Properties

Label 8023.2.a.c.1.14
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.51950 q^{2}\) \(-2.51323 q^{3}\) \(+4.34790 q^{4}\) \(+1.49157 q^{5}\) \(+6.33210 q^{6}\) \(-1.81281 q^{7}\) \(-5.91556 q^{8}\) \(+3.31634 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.51950 q^{2}\) \(-2.51323 q^{3}\) \(+4.34790 q^{4}\) \(+1.49157 q^{5}\) \(+6.33210 q^{6}\) \(-1.81281 q^{7}\) \(-5.91556 q^{8}\) \(+3.31634 q^{9}\) \(-3.75802 q^{10}\) \(+0.112037 q^{11}\) \(-10.9273 q^{12}\) \(-2.05744 q^{13}\) \(+4.56738 q^{14}\) \(-3.74866 q^{15}\) \(+6.20847 q^{16}\) \(-0.998471 q^{17}\) \(-8.35554 q^{18}\) \(+2.42110 q^{19}\) \(+6.48521 q^{20}\) \(+4.55601 q^{21}\) \(-0.282278 q^{22}\) \(-4.58166 q^{23}\) \(+14.8672 q^{24}\) \(-2.77522 q^{25}\) \(+5.18373 q^{26}\) \(-0.795043 q^{27}\) \(-7.88192 q^{28}\) \(-1.78517 q^{29}\) \(+9.44478 q^{30}\) \(-1.50305 q^{31}\) \(-3.81115 q^{32}\) \(-0.281575 q^{33}\) \(+2.51565 q^{34}\) \(-2.70393 q^{35}\) \(+14.4191 q^{36}\) \(+1.83538 q^{37}\) \(-6.09997 q^{38}\) \(+5.17083 q^{39}\) \(-8.82347 q^{40}\) \(+3.52083 q^{41}\) \(-11.4789 q^{42}\) \(+1.61704 q^{43}\) \(+0.487126 q^{44}\) \(+4.94656 q^{45}\) \(+11.5435 q^{46}\) \(+3.42421 q^{47}\) \(-15.6033 q^{48}\) \(-3.71372 q^{49}\) \(+6.99217 q^{50}\) \(+2.50939 q^{51}\) \(-8.94556 q^{52}\) \(-7.80459 q^{53}\) \(+2.00311 q^{54}\) \(+0.167111 q^{55}\) \(+10.7238 q^{56}\) \(-6.08478 q^{57}\) \(+4.49775 q^{58}\) \(+9.72052 q^{59}\) \(-16.2988 q^{60}\) \(+6.10379 q^{61}\) \(+3.78695 q^{62}\) \(-6.01189 q^{63}\) \(-2.81473 q^{64}\) \(-3.06882 q^{65}\) \(+0.709429 q^{66}\) \(-4.61058 q^{67}\) \(-4.34126 q^{68}\) \(+11.5148 q^{69}\) \(+6.81257 q^{70}\) \(-1.00000 q^{71}\) \(-19.6180 q^{72}\) \(+15.7775 q^{73}\) \(-4.62425 q^{74}\) \(+6.97477 q^{75}\) \(+10.5267 q^{76}\) \(-0.203101 q^{77}\) \(-13.0279 q^{78}\) \(+12.0908 q^{79}\) \(+9.26037 q^{80}\) \(-7.95090 q^{81}\) \(-8.87074 q^{82}\) \(+11.6775 q^{83}\) \(+19.8091 q^{84}\) \(-1.48929 q^{85}\) \(-4.07413 q^{86}\) \(+4.48655 q^{87}\) \(-0.662761 q^{88}\) \(+9.20666 q^{89}\) \(-12.4629 q^{90}\) \(+3.72975 q^{91}\) \(-19.9206 q^{92}\) \(+3.77753 q^{93}\) \(-8.62733 q^{94}\) \(+3.61124 q^{95}\) \(+9.57831 q^{96}\) \(-1.36224 q^{97}\) \(+9.35675 q^{98}\) \(+0.371553 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51950 −1.78156 −0.890780 0.454436i \(-0.849841\pi\)
−0.890780 + 0.454436i \(0.849841\pi\)
\(3\) −2.51323 −1.45102 −0.725508 0.688214i \(-0.758395\pi\)
−0.725508 + 0.688214i \(0.758395\pi\)
\(4\) 4.34790 2.17395
\(5\) 1.49157 0.667051 0.333525 0.942741i \(-0.391762\pi\)
0.333525 + 0.942741i \(0.391762\pi\)
\(6\) 6.33210 2.58507
\(7\) −1.81281 −0.685177 −0.342589 0.939486i \(-0.611304\pi\)
−0.342589 + 0.939486i \(0.611304\pi\)
\(8\) −5.91556 −2.09147
\(9\) 3.31634 1.10545
\(10\) −3.75802 −1.18839
\(11\) 0.112037 0.0337804 0.0168902 0.999857i \(-0.494623\pi\)
0.0168902 + 0.999857i \(0.494623\pi\)
\(12\) −10.9273 −3.15444
\(13\) −2.05744 −0.570631 −0.285316 0.958434i \(-0.592098\pi\)
−0.285316 + 0.958434i \(0.592098\pi\)
\(14\) 4.56738 1.22068
\(15\) −3.74866 −0.967901
\(16\) 6.20847 1.55212
\(17\) −0.998471 −0.242165 −0.121082 0.992642i \(-0.538637\pi\)
−0.121082 + 0.992642i \(0.538637\pi\)
\(18\) −8.35554 −1.96942
\(19\) 2.42110 0.555438 0.277719 0.960662i \(-0.410422\pi\)
0.277719 + 0.960662i \(0.410422\pi\)
\(20\) 6.48521 1.45014
\(21\) 4.55601 0.994203
\(22\) −0.282278 −0.0601818
\(23\) −4.58166 −0.955343 −0.477672 0.878539i \(-0.658519\pi\)
−0.477672 + 0.878539i \(0.658519\pi\)
\(24\) 14.8672 3.03475
\(25\) −2.77522 −0.555044
\(26\) 5.18373 1.01661
\(27\) −0.795043 −0.153006
\(28\) −7.88192 −1.48954
\(29\) −1.78517 −0.331498 −0.165749 0.986168i \(-0.553004\pi\)
−0.165749 + 0.986168i \(0.553004\pi\)
\(30\) 9.44478 1.72437
\(31\) −1.50305 −0.269957 −0.134978 0.990849i \(-0.543096\pi\)
−0.134978 + 0.990849i \(0.543096\pi\)
\(32\) −3.81115 −0.673722
\(33\) −0.281575 −0.0490159
\(34\) 2.51565 0.431431
\(35\) −2.70393 −0.457048
\(36\) 14.4191 2.40319
\(37\) 1.83538 0.301735 0.150867 0.988554i \(-0.451793\pi\)
0.150867 + 0.988554i \(0.451793\pi\)
\(38\) −6.09997 −0.989545
\(39\) 5.17083 0.827995
\(40\) −8.82347 −1.39511
\(41\) 3.52083 0.549861 0.274930 0.961464i \(-0.411345\pi\)
0.274930 + 0.961464i \(0.411345\pi\)
\(42\) −11.4789 −1.77123
\(43\) 1.61704 0.246596 0.123298 0.992370i \(-0.460653\pi\)
0.123298 + 0.992370i \(0.460653\pi\)
\(44\) 0.487126 0.0734370
\(45\) 4.94656 0.737389
\(46\) 11.5435 1.70200
\(47\) 3.42421 0.499473 0.249737 0.968314i \(-0.419656\pi\)
0.249737 + 0.968314i \(0.419656\pi\)
\(48\) −15.6033 −2.25215
\(49\) −3.71372 −0.530532
\(50\) 6.99217 0.988843
\(51\) 2.50939 0.351385
\(52\) −8.94556 −1.24053
\(53\) −7.80459 −1.07204 −0.536022 0.844204i \(-0.680073\pi\)
−0.536022 + 0.844204i \(0.680073\pi\)
\(54\) 2.00311 0.272589
\(55\) 0.167111 0.0225332
\(56\) 10.7238 1.43302
\(57\) −6.08478 −0.805949
\(58\) 4.49775 0.590583
\(59\) 9.72052 1.26550 0.632752 0.774354i \(-0.281925\pi\)
0.632752 + 0.774354i \(0.281925\pi\)
\(60\) −16.2988 −2.10417
\(61\) 6.10379 0.781511 0.390755 0.920495i \(-0.372214\pi\)
0.390755 + 0.920495i \(0.372214\pi\)
\(62\) 3.78695 0.480944
\(63\) −6.01189 −0.757428
\(64\) −2.81473 −0.351841
\(65\) −3.06882 −0.380640
\(66\) 0.709429 0.0873247
\(67\) −4.61058 −0.563272 −0.281636 0.959521i \(-0.590877\pi\)
−0.281636 + 0.959521i \(0.590877\pi\)
\(68\) −4.34126 −0.526455
\(69\) 11.5148 1.38622
\(70\) 6.81257 0.814258
\(71\) −1.00000 −0.118678
\(72\) −19.6180 −2.31201
\(73\) 15.7775 1.84661 0.923306 0.384066i \(-0.125476\pi\)
0.923306 + 0.384066i \(0.125476\pi\)
\(74\) −4.62425 −0.537559
\(75\) 6.97477 0.805377
\(76\) 10.5267 1.20750
\(77\) −0.203101 −0.0231456
\(78\) −13.0279 −1.47512
\(79\) 12.0908 1.36033 0.680163 0.733061i \(-0.261909\pi\)
0.680163 + 0.733061i \(0.261909\pi\)
\(80\) 9.26037 1.03534
\(81\) −7.95090 −0.883433
\(82\) −8.87074 −0.979609
\(83\) 11.6775 1.28178 0.640888 0.767634i \(-0.278566\pi\)
0.640888 + 0.767634i \(0.278566\pi\)
\(84\) 19.8091 2.16135
\(85\) −1.48929 −0.161536
\(86\) −4.07413 −0.439325
\(87\) 4.48655 0.481009
\(88\) −0.662761 −0.0706505
\(89\) 9.20666 0.975904 0.487952 0.872871i \(-0.337744\pi\)
0.487952 + 0.872871i \(0.337744\pi\)
\(90\) −12.4629 −1.31370
\(91\) 3.72975 0.390984
\(92\) −19.9206 −2.07687
\(93\) 3.77753 0.391711
\(94\) −8.62733 −0.889841
\(95\) 3.61124 0.370505
\(96\) 9.57831 0.977582
\(97\) −1.36224 −0.138315 −0.0691574 0.997606i \(-0.522031\pi\)
−0.0691574 + 0.997606i \(0.522031\pi\)
\(98\) 9.35675 0.945174
\(99\) 0.371553 0.0373425
\(100\) −12.0664 −1.20664
\(101\) −6.66565 −0.663257 −0.331629 0.943410i \(-0.607598\pi\)
−0.331629 + 0.943410i \(0.607598\pi\)
\(102\) −6.32242 −0.626013
\(103\) −12.4447 −1.22621 −0.613104 0.790002i \(-0.710079\pi\)
−0.613104 + 0.790002i \(0.710079\pi\)
\(104\) 12.1709 1.19346
\(105\) 6.79561 0.663184
\(106\) 19.6637 1.90991
\(107\) −4.02551 −0.389160 −0.194580 0.980887i \(-0.562334\pi\)
−0.194580 + 0.980887i \(0.562334\pi\)
\(108\) −3.45677 −0.332628
\(109\) 0.903714 0.0865601 0.0432801 0.999063i \(-0.486219\pi\)
0.0432801 + 0.999063i \(0.486219\pi\)
\(110\) −0.421037 −0.0401443
\(111\) −4.61274 −0.437822
\(112\) −11.2548 −1.06348
\(113\) −1.00000 −0.0940721
\(114\) 15.3306 1.43585
\(115\) −6.83387 −0.637262
\(116\) −7.76176 −0.720661
\(117\) −6.82318 −0.630803
\(118\) −24.4909 −2.25457
\(119\) 1.81004 0.165926
\(120\) 22.1754 2.02433
\(121\) −10.9874 −0.998859
\(122\) −15.3785 −1.39231
\(123\) −8.84866 −0.797856
\(124\) −6.53514 −0.586873
\(125\) −11.5973 −1.03729
\(126\) 15.1470 1.34940
\(127\) −12.1269 −1.07609 −0.538045 0.842916i \(-0.680837\pi\)
−0.538045 + 0.842916i \(0.680837\pi\)
\(128\) 14.7140 1.30055
\(129\) −4.06399 −0.357815
\(130\) 7.73190 0.678133
\(131\) 3.93681 0.343961 0.171980 0.985100i \(-0.444983\pi\)
0.171980 + 0.985100i \(0.444983\pi\)
\(132\) −1.22426 −0.106558
\(133\) −4.38899 −0.380573
\(134\) 11.6164 1.00350
\(135\) −1.18586 −0.102063
\(136\) 5.90651 0.506479
\(137\) −3.95166 −0.337613 −0.168807 0.985649i \(-0.553991\pi\)
−0.168807 + 0.985649i \(0.553991\pi\)
\(138\) −29.0116 −2.46963
\(139\) 6.91616 0.586621 0.293310 0.956017i \(-0.405243\pi\)
0.293310 + 0.956017i \(0.405243\pi\)
\(140\) −11.7564 −0.993601
\(141\) −8.60585 −0.724743
\(142\) 2.51950 0.211432
\(143\) −0.230509 −0.0192762
\(144\) 20.5894 1.71578
\(145\) −2.66271 −0.221126
\(146\) −39.7514 −3.28985
\(147\) 9.33346 0.769810
\(148\) 7.98007 0.655957
\(149\) −21.6485 −1.77351 −0.886757 0.462236i \(-0.847047\pi\)
−0.886757 + 0.462236i \(0.847047\pi\)
\(150\) −17.5730 −1.43483
\(151\) 12.1857 0.991655 0.495828 0.868421i \(-0.334865\pi\)
0.495828 + 0.868421i \(0.334865\pi\)
\(152\) −14.3221 −1.16168
\(153\) −3.31127 −0.267700
\(154\) 0.511715 0.0412352
\(155\) −2.24191 −0.180075
\(156\) 22.4823 1.80002
\(157\) 23.1601 1.84838 0.924188 0.381938i \(-0.124743\pi\)
0.924188 + 0.381938i \(0.124743\pi\)
\(158\) −30.4630 −2.42350
\(159\) 19.6148 1.55555
\(160\) −5.68460 −0.449407
\(161\) 8.30568 0.654579
\(162\) 20.0323 1.57389
\(163\) −13.8010 −1.08098 −0.540488 0.841351i \(-0.681761\pi\)
−0.540488 + 0.841351i \(0.681761\pi\)
\(164\) 15.3082 1.19537
\(165\) −0.419989 −0.0326961
\(166\) −29.4216 −2.28356
\(167\) 1.67578 0.129676 0.0648378 0.997896i \(-0.479347\pi\)
0.0648378 + 0.997896i \(0.479347\pi\)
\(168\) −26.9514 −2.07934
\(169\) −8.76694 −0.674380
\(170\) 3.75227 0.287786
\(171\) 8.02919 0.614007
\(172\) 7.03073 0.536088
\(173\) −15.0424 −1.14365 −0.571827 0.820374i \(-0.693765\pi\)
−0.571827 + 0.820374i \(0.693765\pi\)
\(174\) −11.3039 −0.856946
\(175\) 5.03094 0.380303
\(176\) 0.695577 0.0524311
\(177\) −24.4299 −1.83627
\(178\) −23.1962 −1.73863
\(179\) −2.71136 −0.202656 −0.101328 0.994853i \(-0.532309\pi\)
−0.101328 + 0.994853i \(0.532309\pi\)
\(180\) 21.5072 1.60305
\(181\) 21.7466 1.61641 0.808205 0.588902i \(-0.200440\pi\)
0.808205 + 0.588902i \(0.200440\pi\)
\(182\) −9.39711 −0.696560
\(183\) −15.3403 −1.13398
\(184\) 27.1031 1.99807
\(185\) 2.73760 0.201272
\(186\) −9.51750 −0.697857
\(187\) −0.111866 −0.00818042
\(188\) 14.8882 1.08583
\(189\) 1.44126 0.104836
\(190\) −9.09853 −0.660077
\(191\) 12.3654 0.894732 0.447366 0.894351i \(-0.352362\pi\)
0.447366 + 0.894351i \(0.352362\pi\)
\(192\) 7.07407 0.510527
\(193\) −1.94654 −0.140115 −0.0700575 0.997543i \(-0.522318\pi\)
−0.0700575 + 0.997543i \(0.522318\pi\)
\(194\) 3.43218 0.246416
\(195\) 7.71266 0.552315
\(196\) −16.1469 −1.15335
\(197\) −27.7265 −1.97543 −0.987714 0.156269i \(-0.950053\pi\)
−0.987714 + 0.156269i \(0.950053\pi\)
\(198\) −0.936129 −0.0665278
\(199\) 27.2259 1.92999 0.964995 0.262269i \(-0.0844709\pi\)
0.964995 + 0.262269i \(0.0844709\pi\)
\(200\) 16.4170 1.16085
\(201\) 11.5875 0.817317
\(202\) 16.7941 1.18163
\(203\) 3.23618 0.227135
\(204\) 10.9106 0.763894
\(205\) 5.25156 0.366785
\(206\) 31.3544 2.18456
\(207\) −15.1944 −1.05608
\(208\) −12.7736 −0.885687
\(209\) 0.271252 0.0187629
\(210\) −17.1216 −1.18150
\(211\) 1.46873 0.101112 0.0505559 0.998721i \(-0.483901\pi\)
0.0505559 + 0.998721i \(0.483901\pi\)
\(212\) −33.9336 −2.33057
\(213\) 2.51323 0.172204
\(214\) 10.1423 0.693312
\(215\) 2.41193 0.164492
\(216\) 4.70312 0.320007
\(217\) 2.72475 0.184968
\(218\) −2.27691 −0.154212
\(219\) −39.6524 −2.67946
\(220\) 0.726582 0.0489862
\(221\) 2.05429 0.138187
\(222\) 11.6218 0.780006
\(223\) −11.5952 −0.776473 −0.388237 0.921560i \(-0.626916\pi\)
−0.388237 + 0.921560i \(0.626916\pi\)
\(224\) 6.90888 0.461619
\(225\) −9.20357 −0.613571
\(226\) 2.51950 0.167595
\(227\) −12.1596 −0.807058 −0.403529 0.914967i \(-0.632217\pi\)
−0.403529 + 0.914967i \(0.632217\pi\)
\(228\) −26.4561 −1.75210
\(229\) 10.0846 0.666406 0.333203 0.942855i \(-0.391871\pi\)
0.333203 + 0.942855i \(0.391871\pi\)
\(230\) 17.2180 1.13532
\(231\) 0.510441 0.0335846
\(232\) 10.5603 0.693317
\(233\) −2.11264 −0.138404 −0.0692020 0.997603i \(-0.522045\pi\)
−0.0692020 + 0.997603i \(0.522045\pi\)
\(234\) 17.1910 1.12381
\(235\) 5.10746 0.333174
\(236\) 42.2639 2.75115
\(237\) −30.3871 −1.97386
\(238\) −4.56040 −0.295607
\(239\) 15.2071 0.983667 0.491834 0.870689i \(-0.336327\pi\)
0.491834 + 0.870689i \(0.336327\pi\)
\(240\) −23.2735 −1.50230
\(241\) 25.4306 1.63813 0.819066 0.573700i \(-0.194492\pi\)
0.819066 + 0.573700i \(0.194492\pi\)
\(242\) 27.6829 1.77953
\(243\) 22.3676 1.43488
\(244\) 26.5387 1.69897
\(245\) −5.53928 −0.353892
\(246\) 22.2942 1.42143
\(247\) −4.98126 −0.316950
\(248\) 8.89141 0.564605
\(249\) −29.3484 −1.85988
\(250\) 29.2194 1.84800
\(251\) 0.115702 0.00730302 0.00365151 0.999993i \(-0.498838\pi\)
0.00365151 + 0.999993i \(0.498838\pi\)
\(252\) −26.1391 −1.64661
\(253\) −0.513315 −0.0322719
\(254\) 30.5538 1.91712
\(255\) 3.74293 0.234392
\(256\) −31.4426 −1.96516
\(257\) 16.3672 1.02096 0.510478 0.859891i \(-0.329468\pi\)
0.510478 + 0.859891i \(0.329468\pi\)
\(258\) 10.2393 0.637468
\(259\) −3.32720 −0.206742
\(260\) −13.3429 −0.827493
\(261\) −5.92024 −0.366454
\(262\) −9.91881 −0.612786
\(263\) 12.3090 0.759008 0.379504 0.925190i \(-0.376095\pi\)
0.379504 + 0.925190i \(0.376095\pi\)
\(264\) 1.66567 0.102515
\(265\) −11.6411 −0.715107
\(266\) 11.0581 0.678014
\(267\) −23.1385 −1.41605
\(268\) −20.0464 −1.22453
\(269\) −17.8838 −1.09039 −0.545197 0.838308i \(-0.683545\pi\)
−0.545197 + 0.838308i \(0.683545\pi\)
\(270\) 2.98779 0.181831
\(271\) 5.26761 0.319985 0.159992 0.987118i \(-0.448853\pi\)
0.159992 + 0.987118i \(0.448853\pi\)
\(272\) −6.19897 −0.375868
\(273\) −9.37372 −0.567324
\(274\) 9.95624 0.601478
\(275\) −0.310927 −0.0187496
\(276\) 50.0652 3.01357
\(277\) −11.4057 −0.685299 −0.342650 0.939463i \(-0.611324\pi\)
−0.342650 + 0.939463i \(0.611324\pi\)
\(278\) −17.4253 −1.04510
\(279\) −4.98464 −0.298423
\(280\) 15.9953 0.955900
\(281\) 7.81009 0.465911 0.232955 0.972487i \(-0.425160\pi\)
0.232955 + 0.972487i \(0.425160\pi\)
\(282\) 21.6825 1.29117
\(283\) 25.4615 1.51353 0.756764 0.653689i \(-0.226779\pi\)
0.756764 + 0.653689i \(0.226779\pi\)
\(284\) −4.34790 −0.258001
\(285\) −9.07588 −0.537609
\(286\) 0.580769 0.0343416
\(287\) −6.38258 −0.376752
\(288\) −12.6391 −0.744765
\(289\) −16.0031 −0.941356
\(290\) 6.70871 0.393949
\(291\) 3.42364 0.200697
\(292\) 68.5989 4.01445
\(293\) −10.2983 −0.601630 −0.300815 0.953682i \(-0.597259\pi\)
−0.300815 + 0.953682i \(0.597259\pi\)
\(294\) −23.5157 −1.37146
\(295\) 14.4988 0.844156
\(296\) −10.8573 −0.631068
\(297\) −0.0890741 −0.00516860
\(298\) 54.5435 3.15962
\(299\) 9.42650 0.545149
\(300\) 30.3256 1.75085
\(301\) −2.93138 −0.168962
\(302\) −30.7018 −1.76669
\(303\) 16.7523 0.962397
\(304\) 15.0313 0.862104
\(305\) 9.10424 0.521307
\(306\) 8.34277 0.476924
\(307\) 2.93345 0.167421 0.0837104 0.996490i \(-0.473323\pi\)
0.0837104 + 0.996490i \(0.473323\pi\)
\(308\) −0.883066 −0.0503173
\(309\) 31.2763 1.77925
\(310\) 5.64851 0.320814
\(311\) −3.54731 −0.201149 −0.100575 0.994930i \(-0.532068\pi\)
−0.100575 + 0.994930i \(0.532068\pi\)
\(312\) −30.5883 −1.73172
\(313\) 15.5425 0.878517 0.439258 0.898361i \(-0.355241\pi\)
0.439258 + 0.898361i \(0.355241\pi\)
\(314\) −58.3520 −3.29299
\(315\) −8.96716 −0.505243
\(316\) 52.5699 2.95729
\(317\) 5.89069 0.330854 0.165427 0.986222i \(-0.447100\pi\)
0.165427 + 0.986222i \(0.447100\pi\)
\(318\) −49.4195 −2.77131
\(319\) −0.200005 −0.0111981
\(320\) −4.19836 −0.234696
\(321\) 10.1170 0.564678
\(322\) −20.9262 −1.16617
\(323\) −2.41740 −0.134507
\(324\) −34.5698 −1.92054
\(325\) 5.70985 0.316725
\(326\) 34.7717 1.92582
\(327\) −2.27124 −0.125600
\(328\) −20.8276 −1.15001
\(329\) −6.20745 −0.342228
\(330\) 1.05816 0.0582500
\(331\) −19.4021 −1.06644 −0.533219 0.845977i \(-0.679018\pi\)
−0.533219 + 0.845977i \(0.679018\pi\)
\(332\) 50.7728 2.78652
\(333\) 6.08675 0.333552
\(334\) −4.22213 −0.231025
\(335\) −6.87701 −0.375731
\(336\) 28.2859 1.54312
\(337\) −32.4584 −1.76812 −0.884060 0.467374i \(-0.845200\pi\)
−0.884060 + 0.467374i \(0.845200\pi\)
\(338\) 22.0883 1.20145
\(339\) 2.51323 0.136500
\(340\) −6.47529 −0.351172
\(341\) −0.168398 −0.00911924
\(342\) −20.2296 −1.09389
\(343\) 19.4219 1.04869
\(344\) −9.56568 −0.515747
\(345\) 17.1751 0.924678
\(346\) 37.8994 2.03749
\(347\) −0.653619 −0.0350881 −0.0175440 0.999846i \(-0.505585\pi\)
−0.0175440 + 0.999846i \(0.505585\pi\)
\(348\) 19.5071 1.04569
\(349\) 13.8769 0.742815 0.371408 0.928470i \(-0.378875\pi\)
0.371408 + 0.928470i \(0.378875\pi\)
\(350\) −12.6755 −0.677533
\(351\) 1.63575 0.0873100
\(352\) −0.426989 −0.0227586
\(353\) 3.33171 0.177329 0.0886646 0.996062i \(-0.471740\pi\)
0.0886646 + 0.996062i \(0.471740\pi\)
\(354\) 61.5514 3.27142
\(355\) −1.49157 −0.0791643
\(356\) 40.0297 2.12157
\(357\) −4.54905 −0.240761
\(358\) 6.83128 0.361044
\(359\) 21.6449 1.14238 0.571188 0.820819i \(-0.306483\pi\)
0.571188 + 0.820819i \(0.306483\pi\)
\(360\) −29.2617 −1.54222
\(361\) −13.1383 −0.691489
\(362\) −54.7906 −2.87973
\(363\) 27.6140 1.44936
\(364\) 16.2166 0.849980
\(365\) 23.5332 1.23178
\(366\) 38.6499 2.02026
\(367\) −8.23227 −0.429721 −0.214860 0.976645i \(-0.568930\pi\)
−0.214860 + 0.976645i \(0.568930\pi\)
\(368\) −28.4451 −1.48280
\(369\) 11.6763 0.607842
\(370\) −6.89740 −0.358579
\(371\) 14.1482 0.734540
\(372\) 16.4243 0.851562
\(373\) 11.7365 0.607695 0.303847 0.952721i \(-0.401729\pi\)
0.303847 + 0.952721i \(0.401729\pi\)
\(374\) 0.281846 0.0145739
\(375\) 29.1467 1.50513
\(376\) −20.2561 −1.04463
\(377\) 3.67288 0.189163
\(378\) −3.63126 −0.186772
\(379\) 14.5218 0.745932 0.372966 0.927845i \(-0.378341\pi\)
0.372966 + 0.927845i \(0.378341\pi\)
\(380\) 15.7013 0.805460
\(381\) 30.4778 1.56142
\(382\) −31.1548 −1.59402
\(383\) 16.5023 0.843228 0.421614 0.906775i \(-0.361464\pi\)
0.421614 + 0.906775i \(0.361464\pi\)
\(384\) −36.9798 −1.88712
\(385\) −0.302940 −0.0154393
\(386\) 4.90432 0.249623
\(387\) 5.36265 0.272599
\(388\) −5.92291 −0.300690
\(389\) −3.38791 −0.171774 −0.0858869 0.996305i \(-0.527372\pi\)
−0.0858869 + 0.996305i \(0.527372\pi\)
\(390\) −19.4321 −0.983981
\(391\) 4.57466 0.231350
\(392\) 21.9688 1.10959
\(393\) −9.89412 −0.499092
\(394\) 69.8570 3.51934
\(395\) 18.0344 0.907407
\(396\) 1.61548 0.0811807
\(397\) 4.63107 0.232427 0.116213 0.993224i \(-0.462924\pi\)
0.116213 + 0.993224i \(0.462924\pi\)
\(398\) −68.5957 −3.43839
\(399\) 11.0305 0.552218
\(400\) −17.2298 −0.861492
\(401\) 23.4815 1.17261 0.586304 0.810091i \(-0.300582\pi\)
0.586304 + 0.810091i \(0.300582\pi\)
\(402\) −29.1947 −1.45610
\(403\) 3.09245 0.154046
\(404\) −28.9816 −1.44189
\(405\) −11.8593 −0.589295
\(406\) −8.15356 −0.404654
\(407\) 0.205630 0.0101927
\(408\) −14.8444 −0.734910
\(409\) 6.82493 0.337471 0.168736 0.985661i \(-0.446032\pi\)
0.168736 + 0.985661i \(0.446032\pi\)
\(410\) −13.2313 −0.653449
\(411\) 9.93145 0.489883
\(412\) −54.1082 −2.66572
\(413\) −17.6215 −0.867095
\(414\) 38.2823 1.88147
\(415\) 17.4179 0.855010
\(416\) 7.84121 0.384447
\(417\) −17.3819 −0.851196
\(418\) −0.683421 −0.0334272
\(419\) −18.4506 −0.901370 −0.450685 0.892683i \(-0.648820\pi\)
−0.450685 + 0.892683i \(0.648820\pi\)
\(420\) 29.5467 1.44173
\(421\) 22.5985 1.10138 0.550691 0.834709i \(-0.314364\pi\)
0.550691 + 0.834709i \(0.314364\pi\)
\(422\) −3.70048 −0.180137
\(423\) 11.3559 0.552141
\(424\) 46.1685 2.24214
\(425\) 2.77097 0.134412
\(426\) −6.33210 −0.306791
\(427\) −11.0650 −0.535473
\(428\) −17.5025 −0.846016
\(429\) 0.579324 0.0279700
\(430\) −6.07686 −0.293052
\(431\) −21.0244 −1.01271 −0.506354 0.862326i \(-0.669007\pi\)
−0.506354 + 0.862326i \(0.669007\pi\)
\(432\) −4.93600 −0.237483
\(433\) −23.0217 −1.10635 −0.553176 0.833064i \(-0.686584\pi\)
−0.553176 + 0.833064i \(0.686584\pi\)
\(434\) −6.86502 −0.329532
\(435\) 6.69201 0.320857
\(436\) 3.92926 0.188178
\(437\) −11.0927 −0.530634
\(438\) 99.9045 4.77362
\(439\) −25.5662 −1.22021 −0.610104 0.792322i \(-0.708872\pi\)
−0.610104 + 0.792322i \(0.708872\pi\)
\(440\) −0.988554 −0.0471275
\(441\) −12.3160 −0.586475
\(442\) −5.17581 −0.246188
\(443\) 23.6798 1.12506 0.562532 0.826776i \(-0.309827\pi\)
0.562532 + 0.826776i \(0.309827\pi\)
\(444\) −20.0558 −0.951805
\(445\) 13.7324 0.650977
\(446\) 29.2142 1.38333
\(447\) 54.4077 2.57340
\(448\) 5.10256 0.241073
\(449\) 10.4198 0.491741 0.245870 0.969303i \(-0.420926\pi\)
0.245870 + 0.969303i \(0.420926\pi\)
\(450\) 23.1884 1.09311
\(451\) 0.394462 0.0185745
\(452\) −4.34790 −0.204508
\(453\) −30.6254 −1.43891
\(454\) 30.6361 1.43782
\(455\) 5.56318 0.260806
\(456\) 35.9949 1.68561
\(457\) 14.6985 0.687569 0.343784 0.939049i \(-0.388291\pi\)
0.343784 + 0.939049i \(0.388291\pi\)
\(458\) −25.4081 −1.18724
\(459\) 0.793827 0.0370527
\(460\) −29.7130 −1.38538
\(461\) 12.4736 0.580951 0.290476 0.956882i \(-0.406186\pi\)
0.290476 + 0.956882i \(0.406186\pi\)
\(462\) −1.28606 −0.0598329
\(463\) 9.88583 0.459433 0.229717 0.973258i \(-0.426220\pi\)
0.229717 + 0.973258i \(0.426220\pi\)
\(464\) −11.0832 −0.514524
\(465\) 5.63445 0.261291
\(466\) 5.32282 0.246575
\(467\) −4.48560 −0.207569 −0.103784 0.994600i \(-0.533095\pi\)
−0.103784 + 0.994600i \(0.533095\pi\)
\(468\) −29.6665 −1.37134
\(469\) 8.35810 0.385941
\(470\) −12.8683 −0.593569
\(471\) −58.2067 −2.68202
\(472\) −57.5023 −2.64676
\(473\) 0.181168 0.00833011
\(474\) 76.5605 3.51654
\(475\) −6.71907 −0.308292
\(476\) 7.86987 0.360715
\(477\) −25.8827 −1.18509
\(478\) −38.3144 −1.75246
\(479\) 19.2893 0.881348 0.440674 0.897667i \(-0.354739\pi\)
0.440674 + 0.897667i \(0.354739\pi\)
\(480\) 14.2867 0.652097
\(481\) −3.77619 −0.172179
\(482\) −64.0726 −2.91843
\(483\) −20.8741 −0.949805
\(484\) −47.7724 −2.17147
\(485\) −2.03188 −0.0922630
\(486\) −56.3553 −2.55633
\(487\) 19.1242 0.866602 0.433301 0.901249i \(-0.357349\pi\)
0.433301 + 0.901249i \(0.357349\pi\)
\(488\) −36.1073 −1.63450
\(489\) 34.6851 1.56851
\(490\) 13.9562 0.630479
\(491\) −4.04055 −0.182347 −0.0911736 0.995835i \(-0.529062\pi\)
−0.0911736 + 0.995835i \(0.529062\pi\)
\(492\) −38.4731 −1.73450
\(493\) 1.78244 0.0802772
\(494\) 12.5503 0.564665
\(495\) 0.554197 0.0249093
\(496\) −9.33167 −0.419004
\(497\) 1.81281 0.0813156
\(498\) 73.9434 3.31348
\(499\) −21.2637 −0.951896 −0.475948 0.879473i \(-0.657895\pi\)
−0.475948 + 0.879473i \(0.657895\pi\)
\(500\) −50.4239 −2.25503
\(501\) −4.21162 −0.188161
\(502\) −0.291511 −0.0130108
\(503\) 9.17310 0.409008 0.204504 0.978866i \(-0.434442\pi\)
0.204504 + 0.978866i \(0.434442\pi\)
\(504\) 35.5637 1.58413
\(505\) −9.94229 −0.442426
\(506\) 1.29330 0.0574942
\(507\) 22.0334 0.978536
\(508\) −52.7267 −2.33937
\(509\) −30.5656 −1.35480 −0.677398 0.735617i \(-0.736892\pi\)
−0.677398 + 0.735617i \(0.736892\pi\)
\(510\) −9.43034 −0.417582
\(511\) −28.6015 −1.26526
\(512\) 49.7917 2.20050
\(513\) −1.92488 −0.0849853
\(514\) −41.2372 −1.81889
\(515\) −18.5621 −0.817943
\(516\) −17.6699 −0.777872
\(517\) 0.383638 0.0168724
\(518\) 8.38289 0.368323
\(519\) 37.8051 1.65946
\(520\) 18.1538 0.796095
\(521\) −3.48867 −0.152842 −0.0764208 0.997076i \(-0.524349\pi\)
−0.0764208 + 0.997076i \(0.524349\pi\)
\(522\) 14.9161 0.652859
\(523\) 38.8187 1.69742 0.848711 0.528857i \(-0.177379\pi\)
0.848711 + 0.528857i \(0.177379\pi\)
\(524\) 17.1169 0.747754
\(525\) −12.6439 −0.551826
\(526\) −31.0127 −1.35222
\(527\) 1.50076 0.0653740
\(528\) −1.74815 −0.0760784
\(529\) −2.00835 −0.0873197
\(530\) 29.3298 1.27401
\(531\) 32.2366 1.39895
\(532\) −19.0829 −0.827348
\(533\) −7.24389 −0.313768
\(534\) 58.2975 2.52278
\(535\) −6.00432 −0.259590
\(536\) 27.2742 1.17806
\(537\) 6.81427 0.294058
\(538\) 45.0583 1.94260
\(539\) −0.416074 −0.0179216
\(540\) −5.15602 −0.221880
\(541\) 13.4545 0.578455 0.289228 0.957260i \(-0.406602\pi\)
0.289228 + 0.957260i \(0.406602\pi\)
\(542\) −13.2718 −0.570071
\(543\) −54.6542 −2.34544
\(544\) 3.80532 0.163152
\(545\) 1.34795 0.0577400
\(546\) 23.6171 1.01072
\(547\) −19.2032 −0.821070 −0.410535 0.911845i \(-0.634658\pi\)
−0.410535 + 0.911845i \(0.634658\pi\)
\(548\) −17.1815 −0.733956
\(549\) 20.2423 0.863919
\(550\) 0.783381 0.0334035
\(551\) −4.32207 −0.184127
\(552\) −68.1164 −2.89923
\(553\) −21.9184 −0.932065
\(554\) 28.7366 1.22090
\(555\) −6.88023 −0.292050
\(556\) 30.0708 1.27529
\(557\) −43.0376 −1.82356 −0.911780 0.410679i \(-0.865292\pi\)
−0.911780 + 0.410679i \(0.865292\pi\)
\(558\) 12.5588 0.531658
\(559\) −3.32696 −0.140715
\(560\) −16.7873 −0.709392
\(561\) 0.281144 0.0118699
\(562\) −19.6776 −0.830047
\(563\) −17.6181 −0.742512 −0.371256 0.928530i \(-0.621073\pi\)
−0.371256 + 0.928530i \(0.621073\pi\)
\(564\) −37.4174 −1.57556
\(565\) −1.49157 −0.0627508
\(566\) −64.1503 −2.69644
\(567\) 14.4135 0.605308
\(568\) 5.91556 0.248211
\(569\) −36.7055 −1.53877 −0.769386 0.638784i \(-0.779438\pi\)
−0.769386 + 0.638784i \(0.779438\pi\)
\(570\) 22.8667 0.957782
\(571\) −10.2738 −0.429945 −0.214972 0.976620i \(-0.568966\pi\)
−0.214972 + 0.976620i \(0.568966\pi\)
\(572\) −1.00223 −0.0419054
\(573\) −31.0772 −1.29827
\(574\) 16.0809 0.671206
\(575\) 12.7151 0.530257
\(576\) −9.33460 −0.388942
\(577\) 13.8926 0.578357 0.289179 0.957275i \(-0.406618\pi\)
0.289179 + 0.957275i \(0.406618\pi\)
\(578\) 40.3198 1.67708
\(579\) 4.89211 0.203309
\(580\) −11.5772 −0.480717
\(581\) −21.1691 −0.878244
\(582\) −8.62587 −0.357554
\(583\) −0.874402 −0.0362140
\(584\) −93.3325 −3.86212
\(585\) −10.1773 −0.420778
\(586\) 25.9465 1.07184
\(587\) 8.37627 0.345726 0.172863 0.984946i \(-0.444698\pi\)
0.172863 + 0.984946i \(0.444698\pi\)
\(588\) 40.5810 1.67353
\(589\) −3.63904 −0.149944
\(590\) −36.5299 −1.50391
\(591\) 69.6831 2.86638
\(592\) 11.3949 0.468328
\(593\) −36.2203 −1.48739 −0.743695 0.668519i \(-0.766929\pi\)
−0.743695 + 0.668519i \(0.766929\pi\)
\(594\) 0.224423 0.00920817
\(595\) 2.69980 0.110681
\(596\) −94.1256 −3.85553
\(597\) −68.4249 −2.80045
\(598\) −23.7501 −0.971215
\(599\) −4.93393 −0.201595 −0.100797 0.994907i \(-0.532139\pi\)
−0.100797 + 0.994907i \(0.532139\pi\)
\(600\) −41.2597 −1.68442
\(601\) −39.1390 −1.59651 −0.798257 0.602317i \(-0.794244\pi\)
−0.798257 + 0.602317i \(0.794244\pi\)
\(602\) 7.38563 0.301016
\(603\) −15.2903 −0.622668
\(604\) 52.9821 2.15581
\(605\) −16.3886 −0.666289
\(606\) −42.2076 −1.71457
\(607\) −27.4186 −1.11289 −0.556444 0.830885i \(-0.687835\pi\)
−0.556444 + 0.830885i \(0.687835\pi\)
\(608\) −9.22716 −0.374211
\(609\) −8.13326 −0.329576
\(610\) −22.9382 −0.928740
\(611\) −7.04512 −0.285015
\(612\) −14.3971 −0.581968
\(613\) 31.0735 1.25505 0.627523 0.778598i \(-0.284069\pi\)
0.627523 + 0.778598i \(0.284069\pi\)
\(614\) −7.39084 −0.298270
\(615\) −13.1984 −0.532211
\(616\) 1.20146 0.0484081
\(617\) 29.6654 1.19428 0.597142 0.802135i \(-0.296303\pi\)
0.597142 + 0.802135i \(0.296303\pi\)
\(618\) −78.8009 −3.16984
\(619\) 41.5777 1.67115 0.835574 0.549378i \(-0.185135\pi\)
0.835574 + 0.549378i \(0.185135\pi\)
\(620\) −9.74762 −0.391474
\(621\) 3.64262 0.146173
\(622\) 8.93746 0.358360
\(623\) −16.6899 −0.668667
\(624\) 32.1029 1.28515
\(625\) −3.42208 −0.136883
\(626\) −39.1595 −1.56513
\(627\) −0.681720 −0.0272253
\(628\) 100.698 4.01828
\(629\) −1.83258 −0.0730696
\(630\) 22.5928 0.900119
\(631\) 47.3417 1.88464 0.942322 0.334708i \(-0.108638\pi\)
0.942322 + 0.334708i \(0.108638\pi\)
\(632\) −71.5241 −2.84508
\(633\) −3.69127 −0.146715
\(634\) −14.8416 −0.589436
\(635\) −18.0882 −0.717806
\(636\) 85.2831 3.38170
\(637\) 7.64077 0.302738
\(638\) 0.503914 0.0199501
\(639\) −3.31634 −0.131192
\(640\) 21.9470 0.867531
\(641\) −38.9648 −1.53902 −0.769509 0.638636i \(-0.779499\pi\)
−0.769509 + 0.638636i \(0.779499\pi\)
\(642\) −25.4899 −1.00601
\(643\) −21.9566 −0.865883 −0.432942 0.901422i \(-0.642524\pi\)
−0.432942 + 0.901422i \(0.642524\pi\)
\(644\) 36.1123 1.42302
\(645\) −6.06173 −0.238680
\(646\) 6.09064 0.239633
\(647\) 3.81388 0.149939 0.0749696 0.997186i \(-0.476114\pi\)
0.0749696 + 0.997186i \(0.476114\pi\)
\(648\) 47.0340 1.84767
\(649\) 1.08906 0.0427492
\(650\) −14.3860 −0.564265
\(651\) −6.84793 −0.268392
\(652\) −60.0054 −2.34999
\(653\) −30.2758 −1.18479 −0.592393 0.805649i \(-0.701817\pi\)
−0.592393 + 0.805649i \(0.701817\pi\)
\(654\) 5.72241 0.223764
\(655\) 5.87203 0.229439
\(656\) 21.8589 0.853448
\(657\) 52.3235 2.04133
\(658\) 15.6397 0.609699
\(659\) −14.0433 −0.547048 −0.273524 0.961865i \(-0.588189\pi\)
−0.273524 + 0.961865i \(0.588189\pi\)
\(660\) −1.82607 −0.0710797
\(661\) −1.43467 −0.0558021 −0.0279010 0.999611i \(-0.508882\pi\)
−0.0279010 + 0.999611i \(0.508882\pi\)
\(662\) 48.8838 1.89992
\(663\) −5.16292 −0.200511
\(664\) −69.0791 −2.68079
\(665\) −6.54648 −0.253862
\(666\) −15.3356 −0.594243
\(667\) 8.17906 0.316694
\(668\) 7.28613 0.281909
\(669\) 29.1415 1.12668
\(670\) 17.3267 0.669387
\(671\) 0.683850 0.0263997
\(672\) −17.3636 −0.669817
\(673\) −11.2622 −0.434126 −0.217063 0.976158i \(-0.569648\pi\)
−0.217063 + 0.976158i \(0.569648\pi\)
\(674\) 81.7790 3.15001
\(675\) 2.20642 0.0849250
\(676\) −38.1178 −1.46607
\(677\) −39.0254 −1.49987 −0.749933 0.661514i \(-0.769914\pi\)
−0.749933 + 0.661514i \(0.769914\pi\)
\(678\) −6.33210 −0.243183
\(679\) 2.46949 0.0947702
\(680\) 8.80998 0.337847
\(681\) 30.5598 1.17105
\(682\) 0.424279 0.0162465
\(683\) −46.5823 −1.78242 −0.891211 0.453588i \(-0.850144\pi\)
−0.891211 + 0.453588i \(0.850144\pi\)
\(684\) 34.9101 1.33482
\(685\) −5.89419 −0.225205
\(686\) −48.9337 −1.86830
\(687\) −25.3448 −0.966966
\(688\) 10.0393 0.382746
\(689\) 16.0575 0.611742
\(690\) −43.2728 −1.64737
\(691\) −6.48614 −0.246744 −0.123372 0.992360i \(-0.539371\pi\)
−0.123372 + 0.992360i \(0.539371\pi\)
\(692\) −65.4030 −2.48625
\(693\) −0.673554 −0.0255862
\(694\) 1.64680 0.0625115
\(695\) 10.3159 0.391306
\(696\) −26.5405 −1.00601
\(697\) −3.51544 −0.133157
\(698\) −34.9630 −1.32337
\(699\) 5.30957 0.200826
\(700\) 21.8740 0.826761
\(701\) −20.5170 −0.774917 −0.387459 0.921887i \(-0.626647\pi\)
−0.387459 + 0.921887i \(0.626647\pi\)
\(702\) −4.12129 −0.155548
\(703\) 4.44364 0.167595
\(704\) −0.315353 −0.0118853
\(705\) −12.8362 −0.483441
\(706\) −8.39427 −0.315922
\(707\) 12.0836 0.454449
\(708\) −106.219 −3.99196
\(709\) 39.6901 1.49059 0.745297 0.666733i \(-0.232308\pi\)
0.745297 + 0.666733i \(0.232308\pi\)
\(710\) 3.75802 0.141036
\(711\) 40.0974 1.50377
\(712\) −54.4625 −2.04107
\(713\) 6.88649 0.257901
\(714\) 11.4613 0.428930
\(715\) −0.343821 −0.0128582
\(716\) −11.7887 −0.440565
\(717\) −38.2191 −1.42732
\(718\) −54.5345 −2.03521
\(719\) −36.4367 −1.35886 −0.679430 0.733740i \(-0.737773\pi\)
−0.679430 + 0.733740i \(0.737773\pi\)
\(720\) 30.7105 1.14451
\(721\) 22.5598 0.840170
\(722\) 33.1020 1.23193
\(723\) −63.9131 −2.37695
\(724\) 94.5520 3.51400
\(725\) 4.95424 0.183996
\(726\) −69.5737 −2.58212
\(727\) 7.37854 0.273655 0.136827 0.990595i \(-0.456309\pi\)
0.136827 + 0.990595i \(0.456309\pi\)
\(728\) −22.0635 −0.817729
\(729\) −32.3623 −1.19860
\(730\) −59.2920 −2.19449
\(731\) −1.61457 −0.0597168
\(732\) −66.6980 −2.46523
\(733\) 26.1846 0.967151 0.483576 0.875303i \(-0.339338\pi\)
0.483576 + 0.875303i \(0.339338\pi\)
\(734\) 20.7412 0.765573
\(735\) 13.9215 0.513503
\(736\) 17.4614 0.643636
\(737\) −0.516555 −0.0190276
\(738\) −29.4184 −1.08291
\(739\) −21.0245 −0.773398 −0.386699 0.922206i \(-0.626385\pi\)
−0.386699 + 0.922206i \(0.626385\pi\)
\(740\) 11.9028 0.437557
\(741\) 12.5191 0.459900
\(742\) −35.6466 −1.30863
\(743\) −2.21400 −0.0812238 −0.0406119 0.999175i \(-0.512931\pi\)
−0.0406119 + 0.999175i \(0.512931\pi\)
\(744\) −22.3462 −0.819251
\(745\) −32.2903 −1.18302
\(746\) −29.5703 −1.08264
\(747\) 38.7267 1.41694
\(748\) −0.486381 −0.0177838
\(749\) 7.29747 0.266644
\(750\) −73.4352 −2.68147
\(751\) 28.6994 1.04726 0.523628 0.851947i \(-0.324578\pi\)
0.523628 + 0.851947i \(0.324578\pi\)
\(752\) 21.2591 0.775241
\(753\) −0.290785 −0.0105968
\(754\) −9.25385 −0.337005
\(755\) 18.1758 0.661484
\(756\) 6.26646 0.227909
\(757\) −4.92786 −0.179106 −0.0895530 0.995982i \(-0.528544\pi\)
−0.0895530 + 0.995982i \(0.528544\pi\)
\(758\) −36.5876 −1.32892
\(759\) 1.29008 0.0468270
\(760\) −21.3625 −0.774899
\(761\) −8.61243 −0.312200 −0.156100 0.987741i \(-0.549892\pi\)
−0.156100 + 0.987741i \(0.549892\pi\)
\(762\) −76.7889 −2.78177
\(763\) −1.63826 −0.0593090
\(764\) 53.7637 1.94510
\(765\) −4.93900 −0.178570
\(766\) −41.5776 −1.50226
\(767\) −19.9994 −0.722137
\(768\) 79.0226 2.85148
\(769\) −9.99362 −0.360379 −0.180190 0.983632i \(-0.557671\pi\)
−0.180190 + 0.983632i \(0.557671\pi\)
\(770\) 0.763259 0.0275060
\(771\) −41.1345 −1.48142
\(772\) −8.46337 −0.304603
\(773\) 23.6651 0.851176 0.425588 0.904917i \(-0.360067\pi\)
0.425588 + 0.904917i \(0.360067\pi\)
\(774\) −13.5112 −0.485651
\(775\) 4.17130 0.149838
\(776\) 8.05843 0.289281
\(777\) 8.36202 0.299986
\(778\) 8.53585 0.306025
\(779\) 8.52426 0.305413
\(780\) 33.5339 1.20071
\(781\) −0.112037 −0.00400900
\(782\) −11.5259 −0.412164
\(783\) 1.41929 0.0507212
\(784\) −23.0565 −0.823448
\(785\) 34.5449 1.23296
\(786\) 24.9283 0.889162
\(787\) 14.2056 0.506375 0.253188 0.967417i \(-0.418521\pi\)
0.253188 + 0.967417i \(0.418521\pi\)
\(788\) −120.552 −4.29449
\(789\) −30.9355 −1.10133
\(790\) −45.4376 −1.61660
\(791\) 1.81281 0.0644561
\(792\) −2.19794 −0.0781005
\(793\) −12.5582 −0.445955
\(794\) −11.6680 −0.414082
\(795\) 29.2568 1.03763
\(796\) 118.375 4.19571
\(797\) −32.7404 −1.15972 −0.579862 0.814714i \(-0.696894\pi\)
−0.579862 + 0.814714i \(0.696894\pi\)
\(798\) −27.7915 −0.983809
\(799\) −3.41898 −0.120955
\(800\) 10.5768 0.373945
\(801\) 30.5324 1.07881
\(802\) −59.1617 −2.08907
\(803\) 1.76766 0.0623793
\(804\) 50.3812 1.77681
\(805\) 12.3885 0.436638
\(806\) −7.79143 −0.274441
\(807\) 44.9462 1.58218
\(808\) 39.4311 1.38718
\(809\) −32.6130 −1.14661 −0.573306 0.819341i \(-0.694339\pi\)
−0.573306 + 0.819341i \(0.694339\pi\)
\(810\) 29.8796 1.04986
\(811\) 14.4438 0.507189 0.253594 0.967311i \(-0.418387\pi\)
0.253594 + 0.967311i \(0.418387\pi\)
\(812\) 14.0706 0.493781
\(813\) −13.2387 −0.464303
\(814\) −0.518087 −0.0181589
\(815\) −20.5851 −0.721066
\(816\) 15.5795 0.545391
\(817\) 3.91501 0.136969
\(818\) −17.1955 −0.601225
\(819\) 12.3691 0.432212
\(820\) 22.8333 0.797373
\(821\) −49.4511 −1.72585 −0.862927 0.505328i \(-0.831372\pi\)
−0.862927 + 0.505328i \(0.831372\pi\)
\(822\) −25.0223 −0.872755
\(823\) 3.53562 0.123244 0.0616219 0.998100i \(-0.480373\pi\)
0.0616219 + 0.998100i \(0.480373\pi\)
\(824\) 73.6171 2.56457
\(825\) 0.781432 0.0272060
\(826\) 44.3973 1.54478
\(827\) 15.8575 0.551419 0.275710 0.961241i \(-0.411087\pi\)
0.275710 + 0.961241i \(0.411087\pi\)
\(828\) −66.0637 −2.29587
\(829\) −6.37825 −0.221526 −0.110763 0.993847i \(-0.535329\pi\)
−0.110763 + 0.993847i \(0.535329\pi\)
\(830\) −43.8844 −1.52325
\(831\) 28.6651 0.994380
\(832\) 5.79113 0.200771
\(833\) 3.70805 0.128476
\(834\) 43.7938 1.51646
\(835\) 2.49954 0.0865002
\(836\) 1.17938 0.0407897
\(837\) 1.19499 0.0413050
\(838\) 46.4863 1.60584
\(839\) −33.3714 −1.15211 −0.576054 0.817411i \(-0.695408\pi\)
−0.576054 + 0.817411i \(0.695408\pi\)
\(840\) −40.1998 −1.38703
\(841\) −25.8132 −0.890109
\(842\) −56.9369 −1.96218
\(843\) −19.6286 −0.676044
\(844\) 6.38591 0.219812
\(845\) −13.0765 −0.449845
\(846\) −28.6112 −0.983672
\(847\) 19.9181 0.684395
\(848\) −48.4546 −1.66394
\(849\) −63.9906 −2.19615
\(850\) −6.98148 −0.239463
\(851\) −8.40910 −0.288260
\(852\) 10.9273 0.374363
\(853\) 6.75493 0.231284 0.115642 0.993291i \(-0.463107\pi\)
0.115642 + 0.993291i \(0.463107\pi\)
\(854\) 27.8784 0.953978
\(855\) 11.9761 0.409574
\(856\) 23.8131 0.813915
\(857\) −15.3282 −0.523600 −0.261800 0.965122i \(-0.584316\pi\)
−0.261800 + 0.965122i \(0.584316\pi\)
\(858\) −1.45961 −0.0498302
\(859\) 2.68990 0.0917781 0.0458891 0.998947i \(-0.485388\pi\)
0.0458891 + 0.998947i \(0.485388\pi\)
\(860\) 10.4868 0.357598
\(861\) 16.0409 0.546673
\(862\) 52.9710 1.80420
\(863\) −9.56976 −0.325758 −0.162879 0.986646i \(-0.552078\pi\)
−0.162879 + 0.986646i \(0.552078\pi\)
\(864\) 3.03003 0.103084
\(865\) −22.4368 −0.762875
\(866\) 58.0033 1.97103
\(867\) 40.2194 1.36592
\(868\) 11.8470 0.402112
\(869\) 1.35462 0.0459524
\(870\) −16.8606 −0.571626
\(871\) 9.48600 0.321421
\(872\) −5.34597 −0.181037
\(873\) −4.51767 −0.152900
\(874\) 27.9480 0.945355
\(875\) 21.0237 0.710729
\(876\) −172.405 −5.82503
\(877\) 9.91033 0.334648 0.167324 0.985902i \(-0.446487\pi\)
0.167324 + 0.985902i \(0.446487\pi\)
\(878\) 64.4141 2.17387
\(879\) 25.8819 0.872975
\(880\) 1.03750 0.0349742
\(881\) 4.73194 0.159423 0.0797116 0.996818i \(-0.474600\pi\)
0.0797116 + 0.996818i \(0.474600\pi\)
\(882\) 31.0302 1.04484
\(883\) 16.7152 0.562510 0.281255 0.959633i \(-0.409249\pi\)
0.281255 + 0.959633i \(0.409249\pi\)
\(884\) 8.93188 0.300412
\(885\) −36.4390 −1.22488
\(886\) −59.6615 −2.00437
\(887\) 20.6408 0.693050 0.346525 0.938041i \(-0.387362\pi\)
0.346525 + 0.938041i \(0.387362\pi\)
\(888\) 27.2869 0.915690
\(889\) 21.9838 0.737312
\(890\) −34.5988 −1.15975
\(891\) −0.890794 −0.0298427
\(892\) −50.4149 −1.68802
\(893\) 8.29036 0.277426
\(894\) −137.081 −4.58466
\(895\) −4.04418 −0.135182
\(896\) −26.6737 −0.891106
\(897\) −23.6910 −0.791019
\(898\) −26.2527 −0.876065
\(899\) 2.68321 0.0894901
\(900\) −40.0163 −1.33388
\(901\) 7.79266 0.259611
\(902\) −0.993850 −0.0330916
\(903\) 7.36724 0.245166
\(904\) 5.91556 0.196749
\(905\) 32.4365 1.07823
\(906\) 77.1609 2.56350
\(907\) −12.4698 −0.414053 −0.207026 0.978335i \(-0.566379\pi\)
−0.207026 + 0.978335i \(0.566379\pi\)
\(908\) −52.8686 −1.75451
\(909\) −22.1056 −0.733196
\(910\) −14.0165 −0.464641
\(911\) 35.2855 1.16906 0.584530 0.811372i \(-0.301279\pi\)
0.584530 + 0.811372i \(0.301279\pi\)
\(912\) −37.7772 −1.25093
\(913\) 1.30831 0.0432989
\(914\) −37.0331 −1.22494
\(915\) −22.8811 −0.756425
\(916\) 43.8467 1.44874
\(917\) −7.13668 −0.235674
\(918\) −2.00005 −0.0660115
\(919\) −41.4040 −1.36579 −0.682896 0.730516i \(-0.739280\pi\)
−0.682896 + 0.730516i \(0.739280\pi\)
\(920\) 40.4262 1.33281
\(921\) −7.37244 −0.242930
\(922\) −31.4272 −1.03500
\(923\) 2.05744 0.0677215
\(924\) 2.21935 0.0730113
\(925\) −5.09358 −0.167476
\(926\) −24.9074 −0.818508
\(927\) −41.2707 −1.35551
\(928\) 6.80356 0.223338
\(929\) −26.4568 −0.868018 −0.434009 0.900909i \(-0.642901\pi\)
−0.434009 + 0.900909i \(0.642901\pi\)
\(930\) −14.1960 −0.465506
\(931\) −8.99129 −0.294678
\(932\) −9.18558 −0.300884
\(933\) 8.91521 0.291871
\(934\) 11.3015 0.369796
\(935\) −0.166855 −0.00545676
\(936\) 40.3629 1.31930
\(937\) −19.7293 −0.644527 −0.322264 0.946650i \(-0.604444\pi\)
−0.322264 + 0.946650i \(0.604444\pi\)
\(938\) −21.0583 −0.687577
\(939\) −39.0620 −1.27474
\(940\) 22.2067 0.724304
\(941\) −17.4689 −0.569470 −0.284735 0.958606i \(-0.591906\pi\)
−0.284735 + 0.958606i \(0.591906\pi\)
\(942\) 146.652 4.77818
\(943\) −16.1312 −0.525305
\(944\) 60.3496 1.96421
\(945\) 2.14974 0.0699311
\(946\) −0.456453 −0.0148406
\(947\) −19.5799 −0.636261 −0.318130 0.948047i \(-0.603055\pi\)
−0.318130 + 0.948047i \(0.603055\pi\)
\(948\) −132.120 −4.29107
\(949\) −32.4612 −1.05373
\(950\) 16.9287 0.549241
\(951\) −14.8047 −0.480075
\(952\) −10.7074 −0.347028
\(953\) −33.5019 −1.08523 −0.542616 0.839981i \(-0.682566\pi\)
−0.542616 + 0.839981i \(0.682566\pi\)
\(954\) 65.2116 2.11130
\(955\) 18.4439 0.596831
\(956\) 66.1191 2.13845
\(957\) 0.502660 0.0162487
\(958\) −48.5994 −1.57017
\(959\) 7.16361 0.231325
\(960\) 10.5515 0.340547
\(961\) −28.7408 −0.927123
\(962\) 9.51413 0.306748
\(963\) −13.3500 −0.430196
\(964\) 110.570 3.56122
\(965\) −2.90340 −0.0934638
\(966\) 52.5924 1.69213
\(967\) 22.0935 0.710479 0.355239 0.934775i \(-0.384399\pi\)
0.355239 + 0.934775i \(0.384399\pi\)
\(968\) 64.9969 2.08908
\(969\) 6.07548 0.195172
\(970\) 5.11934 0.164372
\(971\) −32.2311 −1.03435 −0.517173 0.855881i \(-0.673016\pi\)
−0.517173 + 0.855881i \(0.673016\pi\)
\(972\) 97.2522 3.11937
\(973\) −12.5377 −0.401939
\(974\) −48.1836 −1.54390
\(975\) −14.3502 −0.459573
\(976\) 37.8952 1.21300
\(977\) 44.6411 1.42820 0.714098 0.700046i \(-0.246837\pi\)
0.714098 + 0.700046i \(0.246837\pi\)
\(978\) −87.3893 −2.79440
\(979\) 1.03149 0.0329664
\(980\) −24.0843 −0.769344
\(981\) 2.99703 0.0956877
\(982\) 10.1802 0.324862
\(983\) −33.1297 −1.05667 −0.528337 0.849035i \(-0.677184\pi\)
−0.528337 + 0.849035i \(0.677184\pi\)
\(984\) 52.3447 1.66869
\(985\) −41.3560 −1.31771
\(986\) −4.49087 −0.143018
\(987\) 15.6008 0.496578
\(988\) −21.6581 −0.689035
\(989\) −7.40872 −0.235584
\(990\) −1.39630 −0.0443774
\(991\) −17.3320 −0.550569 −0.275284 0.961363i \(-0.588772\pi\)
−0.275284 + 0.961363i \(0.588772\pi\)
\(992\) 5.72836 0.181876
\(993\) 48.7621 1.54742
\(994\) −4.56738 −0.144869
\(995\) 40.6093 1.28740
\(996\) −127.604 −4.04329
\(997\) −15.2928 −0.484329 −0.242165 0.970235i \(-0.577857\pi\)
−0.242165 + 0.970235i \(0.577857\pi\)
\(998\) 53.5741 1.69586
\(999\) −1.45921 −0.0461673
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 \(a_p\))