Properties

Label 8046.2.a.h.1.1
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 1.1
Root \(1.05829\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -3.80777 q^{5} +0.515673 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -3.80777 q^{5} +0.515673 q^{7} +1.00000 q^{8} -3.80777 q^{10} -0.940941 q^{11} -2.83646 q^{13} +0.515673 q^{14} +1.00000 q^{16} +3.93453 q^{17} -3.57365 q^{19} -3.80777 q^{20} -0.940941 q^{22} +1.39239 q^{23} +9.49910 q^{25} -2.83646 q^{26} +0.515673 q^{28} +8.36889 q^{29} +2.17513 q^{31} +1.00000 q^{32} +3.93453 q^{34} -1.96357 q^{35} +3.67086 q^{37} -3.57365 q^{38} -3.80777 q^{40} +9.56071 q^{41} -9.00371 q^{43} -0.940941 q^{44} +1.39239 q^{46} -2.89701 q^{47} -6.73408 q^{49} +9.49910 q^{50} -2.83646 q^{52} -1.17075 q^{53} +3.58289 q^{55} +0.515673 q^{56} +8.36889 q^{58} -12.3747 q^{59} +2.12700 q^{61} +2.17513 q^{62} +1.00000 q^{64} +10.8006 q^{65} -10.2760 q^{67} +3.93453 q^{68} -1.96357 q^{70} -2.35223 q^{71} +10.1300 q^{73} +3.67086 q^{74} -3.57365 q^{76} -0.485218 q^{77} -5.14150 q^{79} -3.80777 q^{80} +9.56071 q^{82} +3.57873 q^{83} -14.9818 q^{85} -9.00371 q^{86} -0.940941 q^{88} +0.00223128 q^{89} -1.46269 q^{91} +1.39239 q^{92} -2.89701 q^{94} +13.6076 q^{95} +3.82873 q^{97} -6.73408 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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
\(5\) −3.80777 −1.70289 −0.851443 0.524447i \(-0.824272\pi\)
−0.851443 + 0.524447i \(0.824272\pi\)
\(6\) 0 0
\(7\) 0.515673 0.194906 0.0974531 0.995240i \(-0.468930\pi\)
0.0974531 + 0.995240i \(0.468930\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −3.80777 −1.20412
\(11\) −0.940941 −0.283704 −0.141852 0.989888i \(-0.545306\pi\)
−0.141852 + 0.989888i \(0.545306\pi\)
\(12\) 0 0
\(13\) −2.83646 −0.786693 −0.393346 0.919390i \(-0.628683\pi\)
−0.393346 + 0.919390i \(0.628683\pi\)
\(14\) 0.515673 0.137820
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.93453 0.954264 0.477132 0.878832i \(-0.341676\pi\)
0.477132 + 0.878832i \(0.341676\pi\)
\(18\) 0 0
\(19\) −3.57365 −0.819852 −0.409926 0.912119i \(-0.634446\pi\)
−0.409926 + 0.912119i \(0.634446\pi\)
\(20\) −3.80777 −0.851443
\(21\) 0 0
\(22\) −0.940941 −0.200609
\(23\) 1.39239 0.290333 0.145167 0.989407i \(-0.453628\pi\)
0.145167 + 0.989407i \(0.453628\pi\)
\(24\) 0 0
\(25\) 9.49910 1.89982
\(26\) −2.83646 −0.556276
\(27\) 0 0
\(28\) 0.515673 0.0974531
\(29\) 8.36889 1.55406 0.777032 0.629461i \(-0.216724\pi\)
0.777032 + 0.629461i \(0.216724\pi\)
\(30\) 0 0
\(31\) 2.17513 0.390666 0.195333 0.980737i \(-0.437421\pi\)
0.195333 + 0.980737i \(0.437421\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 3.93453 0.674766
\(35\) −1.96357 −0.331903
\(36\) 0 0
\(37\) 3.67086 0.603486 0.301743 0.953389i \(-0.402432\pi\)
0.301743 + 0.953389i \(0.402432\pi\)
\(38\) −3.57365 −0.579723
\(39\) 0 0
\(40\) −3.80777 −0.602061
\(41\) 9.56071 1.49313 0.746566 0.665312i \(-0.231701\pi\)
0.746566 + 0.665312i \(0.231701\pi\)
\(42\) 0 0
\(43\) −9.00371 −1.37305 −0.686526 0.727105i \(-0.740865\pi\)
−0.686526 + 0.727105i \(0.740865\pi\)
\(44\) −0.940941 −0.141852
\(45\) 0 0
\(46\) 1.39239 0.205297
\(47\) −2.89701 −0.422573 −0.211286 0.977424i \(-0.567765\pi\)
−0.211286 + 0.977424i \(0.567765\pi\)
\(48\) 0 0
\(49\) −6.73408 −0.962012
\(50\) 9.49910 1.34338
\(51\) 0 0
\(52\) −2.83646 −0.393346
\(53\) −1.17075 −0.160815 −0.0804076 0.996762i \(-0.525622\pi\)
−0.0804076 + 0.996762i \(0.525622\pi\)
\(54\) 0 0
\(55\) 3.58289 0.483116
\(56\) 0.515673 0.0689098
\(57\) 0 0
\(58\) 8.36889 1.09889
\(59\) −12.3747 −1.61105 −0.805523 0.592564i \(-0.798116\pi\)
−0.805523 + 0.592564i \(0.798116\pi\)
\(60\) 0 0
\(61\) 2.12700 0.272334 0.136167 0.990686i \(-0.456522\pi\)
0.136167 + 0.990686i \(0.456522\pi\)
\(62\) 2.17513 0.276242
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 10.8006 1.33965
\(66\) 0 0
\(67\) −10.2760 −1.25542 −0.627709 0.778448i \(-0.716007\pi\)
−0.627709 + 0.778448i \(0.716007\pi\)
\(68\) 3.93453 0.477132
\(69\) 0 0
\(70\) −1.96357 −0.234691
\(71\) −2.35223 −0.279158 −0.139579 0.990211i \(-0.544575\pi\)
−0.139579 + 0.990211i \(0.544575\pi\)
\(72\) 0 0
\(73\) 10.1300 1.18562 0.592812 0.805341i \(-0.298018\pi\)
0.592812 + 0.805341i \(0.298018\pi\)
\(74\) 3.67086 0.426729
\(75\) 0 0
\(76\) −3.57365 −0.409926
\(77\) −0.485218 −0.0552958
\(78\) 0 0
\(79\) −5.14150 −0.578464 −0.289232 0.957259i \(-0.593400\pi\)
−0.289232 + 0.957259i \(0.593400\pi\)
\(80\) −3.80777 −0.425721
\(81\) 0 0
\(82\) 9.56071 1.05580
\(83\) 3.57873 0.392816 0.196408 0.980522i \(-0.437072\pi\)
0.196408 + 0.980522i \(0.437072\pi\)
\(84\) 0 0
\(85\) −14.9818 −1.62500
\(86\) −9.00371 −0.970895
\(87\) 0 0
\(88\) −0.940941 −0.100305
\(89\) 0.00223128 0.000236515 0 0.000118258 1.00000i \(-0.499962\pi\)
0.000118258 1.00000i \(0.499962\pi\)
\(90\) 0 0
\(91\) −1.46269 −0.153331
\(92\) 1.39239 0.145167
\(93\) 0 0
\(94\) −2.89701 −0.298804
\(95\) 13.6076 1.39611
\(96\) 0 0
\(97\) 3.82873 0.388749 0.194374 0.980927i \(-0.437732\pi\)
0.194374 + 0.980927i \(0.437732\pi\)
\(98\) −6.73408 −0.680245
\(99\) 0 0
\(100\) 9.49910 0.949910
\(101\) 2.22598 0.221494 0.110747 0.993849i \(-0.464676\pi\)
0.110747 + 0.993849i \(0.464676\pi\)
\(102\) 0 0
\(103\) −13.3755 −1.31793 −0.658966 0.752173i \(-0.729006\pi\)
−0.658966 + 0.752173i \(0.729006\pi\)
\(104\) −2.83646 −0.278138
\(105\) 0 0
\(106\) −1.17075 −0.113714
\(107\) −4.96212 −0.479707 −0.239853 0.970809i \(-0.577099\pi\)
−0.239853 + 0.970809i \(0.577099\pi\)
\(108\) 0 0
\(109\) −2.01553 −0.193053 −0.0965264 0.995330i \(-0.530773\pi\)
−0.0965264 + 0.995330i \(0.530773\pi\)
\(110\) 3.58289 0.341615
\(111\) 0 0
\(112\) 0.515673 0.0487266
\(113\) −7.87785 −0.741086 −0.370543 0.928815i \(-0.620828\pi\)
−0.370543 + 0.928815i \(0.620828\pi\)
\(114\) 0 0
\(115\) −5.30190 −0.494404
\(116\) 8.36889 0.777032
\(117\) 0 0
\(118\) −12.3747 −1.13918
\(119\) 2.02893 0.185992
\(120\) 0 0
\(121\) −10.1146 −0.919512
\(122\) 2.12700 0.192569
\(123\) 0 0
\(124\) 2.17513 0.195333
\(125\) −17.1315 −1.53229
\(126\) 0 0
\(127\) −19.7227 −1.75011 −0.875054 0.484025i \(-0.839174\pi\)
−0.875054 + 0.484025i \(0.839174\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 10.8006 0.947274
\(131\) 10.9019 0.952504 0.476252 0.879309i \(-0.341995\pi\)
0.476252 + 0.879309i \(0.341995\pi\)
\(132\) 0 0
\(133\) −1.84284 −0.159794
\(134\) −10.2760 −0.887715
\(135\) 0 0
\(136\) 3.93453 0.337383
\(137\) 6.40820 0.547489 0.273745 0.961802i \(-0.411738\pi\)
0.273745 + 0.961802i \(0.411738\pi\)
\(138\) 0 0
\(139\) −17.0897 −1.44953 −0.724763 0.688998i \(-0.758051\pi\)
−0.724763 + 0.688998i \(0.758051\pi\)
\(140\) −1.96357 −0.165952
\(141\) 0 0
\(142\) −2.35223 −0.197394
\(143\) 2.66894 0.223188
\(144\) 0 0
\(145\) −31.8668 −2.64639
\(146\) 10.1300 0.838363
\(147\) 0 0
\(148\) 3.67086 0.301743
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −13.2487 −1.07816 −0.539081 0.842254i \(-0.681228\pi\)
−0.539081 + 0.842254i \(0.681228\pi\)
\(152\) −3.57365 −0.289862
\(153\) 0 0
\(154\) −0.485218 −0.0391000
\(155\) −8.28241 −0.665259
\(156\) 0 0
\(157\) 10.5613 0.842883 0.421442 0.906855i \(-0.361524\pi\)
0.421442 + 0.906855i \(0.361524\pi\)
\(158\) −5.14150 −0.409036
\(159\) 0 0
\(160\) −3.80777 −0.301030
\(161\) 0.718018 0.0565878
\(162\) 0 0
\(163\) −12.9514 −1.01443 −0.507216 0.861819i \(-0.669325\pi\)
−0.507216 + 0.861819i \(0.669325\pi\)
\(164\) 9.56071 0.746566
\(165\) 0 0
\(166\) 3.57873 0.277763
\(167\) −11.4775 −0.888159 −0.444079 0.895987i \(-0.646469\pi\)
−0.444079 + 0.895987i \(0.646469\pi\)
\(168\) 0 0
\(169\) −4.95449 −0.381114
\(170\) −14.9818 −1.14905
\(171\) 0 0
\(172\) −9.00371 −0.686526
\(173\) 24.8186 1.88692 0.943461 0.331485i \(-0.107550\pi\)
0.943461 + 0.331485i \(0.107550\pi\)
\(174\) 0 0
\(175\) 4.89843 0.370287
\(176\) −0.940941 −0.0709261
\(177\) 0 0
\(178\) 0.00223128 0.000167242 0
\(179\) −9.86161 −0.737091 −0.368546 0.929610i \(-0.620144\pi\)
−0.368546 + 0.929610i \(0.620144\pi\)
\(180\) 0 0
\(181\) −15.6306 −1.16182 −0.580908 0.813969i \(-0.697302\pi\)
−0.580908 + 0.813969i \(0.697302\pi\)
\(182\) −1.46269 −0.108422
\(183\) 0 0
\(184\) 1.39239 0.102648
\(185\) −13.9778 −1.02767
\(186\) 0 0
\(187\) −3.70216 −0.270729
\(188\) −2.89701 −0.211286
\(189\) 0 0
\(190\) 13.6076 0.987202
\(191\) −8.22930 −0.595451 −0.297726 0.954651i \(-0.596228\pi\)
−0.297726 + 0.954651i \(0.596228\pi\)
\(192\) 0 0
\(193\) −3.29466 −0.237155 −0.118577 0.992945i \(-0.537833\pi\)
−0.118577 + 0.992945i \(0.537833\pi\)
\(194\) 3.82873 0.274887
\(195\) 0 0
\(196\) −6.73408 −0.481006
\(197\) −13.7739 −0.981348 −0.490674 0.871343i \(-0.663249\pi\)
−0.490674 + 0.871343i \(0.663249\pi\)
\(198\) 0 0
\(199\) 2.93461 0.208029 0.104014 0.994576i \(-0.466831\pi\)
0.104014 + 0.994576i \(0.466831\pi\)
\(200\) 9.49910 0.671688
\(201\) 0 0
\(202\) 2.22598 0.156620
\(203\) 4.31562 0.302897
\(204\) 0 0
\(205\) −36.4050 −2.54263
\(206\) −13.3755 −0.931918
\(207\) 0 0
\(208\) −2.83646 −0.196673
\(209\) 3.36260 0.232596
\(210\) 0 0
\(211\) 13.5697 0.934175 0.467088 0.884211i \(-0.345303\pi\)
0.467088 + 0.884211i \(0.345303\pi\)
\(212\) −1.17075 −0.0804076
\(213\) 0 0
\(214\) −4.96212 −0.339204
\(215\) 34.2840 2.33815
\(216\) 0 0
\(217\) 1.12166 0.0761432
\(218\) −2.01553 −0.136509
\(219\) 0 0
\(220\) 3.58289 0.241558
\(221\) −11.1601 −0.750712
\(222\) 0 0
\(223\) 0.372556 0.0249482 0.0124741 0.999922i \(-0.496029\pi\)
0.0124741 + 0.999922i \(0.496029\pi\)
\(224\) 0.515673 0.0344549
\(225\) 0 0
\(226\) −7.87785 −0.524027
\(227\) 12.9343 0.858478 0.429239 0.903191i \(-0.358782\pi\)
0.429239 + 0.903191i \(0.358782\pi\)
\(228\) 0 0
\(229\) −6.44573 −0.425946 −0.212973 0.977058i \(-0.568315\pi\)
−0.212973 + 0.977058i \(0.568315\pi\)
\(230\) −5.30190 −0.349597
\(231\) 0 0
\(232\) 8.36889 0.549445
\(233\) −7.75366 −0.507959 −0.253980 0.967210i \(-0.581740\pi\)
−0.253980 + 0.967210i \(0.581740\pi\)
\(234\) 0 0
\(235\) 11.0311 0.719593
\(236\) −12.3747 −0.805523
\(237\) 0 0
\(238\) 2.02893 0.131516
\(239\) −14.3567 −0.928660 −0.464330 0.885662i \(-0.653705\pi\)
−0.464330 + 0.885662i \(0.653705\pi\)
\(240\) 0 0
\(241\) 12.1139 0.780323 0.390162 0.920746i \(-0.372419\pi\)
0.390162 + 0.920746i \(0.372419\pi\)
\(242\) −10.1146 −0.650193
\(243\) 0 0
\(244\) 2.12700 0.136167
\(245\) 25.6418 1.63820
\(246\) 0 0
\(247\) 10.1365 0.644972
\(248\) 2.17513 0.138121
\(249\) 0 0
\(250\) −17.1315 −1.08349
\(251\) −16.3635 −1.03286 −0.516428 0.856331i \(-0.672739\pi\)
−0.516428 + 0.856331i \(0.672739\pi\)
\(252\) 0 0
\(253\) −1.31016 −0.0823688
\(254\) −19.7227 −1.23751
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −0.104679 −0.00652969 −0.00326484 0.999995i \(-0.501039\pi\)
−0.00326484 + 0.999995i \(0.501039\pi\)
\(258\) 0 0
\(259\) 1.89297 0.117623
\(260\) 10.8006 0.669824
\(261\) 0 0
\(262\) 10.9019 0.673522
\(263\) −21.3035 −1.31363 −0.656815 0.754052i \(-0.728097\pi\)
−0.656815 + 0.754052i \(0.728097\pi\)
\(264\) 0 0
\(265\) 4.45795 0.273850
\(266\) −1.84284 −0.112992
\(267\) 0 0
\(268\) −10.2760 −0.627709
\(269\) 9.61799 0.586419 0.293210 0.956048i \(-0.405277\pi\)
0.293210 + 0.956048i \(0.405277\pi\)
\(270\) 0 0
\(271\) 14.1277 0.858195 0.429097 0.903258i \(-0.358832\pi\)
0.429097 + 0.903258i \(0.358832\pi\)
\(272\) 3.93453 0.238566
\(273\) 0 0
\(274\) 6.40820 0.387133
\(275\) −8.93809 −0.538987
\(276\) 0 0
\(277\) −20.2247 −1.21519 −0.607593 0.794248i \(-0.707865\pi\)
−0.607593 + 0.794248i \(0.707865\pi\)
\(278\) −17.0897 −1.02497
\(279\) 0 0
\(280\) −1.96357 −0.117345
\(281\) 19.8872 1.18637 0.593184 0.805067i \(-0.297871\pi\)
0.593184 + 0.805067i \(0.297871\pi\)
\(282\) 0 0
\(283\) 17.9462 1.06679 0.533395 0.845866i \(-0.320916\pi\)
0.533395 + 0.845866i \(0.320916\pi\)
\(284\) −2.35223 −0.139579
\(285\) 0 0
\(286\) 2.66894 0.157818
\(287\) 4.93020 0.291021
\(288\) 0 0
\(289\) −1.51947 −0.0893807
\(290\) −31.8668 −1.87128
\(291\) 0 0
\(292\) 10.1300 0.592812
\(293\) −3.06625 −0.179132 −0.0895661 0.995981i \(-0.528548\pi\)
−0.0895661 + 0.995981i \(0.528548\pi\)
\(294\) 0 0
\(295\) 47.1199 2.74343
\(296\) 3.67086 0.213365
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −3.94946 −0.228403
\(300\) 0 0
\(301\) −4.64297 −0.267617
\(302\) −13.2487 −0.762375
\(303\) 0 0
\(304\) −3.57365 −0.204963
\(305\) −8.09911 −0.463754
\(306\) 0 0
\(307\) 6.82680 0.389626 0.194813 0.980840i \(-0.437590\pi\)
0.194813 + 0.980840i \(0.437590\pi\)
\(308\) −0.485218 −0.0276479
\(309\) 0 0
\(310\) −8.28241 −0.470409
\(311\) 11.5998 0.657765 0.328882 0.944371i \(-0.393328\pi\)
0.328882 + 0.944371i \(0.393328\pi\)
\(312\) 0 0
\(313\) 16.4325 0.928818 0.464409 0.885621i \(-0.346267\pi\)
0.464409 + 0.885621i \(0.346267\pi\)
\(314\) 10.5613 0.596009
\(315\) 0 0
\(316\) −5.14150 −0.289232
\(317\) −12.2930 −0.690445 −0.345222 0.938521i \(-0.612197\pi\)
−0.345222 + 0.938521i \(0.612197\pi\)
\(318\) 0 0
\(319\) −7.87463 −0.440895
\(320\) −3.80777 −0.212861
\(321\) 0 0
\(322\) 0.718018 0.0400136
\(323\) −14.0606 −0.782355
\(324\) 0 0
\(325\) −26.9438 −1.49457
\(326\) −12.9514 −0.717312
\(327\) 0 0
\(328\) 9.56071 0.527902
\(329\) −1.49391 −0.0823620
\(330\) 0 0
\(331\) −18.3673 −1.00956 −0.504779 0.863248i \(-0.668426\pi\)
−0.504779 + 0.863248i \(0.668426\pi\)
\(332\) 3.57873 0.196408
\(333\) 0 0
\(334\) −11.4775 −0.628023
\(335\) 39.1288 2.13783
\(336\) 0 0
\(337\) 26.3649 1.43619 0.718094 0.695946i \(-0.245015\pi\)
0.718094 + 0.695946i \(0.245015\pi\)
\(338\) −4.95449 −0.269489
\(339\) 0 0
\(340\) −14.9818 −0.812501
\(341\) −2.04667 −0.110834
\(342\) 0 0
\(343\) −7.08230 −0.382408
\(344\) −9.00371 −0.485448
\(345\) 0 0
\(346\) 24.8186 1.33425
\(347\) −31.6944 −1.70144 −0.850721 0.525617i \(-0.823835\pi\)
−0.850721 + 0.525617i \(0.823835\pi\)
\(348\) 0 0
\(349\) −13.0175 −0.696809 −0.348404 0.937344i \(-0.613276\pi\)
−0.348404 + 0.937344i \(0.613276\pi\)
\(350\) 4.89843 0.261832
\(351\) 0 0
\(352\) −0.940941 −0.0501523
\(353\) 24.8615 1.32324 0.661622 0.749837i \(-0.269868\pi\)
0.661622 + 0.749837i \(0.269868\pi\)
\(354\) 0 0
\(355\) 8.95673 0.475374
\(356\) 0.00223128 0.000118258 0
\(357\) 0 0
\(358\) −9.86161 −0.521202
\(359\) 8.53896 0.450669 0.225335 0.974281i \(-0.427653\pi\)
0.225335 + 0.974281i \(0.427653\pi\)
\(360\) 0 0
\(361\) −6.22900 −0.327842
\(362\) −15.6306 −0.821527
\(363\) 0 0
\(364\) −1.46269 −0.0766657
\(365\) −38.5726 −2.01898
\(366\) 0 0
\(367\) 22.8141 1.19089 0.595443 0.803397i \(-0.296976\pi\)
0.595443 + 0.803397i \(0.296976\pi\)
\(368\) 1.39239 0.0725833
\(369\) 0 0
\(370\) −13.9778 −0.726671
\(371\) −0.603726 −0.0313439
\(372\) 0 0
\(373\) −34.0227 −1.76163 −0.880813 0.473464i \(-0.843003\pi\)
−0.880813 + 0.473464i \(0.843003\pi\)
\(374\) −3.70216 −0.191434
\(375\) 0 0
\(376\) −2.89701 −0.149402
\(377\) −23.7380 −1.22257
\(378\) 0 0
\(379\) 3.03351 0.155821 0.0779105 0.996960i \(-0.475175\pi\)
0.0779105 + 0.996960i \(0.475175\pi\)
\(380\) 13.6076 0.698057
\(381\) 0 0
\(382\) −8.22930 −0.421048
\(383\) 22.2167 1.13522 0.567609 0.823298i \(-0.307869\pi\)
0.567609 + 0.823298i \(0.307869\pi\)
\(384\) 0 0
\(385\) 1.84760 0.0941624
\(386\) −3.29466 −0.167694
\(387\) 0 0
\(388\) 3.82873 0.194374
\(389\) −34.5062 −1.74954 −0.874768 0.484543i \(-0.838986\pi\)
−0.874768 + 0.484543i \(0.838986\pi\)
\(390\) 0 0
\(391\) 5.47840 0.277055
\(392\) −6.73408 −0.340122
\(393\) 0 0
\(394\) −13.7739 −0.693918
\(395\) 19.5776 0.985058
\(396\) 0 0
\(397\) −29.6718 −1.48918 −0.744592 0.667520i \(-0.767356\pi\)
−0.744592 + 0.667520i \(0.767356\pi\)
\(398\) 2.93461 0.147099
\(399\) 0 0
\(400\) 9.49910 0.474955
\(401\) 18.1554 0.906637 0.453318 0.891349i \(-0.350240\pi\)
0.453318 + 0.891349i \(0.350240\pi\)
\(402\) 0 0
\(403\) −6.16968 −0.307334
\(404\) 2.22598 0.110747
\(405\) 0 0
\(406\) 4.31562 0.214180
\(407\) −3.45407 −0.171212
\(408\) 0 0
\(409\) −25.9816 −1.28471 −0.642355 0.766408i \(-0.722042\pi\)
−0.642355 + 0.766408i \(0.722042\pi\)
\(410\) −36.4050 −1.79791
\(411\) 0 0
\(412\) −13.3755 −0.658966
\(413\) −6.38130 −0.314003
\(414\) 0 0
\(415\) −13.6270 −0.668921
\(416\) −2.83646 −0.139069
\(417\) 0 0
\(418\) 3.36260 0.164470
\(419\) −30.8938 −1.50926 −0.754629 0.656151i \(-0.772183\pi\)
−0.754629 + 0.656151i \(0.772183\pi\)
\(420\) 0 0
\(421\) 17.9253 0.873625 0.436812 0.899553i \(-0.356107\pi\)
0.436812 + 0.899553i \(0.356107\pi\)
\(422\) 13.5697 0.660562
\(423\) 0 0
\(424\) −1.17075 −0.0568568
\(425\) 37.3745 1.81293
\(426\) 0 0
\(427\) 1.09684 0.0530796
\(428\) −4.96212 −0.239853
\(429\) 0 0
\(430\) 34.2840 1.65332
\(431\) −9.24825 −0.445472 −0.222736 0.974879i \(-0.571499\pi\)
−0.222736 + 0.974879i \(0.571499\pi\)
\(432\) 0 0
\(433\) −9.35001 −0.449333 −0.224666 0.974436i \(-0.572129\pi\)
−0.224666 + 0.974436i \(0.572129\pi\)
\(434\) 1.12166 0.0538413
\(435\) 0 0
\(436\) −2.01553 −0.0965264
\(437\) −4.97592 −0.238030
\(438\) 0 0
\(439\) 0.0383341 0.00182959 0.000914793 1.00000i \(-0.499709\pi\)
0.000914793 1.00000i \(0.499709\pi\)
\(440\) 3.58289 0.170807
\(441\) 0 0
\(442\) −11.1601 −0.530834
\(443\) 7.37697 0.350490 0.175245 0.984525i \(-0.443928\pi\)
0.175245 + 0.984525i \(0.443928\pi\)
\(444\) 0 0
\(445\) −0.00849621 −0.000402759 0
\(446\) 0.372556 0.0176411
\(447\) 0 0
\(448\) 0.515673 0.0243633
\(449\) 14.1872 0.669534 0.334767 0.942301i \(-0.391342\pi\)
0.334767 + 0.942301i \(0.391342\pi\)
\(450\) 0 0
\(451\) −8.99606 −0.423608
\(452\) −7.87785 −0.370543
\(453\) 0 0
\(454\) 12.9343 0.607035
\(455\) 5.56958 0.261106
\(456\) 0 0
\(457\) 9.03586 0.422680 0.211340 0.977413i \(-0.432217\pi\)
0.211340 + 0.977413i \(0.432217\pi\)
\(458\) −6.44573 −0.301189
\(459\) 0 0
\(460\) −5.30190 −0.247202
\(461\) 9.78904 0.455921 0.227961 0.973670i \(-0.426794\pi\)
0.227961 + 0.973670i \(0.426794\pi\)
\(462\) 0 0
\(463\) 11.6439 0.541136 0.270568 0.962701i \(-0.412788\pi\)
0.270568 + 0.962701i \(0.412788\pi\)
\(464\) 8.36889 0.388516
\(465\) 0 0
\(466\) −7.75366 −0.359181
\(467\) −9.99358 −0.462448 −0.231224 0.972901i \(-0.574273\pi\)
−0.231224 + 0.972901i \(0.574273\pi\)
\(468\) 0 0
\(469\) −5.29908 −0.244689
\(470\) 11.0311 0.508829
\(471\) 0 0
\(472\) −12.3747 −0.569591
\(473\) 8.47196 0.389541
\(474\) 0 0
\(475\) −33.9465 −1.55757
\(476\) 2.02893 0.0929960
\(477\) 0 0
\(478\) −14.3567 −0.656662
\(479\) 22.4494 1.02574 0.512871 0.858466i \(-0.328582\pi\)
0.512871 + 0.858466i \(0.328582\pi\)
\(480\) 0 0
\(481\) −10.4123 −0.474758
\(482\) 12.1139 0.551772
\(483\) 0 0
\(484\) −10.1146 −0.459756
\(485\) −14.5789 −0.661995
\(486\) 0 0
\(487\) 9.74065 0.441391 0.220695 0.975343i \(-0.429167\pi\)
0.220695 + 0.975343i \(0.429167\pi\)
\(488\) 2.12700 0.0962847
\(489\) 0 0
\(490\) 25.6418 1.15838
\(491\) −31.6763 −1.42953 −0.714766 0.699364i \(-0.753467\pi\)
−0.714766 + 0.699364i \(0.753467\pi\)
\(492\) 0 0
\(493\) 32.9277 1.48299
\(494\) 10.1365 0.456064
\(495\) 0 0
\(496\) 2.17513 0.0976664
\(497\) −1.21298 −0.0544096
\(498\) 0 0
\(499\) 6.13481 0.274632 0.137316 0.990527i \(-0.456152\pi\)
0.137316 + 0.990527i \(0.456152\pi\)
\(500\) −17.1315 −0.766145
\(501\) 0 0
\(502\) −16.3635 −0.730339
\(503\) 5.23723 0.233517 0.116758 0.993160i \(-0.462750\pi\)
0.116758 + 0.993160i \(0.462750\pi\)
\(504\) 0 0
\(505\) −8.47603 −0.377178
\(506\) −1.31016 −0.0582436
\(507\) 0 0
\(508\) −19.7227 −0.875054
\(509\) −31.0989 −1.37844 −0.689218 0.724554i \(-0.742046\pi\)
−0.689218 + 0.724554i \(0.742046\pi\)
\(510\) 0 0
\(511\) 5.22376 0.231086
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −0.104679 −0.00461719
\(515\) 50.9310 2.24429
\(516\) 0 0
\(517\) 2.72592 0.119886
\(518\) 1.89297 0.0831722
\(519\) 0 0
\(520\) 10.8006 0.473637
\(521\) −8.77765 −0.384556 −0.192278 0.981341i \(-0.561588\pi\)
−0.192278 + 0.981341i \(0.561588\pi\)
\(522\) 0 0
\(523\) 33.8192 1.47881 0.739406 0.673260i \(-0.235106\pi\)
0.739406 + 0.673260i \(0.235106\pi\)
\(524\) 10.9019 0.476252
\(525\) 0 0
\(526\) −21.3035 −0.928876
\(527\) 8.55813 0.372798
\(528\) 0 0
\(529\) −21.0613 −0.915707
\(530\) 4.45795 0.193641
\(531\) 0 0
\(532\) −1.84284 −0.0798972
\(533\) −27.1186 −1.17464
\(534\) 0 0
\(535\) 18.8946 0.816886
\(536\) −10.2760 −0.443857
\(537\) 0 0
\(538\) 9.61799 0.414661
\(539\) 6.33637 0.272927
\(540\) 0 0
\(541\) 28.0587 1.20634 0.603170 0.797613i \(-0.293904\pi\)
0.603170 + 0.797613i \(0.293904\pi\)
\(542\) 14.1277 0.606835
\(543\) 0 0
\(544\) 3.93453 0.168692
\(545\) 7.67468 0.328747
\(546\) 0 0
\(547\) 13.7186 0.586565 0.293282 0.956026i \(-0.405252\pi\)
0.293282 + 0.956026i \(0.405252\pi\)
\(548\) 6.40820 0.273745
\(549\) 0 0
\(550\) −8.93809 −0.381121
\(551\) −29.9075 −1.27410
\(552\) 0 0
\(553\) −2.65134 −0.112746
\(554\) −20.2247 −0.859267
\(555\) 0 0
\(556\) −17.0897 −0.724763
\(557\) −38.7258 −1.64087 −0.820433 0.571743i \(-0.806267\pi\)
−0.820433 + 0.571743i \(0.806267\pi\)
\(558\) 0 0
\(559\) 25.5387 1.08017
\(560\) −1.96357 −0.0829758
\(561\) 0 0
\(562\) 19.8872 0.838889
\(563\) 27.0005 1.13793 0.568967 0.822360i \(-0.307343\pi\)
0.568967 + 0.822360i \(0.307343\pi\)
\(564\) 0 0
\(565\) 29.9970 1.26198
\(566\) 17.9462 0.754335
\(567\) 0 0
\(568\) −2.35223 −0.0986972
\(569\) 44.4013 1.86140 0.930700 0.365784i \(-0.119199\pi\)
0.930700 + 0.365784i \(0.119199\pi\)
\(570\) 0 0
\(571\) 16.1826 0.677220 0.338610 0.940927i \(-0.390043\pi\)
0.338610 + 0.940927i \(0.390043\pi\)
\(572\) 2.66894 0.111594
\(573\) 0 0
\(574\) 4.93020 0.205783
\(575\) 13.2264 0.551581
\(576\) 0 0
\(577\) −38.4291 −1.59983 −0.799913 0.600116i \(-0.795121\pi\)
−0.799913 + 0.600116i \(0.795121\pi\)
\(578\) −1.51947 −0.0632017
\(579\) 0 0
\(580\) −31.8668 −1.32320
\(581\) 1.84545 0.0765623
\(582\) 0 0
\(583\) 1.10161 0.0456240
\(584\) 10.1300 0.419182
\(585\) 0 0
\(586\) −3.06625 −0.126666
\(587\) −45.0593 −1.85980 −0.929898 0.367816i \(-0.880105\pi\)
−0.929898 + 0.367816i \(0.880105\pi\)
\(588\) 0 0
\(589\) −7.77318 −0.320288
\(590\) 47.1199 1.93990
\(591\) 0 0
\(592\) 3.67086 0.150872
\(593\) 6.82079 0.280096 0.140048 0.990145i \(-0.455274\pi\)
0.140048 + 0.990145i \(0.455274\pi\)
\(594\) 0 0
\(595\) −7.72571 −0.316723
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) −3.94946 −0.161505
\(599\) −34.9813 −1.42930 −0.714648 0.699485i \(-0.753413\pi\)
−0.714648 + 0.699485i \(0.753413\pi\)
\(600\) 0 0
\(601\) −7.13369 −0.290989 −0.145495 0.989359i \(-0.546477\pi\)
−0.145495 + 0.989359i \(0.546477\pi\)
\(602\) −4.64297 −0.189234
\(603\) 0 0
\(604\) −13.2487 −0.539081
\(605\) 38.5142 1.56582
\(606\) 0 0
\(607\) −15.1999 −0.616946 −0.308473 0.951233i \(-0.599818\pi\)
−0.308473 + 0.951233i \(0.599818\pi\)
\(608\) −3.57365 −0.144931
\(609\) 0 0
\(610\) −8.09911 −0.327924
\(611\) 8.21726 0.332435
\(612\) 0 0
\(613\) −2.50818 −0.101304 −0.0506521 0.998716i \(-0.516130\pi\)
−0.0506521 + 0.998716i \(0.516130\pi\)
\(614\) 6.82680 0.275507
\(615\) 0 0
\(616\) −0.485218 −0.0195500
\(617\) −21.9733 −0.884612 −0.442306 0.896864i \(-0.645839\pi\)
−0.442306 + 0.896864i \(0.645839\pi\)
\(618\) 0 0
\(619\) −19.0935 −0.767432 −0.383716 0.923451i \(-0.625356\pi\)
−0.383716 + 0.923451i \(0.625356\pi\)
\(620\) −8.28241 −0.332629
\(621\) 0 0
\(622\) 11.5998 0.465110
\(623\) 0.00115061 4.60983e−5 0
\(624\) 0 0
\(625\) 17.7374 0.709494
\(626\) 16.4325 0.656773
\(627\) 0 0
\(628\) 10.5613 0.421442
\(629\) 14.4431 0.575885
\(630\) 0 0
\(631\) −42.9622 −1.71030 −0.855149 0.518382i \(-0.826534\pi\)
−0.855149 + 0.518382i \(0.826534\pi\)
\(632\) −5.14150 −0.204518
\(633\) 0 0
\(634\) −12.2930 −0.488218
\(635\) 75.0996 2.98023
\(636\) 0 0
\(637\) 19.1010 0.756808
\(638\) −7.87463 −0.311760
\(639\) 0 0
\(640\) −3.80777 −0.150515
\(641\) −2.70665 −0.106906 −0.0534532 0.998570i \(-0.517023\pi\)
−0.0534532 + 0.998570i \(0.517023\pi\)
\(642\) 0 0
\(643\) 14.2882 0.563472 0.281736 0.959492i \(-0.409090\pi\)
0.281736 + 0.959492i \(0.409090\pi\)
\(644\) 0.718018 0.0282939
\(645\) 0 0
\(646\) −14.0606 −0.553209
\(647\) −17.7134 −0.696387 −0.348194 0.937423i \(-0.613205\pi\)
−0.348194 + 0.937423i \(0.613205\pi\)
\(648\) 0 0
\(649\) 11.6438 0.457061
\(650\) −26.9438 −1.05682
\(651\) 0 0
\(652\) −12.9514 −0.507216
\(653\) 13.0562 0.510927 0.255463 0.966819i \(-0.417772\pi\)
0.255463 + 0.966819i \(0.417772\pi\)
\(654\) 0 0
\(655\) −41.5119 −1.62200
\(656\) 9.56071 0.373283
\(657\) 0 0
\(658\) −1.49391 −0.0582387
\(659\) 5.96324 0.232295 0.116147 0.993232i \(-0.462945\pi\)
0.116147 + 0.993232i \(0.462945\pi\)
\(660\) 0 0
\(661\) −15.6385 −0.608267 −0.304133 0.952629i \(-0.598367\pi\)
−0.304133 + 0.952629i \(0.598367\pi\)
\(662\) −18.3673 −0.713866
\(663\) 0 0
\(664\) 3.57873 0.138881
\(665\) 7.01710 0.272112
\(666\) 0 0
\(667\) 11.6528 0.451197
\(668\) −11.4775 −0.444079
\(669\) 0 0
\(670\) 39.1288 1.51168
\(671\) −2.00138 −0.0772624
\(672\) 0 0
\(673\) 13.3684 0.515315 0.257657 0.966236i \(-0.417049\pi\)
0.257657 + 0.966236i \(0.417049\pi\)
\(674\) 26.3649 1.01554
\(675\) 0 0
\(676\) −4.95449 −0.190557
\(677\) −0.501351 −0.0192685 −0.00963424 0.999954i \(-0.503067\pi\)
−0.00963424 + 0.999954i \(0.503067\pi\)
\(678\) 0 0
\(679\) 1.97438 0.0757696
\(680\) −14.9818 −0.574525
\(681\) 0 0
\(682\) −2.04667 −0.0783711
\(683\) −38.7401 −1.48235 −0.741174 0.671313i \(-0.765731\pi\)
−0.741174 + 0.671313i \(0.765731\pi\)
\(684\) 0 0
\(685\) −24.4009 −0.932311
\(686\) −7.08230 −0.270404
\(687\) 0 0
\(688\) −9.00371 −0.343263
\(689\) 3.32079 0.126512
\(690\) 0 0
\(691\) 17.5941 0.669310 0.334655 0.942341i \(-0.391380\pi\)
0.334655 + 0.942341i \(0.391380\pi\)
\(692\) 24.8186 0.943461
\(693\) 0 0
\(694\) −31.6944 −1.20310
\(695\) 65.0735 2.46838
\(696\) 0 0
\(697\) 37.6169 1.42484
\(698\) −13.0175 −0.492718
\(699\) 0 0
\(700\) 4.89843 0.185143
\(701\) 47.1097 1.77931 0.889655 0.456633i \(-0.150945\pi\)
0.889655 + 0.456633i \(0.150945\pi\)
\(702\) 0 0
\(703\) −13.1184 −0.494769
\(704\) −0.940941 −0.0354630
\(705\) 0 0
\(706\) 24.8615 0.935675
\(707\) 1.14788 0.0431705
\(708\) 0 0
\(709\) −32.4176 −1.21747 −0.608734 0.793374i \(-0.708322\pi\)
−0.608734 + 0.793374i \(0.708322\pi\)
\(710\) 8.95673 0.336140
\(711\) 0 0
\(712\) 0.00223128 8.36209e−5 0
\(713\) 3.02863 0.113423
\(714\) 0 0
\(715\) −10.1627 −0.380064
\(716\) −9.86161 −0.368546
\(717\) 0 0
\(718\) 8.53896 0.318671
\(719\) 8.71247 0.324920 0.162460 0.986715i \(-0.448057\pi\)
0.162460 + 0.986715i \(0.448057\pi\)
\(720\) 0 0
\(721\) −6.89741 −0.256873
\(722\) −6.22900 −0.231819
\(723\) 0 0
\(724\) −15.6306 −0.580908
\(725\) 79.4969 2.95244
\(726\) 0 0
\(727\) −26.3912 −0.978795 −0.489398 0.872061i \(-0.662783\pi\)
−0.489398 + 0.872061i \(0.662783\pi\)
\(728\) −1.46269 −0.0542108
\(729\) 0 0
\(730\) −38.5726 −1.42764
\(731\) −35.4254 −1.31025
\(732\) 0 0
\(733\) 9.01175 0.332856 0.166428 0.986054i \(-0.446777\pi\)
0.166428 + 0.986054i \(0.446777\pi\)
\(734\) 22.8141 0.842084
\(735\) 0 0
\(736\) 1.39239 0.0513242
\(737\) 9.66915 0.356168
\(738\) 0 0
\(739\) 22.9160 0.842980 0.421490 0.906833i \(-0.361507\pi\)
0.421490 + 0.906833i \(0.361507\pi\)
\(740\) −13.9778 −0.513834
\(741\) 0 0
\(742\) −0.603726 −0.0221635
\(743\) 7.25666 0.266221 0.133111 0.991101i \(-0.457503\pi\)
0.133111 + 0.991101i \(0.457503\pi\)
\(744\) 0 0
\(745\) 3.80777 0.139506
\(746\) −34.0227 −1.24566
\(747\) 0 0
\(748\) −3.70216 −0.135364
\(749\) −2.55884 −0.0934978
\(750\) 0 0
\(751\) −26.0409 −0.950244 −0.475122 0.879920i \(-0.657596\pi\)
−0.475122 + 0.879920i \(0.657596\pi\)
\(752\) −2.89701 −0.105643
\(753\) 0 0
\(754\) −23.7380 −0.864488
\(755\) 50.4479 1.83599
\(756\) 0 0
\(757\) −23.4919 −0.853829 −0.426915 0.904292i \(-0.640400\pi\)
−0.426915 + 0.904292i \(0.640400\pi\)
\(758\) 3.03351 0.110182
\(759\) 0 0
\(760\) 13.6076 0.493601
\(761\) 42.5099 1.54098 0.770491 0.637451i \(-0.220011\pi\)
0.770491 + 0.637451i \(0.220011\pi\)
\(762\) 0 0
\(763\) −1.03936 −0.0376272
\(764\) −8.22930 −0.297726
\(765\) 0 0
\(766\) 22.2167 0.802720
\(767\) 35.1003 1.26740
\(768\) 0 0
\(769\) −0.651559 −0.0234958 −0.0117479 0.999931i \(-0.503740\pi\)
−0.0117479 + 0.999931i \(0.503740\pi\)
\(770\) 1.84760 0.0665828
\(771\) 0 0
\(772\) −3.29466 −0.118577
\(773\) −2.37546 −0.0854393 −0.0427196 0.999087i \(-0.513602\pi\)
−0.0427196 + 0.999087i \(0.513602\pi\)
\(774\) 0 0
\(775\) 20.6618 0.742194
\(776\) 3.82873 0.137444
\(777\) 0 0
\(778\) −34.5062 −1.23711
\(779\) −34.1667 −1.22415
\(780\) 0 0
\(781\) 2.21331 0.0791983
\(782\) 5.47840 0.195907
\(783\) 0 0
\(784\) −6.73408 −0.240503
\(785\) −40.2150 −1.43533
\(786\) 0 0
\(787\) 5.98295 0.213269 0.106635 0.994298i \(-0.465993\pi\)
0.106635 + 0.994298i \(0.465993\pi\)
\(788\) −13.7739 −0.490674
\(789\) 0 0
\(790\) 19.5776 0.696541
\(791\) −4.06240 −0.144442
\(792\) 0 0
\(793\) −6.03315 −0.214243
\(794\) −29.6718 −1.05301
\(795\) 0 0
\(796\) 2.93461 0.104014
\(797\) 28.4827 1.00891 0.504455 0.863438i \(-0.331694\pi\)
0.504455 + 0.863438i \(0.331694\pi\)
\(798\) 0 0
\(799\) −11.3984 −0.403246
\(800\) 9.49910 0.335844
\(801\) 0 0
\(802\) 18.1554 0.641089
\(803\) −9.53171 −0.336367
\(804\) 0 0
\(805\) −2.73405 −0.0963625
\(806\) −6.16968 −0.217318
\(807\) 0 0
\(808\) 2.22598 0.0783098
\(809\) −20.2110 −0.710582 −0.355291 0.934756i \(-0.615618\pi\)
−0.355291 + 0.934756i \(0.615618\pi\)
\(810\) 0 0
\(811\) −9.44577 −0.331686 −0.165843 0.986152i \(-0.553034\pi\)
−0.165843 + 0.986152i \(0.553034\pi\)
\(812\) 4.31562 0.151448
\(813\) 0 0
\(814\) −3.45407 −0.121065
\(815\) 49.3159 1.72746
\(816\) 0 0
\(817\) 32.1761 1.12570
\(818\) −25.9816 −0.908426
\(819\) 0 0
\(820\) −36.4050 −1.27132
\(821\) 3.74294 0.130629 0.0653147 0.997865i \(-0.479195\pi\)
0.0653147 + 0.997865i \(0.479195\pi\)
\(822\) 0 0
\(823\) 35.8071 1.24816 0.624078 0.781362i \(-0.285475\pi\)
0.624078 + 0.781362i \(0.285475\pi\)
\(824\) −13.3755 −0.465959
\(825\) 0 0
\(826\) −6.38130 −0.222034
\(827\) 18.6515 0.648577 0.324289 0.945958i \(-0.394875\pi\)
0.324289 + 0.945958i \(0.394875\pi\)
\(828\) 0 0
\(829\) −46.9704 −1.63135 −0.815674 0.578512i \(-0.803634\pi\)
−0.815674 + 0.578512i \(0.803634\pi\)
\(830\) −13.6270 −0.472999
\(831\) 0 0
\(832\) −2.83646 −0.0983366
\(833\) −26.4954 −0.918013
\(834\) 0 0
\(835\) 43.7038 1.51243
\(836\) 3.36260 0.116298
\(837\) 0 0
\(838\) −30.8938 −1.06721
\(839\) −35.3679 −1.22104 −0.610518 0.792002i \(-0.709039\pi\)
−0.610518 + 0.792002i \(0.709039\pi\)
\(840\) 0 0
\(841\) 41.0384 1.41512
\(842\) 17.9253 0.617746
\(843\) 0 0
\(844\) 13.5697 0.467088
\(845\) 18.8655 0.648994
\(846\) 0 0
\(847\) −5.21585 −0.179219
\(848\) −1.17075 −0.0402038
\(849\) 0 0
\(850\) 37.3745 1.28193
\(851\) 5.11127 0.175212
\(852\) 0 0
\(853\) −36.2844 −1.24236 −0.621178 0.783670i \(-0.713345\pi\)
−0.621178 + 0.783670i \(0.713345\pi\)
\(854\) 1.09684 0.0375330
\(855\) 0 0
\(856\) −4.96212 −0.169602
\(857\) −41.3401 −1.41215 −0.706076 0.708136i \(-0.749536\pi\)
−0.706076 + 0.708136i \(0.749536\pi\)
\(858\) 0 0
\(859\) 12.1747 0.415395 0.207697 0.978193i \(-0.433403\pi\)
0.207697 + 0.978193i \(0.433403\pi\)
\(860\) 34.2840 1.16908
\(861\) 0 0
\(862\) −9.24825 −0.314996
\(863\) 26.6836 0.908319 0.454160 0.890920i \(-0.349940\pi\)
0.454160 + 0.890920i \(0.349940\pi\)
\(864\) 0 0
\(865\) −94.5034 −3.21321
\(866\) −9.35001 −0.317726
\(867\) 0 0
\(868\) 1.12166 0.0380716
\(869\) 4.83785 0.164113
\(870\) 0 0
\(871\) 29.1476 0.987628
\(872\) −2.01553 −0.0682545
\(873\) 0 0
\(874\) −4.97592 −0.168313
\(875\) −8.83427 −0.298653
\(876\) 0 0
\(877\) −23.8159 −0.804205 −0.402103 0.915595i \(-0.631720\pi\)
−0.402103 + 0.915595i \(0.631720\pi\)
\(878\) 0.0383341 0.00129371
\(879\) 0 0
\(880\) 3.58289 0.120779
\(881\) 27.5213 0.927216 0.463608 0.886040i \(-0.346555\pi\)
0.463608 + 0.886040i \(0.346555\pi\)
\(882\) 0 0
\(883\) 33.0700 1.11289 0.556447 0.830883i \(-0.312164\pi\)
0.556447 + 0.830883i \(0.312164\pi\)
\(884\) −11.1601 −0.375356
\(885\) 0 0
\(886\) 7.37697 0.247834
\(887\) −23.4709 −0.788074 −0.394037 0.919095i \(-0.628922\pi\)
−0.394037 + 0.919095i \(0.628922\pi\)
\(888\) 0 0
\(889\) −10.1705 −0.341107
\(890\) −0.00849621 −0.000284793 0
\(891\) 0 0
\(892\) 0.372556 0.0124741
\(893\) 10.3529 0.346447
\(894\) 0 0
\(895\) 37.5507 1.25518
\(896\) 0.515673 0.0172274
\(897\) 0 0
\(898\) 14.1872 0.473432
\(899\) 18.2035 0.607119
\(900\) 0 0
\(901\) −4.60636 −0.153460
\(902\) −8.99606 −0.299536
\(903\) 0 0
\(904\) −7.87785 −0.262014
\(905\) 59.5178 1.97844
\(906\) 0 0
\(907\) −51.5516 −1.71174 −0.855871 0.517189i \(-0.826978\pi\)
−0.855871 + 0.517189i \(0.826978\pi\)
\(908\) 12.9343 0.429239
\(909\) 0 0
\(910\) 5.56958 0.184630
\(911\) −44.9739 −1.49005 −0.745027 0.667035i \(-0.767563\pi\)
−0.745027 + 0.667035i \(0.767563\pi\)
\(912\) 0 0
\(913\) −3.36737 −0.111444
\(914\) 9.03586 0.298880
\(915\) 0 0
\(916\) −6.44573 −0.212973
\(917\) 5.62182 0.185649
\(918\) 0 0
\(919\) 31.1582 1.02781 0.513907 0.857846i \(-0.328198\pi\)
0.513907 + 0.857846i \(0.328198\pi\)
\(920\) −5.30190 −0.174798
\(921\) 0 0
\(922\) 9.78904 0.322385
\(923\) 6.67200 0.219611
\(924\) 0 0
\(925\) 34.8699 1.14651
\(926\) 11.6439 0.382641
\(927\) 0 0
\(928\) 8.36889 0.274722
\(929\) 28.6933 0.941397 0.470699 0.882294i \(-0.344002\pi\)
0.470699 + 0.882294i \(0.344002\pi\)
\(930\) 0 0
\(931\) 24.0653 0.788707
\(932\) −7.75366 −0.253980
\(933\) 0 0
\(934\) −9.99358 −0.327000
\(935\) 14.0970 0.461020
\(936\) 0 0
\(937\) −47.8718 −1.56390 −0.781951 0.623339i \(-0.785776\pi\)
−0.781951 + 0.623339i \(0.785776\pi\)
\(938\) −5.29908 −0.173021
\(939\) 0 0
\(940\) 11.0311 0.359796
\(941\) −4.61707 −0.150512 −0.0752561 0.997164i \(-0.523977\pi\)
−0.0752561 + 0.997164i \(0.523977\pi\)
\(942\) 0 0
\(943\) 13.3122 0.433506
\(944\) −12.3747 −0.402762
\(945\) 0 0
\(946\) 8.47196 0.275447
\(947\) 37.4692 1.21759 0.608793 0.793329i \(-0.291654\pi\)
0.608793 + 0.793329i \(0.291654\pi\)
\(948\) 0 0
\(949\) −28.7333 −0.932722
\(950\) −33.9465 −1.10137
\(951\) 0 0
\(952\) 2.02893 0.0657581
\(953\) 38.7731 1.25598 0.627992 0.778219i \(-0.283877\pi\)
0.627992 + 0.778219i \(0.283877\pi\)
\(954\) 0 0
\(955\) 31.3353 1.01399
\(956\) −14.3567 −0.464330
\(957\) 0 0
\(958\) 22.4494 0.725308
\(959\) 3.30454 0.106709
\(960\) 0 0
\(961\) −26.2688 −0.847380
\(962\) −10.4123 −0.335705
\(963\) 0 0
\(964\) 12.1139 0.390162
\(965\) 12.5453 0.403848
\(966\) 0 0
\(967\) 23.4848 0.755221 0.377610 0.925965i \(-0.376746\pi\)
0.377610 + 0.925965i \(0.376746\pi\)
\(968\) −10.1146 −0.325097
\(969\) 0 0
\(970\) −14.5789 −0.468101
\(971\) 33.1490 1.06380 0.531901 0.846806i \(-0.321478\pi\)
0.531901 + 0.846806i \(0.321478\pi\)
\(972\) 0 0
\(973\) −8.81269 −0.282522
\(974\) 9.74065 0.312111
\(975\) 0 0
\(976\) 2.12700 0.0680835
\(977\) 5.41485 0.173236 0.0866182 0.996242i \(-0.472394\pi\)
0.0866182 + 0.996242i \(0.472394\pi\)
\(978\) 0 0
\(979\) −0.00209951 −6.71005e−5 0
\(980\) 25.6418 0.819098
\(981\) 0 0
\(982\) −31.6763 −1.01083
\(983\) 43.8075 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(984\) 0 0
\(985\) 52.4477 1.67112
\(986\) 32.9277 1.04863
\(987\) 0 0
\(988\) 10.1365 0.322486
\(989\) −12.5367 −0.398643
\(990\) 0 0
\(991\) 7.59749 0.241342 0.120671 0.992693i \(-0.461495\pi\)
0.120671 + 0.992693i \(0.461495\pi\)
\(992\) 2.17513 0.0690606
\(993\) 0 0
\(994\) −1.21298 −0.0384734
\(995\) −11.1743 −0.354249
\(996\) 0 0
\(997\) 47.1875 1.49444 0.747221 0.664575i \(-0.231387\pi\)
0.747221 + 0.664575i \(0.231387\pi\)
\(998\) 6.13481 0.194194
\(999\) 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 \(a_p\))