Properties

Label 8018.2.a.j.1.4
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.90959 q^{3}\) \(+1.00000 q^{4}\) \(-4.15278 q^{5}\) \(-2.90959 q^{6}\) \(+3.02073 q^{7}\) \(+1.00000 q^{8}\) \(+5.46571 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.90959 q^{3}\) \(+1.00000 q^{4}\) \(-4.15278 q^{5}\) \(-2.90959 q^{6}\) \(+3.02073 q^{7}\) \(+1.00000 q^{8}\) \(+5.46571 q^{9}\) \(-4.15278 q^{10}\) \(+1.94973 q^{11}\) \(-2.90959 q^{12}\) \(+7.15763 q^{13}\) \(+3.02073 q^{14}\) \(+12.0829 q^{15}\) \(+1.00000 q^{16}\) \(+1.01914 q^{17}\) \(+5.46571 q^{18}\) \(-1.00000 q^{19}\) \(-4.15278 q^{20}\) \(-8.78908 q^{21}\) \(+1.94973 q^{22}\) \(+3.81312 q^{23}\) \(-2.90959 q^{24}\) \(+12.2456 q^{25}\) \(+7.15763 q^{26}\) \(-7.17419 q^{27}\) \(+3.02073 q^{28}\) \(+10.1658 q^{29}\) \(+12.0829 q^{30}\) \(+4.20950 q^{31}\) \(+1.00000 q^{32}\) \(-5.67292 q^{33}\) \(+1.01914 q^{34}\) \(-12.5444 q^{35}\) \(+5.46571 q^{36}\) \(+9.42107 q^{37}\) \(-1.00000 q^{38}\) \(-20.8257 q^{39}\) \(-4.15278 q^{40}\) \(+0.697666 q^{41}\) \(-8.78908 q^{42}\) \(+7.53762 q^{43}\) \(+1.94973 q^{44}\) \(-22.6979 q^{45}\) \(+3.81312 q^{46}\) \(-5.51721 q^{47}\) \(-2.90959 q^{48}\) \(+2.12481 q^{49}\) \(+12.2456 q^{50}\) \(-2.96528 q^{51}\) \(+7.15763 q^{52}\) \(-3.63798 q^{53}\) \(-7.17419 q^{54}\) \(-8.09681 q^{55}\) \(+3.02073 q^{56}\) \(+2.90959 q^{57}\) \(+10.1658 q^{58}\) \(+7.99315 q^{59}\) \(+12.0829 q^{60}\) \(-1.55823 q^{61}\) \(+4.20950 q^{62}\) \(+16.5104 q^{63}\) \(+1.00000 q^{64}\) \(-29.7241 q^{65}\) \(-5.67292 q^{66}\) \(+1.68379 q^{67}\) \(+1.01914 q^{68}\) \(-11.0946 q^{69}\) \(-12.5444 q^{70}\) \(-11.8559 q^{71}\) \(+5.46571 q^{72}\) \(+3.13570 q^{73}\) \(+9.42107 q^{74}\) \(-35.6296 q^{75}\) \(-1.00000 q^{76}\) \(+5.88961 q^{77}\) \(-20.8257 q^{78}\) \(-1.68328 q^{79}\) \(-4.15278 q^{80}\) \(+4.47682 q^{81}\) \(+0.697666 q^{82}\) \(-5.75209 q^{83}\) \(-8.78908 q^{84}\) \(-4.23226 q^{85}\) \(+7.53762 q^{86}\) \(-29.5784 q^{87}\) \(+1.94973 q^{88}\) \(-8.16873 q^{89}\) \(-22.6979 q^{90}\) \(+21.6213 q^{91}\) \(+3.81312 q^{92}\) \(-12.2479 q^{93}\) \(-5.51721 q^{94}\) \(+4.15278 q^{95}\) \(-2.90959 q^{96}\) \(+11.4176 q^{97}\) \(+2.12481 q^{98}\) \(+10.6567 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.90959 −1.67985 −0.839926 0.542701i \(-0.817402\pi\)
−0.839926 + 0.542701i \(0.817402\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.15278 −1.85718 −0.928590 0.371107i \(-0.878978\pi\)
−0.928590 + 0.371107i \(0.878978\pi\)
\(6\) −2.90959 −1.18783
\(7\) 3.02073 1.14173 0.570864 0.821044i \(-0.306608\pi\)
0.570864 + 0.821044i \(0.306608\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.46571 1.82190
\(10\) −4.15278 −1.31322
\(11\) 1.94973 0.587866 0.293933 0.955826i \(-0.405036\pi\)
0.293933 + 0.955826i \(0.405036\pi\)
\(12\) −2.90959 −0.839926
\(13\) 7.15763 1.98517 0.992584 0.121560i \(-0.0387895\pi\)
0.992584 + 0.121560i \(0.0387895\pi\)
\(14\) 3.02073 0.807324
\(15\) 12.0829 3.11979
\(16\) 1.00000 0.250000
\(17\) 1.01914 0.247178 0.123589 0.992334i \(-0.460560\pi\)
0.123589 + 0.992334i \(0.460560\pi\)
\(18\) 5.46571 1.28828
\(19\) −1.00000 −0.229416
\(20\) −4.15278 −0.928590
\(21\) −8.78908 −1.91793
\(22\) 1.94973 0.415684
\(23\) 3.81312 0.795091 0.397545 0.917583i \(-0.369862\pi\)
0.397545 + 0.917583i \(0.369862\pi\)
\(24\) −2.90959 −0.593917
\(25\) 12.2456 2.44912
\(26\) 7.15763 1.40373
\(27\) −7.17419 −1.38067
\(28\) 3.02073 0.570864
\(29\) 10.1658 1.88775 0.943875 0.330302i \(-0.107151\pi\)
0.943875 + 0.330302i \(0.107151\pi\)
\(30\) 12.0829 2.20602
\(31\) 4.20950 0.756049 0.378024 0.925796i \(-0.376604\pi\)
0.378024 + 0.925796i \(0.376604\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.67292 −0.987528
\(34\) 1.01914 0.174781
\(35\) −12.5444 −2.12040
\(36\) 5.46571 0.910951
\(37\) 9.42107 1.54881 0.774407 0.632688i \(-0.218048\pi\)
0.774407 + 0.632688i \(0.218048\pi\)
\(38\) −1.00000 −0.162221
\(39\) −20.8257 −3.33479
\(40\) −4.15278 −0.656612
\(41\) 0.697666 0.108957 0.0544786 0.998515i \(-0.482650\pi\)
0.0544786 + 0.998515i \(0.482650\pi\)
\(42\) −8.78908 −1.35618
\(43\) 7.53762 1.14948 0.574738 0.818338i \(-0.305104\pi\)
0.574738 + 0.818338i \(0.305104\pi\)
\(44\) 1.94973 0.293933
\(45\) −22.6979 −3.38360
\(46\) 3.81312 0.562214
\(47\) −5.51721 −0.804768 −0.402384 0.915471i \(-0.631818\pi\)
−0.402384 + 0.915471i \(0.631818\pi\)
\(48\) −2.90959 −0.419963
\(49\) 2.12481 0.303544
\(50\) 12.2456 1.73179
\(51\) −2.96528 −0.415222
\(52\) 7.15763 0.992584
\(53\) −3.63798 −0.499715 −0.249857 0.968283i \(-0.580384\pi\)
−0.249857 + 0.968283i \(0.580384\pi\)
\(54\) −7.17419 −0.976283
\(55\) −8.09681 −1.09177
\(56\) 3.02073 0.403662
\(57\) 2.90959 0.385384
\(58\) 10.1658 1.33484
\(59\) 7.99315 1.04062 0.520309 0.853978i \(-0.325817\pi\)
0.520309 + 0.853978i \(0.325817\pi\)
\(60\) 12.0829 1.55989
\(61\) −1.55823 −0.199511 −0.0997557 0.995012i \(-0.531806\pi\)
−0.0997557 + 0.995012i \(0.531806\pi\)
\(62\) 4.20950 0.534607
\(63\) 16.5104 2.08012
\(64\) 1.00000 0.125000
\(65\) −29.7241 −3.68682
\(66\) −5.67292 −0.698288
\(67\) 1.68379 0.205708 0.102854 0.994696i \(-0.467203\pi\)
0.102854 + 0.994696i \(0.467203\pi\)
\(68\) 1.01914 0.123589
\(69\) −11.0946 −1.33563
\(70\) −12.5444 −1.49935
\(71\) −11.8559 −1.40704 −0.703518 0.710678i \(-0.748388\pi\)
−0.703518 + 0.710678i \(0.748388\pi\)
\(72\) 5.46571 0.644140
\(73\) 3.13570 0.367006 0.183503 0.983019i \(-0.441256\pi\)
0.183503 + 0.983019i \(0.441256\pi\)
\(74\) 9.42107 1.09518
\(75\) −35.6296 −4.11415
\(76\) −1.00000 −0.114708
\(77\) 5.88961 0.671183
\(78\) −20.8257 −2.35805
\(79\) −1.68328 −0.189384 −0.0946918 0.995507i \(-0.530187\pi\)
−0.0946918 + 0.995507i \(0.530187\pi\)
\(80\) −4.15278 −0.464295
\(81\) 4.47682 0.497424
\(82\) 0.697666 0.0770443
\(83\) −5.75209 −0.631374 −0.315687 0.948863i \(-0.602235\pi\)
−0.315687 + 0.948863i \(0.602235\pi\)
\(84\) −8.78908 −0.958967
\(85\) −4.23226 −0.459053
\(86\) 7.53762 0.812802
\(87\) −29.5784 −3.17114
\(88\) 1.94973 0.207842
\(89\) −8.16873 −0.865884 −0.432942 0.901422i \(-0.642524\pi\)
−0.432942 + 0.901422i \(0.642524\pi\)
\(90\) −22.6979 −2.39257
\(91\) 21.6213 2.26652
\(92\) 3.81312 0.397545
\(93\) −12.2479 −1.27005
\(94\) −5.51721 −0.569057
\(95\) 4.15278 0.426066
\(96\) −2.90959 −0.296959
\(97\) 11.4176 1.15928 0.579642 0.814871i \(-0.303193\pi\)
0.579642 + 0.814871i \(0.303193\pi\)
\(98\) 2.12481 0.214638
\(99\) 10.6567 1.07103
\(100\) 12.2456 1.22456
\(101\) 17.1859 1.71006 0.855031 0.518577i \(-0.173538\pi\)
0.855031 + 0.518577i \(0.173538\pi\)
\(102\) −2.96528 −0.293606
\(103\) −0.905175 −0.0891896 −0.0445948 0.999005i \(-0.514200\pi\)
−0.0445948 + 0.999005i \(0.514200\pi\)
\(104\) 7.15763 0.701863
\(105\) 36.4991 3.56195
\(106\) −3.63798 −0.353352
\(107\) −6.25612 −0.604802 −0.302401 0.953181i \(-0.597788\pi\)
−0.302401 + 0.953181i \(0.597788\pi\)
\(108\) −7.17419 −0.690337
\(109\) 6.87919 0.658907 0.329453 0.944172i \(-0.393136\pi\)
0.329453 + 0.944172i \(0.393136\pi\)
\(110\) −8.09681 −0.772000
\(111\) −27.4114 −2.60178
\(112\) 3.02073 0.285432
\(113\) −15.0441 −1.41523 −0.707616 0.706598i \(-0.750229\pi\)
−0.707616 + 0.706598i \(0.750229\pi\)
\(114\) 2.90959 0.272508
\(115\) −15.8351 −1.47663
\(116\) 10.1658 0.943875
\(117\) 39.1215 3.61678
\(118\) 7.99315 0.735829
\(119\) 3.07854 0.282210
\(120\) 12.0829 1.10301
\(121\) −7.19855 −0.654413
\(122\) −1.55823 −0.141076
\(123\) −2.02992 −0.183032
\(124\) 4.20950 0.378024
\(125\) −30.0893 −2.69127
\(126\) 16.5104 1.47086
\(127\) −15.5694 −1.38156 −0.690779 0.723066i \(-0.742732\pi\)
−0.690779 + 0.723066i \(0.742732\pi\)
\(128\) 1.00000 0.0883883
\(129\) −21.9314 −1.93095
\(130\) −29.7241 −2.60697
\(131\) −15.0676 −1.31646 −0.658229 0.752818i \(-0.728694\pi\)
−0.658229 + 0.752818i \(0.728694\pi\)
\(132\) −5.67292 −0.493764
\(133\) −3.02073 −0.261930
\(134\) 1.68379 0.145457
\(135\) 29.7928 2.56416
\(136\) 1.01914 0.0873905
\(137\) 3.33949 0.285312 0.142656 0.989772i \(-0.454436\pi\)
0.142656 + 0.989772i \(0.454436\pi\)
\(138\) −11.0946 −0.944436
\(139\) 19.3076 1.63765 0.818826 0.574042i \(-0.194625\pi\)
0.818826 + 0.574042i \(0.194625\pi\)
\(140\) −12.5444 −1.06020
\(141\) 16.0528 1.35189
\(142\) −11.8559 −0.994924
\(143\) 13.9554 1.16701
\(144\) 5.46571 0.455475
\(145\) −42.2165 −3.50589
\(146\) 3.13570 0.259513
\(147\) −6.18231 −0.509909
\(148\) 9.42107 0.774407
\(149\) 5.10176 0.417953 0.208976 0.977921i \(-0.432987\pi\)
0.208976 + 0.977921i \(0.432987\pi\)
\(150\) −35.6296 −2.90915
\(151\) 12.0241 0.978505 0.489252 0.872142i \(-0.337270\pi\)
0.489252 + 0.872142i \(0.337270\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 5.57031 0.450333
\(154\) 5.88961 0.474598
\(155\) −17.4811 −1.40412
\(156\) −20.8257 −1.66739
\(157\) −2.70273 −0.215701 −0.107851 0.994167i \(-0.534397\pi\)
−0.107851 + 0.994167i \(0.534397\pi\)
\(158\) −1.68328 −0.133914
\(159\) 10.5850 0.839447
\(160\) −4.15278 −0.328306
\(161\) 11.5184 0.907778
\(162\) 4.47682 0.351732
\(163\) 13.4310 1.05200 0.525999 0.850485i \(-0.323692\pi\)
0.525999 + 0.850485i \(0.323692\pi\)
\(164\) 0.697666 0.0544786
\(165\) 23.5584 1.83402
\(166\) −5.75209 −0.446449
\(167\) −9.30505 −0.720046 −0.360023 0.932943i \(-0.617231\pi\)
−0.360023 + 0.932943i \(0.617231\pi\)
\(168\) −8.78908 −0.678092
\(169\) 38.2316 2.94089
\(170\) −4.23226 −0.324600
\(171\) −5.46571 −0.417973
\(172\) 7.53762 0.574738
\(173\) −5.62614 −0.427747 −0.213874 0.976861i \(-0.568608\pi\)
−0.213874 + 0.976861i \(0.568608\pi\)
\(174\) −29.5784 −2.24234
\(175\) 36.9906 2.79623
\(176\) 1.94973 0.146967
\(177\) −23.2568 −1.74809
\(178\) −8.16873 −0.612272
\(179\) 6.67942 0.499243 0.249622 0.968343i \(-0.419694\pi\)
0.249622 + 0.968343i \(0.419694\pi\)
\(180\) −22.6979 −1.69180
\(181\) −16.2828 −1.21029 −0.605145 0.796116i \(-0.706885\pi\)
−0.605145 + 0.796116i \(0.706885\pi\)
\(182\) 21.6213 1.60267
\(183\) 4.53382 0.335149
\(184\) 3.81312 0.281107
\(185\) −39.1236 −2.87643
\(186\) −12.2479 −0.898061
\(187\) 1.98705 0.145307
\(188\) −5.51721 −0.402384
\(189\) −21.6713 −1.57635
\(190\) 4.15278 0.301274
\(191\) 16.0005 1.15775 0.578877 0.815415i \(-0.303491\pi\)
0.578877 + 0.815415i \(0.303491\pi\)
\(192\) −2.90959 −0.209981
\(193\) −12.4466 −0.895926 −0.447963 0.894052i \(-0.647850\pi\)
−0.447963 + 0.894052i \(0.647850\pi\)
\(194\) 11.4176 0.819737
\(195\) 86.4848 6.19330
\(196\) 2.12481 0.151772
\(197\) 14.3766 1.02429 0.512144 0.858899i \(-0.328851\pi\)
0.512144 + 0.858899i \(0.328851\pi\)
\(198\) 10.6567 0.757336
\(199\) 19.1040 1.35425 0.677125 0.735868i \(-0.263226\pi\)
0.677125 + 0.735868i \(0.263226\pi\)
\(200\) 12.2456 0.865894
\(201\) −4.89914 −0.345558
\(202\) 17.1859 1.20920
\(203\) 30.7083 2.15530
\(204\) −2.96528 −0.207611
\(205\) −2.89725 −0.202353
\(206\) −0.905175 −0.0630665
\(207\) 20.8414 1.44858
\(208\) 7.15763 0.496292
\(209\) −1.94973 −0.134866
\(210\) 36.4991 2.51868
\(211\) −1.00000 −0.0688428
\(212\) −3.63798 −0.249857
\(213\) 34.4958 2.36361
\(214\) −6.25612 −0.427660
\(215\) −31.3021 −2.13478
\(216\) −7.17419 −0.488142
\(217\) 12.7158 0.863203
\(218\) 6.87919 0.465917
\(219\) −9.12361 −0.616516
\(220\) −8.09681 −0.545887
\(221\) 7.29462 0.490689
\(222\) −27.4114 −1.83974
\(223\) −17.1649 −1.14945 −0.574724 0.818347i \(-0.694891\pi\)
−0.574724 + 0.818347i \(0.694891\pi\)
\(224\) 3.02073 0.201831
\(225\) 66.9308 4.46205
\(226\) −15.0441 −1.00072
\(227\) −14.3527 −0.952622 −0.476311 0.879277i \(-0.658026\pi\)
−0.476311 + 0.879277i \(0.658026\pi\)
\(228\) 2.90959 0.192692
\(229\) 6.65984 0.440095 0.220047 0.975489i \(-0.429379\pi\)
0.220047 + 0.975489i \(0.429379\pi\)
\(230\) −15.8351 −1.04413
\(231\) −17.1363 −1.12749
\(232\) 10.1658 0.667421
\(233\) 9.07581 0.594576 0.297288 0.954788i \(-0.403918\pi\)
0.297288 + 0.954788i \(0.403918\pi\)
\(234\) 39.1215 2.55745
\(235\) 22.9118 1.49460
\(236\) 7.99315 0.520309
\(237\) 4.89764 0.318136
\(238\) 3.07854 0.199552
\(239\) −14.6906 −0.950257 −0.475128 0.879916i \(-0.657598\pi\)
−0.475128 + 0.879916i \(0.657598\pi\)
\(240\) 12.0829 0.779947
\(241\) −23.1588 −1.49179 −0.745894 0.666065i \(-0.767977\pi\)
−0.745894 + 0.666065i \(0.767977\pi\)
\(242\) −7.19855 −0.462740
\(243\) 8.49686 0.545074
\(244\) −1.55823 −0.0997557
\(245\) −8.82386 −0.563736
\(246\) −2.02992 −0.129423
\(247\) −7.15763 −0.455429
\(248\) 4.20950 0.267304
\(249\) 16.7362 1.06061
\(250\) −30.0893 −1.90302
\(251\) −12.5886 −0.794588 −0.397294 0.917691i \(-0.630051\pi\)
−0.397294 + 0.917691i \(0.630051\pi\)
\(252\) 16.5104 1.04006
\(253\) 7.43456 0.467407
\(254\) −15.5694 −0.976909
\(255\) 12.3141 0.771141
\(256\) 1.00000 0.0625000
\(257\) −23.4693 −1.46397 −0.731986 0.681319i \(-0.761406\pi\)
−0.731986 + 0.681319i \(0.761406\pi\)
\(258\) −21.9314 −1.36539
\(259\) 28.4585 1.76833
\(260\) −29.7241 −1.84341
\(261\) 55.5635 3.43930
\(262\) −15.0676 −0.930877
\(263\) 6.34196 0.391062 0.195531 0.980698i \(-0.437357\pi\)
0.195531 + 0.980698i \(0.437357\pi\)
\(264\) −5.67292 −0.349144
\(265\) 15.1077 0.928060
\(266\) −3.02073 −0.185213
\(267\) 23.7676 1.45456
\(268\) 1.68379 0.102854
\(269\) 19.2182 1.17176 0.585878 0.810400i \(-0.300750\pi\)
0.585878 + 0.810400i \(0.300750\pi\)
\(270\) 29.7928 1.81313
\(271\) −27.7948 −1.68842 −0.844208 0.536015i \(-0.819929\pi\)
−0.844208 + 0.536015i \(0.819929\pi\)
\(272\) 1.01914 0.0617944
\(273\) −62.9089 −3.80742
\(274\) 3.33949 0.201746
\(275\) 23.8756 1.43975
\(276\) −11.0946 −0.667817
\(277\) −8.51136 −0.511398 −0.255699 0.966756i \(-0.582306\pi\)
−0.255699 + 0.966756i \(0.582306\pi\)
\(278\) 19.3076 1.15799
\(279\) 23.0079 1.37745
\(280\) −12.5444 −0.749673
\(281\) 29.3230 1.74926 0.874632 0.484787i \(-0.161103\pi\)
0.874632 + 0.484787i \(0.161103\pi\)
\(282\) 16.0528 0.955931
\(283\) 1.05656 0.0628062 0.0314031 0.999507i \(-0.490002\pi\)
0.0314031 + 0.999507i \(0.490002\pi\)
\(284\) −11.8559 −0.703518
\(285\) −12.0829 −0.715728
\(286\) 13.9554 0.825203
\(287\) 2.10746 0.124399
\(288\) 5.46571 0.322070
\(289\) −15.9614 −0.938903
\(290\) −42.2165 −2.47904
\(291\) −33.2206 −1.94742
\(292\) 3.13570 0.183503
\(293\) −12.4399 −0.726745 −0.363373 0.931644i \(-0.618375\pi\)
−0.363373 + 0.931644i \(0.618375\pi\)
\(294\) −6.18231 −0.360560
\(295\) −33.1938 −1.93262
\(296\) 9.42107 0.547589
\(297\) −13.9877 −0.811651
\(298\) 5.10176 0.295537
\(299\) 27.2929 1.57839
\(300\) −35.6296 −2.05708
\(301\) 22.7691 1.31239
\(302\) 12.0241 0.691907
\(303\) −50.0039 −2.87265
\(304\) −1.00000 −0.0573539
\(305\) 6.47100 0.370528
\(306\) 5.57031 0.318434
\(307\) −17.3312 −0.989141 −0.494571 0.869137i \(-0.664675\pi\)
−0.494571 + 0.869137i \(0.664675\pi\)
\(308\) 5.88961 0.335592
\(309\) 2.63369 0.149825
\(310\) −17.4811 −0.992862
\(311\) −2.20615 −0.125099 −0.0625496 0.998042i \(-0.519923\pi\)
−0.0625496 + 0.998042i \(0.519923\pi\)
\(312\) −20.8257 −1.17903
\(313\) 18.6570 1.05456 0.527278 0.849693i \(-0.323213\pi\)
0.527278 + 0.849693i \(0.323213\pi\)
\(314\) −2.70273 −0.152524
\(315\) −68.5641 −3.86315
\(316\) −1.68328 −0.0946918
\(317\) 4.76007 0.267352 0.133676 0.991025i \(-0.457322\pi\)
0.133676 + 0.991025i \(0.457322\pi\)
\(318\) 10.5850 0.593578
\(319\) 19.8207 1.10974
\(320\) −4.15278 −0.232148
\(321\) 18.2027 1.01598
\(322\) 11.5184 0.641896
\(323\) −1.01914 −0.0567064
\(324\) 4.47682 0.248712
\(325\) 87.6494 4.86191
\(326\) 13.4310 0.743875
\(327\) −20.0156 −1.10687
\(328\) 0.697666 0.0385222
\(329\) −16.6660 −0.918826
\(330\) 23.5584 1.29685
\(331\) 11.8428 0.650938 0.325469 0.945553i \(-0.394478\pi\)
0.325469 + 0.945553i \(0.394478\pi\)
\(332\) −5.75209 −0.315687
\(333\) 51.4928 2.82179
\(334\) −9.30505 −0.509150
\(335\) −6.99241 −0.382036
\(336\) −8.78908 −0.479484
\(337\) −23.8124 −1.29714 −0.648572 0.761153i \(-0.724634\pi\)
−0.648572 + 0.761153i \(0.724634\pi\)
\(338\) 38.2316 2.07953
\(339\) 43.7722 2.37738
\(340\) −4.23226 −0.229527
\(341\) 8.20740 0.444455
\(342\) −5.46571 −0.295551
\(343\) −14.7266 −0.795164
\(344\) 7.53762 0.406401
\(345\) 46.0735 2.48051
\(346\) −5.62614 −0.302463
\(347\) 34.6997 1.86278 0.931388 0.364027i \(-0.118599\pi\)
0.931388 + 0.364027i \(0.118599\pi\)
\(348\) −29.5784 −1.58557
\(349\) −29.2926 −1.56800 −0.784000 0.620761i \(-0.786824\pi\)
−0.784000 + 0.620761i \(0.786824\pi\)
\(350\) 36.9906 1.97723
\(351\) −51.3502 −2.74087
\(352\) 1.94973 0.103921
\(353\) −5.86582 −0.312206 −0.156103 0.987741i \(-0.549893\pi\)
−0.156103 + 0.987741i \(0.549893\pi\)
\(354\) −23.2568 −1.23608
\(355\) 49.2349 2.61312
\(356\) −8.16873 −0.432942
\(357\) −8.95730 −0.474070
\(358\) 6.67942 0.353018
\(359\) −0.441918 −0.0233235 −0.0116618 0.999932i \(-0.503712\pi\)
−0.0116618 + 0.999932i \(0.503712\pi\)
\(360\) −22.6979 −1.19628
\(361\) 1.00000 0.0526316
\(362\) −16.2828 −0.855804
\(363\) 20.9448 1.09932
\(364\) 21.6213 1.13326
\(365\) −13.0219 −0.681597
\(366\) 4.53382 0.236986
\(367\) 17.2015 0.897911 0.448955 0.893554i \(-0.351796\pi\)
0.448955 + 0.893554i \(0.351796\pi\)
\(368\) 3.81312 0.198773
\(369\) 3.81324 0.198509
\(370\) −39.1236 −2.03394
\(371\) −10.9893 −0.570539
\(372\) −12.2479 −0.635025
\(373\) 10.6175 0.549755 0.274877 0.961479i \(-0.411363\pi\)
0.274877 + 0.961479i \(0.411363\pi\)
\(374\) 1.98705 0.102748
\(375\) 87.5476 4.52094
\(376\) −5.51721 −0.284528
\(377\) 72.7633 3.74750
\(378\) −21.6713 −1.11465
\(379\) −17.9307 −0.921037 −0.460519 0.887650i \(-0.652337\pi\)
−0.460519 + 0.887650i \(0.652337\pi\)
\(380\) 4.15278 0.213033
\(381\) 45.3004 2.32081
\(382\) 16.0005 0.818655
\(383\) 17.9992 0.919716 0.459858 0.887992i \(-0.347900\pi\)
0.459858 + 0.887992i \(0.347900\pi\)
\(384\) −2.90959 −0.148479
\(385\) −24.4583 −1.24651
\(386\) −12.4466 −0.633515
\(387\) 41.1984 2.09423
\(388\) 11.4176 0.579642
\(389\) −31.9610 −1.62049 −0.810243 0.586094i \(-0.800665\pi\)
−0.810243 + 0.586094i \(0.800665\pi\)
\(390\) 86.4848 4.37933
\(391\) 3.88610 0.196529
\(392\) 2.12481 0.107319
\(393\) 43.8404 2.21145
\(394\) 14.3766 0.724281
\(395\) 6.99028 0.351719
\(396\) 10.6567 0.535517
\(397\) 7.68750 0.385825 0.192912 0.981216i \(-0.438207\pi\)
0.192912 + 0.981216i \(0.438207\pi\)
\(398\) 19.1040 0.957599
\(399\) 8.78908 0.440004
\(400\) 12.2456 0.612279
\(401\) 31.2202 1.55906 0.779532 0.626362i \(-0.215457\pi\)
0.779532 + 0.626362i \(0.215457\pi\)
\(402\) −4.89914 −0.244347
\(403\) 30.1300 1.50088
\(404\) 17.1859 0.855031
\(405\) −18.5912 −0.923807
\(406\) 30.7083 1.52403
\(407\) 18.3686 0.910495
\(408\) −2.96528 −0.146803
\(409\) 33.3660 1.64984 0.824921 0.565249i \(-0.191220\pi\)
0.824921 + 0.565249i \(0.191220\pi\)
\(410\) −2.89725 −0.143085
\(411\) −9.71653 −0.479281
\(412\) −0.905175 −0.0445948
\(413\) 24.1451 1.18810
\(414\) 20.8414 1.02430
\(415\) 23.8872 1.17258
\(416\) 7.15763 0.350931
\(417\) −56.1773 −2.75101
\(418\) −1.94973 −0.0953645
\(419\) −13.8340 −0.675837 −0.337919 0.941175i \(-0.609723\pi\)
−0.337919 + 0.941175i \(0.609723\pi\)
\(420\) 36.4991 1.78097
\(421\) 17.9771 0.876152 0.438076 0.898938i \(-0.355660\pi\)
0.438076 + 0.898938i \(0.355660\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −30.1554 −1.46621
\(424\) −3.63798 −0.176676
\(425\) 12.4800 0.605367
\(426\) 34.4958 1.67132
\(427\) −4.70700 −0.227788
\(428\) −6.25612 −0.302401
\(429\) −40.6046 −1.96041
\(430\) −31.3021 −1.50952
\(431\) 34.4107 1.65750 0.828752 0.559616i \(-0.189052\pi\)
0.828752 + 0.559616i \(0.189052\pi\)
\(432\) −7.17419 −0.345168
\(433\) −32.8764 −1.57994 −0.789969 0.613147i \(-0.789903\pi\)
−0.789969 + 0.613147i \(0.789903\pi\)
\(434\) 12.7158 0.610376
\(435\) 122.833 5.88938
\(436\) 6.87919 0.329453
\(437\) −3.81312 −0.182406
\(438\) −9.12361 −0.435943
\(439\) 12.5408 0.598539 0.299270 0.954169i \(-0.403257\pi\)
0.299270 + 0.954169i \(0.403257\pi\)
\(440\) −8.09681 −0.386000
\(441\) 11.6136 0.553027
\(442\) 7.29462 0.346970
\(443\) −7.63728 −0.362858 −0.181429 0.983404i \(-0.558072\pi\)
−0.181429 + 0.983404i \(0.558072\pi\)
\(444\) −27.4114 −1.30089
\(445\) 33.9229 1.60810
\(446\) −17.1649 −0.812783
\(447\) −14.8440 −0.702098
\(448\) 3.02073 0.142716
\(449\) −16.9124 −0.798148 −0.399074 0.916919i \(-0.630668\pi\)
−0.399074 + 0.916919i \(0.630668\pi\)
\(450\) 66.9308 3.15515
\(451\) 1.36026 0.0640522
\(452\) −15.0441 −0.707616
\(453\) −34.9851 −1.64374
\(454\) −14.3527 −0.673606
\(455\) −89.7883 −4.20934
\(456\) 2.90959 0.136254
\(457\) −17.7455 −0.830102 −0.415051 0.909798i \(-0.636236\pi\)
−0.415051 + 0.909798i \(0.636236\pi\)
\(458\) 6.65984 0.311194
\(459\) −7.31150 −0.341271
\(460\) −15.8351 −0.738313
\(461\) −28.6682 −1.33521 −0.667606 0.744515i \(-0.732681\pi\)
−0.667606 + 0.744515i \(0.732681\pi\)
\(462\) −17.1363 −0.797255
\(463\) 2.56062 0.119002 0.0595011 0.998228i \(-0.481049\pi\)
0.0595011 + 0.998228i \(0.481049\pi\)
\(464\) 10.1658 0.471938
\(465\) 50.8629 2.35871
\(466\) 9.07581 0.420429
\(467\) −20.0042 −0.925682 −0.462841 0.886441i \(-0.653170\pi\)
−0.462841 + 0.886441i \(0.653170\pi\)
\(468\) 39.1215 1.80839
\(469\) 5.08627 0.234862
\(470\) 22.9118 1.05684
\(471\) 7.86384 0.362346
\(472\) 7.99315 0.367914
\(473\) 14.6963 0.675738
\(474\) 4.89764 0.224956
\(475\) −12.2456 −0.561866
\(476\) 3.07854 0.141105
\(477\) −19.8841 −0.910431
\(478\) −14.6906 −0.671933
\(479\) 5.04331 0.230435 0.115217 0.993340i \(-0.463244\pi\)
0.115217 + 0.993340i \(0.463244\pi\)
\(480\) 12.0829 0.551506
\(481\) 67.4325 3.07466
\(482\) −23.1588 −1.05485
\(483\) −33.5138 −1.52493
\(484\) −7.19855 −0.327207
\(485\) −47.4149 −2.15300
\(486\) 8.49686 0.385426
\(487\) 11.0808 0.502118 0.251059 0.967972i \(-0.419221\pi\)
0.251059 + 0.967972i \(0.419221\pi\)
\(488\) −1.55823 −0.0705379
\(489\) −39.0787 −1.76720
\(490\) −8.82386 −0.398621
\(491\) 9.19476 0.414954 0.207477 0.978240i \(-0.433475\pi\)
0.207477 + 0.978240i \(0.433475\pi\)
\(492\) −2.02992 −0.0915159
\(493\) 10.3604 0.466610
\(494\) −7.15763 −0.322037
\(495\) −44.2548 −1.98910
\(496\) 4.20950 0.189012
\(497\) −35.8134 −1.60645
\(498\) 16.7362 0.749968
\(499\) −29.6428 −1.32699 −0.663496 0.748180i \(-0.730928\pi\)
−0.663496 + 0.748180i \(0.730928\pi\)
\(500\) −30.0893 −1.34564
\(501\) 27.0739 1.20957
\(502\) −12.5886 −0.561859
\(503\) 3.40931 0.152013 0.0760067 0.997107i \(-0.475783\pi\)
0.0760067 + 0.997107i \(0.475783\pi\)
\(504\) 16.5104 0.735432
\(505\) −71.3693 −3.17589
\(506\) 7.43456 0.330507
\(507\) −111.238 −4.94026
\(508\) −15.5694 −0.690779
\(509\) 32.1399 1.42458 0.712289 0.701886i \(-0.247659\pi\)
0.712289 + 0.701886i \(0.247659\pi\)
\(510\) 12.3141 0.545279
\(511\) 9.47211 0.419022
\(512\) 1.00000 0.0441942
\(513\) 7.17419 0.316748
\(514\) −23.4693 −1.03518
\(515\) 3.75899 0.165641
\(516\) −21.9314 −0.965474
\(517\) −10.7571 −0.473096
\(518\) 28.4585 1.25039
\(519\) 16.3697 0.718552
\(520\) −29.7241 −1.30349
\(521\) −3.70118 −0.162152 −0.0810759 0.996708i \(-0.525836\pi\)
−0.0810759 + 0.996708i \(0.525836\pi\)
\(522\) 55.5635 2.43195
\(523\) −16.1140 −0.704614 −0.352307 0.935884i \(-0.614603\pi\)
−0.352307 + 0.935884i \(0.614603\pi\)
\(524\) −15.0676 −0.658229
\(525\) −107.627 −4.69725
\(526\) 6.34196 0.276522
\(527\) 4.29007 0.186878
\(528\) −5.67292 −0.246882
\(529\) −8.46011 −0.367831
\(530\) 15.1077 0.656238
\(531\) 43.6882 1.89591
\(532\) −3.02073 −0.130965
\(533\) 4.99363 0.216298
\(534\) 23.7676 1.02853
\(535\) 25.9803 1.12323
\(536\) 1.68379 0.0727287
\(537\) −19.4344 −0.838655
\(538\) 19.2182 0.828556
\(539\) 4.14280 0.178443
\(540\) 29.7928 1.28208
\(541\) −26.9278 −1.15772 −0.578859 0.815428i \(-0.696502\pi\)
−0.578859 + 0.815428i \(0.696502\pi\)
\(542\) −27.7948 −1.19389
\(543\) 47.3762 2.03311
\(544\) 1.01914 0.0436952
\(545\) −28.5678 −1.22371
\(546\) −62.9089 −2.69225
\(547\) −3.90587 −0.167003 −0.0835016 0.996508i \(-0.526610\pi\)
−0.0835016 + 0.996508i \(0.526610\pi\)
\(548\) 3.33949 0.142656
\(549\) −8.51684 −0.363490
\(550\) 23.8756 1.01806
\(551\) −10.1658 −0.433080
\(552\) −11.0946 −0.472218
\(553\) −5.08473 −0.216225
\(554\) −8.51136 −0.361613
\(555\) 113.834 4.83197
\(556\) 19.3076 0.818826
\(557\) 38.7742 1.64292 0.821458 0.570269i \(-0.193161\pi\)
0.821458 + 0.570269i \(0.193161\pi\)
\(558\) 23.0079 0.974002
\(559\) 53.9514 2.28190
\(560\) −12.5444 −0.530099
\(561\) −5.78149 −0.244095
\(562\) 29.3230 1.23692
\(563\) 34.8720 1.46968 0.734840 0.678240i \(-0.237257\pi\)
0.734840 + 0.678240i \(0.237257\pi\)
\(564\) 16.0528 0.675945
\(565\) 62.4749 2.62834
\(566\) 1.05656 0.0444107
\(567\) 13.5233 0.567924
\(568\) −11.8559 −0.497462
\(569\) −14.2554 −0.597616 −0.298808 0.954313i \(-0.596589\pi\)
−0.298808 + 0.954313i \(0.596589\pi\)
\(570\) −12.0829 −0.506096
\(571\) 5.78533 0.242109 0.121054 0.992646i \(-0.461372\pi\)
0.121054 + 0.992646i \(0.461372\pi\)
\(572\) 13.9554 0.583507
\(573\) −46.5548 −1.94485
\(574\) 2.10746 0.0879637
\(575\) 46.6939 1.94727
\(576\) 5.46571 0.227738
\(577\) −28.9710 −1.20608 −0.603038 0.797712i \(-0.706043\pi\)
−0.603038 + 0.797712i \(0.706043\pi\)
\(578\) −15.9614 −0.663905
\(579\) 36.2145 1.50502
\(580\) −42.2165 −1.75295
\(581\) −17.3755 −0.720858
\(582\) −33.2206 −1.37704
\(583\) −7.09308 −0.293765
\(584\) 3.13570 0.129756
\(585\) −162.463 −6.71701
\(586\) −12.4399 −0.513886
\(587\) −45.7854 −1.88976 −0.944882 0.327410i \(-0.893824\pi\)
−0.944882 + 0.327410i \(0.893824\pi\)
\(588\) −6.18231 −0.254954
\(589\) −4.20950 −0.173450
\(590\) −33.1938 −1.36657
\(591\) −41.8299 −1.72065
\(592\) 9.42107 0.387204
\(593\) 10.5318 0.432489 0.216244 0.976339i \(-0.430619\pi\)
0.216244 + 0.976339i \(0.430619\pi\)
\(594\) −13.9877 −0.573924
\(595\) −12.7845 −0.524114
\(596\) 5.10176 0.208976
\(597\) −55.5849 −2.27494
\(598\) 27.2929 1.11609
\(599\) −35.3648 −1.44497 −0.722483 0.691389i \(-0.756999\pi\)
−0.722483 + 0.691389i \(0.756999\pi\)
\(600\) −35.6296 −1.45457
\(601\) −21.9281 −0.894464 −0.447232 0.894418i \(-0.647590\pi\)
−0.447232 + 0.894418i \(0.647590\pi\)
\(602\) 22.7691 0.927999
\(603\) 9.20310 0.374779
\(604\) 12.0241 0.489252
\(605\) 29.8940 1.21536
\(606\) −50.0039 −2.03127
\(607\) 19.6293 0.796728 0.398364 0.917228i \(-0.369578\pi\)
0.398364 + 0.917228i \(0.369578\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −89.3485 −3.62058
\(610\) 6.47100 0.262003
\(611\) −39.4901 −1.59760
\(612\) 5.57031 0.225167
\(613\) −33.3190 −1.34574 −0.672870 0.739760i \(-0.734939\pi\)
−0.672870 + 0.739760i \(0.734939\pi\)
\(614\) −17.3312 −0.699429
\(615\) 8.42982 0.339923
\(616\) 5.88961 0.237299
\(617\) −2.01887 −0.0812767 −0.0406384 0.999174i \(-0.512939\pi\)
−0.0406384 + 0.999174i \(0.512939\pi\)
\(618\) 2.63369 0.105942
\(619\) 15.6910 0.630676 0.315338 0.948979i \(-0.397882\pi\)
0.315338 + 0.948979i \(0.397882\pi\)
\(620\) −17.4811 −0.702059
\(621\) −27.3560 −1.09776
\(622\) −2.20615 −0.0884584
\(623\) −24.6755 −0.988604
\(624\) −20.8257 −0.833697
\(625\) 63.7265 2.54906
\(626\) 18.6570 0.745683
\(627\) 5.67292 0.226554
\(628\) −2.70273 −0.107851
\(629\) 9.60138 0.382832
\(630\) −68.5641 −2.73166
\(631\) −20.2060 −0.804390 −0.402195 0.915554i \(-0.631753\pi\)
−0.402195 + 0.915554i \(0.631753\pi\)
\(632\) −1.68328 −0.0669572
\(633\) 2.90959 0.115646
\(634\) 4.76007 0.189047
\(635\) 64.6561 2.56580
\(636\) 10.5850 0.419723
\(637\) 15.2086 0.602586
\(638\) 19.8207 0.784708
\(639\) −64.8008 −2.56348
\(640\) −4.15278 −0.164153
\(641\) 7.16583 0.283033 0.141517 0.989936i \(-0.454802\pi\)
0.141517 + 0.989936i \(0.454802\pi\)
\(642\) 18.2027 0.718405
\(643\) −28.5747 −1.12687 −0.563437 0.826159i \(-0.690521\pi\)
−0.563437 + 0.826159i \(0.690521\pi\)
\(644\) 11.5184 0.453889
\(645\) 91.0761 3.58612
\(646\) −1.01914 −0.0400975
\(647\) −19.5375 −0.768099 −0.384049 0.923313i \(-0.625471\pi\)
−0.384049 + 0.923313i \(0.625471\pi\)
\(648\) 4.47682 0.175866
\(649\) 15.5845 0.611745
\(650\) 87.6494 3.43789
\(651\) −36.9976 −1.45005
\(652\) 13.4310 0.525999
\(653\) 31.5416 1.23432 0.617160 0.786838i \(-0.288283\pi\)
0.617160 + 0.786838i \(0.288283\pi\)
\(654\) −20.0156 −0.782672
\(655\) 62.5723 2.44490
\(656\) 0.697666 0.0272393
\(657\) 17.1388 0.668650
\(658\) −16.6660 −0.649708
\(659\) −21.0459 −0.819831 −0.409916 0.912123i \(-0.634442\pi\)
−0.409916 + 0.912123i \(0.634442\pi\)
\(660\) 23.5584 0.917009
\(661\) 1.86235 0.0724369 0.0362184 0.999344i \(-0.488469\pi\)
0.0362184 + 0.999344i \(0.488469\pi\)
\(662\) 11.8428 0.460283
\(663\) −21.2243 −0.824285
\(664\) −5.75209 −0.223224
\(665\) 12.5444 0.486452
\(666\) 51.4928 1.99531
\(667\) 38.7636 1.50093
\(668\) −9.30505 −0.360023
\(669\) 49.9429 1.93090
\(670\) −6.99241 −0.270140
\(671\) −3.03814 −0.117286
\(672\) −8.78908 −0.339046
\(673\) 20.7209 0.798734 0.399367 0.916791i \(-0.369230\pi\)
0.399367 + 0.916791i \(0.369230\pi\)
\(674\) −23.8124 −0.917220
\(675\) −87.8522 −3.38143
\(676\) 38.2316 1.47045
\(677\) 38.2054 1.46835 0.734177 0.678958i \(-0.237568\pi\)
0.734177 + 0.678958i \(0.237568\pi\)
\(678\) 43.7722 1.68106
\(679\) 34.4895 1.32359
\(680\) −4.23226 −0.162300
\(681\) 41.7605 1.60026
\(682\) 8.20740 0.314277
\(683\) −24.4622 −0.936022 −0.468011 0.883723i \(-0.655029\pi\)
−0.468011 + 0.883723i \(0.655029\pi\)
\(684\) −5.46571 −0.208986
\(685\) −13.8682 −0.529875
\(686\) −14.7266 −0.562266
\(687\) −19.3774 −0.739294
\(688\) 7.53762 0.287369
\(689\) −26.0393 −0.992018
\(690\) 46.0735 1.75399
\(691\) −36.0523 −1.37149 −0.685746 0.727841i \(-0.740524\pi\)
−0.685746 + 0.727841i \(0.740524\pi\)
\(692\) −5.62614 −0.213874
\(693\) 32.1909 1.22283
\(694\) 34.6997 1.31718
\(695\) −80.1804 −3.04141
\(696\) −29.5784 −1.12117
\(697\) 0.711019 0.0269318
\(698\) −29.2926 −1.10874
\(699\) −26.4069 −0.998800
\(700\) 36.9906 1.39811
\(701\) −28.0614 −1.05986 −0.529932 0.848040i \(-0.677782\pi\)
−0.529932 + 0.848040i \(0.677782\pi\)
\(702\) −51.3502 −1.93809
\(703\) −9.42107 −0.355322
\(704\) 1.94973 0.0734833
\(705\) −66.6638 −2.51070
\(706\) −5.86582 −0.220763
\(707\) 51.9140 1.95243
\(708\) −23.2568 −0.874043
\(709\) −13.5688 −0.509586 −0.254793 0.966996i \(-0.582007\pi\)
−0.254793 + 0.966996i \(0.582007\pi\)
\(710\) 49.2349 1.84775
\(711\) −9.20030 −0.345038
\(712\) −8.16873 −0.306136
\(713\) 16.0513 0.601127
\(714\) −8.95730 −0.335218
\(715\) −57.9539 −2.16735
\(716\) 6.67942 0.249622
\(717\) 42.7436 1.59629
\(718\) −0.441918 −0.0164922
\(719\) −45.3428 −1.69100 −0.845500 0.533975i \(-0.820698\pi\)
−0.845500 + 0.533975i \(0.820698\pi\)
\(720\) −22.6979 −0.845900
\(721\) −2.73429 −0.101830
\(722\) 1.00000 0.0372161
\(723\) 67.3825 2.50598
\(724\) −16.2828 −0.605145
\(725\) 124.487 4.62332
\(726\) 20.9448 0.777335
\(727\) 2.59966 0.0964162 0.0482081 0.998837i \(-0.484649\pi\)
0.0482081 + 0.998837i \(0.484649\pi\)
\(728\) 21.6213 0.801337
\(729\) −38.1528 −1.41307
\(730\) −13.0219 −0.481962
\(731\) 7.68188 0.284125
\(732\) 4.53382 0.167575
\(733\) 50.3954 1.86140 0.930698 0.365788i \(-0.119201\pi\)
0.930698 + 0.365788i \(0.119201\pi\)
\(734\) 17.2015 0.634919
\(735\) 25.6738 0.946992
\(736\) 3.81312 0.140553
\(737\) 3.28294 0.120929
\(738\) 3.81324 0.140367
\(739\) −51.5853 −1.89759 −0.948797 0.315885i \(-0.897699\pi\)
−0.948797 + 0.315885i \(0.897699\pi\)
\(740\) −39.1236 −1.43821
\(741\) 20.8257 0.765053
\(742\) −10.9893 −0.403432
\(743\) 12.8723 0.472240 0.236120 0.971724i \(-0.424124\pi\)
0.236120 + 0.971724i \(0.424124\pi\)
\(744\) −12.2479 −0.449030
\(745\) −21.1865 −0.776213
\(746\) 10.6175 0.388735
\(747\) −31.4392 −1.15030
\(748\) 1.98705 0.0726536
\(749\) −18.8981 −0.690520
\(750\) 87.5476 3.19679
\(751\) −40.4289 −1.47527 −0.737635 0.675199i \(-0.764058\pi\)
−0.737635 + 0.675199i \(0.764058\pi\)
\(752\) −5.51721 −0.201192
\(753\) 36.6278 1.33479
\(754\) 72.7633 2.64988
\(755\) −49.9333 −1.81726
\(756\) −21.6713 −0.788177
\(757\) 24.2399 0.881014 0.440507 0.897749i \(-0.354799\pi\)
0.440507 + 0.897749i \(0.354799\pi\)
\(758\) −17.9307 −0.651272
\(759\) −21.6315 −0.785174
\(760\) 4.15278 0.150637
\(761\) −9.40814 −0.341045 −0.170522 0.985354i \(-0.554546\pi\)
−0.170522 + 0.985354i \(0.554546\pi\)
\(762\) 45.3004 1.64106
\(763\) 20.7802 0.752293
\(764\) 16.0005 0.578877
\(765\) −23.1323 −0.836350
\(766\) 17.9992 0.650338
\(767\) 57.2119 2.06580
\(768\) −2.90959 −0.104991
\(769\) −46.7257 −1.68497 −0.842485 0.538720i \(-0.818908\pi\)
−0.842485 + 0.538720i \(0.818908\pi\)
\(770\) −24.4583 −0.881415
\(771\) 68.2859 2.45926
\(772\) −12.4466 −0.447963
\(773\) −23.5066 −0.845473 −0.422736 0.906253i \(-0.638930\pi\)
−0.422736 + 0.906253i \(0.638930\pi\)
\(774\) 41.1984 1.48085
\(775\) 51.5478 1.85165
\(776\) 11.4176 0.409869
\(777\) −82.8025 −2.97052
\(778\) −31.9610 −1.14586
\(779\) −0.697666 −0.0249965
\(780\) 86.4848 3.09665
\(781\) −23.1158 −0.827148
\(782\) 3.88610 0.138967
\(783\) −72.9317 −2.60637
\(784\) 2.12481 0.0758860
\(785\) 11.2239 0.400596
\(786\) 43.8404 1.56373
\(787\) −6.72057 −0.239563 −0.119781 0.992800i \(-0.538219\pi\)
−0.119781 + 0.992800i \(0.538219\pi\)
\(788\) 14.3766 0.512144
\(789\) −18.4525 −0.656926
\(790\) 6.99028 0.248703
\(791\) −45.4442 −1.61581
\(792\) 10.6567 0.378668
\(793\) −11.1533 −0.396064
\(794\) 7.68750 0.272819
\(795\) −43.9573 −1.55900
\(796\) 19.1040 0.677125
\(797\) 28.2983 1.00238 0.501189 0.865338i \(-0.332896\pi\)
0.501189 + 0.865338i \(0.332896\pi\)
\(798\) 8.78908 0.311130
\(799\) −5.62280 −0.198920
\(800\) 12.2456 0.432947
\(801\) −44.6479 −1.57756
\(802\) 31.2202 1.10243
\(803\) 6.11378 0.215751
\(804\) −4.89914 −0.172779
\(805\) −47.8334 −1.68591
\(806\) 30.1300 1.06129
\(807\) −55.9171 −1.96837
\(808\) 17.1859 0.604598
\(809\) 1.85205 0.0651146 0.0325573 0.999470i \(-0.489635\pi\)
0.0325573 + 0.999470i \(0.489635\pi\)
\(810\) −18.5912 −0.653230
\(811\) 45.4507 1.59599 0.797995 0.602664i \(-0.205894\pi\)
0.797995 + 0.602664i \(0.205894\pi\)
\(812\) 30.7083 1.07765
\(813\) 80.8716 2.83629
\(814\) 18.3686 0.643817
\(815\) −55.7760 −1.95375
\(816\) −2.96528 −0.103805
\(817\) −7.53762 −0.263708
\(818\) 33.3660 1.16661
\(819\) 118.175 4.12938
\(820\) −2.89725 −0.101177
\(821\) −5.32174 −0.185730 −0.0928651 0.995679i \(-0.529603\pi\)
−0.0928651 + 0.995679i \(0.529603\pi\)
\(822\) −9.71653 −0.338903
\(823\) −13.8074 −0.481294 −0.240647 0.970613i \(-0.577360\pi\)
−0.240647 + 0.970613i \(0.577360\pi\)
\(824\) −0.905175 −0.0315333
\(825\) −69.4682 −2.41857
\(826\) 24.1451 0.840117
\(827\) −35.4391 −1.23234 −0.616170 0.787614i \(-0.711316\pi\)
−0.616170 + 0.787614i \(0.711316\pi\)
\(828\) 20.8414 0.724289
\(829\) 26.9862 0.937271 0.468636 0.883392i \(-0.344746\pi\)
0.468636 + 0.883392i \(0.344746\pi\)
\(830\) 23.8872 0.829136
\(831\) 24.7646 0.859073
\(832\) 7.15763 0.248146
\(833\) 2.16547 0.0750292
\(834\) −56.1773 −1.94526
\(835\) 38.6418 1.33726
\(836\) −1.94973 −0.0674329
\(837\) −30.1998 −1.04386
\(838\) −13.8340 −0.477889
\(839\) 5.72977 0.197814 0.0989068 0.995097i \(-0.468465\pi\)
0.0989068 + 0.995097i \(0.468465\pi\)
\(840\) 36.4991 1.25934
\(841\) 74.3445 2.56360
\(842\) 17.9771 0.619533
\(843\) −85.3179 −2.93851
\(844\) −1.00000 −0.0344214
\(845\) −158.768 −5.46177
\(846\) −30.1554 −1.03677
\(847\) −21.7449 −0.747162
\(848\) −3.63798 −0.124929
\(849\) −3.07417 −0.105505
\(850\) 12.4800 0.428059
\(851\) 35.9237 1.23145
\(852\) 34.4958 1.18181
\(853\) 9.82818 0.336510 0.168255 0.985743i \(-0.446187\pi\)
0.168255 + 0.985743i \(0.446187\pi\)
\(854\) −4.70700 −0.161070
\(855\) 22.6979 0.776251
\(856\) −6.25612 −0.213830
\(857\) 25.3796 0.866950 0.433475 0.901166i \(-0.357287\pi\)
0.433475 + 0.901166i \(0.357287\pi\)
\(858\) −40.6046 −1.38622
\(859\) −9.13659 −0.311736 −0.155868 0.987778i \(-0.549817\pi\)
−0.155868 + 0.987778i \(0.549817\pi\)
\(860\) −31.3021 −1.06739
\(861\) −6.13184 −0.208973
\(862\) 34.4107 1.17203
\(863\) −22.9804 −0.782263 −0.391131 0.920335i \(-0.627916\pi\)
−0.391131 + 0.920335i \(0.627916\pi\)
\(864\) −7.17419 −0.244071
\(865\) 23.3641 0.794404
\(866\) −32.8764 −1.11719
\(867\) 46.4410 1.57722
\(868\) 12.7158 0.431601
\(869\) −3.28194 −0.111332
\(870\) 122.833 4.16442
\(871\) 12.0519 0.408364
\(872\) 6.87919 0.232959
\(873\) 62.4053 2.11210
\(874\) −3.81312 −0.128981
\(875\) −90.8918 −3.07270
\(876\) −9.12361 −0.308258
\(877\) −38.9306 −1.31459 −0.657296 0.753632i \(-0.728300\pi\)
−0.657296 + 0.753632i \(0.728300\pi\)
\(878\) 12.5408 0.423231
\(879\) 36.1949 1.22082
\(880\) −8.09681 −0.272943
\(881\) −23.5053 −0.791912 −0.395956 0.918269i \(-0.629587\pi\)
−0.395956 + 0.918269i \(0.629587\pi\)
\(882\) 11.6136 0.391049
\(883\) −13.9825 −0.470548 −0.235274 0.971929i \(-0.575599\pi\)
−0.235274 + 0.971929i \(0.575599\pi\)
\(884\) 7.29462 0.245345
\(885\) 96.5803 3.24651
\(886\) −7.63728 −0.256580
\(887\) −19.4188 −0.652021 −0.326010 0.945366i \(-0.605704\pi\)
−0.326010 + 0.945366i \(0.605704\pi\)
\(888\) −27.4114 −0.919868
\(889\) −47.0308 −1.57736
\(890\) 33.9229 1.13710
\(891\) 8.72859 0.292419
\(892\) −17.1649 −0.574724
\(893\) 5.51721 0.184626
\(894\) −14.8440 −0.496459
\(895\) −27.7382 −0.927185
\(896\) 3.02073 0.100915
\(897\) −79.4111 −2.65146
\(898\) −16.9124 −0.564376
\(899\) 42.7932 1.42723
\(900\) 66.9308 2.23103
\(901\) −3.70761 −0.123518
\(902\) 1.36026 0.0452917
\(903\) −66.2487 −2.20462
\(904\) −15.0441 −0.500360
\(905\) 67.6188 2.24772
\(906\) −34.9851 −1.16230
\(907\) 28.6747 0.952126 0.476063 0.879411i \(-0.342063\pi\)
0.476063 + 0.879411i \(0.342063\pi\)
\(908\) −14.3527 −0.476311
\(909\) 93.9331 3.11556
\(910\) −89.7883 −2.97645
\(911\) −30.8665 −1.02265 −0.511327 0.859386i \(-0.670846\pi\)
−0.511327 + 0.859386i \(0.670846\pi\)
\(912\) 2.90959 0.0963461
\(913\) −11.2150 −0.371163
\(914\) −17.7455 −0.586970
\(915\) −18.8280 −0.622433
\(916\) 6.65984 0.220047
\(917\) −45.5150 −1.50304
\(918\) −7.31150 −0.241315
\(919\) −25.9388 −0.855643 −0.427821 0.903863i \(-0.640719\pi\)
−0.427821 + 0.903863i \(0.640719\pi\)
\(920\) −15.8351 −0.522066
\(921\) 50.4265 1.66161
\(922\) −28.6682 −0.944137
\(923\) −84.8600 −2.79320
\(924\) −17.1363 −0.563744
\(925\) 115.367 3.79323
\(926\) 2.56062 0.0841473
\(927\) −4.94742 −0.162495
\(928\) 10.1658 0.333710
\(929\) −32.5571 −1.06816 −0.534082 0.845433i \(-0.679343\pi\)
−0.534082 + 0.845433i \(0.679343\pi\)
\(930\) 50.8629 1.66786
\(931\) −2.12481 −0.0696377
\(932\) 9.07581 0.297288
\(933\) 6.41898 0.210148
\(934\) −20.0042 −0.654556
\(935\) −8.25177 −0.269862
\(936\) 39.1215 1.27873
\(937\) 20.4620 0.668464 0.334232 0.942491i \(-0.391523\pi\)
0.334232 + 0.942491i \(0.391523\pi\)
\(938\) 5.08627 0.166073
\(939\) −54.2842 −1.77150
\(940\) 22.9118 0.747299
\(941\) 33.0659 1.07792 0.538958 0.842333i \(-0.318818\pi\)
0.538958 + 0.842333i \(0.318818\pi\)
\(942\) 7.86384 0.256218
\(943\) 2.66029 0.0866308
\(944\) 7.99315 0.260155
\(945\) 89.9961 2.92757
\(946\) 14.6963 0.477819
\(947\) −7.41391 −0.240920 −0.120460 0.992718i \(-0.538437\pi\)
−0.120460 + 0.992718i \(0.538437\pi\)
\(948\) 4.89764 0.159068
\(949\) 22.4442 0.728569
\(950\) −12.2456 −0.397299
\(951\) −13.8499 −0.449112
\(952\) 3.07854 0.0997762
\(953\) −15.8671 −0.513987 −0.256994 0.966413i \(-0.582732\pi\)
−0.256994 + 0.966413i \(0.582732\pi\)
\(954\) −19.8841 −0.643772
\(955\) −66.4465 −2.15016
\(956\) −14.6906 −0.475128
\(957\) −57.6700 −1.86421
\(958\) 5.04331 0.162942
\(959\) 10.0877 0.325748
\(960\) 12.0829 0.389973
\(961\) −13.2801 −0.428390
\(962\) 67.4325 2.17411
\(963\) −34.1941 −1.10189
\(964\) −23.1588 −0.745894
\(965\) 51.6880 1.66390
\(966\) −33.5138 −1.07829
\(967\) 9.86280 0.317166 0.158583 0.987346i \(-0.449307\pi\)
0.158583 + 0.987346i \(0.449307\pi\)
\(968\) −7.19855 −0.231370
\(969\) 2.96528 0.0952584
\(970\) −47.4149 −1.52240
\(971\) 0.323688 0.0103876 0.00519382 0.999987i \(-0.498347\pi\)
0.00519382 + 0.999987i \(0.498347\pi\)
\(972\) 8.49686 0.272537
\(973\) 58.3231 1.86975
\(974\) 11.0808 0.355051
\(975\) −255.024 −8.16729
\(976\) −1.55823 −0.0498778
\(977\) 22.5466 0.721331 0.360665 0.932695i \(-0.382550\pi\)
0.360665 + 0.932695i \(0.382550\pi\)
\(978\) −39.0787 −1.24960
\(979\) −15.9268 −0.509024
\(980\) −8.82386 −0.281868
\(981\) 37.5996 1.20046
\(982\) 9.19476 0.293417
\(983\) 15.5583 0.496233 0.248116 0.968730i \(-0.420188\pi\)
0.248116 + 0.968730i \(0.420188\pi\)
\(984\) −2.02992 −0.0647115
\(985\) −59.7028 −1.90229
\(986\) 10.3604 0.329943
\(987\) 48.4912 1.54349
\(988\) −7.15763 −0.227714
\(989\) 28.7418 0.913937
\(990\) −44.2548 −1.40651
\(991\) −5.67356 −0.180227 −0.0901133 0.995932i \(-0.528723\pi\)
−0.0901133 + 0.995932i \(0.528723\pi\)
\(992\) 4.20950 0.133652
\(993\) −34.4576 −1.09348
\(994\) −35.8134 −1.13593
\(995\) −79.3349 −2.51509
\(996\) 16.7362 0.530307
\(997\) 24.7691 0.784445 0.392223 0.919870i \(-0.371706\pi\)
0.392223 + 0.919870i \(0.371706\pi\)
\(998\) −29.6428 −0.938325
\(999\) −67.5885 −2.13841
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 \(a_p\))