Properties

Label 8007.2.a.j.1.2
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69942 q^{2}\) \(-1.00000 q^{3}\) \(+5.28690 q^{4}\) \(+3.29410 q^{5}\) \(+2.69942 q^{6}\) \(+4.13717 q^{7}\) \(-8.87273 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69942 q^{2}\) \(-1.00000 q^{3}\) \(+5.28690 q^{4}\) \(+3.29410 q^{5}\) \(+2.69942 q^{6}\) \(+4.13717 q^{7}\) \(-8.87273 q^{8}\) \(+1.00000 q^{9}\) \(-8.89217 q^{10}\) \(+1.26440 q^{11}\) \(-5.28690 q^{12}\) \(+5.50466 q^{13}\) \(-11.1680 q^{14}\) \(-3.29410 q^{15}\) \(+13.3775 q^{16}\) \(+1.00000 q^{17}\) \(-2.69942 q^{18}\) \(+3.75022 q^{19}\) \(+17.4156 q^{20}\) \(-4.13717 q^{21}\) \(-3.41316 q^{22}\) \(-5.79289 q^{23}\) \(+8.87273 q^{24}\) \(+5.85108 q^{25}\) \(-14.8594 q^{26}\) \(-1.00000 q^{27}\) \(+21.8728 q^{28}\) \(+1.48332 q^{29}\) \(+8.89217 q^{30}\) \(-5.62716 q^{31}\) \(-18.3660 q^{32}\) \(-1.26440 q^{33}\) \(-2.69942 q^{34}\) \(+13.6282 q^{35}\) \(+5.28690 q^{36}\) \(+9.89414 q^{37}\) \(-10.1234 q^{38}\) \(-5.50466 q^{39}\) \(-29.2276 q^{40}\) \(+3.72683 q^{41}\) \(+11.1680 q^{42}\) \(-3.23636 q^{43}\) \(+6.68477 q^{44}\) \(+3.29410 q^{45}\) \(+15.6375 q^{46}\) \(+1.75649 q^{47}\) \(-13.3775 q^{48}\) \(+10.1162 q^{49}\) \(-15.7946 q^{50}\) \(-1.00000 q^{51}\) \(+29.1025 q^{52}\) \(-6.58226 q^{53}\) \(+2.69942 q^{54}\) \(+4.16507 q^{55}\) \(-36.7080 q^{56}\) \(-3.75022 q^{57}\) \(-4.00411 q^{58}\) \(-13.0815 q^{59}\) \(-17.4156 q^{60}\) \(-1.45833 q^{61}\) \(+15.1901 q^{62}\) \(+4.13717 q^{63}\) \(+22.8228 q^{64}\) \(+18.1329 q^{65}\) \(+3.41316 q^{66}\) \(-15.7266 q^{67}\) \(+5.28690 q^{68}\) \(+5.79289 q^{69}\) \(-36.7884 q^{70}\) \(-0.751536 q^{71}\) \(-8.87273 q^{72}\) \(+8.74535 q^{73}\) \(-26.7085 q^{74}\) \(-5.85108 q^{75}\) \(+19.8270 q^{76}\) \(+5.23105 q^{77}\) \(+14.8594 q^{78}\) \(-8.70356 q^{79}\) \(+44.0667 q^{80}\) \(+1.00000 q^{81}\) \(-10.0603 q^{82}\) \(-8.79348 q^{83}\) \(-21.8728 q^{84}\) \(+3.29410 q^{85}\) \(+8.73632 q^{86}\) \(-1.48332 q^{87}\) \(-11.2187 q^{88}\) \(+4.33618 q^{89}\) \(-8.89217 q^{90}\) \(+22.7737 q^{91}\) \(-30.6264 q^{92}\) \(+5.62716 q^{93}\) \(-4.74151 q^{94}\) \(+12.3536 q^{95}\) \(+18.3660 q^{96}\) \(+12.3848 q^{97}\) \(-27.3078 q^{98}\) \(+1.26440 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69942 −1.90878 −0.954391 0.298560i \(-0.903494\pi\)
−0.954391 + 0.298560i \(0.903494\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.28690 2.64345
\(5\) 3.29410 1.47317 0.736583 0.676347i \(-0.236438\pi\)
0.736583 + 0.676347i \(0.236438\pi\)
\(6\) 2.69942 1.10204
\(7\) 4.13717 1.56370 0.781851 0.623465i \(-0.214276\pi\)
0.781851 + 0.623465i \(0.214276\pi\)
\(8\) −8.87273 −3.13698
\(9\) 1.00000 0.333333
\(10\) −8.89217 −2.81195
\(11\) 1.26440 0.381232 0.190616 0.981665i \(-0.438951\pi\)
0.190616 + 0.981665i \(0.438951\pi\)
\(12\) −5.28690 −1.52620
\(13\) 5.50466 1.52672 0.763359 0.645975i \(-0.223549\pi\)
0.763359 + 0.645975i \(0.223549\pi\)
\(14\) −11.1680 −2.98477
\(15\) −3.29410 −0.850532
\(16\) 13.3775 3.34437
\(17\) 1.00000 0.242536
\(18\) −2.69942 −0.636261
\(19\) 3.75022 0.860359 0.430179 0.902743i \(-0.358450\pi\)
0.430179 + 0.902743i \(0.358450\pi\)
\(20\) 17.4156 3.89424
\(21\) −4.13717 −0.902804
\(22\) −3.41316 −0.727689
\(23\) −5.79289 −1.20790 −0.603951 0.797022i \(-0.706408\pi\)
−0.603951 + 0.797022i \(0.706408\pi\)
\(24\) 8.87273 1.81114
\(25\) 5.85108 1.17022
\(26\) −14.8594 −2.91417
\(27\) −1.00000 −0.192450
\(28\) 21.8728 4.13357
\(29\) 1.48332 0.275445 0.137723 0.990471i \(-0.456022\pi\)
0.137723 + 0.990471i \(0.456022\pi\)
\(30\) 8.89217 1.62348
\(31\) −5.62716 −1.01067 −0.505334 0.862924i \(-0.668631\pi\)
−0.505334 + 0.862924i \(0.668631\pi\)
\(32\) −18.3660 −3.24668
\(33\) −1.26440 −0.220105
\(34\) −2.69942 −0.462948
\(35\) 13.6282 2.30359
\(36\) 5.28690 0.881149
\(37\) 9.89414 1.62659 0.813293 0.581854i \(-0.197672\pi\)
0.813293 + 0.581854i \(0.197672\pi\)
\(38\) −10.1234 −1.64224
\(39\) −5.50466 −0.881451
\(40\) −29.2276 −4.62129
\(41\) 3.72683 0.582033 0.291017 0.956718i \(-0.406007\pi\)
0.291017 + 0.956718i \(0.406007\pi\)
\(42\) 11.1680 1.72326
\(43\) −3.23636 −0.493541 −0.246770 0.969074i \(-0.579369\pi\)
−0.246770 + 0.969074i \(0.579369\pi\)
\(44\) 6.68477 1.00777
\(45\) 3.29410 0.491055
\(46\) 15.6375 2.30562
\(47\) 1.75649 0.256210 0.128105 0.991761i \(-0.459111\pi\)
0.128105 + 0.991761i \(0.459111\pi\)
\(48\) −13.3775 −1.93087
\(49\) 10.1162 1.44517
\(50\) −15.7946 −2.23369
\(51\) −1.00000 −0.140028
\(52\) 29.1025 4.03580
\(53\) −6.58226 −0.904143 −0.452071 0.891982i \(-0.649315\pi\)
−0.452071 + 0.891982i \(0.649315\pi\)
\(54\) 2.69942 0.367345
\(55\) 4.16507 0.561618
\(56\) −36.7080 −4.90531
\(57\) −3.75022 −0.496728
\(58\) −4.00411 −0.525765
\(59\) −13.0815 −1.70307 −0.851536 0.524296i \(-0.824328\pi\)
−0.851536 + 0.524296i \(0.824328\pi\)
\(60\) −17.4156 −2.24834
\(61\) −1.45833 −0.186721 −0.0933603 0.995632i \(-0.529761\pi\)
−0.0933603 + 0.995632i \(0.529761\pi\)
\(62\) 15.1901 1.92915
\(63\) 4.13717 0.521234
\(64\) 22.8228 2.85285
\(65\) 18.1329 2.24911
\(66\) 3.41316 0.420132
\(67\) −15.7266 −1.92131 −0.960653 0.277751i \(-0.910411\pi\)
−0.960653 + 0.277751i \(0.910411\pi\)
\(68\) 5.28690 0.641130
\(69\) 5.79289 0.697382
\(70\) −36.7884 −4.39706
\(71\) −0.751536 −0.0891910 −0.0445955 0.999005i \(-0.514200\pi\)
−0.0445955 + 0.999005i \(0.514200\pi\)
\(72\) −8.87273 −1.04566
\(73\) 8.74535 1.02357 0.511783 0.859115i \(-0.328985\pi\)
0.511783 + 0.859115i \(0.328985\pi\)
\(74\) −26.7085 −3.10480
\(75\) −5.85108 −0.675625
\(76\) 19.8270 2.27431
\(77\) 5.23105 0.596134
\(78\) 14.8594 1.68250
\(79\) −8.70356 −0.979227 −0.489614 0.871939i \(-0.662862\pi\)
−0.489614 + 0.871939i \(0.662862\pi\)
\(80\) 44.0667 4.92681
\(81\) 1.00000 0.111111
\(82\) −10.0603 −1.11097
\(83\) −8.79348 −0.965210 −0.482605 0.875838i \(-0.660309\pi\)
−0.482605 + 0.875838i \(0.660309\pi\)
\(84\) −21.8728 −2.38652
\(85\) 3.29410 0.357295
\(86\) 8.73632 0.942062
\(87\) −1.48332 −0.159029
\(88\) −11.2187 −1.19592
\(89\) 4.33618 0.459634 0.229817 0.973234i \(-0.426187\pi\)
0.229817 + 0.973234i \(0.426187\pi\)
\(90\) −8.89217 −0.937317
\(91\) 22.7737 2.38733
\(92\) −30.6264 −3.19302
\(93\) 5.62716 0.583510
\(94\) −4.74151 −0.489049
\(95\) 12.3536 1.26745
\(96\) 18.3660 1.87447
\(97\) 12.3848 1.25749 0.628744 0.777612i \(-0.283569\pi\)
0.628744 + 0.777612i \(0.283569\pi\)
\(98\) −27.3078 −2.75851
\(99\) 1.26440 0.127077
\(100\) 30.9341 3.09341
\(101\) 9.24128 0.919542 0.459771 0.888038i \(-0.347932\pi\)
0.459771 + 0.888038i \(0.347932\pi\)
\(102\) 2.69942 0.267283
\(103\) −8.06351 −0.794521 −0.397261 0.917706i \(-0.630039\pi\)
−0.397261 + 0.917706i \(0.630039\pi\)
\(104\) −48.8413 −4.78929
\(105\) −13.6282 −1.32998
\(106\) 17.7683 1.72581
\(107\) 19.4006 1.87553 0.937763 0.347277i \(-0.112894\pi\)
0.937763 + 0.347277i \(0.112894\pi\)
\(108\) −5.28690 −0.508732
\(109\) −8.87914 −0.850467 −0.425234 0.905084i \(-0.639808\pi\)
−0.425234 + 0.905084i \(0.639808\pi\)
\(110\) −11.2433 −1.07201
\(111\) −9.89414 −0.939110
\(112\) 55.3448 5.22960
\(113\) 12.5063 1.17650 0.588249 0.808680i \(-0.299818\pi\)
0.588249 + 0.808680i \(0.299818\pi\)
\(114\) 10.1234 0.948146
\(115\) −19.0824 −1.77944
\(116\) 7.84215 0.728126
\(117\) 5.50466 0.508906
\(118\) 35.3126 3.25079
\(119\) 4.13717 0.379254
\(120\) 29.2276 2.66811
\(121\) −9.40128 −0.854662
\(122\) 3.93666 0.356409
\(123\) −3.72683 −0.336037
\(124\) −29.7502 −2.67165
\(125\) 2.80355 0.250757
\(126\) −11.1680 −0.994922
\(127\) 2.80959 0.249311 0.124655 0.992200i \(-0.460217\pi\)
0.124655 + 0.992200i \(0.460217\pi\)
\(128\) −24.8763 −2.19877
\(129\) 3.23636 0.284946
\(130\) −48.9484 −4.29305
\(131\) 13.3474 1.16617 0.583086 0.812410i \(-0.301845\pi\)
0.583086 + 0.812410i \(0.301845\pi\)
\(132\) −6.68477 −0.581835
\(133\) 15.5153 1.34535
\(134\) 42.4527 3.66735
\(135\) −3.29410 −0.283511
\(136\) −8.87273 −0.760830
\(137\) −12.2063 −1.04285 −0.521426 0.853296i \(-0.674600\pi\)
−0.521426 + 0.853296i \(0.674600\pi\)
\(138\) −15.6375 −1.33115
\(139\) 14.7339 1.24971 0.624856 0.780740i \(-0.285158\pi\)
0.624856 + 0.780740i \(0.285158\pi\)
\(140\) 72.0511 6.08943
\(141\) −1.75649 −0.147923
\(142\) 2.02872 0.170246
\(143\) 6.96011 0.582034
\(144\) 13.3775 1.11479
\(145\) 4.88620 0.405777
\(146\) −23.6074 −1.95376
\(147\) −10.1162 −0.834367
\(148\) 52.3093 4.29980
\(149\) 3.66511 0.300257 0.150129 0.988666i \(-0.452031\pi\)
0.150129 + 0.988666i \(0.452031\pi\)
\(150\) 15.7946 1.28962
\(151\) 5.80463 0.472374 0.236187 0.971708i \(-0.424102\pi\)
0.236187 + 0.971708i \(0.424102\pi\)
\(152\) −33.2747 −2.69893
\(153\) 1.00000 0.0808452
\(154\) −14.1208 −1.13789
\(155\) −18.5364 −1.48888
\(156\) −29.1025 −2.33007
\(157\) −1.00000 −0.0798087
\(158\) 23.4946 1.86913
\(159\) 6.58226 0.522007
\(160\) −60.4995 −4.78290
\(161\) −23.9662 −1.88880
\(162\) −2.69942 −0.212087
\(163\) 16.4903 1.29162 0.645812 0.763497i \(-0.276519\pi\)
0.645812 + 0.763497i \(0.276519\pi\)
\(164\) 19.7034 1.53857
\(165\) −4.16507 −0.324250
\(166\) 23.7373 1.84238
\(167\) −2.85685 −0.221070 −0.110535 0.993872i \(-0.535256\pi\)
−0.110535 + 0.993872i \(0.535256\pi\)
\(168\) 36.7080 2.83208
\(169\) 17.3013 1.33087
\(170\) −8.89217 −0.681998
\(171\) 3.75022 0.286786
\(172\) −17.1103 −1.30465
\(173\) 24.1347 1.83493 0.917464 0.397819i \(-0.130233\pi\)
0.917464 + 0.397819i \(0.130233\pi\)
\(174\) 4.00411 0.303551
\(175\) 24.2069 1.82987
\(176\) 16.9145 1.27498
\(177\) 13.0815 0.983269
\(178\) −11.7052 −0.877341
\(179\) −16.6698 −1.24596 −0.622978 0.782239i \(-0.714077\pi\)
−0.622978 + 0.782239i \(0.714077\pi\)
\(180\) 17.4156 1.29808
\(181\) 6.75382 0.502007 0.251004 0.967986i \(-0.419239\pi\)
0.251004 + 0.967986i \(0.419239\pi\)
\(182\) −61.4759 −4.55690
\(183\) 1.45833 0.107803
\(184\) 51.3988 3.78917
\(185\) 32.5923 2.39623
\(186\) −15.1901 −1.11379
\(187\) 1.26440 0.0924624
\(188\) 9.28637 0.677278
\(189\) −4.13717 −0.300935
\(190\) −33.3476 −2.41929
\(191\) 9.45313 0.684004 0.342002 0.939699i \(-0.388895\pi\)
0.342002 + 0.939699i \(0.388895\pi\)
\(192\) −22.8228 −1.64709
\(193\) 12.3474 0.888786 0.444393 0.895832i \(-0.353419\pi\)
0.444393 + 0.895832i \(0.353419\pi\)
\(194\) −33.4319 −2.40027
\(195\) −18.1329 −1.29852
\(196\) 53.4831 3.82022
\(197\) 13.4501 0.958279 0.479140 0.877739i \(-0.340949\pi\)
0.479140 + 0.877739i \(0.340949\pi\)
\(198\) −3.41316 −0.242563
\(199\) 11.4664 0.812830 0.406415 0.913689i \(-0.366779\pi\)
0.406415 + 0.913689i \(0.366779\pi\)
\(200\) −51.9151 −3.67095
\(201\) 15.7266 1.10927
\(202\) −24.9461 −1.75520
\(203\) 6.13674 0.430715
\(204\) −5.28690 −0.370157
\(205\) 12.2765 0.857431
\(206\) 21.7668 1.51657
\(207\) −5.79289 −0.402634
\(208\) 73.6384 5.10590
\(209\) 4.74179 0.327997
\(210\) 36.7884 2.53864
\(211\) −16.7940 −1.15615 −0.578074 0.815985i \(-0.696195\pi\)
−0.578074 + 0.815985i \(0.696195\pi\)
\(212\) −34.7997 −2.39005
\(213\) 0.751536 0.0514944
\(214\) −52.3704 −3.57997
\(215\) −10.6609 −0.727067
\(216\) 8.87273 0.603713
\(217\) −23.2805 −1.58038
\(218\) 23.9686 1.62336
\(219\) −8.74535 −0.590956
\(220\) 22.0203 1.48461
\(221\) 5.50466 0.370283
\(222\) 26.7085 1.79256
\(223\) 12.6977 0.850299 0.425149 0.905123i \(-0.360222\pi\)
0.425149 + 0.905123i \(0.360222\pi\)
\(224\) −75.9833 −5.07685
\(225\) 5.85108 0.390072
\(226\) −33.7599 −2.24568
\(227\) 6.99675 0.464390 0.232195 0.972669i \(-0.425409\pi\)
0.232195 + 0.972669i \(0.425409\pi\)
\(228\) −19.8270 −1.31308
\(229\) 23.4790 1.55154 0.775769 0.631017i \(-0.217362\pi\)
0.775769 + 0.631017i \(0.217362\pi\)
\(230\) 51.5114 3.39656
\(231\) −5.23105 −0.344178
\(232\) −13.1611 −0.864068
\(233\) −0.513616 −0.0336481 −0.0168240 0.999858i \(-0.505356\pi\)
−0.0168240 + 0.999858i \(0.505356\pi\)
\(234\) −14.8594 −0.971390
\(235\) 5.78604 0.377440
\(236\) −69.1607 −4.50198
\(237\) 8.70356 0.565357
\(238\) −11.1680 −0.723912
\(239\) 1.99661 0.129150 0.0645750 0.997913i \(-0.479431\pi\)
0.0645750 + 0.997913i \(0.479431\pi\)
\(240\) −44.0667 −2.84449
\(241\) 8.78995 0.566211 0.283105 0.959089i \(-0.408635\pi\)
0.283105 + 0.959089i \(0.408635\pi\)
\(242\) 25.3781 1.63136
\(243\) −1.00000 −0.0641500
\(244\) −7.71006 −0.493586
\(245\) 33.3236 2.12897
\(246\) 10.0603 0.641421
\(247\) 20.6437 1.31352
\(248\) 49.9283 3.17045
\(249\) 8.79348 0.557264
\(250\) −7.56797 −0.478640
\(251\) 15.1706 0.957559 0.478780 0.877935i \(-0.341079\pi\)
0.478780 + 0.877935i \(0.341079\pi\)
\(252\) 21.8728 1.37786
\(253\) −7.32456 −0.460491
\(254\) −7.58428 −0.475880
\(255\) −3.29410 −0.206284
\(256\) 21.5061 1.34413
\(257\) −6.41622 −0.400233 −0.200116 0.979772i \(-0.564132\pi\)
−0.200116 + 0.979772i \(0.564132\pi\)
\(258\) −8.73632 −0.543900
\(259\) 40.9337 2.54350
\(260\) 95.8666 5.94540
\(261\) 1.48332 0.0918152
\(262\) −36.0304 −2.22597
\(263\) −13.0807 −0.806588 −0.403294 0.915070i \(-0.632135\pi\)
−0.403294 + 0.915070i \(0.632135\pi\)
\(264\) 11.2187 0.690464
\(265\) −21.6826 −1.33195
\(266\) −41.8823 −2.56797
\(267\) −4.33618 −0.265370
\(268\) −83.1447 −5.07887
\(269\) −23.3216 −1.42194 −0.710971 0.703221i \(-0.751744\pi\)
−0.710971 + 0.703221i \(0.751744\pi\)
\(270\) 8.89217 0.541160
\(271\) 14.2253 0.864125 0.432062 0.901844i \(-0.357786\pi\)
0.432062 + 0.901844i \(0.357786\pi\)
\(272\) 13.3775 0.811128
\(273\) −22.7737 −1.37833
\(274\) 32.9499 1.99058
\(275\) 7.39813 0.446124
\(276\) 30.6264 1.84349
\(277\) −14.6727 −0.881598 −0.440799 0.897606i \(-0.645305\pi\)
−0.440799 + 0.897606i \(0.645305\pi\)
\(278\) −39.7730 −2.38543
\(279\) −5.62716 −0.336889
\(280\) −120.920 −7.22633
\(281\) −21.5555 −1.28589 −0.642946 0.765912i \(-0.722288\pi\)
−0.642946 + 0.765912i \(0.722288\pi\)
\(282\) 4.74151 0.282353
\(283\) 23.2166 1.38008 0.690042 0.723769i \(-0.257592\pi\)
0.690042 + 0.723769i \(0.257592\pi\)
\(284\) −3.97329 −0.235772
\(285\) −12.3536 −0.731763
\(286\) −18.7883 −1.11098
\(287\) 15.4185 0.910127
\(288\) −18.3660 −1.08223
\(289\) 1.00000 0.0588235
\(290\) −13.1899 −0.774539
\(291\) −12.3848 −0.726011
\(292\) 46.2357 2.70574
\(293\) −26.1234 −1.52615 −0.763073 0.646312i \(-0.776310\pi\)
−0.763073 + 0.646312i \(0.776310\pi\)
\(294\) 27.3078 1.59262
\(295\) −43.0919 −2.50891
\(296\) −87.7880 −5.10257
\(297\) −1.26440 −0.0733682
\(298\) −9.89368 −0.573126
\(299\) −31.8879 −1.84412
\(300\) −30.9341 −1.78598
\(301\) −13.3894 −0.771751
\(302\) −15.6692 −0.901659
\(303\) −9.24128 −0.530898
\(304\) 50.1684 2.87736
\(305\) −4.80390 −0.275070
\(306\) −2.69942 −0.154316
\(307\) 25.8888 1.47755 0.738776 0.673951i \(-0.235404\pi\)
0.738776 + 0.673951i \(0.235404\pi\)
\(308\) 27.6560 1.57585
\(309\) 8.06351 0.458717
\(310\) 50.0377 2.84195
\(311\) −6.70284 −0.380083 −0.190041 0.981776i \(-0.560862\pi\)
−0.190041 + 0.981776i \(0.560862\pi\)
\(312\) 48.8413 2.76510
\(313\) 10.8671 0.614243 0.307121 0.951670i \(-0.400634\pi\)
0.307121 + 0.951670i \(0.400634\pi\)
\(314\) 2.69942 0.152337
\(315\) 13.6282 0.767864
\(316\) −46.0148 −2.58854
\(317\) 21.2873 1.19561 0.597806 0.801641i \(-0.296039\pi\)
0.597806 + 0.801641i \(0.296039\pi\)
\(318\) −17.7683 −0.996397
\(319\) 1.87552 0.105009
\(320\) 75.1804 4.20271
\(321\) −19.4006 −1.08283
\(322\) 64.6949 3.60530
\(323\) 3.75022 0.208668
\(324\) 5.28690 0.293716
\(325\) 32.2082 1.78659
\(326\) −44.5144 −2.46543
\(327\) 8.87914 0.491018
\(328\) −33.0672 −1.82583
\(329\) 7.26689 0.400636
\(330\) 11.2433 0.618923
\(331\) 6.85976 0.377047 0.188523 0.982069i \(-0.439630\pi\)
0.188523 + 0.982069i \(0.439630\pi\)
\(332\) −46.4902 −2.55148
\(333\) 9.89414 0.542196
\(334\) 7.71185 0.421974
\(335\) −51.8049 −2.83040
\(336\) −55.3448 −3.01931
\(337\) −17.9501 −0.977802 −0.488901 0.872339i \(-0.662602\pi\)
−0.488901 + 0.872339i \(0.662602\pi\)
\(338\) −46.7034 −2.54033
\(339\) −12.5063 −0.679251
\(340\) 17.4156 0.944491
\(341\) −7.11501 −0.385299
\(342\) −10.1234 −0.547412
\(343\) 12.8921 0.696108
\(344\) 28.7154 1.54823
\(345\) 19.0824 1.02736
\(346\) −65.1498 −3.50248
\(347\) 12.8958 0.692280 0.346140 0.938183i \(-0.387492\pi\)
0.346140 + 0.938183i \(0.387492\pi\)
\(348\) −7.84215 −0.420384
\(349\) −24.5721 −1.31531 −0.657657 0.753317i \(-0.728453\pi\)
−0.657657 + 0.753317i \(0.728453\pi\)
\(350\) −65.3447 −3.49282
\(351\) −5.50466 −0.293817
\(352\) −23.2221 −1.23774
\(353\) 16.8630 0.897525 0.448762 0.893651i \(-0.351865\pi\)
0.448762 + 0.893651i \(0.351865\pi\)
\(354\) −35.3126 −1.87685
\(355\) −2.47563 −0.131393
\(356\) 22.9249 1.21502
\(357\) −4.13717 −0.218962
\(358\) 44.9988 2.37826
\(359\) −32.0361 −1.69080 −0.845400 0.534133i \(-0.820638\pi\)
−0.845400 + 0.534133i \(0.820638\pi\)
\(360\) −29.2276 −1.54043
\(361\) −4.93587 −0.259783
\(362\) −18.2314 −0.958222
\(363\) 9.40128 0.493439
\(364\) 120.402 6.31079
\(365\) 28.8080 1.50788
\(366\) −3.93666 −0.205773
\(367\) −6.99587 −0.365181 −0.182591 0.983189i \(-0.558448\pi\)
−0.182591 + 0.983189i \(0.558448\pi\)
\(368\) −77.4942 −4.03967
\(369\) 3.72683 0.194011
\(370\) −87.9804 −4.57388
\(371\) −27.2319 −1.41381
\(372\) 29.7502 1.54248
\(373\) −13.1290 −0.679796 −0.339898 0.940462i \(-0.610393\pi\)
−0.339898 + 0.940462i \(0.610393\pi\)
\(374\) −3.41316 −0.176491
\(375\) −2.80355 −0.144775
\(376\) −15.5848 −0.803727
\(377\) 8.16516 0.420527
\(378\) 11.1680 0.574419
\(379\) −14.3639 −0.737822 −0.368911 0.929465i \(-0.620269\pi\)
−0.368911 + 0.929465i \(0.620269\pi\)
\(380\) 65.3121 3.35044
\(381\) −2.80959 −0.143940
\(382\) −25.5180 −1.30562
\(383\) −15.1396 −0.773598 −0.386799 0.922164i \(-0.626419\pi\)
−0.386799 + 0.922164i \(0.626419\pi\)
\(384\) 24.8763 1.26946
\(385\) 17.2316 0.878204
\(386\) −33.3309 −1.69650
\(387\) −3.23636 −0.164514
\(388\) 65.4772 3.32410
\(389\) −10.9027 −0.552790 −0.276395 0.961044i \(-0.589140\pi\)
−0.276395 + 0.961044i \(0.589140\pi\)
\(390\) 48.9484 2.47860
\(391\) −5.79289 −0.292959
\(392\) −89.7580 −4.53346
\(393\) −13.3474 −0.673290
\(394\) −36.3075 −1.82915
\(395\) −28.6704 −1.44256
\(396\) 6.68477 0.335923
\(397\) −33.6495 −1.68882 −0.844409 0.535699i \(-0.820048\pi\)
−0.844409 + 0.535699i \(0.820048\pi\)
\(398\) −30.9526 −1.55151
\(399\) −15.5153 −0.776736
\(400\) 78.2727 3.91363
\(401\) 15.4442 0.771244 0.385622 0.922657i \(-0.373987\pi\)
0.385622 + 0.922657i \(0.373987\pi\)
\(402\) −42.4527 −2.11735
\(403\) −30.9756 −1.54300
\(404\) 48.8577 2.43076
\(405\) 3.29410 0.163685
\(406\) −16.5657 −0.822141
\(407\) 12.5102 0.620107
\(408\) 8.87273 0.439265
\(409\) −34.8077 −1.72113 −0.860565 0.509340i \(-0.829890\pi\)
−0.860565 + 0.509340i \(0.829890\pi\)
\(410\) −33.1396 −1.63665
\(411\) 12.2063 0.602091
\(412\) −42.6309 −2.10028
\(413\) −54.1205 −2.66310
\(414\) 15.6375 0.768540
\(415\) −28.9666 −1.42191
\(416\) −101.099 −4.95677
\(417\) −14.7339 −0.721521
\(418\) −12.8001 −0.626074
\(419\) −23.5329 −1.14966 −0.574829 0.818273i \(-0.694932\pi\)
−0.574829 + 0.818273i \(0.694932\pi\)
\(420\) −72.0511 −3.51573
\(421\) 0.165111 0.00804701 0.00402350 0.999992i \(-0.498719\pi\)
0.00402350 + 0.999992i \(0.498719\pi\)
\(422\) 45.3342 2.20683
\(423\) 1.75649 0.0854034
\(424\) 58.4026 2.83628
\(425\) 5.85108 0.283819
\(426\) −2.02872 −0.0982916
\(427\) −6.03337 −0.291975
\(428\) 102.569 4.95785
\(429\) −6.96011 −0.336037
\(430\) 28.7783 1.38781
\(431\) 16.3564 0.787859 0.393929 0.919141i \(-0.371115\pi\)
0.393929 + 0.919141i \(0.371115\pi\)
\(432\) −13.3775 −0.643624
\(433\) −21.1189 −1.01491 −0.507454 0.861679i \(-0.669413\pi\)
−0.507454 + 0.861679i \(0.669413\pi\)
\(434\) 62.8440 3.01661
\(435\) −4.88620 −0.234275
\(436\) −46.9431 −2.24817
\(437\) −21.7246 −1.03923
\(438\) 23.6074 1.12801
\(439\) −7.14242 −0.340889 −0.170445 0.985367i \(-0.554520\pi\)
−0.170445 + 0.985367i \(0.554520\pi\)
\(440\) −36.9555 −1.76179
\(441\) 10.1162 0.481722
\(442\) −14.8594 −0.706790
\(443\) 22.1067 1.05032 0.525159 0.851004i \(-0.324006\pi\)
0.525159 + 0.851004i \(0.324006\pi\)
\(444\) −52.3093 −2.48249
\(445\) 14.2838 0.677117
\(446\) −34.2764 −1.62303
\(447\) −3.66511 −0.173354
\(448\) 94.4216 4.46100
\(449\) 8.84021 0.417195 0.208598 0.978002i \(-0.433110\pi\)
0.208598 + 0.978002i \(0.433110\pi\)
\(450\) −15.7946 −0.744563
\(451\) 4.71222 0.221890
\(452\) 66.1197 3.11001
\(453\) −5.80463 −0.272725
\(454\) −18.8872 −0.886420
\(455\) 75.0188 3.51693
\(456\) 33.2747 1.55823
\(457\) 7.66476 0.358542 0.179271 0.983800i \(-0.442626\pi\)
0.179271 + 0.983800i \(0.442626\pi\)
\(458\) −63.3799 −2.96155
\(459\) −1.00000 −0.0466760
\(460\) −100.886 −4.70385
\(461\) 35.1633 1.63772 0.818860 0.573994i \(-0.194607\pi\)
0.818860 + 0.573994i \(0.194607\pi\)
\(462\) 14.1208 0.656961
\(463\) 19.5807 0.909992 0.454996 0.890493i \(-0.349641\pi\)
0.454996 + 0.890493i \(0.349641\pi\)
\(464\) 19.8431 0.921191
\(465\) 18.5364 0.859606
\(466\) 1.38647 0.0642268
\(467\) 13.9284 0.644532 0.322266 0.946649i \(-0.395556\pi\)
0.322266 + 0.946649i \(0.395556\pi\)
\(468\) 29.1025 1.34527
\(469\) −65.0635 −3.00435
\(470\) −15.6190 −0.720450
\(471\) 1.00000 0.0460776
\(472\) 116.069 5.34251
\(473\) −4.09207 −0.188154
\(474\) −23.4946 −1.07914
\(475\) 21.9428 1.00681
\(476\) 21.8728 1.00254
\(477\) −6.58226 −0.301381
\(478\) −5.38970 −0.246519
\(479\) 24.4521 1.11725 0.558623 0.829422i \(-0.311330\pi\)
0.558623 + 0.829422i \(0.311330\pi\)
\(480\) 60.4995 2.76141
\(481\) 54.4639 2.48334
\(482\) −23.7278 −1.08077
\(483\) 23.9662 1.09050
\(484\) −49.7036 −2.25925
\(485\) 40.7968 1.85249
\(486\) 2.69942 0.122448
\(487\) −23.0199 −1.04313 −0.521566 0.853211i \(-0.674652\pi\)
−0.521566 + 0.853211i \(0.674652\pi\)
\(488\) 12.9394 0.585739
\(489\) −16.4903 −0.745719
\(490\) −89.9547 −4.06374
\(491\) 41.0352 1.85189 0.925947 0.377654i \(-0.123269\pi\)
0.925947 + 0.377654i \(0.123269\pi\)
\(492\) −19.7034 −0.888296
\(493\) 1.48332 0.0668053
\(494\) −55.7260 −2.50723
\(495\) 4.16507 0.187206
\(496\) −75.2772 −3.38005
\(497\) −3.10923 −0.139468
\(498\) −23.7373 −1.06370
\(499\) −39.1034 −1.75051 −0.875254 0.483663i \(-0.839306\pi\)
−0.875254 + 0.483663i \(0.839306\pi\)
\(500\) 14.8221 0.662863
\(501\) 2.85685 0.127635
\(502\) −40.9519 −1.82777
\(503\) 0.772059 0.0344244 0.0172122 0.999852i \(-0.494521\pi\)
0.0172122 + 0.999852i \(0.494521\pi\)
\(504\) −36.7080 −1.63510
\(505\) 30.4417 1.35464
\(506\) 19.7721 0.878977
\(507\) −17.3013 −0.768376
\(508\) 14.8540 0.659040
\(509\) −36.1631 −1.60290 −0.801450 0.598061i \(-0.795938\pi\)
−0.801450 + 0.598061i \(0.795938\pi\)
\(510\) 8.89217 0.393752
\(511\) 36.1810 1.60055
\(512\) −8.30164 −0.366884
\(513\) −3.75022 −0.165576
\(514\) 17.3201 0.763957
\(515\) −26.5620 −1.17046
\(516\) 17.1103 0.753240
\(517\) 2.22091 0.0976756
\(518\) −110.498 −4.85498
\(519\) −24.1347 −1.05940
\(520\) −160.888 −7.05541
\(521\) 15.7118 0.688346 0.344173 0.938906i \(-0.388159\pi\)
0.344173 + 0.938906i \(0.388159\pi\)
\(522\) −4.00411 −0.175255
\(523\) 35.2225 1.54017 0.770087 0.637939i \(-0.220213\pi\)
0.770087 + 0.637939i \(0.220213\pi\)
\(524\) 70.5666 3.08271
\(525\) −24.2069 −1.05648
\(526\) 35.3103 1.53960
\(527\) −5.62716 −0.245123
\(528\) −16.9145 −0.736111
\(529\) 10.5576 0.459026
\(530\) 58.5306 2.54240
\(531\) −13.0815 −0.567691
\(532\) 82.0277 3.55635
\(533\) 20.5149 0.888600
\(534\) 11.7052 0.506533
\(535\) 63.9074 2.76296
\(536\) 139.538 6.02710
\(537\) 16.6698 0.719353
\(538\) 62.9549 2.71418
\(539\) 12.7909 0.550944
\(540\) −17.4156 −0.749446
\(541\) −18.0113 −0.774367 −0.387183 0.922003i \(-0.626552\pi\)
−0.387183 + 0.922003i \(0.626552\pi\)
\(542\) −38.4001 −1.64943
\(543\) −6.75382 −0.289834
\(544\) −18.3660 −0.787437
\(545\) −29.2488 −1.25288
\(546\) 61.4759 2.63092
\(547\) 19.9297 0.852133 0.426066 0.904692i \(-0.359899\pi\)
0.426066 + 0.904692i \(0.359899\pi\)
\(548\) −64.5333 −2.75673
\(549\) −1.45833 −0.0622402
\(550\) −19.9707 −0.851554
\(551\) 5.56277 0.236982
\(552\) −51.3988 −2.18768
\(553\) −36.0081 −1.53122
\(554\) 39.6079 1.68278
\(555\) −32.5923 −1.38346
\(556\) 77.8965 3.30355
\(557\) −12.8291 −0.543586 −0.271793 0.962356i \(-0.587617\pi\)
−0.271793 + 0.962356i \(0.587617\pi\)
\(558\) 15.1901 0.643048
\(559\) −17.8151 −0.753497
\(560\) 182.311 7.70406
\(561\) −1.26440 −0.0533832
\(562\) 58.1874 2.45449
\(563\) −26.8621 −1.13210 −0.566052 0.824370i \(-0.691530\pi\)
−0.566052 + 0.824370i \(0.691530\pi\)
\(564\) −9.28637 −0.391027
\(565\) 41.1971 1.73318
\(566\) −62.6715 −2.63428
\(567\) 4.13717 0.173745
\(568\) 6.66818 0.279790
\(569\) −11.9965 −0.502920 −0.251460 0.967868i \(-0.580911\pi\)
−0.251460 + 0.967868i \(0.580911\pi\)
\(570\) 33.3476 1.39678
\(571\) 9.73093 0.407227 0.203613 0.979051i \(-0.434731\pi\)
0.203613 + 0.979051i \(0.434731\pi\)
\(572\) 36.7974 1.53858
\(573\) −9.45313 −0.394910
\(574\) −41.6212 −1.73723
\(575\) −33.8947 −1.41351
\(576\) 22.8228 0.950948
\(577\) 44.0985 1.83584 0.917922 0.396760i \(-0.129865\pi\)
0.917922 + 0.396760i \(0.129865\pi\)
\(578\) −2.69942 −0.112281
\(579\) −12.3474 −0.513141
\(580\) 25.8328 1.07265
\(581\) −36.3801 −1.50930
\(582\) 33.4319 1.38580
\(583\) −8.32264 −0.344688
\(584\) −77.5951 −3.21091
\(585\) 18.1329 0.749702
\(586\) 70.5182 2.91308
\(587\) −6.53569 −0.269757 −0.134878 0.990862i \(-0.543064\pi\)
−0.134878 + 0.990862i \(0.543064\pi\)
\(588\) −53.4831 −2.20561
\(589\) −21.1031 −0.869537
\(590\) 116.323 4.78895
\(591\) −13.4501 −0.553263
\(592\) 132.359 5.43990
\(593\) 31.7624 1.30432 0.652162 0.758080i \(-0.273862\pi\)
0.652162 + 0.758080i \(0.273862\pi\)
\(594\) 3.41316 0.140044
\(595\) 13.6282 0.558703
\(596\) 19.3770 0.793714
\(597\) −11.4664 −0.469287
\(598\) 86.0790 3.52003
\(599\) −15.8996 −0.649640 −0.324820 0.945776i \(-0.605304\pi\)
−0.324820 + 0.945776i \(0.605304\pi\)
\(600\) 51.9151 2.11942
\(601\) 21.8923 0.893006 0.446503 0.894782i \(-0.352669\pi\)
0.446503 + 0.894782i \(0.352669\pi\)
\(602\) 36.1436 1.47310
\(603\) −15.7266 −0.640435
\(604\) 30.6885 1.24870
\(605\) −30.9687 −1.25906
\(606\) 24.9461 1.01337
\(607\) −39.9993 −1.62352 −0.811761 0.583990i \(-0.801491\pi\)
−0.811761 + 0.583990i \(0.801491\pi\)
\(608\) −68.8766 −2.79331
\(609\) −6.13674 −0.248673
\(610\) 12.9678 0.525049
\(611\) 9.66886 0.391160
\(612\) 5.28690 0.213710
\(613\) 10.2120 0.412458 0.206229 0.978504i \(-0.433881\pi\)
0.206229 + 0.978504i \(0.433881\pi\)
\(614\) −69.8849 −2.82032
\(615\) −12.2765 −0.495038
\(616\) −46.4137 −1.87006
\(617\) 23.5999 0.950096 0.475048 0.879960i \(-0.342431\pi\)
0.475048 + 0.879960i \(0.342431\pi\)
\(618\) −21.7668 −0.875591
\(619\) 13.6338 0.547988 0.273994 0.961731i \(-0.411655\pi\)
0.273994 + 0.961731i \(0.411655\pi\)
\(620\) −98.0001 −3.93578
\(621\) 5.79289 0.232461
\(622\) 18.0938 0.725495
\(623\) 17.9395 0.718731
\(624\) −73.6384 −2.94789
\(625\) −20.0202 −0.800810
\(626\) −29.3348 −1.17246
\(627\) −4.74179 −0.189369
\(628\) −5.28690 −0.210970
\(629\) 9.89414 0.394505
\(630\) −36.7884 −1.46569
\(631\) −45.5123 −1.81182 −0.905909 0.423472i \(-0.860811\pi\)
−0.905909 + 0.423472i \(0.860811\pi\)
\(632\) 77.2243 3.07182
\(633\) 16.7940 0.667502
\(634\) −57.4634 −2.28216
\(635\) 9.25507 0.367276
\(636\) 34.7997 1.37990
\(637\) 55.6860 2.20636
\(638\) −5.06281 −0.200439
\(639\) −0.751536 −0.0297303
\(640\) −81.9449 −3.23916
\(641\) −33.4518 −1.32127 −0.660633 0.750709i \(-0.729712\pi\)
−0.660633 + 0.750709i \(0.729712\pi\)
\(642\) 52.3704 2.06690
\(643\) 7.51082 0.296198 0.148099 0.988973i \(-0.452685\pi\)
0.148099 + 0.988973i \(0.452685\pi\)
\(644\) −126.707 −4.99294
\(645\) 10.6609 0.419773
\(646\) −10.1234 −0.398301
\(647\) −16.9500 −0.666374 −0.333187 0.942861i \(-0.608124\pi\)
−0.333187 + 0.942861i \(0.608124\pi\)
\(648\) −8.87273 −0.348554
\(649\) −16.5404 −0.649266
\(650\) −86.9436 −3.41021
\(651\) 23.2805 0.912436
\(652\) 87.1827 3.41434
\(653\) −32.0471 −1.25410 −0.627049 0.778980i \(-0.715738\pi\)
−0.627049 + 0.778980i \(0.715738\pi\)
\(654\) −23.9686 −0.937245
\(655\) 43.9678 1.71796
\(656\) 49.8556 1.94653
\(657\) 8.74535 0.341188
\(658\) −19.6164 −0.764728
\(659\) 12.3092 0.479497 0.239749 0.970835i \(-0.422935\pi\)
0.239749 + 0.970835i \(0.422935\pi\)
\(660\) −22.0203 −0.857139
\(661\) −17.5377 −0.682138 −0.341069 0.940038i \(-0.610789\pi\)
−0.341069 + 0.940038i \(0.610789\pi\)
\(662\) −18.5174 −0.719700
\(663\) −5.50466 −0.213783
\(664\) 78.0222 3.02785
\(665\) 51.1089 1.98192
\(666\) −26.7085 −1.03493
\(667\) −8.59271 −0.332711
\(668\) −15.1039 −0.584386
\(669\) −12.6977 −0.490920
\(670\) 139.843 5.40262
\(671\) −1.84392 −0.0711839
\(672\) 75.9833 2.93112
\(673\) −10.9126 −0.420648 −0.210324 0.977632i \(-0.567452\pi\)
−0.210324 + 0.977632i \(0.567452\pi\)
\(674\) 48.4548 1.86641
\(675\) −5.85108 −0.225208
\(676\) 91.4699 3.51807
\(677\) 16.7562 0.643994 0.321997 0.946741i \(-0.395646\pi\)
0.321997 + 0.946741i \(0.395646\pi\)
\(678\) 33.7599 1.29654
\(679\) 51.2381 1.96634
\(680\) −29.2276 −1.12083
\(681\) −6.99675 −0.268116
\(682\) 19.2064 0.735452
\(683\) 43.1298 1.65031 0.825157 0.564903i \(-0.191086\pi\)
0.825157 + 0.564903i \(0.191086\pi\)
\(684\) 19.8270 0.758105
\(685\) −40.2087 −1.53629
\(686\) −34.8013 −1.32872
\(687\) −23.4790 −0.895781
\(688\) −43.2944 −1.65058
\(689\) −36.2331 −1.38037
\(690\) −51.5114 −1.96101
\(691\) 28.0457 1.06691 0.533455 0.845829i \(-0.320893\pi\)
0.533455 + 0.845829i \(0.320893\pi\)
\(692\) 127.598 4.85054
\(693\) 5.23105 0.198711
\(694\) −34.8111 −1.32141
\(695\) 48.5348 1.84103
\(696\) 13.1611 0.498870
\(697\) 3.72683 0.141164
\(698\) 66.3306 2.51065
\(699\) 0.513616 0.0194267
\(700\) 127.979 4.83717
\(701\) −47.0710 −1.77785 −0.888924 0.458056i \(-0.848546\pi\)
−0.888924 + 0.458056i \(0.848546\pi\)
\(702\) 14.8594 0.560832
\(703\) 37.1052 1.39945
\(704\) 28.8572 1.08760
\(705\) −5.78604 −0.217915
\(706\) −45.5203 −1.71318
\(707\) 38.2327 1.43789
\(708\) 69.1607 2.59922
\(709\) 47.8561 1.79727 0.898637 0.438693i \(-0.144558\pi\)
0.898637 + 0.438693i \(0.144558\pi\)
\(710\) 6.68279 0.250801
\(711\) −8.70356 −0.326409
\(712\) −38.4737 −1.44186
\(713\) 32.5975 1.22079
\(714\) 11.1680 0.417951
\(715\) 22.9273 0.857432
\(716\) −88.1313 −3.29362
\(717\) −1.99661 −0.0745648
\(718\) 86.4790 3.22737
\(719\) −36.5954 −1.36478 −0.682389 0.730989i \(-0.739059\pi\)
−0.682389 + 0.730989i \(0.739059\pi\)
\(720\) 44.0667 1.64227
\(721\) −33.3601 −1.24240
\(722\) 13.3240 0.495868
\(723\) −8.78995 −0.326902
\(724\) 35.7067 1.32703
\(725\) 8.67902 0.322331
\(726\) −25.3781 −0.941868
\(727\) −47.6172 −1.76602 −0.883011 0.469352i \(-0.844488\pi\)
−0.883011 + 0.469352i \(0.844488\pi\)
\(728\) −202.065 −7.48902
\(729\) 1.00000 0.0370370
\(730\) −77.7651 −2.87822
\(731\) −3.23636 −0.119701
\(732\) 7.71006 0.284972
\(733\) 24.2235 0.894714 0.447357 0.894355i \(-0.352365\pi\)
0.447357 + 0.894355i \(0.352365\pi\)
\(734\) 18.8848 0.697051
\(735\) −33.3236 −1.22916
\(736\) 106.392 3.92168
\(737\) −19.8847 −0.732464
\(738\) −10.0603 −0.370325
\(739\) −22.0238 −0.810160 −0.405080 0.914281i \(-0.632756\pi\)
−0.405080 + 0.914281i \(0.632756\pi\)
\(740\) 172.312 6.33431
\(741\) −20.6437 −0.758364
\(742\) 73.5105 2.69866
\(743\) −35.8856 −1.31652 −0.658258 0.752792i \(-0.728707\pi\)
−0.658258 + 0.752792i \(0.728707\pi\)
\(744\) −49.9283 −1.83046
\(745\) 12.0732 0.442329
\(746\) 35.4409 1.29758
\(747\) −8.79348 −0.321737
\(748\) 6.68477 0.244420
\(749\) 80.2635 2.93276
\(750\) 7.56797 0.276343
\(751\) −5.11360 −0.186598 −0.0932989 0.995638i \(-0.529741\pi\)
−0.0932989 + 0.995638i \(0.529741\pi\)
\(752\) 23.4974 0.856861
\(753\) −15.1706 −0.552847
\(754\) −22.0412 −0.802695
\(755\) 19.1210 0.695885
\(756\) −21.8728 −0.795505
\(757\) 38.7193 1.40728 0.703638 0.710558i \(-0.251557\pi\)
0.703638 + 0.710558i \(0.251557\pi\)
\(758\) 38.7742 1.40834
\(759\) 7.32456 0.265865
\(760\) −109.610 −3.97597
\(761\) 15.8585 0.574870 0.287435 0.957800i \(-0.407198\pi\)
0.287435 + 0.957800i \(0.407198\pi\)
\(762\) 7.58428 0.274749
\(763\) −36.7345 −1.32988
\(764\) 49.9777 1.80813
\(765\) 3.29410 0.119098
\(766\) 40.8682 1.47663
\(767\) −72.0094 −2.60011
\(768\) −21.5061 −0.776036
\(769\) 14.1488 0.510221 0.255110 0.966912i \(-0.417888\pi\)
0.255110 + 0.966912i \(0.417888\pi\)
\(770\) −46.5154 −1.67630
\(771\) 6.41622 0.231074
\(772\) 65.2795 2.34946
\(773\) −51.4829 −1.85171 −0.925855 0.377879i \(-0.876654\pi\)
−0.925855 + 0.377879i \(0.876654\pi\)
\(774\) 8.73632 0.314021
\(775\) −32.9250 −1.18270
\(776\) −109.887 −3.94472
\(777\) −40.9337 −1.46849
\(778\) 29.4311 1.05515
\(779\) 13.9764 0.500757
\(780\) −95.8666 −3.43258
\(781\) −0.950246 −0.0340025
\(782\) 15.6375 0.559195
\(783\) −1.48332 −0.0530095
\(784\) 135.329 4.83317
\(785\) −3.29410 −0.117571
\(786\) 36.0304 1.28516
\(787\) 22.7733 0.811782 0.405891 0.913922i \(-0.366961\pi\)
0.405891 + 0.913922i \(0.366961\pi\)
\(788\) 71.1092 2.53316
\(789\) 13.0807 0.465684
\(790\) 77.3936 2.75354
\(791\) 51.7408 1.83969
\(792\) −11.2187 −0.398640
\(793\) −8.02763 −0.285069
\(794\) 90.8342 3.22358
\(795\) 21.6826 0.769003
\(796\) 60.6215 2.14867
\(797\) −25.9350 −0.918667 −0.459333 0.888264i \(-0.651912\pi\)
−0.459333 + 0.888264i \(0.651912\pi\)
\(798\) 41.8823 1.48262
\(799\) 1.75649 0.0621401
\(800\) −107.461 −3.79932
\(801\) 4.33618 0.153211
\(802\) −41.6903 −1.47214
\(803\) 11.0577 0.390216
\(804\) 83.1447 2.93229
\(805\) −78.9469 −2.78251
\(806\) 83.6163 2.94526
\(807\) 23.3216 0.820958
\(808\) −81.9954 −2.88459
\(809\) −35.4632 −1.24682 −0.623410 0.781895i \(-0.714253\pi\)
−0.623410 + 0.781895i \(0.714253\pi\)
\(810\) −8.89217 −0.312439
\(811\) −16.2439 −0.570399 −0.285200 0.958468i \(-0.592060\pi\)
−0.285200 + 0.958468i \(0.592060\pi\)
\(812\) 32.4443 1.13857
\(813\) −14.2253 −0.498903
\(814\) −33.7703 −1.18365
\(815\) 54.3208 1.90277
\(816\) −13.3775 −0.468305
\(817\) −12.1371 −0.424622
\(818\) 93.9608 3.28526
\(819\) 22.7737 0.795777
\(820\) 64.9048 2.26657
\(821\) −15.2862 −0.533491 −0.266745 0.963767i \(-0.585948\pi\)
−0.266745 + 0.963767i \(0.585948\pi\)
\(822\) −32.9499 −1.14926
\(823\) 54.5763 1.90241 0.951204 0.308562i \(-0.0998477\pi\)
0.951204 + 0.308562i \(0.0998477\pi\)
\(824\) 71.5453 2.49240
\(825\) −7.39813 −0.257570
\(826\) 146.094 5.08327
\(827\) −29.6884 −1.03237 −0.516184 0.856478i \(-0.672648\pi\)
−0.516184 + 0.856478i \(0.672648\pi\)
\(828\) −30.6264 −1.06434
\(829\) −20.6662 −0.717767 −0.358884 0.933382i \(-0.616842\pi\)
−0.358884 + 0.933382i \(0.616842\pi\)
\(830\) 78.1931 2.71412
\(831\) 14.6727 0.508991
\(832\) 125.631 4.35549
\(833\) 10.1162 0.350504
\(834\) 39.7730 1.37723
\(835\) −9.41074 −0.325672
\(836\) 25.0694 0.867042
\(837\) 5.62716 0.194503
\(838\) 63.5254 2.19445
\(839\) −4.74449 −0.163798 −0.0818990 0.996641i \(-0.526098\pi\)
−0.0818990 + 0.996641i \(0.526098\pi\)
\(840\) 120.920 4.17212
\(841\) −26.7998 −0.924130
\(842\) −0.445704 −0.0153600
\(843\) 21.5555 0.742410
\(844\) −88.7881 −3.05621
\(845\) 56.9920 1.96059
\(846\) −4.74151 −0.163016
\(847\) −38.8947 −1.33644
\(848\) −88.0540 −3.02379
\(849\) −23.2166 −0.796792
\(850\) −15.7946 −0.541749
\(851\) −57.3157 −1.96476
\(852\) 3.97329 0.136123
\(853\) 51.6619 1.76887 0.884434 0.466664i \(-0.154544\pi\)
0.884434 + 0.466664i \(0.154544\pi\)
\(854\) 16.2866 0.557317
\(855\) 12.3536 0.422484
\(856\) −172.136 −5.88349
\(857\) 3.30949 0.113050 0.0565250 0.998401i \(-0.481998\pi\)
0.0565250 + 0.998401i \(0.481998\pi\)
\(858\) 18.7883 0.641422
\(859\) 9.46105 0.322807 0.161403 0.986889i \(-0.448398\pi\)
0.161403 + 0.986889i \(0.448398\pi\)
\(860\) −56.3631 −1.92196
\(861\) −15.4185 −0.525462
\(862\) −44.1528 −1.50385
\(863\) −32.3737 −1.10201 −0.551007 0.834501i \(-0.685756\pi\)
−0.551007 + 0.834501i \(0.685756\pi\)
\(864\) 18.3660 0.624825
\(865\) 79.5021 2.70315
\(866\) 57.0088 1.93724
\(867\) −1.00000 −0.0339618
\(868\) −123.082 −4.17766
\(869\) −11.0048 −0.373313
\(870\) 13.1899 0.447180
\(871\) −86.5694 −2.93329
\(872\) 78.7822 2.66790
\(873\) 12.3848 0.419163
\(874\) 58.6439 1.98366
\(875\) 11.5988 0.392109
\(876\) −46.2357 −1.56216
\(877\) 28.0649 0.947683 0.473842 0.880610i \(-0.342867\pi\)
0.473842 + 0.880610i \(0.342867\pi\)
\(878\) 19.2804 0.650683
\(879\) 26.1234 0.881121
\(880\) 55.7181 1.87826
\(881\) 11.9638 0.403072 0.201536 0.979481i \(-0.435407\pi\)
0.201536 + 0.979481i \(0.435407\pi\)
\(882\) −27.3078 −0.919502
\(883\) 37.9825 1.27821 0.639107 0.769118i \(-0.279304\pi\)
0.639107 + 0.769118i \(0.279304\pi\)
\(884\) 29.1025 0.978825
\(885\) 43.0919 1.44852
\(886\) −59.6753 −2.00483
\(887\) 47.2865 1.58772 0.793862 0.608098i \(-0.208067\pi\)
0.793862 + 0.608098i \(0.208067\pi\)
\(888\) 87.7880 2.94597
\(889\) 11.6238 0.389848
\(890\) −38.5580 −1.29247
\(891\) 1.26440 0.0423591
\(892\) 67.1312 2.24772
\(893\) 6.58721 0.220433
\(894\) 9.89368 0.330894
\(895\) −54.9118 −1.83550
\(896\) −102.917 −3.43823
\(897\) 31.8879 1.06471
\(898\) −23.8635 −0.796335
\(899\) −8.34688 −0.278384
\(900\) 30.9341 1.03114
\(901\) −6.58226 −0.219287
\(902\) −12.7203 −0.423539
\(903\) 13.3894 0.445571
\(904\) −110.965 −3.69065
\(905\) 22.2477 0.739540
\(906\) 15.6692 0.520573
\(907\) −31.8598 −1.05789 −0.528943 0.848657i \(-0.677412\pi\)
−0.528943 + 0.848657i \(0.677412\pi\)
\(908\) 36.9911 1.22759
\(909\) 9.24128 0.306514
\(910\) −202.508 −6.71306
\(911\) 47.7384 1.58164 0.790822 0.612046i \(-0.209653\pi\)
0.790822 + 0.612046i \(0.209653\pi\)
\(912\) −50.1684 −1.66124
\(913\) −11.1185 −0.367969
\(914\) −20.6904 −0.684379
\(915\) 4.80390 0.158812
\(916\) 124.131 4.10141
\(917\) 55.2206 1.82355
\(918\) 2.69942 0.0890943
\(919\) −52.6185 −1.73573 −0.867863 0.496804i \(-0.834507\pi\)
−0.867863 + 0.496804i \(0.834507\pi\)
\(920\) 169.313 5.58207
\(921\) −25.8888 −0.853065
\(922\) −94.9208 −3.12605
\(923\) −4.13695 −0.136169
\(924\) −27.6560 −0.909817
\(925\) 57.8914 1.90346
\(926\) −52.8566 −1.73698
\(927\) −8.06351 −0.264840
\(928\) −27.2427 −0.894285
\(929\) −4.06466 −0.133357 −0.0666786 0.997775i \(-0.521240\pi\)
−0.0666786 + 0.997775i \(0.521240\pi\)
\(930\) −50.0377 −1.64080
\(931\) 37.9378 1.24336
\(932\) −2.71543 −0.0889469
\(933\) 6.70284 0.219441
\(934\) −37.5988 −1.23027
\(935\) 4.16507 0.136212
\(936\) −48.8413 −1.59643
\(937\) −31.1634 −1.01807 −0.509033 0.860747i \(-0.669997\pi\)
−0.509033 + 0.860747i \(0.669997\pi\)
\(938\) 175.634 5.73465
\(939\) −10.8671 −0.354633
\(940\) 30.5902 0.997743
\(941\) 23.8033 0.775965 0.387983 0.921667i \(-0.373172\pi\)
0.387983 + 0.921667i \(0.373172\pi\)
\(942\) −2.69942 −0.0879520
\(943\) −21.5891 −0.703039
\(944\) −174.998 −5.69570
\(945\) −13.6282 −0.443327
\(946\) 11.0462 0.359144
\(947\) 23.4461 0.761895 0.380948 0.924597i \(-0.375598\pi\)
0.380948 + 0.924597i \(0.375598\pi\)
\(948\) 46.0148 1.49449
\(949\) 48.1401 1.56269
\(950\) −59.2330 −1.92177
\(951\) −21.2873 −0.690287
\(952\) −36.7080 −1.18971
\(953\) 10.6565 0.345197 0.172599 0.984992i \(-0.444784\pi\)
0.172599 + 0.984992i \(0.444784\pi\)
\(954\) 17.7683 0.575270
\(955\) 31.1395 1.00765
\(956\) 10.5559 0.341401
\(957\) −1.87552 −0.0606268
\(958\) −66.0066 −2.13258
\(959\) −50.4994 −1.63071
\(960\) −75.1804 −2.42644
\(961\) 0.664961 0.0214504
\(962\) −147.021 −4.74015
\(963\) 19.4006 0.625175
\(964\) 46.4716 1.49675
\(965\) 40.6736 1.30933
\(966\) −64.6949 −2.08152
\(967\) 5.48941 0.176528 0.0882638 0.996097i \(-0.471868\pi\)
0.0882638 + 0.996097i \(0.471868\pi\)
\(968\) 83.4150 2.68106
\(969\) −3.75022 −0.120474
\(970\) −110.128 −3.53599
\(971\) −42.0415 −1.34918 −0.674588 0.738195i \(-0.735679\pi\)
−0.674588 + 0.738195i \(0.735679\pi\)
\(972\) −5.28690 −0.169577
\(973\) 60.9566 1.95418
\(974\) 62.1405 1.99111
\(975\) −32.2082 −1.03149
\(976\) −19.5088 −0.624462
\(977\) 50.2521 1.60771 0.803854 0.594827i \(-0.202779\pi\)
0.803854 + 0.594827i \(0.202779\pi\)
\(978\) 44.5144 1.42341
\(979\) 5.48268 0.175227
\(980\) 176.179 5.62782
\(981\) −8.87914 −0.283489
\(982\) −110.772 −3.53486
\(983\) 23.2261 0.740797 0.370398 0.928873i \(-0.379221\pi\)
0.370398 + 0.928873i \(0.379221\pi\)
\(984\) 33.0672 1.05414
\(985\) 44.3059 1.41170
\(986\) −4.00411 −0.127517
\(987\) −7.26689 −0.231308
\(988\) 109.141 3.47223
\(989\) 18.7479 0.596149
\(990\) −11.2433 −0.357336
\(991\) −35.1600 −1.11689 −0.558447 0.829540i \(-0.688603\pi\)
−0.558447 + 0.829540i \(0.688603\pi\)
\(992\) 103.349 3.28132
\(993\) −6.85976 −0.217688
\(994\) 8.39314 0.266214
\(995\) 37.7714 1.19743
\(996\) 46.4902 1.47310
\(997\) −46.4104 −1.46983 −0.734917 0.678157i \(-0.762779\pi\)
−0.734917 + 0.678157i \(0.762779\pi\)
\(998\) 105.557 3.34134
\(999\) −9.89414 −0.313037
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 \(a_p\))