Properties

Label 4009.2.a.c.1.19
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.74061 q^{2}\) \(-3.34117 q^{3}\) \(+1.02972 q^{4}\) \(-2.66559 q^{5}\) \(+5.81567 q^{6}\) \(+0.0455688 q^{7}\) \(+1.68888 q^{8}\) \(+8.16342 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.74061 q^{2}\) \(-3.34117 q^{3}\) \(+1.02972 q^{4}\) \(-2.66559 q^{5}\) \(+5.81567 q^{6}\) \(+0.0455688 q^{7}\) \(+1.68888 q^{8}\) \(+8.16342 q^{9}\) \(+4.63975 q^{10}\) \(-5.77378 q^{11}\) \(-3.44046 q^{12}\) \(+5.44313 q^{13}\) \(-0.0793174 q^{14}\) \(+8.90619 q^{15}\) \(-4.99912 q^{16}\) \(-2.61660 q^{17}\) \(-14.2093 q^{18}\) \(+1.00000 q^{19}\) \(-2.74481 q^{20}\) \(-0.152253 q^{21}\) \(+10.0499 q^{22}\) \(-5.93212 q^{23}\) \(-5.64284 q^{24}\) \(+2.10537 q^{25}\) \(-9.47436 q^{26}\) \(-17.2519 q^{27}\) \(+0.0469230 q^{28}\) \(-1.01835 q^{29}\) \(-15.5022 q^{30}\) \(+5.87824 q^{31}\) \(+5.32374 q^{32}\) \(+19.2912 q^{33}\) \(+4.55448 q^{34}\) \(-0.121468 q^{35}\) \(+8.40602 q^{36}\) \(-5.35484 q^{37}\) \(-1.74061 q^{38}\) \(-18.1864 q^{39}\) \(-4.50187 q^{40}\) \(-6.75452 q^{41}\) \(+0.265013 q^{42}\) \(+8.74809 q^{43}\) \(-5.94537 q^{44}\) \(-21.7603 q^{45}\) \(+10.3255 q^{46}\) \(-9.44683 q^{47}\) \(+16.7029 q^{48}\) \(-6.99792 q^{49}\) \(-3.66463 q^{50}\) \(+8.74252 q^{51}\) \(+5.60489 q^{52}\) \(+0.930586 q^{53}\) \(+30.0287 q^{54}\) \(+15.3905 q^{55}\) \(+0.0769603 q^{56}\) \(-3.34117 q^{57}\) \(+1.77254 q^{58}\) \(+6.84591 q^{59}\) \(+9.17087 q^{60}\) \(+3.42660 q^{61}\) \(-10.2317 q^{62}\) \(+0.371997 q^{63}\) \(+0.731682 q^{64}\) \(-14.5092 q^{65}\) \(-33.5784 q^{66}\) \(+12.3645 q^{67}\) \(-2.69436 q^{68}\) \(+19.8202 q^{69}\) \(+0.211428 q^{70}\) \(+1.90288 q^{71}\) \(+13.7870 q^{72}\) \(+0.651226 q^{73}\) \(+9.32067 q^{74}\) \(-7.03441 q^{75}\) \(+1.02972 q^{76}\) \(-0.263104 q^{77}\) \(+31.6554 q^{78}\) \(-8.80260 q^{79}\) \(+13.3256 q^{80}\) \(+33.1512 q^{81}\) \(+11.7570 q^{82}\) \(-2.19419 q^{83}\) \(-0.156778 q^{84}\) \(+6.97480 q^{85}\) \(-15.2270 q^{86}\) \(+3.40247 q^{87}\) \(-9.75123 q^{88}\) \(-5.58740 q^{89}\) \(+37.8762 q^{90}\) \(+0.248037 q^{91}\) \(-6.10841 q^{92}\) \(-19.6402 q^{93}\) \(+16.4432 q^{94}\) \(-2.66559 q^{95}\) \(-17.7875 q^{96}\) \(+15.4317 q^{97}\) \(+12.1806 q^{98}\) \(-47.1338 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74061 −1.23080 −0.615398 0.788217i \(-0.711005\pi\)
−0.615398 + 0.788217i \(0.711005\pi\)
\(3\) −3.34117 −1.92903 −0.964513 0.264036i \(-0.914946\pi\)
−0.964513 + 0.264036i \(0.914946\pi\)
\(4\) 1.02972 0.514859
\(5\) −2.66559 −1.19209 −0.596044 0.802952i \(-0.703262\pi\)
−0.596044 + 0.802952i \(0.703262\pi\)
\(6\) 5.81567 2.37424
\(7\) 0.0455688 0.0172234 0.00861169 0.999963i \(-0.497259\pi\)
0.00861169 + 0.999963i \(0.497259\pi\)
\(8\) 1.68888 0.597110
\(9\) 8.16342 2.72114
\(10\) 4.63975 1.46722
\(11\) −5.77378 −1.74086 −0.870430 0.492292i \(-0.836159\pi\)
−0.870430 + 0.492292i \(0.836159\pi\)
\(12\) −3.44046 −0.993176
\(13\) 5.44313 1.50965 0.754826 0.655925i \(-0.227721\pi\)
0.754826 + 0.655925i \(0.227721\pi\)
\(14\) −0.0793174 −0.0211985
\(15\) 8.90619 2.29957
\(16\) −4.99912 −1.24978
\(17\) −2.61660 −0.634620 −0.317310 0.948322i \(-0.602780\pi\)
−0.317310 + 0.948322i \(0.602780\pi\)
\(18\) −14.2093 −3.34917
\(19\) 1.00000 0.229416
\(20\) −2.74481 −0.613757
\(21\) −0.152253 −0.0332244
\(22\) 10.0499 2.14264
\(23\) −5.93212 −1.23693 −0.618466 0.785812i \(-0.712246\pi\)
−0.618466 + 0.785812i \(0.712246\pi\)
\(24\) −5.64284 −1.15184
\(25\) 2.10537 0.421075
\(26\) −9.47436 −1.85807
\(27\) −17.2519 −3.32012
\(28\) 0.0469230 0.00886761
\(29\) −1.01835 −0.189102 −0.0945510 0.995520i \(-0.530142\pi\)
−0.0945510 + 0.995520i \(0.530142\pi\)
\(30\) −15.5022 −2.83030
\(31\) 5.87824 1.05576 0.527881 0.849318i \(-0.322987\pi\)
0.527881 + 0.849318i \(0.322987\pi\)
\(32\) 5.32374 0.941114
\(33\) 19.2912 3.35816
\(34\) 4.55448 0.781087
\(35\) −0.121468 −0.0205318
\(36\) 8.40602 1.40100
\(37\) −5.35484 −0.880330 −0.440165 0.897917i \(-0.645080\pi\)
−0.440165 + 0.897917i \(0.645080\pi\)
\(38\) −1.74061 −0.282364
\(39\) −18.1864 −2.91216
\(40\) −4.50187 −0.711808
\(41\) −6.75452 −1.05488 −0.527439 0.849593i \(-0.676848\pi\)
−0.527439 + 0.849593i \(0.676848\pi\)
\(42\) 0.265013 0.0408924
\(43\) 8.74809 1.33407 0.667036 0.745026i \(-0.267563\pi\)
0.667036 + 0.745026i \(0.267563\pi\)
\(44\) −5.94537 −0.896298
\(45\) −21.7603 −3.24384
\(46\) 10.3255 1.52241
\(47\) −9.44683 −1.37796 −0.688981 0.724779i \(-0.741942\pi\)
−0.688981 + 0.724779i \(0.741942\pi\)
\(48\) 16.7029 2.41086
\(49\) −6.99792 −0.999703
\(50\) −3.66463 −0.518257
\(51\) 8.74252 1.22420
\(52\) 5.60489 0.777258
\(53\) 0.930586 0.127826 0.0639129 0.997955i \(-0.479642\pi\)
0.0639129 + 0.997955i \(0.479642\pi\)
\(54\) 30.0287 4.08639
\(55\) 15.3905 2.07526
\(56\) 0.0769603 0.0102843
\(57\) −3.34117 −0.442549
\(58\) 1.77254 0.232746
\(59\) 6.84591 0.891261 0.445631 0.895217i \(-0.352979\pi\)
0.445631 + 0.895217i \(0.352979\pi\)
\(60\) 9.17087 1.18395
\(61\) 3.42660 0.438731 0.219366 0.975643i \(-0.429601\pi\)
0.219366 + 0.975643i \(0.429601\pi\)
\(62\) −10.2317 −1.29943
\(63\) 0.371997 0.0468672
\(64\) 0.731682 0.0914603
\(65\) −14.5092 −1.79964
\(66\) −33.5784 −4.13322
\(67\) 12.3645 1.51057 0.755285 0.655397i \(-0.227499\pi\)
0.755285 + 0.655397i \(0.227499\pi\)
\(68\) −2.69436 −0.326740
\(69\) 19.8202 2.38607
\(70\) 0.211428 0.0252705
\(71\) 1.90288 0.225831 0.112915 0.993605i \(-0.463981\pi\)
0.112915 + 0.993605i \(0.463981\pi\)
\(72\) 13.7870 1.62482
\(73\) 0.651226 0.0762203 0.0381101 0.999274i \(-0.487866\pi\)
0.0381101 + 0.999274i \(0.487866\pi\)
\(74\) 9.32067 1.08351
\(75\) −7.03441 −0.812264
\(76\) 1.02972 0.118117
\(77\) −0.263104 −0.0299835
\(78\) 31.6554 3.58427
\(79\) −8.80260 −0.990370 −0.495185 0.868788i \(-0.664900\pi\)
−0.495185 + 0.868788i \(0.664900\pi\)
\(80\) 13.3256 1.48985
\(81\) 33.1512 3.68346
\(82\) 11.7570 1.29834
\(83\) −2.19419 −0.240843 −0.120422 0.992723i \(-0.538425\pi\)
−0.120422 + 0.992723i \(0.538425\pi\)
\(84\) −0.156778 −0.0171059
\(85\) 6.97480 0.756523
\(86\) −15.2270 −1.64197
\(87\) 3.40247 0.364783
\(88\) −9.75123 −1.03948
\(89\) −5.58740 −0.592264 −0.296132 0.955147i \(-0.595697\pi\)
−0.296132 + 0.955147i \(0.595697\pi\)
\(90\) 37.8762 3.99250
\(91\) 0.248037 0.0260013
\(92\) −6.10841 −0.636846
\(93\) −19.6402 −2.03659
\(94\) 16.4432 1.69599
\(95\) −2.66559 −0.273484
\(96\) −17.7875 −1.81543
\(97\) 15.4317 1.56685 0.783427 0.621484i \(-0.213470\pi\)
0.783427 + 0.621484i \(0.213470\pi\)
\(98\) 12.1806 1.23043
\(99\) −47.1338 −4.73713
\(100\) 2.16794 0.216794
\(101\) 16.2442 1.61636 0.808181 0.588934i \(-0.200452\pi\)
0.808181 + 0.588934i \(0.200452\pi\)
\(102\) −15.2173 −1.50674
\(103\) −19.4403 −1.91551 −0.957753 0.287592i \(-0.907145\pi\)
−0.957753 + 0.287592i \(0.907145\pi\)
\(104\) 9.19280 0.901428
\(105\) 0.405845 0.0396064
\(106\) −1.61979 −0.157327
\(107\) 19.9334 1.92704 0.963519 0.267641i \(-0.0862442\pi\)
0.963519 + 0.267641i \(0.0862442\pi\)
\(108\) −17.7646 −1.70939
\(109\) 3.64550 0.349176 0.174588 0.984642i \(-0.444141\pi\)
0.174588 + 0.984642i \(0.444141\pi\)
\(110\) −26.7889 −2.55422
\(111\) 17.8914 1.69818
\(112\) −0.227804 −0.0215254
\(113\) 16.2367 1.52742 0.763710 0.645559i \(-0.223376\pi\)
0.763710 + 0.645559i \(0.223376\pi\)
\(114\) 5.81567 0.544687
\(115\) 15.8126 1.47453
\(116\) −1.04861 −0.0973609
\(117\) 44.4345 4.10798
\(118\) −11.9160 −1.09696
\(119\) −0.119236 −0.0109303
\(120\) 15.0415 1.37310
\(121\) 22.3366 2.03060
\(122\) −5.96437 −0.539989
\(123\) 22.5680 2.03489
\(124\) 6.05293 0.543569
\(125\) 7.71589 0.690130
\(126\) −0.647502 −0.0576840
\(127\) −9.77740 −0.867604 −0.433802 0.901008i \(-0.642828\pi\)
−0.433802 + 0.901008i \(0.642828\pi\)
\(128\) −11.9211 −1.05368
\(129\) −29.2289 −2.57346
\(130\) 25.2548 2.21499
\(131\) −3.36722 −0.294196 −0.147098 0.989122i \(-0.546993\pi\)
−0.147098 + 0.989122i \(0.546993\pi\)
\(132\) 19.8645 1.72898
\(133\) 0.0455688 0.00395132
\(134\) −21.5218 −1.85920
\(135\) 45.9864 3.95788
\(136\) −4.41913 −0.378938
\(137\) 12.3070 1.05145 0.525727 0.850653i \(-0.323793\pi\)
0.525727 + 0.850653i \(0.323793\pi\)
\(138\) −34.4992 −2.93677
\(139\) −5.54031 −0.469923 −0.234962 0.972005i \(-0.575496\pi\)
−0.234962 + 0.972005i \(0.575496\pi\)
\(140\) −0.125078 −0.0105710
\(141\) 31.5635 2.65812
\(142\) −3.31217 −0.277951
\(143\) −31.4274 −2.62809
\(144\) −40.8099 −3.40082
\(145\) 2.71449 0.225426
\(146\) −1.13353 −0.0938116
\(147\) 23.3813 1.92845
\(148\) −5.51397 −0.453246
\(149\) 4.46211 0.365551 0.182775 0.983155i \(-0.441492\pi\)
0.182775 + 0.983155i \(0.441492\pi\)
\(150\) 12.2442 0.999732
\(151\) −16.9640 −1.38051 −0.690257 0.723564i \(-0.742503\pi\)
−0.690257 + 0.723564i \(0.742503\pi\)
\(152\) 1.68888 0.136986
\(153\) −21.3604 −1.72689
\(154\) 0.457962 0.0369036
\(155\) −15.6690 −1.25856
\(156\) −18.7269 −1.49935
\(157\) 6.02503 0.480849 0.240425 0.970668i \(-0.422713\pi\)
0.240425 + 0.970668i \(0.422713\pi\)
\(158\) 15.3219 1.21894
\(159\) −3.10925 −0.246579
\(160\) −14.1909 −1.12189
\(161\) −0.270319 −0.0213042
\(162\) −57.7032 −4.53359
\(163\) 0.00745152 0.000583648 0 0.000291824 1.00000i \(-0.499907\pi\)
0.000291824 1.00000i \(0.499907\pi\)
\(164\) −6.95525 −0.543114
\(165\) −51.4224 −4.00323
\(166\) 3.81922 0.296429
\(167\) 19.1424 1.48128 0.740642 0.671900i \(-0.234521\pi\)
0.740642 + 0.671900i \(0.234521\pi\)
\(168\) −0.257137 −0.0198386
\(169\) 16.6277 1.27905
\(170\) −12.1404 −0.931125
\(171\) 8.16342 0.624272
\(172\) 9.00807 0.686859
\(173\) −0.0597609 −0.00454354 −0.00227177 0.999997i \(-0.500723\pi\)
−0.00227177 + 0.999997i \(0.500723\pi\)
\(174\) −5.92236 −0.448973
\(175\) 0.0959394 0.00725234
\(176\) 28.8638 2.17569
\(177\) −22.8733 −1.71927
\(178\) 9.72548 0.728956
\(179\) −13.8722 −1.03685 −0.518427 0.855122i \(-0.673482\pi\)
−0.518427 + 0.855122i \(0.673482\pi\)
\(180\) −22.4070 −1.67012
\(181\) 3.34790 0.248848 0.124424 0.992229i \(-0.460292\pi\)
0.124424 + 0.992229i \(0.460292\pi\)
\(182\) −0.431735 −0.0320023
\(183\) −11.4489 −0.846324
\(184\) −10.0186 −0.738584
\(185\) 14.2738 1.04943
\(186\) 34.1859 2.50663
\(187\) 15.1077 1.10478
\(188\) −9.72757 −0.709456
\(189\) −0.786147 −0.0571838
\(190\) 4.63975 0.336603
\(191\) 21.5384 1.55846 0.779231 0.626736i \(-0.215610\pi\)
0.779231 + 0.626736i \(0.215610\pi\)
\(192\) −2.44467 −0.176429
\(193\) 1.73663 0.125005 0.0625026 0.998045i \(-0.480092\pi\)
0.0625026 + 0.998045i \(0.480092\pi\)
\(194\) −26.8606 −1.92848
\(195\) 48.4776 3.47155
\(196\) −7.20589 −0.514706
\(197\) −22.6717 −1.61529 −0.807644 0.589670i \(-0.799258\pi\)
−0.807644 + 0.589670i \(0.799258\pi\)
\(198\) 82.0415 5.83044
\(199\) −14.8533 −1.05292 −0.526460 0.850200i \(-0.676481\pi\)
−0.526460 + 0.850200i \(0.676481\pi\)
\(200\) 3.55573 0.251428
\(201\) −41.3120 −2.91393
\(202\) −28.2749 −1.98941
\(203\) −0.0464048 −0.00325698
\(204\) 9.00233 0.630289
\(205\) 18.0048 1.25751
\(206\) 33.8379 2.35760
\(207\) −48.4264 −3.36587
\(208\) −27.2108 −1.88673
\(209\) −5.77378 −0.399381
\(210\) −0.706416 −0.0487474
\(211\) 1.00000 0.0688428
\(212\) 0.958241 0.0658123
\(213\) −6.35785 −0.435633
\(214\) −34.6963 −2.37179
\(215\) −23.3188 −1.59033
\(216\) −29.1364 −1.98248
\(217\) 0.267864 0.0181838
\(218\) −6.34539 −0.429764
\(219\) −2.17586 −0.147031
\(220\) 15.8479 1.06847
\(221\) −14.2425 −0.958055
\(222\) −31.1420 −2.09011
\(223\) 7.03060 0.470804 0.235402 0.971898i \(-0.424359\pi\)
0.235402 + 0.971898i \(0.424359\pi\)
\(224\) 0.242597 0.0162092
\(225\) 17.1871 1.14580
\(226\) −28.2617 −1.87994
\(227\) −20.5078 −1.36115 −0.680576 0.732677i \(-0.738271\pi\)
−0.680576 + 0.732677i \(0.738271\pi\)
\(228\) −3.44046 −0.227850
\(229\) 18.4436 1.21879 0.609395 0.792867i \(-0.291413\pi\)
0.609395 + 0.792867i \(0.291413\pi\)
\(230\) −27.5235 −1.81485
\(231\) 0.879076 0.0578390
\(232\) −1.71986 −0.112915
\(233\) 23.4767 1.53801 0.769004 0.639244i \(-0.220753\pi\)
0.769004 + 0.639244i \(0.220753\pi\)
\(234\) −77.3431 −5.05608
\(235\) 25.1814 1.64265
\(236\) 7.04935 0.458874
\(237\) 29.4110 1.91045
\(238\) 0.207542 0.0134530
\(239\) −9.84627 −0.636902 −0.318451 0.947939i \(-0.603163\pi\)
−0.318451 + 0.947939i \(0.603163\pi\)
\(240\) −44.5231 −2.87395
\(241\) −1.95165 −0.125717 −0.0628584 0.998022i \(-0.520022\pi\)
−0.0628584 + 0.998022i \(0.520022\pi\)
\(242\) −38.8792 −2.49925
\(243\) −59.0081 −3.78537
\(244\) 3.52843 0.225885
\(245\) 18.6536 1.19173
\(246\) −39.2821 −2.50453
\(247\) 5.44313 0.346338
\(248\) 9.92765 0.630406
\(249\) 7.33115 0.464593
\(250\) −13.4303 −0.849409
\(251\) −0.0590057 −0.00372441 −0.00186220 0.999998i \(-0.500593\pi\)
−0.00186220 + 0.999998i \(0.500593\pi\)
\(252\) 0.383052 0.0241300
\(253\) 34.2508 2.15333
\(254\) 17.0186 1.06784
\(255\) −23.3040 −1.45935
\(256\) 19.2865 1.20541
\(257\) 13.9070 0.867495 0.433747 0.901035i \(-0.357191\pi\)
0.433747 + 0.901035i \(0.357191\pi\)
\(258\) 50.8760 3.16740
\(259\) −0.244013 −0.0151623
\(260\) −14.9403 −0.926560
\(261\) −8.31318 −0.514573
\(262\) 5.86102 0.362095
\(263\) 21.7293 1.33988 0.669942 0.742413i \(-0.266319\pi\)
0.669942 + 0.742413i \(0.266319\pi\)
\(264\) 32.5805 2.00519
\(265\) −2.48056 −0.152380
\(266\) −0.0793174 −0.00486326
\(267\) 18.6685 1.14249
\(268\) 12.7320 0.777730
\(269\) −24.6374 −1.50217 −0.751084 0.660207i \(-0.770468\pi\)
−0.751084 + 0.660207i \(0.770468\pi\)
\(270\) −80.0443 −4.87134
\(271\) −19.3262 −1.17399 −0.586993 0.809592i \(-0.699688\pi\)
−0.586993 + 0.809592i \(0.699688\pi\)
\(272\) 13.0807 0.793134
\(273\) −0.828733 −0.0501572
\(274\) −21.4216 −1.29413
\(275\) −12.1560 −0.733033
\(276\) 20.4092 1.22849
\(277\) −5.80451 −0.348759 −0.174380 0.984679i \(-0.555792\pi\)
−0.174380 + 0.984679i \(0.555792\pi\)
\(278\) 9.64351 0.578380
\(279\) 47.9865 2.87288
\(280\) −0.205145 −0.0122597
\(281\) 2.12615 0.126836 0.0634178 0.997987i \(-0.479800\pi\)
0.0634178 + 0.997987i \(0.479800\pi\)
\(282\) −54.9397 −3.27161
\(283\) −2.58168 −0.153465 −0.0767326 0.997052i \(-0.524449\pi\)
−0.0767326 + 0.997052i \(0.524449\pi\)
\(284\) 1.95943 0.116271
\(285\) 8.90619 0.527557
\(286\) 54.7029 3.23465
\(287\) −0.307795 −0.0181686
\(288\) 43.4599 2.56090
\(289\) −10.1534 −0.597258
\(290\) −4.72487 −0.277454
\(291\) −51.5600 −3.02250
\(292\) 0.670580 0.0392427
\(293\) 21.6572 1.26523 0.632614 0.774468i \(-0.281982\pi\)
0.632614 + 0.774468i \(0.281982\pi\)
\(294\) −40.6976 −2.37353
\(295\) −18.2484 −1.06246
\(296\) −9.04368 −0.525653
\(297\) 99.6085 5.77987
\(298\) −7.76679 −0.449918
\(299\) −32.2893 −1.86734
\(300\) −7.24346 −0.418201
\(301\) 0.398640 0.0229772
\(302\) 29.5278 1.69913
\(303\) −54.2748 −3.11800
\(304\) −4.99912 −0.286719
\(305\) −9.13392 −0.523007
\(306\) 37.1802 2.12545
\(307\) 27.9345 1.59430 0.797152 0.603779i \(-0.206339\pi\)
0.797152 + 0.603779i \(0.206339\pi\)
\(308\) −0.270923 −0.0154373
\(309\) 64.9532 3.69506
\(310\) 27.2736 1.54903
\(311\) 11.4609 0.649886 0.324943 0.945734i \(-0.394655\pi\)
0.324943 + 0.945734i \(0.394655\pi\)
\(312\) −30.7147 −1.73888
\(313\) −5.97637 −0.337804 −0.168902 0.985633i \(-0.554022\pi\)
−0.168902 + 0.985633i \(0.554022\pi\)
\(314\) −10.4872 −0.591828
\(315\) −0.991592 −0.0558699
\(316\) −9.06419 −0.509901
\(317\) 12.0415 0.676320 0.338160 0.941089i \(-0.390195\pi\)
0.338160 + 0.941089i \(0.390195\pi\)
\(318\) 5.41198 0.303489
\(319\) 5.87970 0.329200
\(320\) −1.95036 −0.109029
\(321\) −66.6010 −3.71730
\(322\) 0.470520 0.0262211
\(323\) −2.61660 −0.145592
\(324\) 34.1363 1.89646
\(325\) 11.4598 0.635677
\(326\) −0.0129702 −0.000718351 0
\(327\) −12.1802 −0.673569
\(328\) −11.4076 −0.629878
\(329\) −0.430481 −0.0237332
\(330\) 89.5063 4.92716
\(331\) −29.6154 −1.62781 −0.813904 0.581000i \(-0.802662\pi\)
−0.813904 + 0.581000i \(0.802662\pi\)
\(332\) −2.25939 −0.124000
\(333\) −43.7138 −2.39550
\(334\) −33.3194 −1.82316
\(335\) −32.9588 −1.80073
\(336\) 0.761131 0.0415231
\(337\) 17.7117 0.964817 0.482409 0.875946i \(-0.339762\pi\)
0.482409 + 0.875946i \(0.339762\pi\)
\(338\) −28.9422 −1.57425
\(339\) −54.2496 −2.94643
\(340\) 7.18207 0.389503
\(341\) −33.9397 −1.83794
\(342\) −14.2093 −0.768352
\(343\) −0.637869 −0.0344417
\(344\) 14.7745 0.796587
\(345\) −52.8326 −2.84441
\(346\) 0.104020 0.00559217
\(347\) 13.0704 0.701658 0.350829 0.936440i \(-0.385900\pi\)
0.350829 + 0.936440i \(0.385900\pi\)
\(348\) 3.50358 0.187812
\(349\) 0.495731 0.0265359 0.0132679 0.999912i \(-0.495777\pi\)
0.0132679 + 0.999912i \(0.495777\pi\)
\(350\) −0.166993 −0.00892615
\(351\) −93.9041 −5.01223
\(352\) −30.7381 −1.63835
\(353\) 21.6028 1.14980 0.574901 0.818223i \(-0.305040\pi\)
0.574901 + 0.818223i \(0.305040\pi\)
\(354\) 39.8135 2.11607
\(355\) −5.07231 −0.269210
\(356\) −5.75345 −0.304932
\(357\) 0.398386 0.0210848
\(358\) 24.1460 1.27616
\(359\) −29.3675 −1.54995 −0.774977 0.631989i \(-0.782239\pi\)
−0.774977 + 0.631989i \(0.782239\pi\)
\(360\) −36.7506 −1.93693
\(361\) 1.00000 0.0526316
\(362\) −5.82739 −0.306281
\(363\) −74.6302 −3.91707
\(364\) 0.255408 0.0133870
\(365\) −1.73590 −0.0908613
\(366\) 19.9280 1.04165
\(367\) 1.84372 0.0962414 0.0481207 0.998842i \(-0.484677\pi\)
0.0481207 + 0.998842i \(0.484677\pi\)
\(368\) 29.6553 1.54589
\(369\) −55.1400 −2.87047
\(370\) −24.8451 −1.29164
\(371\) 0.0424057 0.00220159
\(372\) −20.2239 −1.04856
\(373\) −5.04481 −0.261210 −0.130605 0.991434i \(-0.541692\pi\)
−0.130605 + 0.991434i \(0.541692\pi\)
\(374\) −26.2966 −1.35976
\(375\) −25.7801 −1.33128
\(376\) −15.9546 −0.822795
\(377\) −5.54299 −0.285478
\(378\) 1.36837 0.0703815
\(379\) 13.9046 0.714233 0.357117 0.934060i \(-0.383760\pi\)
0.357117 + 0.934060i \(0.383760\pi\)
\(380\) −2.74481 −0.140806
\(381\) 32.6680 1.67363
\(382\) −37.4899 −1.91815
\(383\) −36.4675 −1.86340 −0.931701 0.363226i \(-0.881675\pi\)
−0.931701 + 0.363226i \(0.881675\pi\)
\(384\) 39.8303 2.03258
\(385\) 0.701328 0.0357430
\(386\) −3.02279 −0.153856
\(387\) 71.4143 3.63020
\(388\) 15.8903 0.806708
\(389\) −27.3415 −1.38627 −0.693134 0.720808i \(-0.743771\pi\)
−0.693134 + 0.720808i \(0.743771\pi\)
\(390\) −84.3805 −4.27277
\(391\) 15.5220 0.784981
\(392\) −11.8187 −0.596933
\(393\) 11.2505 0.567511
\(394\) 39.4625 1.98809
\(395\) 23.4641 1.18061
\(396\) −48.5345 −2.43895
\(397\) 6.47117 0.324779 0.162389 0.986727i \(-0.448080\pi\)
0.162389 + 0.986727i \(0.448080\pi\)
\(398\) 25.8537 1.29593
\(399\) −0.152253 −0.00762219
\(400\) −10.5250 −0.526251
\(401\) −22.4117 −1.11919 −0.559594 0.828767i \(-0.689043\pi\)
−0.559594 + 0.828767i \(0.689043\pi\)
\(402\) 71.9081 3.58645
\(403\) 31.9960 1.59383
\(404\) 16.7270 0.832198
\(405\) −88.3674 −4.39101
\(406\) 0.0807725 0.00400867
\(407\) 30.9177 1.53253
\(408\) 14.7651 0.730980
\(409\) 36.2751 1.79369 0.896845 0.442345i \(-0.145853\pi\)
0.896845 + 0.442345i \(0.145853\pi\)
\(410\) −31.3393 −1.54774
\(411\) −41.1196 −2.02828
\(412\) −20.0180 −0.986216
\(413\) 0.311960 0.0153505
\(414\) 84.2913 4.14269
\(415\) 5.84880 0.287106
\(416\) 28.9778 1.42075
\(417\) 18.5111 0.906494
\(418\) 10.0499 0.491556
\(419\) −15.5144 −0.757928 −0.378964 0.925411i \(-0.623720\pi\)
−0.378964 + 0.925411i \(0.623720\pi\)
\(420\) 0.417905 0.0203917
\(421\) 4.98991 0.243193 0.121597 0.992580i \(-0.461199\pi\)
0.121597 + 0.992580i \(0.461199\pi\)
\(422\) −1.74061 −0.0847315
\(423\) −77.1185 −3.74963
\(424\) 1.57165 0.0763260
\(425\) −5.50893 −0.267222
\(426\) 11.0665 0.536175
\(427\) 0.156146 0.00755644
\(428\) 20.5258 0.992152
\(429\) 105.004 5.06966
\(430\) 40.5890 1.95737
\(431\) −0.927561 −0.0446791 −0.0223395 0.999750i \(-0.507111\pi\)
−0.0223395 + 0.999750i \(0.507111\pi\)
\(432\) 86.2441 4.14942
\(433\) 4.49916 0.216216 0.108108 0.994139i \(-0.465521\pi\)
0.108108 + 0.994139i \(0.465521\pi\)
\(434\) −0.466247 −0.0223806
\(435\) −9.06958 −0.434853
\(436\) 3.75384 0.179776
\(437\) −5.93212 −0.283772
\(438\) 3.78732 0.180965
\(439\) −20.3729 −0.972345 −0.486172 0.873863i \(-0.661607\pi\)
−0.486172 + 0.873863i \(0.661607\pi\)
\(440\) 25.9928 1.23916
\(441\) −57.1270 −2.72033
\(442\) 24.7906 1.17917
\(443\) 39.2967 1.86704 0.933522 0.358521i \(-0.116719\pi\)
0.933522 + 0.358521i \(0.116719\pi\)
\(444\) 18.4231 0.874322
\(445\) 14.8937 0.706031
\(446\) −12.2375 −0.579464
\(447\) −14.9087 −0.705156
\(448\) 0.0333419 0.00157526
\(449\) 15.8914 0.749964 0.374982 0.927032i \(-0.377649\pi\)
0.374982 + 0.927032i \(0.377649\pi\)
\(450\) −29.9159 −1.41025
\(451\) 38.9991 1.83640
\(452\) 16.7192 0.786406
\(453\) 56.6798 2.66305
\(454\) 35.6961 1.67530
\(455\) −0.661165 −0.0309959
\(456\) −5.64284 −0.264250
\(457\) −14.8024 −0.692426 −0.346213 0.938156i \(-0.612533\pi\)
−0.346213 + 0.938156i \(0.612533\pi\)
\(458\) −32.1031 −1.50008
\(459\) 45.1413 2.10702
\(460\) 16.2825 0.759176
\(461\) 31.9799 1.48945 0.744726 0.667371i \(-0.232580\pi\)
0.744726 + 0.667371i \(0.232580\pi\)
\(462\) −1.53013 −0.0711880
\(463\) 9.86644 0.458532 0.229266 0.973364i \(-0.426367\pi\)
0.229266 + 0.973364i \(0.426367\pi\)
\(464\) 5.09083 0.236336
\(465\) 52.3527 2.42780
\(466\) −40.8637 −1.89297
\(467\) 28.9588 1.34005 0.670026 0.742337i \(-0.266283\pi\)
0.670026 + 0.742337i \(0.266283\pi\)
\(468\) 45.7550 2.11503
\(469\) 0.563437 0.0260171
\(470\) −43.8310 −2.02177
\(471\) −20.1306 −0.927571
\(472\) 11.5619 0.532181
\(473\) −50.5096 −2.32243
\(474\) −51.1930 −2.35137
\(475\) 2.10537 0.0966012
\(476\) −0.122779 −0.00562756
\(477\) 7.59676 0.347832
\(478\) 17.1385 0.783897
\(479\) −12.6325 −0.577193 −0.288597 0.957451i \(-0.593189\pi\)
−0.288597 + 0.957451i \(0.593189\pi\)
\(480\) 47.4143 2.16416
\(481\) −29.1471 −1.32899
\(482\) 3.39706 0.154732
\(483\) 0.903183 0.0410963
\(484\) 23.0004 1.04547
\(485\) −41.1346 −1.86783
\(486\) 102.710 4.65902
\(487\) −23.9161 −1.08374 −0.541870 0.840462i \(-0.682283\pi\)
−0.541870 + 0.840462i \(0.682283\pi\)
\(488\) 5.78712 0.261971
\(489\) −0.0248968 −0.00112587
\(490\) −32.4686 −1.46678
\(491\) 1.45598 0.0657076 0.0328538 0.999460i \(-0.489540\pi\)
0.0328538 + 0.999460i \(0.489540\pi\)
\(492\) 23.2387 1.04768
\(493\) 2.66461 0.120008
\(494\) −9.47436 −0.426271
\(495\) 125.639 5.64707
\(496\) −29.3860 −1.31947
\(497\) 0.0867121 0.00388957
\(498\) −12.7607 −0.571819
\(499\) −15.2554 −0.682925 −0.341463 0.939895i \(-0.610922\pi\)
−0.341463 + 0.939895i \(0.610922\pi\)
\(500\) 7.94519 0.355320
\(501\) −63.9581 −2.85744
\(502\) 0.102706 0.00458399
\(503\) 28.9694 1.29168 0.645842 0.763471i \(-0.276507\pi\)
0.645842 + 0.763471i \(0.276507\pi\)
\(504\) 0.628259 0.0279849
\(505\) −43.3005 −1.92685
\(506\) −59.6172 −2.65031
\(507\) −55.5558 −2.46732
\(508\) −10.0680 −0.446694
\(509\) 4.96622 0.220124 0.110062 0.993925i \(-0.464895\pi\)
0.110062 + 0.993925i \(0.464895\pi\)
\(510\) 40.5631 1.79616
\(511\) 0.0296756 0.00131277
\(512\) −9.72818 −0.429929
\(513\) −17.2519 −0.761688
\(514\) −24.2066 −1.06771
\(515\) 51.8198 2.28345
\(516\) −30.0975 −1.32497
\(517\) 54.5440 2.39884
\(518\) 0.424732 0.0186616
\(519\) 0.199671 0.00876460
\(520\) −24.5042 −1.07458
\(521\) 14.7790 0.647481 0.323741 0.946146i \(-0.395059\pi\)
0.323741 + 0.946146i \(0.395059\pi\)
\(522\) 14.4700 0.633334
\(523\) −4.11833 −0.180082 −0.0900410 0.995938i \(-0.528700\pi\)
−0.0900410 + 0.995938i \(0.528700\pi\)
\(524\) −3.46729 −0.151469
\(525\) −0.320550 −0.0139899
\(526\) −37.8222 −1.64912
\(527\) −15.3810 −0.670008
\(528\) −96.4389 −4.19696
\(529\) 12.1900 0.530001
\(530\) 4.31769 0.187548
\(531\) 55.8860 2.42525
\(532\) 0.0469230 0.00203437
\(533\) −36.7657 −1.59250
\(534\) −32.4945 −1.40617
\(535\) −53.1344 −2.29720
\(536\) 20.8822 0.901975
\(537\) 46.3492 2.00012
\(538\) 42.8840 1.84886
\(539\) 40.4045 1.74034
\(540\) 47.3530 2.03775
\(541\) −12.5585 −0.539933 −0.269967 0.962870i \(-0.587013\pi\)
−0.269967 + 0.962870i \(0.587013\pi\)
\(542\) 33.6394 1.44494
\(543\) −11.1859 −0.480033
\(544\) −13.9301 −0.597249
\(545\) −9.71741 −0.416248
\(546\) 1.44250 0.0617333
\(547\) −4.37116 −0.186897 −0.0934486 0.995624i \(-0.529789\pi\)
−0.0934486 + 0.995624i \(0.529789\pi\)
\(548\) 12.6727 0.541351
\(549\) 27.9728 1.19385
\(550\) 21.1588 0.902214
\(551\) −1.01835 −0.0433830
\(552\) 33.4740 1.42475
\(553\) −0.401124 −0.0170575
\(554\) 10.1034 0.429251
\(555\) −47.6912 −2.02438
\(556\) −5.70496 −0.241944
\(557\) −26.0003 −1.10167 −0.550835 0.834614i \(-0.685690\pi\)
−0.550835 + 0.834614i \(0.685690\pi\)
\(558\) −83.5257 −3.53593
\(559\) 47.6170 2.01398
\(560\) 0.607232 0.0256602
\(561\) −50.4774 −2.13116
\(562\) −3.70080 −0.156109
\(563\) −16.9417 −0.714007 −0.357004 0.934103i \(-0.616202\pi\)
−0.357004 + 0.934103i \(0.616202\pi\)
\(564\) 32.5015 1.36856
\(565\) −43.2804 −1.82082
\(566\) 4.49370 0.188884
\(567\) 1.51066 0.0634417
\(568\) 3.21374 0.134846
\(569\) −39.1407 −1.64086 −0.820431 0.571745i \(-0.806267\pi\)
−0.820431 + 0.571745i \(0.806267\pi\)
\(570\) −15.5022 −0.649316
\(571\) −14.0289 −0.587090 −0.293545 0.955945i \(-0.594835\pi\)
−0.293545 + 0.955945i \(0.594835\pi\)
\(572\) −32.3614 −1.35310
\(573\) −71.9634 −3.00631
\(574\) 0.535751 0.0223618
\(575\) −12.4893 −0.520841
\(576\) 5.97303 0.248876
\(577\) −37.9296 −1.57903 −0.789515 0.613731i \(-0.789668\pi\)
−0.789515 + 0.613731i \(0.789668\pi\)
\(578\) 17.6731 0.735103
\(579\) −5.80237 −0.241138
\(580\) 2.79516 0.116063
\(581\) −0.0999864 −0.00414814
\(582\) 89.7458 3.72008
\(583\) −5.37300 −0.222527
\(584\) 1.09984 0.0455119
\(585\) −118.444 −4.89707
\(586\) −37.6967 −1.55724
\(587\) −1.21754 −0.0502534 −0.0251267 0.999684i \(-0.507999\pi\)
−0.0251267 + 0.999684i \(0.507999\pi\)
\(588\) 24.0761 0.992881
\(589\) 5.87824 0.242209
\(590\) 31.7633 1.30767
\(591\) 75.7499 3.11593
\(592\) 26.7695 1.10022
\(593\) 38.6941 1.58898 0.794488 0.607279i \(-0.207739\pi\)
0.794488 + 0.607279i \(0.207739\pi\)
\(594\) −173.379 −7.11384
\(595\) 0.317833 0.0130299
\(596\) 4.59472 0.188207
\(597\) 49.6273 2.03111
\(598\) 56.2030 2.29831
\(599\) 16.5459 0.676048 0.338024 0.941137i \(-0.390242\pi\)
0.338024 + 0.941137i \(0.390242\pi\)
\(600\) −11.8803 −0.485011
\(601\) −32.3580 −1.31991 −0.659954 0.751306i \(-0.729424\pi\)
−0.659954 + 0.751306i \(0.729424\pi\)
\(602\) −0.693876 −0.0282803
\(603\) 100.937 4.11047
\(604\) −17.4682 −0.710770
\(605\) −59.5401 −2.42065
\(606\) 94.4711 3.83763
\(607\) 34.4933 1.40004 0.700019 0.714124i \(-0.253175\pi\)
0.700019 + 0.714124i \(0.253175\pi\)
\(608\) 5.32374 0.215906
\(609\) 0.155046 0.00628279
\(610\) 15.8986 0.643714
\(611\) −51.4203 −2.08024
\(612\) −21.9952 −0.889104
\(613\) −1.13192 −0.0457177 −0.0228589 0.999739i \(-0.507277\pi\)
−0.0228589 + 0.999739i \(0.507277\pi\)
\(614\) −48.6230 −1.96226
\(615\) −60.1570 −2.42577
\(616\) −0.444352 −0.0179034
\(617\) 9.00443 0.362505 0.181252 0.983437i \(-0.441985\pi\)
0.181252 + 0.983437i \(0.441985\pi\)
\(618\) −113.058 −4.54787
\(619\) 20.1918 0.811579 0.405789 0.913967i \(-0.366997\pi\)
0.405789 + 0.913967i \(0.366997\pi\)
\(620\) −16.1346 −0.647982
\(621\) 102.340 4.10677
\(622\) −19.9489 −0.799877
\(623\) −0.254611 −0.0102008
\(624\) 90.9160 3.63955
\(625\) −31.0943 −1.24377
\(626\) 10.4025 0.415768
\(627\) 19.2912 0.770416
\(628\) 6.20408 0.247570
\(629\) 14.0115 0.558674
\(630\) 1.72597 0.0687645
\(631\) −32.4333 −1.29115 −0.645575 0.763696i \(-0.723382\pi\)
−0.645575 + 0.763696i \(0.723382\pi\)
\(632\) −14.8665 −0.591359
\(633\) −3.34117 −0.132800
\(634\) −20.9596 −0.832413
\(635\) 26.0626 1.03426
\(636\) −3.20165 −0.126954
\(637\) −38.0906 −1.50920
\(638\) −10.2343 −0.405178
\(639\) 15.5340 0.614517
\(640\) 31.7767 1.25608
\(641\) 11.0757 0.437462 0.218731 0.975785i \(-0.429808\pi\)
0.218731 + 0.975785i \(0.429808\pi\)
\(642\) 115.926 4.57524
\(643\) 10.7261 0.422995 0.211498 0.977378i \(-0.432166\pi\)
0.211498 + 0.977378i \(0.432166\pi\)
\(644\) −0.278353 −0.0109686
\(645\) 77.9122 3.06779
\(646\) 4.55448 0.179194
\(647\) −7.37626 −0.289991 −0.144995 0.989432i \(-0.546317\pi\)
−0.144995 + 0.989432i \(0.546317\pi\)
\(648\) 55.9884 2.19943
\(649\) −39.5268 −1.55156
\(650\) −19.9471 −0.782388
\(651\) −0.894980 −0.0350770
\(652\) 0.00767296 0.000300496 0
\(653\) 21.5605 0.843726 0.421863 0.906660i \(-0.361376\pi\)
0.421863 + 0.906660i \(0.361376\pi\)
\(654\) 21.2010 0.829026
\(655\) 8.97564 0.350707
\(656\) 33.7666 1.31837
\(657\) 5.31623 0.207406
\(658\) 0.749299 0.0292107
\(659\) −13.1817 −0.513488 −0.256744 0.966480i \(-0.582650\pi\)
−0.256744 + 0.966480i \(0.582650\pi\)
\(660\) −52.9506 −2.06110
\(661\) 40.8506 1.58890 0.794452 0.607326i \(-0.207758\pi\)
0.794452 + 0.607326i \(0.207758\pi\)
\(662\) 51.5487 2.00350
\(663\) 47.5867 1.84811
\(664\) −3.70572 −0.143810
\(665\) −0.121468 −0.00471032
\(666\) 76.0886 2.94837
\(667\) 6.04094 0.233906
\(668\) 19.7113 0.762652
\(669\) −23.4904 −0.908193
\(670\) 57.3684 2.21633
\(671\) −19.7844 −0.763770
\(672\) −0.810556 −0.0312679
\(673\) −12.9417 −0.498865 −0.249432 0.968392i \(-0.580244\pi\)
−0.249432 + 0.968392i \(0.580244\pi\)
\(674\) −30.8291 −1.18749
\(675\) −36.3216 −1.39802
\(676\) 17.1218 0.658531
\(677\) −42.5408 −1.63498 −0.817488 0.575946i \(-0.804634\pi\)
−0.817488 + 0.575946i \(0.804634\pi\)
\(678\) 94.4273 3.62646
\(679\) 0.703205 0.0269865
\(680\) 11.7796 0.451727
\(681\) 68.5202 2.62570
\(682\) 59.0757 2.26212
\(683\) −22.0731 −0.844603 −0.422301 0.906455i \(-0.638778\pi\)
−0.422301 + 0.906455i \(0.638778\pi\)
\(684\) 8.40602 0.321412
\(685\) −32.8053 −1.25343
\(686\) 1.11028 0.0423907
\(687\) −61.6233 −2.35108
\(688\) −43.7327 −1.66729
\(689\) 5.06530 0.192973
\(690\) 91.9608 3.50089
\(691\) −18.0550 −0.686845 −0.343422 0.939181i \(-0.611586\pi\)
−0.343422 + 0.939181i \(0.611586\pi\)
\(692\) −0.0615369 −0.00233928
\(693\) −2.14783 −0.0815893
\(694\) −22.7505 −0.863598
\(695\) 14.7682 0.560190
\(696\) 5.74636 0.217815
\(697\) 17.6739 0.669447
\(698\) −0.862874 −0.0326603
\(699\) −78.4395 −2.96686
\(700\) 0.0987905 0.00373393
\(701\) 6.75406 0.255097 0.127549 0.991832i \(-0.459289\pi\)
0.127549 + 0.991832i \(0.459289\pi\)
\(702\) 163.450 6.16903
\(703\) −5.35484 −0.201961
\(704\) −4.22457 −0.159220
\(705\) −84.1353 −3.16872
\(706\) −37.6021 −1.41517
\(707\) 0.740230 0.0278392
\(708\) −23.5531 −0.885179
\(709\) −20.9893 −0.788268 −0.394134 0.919053i \(-0.628955\pi\)
−0.394134 + 0.919053i \(0.628955\pi\)
\(710\) 8.82890 0.331343
\(711\) −71.8593 −2.69493
\(712\) −9.43646 −0.353646
\(713\) −34.8704 −1.30591
\(714\) −0.693434 −0.0259511
\(715\) 83.7727 3.13292
\(716\) −14.2844 −0.533833
\(717\) 32.8981 1.22860
\(718\) 51.1172 1.90768
\(719\) 22.2685 0.830476 0.415238 0.909713i \(-0.363698\pi\)
0.415238 + 0.909713i \(0.363698\pi\)
\(720\) 108.782 4.05408
\(721\) −0.885870 −0.0329915
\(722\) −1.74061 −0.0647787
\(723\) 6.52079 0.242511
\(724\) 3.44739 0.128121
\(725\) −2.14400 −0.0796261
\(726\) 129.902 4.82112
\(727\) −35.3705 −1.31182 −0.655910 0.754839i \(-0.727715\pi\)
−0.655910 + 0.754839i \(0.727715\pi\)
\(728\) 0.418905 0.0155256
\(729\) 97.7026 3.61861
\(730\) 3.02153 0.111832
\(731\) −22.8903 −0.846628
\(732\) −11.7891 −0.435737
\(733\) 44.8057 1.65494 0.827469 0.561511i \(-0.189780\pi\)
0.827469 + 0.561511i \(0.189780\pi\)
\(734\) −3.20919 −0.118454
\(735\) −62.3249 −2.29889
\(736\) −31.5811 −1.16409
\(737\) −71.3902 −2.62969
\(738\) 95.9771 3.53297
\(739\) 11.3703 0.418263 0.209132 0.977887i \(-0.432936\pi\)
0.209132 + 0.977887i \(0.432936\pi\)
\(740\) 14.6980 0.540309
\(741\) −18.1864 −0.668095
\(742\) −0.0738117 −0.00270971
\(743\) −48.6553 −1.78499 −0.892496 0.451056i \(-0.851047\pi\)
−0.892496 + 0.451056i \(0.851047\pi\)
\(744\) −33.1700 −1.21607
\(745\) −11.8942 −0.435769
\(746\) 8.78103 0.321496
\(747\) −17.9121 −0.655368
\(748\) 15.5567 0.568808
\(749\) 0.908342 0.0331901
\(750\) 44.8731 1.63853
\(751\) 22.6187 0.825369 0.412685 0.910874i \(-0.364591\pi\)
0.412685 + 0.910874i \(0.364591\pi\)
\(752\) 47.2258 1.72215
\(753\) 0.197148 0.00718448
\(754\) 9.64817 0.351366
\(755\) 45.2192 1.64570
\(756\) −0.809509 −0.0294416
\(757\) −40.2314 −1.46223 −0.731117 0.682252i \(-0.761001\pi\)
−0.731117 + 0.682252i \(0.761001\pi\)
\(758\) −24.2025 −0.879075
\(759\) −114.438 −4.15382
\(760\) −4.50187 −0.163300
\(761\) 10.9158 0.395696 0.197848 0.980233i \(-0.436605\pi\)
0.197848 + 0.980233i \(0.436605\pi\)
\(762\) −56.8621 −2.05990
\(763\) 0.166121 0.00601399
\(764\) 22.1785 0.802388
\(765\) 56.9382 2.05860
\(766\) 63.4756 2.29347
\(767\) 37.2632 1.34549
\(768\) −64.4396 −2.32526
\(769\) −40.0451 −1.44406 −0.722031 0.691861i \(-0.756791\pi\)
−0.722031 + 0.691861i \(0.756791\pi\)
\(770\) −1.22074 −0.0439924
\(771\) −46.4657 −1.67342
\(772\) 1.78824 0.0643600
\(773\) 15.4759 0.556630 0.278315 0.960490i \(-0.410224\pi\)
0.278315 + 0.960490i \(0.410224\pi\)
\(774\) −124.304 −4.46803
\(775\) 12.3759 0.444555
\(776\) 26.0623 0.935583
\(777\) 0.815291 0.0292484
\(778\) 47.5908 1.70621
\(779\) −6.75452 −0.242006
\(780\) 49.9182 1.78736
\(781\) −10.9868 −0.393140
\(782\) −27.0177 −0.966152
\(783\) 17.5684 0.627842
\(784\) 34.9834 1.24941
\(785\) −16.0603 −0.573215
\(786\) −19.5827 −0.698490
\(787\) 25.3333 0.903036 0.451518 0.892262i \(-0.350883\pi\)
0.451518 + 0.892262i \(0.350883\pi\)
\(788\) −23.3454 −0.831646
\(789\) −72.6012 −2.58467
\(790\) −40.8418 −1.45309
\(791\) 0.739887 0.0263074
\(792\) −79.6034 −2.82858
\(793\) 18.6514 0.662332
\(794\) −11.2638 −0.399736
\(795\) 8.28798 0.293944
\(796\) −15.2947 −0.542105
\(797\) −15.9386 −0.564573 −0.282286 0.959330i \(-0.591093\pi\)
−0.282286 + 0.959330i \(0.591093\pi\)
\(798\) 0.265013 0.00938136
\(799\) 24.7186 0.874482
\(800\) 11.2085 0.396279
\(801\) −45.6123 −1.61163
\(802\) 39.0100 1.37749
\(803\) −3.76004 −0.132689
\(804\) −42.5397 −1.50026
\(805\) 0.720561 0.0253964
\(806\) −55.6925 −1.96169
\(807\) 82.3177 2.89772
\(808\) 27.4346 0.965145
\(809\) 21.5734 0.758481 0.379240 0.925298i \(-0.376185\pi\)
0.379240 + 0.925298i \(0.376185\pi\)
\(810\) 153.813 5.40444
\(811\) −28.2124 −0.990673 −0.495336 0.868701i \(-0.664955\pi\)
−0.495336 + 0.868701i \(0.664955\pi\)
\(812\) −0.0477838 −0.00167688
\(813\) 64.5723 2.26465
\(814\) −53.8155 −1.88623
\(815\) −0.0198627 −0.000695760 0
\(816\) −43.7049 −1.52998
\(817\) 8.74809 0.306057
\(818\) −63.1408 −2.20767
\(819\) 2.02483 0.0707532
\(820\) 18.5398 0.647440
\(821\) 14.2937 0.498853 0.249426 0.968394i \(-0.419758\pi\)
0.249426 + 0.968394i \(0.419758\pi\)
\(822\) 71.5732 2.49640
\(823\) 8.02738 0.279817 0.139908 0.990164i \(-0.455319\pi\)
0.139908 + 0.990164i \(0.455319\pi\)
\(824\) −32.8323 −1.14377
\(825\) 40.6152 1.41404
\(826\) −0.543000 −0.0188934
\(827\) 35.4635 1.23319 0.616594 0.787281i \(-0.288512\pi\)
0.616594 + 0.787281i \(0.288512\pi\)
\(828\) −49.8655 −1.73295
\(829\) 1.85139 0.0643013 0.0321507 0.999483i \(-0.489764\pi\)
0.0321507 + 0.999483i \(0.489764\pi\)
\(830\) −10.1805 −0.353369
\(831\) 19.3939 0.672765
\(832\) 3.98264 0.138073
\(833\) 18.3108 0.634431
\(834\) −32.2206 −1.11571
\(835\) −51.0258 −1.76582
\(836\) −5.94537 −0.205625
\(837\) −101.411 −3.50526
\(838\) 27.0045 0.932855
\(839\) −15.8569 −0.547440 −0.273720 0.961809i \(-0.588254\pi\)
−0.273720 + 0.961809i \(0.588254\pi\)
\(840\) 0.685423 0.0236493
\(841\) −27.9630 −0.964240
\(842\) −8.68548 −0.299321
\(843\) −7.10383 −0.244669
\(844\) 1.02972 0.0354444
\(845\) −44.3225 −1.52474
\(846\) 134.233 4.61503
\(847\) 1.01785 0.0349737
\(848\) −4.65211 −0.159754
\(849\) 8.62584 0.296038
\(850\) 9.58889 0.328896
\(851\) 31.7655 1.08891
\(852\) −6.54680 −0.224290
\(853\) 37.3340 1.27829 0.639146 0.769085i \(-0.279288\pi\)
0.639146 + 0.769085i \(0.279288\pi\)
\(854\) −0.271789 −0.00930044
\(855\) −21.7603 −0.744188
\(856\) 33.6652 1.15065
\(857\) −29.6198 −1.01179 −0.505896 0.862594i \(-0.668838\pi\)
−0.505896 + 0.862594i \(0.668838\pi\)
\(858\) −182.772 −6.23972
\(859\) 42.0851 1.43593 0.717963 0.696082i \(-0.245075\pi\)
0.717963 + 0.696082i \(0.245075\pi\)
\(860\) −24.0118 −0.818796
\(861\) 1.02840 0.0350477
\(862\) 1.61452 0.0549908
\(863\) 5.08070 0.172949 0.0864745 0.996254i \(-0.472440\pi\)
0.0864745 + 0.996254i \(0.472440\pi\)
\(864\) −91.8445 −3.12461
\(865\) 0.159298 0.00541630
\(866\) −7.83127 −0.266117
\(867\) 33.9242 1.15213
\(868\) 0.275825 0.00936210
\(869\) 50.8243 1.72410
\(870\) 15.7866 0.535215
\(871\) 67.3018 2.28043
\(872\) 6.15682 0.208496
\(873\) 125.976 4.26363
\(874\) 10.3255 0.349265
\(875\) 0.351604 0.0118864
\(876\) −2.24052 −0.0757002
\(877\) 31.7332 1.07155 0.535777 0.844359i \(-0.320019\pi\)
0.535777 + 0.844359i \(0.320019\pi\)
\(878\) 35.4612 1.19676
\(879\) −72.3604 −2.44066
\(880\) −76.9391 −2.59362
\(881\) −17.1482 −0.577737 −0.288868 0.957369i \(-0.593279\pi\)
−0.288868 + 0.957369i \(0.593279\pi\)
\(882\) 99.4357 3.34817
\(883\) −29.1692 −0.981622 −0.490811 0.871266i \(-0.663300\pi\)
−0.490811 + 0.871266i \(0.663300\pi\)
\(884\) −14.6658 −0.493263
\(885\) 60.9710 2.04952
\(886\) −68.4002 −2.29795
\(887\) 8.50695 0.285635 0.142818 0.989749i \(-0.454384\pi\)
0.142818 + 0.989749i \(0.454384\pi\)
\(888\) 30.2165 1.01400
\(889\) −0.445544 −0.0149431
\(890\) −25.9242 −0.868980
\(891\) −191.408 −6.41239
\(892\) 7.23954 0.242398
\(893\) −9.44683 −0.316126
\(894\) 25.9502 0.867904
\(895\) 36.9775 1.23602
\(896\) −0.543228 −0.0181480
\(897\) 107.884 3.60214
\(898\) −27.6608 −0.923052
\(899\) −5.98608 −0.199647
\(900\) 17.6978 0.589927
\(901\) −2.43497 −0.0811208
\(902\) −67.8822 −2.26023
\(903\) −1.33192 −0.0443237
\(904\) 27.4219 0.912038
\(905\) −8.92414 −0.296648
\(906\) −98.6573 −3.27767
\(907\) −33.1020 −1.09913 −0.549566 0.835450i \(-0.685207\pi\)
−0.549566 + 0.835450i \(0.685207\pi\)
\(908\) −21.1173 −0.700802
\(909\) 132.609 4.39835
\(910\) 1.15083 0.0381496
\(911\) 13.7116 0.454285 0.227143 0.973861i \(-0.427062\pi\)
0.227143 + 0.973861i \(0.427062\pi\)
\(912\) 16.7029 0.553088
\(913\) 12.6688 0.419274
\(914\) 25.7651 0.852235
\(915\) 30.5180 1.00889
\(916\) 18.9917 0.627504
\(917\) −0.153440 −0.00506705
\(918\) −78.5733 −2.59331
\(919\) −22.0703 −0.728031 −0.364016 0.931393i \(-0.618594\pi\)
−0.364016 + 0.931393i \(0.618594\pi\)
\(920\) 26.7056 0.880458
\(921\) −93.3338 −3.07545
\(922\) −55.6644 −1.83321
\(923\) 10.3576 0.340926
\(924\) 0.905201 0.0297789
\(925\) −11.2739 −0.370685
\(926\) −17.1736 −0.564360
\(927\) −158.699 −5.21236
\(928\) −5.42141 −0.177966
\(929\) −20.5367 −0.673788 −0.336894 0.941543i \(-0.609376\pi\)
−0.336894 + 0.941543i \(0.609376\pi\)
\(930\) −91.1256 −2.98813
\(931\) −6.99792 −0.229348
\(932\) 24.1743 0.791857
\(933\) −38.2927 −1.25365
\(934\) −50.4059 −1.64933
\(935\) −40.2709 −1.31700
\(936\) 75.0447 2.45291
\(937\) −39.4019 −1.28720 −0.643602 0.765360i \(-0.722561\pi\)
−0.643602 + 0.765360i \(0.722561\pi\)
\(938\) −0.980724 −0.0320218
\(939\) 19.9681 0.651633
\(940\) 25.9297 0.845735
\(941\) −28.9711 −0.944432 −0.472216 0.881483i \(-0.656546\pi\)
−0.472216 + 0.881483i \(0.656546\pi\)
\(942\) 35.0396 1.14165
\(943\) 40.0686 1.30481
\(944\) −34.2235 −1.11388
\(945\) 2.09555 0.0681681
\(946\) 87.9174 2.85844
\(947\) 8.24181 0.267823 0.133911 0.990993i \(-0.457246\pi\)
0.133911 + 0.990993i \(0.457246\pi\)
\(948\) 30.2850 0.983611
\(949\) 3.54471 0.115066
\(950\) −3.66463 −0.118896
\(951\) −40.2328 −1.30464
\(952\) −0.201375 −0.00652659
\(953\) −28.2162 −0.914012 −0.457006 0.889463i \(-0.651078\pi\)
−0.457006 + 0.889463i \(0.651078\pi\)
\(954\) −13.2230 −0.428110
\(955\) −57.4125 −1.85783
\(956\) −10.1389 −0.327915
\(957\) −19.6451 −0.635036
\(958\) 21.9882 0.710407
\(959\) 0.560813 0.0181096
\(960\) 6.51650 0.210319
\(961\) 3.55368 0.114635
\(962\) 50.7336 1.63572
\(963\) 162.725 5.24374
\(964\) −2.00965 −0.0647264
\(965\) −4.62914 −0.149017
\(966\) −1.57209 −0.0505811
\(967\) −24.0414 −0.773120 −0.386560 0.922264i \(-0.626337\pi\)
−0.386560 + 0.922264i \(0.626337\pi\)
\(968\) 37.7238 1.21249
\(969\) 8.74252 0.280850
\(970\) 71.5993 2.29892
\(971\) 47.5150 1.52483 0.762415 0.647089i \(-0.224014\pi\)
0.762415 + 0.647089i \(0.224014\pi\)
\(972\) −60.7617 −1.94893
\(973\) −0.252465 −0.00809367
\(974\) 41.6285 1.33386
\(975\) −38.2892 −1.22624
\(976\) −17.1300 −0.548317
\(977\) −50.4242 −1.61321 −0.806607 0.591088i \(-0.798698\pi\)
−0.806607 + 0.591088i \(0.798698\pi\)
\(978\) 0.0433356 0.00138572
\(979\) 32.2604 1.03105
\(980\) 19.2079 0.613575
\(981\) 29.7598 0.950156
\(982\) −2.53430 −0.0808726
\(983\) −37.6059 −1.19944 −0.599722 0.800209i \(-0.704722\pi\)
−0.599722 + 0.800209i \(0.704722\pi\)
\(984\) 38.1147 1.21505
\(985\) 60.4334 1.92557
\(986\) −4.63804 −0.147705
\(987\) 1.43831 0.0457819
\(988\) 5.60489 0.178315
\(989\) −51.8947 −1.65016
\(990\) −218.689 −6.95039
\(991\) −24.7989 −0.787763 −0.393882 0.919161i \(-0.628868\pi\)
−0.393882 + 0.919161i \(0.628868\pi\)
\(992\) 31.2942 0.993593
\(993\) 98.9499 3.14008
\(994\) −0.150932 −0.00478727
\(995\) 39.5927 1.25517
\(996\) 7.54901 0.239200
\(997\) 31.1879 0.987732 0.493866 0.869538i \(-0.335583\pi\)
0.493866 + 0.869538i \(0.335583\pi\)
\(998\) 26.5537 0.840542
\(999\) 92.3809 2.92280
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 \(a_p\))