Properties

Label 8015.2.a.l.1.55
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.55
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} +O(q^{10})\) \(q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} -2.36805 q^{10} -4.69124 q^{11} -7.25001 q^{12} -0.376745 q^{13} -2.36805 q^{14} +2.00963 q^{15} +1.79977 q^{16} -6.64858 q^{17} +2.45947 q^{18} +6.10646 q^{19} -3.60764 q^{20} +2.00963 q^{21} -11.1091 q^{22} -7.22433 q^{23} -7.65057 q^{24} +1.00000 q^{25} -0.892148 q^{26} +3.94167 q^{27} -3.60764 q^{28} +4.12509 q^{29} +4.75889 q^{30} -5.11724 q^{31} -3.35197 q^{32} +9.42765 q^{33} -15.7441 q^{34} +1.00000 q^{35} +3.74692 q^{36} +6.31706 q^{37} +14.4604 q^{38} +0.757117 q^{39} -3.80696 q^{40} +1.38450 q^{41} +4.75889 q^{42} +3.57663 q^{43} -16.9243 q^{44} -1.03861 q^{45} -17.1075 q^{46} +9.57906 q^{47} -3.61687 q^{48} +1.00000 q^{49} +2.36805 q^{50} +13.3612 q^{51} -1.35916 q^{52} -2.34354 q^{53} +9.33406 q^{54} +4.69124 q^{55} -3.80696 q^{56} -12.2717 q^{57} +9.76840 q^{58} +10.2410 q^{59} +7.25001 q^{60} +1.00073 q^{61} -12.1179 q^{62} -1.03861 q^{63} -11.5372 q^{64} +0.376745 q^{65} +22.3251 q^{66} +0.542699 q^{67} -23.9857 q^{68} +14.5182 q^{69} +2.36805 q^{70} -14.9311 q^{71} +3.95393 q^{72} +15.6290 q^{73} +14.9591 q^{74} -2.00963 q^{75} +22.0299 q^{76} +4.69124 q^{77} +1.79289 q^{78} -6.35712 q^{79} -1.79977 q^{80} -11.0371 q^{81} +3.27855 q^{82} +14.3897 q^{83} +7.25001 q^{84} +6.64858 q^{85} +8.46961 q^{86} -8.28990 q^{87} -17.8594 q^{88} +6.09510 q^{89} -2.45947 q^{90} +0.376745 q^{91} -26.0628 q^{92} +10.2838 q^{93} +22.6836 q^{94} -6.10646 q^{95} +6.73622 q^{96} -15.5793 q^{97} +2.36805 q^{98} -4.87235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.36805 1.67446 0.837230 0.546850i \(-0.184173\pi\)
0.837230 + 0.546850i \(0.184173\pi\)
\(3\) −2.00963 −1.16026 −0.580130 0.814524i \(-0.696998\pi\)
−0.580130 + 0.814524i \(0.696998\pi\)
\(4\) 3.60764 1.80382
\(5\) −1.00000 −0.447214
\(6\) −4.75889 −1.94281
\(7\) −1.00000 −0.377964
\(8\) 3.80696 1.34596
\(9\) 1.03861 0.346202
\(10\) −2.36805 −0.748842
\(11\) −4.69124 −1.41446 −0.707231 0.706982i \(-0.750056\pi\)
−0.707231 + 0.706982i \(0.750056\pi\)
\(12\) −7.25001 −2.09290
\(13\) −0.376745 −0.104490 −0.0522451 0.998634i \(-0.516638\pi\)
−0.0522451 + 0.998634i \(0.516638\pi\)
\(14\) −2.36805 −0.632887
\(15\) 2.00963 0.518884
\(16\) 1.79977 0.449943
\(17\) −6.64858 −1.61252 −0.806259 0.591563i \(-0.798511\pi\)
−0.806259 + 0.591563i \(0.798511\pi\)
\(18\) 2.45947 0.579702
\(19\) 6.10646 1.40092 0.700458 0.713693i \(-0.252979\pi\)
0.700458 + 0.713693i \(0.252979\pi\)
\(20\) −3.60764 −0.806692
\(21\) 2.00963 0.438537
\(22\) −11.1091 −2.36846
\(23\) −7.22433 −1.50638 −0.753189 0.657804i \(-0.771485\pi\)
−0.753189 + 0.657804i \(0.771485\pi\)
\(24\) −7.65057 −1.56167
\(25\) 1.00000 0.200000
\(26\) −0.892148 −0.174965
\(27\) 3.94167 0.758575
\(28\) −3.60764 −0.681779
\(29\) 4.12509 0.766010 0.383005 0.923746i \(-0.374889\pi\)
0.383005 + 0.923746i \(0.374889\pi\)
\(30\) 4.75889 0.868851
\(31\) −5.11724 −0.919084 −0.459542 0.888156i \(-0.651986\pi\)
−0.459542 + 0.888156i \(0.651986\pi\)
\(32\) −3.35197 −0.592551
\(33\) 9.42765 1.64114
\(34\) −15.7441 −2.70010
\(35\) 1.00000 0.169031
\(36\) 3.74692 0.624486
\(37\) 6.31706 1.03852 0.519259 0.854617i \(-0.326208\pi\)
0.519259 + 0.854617i \(0.326208\pi\)
\(38\) 14.4604 2.34578
\(39\) 0.757117 0.121236
\(40\) −3.80696 −0.601933
\(41\) 1.38450 0.216222 0.108111 0.994139i \(-0.465520\pi\)
0.108111 + 0.994139i \(0.465520\pi\)
\(42\) 4.75889 0.734313
\(43\) 3.57663 0.545430 0.272715 0.962095i \(-0.412078\pi\)
0.272715 + 0.962095i \(0.412078\pi\)
\(44\) −16.9243 −2.55143
\(45\) −1.03861 −0.154826
\(46\) −17.1075 −2.52237
\(47\) 9.57906 1.39725 0.698625 0.715488i \(-0.253796\pi\)
0.698625 + 0.715488i \(0.253796\pi\)
\(48\) −3.61687 −0.522051
\(49\) 1.00000 0.142857
\(50\) 2.36805 0.334892
\(51\) 13.3612 1.87094
\(52\) −1.35916 −0.188481
\(53\) −2.34354 −0.321909 −0.160955 0.986962i \(-0.551457\pi\)
−0.160955 + 0.986962i \(0.551457\pi\)
\(54\) 9.33406 1.27020
\(55\) 4.69124 0.632567
\(56\) −3.80696 −0.508726
\(57\) −12.2717 −1.62543
\(58\) 9.76840 1.28265
\(59\) 10.2410 1.33326 0.666632 0.745387i \(-0.267735\pi\)
0.666632 + 0.745387i \(0.267735\pi\)
\(60\) 7.25001 0.935972
\(61\) 1.00073 0.128130 0.0640649 0.997946i \(-0.479594\pi\)
0.0640649 + 0.997946i \(0.479594\pi\)
\(62\) −12.1179 −1.53897
\(63\) −1.03861 −0.130852
\(64\) −11.5372 −1.44215
\(65\) 0.376745 0.0467294
\(66\) 22.3251 2.74803
\(67\) 0.542699 0.0663012 0.0331506 0.999450i \(-0.489446\pi\)
0.0331506 + 0.999450i \(0.489446\pi\)
\(68\) −23.9857 −2.90869
\(69\) 14.5182 1.74779
\(70\) 2.36805 0.283036
\(71\) −14.9311 −1.77200 −0.886000 0.463686i \(-0.846527\pi\)
−0.886000 + 0.463686i \(0.846527\pi\)
\(72\) 3.95393 0.465975
\(73\) 15.6290 1.82923 0.914615 0.404325i \(-0.132493\pi\)
0.914615 + 0.404325i \(0.132493\pi\)
\(74\) 14.9591 1.73896
\(75\) −2.00963 −0.232052
\(76\) 22.0299 2.52700
\(77\) 4.69124 0.534616
\(78\) 1.79289 0.203004
\(79\) −6.35712 −0.715232 −0.357616 0.933869i \(-0.616410\pi\)
−0.357616 + 0.933869i \(0.616410\pi\)
\(80\) −1.79977 −0.201221
\(81\) −11.0371 −1.22635
\(82\) 3.27855 0.362056
\(83\) 14.3897 1.57948 0.789738 0.613444i \(-0.210216\pi\)
0.789738 + 0.613444i \(0.210216\pi\)
\(84\) 7.25001 0.791041
\(85\) 6.64858 0.721140
\(86\) 8.46961 0.913302
\(87\) −8.28990 −0.888771
\(88\) −17.8594 −1.90381
\(89\) 6.09510 0.646080 0.323040 0.946385i \(-0.395295\pi\)
0.323040 + 0.946385i \(0.395295\pi\)
\(90\) −2.45947 −0.259251
\(91\) 0.376745 0.0394936
\(92\) −26.0628 −2.71723
\(93\) 10.2838 1.06638
\(94\) 22.6836 2.33964
\(95\) −6.10646 −0.626509
\(96\) 6.73622 0.687513
\(97\) −15.5793 −1.58184 −0.790921 0.611918i \(-0.790398\pi\)
−0.790921 + 0.611918i \(0.790398\pi\)
\(98\) 2.36805 0.239209
\(99\) −4.87235 −0.489690
\(100\) 3.60764 0.360764
\(101\) −17.4321 −1.73455 −0.867277 0.497826i \(-0.834132\pi\)
−0.867277 + 0.497826i \(0.834132\pi\)
\(102\) 31.6399 3.13281
\(103\) 11.3428 1.11764 0.558818 0.829290i \(-0.311255\pi\)
0.558818 + 0.829290i \(0.311255\pi\)
\(104\) −1.43425 −0.140640
\(105\) −2.00963 −0.196120
\(106\) −5.54960 −0.539025
\(107\) 15.5472 1.50301 0.751504 0.659729i \(-0.229329\pi\)
0.751504 + 0.659729i \(0.229329\pi\)
\(108\) 14.2201 1.36833
\(109\) 18.2251 1.74565 0.872826 0.488032i \(-0.162285\pi\)
0.872826 + 0.488032i \(0.162285\pi\)
\(110\) 11.1091 1.05921
\(111\) −12.6949 −1.20495
\(112\) −1.79977 −0.170063
\(113\) −5.14934 −0.484410 −0.242205 0.970225i \(-0.577871\pi\)
−0.242205 + 0.970225i \(0.577871\pi\)
\(114\) −29.0600 −2.72171
\(115\) 7.22433 0.673672
\(116\) 14.8818 1.38174
\(117\) −0.391289 −0.0361747
\(118\) 24.2511 2.23250
\(119\) 6.64858 0.609474
\(120\) 7.65057 0.698398
\(121\) 11.0077 1.00070
\(122\) 2.36976 0.214548
\(123\) −2.78233 −0.250874
\(124\) −18.4612 −1.65786
\(125\) −1.00000 −0.0894427
\(126\) −2.45947 −0.219107
\(127\) −4.02935 −0.357547 −0.178774 0.983890i \(-0.557213\pi\)
−0.178774 + 0.983890i \(0.557213\pi\)
\(128\) −20.6166 −1.82227
\(129\) −7.18769 −0.632841
\(130\) 0.892148 0.0782466
\(131\) 3.16807 0.276796 0.138398 0.990377i \(-0.455805\pi\)
0.138398 + 0.990377i \(0.455805\pi\)
\(132\) 34.0115 2.96032
\(133\) −6.10646 −0.529497
\(134\) 1.28514 0.111019
\(135\) −3.94167 −0.339245
\(136\) −25.3109 −2.17039
\(137\) 6.48851 0.554351 0.277175 0.960819i \(-0.410602\pi\)
0.277175 + 0.960819i \(0.410602\pi\)
\(138\) 34.3798 2.92660
\(139\) 11.1111 0.942431 0.471216 0.882018i \(-0.343815\pi\)
0.471216 + 0.882018i \(0.343815\pi\)
\(140\) 3.60764 0.304901
\(141\) −19.2503 −1.62117
\(142\) −35.3576 −2.96714
\(143\) 1.76740 0.147797
\(144\) 1.86926 0.155771
\(145\) −4.12509 −0.342570
\(146\) 37.0101 3.06298
\(147\) −2.00963 −0.165751
\(148\) 22.7897 1.87330
\(149\) 8.01375 0.656512 0.328256 0.944589i \(-0.393539\pi\)
0.328256 + 0.944589i \(0.393539\pi\)
\(150\) −4.75889 −0.388562
\(151\) 4.61444 0.375518 0.187759 0.982215i \(-0.439878\pi\)
0.187759 + 0.982215i \(0.439878\pi\)
\(152\) 23.2470 1.88558
\(153\) −6.90526 −0.558257
\(154\) 11.1091 0.895194
\(155\) 5.11724 0.411027
\(156\) 2.73140 0.218687
\(157\) 13.5849 1.08419 0.542096 0.840317i \(-0.317631\pi\)
0.542096 + 0.840317i \(0.317631\pi\)
\(158\) −15.0540 −1.19763
\(159\) 4.70964 0.373498
\(160\) 3.35197 0.264997
\(161\) 7.22433 0.569357
\(162\) −26.1364 −2.05347
\(163\) −22.7320 −1.78051 −0.890255 0.455462i \(-0.849474\pi\)
−0.890255 + 0.455462i \(0.849474\pi\)
\(164\) 4.99476 0.390026
\(165\) −9.42765 −0.733942
\(166\) 34.0755 2.64477
\(167\) −8.75142 −0.677205 −0.338602 0.940930i \(-0.609954\pi\)
−0.338602 + 0.940930i \(0.609954\pi\)
\(168\) 7.65057 0.590254
\(169\) −12.8581 −0.989082
\(170\) 15.7441 1.20752
\(171\) 6.34220 0.485000
\(172\) 12.9032 0.983857
\(173\) 2.35809 0.179282 0.0896410 0.995974i \(-0.471428\pi\)
0.0896410 + 0.995974i \(0.471428\pi\)
\(174\) −19.6309 −1.48821
\(175\) −1.00000 −0.0755929
\(176\) −8.44316 −0.636427
\(177\) −20.5806 −1.54693
\(178\) 14.4335 1.08184
\(179\) 1.74198 0.130202 0.0651009 0.997879i \(-0.479263\pi\)
0.0651009 + 0.997879i \(0.479263\pi\)
\(180\) −3.74692 −0.279279
\(181\) 17.1861 1.27743 0.638716 0.769442i \(-0.279466\pi\)
0.638716 + 0.769442i \(0.279466\pi\)
\(182\) 0.892148 0.0661304
\(183\) −2.01109 −0.148664
\(184\) −27.5027 −2.02753
\(185\) −6.31706 −0.464439
\(186\) 24.3524 1.78560
\(187\) 31.1901 2.28085
\(188\) 34.5578 2.52038
\(189\) −3.94167 −0.286714
\(190\) −14.4604 −1.04906
\(191\) 2.55093 0.184579 0.0922894 0.995732i \(-0.470581\pi\)
0.0922894 + 0.995732i \(0.470581\pi\)
\(192\) 23.1854 1.67326
\(193\) 6.15597 0.443117 0.221558 0.975147i \(-0.428886\pi\)
0.221558 + 0.975147i \(0.428886\pi\)
\(194\) −36.8926 −2.64873
\(195\) −0.757117 −0.0542182
\(196\) 3.60764 0.257688
\(197\) −1.00610 −0.0716814 −0.0358407 0.999358i \(-0.511411\pi\)
−0.0358407 + 0.999358i \(0.511411\pi\)
\(198\) −11.5379 −0.819966
\(199\) −23.3335 −1.65407 −0.827033 0.562153i \(-0.809973\pi\)
−0.827033 + 0.562153i \(0.809973\pi\)
\(200\) 3.80696 0.269193
\(201\) −1.09062 −0.0769266
\(202\) −41.2799 −2.90444
\(203\) −4.12509 −0.289525
\(204\) 48.2023 3.37484
\(205\) −1.38450 −0.0966975
\(206\) 26.8602 1.87144
\(207\) −7.50324 −0.521511
\(208\) −0.678054 −0.0470146
\(209\) −28.6468 −1.98154
\(210\) −4.75889 −0.328395
\(211\) −19.4796 −1.34103 −0.670515 0.741896i \(-0.733927\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(212\) −8.45463 −0.580666
\(213\) 30.0060 2.05598
\(214\) 36.8165 2.51673
\(215\) −3.57663 −0.243924
\(216\) 15.0058 1.02101
\(217\) 5.11724 0.347381
\(218\) 43.1579 2.92302
\(219\) −31.4084 −2.12238
\(220\) 16.9243 1.14104
\(221\) 2.50482 0.168492
\(222\) −30.0622 −2.01764
\(223\) −7.44201 −0.498354 −0.249177 0.968458i \(-0.580160\pi\)
−0.249177 + 0.968458i \(0.580160\pi\)
\(224\) 3.35197 0.223963
\(225\) 1.03861 0.0692404
\(226\) −12.1939 −0.811125
\(227\) −4.15200 −0.275578 −0.137789 0.990462i \(-0.544000\pi\)
−0.137789 + 0.990462i \(0.544000\pi\)
\(228\) −44.2719 −2.93198
\(229\) 1.00000 0.0660819
\(230\) 17.1075 1.12804
\(231\) −9.42765 −0.620294
\(232\) 15.7040 1.03102
\(233\) 13.3866 0.876986 0.438493 0.898735i \(-0.355512\pi\)
0.438493 + 0.898735i \(0.355512\pi\)
\(234\) −0.926591 −0.0605731
\(235\) −9.57906 −0.624869
\(236\) 36.9458 2.40497
\(237\) 12.7755 0.829855
\(238\) 15.7441 1.02054
\(239\) −14.8815 −0.962603 −0.481301 0.876555i \(-0.659836\pi\)
−0.481301 + 0.876555i \(0.659836\pi\)
\(240\) 3.61687 0.233468
\(241\) 2.16867 0.139696 0.0698482 0.997558i \(-0.477749\pi\)
0.0698482 + 0.997558i \(0.477749\pi\)
\(242\) 26.0668 1.67564
\(243\) 10.3555 0.664305
\(244\) 3.61026 0.231123
\(245\) −1.00000 −0.0638877
\(246\) −6.58867 −0.420078
\(247\) −2.30057 −0.146382
\(248\) −19.4811 −1.23705
\(249\) −28.9180 −1.83260
\(250\) −2.36805 −0.149768
\(251\) 9.83789 0.620962 0.310481 0.950580i \(-0.399510\pi\)
0.310481 + 0.950580i \(0.399510\pi\)
\(252\) −3.74692 −0.236033
\(253\) 33.8911 2.13071
\(254\) −9.54169 −0.598699
\(255\) −13.3612 −0.836709
\(256\) −25.7467 −1.60917
\(257\) 24.6991 1.54069 0.770345 0.637627i \(-0.220084\pi\)
0.770345 + 0.637627i \(0.220084\pi\)
\(258\) −17.0208 −1.05967
\(259\) −6.31706 −0.392523
\(260\) 1.35916 0.0842914
\(261\) 4.28435 0.265194
\(262\) 7.50214 0.463484
\(263\) 13.8033 0.851148 0.425574 0.904924i \(-0.360072\pi\)
0.425574 + 0.904924i \(0.360072\pi\)
\(264\) 35.8907 2.20892
\(265\) 2.34354 0.143962
\(266\) −14.4604 −0.886622
\(267\) −12.2489 −0.749620
\(268\) 1.95786 0.119595
\(269\) −22.4237 −1.36719 −0.683597 0.729859i \(-0.739586\pi\)
−0.683597 + 0.729859i \(0.739586\pi\)
\(270\) −9.33406 −0.568053
\(271\) −30.1213 −1.82974 −0.914869 0.403750i \(-0.867706\pi\)
−0.914869 + 0.403750i \(0.867706\pi\)
\(272\) −11.9659 −0.725541
\(273\) −0.757117 −0.0458228
\(274\) 15.3651 0.928239
\(275\) −4.69124 −0.282892
\(276\) 52.3765 3.15269
\(277\) 7.18602 0.431766 0.215883 0.976419i \(-0.430737\pi\)
0.215883 + 0.976419i \(0.430737\pi\)
\(278\) 26.3116 1.57806
\(279\) −5.31480 −0.318189
\(280\) 3.80696 0.227509
\(281\) −16.8806 −1.00701 −0.503507 0.863991i \(-0.667957\pi\)
−0.503507 + 0.863991i \(0.667957\pi\)
\(282\) −45.5857 −2.71459
\(283\) 22.7190 1.35050 0.675252 0.737587i \(-0.264035\pi\)
0.675252 + 0.737587i \(0.264035\pi\)
\(284\) −53.8661 −3.19637
\(285\) 12.2717 0.726913
\(286\) 4.18528 0.247481
\(287\) −1.38450 −0.0817243
\(288\) −3.48138 −0.205142
\(289\) 27.2036 1.60021
\(290\) −9.76840 −0.573620
\(291\) 31.3087 1.83535
\(292\) 56.3836 3.29960
\(293\) −3.31644 −0.193749 −0.0968743 0.995297i \(-0.530884\pi\)
−0.0968743 + 0.995297i \(0.530884\pi\)
\(294\) −4.75889 −0.277544
\(295\) −10.2410 −0.596254
\(296\) 24.0488 1.39781
\(297\) −18.4913 −1.07298
\(298\) 18.9769 1.09930
\(299\) 2.72173 0.157402
\(300\) −7.25001 −0.418580
\(301\) −3.57663 −0.206153
\(302\) 10.9272 0.628790
\(303\) 35.0320 2.01253
\(304\) 10.9902 0.630333
\(305\) −1.00073 −0.0573014
\(306\) −16.3520 −0.934780
\(307\) 23.5246 1.34262 0.671309 0.741178i \(-0.265733\pi\)
0.671309 + 0.741178i \(0.265733\pi\)
\(308\) 16.9243 0.964351
\(309\) −22.7947 −1.29675
\(310\) 12.1179 0.688248
\(311\) 15.1484 0.858986 0.429493 0.903070i \(-0.358692\pi\)
0.429493 + 0.903070i \(0.358692\pi\)
\(312\) 2.88231 0.163179
\(313\) −8.61928 −0.487191 −0.243595 0.969877i \(-0.578327\pi\)
−0.243595 + 0.969877i \(0.578327\pi\)
\(314\) 32.1696 1.81544
\(315\) 1.03861 0.0585188
\(316\) −22.9342 −1.29015
\(317\) 14.5008 0.814446 0.407223 0.913329i \(-0.366497\pi\)
0.407223 + 0.913329i \(0.366497\pi\)
\(318\) 11.1526 0.625409
\(319\) −19.3518 −1.08349
\(320\) 11.5372 0.644947
\(321\) −31.2441 −1.74388
\(322\) 17.1075 0.953366
\(323\) −40.5993 −2.25900
\(324\) −39.8179 −2.21211
\(325\) −0.376745 −0.0208980
\(326\) −53.8305 −2.98139
\(327\) −36.6257 −2.02541
\(328\) 5.27072 0.291027
\(329\) −9.57906 −0.528111
\(330\) −22.3251 −1.22896
\(331\) 25.7306 1.41428 0.707140 0.707073i \(-0.249985\pi\)
0.707140 + 0.707073i \(0.249985\pi\)
\(332\) 51.9129 2.84909
\(333\) 6.56094 0.359537
\(334\) −20.7237 −1.13395
\(335\) −0.542699 −0.0296508
\(336\) 3.61687 0.197317
\(337\) 24.0813 1.31179 0.655896 0.754851i \(-0.272291\pi\)
0.655896 + 0.754851i \(0.272291\pi\)
\(338\) −30.4485 −1.65618
\(339\) 10.3483 0.562041
\(340\) 23.9857 1.30081
\(341\) 24.0062 1.30001
\(342\) 15.0186 0.812114
\(343\) −1.00000 −0.0539949
\(344\) 13.6161 0.734129
\(345\) −14.5182 −0.781635
\(346\) 5.58405 0.300201
\(347\) −4.03005 −0.216344 −0.108172 0.994132i \(-0.534500\pi\)
−0.108172 + 0.994132i \(0.534500\pi\)
\(348\) −29.9070 −1.60318
\(349\) 27.1577 1.45372 0.726860 0.686786i \(-0.240979\pi\)
0.726860 + 0.686786i \(0.240979\pi\)
\(350\) −2.36805 −0.126577
\(351\) −1.48500 −0.0792636
\(352\) 15.7249 0.838141
\(353\) 34.4127 1.83160 0.915802 0.401631i \(-0.131556\pi\)
0.915802 + 0.401631i \(0.131556\pi\)
\(354\) −48.7358 −2.59028
\(355\) 14.9311 0.792462
\(356\) 21.9889 1.16541
\(357\) −13.3612 −0.707149
\(358\) 4.12509 0.218018
\(359\) 14.8877 0.785743 0.392871 0.919593i \(-0.371482\pi\)
0.392871 + 0.919593i \(0.371482\pi\)
\(360\) −3.95393 −0.208390
\(361\) 18.2888 0.962568
\(362\) 40.6974 2.13901
\(363\) −22.1215 −1.16108
\(364\) 1.35916 0.0712392
\(365\) −15.6290 −0.818057
\(366\) −4.76235 −0.248932
\(367\) −20.0982 −1.04912 −0.524559 0.851374i \(-0.675770\pi\)
−0.524559 + 0.851374i \(0.675770\pi\)
\(368\) −13.0022 −0.677784
\(369\) 1.43795 0.0748566
\(370\) −14.9591 −0.777686
\(371\) 2.34354 0.121670
\(372\) 37.1001 1.92355
\(373\) 18.0717 0.935719 0.467860 0.883803i \(-0.345025\pi\)
0.467860 + 0.883803i \(0.345025\pi\)
\(374\) 73.8595 3.81919
\(375\) 2.00963 0.103777
\(376\) 36.4671 1.88065
\(377\) −1.55411 −0.0800405
\(378\) −9.33406 −0.480092
\(379\) −2.04815 −0.105206 −0.0526031 0.998615i \(-0.516752\pi\)
−0.0526031 + 0.998615i \(0.516752\pi\)
\(380\) −22.0299 −1.13011
\(381\) 8.09750 0.414848
\(382\) 6.04072 0.309070
\(383\) 14.0790 0.719404 0.359702 0.933067i \(-0.382878\pi\)
0.359702 + 0.933067i \(0.382878\pi\)
\(384\) 41.4317 2.11430
\(385\) −4.69124 −0.239088
\(386\) 14.5776 0.741982
\(387\) 3.71471 0.188829
\(388\) −56.2046 −2.85336
\(389\) −16.5297 −0.838087 −0.419043 0.907966i \(-0.637634\pi\)
−0.419043 + 0.907966i \(0.637634\pi\)
\(390\) −1.79289 −0.0907863
\(391\) 48.0316 2.42906
\(392\) 3.80696 0.192280
\(393\) −6.36665 −0.321155
\(394\) −2.38248 −0.120028
\(395\) 6.35712 0.319862
\(396\) −17.5777 −0.883312
\(397\) −15.7218 −0.789053 −0.394527 0.918884i \(-0.629091\pi\)
−0.394527 + 0.918884i \(0.629091\pi\)
\(398\) −55.2547 −2.76967
\(399\) 12.2717 0.614354
\(400\) 1.79977 0.0899886
\(401\) −25.8659 −1.29168 −0.645842 0.763471i \(-0.723493\pi\)
−0.645842 + 0.763471i \(0.723493\pi\)
\(402\) −2.58264 −0.128811
\(403\) 1.92789 0.0960352
\(404\) −62.8885 −3.12882
\(405\) 11.0371 0.548439
\(406\) −9.76840 −0.484798
\(407\) −29.6348 −1.46894
\(408\) 50.8654 2.51821
\(409\) 29.8263 1.47482 0.737408 0.675448i \(-0.236050\pi\)
0.737408 + 0.675448i \(0.236050\pi\)
\(410\) −3.27855 −0.161916
\(411\) −13.0395 −0.643191
\(412\) 40.9206 2.01601
\(413\) −10.2410 −0.503927
\(414\) −17.7680 −0.873250
\(415\) −14.3897 −0.706363
\(416\) 1.26284 0.0619157
\(417\) −22.3292 −1.09346
\(418\) −67.8370 −3.31802
\(419\) −20.1673 −0.985236 −0.492618 0.870246i \(-0.663960\pi\)
−0.492618 + 0.870246i \(0.663960\pi\)
\(420\) −7.25001 −0.353764
\(421\) 25.1716 1.22679 0.613394 0.789777i \(-0.289804\pi\)
0.613394 + 0.789777i \(0.289804\pi\)
\(422\) −46.1285 −2.24550
\(423\) 9.94887 0.483731
\(424\) −8.92174 −0.433278
\(425\) −6.64858 −0.322504
\(426\) 71.0556 3.44266
\(427\) −1.00073 −0.0484285
\(428\) 56.0888 2.71115
\(429\) −3.55182 −0.171483
\(430\) −8.46961 −0.408441
\(431\) 8.74040 0.421010 0.210505 0.977593i \(-0.432489\pi\)
0.210505 + 0.977593i \(0.432489\pi\)
\(432\) 7.09411 0.341316
\(433\) 34.9109 1.67771 0.838855 0.544354i \(-0.183225\pi\)
0.838855 + 0.544354i \(0.183225\pi\)
\(434\) 12.1179 0.581676
\(435\) 8.28990 0.397470
\(436\) 65.7497 3.14884
\(437\) −44.1151 −2.11031
\(438\) −74.3765 −3.55385
\(439\) −16.8518 −0.804292 −0.402146 0.915575i \(-0.631736\pi\)
−0.402146 + 0.915575i \(0.631736\pi\)
\(440\) 17.8594 0.851411
\(441\) 1.03861 0.0494574
\(442\) 5.93152 0.282134
\(443\) −4.51871 −0.214690 −0.107345 0.994222i \(-0.534235\pi\)
−0.107345 + 0.994222i \(0.534235\pi\)
\(444\) −45.7987 −2.17351
\(445\) −6.09510 −0.288936
\(446\) −17.6230 −0.834473
\(447\) −16.1047 −0.761725
\(448\) 11.5372 0.545080
\(449\) 20.1871 0.952687 0.476344 0.879259i \(-0.341962\pi\)
0.476344 + 0.879259i \(0.341962\pi\)
\(450\) 2.45947 0.115940
\(451\) −6.49501 −0.305838
\(452\) −18.5770 −0.873787
\(453\) −9.27331 −0.435698
\(454\) −9.83211 −0.461444
\(455\) −0.376745 −0.0176621
\(456\) −46.7179 −2.18776
\(457\) −6.24911 −0.292321 −0.146161 0.989261i \(-0.546692\pi\)
−0.146161 + 0.989261i \(0.546692\pi\)
\(458\) 2.36805 0.110651
\(459\) −26.2065 −1.22322
\(460\) 26.0628 1.21518
\(461\) −36.9391 −1.72042 −0.860212 0.509936i \(-0.829669\pi\)
−0.860212 + 0.509936i \(0.829669\pi\)
\(462\) −22.3251 −1.03866
\(463\) −20.7951 −0.966432 −0.483216 0.875501i \(-0.660531\pi\)
−0.483216 + 0.875501i \(0.660531\pi\)
\(464\) 7.42423 0.344661
\(465\) −10.2838 −0.476898
\(466\) 31.7001 1.46848
\(467\) 15.7121 0.727068 0.363534 0.931581i \(-0.381570\pi\)
0.363534 + 0.931581i \(0.381570\pi\)
\(468\) −1.41163 −0.0652526
\(469\) −0.542699 −0.0250595
\(470\) −22.6836 −1.04632
\(471\) −27.3006 −1.25794
\(472\) 38.9870 1.79452
\(473\) −16.7788 −0.771490
\(474\) 30.2529 1.38956
\(475\) 6.10646 0.280183
\(476\) 23.9857 1.09938
\(477\) −2.43401 −0.111446
\(478\) −35.2400 −1.61184
\(479\) −4.79325 −0.219009 −0.109505 0.993986i \(-0.534926\pi\)
−0.109505 + 0.993986i \(0.534926\pi\)
\(480\) −6.73622 −0.307465
\(481\) −2.37992 −0.108515
\(482\) 5.13551 0.233916
\(483\) −14.5182 −0.660602
\(484\) 39.7119 1.80509
\(485\) 15.5793 0.707421
\(486\) 24.5223 1.11235
\(487\) 13.6442 0.618277 0.309138 0.951017i \(-0.399959\pi\)
0.309138 + 0.951017i \(0.399959\pi\)
\(488\) 3.80972 0.172458
\(489\) 45.6829 2.06585
\(490\) −2.36805 −0.106977
\(491\) −5.82875 −0.263048 −0.131524 0.991313i \(-0.541987\pi\)
−0.131524 + 0.991313i \(0.541987\pi\)
\(492\) −10.0376 −0.452531
\(493\) −27.4260 −1.23521
\(494\) −5.44786 −0.245111
\(495\) 4.87235 0.218996
\(496\) −9.20987 −0.413535
\(497\) 14.9311 0.669753
\(498\) −68.4791 −3.06862
\(499\) 16.3292 0.730994 0.365497 0.930812i \(-0.380899\pi\)
0.365497 + 0.930812i \(0.380899\pi\)
\(500\) −3.60764 −0.161338
\(501\) 17.5871 0.785733
\(502\) 23.2966 1.03978
\(503\) −16.8141 −0.749704 −0.374852 0.927085i \(-0.622307\pi\)
−0.374852 + 0.927085i \(0.622307\pi\)
\(504\) −3.95393 −0.176122
\(505\) 17.4321 0.775716
\(506\) 80.2556 3.56780
\(507\) 25.8399 1.14759
\(508\) −14.5364 −0.644951
\(509\) −18.5008 −0.820035 −0.410017 0.912078i \(-0.634477\pi\)
−0.410017 + 0.912078i \(0.634477\pi\)
\(510\) −31.6399 −1.40104
\(511\) −15.6290 −0.691384
\(512\) −19.7361 −0.872221
\(513\) 24.0696 1.06270
\(514\) 58.4887 2.57982
\(515\) −11.3428 −0.499822
\(516\) −25.9306 −1.14153
\(517\) −44.9377 −1.97636
\(518\) −14.9591 −0.657264
\(519\) −4.73888 −0.208014
\(520\) 1.43425 0.0628960
\(521\) −26.6985 −1.16968 −0.584842 0.811147i \(-0.698843\pi\)
−0.584842 + 0.811147i \(0.698843\pi\)
\(522\) 10.1455 0.444058
\(523\) 6.24610 0.273123 0.136561 0.990632i \(-0.456395\pi\)
0.136561 + 0.990632i \(0.456395\pi\)
\(524\) 11.4293 0.499289
\(525\) 2.00963 0.0877074
\(526\) 32.6868 1.42521
\(527\) 34.0224 1.48204
\(528\) 16.9676 0.738421
\(529\) 29.1910 1.26917
\(530\) 5.54960 0.241059
\(531\) 10.6364 0.461579
\(532\) −22.0299 −0.955116
\(533\) −0.521602 −0.0225931
\(534\) −29.0059 −1.25521
\(535\) −15.5472 −0.672165
\(536\) 2.06603 0.0892390
\(537\) −3.50073 −0.151068
\(538\) −53.1002 −2.28931
\(539\) −4.69124 −0.202066
\(540\) −14.2201 −0.611937
\(541\) 24.4866 1.05276 0.526381 0.850249i \(-0.323548\pi\)
0.526381 + 0.850249i \(0.323548\pi\)
\(542\) −71.3286 −3.06383
\(543\) −34.5377 −1.48215
\(544\) 22.2859 0.955499
\(545\) −18.2251 −0.780679
\(546\) −1.79289 −0.0767284
\(547\) 21.1362 0.903717 0.451859 0.892090i \(-0.350761\pi\)
0.451859 + 0.892090i \(0.350761\pi\)
\(548\) 23.4082 0.999948
\(549\) 1.03936 0.0443588
\(550\) −11.1091 −0.473692
\(551\) 25.1897 1.07312
\(552\) 55.2703 2.35246
\(553\) 6.35712 0.270332
\(554\) 17.0168 0.722975
\(555\) 12.6949 0.538870
\(556\) 40.0848 1.69997
\(557\) −11.3102 −0.479228 −0.239614 0.970868i \(-0.577021\pi\)
−0.239614 + 0.970868i \(0.577021\pi\)
\(558\) −12.5857 −0.532795
\(559\) −1.34747 −0.0569921
\(560\) 1.79977 0.0760543
\(561\) −62.6805 −2.64637
\(562\) −39.9741 −1.68621
\(563\) −37.6529 −1.58688 −0.793440 0.608649i \(-0.791712\pi\)
−0.793440 + 0.608649i \(0.791712\pi\)
\(564\) −69.4483 −2.92430
\(565\) 5.14934 0.216635
\(566\) 53.7996 2.26137
\(567\) 11.0371 0.463515
\(568\) −56.8422 −2.38505
\(569\) −3.26326 −0.136803 −0.0684015 0.997658i \(-0.521790\pi\)
−0.0684015 + 0.997658i \(0.521790\pi\)
\(570\) 29.0600 1.21719
\(571\) 39.9899 1.67353 0.836763 0.547566i \(-0.184445\pi\)
0.836763 + 0.547566i \(0.184445\pi\)
\(572\) 6.37614 0.266600
\(573\) −5.12642 −0.214159
\(574\) −3.27855 −0.136844
\(575\) −7.22433 −0.301275
\(576\) −11.9826 −0.499274
\(577\) −12.5128 −0.520916 −0.260458 0.965485i \(-0.583874\pi\)
−0.260458 + 0.965485i \(0.583874\pi\)
\(578\) 64.4194 2.67950
\(579\) −12.3712 −0.514130
\(580\) −14.8818 −0.617934
\(581\) −14.3897 −0.596986
\(582\) 74.1404 3.07322
\(583\) 10.9941 0.455329
\(584\) 59.4988 2.46208
\(585\) 0.391289 0.0161778
\(586\) −7.85348 −0.324424
\(587\) −32.8279 −1.35495 −0.677477 0.735544i \(-0.736927\pi\)
−0.677477 + 0.735544i \(0.736927\pi\)
\(588\) −7.25001 −0.298985
\(589\) −31.2482 −1.28756
\(590\) −24.2511 −0.998404
\(591\) 2.02188 0.0831690
\(592\) 11.3693 0.467274
\(593\) 16.6581 0.684068 0.342034 0.939688i \(-0.388884\pi\)
0.342034 + 0.939688i \(0.388884\pi\)
\(594\) −43.7883 −1.79666
\(595\) −6.64858 −0.272565
\(596\) 28.9107 1.18423
\(597\) 46.8916 1.91915
\(598\) 6.44517 0.263563
\(599\) −13.7946 −0.563631 −0.281815 0.959469i \(-0.590937\pi\)
−0.281815 + 0.959469i \(0.590937\pi\)
\(600\) −7.65057 −0.312333
\(601\) 36.4800 1.48805 0.744026 0.668151i \(-0.232914\pi\)
0.744026 + 0.668151i \(0.232914\pi\)
\(602\) −8.46961 −0.345196
\(603\) 0.563651 0.0229536
\(604\) 16.6472 0.677366
\(605\) −11.0077 −0.447528
\(606\) 82.9572 3.36991
\(607\) −17.8226 −0.723395 −0.361698 0.932295i \(-0.617803\pi\)
−0.361698 + 0.932295i \(0.617803\pi\)
\(608\) −20.4687 −0.830114
\(609\) 8.28990 0.335924
\(610\) −2.36976 −0.0959489
\(611\) −3.60886 −0.145999
\(612\) −24.9117 −1.00699
\(613\) −31.6961 −1.28019 −0.640096 0.768295i \(-0.721105\pi\)
−0.640096 + 0.768295i \(0.721105\pi\)
\(614\) 55.7072 2.24816
\(615\) 2.78233 0.112194
\(616\) 17.8594 0.719574
\(617\) 24.2049 0.974453 0.487227 0.873276i \(-0.338009\pi\)
0.487227 + 0.873276i \(0.338009\pi\)
\(618\) −53.9790 −2.17135
\(619\) 47.4595 1.90756 0.953779 0.300508i \(-0.0971561\pi\)
0.953779 + 0.300508i \(0.0971561\pi\)
\(620\) 18.4612 0.741418
\(621\) −28.4760 −1.14270
\(622\) 35.8721 1.43834
\(623\) −6.09510 −0.244195
\(624\) 1.36264 0.0545492
\(625\) 1.00000 0.0400000
\(626\) −20.4109 −0.815782
\(627\) 57.5695 2.29911
\(628\) 49.0093 1.95568
\(629\) −41.9995 −1.67463
\(630\) 2.45947 0.0979875
\(631\) −31.9477 −1.27182 −0.635909 0.771764i \(-0.719375\pi\)
−0.635909 + 0.771764i \(0.719375\pi\)
\(632\) −24.2013 −0.962676
\(633\) 39.1467 1.55594
\(634\) 34.3386 1.36376
\(635\) 4.02935 0.159900
\(636\) 16.9907 0.673724
\(637\) −0.376745 −0.0149272
\(638\) −45.8259 −1.81427
\(639\) −15.5076 −0.613470
\(640\) 20.6166 0.814942
\(641\) 26.5351 1.04807 0.524037 0.851695i \(-0.324425\pi\)
0.524037 + 0.851695i \(0.324425\pi\)
\(642\) −73.9876 −2.92006
\(643\) 6.20130 0.244555 0.122278 0.992496i \(-0.460980\pi\)
0.122278 + 0.992496i \(0.460980\pi\)
\(644\) 26.0628 1.02702
\(645\) 7.18769 0.283015
\(646\) −96.1409 −3.78261
\(647\) −5.07861 −0.199661 −0.0998304 0.995004i \(-0.531830\pi\)
−0.0998304 + 0.995004i \(0.531830\pi\)
\(648\) −42.0178 −1.65062
\(649\) −48.0430 −1.88585
\(650\) −0.892148 −0.0349929
\(651\) −10.2838 −0.403052
\(652\) −82.0089 −3.21172
\(653\) −14.9145 −0.583650 −0.291825 0.956472i \(-0.594262\pi\)
−0.291825 + 0.956472i \(0.594262\pi\)
\(654\) −86.7314 −3.39147
\(655\) −3.16807 −0.123787
\(656\) 2.49178 0.0972877
\(657\) 16.2323 0.633284
\(658\) −22.6836 −0.884300
\(659\) −0.233973 −0.00911431 −0.00455716 0.999990i \(-0.501451\pi\)
−0.00455716 + 0.999990i \(0.501451\pi\)
\(660\) −34.0115 −1.32390
\(661\) −12.3365 −0.479833 −0.239916 0.970794i \(-0.577120\pi\)
−0.239916 + 0.970794i \(0.577120\pi\)
\(662\) 60.9312 2.36816
\(663\) −5.03375 −0.195495
\(664\) 54.7810 2.12592
\(665\) 6.10646 0.236798
\(666\) 15.5366 0.602031
\(667\) −29.8010 −1.15390
\(668\) −31.5719 −1.22155
\(669\) 14.9557 0.578219
\(670\) −1.28514 −0.0496491
\(671\) −4.69465 −0.181235
\(672\) −6.73622 −0.259855
\(673\) −17.5703 −0.677284 −0.338642 0.940915i \(-0.609967\pi\)
−0.338642 + 0.940915i \(0.609967\pi\)
\(674\) 57.0256 2.19654
\(675\) 3.94167 0.151715
\(676\) −46.3872 −1.78412
\(677\) 40.2015 1.54507 0.772535 0.634972i \(-0.218988\pi\)
0.772535 + 0.634972i \(0.218988\pi\)
\(678\) 24.5052 0.941115
\(679\) 15.5793 0.597880
\(680\) 25.3109 0.970628
\(681\) 8.34397 0.319742
\(682\) 56.8478 2.17681
\(683\) −48.7564 −1.86561 −0.932805 0.360381i \(-0.882647\pi\)
−0.932805 + 0.360381i \(0.882647\pi\)
\(684\) 22.8804 0.874853
\(685\) −6.48851 −0.247913
\(686\) −2.36805 −0.0904124
\(687\) −2.00963 −0.0766721
\(688\) 6.43711 0.245413
\(689\) 0.882914 0.0336364
\(690\) −34.3798 −1.30882
\(691\) 2.37863 0.0904873 0.0452437 0.998976i \(-0.485594\pi\)
0.0452437 + 0.998976i \(0.485594\pi\)
\(692\) 8.50712 0.323392
\(693\) 4.87235 0.185085
\(694\) −9.54334 −0.362260
\(695\) −11.1111 −0.421468
\(696\) −31.5593 −1.19625
\(697\) −9.20494 −0.348662
\(698\) 64.3107 2.43420
\(699\) −26.9021 −1.01753
\(700\) −3.60764 −0.136356
\(701\) −32.5555 −1.22960 −0.614802 0.788682i \(-0.710764\pi\)
−0.614802 + 0.788682i \(0.710764\pi\)
\(702\) −3.51656 −0.132724
\(703\) 38.5748 1.45488
\(704\) 54.1236 2.03986
\(705\) 19.2503 0.725010
\(706\) 81.4908 3.06695
\(707\) 17.4321 0.655600
\(708\) −74.2473 −2.79039
\(709\) −17.5172 −0.657873 −0.328937 0.944352i \(-0.606690\pi\)
−0.328937 + 0.944352i \(0.606690\pi\)
\(710\) 35.3576 1.32695
\(711\) −6.60255 −0.247615
\(712\) 23.2038 0.869599
\(713\) 36.9687 1.38449
\(714\) −31.6399 −1.18409
\(715\) −1.76740 −0.0660970
\(716\) 6.28443 0.234860
\(717\) 29.9062 1.11687
\(718\) 35.2547 1.31570
\(719\) 19.8162 0.739020 0.369510 0.929227i \(-0.379526\pi\)
0.369510 + 0.929227i \(0.379526\pi\)
\(720\) −1.86926 −0.0696630
\(721\) −11.3428 −0.422427
\(722\) 43.3087 1.61178
\(723\) −4.35822 −0.162084
\(724\) 62.0012 2.30426
\(725\) 4.12509 0.153202
\(726\) −52.3846 −1.94417
\(727\) 31.0854 1.15289 0.576447 0.817135i \(-0.304439\pi\)
0.576447 + 0.817135i \(0.304439\pi\)
\(728\) 1.43425 0.0531569
\(729\) 12.3007 0.455580
\(730\) −37.0101 −1.36980
\(731\) −23.7795 −0.879516
\(732\) −7.25527 −0.268163
\(733\) 41.7165 1.54083 0.770417 0.637540i \(-0.220048\pi\)
0.770417 + 0.637540i \(0.220048\pi\)
\(734\) −47.5935 −1.75671
\(735\) 2.00963 0.0741263
\(736\) 24.2158 0.892605
\(737\) −2.54593 −0.0937806
\(738\) 3.40513 0.125344
\(739\) −9.63419 −0.354399 −0.177200 0.984175i \(-0.556704\pi\)
−0.177200 + 0.984175i \(0.556704\pi\)
\(740\) −22.7897 −0.837764
\(741\) 4.62330 0.169841
\(742\) 5.54960 0.203732
\(743\) −9.17856 −0.336729 −0.168364 0.985725i \(-0.553849\pi\)
−0.168364 + 0.985725i \(0.553849\pi\)
\(744\) 39.1498 1.43530
\(745\) −8.01375 −0.293601
\(746\) 42.7947 1.56683
\(747\) 14.9452 0.546818
\(748\) 112.523 4.11423
\(749\) −15.5472 −0.568083
\(750\) 4.75889 0.173770
\(751\) 31.3039 1.14230 0.571149 0.820847i \(-0.306498\pi\)
0.571149 + 0.820847i \(0.306498\pi\)
\(752\) 17.2401 0.628683
\(753\) −19.7705 −0.720477
\(754\) −3.68019 −0.134025
\(755\) −4.61444 −0.167937
\(756\) −14.2201 −0.517181
\(757\) 18.8826 0.686300 0.343150 0.939281i \(-0.388506\pi\)
0.343150 + 0.939281i \(0.388506\pi\)
\(758\) −4.85010 −0.176164
\(759\) −68.1085 −2.47218
\(760\) −23.2470 −0.843258
\(761\) −1.40659 −0.0509889 −0.0254945 0.999675i \(-0.508116\pi\)
−0.0254945 + 0.999675i \(0.508116\pi\)
\(762\) 19.1753 0.694646
\(763\) −18.2251 −0.659794
\(764\) 9.20283 0.332947
\(765\) 6.90526 0.249660
\(766\) 33.3397 1.20461
\(767\) −3.85824 −0.139313
\(768\) 51.7412 1.86705
\(769\) −7.04453 −0.254032 −0.127016 0.991901i \(-0.540540\pi\)
−0.127016 + 0.991901i \(0.540540\pi\)
\(770\) −11.1091 −0.400343
\(771\) −49.6361 −1.78760
\(772\) 22.2085 0.799302
\(773\) 19.4599 0.699923 0.349961 0.936764i \(-0.386195\pi\)
0.349961 + 0.936764i \(0.386195\pi\)
\(774\) 8.79659 0.316187
\(775\) −5.11724 −0.183817
\(776\) −59.3099 −2.12910
\(777\) 12.6949 0.455428
\(778\) −39.1430 −1.40334
\(779\) 8.45437 0.302909
\(780\) −2.73140 −0.0977999
\(781\) 70.0455 2.50643
\(782\) 113.741 4.06737
\(783\) 16.2598 0.581076
\(784\) 1.79977 0.0642776
\(785\) −13.5849 −0.484865
\(786\) −15.0765 −0.537761
\(787\) 45.5140 1.62240 0.811199 0.584770i \(-0.198815\pi\)
0.811199 + 0.584770i \(0.198815\pi\)
\(788\) −3.62963 −0.129300
\(789\) −27.7395 −0.987553
\(790\) 15.0540 0.535596
\(791\) 5.14934 0.183090
\(792\) −18.5488 −0.659104
\(793\) −0.377018 −0.0133883
\(794\) −37.2299 −1.32124
\(795\) −4.70964 −0.167034
\(796\) −84.1787 −2.98364
\(797\) 24.4638 0.866553 0.433277 0.901261i \(-0.357357\pi\)
0.433277 + 0.901261i \(0.357357\pi\)
\(798\) 29.0600 1.02871
\(799\) −63.6872 −2.25309
\(800\) −3.35197 −0.118510
\(801\) 6.33041 0.223674
\(802\) −61.2517 −2.16287
\(803\) −73.3192 −2.58738
\(804\) −3.93457 −0.138762
\(805\) −7.22433 −0.254624
\(806\) 4.56534 0.160807
\(807\) 45.0632 1.58630
\(808\) −66.3631 −2.33465
\(809\) −0.911420 −0.0320438 −0.0160219 0.999872i \(-0.505100\pi\)
−0.0160219 + 0.999872i \(0.505100\pi\)
\(810\) 26.1364 0.918339
\(811\) 40.0862 1.40762 0.703808 0.710390i \(-0.251482\pi\)
0.703808 + 0.710390i \(0.251482\pi\)
\(812\) −14.8818 −0.522250
\(813\) 60.5326 2.12297
\(814\) −70.1766 −2.45969
\(815\) 22.7320 0.796268
\(816\) 24.0471 0.841816
\(817\) 21.8405 0.764103
\(818\) 70.6300 2.46952
\(819\) 0.391289 0.0136728
\(820\) −4.99476 −0.174425
\(821\) 3.19163 0.111389 0.0556944 0.998448i \(-0.482263\pi\)
0.0556944 + 0.998448i \(0.482263\pi\)
\(822\) −30.8781 −1.07700
\(823\) −44.8559 −1.56358 −0.781790 0.623542i \(-0.785693\pi\)
−0.781790 + 0.623542i \(0.785693\pi\)
\(824\) 43.1814 1.50430
\(825\) 9.42765 0.328229
\(826\) −24.2511 −0.843805
\(827\) −15.2603 −0.530653 −0.265327 0.964159i \(-0.585480\pi\)
−0.265327 + 0.964159i \(0.585480\pi\)
\(828\) −27.0690 −0.940711
\(829\) −16.3321 −0.567239 −0.283619 0.958937i \(-0.591535\pi\)
−0.283619 + 0.958937i \(0.591535\pi\)
\(830\) −34.0755 −1.18278
\(831\) −14.4412 −0.500961
\(832\) 4.34657 0.150690
\(833\) −6.64858 −0.230360
\(834\) −52.8765 −1.83096
\(835\) 8.75142 0.302855
\(836\) −103.347 −3.57435
\(837\) −20.1705 −0.697194
\(838\) −47.7570 −1.64974
\(839\) 13.4052 0.462800 0.231400 0.972859i \(-0.425669\pi\)
0.231400 + 0.972859i \(0.425669\pi\)
\(840\) −7.65057 −0.263970
\(841\) −11.9836 −0.413228
\(842\) 59.6075 2.05421
\(843\) 33.9238 1.16840
\(844\) −70.2752 −2.41897
\(845\) 12.8581 0.442331
\(846\) 23.5594 0.809988
\(847\) −11.0077 −0.378230
\(848\) −4.21783 −0.144841
\(849\) −45.6567 −1.56693
\(850\) −15.7441 −0.540020
\(851\) −45.6365 −1.56440
\(852\) 108.251 3.70861
\(853\) −18.1022 −0.619806 −0.309903 0.950768i \(-0.600297\pi\)
−0.309903 + 0.950768i \(0.600297\pi\)
\(854\) −2.36976 −0.0810917
\(855\) −6.34220 −0.216899
\(856\) 59.1876 2.02299
\(857\) 22.8699 0.781220 0.390610 0.920556i \(-0.372264\pi\)
0.390610 + 0.920556i \(0.372264\pi\)
\(858\) −8.41086 −0.287142
\(859\) −21.6994 −0.740374 −0.370187 0.928957i \(-0.620706\pi\)
−0.370187 + 0.928957i \(0.620706\pi\)
\(860\) −12.9032 −0.439994
\(861\) 2.78233 0.0948214
\(862\) 20.6977 0.704965
\(863\) −46.1103 −1.56961 −0.784806 0.619742i \(-0.787237\pi\)
−0.784806 + 0.619742i \(0.787237\pi\)
\(864\) −13.2124 −0.449494
\(865\) −2.35809 −0.0801773
\(866\) 82.6706 2.80926
\(867\) −54.6692 −1.85666
\(868\) 18.4612 0.626612
\(869\) 29.8228 1.01167
\(870\) 19.6309 0.665548
\(871\) −0.204459 −0.00692782
\(872\) 69.3823 2.34958
\(873\) −16.1808 −0.547637
\(874\) −104.466 −3.53363
\(875\) 1.00000 0.0338062
\(876\) −113.310 −3.82839
\(877\) 17.2910 0.583875 0.291937 0.956437i \(-0.405700\pi\)
0.291937 + 0.956437i \(0.405700\pi\)
\(878\) −39.9058 −1.34676
\(879\) 6.66481 0.224799
\(880\) 8.44316 0.284619
\(881\) −33.6305 −1.13304 −0.566520 0.824048i \(-0.691711\pi\)
−0.566520 + 0.824048i \(0.691711\pi\)
\(882\) 2.45947 0.0828146
\(883\) −20.1033 −0.676531 −0.338266 0.941051i \(-0.609840\pi\)
−0.338266 + 0.941051i \(0.609840\pi\)
\(884\) 9.03647 0.303929
\(885\) 20.5806 0.691809
\(886\) −10.7005 −0.359490
\(887\) 17.3102 0.581219 0.290610 0.956842i \(-0.406142\pi\)
0.290610 + 0.956842i \(0.406142\pi\)
\(888\) −48.3291 −1.62182
\(889\) 4.02935 0.135140
\(890\) −14.4335 −0.483811
\(891\) 51.7778 1.73462
\(892\) −26.8481 −0.898939
\(893\) 58.4941 1.95743
\(894\) −38.1366 −1.27548
\(895\) −1.74198 −0.0582280
\(896\) 20.6166 0.688752
\(897\) −5.46966 −0.182627
\(898\) 47.8039 1.59524
\(899\) −21.1091 −0.704027
\(900\) 3.74692 0.124897
\(901\) 15.5812 0.519085
\(902\) −15.3805 −0.512114
\(903\) 7.18769 0.239191
\(904\) −19.6033 −0.651997
\(905\) −17.1861 −0.571285
\(906\) −21.9596 −0.729560
\(907\) −48.7931 −1.62015 −0.810075 0.586327i \(-0.800573\pi\)
−0.810075 + 0.586327i \(0.800573\pi\)
\(908\) −14.9789 −0.497092
\(909\) −18.1050 −0.600506
\(910\) −0.892148 −0.0295744
\(911\) 9.01521 0.298687 0.149344 0.988785i \(-0.452284\pi\)
0.149344 + 0.988785i \(0.452284\pi\)
\(912\) −22.0863 −0.731350
\(913\) −67.5056 −2.23411
\(914\) −14.7982 −0.489480
\(915\) 2.01109 0.0664845
\(916\) 3.60764 0.119200
\(917\) −3.16807 −0.104619
\(918\) −62.0582 −2.04823
\(919\) −34.2171 −1.12872 −0.564358 0.825530i \(-0.690876\pi\)
−0.564358 + 0.825530i \(0.690876\pi\)
\(920\) 27.5027 0.906738
\(921\) −47.2756 −1.55778
\(922\) −87.4734 −2.88078
\(923\) 5.62522 0.185156
\(924\) −34.0115 −1.11890
\(925\) 6.31706 0.207704
\(926\) −49.2438 −1.61825
\(927\) 11.7807 0.386928
\(928\) −13.8272 −0.453900
\(929\) 41.1258 1.34930 0.674648 0.738140i \(-0.264296\pi\)
0.674648 + 0.738140i \(0.264296\pi\)
\(930\) −24.3524 −0.798546
\(931\) 6.10646 0.200131
\(932\) 48.2940 1.58192
\(933\) −30.4426 −0.996647
\(934\) 37.2069 1.21745
\(935\) −31.1901 −1.02003
\(936\) −1.48962 −0.0486898
\(937\) −10.8224 −0.353551 −0.176776 0.984251i \(-0.556567\pi\)
−0.176776 + 0.984251i \(0.556567\pi\)
\(938\) −1.28514 −0.0419612
\(939\) 17.3216 0.565268
\(940\) −34.5578 −1.12715
\(941\) 1.16687 0.0380387 0.0190194 0.999819i \(-0.493946\pi\)
0.0190194 + 0.999819i \(0.493946\pi\)
\(942\) −64.6489 −2.10638
\(943\) −10.0021 −0.325712
\(944\) 18.4315 0.599893
\(945\) 3.94167 0.128223
\(946\) −39.7330 −1.29183
\(947\) 5.05122 0.164143 0.0820713 0.996626i \(-0.473846\pi\)
0.0820713 + 0.996626i \(0.473846\pi\)
\(948\) 46.0892 1.49691
\(949\) −5.88812 −0.191137
\(950\) 14.4604 0.469156
\(951\) −29.1412 −0.944969
\(952\) 25.3109 0.820330
\(953\) 9.55535 0.309528 0.154764 0.987951i \(-0.450538\pi\)
0.154764 + 0.987951i \(0.450538\pi\)
\(954\) −5.76385 −0.186612
\(955\) −2.55093 −0.0825462
\(956\) −53.6870 −1.73636
\(957\) 38.8899 1.25713
\(958\) −11.3506 −0.366722
\(959\) −6.48851 −0.209525
\(960\) −23.1854 −0.748306
\(961\) −4.81384 −0.155285
\(962\) −5.63575 −0.181704
\(963\) 16.1474 0.520344
\(964\) 7.82377 0.251987
\(965\) −6.15597 −0.198168
\(966\) −34.3798 −1.10615
\(967\) −7.81947 −0.251457 −0.125729 0.992065i \(-0.540127\pi\)
−0.125729 + 0.992065i \(0.540127\pi\)
\(968\) 41.9060 1.34691
\(969\) 81.5894 2.62103
\(970\) 36.8926 1.18455
\(971\) 7.19810 0.230998 0.115499 0.993308i \(-0.463153\pi\)
0.115499 + 0.993308i \(0.463153\pi\)
\(972\) 37.3588 1.19829
\(973\) −11.1111 −0.356205
\(974\) 32.3100 1.03528
\(975\) 0.757117 0.0242471
\(976\) 1.80108 0.0576511
\(977\) −46.7002 −1.49407 −0.747036 0.664784i \(-0.768524\pi\)
−0.747036 + 0.664784i \(0.768524\pi\)
\(978\) 108.179 3.45919
\(979\) −28.5936 −0.913855
\(980\) −3.60764 −0.115242
\(981\) 18.9287 0.604348
\(982\) −13.8027 −0.440463
\(983\) −56.9979 −1.81795 −0.908976 0.416849i \(-0.863134\pi\)
−0.908976 + 0.416849i \(0.863134\pi\)
\(984\) −10.5922 −0.337667
\(985\) 1.00610 0.0320569
\(986\) −64.9460 −2.06830
\(987\) 19.2503 0.612745
\(988\) −8.29964 −0.264047
\(989\) −25.8387 −0.821624
\(990\) 11.5379 0.366700
\(991\) 3.29027 0.104519 0.0522594 0.998634i \(-0.483358\pi\)
0.0522594 + 0.998634i \(0.483358\pi\)
\(992\) 17.1529 0.544604
\(993\) −51.7089 −1.64093
\(994\) 35.3576 1.12147
\(995\) 23.3335 0.739721
\(996\) −104.326 −3.30568
\(997\) 25.3405 0.802542 0.401271 0.915959i \(-0.368569\pi\)
0.401271 + 0.915959i \(0.368569\pi\)
\(998\) 38.6682 1.22402
\(999\) 24.8998 0.787794
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 \(a_p\))