Properties

Label 8018.2.a.j.1.22
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 1.22
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.00179563 q^{3} +1.00000 q^{4} -2.84522 q^{5} -0.00179563 q^{6} +2.42071 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.00179563 q^{3} +1.00000 q^{4} -2.84522 q^{5} -0.00179563 q^{6} +2.42071 q^{7} +1.00000 q^{8} -3.00000 q^{9} -2.84522 q^{10} -4.79658 q^{11} -0.00179563 q^{12} +0.240087 q^{13} +2.42071 q^{14} +0.00510896 q^{15} +1.00000 q^{16} +0.878242 q^{17} -3.00000 q^{18} -1.00000 q^{19} -2.84522 q^{20} -0.00434669 q^{21} -4.79658 q^{22} -5.60385 q^{23} -0.00179563 q^{24} +3.09529 q^{25} +0.240087 q^{26} +0.0107738 q^{27} +2.42071 q^{28} -4.45888 q^{29} +0.00510896 q^{30} +9.50296 q^{31} +1.00000 q^{32} +0.00861287 q^{33} +0.878242 q^{34} -6.88745 q^{35} -3.00000 q^{36} +3.05886 q^{37} -1.00000 q^{38} -0.000431107 q^{39} -2.84522 q^{40} +9.19476 q^{41} -0.00434669 q^{42} +8.02831 q^{43} -4.79658 q^{44} +8.53566 q^{45} -5.60385 q^{46} -3.46726 q^{47} -0.00179563 q^{48} -1.14017 q^{49} +3.09529 q^{50} -0.00157699 q^{51} +0.240087 q^{52} -8.34252 q^{53} +0.0107738 q^{54} +13.6473 q^{55} +2.42071 q^{56} +0.00179563 q^{57} -4.45888 q^{58} +5.86612 q^{59} +0.00510896 q^{60} -5.52647 q^{61} +9.50296 q^{62} -7.26212 q^{63} +1.00000 q^{64} -0.683101 q^{65} +0.00861287 q^{66} -1.60425 q^{67} +0.878242 q^{68} +0.0100624 q^{69} -6.88745 q^{70} -11.9998 q^{71} -3.00000 q^{72} -4.81238 q^{73} +3.05886 q^{74} -0.00555799 q^{75} -1.00000 q^{76} -11.6111 q^{77} -0.000431107 q^{78} -11.5750 q^{79} -2.84522 q^{80} +8.99997 q^{81} +9.19476 q^{82} +17.6067 q^{83} -0.00434669 q^{84} -2.49879 q^{85} +8.02831 q^{86} +0.00800649 q^{87} -4.79658 q^{88} +9.62818 q^{89} +8.53566 q^{90} +0.581180 q^{91} -5.60385 q^{92} -0.0170638 q^{93} -3.46726 q^{94} +2.84522 q^{95} -0.00179563 q^{96} +11.6368 q^{97} -1.14017 q^{98} +14.3897 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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
\(3\) −0.00179563 −0.00103671 −0.000518353 1.00000i \(-0.500165\pi\)
−0.000518353 1.00000i \(0.500165\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.84522 −1.27242 −0.636211 0.771515i \(-0.719499\pi\)
−0.636211 + 0.771515i \(0.719499\pi\)
\(6\) −0.00179563 −0.000733062 0
\(7\) 2.42071 0.914942 0.457471 0.889225i \(-0.348755\pi\)
0.457471 + 0.889225i \(0.348755\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.00000 −0.999999
\(10\) −2.84522 −0.899738
\(11\) −4.79658 −1.44622 −0.723111 0.690731i \(-0.757289\pi\)
−0.723111 + 0.690731i \(0.757289\pi\)
\(12\) −0.00179563 −0.000518353 0
\(13\) 0.240087 0.0665881 0.0332941 0.999446i \(-0.489400\pi\)
0.0332941 + 0.999446i \(0.489400\pi\)
\(14\) 2.42071 0.646961
\(15\) 0.00510896 0.00131913
\(16\) 1.00000 0.250000
\(17\) 0.878242 0.213005 0.106502 0.994312i \(-0.466035\pi\)
0.106502 + 0.994312i \(0.466035\pi\)
\(18\) −3.00000 −0.707106
\(19\) −1.00000 −0.229416
\(20\) −2.84522 −0.636211
\(21\) −0.00434669 −0.000948525 0
\(22\) −4.79658 −1.02263
\(23\) −5.60385 −1.16848 −0.584242 0.811580i \(-0.698608\pi\)
−0.584242 + 0.811580i \(0.698608\pi\)
\(24\) −0.00179563 −0.000366531 0
\(25\) 3.09529 0.619058
\(26\) 0.240087 0.0470849
\(27\) 0.0107738 0.00207341
\(28\) 2.42071 0.457471
\(29\) −4.45888 −0.827993 −0.413997 0.910278i \(-0.635867\pi\)
−0.413997 + 0.910278i \(0.635867\pi\)
\(30\) 0.00510896 0.000932764 0
\(31\) 9.50296 1.70678 0.853391 0.521272i \(-0.174542\pi\)
0.853391 + 0.521272i \(0.174542\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.00861287 0.00149931
\(34\) 0.878242 0.150617
\(35\) −6.88745 −1.16419
\(36\) −3.00000 −0.499999
\(37\) 3.05886 0.502874 0.251437 0.967874i \(-0.419097\pi\)
0.251437 + 0.967874i \(0.419097\pi\)
\(38\) −1.00000 −0.162221
\(39\) −0.000431107 0 −6.90323e−5 0
\(40\) −2.84522 −0.449869
\(41\) 9.19476 1.43598 0.717990 0.696053i \(-0.245062\pi\)
0.717990 + 0.696053i \(0.245062\pi\)
\(42\) −0.00434669 −0.000670709 0
\(43\) 8.02831 1.22431 0.612153 0.790740i \(-0.290304\pi\)
0.612153 + 0.790740i \(0.290304\pi\)
\(44\) −4.79658 −0.723111
\(45\) 8.53566 1.27242
\(46\) −5.60385 −0.826243
\(47\) −3.46726 −0.505753 −0.252876 0.967499i \(-0.581377\pi\)
−0.252876 + 0.967499i \(0.581377\pi\)
\(48\) −0.00179563 −0.000259176 0
\(49\) −1.14017 −0.162882
\(50\) 3.09529 0.437740
\(51\) −0.00157699 −0.000220823 0
\(52\) 0.240087 0.0332941
\(53\) −8.34252 −1.14593 −0.572966 0.819579i \(-0.694207\pi\)
−0.572966 + 0.819579i \(0.694207\pi\)
\(54\) 0.0107738 0.00146612
\(55\) 13.6473 1.84021
\(56\) 2.42071 0.323481
\(57\) 0.00179563 0.000237837 0
\(58\) −4.45888 −0.585479
\(59\) 5.86612 0.763704 0.381852 0.924223i \(-0.375286\pi\)
0.381852 + 0.924223i \(0.375286\pi\)
\(60\) 0.00510896 0.000659564 0
\(61\) −5.52647 −0.707592 −0.353796 0.935323i \(-0.615109\pi\)
−0.353796 + 0.935323i \(0.615109\pi\)
\(62\) 9.50296 1.20688
\(63\) −7.26212 −0.914941
\(64\) 1.00000 0.125000
\(65\) −0.683101 −0.0847282
\(66\) 0.00861287 0.00106017
\(67\) −1.60425 −0.195991 −0.0979954 0.995187i \(-0.531243\pi\)
−0.0979954 + 0.995187i \(0.531243\pi\)
\(68\) 0.878242 0.106502
\(69\) 0.0100624 0.00121137
\(70\) −6.88745 −0.823208
\(71\) −11.9998 −1.42412 −0.712058 0.702121i \(-0.752237\pi\)
−0.712058 + 0.702121i \(0.752237\pi\)
\(72\) −3.00000 −0.353553
\(73\) −4.81238 −0.563246 −0.281623 0.959525i \(-0.590873\pi\)
−0.281623 + 0.959525i \(0.590873\pi\)
\(74\) 3.05886 0.355585
\(75\) −0.00555799 −0.000641782 0
\(76\) −1.00000 −0.114708
\(77\) −11.6111 −1.32321
\(78\) −0.000431107 0 −4.88132e−5 0
\(79\) −11.5750 −1.30229 −0.651143 0.758955i \(-0.725710\pi\)
−0.651143 + 0.758955i \(0.725710\pi\)
\(80\) −2.84522 −0.318106
\(81\) 8.99997 0.999997
\(82\) 9.19476 1.01539
\(83\) 17.6067 1.93258 0.966292 0.257447i \(-0.0828813\pi\)
0.966292 + 0.257447i \(0.0828813\pi\)
\(84\) −0.00434669 −0.000474263 0
\(85\) −2.49879 −0.271032
\(86\) 8.02831 0.865714
\(87\) 0.00800649 0.000858385 0
\(88\) −4.79658 −0.511317
\(89\) 9.62818 1.02058 0.510292 0.860001i \(-0.329537\pi\)
0.510292 + 0.860001i \(0.329537\pi\)
\(90\) 8.53566 0.899737
\(91\) 0.581180 0.0609242
\(92\) −5.60385 −0.584242
\(93\) −0.0170638 −0.00176943
\(94\) −3.46726 −0.357621
\(95\) 2.84522 0.291914
\(96\) −0.00179563 −0.000183265 0
\(97\) 11.6368 1.18153 0.590767 0.806842i \(-0.298825\pi\)
0.590767 + 0.806842i \(0.298825\pi\)
\(98\) −1.14017 −0.115175
\(99\) 14.3897 1.44622
\(100\) 3.09529 0.309529
\(101\) 14.9281 1.48540 0.742700 0.669624i \(-0.233545\pi\)
0.742700 + 0.669624i \(0.233545\pi\)
\(102\) −0.00157699 −0.000156146 0
\(103\) 5.38404 0.530505 0.265253 0.964179i \(-0.414545\pi\)
0.265253 + 0.964179i \(0.414545\pi\)
\(104\) 0.240087 0.0235425
\(105\) 0.0123673 0.00120692
\(106\) −8.34252 −0.810297
\(107\) 7.38286 0.713728 0.356864 0.934156i \(-0.383846\pi\)
0.356864 + 0.934156i \(0.383846\pi\)
\(108\) 0.0107738 0.00103671
\(109\) 13.4481 1.28809 0.644047 0.764986i \(-0.277254\pi\)
0.644047 + 0.764986i \(0.277254\pi\)
\(110\) 13.6473 1.30122
\(111\) −0.00549258 −0.000521332 0
\(112\) 2.42071 0.228735
\(113\) 5.91656 0.556583 0.278292 0.960497i \(-0.410232\pi\)
0.278292 + 0.960497i \(0.410232\pi\)
\(114\) 0.00179563 0.000168176 0
\(115\) 15.9442 1.48680
\(116\) −4.45888 −0.413997
\(117\) −0.720260 −0.0665881
\(118\) 5.86612 0.540021
\(119\) 2.12597 0.194887
\(120\) 0.00510896 0.000466382 0
\(121\) 12.0072 1.09156
\(122\) −5.52647 −0.500343
\(123\) −0.0165104 −0.00148869
\(124\) 9.50296 0.853391
\(125\) 5.41932 0.484719
\(126\) −7.26212 −0.646961
\(127\) 9.34529 0.829260 0.414630 0.909990i \(-0.363911\pi\)
0.414630 + 0.909990i \(0.363911\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.0144158 −0.00126924
\(130\) −0.683101 −0.0599119
\(131\) −5.43634 −0.474975 −0.237488 0.971391i \(-0.576324\pi\)
−0.237488 + 0.971391i \(0.576324\pi\)
\(132\) 0.00861287 0.000749654 0
\(133\) −2.42071 −0.209902
\(134\) −1.60425 −0.138586
\(135\) −0.0306537 −0.00263825
\(136\) 0.878242 0.0753086
\(137\) −4.48249 −0.382965 −0.191482 0.981496i \(-0.561329\pi\)
−0.191482 + 0.981496i \(0.561329\pi\)
\(138\) 0.0100624 0.000856571 0
\(139\) 12.5442 1.06398 0.531992 0.846750i \(-0.321444\pi\)
0.531992 + 0.846750i \(0.321444\pi\)
\(140\) −6.88745 −0.582096
\(141\) 0.00622592 0.000524317 0
\(142\) −11.9998 −1.00700
\(143\) −1.15160 −0.0963013
\(144\) −3.00000 −0.250000
\(145\) 12.6865 1.05356
\(146\) −4.81238 −0.398275
\(147\) 0.00204733 0.000168861 0
\(148\) 3.05886 0.251437
\(149\) −0.954574 −0.0782017 −0.0391009 0.999235i \(-0.512449\pi\)
−0.0391009 + 0.999235i \(0.512449\pi\)
\(150\) −0.00555799 −0.000453808 0
\(151\) −3.99230 −0.324889 −0.162444 0.986718i \(-0.551938\pi\)
−0.162444 + 0.986718i \(0.551938\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −2.63472 −0.213005
\(154\) −11.6111 −0.935650
\(155\) −27.0380 −2.17175
\(156\) −0.000431107 0 −3.45162e−5 0
\(157\) 2.42485 0.193524 0.0967619 0.995308i \(-0.469151\pi\)
0.0967619 + 0.995308i \(0.469151\pi\)
\(158\) −11.5750 −0.920856
\(159\) 0.0149801 0.00118800
\(160\) −2.84522 −0.224935
\(161\) −13.5653 −1.06909
\(162\) 8.99997 0.707105
\(163\) 15.9239 1.24726 0.623628 0.781721i \(-0.285658\pi\)
0.623628 + 0.781721i \(0.285658\pi\)
\(164\) 9.19476 0.717990
\(165\) −0.0245055 −0.00190775
\(166\) 17.6067 1.36654
\(167\) 8.25446 0.638750 0.319375 0.947628i \(-0.396527\pi\)
0.319375 + 0.947628i \(0.396527\pi\)
\(168\) −0.00434669 −0.000335354 0
\(169\) −12.9424 −0.995566
\(170\) −2.49879 −0.191649
\(171\) 3.00000 0.229415
\(172\) 8.02831 0.612153
\(173\) 3.45938 0.263012 0.131506 0.991315i \(-0.458019\pi\)
0.131506 + 0.991315i \(0.458019\pi\)
\(174\) 0.00800649 0.000606970 0
\(175\) 7.49280 0.566402
\(176\) −4.79658 −0.361556
\(177\) −0.0105334 −0.000791737 0
\(178\) 9.62818 0.721663
\(179\) −13.0489 −0.975320 −0.487660 0.873034i \(-0.662149\pi\)
−0.487660 + 0.873034i \(0.662149\pi\)
\(180\) 8.53566 0.636210
\(181\) 17.2368 1.28120 0.640602 0.767873i \(-0.278685\pi\)
0.640602 + 0.767873i \(0.278685\pi\)
\(182\) 0.581180 0.0430799
\(183\) 0.00992348 0.000733564 0
\(184\) −5.60385 −0.413121
\(185\) −8.70314 −0.639868
\(186\) −0.0170638 −0.00125118
\(187\) −4.21256 −0.308053
\(188\) −3.46726 −0.252876
\(189\) 0.0260801 0.00189705
\(190\) 2.84522 0.206414
\(191\) −13.5373 −0.979525 −0.489762 0.871856i \(-0.662916\pi\)
−0.489762 + 0.871856i \(0.662916\pi\)
\(192\) −0.00179563 −0.000129588 0
\(193\) −4.75134 −0.342009 −0.171004 0.985270i \(-0.554701\pi\)
−0.171004 + 0.985270i \(0.554701\pi\)
\(194\) 11.6368 0.835470
\(195\) 0.00122659 8.78382e−5 0
\(196\) −1.14017 −0.0814410
\(197\) −3.71388 −0.264603 −0.132301 0.991210i \(-0.542237\pi\)
−0.132301 + 0.991210i \(0.542237\pi\)
\(198\) 14.3897 1.02263
\(199\) −21.9493 −1.55594 −0.777972 0.628298i \(-0.783752\pi\)
−0.777972 + 0.628298i \(0.783752\pi\)
\(200\) 3.09529 0.218870
\(201\) 0.00288064 0.000203185 0
\(202\) 14.9281 1.05034
\(203\) −10.7936 −0.757565
\(204\) −0.00157699 −0.000110412 0
\(205\) −26.1611 −1.82717
\(206\) 5.38404 0.375124
\(207\) 16.8115 1.16848
\(208\) 0.240087 0.0166470
\(209\) 4.79658 0.331786
\(210\) 0.0123673 0.000853425 0
\(211\) −1.00000 −0.0688428
\(212\) −8.34252 −0.572966
\(213\) 0.0215472 0.00147639
\(214\) 7.38286 0.504682
\(215\) −22.8423 −1.55783
\(216\) 0.0107738 0.000733061 0
\(217\) 23.0039 1.56161
\(218\) 13.4481 0.910820
\(219\) 0.00864123 0.000583920 0
\(220\) 13.6473 0.920103
\(221\) 0.210854 0.0141836
\(222\) −0.00549258 −0.000368638 0
\(223\) 10.9423 0.732752 0.366376 0.930467i \(-0.380598\pi\)
0.366376 + 0.930467i \(0.380598\pi\)
\(224\) 2.42071 0.161740
\(225\) −9.28587 −0.619058
\(226\) 5.91656 0.393564
\(227\) 27.4565 1.82235 0.911175 0.412020i \(-0.135177\pi\)
0.911175 + 0.412020i \(0.135177\pi\)
\(228\) 0.00179563 0.000118918 0
\(229\) 23.5037 1.55317 0.776584 0.630014i \(-0.216951\pi\)
0.776584 + 0.630014i \(0.216951\pi\)
\(230\) 15.9442 1.05133
\(231\) 0.0208492 0.00137178
\(232\) −4.45888 −0.292740
\(233\) −20.9100 −1.36986 −0.684930 0.728609i \(-0.740167\pi\)
−0.684930 + 0.728609i \(0.740167\pi\)
\(234\) −0.720260 −0.0470849
\(235\) 9.86514 0.643531
\(236\) 5.86612 0.381852
\(237\) 0.0207843 0.00135009
\(238\) 2.12597 0.137806
\(239\) −5.68156 −0.367510 −0.183755 0.982972i \(-0.558825\pi\)
−0.183755 + 0.982972i \(0.558825\pi\)
\(240\) 0.00510896 0.000329782 0
\(241\) 9.05353 0.583189 0.291594 0.956542i \(-0.405814\pi\)
0.291594 + 0.956542i \(0.405814\pi\)
\(242\) 12.0072 0.771850
\(243\) −0.0484819 −0.00311011
\(244\) −5.52647 −0.353796
\(245\) 3.24405 0.207255
\(246\) −0.0165104 −0.00105266
\(247\) −0.240087 −0.0152764
\(248\) 9.50296 0.603438
\(249\) −0.0316150 −0.00200352
\(250\) 5.41932 0.342748
\(251\) 10.5940 0.668690 0.334345 0.942451i \(-0.391485\pi\)
0.334345 + 0.942451i \(0.391485\pi\)
\(252\) −7.26212 −0.457470
\(253\) 26.8793 1.68989
\(254\) 9.34529 0.586375
\(255\) 0.00448690 0.000280981 0
\(256\) 1.00000 0.0625000
\(257\) −23.5918 −1.47161 −0.735806 0.677192i \(-0.763197\pi\)
−0.735806 + 0.677192i \(0.763197\pi\)
\(258\) −0.0144158 −0.000897491 0
\(259\) 7.40461 0.460100
\(260\) −0.683101 −0.0423641
\(261\) 13.3766 0.827992
\(262\) −5.43634 −0.335858
\(263\) 28.7438 1.77242 0.886210 0.463285i \(-0.153329\pi\)
0.886210 + 0.463285i \(0.153329\pi\)
\(264\) 0.00861287 0.000530085 0
\(265\) 23.7363 1.45811
\(266\) −2.42071 −0.148423
\(267\) −0.0172886 −0.00105805
\(268\) −1.60425 −0.0979954
\(269\) −14.8139 −0.903218 −0.451609 0.892216i \(-0.649150\pi\)
−0.451609 + 0.892216i \(0.649150\pi\)
\(270\) −0.0306537 −0.00186553
\(271\) −0.836191 −0.0507950 −0.0253975 0.999677i \(-0.508085\pi\)
−0.0253975 + 0.999677i \(0.508085\pi\)
\(272\) 0.878242 0.0532512
\(273\) −0.00104358 −6.31605e−5 0
\(274\) −4.48249 −0.270797
\(275\) −14.8468 −0.895296
\(276\) 0.0100624 0.000605687 0
\(277\) 12.4906 0.750488 0.375244 0.926926i \(-0.377559\pi\)
0.375244 + 0.926926i \(0.377559\pi\)
\(278\) 12.5442 0.752350
\(279\) −28.5088 −1.70678
\(280\) −6.88745 −0.411604
\(281\) −20.4648 −1.22083 −0.610414 0.792082i \(-0.708997\pi\)
−0.610414 + 0.792082i \(0.708997\pi\)
\(282\) 0.00622592 0.000370748 0
\(283\) −21.7664 −1.29388 −0.646938 0.762542i \(-0.723951\pi\)
−0.646938 + 0.762542i \(0.723951\pi\)
\(284\) −11.9998 −0.712058
\(285\) −0.00510896 −0.000302629 0
\(286\) −1.15160 −0.0680953
\(287\) 22.2578 1.31384
\(288\) −3.00000 −0.176777
\(289\) −16.2287 −0.954629
\(290\) 12.6865 0.744977
\(291\) −0.0208953 −0.00122490
\(292\) −4.81238 −0.281623
\(293\) −30.4844 −1.78092 −0.890458 0.455065i \(-0.849616\pi\)
−0.890458 + 0.455065i \(0.849616\pi\)
\(294\) 0.00204733 0.000119403 0
\(295\) −16.6904 −0.971754
\(296\) 3.05886 0.177793
\(297\) −0.0516772 −0.00299861
\(298\) −0.954574 −0.0552970
\(299\) −1.34541 −0.0778072
\(300\) −0.00555799 −0.000320891 0
\(301\) 19.4342 1.12017
\(302\) −3.99230 −0.229731
\(303\) −0.0268053 −0.00153992
\(304\) −1.00000 −0.0573539
\(305\) 15.7240 0.900355
\(306\) −2.63472 −0.150617
\(307\) 8.11465 0.463128 0.231564 0.972820i \(-0.425616\pi\)
0.231564 + 0.972820i \(0.425616\pi\)
\(308\) −11.6111 −0.661605
\(309\) −0.00966773 −0.000549978 0
\(310\) −27.0380 −1.53566
\(311\) 0.0140801 0.000798407 0 0.000399203 1.00000i \(-0.499873\pi\)
0.000399203 1.00000i \(0.499873\pi\)
\(312\) −0.000431107 0 −2.44066e−5 0
\(313\) 10.1958 0.576302 0.288151 0.957585i \(-0.406959\pi\)
0.288151 + 0.957585i \(0.406959\pi\)
\(314\) 2.42485 0.136842
\(315\) 20.6623 1.16419
\(316\) −11.5750 −0.651143
\(317\) 2.49278 0.140008 0.0700042 0.997547i \(-0.477699\pi\)
0.0700042 + 0.997547i \(0.477699\pi\)
\(318\) 0.0149801 0.000840040 0
\(319\) 21.3874 1.19746
\(320\) −2.84522 −0.159053
\(321\) −0.0132569 −0.000739926 0
\(322\) −13.5653 −0.755964
\(323\) −0.878242 −0.0488667
\(324\) 8.99997 0.499998
\(325\) 0.743139 0.0412219
\(326\) 15.9239 0.881943
\(327\) −0.0241478 −0.00133537
\(328\) 9.19476 0.507696
\(329\) −8.39323 −0.462734
\(330\) −0.0245055 −0.00134898
\(331\) 25.2820 1.38962 0.694811 0.719192i \(-0.255488\pi\)
0.694811 + 0.719192i \(0.255488\pi\)
\(332\) 17.6067 0.966292
\(333\) −9.17657 −0.502873
\(334\) 8.25446 0.451664
\(335\) 4.56446 0.249383
\(336\) −0.00434669 −0.000237131 0
\(337\) 20.4478 1.11386 0.556932 0.830558i \(-0.311978\pi\)
0.556932 + 0.830558i \(0.311978\pi\)
\(338\) −12.9424 −0.703971
\(339\) −0.0106239 −0.000577013 0
\(340\) −2.49879 −0.135516
\(341\) −45.5817 −2.46839
\(342\) 3.00000 0.162221
\(343\) −19.7050 −1.06397
\(344\) 8.02831 0.432857
\(345\) −0.0286299 −0.00154138
\(346\) 3.45938 0.185977
\(347\) 26.2910 1.41138 0.705688 0.708523i \(-0.250638\pi\)
0.705688 + 0.708523i \(0.250638\pi\)
\(348\) 0.00800649 0.000429193 0
\(349\) 24.8585 1.33065 0.665323 0.746556i \(-0.268294\pi\)
0.665323 + 0.746556i \(0.268294\pi\)
\(350\) 7.49280 0.400507
\(351\) 0.00258664 0.000138065 0
\(352\) −4.79658 −0.255658
\(353\) 17.0158 0.905661 0.452831 0.891597i \(-0.350414\pi\)
0.452831 + 0.891597i \(0.350414\pi\)
\(354\) −0.0105334 −0.000559842 0
\(355\) 34.1421 1.81208
\(356\) 9.62818 0.510292
\(357\) −0.00381744 −0.000202041 0
\(358\) −13.0489 −0.689656
\(359\) 10.3032 0.543782 0.271891 0.962328i \(-0.412351\pi\)
0.271891 + 0.962328i \(0.412351\pi\)
\(360\) 8.53566 0.449869
\(361\) 1.00000 0.0526316
\(362\) 17.2368 0.905949
\(363\) −0.0215604 −0.00113163
\(364\) 0.581180 0.0304621
\(365\) 13.6923 0.716687
\(366\) 0.00992348 0.000518708 0
\(367\) −27.4401 −1.43236 −0.716180 0.697915i \(-0.754111\pi\)
−0.716180 + 0.697915i \(0.754111\pi\)
\(368\) −5.60385 −0.292121
\(369\) −27.5843 −1.43598
\(370\) −8.70314 −0.452455
\(371\) −20.1948 −1.04846
\(372\) −0.0170638 −0.000884715 0
\(373\) −28.9544 −1.49920 −0.749601 0.661890i \(-0.769755\pi\)
−0.749601 + 0.661890i \(0.769755\pi\)
\(374\) −4.21256 −0.217826
\(375\) −0.00973108 −0.000502511 0
\(376\) −3.46726 −0.178811
\(377\) −1.07052 −0.0551345
\(378\) 0.0260801 0.00134142
\(379\) 24.8584 1.27689 0.638445 0.769667i \(-0.279578\pi\)
0.638445 + 0.769667i \(0.279578\pi\)
\(380\) 2.84522 0.145957
\(381\) −0.0167807 −0.000859699 0
\(382\) −13.5373 −0.692629
\(383\) −20.3027 −1.03742 −0.518710 0.854950i \(-0.673588\pi\)
−0.518710 + 0.854950i \(0.673588\pi\)
\(384\) −0.00179563 −9.16327e−5 0
\(385\) 33.0362 1.68368
\(386\) −4.75134 −0.241837
\(387\) −24.0849 −1.22430
\(388\) 11.6368 0.590767
\(389\) 23.5299 1.19301 0.596506 0.802608i \(-0.296555\pi\)
0.596506 + 0.802608i \(0.296555\pi\)
\(390\) 0.00122659 6.21110e−5 0
\(391\) −4.92154 −0.248893
\(392\) −1.14017 −0.0575875
\(393\) 0.00976164 0.000492409 0
\(394\) −3.71388 −0.187102
\(395\) 32.9334 1.65706
\(396\) 14.3897 0.723111
\(397\) 10.6764 0.535832 0.267916 0.963442i \(-0.413665\pi\)
0.267916 + 0.963442i \(0.413665\pi\)
\(398\) −21.9493 −1.10022
\(399\) 0.00434669 0.000217607 0
\(400\) 3.09529 0.154765
\(401\) −5.14678 −0.257018 −0.128509 0.991708i \(-0.541019\pi\)
−0.128509 + 0.991708i \(0.541019\pi\)
\(402\) 0.00288064 0.000143673 0
\(403\) 2.28154 0.113651
\(404\) 14.9281 0.742700
\(405\) −25.6069 −1.27242
\(406\) −10.7936 −0.535680
\(407\) −14.6721 −0.727267
\(408\) −0.00157699 −7.80729e−5 0
\(409\) 1.35507 0.0670037 0.0335018 0.999439i \(-0.489334\pi\)
0.0335018 + 0.999439i \(0.489334\pi\)
\(410\) −26.1611 −1.29201
\(411\) 0.00804888 0.000397022 0
\(412\) 5.38404 0.265253
\(413\) 14.2002 0.698745
\(414\) 16.8115 0.826242
\(415\) −50.0949 −2.45906
\(416\) 0.240087 0.0117712
\(417\) −0.0225247 −0.00110304
\(418\) 4.79658 0.234608
\(419\) 32.8620 1.60541 0.802706 0.596375i \(-0.203393\pi\)
0.802706 + 0.596375i \(0.203393\pi\)
\(420\) 0.0123673 0.000603462 0
\(421\) 19.3852 0.944775 0.472388 0.881391i \(-0.343392\pi\)
0.472388 + 0.881391i \(0.343392\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 10.4018 0.505752
\(424\) −8.34252 −0.405148
\(425\) 2.71841 0.131862
\(426\) 0.0215472 0.00104396
\(427\) −13.3780 −0.647405
\(428\) 7.38286 0.356864
\(429\) 0.00206784 9.98361e−5 0
\(430\) −22.8423 −1.10155
\(431\) 19.3947 0.934210 0.467105 0.884202i \(-0.345297\pi\)
0.467105 + 0.884202i \(0.345297\pi\)
\(432\) 0.0107738 0.000518353 0
\(433\) −15.6643 −0.752781 −0.376390 0.926461i \(-0.622835\pi\)
−0.376390 + 0.926461i \(0.622835\pi\)
\(434\) 23.0039 1.10422
\(435\) −0.0227802 −0.00109223
\(436\) 13.4481 0.644047
\(437\) 5.60385 0.268069
\(438\) 0.00864123 0.000412894 0
\(439\) 15.1152 0.721408 0.360704 0.932680i \(-0.382536\pi\)
0.360704 + 0.932680i \(0.382536\pi\)
\(440\) 13.6473 0.650611
\(441\) 3.42052 0.162882
\(442\) 0.210854 0.0100293
\(443\) 3.94271 0.187324 0.0936620 0.995604i \(-0.470143\pi\)
0.0936620 + 0.995604i \(0.470143\pi\)
\(444\) −0.00549258 −0.000260666 0
\(445\) −27.3943 −1.29861
\(446\) 10.9423 0.518134
\(447\) 0.00171406 8.10722e−5 0
\(448\) 2.42071 0.114368
\(449\) −4.88432 −0.230505 −0.115253 0.993336i \(-0.536768\pi\)
−0.115253 + 0.993336i \(0.536768\pi\)
\(450\) −9.28587 −0.437740
\(451\) −44.1034 −2.07675
\(452\) 5.91656 0.278292
\(453\) 0.00716869 0.000336814 0
\(454\) 27.4565 1.28860
\(455\) −1.65359 −0.0775214
\(456\) 0.00179563 8.40880e−5 0
\(457\) 1.82125 0.0851946 0.0425973 0.999092i \(-0.486437\pi\)
0.0425973 + 0.999092i \(0.486437\pi\)
\(458\) 23.5037 1.09826
\(459\) 0.00946196 0.000441647 0
\(460\) 15.9442 0.743402
\(461\) −36.7344 −1.71089 −0.855446 0.517892i \(-0.826717\pi\)
−0.855446 + 0.517892i \(0.826717\pi\)
\(462\) 0.0208492 0.000969994 0
\(463\) 29.4545 1.36886 0.684432 0.729076i \(-0.260050\pi\)
0.684432 + 0.729076i \(0.260050\pi\)
\(464\) −4.45888 −0.206998
\(465\) 0.0485502 0.00225146
\(466\) −20.9100 −0.968637
\(467\) 22.3819 1.03571 0.517855 0.855468i \(-0.326731\pi\)
0.517855 + 0.855468i \(0.326731\pi\)
\(468\) −0.720260 −0.0332940
\(469\) −3.88343 −0.179320
\(470\) 9.86514 0.455045
\(471\) −0.00435412 −0.000200627 0
\(472\) 5.86612 0.270010
\(473\) −38.5084 −1.77062
\(474\) 0.0207843 0.000954656 0
\(475\) −3.09529 −0.142022
\(476\) 2.12597 0.0974435
\(477\) 25.0275 1.14593
\(478\) −5.68156 −0.259869
\(479\) 36.1413 1.65134 0.825669 0.564155i \(-0.190798\pi\)
0.825669 + 0.564155i \(0.190798\pi\)
\(480\) 0.00510896 0.000233191 0
\(481\) 0.734393 0.0334854
\(482\) 9.05353 0.412377
\(483\) 0.0243582 0.00110834
\(484\) 12.0072 0.545780
\(485\) −33.1092 −1.50341
\(486\) −0.0484819 −0.00219918
\(487\) −4.85599 −0.220046 −0.110023 0.993929i \(-0.535092\pi\)
−0.110023 + 0.993929i \(0.535092\pi\)
\(488\) −5.52647 −0.250171
\(489\) −0.0285934 −0.00129304
\(490\) 3.24405 0.146551
\(491\) 34.0613 1.53717 0.768583 0.639750i \(-0.220962\pi\)
0.768583 + 0.639750i \(0.220962\pi\)
\(492\) −0.0165104 −0.000744345 0
\(493\) −3.91597 −0.176367
\(494\) −0.240087 −0.0108020
\(495\) −40.9420 −1.84020
\(496\) 9.50296 0.426695
\(497\) −29.0480 −1.30298
\(498\) −0.0316150 −0.00141670
\(499\) −35.6636 −1.59652 −0.798260 0.602312i \(-0.794246\pi\)
−0.798260 + 0.602312i \(0.794246\pi\)
\(500\) 5.41932 0.242359
\(501\) −0.0148219 −0.000662196 0
\(502\) 10.5940 0.472835
\(503\) 18.6709 0.832493 0.416247 0.909252i \(-0.363345\pi\)
0.416247 + 0.909252i \(0.363345\pi\)
\(504\) −7.26212 −0.323480
\(505\) −42.4737 −1.89006
\(506\) 26.8793 1.19493
\(507\) 0.0232397 0.00103211
\(508\) 9.34529 0.414630
\(509\) 10.5431 0.467315 0.233658 0.972319i \(-0.424931\pi\)
0.233658 + 0.972319i \(0.424931\pi\)
\(510\) 0.00448690 0.000198683 0
\(511\) −11.6494 −0.515337
\(512\) 1.00000 0.0441942
\(513\) −0.0107738 −0.000475673 0
\(514\) −23.5918 −1.04059
\(515\) −15.3188 −0.675027
\(516\) −0.0144158 −0.000634622 0
\(517\) 16.6310 0.731431
\(518\) 7.40461 0.325340
\(519\) −0.00621176 −0.000272666 0
\(520\) −0.683101 −0.0299559
\(521\) −19.2105 −0.841627 −0.420814 0.907147i \(-0.638255\pi\)
−0.420814 + 0.907147i \(0.638255\pi\)
\(522\) 13.3766 0.585479
\(523\) −32.8940 −1.43835 −0.719177 0.694827i \(-0.755481\pi\)
−0.719177 + 0.694827i \(0.755481\pi\)
\(524\) −5.43634 −0.237488
\(525\) −0.0134543 −0.000587193 0
\(526\) 28.7438 1.25329
\(527\) 8.34589 0.363553
\(528\) 0.00861287 0.000374827 0
\(529\) 8.40316 0.365355
\(530\) 23.7363 1.03104
\(531\) −17.5984 −0.763704
\(532\) −2.42071 −0.104951
\(533\) 2.20754 0.0956192
\(534\) −0.0172886 −0.000748152 0
\(535\) −21.0059 −0.908163
\(536\) −1.60425 −0.0692932
\(537\) 0.0234310 0.00101112
\(538\) −14.8139 −0.638672
\(539\) 5.46893 0.235564
\(540\) −0.0306537 −0.00131913
\(541\) 38.9807 1.67591 0.837955 0.545740i \(-0.183751\pi\)
0.837955 + 0.545740i \(0.183751\pi\)
\(542\) −0.836191 −0.0359175
\(543\) −0.0309510 −0.00132823
\(544\) 0.878242 0.0376543
\(545\) −38.2628 −1.63900
\(546\) −0.00104358 −4.46612e−5 0
\(547\) 0.492857 0.0210730 0.0105365 0.999944i \(-0.496646\pi\)
0.0105365 + 0.999944i \(0.496646\pi\)
\(548\) −4.48249 −0.191482
\(549\) 16.5794 0.707591
\(550\) −14.8468 −0.633070
\(551\) 4.45888 0.189955
\(552\) 0.0100624 0.000428285 0
\(553\) −28.0196 −1.19152
\(554\) 12.4906 0.530675
\(555\) 0.0156276 0.000663355 0
\(556\) 12.5442 0.531992
\(557\) −12.5752 −0.532828 −0.266414 0.963859i \(-0.585839\pi\)
−0.266414 + 0.963859i \(0.585839\pi\)
\(558\) −28.5088 −1.20688
\(559\) 1.92749 0.0815242
\(560\) −6.88745 −0.291048
\(561\) 0.00756418 0.000319360 0
\(562\) −20.4648 −0.863256
\(563\) −25.9381 −1.09316 −0.546580 0.837407i \(-0.684071\pi\)
−0.546580 + 0.837407i \(0.684071\pi\)
\(564\) 0.00622592 0.000262158 0
\(565\) −16.8339 −0.708209
\(566\) −21.7664 −0.914909
\(567\) 21.7863 0.914939
\(568\) −11.9998 −0.503501
\(569\) 6.72278 0.281833 0.140917 0.990021i \(-0.454995\pi\)
0.140917 + 0.990021i \(0.454995\pi\)
\(570\) −0.00510896 −0.000213991 0
\(571\) −16.7539 −0.701129 −0.350564 0.936539i \(-0.614010\pi\)
−0.350564 + 0.936539i \(0.614010\pi\)
\(572\) −1.15160 −0.0481506
\(573\) 0.0243079 0.00101548
\(574\) 22.2578 0.929024
\(575\) −17.3456 −0.723360
\(576\) −3.00000 −0.125000
\(577\) −35.7934 −1.49010 −0.745049 0.667010i \(-0.767574\pi\)
−0.745049 + 0.667010i \(0.767574\pi\)
\(578\) −16.2287 −0.675025
\(579\) 0.00853164 0.000354563 0
\(580\) 12.6865 0.526778
\(581\) 42.6206 1.76820
\(582\) −0.0208953 −0.000866137 0
\(583\) 40.0155 1.65727
\(584\) −4.81238 −0.199138
\(585\) 2.04930 0.0847281
\(586\) −30.4844 −1.25930
\(587\) −5.08519 −0.209888 −0.104944 0.994478i \(-0.533466\pi\)
−0.104944 + 0.994478i \(0.533466\pi\)
\(588\) 0.00204733 8.44304e−5 0
\(589\) −9.50296 −0.391562
\(590\) −16.6904 −0.687134
\(591\) 0.00666874 0.000274315 0
\(592\) 3.05886 0.125718
\(593\) 2.28232 0.0937238 0.0468619 0.998901i \(-0.485078\pi\)
0.0468619 + 0.998901i \(0.485078\pi\)
\(594\) −0.0516772 −0.00212034
\(595\) −6.04885 −0.247979
\(596\) −0.954574 −0.0391009
\(597\) 0.0394128 0.00161306
\(598\) −1.34541 −0.0550180
\(599\) −20.9805 −0.857238 −0.428619 0.903485i \(-0.641000\pi\)
−0.428619 + 0.903485i \(0.641000\pi\)
\(600\) −0.00555799 −0.000226904 0
\(601\) 39.4205 1.60800 0.803998 0.594632i \(-0.202702\pi\)
0.803998 + 0.594632i \(0.202702\pi\)
\(602\) 19.4342 0.792078
\(603\) 4.81276 0.195991
\(604\) −3.99230 −0.162444
\(605\) −34.1631 −1.38893
\(606\) −0.0268053 −0.00108889
\(607\) 27.7390 1.12589 0.562946 0.826494i \(-0.309668\pi\)
0.562946 + 0.826494i \(0.309668\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0.0193814 0.000785372 0
\(610\) 15.7240 0.636647
\(611\) −0.832445 −0.0336771
\(612\) −2.63472 −0.106502
\(613\) 25.5132 1.03047 0.515235 0.857049i \(-0.327705\pi\)
0.515235 + 0.857049i \(0.327705\pi\)
\(614\) 8.11465 0.327481
\(615\) 0.0469757 0.00189424
\(616\) −11.6111 −0.467825
\(617\) −3.27412 −0.131811 −0.0659056 0.997826i \(-0.520994\pi\)
−0.0659056 + 0.997826i \(0.520994\pi\)
\(618\) −0.00966773 −0.000388893 0
\(619\) −1.84005 −0.0739578 −0.0369789 0.999316i \(-0.511773\pi\)
−0.0369789 + 0.999316i \(0.511773\pi\)
\(620\) −27.0380 −1.08587
\(621\) −0.0603746 −0.00242275
\(622\) 0.0140801 0.000564559 0
\(623\) 23.3070 0.933776
\(624\) −0.000431107 0 −1.72581e−5 0
\(625\) −30.8956 −1.23583
\(626\) 10.1958 0.407507
\(627\) −0.00861287 −0.000343965 0
\(628\) 2.42485 0.0967619
\(629\) 2.68642 0.107115
\(630\) 20.6623 0.823207
\(631\) 40.3974 1.60819 0.804097 0.594498i \(-0.202649\pi\)
0.804097 + 0.594498i \(0.202649\pi\)
\(632\) −11.5750 −0.460428
\(633\) 0.00179563 7.13698e−5 0
\(634\) 2.49278 0.0990009
\(635\) −26.5894 −1.05517
\(636\) 0.0149801 0.000593998 0
\(637\) −0.273741 −0.0108460
\(638\) 21.3874 0.846734
\(639\) 35.9994 1.42411
\(640\) −2.84522 −0.112467
\(641\) −38.7155 −1.52917 −0.764586 0.644522i \(-0.777057\pi\)
−0.764586 + 0.644522i \(0.777057\pi\)
\(642\) −0.0132569 −0.000523207 0
\(643\) 41.7031 1.64461 0.822306 0.569046i \(-0.192687\pi\)
0.822306 + 0.569046i \(0.192687\pi\)
\(644\) −13.5653 −0.534547
\(645\) 0.0410163 0.00161501
\(646\) −0.878242 −0.0345540
\(647\) −42.4389 −1.66844 −0.834222 0.551429i \(-0.814083\pi\)
−0.834222 + 0.551429i \(0.814083\pi\)
\(648\) 8.99997 0.353552
\(649\) −28.1373 −1.10449
\(650\) 0.743139 0.0291483
\(651\) −0.0413064 −0.00161893
\(652\) 15.9239 0.623628
\(653\) 23.9430 0.936962 0.468481 0.883474i \(-0.344802\pi\)
0.468481 + 0.883474i \(0.344802\pi\)
\(654\) −0.0241478 −0.000944252 0
\(655\) 15.4676 0.604369
\(656\) 9.19476 0.358995
\(657\) 14.4371 0.563245
\(658\) −8.39323 −0.327202
\(659\) −35.3540 −1.37719 −0.688597 0.725144i \(-0.741773\pi\)
−0.688597 + 0.725144i \(0.741773\pi\)
\(660\) −0.0245055 −0.000953876 0
\(661\) 17.0210 0.662041 0.331021 0.943624i \(-0.392607\pi\)
0.331021 + 0.943624i \(0.392607\pi\)
\(662\) 25.2820 0.982612
\(663\) −0.000378616 0 −1.47042e−5 0
\(664\) 17.6067 0.683272
\(665\) 6.88745 0.267084
\(666\) −9.17657 −0.355585
\(667\) 24.9869 0.967497
\(668\) 8.25446 0.319375
\(669\) −0.0196483 −0.000759648 0
\(670\) 4.56446 0.176341
\(671\) 26.5081 1.02334
\(672\) −0.00434669 −0.000167677 0
\(673\) −50.3333 −1.94021 −0.970104 0.242691i \(-0.921970\pi\)
−0.970104 + 0.242691i \(0.921970\pi\)
\(674\) 20.4478 0.787621
\(675\) 0.0333479 0.00128356
\(676\) −12.9424 −0.497783
\(677\) −4.24362 −0.163095 −0.0815477 0.996669i \(-0.525986\pi\)
−0.0815477 + 0.996669i \(0.525986\pi\)
\(678\) −0.0106239 −0.000408010 0
\(679\) 28.1692 1.08103
\(680\) −2.49879 −0.0958243
\(681\) −0.0493016 −0.00188924
\(682\) −45.5817 −1.74541
\(683\) 17.5799 0.672676 0.336338 0.941741i \(-0.390812\pi\)
0.336338 + 0.941741i \(0.390812\pi\)
\(684\) 3.00000 0.114708
\(685\) 12.7537 0.487293
\(686\) −19.7050 −0.752340
\(687\) −0.0422039 −0.00161018
\(688\) 8.02831 0.306076
\(689\) −2.00293 −0.0763055
\(690\) −0.0286299 −0.00108992
\(691\) 21.3157 0.810886 0.405443 0.914120i \(-0.367117\pi\)
0.405443 + 0.914120i \(0.367117\pi\)
\(692\) 3.45938 0.131506
\(693\) 34.8333 1.32321
\(694\) 26.2910 0.997993
\(695\) −35.6910 −1.35384
\(696\) 0.00800649 0.000303485 0
\(697\) 8.07522 0.305871
\(698\) 24.8585 0.940909
\(699\) 0.0375466 0.00142014
\(700\) 7.49280 0.283201
\(701\) 49.4369 1.86721 0.933603 0.358309i \(-0.116647\pi\)
0.933603 + 0.358309i \(0.116647\pi\)
\(702\) 0.00258664 9.76264e−5 0
\(703\) −3.05886 −0.115367
\(704\) −4.79658 −0.180778
\(705\) −0.0177141 −0.000667152 0
\(706\) 17.0158 0.640399
\(707\) 36.1365 1.35905
\(708\) −0.0105334 −0.000395868 0
\(709\) −26.2836 −0.987103 −0.493551 0.869717i \(-0.664302\pi\)
−0.493551 + 0.869717i \(0.664302\pi\)
\(710\) 34.1421 1.28133
\(711\) 34.7249 1.30228
\(712\) 9.62818 0.360831
\(713\) −53.2532 −1.99435
\(714\) −0.00381744 −0.000142864 0
\(715\) 3.27655 0.122536
\(716\) −13.0489 −0.487660
\(717\) 0.0102020 0.000381000 0
\(718\) 10.3032 0.384512
\(719\) −18.7008 −0.697422 −0.348711 0.937230i \(-0.613380\pi\)
−0.348711 + 0.937230i \(0.613380\pi\)
\(720\) 8.53566 0.318105
\(721\) 13.0332 0.485381
\(722\) 1.00000 0.0372161
\(723\) −0.0162568 −0.000604595 0
\(724\) 17.2368 0.640602
\(725\) −13.8015 −0.512576
\(726\) −0.0215604 −0.000800181 0
\(727\) −17.2064 −0.638149 −0.319074 0.947730i \(-0.603372\pi\)
−0.319074 + 0.947730i \(0.603372\pi\)
\(728\) 0.581180 0.0215400
\(729\) −26.9998 −0.999994
\(730\) 13.6923 0.506774
\(731\) 7.05079 0.260783
\(732\) 0.00992348 0.000366782 0
\(733\) −51.7474 −1.91133 −0.955667 0.294449i \(-0.904864\pi\)
−0.955667 + 0.294449i \(0.904864\pi\)
\(734\) −27.4401 −1.01283
\(735\) −0.00582510 −0.000214862 0
\(736\) −5.60385 −0.206561
\(737\) 7.69493 0.283446
\(738\) −27.5843 −1.01539
\(739\) −22.1750 −0.815721 −0.407860 0.913044i \(-0.633725\pi\)
−0.407860 + 0.913044i \(0.633725\pi\)
\(740\) −8.70314 −0.319934
\(741\) 0.000431107 0 1.58371e−5 0
\(742\) −20.1948 −0.741374
\(743\) −2.68077 −0.0983477 −0.0491739 0.998790i \(-0.515659\pi\)
−0.0491739 + 0.998790i \(0.515659\pi\)
\(744\) −0.0170638 −0.000625588 0
\(745\) 2.71598 0.0995056
\(746\) −28.9544 −1.06010
\(747\) −52.8200 −1.93258
\(748\) −4.21256 −0.154026
\(749\) 17.8717 0.653019
\(750\) −0.00973108 −0.000355329 0
\(751\) −21.4368 −0.782240 −0.391120 0.920340i \(-0.627912\pi\)
−0.391120 + 0.920340i \(0.627912\pi\)
\(752\) −3.46726 −0.126438
\(753\) −0.0190229 −0.000693235 0
\(754\) −1.07052 −0.0389860
\(755\) 11.3590 0.413396
\(756\) 0.0260801 0.000948525 0
\(757\) 13.3428 0.484952 0.242476 0.970157i \(-0.422040\pi\)
0.242476 + 0.970157i \(0.422040\pi\)
\(758\) 24.8584 0.902898
\(759\) −0.0482652 −0.00175192
\(760\) 2.84522 0.103207
\(761\) 44.2849 1.60533 0.802664 0.596432i \(-0.203415\pi\)
0.802664 + 0.596432i \(0.203415\pi\)
\(762\) −0.0167807 −0.000607899 0
\(763\) 32.5539 1.17853
\(764\) −13.5373 −0.489762
\(765\) 7.49637 0.271032
\(766\) −20.3027 −0.733567
\(767\) 1.40838 0.0508536
\(768\) −0.00179563 −6.47941e−5 0
\(769\) 3.60467 0.129988 0.0649939 0.997886i \(-0.479297\pi\)
0.0649939 + 0.997886i \(0.479297\pi\)
\(770\) 33.0362 1.19054
\(771\) 0.0423620 0.00152563
\(772\) −4.75134 −0.171004
\(773\) −7.12506 −0.256271 −0.128135 0.991757i \(-0.540899\pi\)
−0.128135 + 0.991757i \(0.540899\pi\)
\(774\) −24.0849 −0.865714
\(775\) 29.4144 1.05660
\(776\) 11.6368 0.417735
\(777\) −0.0132959 −0.000476988 0
\(778\) 23.5299 0.843587
\(779\) −9.19476 −0.329436
\(780\) 0.00122659 4.39191e−5 0
\(781\) 57.5580 2.05959
\(782\) −4.92154 −0.175994
\(783\) −0.0480389 −0.00171677
\(784\) −1.14017 −0.0407205
\(785\) −6.89923 −0.246244
\(786\) 0.00976164 0.000348186 0
\(787\) 22.8348 0.813971 0.406986 0.913435i \(-0.366580\pi\)
0.406986 + 0.913435i \(0.366580\pi\)
\(788\) −3.71388 −0.132301
\(789\) −0.0516132 −0.00183748
\(790\) 32.9334 1.17172
\(791\) 14.3223 0.509241
\(792\) 14.3897 0.511316
\(793\) −1.32683 −0.0471172
\(794\) 10.6764 0.378890
\(795\) −0.0426216 −0.00151163
\(796\) −21.9493 −0.777972
\(797\) −18.7724 −0.664952 −0.332476 0.943112i \(-0.607884\pi\)
−0.332476 + 0.943112i \(0.607884\pi\)
\(798\) 0.00434669 0.000153871 0
\(799\) −3.04510 −0.107728
\(800\) 3.09529 0.109435
\(801\) −28.8845 −1.02058
\(802\) −5.14678 −0.181739
\(803\) 23.0829 0.814579
\(804\) 0.00288064 0.000101592 0
\(805\) 38.5963 1.36034
\(806\) 2.28154 0.0803636
\(807\) 0.0266002 0.000936372 0
\(808\) 14.9281 0.525168
\(809\) 26.7279 0.939704 0.469852 0.882745i \(-0.344307\pi\)
0.469852 + 0.882745i \(0.344307\pi\)
\(810\) −25.6069 −0.899736
\(811\) 8.06370 0.283155 0.141577 0.989927i \(-0.454783\pi\)
0.141577 + 0.989927i \(0.454783\pi\)
\(812\) −10.7936 −0.378783
\(813\) 0.00150149 5.26595e−5 0
\(814\) −14.6721 −0.514256
\(815\) −45.3070 −1.58704
\(816\) −0.00157699 −5.52059e−5 0
\(817\) −8.02831 −0.280875
\(818\) 1.35507 0.0473787
\(819\) −1.74354 −0.0609242
\(820\) −26.1611 −0.913587
\(821\) −20.8937 −0.729195 −0.364597 0.931165i \(-0.618793\pi\)
−0.364597 + 0.931165i \(0.618793\pi\)
\(822\) 0.00804888 0.000280737 0
\(823\) −9.56812 −0.333524 −0.166762 0.985997i \(-0.553331\pi\)
−0.166762 + 0.985997i \(0.553331\pi\)
\(824\) 5.38404 0.187562
\(825\) 0.0266593 0.000928159 0
\(826\) 14.2002 0.494087
\(827\) −16.1182 −0.560486 −0.280243 0.959929i \(-0.590415\pi\)
−0.280243 + 0.959929i \(0.590415\pi\)
\(828\) 16.8115 0.584241
\(829\) 3.99510 0.138756 0.0693778 0.997590i \(-0.477899\pi\)
0.0693778 + 0.997590i \(0.477899\pi\)
\(830\) −50.0949 −1.73882
\(831\) −0.0224285 −0.000778036 0
\(832\) 0.240087 0.00832352
\(833\) −1.00135 −0.0346947
\(834\) −0.0225247 −0.000779966 0
\(835\) −23.4858 −0.812759
\(836\) 4.79658 0.165893
\(837\) 0.102383 0.00353886
\(838\) 32.8620 1.13520
\(839\) −51.3694 −1.77347 −0.886734 0.462280i \(-0.847031\pi\)
−0.886734 + 0.462280i \(0.847031\pi\)
\(840\) 0.0123673 0.000426712 0
\(841\) −9.11840 −0.314428
\(842\) 19.3852 0.668057
\(843\) 0.0367472 0.00126564
\(844\) −1.00000 −0.0344214
\(845\) 36.8239 1.26678
\(846\) 10.4018 0.357621
\(847\) 29.0658 0.998714
\(848\) −8.34252 −0.286483
\(849\) 0.0390843 0.00134137
\(850\) 2.71841 0.0932409
\(851\) −17.1414 −0.587600
\(852\) 0.0215472 0.000738195 0
\(853\) 36.6607 1.25524 0.627619 0.778521i \(-0.284030\pi\)
0.627619 + 0.778521i \(0.284030\pi\)
\(854\) −13.3780 −0.457784
\(855\) −8.53566 −0.291913
\(856\) 7.38286 0.252341
\(857\) −7.94393 −0.271359 −0.135680 0.990753i \(-0.543322\pi\)
−0.135680 + 0.990753i \(0.543322\pi\)
\(858\) 0.00206784 7.05948e−5 0
\(859\) 14.3412 0.489316 0.244658 0.969609i \(-0.421324\pi\)
0.244658 + 0.969609i \(0.421324\pi\)
\(860\) −22.8423 −0.778917
\(861\) −0.0399668 −0.00136206
\(862\) 19.3947 0.660586
\(863\) −32.4626 −1.10504 −0.552520 0.833500i \(-0.686334\pi\)
−0.552520 + 0.833500i \(0.686334\pi\)
\(864\) 0.0107738 0.000366531 0
\(865\) −9.84270 −0.334662
\(866\) −15.6643 −0.532296
\(867\) 0.0291407 0.000989670 0
\(868\) 23.0039 0.780803
\(869\) 55.5203 1.88340
\(870\) −0.0227802 −0.000772322 0
\(871\) −0.385160 −0.0130507
\(872\) 13.4481 0.455410
\(873\) −34.9102 −1.18153
\(874\) 5.60385 0.189553
\(875\) 13.1186 0.443489
\(876\) 0.00864123 0.000291960 0
\(877\) 23.1183 0.780649 0.390324 0.920677i \(-0.372363\pi\)
0.390324 + 0.920677i \(0.372363\pi\)
\(878\) 15.1152 0.510112
\(879\) 0.0547386 0.00184629
\(880\) 13.6473 0.460052
\(881\) 10.2682 0.345944 0.172972 0.984927i \(-0.444663\pi\)
0.172972 + 0.984927i \(0.444663\pi\)
\(882\) 3.42052 0.115175
\(883\) 0.913466 0.0307406 0.0153703 0.999882i \(-0.495107\pi\)
0.0153703 + 0.999882i \(0.495107\pi\)
\(884\) 0.210854 0.00709180
\(885\) 0.0299698 0.00100742
\(886\) 3.94271 0.132458
\(887\) 48.0970 1.61494 0.807469 0.589910i \(-0.200837\pi\)
0.807469 + 0.589910i \(0.200837\pi\)
\(888\) −0.00549258 −0.000184319 0
\(889\) 22.6222 0.758724
\(890\) −27.3943 −0.918259
\(891\) −43.1691 −1.44622
\(892\) 10.9423 0.366376
\(893\) 3.46726 0.116028
\(894\) 0.00171406 5.73267e−5 0
\(895\) 37.1270 1.24102
\(896\) 2.42071 0.0808702
\(897\) 0.00241586 8.06631e−5 0
\(898\) −4.88432 −0.162992
\(899\) −42.3725 −1.41320
\(900\) −9.28587 −0.309529
\(901\) −7.32675 −0.244089
\(902\) −44.1034 −1.46848
\(903\) −0.0348965 −0.00116128
\(904\) 5.91656 0.196782
\(905\) −49.0427 −1.63023
\(906\) 0.00716869 0.000238164 0
\(907\) −11.6383 −0.386444 −0.193222 0.981155i \(-0.561894\pi\)
−0.193222 + 0.981155i \(0.561894\pi\)
\(908\) 27.4565 0.911175
\(909\) −44.7842 −1.48540
\(910\) −1.65359 −0.0548159
\(911\) 3.53423 0.117094 0.0585471 0.998285i \(-0.481353\pi\)
0.0585471 + 0.998285i \(0.481353\pi\)
\(912\) 0.00179563 5.94592e−5 0
\(913\) −84.4518 −2.79495
\(914\) 1.82125 0.0602417
\(915\) −0.0282345 −0.000933404 0
\(916\) 23.5037 0.776584
\(917\) −13.1598 −0.434574
\(918\) 0.00946196 0.000312291 0
\(919\) −2.87305 −0.0947732 −0.0473866 0.998877i \(-0.515089\pi\)
−0.0473866 + 0.998877i \(0.515089\pi\)
\(920\) 15.9442 0.525665
\(921\) −0.0145709 −0.000480127 0
\(922\) −36.7344 −1.20978
\(923\) −2.88100 −0.0948292
\(924\) 0.0208492 0.000685889 0
\(925\) 9.46807 0.311308
\(926\) 29.4545 0.967934
\(927\) −16.1521 −0.530505
\(928\) −4.45888 −0.146370
\(929\) −15.3309 −0.502992 −0.251496 0.967858i \(-0.580922\pi\)
−0.251496 + 0.967858i \(0.580922\pi\)
\(930\) 0.0485502 0.00159202
\(931\) 1.14017 0.0373677
\(932\) −20.9100 −0.684930
\(933\) −2.52825e−5 0 −8.27713e−7 0
\(934\) 22.3819 0.732357
\(935\) 11.9857 0.391973
\(936\) −0.720260 −0.0235424
\(937\) −16.5432 −0.540443 −0.270221 0.962798i \(-0.587097\pi\)
−0.270221 + 0.962798i \(0.587097\pi\)
\(938\) −3.88343 −0.126799
\(939\) −0.0183079 −0.000597456 0
\(940\) 9.86514 0.321765
\(941\) −27.8624 −0.908289 −0.454145 0.890928i \(-0.650055\pi\)
−0.454145 + 0.890928i \(0.650055\pi\)
\(942\) −0.00435412 −0.000141865 0
\(943\) −51.5261 −1.67792
\(944\) 5.86612 0.190926
\(945\) −0.0742038 −0.00241385
\(946\) −38.5084 −1.25202
\(947\) −0.522227 −0.0169701 −0.00848505 0.999964i \(-0.502701\pi\)
−0.00848505 + 0.999964i \(0.502701\pi\)
\(948\) 0.0207843 0.000675044 0
\(949\) −1.15539 −0.0375055
\(950\) −3.09529 −0.100425
\(951\) −0.00447610 −0.000145148 0
\(952\) 2.12597 0.0689030
\(953\) 25.0170 0.810379 0.405190 0.914233i \(-0.367205\pi\)
0.405190 + 0.914233i \(0.367205\pi\)
\(954\) 25.0275 0.810296
\(955\) 38.5166 1.24637
\(956\) −5.68156 −0.183755
\(957\) −0.0384037 −0.00124142
\(958\) 36.1413 1.16767
\(959\) −10.8508 −0.350390
\(960\) 0.00510896 0.000164891 0
\(961\) 59.3062 1.91310
\(962\) 0.734393 0.0236778
\(963\) −22.1486 −0.713727
\(964\) 9.05353 0.291594
\(965\) 13.5186 0.435180
\(966\) 0.0243582 0.000783712 0
\(967\) −17.6698 −0.568222 −0.284111 0.958791i \(-0.591698\pi\)
−0.284111 + 0.958791i \(0.591698\pi\)
\(968\) 12.0072 0.385925
\(969\) 0.00157699 5.06604e−5 0
\(970\) −33.1092 −1.06307
\(971\) 3.42041 0.109766 0.0548831 0.998493i \(-0.482521\pi\)
0.0548831 + 0.998493i \(0.482521\pi\)
\(972\) −0.0484819 −0.00155506
\(973\) 30.3658 0.973483
\(974\) −4.85599 −0.155596
\(975\) −0.00133440 −4.27350e−5 0
\(976\) −5.52647 −0.176898
\(977\) 25.7862 0.824974 0.412487 0.910963i \(-0.364660\pi\)
0.412487 + 0.910963i \(0.364660\pi\)
\(978\) −0.0285934 −0.000914316 0
\(979\) −46.1823 −1.47599
\(980\) 3.24405 0.103627
\(981\) −40.3442 −1.28809
\(982\) 34.0613 1.08694
\(983\) 20.1953 0.644129 0.322064 0.946718i \(-0.395623\pi\)
0.322064 + 0.946718i \(0.395623\pi\)
\(984\) −0.0165104 −0.000526331 0
\(985\) 10.5668 0.336686
\(986\) −3.91597 −0.124710
\(987\) 0.0150711 0.000479719 0
\(988\) −0.240087 −0.00763818
\(989\) −44.9894 −1.43058
\(990\) −40.9420 −1.30122
\(991\) 55.2073 1.75372 0.876860 0.480747i \(-0.159634\pi\)
0.876860 + 0.480747i \(0.159634\pi\)
\(992\) 9.50296 0.301719
\(993\) −0.0453970 −0.00144063
\(994\) −29.0480 −0.921348
\(995\) 62.4507 1.97982
\(996\) −0.0316150 −0.00100176
\(997\) −22.2158 −0.703582 −0.351791 0.936079i \(-0.614427\pi\)
−0.351791 + 0.936079i \(0.614427\pi\)
\(998\) −35.6636 −1.12891
\(999\) 0.0329554 0.00104266
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 \(a_p\))