Properties

Label 8018.2.a.j.1.11
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.99735 q^{3}\) \(+1.00000 q^{4}\) \(-0.291796 q^{5}\) \(-1.99735 q^{6}\) \(-0.492820 q^{7}\) \(+1.00000 q^{8}\) \(+0.989407 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.99735 q^{3}\) \(+1.00000 q^{4}\) \(-0.291796 q^{5}\) \(-1.99735 q^{6}\) \(-0.492820 q^{7}\) \(+1.00000 q^{8}\) \(+0.989407 q^{9}\) \(-0.291796 q^{10}\) \(-5.82808 q^{11}\) \(-1.99735 q^{12}\) \(-2.76888 q^{13}\) \(-0.492820 q^{14}\) \(+0.582818 q^{15}\) \(+1.00000 q^{16}\) \(-7.53438 q^{17}\) \(+0.989407 q^{18}\) \(-1.00000 q^{19}\) \(-0.291796 q^{20}\) \(+0.984334 q^{21}\) \(-5.82808 q^{22}\) \(-1.16315 q^{23}\) \(-1.99735 q^{24}\) \(-4.91486 q^{25}\) \(-2.76888 q^{26}\) \(+4.01586 q^{27}\) \(-0.492820 q^{28}\) \(-5.53317 q^{29}\) \(+0.582818 q^{30}\) \(+0.123478 q^{31}\) \(+1.00000 q^{32}\) \(+11.6407 q^{33}\) \(-7.53438 q^{34}\) \(+0.143803 q^{35}\) \(+0.989407 q^{36}\) \(+0.138353 q^{37}\) \(-1.00000 q^{38}\) \(+5.53041 q^{39}\) \(-0.291796 q^{40}\) \(-0.934090 q^{41}\) \(+0.984334 q^{42}\) \(+1.73877 q^{43}\) \(-5.82808 q^{44}\) \(-0.288705 q^{45}\) \(-1.16315 q^{46}\) \(+3.19055 q^{47}\) \(-1.99735 q^{48}\) \(-6.75713 q^{49}\) \(-4.91486 q^{50}\) \(+15.0488 q^{51}\) \(-2.76888 q^{52}\) \(+0.526470 q^{53}\) \(+4.01586 q^{54}\) \(+1.70061 q^{55}\) \(-0.492820 q^{56}\) \(+1.99735 q^{57}\) \(-5.53317 q^{58}\) \(-7.55977 q^{59}\) \(+0.582818 q^{60}\) \(+5.41561 q^{61}\) \(+0.123478 q^{62}\) \(-0.487600 q^{63}\) \(+1.00000 q^{64}\) \(+0.807946 q^{65}\) \(+11.6407 q^{66}\) \(-2.44673 q^{67}\) \(-7.53438 q^{68}\) \(+2.32322 q^{69}\) \(+0.143803 q^{70}\) \(-5.21157 q^{71}\) \(+0.989407 q^{72}\) \(+10.6474 q^{73}\) \(+0.138353 q^{74}\) \(+9.81669 q^{75}\) \(-1.00000 q^{76}\) \(+2.87219 q^{77}\) \(+5.53041 q^{78}\) \(+6.09239 q^{79}\) \(-0.291796 q^{80}\) \(-10.9893 q^{81}\) \(-0.934090 q^{82}\) \(+0.696438 q^{83}\) \(+0.984334 q^{84}\) \(+2.19850 q^{85}\) \(+1.73877 q^{86}\) \(+11.0517 q^{87}\) \(-5.82808 q^{88}\) \(+15.6407 q^{89}\) \(-0.288705 q^{90}\) \(+1.36456 q^{91}\) \(-1.16315 q^{92}\) \(-0.246628 q^{93}\) \(+3.19055 q^{94}\) \(+0.291796 q^{95}\) \(-1.99735 q^{96}\) \(+3.77181 q^{97}\) \(-6.75713 q^{98}\) \(-5.76634 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.99735 −1.15317 −0.576585 0.817037i \(-0.695615\pi\)
−0.576585 + 0.817037i \(0.695615\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.291796 −0.130495 −0.0652475 0.997869i \(-0.520784\pi\)
−0.0652475 + 0.997869i \(0.520784\pi\)
\(6\) −1.99735 −0.815415
\(7\) −0.492820 −0.186268 −0.0931342 0.995654i \(-0.529689\pi\)
−0.0931342 + 0.995654i \(0.529689\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.989407 0.329802
\(10\) −0.291796 −0.0922739
\(11\) −5.82808 −1.75723 −0.878616 0.477529i \(-0.841532\pi\)
−0.878616 + 0.477529i \(0.841532\pi\)
\(12\) −1.99735 −0.576585
\(13\) −2.76888 −0.767948 −0.383974 0.923344i \(-0.625445\pi\)
−0.383974 + 0.923344i \(0.625445\pi\)
\(14\) −0.492820 −0.131712
\(15\) 0.582818 0.150483
\(16\) 1.00000 0.250000
\(17\) −7.53438 −1.82736 −0.913678 0.406438i \(-0.866771\pi\)
−0.913678 + 0.406438i \(0.866771\pi\)
\(18\) 0.989407 0.233206
\(19\) −1.00000 −0.229416
\(20\) −0.291796 −0.0652475
\(21\) 0.984334 0.214799
\(22\) −5.82808 −1.24255
\(23\) −1.16315 −0.242534 −0.121267 0.992620i \(-0.538696\pi\)
−0.121267 + 0.992620i \(0.538696\pi\)
\(24\) −1.99735 −0.407707
\(25\) −4.91486 −0.982971
\(26\) −2.76888 −0.543021
\(27\) 4.01586 0.772852
\(28\) −0.492820 −0.0931342
\(29\) −5.53317 −1.02748 −0.513742 0.857945i \(-0.671741\pi\)
−0.513742 + 0.857945i \(0.671741\pi\)
\(30\) 0.582818 0.106408
\(31\) 0.123478 0.0221772 0.0110886 0.999939i \(-0.496470\pi\)
0.0110886 + 0.999939i \(0.496470\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.6407 2.02639
\(34\) −7.53438 −1.29214
\(35\) 0.143803 0.0243071
\(36\) 0.989407 0.164901
\(37\) 0.138353 0.0227451 0.0113726 0.999935i \(-0.496380\pi\)
0.0113726 + 0.999935i \(0.496380\pi\)
\(38\) −1.00000 −0.162221
\(39\) 5.53041 0.885575
\(40\) −0.291796 −0.0461369
\(41\) −0.934090 −0.145880 −0.0729402 0.997336i \(-0.523238\pi\)
−0.0729402 + 0.997336i \(0.523238\pi\)
\(42\) 0.984334 0.151886
\(43\) 1.73877 0.265160 0.132580 0.991172i \(-0.457674\pi\)
0.132580 + 0.991172i \(0.457674\pi\)
\(44\) −5.82808 −0.878616
\(45\) −0.288705 −0.0430376
\(46\) −1.16315 −0.171497
\(47\) 3.19055 0.465390 0.232695 0.972550i \(-0.425246\pi\)
0.232695 + 0.972550i \(0.425246\pi\)
\(48\) −1.99735 −0.288293
\(49\) −6.75713 −0.965304
\(50\) −4.91486 −0.695066
\(51\) 15.0488 2.10725
\(52\) −2.76888 −0.383974
\(53\) 0.526470 0.0723162 0.0361581 0.999346i \(-0.488488\pi\)
0.0361581 + 0.999346i \(0.488488\pi\)
\(54\) 4.01586 0.546489
\(55\) 1.70061 0.229310
\(56\) −0.492820 −0.0658558
\(57\) 1.99735 0.264555
\(58\) −5.53317 −0.726540
\(59\) −7.55977 −0.984198 −0.492099 0.870539i \(-0.663770\pi\)
−0.492099 + 0.870539i \(0.663770\pi\)
\(60\) 0.582818 0.0752415
\(61\) 5.41561 0.693398 0.346699 0.937976i \(-0.387303\pi\)
0.346699 + 0.937976i \(0.387303\pi\)
\(62\) 0.123478 0.0156817
\(63\) −0.487600 −0.0614318
\(64\) 1.00000 0.125000
\(65\) 0.807946 0.100213
\(66\) 11.6407 1.43287
\(67\) −2.44673 −0.298915 −0.149458 0.988768i \(-0.547753\pi\)
−0.149458 + 0.988768i \(0.547753\pi\)
\(68\) −7.53438 −0.913678
\(69\) 2.32322 0.279683
\(70\) 0.143803 0.0171877
\(71\) −5.21157 −0.618500 −0.309250 0.950981i \(-0.600078\pi\)
−0.309250 + 0.950981i \(0.600078\pi\)
\(72\) 0.989407 0.116603
\(73\) 10.6474 1.24619 0.623094 0.782147i \(-0.285875\pi\)
0.623094 + 0.782147i \(0.285875\pi\)
\(74\) 0.138353 0.0160832
\(75\) 9.81669 1.13353
\(76\) −1.00000 −0.114708
\(77\) 2.87219 0.327317
\(78\) 5.53041 0.626196
\(79\) 6.09239 0.685448 0.342724 0.939436i \(-0.388650\pi\)
0.342724 + 0.939436i \(0.388650\pi\)
\(80\) −0.291796 −0.0326237
\(81\) −10.9893 −1.22103
\(82\) −0.934090 −0.103153
\(83\) 0.696438 0.0764440 0.0382220 0.999269i \(-0.487831\pi\)
0.0382220 + 0.999269i \(0.487831\pi\)
\(84\) 0.984334 0.107400
\(85\) 2.19850 0.238461
\(86\) 1.73877 0.187496
\(87\) 11.0517 1.18486
\(88\) −5.82808 −0.621275
\(89\) 15.6407 1.65791 0.828954 0.559317i \(-0.188937\pi\)
0.828954 + 0.559317i \(0.188937\pi\)
\(90\) −0.288705 −0.0304321
\(91\) 1.36456 0.143044
\(92\) −1.16315 −0.121267
\(93\) −0.246628 −0.0255741
\(94\) 3.19055 0.329081
\(95\) 0.291796 0.0299376
\(96\) −1.99735 −0.203854
\(97\) 3.77181 0.382969 0.191485 0.981496i \(-0.438670\pi\)
0.191485 + 0.981496i \(0.438670\pi\)
\(98\) −6.75713 −0.682573
\(99\) −5.76634 −0.579539
\(100\) −4.91486 −0.491486
\(101\) −14.1513 −1.40811 −0.704055 0.710146i \(-0.748629\pi\)
−0.704055 + 0.710146i \(0.748629\pi\)
\(102\) 15.0488 1.49005
\(103\) 13.1376 1.29448 0.647242 0.762285i \(-0.275922\pi\)
0.647242 + 0.762285i \(0.275922\pi\)
\(104\) −2.76888 −0.271511
\(105\) −0.287224 −0.0280302
\(106\) 0.526470 0.0511352
\(107\) 3.34526 0.323398 0.161699 0.986840i \(-0.448303\pi\)
0.161699 + 0.986840i \(0.448303\pi\)
\(108\) 4.01586 0.386426
\(109\) 15.5871 1.49297 0.746486 0.665401i \(-0.231739\pi\)
0.746486 + 0.665401i \(0.231739\pi\)
\(110\) 1.70061 0.162147
\(111\) −0.276340 −0.0262290
\(112\) −0.492820 −0.0465671
\(113\) −18.5105 −1.74132 −0.870659 0.491887i \(-0.836307\pi\)
−0.870659 + 0.491887i \(0.836307\pi\)
\(114\) 1.99735 0.187069
\(115\) 0.339403 0.0316495
\(116\) −5.53317 −0.513742
\(117\) −2.73955 −0.253271
\(118\) −7.55977 −0.695933
\(119\) 3.71310 0.340379
\(120\) 0.582818 0.0532038
\(121\) 22.9665 2.08786
\(122\) 5.41561 0.490306
\(123\) 1.86570 0.168225
\(124\) 0.123478 0.0110886
\(125\) 2.89311 0.258768
\(126\) −0.487600 −0.0434388
\(127\) −14.9790 −1.32918 −0.664588 0.747210i \(-0.731393\pi\)
−0.664588 + 0.747210i \(0.731393\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.47293 −0.305774
\(130\) 0.807946 0.0708615
\(131\) 4.23736 0.370220 0.185110 0.982718i \(-0.440736\pi\)
0.185110 + 0.982718i \(0.440736\pi\)
\(132\) 11.6407 1.01319
\(133\) 0.492820 0.0427329
\(134\) −2.44673 −0.211365
\(135\) −1.17181 −0.100853
\(136\) −7.53438 −0.646068
\(137\) 13.9778 1.19420 0.597101 0.802166i \(-0.296319\pi\)
0.597101 + 0.802166i \(0.296319\pi\)
\(138\) 2.32322 0.197766
\(139\) 8.05368 0.683104 0.341552 0.939863i \(-0.389047\pi\)
0.341552 + 0.939863i \(0.389047\pi\)
\(140\) 0.143803 0.0121535
\(141\) −6.37265 −0.536674
\(142\) −5.21157 −0.437346
\(143\) 16.1372 1.34946
\(144\) 0.989407 0.0824506
\(145\) 1.61455 0.134081
\(146\) 10.6474 0.881188
\(147\) 13.4964 1.11316
\(148\) 0.138353 0.0113726
\(149\) 24.1329 1.97704 0.988520 0.151087i \(-0.0482774\pi\)
0.988520 + 0.151087i \(0.0482774\pi\)
\(150\) 9.81669 0.801529
\(151\) −11.8434 −0.963803 −0.481901 0.876226i \(-0.660054\pi\)
−0.481901 + 0.876226i \(0.660054\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −7.45457 −0.602667
\(154\) 2.87219 0.231448
\(155\) −0.0360302 −0.00289402
\(156\) 5.53041 0.442787
\(157\) −11.3220 −0.903594 −0.451797 0.892121i \(-0.649217\pi\)
−0.451797 + 0.892121i \(0.649217\pi\)
\(158\) 6.09239 0.484685
\(159\) −1.05154 −0.0833929
\(160\) −0.291796 −0.0230685
\(161\) 0.573225 0.0451764
\(162\) −10.9893 −0.863401
\(163\) −6.96207 −0.545311 −0.272656 0.962112i \(-0.587902\pi\)
−0.272656 + 0.962112i \(0.587902\pi\)
\(164\) −0.934090 −0.0729402
\(165\) −3.39671 −0.264433
\(166\) 0.696438 0.0540541
\(167\) −20.3291 −1.57311 −0.786557 0.617518i \(-0.788138\pi\)
−0.786557 + 0.617518i \(0.788138\pi\)
\(168\) 0.984334 0.0759430
\(169\) −5.33333 −0.410256
\(170\) 2.19850 0.168617
\(171\) −0.989407 −0.0756619
\(172\) 1.73877 0.132580
\(173\) −12.3099 −0.935906 −0.467953 0.883753i \(-0.655008\pi\)
−0.467953 + 0.883753i \(0.655008\pi\)
\(174\) 11.0517 0.837825
\(175\) 2.42214 0.183097
\(176\) −5.82808 −0.439308
\(177\) 15.0995 1.13495
\(178\) 15.6407 1.17232
\(179\) −22.9118 −1.71251 −0.856253 0.516557i \(-0.827213\pi\)
−0.856253 + 0.516557i \(0.827213\pi\)
\(180\) −0.288705 −0.0215188
\(181\) 16.3957 1.21868 0.609341 0.792908i \(-0.291434\pi\)
0.609341 + 0.792908i \(0.291434\pi\)
\(182\) 1.36456 0.101148
\(183\) −10.8169 −0.799606
\(184\) −1.16315 −0.0857487
\(185\) −0.0403709 −0.00296813
\(186\) −0.246628 −0.0180836
\(187\) 43.9110 3.21109
\(188\) 3.19055 0.232695
\(189\) −1.97910 −0.143958
\(190\) 0.291796 0.0211691
\(191\) 19.1529 1.38586 0.692928 0.721007i \(-0.256320\pi\)
0.692928 + 0.721007i \(0.256320\pi\)
\(192\) −1.99735 −0.144146
\(193\) −23.7671 −1.71079 −0.855396 0.517974i \(-0.826686\pi\)
−0.855396 + 0.517974i \(0.826686\pi\)
\(194\) 3.77181 0.270800
\(195\) −1.61375 −0.115563
\(196\) −6.75713 −0.482652
\(197\) −3.50954 −0.250044 −0.125022 0.992154i \(-0.539900\pi\)
−0.125022 + 0.992154i \(0.539900\pi\)
\(198\) −5.76634 −0.409796
\(199\) −12.7834 −0.906191 −0.453095 0.891462i \(-0.649680\pi\)
−0.453095 + 0.891462i \(0.649680\pi\)
\(200\) −4.91486 −0.347533
\(201\) 4.88697 0.344700
\(202\) −14.1513 −0.995684
\(203\) 2.72686 0.191388
\(204\) 15.0488 1.05363
\(205\) 0.272563 0.0190366
\(206\) 13.1376 0.915338
\(207\) −1.15083 −0.0799883
\(208\) −2.76888 −0.191987
\(209\) 5.82808 0.403137
\(210\) −0.287224 −0.0198204
\(211\) −1.00000 −0.0688428
\(212\) 0.526470 0.0361581
\(213\) 10.4093 0.713236
\(214\) 3.34526 0.228677
\(215\) −0.507365 −0.0346020
\(216\) 4.01586 0.273244
\(217\) −0.0608522 −0.00413092
\(218\) 15.5871 1.05569
\(219\) −21.2666 −1.43707
\(220\) 1.70061 0.114655
\(221\) 20.8618 1.40331
\(222\) −0.276340 −0.0185467
\(223\) −24.5778 −1.64585 −0.822927 0.568148i \(-0.807660\pi\)
−0.822927 + 0.568148i \(0.807660\pi\)
\(224\) −0.492820 −0.0329279
\(225\) −4.86279 −0.324186
\(226\) −18.5105 −1.23130
\(227\) −21.9324 −1.45570 −0.727852 0.685735i \(-0.759481\pi\)
−0.727852 + 0.685735i \(0.759481\pi\)
\(228\) 1.99735 0.132278
\(229\) 12.8876 0.851634 0.425817 0.904809i \(-0.359987\pi\)
0.425817 + 0.904809i \(0.359987\pi\)
\(230\) 0.339403 0.0223795
\(231\) −5.73678 −0.377452
\(232\) −5.53317 −0.363270
\(233\) 3.47952 0.227951 0.113975 0.993484i \(-0.463642\pi\)
0.113975 + 0.993484i \(0.463642\pi\)
\(234\) −2.73955 −0.179090
\(235\) −0.930990 −0.0607311
\(236\) −7.55977 −0.492099
\(237\) −12.1686 −0.790438
\(238\) 3.71310 0.240684
\(239\) 13.0297 0.842819 0.421410 0.906870i \(-0.361535\pi\)
0.421410 + 0.906870i \(0.361535\pi\)
\(240\) 0.582818 0.0376207
\(241\) −15.5204 −0.999757 −0.499878 0.866096i \(-0.666622\pi\)
−0.499878 + 0.866096i \(0.666622\pi\)
\(242\) 22.9665 1.47634
\(243\) 9.90190 0.635207
\(244\) 5.41561 0.346699
\(245\) 1.97170 0.125967
\(246\) 1.86570 0.118953
\(247\) 2.76888 0.176179
\(248\) 0.123478 0.00784083
\(249\) −1.39103 −0.0881530
\(250\) 2.89311 0.182976
\(251\) −27.0675 −1.70849 −0.854243 0.519873i \(-0.825979\pi\)
−0.854243 + 0.519873i \(0.825979\pi\)
\(252\) −0.487600 −0.0307159
\(253\) 6.77894 0.426188
\(254\) −14.9790 −0.939869
\(255\) −4.39117 −0.274986
\(256\) 1.00000 0.0625000
\(257\) −15.5280 −0.968608 −0.484304 0.874900i \(-0.660927\pi\)
−0.484304 + 0.874900i \(0.660927\pi\)
\(258\) −3.47293 −0.216215
\(259\) −0.0681833 −0.00423670
\(260\) 0.807946 0.0501067
\(261\) −5.47456 −0.338866
\(262\) 4.23736 0.261785
\(263\) 7.97221 0.491588 0.245794 0.969322i \(-0.420951\pi\)
0.245794 + 0.969322i \(0.420951\pi\)
\(264\) 11.6407 0.716436
\(265\) −0.153621 −0.00943689
\(266\) 0.492820 0.0302167
\(267\) −31.2399 −1.91185
\(268\) −2.44673 −0.149458
\(269\) 18.4928 1.12752 0.563762 0.825937i \(-0.309353\pi\)
0.563762 + 0.825937i \(0.309353\pi\)
\(270\) −1.17181 −0.0713141
\(271\) −28.4817 −1.73014 −0.865069 0.501653i \(-0.832726\pi\)
−0.865069 + 0.501653i \(0.832726\pi\)
\(272\) −7.53438 −0.456839
\(273\) −2.72550 −0.164955
\(274\) 13.9778 0.844429
\(275\) 28.6442 1.72731
\(276\) 2.32322 0.139842
\(277\) 31.9367 1.91889 0.959444 0.281900i \(-0.0909646\pi\)
0.959444 + 0.281900i \(0.0909646\pi\)
\(278\) 8.05368 0.483027
\(279\) 0.122170 0.00731410
\(280\) 0.143803 0.00859386
\(281\) 16.0852 0.959563 0.479781 0.877388i \(-0.340716\pi\)
0.479781 + 0.877388i \(0.340716\pi\)
\(282\) −6.37265 −0.379486
\(283\) 26.7258 1.58868 0.794342 0.607471i \(-0.207816\pi\)
0.794342 + 0.607471i \(0.207816\pi\)
\(284\) −5.21157 −0.309250
\(285\) −0.582818 −0.0345232
\(286\) 16.1372 0.954214
\(287\) 0.460338 0.0271729
\(288\) 0.989407 0.0583014
\(289\) 39.7669 2.33923
\(290\) 1.61455 0.0948099
\(291\) −7.53363 −0.441629
\(292\) 10.6474 0.623094
\(293\) −6.32828 −0.369702 −0.184851 0.982767i \(-0.559180\pi\)
−0.184851 + 0.982767i \(0.559180\pi\)
\(294\) 13.4964 0.787123
\(295\) 2.20591 0.128433
\(296\) 0.138353 0.00804162
\(297\) −23.4047 −1.35808
\(298\) 24.1329 1.39798
\(299\) 3.22062 0.186253
\(300\) 9.81669 0.566767
\(301\) −0.856900 −0.0493909
\(302\) −11.8434 −0.681511
\(303\) 28.2651 1.62379
\(304\) −1.00000 −0.0573539
\(305\) −1.58025 −0.0904849
\(306\) −7.45457 −0.426150
\(307\) 21.8190 1.24527 0.622637 0.782511i \(-0.286061\pi\)
0.622637 + 0.782511i \(0.286061\pi\)
\(308\) 2.87219 0.163658
\(309\) −26.2403 −1.49276
\(310\) −0.0360302 −0.00204638
\(311\) 0.448831 0.0254509 0.0127254 0.999919i \(-0.495949\pi\)
0.0127254 + 0.999919i \(0.495949\pi\)
\(312\) 5.53041 0.313098
\(313\) −7.58291 −0.428611 −0.214306 0.976767i \(-0.568749\pi\)
−0.214306 + 0.976767i \(0.568749\pi\)
\(314\) −11.3220 −0.638938
\(315\) 0.142279 0.00801654
\(316\) 6.09239 0.342724
\(317\) −5.26198 −0.295543 −0.147771 0.989022i \(-0.547210\pi\)
−0.147771 + 0.989022i \(0.547210\pi\)
\(318\) −1.05154 −0.0589677
\(319\) 32.2477 1.80553
\(320\) −0.291796 −0.0163119
\(321\) −6.68165 −0.372933
\(322\) 0.573225 0.0319446
\(323\) 7.53438 0.419224
\(324\) −10.9893 −0.610516
\(325\) 13.6086 0.754870
\(326\) −6.96207 −0.385593
\(327\) −31.1329 −1.72165
\(328\) −0.934090 −0.0515765
\(329\) −1.57237 −0.0866875
\(330\) −3.39671 −0.186983
\(331\) −6.85598 −0.376839 −0.188419 0.982089i \(-0.560336\pi\)
−0.188419 + 0.982089i \(0.560336\pi\)
\(332\) 0.696438 0.0382220
\(333\) 0.136888 0.00750140
\(334\) −20.3291 −1.11236
\(335\) 0.713944 0.0390069
\(336\) 0.984334 0.0536998
\(337\) −25.1687 −1.37103 −0.685515 0.728059i \(-0.740423\pi\)
−0.685515 + 0.728059i \(0.740423\pi\)
\(338\) −5.33333 −0.290095
\(339\) 36.9719 2.00804
\(340\) 2.19850 0.119230
\(341\) −0.719637 −0.0389705
\(342\) −0.989407 −0.0535010
\(343\) 6.77979 0.366074
\(344\) 1.73877 0.0937481
\(345\) −0.677906 −0.0364972
\(346\) −12.3099 −0.661785
\(347\) 12.2928 0.659910 0.329955 0.943997i \(-0.392966\pi\)
0.329955 + 0.943997i \(0.392966\pi\)
\(348\) 11.0517 0.592432
\(349\) 14.6723 0.785389 0.392694 0.919669i \(-0.371543\pi\)
0.392694 + 0.919669i \(0.371543\pi\)
\(350\) 2.42214 0.129469
\(351\) −11.1194 −0.593510
\(352\) −5.82808 −0.310638
\(353\) 12.8028 0.681422 0.340711 0.940168i \(-0.389332\pi\)
0.340711 + 0.940168i \(0.389332\pi\)
\(354\) 15.0995 0.802530
\(355\) 1.52071 0.0807111
\(356\) 15.6407 0.828954
\(357\) −7.41635 −0.392515
\(358\) −22.9118 −1.21092
\(359\) −30.8014 −1.62564 −0.812819 0.582516i \(-0.802068\pi\)
−0.812819 + 0.582516i \(0.802068\pi\)
\(360\) −0.288705 −0.0152161
\(361\) 1.00000 0.0526316
\(362\) 16.3957 0.861739
\(363\) −45.8721 −2.40766
\(364\) 1.36456 0.0715222
\(365\) −3.10687 −0.162621
\(366\) −10.8169 −0.565407
\(367\) −0.442858 −0.0231170 −0.0115585 0.999933i \(-0.503679\pi\)
−0.0115585 + 0.999933i \(0.503679\pi\)
\(368\) −1.16315 −0.0606335
\(369\) −0.924195 −0.0481117
\(370\) −0.0403709 −0.00209878
\(371\) −0.259455 −0.0134702
\(372\) −0.246628 −0.0127871
\(373\) 29.7502 1.54041 0.770204 0.637797i \(-0.220154\pi\)
0.770204 + 0.637797i \(0.220154\pi\)
\(374\) 43.9110 2.27058
\(375\) −5.77856 −0.298403
\(376\) 3.19055 0.164540
\(377\) 15.3206 0.789054
\(378\) −1.97910 −0.101794
\(379\) 11.9391 0.613271 0.306636 0.951827i \(-0.400797\pi\)
0.306636 + 0.951827i \(0.400797\pi\)
\(380\) 0.291796 0.0149688
\(381\) 29.9184 1.53277
\(382\) 19.1529 0.979948
\(383\) 7.06516 0.361013 0.180506 0.983574i \(-0.442226\pi\)
0.180506 + 0.983574i \(0.442226\pi\)
\(384\) −1.99735 −0.101927
\(385\) −0.838093 −0.0427132
\(386\) −23.7671 −1.20971
\(387\) 1.72035 0.0874503
\(388\) 3.77181 0.191485
\(389\) 0.804055 0.0407672 0.0203836 0.999792i \(-0.493511\pi\)
0.0203836 + 0.999792i \(0.493511\pi\)
\(390\) −1.61375 −0.0817154
\(391\) 8.76363 0.443196
\(392\) −6.75713 −0.341287
\(393\) −8.46349 −0.426927
\(394\) −3.50954 −0.176808
\(395\) −1.77773 −0.0894475
\(396\) −5.76634 −0.289770
\(397\) −7.48659 −0.375741 −0.187870 0.982194i \(-0.560159\pi\)
−0.187870 + 0.982194i \(0.560159\pi\)
\(398\) −12.7834 −0.640774
\(399\) −0.984334 −0.0492783
\(400\) −4.91486 −0.245743
\(401\) 30.1926 1.50775 0.753874 0.657019i \(-0.228183\pi\)
0.753874 + 0.657019i \(0.228183\pi\)
\(402\) 4.88697 0.243740
\(403\) −0.341894 −0.0170310
\(404\) −14.1513 −0.704055
\(405\) 3.20663 0.159339
\(406\) 2.72686 0.135332
\(407\) −0.806333 −0.0399685
\(408\) 15.0488 0.745027
\(409\) 14.6143 0.722632 0.361316 0.932443i \(-0.382328\pi\)
0.361316 + 0.932443i \(0.382328\pi\)
\(410\) 0.272563 0.0134609
\(411\) −27.9185 −1.37712
\(412\) 13.1376 0.647242
\(413\) 3.72561 0.183325
\(414\) −1.15083 −0.0565603
\(415\) −0.203218 −0.00997556
\(416\) −2.76888 −0.135755
\(417\) −16.0860 −0.787735
\(418\) 5.82808 0.285061
\(419\) −31.7737 −1.55225 −0.776123 0.630581i \(-0.782816\pi\)
−0.776123 + 0.630581i \(0.782816\pi\)
\(420\) −0.287224 −0.0140151
\(421\) 35.8484 1.74715 0.873573 0.486694i \(-0.161797\pi\)
0.873573 + 0.486694i \(0.161797\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 3.15676 0.153487
\(424\) 0.526470 0.0255676
\(425\) 37.0304 1.79624
\(426\) 10.4093 0.504334
\(427\) −2.66892 −0.129158
\(428\) 3.34526 0.161699
\(429\) −32.2317 −1.55616
\(430\) −0.507365 −0.0244673
\(431\) 2.41840 0.116490 0.0582450 0.998302i \(-0.481450\pi\)
0.0582450 + 0.998302i \(0.481450\pi\)
\(432\) 4.01586 0.193213
\(433\) 26.0821 1.25343 0.626713 0.779250i \(-0.284400\pi\)
0.626713 + 0.779250i \(0.284400\pi\)
\(434\) −0.0608522 −0.00292100
\(435\) −3.22483 −0.154619
\(436\) 15.5871 0.746486
\(437\) 1.16315 0.0556411
\(438\) −21.2666 −1.01616
\(439\) 9.81398 0.468396 0.234198 0.972189i \(-0.424754\pi\)
0.234198 + 0.972189i \(0.424754\pi\)
\(440\) 1.70061 0.0810733
\(441\) −6.68555 −0.318360
\(442\) 20.8618 0.992293
\(443\) −7.96518 −0.378437 −0.189219 0.981935i \(-0.560595\pi\)
−0.189219 + 0.981935i \(0.560595\pi\)
\(444\) −0.276340 −0.0131145
\(445\) −4.56388 −0.216349
\(446\) −24.5778 −1.16379
\(447\) −48.2018 −2.27987
\(448\) −0.492820 −0.0232836
\(449\) 41.7261 1.96917 0.984587 0.174894i \(-0.0559581\pi\)
0.984587 + 0.174894i \(0.0559581\pi\)
\(450\) −4.86279 −0.229234
\(451\) 5.44395 0.256345
\(452\) −18.5105 −0.870659
\(453\) 23.6554 1.11143
\(454\) −21.9324 −1.02934
\(455\) −0.398172 −0.0186666
\(456\) 1.99735 0.0935345
\(457\) 1.15273 0.0539224 0.0269612 0.999636i \(-0.491417\pi\)
0.0269612 + 0.999636i \(0.491417\pi\)
\(458\) 12.8876 0.602196
\(459\) −30.2570 −1.41228
\(460\) 0.339403 0.0158247
\(461\) 10.4866 0.488410 0.244205 0.969724i \(-0.421473\pi\)
0.244205 + 0.969724i \(0.421473\pi\)
\(462\) −5.73678 −0.266899
\(463\) 12.0262 0.558904 0.279452 0.960160i \(-0.409847\pi\)
0.279452 + 0.960160i \(0.409847\pi\)
\(464\) −5.53317 −0.256871
\(465\) 0.0719649 0.00333729
\(466\) 3.47952 0.161186
\(467\) 3.99432 0.184835 0.0924175 0.995720i \(-0.470541\pi\)
0.0924175 + 0.995720i \(0.470541\pi\)
\(468\) −2.73955 −0.126636
\(469\) 1.20580 0.0556785
\(470\) −0.930990 −0.0429433
\(471\) 22.6140 1.04200
\(472\) −7.55977 −0.347967
\(473\) −10.1337 −0.465947
\(474\) −12.1686 −0.558924
\(475\) 4.91486 0.225509
\(476\) 3.71310 0.170189
\(477\) 0.520893 0.0238500
\(478\) 13.0297 0.595963
\(479\) −25.3246 −1.15711 −0.578556 0.815643i \(-0.696383\pi\)
−0.578556 + 0.815643i \(0.696383\pi\)
\(480\) 0.582818 0.0266019
\(481\) −0.383083 −0.0174671
\(482\) −15.5204 −0.706935
\(483\) −1.14493 −0.0520961
\(484\) 22.9665 1.04393
\(485\) −1.10060 −0.0499756
\(486\) 9.90190 0.449159
\(487\) 8.66907 0.392833 0.196417 0.980521i \(-0.437070\pi\)
0.196417 + 0.980521i \(0.437070\pi\)
\(488\) 5.41561 0.245153
\(489\) 13.9057 0.628837
\(490\) 1.97170 0.0890723
\(491\) −19.3277 −0.872248 −0.436124 0.899887i \(-0.643649\pi\)
−0.436124 + 0.899887i \(0.643649\pi\)
\(492\) 1.86570 0.0841124
\(493\) 41.6890 1.87758
\(494\) 2.76888 0.124578
\(495\) 1.68259 0.0756269
\(496\) 0.123478 0.00554431
\(497\) 2.56837 0.115207
\(498\) −1.39103 −0.0623336
\(499\) −36.3023 −1.62511 −0.812556 0.582883i \(-0.801925\pi\)
−0.812556 + 0.582883i \(0.801925\pi\)
\(500\) 2.89311 0.129384
\(501\) 40.6043 1.81407
\(502\) −27.0675 −1.20808
\(503\) 10.2155 0.455487 0.227744 0.973721i \(-0.426865\pi\)
0.227744 + 0.973721i \(0.426865\pi\)
\(504\) −0.487600 −0.0217194
\(505\) 4.12929 0.183751
\(506\) 6.77894 0.301361
\(507\) 10.6525 0.473095
\(508\) −14.9790 −0.664588
\(509\) −21.1152 −0.935915 −0.467958 0.883751i \(-0.655010\pi\)
−0.467958 + 0.883751i \(0.655010\pi\)
\(510\) −4.39117 −0.194444
\(511\) −5.24727 −0.232125
\(512\) 1.00000 0.0441942
\(513\) −4.01586 −0.177304
\(514\) −15.5280 −0.684909
\(515\) −3.83349 −0.168924
\(516\) −3.47293 −0.152887
\(517\) −18.5948 −0.817798
\(518\) −0.0681833 −0.00299580
\(519\) 24.5872 1.07926
\(520\) 0.807946 0.0354308
\(521\) −33.4775 −1.46668 −0.733339 0.679863i \(-0.762039\pi\)
−0.733339 + 0.679863i \(0.762039\pi\)
\(522\) −5.47456 −0.239615
\(523\) 9.79291 0.428214 0.214107 0.976810i \(-0.431316\pi\)
0.214107 + 0.976810i \(0.431316\pi\)
\(524\) 4.23736 0.185110
\(525\) −4.83786 −0.211142
\(526\) 7.97221 0.347605
\(527\) −0.930327 −0.0405257
\(528\) 11.6407 0.506597
\(529\) −21.6471 −0.941177
\(530\) −0.153621 −0.00667289
\(531\) −7.47969 −0.324591
\(532\) 0.492820 0.0213665
\(533\) 2.58638 0.112028
\(534\) −31.2399 −1.35188
\(535\) −0.976131 −0.0422018
\(536\) −2.44673 −0.105683
\(537\) 45.7628 1.97481
\(538\) 18.4928 0.797280
\(539\) 39.3811 1.69626
\(540\) −1.17181 −0.0504267
\(541\) 13.5677 0.583322 0.291661 0.956522i \(-0.405792\pi\)
0.291661 + 0.956522i \(0.405792\pi\)
\(542\) −28.4817 −1.22339
\(543\) −32.7479 −1.40535
\(544\) −7.53438 −0.323034
\(545\) −4.54824 −0.194825
\(546\) −2.72550 −0.116641
\(547\) 28.3311 1.21135 0.605676 0.795712i \(-0.292903\pi\)
0.605676 + 0.795712i \(0.292903\pi\)
\(548\) 13.9778 0.597101
\(549\) 5.35824 0.228684
\(550\) 28.6442 1.22139
\(551\) 5.53317 0.235721
\(552\) 2.32322 0.0988829
\(553\) −3.00245 −0.127677
\(554\) 31.9367 1.35686
\(555\) 0.0806348 0.00342275
\(556\) 8.05368 0.341552
\(557\) −5.25046 −0.222469 −0.111235 0.993794i \(-0.535480\pi\)
−0.111235 + 0.993794i \(0.535480\pi\)
\(558\) 0.122170 0.00517185
\(559\) −4.81443 −0.203629
\(560\) 0.143803 0.00607677
\(561\) −87.7056 −3.70293
\(562\) 16.0852 0.678513
\(563\) −42.7066 −1.79987 −0.899935 0.436024i \(-0.856386\pi\)
−0.899935 + 0.436024i \(0.856386\pi\)
\(564\) −6.37265 −0.268337
\(565\) 5.40127 0.227233
\(566\) 26.7258 1.12337
\(567\) 5.41574 0.227440
\(568\) −5.21157 −0.218673
\(569\) 19.9747 0.837382 0.418691 0.908129i \(-0.362489\pi\)
0.418691 + 0.908129i \(0.362489\pi\)
\(570\) −0.582818 −0.0244116
\(571\) −45.3844 −1.89928 −0.949640 0.313343i \(-0.898551\pi\)
−0.949640 + 0.313343i \(0.898551\pi\)
\(572\) 16.1372 0.674731
\(573\) −38.2551 −1.59813
\(574\) 0.460338 0.0192141
\(575\) 5.71672 0.238404
\(576\) 0.989407 0.0412253
\(577\) −5.22582 −0.217554 −0.108777 0.994066i \(-0.534693\pi\)
−0.108777 + 0.994066i \(0.534693\pi\)
\(578\) 39.7669 1.65409
\(579\) 47.4712 1.97284
\(580\) 1.61455 0.0670407
\(581\) −0.343219 −0.0142391
\(582\) −7.53363 −0.312279
\(583\) −3.06831 −0.127076
\(584\) 10.6474 0.440594
\(585\) 0.799387 0.0330506
\(586\) −6.32828 −0.261419
\(587\) 40.9700 1.69101 0.845506 0.533966i \(-0.179299\pi\)
0.845506 + 0.533966i \(0.179299\pi\)
\(588\) 13.4964 0.556580
\(589\) −0.123478 −0.00508780
\(590\) 2.20591 0.0908158
\(591\) 7.00978 0.288344
\(592\) 0.138353 0.00568628
\(593\) −11.5644 −0.474892 −0.237446 0.971401i \(-0.576310\pi\)
−0.237446 + 0.971401i \(0.576310\pi\)
\(594\) −23.4047 −0.960308
\(595\) −1.08346 −0.0444177
\(596\) 24.1329 0.988520
\(597\) 25.5329 1.04499
\(598\) 3.22062 0.131701
\(599\) 18.8113 0.768610 0.384305 0.923206i \(-0.374441\pi\)
0.384305 + 0.923206i \(0.374441\pi\)
\(600\) 9.81669 0.400765
\(601\) −9.98897 −0.407459 −0.203729 0.979027i \(-0.565306\pi\)
−0.203729 + 0.979027i \(0.565306\pi\)
\(602\) −0.856900 −0.0349246
\(603\) −2.42081 −0.0985830
\(604\) −11.8434 −0.481901
\(605\) −6.70152 −0.272456
\(606\) 28.2651 1.14819
\(607\) 22.6819 0.920631 0.460316 0.887755i \(-0.347736\pi\)
0.460316 + 0.887755i \(0.347736\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −5.44649 −0.220703
\(610\) −1.58025 −0.0639825
\(611\) −8.83425 −0.357395
\(612\) −7.45457 −0.301333
\(613\) 13.6552 0.551527 0.275764 0.961225i \(-0.411069\pi\)
0.275764 + 0.961225i \(0.411069\pi\)
\(614\) 21.8190 0.880542
\(615\) −0.544404 −0.0219525
\(616\) 2.87219 0.115724
\(617\) −11.4070 −0.459230 −0.229615 0.973282i \(-0.573747\pi\)
−0.229615 + 0.973282i \(0.573747\pi\)
\(618\) −26.2403 −1.05554
\(619\) −20.2291 −0.813078 −0.406539 0.913633i \(-0.633264\pi\)
−0.406539 + 0.913633i \(0.633264\pi\)
\(620\) −0.0360302 −0.00144701
\(621\) −4.67105 −0.187443
\(622\) 0.448831 0.0179965
\(623\) −7.70804 −0.308816
\(624\) 5.53041 0.221394
\(625\) 23.7301 0.949203
\(626\) −7.58291 −0.303074
\(627\) −11.6407 −0.464885
\(628\) −11.3220 −0.451797
\(629\) −1.04241 −0.0415635
\(630\) 0.142279 0.00566855
\(631\) 3.14265 0.125107 0.0625534 0.998042i \(-0.480076\pi\)
0.0625534 + 0.998042i \(0.480076\pi\)
\(632\) 6.09239 0.242342
\(633\) 1.99735 0.0793875
\(634\) −5.26198 −0.208980
\(635\) 4.37082 0.173451
\(636\) −1.05154 −0.0416964
\(637\) 18.7096 0.741303
\(638\) 32.2477 1.27670
\(639\) −5.15637 −0.203983
\(640\) −0.291796 −0.0115342
\(641\) 23.2901 0.919904 0.459952 0.887944i \(-0.347867\pi\)
0.459952 + 0.887944i \(0.347867\pi\)
\(642\) −6.68165 −0.263704
\(643\) 29.5873 1.16681 0.583404 0.812182i \(-0.301720\pi\)
0.583404 + 0.812182i \(0.301720\pi\)
\(644\) 0.573225 0.0225882
\(645\) 1.01339 0.0399020
\(646\) 7.53438 0.296436
\(647\) 21.9890 0.864476 0.432238 0.901760i \(-0.357724\pi\)
0.432238 + 0.901760i \(0.357724\pi\)
\(648\) −10.9893 −0.431700
\(649\) 44.0589 1.72946
\(650\) 13.6086 0.533774
\(651\) 0.121543 0.00476365
\(652\) −6.96207 −0.272656
\(653\) −39.6858 −1.55303 −0.776513 0.630102i \(-0.783013\pi\)
−0.776513 + 0.630102i \(0.783013\pi\)
\(654\) −31.1329 −1.21739
\(655\) −1.23644 −0.0483118
\(656\) −0.934090 −0.0364701
\(657\) 10.5346 0.410996
\(658\) −1.57237 −0.0612973
\(659\) 3.50378 0.136488 0.0682440 0.997669i \(-0.478260\pi\)
0.0682440 + 0.997669i \(0.478260\pi\)
\(660\) −3.39671 −0.132217
\(661\) −35.1467 −1.36705 −0.683524 0.729928i \(-0.739553\pi\)
−0.683524 + 0.729928i \(0.739553\pi\)
\(662\) −6.85598 −0.266465
\(663\) −41.6683 −1.61826
\(664\) 0.696438 0.0270270
\(665\) −0.143803 −0.00557643
\(666\) 0.136888 0.00530429
\(667\) 6.43592 0.249200
\(668\) −20.3291 −0.786557
\(669\) 49.0905 1.89795
\(670\) 0.713944 0.0275821
\(671\) −31.5626 −1.21846
\(672\) 0.984334 0.0379715
\(673\) −9.52050 −0.366988 −0.183494 0.983021i \(-0.558741\pi\)
−0.183494 + 0.983021i \(0.558741\pi\)
\(674\) −25.1687 −0.969464
\(675\) −19.7374 −0.759691
\(676\) −5.33333 −0.205128
\(677\) −25.6306 −0.985063 −0.492531 0.870295i \(-0.663928\pi\)
−0.492531 + 0.870295i \(0.663928\pi\)
\(678\) 36.9719 1.41990
\(679\) −1.85882 −0.0713351
\(680\) 2.19850 0.0843086
\(681\) 43.8066 1.67867
\(682\) −0.719637 −0.0275563
\(683\) −19.4007 −0.742347 −0.371174 0.928564i \(-0.621045\pi\)
−0.371174 + 0.928564i \(0.621045\pi\)
\(684\) −0.989407 −0.0378309
\(685\) −4.07866 −0.155837
\(686\) 6.77979 0.258854
\(687\) −25.7410 −0.982079
\(688\) 1.73877 0.0662899
\(689\) −1.45773 −0.0555350
\(690\) −0.677906 −0.0258074
\(691\) −29.1286 −1.10810 −0.554052 0.832482i \(-0.686919\pi\)
−0.554052 + 0.832482i \(0.686919\pi\)
\(692\) −12.3099 −0.467953
\(693\) 2.84177 0.107950
\(694\) 12.2928 0.466627
\(695\) −2.35003 −0.0891416
\(696\) 11.0517 0.418913
\(697\) 7.03779 0.266575
\(698\) 14.6723 0.555354
\(699\) −6.94981 −0.262866
\(700\) 2.42214 0.0915483
\(701\) 44.0043 1.66202 0.831009 0.556259i \(-0.187764\pi\)
0.831009 + 0.556259i \(0.187764\pi\)
\(702\) −11.1194 −0.419675
\(703\) −0.138353 −0.00521809
\(704\) −5.82808 −0.219654
\(705\) 1.85951 0.0700333
\(706\) 12.8028 0.481838
\(707\) 6.97406 0.262286
\(708\) 15.0995 0.567474
\(709\) 41.3975 1.55472 0.777358 0.629058i \(-0.216559\pi\)
0.777358 + 0.629058i \(0.216559\pi\)
\(710\) 1.52071 0.0570714
\(711\) 6.02786 0.226062
\(712\) 15.6407 0.586159
\(713\) −0.143623 −0.00537873
\(714\) −7.41635 −0.277550
\(715\) −4.70877 −0.176098
\(716\) −22.9118 −0.856253
\(717\) −26.0248 −0.971914
\(718\) −30.8014 −1.14950
\(719\) −6.53979 −0.243893 −0.121947 0.992537i \(-0.538914\pi\)
−0.121947 + 0.992537i \(0.538914\pi\)
\(720\) −0.288705 −0.0107594
\(721\) −6.47446 −0.241122
\(722\) 1.00000 0.0372161
\(723\) 30.9997 1.15289
\(724\) 16.3957 0.609341
\(725\) 27.1947 1.00999
\(726\) −45.8721 −1.70247
\(727\) 5.24387 0.194484 0.0972422 0.995261i \(-0.468998\pi\)
0.0972422 + 0.995261i \(0.468998\pi\)
\(728\) 1.36456 0.0505739
\(729\) 13.1903 0.488531
\(730\) −3.10687 −0.114991
\(731\) −13.1005 −0.484541
\(732\) −10.8169 −0.399803
\(733\) 19.1105 0.705864 0.352932 0.935649i \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(734\) −0.442858 −0.0163462
\(735\) −3.93818 −0.145262
\(736\) −1.16315 −0.0428744
\(737\) 14.2597 0.525263
\(738\) −0.924195 −0.0340201
\(739\) −41.0095 −1.50856 −0.754280 0.656553i \(-0.772014\pi\)
−0.754280 + 0.656553i \(0.772014\pi\)
\(740\) −0.0403709 −0.00148406
\(741\) −5.53041 −0.203165
\(742\) −0.259455 −0.00952488
\(743\) 14.9024 0.546714 0.273357 0.961913i \(-0.411866\pi\)
0.273357 + 0.961913i \(0.411866\pi\)
\(744\) −0.246628 −0.00904182
\(745\) −7.04186 −0.257994
\(746\) 29.7502 1.08923
\(747\) 0.689061 0.0252114
\(748\) 43.9110 1.60554
\(749\) −1.64861 −0.0602389
\(750\) −5.77856 −0.211003
\(751\) 32.5307 1.18706 0.593531 0.804811i \(-0.297733\pi\)
0.593531 + 0.804811i \(0.297733\pi\)
\(752\) 3.19055 0.116348
\(753\) 54.0633 1.97018
\(754\) 15.3206 0.557945
\(755\) 3.45585 0.125771
\(756\) −1.97910 −0.0719790
\(757\) 20.6242 0.749599 0.374799 0.927106i \(-0.377712\pi\)
0.374799 + 0.927106i \(0.377712\pi\)
\(758\) 11.9391 0.433648
\(759\) −13.5399 −0.491468
\(760\) 0.291796 0.0105845
\(761\) −47.8520 −1.73463 −0.867317 0.497757i \(-0.834157\pi\)
−0.867317 + 0.497757i \(0.834157\pi\)
\(762\) 29.9184 1.08383
\(763\) −7.68163 −0.278094
\(764\) 19.1529 0.692928
\(765\) 2.17521 0.0786449
\(766\) 7.06516 0.255275
\(767\) 20.9321 0.755813
\(768\) −1.99735 −0.0720732
\(769\) −45.9438 −1.65677 −0.828387 0.560156i \(-0.810741\pi\)
−0.828387 + 0.560156i \(0.810741\pi\)
\(770\) −0.838093 −0.0302028
\(771\) 31.0148 1.11697
\(772\) −23.7671 −0.855396
\(773\) 30.3210 1.09057 0.545285 0.838251i \(-0.316421\pi\)
0.545285 + 0.838251i \(0.316421\pi\)
\(774\) 1.72035 0.0618367
\(775\) −0.606874 −0.0217996
\(776\) 3.77181 0.135400
\(777\) 0.136186 0.00488564
\(778\) 0.804055 0.0288268
\(779\) 0.934090 0.0334672
\(780\) −1.61375 −0.0577815
\(781\) 30.3735 1.08685
\(782\) 8.76363 0.313387
\(783\) −22.2204 −0.794093
\(784\) −6.75713 −0.241326
\(785\) 3.30371 0.117914
\(786\) −8.46349 −0.301883
\(787\) 43.9118 1.56529 0.782644 0.622470i \(-0.213871\pi\)
0.782644 + 0.622470i \(0.213871\pi\)
\(788\) −3.50954 −0.125022
\(789\) −15.9233 −0.566884
\(790\) −1.77773 −0.0632489
\(791\) 9.12233 0.324353
\(792\) −5.76634 −0.204898
\(793\) −14.9951 −0.532493
\(794\) −7.48659 −0.265689
\(795\) 0.306836 0.0108823
\(796\) −12.7834 −0.453095
\(797\) −49.2267 −1.74370 −0.871849 0.489775i \(-0.837079\pi\)
−0.871849 + 0.489775i \(0.837079\pi\)
\(798\) −0.984334 −0.0348451
\(799\) −24.0389 −0.850434
\(800\) −4.91486 −0.173766
\(801\) 15.4750 0.546782
\(802\) 30.1926 1.06614
\(803\) −62.0541 −2.18984
\(804\) 4.88697 0.172350
\(805\) −0.167264 −0.00589530
\(806\) −0.341894 −0.0120427
\(807\) −36.9366 −1.30023
\(808\) −14.1513 −0.497842
\(809\) −11.2883 −0.396876 −0.198438 0.980113i \(-0.563587\pi\)
−0.198438 + 0.980113i \(0.563587\pi\)
\(810\) 3.20663 0.112669
\(811\) 35.0290 1.23003 0.615016 0.788514i \(-0.289149\pi\)
0.615016 + 0.788514i \(0.289149\pi\)
\(812\) 2.72686 0.0956939
\(813\) 56.8879 1.99514
\(814\) −0.806333 −0.0282620
\(815\) 2.03150 0.0711603
\(816\) 15.0488 0.526813
\(817\) −1.73877 −0.0608318
\(818\) 14.6143 0.510978
\(819\) 1.35010 0.0471764
\(820\) 0.272563 0.00951832
\(821\) 30.2946 1.05729 0.528644 0.848844i \(-0.322701\pi\)
0.528644 + 0.848844i \(0.322701\pi\)
\(822\) −27.9185 −0.973770
\(823\) 40.8349 1.42342 0.711708 0.702475i \(-0.247922\pi\)
0.711708 + 0.702475i \(0.247922\pi\)
\(824\) 13.1376 0.457669
\(825\) −57.2124 −1.99188
\(826\) 3.72561 0.129630
\(827\) −36.9776 −1.28584 −0.642918 0.765935i \(-0.722276\pi\)
−0.642918 + 0.765935i \(0.722276\pi\)
\(828\) −1.15083 −0.0399941
\(829\) −32.7871 −1.13874 −0.569371 0.822081i \(-0.692813\pi\)
−0.569371 + 0.822081i \(0.692813\pi\)
\(830\) −0.203218 −0.00705378
\(831\) −63.7887 −2.21280
\(832\) −2.76888 −0.0959935
\(833\) 50.9108 1.76395
\(834\) −16.0860 −0.557013
\(835\) 5.93194 0.205283
\(836\) 5.82808 0.201568
\(837\) 0.495868 0.0171397
\(838\) −31.7737 −1.09760
\(839\) −42.8184 −1.47826 −0.739128 0.673565i \(-0.764762\pi\)
−0.739128 + 0.673565i \(0.764762\pi\)
\(840\) −0.287224 −0.00991018
\(841\) 1.61594 0.0557220
\(842\) 35.8484 1.23542
\(843\) −32.1278 −1.10654
\(844\) −1.00000 −0.0344214
\(845\) 1.55624 0.0535364
\(846\) 3.15676 0.108532
\(847\) −11.3183 −0.388903
\(848\) 0.526470 0.0180790
\(849\) −53.3808 −1.83202
\(850\) 37.0304 1.27013
\(851\) −0.160926 −0.00551647
\(852\) 10.4093 0.356618
\(853\) −29.9914 −1.02689 −0.513443 0.858124i \(-0.671630\pi\)
−0.513443 + 0.858124i \(0.671630\pi\)
\(854\) −2.66892 −0.0913286
\(855\) 0.288705 0.00987349
\(856\) 3.34526 0.114339
\(857\) 39.7381 1.35743 0.678714 0.734402i \(-0.262537\pi\)
0.678714 + 0.734402i \(0.262537\pi\)
\(858\) −32.2317 −1.10037
\(859\) −21.3667 −0.729021 −0.364510 0.931199i \(-0.618764\pi\)
−0.364510 + 0.931199i \(0.618764\pi\)
\(860\) −0.507365 −0.0173010
\(861\) −0.919456 −0.0313350
\(862\) 2.41840 0.0823709
\(863\) 46.9898 1.59955 0.799775 0.600299i \(-0.204952\pi\)
0.799775 + 0.600299i \(0.204952\pi\)
\(864\) 4.01586 0.136622
\(865\) 3.59198 0.122131
\(866\) 26.0821 0.886306
\(867\) −79.4285 −2.69753
\(868\) −0.0608522 −0.00206546
\(869\) −35.5069 −1.20449
\(870\) −3.22483 −0.109332
\(871\) 6.77468 0.229551
\(872\) 15.5871 0.527846
\(873\) 3.73186 0.126304
\(874\) 1.16315 0.0393442
\(875\) −1.42578 −0.0482003
\(876\) −21.2666 −0.718533
\(877\) −22.0920 −0.745993 −0.372996 0.927833i \(-0.621670\pi\)
−0.372996 + 0.927833i \(0.621670\pi\)
\(878\) 9.81398 0.331206
\(879\) 12.6398 0.426330
\(880\) 1.70061 0.0573275
\(881\) −30.5795 −1.03025 −0.515124 0.857116i \(-0.672254\pi\)
−0.515124 + 0.857116i \(0.672254\pi\)
\(882\) −6.68555 −0.225114
\(883\) −56.7209 −1.90881 −0.954405 0.298515i \(-0.903509\pi\)
−0.954405 + 0.298515i \(0.903509\pi\)
\(884\) 20.8618 0.701657
\(885\) −4.40597 −0.148105
\(886\) −7.96518 −0.267596
\(887\) −54.6134 −1.83374 −0.916869 0.399189i \(-0.869292\pi\)
−0.916869 + 0.399189i \(0.869292\pi\)
\(888\) −0.276340 −0.00927336
\(889\) 7.38198 0.247584
\(890\) −4.56388 −0.152982
\(891\) 64.0465 2.14564
\(892\) −24.5778 −0.822927
\(893\) −3.19055 −0.106768
\(894\) −48.2018 −1.61211
\(895\) 6.68555 0.223473
\(896\) −0.492820 −0.0164640
\(897\) −6.43271 −0.214782
\(898\) 41.7261 1.39242
\(899\) −0.683222 −0.0227867
\(900\) −4.86279 −0.162093
\(901\) −3.96662 −0.132147
\(902\) 5.44395 0.181264
\(903\) 1.71153 0.0569561
\(904\) −18.5105 −0.615649
\(905\) −4.78419 −0.159032
\(906\) 23.6554 0.785899
\(907\) 5.59601 0.185813 0.0929063 0.995675i \(-0.470384\pi\)
0.0929063 + 0.995675i \(0.470384\pi\)
\(908\) −21.9324 −0.727852
\(909\) −14.0014 −0.464398
\(910\) −0.398172 −0.0131993
\(911\) 13.8939 0.460325 0.230162 0.973152i \(-0.426074\pi\)
0.230162 + 0.973152i \(0.426074\pi\)
\(912\) 1.99735 0.0661389
\(913\) −4.05889 −0.134330
\(914\) 1.15273 0.0381289
\(915\) 3.15631 0.104345
\(916\) 12.8876 0.425817
\(917\) −2.08826 −0.0689603
\(918\) −30.2570 −0.998630
\(919\) −44.0034 −1.45154 −0.725768 0.687939i \(-0.758516\pi\)
−0.725768 + 0.687939i \(0.758516\pi\)
\(920\) 0.339403 0.0111898
\(921\) −43.5801 −1.43601
\(922\) 10.4866 0.345358
\(923\) 14.4302 0.474976
\(924\) −5.73678 −0.188726
\(925\) −0.679986 −0.0223578
\(926\) 12.0262 0.395205
\(927\) 12.9984 0.426924
\(928\) −5.53317 −0.181635
\(929\) −35.7726 −1.17366 −0.586830 0.809710i \(-0.699624\pi\)
−0.586830 + 0.809710i \(0.699624\pi\)
\(930\) 0.0719649 0.00235982
\(931\) 6.75713 0.221456
\(932\) 3.47952 0.113975
\(933\) −0.896473 −0.0293492
\(934\) 3.99432 0.130698
\(935\) −12.8130 −0.419031
\(936\) −2.73955 −0.0895448
\(937\) 22.5479 0.736606 0.368303 0.929706i \(-0.379939\pi\)
0.368303 + 0.929706i \(0.379939\pi\)
\(938\) 1.20580 0.0393706
\(939\) 15.1457 0.494262
\(940\) −0.930990 −0.0303655
\(941\) 34.4137 1.12186 0.560928 0.827865i \(-0.310445\pi\)
0.560928 + 0.827865i \(0.310445\pi\)
\(942\) 22.6140 0.736804
\(943\) 1.08649 0.0353809
\(944\) −7.55977 −0.246050
\(945\) 0.577491 0.0187858
\(946\) −10.1337 −0.329474
\(947\) 53.6411 1.74310 0.871551 0.490304i \(-0.163114\pi\)
0.871551 + 0.490304i \(0.163114\pi\)
\(948\) −12.1686 −0.395219
\(949\) −29.4814 −0.957007
\(950\) 4.91486 0.159459
\(951\) 10.5100 0.340811
\(952\) 3.71310 0.120342
\(953\) 8.28280 0.268306 0.134153 0.990961i \(-0.457169\pi\)
0.134153 + 0.990961i \(0.457169\pi\)
\(954\) 0.520893 0.0168645
\(955\) −5.58873 −0.180847
\(956\) 13.0297 0.421410
\(957\) −64.4100 −2.08208
\(958\) −25.3246 −0.818201
\(959\) −6.88853 −0.222442
\(960\) 0.582818 0.0188104
\(961\) −30.9848 −0.999508
\(962\) −0.383083 −0.0123511
\(963\) 3.30982 0.106658
\(964\) −15.5204 −0.499878
\(965\) 6.93513 0.223250
\(966\) −1.14493 −0.0368375
\(967\) −24.0647 −0.773868 −0.386934 0.922107i \(-0.626466\pi\)
−0.386934 + 0.922107i \(0.626466\pi\)
\(968\) 22.9665 0.738171
\(969\) −15.0488 −0.483437
\(970\) −1.10060 −0.0353381
\(971\) 25.9691 0.833390 0.416695 0.909046i \(-0.363188\pi\)
0.416695 + 0.909046i \(0.363188\pi\)
\(972\) 9.90190 0.317603
\(973\) −3.96901 −0.127241
\(974\) 8.66907 0.277775
\(975\) −27.1812 −0.870494
\(976\) 5.41561 0.173349
\(977\) −21.5467 −0.689340 −0.344670 0.938724i \(-0.612009\pi\)
−0.344670 + 0.938724i \(0.612009\pi\)
\(978\) 13.9057 0.444655
\(979\) −91.1550 −2.91333
\(980\) 1.97170 0.0629837
\(981\) 15.4220 0.492386
\(982\) −19.3277 −0.616772
\(983\) 24.1055 0.768845 0.384422 0.923157i \(-0.374401\pi\)
0.384422 + 0.923157i \(0.374401\pi\)
\(984\) 1.86570 0.0594765
\(985\) 1.02407 0.0326295
\(986\) 41.6890 1.32765
\(987\) 3.14057 0.0999655
\(988\) 2.76888 0.0880897
\(989\) −2.02245 −0.0643102
\(990\) 1.68259 0.0534763
\(991\) −24.2137 −0.769174 −0.384587 0.923089i \(-0.625656\pi\)
−0.384587 + 0.923089i \(0.625656\pi\)
\(992\) 0.123478 0.00392042
\(993\) 13.6938 0.434559
\(994\) 2.56837 0.0814637
\(995\) 3.73014 0.118253
\(996\) −1.39103 −0.0440765
\(997\) 45.9058 1.45385 0.726926 0.686716i \(-0.240948\pi\)
0.726926 + 0.686716i \(0.240948\pi\)
\(998\) −36.3023 −1.14913
\(999\) 0.555607 0.0175786
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 \(a_p\))