Properties

Label 8024.2.a.y.1.17
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.25653 q^{3} +3.93457 q^{5} -3.56420 q^{7} -1.42113 q^{9} +O(q^{10})\) \(q+1.25653 q^{3} +3.93457 q^{5} -3.56420 q^{7} -1.42113 q^{9} -3.07833 q^{11} +2.74994 q^{13} +4.94392 q^{15} -1.00000 q^{17} +2.16402 q^{19} -4.47854 q^{21} -5.55312 q^{23} +10.4809 q^{25} -5.55529 q^{27} -2.25685 q^{29} -0.00422060 q^{31} -3.86802 q^{33} -14.0236 q^{35} +5.75808 q^{37} +3.45539 q^{39} -2.70729 q^{41} -11.1211 q^{43} -5.59152 q^{45} +3.90158 q^{47} +5.70355 q^{49} -1.25653 q^{51} -6.71321 q^{53} -12.1119 q^{55} +2.71917 q^{57} -1.00000 q^{59} -11.2654 q^{61} +5.06518 q^{63} +10.8198 q^{65} -5.44196 q^{67} -6.97767 q^{69} -3.00896 q^{71} -0.207216 q^{73} +13.1695 q^{75} +10.9718 q^{77} -3.57390 q^{79} -2.71703 q^{81} -4.16115 q^{83} -3.93457 q^{85} -2.83581 q^{87} +5.88005 q^{89} -9.80134 q^{91} -0.00530333 q^{93} +8.51450 q^{95} -9.10944 q^{97} +4.37469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.25653 0.725460 0.362730 0.931894i \(-0.381845\pi\)
0.362730 + 0.931894i \(0.381845\pi\)
\(4\) 0 0
\(5\) 3.93457 1.75959 0.879797 0.475350i \(-0.157678\pi\)
0.879797 + 0.475350i \(0.157678\pi\)
\(6\) 0 0
\(7\) −3.56420 −1.34714 −0.673571 0.739122i \(-0.735241\pi\)
−0.673571 + 0.739122i \(0.735241\pi\)
\(8\) 0 0
\(9\) −1.42113 −0.473708
\(10\) 0 0
\(11\) −3.07833 −0.928151 −0.464075 0.885796i \(-0.653613\pi\)
−0.464075 + 0.885796i \(0.653613\pi\)
\(12\) 0 0
\(13\) 2.74994 0.762695 0.381348 0.924432i \(-0.375460\pi\)
0.381348 + 0.924432i \(0.375460\pi\)
\(14\) 0 0
\(15\) 4.94392 1.27651
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 2.16402 0.496461 0.248230 0.968701i \(-0.420151\pi\)
0.248230 + 0.968701i \(0.420151\pi\)
\(20\) 0 0
\(21\) −4.47854 −0.977297
\(22\) 0 0
\(23\) −5.55312 −1.15790 −0.578952 0.815361i \(-0.696538\pi\)
−0.578952 + 0.815361i \(0.696538\pi\)
\(24\) 0 0
\(25\) 10.4809 2.09617
\(26\) 0 0
\(27\) −5.55529 −1.06912
\(28\) 0 0
\(29\) −2.25685 −0.419086 −0.209543 0.977799i \(-0.567198\pi\)
−0.209543 + 0.977799i \(0.567198\pi\)
\(30\) 0 0
\(31\) −0.00422060 −0.000758043 0 −0.000379021 1.00000i \(-0.500121\pi\)
−0.000379021 1.00000i \(0.500121\pi\)
\(32\) 0 0
\(33\) −3.86802 −0.673336
\(34\) 0 0
\(35\) −14.0236 −2.37042
\(36\) 0 0
\(37\) 5.75808 0.946622 0.473311 0.880895i \(-0.343059\pi\)
0.473311 + 0.880895i \(0.343059\pi\)
\(38\) 0 0
\(39\) 3.45539 0.553305
\(40\) 0 0
\(41\) −2.70729 −0.422807 −0.211404 0.977399i \(-0.567803\pi\)
−0.211404 + 0.977399i \(0.567803\pi\)
\(42\) 0 0
\(43\) −11.1211 −1.69595 −0.847976 0.530034i \(-0.822179\pi\)
−0.847976 + 0.530034i \(0.822179\pi\)
\(44\) 0 0
\(45\) −5.59152 −0.833534
\(46\) 0 0
\(47\) 3.90158 0.569104 0.284552 0.958661i \(-0.408155\pi\)
0.284552 + 0.958661i \(0.408155\pi\)
\(48\) 0 0
\(49\) 5.70355 0.814792
\(50\) 0 0
\(51\) −1.25653 −0.175950
\(52\) 0 0
\(53\) −6.71321 −0.922130 −0.461065 0.887366i \(-0.652533\pi\)
−0.461065 + 0.887366i \(0.652533\pi\)
\(54\) 0 0
\(55\) −12.1119 −1.63317
\(56\) 0 0
\(57\) 2.71917 0.360162
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −11.2654 −1.44239 −0.721193 0.692734i \(-0.756406\pi\)
−0.721193 + 0.692734i \(0.756406\pi\)
\(62\) 0 0
\(63\) 5.06518 0.638153
\(64\) 0 0
\(65\) 10.8198 1.34203
\(66\) 0 0
\(67\) −5.44196 −0.664841 −0.332421 0.943131i \(-0.607865\pi\)
−0.332421 + 0.943131i \(0.607865\pi\)
\(68\) 0 0
\(69\) −6.97767 −0.840013
\(70\) 0 0
\(71\) −3.00896 −0.357098 −0.178549 0.983931i \(-0.557140\pi\)
−0.178549 + 0.983931i \(0.557140\pi\)
\(72\) 0 0
\(73\) −0.207216 −0.0242527 −0.0121264 0.999926i \(-0.503860\pi\)
−0.0121264 + 0.999926i \(0.503860\pi\)
\(74\) 0 0
\(75\) 13.1695 1.52069
\(76\) 0 0
\(77\) 10.9718 1.25035
\(78\) 0 0
\(79\) −3.57390 −0.402096 −0.201048 0.979581i \(-0.564435\pi\)
−0.201048 + 0.979581i \(0.564435\pi\)
\(80\) 0 0
\(81\) −2.71703 −0.301892
\(82\) 0 0
\(83\) −4.16115 −0.456746 −0.228373 0.973574i \(-0.573341\pi\)
−0.228373 + 0.973574i \(0.573341\pi\)
\(84\) 0 0
\(85\) −3.93457 −0.426764
\(86\) 0 0
\(87\) −2.83581 −0.304030
\(88\) 0 0
\(89\) 5.88005 0.623284 0.311642 0.950200i \(-0.399121\pi\)
0.311642 + 0.950200i \(0.399121\pi\)
\(90\) 0 0
\(91\) −9.80134 −1.02746
\(92\) 0 0
\(93\) −0.00530333 −0.000549929 0
\(94\) 0 0
\(95\) 8.51450 0.873569
\(96\) 0 0
\(97\) −9.10944 −0.924923 −0.462462 0.886639i \(-0.653034\pi\)
−0.462462 + 0.886639i \(0.653034\pi\)
\(98\) 0 0
\(99\) 4.37469 0.439673
\(100\) 0 0
\(101\) 3.36167 0.334499 0.167249 0.985915i \(-0.446512\pi\)
0.167249 + 0.985915i \(0.446512\pi\)
\(102\) 0 0
\(103\) 8.82433 0.869487 0.434744 0.900554i \(-0.356839\pi\)
0.434744 + 0.900554i \(0.356839\pi\)
\(104\) 0 0
\(105\) −17.6211 −1.71965
\(106\) 0 0
\(107\) −2.28460 −0.220861 −0.110430 0.993884i \(-0.535223\pi\)
−0.110430 + 0.993884i \(0.535223\pi\)
\(108\) 0 0
\(109\) 5.60607 0.536964 0.268482 0.963285i \(-0.413478\pi\)
0.268482 + 0.963285i \(0.413478\pi\)
\(110\) 0 0
\(111\) 7.23522 0.686736
\(112\) 0 0
\(113\) −4.76980 −0.448705 −0.224353 0.974508i \(-0.572027\pi\)
−0.224353 + 0.974508i \(0.572027\pi\)
\(114\) 0 0
\(115\) −21.8491 −2.03744
\(116\) 0 0
\(117\) −3.90800 −0.361295
\(118\) 0 0
\(119\) 3.56420 0.326730
\(120\) 0 0
\(121\) −1.52390 −0.138536
\(122\) 0 0
\(123\) −3.40179 −0.306730
\(124\) 0 0
\(125\) 21.5648 1.92881
\(126\) 0 0
\(127\) 7.44183 0.660355 0.330178 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(128\) 0 0
\(129\) −13.9740 −1.23035
\(130\) 0 0
\(131\) 9.99213 0.873017 0.436508 0.899700i \(-0.356215\pi\)
0.436508 + 0.899700i \(0.356215\pi\)
\(132\) 0 0
\(133\) −7.71302 −0.668803
\(134\) 0 0
\(135\) −21.8577 −1.88121
\(136\) 0 0
\(137\) 20.7866 1.77592 0.887960 0.459920i \(-0.152122\pi\)
0.887960 + 0.459920i \(0.152122\pi\)
\(138\) 0 0
\(139\) −17.9028 −1.51850 −0.759248 0.650802i \(-0.774433\pi\)
−0.759248 + 0.650802i \(0.774433\pi\)
\(140\) 0 0
\(141\) 4.90247 0.412862
\(142\) 0 0
\(143\) −8.46521 −0.707896
\(144\) 0 0
\(145\) −8.87974 −0.737422
\(146\) 0 0
\(147\) 7.16669 0.591099
\(148\) 0 0
\(149\) −5.86005 −0.480074 −0.240037 0.970764i \(-0.577160\pi\)
−0.240037 + 0.970764i \(0.577160\pi\)
\(150\) 0 0
\(151\) −5.31582 −0.432595 −0.216297 0.976328i \(-0.569398\pi\)
−0.216297 + 0.976328i \(0.569398\pi\)
\(152\) 0 0
\(153\) 1.42113 0.114891
\(154\) 0 0
\(155\) −0.0166063 −0.00133385
\(156\) 0 0
\(157\) −7.46330 −0.595636 −0.297818 0.954623i \(-0.596259\pi\)
−0.297818 + 0.954623i \(0.596259\pi\)
\(158\) 0 0
\(159\) −8.43537 −0.668968
\(160\) 0 0
\(161\) 19.7924 1.55986
\(162\) 0 0
\(163\) −3.30975 −0.259240 −0.129620 0.991564i \(-0.541376\pi\)
−0.129620 + 0.991564i \(0.541376\pi\)
\(164\) 0 0
\(165\) −15.2190 −1.18480
\(166\) 0 0
\(167\) −0.270878 −0.0209612 −0.0104806 0.999945i \(-0.503336\pi\)
−0.0104806 + 0.999945i \(0.503336\pi\)
\(168\) 0 0
\(169\) −5.43785 −0.418296
\(170\) 0 0
\(171\) −3.07535 −0.235178
\(172\) 0 0
\(173\) 4.72125 0.358950 0.179475 0.983763i \(-0.442560\pi\)
0.179475 + 0.983763i \(0.442560\pi\)
\(174\) 0 0
\(175\) −37.3559 −2.82384
\(176\) 0 0
\(177\) −1.25653 −0.0944468
\(178\) 0 0
\(179\) −13.6902 −1.02325 −0.511625 0.859209i \(-0.670956\pi\)
−0.511625 + 0.859209i \(0.670956\pi\)
\(180\) 0 0
\(181\) 0.731964 0.0544065 0.0272032 0.999630i \(-0.491340\pi\)
0.0272032 + 0.999630i \(0.491340\pi\)
\(182\) 0 0
\(183\) −14.1553 −1.04639
\(184\) 0 0
\(185\) 22.6556 1.66567
\(186\) 0 0
\(187\) 3.07833 0.225110
\(188\) 0 0
\(189\) 19.8002 1.44025
\(190\) 0 0
\(191\) −21.2217 −1.53555 −0.767775 0.640720i \(-0.778636\pi\)
−0.767775 + 0.640720i \(0.778636\pi\)
\(192\) 0 0
\(193\) −20.5205 −1.47710 −0.738550 0.674199i \(-0.764489\pi\)
−0.738550 + 0.674199i \(0.764489\pi\)
\(194\) 0 0
\(195\) 13.5955 0.973591
\(196\) 0 0
\(197\) −11.6131 −0.827398 −0.413699 0.910414i \(-0.635763\pi\)
−0.413699 + 0.910414i \(0.635763\pi\)
\(198\) 0 0
\(199\) 16.4856 1.16863 0.584315 0.811527i \(-0.301363\pi\)
0.584315 + 0.811527i \(0.301363\pi\)
\(200\) 0 0
\(201\) −6.83800 −0.482316
\(202\) 0 0
\(203\) 8.04387 0.564569
\(204\) 0 0
\(205\) −10.6520 −0.743969
\(206\) 0 0
\(207\) 7.89167 0.548509
\(208\) 0 0
\(209\) −6.66157 −0.460790
\(210\) 0 0
\(211\) 14.3344 0.986818 0.493409 0.869797i \(-0.335751\pi\)
0.493409 + 0.869797i \(0.335751\pi\)
\(212\) 0 0
\(213\) −3.78086 −0.259060
\(214\) 0 0
\(215\) −43.7568 −2.98419
\(216\) 0 0
\(217\) 0.0150431 0.00102119
\(218\) 0 0
\(219\) −0.260373 −0.0175944
\(220\) 0 0
\(221\) −2.74994 −0.184981
\(222\) 0 0
\(223\) −6.09525 −0.408168 −0.204084 0.978953i \(-0.565422\pi\)
−0.204084 + 0.978953i \(0.565422\pi\)
\(224\) 0 0
\(225\) −14.8946 −0.992973
\(226\) 0 0
\(227\) −9.70183 −0.643933 −0.321967 0.946751i \(-0.604344\pi\)
−0.321967 + 0.946751i \(0.604344\pi\)
\(228\) 0 0
\(229\) −3.16516 −0.209159 −0.104580 0.994517i \(-0.533350\pi\)
−0.104580 + 0.994517i \(0.533350\pi\)
\(230\) 0 0
\(231\) 13.7864 0.907079
\(232\) 0 0
\(233\) −0.535750 −0.0350982 −0.0175491 0.999846i \(-0.505586\pi\)
−0.0175491 + 0.999846i \(0.505586\pi\)
\(234\) 0 0
\(235\) 15.3511 1.00139
\(236\) 0 0
\(237\) −4.49073 −0.291704
\(238\) 0 0
\(239\) −3.70234 −0.239485 −0.119742 0.992805i \(-0.538207\pi\)
−0.119742 + 0.992805i \(0.538207\pi\)
\(240\) 0 0
\(241\) 8.15946 0.525597 0.262798 0.964851i \(-0.415355\pi\)
0.262798 + 0.964851i \(0.415355\pi\)
\(242\) 0 0
\(243\) 13.2518 0.850105
\(244\) 0 0
\(245\) 22.4410 1.43370
\(246\) 0 0
\(247\) 5.95093 0.378648
\(248\) 0 0
\(249\) −5.22862 −0.331351
\(250\) 0 0
\(251\) −25.5064 −1.60995 −0.804974 0.593310i \(-0.797821\pi\)
−0.804974 + 0.593310i \(0.797821\pi\)
\(252\) 0 0
\(253\) 17.0943 1.07471
\(254\) 0 0
\(255\) −4.94392 −0.309600
\(256\) 0 0
\(257\) −10.2586 −0.639914 −0.319957 0.947432i \(-0.603669\pi\)
−0.319957 + 0.947432i \(0.603669\pi\)
\(258\) 0 0
\(259\) −20.5230 −1.27523
\(260\) 0 0
\(261\) 3.20727 0.198525
\(262\) 0 0
\(263\) 13.6021 0.838742 0.419371 0.907815i \(-0.362251\pi\)
0.419371 + 0.907815i \(0.362251\pi\)
\(264\) 0 0
\(265\) −26.4136 −1.62257
\(266\) 0 0
\(267\) 7.38848 0.452168
\(268\) 0 0
\(269\) 29.5611 1.80237 0.901187 0.433431i \(-0.142697\pi\)
0.901187 + 0.433431i \(0.142697\pi\)
\(270\) 0 0
\(271\) −30.3524 −1.84378 −0.921890 0.387452i \(-0.873355\pi\)
−0.921890 + 0.387452i \(0.873355\pi\)
\(272\) 0 0
\(273\) −12.3157 −0.745380
\(274\) 0 0
\(275\) −32.2635 −1.94556
\(276\) 0 0
\(277\) −3.89540 −0.234052 −0.117026 0.993129i \(-0.537336\pi\)
−0.117026 + 0.993129i \(0.537336\pi\)
\(278\) 0 0
\(279\) 0.00599801 0.000359091 0
\(280\) 0 0
\(281\) 6.74069 0.402116 0.201058 0.979579i \(-0.435562\pi\)
0.201058 + 0.979579i \(0.435562\pi\)
\(282\) 0 0
\(283\) −10.1403 −0.602778 −0.301389 0.953501i \(-0.597450\pi\)
−0.301389 + 0.953501i \(0.597450\pi\)
\(284\) 0 0
\(285\) 10.6987 0.633739
\(286\) 0 0
\(287\) 9.64932 0.569581
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −11.4463 −0.670995
\(292\) 0 0
\(293\) −26.3820 −1.54125 −0.770627 0.637287i \(-0.780057\pi\)
−0.770627 + 0.637287i \(0.780057\pi\)
\(294\) 0 0
\(295\) −3.93457 −0.229080
\(296\) 0 0
\(297\) 17.1010 0.992301
\(298\) 0 0
\(299\) −15.2707 −0.883129
\(300\) 0 0
\(301\) 39.6379 2.28469
\(302\) 0 0
\(303\) 4.22405 0.242665
\(304\) 0 0
\(305\) −44.3245 −2.53802
\(306\) 0 0
\(307\) −11.4704 −0.654652 −0.327326 0.944911i \(-0.606148\pi\)
−0.327326 + 0.944911i \(0.606148\pi\)
\(308\) 0 0
\(309\) 11.0881 0.630778
\(310\) 0 0
\(311\) 0.376698 0.0213606 0.0106803 0.999943i \(-0.496600\pi\)
0.0106803 + 0.999943i \(0.496600\pi\)
\(312\) 0 0
\(313\) 13.2217 0.747337 0.373669 0.927562i \(-0.378100\pi\)
0.373669 + 0.927562i \(0.378100\pi\)
\(314\) 0 0
\(315\) 19.9293 1.12289
\(316\) 0 0
\(317\) 19.2248 1.07977 0.539887 0.841737i \(-0.318467\pi\)
0.539887 + 0.841737i \(0.318467\pi\)
\(318\) 0 0
\(319\) 6.94732 0.388975
\(320\) 0 0
\(321\) −2.87068 −0.160226
\(322\) 0 0
\(323\) −2.16402 −0.120409
\(324\) 0 0
\(325\) 28.8217 1.59874
\(326\) 0 0
\(327\) 7.04422 0.389546
\(328\) 0 0
\(329\) −13.9060 −0.766665
\(330\) 0 0
\(331\) 17.4854 0.961083 0.480541 0.876972i \(-0.340440\pi\)
0.480541 + 0.876972i \(0.340440\pi\)
\(332\) 0 0
\(333\) −8.18295 −0.448423
\(334\) 0 0
\(335\) −21.4118 −1.16985
\(336\) 0 0
\(337\) 12.9599 0.705969 0.352984 0.935629i \(-0.385167\pi\)
0.352984 + 0.935629i \(0.385167\pi\)
\(338\) 0 0
\(339\) −5.99341 −0.325517
\(340\) 0 0
\(341\) 0.0129924 0.000703578 0
\(342\) 0 0
\(343\) 4.62082 0.249501
\(344\) 0 0
\(345\) −27.4542 −1.47808
\(346\) 0 0
\(347\) 20.0786 1.07788 0.538938 0.842345i \(-0.318826\pi\)
0.538938 + 0.842345i \(0.318826\pi\)
\(348\) 0 0
\(349\) −29.7123 −1.59046 −0.795230 0.606308i \(-0.792650\pi\)
−0.795230 + 0.606308i \(0.792650\pi\)
\(350\) 0 0
\(351\) −15.2767 −0.815410
\(352\) 0 0
\(353\) −31.3807 −1.67023 −0.835114 0.550076i \(-0.814599\pi\)
−0.835114 + 0.550076i \(0.814599\pi\)
\(354\) 0 0
\(355\) −11.8390 −0.628348
\(356\) 0 0
\(357\) 4.47854 0.237029
\(358\) 0 0
\(359\) 7.60943 0.401610 0.200805 0.979631i \(-0.435644\pi\)
0.200805 + 0.979631i \(0.435644\pi\)
\(360\) 0 0
\(361\) −14.3170 −0.753527
\(362\) 0 0
\(363\) −1.91483 −0.100503
\(364\) 0 0
\(365\) −0.815305 −0.0426750
\(366\) 0 0
\(367\) 4.28204 0.223521 0.111760 0.993735i \(-0.464351\pi\)
0.111760 + 0.993735i \(0.464351\pi\)
\(368\) 0 0
\(369\) 3.84739 0.200287
\(370\) 0 0
\(371\) 23.9272 1.24224
\(372\) 0 0
\(373\) −5.76119 −0.298303 −0.149152 0.988814i \(-0.547654\pi\)
−0.149152 + 0.988814i \(0.547654\pi\)
\(374\) 0 0
\(375\) 27.0969 1.39928
\(376\) 0 0
\(377\) −6.20619 −0.319635
\(378\) 0 0
\(379\) −4.74598 −0.243785 −0.121892 0.992543i \(-0.538896\pi\)
−0.121892 + 0.992543i \(0.538896\pi\)
\(380\) 0 0
\(381\) 9.35090 0.479061
\(382\) 0 0
\(383\) 22.8239 1.16625 0.583125 0.812383i \(-0.301830\pi\)
0.583125 + 0.812383i \(0.301830\pi\)
\(384\) 0 0
\(385\) 43.1693 2.20011
\(386\) 0 0
\(387\) 15.8045 0.803387
\(388\) 0 0
\(389\) 7.05806 0.357858 0.178929 0.983862i \(-0.442737\pi\)
0.178929 + 0.983862i \(0.442737\pi\)
\(390\) 0 0
\(391\) 5.55312 0.280833
\(392\) 0 0
\(393\) 12.5554 0.633338
\(394\) 0 0
\(395\) −14.0618 −0.707525
\(396\) 0 0
\(397\) 35.6750 1.79048 0.895239 0.445587i \(-0.147005\pi\)
0.895239 + 0.445587i \(0.147005\pi\)
\(398\) 0 0
\(399\) −9.69166 −0.485190
\(400\) 0 0
\(401\) −0.811108 −0.0405048 −0.0202524 0.999795i \(-0.506447\pi\)
−0.0202524 + 0.999795i \(0.506447\pi\)
\(402\) 0 0
\(403\) −0.0116064 −0.000578156 0
\(404\) 0 0
\(405\) −10.6903 −0.531207
\(406\) 0 0
\(407\) −17.7253 −0.878608
\(408\) 0 0
\(409\) 25.8513 1.27826 0.639131 0.769098i \(-0.279294\pi\)
0.639131 + 0.769098i \(0.279294\pi\)
\(410\) 0 0
\(411\) 26.1191 1.28836
\(412\) 0 0
\(413\) 3.56420 0.175383
\(414\) 0 0
\(415\) −16.3723 −0.803687
\(416\) 0 0
\(417\) −22.4955 −1.10161
\(418\) 0 0
\(419\) 36.4443 1.78042 0.890210 0.455550i \(-0.150557\pi\)
0.890210 + 0.455550i \(0.150557\pi\)
\(420\) 0 0
\(421\) 12.2534 0.597196 0.298598 0.954379i \(-0.403481\pi\)
0.298598 + 0.954379i \(0.403481\pi\)
\(422\) 0 0
\(423\) −5.54464 −0.269590
\(424\) 0 0
\(425\) −10.4809 −0.508396
\(426\) 0 0
\(427\) 40.1522 1.94310
\(428\) 0 0
\(429\) −10.6368 −0.513550
\(430\) 0 0
\(431\) 18.8301 0.907014 0.453507 0.891253i \(-0.350173\pi\)
0.453507 + 0.891253i \(0.350173\pi\)
\(432\) 0 0
\(433\) −24.7361 −1.18874 −0.594371 0.804191i \(-0.702599\pi\)
−0.594371 + 0.804191i \(0.702599\pi\)
\(434\) 0 0
\(435\) −11.1577 −0.534970
\(436\) 0 0
\(437\) −12.0171 −0.574854
\(438\) 0 0
\(439\) −11.7338 −0.560023 −0.280011 0.959997i \(-0.590338\pi\)
−0.280011 + 0.959997i \(0.590338\pi\)
\(440\) 0 0
\(441\) −8.10545 −0.385974
\(442\) 0 0
\(443\) 28.7954 1.36811 0.684056 0.729429i \(-0.260214\pi\)
0.684056 + 0.729429i \(0.260214\pi\)
\(444\) 0 0
\(445\) 23.1355 1.09673
\(446\) 0 0
\(447\) −7.36335 −0.348275
\(448\) 0 0
\(449\) −10.5553 −0.498136 −0.249068 0.968486i \(-0.580124\pi\)
−0.249068 + 0.968486i \(0.580124\pi\)
\(450\) 0 0
\(451\) 8.33392 0.392429
\(452\) 0 0
\(453\) −6.67950 −0.313830
\(454\) 0 0
\(455\) −38.5641 −1.80791
\(456\) 0 0
\(457\) −21.3776 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 5.55529 0.259299
\(460\) 0 0
\(461\) −16.4658 −0.766890 −0.383445 0.923564i \(-0.625262\pi\)
−0.383445 + 0.923564i \(0.625262\pi\)
\(462\) 0 0
\(463\) 3.46666 0.161109 0.0805547 0.996750i \(-0.474331\pi\)
0.0805547 + 0.996750i \(0.474331\pi\)
\(464\) 0 0
\(465\) −0.0208663 −0.000967652 0
\(466\) 0 0
\(467\) −7.16923 −0.331753 −0.165876 0.986147i \(-0.553045\pi\)
−0.165876 + 0.986147i \(0.553045\pi\)
\(468\) 0 0
\(469\) 19.3963 0.895636
\(470\) 0 0
\(471\) −9.37788 −0.432110
\(472\) 0 0
\(473\) 34.2344 1.57410
\(474\) 0 0
\(475\) 22.6808 1.04067
\(476\) 0 0
\(477\) 9.54031 0.436821
\(478\) 0 0
\(479\) −10.5300 −0.481128 −0.240564 0.970633i \(-0.577332\pi\)
−0.240564 + 0.970633i \(0.577332\pi\)
\(480\) 0 0
\(481\) 15.8344 0.721984
\(482\) 0 0
\(483\) 24.8698 1.13162
\(484\) 0 0
\(485\) −35.8417 −1.62749
\(486\) 0 0
\(487\) 15.2222 0.689783 0.344892 0.938643i \(-0.387916\pi\)
0.344892 + 0.938643i \(0.387916\pi\)
\(488\) 0 0
\(489\) −4.15882 −0.188068
\(490\) 0 0
\(491\) −6.06208 −0.273578 −0.136789 0.990600i \(-0.543678\pi\)
−0.136789 + 0.990600i \(0.543678\pi\)
\(492\) 0 0
\(493\) 2.25685 0.101643
\(494\) 0 0
\(495\) 17.2125 0.773645
\(496\) 0 0
\(497\) 10.7246 0.481062
\(498\) 0 0
\(499\) 29.3216 1.31261 0.656307 0.754494i \(-0.272118\pi\)
0.656307 + 0.754494i \(0.272118\pi\)
\(500\) 0 0
\(501\) −0.340368 −0.0152065
\(502\) 0 0
\(503\) 5.46335 0.243599 0.121799 0.992555i \(-0.461134\pi\)
0.121799 + 0.992555i \(0.461134\pi\)
\(504\) 0 0
\(505\) 13.2267 0.588582
\(506\) 0 0
\(507\) −6.83283 −0.303457
\(508\) 0 0
\(509\) −15.8506 −0.702564 −0.351282 0.936270i \(-0.614254\pi\)
−0.351282 + 0.936270i \(0.614254\pi\)
\(510\) 0 0
\(511\) 0.738559 0.0326719
\(512\) 0 0
\(513\) −12.0218 −0.530774
\(514\) 0 0
\(515\) 34.7200 1.52994
\(516\) 0 0
\(517\) −12.0104 −0.528215
\(518\) 0 0
\(519\) 5.93240 0.260404
\(520\) 0 0
\(521\) 36.7668 1.61078 0.805392 0.592742i \(-0.201955\pi\)
0.805392 + 0.592742i \(0.201955\pi\)
\(522\) 0 0
\(523\) 39.5785 1.73065 0.865324 0.501213i \(-0.167113\pi\)
0.865324 + 0.501213i \(0.167113\pi\)
\(524\) 0 0
\(525\) −46.9389 −2.04858
\(526\) 0 0
\(527\) 0.00422060 0.000183852 0
\(528\) 0 0
\(529\) 7.83710 0.340743
\(530\) 0 0
\(531\) 1.42113 0.0616716
\(532\) 0 0
\(533\) −7.44487 −0.322473
\(534\) 0 0
\(535\) −8.98893 −0.388625
\(536\) 0 0
\(537\) −17.2021 −0.742327
\(538\) 0 0
\(539\) −17.5574 −0.756250
\(540\) 0 0
\(541\) 5.85716 0.251819 0.125909 0.992042i \(-0.459815\pi\)
0.125909 + 0.992042i \(0.459815\pi\)
\(542\) 0 0
\(543\) 0.919737 0.0394697
\(544\) 0 0
\(545\) 22.0575 0.944839
\(546\) 0 0
\(547\) 13.8724 0.593140 0.296570 0.955011i \(-0.404157\pi\)
0.296570 + 0.955011i \(0.404157\pi\)
\(548\) 0 0
\(549\) 16.0095 0.683271
\(550\) 0 0
\(551\) −4.88387 −0.208060
\(552\) 0 0
\(553\) 12.7381 0.541680
\(554\) 0 0
\(555\) 28.4675 1.20838
\(556\) 0 0
\(557\) −9.00157 −0.381409 −0.190704 0.981648i \(-0.561077\pi\)
−0.190704 + 0.981648i \(0.561077\pi\)
\(558\) 0 0
\(559\) −30.5823 −1.29350
\(560\) 0 0
\(561\) 3.86802 0.163308
\(562\) 0 0
\(563\) 5.20078 0.219187 0.109593 0.993977i \(-0.465045\pi\)
0.109593 + 0.993977i \(0.465045\pi\)
\(564\) 0 0
\(565\) −18.7671 −0.789539
\(566\) 0 0
\(567\) 9.68404 0.406692
\(568\) 0 0
\(569\) −28.1274 −1.17916 −0.589580 0.807710i \(-0.700707\pi\)
−0.589580 + 0.807710i \(0.700707\pi\)
\(570\) 0 0
\(571\) −8.55424 −0.357984 −0.178992 0.983851i \(-0.557284\pi\)
−0.178992 + 0.983851i \(0.557284\pi\)
\(572\) 0 0
\(573\) −26.6658 −1.11398
\(574\) 0 0
\(575\) −58.2014 −2.42717
\(576\) 0 0
\(577\) −31.2295 −1.30010 −0.650052 0.759890i \(-0.725253\pi\)
−0.650052 + 0.759890i \(0.725253\pi\)
\(578\) 0 0
\(579\) −25.7847 −1.07158
\(580\) 0 0
\(581\) 14.8312 0.615301
\(582\) 0 0
\(583\) 20.6655 0.855876
\(584\) 0 0
\(585\) −15.3763 −0.635733
\(586\) 0 0
\(587\) −16.9886 −0.701195 −0.350598 0.936526i \(-0.614021\pi\)
−0.350598 + 0.936526i \(0.614021\pi\)
\(588\) 0 0
\(589\) −0.00913348 −0.000376339 0
\(590\) 0 0
\(591\) −14.5922 −0.600244
\(592\) 0 0
\(593\) 21.8405 0.896883 0.448441 0.893812i \(-0.351979\pi\)
0.448441 + 0.893812i \(0.351979\pi\)
\(594\) 0 0
\(595\) 14.0236 0.574912
\(596\) 0 0
\(597\) 20.7146 0.847794
\(598\) 0 0
\(599\) 13.4138 0.548073 0.274037 0.961719i \(-0.411641\pi\)
0.274037 + 0.961719i \(0.411641\pi\)
\(600\) 0 0
\(601\) 18.3687 0.749273 0.374637 0.927172i \(-0.377768\pi\)
0.374637 + 0.927172i \(0.377768\pi\)
\(602\) 0 0
\(603\) 7.73371 0.314941
\(604\) 0 0
\(605\) −5.99589 −0.243768
\(606\) 0 0
\(607\) 33.6872 1.36732 0.683661 0.729799i \(-0.260386\pi\)
0.683661 + 0.729799i \(0.260386\pi\)
\(608\) 0 0
\(609\) 10.1074 0.409572
\(610\) 0 0
\(611\) 10.7291 0.434053
\(612\) 0 0
\(613\) 16.2898 0.657938 0.328969 0.944341i \(-0.393299\pi\)
0.328969 + 0.944341i \(0.393299\pi\)
\(614\) 0 0
\(615\) −13.3846 −0.539719
\(616\) 0 0
\(617\) −18.7025 −0.752934 −0.376467 0.926430i \(-0.622861\pi\)
−0.376467 + 0.926430i \(0.622861\pi\)
\(618\) 0 0
\(619\) −12.5456 −0.504251 −0.252125 0.967695i \(-0.581130\pi\)
−0.252125 + 0.967695i \(0.581130\pi\)
\(620\) 0 0
\(621\) 30.8492 1.23793
\(622\) 0 0
\(623\) −20.9577 −0.839653
\(624\) 0 0
\(625\) 32.4440 1.29776
\(626\) 0 0
\(627\) −8.37048 −0.334285
\(628\) 0 0
\(629\) −5.75808 −0.229590
\(630\) 0 0
\(631\) 24.8839 0.990614 0.495307 0.868718i \(-0.335056\pi\)
0.495307 + 0.868718i \(0.335056\pi\)
\(632\) 0 0
\(633\) 18.0116 0.715897
\(634\) 0 0
\(635\) 29.2804 1.16196
\(636\) 0 0
\(637\) 15.6844 0.621438
\(638\) 0 0
\(639\) 4.27611 0.169160
\(640\) 0 0
\(641\) −1.43843 −0.0568145 −0.0284073 0.999596i \(-0.509044\pi\)
−0.0284073 + 0.999596i \(0.509044\pi\)
\(642\) 0 0
\(643\) 24.2853 0.957720 0.478860 0.877891i \(-0.341050\pi\)
0.478860 + 0.877891i \(0.341050\pi\)
\(644\) 0 0
\(645\) −54.9818 −2.16491
\(646\) 0 0
\(647\) −37.6283 −1.47932 −0.739660 0.672981i \(-0.765014\pi\)
−0.739660 + 0.672981i \(0.765014\pi\)
\(648\) 0 0
\(649\) 3.07833 0.120835
\(650\) 0 0
\(651\) 0.0189021 0.000740833 0
\(652\) 0 0
\(653\) 35.0033 1.36979 0.684893 0.728644i \(-0.259849\pi\)
0.684893 + 0.728644i \(0.259849\pi\)
\(654\) 0 0
\(655\) 39.3148 1.53615
\(656\) 0 0
\(657\) 0.294479 0.0114887
\(658\) 0 0
\(659\) −39.9805 −1.55742 −0.778710 0.627384i \(-0.784126\pi\)
−0.778710 + 0.627384i \(0.784126\pi\)
\(660\) 0 0
\(661\) −21.0305 −0.817991 −0.408995 0.912536i \(-0.634121\pi\)
−0.408995 + 0.912536i \(0.634121\pi\)
\(662\) 0 0
\(663\) −3.45539 −0.134196
\(664\) 0 0
\(665\) −30.3474 −1.17682
\(666\) 0 0
\(667\) 12.5325 0.485262
\(668\) 0 0
\(669\) −7.65888 −0.296109
\(670\) 0 0
\(671\) 34.6786 1.33875
\(672\) 0 0
\(673\) 24.4543 0.942643 0.471322 0.881961i \(-0.343777\pi\)
0.471322 + 0.881961i \(0.343777\pi\)
\(674\) 0 0
\(675\) −58.2242 −2.24105
\(676\) 0 0
\(677\) −13.5133 −0.519357 −0.259679 0.965695i \(-0.583617\pi\)
−0.259679 + 0.965695i \(0.583617\pi\)
\(678\) 0 0
\(679\) 32.4679 1.24600
\(680\) 0 0
\(681\) −12.1907 −0.467148
\(682\) 0 0
\(683\) 35.1926 1.34661 0.673304 0.739366i \(-0.264874\pi\)
0.673304 + 0.739366i \(0.264874\pi\)
\(684\) 0 0
\(685\) 81.7864 3.12490
\(686\) 0 0
\(687\) −3.97712 −0.151737
\(688\) 0 0
\(689\) −18.4609 −0.703304
\(690\) 0 0
\(691\) −32.3054 −1.22896 −0.614478 0.788934i \(-0.710633\pi\)
−0.614478 + 0.788934i \(0.710633\pi\)
\(692\) 0 0
\(693\) −15.5923 −0.592302
\(694\) 0 0
\(695\) −70.4398 −2.67193
\(696\) 0 0
\(697\) 2.70729 0.102546
\(698\) 0 0
\(699\) −0.673188 −0.0254623
\(700\) 0 0
\(701\) 4.10932 0.155207 0.0776034 0.996984i \(-0.475273\pi\)
0.0776034 + 0.996984i \(0.475273\pi\)
\(702\) 0 0
\(703\) 12.4606 0.469961
\(704\) 0 0
\(705\) 19.2891 0.726470
\(706\) 0 0
\(707\) −11.9817 −0.450617
\(708\) 0 0
\(709\) −33.2063 −1.24709 −0.623545 0.781787i \(-0.714308\pi\)
−0.623545 + 0.781787i \(0.714308\pi\)
\(710\) 0 0
\(711\) 5.07897 0.190476
\(712\) 0 0
\(713\) 0.0234375 0.000877741 0
\(714\) 0 0
\(715\) −33.3070 −1.24561
\(716\) 0 0
\(717\) −4.65212 −0.173736
\(718\) 0 0
\(719\) −18.9088 −0.705181 −0.352591 0.935778i \(-0.614699\pi\)
−0.352591 + 0.935778i \(0.614699\pi\)
\(720\) 0 0
\(721\) −31.4517 −1.17132
\(722\) 0 0
\(723\) 10.2526 0.381299
\(724\) 0 0
\(725\) −23.6537 −0.878477
\(726\) 0 0
\(727\) −38.0421 −1.41090 −0.705452 0.708758i \(-0.749256\pi\)
−0.705452 + 0.708758i \(0.749256\pi\)
\(728\) 0 0
\(729\) 24.8024 0.918609
\(730\) 0 0
\(731\) 11.1211 0.411329
\(732\) 0 0
\(733\) 5.15052 0.190239 0.0951194 0.995466i \(-0.469677\pi\)
0.0951194 + 0.995466i \(0.469677\pi\)
\(734\) 0 0
\(735\) 28.1979 1.04009
\(736\) 0 0
\(737\) 16.7521 0.617073
\(738\) 0 0
\(739\) 20.6112 0.758196 0.379098 0.925356i \(-0.376234\pi\)
0.379098 + 0.925356i \(0.376234\pi\)
\(740\) 0 0
\(741\) 7.47753 0.274694
\(742\) 0 0
\(743\) −5.34340 −0.196030 −0.0980152 0.995185i \(-0.531249\pi\)
−0.0980152 + 0.995185i \(0.531249\pi\)
\(744\) 0 0
\(745\) −23.0568 −0.844736
\(746\) 0 0
\(747\) 5.91352 0.216364
\(748\) 0 0
\(749\) 8.14279 0.297531
\(750\) 0 0
\(751\) −5.59110 −0.204022 −0.102011 0.994783i \(-0.532528\pi\)
−0.102011 + 0.994783i \(0.532528\pi\)
\(752\) 0 0
\(753\) −32.0496 −1.16795
\(754\) 0 0
\(755\) −20.9155 −0.761191
\(756\) 0 0
\(757\) 33.6951 1.22467 0.612335 0.790598i \(-0.290230\pi\)
0.612335 + 0.790598i \(0.290230\pi\)
\(758\) 0 0
\(759\) 21.4796 0.779659
\(760\) 0 0
\(761\) −5.38882 −0.195344 −0.0976722 0.995219i \(-0.531140\pi\)
−0.0976722 + 0.995219i \(0.531140\pi\)
\(762\) 0 0
\(763\) −19.9812 −0.723368
\(764\) 0 0
\(765\) 5.59152 0.202162
\(766\) 0 0
\(767\) −2.74994 −0.0992945
\(768\) 0 0
\(769\) 28.2792 1.01977 0.509886 0.860242i \(-0.329688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(770\) 0 0
\(771\) −12.8903 −0.464232
\(772\) 0 0
\(773\) −44.2573 −1.59182 −0.795911 0.605413i \(-0.793008\pi\)
−0.795911 + 0.605413i \(0.793008\pi\)
\(774\) 0 0
\(775\) −0.0442355 −0.00158899
\(776\) 0 0
\(777\) −25.7878 −0.925131
\(778\) 0 0
\(779\) −5.85863 −0.209907
\(780\) 0 0
\(781\) 9.26257 0.331441
\(782\) 0 0
\(783\) 12.5375 0.448052
\(784\) 0 0
\(785\) −29.3649 −1.04808
\(786\) 0 0
\(787\) −39.5510 −1.40984 −0.704920 0.709287i \(-0.749017\pi\)
−0.704920 + 0.709287i \(0.749017\pi\)
\(788\) 0 0
\(789\) 17.0915 0.608474
\(790\) 0 0
\(791\) 17.0005 0.604470
\(792\) 0 0
\(793\) −30.9791 −1.10010
\(794\) 0 0
\(795\) −33.1896 −1.17711
\(796\) 0 0
\(797\) 16.6094 0.588336 0.294168 0.955754i \(-0.404957\pi\)
0.294168 + 0.955754i \(0.404957\pi\)
\(798\) 0 0
\(799\) −3.90158 −0.138028
\(800\) 0 0
\(801\) −8.35629 −0.295255
\(802\) 0 0
\(803\) 0.637877 0.0225102
\(804\) 0 0
\(805\) 77.8748 2.74472
\(806\) 0 0
\(807\) 37.1445 1.30755
\(808\) 0 0
\(809\) −26.7324 −0.939862 −0.469931 0.882703i \(-0.655721\pi\)
−0.469931 + 0.882703i \(0.655721\pi\)
\(810\) 0 0
\(811\) −24.8178 −0.871470 −0.435735 0.900075i \(-0.643511\pi\)
−0.435735 + 0.900075i \(0.643511\pi\)
\(812\) 0 0
\(813\) −38.1389 −1.33759
\(814\) 0 0
\(815\) −13.0225 −0.456157
\(816\) 0 0
\(817\) −24.0663 −0.841974
\(818\) 0 0
\(819\) 13.9289 0.486716
\(820\) 0 0
\(821\) −42.0803 −1.46861 −0.734306 0.678819i \(-0.762492\pi\)
−0.734306 + 0.678819i \(0.762492\pi\)
\(822\) 0 0
\(823\) −20.8093 −0.725366 −0.362683 0.931912i \(-0.618139\pi\)
−0.362683 + 0.931912i \(0.618139\pi\)
\(824\) 0 0
\(825\) −40.5401 −1.41143
\(826\) 0 0
\(827\) 6.28377 0.218508 0.109254 0.994014i \(-0.465154\pi\)
0.109254 + 0.994014i \(0.465154\pi\)
\(828\) 0 0
\(829\) 32.7063 1.13594 0.567969 0.823050i \(-0.307730\pi\)
0.567969 + 0.823050i \(0.307730\pi\)
\(830\) 0 0
\(831\) −4.89470 −0.169795
\(832\) 0 0
\(833\) −5.70355 −0.197616
\(834\) 0 0
\(835\) −1.06579 −0.0368832
\(836\) 0 0
\(837\) 0.0234467 0.000810436 0
\(838\) 0 0
\(839\) 0.383506 0.0132401 0.00662005 0.999978i \(-0.497893\pi\)
0.00662005 + 0.999978i \(0.497893\pi\)
\(840\) 0 0
\(841\) −23.9066 −0.824367
\(842\) 0 0
\(843\) 8.46990 0.291719
\(844\) 0 0
\(845\) −21.3956 −0.736031
\(846\) 0 0
\(847\) 5.43149 0.186628
\(848\) 0 0
\(849\) −12.7416 −0.437291
\(850\) 0 0
\(851\) −31.9753 −1.09610
\(852\) 0 0
\(853\) 22.1179 0.757301 0.378651 0.925540i \(-0.376388\pi\)
0.378651 + 0.925540i \(0.376388\pi\)
\(854\) 0 0
\(855\) −12.1002 −0.413817
\(856\) 0 0
\(857\) 43.2225 1.47645 0.738227 0.674552i \(-0.235663\pi\)
0.738227 + 0.674552i \(0.235663\pi\)
\(858\) 0 0
\(859\) −0.633535 −0.0216159 −0.0108080 0.999942i \(-0.503440\pi\)
−0.0108080 + 0.999942i \(0.503440\pi\)
\(860\) 0 0
\(861\) 12.1247 0.413208
\(862\) 0 0
\(863\) 16.2376 0.552736 0.276368 0.961052i \(-0.410869\pi\)
0.276368 + 0.961052i \(0.410869\pi\)
\(864\) 0 0
\(865\) 18.5761 0.631606
\(866\) 0 0
\(867\) 1.25653 0.0426741
\(868\) 0 0
\(869\) 11.0016 0.373205
\(870\) 0 0
\(871\) −14.9651 −0.507071
\(872\) 0 0
\(873\) 12.9457 0.438144
\(874\) 0 0
\(875\) −76.8613 −2.59839
\(876\) 0 0
\(877\) −43.7849 −1.47851 −0.739256 0.673424i \(-0.764823\pi\)
−0.739256 + 0.673424i \(0.764823\pi\)
\(878\) 0 0
\(879\) −33.1499 −1.11812
\(880\) 0 0
\(881\) 48.8665 1.64635 0.823176 0.567786i \(-0.192200\pi\)
0.823176 + 0.567786i \(0.192200\pi\)
\(882\) 0 0
\(883\) −33.4586 −1.12597 −0.562985 0.826467i \(-0.690347\pi\)
−0.562985 + 0.826467i \(0.690347\pi\)
\(884\) 0 0
\(885\) −4.94392 −0.166188
\(886\) 0 0
\(887\) −55.1309 −1.85111 −0.925557 0.378609i \(-0.876402\pi\)
−0.925557 + 0.378609i \(0.876402\pi\)
\(888\) 0 0
\(889\) −26.5242 −0.889593
\(890\) 0 0
\(891\) 8.36390 0.280201
\(892\) 0 0
\(893\) 8.44311 0.282538
\(894\) 0 0
\(895\) −53.8649 −1.80051
\(896\) 0 0
\(897\) −19.1882 −0.640674
\(898\) 0 0
\(899\) 0.00952527 0.000317685 0
\(900\) 0 0
\(901\) 6.71321 0.223649
\(902\) 0 0
\(903\) 49.8063 1.65745
\(904\) 0 0
\(905\) 2.87996 0.0957333
\(906\) 0 0
\(907\) −30.8505 −1.02438 −0.512188 0.858874i \(-0.671165\pi\)
−0.512188 + 0.858874i \(0.671165\pi\)
\(908\) 0 0
\(909\) −4.77735 −0.158455
\(910\) 0 0
\(911\) −20.6821 −0.685229 −0.342614 0.939476i \(-0.611312\pi\)
−0.342614 + 0.939476i \(0.611312\pi\)
\(912\) 0 0
\(913\) 12.8094 0.423929
\(914\) 0 0
\(915\) −55.6952 −1.84123
\(916\) 0 0
\(917\) −35.6140 −1.17608
\(918\) 0 0
\(919\) −59.6795 −1.96864 −0.984322 0.176378i \(-0.943562\pi\)
−0.984322 + 0.176378i \(0.943562\pi\)
\(920\) 0 0
\(921\) −14.4130 −0.474924
\(922\) 0 0
\(923\) −8.27446 −0.272357
\(924\) 0 0
\(925\) 60.3496 1.98428
\(926\) 0 0
\(927\) −12.5405 −0.411883
\(928\) 0 0
\(929\) 16.2162 0.532035 0.266017 0.963968i \(-0.414292\pi\)
0.266017 + 0.963968i \(0.414292\pi\)
\(930\) 0 0
\(931\) 12.3426 0.404512
\(932\) 0 0
\(933\) 0.473333 0.0154962
\(934\) 0 0
\(935\) 12.1119 0.396101
\(936\) 0 0
\(937\) 19.3249 0.631315 0.315658 0.948873i \(-0.397775\pi\)
0.315658 + 0.948873i \(0.397775\pi\)
\(938\) 0 0
\(939\) 16.6136 0.542163
\(940\) 0 0
\(941\) 38.3566 1.25039 0.625195 0.780468i \(-0.285019\pi\)
0.625195 + 0.780468i \(0.285019\pi\)
\(942\) 0 0
\(943\) 15.0339 0.489570
\(944\) 0 0
\(945\) 77.9052 2.53426
\(946\) 0 0
\(947\) 3.83161 0.124511 0.0622553 0.998060i \(-0.480171\pi\)
0.0622553 + 0.998060i \(0.480171\pi\)
\(948\) 0 0
\(949\) −0.569830 −0.0184975
\(950\) 0 0
\(951\) 24.1566 0.783333
\(952\) 0 0
\(953\) 33.9178 1.09871 0.549353 0.835590i \(-0.314874\pi\)
0.549353 + 0.835590i \(0.314874\pi\)
\(954\) 0 0
\(955\) −83.4984 −2.70194
\(956\) 0 0
\(957\) 8.72954 0.282186
\(958\) 0 0
\(959\) −74.0877 −2.39242
\(960\) 0 0
\(961\) −31.0000 −0.999999
\(962\) 0 0
\(963\) 3.24671 0.104624
\(964\) 0 0
\(965\) −80.7395 −2.59910
\(966\) 0 0
\(967\) −7.04620 −0.226591 −0.113295 0.993561i \(-0.536141\pi\)
−0.113295 + 0.993561i \(0.536141\pi\)
\(968\) 0 0
\(969\) −2.71917 −0.0873522
\(970\) 0 0
\(971\) 40.7548 1.30788 0.653942 0.756545i \(-0.273114\pi\)
0.653942 + 0.756545i \(0.273114\pi\)
\(972\) 0 0
\(973\) 63.8092 2.04563
\(974\) 0 0
\(975\) 36.2154 1.15982
\(976\) 0 0
\(977\) −47.2211 −1.51074 −0.755368 0.655301i \(-0.772542\pi\)
−0.755368 + 0.655301i \(0.772542\pi\)
\(978\) 0 0
\(979\) −18.1007 −0.578502
\(980\) 0 0
\(981\) −7.96693 −0.254365
\(982\) 0 0
\(983\) −30.9654 −0.987642 −0.493821 0.869564i \(-0.664400\pi\)
−0.493821 + 0.869564i \(0.664400\pi\)
\(984\) 0 0
\(985\) −45.6925 −1.45588
\(986\) 0 0
\(987\) −17.4734 −0.556184
\(988\) 0 0
\(989\) 61.7568 1.96375
\(990\) 0 0
\(991\) 19.7724 0.628092 0.314046 0.949408i \(-0.398315\pi\)
0.314046 + 0.949408i \(0.398315\pi\)
\(992\) 0 0
\(993\) 21.9709 0.697227
\(994\) 0 0
\(995\) 64.8636 2.05631
\(996\) 0 0
\(997\) −37.6434 −1.19218 −0.596090 0.802918i \(-0.703280\pi\)
−0.596090 + 0.802918i \(0.703280\pi\)
\(998\) 0 0
\(999\) −31.9878 −1.01205
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 \(a_p\))