Properties

Label 8003.2.a.c.1.14
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49180 q^{2}\) \(+1.26406 q^{3}\) \(+4.20905 q^{4}\) \(-3.18748 q^{5}\) \(-3.14979 q^{6}\) \(+4.16576 q^{7}\) \(-5.50450 q^{8}\) \(-1.40214 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49180 q^{2}\) \(+1.26406 q^{3}\) \(+4.20905 q^{4}\) \(-3.18748 q^{5}\) \(-3.14979 q^{6}\) \(+4.16576 q^{7}\) \(-5.50450 q^{8}\) \(-1.40214 q^{9}\) \(+7.94255 q^{10}\) \(+4.10364 q^{11}\) \(+5.32050 q^{12}\) \(-2.81118 q^{13}\) \(-10.3802 q^{14}\) \(-4.02918 q^{15}\) \(+5.29800 q^{16}\) \(-5.22651 q^{17}\) \(+3.49386 q^{18}\) \(+4.32766 q^{19}\) \(-13.4163 q^{20}\) \(+5.26579 q^{21}\) \(-10.2254 q^{22}\) \(-2.96556 q^{23}\) \(-6.95804 q^{24}\) \(+5.16002 q^{25}\) \(+7.00490 q^{26}\) \(-5.56459 q^{27}\) \(+17.5339 q^{28}\) \(+0.134462 q^{29}\) \(+10.0399 q^{30}\) \(-2.32765 q^{31}\) \(-2.19253 q^{32}\) \(+5.18726 q^{33}\) \(+13.0234 q^{34}\) \(-13.2783 q^{35}\) \(-5.90169 q^{36}\) \(-3.13194 q^{37}\) \(-10.7837 q^{38}\) \(-3.55351 q^{39}\) \(+17.5455 q^{40}\) \(-0.709502 q^{41}\) \(-13.1213 q^{42}\) \(+2.15254 q^{43}\) \(+17.2724 q^{44}\) \(+4.46931 q^{45}\) \(+7.38958 q^{46}\) \(+5.65906 q^{47}\) \(+6.69701 q^{48}\) \(+10.3536 q^{49}\) \(-12.8577 q^{50}\) \(-6.60663 q^{51}\) \(-11.8324 q^{52}\) \(-1.00000 q^{53}\) \(+13.8658 q^{54}\) \(-13.0803 q^{55}\) \(-22.9304 q^{56}\) \(+5.47044 q^{57}\) \(-0.335053 q^{58}\) \(-13.8862 q^{59}\) \(-16.9590 q^{60}\) \(+2.60754 q^{61}\) \(+5.80002 q^{62}\) \(-5.84100 q^{63}\) \(-5.13266 q^{64}\) \(+8.96059 q^{65}\) \(-12.9256 q^{66}\) \(+7.18915 q^{67}\) \(-21.9986 q^{68}\) \(-3.74866 q^{69}\) \(+33.0868 q^{70}\) \(-11.1229 q^{71}\) \(+7.71811 q^{72}\) \(+6.14128 q^{73}\) \(+7.80416 q^{74}\) \(+6.52260 q^{75}\) \(+18.2154 q^{76}\) \(+17.0948 q^{77}\) \(+8.85463 q^{78}\) \(+10.3746 q^{79}\) \(-16.8873 q^{80}\) \(-2.82756 q^{81}\) \(+1.76793 q^{82}\) \(-4.78580 q^{83}\) \(+22.1640 q^{84}\) \(+16.6594 q^{85}\) \(-5.36369 q^{86}\) \(+0.169969 q^{87}\) \(-22.5885 q^{88}\) \(-0.627918 q^{89}\) \(-11.1366 q^{90}\) \(-11.7107 q^{91}\) \(-12.4822 q^{92}\) \(-2.94229 q^{93}\) \(-14.1012 q^{94}\) \(-13.7943 q^{95}\) \(-2.77150 q^{96}\) \(-9.52135 q^{97}\) \(-25.7990 q^{98}\) \(-5.75389 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49180 −1.76197 −0.880983 0.473148i \(-0.843118\pi\)
−0.880983 + 0.473148i \(0.843118\pi\)
\(3\) 1.26406 0.729807 0.364904 0.931045i \(-0.381102\pi\)
0.364904 + 0.931045i \(0.381102\pi\)
\(4\) 4.20905 2.10452
\(5\) −3.18748 −1.42548 −0.712742 0.701426i \(-0.752547\pi\)
−0.712742 + 0.701426i \(0.752547\pi\)
\(6\) −3.14979 −1.28590
\(7\) 4.16576 1.57451 0.787255 0.616628i \(-0.211502\pi\)
0.787255 + 0.616628i \(0.211502\pi\)
\(8\) −5.50450 −1.94614
\(9\) −1.40214 −0.467381
\(10\) 7.94255 2.51165
\(11\) 4.10364 1.23729 0.618647 0.785669i \(-0.287681\pi\)
0.618647 + 0.785669i \(0.287681\pi\)
\(12\) 5.32050 1.53590
\(13\) −2.81118 −0.779682 −0.389841 0.920882i \(-0.627470\pi\)
−0.389841 + 0.920882i \(0.627470\pi\)
\(14\) −10.3802 −2.77423
\(15\) −4.02918 −1.04033
\(16\) 5.29800 1.32450
\(17\) −5.22651 −1.26761 −0.633807 0.773491i \(-0.718509\pi\)
−0.633807 + 0.773491i \(0.718509\pi\)
\(18\) 3.49386 0.823510
\(19\) 4.32766 0.992834 0.496417 0.868084i \(-0.334649\pi\)
0.496417 + 0.868084i \(0.334649\pi\)
\(20\) −13.4163 −2.99997
\(21\) 5.26579 1.14909
\(22\) −10.2254 −2.18007
\(23\) −2.96556 −0.618363 −0.309181 0.951003i \(-0.600055\pi\)
−0.309181 + 0.951003i \(0.600055\pi\)
\(24\) −6.95804 −1.42030
\(25\) 5.16002 1.03200
\(26\) 7.00490 1.37377
\(27\) −5.56459 −1.07091
\(28\) 17.5339 3.31360
\(29\) 0.134462 0.0249690 0.0124845 0.999922i \(-0.496026\pi\)
0.0124845 + 0.999922i \(0.496026\pi\)
\(30\) 10.0399 1.83302
\(31\) −2.32765 −0.418058 −0.209029 0.977909i \(-0.567030\pi\)
−0.209029 + 0.977909i \(0.567030\pi\)
\(32\) −2.19253 −0.387589
\(33\) 5.18726 0.902986
\(34\) 13.0234 2.23349
\(35\) −13.2783 −2.24444
\(36\) −5.90169 −0.983616
\(37\) −3.13194 −0.514888 −0.257444 0.966293i \(-0.582880\pi\)
−0.257444 + 0.966293i \(0.582880\pi\)
\(38\) −10.7837 −1.74934
\(39\) −3.55351 −0.569018
\(40\) 17.5455 2.77418
\(41\) −0.709502 −0.110806 −0.0554028 0.998464i \(-0.517644\pi\)
−0.0554028 + 0.998464i \(0.517644\pi\)
\(42\) −13.1213 −2.02466
\(43\) 2.15254 0.328259 0.164129 0.986439i \(-0.447519\pi\)
0.164129 + 0.986439i \(0.447519\pi\)
\(44\) 17.2724 2.60391
\(45\) 4.46931 0.666245
\(46\) 7.38958 1.08953
\(47\) 5.65906 0.825458 0.412729 0.910854i \(-0.364576\pi\)
0.412729 + 0.910854i \(0.364576\pi\)
\(48\) 6.69701 0.966630
\(49\) 10.3536 1.47908
\(50\) −12.8577 −1.81836
\(51\) −6.60663 −0.925114
\(52\) −11.8324 −1.64086
\(53\) −1.00000 −0.137361
\(54\) 13.8658 1.88690
\(55\) −13.0803 −1.76374
\(56\) −22.9304 −3.06421
\(57\) 5.47044 0.724578
\(58\) −0.335053 −0.0439946
\(59\) −13.8862 −1.80783 −0.903913 0.427716i \(-0.859318\pi\)
−0.903913 + 0.427716i \(0.859318\pi\)
\(60\) −16.9590 −2.18940
\(61\) 2.60754 0.333862 0.166931 0.985969i \(-0.446614\pi\)
0.166931 + 0.985969i \(0.446614\pi\)
\(62\) 5.80002 0.736604
\(63\) −5.84100 −0.735897
\(64\) −5.13266 −0.641582
\(65\) 8.96059 1.11142
\(66\) −12.9256 −1.59103
\(67\) 7.18915 0.878294 0.439147 0.898415i \(-0.355281\pi\)
0.439147 + 0.898415i \(0.355281\pi\)
\(68\) −21.9986 −2.66773
\(69\) −3.74866 −0.451286
\(70\) 33.0868 3.95463
\(71\) −11.1229 −1.32004 −0.660022 0.751247i \(-0.729453\pi\)
−0.660022 + 0.751247i \(0.729453\pi\)
\(72\) 7.71811 0.909587
\(73\) 6.14128 0.718782 0.359391 0.933187i \(-0.382984\pi\)
0.359391 + 0.933187i \(0.382984\pi\)
\(74\) 7.80416 0.907215
\(75\) 6.52260 0.753165
\(76\) 18.2154 2.08944
\(77\) 17.0948 1.94813
\(78\) 8.85463 1.00259
\(79\) 10.3746 1.16723 0.583614 0.812031i \(-0.301638\pi\)
0.583614 + 0.812031i \(0.301638\pi\)
\(80\) −16.8873 −1.88805
\(81\) −2.82756 −0.314173
\(82\) 1.76793 0.195236
\(83\) −4.78580 −0.525310 −0.262655 0.964890i \(-0.584598\pi\)
−0.262655 + 0.964890i \(0.584598\pi\)
\(84\) 22.1640 2.41829
\(85\) 16.6594 1.80696
\(86\) −5.36369 −0.578381
\(87\) 0.169969 0.0182226
\(88\) −22.5885 −2.40794
\(89\) −0.627918 −0.0665592 −0.0332796 0.999446i \(-0.510595\pi\)
−0.0332796 + 0.999446i \(0.510595\pi\)
\(90\) −11.1366 −1.17390
\(91\) −11.7107 −1.22762
\(92\) −12.4822 −1.30136
\(93\) −2.94229 −0.305102
\(94\) −14.1012 −1.45443
\(95\) −13.7943 −1.41527
\(96\) −2.77150 −0.282865
\(97\) −9.52135 −0.966747 −0.483374 0.875414i \(-0.660589\pi\)
−0.483374 + 0.875414i \(0.660589\pi\)
\(98\) −25.7990 −2.60609
\(99\) −5.75389 −0.578288
\(100\) 21.7188 2.17188
\(101\) 17.6646 1.75770 0.878848 0.477102i \(-0.158313\pi\)
0.878848 + 0.477102i \(0.158313\pi\)
\(102\) 16.4624 1.63002
\(103\) 12.3226 1.21418 0.607090 0.794633i \(-0.292337\pi\)
0.607090 + 0.794633i \(0.292337\pi\)
\(104\) 15.4742 1.51737
\(105\) −16.7846 −1.63801
\(106\) 2.49180 0.242025
\(107\) 14.6702 1.41822 0.709110 0.705098i \(-0.249097\pi\)
0.709110 + 0.705098i \(0.249097\pi\)
\(108\) −23.4216 −2.25375
\(109\) 4.09509 0.392238 0.196119 0.980580i \(-0.437166\pi\)
0.196119 + 0.980580i \(0.437166\pi\)
\(110\) 32.5934 3.10765
\(111\) −3.95897 −0.375769
\(112\) 22.0702 2.08544
\(113\) 7.60429 0.715352 0.357676 0.933846i \(-0.383569\pi\)
0.357676 + 0.933846i \(0.383569\pi\)
\(114\) −13.6312 −1.27668
\(115\) 9.45267 0.881466
\(116\) 0.565959 0.0525479
\(117\) 3.94169 0.364409
\(118\) 34.6015 3.18533
\(119\) −21.7724 −1.99587
\(120\) 22.1786 2.02462
\(121\) 5.83985 0.530895
\(122\) −6.49747 −0.588253
\(123\) −0.896855 −0.0808667
\(124\) −9.79718 −0.879813
\(125\) −0.510075 −0.0456225
\(126\) 14.5546 1.29663
\(127\) −5.15412 −0.457354 −0.228677 0.973502i \(-0.573440\pi\)
−0.228677 + 0.973502i \(0.573440\pi\)
\(128\) 17.1746 1.51803
\(129\) 2.72094 0.239566
\(130\) −22.3280 −1.95829
\(131\) 0.813284 0.0710570 0.0355285 0.999369i \(-0.488689\pi\)
0.0355285 + 0.999369i \(0.488689\pi\)
\(132\) 21.8334 1.90036
\(133\) 18.0280 1.56323
\(134\) −17.9139 −1.54752
\(135\) 17.7370 1.52656
\(136\) 28.7693 2.46695
\(137\) 11.1819 0.955338 0.477669 0.878540i \(-0.341482\pi\)
0.477669 + 0.878540i \(0.341482\pi\)
\(138\) 9.34090 0.795150
\(139\) 7.44775 0.631710 0.315855 0.948807i \(-0.397709\pi\)
0.315855 + 0.948807i \(0.397709\pi\)
\(140\) −55.8889 −4.72348
\(141\) 7.15340 0.602425
\(142\) 27.7160 2.32587
\(143\) −11.5361 −0.964696
\(144\) −7.42856 −0.619047
\(145\) −0.428596 −0.0355930
\(146\) −15.3028 −1.26647
\(147\) 13.0876 1.07944
\(148\) −13.1825 −1.08359
\(149\) −7.58476 −0.621368 −0.310684 0.950513i \(-0.600558\pi\)
−0.310684 + 0.950513i \(0.600558\pi\)
\(150\) −16.2530 −1.32705
\(151\) 1.00000 0.0813788
\(152\) −23.8216 −1.93219
\(153\) 7.32832 0.592459
\(154\) −42.5967 −3.43254
\(155\) 7.41933 0.595935
\(156\) −14.9569 −1.19751
\(157\) −12.5367 −1.00053 −0.500267 0.865871i \(-0.666765\pi\)
−0.500267 + 0.865871i \(0.666765\pi\)
\(158\) −25.8513 −2.05662
\(159\) −1.26406 −0.100247
\(160\) 6.98865 0.552501
\(161\) −12.3538 −0.973618
\(162\) 7.04570 0.553563
\(163\) 8.33588 0.652916 0.326458 0.945212i \(-0.394145\pi\)
0.326458 + 0.945212i \(0.394145\pi\)
\(164\) −2.98633 −0.233193
\(165\) −16.5343 −1.28719
\(166\) 11.9252 0.925578
\(167\) 2.19756 0.170053 0.0850263 0.996379i \(-0.472903\pi\)
0.0850263 + 0.996379i \(0.472903\pi\)
\(168\) −28.9855 −2.23628
\(169\) −5.09725 −0.392096
\(170\) −41.5118 −3.18381
\(171\) −6.06801 −0.464032
\(172\) 9.06014 0.690829
\(173\) 16.7651 1.27463 0.637315 0.770603i \(-0.280045\pi\)
0.637315 + 0.770603i \(0.280045\pi\)
\(174\) −0.423528 −0.0321076
\(175\) 21.4954 1.62490
\(176\) 21.7411 1.63880
\(177\) −17.5530 −1.31936
\(178\) 1.56464 0.117275
\(179\) −3.90391 −0.291792 −0.145896 0.989300i \(-0.546606\pi\)
−0.145896 + 0.989300i \(0.546606\pi\)
\(180\) 18.8115 1.40213
\(181\) 6.81301 0.506407 0.253204 0.967413i \(-0.418516\pi\)
0.253204 + 0.967413i \(0.418516\pi\)
\(182\) 29.1807 2.16302
\(183\) 3.29610 0.243655
\(184\) 16.3239 1.20342
\(185\) 9.98299 0.733964
\(186\) 7.33159 0.537579
\(187\) −21.4477 −1.56841
\(188\) 23.8192 1.73720
\(189\) −23.1808 −1.68615
\(190\) 34.3727 2.49366
\(191\) −12.8363 −0.928801 −0.464401 0.885625i \(-0.653730\pi\)
−0.464401 + 0.885625i \(0.653730\pi\)
\(192\) −6.48800 −0.468231
\(193\) 15.6298 1.12506 0.562528 0.826778i \(-0.309829\pi\)
0.562528 + 0.826778i \(0.309829\pi\)
\(194\) 23.7253 1.70338
\(195\) 11.3268 0.811126
\(196\) 43.5787 3.11276
\(197\) 10.8051 0.769833 0.384916 0.922951i \(-0.374230\pi\)
0.384916 + 0.922951i \(0.374230\pi\)
\(198\) 14.3375 1.01892
\(199\) 6.76148 0.479309 0.239654 0.970858i \(-0.422966\pi\)
0.239654 + 0.970858i \(0.422966\pi\)
\(200\) −28.4034 −2.00842
\(201\) 9.08754 0.640985
\(202\) −44.0167 −3.09700
\(203\) 0.560138 0.0393140
\(204\) −27.8077 −1.94693
\(205\) 2.26152 0.157952
\(206\) −30.7053 −2.13934
\(207\) 4.15815 0.289011
\(208\) −14.8936 −1.03269
\(209\) 17.7592 1.22843
\(210\) 41.8238 2.88611
\(211\) −13.3505 −0.919084 −0.459542 0.888156i \(-0.651987\pi\)
−0.459542 + 0.888156i \(0.651987\pi\)
\(212\) −4.20905 −0.289079
\(213\) −14.0600 −0.963377
\(214\) −36.5551 −2.49885
\(215\) −6.86117 −0.467928
\(216\) 30.6303 2.08413
\(217\) −9.69642 −0.658236
\(218\) −10.2041 −0.691111
\(219\) 7.76296 0.524572
\(220\) −55.0555 −3.71184
\(221\) 14.6927 0.988336
\(222\) 9.86495 0.662092
\(223\) 13.9086 0.931389 0.465694 0.884946i \(-0.345805\pi\)
0.465694 + 0.884946i \(0.345805\pi\)
\(224\) −9.13357 −0.610262
\(225\) −7.23510 −0.482340
\(226\) −18.9483 −1.26043
\(227\) −26.1232 −1.73386 −0.866928 0.498434i \(-0.833909\pi\)
−0.866928 + 0.498434i \(0.833909\pi\)
\(228\) 23.0254 1.52489
\(229\) −26.1587 −1.72862 −0.864309 0.502961i \(-0.832244\pi\)
−0.864309 + 0.502961i \(0.832244\pi\)
\(230\) −23.5541 −1.55311
\(231\) 21.6089 1.42176
\(232\) −0.740148 −0.0485931
\(233\) −8.08685 −0.529787 −0.264893 0.964278i \(-0.585337\pi\)
−0.264893 + 0.964278i \(0.585337\pi\)
\(234\) −9.82188 −0.642076
\(235\) −18.0381 −1.17668
\(236\) −58.4476 −3.80461
\(237\) 13.1141 0.851852
\(238\) 54.2523 3.51666
\(239\) −9.17856 −0.593712 −0.296856 0.954922i \(-0.595938\pi\)
−0.296856 + 0.954922i \(0.595938\pi\)
\(240\) −21.3466 −1.37792
\(241\) −5.75828 −0.370923 −0.185462 0.982651i \(-0.559378\pi\)
−0.185462 + 0.982651i \(0.559378\pi\)
\(242\) −14.5517 −0.935420
\(243\) 13.1196 0.841620
\(244\) 10.9753 0.702620
\(245\) −33.0018 −2.10841
\(246\) 2.23478 0.142484
\(247\) −12.1659 −0.774095
\(248\) 12.8125 0.813597
\(249\) −6.04956 −0.383375
\(250\) 1.27100 0.0803853
\(251\) 13.2244 0.834718 0.417359 0.908742i \(-0.362956\pi\)
0.417359 + 0.908742i \(0.362956\pi\)
\(252\) −24.5851 −1.54871
\(253\) −12.1696 −0.765096
\(254\) 12.8430 0.805843
\(255\) 21.0585 1.31874
\(256\) −32.5303 −2.03314
\(257\) 12.5160 0.780725 0.390363 0.920661i \(-0.372350\pi\)
0.390363 + 0.920661i \(0.372350\pi\)
\(258\) −6.78004 −0.422107
\(259\) −13.0469 −0.810696
\(260\) 37.7156 2.33902
\(261\) −0.188536 −0.0116701
\(262\) −2.02654 −0.125200
\(263\) 3.01417 0.185862 0.0929308 0.995673i \(-0.470376\pi\)
0.0929308 + 0.995673i \(0.470376\pi\)
\(264\) −28.5533 −1.75733
\(265\) 3.18748 0.195805
\(266\) −44.9222 −2.75435
\(267\) −0.793728 −0.0485754
\(268\) 30.2595 1.84839
\(269\) −8.44611 −0.514968 −0.257484 0.966283i \(-0.582894\pi\)
−0.257484 + 0.966283i \(0.582894\pi\)
\(270\) −44.1970 −2.68975
\(271\) 12.0600 0.732591 0.366295 0.930499i \(-0.380626\pi\)
0.366295 + 0.930499i \(0.380626\pi\)
\(272\) −27.6900 −1.67895
\(273\) −14.8031 −0.895924
\(274\) −27.8631 −1.68327
\(275\) 21.1749 1.27689
\(276\) −15.7783 −0.949742
\(277\) 21.1705 1.27201 0.636005 0.771685i \(-0.280586\pi\)
0.636005 + 0.771685i \(0.280586\pi\)
\(278\) −18.5583 −1.11305
\(279\) 3.26370 0.195392
\(280\) 73.0903 4.36798
\(281\) 18.6566 1.11296 0.556479 0.830862i \(-0.312152\pi\)
0.556479 + 0.830862i \(0.312152\pi\)
\(282\) −17.8248 −1.06145
\(283\) 16.1998 0.962975 0.481488 0.876453i \(-0.340097\pi\)
0.481488 + 0.876453i \(0.340097\pi\)
\(284\) −46.8168 −2.77806
\(285\) −17.4369 −1.03287
\(286\) 28.7456 1.69976
\(287\) −2.95562 −0.174465
\(288\) 3.07425 0.181152
\(289\) 10.3164 0.606845
\(290\) 1.06797 0.0627136
\(291\) −12.0356 −0.705539
\(292\) 25.8489 1.51269
\(293\) 10.5898 0.618662 0.309331 0.950954i \(-0.399895\pi\)
0.309331 + 0.950954i \(0.399895\pi\)
\(294\) −32.6116 −1.90195
\(295\) 44.2619 2.57703
\(296\) 17.2398 1.00204
\(297\) −22.8351 −1.32502
\(298\) 18.8997 1.09483
\(299\) 8.33674 0.482126
\(300\) 27.4539 1.58505
\(301\) 8.96696 0.516847
\(302\) −2.49180 −0.143387
\(303\) 22.3292 1.28278
\(304\) 22.9280 1.31501
\(305\) −8.31149 −0.475915
\(306\) −18.2607 −1.04389
\(307\) 6.18948 0.353252 0.176626 0.984278i \(-0.443482\pi\)
0.176626 + 0.984278i \(0.443482\pi\)
\(308\) 71.9528 4.09989
\(309\) 15.5765 0.886117
\(310\) −18.4875 −1.05002
\(311\) −10.9586 −0.621405 −0.310703 0.950507i \(-0.600564\pi\)
−0.310703 + 0.950507i \(0.600564\pi\)
\(312\) 19.5603 1.10739
\(313\) 11.0319 0.623562 0.311781 0.950154i \(-0.399075\pi\)
0.311781 + 0.950154i \(0.399075\pi\)
\(314\) 31.2388 1.76291
\(315\) 18.6181 1.04901
\(316\) 43.6670 2.45646
\(317\) 16.6097 0.932892 0.466446 0.884550i \(-0.345534\pi\)
0.466446 + 0.884550i \(0.345534\pi\)
\(318\) 3.14979 0.176631
\(319\) 0.551785 0.0308940
\(320\) 16.3602 0.914565
\(321\) 18.5440 1.03503
\(322\) 30.7832 1.71548
\(323\) −22.6186 −1.25853
\(324\) −11.9013 −0.661185
\(325\) −14.5058 −0.804636
\(326\) −20.7713 −1.15042
\(327\) 5.17645 0.286258
\(328\) 3.90546 0.215643
\(329\) 23.5743 1.29969
\(330\) 41.2001 2.26799
\(331\) −8.51012 −0.467758 −0.233879 0.972266i \(-0.575142\pi\)
−0.233879 + 0.972266i \(0.575142\pi\)
\(332\) −20.1437 −1.10553
\(333\) 4.39143 0.240649
\(334\) −5.47588 −0.299627
\(335\) −22.9153 −1.25199
\(336\) 27.8981 1.52197
\(337\) 20.5446 1.11913 0.559567 0.828785i \(-0.310968\pi\)
0.559567 + 0.828785i \(0.310968\pi\)
\(338\) 12.7013 0.690860
\(339\) 9.61231 0.522069
\(340\) 70.1202 3.80280
\(341\) −9.55182 −0.517260
\(342\) 15.1202 0.817609
\(343\) 13.9702 0.754319
\(344\) −11.8487 −0.638836
\(345\) 11.9488 0.643300
\(346\) −41.7753 −2.24586
\(347\) −7.43683 −0.399230 −0.199615 0.979874i \(-0.563969\pi\)
−0.199615 + 0.979874i \(0.563969\pi\)
\(348\) 0.715408 0.0383499
\(349\) 29.2579 1.56614 0.783069 0.621935i \(-0.213653\pi\)
0.783069 + 0.621935i \(0.213653\pi\)
\(350\) −53.5622 −2.86302
\(351\) 15.6431 0.834966
\(352\) −8.99736 −0.479561
\(353\) −2.38165 −0.126763 −0.0633813 0.997989i \(-0.520188\pi\)
−0.0633813 + 0.997989i \(0.520188\pi\)
\(354\) 43.7385 2.32468
\(355\) 35.4540 1.88170
\(356\) −2.64294 −0.140076
\(357\) −27.5217 −1.45660
\(358\) 9.72774 0.514127
\(359\) 15.8310 0.835527 0.417763 0.908556i \(-0.362814\pi\)
0.417763 + 0.908556i \(0.362814\pi\)
\(360\) −24.6013 −1.29660
\(361\) −0.271326 −0.0142803
\(362\) −16.9766 −0.892272
\(363\) 7.38194 0.387451
\(364\) −49.2910 −2.58355
\(365\) −19.5752 −1.02461
\(366\) −8.21321 −0.429311
\(367\) 23.4348 1.22329 0.611644 0.791133i \(-0.290509\pi\)
0.611644 + 0.791133i \(0.290509\pi\)
\(368\) −15.7116 −0.819021
\(369\) 0.994824 0.0517885
\(370\) −24.8756 −1.29322
\(371\) −4.16576 −0.216276
\(372\) −12.3843 −0.642094
\(373\) −11.1955 −0.579679 −0.289840 0.957075i \(-0.593602\pi\)
−0.289840 + 0.957075i \(0.593602\pi\)
\(374\) 53.4433 2.76349
\(375\) −0.644767 −0.0332956
\(376\) −31.1503 −1.60645
\(377\) −0.377998 −0.0194679
\(378\) 57.7617 2.97094
\(379\) 4.03176 0.207098 0.103549 0.994624i \(-0.466980\pi\)
0.103549 + 0.994624i \(0.466980\pi\)
\(380\) −58.0611 −2.97847
\(381\) −6.51514 −0.333781
\(382\) 31.9854 1.63652
\(383\) 24.5794 1.25595 0.627975 0.778234i \(-0.283884\pi\)
0.627975 + 0.778234i \(0.283884\pi\)
\(384\) 21.7098 1.10787
\(385\) −54.4893 −2.77703
\(386\) −38.9462 −1.98231
\(387\) −3.01817 −0.153422
\(388\) −40.0759 −2.03454
\(389\) −21.4147 −1.08577 −0.542884 0.839808i \(-0.682668\pi\)
−0.542884 + 0.839808i \(0.682668\pi\)
\(390\) −28.2240 −1.42918
\(391\) 15.4995 0.783845
\(392\) −56.9913 −2.87849
\(393\) 1.02804 0.0518579
\(394\) −26.9242 −1.35642
\(395\) −33.0687 −1.66387
\(396\) −24.2184 −1.21702
\(397\) −18.7397 −0.940520 −0.470260 0.882528i \(-0.655840\pi\)
−0.470260 + 0.882528i \(0.655840\pi\)
\(398\) −16.8482 −0.844526
\(399\) 22.7886 1.14085
\(400\) 27.3378 1.36689
\(401\) −8.68392 −0.433654 −0.216827 0.976210i \(-0.569571\pi\)
−0.216827 + 0.976210i \(0.569571\pi\)
\(402\) −22.6443 −1.12939
\(403\) 6.54344 0.325952
\(404\) 74.3513 3.69912
\(405\) 9.01279 0.447849
\(406\) −1.39575 −0.0692699
\(407\) −12.8524 −0.637067
\(408\) 36.3662 1.80040
\(409\) −5.13024 −0.253674 −0.126837 0.991924i \(-0.540483\pi\)
−0.126837 + 0.991924i \(0.540483\pi\)
\(410\) −5.63526 −0.278305
\(411\) 14.1347 0.697213
\(412\) 51.8663 2.55527
\(413\) −57.8465 −2.84644
\(414\) −10.3613 −0.509228
\(415\) 15.2546 0.748821
\(416\) 6.16361 0.302196
\(417\) 9.41443 0.461026
\(418\) −44.2522 −2.16445
\(419\) −7.99070 −0.390371 −0.195186 0.980766i \(-0.562531\pi\)
−0.195186 + 0.980766i \(0.562531\pi\)
\(420\) −70.6472 −3.44723
\(421\) −33.6184 −1.63846 −0.819231 0.573464i \(-0.805599\pi\)
−0.819231 + 0.573464i \(0.805599\pi\)
\(422\) 33.2667 1.61940
\(423\) −7.93481 −0.385804
\(424\) 5.50450 0.267322
\(425\) −26.9689 −1.30818
\(426\) 35.0347 1.69744
\(427\) 10.8624 0.525669
\(428\) 61.7475 2.98468
\(429\) −14.5823 −0.704042
\(430\) 17.0966 0.824473
\(431\) 23.5648 1.13508 0.567539 0.823347i \(-0.307896\pi\)
0.567539 + 0.823347i \(0.307896\pi\)
\(432\) −29.4812 −1.41841
\(433\) −8.70169 −0.418177 −0.209088 0.977897i \(-0.567050\pi\)
−0.209088 + 0.977897i \(0.567050\pi\)
\(434\) 24.1615 1.15979
\(435\) −0.541772 −0.0259760
\(436\) 17.2364 0.825475
\(437\) −12.8340 −0.613932
\(438\) −19.3437 −0.924279
\(439\) 32.2037 1.53700 0.768500 0.639849i \(-0.221003\pi\)
0.768500 + 0.639849i \(0.221003\pi\)
\(440\) 72.0003 3.43248
\(441\) −14.5172 −0.691295
\(442\) −36.6111 −1.74141
\(443\) −0.974585 −0.0463039 −0.0231520 0.999732i \(-0.507370\pi\)
−0.0231520 + 0.999732i \(0.507370\pi\)
\(444\) −16.6635 −0.790815
\(445\) 2.00148 0.0948791
\(446\) −34.6574 −1.64108
\(447\) −9.58761 −0.453479
\(448\) −21.3814 −1.01018
\(449\) −13.5707 −0.640443 −0.320221 0.947343i \(-0.603757\pi\)
−0.320221 + 0.947343i \(0.603757\pi\)
\(450\) 18.0284 0.849867
\(451\) −2.91154 −0.137099
\(452\) 32.0068 1.50548
\(453\) 1.26406 0.0593909
\(454\) 65.0936 3.05500
\(455\) 37.3277 1.74995
\(456\) −30.1121 −1.41013
\(457\) −14.4128 −0.674203 −0.337101 0.941468i \(-0.609447\pi\)
−0.337101 + 0.941468i \(0.609447\pi\)
\(458\) 65.1823 3.04577
\(459\) 29.0834 1.35749
\(460\) 39.7868 1.85507
\(461\) 14.7973 0.689178 0.344589 0.938754i \(-0.388018\pi\)
0.344589 + 0.938754i \(0.388018\pi\)
\(462\) −53.8449 −2.50509
\(463\) −35.3938 −1.64489 −0.822445 0.568845i \(-0.807391\pi\)
−0.822445 + 0.568845i \(0.807391\pi\)
\(464\) 0.712381 0.0330715
\(465\) 9.37850 0.434917
\(466\) 20.1508 0.933467
\(467\) −18.4797 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(468\) 16.5907 0.766908
\(469\) 29.9483 1.38288
\(470\) 44.9473 2.07327
\(471\) −15.8471 −0.730197
\(472\) 76.4365 3.51827
\(473\) 8.83324 0.406153
\(474\) −32.6776 −1.50093
\(475\) 22.3309 1.02461
\(476\) −91.6410 −4.20036
\(477\) 1.40214 0.0641998
\(478\) 22.8711 1.04610
\(479\) 21.2658 0.971659 0.485830 0.874054i \(-0.338518\pi\)
0.485830 + 0.874054i \(0.338518\pi\)
\(480\) 8.83409 0.403219
\(481\) 8.80446 0.401449
\(482\) 14.3485 0.653554
\(483\) −15.6160 −0.710554
\(484\) 24.5802 1.11728
\(485\) 30.3491 1.37808
\(486\) −32.6913 −1.48291
\(487\) 0.153923 0.00697490 0.00348745 0.999994i \(-0.498890\pi\)
0.00348745 + 0.999994i \(0.498890\pi\)
\(488\) −14.3532 −0.649740
\(489\) 10.5371 0.476503
\(490\) 82.2338 3.71494
\(491\) −2.95347 −0.133288 −0.0666440 0.997777i \(-0.521229\pi\)
−0.0666440 + 0.997777i \(0.521229\pi\)
\(492\) −3.77491 −0.170186
\(493\) −0.702768 −0.0316511
\(494\) 30.3148 1.36393
\(495\) 18.3404 0.824340
\(496\) −12.3319 −0.553717
\(497\) −46.3353 −2.07842
\(498\) 15.0743 0.675494
\(499\) −17.8334 −0.798335 −0.399167 0.916878i \(-0.630701\pi\)
−0.399167 + 0.916878i \(0.630701\pi\)
\(500\) −2.14693 −0.0960137
\(501\) 2.77786 0.124106
\(502\) −32.9526 −1.47075
\(503\) −3.88433 −0.173194 −0.0865970 0.996243i \(-0.527599\pi\)
−0.0865970 + 0.996243i \(0.527599\pi\)
\(504\) 32.1518 1.43215
\(505\) −56.3056 −2.50557
\(506\) 30.3242 1.34807
\(507\) −6.44324 −0.286154
\(508\) −21.6940 −0.962514
\(509\) 29.1538 1.29222 0.646109 0.763245i \(-0.276395\pi\)
0.646109 + 0.763245i \(0.276395\pi\)
\(510\) −52.4735 −2.32357
\(511\) 25.5831 1.13173
\(512\) 46.7097 2.06429
\(513\) −24.0817 −1.06323
\(514\) −31.1873 −1.37561
\(515\) −39.2780 −1.73079
\(516\) 11.4526 0.504172
\(517\) 23.2227 1.02133
\(518\) 32.5103 1.42842
\(519\) 21.1922 0.930235
\(520\) −49.3236 −2.16298
\(521\) −25.3515 −1.11067 −0.555335 0.831627i \(-0.687410\pi\)
−0.555335 + 0.831627i \(0.687410\pi\)
\(522\) 0.469792 0.0205623
\(523\) −36.8932 −1.61323 −0.806613 0.591080i \(-0.798702\pi\)
−0.806613 + 0.591080i \(0.798702\pi\)
\(524\) 3.42315 0.149541
\(525\) 27.1716 1.18587
\(526\) −7.51069 −0.327482
\(527\) 12.1655 0.529936
\(528\) 27.4821 1.19600
\(529\) −14.2054 −0.617628
\(530\) −7.94255 −0.345002
\(531\) 19.4704 0.844944
\(532\) 75.8808 3.28985
\(533\) 1.99454 0.0863932
\(534\) 1.97781 0.0855882
\(535\) −46.7609 −2.02165
\(536\) −39.5727 −1.70928
\(537\) −4.93478 −0.212952
\(538\) 21.0460 0.907357
\(539\) 42.4873 1.83006
\(540\) 74.6560 3.21268
\(541\) −31.7376 −1.36451 −0.682254 0.731116i \(-0.739000\pi\)
−0.682254 + 0.731116i \(0.739000\pi\)
\(542\) −30.0510 −1.29080
\(543\) 8.61208 0.369580
\(544\) 11.4593 0.491313
\(545\) −13.0530 −0.559129
\(546\) 36.8863 1.57859
\(547\) 9.95062 0.425458 0.212729 0.977111i \(-0.431765\pi\)
0.212729 + 0.977111i \(0.431765\pi\)
\(548\) 47.0654 2.01053
\(549\) −3.65615 −0.156041
\(550\) −52.7635 −2.24984
\(551\) 0.581908 0.0247901
\(552\) 20.6345 0.878263
\(553\) 43.2179 1.83781
\(554\) −52.7525 −2.24124
\(555\) 12.6191 0.535653
\(556\) 31.3480 1.32945
\(557\) −4.37679 −0.185451 −0.0927254 0.995692i \(-0.529558\pi\)
−0.0927254 + 0.995692i \(0.529558\pi\)
\(558\) −8.13247 −0.344275
\(559\) −6.05118 −0.255938
\(560\) −70.3483 −2.97276
\(561\) −27.1112 −1.14464
\(562\) −46.4884 −1.96099
\(563\) 29.1109 1.22688 0.613438 0.789743i \(-0.289786\pi\)
0.613438 + 0.789743i \(0.289786\pi\)
\(564\) 30.1090 1.26782
\(565\) −24.2385 −1.01972
\(566\) −40.3665 −1.69673
\(567\) −11.7789 −0.494669
\(568\) 61.2259 2.56898
\(569\) 39.6007 1.66015 0.830074 0.557653i \(-0.188298\pi\)
0.830074 + 0.557653i \(0.188298\pi\)
\(570\) 43.4492 1.81989
\(571\) 32.1103 1.34378 0.671888 0.740653i \(-0.265484\pi\)
0.671888 + 0.740653i \(0.265484\pi\)
\(572\) −48.5559 −2.03023
\(573\) −16.2259 −0.677846
\(574\) 7.36480 0.307401
\(575\) −15.3024 −0.638153
\(576\) 7.19672 0.299863
\(577\) 2.56038 0.106590 0.0532949 0.998579i \(-0.483028\pi\)
0.0532949 + 0.998579i \(0.483028\pi\)
\(578\) −25.7063 −1.06924
\(579\) 19.7570 0.821074
\(580\) −1.80398 −0.0749063
\(581\) −19.9365 −0.827106
\(582\) 29.9903 1.24314
\(583\) −4.10364 −0.169955
\(584\) −33.8047 −1.39885
\(585\) −12.5640 −0.519459
\(586\) −26.3876 −1.09006
\(587\) 19.0670 0.786979 0.393489 0.919329i \(-0.371268\pi\)
0.393489 + 0.919329i \(0.371268\pi\)
\(588\) 55.0862 2.27172
\(589\) −10.0733 −0.415062
\(590\) −110.292 −4.54063
\(591\) 13.6584 0.561830
\(592\) −16.5930 −0.681969
\(593\) 40.4771 1.66219 0.831097 0.556127i \(-0.187713\pi\)
0.831097 + 0.556127i \(0.187713\pi\)
\(594\) 56.9003 2.33465
\(595\) 69.3990 2.84508
\(596\) −31.9246 −1.30768
\(597\) 8.54694 0.349803
\(598\) −20.7735 −0.849490
\(599\) 28.5911 1.16820 0.584101 0.811681i \(-0.301447\pi\)
0.584101 + 0.811681i \(0.301447\pi\)
\(600\) −35.9036 −1.46576
\(601\) 44.4009 1.81115 0.905574 0.424188i \(-0.139440\pi\)
0.905574 + 0.424188i \(0.139440\pi\)
\(602\) −22.3438 −0.910667
\(603\) −10.0802 −0.410498
\(604\) 4.20905 0.171264
\(605\) −18.6144 −0.756783
\(606\) −55.6398 −2.26021
\(607\) 24.0745 0.977156 0.488578 0.872520i \(-0.337516\pi\)
0.488578 + 0.872520i \(0.337516\pi\)
\(608\) −9.48854 −0.384811
\(609\) 0.708050 0.0286916
\(610\) 20.7105 0.838545
\(611\) −15.9086 −0.643595
\(612\) 30.8452 1.24685
\(613\) −48.4394 −1.95645 −0.978225 0.207548i \(-0.933452\pi\)
−0.978225 + 0.207548i \(0.933452\pi\)
\(614\) −15.4229 −0.622419
\(615\) 2.85871 0.115274
\(616\) −94.0983 −3.79133
\(617\) 42.9999 1.73111 0.865555 0.500814i \(-0.166966\pi\)
0.865555 + 0.500814i \(0.166966\pi\)
\(618\) −38.8135 −1.56131
\(619\) −23.9449 −0.962425 −0.481213 0.876604i \(-0.659803\pi\)
−0.481213 + 0.876604i \(0.659803\pi\)
\(620\) 31.2283 1.25416
\(621\) 16.5021 0.662208
\(622\) 27.3066 1.09489
\(623\) −2.61576 −0.104798
\(624\) −18.8265 −0.753664
\(625\) −24.1743 −0.966971
\(626\) −27.4893 −1.09869
\(627\) 22.4487 0.896515
\(628\) −52.7674 −2.10565
\(629\) 16.3691 0.652679
\(630\) −46.3924 −1.84832
\(631\) 12.4916 0.497281 0.248641 0.968596i \(-0.420016\pi\)
0.248641 + 0.968596i \(0.420016\pi\)
\(632\) −57.1067 −2.27158
\(633\) −16.8758 −0.670754
\(634\) −41.3879 −1.64372
\(635\) 16.4287 0.651951
\(636\) −5.32050 −0.210972
\(637\) −29.1058 −1.15321
\(638\) −1.37494 −0.0544342
\(639\) 15.5959 0.616964
\(640\) −54.7437 −2.16393
\(641\) −45.9442 −1.81469 −0.907344 0.420389i \(-0.861894\pi\)
−0.907344 + 0.420389i \(0.861894\pi\)
\(642\) −46.2080 −1.82368
\(643\) 2.45027 0.0966291 0.0483146 0.998832i \(-0.484615\pi\)
0.0483146 + 0.998832i \(0.484615\pi\)
\(644\) −51.9979 −2.04900
\(645\) −8.67295 −0.341497
\(646\) 56.3609 2.21749
\(647\) −33.9834 −1.33603 −0.668013 0.744150i \(-0.732855\pi\)
−0.668013 + 0.744150i \(0.732855\pi\)
\(648\) 15.5643 0.611424
\(649\) −56.9838 −2.23681
\(650\) 36.1454 1.41774
\(651\) −12.2569 −0.480385
\(652\) 35.0861 1.37408
\(653\) −23.0437 −0.901770 −0.450885 0.892582i \(-0.648892\pi\)
−0.450885 + 0.892582i \(0.648892\pi\)
\(654\) −12.8987 −0.504377
\(655\) −2.59233 −0.101291
\(656\) −3.75894 −0.146762
\(657\) −8.61096 −0.335945
\(658\) −58.7423 −2.29001
\(659\) −6.76293 −0.263446 −0.131723 0.991287i \(-0.542051\pi\)
−0.131723 + 0.991287i \(0.542051\pi\)
\(660\) −69.5936 −2.70893
\(661\) 14.8145 0.576216 0.288108 0.957598i \(-0.406974\pi\)
0.288108 + 0.957598i \(0.406974\pi\)
\(662\) 21.2055 0.824174
\(663\) 18.5725 0.721295
\(664\) 26.3435 1.02232
\(665\) −57.4639 −2.22836
\(666\) −10.9426 −0.424015
\(667\) −0.398757 −0.0154399
\(668\) 9.24965 0.357880
\(669\) 17.5814 0.679734
\(670\) 57.1002 2.20597
\(671\) 10.7004 0.413085
\(672\) −11.5454 −0.445374
\(673\) 30.1769 1.16323 0.581617 0.813463i \(-0.302420\pi\)
0.581617 + 0.813463i \(0.302420\pi\)
\(674\) −51.1928 −1.97187
\(675\) −28.7134 −1.10518
\(676\) −21.4546 −0.825175
\(677\) 0.900879 0.0346236 0.0173118 0.999850i \(-0.494489\pi\)
0.0173118 + 0.999850i \(0.494489\pi\)
\(678\) −23.9519 −0.919867
\(679\) −39.6637 −1.52215
\(680\) −91.7016 −3.51660
\(681\) −33.0213 −1.26538
\(682\) 23.8012 0.911395
\(683\) −16.6953 −0.638827 −0.319413 0.947615i \(-0.603486\pi\)
−0.319413 + 0.947615i \(0.603486\pi\)
\(684\) −25.5406 −0.976567
\(685\) −35.6422 −1.36182
\(686\) −34.8109 −1.32909
\(687\) −33.0663 −1.26156
\(688\) 11.4041 0.434779
\(689\) 2.81118 0.107098
\(690\) −29.7739 −1.13347
\(691\) 37.7331 1.43543 0.717717 0.696335i \(-0.245187\pi\)
0.717717 + 0.696335i \(0.245187\pi\)
\(692\) 70.5653 2.68249
\(693\) −23.9693 −0.910520
\(694\) 18.5311 0.703430
\(695\) −23.7396 −0.900492
\(696\) −0.935594 −0.0354636
\(697\) 3.70822 0.140459
\(698\) −72.9047 −2.75948
\(699\) −10.2223 −0.386642
\(700\) 90.4754 3.41965
\(701\) −22.9477 −0.866721 −0.433361 0.901221i \(-0.642672\pi\)
−0.433361 + 0.901221i \(0.642672\pi\)
\(702\) −38.9794 −1.47118
\(703\) −13.5540 −0.511198
\(704\) −21.0626 −0.793825
\(705\) −22.8013 −0.858748
\(706\) 5.93459 0.223351
\(707\) 73.5866 2.76751
\(708\) −73.8815 −2.77664
\(709\) 31.7281 1.19157 0.595787 0.803143i \(-0.296840\pi\)
0.595787 + 0.803143i \(0.296840\pi\)
\(710\) −88.3441 −3.31549
\(711\) −14.5466 −0.545541
\(712\) 3.45638 0.129533
\(713\) 6.90278 0.258511
\(714\) 68.5784 2.56648
\(715\) 36.7710 1.37516
\(716\) −16.4317 −0.614083
\(717\) −11.6023 −0.433295
\(718\) −39.4476 −1.47217
\(719\) 38.6189 1.44024 0.720121 0.693849i \(-0.244086\pi\)
0.720121 + 0.693849i \(0.244086\pi\)
\(720\) 23.6784 0.882441
\(721\) 51.3329 1.91174
\(722\) 0.676089 0.0251614
\(723\) −7.27883 −0.270703
\(724\) 28.6763 1.06575
\(725\) 0.693829 0.0257682
\(726\) −18.3943 −0.682676
\(727\) −39.7665 −1.47486 −0.737429 0.675425i \(-0.763960\pi\)
−0.737429 + 0.675425i \(0.763960\pi\)
\(728\) 64.4617 2.38911
\(729\) 25.0666 0.928393
\(730\) 48.7774 1.80533
\(731\) −11.2503 −0.416106
\(732\) 13.8734 0.512777
\(733\) 31.9318 1.17943 0.589714 0.807612i \(-0.299240\pi\)
0.589714 + 0.807612i \(0.299240\pi\)
\(734\) −58.3948 −2.15539
\(735\) −41.7164 −1.53873
\(736\) 6.50209 0.239670
\(737\) 29.5017 1.08671
\(738\) −2.47890 −0.0912496
\(739\) 35.8263 1.31789 0.658945 0.752191i \(-0.271003\pi\)
0.658945 + 0.752191i \(0.271003\pi\)
\(740\) 42.0189 1.54465
\(741\) −15.3784 −0.564940
\(742\) 10.3802 0.381070
\(743\) 39.3413 1.44329 0.721647 0.692261i \(-0.243385\pi\)
0.721647 + 0.692261i \(0.243385\pi\)
\(744\) 16.1959 0.593769
\(745\) 24.1763 0.885750
\(746\) 27.8968 1.02138
\(747\) 6.71038 0.245520
\(748\) −90.2744 −3.30076
\(749\) 61.1125 2.23300
\(750\) 1.60663 0.0586658
\(751\) 35.8871 1.30954 0.654769 0.755829i \(-0.272766\pi\)
0.654769 + 0.755829i \(0.272766\pi\)
\(752\) 29.9817 1.09332
\(753\) 16.7165 0.609183
\(754\) 0.941895 0.0343018
\(755\) −3.18748 −0.116004
\(756\) −97.5689 −3.54855
\(757\) 36.0322 1.30961 0.654807 0.755796i \(-0.272750\pi\)
0.654807 + 0.755796i \(0.272750\pi\)
\(758\) −10.0463 −0.364899
\(759\) −15.3831 −0.558373
\(760\) 75.9310 2.75431
\(761\) −26.9295 −0.976194 −0.488097 0.872790i \(-0.662309\pi\)
−0.488097 + 0.872790i \(0.662309\pi\)
\(762\) 16.2344 0.588110
\(763\) 17.0592 0.617583
\(764\) −54.0286 −1.95468
\(765\) −23.3589 −0.844541
\(766\) −61.2469 −2.21294
\(767\) 39.0366 1.40953
\(768\) −41.1203 −1.48380
\(769\) −8.52525 −0.307428 −0.153714 0.988115i \(-0.549123\pi\)
−0.153714 + 0.988115i \(0.549123\pi\)
\(770\) 135.776 4.89303
\(771\) 15.8210 0.569779
\(772\) 65.7865 2.36771
\(773\) 19.6527 0.706860 0.353430 0.935461i \(-0.385015\pi\)
0.353430 + 0.935461i \(0.385015\pi\)
\(774\) 7.52066 0.270325
\(775\) −12.0107 −0.431438
\(776\) 52.4103 1.88142
\(777\) −16.4921 −0.591652
\(778\) 53.3611 1.91309
\(779\) −3.07049 −0.110012
\(780\) 47.6749 1.70703
\(781\) −45.6443 −1.63328
\(782\) −38.6217 −1.38111
\(783\) −0.748228 −0.0267395
\(784\) 54.8532 1.95904
\(785\) 39.9604 1.42625
\(786\) −2.56167 −0.0913719
\(787\) 31.7575 1.13203 0.566016 0.824394i \(-0.308484\pi\)
0.566016 + 0.824394i \(0.308484\pi\)
\(788\) 45.4793 1.62013
\(789\) 3.81010 0.135643
\(790\) 82.4004 2.93167
\(791\) 31.6777 1.12633
\(792\) 31.6723 1.12543
\(793\) −7.33028 −0.260306
\(794\) 46.6956 1.65717
\(795\) 4.02918 0.142900
\(796\) 28.4594 1.00872
\(797\) 30.1618 1.06838 0.534192 0.845363i \(-0.320616\pi\)
0.534192 + 0.845363i \(0.320616\pi\)
\(798\) −56.7844 −2.01015
\(799\) −29.5771 −1.04636
\(800\) −11.3135 −0.399993
\(801\) 0.880432 0.0311085
\(802\) 21.6386 0.764085
\(803\) 25.2016 0.889344
\(804\) 38.2499 1.34897
\(805\) 39.3776 1.38788
\(806\) −16.3049 −0.574317
\(807\) −10.6764 −0.375828
\(808\) −97.2350 −3.42071
\(809\) −29.1829 −1.02602 −0.513008 0.858384i \(-0.671469\pi\)
−0.513008 + 0.858384i \(0.671469\pi\)
\(810\) −22.4580 −0.789095
\(811\) 28.3849 0.996727 0.498364 0.866968i \(-0.333934\pi\)
0.498364 + 0.866968i \(0.333934\pi\)
\(812\) 2.35765 0.0827373
\(813\) 15.2446 0.534650
\(814\) 32.0254 1.12249
\(815\) −26.5704 −0.930722
\(816\) −35.0019 −1.22531
\(817\) 9.31546 0.325907
\(818\) 12.7835 0.446965
\(819\) 16.4201 0.573766
\(820\) 9.51886 0.332413
\(821\) −48.3636 −1.68790 −0.843951 0.536420i \(-0.819776\pi\)
−0.843951 + 0.536420i \(0.819776\pi\)
\(822\) −35.2208 −1.22847
\(823\) 16.2186 0.565346 0.282673 0.959216i \(-0.408779\pi\)
0.282673 + 0.959216i \(0.408779\pi\)
\(824\) −67.8296 −2.36296
\(825\) 26.7664 0.931886
\(826\) 144.142 5.01533
\(827\) −38.9798 −1.35546 −0.677731 0.735310i \(-0.737036\pi\)
−0.677731 + 0.735310i \(0.737036\pi\)
\(828\) 17.5018 0.608231
\(829\) 28.4786 0.989104 0.494552 0.869148i \(-0.335332\pi\)
0.494552 + 0.869148i \(0.335332\pi\)
\(830\) −38.0115 −1.31940
\(831\) 26.7608 0.928322
\(832\) 14.4288 0.500230
\(833\) −54.1130 −1.87491
\(834\) −23.4588 −0.812313
\(835\) −7.00469 −0.242407
\(836\) 74.7492 2.58526
\(837\) 12.9524 0.447700
\(838\) 19.9112 0.687821
\(839\) 1.61826 0.0558687 0.0279344 0.999610i \(-0.491107\pi\)
0.0279344 + 0.999610i \(0.491107\pi\)
\(840\) 92.3908 3.18778
\(841\) −28.9819 −0.999377
\(842\) 83.7703 2.88691
\(843\) 23.5831 0.812245
\(844\) −56.1928 −1.93424
\(845\) 16.2474 0.558926
\(846\) 19.7719 0.679773
\(847\) 24.3274 0.835900
\(848\) −5.29800 −0.181934
\(849\) 20.4775 0.702786
\(850\) 67.2010 2.30498
\(851\) 9.28797 0.318387
\(852\) −59.1794 −2.02745
\(853\) 39.3926 1.34878 0.674389 0.738376i \(-0.264407\pi\)
0.674389 + 0.738376i \(0.264407\pi\)
\(854\) −27.0669 −0.926210
\(855\) 19.3417 0.661471
\(856\) −80.7520 −2.76005
\(857\) −11.3883 −0.389018 −0.194509 0.980901i \(-0.562311\pi\)
−0.194509 + 0.980901i \(0.562311\pi\)
\(858\) 36.3362 1.24050
\(859\) −18.5054 −0.631396 −0.315698 0.948860i \(-0.602239\pi\)
−0.315698 + 0.948860i \(0.602239\pi\)
\(860\) −28.8790 −0.984766
\(861\) −3.73609 −0.127325
\(862\) −58.7187 −1.99997
\(863\) −15.4435 −0.525703 −0.262851 0.964836i \(-0.584663\pi\)
−0.262851 + 0.964836i \(0.584663\pi\)
\(864\) 12.2005 0.415071
\(865\) −53.4386 −1.81697
\(866\) 21.6829 0.736813
\(867\) 13.0405 0.442880
\(868\) −40.8127 −1.38527
\(869\) 42.5734 1.44420
\(870\) 1.34999 0.0457688
\(871\) −20.2100 −0.684790
\(872\) −22.5414 −0.763349
\(873\) 13.3503 0.451840
\(874\) 31.9796 1.08173
\(875\) −2.12485 −0.0718331
\(876\) 32.6747 1.10398
\(877\) 28.0432 0.946952 0.473476 0.880807i \(-0.342999\pi\)
0.473476 + 0.880807i \(0.342999\pi\)
\(878\) −80.2452 −2.70814
\(879\) 13.3862 0.451504
\(880\) −69.2992 −2.33608
\(881\) 22.2709 0.750326 0.375163 0.926959i \(-0.377587\pi\)
0.375163 + 0.926959i \(0.377587\pi\)
\(882\) 36.1739 1.21804
\(883\) 12.6402 0.425377 0.212689 0.977120i \(-0.431778\pi\)
0.212689 + 0.977120i \(0.431778\pi\)
\(884\) 61.8422 2.07998
\(885\) 55.9498 1.88073
\(886\) 2.42847 0.0815859
\(887\) 3.62958 0.121869 0.0609347 0.998142i \(-0.480592\pi\)
0.0609347 + 0.998142i \(0.480592\pi\)
\(888\) 21.7922 0.731297
\(889\) −21.4708 −0.720109
\(890\) −4.98727 −0.167174
\(891\) −11.6033 −0.388724
\(892\) 58.5420 1.96013
\(893\) 24.4905 0.819543
\(894\) 23.8904 0.799014
\(895\) 12.4436 0.415944
\(896\) 71.5453 2.39016
\(897\) 10.5382 0.351859
\(898\) 33.8155 1.12844
\(899\) −0.312981 −0.0104385
\(900\) −30.4529 −1.01510
\(901\) 5.22651 0.174120
\(902\) 7.25497 0.241564
\(903\) 11.3348 0.377199
\(904\) −41.8578 −1.39217
\(905\) −21.7163 −0.721875
\(906\) −3.14979 −0.104645
\(907\) −19.2521 −0.639255 −0.319628 0.947543i \(-0.603558\pi\)
−0.319628 + 0.947543i \(0.603558\pi\)
\(908\) −109.954 −3.64894
\(909\) −24.7684 −0.821515
\(910\) −93.0130 −3.08335
\(911\) −1.19834 −0.0397029 −0.0198515 0.999803i \(-0.506319\pi\)
−0.0198515 + 0.999803i \(0.506319\pi\)
\(912\) 28.9824 0.959703
\(913\) −19.6392 −0.649963
\(914\) 35.9138 1.18792
\(915\) −10.5062 −0.347326
\(916\) −110.103 −3.63792
\(917\) 3.38795 0.111880
\(918\) −72.4698 −2.39186
\(919\) 5.45436 0.179923 0.0899614 0.995945i \(-0.471326\pi\)
0.0899614 + 0.995945i \(0.471326\pi\)
\(920\) −52.0322 −1.71545
\(921\) 7.82389 0.257806
\(922\) −36.8718 −1.21431
\(923\) 31.2685 1.02921
\(924\) 90.9529 2.99213
\(925\) −16.1609 −0.531367
\(926\) 88.1942 2.89824
\(927\) −17.2780 −0.567485
\(928\) −0.294813 −0.00967771
\(929\) −21.3826 −0.701542 −0.350771 0.936461i \(-0.614080\pi\)
−0.350771 + 0.936461i \(0.614080\pi\)
\(930\) −23.3693 −0.766310
\(931\) 44.8068 1.46848
\(932\) −34.0379 −1.11495
\(933\) −13.8524 −0.453506
\(934\) 46.0476 1.50672
\(935\) 68.3641 2.23574
\(936\) −21.6970 −0.709189
\(937\) −1.25136 −0.0408803 −0.0204401 0.999791i \(-0.506507\pi\)
−0.0204401 + 0.999791i \(0.506507\pi\)
\(938\) −74.6250 −2.43659
\(939\) 13.9451 0.455080
\(940\) −75.9234 −2.47635
\(941\) −38.3328 −1.24961 −0.624806 0.780780i \(-0.714822\pi\)
−0.624806 + 0.780780i \(0.714822\pi\)
\(942\) 39.4878 1.28658
\(943\) 2.10407 0.0685181
\(944\) −73.5689 −2.39447
\(945\) 73.8882 2.40358
\(946\) −22.0106 −0.715627
\(947\) 34.7326 1.12866 0.564329 0.825550i \(-0.309135\pi\)
0.564329 + 0.825550i \(0.309135\pi\)
\(948\) 55.1979 1.79274
\(949\) −17.2643 −0.560422
\(950\) −55.6439 −1.80533
\(951\) 20.9957 0.680831
\(952\) 119.846 3.88424
\(953\) −20.0005 −0.647878 −0.323939 0.946078i \(-0.605007\pi\)
−0.323939 + 0.946078i \(0.605007\pi\)
\(954\) −3.49386 −0.113118
\(955\) 40.9154 1.32399
\(956\) −38.6330 −1.24948
\(957\) 0.697491 0.0225467
\(958\) −52.9900 −1.71203
\(959\) 46.5813 1.50419
\(960\) 20.6804 0.667456
\(961\) −25.5821 −0.825228
\(962\) −21.9389 −0.707339
\(963\) −20.5697 −0.662849
\(964\) −24.2369 −0.780617
\(965\) −49.8196 −1.60375
\(966\) 38.9119 1.25197
\(967\) −1.84170 −0.0592252 −0.0296126 0.999561i \(-0.509427\pi\)
−0.0296126 + 0.999561i \(0.509427\pi\)
\(968\) −32.1455 −1.03319
\(969\) −28.5913 −0.918485
\(970\) −75.6238 −2.42813
\(971\) 40.6756 1.30534 0.652671 0.757642i \(-0.273649\pi\)
0.652671 + 0.757642i \(0.273649\pi\)
\(972\) 55.2208 1.77121
\(973\) 31.0256 0.994634
\(974\) −0.383544 −0.0122895
\(975\) −18.3362 −0.587229
\(976\) 13.8148 0.442200
\(977\) 47.3886 1.51610 0.758048 0.652199i \(-0.226153\pi\)
0.758048 + 0.652199i \(0.226153\pi\)
\(978\) −26.2562 −0.839582
\(979\) −2.57675 −0.0823533
\(980\) −138.906 −4.43720
\(981\) −5.74190 −0.183325
\(982\) 7.35943 0.234849
\(983\) 57.8968 1.84662 0.923310 0.384055i \(-0.125473\pi\)
0.923310 + 0.384055i \(0.125473\pi\)
\(984\) 4.93674 0.157378
\(985\) −34.4411 −1.09738
\(986\) 1.75116 0.0557682
\(987\) 29.7994 0.948525
\(988\) −51.2067 −1.62910
\(989\) −6.38349 −0.202983
\(990\) −45.7006 −1.45246
\(991\) 20.6340 0.655462 0.327731 0.944771i \(-0.393716\pi\)
0.327731 + 0.944771i \(0.393716\pi\)
\(992\) 5.10344 0.162034
\(993\) −10.7573 −0.341373
\(994\) 115.458 3.66211
\(995\) −21.5521 −0.683247
\(996\) −25.4629 −0.806822
\(997\) 61.6139 1.95133 0.975666 0.219260i \(-0.0703644\pi\)
0.975666 + 0.219260i \(0.0703644\pi\)
\(998\) 44.4373 1.40664
\(999\) 17.4280 0.551396
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 \(a_p\))