Properties

Label 8018.2.a.j.1.13
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 1.13
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +2.14418 q^{10} -4.14345 q^{11} -1.46195 q^{12} +5.72765 q^{13} +2.84565 q^{14} -3.13468 q^{15} +1.00000 q^{16} +0.828433 q^{17} -0.862709 q^{18} -1.00000 q^{19} +2.14418 q^{20} -4.16019 q^{21} -4.14345 q^{22} +4.11173 q^{23} -1.46195 q^{24} -0.402477 q^{25} +5.72765 q^{26} +5.64708 q^{27} +2.84565 q^{28} +5.07697 q^{29} -3.13468 q^{30} +3.20401 q^{31} +1.00000 q^{32} +6.05751 q^{33} +0.828433 q^{34} +6.10160 q^{35} -0.862709 q^{36} -1.30300 q^{37} -1.00000 q^{38} -8.37352 q^{39} +2.14418 q^{40} -9.49007 q^{41} -4.16019 q^{42} +1.76733 q^{43} -4.14345 q^{44} -1.84981 q^{45} +4.11173 q^{46} +6.02255 q^{47} -1.46195 q^{48} +1.09774 q^{49} -0.402477 q^{50} -1.21113 q^{51} +5.72765 q^{52} -9.71241 q^{53} +5.64708 q^{54} -8.88433 q^{55} +2.84565 q^{56} +1.46195 q^{57} +5.07697 q^{58} -1.16819 q^{59} -3.13468 q^{60} -0.741864 q^{61} +3.20401 q^{62} -2.45497 q^{63} +1.00000 q^{64} +12.2811 q^{65} +6.05751 q^{66} +12.6141 q^{67} +0.828433 q^{68} -6.01113 q^{69} +6.10160 q^{70} +1.20025 q^{71} -0.862709 q^{72} +14.2635 q^{73} -1.30300 q^{74} +0.588401 q^{75} -1.00000 q^{76} -11.7908 q^{77} -8.37352 q^{78} +0.0154584 q^{79} +2.14418 q^{80} -5.66760 q^{81} -9.49007 q^{82} +5.25605 q^{83} -4.16019 q^{84} +1.77631 q^{85} +1.76733 q^{86} -7.42227 q^{87} -4.14345 q^{88} +15.8470 q^{89} -1.84981 q^{90} +16.2989 q^{91} +4.11173 q^{92} -4.68409 q^{93} +6.02255 q^{94} -2.14418 q^{95} -1.46195 q^{96} -9.00620 q^{97} +1.09774 q^{98} +3.57460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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
\(3\) −1.46195 −0.844056 −0.422028 0.906583i \(-0.638682\pi\)
−0.422028 + 0.906583i \(0.638682\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.14418 0.958908 0.479454 0.877567i \(-0.340835\pi\)
0.479454 + 0.877567i \(0.340835\pi\)
\(6\) −1.46195 −0.596838
\(7\) 2.84565 1.07556 0.537778 0.843087i \(-0.319264\pi\)
0.537778 + 0.843087i \(0.319264\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.862709 −0.287570
\(10\) 2.14418 0.678050
\(11\) −4.14345 −1.24930 −0.624649 0.780905i \(-0.714758\pi\)
−0.624649 + 0.780905i \(0.714758\pi\)
\(12\) −1.46195 −0.422028
\(13\) 5.72765 1.58856 0.794282 0.607549i \(-0.207847\pi\)
0.794282 + 0.607549i \(0.207847\pi\)
\(14\) 2.84565 0.760533
\(15\) −3.13468 −0.809372
\(16\) 1.00000 0.250000
\(17\) 0.828433 0.200925 0.100462 0.994941i \(-0.467968\pi\)
0.100462 + 0.994941i \(0.467968\pi\)
\(18\) −0.862709 −0.203343
\(19\) −1.00000 −0.229416
\(20\) 2.14418 0.479454
\(21\) −4.16019 −0.907829
\(22\) −4.14345 −0.883388
\(23\) 4.11173 0.857355 0.428678 0.903458i \(-0.358980\pi\)
0.428678 + 0.903458i \(0.358980\pi\)
\(24\) −1.46195 −0.298419
\(25\) −0.402477 −0.0804955
\(26\) 5.72765 1.12328
\(27\) 5.64708 1.08678
\(28\) 2.84565 0.537778
\(29\) 5.07697 0.942770 0.471385 0.881928i \(-0.343754\pi\)
0.471385 + 0.881928i \(0.343754\pi\)
\(30\) −3.13468 −0.572312
\(31\) 3.20401 0.575456 0.287728 0.957712i \(-0.407100\pi\)
0.287728 + 0.957712i \(0.407100\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.05751 1.05448
\(34\) 0.828433 0.142075
\(35\) 6.10160 1.03136
\(36\) −0.862709 −0.143785
\(37\) −1.30300 −0.214211 −0.107106 0.994248i \(-0.534158\pi\)
−0.107106 + 0.994248i \(0.534158\pi\)
\(38\) −1.00000 −0.162221
\(39\) −8.37352 −1.34084
\(40\) 2.14418 0.339025
\(41\) −9.49007 −1.48210 −0.741050 0.671450i \(-0.765672\pi\)
−0.741050 + 0.671450i \(0.765672\pi\)
\(42\) −4.16019 −0.641932
\(43\) 1.76733 0.269515 0.134758 0.990879i \(-0.456974\pi\)
0.134758 + 0.990879i \(0.456974\pi\)
\(44\) −4.14345 −0.624649
\(45\) −1.84981 −0.275753
\(46\) 4.11173 0.606242
\(47\) 6.02255 0.878479 0.439239 0.898370i \(-0.355248\pi\)
0.439239 + 0.898370i \(0.355248\pi\)
\(48\) −1.46195 −0.211014
\(49\) 1.09774 0.156820
\(50\) −0.402477 −0.0569189
\(51\) −1.21113 −0.169592
\(52\) 5.72765 0.794282
\(53\) −9.71241 −1.33410 −0.667051 0.745012i \(-0.732444\pi\)
−0.667051 + 0.745012i \(0.732444\pi\)
\(54\) 5.64708 0.768470
\(55\) −8.88433 −1.19796
\(56\) 2.84565 0.380266
\(57\) 1.46195 0.193640
\(58\) 5.07697 0.666639
\(59\) −1.16819 −0.152086 −0.0760430 0.997105i \(-0.524229\pi\)
−0.0760430 + 0.997105i \(0.524229\pi\)
\(60\) −3.13468 −0.404686
\(61\) −0.741864 −0.0949860 −0.0474930 0.998872i \(-0.515123\pi\)
−0.0474930 + 0.998872i \(0.515123\pi\)
\(62\) 3.20401 0.406909
\(63\) −2.45497 −0.309297
\(64\) 1.00000 0.125000
\(65\) 12.2811 1.52329
\(66\) 6.05751 0.745628
\(67\) 12.6141 1.54106 0.770528 0.637406i \(-0.219992\pi\)
0.770528 + 0.637406i \(0.219992\pi\)
\(68\) 0.828433 0.100462
\(69\) −6.01113 −0.723656
\(70\) 6.10160 0.729281
\(71\) 1.20025 0.142444 0.0712219 0.997460i \(-0.477310\pi\)
0.0712219 + 0.997460i \(0.477310\pi\)
\(72\) −0.862709 −0.101671
\(73\) 14.2635 1.66942 0.834710 0.550690i \(-0.185635\pi\)
0.834710 + 0.550690i \(0.185635\pi\)
\(74\) −1.30300 −0.151470
\(75\) 0.588401 0.0679427
\(76\) −1.00000 −0.114708
\(77\) −11.7908 −1.34369
\(78\) −8.37352 −0.948115
\(79\) 0.0154584 0.00173920 0.000869600 1.00000i \(-0.499723\pi\)
0.000869600 1.00000i \(0.499723\pi\)
\(80\) 2.14418 0.239727
\(81\) −5.66760 −0.629734
\(82\) −9.49007 −1.04800
\(83\) 5.25605 0.576926 0.288463 0.957491i \(-0.406856\pi\)
0.288463 + 0.957491i \(0.406856\pi\)
\(84\) −4.16019 −0.453914
\(85\) 1.77631 0.192668
\(86\) 1.76733 0.190576
\(87\) −7.42227 −0.795750
\(88\) −4.14345 −0.441694
\(89\) 15.8470 1.67978 0.839888 0.542759i \(-0.182620\pi\)
0.839888 + 0.542759i \(0.182620\pi\)
\(90\) −1.84981 −0.194987
\(91\) 16.2989 1.70859
\(92\) 4.11173 0.428678
\(93\) −4.68409 −0.485717
\(94\) 6.02255 0.621178
\(95\) −2.14418 −0.219989
\(96\) −1.46195 −0.149209
\(97\) −9.00620 −0.914441 −0.457221 0.889353i \(-0.651155\pi\)
−0.457221 + 0.889353i \(0.651155\pi\)
\(98\) 1.09774 0.110888
\(99\) 3.57460 0.359261
\(100\) −0.402477 −0.0402477
\(101\) 9.96408 0.991464 0.495732 0.868476i \(-0.334900\pi\)
0.495732 + 0.868476i \(0.334900\pi\)
\(102\) −1.21113 −0.119919
\(103\) −7.91932 −0.780313 −0.390157 0.920748i \(-0.627579\pi\)
−0.390157 + 0.920748i \(0.627579\pi\)
\(104\) 5.72765 0.561642
\(105\) −8.92022 −0.870524
\(106\) −9.71241 −0.943353
\(107\) −19.5270 −1.88775 −0.943875 0.330302i \(-0.892849\pi\)
−0.943875 + 0.330302i \(0.892849\pi\)
\(108\) 5.64708 0.543390
\(109\) 2.14391 0.205349 0.102674 0.994715i \(-0.467260\pi\)
0.102674 + 0.994715i \(0.467260\pi\)
\(110\) −8.88433 −0.847087
\(111\) 1.90491 0.180806
\(112\) 2.84565 0.268889
\(113\) 17.2207 1.61999 0.809993 0.586440i \(-0.199471\pi\)
0.809993 + 0.586440i \(0.199471\pi\)
\(114\) 1.46195 0.136924
\(115\) 8.81631 0.822125
\(116\) 5.07697 0.471385
\(117\) −4.94130 −0.456823
\(118\) −1.16819 −0.107541
\(119\) 2.35743 0.216106
\(120\) −3.13468 −0.286156
\(121\) 6.16822 0.560747
\(122\) −0.741864 −0.0671652
\(123\) 13.8740 1.25097
\(124\) 3.20401 0.287728
\(125\) −11.5839 −1.03610
\(126\) −2.45497 −0.218706
\(127\) −0.744794 −0.0660897 −0.0330449 0.999454i \(-0.510520\pi\)
−0.0330449 + 0.999454i \(0.510520\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.58374 −0.227486
\(130\) 12.2811 1.07713
\(131\) 0.775074 0.0677185 0.0338592 0.999427i \(-0.489220\pi\)
0.0338592 + 0.999427i \(0.489220\pi\)
\(132\) 6.05751 0.527239
\(133\) −2.84565 −0.246749
\(134\) 12.6141 1.08969
\(135\) 12.1084 1.04212
\(136\) 0.828433 0.0710376
\(137\) −10.8225 −0.924630 −0.462315 0.886716i \(-0.652981\pi\)
−0.462315 + 0.886716i \(0.652981\pi\)
\(138\) −6.01113 −0.511702
\(139\) −5.75291 −0.487955 −0.243978 0.969781i \(-0.578452\pi\)
−0.243978 + 0.969781i \(0.578452\pi\)
\(140\) 6.10160 0.515679
\(141\) −8.80465 −0.741485
\(142\) 1.20025 0.100723
\(143\) −23.7323 −1.98459
\(144\) −0.862709 −0.0718925
\(145\) 10.8860 0.904030
\(146\) 14.2635 1.18046
\(147\) −1.60484 −0.132365
\(148\) −1.30300 −0.107106
\(149\) 17.6403 1.44515 0.722574 0.691294i \(-0.242959\pi\)
0.722574 + 0.691294i \(0.242959\pi\)
\(150\) 0.588401 0.0480427
\(151\) −11.6954 −0.951755 −0.475877 0.879512i \(-0.657869\pi\)
−0.475877 + 0.879512i \(0.657869\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −0.714697 −0.0577798
\(154\) −11.7908 −0.950132
\(155\) 6.86997 0.551810
\(156\) −8.37352 −0.670418
\(157\) 19.0859 1.52322 0.761611 0.648034i \(-0.224409\pi\)
0.761611 + 0.648034i \(0.224409\pi\)
\(158\) 0.0154584 0.00122980
\(159\) 14.1990 1.12606
\(160\) 2.14418 0.169513
\(161\) 11.7006 0.922133
\(162\) −5.66760 −0.445289
\(163\) −4.38341 −0.343335 −0.171668 0.985155i \(-0.554916\pi\)
−0.171668 + 0.985155i \(0.554916\pi\)
\(164\) −9.49007 −0.741050
\(165\) 12.9884 1.01115
\(166\) 5.25605 0.407948
\(167\) 12.6831 0.981444 0.490722 0.871316i \(-0.336733\pi\)
0.490722 + 0.871316i \(0.336733\pi\)
\(168\) −4.16019 −0.320966
\(169\) 19.8060 1.52354
\(170\) 1.77631 0.136237
\(171\) 0.862709 0.0659730
\(172\) 1.76733 0.134758
\(173\) 14.5957 1.10969 0.554846 0.831953i \(-0.312777\pi\)
0.554846 + 0.831953i \(0.312777\pi\)
\(174\) −7.42227 −0.562681
\(175\) −1.14531 −0.0865774
\(176\) −4.14345 −0.312325
\(177\) 1.70784 0.128369
\(178\) 15.8470 1.18778
\(179\) −7.01955 −0.524666 −0.262333 0.964977i \(-0.584492\pi\)
−0.262333 + 0.964977i \(0.584492\pi\)
\(180\) −1.84981 −0.137877
\(181\) 6.98602 0.519267 0.259633 0.965707i \(-0.416398\pi\)
0.259633 + 0.965707i \(0.416398\pi\)
\(182\) 16.2989 1.20815
\(183\) 1.08457 0.0801735
\(184\) 4.11173 0.303121
\(185\) −2.79386 −0.205409
\(186\) −4.68409 −0.343454
\(187\) −3.43258 −0.251015
\(188\) 6.02255 0.439239
\(189\) 16.0696 1.16889
\(190\) −2.14418 −0.155555
\(191\) −4.48856 −0.324781 −0.162391 0.986727i \(-0.551920\pi\)
−0.162391 + 0.986727i \(0.551920\pi\)
\(192\) −1.46195 −0.105507
\(193\) 15.3315 1.10358 0.551791 0.833982i \(-0.313945\pi\)
0.551791 + 0.833982i \(0.313945\pi\)
\(194\) −9.00620 −0.646608
\(195\) −17.9544 −1.28574
\(196\) 1.09774 0.0784099
\(197\) −14.0812 −1.00325 −0.501623 0.865086i \(-0.667264\pi\)
−0.501623 + 0.865086i \(0.667264\pi\)
\(198\) 3.57460 0.254036
\(199\) −7.77841 −0.551397 −0.275699 0.961244i \(-0.588909\pi\)
−0.275699 + 0.961244i \(0.588909\pi\)
\(200\) −0.402477 −0.0284595
\(201\) −18.4411 −1.30074
\(202\) 9.96408 0.701071
\(203\) 14.4473 1.01400
\(204\) −1.21113 −0.0847958
\(205\) −20.3484 −1.42120
\(206\) −7.91932 −0.551765
\(207\) −3.54723 −0.246549
\(208\) 5.72765 0.397141
\(209\) 4.14345 0.286609
\(210\) −8.92022 −0.615554
\(211\) −1.00000 −0.0688428
\(212\) −9.71241 −0.667051
\(213\) −1.75471 −0.120231
\(214\) −19.5270 −1.33484
\(215\) 3.78948 0.258440
\(216\) 5.64708 0.384235
\(217\) 9.11749 0.618935
\(218\) 2.14391 0.145204
\(219\) −20.8525 −1.40908
\(220\) −8.88433 −0.598981
\(221\) 4.74497 0.319182
\(222\) 1.90491 0.127849
\(223\) −25.6890 −1.72026 −0.860130 0.510075i \(-0.829618\pi\)
−0.860130 + 0.510075i \(0.829618\pi\)
\(224\) 2.84565 0.190133
\(225\) 0.347221 0.0231481
\(226\) 17.2207 1.14550
\(227\) −0.630959 −0.0418782 −0.0209391 0.999781i \(-0.506666\pi\)
−0.0209391 + 0.999781i \(0.506666\pi\)
\(228\) 1.46195 0.0968198
\(229\) 15.0811 0.996588 0.498294 0.867008i \(-0.333960\pi\)
0.498294 + 0.867008i \(0.333960\pi\)
\(230\) 8.81631 0.581330
\(231\) 17.2376 1.13415
\(232\) 5.07697 0.333320
\(233\) 9.27718 0.607768 0.303884 0.952709i \(-0.401716\pi\)
0.303884 + 0.952709i \(0.401716\pi\)
\(234\) −4.94130 −0.323023
\(235\) 12.9134 0.842380
\(236\) −1.16819 −0.0760430
\(237\) −0.0225993 −0.00146798
\(238\) 2.35743 0.152810
\(239\) −3.55667 −0.230062 −0.115031 0.993362i \(-0.536697\pi\)
−0.115031 + 0.993362i \(0.536697\pi\)
\(240\) −3.13468 −0.202343
\(241\) 22.0482 1.42025 0.710125 0.704075i \(-0.248638\pi\)
0.710125 + 0.704075i \(0.248638\pi\)
\(242\) 6.16822 0.396508
\(243\) −8.65550 −0.555250
\(244\) −0.741864 −0.0474930
\(245\) 2.35375 0.150376
\(246\) 13.8740 0.884573
\(247\) −5.72765 −0.364442
\(248\) 3.20401 0.203455
\(249\) −7.68406 −0.486958
\(250\) −11.5839 −0.732630
\(251\) −20.7095 −1.30717 −0.653587 0.756851i \(-0.726737\pi\)
−0.653587 + 0.756851i \(0.726737\pi\)
\(252\) −2.45497 −0.154649
\(253\) −17.0368 −1.07109
\(254\) −0.744794 −0.0467325
\(255\) −2.59688 −0.162623
\(256\) 1.00000 0.0625000
\(257\) 27.8267 1.73578 0.867891 0.496754i \(-0.165475\pi\)
0.867891 + 0.496754i \(0.165475\pi\)
\(258\) −2.58374 −0.160857
\(259\) −3.70787 −0.230396
\(260\) 12.2811 0.761643
\(261\) −4.37995 −0.271112
\(262\) 0.775074 0.0478842
\(263\) −25.6234 −1.58001 −0.790003 0.613103i \(-0.789921\pi\)
−0.790003 + 0.613103i \(0.789921\pi\)
\(264\) 6.05751 0.372814
\(265\) −20.8252 −1.27928
\(266\) −2.84565 −0.174478
\(267\) −23.1675 −1.41783
\(268\) 12.6141 0.770528
\(269\) −13.2302 −0.806658 −0.403329 0.915055i \(-0.632147\pi\)
−0.403329 + 0.915055i \(0.632147\pi\)
\(270\) 12.1084 0.736892
\(271\) 16.9638 1.03048 0.515240 0.857046i \(-0.327703\pi\)
0.515240 + 0.857046i \(0.327703\pi\)
\(272\) 0.828433 0.0502311
\(273\) −23.8281 −1.44214
\(274\) −10.8225 −0.653812
\(275\) 1.66765 0.100563
\(276\) −6.01113 −0.361828
\(277\) −5.90568 −0.354838 −0.177419 0.984135i \(-0.556775\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(278\) −5.75291 −0.345037
\(279\) −2.76413 −0.165484
\(280\) 6.10160 0.364640
\(281\) −20.4261 −1.21852 −0.609261 0.792970i \(-0.708534\pi\)
−0.609261 + 0.792970i \(0.708534\pi\)
\(282\) −8.80465 −0.524309
\(283\) 4.60453 0.273711 0.136855 0.990591i \(-0.456300\pi\)
0.136855 + 0.990591i \(0.456300\pi\)
\(284\) 1.20025 0.0712219
\(285\) 3.13468 0.185683
\(286\) −23.7323 −1.40332
\(287\) −27.0054 −1.59408
\(288\) −0.862709 −0.0508356
\(289\) −16.3137 −0.959629
\(290\) 10.8860 0.639245
\(291\) 13.1666 0.771839
\(292\) 14.2635 0.834710
\(293\) −16.3422 −0.954723 −0.477362 0.878707i \(-0.658407\pi\)
−0.477362 + 0.878707i \(0.658407\pi\)
\(294\) −1.60484 −0.0935959
\(295\) −2.50482 −0.145836
\(296\) −1.30300 −0.0757351
\(297\) −23.3984 −1.35771
\(298\) 17.6403 1.02187
\(299\) 23.5506 1.36196
\(300\) 0.588401 0.0339713
\(301\) 5.02920 0.289879
\(302\) −11.6954 −0.672992
\(303\) −14.5670 −0.836851
\(304\) −1.00000 −0.0573539
\(305\) −1.59069 −0.0910828
\(306\) −0.714697 −0.0408565
\(307\) 4.35094 0.248321 0.124161 0.992262i \(-0.460376\pi\)
0.124161 + 0.992262i \(0.460376\pi\)
\(308\) −11.7908 −0.671845
\(309\) 11.5776 0.658628
\(310\) 6.86997 0.390188
\(311\) −1.44045 −0.0816803 −0.0408402 0.999166i \(-0.513003\pi\)
−0.0408402 + 0.999166i \(0.513003\pi\)
\(312\) −8.37352 −0.474057
\(313\) 17.9598 1.01515 0.507575 0.861608i \(-0.330542\pi\)
0.507575 + 0.861608i \(0.330542\pi\)
\(314\) 19.0859 1.07708
\(315\) −5.26391 −0.296588
\(316\) 0.0154584 0.000869600 0
\(317\) 4.35186 0.244425 0.122212 0.992504i \(-0.461001\pi\)
0.122212 + 0.992504i \(0.461001\pi\)
\(318\) 14.1990 0.796242
\(319\) −21.0362 −1.17780
\(320\) 2.14418 0.119863
\(321\) 28.5475 1.59337
\(322\) 11.7006 0.652047
\(323\) −0.828433 −0.0460953
\(324\) −5.66760 −0.314867
\(325\) −2.30525 −0.127872
\(326\) −4.38341 −0.242775
\(327\) −3.13428 −0.173326
\(328\) −9.49007 −0.524001
\(329\) 17.1381 0.944853
\(330\) 12.9884 0.714989
\(331\) 11.8181 0.649582 0.324791 0.945786i \(-0.394706\pi\)
0.324791 + 0.945786i \(0.394706\pi\)
\(332\) 5.25605 0.288463
\(333\) 1.12411 0.0616007
\(334\) 12.6831 0.693986
\(335\) 27.0469 1.47773
\(336\) −4.16019 −0.226957
\(337\) −19.4839 −1.06135 −0.530677 0.847574i \(-0.678062\pi\)
−0.530677 + 0.847574i \(0.678062\pi\)
\(338\) 19.8060 1.07730
\(339\) −25.1757 −1.36736
\(340\) 1.77631 0.0963341
\(341\) −13.2757 −0.718917
\(342\) 0.862709 0.0466500
\(343\) −16.7958 −0.906887
\(344\) 1.76733 0.0952880
\(345\) −12.8890 −0.693919
\(346\) 14.5957 0.784671
\(347\) 10.4554 0.561274 0.280637 0.959814i \(-0.409454\pi\)
0.280637 + 0.959814i \(0.409454\pi\)
\(348\) −7.42227 −0.397875
\(349\) 30.9932 1.65903 0.829515 0.558485i \(-0.188617\pi\)
0.829515 + 0.558485i \(0.188617\pi\)
\(350\) −1.14531 −0.0612194
\(351\) 32.3445 1.72642
\(352\) −4.14345 −0.220847
\(353\) 31.9801 1.70213 0.851064 0.525061i \(-0.175958\pi\)
0.851064 + 0.525061i \(0.175958\pi\)
\(354\) 1.70784 0.0907706
\(355\) 2.57356 0.136590
\(356\) 15.8470 0.839888
\(357\) −3.44644 −0.182405
\(358\) −7.01955 −0.370995
\(359\) 11.4813 0.605958 0.302979 0.952997i \(-0.402019\pi\)
0.302979 + 0.952997i \(0.402019\pi\)
\(360\) −1.84981 −0.0974934
\(361\) 1.00000 0.0526316
\(362\) 6.98602 0.367177
\(363\) −9.01761 −0.473302
\(364\) 16.2989 0.854295
\(365\) 30.5836 1.60082
\(366\) 1.08457 0.0566912
\(367\) 4.21857 0.220207 0.110104 0.993920i \(-0.464882\pi\)
0.110104 + 0.993920i \(0.464882\pi\)
\(368\) 4.11173 0.214339
\(369\) 8.18717 0.426207
\(370\) −2.79386 −0.145246
\(371\) −27.6381 −1.43490
\(372\) −4.68409 −0.242859
\(373\) 18.0156 0.932812 0.466406 0.884571i \(-0.345549\pi\)
0.466406 + 0.884571i \(0.345549\pi\)
\(374\) −3.43258 −0.177494
\(375\) 16.9351 0.874523
\(376\) 6.02255 0.310589
\(377\) 29.0791 1.49765
\(378\) 16.0696 0.826532
\(379\) 11.2182 0.576242 0.288121 0.957594i \(-0.406970\pi\)
0.288121 + 0.957594i \(0.406970\pi\)
\(380\) −2.14418 −0.109994
\(381\) 1.08885 0.0557834
\(382\) −4.48856 −0.229655
\(383\) −1.60731 −0.0821299 −0.0410650 0.999156i \(-0.513075\pi\)
−0.0410650 + 0.999156i \(0.513075\pi\)
\(384\) −1.46195 −0.0746047
\(385\) −25.2817 −1.28848
\(386\) 15.3315 0.780351
\(387\) −1.52469 −0.0775044
\(388\) −9.00620 −0.457221
\(389\) −17.5609 −0.890375 −0.445187 0.895437i \(-0.646863\pi\)
−0.445187 + 0.895437i \(0.646863\pi\)
\(390\) −17.9544 −0.909155
\(391\) 3.40629 0.172264
\(392\) 1.09774 0.0554442
\(393\) −1.13312 −0.0571582
\(394\) −14.0812 −0.709402
\(395\) 0.0331455 0.00166773
\(396\) 3.57460 0.179630
\(397\) −0.150873 −0.00757208 −0.00378604 0.999993i \(-0.501205\pi\)
−0.00378604 + 0.999993i \(0.501205\pi\)
\(398\) −7.77841 −0.389897
\(399\) 4.16019 0.208270
\(400\) −0.402477 −0.0201239
\(401\) −5.06306 −0.252837 −0.126418 0.991977i \(-0.540348\pi\)
−0.126418 + 0.991977i \(0.540348\pi\)
\(402\) −18.4411 −0.919760
\(403\) 18.3514 0.914149
\(404\) 9.96408 0.495732
\(405\) −12.1524 −0.603857
\(406\) 14.4473 0.717007
\(407\) 5.39891 0.267614
\(408\) −1.21113 −0.0599597
\(409\) 29.5594 1.46162 0.730809 0.682581i \(-0.239143\pi\)
0.730809 + 0.682581i \(0.239143\pi\)
\(410\) −20.3484 −1.00494
\(411\) 15.8219 0.780439
\(412\) −7.91932 −0.390157
\(413\) −3.32427 −0.163577
\(414\) −3.54723 −0.174337
\(415\) 11.2699 0.553219
\(416\) 5.72765 0.280821
\(417\) 8.41045 0.411862
\(418\) 4.14345 0.202663
\(419\) −10.8629 −0.530687 −0.265343 0.964154i \(-0.585485\pi\)
−0.265343 + 0.964154i \(0.585485\pi\)
\(420\) −8.92022 −0.435262
\(421\) 20.9345 1.02029 0.510143 0.860090i \(-0.329593\pi\)
0.510143 + 0.860090i \(0.329593\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −5.19571 −0.252624
\(424\) −9.71241 −0.471676
\(425\) −0.333426 −0.0161735
\(426\) −1.75471 −0.0850158
\(427\) −2.11109 −0.102163
\(428\) −19.5270 −0.943875
\(429\) 34.6953 1.67511
\(430\) 3.78948 0.182745
\(431\) −24.5708 −1.18353 −0.591767 0.806109i \(-0.701569\pi\)
−0.591767 + 0.806109i \(0.701569\pi\)
\(432\) 5.64708 0.271695
\(433\) −10.2969 −0.494836 −0.247418 0.968909i \(-0.579582\pi\)
−0.247418 + 0.968909i \(0.579582\pi\)
\(434\) 9.11749 0.437653
\(435\) −15.9147 −0.763051
\(436\) 2.14391 0.102674
\(437\) −4.11173 −0.196691
\(438\) −20.8525 −0.996372
\(439\) 23.3441 1.11415 0.557077 0.830461i \(-0.311923\pi\)
0.557077 + 0.830461i \(0.311923\pi\)
\(440\) −8.88433 −0.423544
\(441\) −0.947029 −0.0450966
\(442\) 4.74497 0.225695
\(443\) −35.5818 −1.69054 −0.845271 0.534338i \(-0.820561\pi\)
−0.845271 + 0.534338i \(0.820561\pi\)
\(444\) 1.90491 0.0904031
\(445\) 33.9788 1.61075
\(446\) −25.6890 −1.21641
\(447\) −25.7892 −1.21979
\(448\) 2.84565 0.134444
\(449\) 25.6489 1.21045 0.605223 0.796056i \(-0.293084\pi\)
0.605223 + 0.796056i \(0.293084\pi\)
\(450\) 0.347221 0.0163682
\(451\) 39.3217 1.85159
\(452\) 17.2207 0.809993
\(453\) 17.0980 0.803334
\(454\) −0.630959 −0.0296124
\(455\) 34.9478 1.63838
\(456\) 1.46195 0.0684620
\(457\) −24.8873 −1.16418 −0.582090 0.813124i \(-0.697765\pi\)
−0.582090 + 0.813124i \(0.697765\pi\)
\(458\) 15.0811 0.704694
\(459\) 4.67823 0.218361
\(460\) 8.81631 0.411062
\(461\) 18.8711 0.878915 0.439457 0.898263i \(-0.355171\pi\)
0.439457 + 0.898263i \(0.355171\pi\)
\(462\) 17.2376 0.801965
\(463\) −4.38457 −0.203768 −0.101884 0.994796i \(-0.532487\pi\)
−0.101884 + 0.994796i \(0.532487\pi\)
\(464\) 5.07697 0.235692
\(465\) −10.0435 −0.465758
\(466\) 9.27718 0.429757
\(467\) −9.98957 −0.462262 −0.231131 0.972923i \(-0.574243\pi\)
−0.231131 + 0.972923i \(0.574243\pi\)
\(468\) −4.94130 −0.228412
\(469\) 35.8953 1.65749
\(470\) 12.9134 0.595653
\(471\) −27.9026 −1.28568
\(472\) −1.16819 −0.0537705
\(473\) −7.32285 −0.336705
\(474\) −0.0225993 −0.00103802
\(475\) 0.402477 0.0184669
\(476\) 2.35743 0.108053
\(477\) 8.37899 0.383648
\(478\) −3.55667 −0.162678
\(479\) 40.2855 1.84069 0.920346 0.391106i \(-0.127907\pi\)
0.920346 + 0.391106i \(0.127907\pi\)
\(480\) −3.13468 −0.143078
\(481\) −7.46311 −0.340288
\(482\) 22.0482 1.00427
\(483\) −17.1056 −0.778332
\(484\) 6.16822 0.280374
\(485\) −19.3109 −0.876865
\(486\) −8.65550 −0.392621
\(487\) 14.0124 0.634964 0.317482 0.948264i \(-0.397163\pi\)
0.317482 + 0.948264i \(0.397163\pi\)
\(488\) −0.741864 −0.0335826
\(489\) 6.40832 0.289794
\(490\) 2.35375 0.106332
\(491\) −12.7909 −0.577243 −0.288622 0.957443i \(-0.593197\pi\)
−0.288622 + 0.957443i \(0.593197\pi\)
\(492\) 13.8740 0.625487
\(493\) 4.20593 0.189426
\(494\) −5.72765 −0.257699
\(495\) 7.66459 0.344498
\(496\) 3.20401 0.143864
\(497\) 3.41550 0.153206
\(498\) −7.68406 −0.344331
\(499\) 2.40267 0.107558 0.0537791 0.998553i \(-0.482873\pi\)
0.0537791 + 0.998553i \(0.482873\pi\)
\(500\) −11.5839 −0.518048
\(501\) −18.5420 −0.828394
\(502\) −20.7095 −0.924312
\(503\) −32.3328 −1.44165 −0.720824 0.693118i \(-0.756237\pi\)
−0.720824 + 0.693118i \(0.756237\pi\)
\(504\) −2.45497 −0.109353
\(505\) 21.3648 0.950722
\(506\) −17.0368 −0.757377
\(507\) −28.9553 −1.28595
\(508\) −0.744794 −0.0330449
\(509\) 30.9450 1.37161 0.685807 0.727783i \(-0.259449\pi\)
0.685807 + 0.727783i \(0.259449\pi\)
\(510\) −2.59688 −0.114992
\(511\) 40.5890 1.79555
\(512\) 1.00000 0.0441942
\(513\) −5.64708 −0.249325
\(514\) 27.8267 1.22738
\(515\) −16.9805 −0.748249
\(516\) −2.58374 −0.113743
\(517\) −24.9542 −1.09748
\(518\) −3.70787 −0.162915
\(519\) −21.3382 −0.936642
\(520\) 12.2811 0.538563
\(521\) 27.0458 1.18490 0.592450 0.805608i \(-0.298161\pi\)
0.592450 + 0.805608i \(0.298161\pi\)
\(522\) −4.37995 −0.191705
\(523\) −12.6584 −0.553514 −0.276757 0.960940i \(-0.589260\pi\)
−0.276757 + 0.960940i \(0.589260\pi\)
\(524\) 0.775074 0.0338592
\(525\) 1.67438 0.0730761
\(526\) −25.6234 −1.11723
\(527\) 2.65430 0.115623
\(528\) 6.05751 0.263619
\(529\) −6.09367 −0.264942
\(530\) −20.8252 −0.904588
\(531\) 1.00781 0.0437353
\(532\) −2.84565 −0.123375
\(533\) −54.3558 −2.35441
\(534\) −23.1675 −1.00255
\(535\) −41.8696 −1.81018
\(536\) 12.6141 0.544846
\(537\) 10.2622 0.442847
\(538\) −13.2302 −0.570393
\(539\) −4.54843 −0.195915
\(540\) 12.1084 0.521061
\(541\) 12.2683 0.527455 0.263727 0.964597i \(-0.415048\pi\)
0.263727 + 0.964597i \(0.415048\pi\)
\(542\) 16.9638 0.728660
\(543\) −10.2132 −0.438290
\(544\) 0.828433 0.0355188
\(545\) 4.59693 0.196911
\(546\) −23.8281 −1.01975
\(547\) −15.9475 −0.681867 −0.340933 0.940087i \(-0.610743\pi\)
−0.340933 + 0.940087i \(0.610743\pi\)
\(548\) −10.8225 −0.462315
\(549\) 0.640013 0.0273151
\(550\) 1.66765 0.0711087
\(551\) −5.07697 −0.216286
\(552\) −6.01113 −0.255851
\(553\) 0.0439891 0.00187061
\(554\) −5.90568 −0.250908
\(555\) 4.08448 0.173377
\(556\) −5.75291 −0.243978
\(557\) −4.10858 −0.174086 −0.0870431 0.996205i \(-0.527742\pi\)
−0.0870431 + 0.996205i \(0.527742\pi\)
\(558\) −2.76413 −0.117015
\(559\) 10.1226 0.428142
\(560\) 6.10160 0.257840
\(561\) 5.01824 0.211870
\(562\) −20.4261 −0.861625
\(563\) 19.4469 0.819591 0.409796 0.912177i \(-0.365600\pi\)
0.409796 + 0.912177i \(0.365600\pi\)
\(564\) −8.80465 −0.370743
\(565\) 36.9243 1.55342
\(566\) 4.60453 0.193543
\(567\) −16.1280 −0.677314
\(568\) 1.20025 0.0503615
\(569\) −27.9325 −1.17099 −0.585496 0.810675i \(-0.699100\pi\)
−0.585496 + 0.810675i \(0.699100\pi\)
\(570\) 3.13468 0.131297
\(571\) 40.9053 1.71184 0.855918 0.517112i \(-0.172993\pi\)
0.855918 + 0.517112i \(0.172993\pi\)
\(572\) −23.7323 −0.992296
\(573\) 6.56204 0.274133
\(574\) −27.0054 −1.12719
\(575\) −1.65488 −0.0690132
\(576\) −0.862709 −0.0359462
\(577\) 29.0254 1.20834 0.604172 0.796854i \(-0.293504\pi\)
0.604172 + 0.796854i \(0.293504\pi\)
\(578\) −16.3137 −0.678560
\(579\) −22.4138 −0.931485
\(580\) 10.8860 0.452015
\(581\) 14.9569 0.620516
\(582\) 13.1666 0.545773
\(583\) 40.2429 1.66669
\(584\) 14.2635 0.590229
\(585\) −10.5950 −0.438051
\(586\) −16.3422 −0.675091
\(587\) −36.9891 −1.52670 −0.763351 0.645984i \(-0.776447\pi\)
−0.763351 + 0.645984i \(0.776447\pi\)
\(588\) −1.60484 −0.0661823
\(589\) −3.20401 −0.132019
\(590\) −2.50482 −0.103122
\(591\) 20.5860 0.846796
\(592\) −1.30300 −0.0535528
\(593\) 14.0042 0.575084 0.287542 0.957768i \(-0.407162\pi\)
0.287542 + 0.957768i \(0.407162\pi\)
\(594\) −23.3984 −0.960049
\(595\) 5.05477 0.207225
\(596\) 17.6403 0.722574
\(597\) 11.3716 0.465410
\(598\) 23.5506 0.963054
\(599\) −21.9668 −0.897540 −0.448770 0.893647i \(-0.648138\pi\)
−0.448770 + 0.893647i \(0.648138\pi\)
\(600\) 0.588401 0.0240214
\(601\) −0.402585 −0.0164218 −0.00821089 0.999966i \(-0.502614\pi\)
−0.00821089 + 0.999966i \(0.502614\pi\)
\(602\) 5.02920 0.204975
\(603\) −10.8823 −0.443161
\(604\) −11.6954 −0.475877
\(605\) 13.2258 0.537705
\(606\) −14.5670 −0.591743
\(607\) −17.8165 −0.723150 −0.361575 0.932343i \(-0.617761\pi\)
−0.361575 + 0.932343i \(0.617761\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −21.1212 −0.855874
\(610\) −1.59069 −0.0644053
\(611\) 34.4950 1.39552
\(612\) −0.714697 −0.0288899
\(613\) 0.241320 0.00974684 0.00487342 0.999988i \(-0.498449\pi\)
0.00487342 + 0.999988i \(0.498449\pi\)
\(614\) 4.35094 0.175590
\(615\) 29.7484 1.19957
\(616\) −11.7908 −0.475066
\(617\) −22.2070 −0.894020 −0.447010 0.894529i \(-0.647511\pi\)
−0.447010 + 0.894529i \(0.647511\pi\)
\(618\) 11.5776 0.465720
\(619\) −43.9613 −1.76695 −0.883476 0.468476i \(-0.844803\pi\)
−0.883476 + 0.468476i \(0.844803\pi\)
\(620\) 6.86997 0.275905
\(621\) 23.2193 0.931757
\(622\) −1.44045 −0.0577567
\(623\) 45.0950 1.80669
\(624\) −8.37352 −0.335209
\(625\) −22.8256 −0.913025
\(626\) 17.9598 0.717819
\(627\) −6.05751 −0.241914
\(628\) 19.0859 0.761611
\(629\) −1.07945 −0.0430403
\(630\) −5.26391 −0.209719
\(631\) 17.9004 0.712603 0.356301 0.934371i \(-0.384038\pi\)
0.356301 + 0.934371i \(0.384038\pi\)
\(632\) 0.0154584 0.000614900 0
\(633\) 1.46195 0.0581072
\(634\) 4.35186 0.172834
\(635\) −1.59697 −0.0633740
\(636\) 14.1990 0.563028
\(637\) 6.28746 0.249118
\(638\) −21.0362 −0.832831
\(639\) −1.03547 −0.0409625
\(640\) 2.14418 0.0847563
\(641\) 19.7232 0.779021 0.389511 0.921022i \(-0.372644\pi\)
0.389511 + 0.921022i \(0.372644\pi\)
\(642\) 28.5475 1.12668
\(643\) 29.3895 1.15901 0.579505 0.814969i \(-0.303246\pi\)
0.579505 + 0.814969i \(0.303246\pi\)
\(644\) 11.7006 0.461067
\(645\) −5.54002 −0.218138
\(646\) −0.828433 −0.0325943
\(647\) −18.7284 −0.736290 −0.368145 0.929768i \(-0.620007\pi\)
−0.368145 + 0.929768i \(0.620007\pi\)
\(648\) −5.66760 −0.222645
\(649\) 4.84036 0.190001
\(650\) −2.30525 −0.0904193
\(651\) −13.3293 −0.522416
\(652\) −4.38341 −0.171668
\(653\) −28.2590 −1.10586 −0.552930 0.833228i \(-0.686490\pi\)
−0.552930 + 0.833228i \(0.686490\pi\)
\(654\) −3.13428 −0.122560
\(655\) 1.66190 0.0649358
\(656\) −9.49007 −0.370525
\(657\) −12.3053 −0.480075
\(658\) 17.1381 0.668112
\(659\) −14.9519 −0.582442 −0.291221 0.956656i \(-0.594061\pi\)
−0.291221 + 0.956656i \(0.594061\pi\)
\(660\) 12.9884 0.505574
\(661\) 33.3340 1.29654 0.648272 0.761409i \(-0.275492\pi\)
0.648272 + 0.761409i \(0.275492\pi\)
\(662\) 11.8181 0.459324
\(663\) −6.93690 −0.269407
\(664\) 5.25605 0.203974
\(665\) −6.10160 −0.236610
\(666\) 1.12411 0.0435583
\(667\) 20.8751 0.808289
\(668\) 12.6831 0.490722
\(669\) 37.5559 1.45200
\(670\) 27.0469 1.04491
\(671\) 3.07388 0.118666
\(672\) −4.16019 −0.160483
\(673\) −15.6909 −0.604839 −0.302419 0.953175i \(-0.597794\pi\)
−0.302419 + 0.953175i \(0.597794\pi\)
\(674\) −19.4839 −0.750490
\(675\) −2.27282 −0.0874809
\(676\) 19.8060 0.761768
\(677\) 2.12121 0.0815246 0.0407623 0.999169i \(-0.487021\pi\)
0.0407623 + 0.999169i \(0.487021\pi\)
\(678\) −25.1757 −0.966868
\(679\) −25.6285 −0.983532
\(680\) 1.77631 0.0681185
\(681\) 0.922429 0.0353476
\(682\) −13.2757 −0.508351
\(683\) 44.9510 1.72000 0.860001 0.510293i \(-0.170463\pi\)
0.860001 + 0.510293i \(0.170463\pi\)
\(684\) 0.862709 0.0329865
\(685\) −23.2055 −0.886635
\(686\) −16.7958 −0.641266
\(687\) −22.0478 −0.841176
\(688\) 1.76733 0.0673788
\(689\) −55.6293 −2.11931
\(690\) −12.8890 −0.490675
\(691\) −30.8647 −1.17415 −0.587074 0.809534i \(-0.699720\pi\)
−0.587074 + 0.809534i \(0.699720\pi\)
\(692\) 14.5957 0.554846
\(693\) 10.1721 0.386405
\(694\) 10.4554 0.396880
\(695\) −12.3353 −0.467904
\(696\) −7.42227 −0.281340
\(697\) −7.86189 −0.297790
\(698\) 30.9932 1.17311
\(699\) −13.5628 −0.512990
\(700\) −1.14531 −0.0432887
\(701\) −13.8059 −0.521441 −0.260721 0.965414i \(-0.583960\pi\)
−0.260721 + 0.965414i \(0.583960\pi\)
\(702\) 32.3445 1.22076
\(703\) 1.30300 0.0491434
\(704\) −4.14345 −0.156162
\(705\) −18.8788 −0.711016
\(706\) 31.9801 1.20359
\(707\) 28.3543 1.06637
\(708\) 1.70784 0.0641845
\(709\) 38.8522 1.45913 0.729563 0.683914i \(-0.239724\pi\)
0.729563 + 0.683914i \(0.239724\pi\)
\(710\) 2.57356 0.0965841
\(711\) −0.0133361 −0.000500142 0
\(712\) 15.8470 0.593891
\(713\) 13.1740 0.493370
\(714\) −3.44644 −0.128980
\(715\) −50.8863 −1.90304
\(716\) −7.01955 −0.262333
\(717\) 5.19967 0.194185
\(718\) 11.4813 0.428477
\(719\) −5.04037 −0.187974 −0.0939870 0.995573i \(-0.529961\pi\)
−0.0939870 + 0.995573i \(0.529961\pi\)
\(720\) −1.84981 −0.0689383
\(721\) −22.5356 −0.839271
\(722\) 1.00000 0.0372161
\(723\) −32.2333 −1.19877
\(724\) 6.98602 0.259633
\(725\) −2.04337 −0.0758887
\(726\) −9.01761 −0.334675
\(727\) 21.3845 0.793106 0.396553 0.918012i \(-0.370206\pi\)
0.396553 + 0.918012i \(0.370206\pi\)
\(728\) 16.2989 0.604077
\(729\) 29.6567 1.09840
\(730\) 30.5836 1.13195
\(731\) 1.46411 0.0541522
\(732\) 1.08457 0.0400867
\(733\) 38.8646 1.43550 0.717748 0.696303i \(-0.245173\pi\)
0.717748 + 0.696303i \(0.245173\pi\)
\(734\) 4.21857 0.155710
\(735\) −3.44106 −0.126926
\(736\) 4.11173 0.151560
\(737\) −52.2659 −1.92524
\(738\) 8.18717 0.301374
\(739\) −13.4327 −0.494129 −0.247064 0.968999i \(-0.579466\pi\)
−0.247064 + 0.968999i \(0.579466\pi\)
\(740\) −2.79386 −0.102704
\(741\) 8.37352 0.307609
\(742\) −27.6381 −1.01463
\(743\) 2.75446 0.101051 0.0505257 0.998723i \(-0.483910\pi\)
0.0505257 + 0.998723i \(0.483910\pi\)
\(744\) −4.68409 −0.171727
\(745\) 37.8240 1.38576
\(746\) 18.0156 0.659598
\(747\) −4.53444 −0.165906
\(748\) −3.43258 −0.125507
\(749\) −55.5672 −2.03038
\(750\) 16.9351 0.618381
\(751\) 33.9990 1.24064 0.620320 0.784349i \(-0.287003\pi\)
0.620320 + 0.784349i \(0.287003\pi\)
\(752\) 6.02255 0.219620
\(753\) 30.2763 1.10333
\(754\) 29.0791 1.05900
\(755\) −25.0770 −0.912645
\(756\) 16.0696 0.584447
\(757\) −22.4250 −0.815049 −0.407524 0.913194i \(-0.633608\pi\)
−0.407524 + 0.913194i \(0.633608\pi\)
\(758\) 11.2182 0.407464
\(759\) 24.9069 0.904062
\(760\) −2.14418 −0.0777777
\(761\) −38.2175 −1.38538 −0.692691 0.721235i \(-0.743575\pi\)
−0.692691 + 0.721235i \(0.743575\pi\)
\(762\) 1.08885 0.0394448
\(763\) 6.10081 0.220864
\(764\) −4.48856 −0.162391
\(765\) −1.53244 −0.0554055
\(766\) −1.60731 −0.0580746
\(767\) −6.69101 −0.241598
\(768\) −1.46195 −0.0527535
\(769\) −18.3195 −0.660618 −0.330309 0.943873i \(-0.607153\pi\)
−0.330309 + 0.943873i \(0.607153\pi\)
\(770\) −25.2817 −0.911090
\(771\) −40.6812 −1.46510
\(772\) 15.3315 0.551791
\(773\) −12.4872 −0.449133 −0.224566 0.974459i \(-0.572097\pi\)
−0.224566 + 0.974459i \(0.572097\pi\)
\(774\) −1.52469 −0.0548039
\(775\) −1.28954 −0.0463216
\(776\) −9.00620 −0.323304
\(777\) 5.42072 0.194467
\(778\) −17.5609 −0.629590
\(779\) 9.49007 0.340017
\(780\) −17.9544 −0.642870
\(781\) −4.97319 −0.177955
\(782\) 3.40629 0.121809
\(783\) 28.6701 1.02458
\(784\) 1.09774 0.0392049
\(785\) 40.9237 1.46063
\(786\) −1.13312 −0.0404169
\(787\) 33.3598 1.18915 0.594575 0.804040i \(-0.297320\pi\)
0.594575 + 0.804040i \(0.297320\pi\)
\(788\) −14.0812 −0.501623
\(789\) 37.4600 1.33361
\(790\) 0.0331455 0.00117927
\(791\) 49.0041 1.74238
\(792\) 3.57460 0.127018
\(793\) −4.24914 −0.150891
\(794\) −0.150873 −0.00535427
\(795\) 30.4453 1.07978
\(796\) −7.77841 −0.275699
\(797\) −19.1245 −0.677424 −0.338712 0.940890i \(-0.609991\pi\)
−0.338712 + 0.940890i \(0.609991\pi\)
\(798\) 4.16019 0.147269
\(799\) 4.98928 0.176508
\(800\) −0.402477 −0.0142297
\(801\) −13.6713 −0.483053
\(802\) −5.06306 −0.178783
\(803\) −59.1003 −2.08560
\(804\) −18.4411 −0.650369
\(805\) 25.0881 0.884241
\(806\) 18.3514 0.646401
\(807\) 19.3418 0.680864
\(808\) 9.96408 0.350535
\(809\) −49.0298 −1.72380 −0.861898 0.507081i \(-0.830725\pi\)
−0.861898 + 0.507081i \(0.830725\pi\)
\(810\) −12.1524 −0.426991
\(811\) 9.58531 0.336586 0.168293 0.985737i \(-0.446175\pi\)
0.168293 + 0.985737i \(0.446175\pi\)
\(812\) 14.4473 0.507001
\(813\) −24.8003 −0.869783
\(814\) 5.39891 0.189232
\(815\) −9.39884 −0.329227
\(816\) −1.21113 −0.0423979
\(817\) −1.76733 −0.0618310
\(818\) 29.5594 1.03352
\(819\) −14.0612 −0.491339
\(820\) −20.3484 −0.710599
\(821\) 25.8400 0.901823 0.450912 0.892569i \(-0.351099\pi\)
0.450912 + 0.892569i \(0.351099\pi\)
\(822\) 15.8219 0.551854
\(823\) −22.3393 −0.778700 −0.389350 0.921090i \(-0.627300\pi\)
−0.389350 + 0.921090i \(0.627300\pi\)
\(824\) −7.91932 −0.275882
\(825\) −2.43801 −0.0848807
\(826\) −3.32427 −0.115666
\(827\) 12.8864 0.448104 0.224052 0.974577i \(-0.428072\pi\)
0.224052 + 0.974577i \(0.428072\pi\)
\(828\) −3.54723 −0.123275
\(829\) 17.9879 0.624747 0.312374 0.949959i \(-0.398876\pi\)
0.312374 + 0.949959i \(0.398876\pi\)
\(830\) 11.2699 0.391185
\(831\) 8.63379 0.299503
\(832\) 5.72765 0.198571
\(833\) 0.909403 0.0315089
\(834\) 8.41045 0.291230
\(835\) 27.1948 0.941115
\(836\) 4.14345 0.143304
\(837\) 18.0933 0.625395
\(838\) −10.8629 −0.375252
\(839\) 15.2591 0.526802 0.263401 0.964686i \(-0.415156\pi\)
0.263401 + 0.964686i \(0.415156\pi\)
\(840\) −8.92022 −0.307777
\(841\) −3.22436 −0.111185
\(842\) 20.9345 0.721450
\(843\) 29.8619 1.02850
\(844\) −1.00000 −0.0344214
\(845\) 42.4676 1.46093
\(846\) −5.19571 −0.178632
\(847\) 17.5526 0.603115
\(848\) −9.71241 −0.333526
\(849\) −6.73158 −0.231027
\(850\) −0.333426 −0.0114364
\(851\) −5.35757 −0.183655
\(852\) −1.75471 −0.0601153
\(853\) 20.0870 0.687764 0.343882 0.939013i \(-0.388258\pi\)
0.343882 + 0.939013i \(0.388258\pi\)
\(854\) −2.11109 −0.0722399
\(855\) 1.84981 0.0632621
\(856\) −19.5270 −0.667421
\(857\) −49.4204 −1.68817 −0.844085 0.536210i \(-0.819856\pi\)
−0.844085 + 0.536210i \(0.819856\pi\)
\(858\) 34.6953 1.18448
\(859\) −14.5429 −0.496198 −0.248099 0.968735i \(-0.579806\pi\)
−0.248099 + 0.968735i \(0.579806\pi\)
\(860\) 3.78948 0.129220
\(861\) 39.4805 1.34549
\(862\) −24.5708 −0.836884
\(863\) −4.16415 −0.141749 −0.0708747 0.997485i \(-0.522579\pi\)
−0.0708747 + 0.997485i \(0.522579\pi\)
\(864\) 5.64708 0.192118
\(865\) 31.2959 1.06409
\(866\) −10.2969 −0.349902
\(867\) 23.8498 0.809981
\(868\) 9.11749 0.309468
\(869\) −0.0640510 −0.00217278
\(870\) −15.9147 −0.539559
\(871\) 72.2491 2.44807
\(872\) 2.14391 0.0726018
\(873\) 7.76973 0.262966
\(874\) −4.11173 −0.139081
\(875\) −32.9638 −1.11438
\(876\) −20.8525 −0.704542
\(877\) −17.1129 −0.577860 −0.288930 0.957350i \(-0.593300\pi\)
−0.288930 + 0.957350i \(0.593300\pi\)
\(878\) 23.3441 0.787826
\(879\) 23.8915 0.805840
\(880\) −8.88433 −0.299491
\(881\) 33.3241 1.12272 0.561358 0.827573i \(-0.310279\pi\)
0.561358 + 0.827573i \(0.310279\pi\)
\(882\) −0.947029 −0.0318881
\(883\) −14.1100 −0.474839 −0.237420 0.971407i \(-0.576302\pi\)
−0.237420 + 0.971407i \(0.576302\pi\)
\(884\) 4.74497 0.159591
\(885\) 3.66192 0.123094
\(886\) −35.5818 −1.19539
\(887\) −2.02756 −0.0680787 −0.0340394 0.999420i \(-0.510837\pi\)
−0.0340394 + 0.999420i \(0.510837\pi\)
\(888\) 1.90491 0.0639247
\(889\) −2.11942 −0.0710832
\(890\) 33.9788 1.13897
\(891\) 23.4835 0.786726
\(892\) −25.6890 −0.860130
\(893\) −6.02255 −0.201537
\(894\) −25.7892 −0.862518
\(895\) −15.0512 −0.503106
\(896\) 2.84565 0.0950666
\(897\) −34.4297 −1.14957
\(898\) 25.6489 0.855915
\(899\) 16.2666 0.542523
\(900\) 0.347221 0.0115740
\(901\) −8.04608 −0.268054
\(902\) 39.3217 1.30927
\(903\) −7.35243 −0.244674
\(904\) 17.2207 0.572751
\(905\) 14.9793 0.497929
\(906\) 17.0980 0.568043
\(907\) −24.9178 −0.827383 −0.413692 0.910417i \(-0.635761\pi\)
−0.413692 + 0.910417i \(0.635761\pi\)
\(908\) −0.630959 −0.0209391
\(909\) −8.59611 −0.285115
\(910\) 34.9478 1.15851
\(911\) −10.1240 −0.335423 −0.167712 0.985836i \(-0.553638\pi\)
−0.167712 + 0.985836i \(0.553638\pi\)
\(912\) 1.46195 0.0484099
\(913\) −21.7782 −0.720753
\(914\) −24.8873 −0.823199
\(915\) 2.32551 0.0768790
\(916\) 15.0811 0.498294
\(917\) 2.20559 0.0728350
\(918\) 4.67823 0.154404
\(919\) 15.2836 0.504160 0.252080 0.967706i \(-0.418885\pi\)
0.252080 + 0.967706i \(0.418885\pi\)
\(920\) 8.81631 0.290665
\(921\) −6.36084 −0.209597
\(922\) 18.8711 0.621486
\(923\) 6.87463 0.226281
\(924\) 17.2376 0.567075
\(925\) 0.524427 0.0172430
\(926\) −4.38457 −0.144086
\(927\) 6.83207 0.224395
\(928\) 5.07697 0.166660
\(929\) 28.5284 0.935985 0.467993 0.883732i \(-0.344977\pi\)
0.467993 + 0.883732i \(0.344977\pi\)
\(930\) −10.0435 −0.329341
\(931\) −1.09774 −0.0359769
\(932\) 9.27718 0.303884
\(933\) 2.10586 0.0689427
\(934\) −9.98957 −0.326869
\(935\) −7.36007 −0.240700
\(936\) −4.94130 −0.161511
\(937\) −50.1429 −1.63810 −0.819048 0.573725i \(-0.805498\pi\)
−0.819048 + 0.573725i \(0.805498\pi\)
\(938\) 35.8953 1.17202
\(939\) −26.2563 −0.856843
\(940\) 12.9134 0.421190
\(941\) −19.0410 −0.620720 −0.310360 0.950619i \(-0.600450\pi\)
−0.310360 + 0.950619i \(0.600450\pi\)
\(942\) −27.9026 −0.909116
\(943\) −39.0206 −1.27069
\(944\) −1.16819 −0.0380215
\(945\) 34.4562 1.12086
\(946\) −7.32285 −0.238086
\(947\) −51.1006 −1.66054 −0.830272 0.557358i \(-0.811815\pi\)
−0.830272 + 0.557358i \(0.811815\pi\)
\(948\) −0.0225993 −0.000733991 0
\(949\) 81.6965 2.65198
\(950\) 0.402477 0.0130581
\(951\) −6.36219 −0.206308
\(952\) 2.35743 0.0764048
\(953\) −30.2817 −0.980922 −0.490461 0.871463i \(-0.663172\pi\)
−0.490461 + 0.871463i \(0.663172\pi\)
\(954\) 8.37899 0.271280
\(955\) −9.62430 −0.311435
\(956\) −3.55667 −0.115031
\(957\) 30.7538 0.994130
\(958\) 40.2855 1.30157
\(959\) −30.7971 −0.994491
\(960\) −3.13468 −0.101171
\(961\) −20.7344 −0.668850
\(962\) −7.46311 −0.240620
\(963\) 16.8462 0.542860
\(964\) 22.0482 0.710125
\(965\) 32.8735 1.05823
\(966\) −17.1056 −0.550364
\(967\) −19.5173 −0.627635 −0.313818 0.949483i \(-0.601608\pi\)
−0.313818 + 0.949483i \(0.601608\pi\)
\(968\) 6.16822 0.198254
\(969\) 1.21113 0.0389070
\(970\) −19.3109 −0.620037
\(971\) −22.1916 −0.712163 −0.356081 0.934455i \(-0.615887\pi\)
−0.356081 + 0.934455i \(0.615887\pi\)
\(972\) −8.65550 −0.277625
\(973\) −16.3708 −0.524823
\(974\) 14.0124 0.448988
\(975\) 3.37015 0.107931
\(976\) −0.741864 −0.0237465
\(977\) 25.5094 0.816118 0.408059 0.912956i \(-0.366206\pi\)
0.408059 + 0.912956i \(0.366206\pi\)
\(978\) 6.40832 0.204915
\(979\) −65.6612 −2.09854
\(980\) 2.35375 0.0751879
\(981\) −1.84957 −0.0590522
\(982\) −12.7909 −0.408173
\(983\) −4.81931 −0.153712 −0.0768560 0.997042i \(-0.524488\pi\)
−0.0768560 + 0.997042i \(0.524488\pi\)
\(984\) 13.8740 0.442286
\(985\) −30.1928 −0.962021
\(986\) 4.20593 0.133944
\(987\) −25.0550 −0.797509
\(988\) −5.72765 −0.182221
\(989\) 7.26678 0.231070
\(990\) 7.66459 0.243597
\(991\) 21.3126 0.677016 0.338508 0.940963i \(-0.390078\pi\)
0.338508 + 0.940963i \(0.390078\pi\)
\(992\) 3.20401 0.101727
\(993\) −17.2775 −0.548283
\(994\) 3.41550 0.108333
\(995\) −16.6783 −0.528739
\(996\) −7.68406 −0.243479
\(997\) −51.5769 −1.63346 −0.816728 0.577023i \(-0.804214\pi\)
−0.816728 + 0.577023i \(0.804214\pi\)
\(998\) 2.40267 0.0760552
\(999\) −7.35812 −0.232801
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 \(a_p\))