Properties

Label 8018.2.a.j.1.2
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 1.2
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +2.17673 q^{10} -0.677923 q^{11} -3.13813 q^{12} -1.92598 q^{13} +2.94096 q^{14} -6.83085 q^{15} +1.00000 q^{16} -0.0568742 q^{17} +6.84787 q^{18} -1.00000 q^{19} +2.17673 q^{20} -9.22911 q^{21} -0.677923 q^{22} -7.41334 q^{23} -3.13813 q^{24} -0.261866 q^{25} -1.92598 q^{26} -12.0751 q^{27} +2.94096 q^{28} +3.72430 q^{29} -6.83085 q^{30} +6.43359 q^{31} +1.00000 q^{32} +2.12741 q^{33} -0.0568742 q^{34} +6.40166 q^{35} +6.84787 q^{36} +3.10884 q^{37} -1.00000 q^{38} +6.04397 q^{39} +2.17673 q^{40} +4.25069 q^{41} -9.22911 q^{42} +0.0900971 q^{43} -0.677923 q^{44} +14.9059 q^{45} -7.41334 q^{46} -9.35894 q^{47} -3.13813 q^{48} +1.64923 q^{49} -0.261866 q^{50} +0.178479 q^{51} -1.92598 q^{52} +9.62968 q^{53} -12.0751 q^{54} -1.47565 q^{55} +2.94096 q^{56} +3.13813 q^{57} +3.72430 q^{58} -2.91543 q^{59} -6.83085 q^{60} +7.57892 q^{61} +6.43359 q^{62} +20.1393 q^{63} +1.00000 q^{64} -4.19232 q^{65} +2.12741 q^{66} +7.50104 q^{67} -0.0568742 q^{68} +23.2640 q^{69} +6.40166 q^{70} -4.17053 q^{71} +6.84787 q^{72} +14.8152 q^{73} +3.10884 q^{74} +0.821770 q^{75} -1.00000 q^{76} -1.99374 q^{77} +6.04397 q^{78} +12.2510 q^{79} +2.17673 q^{80} +17.3497 q^{81} +4.25069 q^{82} +14.2160 q^{83} -9.22911 q^{84} -0.123800 q^{85} +0.0900971 q^{86} -11.6873 q^{87} -0.677923 q^{88} -2.98084 q^{89} +14.9059 q^{90} -5.66422 q^{91} -7.41334 q^{92} -20.1895 q^{93} -9.35894 q^{94} -2.17673 q^{95} -3.13813 q^{96} +1.69741 q^{97} +1.64923 q^{98} -4.64233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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
\(3\) −3.13813 −1.81180 −0.905901 0.423490i \(-0.860805\pi\)
−0.905901 + 0.423490i \(0.860805\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.17673 0.973461 0.486731 0.873552i \(-0.338189\pi\)
0.486731 + 0.873552i \(0.338189\pi\)
\(6\) −3.13813 −1.28114
\(7\) 2.94096 1.11158 0.555789 0.831324i \(-0.312416\pi\)
0.555789 + 0.831324i \(0.312416\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.84787 2.28262
\(10\) 2.17673 0.688341
\(11\) −0.677923 −0.204401 −0.102201 0.994764i \(-0.532588\pi\)
−0.102201 + 0.994764i \(0.532588\pi\)
\(12\) −3.13813 −0.905901
\(13\) −1.92598 −0.534170 −0.267085 0.963673i \(-0.586060\pi\)
−0.267085 + 0.963673i \(0.586060\pi\)
\(14\) 2.94096 0.786004
\(15\) −6.83085 −1.76372
\(16\) 1.00000 0.250000
\(17\) −0.0568742 −0.0137940 −0.00689701 0.999976i \(-0.502195\pi\)
−0.00689701 + 0.999976i \(0.502195\pi\)
\(18\) 6.84787 1.61406
\(19\) −1.00000 −0.229416
\(20\) 2.17673 0.486731
\(21\) −9.22911 −2.01396
\(22\) −0.677923 −0.144534
\(23\) −7.41334 −1.54579 −0.772894 0.634535i \(-0.781192\pi\)
−0.772894 + 0.634535i \(0.781192\pi\)
\(24\) −3.13813 −0.640569
\(25\) −0.261866 −0.0523732
\(26\) −1.92598 −0.377715
\(27\) −12.0751 −2.32386
\(28\) 2.94096 0.555789
\(29\) 3.72430 0.691585 0.345793 0.938311i \(-0.387610\pi\)
0.345793 + 0.938311i \(0.387610\pi\)
\(30\) −6.83085 −1.24714
\(31\) 6.43359 1.15551 0.577753 0.816211i \(-0.303930\pi\)
0.577753 + 0.816211i \(0.303930\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.12741 0.370335
\(34\) −0.0568742 −0.00975384
\(35\) 6.40166 1.08208
\(36\) 6.84787 1.14131
\(37\) 3.10884 0.511090 0.255545 0.966797i \(-0.417745\pi\)
0.255545 + 0.966797i \(0.417745\pi\)
\(38\) −1.00000 −0.162221
\(39\) 6.04397 0.967810
\(40\) 2.17673 0.344171
\(41\) 4.25069 0.663847 0.331923 0.943306i \(-0.392302\pi\)
0.331923 + 0.943306i \(0.392302\pi\)
\(42\) −9.22911 −1.42408
\(43\) 0.0900971 0.0137397 0.00686984 0.999976i \(-0.497813\pi\)
0.00686984 + 0.999976i \(0.497813\pi\)
\(44\) −0.677923 −0.102201
\(45\) 14.9059 2.22205
\(46\) −7.41334 −1.09304
\(47\) −9.35894 −1.36514 −0.682571 0.730819i \(-0.739138\pi\)
−0.682571 + 0.730819i \(0.739138\pi\)
\(48\) −3.13813 −0.452950
\(49\) 1.64923 0.235605
\(50\) −0.261866 −0.0370334
\(51\) 0.178479 0.0249920
\(52\) −1.92598 −0.267085
\(53\) 9.62968 1.32274 0.661369 0.750061i \(-0.269976\pi\)
0.661369 + 0.750061i \(0.269976\pi\)
\(54\) −12.0751 −1.64322
\(55\) −1.47565 −0.198977
\(56\) 2.94096 0.393002
\(57\) 3.13813 0.415656
\(58\) 3.72430 0.489025
\(59\) −2.91543 −0.379557 −0.189779 0.981827i \(-0.560777\pi\)
−0.189779 + 0.981827i \(0.560777\pi\)
\(60\) −6.83085 −0.881859
\(61\) 7.57892 0.970381 0.485190 0.874409i \(-0.338750\pi\)
0.485190 + 0.874409i \(0.338750\pi\)
\(62\) 6.43359 0.817067
\(63\) 20.1393 2.53731
\(64\) 1.00000 0.125000
\(65\) −4.19232 −0.519994
\(66\) 2.12741 0.261866
\(67\) 7.50104 0.916398 0.458199 0.888850i \(-0.348495\pi\)
0.458199 + 0.888850i \(0.348495\pi\)
\(68\) −0.0568742 −0.00689701
\(69\) 23.2640 2.80066
\(70\) 6.40166 0.765144
\(71\) −4.17053 −0.494951 −0.247475 0.968894i \(-0.579601\pi\)
−0.247475 + 0.968894i \(0.579601\pi\)
\(72\) 6.84787 0.807030
\(73\) 14.8152 1.73398 0.866991 0.498323i \(-0.166051\pi\)
0.866991 + 0.498323i \(0.166051\pi\)
\(74\) 3.10884 0.361395
\(75\) 0.821770 0.0948898
\(76\) −1.00000 −0.114708
\(77\) −1.99374 −0.227208
\(78\) 6.04397 0.684345
\(79\) 12.2510 1.37835 0.689173 0.724597i \(-0.257974\pi\)
0.689173 + 0.724597i \(0.257974\pi\)
\(80\) 2.17673 0.243365
\(81\) 17.3497 1.92775
\(82\) 4.25069 0.469410
\(83\) 14.2160 1.56041 0.780205 0.625523i \(-0.215115\pi\)
0.780205 + 0.625523i \(0.215115\pi\)
\(84\) −9.22911 −1.00698
\(85\) −0.123800 −0.0134279
\(86\) 0.0900971 0.00971542
\(87\) −11.6873 −1.25301
\(88\) −0.677923 −0.0722668
\(89\) −2.98084 −0.315968 −0.157984 0.987442i \(-0.550499\pi\)
−0.157984 + 0.987442i \(0.550499\pi\)
\(90\) 14.9059 1.57122
\(91\) −5.66422 −0.593771
\(92\) −7.41334 −0.772894
\(93\) −20.1895 −2.09355
\(94\) −9.35894 −0.965301
\(95\) −2.17673 −0.223327
\(96\) −3.13813 −0.320284
\(97\) 1.69741 0.172346 0.0861729 0.996280i \(-0.472536\pi\)
0.0861729 + 0.996280i \(0.472536\pi\)
\(98\) 1.64923 0.166598
\(99\) −4.64233 −0.466572
\(100\) −0.261866 −0.0261866
\(101\) −14.0189 −1.39493 −0.697466 0.716618i \(-0.745689\pi\)
−0.697466 + 0.716618i \(0.745689\pi\)
\(102\) 0.178479 0.0176720
\(103\) 6.57765 0.648115 0.324058 0.946037i \(-0.394953\pi\)
0.324058 + 0.946037i \(0.394953\pi\)
\(104\) −1.92598 −0.188858
\(105\) −20.0892 −1.96051
\(106\) 9.62968 0.935317
\(107\) 6.18607 0.598030 0.299015 0.954248i \(-0.403342\pi\)
0.299015 + 0.954248i \(0.403342\pi\)
\(108\) −12.0751 −1.16193
\(109\) 6.65064 0.637015 0.318508 0.947920i \(-0.396818\pi\)
0.318508 + 0.947920i \(0.396818\pi\)
\(110\) −1.47565 −0.140698
\(111\) −9.75595 −0.925994
\(112\) 2.94096 0.277894
\(113\) −0.172612 −0.0162380 −0.00811900 0.999967i \(-0.502584\pi\)
−0.00811900 + 0.999967i \(0.502584\pi\)
\(114\) 3.13813 0.293913
\(115\) −16.1368 −1.50477
\(116\) 3.72430 0.345793
\(117\) −13.1889 −1.21931
\(118\) −2.91543 −0.268387
\(119\) −0.167265 −0.0153331
\(120\) −6.83085 −0.623569
\(121\) −10.5404 −0.958220
\(122\) 7.57892 0.686163
\(123\) −13.3392 −1.20276
\(124\) 6.43359 0.577753
\(125\) −11.4536 −1.02444
\(126\) 20.1393 1.79415
\(127\) −0.0366627 −0.00325329 −0.00162664 0.999999i \(-0.500518\pi\)
−0.00162664 + 0.999999i \(0.500518\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.282737 −0.0248936
\(130\) −4.19232 −0.367691
\(131\) −15.5217 −1.35614 −0.678068 0.734999i \(-0.737183\pi\)
−0.678068 + 0.734999i \(0.737183\pi\)
\(132\) 2.12741 0.185167
\(133\) −2.94096 −0.255013
\(134\) 7.50104 0.647991
\(135\) −26.2842 −2.26219
\(136\) −0.0568742 −0.00487692
\(137\) −0.603727 −0.0515799 −0.0257899 0.999667i \(-0.508210\pi\)
−0.0257899 + 0.999667i \(0.508210\pi\)
\(138\) 23.2640 1.98037
\(139\) −7.67314 −0.650827 −0.325413 0.945572i \(-0.605503\pi\)
−0.325413 + 0.945572i \(0.605503\pi\)
\(140\) 6.40166 0.541039
\(141\) 29.3696 2.47337
\(142\) −4.17053 −0.349983
\(143\) 1.30566 0.109185
\(144\) 6.84787 0.570656
\(145\) 8.10678 0.673231
\(146\) 14.8152 1.22611
\(147\) −5.17551 −0.426869
\(148\) 3.10884 0.255545
\(149\) 17.8478 1.46214 0.731072 0.682300i \(-0.239020\pi\)
0.731072 + 0.682300i \(0.239020\pi\)
\(150\) 0.821770 0.0670972
\(151\) 1.96512 0.159920 0.0799598 0.996798i \(-0.474521\pi\)
0.0799598 + 0.996798i \(0.474521\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −0.389467 −0.0314866
\(154\) −1.99374 −0.160660
\(155\) 14.0042 1.12484
\(156\) 6.04397 0.483905
\(157\) 20.4528 1.63231 0.816155 0.577832i \(-0.196101\pi\)
0.816155 + 0.577832i \(0.196101\pi\)
\(158\) 12.2510 0.974637
\(159\) −30.2192 −2.39654
\(160\) 2.17673 0.172085
\(161\) −21.8023 −1.71826
\(162\) 17.3497 1.36312
\(163\) −1.83432 −0.143675 −0.0718377 0.997416i \(-0.522886\pi\)
−0.0718377 + 0.997416i \(0.522886\pi\)
\(164\) 4.25069 0.331923
\(165\) 4.63079 0.360507
\(166\) 14.2160 1.10338
\(167\) −5.63314 −0.435906 −0.217953 0.975959i \(-0.569938\pi\)
−0.217953 + 0.975959i \(0.569938\pi\)
\(168\) −9.22911 −0.712042
\(169\) −9.29061 −0.714662
\(170\) −0.123800 −0.00949499
\(171\) −6.84787 −0.523670
\(172\) 0.0900971 0.00686984
\(173\) 18.5062 1.40700 0.703499 0.710697i \(-0.251620\pi\)
0.703499 + 0.710697i \(0.251620\pi\)
\(174\) −11.6873 −0.886015
\(175\) −0.770136 −0.0582168
\(176\) −0.677923 −0.0511004
\(177\) 9.14902 0.687682
\(178\) −2.98084 −0.223423
\(179\) 10.1095 0.755621 0.377810 0.925883i \(-0.376677\pi\)
0.377810 + 0.925883i \(0.376677\pi\)
\(180\) 14.9059 1.11102
\(181\) −14.1473 −1.05156 −0.525780 0.850621i \(-0.676226\pi\)
−0.525780 + 0.850621i \(0.676226\pi\)
\(182\) −5.66422 −0.419860
\(183\) −23.7836 −1.75814
\(184\) −7.41334 −0.546519
\(185\) 6.76709 0.497527
\(186\) −20.1895 −1.48036
\(187\) 0.0385563 0.00281952
\(188\) −9.35894 −0.682571
\(189\) −35.5125 −2.58315
\(190\) −2.17673 −0.157916
\(191\) −7.02060 −0.507993 −0.253997 0.967205i \(-0.581745\pi\)
−0.253997 + 0.967205i \(0.581745\pi\)
\(192\) −3.13813 −0.226475
\(193\) 8.20378 0.590521 0.295260 0.955417i \(-0.404594\pi\)
0.295260 + 0.955417i \(0.404594\pi\)
\(194\) 1.69741 0.121867
\(195\) 13.1561 0.942126
\(196\) 1.64923 0.117802
\(197\) 17.7254 1.26288 0.631441 0.775424i \(-0.282464\pi\)
0.631441 + 0.775424i \(0.282464\pi\)
\(198\) −4.64233 −0.329916
\(199\) 13.9359 0.987890 0.493945 0.869493i \(-0.335554\pi\)
0.493945 + 0.869493i \(0.335554\pi\)
\(200\) −0.261866 −0.0185167
\(201\) −23.5392 −1.66033
\(202\) −14.0189 −0.986366
\(203\) 10.9530 0.768750
\(204\) 0.178479 0.0124960
\(205\) 9.25259 0.646229
\(206\) 6.57765 0.458287
\(207\) −50.7656 −3.52845
\(208\) −1.92598 −0.133543
\(209\) 0.677923 0.0468929
\(210\) −20.0892 −1.38629
\(211\) −1.00000 −0.0688428
\(212\) 9.62968 0.661369
\(213\) 13.0877 0.896753
\(214\) 6.18607 0.422871
\(215\) 0.196117 0.0133750
\(216\) −12.0751 −0.821609
\(217\) 18.9209 1.28444
\(218\) 6.65064 0.450438
\(219\) −46.4919 −3.14163
\(220\) −1.47565 −0.0994884
\(221\) 0.109538 0.00736835
\(222\) −9.75595 −0.654777
\(223\) 22.6646 1.51774 0.758868 0.651245i \(-0.225753\pi\)
0.758868 + 0.651245i \(0.225753\pi\)
\(224\) 2.94096 0.196501
\(225\) −1.79322 −0.119548
\(226\) −0.172612 −0.0114820
\(227\) −27.0609 −1.79609 −0.898047 0.439899i \(-0.855014\pi\)
−0.898047 + 0.439899i \(0.855014\pi\)
\(228\) 3.13813 0.207828
\(229\) −17.9654 −1.18718 −0.593592 0.804766i \(-0.702291\pi\)
−0.593592 + 0.804766i \(0.702291\pi\)
\(230\) −16.1368 −1.06403
\(231\) 6.25663 0.411656
\(232\) 3.72430 0.244512
\(233\) 12.5585 0.822736 0.411368 0.911469i \(-0.365051\pi\)
0.411368 + 0.911469i \(0.365051\pi\)
\(234\) −13.1889 −0.862182
\(235\) −20.3718 −1.32891
\(236\) −2.91543 −0.189779
\(237\) −38.4453 −2.49729
\(238\) −0.167265 −0.0108422
\(239\) 1.08193 0.0699840 0.0349920 0.999388i \(-0.488859\pi\)
0.0349920 + 0.999388i \(0.488859\pi\)
\(240\) −6.83085 −0.440930
\(241\) 7.91764 0.510020 0.255010 0.966938i \(-0.417921\pi\)
0.255010 + 0.966938i \(0.417921\pi\)
\(242\) −10.5404 −0.677564
\(243\) −18.2204 −1.16884
\(244\) 7.57892 0.485190
\(245\) 3.58993 0.229352
\(246\) −13.3392 −0.850479
\(247\) 1.92598 0.122547
\(248\) 6.43359 0.408533
\(249\) −44.6117 −2.82715
\(250\) −11.4536 −0.724392
\(251\) −1.15591 −0.0729601 −0.0364801 0.999334i \(-0.511615\pi\)
−0.0364801 + 0.999334i \(0.511615\pi\)
\(252\) 20.1393 1.26866
\(253\) 5.02567 0.315961
\(254\) −0.0366627 −0.00230042
\(255\) 0.388499 0.0243288
\(256\) 1.00000 0.0625000
\(257\) 25.7438 1.60585 0.802926 0.596079i \(-0.203275\pi\)
0.802926 + 0.596079i \(0.203275\pi\)
\(258\) −0.282737 −0.0176024
\(259\) 9.14297 0.568117
\(260\) −4.19232 −0.259997
\(261\) 25.5035 1.57863
\(262\) −15.5217 −0.958933
\(263\) 9.07220 0.559416 0.279708 0.960085i \(-0.409762\pi\)
0.279708 + 0.960085i \(0.409762\pi\)
\(264\) 2.12741 0.130933
\(265\) 20.9612 1.28763
\(266\) −2.94096 −0.180322
\(267\) 9.35426 0.572472
\(268\) 7.50104 0.458199
\(269\) −1.42081 −0.0866282 −0.0433141 0.999062i \(-0.513792\pi\)
−0.0433141 + 0.999062i \(0.513792\pi\)
\(270\) −26.2842 −1.59961
\(271\) 0.387319 0.0235279 0.0117640 0.999931i \(-0.496255\pi\)
0.0117640 + 0.999931i \(0.496255\pi\)
\(272\) −0.0568742 −0.00344850
\(273\) 17.7751 1.07580
\(274\) −0.603727 −0.0364725
\(275\) 0.177525 0.0107052
\(276\) 23.2640 1.40033
\(277\) −21.4747 −1.29029 −0.645145 0.764060i \(-0.723203\pi\)
−0.645145 + 0.764060i \(0.723203\pi\)
\(278\) −7.67314 −0.460204
\(279\) 44.0564 2.63759
\(280\) 6.40166 0.382572
\(281\) −6.86911 −0.409777 −0.204889 0.978785i \(-0.565683\pi\)
−0.204889 + 0.978785i \(0.565683\pi\)
\(282\) 29.3696 1.74893
\(283\) −23.6913 −1.40830 −0.704151 0.710050i \(-0.748672\pi\)
−0.704151 + 0.710050i \(0.748672\pi\)
\(284\) −4.17053 −0.247475
\(285\) 6.83085 0.404625
\(286\) 1.30566 0.0772056
\(287\) 12.5011 0.737917
\(288\) 6.84787 0.403515
\(289\) −16.9968 −0.999810
\(290\) 8.10678 0.476046
\(291\) −5.32670 −0.312256
\(292\) 14.8152 0.866991
\(293\) 18.2346 1.06528 0.532639 0.846342i \(-0.321200\pi\)
0.532639 + 0.846342i \(0.321200\pi\)
\(294\) −5.17551 −0.301842
\(295\) −6.34610 −0.369484
\(296\) 3.10884 0.180698
\(297\) 8.18601 0.475000
\(298\) 17.8478 1.03389
\(299\) 14.2779 0.825714
\(300\) 0.821770 0.0474449
\(301\) 0.264972 0.0152727
\(302\) 1.96512 0.113080
\(303\) 43.9931 2.52734
\(304\) −1.00000 −0.0573539
\(305\) 16.4972 0.944628
\(306\) −0.389467 −0.0222644
\(307\) 19.7289 1.12599 0.562993 0.826461i \(-0.309650\pi\)
0.562993 + 0.826461i \(0.309650\pi\)
\(308\) −1.99374 −0.113604
\(309\) −20.6415 −1.17426
\(310\) 14.0042 0.795383
\(311\) −16.4419 −0.932337 −0.466169 0.884696i \(-0.654366\pi\)
−0.466169 + 0.884696i \(0.654366\pi\)
\(312\) 6.04397 0.342173
\(313\) 30.1407 1.70365 0.851827 0.523824i \(-0.175495\pi\)
0.851827 + 0.523824i \(0.175495\pi\)
\(314\) 20.4528 1.15422
\(315\) 43.8377 2.46998
\(316\) 12.2510 0.689173
\(317\) 2.60261 0.146177 0.0730886 0.997325i \(-0.476714\pi\)
0.0730886 + 0.997325i \(0.476714\pi\)
\(318\) −30.2192 −1.69461
\(319\) −2.52479 −0.141361
\(320\) 2.17673 0.121683
\(321\) −19.4127 −1.08351
\(322\) −21.8023 −1.21500
\(323\) 0.0568742 0.00316457
\(324\) 17.3497 0.963875
\(325\) 0.504348 0.0279762
\(326\) −1.83432 −0.101594
\(327\) −20.8706 −1.15415
\(328\) 4.25069 0.234705
\(329\) −27.5243 −1.51746
\(330\) 4.63079 0.254917
\(331\) 15.7023 0.863078 0.431539 0.902094i \(-0.357971\pi\)
0.431539 + 0.902094i \(0.357971\pi\)
\(332\) 14.2160 0.780205
\(333\) 21.2890 1.16663
\(334\) −5.63314 −0.308232
\(335\) 16.3277 0.892078
\(336\) −9.22911 −0.503489
\(337\) −7.79959 −0.424871 −0.212435 0.977175i \(-0.568139\pi\)
−0.212435 + 0.977175i \(0.568139\pi\)
\(338\) −9.29061 −0.505343
\(339\) 0.541680 0.0294200
\(340\) −0.123800 −0.00671397
\(341\) −4.36148 −0.236187
\(342\) −6.84787 −0.370291
\(343\) −15.7364 −0.849685
\(344\) 0.0900971 0.00485771
\(345\) 50.6394 2.72634
\(346\) 18.5062 0.994897
\(347\) −0.207988 −0.0111654 −0.00558268 0.999984i \(-0.501777\pi\)
−0.00558268 + 0.999984i \(0.501777\pi\)
\(348\) −11.6873 −0.626507
\(349\) 8.01503 0.429035 0.214517 0.976720i \(-0.431182\pi\)
0.214517 + 0.976720i \(0.431182\pi\)
\(350\) −0.770136 −0.0411655
\(351\) 23.2564 1.24134
\(352\) −0.677923 −0.0361334
\(353\) 1.32594 0.0705726 0.0352863 0.999377i \(-0.488766\pi\)
0.0352863 + 0.999377i \(0.488766\pi\)
\(354\) 9.14902 0.486265
\(355\) −9.07810 −0.481816
\(356\) −2.98084 −0.157984
\(357\) 0.524898 0.0277806
\(358\) 10.1095 0.534305
\(359\) 32.4982 1.71519 0.857595 0.514325i \(-0.171958\pi\)
0.857595 + 0.514325i \(0.171958\pi\)
\(360\) 14.9059 0.785612
\(361\) 1.00000 0.0526316
\(362\) −14.1473 −0.743565
\(363\) 33.0772 1.73610
\(364\) −5.66422 −0.296886
\(365\) 32.2485 1.68796
\(366\) −23.7836 −1.24319
\(367\) −13.7239 −0.716382 −0.358191 0.933648i \(-0.616606\pi\)
−0.358191 + 0.933648i \(0.616606\pi\)
\(368\) −7.41334 −0.386447
\(369\) 29.1082 1.51531
\(370\) 6.76709 0.351804
\(371\) 28.3205 1.47033
\(372\) −20.1895 −1.04677
\(373\) 9.46516 0.490087 0.245044 0.969512i \(-0.421198\pi\)
0.245044 + 0.969512i \(0.421198\pi\)
\(374\) 0.0385563 0.00199370
\(375\) 35.9430 1.85609
\(376\) −9.35894 −0.482651
\(377\) −7.17292 −0.369424
\(378\) −35.5125 −1.82656
\(379\) 20.3600 1.04582 0.522911 0.852387i \(-0.324846\pi\)
0.522911 + 0.852387i \(0.324846\pi\)
\(380\) −2.17673 −0.111664
\(381\) 0.115052 0.00589431
\(382\) −7.02060 −0.359205
\(383\) −24.3490 −1.24418 −0.622088 0.782948i \(-0.713715\pi\)
−0.622088 + 0.782948i \(0.713715\pi\)
\(384\) −3.13813 −0.160142
\(385\) −4.33983 −0.221178
\(386\) 8.20378 0.417561
\(387\) 0.616974 0.0313625
\(388\) 1.69741 0.0861729
\(389\) −24.8707 −1.26099 −0.630496 0.776192i \(-0.717149\pi\)
−0.630496 + 0.776192i \(0.717149\pi\)
\(390\) 13.1561 0.666183
\(391\) 0.421628 0.0213226
\(392\) 1.64923 0.0832988
\(393\) 48.7091 2.45705
\(394\) 17.7254 0.892993
\(395\) 26.6671 1.34177
\(396\) −4.64233 −0.233286
\(397\) 5.94481 0.298362 0.149181 0.988810i \(-0.452336\pi\)
0.149181 + 0.988810i \(0.452336\pi\)
\(398\) 13.9359 0.698544
\(399\) 9.22911 0.462034
\(400\) −0.261866 −0.0130933
\(401\) −32.5793 −1.62693 −0.813467 0.581611i \(-0.802423\pi\)
−0.813467 + 0.581611i \(0.802423\pi\)
\(402\) −23.5392 −1.17403
\(403\) −12.3910 −0.617237
\(404\) −14.0189 −0.697466
\(405\) 37.7656 1.87659
\(406\) 10.9530 0.543589
\(407\) −2.10755 −0.104468
\(408\) 0.178479 0.00883601
\(409\) −8.21196 −0.406055 −0.203028 0.979173i \(-0.565078\pi\)
−0.203028 + 0.979173i \(0.565078\pi\)
\(410\) 9.25259 0.456953
\(411\) 1.89458 0.0934525
\(412\) 6.57765 0.324058
\(413\) −8.57417 −0.421907
\(414\) −50.7656 −2.49499
\(415\) 30.9444 1.51900
\(416\) −1.92598 −0.0944288
\(417\) 24.0793 1.17917
\(418\) 0.677923 0.0331583
\(419\) 6.67006 0.325854 0.162927 0.986638i \(-0.447907\pi\)
0.162927 + 0.986638i \(0.447907\pi\)
\(420\) −20.0892 −0.980255
\(421\) 31.9362 1.55647 0.778237 0.627970i \(-0.216114\pi\)
0.778237 + 0.627970i \(0.216114\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −64.0888 −3.11611
\(424\) 9.62968 0.467658
\(425\) 0.0148934 0.000722437 0
\(426\) 13.0877 0.634100
\(427\) 22.2893 1.07865
\(428\) 6.18607 0.299015
\(429\) −4.09735 −0.197822
\(430\) 0.196117 0.00945759
\(431\) 3.40300 0.163917 0.0819584 0.996636i \(-0.473883\pi\)
0.0819584 + 0.996636i \(0.473883\pi\)
\(432\) −12.0751 −0.580965
\(433\) 32.9384 1.58292 0.791460 0.611221i \(-0.209321\pi\)
0.791460 + 0.611221i \(0.209321\pi\)
\(434\) 18.9209 0.908233
\(435\) −25.4401 −1.21976
\(436\) 6.65064 0.318508
\(437\) 7.41334 0.354628
\(438\) −46.4919 −2.22147
\(439\) −36.8895 −1.76064 −0.880319 0.474382i \(-0.842672\pi\)
−0.880319 + 0.474382i \(0.842672\pi\)
\(440\) −1.47565 −0.0703490
\(441\) 11.2937 0.537797
\(442\) 0.109538 0.00521021
\(443\) 5.25207 0.249534 0.124767 0.992186i \(-0.460182\pi\)
0.124767 + 0.992186i \(0.460182\pi\)
\(444\) −9.75595 −0.462997
\(445\) −6.48847 −0.307583
\(446\) 22.6646 1.07320
\(447\) −56.0086 −2.64912
\(448\) 2.94096 0.138947
\(449\) −16.5954 −0.783184 −0.391592 0.920139i \(-0.628075\pi\)
−0.391592 + 0.920139i \(0.628075\pi\)
\(450\) −1.79322 −0.0845334
\(451\) −2.88164 −0.135691
\(452\) −0.172612 −0.00811900
\(453\) −6.16682 −0.289743
\(454\) −27.0609 −1.27003
\(455\) −12.3295 −0.578014
\(456\) 3.13813 0.146956
\(457\) 21.1449 0.989119 0.494559 0.869144i \(-0.335329\pi\)
0.494559 + 0.869144i \(0.335329\pi\)
\(458\) −17.9654 −0.839466
\(459\) 0.686764 0.0320554
\(460\) −16.1368 −0.752383
\(461\) 3.07268 0.143109 0.0715544 0.997437i \(-0.477204\pi\)
0.0715544 + 0.997437i \(0.477204\pi\)
\(462\) 6.25663 0.291085
\(463\) 27.7827 1.29117 0.645587 0.763687i \(-0.276613\pi\)
0.645587 + 0.763687i \(0.276613\pi\)
\(464\) 3.72430 0.172896
\(465\) −43.9469 −2.03799
\(466\) 12.5585 0.581763
\(467\) −4.37619 −0.202506 −0.101253 0.994861i \(-0.532285\pi\)
−0.101253 + 0.994861i \(0.532285\pi\)
\(468\) −13.1889 −0.609655
\(469\) 22.0602 1.01865
\(470\) −20.3718 −0.939683
\(471\) −64.1836 −2.95742
\(472\) −2.91543 −0.134194
\(473\) −0.0610789 −0.00280841
\(474\) −38.4453 −1.76585
\(475\) 0.261866 0.0120152
\(476\) −0.167265 −0.00766656
\(477\) 65.9428 3.01931
\(478\) 1.08193 0.0494862
\(479\) −12.2778 −0.560989 −0.280494 0.959856i \(-0.590498\pi\)
−0.280494 + 0.959856i \(0.590498\pi\)
\(480\) −6.83085 −0.311784
\(481\) −5.98756 −0.273009
\(482\) 7.91764 0.360639
\(483\) 68.4186 3.11315
\(484\) −10.5404 −0.479110
\(485\) 3.69480 0.167772
\(486\) −18.2204 −0.826493
\(487\) −18.3877 −0.833226 −0.416613 0.909084i \(-0.636783\pi\)
−0.416613 + 0.909084i \(0.636783\pi\)
\(488\) 7.57892 0.343081
\(489\) 5.75635 0.260311
\(490\) 3.58993 0.162176
\(491\) 29.5824 1.33503 0.667517 0.744595i \(-0.267357\pi\)
0.667517 + 0.744595i \(0.267357\pi\)
\(492\) −13.3392 −0.601379
\(493\) −0.211817 −0.00953974
\(494\) 1.92598 0.0866538
\(495\) −10.1051 −0.454189
\(496\) 6.43359 0.288877
\(497\) −12.2654 −0.550176
\(498\) −44.6117 −1.99910
\(499\) 10.7603 0.481696 0.240848 0.970563i \(-0.422574\pi\)
0.240848 + 0.970563i \(0.422574\pi\)
\(500\) −11.4536 −0.512222
\(501\) 17.6775 0.789775
\(502\) −1.15591 −0.0515906
\(503\) −6.26370 −0.279284 −0.139642 0.990202i \(-0.544595\pi\)
−0.139642 + 0.990202i \(0.544595\pi\)
\(504\) 20.1393 0.897076
\(505\) −30.5153 −1.35791
\(506\) 5.02567 0.223418
\(507\) 29.1552 1.29483
\(508\) −0.0366627 −0.00162664
\(509\) 43.2024 1.91491 0.957455 0.288581i \(-0.0931836\pi\)
0.957455 + 0.288581i \(0.0931836\pi\)
\(510\) 0.388499 0.0172030
\(511\) 43.5707 1.92746
\(512\) 1.00000 0.0441942
\(513\) 12.0751 0.533130
\(514\) 25.7438 1.13551
\(515\) 14.3177 0.630915
\(516\) −0.282737 −0.0124468
\(517\) 6.34464 0.279037
\(518\) 9.14297 0.401719
\(519\) −58.0748 −2.54920
\(520\) −4.19232 −0.183846
\(521\) −23.2818 −1.01999 −0.509997 0.860176i \(-0.670354\pi\)
−0.509997 + 0.860176i \(0.670354\pi\)
\(522\) 25.5035 1.11626
\(523\) −10.0037 −0.437431 −0.218715 0.975789i \(-0.570187\pi\)
−0.218715 + 0.975789i \(0.570187\pi\)
\(524\) −15.5217 −0.678068
\(525\) 2.41679 0.105477
\(526\) 9.07220 0.395567
\(527\) −0.365905 −0.0159391
\(528\) 2.12741 0.0925837
\(529\) 31.9576 1.38946
\(530\) 20.9612 0.910495
\(531\) −19.9645 −0.866387
\(532\) −2.94096 −0.127507
\(533\) −8.18674 −0.354607
\(534\) 9.35426 0.404799
\(535\) 13.4654 0.582159
\(536\) 7.50104 0.323996
\(537\) −31.7250 −1.36904
\(538\) −1.42081 −0.0612554
\(539\) −1.11805 −0.0481579
\(540\) −26.2842 −1.13109
\(541\) 16.1434 0.694061 0.347030 0.937854i \(-0.387190\pi\)
0.347030 + 0.937854i \(0.387190\pi\)
\(542\) 0.387319 0.0166368
\(543\) 44.3960 1.90522
\(544\) −0.0568742 −0.00243846
\(545\) 14.4766 0.620110
\(546\) 17.7751 0.760703
\(547\) 8.59487 0.367490 0.183745 0.982974i \(-0.441178\pi\)
0.183745 + 0.982974i \(0.441178\pi\)
\(548\) −0.603727 −0.0257899
\(549\) 51.8995 2.21501
\(550\) 0.177525 0.00756969
\(551\) −3.72430 −0.158661
\(552\) 23.2640 0.990184
\(553\) 36.0297 1.53214
\(554\) −21.4747 −0.912373
\(555\) −21.2360 −0.901420
\(556\) −7.67314 −0.325413
\(557\) 22.5177 0.954104 0.477052 0.878875i \(-0.341705\pi\)
0.477052 + 0.878875i \(0.341705\pi\)
\(558\) 44.0564 1.86506
\(559\) −0.173525 −0.00733933
\(560\) 6.40166 0.270519
\(561\) −0.120995 −0.00510841
\(562\) −6.86911 −0.289756
\(563\) −37.5767 −1.58367 −0.791835 0.610736i \(-0.790874\pi\)
−0.791835 + 0.610736i \(0.790874\pi\)
\(564\) 29.3696 1.23668
\(565\) −0.375730 −0.0158071
\(566\) −23.6913 −0.995821
\(567\) 51.0249 2.14284
\(568\) −4.17053 −0.174992
\(569\) 3.93013 0.164760 0.0823798 0.996601i \(-0.473748\pi\)
0.0823798 + 0.996601i \(0.473748\pi\)
\(570\) 6.83085 0.286113
\(571\) 7.07265 0.295981 0.147991 0.988989i \(-0.452719\pi\)
0.147991 + 0.988989i \(0.452719\pi\)
\(572\) 1.30566 0.0545926
\(573\) 22.0316 0.920383
\(574\) 12.5011 0.521786
\(575\) 1.94130 0.0809579
\(576\) 6.84787 0.285328
\(577\) −11.7591 −0.489537 −0.244768 0.969582i \(-0.578712\pi\)
−0.244768 + 0.969582i \(0.578712\pi\)
\(578\) −16.9968 −0.706972
\(579\) −25.7445 −1.06991
\(580\) 8.10678 0.336616
\(581\) 41.8087 1.73452
\(582\) −5.32670 −0.220799
\(583\) −6.52818 −0.270369
\(584\) 14.8152 0.613055
\(585\) −28.7085 −1.18695
\(586\) 18.2346 0.753265
\(587\) 8.29118 0.342214 0.171107 0.985252i \(-0.445266\pi\)
0.171107 + 0.985252i \(0.445266\pi\)
\(588\) −5.17551 −0.213434
\(589\) −6.43359 −0.265091
\(590\) −6.34610 −0.261265
\(591\) −55.6246 −2.28809
\(592\) 3.10884 0.127773
\(593\) −10.3414 −0.424669 −0.212334 0.977197i \(-0.568107\pi\)
−0.212334 + 0.977197i \(0.568107\pi\)
\(594\) 8.18601 0.335876
\(595\) −0.364089 −0.0149262
\(596\) 17.8478 0.731072
\(597\) −43.7327 −1.78986
\(598\) 14.2779 0.583868
\(599\) 40.2651 1.64519 0.822594 0.568629i \(-0.192526\pi\)
0.822594 + 0.568629i \(0.192526\pi\)
\(600\) 0.821770 0.0335486
\(601\) −22.1721 −0.904420 −0.452210 0.891912i \(-0.649364\pi\)
−0.452210 + 0.891912i \(0.649364\pi\)
\(602\) 0.264972 0.0107994
\(603\) 51.3662 2.09179
\(604\) 1.96512 0.0799598
\(605\) −22.9436 −0.932790
\(606\) 43.9931 1.78710
\(607\) −22.3686 −0.907912 −0.453956 0.891024i \(-0.649988\pi\)
−0.453956 + 0.891024i \(0.649988\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −34.3720 −1.39282
\(610\) 16.4972 0.667953
\(611\) 18.0251 0.729218
\(612\) −0.389467 −0.0157433
\(613\) 32.2960 1.30442 0.652211 0.758037i \(-0.273842\pi\)
0.652211 + 0.758037i \(0.273842\pi\)
\(614\) 19.7289 0.796193
\(615\) −29.0359 −1.17084
\(616\) −1.99374 −0.0803302
\(617\) 8.60952 0.346606 0.173303 0.984869i \(-0.444556\pi\)
0.173303 + 0.984869i \(0.444556\pi\)
\(618\) −20.6415 −0.830325
\(619\) 2.71059 0.108948 0.0544739 0.998515i \(-0.482652\pi\)
0.0544739 + 0.998515i \(0.482652\pi\)
\(620\) 14.0042 0.562421
\(621\) 89.5171 3.59220
\(622\) −16.4419 −0.659262
\(623\) −8.76652 −0.351223
\(624\) 6.04397 0.241953
\(625\) −23.6221 −0.944884
\(626\) 30.1407 1.20467
\(627\) −2.12741 −0.0849606
\(628\) 20.4528 0.816155
\(629\) −0.176813 −0.00704999
\(630\) 43.8377 1.74654
\(631\) −14.7800 −0.588381 −0.294190 0.955747i \(-0.595050\pi\)
−0.294190 + 0.955747i \(0.595050\pi\)
\(632\) 12.2510 0.487319
\(633\) 3.13813 0.124730
\(634\) 2.60261 0.103363
\(635\) −0.0798046 −0.00316695
\(636\) −30.2192 −1.19827
\(637\) −3.17638 −0.125853
\(638\) −2.52479 −0.0999573
\(639\) −28.5593 −1.12979
\(640\) 2.17673 0.0860426
\(641\) −10.9253 −0.431524 −0.215762 0.976446i \(-0.569223\pi\)
−0.215762 + 0.976446i \(0.569223\pi\)
\(642\) −19.4127 −0.766158
\(643\) −6.49059 −0.255964 −0.127982 0.991776i \(-0.540850\pi\)
−0.127982 + 0.991776i \(0.540850\pi\)
\(644\) −21.8023 −0.859132
\(645\) −0.615440 −0.0242329
\(646\) 0.0568742 0.00223769
\(647\) 33.8660 1.33141 0.665705 0.746215i \(-0.268131\pi\)
0.665705 + 0.746215i \(0.268131\pi\)
\(648\) 17.3497 0.681562
\(649\) 1.97644 0.0775820
\(650\) 0.504348 0.0197821
\(651\) −59.3763 −2.32714
\(652\) −1.83432 −0.0718377
\(653\) 20.3926 0.798024 0.399012 0.916946i \(-0.369353\pi\)
0.399012 + 0.916946i \(0.369353\pi\)
\(654\) −20.8706 −0.816104
\(655\) −33.7865 −1.32015
\(656\) 4.25069 0.165962
\(657\) 101.452 3.95803
\(658\) −27.5243 −1.07301
\(659\) −10.3240 −0.402165 −0.201083 0.979574i \(-0.564446\pi\)
−0.201083 + 0.979574i \(0.564446\pi\)
\(660\) 4.63079 0.180253
\(661\) −0.578727 −0.0225099 −0.0112549 0.999937i \(-0.503583\pi\)
−0.0112549 + 0.999937i \(0.503583\pi\)
\(662\) 15.7023 0.610288
\(663\) −0.343746 −0.0133500
\(664\) 14.2160 0.551689
\(665\) −6.40166 −0.248246
\(666\) 21.2890 0.824930
\(667\) −27.6095 −1.06904
\(668\) −5.63314 −0.217953
\(669\) −71.1246 −2.74983
\(670\) 16.3277 0.630794
\(671\) −5.13792 −0.198347
\(672\) −9.22911 −0.356021
\(673\) 15.0961 0.581910 0.290955 0.956737i \(-0.406027\pi\)
0.290955 + 0.956737i \(0.406027\pi\)
\(674\) −7.79959 −0.300429
\(675\) 3.16206 0.121708
\(676\) −9.29061 −0.357331
\(677\) 47.2522 1.81605 0.908025 0.418916i \(-0.137590\pi\)
0.908025 + 0.418916i \(0.137590\pi\)
\(678\) 0.541680 0.0208031
\(679\) 4.99201 0.191576
\(680\) −0.123800 −0.00474750
\(681\) 84.9207 3.25417
\(682\) −4.36148 −0.167010
\(683\) −35.4713 −1.35727 −0.678636 0.734475i \(-0.737429\pi\)
−0.678636 + 0.734475i \(0.737429\pi\)
\(684\) −6.84787 −0.261835
\(685\) −1.31415 −0.0502110
\(686\) −15.7364 −0.600818
\(687\) 56.3777 2.15094
\(688\) 0.0900971 0.00343492
\(689\) −18.5465 −0.706567
\(690\) 50.6394 1.92781
\(691\) 4.43469 0.168704 0.0843519 0.996436i \(-0.473118\pi\)
0.0843519 + 0.996436i \(0.473118\pi\)
\(692\) 18.5062 0.703499
\(693\) −13.6529 −0.518631
\(694\) −0.207988 −0.00789510
\(695\) −16.7023 −0.633555
\(696\) −11.6873 −0.443008
\(697\) −0.241755 −0.00915711
\(698\) 8.01503 0.303373
\(699\) −39.4103 −1.49064
\(700\) −0.770136 −0.0291084
\(701\) 10.8854 0.411136 0.205568 0.978643i \(-0.434096\pi\)
0.205568 + 0.978643i \(0.434096\pi\)
\(702\) 23.2564 0.877758
\(703\) −3.10884 −0.117252
\(704\) −0.677923 −0.0255502
\(705\) 63.9295 2.40773
\(706\) 1.32594 0.0499023
\(707\) −41.2290 −1.55057
\(708\) 9.14902 0.343841
\(709\) −39.3745 −1.47874 −0.739370 0.673299i \(-0.764877\pi\)
−0.739370 + 0.673299i \(0.764877\pi\)
\(710\) −9.07810 −0.340695
\(711\) 83.8933 3.14624
\(712\) −2.98084 −0.111712
\(713\) −47.6944 −1.78617
\(714\) 0.524898 0.0196438
\(715\) 2.84207 0.106288
\(716\) 10.1095 0.377810
\(717\) −3.39523 −0.126797
\(718\) 32.4982 1.21282
\(719\) 9.68910 0.361342 0.180671 0.983544i \(-0.442173\pi\)
0.180671 + 0.983544i \(0.442173\pi\)
\(720\) 14.9059 0.555512
\(721\) 19.3446 0.720431
\(722\) 1.00000 0.0372161
\(723\) −24.8466 −0.924055
\(724\) −14.1473 −0.525780
\(725\) −0.975267 −0.0362205
\(726\) 33.0772 1.22761
\(727\) −38.6933 −1.43506 −0.717528 0.696530i \(-0.754726\pi\)
−0.717528 + 0.696530i \(0.754726\pi\)
\(728\) −5.66422 −0.209930
\(729\) 5.12874 0.189954
\(730\) 32.2485 1.19357
\(731\) −0.00512420 −0.000189525 0
\(732\) −23.7836 −0.879069
\(733\) −41.7858 −1.54339 −0.771696 0.635991i \(-0.780591\pi\)
−0.771696 + 0.635991i \(0.780591\pi\)
\(734\) −13.7239 −0.506558
\(735\) −11.2657 −0.415540
\(736\) −7.41334 −0.273259
\(737\) −5.08513 −0.187313
\(738\) 29.1082 1.07149
\(739\) −12.2027 −0.448882 −0.224441 0.974488i \(-0.572056\pi\)
−0.224441 + 0.974488i \(0.572056\pi\)
\(740\) 6.76709 0.248763
\(741\) −6.04397 −0.222031
\(742\) 28.3205 1.03968
\(743\) −42.9444 −1.57548 −0.787738 0.616011i \(-0.788748\pi\)
−0.787738 + 0.616011i \(0.788748\pi\)
\(744\) −20.1895 −0.740181
\(745\) 38.8497 1.42334
\(746\) 9.46516 0.346544
\(747\) 97.3495 3.56183
\(748\) 0.0385563 0.00140976
\(749\) 18.1930 0.664757
\(750\) 35.9430 1.31245
\(751\) −7.76923 −0.283503 −0.141752 0.989902i \(-0.545273\pi\)
−0.141752 + 0.989902i \(0.545273\pi\)
\(752\) −9.35894 −0.341285
\(753\) 3.62738 0.132189
\(754\) −7.17292 −0.261222
\(755\) 4.27754 0.155676
\(756\) −35.5125 −1.29158
\(757\) 9.84299 0.357749 0.178875 0.983872i \(-0.442754\pi\)
0.178875 + 0.983872i \(0.442754\pi\)
\(758\) 20.3600 0.739508
\(759\) −15.7712 −0.572459
\(760\) −2.17673 −0.0789581
\(761\) 19.2000 0.695999 0.348000 0.937495i \(-0.386861\pi\)
0.348000 + 0.937495i \(0.386861\pi\)
\(762\) 0.115052 0.00416791
\(763\) 19.5592 0.708092
\(764\) −7.02060 −0.253997
\(765\) −0.847763 −0.0306510
\(766\) −24.3490 −0.879765
\(767\) 5.61506 0.202748
\(768\) −3.13813 −0.113238
\(769\) −6.79690 −0.245102 −0.122551 0.992462i \(-0.539108\pi\)
−0.122551 + 0.992462i \(0.539108\pi\)
\(770\) −4.33983 −0.156397
\(771\) −80.7873 −2.90948
\(772\) 8.20378 0.295260
\(773\) −11.9514 −0.429862 −0.214931 0.976629i \(-0.568953\pi\)
−0.214931 + 0.976629i \(0.568953\pi\)
\(774\) 0.616974 0.0221767
\(775\) −1.68474 −0.0605176
\(776\) 1.69741 0.0609335
\(777\) −28.6919 −1.02931
\(778\) −24.8707 −0.891656
\(779\) −4.25069 −0.152297
\(780\) 13.1561 0.471063
\(781\) 2.82730 0.101169
\(782\) 0.421628 0.0150774
\(783\) −44.9714 −1.60715
\(784\) 1.64923 0.0589011
\(785\) 44.5201 1.58899
\(786\) 48.7091 1.73740
\(787\) 35.1604 1.25333 0.626667 0.779287i \(-0.284419\pi\)
0.626667 + 0.779287i \(0.284419\pi\)
\(788\) 17.7254 0.631441
\(789\) −28.4698 −1.01355
\(790\) 26.6671 0.948772
\(791\) −0.507645 −0.0180498
\(792\) −4.64233 −0.164958
\(793\) −14.5968 −0.518348
\(794\) 5.94481 0.210974
\(795\) −65.7789 −2.33294
\(796\) 13.9359 0.493945
\(797\) −7.07338 −0.250552 −0.125276 0.992122i \(-0.539982\pi\)
−0.125276 + 0.992122i \(0.539982\pi\)
\(798\) 9.22911 0.326707
\(799\) 0.532282 0.0188308
\(800\) −0.261866 −0.00925836
\(801\) −20.4124 −0.721237
\(802\) −32.5793 −1.15042
\(803\) −10.0435 −0.354429
\(804\) −23.5392 −0.830165
\(805\) −47.4577 −1.67266
\(806\) −12.3910 −0.436453
\(807\) 4.45868 0.156953
\(808\) −14.0189 −0.493183
\(809\) −19.5805 −0.688415 −0.344208 0.938894i \(-0.611852\pi\)
−0.344208 + 0.938894i \(0.611852\pi\)
\(810\) 37.7656 1.32695
\(811\) −20.4619 −0.718514 −0.359257 0.933239i \(-0.616970\pi\)
−0.359257 + 0.933239i \(0.616970\pi\)
\(812\) 10.9530 0.384375
\(813\) −1.21546 −0.0426279
\(814\) −2.10755 −0.0738698
\(815\) −3.99282 −0.139862
\(816\) 0.178479 0.00624801
\(817\) −0.0900971 −0.00315210
\(818\) −8.21196 −0.287124
\(819\) −38.7879 −1.35536
\(820\) 9.25259 0.323115
\(821\) 33.9776 1.18583 0.592913 0.805267i \(-0.297978\pi\)
0.592913 + 0.805267i \(0.297978\pi\)
\(822\) 1.89458 0.0660809
\(823\) −20.7767 −0.724232 −0.362116 0.932133i \(-0.617946\pi\)
−0.362116 + 0.932133i \(0.617946\pi\)
\(824\) 6.57765 0.229143
\(825\) −0.557096 −0.0193956
\(826\) −8.57417 −0.298334
\(827\) 25.4596 0.885316 0.442658 0.896691i \(-0.354036\pi\)
0.442658 + 0.896691i \(0.354036\pi\)
\(828\) −50.7656 −1.76423
\(829\) −23.4750 −0.815322 −0.407661 0.913133i \(-0.633656\pi\)
−0.407661 + 0.913133i \(0.633656\pi\)
\(830\) 30.9444 1.07409
\(831\) 67.3905 2.33775
\(832\) −1.92598 −0.0667713
\(833\) −0.0937988 −0.00324993
\(834\) 24.0793 0.833799
\(835\) −12.2618 −0.424337
\(836\) 0.677923 0.0234465
\(837\) −77.6865 −2.68524
\(838\) 6.67006 0.230413
\(839\) −49.5773 −1.71160 −0.855800 0.517307i \(-0.826934\pi\)
−0.855800 + 0.517307i \(0.826934\pi\)
\(840\) −20.0892 −0.693145
\(841\) −15.1296 −0.521710
\(842\) 31.9362 1.10059
\(843\) 21.5562 0.742435
\(844\) −1.00000 −0.0344214
\(845\) −20.2231 −0.695696
\(846\) −64.0888 −2.20342
\(847\) −30.9989 −1.06514
\(848\) 9.62968 0.330684
\(849\) 74.3465 2.55157
\(850\) 0.0148934 0.000510840 0
\(851\) −23.0469 −0.790038
\(852\) 13.0877 0.448376
\(853\) 42.7692 1.46439 0.732195 0.681095i \(-0.238496\pi\)
0.732195 + 0.681095i \(0.238496\pi\)
\(854\) 22.2893 0.762723
\(855\) −14.9059 −0.509772
\(856\) 6.18607 0.211436
\(857\) −6.49610 −0.221903 −0.110951 0.993826i \(-0.535390\pi\)
−0.110951 + 0.993826i \(0.535390\pi\)
\(858\) −4.09735 −0.139881
\(859\) −25.4880 −0.869640 −0.434820 0.900517i \(-0.643188\pi\)
−0.434820 + 0.900517i \(0.643188\pi\)
\(860\) 0.196117 0.00668752
\(861\) −39.2301 −1.33696
\(862\) 3.40300 0.115907
\(863\) −6.89141 −0.234586 −0.117293 0.993097i \(-0.537422\pi\)
−0.117293 + 0.993097i \(0.537422\pi\)
\(864\) −12.0751 −0.410804
\(865\) 40.2828 1.36966
\(866\) 32.9384 1.11929
\(867\) 53.3381 1.81146
\(868\) 18.9209 0.642218
\(869\) −8.30524 −0.281736
\(870\) −25.4401 −0.862502
\(871\) −14.4468 −0.489512
\(872\) 6.65064 0.225219
\(873\) 11.6236 0.393401
\(874\) 7.41334 0.250760
\(875\) −33.6847 −1.13875
\(876\) −46.4919 −1.57082
\(877\) −28.0141 −0.945968 −0.472984 0.881071i \(-0.656823\pi\)
−0.472984 + 0.881071i \(0.656823\pi\)
\(878\) −36.8895 −1.24496
\(879\) −57.2227 −1.93007
\(880\) −1.47565 −0.0497442
\(881\) 2.18960 0.0737696 0.0368848 0.999320i \(-0.488257\pi\)
0.0368848 + 0.999320i \(0.488257\pi\)
\(882\) 11.2937 0.380280
\(883\) 25.2565 0.849948 0.424974 0.905206i \(-0.360283\pi\)
0.424974 + 0.905206i \(0.360283\pi\)
\(884\) 0.109538 0.00368418
\(885\) 19.9149 0.669432
\(886\) 5.25207 0.176447
\(887\) −14.1888 −0.476414 −0.238207 0.971214i \(-0.576560\pi\)
−0.238207 + 0.971214i \(0.576560\pi\)
\(888\) −9.75595 −0.327388
\(889\) −0.107823 −0.00361628
\(890\) −6.48847 −0.217494
\(891\) −11.7618 −0.394035
\(892\) 22.6646 0.758868
\(893\) 9.35894 0.313185
\(894\) −56.0086 −1.87321
\(895\) 22.0056 0.735568
\(896\) 2.94096 0.0982505
\(897\) −44.8060 −1.49603
\(898\) −16.5954 −0.553794
\(899\) 23.9606 0.799131
\(900\) −1.79322 −0.0597741
\(901\) −0.547680 −0.0182459
\(902\) −2.88164 −0.0959482
\(903\) −0.831516 −0.0276711
\(904\) −0.172612 −0.00574100
\(905\) −30.7948 −1.02365
\(906\) −6.16682 −0.204879
\(907\) 25.5966 0.849920 0.424960 0.905212i \(-0.360288\pi\)
0.424960 + 0.905212i \(0.360288\pi\)
\(908\) −27.0609 −0.898047
\(909\) −95.9996 −3.18411
\(910\) −12.3295 −0.408717
\(911\) 18.9005 0.626203 0.313102 0.949720i \(-0.398632\pi\)
0.313102 + 0.949720i \(0.398632\pi\)
\(912\) 3.13813 0.103914
\(913\) −9.63737 −0.318950
\(914\) 21.1449 0.699412
\(915\) −51.7705 −1.71148
\(916\) −17.9654 −0.593592
\(917\) −45.6486 −1.50745
\(918\) 0.686764 0.0226666
\(919\) −20.7549 −0.684640 −0.342320 0.939583i \(-0.611213\pi\)
−0.342320 + 0.939583i \(0.611213\pi\)
\(920\) −16.1368 −0.532015
\(921\) −61.9118 −2.04006
\(922\) 3.07268 0.101193
\(923\) 8.03235 0.264388
\(924\) 6.25663 0.205828
\(925\) −0.814099 −0.0267674
\(926\) 27.7827 0.912998
\(927\) 45.0429 1.47940
\(928\) 3.72430 0.122256
\(929\) −33.7447 −1.10713 −0.553564 0.832807i \(-0.686732\pi\)
−0.553564 + 0.832807i \(0.686732\pi\)
\(930\) −43.9469 −1.44108
\(931\) −1.64923 −0.0540514
\(932\) 12.5585 0.411368
\(933\) 51.5970 1.68921
\(934\) −4.37619 −0.143193
\(935\) 0.0839265 0.00274469
\(936\) −13.1889 −0.431091
\(937\) 25.1692 0.822241 0.411121 0.911581i \(-0.365138\pi\)
0.411121 + 0.911581i \(0.365138\pi\)
\(938\) 22.0602 0.720292
\(939\) −94.5855 −3.08668
\(940\) −20.3718 −0.664456
\(941\) −3.23958 −0.105607 −0.0528036 0.998605i \(-0.516816\pi\)
−0.0528036 + 0.998605i \(0.516816\pi\)
\(942\) −64.1836 −2.09121
\(943\) −31.5118 −1.02617
\(944\) −2.91543 −0.0948893
\(945\) −77.3009 −2.51460
\(946\) −0.0610789 −0.00198585
\(947\) 34.0316 1.10588 0.552939 0.833222i \(-0.313506\pi\)
0.552939 + 0.833222i \(0.313506\pi\)
\(948\) −38.4453 −1.24864
\(949\) −28.5337 −0.926242
\(950\) 0.261866 0.00849605
\(951\) −8.16734 −0.264844
\(952\) −0.167265 −0.00542108
\(953\) −47.5069 −1.53890 −0.769450 0.638707i \(-0.779469\pi\)
−0.769450 + 0.638707i \(0.779469\pi\)
\(954\) 65.9428 2.13498
\(955\) −15.2819 −0.494512
\(956\) 1.08193 0.0349920
\(957\) 7.92312 0.256118
\(958\) −12.2778 −0.396679
\(959\) −1.77554 −0.0573351
\(960\) −6.83085 −0.220465
\(961\) 10.3911 0.335196
\(962\) −5.98756 −0.193047
\(963\) 42.3614 1.36508
\(964\) 7.91764 0.255010
\(965\) 17.8574 0.574849
\(966\) 68.4186 2.20133
\(967\) −41.1823 −1.32433 −0.662167 0.749356i \(-0.730363\pi\)
−0.662167 + 0.749356i \(0.730363\pi\)
\(968\) −10.5404 −0.338782
\(969\) −0.178479 −0.00573356
\(970\) 3.69480 0.118633
\(971\) 34.8476 1.11831 0.559156 0.829063i \(-0.311125\pi\)
0.559156 + 0.829063i \(0.311125\pi\)
\(972\) −18.2204 −0.584419
\(973\) −22.5664 −0.723445
\(974\) −18.3877 −0.589180
\(975\) −1.58271 −0.0506873
\(976\) 7.57892 0.242595
\(977\) −45.8194 −1.46589 −0.732947 0.680286i \(-0.761856\pi\)
−0.732947 + 0.680286i \(0.761856\pi\)
\(978\) 5.75635 0.184068
\(979\) 2.02078 0.0645844
\(980\) 3.58993 0.114676
\(981\) 45.5427 1.45407
\(982\) 29.5824 0.944012
\(983\) 9.81624 0.313090 0.156545 0.987671i \(-0.449964\pi\)
0.156545 + 0.987671i \(0.449964\pi\)
\(984\) −13.3392 −0.425239
\(985\) 38.5833 1.22937
\(986\) −0.211817 −0.00674561
\(987\) 86.3747 2.74934
\(988\) 1.92598 0.0612735
\(989\) −0.667921 −0.0212386
\(990\) −10.1051 −0.321160
\(991\) 18.0515 0.573425 0.286713 0.958017i \(-0.407437\pi\)
0.286713 + 0.958017i \(0.407437\pi\)
\(992\) 6.43359 0.204267
\(993\) −49.2760 −1.56373
\(994\) −12.2654 −0.389033
\(995\) 30.3346 0.961673
\(996\) −44.6117 −1.41358
\(997\) −2.53260 −0.0802082 −0.0401041 0.999196i \(-0.512769\pi\)
−0.0401041 + 0.999196i \(0.512769\pi\)
\(998\) 10.7603 0.340611
\(999\) −37.5397 −1.18770
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 \(a_p\))