Properties

Label 8018.2.a.f.1.4
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
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: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.08799 q^{3}\) \(+1.00000 q^{4}\) \(+2.62819 q^{5}\) \(+3.08799 q^{6}\) \(-3.66609 q^{7}\) \(-1.00000 q^{8}\) \(+6.53566 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.08799 q^{3}\) \(+1.00000 q^{4}\) \(+2.62819 q^{5}\) \(+3.08799 q^{6}\) \(-3.66609 q^{7}\) \(-1.00000 q^{8}\) \(+6.53566 q^{9}\) \(-2.62819 q^{10}\) \(+1.21778 q^{11}\) \(-3.08799 q^{12}\) \(-4.51494 q^{13}\) \(+3.66609 q^{14}\) \(-8.11583 q^{15}\) \(+1.00000 q^{16}\) \(+4.39274 q^{17}\) \(-6.53566 q^{18}\) \(-1.00000 q^{19}\) \(+2.62819 q^{20}\) \(+11.3208 q^{21}\) \(-1.21778 q^{22}\) \(+2.40206 q^{23}\) \(+3.08799 q^{24}\) \(+1.90741 q^{25}\) \(+4.51494 q^{26}\) \(-10.9181 q^{27}\) \(-3.66609 q^{28}\) \(-1.07536 q^{29}\) \(+8.11583 q^{30}\) \(-0.440740 q^{31}\) \(-1.00000 q^{32}\) \(-3.76050 q^{33}\) \(-4.39274 q^{34}\) \(-9.63519 q^{35}\) \(+6.53566 q^{36}\) \(+2.89756 q^{37}\) \(+1.00000 q^{38}\) \(+13.9421 q^{39}\) \(-2.62819 q^{40}\) \(-2.67431 q^{41}\) \(-11.3208 q^{42}\) \(-7.06259 q^{43}\) \(+1.21778 q^{44}\) \(+17.1770 q^{45}\) \(-2.40206 q^{46}\) \(-3.18475 q^{47}\) \(-3.08799 q^{48}\) \(+6.44020 q^{49}\) \(-1.90741 q^{50}\) \(-13.5647 q^{51}\) \(-4.51494 q^{52}\) \(+0.511348 q^{53}\) \(+10.9181 q^{54}\) \(+3.20057 q^{55}\) \(+3.66609 q^{56}\) \(+3.08799 q^{57}\) \(+1.07536 q^{58}\) \(+4.68732 q^{59}\) \(-8.11583 q^{60}\) \(+12.8591 q^{61}\) \(+0.440740 q^{62}\) \(-23.9603 q^{63}\) \(+1.00000 q^{64}\) \(-11.8661 q^{65}\) \(+3.76050 q^{66}\) \(+1.04627 q^{67}\) \(+4.39274 q^{68}\) \(-7.41754 q^{69}\) \(+9.63519 q^{70}\) \(-4.69860 q^{71}\) \(-6.53566 q^{72}\) \(+5.06591 q^{73}\) \(-2.89756 q^{74}\) \(-5.89004 q^{75}\) \(-1.00000 q^{76}\) \(-4.46450 q^{77}\) \(-13.9421 q^{78}\) \(+10.7461 q^{79}\) \(+2.62819 q^{80}\) \(+14.1079 q^{81}\) \(+2.67431 q^{82}\) \(+2.37602 q^{83}\) \(+11.3208 q^{84}\) \(+11.5450 q^{85}\) \(+7.06259 q^{86}\) \(+3.32071 q^{87}\) \(-1.21778 q^{88}\) \(+10.6548 q^{89}\) \(-17.1770 q^{90}\) \(+16.5522 q^{91}\) \(+2.40206 q^{92}\) \(+1.36100 q^{93}\) \(+3.18475 q^{94}\) \(-2.62819 q^{95}\) \(+3.08799 q^{96}\) \(-2.91374 q^{97}\) \(-6.44020 q^{98}\) \(+7.95902 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.08799 −1.78285 −0.891425 0.453168i \(-0.850294\pi\)
−0.891425 + 0.453168i \(0.850294\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.62819 1.17536 0.587682 0.809092i \(-0.300041\pi\)
0.587682 + 0.809092i \(0.300041\pi\)
\(6\) 3.08799 1.26067
\(7\) −3.66609 −1.38565 −0.692826 0.721105i \(-0.743634\pi\)
−0.692826 + 0.721105i \(0.743634\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.53566 2.17855
\(10\) −2.62819 −0.831108
\(11\) 1.21778 0.367176 0.183588 0.983003i \(-0.441229\pi\)
0.183588 + 0.983003i \(0.441229\pi\)
\(12\) −3.08799 −0.891425
\(13\) −4.51494 −1.25222 −0.626109 0.779736i \(-0.715353\pi\)
−0.626109 + 0.779736i \(0.715353\pi\)
\(14\) 3.66609 0.979803
\(15\) −8.11583 −2.09550
\(16\) 1.00000 0.250000
\(17\) 4.39274 1.06540 0.532698 0.846305i \(-0.321178\pi\)
0.532698 + 0.846305i \(0.321178\pi\)
\(18\) −6.53566 −1.54047
\(19\) −1.00000 −0.229416
\(20\) 2.62819 0.587682
\(21\) 11.3208 2.47041
\(22\) −1.21778 −0.259632
\(23\) 2.40206 0.500865 0.250432 0.968134i \(-0.419427\pi\)
0.250432 + 0.968134i \(0.419427\pi\)
\(24\) 3.08799 0.630333
\(25\) 1.90741 0.381481
\(26\) 4.51494 0.885452
\(27\) −10.9181 −2.10118
\(28\) −3.66609 −0.692826
\(29\) −1.07536 −0.199690 −0.0998451 0.995003i \(-0.531835\pi\)
−0.0998451 + 0.995003i \(0.531835\pi\)
\(30\) 8.11583 1.48174
\(31\) −0.440740 −0.0791592 −0.0395796 0.999216i \(-0.512602\pi\)
−0.0395796 + 0.999216i \(0.512602\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.76050 −0.654619
\(34\) −4.39274 −0.753349
\(35\) −9.63519 −1.62864
\(36\) 6.53566 1.08928
\(37\) 2.89756 0.476357 0.238178 0.971221i \(-0.423450\pi\)
0.238178 + 0.971221i \(0.423450\pi\)
\(38\) 1.00000 0.162221
\(39\) 13.9421 2.23252
\(40\) −2.62819 −0.415554
\(41\) −2.67431 −0.417657 −0.208828 0.977952i \(-0.566965\pi\)
−0.208828 + 0.977952i \(0.566965\pi\)
\(42\) −11.3208 −1.74684
\(43\) −7.06259 −1.07703 −0.538517 0.842615i \(-0.681015\pi\)
−0.538517 + 0.842615i \(0.681015\pi\)
\(44\) 1.21778 0.183588
\(45\) 17.1770 2.56059
\(46\) −2.40206 −0.354165
\(47\) −3.18475 −0.464543 −0.232271 0.972651i \(-0.574616\pi\)
−0.232271 + 0.972651i \(0.574616\pi\)
\(48\) −3.08799 −0.445712
\(49\) 6.44020 0.920029
\(50\) −1.90741 −0.269748
\(51\) −13.5647 −1.89944
\(52\) −4.51494 −0.626109
\(53\) 0.511348 0.0702390 0.0351195 0.999383i \(-0.488819\pi\)
0.0351195 + 0.999383i \(0.488819\pi\)
\(54\) 10.9181 1.48576
\(55\) 3.20057 0.431565
\(56\) 3.66609 0.489902
\(57\) 3.08799 0.409014
\(58\) 1.07536 0.141202
\(59\) 4.68732 0.610237 0.305119 0.952314i \(-0.401304\pi\)
0.305119 + 0.952314i \(0.401304\pi\)
\(60\) −8.11583 −1.04775
\(61\) 12.8591 1.64644 0.823221 0.567721i \(-0.192175\pi\)
0.823221 + 0.567721i \(0.192175\pi\)
\(62\) 0.440740 0.0559740
\(63\) −23.9603 −3.01871
\(64\) 1.00000 0.125000
\(65\) −11.8661 −1.47181
\(66\) 3.76050 0.462885
\(67\) 1.04627 0.127822 0.0639112 0.997956i \(-0.479643\pi\)
0.0639112 + 0.997956i \(0.479643\pi\)
\(68\) 4.39274 0.532698
\(69\) −7.41754 −0.892967
\(70\) 9.63519 1.15163
\(71\) −4.69860 −0.557622 −0.278811 0.960346i \(-0.589940\pi\)
−0.278811 + 0.960346i \(0.589940\pi\)
\(72\) −6.53566 −0.770235
\(73\) 5.06591 0.592920 0.296460 0.955045i \(-0.404194\pi\)
0.296460 + 0.955045i \(0.404194\pi\)
\(74\) −2.89756 −0.336835
\(75\) −5.89004 −0.680124
\(76\) −1.00000 −0.114708
\(77\) −4.46450 −0.508777
\(78\) −13.9421 −1.57863
\(79\) 10.7461 1.20903 0.604517 0.796593i \(-0.293366\pi\)
0.604517 + 0.796593i \(0.293366\pi\)
\(80\) 2.62819 0.293841
\(81\) 14.1079 1.56754
\(82\) 2.67431 0.295328
\(83\) 2.37602 0.260802 0.130401 0.991461i \(-0.458374\pi\)
0.130401 + 0.991461i \(0.458374\pi\)
\(84\) 11.3208 1.23520
\(85\) 11.5450 1.25223
\(86\) 7.06259 0.761578
\(87\) 3.32071 0.356017
\(88\) −1.21778 −0.129816
\(89\) 10.6548 1.12940 0.564701 0.825295i \(-0.308991\pi\)
0.564701 + 0.825295i \(0.308991\pi\)
\(90\) −17.1770 −1.81061
\(91\) 16.5522 1.73514
\(92\) 2.40206 0.250432
\(93\) 1.36100 0.141129
\(94\) 3.18475 0.328481
\(95\) −2.62819 −0.269647
\(96\) 3.08799 0.315166
\(97\) −2.91374 −0.295846 −0.147923 0.988999i \(-0.547259\pi\)
−0.147923 + 0.988999i \(0.547259\pi\)
\(98\) −6.44020 −0.650559
\(99\) 7.95902 0.799912
\(100\) 1.90741 0.190741
\(101\) −9.39603 −0.934940 −0.467470 0.884009i \(-0.654834\pi\)
−0.467470 + 0.884009i \(0.654834\pi\)
\(102\) 13.5647 1.34311
\(103\) −18.5476 −1.82755 −0.913775 0.406220i \(-0.866847\pi\)
−0.913775 + 0.406220i \(0.866847\pi\)
\(104\) 4.51494 0.442726
\(105\) 29.7533 2.90363
\(106\) −0.511348 −0.0496665
\(107\) −16.6286 −1.60755 −0.803774 0.594934i \(-0.797178\pi\)
−0.803774 + 0.594934i \(0.797178\pi\)
\(108\) −10.9181 −1.05059
\(109\) 1.39080 0.133214 0.0666071 0.997779i \(-0.478783\pi\)
0.0666071 + 0.997779i \(0.478783\pi\)
\(110\) −3.20057 −0.305163
\(111\) −8.94764 −0.849272
\(112\) −3.66609 −0.346413
\(113\) −7.52173 −0.707584 −0.353792 0.935324i \(-0.615108\pi\)
−0.353792 + 0.935324i \(0.615108\pi\)
\(114\) −3.08799 −0.289216
\(115\) 6.31309 0.588699
\(116\) −1.07536 −0.0998451
\(117\) −29.5081 −2.72802
\(118\) −4.68732 −0.431503
\(119\) −16.1042 −1.47627
\(120\) 8.11583 0.740870
\(121\) −9.51700 −0.865182
\(122\) −12.8591 −1.16421
\(123\) 8.25823 0.744620
\(124\) −0.440740 −0.0395796
\(125\) −8.12794 −0.726985
\(126\) 23.9603 2.13455
\(127\) −1.39395 −0.123693 −0.0618465 0.998086i \(-0.519699\pi\)
−0.0618465 + 0.998086i \(0.519699\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 21.8092 1.92019
\(130\) 11.8661 1.04073
\(131\) −8.42358 −0.735972 −0.367986 0.929831i \(-0.619953\pi\)
−0.367986 + 0.929831i \(0.619953\pi\)
\(132\) −3.76050 −0.327309
\(133\) 3.66609 0.317890
\(134\) −1.04627 −0.0903841
\(135\) −28.6948 −2.46966
\(136\) −4.39274 −0.376675
\(137\) 9.94835 0.849945 0.424972 0.905206i \(-0.360284\pi\)
0.424972 + 0.905206i \(0.360284\pi\)
\(138\) 7.41754 0.631423
\(139\) 17.3629 1.47270 0.736352 0.676599i \(-0.236547\pi\)
0.736352 + 0.676599i \(0.236547\pi\)
\(140\) −9.63519 −0.814322
\(141\) 9.83445 0.828210
\(142\) 4.69860 0.394298
\(143\) −5.49821 −0.459784
\(144\) 6.53566 0.544638
\(145\) −2.82627 −0.234709
\(146\) −5.06591 −0.419258
\(147\) −19.8873 −1.64027
\(148\) 2.89756 0.238178
\(149\) −0.0832650 −0.00682133 −0.00341067 0.999994i \(-0.501086\pi\)
−0.00341067 + 0.999994i \(0.501086\pi\)
\(150\) 5.89004 0.480920
\(151\) 6.80702 0.553948 0.276974 0.960877i \(-0.410668\pi\)
0.276974 + 0.960877i \(0.410668\pi\)
\(152\) 1.00000 0.0811107
\(153\) 28.7095 2.32102
\(154\) 4.46450 0.359760
\(155\) −1.15835 −0.0930409
\(156\) 13.9421 1.11626
\(157\) −5.41689 −0.432315 −0.216157 0.976359i \(-0.569352\pi\)
−0.216157 + 0.976359i \(0.569352\pi\)
\(158\) −10.7461 −0.854916
\(159\) −1.57904 −0.125226
\(160\) −2.62819 −0.207777
\(161\) −8.80618 −0.694024
\(162\) −14.1079 −1.10842
\(163\) 7.28377 0.570509 0.285255 0.958452i \(-0.407922\pi\)
0.285255 + 0.958452i \(0.407922\pi\)
\(164\) −2.67431 −0.208828
\(165\) −9.88332 −0.769416
\(166\) −2.37602 −0.184415
\(167\) −5.95964 −0.461171 −0.230586 0.973052i \(-0.574064\pi\)
−0.230586 + 0.973052i \(0.574064\pi\)
\(168\) −11.3208 −0.873421
\(169\) 7.38464 0.568049
\(170\) −11.5450 −0.885460
\(171\) −6.53566 −0.499794
\(172\) −7.06259 −0.538517
\(173\) 9.57800 0.728202 0.364101 0.931360i \(-0.381376\pi\)
0.364101 + 0.931360i \(0.381376\pi\)
\(174\) −3.32071 −0.251742
\(175\) −6.99272 −0.528600
\(176\) 1.21778 0.0917939
\(177\) −14.4744 −1.08796
\(178\) −10.6548 −0.798608
\(179\) −15.0901 −1.12788 −0.563942 0.825815i \(-0.690716\pi\)
−0.563942 + 0.825815i \(0.690716\pi\)
\(180\) 17.1770 1.28030
\(181\) 24.1491 1.79499 0.897496 0.441023i \(-0.145384\pi\)
0.897496 + 0.441023i \(0.145384\pi\)
\(182\) −16.5522 −1.22693
\(183\) −39.7088 −2.93536
\(184\) −2.40206 −0.177082
\(185\) 7.61536 0.559893
\(186\) −1.36100 −0.0997932
\(187\) 5.34941 0.391188
\(188\) −3.18475 −0.232271
\(189\) 40.0266 2.91151
\(190\) 2.62819 0.190669
\(191\) 12.8860 0.932396 0.466198 0.884680i \(-0.345623\pi\)
0.466198 + 0.884680i \(0.345623\pi\)
\(192\) −3.08799 −0.222856
\(193\) 6.86465 0.494128 0.247064 0.968999i \(-0.420534\pi\)
0.247064 + 0.968999i \(0.420534\pi\)
\(194\) 2.91374 0.209195
\(195\) 36.6424 2.62402
\(196\) 6.44020 0.460014
\(197\) 18.7442 1.33547 0.667735 0.744399i \(-0.267264\pi\)
0.667735 + 0.744399i \(0.267264\pi\)
\(198\) −7.95902 −0.565623
\(199\) −7.50235 −0.531827 −0.265914 0.963997i \(-0.585674\pi\)
−0.265914 + 0.963997i \(0.585674\pi\)
\(200\) −1.90741 −0.134874
\(201\) −3.23087 −0.227888
\(202\) 9.39603 0.661102
\(203\) 3.94238 0.276701
\(204\) −13.5647 −0.949721
\(205\) −7.02860 −0.490899
\(206\) 18.5476 1.29227
\(207\) 15.6991 1.09116
\(208\) −4.51494 −0.313054
\(209\) −1.21778 −0.0842358
\(210\) −29.7533 −2.05318
\(211\) −1.00000 −0.0688428
\(212\) 0.511348 0.0351195
\(213\) 14.5092 0.994155
\(214\) 16.6286 1.13671
\(215\) −18.5619 −1.26591
\(216\) 10.9181 0.742881
\(217\) 1.61579 0.109687
\(218\) −1.39080 −0.0941967
\(219\) −15.6435 −1.05709
\(220\) 3.20057 0.215783
\(221\) −19.8330 −1.33411
\(222\) 8.94764 0.600526
\(223\) −3.95401 −0.264780 −0.132390 0.991198i \(-0.542265\pi\)
−0.132390 + 0.991198i \(0.542265\pi\)
\(224\) 3.66609 0.244951
\(225\) 12.4662 0.831077
\(226\) 7.52173 0.500338
\(227\) −5.64190 −0.374466 −0.187233 0.982316i \(-0.559952\pi\)
−0.187233 + 0.982316i \(0.559952\pi\)
\(228\) 3.08799 0.204507
\(229\) 18.7325 1.23788 0.618939 0.785439i \(-0.287563\pi\)
0.618939 + 0.785439i \(0.287563\pi\)
\(230\) −6.31309 −0.416273
\(231\) 13.7863 0.907073
\(232\) 1.07536 0.0706011
\(233\) 6.12670 0.401373 0.200687 0.979655i \(-0.435683\pi\)
0.200687 + 0.979655i \(0.435683\pi\)
\(234\) 29.5081 1.92900
\(235\) −8.37013 −0.546007
\(236\) 4.68732 0.305119
\(237\) −33.1839 −2.15552
\(238\) 16.1042 1.04388
\(239\) 13.0668 0.845223 0.422612 0.906311i \(-0.361113\pi\)
0.422612 + 0.906311i \(0.361113\pi\)
\(240\) −8.11583 −0.523874
\(241\) 22.5244 1.45093 0.725463 0.688261i \(-0.241626\pi\)
0.725463 + 0.688261i \(0.241626\pi\)
\(242\) 9.51700 0.611776
\(243\) −10.8107 −0.693507
\(244\) 12.8591 0.823221
\(245\) 16.9261 1.08137
\(246\) −8.25823 −0.526526
\(247\) 4.51494 0.287278
\(248\) 0.440740 0.0279870
\(249\) −7.33711 −0.464970
\(250\) 8.12794 0.514056
\(251\) 3.60825 0.227751 0.113875 0.993495i \(-0.463674\pi\)
0.113875 + 0.993495i \(0.463674\pi\)
\(252\) −23.9603 −1.50936
\(253\) 2.92519 0.183905
\(254\) 1.39395 0.0874642
\(255\) −35.6508 −2.23254
\(256\) 1.00000 0.0625000
\(257\) −22.7225 −1.41739 −0.708696 0.705514i \(-0.750716\pi\)
−0.708696 + 0.705514i \(0.750716\pi\)
\(258\) −21.8092 −1.35778
\(259\) −10.6227 −0.660064
\(260\) −11.8661 −0.735906
\(261\) −7.02821 −0.435036
\(262\) 8.42358 0.520411
\(263\) 29.1911 1.80000 0.899999 0.435892i \(-0.143567\pi\)
0.899999 + 0.435892i \(0.143567\pi\)
\(264\) 3.76050 0.231443
\(265\) 1.34392 0.0825564
\(266\) −3.66609 −0.224782
\(267\) −32.9018 −2.01356
\(268\) 1.04627 0.0639112
\(269\) −7.41146 −0.451885 −0.225942 0.974141i \(-0.572546\pi\)
−0.225942 + 0.974141i \(0.572546\pi\)
\(270\) 28.6948 1.74631
\(271\) −15.3350 −0.931535 −0.465768 0.884907i \(-0.654222\pi\)
−0.465768 + 0.884907i \(0.654222\pi\)
\(272\) 4.39274 0.266349
\(273\) −51.1128 −3.09349
\(274\) −9.94835 −0.601002
\(275\) 2.32281 0.140071
\(276\) −7.41754 −0.446483
\(277\) −1.64228 −0.0986748 −0.0493374 0.998782i \(-0.515711\pi\)
−0.0493374 + 0.998782i \(0.515711\pi\)
\(278\) −17.3629 −1.04136
\(279\) −2.88053 −0.172453
\(280\) 9.63519 0.575813
\(281\) −20.1260 −1.20062 −0.600310 0.799768i \(-0.704956\pi\)
−0.600310 + 0.799768i \(0.704956\pi\)
\(282\) −9.83445 −0.585633
\(283\) 13.4278 0.798200 0.399100 0.916907i \(-0.369323\pi\)
0.399100 + 0.916907i \(0.369323\pi\)
\(284\) −4.69860 −0.278811
\(285\) 8.11583 0.480740
\(286\) 5.49821 0.325116
\(287\) 9.80425 0.578727
\(288\) −6.53566 −0.385117
\(289\) 2.29620 0.135070
\(290\) 2.82627 0.165964
\(291\) 8.99760 0.527449
\(292\) 5.06591 0.296460
\(293\) 22.7545 1.32933 0.664667 0.747140i \(-0.268573\pi\)
0.664667 + 0.747140i \(0.268573\pi\)
\(294\) 19.8873 1.15985
\(295\) 12.3192 0.717251
\(296\) −2.89756 −0.168418
\(297\) −13.2958 −0.771503
\(298\) 0.0832650 0.00482341
\(299\) −10.8452 −0.627192
\(300\) −5.89004 −0.340062
\(301\) 25.8921 1.49239
\(302\) −6.80702 −0.391700
\(303\) 29.0148 1.66686
\(304\) −1.00000 −0.0573539
\(305\) 33.7963 1.93517
\(306\) −28.7095 −1.64121
\(307\) 9.59394 0.547555 0.273777 0.961793i \(-0.411727\pi\)
0.273777 + 0.961793i \(0.411727\pi\)
\(308\) −4.46450 −0.254389
\(309\) 57.2748 3.25825
\(310\) 1.15835 0.0657898
\(311\) 0.409447 0.0232176 0.0116088 0.999933i \(-0.496305\pi\)
0.0116088 + 0.999933i \(0.496305\pi\)
\(312\) −13.9421 −0.789314
\(313\) −22.1881 −1.25415 −0.627074 0.778960i \(-0.715747\pi\)
−0.627074 + 0.778960i \(0.715747\pi\)
\(314\) 5.41689 0.305693
\(315\) −62.9723 −3.54809
\(316\) 10.7461 0.604517
\(317\) 10.9131 0.612940 0.306470 0.951880i \(-0.400852\pi\)
0.306470 + 0.951880i \(0.400852\pi\)
\(318\) 1.57904 0.0885479
\(319\) −1.30956 −0.0733213
\(320\) 2.62819 0.146921
\(321\) 51.3489 2.86602
\(322\) 8.80618 0.490749
\(323\) −4.39274 −0.244419
\(324\) 14.1079 0.783771
\(325\) −8.61181 −0.477697
\(326\) −7.28377 −0.403411
\(327\) −4.29477 −0.237501
\(328\) 2.67431 0.147664
\(329\) 11.6756 0.643694
\(330\) 9.88332 0.544059
\(331\) −24.1998 −1.33014 −0.665069 0.746782i \(-0.731598\pi\)
−0.665069 + 0.746782i \(0.731598\pi\)
\(332\) 2.37602 0.130401
\(333\) 18.9375 1.03777
\(334\) 5.95964 0.326097
\(335\) 2.74981 0.150238
\(336\) 11.3208 0.617602
\(337\) 2.17669 0.118572 0.0592858 0.998241i \(-0.481118\pi\)
0.0592858 + 0.998241i \(0.481118\pi\)
\(338\) −7.38464 −0.401672
\(339\) 23.2270 1.26152
\(340\) 11.5450 0.626115
\(341\) −0.536726 −0.0290653
\(342\) 6.53566 0.353408
\(343\) 2.05227 0.110812
\(344\) 7.06259 0.380789
\(345\) −19.4947 −1.04956
\(346\) −9.57800 −0.514916
\(347\) 20.4315 1.09682 0.548411 0.836209i \(-0.315233\pi\)
0.548411 + 0.836209i \(0.315233\pi\)
\(348\) 3.32071 0.178009
\(349\) −10.6675 −0.571021 −0.285510 0.958376i \(-0.592163\pi\)
−0.285510 + 0.958376i \(0.592163\pi\)
\(350\) 6.99272 0.373776
\(351\) 49.2944 2.63114
\(352\) −1.21778 −0.0649081
\(353\) −11.1690 −0.594468 −0.297234 0.954805i \(-0.596064\pi\)
−0.297234 + 0.954805i \(0.596064\pi\)
\(354\) 14.4744 0.769305
\(355\) −12.3488 −0.655408
\(356\) 10.6548 0.564701
\(357\) 49.7295 2.63196
\(358\) 15.0901 0.797534
\(359\) −15.7595 −0.831752 −0.415876 0.909421i \(-0.636525\pi\)
−0.415876 + 0.909421i \(0.636525\pi\)
\(360\) −17.1770 −0.905307
\(361\) 1.00000 0.0526316
\(362\) −24.1491 −1.26925
\(363\) 29.3884 1.54249
\(364\) 16.5522 0.867568
\(365\) 13.3142 0.696898
\(366\) 39.7088 2.07561
\(367\) 26.4309 1.37968 0.689840 0.723962i \(-0.257681\pi\)
0.689840 + 0.723962i \(0.257681\pi\)
\(368\) 2.40206 0.125216
\(369\) −17.4784 −0.909888
\(370\) −7.61536 −0.395904
\(371\) −1.87465 −0.0973268
\(372\) 1.36100 0.0705645
\(373\) −5.99275 −0.310293 −0.155146 0.987891i \(-0.549585\pi\)
−0.155146 + 0.987891i \(0.549585\pi\)
\(374\) −5.34941 −0.276611
\(375\) 25.0990 1.29611
\(376\) 3.18475 0.164241
\(377\) 4.85520 0.250056
\(378\) −40.0266 −2.05875
\(379\) 22.9513 1.17893 0.589464 0.807795i \(-0.299339\pi\)
0.589464 + 0.807795i \(0.299339\pi\)
\(380\) −2.62819 −0.134824
\(381\) 4.30450 0.220526
\(382\) −12.8860 −0.659303
\(383\) −20.7028 −1.05786 −0.528932 0.848664i \(-0.677407\pi\)
−0.528932 + 0.848664i \(0.677407\pi\)
\(384\) 3.08799 0.157583
\(385\) −11.7336 −0.597999
\(386\) −6.86465 −0.349402
\(387\) −46.1587 −2.34638
\(388\) −2.91374 −0.147923
\(389\) −3.59719 −0.182385 −0.0911923 0.995833i \(-0.529068\pi\)
−0.0911923 + 0.995833i \(0.529068\pi\)
\(390\) −36.6424 −1.85546
\(391\) 10.5516 0.533620
\(392\) −6.44020 −0.325279
\(393\) 26.0119 1.31213
\(394\) −18.7442 −0.944319
\(395\) 28.2429 1.42105
\(396\) 7.95902 0.399956
\(397\) 5.55478 0.278786 0.139393 0.990237i \(-0.455485\pi\)
0.139393 + 0.990237i \(0.455485\pi\)
\(398\) 7.50235 0.376059
\(399\) −11.3208 −0.566750
\(400\) 1.90741 0.0953703
\(401\) −17.0328 −0.850575 −0.425288 0.905058i \(-0.639827\pi\)
−0.425288 + 0.905058i \(0.639827\pi\)
\(402\) 3.23087 0.161141
\(403\) 1.98991 0.0991246
\(404\) −9.39603 −0.467470
\(405\) 37.0782 1.84243
\(406\) −3.94238 −0.195657
\(407\) 3.52861 0.174907
\(408\) 13.5647 0.671554
\(409\) −17.9167 −0.885924 −0.442962 0.896540i \(-0.646072\pi\)
−0.442962 + 0.896540i \(0.646072\pi\)
\(410\) 7.02860 0.347118
\(411\) −30.7204 −1.51532
\(412\) −18.5476 −0.913775
\(413\) −17.1841 −0.845576
\(414\) −15.6991 −0.771567
\(415\) 6.24464 0.306537
\(416\) 4.51494 0.221363
\(417\) −53.6165 −2.62561
\(418\) 1.21778 0.0595637
\(419\) −3.33924 −0.163133 −0.0815663 0.996668i \(-0.525992\pi\)
−0.0815663 + 0.996668i \(0.525992\pi\)
\(420\) 29.7533 1.45181
\(421\) −17.3270 −0.844468 −0.422234 0.906487i \(-0.638754\pi\)
−0.422234 + 0.906487i \(0.638754\pi\)
\(422\) 1.00000 0.0486792
\(423\) −20.8144 −1.01203
\(424\) −0.511348 −0.0248332
\(425\) 8.37874 0.406429
\(426\) −14.5092 −0.702974
\(427\) −47.1427 −2.28139
\(428\) −16.6286 −0.803774
\(429\) 16.9784 0.819725
\(430\) 18.5619 0.895132
\(431\) −21.7260 −1.04650 −0.523252 0.852178i \(-0.675281\pi\)
−0.523252 + 0.852178i \(0.675281\pi\)
\(432\) −10.9181 −0.525296
\(433\) −29.4313 −1.41438 −0.707188 0.707025i \(-0.750037\pi\)
−0.707188 + 0.707025i \(0.750037\pi\)
\(434\) −1.61579 −0.0775604
\(435\) 8.72747 0.418450
\(436\) 1.39080 0.0666071
\(437\) −2.40206 −0.114906
\(438\) 15.6435 0.747474
\(439\) −13.5207 −0.645306 −0.322653 0.946517i \(-0.604575\pi\)
−0.322653 + 0.946517i \(0.604575\pi\)
\(440\) −3.20057 −0.152581
\(441\) 42.0910 2.00433
\(442\) 19.8330 0.943357
\(443\) −10.5641 −0.501915 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(444\) −8.94764 −0.424636
\(445\) 28.0028 1.32746
\(446\) 3.95401 0.187228
\(447\) 0.257121 0.0121614
\(448\) −3.66609 −0.173206
\(449\) −35.2338 −1.66279 −0.831393 0.555685i \(-0.812456\pi\)
−0.831393 + 0.555685i \(0.812456\pi\)
\(450\) −12.4662 −0.587660
\(451\) −3.25673 −0.153353
\(452\) −7.52173 −0.353792
\(453\) −21.0200 −0.987605
\(454\) 5.64190 0.264788
\(455\) 43.5023 2.03942
\(456\) −3.08799 −0.144608
\(457\) −16.5664 −0.774942 −0.387471 0.921882i \(-0.626651\pi\)
−0.387471 + 0.921882i \(0.626651\pi\)
\(458\) −18.7325 −0.875312
\(459\) −47.9603 −2.23859
\(460\) 6.31309 0.294349
\(461\) −4.59128 −0.213837 −0.106919 0.994268i \(-0.534098\pi\)
−0.106919 + 0.994268i \(0.534098\pi\)
\(462\) −13.7863 −0.641398
\(463\) −21.5547 −1.00173 −0.500865 0.865525i \(-0.666985\pi\)
−0.500865 + 0.865525i \(0.666985\pi\)
\(464\) −1.07536 −0.0499225
\(465\) 3.57697 0.165878
\(466\) −6.12670 −0.283814
\(467\) −34.2095 −1.58303 −0.791513 0.611152i \(-0.790706\pi\)
−0.791513 + 0.611152i \(0.790706\pi\)
\(468\) −29.5081 −1.36401
\(469\) −3.83572 −0.177117
\(470\) 8.37013 0.386085
\(471\) 16.7273 0.770752
\(472\) −4.68732 −0.215751
\(473\) −8.60070 −0.395461
\(474\) 33.1839 1.52419
\(475\) −1.90741 −0.0875178
\(476\) −16.1042 −0.738134
\(477\) 3.34200 0.153019
\(478\) −13.0668 −0.597663
\(479\) 7.21220 0.329534 0.164767 0.986333i \(-0.447313\pi\)
0.164767 + 0.986333i \(0.447313\pi\)
\(480\) 8.11583 0.370435
\(481\) −13.0823 −0.596502
\(482\) −22.5244 −1.02596
\(483\) 27.1934 1.23734
\(484\) −9.51700 −0.432591
\(485\) −7.65789 −0.347727
\(486\) 10.8107 0.490384
\(487\) −28.7120 −1.30106 −0.650532 0.759478i \(-0.725454\pi\)
−0.650532 + 0.759478i \(0.725454\pi\)
\(488\) −12.8591 −0.582105
\(489\) −22.4922 −1.01713
\(490\) −16.9261 −0.764643
\(491\) −18.1445 −0.818849 −0.409424 0.912344i \(-0.634270\pi\)
−0.409424 + 0.912344i \(0.634270\pi\)
\(492\) 8.25823 0.372310
\(493\) −4.72380 −0.212749
\(494\) −4.51494 −0.203137
\(495\) 20.9178 0.940187
\(496\) −0.440740 −0.0197898
\(497\) 17.2255 0.772669
\(498\) 7.33711 0.328784
\(499\) −10.9783 −0.491455 −0.245727 0.969339i \(-0.579027\pi\)
−0.245727 + 0.969339i \(0.579027\pi\)
\(500\) −8.12794 −0.363492
\(501\) 18.4033 0.822199
\(502\) −3.60825 −0.161044
\(503\) −7.46339 −0.332776 −0.166388 0.986060i \(-0.553210\pi\)
−0.166388 + 0.986060i \(0.553210\pi\)
\(504\) 23.9603 1.06728
\(505\) −24.6946 −1.09889
\(506\) −2.92519 −0.130041
\(507\) −22.8037 −1.01275
\(508\) −1.39395 −0.0618465
\(509\) −4.78477 −0.212081 −0.106041 0.994362i \(-0.533817\pi\)
−0.106041 + 0.994362i \(0.533817\pi\)
\(510\) 35.6508 1.57864
\(511\) −18.5721 −0.821581
\(512\) −1.00000 −0.0441942
\(513\) 10.9181 0.482045
\(514\) 22.7225 1.00225
\(515\) −48.7467 −2.14804
\(516\) 21.8092 0.960095
\(517\) −3.87833 −0.170569
\(518\) 10.6227 0.466736
\(519\) −29.5767 −1.29827
\(520\) 11.8661 0.520364
\(521\) 25.6000 1.12156 0.560779 0.827966i \(-0.310502\pi\)
0.560779 + 0.827966i \(0.310502\pi\)
\(522\) 7.02821 0.307617
\(523\) 13.5908 0.594284 0.297142 0.954833i \(-0.403967\pi\)
0.297142 + 0.954833i \(0.403967\pi\)
\(524\) −8.42358 −0.367986
\(525\) 21.5934 0.942414
\(526\) −29.1911 −1.27279
\(527\) −1.93606 −0.0843360
\(528\) −3.76050 −0.163655
\(529\) −17.2301 −0.749134
\(530\) −1.34392 −0.0583762
\(531\) 30.6347 1.32943
\(532\) 3.66609 0.158945
\(533\) 12.0743 0.522997
\(534\) 32.9018 1.42380
\(535\) −43.7032 −1.88946
\(536\) −1.04627 −0.0451921
\(537\) 46.5979 2.01085
\(538\) 7.41146 0.319531
\(539\) 7.84277 0.337812
\(540\) −28.6948 −1.23483
\(541\) −32.3680 −1.39161 −0.695804 0.718231i \(-0.744952\pi\)
−0.695804 + 0.718231i \(0.744952\pi\)
\(542\) 15.3350 0.658695
\(543\) −74.5722 −3.20020
\(544\) −4.39274 −0.188337
\(545\) 3.65529 0.156575
\(546\) 51.1128 2.18743
\(547\) −22.5544 −0.964357 −0.482178 0.876073i \(-0.660154\pi\)
−0.482178 + 0.876073i \(0.660154\pi\)
\(548\) 9.94835 0.424972
\(549\) 84.0428 3.58686
\(550\) −2.32281 −0.0990448
\(551\) 1.07536 0.0458121
\(552\) 7.41754 0.315711
\(553\) −39.3962 −1.67530
\(554\) 1.64228 0.0697736
\(555\) −23.5161 −0.998204
\(556\) 17.3629 0.736352
\(557\) −38.8474 −1.64602 −0.823009 0.568028i \(-0.807706\pi\)
−0.823009 + 0.568028i \(0.807706\pi\)
\(558\) 2.88053 0.121942
\(559\) 31.8871 1.34868
\(560\) −9.63519 −0.407161
\(561\) −16.5189 −0.697429
\(562\) 20.1260 0.848966
\(563\) −0.502612 −0.0211826 −0.0105913 0.999944i \(-0.503371\pi\)
−0.0105913 + 0.999944i \(0.503371\pi\)
\(564\) 9.83445 0.414105
\(565\) −19.7686 −0.831669
\(566\) −13.4278 −0.564413
\(567\) −51.7207 −2.17207
\(568\) 4.69860 0.197149
\(569\) −6.02493 −0.252578 −0.126289 0.991993i \(-0.540307\pi\)
−0.126289 + 0.991993i \(0.540307\pi\)
\(570\) −8.11583 −0.339935
\(571\) 17.5909 0.736157 0.368078 0.929795i \(-0.380016\pi\)
0.368078 + 0.929795i \(0.380016\pi\)
\(572\) −5.49821 −0.229892
\(573\) −39.7917 −1.66232
\(574\) −9.80425 −0.409222
\(575\) 4.58171 0.191070
\(576\) 6.53566 0.272319
\(577\) 17.6746 0.735803 0.367902 0.929865i \(-0.380076\pi\)
0.367902 + 0.929865i \(0.380076\pi\)
\(578\) −2.29620 −0.0955092
\(579\) −21.1979 −0.880957
\(580\) −2.82627 −0.117354
\(581\) −8.71069 −0.361380
\(582\) −8.99760 −0.372963
\(583\) 0.622711 0.0257901
\(584\) −5.06591 −0.209629
\(585\) −77.5530 −3.20642
\(586\) −22.7545 −0.939981
\(587\) −2.61022 −0.107735 −0.0538676 0.998548i \(-0.517155\pi\)
−0.0538676 + 0.998548i \(0.517155\pi\)
\(588\) −19.8873 −0.820137
\(589\) 0.440740 0.0181604
\(590\) −12.3192 −0.507173
\(591\) −57.8818 −2.38094
\(592\) 2.89756 0.119089
\(593\) 33.6988 1.38384 0.691921 0.721973i \(-0.256765\pi\)
0.691921 + 0.721973i \(0.256765\pi\)
\(594\) 13.2958 0.545535
\(595\) −42.3249 −1.73515
\(596\) −0.0832650 −0.00341067
\(597\) 23.1672 0.948168
\(598\) 10.8452 0.443492
\(599\) 5.72946 0.234099 0.117050 0.993126i \(-0.462656\pi\)
0.117050 + 0.993126i \(0.462656\pi\)
\(600\) 5.89004 0.240460
\(601\) 8.50040 0.346738 0.173369 0.984857i \(-0.444535\pi\)
0.173369 + 0.984857i \(0.444535\pi\)
\(602\) −25.8921 −1.05528
\(603\) 6.83808 0.278468
\(604\) 6.80702 0.276974
\(605\) −25.0125 −1.01690
\(606\) −29.0148 −1.17865
\(607\) −5.05944 −0.205356 −0.102678 0.994715i \(-0.532741\pi\)
−0.102678 + 0.994715i \(0.532741\pi\)
\(608\) 1.00000 0.0405554
\(609\) −12.1740 −0.493316
\(610\) −33.7963 −1.36837
\(611\) 14.3789 0.581709
\(612\) 28.7095 1.16051
\(613\) 0.644516 0.0260317 0.0130159 0.999915i \(-0.495857\pi\)
0.0130159 + 0.999915i \(0.495857\pi\)
\(614\) −9.59394 −0.387180
\(615\) 21.7042 0.875199
\(616\) 4.46450 0.179880
\(617\) −16.6540 −0.670464 −0.335232 0.942136i \(-0.608815\pi\)
−0.335232 + 0.942136i \(0.608815\pi\)
\(618\) −57.2748 −2.30393
\(619\) −18.1547 −0.729699 −0.364850 0.931066i \(-0.618880\pi\)
−0.364850 + 0.931066i \(0.618880\pi\)
\(620\) −1.15835 −0.0465204
\(621\) −26.2259 −1.05241
\(622\) −0.409447 −0.0164173
\(623\) −39.0613 −1.56496
\(624\) 13.9421 0.558129
\(625\) −30.8988 −1.23595
\(626\) 22.1881 0.886816
\(627\) 3.76050 0.150180
\(628\) −5.41689 −0.216157
\(629\) 12.7283 0.507509
\(630\) 62.9723 2.50888
\(631\) 29.4106 1.17082 0.585408 0.810739i \(-0.300934\pi\)
0.585408 + 0.810739i \(0.300934\pi\)
\(632\) −10.7461 −0.427458
\(633\) 3.08799 0.122736
\(634\) −10.9131 −0.433414
\(635\) −3.66357 −0.145384
\(636\) −1.57904 −0.0626128
\(637\) −29.0771 −1.15208
\(638\) 1.30956 0.0518460
\(639\) −30.7085 −1.21481
\(640\) −2.62819 −0.103889
\(641\) 10.7521 0.424683 0.212342 0.977196i \(-0.431891\pi\)
0.212342 + 0.977196i \(0.431891\pi\)
\(642\) −51.3489 −2.02658
\(643\) −9.26214 −0.365263 −0.182632 0.983181i \(-0.558462\pi\)
−0.182632 + 0.983181i \(0.558462\pi\)
\(644\) −8.80618 −0.347012
\(645\) 57.3187 2.25692
\(646\) 4.39274 0.172830
\(647\) −15.4901 −0.608978 −0.304489 0.952516i \(-0.598486\pi\)
−0.304489 + 0.952516i \(0.598486\pi\)
\(648\) −14.1079 −0.554210
\(649\) 5.70814 0.224064
\(650\) 8.61181 0.337783
\(651\) −4.98954 −0.195556
\(652\) 7.28377 0.285255
\(653\) 12.5699 0.491899 0.245949 0.969283i \(-0.420900\pi\)
0.245949 + 0.969283i \(0.420900\pi\)
\(654\) 4.29477 0.167939
\(655\) −22.1388 −0.865035
\(656\) −2.67431 −0.104414
\(657\) 33.1091 1.29171
\(658\) −11.6756 −0.455161
\(659\) −19.8788 −0.774368 −0.387184 0.922002i \(-0.626552\pi\)
−0.387184 + 0.922002i \(0.626552\pi\)
\(660\) −9.88332 −0.384708
\(661\) 11.9688 0.465533 0.232766 0.972533i \(-0.425222\pi\)
0.232766 + 0.972533i \(0.425222\pi\)
\(662\) 24.1998 0.940550
\(663\) 61.2439 2.37852
\(664\) −2.37602 −0.0922074
\(665\) 9.63519 0.373637
\(666\) −18.9375 −0.733813
\(667\) −2.58309 −0.100018
\(668\) −5.95964 −0.230586
\(669\) 12.2099 0.472063
\(670\) −2.74981 −0.106234
\(671\) 15.6596 0.604533
\(672\) −11.3208 −0.436711
\(673\) 24.3321 0.937934 0.468967 0.883216i \(-0.344626\pi\)
0.468967 + 0.883216i \(0.344626\pi\)
\(674\) −2.17669 −0.0838428
\(675\) −20.8252 −0.801562
\(676\) 7.38464 0.284025
\(677\) 29.1809 1.12151 0.560756 0.827981i \(-0.310510\pi\)
0.560756 + 0.827981i \(0.310510\pi\)
\(678\) −23.2270 −0.892027
\(679\) 10.6820 0.409939
\(680\) −11.5450 −0.442730
\(681\) 17.4221 0.667617
\(682\) 0.536726 0.0205523
\(683\) 21.4723 0.821615 0.410808 0.911722i \(-0.365247\pi\)
0.410808 + 0.911722i \(0.365247\pi\)
\(684\) −6.53566 −0.249897
\(685\) 26.1462 0.998995
\(686\) −2.05227 −0.0783559
\(687\) −57.8457 −2.20695
\(688\) −7.06259 −0.269259
\(689\) −2.30870 −0.0879546
\(690\) 19.4947 0.742152
\(691\) 4.17677 0.158892 0.0794460 0.996839i \(-0.474685\pi\)
0.0794460 + 0.996839i \(0.474685\pi\)
\(692\) 9.57800 0.364101
\(693\) −29.1785 −1.10840
\(694\) −20.4315 −0.775570
\(695\) 45.6331 1.73096
\(696\) −3.32071 −0.125871
\(697\) −11.7476 −0.444970
\(698\) 10.6675 0.403773
\(699\) −18.9192 −0.715588
\(700\) −6.99272 −0.264300
\(701\) −9.83263 −0.371373 −0.185687 0.982609i \(-0.559451\pi\)
−0.185687 + 0.982609i \(0.559451\pi\)
\(702\) −49.2944 −1.86050
\(703\) −2.89756 −0.109284
\(704\) 1.21778 0.0458969
\(705\) 25.8468 0.973449
\(706\) 11.1690 0.420353
\(707\) 34.4467 1.29550
\(708\) −14.4744 −0.543981
\(709\) 2.28208 0.0857052 0.0428526 0.999081i \(-0.486355\pi\)
0.0428526 + 0.999081i \(0.486355\pi\)
\(710\) 12.3488 0.463444
\(711\) 70.2330 2.63394
\(712\) −10.6548 −0.399304
\(713\) −1.05868 −0.0396481
\(714\) −49.7295 −1.86108
\(715\) −14.4504 −0.540413
\(716\) −15.0901 −0.563942
\(717\) −40.3502 −1.50691
\(718\) 15.7595 0.588137
\(719\) −49.5877 −1.84931 −0.924655 0.380806i \(-0.875647\pi\)
−0.924655 + 0.380806i \(0.875647\pi\)
\(720\) 17.1770 0.640148
\(721\) 67.9972 2.53235
\(722\) −1.00000 −0.0372161
\(723\) −69.5551 −2.58678
\(724\) 24.1491 0.897496
\(725\) −2.05116 −0.0761780
\(726\) −29.3884 −1.09070
\(727\) −22.7388 −0.843335 −0.421667 0.906751i \(-0.638555\pi\)
−0.421667 + 0.906751i \(0.638555\pi\)
\(728\) −16.5522 −0.613464
\(729\) −8.94029 −0.331122
\(730\) −13.3142 −0.492781
\(731\) −31.0241 −1.14747
\(732\) −39.7088 −1.46768
\(733\) −51.0654 −1.88614 −0.943072 0.332589i \(-0.892078\pi\)
−0.943072 + 0.332589i \(0.892078\pi\)
\(734\) −26.4309 −0.975581
\(735\) −52.2676 −1.92792
\(736\) −2.40206 −0.0885412
\(737\) 1.27413 0.0469333
\(738\) 17.4784 0.643388
\(739\) −30.3608 −1.11684 −0.558419 0.829559i \(-0.688592\pi\)
−0.558419 + 0.829559i \(0.688592\pi\)
\(740\) 7.61536 0.279946
\(741\) −13.9421 −0.512174
\(742\) 1.87465 0.0688204
\(743\) 49.4246 1.81321 0.906606 0.421977i \(-0.138664\pi\)
0.906606 + 0.421977i \(0.138664\pi\)
\(744\) −1.36100 −0.0498966
\(745\) −0.218837 −0.00801755
\(746\) 5.99275 0.219410
\(747\) 15.5288 0.568171
\(748\) 5.34941 0.195594
\(749\) 60.9620 2.22750
\(750\) −25.0990 −0.916485
\(751\) −19.2237 −0.701482 −0.350741 0.936473i \(-0.614070\pi\)
−0.350741 + 0.936473i \(0.614070\pi\)
\(752\) −3.18475 −0.116136
\(753\) −11.1422 −0.406045
\(754\) −4.85520 −0.176816
\(755\) 17.8902 0.651090
\(756\) 40.0266 1.45575
\(757\) 3.35485 0.121934 0.0609670 0.998140i \(-0.480582\pi\)
0.0609670 + 0.998140i \(0.480582\pi\)
\(758\) −22.9513 −0.833628
\(759\) −9.03296 −0.327876
\(760\) 2.62819 0.0953346
\(761\) 12.2456 0.443904 0.221952 0.975058i \(-0.428757\pi\)
0.221952 + 0.975058i \(0.428757\pi\)
\(762\) −4.30450 −0.155936
\(763\) −5.09879 −0.184589
\(764\) 12.8860 0.466198
\(765\) 75.4541 2.72805
\(766\) 20.7028 0.748023
\(767\) −21.1630 −0.764150
\(768\) −3.08799 −0.111428
\(769\) −29.4617 −1.06241 −0.531207 0.847242i \(-0.678261\pi\)
−0.531207 + 0.847242i \(0.678261\pi\)
\(770\) 11.7336 0.422849
\(771\) 70.1669 2.52700
\(772\) 6.86465 0.247064
\(773\) −41.5818 −1.49559 −0.747796 0.663929i \(-0.768888\pi\)
−0.747796 + 0.663929i \(0.768888\pi\)
\(774\) 46.1587 1.65914
\(775\) −0.840669 −0.0301977
\(776\) 2.91374 0.104597
\(777\) 32.8028 1.17680
\(778\) 3.59719 0.128965
\(779\) 2.67431 0.0958171
\(780\) 36.6424 1.31201
\(781\) −5.72188 −0.204745
\(782\) −10.5516 −0.377326
\(783\) 11.7409 0.419586
\(784\) 6.44020 0.230007
\(785\) −14.2366 −0.508127
\(786\) −26.0119 −0.927814
\(787\) 19.2280 0.685404 0.342702 0.939444i \(-0.388658\pi\)
0.342702 + 0.939444i \(0.388658\pi\)
\(788\) 18.7442 0.667735
\(789\) −90.1416 −3.20913
\(790\) −28.2429 −1.00484
\(791\) 27.5753 0.980465
\(792\) −7.95902 −0.282811
\(793\) −58.0581 −2.06170
\(794\) −5.55478 −0.197132
\(795\) −4.15001 −0.147186
\(796\) −7.50235 −0.265914
\(797\) −42.5483 −1.50714 −0.753569 0.657369i \(-0.771669\pi\)
−0.753569 + 0.657369i \(0.771669\pi\)
\(798\) 11.3208 0.400753
\(799\) −13.9898 −0.494922
\(800\) −1.90741 −0.0674370
\(801\) 69.6359 2.46046
\(802\) 17.0328 0.601448
\(803\) 6.16919 0.217706
\(804\) −3.23087 −0.113944
\(805\) −23.1443 −0.815731
\(806\) −1.98991 −0.0700916
\(807\) 22.8865 0.805642
\(808\) 9.39603 0.330551
\(809\) 42.0980 1.48009 0.740044 0.672558i \(-0.234805\pi\)
0.740044 + 0.672558i \(0.234805\pi\)
\(810\) −37.0782 −1.30280
\(811\) −16.7806 −0.589246 −0.294623 0.955614i \(-0.595194\pi\)
−0.294623 + 0.955614i \(0.595194\pi\)
\(812\) 3.94238 0.138350
\(813\) 47.3543 1.66079
\(814\) −3.52861 −0.123678
\(815\) 19.1432 0.670556
\(816\) −13.5647 −0.474861
\(817\) 7.06259 0.247089
\(818\) 17.9167 0.626443
\(819\) 108.179 3.78009
\(820\) −7.02860 −0.245450
\(821\) −45.6207 −1.59217 −0.796087 0.605182i \(-0.793100\pi\)
−0.796087 + 0.605182i \(0.793100\pi\)
\(822\) 30.7204 1.07150
\(823\) −8.12703 −0.283290 −0.141645 0.989917i \(-0.545239\pi\)
−0.141645 + 0.989917i \(0.545239\pi\)
\(824\) 18.5476 0.646137
\(825\) −7.17280 −0.249725
\(826\) 17.1841 0.597912
\(827\) 38.1225 1.32565 0.662824 0.748775i \(-0.269358\pi\)
0.662824 + 0.748775i \(0.269358\pi\)
\(828\) 15.6991 0.545580
\(829\) 12.8740 0.447133 0.223566 0.974689i \(-0.428230\pi\)
0.223566 + 0.974689i \(0.428230\pi\)
\(830\) −6.24464 −0.216754
\(831\) 5.07133 0.175922
\(832\) −4.51494 −0.156527
\(833\) 28.2902 0.980196
\(834\) 53.6165 1.85659
\(835\) −15.6631 −0.542044
\(836\) −1.21778 −0.0421179
\(837\) 4.81203 0.166328
\(838\) 3.33924 0.115352
\(839\) 7.18863 0.248179 0.124089 0.992271i \(-0.460399\pi\)
0.124089 + 0.992271i \(0.460399\pi\)
\(840\) −29.7533 −1.02659
\(841\) −27.8436 −0.960124
\(842\) 17.3270 0.597129
\(843\) 62.1490 2.14052
\(844\) −1.00000 −0.0344214
\(845\) 19.4083 0.667665
\(846\) 20.8144 0.715614
\(847\) 34.8902 1.19884
\(848\) 0.511348 0.0175598
\(849\) −41.4649 −1.42307
\(850\) −8.37874 −0.287389
\(851\) 6.96013 0.238590
\(852\) 14.5092 0.497078
\(853\) −10.4064 −0.356310 −0.178155 0.984002i \(-0.557013\pi\)
−0.178155 + 0.984002i \(0.557013\pi\)
\(854\) 47.1427 1.61319
\(855\) −17.1770 −0.587441
\(856\) 16.6286 0.568354
\(857\) 16.8774 0.576521 0.288260 0.957552i \(-0.406923\pi\)
0.288260 + 0.957552i \(0.406923\pi\)
\(858\) −16.9784 −0.579633
\(859\) 40.4695 1.38080 0.690400 0.723427i \(-0.257434\pi\)
0.690400 + 0.723427i \(0.257434\pi\)
\(860\) −18.5619 −0.632954
\(861\) −30.2754 −1.03178
\(862\) 21.7260 0.739990
\(863\) −18.5964 −0.633028 −0.316514 0.948588i \(-0.602512\pi\)
−0.316514 + 0.948588i \(0.602512\pi\)
\(864\) 10.9181 0.371440
\(865\) 25.1728 0.855902
\(866\) 29.4313 1.00012
\(867\) −7.09062 −0.240810
\(868\) 1.61579 0.0548435
\(869\) 13.0864 0.443927
\(870\) −8.72747 −0.295889
\(871\) −4.72385 −0.160062
\(872\) −1.39080 −0.0470984
\(873\) −19.0432 −0.644516
\(874\) 2.40206 0.0812510
\(875\) 29.7977 1.00735
\(876\) −15.6435 −0.528544
\(877\) −2.54066 −0.0857918 −0.0428959 0.999080i \(-0.513658\pi\)
−0.0428959 + 0.999080i \(0.513658\pi\)
\(878\) 13.5207 0.456300
\(879\) −70.2657 −2.37000
\(880\) 3.20057 0.107891
\(881\) −36.2230 −1.22038 −0.610192 0.792254i \(-0.708908\pi\)
−0.610192 + 0.792254i \(0.708908\pi\)
\(882\) −42.0910 −1.41728
\(883\) −22.7915 −0.766996 −0.383498 0.923542i \(-0.625281\pi\)
−0.383498 + 0.923542i \(0.625281\pi\)
\(884\) −19.8330 −0.667054
\(885\) −38.0415 −1.27875
\(886\) 10.5641 0.354907
\(887\) −59.3005 −1.99112 −0.995558 0.0941485i \(-0.969987\pi\)
−0.995558 + 0.0941485i \(0.969987\pi\)
\(888\) 8.94764 0.300263
\(889\) 5.11034 0.171395
\(890\) −28.0028 −0.938656
\(891\) 17.1803 0.575563
\(892\) −3.95401 −0.132390
\(893\) 3.18475 0.106573
\(894\) −0.257121 −0.00859942
\(895\) −39.6596 −1.32567
\(896\) 3.66609 0.122475
\(897\) 33.4897 1.11819
\(898\) 35.2338 1.17577
\(899\) 0.473956 0.0158073
\(900\) 12.4662 0.415538
\(901\) 2.24622 0.0748324
\(902\) 3.25673 0.108437
\(903\) −79.9543 −2.66071
\(904\) 7.52173 0.250169
\(905\) 63.4687 2.10977
\(906\) 21.0200 0.698342
\(907\) −44.0321 −1.46206 −0.731031 0.682344i \(-0.760961\pi\)
−0.731031 + 0.682344i \(0.760961\pi\)
\(908\) −5.64190 −0.187233
\(909\) −61.4093 −2.03682
\(910\) −43.5023 −1.44209
\(911\) 12.8796 0.426721 0.213361 0.976974i \(-0.431559\pi\)
0.213361 + 0.976974i \(0.431559\pi\)
\(912\) 3.08799 0.102253
\(913\) 2.89347 0.0957600
\(914\) 16.5664 0.547967
\(915\) −104.362 −3.45011
\(916\) 18.7325 0.618939
\(917\) 30.8816 1.01980
\(918\) 47.9603 1.58293
\(919\) 15.4887 0.510925 0.255463 0.966819i \(-0.417772\pi\)
0.255463 + 0.966819i \(0.417772\pi\)
\(920\) −6.31309 −0.208136
\(921\) −29.6259 −0.976208
\(922\) 4.59128 0.151206
\(923\) 21.2139 0.698264
\(924\) 13.7863 0.453537
\(925\) 5.52683 0.181721
\(926\) 21.5547 0.708330
\(927\) −121.221 −3.98142
\(928\) 1.07536 0.0353006
\(929\) −7.21008 −0.236555 −0.118278 0.992981i \(-0.537737\pi\)
−0.118278 + 0.992981i \(0.537737\pi\)
\(930\) −3.57697 −0.117293
\(931\) −6.44020 −0.211069
\(932\) 6.12670 0.200687
\(933\) −1.26437 −0.0413935
\(934\) 34.2095 1.11937
\(935\) 14.0593 0.459788
\(936\) 29.5081 0.964502
\(937\) −26.8336 −0.876615 −0.438308 0.898825i \(-0.644422\pi\)
−0.438308 + 0.898825i \(0.644422\pi\)
\(938\) 3.83572 0.125241
\(939\) 68.5166 2.23596
\(940\) −8.37013 −0.273004
\(941\) −18.0314 −0.587806 −0.293903 0.955835i \(-0.594954\pi\)
−0.293903 + 0.955835i \(0.594954\pi\)
\(942\) −16.7273 −0.545004
\(943\) −6.42386 −0.209190
\(944\) 4.68732 0.152559
\(945\) 105.198 3.42208
\(946\) 8.60070 0.279633
\(947\) −24.6484 −0.800966 −0.400483 0.916304i \(-0.631158\pi\)
−0.400483 + 0.916304i \(0.631158\pi\)
\(948\) −33.1839 −1.07776
\(949\) −22.8723 −0.742466
\(950\) 1.90741 0.0618844
\(951\) −33.6994 −1.09278
\(952\) 16.1042 0.521940
\(953\) 50.3498 1.63099 0.815495 0.578764i \(-0.196465\pi\)
0.815495 + 0.578764i \(0.196465\pi\)
\(954\) −3.34200 −0.108201
\(955\) 33.8668 1.09590
\(956\) 13.0668 0.422612
\(957\) 4.04391 0.130721
\(958\) −7.21220 −0.233016
\(959\) −36.4715 −1.17773
\(960\) −8.11583 −0.261937
\(961\) −30.8057 −0.993734
\(962\) 13.0823 0.421791
\(963\) −108.679 −3.50213
\(964\) 22.5244 0.725463
\(965\) 18.0416 0.580781
\(966\) −27.1934 −0.874932
\(967\) −1.26019 −0.0405250 −0.0202625 0.999795i \(-0.506450\pi\)
−0.0202625 + 0.999795i \(0.506450\pi\)
\(968\) 9.51700 0.305888
\(969\) 13.5647 0.435762
\(970\) 7.65789 0.245880
\(971\) 19.6863 0.631763 0.315881 0.948799i \(-0.397700\pi\)
0.315881 + 0.948799i \(0.397700\pi\)
\(972\) −10.8107 −0.346754
\(973\) −63.6540 −2.04065
\(974\) 28.7120 0.919992
\(975\) 26.5932 0.851663
\(976\) 12.8591 0.411610
\(977\) −55.5694 −1.77782 −0.888911 0.458080i \(-0.848537\pi\)
−0.888911 + 0.458080i \(0.848537\pi\)
\(978\) 22.4922 0.719221
\(979\) 12.9752 0.414689
\(980\) 16.9261 0.540685
\(981\) 9.08978 0.290214
\(982\) 18.1445 0.579014
\(983\) −34.8075 −1.11019 −0.555093 0.831788i \(-0.687317\pi\)
−0.555093 + 0.831788i \(0.687317\pi\)
\(984\) −8.25823 −0.263263
\(985\) 49.2634 1.56966
\(986\) 4.72380 0.150436
\(987\) −36.0540 −1.14761
\(988\) 4.51494 0.143639
\(989\) −16.9648 −0.539449
\(990\) −20.9178 −0.664813
\(991\) 14.7837 0.469619 0.234809 0.972041i \(-0.424553\pi\)
0.234809 + 0.972041i \(0.424553\pi\)
\(992\) 0.440740 0.0139935
\(993\) 74.7285 2.37144
\(994\) −17.2255 −0.546359
\(995\) −19.7176 −0.625091
\(996\) −7.33711 −0.232485
\(997\) −11.8243 −0.374480 −0.187240 0.982314i \(-0.559954\pi\)
−0.187240 + 0.982314i \(0.559954\pi\)
\(998\) 10.9783 0.347511
\(999\) −31.6358 −1.00091
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 \(a_p\))