Properties

Label 8042.2.a.c.1.12
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.38541 q^{3}\) \(+1.00000 q^{4}\) \(+2.54225 q^{5}\) \(+2.38541 q^{6}\) \(+3.05592 q^{7}\) \(-1.00000 q^{8}\) \(+2.69019 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.38541 q^{3}\) \(+1.00000 q^{4}\) \(+2.54225 q^{5}\) \(+2.38541 q^{6}\) \(+3.05592 q^{7}\) \(-1.00000 q^{8}\) \(+2.69019 q^{9}\) \(-2.54225 q^{10}\) \(+5.40659 q^{11}\) \(-2.38541 q^{12}\) \(+2.16059 q^{13}\) \(-3.05592 q^{14}\) \(-6.06432 q^{15}\) \(+1.00000 q^{16}\) \(+0.860456 q^{17}\) \(-2.69019 q^{18}\) \(-6.33765 q^{19}\) \(+2.54225 q^{20}\) \(-7.28963 q^{21}\) \(-5.40659 q^{22}\) \(-2.60042 q^{23}\) \(+2.38541 q^{24}\) \(+1.46305 q^{25}\) \(-2.16059 q^{26}\) \(+0.739034 q^{27}\) \(+3.05592 q^{28}\) \(-9.11723 q^{29}\) \(+6.06432 q^{30}\) \(+5.79999 q^{31}\) \(-1.00000 q^{32}\) \(-12.8969 q^{33}\) \(-0.860456 q^{34}\) \(+7.76893 q^{35}\) \(+2.69019 q^{36}\) \(-3.68703 q^{37}\) \(+6.33765 q^{38}\) \(-5.15389 q^{39}\) \(-2.54225 q^{40}\) \(-2.55894 q^{41}\) \(+7.28963 q^{42}\) \(-2.74552 q^{43}\) \(+5.40659 q^{44}\) \(+6.83913 q^{45}\) \(+2.60042 q^{46}\) \(-8.15126 q^{47}\) \(-2.38541 q^{48}\) \(+2.33866 q^{49}\) \(-1.46305 q^{50}\) \(-2.05254 q^{51}\) \(+2.16059 q^{52}\) \(+13.6247 q^{53}\) \(-0.739034 q^{54}\) \(+13.7449 q^{55}\) \(-3.05592 q^{56}\) \(+15.1179 q^{57}\) \(+9.11723 q^{58}\) \(+4.92751 q^{59}\) \(-6.06432 q^{60}\) \(+8.90175 q^{61}\) \(-5.79999 q^{62}\) \(+8.22100 q^{63}\) \(+1.00000 q^{64}\) \(+5.49276 q^{65}\) \(+12.8969 q^{66}\) \(-8.71794 q^{67}\) \(+0.860456 q^{68}\) \(+6.20308 q^{69}\) \(-7.76893 q^{70}\) \(-5.52150 q^{71}\) \(-2.69019 q^{72}\) \(-1.03624 q^{73}\) \(+3.68703 q^{74}\) \(-3.48998 q^{75}\) \(-6.33765 q^{76}\) \(+16.5221 q^{77}\) \(+5.15389 q^{78}\) \(+15.5592 q^{79}\) \(+2.54225 q^{80}\) \(-9.83346 q^{81}\) \(+2.55894 q^{82}\) \(+6.14988 q^{83}\) \(-7.28963 q^{84}\) \(+2.18750 q^{85}\) \(+2.74552 q^{86}\) \(+21.7483 q^{87}\) \(-5.40659 q^{88}\) \(+15.3032 q^{89}\) \(-6.83913 q^{90}\) \(+6.60259 q^{91}\) \(-2.60042 q^{92}\) \(-13.8354 q^{93}\) \(+8.15126 q^{94}\) \(-16.1119 q^{95}\) \(+2.38541 q^{96}\) \(-10.1728 q^{97}\) \(-2.33866 q^{98}\) \(+14.5447 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.38541 −1.37722 −0.688609 0.725133i \(-0.741778\pi\)
−0.688609 + 0.725133i \(0.741778\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.54225 1.13693 0.568465 0.822707i \(-0.307537\pi\)
0.568465 + 0.822707i \(0.307537\pi\)
\(6\) 2.38541 0.973840
\(7\) 3.05592 1.15503 0.577515 0.816380i \(-0.304023\pi\)
0.577515 + 0.816380i \(0.304023\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.69019 0.896729
\(10\) −2.54225 −0.803931
\(11\) 5.40659 1.63015 0.815075 0.579356i \(-0.196696\pi\)
0.815075 + 0.579356i \(0.196696\pi\)
\(12\) −2.38541 −0.688609
\(13\) 2.16059 0.599239 0.299620 0.954059i \(-0.403140\pi\)
0.299620 + 0.954059i \(0.403140\pi\)
\(14\) −3.05592 −0.816730
\(15\) −6.06432 −1.56580
\(16\) 1.00000 0.250000
\(17\) 0.860456 0.208691 0.104346 0.994541i \(-0.466725\pi\)
0.104346 + 0.994541i \(0.466725\pi\)
\(18\) −2.69019 −0.634083
\(19\) −6.33765 −1.45396 −0.726978 0.686661i \(-0.759076\pi\)
−0.726978 + 0.686661i \(0.759076\pi\)
\(20\) 2.54225 0.568465
\(21\) −7.28963 −1.59073
\(22\) −5.40659 −1.15269
\(23\) −2.60042 −0.542226 −0.271113 0.962548i \(-0.587392\pi\)
−0.271113 + 0.962548i \(0.587392\pi\)
\(24\) 2.38541 0.486920
\(25\) 1.46305 0.292610
\(26\) −2.16059 −0.423726
\(27\) 0.739034 0.142227
\(28\) 3.05592 0.577515
\(29\) −9.11723 −1.69303 −0.846513 0.532367i \(-0.821302\pi\)
−0.846513 + 0.532367i \(0.821302\pi\)
\(30\) 6.06432 1.10719
\(31\) 5.79999 1.04171 0.520855 0.853645i \(-0.325613\pi\)
0.520855 + 0.853645i \(0.325613\pi\)
\(32\) −1.00000 −0.176777
\(33\) −12.8969 −2.24507
\(34\) −0.860456 −0.147567
\(35\) 7.76893 1.31319
\(36\) 2.69019 0.448364
\(37\) −3.68703 −0.606145 −0.303072 0.952968i \(-0.598012\pi\)
−0.303072 + 0.952968i \(0.598012\pi\)
\(38\) 6.33765 1.02810
\(39\) −5.15389 −0.825283
\(40\) −2.54225 −0.401966
\(41\) −2.55894 −0.399639 −0.199820 0.979833i \(-0.564036\pi\)
−0.199820 + 0.979833i \(0.564036\pi\)
\(42\) 7.28963 1.12481
\(43\) −2.74552 −0.418688 −0.209344 0.977842i \(-0.567133\pi\)
−0.209344 + 0.977842i \(0.567133\pi\)
\(44\) 5.40659 0.815075
\(45\) 6.83913 1.01952
\(46\) 2.60042 0.383411
\(47\) −8.15126 −1.18898 −0.594492 0.804102i \(-0.702647\pi\)
−0.594492 + 0.804102i \(0.702647\pi\)
\(48\) −2.38541 −0.344304
\(49\) 2.33866 0.334094
\(50\) −1.46305 −0.206907
\(51\) −2.05254 −0.287413
\(52\) 2.16059 0.299620
\(53\) 13.6247 1.87149 0.935746 0.352674i \(-0.114728\pi\)
0.935746 + 0.352674i \(0.114728\pi\)
\(54\) −0.739034 −0.100570
\(55\) 13.7449 1.85337
\(56\) −3.05592 −0.408365
\(57\) 15.1179 2.00241
\(58\) 9.11723 1.19715
\(59\) 4.92751 0.641507 0.320754 0.947163i \(-0.396064\pi\)
0.320754 + 0.947163i \(0.396064\pi\)
\(60\) −6.06432 −0.782900
\(61\) 8.90175 1.13975 0.569876 0.821730i \(-0.306991\pi\)
0.569876 + 0.821730i \(0.306991\pi\)
\(62\) −5.79999 −0.736600
\(63\) 8.22100 1.03575
\(64\) 1.00000 0.125000
\(65\) 5.49276 0.681293
\(66\) 12.8969 1.58750
\(67\) −8.71794 −1.06507 −0.532533 0.846409i \(-0.678760\pi\)
−0.532533 + 0.846409i \(0.678760\pi\)
\(68\) 0.860456 0.104346
\(69\) 6.20308 0.746763
\(70\) −7.76893 −0.928564
\(71\) −5.52150 −0.655282 −0.327641 0.944802i \(-0.606254\pi\)
−0.327641 + 0.944802i \(0.606254\pi\)
\(72\) −2.69019 −0.317041
\(73\) −1.03624 −0.121283 −0.0606413 0.998160i \(-0.519315\pi\)
−0.0606413 + 0.998160i \(0.519315\pi\)
\(74\) 3.68703 0.428609
\(75\) −3.48998 −0.402988
\(76\) −6.33765 −0.726978
\(77\) 16.5221 1.88287
\(78\) 5.15389 0.583563
\(79\) 15.5592 1.75055 0.875276 0.483624i \(-0.160680\pi\)
0.875276 + 0.483624i \(0.160680\pi\)
\(80\) 2.54225 0.284233
\(81\) −9.83346 −1.09261
\(82\) 2.55894 0.282588
\(83\) 6.14988 0.675037 0.337519 0.941319i \(-0.390412\pi\)
0.337519 + 0.941319i \(0.390412\pi\)
\(84\) −7.28963 −0.795364
\(85\) 2.18750 0.237267
\(86\) 2.74552 0.296057
\(87\) 21.7483 2.33167
\(88\) −5.40659 −0.576345
\(89\) 15.3032 1.62213 0.811067 0.584953i \(-0.198887\pi\)
0.811067 + 0.584953i \(0.198887\pi\)
\(90\) −6.83913 −0.720908
\(91\) 6.60259 0.692139
\(92\) −2.60042 −0.271113
\(93\) −13.8354 −1.43466
\(94\) 8.15126 0.840738
\(95\) −16.1119 −1.65305
\(96\) 2.38541 0.243460
\(97\) −10.1728 −1.03289 −0.516445 0.856320i \(-0.672745\pi\)
−0.516445 + 0.856320i \(0.672745\pi\)
\(98\) −2.33866 −0.236240
\(99\) 14.5447 1.46180
\(100\) 1.46305 0.146305
\(101\) −6.81110 −0.677730 −0.338865 0.940835i \(-0.610043\pi\)
−0.338865 + 0.940835i \(0.610043\pi\)
\(102\) 2.05254 0.203232
\(103\) 17.4455 1.71896 0.859479 0.511171i \(-0.170788\pi\)
0.859479 + 0.511171i \(0.170788\pi\)
\(104\) −2.16059 −0.211863
\(105\) −18.5321 −1.80855
\(106\) −13.6247 −1.32335
\(107\) 10.7161 1.03597 0.517983 0.855391i \(-0.326683\pi\)
0.517983 + 0.855391i \(0.326683\pi\)
\(108\) 0.739034 0.0711136
\(109\) 11.1958 1.07237 0.536184 0.844101i \(-0.319865\pi\)
0.536184 + 0.844101i \(0.319865\pi\)
\(110\) −13.7449 −1.31053
\(111\) 8.79509 0.834793
\(112\) 3.05592 0.288757
\(113\) 18.7388 1.76280 0.881398 0.472375i \(-0.156603\pi\)
0.881398 + 0.472375i \(0.156603\pi\)
\(114\) −15.1179 −1.41592
\(115\) −6.61093 −0.616473
\(116\) −9.11723 −0.846513
\(117\) 5.81238 0.537355
\(118\) −4.92751 −0.453614
\(119\) 2.62949 0.241045
\(120\) 6.06432 0.553594
\(121\) 18.2313 1.65739
\(122\) −8.90175 −0.805927
\(123\) 6.10413 0.550390
\(124\) 5.79999 0.520855
\(125\) −8.99182 −0.804253
\(126\) −8.22100 −0.732385
\(127\) −3.66483 −0.325201 −0.162600 0.986692i \(-0.551988\pi\)
−0.162600 + 0.986692i \(0.551988\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.54920 0.576625
\(130\) −5.49276 −0.481747
\(131\) −17.9734 −1.57034 −0.785172 0.619277i \(-0.787426\pi\)
−0.785172 + 0.619277i \(0.787426\pi\)
\(132\) −12.8969 −1.12254
\(133\) −19.3674 −1.67936
\(134\) 8.71794 0.753116
\(135\) 1.87881 0.161702
\(136\) −0.860456 −0.0737835
\(137\) 0.651530 0.0556640 0.0278320 0.999613i \(-0.491140\pi\)
0.0278320 + 0.999613i \(0.491140\pi\)
\(138\) −6.20308 −0.528041
\(139\) 6.35989 0.539438 0.269719 0.962939i \(-0.413069\pi\)
0.269719 + 0.962939i \(0.413069\pi\)
\(140\) 7.76893 0.656594
\(141\) 19.4441 1.63749
\(142\) 5.52150 0.463354
\(143\) 11.6814 0.976849
\(144\) 2.69019 0.224182
\(145\) −23.1783 −1.92485
\(146\) 1.03624 0.0857597
\(147\) −5.57866 −0.460120
\(148\) −3.68703 −0.303072
\(149\) −0.224420 −0.0183852 −0.00919260 0.999958i \(-0.502926\pi\)
−0.00919260 + 0.999958i \(0.502926\pi\)
\(150\) 3.48998 0.284956
\(151\) 2.55670 0.208061 0.104031 0.994574i \(-0.466826\pi\)
0.104031 + 0.994574i \(0.466826\pi\)
\(152\) 6.33765 0.514051
\(153\) 2.31479 0.187139
\(154\) −16.5221 −1.33139
\(155\) 14.7450 1.18435
\(156\) −5.15389 −0.412641
\(157\) 1.52156 0.121434 0.0607170 0.998155i \(-0.480661\pi\)
0.0607170 + 0.998155i \(0.480661\pi\)
\(158\) −15.5592 −1.23783
\(159\) −32.5004 −2.57745
\(160\) −2.54225 −0.200983
\(161\) −7.94669 −0.626287
\(162\) 9.83346 0.772589
\(163\) 12.0908 0.947028 0.473514 0.880786i \(-0.342985\pi\)
0.473514 + 0.880786i \(0.342985\pi\)
\(164\) −2.55894 −0.199820
\(165\) −32.7873 −2.55249
\(166\) −6.14988 −0.477324
\(167\) −0.854626 −0.0661329 −0.0330665 0.999453i \(-0.510527\pi\)
−0.0330665 + 0.999453i \(0.510527\pi\)
\(168\) 7.28963 0.562407
\(169\) −8.33186 −0.640912
\(170\) −2.18750 −0.167773
\(171\) −17.0494 −1.30380
\(172\) −2.74552 −0.209344
\(173\) 18.2898 1.39055 0.695274 0.718745i \(-0.255283\pi\)
0.695274 + 0.718745i \(0.255283\pi\)
\(174\) −21.7483 −1.64874
\(175\) 4.47097 0.337974
\(176\) 5.40659 0.407537
\(177\) −11.7541 −0.883495
\(178\) −15.3032 −1.14702
\(179\) 11.6079 0.867615 0.433807 0.901006i \(-0.357170\pi\)
0.433807 + 0.901006i \(0.357170\pi\)
\(180\) 6.83913 0.509759
\(181\) 11.7305 0.871918 0.435959 0.899967i \(-0.356409\pi\)
0.435959 + 0.899967i \(0.356409\pi\)
\(182\) −6.60259 −0.489416
\(183\) −21.2343 −1.56969
\(184\) 2.60042 0.191706
\(185\) −9.37337 −0.689144
\(186\) 13.8354 1.01446
\(187\) 4.65214 0.340198
\(188\) −8.15126 −0.594492
\(189\) 2.25843 0.164277
\(190\) 16.1119 1.16888
\(191\) 18.4808 1.33722 0.668611 0.743612i \(-0.266889\pi\)
0.668611 + 0.743612i \(0.266889\pi\)
\(192\) −2.38541 −0.172152
\(193\) −5.84771 −0.420928 −0.210464 0.977602i \(-0.567497\pi\)
−0.210464 + 0.977602i \(0.567497\pi\)
\(194\) 10.1728 0.730364
\(195\) −13.1025 −0.938289
\(196\) 2.33866 0.167047
\(197\) 19.8406 1.41358 0.706790 0.707423i \(-0.250142\pi\)
0.706790 + 0.707423i \(0.250142\pi\)
\(198\) −14.5447 −1.03365
\(199\) 25.3449 1.79665 0.898326 0.439329i \(-0.144784\pi\)
0.898326 + 0.439329i \(0.144784\pi\)
\(200\) −1.46305 −0.103453
\(201\) 20.7959 1.46683
\(202\) 6.81110 0.479227
\(203\) −27.8615 −1.95550
\(204\) −2.05254 −0.143707
\(205\) −6.50548 −0.454362
\(206\) −17.4455 −1.21549
\(207\) −6.99562 −0.486229
\(208\) 2.16059 0.149810
\(209\) −34.2651 −2.37016
\(210\) 18.5321 1.27884
\(211\) −9.99447 −0.688048 −0.344024 0.938961i \(-0.611790\pi\)
−0.344024 + 0.938961i \(0.611790\pi\)
\(212\) 13.6247 0.935746
\(213\) 13.1711 0.902466
\(214\) −10.7161 −0.732539
\(215\) −6.97982 −0.476020
\(216\) −0.739034 −0.0502849
\(217\) 17.7243 1.20321
\(218\) −11.1958 −0.758279
\(219\) 2.47185 0.167032
\(220\) 13.7449 0.926683
\(221\) 1.85909 0.125056
\(222\) −8.79509 −0.590288
\(223\) 15.3316 1.02668 0.513341 0.858185i \(-0.328408\pi\)
0.513341 + 0.858185i \(0.328408\pi\)
\(224\) −3.05592 −0.204182
\(225\) 3.93588 0.262392
\(226\) −18.7388 −1.24648
\(227\) 11.8746 0.788148 0.394074 0.919079i \(-0.371065\pi\)
0.394074 + 0.919079i \(0.371065\pi\)
\(228\) 15.1179 1.00121
\(229\) −14.3238 −0.946540 −0.473270 0.880917i \(-0.656927\pi\)
−0.473270 + 0.880917i \(0.656927\pi\)
\(230\) 6.61093 0.435912
\(231\) −39.4121 −2.59312
\(232\) 9.11723 0.598575
\(233\) 20.7093 1.35671 0.678356 0.734733i \(-0.262693\pi\)
0.678356 + 0.734733i \(0.262693\pi\)
\(234\) −5.81238 −0.379967
\(235\) −20.7226 −1.35179
\(236\) 4.92751 0.320754
\(237\) −37.1152 −2.41089
\(238\) −2.62949 −0.170444
\(239\) −20.9530 −1.35534 −0.677668 0.735368i \(-0.737009\pi\)
−0.677668 + 0.735368i \(0.737009\pi\)
\(240\) −6.06432 −0.391450
\(241\) −21.7198 −1.39910 −0.699548 0.714586i \(-0.746615\pi\)
−0.699548 + 0.714586i \(0.746615\pi\)
\(242\) −18.2313 −1.17195
\(243\) 21.2397 1.36253
\(244\) 8.90175 0.569876
\(245\) 5.94546 0.379842
\(246\) −6.10413 −0.389185
\(247\) −13.6930 −0.871267
\(248\) −5.79999 −0.368300
\(249\) −14.6700 −0.929674
\(250\) 8.99182 0.568693
\(251\) −15.1485 −0.956163 −0.478082 0.878315i \(-0.658668\pi\)
−0.478082 + 0.878315i \(0.658668\pi\)
\(252\) 8.22100 0.517874
\(253\) −14.0594 −0.883909
\(254\) 3.66483 0.229952
\(255\) −5.21808 −0.326769
\(256\) 1.00000 0.0625000
\(257\) −27.7721 −1.73237 −0.866187 0.499720i \(-0.833436\pi\)
−0.866187 + 0.499720i \(0.833436\pi\)
\(258\) −6.54920 −0.407736
\(259\) −11.2673 −0.700115
\(260\) 5.49276 0.340647
\(261\) −24.5270 −1.51819
\(262\) 17.9734 1.11040
\(263\) −0.192744 −0.0118851 −0.00594254 0.999982i \(-0.501892\pi\)
−0.00594254 + 0.999982i \(0.501892\pi\)
\(264\) 12.8969 0.793752
\(265\) 34.6374 2.12776
\(266\) 19.3674 1.18749
\(267\) −36.5044 −2.23403
\(268\) −8.71794 −0.532533
\(269\) 11.7799 0.718233 0.359116 0.933293i \(-0.383078\pi\)
0.359116 + 0.933293i \(0.383078\pi\)
\(270\) −1.87881 −0.114341
\(271\) 24.8245 1.50798 0.753991 0.656885i \(-0.228126\pi\)
0.753991 + 0.656885i \(0.228126\pi\)
\(272\) 0.860456 0.0521728
\(273\) −15.7499 −0.953227
\(274\) −0.651530 −0.0393604
\(275\) 7.91013 0.476999
\(276\) 6.20308 0.373381
\(277\) −28.3862 −1.70556 −0.852780 0.522270i \(-0.825085\pi\)
−0.852780 + 0.522270i \(0.825085\pi\)
\(278\) −6.35989 −0.381441
\(279\) 15.6031 0.934130
\(280\) −7.76893 −0.464282
\(281\) 7.51813 0.448494 0.224247 0.974532i \(-0.428008\pi\)
0.224247 + 0.974532i \(0.428008\pi\)
\(282\) −19.4441 −1.15788
\(283\) 28.0175 1.66547 0.832735 0.553672i \(-0.186774\pi\)
0.832735 + 0.553672i \(0.186774\pi\)
\(284\) −5.52150 −0.327641
\(285\) 38.4335 2.27660
\(286\) −11.6814 −0.690737
\(287\) −7.81992 −0.461595
\(288\) −2.69019 −0.158521
\(289\) −16.2596 −0.956448
\(290\) 23.1783 1.36108
\(291\) 24.2663 1.42252
\(292\) −1.03624 −0.0606413
\(293\) −15.7191 −0.918318 −0.459159 0.888354i \(-0.651849\pi\)
−0.459159 + 0.888354i \(0.651849\pi\)
\(294\) 5.57866 0.325354
\(295\) 12.5270 0.729349
\(296\) 3.68703 0.214304
\(297\) 3.99566 0.231852
\(298\) 0.224420 0.0130003
\(299\) −5.61844 −0.324923
\(300\) −3.48998 −0.201494
\(301\) −8.39011 −0.483598
\(302\) −2.55670 −0.147121
\(303\) 16.2473 0.933381
\(304\) −6.33765 −0.363489
\(305\) 22.6305 1.29582
\(306\) −2.31479 −0.132328
\(307\) 24.0414 1.37212 0.686059 0.727546i \(-0.259339\pi\)
0.686059 + 0.727546i \(0.259339\pi\)
\(308\) 16.5221 0.941436
\(309\) −41.6147 −2.36738
\(310\) −14.7450 −0.837462
\(311\) −12.2328 −0.693661 −0.346831 0.937928i \(-0.612742\pi\)
−0.346831 + 0.937928i \(0.612742\pi\)
\(312\) 5.15389 0.291782
\(313\) −14.1524 −0.799941 −0.399970 0.916528i \(-0.630980\pi\)
−0.399970 + 0.916528i \(0.630980\pi\)
\(314\) −1.52156 −0.0858668
\(315\) 20.8999 1.17757
\(316\) 15.5592 0.875276
\(317\) 17.2514 0.968936 0.484468 0.874809i \(-0.339013\pi\)
0.484468 + 0.874809i \(0.339013\pi\)
\(318\) 32.5004 1.82253
\(319\) −49.2931 −2.75989
\(320\) 2.54225 0.142116
\(321\) −25.5623 −1.42675
\(322\) 7.94669 0.442852
\(323\) −5.45327 −0.303428
\(324\) −9.83346 −0.546303
\(325\) 3.16105 0.175344
\(326\) −12.0908 −0.669650
\(327\) −26.7067 −1.47688
\(328\) 2.55894 0.141294
\(329\) −24.9096 −1.37331
\(330\) 32.7873 1.80488
\(331\) 3.91181 0.215013 0.107506 0.994204i \(-0.465713\pi\)
0.107506 + 0.994204i \(0.465713\pi\)
\(332\) 6.14988 0.337519
\(333\) −9.91880 −0.543547
\(334\) 0.854626 0.0467630
\(335\) −22.1632 −1.21091
\(336\) −7.28963 −0.397682
\(337\) 5.89251 0.320986 0.160493 0.987037i \(-0.448692\pi\)
0.160493 + 0.987037i \(0.448692\pi\)
\(338\) 8.33186 0.453193
\(339\) −44.6997 −2.42775
\(340\) 2.18750 0.118634
\(341\) 31.3582 1.69814
\(342\) 17.0494 0.921928
\(343\) −14.2447 −0.769141
\(344\) 2.74552 0.148029
\(345\) 15.7698 0.849017
\(346\) −18.2898 −0.983266
\(347\) −4.25322 −0.228325 −0.114162 0.993462i \(-0.536418\pi\)
−0.114162 + 0.993462i \(0.536418\pi\)
\(348\) 21.7483 1.16583
\(349\) −29.7292 −1.59137 −0.795683 0.605714i \(-0.792888\pi\)
−0.795683 + 0.605714i \(0.792888\pi\)
\(350\) −4.47097 −0.238984
\(351\) 1.59675 0.0852282
\(352\) −5.40659 −0.288172
\(353\) 3.01361 0.160398 0.0801991 0.996779i \(-0.474444\pi\)
0.0801991 + 0.996779i \(0.474444\pi\)
\(354\) 11.7541 0.624725
\(355\) −14.0371 −0.745010
\(356\) 15.3032 0.811067
\(357\) −6.27241 −0.331971
\(358\) −11.6079 −0.613496
\(359\) 17.5768 0.927669 0.463834 0.885922i \(-0.346473\pi\)
0.463834 + 0.885922i \(0.346473\pi\)
\(360\) −6.83913 −0.360454
\(361\) 21.1658 1.11399
\(362\) −11.7305 −0.616539
\(363\) −43.4890 −2.28258
\(364\) 6.60259 0.346070
\(365\) −2.63438 −0.137890
\(366\) 21.2343 1.10994
\(367\) 25.6358 1.33818 0.669089 0.743182i \(-0.266684\pi\)
0.669089 + 0.743182i \(0.266684\pi\)
\(368\) −2.60042 −0.135556
\(369\) −6.88403 −0.358368
\(370\) 9.37337 0.487298
\(371\) 41.6359 2.16163
\(372\) −13.8354 −0.717330
\(373\) 10.4814 0.542705 0.271353 0.962480i \(-0.412529\pi\)
0.271353 + 0.962480i \(0.412529\pi\)
\(374\) −4.65214 −0.240556
\(375\) 21.4492 1.10763
\(376\) 8.15126 0.420369
\(377\) −19.6986 −1.01453
\(378\) −2.25843 −0.116161
\(379\) −12.4358 −0.638786 −0.319393 0.947622i \(-0.603479\pi\)
−0.319393 + 0.947622i \(0.603479\pi\)
\(380\) −16.1119 −0.826523
\(381\) 8.74211 0.447872
\(382\) −18.4808 −0.945559
\(383\) 18.2512 0.932593 0.466297 0.884628i \(-0.345588\pi\)
0.466297 + 0.884628i \(0.345588\pi\)
\(384\) 2.38541 0.121730
\(385\) 42.0034 2.14069
\(386\) 5.84771 0.297641
\(387\) −7.38597 −0.375450
\(388\) −10.1728 −0.516445
\(389\) 14.5636 0.738406 0.369203 0.929349i \(-0.379631\pi\)
0.369203 + 0.929349i \(0.379631\pi\)
\(390\) 13.1025 0.663471
\(391\) −2.23755 −0.113158
\(392\) −2.33866 −0.118120
\(393\) 42.8740 2.16271
\(394\) −19.8406 −0.999553
\(395\) 39.5555 1.99026
\(396\) 14.5447 0.730901
\(397\) −3.75094 −0.188254 −0.0941272 0.995560i \(-0.530006\pi\)
−0.0941272 + 0.995560i \(0.530006\pi\)
\(398\) −25.3449 −1.27043
\(399\) 46.1991 2.31285
\(400\) 1.46305 0.0731526
\(401\) −24.8048 −1.23869 −0.619347 0.785117i \(-0.712603\pi\)
−0.619347 + 0.785117i \(0.712603\pi\)
\(402\) −20.7959 −1.03720
\(403\) 12.5314 0.624233
\(404\) −6.81110 −0.338865
\(405\) −24.9991 −1.24222
\(406\) 27.8615 1.38274
\(407\) −19.9343 −0.988106
\(408\) 2.05254 0.101616
\(409\) 25.0789 1.24007 0.620036 0.784574i \(-0.287118\pi\)
0.620036 + 0.784574i \(0.287118\pi\)
\(410\) 6.50548 0.321283
\(411\) −1.55417 −0.0766614
\(412\) 17.4455 0.859479
\(413\) 15.0581 0.740960
\(414\) 6.99562 0.343816
\(415\) 15.6346 0.767471
\(416\) −2.16059 −0.105932
\(417\) −15.1709 −0.742924
\(418\) 34.2651 1.67596
\(419\) 17.8485 0.871955 0.435978 0.899957i \(-0.356403\pi\)
0.435978 + 0.899957i \(0.356403\pi\)
\(420\) −18.5321 −0.904273
\(421\) 18.9872 0.925381 0.462690 0.886520i \(-0.346884\pi\)
0.462690 + 0.886520i \(0.346884\pi\)
\(422\) 9.99447 0.486523
\(423\) −21.9284 −1.06620
\(424\) −13.6247 −0.661673
\(425\) 1.25889 0.0610652
\(426\) −13.1711 −0.638140
\(427\) 27.2031 1.31645
\(428\) 10.7161 0.517983
\(429\) −27.8650 −1.34533
\(430\) 6.97982 0.336597
\(431\) 26.1878 1.26142 0.630710 0.776018i \(-0.282764\pi\)
0.630710 + 0.776018i \(0.282764\pi\)
\(432\) 0.739034 0.0355568
\(433\) −20.0820 −0.965077 −0.482539 0.875875i \(-0.660285\pi\)
−0.482539 + 0.875875i \(0.660285\pi\)
\(434\) −17.7243 −0.850795
\(435\) 55.2898 2.65094
\(436\) 11.1958 0.536184
\(437\) 16.4806 0.788372
\(438\) −2.47185 −0.118110
\(439\) 39.1621 1.86911 0.934553 0.355824i \(-0.115800\pi\)
0.934553 + 0.355824i \(0.115800\pi\)
\(440\) −13.7449 −0.655264
\(441\) 6.29143 0.299592
\(442\) −1.85909 −0.0884280
\(443\) −20.4838 −0.973217 −0.486608 0.873620i \(-0.661766\pi\)
−0.486608 + 0.873620i \(0.661766\pi\)
\(444\) 8.79509 0.417397
\(445\) 38.9046 1.84425
\(446\) −15.3316 −0.725973
\(447\) 0.535334 0.0253204
\(448\) 3.05592 0.144379
\(449\) −8.81757 −0.416127 −0.208063 0.978115i \(-0.566716\pi\)
−0.208063 + 0.978115i \(0.566716\pi\)
\(450\) −3.93588 −0.185539
\(451\) −13.8352 −0.651472
\(452\) 18.7388 0.881398
\(453\) −6.09877 −0.286545
\(454\) −11.8746 −0.557305
\(455\) 16.7855 0.786914
\(456\) −15.1179 −0.707960
\(457\) 13.0062 0.608403 0.304201 0.952608i \(-0.401610\pi\)
0.304201 + 0.952608i \(0.401610\pi\)
\(458\) 14.3238 0.669305
\(459\) 0.635907 0.0296816
\(460\) −6.61093 −0.308236
\(461\) 7.97413 0.371392 0.185696 0.982607i \(-0.440546\pi\)
0.185696 + 0.982607i \(0.440546\pi\)
\(462\) 39.4121 1.83362
\(463\) 16.7681 0.779278 0.389639 0.920968i \(-0.372600\pi\)
0.389639 + 0.920968i \(0.372600\pi\)
\(464\) −9.11723 −0.423257
\(465\) −35.1730 −1.63111
\(466\) −20.7093 −0.959340
\(467\) −29.8711 −1.38227 −0.691134 0.722726i \(-0.742889\pi\)
−0.691134 + 0.722726i \(0.742889\pi\)
\(468\) 5.81238 0.268677
\(469\) −26.6414 −1.23018
\(470\) 20.7226 0.955861
\(471\) −3.62955 −0.167241
\(472\) −4.92751 −0.226807
\(473\) −14.8439 −0.682525
\(474\) 37.1152 1.70476
\(475\) −9.27230 −0.425442
\(476\) 2.62949 0.120522
\(477\) 36.6529 1.67822
\(478\) 20.9530 0.958368
\(479\) −32.0686 −1.46525 −0.732625 0.680632i \(-0.761705\pi\)
−0.732625 + 0.680632i \(0.761705\pi\)
\(480\) 6.06432 0.276797
\(481\) −7.96616 −0.363226
\(482\) 21.7198 0.989310
\(483\) 18.9561 0.862533
\(484\) 18.2313 0.828693
\(485\) −25.8618 −1.17432
\(486\) −21.2397 −0.963454
\(487\) 8.43016 0.382007 0.191003 0.981589i \(-0.438826\pi\)
0.191003 + 0.981589i \(0.438826\pi\)
\(488\) −8.90175 −0.402963
\(489\) −28.8416 −1.30426
\(490\) −5.94546 −0.268589
\(491\) 41.9399 1.89272 0.946360 0.323115i \(-0.104730\pi\)
0.946360 + 0.323115i \(0.104730\pi\)
\(492\) 6.10413 0.275195
\(493\) −7.84498 −0.353320
\(494\) 13.6930 0.616079
\(495\) 36.9764 1.66197
\(496\) 5.79999 0.260427
\(497\) −16.8733 −0.756870
\(498\) 14.6700 0.657378
\(499\) 28.2315 1.26382 0.631908 0.775043i \(-0.282272\pi\)
0.631908 + 0.775043i \(0.282272\pi\)
\(500\) −8.99182 −0.402126
\(501\) 2.03863 0.0910794
\(502\) 15.1485 0.676110
\(503\) −1.57312 −0.0701420 −0.0350710 0.999385i \(-0.511166\pi\)
−0.0350710 + 0.999385i \(0.511166\pi\)
\(504\) −8.22100 −0.366192
\(505\) −17.3155 −0.770531
\(506\) 14.0594 0.625018
\(507\) 19.8749 0.882676
\(508\) −3.66483 −0.162600
\(509\) −29.4176 −1.30391 −0.651956 0.758257i \(-0.726051\pi\)
−0.651956 + 0.758257i \(0.726051\pi\)
\(510\) 5.21808 0.231060
\(511\) −3.16666 −0.140085
\(512\) −1.00000 −0.0441942
\(513\) −4.68374 −0.206792
\(514\) 27.7721 1.22497
\(515\) 44.3509 1.95434
\(516\) 6.54920 0.288313
\(517\) −44.0705 −1.93822
\(518\) 11.2673 0.495056
\(519\) −43.6287 −1.91509
\(520\) −5.49276 −0.240874
\(521\) −11.6727 −0.511388 −0.255694 0.966758i \(-0.582304\pi\)
−0.255694 + 0.966758i \(0.582304\pi\)
\(522\) 24.5270 1.07352
\(523\) 25.8144 1.12878 0.564392 0.825507i \(-0.309111\pi\)
0.564392 + 0.825507i \(0.309111\pi\)
\(524\) −17.9734 −0.785172
\(525\) −10.6651 −0.465463
\(526\) 0.192744 0.00840402
\(527\) 4.99064 0.217396
\(528\) −12.8969 −0.561268
\(529\) −16.2378 −0.705991
\(530\) −34.6374 −1.50455
\(531\) 13.2559 0.575258
\(532\) −19.3674 −0.839681
\(533\) −5.52882 −0.239480
\(534\) 36.5044 1.57970
\(535\) 27.2431 1.17782
\(536\) 8.71794 0.376558
\(537\) −27.6896 −1.19489
\(538\) −11.7799 −0.507867
\(539\) 12.6442 0.544623
\(540\) 1.87881 0.0808512
\(541\) −6.36999 −0.273867 −0.136934 0.990580i \(-0.543725\pi\)
−0.136934 + 0.990580i \(0.543725\pi\)
\(542\) −24.8245 −1.06630
\(543\) −27.9820 −1.20082
\(544\) −0.860456 −0.0368918
\(545\) 28.4627 1.21921
\(546\) 15.7499 0.674033
\(547\) −15.3332 −0.655602 −0.327801 0.944747i \(-0.606308\pi\)
−0.327801 + 0.944747i \(0.606308\pi\)
\(548\) 0.651530 0.0278320
\(549\) 23.9474 1.02205
\(550\) −7.91013 −0.337289
\(551\) 57.7818 2.46159
\(552\) −6.20308 −0.264021
\(553\) 47.5478 2.02194
\(554\) 28.3862 1.20601
\(555\) 22.3593 0.949101
\(556\) 6.35989 0.269719
\(557\) −44.6158 −1.89043 −0.945215 0.326448i \(-0.894148\pi\)
−0.945215 + 0.326448i \(0.894148\pi\)
\(558\) −15.6031 −0.660530
\(559\) −5.93195 −0.250895
\(560\) 7.76893 0.328297
\(561\) −11.0973 −0.468527
\(562\) −7.51813 −0.317133
\(563\) −6.50862 −0.274306 −0.137153 0.990550i \(-0.543795\pi\)
−0.137153 + 0.990550i \(0.543795\pi\)
\(564\) 19.4441 0.818744
\(565\) 47.6387 2.00418
\(566\) −28.0175 −1.17767
\(567\) −30.0503 −1.26199
\(568\) 5.52150 0.231677
\(569\) −33.2160 −1.39249 −0.696243 0.717806i \(-0.745147\pi\)
−0.696243 + 0.717806i \(0.745147\pi\)
\(570\) −38.4335 −1.60980
\(571\) −9.69938 −0.405906 −0.202953 0.979188i \(-0.565054\pi\)
−0.202953 + 0.979188i \(0.565054\pi\)
\(572\) 11.6814 0.488425
\(573\) −44.0843 −1.84165
\(574\) 7.81992 0.326397
\(575\) −3.80455 −0.158661
\(576\) 2.69019 0.112091
\(577\) 36.1366 1.50439 0.752194 0.658942i \(-0.228996\pi\)
0.752194 + 0.658942i \(0.228996\pi\)
\(578\) 16.2596 0.676311
\(579\) 13.9492 0.579709
\(580\) −23.1783 −0.962427
\(581\) 18.7936 0.779688
\(582\) −24.2663 −1.00587
\(583\) 73.6631 3.05081
\(584\) 1.03624 0.0428799
\(585\) 14.7765 0.610935
\(586\) 15.7191 0.649349
\(587\) 17.2526 0.712093 0.356046 0.934468i \(-0.384125\pi\)
0.356046 + 0.934468i \(0.384125\pi\)
\(588\) −5.57866 −0.230060
\(589\) −36.7583 −1.51460
\(590\) −12.5270 −0.515727
\(591\) −47.3279 −1.94681
\(592\) −3.68703 −0.151536
\(593\) 9.74335 0.400112 0.200056 0.979785i \(-0.435888\pi\)
0.200056 + 0.979785i \(0.435888\pi\)
\(594\) −3.99566 −0.163944
\(595\) 6.68482 0.274051
\(596\) −0.224420 −0.00919260
\(597\) −60.4580 −2.47438
\(598\) 5.61844 0.229755
\(599\) −1.69261 −0.0691582 −0.0345791 0.999402i \(-0.511009\pi\)
−0.0345791 + 0.999402i \(0.511009\pi\)
\(600\) 3.48998 0.142478
\(601\) 37.1925 1.51712 0.758558 0.651606i \(-0.225904\pi\)
0.758558 + 0.651606i \(0.225904\pi\)
\(602\) 8.39011 0.341955
\(603\) −23.4529 −0.955075
\(604\) 2.55670 0.104031
\(605\) 46.3485 1.88433
\(606\) −16.2473 −0.660000
\(607\) 6.99304 0.283839 0.141919 0.989878i \(-0.454673\pi\)
0.141919 + 0.989878i \(0.454673\pi\)
\(608\) 6.33765 0.257025
\(609\) 66.4612 2.69314
\(610\) −22.6305 −0.916283
\(611\) −17.6115 −0.712486
\(612\) 2.31479 0.0935697
\(613\) −4.78897 −0.193425 −0.0967123 0.995312i \(-0.530833\pi\)
−0.0967123 + 0.995312i \(0.530833\pi\)
\(614\) −24.0414 −0.970233
\(615\) 15.5182 0.625756
\(616\) −16.5221 −0.665696
\(617\) −37.1562 −1.49585 −0.747926 0.663782i \(-0.768950\pi\)
−0.747926 + 0.663782i \(0.768950\pi\)
\(618\) 41.6147 1.67399
\(619\) 0.270313 0.0108648 0.00543239 0.999985i \(-0.498271\pi\)
0.00543239 + 0.999985i \(0.498271\pi\)
\(620\) 14.7450 0.592175
\(621\) −1.92180 −0.0771193
\(622\) 12.2328 0.490493
\(623\) 46.7653 1.87361
\(624\) −5.15389 −0.206321
\(625\) −30.1747 −1.20699
\(626\) 14.1524 0.565643
\(627\) 81.7363 3.26423
\(628\) 1.52156 0.0607170
\(629\) −3.17253 −0.126497
\(630\) −20.8999 −0.832670
\(631\) −38.4507 −1.53070 −0.765348 0.643616i \(-0.777433\pi\)
−0.765348 + 0.643616i \(0.777433\pi\)
\(632\) −15.5592 −0.618914
\(633\) 23.8409 0.947592
\(634\) −17.2514 −0.685141
\(635\) −9.31691 −0.369730
\(636\) −32.5004 −1.28873
\(637\) 5.05288 0.200202
\(638\) 49.2931 1.95153
\(639\) −14.8539 −0.587610
\(640\) −2.54225 −0.100491
\(641\) 0.745939 0.0294628 0.0147314 0.999891i \(-0.495311\pi\)
0.0147314 + 0.999891i \(0.495311\pi\)
\(642\) 25.5623 1.00887
\(643\) 0.745265 0.0293904 0.0146952 0.999892i \(-0.495322\pi\)
0.0146952 + 0.999892i \(0.495322\pi\)
\(644\) −7.94669 −0.313143
\(645\) 16.6497 0.655583
\(646\) 5.45327 0.214556
\(647\) 35.5757 1.39863 0.699313 0.714815i \(-0.253489\pi\)
0.699313 + 0.714815i \(0.253489\pi\)
\(648\) 9.83346 0.386295
\(649\) 26.6410 1.04575
\(650\) −3.16105 −0.123987
\(651\) −42.2798 −1.65708
\(652\) 12.0908 0.473514
\(653\) −29.0244 −1.13581 −0.567907 0.823093i \(-0.692246\pi\)
−0.567907 + 0.823093i \(0.692246\pi\)
\(654\) 26.7067 1.04431
\(655\) −45.6930 −1.78537
\(656\) −2.55894 −0.0999098
\(657\) −2.78767 −0.108758
\(658\) 24.9096 0.971078
\(659\) 6.70174 0.261063 0.130531 0.991444i \(-0.458332\pi\)
0.130531 + 0.991444i \(0.458332\pi\)
\(660\) −32.7873 −1.27624
\(661\) −32.0963 −1.24840 −0.624201 0.781264i \(-0.714575\pi\)
−0.624201 + 0.781264i \(0.714575\pi\)
\(662\) −3.91181 −0.152037
\(663\) −4.43470 −0.172229
\(664\) −6.14988 −0.238662
\(665\) −49.2367 −1.90932
\(666\) 9.91880 0.384346
\(667\) 23.7087 0.918003
\(668\) −0.854626 −0.0330665
\(669\) −36.5722 −1.41396
\(670\) 22.1632 0.856240
\(671\) 48.1282 1.85797
\(672\) 7.28963 0.281204
\(673\) 18.8382 0.726159 0.363080 0.931758i \(-0.381725\pi\)
0.363080 + 0.931758i \(0.381725\pi\)
\(674\) −5.89251 −0.226971
\(675\) 1.08125 0.0416172
\(676\) −8.33186 −0.320456
\(677\) 35.2051 1.35304 0.676521 0.736423i \(-0.263487\pi\)
0.676521 + 0.736423i \(0.263487\pi\)
\(678\) 44.6997 1.71668
\(679\) −31.0873 −1.19302
\(680\) −2.18750 −0.0838867
\(681\) −28.3259 −1.08545
\(682\) −31.3582 −1.20077
\(683\) 29.5822 1.13193 0.565966 0.824429i \(-0.308503\pi\)
0.565966 + 0.824429i \(0.308503\pi\)
\(684\) −17.0494 −0.651902
\(685\) 1.65636 0.0632861
\(686\) 14.2447 0.543865
\(687\) 34.1680 1.30359
\(688\) −2.74552 −0.104672
\(689\) 29.4373 1.12147
\(690\) −15.7698 −0.600346
\(691\) 11.6370 0.442692 0.221346 0.975195i \(-0.428955\pi\)
0.221346 + 0.975195i \(0.428955\pi\)
\(692\) 18.2898 0.695274
\(693\) 44.4476 1.68842
\(694\) 4.25322 0.161450
\(695\) 16.1684 0.613304
\(696\) −21.7483 −0.824369
\(697\) −2.20186 −0.0834013
\(698\) 29.7292 1.12527
\(699\) −49.4002 −1.86849
\(700\) 4.47097 0.168987
\(701\) −51.3777 −1.94051 −0.970255 0.242086i \(-0.922168\pi\)
−0.970255 + 0.242086i \(0.922168\pi\)
\(702\) −1.59675 −0.0602654
\(703\) 23.3671 0.881307
\(704\) 5.40659 0.203769
\(705\) 49.4318 1.86171
\(706\) −3.01361 −0.113419
\(707\) −20.8142 −0.782798
\(708\) −11.7541 −0.441747
\(709\) 17.6913 0.664409 0.332205 0.943207i \(-0.392208\pi\)
0.332205 + 0.943207i \(0.392208\pi\)
\(710\) 14.0371 0.526801
\(711\) 41.8573 1.56977
\(712\) −15.3032 −0.573511
\(713\) −15.0824 −0.564842
\(714\) 6.27241 0.234739
\(715\) 29.6971 1.11061
\(716\) 11.6079 0.433807
\(717\) 49.9815 1.86659
\(718\) −17.5768 −0.655961
\(719\) −32.1842 −1.20027 −0.600134 0.799899i \(-0.704886\pi\)
−0.600134 + 0.799899i \(0.704886\pi\)
\(720\) 6.83913 0.254879
\(721\) 53.3122 1.98545
\(722\) −21.1658 −0.787708
\(723\) 51.8106 1.92686
\(724\) 11.7305 0.435959
\(725\) −13.3390 −0.495397
\(726\) 43.4890 1.61403
\(727\) −22.1568 −0.821750 −0.410875 0.911692i \(-0.634777\pi\)
−0.410875 + 0.911692i \(0.634777\pi\)
\(728\) −6.60259 −0.244708
\(729\) −21.1651 −0.783894
\(730\) 2.63438 0.0975028
\(731\) −2.36240 −0.0873766
\(732\) −21.2343 −0.784844
\(733\) 25.1291 0.928163 0.464081 0.885793i \(-0.346385\pi\)
0.464081 + 0.885793i \(0.346385\pi\)
\(734\) −25.6358 −0.946235
\(735\) −14.1824 −0.523125
\(736\) 2.60042 0.0958529
\(737\) −47.1344 −1.73622
\(738\) 6.88403 0.253404
\(739\) 32.5495 1.19735 0.598676 0.800991i \(-0.295694\pi\)
0.598676 + 0.800991i \(0.295694\pi\)
\(740\) −9.37337 −0.344572
\(741\) 32.6635 1.19992
\(742\) −41.6359 −1.52850
\(743\) −7.62050 −0.279569 −0.139785 0.990182i \(-0.544641\pi\)
−0.139785 + 0.990182i \(0.544641\pi\)
\(744\) 13.8354 0.507229
\(745\) −0.570532 −0.0209027
\(746\) −10.4814 −0.383750
\(747\) 16.5443 0.605325
\(748\) 4.65214 0.170099
\(749\) 32.7476 1.19657
\(750\) −21.4492 −0.783213
\(751\) −38.4999 −1.40488 −0.702440 0.711742i \(-0.747906\pi\)
−0.702440 + 0.711742i \(0.747906\pi\)
\(752\) −8.15126 −0.297246
\(753\) 36.1353 1.31685
\(754\) 19.6986 0.717380
\(755\) 6.49977 0.236551
\(756\) 2.25843 0.0821384
\(757\) −0.692942 −0.0251854 −0.0125927 0.999921i \(-0.504008\pi\)
−0.0125927 + 0.999921i \(0.504008\pi\)
\(758\) 12.4358 0.451690
\(759\) 33.5375 1.21733
\(760\) 16.1119 0.584440
\(761\) 54.8971 1.99002 0.995010 0.0997772i \(-0.0318130\pi\)
0.995010 + 0.0997772i \(0.0318130\pi\)
\(762\) −8.74211 −0.316693
\(763\) 34.2136 1.23862
\(764\) 18.4808 0.668611
\(765\) 5.88477 0.212764
\(766\) −18.2512 −0.659443
\(767\) 10.6463 0.384416
\(768\) −2.38541 −0.0860761
\(769\) −30.4304 −1.09735 −0.548674 0.836036i \(-0.684867\pi\)
−0.548674 + 0.836036i \(0.684867\pi\)
\(770\) −42.0034 −1.51370
\(771\) 66.2478 2.38586
\(772\) −5.84771 −0.210464
\(773\) 40.5910 1.45996 0.729978 0.683471i \(-0.239530\pi\)
0.729978 + 0.683471i \(0.239530\pi\)
\(774\) 7.38597 0.265483
\(775\) 8.48569 0.304815
\(776\) 10.1728 0.365182
\(777\) 26.8771 0.964211
\(778\) −14.5636 −0.522132
\(779\) 16.2177 0.581058
\(780\) −13.1025 −0.469145
\(781\) −29.8525 −1.06821
\(782\) 2.23755 0.0800146
\(783\) −6.73795 −0.240795
\(784\) 2.33866 0.0835236
\(785\) 3.86820 0.138062
\(786\) −42.8740 −1.52926
\(787\) 37.4883 1.33631 0.668157 0.744020i \(-0.267083\pi\)
0.668157 + 0.744020i \(0.267083\pi\)
\(788\) 19.8406 0.706790
\(789\) 0.459773 0.0163683
\(790\) −39.5555 −1.40732
\(791\) 57.2642 2.03608
\(792\) −14.5447 −0.516825
\(793\) 19.2330 0.682985
\(794\) 3.75094 0.133116
\(795\) −82.6243 −2.93038
\(796\) 25.3449 0.898326
\(797\) 50.1042 1.77478 0.887390 0.461019i \(-0.152516\pi\)
0.887390 + 0.461019i \(0.152516\pi\)
\(798\) −46.1991 −1.63543
\(799\) −7.01380 −0.248130
\(800\) −1.46305 −0.0517267
\(801\) 41.1684 1.45461
\(802\) 24.8048 0.875889
\(803\) −5.60252 −0.197709
\(804\) 20.7959 0.733414
\(805\) −20.2025 −0.712045
\(806\) −12.5314 −0.441399
\(807\) −28.0999 −0.989163
\(808\) 6.81110 0.239614
\(809\) −55.8553 −1.96377 −0.981883 0.189486i \(-0.939318\pi\)
−0.981883 + 0.189486i \(0.939318\pi\)
\(810\) 24.9991 0.878380
\(811\) −8.41451 −0.295473 −0.147737 0.989027i \(-0.547199\pi\)
−0.147737 + 0.989027i \(0.547199\pi\)
\(812\) −27.8615 −0.977748
\(813\) −59.2167 −2.07682
\(814\) 19.9343 0.698697
\(815\) 30.7380 1.07671
\(816\) −2.05254 −0.0718533
\(817\) 17.4002 0.608754
\(818\) −25.0789 −0.876863
\(819\) 17.7622 0.620661
\(820\) −6.50548 −0.227181
\(821\) −20.8210 −0.726658 −0.363329 0.931661i \(-0.618360\pi\)
−0.363329 + 0.931661i \(0.618360\pi\)
\(822\) 1.55417 0.0542078
\(823\) 31.1649 1.08634 0.543171 0.839622i \(-0.317224\pi\)
0.543171 + 0.839622i \(0.317224\pi\)
\(824\) −17.4455 −0.607744
\(825\) −18.8689 −0.656931
\(826\) −15.0581 −0.523938
\(827\) −19.4331 −0.675754 −0.337877 0.941190i \(-0.609709\pi\)
−0.337877 + 0.941190i \(0.609709\pi\)
\(828\) −6.99562 −0.243115
\(829\) −16.6418 −0.577992 −0.288996 0.957330i \(-0.593321\pi\)
−0.288996 + 0.957330i \(0.593321\pi\)
\(830\) −15.6346 −0.542684
\(831\) 67.7127 2.34893
\(832\) 2.16059 0.0749049
\(833\) 2.01231 0.0697225
\(834\) 15.1709 0.525327
\(835\) −2.17267 −0.0751885
\(836\) −34.2651 −1.18508
\(837\) 4.28639 0.148159
\(838\) −17.8485 −0.616566
\(839\) 3.75459 0.129623 0.0648115 0.997898i \(-0.479355\pi\)
0.0648115 + 0.997898i \(0.479355\pi\)
\(840\) 18.5321 0.639418
\(841\) 54.1239 1.86634
\(842\) −18.9872 −0.654343
\(843\) −17.9338 −0.617674
\(844\) −9.99447 −0.344024
\(845\) −21.1817 −0.728673
\(846\) 21.9284 0.753914
\(847\) 55.7133 1.91433
\(848\) 13.6247 0.467873
\(849\) −66.8334 −2.29371
\(850\) −1.25889 −0.0431796
\(851\) 9.58785 0.328667
\(852\) 13.1711 0.451233
\(853\) −34.0340 −1.16530 −0.582652 0.812722i \(-0.697985\pi\)
−0.582652 + 0.812722i \(0.697985\pi\)
\(854\) −27.2031 −0.930870
\(855\) −43.3440 −1.48233
\(856\) −10.7161 −0.366269
\(857\) −39.1928 −1.33880 −0.669400 0.742902i \(-0.733449\pi\)
−0.669400 + 0.742902i \(0.733449\pi\)
\(858\) 27.8650 0.951295
\(859\) −30.6985 −1.04742 −0.523710 0.851896i \(-0.675453\pi\)
−0.523710 + 0.851896i \(0.675453\pi\)
\(860\) −6.97982 −0.238010
\(861\) 18.6537 0.635717
\(862\) −26.1878 −0.891959
\(863\) −28.1492 −0.958210 −0.479105 0.877758i \(-0.659039\pi\)
−0.479105 + 0.877758i \(0.659039\pi\)
\(864\) −0.739034 −0.0251425
\(865\) 46.4973 1.58096
\(866\) 20.0820 0.682413
\(867\) 38.7859 1.31724
\(868\) 17.7243 0.601603
\(869\) 84.1225 2.85366
\(870\) −55.2898 −1.87450
\(871\) −18.8359 −0.638230
\(872\) −11.1958 −0.379139
\(873\) −27.3667 −0.926223
\(874\) −16.4806 −0.557463
\(875\) −27.4783 −0.928936
\(876\) 2.47185 0.0835162
\(877\) 43.4027 1.46561 0.732803 0.680441i \(-0.238212\pi\)
0.732803 + 0.680441i \(0.238212\pi\)
\(878\) −39.1621 −1.32166
\(879\) 37.4964 1.26472
\(880\) 13.7449 0.463341
\(881\) −19.9136 −0.670906 −0.335453 0.942057i \(-0.608889\pi\)
−0.335453 + 0.942057i \(0.608889\pi\)
\(882\) −6.29143 −0.211843
\(883\) 27.1883 0.914961 0.457480 0.889220i \(-0.348752\pi\)
0.457480 + 0.889220i \(0.348752\pi\)
\(884\) 1.85909 0.0625280
\(885\) −29.8820 −1.00447
\(886\) 20.4838 0.688168
\(887\) −31.7353 −1.06557 −0.532783 0.846252i \(-0.678854\pi\)
−0.532783 + 0.846252i \(0.678854\pi\)
\(888\) −8.79509 −0.295144
\(889\) −11.1994 −0.375617
\(890\) −38.9046 −1.30408
\(891\) −53.1655 −1.78111
\(892\) 15.3316 0.513341
\(893\) 51.6598 1.72873
\(894\) −0.535334 −0.0179042
\(895\) 29.5102 0.986417
\(896\) −3.05592 −0.102091
\(897\) 13.4023 0.447490
\(898\) 8.81757 0.294246
\(899\) −52.8798 −1.76364
\(900\) 3.93588 0.131196
\(901\) 11.7234 0.390564
\(902\) 13.8352 0.460660
\(903\) 20.0139 0.666019
\(904\) −18.7388 −0.623242
\(905\) 29.8218 0.991310
\(906\) 6.09877 0.202618
\(907\) −11.3881 −0.378137 −0.189069 0.981964i \(-0.560547\pi\)
−0.189069 + 0.981964i \(0.560547\pi\)
\(908\) 11.8746 0.394074
\(909\) −18.3231 −0.607740
\(910\) −16.7855 −0.556432
\(911\) 7.02167 0.232638 0.116319 0.993212i \(-0.462890\pi\)
0.116319 + 0.993212i \(0.462890\pi\)
\(912\) 15.1179 0.500603
\(913\) 33.2499 1.10041
\(914\) −13.0062 −0.430206
\(915\) −53.9831 −1.78463
\(916\) −14.3238 −0.473270
\(917\) −54.9254 −1.81380
\(918\) −0.635907 −0.0209881
\(919\) 17.8583 0.589092 0.294546 0.955637i \(-0.404832\pi\)
0.294546 + 0.955637i \(0.404832\pi\)
\(920\) 6.61093 0.217956
\(921\) −57.3487 −1.88970
\(922\) −7.97413 −0.262614
\(923\) −11.9297 −0.392671
\(924\) −39.4121 −1.29656
\(925\) −5.39432 −0.177364
\(926\) −16.7681 −0.551033
\(927\) 46.9317 1.54144
\(928\) 9.11723 0.299288
\(929\) 18.6170 0.610804 0.305402 0.952224i \(-0.401209\pi\)
0.305402 + 0.952224i \(0.401209\pi\)
\(930\) 35.1730 1.15337
\(931\) −14.8216 −0.485758
\(932\) 20.7093 0.678356
\(933\) 29.1804 0.955323
\(934\) 29.8711 0.977412
\(935\) 11.8269 0.386781
\(936\) −5.81238 −0.189984
\(937\) −1.49264 −0.0487624 −0.0243812 0.999703i \(-0.507762\pi\)
−0.0243812 + 0.999703i \(0.507762\pi\)
\(938\) 26.6414 0.869871
\(939\) 33.7593 1.10169
\(940\) −20.7226 −0.675896
\(941\) −33.8954 −1.10496 −0.552480 0.833526i \(-0.686318\pi\)
−0.552480 + 0.833526i \(0.686318\pi\)
\(942\) 3.62955 0.118257
\(943\) 6.65433 0.216695
\(944\) 4.92751 0.160377
\(945\) 5.74151 0.186771
\(946\) 14.8439 0.482618
\(947\) −46.8040 −1.52093 −0.760463 0.649382i \(-0.775028\pi\)
−0.760463 + 0.649382i \(0.775028\pi\)
\(948\) −37.1152 −1.20545
\(949\) −2.23888 −0.0726773
\(950\) 9.27230 0.300833
\(951\) −41.1517 −1.33444
\(952\) −2.62949 −0.0852222
\(953\) 51.2378 1.65975 0.829877 0.557946i \(-0.188410\pi\)
0.829877 + 0.557946i \(0.188410\pi\)
\(954\) −36.6529 −1.18668
\(955\) 46.9828 1.52033
\(956\) −20.9530 −0.677668
\(957\) 117.584 3.80096
\(958\) 32.0686 1.03609
\(959\) 1.99103 0.0642936
\(960\) −6.06432 −0.195725
\(961\) 2.63990 0.0851581
\(962\) 7.96616 0.256839
\(963\) 28.8283 0.928980
\(964\) −21.7198 −0.699548
\(965\) −14.8664 −0.478565
\(966\) −18.9561 −0.609903
\(967\) 40.2837 1.29544 0.647718 0.761880i \(-0.275724\pi\)
0.647718 + 0.761880i \(0.275724\pi\)
\(968\) −18.2313 −0.585975
\(969\) 13.0083 0.417886
\(970\) 25.8618 0.830373
\(971\) 50.6728 1.62617 0.813084 0.582146i \(-0.197787\pi\)
0.813084 + 0.582146i \(0.197787\pi\)
\(972\) 21.2397 0.681265
\(973\) 19.4353 0.623068
\(974\) −8.43016 −0.270120
\(975\) −7.54041 −0.241486
\(976\) 8.90175 0.284938
\(977\) 4.90163 0.156817 0.0784085 0.996921i \(-0.475016\pi\)
0.0784085 + 0.996921i \(0.475016\pi\)
\(978\) 28.8416 0.922254
\(979\) 82.7381 2.64432
\(980\) 5.94546 0.189921
\(981\) 30.1189 0.961623
\(982\) −41.9399 −1.33835
\(983\) −7.97058 −0.254222 −0.127111 0.991888i \(-0.540570\pi\)
−0.127111 + 0.991888i \(0.540570\pi\)
\(984\) −6.10413 −0.194592
\(985\) 50.4397 1.60714
\(986\) 7.84498 0.249835
\(987\) 59.4197 1.89135
\(988\) −13.6930 −0.435634
\(989\) 7.13952 0.227024
\(990\) −36.9764 −1.17519
\(991\) −32.1858 −1.02242 −0.511208 0.859457i \(-0.670802\pi\)
−0.511208 + 0.859457i \(0.670802\pi\)
\(992\) −5.79999 −0.184150
\(993\) −9.33128 −0.296119
\(994\) 16.8733 0.535188
\(995\) 64.4332 2.04267
\(996\) −14.6700 −0.464837
\(997\) 20.8543 0.660462 0.330231 0.943900i \(-0.392873\pi\)
0.330231 + 0.943900i \(0.392873\pi\)
\(998\) −28.2315 −0.893653
\(999\) −2.72484 −0.0862103
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 \(a_p\))