Properties

Label 4019.2.a.b.1.9
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62160 q^{2}\) \(-1.74677 q^{3}\) \(+4.87277 q^{4}\) \(-3.59409 q^{5}\) \(+4.57932 q^{6}\) \(+5.00470 q^{7}\) \(-7.53124 q^{8}\) \(+0.0512031 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62160 q^{2}\) \(-1.74677 q^{3}\) \(+4.87277 q^{4}\) \(-3.59409 q^{5}\) \(+4.57932 q^{6}\) \(+5.00470 q^{7}\) \(-7.53124 q^{8}\) \(+0.0512031 q^{9}\) \(+9.42226 q^{10}\) \(+4.83308 q^{11}\) \(-8.51160 q^{12}\) \(+2.69395 q^{13}\) \(-13.1203 q^{14}\) \(+6.27805 q^{15}\) \(+9.99834 q^{16}\) \(+4.49415 q^{17}\) \(-0.134234 q^{18}\) \(-4.49596 q^{19}\) \(-17.5132 q^{20}\) \(-8.74206 q^{21}\) \(-12.6704 q^{22}\) \(-1.03340 q^{23}\) \(+13.1553 q^{24}\) \(+7.91749 q^{25}\) \(-7.06245 q^{26}\) \(+5.15087 q^{27}\) \(+24.3868 q^{28}\) \(+5.52907 q^{29}\) \(-16.4585 q^{30}\) \(+7.30673 q^{31}\) \(-11.1491 q^{32}\) \(-8.44228 q^{33}\) \(-11.7819 q^{34}\) \(-17.9874 q^{35}\) \(+0.249501 q^{36}\) \(+7.95655 q^{37}\) \(+11.7866 q^{38}\) \(-4.70571 q^{39}\) \(+27.0680 q^{40}\) \(+10.5430 q^{41}\) \(+22.9182 q^{42}\) \(+11.3587 q^{43}\) \(+23.5505 q^{44}\) \(-0.184029 q^{45}\) \(+2.70917 q^{46}\) \(-1.42485 q^{47}\) \(-17.4648 q^{48}\) \(+18.0470 q^{49}\) \(-20.7565 q^{50}\) \(-7.85025 q^{51}\) \(+13.1270 q^{52}\) \(-2.96560 q^{53}\) \(-13.5035 q^{54}\) \(-17.3705 q^{55}\) \(-37.6916 q^{56}\) \(+7.85340 q^{57}\) \(-14.4950 q^{58}\) \(+5.22309 q^{59}\) \(+30.5915 q^{60}\) \(+10.0176 q^{61}\) \(-19.1553 q^{62}\) \(+0.256256 q^{63}\) \(+9.23185 q^{64}\) \(-9.68230 q^{65}\) \(+22.1323 q^{66}\) \(+1.46016 q^{67}\) \(+21.8990 q^{68}\) \(+1.80512 q^{69}\) \(+47.1556 q^{70}\) \(+4.84033 q^{71}\) \(-0.385623 q^{72}\) \(-0.166246 q^{73}\) \(-20.8589 q^{74}\) \(-13.8300 q^{75}\) \(-21.9078 q^{76}\) \(+24.1881 q^{77}\) \(+12.3365 q^{78}\) \(-6.67132 q^{79}\) \(-35.9349 q^{80}\) \(-9.15099 q^{81}\) \(-27.6396 q^{82}\) \(+3.94157 q^{83}\) \(-42.5980 q^{84}\) \(-16.1524 q^{85}\) \(-29.7779 q^{86}\) \(-9.65801 q^{87}\) \(-36.3991 q^{88}\) \(-12.1444 q^{89}\) \(+0.482449 q^{90}\) \(+13.4824 q^{91}\) \(-5.03553 q^{92}\) \(-12.7632 q^{93}\) \(+3.73537 q^{94}\) \(+16.1589 q^{95}\) \(+19.4750 q^{96}\) \(-5.94555 q^{97}\) \(-47.3121 q^{98}\) \(+0.247469 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62160 −1.85375 −0.926874 0.375372i \(-0.877515\pi\)
−0.926874 + 0.375372i \(0.877515\pi\)
\(3\) −1.74677 −1.00850 −0.504249 0.863558i \(-0.668231\pi\)
−0.504249 + 0.863558i \(0.668231\pi\)
\(4\) 4.87277 2.43638
\(5\) −3.59409 −1.60733 −0.803663 0.595084i \(-0.797119\pi\)
−0.803663 + 0.595084i \(0.797119\pi\)
\(6\) 4.57932 1.86950
\(7\) 5.00470 1.89160 0.945800 0.324750i \(-0.105280\pi\)
0.945800 + 0.324750i \(0.105280\pi\)
\(8\) −7.53124 −2.66270
\(9\) 0.0512031 0.0170677
\(10\) 9.42226 2.97958
\(11\) 4.83308 1.45723 0.728615 0.684924i \(-0.240164\pi\)
0.728615 + 0.684924i \(0.240164\pi\)
\(12\) −8.51160 −2.45709
\(13\) 2.69395 0.747167 0.373584 0.927597i \(-0.378129\pi\)
0.373584 + 0.927597i \(0.378129\pi\)
\(14\) −13.1203 −3.50655
\(15\) 6.27805 1.62099
\(16\) 9.99834 2.49958
\(17\) 4.49415 1.08999 0.544996 0.838438i \(-0.316531\pi\)
0.544996 + 0.838438i \(0.316531\pi\)
\(18\) −0.134234 −0.0316392
\(19\) −4.49596 −1.03144 −0.515722 0.856756i \(-0.672476\pi\)
−0.515722 + 0.856756i \(0.672476\pi\)
\(20\) −17.5132 −3.91607
\(21\) −8.74206 −1.90767
\(22\) −12.6704 −2.70134
\(23\) −1.03340 −0.215479 −0.107740 0.994179i \(-0.534361\pi\)
−0.107740 + 0.994179i \(0.534361\pi\)
\(24\) 13.1553 2.68532
\(25\) 7.91749 1.58350
\(26\) −7.06245 −1.38506
\(27\) 5.15087 0.991285
\(28\) 24.3868 4.60866
\(29\) 5.52907 1.02672 0.513361 0.858173i \(-0.328400\pi\)
0.513361 + 0.858173i \(0.328400\pi\)
\(30\) −16.4585 −3.00490
\(31\) 7.30673 1.31233 0.656164 0.754619i \(-0.272178\pi\)
0.656164 + 0.754619i \(0.272178\pi\)
\(32\) −11.1491 −1.97091
\(33\) −8.44228 −1.46961
\(34\) −11.7819 −2.02057
\(35\) −17.9874 −3.04042
\(36\) 0.249501 0.0415835
\(37\) 7.95655 1.30805 0.654024 0.756474i \(-0.273079\pi\)
0.654024 + 0.756474i \(0.273079\pi\)
\(38\) 11.7866 1.91204
\(39\) −4.70571 −0.753516
\(40\) 27.0680 4.27982
\(41\) 10.5430 1.64655 0.823273 0.567646i \(-0.192146\pi\)
0.823273 + 0.567646i \(0.192146\pi\)
\(42\) 22.9182 3.53635
\(43\) 11.3587 1.73218 0.866091 0.499887i \(-0.166625\pi\)
0.866091 + 0.499887i \(0.166625\pi\)
\(44\) 23.5505 3.55037
\(45\) −0.184029 −0.0274334
\(46\) 2.70917 0.399445
\(47\) −1.42485 −0.207835 −0.103918 0.994586i \(-0.533138\pi\)
−0.103918 + 0.994586i \(0.533138\pi\)
\(48\) −17.4648 −2.52083
\(49\) 18.0470 2.57815
\(50\) −20.7565 −2.93541
\(51\) −7.85025 −1.09926
\(52\) 13.1270 1.82039
\(53\) −2.96560 −0.407357 −0.203678 0.979038i \(-0.565290\pi\)
−0.203678 + 0.979038i \(0.565290\pi\)
\(54\) −13.5035 −1.83759
\(55\) −17.3705 −2.34224
\(56\) −37.6916 −5.03676
\(57\) 7.85340 1.04021
\(58\) −14.4950 −1.90329
\(59\) 5.22309 0.679988 0.339994 0.940428i \(-0.389575\pi\)
0.339994 + 0.940428i \(0.389575\pi\)
\(60\) 30.5915 3.94934
\(61\) 10.0176 1.28262 0.641311 0.767281i \(-0.278391\pi\)
0.641311 + 0.767281i \(0.278391\pi\)
\(62\) −19.1553 −2.43273
\(63\) 0.256256 0.0322853
\(64\) 9.23185 1.15398
\(65\) −9.68230 −1.20094
\(66\) 22.1323 2.72429
\(67\) 1.46016 0.178387 0.0891936 0.996014i \(-0.471571\pi\)
0.0891936 + 0.996014i \(0.471571\pi\)
\(68\) 21.8990 2.65564
\(69\) 1.80512 0.217311
\(70\) 47.1556 5.63617
\(71\) 4.84033 0.574441 0.287220 0.957864i \(-0.407269\pi\)
0.287220 + 0.957864i \(0.407269\pi\)
\(72\) −0.385623 −0.0454461
\(73\) −0.166246 −0.0194577 −0.00972884 0.999953i \(-0.503097\pi\)
−0.00972884 + 0.999953i \(0.503097\pi\)
\(74\) −20.8589 −2.42479
\(75\) −13.8300 −1.59696
\(76\) −21.9078 −2.51299
\(77\) 24.1881 2.75650
\(78\) 12.3365 1.39683
\(79\) −6.67132 −0.750582 −0.375291 0.926907i \(-0.622457\pi\)
−0.375291 + 0.926907i \(0.622457\pi\)
\(80\) −35.9349 −4.01765
\(81\) −9.15099 −1.01678
\(82\) −27.6396 −3.05228
\(83\) 3.94157 0.432643 0.216322 0.976322i \(-0.430594\pi\)
0.216322 + 0.976322i \(0.430594\pi\)
\(84\) −42.5980 −4.64783
\(85\) −16.1524 −1.75197
\(86\) −29.7779 −3.21103
\(87\) −9.65801 −1.03545
\(88\) −36.3991 −3.88016
\(89\) −12.1444 −1.28731 −0.643653 0.765318i \(-0.722582\pi\)
−0.643653 + 0.765318i \(0.722582\pi\)
\(90\) 0.482449 0.0508546
\(91\) 13.4824 1.41334
\(92\) −5.03553 −0.524991
\(93\) −12.7632 −1.32348
\(94\) 3.73537 0.385274
\(95\) 16.1589 1.65787
\(96\) 19.4750 1.98765
\(97\) −5.94555 −0.603679 −0.301840 0.953359i \(-0.597601\pi\)
−0.301840 + 0.953359i \(0.597601\pi\)
\(98\) −47.3121 −4.77924
\(99\) 0.247469 0.0248716
\(100\) 38.5801 3.85801
\(101\) −6.31979 −0.628842 −0.314421 0.949284i \(-0.601810\pi\)
−0.314421 + 0.949284i \(0.601810\pi\)
\(102\) 20.5802 2.03774
\(103\) 11.4102 1.12428 0.562141 0.827041i \(-0.309978\pi\)
0.562141 + 0.827041i \(0.309978\pi\)
\(104\) −20.2888 −1.98948
\(105\) 31.4198 3.06626
\(106\) 7.77461 0.755137
\(107\) −3.19930 −0.309288 −0.154644 0.987970i \(-0.549423\pi\)
−0.154644 + 0.987970i \(0.549423\pi\)
\(108\) 25.0990 2.41515
\(109\) 16.7146 1.60097 0.800486 0.599352i \(-0.204575\pi\)
0.800486 + 0.599352i \(0.204575\pi\)
\(110\) 45.5386 4.34193
\(111\) −13.8983 −1.31916
\(112\) 50.0387 4.72821
\(113\) −20.1898 −1.89930 −0.949649 0.313317i \(-0.898560\pi\)
−0.949649 + 0.313317i \(0.898560\pi\)
\(114\) −20.5884 −1.92828
\(115\) 3.71414 0.346346
\(116\) 26.9419 2.50149
\(117\) 0.137939 0.0127524
\(118\) −13.6928 −1.26053
\(119\) 22.4919 2.06183
\(120\) −47.2815 −4.31619
\(121\) 12.3587 1.12352
\(122\) −26.2621 −2.37766
\(123\) −18.4162 −1.66054
\(124\) 35.6040 3.19733
\(125\) −10.4857 −0.937873
\(126\) −0.671801 −0.0598488
\(127\) −1.67283 −0.148439 −0.0742196 0.997242i \(-0.523647\pi\)
−0.0742196 + 0.997242i \(0.523647\pi\)
\(128\) −1.90391 −0.168284
\(129\) −19.8410 −1.74690
\(130\) 25.3831 2.22624
\(131\) 10.4782 0.915483 0.457741 0.889085i \(-0.348659\pi\)
0.457741 + 0.889085i \(0.348659\pi\)
\(132\) −41.1373 −3.58054
\(133\) −22.5009 −1.95108
\(134\) −3.82796 −0.330685
\(135\) −18.5127 −1.59332
\(136\) −33.8466 −2.90232
\(137\) −2.12717 −0.181736 −0.0908681 0.995863i \(-0.528964\pi\)
−0.0908681 + 0.995863i \(0.528964\pi\)
\(138\) −4.73229 −0.402839
\(139\) 11.8479 1.00493 0.502463 0.864599i \(-0.332427\pi\)
0.502463 + 0.864599i \(0.332427\pi\)
\(140\) −87.6483 −7.40763
\(141\) 2.48888 0.209601
\(142\) −12.6894 −1.06487
\(143\) 13.0201 1.08879
\(144\) 0.511946 0.0426622
\(145\) −19.8720 −1.65028
\(146\) 0.435831 0.0360696
\(147\) −31.5240 −2.60006
\(148\) 38.7704 3.18691
\(149\) 6.58977 0.539855 0.269927 0.962881i \(-0.413000\pi\)
0.269927 + 0.962881i \(0.413000\pi\)
\(150\) 36.2568 2.96035
\(151\) −20.3780 −1.65834 −0.829169 0.558998i \(-0.811186\pi\)
−0.829169 + 0.558998i \(0.811186\pi\)
\(152\) 33.8601 2.74642
\(153\) 0.230115 0.0186037
\(154\) −63.4116 −5.10985
\(155\) −26.2611 −2.10934
\(156\) −22.9298 −1.83586
\(157\) −16.0314 −1.27945 −0.639724 0.768605i \(-0.720951\pi\)
−0.639724 + 0.768605i \(0.720951\pi\)
\(158\) 17.4895 1.39139
\(159\) 5.18022 0.410818
\(160\) 40.0710 3.16789
\(161\) −5.17187 −0.407601
\(162\) 23.9902 1.88485
\(163\) −10.1731 −0.796818 −0.398409 0.917208i \(-0.630438\pi\)
−0.398409 + 0.917208i \(0.630438\pi\)
\(164\) 51.3738 4.01162
\(165\) 30.3423 2.36215
\(166\) −10.3332 −0.802012
\(167\) −14.4360 −1.11709 −0.558546 0.829474i \(-0.688641\pi\)
−0.558546 + 0.829474i \(0.688641\pi\)
\(168\) 65.8386 5.07956
\(169\) −5.74264 −0.441741
\(170\) 42.3451 3.24772
\(171\) −0.230207 −0.0176044
\(172\) 55.3482 4.22026
\(173\) 14.1050 1.07239 0.536193 0.844095i \(-0.319862\pi\)
0.536193 + 0.844095i \(0.319862\pi\)
\(174\) 25.3194 1.91946
\(175\) 39.6247 2.99535
\(176\) 48.3228 3.64247
\(177\) −9.12353 −0.685766
\(178\) 31.8378 2.38634
\(179\) 22.6885 1.69582 0.847908 0.530144i \(-0.177862\pi\)
0.847908 + 0.530144i \(0.177862\pi\)
\(180\) −0.896730 −0.0668383
\(181\) −13.4078 −0.996592 −0.498296 0.867007i \(-0.666041\pi\)
−0.498296 + 0.867007i \(0.666041\pi\)
\(182\) −35.3455 −2.61998
\(183\) −17.4984 −1.29352
\(184\) 7.78281 0.573756
\(185\) −28.5966 −2.10246
\(186\) 33.4599 2.45340
\(187\) 21.7206 1.58837
\(188\) −6.94295 −0.506367
\(189\) 25.7786 1.87511
\(190\) −42.3621 −3.07327
\(191\) −9.75439 −0.705803 −0.352901 0.935661i \(-0.614805\pi\)
−0.352901 + 0.935661i \(0.614805\pi\)
\(192\) −16.1259 −1.16379
\(193\) −23.0795 −1.66130 −0.830651 0.556793i \(-0.812032\pi\)
−0.830651 + 0.556793i \(0.812032\pi\)
\(194\) 15.5868 1.11907
\(195\) 16.9127 1.21115
\(196\) 87.9391 6.28136
\(197\) −15.4919 −1.10375 −0.551875 0.833927i \(-0.686087\pi\)
−0.551875 + 0.833927i \(0.686087\pi\)
\(198\) −0.648764 −0.0461057
\(199\) 0.714014 0.0506151 0.0253076 0.999680i \(-0.491943\pi\)
0.0253076 + 0.999680i \(0.491943\pi\)
\(200\) −59.6286 −4.21638
\(201\) −2.55057 −0.179903
\(202\) 16.5679 1.16572
\(203\) 27.6713 1.94215
\(204\) −38.2525 −2.67821
\(205\) −37.8926 −2.64654
\(206\) −29.9130 −2.08414
\(207\) −0.0529135 −0.00367774
\(208\) 26.9350 1.86761
\(209\) −21.7293 −1.50305
\(210\) −82.3700 −5.68407
\(211\) −2.03028 −0.139770 −0.0698852 0.997555i \(-0.522263\pi\)
−0.0698852 + 0.997555i \(0.522263\pi\)
\(212\) −14.4507 −0.992478
\(213\) −8.45493 −0.579322
\(214\) 8.38726 0.573342
\(215\) −40.8241 −2.78418
\(216\) −38.7924 −2.63949
\(217\) 36.5680 2.48240
\(218\) −43.8190 −2.96780
\(219\) 0.290394 0.0196230
\(220\) −84.6427 −5.70661
\(221\) 12.1070 0.814407
\(222\) 36.4356 2.44540
\(223\) −25.6355 −1.71668 −0.858340 0.513082i \(-0.828504\pi\)
−0.858340 + 0.513082i \(0.828504\pi\)
\(224\) −55.7981 −3.72817
\(225\) 0.405401 0.0270267
\(226\) 52.9295 3.52082
\(227\) 11.9297 0.791805 0.395903 0.918293i \(-0.370432\pi\)
0.395903 + 0.918293i \(0.370432\pi\)
\(228\) 38.2678 2.53435
\(229\) 24.6375 1.62809 0.814047 0.580798i \(-0.197260\pi\)
0.814047 + 0.580798i \(0.197260\pi\)
\(230\) −9.73699 −0.642038
\(231\) −42.2511 −2.77992
\(232\) −41.6408 −2.73385
\(233\) −1.05780 −0.0692990 −0.0346495 0.999400i \(-0.511031\pi\)
−0.0346495 + 0.999400i \(0.511031\pi\)
\(234\) −0.361620 −0.0236398
\(235\) 5.12103 0.334059
\(236\) 25.4509 1.65671
\(237\) 11.6533 0.756961
\(238\) −58.9647 −3.82211
\(239\) 20.6100 1.33315 0.666576 0.745437i \(-0.267759\pi\)
0.666576 + 0.745437i \(0.267759\pi\)
\(240\) 62.7701 4.05179
\(241\) 13.9640 0.899499 0.449750 0.893155i \(-0.351513\pi\)
0.449750 + 0.893155i \(0.351513\pi\)
\(242\) −32.3995 −2.08272
\(243\) 0.532061 0.0341317
\(244\) 48.8135 3.12496
\(245\) −64.8627 −4.14393
\(246\) 48.2800 3.07822
\(247\) −12.1119 −0.770661
\(248\) −55.0287 −3.49433
\(249\) −6.88501 −0.436320
\(250\) 27.4894 1.73858
\(251\) 16.4612 1.03902 0.519509 0.854465i \(-0.326115\pi\)
0.519509 + 0.854465i \(0.326115\pi\)
\(252\) 1.24868 0.0786594
\(253\) −4.99452 −0.314003
\(254\) 4.38547 0.275169
\(255\) 28.2145 1.76686
\(256\) −13.4724 −0.842025
\(257\) 6.16096 0.384310 0.192155 0.981365i \(-0.438452\pi\)
0.192155 + 0.981365i \(0.438452\pi\)
\(258\) 52.0151 3.23832
\(259\) 39.8202 2.47430
\(260\) −47.1796 −2.92596
\(261\) 0.283106 0.0175238
\(262\) −27.4696 −1.69707
\(263\) −21.7710 −1.34246 −0.671229 0.741250i \(-0.734233\pi\)
−0.671229 + 0.741250i \(0.734233\pi\)
\(264\) 63.5809 3.91313
\(265\) 10.6586 0.654755
\(266\) 58.9884 3.61681
\(267\) 21.2135 1.29824
\(268\) 7.11503 0.434620
\(269\) −27.1690 −1.65652 −0.828262 0.560341i \(-0.810670\pi\)
−0.828262 + 0.560341i \(0.810670\pi\)
\(270\) 48.5328 2.95361
\(271\) 10.7469 0.652830 0.326415 0.945227i \(-0.394159\pi\)
0.326415 + 0.945227i \(0.394159\pi\)
\(272\) 44.9341 2.72453
\(273\) −23.5507 −1.42535
\(274\) 5.57657 0.336893
\(275\) 38.2659 2.30752
\(276\) 8.79592 0.529452
\(277\) 12.9230 0.776469 0.388234 0.921561i \(-0.373085\pi\)
0.388234 + 0.921561i \(0.373085\pi\)
\(278\) −31.0604 −1.86288
\(279\) 0.374127 0.0223984
\(280\) 135.467 8.09571
\(281\) −21.7945 −1.30015 −0.650075 0.759870i \(-0.725263\pi\)
−0.650075 + 0.759870i \(0.725263\pi\)
\(282\) −6.52483 −0.388548
\(283\) −13.5466 −0.805259 −0.402630 0.915363i \(-0.631904\pi\)
−0.402630 + 0.915363i \(0.631904\pi\)
\(284\) 23.5858 1.39956
\(285\) −28.2258 −1.67195
\(286\) −34.1334 −2.01835
\(287\) 52.7647 3.11460
\(288\) −0.570870 −0.0336389
\(289\) 3.19743 0.188084
\(290\) 52.0963 3.05920
\(291\) 10.3855 0.608809
\(292\) −0.810080 −0.0474064
\(293\) −18.3408 −1.07148 −0.535742 0.844382i \(-0.679968\pi\)
−0.535742 + 0.844382i \(0.679968\pi\)
\(294\) 82.6433 4.81985
\(295\) −18.7722 −1.09296
\(296\) −59.9227 −3.48294
\(297\) 24.8946 1.44453
\(298\) −17.2757 −1.00075
\(299\) −2.78394 −0.160999
\(300\) −67.3906 −3.89080
\(301\) 56.8468 3.27659
\(302\) 53.4229 3.07414
\(303\) 11.0392 0.634186
\(304\) −44.9521 −2.57818
\(305\) −36.0042 −2.06159
\(306\) −0.603268 −0.0344865
\(307\) −11.7553 −0.670913 −0.335457 0.942056i \(-0.608891\pi\)
−0.335457 + 0.942056i \(0.608891\pi\)
\(308\) 117.863 6.71588
\(309\) −19.9310 −1.13384
\(310\) 68.8459 3.91018
\(311\) 5.02533 0.284960 0.142480 0.989798i \(-0.454492\pi\)
0.142480 + 0.989798i \(0.454492\pi\)
\(312\) 35.4398 2.00639
\(313\) −28.9391 −1.63574 −0.817868 0.575406i \(-0.804844\pi\)
−0.817868 + 0.575406i \(0.804844\pi\)
\(314\) 42.0279 2.37177
\(315\) −0.921009 −0.0518930
\(316\) −32.5078 −1.82871
\(317\) 8.02755 0.450872 0.225436 0.974258i \(-0.427619\pi\)
0.225436 + 0.974258i \(0.427619\pi\)
\(318\) −13.5805 −0.761554
\(319\) 26.7225 1.49617
\(320\) −33.1801 −1.85482
\(321\) 5.58843 0.311916
\(322\) 13.5586 0.755590
\(323\) −20.2055 −1.12427
\(324\) −44.5906 −2.47726
\(325\) 21.3293 1.18314
\(326\) 26.6698 1.47710
\(327\) −29.1966 −1.61458
\(328\) −79.4021 −4.38425
\(329\) −7.13093 −0.393141
\(330\) −79.5454 −4.37883
\(331\) −3.64933 −0.200585 −0.100293 0.994958i \(-0.531978\pi\)
−0.100293 + 0.994958i \(0.531978\pi\)
\(332\) 19.2064 1.05409
\(333\) 0.407400 0.0223254
\(334\) 37.8454 2.07081
\(335\) −5.24796 −0.286727
\(336\) −87.4061 −4.76839
\(337\) −25.3134 −1.37891 −0.689453 0.724330i \(-0.742149\pi\)
−0.689453 + 0.724330i \(0.742149\pi\)
\(338\) 15.0549 0.818877
\(339\) 35.2669 1.91544
\(340\) −78.7069 −4.26848
\(341\) 35.3140 1.91236
\(342\) 0.603510 0.0326341
\(343\) 55.2872 2.98523
\(344\) −85.5449 −4.61227
\(345\) −6.48775 −0.349289
\(346\) −36.9777 −1.98793
\(347\) 22.6162 1.21410 0.607051 0.794663i \(-0.292352\pi\)
0.607051 + 0.794663i \(0.292352\pi\)
\(348\) −47.0612 −2.52275
\(349\) 18.6963 1.00079 0.500396 0.865797i \(-0.333188\pi\)
0.500396 + 0.865797i \(0.333188\pi\)
\(350\) −103.880 −5.55262
\(351\) 13.8762 0.740656
\(352\) −53.8847 −2.87206
\(353\) 13.9921 0.744723 0.372362 0.928088i \(-0.378548\pi\)
0.372362 + 0.928088i \(0.378548\pi\)
\(354\) 23.9182 1.27124
\(355\) −17.3966 −0.923314
\(356\) −59.1769 −3.13637
\(357\) −39.2882 −2.07935
\(358\) −59.4800 −3.14362
\(359\) −15.7751 −0.832578 −0.416289 0.909232i \(-0.636670\pi\)
−0.416289 + 0.909232i \(0.636670\pi\)
\(360\) 1.38596 0.0730468
\(361\) 1.21363 0.0638755
\(362\) 35.1498 1.84743
\(363\) −21.5878 −1.13307
\(364\) 65.6967 3.44344
\(365\) 0.597505 0.0312748
\(366\) 45.8738 2.39786
\(367\) 25.0061 1.30531 0.652654 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(368\) −10.3323 −0.538609
\(369\) 0.539836 0.0281028
\(370\) 74.9686 3.89743
\(371\) −14.8420 −0.770556
\(372\) −62.1920 −3.22450
\(373\) −18.2775 −0.946373 −0.473187 0.880962i \(-0.656896\pi\)
−0.473187 + 0.880962i \(0.656896\pi\)
\(374\) −56.9427 −2.94444
\(375\) 18.3162 0.945843
\(376\) 10.7309 0.553402
\(377\) 14.8950 0.767133
\(378\) −67.5810 −3.47599
\(379\) 1.91196 0.0982107 0.0491054 0.998794i \(-0.484363\pi\)
0.0491054 + 0.998794i \(0.484363\pi\)
\(380\) 78.7385 4.03920
\(381\) 2.92204 0.149701
\(382\) 25.5721 1.30838
\(383\) −8.87430 −0.453456 −0.226728 0.973958i \(-0.572803\pi\)
−0.226728 + 0.973958i \(0.572803\pi\)
\(384\) 3.32570 0.169714
\(385\) −86.9344 −4.43059
\(386\) 60.5053 3.07964
\(387\) 0.581600 0.0295644
\(388\) −28.9713 −1.47080
\(389\) 21.5022 1.09021 0.545103 0.838369i \(-0.316491\pi\)
0.545103 + 0.838369i \(0.316491\pi\)
\(390\) −44.3384 −2.24516
\(391\) −4.64427 −0.234871
\(392\) −135.917 −6.86483
\(393\) −18.3030 −0.923262
\(394\) 40.6134 2.04607
\(395\) 23.9773 1.20643
\(396\) 1.20586 0.0605967
\(397\) −0.646998 −0.0324719 −0.0162359 0.999868i \(-0.505168\pi\)
−0.0162359 + 0.999868i \(0.505168\pi\)
\(398\) −1.87186 −0.0938277
\(399\) 39.3039 1.96766
\(400\) 79.1618 3.95809
\(401\) 2.92636 0.146135 0.0730677 0.997327i \(-0.476721\pi\)
0.0730677 + 0.997327i \(0.476721\pi\)
\(402\) 6.68656 0.333495
\(403\) 19.6840 0.980528
\(404\) −30.7949 −1.53210
\(405\) 32.8895 1.63429
\(406\) −72.5431 −3.60025
\(407\) 38.4547 1.90613
\(408\) 59.1221 2.92698
\(409\) 5.97515 0.295452 0.147726 0.989028i \(-0.452805\pi\)
0.147726 + 0.989028i \(0.452805\pi\)
\(410\) 99.3392 4.90601
\(411\) 3.71567 0.183280
\(412\) 55.5994 2.73918
\(413\) 26.1400 1.28626
\(414\) 0.138718 0.00681761
\(415\) −14.1664 −0.695399
\(416\) −30.0352 −1.47260
\(417\) −20.6956 −1.01347
\(418\) 56.9656 2.78628
\(419\) −1.92065 −0.0938298 −0.0469149 0.998899i \(-0.514939\pi\)
−0.0469149 + 0.998899i \(0.514939\pi\)
\(420\) 153.101 7.47058
\(421\) −26.6011 −1.29646 −0.648228 0.761446i \(-0.724490\pi\)
−0.648228 + 0.761446i \(0.724490\pi\)
\(422\) 5.32258 0.259099
\(423\) −0.0729566 −0.00354727
\(424\) 22.3347 1.08467
\(425\) 35.5824 1.72600
\(426\) 22.1654 1.07392
\(427\) 50.1351 2.42621
\(428\) −15.5894 −0.753544
\(429\) −22.7431 −1.09805
\(430\) 107.024 5.16117
\(431\) 21.1280 1.01770 0.508850 0.860855i \(-0.330071\pi\)
0.508850 + 0.860855i \(0.330071\pi\)
\(432\) 51.5001 2.47780
\(433\) 27.8264 1.33725 0.668625 0.743600i \(-0.266883\pi\)
0.668625 + 0.743600i \(0.266883\pi\)
\(434\) −95.8666 −4.60174
\(435\) 34.7118 1.66430
\(436\) 81.4465 3.90058
\(437\) 4.64614 0.222255
\(438\) −0.761296 −0.0363761
\(439\) −12.1390 −0.579362 −0.289681 0.957123i \(-0.593549\pi\)
−0.289681 + 0.957123i \(0.593549\pi\)
\(440\) 130.822 6.23668
\(441\) 0.924065 0.0440031
\(442\) −31.7397 −1.50971
\(443\) −21.0719 −1.00116 −0.500579 0.865691i \(-0.666879\pi\)
−0.500579 + 0.865691i \(0.666879\pi\)
\(444\) −67.7230 −3.21399
\(445\) 43.6481 2.06912
\(446\) 67.2059 3.18229
\(447\) −11.5108 −0.544442
\(448\) 46.2026 2.18287
\(449\) 8.85250 0.417775 0.208888 0.977940i \(-0.433016\pi\)
0.208888 + 0.977940i \(0.433016\pi\)
\(450\) −1.06280 −0.0501007
\(451\) 50.9554 2.39939
\(452\) −98.3803 −4.62742
\(453\) 35.5957 1.67243
\(454\) −31.2750 −1.46781
\(455\) −48.4570 −2.27170
\(456\) −59.1459 −2.76976
\(457\) −9.49040 −0.443942 −0.221971 0.975053i \(-0.571249\pi\)
−0.221971 + 0.975053i \(0.571249\pi\)
\(458\) −64.5897 −3.01808
\(459\) 23.1488 1.08049
\(460\) 18.0982 0.843832
\(461\) 5.91355 0.275422 0.137711 0.990472i \(-0.456026\pi\)
0.137711 + 0.990472i \(0.456026\pi\)
\(462\) 110.765 5.15327
\(463\) −1.20527 −0.0560137 −0.0280068 0.999608i \(-0.508916\pi\)
−0.0280068 + 0.999608i \(0.508916\pi\)
\(464\) 55.2815 2.56638
\(465\) 45.8720 2.12726
\(466\) 2.77313 0.128463
\(467\) 16.7156 0.773506 0.386753 0.922183i \(-0.373597\pi\)
0.386753 + 0.922183i \(0.373597\pi\)
\(468\) 0.672143 0.0310698
\(469\) 7.30768 0.337437
\(470\) −13.4253 −0.619262
\(471\) 28.0032 1.29032
\(472\) −39.3363 −1.81060
\(473\) 54.8974 2.52419
\(474\) −30.5501 −1.40321
\(475\) −35.5967 −1.63329
\(476\) 109.598 5.02341
\(477\) −0.151848 −0.00695265
\(478\) −54.0312 −2.47133
\(479\) −17.9870 −0.821848 −0.410924 0.911670i \(-0.634794\pi\)
−0.410924 + 0.911670i \(0.634794\pi\)
\(480\) −69.9948 −3.19481
\(481\) 21.4345 0.977331
\(482\) −36.6079 −1.66745
\(483\) 9.03407 0.411065
\(484\) 60.2211 2.73732
\(485\) 21.3689 0.970310
\(486\) −1.39485 −0.0632716
\(487\) 17.1059 0.775144 0.387572 0.921839i \(-0.373314\pi\)
0.387572 + 0.921839i \(0.373314\pi\)
\(488\) −75.4450 −3.41523
\(489\) 17.7701 0.803589
\(490\) 170.044 7.68180
\(491\) −24.2680 −1.09520 −0.547599 0.836741i \(-0.684458\pi\)
−0.547599 + 0.836741i \(0.684458\pi\)
\(492\) −89.7381 −4.04571
\(493\) 24.8485 1.11912
\(494\) 31.7525 1.42861
\(495\) −0.889426 −0.0399767
\(496\) 73.0552 3.28027
\(497\) 24.2244 1.08661
\(498\) 18.0497 0.808827
\(499\) −16.9863 −0.760413 −0.380206 0.924902i \(-0.624147\pi\)
−0.380206 + 0.924902i \(0.624147\pi\)
\(500\) −51.0946 −2.28502
\(501\) 25.2164 1.12658
\(502\) −43.1545 −1.92608
\(503\) −15.2632 −0.680552 −0.340276 0.940326i \(-0.610520\pi\)
−0.340276 + 0.940326i \(0.610520\pi\)
\(504\) −1.92993 −0.0859659
\(505\) 22.7139 1.01075
\(506\) 13.0936 0.582083
\(507\) 10.0311 0.445495
\(508\) −8.15129 −0.361655
\(509\) −0.311340 −0.0137999 −0.00689996 0.999976i \(-0.502196\pi\)
−0.00689996 + 0.999976i \(0.502196\pi\)
\(510\) −73.9671 −3.27532
\(511\) −0.832014 −0.0368061
\(512\) 39.1270 1.72919
\(513\) −23.1581 −1.02245
\(514\) −16.1515 −0.712414
\(515\) −41.0094 −1.80709
\(516\) −96.6805 −4.25612
\(517\) −6.88640 −0.302864
\(518\) −104.392 −4.58674
\(519\) −24.6383 −1.08150
\(520\) 72.9198 3.19774
\(521\) 8.09571 0.354680 0.177340 0.984150i \(-0.443251\pi\)
0.177340 + 0.984150i \(0.443251\pi\)
\(522\) −0.742189 −0.0324847
\(523\) −1.50381 −0.0657570 −0.0328785 0.999459i \(-0.510467\pi\)
−0.0328785 + 0.999459i \(0.510467\pi\)
\(524\) 51.0577 2.23047
\(525\) −69.2152 −3.02080
\(526\) 57.0748 2.48858
\(527\) 32.8376 1.43043
\(528\) −84.4088 −3.67342
\(529\) −21.9321 −0.953569
\(530\) −27.9427 −1.21375
\(531\) 0.267438 0.0116058
\(532\) −109.642 −4.75358
\(533\) 28.4024 1.23024
\(534\) −55.6132 −2.40662
\(535\) 11.4986 0.497126
\(536\) −10.9968 −0.474991
\(537\) −39.6315 −1.71023
\(538\) 71.2262 3.07078
\(539\) 87.2229 3.75696
\(540\) −90.2081 −3.88194
\(541\) 27.3025 1.17382 0.586912 0.809651i \(-0.300343\pi\)
0.586912 + 0.809651i \(0.300343\pi\)
\(542\) −28.1741 −1.21018
\(543\) 23.4203 1.00506
\(544\) −50.1059 −2.14827
\(545\) −60.0739 −2.57328
\(546\) 61.7404 2.64224
\(547\) 7.56196 0.323326 0.161663 0.986846i \(-0.448314\pi\)
0.161663 + 0.986846i \(0.448314\pi\)
\(548\) −10.3652 −0.442779
\(549\) 0.512933 0.0218914
\(550\) −100.318 −4.27757
\(551\) −24.8585 −1.05901
\(552\) −13.5948 −0.578632
\(553\) −33.3880 −1.41980
\(554\) −33.8789 −1.43938
\(555\) 49.9516 2.12033
\(556\) 57.7321 2.44839
\(557\) −5.45719 −0.231229 −0.115614 0.993294i \(-0.536884\pi\)
−0.115614 + 0.993294i \(0.536884\pi\)
\(558\) −0.980811 −0.0415210
\(559\) 30.5997 1.29423
\(560\) −179.844 −7.59979
\(561\) −37.9409 −1.60187
\(562\) 57.1364 2.41015
\(563\) 12.2065 0.514444 0.257222 0.966352i \(-0.417193\pi\)
0.257222 + 0.966352i \(0.417193\pi\)
\(564\) 12.1277 0.510670
\(565\) 72.5640 3.05279
\(566\) 35.5136 1.49275
\(567\) −45.7980 −1.92333
\(568\) −36.4537 −1.52956
\(569\) −2.95666 −0.123950 −0.0619748 0.998078i \(-0.519740\pi\)
−0.0619748 + 0.998078i \(0.519740\pi\)
\(570\) 73.9968 3.09938
\(571\) −25.8570 −1.08208 −0.541041 0.840996i \(-0.681970\pi\)
−0.541041 + 0.840996i \(0.681970\pi\)
\(572\) 63.4439 2.65272
\(573\) 17.0387 0.711800
\(574\) −138.328 −5.77369
\(575\) −8.18196 −0.341211
\(576\) 0.472699 0.0196958
\(577\) −8.12175 −0.338113 −0.169056 0.985606i \(-0.554072\pi\)
−0.169056 + 0.985606i \(0.554072\pi\)
\(578\) −8.38237 −0.348661
\(579\) 40.3146 1.67542
\(580\) −96.8316 −4.02071
\(581\) 19.7264 0.818388
\(582\) −27.2266 −1.12858
\(583\) −14.3330 −0.593612
\(584\) 1.25204 0.0518099
\(585\) −0.495764 −0.0204973
\(586\) 48.0823 1.98626
\(587\) −22.7370 −0.938458 −0.469229 0.883077i \(-0.655468\pi\)
−0.469229 + 0.883077i \(0.655468\pi\)
\(588\) −153.609 −6.33474
\(589\) −32.8507 −1.35359
\(590\) 49.2133 2.02608
\(591\) 27.0607 1.11313
\(592\) 79.5523 3.26958
\(593\) 21.4016 0.878860 0.439430 0.898277i \(-0.355180\pi\)
0.439430 + 0.898277i \(0.355180\pi\)
\(594\) −65.2635 −2.67780
\(595\) −80.8380 −3.31403
\(596\) 32.1104 1.31529
\(597\) −1.24722 −0.0510452
\(598\) 7.29836 0.298452
\(599\) 5.52344 0.225682 0.112841 0.993613i \(-0.464005\pi\)
0.112841 + 0.993613i \(0.464005\pi\)
\(600\) 104.157 4.25221
\(601\) −13.6050 −0.554959 −0.277479 0.960732i \(-0.589499\pi\)
−0.277479 + 0.960732i \(0.589499\pi\)
\(602\) −149.029 −6.07398
\(603\) 0.0747649 0.00304466
\(604\) −99.2973 −4.04035
\(605\) −44.4183 −1.80586
\(606\) −28.9404 −1.17562
\(607\) −28.2370 −1.14610 −0.573052 0.819519i \(-0.694241\pi\)
−0.573052 + 0.819519i \(0.694241\pi\)
\(608\) 50.1260 2.03288
\(609\) −48.3355 −1.95865
\(610\) 94.3884 3.82168
\(611\) −3.83846 −0.155288
\(612\) 1.12130 0.0453257
\(613\) −20.4912 −0.827634 −0.413817 0.910360i \(-0.635805\pi\)
−0.413817 + 0.910360i \(0.635805\pi\)
\(614\) 30.8178 1.24370
\(615\) 66.1897 2.66903
\(616\) −182.167 −7.33971
\(617\) 22.5927 0.909548 0.454774 0.890607i \(-0.349720\pi\)
0.454774 + 0.890607i \(0.349720\pi\)
\(618\) 52.2511 2.10185
\(619\) −13.9119 −0.559167 −0.279583 0.960121i \(-0.590196\pi\)
−0.279583 + 0.960121i \(0.590196\pi\)
\(620\) −127.964 −5.13916
\(621\) −5.32292 −0.213602
\(622\) −13.1744 −0.528245
\(623\) −60.7792 −2.43507
\(624\) −47.0493 −1.88348
\(625\) −1.90075 −0.0760301
\(626\) 75.8667 3.03224
\(627\) 37.9561 1.51582
\(628\) −78.1175 −3.11723
\(629\) 35.7580 1.42576
\(630\) 2.41451 0.0961966
\(631\) 23.0393 0.917181 0.458590 0.888648i \(-0.348355\pi\)
0.458590 + 0.888648i \(0.348355\pi\)
\(632\) 50.2433 1.99857
\(633\) 3.54643 0.140958
\(634\) −21.0450 −0.835803
\(635\) 6.01229 0.238590
\(636\) 25.2420 1.00091
\(637\) 48.6178 1.92631
\(638\) −70.0555 −2.77352
\(639\) 0.247840 0.00980439
\(640\) 6.84284 0.270487
\(641\) 44.0942 1.74162 0.870808 0.491623i \(-0.163596\pi\)
0.870808 + 0.491623i \(0.163596\pi\)
\(642\) −14.6506 −0.578214
\(643\) −10.7601 −0.424336 −0.212168 0.977233i \(-0.568052\pi\)
−0.212168 + 0.977233i \(0.568052\pi\)
\(644\) −25.2014 −0.993072
\(645\) 71.3103 2.80784
\(646\) 52.9707 2.08411
\(647\) 36.2437 1.42489 0.712443 0.701730i \(-0.247589\pi\)
0.712443 + 0.701730i \(0.247589\pi\)
\(648\) 68.9183 2.70737
\(649\) 25.2436 0.990898
\(650\) −55.9169 −2.19324
\(651\) −63.8759 −2.50349
\(652\) −49.5711 −1.94136
\(653\) 34.5179 1.35079 0.675396 0.737456i \(-0.263973\pi\)
0.675396 + 0.737456i \(0.263973\pi\)
\(654\) 76.5417 2.99302
\(655\) −37.6595 −1.47148
\(656\) 105.413 4.11568
\(657\) −0.00851234 −0.000332098 0
\(658\) 18.6944 0.728785
\(659\) −12.2573 −0.477478 −0.238739 0.971084i \(-0.576734\pi\)
−0.238739 + 0.971084i \(0.576734\pi\)
\(660\) 147.851 5.75510
\(661\) 6.76439 0.263104 0.131552 0.991309i \(-0.458004\pi\)
0.131552 + 0.991309i \(0.458004\pi\)
\(662\) 9.56706 0.371834
\(663\) −21.1482 −0.821327
\(664\) −29.6849 −1.15200
\(665\) 80.8704 3.13602
\(666\) −1.06804 −0.0413857
\(667\) −5.71376 −0.221238
\(668\) −70.3433 −2.72167
\(669\) 44.7793 1.73127
\(670\) 13.7580 0.531519
\(671\) 48.4159 1.86908
\(672\) 97.4664 3.75985
\(673\) −16.3569 −0.630514 −0.315257 0.949006i \(-0.602091\pi\)
−0.315257 + 0.949006i \(0.602091\pi\)
\(674\) 66.3614 2.55615
\(675\) 40.7820 1.56970
\(676\) −27.9825 −1.07625
\(677\) −47.1334 −1.81148 −0.905742 0.423829i \(-0.860686\pi\)
−0.905742 + 0.423829i \(0.860686\pi\)
\(678\) −92.4557 −3.55074
\(679\) −29.7557 −1.14192
\(680\) 121.648 4.66497
\(681\) −20.8385 −0.798534
\(682\) −92.5792 −3.54504
\(683\) −38.1299 −1.45900 −0.729499 0.683982i \(-0.760247\pi\)
−0.729499 + 0.683982i \(0.760247\pi\)
\(684\) −1.12175 −0.0428910
\(685\) 7.64523 0.292109
\(686\) −144.941 −5.53386
\(687\) −43.0361 −1.64193
\(688\) 113.568 4.32974
\(689\) −7.98918 −0.304364
\(690\) 17.0083 0.647494
\(691\) −27.6199 −1.05071 −0.525356 0.850883i \(-0.676068\pi\)
−0.525356 + 0.850883i \(0.676068\pi\)
\(692\) 68.7306 2.61275
\(693\) 1.23851 0.0470471
\(694\) −59.2906 −2.25064
\(695\) −42.5825 −1.61525
\(696\) 72.7368 2.75708
\(697\) 47.3820 1.79472
\(698\) −49.0143 −1.85522
\(699\) 1.84774 0.0698879
\(700\) 193.082 7.29782
\(701\) −51.1254 −1.93098 −0.965490 0.260441i \(-0.916132\pi\)
−0.965490 + 0.260441i \(0.916132\pi\)
\(702\) −36.3777 −1.37299
\(703\) −35.7723 −1.34918
\(704\) 44.6183 1.68161
\(705\) −8.94526 −0.336898
\(706\) −36.6816 −1.38053
\(707\) −31.6287 −1.18952
\(708\) −44.4568 −1.67079
\(709\) 6.24782 0.234642 0.117321 0.993094i \(-0.462569\pi\)
0.117321 + 0.993094i \(0.462569\pi\)
\(710\) 45.6068 1.71159
\(711\) −0.341593 −0.0128107
\(712\) 91.4625 3.42770
\(713\) −7.55080 −0.282780
\(714\) 102.998 3.85459
\(715\) −46.7954 −1.75005
\(716\) 110.556 4.13166
\(717\) −36.0010 −1.34448
\(718\) 41.3559 1.54339
\(719\) 28.1094 1.04830 0.524152 0.851625i \(-0.324382\pi\)
0.524152 + 0.851625i \(0.324382\pi\)
\(720\) −1.83998 −0.0685721
\(721\) 57.1048 2.12669
\(722\) −3.18166 −0.118409
\(723\) −24.3919 −0.907143
\(724\) −65.3330 −2.42808
\(725\) 43.7764 1.62581
\(726\) 56.5945 2.10042
\(727\) −34.0068 −1.26124 −0.630621 0.776091i \(-0.717200\pi\)
−0.630621 + 0.776091i \(0.717200\pi\)
\(728\) −101.539 −3.76330
\(729\) 26.5236 0.982355
\(730\) −1.56642 −0.0579757
\(731\) 51.0476 1.88807
\(732\) −85.2659 −3.15152
\(733\) −1.37261 −0.0506984 −0.0253492 0.999679i \(-0.508070\pi\)
−0.0253492 + 0.999679i \(0.508070\pi\)
\(734\) −65.5559 −2.41971
\(735\) 113.300 4.17914
\(736\) 11.5215 0.424690
\(737\) 7.05709 0.259951
\(738\) −1.41523 −0.0520954
\(739\) −51.5090 −1.89479 −0.947394 0.320070i \(-0.896294\pi\)
−0.947394 + 0.320070i \(0.896294\pi\)
\(740\) −139.344 −5.12240
\(741\) 21.1567 0.777210
\(742\) 38.9096 1.42842
\(743\) 8.77792 0.322031 0.161015 0.986952i \(-0.448523\pi\)
0.161015 + 0.986952i \(0.448523\pi\)
\(744\) 96.1225 3.52402
\(745\) −23.6842 −0.867723
\(746\) 47.9162 1.75434
\(747\) 0.201821 0.00738423
\(748\) 105.840 3.86988
\(749\) −16.0115 −0.585048
\(750\) −48.0176 −1.75336
\(751\) −47.4783 −1.73251 −0.866255 0.499603i \(-0.833479\pi\)
−0.866255 + 0.499603i \(0.833479\pi\)
\(752\) −14.2461 −0.519502
\(753\) −28.7538 −1.04785
\(754\) −39.0488 −1.42207
\(755\) 73.2404 2.66549
\(756\) 125.613 4.56850
\(757\) 21.9311 0.797100 0.398550 0.917147i \(-0.369514\pi\)
0.398550 + 0.917147i \(0.369514\pi\)
\(758\) −5.01238 −0.182058
\(759\) 8.72428 0.316671
\(760\) −121.696 −4.41439
\(761\) 23.2955 0.844461 0.422231 0.906488i \(-0.361247\pi\)
0.422231 + 0.906488i \(0.361247\pi\)
\(762\) −7.66041 −0.277507
\(763\) 83.6518 3.02840
\(764\) −47.5309 −1.71961
\(765\) −0.827054 −0.0299022
\(766\) 23.2648 0.840593
\(767\) 14.0707 0.508065
\(768\) 23.5332 0.849180
\(769\) 21.3481 0.769832 0.384916 0.922952i \(-0.374230\pi\)
0.384916 + 0.922952i \(0.374230\pi\)
\(770\) 227.907 8.21320
\(771\) −10.7618 −0.387576
\(772\) −112.461 −4.04757
\(773\) 32.1762 1.15730 0.578649 0.815576i \(-0.303580\pi\)
0.578649 + 0.815576i \(0.303580\pi\)
\(774\) −1.52472 −0.0548049
\(775\) 57.8510 2.07807
\(776\) 44.7774 1.60742
\(777\) −69.5566 −2.49533
\(778\) −56.3701 −2.02097
\(779\) −47.4010 −1.69832
\(780\) 82.4119 2.95082
\(781\) 23.3937 0.837092
\(782\) 12.1754 0.435392
\(783\) 28.4795 1.01777
\(784\) 180.441 6.44430
\(785\) 57.6184 2.05649
\(786\) 47.9830 1.71150
\(787\) 17.9477 0.639765 0.319883 0.947457i \(-0.396356\pi\)
0.319883 + 0.947457i \(0.396356\pi\)
\(788\) −75.4883 −2.68916
\(789\) 38.0289 1.35387
\(790\) −62.8589 −2.23642
\(791\) −101.044 −3.59271
\(792\) −1.86375 −0.0662254
\(793\) 26.9869 0.958333
\(794\) 1.69617 0.0601947
\(795\) −18.6182 −0.660319
\(796\) 3.47923 0.123318
\(797\) −1.71188 −0.0606378 −0.0303189 0.999540i \(-0.509652\pi\)
−0.0303189 + 0.999540i \(0.509652\pi\)
\(798\) −103.039 −3.64754
\(799\) −6.40348 −0.226539
\(800\) −88.2732 −3.12093
\(801\) −0.621832 −0.0219714
\(802\) −7.67173 −0.270898
\(803\) −0.803483 −0.0283543
\(804\) −12.4283 −0.438313
\(805\) 18.5882 0.655148
\(806\) −51.6034 −1.81765
\(807\) 47.4580 1.67060
\(808\) 47.5958 1.67442
\(809\) −31.7245 −1.11537 −0.557686 0.830052i \(-0.688311\pi\)
−0.557686 + 0.830052i \(0.688311\pi\)
\(810\) −86.2230 −3.02957
\(811\) −49.9569 −1.75422 −0.877112 0.480285i \(-0.840533\pi\)
−0.877112 + 0.480285i \(0.840533\pi\)
\(812\) 134.836 4.73182
\(813\) −18.7724 −0.658377
\(814\) −100.813 −3.53348
\(815\) 36.5630 1.28075
\(816\) −78.4895 −2.74768
\(817\) −51.0681 −1.78665
\(818\) −15.6644 −0.547694
\(819\) 0.690342 0.0241225
\(820\) −184.642 −6.44798
\(821\) 9.39202 0.327784 0.163892 0.986478i \(-0.447595\pi\)
0.163892 + 0.986478i \(0.447595\pi\)
\(822\) −9.74099 −0.339756
\(823\) 46.5051 1.62107 0.810533 0.585692i \(-0.199177\pi\)
0.810533 + 0.585692i \(0.199177\pi\)
\(824\) −85.9331 −2.99362
\(825\) −66.8417 −2.32713
\(826\) −68.5285 −2.38441
\(827\) 44.7603 1.55647 0.778234 0.627975i \(-0.216116\pi\)
0.778234 + 0.627975i \(0.216116\pi\)
\(828\) −0.257835 −0.00896039
\(829\) −18.6308 −0.647074 −0.323537 0.946216i \(-0.604872\pi\)
−0.323537 + 0.946216i \(0.604872\pi\)
\(830\) 37.1385 1.28910
\(831\) −22.5735 −0.783067
\(832\) 24.8701 0.862216
\(833\) 81.1062 2.81016
\(834\) 54.2554 1.87871
\(835\) 51.8843 1.79553
\(836\) −105.882 −3.66201
\(837\) 37.6360 1.30089
\(838\) 5.03517 0.173937
\(839\) 18.0186 0.622072 0.311036 0.950398i \(-0.399324\pi\)
0.311036 + 0.950398i \(0.399324\pi\)
\(840\) −236.630 −8.16451
\(841\) 1.57060 0.0541587
\(842\) 69.7372 2.40330
\(843\) 38.0700 1.31120
\(844\) −9.89309 −0.340534
\(845\) 20.6396 0.710022
\(846\) 0.191263 0.00657575
\(847\) 61.8516 2.12525
\(848\) −29.6511 −1.01822
\(849\) 23.6627 0.812102
\(850\) −93.2828 −3.19957
\(851\) −8.22232 −0.281857
\(852\) −41.1989 −1.41145
\(853\) −38.5727 −1.32070 −0.660352 0.750956i \(-0.729593\pi\)
−0.660352 + 0.750956i \(0.729593\pi\)
\(854\) −131.434 −4.49758
\(855\) 0.827385 0.0282960
\(856\) 24.0947 0.823539
\(857\) 20.0781 0.685855 0.342927 0.939362i \(-0.388582\pi\)
0.342927 + 0.939362i \(0.388582\pi\)
\(858\) 59.6232 2.03550
\(859\) 54.9282 1.87413 0.937063 0.349160i \(-0.113533\pi\)
0.937063 + 0.349160i \(0.113533\pi\)
\(860\) −198.926 −6.78334
\(861\) −92.1678 −3.14107
\(862\) −55.3891 −1.88656
\(863\) −33.1526 −1.12853 −0.564264 0.825594i \(-0.690840\pi\)
−0.564264 + 0.825594i \(0.690840\pi\)
\(864\) −57.4277 −1.95373
\(865\) −50.6948 −1.72368
\(866\) −72.9495 −2.47892
\(867\) −5.58517 −0.189682
\(868\) 178.187 6.04808
\(869\) −32.2431 −1.09377
\(870\) −91.0002 −3.08520
\(871\) 3.93360 0.133285
\(872\) −125.882 −4.26290
\(873\) −0.304431 −0.0103034
\(874\) −12.1803 −0.412005
\(875\) −52.4780 −1.77408
\(876\) 1.41502 0.0478092
\(877\) −12.3301 −0.416357 −0.208179 0.978091i \(-0.566754\pi\)
−0.208179 + 0.978091i \(0.566754\pi\)
\(878\) 31.8235 1.07399
\(879\) 32.0372 1.08059
\(880\) −173.677 −5.85464
\(881\) 35.5259 1.19690 0.598450 0.801160i \(-0.295784\pi\)
0.598450 + 0.801160i \(0.295784\pi\)
\(882\) −2.42253 −0.0815707
\(883\) −0.878130 −0.0295514 −0.0147757 0.999891i \(-0.504703\pi\)
−0.0147757 + 0.999891i \(0.504703\pi\)
\(884\) 58.9947 1.98421
\(885\) 32.7908 1.10225
\(886\) 55.2421 1.85589
\(887\) −16.6357 −0.558572 −0.279286 0.960208i \(-0.590098\pi\)
−0.279286 + 0.960208i \(0.590098\pi\)
\(888\) 104.671 3.51253
\(889\) −8.37199 −0.280788
\(890\) −114.428 −3.83563
\(891\) −44.2275 −1.48168
\(892\) −124.916 −4.18249
\(893\) 6.40605 0.214370
\(894\) 30.1767 1.00926
\(895\) −81.5444 −2.72573
\(896\) −9.52852 −0.318325
\(897\) 4.86289 0.162367
\(898\) −23.2077 −0.774450
\(899\) 40.3994 1.34740
\(900\) 1.97542 0.0658474
\(901\) −13.3279 −0.444016
\(902\) −133.584 −4.44787
\(903\) −99.2982 −3.30444
\(904\) 152.054 5.05725
\(905\) 48.1888 1.60185
\(906\) −93.3175 −3.10027
\(907\) 34.1227 1.13303 0.566513 0.824053i \(-0.308292\pi\)
0.566513 + 0.824053i \(0.308292\pi\)
\(908\) 58.1309 1.92914
\(909\) −0.323593 −0.0107329
\(910\) 127.035 4.21116
\(911\) −50.5156 −1.67366 −0.836829 0.547465i \(-0.815593\pi\)
−0.836829 + 0.547465i \(0.815593\pi\)
\(912\) 78.5210 2.60009
\(913\) 19.0499 0.630461
\(914\) 24.8800 0.822958
\(915\) 62.8910 2.07911
\(916\) 120.053 3.96667
\(917\) 52.4402 1.73173
\(918\) −60.6868 −2.00296
\(919\) 23.3013 0.768640 0.384320 0.923200i \(-0.374436\pi\)
0.384320 + 0.923200i \(0.374436\pi\)
\(920\) −27.9721 −0.922214
\(921\) 20.5339 0.676614
\(922\) −15.5029 −0.510562
\(923\) 13.0396 0.429203
\(924\) −205.880 −6.77295
\(925\) 62.9959 2.07129
\(926\) 3.15973 0.103835
\(927\) 0.584239 0.0191889
\(928\) −61.6443 −2.02357
\(929\) −32.9585 −1.08133 −0.540666 0.841237i \(-0.681828\pi\)
−0.540666 + 0.841237i \(0.681828\pi\)
\(930\) −120.258 −3.94341
\(931\) −81.1388 −2.65922
\(932\) −5.15443 −0.168839
\(933\) −8.77809 −0.287382
\(934\) −43.8216 −1.43388
\(935\) −78.0659 −2.55303
\(936\) −1.03885 −0.0339559
\(937\) −46.0785 −1.50532 −0.752659 0.658411i \(-0.771229\pi\)
−0.752659 + 0.658411i \(0.771229\pi\)
\(938\) −19.1578 −0.625524
\(939\) 50.5500 1.64964
\(940\) 24.9536 0.813896
\(941\) −44.5795 −1.45325 −0.726624 0.687035i \(-0.758912\pi\)
−0.726624 + 0.687035i \(0.758912\pi\)
\(942\) −73.4131 −2.39193
\(943\) −10.8952 −0.354797
\(944\) 52.2222 1.69969
\(945\) −92.6505 −3.01392
\(946\) −143.919 −4.67921
\(947\) −0.707003 −0.0229745 −0.0114873 0.999934i \(-0.503657\pi\)
−0.0114873 + 0.999934i \(0.503657\pi\)
\(948\) 56.7836 1.84425
\(949\) −0.447859 −0.0145381
\(950\) 93.3202 3.02771
\(951\) −14.0223 −0.454703
\(952\) −169.392 −5.49003
\(953\) −49.5961 −1.60657 −0.803287 0.595592i \(-0.796917\pi\)
−0.803287 + 0.595592i \(0.796917\pi\)
\(954\) 0.398084 0.0128885
\(955\) 35.0582 1.13446
\(956\) 100.428 3.24807
\(957\) −46.6780 −1.50888
\(958\) 47.1547 1.52350
\(959\) −10.6458 −0.343772
\(960\) 57.9580 1.87059
\(961\) 22.3883 0.722203
\(962\) −56.1927 −1.81173
\(963\) −0.163814 −0.00527883
\(964\) 68.0433 2.19153
\(965\) 82.9500 2.67026
\(966\) −23.6837 −0.762010
\(967\) −1.42966 −0.0459747 −0.0229874 0.999736i \(-0.507318\pi\)
−0.0229874 + 0.999736i \(0.507318\pi\)
\(968\) −93.0764 −2.99159
\(969\) 35.2944 1.13382
\(970\) −56.0205 −1.79871
\(971\) 35.8930 1.15186 0.575931 0.817498i \(-0.304640\pi\)
0.575931 + 0.817498i \(0.304640\pi\)
\(972\) 2.59261 0.0831580
\(973\) 59.2953 1.90092
\(974\) −44.8449 −1.43692
\(975\) −37.2574 −1.19319
\(976\) 100.159 3.20602
\(977\) 1.54033 0.0492796 0.0246398 0.999696i \(-0.492156\pi\)
0.0246398 + 0.999696i \(0.492156\pi\)
\(978\) −46.5859 −1.48965
\(979\) −58.6950 −1.87590
\(980\) −316.061 −10.0962
\(981\) 0.855842 0.0273249
\(982\) 63.6208 2.03022
\(983\) −33.4724 −1.06760 −0.533801 0.845610i \(-0.679237\pi\)
−0.533801 + 0.845610i \(0.679237\pi\)
\(984\) 138.697 4.42151
\(985\) 55.6792 1.77409
\(986\) −65.1427 −2.07457
\(987\) 12.4561 0.396482
\(988\) −59.0184 −1.87763
\(989\) −11.7381 −0.373249
\(990\) 2.33172 0.0741068
\(991\) −16.6246 −0.528097 −0.264049 0.964509i \(-0.585058\pi\)
−0.264049 + 0.964509i \(0.585058\pi\)
\(992\) −81.4637 −2.58647
\(993\) 6.37453 0.202290
\(994\) −63.5066 −2.01431
\(995\) −2.56623 −0.0813550
\(996\) −33.5491 −1.06304
\(997\) −2.00053 −0.0633574 −0.0316787 0.999498i \(-0.510085\pi\)
−0.0316787 + 0.999498i \(0.510085\pi\)
\(998\) 44.5313 1.40961
\(999\) 40.9831 1.29665
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 \(a_p\))