14.4257 −0.963857
\(225\) 10.0349 0.668994
\(226\) −20.5521 −1.36711
\(227\) 6.98626 0.463695 0.231847 0.972752i \(-0.425523\pi\)
0.231847 + 0.972752i \(0.425523\pi\)
\(228\) −12.4396 −0.823833
\(229\) 7.62415 0.503818 0.251909 0.967751i \(-0.418942\pi\)
0.251909 + 0.967751i \(0.418942\pi\)
\(230\) −35.4041 −2.33448
\(231\) −8.99771 −0.592006
\(232\) −3.59342 −0.235920
\(233\) −18.9266 −1.23992 −0.619960 0.784633i \(-0.712851\pi\)
−0.619960 + 0.784633i \(0.712851\pi\)
\(234\) −29.0232 −1.89731
\(235\) 14.6207 0.953752
\(236\) 2.77278 0.180493
\(237\) 30.5047 1.98149
\(238\) −5.11310 −0.331433
\(239\) 1.97805 0.127950 0.0639748 0.997952i \(-0.479622\pi\)
0.0639748 + 0.997952i \(0.479622\pi\)
\(240\) −38.7230 −2.49956
\(241\) 5.15695 0.332189 0.166094 0.986110i \(-0.446884\pi\)
0.166094 + 0.986110i \(0.446884\pi\)
\(242\) −1.70714 −0.109739
\(243\) 0.447607 0.0287140
\(244\) 6.72091 0.430262
\(245\) 5.08811 0.325067
\(246\) 17.4935 1.11535
\(247\) −12.7798 −0.813162
\(248\) −7.43866 −0.472355
\(249\) −2.23270 −0.141492
\(250\) 14.6962 0.929468
\(251\) 24.0312 1.51683 0.758417 0.651769i \(-0.225973\pi\)
0.758417 + 0.651769i \(0.225973\pi\)
\(252\) −16.4989 −1.03933
\(253\) 8.03274 0.505014
\(254\) 26.3989 1.65641
\(255\) −7.75599 −0.485699
\(256\) 18.0565 1.12853
\(257\) −5.40174 −0.336951 −0.168476 0.985706i \(-0.553884\pi\)
−0.168476 + 0.985706i \(0.553884\pi\)
\(258\) 5.12845 0.319284
\(259\) −10.7749 −0.669517
\(260\) 6.66134 0.413119
\(261\) −11.6810 −0.723033
\(262\) −5.12534 −0.316645
\(263\) 9.40836 0.580144 0.290072 0.957005i \(-0.406321\pi\)
0.290072 + 0.957005i \(0.406321\pi\)
\(264\) 5.56781 0.342675
\(265\) −8.50408 −0.522401
\(266\) −23.1564 −1.41981
\(267\) 6.43612 0.393884
\(268\) 11.7709 0.719022
\(269\) −8.71453 −0.531334 −0.265667 0.964065i \(-0.585592\pi\)
−0.265667 + 0.964065i \(0.585592\pi\)
\(270\) −40.0492 −2.43731
\(271\) −19.2783 −1.17107 −0.585536 0.810646i \(-0.699116\pi\)
−0.585536 + 0.810646i \(0.699116\pi\)
\(272\) 4.99266 0.302725
\(273\) −25.3905 −1.53670
\(274\) 8.60927 0.520105
\(275\) 1.66562 0.100441
\(276\) 22.0640 1.32809
\(277\) 28.6412 1.72088 0.860441 0.509550i \(-0.170188\pi\)
0.860441 + 0.509550i \(0.170188\pi\)
\(278\) −10.9590 −0.657277
\(279\) −24.1805 −1.44765
\(280\) −14.3319 −0.856492
\(281\) −3.53038 −0.210605 −0.105302 0.994440i \(-0.533581\pi\)
−0.105302 + 0.994440i \(0.533581\pi\)
\(282\) −29.0426 −1.72946
\(283\) −28.9441 −1.72055 −0.860275 0.509831i \(-0.829708\pi\)
−0.860275 + 0.509831i \(0.829708\pi\)
\(284\) −1.59335 −0.0945482
\(285\) −35.1256 −2.08066
\(286\) −4.81735 −0.284856
\(287\) 10.2166 0.603066
\(288\) 29.0174 1.70987
\(289\) 1.00000 0.0588235
\(290\) 8.54536 0.501801
\(291\) 22.3575 1.31062
\(292\) 8.89277 0.520410
\(293\) 19.8993 1.16253 0.581266 0.813714i \(-0.302558\pi\)
0.581266 + 0.813714i \(0.302558\pi\)
\(294\) −10.1070 −0.589452
\(295\) 7.82949 0.455851
\(296\) 6.66752 0.387542
\(297\) 9.08665 0.527261
\(298\) −5.27603 −0.305632
\(299\) 22.6674 1.31089
\(300\) 4.57505 0.264141
\(301\) 2.99512 0.172636
\(302\) −3.21553 −0.185033
\(303\) −29.4990 −1.69467
\(304\) 22.6109 1.29683
\(305\) 18.9778 1.08666
\(306\) 10.2851 0.587958
\(307\) 26.2441 1.49783 0.748914 0.662667i \(-0.230575\pi\)
0.748914 + 0.662667i \(0.230575\pi\)
\(308\) −2.73853 −0.156042
\(309\) 26.7199 1.52004
\(310\) 17.6895 1.00470
\(311\) 3.43363 0.194703 0.0973515 0.995250i \(-0.468963\pi\)
0.0973515 + 0.995250i \(0.468963\pi\)
\(312\) 15.7117 0.889500
\(313\) 16.7662 0.947684 0.473842 0.880610i \(-0.342867\pi\)
0.473842 + 0.880610i \(0.342867\pi\)
\(314\) −23.7110 −1.33809
\(315\) −46.5879 −2.62493
\(316\) 9.28437 0.522287
\(317\) 5.20653 0.292428 0.146214 0.989253i \(-0.453291\pi\)
0.146214 + 0.989253i \(0.453291\pi\)
\(318\) 16.8925 0.947283
\(319\) −1.93883 −0.108554
\(320\) 4.55186 0.254457
\(321\) 58.4766 3.26385
\(322\) 41.0722 2.28886
\(323\) 4.52884 0.251991
\(324\) 8.43303 0.468502
\(325\) 4.70018 0.260719
\(326\) −30.1875 −1.67193
\(327\) 27.9747 1.54701
\(328\) −6.32206 −0.349077
\(329\) −16.9615 −0.935117
\(330\) −13.2406 −0.728869
\(331\) −0.264100 −0.0145162 −0.00725811 0.999974i \(-0.502310\pi\)
−0.00725811 + 0.999974i \(0.502310\pi\)
\(332\) −0.679543 −0.0372947
\(333\) 21.6738 1.18772
\(334\) 11.6894 0.639616
\(335\) 33.2374 1.81595
\(336\) 44.9225 2.45072
\(337\) 4.95839 0.270101 0.135050 0.990839i \(-0.456880\pi\)
0.135050 + 0.990839i \(0.456880\pi\)
\(338\) 8.59884 0.467715
\(339\) 36.1664 1.96429
\(340\) −2.36060 −0.128022
\(341\) −4.01354 −0.217345
\(342\) 46.5794 2.51872
\(343\) 15.0632 0.813335
\(344\) −1.85339 −0.0999282
\(345\) 62.3019 3.35422
\(346\) −2.15465 −0.115834
\(347\) −4.37562 −0.234896 −0.117448 0.993079i \(-0.537471\pi\)
−0.117448 + 0.993079i \(0.537471\pi\)
\(348\) −5.32550 −0.285477
\(349\) −19.2040 −1.02796 −0.513982 0.857801i \(-0.671830\pi\)
−0.513982 + 0.857801i \(0.671830\pi\)
\(350\) 8.51648 0.455225
\(351\) 25.6415 1.36864
\(352\) 4.81639 0.256714
\(353\) 27.3704 1.45678 0.728390 0.685162i \(-0.240269\pi\)
0.728390 + 0.685162i \(0.240269\pi\)
\(354\) −15.5525 −0.826605
\(355\) −4.49915 −0.238790
\(356\) 1.95889 0.103821
\(357\) 8.99771 0.476209
\(358\) −14.6164 −0.772501
\(359\) −13.1360 −0.693293 −0.346646 0.937996i \(-0.612680\pi\)
−0.346646 + 0.937996i \(0.612680\pi\)
\(360\) 28.8287 1.51941
\(361\) 1.51036 0.0794926
\(362\) 29.3511 1.54266
\(363\) 3.00412 0.157675
\(364\) −7.72781 −0.405047
\(365\) 25.1105 1.31434
\(366\) −37.6974 −1.97048
\(367\) 4.30071 0.224495 0.112248 0.993680i \(-0.464195\pi\)
0.112248 + 0.993680i \(0.464195\pi\)
\(368\) −40.1047 −2.09060
\(369\) −20.5508 −1.06983
\(370\) −15.8557 −0.824300
\(371\) 9.86556 0.512194
\(372\) −11.0242 −0.571578
\(373\) 11.7573 0.608771 0.304385 0.952549i \(-0.401549\pi\)
0.304385 + 0.952549i \(0.401549\pi\)
\(374\) 1.70714 0.0882741
\(375\) −25.8614 −1.33548
\(376\) 10.4958 0.541281
\(377\) −5.47116 −0.281779
\(378\) 46.4609 2.38969
\(379\) −20.9215 −1.07466 −0.537332 0.843371i \(-0.680568\pi\)
−0.537332 + 0.843371i \(0.680568\pi\)
\(380\) −10.6908 −0.548426
\(381\) −46.4551 −2.37997
\(382\) 29.6285 1.51593
\(383\) 0.294128 0.0150293 0.00751463 0.999972i \(-0.497608\pi\)
0.00751463 + 0.999972i \(0.497608\pi\)
\(384\) −37.9798 −1.93815
\(385\) −7.73277 −0.394098
\(386\) 10.6050 0.539781
\(387\) −6.02473 −0.306254
\(388\) 6.80470 0.345457
\(389\) 8.77705 0.445014 0.222507 0.974931i \(-0.428576\pi\)
0.222507 + 0.974931i \(0.428576\pi\)
\(390\) −37.3633 −1.89197
\(391\) −8.03274 −0.406233
\(392\) 3.65261 0.184485
\(393\) 9.01925 0.454961
\(394\) −4.37920 −0.220621
\(395\) 26.2162 1.31908
\(396\) 5.50859 0.276817
\(397\) 25.2836 1.26895 0.634473 0.772945i \(-0.281217\pi\)
0.634473 + 0.772945i \(0.281217\pi\)
\(398\) 25.0737 1.25683
\(399\) 40.7492 2.04001
\(400\) −8.31588 −0.415794
\(401\) −22.5865 −1.12792 −0.563959 0.825803i \(-0.690722\pi\)
−0.563959 + 0.825803i \(0.690722\pi\)
\(402\) −66.0228 −3.29292
\(403\) −11.3257 −0.564174
\(404\) −8.97827 −0.446686
\(405\) 23.8123 1.18324
\(406\) −9.91345 −0.491996
\(407\) 3.59747 0.178320
\(408\) −5.56781 −0.275648
\(409\) 2.30505 0.113977 0.0569887 0.998375i \(-0.481850\pi\)
0.0569887 + 0.998375i \(0.481850\pi\)
\(410\) 15.0342 0.742487
\(411\) −15.1501 −0.747297
\(412\) 8.13244 0.400657
\(413\) −9.08298 −0.446944
\(414\) −82.6172 −4.06042
\(415\) −1.91882 −0.0941912
\(416\) 13.5913 0.666367
\(417\) 19.2850 0.944388
\(418\) 7.73136 0.378153
\(419\) −32.3226 −1.57906 −0.789531 0.613711i \(-0.789676\pi\)
−0.789531 + 0.613711i \(0.789676\pi\)
\(420\) −21.2400 −1.03641
\(421\) 3.05398 0.148842 0.0744210 0.997227i \(-0.476289\pi\)
0.0744210 + 0.997227i \(0.476289\pi\)
\(422\) 27.9368 1.35994
\(423\) 34.1182 1.65889
\(424\) −6.10484 −0.296477
\(425\) −1.66562 −0.0807945
\(426\) 8.93709 0.433004
\(427\) −22.0161 −1.06543
\(428\) 17.7979 0.860292
\(429\) 8.47727 0.409286
\(430\) 4.40747 0.212547
\(431\) −34.4829 −1.66098 −0.830491 0.557032i \(-0.811940\pi\)
−0.830491 + 0.557032i \(0.811940\pi\)
\(432\) −45.3666 −2.18270
\(433\) −28.2661 −1.35838 −0.679192 0.733961i \(-0.737669\pi\)
−0.679192 + 0.733961i \(0.737669\pi\)
\(434\) −20.5216 −0.985068
\(435\) −15.0376 −0.720997
\(436\) 8.51435 0.407763
\(437\) −36.3790 −1.74024
\(438\) −49.8794 −2.38333
\(439\) −2.85011 −0.136028 −0.0680141 0.997684i \(-0.521666\pi\)
−0.0680141 + 0.997684i \(0.521666\pi\)
\(440\) 4.78506 0.228119
\(441\) 11.8734 0.565398
\(442\) 4.81735 0.229138
\(443\) −37.9460 −1.80287 −0.901435 0.432914i \(-0.857485\pi\)
−0.901435 + 0.432914i \(0.857485\pi\)
\(444\) 9.88136 0.468948
\(445\) 5.53130 0.262209
\(446\) −4.36436 −0.206658
\(447\) 9.28443 0.439139
\(448\) −5.28061 −0.249485
\(449\) −1.63603 −0.0772090 −0.0386045 0.999255i \(-0.512291\pi\)
−0.0386045 + 0.999255i \(0.512291\pi\)
\(450\) −17.1310 −0.807564
\(451\) −3.41107 −0.160621
\(452\) 11.0075 0.517751
\(453\) 5.65849 0.265859
\(454\) −11.9265 −0.559740
\(455\) −21.8210 −1.02298
\(456\) −25.2157 −1.18083
\(457\) −6.96222 −0.325679 −0.162839 0.986653i \(-0.552065\pi\)
−0.162839 + 0.986653i \(0.552065\pi\)
\(458\) −13.0155 −0.608174
\(459\) −9.08665 −0.424129
\(460\) 18.9621 0.884113
\(461\) −1.33882 −0.0623550 −0.0311775 0.999514i \(-0.509926\pi\)
−0.0311775 + 0.999514i \(0.509926\pi\)
\(462\) 15.3604 0.714628
\(463\) 14.5799 0.677584 0.338792 0.940861i \(-0.389982\pi\)
0.338792 + 0.940861i \(0.389982\pi\)
\(464\) 9.67994 0.449380
\(465\) −31.1290 −1.44357
\(466\) 32.3103 1.49675
\(467\) 33.4252 1.54674 0.773368 0.633958i \(-0.218571\pi\)
0.773368 + 0.633958i \(0.218571\pi\)
\(468\) 15.5446 0.718549
\(469\) −38.5587 −1.78047
\(470\) −24.9597 −1.15130
\(471\) 41.7252 1.92260
\(472\) 5.62057 0.258708
\(473\) −1.00000 −0.0459800
\(474\) −52.0759 −2.39192
\(475\) −7.54332 −0.346111
\(476\) 2.73853 0.125520
\(477\) −19.8447 −0.908627
\(478\) −3.37681 −0.154452
\(479\) −5.30744 −0.242503 −0.121252 0.992622i \(-0.538691\pi\)
−0.121252 + 0.992622i \(0.538691\pi\)
\(480\) 37.3559 1.70505
\(481\) 10.1516 0.462874
\(482\) −8.80365 −0.400995
\(483\) −72.2763 −3.28868
\(484\) 0.914329 0.0415604
\(485\) 19.2144 0.872481
\(486\) −0.764129 −0.0346616
\(487\) −32.8945 −1.49059 −0.745295 0.666734i \(-0.767692\pi\)
−0.745295 + 0.666734i \(0.767692\pi\)
\(488\) 13.6236 0.616712
\(489\) 53.1220 2.40226
\(490\) −8.68611 −0.392399
\(491\) −1.94836 −0.0879283 −0.0439641 0.999033i \(-0.513999\pi\)
−0.0439641 + 0.999033i \(0.513999\pi\)
\(492\) −9.36938 −0.422404
\(493\) 1.93883 0.0873207
\(494\) 21.8170 0.981593
\(495\) 15.5546 0.699126
\(496\) 20.0382 0.899743
\(497\) 5.21945 0.234124
\(498\) 3.81154 0.170799
\(499\) 25.4596 1.13973 0.569863 0.821740i \(-0.306996\pi\)
0.569863 + 0.821740i \(0.306996\pi\)
\(500\) −7.87115 −0.352008
\(501\) −20.5703 −0.919013
\(502\) −41.0246 −1.83102
\(503\) −29.9609 −1.33589 −0.667945 0.744211i \(-0.732826\pi\)
−0.667945 + 0.744211i \(0.732826\pi\)
\(504\) −33.4441 −1.48972
\(505\) −25.3519 −1.12814
\(506\) −13.7130 −0.609618
\(507\) −15.1317 −0.672023
\(508\) −14.1390 −0.627318
\(509\) −23.3208 −1.03368 −0.516838 0.856083i \(-0.672891\pi\)
−0.516838 + 0.856083i \(0.672891\pi\)
\(510\) 13.2406 0.586302
\(511\) −29.1306 −1.28866
\(512\) −5.53988 −0.244830
\(513\) −41.1520 −1.81690
\(514\) 9.22152 0.406744
\(515\) 22.9635 1.01189
\(516\) −2.74675 −0.120919
\(517\) 5.66303 0.249060
\(518\) 18.3942 0.808195
\(519\) 3.79161 0.166433
\(520\) 13.5029 0.592140
\(521\) −40.1913 −1.76081 −0.880407 0.474218i \(-0.842731\pi\)
−0.880407 + 0.474218i \(0.842731\pi\)
\(522\) 19.9410 0.872795
\(523\) 28.2217 1.23405 0.617024 0.786944i \(-0.288338\pi\)
0.617024 + 0.786944i \(0.288338\pi\)
\(524\) 2.74509 0.119920
\(525\) −14.9868 −0.654076
\(526\) −16.0614 −0.700310
\(527\) 4.01354 0.174832
\(528\) −14.9985 −0.652728
\(529\) 41.5249 1.80543
\(530\) 14.5177 0.630607
\(531\) 18.2705 0.792873
\(532\) 12.4024 0.537710
\(533\) −9.62564 −0.416933
\(534\) −10.9874 −0.475470
\(535\) 50.2557 2.17274
\(536\) 23.8602 1.03060
\(537\) 25.7210 1.10994
\(538\) 14.8769 0.641390
\(539\) 1.97077 0.0848870
\(540\) 21.4500 0.923060
\(541\) −18.5299 −0.796663 −0.398331 0.917242i \(-0.630411\pi\)
−0.398331 + 0.917242i \(0.630411\pi\)
\(542\) 32.9107 1.41364
\(543\) −51.6502 −2.21652
\(544\) −4.81639 −0.206501
\(545\) 24.0419 1.02984
\(546\) 43.3451 1.85500
\(547\) 12.0252 0.514158 0.257079 0.966390i \(-0.417240\pi\)
0.257079 + 0.966390i \(0.417240\pi\)
\(548\) −4.61105 −0.196974
\(549\) 44.2856 1.89006
\(550\) −2.84345 −0.121245
\(551\) 8.78066 0.374069
\(552\) 44.7248 1.90361
\(553\) −30.4134 −1.29331
\(554\) −48.8945 −2.07733
\(555\) 27.9019 1.18437
\(556\) 5.86954 0.248924
\(557\) 16.9330 0.717472 0.358736 0.933439i \(-0.383208\pi\)
0.358736 + 0.933439i \(0.383208\pi\)
\(558\) 41.2795 1.74750
\(559\) −2.82188 −0.119353
\(560\) 38.6071 1.63145
\(561\) −3.00412 −0.126834
\(562\) 6.02686 0.254228
\(563\) 38.2466 1.61190 0.805952 0.591981i \(-0.201654\pi\)
0.805952 + 0.591981i \(0.201654\pi\)
\(564\) 15.5550 0.654982
\(565\) 31.0819 1.30763
\(566\) 49.4117 2.07693
\(567\) −27.6246 −1.16012
\(568\) −3.22981 −0.135520
\(569\) −13.3812 −0.560969 −0.280485 0.959859i \(-0.590495\pi\)
−0.280485 + 0.959859i \(0.590495\pi\)
\(570\) 59.9644 2.51163
\(571\) −8.54519 −0.357605 −0.178802 0.983885i \(-0.557222\pi\)
−0.178802 + 0.983885i \(0.557222\pi\)
\(572\) 2.58013 0.107881
\(573\) −52.1384 −2.17811
\(574\) −17.4411 −0.727979
\(575\) 13.3795 0.557963
\(576\) 10.6220 0.442584
\(577\) −15.5254 −0.646332 −0.323166 0.946342i \(-0.604747\pi\)
−0.323166 + 0.946342i \(0.604747\pi\)
\(578\) −1.70714 −0.0710077
\(579\) −18.6621 −0.775568
\(580\) −4.57682 −0.190042
\(581\) 2.22602 0.0923508
\(582\) −38.1674 −1.58209
\(583\) −3.29387 −0.136418
\(584\) 18.0261 0.745926
\(585\) 43.8931 1.81476
\(586\) −33.9710 −1.40333
\(587\) −13.9457 −0.575601 −0.287801 0.957690i \(-0.592924\pi\)
−0.287801 + 0.957690i \(0.592924\pi\)
\(588\) 5.41322 0.223237
\(589\) 18.1766 0.748956
\(590\) −13.3660 −0.550271
\(591\) 7.70625 0.316993
\(592\) −17.9609 −0.738190
\(593\) 1.69391 0.0695604 0.0347802 0.999395i \(-0.488927\pi\)
0.0347802 + 0.999395i \(0.488927\pi\)
\(594\) −15.5122 −0.636473
\(595\) 7.73277 0.317013
\(596\) 2.82580 0.115749
\(597\) −44.1231 −1.80584
\(598\) −38.6965 −1.58242
\(599\) −17.0080 −0.694930 −0.347465 0.937693i \(-0.612957\pi\)
−0.347465 + 0.937693i \(0.612957\pi\)
\(600\) 9.27386 0.378604
\(601\) −22.6958 −0.925782 −0.462891 0.886415i \(-0.653188\pi\)
−0.462891 + 0.886415i \(0.653188\pi\)
\(602\) −5.11310 −0.208394
\(603\) 77.5613 3.15854
\(604\) 1.72221 0.0700758
\(605\) 2.58179 0.104965
\(606\) 50.3589 2.04569
\(607\) −9.84320 −0.399523 −0.199762 0.979845i \(-0.564017\pi\)
−0.199762 + 0.979845i \(0.564017\pi\)
\(608\) −21.8126 −0.884619
\(609\) 17.4451 0.706910
\(610\) −32.3977 −1.31175
\(611\) 15.9804 0.646498
\(612\) −5.50859 −0.222672
\(613\) −32.3597 −1.30700 −0.653498 0.756928i \(-0.726699\pi\)
−0.653498 + 0.756928i \(0.726699\pi\)
\(614\) −44.8023 −1.80807
\(615\) −26.4563 −1.06682
\(616\) −5.55114 −0.223662
\(617\) −28.0622 −1.12974 −0.564872 0.825179i \(-0.691074\pi\)
−0.564872 + 0.825179i \(0.691074\pi\)
\(618\) −45.6147 −1.83489
\(619\) 28.0533 1.12756 0.563778 0.825926i \(-0.309347\pi\)
0.563778 + 0.825926i \(0.309347\pi\)
\(620\) −9.47436 −0.380500
\(621\) 72.9907 2.92902
\(622\) −5.86168 −0.235032
\(623\) −6.41685 −0.257086
\(624\) −42.3241 −1.69432
\(625\) −30.5538 −1.22215
\(626\) −28.6223 −1.14398
\(627\) −13.6052 −0.543338
\(628\) 12.6994 0.506762
\(629\) −3.59747 −0.143440
\(630\) 79.5320 3.16863
\(631\) −13.5333 −0.538752 −0.269376 0.963035i \(-0.586817\pi\)
−0.269376 + 0.963035i \(0.586817\pi\)
\(632\) 18.8199 0.748616
\(633\) −49.1615 −1.95399
\(634\) −8.88829 −0.352999
\(635\) −39.9243 −1.58435
\(636\) −9.04746 −0.358755
\(637\) 5.56128 0.220346
\(638\) 3.30986 0.131039
\(639\) −10.4990 −0.415334
\(640\) −32.6404 −1.29023
\(641\) 2.21452 0.0874683 0.0437341 0.999043i \(-0.486075\pi\)
0.0437341 + 0.999043i \(0.486075\pi\)
\(642\) −99.8278 −3.93989
\(643\) −4.55377 −0.179583 −0.0897916 0.995961i \(-0.528620\pi\)
−0.0897916 + 0.995961i \(0.528620\pi\)
\(644\) −21.9979 −0.866839
\(645\) −7.75599 −0.305392
\(646\) −7.73136 −0.304186
\(647\) 15.8632 0.623647 0.311824 0.950140i \(-0.399060\pi\)
0.311824 + 0.950140i \(0.399060\pi\)
\(648\) 17.0942 0.671523
\(649\) 3.03259 0.119039
\(650\) −8.02387 −0.314722
\(651\) 36.1126 1.41537
\(652\) 16.1681 0.633193
\(653\) −21.9593 −0.859332 −0.429666 0.902988i \(-0.641369\pi\)
−0.429666 + 0.902988i \(0.641369\pi\)
\(654\) −47.7568 −1.86744
\(655\) 7.75128 0.302868
\(656\) 17.0303 0.664922
\(657\) 58.5966 2.28607
\(658\) 28.9556 1.12881
\(659\) −9.64737 −0.375808 −0.187904 0.982187i \(-0.560169\pi\)
−0.187904 + 0.982187i \(0.560169\pi\)
\(660\) 7.09153 0.276038
\(661\) 30.9915 1.20543 0.602715 0.797957i \(-0.294086\pi\)
0.602715 + 0.797957i \(0.294086\pi\)
\(662\) 0.450855 0.0175230
\(663\) −8.47727 −0.329230
\(664\) −1.37747 −0.0534561
\(665\) 35.0205 1.35803
\(666\) −37.0002 −1.43373
\(667\) −15.5741 −0.603033
\(668\) −6.26075 −0.242236
\(669\) 7.68012 0.296931
\(670\) −56.7410 −2.19210
\(671\) 7.35064 0.283768
\(672\) −43.3365 −1.67174
\(673\) 8.15023 0.314168 0.157084 0.987585i \(-0.449791\pi\)
0.157084 + 0.987585i \(0.449791\pi\)
\(674\) −8.46467 −0.326047
\(675\) 15.1349 0.582543
\(676\) −4.60546 −0.177133
\(677\) 18.3783 0.706337 0.353168 0.935560i \(-0.385104\pi\)
0.353168 + 0.935560i \(0.385104\pi\)
\(678\) −61.7411 −2.37115
\(679\) −22.2906 −0.855434
\(680\) −4.78506 −0.183499
\(681\) 20.9876 0.804245
\(682\) 6.85167 0.262364
\(683\) 19.3461 0.740260 0.370130 0.928980i \(-0.379313\pi\)
0.370130 + 0.928980i \(0.379313\pi\)
\(684\) −24.9475 −0.953891
\(685\) −13.0202 −0.497476
\(686\) −25.7150 −0.981801
\(687\) 22.9038 0.873836
\(688\) 4.99266 0.190343
\(689\) −9.29492 −0.354108
\(690\) −106.358 −4.04898
\(691\) −22.1628 −0.843115 −0.421557 0.906802i \(-0.638516\pi\)
−0.421557 + 0.906802i \(0.638516\pi\)
\(692\) 1.15401 0.0438688
\(693\) −18.0448 −0.685466
\(694\) 7.46981 0.283550
\(695\) 16.5738 0.628679
\(696\) −10.7951 −0.409186
\(697\) 3.41107 0.129204
\(698\) 32.7839 1.24089
\(699\) −56.8577 −2.15055
\(700\) −4.56135 −0.172403
\(701\) −1.91078 −0.0721691 −0.0360846 0.999349i \(-0.511489\pi\)
−0.0360846 + 0.999349i \(0.511489\pi\)
\(702\) −43.7736 −1.65213
\(703\) −16.2923 −0.614477
\(704\) 1.76307 0.0664481
\(705\) 43.9224 1.65421
\(706\) −46.7252 −1.75853
\(707\) 29.4107 1.10610
\(708\) 8.32977 0.313052
\(709\) −37.6792 −1.41507 −0.707537 0.706676i \(-0.750194\pi\)
−0.707537 + 0.706676i \(0.750194\pi\)
\(710\) 7.68067 0.288251
\(711\) 61.1769 2.29431
\(712\) 3.97077 0.148811
\(713\) −32.2397 −1.20739
\(714\) −15.3604 −0.574847
\(715\) 7.28549 0.272462
\(716\) 7.82841 0.292562
\(717\) 5.94230 0.221919
\(718\) 22.4250 0.836895
\(719\) 9.48956 0.353901 0.176950 0.984220i \(-0.443377\pi\)
0.176950 + 0.984220i \(0.443377\pi\)
\(720\) −77.6587 −2.89417
\(721\) −26.6399 −0.992123
\(722\) −2.57840 −0.0959580
\(723\) 15.4921 0.576158
\(724\) −15.7202 −0.584235
\(725\) −3.22936 −0.119935
\(726\) −5.12845 −0.190335
\(727\) 13.3855 0.496439 0.248220 0.968704i \(-0.420155\pi\)
0.248220 + 0.968704i \(0.420155\pi\)
\(728\) −15.6647 −0.580571
\(729\) −26.3249 −0.974997
\(730\) −42.8671 −1.58658
\(731\) 1.00000 0.0369863
\(732\) 20.1904 0.746259
\(733\) 50.9164 1.88064 0.940320 0.340293i \(-0.110526\pi\)
0.940320 + 0.340293i \(0.110526\pi\)
\(734\) −7.34192 −0.270995
\(735\) 15.2853 0.563806
\(736\) 38.6888 1.42609
\(737\) 12.8738 0.474213
\(738\) 35.0831 1.29143
\(739\) 17.6718 0.650068 0.325034 0.945702i \(-0.394624\pi\)
0.325034 + 0.945702i \(0.394624\pi\)
\(740\) 8.49219 0.312179
\(741\) −38.3922 −1.41037
\(742\) −16.8419 −0.618286
\(743\) 35.6520 1.30795 0.653973 0.756518i \(-0.273101\pi\)
0.653973 + 0.756518i \(0.273101\pi\)
\(744\) −22.3466 −0.819266
\(745\) 7.97919 0.292335
\(746\) −20.0714 −0.734866
\(747\) −4.47767 −0.163829
\(748\) −0.914329 −0.0334312
\(749\) −58.3015 −2.13029
\(750\) 44.1491 1.61210
\(751\) −8.38924 −0.306128 −0.153064 0.988216i \(-0.548914\pi\)
−0.153064 + 0.988216i \(0.548914\pi\)
\(752\) −28.2736 −1.03103
\(753\) 72.1925 2.63084
\(754\) 9.34004 0.340144
\(755\) 4.86300 0.176983
\(756\) −24.8841 −0.905025
\(757\) −38.2639 −1.39073 −0.695363 0.718659i \(-0.744756\pi\)
−0.695363 + 0.718659i \(0.744756\pi\)
\(758\) 35.7159 1.29726
\(759\) 24.1313 0.875911
\(760\) −21.6708 −0.786081
\(761\) 28.0751 1.01772 0.508860 0.860849i \(-0.330067\pi\)
0.508860 + 0.860849i \(0.330067\pi\)
\(762\) 79.3055 2.87293
\(763\) −27.8910 −1.00972
\(764\) −15.8688 −0.574112
\(765\) −15.5546 −0.562377
\(766\) −0.502119 −0.0181423
\(767\) 8.55760 0.308997
\(768\) 54.2440 1.95736
\(769\) −23.6111 −0.851439 −0.425719 0.904855i \(-0.639979\pi\)
−0.425719 + 0.904855i \(0.639979\pi\)
\(770\) 13.2009 0.475728
\(771\) −16.2275 −0.584418
\(772\) −5.67996 −0.204426
\(773\) 4.89139 0.175931 0.0879655 0.996124i \(-0.471963\pi\)
0.0879655 + 0.996124i \(0.471963\pi\)
\(774\) 10.2851 0.369689
\(775\) −6.68503 −0.240133
\(776\) 13.7935 0.495157
\(777\) −32.3690 −1.16123
\(778\) −14.9837 −0.537190
\(779\) 15.4482 0.553489
\(780\) 20.0115 0.716525
\(781\) −1.74265 −0.0623569
\(782\) 13.7130 0.490376
\(783\) −17.6175 −0.629598
\(784\) −9.83938 −0.351406
\(785\) 35.8593 1.27987
\(786\) −15.3971 −0.549197
\(787\) −36.6731 −1.30726 −0.653628 0.756816i \(-0.726754\pi\)
−0.653628 + 0.756816i \(0.726754\pi\)
\(788\) 2.34546 0.0835536
\(789\) 28.2638 1.00622
\(790\) −44.7548 −1.59230
\(791\) −36.0581 −1.28208
\(792\) 11.1662 0.396773
\(793\) 20.7426 0.736592
\(794\) −43.1626 −1.53178
\(795\) −25.5473 −0.906068
\(796\) −13.4292 −0.475987
\(797\) 16.1462 0.571926 0.285963 0.958241i \(-0.407686\pi\)
0.285963 + 0.958241i \(0.407686\pi\)
\(798\) −69.5645 −2.46256
\(799\) −5.66303 −0.200344
\(800\) 8.02228 0.283630
\(801\) 12.9076 0.456067
\(802\) 38.5584 1.36154
\(803\) 9.72601 0.343223
\(804\) 35.3612 1.24709
\(805\) −62.1153 −2.18928
\(806\) 19.3346 0.681032
\(807\) −26.1795 −0.921561
\(808\) −18.1994 −0.640253
\(809\) 23.7534 0.835125 0.417563 0.908648i \(-0.362884\pi\)
0.417563 + 0.908648i \(0.362884\pi\)
\(810\) −40.6510 −1.42833
\(811\) 41.4907 1.45693 0.728467 0.685081i \(-0.240233\pi\)
0.728467 + 0.685081i \(0.240233\pi\)
\(812\) 5.30956 0.186329
\(813\) −57.9143 −2.03114
\(814\) −6.14138 −0.215255
\(815\) 45.6539 1.59918
\(816\) 14.9985 0.525054
\(817\) 4.52884 0.158444
\(818\) −3.93504 −0.137586
\(819\) −50.9203 −1.77930
\(820\) −8.05219 −0.281195
\(821\) 21.6232 0.754655 0.377327 0.926080i \(-0.376843\pi\)
0.377327 + 0.926080i \(0.376843\pi\)
\(822\) 25.8633 0.902085
\(823\) 40.3891 1.40787 0.703937 0.710262i \(-0.251424\pi\)
0.703937 + 0.710262i \(0.251424\pi\)
\(824\) 16.4849 0.574278
\(825\) 5.00372 0.174207
\(826\) 15.5059 0.539520
\(827\) −54.7476 −1.90376 −0.951880 0.306472i \(-0.900851\pi\)
−0.951880 + 0.306472i \(0.900851\pi\)
\(828\) 44.2491 1.53776
\(829\) −0.207335 −0.00720105 −0.00360053 0.999994i \(-0.501146\pi\)
−0.00360053 + 0.999994i \(0.501146\pi\)
\(830\) 3.27570 0.113701
\(831\) 86.0416 2.98475
\(832\) 4.97517 0.172483
\(833\) −1.97077 −0.0682831
\(834\) −32.9221 −1.14000
\(835\) −17.6784 −0.611787
\(836\) −4.14085 −0.143214
\(837\) −36.4696 −1.26057
\(838\) 55.1792 1.90613
\(839\) 21.6296 0.746738 0.373369 0.927683i \(-0.378203\pi\)
0.373369 + 0.927683i \(0.378203\pi\)
\(840\) −43.0546 −1.48553
\(841\) −25.2409 −0.870377
\(842\) −5.21358 −0.179672
\(843\) −10.6057 −0.365279
\(844\) −14.9627 −0.515038
\(845\) −13.0044 −0.447366
\(846\) −58.2446 −2.00249
\(847\) −2.99512 −0.102914
\(848\) 16.4452 0.564730
\(849\) −86.9516 −2.98417
\(850\) 2.84345 0.0975295
\(851\) 28.8975 0.990594
\(852\) −4.78663 −0.163987
\(853\) 30.0205 1.02788 0.513941 0.857826i \(-0.328185\pi\)
0.513941 + 0.857826i \(0.328185\pi\)
\(854\) 37.5845 1.28612
\(855\) −70.4441 −2.40914
\(856\) 36.0772 1.23309
\(857\) 29.4546 1.00615 0.503074 0.864243i \(-0.332202\pi\)
0.503074 + 0.864243i \(0.332202\pi\)
\(858\) −14.4719 −0.494062
\(859\) 0.816990 0.0278753 0.0139377 0.999903i \(-0.495563\pi\)
0.0139377 + 0.999903i \(0.495563\pi\)
\(860\) −2.36060 −0.0804959
\(861\) 30.6918 1.04597
\(862\) 58.8671 2.00502
\(863\) −35.6036 −1.21196 −0.605980 0.795480i \(-0.707219\pi\)
−0.605980 + 0.795480i \(0.707219\pi\)
\(864\) 43.7649 1.48891
\(865\) 3.25857 0.110795
\(866\) 48.2542 1.63975
\(867\) 3.00412 0.102025
\(868\) 10.9912 0.373065
\(869\) 10.1543 0.344461
\(870\) 25.6713 0.870338
\(871\) 36.3284 1.23094
\(872\) 17.2590 0.584464
\(873\) 44.8378 1.51753
\(874\) 62.1040 2.10070
\(875\) 25.7840 0.871658
\(876\) 26.7150 0.902615
\(877\) −38.9840 −1.31639 −0.658197 0.752845i \(-0.728681\pi\)
−0.658197 + 0.752845i \(0.728681\pi\)
\(878\) 4.86553 0.164204
\(879\) 59.7800 2.01633
\(880\) −12.8900 −0.434521
\(881\) −48.4968 −1.63390 −0.816949 0.576709i \(-0.804337\pi\)
−0.816949 + 0.576709i \(0.804337\pi\)
\(882\) −20.2695 −0.682509
\(883\) −43.2022 −1.45387 −0.726935 0.686707i \(-0.759056\pi\)
−0.726935 + 0.686707i \(0.759056\pi\)
\(884\) −2.58013 −0.0867791
\(885\) 23.5207 0.790641
\(886\) 64.7792 2.17630
\(887\) 1.97748 0.0663972 0.0331986 0.999449i \(-0.489431\pi\)
0.0331986 + 0.999449i \(0.489431\pi\)
\(888\) 20.0300 0.672163
\(889\) 46.3160 1.55339
\(890\) −9.44271 −0.316520
\(891\) 9.22319 0.308989
\(892\) 2.33751 0.0782656
\(893\) −25.6469 −0.858242
\(894\) −15.8498 −0.530098
\(895\) 22.1050 0.738890
\(896\) 37.8661 1.26502
\(897\) 68.0957 2.27365
\(898\) 2.79293 0.0932013
\(899\) 7.78158 0.259530
\(900\) 9.17522 0.305841
\(901\) 3.29387 0.109735
\(902\) 5.82318 0.193891
\(903\) 8.99771 0.299425
\(904\) 22.3128 0.742114
\(905\) −44.3889 −1.47554
\(906\) −9.65985 −0.320927
\(907\) −47.8605 −1.58918 −0.794590 0.607146i \(-0.792314\pi\)
−0.794590 + 0.607146i \(0.792314\pi\)
\(908\) 6.38775 0.211985
\(909\) −59.1599 −1.96221
\(910\) 37.2515 1.23487
\(911\) 18.5057 0.613122 0.306561 0.951851i \(-0.400822\pi\)
0.306561 + 0.951851i \(0.400822\pi\)
\(912\) 67.9260 2.24925
\(913\) −0.743214 −0.0245968
\(914\) 11.8855 0.393137
\(915\) 57.0115 1.88474
\(916\) 6.97098 0.230328
\(917\) −8.99225 −0.296950
\(918\) 15.5122 0.511979
\(919\) −0.473425 −0.0156168 −0.00780842 0.999970i \(-0.502486\pi\)
−0.00780842 + 0.999970i \(0.502486\pi\)
\(920\) 38.4372 1.26724
\(921\) 78.8403 2.59788
\(922\) 2.28555 0.0752706
\(923\) −4.91755 −0.161863
\(924\) −8.22687 −0.270644
\(925\) 5.99201 0.197016
\(926\) −24.8899 −0.817932
\(927\) 53.5866 1.76001
\(928\) −9.33818 −0.306541
\(929\) 24.9772 0.819477 0.409738 0.912203i \(-0.365620\pi\)
0.409738 + 0.912203i \(0.365620\pi\)
\(930\) 53.1415 1.74258
\(931\) −8.92529 −0.292515
\(932\) −17.3051 −0.566848
\(933\) 10.3150 0.337699
\(934\) −57.0616 −1.86711
\(935\) −2.58179 −0.0844334
\(936\) 31.5097 1.02993
\(937\) −37.5992 −1.22831 −0.614155 0.789185i \(-0.710503\pi\)
−0.614155 + 0.789185i \(0.710503\pi\)
\(938\) 65.8251 2.14926
\(939\) 50.3678 1.64369
\(940\) 13.3682 0.436022
\(941\) −50.1251 −1.63403 −0.817016 0.576615i \(-0.804373\pi\)
−0.817016 + 0.576615i \(0.804373\pi\)
\(942\) −71.2308 −2.32082
\(943\) −27.4003 −0.892275
\(944\) −15.1407 −0.492787
\(945\) −70.2650 −2.28572
\(946\) 1.70714 0.0555039
\(947\) −4.46578 −0.145118 −0.0725592 0.997364i \(-0.523117\pi\)
−0.0725592 + 0.997364i \(0.523117\pi\)
\(948\) 27.8914 0.905869
\(949\) 27.4456 0.890923
\(950\) 12.8775 0.417802
\(951\) 15.6410 0.507196
\(952\) 5.55114 0.179914
\(953\) −25.1351 −0.814206 −0.407103 0.913382i \(-0.633461\pi\)
−0.407103 + 0.913382i \(0.633461\pi\)
\(954\) 33.8777 1.09683
\(955\) −44.8086 −1.44997
\(956\) 1.80859 0.0584940
\(957\) −5.82449 −0.188279
\(958\) 9.06055 0.292733
\(959\) 15.1047 0.487756
\(960\) 13.6743 0.441337
\(961\) −14.8915 −0.480372
\(962\) −17.3302 −0.558750
\(963\) 117.274 3.77911
\(964\) 4.71516 0.151865
\(965\) −16.0385 −0.516296
\(966\) 123.386 3.96987
\(967\) 26.5789 0.854720 0.427360 0.904082i \(-0.359444\pi\)
0.427360 + 0.904082i \(0.359444\pi\)
\(968\) 1.85339 0.0595703
\(969\) 13.6052 0.437061
\(970\) −32.8017 −1.05320
\(971\) −12.3495 −0.396314 −0.198157 0.980170i \(-0.563496\pi\)
−0.198157 + 0.980170i \(0.563496\pi\)
\(972\) 0.409261 0.0131270
\(973\) −19.2272 −0.616396
\(974\) 56.1555 1.79934
\(975\) 14.1199 0.452199
\(976\) −36.6992 −1.17471
\(977\) −0.773179 −0.0247362 −0.0123681 0.999924i \(-0.503937\pi\)
−0.0123681 + 0.999924i \(0.503937\pi\)
\(978\) −90.6867 −2.89984
\(979\) 2.14243 0.0684724
\(980\) 4.65220 0.148609
\(981\) 56.1030 1.79123
\(982\) 3.32613 0.106141
\(983\) 44.2292 1.41069 0.705347 0.708863i \(-0.250791\pi\)
0.705347 + 0.708863i \(0.250791\pi\)
\(984\) −18.9922 −0.605449
\(985\) 6.62287 0.211022
\(986\) −3.30986 −0.105407
\(987\) −50.9543 −1.62189
\(988\) −11.6850 −0.371749
\(989\) −8.03274 −0.255426
\(990\) −26.5538 −0.843936
\(991\) 41.3435 1.31332 0.656659 0.754187i \(-0.271969\pi\)
0.656659 + 0.754187i \(0.271969\pi\)
\(992\) −19.3307 −0.613752
\(993\) −0.793386 −0.0251774
\(994\) −8.91033 −0.282619
\(995\) −37.9201 −1.20215
\(996\) −2.04143 −0.0646851
\(997\) −7.19869 −0.227985 −0.113992 0.993482i \(-0.536364\pi\)
−0.113992 + 0.993482i \(0.536364\pi\)
\(998\) −43.4631 −1.37580
\(999\) 32.6889 1.03423
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 \(a_p\))