Properties

Label 8046.2.a.h.1.3
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 1.3
Root \(-2.13687\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.65274 q^{5} +0.0358535 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.65274 q^{5} +0.0358535 q^{7} +1.00000 q^{8} -1.65274 q^{10} +1.10979 q^{11} +1.20305 q^{13} +0.0358535 q^{14} +1.00000 q^{16} -3.50418 q^{17} +4.17906 q^{19} -1.65274 q^{20} +1.10979 q^{22} -5.77941 q^{23} -2.26846 q^{25} +1.20305 q^{26} +0.0358535 q^{28} +8.50659 q^{29} -7.39492 q^{31} +1.00000 q^{32} -3.50418 q^{34} -0.0592564 q^{35} -8.83693 q^{37} +4.17906 q^{38} -1.65274 q^{40} -5.77287 q^{41} -7.59277 q^{43} +1.10979 q^{44} -5.77941 q^{46} +11.7891 q^{47} -6.99871 q^{49} -2.26846 q^{50} +1.20305 q^{52} +8.49664 q^{53} -1.83419 q^{55} +0.0358535 q^{56} +8.50659 q^{58} +9.24179 q^{59} -6.48240 q^{61} -7.39492 q^{62} +1.00000 q^{64} -1.98832 q^{65} -3.00093 q^{67} -3.50418 q^{68} -0.0592564 q^{70} -10.9241 q^{71} +3.64076 q^{73} -8.83693 q^{74} +4.17906 q^{76} +0.0397898 q^{77} +4.74320 q^{79} -1.65274 q^{80} -5.77287 q^{82} +2.78704 q^{83} +5.79149 q^{85} -7.59277 q^{86} +1.10979 q^{88} -6.07566 q^{89} +0.0431334 q^{91} -5.77941 q^{92} +11.7891 q^{94} -6.90688 q^{95} +0.383046 q^{97} -6.99871 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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
\(5\) −1.65274 −0.739126 −0.369563 0.929206i \(-0.620493\pi\)
−0.369563 + 0.929206i \(0.620493\pi\)
\(6\) 0 0
\(7\) 0.0358535 0.0135514 0.00677568 0.999977i \(-0.497843\pi\)
0.00677568 + 0.999977i \(0.497843\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.65274 −0.522641
\(11\) 1.10979 0.334614 0.167307 0.985905i \(-0.446493\pi\)
0.167307 + 0.985905i \(0.446493\pi\)
\(12\) 0 0
\(13\) 1.20305 0.333665 0.166832 0.985985i \(-0.446646\pi\)
0.166832 + 0.985985i \(0.446646\pi\)
\(14\) 0.0358535 0.00958226
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.50418 −0.849889 −0.424944 0.905219i \(-0.639706\pi\)
−0.424944 + 0.905219i \(0.639706\pi\)
\(18\) 0 0
\(19\) 4.17906 0.958741 0.479371 0.877613i \(-0.340865\pi\)
0.479371 + 0.877613i \(0.340865\pi\)
\(20\) −1.65274 −0.369563
\(21\) 0 0
\(22\) 1.10979 0.236608
\(23\) −5.77941 −1.20509 −0.602545 0.798085i \(-0.705847\pi\)
−0.602545 + 0.798085i \(0.705847\pi\)
\(24\) 0 0
\(25\) −2.26846 −0.453692
\(26\) 1.20305 0.235937
\(27\) 0 0
\(28\) 0.0358535 0.00677568
\(29\) 8.50659 1.57963 0.789817 0.613342i \(-0.210175\pi\)
0.789817 + 0.613342i \(0.210175\pi\)
\(30\) 0 0
\(31\) −7.39492 −1.32817 −0.664083 0.747659i \(-0.731178\pi\)
−0.664083 + 0.747659i \(0.731178\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.50418 −0.600962
\(35\) −0.0592564 −0.0100162
\(36\) 0 0
\(37\) −8.83693 −1.45278 −0.726391 0.687282i \(-0.758804\pi\)
−0.726391 + 0.687282i \(0.758804\pi\)
\(38\) 4.17906 0.677933
\(39\) 0 0
\(40\) −1.65274 −0.261321
\(41\) −5.77287 −0.901571 −0.450786 0.892632i \(-0.648856\pi\)
−0.450786 + 0.892632i \(0.648856\pi\)
\(42\) 0 0
\(43\) −7.59277 −1.15789 −0.578943 0.815368i \(-0.696535\pi\)
−0.578943 + 0.815368i \(0.696535\pi\)
\(44\) 1.10979 0.167307
\(45\) 0 0
\(46\) −5.77941 −0.852127
\(47\) 11.7891 1.71962 0.859810 0.510615i \(-0.170582\pi\)
0.859810 + 0.510615i \(0.170582\pi\)
\(48\) 0 0
\(49\) −6.99871 −0.999816
\(50\) −2.26846 −0.320809
\(51\) 0 0
\(52\) 1.20305 0.166832
\(53\) 8.49664 1.16710 0.583552 0.812076i \(-0.301662\pi\)
0.583552 + 0.812076i \(0.301662\pi\)
\(54\) 0 0
\(55\) −1.83419 −0.247322
\(56\) 0.0358535 0.00479113
\(57\) 0 0
\(58\) 8.50659 1.11697
\(59\) 9.24179 1.20318 0.601590 0.798805i \(-0.294534\pi\)
0.601590 + 0.798805i \(0.294534\pi\)
\(60\) 0 0
\(61\) −6.48240 −0.829986 −0.414993 0.909825i \(-0.636216\pi\)
−0.414993 + 0.909825i \(0.636216\pi\)
\(62\) −7.39492 −0.939156
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.98832 −0.246620
\(66\) 0 0
\(67\) −3.00093 −0.366622 −0.183311 0.983055i \(-0.558682\pi\)
−0.183311 + 0.983055i \(0.558682\pi\)
\(68\) −3.50418 −0.424944
\(69\) 0 0
\(70\) −0.0592564 −0.00708250
\(71\) −10.9241 −1.29645 −0.648226 0.761448i \(-0.724489\pi\)
−0.648226 + 0.761448i \(0.724489\pi\)
\(72\) 0 0
\(73\) 3.64076 0.426118 0.213059 0.977039i \(-0.431657\pi\)
0.213059 + 0.977039i \(0.431657\pi\)
\(74\) −8.83693 −1.02727
\(75\) 0 0
\(76\) 4.17906 0.479371
\(77\) 0.0397898 0.00453447
\(78\) 0 0
\(79\) 4.74320 0.533651 0.266826 0.963745i \(-0.414025\pi\)
0.266826 + 0.963745i \(0.414025\pi\)
\(80\) −1.65274 −0.184782
\(81\) 0 0
\(82\) −5.77287 −0.637507
\(83\) 2.78704 0.305918 0.152959 0.988233i \(-0.451120\pi\)
0.152959 + 0.988233i \(0.451120\pi\)
\(84\) 0 0
\(85\) 5.79149 0.628175
\(86\) −7.59277 −0.818749
\(87\) 0 0
\(88\) 1.10979 0.118304
\(89\) −6.07566 −0.644019 −0.322010 0.946736i \(-0.604358\pi\)
−0.322010 + 0.946736i \(0.604358\pi\)
\(90\) 0 0
\(91\) 0.0431334 0.00452161
\(92\) −5.77941 −0.602545
\(93\) 0 0
\(94\) 11.7891 1.21595
\(95\) −6.90688 −0.708631
\(96\) 0 0
\(97\) 0.383046 0.0388924 0.0194462 0.999811i \(-0.493810\pi\)
0.0194462 + 0.999811i \(0.493810\pi\)
\(98\) −6.99871 −0.706977
\(99\) 0 0
\(100\) −2.26846 −0.226846
\(101\) −6.26977 −0.623865 −0.311933 0.950104i \(-0.600976\pi\)
−0.311933 + 0.950104i \(0.600976\pi\)
\(102\) 0 0
\(103\) −11.5950 −1.14249 −0.571244 0.820780i \(-0.693539\pi\)
−0.571244 + 0.820780i \(0.693539\pi\)
\(104\) 1.20305 0.117968
\(105\) 0 0
\(106\) 8.49664 0.825267
\(107\) −9.58849 −0.926954 −0.463477 0.886109i \(-0.653398\pi\)
−0.463477 + 0.886109i \(0.653398\pi\)
\(108\) 0 0
\(109\) 7.07628 0.677784 0.338892 0.940825i \(-0.389948\pi\)
0.338892 + 0.940825i \(0.389948\pi\)
\(110\) −1.83419 −0.174883
\(111\) 0 0
\(112\) 0.0358535 0.00338784
\(113\) 1.56605 0.147322 0.0736609 0.997283i \(-0.476532\pi\)
0.0736609 + 0.997283i \(0.476532\pi\)
\(114\) 0 0
\(115\) 9.55184 0.890713
\(116\) 8.50659 0.789817
\(117\) 0 0
\(118\) 9.24179 0.850776
\(119\) −0.125637 −0.0115172
\(120\) 0 0
\(121\) −9.76837 −0.888034
\(122\) −6.48240 −0.586889
\(123\) 0 0
\(124\) −7.39492 −0.664083
\(125\) 12.0129 1.07446
\(126\) 0 0
\(127\) −4.38796 −0.389368 −0.194684 0.980866i \(-0.562368\pi\)
−0.194684 + 0.980866i \(0.562368\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −1.98832 −0.174387
\(131\) 11.9230 1.04172 0.520859 0.853643i \(-0.325612\pi\)
0.520859 + 0.853643i \(0.325612\pi\)
\(132\) 0 0
\(133\) 0.149834 0.0129923
\(134\) −3.00093 −0.259241
\(135\) 0 0
\(136\) −3.50418 −0.300481
\(137\) 7.57559 0.647226 0.323613 0.946190i \(-0.395102\pi\)
0.323613 + 0.946190i \(0.395102\pi\)
\(138\) 0 0
\(139\) 4.27059 0.362227 0.181113 0.983462i \(-0.442030\pi\)
0.181113 + 0.983462i \(0.442030\pi\)
\(140\) −0.0592564 −0.00500808
\(141\) 0 0
\(142\) −10.9241 −0.916730
\(143\) 1.33513 0.111649
\(144\) 0 0
\(145\) −14.0592 −1.16755
\(146\) 3.64076 0.301311
\(147\) 0 0
\(148\) −8.83693 −0.726391
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −12.1677 −0.990194 −0.495097 0.868838i \(-0.664868\pi\)
−0.495097 + 0.868838i \(0.664868\pi\)
\(152\) 4.17906 0.338966
\(153\) 0 0
\(154\) 0.0397898 0.00320636
\(155\) 12.2219 0.981683
\(156\) 0 0
\(157\) 5.15135 0.411122 0.205561 0.978644i \(-0.434098\pi\)
0.205561 + 0.978644i \(0.434098\pi\)
\(158\) 4.74320 0.377348
\(159\) 0 0
\(160\) −1.65274 −0.130660
\(161\) −0.207212 −0.0163306
\(162\) 0 0
\(163\) 20.4207 1.59947 0.799735 0.600353i \(-0.204973\pi\)
0.799735 + 0.600353i \(0.204973\pi\)
\(164\) −5.77287 −0.450786
\(165\) 0 0
\(166\) 2.78704 0.216316
\(167\) −16.9356 −1.31052 −0.655259 0.755404i \(-0.727441\pi\)
−0.655259 + 0.755404i \(0.727441\pi\)
\(168\) 0 0
\(169\) −11.5527 −0.888668
\(170\) 5.79149 0.444187
\(171\) 0 0
\(172\) −7.59277 −0.578943
\(173\) −22.2660 −1.69285 −0.846427 0.532505i \(-0.821251\pi\)
−0.846427 + 0.532505i \(0.821251\pi\)
\(174\) 0 0
\(175\) −0.0813324 −0.00614815
\(176\) 1.10979 0.0836534
\(177\) 0 0
\(178\) −6.07566 −0.455390
\(179\) 4.06027 0.303478 0.151739 0.988421i \(-0.451513\pi\)
0.151739 + 0.988421i \(0.451513\pi\)
\(180\) 0 0
\(181\) −13.2135 −0.982154 −0.491077 0.871116i \(-0.663397\pi\)
−0.491077 + 0.871116i \(0.663397\pi\)
\(182\) 0.0431334 0.00319726
\(183\) 0 0
\(184\) −5.77941 −0.426064
\(185\) 14.6051 1.07379
\(186\) 0 0
\(187\) −3.88890 −0.284384
\(188\) 11.7891 0.859810
\(189\) 0 0
\(190\) −6.90688 −0.501078
\(191\) −10.4427 −0.755605 −0.377803 0.925886i \(-0.623320\pi\)
−0.377803 + 0.925886i \(0.623320\pi\)
\(192\) 0 0
\(193\) −10.2254 −0.736042 −0.368021 0.929817i \(-0.619965\pi\)
−0.368021 + 0.929817i \(0.619965\pi\)
\(194\) 0.383046 0.0275011
\(195\) 0 0
\(196\) −6.99871 −0.499908
\(197\) −22.4981 −1.60292 −0.801460 0.598048i \(-0.795943\pi\)
−0.801460 + 0.598048i \(0.795943\pi\)
\(198\) 0 0
\(199\) −1.33281 −0.0944802 −0.0472401 0.998884i \(-0.515043\pi\)
−0.0472401 + 0.998884i \(0.515043\pi\)
\(200\) −2.26846 −0.160404
\(201\) 0 0
\(202\) −6.26977 −0.441140
\(203\) 0.304991 0.0214062
\(204\) 0 0
\(205\) 9.54104 0.666375
\(206\) −11.5950 −0.807861
\(207\) 0 0
\(208\) 1.20305 0.0834162
\(209\) 4.63787 0.320808
\(210\) 0 0
\(211\) −14.2623 −0.981857 −0.490928 0.871200i \(-0.663342\pi\)
−0.490928 + 0.871200i \(0.663342\pi\)
\(212\) 8.49664 0.583552
\(213\) 0 0
\(214\) −9.58849 −0.655455
\(215\) 12.5488 0.855824
\(216\) 0 0
\(217\) −0.265134 −0.0179985
\(218\) 7.07628 0.479266
\(219\) 0 0
\(220\) −1.83419 −0.123661
\(221\) −4.21569 −0.283578
\(222\) 0 0
\(223\) −28.6033 −1.91542 −0.957710 0.287734i \(-0.907098\pi\)
−0.957710 + 0.287734i \(0.907098\pi\)
\(224\) 0.0358535 0.00239557
\(225\) 0 0
\(226\) 1.56605 0.104172
\(227\) 2.37525 0.157651 0.0788253 0.996888i \(-0.474883\pi\)
0.0788253 + 0.996888i \(0.474883\pi\)
\(228\) 0 0
\(229\) 9.02486 0.596380 0.298190 0.954507i \(-0.403617\pi\)
0.298190 + 0.954507i \(0.403617\pi\)
\(230\) 9.55184 0.629829
\(231\) 0 0
\(232\) 8.50659 0.558485
\(233\) 14.5151 0.950918 0.475459 0.879738i \(-0.342282\pi\)
0.475459 + 0.879738i \(0.342282\pi\)
\(234\) 0 0
\(235\) −19.4843 −1.27102
\(236\) 9.24179 0.601590
\(237\) 0 0
\(238\) −0.125637 −0.00814386
\(239\) −3.69277 −0.238865 −0.119433 0.992842i \(-0.538108\pi\)
−0.119433 + 0.992842i \(0.538108\pi\)
\(240\) 0 0
\(241\) −30.9002 −1.99045 −0.995227 0.0975856i \(-0.968888\pi\)
−0.995227 + 0.0975856i \(0.968888\pi\)
\(242\) −9.76837 −0.627935
\(243\) 0 0
\(244\) −6.48240 −0.414993
\(245\) 11.5670 0.738991
\(246\) 0 0
\(247\) 5.02760 0.319898
\(248\) −7.39492 −0.469578
\(249\) 0 0
\(250\) 12.0129 0.759760
\(251\) −27.6898 −1.74777 −0.873884 0.486135i \(-0.838406\pi\)
−0.873884 + 0.486135i \(0.838406\pi\)
\(252\) 0 0
\(253\) −6.41392 −0.403239
\(254\) −4.38796 −0.275325
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −20.6618 −1.28884 −0.644422 0.764670i \(-0.722902\pi\)
−0.644422 + 0.764670i \(0.722902\pi\)
\(258\) 0 0
\(259\) −0.316835 −0.0196872
\(260\) −1.98832 −0.123310
\(261\) 0 0
\(262\) 11.9230 0.736606
\(263\) 30.9793 1.91027 0.955134 0.296174i \(-0.0957108\pi\)
0.955134 + 0.296174i \(0.0957108\pi\)
\(264\) 0 0
\(265\) −14.0427 −0.862637
\(266\) 0.149834 0.00918691
\(267\) 0 0
\(268\) −3.00093 −0.183311
\(269\) −10.4072 −0.634537 −0.317268 0.948336i \(-0.602766\pi\)
−0.317268 + 0.948336i \(0.602766\pi\)
\(270\) 0 0
\(271\) 4.03824 0.245306 0.122653 0.992450i \(-0.460860\pi\)
0.122653 + 0.992450i \(0.460860\pi\)
\(272\) −3.50418 −0.212472
\(273\) 0 0
\(274\) 7.57559 0.457658
\(275\) −2.51751 −0.151812
\(276\) 0 0
\(277\) 22.8113 1.37060 0.685300 0.728261i \(-0.259671\pi\)
0.685300 + 0.728261i \(0.259671\pi\)
\(278\) 4.27059 0.256133
\(279\) 0 0
\(280\) −0.0592564 −0.00354125
\(281\) 13.2889 0.792750 0.396375 0.918089i \(-0.370268\pi\)
0.396375 + 0.918089i \(0.370268\pi\)
\(282\) 0 0
\(283\) 2.74147 0.162963 0.0814817 0.996675i \(-0.474035\pi\)
0.0814817 + 0.996675i \(0.474035\pi\)
\(284\) −10.9241 −0.648226
\(285\) 0 0
\(286\) 1.33513 0.0789476
\(287\) −0.206978 −0.0122175
\(288\) 0 0
\(289\) −4.72071 −0.277689
\(290\) −14.0592 −0.825582
\(291\) 0 0
\(292\) 3.64076 0.213059
\(293\) −1.14676 −0.0669942 −0.0334971 0.999439i \(-0.510664\pi\)
−0.0334971 + 0.999439i \(0.510664\pi\)
\(294\) 0 0
\(295\) −15.2742 −0.889301
\(296\) −8.83693 −0.513636
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −6.95289 −0.402096
\(300\) 0 0
\(301\) −0.272227 −0.0156909
\(302\) −12.1677 −0.700173
\(303\) 0 0
\(304\) 4.17906 0.239685
\(305\) 10.7137 0.613465
\(306\) 0 0
\(307\) −9.96224 −0.568575 −0.284288 0.958739i \(-0.591757\pi\)
−0.284288 + 0.958739i \(0.591757\pi\)
\(308\) 0.0397898 0.00226724
\(309\) 0 0
\(310\) 12.2219 0.694155
\(311\) −3.58000 −0.203003 −0.101502 0.994835i \(-0.532365\pi\)
−0.101502 + 0.994835i \(0.532365\pi\)
\(312\) 0 0
\(313\) −1.86731 −0.105547 −0.0527733 0.998607i \(-0.516806\pi\)
−0.0527733 + 0.998607i \(0.516806\pi\)
\(314\) 5.15135 0.290707
\(315\) 0 0
\(316\) 4.74320 0.266826
\(317\) 18.7083 1.05076 0.525382 0.850867i \(-0.323923\pi\)
0.525382 + 0.850867i \(0.323923\pi\)
\(318\) 0 0
\(319\) 9.44051 0.528567
\(320\) −1.65274 −0.0923908
\(321\) 0 0
\(322\) −0.207212 −0.0115475
\(323\) −14.6442 −0.814824
\(324\) 0 0
\(325\) −2.72906 −0.151381
\(326\) 20.4207 1.13100
\(327\) 0 0
\(328\) −5.77287 −0.318754
\(329\) 0.422681 0.0233032
\(330\) 0 0
\(331\) 26.2800 1.44448 0.722239 0.691644i \(-0.243113\pi\)
0.722239 + 0.691644i \(0.243113\pi\)
\(332\) 2.78704 0.152959
\(333\) 0 0
\(334\) −16.9356 −0.926676
\(335\) 4.95975 0.270980
\(336\) 0 0
\(337\) −24.4996 −1.33458 −0.667288 0.744799i \(-0.732545\pi\)
−0.667288 + 0.744799i \(0.732545\pi\)
\(338\) −11.5527 −0.628383
\(339\) 0 0
\(340\) 5.79149 0.314088
\(341\) −8.20679 −0.444423
\(342\) 0 0
\(343\) −0.501903 −0.0271002
\(344\) −7.59277 −0.409374
\(345\) 0 0
\(346\) −22.2660 −1.19703
\(347\) 8.34721 0.448102 0.224051 0.974577i \(-0.428072\pi\)
0.224051 + 0.974577i \(0.428072\pi\)
\(348\) 0 0
\(349\) 10.1250 0.541977 0.270988 0.962583i \(-0.412650\pi\)
0.270988 + 0.962583i \(0.412650\pi\)
\(350\) −0.0813324 −0.00434740
\(351\) 0 0
\(352\) 1.10979 0.0591519
\(353\) −12.9436 −0.688916 −0.344458 0.938802i \(-0.611937\pi\)
−0.344458 + 0.938802i \(0.611937\pi\)
\(354\) 0 0
\(355\) 18.0547 0.958241
\(356\) −6.07566 −0.322010
\(357\) 0 0
\(358\) 4.06027 0.214592
\(359\) −12.7585 −0.673369 −0.336685 0.941617i \(-0.609306\pi\)
−0.336685 + 0.941617i \(0.609306\pi\)
\(360\) 0 0
\(361\) −1.53548 −0.0808148
\(362\) −13.2135 −0.694488
\(363\) 0 0
\(364\) 0.0431334 0.00226081
\(365\) −6.01721 −0.314955
\(366\) 0 0
\(367\) −5.74079 −0.299667 −0.149833 0.988711i \(-0.547874\pi\)
−0.149833 + 0.988711i \(0.547874\pi\)
\(368\) −5.77941 −0.301272
\(369\) 0 0
\(370\) 14.6051 0.759284
\(371\) 0.304635 0.0158158
\(372\) 0 0
\(373\) 20.9995 1.08731 0.543655 0.839309i \(-0.317040\pi\)
0.543655 + 0.839309i \(0.317040\pi\)
\(374\) −3.88890 −0.201090
\(375\) 0 0
\(376\) 11.7891 0.607977
\(377\) 10.2338 0.527068
\(378\) 0 0
\(379\) −19.9938 −1.02701 −0.513506 0.858086i \(-0.671653\pi\)
−0.513506 + 0.858086i \(0.671653\pi\)
\(380\) −6.90688 −0.354315
\(381\) 0 0
\(382\) −10.4427 −0.534294
\(383\) −4.52949 −0.231446 −0.115723 0.993282i \(-0.536918\pi\)
−0.115723 + 0.993282i \(0.536918\pi\)
\(384\) 0 0
\(385\) −0.0657621 −0.00335155
\(386\) −10.2254 −0.520460
\(387\) 0 0
\(388\) 0.383046 0.0194462
\(389\) 20.0034 1.01421 0.507106 0.861884i \(-0.330715\pi\)
0.507106 + 0.861884i \(0.330715\pi\)
\(390\) 0 0
\(391\) 20.2521 1.02419
\(392\) −6.99871 −0.353488
\(393\) 0 0
\(394\) −22.4981 −1.13344
\(395\) −7.83925 −0.394436
\(396\) 0 0
\(397\) −14.0741 −0.706357 −0.353178 0.935556i \(-0.614899\pi\)
−0.353178 + 0.935556i \(0.614899\pi\)
\(398\) −1.33281 −0.0668076
\(399\) 0 0
\(400\) −2.26846 −0.113423
\(401\) 7.17872 0.358488 0.179244 0.983805i \(-0.442635\pi\)
0.179244 + 0.983805i \(0.442635\pi\)
\(402\) 0 0
\(403\) −8.89642 −0.443162
\(404\) −6.26977 −0.311933
\(405\) 0 0
\(406\) 0.304991 0.0151365
\(407\) −9.80711 −0.486121
\(408\) 0 0
\(409\) −12.2911 −0.607755 −0.303878 0.952711i \(-0.598281\pi\)
−0.303878 + 0.952711i \(0.598281\pi\)
\(410\) 9.54104 0.471198
\(411\) 0 0
\(412\) −11.5950 −0.571244
\(413\) 0.331351 0.0163047
\(414\) 0 0
\(415\) −4.60625 −0.226112
\(416\) 1.20305 0.0589842
\(417\) 0 0
\(418\) 4.63787 0.226845
\(419\) −11.9663 −0.584594 −0.292297 0.956328i \(-0.594420\pi\)
−0.292297 + 0.956328i \(0.594420\pi\)
\(420\) 0 0
\(421\) 0.00355896 0.000173453 0 8.67265e−5 1.00000i \(-0.499972\pi\)
8.67265e−5 1.00000i \(0.499972\pi\)
\(422\) −14.2623 −0.694278
\(423\) 0 0
\(424\) 8.49664 0.412634
\(425\) 7.94910 0.385588
\(426\) 0 0
\(427\) −0.232417 −0.0112474
\(428\) −9.58849 −0.463477
\(429\) 0 0
\(430\) 12.5488 0.605159
\(431\) −31.6067 −1.52244 −0.761220 0.648494i \(-0.775399\pi\)
−0.761220 + 0.648494i \(0.775399\pi\)
\(432\) 0 0
\(433\) 2.95878 0.142190 0.0710950 0.997470i \(-0.477351\pi\)
0.0710950 + 0.997470i \(0.477351\pi\)
\(434\) −0.265134 −0.0127268
\(435\) 0 0
\(436\) 7.07628 0.338892
\(437\) −24.1525 −1.15537
\(438\) 0 0
\(439\) 34.0207 1.62372 0.811860 0.583852i \(-0.198455\pi\)
0.811860 + 0.583852i \(0.198455\pi\)
\(440\) −1.83419 −0.0874414
\(441\) 0 0
\(442\) −4.21569 −0.200520
\(443\) −5.70534 −0.271069 −0.135534 0.990773i \(-0.543275\pi\)
−0.135534 + 0.990773i \(0.543275\pi\)
\(444\) 0 0
\(445\) 10.0415 0.476011
\(446\) −28.6033 −1.35441
\(447\) 0 0
\(448\) 0.0358535 0.00169392
\(449\) 10.8071 0.510018 0.255009 0.966939i \(-0.417922\pi\)
0.255009 + 0.966939i \(0.417922\pi\)
\(450\) 0 0
\(451\) −6.40667 −0.301678
\(452\) 1.56605 0.0736609
\(453\) 0 0
\(454\) 2.37525 0.111476
\(455\) −0.0712882 −0.00334204
\(456\) 0 0
\(457\) −26.9583 −1.26106 −0.630528 0.776167i \(-0.717162\pi\)
−0.630528 + 0.776167i \(0.717162\pi\)
\(458\) 9.02486 0.421704
\(459\) 0 0
\(460\) 9.55184 0.445357
\(461\) 30.0843 1.40117 0.700583 0.713571i \(-0.252923\pi\)
0.700583 + 0.713571i \(0.252923\pi\)
\(462\) 0 0
\(463\) 40.5192 1.88309 0.941543 0.336893i \(-0.109376\pi\)
0.941543 + 0.336893i \(0.109376\pi\)
\(464\) 8.50659 0.394909
\(465\) 0 0
\(466\) 14.5151 0.672401
\(467\) 15.9889 0.739876 0.369938 0.929056i \(-0.379379\pi\)
0.369938 + 0.929056i \(0.379379\pi\)
\(468\) 0 0
\(469\) −0.107594 −0.00496823
\(470\) −19.4843 −0.898744
\(471\) 0 0
\(472\) 9.24179 0.425388
\(473\) −8.42636 −0.387444
\(474\) 0 0
\(475\) −9.48003 −0.434974
\(476\) −0.125637 −0.00575858
\(477\) 0 0
\(478\) −3.69277 −0.168903
\(479\) −26.4486 −1.20847 −0.604235 0.796807i \(-0.706521\pi\)
−0.604235 + 0.796807i \(0.706521\pi\)
\(480\) 0 0
\(481\) −10.6312 −0.484742
\(482\) −30.9002 −1.40746
\(483\) 0 0
\(484\) −9.76837 −0.444017
\(485\) −0.633073 −0.0287464
\(486\) 0 0
\(487\) −43.0978 −1.95295 −0.976473 0.215638i \(-0.930817\pi\)
−0.976473 + 0.215638i \(0.930817\pi\)
\(488\) −6.48240 −0.293444
\(489\) 0 0
\(490\) 11.5670 0.522545
\(491\) −20.3362 −0.917758 −0.458879 0.888499i \(-0.651749\pi\)
−0.458879 + 0.888499i \(0.651749\pi\)
\(492\) 0 0
\(493\) −29.8086 −1.34251
\(494\) 5.02760 0.226202
\(495\) 0 0
\(496\) −7.39492 −0.332042
\(497\) −0.391667 −0.0175687
\(498\) 0 0
\(499\) −28.4668 −1.27435 −0.637174 0.770720i \(-0.719897\pi\)
−0.637174 + 0.770720i \(0.719897\pi\)
\(500\) 12.0129 0.537231
\(501\) 0 0
\(502\) −27.6898 −1.23586
\(503\) 12.0413 0.536895 0.268448 0.963294i \(-0.413489\pi\)
0.268448 + 0.963294i \(0.413489\pi\)
\(504\) 0 0
\(505\) 10.3623 0.461115
\(506\) −6.41392 −0.285133
\(507\) 0 0
\(508\) −4.38796 −0.194684
\(509\) 16.8133 0.745236 0.372618 0.927985i \(-0.378460\pi\)
0.372618 + 0.927985i \(0.378460\pi\)
\(510\) 0 0
\(511\) 0.130534 0.00577449
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −20.6618 −0.911351
\(515\) 19.1635 0.844443
\(516\) 0 0
\(517\) 13.0834 0.575408
\(518\) −0.316835 −0.0139209
\(519\) 0 0
\(520\) −1.98832 −0.0871935
\(521\) 19.6095 0.859109 0.429554 0.903041i \(-0.358671\pi\)
0.429554 + 0.903041i \(0.358671\pi\)
\(522\) 0 0
\(523\) 13.7743 0.602306 0.301153 0.953576i \(-0.402628\pi\)
0.301153 + 0.953576i \(0.402628\pi\)
\(524\) 11.9230 0.520859
\(525\) 0 0
\(526\) 30.9793 1.35076
\(527\) 25.9131 1.12879
\(528\) 0 0
\(529\) 10.4015 0.452241
\(530\) −14.0427 −0.609977
\(531\) 0 0
\(532\) 0.149834 0.00649613
\(533\) −6.94503 −0.300823
\(534\) 0 0
\(535\) 15.8472 0.685136
\(536\) −3.00093 −0.129621
\(537\) 0 0
\(538\) −10.4072 −0.448685
\(539\) −7.76709 −0.334552
\(540\) 0 0
\(541\) −34.1862 −1.46978 −0.734890 0.678186i \(-0.762766\pi\)
−0.734890 + 0.678186i \(0.762766\pi\)
\(542\) 4.03824 0.173457
\(543\) 0 0
\(544\) −3.50418 −0.150241
\(545\) −11.6952 −0.500968
\(546\) 0 0
\(547\) 38.2519 1.63553 0.817766 0.575551i \(-0.195212\pi\)
0.817766 + 0.575551i \(0.195212\pi\)
\(548\) 7.57559 0.323613
\(549\) 0 0
\(550\) −2.51751 −0.107347
\(551\) 35.5495 1.51446
\(552\) 0 0
\(553\) 0.170060 0.00723170
\(554\) 22.8113 0.969161
\(555\) 0 0
\(556\) 4.27059 0.181113
\(557\) 8.45230 0.358136 0.179068 0.983837i \(-0.442692\pi\)
0.179068 + 0.983837i \(0.442692\pi\)
\(558\) 0 0
\(559\) −9.13444 −0.386346
\(560\) −0.0592564 −0.00250404
\(561\) 0 0
\(562\) 13.2889 0.560559
\(563\) 41.2408 1.73809 0.869047 0.494729i \(-0.164733\pi\)
0.869047 + 0.494729i \(0.164733\pi\)
\(564\) 0 0
\(565\) −2.58827 −0.108889
\(566\) 2.74147 0.115233
\(567\) 0 0
\(568\) −10.9241 −0.458365
\(569\) −31.1589 −1.30625 −0.653124 0.757251i \(-0.726542\pi\)
−0.653124 + 0.757251i \(0.726542\pi\)
\(570\) 0 0
\(571\) 5.09780 0.213336 0.106668 0.994295i \(-0.465982\pi\)
0.106668 + 0.994295i \(0.465982\pi\)
\(572\) 1.33513 0.0558244
\(573\) 0 0
\(574\) −0.206978 −0.00863909
\(575\) 13.1104 0.546740
\(576\) 0 0
\(577\) −26.7328 −1.11290 −0.556451 0.830880i \(-0.687837\pi\)
−0.556451 + 0.830880i \(0.687837\pi\)
\(578\) −4.72071 −0.196356
\(579\) 0 0
\(580\) −14.0592 −0.583775
\(581\) 0.0999253 0.00414560
\(582\) 0 0
\(583\) 9.42947 0.390529
\(584\) 3.64076 0.150656
\(585\) 0 0
\(586\) −1.14676 −0.0473721
\(587\) 42.7943 1.76631 0.883155 0.469081i \(-0.155415\pi\)
0.883155 + 0.469081i \(0.155415\pi\)
\(588\) 0 0
\(589\) −30.9038 −1.27337
\(590\) −15.2742 −0.628831
\(591\) 0 0
\(592\) −8.83693 −0.363195
\(593\) 47.7664 1.96153 0.980765 0.195194i \(-0.0625337\pi\)
0.980765 + 0.195194i \(0.0625337\pi\)
\(594\) 0 0
\(595\) 0.207645 0.00851263
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) −6.95289 −0.284325
\(599\) −4.56549 −0.186541 −0.0932703 0.995641i \(-0.529732\pi\)
−0.0932703 + 0.995641i \(0.529732\pi\)
\(600\) 0 0
\(601\) 24.5480 1.00133 0.500667 0.865640i \(-0.333088\pi\)
0.500667 + 0.865640i \(0.333088\pi\)
\(602\) −0.272227 −0.0110952
\(603\) 0 0
\(604\) −12.1677 −0.495097
\(605\) 16.1445 0.656369
\(606\) 0 0
\(607\) 44.1390 1.79154 0.895772 0.444513i \(-0.146623\pi\)
0.895772 + 0.444513i \(0.146623\pi\)
\(608\) 4.17906 0.169483
\(609\) 0 0
\(610\) 10.7137 0.433785
\(611\) 14.1828 0.573776
\(612\) 0 0
\(613\) −8.56263 −0.345841 −0.172921 0.984936i \(-0.555320\pi\)
−0.172921 + 0.984936i \(0.555320\pi\)
\(614\) −9.96224 −0.402043
\(615\) 0 0
\(616\) 0.0397898 0.00160318
\(617\) 34.3672 1.38357 0.691785 0.722103i \(-0.256825\pi\)
0.691785 + 0.722103i \(0.256825\pi\)
\(618\) 0 0
\(619\) 35.5991 1.43085 0.715424 0.698690i \(-0.246234\pi\)
0.715424 + 0.698690i \(0.246234\pi\)
\(620\) 12.2219 0.490841
\(621\) 0 0
\(622\) −3.58000 −0.143545
\(623\) −0.217834 −0.00872734
\(624\) 0 0
\(625\) −8.51177 −0.340471
\(626\) −1.86731 −0.0746328
\(627\) 0 0
\(628\) 5.15135 0.205561
\(629\) 30.9662 1.23470
\(630\) 0 0
\(631\) −7.47160 −0.297440 −0.148720 0.988879i \(-0.547515\pi\)
−0.148720 + 0.988879i \(0.547515\pi\)
\(632\) 4.74320 0.188674
\(633\) 0 0
\(634\) 18.7083 0.743002
\(635\) 7.25214 0.287792
\(636\) 0 0
\(637\) −8.41977 −0.333604
\(638\) 9.44051 0.373753
\(639\) 0 0
\(640\) −1.65274 −0.0653301
\(641\) −28.8283 −1.13865 −0.569324 0.822113i \(-0.692795\pi\)
−0.569324 + 0.822113i \(0.692795\pi\)
\(642\) 0 0
\(643\) 26.5086 1.04540 0.522700 0.852517i \(-0.324925\pi\)
0.522700 + 0.852517i \(0.324925\pi\)
\(644\) −0.207212 −0.00816530
\(645\) 0 0
\(646\) −14.6442 −0.576167
\(647\) 12.6198 0.496134 0.248067 0.968743i \(-0.420205\pi\)
0.248067 + 0.968743i \(0.420205\pi\)
\(648\) 0 0
\(649\) 10.2564 0.402600
\(650\) −2.72906 −0.107043
\(651\) 0 0
\(652\) 20.4207 0.799735
\(653\) 5.31321 0.207922 0.103961 0.994581i \(-0.466848\pi\)
0.103961 + 0.994581i \(0.466848\pi\)
\(654\) 0 0
\(655\) −19.7056 −0.769961
\(656\) −5.77287 −0.225393
\(657\) 0 0
\(658\) 0.422681 0.0164778
\(659\) −22.4705 −0.875327 −0.437663 0.899139i \(-0.644194\pi\)
−0.437663 + 0.899139i \(0.644194\pi\)
\(660\) 0 0
\(661\) −37.9144 −1.47470 −0.737349 0.675511i \(-0.763923\pi\)
−0.737349 + 0.675511i \(0.763923\pi\)
\(662\) 26.2800 1.02140
\(663\) 0 0
\(664\) 2.78704 0.108158
\(665\) −0.247636 −0.00960292
\(666\) 0 0
\(667\) −49.1631 −1.90360
\(668\) −16.9356 −0.655259
\(669\) 0 0
\(670\) 4.95975 0.191612
\(671\) −7.19409 −0.277725
\(672\) 0 0
\(673\) −34.3673 −1.32476 −0.662381 0.749167i \(-0.730454\pi\)
−0.662381 + 0.749167i \(0.730454\pi\)
\(674\) −24.4996 −0.943688
\(675\) 0 0
\(676\) −11.5527 −0.444334
\(677\) 29.1518 1.12039 0.560197 0.828360i \(-0.310726\pi\)
0.560197 + 0.828360i \(0.310726\pi\)
\(678\) 0 0
\(679\) 0.0137335 0.000527045 0
\(680\) 5.79149 0.222093
\(681\) 0 0
\(682\) −8.20679 −0.314254
\(683\) −15.1256 −0.578766 −0.289383 0.957213i \(-0.593450\pi\)
−0.289383 + 0.957213i \(0.593450\pi\)
\(684\) 0 0
\(685\) −12.5205 −0.478382
\(686\) −0.501903 −0.0191628
\(687\) 0 0
\(688\) −7.59277 −0.289471
\(689\) 10.2219 0.389421
\(690\) 0 0
\(691\) −42.7381 −1.62584 −0.812918 0.582378i \(-0.802122\pi\)
−0.812918 + 0.582378i \(0.802122\pi\)
\(692\) −22.2660 −0.846427
\(693\) 0 0
\(694\) 8.34721 0.316856
\(695\) −7.05816 −0.267731
\(696\) 0 0
\(697\) 20.2292 0.766235
\(698\) 10.1250 0.383235
\(699\) 0 0
\(700\) −0.0813324 −0.00307408
\(701\) −15.0197 −0.567285 −0.283642 0.958930i \(-0.591543\pi\)
−0.283642 + 0.958930i \(0.591543\pi\)
\(702\) 0 0
\(703\) −36.9300 −1.39284
\(704\) 1.10979 0.0418267
\(705\) 0 0
\(706\) −12.9436 −0.487137
\(707\) −0.224793 −0.00845423
\(708\) 0 0
\(709\) 35.9651 1.35070 0.675349 0.737498i \(-0.263993\pi\)
0.675349 + 0.737498i \(0.263993\pi\)
\(710\) 18.0547 0.677579
\(711\) 0 0
\(712\) −6.07566 −0.227695
\(713\) 42.7382 1.60056
\(714\) 0 0
\(715\) −2.20661 −0.0825226
\(716\) 4.06027 0.151739
\(717\) 0 0
\(718\) −12.7585 −0.476144
\(719\) 0.962903 0.0359102 0.0179551 0.999839i \(-0.494284\pi\)
0.0179551 + 0.999839i \(0.494284\pi\)
\(720\) 0 0
\(721\) −0.415722 −0.0154823
\(722\) −1.53548 −0.0571447
\(723\) 0 0
\(724\) −13.2135 −0.491077
\(725\) −19.2969 −0.716668
\(726\) 0 0
\(727\) 52.3053 1.93990 0.969948 0.243312i \(-0.0782340\pi\)
0.969948 + 0.243312i \(0.0782340\pi\)
\(728\) 0.0431334 0.00159863
\(729\) 0 0
\(730\) −6.01721 −0.222707
\(731\) 26.6064 0.984074
\(732\) 0 0
\(733\) −5.25248 −0.194005 −0.0970024 0.995284i \(-0.530925\pi\)
−0.0970024 + 0.995284i \(0.530925\pi\)
\(734\) −5.74079 −0.211896
\(735\) 0 0
\(736\) −5.77941 −0.213032
\(737\) −3.33040 −0.122677
\(738\) 0 0
\(739\) −5.09563 −0.187446 −0.0937229 0.995598i \(-0.529877\pi\)
−0.0937229 + 0.995598i \(0.529877\pi\)
\(740\) 14.6051 0.536895
\(741\) 0 0
\(742\) 0.304635 0.0111835
\(743\) −38.6427 −1.41766 −0.708832 0.705378i \(-0.750777\pi\)
−0.708832 + 0.705378i \(0.750777\pi\)
\(744\) 0 0
\(745\) 1.65274 0.0605516
\(746\) 20.9995 0.768845
\(747\) 0 0
\(748\) −3.88890 −0.142192
\(749\) −0.343781 −0.0125615
\(750\) 0 0
\(751\) −30.7607 −1.12247 −0.561237 0.827655i \(-0.689674\pi\)
−0.561237 + 0.827655i \(0.689674\pi\)
\(752\) 11.7891 0.429905
\(753\) 0 0
\(754\) 10.2338 0.372694
\(755\) 20.1100 0.731878
\(756\) 0 0
\(757\) 48.3050 1.75568 0.877838 0.478957i \(-0.158985\pi\)
0.877838 + 0.478957i \(0.158985\pi\)
\(758\) −19.9938 −0.726207
\(759\) 0 0
\(760\) −6.90688 −0.250539
\(761\) −22.0555 −0.799512 −0.399756 0.916622i \(-0.630905\pi\)
−0.399756 + 0.916622i \(0.630905\pi\)
\(762\) 0 0
\(763\) 0.253710 0.00918490
\(764\) −10.4427 −0.377803
\(765\) 0 0
\(766\) −4.52949 −0.163657
\(767\) 11.1183 0.401458
\(768\) 0 0
\(769\) 9.38769 0.338529 0.169264 0.985571i \(-0.445861\pi\)
0.169264 + 0.985571i \(0.445861\pi\)
\(770\) −0.0657621 −0.00236990
\(771\) 0 0
\(772\) −10.2254 −0.368021
\(773\) −28.4620 −1.02371 −0.511854 0.859073i \(-0.671041\pi\)
−0.511854 + 0.859073i \(0.671041\pi\)
\(774\) 0 0
\(775\) 16.7751 0.602579
\(776\) 0.383046 0.0137505
\(777\) 0 0
\(778\) 20.0034 0.717156
\(779\) −24.1252 −0.864374
\(780\) 0 0
\(781\) −12.1234 −0.433810
\(782\) 20.2521 0.724213
\(783\) 0 0
\(784\) −6.99871 −0.249954
\(785\) −8.51382 −0.303871
\(786\) 0 0
\(787\) 51.5947 1.83915 0.919577 0.392911i \(-0.128532\pi\)
0.919577 + 0.392911i \(0.128532\pi\)
\(788\) −22.4981 −0.801460
\(789\) 0 0
\(790\) −7.83925 −0.278908
\(791\) 0.0561485 0.00199641
\(792\) 0 0
\(793\) −7.79862 −0.276937
\(794\) −14.0741 −0.499470
\(795\) 0 0
\(796\) −1.33281 −0.0472401
\(797\) 11.3644 0.402546 0.201273 0.979535i \(-0.435492\pi\)
0.201273 + 0.979535i \(0.435492\pi\)
\(798\) 0 0
\(799\) −41.3112 −1.46148
\(800\) −2.26846 −0.0802022
\(801\) 0 0
\(802\) 7.17872 0.253489
\(803\) 4.04047 0.142585
\(804\) 0 0
\(805\) 0.342467 0.0120704
\(806\) −8.89642 −0.313363
\(807\) 0 0
\(808\) −6.26977 −0.220570
\(809\) 9.11122 0.320334 0.160167 0.987090i \(-0.448797\pi\)
0.160167 + 0.987090i \(0.448797\pi\)
\(810\) 0 0
\(811\) 39.0028 1.36957 0.684787 0.728744i \(-0.259895\pi\)
0.684787 + 0.728744i \(0.259895\pi\)
\(812\) 0.304991 0.0107031
\(813\) 0 0
\(814\) −9.80711 −0.343739
\(815\) −33.7500 −1.18221
\(816\) 0 0
\(817\) −31.7306 −1.11011
\(818\) −12.2911 −0.429748
\(819\) 0 0
\(820\) 9.54104 0.333188
\(821\) −1.67739 −0.0585412 −0.0292706 0.999572i \(-0.509318\pi\)
−0.0292706 + 0.999572i \(0.509318\pi\)
\(822\) 0 0
\(823\) −3.48182 −0.121368 −0.0606842 0.998157i \(-0.519328\pi\)
−0.0606842 + 0.998157i \(0.519328\pi\)
\(824\) −11.5950 −0.403931
\(825\) 0 0
\(826\) 0.331351 0.0115292
\(827\) 14.9045 0.518282 0.259141 0.965840i \(-0.416561\pi\)
0.259141 + 0.965840i \(0.416561\pi\)
\(828\) 0 0
\(829\) −46.2140 −1.60508 −0.802538 0.596600i \(-0.796518\pi\)
−0.802538 + 0.596600i \(0.796518\pi\)
\(830\) −4.60625 −0.159885
\(831\) 0 0
\(832\) 1.20305 0.0417081
\(833\) 24.5248 0.849733
\(834\) 0 0
\(835\) 27.9901 0.968639
\(836\) 4.63787 0.160404
\(837\) 0 0
\(838\) −11.9663 −0.413370
\(839\) −3.27807 −0.113171 −0.0565857 0.998398i \(-0.518021\pi\)
−0.0565857 + 0.998398i \(0.518021\pi\)
\(840\) 0 0
\(841\) 43.3621 1.49524
\(842\) 0.00355896 0.000122650 0
\(843\) 0 0
\(844\) −14.2623 −0.490928
\(845\) 19.0935 0.656838
\(846\) 0 0
\(847\) −0.350231 −0.0120341
\(848\) 8.49664 0.291776
\(849\) 0 0
\(850\) 7.94910 0.272652
\(851\) 51.0722 1.75073
\(852\) 0 0
\(853\) 46.6604 1.59762 0.798810 0.601583i \(-0.205463\pi\)
0.798810 + 0.601583i \(0.205463\pi\)
\(854\) −0.232417 −0.00795315
\(855\) 0 0
\(856\) −9.58849 −0.327728
\(857\) 41.9297 1.43229 0.716145 0.697952i \(-0.245905\pi\)
0.716145 + 0.697952i \(0.245905\pi\)
\(858\) 0 0
\(859\) 2.38586 0.0814044 0.0407022 0.999171i \(-0.487041\pi\)
0.0407022 + 0.999171i \(0.487041\pi\)
\(860\) 12.5488 0.427912
\(861\) 0 0
\(862\) −31.6067 −1.07653
\(863\) 32.0932 1.09247 0.546233 0.837633i \(-0.316061\pi\)
0.546233 + 0.837633i \(0.316061\pi\)
\(864\) 0 0
\(865\) 36.7999 1.25123
\(866\) 2.95878 0.100544
\(867\) 0 0
\(868\) −0.265134 −0.00899923
\(869\) 5.26394 0.178567
\(870\) 0 0
\(871\) −3.61026 −0.122329
\(872\) 7.07628 0.239633
\(873\) 0 0
\(874\) −24.1525 −0.816970
\(875\) 0.430703 0.0145604
\(876\) 0 0
\(877\) −42.7400 −1.44323 −0.721614 0.692296i \(-0.756599\pi\)
−0.721614 + 0.692296i \(0.756599\pi\)
\(878\) 34.0207 1.14814
\(879\) 0 0
\(880\) −1.83419 −0.0618304
\(881\) 34.7863 1.17198 0.585990 0.810318i \(-0.300706\pi\)
0.585990 + 0.810318i \(0.300706\pi\)
\(882\) 0 0
\(883\) 50.0834 1.68544 0.842720 0.538352i \(-0.180953\pi\)
0.842720 + 0.538352i \(0.180953\pi\)
\(884\) −4.21569 −0.141789
\(885\) 0 0
\(886\) −5.70534 −0.191675
\(887\) −37.3808 −1.25512 −0.627562 0.778566i \(-0.715947\pi\)
−0.627562 + 0.778566i \(0.715947\pi\)
\(888\) 0 0
\(889\) −0.157324 −0.00527647
\(890\) 10.0415 0.336591
\(891\) 0 0
\(892\) −28.6033 −0.957710
\(893\) 49.2674 1.64867
\(894\) 0 0
\(895\) −6.71055 −0.224309
\(896\) 0.0358535 0.00119778
\(897\) 0 0
\(898\) 10.8071 0.360637
\(899\) −62.9056 −2.09802
\(900\) 0 0
\(901\) −29.7738 −0.991909
\(902\) −6.40667 −0.213319
\(903\) 0 0
\(904\) 1.56605 0.0520861
\(905\) 21.8385 0.725936
\(906\) 0 0
\(907\) 18.0117 0.598069 0.299035 0.954242i \(-0.403335\pi\)
0.299035 + 0.954242i \(0.403335\pi\)
\(908\) 2.37525 0.0788253
\(909\) 0 0
\(910\) −0.0712882 −0.00236318
\(911\) −29.2095 −0.967753 −0.483877 0.875136i \(-0.660772\pi\)
−0.483877 + 0.875136i \(0.660772\pi\)
\(912\) 0 0
\(913\) 3.09303 0.102364
\(914\) −26.9583 −0.891701
\(915\) 0 0
\(916\) 9.02486 0.298190
\(917\) 0.427482 0.0141167
\(918\) 0 0
\(919\) −9.48599 −0.312914 −0.156457 0.987685i \(-0.550007\pi\)
−0.156457 + 0.987685i \(0.550007\pi\)
\(920\) 9.55184 0.314915
\(921\) 0 0
\(922\) 30.0843 0.990774
\(923\) −13.1422 −0.432580
\(924\) 0 0
\(925\) 20.0462 0.659116
\(926\) 40.5192 1.33154
\(927\) 0 0
\(928\) 8.50659 0.279243
\(929\) −9.36643 −0.307302 −0.153651 0.988125i \(-0.549103\pi\)
−0.153651 + 0.988125i \(0.549103\pi\)
\(930\) 0 0
\(931\) −29.2480 −0.958565
\(932\) 14.5151 0.475459
\(933\) 0 0
\(934\) 15.9889 0.523171
\(935\) 6.42732 0.210196
\(936\) 0 0
\(937\) 34.3928 1.12356 0.561782 0.827285i \(-0.310116\pi\)
0.561782 + 0.827285i \(0.310116\pi\)
\(938\) −0.107594 −0.00351307
\(939\) 0 0
\(940\) −19.4843 −0.635508
\(941\) 22.1703 0.722730 0.361365 0.932424i \(-0.382311\pi\)
0.361365 + 0.932424i \(0.382311\pi\)
\(942\) 0 0
\(943\) 33.3638 1.08647
\(944\) 9.24179 0.300795
\(945\) 0 0
\(946\) −8.42636 −0.273965
\(947\) −10.6321 −0.345495 −0.172748 0.984966i \(-0.555265\pi\)
−0.172748 + 0.984966i \(0.555265\pi\)
\(948\) 0 0
\(949\) 4.38000 0.142181
\(950\) −9.48003 −0.307573
\(951\) 0 0
\(952\) −0.125637 −0.00407193
\(953\) −32.0340 −1.03768 −0.518841 0.854871i \(-0.673636\pi\)
−0.518841 + 0.854871i \(0.673636\pi\)
\(954\) 0 0
\(955\) 17.2590 0.558488
\(956\) −3.69277 −0.119433
\(957\) 0 0
\(958\) −26.4486 −0.854517
\(959\) 0.271612 0.00877080
\(960\) 0 0
\(961\) 23.6848 0.764027
\(962\) −10.6312 −0.342764
\(963\) 0 0
\(964\) −30.9002 −0.995227
\(965\) 16.8999 0.544028
\(966\) 0 0
\(967\) 9.52983 0.306459 0.153229 0.988191i \(-0.451033\pi\)
0.153229 + 0.988191i \(0.451033\pi\)
\(968\) −9.76837 −0.313967
\(969\) 0 0
\(970\) −0.633073 −0.0203268
\(971\) 40.8006 1.30935 0.654677 0.755909i \(-0.272805\pi\)
0.654677 + 0.755909i \(0.272805\pi\)
\(972\) 0 0
\(973\) 0.153116 0.00490867
\(974\) −43.0978 −1.38094
\(975\) 0 0
\(976\) −6.48240 −0.207497
\(977\) −16.4171 −0.525228 −0.262614 0.964901i \(-0.584585\pi\)
−0.262614 + 0.964901i \(0.584585\pi\)
\(978\) 0 0
\(979\) −6.74270 −0.215498
\(980\) 11.5670 0.369495
\(981\) 0 0
\(982\) −20.3362 −0.648953
\(983\) −35.1472 −1.12102 −0.560510 0.828148i \(-0.689395\pi\)
−0.560510 + 0.828148i \(0.689395\pi\)
\(984\) 0 0
\(985\) 37.1834 1.18476
\(986\) −29.8086 −0.949300
\(987\) 0 0
\(988\) 5.02760 0.159949
\(989\) 43.8817 1.39536
\(990\) 0 0
\(991\) −49.7613 −1.58072 −0.790361 0.612642i \(-0.790107\pi\)
−0.790361 + 0.612642i \(0.790107\pi\)
\(992\) −7.39492 −0.234789
\(993\) 0 0
\(994\) −0.391667 −0.0124229
\(995\) 2.20278 0.0698328
\(996\) 0 0
\(997\) −41.4428 −1.31251 −0.656254 0.754540i \(-0.727860\pi\)
−0.656254 + 0.754540i \(0.727860\pi\)
\(998\) −28.4668 −0.901101
\(999\) 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 \(a_p\))