Properties

Label 8023.2.a.c.1.5
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 1.5
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.74512 q^{2}\) \(+2.49890 q^{3}\) \(+5.53568 q^{4}\) \(+0.133996 q^{5}\) \(-6.85979 q^{6}\) \(+0.778013 q^{7}\) \(-9.70588 q^{8}\) \(+3.24451 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.74512 q^{2}\) \(+2.49890 q^{3}\) \(+5.53568 q^{4}\) \(+0.133996 q^{5}\) \(-6.85979 q^{6}\) \(+0.778013 q^{7}\) \(-9.70588 q^{8}\) \(+3.24451 q^{9}\) \(-0.367836 q^{10}\) \(+5.21472 q^{11}\) \(+13.8331 q^{12}\) \(-3.44123 q^{13}\) \(-2.13574 q^{14}\) \(+0.334844 q^{15}\) \(+15.5724 q^{16}\) \(-3.95432 q^{17}\) \(-8.90657 q^{18}\) \(+2.36206 q^{19}\) \(+0.741761 q^{20}\) \(+1.94418 q^{21}\) \(-14.3150 q^{22}\) \(-9.52848 q^{23}\) \(-24.2540 q^{24}\) \(-4.98204 q^{25}\) \(+9.44659 q^{26}\) \(+0.611007 q^{27}\) \(+4.30683 q^{28}\) \(+2.75153 q^{29}\) \(-0.919186 q^{30}\) \(+5.63718 q^{31}\) \(-23.3364 q^{32}\) \(+13.0311 q^{33}\) \(+10.8551 q^{34}\) \(+0.104251 q^{35}\) \(+17.9606 q^{36}\) \(-0.680380 q^{37}\) \(-6.48414 q^{38}\) \(-8.59929 q^{39}\) \(-1.30055 q^{40}\) \(-11.8771 q^{41}\) \(-5.33700 q^{42}\) \(+1.80337 q^{43}\) \(+28.8671 q^{44}\) \(+0.434752 q^{45}\) \(+26.1568 q^{46}\) \(-6.64581 q^{47}\) \(+38.9140 q^{48}\) \(-6.39470 q^{49}\) \(+13.6763 q^{50}\) \(-9.88145 q^{51}\) \(-19.0496 q^{52}\) \(+7.46761 q^{53}\) \(-1.67729 q^{54}\) \(+0.698754 q^{55}\) \(-7.55130 q^{56}\) \(+5.90256 q^{57}\) \(-7.55328 q^{58}\) \(+8.15971 q^{59}\) \(+1.85359 q^{60}\) \(-7.71717 q^{61}\) \(-15.4747 q^{62}\) \(+2.52427 q^{63}\) \(+32.9165 q^{64}\) \(-0.461112 q^{65}\) \(-35.7719 q^{66}\) \(+11.0607 q^{67}\) \(-21.8898 q^{68}\) \(-23.8107 q^{69}\) \(-0.286181 q^{70}\) \(-1.00000 q^{71}\) \(-31.4908 q^{72}\) \(-10.1689 q^{73}\) \(+1.86773 q^{74}\) \(-12.4496 q^{75}\) \(+13.0756 q^{76}\) \(+4.05712 q^{77}\) \(+23.6061 q^{78}\) \(-14.8433 q^{79}\) \(+2.08665 q^{80}\) \(-8.20668 q^{81}\) \(+32.6042 q^{82}\) \(-3.41548 q^{83}\) \(+10.7624 q^{84}\) \(-0.529864 q^{85}\) \(-4.95048 q^{86}\) \(+6.87581 q^{87}\) \(-50.6135 q^{88}\) \(-7.86279 q^{89}\) \(-1.19345 q^{90}\) \(-2.67732 q^{91}\) \(-52.7467 q^{92}\) \(+14.0868 q^{93}\) \(+18.2436 q^{94}\) \(+0.316507 q^{95}\) \(-58.3155 q^{96}\) \(-1.61476 q^{97}\) \(+17.5542 q^{98}\) \(+16.9192 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74512 −1.94109 −0.970546 0.240914i \(-0.922553\pi\)
−0.970546 + 0.240914i \(0.922553\pi\)
\(3\) 2.49890 1.44274 0.721371 0.692549i \(-0.243512\pi\)
0.721371 + 0.692549i \(0.243512\pi\)
\(4\) 5.53568 2.76784
\(5\) 0.133996 0.0599250 0.0299625 0.999551i \(-0.490461\pi\)
0.0299625 + 0.999551i \(0.490461\pi\)
\(6\) −6.85979 −2.80050
\(7\) 0.778013 0.294061 0.147031 0.989132i \(-0.453028\pi\)
0.147031 + 0.989132i \(0.453028\pi\)
\(8\) −9.70588 −3.43155
\(9\) 3.24451 1.08150
\(10\) −0.367836 −0.116320
\(11\) 5.21472 1.57230 0.786149 0.618037i \(-0.212072\pi\)
0.786149 + 0.618037i \(0.212072\pi\)
\(12\) 13.8331 3.99328
\(13\) −3.44123 −0.954425 −0.477213 0.878788i \(-0.658353\pi\)
−0.477213 + 0.878788i \(0.658353\pi\)
\(14\) −2.13574 −0.570800
\(15\) 0.334844 0.0864563
\(16\) 15.5724 3.89311
\(17\) −3.95432 −0.959063 −0.479531 0.877525i \(-0.659193\pi\)
−0.479531 + 0.877525i \(0.659193\pi\)
\(18\) −8.90657 −2.09930
\(19\) 2.36206 0.541894 0.270947 0.962594i \(-0.412663\pi\)
0.270947 + 0.962594i \(0.412663\pi\)
\(20\) 0.741761 0.165863
\(21\) 1.94418 0.424254
\(22\) −14.3150 −3.05198
\(23\) −9.52848 −1.98683 −0.993413 0.114590i \(-0.963445\pi\)
−0.993413 + 0.114590i \(0.963445\pi\)
\(24\) −24.2540 −4.95083
\(25\) −4.98204 −0.996409
\(26\) 9.44659 1.85263
\(27\) 0.611007 0.117588
\(28\) 4.30683 0.813915
\(29\) 2.75153 0.510947 0.255473 0.966816i \(-0.417769\pi\)
0.255473 + 0.966816i \(0.417769\pi\)
\(30\) −0.919186 −0.167820
\(31\) 5.63718 1.01247 0.506234 0.862396i \(-0.331037\pi\)
0.506234 + 0.862396i \(0.331037\pi\)
\(32\) −23.3364 −4.12534
\(33\) 13.0311 2.26842
\(34\) 10.8551 1.86163
\(35\) 0.104251 0.0176216
\(36\) 17.9606 2.99343
\(37\) −0.680380 −0.111854 −0.0559269 0.998435i \(-0.517811\pi\)
−0.0559269 + 0.998435i \(0.517811\pi\)
\(38\) −6.48414 −1.05187
\(39\) −8.59929 −1.37699
\(40\) −1.30055 −0.205635
\(41\) −11.8771 −1.85490 −0.927449 0.373951i \(-0.878003\pi\)
−0.927449 + 0.373951i \(0.878003\pi\)
\(42\) −5.33700 −0.823517
\(43\) 1.80337 0.275012 0.137506 0.990501i \(-0.456091\pi\)
0.137506 + 0.990501i \(0.456091\pi\)
\(44\) 28.8671 4.35187
\(45\) 0.434752 0.0648091
\(46\) 26.1568 3.85661
\(47\) −6.64581 −0.969392 −0.484696 0.874683i \(-0.661070\pi\)
−0.484696 + 0.874683i \(0.661070\pi\)
\(48\) 38.9140 5.61675
\(49\) −6.39470 −0.913528
\(50\) 13.6763 1.93412
\(51\) −9.88145 −1.38368
\(52\) −19.0496 −2.64170
\(53\) 7.46761 1.02576 0.512878 0.858462i \(-0.328579\pi\)
0.512878 + 0.858462i \(0.328579\pi\)
\(54\) −1.67729 −0.228250
\(55\) 0.698754 0.0942199
\(56\) −7.55130 −1.00908
\(57\) 5.90256 0.781813
\(58\) −7.55328 −0.991795
\(59\) 8.15971 1.06230 0.531152 0.847277i \(-0.321759\pi\)
0.531152 + 0.847277i \(0.321759\pi\)
\(60\) 1.85359 0.239297
\(61\) −7.71717 −0.988082 −0.494041 0.869439i \(-0.664481\pi\)
−0.494041 + 0.869439i \(0.664481\pi\)
\(62\) −15.4747 −1.96529
\(63\) 2.52427 0.318028
\(64\) 32.9165 4.11456
\(65\) −0.461112 −0.0571939
\(66\) −35.7719 −4.40322
\(67\) 11.0607 1.35128 0.675641 0.737230i \(-0.263867\pi\)
0.675641 + 0.737230i \(0.263867\pi\)
\(68\) −21.8898 −2.65453
\(69\) −23.8107 −2.86648
\(70\) −0.286181 −0.0342052
\(71\) −1.00000 −0.118678
\(72\) −31.4908 −3.71123
\(73\) −10.1689 −1.19018 −0.595091 0.803658i \(-0.702884\pi\)
−0.595091 + 0.803658i \(0.702884\pi\)
\(74\) 1.86773 0.217119
\(75\) −12.4496 −1.43756
\(76\) 13.0756 1.49988
\(77\) 4.05712 0.462352
\(78\) 23.6061 2.67286
\(79\) −14.8433 −1.67000 −0.834999 0.550252i \(-0.814532\pi\)
−0.834999 + 0.550252i \(0.814532\pi\)
\(80\) 2.08665 0.233294
\(81\) −8.20668 −0.911854
\(82\) 32.6042 3.60053
\(83\) −3.41548 −0.374898 −0.187449 0.982274i \(-0.560022\pi\)
−0.187449 + 0.982274i \(0.560022\pi\)
\(84\) 10.7624 1.17427
\(85\) −0.529864 −0.0574718
\(86\) −4.95048 −0.533823
\(87\) 6.87581 0.737164
\(88\) −50.6135 −5.39541
\(89\) −7.86279 −0.833454 −0.416727 0.909032i \(-0.636823\pi\)
−0.416727 + 0.909032i \(0.636823\pi\)
\(90\) −1.19345 −0.125800
\(91\) −2.67732 −0.280659
\(92\) −52.7467 −5.49922
\(93\) 14.0868 1.46073
\(94\) 18.2436 1.88168
\(95\) 0.316507 0.0324730
\(96\) −58.3155 −5.95180
\(97\) −1.61476 −0.163954 −0.0819772 0.996634i \(-0.526123\pi\)
−0.0819772 + 0.996634i \(0.526123\pi\)
\(98\) 17.5542 1.77324
\(99\) 16.9192 1.70045
\(100\) −27.5790 −2.75790
\(101\) −5.57692 −0.554924 −0.277462 0.960737i \(-0.589493\pi\)
−0.277462 + 0.960737i \(0.589493\pi\)
\(102\) 27.1258 2.68585
\(103\) −6.98037 −0.687796 −0.343898 0.939007i \(-0.611747\pi\)
−0.343898 + 0.939007i \(0.611747\pi\)
\(104\) 33.4001 3.27515
\(105\) 0.260513 0.0254234
\(106\) −20.4995 −1.99109
\(107\) −11.9078 −1.15117 −0.575586 0.817741i \(-0.695226\pi\)
−0.575586 + 0.817741i \(0.695226\pi\)
\(108\) 3.38234 0.325466
\(109\) 14.4032 1.37958 0.689789 0.724010i \(-0.257703\pi\)
0.689789 + 0.724010i \(0.257703\pi\)
\(110\) −1.91816 −0.182890
\(111\) −1.70020 −0.161376
\(112\) 12.1156 1.14481
\(113\) −1.00000 −0.0940721
\(114\) −16.2032 −1.51757
\(115\) −1.27678 −0.119060
\(116\) 15.2316 1.41422
\(117\) −11.1651 −1.03221
\(118\) −22.3994 −2.06203
\(119\) −3.07651 −0.282023
\(120\) −3.24995 −0.296679
\(121\) 16.1934 1.47212
\(122\) 21.1846 1.91796
\(123\) −29.6798 −2.67614
\(124\) 31.2057 2.80235
\(125\) −1.33756 −0.119635
\(126\) −6.92943 −0.617323
\(127\) −2.52082 −0.223687 −0.111843 0.993726i \(-0.535676\pi\)
−0.111843 + 0.993726i \(0.535676\pi\)
\(128\) −43.6867 −3.86140
\(129\) 4.50645 0.396771
\(130\) 1.26581 0.111019
\(131\) 5.36752 0.468962 0.234481 0.972121i \(-0.424661\pi\)
0.234481 + 0.972121i \(0.424661\pi\)
\(132\) 72.1360 6.27863
\(133\) 1.83771 0.159350
\(134\) −30.3630 −2.62297
\(135\) 0.0818727 0.00704648
\(136\) 38.3801 3.29107
\(137\) 1.56581 0.133776 0.0668882 0.997760i \(-0.478693\pi\)
0.0668882 + 0.997760i \(0.478693\pi\)
\(138\) 65.3633 5.56410
\(139\) 13.1312 1.11377 0.556886 0.830589i \(-0.311996\pi\)
0.556886 + 0.830589i \(0.311996\pi\)
\(140\) 0.577100 0.0487738
\(141\) −16.6072 −1.39858
\(142\) 2.74512 0.230365
\(143\) −17.9451 −1.50064
\(144\) 50.5249 4.21041
\(145\) 0.368695 0.0306185
\(146\) 27.9149 2.31025
\(147\) −15.9797 −1.31798
\(148\) −3.76637 −0.309594
\(149\) −9.21209 −0.754684 −0.377342 0.926074i \(-0.623162\pi\)
−0.377342 + 0.926074i \(0.623162\pi\)
\(150\) 34.1758 2.79044
\(151\) 20.8538 1.69706 0.848531 0.529146i \(-0.177487\pi\)
0.848531 + 0.529146i \(0.177487\pi\)
\(152\) −22.9259 −1.85953
\(153\) −12.8298 −1.03723
\(154\) −11.1373 −0.897469
\(155\) 0.755362 0.0606721
\(156\) −47.6030 −3.81129
\(157\) 16.1024 1.28511 0.642557 0.766238i \(-0.277874\pi\)
0.642557 + 0.766238i \(0.277874\pi\)
\(158\) 40.7465 3.24162
\(159\) 18.6608 1.47990
\(160\) −3.12700 −0.247211
\(161\) −7.41328 −0.584249
\(162\) 22.5283 1.76999
\(163\) −11.4096 −0.893671 −0.446836 0.894616i \(-0.647449\pi\)
−0.446836 + 0.894616i \(0.647449\pi\)
\(164\) −65.7481 −5.13406
\(165\) 1.74612 0.135935
\(166\) 9.37591 0.727712
\(167\) −8.57532 −0.663578 −0.331789 0.943354i \(-0.607652\pi\)
−0.331789 + 0.943354i \(0.607652\pi\)
\(168\) −18.8700 −1.45585
\(169\) −1.15795 −0.0890728
\(170\) 1.45454 0.111558
\(171\) 7.66373 0.586060
\(172\) 9.98290 0.761189
\(173\) 0.451920 0.0343588 0.0171794 0.999852i \(-0.494531\pi\)
0.0171794 + 0.999852i \(0.494531\pi\)
\(174\) −18.8749 −1.43090
\(175\) −3.87610 −0.293005
\(176\) 81.2059 6.12113
\(177\) 20.3903 1.53263
\(178\) 21.5843 1.61781
\(179\) −15.9262 −1.19038 −0.595191 0.803584i \(-0.702924\pi\)
−0.595191 + 0.803584i \(0.702924\pi\)
\(180\) 2.40665 0.179381
\(181\) 17.9545 1.33455 0.667274 0.744812i \(-0.267461\pi\)
0.667274 + 0.744812i \(0.267461\pi\)
\(182\) 7.34957 0.544786
\(183\) −19.2844 −1.42555
\(184\) 92.4823 6.81788
\(185\) −0.0911684 −0.00670284
\(186\) −38.6699 −2.83541
\(187\) −20.6207 −1.50793
\(188\) −36.7891 −2.68312
\(189\) 0.475372 0.0345782
\(190\) −0.868851 −0.0630330
\(191\) −22.5692 −1.63305 −0.816525 0.577310i \(-0.804102\pi\)
−0.816525 + 0.577310i \(0.804102\pi\)
\(192\) 82.2550 5.93624
\(193\) −26.8265 −1.93101 −0.965506 0.260382i \(-0.916152\pi\)
−0.965506 + 0.260382i \(0.916152\pi\)
\(194\) 4.43272 0.318251
\(195\) −1.15227 −0.0825160
\(196\) −35.3990 −2.52850
\(197\) −8.07047 −0.574998 −0.287499 0.957781i \(-0.592824\pi\)
−0.287499 + 0.957781i \(0.592824\pi\)
\(198\) −46.4453 −3.30072
\(199\) 10.8653 0.770223 0.385111 0.922870i \(-0.374163\pi\)
0.385111 + 0.922870i \(0.374163\pi\)
\(200\) 48.3551 3.41922
\(201\) 27.6397 1.94955
\(202\) 15.3093 1.07716
\(203\) 2.14073 0.150250
\(204\) −54.7006 −3.82981
\(205\) −1.59149 −0.111155
\(206\) 19.1620 1.33508
\(207\) −30.9153 −2.14876
\(208\) −53.5883 −3.71568
\(209\) 12.3175 0.852019
\(210\) −0.715139 −0.0493493
\(211\) −0.168646 −0.0116100 −0.00580502 0.999983i \(-0.501848\pi\)
−0.00580502 + 0.999983i \(0.501848\pi\)
\(212\) 41.3383 2.83913
\(213\) −2.49890 −0.171222
\(214\) 32.6884 2.23453
\(215\) 0.241645 0.0164801
\(216\) −5.93036 −0.403510
\(217\) 4.38580 0.297728
\(218\) −39.5386 −2.67789
\(219\) −25.4111 −1.71713
\(220\) 3.86808 0.260786
\(221\) 13.6077 0.915353
\(222\) 4.66726 0.313246
\(223\) 26.7387 1.79056 0.895279 0.445505i \(-0.146976\pi\)
0.895279 + 0.445505i \(0.146976\pi\)
\(224\) −18.1561 −1.21310
\(225\) −16.1643 −1.07762
\(226\) 2.74512 0.182603
\(227\) 8.83141 0.586161 0.293081 0.956088i \(-0.405320\pi\)
0.293081 + 0.956088i \(0.405320\pi\)
\(228\) 32.6747 2.16393
\(229\) −23.2357 −1.53546 −0.767728 0.640776i \(-0.778613\pi\)
−0.767728 + 0.640776i \(0.778613\pi\)
\(230\) 3.50492 0.231107
\(231\) 10.1384 0.667055
\(232\) −26.7060 −1.75334
\(233\) 4.59897 0.301289 0.150644 0.988588i \(-0.451865\pi\)
0.150644 + 0.988588i \(0.451865\pi\)
\(234\) 30.6495 2.00362
\(235\) −0.890515 −0.0580908
\(236\) 45.1695 2.94029
\(237\) −37.0919 −2.40938
\(238\) 8.44539 0.547433
\(239\) −8.11859 −0.525148 −0.262574 0.964912i \(-0.584571\pi\)
−0.262574 + 0.964912i \(0.584571\pi\)
\(240\) 5.21433 0.336583
\(241\) −5.93005 −0.381988 −0.190994 0.981591i \(-0.561171\pi\)
−0.190994 + 0.981591i \(0.561171\pi\)
\(242\) −44.4527 −2.85753
\(243\) −22.3407 −1.43316
\(244\) −42.7198 −2.73486
\(245\) −0.856866 −0.0547431
\(246\) 81.4746 5.19463
\(247\) −8.12839 −0.517197
\(248\) −54.7138 −3.47433
\(249\) −8.53496 −0.540881
\(250\) 3.67176 0.232222
\(251\) 0.929672 0.0586804 0.0293402 0.999569i \(-0.490659\pi\)
0.0293402 + 0.999569i \(0.490659\pi\)
\(252\) 13.9736 0.880252
\(253\) −49.6884 −3.12388
\(254\) 6.91996 0.434197
\(255\) −1.32408 −0.0829170
\(256\) 54.0925 3.38078
\(257\) 9.60806 0.599334 0.299667 0.954044i \(-0.403124\pi\)
0.299667 + 0.954044i \(0.403124\pi\)
\(258\) −12.3708 −0.770169
\(259\) −0.529345 −0.0328919
\(260\) −2.55257 −0.158304
\(261\) 8.92737 0.552590
\(262\) −14.7345 −0.910299
\(263\) −10.7085 −0.660317 −0.330159 0.943925i \(-0.607102\pi\)
−0.330159 + 0.943925i \(0.607102\pi\)
\(264\) −126.478 −7.78419
\(265\) 1.00063 0.0614684
\(266\) −5.04474 −0.309313
\(267\) −19.6483 −1.20246
\(268\) 61.2287 3.74014
\(269\) 9.96734 0.607719 0.303860 0.952717i \(-0.401725\pi\)
0.303860 + 0.952717i \(0.401725\pi\)
\(270\) −0.224750 −0.0136779
\(271\) 16.3909 0.995674 0.497837 0.867271i \(-0.334128\pi\)
0.497837 + 0.867271i \(0.334128\pi\)
\(272\) −61.5783 −3.73373
\(273\) −6.69036 −0.404919
\(274\) −4.29834 −0.259672
\(275\) −25.9800 −1.56665
\(276\) −131.809 −7.93395
\(277\) 18.6461 1.12033 0.560167 0.828379i \(-0.310737\pi\)
0.560167 + 0.828379i \(0.310737\pi\)
\(278\) −36.0467 −2.16194
\(279\) 18.2899 1.09499
\(280\) −1.01185 −0.0604694
\(281\) −5.47560 −0.326647 −0.163324 0.986573i \(-0.552221\pi\)
−0.163324 + 0.986573i \(0.552221\pi\)
\(282\) 45.5889 2.71478
\(283\) −24.9385 −1.48244 −0.741221 0.671262i \(-0.765753\pi\)
−0.741221 + 0.671262i \(0.765753\pi\)
\(284\) −5.53568 −0.328482
\(285\) 0.790921 0.0468501
\(286\) 49.2613 2.91288
\(287\) −9.24057 −0.545453
\(288\) −75.7153 −4.46157
\(289\) −1.36338 −0.0801990
\(290\) −1.01211 −0.0594333
\(291\) −4.03513 −0.236544
\(292\) −56.2919 −3.29424
\(293\) 1.27120 0.0742640 0.0371320 0.999310i \(-0.488178\pi\)
0.0371320 + 0.999310i \(0.488178\pi\)
\(294\) 43.8662 2.55833
\(295\) 1.09337 0.0636585
\(296\) 6.60369 0.383832
\(297\) 3.18623 0.184884
\(298\) 25.2883 1.46491
\(299\) 32.7897 1.89628
\(300\) −68.9173 −3.97894
\(301\) 1.40305 0.0808703
\(302\) −57.2463 −3.29416
\(303\) −13.9362 −0.800612
\(304\) 36.7830 2.10965
\(305\) −1.03407 −0.0592108
\(306\) 35.2194 2.01336
\(307\) −22.7215 −1.29678 −0.648392 0.761307i \(-0.724558\pi\)
−0.648392 + 0.761307i \(0.724558\pi\)
\(308\) 22.4590 1.27972
\(309\) −17.4433 −0.992312
\(310\) −2.07356 −0.117770
\(311\) 2.12491 0.120493 0.0602463 0.998184i \(-0.480811\pi\)
0.0602463 + 0.998184i \(0.480811\pi\)
\(312\) 83.4637 4.72520
\(313\) 5.69184 0.321722 0.160861 0.986977i \(-0.448573\pi\)
0.160861 + 0.986977i \(0.448573\pi\)
\(314\) −44.2031 −2.49453
\(315\) 0.338243 0.0190578
\(316\) −82.1676 −4.62229
\(317\) −25.3083 −1.42146 −0.710729 0.703466i \(-0.751635\pi\)
−0.710729 + 0.703466i \(0.751635\pi\)
\(318\) −51.2262 −2.87262
\(319\) 14.3485 0.803361
\(320\) 4.41068 0.246565
\(321\) −29.7565 −1.66084
\(322\) 20.3504 1.13408
\(323\) −9.34033 −0.519710
\(324\) −45.4296 −2.52387
\(325\) 17.1444 0.950998
\(326\) 31.3208 1.73470
\(327\) 35.9922 1.99038
\(328\) 115.278 6.36516
\(329\) −5.17053 −0.285061
\(330\) −4.79330 −0.263863
\(331\) 3.90131 0.214435 0.107218 0.994236i \(-0.465806\pi\)
0.107218 + 0.994236i \(0.465806\pi\)
\(332\) −18.9070 −1.03766
\(333\) −2.20750 −0.120970
\(334\) 23.5403 1.28807
\(335\) 1.48210 0.0809756
\(336\) 30.2756 1.65167
\(337\) −9.17818 −0.499968 −0.249984 0.968250i \(-0.580425\pi\)
−0.249984 + 0.968250i \(0.580425\pi\)
\(338\) 3.17870 0.172899
\(339\) −2.49890 −0.135722
\(340\) −2.93316 −0.159073
\(341\) 29.3964 1.59190
\(342\) −21.0379 −1.13760
\(343\) −10.4212 −0.562695
\(344\) −17.5033 −0.943716
\(345\) −3.19055 −0.171774
\(346\) −1.24057 −0.0666937
\(347\) −11.6563 −0.625746 −0.312873 0.949795i \(-0.601291\pi\)
−0.312873 + 0.949795i \(0.601291\pi\)
\(348\) 38.0623 2.04035
\(349\) −4.27529 −0.228851 −0.114425 0.993432i \(-0.536503\pi\)
−0.114425 + 0.993432i \(0.536503\pi\)
\(350\) 10.6403 0.568751
\(351\) −2.10262 −0.112229
\(352\) −121.693 −6.48626
\(353\) −15.1145 −0.804464 −0.402232 0.915538i \(-0.631765\pi\)
−0.402232 + 0.915538i \(0.631765\pi\)
\(354\) −55.9738 −2.97498
\(355\) −0.133996 −0.00711179
\(356\) −43.5259 −2.30687
\(357\) −7.68790 −0.406887
\(358\) 43.7194 2.31064
\(359\) −25.0019 −1.31955 −0.659774 0.751464i \(-0.729348\pi\)
−0.659774 + 0.751464i \(0.729348\pi\)
\(360\) −4.21965 −0.222395
\(361\) −13.4207 −0.706351
\(362\) −49.2873 −2.59048
\(363\) 40.4656 2.12389
\(364\) −14.8208 −0.776821
\(365\) −1.36260 −0.0713216
\(366\) 52.9381 2.76712
\(367\) 36.5969 1.91035 0.955173 0.296050i \(-0.0956694\pi\)
0.955173 + 0.296050i \(0.0956694\pi\)
\(368\) −148.382 −7.73493
\(369\) −38.5355 −2.00608
\(370\) 0.250268 0.0130108
\(371\) 5.80990 0.301635
\(372\) 77.9799 4.04307
\(373\) 30.2192 1.56469 0.782345 0.622845i \(-0.214023\pi\)
0.782345 + 0.622845i \(0.214023\pi\)
\(374\) 56.6062 2.92704
\(375\) −3.34242 −0.172602
\(376\) 64.5035 3.32651
\(377\) −9.46865 −0.487660
\(378\) −1.30495 −0.0671195
\(379\) −3.47290 −0.178391 −0.0891955 0.996014i \(-0.528430\pi\)
−0.0891955 + 0.996014i \(0.528430\pi\)
\(380\) 1.75208 0.0898800
\(381\) −6.29929 −0.322722
\(382\) 61.9552 3.16990
\(383\) 29.8244 1.52396 0.761978 0.647603i \(-0.224228\pi\)
0.761978 + 0.647603i \(0.224228\pi\)
\(384\) −109.169 −5.57100
\(385\) 0.543640 0.0277064
\(386\) 73.6419 3.74827
\(387\) 5.85106 0.297426
\(388\) −8.93882 −0.453800
\(389\) 24.5717 1.24584 0.622918 0.782287i \(-0.285947\pi\)
0.622918 + 0.782287i \(0.285947\pi\)
\(390\) 3.16313 0.160171
\(391\) 37.6786 1.90549
\(392\) 62.0661 3.13481
\(393\) 13.4129 0.676591
\(394\) 22.1544 1.11612
\(395\) −1.98894 −0.100075
\(396\) 93.6595 4.70657
\(397\) 11.6193 0.583154 0.291577 0.956547i \(-0.405820\pi\)
0.291577 + 0.956547i \(0.405820\pi\)
\(398\) −29.8266 −1.49507
\(399\) 4.59227 0.229901
\(400\) −77.5825 −3.87913
\(401\) 14.4123 0.719716 0.359858 0.933007i \(-0.382825\pi\)
0.359858 + 0.933007i \(0.382825\pi\)
\(402\) −75.8742 −3.78426
\(403\) −19.3988 −0.966325
\(404\) −30.8721 −1.53594
\(405\) −1.09967 −0.0546428
\(406\) −5.87655 −0.291648
\(407\) −3.54800 −0.175868
\(408\) 95.9081 4.74816
\(409\) 22.3649 1.10587 0.552936 0.833224i \(-0.313508\pi\)
0.552936 + 0.833224i \(0.313508\pi\)
\(410\) 4.36884 0.215762
\(411\) 3.91281 0.193005
\(412\) −38.6411 −1.90371
\(413\) 6.34836 0.312382
\(414\) 84.8661 4.17094
\(415\) −0.457662 −0.0224658
\(416\) 80.3060 3.93733
\(417\) 32.8135 1.60689
\(418\) −33.8130 −1.65385
\(419\) 17.0073 0.830863 0.415431 0.909624i \(-0.363631\pi\)
0.415431 + 0.909624i \(0.363631\pi\)
\(420\) 1.44212 0.0703681
\(421\) −14.5662 −0.709913 −0.354957 0.934883i \(-0.615504\pi\)
−0.354957 + 0.934883i \(0.615504\pi\)
\(422\) 0.462952 0.0225362
\(423\) −21.5624 −1.04840
\(424\) −72.4797 −3.51993
\(425\) 19.7006 0.955619
\(426\) 6.85979 0.332358
\(427\) −6.00406 −0.290557
\(428\) −65.9179 −3.18626
\(429\) −44.8429 −2.16504
\(430\) −0.663345 −0.0319894
\(431\) −16.9661 −0.817226 −0.408613 0.912708i \(-0.633987\pi\)
−0.408613 + 0.912708i \(0.633987\pi\)
\(432\) 9.51487 0.457784
\(433\) 5.11657 0.245886 0.122943 0.992414i \(-0.460767\pi\)
0.122943 + 0.992414i \(0.460767\pi\)
\(434\) −12.0396 −0.577917
\(435\) 0.921333 0.0441745
\(436\) 79.7317 3.81846
\(437\) −22.5068 −1.07665
\(438\) 69.7566 3.33310
\(439\) 18.6871 0.891886 0.445943 0.895061i \(-0.352868\pi\)
0.445943 + 0.895061i \(0.352868\pi\)
\(440\) −6.78202 −0.323320
\(441\) −20.7477 −0.987984
\(442\) −37.3548 −1.77679
\(443\) −12.0757 −0.573733 −0.286866 0.957971i \(-0.592614\pi\)
−0.286866 + 0.957971i \(0.592614\pi\)
\(444\) −9.41179 −0.446664
\(445\) −1.05358 −0.0499447
\(446\) −73.4011 −3.47564
\(447\) −23.0201 −1.08881
\(448\) 25.6094 1.20993
\(449\) −17.6418 −0.832569 −0.416285 0.909234i \(-0.636668\pi\)
−0.416285 + 0.909234i \(0.636668\pi\)
\(450\) 44.3729 2.09176
\(451\) −61.9360 −2.91645
\(452\) −5.53568 −0.260377
\(453\) 52.1117 2.44842
\(454\) −24.2433 −1.13779
\(455\) −0.358751 −0.0168185
\(456\) −57.2895 −2.68283
\(457\) 22.1992 1.03844 0.519218 0.854642i \(-0.326223\pi\)
0.519218 + 0.854642i \(0.326223\pi\)
\(458\) 63.7847 2.98046
\(459\) −2.41612 −0.112775
\(460\) −7.06786 −0.329541
\(461\) −25.5060 −1.18793 −0.593966 0.804490i \(-0.702439\pi\)
−0.593966 + 0.804490i \(0.702439\pi\)
\(462\) −27.8310 −1.29482
\(463\) −18.3410 −0.852377 −0.426188 0.904634i \(-0.640144\pi\)
−0.426188 + 0.904634i \(0.640144\pi\)
\(464\) 42.8480 1.98917
\(465\) 1.88757 0.0875342
\(466\) −12.6247 −0.584830
\(467\) −4.95595 −0.229334 −0.114667 0.993404i \(-0.536580\pi\)
−0.114667 + 0.993404i \(0.536580\pi\)
\(468\) −61.8065 −2.85701
\(469\) 8.60539 0.397360
\(470\) 2.44457 0.112760
\(471\) 40.2384 1.85409
\(472\) −79.1971 −3.64534
\(473\) 9.40409 0.432401
\(474\) 101.822 4.67682
\(475\) −11.7679 −0.539948
\(476\) −17.0306 −0.780596
\(477\) 24.2287 1.10936
\(478\) 22.2865 1.01936
\(479\) 17.1674 0.784399 0.392199 0.919880i \(-0.371714\pi\)
0.392199 + 0.919880i \(0.371714\pi\)
\(480\) −7.81406 −0.356661
\(481\) 2.34134 0.106756
\(482\) 16.2787 0.741475
\(483\) −18.5251 −0.842920
\(484\) 89.6413 4.07460
\(485\) −0.216372 −0.00982496
\(486\) 61.3280 2.78189
\(487\) 36.1274 1.63709 0.818544 0.574444i \(-0.194782\pi\)
0.818544 + 0.574444i \(0.194782\pi\)
\(488\) 74.9019 3.39065
\(489\) −28.5115 −1.28934
\(490\) 2.35220 0.106262
\(491\) 21.1017 0.952304 0.476152 0.879363i \(-0.342031\pi\)
0.476152 + 0.879363i \(0.342031\pi\)
\(492\) −164.298 −7.40713
\(493\) −10.8804 −0.490030
\(494\) 22.3134 1.00393
\(495\) 2.26711 0.101899
\(496\) 87.7846 3.94165
\(497\) −0.778013 −0.0348987
\(498\) 23.4295 1.04990
\(499\) 6.20555 0.277798 0.138899 0.990307i \(-0.455644\pi\)
0.138899 + 0.990307i \(0.455644\pi\)
\(500\) −7.40429 −0.331130
\(501\) −21.4289 −0.957372
\(502\) −2.55206 −0.113904
\(503\) 5.41034 0.241235 0.120618 0.992699i \(-0.461513\pi\)
0.120618 + 0.992699i \(0.461513\pi\)
\(504\) −24.5003 −1.09133
\(505\) −0.747287 −0.0332538
\(506\) 136.401 6.06375
\(507\) −2.89359 −0.128509
\(508\) −13.9545 −0.619130
\(509\) 34.8140 1.54310 0.771551 0.636168i \(-0.219481\pi\)
0.771551 + 0.636168i \(0.219481\pi\)
\(510\) 3.63475 0.160950
\(511\) −7.91155 −0.349986
\(512\) −61.1168 −2.70101
\(513\) 1.44324 0.0637204
\(514\) −26.3753 −1.16336
\(515\) −0.935344 −0.0412162
\(516\) 24.9463 1.09820
\(517\) −34.6561 −1.52417
\(518\) 1.45311 0.0638462
\(519\) 1.12930 0.0495709
\(520\) 4.47550 0.196263
\(521\) 37.9754 1.66373 0.831867 0.554975i \(-0.187272\pi\)
0.831867 + 0.554975i \(0.187272\pi\)
\(522\) −24.5067 −1.07263
\(523\) −18.6861 −0.817087 −0.408543 0.912739i \(-0.633963\pi\)
−0.408543 + 0.912739i \(0.633963\pi\)
\(524\) 29.7129 1.29801
\(525\) −9.68598 −0.422731
\(526\) 29.3962 1.28174
\(527\) −22.2912 −0.971020
\(528\) 202.926 8.83120
\(529\) 67.7920 2.94748
\(530\) −2.74686 −0.119316
\(531\) 26.4742 1.14888
\(532\) 10.1730 0.441056
\(533\) 40.8719 1.77036
\(534\) 53.9370 2.33408
\(535\) −1.59560 −0.0689840
\(536\) −107.354 −4.63699
\(537\) −39.7981 −1.71741
\(538\) −27.3615 −1.17964
\(539\) −33.3466 −1.43634
\(540\) 0.453221 0.0195035
\(541\) −23.4288 −1.00728 −0.503642 0.863912i \(-0.668007\pi\)
−0.503642 + 0.863912i \(0.668007\pi\)
\(542\) −44.9949 −1.93270
\(543\) 44.8666 1.92541
\(544\) 92.2796 3.95646
\(545\) 1.92998 0.0826712
\(546\) 18.3658 0.785986
\(547\) −24.9088 −1.06502 −0.532512 0.846422i \(-0.678752\pi\)
−0.532512 + 0.846422i \(0.678752\pi\)
\(548\) 8.66784 0.370272
\(549\) −25.0384 −1.06861
\(550\) 71.3182 3.04102
\(551\) 6.49928 0.276879
\(552\) 231.104 9.83644
\(553\) −11.5483 −0.491082
\(554\) −51.1857 −2.17467
\(555\) −0.227821 −0.00967046
\(556\) 72.6901 3.08275
\(557\) 1.19087 0.0504587 0.0252294 0.999682i \(-0.491968\pi\)
0.0252294 + 0.999682i \(0.491968\pi\)
\(558\) −50.2080 −2.12547
\(559\) −6.20582 −0.262478
\(560\) 1.62344 0.0686028
\(561\) −51.5290 −2.17556
\(562\) 15.0312 0.634052
\(563\) 5.68885 0.239756 0.119878 0.992789i \(-0.461750\pi\)
0.119878 + 0.992789i \(0.461750\pi\)
\(564\) −91.9324 −3.87105
\(565\) −0.133996 −0.00563727
\(566\) 68.4592 2.87756
\(567\) −6.38491 −0.268141
\(568\) 9.70588 0.407250
\(569\) −4.84561 −0.203138 −0.101569 0.994828i \(-0.532386\pi\)
−0.101569 + 0.994828i \(0.532386\pi\)
\(570\) −2.17117 −0.0909404
\(571\) −30.1348 −1.26110 −0.630551 0.776148i \(-0.717171\pi\)
−0.630551 + 0.776148i \(0.717171\pi\)
\(572\) −99.3382 −4.15354
\(573\) −56.3982 −2.35607
\(574\) 25.3665 1.05878
\(575\) 47.4713 1.97969
\(576\) 106.798 4.44991
\(577\) −22.3183 −0.929123 −0.464561 0.885541i \(-0.653788\pi\)
−0.464561 + 0.885541i \(0.653788\pi\)
\(578\) 3.74265 0.155674
\(579\) −67.0367 −2.78595
\(580\) 2.04098 0.0847471
\(581\) −2.65729 −0.110243
\(582\) 11.0769 0.459154
\(583\) 38.9415 1.61279
\(584\) 98.6983 4.08416
\(585\) −1.49608 −0.0618554
\(586\) −3.48958 −0.144153
\(587\) −18.6554 −0.769993 −0.384996 0.922918i \(-0.625797\pi\)
−0.384996 + 0.922918i \(0.625797\pi\)
\(588\) −88.4587 −3.64797
\(589\) 13.3154 0.548650
\(590\) −3.00143 −0.123567
\(591\) −20.1673 −0.829573
\(592\) −10.5952 −0.435459
\(593\) 47.5299 1.95182 0.975909 0.218179i \(-0.0700118\pi\)
0.975909 + 0.218179i \(0.0700118\pi\)
\(594\) −8.74660 −0.358877
\(595\) −0.412241 −0.0169002
\(596\) −50.9952 −2.08885
\(597\) 27.1514 1.11123
\(598\) −90.0116 −3.68085
\(599\) −24.6595 −1.00756 −0.503781 0.863832i \(-0.668058\pi\)
−0.503781 + 0.863832i \(0.668058\pi\)
\(600\) 120.835 4.93306
\(601\) −17.5527 −0.715989 −0.357995 0.933724i \(-0.616539\pi\)
−0.357995 + 0.933724i \(0.616539\pi\)
\(602\) −3.85153 −0.156977
\(603\) 35.8866 1.46142
\(604\) 115.440 4.69720
\(605\) 2.16985 0.0882169
\(606\) 38.2565 1.55406
\(607\) −5.15250 −0.209133 −0.104567 0.994518i \(-0.533346\pi\)
−0.104567 + 0.994518i \(0.533346\pi\)
\(608\) −55.1221 −2.23549
\(609\) 5.34947 0.216771
\(610\) 2.83865 0.114934
\(611\) 22.8698 0.925212
\(612\) −71.0218 −2.87089
\(613\) 31.1573 1.25843 0.629216 0.777231i \(-0.283376\pi\)
0.629216 + 0.777231i \(0.283376\pi\)
\(614\) 62.3732 2.51718
\(615\) −3.97698 −0.160367
\(616\) −39.3779 −1.58658
\(617\) 35.9892 1.44887 0.724435 0.689343i \(-0.242101\pi\)
0.724435 + 0.689343i \(0.242101\pi\)
\(618\) 47.8838 1.92617
\(619\) 14.7207 0.591676 0.295838 0.955238i \(-0.404401\pi\)
0.295838 + 0.955238i \(0.404401\pi\)
\(620\) 4.18144 0.167931
\(621\) −5.82197 −0.233628
\(622\) −5.83313 −0.233887
\(623\) −6.11735 −0.245087
\(624\) −133.912 −5.36077
\(625\) 24.7310 0.989240
\(626\) −15.6248 −0.624491
\(627\) 30.7802 1.22924
\(628\) 89.1380 3.55699
\(629\) 2.69044 0.107275
\(630\) −0.928518 −0.0369930
\(631\) 35.7762 1.42423 0.712114 0.702063i \(-0.247738\pi\)
0.712114 + 0.702063i \(0.247738\pi\)
\(632\) 144.067 5.73067
\(633\) −0.421429 −0.0167503
\(634\) 69.4744 2.75918
\(635\) −0.337781 −0.0134044
\(636\) 103.300 4.09613
\(637\) 22.0056 0.871894
\(638\) −39.3883 −1.55940
\(639\) −3.24451 −0.128351
\(640\) −5.85386 −0.231394
\(641\) 33.2094 1.31169 0.655847 0.754894i \(-0.272312\pi\)
0.655847 + 0.754894i \(0.272312\pi\)
\(642\) 81.6851 3.22385
\(643\) −38.0963 −1.50237 −0.751186 0.660090i \(-0.770518\pi\)
−0.751186 + 0.660090i \(0.770518\pi\)
\(644\) −41.0376 −1.61711
\(645\) 0.603848 0.0237765
\(646\) 25.6403 1.00881
\(647\) −21.3540 −0.839511 −0.419756 0.907637i \(-0.637884\pi\)
−0.419756 + 0.907637i \(0.637884\pi\)
\(648\) 79.6531 3.12907
\(649\) 42.5506 1.67026
\(650\) −47.0633 −1.84598
\(651\) 10.9597 0.429544
\(652\) −63.1601 −2.47354
\(653\) 37.7905 1.47886 0.739428 0.673236i \(-0.235096\pi\)
0.739428 + 0.673236i \(0.235096\pi\)
\(654\) −98.8030 −3.86350
\(655\) 0.719227 0.0281025
\(656\) −184.956 −7.22131
\(657\) −32.9932 −1.28719
\(658\) 14.1937 0.553329
\(659\) 11.4690 0.446768 0.223384 0.974731i \(-0.428290\pi\)
0.223384 + 0.974731i \(0.428290\pi\)
\(660\) 9.66595 0.376247
\(661\) −16.4583 −0.640155 −0.320078 0.947391i \(-0.603709\pi\)
−0.320078 + 0.947391i \(0.603709\pi\)
\(662\) −10.7096 −0.416239
\(663\) 34.0043 1.32062
\(664\) 33.1503 1.28648
\(665\) 0.246247 0.00954904
\(666\) 6.05985 0.234815
\(667\) −26.2179 −1.01516
\(668\) −47.4703 −1.83668
\(669\) 66.8175 2.58331
\(670\) −4.06853 −0.157181
\(671\) −40.2429 −1.55356
\(672\) −45.3702 −1.75019
\(673\) −10.1133 −0.389840 −0.194920 0.980819i \(-0.562445\pi\)
−0.194920 + 0.980819i \(0.562445\pi\)
\(674\) 25.1952 0.970483
\(675\) −3.04407 −0.117166
\(676\) −6.41002 −0.246539
\(677\) −40.7602 −1.56654 −0.783270 0.621681i \(-0.786450\pi\)
−0.783270 + 0.621681i \(0.786450\pi\)
\(678\) 6.85979 0.263448
\(679\) −1.25631 −0.0482126
\(680\) 5.14279 0.197217
\(681\) 22.0688 0.845679
\(682\) −80.6965 −3.09003
\(683\) −15.9445 −0.610101 −0.305051 0.952336i \(-0.598673\pi\)
−0.305051 + 0.952336i \(0.598673\pi\)
\(684\) 42.4240 1.62212
\(685\) 0.209813 0.00801655
\(686\) 28.6076 1.09224
\(687\) −58.0636 −2.21527
\(688\) 28.0829 1.07065
\(689\) −25.6978 −0.979007
\(690\) 8.75845 0.333428
\(691\) 50.1087 1.90623 0.953113 0.302614i \(-0.0978594\pi\)
0.953113 + 0.302614i \(0.0978594\pi\)
\(692\) 2.50169 0.0950998
\(693\) 13.1634 0.500035
\(694\) 31.9981 1.21463
\(695\) 1.75953 0.0667428
\(696\) −66.7357 −2.52961
\(697\) 46.9660 1.77896
\(698\) 11.7362 0.444221
\(699\) 11.4924 0.434682
\(700\) −21.4568 −0.810992
\(701\) −3.38467 −0.127837 −0.0639185 0.997955i \(-0.520360\pi\)
−0.0639185 + 0.997955i \(0.520360\pi\)
\(702\) 5.77193 0.217848
\(703\) −1.60710 −0.0606129
\(704\) 171.650 6.46931
\(705\) −2.22531 −0.0838100
\(706\) 41.4911 1.56154
\(707\) −4.33892 −0.163182
\(708\) 112.874 4.24207
\(709\) −4.55041 −0.170894 −0.0854471 0.996343i \(-0.527232\pi\)
−0.0854471 + 0.996343i \(0.527232\pi\)
\(710\) 0.367836 0.0138046
\(711\) −48.1591 −1.80611
\(712\) 76.3152 2.86003
\(713\) −53.7138 −2.01160
\(714\) 21.1042 0.789805
\(715\) −2.40457 −0.0899259
\(716\) −88.1625 −3.29479
\(717\) −20.2875 −0.757652
\(718\) 68.6331 2.56136
\(719\) 5.05785 0.188626 0.0943129 0.995543i \(-0.469935\pi\)
0.0943129 + 0.995543i \(0.469935\pi\)
\(720\) 6.77015 0.252309
\(721\) −5.43082 −0.202254
\(722\) 36.8414 1.37109
\(723\) −14.8186 −0.551111
\(724\) 99.3905 3.69382
\(725\) −13.7083 −0.509112
\(726\) −111.083 −4.12267
\(727\) −12.1437 −0.450384 −0.225192 0.974314i \(-0.572301\pi\)
−0.225192 + 0.974314i \(0.572301\pi\)
\(728\) 25.9857 0.963096
\(729\) −31.2072 −1.15582
\(730\) 3.74049 0.138442
\(731\) −7.13111 −0.263754
\(732\) −106.753 −3.94569
\(733\) −32.0282 −1.18299 −0.591493 0.806310i \(-0.701461\pi\)
−0.591493 + 0.806310i \(0.701461\pi\)
\(734\) −100.463 −3.70816
\(735\) −2.14122 −0.0789802
\(736\) 222.361 8.19633
\(737\) 57.6786 2.12462
\(738\) 105.785 3.89398
\(739\) −8.47985 −0.311936 −0.155968 0.987762i \(-0.549850\pi\)
−0.155968 + 0.987762i \(0.549850\pi\)
\(740\) −0.504680 −0.0185524
\(741\) −20.3120 −0.746182
\(742\) −15.9489 −0.585502
\(743\) −32.4699 −1.19120 −0.595602 0.803280i \(-0.703086\pi\)
−0.595602 + 0.803280i \(0.703086\pi\)
\(744\) −136.724 −5.01256
\(745\) −1.23439 −0.0452244
\(746\) −82.9553 −3.03721
\(747\) −11.0816 −0.405453
\(748\) −114.150 −4.17372
\(749\) −9.26444 −0.338515
\(750\) 9.17536 0.335037
\(751\) −51.0343 −1.86227 −0.931134 0.364676i \(-0.881180\pi\)
−0.931134 + 0.364676i \(0.881180\pi\)
\(752\) −103.491 −3.77395
\(753\) 2.32316 0.0846606
\(754\) 25.9926 0.946594
\(755\) 2.79434 0.101696
\(756\) 2.63151 0.0957070
\(757\) −2.85432 −0.103742 −0.0518710 0.998654i \(-0.516518\pi\)
−0.0518710 + 0.998654i \(0.516518\pi\)
\(758\) 9.53353 0.346273
\(759\) −124.166 −4.50696
\(760\) −3.07198 −0.111432
\(761\) 37.3657 1.35450 0.677252 0.735751i \(-0.263170\pi\)
0.677252 + 0.735751i \(0.263170\pi\)
\(762\) 17.2923 0.626434
\(763\) 11.2059 0.405681
\(764\) −124.936 −4.52003
\(765\) −1.71915 −0.0621559
\(766\) −81.8716 −2.95814
\(767\) −28.0794 −1.01389
\(768\) 135.172 4.87759
\(769\) −6.13271 −0.221151 −0.110576 0.993868i \(-0.535269\pi\)
−0.110576 + 0.993868i \(0.535269\pi\)
\(770\) −1.49236 −0.0537808
\(771\) 24.0096 0.864684
\(772\) −148.503 −5.34473
\(773\) −28.4469 −1.02316 −0.511581 0.859235i \(-0.670940\pi\)
−0.511581 + 0.859235i \(0.670940\pi\)
\(774\) −16.0619 −0.577332
\(775\) −28.0847 −1.00883
\(776\) 15.6727 0.562617
\(777\) −1.32278 −0.0474545
\(778\) −67.4523 −2.41828
\(779\) −28.0545 −1.00516
\(780\) −6.37862 −0.228391
\(781\) −5.21472 −0.186598
\(782\) −103.432 −3.69873
\(783\) 1.68121 0.0600814
\(784\) −99.5809 −3.55646
\(785\) 2.15767 0.0770104
\(786\) −36.8200 −1.31333
\(787\) 3.62360 0.129167 0.0645836 0.997912i \(-0.479428\pi\)
0.0645836 + 0.997912i \(0.479428\pi\)
\(788\) −44.6756 −1.59150
\(789\) −26.7596 −0.952667
\(790\) 5.45989 0.194254
\(791\) −0.778013 −0.0276630
\(792\) −164.216 −5.83516
\(793\) 26.5565 0.943050
\(794\) −31.8963 −1.13196
\(795\) 2.50048 0.0886830
\(796\) 60.1470 2.13185
\(797\) 37.8531 1.34082 0.670412 0.741989i \(-0.266117\pi\)
0.670412 + 0.741989i \(0.266117\pi\)
\(798\) −12.6063 −0.446259
\(799\) 26.2797 0.929707
\(800\) 116.263 4.11052
\(801\) −25.5109 −0.901383
\(802\) −39.5635 −1.39704
\(803\) −53.0281 −1.87132
\(804\) 153.004 5.39605
\(805\) −0.993353 −0.0350111
\(806\) 53.2521 1.87573
\(807\) 24.9074 0.876782
\(808\) 54.1289 1.90425
\(809\) −37.6959 −1.32532 −0.662659 0.748921i \(-0.730572\pi\)
−0.662659 + 0.748921i \(0.730572\pi\)
\(810\) 3.01871 0.106067
\(811\) −46.3074 −1.62607 −0.813036 0.582213i \(-0.802187\pi\)
−0.813036 + 0.582213i \(0.802187\pi\)
\(812\) 11.8504 0.415867
\(813\) 40.9592 1.43650
\(814\) 9.73967 0.341375
\(815\) −1.52885 −0.0535532
\(816\) −153.878 −5.38681
\(817\) 4.25967 0.149027
\(818\) −61.3942 −2.14660
\(819\) −8.68659 −0.303534
\(820\) −8.81000 −0.307659
\(821\) −17.4335 −0.608432 −0.304216 0.952603i \(-0.598394\pi\)
−0.304216 + 0.952603i \(0.598394\pi\)
\(822\) −10.7411 −0.374640
\(823\) 41.3021 1.43970 0.719851 0.694129i \(-0.244210\pi\)
0.719851 + 0.694129i \(0.244210\pi\)
\(824\) 67.7506 2.36020
\(825\) −64.9214 −2.26027
\(826\) −17.4270 −0.606363
\(827\) −17.4628 −0.607240 −0.303620 0.952793i \(-0.598195\pi\)
−0.303620 + 0.952793i \(0.598195\pi\)
\(828\) −171.137 −5.94743
\(829\) −38.6660 −1.34293 −0.671463 0.741038i \(-0.734334\pi\)
−0.671463 + 0.741038i \(0.734334\pi\)
\(830\) 1.25634 0.0436081
\(831\) 46.5947 1.61635
\(832\) −113.273 −3.92704
\(833\) 25.2866 0.876130
\(834\) −90.0771 −3.11912
\(835\) −1.14906 −0.0397649
\(836\) 68.1857 2.35825
\(837\) 3.44436 0.119054
\(838\) −46.6872 −1.61278
\(839\) −48.6760 −1.68048 −0.840240 0.542214i \(-0.817586\pi\)
−0.840240 + 0.542214i \(0.817586\pi\)
\(840\) −2.52850 −0.0872417
\(841\) −21.4291 −0.738934
\(842\) 39.9860 1.37801
\(843\) −13.6830 −0.471267
\(844\) −0.933569 −0.0321348
\(845\) −0.155161 −0.00533768
\(846\) 59.1914 2.03504
\(847\) 12.5986 0.432894
\(848\) 116.289 3.99338
\(849\) −62.3189 −2.13878
\(850\) −54.0805 −1.85494
\(851\) 6.48299 0.222234
\(852\) −13.8331 −0.473915
\(853\) 22.0058 0.753464 0.376732 0.926322i \(-0.377048\pi\)
0.376732 + 0.926322i \(0.377048\pi\)
\(854\) 16.4819 0.563998
\(855\) 1.02691 0.0351196
\(856\) 115.576 3.95030
\(857\) −20.6128 −0.704119 −0.352060 0.935978i \(-0.614519\pi\)
−0.352060 + 0.935978i \(0.614519\pi\)
\(858\) 123.099 4.20254
\(859\) 28.2277 0.963115 0.481558 0.876414i \(-0.340071\pi\)
0.481558 + 0.876414i \(0.340071\pi\)
\(860\) 1.33767 0.0456142
\(861\) −23.0913 −0.786948
\(862\) 46.5739 1.58631
\(863\) 14.2756 0.485946 0.242973 0.970033i \(-0.421877\pi\)
0.242973 + 0.970033i \(0.421877\pi\)
\(864\) −14.2587 −0.485092
\(865\) 0.0605556 0.00205895
\(866\) −14.0456 −0.477289
\(867\) −3.40696 −0.115706
\(868\) 24.2784 0.824063
\(869\) −77.4035 −2.62573
\(870\) −2.52917 −0.0857469
\(871\) −38.0625 −1.28970
\(872\) −139.796 −4.73409
\(873\) −5.23912 −0.177317
\(874\) 61.7840 2.08987
\(875\) −1.04064 −0.0351800
\(876\) −140.668 −4.75273
\(877\) 28.6359 0.966964 0.483482 0.875354i \(-0.339372\pi\)
0.483482 + 0.875354i \(0.339372\pi\)
\(878\) −51.2983 −1.73123
\(879\) 3.17659 0.107144
\(880\) 10.8813 0.366808
\(881\) −50.8714 −1.71390 −0.856951 0.515399i \(-0.827644\pi\)
−0.856951 + 0.515399i \(0.827644\pi\)
\(882\) 56.9548 1.91777
\(883\) 12.0825 0.406608 0.203304 0.979116i \(-0.434832\pi\)
0.203304 + 0.979116i \(0.434832\pi\)
\(884\) 75.3280 2.53355
\(885\) 2.73223 0.0918427
\(886\) 33.1492 1.11367
\(887\) −5.86444 −0.196909 −0.0984543 0.995142i \(-0.531390\pi\)
−0.0984543 + 0.995142i \(0.531390\pi\)
\(888\) 16.5020 0.553770
\(889\) −1.96123 −0.0657777
\(890\) 2.89222 0.0969473
\(891\) −42.7956 −1.43371
\(892\) 148.017 4.95598
\(893\) −15.6978 −0.525307
\(894\) 63.1930 2.11349
\(895\) −2.13405 −0.0713336
\(896\) −33.9889 −1.13549
\(897\) 81.9382 2.73584
\(898\) 48.4289 1.61609
\(899\) 15.5109 0.517317
\(900\) −89.4804 −2.98268
\(901\) −29.5293 −0.983764
\(902\) 170.022 5.66111
\(903\) 3.50608 0.116675
\(904\) 9.70588 0.322813
\(905\) 2.40584 0.0799728
\(906\) −143.053 −4.75261
\(907\) −34.5248 −1.14638 −0.573188 0.819424i \(-0.694293\pi\)
−0.573188 + 0.819424i \(0.694293\pi\)
\(908\) 48.8879 1.62240
\(909\) −18.0944 −0.600153
\(910\) 0.984815 0.0326463
\(911\) 12.7656 0.422944 0.211472 0.977384i \(-0.432174\pi\)
0.211472 + 0.977384i \(0.432174\pi\)
\(912\) 91.9171 3.04368
\(913\) −17.8108 −0.589452
\(914\) −60.9396 −2.01570
\(915\) −2.58404 −0.0854259
\(916\) −128.625 −4.24990
\(917\) 4.17600 0.137904
\(918\) 6.63253 0.218906
\(919\) 37.9051 1.25038 0.625188 0.780474i \(-0.285022\pi\)
0.625188 + 0.780474i \(0.285022\pi\)
\(920\) 12.3923 0.408561
\(921\) −56.7787 −1.87092
\(922\) 70.0170 2.30589
\(923\) 3.44123 0.113269
\(924\) 56.1227 1.84630
\(925\) 3.38969 0.111452
\(926\) 50.3481 1.65454
\(927\) −22.6479 −0.743854
\(928\) −64.2109 −2.10783
\(929\) 54.5941 1.79118 0.895588 0.444884i \(-0.146755\pi\)
0.895588 + 0.444884i \(0.146755\pi\)
\(930\) −5.18162 −0.169912
\(931\) −15.1047 −0.495035
\(932\) 25.4585 0.833920
\(933\) 5.30994 0.173840
\(934\) 13.6047 0.445159
\(935\) −2.76309 −0.0903628
\(936\) 108.367 3.54209
\(937\) 49.7854 1.62642 0.813209 0.581971i \(-0.197718\pi\)
0.813209 + 0.581971i \(0.197718\pi\)
\(938\) −23.6228 −0.771313
\(939\) 14.2233 0.464161
\(940\) −4.92961 −0.160786
\(941\) 1.53077 0.0499018 0.0249509 0.999689i \(-0.492057\pi\)
0.0249509 + 0.999689i \(0.492057\pi\)
\(942\) −110.459 −3.59896
\(943\) 113.171 3.68536
\(944\) 127.066 4.13566
\(945\) 0.0636980 0.00207210
\(946\) −25.8154 −0.839330
\(947\) −11.0910 −0.360410 −0.180205 0.983629i \(-0.557676\pi\)
−0.180205 + 0.983629i \(0.557676\pi\)
\(948\) −205.329 −6.66877
\(949\) 34.9936 1.13594
\(950\) 32.3043 1.04809
\(951\) −63.2431 −2.05080
\(952\) 29.8602 0.967775
\(953\) 19.6338 0.636001 0.318001 0.948090i \(-0.396989\pi\)
0.318001 + 0.948090i \(0.396989\pi\)
\(954\) −66.5108 −2.15337
\(955\) −3.02419 −0.0978605
\(956\) −44.9419 −1.45353
\(957\) 35.8554 1.15904
\(958\) −47.1266 −1.52259
\(959\) 1.21822 0.0393385
\(960\) 11.0219 0.355729
\(961\) 0.777834 0.0250914
\(962\) −6.42727 −0.207224
\(963\) −38.6350 −1.24500
\(964\) −32.8269 −1.05728
\(965\) −3.59465 −0.115716
\(966\) 50.8535 1.63619
\(967\) 9.40582 0.302471 0.151235 0.988498i \(-0.451675\pi\)
0.151235 + 0.988498i \(0.451675\pi\)
\(968\) −157.171 −5.05166
\(969\) −23.3406 −0.749807
\(970\) 0.593968 0.0190712
\(971\) −24.4561 −0.784833 −0.392417 0.919788i \(-0.628361\pi\)
−0.392417 + 0.919788i \(0.628361\pi\)
\(972\) −123.671 −3.96675
\(973\) 10.2162 0.327517
\(974\) −99.1740 −3.17774
\(975\) 42.8421 1.37204
\(976\) −120.175 −3.84671
\(977\) −27.5757 −0.882225 −0.441112 0.897452i \(-0.645416\pi\)
−0.441112 + 0.897452i \(0.645416\pi\)
\(978\) 78.2676 2.50272
\(979\) −41.0023 −1.31044
\(980\) −4.74334 −0.151520
\(981\) 46.7314 1.49202
\(982\) −57.9266 −1.84851
\(983\) −28.2464 −0.900919 −0.450460 0.892797i \(-0.648740\pi\)
−0.450460 + 0.892797i \(0.648740\pi\)
\(984\) 288.068 9.18329
\(985\) −1.08141 −0.0344567
\(986\) 29.8681 0.951193
\(987\) −12.9206 −0.411269
\(988\) −44.9962 −1.43152
\(989\) −17.1834 −0.546401
\(990\) −6.22350 −0.197796
\(991\) −6.91095 −0.219534 −0.109767 0.993957i \(-0.535010\pi\)
−0.109767 + 0.993957i \(0.535010\pi\)
\(992\) −131.552 −4.17677
\(993\) 9.74898 0.309375
\(994\) 2.13574 0.0677415
\(995\) 1.45591 0.0461556
\(996\) −47.2468 −1.49707
\(997\) −17.7333 −0.561620 −0.280810 0.959763i \(-0.590603\pi\)
−0.280810 + 0.959763i \(0.590603\pi\)
\(998\) −17.0350 −0.539233
\(999\) −0.415717 −0.0131527
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 \(a_p\))