Properties

Label 8015.2.a.l.1.59
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 1.59
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} +O(q^{10})\) \(q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} -2.62755 q^{10} -5.79150 q^{11} -5.83004 q^{12} -6.84400 q^{13} -2.62755 q^{14} +1.18883 q^{15} +10.2415 q^{16} +6.86984 q^{17} -4.16912 q^{18} +6.33777 q^{19} -4.90404 q^{20} +1.18883 q^{21} -15.2175 q^{22} +7.14073 q^{23} -9.07135 q^{24} +1.00000 q^{25} -17.9830 q^{26} +5.45278 q^{27} -4.90404 q^{28} -2.28122 q^{29} +3.12370 q^{30} +3.85963 q^{31} +11.6491 q^{32} +6.88508 q^{33} +18.0509 q^{34} +1.00000 q^{35} -7.78120 q^{36} -0.186449 q^{37} +16.6528 q^{38} +8.13632 q^{39} -7.63051 q^{40} +1.16571 q^{41} +3.12370 q^{42} +3.17391 q^{43} -28.4017 q^{44} +1.58669 q^{45} +18.7626 q^{46} +0.258848 q^{47} -12.1754 q^{48} +1.00000 q^{49} +2.62755 q^{50} -8.16704 q^{51} -33.5632 q^{52} -8.96737 q^{53} +14.3275 q^{54} +5.79150 q^{55} -7.63051 q^{56} -7.53451 q^{57} -5.99402 q^{58} +2.12258 q^{59} +5.83004 q^{60} -5.73197 q^{61} +10.1414 q^{62} +1.58669 q^{63} +10.1255 q^{64} +6.84400 q^{65} +18.0909 q^{66} +0.485444 q^{67} +33.6899 q^{68} -8.48908 q^{69} +2.62755 q^{70} +12.9055 q^{71} -12.1073 q^{72} +0.306248 q^{73} -0.489904 q^{74} -1.18883 q^{75} +31.0807 q^{76} +5.79150 q^{77} +21.3786 q^{78} -4.98220 q^{79} -10.2415 q^{80} -1.72233 q^{81} +3.06297 q^{82} +12.3172 q^{83} +5.83004 q^{84} -6.86984 q^{85} +8.33963 q^{86} +2.71197 q^{87} -44.1921 q^{88} +12.0055 q^{89} +4.16912 q^{90} +6.84400 q^{91} +35.0184 q^{92} -4.58843 q^{93} +0.680136 q^{94} -6.33777 q^{95} -13.8487 q^{96} +12.7617 q^{97} +2.62755 q^{98} +9.18933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62755 1.85796 0.928980 0.370129i \(-0.120687\pi\)
0.928980 + 0.370129i \(0.120687\pi\)
\(3\) −1.18883 −0.686369 −0.343184 0.939268i \(-0.611506\pi\)
−0.343184 + 0.939268i \(0.611506\pi\)
\(4\) 4.90404 2.45202
\(5\) −1.00000 −0.447214
\(6\) −3.12370 −1.27525
\(7\) −1.00000 −0.377964
\(8\) 7.63051 2.69779
\(9\) −1.58669 −0.528898
\(10\) −2.62755 −0.830905
\(11\) −5.79150 −1.74620 −0.873101 0.487539i \(-0.837895\pi\)
−0.873101 + 0.487539i \(0.837895\pi\)
\(12\) −5.83004 −1.68299
\(13\) −6.84400 −1.89818 −0.949092 0.314999i \(-0.897996\pi\)
−0.949092 + 0.314999i \(0.897996\pi\)
\(14\) −2.62755 −0.702243
\(15\) 1.18883 0.306954
\(16\) 10.2415 2.56037
\(17\) 6.86984 1.66618 0.833090 0.553138i \(-0.186570\pi\)
0.833090 + 0.553138i \(0.186570\pi\)
\(18\) −4.16912 −0.982671
\(19\) 6.33777 1.45398 0.726992 0.686646i \(-0.240918\pi\)
0.726992 + 0.686646i \(0.240918\pi\)
\(20\) −4.90404 −1.09658
\(21\) 1.18883 0.259423
\(22\) −15.2175 −3.24437
\(23\) 7.14073 1.48894 0.744472 0.667654i \(-0.232701\pi\)
0.744472 + 0.667654i \(0.232701\pi\)
\(24\) −9.07135 −1.85168
\(25\) 1.00000 0.200000
\(26\) −17.9830 −3.52675
\(27\) 5.45278 1.04939
\(28\) −4.90404 −0.926776
\(29\) −2.28122 −0.423611 −0.211806 0.977312i \(-0.567934\pi\)
−0.211806 + 0.977312i \(0.567934\pi\)
\(30\) 3.12370 0.570308
\(31\) 3.85963 0.693211 0.346605 0.938011i \(-0.387334\pi\)
0.346605 + 0.938011i \(0.387334\pi\)
\(32\) 11.6491 2.05928
\(33\) 6.88508 1.19854
\(34\) 18.0509 3.09570
\(35\) 1.00000 0.169031
\(36\) −7.78120 −1.29687
\(37\) −0.186449 −0.0306520 −0.0153260 0.999883i \(-0.504879\pi\)
−0.0153260 + 0.999883i \(0.504879\pi\)
\(38\) 16.6528 2.70145
\(39\) 8.13632 1.30285
\(40\) −7.63051 −1.20649
\(41\) 1.16571 0.182053 0.0910267 0.995848i \(-0.470985\pi\)
0.0910267 + 0.995848i \(0.470985\pi\)
\(42\) 3.12370 0.481998
\(43\) 3.17391 0.484017 0.242009 0.970274i \(-0.422194\pi\)
0.242009 + 0.970274i \(0.422194\pi\)
\(44\) −28.4017 −4.28172
\(45\) 1.58669 0.236530
\(46\) 18.7626 2.76640
\(47\) 0.258848 0.0377568 0.0188784 0.999822i \(-0.493990\pi\)
0.0188784 + 0.999822i \(0.493990\pi\)
\(48\) −12.1754 −1.75736
\(49\) 1.00000 0.142857
\(50\) 2.62755 0.371592
\(51\) −8.16704 −1.14361
\(52\) −33.5632 −4.65438
\(53\) −8.96737 −1.23176 −0.615881 0.787839i \(-0.711200\pi\)
−0.615881 + 0.787839i \(0.711200\pi\)
\(54\) 14.3275 1.94972
\(55\) 5.79150 0.780925
\(56\) −7.63051 −1.01967
\(57\) −7.53451 −0.997970
\(58\) −5.99402 −0.787053
\(59\) 2.12258 0.276336 0.138168 0.990409i \(-0.455879\pi\)
0.138168 + 0.990409i \(0.455879\pi\)
\(60\) 5.83004 0.752656
\(61\) −5.73197 −0.733903 −0.366952 0.930240i \(-0.619599\pi\)
−0.366952 + 0.930240i \(0.619599\pi\)
\(62\) 10.1414 1.28796
\(63\) 1.58669 0.199905
\(64\) 10.1255 1.26569
\(65\) 6.84400 0.848894
\(66\) 18.0909 2.22684
\(67\) 0.485444 0.0593064 0.0296532 0.999560i \(-0.490560\pi\)
0.0296532 + 0.999560i \(0.490560\pi\)
\(68\) 33.6899 4.08550
\(69\) −8.48908 −1.02197
\(70\) 2.62755 0.314053
\(71\) 12.9055 1.53160 0.765802 0.643076i \(-0.222342\pi\)
0.765802 + 0.643076i \(0.222342\pi\)
\(72\) −12.1073 −1.42686
\(73\) 0.306248 0.0358436 0.0179218 0.999839i \(-0.494295\pi\)
0.0179218 + 0.999839i \(0.494295\pi\)
\(74\) −0.489904 −0.0569502
\(75\) −1.18883 −0.137274
\(76\) 31.0807 3.56520
\(77\) 5.79150 0.660002
\(78\) 21.3786 2.42065
\(79\) −4.98220 −0.560541 −0.280270 0.959921i \(-0.590424\pi\)
−0.280270 + 0.959921i \(0.590424\pi\)
\(80\) −10.2415 −1.14503
\(81\) −1.72233 −0.191370
\(82\) 3.06297 0.338248
\(83\) 12.3172 1.35199 0.675993 0.736908i \(-0.263715\pi\)
0.675993 + 0.736908i \(0.263715\pi\)
\(84\) 5.83004 0.636110
\(85\) −6.86984 −0.745138
\(86\) 8.33963 0.899285
\(87\) 2.71197 0.290754
\(88\) −44.1921 −4.71089
\(89\) 12.0055 1.27258 0.636288 0.771452i \(-0.280469\pi\)
0.636288 + 0.771452i \(0.280469\pi\)
\(90\) 4.16912 0.439464
\(91\) 6.84400 0.717446
\(92\) 35.0184 3.65092
\(93\) −4.58843 −0.475798
\(94\) 0.680136 0.0701507
\(95\) −6.33777 −0.650242
\(96\) −13.8487 −1.41343
\(97\) 12.7617 1.29576 0.647879 0.761743i \(-0.275656\pi\)
0.647879 + 0.761743i \(0.275656\pi\)
\(98\) 2.62755 0.265423
\(99\) 9.18933 0.923562
\(100\) 4.90404 0.490404
\(101\) 18.3388 1.82478 0.912391 0.409319i \(-0.134234\pi\)
0.912391 + 0.409319i \(0.134234\pi\)
\(102\) −21.4593 −2.12479
\(103\) 0.620124 0.0611027 0.0305513 0.999533i \(-0.490274\pi\)
0.0305513 + 0.999533i \(0.490274\pi\)
\(104\) −52.2232 −5.12091
\(105\) −1.18883 −0.116018
\(106\) −23.5622 −2.28857
\(107\) −2.87994 −0.278414 −0.139207 0.990263i \(-0.544455\pi\)
−0.139207 + 0.990263i \(0.544455\pi\)
\(108\) 26.7406 2.57312
\(109\) −17.2756 −1.65470 −0.827350 0.561686i \(-0.810153\pi\)
−0.827350 + 0.561686i \(0.810153\pi\)
\(110\) 15.2175 1.45093
\(111\) 0.221655 0.0210386
\(112\) −10.2415 −0.967731
\(113\) 17.7719 1.67184 0.835920 0.548851i \(-0.184935\pi\)
0.835920 + 0.548851i \(0.184935\pi\)
\(114\) −19.7973 −1.85419
\(115\) −7.14073 −0.665876
\(116\) −11.1872 −1.03870
\(117\) 10.8593 1.00395
\(118\) 5.57719 0.513422
\(119\) −6.86984 −0.629757
\(120\) 9.07135 0.828097
\(121\) 22.5414 2.04922
\(122\) −15.0610 −1.36356
\(123\) −1.38583 −0.124956
\(124\) 18.9278 1.69976
\(125\) −1.00000 −0.0894427
\(126\) 4.16912 0.371415
\(127\) −18.1704 −1.61236 −0.806180 0.591670i \(-0.798469\pi\)
−0.806180 + 0.591670i \(0.798469\pi\)
\(128\) 3.30725 0.292323
\(129\) −3.77323 −0.332214
\(130\) 17.9830 1.57721
\(131\) 19.2511 1.68198 0.840990 0.541051i \(-0.181973\pi\)
0.840990 + 0.541051i \(0.181973\pi\)
\(132\) 33.7647 2.93884
\(133\) −6.33777 −0.549555
\(134\) 1.27553 0.110189
\(135\) −5.45278 −0.469301
\(136\) 52.4203 4.49501
\(137\) −15.3632 −1.31257 −0.656283 0.754515i \(-0.727872\pi\)
−0.656283 + 0.754515i \(0.727872\pi\)
\(138\) −22.3055 −1.89877
\(139\) 12.6073 1.06934 0.534668 0.845062i \(-0.320436\pi\)
0.534668 + 0.845062i \(0.320436\pi\)
\(140\) 4.90404 0.414467
\(141\) −0.307725 −0.0259151
\(142\) 33.9100 2.84566
\(143\) 39.6370 3.31461
\(144\) −16.2501 −1.35418
\(145\) 2.28122 0.189445
\(146\) 0.804683 0.0665961
\(147\) −1.18883 −0.0980527
\(148\) −0.914351 −0.0751592
\(149\) 20.3870 1.67017 0.835085 0.550121i \(-0.185419\pi\)
0.835085 + 0.550121i \(0.185419\pi\)
\(150\) −3.12370 −0.255049
\(151\) 0.314224 0.0255712 0.0127856 0.999918i \(-0.495930\pi\)
0.0127856 + 0.999918i \(0.495930\pi\)
\(152\) 48.3604 3.92255
\(153\) −10.9003 −0.881239
\(154\) 15.2175 1.22626
\(155\) −3.85963 −0.310013
\(156\) 39.9008 3.19462
\(157\) −7.24442 −0.578168 −0.289084 0.957304i \(-0.593351\pi\)
−0.289084 + 0.957304i \(0.593351\pi\)
\(158\) −13.0910 −1.04146
\(159\) 10.6606 0.845444
\(160\) −11.6491 −0.920939
\(161\) −7.14073 −0.562768
\(162\) −4.52550 −0.355557
\(163\) 14.9142 1.16817 0.584083 0.811694i \(-0.301454\pi\)
0.584083 + 0.811694i \(0.301454\pi\)
\(164\) 5.71668 0.446398
\(165\) −6.88508 −0.536003
\(166\) 32.3640 2.51194
\(167\) −4.61121 −0.356826 −0.178413 0.983956i \(-0.557096\pi\)
−0.178413 + 0.983956i \(0.557096\pi\)
\(168\) 9.07135 0.699870
\(169\) 33.8403 2.60310
\(170\) −18.0509 −1.38444
\(171\) −10.0561 −0.769009
\(172\) 15.5650 1.18682
\(173\) −10.3015 −0.783205 −0.391602 0.920135i \(-0.628079\pi\)
−0.391602 + 0.920135i \(0.628079\pi\)
\(174\) 7.12584 0.540209
\(175\) −1.00000 −0.0755929
\(176\) −59.3136 −4.47093
\(177\) −2.52338 −0.189669
\(178\) 31.5450 2.36440
\(179\) 18.8850 1.41153 0.705764 0.708447i \(-0.250604\pi\)
0.705764 + 0.708447i \(0.250604\pi\)
\(180\) 7.78120 0.579976
\(181\) −11.5182 −0.856140 −0.428070 0.903745i \(-0.640806\pi\)
−0.428070 + 0.903745i \(0.640806\pi\)
\(182\) 17.9830 1.33299
\(183\) 6.81431 0.503728
\(184\) 54.4874 4.01686
\(185\) 0.186449 0.0137080
\(186\) −12.0563 −0.884014
\(187\) −39.7866 −2.90949
\(188\) 1.26940 0.0925804
\(189\) −5.45278 −0.396631
\(190\) −16.6528 −1.20812
\(191\) −17.7914 −1.28734 −0.643669 0.765304i \(-0.722588\pi\)
−0.643669 + 0.765304i \(0.722588\pi\)
\(192\) −12.0375 −0.868731
\(193\) 8.44371 0.607791 0.303896 0.952705i \(-0.401713\pi\)
0.303896 + 0.952705i \(0.401713\pi\)
\(194\) 33.5321 2.40747
\(195\) −8.13632 −0.582654
\(196\) 4.90404 0.350288
\(197\) −10.1837 −0.725558 −0.362779 0.931875i \(-0.618172\pi\)
−0.362779 + 0.931875i \(0.618172\pi\)
\(198\) 24.1454 1.71594
\(199\) 2.88689 0.204646 0.102323 0.994751i \(-0.467372\pi\)
0.102323 + 0.994751i \(0.467372\pi\)
\(200\) 7.63051 0.539558
\(201\) −0.577108 −0.0407060
\(202\) 48.1863 3.39037
\(203\) 2.28122 0.160110
\(204\) −40.0514 −2.80416
\(205\) −1.16571 −0.0814167
\(206\) 1.62941 0.113526
\(207\) −11.3301 −0.787499
\(208\) −70.0928 −4.86006
\(209\) −36.7052 −2.53895
\(210\) −3.12370 −0.215556
\(211\) 0.598480 0.0412011 0.0206005 0.999788i \(-0.493442\pi\)
0.0206005 + 0.999788i \(0.493442\pi\)
\(212\) −43.9763 −3.02030
\(213\) −15.3424 −1.05125
\(214\) −7.56719 −0.517282
\(215\) −3.17391 −0.216459
\(216\) 41.6075 2.83103
\(217\) −3.85963 −0.262009
\(218\) −45.3925 −3.07437
\(219\) −0.364076 −0.0246020
\(220\) 28.4017 1.91484
\(221\) −47.0172 −3.16272
\(222\) 0.582410 0.0390888
\(223\) 24.7467 1.65716 0.828580 0.559871i \(-0.189149\pi\)
0.828580 + 0.559871i \(0.189149\pi\)
\(224\) −11.6491 −0.778336
\(225\) −1.58669 −0.105780
\(226\) 46.6966 3.10621
\(227\) 3.30995 0.219689 0.109845 0.993949i \(-0.464965\pi\)
0.109845 + 0.993949i \(0.464965\pi\)
\(228\) −36.9495 −2.44704
\(229\) 1.00000 0.0660819
\(230\) −18.7626 −1.23717
\(231\) −6.88508 −0.453005
\(232\) −17.4068 −1.14282
\(233\) 27.8189 1.82248 0.911240 0.411876i \(-0.135126\pi\)
0.911240 + 0.411876i \(0.135126\pi\)
\(234\) 28.5335 1.86529
\(235\) −0.258848 −0.0168854
\(236\) 10.4092 0.677581
\(237\) 5.92296 0.384738
\(238\) −18.0509 −1.17006
\(239\) −18.9879 −1.22822 −0.614111 0.789219i \(-0.710485\pi\)
−0.614111 + 0.789219i \(0.710485\pi\)
\(240\) 12.1754 0.785916
\(241\) −8.52555 −0.549179 −0.274590 0.961562i \(-0.588542\pi\)
−0.274590 + 0.961562i \(0.588542\pi\)
\(242\) 59.2288 3.80737
\(243\) −14.3108 −0.918038
\(244\) −28.1098 −1.79954
\(245\) −1.00000 −0.0638877
\(246\) −3.64133 −0.232163
\(247\) −43.3757 −2.75993
\(248\) 29.4510 1.87014
\(249\) −14.6430 −0.927961
\(250\) −2.62755 −0.166181
\(251\) 7.55193 0.476674 0.238337 0.971183i \(-0.423398\pi\)
0.238337 + 0.971183i \(0.423398\pi\)
\(252\) 7.78120 0.490170
\(253\) −41.3555 −2.60000
\(254\) −47.7437 −2.99570
\(255\) 8.16704 0.511440
\(256\) −11.5611 −0.722567
\(257\) −20.9456 −1.30655 −0.653275 0.757121i \(-0.726605\pi\)
−0.653275 + 0.757121i \(0.726605\pi\)
\(258\) −9.91437 −0.617241
\(259\) 0.186449 0.0115854
\(260\) 33.5632 2.08150
\(261\) 3.61959 0.224047
\(262\) 50.5834 3.12505
\(263\) 7.08415 0.436827 0.218414 0.975856i \(-0.429912\pi\)
0.218414 + 0.975856i \(0.429912\pi\)
\(264\) 52.5367 3.23341
\(265\) 8.96737 0.550861
\(266\) −16.6528 −1.02105
\(267\) −14.2724 −0.873457
\(268\) 2.38063 0.145420
\(269\) −25.1463 −1.53320 −0.766598 0.642128i \(-0.778052\pi\)
−0.766598 + 0.642128i \(0.778052\pi\)
\(270\) −14.3275 −0.871942
\(271\) −1.88111 −0.114269 −0.0571347 0.998366i \(-0.518196\pi\)
−0.0571347 + 0.998366i \(0.518196\pi\)
\(272\) 70.3574 4.26604
\(273\) −8.13632 −0.492433
\(274\) −40.3676 −2.43869
\(275\) −5.79150 −0.349240
\(276\) −41.6307 −2.50588
\(277\) −13.7162 −0.824126 −0.412063 0.911155i \(-0.635192\pi\)
−0.412063 + 0.911155i \(0.635192\pi\)
\(278\) 33.1263 1.98679
\(279\) −6.12405 −0.366637
\(280\) 7.63051 0.456010
\(281\) −13.3574 −0.796834 −0.398417 0.917204i \(-0.630440\pi\)
−0.398417 + 0.917204i \(0.630440\pi\)
\(282\) −0.808563 −0.0481493
\(283\) 14.1780 0.842797 0.421398 0.906876i \(-0.361539\pi\)
0.421398 + 0.906876i \(0.361539\pi\)
\(284\) 63.2892 3.75552
\(285\) 7.53451 0.446306
\(286\) 104.148 6.15842
\(287\) −1.16571 −0.0688097
\(288\) −18.4835 −1.08915
\(289\) 30.1946 1.77616
\(290\) 5.99402 0.351981
\(291\) −15.1715 −0.889368
\(292\) 1.50185 0.0878892
\(293\) 14.3343 0.837419 0.418709 0.908120i \(-0.362483\pi\)
0.418709 + 0.908120i \(0.362483\pi\)
\(294\) −3.12370 −0.182178
\(295\) −2.12258 −0.123581
\(296\) −1.42270 −0.0826927
\(297\) −31.5798 −1.83244
\(298\) 53.5680 3.10311
\(299\) −48.8711 −2.82629
\(300\) −5.83004 −0.336598
\(301\) −3.17391 −0.182941
\(302\) 0.825640 0.0475103
\(303\) −21.8017 −1.25247
\(304\) 64.9083 3.72275
\(305\) 5.73197 0.328211
\(306\) −28.6412 −1.63731
\(307\) 4.82370 0.275303 0.137651 0.990481i \(-0.456045\pi\)
0.137651 + 0.990481i \(0.456045\pi\)
\(308\) 28.4017 1.61834
\(309\) −0.737220 −0.0419390
\(310\) −10.1414 −0.575992
\(311\) 8.50918 0.482512 0.241256 0.970462i \(-0.422441\pi\)
0.241256 + 0.970462i \(0.422441\pi\)
\(312\) 62.0843 3.51483
\(313\) −4.71402 −0.266452 −0.133226 0.991086i \(-0.542534\pi\)
−0.133226 + 0.991086i \(0.542534\pi\)
\(314\) −19.0351 −1.07421
\(315\) −1.58669 −0.0894000
\(316\) −24.4329 −1.37446
\(317\) 12.8147 0.719744 0.359872 0.933002i \(-0.382820\pi\)
0.359872 + 0.933002i \(0.382820\pi\)
\(318\) 28.0114 1.57080
\(319\) 13.2117 0.739711
\(320\) −10.1255 −0.566034
\(321\) 3.42374 0.191095
\(322\) −18.7626 −1.04560
\(323\) 43.5395 2.42260
\(324\) −8.44635 −0.469242
\(325\) −6.84400 −0.379637
\(326\) 39.1877 2.17041
\(327\) 20.5377 1.13573
\(328\) 8.89496 0.491142
\(329\) −0.258848 −0.0142707
\(330\) −18.0909 −0.995872
\(331\) 11.1087 0.610587 0.305294 0.952258i \(-0.401245\pi\)
0.305294 + 0.952258i \(0.401245\pi\)
\(332\) 60.4039 3.31509
\(333\) 0.295837 0.0162118
\(334\) −12.1162 −0.662969
\(335\) −0.485444 −0.0265226
\(336\) 12.1754 0.664220
\(337\) 10.3858 0.565752 0.282876 0.959156i \(-0.408711\pi\)
0.282876 + 0.959156i \(0.408711\pi\)
\(338\) 88.9173 4.83646
\(339\) −21.1277 −1.14750
\(340\) −33.6899 −1.82709
\(341\) −22.3531 −1.21049
\(342\) −26.4229 −1.42879
\(343\) −1.00000 −0.0539949
\(344\) 24.2186 1.30578
\(345\) 8.48908 0.457037
\(346\) −27.0676 −1.45516
\(347\) −11.3891 −0.611401 −0.305701 0.952128i \(-0.598891\pi\)
−0.305701 + 0.952128i \(0.598891\pi\)
\(348\) 13.2996 0.712933
\(349\) −24.9331 −1.33464 −0.667318 0.744773i \(-0.732558\pi\)
−0.667318 + 0.744773i \(0.732558\pi\)
\(350\) −2.62755 −0.140449
\(351\) −37.3188 −1.99193
\(352\) −67.4655 −3.59592
\(353\) −26.4654 −1.40861 −0.704305 0.709898i \(-0.748741\pi\)
−0.704305 + 0.709898i \(0.748741\pi\)
\(354\) −6.63031 −0.352397
\(355\) −12.9055 −0.684954
\(356\) 58.8752 3.12038
\(357\) 8.16704 0.432246
\(358\) 49.6212 2.62256
\(359\) 13.0631 0.689446 0.344723 0.938704i \(-0.387973\pi\)
0.344723 + 0.938704i \(0.387973\pi\)
\(360\) 12.1073 0.638109
\(361\) 21.1674 1.11407
\(362\) −30.2647 −1.59068
\(363\) −26.7978 −1.40652
\(364\) 33.5632 1.75919
\(365\) −0.306248 −0.0160298
\(366\) 17.9050 0.935907
\(367\) 13.0031 0.678757 0.339379 0.940650i \(-0.389783\pi\)
0.339379 + 0.940650i \(0.389783\pi\)
\(368\) 73.1317 3.81225
\(369\) −1.84962 −0.0962876
\(370\) 0.489904 0.0254689
\(371\) 8.96737 0.465563
\(372\) −22.5018 −1.16667
\(373\) −8.17554 −0.423313 −0.211657 0.977344i \(-0.567886\pi\)
−0.211657 + 0.977344i \(0.567886\pi\)
\(374\) −104.541 −5.40571
\(375\) 1.18883 0.0613907
\(376\) 1.97514 0.101860
\(377\) 15.6126 0.804092
\(378\) −14.3275 −0.736925
\(379\) −13.3000 −0.683176 −0.341588 0.939850i \(-0.610965\pi\)
−0.341588 + 0.939850i \(0.610965\pi\)
\(380\) −31.0807 −1.59440
\(381\) 21.6014 1.10667
\(382\) −46.7477 −2.39182
\(383\) −11.6799 −0.596816 −0.298408 0.954438i \(-0.596456\pi\)
−0.298408 + 0.954438i \(0.596456\pi\)
\(384\) −3.93175 −0.200641
\(385\) −5.79150 −0.295162
\(386\) 22.1863 1.12925
\(387\) −5.03603 −0.255996
\(388\) 62.5840 3.17722
\(389\) −1.82009 −0.0922823 −0.0461411 0.998935i \(-0.514692\pi\)
−0.0461411 + 0.998935i \(0.514692\pi\)
\(390\) −21.3786 −1.08255
\(391\) 49.0556 2.48085
\(392\) 7.63051 0.385399
\(393\) −22.8863 −1.15446
\(394\) −26.7582 −1.34806
\(395\) 4.98220 0.250681
\(396\) 45.0648 2.26459
\(397\) −5.10154 −0.256039 −0.128020 0.991772i \(-0.540862\pi\)
−0.128020 + 0.991772i \(0.540862\pi\)
\(398\) 7.58546 0.380225
\(399\) 7.53451 0.377197
\(400\) 10.2415 0.512075
\(401\) −5.52804 −0.276057 −0.138029 0.990428i \(-0.544077\pi\)
−0.138029 + 0.990428i \(0.544077\pi\)
\(402\) −1.51638 −0.0756302
\(403\) −26.4153 −1.31584
\(404\) 89.9343 4.47440
\(405\) 1.72233 0.0855831
\(406\) 5.99402 0.297478
\(407\) 1.07982 0.0535245
\(408\) −62.3187 −3.08523
\(409\) 35.0555 1.73338 0.866691 0.498846i \(-0.166243\pi\)
0.866691 + 0.498846i \(0.166243\pi\)
\(410\) −3.06297 −0.151269
\(411\) 18.2641 0.900904
\(412\) 3.04111 0.149825
\(413\) −2.12258 −0.104445
\(414\) −29.7705 −1.46314
\(415\) −12.3172 −0.604626
\(416\) −79.7262 −3.90890
\(417\) −14.9879 −0.733960
\(418\) −96.4448 −4.71727
\(419\) −24.4471 −1.19432 −0.597159 0.802123i \(-0.703704\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(420\) −5.83004 −0.284477
\(421\) −1.20577 −0.0587657 −0.0293828 0.999568i \(-0.509354\pi\)
−0.0293828 + 0.999568i \(0.509354\pi\)
\(422\) 1.57254 0.0765500
\(423\) −0.410712 −0.0199695
\(424\) −68.4256 −3.32304
\(425\) 6.86984 0.333236
\(426\) −40.3130 −1.95317
\(427\) 5.73197 0.277389
\(428\) −14.1233 −0.682676
\(429\) −47.1215 −2.27505
\(430\) −8.33963 −0.402173
\(431\) −10.5721 −0.509239 −0.254619 0.967041i \(-0.581950\pi\)
−0.254619 + 0.967041i \(0.581950\pi\)
\(432\) 55.8446 2.68683
\(433\) 22.4565 1.07919 0.539596 0.841924i \(-0.318577\pi\)
0.539596 + 0.841924i \(0.318577\pi\)
\(434\) −10.1414 −0.486802
\(435\) −2.71197 −0.130029
\(436\) −84.7201 −4.05736
\(437\) 45.2563 2.16490
\(438\) −0.956628 −0.0457095
\(439\) 11.1113 0.530312 0.265156 0.964206i \(-0.414577\pi\)
0.265156 + 0.964206i \(0.414577\pi\)
\(440\) 44.1921 2.10677
\(441\) −1.58669 −0.0755568
\(442\) −123.540 −5.87620
\(443\) −5.79272 −0.275221 −0.137610 0.990486i \(-0.543942\pi\)
−0.137610 + 0.990486i \(0.543942\pi\)
\(444\) 1.08700 0.0515869
\(445\) −12.0055 −0.569113
\(446\) 65.0232 3.07894
\(447\) −24.2366 −1.14635
\(448\) −10.1255 −0.478386
\(449\) −31.0356 −1.46466 −0.732331 0.680949i \(-0.761568\pi\)
−0.732331 + 0.680949i \(0.761568\pi\)
\(450\) −4.16912 −0.196534
\(451\) −6.75121 −0.317902
\(452\) 87.1541 4.09938
\(453\) −0.373558 −0.0175513
\(454\) 8.69708 0.408174
\(455\) −6.84400 −0.320852
\(456\) −57.4921 −2.69232
\(457\) 34.4713 1.61250 0.806250 0.591574i \(-0.201493\pi\)
0.806250 + 0.591574i \(0.201493\pi\)
\(458\) 2.62755 0.122777
\(459\) 37.4597 1.74847
\(460\) −35.0184 −1.63274
\(461\) −10.6385 −0.495486 −0.247743 0.968826i \(-0.579689\pi\)
−0.247743 + 0.968826i \(0.579689\pi\)
\(462\) −18.0909 −0.841666
\(463\) −5.24396 −0.243707 −0.121854 0.992548i \(-0.538884\pi\)
−0.121854 + 0.992548i \(0.538884\pi\)
\(464\) −23.3631 −1.08460
\(465\) 4.58843 0.212783
\(466\) 73.0958 3.38610
\(467\) 19.1867 0.887856 0.443928 0.896063i \(-0.353585\pi\)
0.443928 + 0.896063i \(0.353585\pi\)
\(468\) 53.2545 2.46169
\(469\) −0.485444 −0.0224157
\(470\) −0.680136 −0.0313723
\(471\) 8.61236 0.396836
\(472\) 16.1964 0.745498
\(473\) −18.3817 −0.845192
\(474\) 15.5629 0.714828
\(475\) 6.33777 0.290797
\(476\) −33.6899 −1.54418
\(477\) 14.2285 0.651476
\(478\) −49.8916 −2.28199
\(479\) −31.9983 −1.46204 −0.731019 0.682357i \(-0.760955\pi\)
−0.731019 + 0.682357i \(0.760955\pi\)
\(480\) 13.8487 0.632104
\(481\) 1.27605 0.0581831
\(482\) −22.4013 −1.02035
\(483\) 8.48908 0.386266
\(484\) 110.544 5.02473
\(485\) −12.7617 −0.579481
\(486\) −37.6024 −1.70568
\(487\) −41.0140 −1.85852 −0.929262 0.369423i \(-0.879555\pi\)
−0.929262 + 0.369423i \(0.879555\pi\)
\(488\) −43.7378 −1.97992
\(489\) −17.7303 −0.801793
\(490\) −2.62755 −0.118701
\(491\) 7.58060 0.342108 0.171054 0.985262i \(-0.445283\pi\)
0.171054 + 0.985262i \(0.445283\pi\)
\(492\) −6.79614 −0.306394
\(493\) −15.6716 −0.705813
\(494\) −113.972 −5.12784
\(495\) −9.18933 −0.413030
\(496\) 39.5284 1.77488
\(497\) −12.9055 −0.578892
\(498\) −38.4752 −1.72411
\(499\) −24.2316 −1.08476 −0.542378 0.840135i \(-0.682476\pi\)
−0.542378 + 0.840135i \(0.682476\pi\)
\(500\) −4.90404 −0.219315
\(501\) 5.48193 0.244915
\(502\) 19.8431 0.885641
\(503\) −37.6231 −1.67753 −0.838765 0.544493i \(-0.816722\pi\)
−0.838765 + 0.544493i \(0.816722\pi\)
\(504\) 12.1073 0.539301
\(505\) −18.3388 −0.816068
\(506\) −108.664 −4.83069
\(507\) −40.2303 −1.78669
\(508\) −89.1082 −3.95354
\(509\) 26.2876 1.16518 0.582588 0.812768i \(-0.302040\pi\)
0.582588 + 0.812768i \(0.302040\pi\)
\(510\) 21.4593 0.950235
\(511\) −0.306248 −0.0135476
\(512\) −36.9919 −1.63482
\(513\) 34.5585 1.52579
\(514\) −55.0356 −2.42752
\(515\) −0.620124 −0.0273259
\(516\) −18.5041 −0.814596
\(517\) −1.49912 −0.0659310
\(518\) 0.489904 0.0215251
\(519\) 12.2466 0.537568
\(520\) 52.2232 2.29014
\(521\) 10.4956 0.459822 0.229911 0.973212i \(-0.426157\pi\)
0.229911 + 0.973212i \(0.426157\pi\)
\(522\) 9.51067 0.416271
\(523\) −21.1160 −0.923340 −0.461670 0.887052i \(-0.652750\pi\)
−0.461670 + 0.887052i \(0.652750\pi\)
\(524\) 94.4083 4.12424
\(525\) 1.18883 0.0518846
\(526\) 18.6140 0.811608
\(527\) 26.5150 1.15501
\(528\) 70.5135 3.06871
\(529\) 27.9900 1.21695
\(530\) 23.5622 1.02348
\(531\) −3.36788 −0.146154
\(532\) −31.0807 −1.34752
\(533\) −7.97812 −0.345571
\(534\) −37.5015 −1.62285
\(535\) 2.87994 0.124511
\(536\) 3.70418 0.159996
\(537\) −22.4509 −0.968829
\(538\) −66.0732 −2.84862
\(539\) −5.79150 −0.249457
\(540\) −26.7406 −1.15073
\(541\) −24.1894 −1.03998 −0.519992 0.854171i \(-0.674065\pi\)
−0.519992 + 0.854171i \(0.674065\pi\)
\(542\) −4.94273 −0.212308
\(543\) 13.6931 0.587628
\(544\) 80.0271 3.43113
\(545\) 17.2756 0.740004
\(546\) −21.3786 −0.914921
\(547\) −39.8056 −1.70197 −0.850983 0.525194i \(-0.823993\pi\)
−0.850983 + 0.525194i \(0.823993\pi\)
\(548\) −75.3416 −3.21843
\(549\) 9.09487 0.388160
\(550\) −15.2175 −0.648875
\(551\) −14.4578 −0.615924
\(552\) −64.7760 −2.75705
\(553\) 4.98220 0.211864
\(554\) −36.0400 −1.53119
\(555\) −0.221655 −0.00940873
\(556\) 61.8266 2.62203
\(557\) 29.2654 1.24002 0.620008 0.784596i \(-0.287130\pi\)
0.620008 + 0.784596i \(0.287130\pi\)
\(558\) −16.0913 −0.681198
\(559\) −21.7223 −0.918754
\(560\) 10.2415 0.432782
\(561\) 47.2994 1.99698
\(562\) −35.0972 −1.48049
\(563\) −24.6297 −1.03802 −0.519010 0.854768i \(-0.673699\pi\)
−0.519010 + 0.854768i \(0.673699\pi\)
\(564\) −1.50909 −0.0635443
\(565\) −17.7719 −0.747670
\(566\) 37.2536 1.56588
\(567\) 1.72233 0.0723309
\(568\) 98.4757 4.13195
\(569\) 37.1633 1.55797 0.778984 0.627043i \(-0.215735\pi\)
0.778984 + 0.627043i \(0.215735\pi\)
\(570\) 19.7973 0.829219
\(571\) 5.05955 0.211736 0.105868 0.994380i \(-0.466238\pi\)
0.105868 + 0.994380i \(0.466238\pi\)
\(572\) 194.381 8.12749
\(573\) 21.1508 0.883588
\(574\) −3.06297 −0.127846
\(575\) 7.14073 0.297789
\(576\) −16.0661 −0.669421
\(577\) −8.43986 −0.351356 −0.175678 0.984448i \(-0.556212\pi\)
−0.175678 + 0.984448i \(0.556212\pi\)
\(578\) 79.3380 3.30003
\(579\) −10.0381 −0.417169
\(580\) 11.1872 0.464522
\(581\) −12.3172 −0.511003
\(582\) −39.8639 −1.65241
\(583\) 51.9345 2.15091
\(584\) 2.33683 0.0966987
\(585\) −10.8593 −0.448978
\(586\) 37.6641 1.55589
\(587\) 9.62193 0.397140 0.198570 0.980087i \(-0.436370\pi\)
0.198570 + 0.980087i \(0.436370\pi\)
\(588\) −5.83004 −0.240427
\(589\) 24.4615 1.00792
\(590\) −5.57719 −0.229609
\(591\) 12.1066 0.498001
\(592\) −1.90951 −0.0784805
\(593\) 41.5647 1.70686 0.853429 0.521209i \(-0.174519\pi\)
0.853429 + 0.521209i \(0.174519\pi\)
\(594\) −82.9775 −3.40461
\(595\) 6.86984 0.281636
\(596\) 99.9787 4.09529
\(597\) −3.43201 −0.140463
\(598\) −128.411 −5.25114
\(599\) 6.04850 0.247135 0.123568 0.992336i \(-0.460566\pi\)
0.123568 + 0.992336i \(0.460566\pi\)
\(600\) −9.07135 −0.370336
\(601\) 2.44556 0.0997566 0.0498783 0.998755i \(-0.484117\pi\)
0.0498783 + 0.998755i \(0.484117\pi\)
\(602\) −8.33963 −0.339898
\(603\) −0.770250 −0.0313670
\(604\) 1.54097 0.0627010
\(605\) −22.5414 −0.916440
\(606\) −57.2851 −2.32705
\(607\) 46.2642 1.87781 0.938903 0.344183i \(-0.111844\pi\)
0.938903 + 0.344183i \(0.111844\pi\)
\(608\) 73.8291 2.99417
\(609\) −2.71197 −0.109895
\(610\) 15.0610 0.609804
\(611\) −1.77155 −0.0716694
\(612\) −53.4556 −2.16081
\(613\) −24.9488 −1.00767 −0.503837 0.863799i \(-0.668079\pi\)
−0.503837 + 0.863799i \(0.668079\pi\)
\(614\) 12.6745 0.511502
\(615\) 1.38583 0.0558819
\(616\) 44.1921 1.78055
\(617\) −17.2331 −0.693777 −0.346889 0.937906i \(-0.612762\pi\)
−0.346889 + 0.937906i \(0.612762\pi\)
\(618\) −1.93708 −0.0779210
\(619\) 0.861823 0.0346396 0.0173198 0.999850i \(-0.494487\pi\)
0.0173198 + 0.999850i \(0.494487\pi\)
\(620\) −18.9278 −0.760158
\(621\) 38.9368 1.56248
\(622\) 22.3583 0.896488
\(623\) −12.0055 −0.480988
\(624\) 83.3281 3.33580
\(625\) 1.00000 0.0400000
\(626\) −12.3863 −0.495058
\(627\) 43.6361 1.74266
\(628\) −35.5269 −1.41768
\(629\) −1.28087 −0.0510717
\(630\) −4.16912 −0.166102
\(631\) 22.8181 0.908373 0.454187 0.890907i \(-0.349930\pi\)
0.454187 + 0.890907i \(0.349930\pi\)
\(632\) −38.0167 −1.51222
\(633\) −0.711489 −0.0282791
\(634\) 33.6713 1.33726
\(635\) 18.1704 0.721070
\(636\) 52.2802 2.07304
\(637\) −6.84400 −0.271169
\(638\) 34.7143 1.37435
\(639\) −20.4771 −0.810062
\(640\) −3.30725 −0.130731
\(641\) −5.11840 −0.202165 −0.101082 0.994878i \(-0.532231\pi\)
−0.101082 + 0.994878i \(0.532231\pi\)
\(642\) 8.99607 0.355046
\(643\) 44.7953 1.76656 0.883278 0.468850i \(-0.155332\pi\)
0.883278 + 0.468850i \(0.155332\pi\)
\(644\) −35.0184 −1.37992
\(645\) 3.77323 0.148571
\(646\) 114.402 4.50110
\(647\) −14.6779 −0.577049 −0.288525 0.957472i \(-0.593165\pi\)
−0.288525 + 0.957472i \(0.593165\pi\)
\(648\) −13.1422 −0.516275
\(649\) −12.2929 −0.482539
\(650\) −17.9830 −0.705350
\(651\) 4.58843 0.179835
\(652\) 73.1396 2.86437
\(653\) 10.9428 0.428226 0.214113 0.976809i \(-0.431314\pi\)
0.214113 + 0.976809i \(0.431314\pi\)
\(654\) 53.9638 2.11015
\(655\) −19.2511 −0.752204
\(656\) 11.9386 0.466125
\(657\) −0.485922 −0.0189576
\(658\) −0.680136 −0.0265145
\(659\) −46.7360 −1.82058 −0.910288 0.413975i \(-0.864140\pi\)
−0.910288 + 0.413975i \(0.864140\pi\)
\(660\) −33.7647 −1.31429
\(661\) 43.9986 1.71135 0.855674 0.517515i \(-0.173143\pi\)
0.855674 + 0.517515i \(0.173143\pi\)
\(662\) 29.1886 1.13445
\(663\) 55.8952 2.17079
\(664\) 93.9863 3.64738
\(665\) 6.33777 0.245768
\(666\) 0.777327 0.0301208
\(667\) −16.2895 −0.630734
\(668\) −22.6136 −0.874945
\(669\) −29.4195 −1.13742
\(670\) −1.27553 −0.0492780
\(671\) 33.1967 1.28154
\(672\) 13.8487 0.534225
\(673\) 48.7221 1.87810 0.939049 0.343784i \(-0.111709\pi\)
0.939049 + 0.343784i \(0.111709\pi\)
\(674\) 27.2893 1.05115
\(675\) 5.45278 0.209878
\(676\) 165.954 6.38285
\(677\) 8.84502 0.339942 0.169971 0.985449i \(-0.445633\pi\)
0.169971 + 0.985449i \(0.445633\pi\)
\(678\) −55.5142 −2.13201
\(679\) −12.7617 −0.489751
\(680\) −52.4203 −2.01023
\(681\) −3.93496 −0.150788
\(682\) −58.7338 −2.24903
\(683\) −25.2971 −0.967968 −0.483984 0.875077i \(-0.660811\pi\)
−0.483984 + 0.875077i \(0.660811\pi\)
\(684\) −49.3155 −1.88562
\(685\) 15.3632 0.586997
\(686\) −2.62755 −0.100320
\(687\) −1.18883 −0.0453565
\(688\) 32.5056 1.23927
\(689\) 61.3727 2.33811
\(690\) 22.3055 0.849156
\(691\) −0.122930 −0.00467648 −0.00233824 0.999997i \(-0.500744\pi\)
−0.00233824 + 0.999997i \(0.500744\pi\)
\(692\) −50.5187 −1.92043
\(693\) −9.18933 −0.349074
\(694\) −29.9256 −1.13596
\(695\) −12.6073 −0.478222
\(696\) 20.6937 0.784393
\(697\) 8.00824 0.303334
\(698\) −65.5129 −2.47970
\(699\) −33.0719 −1.25089
\(700\) −4.90404 −0.185355
\(701\) 47.3854 1.78972 0.894861 0.446344i \(-0.147274\pi\)
0.894861 + 0.446344i \(0.147274\pi\)
\(702\) −98.0572 −3.70093
\(703\) −1.18167 −0.0445675
\(704\) −58.6420 −2.21015
\(705\) 0.307725 0.0115896
\(706\) −69.5392 −2.61714
\(707\) −18.3388 −0.689703
\(708\) −12.3747 −0.465071
\(709\) −39.5547 −1.48551 −0.742753 0.669565i \(-0.766480\pi\)
−0.742753 + 0.669565i \(0.766480\pi\)
\(710\) −33.9100 −1.27262
\(711\) 7.90521 0.296469
\(712\) 91.6078 3.43315
\(713\) 27.5606 1.03215
\(714\) 21.4593 0.803095
\(715\) −39.6370 −1.48234
\(716\) 92.6125 3.46109
\(717\) 22.5733 0.843014
\(718\) 34.3241 1.28096
\(719\) −32.6521 −1.21772 −0.608859 0.793279i \(-0.708372\pi\)
−0.608859 + 0.793279i \(0.708372\pi\)
\(720\) 16.2501 0.605606
\(721\) −0.620124 −0.0230946
\(722\) 55.6184 2.06990
\(723\) 10.1354 0.376940
\(724\) −56.4856 −2.09927
\(725\) −2.28122 −0.0847223
\(726\) −70.4127 −2.61326
\(727\) 27.6870 1.02685 0.513427 0.858134i \(-0.328376\pi\)
0.513427 + 0.858134i \(0.328376\pi\)
\(728\) 52.2232 1.93552
\(729\) 22.1800 0.821482
\(730\) −0.804683 −0.0297827
\(731\) 21.8043 0.806460
\(732\) 33.4176 1.23515
\(733\) −26.3705 −0.974018 −0.487009 0.873397i \(-0.661912\pi\)
−0.487009 + 0.873397i \(0.661912\pi\)
\(734\) 34.1664 1.26110
\(735\) 1.18883 0.0438505
\(736\) 83.1827 3.06616
\(737\) −2.81144 −0.103561
\(738\) −4.85999 −0.178899
\(739\) 16.6013 0.610690 0.305345 0.952242i \(-0.401228\pi\)
0.305345 + 0.952242i \(0.401228\pi\)
\(740\) 0.914351 0.0336122
\(741\) 51.5662 1.89433
\(742\) 23.5622 0.864997
\(743\) 2.68069 0.0983451 0.0491726 0.998790i \(-0.484342\pi\)
0.0491726 + 0.998790i \(0.484342\pi\)
\(744\) −35.0121 −1.28360
\(745\) −20.3870 −0.746922
\(746\) −21.4817 −0.786499
\(747\) −19.5436 −0.715062
\(748\) −195.115 −7.13411
\(749\) 2.87994 0.105231
\(750\) 3.12370 0.114062
\(751\) −14.6552 −0.534777 −0.267389 0.963589i \(-0.586161\pi\)
−0.267389 + 0.963589i \(0.586161\pi\)
\(752\) 2.65099 0.0966716
\(753\) −8.97793 −0.327174
\(754\) 41.0231 1.49397
\(755\) −0.314224 −0.0114358
\(756\) −26.7406 −0.972547
\(757\) 0.542768 0.0197272 0.00986362 0.999951i \(-0.496860\pi\)
0.00986362 + 0.999951i \(0.496860\pi\)
\(758\) −34.9465 −1.26931
\(759\) 49.1645 1.78456
\(760\) −48.3604 −1.75422
\(761\) −27.3323 −0.990796 −0.495398 0.868666i \(-0.664978\pi\)
−0.495398 + 0.868666i \(0.664978\pi\)
\(762\) 56.7589 2.05616
\(763\) 17.2756 0.625418
\(764\) −87.2494 −3.15657
\(765\) 10.9003 0.394102
\(766\) −30.6896 −1.10886
\(767\) −14.5269 −0.524537
\(768\) 13.7441 0.495948
\(769\) 40.9702 1.47742 0.738711 0.674023i \(-0.235435\pi\)
0.738711 + 0.674023i \(0.235435\pi\)
\(770\) −15.2175 −0.548399
\(771\) 24.9007 0.896775
\(772\) 41.4082 1.49032
\(773\) 17.9717 0.646398 0.323199 0.946331i \(-0.395242\pi\)
0.323199 + 0.946331i \(0.395242\pi\)
\(774\) −13.2324 −0.475630
\(775\) 3.85963 0.138642
\(776\) 97.3785 3.49569
\(777\) −0.221655 −0.00795183
\(778\) −4.78239 −0.171457
\(779\) 7.38801 0.264703
\(780\) −39.9008 −1.42868
\(781\) −74.7423 −2.67449
\(782\) 128.896 4.60932
\(783\) −12.4390 −0.444533
\(784\) 10.2415 0.365768
\(785\) 7.24442 0.258565
\(786\) −60.1348 −2.14494
\(787\) −1.49512 −0.0532953 −0.0266476 0.999645i \(-0.508483\pi\)
−0.0266476 + 0.999645i \(0.508483\pi\)
\(788\) −49.9412 −1.77908
\(789\) −8.42182 −0.299825
\(790\) 13.0910 0.465756
\(791\) −17.7719 −0.631896
\(792\) 70.1192 2.49158
\(793\) 39.2296 1.39308
\(794\) −13.4046 −0.475711
\(795\) −10.6606 −0.378094
\(796\) 14.1574 0.501796
\(797\) 14.7465 0.522348 0.261174 0.965292i \(-0.415890\pi\)
0.261174 + 0.965292i \(0.415890\pi\)
\(798\) 19.7973 0.700818
\(799\) 1.77824 0.0629097
\(800\) 11.6491 0.411856
\(801\) −19.0490 −0.673062
\(802\) −14.5252 −0.512903
\(803\) −1.77363 −0.0625902
\(804\) −2.83016 −0.0998120
\(805\) 7.14073 0.251678
\(806\) −69.4077 −2.44478
\(807\) 29.8945 1.05234
\(808\) 139.935 4.92288
\(809\) −20.9984 −0.738266 −0.369133 0.929377i \(-0.620345\pi\)
−0.369133 + 0.929377i \(0.620345\pi\)
\(810\) 4.52550 0.159010
\(811\) −37.2560 −1.30823 −0.654117 0.756394i \(-0.726960\pi\)
−0.654117 + 0.756394i \(0.726960\pi\)
\(812\) 11.1872 0.392593
\(813\) 2.23632 0.0784310
\(814\) 2.83728 0.0994465
\(815\) −14.9142 −0.522420
\(816\) −83.6427 −2.92808
\(817\) 20.1155 0.703754
\(818\) 92.1101 3.22056
\(819\) −10.8593 −0.379456
\(820\) −5.71668 −0.199635
\(821\) 27.1081 0.946078 0.473039 0.881042i \(-0.343157\pi\)
0.473039 + 0.881042i \(0.343157\pi\)
\(822\) 47.9900 1.67384
\(823\) −8.90373 −0.310365 −0.155182 0.987886i \(-0.549597\pi\)
−0.155182 + 0.987886i \(0.549597\pi\)
\(824\) 4.73186 0.164842
\(825\) 6.88508 0.239708
\(826\) −5.57719 −0.194055
\(827\) 10.7227 0.372865 0.186433 0.982468i \(-0.440307\pi\)
0.186433 + 0.982468i \(0.440307\pi\)
\(828\) −55.5634 −1.93096
\(829\) 28.0878 0.975531 0.487766 0.872975i \(-0.337812\pi\)
0.487766 + 0.872975i \(0.337812\pi\)
\(830\) −32.3640 −1.12337
\(831\) 16.3062 0.565655
\(832\) −69.2991 −2.40252
\(833\) 6.86984 0.238026
\(834\) −39.3815 −1.36367
\(835\) 4.61121 0.159578
\(836\) −180.004 −6.22555
\(837\) 21.0457 0.727447
\(838\) −64.2360 −2.21900
\(839\) 0.419278 0.0144751 0.00723754 0.999974i \(-0.497696\pi\)
0.00723754 + 0.999974i \(0.497696\pi\)
\(840\) −9.07135 −0.312991
\(841\) −23.7960 −0.820553
\(842\) −3.16823 −0.109184
\(843\) 15.8796 0.546922
\(844\) 2.93497 0.101026
\(845\) −33.8403 −1.16414
\(846\) −1.07917 −0.0371025
\(847\) −22.5414 −0.774533
\(848\) −91.8393 −3.15377
\(849\) −16.8552 −0.578470
\(850\) 18.0509 0.619139
\(851\) −1.33138 −0.0456391
\(852\) −75.2398 −2.57767
\(853\) 29.8683 1.02267 0.511335 0.859382i \(-0.329151\pi\)
0.511335 + 0.859382i \(0.329151\pi\)
\(854\) 15.0610 0.515378
\(855\) 10.0561 0.343911
\(856\) −21.9754 −0.751103
\(857\) 27.7454 0.947765 0.473883 0.880588i \(-0.342852\pi\)
0.473883 + 0.880588i \(0.342852\pi\)
\(858\) −123.814 −4.22695
\(859\) −40.0095 −1.36511 −0.682554 0.730835i \(-0.739131\pi\)
−0.682554 + 0.730835i \(0.739131\pi\)
\(860\) −15.5650 −0.530762
\(861\) 1.38583 0.0472288
\(862\) −27.7787 −0.946145
\(863\) 37.9907 1.29322 0.646609 0.762822i \(-0.276187\pi\)
0.646609 + 0.762822i \(0.276187\pi\)
\(864\) 63.5198 2.16099
\(865\) 10.3015 0.350260
\(866\) 59.0058 2.00510
\(867\) −35.8962 −1.21910
\(868\) −18.9278 −0.642451
\(869\) 28.8544 0.978817
\(870\) −7.12584 −0.241589
\(871\) −3.32238 −0.112574
\(872\) −131.821 −4.46404
\(873\) −20.2490 −0.685323
\(874\) 118.913 4.02230
\(875\) 1.00000 0.0338062
\(876\) −1.78544 −0.0603244
\(877\) 21.3492 0.720913 0.360456 0.932776i \(-0.382621\pi\)
0.360456 + 0.932776i \(0.382621\pi\)
\(878\) 29.1955 0.985299
\(879\) −17.0410 −0.574778
\(880\) 59.3136 1.99946
\(881\) 6.33071 0.213287 0.106644 0.994297i \(-0.465990\pi\)
0.106644 + 0.994297i \(0.465990\pi\)
\(882\) −4.16912 −0.140382
\(883\) 22.9572 0.772573 0.386286 0.922379i \(-0.373758\pi\)
0.386286 + 0.922379i \(0.373758\pi\)
\(884\) −230.574 −7.75504
\(885\) 2.52338 0.0848224
\(886\) −15.2207 −0.511349
\(887\) 30.6220 1.02819 0.514093 0.857734i \(-0.328129\pi\)
0.514093 + 0.857734i \(0.328129\pi\)
\(888\) 1.69134 0.0567577
\(889\) 18.1704 0.609415
\(890\) −31.5450 −1.05739
\(891\) 9.97485 0.334170
\(892\) 121.359 4.06338
\(893\) 1.64052 0.0548978
\(894\) −63.6830 −2.12988
\(895\) −18.8850 −0.631255
\(896\) −3.30725 −0.110488
\(897\) 58.0993 1.93988
\(898\) −81.5478 −2.72128
\(899\) −8.80466 −0.293652
\(900\) −7.78120 −0.259373
\(901\) −61.6043 −2.05234
\(902\) −17.7392 −0.590649
\(903\) 3.77323 0.125565
\(904\) 135.609 4.51028
\(905\) 11.5182 0.382878
\(906\) −0.981543 −0.0326096
\(907\) 41.9465 1.39281 0.696405 0.717649i \(-0.254782\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(908\) 16.2321 0.538682
\(909\) −29.0981 −0.965123
\(910\) −17.9830 −0.596130
\(911\) 20.7130 0.686252 0.343126 0.939289i \(-0.388514\pi\)
0.343126 + 0.939289i \(0.388514\pi\)
\(912\) −77.1646 −2.55518
\(913\) −71.3349 −2.36084
\(914\) 90.5753 2.99596
\(915\) −6.81431 −0.225274
\(916\) 4.90404 0.162034
\(917\) −19.2511 −0.635729
\(918\) 98.4274 3.24859
\(919\) −16.2776 −0.536948 −0.268474 0.963287i \(-0.586519\pi\)
−0.268474 + 0.963287i \(0.586519\pi\)
\(920\) −54.4874 −1.79640
\(921\) −5.73453 −0.188959
\(922\) −27.9533 −0.920594
\(923\) −88.3254 −2.90727
\(924\) −33.7647 −1.11078
\(925\) −0.186449 −0.00613040
\(926\) −13.7788 −0.452799
\(927\) −0.983947 −0.0323171
\(928\) −26.5740 −0.872335
\(929\) −11.9753 −0.392896 −0.196448 0.980514i \(-0.562941\pi\)
−0.196448 + 0.980514i \(0.562941\pi\)
\(930\) 12.0563 0.395343
\(931\) 6.33777 0.207712
\(932\) 136.425 4.46875
\(933\) −10.1159 −0.331181
\(934\) 50.4141 1.64960
\(935\) 39.7866 1.30116
\(936\) 82.8622 2.70844
\(937\) −14.1989 −0.463856 −0.231928 0.972733i \(-0.574503\pi\)
−0.231928 + 0.972733i \(0.574503\pi\)
\(938\) −1.27553 −0.0416475
\(939\) 5.60415 0.182884
\(940\) −1.26940 −0.0414032
\(941\) −28.5715 −0.931405 −0.465703 0.884941i \(-0.654198\pi\)
−0.465703 + 0.884941i \(0.654198\pi\)
\(942\) 22.6294 0.737307
\(943\) 8.32402 0.271067
\(944\) 21.7384 0.707524
\(945\) 5.45278 0.177379
\(946\) −48.2989 −1.57033
\(947\) 54.1215 1.75871 0.879356 0.476164i \(-0.157973\pi\)
0.879356 + 0.476164i \(0.157973\pi\)
\(948\) 29.0464 0.943384
\(949\) −2.09596 −0.0680378
\(950\) 16.6528 0.540289
\(951\) −15.2344 −0.494010
\(952\) −52.4203 −1.69895
\(953\) 37.0139 1.19900 0.599499 0.800375i \(-0.295366\pi\)
0.599499 + 0.800375i \(0.295366\pi\)
\(954\) 37.3860 1.21042
\(955\) 17.7914 0.575715
\(956\) −93.1172 −3.01162
\(957\) −15.7064 −0.507715
\(958\) −84.0772 −2.71641
\(959\) 15.3632 0.496103
\(960\) 12.0375 0.388508
\(961\) −16.1032 −0.519459
\(962\) 3.35290 0.108102
\(963\) 4.56958 0.147253
\(964\) −41.8096 −1.34660
\(965\) −8.44371 −0.271813
\(966\) 22.3055 0.717668
\(967\) −15.1097 −0.485896 −0.242948 0.970039i \(-0.578114\pi\)
−0.242948 + 0.970039i \(0.578114\pi\)
\(968\) 172.003 5.52837
\(969\) −51.7608 −1.66280
\(970\) −33.5321 −1.07665
\(971\) 33.9003 1.08791 0.543956 0.839114i \(-0.316926\pi\)
0.543956 + 0.839114i \(0.316926\pi\)
\(972\) −70.1806 −2.25105
\(973\) −12.6073 −0.404171
\(974\) −107.767 −3.45306
\(975\) 8.13632 0.260571
\(976\) −58.7039 −1.87907
\(977\) 40.5575 1.29755 0.648774 0.760981i \(-0.275282\pi\)
0.648774 + 0.760981i \(0.275282\pi\)
\(978\) −46.5874 −1.48970
\(979\) −69.5296 −2.22217
\(980\) −4.90404 −0.156654
\(981\) 27.4110 0.875167
\(982\) 19.9184 0.635623
\(983\) −33.5434 −1.06987 −0.534934 0.844894i \(-0.679664\pi\)
−0.534934 + 0.844894i \(0.679664\pi\)
\(984\) −10.5746 −0.337105
\(985\) 10.1837 0.324479
\(986\) −41.1779 −1.31137
\(987\) 0.307725 0.00979499
\(988\) −212.716 −6.76740
\(989\) 22.6640 0.720675
\(990\) −24.1454 −0.767393
\(991\) 40.6860 1.29243 0.646217 0.763154i \(-0.276350\pi\)
0.646217 + 0.763154i \(0.276350\pi\)
\(992\) 44.9611 1.42752
\(993\) −13.2063 −0.419088
\(994\) −33.9100 −1.07556
\(995\) −2.88689 −0.0915206
\(996\) −71.8097 −2.27538
\(997\) 17.4231 0.551795 0.275898 0.961187i \(-0.411025\pi\)
0.275898 + 0.961187i \(0.411025\pi\)
\(998\) −63.6698 −2.01543
\(999\) −1.01666 −0.0321658
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 \(a_p\))