Properties

Label 4028.2.a.d.1.4
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.40459\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.40459 q^{3} -0.489610 q^{5} +4.26722 q^{7} +2.78204 q^{9} +O(q^{10})\) \(q-2.40459 q^{3} -0.489610 q^{5} +4.26722 q^{7} +2.78204 q^{9} -0.593113 q^{11} -1.15631 q^{13} +1.17731 q^{15} -0.567069 q^{17} -1.00000 q^{19} -10.2609 q^{21} -0.283453 q^{23} -4.76028 q^{25} +0.524106 q^{27} +7.84950 q^{29} -1.45614 q^{31} +1.42619 q^{33} -2.08928 q^{35} -10.2044 q^{37} +2.78046 q^{39} -1.80512 q^{41} -10.9526 q^{43} -1.36212 q^{45} -0.268056 q^{47} +11.2092 q^{49} +1.36357 q^{51} +1.00000 q^{53} +0.290395 q^{55} +2.40459 q^{57} -7.12660 q^{59} -3.60308 q^{61} +11.8716 q^{63} +0.566143 q^{65} +13.0044 q^{67} +0.681587 q^{69} +5.30469 q^{71} +6.82454 q^{73} +11.4465 q^{75} -2.53095 q^{77} +6.03777 q^{79} -9.60638 q^{81} -18.1576 q^{83} +0.277643 q^{85} -18.8748 q^{87} +11.2560 q^{89} -4.93425 q^{91} +3.50142 q^{93} +0.489610 q^{95} +16.7957 q^{97} -1.65006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) −2.40459 −1.38829 −0.694144 0.719836i \(-0.744217\pi\)
−0.694144 + 0.719836i \(0.744217\pi\)
\(4\) 0 0
\(5\) −0.489610 −0.218960 −0.109480 0.993989i \(-0.534919\pi\)
−0.109480 + 0.993989i \(0.534919\pi\)
\(6\) 0 0
\(7\) 4.26722 1.61286 0.806429 0.591331i \(-0.201397\pi\)
0.806429 + 0.591331i \(0.201397\pi\)
\(8\) 0 0
\(9\) 2.78204 0.927346
\(10\) 0 0
\(11\) −0.593113 −0.178830 −0.0894152 0.995994i \(-0.528500\pi\)
−0.0894152 + 0.995994i \(0.528500\pi\)
\(12\) 0 0
\(13\) −1.15631 −0.320704 −0.160352 0.987060i \(-0.551263\pi\)
−0.160352 + 0.987060i \(0.551263\pi\)
\(14\) 0 0
\(15\) 1.17731 0.303980
\(16\) 0 0
\(17\) −0.567069 −0.137534 −0.0687672 0.997633i \(-0.521907\pi\)
−0.0687672 + 0.997633i \(0.521907\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −10.2609 −2.23911
\(22\) 0 0
\(23\) −0.283453 −0.0591040 −0.0295520 0.999563i \(-0.509408\pi\)
−0.0295520 + 0.999563i \(0.509408\pi\)
\(24\) 0 0
\(25\) −4.76028 −0.952056
\(26\) 0 0
\(27\) 0.524106 0.100864
\(28\) 0 0
\(29\) 7.84950 1.45762 0.728808 0.684718i \(-0.240075\pi\)
0.728808 + 0.684718i \(0.240075\pi\)
\(30\) 0 0
\(31\) −1.45614 −0.261531 −0.130765 0.991413i \(-0.541743\pi\)
−0.130765 + 0.991413i \(0.541743\pi\)
\(32\) 0 0
\(33\) 1.42619 0.248268
\(34\) 0 0
\(35\) −2.08928 −0.353152
\(36\) 0 0
\(37\) −10.2044 −1.67759 −0.838796 0.544446i \(-0.816740\pi\)
−0.838796 + 0.544446i \(0.816740\pi\)
\(38\) 0 0
\(39\) 2.78046 0.445229
\(40\) 0 0
\(41\) −1.80512 −0.281912 −0.140956 0.990016i \(-0.545018\pi\)
−0.140956 + 0.990016i \(0.545018\pi\)
\(42\) 0 0
\(43\) −10.9526 −1.67025 −0.835126 0.550059i \(-0.814605\pi\)
−0.835126 + 0.550059i \(0.814605\pi\)
\(44\) 0 0
\(45\) −1.36212 −0.203052
\(46\) 0 0
\(47\) −0.268056 −0.0391000 −0.0195500 0.999809i \(-0.506223\pi\)
−0.0195500 + 0.999809i \(0.506223\pi\)
\(48\) 0 0
\(49\) 11.2092 1.60131
\(50\) 0 0
\(51\) 1.36357 0.190937
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 0.290395 0.0391568
\(56\) 0 0
\(57\) 2.40459 0.318495
\(58\) 0 0
\(59\) −7.12660 −0.927804 −0.463902 0.885887i \(-0.653551\pi\)
−0.463902 + 0.885887i \(0.653551\pi\)
\(60\) 0 0
\(61\) −3.60308 −0.461327 −0.230664 0.973034i \(-0.574090\pi\)
−0.230664 + 0.973034i \(0.574090\pi\)
\(62\) 0 0
\(63\) 11.8716 1.49568
\(64\) 0 0
\(65\) 0.566143 0.0702214
\(66\) 0 0
\(67\) 13.0044 1.58874 0.794369 0.607436i \(-0.207802\pi\)
0.794369 + 0.607436i \(0.207802\pi\)
\(68\) 0 0
\(69\) 0.681587 0.0820534
\(70\) 0 0
\(71\) 5.30469 0.629551 0.314776 0.949166i \(-0.398071\pi\)
0.314776 + 0.949166i \(0.398071\pi\)
\(72\) 0 0
\(73\) 6.82454 0.798752 0.399376 0.916787i \(-0.369227\pi\)
0.399376 + 0.916787i \(0.369227\pi\)
\(74\) 0 0
\(75\) 11.4465 1.32173
\(76\) 0 0
\(77\) −2.53095 −0.288428
\(78\) 0 0
\(79\) 6.03777 0.679302 0.339651 0.940552i \(-0.389691\pi\)
0.339651 + 0.940552i \(0.389691\pi\)
\(80\) 0 0
\(81\) −9.60638 −1.06738
\(82\) 0 0
\(83\) −18.1576 −1.99305 −0.996526 0.0832803i \(-0.973460\pi\)
−0.996526 + 0.0832803i \(0.973460\pi\)
\(84\) 0 0
\(85\) 0.277643 0.0301146
\(86\) 0 0
\(87\) −18.8748 −2.02359
\(88\) 0 0
\(89\) 11.2560 1.19314 0.596568 0.802563i \(-0.296531\pi\)
0.596568 + 0.802563i \(0.296531\pi\)
\(90\) 0 0
\(91\) −4.93425 −0.517250
\(92\) 0 0
\(93\) 3.50142 0.363080
\(94\) 0 0
\(95\) 0.489610 0.0502330
\(96\) 0 0
\(97\) 16.7957 1.70534 0.852671 0.522448i \(-0.174981\pi\)
0.852671 + 0.522448i \(0.174981\pi\)
\(98\) 0 0
\(99\) −1.65006 −0.165838
\(100\) 0 0
\(101\) −6.59077 −0.655807 −0.327903 0.944711i \(-0.606342\pi\)
−0.327903 + 0.944711i \(0.606342\pi\)
\(102\) 0 0
\(103\) 3.34526 0.329618 0.164809 0.986325i \(-0.447299\pi\)
0.164809 + 0.986325i \(0.447299\pi\)
\(104\) 0 0
\(105\) 5.02385 0.490277
\(106\) 0 0
\(107\) −9.55246 −0.923471 −0.461736 0.887018i \(-0.652773\pi\)
−0.461736 + 0.887018i \(0.652773\pi\)
\(108\) 0 0
\(109\) 0.195040 0.0186815 0.00934074 0.999956i \(-0.497027\pi\)
0.00934074 + 0.999956i \(0.497027\pi\)
\(110\) 0 0
\(111\) 24.5373 2.32898
\(112\) 0 0
\(113\) −13.8267 −1.30070 −0.650352 0.759633i \(-0.725379\pi\)
−0.650352 + 0.759633i \(0.725379\pi\)
\(114\) 0 0
\(115\) 0.138781 0.0129414
\(116\) 0 0
\(117\) −3.21691 −0.297403
\(118\) 0 0
\(119\) −2.41981 −0.221823
\(120\) 0 0
\(121\) −10.6482 −0.968020
\(122\) 0 0
\(123\) 4.34057 0.391376
\(124\) 0 0
\(125\) 4.77874 0.427423
\(126\) 0 0
\(127\) 13.5583 1.20311 0.601553 0.798833i \(-0.294549\pi\)
0.601553 + 0.798833i \(0.294549\pi\)
\(128\) 0 0
\(129\) 26.3364 2.31879
\(130\) 0 0
\(131\) 11.3534 0.991953 0.495977 0.868336i \(-0.334810\pi\)
0.495977 + 0.868336i \(0.334810\pi\)
\(132\) 0 0
\(133\) −4.26722 −0.370015
\(134\) 0 0
\(135\) −0.256608 −0.0220853
\(136\) 0 0
\(137\) 10.2091 0.872223 0.436112 0.899893i \(-0.356355\pi\)
0.436112 + 0.899893i \(0.356355\pi\)
\(138\) 0 0
\(139\) 0.848744 0.0719895 0.0359947 0.999352i \(-0.488540\pi\)
0.0359947 + 0.999352i \(0.488540\pi\)
\(140\) 0 0
\(141\) 0.644564 0.0542821
\(142\) 0 0
\(143\) 0.685825 0.0573516
\(144\) 0 0
\(145\) −3.84320 −0.319160
\(146\) 0 0
\(147\) −26.9534 −2.22308
\(148\) 0 0
\(149\) 19.7506 1.61803 0.809015 0.587788i \(-0.200001\pi\)
0.809015 + 0.587788i \(0.200001\pi\)
\(150\) 0 0
\(151\) −17.9990 −1.46474 −0.732368 0.680909i \(-0.761585\pi\)
−0.732368 + 0.680909i \(0.761585\pi\)
\(152\) 0 0
\(153\) −1.57761 −0.127542
\(154\) 0 0
\(155\) 0.712942 0.0572649
\(156\) 0 0
\(157\) −5.29269 −0.422402 −0.211201 0.977443i \(-0.567738\pi\)
−0.211201 + 0.977443i \(0.567738\pi\)
\(158\) 0 0
\(159\) −2.40459 −0.190696
\(160\) 0 0
\(161\) −1.20956 −0.0953263
\(162\) 0 0
\(163\) −22.9884 −1.80059 −0.900296 0.435278i \(-0.856650\pi\)
−0.900296 + 0.435278i \(0.856650\pi\)
\(164\) 0 0
\(165\) −0.698279 −0.0543609
\(166\) 0 0
\(167\) −18.0882 −1.39971 −0.699855 0.714285i \(-0.746752\pi\)
−0.699855 + 0.714285i \(0.746752\pi\)
\(168\) 0 0
\(169\) −11.6629 −0.897149
\(170\) 0 0
\(171\) −2.78204 −0.212748
\(172\) 0 0
\(173\) 10.3205 0.784651 0.392325 0.919827i \(-0.371671\pi\)
0.392325 + 0.919827i \(0.371671\pi\)
\(174\) 0 0
\(175\) −20.3132 −1.53553
\(176\) 0 0
\(177\) 17.1365 1.28806
\(178\) 0 0
\(179\) −11.7825 −0.880666 −0.440333 0.897834i \(-0.645140\pi\)
−0.440333 + 0.897834i \(0.645140\pi\)
\(180\) 0 0
\(181\) −10.7511 −0.799125 −0.399562 0.916706i \(-0.630838\pi\)
−0.399562 + 0.916706i \(0.630838\pi\)
\(182\) 0 0
\(183\) 8.66392 0.640456
\(184\) 0 0
\(185\) 4.99618 0.367326
\(186\) 0 0
\(187\) 0.336336 0.0245953
\(188\) 0 0
\(189\) 2.23648 0.162680
\(190\) 0 0
\(191\) −17.9185 −1.29654 −0.648268 0.761412i \(-0.724506\pi\)
−0.648268 + 0.761412i \(0.724506\pi\)
\(192\) 0 0
\(193\) −14.7314 −1.06039 −0.530195 0.847876i \(-0.677881\pi\)
−0.530195 + 0.847876i \(0.677881\pi\)
\(194\) 0 0
\(195\) −1.36134 −0.0974876
\(196\) 0 0
\(197\) 8.16837 0.581973 0.290986 0.956727i \(-0.406017\pi\)
0.290986 + 0.956727i \(0.406017\pi\)
\(198\) 0 0
\(199\) −26.2015 −1.85738 −0.928688 0.370861i \(-0.879062\pi\)
−0.928688 + 0.370861i \(0.879062\pi\)
\(200\) 0 0
\(201\) −31.2702 −2.20563
\(202\) 0 0
\(203\) 33.4956 2.35093
\(204\) 0 0
\(205\) 0.883805 0.0617276
\(206\) 0 0
\(207\) −0.788577 −0.0548099
\(208\) 0 0
\(209\) 0.593113 0.0410265
\(210\) 0 0
\(211\) −24.1902 −1.66532 −0.832661 0.553782i \(-0.813184\pi\)
−0.832661 + 0.553782i \(0.813184\pi\)
\(212\) 0 0
\(213\) −12.7556 −0.873999
\(214\) 0 0
\(215\) 5.36249 0.365719
\(216\) 0 0
\(217\) −6.21368 −0.421812
\(218\) 0 0
\(219\) −16.4102 −1.10890
\(220\) 0 0
\(221\) 0.655709 0.0441078
\(222\) 0 0
\(223\) −3.32596 −0.222723 −0.111361 0.993780i \(-0.535521\pi\)
−0.111361 + 0.993780i \(0.535521\pi\)
\(224\) 0 0
\(225\) −13.2433 −0.882886
\(226\) 0 0
\(227\) −13.7421 −0.912096 −0.456048 0.889955i \(-0.650735\pi\)
−0.456048 + 0.889955i \(0.650735\pi\)
\(228\) 0 0
\(229\) −28.4253 −1.87840 −0.939200 0.343371i \(-0.888431\pi\)
−0.939200 + 0.343371i \(0.888431\pi\)
\(230\) 0 0
\(231\) 6.08588 0.400422
\(232\) 0 0
\(233\) −25.2345 −1.65316 −0.826582 0.562816i \(-0.809718\pi\)
−0.826582 + 0.562816i \(0.809718\pi\)
\(234\) 0 0
\(235\) 0.131243 0.00856136
\(236\) 0 0
\(237\) −14.5183 −0.943067
\(238\) 0 0
\(239\) 19.4760 1.25980 0.629900 0.776676i \(-0.283096\pi\)
0.629900 + 0.776676i \(0.283096\pi\)
\(240\) 0 0
\(241\) 6.36949 0.410295 0.205147 0.978731i \(-0.434233\pi\)
0.205147 + 0.978731i \(0.434233\pi\)
\(242\) 0 0
\(243\) 21.5270 1.38096
\(244\) 0 0
\(245\) −5.48813 −0.350624
\(246\) 0 0
\(247\) 1.15631 0.0735745
\(248\) 0 0
\(249\) 43.6615 2.76693
\(250\) 0 0
\(251\) −14.0762 −0.888479 −0.444240 0.895908i \(-0.646526\pi\)
−0.444240 + 0.895908i \(0.646526\pi\)
\(252\) 0 0
\(253\) 0.168120 0.0105696
\(254\) 0 0
\(255\) −0.667616 −0.0418077
\(256\) 0 0
\(257\) 23.6236 1.47360 0.736801 0.676110i \(-0.236336\pi\)
0.736801 + 0.676110i \(0.236336\pi\)
\(258\) 0 0
\(259\) −43.5444 −2.70572
\(260\) 0 0
\(261\) 21.8376 1.35171
\(262\) 0 0
\(263\) −25.3321 −1.56204 −0.781022 0.624503i \(-0.785301\pi\)
−0.781022 + 0.624503i \(0.785301\pi\)
\(264\) 0 0
\(265\) −0.489610 −0.0300765
\(266\) 0 0
\(267\) −27.0661 −1.65642
\(268\) 0 0
\(269\) 10.0059 0.610072 0.305036 0.952341i \(-0.401331\pi\)
0.305036 + 0.952341i \(0.401331\pi\)
\(270\) 0 0
\(271\) −8.45285 −0.513474 −0.256737 0.966481i \(-0.582647\pi\)
−0.256737 + 0.966481i \(0.582647\pi\)
\(272\) 0 0
\(273\) 11.8648 0.718092
\(274\) 0 0
\(275\) 2.82339 0.170257
\(276\) 0 0
\(277\) 13.6319 0.819063 0.409531 0.912296i \(-0.365692\pi\)
0.409531 + 0.912296i \(0.365692\pi\)
\(278\) 0 0
\(279\) −4.05104 −0.242530
\(280\) 0 0
\(281\) 8.21933 0.490324 0.245162 0.969482i \(-0.421159\pi\)
0.245162 + 0.969482i \(0.421159\pi\)
\(282\) 0 0
\(283\) −17.9266 −1.06562 −0.532812 0.846234i \(-0.678865\pi\)
−0.532812 + 0.846234i \(0.678865\pi\)
\(284\) 0 0
\(285\) −1.17731 −0.0697379
\(286\) 0 0
\(287\) −7.70284 −0.454684
\(288\) 0 0
\(289\) −16.6784 −0.981084
\(290\) 0 0
\(291\) −40.3867 −2.36751
\(292\) 0 0
\(293\) 25.3915 1.48339 0.741694 0.670739i \(-0.234023\pi\)
0.741694 + 0.670739i \(0.234023\pi\)
\(294\) 0 0
\(295\) 3.48926 0.203152
\(296\) 0 0
\(297\) −0.310854 −0.0180376
\(298\) 0 0
\(299\) 0.327760 0.0189549
\(300\) 0 0
\(301\) −46.7370 −2.69388
\(302\) 0 0
\(303\) 15.8481 0.910449
\(304\) 0 0
\(305\) 1.76411 0.101012
\(306\) 0 0
\(307\) −6.58449 −0.375797 −0.187898 0.982188i \(-0.560168\pi\)
−0.187898 + 0.982188i \(0.560168\pi\)
\(308\) 0 0
\(309\) −8.04397 −0.457605
\(310\) 0 0
\(311\) 3.50525 0.198765 0.0993823 0.995049i \(-0.468313\pi\)
0.0993823 + 0.995049i \(0.468313\pi\)
\(312\) 0 0
\(313\) 11.0456 0.624337 0.312168 0.950027i \(-0.398945\pi\)
0.312168 + 0.950027i \(0.398945\pi\)
\(314\) 0 0
\(315\) −5.81245 −0.327494
\(316\) 0 0
\(317\) −8.51919 −0.478486 −0.239243 0.970960i \(-0.576899\pi\)
−0.239243 + 0.970960i \(0.576899\pi\)
\(318\) 0 0
\(319\) −4.65565 −0.260666
\(320\) 0 0
\(321\) 22.9697 1.28204
\(322\) 0 0
\(323\) 0.567069 0.0315525
\(324\) 0 0
\(325\) 5.50438 0.305328
\(326\) 0 0
\(327\) −0.468992 −0.0259353
\(328\) 0 0
\(329\) −1.14386 −0.0630628
\(330\) 0 0
\(331\) 15.8010 0.868503 0.434252 0.900792i \(-0.357013\pi\)
0.434252 + 0.900792i \(0.357013\pi\)
\(332\) 0 0
\(333\) −28.3890 −1.55571
\(334\) 0 0
\(335\) −6.36708 −0.347871
\(336\) 0 0
\(337\) −5.91933 −0.322446 −0.161223 0.986918i \(-0.551544\pi\)
−0.161223 + 0.986918i \(0.551544\pi\)
\(338\) 0 0
\(339\) 33.2474 1.80575
\(340\) 0 0
\(341\) 0.863657 0.0467697
\(342\) 0 0
\(343\) 17.9615 0.969829
\(344\) 0 0
\(345\) −0.333712 −0.0179665
\(346\) 0 0
\(347\) −33.3477 −1.79020 −0.895100 0.445865i \(-0.852896\pi\)
−0.895100 + 0.445865i \(0.852896\pi\)
\(348\) 0 0
\(349\) 16.4860 0.882475 0.441238 0.897390i \(-0.354540\pi\)
0.441238 + 0.897390i \(0.354540\pi\)
\(350\) 0 0
\(351\) −0.606031 −0.0323475
\(352\) 0 0
\(353\) −26.5765 −1.41453 −0.707263 0.706950i \(-0.750071\pi\)
−0.707263 + 0.706950i \(0.750071\pi\)
\(354\) 0 0
\(355\) −2.59723 −0.137847
\(356\) 0 0
\(357\) 5.81864 0.307955
\(358\) 0 0
\(359\) 26.3425 1.39030 0.695152 0.718863i \(-0.255337\pi\)
0.695152 + 0.718863i \(0.255337\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 25.6046 1.34389
\(364\) 0 0
\(365\) −3.34137 −0.174895
\(366\) 0 0
\(367\) 7.93086 0.413987 0.206994 0.978342i \(-0.433632\pi\)
0.206994 + 0.978342i \(0.433632\pi\)
\(368\) 0 0
\(369\) −5.02191 −0.261430
\(370\) 0 0
\(371\) 4.26722 0.221543
\(372\) 0 0
\(373\) −20.1490 −1.04328 −0.521638 0.853167i \(-0.674679\pi\)
−0.521638 + 0.853167i \(0.674679\pi\)
\(374\) 0 0
\(375\) −11.4909 −0.593387
\(376\) 0 0
\(377\) −9.07649 −0.467463
\(378\) 0 0
\(379\) 2.74775 0.141142 0.0705712 0.997507i \(-0.477518\pi\)
0.0705712 + 0.997507i \(0.477518\pi\)
\(380\) 0 0
\(381\) −32.6022 −1.67026
\(382\) 0 0
\(383\) 18.5199 0.946321 0.473160 0.880976i \(-0.343113\pi\)
0.473160 + 0.880976i \(0.343113\pi\)
\(384\) 0 0
\(385\) 1.23918 0.0631543
\(386\) 0 0
\(387\) −30.4705 −1.54890
\(388\) 0 0
\(389\) 16.0162 0.812052 0.406026 0.913861i \(-0.366914\pi\)
0.406026 + 0.913861i \(0.366914\pi\)
\(390\) 0 0
\(391\) 0.160737 0.00812883
\(392\) 0 0
\(393\) −27.3003 −1.37712
\(394\) 0 0
\(395\) −2.95615 −0.148740
\(396\) 0 0
\(397\) −26.7822 −1.34416 −0.672080 0.740479i \(-0.734599\pi\)
−0.672080 + 0.740479i \(0.734599\pi\)
\(398\) 0 0
\(399\) 10.2609 0.513688
\(400\) 0 0
\(401\) 11.0341 0.551018 0.275509 0.961299i \(-0.411154\pi\)
0.275509 + 0.961299i \(0.411154\pi\)
\(402\) 0 0
\(403\) 1.68376 0.0838739
\(404\) 0 0
\(405\) 4.70338 0.233713
\(406\) 0 0
\(407\) 6.05236 0.300004
\(408\) 0 0
\(409\) −5.49748 −0.271833 −0.135916 0.990720i \(-0.543398\pi\)
−0.135916 + 0.990720i \(0.543398\pi\)
\(410\) 0 0
\(411\) −24.5487 −1.21090
\(412\) 0 0
\(413\) −30.4108 −1.49642
\(414\) 0 0
\(415\) 8.89014 0.436400
\(416\) 0 0
\(417\) −2.04088 −0.0999422
\(418\) 0 0
\(419\) −18.5023 −0.903897 −0.451949 0.892044i \(-0.649271\pi\)
−0.451949 + 0.892044i \(0.649271\pi\)
\(420\) 0 0
\(421\) −28.2312 −1.37591 −0.687953 0.725755i \(-0.741490\pi\)
−0.687953 + 0.725755i \(0.741490\pi\)
\(422\) 0 0
\(423\) −0.745743 −0.0362593
\(424\) 0 0
\(425\) 2.69941 0.130940
\(426\) 0 0
\(427\) −15.3751 −0.744055
\(428\) 0 0
\(429\) −1.64913 −0.0796206
\(430\) 0 0
\(431\) −2.69590 −0.129857 −0.0649285 0.997890i \(-0.520682\pi\)
−0.0649285 + 0.997890i \(0.520682\pi\)
\(432\) 0 0
\(433\) 19.3997 0.932291 0.466145 0.884708i \(-0.345642\pi\)
0.466145 + 0.884708i \(0.345642\pi\)
\(434\) 0 0
\(435\) 9.24130 0.443087
\(436\) 0 0
\(437\) 0.283453 0.0135594
\(438\) 0 0
\(439\) −36.3458 −1.73469 −0.867344 0.497708i \(-0.834175\pi\)
−0.867344 + 0.497708i \(0.834175\pi\)
\(440\) 0 0
\(441\) 31.1844 1.48497
\(442\) 0 0
\(443\) −19.9977 −0.950120 −0.475060 0.879953i \(-0.657574\pi\)
−0.475060 + 0.879953i \(0.657574\pi\)
\(444\) 0 0
\(445\) −5.51106 −0.261249
\(446\) 0 0
\(447\) −47.4920 −2.24629
\(448\) 0 0
\(449\) −9.85329 −0.465006 −0.232503 0.972596i \(-0.574691\pi\)
−0.232503 + 0.972596i \(0.574691\pi\)
\(450\) 0 0
\(451\) 1.07064 0.0504145
\(452\) 0 0
\(453\) 43.2801 2.03348
\(454\) 0 0
\(455\) 2.41586 0.113257
\(456\) 0 0
\(457\) 24.0250 1.12384 0.561922 0.827190i \(-0.310062\pi\)
0.561922 + 0.827190i \(0.310062\pi\)
\(458\) 0 0
\(459\) −0.297204 −0.0138723
\(460\) 0 0
\(461\) 26.0400 1.21280 0.606401 0.795159i \(-0.292613\pi\)
0.606401 + 0.795159i \(0.292613\pi\)
\(462\) 0 0
\(463\) 12.1893 0.566483 0.283241 0.959049i \(-0.408590\pi\)
0.283241 + 0.959049i \(0.408590\pi\)
\(464\) 0 0
\(465\) −1.71433 −0.0795002
\(466\) 0 0
\(467\) 11.9943 0.555030 0.277515 0.960721i \(-0.410489\pi\)
0.277515 + 0.960721i \(0.410489\pi\)
\(468\) 0 0
\(469\) 55.4925 2.56241
\(470\) 0 0
\(471\) 12.7267 0.586416
\(472\) 0 0
\(473\) 6.49612 0.298692
\(474\) 0 0
\(475\) 4.76028 0.218417
\(476\) 0 0
\(477\) 2.78204 0.127381
\(478\) 0 0
\(479\) 37.4019 1.70894 0.854469 0.519503i \(-0.173883\pi\)
0.854469 + 0.519503i \(0.173883\pi\)
\(480\) 0 0
\(481\) 11.7995 0.538010
\(482\) 0 0
\(483\) 2.90848 0.132341
\(484\) 0 0
\(485\) −8.22334 −0.373403
\(486\) 0 0
\(487\) −5.58556 −0.253106 −0.126553 0.991960i \(-0.540391\pi\)
−0.126553 + 0.991960i \(0.540391\pi\)
\(488\) 0 0
\(489\) 55.2777 2.49974
\(490\) 0 0
\(491\) −0.376459 −0.0169893 −0.00849467 0.999964i \(-0.502704\pi\)
−0.00849467 + 0.999964i \(0.502704\pi\)
\(492\) 0 0
\(493\) −4.45121 −0.200472
\(494\) 0 0
\(495\) 0.807889 0.0363119
\(496\) 0 0
\(497\) 22.6363 1.01538
\(498\) 0 0
\(499\) 4.55394 0.203862 0.101931 0.994791i \(-0.467498\pi\)
0.101931 + 0.994791i \(0.467498\pi\)
\(500\) 0 0
\(501\) 43.4948 1.94320
\(502\) 0 0
\(503\) 21.1855 0.944616 0.472308 0.881433i \(-0.343421\pi\)
0.472308 + 0.881433i \(0.343421\pi\)
\(504\) 0 0
\(505\) 3.22691 0.143596
\(506\) 0 0
\(507\) 28.0446 1.24550
\(508\) 0 0
\(509\) 23.8635 1.05773 0.528865 0.848706i \(-0.322618\pi\)
0.528865 + 0.848706i \(0.322618\pi\)
\(510\) 0 0
\(511\) 29.1218 1.28827
\(512\) 0 0
\(513\) −0.524106 −0.0231398
\(514\) 0 0
\(515\) −1.63787 −0.0721733
\(516\) 0 0
\(517\) 0.158988 0.00699227
\(518\) 0 0
\(519\) −24.8165 −1.08932
\(520\) 0 0
\(521\) 32.2098 1.41114 0.705568 0.708642i \(-0.250692\pi\)
0.705568 + 0.708642i \(0.250692\pi\)
\(522\) 0 0
\(523\) −2.73250 −0.119484 −0.0597420 0.998214i \(-0.519028\pi\)
−0.0597420 + 0.998214i \(0.519028\pi\)
\(524\) 0 0
\(525\) 48.8448 2.13176
\(526\) 0 0
\(527\) 0.825732 0.0359695
\(528\) 0 0
\(529\) −22.9197 −0.996507
\(530\) 0 0
\(531\) −19.8265 −0.860396
\(532\) 0 0
\(533\) 2.08728 0.0904103
\(534\) 0 0
\(535\) 4.67698 0.202204
\(536\) 0 0
\(537\) 28.3321 1.22262
\(538\) 0 0
\(539\) −6.64831 −0.286363
\(540\) 0 0
\(541\) −21.6113 −0.929143 −0.464572 0.885536i \(-0.653792\pi\)
−0.464572 + 0.885536i \(0.653792\pi\)
\(542\) 0 0
\(543\) 25.8520 1.10942
\(544\) 0 0
\(545\) −0.0954939 −0.00409051
\(546\) 0 0
\(547\) −14.0368 −0.600168 −0.300084 0.953913i \(-0.597015\pi\)
−0.300084 + 0.953913i \(0.597015\pi\)
\(548\) 0 0
\(549\) −10.0239 −0.427810
\(550\) 0 0
\(551\) −7.84950 −0.334400
\(552\) 0 0
\(553\) 25.7645 1.09562
\(554\) 0 0
\(555\) −12.0137 −0.509955
\(556\) 0 0
\(557\) 17.4768 0.740517 0.370258 0.928929i \(-0.379269\pi\)
0.370258 + 0.928929i \(0.379269\pi\)
\(558\) 0 0
\(559\) 12.6646 0.535656
\(560\) 0 0
\(561\) −0.808749 −0.0341454
\(562\) 0 0
\(563\) 5.49829 0.231725 0.115863 0.993265i \(-0.463037\pi\)
0.115863 + 0.993265i \(0.463037\pi\)
\(564\) 0 0
\(565\) 6.76968 0.284803
\(566\) 0 0
\(567\) −40.9925 −1.72152
\(568\) 0 0
\(569\) −0.659955 −0.0276668 −0.0138334 0.999904i \(-0.504403\pi\)
−0.0138334 + 0.999904i \(0.504403\pi\)
\(570\) 0 0
\(571\) 40.4557 1.69302 0.846509 0.532374i \(-0.178700\pi\)
0.846509 + 0.532374i \(0.178700\pi\)
\(572\) 0 0
\(573\) 43.0866 1.79997
\(574\) 0 0
\(575\) 1.34931 0.0562703
\(576\) 0 0
\(577\) −10.5897 −0.440855 −0.220428 0.975403i \(-0.570745\pi\)
−0.220428 + 0.975403i \(0.570745\pi\)
\(578\) 0 0
\(579\) 35.4230 1.47213
\(580\) 0 0
\(581\) −77.4824 −3.21451
\(582\) 0 0
\(583\) −0.593113 −0.0245642
\(584\) 0 0
\(585\) 1.57503 0.0651196
\(586\) 0 0
\(587\) −26.2330 −1.08275 −0.541376 0.840780i \(-0.682097\pi\)
−0.541376 + 0.840780i \(0.682097\pi\)
\(588\) 0 0
\(589\) 1.45614 0.0599993
\(590\) 0 0
\(591\) −19.6416 −0.807946
\(592\) 0 0
\(593\) 42.9710 1.76461 0.882304 0.470680i \(-0.155991\pi\)
0.882304 + 0.470680i \(0.155991\pi\)
\(594\) 0 0
\(595\) 1.18476 0.0485705
\(596\) 0 0
\(597\) 63.0038 2.57858
\(598\) 0 0
\(599\) −20.4694 −0.836355 −0.418178 0.908365i \(-0.637331\pi\)
−0.418178 + 0.908365i \(0.637331\pi\)
\(600\) 0 0
\(601\) 8.64710 0.352723 0.176361 0.984325i \(-0.443567\pi\)
0.176361 + 0.984325i \(0.443567\pi\)
\(602\) 0 0
\(603\) 36.1787 1.47331
\(604\) 0 0
\(605\) 5.21348 0.211958
\(606\) 0 0
\(607\) −29.5194 −1.19815 −0.599077 0.800691i \(-0.704466\pi\)
−0.599077 + 0.800691i \(0.704466\pi\)
\(608\) 0 0
\(609\) −80.5430 −3.26377
\(610\) 0 0
\(611\) 0.309957 0.0125395
\(612\) 0 0
\(613\) −14.6360 −0.591144 −0.295572 0.955320i \(-0.595510\pi\)
−0.295572 + 0.955320i \(0.595510\pi\)
\(614\) 0 0
\(615\) −2.12519 −0.0856958
\(616\) 0 0
\(617\) −5.60037 −0.225462 −0.112731 0.993626i \(-0.535960\pi\)
−0.112731 + 0.993626i \(0.535960\pi\)
\(618\) 0 0
\(619\) −10.0552 −0.404151 −0.202075 0.979370i \(-0.564769\pi\)
−0.202075 + 0.979370i \(0.564769\pi\)
\(620\) 0 0
\(621\) −0.148559 −0.00596148
\(622\) 0 0
\(623\) 48.0319 1.92436
\(624\) 0 0
\(625\) 21.4617 0.858468
\(626\) 0 0
\(627\) −1.42619 −0.0569567
\(628\) 0 0
\(629\) 5.78659 0.230726
\(630\) 0 0
\(631\) 42.9043 1.70799 0.853996 0.520280i \(-0.174172\pi\)
0.853996 + 0.520280i \(0.174172\pi\)
\(632\) 0 0
\(633\) 58.1675 2.31195
\(634\) 0 0
\(635\) −6.63829 −0.263433
\(636\) 0 0
\(637\) −12.9613 −0.513546
\(638\) 0 0
\(639\) 14.7579 0.583812
\(640\) 0 0
\(641\) −13.7730 −0.544003 −0.272001 0.962297i \(-0.587686\pi\)
−0.272001 + 0.962297i \(0.587686\pi\)
\(642\) 0 0
\(643\) −33.2396 −1.31084 −0.655421 0.755263i \(-0.727509\pi\)
−0.655421 + 0.755263i \(0.727509\pi\)
\(644\) 0 0
\(645\) −12.8946 −0.507724
\(646\) 0 0
\(647\) −37.8612 −1.48848 −0.744238 0.667914i \(-0.767187\pi\)
−0.744238 + 0.667914i \(0.767187\pi\)
\(648\) 0 0
\(649\) 4.22688 0.165920
\(650\) 0 0
\(651\) 14.9413 0.585597
\(652\) 0 0
\(653\) 24.1029 0.943219 0.471610 0.881807i \(-0.343673\pi\)
0.471610 + 0.881807i \(0.343673\pi\)
\(654\) 0 0
\(655\) −5.55875 −0.217199
\(656\) 0 0
\(657\) 18.9861 0.740720
\(658\) 0 0
\(659\) −46.9261 −1.82798 −0.913991 0.405735i \(-0.867016\pi\)
−0.913991 + 0.405735i \(0.867016\pi\)
\(660\) 0 0
\(661\) 11.8119 0.459431 0.229715 0.973258i \(-0.426220\pi\)
0.229715 + 0.973258i \(0.426220\pi\)
\(662\) 0 0
\(663\) −1.57671 −0.0612343
\(664\) 0 0
\(665\) 2.08928 0.0810186
\(666\) 0 0
\(667\) −2.22496 −0.0861509
\(668\) 0 0
\(669\) 7.99757 0.309204
\(670\) 0 0
\(671\) 2.13704 0.0824994
\(672\) 0 0
\(673\) −27.1703 −1.04734 −0.523668 0.851922i \(-0.675437\pi\)
−0.523668 + 0.851922i \(0.675437\pi\)
\(674\) 0 0
\(675\) −2.49489 −0.0960285
\(676\) 0 0
\(677\) −24.4682 −0.940390 −0.470195 0.882563i \(-0.655816\pi\)
−0.470195 + 0.882563i \(0.655816\pi\)
\(678\) 0 0
\(679\) 71.6709 2.75048
\(680\) 0 0
\(681\) 33.0441 1.26625
\(682\) 0 0
\(683\) −28.7130 −1.09867 −0.549337 0.835601i \(-0.685120\pi\)
−0.549337 + 0.835601i \(0.685120\pi\)
\(684\) 0 0
\(685\) −4.99849 −0.190982
\(686\) 0 0
\(687\) 68.3512 2.60776
\(688\) 0 0
\(689\) −1.15631 −0.0440520
\(690\) 0 0
\(691\) −23.2097 −0.882938 −0.441469 0.897276i \(-0.645543\pi\)
−0.441469 + 0.897276i \(0.645543\pi\)
\(692\) 0 0
\(693\) −7.04119 −0.267473
\(694\) 0 0
\(695\) −0.415554 −0.0157629
\(696\) 0 0
\(697\) 1.02363 0.0387726
\(698\) 0 0
\(699\) 60.6785 2.29507
\(700\) 0 0
\(701\) 14.2814 0.539402 0.269701 0.962944i \(-0.413075\pi\)
0.269701 + 0.962944i \(0.413075\pi\)
\(702\) 0 0
\(703\) 10.2044 0.384866
\(704\) 0 0
\(705\) −0.315585 −0.0118856
\(706\) 0 0
\(707\) −28.1243 −1.05772
\(708\) 0 0
\(709\) −14.5116 −0.544993 −0.272497 0.962157i \(-0.587849\pi\)
−0.272497 + 0.962157i \(0.587849\pi\)
\(710\) 0 0
\(711\) 16.7973 0.629948
\(712\) 0 0
\(713\) 0.412747 0.0154575
\(714\) 0 0
\(715\) −0.335787 −0.0125577
\(716\) 0 0
\(717\) −46.8318 −1.74897
\(718\) 0 0
\(719\) 49.2609 1.83712 0.918561 0.395280i \(-0.129353\pi\)
0.918561 + 0.395280i \(0.129353\pi\)
\(720\) 0 0
\(721\) 14.2750 0.531627
\(722\) 0 0
\(723\) −15.3160 −0.569608
\(724\) 0 0
\(725\) −37.3658 −1.38773
\(726\) 0 0
\(727\) −17.9463 −0.665593 −0.332796 0.942999i \(-0.607992\pi\)
−0.332796 + 0.942999i \(0.607992\pi\)
\(728\) 0 0
\(729\) −22.9445 −0.849798
\(730\) 0 0
\(731\) 6.21086 0.229717
\(732\) 0 0
\(733\) −14.7118 −0.543393 −0.271697 0.962383i \(-0.587585\pi\)
−0.271697 + 0.962383i \(0.587585\pi\)
\(734\) 0 0
\(735\) 13.1967 0.486767
\(736\) 0 0
\(737\) −7.71307 −0.284115
\(738\) 0 0
\(739\) −13.6777 −0.503141 −0.251570 0.967839i \(-0.580947\pi\)
−0.251570 + 0.967839i \(0.580947\pi\)
\(740\) 0 0
\(741\) −2.78046 −0.102143
\(742\) 0 0
\(743\) 33.9122 1.24412 0.622059 0.782971i \(-0.286296\pi\)
0.622059 + 0.782971i \(0.286296\pi\)
\(744\) 0 0
\(745\) −9.67008 −0.354284
\(746\) 0 0
\(747\) −50.5151 −1.84825
\(748\) 0 0
\(749\) −40.7625 −1.48943
\(750\) 0 0
\(751\) 20.4999 0.748050 0.374025 0.927419i \(-0.377977\pi\)
0.374025 + 0.927419i \(0.377977\pi\)
\(752\) 0 0
\(753\) 33.8473 1.23347
\(754\) 0 0
\(755\) 8.81249 0.320719
\(756\) 0 0
\(757\) −31.6654 −1.15090 −0.575450 0.817837i \(-0.695173\pi\)
−0.575450 + 0.817837i \(0.695173\pi\)
\(758\) 0 0
\(759\) −0.404258 −0.0146736
\(760\) 0 0
\(761\) −12.6218 −0.457540 −0.228770 0.973480i \(-0.573470\pi\)
−0.228770 + 0.973480i \(0.573470\pi\)
\(762\) 0 0
\(763\) 0.832281 0.0301306
\(764\) 0 0
\(765\) 0.772413 0.0279266
\(766\) 0 0
\(767\) 8.24058 0.297550
\(768\) 0 0
\(769\) −47.2496 −1.70386 −0.851932 0.523652i \(-0.824569\pi\)
−0.851932 + 0.523652i \(0.824569\pi\)
\(770\) 0 0
\(771\) −56.8051 −2.04579
\(772\) 0 0
\(773\) 39.3017 1.41358 0.706791 0.707422i \(-0.250142\pi\)
0.706791 + 0.707422i \(0.250142\pi\)
\(774\) 0 0
\(775\) 6.93165 0.248992
\(776\) 0 0
\(777\) 104.706 3.75632
\(778\) 0 0
\(779\) 1.80512 0.0646751
\(780\) 0 0
\(781\) −3.14628 −0.112583
\(782\) 0 0
\(783\) 4.11397 0.147021
\(784\) 0 0
\(785\) 2.59135 0.0924894
\(786\) 0 0
\(787\) 16.7525 0.597163 0.298581 0.954384i \(-0.403487\pi\)
0.298581 + 0.954384i \(0.403487\pi\)
\(788\) 0 0
\(789\) 60.9133 2.16857
\(790\) 0 0
\(791\) −59.0015 −2.09785
\(792\) 0 0
\(793\) 4.16629 0.147949
\(794\) 0 0
\(795\) 1.17731 0.0417549
\(796\) 0 0
\(797\) 43.4218 1.53808 0.769039 0.639202i \(-0.220735\pi\)
0.769039 + 0.639202i \(0.220735\pi\)
\(798\) 0 0
\(799\) 0.152006 0.00537759
\(800\) 0 0
\(801\) 31.3147 1.10645
\(802\) 0 0
\(803\) −4.04773 −0.142841
\(804\) 0 0
\(805\) 0.592211 0.0208727
\(806\) 0 0
\(807\) −24.0601 −0.846956
\(808\) 0 0
\(809\) −42.1872 −1.48322 −0.741611 0.670831i \(-0.765938\pi\)
−0.741611 + 0.670831i \(0.765938\pi\)
\(810\) 0 0
\(811\) 5.39281 0.189367 0.0946837 0.995507i \(-0.469816\pi\)
0.0946837 + 0.995507i \(0.469816\pi\)
\(812\) 0 0
\(813\) 20.3256 0.712850
\(814\) 0 0
\(815\) 11.2554 0.394258
\(816\) 0 0
\(817\) 10.9526 0.383182
\(818\) 0 0
\(819\) −13.7273 −0.479669
\(820\) 0 0
\(821\) 37.9182 1.32335 0.661677 0.749789i \(-0.269845\pi\)
0.661677 + 0.749789i \(0.269845\pi\)
\(822\) 0 0
\(823\) −42.2072 −1.47125 −0.735625 0.677389i \(-0.763111\pi\)
−0.735625 + 0.677389i \(0.763111\pi\)
\(824\) 0 0
\(825\) −6.78908 −0.236365
\(826\) 0 0
\(827\) 9.53128 0.331435 0.165718 0.986173i \(-0.447006\pi\)
0.165718 + 0.986173i \(0.447006\pi\)
\(828\) 0 0
\(829\) −7.77654 −0.270091 −0.135045 0.990839i \(-0.543118\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(830\) 0 0
\(831\) −32.7791 −1.13710
\(832\) 0 0
\(833\) −6.35637 −0.220235
\(834\) 0 0
\(835\) 8.85619 0.306481
\(836\) 0 0
\(837\) −0.763173 −0.0263791
\(838\) 0 0
\(839\) −9.60525 −0.331610 −0.165805 0.986159i \(-0.553022\pi\)
−0.165805 + 0.986159i \(0.553022\pi\)
\(840\) 0 0
\(841\) 32.6147 1.12464
\(842\) 0 0
\(843\) −19.7641 −0.680712
\(844\) 0 0
\(845\) 5.71030 0.196440
\(846\) 0 0
\(847\) −45.4383 −1.56128
\(848\) 0 0
\(849\) 43.1060 1.47939
\(850\) 0 0
\(851\) 2.89246 0.0991523
\(852\) 0 0
\(853\) −3.76954 −0.129066 −0.0645332 0.997916i \(-0.520556\pi\)
−0.0645332 + 0.997916i \(0.520556\pi\)
\(854\) 0 0
\(855\) 1.36212 0.0465834
\(856\) 0 0
\(857\) −31.8511 −1.08801 −0.544007 0.839081i \(-0.683094\pi\)
−0.544007 + 0.839081i \(0.683094\pi\)
\(858\) 0 0
\(859\) −45.7453 −1.56081 −0.780404 0.625275i \(-0.784987\pi\)
−0.780404 + 0.625275i \(0.784987\pi\)
\(860\) 0 0
\(861\) 18.5222 0.631233
\(862\) 0 0
\(863\) 14.2650 0.485586 0.242793 0.970078i \(-0.421936\pi\)
0.242793 + 0.970078i \(0.421936\pi\)
\(864\) 0 0
\(865\) −5.05301 −0.171807
\(866\) 0 0
\(867\) 40.1047 1.36203
\(868\) 0 0
\(869\) −3.58108 −0.121480
\(870\) 0 0
\(871\) −15.0371 −0.509514
\(872\) 0 0
\(873\) 46.7262 1.58144
\(874\) 0 0
\(875\) 20.3919 0.689373
\(876\) 0 0
\(877\) 4.98368 0.168287 0.0841434 0.996454i \(-0.473185\pi\)
0.0841434 + 0.996454i \(0.473185\pi\)
\(878\) 0 0
\(879\) −61.0561 −2.05937
\(880\) 0 0
\(881\) −35.2448 −1.18743 −0.593713 0.804677i \(-0.702339\pi\)
−0.593713 + 0.804677i \(0.702339\pi\)
\(882\) 0 0
\(883\) 17.1327 0.576562 0.288281 0.957546i \(-0.406916\pi\)
0.288281 + 0.957546i \(0.406916\pi\)
\(884\) 0 0
\(885\) −8.39022 −0.282034
\(886\) 0 0
\(887\) −12.7821 −0.429180 −0.214590 0.976704i \(-0.568841\pi\)
−0.214590 + 0.976704i \(0.568841\pi\)
\(888\) 0 0
\(889\) 57.8563 1.94044
\(890\) 0 0
\(891\) 5.69767 0.190879
\(892\) 0 0
\(893\) 0.268056 0.00897016
\(894\) 0 0
\(895\) 5.76884 0.192831
\(896\) 0 0
\(897\) −0.788128 −0.0263148
\(898\) 0 0
\(899\) −11.4300 −0.381211
\(900\) 0 0
\(901\) −0.567069 −0.0188918
\(902\) 0 0
\(903\) 112.383 3.73988
\(904\) 0 0
\(905\) 5.26386 0.174977
\(906\) 0 0
\(907\) −40.2799 −1.33747 −0.668735 0.743501i \(-0.733164\pi\)
−0.668735 + 0.743501i \(0.733164\pi\)
\(908\) 0 0
\(909\) −18.3358 −0.608160
\(910\) 0 0
\(911\) 41.3166 1.36888 0.684440 0.729069i \(-0.260047\pi\)
0.684440 + 0.729069i \(0.260047\pi\)
\(912\) 0 0
\(913\) 10.7695 0.356418
\(914\) 0 0
\(915\) −4.24195 −0.140234
\(916\) 0 0
\(917\) 48.4476 1.59988
\(918\) 0 0
\(919\) 56.6644 1.86919 0.934593 0.355720i \(-0.115764\pi\)
0.934593 + 0.355720i \(0.115764\pi\)
\(920\) 0 0
\(921\) 15.8330 0.521714
\(922\) 0 0
\(923\) −6.13389 −0.201899
\(924\) 0 0
\(925\) 48.5758 1.59716
\(926\) 0 0
\(927\) 9.30664 0.305670
\(928\) 0 0
\(929\) 41.3730 1.35740 0.678702 0.734414i \(-0.262543\pi\)
0.678702 + 0.734414i \(0.262543\pi\)
\(930\) 0 0
\(931\) −11.2092 −0.367366
\(932\) 0 0
\(933\) −8.42868 −0.275943
\(934\) 0 0
\(935\) −0.164674 −0.00538540
\(936\) 0 0
\(937\) 4.98784 0.162946 0.0814728 0.996676i \(-0.474038\pi\)
0.0814728 + 0.996676i \(0.474038\pi\)
\(938\) 0 0
\(939\) −26.5602 −0.866760
\(940\) 0 0
\(941\) −17.1052 −0.557612 −0.278806 0.960347i \(-0.589939\pi\)
−0.278806 + 0.960347i \(0.589939\pi\)
\(942\) 0 0
\(943\) 0.511666 0.0166621
\(944\) 0 0
\(945\) −1.09500 −0.0356204
\(946\) 0 0
\(947\) −0.775986 −0.0252162 −0.0126081 0.999921i \(-0.504013\pi\)
−0.0126081 + 0.999921i \(0.504013\pi\)
\(948\) 0 0
\(949\) −7.89131 −0.256163
\(950\) 0 0
\(951\) 20.4851 0.664276
\(952\) 0 0
\(953\) −24.0180 −0.778018 −0.389009 0.921234i \(-0.627182\pi\)
−0.389009 + 0.921234i \(0.627182\pi\)
\(954\) 0 0
\(955\) 8.77308 0.283890
\(956\) 0 0
\(957\) 11.1949 0.361880
\(958\) 0 0
\(959\) 43.5645 1.40677
\(960\) 0 0
\(961\) −28.8797 −0.931602
\(962\) 0 0
\(963\) −26.5753 −0.856378
\(964\) 0 0
\(965\) 7.21265 0.232183
\(966\) 0 0
\(967\) 7.13796 0.229541 0.114771 0.993392i \(-0.463387\pi\)
0.114771 + 0.993392i \(0.463387\pi\)
\(968\) 0 0
\(969\) −1.36357 −0.0438040
\(970\) 0 0
\(971\) −14.3344 −0.460014 −0.230007 0.973189i \(-0.573875\pi\)
−0.230007 + 0.973189i \(0.573875\pi\)
\(972\) 0 0
\(973\) 3.62178 0.116109
\(974\) 0 0
\(975\) −13.2358 −0.423884
\(976\) 0 0
\(977\) −38.5586 −1.23360 −0.616800 0.787120i \(-0.711571\pi\)
−0.616800 + 0.787120i \(0.711571\pi\)
\(978\) 0 0
\(979\) −6.67610 −0.213369
\(980\) 0 0
\(981\) 0.542610 0.0173242
\(982\) 0 0
\(983\) −17.3991 −0.554944 −0.277472 0.960734i \(-0.589497\pi\)
−0.277472 + 0.960734i \(0.589497\pi\)
\(984\) 0 0
\(985\) −3.99932 −0.127429
\(986\) 0 0
\(987\) 2.75050 0.0875493
\(988\) 0 0
\(989\) 3.10454 0.0987185
\(990\) 0 0
\(991\) 47.6058 1.51225 0.756123 0.654429i \(-0.227091\pi\)
0.756123 + 0.654429i \(0.227091\pi\)
\(992\) 0 0
\(993\) −37.9950 −1.20573
\(994\) 0 0
\(995\) 12.8285 0.406692
\(996\) 0 0
\(997\) −50.9178 −1.61258 −0.806292 0.591518i \(-0.798529\pi\)
−0.806292 + 0.591518i \(0.798529\pi\)
\(998\) 0 0
\(999\) −5.34818 −0.169209
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 \(a_p\))