Properties

Label 6008.2.a.e.1.42
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.42
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.26355 q^{3} -2.03106 q^{5} +2.84873 q^{7} +2.12365 q^{9} +O(q^{10})\) \(q+2.26355 q^{3} -2.03106 q^{5} +2.84873 q^{7} +2.12365 q^{9} +5.94130 q^{11} +3.06346 q^{13} -4.59739 q^{15} +5.90773 q^{17} +2.58062 q^{19} +6.44823 q^{21} +1.10477 q^{23} -0.874809 q^{25} -1.98367 q^{27} +6.71326 q^{29} -6.73786 q^{31} +13.4484 q^{33} -5.78593 q^{35} +4.99862 q^{37} +6.93430 q^{39} -8.52835 q^{41} -5.24692 q^{43} -4.31325 q^{45} +10.6005 q^{47} +1.11525 q^{49} +13.3724 q^{51} -10.2822 q^{53} -12.0671 q^{55} +5.84136 q^{57} -2.18420 q^{59} -7.25388 q^{61} +6.04970 q^{63} -6.22207 q^{65} +7.02358 q^{67} +2.50070 q^{69} +11.8016 q^{71} -8.01357 q^{73} -1.98017 q^{75} +16.9252 q^{77} +11.6831 q^{79} -10.8611 q^{81} -4.69026 q^{83} -11.9989 q^{85} +15.1958 q^{87} -12.4148 q^{89} +8.72698 q^{91} -15.2515 q^{93} -5.24139 q^{95} -11.9835 q^{97} +12.6172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.26355 1.30686 0.653430 0.756987i \(-0.273329\pi\)
0.653430 + 0.756987i \(0.273329\pi\)
\(4\) 0 0
\(5\) −2.03106 −0.908316 −0.454158 0.890921i \(-0.650060\pi\)
−0.454158 + 0.890921i \(0.650060\pi\)
\(6\) 0 0
\(7\) 2.84873 1.07672 0.538359 0.842716i \(-0.319044\pi\)
0.538359 + 0.842716i \(0.319044\pi\)
\(8\) 0 0
\(9\) 2.12365 0.707883
\(10\) 0 0
\(11\) 5.94130 1.79137 0.895685 0.444689i \(-0.146686\pi\)
0.895685 + 0.444689i \(0.146686\pi\)
\(12\) 0 0
\(13\) 3.06346 0.849652 0.424826 0.905275i \(-0.360335\pi\)
0.424826 + 0.905275i \(0.360335\pi\)
\(14\) 0 0
\(15\) −4.59739 −1.18704
\(16\) 0 0
\(17\) 5.90773 1.43283 0.716417 0.697672i \(-0.245781\pi\)
0.716417 + 0.697672i \(0.245781\pi\)
\(18\) 0 0
\(19\) 2.58062 0.592035 0.296017 0.955183i \(-0.404341\pi\)
0.296017 + 0.955183i \(0.404341\pi\)
\(20\) 0 0
\(21\) 6.44823 1.40712
\(22\) 0 0
\(23\) 1.10477 0.230361 0.115180 0.993345i \(-0.463255\pi\)
0.115180 + 0.993345i \(0.463255\pi\)
\(24\) 0 0
\(25\) −0.874809 −0.174962
\(26\) 0 0
\(27\) −1.98367 −0.381757
\(28\) 0 0
\(29\) 6.71326 1.24662 0.623310 0.781974i \(-0.285787\pi\)
0.623310 + 0.781974i \(0.285787\pi\)
\(30\) 0 0
\(31\) −6.73786 −1.21015 −0.605077 0.796167i \(-0.706858\pi\)
−0.605077 + 0.796167i \(0.706858\pi\)
\(32\) 0 0
\(33\) 13.4484 2.34107
\(34\) 0 0
\(35\) −5.78593 −0.978001
\(36\) 0 0
\(37\) 4.99862 0.821767 0.410884 0.911688i \(-0.365220\pi\)
0.410884 + 0.911688i \(0.365220\pi\)
\(38\) 0 0
\(39\) 6.93430 1.11038
\(40\) 0 0
\(41\) −8.52835 −1.33190 −0.665952 0.745995i \(-0.731974\pi\)
−0.665952 + 0.745995i \(0.731974\pi\)
\(42\) 0 0
\(43\) −5.24692 −0.800147 −0.400074 0.916483i \(-0.631015\pi\)
−0.400074 + 0.916483i \(0.631015\pi\)
\(44\) 0 0
\(45\) −4.31325 −0.642981
\(46\) 0 0
\(47\) 10.6005 1.54624 0.773122 0.634258i \(-0.218694\pi\)
0.773122 + 0.634258i \(0.218694\pi\)
\(48\) 0 0
\(49\) 1.11525 0.159322
\(50\) 0 0
\(51\) 13.3724 1.87251
\(52\) 0 0
\(53\) −10.2822 −1.41237 −0.706183 0.708030i \(-0.749584\pi\)
−0.706183 + 0.708030i \(0.749584\pi\)
\(54\) 0 0
\(55\) −12.0671 −1.62713
\(56\) 0 0
\(57\) 5.84136 0.773707
\(58\) 0 0
\(59\) −2.18420 −0.284359 −0.142180 0.989841i \(-0.545411\pi\)
−0.142180 + 0.989841i \(0.545411\pi\)
\(60\) 0 0
\(61\) −7.25388 −0.928765 −0.464382 0.885635i \(-0.653724\pi\)
−0.464382 + 0.885635i \(0.653724\pi\)
\(62\) 0 0
\(63\) 6.04970 0.762190
\(64\) 0 0
\(65\) −6.22207 −0.771753
\(66\) 0 0
\(67\) 7.02358 0.858066 0.429033 0.903289i \(-0.358854\pi\)
0.429033 + 0.903289i \(0.358854\pi\)
\(68\) 0 0
\(69\) 2.50070 0.301049
\(70\) 0 0
\(71\) 11.8016 1.40059 0.700296 0.713853i \(-0.253051\pi\)
0.700296 + 0.713853i \(0.253051\pi\)
\(72\) 0 0
\(73\) −8.01357 −0.937918 −0.468959 0.883220i \(-0.655371\pi\)
−0.468959 + 0.883220i \(0.655371\pi\)
\(74\) 0 0
\(75\) −1.98017 −0.228650
\(76\) 0 0
\(77\) 16.9252 1.92880
\(78\) 0 0
\(79\) 11.6831 1.31445 0.657226 0.753693i \(-0.271730\pi\)
0.657226 + 0.753693i \(0.271730\pi\)
\(80\) 0 0
\(81\) −10.8611 −1.20678
\(82\) 0 0
\(83\) −4.69026 −0.514823 −0.257411 0.966302i \(-0.582870\pi\)
−0.257411 + 0.966302i \(0.582870\pi\)
\(84\) 0 0
\(85\) −11.9989 −1.30147
\(86\) 0 0
\(87\) 15.1958 1.62916
\(88\) 0 0
\(89\) −12.4148 −1.31597 −0.657984 0.753032i \(-0.728590\pi\)
−0.657984 + 0.753032i \(0.728590\pi\)
\(90\) 0 0
\(91\) 8.72698 0.914836
\(92\) 0 0
\(93\) −15.2515 −1.58150
\(94\) 0 0
\(95\) −5.24139 −0.537755
\(96\) 0 0
\(97\) −11.9835 −1.21675 −0.608373 0.793652i \(-0.708177\pi\)
−0.608373 + 0.793652i \(0.708177\pi\)
\(98\) 0 0
\(99\) 12.6172 1.26808
\(100\) 0 0
\(101\) 6.56478 0.653220 0.326610 0.945159i \(-0.394094\pi\)
0.326610 + 0.945159i \(0.394094\pi\)
\(102\) 0 0
\(103\) 16.0425 1.58072 0.790359 0.612644i \(-0.209894\pi\)
0.790359 + 0.612644i \(0.209894\pi\)
\(104\) 0 0
\(105\) −13.0967 −1.27811
\(106\) 0 0
\(107\) −16.0761 −1.55413 −0.777067 0.629418i \(-0.783294\pi\)
−0.777067 + 0.629418i \(0.783294\pi\)
\(108\) 0 0
\(109\) −7.58352 −0.726370 −0.363185 0.931717i \(-0.618311\pi\)
−0.363185 + 0.931717i \(0.618311\pi\)
\(110\) 0 0
\(111\) 11.3146 1.07393
\(112\) 0 0
\(113\) −5.95235 −0.559950 −0.279975 0.960007i \(-0.590326\pi\)
−0.279975 + 0.960007i \(0.590326\pi\)
\(114\) 0 0
\(115\) −2.24385 −0.209240
\(116\) 0 0
\(117\) 6.50572 0.601454
\(118\) 0 0
\(119\) 16.8295 1.54276
\(120\) 0 0
\(121\) 24.2991 2.20901
\(122\) 0 0
\(123\) −19.3043 −1.74061
\(124\) 0 0
\(125\) 11.9321 1.06724
\(126\) 0 0
\(127\) 3.80739 0.337852 0.168926 0.985629i \(-0.445970\pi\)
0.168926 + 0.985629i \(0.445970\pi\)
\(128\) 0 0
\(129\) −11.8766 −1.04568
\(130\) 0 0
\(131\) −18.0150 −1.57398 −0.786988 0.616968i \(-0.788361\pi\)
−0.786988 + 0.616968i \(0.788361\pi\)
\(132\) 0 0
\(133\) 7.35149 0.637455
\(134\) 0 0
\(135\) 4.02894 0.346756
\(136\) 0 0
\(137\) 11.1942 0.956385 0.478192 0.878255i \(-0.341292\pi\)
0.478192 + 0.878255i \(0.341292\pi\)
\(138\) 0 0
\(139\) 18.1484 1.53933 0.769665 0.638449i \(-0.220423\pi\)
0.769665 + 0.638449i \(0.220423\pi\)
\(140\) 0 0
\(141\) 23.9948 2.02072
\(142\) 0 0
\(143\) 18.2010 1.52204
\(144\) 0 0
\(145\) −13.6350 −1.13233
\(146\) 0 0
\(147\) 2.52443 0.208212
\(148\) 0 0
\(149\) −6.10842 −0.500421 −0.250210 0.968191i \(-0.580500\pi\)
−0.250210 + 0.968191i \(0.580500\pi\)
\(150\) 0 0
\(151\) −1.68762 −0.137337 −0.0686683 0.997640i \(-0.521875\pi\)
−0.0686683 + 0.997640i \(0.521875\pi\)
\(152\) 0 0
\(153\) 12.5459 1.01428
\(154\) 0 0
\(155\) 13.6850 1.09920
\(156\) 0 0
\(157\) −1.12522 −0.0898023 −0.0449012 0.998991i \(-0.514297\pi\)
−0.0449012 + 0.998991i \(0.514297\pi\)
\(158\) 0 0
\(159\) −23.2742 −1.84576
\(160\) 0 0
\(161\) 3.14719 0.248033
\(162\) 0 0
\(163\) −10.1769 −0.797114 −0.398557 0.917144i \(-0.630489\pi\)
−0.398557 + 0.917144i \(0.630489\pi\)
\(164\) 0 0
\(165\) −27.3145 −2.12643
\(166\) 0 0
\(167\) 0.563580 0.0436111 0.0218056 0.999762i \(-0.493059\pi\)
0.0218056 + 0.999762i \(0.493059\pi\)
\(168\) 0 0
\(169\) −3.61518 −0.278091
\(170\) 0 0
\(171\) 5.48033 0.419091
\(172\) 0 0
\(173\) 15.1488 1.15174 0.575869 0.817542i \(-0.304664\pi\)
0.575869 + 0.817542i \(0.304664\pi\)
\(174\) 0 0
\(175\) −2.49209 −0.188384
\(176\) 0 0
\(177\) −4.94405 −0.371618
\(178\) 0 0
\(179\) −22.6839 −1.69548 −0.847738 0.530415i \(-0.822036\pi\)
−0.847738 + 0.530415i \(0.822036\pi\)
\(180\) 0 0
\(181\) −23.4230 −1.74102 −0.870508 0.492154i \(-0.836210\pi\)
−0.870508 + 0.492154i \(0.836210\pi\)
\(182\) 0 0
\(183\) −16.4195 −1.21377
\(184\) 0 0
\(185\) −10.1525 −0.746425
\(186\) 0 0
\(187\) 35.0996 2.56674
\(188\) 0 0
\(189\) −5.65092 −0.411044
\(190\) 0 0
\(191\) 15.6670 1.13363 0.566813 0.823847i \(-0.308176\pi\)
0.566813 + 0.823847i \(0.308176\pi\)
\(192\) 0 0
\(193\) 10.9595 0.788882 0.394441 0.918921i \(-0.370938\pi\)
0.394441 + 0.918921i \(0.370938\pi\)
\(194\) 0 0
\(195\) −14.0840 −1.00857
\(196\) 0 0
\(197\) −7.32665 −0.522002 −0.261001 0.965339i \(-0.584053\pi\)
−0.261001 + 0.965339i \(0.584053\pi\)
\(198\) 0 0
\(199\) 1.96696 0.139434 0.0697172 0.997567i \(-0.477790\pi\)
0.0697172 + 0.997567i \(0.477790\pi\)
\(200\) 0 0
\(201\) 15.8982 1.12137
\(202\) 0 0
\(203\) 19.1243 1.34226
\(204\) 0 0
\(205\) 17.3216 1.20979
\(206\) 0 0
\(207\) 2.34614 0.163068
\(208\) 0 0
\(209\) 15.3322 1.06055
\(210\) 0 0
\(211\) 17.9708 1.23716 0.618579 0.785722i \(-0.287709\pi\)
0.618579 + 0.785722i \(0.287709\pi\)
\(212\) 0 0
\(213\) 26.7135 1.83038
\(214\) 0 0
\(215\) 10.6568 0.726787
\(216\) 0 0
\(217\) −19.1943 −1.30300
\(218\) 0 0
\(219\) −18.1391 −1.22573
\(220\) 0 0
\(221\) 18.0981 1.21741
\(222\) 0 0
\(223\) 0.871055 0.0583302 0.0291651 0.999575i \(-0.490715\pi\)
0.0291651 + 0.999575i \(0.490715\pi\)
\(224\) 0 0
\(225\) −1.85779 −0.123852
\(226\) 0 0
\(227\) −12.0084 −0.797024 −0.398512 0.917163i \(-0.630473\pi\)
−0.398512 + 0.917163i \(0.630473\pi\)
\(228\) 0 0
\(229\) −2.26262 −0.149518 −0.0747590 0.997202i \(-0.523819\pi\)
−0.0747590 + 0.997202i \(0.523819\pi\)
\(230\) 0 0
\(231\) 38.3109 2.52067
\(232\) 0 0
\(233\) −5.68168 −0.372219 −0.186110 0.982529i \(-0.559588\pi\)
−0.186110 + 0.982529i \(0.559588\pi\)
\(234\) 0 0
\(235\) −21.5302 −1.40448
\(236\) 0 0
\(237\) 26.4453 1.71780
\(238\) 0 0
\(239\) −12.2544 −0.792670 −0.396335 0.918106i \(-0.629718\pi\)
−0.396335 + 0.918106i \(0.629718\pi\)
\(240\) 0 0
\(241\) 25.1614 1.62079 0.810393 0.585886i \(-0.199253\pi\)
0.810393 + 0.585886i \(0.199253\pi\)
\(242\) 0 0
\(243\) −18.6335 −1.19534
\(244\) 0 0
\(245\) −2.26515 −0.144715
\(246\) 0 0
\(247\) 7.90564 0.503024
\(248\) 0 0
\(249\) −10.6166 −0.672801
\(250\) 0 0
\(251\) 14.6366 0.923854 0.461927 0.886918i \(-0.347158\pi\)
0.461927 + 0.886918i \(0.347158\pi\)
\(252\) 0 0
\(253\) 6.56378 0.412661
\(254\) 0 0
\(255\) −27.1601 −1.70083
\(256\) 0 0
\(257\) −2.45719 −0.153275 −0.0766377 0.997059i \(-0.524418\pi\)
−0.0766377 + 0.997059i \(0.524418\pi\)
\(258\) 0 0
\(259\) 14.2397 0.884812
\(260\) 0 0
\(261\) 14.2566 0.882461
\(262\) 0 0
\(263\) −13.7817 −0.849814 −0.424907 0.905237i \(-0.639693\pi\)
−0.424907 + 0.905237i \(0.639693\pi\)
\(264\) 0 0
\(265\) 20.8837 1.28287
\(266\) 0 0
\(267\) −28.1015 −1.71978
\(268\) 0 0
\(269\) 8.31451 0.506945 0.253472 0.967343i \(-0.418427\pi\)
0.253472 + 0.967343i \(0.418427\pi\)
\(270\) 0 0
\(271\) 11.2719 0.684716 0.342358 0.939570i \(-0.388774\pi\)
0.342358 + 0.939570i \(0.388774\pi\)
\(272\) 0 0
\(273\) 19.7539 1.19556
\(274\) 0 0
\(275\) −5.19750 −0.313421
\(276\) 0 0
\(277\) 5.85187 0.351605 0.175803 0.984425i \(-0.443748\pi\)
0.175803 + 0.984425i \(0.443748\pi\)
\(278\) 0 0
\(279\) −14.3088 −0.856647
\(280\) 0 0
\(281\) −2.72235 −0.162402 −0.0812010 0.996698i \(-0.525876\pi\)
−0.0812010 + 0.996698i \(0.525876\pi\)
\(282\) 0 0
\(283\) 26.8627 1.59682 0.798410 0.602114i \(-0.205675\pi\)
0.798410 + 0.602114i \(0.205675\pi\)
\(284\) 0 0
\(285\) −11.8641 −0.702770
\(286\) 0 0
\(287\) −24.2949 −1.43409
\(288\) 0 0
\(289\) 17.9012 1.05301
\(290\) 0 0
\(291\) −27.1253 −1.59012
\(292\) 0 0
\(293\) 3.57249 0.208707 0.104353 0.994540i \(-0.466723\pi\)
0.104353 + 0.994540i \(0.466723\pi\)
\(294\) 0 0
\(295\) 4.43624 0.258288
\(296\) 0 0
\(297\) −11.7856 −0.683867
\(298\) 0 0
\(299\) 3.38442 0.195726
\(300\) 0 0
\(301\) −14.9470 −0.861533
\(302\) 0 0
\(303\) 14.8597 0.853667
\(304\) 0 0
\(305\) 14.7330 0.843612
\(306\) 0 0
\(307\) 31.1639 1.77862 0.889310 0.457306i \(-0.151185\pi\)
0.889310 + 0.457306i \(0.151185\pi\)
\(308\) 0 0
\(309\) 36.3131 2.06578
\(310\) 0 0
\(311\) −0.829003 −0.0470085 −0.0235042 0.999724i \(-0.507482\pi\)
−0.0235042 + 0.999724i \(0.507482\pi\)
\(312\) 0 0
\(313\) 14.9858 0.847046 0.423523 0.905885i \(-0.360793\pi\)
0.423523 + 0.905885i \(0.360793\pi\)
\(314\) 0 0
\(315\) −12.2873 −0.692310
\(316\) 0 0
\(317\) −30.1502 −1.69340 −0.846701 0.532069i \(-0.821415\pi\)
−0.846701 + 0.532069i \(0.821415\pi\)
\(318\) 0 0
\(319\) 39.8855 2.23316
\(320\) 0 0
\(321\) −36.3890 −2.03104
\(322\) 0 0
\(323\) 15.2456 0.848288
\(324\) 0 0
\(325\) −2.67995 −0.148657
\(326\) 0 0
\(327\) −17.1657 −0.949263
\(328\) 0 0
\(329\) 30.1980 1.66487
\(330\) 0 0
\(331\) 4.10175 0.225452 0.112726 0.993626i \(-0.464042\pi\)
0.112726 + 0.993626i \(0.464042\pi\)
\(332\) 0 0
\(333\) 10.6153 0.581715
\(334\) 0 0
\(335\) −14.2653 −0.779395
\(336\) 0 0
\(337\) 15.0504 0.819848 0.409924 0.912120i \(-0.365555\pi\)
0.409924 + 0.912120i \(0.365555\pi\)
\(338\) 0 0
\(339\) −13.4734 −0.731776
\(340\) 0 0
\(341\) −40.0317 −2.16784
\(342\) 0 0
\(343\) −16.7640 −0.905173
\(344\) 0 0
\(345\) −5.07906 −0.273448
\(346\) 0 0
\(347\) −16.0676 −0.862555 −0.431278 0.902219i \(-0.641937\pi\)
−0.431278 + 0.902219i \(0.641937\pi\)
\(348\) 0 0
\(349\) 10.9027 0.583607 0.291803 0.956478i \(-0.405745\pi\)
0.291803 + 0.956478i \(0.405745\pi\)
\(350\) 0 0
\(351\) −6.07689 −0.324360
\(352\) 0 0
\(353\) −9.01265 −0.479695 −0.239848 0.970811i \(-0.577097\pi\)
−0.239848 + 0.970811i \(0.577097\pi\)
\(354\) 0 0
\(355\) −23.9697 −1.27218
\(356\) 0 0
\(357\) 38.0944 2.01617
\(358\) 0 0
\(359\) 34.8170 1.83757 0.918784 0.394760i \(-0.129172\pi\)
0.918784 + 0.394760i \(0.129172\pi\)
\(360\) 0 0
\(361\) −12.3404 −0.649495
\(362\) 0 0
\(363\) 55.0021 2.88686
\(364\) 0 0
\(365\) 16.2760 0.851926
\(366\) 0 0
\(367\) −35.2245 −1.83871 −0.919353 0.393434i \(-0.871287\pi\)
−0.919353 + 0.393434i \(0.871287\pi\)
\(368\) 0 0
\(369\) −18.1112 −0.942832
\(370\) 0 0
\(371\) −29.2911 −1.52072
\(372\) 0 0
\(373\) −19.8146 −1.02596 −0.512981 0.858400i \(-0.671459\pi\)
−0.512981 + 0.858400i \(0.671459\pi\)
\(374\) 0 0
\(375\) 27.0088 1.39473
\(376\) 0 0
\(377\) 20.5658 1.05919
\(378\) 0 0
\(379\) 19.8202 1.01810 0.509048 0.860738i \(-0.329997\pi\)
0.509048 + 0.860738i \(0.329997\pi\)
\(380\) 0 0
\(381\) 8.61822 0.441525
\(382\) 0 0
\(383\) 14.2166 0.726434 0.363217 0.931705i \(-0.381678\pi\)
0.363217 + 0.931705i \(0.381678\pi\)
\(384\) 0 0
\(385\) −34.3760 −1.75196
\(386\) 0 0
\(387\) −11.1426 −0.566410
\(388\) 0 0
\(389\) 22.8295 1.15750 0.578751 0.815504i \(-0.303540\pi\)
0.578751 + 0.815504i \(0.303540\pi\)
\(390\) 0 0
\(391\) 6.52668 0.330068
\(392\) 0 0
\(393\) −40.7778 −2.05697
\(394\) 0 0
\(395\) −23.7291 −1.19394
\(396\) 0 0
\(397\) 17.5329 0.879951 0.439975 0.898010i \(-0.354987\pi\)
0.439975 + 0.898010i \(0.354987\pi\)
\(398\) 0 0
\(399\) 16.6404 0.833064
\(400\) 0 0
\(401\) −30.2366 −1.50994 −0.754971 0.655758i \(-0.772349\pi\)
−0.754971 + 0.655758i \(0.772349\pi\)
\(402\) 0 0
\(403\) −20.6412 −1.02821
\(404\) 0 0
\(405\) 22.0594 1.09614
\(406\) 0 0
\(407\) 29.6983 1.47209
\(408\) 0 0
\(409\) 20.6540 1.02127 0.510636 0.859797i \(-0.329410\pi\)
0.510636 + 0.859797i \(0.329410\pi\)
\(410\) 0 0
\(411\) 25.3386 1.24986
\(412\) 0 0
\(413\) −6.22221 −0.306175
\(414\) 0 0
\(415\) 9.52618 0.467622
\(416\) 0 0
\(417\) 41.0798 2.01169
\(418\) 0 0
\(419\) 35.0027 1.70999 0.854996 0.518634i \(-0.173559\pi\)
0.854996 + 0.518634i \(0.173559\pi\)
\(420\) 0 0
\(421\) −17.6641 −0.860894 −0.430447 0.902616i \(-0.641644\pi\)
−0.430447 + 0.902616i \(0.641644\pi\)
\(422\) 0 0
\(423\) 22.5118 1.09456
\(424\) 0 0
\(425\) −5.16813 −0.250691
\(426\) 0 0
\(427\) −20.6643 −1.00002
\(428\) 0 0
\(429\) 41.1988 1.98910
\(430\) 0 0
\(431\) 1.44029 0.0693761 0.0346881 0.999398i \(-0.488956\pi\)
0.0346881 + 0.999398i \(0.488956\pi\)
\(432\) 0 0
\(433\) −15.4980 −0.744788 −0.372394 0.928075i \(-0.621463\pi\)
−0.372394 + 0.928075i \(0.621463\pi\)
\(434\) 0 0
\(435\) −30.8635 −1.47979
\(436\) 0 0
\(437\) 2.85099 0.136381
\(438\) 0 0
\(439\) 13.9160 0.664174 0.332087 0.943249i \(-0.392247\pi\)
0.332087 + 0.943249i \(0.392247\pi\)
\(440\) 0 0
\(441\) 2.36841 0.112781
\(442\) 0 0
\(443\) −29.3742 −1.39561 −0.697806 0.716287i \(-0.745840\pi\)
−0.697806 + 0.716287i \(0.745840\pi\)
\(444\) 0 0
\(445\) 25.2152 1.19531
\(446\) 0 0
\(447\) −13.8267 −0.653980
\(448\) 0 0
\(449\) −11.9746 −0.565118 −0.282559 0.959250i \(-0.591183\pi\)
−0.282559 + 0.959250i \(0.591183\pi\)
\(450\) 0 0
\(451\) −50.6695 −2.38593
\(452\) 0 0
\(453\) −3.82001 −0.179480
\(454\) 0 0
\(455\) −17.7250 −0.830960
\(456\) 0 0
\(457\) −19.0554 −0.891376 −0.445688 0.895188i \(-0.647041\pi\)
−0.445688 + 0.895188i \(0.647041\pi\)
\(458\) 0 0
\(459\) −11.7190 −0.546994
\(460\) 0 0
\(461\) 19.9012 0.926892 0.463446 0.886125i \(-0.346613\pi\)
0.463446 + 0.886125i \(0.346613\pi\)
\(462\) 0 0
\(463\) −14.2887 −0.664053 −0.332027 0.943270i \(-0.607732\pi\)
−0.332027 + 0.943270i \(0.607732\pi\)
\(464\) 0 0
\(465\) 30.9766 1.43650
\(466\) 0 0
\(467\) 12.2255 0.565728 0.282864 0.959160i \(-0.408715\pi\)
0.282864 + 0.959160i \(0.408715\pi\)
\(468\) 0 0
\(469\) 20.0083 0.923896
\(470\) 0 0
\(471\) −2.54699 −0.117359
\(472\) 0 0
\(473\) −31.1735 −1.43336
\(474\) 0 0
\(475\) −2.25755 −0.103583
\(476\) 0 0
\(477\) −21.8357 −0.999789
\(478\) 0 0
\(479\) −31.2654 −1.42855 −0.714277 0.699863i \(-0.753244\pi\)
−0.714277 + 0.699863i \(0.753244\pi\)
\(480\) 0 0
\(481\) 15.3131 0.698217
\(482\) 0 0
\(483\) 7.12382 0.324145
\(484\) 0 0
\(485\) 24.3393 1.10519
\(486\) 0 0
\(487\) −20.0752 −0.909694 −0.454847 0.890570i \(-0.650306\pi\)
−0.454847 + 0.890570i \(0.650306\pi\)
\(488\) 0 0
\(489\) −23.0358 −1.04172
\(490\) 0 0
\(491\) −24.5106 −1.10615 −0.553075 0.833132i \(-0.686546\pi\)
−0.553075 + 0.833132i \(0.686546\pi\)
\(492\) 0 0
\(493\) 39.6601 1.78620
\(494\) 0 0
\(495\) −25.6263 −1.15182
\(496\) 0 0
\(497\) 33.6195 1.50804
\(498\) 0 0
\(499\) −37.9735 −1.69993 −0.849965 0.526840i \(-0.823377\pi\)
−0.849965 + 0.526840i \(0.823377\pi\)
\(500\) 0 0
\(501\) 1.27569 0.0569936
\(502\) 0 0
\(503\) −0.416077 −0.0185520 −0.00927599 0.999957i \(-0.502953\pi\)
−0.00927599 + 0.999957i \(0.502953\pi\)
\(504\) 0 0
\(505\) −13.3334 −0.593330
\(506\) 0 0
\(507\) −8.18314 −0.363426
\(508\) 0 0
\(509\) −24.0031 −1.06392 −0.531959 0.846770i \(-0.678544\pi\)
−0.531959 + 0.846770i \(0.678544\pi\)
\(510\) 0 0
\(511\) −22.8285 −1.00987
\(512\) 0 0
\(513\) −5.11909 −0.226013
\(514\) 0 0
\(515\) −32.5833 −1.43579
\(516\) 0 0
\(517\) 62.9809 2.76990
\(518\) 0 0
\(519\) 34.2899 1.50516
\(520\) 0 0
\(521\) −14.4262 −0.632025 −0.316012 0.948755i \(-0.602344\pi\)
−0.316012 + 0.948755i \(0.602344\pi\)
\(522\) 0 0
\(523\) 41.7897 1.82734 0.913669 0.406460i \(-0.133237\pi\)
0.913669 + 0.406460i \(0.133237\pi\)
\(524\) 0 0
\(525\) −5.64097 −0.246192
\(526\) 0 0
\(527\) −39.8054 −1.73395
\(528\) 0 0
\(529\) −21.7795 −0.946934
\(530\) 0 0
\(531\) −4.63848 −0.201293
\(532\) 0 0
\(533\) −26.1263 −1.13166
\(534\) 0 0
\(535\) 32.6515 1.41165
\(536\) 0 0
\(537\) −51.3461 −2.21575
\(538\) 0 0
\(539\) 6.62607 0.285405
\(540\) 0 0
\(541\) 31.1607 1.33970 0.669852 0.742495i \(-0.266358\pi\)
0.669852 + 0.742495i \(0.266358\pi\)
\(542\) 0 0
\(543\) −53.0190 −2.27526
\(544\) 0 0
\(545\) 15.4026 0.659773
\(546\) 0 0
\(547\) 23.8696 1.02059 0.510295 0.859999i \(-0.329536\pi\)
0.510295 + 0.859999i \(0.329536\pi\)
\(548\) 0 0
\(549\) −15.4047 −0.657456
\(550\) 0 0
\(551\) 17.3244 0.738043
\(552\) 0 0
\(553\) 33.2820 1.41529
\(554\) 0 0
\(555\) −22.9806 −0.975472
\(556\) 0 0
\(557\) 4.87995 0.206770 0.103385 0.994641i \(-0.467033\pi\)
0.103385 + 0.994641i \(0.467033\pi\)
\(558\) 0 0
\(559\) −16.0737 −0.679847
\(560\) 0 0
\(561\) 79.4496 3.35437
\(562\) 0 0
\(563\) 34.0486 1.43498 0.717488 0.696571i \(-0.245292\pi\)
0.717488 + 0.696571i \(0.245292\pi\)
\(564\) 0 0
\(565\) 12.0896 0.508612
\(566\) 0 0
\(567\) −30.9402 −1.29937
\(568\) 0 0
\(569\) −37.1262 −1.55641 −0.778205 0.628010i \(-0.783870\pi\)
−0.778205 + 0.628010i \(0.783870\pi\)
\(570\) 0 0
\(571\) 2.54908 0.106676 0.0533379 0.998577i \(-0.483014\pi\)
0.0533379 + 0.998577i \(0.483014\pi\)
\(572\) 0 0
\(573\) 35.4630 1.48149
\(574\) 0 0
\(575\) −0.966463 −0.0403043
\(576\) 0 0
\(577\) 7.33113 0.305199 0.152599 0.988288i \(-0.451236\pi\)
0.152599 + 0.988288i \(0.451236\pi\)
\(578\) 0 0
\(579\) 24.8073 1.03096
\(580\) 0 0
\(581\) −13.3613 −0.554319
\(582\) 0 0
\(583\) −61.0895 −2.53007
\(584\) 0 0
\(585\) −13.2135 −0.546310
\(586\) 0 0
\(587\) −35.0156 −1.44525 −0.722625 0.691240i \(-0.757065\pi\)
−0.722625 + 0.691240i \(0.757065\pi\)
\(588\) 0 0
\(589\) −17.3879 −0.716454
\(590\) 0 0
\(591\) −16.5842 −0.682183
\(592\) 0 0
\(593\) −23.5914 −0.968781 −0.484391 0.874852i \(-0.660959\pi\)
−0.484391 + 0.874852i \(0.660959\pi\)
\(594\) 0 0
\(595\) −34.1817 −1.40131
\(596\) 0 0
\(597\) 4.45232 0.182221
\(598\) 0 0
\(599\) −26.1880 −1.07001 −0.535006 0.844848i \(-0.679691\pi\)
−0.535006 + 0.844848i \(0.679691\pi\)
\(600\) 0 0
\(601\) 1.98654 0.0810328 0.0405164 0.999179i \(-0.487100\pi\)
0.0405164 + 0.999179i \(0.487100\pi\)
\(602\) 0 0
\(603\) 14.9156 0.607410
\(604\) 0 0
\(605\) −49.3528 −2.00648
\(606\) 0 0
\(607\) 8.92706 0.362338 0.181169 0.983452i \(-0.442012\pi\)
0.181169 + 0.983452i \(0.442012\pi\)
\(608\) 0 0
\(609\) 43.2887 1.75415
\(610\) 0 0
\(611\) 32.4743 1.31377
\(612\) 0 0
\(613\) −28.3094 −1.14341 −0.571703 0.820460i \(-0.693717\pi\)
−0.571703 + 0.820460i \(0.693717\pi\)
\(614\) 0 0
\(615\) 39.2082 1.58103
\(616\) 0 0
\(617\) −19.8166 −0.797787 −0.398894 0.916997i \(-0.630606\pi\)
−0.398894 + 0.916997i \(0.630606\pi\)
\(618\) 0 0
\(619\) 5.77849 0.232257 0.116129 0.993234i \(-0.462952\pi\)
0.116129 + 0.993234i \(0.462952\pi\)
\(620\) 0 0
\(621\) −2.19149 −0.0879416
\(622\) 0 0
\(623\) −35.3664 −1.41693
\(624\) 0 0
\(625\) −19.8607 −0.794427
\(626\) 0 0
\(627\) 34.7053 1.38600
\(628\) 0 0
\(629\) 29.5305 1.17746
\(630\) 0 0
\(631\) −48.0493 −1.91281 −0.956406 0.292040i \(-0.905666\pi\)
−0.956406 + 0.292040i \(0.905666\pi\)
\(632\) 0 0
\(633\) 40.6777 1.61679
\(634\) 0 0
\(635\) −7.73303 −0.306876
\(636\) 0 0
\(637\) 3.41654 0.135368
\(638\) 0 0
\(639\) 25.0624 0.991455
\(640\) 0 0
\(641\) 28.2296 1.11500 0.557501 0.830176i \(-0.311760\pi\)
0.557501 + 0.830176i \(0.311760\pi\)
\(642\) 0 0
\(643\) 30.6110 1.20718 0.603589 0.797295i \(-0.293737\pi\)
0.603589 + 0.797295i \(0.293737\pi\)
\(644\) 0 0
\(645\) 24.1221 0.949808
\(646\) 0 0
\(647\) −34.7903 −1.36775 −0.683873 0.729601i \(-0.739706\pi\)
−0.683873 + 0.729601i \(0.739706\pi\)
\(648\) 0 0
\(649\) −12.9770 −0.509393
\(650\) 0 0
\(651\) −43.4473 −1.70283
\(652\) 0 0
\(653\) −16.4855 −0.645128 −0.322564 0.946548i \(-0.604545\pi\)
−0.322564 + 0.946548i \(0.604545\pi\)
\(654\) 0 0
\(655\) 36.5894 1.42967
\(656\) 0 0
\(657\) −17.0180 −0.663936
\(658\) 0 0
\(659\) −3.56024 −0.138687 −0.0693437 0.997593i \(-0.522091\pi\)
−0.0693437 + 0.997593i \(0.522091\pi\)
\(660\) 0 0
\(661\) −35.1172 −1.36590 −0.682950 0.730466i \(-0.739303\pi\)
−0.682950 + 0.730466i \(0.739303\pi\)
\(662\) 0 0
\(663\) 40.9659 1.59099
\(664\) 0 0
\(665\) −14.9313 −0.579010
\(666\) 0 0
\(667\) 7.41661 0.287172
\(668\) 0 0
\(669\) 1.97167 0.0762293
\(670\) 0 0
\(671\) −43.0975 −1.66376
\(672\) 0 0
\(673\) 11.6622 0.449546 0.224773 0.974411i \(-0.427836\pi\)
0.224773 + 0.974411i \(0.427836\pi\)
\(674\) 0 0
\(675\) 1.73533 0.0667928
\(676\) 0 0
\(677\) −19.2277 −0.738980 −0.369490 0.929235i \(-0.620468\pi\)
−0.369490 + 0.929235i \(0.620468\pi\)
\(678\) 0 0
\(679\) −34.1379 −1.31009
\(680\) 0 0
\(681\) −27.1815 −1.04160
\(682\) 0 0
\(683\) 3.35587 0.128409 0.0642043 0.997937i \(-0.479549\pi\)
0.0642043 + 0.997937i \(0.479549\pi\)
\(684\) 0 0
\(685\) −22.7361 −0.868700
\(686\) 0 0
\(687\) −5.12154 −0.195399
\(688\) 0 0
\(689\) −31.4991 −1.20002
\(690\) 0 0
\(691\) −26.9912 −1.02679 −0.513397 0.858152i \(-0.671613\pi\)
−0.513397 + 0.858152i \(0.671613\pi\)
\(692\) 0 0
\(693\) 35.9431 1.36536
\(694\) 0 0
\(695\) −36.8605 −1.39820
\(696\) 0 0
\(697\) −50.3832 −1.90840
\(698\) 0 0
\(699\) −12.8608 −0.486438
\(700\) 0 0
\(701\) 9.34446 0.352935 0.176468 0.984306i \(-0.443533\pi\)
0.176468 + 0.984306i \(0.443533\pi\)
\(702\) 0 0
\(703\) 12.8995 0.486515
\(704\) 0 0
\(705\) −48.7347 −1.83546
\(706\) 0 0
\(707\) 18.7013 0.703334
\(708\) 0 0
\(709\) 16.9833 0.637820 0.318910 0.947785i \(-0.396683\pi\)
0.318910 + 0.947785i \(0.396683\pi\)
\(710\) 0 0
\(711\) 24.8108 0.930478
\(712\) 0 0
\(713\) −7.44378 −0.278772
\(714\) 0 0
\(715\) −36.9672 −1.38250
\(716\) 0 0
\(717\) −27.7384 −1.03591
\(718\) 0 0
\(719\) −19.0904 −0.711951 −0.355976 0.934495i \(-0.615851\pi\)
−0.355976 + 0.934495i \(0.615851\pi\)
\(720\) 0 0
\(721\) 45.7008 1.70199
\(722\) 0 0
\(723\) 56.9540 2.11814
\(724\) 0 0
\(725\) −5.87282 −0.218111
\(726\) 0 0
\(727\) −13.6110 −0.504803 −0.252402 0.967623i \(-0.581220\pi\)
−0.252402 + 0.967623i \(0.581220\pi\)
\(728\) 0 0
\(729\) −9.59471 −0.355360
\(730\) 0 0
\(731\) −30.9973 −1.14648
\(732\) 0 0
\(733\) 14.2251 0.525416 0.262708 0.964875i \(-0.415384\pi\)
0.262708 + 0.964875i \(0.415384\pi\)
\(734\) 0 0
\(735\) −5.12726 −0.189122
\(736\) 0 0
\(737\) 41.7292 1.53711
\(738\) 0 0
\(739\) 41.4200 1.52366 0.761830 0.647777i \(-0.224301\pi\)
0.761830 + 0.647777i \(0.224301\pi\)
\(740\) 0 0
\(741\) 17.8948 0.657382
\(742\) 0 0
\(743\) 2.14855 0.0788227 0.0394114 0.999223i \(-0.487452\pi\)
0.0394114 + 0.999223i \(0.487452\pi\)
\(744\) 0 0
\(745\) 12.4065 0.454540
\(746\) 0 0
\(747\) −9.96045 −0.364434
\(748\) 0 0
\(749\) −45.7964 −1.67336
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 33.1306 1.20735
\(754\) 0 0
\(755\) 3.42765 0.124745
\(756\) 0 0
\(757\) 11.1801 0.406347 0.203173 0.979143i \(-0.434875\pi\)
0.203173 + 0.979143i \(0.434875\pi\)
\(758\) 0 0
\(759\) 14.8574 0.539290
\(760\) 0 0
\(761\) −26.5107 −0.961011 −0.480506 0.876992i \(-0.659547\pi\)
−0.480506 + 0.876992i \(0.659547\pi\)
\(762\) 0 0
\(763\) −21.6034 −0.782095
\(764\) 0 0
\(765\) −25.4815 −0.921286
\(766\) 0 0
\(767\) −6.69123 −0.241606
\(768\) 0 0
\(769\) −25.7752 −0.929477 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(770\) 0 0
\(771\) −5.56197 −0.200309
\(772\) 0 0
\(773\) −10.7241 −0.385719 −0.192860 0.981226i \(-0.561776\pi\)
−0.192860 + 0.981226i \(0.561776\pi\)
\(774\) 0 0
\(775\) 5.89434 0.211731
\(776\) 0 0
\(777\) 32.2322 1.15633
\(778\) 0 0
\(779\) −22.0084 −0.788534
\(780\) 0 0
\(781\) 70.1169 2.50898
\(782\) 0 0
\(783\) −13.3169 −0.475906
\(784\) 0 0
\(785\) 2.28539 0.0815689
\(786\) 0 0
\(787\) 9.80761 0.349603 0.174802 0.984604i \(-0.444072\pi\)
0.174802 + 0.984604i \(0.444072\pi\)
\(788\) 0 0
\(789\) −31.1955 −1.11059
\(790\) 0 0
\(791\) −16.9566 −0.602909
\(792\) 0 0
\(793\) −22.2220 −0.789127
\(794\) 0 0
\(795\) 47.2712 1.67654
\(796\) 0 0
\(797\) 14.4353 0.511326 0.255663 0.966766i \(-0.417706\pi\)
0.255663 + 0.966766i \(0.417706\pi\)
\(798\) 0 0
\(799\) 62.6249 2.21551
\(800\) 0 0
\(801\) −26.3647 −0.931550
\(802\) 0 0
\(803\) −47.6111 −1.68016
\(804\) 0 0
\(805\) −6.39212 −0.225293
\(806\) 0 0
\(807\) 18.8203 0.662506
\(808\) 0 0
\(809\) −17.7583 −0.624348 −0.312174 0.950025i \(-0.601057\pi\)
−0.312174 + 0.950025i \(0.601057\pi\)
\(810\) 0 0
\(811\) −42.2433 −1.48336 −0.741682 0.670752i \(-0.765972\pi\)
−0.741682 + 0.670752i \(0.765972\pi\)
\(812\) 0 0
\(813\) 25.5144 0.894828
\(814\) 0 0
\(815\) 20.6698 0.724032
\(816\) 0 0
\(817\) −13.5403 −0.473715
\(818\) 0 0
\(819\) 18.5330 0.647596
\(820\) 0 0
\(821\) −13.0015 −0.453756 −0.226878 0.973923i \(-0.572852\pi\)
−0.226878 + 0.973923i \(0.572852\pi\)
\(822\) 0 0
\(823\) −29.7993 −1.03874 −0.519369 0.854550i \(-0.673833\pi\)
−0.519369 + 0.854550i \(0.673833\pi\)
\(824\) 0 0
\(825\) −11.7648 −0.409598
\(826\) 0 0
\(827\) 32.0935 1.11600 0.557999 0.829841i \(-0.311569\pi\)
0.557999 + 0.829841i \(0.311569\pi\)
\(828\) 0 0
\(829\) 24.2528 0.842334 0.421167 0.906983i \(-0.361621\pi\)
0.421167 + 0.906983i \(0.361621\pi\)
\(830\) 0 0
\(831\) 13.2460 0.459498
\(832\) 0 0
\(833\) 6.58862 0.228282
\(834\) 0 0
\(835\) −1.14466 −0.0396127
\(836\) 0 0
\(837\) 13.3657 0.461985
\(838\) 0 0
\(839\) −7.51319 −0.259384 −0.129692 0.991554i \(-0.541399\pi\)
−0.129692 + 0.991554i \(0.541399\pi\)
\(840\) 0 0
\(841\) 16.0679 0.554064
\(842\) 0 0
\(843\) −6.16217 −0.212237
\(844\) 0 0
\(845\) 7.34264 0.252595
\(846\) 0 0
\(847\) 69.2215 2.37848
\(848\) 0 0
\(849\) 60.8049 2.08682
\(850\) 0 0
\(851\) 5.52232 0.189303
\(852\) 0 0
\(853\) −7.77565 −0.266233 −0.133117 0.991100i \(-0.542498\pi\)
−0.133117 + 0.991100i \(0.542498\pi\)
\(854\) 0 0
\(855\) −11.1309 −0.380667
\(856\) 0 0
\(857\) −31.5852 −1.07893 −0.539466 0.842008i \(-0.681374\pi\)
−0.539466 + 0.842008i \(0.681374\pi\)
\(858\) 0 0
\(859\) 47.5576 1.62264 0.811321 0.584600i \(-0.198749\pi\)
0.811321 + 0.584600i \(0.198749\pi\)
\(860\) 0 0
\(861\) −54.9928 −1.87415
\(862\) 0 0
\(863\) 29.4008 1.00082 0.500408 0.865790i \(-0.333183\pi\)
0.500408 + 0.865790i \(0.333183\pi\)
\(864\) 0 0
\(865\) −30.7680 −1.04614
\(866\) 0 0
\(867\) 40.5203 1.37614
\(868\) 0 0
\(869\) 69.4129 2.35467
\(870\) 0 0
\(871\) 21.5165 0.729058
\(872\) 0 0
\(873\) −25.4488 −0.861313
\(874\) 0 0
\(875\) 33.9912 1.14911
\(876\) 0 0
\(877\) 38.9880 1.31653 0.658265 0.752786i \(-0.271291\pi\)
0.658265 + 0.752786i \(0.271291\pi\)
\(878\) 0 0
\(879\) 8.08649 0.272751
\(880\) 0 0
\(881\) −24.9847 −0.841755 −0.420878 0.907117i \(-0.638278\pi\)
−0.420878 + 0.907117i \(0.638278\pi\)
\(882\) 0 0
\(883\) 28.7179 0.966433 0.483217 0.875501i \(-0.339468\pi\)
0.483217 + 0.875501i \(0.339468\pi\)
\(884\) 0 0
\(885\) 10.0416 0.337546
\(886\) 0 0
\(887\) 18.0783 0.607011 0.303506 0.952830i \(-0.401843\pi\)
0.303506 + 0.952830i \(0.401843\pi\)
\(888\) 0 0
\(889\) 10.8462 0.363771
\(890\) 0 0
\(891\) −64.5289 −2.16180
\(892\) 0 0
\(893\) 27.3559 0.915430
\(894\) 0 0
\(895\) 46.0723 1.54003
\(896\) 0 0
\(897\) 7.66081 0.255787
\(898\) 0 0
\(899\) −45.2330 −1.50860
\(900\) 0 0
\(901\) −60.7443 −2.02369
\(902\) 0 0
\(903\) −33.8333 −1.12590
\(904\) 0 0
\(905\) 47.5734 1.58139
\(906\) 0 0
\(907\) 9.19940 0.305461 0.152730 0.988268i \(-0.451193\pi\)
0.152730 + 0.988268i \(0.451193\pi\)
\(908\) 0 0
\(909\) 13.9413 0.462403
\(910\) 0 0
\(911\) 5.85991 0.194148 0.0970738 0.995277i \(-0.469052\pi\)
0.0970738 + 0.995277i \(0.469052\pi\)
\(912\) 0 0
\(913\) −27.8662 −0.922238
\(914\) 0 0
\(915\) 33.3490 1.10248
\(916\) 0 0
\(917\) −51.3198 −1.69473
\(918\) 0 0
\(919\) 31.2584 1.03112 0.515560 0.856854i \(-0.327584\pi\)
0.515560 + 0.856854i \(0.327584\pi\)
\(920\) 0 0
\(921\) 70.5410 2.32441
\(922\) 0 0
\(923\) 36.1538 1.19002
\(924\) 0 0
\(925\) −4.37283 −0.143778
\(926\) 0 0
\(927\) 34.0687 1.11896
\(928\) 0 0
\(929\) 31.3616 1.02894 0.514470 0.857508i \(-0.327989\pi\)
0.514470 + 0.857508i \(0.327989\pi\)
\(930\) 0 0
\(931\) 2.87805 0.0943243
\(932\) 0 0
\(933\) −1.87649 −0.0614335
\(934\) 0 0
\(935\) −71.2893 −2.33141
\(936\) 0 0
\(937\) 5.35220 0.174849 0.0874244 0.996171i \(-0.472136\pi\)
0.0874244 + 0.996171i \(0.472136\pi\)
\(938\) 0 0
\(939\) 33.9210 1.10697
\(940\) 0 0
\(941\) −13.4723 −0.439186 −0.219593 0.975592i \(-0.570473\pi\)
−0.219593 + 0.975592i \(0.570473\pi\)
\(942\) 0 0
\(943\) −9.42186 −0.306818
\(944\) 0 0
\(945\) 11.4773 0.373358
\(946\) 0 0
\(947\) −33.5555 −1.09041 −0.545204 0.838303i \(-0.683548\pi\)
−0.545204 + 0.838303i \(0.683548\pi\)
\(948\) 0 0
\(949\) −24.5493 −0.796904
\(950\) 0 0
\(951\) −68.2463 −2.21304
\(952\) 0 0
\(953\) 36.4805 1.18172 0.590860 0.806774i \(-0.298789\pi\)
0.590860 + 0.806774i \(0.298789\pi\)
\(954\) 0 0
\(955\) −31.8206 −1.02969
\(956\) 0 0
\(957\) 90.2828 2.91843
\(958\) 0 0
\(959\) 31.8892 1.02976
\(960\) 0 0
\(961\) 14.3987 0.464475
\(962\) 0 0
\(963\) −34.1400 −1.10014
\(964\) 0 0
\(965\) −22.2594 −0.716554
\(966\) 0 0
\(967\) 46.5393 1.49660 0.748302 0.663359i \(-0.230870\pi\)
0.748302 + 0.663359i \(0.230870\pi\)
\(968\) 0 0
\(969\) 34.5091 1.10859
\(970\) 0 0
\(971\) −39.2402 −1.25928 −0.629639 0.776888i \(-0.716797\pi\)
−0.629639 + 0.776888i \(0.716797\pi\)
\(972\) 0 0
\(973\) 51.6999 1.65742
\(974\) 0 0
\(975\) −6.06618 −0.194273
\(976\) 0 0
\(977\) 42.5085 1.35997 0.679983 0.733228i \(-0.261987\pi\)
0.679983 + 0.733228i \(0.261987\pi\)
\(978\) 0 0
\(979\) −73.7601 −2.35738
\(980\) 0 0
\(981\) −16.1047 −0.514184
\(982\) 0 0
\(983\) 9.68313 0.308844 0.154422 0.988005i \(-0.450648\pi\)
0.154422 + 0.988005i \(0.450648\pi\)
\(984\) 0 0
\(985\) 14.8808 0.474143
\(986\) 0 0
\(987\) 68.3546 2.17575
\(988\) 0 0
\(989\) −5.79664 −0.184322
\(990\) 0 0
\(991\) 26.7828 0.850783 0.425392 0.905009i \(-0.360136\pi\)
0.425392 + 0.905009i \(0.360136\pi\)
\(992\) 0 0
\(993\) 9.28450 0.294635
\(994\) 0 0
\(995\) −3.99501 −0.126650
\(996\) 0 0
\(997\) 23.2881 0.737541 0.368770 0.929520i \(-0.379779\pi\)
0.368770 + 0.929520i \(0.379779\pi\)
\(998\) 0 0
\(999\) −9.91558 −0.313715
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 \(a_p\))