Properties

Label 8042.2.a.c.1.19
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.95612 q^{3}\) \(+1.00000 q^{4}\) \(+0.359780 q^{5}\) \(+1.95612 q^{6}\) \(-1.34656 q^{7}\) \(-1.00000 q^{8}\) \(+0.826410 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.95612 q^{3}\) \(+1.00000 q^{4}\) \(+0.359780 q^{5}\) \(+1.95612 q^{6}\) \(-1.34656 q^{7}\) \(-1.00000 q^{8}\) \(+0.826410 q^{9}\) \(-0.359780 q^{10}\) \(-1.45863 q^{11}\) \(-1.95612 q^{12}\) \(-1.46403 q^{13}\) \(+1.34656 q^{14}\) \(-0.703774 q^{15}\) \(+1.00000 q^{16}\) \(+2.18699 q^{17}\) \(-0.826410 q^{18}\) \(-0.0167571 q^{19}\) \(+0.359780 q^{20}\) \(+2.63403 q^{21}\) \(+1.45863 q^{22}\) \(+2.73171 q^{23}\) \(+1.95612 q^{24}\) \(-4.87056 q^{25}\) \(+1.46403 q^{26}\) \(+4.25180 q^{27}\) \(-1.34656 q^{28}\) \(+8.45751 q^{29}\) \(+0.703774 q^{30}\) \(+1.90088 q^{31}\) \(-1.00000 q^{32}\) \(+2.85326 q^{33}\) \(-2.18699 q^{34}\) \(-0.484464 q^{35}\) \(+0.826410 q^{36}\) \(-4.97197 q^{37}\) \(+0.0167571 q^{38}\) \(+2.86382 q^{39}\) \(-0.359780 q^{40}\) \(+0.347278 q^{41}\) \(-2.63403 q^{42}\) \(-6.02157 q^{43}\) \(-1.45863 q^{44}\) \(+0.297326 q^{45}\) \(-2.73171 q^{46}\) \(+11.8533 q^{47}\) \(-1.95612 q^{48}\) \(-5.18679 q^{49}\) \(+4.87056 q^{50}\) \(-4.27803 q^{51}\) \(-1.46403 q^{52}\) \(-8.10403 q^{53}\) \(-4.25180 q^{54}\) \(-0.524787 q^{55}\) \(+1.34656 q^{56}\) \(+0.0327789 q^{57}\) \(-8.45751 q^{58}\) \(+0.940926 q^{59}\) \(-0.703774 q^{60}\) \(-0.574197 q^{61}\) \(-1.90088 q^{62}\) \(-1.11281 q^{63}\) \(+1.00000 q^{64}\) \(-0.526729 q^{65}\) \(-2.85326 q^{66}\) \(-9.88107 q^{67}\) \(+2.18699 q^{68}\) \(-5.34355 q^{69}\) \(+0.484464 q^{70}\) \(-13.0279 q^{71}\) \(-0.826410 q^{72}\) \(-6.35541 q^{73}\) \(+4.97197 q^{74}\) \(+9.52740 q^{75}\) \(-0.0167571 q^{76}\) \(+1.96413 q^{77}\) \(-2.86382 q^{78}\) \(-8.79048 q^{79}\) \(+0.359780 q^{80}\) \(-10.7963 q^{81}\) \(-0.347278 q^{82}\) \(+10.2256 q^{83}\) \(+2.63403 q^{84}\) \(+0.786837 q^{85}\) \(+6.02157 q^{86}\) \(-16.5439 q^{87}\) \(+1.45863 q^{88}\) \(+7.08705 q^{89}\) \(-0.297326 q^{90}\) \(+1.97140 q^{91}\) \(+2.73171 q^{92}\) \(-3.71835 q^{93}\) \(-11.8533 q^{94}\) \(-0.00602887 q^{95}\) \(+1.95612 q^{96}\) \(+18.5745 q^{97}\) \(+5.18679 q^{98}\) \(-1.20543 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.95612 −1.12937 −0.564684 0.825307i \(-0.691002\pi\)
−0.564684 + 0.825307i \(0.691002\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.359780 0.160899 0.0804493 0.996759i \(-0.474364\pi\)
0.0804493 + 0.996759i \(0.474364\pi\)
\(6\) 1.95612 0.798583
\(7\) −1.34656 −0.508950 −0.254475 0.967079i \(-0.581903\pi\)
−0.254475 + 0.967079i \(0.581903\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.826410 0.275470
\(10\) −0.359780 −0.113772
\(11\) −1.45863 −0.439794 −0.219897 0.975523i \(-0.570572\pi\)
−0.219897 + 0.975523i \(0.570572\pi\)
\(12\) −1.95612 −0.564684
\(13\) −1.46403 −0.406049 −0.203025 0.979174i \(-0.565077\pi\)
−0.203025 + 0.979174i \(0.565077\pi\)
\(14\) 1.34656 0.359882
\(15\) −0.703774 −0.181714
\(16\) 1.00000 0.250000
\(17\) 2.18699 0.530424 0.265212 0.964190i \(-0.414558\pi\)
0.265212 + 0.964190i \(0.414558\pi\)
\(18\) −0.826410 −0.194787
\(19\) −0.0167571 −0.00384434 −0.00192217 0.999998i \(-0.500612\pi\)
−0.00192217 + 0.999998i \(0.500612\pi\)
\(20\) 0.359780 0.0804493
\(21\) 2.63403 0.574792
\(22\) 1.45863 0.310982
\(23\) 2.73171 0.569600 0.284800 0.958587i \(-0.408073\pi\)
0.284800 + 0.958587i \(0.408073\pi\)
\(24\) 1.95612 0.399292
\(25\) −4.87056 −0.974112
\(26\) 1.46403 0.287120
\(27\) 4.25180 0.818260
\(28\) −1.34656 −0.254475
\(29\) 8.45751 1.57052 0.785260 0.619166i \(-0.212529\pi\)
0.785260 + 0.619166i \(0.212529\pi\)
\(30\) 0.703774 0.128491
\(31\) 1.90088 0.341408 0.170704 0.985322i \(-0.445396\pi\)
0.170704 + 0.985322i \(0.445396\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.85326 0.496689
\(34\) −2.18699 −0.375066
\(35\) −0.484464 −0.0818894
\(36\) 0.826410 0.137735
\(37\) −4.97197 −0.817387 −0.408693 0.912672i \(-0.634015\pi\)
−0.408693 + 0.912672i \(0.634015\pi\)
\(38\) 0.0167571 0.00271836
\(39\) 2.86382 0.458579
\(40\) −0.359780 −0.0568862
\(41\) 0.347278 0.0542356 0.0271178 0.999632i \(-0.491367\pi\)
0.0271178 + 0.999632i \(0.491367\pi\)
\(42\) −2.63403 −0.406439
\(43\) −6.02157 −0.918281 −0.459140 0.888364i \(-0.651843\pi\)
−0.459140 + 0.888364i \(0.651843\pi\)
\(44\) −1.45863 −0.219897
\(45\) 0.297326 0.0443228
\(46\) −2.73171 −0.402768
\(47\) 11.8533 1.72898 0.864490 0.502650i \(-0.167642\pi\)
0.864490 + 0.502650i \(0.167642\pi\)
\(48\) −1.95612 −0.282342
\(49\) −5.18679 −0.740970
\(50\) 4.87056 0.688801
\(51\) −4.27803 −0.599043
\(52\) −1.46403 −0.203025
\(53\) −8.10403 −1.11317 −0.556587 0.830789i \(-0.687889\pi\)
−0.556587 + 0.830789i \(0.687889\pi\)
\(54\) −4.25180 −0.578597
\(55\) −0.524787 −0.0707623
\(56\) 1.34656 0.179941
\(57\) 0.0327789 0.00434167
\(58\) −8.45751 −1.11053
\(59\) 0.940926 0.122498 0.0612491 0.998123i \(-0.480492\pi\)
0.0612491 + 0.998123i \(0.480492\pi\)
\(60\) −0.703774 −0.0908568
\(61\) −0.574197 −0.0735184 −0.0367592 0.999324i \(-0.511703\pi\)
−0.0367592 + 0.999324i \(0.511703\pi\)
\(62\) −1.90088 −0.241412
\(63\) −1.11281 −0.140201
\(64\) 1.00000 0.125000
\(65\) −0.526729 −0.0653327
\(66\) −2.85326 −0.351212
\(67\) −9.88107 −1.20716 −0.603582 0.797301i \(-0.706261\pi\)
−0.603582 + 0.797301i \(0.706261\pi\)
\(68\) 2.18699 0.265212
\(69\) −5.34355 −0.643288
\(70\) 0.484464 0.0579045
\(71\) −13.0279 −1.54613 −0.773065 0.634326i \(-0.781278\pi\)
−0.773065 + 0.634326i \(0.781278\pi\)
\(72\) −0.826410 −0.0973934
\(73\) −6.35541 −0.743845 −0.371922 0.928264i \(-0.621301\pi\)
−0.371922 + 0.928264i \(0.621301\pi\)
\(74\) 4.97197 0.577980
\(75\) 9.52740 1.10013
\(76\) −0.0167571 −0.00192217
\(77\) 1.96413 0.223834
\(78\) −2.86382 −0.324264
\(79\) −8.79048 −0.989006 −0.494503 0.869176i \(-0.664650\pi\)
−0.494503 + 0.869176i \(0.664650\pi\)
\(80\) 0.359780 0.0402247
\(81\) −10.7963 −1.19959
\(82\) −0.347278 −0.0383504
\(83\) 10.2256 1.12241 0.561204 0.827678i \(-0.310338\pi\)
0.561204 + 0.827678i \(0.310338\pi\)
\(84\) 2.63403 0.287396
\(85\) 0.786837 0.0853445
\(86\) 6.02157 0.649323
\(87\) −16.5439 −1.77369
\(88\) 1.45863 0.155491
\(89\) 7.08705 0.751225 0.375613 0.926777i \(-0.377432\pi\)
0.375613 + 0.926777i \(0.377432\pi\)
\(90\) −0.297326 −0.0313409
\(91\) 1.97140 0.206659
\(92\) 2.73171 0.284800
\(93\) −3.71835 −0.385575
\(94\) −11.8533 −1.22257
\(95\) −0.00602887 −0.000618549 0
\(96\) 1.95612 0.199646
\(97\) 18.5745 1.88595 0.942977 0.332857i \(-0.108013\pi\)
0.942977 + 0.332857i \(0.108013\pi\)
\(98\) 5.18679 0.523945
\(99\) −1.20543 −0.121150
\(100\) −4.87056 −0.487056
\(101\) −15.6453 −1.55677 −0.778384 0.627789i \(-0.783960\pi\)
−0.778384 + 0.627789i \(0.783960\pi\)
\(102\) 4.27803 0.423588
\(103\) 4.00189 0.394318 0.197159 0.980372i \(-0.436828\pi\)
0.197159 + 0.980372i \(0.436828\pi\)
\(104\) 1.46403 0.143560
\(105\) 0.947671 0.0924832
\(106\) 8.10403 0.787133
\(107\) −4.20779 −0.406782 −0.203391 0.979098i \(-0.565196\pi\)
−0.203391 + 0.979098i \(0.565196\pi\)
\(108\) 4.25180 0.409130
\(109\) 3.42355 0.327917 0.163958 0.986467i \(-0.447574\pi\)
0.163958 + 0.986467i \(0.447574\pi\)
\(110\) 0.524787 0.0500365
\(111\) 9.72577 0.923130
\(112\) −1.34656 −0.127238
\(113\) 13.9681 1.31401 0.657004 0.753887i \(-0.271823\pi\)
0.657004 + 0.753887i \(0.271823\pi\)
\(114\) −0.0327789 −0.00307002
\(115\) 0.982814 0.0916479
\(116\) 8.45751 0.785260
\(117\) −1.20989 −0.111854
\(118\) −0.940926 −0.0866193
\(119\) −2.94491 −0.269959
\(120\) 0.703774 0.0642455
\(121\) −8.87239 −0.806581
\(122\) 0.574197 0.0519853
\(123\) −0.679317 −0.0612520
\(124\) 1.90088 0.170704
\(125\) −3.55123 −0.317632
\(126\) 1.11281 0.0991368
\(127\) −4.15073 −0.368318 −0.184159 0.982896i \(-0.558956\pi\)
−0.184159 + 0.982896i \(0.558956\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.7789 1.03708
\(130\) 0.526729 0.0461972
\(131\) 4.50989 0.394031 0.197016 0.980400i \(-0.436875\pi\)
0.197016 + 0.980400i \(0.436875\pi\)
\(132\) 2.85326 0.248345
\(133\) 0.0225643 0.00195658
\(134\) 9.88107 0.853594
\(135\) 1.52972 0.131657
\(136\) −2.18699 −0.187533
\(137\) −3.36358 −0.287370 −0.143685 0.989623i \(-0.545895\pi\)
−0.143685 + 0.989623i \(0.545895\pi\)
\(138\) 5.34355 0.454873
\(139\) 21.6408 1.83555 0.917773 0.397104i \(-0.129985\pi\)
0.917773 + 0.397104i \(0.129985\pi\)
\(140\) −0.484464 −0.0409447
\(141\) −23.1865 −1.95265
\(142\) 13.0279 1.09328
\(143\) 2.13548 0.178578
\(144\) 0.826410 0.0688675
\(145\) 3.04285 0.252695
\(146\) 6.35541 0.525978
\(147\) 10.1460 0.836827
\(148\) −4.97197 −0.408693
\(149\) −22.9120 −1.87703 −0.938514 0.345242i \(-0.887797\pi\)
−0.938514 + 0.345242i \(0.887797\pi\)
\(150\) −9.52740 −0.777909
\(151\) −24.2613 −1.97436 −0.987180 0.159610i \(-0.948976\pi\)
−0.987180 + 0.159610i \(0.948976\pi\)
\(152\) 0.0167571 0.00135918
\(153\) 1.80735 0.146116
\(154\) −1.96413 −0.158274
\(155\) 0.683899 0.0549321
\(156\) 2.86382 0.229289
\(157\) 1.11609 0.0890734 0.0445367 0.999008i \(-0.485819\pi\)
0.0445367 + 0.999008i \(0.485819\pi\)
\(158\) 8.79048 0.699333
\(159\) 15.8525 1.25718
\(160\) −0.359780 −0.0284431
\(161\) −3.67840 −0.289898
\(162\) 10.7963 0.848236
\(163\) 20.8506 1.63315 0.816574 0.577241i \(-0.195871\pi\)
0.816574 + 0.577241i \(0.195871\pi\)
\(164\) 0.347278 0.0271178
\(165\) 1.02655 0.0799166
\(166\) −10.2256 −0.793662
\(167\) −6.69157 −0.517809 −0.258904 0.965903i \(-0.583361\pi\)
−0.258904 + 0.965903i \(0.583361\pi\)
\(168\) −2.63403 −0.203220
\(169\) −10.8566 −0.835124
\(170\) −0.786837 −0.0603477
\(171\) −0.0138482 −0.00105900
\(172\) −6.02157 −0.459140
\(173\) 0.619997 0.0471375 0.0235687 0.999722i \(-0.492497\pi\)
0.0235687 + 0.999722i \(0.492497\pi\)
\(174\) 16.5439 1.25419
\(175\) 6.55848 0.495774
\(176\) −1.45863 −0.109949
\(177\) −1.84057 −0.138345
\(178\) −7.08705 −0.531197
\(179\) 7.23870 0.541046 0.270523 0.962714i \(-0.412803\pi\)
0.270523 + 0.962714i \(0.412803\pi\)
\(180\) 0.297326 0.0221614
\(181\) 14.1704 1.05328 0.526639 0.850089i \(-0.323452\pi\)
0.526639 + 0.850089i \(0.323452\pi\)
\(182\) −1.97140 −0.146130
\(183\) 1.12320 0.0830292
\(184\) −2.73171 −0.201384
\(185\) −1.78882 −0.131516
\(186\) 3.71835 0.272643
\(187\) −3.19002 −0.233277
\(188\) 11.8533 0.864490
\(189\) −5.72529 −0.416454
\(190\) 0.00602887 0.000437380 0
\(191\) −19.3279 −1.39852 −0.699258 0.714869i \(-0.746486\pi\)
−0.699258 + 0.714869i \(0.746486\pi\)
\(192\) −1.95612 −0.141171
\(193\) −2.91199 −0.209610 −0.104805 0.994493i \(-0.533422\pi\)
−0.104805 + 0.994493i \(0.533422\pi\)
\(194\) −18.5745 −1.33357
\(195\) 1.03035 0.0737847
\(196\) −5.18679 −0.370485
\(197\) 15.0270 1.07063 0.535315 0.844653i \(-0.320193\pi\)
0.535315 + 0.844653i \(0.320193\pi\)
\(198\) 1.20543 0.0856662
\(199\) −5.23835 −0.371337 −0.185668 0.982612i \(-0.559445\pi\)
−0.185668 + 0.982612i \(0.559445\pi\)
\(200\) 4.87056 0.344400
\(201\) 19.3286 1.36333
\(202\) 15.6453 1.10080
\(203\) −11.3885 −0.799317
\(204\) −4.27803 −0.299522
\(205\) 0.124944 0.00872644
\(206\) −4.00189 −0.278825
\(207\) 2.25751 0.156908
\(208\) −1.46403 −0.101512
\(209\) 0.0244424 0.00169072
\(210\) −0.947671 −0.0653955
\(211\) 12.3093 0.847410 0.423705 0.905800i \(-0.360729\pi\)
0.423705 + 0.905800i \(0.360729\pi\)
\(212\) −8.10403 −0.556587
\(213\) 25.4842 1.74615
\(214\) 4.20779 0.287639
\(215\) −2.16644 −0.147750
\(216\) −4.25180 −0.289299
\(217\) −2.55964 −0.173760
\(218\) −3.42355 −0.231872
\(219\) 12.4320 0.840074
\(220\) −0.524787 −0.0353812
\(221\) −3.20183 −0.215378
\(222\) −9.72577 −0.652751
\(223\) 21.2435 1.42257 0.711284 0.702905i \(-0.248114\pi\)
0.711284 + 0.702905i \(0.248114\pi\)
\(224\) 1.34656 0.0899705
\(225\) −4.02508 −0.268339
\(226\) −13.9681 −0.929144
\(227\) −19.4120 −1.28842 −0.644211 0.764848i \(-0.722814\pi\)
−0.644211 + 0.764848i \(0.722814\pi\)
\(228\) 0.0327789 0.00217083
\(229\) −7.72343 −0.510378 −0.255189 0.966891i \(-0.582138\pi\)
−0.255189 + 0.966891i \(0.582138\pi\)
\(230\) −0.982814 −0.0648048
\(231\) −3.84208 −0.252790
\(232\) −8.45751 −0.555263
\(233\) −9.42994 −0.617776 −0.308888 0.951098i \(-0.599957\pi\)
−0.308888 + 0.951098i \(0.599957\pi\)
\(234\) 1.20989 0.0790930
\(235\) 4.26458 0.278190
\(236\) 0.940926 0.0612491
\(237\) 17.1952 1.11695
\(238\) 2.94491 0.190890
\(239\) 7.35695 0.475882 0.237941 0.971280i \(-0.423528\pi\)
0.237941 + 0.971280i \(0.423528\pi\)
\(240\) −0.703774 −0.0454284
\(241\) 12.0103 0.773654 0.386827 0.922152i \(-0.373571\pi\)
0.386827 + 0.922152i \(0.373571\pi\)
\(242\) 8.87239 0.570339
\(243\) 8.36341 0.536513
\(244\) −0.574197 −0.0367592
\(245\) −1.86610 −0.119221
\(246\) 0.679317 0.0433117
\(247\) 0.0245329 0.00156099
\(248\) −1.90088 −0.120706
\(249\) −20.0026 −1.26761
\(250\) 3.55123 0.224600
\(251\) 8.28533 0.522966 0.261483 0.965208i \(-0.415789\pi\)
0.261483 + 0.965208i \(0.415789\pi\)
\(252\) −1.11281 −0.0701003
\(253\) −3.98456 −0.250507
\(254\) 4.15073 0.260440
\(255\) −1.53915 −0.0963852
\(256\) 1.00000 0.0625000
\(257\) −20.6325 −1.28702 −0.643511 0.765437i \(-0.722523\pi\)
−0.643511 + 0.765437i \(0.722523\pi\)
\(258\) −11.7789 −0.733324
\(259\) 6.69503 0.416009
\(260\) −0.526729 −0.0326664
\(261\) 6.98938 0.432632
\(262\) −4.50989 −0.278622
\(263\) 3.96611 0.244561 0.122280 0.992496i \(-0.460979\pi\)
0.122280 + 0.992496i \(0.460979\pi\)
\(264\) −2.85326 −0.175606
\(265\) −2.91567 −0.179108
\(266\) −0.0225643 −0.00138351
\(267\) −13.8631 −0.848409
\(268\) −9.88107 −0.603582
\(269\) −11.8496 −0.722485 −0.361243 0.932472i \(-0.617647\pi\)
−0.361243 + 0.932472i \(0.617647\pi\)
\(270\) −1.52972 −0.0930955
\(271\) −4.66837 −0.283583 −0.141792 0.989897i \(-0.545286\pi\)
−0.141792 + 0.989897i \(0.545286\pi\)
\(272\) 2.18699 0.132606
\(273\) −3.85630 −0.233394
\(274\) 3.36358 0.203202
\(275\) 7.10436 0.428409
\(276\) −5.34355 −0.321644
\(277\) 19.0624 1.14535 0.572675 0.819782i \(-0.305906\pi\)
0.572675 + 0.819782i \(0.305906\pi\)
\(278\) −21.6408 −1.29793
\(279\) 1.57091 0.0940478
\(280\) 0.484464 0.0289523
\(281\) 1.48411 0.0885344 0.0442672 0.999020i \(-0.485905\pi\)
0.0442672 + 0.999020i \(0.485905\pi\)
\(282\) 23.1865 1.38073
\(283\) 25.8606 1.53725 0.768625 0.639699i \(-0.220941\pi\)
0.768625 + 0.639699i \(0.220941\pi\)
\(284\) −13.0279 −0.773065
\(285\) 0.0117932 0.000698569 0
\(286\) −2.13548 −0.126274
\(287\) −0.467629 −0.0276032
\(288\) −0.826410 −0.0486967
\(289\) −12.2171 −0.718650
\(290\) −3.04285 −0.178682
\(291\) −36.3340 −2.12993
\(292\) −6.35541 −0.371922
\(293\) 16.7854 0.980616 0.490308 0.871549i \(-0.336884\pi\)
0.490308 + 0.871549i \(0.336884\pi\)
\(294\) −10.1460 −0.591726
\(295\) 0.338527 0.0197098
\(296\) 4.97197 0.288990
\(297\) −6.20182 −0.359866
\(298\) 22.9120 1.32726
\(299\) −3.99930 −0.231286
\(300\) 9.52740 0.550065
\(301\) 8.10838 0.467359
\(302\) 24.2613 1.39608
\(303\) 30.6041 1.75816
\(304\) −0.0167571 −0.000961085 0
\(305\) −0.206585 −0.0118290
\(306\) −1.80735 −0.103320
\(307\) −6.29542 −0.359299 −0.179649 0.983731i \(-0.557496\pi\)
−0.179649 + 0.983731i \(0.557496\pi\)
\(308\) 1.96413 0.111917
\(309\) −7.82819 −0.445330
\(310\) −0.683899 −0.0388429
\(311\) 10.7360 0.608785 0.304392 0.952547i \(-0.401547\pi\)
0.304392 + 0.952547i \(0.401547\pi\)
\(312\) −2.86382 −0.162132
\(313\) 3.22213 0.182126 0.0910628 0.995845i \(-0.470974\pi\)
0.0910628 + 0.995845i \(0.470974\pi\)
\(314\) −1.11609 −0.0629844
\(315\) −0.400366 −0.0225581
\(316\) −8.79048 −0.494503
\(317\) −24.9930 −1.40375 −0.701874 0.712301i \(-0.747653\pi\)
−0.701874 + 0.712301i \(0.747653\pi\)
\(318\) −15.8525 −0.888962
\(319\) −12.3364 −0.690706
\(320\) 0.359780 0.0201123
\(321\) 8.23094 0.459407
\(322\) 3.67840 0.204989
\(323\) −0.0366476 −0.00203913
\(324\) −10.7963 −0.599793
\(325\) 7.13065 0.395537
\(326\) −20.8506 −1.15481
\(327\) −6.69688 −0.370339
\(328\) −0.347278 −0.0191752
\(329\) −15.9611 −0.879965
\(330\) −1.02655 −0.0565096
\(331\) 13.6179 0.748508 0.374254 0.927326i \(-0.377899\pi\)
0.374254 + 0.927326i \(0.377899\pi\)
\(332\) 10.2256 0.561204
\(333\) −4.10889 −0.225166
\(334\) 6.69157 0.366146
\(335\) −3.55501 −0.194231
\(336\) 2.63403 0.143698
\(337\) −15.8385 −0.862779 −0.431390 0.902166i \(-0.641977\pi\)
−0.431390 + 0.902166i \(0.641977\pi\)
\(338\) 10.8566 0.590522
\(339\) −27.3233 −1.48400
\(340\) 0.786837 0.0426722
\(341\) −2.77269 −0.150149
\(342\) 0.0138482 0.000748826 0
\(343\) 16.4102 0.886067
\(344\) 6.02157 0.324661
\(345\) −1.92250 −0.103504
\(346\) −0.619997 −0.0333312
\(347\) 22.0889 1.18580 0.592898 0.805278i \(-0.297984\pi\)
0.592898 + 0.805278i \(0.297984\pi\)
\(348\) −16.5439 −0.886847
\(349\) 3.46238 0.185337 0.0926685 0.995697i \(-0.470460\pi\)
0.0926685 + 0.995697i \(0.470460\pi\)
\(350\) −6.55848 −0.350565
\(351\) −6.22477 −0.332254
\(352\) 1.45863 0.0777454
\(353\) −31.3704 −1.66968 −0.834839 0.550495i \(-0.814439\pi\)
−0.834839 + 0.550495i \(0.814439\pi\)
\(354\) 1.84057 0.0978250
\(355\) −4.68719 −0.248770
\(356\) 7.08705 0.375613
\(357\) 5.76060 0.304883
\(358\) −7.23870 −0.382577
\(359\) 18.2289 0.962085 0.481042 0.876697i \(-0.340258\pi\)
0.481042 + 0.876697i \(0.340258\pi\)
\(360\) −0.297326 −0.0156705
\(361\) −18.9997 −0.999985
\(362\) −14.1704 −0.744779
\(363\) 17.3555 0.910926
\(364\) 1.97140 0.103329
\(365\) −2.28655 −0.119684
\(366\) −1.12320 −0.0587105
\(367\) 29.8011 1.55560 0.777801 0.628510i \(-0.216335\pi\)
0.777801 + 0.628510i \(0.216335\pi\)
\(368\) 2.73171 0.142400
\(369\) 0.286994 0.0149403
\(370\) 1.78882 0.0929961
\(371\) 10.9125 0.566550
\(372\) −3.71835 −0.192788
\(373\) −0.215926 −0.0111802 −0.00559011 0.999984i \(-0.501779\pi\)
−0.00559011 + 0.999984i \(0.501779\pi\)
\(374\) 3.19002 0.164952
\(375\) 6.94664 0.358723
\(376\) −11.8533 −0.611287
\(377\) −12.3821 −0.637709
\(378\) 5.72529 0.294477
\(379\) −4.94510 −0.254013 −0.127006 0.991902i \(-0.540537\pi\)
−0.127006 + 0.991902i \(0.540537\pi\)
\(380\) −0.00602887 −0.000309274 0
\(381\) 8.11933 0.415966
\(382\) 19.3279 0.988900
\(383\) 38.5669 1.97068 0.985338 0.170614i \(-0.0545751\pi\)
0.985338 + 0.170614i \(0.0545751\pi\)
\(384\) 1.95612 0.0998229
\(385\) 0.706656 0.0360145
\(386\) 2.91199 0.148216
\(387\) −4.97629 −0.252959
\(388\) 18.5745 0.942977
\(389\) 27.1464 1.37638 0.688190 0.725531i \(-0.258406\pi\)
0.688190 + 0.725531i \(0.258406\pi\)
\(390\) −1.03035 −0.0521736
\(391\) 5.97423 0.302130
\(392\) 5.18679 0.261972
\(393\) −8.82190 −0.445006
\(394\) −15.0270 −0.757049
\(395\) −3.16264 −0.159130
\(396\) −1.20543 −0.0605751
\(397\) 1.22440 0.0614508 0.0307254 0.999528i \(-0.490218\pi\)
0.0307254 + 0.999528i \(0.490218\pi\)
\(398\) 5.23835 0.262575
\(399\) −0.0441386 −0.00220969
\(400\) −4.87056 −0.243528
\(401\) 3.20701 0.160151 0.0800753 0.996789i \(-0.474484\pi\)
0.0800753 + 0.996789i \(0.474484\pi\)
\(402\) −19.3286 −0.964021
\(403\) −2.78295 −0.138629
\(404\) −15.6453 −0.778384
\(405\) −3.88429 −0.193012
\(406\) 11.3885 0.565203
\(407\) 7.25228 0.359482
\(408\) 4.27803 0.211794
\(409\) 16.2981 0.805890 0.402945 0.915224i \(-0.367987\pi\)
0.402945 + 0.915224i \(0.367987\pi\)
\(410\) −0.124944 −0.00617052
\(411\) 6.57958 0.324547
\(412\) 4.00189 0.197159
\(413\) −1.26701 −0.0623455
\(414\) −2.25751 −0.110951
\(415\) 3.67898 0.180594
\(416\) 1.46403 0.0717800
\(417\) −42.3320 −2.07301
\(418\) −0.0244424 −0.00119552
\(419\) −37.3045 −1.82244 −0.911221 0.411917i \(-0.864859\pi\)
−0.911221 + 0.411917i \(0.864859\pi\)
\(420\) 0.947671 0.0462416
\(421\) 0.961923 0.0468813 0.0234406 0.999725i \(-0.492538\pi\)
0.0234406 + 0.999725i \(0.492538\pi\)
\(422\) −12.3093 −0.599210
\(423\) 9.79568 0.476282
\(424\) 8.10403 0.393567
\(425\) −10.6519 −0.516692
\(426\) −25.4842 −1.23471
\(427\) 0.773188 0.0374172
\(428\) −4.20779 −0.203391
\(429\) −4.17727 −0.201680
\(430\) 2.16644 0.104475
\(431\) 1.54267 0.0743077 0.0371538 0.999310i \(-0.488171\pi\)
0.0371538 + 0.999310i \(0.488171\pi\)
\(432\) 4.25180 0.204565
\(433\) −6.74748 −0.324263 −0.162131 0.986769i \(-0.551837\pi\)
−0.162131 + 0.986769i \(0.551837\pi\)
\(434\) 2.55964 0.122867
\(435\) −5.95218 −0.285385
\(436\) 3.42355 0.163958
\(437\) −0.0457754 −0.00218974
\(438\) −12.4320 −0.594022
\(439\) 28.3413 1.35266 0.676328 0.736601i \(-0.263570\pi\)
0.676328 + 0.736601i \(0.263570\pi\)
\(440\) 0.524787 0.0250183
\(441\) −4.28642 −0.204115
\(442\) 3.20183 0.152295
\(443\) −29.1627 −1.38556 −0.692780 0.721149i \(-0.743614\pi\)
−0.692780 + 0.721149i \(0.743614\pi\)
\(444\) 9.72577 0.461565
\(445\) 2.54978 0.120871
\(446\) −21.2435 −1.00591
\(447\) 44.8187 2.11985
\(448\) −1.34656 −0.0636188
\(449\) −26.6477 −1.25758 −0.628791 0.777575i \(-0.716450\pi\)
−0.628791 + 0.777575i \(0.716450\pi\)
\(450\) 4.02508 0.189744
\(451\) −0.506551 −0.0238525
\(452\) 13.9681 0.657004
\(453\) 47.4581 2.22978
\(454\) 19.4120 0.911052
\(455\) 0.709271 0.0332511
\(456\) −0.0327789 −0.00153501
\(457\) 19.1923 0.897779 0.448890 0.893587i \(-0.351820\pi\)
0.448890 + 0.893587i \(0.351820\pi\)
\(458\) 7.72343 0.360892
\(459\) 9.29867 0.434025
\(460\) 0.982814 0.0458239
\(461\) 13.5409 0.630662 0.315331 0.948982i \(-0.397884\pi\)
0.315331 + 0.948982i \(0.397884\pi\)
\(462\) 3.84208 0.178750
\(463\) 15.1001 0.701759 0.350880 0.936421i \(-0.385883\pi\)
0.350880 + 0.936421i \(0.385883\pi\)
\(464\) 8.45751 0.392630
\(465\) −1.33779 −0.0620385
\(466\) 9.42994 0.436833
\(467\) −0.676254 −0.0312933 −0.0156467 0.999878i \(-0.504981\pi\)
−0.0156467 + 0.999878i \(0.504981\pi\)
\(468\) −1.20989 −0.0559272
\(469\) 13.3054 0.614387
\(470\) −4.26458 −0.196710
\(471\) −2.18320 −0.100597
\(472\) −0.940926 −0.0433096
\(473\) 8.78326 0.403855
\(474\) −17.1952 −0.789804
\(475\) 0.0816163 0.00374481
\(476\) −2.94491 −0.134980
\(477\) −6.69726 −0.306646
\(478\) −7.35695 −0.336499
\(479\) 29.0847 1.32891 0.664456 0.747327i \(-0.268663\pi\)
0.664456 + 0.747327i \(0.268663\pi\)
\(480\) 0.703774 0.0321227
\(481\) 7.27912 0.331899
\(482\) −12.0103 −0.547056
\(483\) 7.19539 0.327401
\(484\) −8.87239 −0.403290
\(485\) 6.68274 0.303447
\(486\) −8.36341 −0.379372
\(487\) 25.0742 1.13622 0.568111 0.822952i \(-0.307674\pi\)
0.568111 + 0.822952i \(0.307674\pi\)
\(488\) 0.574197 0.0259927
\(489\) −40.7864 −1.84442
\(490\) 1.86610 0.0843020
\(491\) 7.09457 0.320174 0.160087 0.987103i \(-0.448823\pi\)
0.160087 + 0.987103i \(0.448823\pi\)
\(492\) −0.679317 −0.0306260
\(493\) 18.4965 0.833042
\(494\) −0.0245329 −0.00110379
\(495\) −0.433690 −0.0194929
\(496\) 1.90088 0.0853521
\(497\) 17.5428 0.786904
\(498\) 20.0026 0.896336
\(499\) 22.1068 0.989638 0.494819 0.868996i \(-0.335234\pi\)
0.494819 + 0.868996i \(0.335234\pi\)
\(500\) −3.55123 −0.158816
\(501\) 13.0895 0.584796
\(502\) −8.28533 −0.369793
\(503\) −10.5907 −0.472216 −0.236108 0.971727i \(-0.575872\pi\)
−0.236108 + 0.971727i \(0.575872\pi\)
\(504\) 1.11281 0.0495684
\(505\) −5.62887 −0.250482
\(506\) 3.98456 0.177135
\(507\) 21.2369 0.943162
\(508\) −4.15073 −0.184159
\(509\) −27.2672 −1.20860 −0.604300 0.796757i \(-0.706547\pi\)
−0.604300 + 0.796757i \(0.706547\pi\)
\(510\) 1.53915 0.0681547
\(511\) 8.55792 0.378580
\(512\) −1.00000 −0.0441942
\(513\) −0.0712478 −0.00314567
\(514\) 20.6325 0.910062
\(515\) 1.43980 0.0634452
\(516\) 11.7789 0.518538
\(517\) −17.2896 −0.760396
\(518\) −6.69503 −0.294163
\(519\) −1.21279 −0.0532355
\(520\) 0.526729 0.0230986
\(521\) 8.83870 0.387231 0.193615 0.981078i \(-0.437979\pi\)
0.193615 + 0.981078i \(0.437979\pi\)
\(522\) −6.98938 −0.305917
\(523\) −32.6487 −1.42763 −0.713813 0.700336i \(-0.753033\pi\)
−0.713813 + 0.700336i \(0.753033\pi\)
\(524\) 4.50989 0.197016
\(525\) −12.8292 −0.559911
\(526\) −3.96611 −0.172931
\(527\) 4.15722 0.181091
\(528\) 2.85326 0.124172
\(529\) −15.5378 −0.675556
\(530\) 2.91567 0.126649
\(531\) 0.777591 0.0337446
\(532\) 0.0225643 0.000978289 0
\(533\) −0.508425 −0.0220223
\(534\) 13.8631 0.599916
\(535\) −1.51388 −0.0654507
\(536\) 9.88107 0.426797
\(537\) −14.1598 −0.611040
\(538\) 11.8496 0.510874
\(539\) 7.56562 0.325874
\(540\) 1.52972 0.0658285
\(541\) −27.6624 −1.18930 −0.594650 0.803985i \(-0.702709\pi\)
−0.594650 + 0.803985i \(0.702709\pi\)
\(542\) 4.66837 0.200524
\(543\) −27.7190 −1.18954
\(544\) −2.18699 −0.0937666
\(545\) 1.23173 0.0527614
\(546\) 3.85630 0.165034
\(547\) 18.6646 0.798042 0.399021 0.916942i \(-0.369350\pi\)
0.399021 + 0.916942i \(0.369350\pi\)
\(548\) −3.36358 −0.143685
\(549\) −0.474522 −0.0202521
\(550\) −7.10436 −0.302931
\(551\) −0.141723 −0.00603761
\(552\) 5.34355 0.227437
\(553\) 11.8369 0.503355
\(554\) −19.0624 −0.809885
\(555\) 3.49914 0.148530
\(556\) 21.6408 0.917773
\(557\) 16.4010 0.694931 0.347465 0.937693i \(-0.387042\pi\)
0.347465 + 0.937693i \(0.387042\pi\)
\(558\) −1.57091 −0.0665018
\(559\) 8.81577 0.372867
\(560\) −0.484464 −0.0204723
\(561\) 6.24007 0.263456
\(562\) −1.48411 −0.0626033
\(563\) 29.1156 1.22708 0.613538 0.789665i \(-0.289746\pi\)
0.613538 + 0.789665i \(0.289746\pi\)
\(564\) −23.1865 −0.976326
\(565\) 5.02545 0.211422
\(566\) −25.8606 −1.08700
\(567\) 14.5378 0.610530
\(568\) 13.0279 0.546640
\(569\) 14.1712 0.594088 0.297044 0.954864i \(-0.403999\pi\)
0.297044 + 0.954864i \(0.403999\pi\)
\(570\) −0.0117932 −0.000493963 0
\(571\) 24.9937 1.04595 0.522976 0.852347i \(-0.324822\pi\)
0.522976 + 0.852347i \(0.324822\pi\)
\(572\) 2.13548 0.0892891
\(573\) 37.8077 1.57944
\(574\) 0.467629 0.0195184
\(575\) −13.3049 −0.554854
\(576\) 0.826410 0.0344338
\(577\) −15.9444 −0.663774 −0.331887 0.943319i \(-0.607685\pi\)
−0.331887 + 0.943319i \(0.607685\pi\)
\(578\) 12.2171 0.508163
\(579\) 5.69620 0.236726
\(580\) 3.04285 0.126347
\(581\) −13.7694 −0.571250
\(582\) 36.3340 1.50609
\(583\) 11.8208 0.489568
\(584\) 6.35541 0.262989
\(585\) −0.435295 −0.0179972
\(586\) −16.7854 −0.693400
\(587\) 0.134590 0.00555514 0.00277757 0.999996i \(-0.499116\pi\)
0.00277757 + 0.999996i \(0.499116\pi\)
\(588\) 10.1460 0.418413
\(589\) −0.0318532 −0.00131249
\(590\) −0.338527 −0.0139369
\(591\) −29.3946 −1.20913
\(592\) −4.97197 −0.204347
\(593\) 19.4114 0.797130 0.398565 0.917140i \(-0.369508\pi\)
0.398565 + 0.917140i \(0.369508\pi\)
\(594\) 6.20182 0.254464
\(595\) −1.05952 −0.0434361
\(596\) −22.9120 −0.938514
\(597\) 10.2469 0.419376
\(598\) 3.99930 0.163544
\(599\) 9.22942 0.377104 0.188552 0.982063i \(-0.439621\pi\)
0.188552 + 0.982063i \(0.439621\pi\)
\(600\) −9.52740 −0.388955
\(601\) 21.6048 0.881276 0.440638 0.897685i \(-0.354752\pi\)
0.440638 + 0.897685i \(0.354752\pi\)
\(602\) −8.10838 −0.330473
\(603\) −8.16582 −0.332538
\(604\) −24.2613 −0.987180
\(605\) −3.19211 −0.129778
\(606\) −30.6041 −1.24321
\(607\) −6.66214 −0.270408 −0.135204 0.990818i \(-0.543169\pi\)
−0.135204 + 0.990818i \(0.543169\pi\)
\(608\) 0.0167571 0.000679589 0
\(609\) 22.2773 0.902722
\(610\) 0.206585 0.00836437
\(611\) −17.3536 −0.702051
\(612\) 1.80735 0.0730580
\(613\) −0.983677 −0.0397303 −0.0198652 0.999803i \(-0.506324\pi\)
−0.0198652 + 0.999803i \(0.506324\pi\)
\(614\) 6.29542 0.254063
\(615\) −0.244405 −0.00985535
\(616\) −1.96413 −0.0791371
\(617\) 27.4150 1.10369 0.551843 0.833948i \(-0.313925\pi\)
0.551843 + 0.833948i \(0.313925\pi\)
\(618\) 7.82819 0.314896
\(619\) 34.1310 1.37184 0.685921 0.727676i \(-0.259399\pi\)
0.685921 + 0.727676i \(0.259399\pi\)
\(620\) 0.683899 0.0274661
\(621\) 11.6147 0.466081
\(622\) −10.7360 −0.430476
\(623\) −9.54310 −0.382336
\(624\) 2.86382 0.114645
\(625\) 23.0751 0.923005
\(626\) −3.22213 −0.128782
\(627\) −0.0478124 −0.00190944
\(628\) 1.11609 0.0445367
\(629\) −10.8737 −0.433561
\(630\) 0.400366 0.0159510
\(631\) −39.5158 −1.57310 −0.786550 0.617526i \(-0.788135\pi\)
−0.786550 + 0.617526i \(0.788135\pi\)
\(632\) 8.79048 0.349666
\(633\) −24.0786 −0.957037
\(634\) 24.9930 0.992599
\(635\) −1.49335 −0.0592618
\(636\) 15.8525 0.628591
\(637\) 7.59362 0.300870
\(638\) 12.3364 0.488403
\(639\) −10.7664 −0.425913
\(640\) −0.359780 −0.0142216
\(641\) 39.7321 1.56932 0.784662 0.619924i \(-0.212837\pi\)
0.784662 + 0.619924i \(0.212837\pi\)
\(642\) −8.23094 −0.324849
\(643\) −16.3885 −0.646297 −0.323149 0.946348i \(-0.604741\pi\)
−0.323149 + 0.946348i \(0.604741\pi\)
\(644\) −3.67840 −0.144949
\(645\) 4.23782 0.166864
\(646\) 0.0366476 0.00144188
\(647\) −3.59219 −0.141224 −0.0706118 0.997504i \(-0.522495\pi\)
−0.0706118 + 0.997504i \(0.522495\pi\)
\(648\) 10.7963 0.424118
\(649\) −1.37247 −0.0538740
\(650\) −7.13065 −0.279687
\(651\) 5.00697 0.196239
\(652\) 20.8506 0.816574
\(653\) −9.64575 −0.377467 −0.188734 0.982028i \(-0.560438\pi\)
−0.188734 + 0.982028i \(0.560438\pi\)
\(654\) 6.69688 0.261869
\(655\) 1.62257 0.0633991
\(656\) 0.347278 0.0135589
\(657\) −5.25218 −0.204907
\(658\) 15.9611 0.622229
\(659\) −12.2049 −0.475435 −0.237717 0.971334i \(-0.576399\pi\)
−0.237717 + 0.971334i \(0.576399\pi\)
\(660\) 1.02655 0.0399583
\(661\) −2.55135 −0.0992362 −0.0496181 0.998768i \(-0.515800\pi\)
−0.0496181 + 0.998768i \(0.515800\pi\)
\(662\) −13.6179 −0.529275
\(663\) 6.26316 0.243241
\(664\) −10.2256 −0.396831
\(665\) 0.00811821 0.000314811 0
\(666\) 4.10889 0.159216
\(667\) 23.1034 0.894569
\(668\) −6.69157 −0.258904
\(669\) −41.5548 −1.60660
\(670\) 3.55501 0.137342
\(671\) 0.837542 0.0323330
\(672\) −2.63403 −0.101610
\(673\) 21.9227 0.845058 0.422529 0.906349i \(-0.361143\pi\)
0.422529 + 0.906349i \(0.361143\pi\)
\(674\) 15.8385 0.610077
\(675\) −20.7087 −0.797077
\(676\) −10.8566 −0.417562
\(677\) 10.6471 0.409201 0.204601 0.978846i \(-0.434410\pi\)
0.204601 + 0.978846i \(0.434410\pi\)
\(678\) 27.3233 1.04934
\(679\) −25.0116 −0.959857
\(680\) −0.786837 −0.0301738
\(681\) 37.9723 1.45510
\(682\) 2.77269 0.106172
\(683\) 8.22433 0.314695 0.157348 0.987543i \(-0.449706\pi\)
0.157348 + 0.987543i \(0.449706\pi\)
\(684\) −0.0138482 −0.000529500 0
\(685\) −1.21015 −0.0462375
\(686\) −16.4102 −0.626544
\(687\) 15.1080 0.576405
\(688\) −6.02157 −0.229570
\(689\) 11.8646 0.452004
\(690\) 1.92250 0.0731885
\(691\) 6.55510 0.249368 0.124684 0.992197i \(-0.460208\pi\)
0.124684 + 0.992197i \(0.460208\pi\)
\(692\) 0.619997 0.0235687
\(693\) 1.62318 0.0616595
\(694\) −22.0889 −0.838484
\(695\) 7.78592 0.295337
\(696\) 16.5439 0.627096
\(697\) 0.759494 0.0287679
\(698\) −3.46238 −0.131053
\(699\) 18.4461 0.697696
\(700\) 6.55848 0.247887
\(701\) 3.06398 0.115725 0.0578625 0.998325i \(-0.481571\pi\)
0.0578625 + 0.998325i \(0.481571\pi\)
\(702\) 6.22477 0.234939
\(703\) 0.0833157 0.00314231
\(704\) −1.45863 −0.0549743
\(705\) −8.34203 −0.314179
\(706\) 31.3704 1.18064
\(707\) 21.0673 0.792317
\(708\) −1.84057 −0.0691727
\(709\) 42.4237 1.59326 0.796628 0.604470i \(-0.206615\pi\)
0.796628 + 0.604470i \(0.206615\pi\)
\(710\) 4.68719 0.175907
\(711\) −7.26454 −0.272442
\(712\) −7.08705 −0.265598
\(713\) 5.19265 0.194466
\(714\) −5.76060 −0.215585
\(715\) 0.768305 0.0287330
\(716\) 7.23870 0.270523
\(717\) −14.3911 −0.537445
\(718\) −18.2289 −0.680297
\(719\) 29.3888 1.09602 0.548008 0.836473i \(-0.315386\pi\)
0.548008 + 0.836473i \(0.315386\pi\)
\(720\) 0.297326 0.0110807
\(721\) −5.38877 −0.200688
\(722\) 18.9997 0.707096
\(723\) −23.4937 −0.873739
\(724\) 14.1704 0.526639
\(725\) −41.1928 −1.52986
\(726\) −17.3555 −0.644122
\(727\) 39.4000 1.46126 0.730632 0.682772i \(-0.239226\pi\)
0.730632 + 0.682772i \(0.239226\pi\)
\(728\) −1.97140 −0.0730649
\(729\) 16.0290 0.593666
\(730\) 2.28655 0.0846290
\(731\) −13.1691 −0.487078
\(732\) 1.12320 0.0415146
\(733\) −24.9413 −0.921227 −0.460614 0.887601i \(-0.652371\pi\)
−0.460614 + 0.887601i \(0.652371\pi\)
\(734\) −29.8011 −1.09998
\(735\) 3.65032 0.134644
\(736\) −2.73171 −0.100692
\(737\) 14.4129 0.530904
\(738\) −0.286994 −0.0105644
\(739\) 8.61742 0.316997 0.158499 0.987359i \(-0.449335\pi\)
0.158499 + 0.987359i \(0.449335\pi\)
\(740\) −1.78882 −0.0657582
\(741\) −0.0479893 −0.00176293
\(742\) −10.9125 −0.400612
\(743\) 35.2099 1.29173 0.645863 0.763453i \(-0.276498\pi\)
0.645863 + 0.763453i \(0.276498\pi\)
\(744\) 3.71835 0.136321
\(745\) −8.24330 −0.302011
\(746\) 0.215926 0.00790561
\(747\) 8.45056 0.309190
\(748\) −3.19002 −0.116639
\(749\) 5.66602 0.207032
\(750\) −6.94664 −0.253655
\(751\) 36.7287 1.34025 0.670124 0.742249i \(-0.266241\pi\)
0.670124 + 0.742249i \(0.266241\pi\)
\(752\) 11.8533 0.432245
\(753\) −16.2071 −0.590620
\(754\) 12.3821 0.450928
\(755\) −8.72875 −0.317672
\(756\) −5.72529 −0.208227
\(757\) 34.1062 1.23961 0.619806 0.784755i \(-0.287211\pi\)
0.619806 + 0.784755i \(0.287211\pi\)
\(758\) 4.94510 0.179614
\(759\) 7.79428 0.282914
\(760\) 0.00602887 0.000218690 0
\(761\) −1.00936 −0.0365894 −0.0182947 0.999833i \(-0.505824\pi\)
−0.0182947 + 0.999833i \(0.505824\pi\)
\(762\) −8.11933 −0.294132
\(763\) −4.61001 −0.166893
\(764\) −19.3279 −0.699258
\(765\) 0.650250 0.0235099
\(766\) −38.5669 −1.39348
\(767\) −1.37755 −0.0497403
\(768\) −1.95612 −0.0705854
\(769\) −15.2602 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(770\) −0.706656 −0.0254661
\(771\) 40.3598 1.45352
\(772\) −2.91199 −0.104805
\(773\) 38.7251 1.39285 0.696423 0.717632i \(-0.254774\pi\)
0.696423 + 0.717632i \(0.254774\pi\)
\(774\) 4.97629 0.178869
\(775\) −9.25835 −0.332570
\(776\) −18.5745 −0.666786
\(777\) −13.0963 −0.469827
\(778\) −27.1464 −0.973247
\(779\) −0.00581936 −0.000208500 0
\(780\) 1.03035 0.0368923
\(781\) 19.0030 0.679980
\(782\) −5.97423 −0.213638
\(783\) 35.9597 1.28509
\(784\) −5.18679 −0.185242
\(785\) 0.401546 0.0143318
\(786\) 8.82190 0.314667
\(787\) 52.5478 1.87313 0.936563 0.350500i \(-0.113988\pi\)
0.936563 + 0.350500i \(0.113988\pi\)
\(788\) 15.0270 0.535315
\(789\) −7.75819 −0.276199
\(790\) 3.16264 0.112522
\(791\) −18.8088 −0.668765
\(792\) 1.20543 0.0428331
\(793\) 0.840642 0.0298521
\(794\) −1.22440 −0.0434522
\(795\) 5.70340 0.202279
\(796\) −5.23835 −0.185668
\(797\) −22.9338 −0.812355 −0.406178 0.913794i \(-0.633139\pi\)
−0.406178 + 0.913794i \(0.633139\pi\)
\(798\) 0.0441386 0.00156249
\(799\) 25.9231 0.917092
\(800\) 4.87056 0.172200
\(801\) 5.85681 0.206940
\(802\) −3.20701 −0.113244
\(803\) 9.27021 0.327139
\(804\) 19.3286 0.681666
\(805\) −1.32341 −0.0466442
\(806\) 2.78295 0.0980252
\(807\) 23.1793 0.815951
\(808\) 15.6453 0.550400
\(809\) 44.4295 1.56206 0.781029 0.624495i \(-0.214695\pi\)
0.781029 + 0.624495i \(0.214695\pi\)
\(810\) 3.88429 0.136480
\(811\) −52.1653 −1.83177 −0.915885 0.401440i \(-0.868510\pi\)
−0.915885 + 0.401440i \(0.868510\pi\)
\(812\) −11.3885 −0.399659
\(813\) 9.13190 0.320270
\(814\) −7.25228 −0.254192
\(815\) 7.50165 0.262771
\(816\) −4.27803 −0.149761
\(817\) 0.100904 0.00353018
\(818\) −16.2981 −0.569850
\(819\) 1.62919 0.0569283
\(820\) 0.124944 0.00436322
\(821\) 20.0147 0.698517 0.349259 0.937026i \(-0.386433\pi\)
0.349259 + 0.937026i \(0.386433\pi\)
\(822\) −6.57958 −0.229489
\(823\) −34.4856 −1.20209 −0.601046 0.799214i \(-0.705249\pi\)
−0.601046 + 0.799214i \(0.705249\pi\)
\(824\) −4.00189 −0.139413
\(825\) −13.8970 −0.483831
\(826\) 1.26701 0.0440849
\(827\) −3.07908 −0.107070 −0.0535351 0.998566i \(-0.517049\pi\)
−0.0535351 + 0.998566i \(0.517049\pi\)
\(828\) 2.25751 0.0784539
\(829\) 30.8419 1.07118 0.535592 0.844477i \(-0.320089\pi\)
0.535592 + 0.844477i \(0.320089\pi\)
\(830\) −3.67898 −0.127699
\(831\) −37.2884 −1.29352
\(832\) −1.46403 −0.0507561
\(833\) −11.3435 −0.393028
\(834\) 42.3320 1.46584
\(835\) −2.40749 −0.0833147
\(836\) 0.0244424 0.000845359 0
\(837\) 8.08218 0.279361
\(838\) 37.3045 1.28866
\(839\) −46.1171 −1.59214 −0.796069 0.605206i \(-0.793091\pi\)
−0.796069 + 0.605206i \(0.793091\pi\)
\(840\) −0.947671 −0.0326977
\(841\) 42.5295 1.46654
\(842\) −0.961923 −0.0331501
\(843\) −2.90309 −0.0999878
\(844\) 12.3093 0.423705
\(845\) −3.90599 −0.134370
\(846\) −9.79568 −0.336782
\(847\) 11.9472 0.410510
\(848\) −8.10403 −0.278294
\(849\) −50.5864 −1.73612
\(850\) 10.6519 0.365356
\(851\) −13.5820 −0.465584
\(852\) 25.4842 0.873075
\(853\) 47.4535 1.62478 0.812389 0.583116i \(-0.198167\pi\)
0.812389 + 0.583116i \(0.198167\pi\)
\(854\) −0.773188 −0.0264579
\(855\) −0.00498232 −0.000170392 0
\(856\) 4.20779 0.143819
\(857\) −47.9501 −1.63794 −0.818971 0.573834i \(-0.805455\pi\)
−0.818971 + 0.573834i \(0.805455\pi\)
\(858\) 4.17727 0.142610
\(859\) 33.2022 1.13284 0.566422 0.824116i \(-0.308327\pi\)
0.566422 + 0.824116i \(0.308327\pi\)
\(860\) −2.16644 −0.0738751
\(861\) 0.914738 0.0311742
\(862\) −1.54267 −0.0525434
\(863\) 42.5475 1.44833 0.724166 0.689626i \(-0.242225\pi\)
0.724166 + 0.689626i \(0.242225\pi\)
\(864\) −4.25180 −0.144649
\(865\) 0.223063 0.00758436
\(866\) 6.74748 0.229289
\(867\) 23.8980 0.811620
\(868\) −2.55964 −0.0868799
\(869\) 12.8221 0.434959
\(870\) 5.95218 0.201798
\(871\) 14.4662 0.490168
\(872\) −3.42355 −0.115936
\(873\) 15.3502 0.519524
\(874\) 0.0457754 0.00154838
\(875\) 4.78193 0.161659
\(876\) 12.4320 0.420037
\(877\) −34.2051 −1.15502 −0.577512 0.816383i \(-0.695976\pi\)
−0.577512 + 0.816383i \(0.695976\pi\)
\(878\) −28.3413 −0.956472
\(879\) −32.8344 −1.10748
\(880\) −0.524787 −0.0176906
\(881\) −2.30736 −0.0777368 −0.0388684 0.999244i \(-0.512375\pi\)
−0.0388684 + 0.999244i \(0.512375\pi\)
\(882\) 4.28642 0.144331
\(883\) −8.85286 −0.297922 −0.148961 0.988843i \(-0.547593\pi\)
−0.148961 + 0.988843i \(0.547593\pi\)
\(884\) −3.20183 −0.107689
\(885\) −0.662199 −0.0222596
\(886\) 29.1627 0.979739
\(887\) 29.3076 0.984052 0.492026 0.870581i \(-0.336257\pi\)
0.492026 + 0.870581i \(0.336257\pi\)
\(888\) −9.72577 −0.326376
\(889\) 5.58919 0.187455
\(890\) −2.54978 −0.0854688
\(891\) 15.7478 0.527571
\(892\) 21.2435 0.711284
\(893\) −0.198627 −0.00664678
\(894\) −44.8187 −1.49896
\(895\) 2.60434 0.0870536
\(896\) 1.34656 0.0449853
\(897\) 7.82312 0.261206
\(898\) 26.6477 0.889244
\(899\) 16.0767 0.536189
\(900\) −4.02508 −0.134169
\(901\) −17.7235 −0.590454
\(902\) 0.506551 0.0168663
\(903\) −15.8610 −0.527820
\(904\) −13.9681 −0.464572
\(905\) 5.09823 0.169471
\(906\) −47.4581 −1.57669
\(907\) 2.74117 0.0910190 0.0455095 0.998964i \(-0.485509\pi\)
0.0455095 + 0.998964i \(0.485509\pi\)
\(908\) −19.4120 −0.644211
\(909\) −12.9295 −0.428843
\(910\) −0.709271 −0.0235121
\(911\) 40.3473 1.33676 0.668382 0.743818i \(-0.266987\pi\)
0.668382 + 0.743818i \(0.266987\pi\)
\(912\) 0.0327789 0.00108542
\(913\) −14.9154 −0.493629
\(914\) −19.1923 −0.634826
\(915\) 0.404105 0.0133593
\(916\) −7.72343 −0.255189
\(917\) −6.07282 −0.200542
\(918\) −9.29867 −0.306902
\(919\) 6.08753 0.200809 0.100405 0.994947i \(-0.467986\pi\)
0.100405 + 0.994947i \(0.467986\pi\)
\(920\) −0.982814 −0.0324024
\(921\) 12.3146 0.405780
\(922\) −13.5409 −0.445945
\(923\) 19.0733 0.627805
\(924\) −3.84208 −0.126395
\(925\) 24.2163 0.796226
\(926\) −15.1001 −0.496219
\(927\) 3.30721 0.108623
\(928\) −8.45751 −0.277631
\(929\) −3.40082 −0.111577 −0.0557887 0.998443i \(-0.517767\pi\)
−0.0557887 + 0.998443i \(0.517767\pi\)
\(930\) 1.33779 0.0438679
\(931\) 0.0869154 0.00284854
\(932\) −9.42994 −0.308888
\(933\) −21.0010 −0.687542
\(934\) 0.676254 0.0221277
\(935\) −1.14771 −0.0375340
\(936\) 1.20989 0.0395465
\(937\) 22.3095 0.728819 0.364409 0.931239i \(-0.381271\pi\)
0.364409 + 0.931239i \(0.381271\pi\)
\(938\) −13.3054 −0.434437
\(939\) −6.30288 −0.205687
\(940\) 4.26458 0.139095
\(941\) −18.7550 −0.611394 −0.305697 0.952129i \(-0.598889\pi\)
−0.305697 + 0.952129i \(0.598889\pi\)
\(942\) 2.18320 0.0711325
\(943\) 0.948661 0.0308926
\(944\) 0.940926 0.0306245
\(945\) −2.05985 −0.0670068
\(946\) −8.78326 −0.285569
\(947\) −12.2526 −0.398156 −0.199078 0.979984i \(-0.563795\pi\)
−0.199078 + 0.979984i \(0.563795\pi\)
\(948\) 17.1952 0.558476
\(949\) 9.30452 0.302037
\(950\) −0.0816163 −0.00264798
\(951\) 48.8894 1.58535
\(952\) 2.94491 0.0954451
\(953\) −9.37517 −0.303691 −0.151846 0.988404i \(-0.548522\pi\)
−0.151846 + 0.988404i \(0.548522\pi\)
\(954\) 6.69726 0.216832
\(955\) −6.95379 −0.225019
\(956\) 7.35695 0.237941
\(957\) 24.1315 0.780061
\(958\) −29.0847 −0.939683
\(959\) 4.52925 0.146257
\(960\) −0.703774 −0.0227142
\(961\) −27.3867 −0.883440
\(962\) −7.27912 −0.234688
\(963\) −3.47736 −0.112056
\(964\) 12.0103 0.386827
\(965\) −1.04768 −0.0337259
\(966\) −7.19539 −0.231508
\(967\) −12.1157 −0.389615 −0.194808 0.980841i \(-0.562408\pi\)
−0.194808 + 0.980841i \(0.562408\pi\)
\(968\) 8.87239 0.285169
\(969\) 0.0716872 0.00230293
\(970\) −6.68274 −0.214570
\(971\) 37.7444 1.21127 0.605637 0.795741i \(-0.292918\pi\)
0.605637 + 0.795741i \(0.292918\pi\)
\(972\) 8.36341 0.268257
\(973\) −29.1405 −0.934202
\(974\) −25.0742 −0.803431
\(975\) −13.9484 −0.446707
\(976\) −0.574197 −0.0183796
\(977\) −28.4122 −0.908987 −0.454493 0.890750i \(-0.650180\pi\)
−0.454493 + 0.890750i \(0.650180\pi\)
\(978\) 40.7864 1.30420
\(979\) −10.3374 −0.330385
\(980\) −1.86610 −0.0596105
\(981\) 2.82926 0.0903313
\(982\) −7.09457 −0.226397
\(983\) −0.148500 −0.00473642 −0.00236821 0.999997i \(-0.500754\pi\)
−0.00236821 + 0.999997i \(0.500754\pi\)
\(984\) 0.679317 0.0216558
\(985\) 5.40642 0.172263
\(986\) −18.4965 −0.589050
\(987\) 31.2219 0.993803
\(988\) 0.0245329 0.000780495 0
\(989\) −16.4492 −0.523053
\(990\) 0.433690 0.0137836
\(991\) −46.4227 −1.47467 −0.737333 0.675530i \(-0.763915\pi\)
−0.737333 + 0.675530i \(0.763915\pi\)
\(992\) −1.90088 −0.0603530
\(993\) −26.6383 −0.845341
\(994\) −17.5428 −0.556425
\(995\) −1.88466 −0.0597476
\(996\) −20.0026 −0.633805
\(997\) 3.56426 0.112881 0.0564406 0.998406i \(-0.482025\pi\)
0.0564406 + 0.998406i \(0.482025\pi\)
\(998\) −22.1068 −0.699780
\(999\) −21.1398 −0.668835
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 \(a_p\))