Properties

Label 8008.2.a.y.1.4
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.97367\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.97367 q^{3} -1.63177 q^{5} +1.00000 q^{7} +0.895375 q^{9} +O(q^{10})\) \(q-1.97367 q^{3} -1.63177 q^{5} +1.00000 q^{7} +0.895375 q^{9} -1.00000 q^{11} -1.00000 q^{13} +3.22057 q^{15} +7.91396 q^{17} -4.55443 q^{19} -1.97367 q^{21} -1.32230 q^{23} -2.33734 q^{25} +4.15384 q^{27} +5.69820 q^{29} -4.04820 q^{31} +1.97367 q^{33} -1.63177 q^{35} -10.2298 q^{37} +1.97367 q^{39} +6.71462 q^{41} -1.42459 q^{43} -1.46104 q^{45} -8.30825 q^{47} +1.00000 q^{49} -15.6196 q^{51} +1.91085 q^{53} +1.63177 q^{55} +8.98894 q^{57} +3.45460 q^{59} +1.01972 q^{61} +0.895375 q^{63} +1.63177 q^{65} +8.79914 q^{67} +2.60979 q^{69} +10.9746 q^{71} +5.48196 q^{73} +4.61313 q^{75} -1.00000 q^{77} +12.9320 q^{79} -10.8844 q^{81} -10.3136 q^{83} -12.9137 q^{85} -11.2464 q^{87} -7.86173 q^{89} -1.00000 q^{91} +7.98981 q^{93} +7.43177 q^{95} -5.14705 q^{97} -0.895375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) −1.97367 −1.13950 −0.569750 0.821818i \(-0.692960\pi\)
−0.569750 + 0.821818i \(0.692960\pi\)
\(4\) 0 0
\(5\) −1.63177 −0.729748 −0.364874 0.931057i \(-0.618888\pi\)
−0.364874 + 0.931057i \(0.618888\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0.895375 0.298458
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 3.22057 0.831548
\(16\) 0 0
\(17\) 7.91396 1.91942 0.959709 0.280996i \(-0.0906649\pi\)
0.959709 + 0.280996i \(0.0906649\pi\)
\(18\) 0 0
\(19\) −4.55443 −1.04486 −0.522429 0.852683i \(-0.674974\pi\)
−0.522429 + 0.852683i \(0.674974\pi\)
\(20\) 0 0
\(21\) −1.97367 −0.430690
\(22\) 0 0
\(23\) −1.32230 −0.275719 −0.137860 0.990452i \(-0.544022\pi\)
−0.137860 + 0.990452i \(0.544022\pi\)
\(24\) 0 0
\(25\) −2.33734 −0.467467
\(26\) 0 0
\(27\) 4.15384 0.799406
\(28\) 0 0
\(29\) 5.69820 1.05813 0.529065 0.848582i \(-0.322543\pi\)
0.529065 + 0.848582i \(0.322543\pi\)
\(30\) 0 0
\(31\) −4.04820 −0.727078 −0.363539 0.931579i \(-0.618432\pi\)
−0.363539 + 0.931579i \(0.618432\pi\)
\(32\) 0 0
\(33\) 1.97367 0.343572
\(34\) 0 0
\(35\) −1.63177 −0.275819
\(36\) 0 0
\(37\) −10.2298 −1.68177 −0.840887 0.541211i \(-0.817966\pi\)
−0.840887 + 0.541211i \(0.817966\pi\)
\(38\) 0 0
\(39\) 1.97367 0.316040
\(40\) 0 0
\(41\) 6.71462 1.04865 0.524324 0.851519i \(-0.324318\pi\)
0.524324 + 0.851519i \(0.324318\pi\)
\(42\) 0 0
\(43\) −1.42459 −0.217249 −0.108624 0.994083i \(-0.534645\pi\)
−0.108624 + 0.994083i \(0.534645\pi\)
\(44\) 0 0
\(45\) −1.46104 −0.217799
\(46\) 0 0
\(47\) −8.30825 −1.21188 −0.605942 0.795509i \(-0.707204\pi\)
−0.605942 + 0.795509i \(0.707204\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −15.6196 −2.18717
\(52\) 0 0
\(53\) 1.91085 0.262475 0.131238 0.991351i \(-0.458105\pi\)
0.131238 + 0.991351i \(0.458105\pi\)
\(54\) 0 0
\(55\) 1.63177 0.220027
\(56\) 0 0
\(57\) 8.98894 1.19061
\(58\) 0 0
\(59\) 3.45460 0.449751 0.224876 0.974387i \(-0.427802\pi\)
0.224876 + 0.974387i \(0.427802\pi\)
\(60\) 0 0
\(61\) 1.01972 0.130561 0.0652806 0.997867i \(-0.479206\pi\)
0.0652806 + 0.997867i \(0.479206\pi\)
\(62\) 0 0
\(63\) 0.895375 0.112807
\(64\) 0 0
\(65\) 1.63177 0.202396
\(66\) 0 0
\(67\) 8.79914 1.07499 0.537493 0.843268i \(-0.319371\pi\)
0.537493 + 0.843268i \(0.319371\pi\)
\(68\) 0 0
\(69\) 2.60979 0.314182
\(70\) 0 0
\(71\) 10.9746 1.30245 0.651223 0.758886i \(-0.274256\pi\)
0.651223 + 0.758886i \(0.274256\pi\)
\(72\) 0 0
\(73\) 5.48196 0.641614 0.320807 0.947145i \(-0.396046\pi\)
0.320807 + 0.947145i \(0.396046\pi\)
\(74\) 0 0
\(75\) 4.61313 0.532679
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 12.9320 1.45497 0.727483 0.686126i \(-0.240690\pi\)
0.727483 + 0.686126i \(0.240690\pi\)
\(80\) 0 0
\(81\) −10.8844 −1.20938
\(82\) 0 0
\(83\) −10.3136 −1.13207 −0.566033 0.824383i \(-0.691523\pi\)
−0.566033 + 0.824383i \(0.691523\pi\)
\(84\) 0 0
\(85\) −12.9137 −1.40069
\(86\) 0 0
\(87\) −11.2464 −1.20574
\(88\) 0 0
\(89\) −7.86173 −0.833342 −0.416671 0.909057i \(-0.636803\pi\)
−0.416671 + 0.909057i \(0.636803\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 7.98981 0.828505
\(94\) 0 0
\(95\) 7.43177 0.762483
\(96\) 0 0
\(97\) −5.14705 −0.522604 −0.261302 0.965257i \(-0.584152\pi\)
−0.261302 + 0.965257i \(0.584152\pi\)
\(98\) 0 0
\(99\) −0.895375 −0.0899885
\(100\) 0 0
\(101\) 4.60174 0.457890 0.228945 0.973439i \(-0.426472\pi\)
0.228945 + 0.973439i \(0.426472\pi\)
\(102\) 0 0
\(103\) 18.2526 1.79848 0.899240 0.437455i \(-0.144120\pi\)
0.899240 + 0.437455i \(0.144120\pi\)
\(104\) 0 0
\(105\) 3.22057 0.314295
\(106\) 0 0
\(107\) −2.08351 −0.201420 −0.100710 0.994916i \(-0.532112\pi\)
−0.100710 + 0.994916i \(0.532112\pi\)
\(108\) 0 0
\(109\) 3.84603 0.368383 0.184191 0.982890i \(-0.441033\pi\)
0.184191 + 0.982890i \(0.441033\pi\)
\(110\) 0 0
\(111\) 20.1903 1.91638
\(112\) 0 0
\(113\) −0.663828 −0.0624477 −0.0312238 0.999512i \(-0.509940\pi\)
−0.0312238 + 0.999512i \(0.509940\pi\)
\(114\) 0 0
\(115\) 2.15769 0.201206
\(116\) 0 0
\(117\) −0.895375 −0.0827774
\(118\) 0 0
\(119\) 7.91396 0.725472
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −13.2524 −1.19493
\(124\) 0 0
\(125\) 11.9728 1.07088
\(126\) 0 0
\(127\) 17.9307 1.59109 0.795547 0.605892i \(-0.207184\pi\)
0.795547 + 0.605892i \(0.207184\pi\)
\(128\) 0 0
\(129\) 2.81168 0.247555
\(130\) 0 0
\(131\) −18.9519 −1.65584 −0.827918 0.560849i \(-0.810475\pi\)
−0.827918 + 0.560849i \(0.810475\pi\)
\(132\) 0 0
\(133\) −4.55443 −0.394919
\(134\) 0 0
\(135\) −6.77809 −0.583365
\(136\) 0 0
\(137\) 15.8019 1.35004 0.675022 0.737798i \(-0.264134\pi\)
0.675022 + 0.737798i \(0.264134\pi\)
\(138\) 0 0
\(139\) −16.3702 −1.38850 −0.694249 0.719735i \(-0.744264\pi\)
−0.694249 + 0.719735i \(0.744264\pi\)
\(140\) 0 0
\(141\) 16.3978 1.38094
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −9.29813 −0.772168
\(146\) 0 0
\(147\) −1.97367 −0.162786
\(148\) 0 0
\(149\) −9.93854 −0.814197 −0.407098 0.913384i \(-0.633459\pi\)
−0.407098 + 0.913384i \(0.633459\pi\)
\(150\) 0 0
\(151\) −17.6747 −1.43834 −0.719172 0.694832i \(-0.755478\pi\)
−0.719172 + 0.694832i \(0.755478\pi\)
\(152\) 0 0
\(153\) 7.08596 0.572866
\(154\) 0 0
\(155\) 6.60572 0.530584
\(156\) 0 0
\(157\) 2.39357 0.191028 0.0955138 0.995428i \(-0.469551\pi\)
0.0955138 + 0.995428i \(0.469551\pi\)
\(158\) 0 0
\(159\) −3.77139 −0.299090
\(160\) 0 0
\(161\) −1.32230 −0.104212
\(162\) 0 0
\(163\) −12.6284 −0.989133 −0.494567 0.869140i \(-0.664673\pi\)
−0.494567 + 0.869140i \(0.664673\pi\)
\(164\) 0 0
\(165\) −3.22057 −0.250721
\(166\) 0 0
\(167\) −5.02641 −0.388955 −0.194478 0.980907i \(-0.562301\pi\)
−0.194478 + 0.980907i \(0.562301\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.07792 −0.311846
\(172\) 0 0
\(173\) 21.1282 1.60635 0.803175 0.595744i \(-0.203143\pi\)
0.803175 + 0.595744i \(0.203143\pi\)
\(174\) 0 0
\(175\) −2.33734 −0.176686
\(176\) 0 0
\(177\) −6.81825 −0.512491
\(178\) 0 0
\(179\) 26.2300 1.96052 0.980261 0.197709i \(-0.0633502\pi\)
0.980261 + 0.197709i \(0.0633502\pi\)
\(180\) 0 0
\(181\) −3.57385 −0.265642 −0.132821 0.991140i \(-0.542404\pi\)
−0.132821 + 0.991140i \(0.542404\pi\)
\(182\) 0 0
\(183\) −2.01258 −0.148774
\(184\) 0 0
\(185\) 16.6927 1.22727
\(186\) 0 0
\(187\) −7.91396 −0.578726
\(188\) 0 0
\(189\) 4.15384 0.302147
\(190\) 0 0
\(191\) −19.5122 −1.41186 −0.705928 0.708283i \(-0.749470\pi\)
−0.705928 + 0.708283i \(0.749470\pi\)
\(192\) 0 0
\(193\) −8.80805 −0.634017 −0.317009 0.948423i \(-0.602678\pi\)
−0.317009 + 0.948423i \(0.602678\pi\)
\(194\) 0 0
\(195\) −3.22057 −0.230630
\(196\) 0 0
\(197\) 8.14547 0.580341 0.290170 0.956975i \(-0.406288\pi\)
0.290170 + 0.956975i \(0.406288\pi\)
\(198\) 0 0
\(199\) −18.7798 −1.33127 −0.665634 0.746278i \(-0.731839\pi\)
−0.665634 + 0.746278i \(0.731839\pi\)
\(200\) 0 0
\(201\) −17.3666 −1.22495
\(202\) 0 0
\(203\) 5.69820 0.399935
\(204\) 0 0
\(205\) −10.9567 −0.765249
\(206\) 0 0
\(207\) −1.18396 −0.0822906
\(208\) 0 0
\(209\) 4.55443 0.315037
\(210\) 0 0
\(211\) −4.75462 −0.327322 −0.163661 0.986517i \(-0.552330\pi\)
−0.163661 + 0.986517i \(0.552330\pi\)
\(212\) 0 0
\(213\) −21.6603 −1.48414
\(214\) 0 0
\(215\) 2.32461 0.158537
\(216\) 0 0
\(217\) −4.04820 −0.274810
\(218\) 0 0
\(219\) −10.8196 −0.731119
\(220\) 0 0
\(221\) −7.91396 −0.532351
\(222\) 0 0
\(223\) −12.2317 −0.819094 −0.409547 0.912289i \(-0.634313\pi\)
−0.409547 + 0.912289i \(0.634313\pi\)
\(224\) 0 0
\(225\) −2.09279 −0.139519
\(226\) 0 0
\(227\) −21.6766 −1.43873 −0.719364 0.694633i \(-0.755567\pi\)
−0.719364 + 0.694633i \(0.755567\pi\)
\(228\) 0 0
\(229\) −9.01919 −0.596005 −0.298002 0.954565i \(-0.596320\pi\)
−0.298002 + 0.954565i \(0.596320\pi\)
\(230\) 0 0
\(231\) 1.97367 0.129858
\(232\) 0 0
\(233\) 14.1749 0.928628 0.464314 0.885671i \(-0.346301\pi\)
0.464314 + 0.885671i \(0.346301\pi\)
\(234\) 0 0
\(235\) 13.5571 0.884370
\(236\) 0 0
\(237\) −25.5235 −1.65793
\(238\) 0 0
\(239\) −1.71344 −0.110834 −0.0554168 0.998463i \(-0.517649\pi\)
−0.0554168 + 0.998463i \(0.517649\pi\)
\(240\) 0 0
\(241\) 3.34256 0.215313 0.107657 0.994188i \(-0.465665\pi\)
0.107657 + 0.994188i \(0.465665\pi\)
\(242\) 0 0
\(243\) 9.02076 0.578682
\(244\) 0 0
\(245\) −1.63177 −0.104250
\(246\) 0 0
\(247\) 4.55443 0.289791
\(248\) 0 0
\(249\) 20.3557 1.28999
\(250\) 0 0
\(251\) −2.72119 −0.171760 −0.0858800 0.996305i \(-0.527370\pi\)
−0.0858800 + 0.996305i \(0.527370\pi\)
\(252\) 0 0
\(253\) 1.32230 0.0831324
\(254\) 0 0
\(255\) 25.4875 1.59609
\(256\) 0 0
\(257\) 8.97818 0.560044 0.280022 0.959994i \(-0.409658\pi\)
0.280022 + 0.959994i \(0.409658\pi\)
\(258\) 0 0
\(259\) −10.2298 −0.635650
\(260\) 0 0
\(261\) 5.10202 0.315807
\(262\) 0 0
\(263\) 13.8429 0.853591 0.426795 0.904348i \(-0.359642\pi\)
0.426795 + 0.904348i \(0.359642\pi\)
\(264\) 0 0
\(265\) −3.11806 −0.191541
\(266\) 0 0
\(267\) 15.5165 0.949592
\(268\) 0 0
\(269\) 16.8771 1.02901 0.514507 0.857486i \(-0.327975\pi\)
0.514507 + 0.857486i \(0.327975\pi\)
\(270\) 0 0
\(271\) 29.2049 1.77407 0.887036 0.461701i \(-0.152761\pi\)
0.887036 + 0.461701i \(0.152761\pi\)
\(272\) 0 0
\(273\) 1.97367 0.119452
\(274\) 0 0
\(275\) 2.33734 0.140947
\(276\) 0 0
\(277\) 13.7805 0.827992 0.413996 0.910279i \(-0.364133\pi\)
0.413996 + 0.910279i \(0.364133\pi\)
\(278\) 0 0
\(279\) −3.62466 −0.217002
\(280\) 0 0
\(281\) −21.6494 −1.29150 −0.645748 0.763550i \(-0.723454\pi\)
−0.645748 + 0.763550i \(0.723454\pi\)
\(282\) 0 0
\(283\) −22.7794 −1.35409 −0.677047 0.735940i \(-0.736740\pi\)
−0.677047 + 0.735940i \(0.736740\pi\)
\(284\) 0 0
\(285\) −14.6679 −0.868849
\(286\) 0 0
\(287\) 6.71462 0.396352
\(288\) 0 0
\(289\) 45.6308 2.68416
\(290\) 0 0
\(291\) 10.1586 0.595507
\(292\) 0 0
\(293\) −11.2136 −0.655104 −0.327552 0.944833i \(-0.606224\pi\)
−0.327552 + 0.944833i \(0.606224\pi\)
\(294\) 0 0
\(295\) −5.63711 −0.328205
\(296\) 0 0
\(297\) −4.15384 −0.241030
\(298\) 0 0
\(299\) 1.32230 0.0764707
\(300\) 0 0
\(301\) −1.42459 −0.0821123
\(302\) 0 0
\(303\) −9.08231 −0.521765
\(304\) 0 0
\(305\) −1.66394 −0.0952769
\(306\) 0 0
\(307\) −23.1176 −1.31939 −0.659696 0.751533i \(-0.729315\pi\)
−0.659696 + 0.751533i \(0.729315\pi\)
\(308\) 0 0
\(309\) −36.0246 −2.04937
\(310\) 0 0
\(311\) −30.6557 −1.73832 −0.869162 0.494527i \(-0.835341\pi\)
−0.869162 + 0.494527i \(0.835341\pi\)
\(312\) 0 0
\(313\) 27.8466 1.57398 0.786991 0.616965i \(-0.211638\pi\)
0.786991 + 0.616965i \(0.211638\pi\)
\(314\) 0 0
\(315\) −1.46104 −0.0823204
\(316\) 0 0
\(317\) −28.7754 −1.61619 −0.808093 0.589055i \(-0.799500\pi\)
−0.808093 + 0.589055i \(0.799500\pi\)
\(318\) 0 0
\(319\) −5.69820 −0.319038
\(320\) 0 0
\(321\) 4.11216 0.229518
\(322\) 0 0
\(323\) −36.0436 −2.00552
\(324\) 0 0
\(325\) 2.33734 0.129652
\(326\) 0 0
\(327\) −7.59080 −0.419772
\(328\) 0 0
\(329\) −8.30825 −0.458049
\(330\) 0 0
\(331\) 17.7925 0.977964 0.488982 0.872294i \(-0.337368\pi\)
0.488982 + 0.872294i \(0.337368\pi\)
\(332\) 0 0
\(333\) −9.15953 −0.501939
\(334\) 0 0
\(335\) −14.3582 −0.784470
\(336\) 0 0
\(337\) −2.33485 −0.127187 −0.0635936 0.997976i \(-0.520256\pi\)
−0.0635936 + 0.997976i \(0.520256\pi\)
\(338\) 0 0
\(339\) 1.31018 0.0711591
\(340\) 0 0
\(341\) 4.04820 0.219222
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −4.25857 −0.229274
\(346\) 0 0
\(347\) −10.4608 −0.561563 −0.280781 0.959772i \(-0.590594\pi\)
−0.280781 + 0.959772i \(0.590594\pi\)
\(348\) 0 0
\(349\) −27.4071 −1.46707 −0.733534 0.679653i \(-0.762131\pi\)
−0.733534 + 0.679653i \(0.762131\pi\)
\(350\) 0 0
\(351\) −4.15384 −0.221715
\(352\) 0 0
\(353\) −22.9597 −1.22202 −0.611011 0.791622i \(-0.709237\pi\)
−0.611011 + 0.791622i \(0.709237\pi\)
\(354\) 0 0
\(355\) −17.9080 −0.950458
\(356\) 0 0
\(357\) −15.6196 −0.826674
\(358\) 0 0
\(359\) −27.1039 −1.43049 −0.715244 0.698875i \(-0.753684\pi\)
−0.715244 + 0.698875i \(0.753684\pi\)
\(360\) 0 0
\(361\) 1.74284 0.0917284
\(362\) 0 0
\(363\) −1.97367 −0.103591
\(364\) 0 0
\(365\) −8.94527 −0.468217
\(366\) 0 0
\(367\) −8.87037 −0.463029 −0.231515 0.972831i \(-0.574368\pi\)
−0.231515 + 0.972831i \(0.574368\pi\)
\(368\) 0 0
\(369\) 6.01210 0.312977
\(370\) 0 0
\(371\) 1.91085 0.0992064
\(372\) 0 0
\(373\) 21.1903 1.09719 0.548596 0.836087i \(-0.315162\pi\)
0.548596 + 0.836087i \(0.315162\pi\)
\(374\) 0 0
\(375\) −23.6304 −1.22027
\(376\) 0 0
\(377\) −5.69820 −0.293472
\(378\) 0 0
\(379\) 6.52876 0.335360 0.167680 0.985841i \(-0.446372\pi\)
0.167680 + 0.985841i \(0.446372\pi\)
\(380\) 0 0
\(381\) −35.3893 −1.81305
\(382\) 0 0
\(383\) −9.46741 −0.483762 −0.241881 0.970306i \(-0.577764\pi\)
−0.241881 + 0.970306i \(0.577764\pi\)
\(384\) 0 0
\(385\) 1.63177 0.0831625
\(386\) 0 0
\(387\) −1.27555 −0.0648396
\(388\) 0 0
\(389\) 15.0556 0.763350 0.381675 0.924297i \(-0.375347\pi\)
0.381675 + 0.924297i \(0.375347\pi\)
\(390\) 0 0
\(391\) −10.4646 −0.529220
\(392\) 0 0
\(393\) 37.4048 1.88682
\(394\) 0 0
\(395\) −21.1020 −1.06176
\(396\) 0 0
\(397\) −33.4831 −1.68047 −0.840234 0.542225i \(-0.817582\pi\)
−0.840234 + 0.542225i \(0.817582\pi\)
\(398\) 0 0
\(399\) 8.98894 0.450010
\(400\) 0 0
\(401\) 22.0425 1.10075 0.550374 0.834918i \(-0.314485\pi\)
0.550374 + 0.834918i \(0.314485\pi\)
\(402\) 0 0
\(403\) 4.04820 0.201655
\(404\) 0 0
\(405\) 17.7609 0.882544
\(406\) 0 0
\(407\) 10.2298 0.507074
\(408\) 0 0
\(409\) 38.9097 1.92396 0.961980 0.273119i \(-0.0880553\pi\)
0.961980 + 0.273119i \(0.0880553\pi\)
\(410\) 0 0
\(411\) −31.1876 −1.53837
\(412\) 0 0
\(413\) 3.45460 0.169990
\(414\) 0 0
\(415\) 16.8294 0.826123
\(416\) 0 0
\(417\) 32.3093 1.58219
\(418\) 0 0
\(419\) −39.6982 −1.93939 −0.969693 0.244326i \(-0.921433\pi\)
−0.969693 + 0.244326i \(0.921433\pi\)
\(420\) 0 0
\(421\) 16.1632 0.787746 0.393873 0.919165i \(-0.371135\pi\)
0.393873 + 0.919165i \(0.371135\pi\)
\(422\) 0 0
\(423\) −7.43900 −0.361697
\(424\) 0 0
\(425\) −18.4976 −0.897265
\(426\) 0 0
\(427\) 1.01972 0.0493475
\(428\) 0 0
\(429\) −1.97367 −0.0952897
\(430\) 0 0
\(431\) −26.3219 −1.26788 −0.633940 0.773383i \(-0.718563\pi\)
−0.633940 + 0.773383i \(0.718563\pi\)
\(432\) 0 0
\(433\) −30.5961 −1.47035 −0.735177 0.677875i \(-0.762901\pi\)
−0.735177 + 0.677875i \(0.762901\pi\)
\(434\) 0 0
\(435\) 18.3515 0.879885
\(436\) 0 0
\(437\) 6.02233 0.288087
\(438\) 0 0
\(439\) −25.6424 −1.22384 −0.611922 0.790918i \(-0.709603\pi\)
−0.611922 + 0.790918i \(0.709603\pi\)
\(440\) 0 0
\(441\) 0.895375 0.0426369
\(442\) 0 0
\(443\) −13.1665 −0.625562 −0.312781 0.949825i \(-0.601261\pi\)
−0.312781 + 0.949825i \(0.601261\pi\)
\(444\) 0 0
\(445\) 12.8285 0.608130
\(446\) 0 0
\(447\) 19.6154 0.927776
\(448\) 0 0
\(449\) −32.3734 −1.52779 −0.763897 0.645338i \(-0.776716\pi\)
−0.763897 + 0.645338i \(0.776716\pi\)
\(450\) 0 0
\(451\) −6.71462 −0.316179
\(452\) 0 0
\(453\) 34.8839 1.63899
\(454\) 0 0
\(455\) 1.63177 0.0764984
\(456\) 0 0
\(457\) 12.7709 0.597396 0.298698 0.954348i \(-0.403448\pi\)
0.298698 + 0.954348i \(0.403448\pi\)
\(458\) 0 0
\(459\) 32.8733 1.53439
\(460\) 0 0
\(461\) −39.8373 −1.85541 −0.927704 0.373316i \(-0.878221\pi\)
−0.927704 + 0.373316i \(0.878221\pi\)
\(462\) 0 0
\(463\) 28.1774 1.30951 0.654757 0.755839i \(-0.272771\pi\)
0.654757 + 0.755839i \(0.272771\pi\)
\(464\) 0 0
\(465\) −13.0375 −0.604600
\(466\) 0 0
\(467\) −26.6860 −1.23488 −0.617441 0.786617i \(-0.711831\pi\)
−0.617441 + 0.786617i \(0.711831\pi\)
\(468\) 0 0
\(469\) 8.79914 0.406307
\(470\) 0 0
\(471\) −4.72412 −0.217676
\(472\) 0 0
\(473\) 1.42459 0.0655029
\(474\) 0 0
\(475\) 10.6452 0.488437
\(476\) 0 0
\(477\) 1.71093 0.0783379
\(478\) 0 0
\(479\) 22.8074 1.04210 0.521048 0.853527i \(-0.325541\pi\)
0.521048 + 0.853527i \(0.325541\pi\)
\(480\) 0 0
\(481\) 10.2298 0.466440
\(482\) 0 0
\(483\) 2.60979 0.118749
\(484\) 0 0
\(485\) 8.39879 0.381369
\(486\) 0 0
\(487\) −19.5802 −0.887266 −0.443633 0.896209i \(-0.646311\pi\)
−0.443633 + 0.896209i \(0.646311\pi\)
\(488\) 0 0
\(489\) 24.9243 1.12712
\(490\) 0 0
\(491\) −20.1212 −0.908056 −0.454028 0.890987i \(-0.650013\pi\)
−0.454028 + 0.890987i \(0.650013\pi\)
\(492\) 0 0
\(493\) 45.0953 2.03099
\(494\) 0 0
\(495\) 1.46104 0.0656690
\(496\) 0 0
\(497\) 10.9746 0.492278
\(498\) 0 0
\(499\) −1.32913 −0.0595003 −0.0297501 0.999557i \(-0.509471\pi\)
−0.0297501 + 0.999557i \(0.509471\pi\)
\(500\) 0 0
\(501\) 9.92047 0.443214
\(502\) 0 0
\(503\) 31.1232 1.38771 0.693857 0.720113i \(-0.255910\pi\)
0.693857 + 0.720113i \(0.255910\pi\)
\(504\) 0 0
\(505\) −7.50896 −0.334144
\(506\) 0 0
\(507\) −1.97367 −0.0876538
\(508\) 0 0
\(509\) 15.3832 0.681847 0.340923 0.940091i \(-0.389260\pi\)
0.340923 + 0.940091i \(0.389260\pi\)
\(510\) 0 0
\(511\) 5.48196 0.242507
\(512\) 0 0
\(513\) −18.9184 −0.835266
\(514\) 0 0
\(515\) −29.7840 −1.31244
\(516\) 0 0
\(517\) 8.30825 0.365397
\(518\) 0 0
\(519\) −41.7002 −1.83043
\(520\) 0 0
\(521\) 29.9337 1.31142 0.655709 0.755013i \(-0.272370\pi\)
0.655709 + 0.755013i \(0.272370\pi\)
\(522\) 0 0
\(523\) −28.9394 −1.26543 −0.632717 0.774383i \(-0.718060\pi\)
−0.632717 + 0.774383i \(0.718060\pi\)
\(524\) 0 0
\(525\) 4.61313 0.201334
\(526\) 0 0
\(527\) −32.0373 −1.39557
\(528\) 0 0
\(529\) −21.2515 −0.923979
\(530\) 0 0
\(531\) 3.09316 0.134232
\(532\) 0 0
\(533\) −6.71462 −0.290842
\(534\) 0 0
\(535\) 3.39980 0.146986
\(536\) 0 0
\(537\) −51.7694 −2.23401
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −2.67878 −0.115170 −0.0575849 0.998341i \(-0.518340\pi\)
−0.0575849 + 0.998341i \(0.518340\pi\)
\(542\) 0 0
\(543\) 7.05360 0.302699
\(544\) 0 0
\(545\) −6.27583 −0.268827
\(546\) 0 0
\(547\) 14.4171 0.616431 0.308216 0.951316i \(-0.400268\pi\)
0.308216 + 0.951316i \(0.400268\pi\)
\(548\) 0 0
\(549\) 0.913028 0.0389671
\(550\) 0 0
\(551\) −25.9521 −1.10559
\(552\) 0 0
\(553\) 12.9320 0.549925
\(554\) 0 0
\(555\) −32.9459 −1.39847
\(556\) 0 0
\(557\) −14.4205 −0.611016 −0.305508 0.952189i \(-0.598826\pi\)
−0.305508 + 0.952189i \(0.598826\pi\)
\(558\) 0 0
\(559\) 1.42459 0.0602539
\(560\) 0 0
\(561\) 15.6196 0.659458
\(562\) 0 0
\(563\) −35.8777 −1.51206 −0.756032 0.654535i \(-0.772864\pi\)
−0.756032 + 0.654535i \(0.772864\pi\)
\(564\) 0 0
\(565\) 1.08321 0.0455711
\(566\) 0 0
\(567\) −10.8844 −0.457103
\(568\) 0 0
\(569\) 13.7034 0.574477 0.287238 0.957859i \(-0.407263\pi\)
0.287238 + 0.957859i \(0.407263\pi\)
\(570\) 0 0
\(571\) −34.6061 −1.44822 −0.724110 0.689685i \(-0.757749\pi\)
−0.724110 + 0.689685i \(0.757749\pi\)
\(572\) 0 0
\(573\) 38.5107 1.60881
\(574\) 0 0
\(575\) 3.09066 0.128890
\(576\) 0 0
\(577\) −27.1806 −1.13154 −0.565772 0.824562i \(-0.691422\pi\)
−0.565772 + 0.824562i \(0.691422\pi\)
\(578\) 0 0
\(579\) 17.3842 0.722462
\(580\) 0 0
\(581\) −10.3136 −0.427881
\(582\) 0 0
\(583\) −1.91085 −0.0791393
\(584\) 0 0
\(585\) 1.46104 0.0604067
\(586\) 0 0
\(587\) 9.85214 0.406641 0.203321 0.979112i \(-0.434827\pi\)
0.203321 + 0.979112i \(0.434827\pi\)
\(588\) 0 0
\(589\) 18.4372 0.759694
\(590\) 0 0
\(591\) −16.0765 −0.661298
\(592\) 0 0
\(593\) −21.2512 −0.872683 −0.436341 0.899781i \(-0.643726\pi\)
−0.436341 + 0.899781i \(0.643726\pi\)
\(594\) 0 0
\(595\) −12.9137 −0.529412
\(596\) 0 0
\(597\) 37.0652 1.51698
\(598\) 0 0
\(599\) 41.4595 1.69399 0.846994 0.531603i \(-0.178410\pi\)
0.846994 + 0.531603i \(0.178410\pi\)
\(600\) 0 0
\(601\) −25.1381 −1.02540 −0.512701 0.858567i \(-0.671355\pi\)
−0.512701 + 0.858567i \(0.671355\pi\)
\(602\) 0 0
\(603\) 7.87853 0.320839
\(604\) 0 0
\(605\) −1.63177 −0.0663408
\(606\) 0 0
\(607\) −31.4276 −1.27561 −0.637804 0.770198i \(-0.720157\pi\)
−0.637804 + 0.770198i \(0.720157\pi\)
\(608\) 0 0
\(609\) −11.2464 −0.455726
\(610\) 0 0
\(611\) 8.30825 0.336116
\(612\) 0 0
\(613\) −38.4188 −1.55172 −0.775861 0.630903i \(-0.782684\pi\)
−0.775861 + 0.630903i \(0.782684\pi\)
\(614\) 0 0
\(615\) 21.6249 0.872000
\(616\) 0 0
\(617\) 28.4404 1.14497 0.572484 0.819916i \(-0.305980\pi\)
0.572484 + 0.819916i \(0.305980\pi\)
\(618\) 0 0
\(619\) 13.9835 0.562046 0.281023 0.959701i \(-0.409326\pi\)
0.281023 + 0.959701i \(0.409326\pi\)
\(620\) 0 0
\(621\) −5.49263 −0.220412
\(622\) 0 0
\(623\) −7.86173 −0.314974
\(624\) 0 0
\(625\) −7.85018 −0.314007
\(626\) 0 0
\(627\) −8.98894 −0.358984
\(628\) 0 0
\(629\) −80.9585 −3.22803
\(630\) 0 0
\(631\) −28.5782 −1.13768 −0.568841 0.822448i \(-0.692608\pi\)
−0.568841 + 0.822448i \(0.692608\pi\)
\(632\) 0 0
\(633\) 9.38406 0.372983
\(634\) 0 0
\(635\) −29.2587 −1.16110
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 9.82638 0.388726
\(640\) 0 0
\(641\) −24.2719 −0.958682 −0.479341 0.877629i \(-0.659124\pi\)
−0.479341 + 0.877629i \(0.659124\pi\)
\(642\) 0 0
\(643\) 33.9912 1.34048 0.670241 0.742144i \(-0.266191\pi\)
0.670241 + 0.742144i \(0.266191\pi\)
\(644\) 0 0
\(645\) −4.58801 −0.180653
\(646\) 0 0
\(647\) −32.0877 −1.26150 −0.630748 0.775987i \(-0.717252\pi\)
−0.630748 + 0.775987i \(0.717252\pi\)
\(648\) 0 0
\(649\) −3.45460 −0.135605
\(650\) 0 0
\(651\) 7.98981 0.313145
\(652\) 0 0
\(653\) −34.4571 −1.34841 −0.674205 0.738544i \(-0.735514\pi\)
−0.674205 + 0.738544i \(0.735514\pi\)
\(654\) 0 0
\(655\) 30.9251 1.20834
\(656\) 0 0
\(657\) 4.90840 0.191495
\(658\) 0 0
\(659\) 11.7802 0.458891 0.229445 0.973322i \(-0.426309\pi\)
0.229445 + 0.973322i \(0.426309\pi\)
\(660\) 0 0
\(661\) 44.3586 1.72535 0.862675 0.505759i \(-0.168787\pi\)
0.862675 + 0.505759i \(0.168787\pi\)
\(662\) 0 0
\(663\) 15.6196 0.606613
\(664\) 0 0
\(665\) 7.43177 0.288192
\(666\) 0 0
\(667\) −7.53474 −0.291746
\(668\) 0 0
\(669\) 24.1413 0.933357
\(670\) 0 0
\(671\) −1.01972 −0.0393657
\(672\) 0 0
\(673\) 9.13784 0.352238 0.176119 0.984369i \(-0.443646\pi\)
0.176119 + 0.984369i \(0.443646\pi\)
\(674\) 0 0
\(675\) −9.70891 −0.373696
\(676\) 0 0
\(677\) −25.2704 −0.971222 −0.485611 0.874175i \(-0.661403\pi\)
−0.485611 + 0.874175i \(0.661403\pi\)
\(678\) 0 0
\(679\) −5.14705 −0.197526
\(680\) 0 0
\(681\) 42.7825 1.63943
\(682\) 0 0
\(683\) 34.4541 1.31835 0.659176 0.751989i \(-0.270905\pi\)
0.659176 + 0.751989i \(0.270905\pi\)
\(684\) 0 0
\(685\) −25.7849 −0.985192
\(686\) 0 0
\(687\) 17.8009 0.679147
\(688\) 0 0
\(689\) −1.91085 −0.0727976
\(690\) 0 0
\(691\) −49.1293 −1.86897 −0.934484 0.356006i \(-0.884138\pi\)
−0.934484 + 0.356006i \(0.884138\pi\)
\(692\) 0 0
\(693\) −0.895375 −0.0340125
\(694\) 0 0
\(695\) 26.7123 1.01325
\(696\) 0 0
\(697\) 53.1392 2.01279
\(698\) 0 0
\(699\) −27.9766 −1.05817
\(700\) 0 0
\(701\) 0.115992 0.00438098 0.00219049 0.999998i \(-0.499303\pi\)
0.00219049 + 0.999998i \(0.499303\pi\)
\(702\) 0 0
\(703\) 46.5910 1.75721
\(704\) 0 0
\(705\) −26.7573 −1.00774
\(706\) 0 0
\(707\) 4.60174 0.173066
\(708\) 0 0
\(709\) −38.8624 −1.45951 −0.729754 0.683710i \(-0.760365\pi\)
−0.729754 + 0.683710i \(0.760365\pi\)
\(710\) 0 0
\(711\) 11.5790 0.434246
\(712\) 0 0
\(713\) 5.35294 0.200469
\(714\) 0 0
\(715\) −1.63177 −0.0610246
\(716\) 0 0
\(717\) 3.38178 0.126295
\(718\) 0 0
\(719\) −43.1487 −1.60918 −0.804588 0.593834i \(-0.797614\pi\)
−0.804588 + 0.593834i \(0.797614\pi\)
\(720\) 0 0
\(721\) 18.2526 0.679762
\(722\) 0 0
\(723\) −6.59712 −0.245349
\(724\) 0 0
\(725\) −13.3186 −0.494641
\(726\) 0 0
\(727\) 46.3882 1.72044 0.860222 0.509920i \(-0.170325\pi\)
0.860222 + 0.509920i \(0.170325\pi\)
\(728\) 0 0
\(729\) 14.8493 0.549973
\(730\) 0 0
\(731\) −11.2742 −0.416991
\(732\) 0 0
\(733\) −0.832725 −0.0307574 −0.0153787 0.999882i \(-0.504895\pi\)
−0.0153787 + 0.999882i \(0.504895\pi\)
\(734\) 0 0
\(735\) 3.22057 0.118793
\(736\) 0 0
\(737\) −8.79914 −0.324121
\(738\) 0 0
\(739\) −0.568658 −0.0209184 −0.0104592 0.999945i \(-0.503329\pi\)
−0.0104592 + 0.999945i \(0.503329\pi\)
\(740\) 0 0
\(741\) −8.98894 −0.330217
\(742\) 0 0
\(743\) −5.94968 −0.218272 −0.109136 0.994027i \(-0.534808\pi\)
−0.109136 + 0.994027i \(0.534808\pi\)
\(744\) 0 0
\(745\) 16.2174 0.594159
\(746\) 0 0
\(747\) −9.23455 −0.337874
\(748\) 0 0
\(749\) −2.08351 −0.0761298
\(750\) 0 0
\(751\) 7.99497 0.291741 0.145870 0.989304i \(-0.453402\pi\)
0.145870 + 0.989304i \(0.453402\pi\)
\(752\) 0 0
\(753\) 5.37073 0.195720
\(754\) 0 0
\(755\) 28.8409 1.04963
\(756\) 0 0
\(757\) −29.9056 −1.08694 −0.543468 0.839430i \(-0.682889\pi\)
−0.543468 + 0.839430i \(0.682889\pi\)
\(758\) 0 0
\(759\) −2.60979 −0.0947293
\(760\) 0 0
\(761\) −50.6230 −1.83508 −0.917542 0.397640i \(-0.869829\pi\)
−0.917542 + 0.397640i \(0.869829\pi\)
\(762\) 0 0
\(763\) 3.84603 0.139236
\(764\) 0 0
\(765\) −11.5626 −0.418048
\(766\) 0 0
\(767\) −3.45460 −0.124739
\(768\) 0 0
\(769\) 26.3260 0.949339 0.474669 0.880164i \(-0.342568\pi\)
0.474669 + 0.880164i \(0.342568\pi\)
\(770\) 0 0
\(771\) −17.7200 −0.638169
\(772\) 0 0
\(773\) 23.6758 0.851559 0.425780 0.904827i \(-0.360000\pi\)
0.425780 + 0.904827i \(0.360000\pi\)
\(774\) 0 0
\(775\) 9.46201 0.339885
\(776\) 0 0
\(777\) 20.1903 0.724323
\(778\) 0 0
\(779\) −30.5813 −1.09569
\(780\) 0 0
\(781\) −10.9746 −0.392702
\(782\) 0 0
\(783\) 23.6694 0.845875
\(784\) 0 0
\(785\) −3.90575 −0.139402
\(786\) 0 0
\(787\) −18.3179 −0.652964 −0.326482 0.945203i \(-0.605863\pi\)
−0.326482 + 0.945203i \(0.605863\pi\)
\(788\) 0 0
\(789\) −27.3213 −0.972666
\(790\) 0 0
\(791\) −0.663828 −0.0236030
\(792\) 0 0
\(793\) −1.01972 −0.0362112
\(794\) 0 0
\(795\) 6.15402 0.218261
\(796\) 0 0
\(797\) −12.7477 −0.451548 −0.225774 0.974180i \(-0.572491\pi\)
−0.225774 + 0.974180i \(0.572491\pi\)
\(798\) 0 0
\(799\) −65.7512 −2.32611
\(800\) 0 0
\(801\) −7.03919 −0.248718
\(802\) 0 0
\(803\) −5.48196 −0.193454
\(804\) 0 0
\(805\) 2.15769 0.0760485
\(806\) 0 0
\(807\) −33.3098 −1.17256
\(808\) 0 0
\(809\) −37.3197 −1.31209 −0.656046 0.754721i \(-0.727772\pi\)
−0.656046 + 0.754721i \(0.727772\pi\)
\(810\) 0 0
\(811\) 12.2325 0.429540 0.214770 0.976665i \(-0.431100\pi\)
0.214770 + 0.976665i \(0.431100\pi\)
\(812\) 0 0
\(813\) −57.6408 −2.02155
\(814\) 0 0
\(815\) 20.6066 0.721818
\(816\) 0 0
\(817\) 6.48822 0.226994
\(818\) 0 0
\(819\) −0.895375 −0.0312869
\(820\) 0 0
\(821\) 31.0371 1.08320 0.541601 0.840636i \(-0.317818\pi\)
0.541601 + 0.840636i \(0.317818\pi\)
\(822\) 0 0
\(823\) 21.1417 0.736952 0.368476 0.929637i \(-0.379880\pi\)
0.368476 + 0.929637i \(0.379880\pi\)
\(824\) 0 0
\(825\) −4.61313 −0.160609
\(826\) 0 0
\(827\) −30.3190 −1.05429 −0.527147 0.849774i \(-0.676738\pi\)
−0.527147 + 0.849774i \(0.676738\pi\)
\(828\) 0 0
\(829\) 32.5980 1.13218 0.566088 0.824345i \(-0.308456\pi\)
0.566088 + 0.824345i \(0.308456\pi\)
\(830\) 0 0
\(831\) −27.1982 −0.943496
\(832\) 0 0
\(833\) 7.91396 0.274203
\(834\) 0 0
\(835\) 8.20193 0.283839
\(836\) 0 0
\(837\) −16.8156 −0.581231
\(838\) 0 0
\(839\) −19.8155 −0.684108 −0.342054 0.939680i \(-0.611123\pi\)
−0.342054 + 0.939680i \(0.611123\pi\)
\(840\) 0 0
\(841\) 3.46948 0.119637
\(842\) 0 0
\(843\) 42.7288 1.47166
\(844\) 0 0
\(845\) −1.63177 −0.0561345
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 44.9590 1.54299
\(850\) 0 0
\(851\) 13.5269 0.463697
\(852\) 0 0
\(853\) 52.8455 1.80940 0.904698 0.426054i \(-0.140097\pi\)
0.904698 + 0.426054i \(0.140097\pi\)
\(854\) 0 0
\(855\) 6.65422 0.227569
\(856\) 0 0
\(857\) −21.5996 −0.737828 −0.368914 0.929464i \(-0.620270\pi\)
−0.368914 + 0.929464i \(0.620270\pi\)
\(858\) 0 0
\(859\) 15.9729 0.544988 0.272494 0.962157i \(-0.412152\pi\)
0.272494 + 0.962157i \(0.412152\pi\)
\(860\) 0 0
\(861\) −13.2524 −0.451642
\(862\) 0 0
\(863\) −19.2812 −0.656341 −0.328170 0.944619i \(-0.606432\pi\)
−0.328170 + 0.944619i \(0.606432\pi\)
\(864\) 0 0
\(865\) −34.4763 −1.17223
\(866\) 0 0
\(867\) −90.0601 −3.05860
\(868\) 0 0
\(869\) −12.9320 −0.438689
\(870\) 0 0
\(871\) −8.79914 −0.298148
\(872\) 0 0
\(873\) −4.60854 −0.155975
\(874\) 0 0
\(875\) 11.9728 0.404755
\(876\) 0 0
\(877\) 16.9170 0.571245 0.285622 0.958342i \(-0.407800\pi\)
0.285622 + 0.958342i \(0.407800\pi\)
\(878\) 0 0
\(879\) 22.1319 0.746490
\(880\) 0 0
\(881\) 37.8704 1.27589 0.637944 0.770083i \(-0.279785\pi\)
0.637944 + 0.770083i \(0.279785\pi\)
\(882\) 0 0
\(883\) 10.5539 0.355168 0.177584 0.984106i \(-0.443172\pi\)
0.177584 + 0.984106i \(0.443172\pi\)
\(884\) 0 0
\(885\) 11.1258 0.373989
\(886\) 0 0
\(887\) 1.23280 0.0413935 0.0206968 0.999786i \(-0.493412\pi\)
0.0206968 + 0.999786i \(0.493412\pi\)
\(888\) 0 0
\(889\) 17.9307 0.601377
\(890\) 0 0
\(891\) 10.8844 0.364642
\(892\) 0 0
\(893\) 37.8394 1.26625
\(894\) 0 0
\(895\) −42.8012 −1.43069
\(896\) 0 0
\(897\) −2.60979 −0.0871383
\(898\) 0 0
\(899\) −23.0675 −0.769343
\(900\) 0 0
\(901\) 15.1224 0.503800
\(902\) 0 0
\(903\) 2.81168 0.0935668
\(904\) 0 0
\(905\) 5.83169 0.193852
\(906\) 0 0
\(907\) −40.4224 −1.34220 −0.671101 0.741366i \(-0.734178\pi\)
−0.671101 + 0.741366i \(0.734178\pi\)
\(908\) 0 0
\(909\) 4.12028 0.136661
\(910\) 0 0
\(911\) −33.6310 −1.11424 −0.557122 0.830431i \(-0.688095\pi\)
−0.557122 + 0.830431i \(0.688095\pi\)
\(912\) 0 0
\(913\) 10.3136 0.341331
\(914\) 0 0
\(915\) 3.28407 0.108568
\(916\) 0 0
\(917\) −18.9519 −0.625847
\(918\) 0 0
\(919\) 51.0307 1.68335 0.841674 0.539985i \(-0.181570\pi\)
0.841674 + 0.539985i \(0.181570\pi\)
\(920\) 0 0
\(921\) 45.6266 1.50345
\(922\) 0 0
\(923\) −10.9746 −0.361234
\(924\) 0 0
\(925\) 23.9105 0.786174
\(926\) 0 0
\(927\) 16.3429 0.536771
\(928\) 0 0
\(929\) 1.83721 0.0602769 0.0301385 0.999546i \(-0.490405\pi\)
0.0301385 + 0.999546i \(0.490405\pi\)
\(930\) 0 0
\(931\) −4.55443 −0.149265
\(932\) 0 0
\(933\) 60.5042 1.98082
\(934\) 0 0
\(935\) 12.9137 0.422325
\(936\) 0 0
\(937\) −41.9904 −1.37176 −0.685882 0.727712i \(-0.740584\pi\)
−0.685882 + 0.727712i \(0.740584\pi\)
\(938\) 0 0
\(939\) −54.9600 −1.79355
\(940\) 0 0
\(941\) −40.8632 −1.33210 −0.666052 0.745905i \(-0.732017\pi\)
−0.666052 + 0.745905i \(0.732017\pi\)
\(942\) 0 0
\(943\) −8.87876 −0.289132
\(944\) 0 0
\(945\) −6.77809 −0.220491
\(946\) 0 0
\(947\) 36.3255 1.18042 0.590210 0.807250i \(-0.299045\pi\)
0.590210 + 0.807250i \(0.299045\pi\)
\(948\) 0 0
\(949\) −5.48196 −0.177952
\(950\) 0 0
\(951\) 56.7931 1.84164
\(952\) 0 0
\(953\) 29.2651 0.947990 0.473995 0.880527i \(-0.342811\pi\)
0.473995 + 0.880527i \(0.342811\pi\)
\(954\) 0 0
\(955\) 31.8394 1.03030
\(956\) 0 0
\(957\) 11.2464 0.363543
\(958\) 0 0
\(959\) 15.8019 0.510268
\(960\) 0 0
\(961\) −14.6121 −0.471357
\(962\) 0 0
\(963\) −1.86552 −0.0601156
\(964\) 0 0
\(965\) 14.3727 0.462673
\(966\) 0 0
\(967\) −12.4407 −0.400065 −0.200032 0.979789i \(-0.564105\pi\)
−0.200032 + 0.979789i \(0.564105\pi\)
\(968\) 0 0
\(969\) 71.1382 2.28529
\(970\) 0 0
\(971\) 44.0812 1.41463 0.707317 0.706897i \(-0.249906\pi\)
0.707317 + 0.706897i \(0.249906\pi\)
\(972\) 0 0
\(973\) −16.3702 −0.524803
\(974\) 0 0
\(975\) −4.61313 −0.147738
\(976\) 0 0
\(977\) −28.2868 −0.904976 −0.452488 0.891770i \(-0.649464\pi\)
−0.452488 + 0.891770i \(0.649464\pi\)
\(978\) 0 0
\(979\) 7.86173 0.251262
\(980\) 0 0
\(981\) 3.44364 0.109947
\(982\) 0 0
\(983\) 28.1927 0.899209 0.449604 0.893228i \(-0.351565\pi\)
0.449604 + 0.893228i \(0.351565\pi\)
\(984\) 0 0
\(985\) −13.2915 −0.423503
\(986\) 0 0
\(987\) 16.3978 0.521946
\(988\) 0 0
\(989\) 1.88374 0.0598996
\(990\) 0 0
\(991\) 53.2688 1.69214 0.846069 0.533073i \(-0.178963\pi\)
0.846069 + 0.533073i \(0.178963\pi\)
\(992\) 0 0
\(993\) −35.1165 −1.11439
\(994\) 0 0
\(995\) 30.6443 0.971491
\(996\) 0 0
\(997\) −31.0211 −0.982448 −0.491224 0.871033i \(-0.663450\pi\)
−0.491224 + 0.871033i \(0.663450\pi\)
\(998\) 0 0
\(999\) −42.4930 −1.34442
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 \(a_p\))