Properties

Label 8046.2.a.h.1.7
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 1.7
Root \(2.89499\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.72525 q^{5} -2.60583 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.72525 q^{5} -2.60583 q^{7} +1.00000 q^{8} +1.72525 q^{10} -5.87208 q^{11} +3.97610 q^{13} -2.60583 q^{14} +1.00000 q^{16} +3.69002 q^{17} -0.972350 q^{19} +1.72525 q^{20} -5.87208 q^{22} -1.45252 q^{23} -2.02352 q^{25} +3.97610 q^{26} -2.60583 q^{28} +0.793752 q^{29} -5.90931 q^{31} +1.00000 q^{32} +3.69002 q^{34} -4.49571 q^{35} -1.91150 q^{37} -0.972350 q^{38} +1.72525 q^{40} +2.77935 q^{41} +0.964786 q^{43} -5.87208 q^{44} -1.45252 q^{46} -5.72077 q^{47} -0.209634 q^{49} -2.02352 q^{50} +3.97610 q^{52} -12.1545 q^{53} -10.1308 q^{55} -2.60583 q^{56} +0.793752 q^{58} +1.69551 q^{59} -8.91875 q^{61} -5.90931 q^{62} +1.00000 q^{64} +6.85976 q^{65} +1.13575 q^{67} +3.69002 q^{68} -4.49571 q^{70} -3.26677 q^{71} +3.64845 q^{73} -1.91150 q^{74} -0.972350 q^{76} +15.3017 q^{77} -6.18956 q^{79} +1.72525 q^{80} +2.77935 q^{82} +14.2544 q^{83} +6.36619 q^{85} +0.964786 q^{86} -5.87208 q^{88} -2.08402 q^{89} -10.3611 q^{91} -1.45252 q^{92} -5.72077 q^{94} -1.67754 q^{95} +4.60522 q^{97} -0.209634 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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
\(5\) 1.72525 0.771554 0.385777 0.922592i \(-0.373933\pi\)
0.385777 + 0.922592i \(0.373933\pi\)
\(6\) 0 0
\(7\) −2.60583 −0.984912 −0.492456 0.870337i \(-0.663901\pi\)
−0.492456 + 0.870337i \(0.663901\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.72525 0.545571
\(11\) −5.87208 −1.77050 −0.885249 0.465117i \(-0.846012\pi\)
−0.885249 + 0.465117i \(0.846012\pi\)
\(12\) 0 0
\(13\) 3.97610 1.10277 0.551386 0.834250i \(-0.314099\pi\)
0.551386 + 0.834250i \(0.314099\pi\)
\(14\) −2.60583 −0.696438
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.69002 0.894961 0.447480 0.894294i \(-0.352321\pi\)
0.447480 + 0.894294i \(0.352321\pi\)
\(18\) 0 0
\(19\) −0.972350 −0.223072 −0.111536 0.993760i \(-0.535577\pi\)
−0.111536 + 0.993760i \(0.535577\pi\)
\(20\) 1.72525 0.385777
\(21\) 0 0
\(22\) −5.87208 −1.25193
\(23\) −1.45252 −0.302871 −0.151436 0.988467i \(-0.548390\pi\)
−0.151436 + 0.988467i \(0.548390\pi\)
\(24\) 0 0
\(25\) −2.02352 −0.404705
\(26\) 3.97610 0.779778
\(27\) 0 0
\(28\) −2.60583 −0.492456
\(29\) 0.793752 0.147396 0.0736980 0.997281i \(-0.476520\pi\)
0.0736980 + 0.997281i \(0.476520\pi\)
\(30\) 0 0
\(31\) −5.90931 −1.06134 −0.530672 0.847578i \(-0.678060\pi\)
−0.530672 + 0.847578i \(0.678060\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 3.69002 0.632833
\(35\) −4.49571 −0.759913
\(36\) 0 0
\(37\) −1.91150 −0.314249 −0.157125 0.987579i \(-0.550222\pi\)
−0.157125 + 0.987579i \(0.550222\pi\)
\(38\) −0.972350 −0.157736
\(39\) 0 0
\(40\) 1.72525 0.272785
\(41\) 2.77935 0.434061 0.217030 0.976165i \(-0.430363\pi\)
0.217030 + 0.976165i \(0.430363\pi\)
\(42\) 0 0
\(43\) 0.964786 0.147128 0.0735642 0.997290i \(-0.476563\pi\)
0.0735642 + 0.997290i \(0.476563\pi\)
\(44\) −5.87208 −0.885249
\(45\) 0 0
\(46\) −1.45252 −0.214162
\(47\) −5.72077 −0.834461 −0.417230 0.908801i \(-0.636999\pi\)
−0.417230 + 0.908801i \(0.636999\pi\)
\(48\) 0 0
\(49\) −0.209634 −0.0299478
\(50\) −2.02352 −0.286169
\(51\) 0 0
\(52\) 3.97610 0.551386
\(53\) −12.1545 −1.66955 −0.834775 0.550592i \(-0.814402\pi\)
−0.834775 + 0.550592i \(0.814402\pi\)
\(54\) 0 0
\(55\) −10.1308 −1.36603
\(56\) −2.60583 −0.348219
\(57\) 0 0
\(58\) 0.793752 0.104225
\(59\) 1.69551 0.220737 0.110368 0.993891i \(-0.464797\pi\)
0.110368 + 0.993891i \(0.464797\pi\)
\(60\) 0 0
\(61\) −8.91875 −1.14193 −0.570965 0.820975i \(-0.693431\pi\)
−0.570965 + 0.820975i \(0.693431\pi\)
\(62\) −5.90931 −0.750483
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.85976 0.850849
\(66\) 0 0
\(67\) 1.13575 0.138754 0.0693770 0.997591i \(-0.477899\pi\)
0.0693770 + 0.997591i \(0.477899\pi\)
\(68\) 3.69002 0.447480
\(69\) 0 0
\(70\) −4.49571 −0.537340
\(71\) −3.26677 −0.387694 −0.193847 0.981032i \(-0.562096\pi\)
−0.193847 + 0.981032i \(0.562096\pi\)
\(72\) 0 0
\(73\) 3.64845 0.427018 0.213509 0.976941i \(-0.431511\pi\)
0.213509 + 0.976941i \(0.431511\pi\)
\(74\) −1.91150 −0.222208
\(75\) 0 0
\(76\) −0.972350 −0.111536
\(77\) 15.3017 1.74379
\(78\) 0 0
\(79\) −6.18956 −0.696380 −0.348190 0.937424i \(-0.613204\pi\)
−0.348190 + 0.937424i \(0.613204\pi\)
\(80\) 1.72525 0.192888
\(81\) 0 0
\(82\) 2.77935 0.306927
\(83\) 14.2544 1.56462 0.782309 0.622890i \(-0.214042\pi\)
0.782309 + 0.622890i \(0.214042\pi\)
\(84\) 0 0
\(85\) 6.36619 0.690510
\(86\) 0.964786 0.104035
\(87\) 0 0
\(88\) −5.87208 −0.625966
\(89\) −2.08402 −0.220906 −0.110453 0.993881i \(-0.535230\pi\)
−0.110453 + 0.993881i \(0.535230\pi\)
\(90\) 0 0
\(91\) −10.3611 −1.08613
\(92\) −1.45252 −0.151436
\(93\) 0 0
\(94\) −5.72077 −0.590053
\(95\) −1.67754 −0.172112
\(96\) 0 0
\(97\) 4.60522 0.467589 0.233795 0.972286i \(-0.424886\pi\)
0.233795 + 0.972286i \(0.424886\pi\)
\(98\) −0.209634 −0.0211763
\(99\) 0 0
\(100\) −2.02352 −0.202352
\(101\) −6.36787 −0.633627 −0.316814 0.948488i \(-0.602613\pi\)
−0.316814 + 0.948488i \(0.602613\pi\)
\(102\) 0 0
\(103\) 0.442994 0.0436495 0.0218248 0.999762i \(-0.493052\pi\)
0.0218248 + 0.999762i \(0.493052\pi\)
\(104\) 3.97610 0.389889
\(105\) 0 0
\(106\) −12.1545 −1.18055
\(107\) −1.20231 −0.116232 −0.0581158 0.998310i \(-0.518509\pi\)
−0.0581158 + 0.998310i \(0.518509\pi\)
\(108\) 0 0
\(109\) 0.528131 0.0505858 0.0252929 0.999680i \(-0.491948\pi\)
0.0252929 + 0.999680i \(0.491948\pi\)
\(110\) −10.1308 −0.965932
\(111\) 0 0
\(112\) −2.60583 −0.246228
\(113\) 3.78400 0.355969 0.177984 0.984033i \(-0.443042\pi\)
0.177984 + 0.984033i \(0.443042\pi\)
\(114\) 0 0
\(115\) −2.50596 −0.233682
\(116\) 0.793752 0.0736980
\(117\) 0 0
\(118\) 1.69551 0.156084
\(119\) −9.61557 −0.881458
\(120\) 0 0
\(121\) 23.4813 2.13466
\(122\) −8.91875 −0.807466
\(123\) 0 0
\(124\) −5.90931 −0.530672
\(125\) −12.1173 −1.08381
\(126\) 0 0
\(127\) −7.25200 −0.643511 −0.321755 0.946823i \(-0.604273\pi\)
−0.321755 + 0.946823i \(0.604273\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 6.85976 0.601641
\(131\) −3.56564 −0.311531 −0.155765 0.987794i \(-0.549784\pi\)
−0.155765 + 0.987794i \(0.549784\pi\)
\(132\) 0 0
\(133\) 2.53378 0.219707
\(134\) 1.13575 0.0981140
\(135\) 0 0
\(136\) 3.69002 0.316416
\(137\) −16.5706 −1.41573 −0.707863 0.706350i \(-0.750341\pi\)
−0.707863 + 0.706350i \(0.750341\pi\)
\(138\) 0 0
\(139\) 10.6385 0.902347 0.451174 0.892436i \(-0.351006\pi\)
0.451174 + 0.892436i \(0.351006\pi\)
\(140\) −4.49571 −0.379956
\(141\) 0 0
\(142\) −3.26677 −0.274141
\(143\) −23.3480 −1.95246
\(144\) 0 0
\(145\) 1.36942 0.113724
\(146\) 3.64845 0.301948
\(147\) 0 0
\(148\) −1.91150 −0.157125
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −11.4508 −0.931854 −0.465927 0.884823i \(-0.654279\pi\)
−0.465927 + 0.884823i \(0.654279\pi\)
\(152\) −0.972350 −0.0788680
\(153\) 0 0
\(154\) 15.3017 1.23304
\(155\) −10.1950 −0.818883
\(156\) 0 0
\(157\) −2.49203 −0.198886 −0.0994428 0.995043i \(-0.531706\pi\)
−0.0994428 + 0.995043i \(0.531706\pi\)
\(158\) −6.18956 −0.492415
\(159\) 0 0
\(160\) 1.72525 0.136393
\(161\) 3.78503 0.298302
\(162\) 0 0
\(163\) −23.2212 −1.81882 −0.909411 0.415899i \(-0.863467\pi\)
−0.909411 + 0.415899i \(0.863467\pi\)
\(164\) 2.77935 0.217030
\(165\) 0 0
\(166\) 14.2544 1.10635
\(167\) −18.5579 −1.43606 −0.718028 0.696014i \(-0.754955\pi\)
−0.718028 + 0.696014i \(0.754955\pi\)
\(168\) 0 0
\(169\) 2.80941 0.216108
\(170\) 6.36619 0.488265
\(171\) 0 0
\(172\) 0.964786 0.0735642
\(173\) −17.3894 −1.32209 −0.661046 0.750345i \(-0.729887\pi\)
−0.661046 + 0.750345i \(0.729887\pi\)
\(174\) 0 0
\(175\) 5.27296 0.398599
\(176\) −5.87208 −0.442625
\(177\) 0 0
\(178\) −2.08402 −0.156204
\(179\) 0.962244 0.0719215 0.0359607 0.999353i \(-0.488551\pi\)
0.0359607 + 0.999353i \(0.488551\pi\)
\(180\) 0 0
\(181\) −15.2649 −1.13463 −0.567314 0.823501i \(-0.692017\pi\)
−0.567314 + 0.823501i \(0.692017\pi\)
\(182\) −10.3611 −0.768013
\(183\) 0 0
\(184\) −1.45252 −0.107081
\(185\) −3.29781 −0.242460
\(186\) 0 0
\(187\) −21.6681 −1.58453
\(188\) −5.72077 −0.417230
\(189\) 0 0
\(190\) −1.67754 −0.121702
\(191\) 13.3385 0.965140 0.482570 0.875858i \(-0.339703\pi\)
0.482570 + 0.875858i \(0.339703\pi\)
\(192\) 0 0
\(193\) −0.978390 −0.0704260 −0.0352130 0.999380i \(-0.511211\pi\)
−0.0352130 + 0.999380i \(0.511211\pi\)
\(194\) 4.60522 0.330636
\(195\) 0 0
\(196\) −0.209634 −0.0149739
\(197\) 15.9854 1.13891 0.569455 0.822023i \(-0.307154\pi\)
0.569455 + 0.822023i \(0.307154\pi\)
\(198\) 0 0
\(199\) 2.31903 0.164392 0.0821959 0.996616i \(-0.473807\pi\)
0.0821959 + 0.996616i \(0.473807\pi\)
\(200\) −2.02352 −0.143085
\(201\) 0 0
\(202\) −6.36787 −0.448042
\(203\) −2.06838 −0.145172
\(204\) 0 0
\(205\) 4.79506 0.334901
\(206\) 0.442994 0.0308649
\(207\) 0 0
\(208\) 3.97610 0.275693
\(209\) 5.70972 0.394949
\(210\) 0 0
\(211\) 12.7331 0.876581 0.438291 0.898833i \(-0.355584\pi\)
0.438291 + 0.898833i \(0.355584\pi\)
\(212\) −12.1545 −0.834775
\(213\) 0 0
\(214\) −1.20231 −0.0821882
\(215\) 1.66449 0.113517
\(216\) 0 0
\(217\) 15.3987 1.04533
\(218\) 0.528131 0.0357696
\(219\) 0 0
\(220\) −10.1308 −0.683017
\(221\) 14.6719 0.986939
\(222\) 0 0
\(223\) −13.1207 −0.878625 −0.439313 0.898334i \(-0.644778\pi\)
−0.439313 + 0.898334i \(0.644778\pi\)
\(224\) −2.60583 −0.174110
\(225\) 0 0
\(226\) 3.78400 0.251708
\(227\) −5.44603 −0.361466 −0.180733 0.983532i \(-0.557847\pi\)
−0.180733 + 0.983532i \(0.557847\pi\)
\(228\) 0 0
\(229\) 13.9568 0.922294 0.461147 0.887324i \(-0.347438\pi\)
0.461147 + 0.887324i \(0.347438\pi\)
\(230\) −2.50596 −0.165238
\(231\) 0 0
\(232\) 0.793752 0.0521124
\(233\) 26.4164 1.73059 0.865297 0.501259i \(-0.167130\pi\)
0.865297 + 0.501259i \(0.167130\pi\)
\(234\) 0 0
\(235\) −9.86975 −0.643831
\(236\) 1.69551 0.110368
\(237\) 0 0
\(238\) −9.61557 −0.623285
\(239\) −3.39802 −0.219800 −0.109900 0.993943i \(-0.535053\pi\)
−0.109900 + 0.993943i \(0.535053\pi\)
\(240\) 0 0
\(241\) −9.84720 −0.634314 −0.317157 0.948373i \(-0.602728\pi\)
−0.317157 + 0.948373i \(0.602728\pi\)
\(242\) 23.4813 1.50944
\(243\) 0 0
\(244\) −8.91875 −0.570965
\(245\) −0.361671 −0.0231063
\(246\) 0 0
\(247\) −3.86617 −0.245998
\(248\) −5.90931 −0.375241
\(249\) 0 0
\(250\) −12.1173 −0.766366
\(251\) 1.91010 0.120565 0.0602823 0.998181i \(-0.480800\pi\)
0.0602823 + 0.998181i \(0.480800\pi\)
\(252\) 0 0
\(253\) 8.52931 0.536233
\(254\) −7.25200 −0.455031
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −13.3629 −0.833553 −0.416777 0.909009i \(-0.636840\pi\)
−0.416777 + 0.909009i \(0.636840\pi\)
\(258\) 0 0
\(259\) 4.98106 0.309508
\(260\) 6.85976 0.425424
\(261\) 0 0
\(262\) −3.56564 −0.220286
\(263\) −14.1629 −0.873320 −0.436660 0.899627i \(-0.643839\pi\)
−0.436660 + 0.899627i \(0.643839\pi\)
\(264\) 0 0
\(265\) −20.9695 −1.28815
\(266\) 2.53378 0.155356
\(267\) 0 0
\(268\) 1.13575 0.0693770
\(269\) 11.7518 0.716522 0.358261 0.933622i \(-0.383370\pi\)
0.358261 + 0.933622i \(0.383370\pi\)
\(270\) 0 0
\(271\) −23.2669 −1.41336 −0.706680 0.707533i \(-0.749808\pi\)
−0.706680 + 0.707533i \(0.749808\pi\)
\(272\) 3.69002 0.223740
\(273\) 0 0
\(274\) −16.5706 −1.00107
\(275\) 11.8823 0.716529
\(276\) 0 0
\(277\) −22.5303 −1.35371 −0.676857 0.736115i \(-0.736658\pi\)
−0.676857 + 0.736115i \(0.736658\pi\)
\(278\) 10.6385 0.638056
\(279\) 0 0
\(280\) −4.49571 −0.268670
\(281\) 26.5178 1.58192 0.790960 0.611868i \(-0.209582\pi\)
0.790960 + 0.611868i \(0.209582\pi\)
\(282\) 0 0
\(283\) 3.43156 0.203985 0.101993 0.994785i \(-0.467478\pi\)
0.101993 + 0.994785i \(0.467478\pi\)
\(284\) −3.26677 −0.193847
\(285\) 0 0
\(286\) −23.3480 −1.38060
\(287\) −7.24251 −0.427512
\(288\) 0 0
\(289\) −3.38377 −0.199045
\(290\) 1.36942 0.0804150
\(291\) 0 0
\(292\) 3.64845 0.213509
\(293\) 6.15832 0.359773 0.179886 0.983687i \(-0.442427\pi\)
0.179886 + 0.983687i \(0.442427\pi\)
\(294\) 0 0
\(295\) 2.92518 0.170310
\(296\) −1.91150 −0.111104
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −5.77537 −0.333998
\(300\) 0 0
\(301\) −2.51407 −0.144909
\(302\) −11.4508 −0.658920
\(303\) 0 0
\(304\) −0.972350 −0.0557681
\(305\) −15.3870 −0.881060
\(306\) 0 0
\(307\) −31.5787 −1.80229 −0.901145 0.433518i \(-0.857272\pi\)
−0.901145 + 0.433518i \(0.857272\pi\)
\(308\) 15.3017 0.871893
\(309\) 0 0
\(310\) −10.1950 −0.579038
\(311\) −10.9006 −0.618114 −0.309057 0.951044i \(-0.600013\pi\)
−0.309057 + 0.951044i \(0.600013\pi\)
\(312\) 0 0
\(313\) 2.80950 0.158803 0.0794013 0.996843i \(-0.474699\pi\)
0.0794013 + 0.996843i \(0.474699\pi\)
\(314\) −2.49203 −0.140633
\(315\) 0 0
\(316\) −6.18956 −0.348190
\(317\) −1.65172 −0.0927696 −0.0463848 0.998924i \(-0.514770\pi\)
−0.0463848 + 0.998924i \(0.514770\pi\)
\(318\) 0 0
\(319\) −4.66097 −0.260964
\(320\) 1.72525 0.0964442
\(321\) 0 0
\(322\) 3.78503 0.210931
\(323\) −3.58799 −0.199641
\(324\) 0 0
\(325\) −8.04574 −0.446297
\(326\) −23.2212 −1.28610
\(327\) 0 0
\(328\) 2.77935 0.153464
\(329\) 14.9074 0.821871
\(330\) 0 0
\(331\) −24.8063 −1.36348 −0.681740 0.731595i \(-0.738776\pi\)
−0.681740 + 0.731595i \(0.738776\pi\)
\(332\) 14.2544 0.782309
\(333\) 0 0
\(334\) −18.5579 −1.01544
\(335\) 1.95945 0.107056
\(336\) 0 0
\(337\) 6.76816 0.368685 0.184343 0.982862i \(-0.440984\pi\)
0.184343 + 0.982862i \(0.440984\pi\)
\(338\) 2.80941 0.152812
\(339\) 0 0
\(340\) 6.36619 0.345255
\(341\) 34.6999 1.87911
\(342\) 0 0
\(343\) 18.7871 1.01441
\(344\) 0.964786 0.0520177
\(345\) 0 0
\(346\) −17.3894 −0.934860
\(347\) 11.1010 0.595932 0.297966 0.954577i \(-0.403692\pi\)
0.297966 + 0.954577i \(0.403692\pi\)
\(348\) 0 0
\(349\) 27.2718 1.45982 0.729912 0.683541i \(-0.239561\pi\)
0.729912 + 0.683541i \(0.239561\pi\)
\(350\) 5.27296 0.281852
\(351\) 0 0
\(352\) −5.87208 −0.312983
\(353\) 0.471858 0.0251145 0.0125572 0.999921i \(-0.496003\pi\)
0.0125572 + 0.999921i \(0.496003\pi\)
\(354\) 0 0
\(355\) −5.63598 −0.299127
\(356\) −2.08402 −0.110453
\(357\) 0 0
\(358\) 0.962244 0.0508562
\(359\) 13.0395 0.688197 0.344099 0.938934i \(-0.388185\pi\)
0.344099 + 0.938934i \(0.388185\pi\)
\(360\) 0 0
\(361\) −18.0545 −0.950239
\(362\) −15.2649 −0.802303
\(363\) 0 0
\(364\) −10.3611 −0.543067
\(365\) 6.29447 0.329468
\(366\) 0 0
\(367\) −3.53216 −0.184377 −0.0921886 0.995742i \(-0.529386\pi\)
−0.0921886 + 0.995742i \(0.529386\pi\)
\(368\) −1.45252 −0.0757179
\(369\) 0 0
\(370\) −3.29781 −0.171445
\(371\) 31.6726 1.64436
\(372\) 0 0
\(373\) −30.5929 −1.58404 −0.792021 0.610494i \(-0.790971\pi\)
−0.792021 + 0.610494i \(0.790971\pi\)
\(374\) −21.6681 −1.12043
\(375\) 0 0
\(376\) −5.72077 −0.295026
\(377\) 3.15604 0.162544
\(378\) 0 0
\(379\) −0.756326 −0.0388499 −0.0194249 0.999811i \(-0.506184\pi\)
−0.0194249 + 0.999811i \(0.506184\pi\)
\(380\) −1.67754 −0.0860562
\(381\) 0 0
\(382\) 13.3385 0.682457
\(383\) −15.5219 −0.793130 −0.396565 0.918007i \(-0.629798\pi\)
−0.396565 + 0.918007i \(0.629798\pi\)
\(384\) 0 0
\(385\) 26.3991 1.34542
\(386\) −0.978390 −0.0497987
\(387\) 0 0
\(388\) 4.60522 0.233795
\(389\) 34.2558 1.73684 0.868420 0.495830i \(-0.165136\pi\)
0.868420 + 0.495830i \(0.165136\pi\)
\(390\) 0 0
\(391\) −5.35983 −0.271058
\(392\) −0.209634 −0.0105881
\(393\) 0 0
\(394\) 15.9854 0.805331
\(395\) −10.6785 −0.537295
\(396\) 0 0
\(397\) −4.32270 −0.216950 −0.108475 0.994099i \(-0.534597\pi\)
−0.108475 + 0.994099i \(0.534597\pi\)
\(398\) 2.31903 0.116243
\(399\) 0 0
\(400\) −2.02352 −0.101176
\(401\) 21.3467 1.06600 0.533002 0.846114i \(-0.321064\pi\)
0.533002 + 0.846114i \(0.321064\pi\)
\(402\) 0 0
\(403\) −23.4960 −1.17042
\(404\) −6.36787 −0.316814
\(405\) 0 0
\(406\) −2.06838 −0.102652
\(407\) 11.2245 0.556377
\(408\) 0 0
\(409\) 33.9729 1.67985 0.839925 0.542702i \(-0.182599\pi\)
0.839925 + 0.542702i \(0.182599\pi\)
\(410\) 4.79506 0.236811
\(411\) 0 0
\(412\) 0.442994 0.0218248
\(413\) −4.41822 −0.217406
\(414\) 0 0
\(415\) 24.5923 1.20719
\(416\) 3.97610 0.194945
\(417\) 0 0
\(418\) 5.70972 0.279271
\(419\) −18.8895 −0.922813 −0.461406 0.887189i \(-0.652655\pi\)
−0.461406 + 0.887189i \(0.652655\pi\)
\(420\) 0 0
\(421\) 11.7138 0.570896 0.285448 0.958394i \(-0.407858\pi\)
0.285448 + 0.958394i \(0.407858\pi\)
\(422\) 12.7331 0.619837
\(423\) 0 0
\(424\) −12.1545 −0.590275
\(425\) −7.46684 −0.362195
\(426\) 0 0
\(427\) 23.2408 1.12470
\(428\) −1.20231 −0.0581158
\(429\) 0 0
\(430\) 1.66449 0.0802690
\(431\) 17.8470 0.859661 0.429830 0.902910i \(-0.358573\pi\)
0.429830 + 0.902910i \(0.358573\pi\)
\(432\) 0 0
\(433\) −34.1206 −1.63973 −0.819866 0.572555i \(-0.805952\pi\)
−0.819866 + 0.572555i \(0.805952\pi\)
\(434\) 15.3987 0.739160
\(435\) 0 0
\(436\) 0.528131 0.0252929
\(437\) 1.41236 0.0675623
\(438\) 0 0
\(439\) −2.87290 −0.137116 −0.0685579 0.997647i \(-0.521840\pi\)
−0.0685579 + 0.997647i \(0.521840\pi\)
\(440\) −10.1308 −0.482966
\(441\) 0 0
\(442\) 14.6719 0.697871
\(443\) 29.2501 1.38971 0.694856 0.719149i \(-0.255468\pi\)
0.694856 + 0.719149i \(0.255468\pi\)
\(444\) 0 0
\(445\) −3.59545 −0.170441
\(446\) −13.1207 −0.621282
\(447\) 0 0
\(448\) −2.60583 −0.123114
\(449\) 11.4354 0.539670 0.269835 0.962907i \(-0.413031\pi\)
0.269835 + 0.962907i \(0.413031\pi\)
\(450\) 0 0
\(451\) −16.3205 −0.768504
\(452\) 3.78400 0.177984
\(453\) 0 0
\(454\) −5.44603 −0.255595
\(455\) −17.8754 −0.838011
\(456\) 0 0
\(457\) 13.2066 0.617781 0.308890 0.951098i \(-0.400042\pi\)
0.308890 + 0.951098i \(0.400042\pi\)
\(458\) 13.9568 0.652160
\(459\) 0 0
\(460\) −2.50596 −0.116841
\(461\) 23.7293 1.10518 0.552592 0.833452i \(-0.313639\pi\)
0.552592 + 0.833452i \(0.313639\pi\)
\(462\) 0 0
\(463\) −6.33611 −0.294464 −0.147232 0.989102i \(-0.547036\pi\)
−0.147232 + 0.989102i \(0.547036\pi\)
\(464\) 0.793752 0.0368490
\(465\) 0 0
\(466\) 26.4164 1.22371
\(467\) 10.5195 0.486782 0.243391 0.969928i \(-0.421740\pi\)
0.243391 + 0.969928i \(0.421740\pi\)
\(468\) 0 0
\(469\) −2.95958 −0.136661
\(470\) −9.86975 −0.455258
\(471\) 0 0
\(472\) 1.69551 0.0780422
\(473\) −5.66530 −0.260491
\(474\) 0 0
\(475\) 1.96757 0.0902784
\(476\) −9.61557 −0.440729
\(477\) 0 0
\(478\) −3.39802 −0.155422
\(479\) 0.598309 0.0273374 0.0136687 0.999907i \(-0.495649\pi\)
0.0136687 + 0.999907i \(0.495649\pi\)
\(480\) 0 0
\(481\) −7.60033 −0.346545
\(482\) −9.84720 −0.448528
\(483\) 0 0
\(484\) 23.4813 1.06733
\(485\) 7.94514 0.360770
\(486\) 0 0
\(487\) 3.97672 0.180203 0.0901013 0.995933i \(-0.471281\pi\)
0.0901013 + 0.995933i \(0.471281\pi\)
\(488\) −8.91875 −0.403733
\(489\) 0 0
\(490\) −0.361671 −0.0163386
\(491\) 12.4900 0.563664 0.281832 0.959464i \(-0.409058\pi\)
0.281832 + 0.959464i \(0.409058\pi\)
\(492\) 0 0
\(493\) 2.92896 0.131914
\(494\) −3.86617 −0.173947
\(495\) 0 0
\(496\) −5.90931 −0.265336
\(497\) 8.51264 0.381844
\(498\) 0 0
\(499\) 30.1380 1.34916 0.674580 0.738202i \(-0.264325\pi\)
0.674580 + 0.738202i \(0.264325\pi\)
\(500\) −12.1173 −0.541903
\(501\) 0 0
\(502\) 1.91010 0.0852520
\(503\) −4.87062 −0.217170 −0.108585 0.994087i \(-0.534632\pi\)
−0.108585 + 0.994087i \(0.534632\pi\)
\(504\) 0 0
\(505\) −10.9862 −0.488877
\(506\) 8.52931 0.379174
\(507\) 0 0
\(508\) −7.25200 −0.321755
\(509\) −0.234024 −0.0103729 −0.00518647 0.999987i \(-0.501651\pi\)
−0.00518647 + 0.999987i \(0.501651\pi\)
\(510\) 0 0
\(511\) −9.50724 −0.420576
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.3629 −0.589411
\(515\) 0.764274 0.0336780
\(516\) 0 0
\(517\) 33.5928 1.47741
\(518\) 4.98106 0.218855
\(519\) 0 0
\(520\) 6.85976 0.300820
\(521\) −37.9004 −1.66045 −0.830223 0.557432i \(-0.811787\pi\)
−0.830223 + 0.557432i \(0.811787\pi\)
\(522\) 0 0
\(523\) −11.1086 −0.485744 −0.242872 0.970058i \(-0.578090\pi\)
−0.242872 + 0.970058i \(0.578090\pi\)
\(524\) −3.56564 −0.155765
\(525\) 0 0
\(526\) −14.1629 −0.617530
\(527\) −21.8055 −0.949861
\(528\) 0 0
\(529\) −20.8902 −0.908269
\(530\) −20.9695 −0.910858
\(531\) 0 0
\(532\) 2.53378 0.109853
\(533\) 11.0510 0.478671
\(534\) 0 0
\(535\) −2.07428 −0.0896790
\(536\) 1.13575 0.0490570
\(537\) 0 0
\(538\) 11.7518 0.506657
\(539\) 1.23099 0.0530225
\(540\) 0 0
\(541\) −32.4740 −1.39617 −0.698084 0.716016i \(-0.745964\pi\)
−0.698084 + 0.716016i \(0.745964\pi\)
\(542\) −23.2669 −0.999397
\(543\) 0 0
\(544\) 3.69002 0.158208
\(545\) 0.911157 0.0390297
\(546\) 0 0
\(547\) −26.9889 −1.15396 −0.576981 0.816757i \(-0.695769\pi\)
−0.576981 + 0.816757i \(0.695769\pi\)
\(548\) −16.5706 −0.707863
\(549\) 0 0
\(550\) 11.8823 0.506662
\(551\) −0.771805 −0.0328800
\(552\) 0 0
\(553\) 16.1290 0.685873
\(554\) −22.5303 −0.957220
\(555\) 0 0
\(556\) 10.6385 0.451174
\(557\) 37.9551 1.60821 0.804105 0.594487i \(-0.202645\pi\)
0.804105 + 0.594487i \(0.202645\pi\)
\(558\) 0 0
\(559\) 3.83609 0.162249
\(560\) −4.49571 −0.189978
\(561\) 0 0
\(562\) 26.5178 1.11859
\(563\) 10.7327 0.452330 0.226165 0.974089i \(-0.427381\pi\)
0.226165 + 0.974089i \(0.427381\pi\)
\(564\) 0 0
\(565\) 6.52833 0.274649
\(566\) 3.43156 0.144239
\(567\) 0 0
\(568\) −3.26677 −0.137070
\(569\) 26.7458 1.12124 0.560621 0.828072i \(-0.310562\pi\)
0.560621 + 0.828072i \(0.310562\pi\)
\(570\) 0 0
\(571\) −32.2845 −1.35106 −0.675532 0.737331i \(-0.736086\pi\)
−0.675532 + 0.737331i \(0.736086\pi\)
\(572\) −23.3480 −0.976229
\(573\) 0 0
\(574\) −7.24251 −0.302297
\(575\) 2.93921 0.122573
\(576\) 0 0
\(577\) 43.5328 1.81230 0.906148 0.422961i \(-0.139009\pi\)
0.906148 + 0.422961i \(0.139009\pi\)
\(578\) −3.38377 −0.140746
\(579\) 0 0
\(580\) 1.36942 0.0568620
\(581\) −37.1445 −1.54101
\(582\) 0 0
\(583\) 71.3722 2.95593
\(584\) 3.64845 0.150974
\(585\) 0 0
\(586\) 6.15832 0.254398
\(587\) 9.91387 0.409189 0.204595 0.978847i \(-0.434412\pi\)
0.204595 + 0.978847i \(0.434412\pi\)
\(588\) 0 0
\(589\) 5.74592 0.236756
\(590\) 2.92518 0.120428
\(591\) 0 0
\(592\) −1.91150 −0.0785623
\(593\) 21.5675 0.885673 0.442836 0.896602i \(-0.353972\pi\)
0.442836 + 0.896602i \(0.353972\pi\)
\(594\) 0 0
\(595\) −16.5892 −0.680092
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) −5.77537 −0.236173
\(599\) 4.47812 0.182971 0.0914854 0.995806i \(-0.470839\pi\)
0.0914854 + 0.995806i \(0.470839\pi\)
\(600\) 0 0
\(601\) −9.29537 −0.379166 −0.189583 0.981865i \(-0.560714\pi\)
−0.189583 + 0.981865i \(0.560714\pi\)
\(602\) −2.51407 −0.102466
\(603\) 0 0
\(604\) −11.4508 −0.465927
\(605\) 40.5110 1.64701
\(606\) 0 0
\(607\) 35.9673 1.45987 0.729933 0.683518i \(-0.239551\pi\)
0.729933 + 0.683518i \(0.239551\pi\)
\(608\) −0.972350 −0.0394340
\(609\) 0 0
\(610\) −15.3870 −0.623003
\(611\) −22.7464 −0.920221
\(612\) 0 0
\(613\) 32.3275 1.30570 0.652849 0.757488i \(-0.273574\pi\)
0.652849 + 0.757488i \(0.273574\pi\)
\(614\) −31.5787 −1.27441
\(615\) 0 0
\(616\) 15.3017 0.616521
\(617\) −33.4194 −1.34541 −0.672707 0.739909i \(-0.734869\pi\)
−0.672707 + 0.739909i \(0.734869\pi\)
\(618\) 0 0
\(619\) −26.3165 −1.05775 −0.528875 0.848700i \(-0.677386\pi\)
−0.528875 + 0.848700i \(0.677386\pi\)
\(620\) −10.1950 −0.409442
\(621\) 0 0
\(622\) −10.9006 −0.437072
\(623\) 5.43061 0.217573
\(624\) 0 0
\(625\) −10.7877 −0.431509
\(626\) 2.80950 0.112290
\(627\) 0 0
\(628\) −2.49203 −0.0994428
\(629\) −7.05348 −0.281241
\(630\) 0 0
\(631\) 0.902840 0.0359415 0.0179707 0.999839i \(-0.494279\pi\)
0.0179707 + 0.999839i \(0.494279\pi\)
\(632\) −6.18956 −0.246208
\(633\) 0 0
\(634\) −1.65172 −0.0655980
\(635\) −12.5115 −0.496503
\(636\) 0 0
\(637\) −0.833528 −0.0330256
\(638\) −4.66097 −0.184530
\(639\) 0 0
\(640\) 1.72525 0.0681964
\(641\) 5.47310 0.216174 0.108087 0.994141i \(-0.465527\pi\)
0.108087 + 0.994141i \(0.465527\pi\)
\(642\) 0 0
\(643\) 14.4305 0.569082 0.284541 0.958664i \(-0.408159\pi\)
0.284541 + 0.958664i \(0.408159\pi\)
\(644\) 3.78503 0.149151
\(645\) 0 0
\(646\) −3.58799 −0.141168
\(647\) −14.4809 −0.569303 −0.284652 0.958631i \(-0.591878\pi\)
−0.284652 + 0.958631i \(0.591878\pi\)
\(648\) 0 0
\(649\) −9.95618 −0.390814
\(650\) −8.04574 −0.315580
\(651\) 0 0
\(652\) −23.2212 −0.909411
\(653\) 2.85456 0.111708 0.0558538 0.998439i \(-0.482212\pi\)
0.0558538 + 0.998439i \(0.482212\pi\)
\(654\) 0 0
\(655\) −6.15160 −0.240363
\(656\) 2.77935 0.108515
\(657\) 0 0
\(658\) 14.9074 0.581150
\(659\) 11.4305 0.445268 0.222634 0.974902i \(-0.428534\pi\)
0.222634 + 0.974902i \(0.428534\pi\)
\(660\) 0 0
\(661\) −25.4333 −0.989243 −0.494621 0.869109i \(-0.664693\pi\)
−0.494621 + 0.869109i \(0.664693\pi\)
\(662\) −24.8063 −0.964126
\(663\) 0 0
\(664\) 14.2544 0.553176
\(665\) 4.37140 0.169516
\(666\) 0 0
\(667\) −1.15294 −0.0446420
\(668\) −18.5579 −0.718028
\(669\) 0 0
\(670\) 1.95945 0.0757002
\(671\) 52.3716 2.02178
\(672\) 0 0
\(673\) 14.5973 0.562686 0.281343 0.959607i \(-0.409220\pi\)
0.281343 + 0.959607i \(0.409220\pi\)
\(674\) 6.76816 0.260700
\(675\) 0 0
\(676\) 2.80941 0.108054
\(677\) 5.17809 0.199010 0.0995051 0.995037i \(-0.468274\pi\)
0.0995051 + 0.995037i \(0.468274\pi\)
\(678\) 0 0
\(679\) −12.0004 −0.460534
\(680\) 6.36619 0.244132
\(681\) 0 0
\(682\) 34.6999 1.32873
\(683\) −19.5785 −0.749151 −0.374575 0.927196i \(-0.622211\pi\)
−0.374575 + 0.927196i \(0.622211\pi\)
\(684\) 0 0
\(685\) −28.5885 −1.09231
\(686\) 18.7871 0.717295
\(687\) 0 0
\(688\) 0.964786 0.0367821
\(689\) −48.3276 −1.84113
\(690\) 0 0
\(691\) 17.8111 0.677567 0.338784 0.940864i \(-0.389985\pi\)
0.338784 + 0.940864i \(0.389985\pi\)
\(692\) −17.3894 −0.661046
\(693\) 0 0
\(694\) 11.1010 0.421387
\(695\) 18.3541 0.696209
\(696\) 0 0
\(697\) 10.2558 0.388468
\(698\) 27.2718 1.03225
\(699\) 0 0
\(700\) 5.27296 0.199299
\(701\) 0.257621 0.00973021 0.00486510 0.999988i \(-0.498451\pi\)
0.00486510 + 0.999988i \(0.498451\pi\)
\(702\) 0 0
\(703\) 1.85865 0.0701003
\(704\) −5.87208 −0.221312
\(705\) 0 0
\(706\) 0.471858 0.0177586
\(707\) 16.5936 0.624067
\(708\) 0 0
\(709\) −50.2989 −1.88902 −0.944508 0.328488i \(-0.893461\pi\)
−0.944508 + 0.328488i \(0.893461\pi\)
\(710\) −5.63598 −0.211514
\(711\) 0 0
\(712\) −2.08402 −0.0781019
\(713\) 8.58339 0.321451
\(714\) 0 0
\(715\) −40.2811 −1.50643
\(716\) 0.962244 0.0359607
\(717\) 0 0
\(718\) 13.0395 0.486629
\(719\) −28.5044 −1.06304 −0.531518 0.847047i \(-0.678378\pi\)
−0.531518 + 0.847047i \(0.678378\pi\)
\(720\) 0 0
\(721\) −1.15437 −0.0429909
\(722\) −18.0545 −0.671920
\(723\) 0 0
\(724\) −15.2649 −0.567314
\(725\) −1.60618 −0.0596519
\(726\) 0 0
\(727\) 45.6430 1.69281 0.846403 0.532543i \(-0.178763\pi\)
0.846403 + 0.532543i \(0.178763\pi\)
\(728\) −10.3611 −0.384007
\(729\) 0 0
\(730\) 6.29447 0.232969
\(731\) 3.56008 0.131674
\(732\) 0 0
\(733\) 15.5822 0.575540 0.287770 0.957700i \(-0.407086\pi\)
0.287770 + 0.957700i \(0.407086\pi\)
\(734\) −3.53216 −0.130374
\(735\) 0 0
\(736\) −1.45252 −0.0535406
\(737\) −6.66922 −0.245664
\(738\) 0 0
\(739\) −0.739981 −0.0272207 −0.0136103 0.999907i \(-0.504332\pi\)
−0.0136103 + 0.999907i \(0.504332\pi\)
\(740\) −3.29781 −0.121230
\(741\) 0 0
\(742\) 31.6726 1.16274
\(743\) 2.42744 0.0890540 0.0445270 0.999008i \(-0.485822\pi\)
0.0445270 + 0.999008i \(0.485822\pi\)
\(744\) 0 0
\(745\) −1.72525 −0.0632082
\(746\) −30.5929 −1.12009
\(747\) 0 0
\(748\) −21.6681 −0.792263
\(749\) 3.13302 0.114478
\(750\) 0 0
\(751\) −43.3867 −1.58320 −0.791601 0.611038i \(-0.790752\pi\)
−0.791601 + 0.611038i \(0.790752\pi\)
\(752\) −5.72077 −0.208615
\(753\) 0 0
\(754\) 3.15604 0.114936
\(755\) −19.7555 −0.718975
\(756\) 0 0
\(757\) 16.9892 0.617481 0.308741 0.951146i \(-0.400092\pi\)
0.308741 + 0.951146i \(0.400092\pi\)
\(758\) −0.756326 −0.0274710
\(759\) 0 0
\(760\) −1.67754 −0.0608509
\(761\) 16.1343 0.584866 0.292433 0.956286i \(-0.405535\pi\)
0.292433 + 0.956286i \(0.405535\pi\)
\(762\) 0 0
\(763\) −1.37622 −0.0498226
\(764\) 13.3385 0.482570
\(765\) 0 0
\(766\) −15.5219 −0.560828
\(767\) 6.74153 0.243423
\(768\) 0 0
\(769\) −22.3888 −0.807360 −0.403680 0.914900i \(-0.632269\pi\)
−0.403680 + 0.914900i \(0.632269\pi\)
\(770\) 26.3991 0.951359
\(771\) 0 0
\(772\) −0.978390 −0.0352130
\(773\) −20.7715 −0.747100 −0.373550 0.927610i \(-0.621859\pi\)
−0.373550 + 0.927610i \(0.621859\pi\)
\(774\) 0 0
\(775\) 11.9576 0.429531
\(776\) 4.60522 0.165318
\(777\) 0 0
\(778\) 34.2558 1.22813
\(779\) −2.70250 −0.0968270
\(780\) 0 0
\(781\) 19.1827 0.686411
\(782\) −5.35983 −0.191667
\(783\) 0 0
\(784\) −0.209634 −0.00748694
\(785\) −4.29937 −0.153451
\(786\) 0 0
\(787\) −3.27862 −0.116870 −0.0584350 0.998291i \(-0.518611\pi\)
−0.0584350 + 0.998291i \(0.518611\pi\)
\(788\) 15.9854 0.569455
\(789\) 0 0
\(790\) −10.6785 −0.379925
\(791\) −9.86047 −0.350598
\(792\) 0 0
\(793\) −35.4619 −1.25929
\(794\) −4.32270 −0.153407
\(795\) 0 0
\(796\) 2.31903 0.0821959
\(797\) −31.0764 −1.10078 −0.550392 0.834906i \(-0.685522\pi\)
−0.550392 + 0.834906i \(0.685522\pi\)
\(798\) 0 0
\(799\) −21.1098 −0.746810
\(800\) −2.02352 −0.0715424
\(801\) 0 0
\(802\) 21.3467 0.753778
\(803\) −21.4240 −0.756035
\(804\) 0 0
\(805\) 6.53010 0.230156
\(806\) −23.4960 −0.827612
\(807\) 0 0
\(808\) −6.36787 −0.224021
\(809\) 51.4149 1.80765 0.903826 0.427901i \(-0.140747\pi\)
0.903826 + 0.427901i \(0.140747\pi\)
\(810\) 0 0
\(811\) 13.6647 0.479831 0.239915 0.970794i \(-0.422880\pi\)
0.239915 + 0.970794i \(0.422880\pi\)
\(812\) −2.06838 −0.0725861
\(813\) 0 0
\(814\) 11.2245 0.393418
\(815\) −40.0622 −1.40332
\(816\) 0 0
\(817\) −0.938109 −0.0328203
\(818\) 33.9729 1.18783
\(819\) 0 0
\(820\) 4.79506 0.167451
\(821\) 37.8782 1.32196 0.660979 0.750404i \(-0.270141\pi\)
0.660979 + 0.750404i \(0.270141\pi\)
\(822\) 0 0
\(823\) 2.26224 0.0788566 0.0394283 0.999222i \(-0.487446\pi\)
0.0394283 + 0.999222i \(0.487446\pi\)
\(824\) 0.442994 0.0154324
\(825\) 0 0
\(826\) −4.41822 −0.153730
\(827\) 31.6475 1.10049 0.550246 0.835003i \(-0.314534\pi\)
0.550246 + 0.835003i \(0.314534\pi\)
\(828\) 0 0
\(829\) 36.3626 1.26293 0.631463 0.775406i \(-0.282455\pi\)
0.631463 + 0.775406i \(0.282455\pi\)
\(830\) 24.5923 0.853611
\(831\) 0 0
\(832\) 3.97610 0.137847
\(833\) −0.773554 −0.0268021
\(834\) 0 0
\(835\) −32.0170 −1.10799
\(836\) 5.70972 0.197475
\(837\) 0 0
\(838\) −18.8895 −0.652527
\(839\) 10.2052 0.352324 0.176162 0.984361i \(-0.443632\pi\)
0.176162 + 0.984361i \(0.443632\pi\)
\(840\) 0 0
\(841\) −28.3700 −0.978274
\(842\) 11.7138 0.403684
\(843\) 0 0
\(844\) 12.7331 0.438291
\(845\) 4.84692 0.166739
\(846\) 0 0
\(847\) −61.1884 −2.10246
\(848\) −12.1545 −0.417387
\(849\) 0 0
\(850\) −7.46684 −0.256110
\(851\) 2.77650 0.0951771
\(852\) 0 0
\(853\) −45.4657 −1.55672 −0.778358 0.627821i \(-0.783947\pi\)
−0.778358 + 0.627821i \(0.783947\pi\)
\(854\) 23.2408 0.795283
\(855\) 0 0
\(856\) −1.20231 −0.0410941
\(857\) 24.5848 0.839800 0.419900 0.907570i \(-0.362065\pi\)
0.419900 + 0.907570i \(0.362065\pi\)
\(858\) 0 0
\(859\) −2.10387 −0.0717832 −0.0358916 0.999356i \(-0.511427\pi\)
−0.0358916 + 0.999356i \(0.511427\pi\)
\(860\) 1.66449 0.0567587
\(861\) 0 0
\(862\) 17.8470 0.607872
\(863\) 21.5707 0.734276 0.367138 0.930166i \(-0.380338\pi\)
0.367138 + 0.930166i \(0.380338\pi\)
\(864\) 0 0
\(865\) −30.0010 −1.02007
\(866\) −34.1206 −1.15947
\(867\) 0 0
\(868\) 15.3987 0.522665
\(869\) 36.3456 1.23294
\(870\) 0 0
\(871\) 4.51587 0.153014
\(872\) 0.528131 0.0178848
\(873\) 0 0
\(874\) 1.41236 0.0477737
\(875\) 31.5757 1.06745
\(876\) 0 0
\(877\) 16.2268 0.547940 0.273970 0.961738i \(-0.411663\pi\)
0.273970 + 0.961738i \(0.411663\pi\)
\(878\) −2.87290 −0.0969556
\(879\) 0 0
\(880\) −10.1308 −0.341509
\(881\) 14.5370 0.489763 0.244882 0.969553i \(-0.421251\pi\)
0.244882 + 0.969553i \(0.421251\pi\)
\(882\) 0 0
\(883\) −17.0988 −0.575421 −0.287711 0.957717i \(-0.592894\pi\)
−0.287711 + 0.957717i \(0.592894\pi\)
\(884\) 14.6719 0.493469
\(885\) 0 0
\(886\) 29.2501 0.982675
\(887\) −52.0091 −1.74629 −0.873147 0.487456i \(-0.837925\pi\)
−0.873147 + 0.487456i \(0.837925\pi\)
\(888\) 0 0
\(889\) 18.8975 0.633802
\(890\) −3.59545 −0.120520
\(891\) 0 0
\(892\) −13.1207 −0.439313
\(893\) 5.56259 0.186145
\(894\) 0 0
\(895\) 1.66011 0.0554913
\(896\) −2.60583 −0.0870548
\(897\) 0 0
\(898\) 11.4354 0.381604
\(899\) −4.69053 −0.156438
\(900\) 0 0
\(901\) −44.8503 −1.49418
\(902\) −16.3205 −0.543415
\(903\) 0 0
\(904\) 3.78400 0.125854
\(905\) −26.3357 −0.875427
\(906\) 0 0
\(907\) −25.0791 −0.832737 −0.416368 0.909196i \(-0.636697\pi\)
−0.416368 + 0.909196i \(0.636697\pi\)
\(908\) −5.44603 −0.180733
\(909\) 0 0
\(910\) −17.8754 −0.592564
\(911\) 5.94833 0.197077 0.0985386 0.995133i \(-0.468583\pi\)
0.0985386 + 0.995133i \(0.468583\pi\)
\(912\) 0 0
\(913\) −83.7027 −2.77015
\(914\) 13.2066 0.436837
\(915\) 0 0
\(916\) 13.9568 0.461147
\(917\) 9.29145 0.306831
\(918\) 0 0
\(919\) 58.6908 1.93603 0.968015 0.250891i \(-0.0807235\pi\)
0.968015 + 0.250891i \(0.0807235\pi\)
\(920\) −2.50596 −0.0826189
\(921\) 0 0
\(922\) 23.7293 0.781483
\(923\) −12.9890 −0.427538
\(924\) 0 0
\(925\) 3.86797 0.127178
\(926\) −6.33611 −0.208218
\(927\) 0 0
\(928\) 0.793752 0.0260562
\(929\) −9.12012 −0.299222 −0.149611 0.988745i \(-0.547802\pi\)
−0.149611 + 0.988745i \(0.547802\pi\)
\(930\) 0 0
\(931\) 0.203838 0.00668052
\(932\) 26.4164 0.865297
\(933\) 0 0
\(934\) 10.5195 0.344207
\(935\) −37.3828 −1.22255
\(936\) 0 0
\(937\) 7.19910 0.235184 0.117592 0.993062i \(-0.462482\pi\)
0.117592 + 0.993062i \(0.462482\pi\)
\(938\) −2.95958 −0.0966336
\(939\) 0 0
\(940\) −9.86975 −0.321916
\(941\) 4.41171 0.143818 0.0719088 0.997411i \(-0.477091\pi\)
0.0719088 + 0.997411i \(0.477091\pi\)
\(942\) 0 0
\(943\) −4.03706 −0.131465
\(944\) 1.69551 0.0551842
\(945\) 0 0
\(946\) −5.66530 −0.184195
\(947\) −2.69955 −0.0877237 −0.0438618 0.999038i \(-0.513966\pi\)
−0.0438618 + 0.999038i \(0.513966\pi\)
\(948\) 0 0
\(949\) 14.5066 0.470904
\(950\) 1.96757 0.0638365
\(951\) 0 0
\(952\) −9.61557 −0.311642
\(953\) −55.7558 −1.80611 −0.903054 0.429528i \(-0.858680\pi\)
−0.903054 + 0.429528i \(0.858680\pi\)
\(954\) 0 0
\(955\) 23.0122 0.744657
\(956\) −3.39802 −0.109900
\(957\) 0 0
\(958\) 0.598309 0.0193305
\(959\) 43.1803 1.39437
\(960\) 0 0
\(961\) 3.91993 0.126449
\(962\) −7.60033 −0.245045
\(963\) 0 0
\(964\) −9.84720 −0.317157
\(965\) −1.68796 −0.0543375
\(966\) 0 0
\(967\) 42.8115 1.37672 0.688362 0.725367i \(-0.258330\pi\)
0.688362 + 0.725367i \(0.258330\pi\)
\(968\) 23.4813 0.754718
\(969\) 0 0
\(970\) 7.94514 0.255103
\(971\) 12.2179 0.392092 0.196046 0.980595i \(-0.437190\pi\)
0.196046 + 0.980595i \(0.437190\pi\)
\(972\) 0 0
\(973\) −27.7222 −0.888733
\(974\) 3.97672 0.127422
\(975\) 0 0
\(976\) −8.91875 −0.285482
\(977\) 23.1547 0.740786 0.370393 0.928875i \(-0.379223\pi\)
0.370393 + 0.928875i \(0.379223\pi\)
\(978\) 0 0
\(979\) 12.2375 0.391113
\(980\) −0.361671 −0.0115532
\(981\) 0 0
\(982\) 12.4900 0.398571
\(983\) −4.54691 −0.145024 −0.0725120 0.997368i \(-0.523102\pi\)
−0.0725120 + 0.997368i \(0.523102\pi\)
\(984\) 0 0
\(985\) 27.5787 0.878730
\(986\) 2.92896 0.0932771
\(987\) 0 0
\(988\) −3.86617 −0.122999
\(989\) −1.40137 −0.0445610
\(990\) 0 0
\(991\) −35.1004 −1.11500 −0.557501 0.830176i \(-0.688240\pi\)
−0.557501 + 0.830176i \(0.688240\pi\)
\(992\) −5.90931 −0.187621
\(993\) 0 0
\(994\) 8.51264 0.270005
\(995\) 4.00090 0.126837
\(996\) 0 0
\(997\) −1.65780 −0.0525031 −0.0262515 0.999655i \(-0.508357\pi\)
−0.0262515 + 0.999655i \(0.508357\pi\)
\(998\) 30.1380 0.954000
\(999\) 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 \(a_p\))