Properties

Label 8021.2.a.a.1.2
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.68511 q^{2}\) \(+2.15795 q^{3}\) \(+5.20984 q^{4}\) \(-0.637263 q^{5}\) \(-5.79434 q^{6}\) \(+0.252834 q^{7}\) \(-8.61877 q^{8}\) \(+1.65675 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.68511 q^{2}\) \(+2.15795 q^{3}\) \(+5.20984 q^{4}\) \(-0.637263 q^{5}\) \(-5.79434 q^{6}\) \(+0.252834 q^{7}\) \(-8.61877 q^{8}\) \(+1.65675 q^{9}\) \(+1.71112 q^{10}\) \(+4.55402 q^{11}\) \(+11.2426 q^{12}\) \(+1.00000 q^{13}\) \(-0.678888 q^{14}\) \(-1.37518 q^{15}\) \(+12.7227 q^{16}\) \(-1.91989 q^{17}\) \(-4.44857 q^{18}\) \(-3.93002 q^{19}\) \(-3.32004 q^{20}\) \(+0.545603 q^{21}\) \(-12.2281 q^{22}\) \(-1.52699 q^{23}\) \(-18.5989 q^{24}\) \(-4.59390 q^{25}\) \(-2.68511 q^{26}\) \(-2.89866 q^{27}\) \(+1.31722 q^{28}\) \(-2.58490 q^{29}\) \(+3.69252 q^{30}\) \(+2.72547 q^{31}\) \(-16.9244 q^{32}\) \(+9.82735 q^{33}\) \(+5.15513 q^{34}\) \(-0.161122 q^{35}\) \(+8.63142 q^{36}\) \(+0.429846 q^{37}\) \(+10.5525 q^{38}\) \(+2.15795 q^{39}\) \(+5.49243 q^{40}\) \(+11.4011 q^{41}\) \(-1.46501 q^{42}\) \(-6.64689 q^{43}\) \(+23.7257 q^{44}\) \(-1.05579 q^{45}\) \(+4.10015 q^{46}\) \(-2.00504 q^{47}\) \(+27.4550 q^{48}\) \(-6.93608 q^{49}\) \(+12.3351 q^{50}\) \(-4.14304 q^{51}\) \(+5.20984 q^{52}\) \(+11.7389 q^{53}\) \(+7.78323 q^{54}\) \(-2.90211 q^{55}\) \(-2.17912 q^{56}\) \(-8.48078 q^{57}\) \(+6.94076 q^{58}\) \(-7.88967 q^{59}\) \(-7.16448 q^{60}\) \(-11.4560 q^{61}\) \(-7.31820 q^{62}\) \(+0.418884 q^{63}\) \(+19.9985 q^{64}\) \(-0.637263 q^{65}\) \(-26.3875 q^{66}\) \(+7.42062 q^{67}\) \(-10.0023 q^{68}\) \(-3.29518 q^{69}\) \(+0.432630 q^{70}\) \(-10.2089 q^{71}\) \(-14.2792 q^{72}\) \(-0.562155 q^{73}\) \(-1.15419 q^{74}\) \(-9.91340 q^{75}\) \(-20.4747 q^{76}\) \(+1.15141 q^{77}\) \(-5.79434 q^{78}\) \(-0.465116 q^{79}\) \(-8.10772 q^{80}\) \(-11.2254 q^{81}\) \(-30.6134 q^{82}\) \(+8.48609 q^{83}\) \(+2.84250 q^{84}\) \(+1.22348 q^{85}\) \(+17.8476 q^{86}\) \(-5.57809 q^{87}\) \(-39.2500 q^{88}\) \(-5.07983 q^{89}\) \(+2.83491 q^{90}\) \(+0.252834 q^{91}\) \(-7.95539 q^{92}\) \(+5.88143 q^{93}\) \(+5.38377 q^{94}\) \(+2.50445 q^{95}\) \(-36.5220 q^{96}\) \(-15.4846 q^{97}\) \(+18.6241 q^{98}\) \(+7.54489 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68511 −1.89866 −0.949331 0.314278i \(-0.898238\pi\)
−0.949331 + 0.314278i \(0.898238\pi\)
\(3\) 2.15795 1.24589 0.622947 0.782264i \(-0.285935\pi\)
0.622947 + 0.782264i \(0.285935\pi\)
\(4\) 5.20984 2.60492
\(5\) −0.637263 −0.284993 −0.142496 0.989795i \(-0.545513\pi\)
−0.142496 + 0.989795i \(0.545513\pi\)
\(6\) −5.79434 −2.36553
\(7\) 0.252834 0.0955622 0.0477811 0.998858i \(-0.484785\pi\)
0.0477811 + 0.998858i \(0.484785\pi\)
\(8\) −8.61877 −3.04720
\(9\) 1.65675 0.552251
\(10\) 1.71112 0.541105
\(11\) 4.55402 1.37309 0.686544 0.727088i \(-0.259127\pi\)
0.686544 + 0.727088i \(0.259127\pi\)
\(12\) 11.2426 3.24545
\(13\) 1.00000 0.277350
\(14\) −0.678888 −0.181440
\(15\) −1.37518 −0.355071
\(16\) 12.7227 3.18068
\(17\) −1.91989 −0.465643 −0.232821 0.972520i \(-0.574796\pi\)
−0.232821 + 0.972520i \(0.574796\pi\)
\(18\) −4.44857 −1.04854
\(19\) −3.93002 −0.901608 −0.450804 0.892623i \(-0.648863\pi\)
−0.450804 + 0.892623i \(0.648863\pi\)
\(20\) −3.32004 −0.742383
\(21\) 0.545603 0.119060
\(22\) −12.2281 −2.60703
\(23\) −1.52699 −0.318400 −0.159200 0.987246i \(-0.550892\pi\)
−0.159200 + 0.987246i \(0.550892\pi\)
\(24\) −18.5989 −3.79648
\(25\) −4.59390 −0.918779
\(26\) −2.68511 −0.526594
\(27\) −2.89866 −0.557847
\(28\) 1.31722 0.248932
\(29\) −2.58490 −0.480004 −0.240002 0.970772i \(-0.577148\pi\)
−0.240002 + 0.970772i \(0.577148\pi\)
\(30\) 3.69252 0.674159
\(31\) 2.72547 0.489509 0.244754 0.969585i \(-0.421293\pi\)
0.244754 + 0.969585i \(0.421293\pi\)
\(32\) −16.9244 −2.99184
\(33\) 9.82735 1.71072
\(34\) 5.15513 0.884098
\(35\) −0.161122 −0.0272345
\(36\) 8.63142 1.43857
\(37\) 0.429846 0.0706663 0.0353331 0.999376i \(-0.488751\pi\)
0.0353331 + 0.999376i \(0.488751\pi\)
\(38\) 10.5525 1.71185
\(39\) 2.15795 0.345549
\(40\) 5.49243 0.868429
\(41\) 11.4011 1.78056 0.890280 0.455413i \(-0.150509\pi\)
0.890280 + 0.455413i \(0.150509\pi\)
\(42\) −1.46501 −0.226055
\(43\) −6.64689 −1.01364 −0.506820 0.862052i \(-0.669179\pi\)
−0.506820 + 0.862052i \(0.669179\pi\)
\(44\) 23.7257 3.57678
\(45\) −1.05579 −0.157388
\(46\) 4.10015 0.604535
\(47\) −2.00504 −0.292466 −0.146233 0.989250i \(-0.546715\pi\)
−0.146233 + 0.989250i \(0.546715\pi\)
\(48\) 27.4550 3.96279
\(49\) −6.93608 −0.990868
\(50\) 12.3351 1.74445
\(51\) −4.14304 −0.580141
\(52\) 5.20984 0.722474
\(53\) 11.7389 1.61246 0.806229 0.591604i \(-0.201505\pi\)
0.806229 + 0.591604i \(0.201505\pi\)
\(54\) 7.78323 1.05916
\(55\) −2.90211 −0.391320
\(56\) −2.17912 −0.291197
\(57\) −8.48078 −1.12331
\(58\) 6.94076 0.911366
\(59\) −7.88967 −1.02715 −0.513573 0.858046i \(-0.671679\pi\)
−0.513573 + 0.858046i \(0.671679\pi\)
\(60\) −7.16448 −0.924930
\(61\) −11.4560 −1.46679 −0.733393 0.679805i \(-0.762065\pi\)
−0.733393 + 0.679805i \(0.762065\pi\)
\(62\) −7.31820 −0.929412
\(63\) 0.418884 0.0527744
\(64\) 19.9985 2.49981
\(65\) −0.637263 −0.0790428
\(66\) −26.3875 −3.24808
\(67\) 7.42062 0.906573 0.453286 0.891365i \(-0.350251\pi\)
0.453286 + 0.891365i \(0.350251\pi\)
\(68\) −10.0023 −1.21296
\(69\) −3.29518 −0.396693
\(70\) 0.432630 0.0517092
\(71\) −10.2089 −1.21157 −0.605785 0.795629i \(-0.707141\pi\)
−0.605785 + 0.795629i \(0.707141\pi\)
\(72\) −14.2792 −1.68282
\(73\) −0.562155 −0.0657952 −0.0328976 0.999459i \(-0.510474\pi\)
−0.0328976 + 0.999459i \(0.510474\pi\)
\(74\) −1.15419 −0.134171
\(75\) −9.91340 −1.14470
\(76\) −20.4747 −2.34861
\(77\) 1.15141 0.131215
\(78\) −5.79434 −0.656080
\(79\) −0.465116 −0.0523296 −0.0261648 0.999658i \(-0.508329\pi\)
−0.0261648 + 0.999658i \(0.508329\pi\)
\(80\) −8.10772 −0.906470
\(81\) −11.2254 −1.24727
\(82\) −30.6134 −3.38068
\(83\) 8.48609 0.931469 0.465735 0.884924i \(-0.345790\pi\)
0.465735 + 0.884924i \(0.345790\pi\)
\(84\) 2.84250 0.310143
\(85\) 1.22348 0.132705
\(86\) 17.8476 1.92456
\(87\) −5.57809 −0.598034
\(88\) −39.2500 −4.18407
\(89\) −5.07983 −0.538461 −0.269230 0.963076i \(-0.586769\pi\)
−0.269230 + 0.963076i \(0.586769\pi\)
\(90\) 2.83491 0.298826
\(91\) 0.252834 0.0265042
\(92\) −7.95539 −0.829407
\(93\) 5.88143 0.609876
\(94\) 5.38377 0.555294
\(95\) 2.50445 0.256952
\(96\) −36.5220 −3.72751
\(97\) −15.4846 −1.57223 −0.786113 0.618083i \(-0.787910\pi\)
−0.786113 + 0.618083i \(0.787910\pi\)
\(98\) 18.6241 1.88132
\(99\) 7.54489 0.758290
\(100\) −23.9334 −2.39334
\(101\) −0.801523 −0.0797545 −0.0398773 0.999205i \(-0.512697\pi\)
−0.0398773 + 0.999205i \(0.512697\pi\)
\(102\) 11.1245 1.10149
\(103\) 10.9803 1.08192 0.540960 0.841048i \(-0.318061\pi\)
0.540960 + 0.841048i \(0.318061\pi\)
\(104\) −8.61877 −0.845140
\(105\) −0.347693 −0.0339314
\(106\) −31.5202 −3.06151
\(107\) −3.22955 −0.312212 −0.156106 0.987740i \(-0.549894\pi\)
−0.156106 + 0.987740i \(0.549894\pi\)
\(108\) −15.1015 −1.45315
\(109\) −3.99266 −0.382427 −0.191214 0.981548i \(-0.561242\pi\)
−0.191214 + 0.981548i \(0.561242\pi\)
\(110\) 7.79249 0.742985
\(111\) 0.927587 0.0880427
\(112\) 3.21673 0.303953
\(113\) −13.3098 −1.25208 −0.626042 0.779790i \(-0.715326\pi\)
−0.626042 + 0.779790i \(0.715326\pi\)
\(114\) 22.7719 2.13278
\(115\) 0.973097 0.0907418
\(116\) −13.4669 −1.25037
\(117\) 1.65675 0.153167
\(118\) 21.1846 1.95020
\(119\) −0.485414 −0.0444978
\(120\) 11.8524 1.08197
\(121\) 9.73907 0.885370
\(122\) 30.7606 2.78493
\(123\) 24.6031 2.21839
\(124\) 14.1993 1.27513
\(125\) 6.11384 0.546838
\(126\) −1.12475 −0.100201
\(127\) −20.7432 −1.84066 −0.920330 0.391143i \(-0.872080\pi\)
−0.920330 + 0.391143i \(0.872080\pi\)
\(128\) −19.8494 −1.75445
\(129\) −14.3437 −1.26289
\(130\) 1.71112 0.150076
\(131\) −11.2061 −0.979078 −0.489539 0.871981i \(-0.662835\pi\)
−0.489539 + 0.871981i \(0.662835\pi\)
\(132\) 51.1989 4.45629
\(133\) −0.993641 −0.0861596
\(134\) −19.9252 −1.72128
\(135\) 1.84721 0.158982
\(136\) 16.5471 1.41890
\(137\) 17.4810 1.49350 0.746750 0.665105i \(-0.231613\pi\)
0.746750 + 0.665105i \(0.231613\pi\)
\(138\) 8.84793 0.753186
\(139\) 18.9688 1.60891 0.804456 0.594013i \(-0.202457\pi\)
0.804456 + 0.594013i \(0.202457\pi\)
\(140\) −0.839418 −0.0709438
\(141\) −4.32679 −0.364381
\(142\) 27.4120 2.30036
\(143\) 4.55402 0.380826
\(144\) 21.0784 1.75653
\(145\) 1.64726 0.136798
\(146\) 1.50945 0.124923
\(147\) −14.9677 −1.23452
\(148\) 2.23943 0.184080
\(149\) −4.23217 −0.346713 −0.173356 0.984859i \(-0.555461\pi\)
−0.173356 + 0.984859i \(0.555461\pi\)
\(150\) 26.6186 2.17340
\(151\) 7.25729 0.590590 0.295295 0.955406i \(-0.404582\pi\)
0.295295 + 0.955406i \(0.404582\pi\)
\(152\) 33.8719 2.74737
\(153\) −3.18079 −0.257152
\(154\) −3.09167 −0.249134
\(155\) −1.73684 −0.139507
\(156\) 11.2426 0.900126
\(157\) −19.5612 −1.56115 −0.780575 0.625062i \(-0.785074\pi\)
−0.780575 + 0.625062i \(0.785074\pi\)
\(158\) 1.24889 0.0993563
\(159\) 25.3319 2.00895
\(160\) 10.7853 0.852652
\(161\) −0.386076 −0.0304270
\(162\) 30.1415 2.36814
\(163\) −20.2291 −1.58446 −0.792232 0.610220i \(-0.791081\pi\)
−0.792232 + 0.610220i \(0.791081\pi\)
\(164\) 59.3981 4.63821
\(165\) −6.26261 −0.487543
\(166\) −22.7861 −1.76855
\(167\) −0.575907 −0.0445650 −0.0222825 0.999752i \(-0.507093\pi\)
−0.0222825 + 0.999752i \(0.507093\pi\)
\(168\) −4.70243 −0.362800
\(169\) 1.00000 0.0769231
\(170\) −3.28518 −0.251961
\(171\) −6.51107 −0.497914
\(172\) −34.6292 −2.64045
\(173\) 15.7678 1.19881 0.599404 0.800447i \(-0.295404\pi\)
0.599404 + 0.800447i \(0.295404\pi\)
\(174\) 14.9778 1.13547
\(175\) −1.16149 −0.0878006
\(176\) 57.9394 4.36735
\(177\) −17.0255 −1.27972
\(178\) 13.6399 1.02235
\(179\) 4.45442 0.332939 0.166469 0.986047i \(-0.446763\pi\)
0.166469 + 0.986047i \(0.446763\pi\)
\(180\) −5.50048 −0.409982
\(181\) −3.61967 −0.269048 −0.134524 0.990910i \(-0.542951\pi\)
−0.134524 + 0.990910i \(0.542951\pi\)
\(182\) −0.678888 −0.0503225
\(183\) −24.7214 −1.82746
\(184\) 13.1608 0.970228
\(185\) −0.273925 −0.0201394
\(186\) −15.7923 −1.15795
\(187\) −8.74323 −0.639368
\(188\) −10.4460 −0.761849
\(189\) −0.732879 −0.0533091
\(190\) −6.72475 −0.487864
\(191\) −23.5442 −1.70360 −0.851801 0.523866i \(-0.824489\pi\)
−0.851801 + 0.523866i \(0.824489\pi\)
\(192\) 43.1557 3.11450
\(193\) 25.3909 1.82768 0.913840 0.406075i \(-0.133103\pi\)
0.913840 + 0.406075i \(0.133103\pi\)
\(194\) 41.5780 2.98513
\(195\) −1.37518 −0.0984789
\(196\) −36.1358 −2.58113
\(197\) 17.5494 1.25035 0.625173 0.780486i \(-0.285028\pi\)
0.625173 + 0.780486i \(0.285028\pi\)
\(198\) −20.2589 −1.43974
\(199\) −21.1071 −1.49624 −0.748121 0.663562i \(-0.769044\pi\)
−0.748121 + 0.663562i \(0.769044\pi\)
\(200\) 39.5937 2.79970
\(201\) 16.0133 1.12949
\(202\) 2.15218 0.151427
\(203\) −0.653551 −0.0458703
\(204\) −21.5845 −1.51122
\(205\) −7.26553 −0.507447
\(206\) −29.4833 −2.05420
\(207\) −2.52985 −0.175837
\(208\) 12.7227 0.882161
\(209\) −17.8974 −1.23799
\(210\) 0.933595 0.0644242
\(211\) −25.9355 −1.78547 −0.892736 0.450580i \(-0.851217\pi\)
−0.892736 + 0.450580i \(0.851217\pi\)
\(212\) 61.1576 4.20032
\(213\) −22.0302 −1.50949
\(214\) 8.67171 0.592786
\(215\) 4.23582 0.288880
\(216\) 24.9829 1.69987
\(217\) 0.689091 0.0467786
\(218\) 10.7207 0.726100
\(219\) −1.21310 −0.0819739
\(220\) −15.1195 −1.01936
\(221\) −1.91989 −0.129146
\(222\) −2.49068 −0.167163
\(223\) −25.4858 −1.70666 −0.853328 0.521374i \(-0.825420\pi\)
−0.853328 + 0.521374i \(0.825420\pi\)
\(224\) −4.27906 −0.285907
\(225\) −7.61096 −0.507397
\(226\) 35.7384 2.37728
\(227\) 5.56747 0.369526 0.184763 0.982783i \(-0.440848\pi\)
0.184763 + 0.982783i \(0.440848\pi\)
\(228\) −44.1835 −2.92612
\(229\) 8.43307 0.557273 0.278637 0.960397i \(-0.410118\pi\)
0.278637 + 0.960397i \(0.410118\pi\)
\(230\) −2.61288 −0.172288
\(231\) 2.48469 0.163480
\(232\) 22.2787 1.46267
\(233\) 27.8546 1.82482 0.912408 0.409281i \(-0.134220\pi\)
0.912408 + 0.409281i \(0.134220\pi\)
\(234\) −4.44857 −0.290812
\(235\) 1.27774 0.0833506
\(236\) −41.1039 −2.67563
\(237\) −1.00370 −0.0651972
\(238\) 1.30339 0.0844864
\(239\) −14.2599 −0.922396 −0.461198 0.887297i \(-0.652580\pi\)
−0.461198 + 0.887297i \(0.652580\pi\)
\(240\) −17.4961 −1.12937
\(241\) −12.9284 −0.832790 −0.416395 0.909184i \(-0.636707\pi\)
−0.416395 + 0.909184i \(0.636707\pi\)
\(242\) −26.1505 −1.68102
\(243\) −15.5280 −0.996119
\(244\) −59.6837 −3.82086
\(245\) 4.42011 0.282390
\(246\) −66.0622 −4.21197
\(247\) −3.93002 −0.250061
\(248\) −23.4902 −1.49163
\(249\) 18.3126 1.16051
\(250\) −16.4163 −1.03826
\(251\) 5.43286 0.342919 0.171460 0.985191i \(-0.445152\pi\)
0.171460 + 0.985191i \(0.445152\pi\)
\(252\) 2.18231 0.137473
\(253\) −6.95396 −0.437192
\(254\) 55.6978 3.49479
\(255\) 2.64020 0.165336
\(256\) 13.3009 0.831309
\(257\) −14.9385 −0.931840 −0.465920 0.884827i \(-0.654277\pi\)
−0.465920 + 0.884827i \(0.654277\pi\)
\(258\) 38.5143 2.39780
\(259\) 0.108680 0.00675303
\(260\) −3.32004 −0.205900
\(261\) −4.28255 −0.265083
\(262\) 30.0895 1.85894
\(263\) 1.77064 0.109182 0.0545912 0.998509i \(-0.482614\pi\)
0.0545912 + 0.998509i \(0.482614\pi\)
\(264\) −84.6997 −5.21290
\(265\) −7.48075 −0.459539
\(266\) 2.66804 0.163588
\(267\) −10.9620 −0.670865
\(268\) 38.6602 2.36155
\(269\) −16.8961 −1.03017 −0.515085 0.857139i \(-0.672240\pi\)
−0.515085 + 0.857139i \(0.672240\pi\)
\(270\) −4.95997 −0.301854
\(271\) −4.66233 −0.283216 −0.141608 0.989923i \(-0.545227\pi\)
−0.141608 + 0.989923i \(0.545227\pi\)
\(272\) −24.4262 −1.48106
\(273\) 0.545603 0.0330214
\(274\) −46.9384 −2.83565
\(275\) −20.9207 −1.26156
\(276\) −17.1673 −1.03335
\(277\) 16.7136 1.00422 0.502111 0.864803i \(-0.332557\pi\)
0.502111 + 0.864803i \(0.332557\pi\)
\(278\) −50.9334 −3.05478
\(279\) 4.51544 0.270332
\(280\) 1.38867 0.0829890
\(281\) 4.28293 0.255498 0.127749 0.991807i \(-0.459225\pi\)
0.127749 + 0.991807i \(0.459225\pi\)
\(282\) 11.6179 0.691837
\(283\) 12.6832 0.753937 0.376968 0.926226i \(-0.376967\pi\)
0.376968 + 0.926226i \(0.376967\pi\)
\(284\) −53.1865 −3.15604
\(285\) 5.40449 0.320134
\(286\) −12.2281 −0.723060
\(287\) 2.88260 0.170154
\(288\) −28.0395 −1.65225
\(289\) −13.3140 −0.783177
\(290\) −4.42309 −0.259733
\(291\) −33.4151 −1.95883
\(292\) −2.92873 −0.171391
\(293\) −25.0148 −1.46138 −0.730690 0.682710i \(-0.760801\pi\)
−0.730690 + 0.682710i \(0.760801\pi\)
\(294\) 40.1900 2.34393
\(295\) 5.02779 0.292729
\(296\) −3.70475 −0.215334
\(297\) −13.2005 −0.765973
\(298\) 11.3638 0.658290
\(299\) −1.52699 −0.0883084
\(300\) −51.6472 −2.98185
\(301\) −1.68056 −0.0968658
\(302\) −19.4866 −1.12133
\(303\) −1.72965 −0.0993657
\(304\) −50.0005 −2.86772
\(305\) 7.30047 0.418024
\(306\) 8.54079 0.488244
\(307\) 25.1299 1.43424 0.717119 0.696951i \(-0.245460\pi\)
0.717119 + 0.696951i \(0.245460\pi\)
\(308\) 5.99866 0.341805
\(309\) 23.6950 1.34796
\(310\) 4.66362 0.264876
\(311\) 32.8063 1.86027 0.930137 0.367212i \(-0.119688\pi\)
0.930137 + 0.367212i \(0.119688\pi\)
\(312\) −18.5989 −1.05295
\(313\) 4.48856 0.253709 0.126854 0.991921i \(-0.459512\pi\)
0.126854 + 0.991921i \(0.459512\pi\)
\(314\) 52.5239 2.96410
\(315\) −0.266939 −0.0150403
\(316\) −2.42318 −0.136314
\(317\) −14.7317 −0.827413 −0.413707 0.910410i \(-0.635766\pi\)
−0.413707 + 0.910410i \(0.635766\pi\)
\(318\) −68.0191 −3.81432
\(319\) −11.7717 −0.659088
\(320\) −12.7443 −0.712427
\(321\) −6.96921 −0.388984
\(322\) 1.03666 0.0577707
\(323\) 7.54521 0.419827
\(324\) −58.4826 −3.24904
\(325\) −4.59390 −0.254823
\(326\) 54.3174 3.00836
\(327\) −8.61596 −0.476463
\(328\) −98.2639 −5.42572
\(329\) −0.506943 −0.0279487
\(330\) 16.8158 0.925680
\(331\) −12.9388 −0.711179 −0.355590 0.934642i \(-0.615720\pi\)
−0.355590 + 0.934642i \(0.615720\pi\)
\(332\) 44.2111 2.42640
\(333\) 0.712150 0.0390256
\(334\) 1.54638 0.0846139
\(335\) −4.72889 −0.258367
\(336\) 6.94155 0.378693
\(337\) 3.70468 0.201807 0.100903 0.994896i \(-0.467827\pi\)
0.100903 + 0.994896i \(0.467827\pi\)
\(338\) −2.68511 −0.146051
\(339\) −28.7220 −1.55996
\(340\) 6.37412 0.345685
\(341\) 12.4118 0.672139
\(342\) 17.4830 0.945370
\(343\) −3.52351 −0.190252
\(344\) 57.2880 3.08876
\(345\) 2.09990 0.113055
\(346\) −42.3385 −2.27613
\(347\) 16.1711 0.868111 0.434056 0.900886i \(-0.357082\pi\)
0.434056 + 0.900886i \(0.357082\pi\)
\(348\) −29.0609 −1.55783
\(349\) −4.87135 −0.260757 −0.130379 0.991464i \(-0.541619\pi\)
−0.130379 + 0.991464i \(0.541619\pi\)
\(350\) 3.11874 0.166704
\(351\) −2.89866 −0.154719
\(352\) −77.0739 −4.10805
\(353\) 20.0979 1.06970 0.534851 0.844946i \(-0.320368\pi\)
0.534851 + 0.844946i \(0.320368\pi\)
\(354\) 45.7154 2.42975
\(355\) 6.50573 0.345289
\(356\) −26.4651 −1.40265
\(357\) −1.04750 −0.0554396
\(358\) −11.9606 −0.632139
\(359\) −1.68017 −0.0886759 −0.0443379 0.999017i \(-0.514118\pi\)
−0.0443379 + 0.999017i \(0.514118\pi\)
\(360\) 9.09960 0.479591
\(361\) −3.55497 −0.187104
\(362\) 9.71923 0.510831
\(363\) 21.0164 1.10308
\(364\) 1.31722 0.0690412
\(365\) 0.358240 0.0187512
\(366\) 66.3798 3.46973
\(367\) −4.20881 −0.219698 −0.109849 0.993948i \(-0.535037\pi\)
−0.109849 + 0.993948i \(0.535037\pi\)
\(368\) −19.4275 −1.01273
\(369\) 18.8889 0.983317
\(370\) 0.735520 0.0382379
\(371\) 2.96798 0.154090
\(372\) 30.6413 1.58868
\(373\) 30.7876 1.59412 0.797060 0.603900i \(-0.206387\pi\)
0.797060 + 0.603900i \(0.206387\pi\)
\(374\) 23.4766 1.21394
\(375\) 13.1934 0.681302
\(376\) 17.2810 0.891201
\(377\) −2.58490 −0.133129
\(378\) 1.96786 0.101216
\(379\) −24.3052 −1.24848 −0.624238 0.781234i \(-0.714590\pi\)
−0.624238 + 0.781234i \(0.714590\pi\)
\(380\) 13.0478 0.669338
\(381\) −44.7628 −2.29327
\(382\) 63.2190 3.23456
\(383\) −21.4090 −1.09395 −0.546974 0.837150i \(-0.684220\pi\)
−0.546974 + 0.837150i \(0.684220\pi\)
\(384\) −42.8340 −2.18586
\(385\) −0.733751 −0.0373954
\(386\) −68.1775 −3.47015
\(387\) −11.0123 −0.559784
\(388\) −80.6724 −4.09552
\(389\) −8.58637 −0.435346 −0.217673 0.976022i \(-0.569847\pi\)
−0.217673 + 0.976022i \(0.569847\pi\)
\(390\) 3.69252 0.186978
\(391\) 2.93167 0.148261
\(392\) 59.7805 3.01937
\(393\) −24.1821 −1.21983
\(394\) −47.1222 −2.37398
\(395\) 0.296401 0.0149136
\(396\) 39.3076 1.97528
\(397\) 10.5533 0.529656 0.264828 0.964296i \(-0.414685\pi\)
0.264828 + 0.964296i \(0.414685\pi\)
\(398\) 56.6750 2.84086
\(399\) −2.14423 −0.107346
\(400\) −58.4468 −2.92234
\(401\) 9.38792 0.468810 0.234405 0.972139i \(-0.424686\pi\)
0.234405 + 0.972139i \(0.424686\pi\)
\(402\) −42.9976 −2.14453
\(403\) 2.72547 0.135765
\(404\) −4.17580 −0.207754
\(405\) 7.15355 0.355463
\(406\) 1.75486 0.0870922
\(407\) 1.95753 0.0970310
\(408\) 35.7079 1.76780
\(409\) −15.7919 −0.780861 −0.390431 0.920632i \(-0.627674\pi\)
−0.390431 + 0.920632i \(0.627674\pi\)
\(410\) 19.5088 0.963470
\(411\) 37.7231 1.86074
\(412\) 57.2055 2.81831
\(413\) −1.99477 −0.0981564
\(414\) 6.79295 0.333855
\(415\) −5.40787 −0.265462
\(416\) −16.9244 −0.829786
\(417\) 40.9337 2.00453
\(418\) 48.0564 2.35052
\(419\) −1.07752 −0.0526404 −0.0263202 0.999654i \(-0.508379\pi\)
−0.0263202 + 0.999654i \(0.508379\pi\)
\(420\) −1.81142 −0.0883884
\(421\) −15.5383 −0.757293 −0.378646 0.925541i \(-0.623610\pi\)
−0.378646 + 0.925541i \(0.623610\pi\)
\(422\) 69.6397 3.39001
\(423\) −3.32187 −0.161515
\(424\) −101.175 −4.91347
\(425\) 8.81979 0.427823
\(426\) 59.1537 2.86601
\(427\) −2.89646 −0.140169
\(428\) −16.8254 −0.813288
\(429\) 9.82735 0.474469
\(430\) −11.3736 −0.548486
\(431\) 28.5437 1.37490 0.687452 0.726230i \(-0.258729\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(432\) −36.8788 −1.77433
\(433\) 14.1783 0.681366 0.340683 0.940178i \(-0.389342\pi\)
0.340683 + 0.940178i \(0.389342\pi\)
\(434\) −1.85029 −0.0888167
\(435\) 3.55471 0.170435
\(436\) −20.8011 −0.996191
\(437\) 6.00111 0.287072
\(438\) 3.25732 0.155641
\(439\) −7.71117 −0.368034 −0.184017 0.982923i \(-0.558910\pi\)
−0.184017 + 0.982923i \(0.558910\pi\)
\(440\) 25.0126 1.19243
\(441\) −11.4914 −0.547208
\(442\) 5.15513 0.245205
\(443\) 14.5757 0.692512 0.346256 0.938140i \(-0.387453\pi\)
0.346256 + 0.938140i \(0.387453\pi\)
\(444\) 4.83258 0.229344
\(445\) 3.23719 0.153457
\(446\) 68.4323 3.24036
\(447\) −9.13281 −0.431967
\(448\) 5.05629 0.238887
\(449\) 18.9524 0.894418 0.447209 0.894429i \(-0.352418\pi\)
0.447209 + 0.894429i \(0.352418\pi\)
\(450\) 20.4363 0.963376
\(451\) 51.9210 2.44487
\(452\) −69.3420 −3.26157
\(453\) 15.6609 0.735812
\(454\) −14.9493 −0.701605
\(455\) −0.161122 −0.00755350
\(456\) 73.0939 3.42294
\(457\) −30.6800 −1.43515 −0.717575 0.696481i \(-0.754748\pi\)
−0.717575 + 0.696481i \(0.754748\pi\)
\(458\) −22.6438 −1.05807
\(459\) 5.56512 0.259757
\(460\) 5.06968 0.236375
\(461\) −32.6936 −1.52269 −0.761347 0.648344i \(-0.775462\pi\)
−0.761347 + 0.648344i \(0.775462\pi\)
\(462\) −6.67167 −0.310394
\(463\) −3.92078 −0.182214 −0.0911069 0.995841i \(-0.529041\pi\)
−0.0911069 + 0.995841i \(0.529041\pi\)
\(464\) −32.8870 −1.52674
\(465\) −3.74802 −0.173810
\(466\) −74.7928 −3.46471
\(467\) 17.2700 0.799162 0.399581 0.916698i \(-0.369156\pi\)
0.399581 + 0.916698i \(0.369156\pi\)
\(468\) 8.63142 0.398987
\(469\) 1.87618 0.0866341
\(470\) −3.43088 −0.158255
\(471\) −42.2120 −1.94503
\(472\) 67.9992 3.12992
\(473\) −30.2700 −1.39182
\(474\) 2.69504 0.123787
\(475\) 18.0541 0.828378
\(476\) −2.52893 −0.115913
\(477\) 19.4484 0.890482
\(478\) 38.2894 1.75132
\(479\) 19.0648 0.871091 0.435545 0.900167i \(-0.356556\pi\)
0.435545 + 0.900167i \(0.356556\pi\)
\(480\) 23.2741 1.06231
\(481\) 0.429846 0.0195993
\(482\) 34.7142 1.58119
\(483\) −0.833133 −0.0379089
\(484\) 50.7390 2.30632
\(485\) 9.86779 0.448073
\(486\) 41.6943 1.89129
\(487\) −15.2044 −0.688978 −0.344489 0.938790i \(-0.611948\pi\)
−0.344489 + 0.938790i \(0.611948\pi\)
\(488\) 98.7364 4.46959
\(489\) −43.6534 −1.97407
\(490\) −11.8685 −0.536164
\(491\) −21.2021 −0.956839 −0.478419 0.878131i \(-0.658790\pi\)
−0.478419 + 0.878131i \(0.658790\pi\)
\(492\) 128.178 5.77872
\(493\) 4.96274 0.223510
\(494\) 10.5525 0.474781
\(495\) −4.80808 −0.216107
\(496\) 34.6754 1.55697
\(497\) −2.58115 −0.115780
\(498\) −49.1713 −2.20342
\(499\) 36.4875 1.63340 0.816702 0.577060i \(-0.195800\pi\)
0.816702 + 0.577060i \(0.195800\pi\)
\(500\) 31.8521 1.42447
\(501\) −1.24278 −0.0555233
\(502\) −14.5878 −0.651087
\(503\) −31.4716 −1.40325 −0.701624 0.712548i \(-0.747541\pi\)
−0.701624 + 0.712548i \(0.747541\pi\)
\(504\) −3.61026 −0.160814
\(505\) 0.510781 0.0227295
\(506\) 18.6722 0.830079
\(507\) 2.15795 0.0958380
\(508\) −108.069 −4.79477
\(509\) 33.3781 1.47946 0.739728 0.672906i \(-0.234954\pi\)
0.739728 + 0.672906i \(0.234954\pi\)
\(510\) −7.08925 −0.313917
\(511\) −0.142132 −0.00628754
\(512\) 3.98426 0.176081
\(513\) 11.3918 0.502959
\(514\) 40.1117 1.76925
\(515\) −6.99734 −0.308340
\(516\) −74.7281 −3.28972
\(517\) −9.13101 −0.401581
\(518\) −0.291817 −0.0128217
\(519\) 34.0262 1.49359
\(520\) 5.49243 0.240859
\(521\) −12.9677 −0.568126 −0.284063 0.958806i \(-0.591682\pi\)
−0.284063 + 0.958806i \(0.591682\pi\)
\(522\) 11.4991 0.503303
\(523\) −20.7433 −0.907041 −0.453520 0.891246i \(-0.649832\pi\)
−0.453520 + 0.891246i \(0.649832\pi\)
\(524\) −58.3817 −2.55042
\(525\) −2.50644 −0.109390
\(526\) −4.75437 −0.207300
\(527\) −5.23261 −0.227936
\(528\) 125.031 5.44125
\(529\) −20.6683 −0.898621
\(530\) 20.0867 0.872509
\(531\) −13.0712 −0.567243
\(532\) −5.17671 −0.224439
\(533\) 11.4011 0.493839
\(534\) 29.4343 1.27375
\(535\) 2.05807 0.0889783
\(536\) −63.9566 −2.76251
\(537\) 9.61242 0.414807
\(538\) 45.3678 1.95595
\(539\) −31.5870 −1.36055
\(540\) 9.62365 0.414136
\(541\) 6.63595 0.285302 0.142651 0.989773i \(-0.454437\pi\)
0.142651 + 0.989773i \(0.454437\pi\)
\(542\) 12.5189 0.537732
\(543\) −7.81107 −0.335205
\(544\) 32.4930 1.39313
\(545\) 2.54437 0.108989
\(546\) −1.46501 −0.0626965
\(547\) −32.6258 −1.39498 −0.697490 0.716595i \(-0.745700\pi\)
−0.697490 + 0.716595i \(0.745700\pi\)
\(548\) 91.0730 3.89045
\(549\) −18.9797 −0.810035
\(550\) 56.1744 2.39528
\(551\) 10.1587 0.432775
\(552\) 28.4004 1.20880
\(553\) −0.117597 −0.00500074
\(554\) −44.8779 −1.90668
\(555\) −0.591117 −0.0250915
\(556\) 98.8243 4.19108
\(557\) −24.3400 −1.03132 −0.515659 0.856794i \(-0.672453\pi\)
−0.515659 + 0.856794i \(0.672453\pi\)
\(558\) −12.1245 −0.513269
\(559\) −6.64689 −0.281133
\(560\) −2.04991 −0.0866243
\(561\) −18.8675 −0.796585
\(562\) −11.5002 −0.485105
\(563\) 15.1593 0.638886 0.319443 0.947605i \(-0.396504\pi\)
0.319443 + 0.947605i \(0.396504\pi\)
\(564\) −22.5419 −0.949183
\(565\) 8.48186 0.356835
\(566\) −34.0558 −1.43147
\(567\) −2.83817 −0.119192
\(568\) 87.9879 3.69189
\(569\) −34.6661 −1.45328 −0.726639 0.687019i \(-0.758919\pi\)
−0.726639 + 0.687019i \(0.758919\pi\)
\(570\) −14.5117 −0.607827
\(571\) 20.4082 0.854055 0.427027 0.904239i \(-0.359561\pi\)
0.427027 + 0.904239i \(0.359561\pi\)
\(572\) 23.7257 0.992020
\(573\) −50.8073 −2.12251
\(574\) −7.74010 −0.323066
\(575\) 7.01485 0.292540
\(576\) 33.1325 1.38052
\(577\) −14.7180 −0.612719 −0.306359 0.951916i \(-0.599111\pi\)
−0.306359 + 0.951916i \(0.599111\pi\)
\(578\) 35.7496 1.48699
\(579\) 54.7924 2.27709
\(580\) 8.58197 0.356347
\(581\) 2.14557 0.0890133
\(582\) 89.7233 3.71915
\(583\) 53.4590 2.21405
\(584\) 4.84508 0.200491
\(585\) −1.05579 −0.0436515
\(586\) 67.1676 2.77467
\(587\) −35.5664 −1.46798 −0.733991 0.679159i \(-0.762344\pi\)
−0.733991 + 0.679159i \(0.762344\pi\)
\(588\) −77.9793 −3.21581
\(589\) −10.7111 −0.441345
\(590\) −13.5002 −0.555794
\(591\) 37.8708 1.55780
\(592\) 5.46881 0.224767
\(593\) 26.9348 1.10608 0.553040 0.833155i \(-0.313468\pi\)
0.553040 + 0.833155i \(0.313468\pi\)
\(594\) 35.4450 1.45432
\(595\) 0.309337 0.0126816
\(596\) −22.0489 −0.903158
\(597\) −45.5481 −1.86416
\(598\) 4.10015 0.167668
\(599\) 10.6388 0.434688 0.217344 0.976095i \(-0.430261\pi\)
0.217344 + 0.976095i \(0.430261\pi\)
\(600\) 85.4414 3.48813
\(601\) −16.0831 −0.656042 −0.328021 0.944670i \(-0.606382\pi\)
−0.328021 + 0.944670i \(0.606382\pi\)
\(602\) 4.51249 0.183915
\(603\) 12.2941 0.500656
\(604\) 37.8093 1.53844
\(605\) −6.20635 −0.252324
\(606\) 4.64430 0.188662
\(607\) 34.7055 1.40865 0.704327 0.709875i \(-0.251249\pi\)
0.704327 + 0.709875i \(0.251249\pi\)
\(608\) 66.5131 2.69746
\(609\) −1.41033 −0.0571495
\(610\) −19.6026 −0.793685
\(611\) −2.00504 −0.0811154
\(612\) −16.5714 −0.669859
\(613\) 24.7501 0.999646 0.499823 0.866128i \(-0.333398\pi\)
0.499823 + 0.866128i \(0.333398\pi\)
\(614\) −67.4766 −2.72313
\(615\) −15.6787 −0.632225
\(616\) −9.92374 −0.399839
\(617\) 1.00000 0.0402585
\(618\) −63.6236 −2.55932
\(619\) 16.9804 0.682501 0.341251 0.939972i \(-0.389150\pi\)
0.341251 + 0.939972i \(0.389150\pi\)
\(620\) −9.04866 −0.363403
\(621\) 4.42624 0.177619
\(622\) −88.0886 −3.53203
\(623\) −1.28435 −0.0514565
\(624\) 27.4550 1.09908
\(625\) 19.0734 0.762934
\(626\) −12.0523 −0.481707
\(627\) −38.6216 −1.54240
\(628\) −101.910 −4.06667
\(629\) −0.825259 −0.0329052
\(630\) 0.716762 0.0285565
\(631\) 33.4061 1.32987 0.664937 0.746899i \(-0.268458\pi\)
0.664937 + 0.746899i \(0.268458\pi\)
\(632\) 4.00873 0.159459
\(633\) −55.9675 −2.22451
\(634\) 39.5562 1.57098
\(635\) 13.2189 0.524575
\(636\) 131.975 5.23315
\(637\) −6.93608 −0.274817
\(638\) 31.6083 1.25139
\(639\) −16.9136 −0.669091
\(640\) 12.6493 0.500007
\(641\) −21.4721 −0.848097 −0.424049 0.905639i \(-0.639391\pi\)
−0.424049 + 0.905639i \(0.639391\pi\)
\(642\) 18.7131 0.738548
\(643\) 38.3323 1.51168 0.755838 0.654758i \(-0.227230\pi\)
0.755838 + 0.654758i \(0.227230\pi\)
\(644\) −2.01139 −0.0792599
\(645\) 9.14069 0.359914
\(646\) −20.2597 −0.797109
\(647\) 44.3485 1.74352 0.871760 0.489933i \(-0.162979\pi\)
0.871760 + 0.489933i \(0.162979\pi\)
\(648\) 96.7494 3.80068
\(649\) −35.9297 −1.41036
\(650\) 12.3351 0.483824
\(651\) 1.48703 0.0582811
\(652\) −105.390 −4.12740
\(653\) −31.7692 −1.24322 −0.621612 0.783325i \(-0.713522\pi\)
−0.621612 + 0.783325i \(0.713522\pi\)
\(654\) 23.1348 0.904643
\(655\) 7.14121 0.279030
\(656\) 145.054 5.66339
\(657\) −0.931352 −0.0363355
\(658\) 1.36120 0.0530651
\(659\) −10.9221 −0.425465 −0.212733 0.977110i \(-0.568236\pi\)
−0.212733 + 0.977110i \(0.568236\pi\)
\(660\) −32.6272 −1.27001
\(661\) −20.0191 −0.778653 −0.389326 0.921100i \(-0.627292\pi\)
−0.389326 + 0.921100i \(0.627292\pi\)
\(662\) 34.7421 1.35029
\(663\) −4.14304 −0.160902
\(664\) −73.1397 −2.83837
\(665\) 0.633211 0.0245549
\(666\) −1.91220 −0.0740964
\(667\) 3.94713 0.152834
\(668\) −3.00038 −0.116088
\(669\) −54.9972 −2.12631
\(670\) 12.6976 0.490551
\(671\) −52.1707 −2.01403
\(672\) −9.23400 −0.356209
\(673\) −22.8913 −0.882393 −0.441197 0.897410i \(-0.645446\pi\)
−0.441197 + 0.897410i \(0.645446\pi\)
\(674\) −9.94748 −0.383163
\(675\) 13.3161 0.512538
\(676\) 5.20984 0.200378
\(677\) −3.16942 −0.121811 −0.0609054 0.998144i \(-0.519399\pi\)
−0.0609054 + 0.998144i \(0.519399\pi\)
\(678\) 77.1217 2.96184
\(679\) −3.91504 −0.150245
\(680\) −10.5449 −0.404377
\(681\) 12.0143 0.460390
\(682\) −33.3272 −1.27616
\(683\) −26.8125 −1.02595 −0.512976 0.858403i \(-0.671457\pi\)
−0.512976 + 0.858403i \(0.671457\pi\)
\(684\) −33.9216 −1.29702
\(685\) −11.1400 −0.425637
\(686\) 9.46103 0.361224
\(687\) 18.1982 0.694303
\(688\) −84.5664 −3.22406
\(689\) 11.7389 0.447215
\(690\) −5.63846 −0.214653
\(691\) −20.2934 −0.771996 −0.385998 0.922500i \(-0.626143\pi\)
−0.385998 + 0.922500i \(0.626143\pi\)
\(692\) 82.1479 3.12279
\(693\) 1.90760 0.0724639
\(694\) −43.4213 −1.64825
\(695\) −12.0881 −0.458528
\(696\) 48.0763 1.82233
\(697\) −21.8890 −0.829104
\(698\) 13.0801 0.495090
\(699\) 60.1089 2.27353
\(700\) −6.05118 −0.228713
\(701\) 22.9408 0.866461 0.433230 0.901283i \(-0.357374\pi\)
0.433230 + 0.901283i \(0.357374\pi\)
\(702\) 7.78323 0.293759
\(703\) −1.68930 −0.0637133
\(704\) 91.0734 3.43246
\(705\) 2.75730 0.103846
\(706\) −53.9651 −2.03100
\(707\) −0.202652 −0.00762152
\(708\) −88.7001 −3.33355
\(709\) 15.3694 0.577209 0.288604 0.957448i \(-0.406809\pi\)
0.288604 + 0.957448i \(0.406809\pi\)
\(710\) −17.4686 −0.655586
\(711\) −0.770583 −0.0288991
\(712\) 43.7819 1.64080
\(713\) −4.16178 −0.155860
\(714\) 2.81266 0.105261
\(715\) −2.90211 −0.108533
\(716\) 23.2068 0.867279
\(717\) −30.7722 −1.14921
\(718\) 4.51144 0.168365
\(719\) −29.7668 −1.11011 −0.555056 0.831813i \(-0.687303\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(720\) −13.4325 −0.500600
\(721\) 2.77619 0.103391
\(722\) 9.54551 0.355247
\(723\) −27.8988 −1.03757
\(724\) −18.8579 −0.700848
\(725\) 11.8748 0.441018
\(726\) −56.4315 −2.09437
\(727\) −11.0946 −0.411476 −0.205738 0.978607i \(-0.565960\pi\)
−0.205738 + 0.978607i \(0.565960\pi\)
\(728\) −2.17912 −0.0807635
\(729\) 0.167720 0.00621186
\(730\) −0.961916 −0.0356021
\(731\) 12.7613 0.471994
\(732\) −128.795 −4.76038
\(733\) −5.47722 −0.202306 −0.101153 0.994871i \(-0.532253\pi\)
−0.101153 + 0.994871i \(0.532253\pi\)
\(734\) 11.3011 0.417133
\(735\) 9.53837 0.351828
\(736\) 25.8434 0.952602
\(737\) 33.7936 1.24480
\(738\) −50.7188 −1.86699
\(739\) −35.8175 −1.31757 −0.658783 0.752333i \(-0.728929\pi\)
−0.658783 + 0.752333i \(0.728929\pi\)
\(740\) −1.42711 −0.0524614
\(741\) −8.48078 −0.311549
\(742\) −7.96937 −0.292565
\(743\) −53.5347 −1.96400 −0.981999 0.188884i \(-0.939513\pi\)
−0.981999 + 0.188884i \(0.939513\pi\)
\(744\) −50.6907 −1.85841
\(745\) 2.69700 0.0988106
\(746\) −82.6681 −3.02670
\(747\) 14.0594 0.514405
\(748\) −45.5508 −1.66550
\(749\) −0.816540 −0.0298357
\(750\) −35.4257 −1.29356
\(751\) 53.8796 1.96609 0.983047 0.183354i \(-0.0586955\pi\)
0.983047 + 0.183354i \(0.0586955\pi\)
\(752\) −25.5096 −0.930239
\(753\) 11.7238 0.427241
\(754\) 6.94076 0.252767
\(755\) −4.62480 −0.168314
\(756\) −3.81818 −0.138866
\(757\) 37.4055 1.35953 0.679764 0.733431i \(-0.262082\pi\)
0.679764 + 0.733431i \(0.262082\pi\)
\(758\) 65.2623 2.37043
\(759\) −15.0063 −0.544694
\(760\) −21.5853 −0.782982
\(761\) 13.6350 0.494268 0.247134 0.968981i \(-0.420511\pi\)
0.247134 + 0.968981i \(0.420511\pi\)
\(762\) 120.193 4.35414
\(763\) −1.00948 −0.0365456
\(764\) −122.662 −4.43774
\(765\) 2.02700 0.0732864
\(766\) 57.4855 2.07704
\(767\) −7.88967 −0.284879
\(768\) 28.7028 1.03572
\(769\) −7.98128 −0.287812 −0.143906 0.989591i \(-0.545966\pi\)
−0.143906 + 0.989591i \(0.545966\pi\)
\(770\) 1.97021 0.0710013
\(771\) −32.2366 −1.16097
\(772\) 132.283 4.76095
\(773\) 7.63243 0.274519 0.137260 0.990535i \(-0.456171\pi\)
0.137260 + 0.990535i \(0.456171\pi\)
\(774\) 29.5692 1.06284
\(775\) −12.5205 −0.449751
\(776\) 133.459 4.79088
\(777\) 0.234526 0.00841356
\(778\) 23.0554 0.826575
\(779\) −44.8067 −1.60537
\(780\) −7.16448 −0.256529
\(781\) −46.4913 −1.66359
\(782\) −7.87186 −0.281497
\(783\) 7.49275 0.267769
\(784\) −88.2457 −3.15163
\(785\) 12.4656 0.444917
\(786\) 64.9318 2.31604
\(787\) 18.0823 0.644565 0.322283 0.946643i \(-0.395550\pi\)
0.322283 + 0.946643i \(0.395550\pi\)
\(788\) 91.4297 3.25705
\(789\) 3.82095 0.136030
\(790\) −0.795871 −0.0283158
\(791\) −3.36518 −0.119652
\(792\) −65.0277 −2.31066
\(793\) −11.4560 −0.406813
\(794\) −28.3369 −1.00564
\(795\) −16.1431 −0.572537
\(796\) −109.965 −3.89759
\(797\) −24.9505 −0.883792 −0.441896 0.897066i \(-0.645694\pi\)
−0.441896 + 0.897066i \(0.645694\pi\)
\(798\) 5.75750 0.203813
\(799\) 3.84947 0.136184
\(800\) 77.7488 2.74884
\(801\) −8.41603 −0.297366
\(802\) −25.2076 −0.890112
\(803\) −2.56006 −0.0903426
\(804\) 83.4268 2.94224
\(805\) 0.246032 0.00867149
\(806\) −7.31820 −0.257773
\(807\) −36.4609 −1.28348
\(808\) 6.90815 0.243028
\(809\) −43.8061 −1.54014 −0.770070 0.637960i \(-0.779779\pi\)
−0.770070 + 0.637960i \(0.779779\pi\)
\(810\) −19.2081 −0.674904
\(811\) 13.3163 0.467597 0.233799 0.972285i \(-0.424884\pi\)
0.233799 + 0.972285i \(0.424884\pi\)
\(812\) −3.40489 −0.119488
\(813\) −10.0611 −0.352858
\(814\) −5.25618 −0.184229
\(815\) 12.8913 0.451561
\(816\) −52.7107 −1.84524
\(817\) 26.1224 0.913906
\(818\) 42.4032 1.48259
\(819\) 0.418884 0.0146370
\(820\) −37.8522 −1.32186
\(821\) 13.3908 0.467341 0.233670 0.972316i \(-0.424926\pi\)
0.233670 + 0.972316i \(0.424926\pi\)
\(822\) −101.291 −3.53292
\(823\) 10.5889 0.369105 0.184552 0.982823i \(-0.440916\pi\)
0.184552 + 0.982823i \(0.440916\pi\)
\(824\) −94.6367 −3.29683
\(825\) −45.1458 −1.57178
\(826\) 5.35620 0.186366
\(827\) 51.8160 1.80182 0.900910 0.434005i \(-0.142900\pi\)
0.900910 + 0.434005i \(0.142900\pi\)
\(828\) −13.1801 −0.458041
\(829\) −13.2274 −0.459405 −0.229703 0.973261i \(-0.573775\pi\)
−0.229703 + 0.973261i \(0.573775\pi\)
\(830\) 14.5208 0.504023
\(831\) 36.0671 1.25115
\(832\) 19.9985 0.693322
\(833\) 13.3165 0.461390
\(834\) −109.912 −3.80593
\(835\) 0.367004 0.0127007
\(836\) −93.2423 −3.22485
\(837\) −7.90021 −0.273071
\(838\) 2.89327 0.0999463
\(839\) 42.7362 1.47542 0.737709 0.675119i \(-0.235908\pi\)
0.737709 + 0.675119i \(0.235908\pi\)
\(840\) 2.99669 0.103395
\(841\) −22.3183 −0.769596
\(842\) 41.7222 1.43784
\(843\) 9.24236 0.318324
\(844\) −135.120 −4.65101
\(845\) −0.637263 −0.0219225
\(846\) 8.91959 0.306662
\(847\) 2.46237 0.0846079
\(848\) 149.350 5.12871
\(849\) 27.3697 0.939325
\(850\) −23.6821 −0.812291
\(851\) −0.656373 −0.0225002
\(852\) −114.774 −3.93209
\(853\) 3.59980 0.123255 0.0616274 0.998099i \(-0.480371\pi\)
0.0616274 + 0.998099i \(0.480371\pi\)
\(854\) 7.77732 0.266134
\(855\) 4.14927 0.141902
\(856\) 27.8348 0.951372
\(857\) −11.1873 −0.382151 −0.191076 0.981575i \(-0.561198\pi\)
−0.191076 + 0.981575i \(0.561198\pi\)
\(858\) −26.3875 −0.900856
\(859\) −51.6410 −1.76197 −0.880984 0.473146i \(-0.843118\pi\)
−0.880984 + 0.473146i \(0.843118\pi\)
\(860\) 22.0679 0.752509
\(861\) 6.22050 0.211994
\(862\) −76.6432 −2.61048
\(863\) 32.9340 1.12109 0.560544 0.828125i \(-0.310592\pi\)
0.560544 + 0.828125i \(0.310592\pi\)
\(864\) 49.0580 1.66899
\(865\) −10.0483 −0.341651
\(866\) −38.0704 −1.29368
\(867\) −28.7310 −0.975755
\(868\) 3.59005 0.121854
\(869\) −2.11815 −0.0718532
\(870\) −9.54481 −0.323599
\(871\) 7.42062 0.251438
\(872\) 34.4118 1.16533
\(873\) −25.6542 −0.868264
\(874\) −16.1137 −0.545053
\(875\) 1.54579 0.0522571
\(876\) −6.32006 −0.213535
\(877\) −36.3204 −1.22645 −0.613227 0.789907i \(-0.710129\pi\)
−0.613227 + 0.789907i \(0.710129\pi\)
\(878\) 20.7054 0.698772
\(879\) −53.9807 −1.82072
\(880\) −36.9227 −1.24466
\(881\) 32.1854 1.08435 0.542176 0.840265i \(-0.317601\pi\)
0.542176 + 0.840265i \(0.317601\pi\)
\(882\) 30.8556 1.03896
\(883\) −25.2868 −0.850969 −0.425485 0.904966i \(-0.639896\pi\)
−0.425485 + 0.904966i \(0.639896\pi\)
\(884\) −10.0023 −0.336415
\(885\) 10.8497 0.364710
\(886\) −39.1374 −1.31485
\(887\) 30.0427 1.00874 0.504368 0.863489i \(-0.331726\pi\)
0.504368 + 0.863489i \(0.331726\pi\)
\(888\) −7.99466 −0.268283
\(889\) −5.24458 −0.175898
\(890\) −8.69222 −0.291364
\(891\) −51.1208 −1.71261
\(892\) −132.777 −4.44570
\(893\) 7.87986 0.263689
\(894\) 24.5226 0.820160
\(895\) −2.83864 −0.0948852
\(896\) −5.01860 −0.167660
\(897\) −3.29518 −0.110023
\(898\) −50.8893 −1.69820
\(899\) −7.04508 −0.234966
\(900\) −39.6518 −1.32173
\(901\) −22.5374 −0.750829
\(902\) −139.414 −4.64197
\(903\) −3.62656 −0.120684
\(904\) 114.714 3.81534
\(905\) 2.30668 0.0766767
\(906\) −42.0512 −1.39706
\(907\) 14.2583 0.473438 0.236719 0.971578i \(-0.423928\pi\)
0.236719 + 0.971578i \(0.423928\pi\)
\(908\) 29.0056 0.962585
\(909\) −1.32793 −0.0440446
\(910\) 0.432630 0.0143416
\(911\) −43.9046 −1.45463 −0.727313 0.686306i \(-0.759231\pi\)
−0.727313 + 0.686306i \(0.759231\pi\)
\(912\) −107.899 −3.57288
\(913\) 38.6458 1.27899
\(914\) 82.3793 2.72486
\(915\) 15.7541 0.520813
\(916\) 43.9349 1.45165
\(917\) −2.83327 −0.0935629
\(918\) −14.9430 −0.493191
\(919\) −14.3638 −0.473819 −0.236910 0.971532i \(-0.576135\pi\)
−0.236910 + 0.971532i \(0.576135\pi\)
\(920\) −8.38690 −0.276508
\(921\) 54.2290 1.78691
\(922\) 87.7861 2.89108
\(923\) −10.2089 −0.336029
\(924\) 12.9448 0.425853
\(925\) −1.97467 −0.0649267
\(926\) 10.5277 0.345963
\(927\) 18.1917 0.597492
\(928\) 43.7479 1.43609
\(929\) 28.0348 0.919792 0.459896 0.887973i \(-0.347887\pi\)
0.459896 + 0.887973i \(0.347887\pi\)
\(930\) 10.0639 0.330007
\(931\) 27.2589 0.893374
\(932\) 145.118 4.75350
\(933\) 70.7944 2.31770
\(934\) −46.3720 −1.51734
\(935\) 5.57174 0.182215
\(936\) −14.2792 −0.466730
\(937\) 18.1258 0.592145 0.296072 0.955165i \(-0.404323\pi\)
0.296072 + 0.955165i \(0.404323\pi\)
\(938\) −5.03777 −0.164489
\(939\) 9.68610 0.316094
\(940\) 6.65682 0.217122
\(941\) −4.51163 −0.147075 −0.0735375 0.997292i \(-0.523429\pi\)
−0.0735375 + 0.997292i \(0.523429\pi\)
\(942\) 113.344 3.69295
\(943\) −17.4095 −0.566931
\(944\) −100.378 −3.26702
\(945\) 0.467037 0.0151927
\(946\) 81.2785 2.64259
\(947\) −20.4014 −0.662956 −0.331478 0.943463i \(-0.607547\pi\)
−0.331478 + 0.943463i \(0.607547\pi\)
\(948\) −5.22910 −0.169833
\(949\) −0.562155 −0.0182483
\(950\) −48.4773 −1.57281
\(951\) −31.7902 −1.03087
\(952\) 4.18367 0.135594
\(953\) 4.65147 0.150676 0.0753379 0.997158i \(-0.475996\pi\)
0.0753379 + 0.997158i \(0.475996\pi\)
\(954\) −52.2212 −1.69072
\(955\) 15.0039 0.485514
\(956\) −74.2917 −2.40276
\(957\) −25.4027 −0.821154
\(958\) −51.1910 −1.65391
\(959\) 4.41978 0.142722
\(960\) −27.5016 −0.887609
\(961\) −23.5718 −0.760381
\(962\) −1.15419 −0.0372125
\(963\) −5.35057 −0.172420
\(964\) −67.3547 −2.16935
\(965\) −16.1807 −0.520876
\(966\) 2.23706 0.0719761
\(967\) −22.9756 −0.738845 −0.369423 0.929262i \(-0.620444\pi\)
−0.369423 + 0.929262i \(0.620444\pi\)
\(968\) −83.9388 −2.69790
\(969\) 16.2822 0.523060
\(970\) −26.4961 −0.850740
\(971\) −45.1797 −1.44988 −0.724942 0.688810i \(-0.758134\pi\)
−0.724942 + 0.688810i \(0.758134\pi\)
\(972\) −80.8981 −2.59481
\(973\) 4.79595 0.153751
\(974\) 40.8256 1.30814
\(975\) −9.91340 −0.317483
\(976\) −145.751 −4.66537
\(977\) −42.7083 −1.36636 −0.683179 0.730251i \(-0.739403\pi\)
−0.683179 + 0.730251i \(0.739403\pi\)
\(978\) 117.214 3.74810
\(979\) −23.1336 −0.739354
\(980\) 23.0280 0.735603
\(981\) −6.61485 −0.211196
\(982\) 56.9301 1.81671
\(983\) −40.3841 −1.28805 −0.644027 0.765003i \(-0.722737\pi\)
−0.644027 + 0.765003i \(0.722737\pi\)
\(984\) −212.049 −6.75987
\(985\) −11.1836 −0.356340
\(986\) −13.3255 −0.424371
\(987\) −1.09396 −0.0348211
\(988\) −20.4747 −0.651388
\(989\) 10.1498 0.322743
\(990\) 12.9102 0.410314
\(991\) 60.0372 1.90714 0.953572 0.301166i \(-0.0973759\pi\)
0.953572 + 0.301166i \(0.0973759\pi\)
\(992\) −46.1269 −1.46453
\(993\) −27.9212 −0.886054
\(994\) 6.93067 0.219828
\(995\) 13.4508 0.426418
\(996\) 95.4055 3.02304
\(997\) −16.7106 −0.529231 −0.264616 0.964354i \(-0.585245\pi\)
−0.264616 + 0.964354i \(0.585245\pi\)
\(998\) −97.9730 −3.10128
\(999\) −1.24598 −0.0394210
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 \(a_p\))