Properties

Label 8018.2.a.j.1.6
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 1.6
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.78985 q^{3}\) \(+1.00000 q^{4}\) \(-2.51493 q^{5}\) \(-2.78985 q^{6}\) \(-0.381461 q^{7}\) \(+1.00000 q^{8}\) \(+4.78329 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.78985 q^{3}\) \(+1.00000 q^{4}\) \(-2.51493 q^{5}\) \(-2.78985 q^{6}\) \(-0.381461 q^{7}\) \(+1.00000 q^{8}\) \(+4.78329 q^{9}\) \(-2.51493 q^{10}\) \(+1.85275 q^{11}\) \(-2.78985 q^{12}\) \(-1.51269 q^{13}\) \(-0.381461 q^{14}\) \(+7.01629 q^{15}\) \(+1.00000 q^{16}\) \(-3.53252 q^{17}\) \(+4.78329 q^{18}\) \(-1.00000 q^{19}\) \(-2.51493 q^{20}\) \(+1.06422 q^{21}\) \(+1.85275 q^{22}\) \(+9.05456 q^{23}\) \(-2.78985 q^{24}\) \(+1.32487 q^{25}\) \(-1.51269 q^{26}\) \(-4.97512 q^{27}\) \(-0.381461 q^{28}\) \(+5.58964 q^{29}\) \(+7.01629 q^{30}\) \(-6.76333 q^{31}\) \(+1.00000 q^{32}\) \(-5.16890 q^{33}\) \(-3.53252 q^{34}\) \(+0.959349 q^{35}\) \(+4.78329 q^{36}\) \(-10.9012 q^{37}\) \(-1.00000 q^{38}\) \(+4.22017 q^{39}\) \(-2.51493 q^{40}\) \(+0.614977 q^{41}\) \(+1.06422 q^{42}\) \(-5.81105 q^{43}\) \(+1.85275 q^{44}\) \(-12.0296 q^{45}\) \(+9.05456 q^{46}\) \(+10.1131 q^{47}\) \(-2.78985 q^{48}\) \(-6.85449 q^{49}\) \(+1.32487 q^{50}\) \(+9.85523 q^{51}\) \(-1.51269 q^{52}\) \(+6.61551 q^{53}\) \(-4.97512 q^{54}\) \(-4.65954 q^{55}\) \(-0.381461 q^{56}\) \(+2.78985 q^{57}\) \(+5.58964 q^{58}\) \(-7.56646 q^{59}\) \(+7.01629 q^{60}\) \(+10.3001 q^{61}\) \(-6.76333 q^{62}\) \(-1.82464 q^{63}\) \(+1.00000 q^{64}\) \(+3.80430 q^{65}\) \(-5.16890 q^{66}\) \(+7.71648 q^{67}\) \(-3.53252 q^{68}\) \(-25.2609 q^{69}\) \(+0.959349 q^{70}\) \(-13.5607 q^{71}\) \(+4.78329 q^{72}\) \(-11.6082 q^{73}\) \(-10.9012 q^{74}\) \(-3.69620 q^{75}\) \(-1.00000 q^{76}\) \(-0.706753 q^{77}\) \(+4.22017 q^{78}\) \(+3.95164 q^{79}\) \(-2.51493 q^{80}\) \(-0.470015 q^{81}\) \(+0.614977 q^{82}\) \(-10.0906 q^{83}\) \(+1.06422 q^{84}\) \(+8.88405 q^{85}\) \(-5.81105 q^{86}\) \(-15.5943 q^{87}\) \(+1.85275 q^{88}\) \(-4.88917 q^{89}\) \(-12.0296 q^{90}\) \(+0.577031 q^{91}\) \(+9.05456 q^{92}\) \(+18.8687 q^{93}\) \(+10.1131 q^{94}\) \(+2.51493 q^{95}\) \(-2.78985 q^{96}\) \(-4.24563 q^{97}\) \(-6.85449 q^{98}\) \(+8.86224 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.78985 −1.61072 −0.805362 0.592784i \(-0.798029\pi\)
−0.805362 + 0.592784i \(0.798029\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.51493 −1.12471 −0.562355 0.826896i \(-0.690105\pi\)
−0.562355 + 0.826896i \(0.690105\pi\)
\(6\) −2.78985 −1.13895
\(7\) −0.381461 −0.144179 −0.0720894 0.997398i \(-0.522967\pi\)
−0.0720894 + 0.997398i \(0.522967\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.78329 1.59443
\(10\) −2.51493 −0.795291
\(11\) 1.85275 0.558625 0.279313 0.960200i \(-0.409893\pi\)
0.279313 + 0.960200i \(0.409893\pi\)
\(12\) −2.78985 −0.805362
\(13\) −1.51269 −0.419544 −0.209772 0.977750i \(-0.567272\pi\)
−0.209772 + 0.977750i \(0.567272\pi\)
\(14\) −0.381461 −0.101950
\(15\) 7.01629 1.81160
\(16\) 1.00000 0.250000
\(17\) −3.53252 −0.856763 −0.428382 0.903598i \(-0.640916\pi\)
−0.428382 + 0.903598i \(0.640916\pi\)
\(18\) 4.78329 1.12743
\(19\) −1.00000 −0.229416
\(20\) −2.51493 −0.562355
\(21\) 1.06422 0.232232
\(22\) 1.85275 0.395008
\(23\) 9.05456 1.88801 0.944003 0.329937i \(-0.107028\pi\)
0.944003 + 0.329937i \(0.107028\pi\)
\(24\) −2.78985 −0.569477
\(25\) 1.32487 0.264975
\(26\) −1.51269 −0.296662
\(27\) −4.97512 −0.957462
\(28\) −0.381461 −0.0720894
\(29\) 5.58964 1.03797 0.518985 0.854783i \(-0.326310\pi\)
0.518985 + 0.854783i \(0.326310\pi\)
\(30\) 7.01629 1.28099
\(31\) −6.76333 −1.21473 −0.607365 0.794423i \(-0.707774\pi\)
−0.607365 + 0.794423i \(0.707774\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.16890 −0.899791
\(34\) −3.53252 −0.605823
\(35\) 0.959349 0.162160
\(36\) 4.78329 0.797215
\(37\) −10.9012 −1.79214 −0.896071 0.443911i \(-0.853591\pi\)
−0.896071 + 0.443911i \(0.853591\pi\)
\(38\) −1.00000 −0.162221
\(39\) 4.22017 0.675769
\(40\) −2.51493 −0.397645
\(41\) 0.614977 0.0960433 0.0480216 0.998846i \(-0.484708\pi\)
0.0480216 + 0.998846i \(0.484708\pi\)
\(42\) 1.06422 0.164213
\(43\) −5.81105 −0.886177 −0.443089 0.896478i \(-0.646117\pi\)
−0.443089 + 0.896478i \(0.646117\pi\)
\(44\) 1.85275 0.279313
\(45\) −12.0296 −1.79327
\(46\) 9.05456 1.33502
\(47\) 10.1131 1.47515 0.737573 0.675268i \(-0.235972\pi\)
0.737573 + 0.675268i \(0.235972\pi\)
\(48\) −2.78985 −0.402681
\(49\) −6.85449 −0.979212
\(50\) 1.32487 0.187365
\(51\) 9.85523 1.38001
\(52\) −1.51269 −0.209772
\(53\) 6.61551 0.908711 0.454355 0.890821i \(-0.349870\pi\)
0.454355 + 0.890821i \(0.349870\pi\)
\(54\) −4.97512 −0.677028
\(55\) −4.65954 −0.628292
\(56\) −0.381461 −0.0509749
\(57\) 2.78985 0.369525
\(58\) 5.58964 0.733956
\(59\) −7.56646 −0.985069 −0.492535 0.870293i \(-0.663929\pi\)
−0.492535 + 0.870293i \(0.663929\pi\)
\(60\) 7.01629 0.905799
\(61\) 10.3001 1.31880 0.659398 0.751794i \(-0.270811\pi\)
0.659398 + 0.751794i \(0.270811\pi\)
\(62\) −6.76333 −0.858944
\(63\) −1.82464 −0.229883
\(64\) 1.00000 0.125000
\(65\) 3.80430 0.471865
\(66\) −5.16890 −0.636248
\(67\) 7.71648 0.942718 0.471359 0.881941i \(-0.343764\pi\)
0.471359 + 0.881941i \(0.343764\pi\)
\(68\) −3.53252 −0.428382
\(69\) −25.2609 −3.04105
\(70\) 0.959349 0.114664
\(71\) −13.5607 −1.60936 −0.804681 0.593707i \(-0.797664\pi\)
−0.804681 + 0.593707i \(0.797664\pi\)
\(72\) 4.78329 0.563716
\(73\) −11.6082 −1.35864 −0.679320 0.733842i \(-0.737725\pi\)
−0.679320 + 0.733842i \(0.737725\pi\)
\(74\) −10.9012 −1.26724
\(75\) −3.69620 −0.426801
\(76\) −1.00000 −0.114708
\(77\) −0.706753 −0.0805420
\(78\) 4.22017 0.477841
\(79\) 3.95164 0.444595 0.222297 0.974979i \(-0.428644\pi\)
0.222297 + 0.974979i \(0.428644\pi\)
\(80\) −2.51493 −0.281178
\(81\) −0.470015 −0.0522239
\(82\) 0.614977 0.0679128
\(83\) −10.0906 −1.10759 −0.553796 0.832653i \(-0.686821\pi\)
−0.553796 + 0.832653i \(0.686821\pi\)
\(84\) 1.06422 0.116116
\(85\) 8.88405 0.963611
\(86\) −5.81105 −0.626622
\(87\) −15.5943 −1.67188
\(88\) 1.85275 0.197504
\(89\) −4.88917 −0.518251 −0.259126 0.965844i \(-0.583434\pi\)
−0.259126 + 0.965844i \(0.583434\pi\)
\(90\) −12.0296 −1.26804
\(91\) 0.577031 0.0604893
\(92\) 9.05456 0.944003
\(93\) 18.8687 1.95660
\(94\) 10.1131 1.04309
\(95\) 2.51493 0.258026
\(96\) −2.78985 −0.284738
\(97\) −4.24563 −0.431078 −0.215539 0.976495i \(-0.569151\pi\)
−0.215539 + 0.976495i \(0.569151\pi\)
\(98\) −6.85449 −0.692408
\(99\) 8.86224 0.890689
\(100\) 1.32487 0.132487
\(101\) −4.66938 −0.464621 −0.232310 0.972642i \(-0.574629\pi\)
−0.232310 + 0.972642i \(0.574629\pi\)
\(102\) 9.85523 0.975813
\(103\) −0.552150 −0.0544050 −0.0272025 0.999630i \(-0.508660\pi\)
−0.0272025 + 0.999630i \(0.508660\pi\)
\(104\) −1.51269 −0.148331
\(105\) −2.67644 −0.261194
\(106\) 6.61551 0.642556
\(107\) 11.7963 1.14040 0.570198 0.821507i \(-0.306867\pi\)
0.570198 + 0.821507i \(0.306867\pi\)
\(108\) −4.97512 −0.478731
\(109\) 12.5577 1.20281 0.601407 0.798943i \(-0.294607\pi\)
0.601407 + 0.798943i \(0.294607\pi\)
\(110\) −4.65954 −0.444270
\(111\) 30.4127 2.88664
\(112\) −0.381461 −0.0360447
\(113\) −2.72236 −0.256098 −0.128049 0.991768i \(-0.540871\pi\)
−0.128049 + 0.991768i \(0.540871\pi\)
\(114\) 2.78985 0.261294
\(115\) −22.7716 −2.12346
\(116\) 5.58964 0.518985
\(117\) −7.23562 −0.668933
\(118\) −7.56646 −0.696549
\(119\) 1.34752 0.123527
\(120\) 7.01629 0.640497
\(121\) −7.56732 −0.687938
\(122\) 10.3001 0.932530
\(123\) −1.71570 −0.154699
\(124\) −6.76333 −0.607365
\(125\) 9.24269 0.826691
\(126\) −1.82464 −0.162552
\(127\) 12.9012 1.14479 0.572397 0.819977i \(-0.306014\pi\)
0.572397 + 0.819977i \(0.306014\pi\)
\(128\) 1.00000 0.0883883
\(129\) 16.2120 1.42739
\(130\) 3.80430 0.333659
\(131\) −16.1220 −1.40859 −0.704294 0.709908i \(-0.748736\pi\)
−0.704294 + 0.709908i \(0.748736\pi\)
\(132\) −5.16890 −0.449895
\(133\) 0.381461 0.0330769
\(134\) 7.71648 0.666603
\(135\) 12.5121 1.07687
\(136\) −3.53252 −0.302911
\(137\) −6.62859 −0.566319 −0.283159 0.959073i \(-0.591383\pi\)
−0.283159 + 0.959073i \(0.591383\pi\)
\(138\) −25.2609 −2.15035
\(139\) −8.67522 −0.735823 −0.367911 0.929861i \(-0.619927\pi\)
−0.367911 + 0.929861i \(0.619927\pi\)
\(140\) 0.959349 0.0810798
\(141\) −28.2141 −2.37605
\(142\) −13.5607 −1.13799
\(143\) −2.80263 −0.234368
\(144\) 4.78329 0.398607
\(145\) −14.0576 −1.16742
\(146\) −11.6082 −0.960704
\(147\) 19.1230 1.57724
\(148\) −10.9012 −0.896071
\(149\) 18.0044 1.47498 0.737490 0.675358i \(-0.236011\pi\)
0.737490 + 0.675358i \(0.236011\pi\)
\(150\) −3.69620 −0.301794
\(151\) −8.47133 −0.689387 −0.344694 0.938715i \(-0.612017\pi\)
−0.344694 + 0.938715i \(0.612017\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −16.8971 −1.36605
\(154\) −0.706753 −0.0569518
\(155\) 17.0093 1.36622
\(156\) 4.22017 0.337884
\(157\) −4.14046 −0.330444 −0.165222 0.986256i \(-0.552834\pi\)
−0.165222 + 0.986256i \(0.552834\pi\)
\(158\) 3.95164 0.314376
\(159\) −18.4563 −1.46368
\(160\) −2.51493 −0.198823
\(161\) −3.45396 −0.272210
\(162\) −0.470015 −0.0369279
\(163\) 16.0818 1.25962 0.629812 0.776748i \(-0.283132\pi\)
0.629812 + 0.776748i \(0.283132\pi\)
\(164\) 0.614977 0.0480216
\(165\) 12.9994 1.01200
\(166\) −10.0906 −0.783186
\(167\) 3.67821 0.284628 0.142314 0.989822i \(-0.454546\pi\)
0.142314 + 0.989822i \(0.454546\pi\)
\(168\) 1.06422 0.0821065
\(169\) −10.7118 −0.823983
\(170\) 8.88405 0.681376
\(171\) −4.78329 −0.365787
\(172\) −5.81105 −0.443089
\(173\) 17.1404 1.30316 0.651582 0.758578i \(-0.274106\pi\)
0.651582 + 0.758578i \(0.274106\pi\)
\(174\) −15.5943 −1.18220
\(175\) −0.505388 −0.0382037
\(176\) 1.85275 0.139656
\(177\) 21.1093 1.58667
\(178\) −4.88917 −0.366459
\(179\) 17.0170 1.27191 0.635954 0.771727i \(-0.280607\pi\)
0.635954 + 0.771727i \(0.280607\pi\)
\(180\) −12.0296 −0.896636
\(181\) 11.4998 0.854774 0.427387 0.904069i \(-0.359434\pi\)
0.427387 + 0.904069i \(0.359434\pi\)
\(182\) 0.577031 0.0427724
\(183\) −28.7359 −2.12422
\(184\) 9.05456 0.667511
\(185\) 27.4157 2.01564
\(186\) 18.8687 1.38352
\(187\) −6.54489 −0.478610
\(188\) 10.1131 0.737573
\(189\) 1.89781 0.138046
\(190\) 2.51493 0.182452
\(191\) 7.79323 0.563898 0.281949 0.959429i \(-0.409019\pi\)
0.281949 + 0.959429i \(0.409019\pi\)
\(192\) −2.78985 −0.201340
\(193\) 10.5128 0.756731 0.378365 0.925656i \(-0.376486\pi\)
0.378365 + 0.925656i \(0.376486\pi\)
\(194\) −4.24563 −0.304818
\(195\) −10.6134 −0.760045
\(196\) −6.85449 −0.489606
\(197\) −24.5742 −1.75084 −0.875420 0.483364i \(-0.839415\pi\)
−0.875420 + 0.483364i \(0.839415\pi\)
\(198\) 8.86224 0.629812
\(199\) −14.5695 −1.03280 −0.516401 0.856347i \(-0.672729\pi\)
−0.516401 + 0.856347i \(0.672729\pi\)
\(200\) 1.32487 0.0936827
\(201\) −21.5279 −1.51846
\(202\) −4.66938 −0.328537
\(203\) −2.13223 −0.149653
\(204\) 9.85523 0.690004
\(205\) −1.54662 −0.108021
\(206\) −0.552150 −0.0384701
\(207\) 43.3106 3.01029
\(208\) −1.51269 −0.104886
\(209\) −1.85275 −0.128157
\(210\) −2.67644 −0.184692
\(211\) −1.00000 −0.0688428
\(212\) 6.61551 0.454355
\(213\) 37.8325 2.59224
\(214\) 11.7963 0.806382
\(215\) 14.6144 0.996693
\(216\) −4.97512 −0.338514
\(217\) 2.57995 0.175138
\(218\) 12.5577 0.850517
\(219\) 32.3853 2.18839
\(220\) −4.65954 −0.314146
\(221\) 5.34360 0.359450
\(222\) 30.4127 2.04117
\(223\) 16.5493 1.10823 0.554113 0.832442i \(-0.313058\pi\)
0.554113 + 0.832442i \(0.313058\pi\)
\(224\) −0.381461 −0.0254875
\(225\) 6.33725 0.422483
\(226\) −2.72236 −0.181089
\(227\) 7.46037 0.495162 0.247581 0.968867i \(-0.420364\pi\)
0.247581 + 0.968867i \(0.420364\pi\)
\(228\) 2.78985 0.184763
\(229\) 27.3715 1.80876 0.904381 0.426725i \(-0.140333\pi\)
0.904381 + 0.426725i \(0.140333\pi\)
\(230\) −22.7716 −1.50151
\(231\) 1.97174 0.129731
\(232\) 5.58964 0.366978
\(233\) −3.38922 −0.222035 −0.111017 0.993818i \(-0.535411\pi\)
−0.111017 + 0.993818i \(0.535411\pi\)
\(234\) −7.23562 −0.473007
\(235\) −25.4337 −1.65911
\(236\) −7.56646 −0.492535
\(237\) −11.0245 −0.716119
\(238\) 1.34752 0.0873469
\(239\) −2.24183 −0.145012 −0.0725060 0.997368i \(-0.523100\pi\)
−0.0725060 + 0.997368i \(0.523100\pi\)
\(240\) 7.01629 0.452900
\(241\) −25.2142 −1.62419 −0.812094 0.583527i \(-0.801672\pi\)
−0.812094 + 0.583527i \(0.801672\pi\)
\(242\) −7.56732 −0.486445
\(243\) 16.2366 1.04158
\(244\) 10.3001 0.659398
\(245\) 17.2386 1.10133
\(246\) −1.71570 −0.109389
\(247\) 1.51269 0.0962499
\(248\) −6.76333 −0.429472
\(249\) 28.1514 1.78402
\(250\) 9.24269 0.584559
\(251\) 25.9381 1.63720 0.818598 0.574367i \(-0.194752\pi\)
0.818598 + 0.574367i \(0.194752\pi\)
\(252\) −1.82464 −0.114942
\(253\) 16.7758 1.05469
\(254\) 12.9012 0.809491
\(255\) −24.7852 −1.55211
\(256\) 1.00000 0.0625000
\(257\) 24.0627 1.50099 0.750494 0.660878i \(-0.229816\pi\)
0.750494 + 0.660878i \(0.229816\pi\)
\(258\) 16.2120 1.00931
\(259\) 4.15838 0.258389
\(260\) 3.80430 0.235933
\(261\) 26.7369 1.65497
\(262\) −16.1220 −0.996022
\(263\) 3.75304 0.231423 0.115711 0.993283i \(-0.463085\pi\)
0.115711 + 0.993283i \(0.463085\pi\)
\(264\) −5.16890 −0.318124
\(265\) −16.6376 −1.02204
\(266\) 0.381461 0.0233889
\(267\) 13.6401 0.834759
\(268\) 7.71648 0.471359
\(269\) 24.9123 1.51893 0.759465 0.650548i \(-0.225461\pi\)
0.759465 + 0.650548i \(0.225461\pi\)
\(270\) 12.5121 0.761460
\(271\) −3.64088 −0.221168 −0.110584 0.993867i \(-0.535272\pi\)
−0.110584 + 0.993867i \(0.535272\pi\)
\(272\) −3.53252 −0.214191
\(273\) −1.60983 −0.0974316
\(274\) −6.62859 −0.400448
\(275\) 2.45466 0.148022
\(276\) −25.2609 −1.52053
\(277\) −16.0293 −0.963108 −0.481554 0.876417i \(-0.659927\pi\)
−0.481554 + 0.876417i \(0.659927\pi\)
\(278\) −8.67522 −0.520305
\(279\) −32.3510 −1.93680
\(280\) 0.959349 0.0573320
\(281\) −11.4881 −0.685322 −0.342661 0.939459i \(-0.611328\pi\)
−0.342661 + 0.939459i \(0.611328\pi\)
\(282\) −28.2141 −1.68012
\(283\) −20.9876 −1.24759 −0.623793 0.781590i \(-0.714409\pi\)
−0.623793 + 0.781590i \(0.714409\pi\)
\(284\) −13.5607 −0.804681
\(285\) −7.01629 −0.415609
\(286\) −2.80263 −0.165723
\(287\) −0.234590 −0.0138474
\(288\) 4.78329 0.281858
\(289\) −4.52127 −0.265957
\(290\) −14.0576 −0.825488
\(291\) 11.8447 0.694348
\(292\) −11.6082 −0.679320
\(293\) 14.2041 0.829812 0.414906 0.909864i \(-0.363814\pi\)
0.414906 + 0.909864i \(0.363814\pi\)
\(294\) 19.1230 1.11528
\(295\) 19.0291 1.10792
\(296\) −10.9012 −0.633618
\(297\) −9.21765 −0.534862
\(298\) 18.0044 1.04297
\(299\) −13.6967 −0.792101
\(300\) −3.69620 −0.213400
\(301\) 2.21669 0.127768
\(302\) −8.47133 −0.487471
\(303\) 13.0269 0.748376
\(304\) −1.00000 −0.0573539
\(305\) −25.9041 −1.48326
\(306\) −16.8971 −0.965942
\(307\) 11.4576 0.653922 0.326961 0.945038i \(-0.393975\pi\)
0.326961 + 0.945038i \(0.393975\pi\)
\(308\) −0.706753 −0.0402710
\(309\) 1.54042 0.0876314
\(310\) 17.0093 0.966064
\(311\) 32.6557 1.85173 0.925866 0.377851i \(-0.123337\pi\)
0.925866 + 0.377851i \(0.123337\pi\)
\(312\) 4.22017 0.238920
\(313\) 16.7725 0.948039 0.474019 0.880514i \(-0.342803\pi\)
0.474019 + 0.880514i \(0.342803\pi\)
\(314\) −4.14046 −0.233659
\(315\) 4.58884 0.258552
\(316\) 3.95164 0.222297
\(317\) 20.6606 1.16041 0.580207 0.814469i \(-0.302972\pi\)
0.580207 + 0.814469i \(0.302972\pi\)
\(318\) −18.4563 −1.03498
\(319\) 10.3562 0.579836
\(320\) −2.51493 −0.140589
\(321\) −32.9101 −1.83686
\(322\) −3.45396 −0.192482
\(323\) 3.53252 0.196555
\(324\) −0.470015 −0.0261119
\(325\) −2.00412 −0.111168
\(326\) 16.0818 0.890688
\(327\) −35.0343 −1.93740
\(328\) 0.614977 0.0339564
\(329\) −3.85775 −0.212685
\(330\) 12.9994 0.715595
\(331\) 20.0656 1.10291 0.551453 0.834206i \(-0.314074\pi\)
0.551453 + 0.834206i \(0.314074\pi\)
\(332\) −10.0906 −0.553796
\(333\) −52.1434 −2.85744
\(334\) 3.67821 0.201263
\(335\) −19.4064 −1.06029
\(336\) 1.06422 0.0580581
\(337\) 18.5215 1.00893 0.504465 0.863432i \(-0.331690\pi\)
0.504465 + 0.863432i \(0.331690\pi\)
\(338\) −10.7118 −0.582644
\(339\) 7.59498 0.412503
\(340\) 8.88405 0.481805
\(341\) −12.5308 −0.678579
\(342\) −4.78329 −0.258651
\(343\) 5.28495 0.285361
\(344\) −5.81105 −0.313311
\(345\) 63.5294 3.42031
\(346\) 17.1404 0.921476
\(347\) −19.1719 −1.02920 −0.514602 0.857429i \(-0.672060\pi\)
−0.514602 + 0.857429i \(0.672060\pi\)
\(348\) −15.5943 −0.835941
\(349\) 14.6746 0.785513 0.392757 0.919642i \(-0.371521\pi\)
0.392757 + 0.919642i \(0.371521\pi\)
\(350\) −0.505388 −0.0270141
\(351\) 7.52579 0.401697
\(352\) 1.85275 0.0987519
\(353\) 24.3574 1.29641 0.648206 0.761465i \(-0.275519\pi\)
0.648206 + 0.761465i \(0.275519\pi\)
\(354\) 21.1093 1.12195
\(355\) 34.1043 1.81007
\(356\) −4.88917 −0.259126
\(357\) −3.75939 −0.198968
\(358\) 17.0170 0.899374
\(359\) −28.7641 −1.51811 −0.759057 0.651024i \(-0.774340\pi\)
−0.759057 + 0.651024i \(0.774340\pi\)
\(360\) −12.0296 −0.634018
\(361\) 1.00000 0.0526316
\(362\) 11.4998 0.604417
\(363\) 21.1117 1.10808
\(364\) 0.577031 0.0302447
\(365\) 29.1939 1.52808
\(366\) −28.7359 −1.50205
\(367\) 23.2429 1.21327 0.606634 0.794981i \(-0.292519\pi\)
0.606634 + 0.794981i \(0.292519\pi\)
\(368\) 9.05456 0.472001
\(369\) 2.94161 0.153134
\(370\) 27.4157 1.42527
\(371\) −2.52356 −0.131017
\(372\) 18.8687 0.978298
\(373\) 18.0135 0.932705 0.466352 0.884599i \(-0.345568\pi\)
0.466352 + 0.884599i \(0.345568\pi\)
\(374\) −6.54489 −0.338428
\(375\) −25.7858 −1.33157
\(376\) 10.1131 0.521543
\(377\) −8.45537 −0.435474
\(378\) 1.89781 0.0976130
\(379\) −0.852570 −0.0437936 −0.0218968 0.999760i \(-0.506971\pi\)
−0.0218968 + 0.999760i \(0.506971\pi\)
\(380\) 2.51493 0.129013
\(381\) −35.9924 −1.84395
\(382\) 7.79323 0.398736
\(383\) −30.7968 −1.57364 −0.786822 0.617180i \(-0.788275\pi\)
−0.786822 + 0.617180i \(0.788275\pi\)
\(384\) −2.78985 −0.142369
\(385\) 1.77743 0.0905864
\(386\) 10.5128 0.535089
\(387\) −27.7959 −1.41295
\(388\) −4.24563 −0.215539
\(389\) 5.99114 0.303763 0.151882 0.988399i \(-0.451467\pi\)
0.151882 + 0.988399i \(0.451467\pi\)
\(390\) −10.6134 −0.537433
\(391\) −31.9854 −1.61757
\(392\) −6.85449 −0.346204
\(393\) 44.9781 2.26885
\(394\) −24.5742 −1.23803
\(395\) −9.93811 −0.500040
\(396\) 8.86224 0.445344
\(397\) 25.0779 1.25862 0.629312 0.777153i \(-0.283337\pi\)
0.629312 + 0.777153i \(0.283337\pi\)
\(398\) −14.5695 −0.730302
\(399\) −1.06422 −0.0532777
\(400\) 1.32487 0.0662437
\(401\) 27.9765 1.39708 0.698540 0.715571i \(-0.253833\pi\)
0.698540 + 0.715571i \(0.253833\pi\)
\(402\) −21.5279 −1.07371
\(403\) 10.2308 0.509633
\(404\) −4.66938 −0.232310
\(405\) 1.18205 0.0587368
\(406\) −2.13223 −0.105821
\(407\) −20.1972 −1.00114
\(408\) 9.85523 0.487907
\(409\) −15.1309 −0.748175 −0.374087 0.927393i \(-0.622044\pi\)
−0.374087 + 0.927393i \(0.622044\pi\)
\(410\) −1.54662 −0.0763823
\(411\) 18.4928 0.912183
\(412\) −0.552150 −0.0272025
\(413\) 2.88631 0.142026
\(414\) 43.3106 2.12860
\(415\) 25.3773 1.24572
\(416\) −1.51269 −0.0741655
\(417\) 24.2026 1.18521
\(418\) −1.85275 −0.0906210
\(419\) 14.2414 0.695737 0.347869 0.937543i \(-0.386906\pi\)
0.347869 + 0.937543i \(0.386906\pi\)
\(420\) −2.67644 −0.130597
\(421\) 1.99964 0.0974566 0.0487283 0.998812i \(-0.484483\pi\)
0.0487283 + 0.998812i \(0.484483\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 48.3738 2.35202
\(424\) 6.61551 0.321278
\(425\) −4.68015 −0.227020
\(426\) 37.8325 1.83299
\(427\) −3.92910 −0.190142
\(428\) 11.7963 0.570198
\(429\) 7.81893 0.377502
\(430\) 14.6144 0.704768
\(431\) −32.2995 −1.55581 −0.777907 0.628379i \(-0.783719\pi\)
−0.777907 + 0.628379i \(0.783719\pi\)
\(432\) −4.97512 −0.239365
\(433\) 9.51355 0.457192 0.228596 0.973521i \(-0.426587\pi\)
0.228596 + 0.973521i \(0.426587\pi\)
\(434\) 2.57995 0.123842
\(435\) 39.2185 1.88038
\(436\) 12.5577 0.601407
\(437\) −9.05456 −0.433138
\(438\) 32.3853 1.54743
\(439\) −39.7801 −1.89860 −0.949300 0.314370i \(-0.898207\pi\)
−0.949300 + 0.314370i \(0.898207\pi\)
\(440\) −4.65954 −0.222135
\(441\) −32.7870 −1.56129
\(442\) 5.34360 0.254169
\(443\) −24.3353 −1.15621 −0.578103 0.815964i \(-0.696207\pi\)
−0.578103 + 0.815964i \(0.696207\pi\)
\(444\) 30.4127 1.44332
\(445\) 12.2959 0.582883
\(446\) 16.5493 0.783634
\(447\) −50.2297 −2.37579
\(448\) −0.381461 −0.0180224
\(449\) −13.8915 −0.655580 −0.327790 0.944751i \(-0.606304\pi\)
−0.327790 + 0.944751i \(0.606304\pi\)
\(450\) 6.33725 0.298741
\(451\) 1.13940 0.0536522
\(452\) −2.72236 −0.128049
\(453\) 23.6338 1.11041
\(454\) 7.46037 0.350133
\(455\) −1.45119 −0.0680330
\(456\) 2.78985 0.130647
\(457\) 41.1067 1.92289 0.961445 0.274996i \(-0.0886767\pi\)
0.961445 + 0.274996i \(0.0886767\pi\)
\(458\) 27.3715 1.27899
\(459\) 17.5747 0.820318
\(460\) −22.7716 −1.06173
\(461\) −7.92899 −0.369290 −0.184645 0.982805i \(-0.559114\pi\)
−0.184645 + 0.982805i \(0.559114\pi\)
\(462\) 1.97174 0.0917335
\(463\) 7.25597 0.337213 0.168607 0.985683i \(-0.446073\pi\)
0.168607 + 0.985683i \(0.446073\pi\)
\(464\) 5.58964 0.259493
\(465\) −47.4535 −2.20060
\(466\) −3.38922 −0.157002
\(467\) −26.2984 −1.21694 −0.608471 0.793576i \(-0.708217\pi\)
−0.608471 + 0.793576i \(0.708217\pi\)
\(468\) −7.23562 −0.334466
\(469\) −2.94354 −0.135920
\(470\) −25.4337 −1.17317
\(471\) 11.5513 0.532254
\(472\) −7.56646 −0.348274
\(473\) −10.7664 −0.495041
\(474\) −11.0245 −0.506372
\(475\) −1.32487 −0.0607893
\(476\) 1.34752 0.0617636
\(477\) 31.6439 1.44888
\(478\) −2.24183 −0.102539
\(479\) 30.9834 1.41567 0.707834 0.706378i \(-0.249672\pi\)
0.707834 + 0.706378i \(0.249672\pi\)
\(480\) 7.01629 0.320248
\(481\) 16.4901 0.751882
\(482\) −25.2142 −1.14847
\(483\) 9.63606 0.438456
\(484\) −7.56732 −0.343969
\(485\) 10.6775 0.484838
\(486\) 16.2366 0.736508
\(487\) 11.5194 0.521992 0.260996 0.965340i \(-0.415949\pi\)
0.260996 + 0.965340i \(0.415949\pi\)
\(488\) 10.3001 0.466265
\(489\) −44.8659 −2.02891
\(490\) 17.2386 0.778759
\(491\) −11.0127 −0.496997 −0.248499 0.968632i \(-0.579937\pi\)
−0.248499 + 0.968632i \(0.579937\pi\)
\(492\) −1.71570 −0.0773496
\(493\) −19.7455 −0.889294
\(494\) 1.51269 0.0680590
\(495\) −22.2879 −1.00177
\(496\) −6.76333 −0.303683
\(497\) 5.17289 0.232036
\(498\) 28.1514 1.26150
\(499\) 7.53530 0.337326 0.168663 0.985674i \(-0.446055\pi\)
0.168663 + 0.985674i \(0.446055\pi\)
\(500\) 9.24269 0.413346
\(501\) −10.2617 −0.458458
\(502\) 25.9381 1.15767
\(503\) 30.0720 1.34085 0.670423 0.741979i \(-0.266113\pi\)
0.670423 + 0.741979i \(0.266113\pi\)
\(504\) −1.82464 −0.0812759
\(505\) 11.7432 0.522564
\(506\) 16.7758 0.745777
\(507\) 29.8843 1.32721
\(508\) 12.9012 0.572397
\(509\) 19.9165 0.882782 0.441391 0.897315i \(-0.354485\pi\)
0.441391 + 0.897315i \(0.354485\pi\)
\(510\) −24.7852 −1.09751
\(511\) 4.42809 0.195887
\(512\) 1.00000 0.0441942
\(513\) 4.97512 0.219657
\(514\) 24.0627 1.06136
\(515\) 1.38862 0.0611899
\(516\) 16.2120 0.713693
\(517\) 18.7370 0.824054
\(518\) 4.15838 0.182709
\(519\) −47.8194 −2.09904
\(520\) 3.80430 0.166830
\(521\) 39.1365 1.71460 0.857301 0.514816i \(-0.172140\pi\)
0.857301 + 0.514816i \(0.172140\pi\)
\(522\) 26.7369 1.17024
\(523\) −16.3609 −0.715413 −0.357707 0.933834i \(-0.616441\pi\)
−0.357707 + 0.933834i \(0.616441\pi\)
\(524\) −16.1220 −0.704294
\(525\) 1.40996 0.0615356
\(526\) 3.75304 0.163640
\(527\) 23.8916 1.04074
\(528\) −5.16890 −0.224948
\(529\) 58.9850 2.56457
\(530\) −16.6376 −0.722689
\(531\) −36.1926 −1.57062
\(532\) 0.381461 0.0165384
\(533\) −0.930267 −0.0402943
\(534\) 13.6401 0.590264
\(535\) −29.6670 −1.28262
\(536\) 7.71648 0.333301
\(537\) −47.4748 −2.04869
\(538\) 24.9123 1.07405
\(539\) −12.6997 −0.547013
\(540\) 12.5121 0.538434
\(541\) −3.90353 −0.167826 −0.0839130 0.996473i \(-0.526742\pi\)
−0.0839130 + 0.996473i \(0.526742\pi\)
\(542\) −3.64088 −0.156389
\(543\) −32.0828 −1.37681
\(544\) −3.53252 −0.151456
\(545\) −31.5818 −1.35282
\(546\) −1.60983 −0.0688945
\(547\) 16.5851 0.709126 0.354563 0.935032i \(-0.384630\pi\)
0.354563 + 0.935032i \(0.384630\pi\)
\(548\) −6.62859 −0.283159
\(549\) 49.2685 2.10273
\(550\) 2.45466 0.104667
\(551\) −5.58964 −0.238127
\(552\) −25.2609 −1.07518
\(553\) −1.50740 −0.0641011
\(554\) −16.0293 −0.681020
\(555\) −76.4858 −3.24664
\(556\) −8.67522 −0.367911
\(557\) −29.7482 −1.26047 −0.630235 0.776404i \(-0.717042\pi\)
−0.630235 + 0.776404i \(0.717042\pi\)
\(558\) −32.3510 −1.36953
\(559\) 8.79030 0.371790
\(560\) 0.959349 0.0405399
\(561\) 18.2593 0.770908
\(562\) −11.4881 −0.484596
\(563\) 15.6976 0.661574 0.330787 0.943705i \(-0.392686\pi\)
0.330787 + 0.943705i \(0.392686\pi\)
\(564\) −28.2141 −1.18803
\(565\) 6.84654 0.288036
\(566\) −20.9876 −0.882176
\(567\) 0.179293 0.00752958
\(568\) −13.5607 −0.568996
\(569\) −21.5637 −0.903997 −0.451998 0.892019i \(-0.649289\pi\)
−0.451998 + 0.892019i \(0.649289\pi\)
\(570\) −7.01629 −0.293880
\(571\) 43.8490 1.83502 0.917512 0.397708i \(-0.130194\pi\)
0.917512 + 0.397708i \(0.130194\pi\)
\(572\) −2.80263 −0.117184
\(573\) −21.7420 −0.908284
\(574\) −0.234590 −0.00979159
\(575\) 11.9961 0.500274
\(576\) 4.78329 0.199304
\(577\) 44.6223 1.85765 0.928826 0.370516i \(-0.120819\pi\)
0.928826 + 0.370516i \(0.120819\pi\)
\(578\) −4.52127 −0.188060
\(579\) −29.3293 −1.21888
\(580\) −14.0576 −0.583708
\(581\) 3.84919 0.159691
\(582\) 11.8447 0.490978
\(583\) 12.2569 0.507629
\(584\) −11.6082 −0.480352
\(585\) 18.1971 0.752356
\(586\) 14.2041 0.586766
\(587\) −45.3034 −1.86987 −0.934936 0.354815i \(-0.884544\pi\)
−0.934936 + 0.354815i \(0.884544\pi\)
\(588\) 19.1230 0.788620
\(589\) 6.76333 0.278678
\(590\) 19.0291 0.783416
\(591\) 68.5584 2.82012
\(592\) −10.9012 −0.448035
\(593\) −38.9167 −1.59812 −0.799059 0.601252i \(-0.794669\pi\)
−0.799059 + 0.601252i \(0.794669\pi\)
\(594\) −9.21765 −0.378205
\(595\) −3.38892 −0.138932
\(596\) 18.0044 0.737490
\(597\) 40.6467 1.66356
\(598\) −13.6967 −0.560100
\(599\) −32.3158 −1.32039 −0.660194 0.751095i \(-0.729526\pi\)
−0.660194 + 0.751095i \(0.729526\pi\)
\(600\) −3.69620 −0.150897
\(601\) −9.53104 −0.388779 −0.194390 0.980924i \(-0.562273\pi\)
−0.194390 + 0.980924i \(0.562273\pi\)
\(602\) 2.21669 0.0903456
\(603\) 36.9102 1.50310
\(604\) −8.47133 −0.344694
\(605\) 19.0313 0.773731
\(606\) 13.0269 0.529182
\(607\) 9.16268 0.371902 0.185951 0.982559i \(-0.440464\pi\)
0.185951 + 0.982559i \(0.440464\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 5.94862 0.241050
\(610\) −25.9041 −1.04883
\(611\) −15.2979 −0.618888
\(612\) −16.8971 −0.683024
\(613\) 31.7215 1.28122 0.640611 0.767866i \(-0.278681\pi\)
0.640611 + 0.767866i \(0.278681\pi\)
\(614\) 11.4576 0.462393
\(615\) 4.31486 0.173992
\(616\) −0.706753 −0.0284759
\(617\) −27.0219 −1.08786 −0.543931 0.839130i \(-0.683065\pi\)
−0.543931 + 0.839130i \(0.683065\pi\)
\(618\) 1.54042 0.0619647
\(619\) −22.9196 −0.921217 −0.460608 0.887603i \(-0.652369\pi\)
−0.460608 + 0.887603i \(0.652369\pi\)
\(620\) 17.0093 0.683110
\(621\) −45.0475 −1.80769
\(622\) 32.6557 1.30937
\(623\) 1.86503 0.0747208
\(624\) 4.22017 0.168942
\(625\) −29.8691 −1.19476
\(626\) 16.7725 0.670365
\(627\) 5.16890 0.206426
\(628\) −4.14046 −0.165222
\(629\) 38.5087 1.53544
\(630\) 4.58884 0.182824
\(631\) 32.1996 1.28184 0.640922 0.767606i \(-0.278552\pi\)
0.640922 + 0.767606i \(0.278552\pi\)
\(632\) 3.95164 0.157188
\(633\) 2.78985 0.110887
\(634\) 20.6606 0.820537
\(635\) −32.4455 −1.28756
\(636\) −18.4563 −0.731841
\(637\) 10.3687 0.410822
\(638\) 10.3562 0.410006
\(639\) −64.8649 −2.56602
\(640\) −2.51493 −0.0994113
\(641\) 16.2029 0.639978 0.319989 0.947421i \(-0.396321\pi\)
0.319989 + 0.947421i \(0.396321\pi\)
\(642\) −32.9101 −1.29886
\(643\) 44.7222 1.76367 0.881835 0.471557i \(-0.156308\pi\)
0.881835 + 0.471557i \(0.156308\pi\)
\(644\) −3.45396 −0.136105
\(645\) −40.7720 −1.60540
\(646\) 3.53252 0.138985
\(647\) 44.0424 1.73149 0.865743 0.500490i \(-0.166847\pi\)
0.865743 + 0.500490i \(0.166847\pi\)
\(648\) −0.470015 −0.0184639
\(649\) −14.0188 −0.550285
\(650\) −2.00412 −0.0786079
\(651\) −7.19769 −0.282100
\(652\) 16.0818 0.629812
\(653\) 21.2712 0.832407 0.416204 0.909271i \(-0.363360\pi\)
0.416204 + 0.909271i \(0.363360\pi\)
\(654\) −35.0343 −1.36995
\(655\) 40.5458 1.58425
\(656\) 0.614977 0.0240108
\(657\) −55.5255 −2.16626
\(658\) −3.85775 −0.150391
\(659\) 3.92847 0.153031 0.0765157 0.997068i \(-0.475620\pi\)
0.0765157 + 0.997068i \(0.475620\pi\)
\(660\) 12.9994 0.506002
\(661\) 42.5418 1.65468 0.827342 0.561699i \(-0.189852\pi\)
0.827342 + 0.561699i \(0.189852\pi\)
\(662\) 20.0656 0.779873
\(663\) −14.9079 −0.578974
\(664\) −10.0906 −0.391593
\(665\) −0.959349 −0.0372019
\(666\) −52.1434 −2.02052
\(667\) 50.6117 1.95969
\(668\) 3.67821 0.142314
\(669\) −46.1702 −1.78504
\(670\) −19.4064 −0.749735
\(671\) 19.0836 0.736713
\(672\) 1.06422 0.0410532
\(673\) 32.8997 1.26819 0.634095 0.773255i \(-0.281373\pi\)
0.634095 + 0.773255i \(0.281373\pi\)
\(674\) 18.5215 0.713421
\(675\) −6.59140 −0.253703
\(676\) −10.7118 −0.411992
\(677\) −3.01893 −0.116027 −0.0580134 0.998316i \(-0.518477\pi\)
−0.0580134 + 0.998316i \(0.518477\pi\)
\(678\) 7.59498 0.291684
\(679\) 1.61954 0.0621524
\(680\) 8.88405 0.340688
\(681\) −20.8134 −0.797569
\(682\) −12.5308 −0.479828
\(683\) 11.0354 0.422259 0.211130 0.977458i \(-0.432286\pi\)
0.211130 + 0.977458i \(0.432286\pi\)
\(684\) −4.78329 −0.182894
\(685\) 16.6704 0.636945
\(686\) 5.28495 0.201780
\(687\) −76.3626 −2.91342
\(688\) −5.81105 −0.221544
\(689\) −10.0072 −0.381244
\(690\) 63.5294 2.41852
\(691\) −37.7357 −1.43553 −0.717767 0.696283i \(-0.754836\pi\)
−0.717767 + 0.696283i \(0.754836\pi\)
\(692\) 17.1404 0.651582
\(693\) −3.38060 −0.128418
\(694\) −19.1719 −0.727757
\(695\) 21.8176 0.827588
\(696\) −15.5943 −0.591100
\(697\) −2.17242 −0.0822863
\(698\) 14.6746 0.555442
\(699\) 9.45542 0.357637
\(700\) −0.505388 −0.0191019
\(701\) −9.85042 −0.372045 −0.186023 0.982545i \(-0.559560\pi\)
−0.186023 + 0.982545i \(0.559560\pi\)
\(702\) 7.52579 0.284043
\(703\) 10.9012 0.411145
\(704\) 1.85275 0.0698282
\(705\) 70.9564 2.67237
\(706\) 24.3574 0.916702
\(707\) 1.78119 0.0669885
\(708\) 21.1093 0.793337
\(709\) −17.8571 −0.670637 −0.335318 0.942105i \(-0.608844\pi\)
−0.335318 + 0.942105i \(0.608844\pi\)
\(710\) 34.1043 1.27991
\(711\) 18.9018 0.708875
\(712\) −4.88917 −0.183229
\(713\) −61.2390 −2.29342
\(714\) −3.75939 −0.140692
\(715\) 7.04842 0.263596
\(716\) 17.0170 0.635954
\(717\) 6.25438 0.233574
\(718\) −28.7641 −1.07347
\(719\) −1.13320 −0.0422613 −0.0211306 0.999777i \(-0.506727\pi\)
−0.0211306 + 0.999777i \(0.506727\pi\)
\(720\) −12.0296 −0.448318
\(721\) 0.210624 0.00784405
\(722\) 1.00000 0.0372161
\(723\) 70.3439 2.61612
\(724\) 11.4998 0.427387
\(725\) 7.40556 0.275036
\(726\) 21.1117 0.783529
\(727\) −22.6380 −0.839598 −0.419799 0.907617i \(-0.637899\pi\)
−0.419799 + 0.907617i \(0.637899\pi\)
\(728\) 0.577031 0.0213862
\(729\) −43.8878 −1.62547
\(730\) 29.1939 1.08051
\(731\) 20.5277 0.759244
\(732\) −28.7359 −1.06211
\(733\) −1.61203 −0.0595415 −0.0297708 0.999557i \(-0.509478\pi\)
−0.0297708 + 0.999557i \(0.509478\pi\)
\(734\) 23.2429 0.857910
\(735\) −48.0931 −1.77394
\(736\) 9.05456 0.333755
\(737\) 14.2967 0.526626
\(738\) 2.94161 0.108282
\(739\) −17.5972 −0.647323 −0.323661 0.946173i \(-0.604914\pi\)
−0.323661 + 0.946173i \(0.604914\pi\)
\(740\) 27.4157 1.00782
\(741\) −4.22017 −0.155032
\(742\) −2.52356 −0.0926429
\(743\) −21.2998 −0.781412 −0.390706 0.920515i \(-0.627769\pi\)
−0.390706 + 0.920515i \(0.627769\pi\)
\(744\) 18.8687 0.691761
\(745\) −45.2799 −1.65893
\(746\) 18.0135 0.659522
\(747\) −48.2664 −1.76598
\(748\) −6.54489 −0.239305
\(749\) −4.49985 −0.164421
\(750\) −25.7858 −0.941563
\(751\) 6.74135 0.245995 0.122998 0.992407i \(-0.460749\pi\)
0.122998 + 0.992407i \(0.460749\pi\)
\(752\) 10.1131 0.368786
\(753\) −72.3634 −2.63707
\(754\) −8.45537 −0.307926
\(755\) 21.3048 0.775362
\(756\) 1.89781 0.0690228
\(757\) −49.8042 −1.81017 −0.905083 0.425236i \(-0.860191\pi\)
−0.905083 + 0.425236i \(0.860191\pi\)
\(758\) −0.852570 −0.0309667
\(759\) −46.8021 −1.69881
\(760\) 2.51493 0.0912261
\(761\) 31.3263 1.13558 0.567789 0.823174i \(-0.307799\pi\)
0.567789 + 0.823174i \(0.307799\pi\)
\(762\) −35.9924 −1.30387
\(763\) −4.79029 −0.173420
\(764\) 7.79323 0.281949
\(765\) 42.4950 1.53641
\(766\) −30.7968 −1.11273
\(767\) 11.4457 0.413279
\(768\) −2.78985 −0.100670
\(769\) −26.5863 −0.958726 −0.479363 0.877617i \(-0.659132\pi\)
−0.479363 + 0.877617i \(0.659132\pi\)
\(770\) 1.77743 0.0640543
\(771\) −67.1313 −2.41768
\(772\) 10.5128 0.378365
\(773\) 30.2003 1.08623 0.543115 0.839659i \(-0.317245\pi\)
0.543115 + 0.839659i \(0.317245\pi\)
\(774\) −27.7959 −0.999104
\(775\) −8.96056 −0.321873
\(776\) −4.24563 −0.152409
\(777\) −11.6013 −0.416193
\(778\) 5.99114 0.214793
\(779\) −0.614977 −0.0220338
\(780\) −10.6134 −0.380022
\(781\) −25.1247 −0.899031
\(782\) −31.9854 −1.14380
\(783\) −27.8091 −0.993816
\(784\) −6.85449 −0.244803
\(785\) 10.4130 0.371654
\(786\) 44.9781 1.60432
\(787\) −14.6882 −0.523576 −0.261788 0.965125i \(-0.584312\pi\)
−0.261788 + 0.965125i \(0.584312\pi\)
\(788\) −24.5742 −0.875420
\(789\) −10.4704 −0.372758
\(790\) −9.93811 −0.353582
\(791\) 1.03847 0.0369239
\(792\) 8.86224 0.314906
\(793\) −15.5809 −0.553293
\(794\) 25.0779 0.889981
\(795\) 46.4164 1.64622
\(796\) −14.5695 −0.516401
\(797\) 40.3293 1.42854 0.714268 0.699872i \(-0.246760\pi\)
0.714268 + 0.699872i \(0.246760\pi\)
\(798\) −1.06422 −0.0376730
\(799\) −35.7247 −1.26385
\(800\) 1.32487 0.0468413
\(801\) −23.3863 −0.826315
\(802\) 27.9765 0.987885
\(803\) −21.5072 −0.758971
\(804\) −21.5279 −0.759229
\(805\) 8.68648 0.306158
\(806\) 10.2308 0.360365
\(807\) −69.5017 −2.44658
\(808\) −4.66938 −0.164268
\(809\) 23.2684 0.818075 0.409038 0.912518i \(-0.365865\pi\)
0.409038 + 0.912518i \(0.365865\pi\)
\(810\) 1.18205 0.0415332
\(811\) −14.6454 −0.514269 −0.257135 0.966376i \(-0.582778\pi\)
−0.257135 + 0.966376i \(0.582778\pi\)
\(812\) −2.13223 −0.0748267
\(813\) 10.1575 0.356240
\(814\) −20.1972 −0.707910
\(815\) −40.4446 −1.41671
\(816\) 9.85523 0.345002
\(817\) 5.81105 0.203303
\(818\) −15.1309 −0.529039
\(819\) 2.76011 0.0964460
\(820\) −1.54662 −0.0540105
\(821\) −28.5448 −0.996221 −0.498111 0.867114i \(-0.665973\pi\)
−0.498111 + 0.867114i \(0.665973\pi\)
\(822\) 18.4928 0.645011
\(823\) 35.8240 1.24875 0.624373 0.781126i \(-0.285355\pi\)
0.624373 + 0.781126i \(0.285355\pi\)
\(824\) −0.552150 −0.0192351
\(825\) −6.84814 −0.238422
\(826\) 2.88631 0.100428
\(827\) −3.00602 −0.104529 −0.0522647 0.998633i \(-0.516644\pi\)
−0.0522647 + 0.998633i \(0.516644\pi\)
\(828\) 43.3106 1.50515
\(829\) −3.99999 −0.138925 −0.0694627 0.997585i \(-0.522128\pi\)
−0.0694627 + 0.997585i \(0.522128\pi\)
\(830\) 25.3773 0.880857
\(831\) 44.7194 1.55130
\(832\) −1.51269 −0.0524430
\(833\) 24.2136 0.838953
\(834\) 24.2026 0.838068
\(835\) −9.25044 −0.320125
\(836\) −1.85275 −0.0640787
\(837\) 33.6484 1.16306
\(838\) 14.2414 0.491961
\(839\) −9.79810 −0.338268 −0.169134 0.985593i \(-0.554097\pi\)
−0.169134 + 0.985593i \(0.554097\pi\)
\(840\) −2.67644 −0.0923461
\(841\) 2.24407 0.0773819
\(842\) 1.99964 0.0689122
\(843\) 32.0501 1.10386
\(844\) −1.00000 −0.0344214
\(845\) 26.9394 0.926743
\(846\) 48.3738 1.66313
\(847\) 2.88664 0.0991861
\(848\) 6.61551 0.227178
\(849\) 58.5525 2.00952
\(850\) −4.68015 −0.160528
\(851\) −98.7053 −3.38357
\(852\) 37.8325 1.29612
\(853\) 29.3378 1.00451 0.502253 0.864721i \(-0.332505\pi\)
0.502253 + 0.864721i \(0.332505\pi\)
\(854\) −3.92910 −0.134451
\(855\) 12.0296 0.411405
\(856\) 11.7963 0.403191
\(857\) −6.83964 −0.233638 −0.116819 0.993153i \(-0.537270\pi\)
−0.116819 + 0.993153i \(0.537270\pi\)
\(858\) 7.81893 0.266934
\(859\) −19.6782 −0.671412 −0.335706 0.941967i \(-0.608975\pi\)
−0.335706 + 0.941967i \(0.608975\pi\)
\(860\) 14.6144 0.498347
\(861\) 0.654472 0.0223043
\(862\) −32.2995 −1.10013
\(863\) −21.5803 −0.734600 −0.367300 0.930102i \(-0.619718\pi\)
−0.367300 + 0.930102i \(0.619718\pi\)
\(864\) −4.97512 −0.169257
\(865\) −43.1070 −1.46568
\(866\) 9.51355 0.323284
\(867\) 12.6137 0.428383
\(868\) 2.57995 0.0875692
\(869\) 7.32141 0.248362
\(870\) 39.2185 1.32963
\(871\) −11.6726 −0.395512
\(872\) 12.5577 0.425259
\(873\) −20.3081 −0.687324
\(874\) −9.05456 −0.306275
\(875\) −3.52573 −0.119191
\(876\) 32.3853 1.09420
\(877\) 30.2120 1.02019 0.510093 0.860119i \(-0.329611\pi\)
0.510093 + 0.860119i \(0.329611\pi\)
\(878\) −39.7801 −1.34251
\(879\) −39.6274 −1.33660
\(880\) −4.65954 −0.157073
\(881\) 9.50022 0.320070 0.160035 0.987111i \(-0.448839\pi\)
0.160035 + 0.987111i \(0.448839\pi\)
\(882\) −32.7870 −1.10400
\(883\) −13.4375 −0.452207 −0.226104 0.974103i \(-0.572599\pi\)
−0.226104 + 0.974103i \(0.572599\pi\)
\(884\) 5.34360 0.179725
\(885\) −53.0885 −1.78455
\(886\) −24.3353 −0.817561
\(887\) 18.9522 0.636351 0.318176 0.948032i \(-0.396930\pi\)
0.318176 + 0.948032i \(0.396930\pi\)
\(888\) 30.4127 1.02058
\(889\) −4.92130 −0.165055
\(890\) 12.2959 0.412160
\(891\) −0.870821 −0.0291736
\(892\) 16.5493 0.554113
\(893\) −10.1131 −0.338422
\(894\) −50.2297 −1.67993
\(895\) −42.7965 −1.43053
\(896\) −0.381461 −0.0127437
\(897\) 38.2118 1.27586
\(898\) −13.8915 −0.463565
\(899\) −37.8046 −1.26085
\(900\) 6.33725 0.211242
\(901\) −23.3695 −0.778550
\(902\) 1.13940 0.0379378
\(903\) −6.18425 −0.205799
\(904\) −2.72236 −0.0905443
\(905\) −28.9212 −0.961374
\(906\) 23.6338 0.785180
\(907\) 10.3122 0.342411 0.171205 0.985235i \(-0.445234\pi\)
0.171205 + 0.985235i \(0.445234\pi\)
\(908\) 7.46037 0.247581
\(909\) −22.3350 −0.740805
\(910\) −1.45119 −0.0481066
\(911\) −58.1985 −1.92820 −0.964101 0.265535i \(-0.914452\pi\)
−0.964101 + 0.265535i \(0.914452\pi\)
\(912\) 2.78985 0.0923813
\(913\) −18.6954 −0.618729
\(914\) 41.1067 1.35969
\(915\) 72.2687 2.38913
\(916\) 27.3715 0.904381
\(917\) 6.14993 0.203089
\(918\) 17.5747 0.580052
\(919\) −58.8412 −1.94099 −0.970495 0.241120i \(-0.922485\pi\)
−0.970495 + 0.241120i \(0.922485\pi\)
\(920\) −22.7716 −0.750757
\(921\) −31.9652 −1.05329
\(922\) −7.92899 −0.261127
\(923\) 20.5131 0.675198
\(924\) 1.97174 0.0648654
\(925\) −14.4427 −0.474872
\(926\) 7.25597 0.238446
\(927\) −2.64109 −0.0867449
\(928\) 5.58964 0.183489
\(929\) −14.6133 −0.479445 −0.239723 0.970841i \(-0.577056\pi\)
−0.239723 + 0.970841i \(0.577056\pi\)
\(930\) −47.4535 −1.55606
\(931\) 6.85449 0.224647
\(932\) −3.38922 −0.111017
\(933\) −91.1045 −2.98263
\(934\) −26.2984 −0.860508
\(935\) 16.4599 0.538297
\(936\) −7.23562 −0.236503
\(937\) −2.83842 −0.0927270 −0.0463635 0.998925i \(-0.514763\pi\)
−0.0463635 + 0.998925i \(0.514763\pi\)
\(938\) −2.94354 −0.0961100
\(939\) −46.7929 −1.52703
\(940\) −25.4337 −0.829556
\(941\) −55.5845 −1.81200 −0.906001 0.423275i \(-0.860880\pi\)
−0.906001 + 0.423275i \(0.860880\pi\)
\(942\) 11.5513 0.376361
\(943\) 5.56834 0.181330
\(944\) −7.56646 −0.246267
\(945\) −4.77287 −0.155262
\(946\) −10.7664 −0.350047
\(947\) 10.4270 0.338832 0.169416 0.985545i \(-0.445812\pi\)
0.169416 + 0.985545i \(0.445812\pi\)
\(948\) −11.0245 −0.358059
\(949\) 17.5596 0.570009
\(950\) −1.32487 −0.0429846
\(951\) −57.6401 −1.86911
\(952\) 1.34752 0.0436734
\(953\) 8.04135 0.260485 0.130242 0.991482i \(-0.458424\pi\)
0.130242 + 0.991482i \(0.458424\pi\)
\(954\) 31.6439 1.02451
\(955\) −19.5994 −0.634223
\(956\) −2.24183 −0.0725060
\(957\) −28.8923 −0.933956
\(958\) 30.9834 1.00103
\(959\) 2.52855 0.0816512
\(960\) 7.01629 0.226450
\(961\) 14.7427 0.475571
\(962\) 16.4901 0.531661
\(963\) 56.4253 1.81828
\(964\) −25.2142 −0.812094
\(965\) −26.4391 −0.851103
\(966\) 9.63606 0.310035
\(967\) −14.9287 −0.480075 −0.240038 0.970764i \(-0.577160\pi\)
−0.240038 + 0.970764i \(0.577160\pi\)
\(968\) −7.56732 −0.243223
\(969\) −9.85523 −0.316596
\(970\) 10.6775 0.342833
\(971\) −11.6150 −0.372742 −0.186371 0.982479i \(-0.559673\pi\)
−0.186371 + 0.982479i \(0.559673\pi\)
\(972\) 16.2366 0.520790
\(973\) 3.30926 0.106090
\(974\) 11.5194 0.369104
\(975\) 5.59120 0.179062
\(976\) 10.3001 0.329699
\(977\) 28.9508 0.926218 0.463109 0.886301i \(-0.346734\pi\)
0.463109 + 0.886301i \(0.346734\pi\)
\(978\) −44.8659 −1.43465
\(979\) −9.05841 −0.289508
\(980\) 17.2386 0.550665
\(981\) 60.0673 1.91780
\(982\) −11.0127 −0.351430
\(983\) −50.4130 −1.60792 −0.803962 0.594681i \(-0.797279\pi\)
−0.803962 + 0.594681i \(0.797279\pi\)
\(984\) −1.71570 −0.0546944
\(985\) 61.8024 1.96919
\(986\) −19.7455 −0.628826
\(987\) 10.7626 0.342576
\(988\) 1.51269 0.0481250
\(989\) −52.6165 −1.67311
\(990\) −22.2879 −0.708356
\(991\) −6.48746 −0.206081 −0.103041 0.994677i \(-0.532857\pi\)
−0.103041 + 0.994677i \(0.532857\pi\)
\(992\) −6.76333 −0.214736
\(993\) −55.9802 −1.77648
\(994\) 5.17289 0.164074
\(995\) 36.6412 1.16160
\(996\) 28.1514 0.892012
\(997\) 0.807451 0.0255722 0.0127861 0.999918i \(-0.495930\pi\)
0.0127861 + 0.999918i \(0.495930\pi\)
\(998\) 7.53530 0.238526
\(999\) 54.2346 1.71591
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 \(a_p\))