Properties

Label 8046.2.a.h.1.6
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.67390\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +0.102080 q^{5} +0.350570 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +0.102080 q^{5} +0.350570 q^{7} +1.00000 q^{8} +0.102080 q^{10} +2.02675 q^{11} -0.0298835 q^{13} +0.350570 q^{14} +1.00000 q^{16} -3.57487 q^{17} -2.36593 q^{19} +0.102080 q^{20} +2.02675 q^{22} -3.59145 q^{23} -4.98958 q^{25} -0.0298835 q^{26} +0.350570 q^{28} -4.55651 q^{29} +0.839401 q^{31} +1.00000 q^{32} -3.57487 q^{34} +0.0357860 q^{35} -3.75798 q^{37} -2.36593 q^{38} +0.102080 q^{40} +1.43684 q^{41} -5.01492 q^{43} +2.02675 q^{44} -3.59145 q^{46} +6.28480 q^{47} -6.87710 q^{49} -4.98958 q^{50} -0.0298835 q^{52} -9.52893 q^{53} +0.206890 q^{55} +0.350570 q^{56} -4.55651 q^{58} -9.78689 q^{59} -7.40365 q^{61} +0.839401 q^{62} +1.00000 q^{64} -0.00305050 q^{65} -4.06800 q^{67} -3.57487 q^{68} +0.0357860 q^{70} +9.49501 q^{71} +7.96509 q^{73} -3.75798 q^{74} -2.36593 q^{76} +0.710518 q^{77} +9.24244 q^{79} +0.102080 q^{80} +1.43684 q^{82} -9.62022 q^{83} -0.364921 q^{85} -5.01492 q^{86} +2.02675 q^{88} -0.871304 q^{89} -0.0104763 q^{91} -3.59145 q^{92} +6.28480 q^{94} -0.241512 q^{95} -12.9918 q^{97} -6.87710 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0.102080 0.0456513 0.0228257 0.999739i \(-0.492734\pi\)
0.0228257 + 0.999739i \(0.492734\pi\)
\(6\) 0 0
\(7\) 0.350570 0.132503 0.0662515 0.997803i \(-0.478896\pi\)
0.0662515 + 0.997803i \(0.478896\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.102080 0.0322804
\(11\) 2.02675 0.611089 0.305544 0.952178i \(-0.401162\pi\)
0.305544 + 0.952178i \(0.401162\pi\)
\(12\) 0 0
\(13\) −0.0298835 −0.00828821 −0.00414410 0.999991i \(-0.501319\pi\)
−0.00414410 + 0.999991i \(0.501319\pi\)
\(14\) 0.350570 0.0936937
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.57487 −0.867033 −0.433516 0.901146i \(-0.642727\pi\)
−0.433516 + 0.901146i \(0.642727\pi\)
\(18\) 0 0
\(19\) −2.36593 −0.542780 −0.271390 0.962469i \(-0.587483\pi\)
−0.271390 + 0.962469i \(0.587483\pi\)
\(20\) 0.102080 0.0228257
\(21\) 0 0
\(22\) 2.02675 0.432105
\(23\) −3.59145 −0.748869 −0.374435 0.927253i \(-0.622163\pi\)
−0.374435 + 0.927253i \(0.622163\pi\)
\(24\) 0 0
\(25\) −4.98958 −0.997916
\(26\) −0.0298835 −0.00586065
\(27\) 0 0
\(28\) 0.350570 0.0662515
\(29\) −4.55651 −0.846122 −0.423061 0.906101i \(-0.639044\pi\)
−0.423061 + 0.906101i \(0.639044\pi\)
\(30\) 0 0
\(31\) 0.839401 0.150761 0.0753805 0.997155i \(-0.475983\pi\)
0.0753805 + 0.997155i \(0.475983\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.57487 −0.613085
\(35\) 0.0357860 0.00604894
\(36\) 0 0
\(37\) −3.75798 −0.617808 −0.308904 0.951093i \(-0.599962\pi\)
−0.308904 + 0.951093i \(0.599962\pi\)
\(38\) −2.36593 −0.383804
\(39\) 0 0
\(40\) 0.102080 0.0161402
\(41\) 1.43684 0.224396 0.112198 0.993686i \(-0.464211\pi\)
0.112198 + 0.993686i \(0.464211\pi\)
\(42\) 0 0
\(43\) −5.01492 −0.764768 −0.382384 0.924003i \(-0.624897\pi\)
−0.382384 + 0.924003i \(0.624897\pi\)
\(44\) 2.02675 0.305544
\(45\) 0 0
\(46\) −3.59145 −0.529531
\(47\) 6.28480 0.916732 0.458366 0.888764i \(-0.348435\pi\)
0.458366 + 0.888764i \(0.348435\pi\)
\(48\) 0 0
\(49\) −6.87710 −0.982443
\(50\) −4.98958 −0.705633
\(51\) 0 0
\(52\) −0.0298835 −0.00414410
\(53\) −9.52893 −1.30890 −0.654449 0.756106i \(-0.727100\pi\)
−0.654449 + 0.756106i \(0.727100\pi\)
\(54\) 0 0
\(55\) 0.206890 0.0278970
\(56\) 0.350570 0.0468469
\(57\) 0 0
\(58\) −4.55651 −0.598299
\(59\) −9.78689 −1.27414 −0.637072 0.770804i \(-0.719855\pi\)
−0.637072 + 0.770804i \(0.719855\pi\)
\(60\) 0 0
\(61\) −7.40365 −0.947941 −0.473970 0.880541i \(-0.657180\pi\)
−0.473970 + 0.880541i \(0.657180\pi\)
\(62\) 0.839401 0.106604
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.00305050 −0.000378368 0
\(66\) 0 0
\(67\) −4.06800 −0.496985 −0.248493 0.968634i \(-0.579935\pi\)
−0.248493 + 0.968634i \(0.579935\pi\)
\(68\) −3.57487 −0.433516
\(69\) 0 0
\(70\) 0.0357860 0.00427724
\(71\) 9.49501 1.12685 0.563425 0.826167i \(-0.309483\pi\)
0.563425 + 0.826167i \(0.309483\pi\)
\(72\) 0 0
\(73\) 7.96509 0.932243 0.466122 0.884721i \(-0.345651\pi\)
0.466122 + 0.884721i \(0.345651\pi\)
\(74\) −3.75798 −0.436856
\(75\) 0 0
\(76\) −2.36593 −0.271390
\(77\) 0.710518 0.0809710
\(78\) 0 0
\(79\) 9.24244 1.03986 0.519928 0.854210i \(-0.325959\pi\)
0.519928 + 0.854210i \(0.325959\pi\)
\(80\) 0.102080 0.0114128
\(81\) 0 0
\(82\) 1.43684 0.158672
\(83\) −9.62022 −1.05596 −0.527978 0.849258i \(-0.677050\pi\)
−0.527978 + 0.849258i \(0.677050\pi\)
\(84\) 0 0
\(85\) −0.364921 −0.0395812
\(86\) −5.01492 −0.540773
\(87\) 0 0
\(88\) 2.02675 0.216052
\(89\) −0.871304 −0.0923580 −0.0461790 0.998933i \(-0.514704\pi\)
−0.0461790 + 0.998933i \(0.514704\pi\)
\(90\) 0 0
\(91\) −0.0104763 −0.00109821
\(92\) −3.59145 −0.374435
\(93\) 0 0
\(94\) 6.28480 0.648227
\(95\) −0.241512 −0.0247787
\(96\) 0 0
\(97\) −12.9918 −1.31912 −0.659559 0.751653i \(-0.729257\pi\)
−0.659559 + 0.751653i \(0.729257\pi\)
\(98\) −6.87710 −0.694692
\(99\) 0 0
\(100\) −4.98958 −0.498958
\(101\) 6.60527 0.657249 0.328624 0.944461i \(-0.393415\pi\)
0.328624 + 0.944461i \(0.393415\pi\)
\(102\) 0 0
\(103\) 5.27651 0.519910 0.259955 0.965621i \(-0.416292\pi\)
0.259955 + 0.965621i \(0.416292\pi\)
\(104\) −0.0298835 −0.00293032
\(105\) 0 0
\(106\) −9.52893 −0.925531
\(107\) 8.42424 0.814402 0.407201 0.913339i \(-0.366505\pi\)
0.407201 + 0.913339i \(0.366505\pi\)
\(108\) 0 0
\(109\) 3.75345 0.359516 0.179758 0.983711i \(-0.442469\pi\)
0.179758 + 0.983711i \(0.442469\pi\)
\(110\) 0.206890 0.0197262
\(111\) 0 0
\(112\) 0.350570 0.0331257
\(113\) 4.46292 0.419836 0.209918 0.977719i \(-0.432680\pi\)
0.209918 + 0.977719i \(0.432680\pi\)
\(114\) 0 0
\(115\) −0.366614 −0.0341869
\(116\) −4.55651 −0.423061
\(117\) 0 0
\(118\) −9.78689 −0.900956
\(119\) −1.25324 −0.114884
\(120\) 0 0
\(121\) −6.89228 −0.626571
\(122\) −7.40365 −0.670295
\(123\) 0 0
\(124\) 0.839401 0.0753805
\(125\) −1.01973 −0.0912075
\(126\) 0 0
\(127\) −1.36720 −0.121320 −0.0606598 0.998158i \(-0.519320\pi\)
−0.0606598 + 0.998158i \(0.519320\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −0.00305050 −0.000267546 0
\(131\) −8.75704 −0.765106 −0.382553 0.923934i \(-0.624955\pi\)
−0.382553 + 0.923934i \(0.624955\pi\)
\(132\) 0 0
\(133\) −0.829422 −0.0719200
\(134\) −4.06800 −0.351422
\(135\) 0 0
\(136\) −3.57487 −0.306542
\(137\) −7.96214 −0.680251 −0.340126 0.940380i \(-0.610470\pi\)
−0.340126 + 0.940380i \(0.610470\pi\)
\(138\) 0 0
\(139\) 3.31018 0.280766 0.140383 0.990097i \(-0.455167\pi\)
0.140383 + 0.990097i \(0.455167\pi\)
\(140\) 0.0357860 0.00302447
\(141\) 0 0
\(142\) 9.49501 0.796804
\(143\) −0.0605665 −0.00506483
\(144\) 0 0
\(145\) −0.465126 −0.0386266
\(146\) 7.96509 0.659196
\(147\) 0 0
\(148\) −3.75798 −0.308904
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) 6.90585 0.561990 0.280995 0.959709i \(-0.409336\pi\)
0.280995 + 0.959709i \(0.409336\pi\)
\(152\) −2.36593 −0.191902
\(153\) 0 0
\(154\) 0.710518 0.0572552
\(155\) 0.0856857 0.00688244
\(156\) 0 0
\(157\) −14.0313 −1.11982 −0.559909 0.828554i \(-0.689164\pi\)
−0.559909 + 0.828554i \(0.689164\pi\)
\(158\) 9.24244 0.735289
\(159\) 0 0
\(160\) 0.102080 0.00807009
\(161\) −1.25905 −0.0992274
\(162\) 0 0
\(163\) −20.7001 −1.62135 −0.810677 0.585494i \(-0.800900\pi\)
−0.810677 + 0.585494i \(0.800900\pi\)
\(164\) 1.43684 0.112198
\(165\) 0 0
\(166\) −9.62022 −0.746674
\(167\) 13.5549 1.04891 0.524455 0.851438i \(-0.324269\pi\)
0.524455 + 0.851438i \(0.324269\pi\)
\(168\) 0 0
\(169\) −12.9991 −0.999931
\(170\) −0.364921 −0.0279881
\(171\) 0 0
\(172\) −5.01492 −0.382384
\(173\) 24.3064 1.84798 0.923991 0.382415i \(-0.124907\pi\)
0.923991 + 0.382415i \(0.124907\pi\)
\(174\) 0 0
\(175\) −1.74920 −0.132227
\(176\) 2.02675 0.152772
\(177\) 0 0
\(178\) −0.871304 −0.0653070
\(179\) −19.8845 −1.48623 −0.743117 0.669162i \(-0.766653\pi\)
−0.743117 + 0.669162i \(0.766653\pi\)
\(180\) 0 0
\(181\) 1.35829 0.100961 0.0504803 0.998725i \(-0.483925\pi\)
0.0504803 + 0.998725i \(0.483925\pi\)
\(182\) −0.0104763 −0.000776553 0
\(183\) 0 0
\(184\) −3.59145 −0.264765
\(185\) −0.383613 −0.0282038
\(186\) 0 0
\(187\) −7.24537 −0.529834
\(188\) 6.28480 0.458366
\(189\) 0 0
\(190\) −0.241512 −0.0175212
\(191\) 12.0574 0.872440 0.436220 0.899840i \(-0.356317\pi\)
0.436220 + 0.899840i \(0.356317\pi\)
\(192\) 0 0
\(193\) 17.1757 1.23634 0.618168 0.786046i \(-0.287875\pi\)
0.618168 + 0.786046i \(0.287875\pi\)
\(194\) −12.9918 −0.932758
\(195\) 0 0
\(196\) −6.87710 −0.491221
\(197\) 15.6315 1.11370 0.556848 0.830614i \(-0.312011\pi\)
0.556848 + 0.830614i \(0.312011\pi\)
\(198\) 0 0
\(199\) −15.7562 −1.11692 −0.558462 0.829530i \(-0.688609\pi\)
−0.558462 + 0.829530i \(0.688609\pi\)
\(200\) −4.98958 −0.352817
\(201\) 0 0
\(202\) 6.60527 0.464745
\(203\) −1.59737 −0.112114
\(204\) 0 0
\(205\) 0.146672 0.0102440
\(206\) 5.27651 0.367632
\(207\) 0 0
\(208\) −0.0298835 −0.00207205
\(209\) −4.79514 −0.331687
\(210\) 0 0
\(211\) 8.83252 0.608056 0.304028 0.952663i \(-0.401668\pi\)
0.304028 + 0.952663i \(0.401668\pi\)
\(212\) −9.52893 −0.654449
\(213\) 0 0
\(214\) 8.42424 0.575869
\(215\) −0.511921 −0.0349127
\(216\) 0 0
\(217\) 0.294269 0.0199763
\(218\) 3.75345 0.254216
\(219\) 0 0
\(220\) 0.206890 0.0139485
\(221\) 0.106830 0.00718614
\(222\) 0 0
\(223\) 20.9511 1.40299 0.701493 0.712676i \(-0.252517\pi\)
0.701493 + 0.712676i \(0.252517\pi\)
\(224\) 0.350570 0.0234234
\(225\) 0 0
\(226\) 4.46292 0.296869
\(227\) 4.91723 0.326368 0.163184 0.986596i \(-0.447824\pi\)
0.163184 + 0.986596i \(0.447824\pi\)
\(228\) 0 0
\(229\) −7.53842 −0.498153 −0.249077 0.968484i \(-0.580127\pi\)
−0.249077 + 0.968484i \(0.580127\pi\)
\(230\) −0.366614 −0.0241738
\(231\) 0 0
\(232\) −4.55651 −0.299149
\(233\) 11.9221 0.781041 0.390521 0.920594i \(-0.372295\pi\)
0.390521 + 0.920594i \(0.372295\pi\)
\(234\) 0 0
\(235\) 0.641549 0.0418500
\(236\) −9.78689 −0.637072
\(237\) 0 0
\(238\) −1.25324 −0.0812355
\(239\) −16.1316 −1.04347 −0.521734 0.853108i \(-0.674715\pi\)
−0.521734 + 0.853108i \(0.674715\pi\)
\(240\) 0 0
\(241\) 20.6366 1.32932 0.664662 0.747144i \(-0.268576\pi\)
0.664662 + 0.747144i \(0.268576\pi\)
\(242\) −6.89228 −0.443052
\(243\) 0 0
\(244\) −7.40365 −0.473970
\(245\) −0.702011 −0.0448498
\(246\) 0 0
\(247\) 0.0707022 0.00449868
\(248\) 0.839401 0.0533020
\(249\) 0 0
\(250\) −1.01973 −0.0644935
\(251\) 4.82748 0.304708 0.152354 0.988326i \(-0.451315\pi\)
0.152354 + 0.988326i \(0.451315\pi\)
\(252\) 0 0
\(253\) −7.27898 −0.457626
\(254\) −1.36720 −0.0857859
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −3.38502 −0.211152 −0.105576 0.994411i \(-0.533669\pi\)
−0.105576 + 0.994411i \(0.533669\pi\)
\(258\) 0 0
\(259\) −1.31743 −0.0818614
\(260\) −0.00305050 −0.000189184 0
\(261\) 0 0
\(262\) −8.75704 −0.541012
\(263\) 15.5141 0.956642 0.478321 0.878185i \(-0.341246\pi\)
0.478321 + 0.878185i \(0.341246\pi\)
\(264\) 0 0
\(265\) −0.972708 −0.0597530
\(266\) −0.829422 −0.0508551
\(267\) 0 0
\(268\) −4.06800 −0.248493
\(269\) −16.6115 −1.01282 −0.506410 0.862293i \(-0.669028\pi\)
−0.506410 + 0.862293i \(0.669028\pi\)
\(270\) 0 0
\(271\) −23.4563 −1.42487 −0.712435 0.701738i \(-0.752408\pi\)
−0.712435 + 0.701738i \(0.752408\pi\)
\(272\) −3.57487 −0.216758
\(273\) 0 0
\(274\) −7.96214 −0.481010
\(275\) −10.1126 −0.609815
\(276\) 0 0
\(277\) −13.5781 −0.815826 −0.407913 0.913021i \(-0.633743\pi\)
−0.407913 + 0.913021i \(0.633743\pi\)
\(278\) 3.31018 0.198532
\(279\) 0 0
\(280\) 0.0357860 0.00213862
\(281\) 8.60505 0.513334 0.256667 0.966500i \(-0.417376\pi\)
0.256667 + 0.966500i \(0.417376\pi\)
\(282\) 0 0
\(283\) −18.6623 −1.10936 −0.554680 0.832063i \(-0.687159\pi\)
−0.554680 + 0.832063i \(0.687159\pi\)
\(284\) 9.49501 0.563425
\(285\) 0 0
\(286\) −0.0605665 −0.00358137
\(287\) 0.503712 0.0297332
\(288\) 0 0
\(289\) −4.22032 −0.248254
\(290\) −0.465126 −0.0273131
\(291\) 0 0
\(292\) 7.96509 0.466122
\(293\) −8.92222 −0.521241 −0.260621 0.965441i \(-0.583927\pi\)
−0.260621 + 0.965441i \(0.583927\pi\)
\(294\) 0 0
\(295\) −0.999041 −0.0581664
\(296\) −3.75798 −0.218428
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 0.107325 0.00620678
\(300\) 0 0
\(301\) −1.75808 −0.101334
\(302\) 6.90585 0.397387
\(303\) 0 0
\(304\) −2.36593 −0.135695
\(305\) −0.755761 −0.0432748
\(306\) 0 0
\(307\) 15.6841 0.895139 0.447570 0.894249i \(-0.352290\pi\)
0.447570 + 0.894249i \(0.352290\pi\)
\(308\) 0.710518 0.0404855
\(309\) 0 0
\(310\) 0.0856857 0.00486662
\(311\) −3.64245 −0.206544 −0.103272 0.994653i \(-0.532931\pi\)
−0.103272 + 0.994653i \(0.532931\pi\)
\(312\) 0 0
\(313\) −31.7926 −1.79703 −0.898513 0.438947i \(-0.855352\pi\)
−0.898513 + 0.438947i \(0.855352\pi\)
\(314\) −14.0313 −0.791830
\(315\) 0 0
\(316\) 9.24244 0.519928
\(317\) −1.50799 −0.0846972 −0.0423486 0.999103i \(-0.513484\pi\)
−0.0423486 + 0.999103i \(0.513484\pi\)
\(318\) 0 0
\(319\) −9.23491 −0.517056
\(320\) 0.102080 0.00570642
\(321\) 0 0
\(322\) −1.25905 −0.0701644
\(323\) 8.45787 0.470608
\(324\) 0 0
\(325\) 0.149106 0.00827093
\(326\) −20.7001 −1.14647
\(327\) 0 0
\(328\) 1.43684 0.0793360
\(329\) 2.20326 0.121470
\(330\) 0 0
\(331\) 1.26926 0.0697647 0.0348824 0.999391i \(-0.488894\pi\)
0.0348824 + 0.999391i \(0.488894\pi\)
\(332\) −9.62022 −0.527978
\(333\) 0 0
\(334\) 13.5549 0.741692
\(335\) −0.415260 −0.0226881
\(336\) 0 0
\(337\) 14.2539 0.776457 0.388229 0.921563i \(-0.373087\pi\)
0.388229 + 0.921563i \(0.373087\pi\)
\(338\) −12.9991 −0.707058
\(339\) 0 0
\(340\) −0.364921 −0.0197906
\(341\) 1.70126 0.0921283
\(342\) 0 0
\(343\) −4.86489 −0.262680
\(344\) −5.01492 −0.270386
\(345\) 0 0
\(346\) 24.3064 1.30672
\(347\) 17.9926 0.965891 0.482945 0.875650i \(-0.339567\pi\)
0.482945 + 0.875650i \(0.339567\pi\)
\(348\) 0 0
\(349\) −30.2747 −1.62057 −0.810284 0.586037i \(-0.800687\pi\)
−0.810284 + 0.586037i \(0.800687\pi\)
\(350\) −1.74920 −0.0934985
\(351\) 0 0
\(352\) 2.02675 0.108026
\(353\) −16.5740 −0.882146 −0.441073 0.897471i \(-0.645402\pi\)
−0.441073 + 0.897471i \(0.645402\pi\)
\(354\) 0 0
\(355\) 0.969246 0.0514422
\(356\) −0.871304 −0.0461790
\(357\) 0 0
\(358\) −19.8845 −1.05093
\(359\) −23.0600 −1.21706 −0.608531 0.793530i \(-0.708241\pi\)
−0.608531 + 0.793530i \(0.708241\pi\)
\(360\) 0 0
\(361\) −13.4024 −0.705389
\(362\) 1.35829 0.0713899
\(363\) 0 0
\(364\) −0.0104763 −0.000549106 0
\(365\) 0.813073 0.0425582
\(366\) 0 0
\(367\) −10.3939 −0.542558 −0.271279 0.962501i \(-0.587447\pi\)
−0.271279 + 0.962501i \(0.587447\pi\)
\(368\) −3.59145 −0.187217
\(369\) 0 0
\(370\) −0.383613 −0.0199431
\(371\) −3.34055 −0.173433
\(372\) 0 0
\(373\) 17.6768 0.915269 0.457634 0.889140i \(-0.348697\pi\)
0.457634 + 0.889140i \(0.348697\pi\)
\(374\) −7.24537 −0.374649
\(375\) 0 0
\(376\) 6.28480 0.324114
\(377\) 0.136165 0.00701284
\(378\) 0 0
\(379\) −6.04973 −0.310754 −0.155377 0.987855i \(-0.549659\pi\)
−0.155377 + 0.987855i \(0.549659\pi\)
\(380\) −0.241512 −0.0123893
\(381\) 0 0
\(382\) 12.0574 0.616908
\(383\) −20.8782 −1.06682 −0.533412 0.845855i \(-0.679091\pi\)
−0.533412 + 0.845855i \(0.679091\pi\)
\(384\) 0 0
\(385\) 0.0725293 0.00369644
\(386\) 17.1757 0.874222
\(387\) 0 0
\(388\) −12.9918 −0.659559
\(389\) 14.4959 0.734971 0.367486 0.930029i \(-0.380219\pi\)
0.367486 + 0.930029i \(0.380219\pi\)
\(390\) 0 0
\(391\) 12.8390 0.649294
\(392\) −6.87710 −0.347346
\(393\) 0 0
\(394\) 15.6315 0.787502
\(395\) 0.943464 0.0474708
\(396\) 0 0
\(397\) −6.17054 −0.309690 −0.154845 0.987939i \(-0.549488\pi\)
−0.154845 + 0.987939i \(0.549488\pi\)
\(398\) −15.7562 −0.789785
\(399\) 0 0
\(400\) −4.98958 −0.249479
\(401\) 10.3024 0.514480 0.257240 0.966348i \(-0.417187\pi\)
0.257240 + 0.966348i \(0.417187\pi\)
\(402\) 0 0
\(403\) −0.0250843 −0.00124954
\(404\) 6.60527 0.328624
\(405\) 0 0
\(406\) −1.59737 −0.0792764
\(407\) −7.61649 −0.377536
\(408\) 0 0
\(409\) 9.18360 0.454100 0.227050 0.973883i \(-0.427092\pi\)
0.227050 + 0.973883i \(0.427092\pi\)
\(410\) 0.146672 0.00724359
\(411\) 0 0
\(412\) 5.27651 0.259955
\(413\) −3.43099 −0.168828
\(414\) 0 0
\(415\) −0.982027 −0.0482058
\(416\) −0.0298835 −0.00146516
\(417\) 0 0
\(418\) −4.79514 −0.234538
\(419\) 23.3723 1.14181 0.570906 0.821015i \(-0.306592\pi\)
0.570906 + 0.821015i \(0.306592\pi\)
\(420\) 0 0
\(421\) −22.5192 −1.09752 −0.548760 0.835980i \(-0.684900\pi\)
−0.548760 + 0.835980i \(0.684900\pi\)
\(422\) 8.83252 0.429960
\(423\) 0 0
\(424\) −9.52893 −0.462766
\(425\) 17.8371 0.865226
\(426\) 0 0
\(427\) −2.59550 −0.125605
\(428\) 8.42424 0.407201
\(429\) 0 0
\(430\) −0.511921 −0.0246870
\(431\) 4.03344 0.194284 0.0971421 0.995271i \(-0.469030\pi\)
0.0971421 + 0.995271i \(0.469030\pi\)
\(432\) 0 0
\(433\) 4.71921 0.226791 0.113395 0.993550i \(-0.463827\pi\)
0.113395 + 0.993550i \(0.463827\pi\)
\(434\) 0.294269 0.0141254
\(435\) 0 0
\(436\) 3.75345 0.179758
\(437\) 8.49711 0.406472
\(438\) 0 0
\(439\) −32.7549 −1.56331 −0.781653 0.623713i \(-0.785623\pi\)
−0.781653 + 0.623713i \(0.785623\pi\)
\(440\) 0.206890 0.00986309
\(441\) 0 0
\(442\) 0.106830 0.00508137
\(443\) −35.0469 −1.66513 −0.832565 0.553927i \(-0.813129\pi\)
−0.832565 + 0.553927i \(0.813129\pi\)
\(444\) 0 0
\(445\) −0.0889423 −0.00421627
\(446\) 20.9511 0.992061
\(447\) 0 0
\(448\) 0.350570 0.0165629
\(449\) 32.0551 1.51278 0.756388 0.654123i \(-0.226962\pi\)
0.756388 + 0.654123i \(0.226962\pi\)
\(450\) 0 0
\(451\) 2.91211 0.137126
\(452\) 4.46292 0.209918
\(453\) 0 0
\(454\) 4.91723 0.230777
\(455\) −0.00106941 −5.01348e−5 0
\(456\) 0 0
\(457\) 24.0443 1.12475 0.562373 0.826884i \(-0.309888\pi\)
0.562373 + 0.826884i \(0.309888\pi\)
\(458\) −7.53842 −0.352247
\(459\) 0 0
\(460\) −0.366614 −0.0170934
\(461\) 7.50713 0.349642 0.174821 0.984600i \(-0.444065\pi\)
0.174821 + 0.984600i \(0.444065\pi\)
\(462\) 0 0
\(463\) −37.7034 −1.75223 −0.876114 0.482105i \(-0.839872\pi\)
−0.876114 + 0.482105i \(0.839872\pi\)
\(464\) −4.55651 −0.211531
\(465\) 0 0
\(466\) 11.9221 0.552280
\(467\) −11.1921 −0.517909 −0.258954 0.965890i \(-0.583378\pi\)
−0.258954 + 0.965890i \(0.583378\pi\)
\(468\) 0 0
\(469\) −1.42612 −0.0658520
\(470\) 0.641549 0.0295925
\(471\) 0 0
\(472\) −9.78689 −0.450478
\(473\) −10.1640 −0.467341
\(474\) 0 0
\(475\) 11.8050 0.541649
\(476\) −1.25324 −0.0574422
\(477\) 0 0
\(478\) −16.1316 −0.737843
\(479\) 37.4425 1.71079 0.855396 0.517975i \(-0.173314\pi\)
0.855396 + 0.517975i \(0.173314\pi\)
\(480\) 0 0
\(481\) 0.112302 0.00512052
\(482\) 20.6366 0.939974
\(483\) 0 0
\(484\) −6.89228 −0.313285
\(485\) −1.32620 −0.0602195
\(486\) 0 0
\(487\) −9.80226 −0.444183 −0.222091 0.975026i \(-0.571288\pi\)
−0.222091 + 0.975026i \(0.571288\pi\)
\(488\) −7.40365 −0.335148
\(489\) 0 0
\(490\) −0.702011 −0.0317136
\(491\) −32.0256 −1.44529 −0.722647 0.691217i \(-0.757075\pi\)
−0.722647 + 0.691217i \(0.757075\pi\)
\(492\) 0 0
\(493\) 16.2889 0.733616
\(494\) 0.0707022 0.00318104
\(495\) 0 0
\(496\) 0.839401 0.0376902
\(497\) 3.32866 0.149311
\(498\) 0 0
\(499\) 13.3658 0.598336 0.299168 0.954201i \(-0.403291\pi\)
0.299168 + 0.954201i \(0.403291\pi\)
\(500\) −1.01973 −0.0456038
\(501\) 0 0
\(502\) 4.82748 0.215461
\(503\) 0.515588 0.0229889 0.0114945 0.999934i \(-0.496341\pi\)
0.0114945 + 0.999934i \(0.496341\pi\)
\(504\) 0 0
\(505\) 0.674262 0.0300043
\(506\) −7.27898 −0.323590
\(507\) 0 0
\(508\) −1.36720 −0.0606598
\(509\) 16.3872 0.726351 0.363176 0.931721i \(-0.381693\pi\)
0.363176 + 0.931721i \(0.381693\pi\)
\(510\) 0 0
\(511\) 2.79232 0.123525
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.38502 −0.149307
\(515\) 0.538624 0.0237346
\(516\) 0 0
\(517\) 12.7377 0.560205
\(518\) −1.31743 −0.0578847
\(519\) 0 0
\(520\) −0.00305050 −0.000133773 0
\(521\) −31.8411 −1.39499 −0.697493 0.716592i \(-0.745701\pi\)
−0.697493 + 0.716592i \(0.745701\pi\)
\(522\) 0 0
\(523\) −7.22133 −0.315766 −0.157883 0.987458i \(-0.550467\pi\)
−0.157883 + 0.987458i \(0.550467\pi\)
\(524\) −8.75704 −0.382553
\(525\) 0 0
\(526\) 15.5141 0.676448
\(527\) −3.00075 −0.130715
\(528\) 0 0
\(529\) −10.1015 −0.439195
\(530\) −0.972708 −0.0422517
\(531\) 0 0
\(532\) −0.829422 −0.0359600
\(533\) −0.0429378 −0.00185984
\(534\) 0 0
\(535\) 0.859942 0.0371786
\(536\) −4.06800 −0.175711
\(537\) 0 0
\(538\) −16.6115 −0.716172
\(539\) −13.9382 −0.600360
\(540\) 0 0
\(541\) −24.9022 −1.07063 −0.535314 0.844653i \(-0.679807\pi\)
−0.535314 + 0.844653i \(0.679807\pi\)
\(542\) −23.4563 −1.00754
\(543\) 0 0
\(544\) −3.57487 −0.153271
\(545\) 0.383151 0.0164124
\(546\) 0 0
\(547\) 31.6658 1.35393 0.676966 0.736014i \(-0.263294\pi\)
0.676966 + 0.736014i \(0.263294\pi\)
\(548\) −7.96214 −0.340126
\(549\) 0 0
\(550\) −10.1126 −0.431204
\(551\) 10.7804 0.459259
\(552\) 0 0
\(553\) 3.24012 0.137784
\(554\) −13.5781 −0.576876
\(555\) 0 0
\(556\) 3.31018 0.140383
\(557\) −28.4674 −1.20620 −0.603101 0.797665i \(-0.706068\pi\)
−0.603101 + 0.797665i \(0.706068\pi\)
\(558\) 0 0
\(559\) 0.149864 0.00633856
\(560\) 0.0357860 0.00151223
\(561\) 0 0
\(562\) 8.60505 0.362982
\(563\) 18.4847 0.779037 0.389518 0.921019i \(-0.372642\pi\)
0.389518 + 0.921019i \(0.372642\pi\)
\(564\) 0 0
\(565\) 0.455572 0.0191661
\(566\) −18.6623 −0.784437
\(567\) 0 0
\(568\) 9.49501 0.398402
\(569\) 30.2299 1.26730 0.633651 0.773619i \(-0.281556\pi\)
0.633651 + 0.773619i \(0.281556\pi\)
\(570\) 0 0
\(571\) −5.28489 −0.221166 −0.110583 0.993867i \(-0.535272\pi\)
−0.110583 + 0.993867i \(0.535272\pi\)
\(572\) −0.0605665 −0.00253241
\(573\) 0 0
\(574\) 0.503712 0.0210245
\(575\) 17.9198 0.747309
\(576\) 0 0
\(577\) −41.7286 −1.73718 −0.868592 0.495527i \(-0.834975\pi\)
−0.868592 + 0.495527i \(0.834975\pi\)
\(578\) −4.22032 −0.175542
\(579\) 0 0
\(580\) −0.465126 −0.0193133
\(581\) −3.37256 −0.139917
\(582\) 0 0
\(583\) −19.3128 −0.799853
\(584\) 7.96509 0.329598
\(585\) 0 0
\(586\) −8.92222 −0.368573
\(587\) 6.32683 0.261136 0.130568 0.991439i \(-0.458320\pi\)
0.130568 + 0.991439i \(0.458320\pi\)
\(588\) 0 0
\(589\) −1.98596 −0.0818301
\(590\) −0.999041 −0.0411299
\(591\) 0 0
\(592\) −3.75798 −0.154452
\(593\) 29.1140 1.19557 0.597784 0.801657i \(-0.296048\pi\)
0.597784 + 0.801657i \(0.296048\pi\)
\(594\) 0 0
\(595\) −0.127930 −0.00524463
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 0.107325 0.00438886
\(599\) −23.2937 −0.951755 −0.475878 0.879511i \(-0.657870\pi\)
−0.475878 + 0.879511i \(0.657870\pi\)
\(600\) 0 0
\(601\) −5.33860 −0.217766 −0.108883 0.994055i \(-0.534727\pi\)
−0.108883 + 0.994055i \(0.534727\pi\)
\(602\) −1.75808 −0.0716540
\(603\) 0 0
\(604\) 6.90585 0.280995
\(605\) −0.703560 −0.0286038
\(606\) 0 0
\(607\) 21.5161 0.873310 0.436655 0.899629i \(-0.356163\pi\)
0.436655 + 0.899629i \(0.356163\pi\)
\(608\) −2.36593 −0.0959509
\(609\) 0 0
\(610\) −0.755761 −0.0305999
\(611\) −0.187812 −0.00759806
\(612\) 0 0
\(613\) 12.2745 0.495762 0.247881 0.968791i \(-0.420266\pi\)
0.247881 + 0.968791i \(0.420266\pi\)
\(614\) 15.6841 0.632959
\(615\) 0 0
\(616\) 0.710518 0.0286276
\(617\) −4.83318 −0.194577 −0.0972883 0.995256i \(-0.531017\pi\)
−0.0972883 + 0.995256i \(0.531017\pi\)
\(618\) 0 0
\(619\) −4.13677 −0.166271 −0.0831353 0.996538i \(-0.526493\pi\)
−0.0831353 + 0.996538i \(0.526493\pi\)
\(620\) 0.0856857 0.00344122
\(621\) 0 0
\(622\) −3.64245 −0.146049
\(623\) −0.305453 −0.0122377
\(624\) 0 0
\(625\) 24.8438 0.993752
\(626\) −31.7926 −1.27069
\(627\) 0 0
\(628\) −14.0313 −0.559909
\(629\) 13.4343 0.535660
\(630\) 0 0
\(631\) 10.8814 0.433182 0.216591 0.976262i \(-0.430506\pi\)
0.216591 + 0.976262i \(0.430506\pi\)
\(632\) 9.24244 0.367645
\(633\) 0 0
\(634\) −1.50799 −0.0598899
\(635\) −0.139563 −0.00553840
\(636\) 0 0
\(637\) 0.205512 0.00814269
\(638\) −9.23491 −0.365614
\(639\) 0 0
\(640\) 0.102080 0.00403505
\(641\) 46.5892 1.84016 0.920081 0.391728i \(-0.128122\pi\)
0.920081 + 0.391728i \(0.128122\pi\)
\(642\) 0 0
\(643\) 18.1726 0.716655 0.358328 0.933596i \(-0.383347\pi\)
0.358328 + 0.933596i \(0.383347\pi\)
\(644\) −1.25905 −0.0496137
\(645\) 0 0
\(646\) 8.45787 0.332770
\(647\) 23.8592 0.938002 0.469001 0.883198i \(-0.344614\pi\)
0.469001 + 0.883198i \(0.344614\pi\)
\(648\) 0 0
\(649\) −19.8356 −0.778615
\(650\) 0.149106 0.00584843
\(651\) 0 0
\(652\) −20.7001 −0.810677
\(653\) −7.62071 −0.298222 −0.149111 0.988820i \(-0.547641\pi\)
−0.149111 + 0.988820i \(0.547641\pi\)
\(654\) 0 0
\(655\) −0.893914 −0.0349281
\(656\) 1.43684 0.0560991
\(657\) 0 0
\(658\) 2.20326 0.0858920
\(659\) 12.4087 0.483376 0.241688 0.970354i \(-0.422299\pi\)
0.241688 + 0.970354i \(0.422299\pi\)
\(660\) 0 0
\(661\) 25.9018 1.00746 0.503732 0.863860i \(-0.331960\pi\)
0.503732 + 0.863860i \(0.331960\pi\)
\(662\) 1.26926 0.0493311
\(663\) 0 0
\(664\) −9.62022 −0.373337
\(665\) −0.0846670 −0.00328324
\(666\) 0 0
\(667\) 16.3645 0.633635
\(668\) 13.5549 0.524455
\(669\) 0 0
\(670\) −0.415260 −0.0160429
\(671\) −15.0054 −0.579276
\(672\) 0 0
\(673\) −7.27877 −0.280576 −0.140288 0.990111i \(-0.544803\pi\)
−0.140288 + 0.990111i \(0.544803\pi\)
\(674\) 14.2539 0.549038
\(675\) 0 0
\(676\) −12.9991 −0.499966
\(677\) 50.8122 1.95287 0.976435 0.215812i \(-0.0692398\pi\)
0.976435 + 0.215812i \(0.0692398\pi\)
\(678\) 0 0
\(679\) −4.55454 −0.174787
\(680\) −0.364921 −0.0139941
\(681\) 0 0
\(682\) 1.70126 0.0651445
\(683\) 42.7539 1.63593 0.817965 0.575267i \(-0.195102\pi\)
0.817965 + 0.575267i \(0.195102\pi\)
\(684\) 0 0
\(685\) −0.812771 −0.0310544
\(686\) −4.86489 −0.185742
\(687\) 0 0
\(688\) −5.01492 −0.191192
\(689\) 0.284758 0.0108484
\(690\) 0 0
\(691\) 0.949122 0.0361063 0.0180532 0.999837i \(-0.494253\pi\)
0.0180532 + 0.999837i \(0.494253\pi\)
\(692\) 24.3064 0.923991
\(693\) 0 0
\(694\) 17.9926 0.682988
\(695\) 0.337902 0.0128174
\(696\) 0 0
\(697\) −5.13650 −0.194559
\(698\) −30.2747 −1.14591
\(699\) 0 0
\(700\) −1.74920 −0.0661134
\(701\) 24.8882 0.940013 0.470006 0.882663i \(-0.344252\pi\)
0.470006 + 0.882663i \(0.344252\pi\)
\(702\) 0 0
\(703\) 8.89110 0.335334
\(704\) 2.02675 0.0763861
\(705\) 0 0
\(706\) −16.5740 −0.623771
\(707\) 2.31561 0.0870874
\(708\) 0 0
\(709\) 15.5052 0.582311 0.291155 0.956676i \(-0.405960\pi\)
0.291155 + 0.956676i \(0.405960\pi\)
\(710\) 0.969246 0.0363752
\(711\) 0 0
\(712\) −0.871304 −0.0326535
\(713\) −3.01467 −0.112900
\(714\) 0 0
\(715\) −0.00618260 −0.000231216 0
\(716\) −19.8845 −0.743117
\(717\) 0 0
\(718\) −23.0600 −0.860593
\(719\) 13.6341 0.508465 0.254233 0.967143i \(-0.418177\pi\)
0.254233 + 0.967143i \(0.418177\pi\)
\(720\) 0 0
\(721\) 1.84979 0.0688896
\(722\) −13.4024 −0.498786
\(723\) 0 0
\(724\) 1.35829 0.0504803
\(725\) 22.7351 0.844359
\(726\) 0 0
\(727\) 9.59451 0.355841 0.177920 0.984045i \(-0.443063\pi\)
0.177920 + 0.984045i \(0.443063\pi\)
\(728\) −0.0104763 −0.000388276 0
\(729\) 0 0
\(730\) 0.813073 0.0300932
\(731\) 17.9277 0.663079
\(732\) 0 0
\(733\) 18.3649 0.678324 0.339162 0.940728i \(-0.389857\pi\)
0.339162 + 0.940728i \(0.389857\pi\)
\(734\) −10.3939 −0.383646
\(735\) 0 0
\(736\) −3.59145 −0.132383
\(737\) −8.24483 −0.303702
\(738\) 0 0
\(739\) −39.9117 −1.46817 −0.734087 0.679055i \(-0.762390\pi\)
−0.734087 + 0.679055i \(0.762390\pi\)
\(740\) −0.383613 −0.0141019
\(741\) 0 0
\(742\) −3.34055 −0.122636
\(743\) −8.04457 −0.295127 −0.147563 0.989053i \(-0.547143\pi\)
−0.147563 + 0.989053i \(0.547143\pi\)
\(744\) 0 0
\(745\) −0.102080 −0.00373990
\(746\) 17.6768 0.647193
\(747\) 0 0
\(748\) −7.24537 −0.264917
\(749\) 2.95328 0.107911
\(750\) 0 0
\(751\) 10.3350 0.377128 0.188564 0.982061i \(-0.439617\pi\)
0.188564 + 0.982061i \(0.439617\pi\)
\(752\) 6.28480 0.229183
\(753\) 0 0
\(754\) 0.136165 0.00495882
\(755\) 0.704946 0.0256556
\(756\) 0 0
\(757\) −49.2360 −1.78951 −0.894756 0.446556i \(-0.852651\pi\)
−0.894756 + 0.446556i \(0.852651\pi\)
\(758\) −6.04973 −0.219736
\(759\) 0 0
\(760\) −0.241512 −0.00876058
\(761\) 8.72729 0.316364 0.158182 0.987410i \(-0.449437\pi\)
0.158182 + 0.987410i \(0.449437\pi\)
\(762\) 0 0
\(763\) 1.31585 0.0476369
\(764\) 12.0574 0.436220
\(765\) 0 0
\(766\) −20.8782 −0.754359
\(767\) 0.292467 0.0105604
\(768\) 0 0
\(769\) −32.5167 −1.17258 −0.586290 0.810101i \(-0.699412\pi\)
−0.586290 + 0.810101i \(0.699412\pi\)
\(770\) 0.0725293 0.00261378
\(771\) 0 0
\(772\) 17.1757 0.618168
\(773\) 30.6093 1.10094 0.550469 0.834855i \(-0.314449\pi\)
0.550469 + 0.834855i \(0.314449\pi\)
\(774\) 0 0
\(775\) −4.18826 −0.150447
\(776\) −12.9918 −0.466379
\(777\) 0 0
\(778\) 14.4959 0.519703
\(779\) −3.39945 −0.121798
\(780\) 0 0
\(781\) 19.2440 0.688606
\(782\) 12.8390 0.459120
\(783\) 0 0
\(784\) −6.87710 −0.245611
\(785\) −1.43231 −0.0511212
\(786\) 0 0
\(787\) −24.9239 −0.888440 −0.444220 0.895918i \(-0.646519\pi\)
−0.444220 + 0.895918i \(0.646519\pi\)
\(788\) 15.6315 0.556848
\(789\) 0 0
\(790\) 0.943464 0.0335669
\(791\) 1.56456 0.0556295
\(792\) 0 0
\(793\) 0.221247 0.00785673
\(794\) −6.17054 −0.218984
\(795\) 0 0
\(796\) −15.7562 −0.558462
\(797\) −21.6064 −0.765338 −0.382669 0.923886i \(-0.624995\pi\)
−0.382669 + 0.923886i \(0.624995\pi\)
\(798\) 0 0
\(799\) −22.4673 −0.794837
\(800\) −4.98958 −0.176408
\(801\) 0 0
\(802\) 10.3024 0.363792
\(803\) 16.1433 0.569683
\(804\) 0 0
\(805\) −0.128524 −0.00452986
\(806\) −0.0250843 −0.000883556 0
\(807\) 0 0
\(808\) 6.60527 0.232373
\(809\) −16.4003 −0.576603 −0.288302 0.957540i \(-0.593091\pi\)
−0.288302 + 0.957540i \(0.593091\pi\)
\(810\) 0 0
\(811\) −11.7483 −0.412539 −0.206269 0.978495i \(-0.566132\pi\)
−0.206269 + 0.978495i \(0.566132\pi\)
\(812\) −1.59737 −0.0560569
\(813\) 0 0
\(814\) −7.61649 −0.266958
\(815\) −2.11305 −0.0740169
\(816\) 0 0
\(817\) 11.8649 0.415101
\(818\) 9.18360 0.321097
\(819\) 0 0
\(820\) 0.146672 0.00512199
\(821\) −51.3053 −1.79057 −0.895284 0.445495i \(-0.853028\pi\)
−0.895284 + 0.445495i \(0.853028\pi\)
\(822\) 0 0
\(823\) −0.892424 −0.0311079 −0.0155540 0.999879i \(-0.504951\pi\)
−0.0155540 + 0.999879i \(0.504951\pi\)
\(824\) 5.27651 0.183816
\(825\) 0 0
\(826\) −3.43099 −0.119379
\(827\) −21.4142 −0.744644 −0.372322 0.928104i \(-0.621438\pi\)
−0.372322 + 0.928104i \(0.621438\pi\)
\(828\) 0 0
\(829\) −10.1286 −0.351782 −0.175891 0.984410i \(-0.556281\pi\)
−0.175891 + 0.984410i \(0.556281\pi\)
\(830\) −0.982027 −0.0340867
\(831\) 0 0
\(832\) −0.0298835 −0.00103603
\(833\) 24.5847 0.851810
\(834\) 0 0
\(835\) 1.38368 0.0478842
\(836\) −4.79514 −0.165843
\(837\) 0 0
\(838\) 23.3723 0.807384
\(839\) 13.1240 0.453091 0.226545 0.974001i \(-0.427257\pi\)
0.226545 + 0.974001i \(0.427257\pi\)
\(840\) 0 0
\(841\) −8.23823 −0.284077
\(842\) −22.5192 −0.776064
\(843\) 0 0
\(844\) 8.83252 0.304028
\(845\) −1.32694 −0.0456482
\(846\) 0 0
\(847\) −2.41622 −0.0830224
\(848\) −9.52893 −0.327225
\(849\) 0 0
\(850\) 17.8371 0.611807
\(851\) 13.4966 0.462658
\(852\) 0 0
\(853\) 24.7181 0.846333 0.423167 0.906052i \(-0.360919\pi\)
0.423167 + 0.906052i \(0.360919\pi\)
\(854\) −2.59550 −0.0888161
\(855\) 0 0
\(856\) 8.42424 0.287935
\(857\) 43.6328 1.49047 0.745234 0.666803i \(-0.232338\pi\)
0.745234 + 0.666803i \(0.232338\pi\)
\(858\) 0 0
\(859\) 43.6531 1.48942 0.744712 0.667386i \(-0.232587\pi\)
0.744712 + 0.667386i \(0.232587\pi\)
\(860\) −0.511921 −0.0174563
\(861\) 0 0
\(862\) 4.03344 0.137380
\(863\) 9.57447 0.325919 0.162959 0.986633i \(-0.447896\pi\)
0.162959 + 0.986633i \(0.447896\pi\)
\(864\) 0 0
\(865\) 2.48119 0.0843628
\(866\) 4.71921 0.160365
\(867\) 0 0
\(868\) 0.294269 0.00998813
\(869\) 18.7321 0.635444
\(870\) 0 0
\(871\) 0.121566 0.00411912
\(872\) 3.75345 0.127108
\(873\) 0 0
\(874\) 8.49711 0.287419
\(875\) −0.357487 −0.0120853
\(876\) 0 0
\(877\) −17.1383 −0.578719 −0.289360 0.957220i \(-0.593442\pi\)
−0.289360 + 0.957220i \(0.593442\pi\)
\(878\) −32.7549 −1.10542
\(879\) 0 0
\(880\) 0.206890 0.00697425
\(881\) −19.2478 −0.648475 −0.324237 0.945976i \(-0.605108\pi\)
−0.324237 + 0.945976i \(0.605108\pi\)
\(882\) 0 0
\(883\) −30.4527 −1.02482 −0.512408 0.858742i \(-0.671246\pi\)
−0.512408 + 0.858742i \(0.671246\pi\)
\(884\) 0.106830 0.00359307
\(885\) 0 0
\(886\) −35.0469 −1.17742
\(887\) −27.3879 −0.919595 −0.459797 0.888024i \(-0.652078\pi\)
−0.459797 + 0.888024i \(0.652078\pi\)
\(888\) 0 0
\(889\) −0.479300 −0.0160752
\(890\) −0.0889423 −0.00298135
\(891\) 0 0
\(892\) 20.9511 0.701493
\(893\) −14.8694 −0.497584
\(894\) 0 0
\(895\) −2.02980 −0.0678486
\(896\) 0.350570 0.0117117
\(897\) 0 0
\(898\) 32.0551 1.06969
\(899\) −3.82474 −0.127562
\(900\) 0 0
\(901\) 34.0646 1.13486
\(902\) 2.91211 0.0969627
\(903\) 0 0
\(904\) 4.46292 0.148434
\(905\) 0.138653 0.00460899
\(906\) 0 0
\(907\) 23.6464 0.785166 0.392583 0.919717i \(-0.371582\pi\)
0.392583 + 0.919717i \(0.371582\pi\)
\(908\) 4.91723 0.163184
\(909\) 0 0
\(910\) −0.00106941 −3.54507e−5 0
\(911\) 40.4265 1.33939 0.669695 0.742636i \(-0.266425\pi\)
0.669695 + 0.742636i \(0.266425\pi\)
\(912\) 0 0
\(913\) −19.4978 −0.645283
\(914\) 24.0443 0.795316
\(915\) 0 0
\(916\) −7.53842 −0.249077
\(917\) −3.06995 −0.101379
\(918\) 0 0
\(919\) −22.4929 −0.741973 −0.370986 0.928638i \(-0.620980\pi\)
−0.370986 + 0.928638i \(0.620980\pi\)
\(920\) −0.366614 −0.0120869
\(921\) 0 0
\(922\) 7.50713 0.247234
\(923\) −0.283745 −0.00933957
\(924\) 0 0
\(925\) 18.7507 0.616521
\(926\) −37.7034 −1.23901
\(927\) 0 0
\(928\) −4.55651 −0.149575
\(929\) −29.1055 −0.954920 −0.477460 0.878653i \(-0.658442\pi\)
−0.477460 + 0.878653i \(0.658442\pi\)
\(930\) 0 0
\(931\) 16.2707 0.533251
\(932\) 11.9221 0.390521
\(933\) 0 0
\(934\) −11.1921 −0.366217
\(935\) −0.739604 −0.0241876
\(936\) 0 0
\(937\) −6.36306 −0.207872 −0.103936 0.994584i \(-0.533144\pi\)
−0.103936 + 0.994584i \(0.533144\pi\)
\(938\) −1.42612 −0.0465644
\(939\) 0 0
\(940\) 0.641549 0.0209250
\(941\) 35.5770 1.15978 0.579889 0.814696i \(-0.303096\pi\)
0.579889 + 0.814696i \(0.303096\pi\)
\(942\) 0 0
\(943\) −5.16033 −0.168043
\(944\) −9.78689 −0.318536
\(945\) 0 0
\(946\) −10.1640 −0.330460
\(947\) 28.1479 0.914684 0.457342 0.889291i \(-0.348802\pi\)
0.457342 + 0.889291i \(0.348802\pi\)
\(948\) 0 0
\(949\) −0.238025 −0.00772663
\(950\) 11.8050 0.383004
\(951\) 0 0
\(952\) −1.25324 −0.0406178
\(953\) 47.8502 1.55002 0.775010 0.631949i \(-0.217745\pi\)
0.775010 + 0.631949i \(0.217745\pi\)
\(954\) 0 0
\(955\) 1.23081 0.0398281
\(956\) −16.1316 −0.521734
\(957\) 0 0
\(958\) 37.4425 1.20971
\(959\) −2.79128 −0.0901353
\(960\) 0 0
\(961\) −30.2954 −0.977271
\(962\) 0.112302 0.00362076
\(963\) 0 0
\(964\) 20.6366 0.664662
\(965\) 1.75329 0.0564404
\(966\) 0 0
\(967\) 11.0594 0.355646 0.177823 0.984063i \(-0.443095\pi\)
0.177823 + 0.984063i \(0.443095\pi\)
\(968\) −6.89228 −0.221526
\(969\) 0 0
\(970\) −1.32620 −0.0425816
\(971\) −11.6714 −0.374552 −0.187276 0.982307i \(-0.559966\pi\)
−0.187276 + 0.982307i \(0.559966\pi\)
\(972\) 0 0
\(973\) 1.16045 0.0372023
\(974\) −9.80226 −0.314085
\(975\) 0 0
\(976\) −7.40365 −0.236985
\(977\) −29.4805 −0.943163 −0.471582 0.881822i \(-0.656317\pi\)
−0.471582 + 0.881822i \(0.656317\pi\)
\(978\) 0 0
\(979\) −1.76592 −0.0564389
\(980\) −0.702011 −0.0224249
\(981\) 0 0
\(982\) −32.0256 −1.02198
\(983\) −28.4486 −0.907371 −0.453685 0.891162i \(-0.649891\pi\)
−0.453685 + 0.891162i \(0.649891\pi\)
\(984\) 0 0
\(985\) 1.59565 0.0508417
\(986\) 16.2889 0.518745
\(987\) 0 0
\(988\) 0.0707022 0.00224934
\(989\) 18.0108 0.572712
\(990\) 0 0
\(991\) −52.8403 −1.67853 −0.839264 0.543724i \(-0.817014\pi\)
−0.839264 + 0.543724i \(0.817014\pi\)
\(992\) 0.839401 0.0266510
\(993\) 0 0
\(994\) 3.32866 0.105579
\(995\) −1.60838 −0.0509891
\(996\) 0 0
\(997\) 21.3350 0.675685 0.337843 0.941203i \(-0.390303\pi\)
0.337843 + 0.941203i \(0.390303\pi\)
\(998\) 13.3658 0.423087
\(999\) 0 0
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 \(a_p\))