Properties

Label 6041.2.a.f.1.1
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.81389 q^{2}\) \(+0.225620 q^{3}\) \(+5.91799 q^{4}\) \(-1.24518 q^{5}\) \(-0.634869 q^{6}\) \(+1.00000 q^{7}\) \(-11.0248 q^{8}\) \(-2.94910 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.81389 q^{2}\) \(+0.225620 q^{3}\) \(+5.91799 q^{4}\) \(-1.24518 q^{5}\) \(-0.634869 q^{6}\) \(+1.00000 q^{7}\) \(-11.0248 q^{8}\) \(-2.94910 q^{9}\) \(+3.50380 q^{10}\) \(+4.12431 q^{11}\) \(+1.33521 q^{12}\) \(+3.68405 q^{13}\) \(-2.81389 q^{14}\) \(-0.280936 q^{15}\) \(+19.1866 q^{16}\) \(-6.21890 q^{17}\) \(+8.29844 q^{18}\) \(-1.83276 q^{19}\) \(-7.36895 q^{20}\) \(+0.225620 q^{21}\) \(-11.6054 q^{22}\) \(-7.83940 q^{23}\) \(-2.48741 q^{24}\) \(-3.44953 q^{25}\) \(-10.3665 q^{26}\) \(-1.34223 q^{27}\) \(+5.91799 q^{28}\) \(-9.64129 q^{29}\) \(+0.790525 q^{30}\) \(+6.68893 q^{31}\) \(-31.9394 q^{32}\) \(+0.930525 q^{33}\) \(+17.4993 q^{34}\) \(-1.24518 q^{35}\) \(-17.4527 q^{36}\) \(+4.67182 q^{37}\) \(+5.15720 q^{38}\) \(+0.831194 q^{39}\) \(+13.7278 q^{40}\) \(-5.34630 q^{41}\) \(-0.634869 q^{42}\) \(-6.30101 q^{43}\) \(+24.4076 q^{44}\) \(+3.67215 q^{45}\) \(+22.0592 q^{46}\) \(-1.19976 q^{47}\) \(+4.32887 q^{48}\) \(+1.00000 q^{49}\) \(+9.70661 q^{50}\) \(-1.40311 q^{51}\) \(+21.8022 q^{52}\) \(+8.21793 q^{53}\) \(+3.77690 q^{54}\) \(-5.13550 q^{55}\) \(-11.0248 q^{56}\) \(-0.413507 q^{57}\) \(+27.1295 q^{58}\) \(+12.7741 q^{59}\) \(-1.66258 q^{60}\) \(-13.8054 q^{61}\) \(-18.8219 q^{62}\) \(-2.94910 q^{63}\) \(+51.5009 q^{64}\) \(-4.58730 q^{65}\) \(-2.61840 q^{66}\) \(+3.40155 q^{67}\) \(-36.8034 q^{68}\) \(-1.76872 q^{69}\) \(+3.50380 q^{70}\) \(+11.9660 q^{71}\) \(+32.5132 q^{72}\) \(-0.0538456 q^{73}\) \(-13.1460 q^{74}\) \(-0.778282 q^{75}\) \(-10.8463 q^{76}\) \(+4.12431 q^{77}\) \(-2.33889 q^{78}\) \(-1.41362 q^{79}\) \(-23.8907 q^{80}\) \(+8.54445 q^{81}\) \(+15.0439 q^{82}\) \(-13.8220 q^{83}\) \(+1.33521 q^{84}\) \(+7.74363 q^{85}\) \(+17.7304 q^{86}\) \(-2.17526 q^{87}\) \(-45.4697 q^{88}\) \(+9.62877 q^{89}\) \(-10.3330 q^{90}\) \(+3.68405 q^{91}\) \(-46.3935 q^{92}\) \(+1.50915 q^{93}\) \(+3.37598 q^{94}\) \(+2.28211 q^{95}\) \(-7.20616 q^{96}\) \(+13.6002 q^{97}\) \(-2.81389 q^{98}\) \(-12.1630 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81389 −1.98972 −0.994861 0.101250i \(-0.967716\pi\)
−0.994861 + 0.101250i \(0.967716\pi\)
\(3\) 0.225620 0.130262 0.0651308 0.997877i \(-0.479254\pi\)
0.0651308 + 0.997877i \(0.479254\pi\)
\(4\) 5.91799 2.95899
\(5\) −1.24518 −0.556860 −0.278430 0.960456i \(-0.589814\pi\)
−0.278430 + 0.960456i \(0.589814\pi\)
\(6\) −0.634869 −0.259184
\(7\) 1.00000 0.377964
\(8\) −11.0248 −3.89785
\(9\) −2.94910 −0.983032
\(10\) 3.50380 1.10800
\(11\) 4.12431 1.24353 0.621763 0.783206i \(-0.286417\pi\)
0.621763 + 0.783206i \(0.286417\pi\)
\(12\) 1.33521 0.385443
\(13\) 3.68405 1.02177 0.510886 0.859649i \(-0.329317\pi\)
0.510886 + 0.859649i \(0.329317\pi\)
\(14\) −2.81389 −0.752044
\(15\) −0.280936 −0.0725375
\(16\) 19.1866 4.79665
\(17\) −6.21890 −1.50830 −0.754152 0.656700i \(-0.771952\pi\)
−0.754152 + 0.656700i \(0.771952\pi\)
\(18\) 8.29844 1.95596
\(19\) −1.83276 −0.420465 −0.210232 0.977651i \(-0.567422\pi\)
−0.210232 + 0.977651i \(0.567422\pi\)
\(20\) −7.36895 −1.64775
\(21\) 0.225620 0.0492342
\(22\) −11.6054 −2.47427
\(23\) −7.83940 −1.63463 −0.817314 0.576193i \(-0.804538\pi\)
−0.817314 + 0.576193i \(0.804538\pi\)
\(24\) −2.48741 −0.507740
\(25\) −3.44953 −0.689907
\(26\) −10.3665 −2.03304
\(27\) −1.34223 −0.258313
\(28\) 5.91799 1.11839
\(29\) −9.64129 −1.79034 −0.895171 0.445723i \(-0.852947\pi\)
−0.895171 + 0.445723i \(0.852947\pi\)
\(30\) 0.790525 0.144329
\(31\) 6.68893 1.20137 0.600684 0.799487i \(-0.294895\pi\)
0.600684 + 0.799487i \(0.294895\pi\)
\(32\) −31.9394 −5.64615
\(33\) 0.930525 0.161984
\(34\) 17.4993 3.00111
\(35\) −1.24518 −0.210473
\(36\) −17.4527 −2.90879
\(37\) 4.67182 0.768042 0.384021 0.923324i \(-0.374539\pi\)
0.384021 + 0.923324i \(0.374539\pi\)
\(38\) 5.15720 0.836608
\(39\) 0.831194 0.133098
\(40\) 13.7278 2.17056
\(41\) −5.34630 −0.834952 −0.417476 0.908688i \(-0.637085\pi\)
−0.417476 + 0.908688i \(0.637085\pi\)
\(42\) −0.634869 −0.0979624
\(43\) −6.30101 −0.960895 −0.480447 0.877024i \(-0.659526\pi\)
−0.480447 + 0.877024i \(0.659526\pi\)
\(44\) 24.4076 3.67959
\(45\) 3.67215 0.547412
\(46\) 22.0592 3.25245
\(47\) −1.19976 −0.175002 −0.0875012 0.996164i \(-0.527888\pi\)
−0.0875012 + 0.996164i \(0.527888\pi\)
\(48\) 4.32887 0.624819
\(49\) 1.00000 0.142857
\(50\) 9.70661 1.37272
\(51\) −1.40311 −0.196474
\(52\) 21.8022 3.02342
\(53\) 8.21793 1.12882 0.564410 0.825495i \(-0.309104\pi\)
0.564410 + 0.825495i \(0.309104\pi\)
\(54\) 3.77690 0.513971
\(55\) −5.13550 −0.692470
\(56\) −11.0248 −1.47325
\(57\) −0.413507 −0.0547703
\(58\) 27.1295 3.56228
\(59\) 12.7741 1.66304 0.831522 0.555492i \(-0.187470\pi\)
0.831522 + 0.555492i \(0.187470\pi\)
\(60\) −1.66258 −0.214638
\(61\) −13.8054 −1.76760 −0.883800 0.467864i \(-0.845024\pi\)
−0.883800 + 0.467864i \(0.845024\pi\)
\(62\) −18.8219 −2.39039
\(63\) −2.94910 −0.371551
\(64\) 51.5009 6.43762
\(65\) −4.58730 −0.568984
\(66\) −2.61840 −0.322302
\(67\) 3.40155 0.415566 0.207783 0.978175i \(-0.433375\pi\)
0.207783 + 0.978175i \(0.433375\pi\)
\(68\) −36.8034 −4.46306
\(69\) −1.76872 −0.212929
\(70\) 3.50380 0.418784
\(71\) 11.9660 1.42010 0.710049 0.704152i \(-0.248673\pi\)
0.710049 + 0.704152i \(0.248673\pi\)
\(72\) 32.5132 3.83171
\(73\) −0.0538456 −0.00630215 −0.00315108 0.999995i \(-0.501003\pi\)
−0.00315108 + 0.999995i \(0.501003\pi\)
\(74\) −13.1460 −1.52819
\(75\) −0.778282 −0.0898683
\(76\) −10.8463 −1.24415
\(77\) 4.12431 0.470009
\(78\) −2.33889 −0.264827
\(79\) −1.41362 −0.159045 −0.0795223 0.996833i \(-0.525339\pi\)
−0.0795223 + 0.996833i \(0.525339\pi\)
\(80\) −23.8907 −2.67106
\(81\) 8.54445 0.949384
\(82\) 15.0439 1.66132
\(83\) −13.8220 −1.51717 −0.758583 0.651576i \(-0.774108\pi\)
−0.758583 + 0.651576i \(0.774108\pi\)
\(84\) 1.33521 0.145684
\(85\) 7.74363 0.839915
\(86\) 17.7304 1.91191
\(87\) −2.17526 −0.233213
\(88\) −45.4697 −4.84708
\(89\) 9.62877 1.02065 0.510324 0.859982i \(-0.329525\pi\)
0.510324 + 0.859982i \(0.329525\pi\)
\(90\) −10.3330 −1.08920
\(91\) 3.68405 0.386193
\(92\) −46.3935 −4.83685
\(93\) 1.50915 0.156492
\(94\) 3.37598 0.348206
\(95\) 2.28211 0.234140
\(96\) −7.20616 −0.735476
\(97\) 13.6002 1.38089 0.690444 0.723385i \(-0.257415\pi\)
0.690444 + 0.723385i \(0.257415\pi\)
\(98\) −2.81389 −0.284246
\(99\) −12.1630 −1.22243
\(100\) −20.4143 −2.04143
\(101\) 2.67785 0.266456 0.133228 0.991085i \(-0.457466\pi\)
0.133228 + 0.991085i \(0.457466\pi\)
\(102\) 3.94819 0.390929
\(103\) −15.8953 −1.56621 −0.783104 0.621891i \(-0.786365\pi\)
−0.783104 + 0.621891i \(0.786365\pi\)
\(104\) −40.6159 −3.98272
\(105\) −0.280936 −0.0274166
\(106\) −23.1244 −2.24604
\(107\) 10.5862 1.02340 0.511702 0.859163i \(-0.329015\pi\)
0.511702 + 0.859163i \(0.329015\pi\)
\(108\) −7.94332 −0.764346
\(109\) −4.53186 −0.434074 −0.217037 0.976163i \(-0.569639\pi\)
−0.217037 + 0.976163i \(0.569639\pi\)
\(110\) 14.4507 1.37782
\(111\) 1.05405 0.100046
\(112\) 19.1866 1.81296
\(113\) 7.19175 0.676543 0.338271 0.941049i \(-0.390158\pi\)
0.338271 + 0.941049i \(0.390158\pi\)
\(114\) 1.16356 0.108978
\(115\) 9.76144 0.910259
\(116\) −57.0570 −5.29761
\(117\) −10.8646 −1.00443
\(118\) −35.9449 −3.30899
\(119\) −6.21890 −0.570086
\(120\) 3.09727 0.282740
\(121\) 6.00992 0.546356
\(122\) 38.8469 3.51703
\(123\) −1.20623 −0.108762
\(124\) 39.5850 3.55484
\(125\) 10.5212 0.941042
\(126\) 8.29844 0.739284
\(127\) −5.07599 −0.450421 −0.225211 0.974310i \(-0.572307\pi\)
−0.225211 + 0.974310i \(0.572307\pi\)
\(128\) −81.0392 −7.16292
\(129\) −1.42163 −0.125168
\(130\) 12.9082 1.13212
\(131\) 7.09883 0.620227 0.310114 0.950699i \(-0.399633\pi\)
0.310114 + 0.950699i \(0.399633\pi\)
\(132\) 5.50683 0.479308
\(133\) −1.83276 −0.158921
\(134\) −9.57161 −0.826861
\(135\) 1.67132 0.143844
\(136\) 68.5621 5.87915
\(137\) 1.13495 0.0969653 0.0484826 0.998824i \(-0.484561\pi\)
0.0484826 + 0.998824i \(0.484561\pi\)
\(138\) 4.97699 0.423670
\(139\) 3.72237 0.315728 0.157864 0.987461i \(-0.449539\pi\)
0.157864 + 0.987461i \(0.449539\pi\)
\(140\) −7.36895 −0.622790
\(141\) −0.270688 −0.0227961
\(142\) −33.6709 −2.82560
\(143\) 15.1942 1.27060
\(144\) −56.5831 −4.71526
\(145\) 12.0051 0.996971
\(146\) 0.151516 0.0125395
\(147\) 0.225620 0.0186088
\(148\) 27.6478 2.27263
\(149\) 18.1708 1.48861 0.744306 0.667839i \(-0.232780\pi\)
0.744306 + 0.667839i \(0.232780\pi\)
\(150\) 2.19000 0.178813
\(151\) 15.8005 1.28582 0.642912 0.765940i \(-0.277726\pi\)
0.642912 + 0.765940i \(0.277726\pi\)
\(152\) 20.2058 1.63891
\(153\) 18.3401 1.48271
\(154\) −11.6054 −0.935186
\(155\) −8.32891 −0.668994
\(156\) 4.91900 0.393835
\(157\) −11.3490 −0.905749 −0.452875 0.891574i \(-0.649601\pi\)
−0.452875 + 0.891574i \(0.649601\pi\)
\(158\) 3.97777 0.316454
\(159\) 1.85413 0.147042
\(160\) 39.7703 3.14412
\(161\) −7.83940 −0.617831
\(162\) −24.0432 −1.88901
\(163\) 4.94342 0.387198 0.193599 0.981081i \(-0.437984\pi\)
0.193599 + 0.981081i \(0.437984\pi\)
\(164\) −31.6393 −2.47062
\(165\) −1.15867 −0.0902022
\(166\) 38.8937 3.01874
\(167\) −4.51158 −0.349117 −0.174558 0.984647i \(-0.555850\pi\)
−0.174558 + 0.984647i \(0.555850\pi\)
\(168\) −2.48741 −0.191908
\(169\) 0.572227 0.0440175
\(170\) −21.7897 −1.67120
\(171\) 5.40499 0.413330
\(172\) −37.2893 −2.84328
\(173\) 18.7126 1.42269 0.711344 0.702844i \(-0.248087\pi\)
0.711344 + 0.702844i \(0.248087\pi\)
\(174\) 6.12096 0.464028
\(175\) −3.44953 −0.260760
\(176\) 79.1315 5.96476
\(177\) 2.88208 0.216631
\(178\) −27.0943 −2.03081
\(179\) −1.65198 −0.123475 −0.0617376 0.998092i \(-0.519664\pi\)
−0.0617376 + 0.998092i \(0.519664\pi\)
\(180\) 21.7317 1.61979
\(181\) 13.8706 1.03099 0.515497 0.856891i \(-0.327607\pi\)
0.515497 + 0.856891i \(0.327607\pi\)
\(182\) −10.3665 −0.768418
\(183\) −3.11477 −0.230250
\(184\) 86.4277 6.37154
\(185\) −5.81724 −0.427692
\(186\) −4.24660 −0.311376
\(187\) −25.6487 −1.87562
\(188\) −7.10014 −0.517831
\(189\) −1.34223 −0.0976330
\(190\) −6.42162 −0.465874
\(191\) −25.6765 −1.85789 −0.928945 0.370219i \(-0.879283\pi\)
−0.928945 + 0.370219i \(0.879283\pi\)
\(192\) 11.6196 0.838574
\(193\) −14.0195 −1.00914 −0.504572 0.863370i \(-0.668350\pi\)
−0.504572 + 0.863370i \(0.668350\pi\)
\(194\) −38.2694 −2.74758
\(195\) −1.03498 −0.0741167
\(196\) 5.91799 0.422713
\(197\) 10.7051 0.762705 0.381353 0.924430i \(-0.375458\pi\)
0.381353 + 0.924430i \(0.375458\pi\)
\(198\) 34.2253 2.43229
\(199\) 19.7333 1.39885 0.699427 0.714704i \(-0.253438\pi\)
0.699427 + 0.714704i \(0.253438\pi\)
\(200\) 38.0304 2.68915
\(201\) 0.767457 0.0541323
\(202\) −7.53517 −0.530172
\(203\) −9.64129 −0.676686
\(204\) −8.30356 −0.581365
\(205\) 6.65709 0.464952
\(206\) 44.7276 3.11632
\(207\) 23.1191 1.60689
\(208\) 70.6844 4.90108
\(209\) −7.55888 −0.522858
\(210\) 0.790525 0.0545514
\(211\) −15.9611 −1.09881 −0.549403 0.835558i \(-0.685145\pi\)
−0.549403 + 0.835558i \(0.685145\pi\)
\(212\) 48.6336 3.34017
\(213\) 2.69976 0.184984
\(214\) −29.7884 −2.03629
\(215\) 7.84588 0.535084
\(216\) 14.7978 1.00687
\(217\) 6.68893 0.454074
\(218\) 12.7522 0.863686
\(219\) −0.0121486 −0.000820928 0
\(220\) −30.3918 −2.04902
\(221\) −22.9107 −1.54114
\(222\) −2.96599 −0.199064
\(223\) −10.0023 −0.669807 −0.334903 0.942253i \(-0.608704\pi\)
−0.334903 + 0.942253i \(0.608704\pi\)
\(224\) −31.9394 −2.13404
\(225\) 10.1730 0.678200
\(226\) −20.2368 −1.34613
\(227\) 28.5169 1.89273 0.946367 0.323094i \(-0.104723\pi\)
0.946367 + 0.323094i \(0.104723\pi\)
\(228\) −2.44713 −0.162065
\(229\) 8.51405 0.562624 0.281312 0.959616i \(-0.409230\pi\)
0.281312 + 0.959616i \(0.409230\pi\)
\(230\) −27.4676 −1.81116
\(231\) 0.930525 0.0612240
\(232\) 106.293 6.97849
\(233\) 6.71699 0.440045 0.220022 0.975495i \(-0.429387\pi\)
0.220022 + 0.975495i \(0.429387\pi\)
\(234\) 30.5719 1.99854
\(235\) 1.49391 0.0974519
\(236\) 75.5968 4.92093
\(237\) −0.318940 −0.0207174
\(238\) 17.4993 1.13431
\(239\) −24.6058 −1.59162 −0.795808 0.605548i \(-0.792954\pi\)
−0.795808 + 0.605548i \(0.792954\pi\)
\(240\) −5.39022 −0.347937
\(241\) 3.12431 0.201255 0.100627 0.994924i \(-0.467915\pi\)
0.100627 + 0.994924i \(0.467915\pi\)
\(242\) −16.9113 −1.08710
\(243\) 5.95449 0.381981
\(244\) −81.7002 −5.23032
\(245\) −1.24518 −0.0795515
\(246\) 3.39420 0.216406
\(247\) −6.75199 −0.429619
\(248\) −73.7441 −4.68276
\(249\) −3.11852 −0.197628
\(250\) −29.6054 −1.87241
\(251\) 6.44258 0.406652 0.203326 0.979111i \(-0.434825\pi\)
0.203326 + 0.979111i \(0.434825\pi\)
\(252\) −17.4527 −1.09942
\(253\) −32.3321 −2.03270
\(254\) 14.2833 0.896213
\(255\) 1.74712 0.109409
\(256\) 125.034 7.81460
\(257\) −2.74640 −0.171316 −0.0856578 0.996325i \(-0.527299\pi\)
−0.0856578 + 0.996325i \(0.527299\pi\)
\(258\) 4.00032 0.249049
\(259\) 4.67182 0.290293
\(260\) −27.1476 −1.68362
\(261\) 28.4331 1.75996
\(262\) −19.9753 −1.23408
\(263\) 5.79836 0.357542 0.178771 0.983891i \(-0.442788\pi\)
0.178771 + 0.983891i \(0.442788\pi\)
\(264\) −10.2588 −0.631388
\(265\) −10.2328 −0.628595
\(266\) 5.15720 0.316208
\(267\) 2.17244 0.132951
\(268\) 20.1304 1.22966
\(269\) −20.1785 −1.23031 −0.615153 0.788408i \(-0.710906\pi\)
−0.615153 + 0.788408i \(0.710906\pi\)
\(270\) −4.70291 −0.286210
\(271\) 29.9023 1.81644 0.908218 0.418498i \(-0.137443\pi\)
0.908218 + 0.418498i \(0.137443\pi\)
\(272\) −119.320 −7.23481
\(273\) 0.831194 0.0503061
\(274\) −3.19363 −0.192934
\(275\) −14.2269 −0.857917
\(276\) −10.4673 −0.630056
\(277\) 1.72153 0.103436 0.0517182 0.998662i \(-0.483530\pi\)
0.0517182 + 0.998662i \(0.483530\pi\)
\(278\) −10.4744 −0.628210
\(279\) −19.7263 −1.18098
\(280\) 13.7278 0.820395
\(281\) 10.2983 0.614344 0.307172 0.951654i \(-0.400617\pi\)
0.307172 + 0.951654i \(0.400617\pi\)
\(282\) 0.761688 0.0453579
\(283\) −12.0010 −0.713388 −0.356694 0.934221i \(-0.616096\pi\)
−0.356694 + 0.934221i \(0.616096\pi\)
\(284\) 70.8144 4.20206
\(285\) 0.514890 0.0304994
\(286\) −42.7547 −2.52814
\(287\) −5.34630 −0.315582
\(288\) 94.1925 5.55034
\(289\) 21.6747 1.27498
\(290\) −33.7811 −1.98369
\(291\) 3.06847 0.179877
\(292\) −0.318658 −0.0186480
\(293\) 29.8631 1.74462 0.872309 0.488954i \(-0.162622\pi\)
0.872309 + 0.488954i \(0.162622\pi\)
\(294\) −0.634869 −0.0370263
\(295\) −15.9060 −0.926083
\(296\) −51.5058 −2.99372
\(297\) −5.53578 −0.321219
\(298\) −51.1307 −2.96192
\(299\) −28.8807 −1.67022
\(300\) −4.60586 −0.265920
\(301\) −6.30101 −0.363184
\(302\) −44.4608 −2.55843
\(303\) 0.604174 0.0347089
\(304\) −35.1645 −2.01682
\(305\) 17.1902 0.984307
\(306\) −51.6071 −2.95018
\(307\) −19.1930 −1.09540 −0.547702 0.836674i \(-0.684497\pi\)
−0.547702 + 0.836674i \(0.684497\pi\)
\(308\) 24.4076 1.39075
\(309\) −3.58629 −0.204017
\(310\) 23.4367 1.33111
\(311\) 3.76320 0.213391 0.106696 0.994292i \(-0.465973\pi\)
0.106696 + 0.994292i \(0.465973\pi\)
\(312\) −9.16374 −0.518795
\(313\) −29.9377 −1.69218 −0.846091 0.533039i \(-0.821050\pi\)
−0.846091 + 0.533039i \(0.821050\pi\)
\(314\) 31.9349 1.80219
\(315\) 3.67215 0.206902
\(316\) −8.36578 −0.470612
\(317\) 19.0952 1.07249 0.536246 0.844062i \(-0.319842\pi\)
0.536246 + 0.844062i \(0.319842\pi\)
\(318\) −5.21731 −0.292572
\(319\) −39.7636 −2.22634
\(320\) −64.1278 −3.58485
\(321\) 2.38845 0.133310
\(322\) 22.0592 1.22931
\(323\) 11.3978 0.634189
\(324\) 50.5660 2.80922
\(325\) −12.7083 −0.704927
\(326\) −13.9102 −0.770417
\(327\) −1.02248 −0.0565431
\(328\) 58.9419 3.25452
\(329\) −1.19976 −0.0661447
\(330\) 3.26037 0.179477
\(331\) 4.28947 0.235771 0.117885 0.993027i \(-0.462388\pi\)
0.117885 + 0.993027i \(0.462388\pi\)
\(332\) −81.7987 −4.48929
\(333\) −13.7776 −0.755010
\(334\) 12.6951 0.694645
\(335\) −4.23554 −0.231412
\(336\) 4.32887 0.236159
\(337\) −6.64071 −0.361743 −0.180871 0.983507i \(-0.557892\pi\)
−0.180871 + 0.983507i \(0.557892\pi\)
\(338\) −1.61019 −0.0875826
\(339\) 1.62260 0.0881275
\(340\) 45.8267 2.48530
\(341\) 27.5872 1.49393
\(342\) −15.2091 −0.822412
\(343\) 1.00000 0.0539949
\(344\) 69.4673 3.74543
\(345\) 2.20237 0.118572
\(346\) −52.6551 −2.83076
\(347\) −18.8861 −1.01386 −0.506929 0.861988i \(-0.669220\pi\)
−0.506929 + 0.861988i \(0.669220\pi\)
\(348\) −12.8732 −0.690075
\(349\) 15.3084 0.819439 0.409719 0.912212i \(-0.365627\pi\)
0.409719 + 0.912212i \(0.365627\pi\)
\(350\) 9.70661 0.518840
\(351\) −4.94485 −0.263937
\(352\) −131.728 −7.02113
\(353\) −23.1957 −1.23458 −0.617292 0.786734i \(-0.711770\pi\)
−0.617292 + 0.786734i \(0.711770\pi\)
\(354\) −8.10987 −0.431035
\(355\) −14.8998 −0.790797
\(356\) 56.9830 3.02009
\(357\) −1.40311 −0.0742602
\(358\) 4.64851 0.245681
\(359\) −27.1701 −1.43398 −0.716991 0.697082i \(-0.754481\pi\)
−0.716991 + 0.697082i \(0.754481\pi\)
\(360\) −40.4847 −2.13373
\(361\) −15.6410 −0.823210
\(362\) −39.0304 −2.05139
\(363\) 1.35596 0.0711692
\(364\) 21.8022 1.14274
\(365\) 0.0670474 0.00350942
\(366\) 8.76462 0.458134
\(367\) −10.8239 −0.565005 −0.282503 0.959267i \(-0.591165\pi\)
−0.282503 + 0.959267i \(0.591165\pi\)
\(368\) −150.411 −7.84074
\(369\) 15.7668 0.820784
\(370\) 16.3691 0.850989
\(371\) 8.21793 0.426654
\(372\) 8.93116 0.463059
\(373\) 16.2909 0.843511 0.421755 0.906710i \(-0.361414\pi\)
0.421755 + 0.906710i \(0.361414\pi\)
\(374\) 72.1726 3.73195
\(375\) 2.37378 0.122582
\(376\) 13.2271 0.682134
\(377\) −35.5190 −1.82932
\(378\) 3.77690 0.194263
\(379\) 5.44932 0.279913 0.139956 0.990158i \(-0.455304\pi\)
0.139956 + 0.990158i \(0.455304\pi\)
\(380\) 13.5055 0.692819
\(381\) −1.14524 −0.0586726
\(382\) 72.2510 3.69668
\(383\) 7.33864 0.374987 0.187494 0.982266i \(-0.439964\pi\)
0.187494 + 0.982266i \(0.439964\pi\)
\(384\) −18.2840 −0.933053
\(385\) −5.13550 −0.261729
\(386\) 39.4493 2.00792
\(387\) 18.5823 0.944590
\(388\) 80.4857 4.08604
\(389\) 13.4449 0.681682 0.340841 0.940121i \(-0.389288\pi\)
0.340841 + 0.940121i \(0.389288\pi\)
\(390\) 2.91233 0.147472
\(391\) 48.7524 2.46552
\(392\) −11.0248 −0.556836
\(393\) 1.60163 0.0807918
\(394\) −30.1229 −1.51757
\(395\) 1.76021 0.0885656
\(396\) −71.9804 −3.61715
\(397\) −10.6630 −0.535160 −0.267580 0.963536i \(-0.586224\pi\)
−0.267580 + 0.963536i \(0.586224\pi\)
\(398\) −55.5273 −2.78333
\(399\) −0.413507 −0.0207012
\(400\) −66.1848 −3.30924
\(401\) 6.09173 0.304206 0.152103 0.988365i \(-0.451395\pi\)
0.152103 + 0.988365i \(0.451395\pi\)
\(402\) −2.15954 −0.107708
\(403\) 24.6424 1.22752
\(404\) 15.8475 0.788440
\(405\) −10.6394 −0.528674
\(406\) 27.1295 1.34642
\(407\) 19.2680 0.955080
\(408\) 15.4689 0.765827
\(409\) −11.0362 −0.545705 −0.272852 0.962056i \(-0.587967\pi\)
−0.272852 + 0.962056i \(0.587967\pi\)
\(410\) −18.7323 −0.925124
\(411\) 0.256067 0.0126308
\(412\) −94.0681 −4.63440
\(413\) 12.7741 0.628571
\(414\) −65.0547 −3.19727
\(415\) 17.2109 0.844850
\(416\) −117.667 −5.76908
\(417\) 0.839840 0.0411272
\(418\) 21.2699 1.04034
\(419\) 24.8513 1.21407 0.607034 0.794676i \(-0.292359\pi\)
0.607034 + 0.794676i \(0.292359\pi\)
\(420\) −1.66258 −0.0811255
\(421\) 19.0847 0.930131 0.465066 0.885276i \(-0.346031\pi\)
0.465066 + 0.885276i \(0.346031\pi\)
\(422\) 44.9127 2.18632
\(423\) 3.53820 0.172033
\(424\) −90.6010 −4.39998
\(425\) 21.4523 1.04059
\(426\) −7.59682 −0.368067
\(427\) −13.8054 −0.668090
\(428\) 62.6489 3.02825
\(429\) 3.42810 0.165510
\(430\) −22.0774 −1.06467
\(431\) 9.14848 0.440667 0.220333 0.975425i \(-0.429285\pi\)
0.220333 + 0.975425i \(0.429285\pi\)
\(432\) −25.7529 −1.23904
\(433\) 19.0731 0.916594 0.458297 0.888799i \(-0.348460\pi\)
0.458297 + 0.888799i \(0.348460\pi\)
\(434\) −18.8219 −0.903482
\(435\) 2.70859 0.129867
\(436\) −26.8195 −1.28442
\(437\) 14.3678 0.687303
\(438\) 0.0341849 0.00163342
\(439\) 16.6094 0.792723 0.396362 0.918094i \(-0.370273\pi\)
0.396362 + 0.918094i \(0.370273\pi\)
\(440\) 56.6178 2.69915
\(441\) −2.94910 −0.140433
\(442\) 64.4683 3.06645
\(443\) 16.5280 0.785270 0.392635 0.919694i \(-0.371564\pi\)
0.392635 + 0.919694i \(0.371564\pi\)
\(444\) 6.23788 0.296036
\(445\) −11.9895 −0.568358
\(446\) 28.1455 1.33273
\(447\) 4.09969 0.193909
\(448\) 51.5009 2.43319
\(449\) −0.869622 −0.0410400 −0.0205200 0.999789i \(-0.506532\pi\)
−0.0205200 + 0.999789i \(0.506532\pi\)
\(450\) −28.6257 −1.34943
\(451\) −22.0498 −1.03828
\(452\) 42.5607 2.00189
\(453\) 3.56489 0.167493
\(454\) −80.2435 −3.76601
\(455\) −4.58730 −0.215056
\(456\) 4.55883 0.213487
\(457\) 6.35781 0.297406 0.148703 0.988882i \(-0.452490\pi\)
0.148703 + 0.988882i \(0.452490\pi\)
\(458\) −23.9576 −1.11947
\(459\) 8.34721 0.389614
\(460\) 57.7681 2.69345
\(461\) 3.94964 0.183953 0.0919765 0.995761i \(-0.470682\pi\)
0.0919765 + 0.995761i \(0.470682\pi\)
\(462\) −2.61840 −0.121819
\(463\) 26.8026 1.24562 0.622810 0.782373i \(-0.285991\pi\)
0.622810 + 0.782373i \(0.285991\pi\)
\(464\) −184.984 −8.58765
\(465\) −1.87917 −0.0871442
\(466\) −18.9009 −0.875567
\(467\) 34.4026 1.59196 0.795982 0.605320i \(-0.206955\pi\)
0.795982 + 0.605320i \(0.206955\pi\)
\(468\) −64.2967 −2.97211
\(469\) 3.40155 0.157069
\(470\) −4.20370 −0.193902
\(471\) −2.56056 −0.117984
\(472\) −140.832 −6.48230
\(473\) −25.9873 −1.19490
\(474\) 0.897463 0.0412218
\(475\) 6.32217 0.290081
\(476\) −36.8034 −1.68688
\(477\) −24.2355 −1.10967
\(478\) 69.2381 3.16688
\(479\) −16.6804 −0.762146 −0.381073 0.924545i \(-0.624445\pi\)
−0.381073 + 0.924545i \(0.624445\pi\)
\(480\) 8.97295 0.409557
\(481\) 17.2112 0.784764
\(482\) −8.79147 −0.400441
\(483\) −1.76872 −0.0804796
\(484\) 35.5666 1.61667
\(485\) −16.9346 −0.768962
\(486\) −16.7553 −0.760036
\(487\) −26.9676 −1.22202 −0.611009 0.791623i \(-0.709236\pi\)
−0.611009 + 0.791623i \(0.709236\pi\)
\(488\) 152.202 6.88985
\(489\) 1.11533 0.0504370
\(490\) 3.50380 0.158285
\(491\) −26.2886 −1.18639 −0.593193 0.805060i \(-0.702133\pi\)
−0.593193 + 0.805060i \(0.702133\pi\)
\(492\) −7.13845 −0.321826
\(493\) 59.9582 2.70038
\(494\) 18.9994 0.854822
\(495\) 15.1451 0.680720
\(496\) 128.338 5.76254
\(497\) 11.9660 0.536747
\(498\) 8.77519 0.393226
\(499\) 12.7873 0.572436 0.286218 0.958165i \(-0.407602\pi\)
0.286218 + 0.958165i \(0.407602\pi\)
\(500\) 62.2641 2.78454
\(501\) −1.01790 −0.0454765
\(502\) −18.1287 −0.809125
\(503\) −37.0549 −1.65220 −0.826098 0.563526i \(-0.809444\pi\)
−0.826098 + 0.563526i \(0.809444\pi\)
\(504\) 32.5132 1.44825
\(505\) −3.33439 −0.148379
\(506\) 90.9790 4.04451
\(507\) 0.129106 0.00573378
\(508\) −30.0397 −1.33279
\(509\) −5.13313 −0.227522 −0.113761 0.993508i \(-0.536290\pi\)
−0.113761 + 0.993508i \(0.536290\pi\)
\(510\) −4.91619 −0.217693
\(511\) −0.0538456 −0.00238199
\(512\) −189.753 −8.38596
\(513\) 2.45999 0.108611
\(514\) 7.72807 0.340870
\(515\) 19.7924 0.872159
\(516\) −8.41319 −0.370370
\(517\) −4.94816 −0.217620
\(518\) −13.1460 −0.577602
\(519\) 4.22192 0.185322
\(520\) 50.5740 2.21782
\(521\) 28.7925 1.26142 0.630712 0.776017i \(-0.282763\pi\)
0.630712 + 0.776017i \(0.282763\pi\)
\(522\) −80.0076 −3.50184
\(523\) 17.7568 0.776450 0.388225 0.921565i \(-0.373088\pi\)
0.388225 + 0.921565i \(0.373088\pi\)
\(524\) 42.0108 1.83525
\(525\) −0.778282 −0.0339670
\(526\) −16.3160 −0.711410
\(527\) −41.5978 −1.81203
\(528\) 17.8536 0.776979
\(529\) 38.4561 1.67201
\(530\) 28.7940 1.25073
\(531\) −37.6720 −1.63482
\(532\) −10.8463 −0.470245
\(533\) −19.6960 −0.853130
\(534\) −6.11301 −0.264536
\(535\) −13.1817 −0.569893
\(536\) −37.5014 −1.61982
\(537\) −0.372720 −0.0160841
\(538\) 56.7802 2.44797
\(539\) 4.12431 0.177647
\(540\) 9.89084 0.425634
\(541\) −18.5554 −0.797757 −0.398878 0.917004i \(-0.630600\pi\)
−0.398878 + 0.917004i \(0.630600\pi\)
\(542\) −84.1419 −3.61420
\(543\) 3.12948 0.134299
\(544\) 198.628 8.51611
\(545\) 5.64298 0.241718
\(546\) −2.33889 −0.100095
\(547\) 29.9525 1.28067 0.640337 0.768094i \(-0.278795\pi\)
0.640337 + 0.768094i \(0.278795\pi\)
\(548\) 6.71662 0.286920
\(549\) 40.7135 1.73761
\(550\) 40.0331 1.70702
\(551\) 17.6702 0.752775
\(552\) 19.4998 0.829966
\(553\) −1.41362 −0.0601132
\(554\) −4.84419 −0.205810
\(555\) −1.31248 −0.0557118
\(556\) 22.0290 0.934236
\(557\) −8.27286 −0.350532 −0.175266 0.984521i \(-0.556079\pi\)
−0.175266 + 0.984521i \(0.556079\pi\)
\(558\) 55.5077 2.34983
\(559\) −23.2132 −0.981815
\(560\) −23.8907 −1.00957
\(561\) −5.78684 −0.244321
\(562\) −28.9783 −1.22237
\(563\) 25.7075 1.08344 0.541721 0.840559i \(-0.317773\pi\)
0.541721 + 0.840559i \(0.317773\pi\)
\(564\) −1.60193 −0.0674534
\(565\) −8.95500 −0.376740
\(566\) 33.7696 1.41944
\(567\) 8.54445 0.358833
\(568\) −131.922 −5.53534
\(569\) −28.1916 −1.18185 −0.590927 0.806725i \(-0.701238\pi\)
−0.590927 + 0.806725i \(0.701238\pi\)
\(570\) −1.44884 −0.0606854
\(571\) 42.4672 1.77720 0.888599 0.458685i \(-0.151679\pi\)
0.888599 + 0.458685i \(0.151679\pi\)
\(572\) 89.9189 3.75970
\(573\) −5.79313 −0.242011
\(574\) 15.0439 0.627921
\(575\) 27.0423 1.12774
\(576\) −151.881 −6.32838
\(577\) 7.28929 0.303457 0.151729 0.988422i \(-0.451516\pi\)
0.151729 + 0.988422i \(0.451516\pi\)
\(578\) −60.9903 −2.53686
\(579\) −3.16307 −0.131453
\(580\) 71.0461 2.95003
\(581\) −13.8220 −0.573435
\(582\) −8.63433 −0.357905
\(583\) 33.8933 1.40372
\(584\) 0.593637 0.0245649
\(585\) 13.5284 0.559330
\(586\) −84.0314 −3.47131
\(587\) 5.98008 0.246824 0.123412 0.992355i \(-0.460616\pi\)
0.123412 + 0.992355i \(0.460616\pi\)
\(588\) 1.33521 0.0550633
\(589\) −12.2592 −0.505133
\(590\) 44.7578 1.84265
\(591\) 2.41528 0.0993512
\(592\) 89.6363 3.68403
\(593\) −6.64002 −0.272673 −0.136336 0.990663i \(-0.543533\pi\)
−0.136336 + 0.990663i \(0.543533\pi\)
\(594\) 15.5771 0.639136
\(595\) 7.74363 0.317458
\(596\) 107.535 4.40479
\(597\) 4.45221 0.182217
\(598\) 81.2673 3.32327
\(599\) −30.7495 −1.25639 −0.628195 0.778056i \(-0.716206\pi\)
−0.628195 + 0.778056i \(0.716206\pi\)
\(600\) 8.58040 0.350293
\(601\) 9.29276 0.379060 0.189530 0.981875i \(-0.439304\pi\)
0.189530 + 0.981875i \(0.439304\pi\)
\(602\) 17.7304 0.722635
\(603\) −10.0315 −0.408515
\(604\) 93.5069 3.80474
\(605\) −7.48342 −0.304244
\(606\) −1.70008 −0.0690611
\(607\) −0.544087 −0.0220838 −0.0110419 0.999939i \(-0.503515\pi\)
−0.0110419 + 0.999939i \(0.503515\pi\)
\(608\) 58.5374 2.37401
\(609\) −2.17526 −0.0881461
\(610\) −48.3713 −1.95850
\(611\) −4.41996 −0.178812
\(612\) 108.537 4.38733
\(613\) 11.7191 0.473331 0.236666 0.971591i \(-0.423945\pi\)
0.236666 + 0.971591i \(0.423945\pi\)
\(614\) 54.0071 2.17955
\(615\) 1.50197 0.0605653
\(616\) −45.4697 −1.83202
\(617\) −2.03619 −0.0819741 −0.0409871 0.999160i \(-0.513050\pi\)
−0.0409871 + 0.999160i \(0.513050\pi\)
\(618\) 10.0914 0.405936
\(619\) 39.5680 1.59037 0.795186 0.606365i \(-0.207373\pi\)
0.795186 + 0.606365i \(0.207373\pi\)
\(620\) −49.2904 −1.97955
\(621\) 10.5223 0.422245
\(622\) −10.5892 −0.424589
\(623\) 9.62877 0.385769
\(624\) 15.9478 0.638422
\(625\) 4.14694 0.165878
\(626\) 84.2416 3.36697
\(627\) −1.70543 −0.0681083
\(628\) −67.1633 −2.68011
\(629\) −29.0536 −1.15844
\(630\) −10.3330 −0.411678
\(631\) 33.4087 1.32998 0.664990 0.746852i \(-0.268436\pi\)
0.664990 + 0.746852i \(0.268436\pi\)
\(632\) 15.5849 0.619932
\(633\) −3.60113 −0.143132
\(634\) −53.7317 −2.13396
\(635\) 6.32051 0.250822
\(636\) 10.9727 0.435096
\(637\) 3.68405 0.145967
\(638\) 111.891 4.42979
\(639\) −35.2888 −1.39600
\(640\) 100.908 3.98874
\(641\) 14.5134 0.573243 0.286621 0.958044i \(-0.407468\pi\)
0.286621 + 0.958044i \(0.407468\pi\)
\(642\) −6.72084 −0.265250
\(643\) −40.1988 −1.58529 −0.792643 0.609687i \(-0.791295\pi\)
−0.792643 + 0.609687i \(0.791295\pi\)
\(644\) −46.3935 −1.82816
\(645\) 1.77018 0.0697009
\(646\) −32.0721 −1.26186
\(647\) −31.5030 −1.23851 −0.619254 0.785190i \(-0.712565\pi\)
−0.619254 + 0.785190i \(0.712565\pi\)
\(648\) −94.2008 −3.70056
\(649\) 52.6842 2.06804
\(650\) 35.7596 1.40261
\(651\) 1.50915 0.0591484
\(652\) 29.2551 1.14572
\(653\) 35.5305 1.39042 0.695208 0.718809i \(-0.255312\pi\)
0.695208 + 0.718809i \(0.255312\pi\)
\(654\) 2.87714 0.112505
\(655\) −8.83930 −0.345380
\(656\) −102.577 −4.00497
\(657\) 0.158796 0.00619522
\(658\) 3.37598 0.131610
\(659\) 23.1778 0.902881 0.451440 0.892301i \(-0.350910\pi\)
0.451440 + 0.892301i \(0.350910\pi\)
\(660\) −6.85699 −0.266908
\(661\) −10.5632 −0.410860 −0.205430 0.978672i \(-0.565859\pi\)
−0.205430 + 0.978672i \(0.565859\pi\)
\(662\) −12.0701 −0.469118
\(663\) −5.16911 −0.200752
\(664\) 152.385 5.91369
\(665\) 2.28211 0.0884966
\(666\) 38.7688 1.50226
\(667\) 75.5819 2.92654
\(668\) −26.6995 −1.03303
\(669\) −2.25672 −0.0872500
\(670\) 11.9183 0.460446
\(671\) −56.9377 −2.19806
\(672\) −7.20616 −0.277984
\(673\) −11.2628 −0.434150 −0.217075 0.976155i \(-0.569652\pi\)
−0.217075 + 0.976155i \(0.569652\pi\)
\(674\) 18.6862 0.719767
\(675\) 4.63007 0.178212
\(676\) 3.38643 0.130247
\(677\) −0.608062 −0.0233697 −0.0116849 0.999932i \(-0.503719\pi\)
−0.0116849 + 0.999932i \(0.503719\pi\)
\(678\) −4.56582 −0.175349
\(679\) 13.6002 0.521927
\(680\) −85.3720 −3.27387
\(681\) 6.43397 0.246550
\(682\) −77.6275 −2.97251
\(683\) −22.0405 −0.843358 −0.421679 0.906745i \(-0.638559\pi\)
−0.421679 + 0.906745i \(0.638559\pi\)
\(684\) 31.9867 1.22304
\(685\) −1.41321 −0.0539961
\(686\) −2.81389 −0.107435
\(687\) 1.92094 0.0732883
\(688\) −120.895 −4.60908
\(689\) 30.2753 1.15340
\(690\) −6.19724 −0.235925
\(691\) −21.1030 −0.802797 −0.401398 0.915904i \(-0.631476\pi\)
−0.401398 + 0.915904i \(0.631476\pi\)
\(692\) 110.741 4.20973
\(693\) −12.1630 −0.462033
\(694\) 53.1434 2.01730
\(695\) −4.63502 −0.175816
\(696\) 23.9818 0.909029
\(697\) 33.2481 1.25936
\(698\) −43.0761 −1.63046
\(699\) 1.51548 0.0573209
\(700\) −20.4143 −0.771588
\(701\) 27.6644 1.04487 0.522435 0.852679i \(-0.325024\pi\)
0.522435 + 0.852679i \(0.325024\pi\)
\(702\) 13.9143 0.525161
\(703\) −8.56233 −0.322934
\(704\) 212.406 8.00534
\(705\) 0.337055 0.0126942
\(706\) 65.2703 2.45648
\(707\) 2.67785 0.100711
\(708\) 17.0561 0.641008
\(709\) 28.3531 1.06482 0.532412 0.846485i \(-0.321286\pi\)
0.532412 + 0.846485i \(0.321286\pi\)
\(710\) 41.9263 1.57347
\(711\) 4.16890 0.156346
\(712\) −106.155 −3.97834
\(713\) −52.4372 −1.96379
\(714\) 3.94819 0.147757
\(715\) −18.9194 −0.707546
\(716\) −9.77643 −0.365362
\(717\) −5.55155 −0.207326
\(718\) 76.4537 2.85323
\(719\) −21.7253 −0.810218 −0.405109 0.914268i \(-0.632766\pi\)
−0.405109 + 0.914268i \(0.632766\pi\)
\(720\) 70.4560 2.62574
\(721\) −15.8953 −0.591971
\(722\) 44.0120 1.63796
\(723\) 0.704906 0.0262157
\(724\) 82.0861 3.05071
\(725\) 33.2579 1.23517
\(726\) −3.81551 −0.141607
\(727\) −5.78059 −0.214390 −0.107195 0.994238i \(-0.534187\pi\)
−0.107195 + 0.994238i \(0.534187\pi\)
\(728\) −40.6159 −1.50533
\(729\) −24.2899 −0.899626
\(730\) −0.188664 −0.00698277
\(731\) 39.1853 1.44932
\(732\) −18.4332 −0.681309
\(733\) −8.04894 −0.297294 −0.148647 0.988890i \(-0.547492\pi\)
−0.148647 + 0.988890i \(0.547492\pi\)
\(734\) 30.4574 1.12420
\(735\) −0.280936 −0.0103625
\(736\) 250.386 9.22935
\(737\) 14.0291 0.516767
\(738\) −44.3659 −1.63313
\(739\) −6.17166 −0.227028 −0.113514 0.993536i \(-0.536211\pi\)
−0.113514 + 0.993536i \(0.536211\pi\)
\(740\) −34.4264 −1.26554
\(741\) −1.52338 −0.0559628
\(742\) −23.1244 −0.848923
\(743\) −21.1424 −0.775640 −0.387820 0.921735i \(-0.626772\pi\)
−0.387820 + 0.921735i \(0.626772\pi\)
\(744\) −16.6381 −0.609983
\(745\) −22.6259 −0.828949
\(746\) −45.8408 −1.67835
\(747\) 40.7625 1.49142
\(748\) −151.788 −5.54994
\(749\) 10.5862 0.386811
\(750\) −6.67956 −0.243903
\(751\) 9.58269 0.349677 0.174839 0.984597i \(-0.444060\pi\)
0.174839 + 0.984597i \(0.444060\pi\)
\(752\) −23.0192 −0.839425
\(753\) 1.45357 0.0529711
\(754\) 99.9466 3.63984
\(755\) −19.6744 −0.716024
\(756\) −7.94332 −0.288896
\(757\) −9.53376 −0.346510 −0.173255 0.984877i \(-0.555429\pi\)
−0.173255 + 0.984877i \(0.555429\pi\)
\(758\) −15.3338 −0.556948
\(759\) −7.29475 −0.264783
\(760\) −25.1598 −0.912644
\(761\) 17.3227 0.627948 0.313974 0.949432i \(-0.398339\pi\)
0.313974 + 0.949432i \(0.398339\pi\)
\(762\) 3.22259 0.116742
\(763\) −4.53186 −0.164064
\(764\) −151.953 −5.49748
\(765\) −22.8367 −0.825663
\(766\) −20.6501 −0.746120
\(767\) 47.0603 1.69925
\(768\) 28.2100 1.01794
\(769\) 7.16435 0.258353 0.129177 0.991622i \(-0.458767\pi\)
0.129177 + 0.991622i \(0.458767\pi\)
\(770\) 14.4507 0.520768
\(771\) −0.619641 −0.0223158
\(772\) −82.9671 −2.98605
\(773\) 37.5855 1.35185 0.675927 0.736968i \(-0.263743\pi\)
0.675927 + 0.736968i \(0.263743\pi\)
\(774\) −52.2885 −1.87947
\(775\) −23.0737 −0.828832
\(776\) −149.939 −5.38250
\(777\) 1.05405 0.0378140
\(778\) −37.8324 −1.35636
\(779\) 9.79850 0.351068
\(780\) −6.12502 −0.219311
\(781\) 49.3513 1.76593
\(782\) −137.184 −4.90569
\(783\) 12.9408 0.462468
\(784\) 19.1866 0.685236
\(785\) 14.1315 0.504376
\(786\) −4.50683 −0.160753
\(787\) −16.1960 −0.577326 −0.288663 0.957431i \(-0.593211\pi\)
−0.288663 + 0.957431i \(0.593211\pi\)
\(788\) 63.3525 2.25684
\(789\) 1.30822 0.0465740
\(790\) −4.95303 −0.176221
\(791\) 7.19175 0.255709
\(792\) 134.094 4.76484
\(793\) −50.8598 −1.80608
\(794\) 30.0045 1.06482
\(795\) −2.30872 −0.0818818
\(796\) 116.781 4.13920
\(797\) −1.54570 −0.0547515 −0.0273758 0.999625i \(-0.508715\pi\)
−0.0273758 + 0.999625i \(0.508715\pi\)
\(798\) 1.16356 0.0411897
\(799\) 7.46116 0.263957
\(800\) 110.176 3.89532
\(801\) −28.3962 −1.00333
\(802\) −17.1415 −0.605286
\(803\) −0.222076 −0.00783689
\(804\) 4.54180 0.160177
\(805\) 9.76144 0.344046
\(806\) −69.3410 −2.44243
\(807\) −4.55267 −0.160262
\(808\) −29.5227 −1.03860
\(809\) 48.5618 1.70734 0.853670 0.520814i \(-0.174372\pi\)
0.853670 + 0.520814i \(0.174372\pi\)
\(810\) 29.9380 1.05191
\(811\) 11.8743 0.416964 0.208482 0.978026i \(-0.433148\pi\)
0.208482 + 0.978026i \(0.433148\pi\)
\(812\) −57.0570 −2.00231
\(813\) 6.74655 0.236612
\(814\) −54.2181 −1.90034
\(815\) −6.15543 −0.215615
\(816\) −26.9208 −0.942417
\(817\) 11.5483 0.404022
\(818\) 31.0547 1.08580
\(819\) −10.8646 −0.379640
\(820\) 39.3966 1.37579
\(821\) 6.75381 0.235709 0.117855 0.993031i \(-0.462398\pi\)
0.117855 + 0.993031i \(0.462398\pi\)
\(822\) −0.720544 −0.0251319
\(823\) −37.4394 −1.30506 −0.652528 0.757764i \(-0.726292\pi\)
−0.652528 + 0.757764i \(0.726292\pi\)
\(824\) 175.242 6.10485
\(825\) −3.20988 −0.111754
\(826\) −35.9449 −1.25068
\(827\) 31.0660 1.08027 0.540135 0.841578i \(-0.318373\pi\)
0.540135 + 0.841578i \(0.318373\pi\)
\(828\) 136.819 4.75478
\(829\) 29.7453 1.03310 0.516548 0.856258i \(-0.327217\pi\)
0.516548 + 0.856258i \(0.327217\pi\)
\(830\) −48.4296 −1.68102
\(831\) 0.388410 0.0134738
\(832\) 189.732 6.57777
\(833\) −6.21890 −0.215472
\(834\) −2.36322 −0.0818316
\(835\) 5.61772 0.194409
\(836\) −44.7333 −1.54714
\(837\) −8.97810 −0.310329
\(838\) −69.9290 −2.41566
\(839\) −23.8695 −0.824067 −0.412033 0.911169i \(-0.635181\pi\)
−0.412033 + 0.911169i \(0.635181\pi\)
\(840\) 3.09727 0.106866
\(841\) 63.9544 2.20533
\(842\) −53.7023 −1.85070
\(843\) 2.32350 0.0800254
\(844\) −94.4575 −3.25136
\(845\) −0.712525 −0.0245116
\(846\) −9.95610 −0.342298
\(847\) 6.00992 0.206503
\(848\) 157.674 5.41456
\(849\) −2.70767 −0.0929270
\(850\) −60.3644 −2.07048
\(851\) −36.6242 −1.25546
\(852\) 15.9771 0.547367
\(853\) −22.5549 −0.772266 −0.386133 0.922443i \(-0.626189\pi\)
−0.386133 + 0.922443i \(0.626189\pi\)
\(854\) 38.8469 1.32931
\(855\) −6.73017 −0.230167
\(856\) −116.710 −3.98908
\(857\) 23.4946 0.802562 0.401281 0.915955i \(-0.368565\pi\)
0.401281 + 0.915955i \(0.368565\pi\)
\(858\) −9.64630 −0.329319
\(859\) −20.5325 −0.700560 −0.350280 0.936645i \(-0.613914\pi\)
−0.350280 + 0.936645i \(0.613914\pi\)
\(860\) 46.4318 1.58331
\(861\) −1.20623 −0.0411082
\(862\) −25.7428 −0.876804
\(863\) −1.00000 −0.0340404
\(864\) 42.8702 1.45847
\(865\) −23.3005 −0.792239
\(866\) −53.6696 −1.82377
\(867\) 4.89024 0.166081
\(868\) 39.5850 1.34360
\(869\) −5.83020 −0.197776
\(870\) −7.62168 −0.258399
\(871\) 12.5315 0.424614
\(872\) 49.9629 1.69196
\(873\) −40.1082 −1.35746
\(874\) −40.4293 −1.36754
\(875\) 10.5212 0.355680
\(876\) −0.0718954 −0.00242912
\(877\) −34.4856 −1.16450 −0.582248 0.813011i \(-0.697827\pi\)
−0.582248 + 0.813011i \(0.697827\pi\)
\(878\) −46.7371 −1.57730
\(879\) 6.73769 0.227257
\(880\) −98.5327 −3.32154
\(881\) 18.0702 0.608802 0.304401 0.952544i \(-0.401544\pi\)
0.304401 + 0.952544i \(0.401544\pi\)
\(882\) 8.29844 0.279423
\(883\) 15.1250 0.508998 0.254499 0.967073i \(-0.418089\pi\)
0.254499 + 0.967073i \(0.418089\pi\)
\(884\) −135.585 −4.56023
\(885\) −3.58870 −0.120633
\(886\) −46.5081 −1.56247
\(887\) −26.2847 −0.882555 −0.441278 0.897371i \(-0.645475\pi\)
−0.441278 + 0.897371i \(0.645475\pi\)
\(888\) −11.6207 −0.389966
\(889\) −5.07599 −0.170243
\(890\) 33.7373 1.13088
\(891\) 35.2400 1.18058
\(892\) −59.1938 −1.98195
\(893\) 2.19887 0.0735823
\(894\) −11.5361 −0.385825
\(895\) 2.05701 0.0687584
\(896\) −81.0392 −2.70733
\(897\) −6.51606 −0.217565
\(898\) 2.44702 0.0816582
\(899\) −64.4899 −2.15086
\(900\) 60.2037 2.00679
\(901\) −51.1065 −1.70260
\(902\) 62.0457 2.06590
\(903\) −1.42163 −0.0473089
\(904\) −79.2875 −2.63706
\(905\) −17.2714 −0.574120
\(906\) −10.0312 −0.333265
\(907\) 50.2750 1.66935 0.834677 0.550739i \(-0.185654\pi\)
0.834677 + 0.550739i \(0.185654\pi\)
\(908\) 168.763 5.60059
\(909\) −7.89722 −0.261934
\(910\) 12.9082 0.427901
\(911\) −0.484125 −0.0160398 −0.00801989 0.999968i \(-0.502553\pi\)
−0.00801989 + 0.999968i \(0.502553\pi\)
\(912\) −7.93380 −0.262714
\(913\) −57.0064 −1.88664
\(914\) −17.8902 −0.591755
\(915\) 3.87844 0.128217
\(916\) 50.3860 1.66480
\(917\) 7.09883 0.234424
\(918\) −23.4881 −0.775224
\(919\) −1.50492 −0.0496426 −0.0248213 0.999692i \(-0.507902\pi\)
−0.0248213 + 0.999692i \(0.507902\pi\)
\(920\) −107.618 −3.54806
\(921\) −4.33032 −0.142689
\(922\) −11.1139 −0.366016
\(923\) 44.0832 1.45102
\(924\) 5.50683 0.181162
\(925\) −16.1156 −0.529877
\(926\) −75.4195 −2.47844
\(927\) 46.8767 1.53963
\(928\) 307.937 10.1085
\(929\) 4.47406 0.146789 0.0733945 0.997303i \(-0.476617\pi\)
0.0733945 + 0.997303i \(0.476617\pi\)
\(930\) 5.28777 0.173393
\(931\) −1.83276 −0.0600664
\(932\) 39.7511 1.30209
\(933\) 0.849051 0.0277967
\(934\) −96.8053 −3.16757
\(935\) 31.9371 1.04446
\(936\) 119.780 3.91514
\(937\) 13.8454 0.452310 0.226155 0.974091i \(-0.427384\pi\)
0.226155 + 0.974091i \(0.427384\pi\)
\(938\) −9.57161 −0.312524
\(939\) −6.75454 −0.220426
\(940\) 8.84094 0.288360
\(941\) −40.9664 −1.33547 −0.667734 0.744400i \(-0.732735\pi\)
−0.667734 + 0.744400i \(0.732735\pi\)
\(942\) 7.20513 0.234756
\(943\) 41.9118 1.36483
\(944\) 245.091 7.97704
\(945\) 1.67132 0.0543680
\(946\) 73.1255 2.37751
\(947\) −48.6265 −1.58015 −0.790075 0.613010i \(-0.789958\pi\)
−0.790075 + 0.613010i \(0.789958\pi\)
\(948\) −1.88748 −0.0613026
\(949\) −0.198370 −0.00643936
\(950\) −17.7899 −0.577181
\(951\) 4.30824 0.139704
\(952\) 68.5621 2.22211
\(953\) 14.9688 0.484888 0.242444 0.970165i \(-0.422051\pi\)
0.242444 + 0.970165i \(0.422051\pi\)
\(954\) 68.1960 2.20793
\(955\) 31.9719 1.03458
\(956\) −145.617 −4.70958
\(957\) −8.97146 −0.290006
\(958\) 46.9368 1.51646
\(959\) 1.13495 0.0366494
\(960\) −14.4685 −0.466968
\(961\) 13.7418 0.443285
\(962\) −48.4305 −1.56146
\(963\) −31.2197 −1.00604
\(964\) 18.4896 0.595511
\(965\) 17.4567 0.561952
\(966\) 4.97699 0.160132
\(967\) 13.1427 0.422641 0.211320 0.977417i \(-0.432224\pi\)
0.211320 + 0.977417i \(0.432224\pi\)
\(968\) −66.2581 −2.12962
\(969\) 2.57156 0.0826104
\(970\) 47.6522 1.53002
\(971\) 22.4397 0.720126 0.360063 0.932928i \(-0.382755\pi\)
0.360063 + 0.932928i \(0.382755\pi\)
\(972\) 35.2386 1.13028
\(973\) 3.72237 0.119334
\(974\) 75.8839 2.43148
\(975\) −2.86723 −0.0918249
\(976\) −264.879 −8.47856
\(977\) 23.8032 0.761533 0.380766 0.924671i \(-0.375660\pi\)
0.380766 + 0.924671i \(0.375660\pi\)
\(978\) −3.13842 −0.100356
\(979\) 39.7120 1.26920
\(980\) −7.36895 −0.235392
\(981\) 13.3649 0.426708
\(982\) 73.9732 2.36058
\(983\) −5.39300 −0.172010 −0.0860050 0.996295i \(-0.527410\pi\)
−0.0860050 + 0.996295i \(0.527410\pi\)
\(984\) 13.2984 0.423939
\(985\) −13.3297 −0.424720
\(986\) −168.716 −5.37301
\(987\) −0.270688 −0.00861611
\(988\) −39.9582 −1.27124
\(989\) 49.3961 1.57070
\(990\) −42.6166 −1.35444
\(991\) 39.3701 1.25063 0.625316 0.780371i \(-0.284970\pi\)
0.625316 + 0.780371i \(0.284970\pi\)
\(992\) −213.641 −6.78310
\(993\) 0.967788 0.0307118
\(994\) −33.6709 −1.06798
\(995\) −24.5714 −0.778967
\(996\) −18.4554 −0.584781
\(997\) −59.4927 −1.88415 −0.942076 0.335400i \(-0.891128\pi\)
−0.942076 + 0.335400i \(0.891128\pi\)
\(998\) −35.9819 −1.13899
\(999\) −6.27067 −0.198395
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 \(a_p\))