Properties

Label 6008.2.a.e.1.47
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 1.47
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.04552 q^{3} +0.431846 q^{5} -0.556871 q^{7} +6.27522 q^{9} +O(q^{10})\) \(q+3.04552 q^{3} +0.431846 q^{5} -0.556871 q^{7} +6.27522 q^{9} +5.64578 q^{11} -1.81308 q^{13} +1.31520 q^{15} -5.52057 q^{17} -2.92722 q^{19} -1.69596 q^{21} +3.66295 q^{23} -4.81351 q^{25} +9.97477 q^{27} +7.96759 q^{29} +10.0264 q^{31} +17.1944 q^{33} -0.240483 q^{35} -8.39654 q^{37} -5.52178 q^{39} -2.60870 q^{41} +7.95510 q^{43} +2.70993 q^{45} +6.97252 q^{47} -6.68989 q^{49} -16.8130 q^{51} +13.4233 q^{53} +2.43811 q^{55} -8.91491 q^{57} +5.82100 q^{59} -5.35030 q^{61} -3.49449 q^{63} -0.782971 q^{65} -1.25200 q^{67} +11.1556 q^{69} +15.4685 q^{71} +6.63973 q^{73} -14.6597 q^{75} -3.14397 q^{77} -8.96461 q^{79} +11.5528 q^{81} +5.14195 q^{83} -2.38404 q^{85} +24.2655 q^{87} -1.35055 q^{89} +1.00965 q^{91} +30.5356 q^{93} -1.26411 q^{95} +9.11507 q^{97} +35.4285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 3.04552 1.75833 0.879167 0.476513i \(-0.158100\pi\)
0.879167 + 0.476513i \(0.158100\pi\)
\(4\) 0 0
\(5\) 0.431846 0.193127 0.0965637 0.995327i \(-0.469215\pi\)
0.0965637 + 0.995327i \(0.469215\pi\)
\(6\) 0 0
\(7\) −0.556871 −0.210477 −0.105239 0.994447i \(-0.533561\pi\)
−0.105239 + 0.994447i \(0.533561\pi\)
\(8\) 0 0
\(9\) 6.27522 2.09174
\(10\) 0 0
\(11\) 5.64578 1.70227 0.851133 0.524950i \(-0.175916\pi\)
0.851133 + 0.524950i \(0.175916\pi\)
\(12\) 0 0
\(13\) −1.81308 −0.502858 −0.251429 0.967876i \(-0.580900\pi\)
−0.251429 + 0.967876i \(0.580900\pi\)
\(14\) 0 0
\(15\) 1.31520 0.339583
\(16\) 0 0
\(17\) −5.52057 −1.33894 −0.669468 0.742841i \(-0.733478\pi\)
−0.669468 + 0.742841i \(0.733478\pi\)
\(18\) 0 0
\(19\) −2.92722 −0.671549 −0.335775 0.941942i \(-0.608998\pi\)
−0.335775 + 0.941942i \(0.608998\pi\)
\(20\) 0 0
\(21\) −1.69596 −0.370090
\(22\) 0 0
\(23\) 3.66295 0.763779 0.381889 0.924208i \(-0.375274\pi\)
0.381889 + 0.924208i \(0.375274\pi\)
\(24\) 0 0
\(25\) −4.81351 −0.962702
\(26\) 0 0
\(27\) 9.97477 1.91965
\(28\) 0 0
\(29\) 7.96759 1.47954 0.739772 0.672857i \(-0.234933\pi\)
0.739772 + 0.672857i \(0.234933\pi\)
\(30\) 0 0
\(31\) 10.0264 1.80079 0.900396 0.435072i \(-0.143277\pi\)
0.900396 + 0.435072i \(0.143277\pi\)
\(32\) 0 0
\(33\) 17.1944 2.99315
\(34\) 0 0
\(35\) −0.240483 −0.0406490
\(36\) 0 0
\(37\) −8.39654 −1.38038 −0.690191 0.723627i \(-0.742474\pi\)
−0.690191 + 0.723627i \(0.742474\pi\)
\(38\) 0 0
\(39\) −5.52178 −0.884192
\(40\) 0 0
\(41\) −2.60870 −0.407411 −0.203706 0.979032i \(-0.565299\pi\)
−0.203706 + 0.979032i \(0.565299\pi\)
\(42\) 0 0
\(43\) 7.95510 1.21314 0.606571 0.795030i \(-0.292545\pi\)
0.606571 + 0.795030i \(0.292545\pi\)
\(44\) 0 0
\(45\) 2.70993 0.403973
\(46\) 0 0
\(47\) 6.97252 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(48\) 0 0
\(49\) −6.68989 −0.955699
\(50\) 0 0
\(51\) −16.8130 −2.35430
\(52\) 0 0
\(53\) 13.4233 1.84384 0.921919 0.387382i \(-0.126620\pi\)
0.921919 + 0.387382i \(0.126620\pi\)
\(54\) 0 0
\(55\) 2.43811 0.328754
\(56\) 0 0
\(57\) −8.91491 −1.18081
\(58\) 0 0
\(59\) 5.82100 0.757830 0.378915 0.925431i \(-0.376297\pi\)
0.378915 + 0.925431i \(0.376297\pi\)
\(60\) 0 0
\(61\) −5.35030 −0.685036 −0.342518 0.939511i \(-0.611280\pi\)
−0.342518 + 0.939511i \(0.611280\pi\)
\(62\) 0 0
\(63\) −3.49449 −0.440264
\(64\) 0 0
\(65\) −0.782971 −0.0971156
\(66\) 0 0
\(67\) −1.25200 −0.152957 −0.0764783 0.997071i \(-0.524368\pi\)
−0.0764783 + 0.997071i \(0.524368\pi\)
\(68\) 0 0
\(69\) 11.1556 1.34298
\(70\) 0 0
\(71\) 15.4685 1.83577 0.917884 0.396849i \(-0.129896\pi\)
0.917884 + 0.396849i \(0.129896\pi\)
\(72\) 0 0
\(73\) 6.63973 0.777122 0.388561 0.921423i \(-0.372972\pi\)
0.388561 + 0.921423i \(0.372972\pi\)
\(74\) 0 0
\(75\) −14.6597 −1.69275
\(76\) 0 0
\(77\) −3.14397 −0.358289
\(78\) 0 0
\(79\) −8.96461 −1.00860 −0.504298 0.863529i \(-0.668249\pi\)
−0.504298 + 0.863529i \(0.668249\pi\)
\(80\) 0 0
\(81\) 11.5528 1.28364
\(82\) 0 0
\(83\) 5.14195 0.564402 0.282201 0.959355i \(-0.408935\pi\)
0.282201 + 0.959355i \(0.408935\pi\)
\(84\) 0 0
\(85\) −2.38404 −0.258585
\(86\) 0 0
\(87\) 24.2655 2.60154
\(88\) 0 0
\(89\) −1.35055 −0.143158 −0.0715788 0.997435i \(-0.522804\pi\)
−0.0715788 + 0.997435i \(0.522804\pi\)
\(90\) 0 0
\(91\) 1.00965 0.105840
\(92\) 0 0
\(93\) 30.5356 3.16639
\(94\) 0 0
\(95\) −1.26411 −0.129695
\(96\) 0 0
\(97\) 9.11507 0.925495 0.462748 0.886490i \(-0.346864\pi\)
0.462748 + 0.886490i \(0.346864\pi\)
\(98\) 0 0
\(99\) 35.4285 3.56070
\(100\) 0 0
\(101\) 14.5297 1.44576 0.722882 0.690972i \(-0.242817\pi\)
0.722882 + 0.690972i \(0.242817\pi\)
\(102\) 0 0
\(103\) 8.50046 0.837575 0.418788 0.908084i \(-0.362455\pi\)
0.418788 + 0.908084i \(0.362455\pi\)
\(104\) 0 0
\(105\) −0.732396 −0.0714745
\(106\) 0 0
\(107\) 3.98351 0.385100 0.192550 0.981287i \(-0.438324\pi\)
0.192550 + 0.981287i \(0.438324\pi\)
\(108\) 0 0
\(109\) −10.1946 −0.976470 −0.488235 0.872712i \(-0.662359\pi\)
−0.488235 + 0.872712i \(0.662359\pi\)
\(110\) 0 0
\(111\) −25.5719 −2.42717
\(112\) 0 0
\(113\) −8.28835 −0.779702 −0.389851 0.920878i \(-0.627474\pi\)
−0.389851 + 0.920878i \(0.627474\pi\)
\(114\) 0 0
\(115\) 1.58183 0.147507
\(116\) 0 0
\(117\) −11.3775 −1.05185
\(118\) 0 0
\(119\) 3.07425 0.281816
\(120\) 0 0
\(121\) 20.8748 1.89771
\(122\) 0 0
\(123\) −7.94487 −0.716365
\(124\) 0 0
\(125\) −4.23793 −0.379052
\(126\) 0 0
\(127\) −11.1908 −0.993020 −0.496510 0.868031i \(-0.665385\pi\)
−0.496510 + 0.868031i \(0.665385\pi\)
\(128\) 0 0
\(129\) 24.2275 2.13311
\(130\) 0 0
\(131\) −15.1151 −1.32061 −0.660307 0.750996i \(-0.729574\pi\)
−0.660307 + 0.750996i \(0.729574\pi\)
\(132\) 0 0
\(133\) 1.63008 0.141346
\(134\) 0 0
\(135\) 4.30757 0.370736
\(136\) 0 0
\(137\) −23.0625 −1.97036 −0.985182 0.171510i \(-0.945136\pi\)
−0.985182 + 0.171510i \(0.945136\pi\)
\(138\) 0 0
\(139\) −1.94126 −0.164656 −0.0823278 0.996605i \(-0.526235\pi\)
−0.0823278 + 0.996605i \(0.526235\pi\)
\(140\) 0 0
\(141\) 21.2350 1.78831
\(142\) 0 0
\(143\) −10.2362 −0.855997
\(144\) 0 0
\(145\) 3.44077 0.285741
\(146\) 0 0
\(147\) −20.3742 −1.68044
\(148\) 0 0
\(149\) −11.1336 −0.912096 −0.456048 0.889955i \(-0.650735\pi\)
−0.456048 + 0.889955i \(0.650735\pi\)
\(150\) 0 0
\(151\) −7.42141 −0.603946 −0.301973 0.953317i \(-0.597645\pi\)
−0.301973 + 0.953317i \(0.597645\pi\)
\(152\) 0 0
\(153\) −34.6428 −2.80071
\(154\) 0 0
\(155\) 4.32985 0.347782
\(156\) 0 0
\(157\) −19.9820 −1.59474 −0.797370 0.603491i \(-0.793776\pi\)
−0.797370 + 0.603491i \(0.793776\pi\)
\(158\) 0 0
\(159\) 40.8811 3.24209
\(160\) 0 0
\(161\) −2.03979 −0.160758
\(162\) 0 0
\(163\) −14.0483 −1.10035 −0.550176 0.835049i \(-0.685439\pi\)
−0.550176 + 0.835049i \(0.685439\pi\)
\(164\) 0 0
\(165\) 7.42531 0.578060
\(166\) 0 0
\(167\) 14.4859 1.12095 0.560477 0.828170i \(-0.310618\pi\)
0.560477 + 0.828170i \(0.310618\pi\)
\(168\) 0 0
\(169\) −9.71274 −0.747134
\(170\) 0 0
\(171\) −18.3689 −1.40471
\(172\) 0 0
\(173\) 15.1810 1.15419 0.577095 0.816677i \(-0.304186\pi\)
0.577095 + 0.816677i \(0.304186\pi\)
\(174\) 0 0
\(175\) 2.68050 0.202627
\(176\) 0 0
\(177\) 17.7280 1.33252
\(178\) 0 0
\(179\) 6.50270 0.486035 0.243017 0.970022i \(-0.421863\pi\)
0.243017 + 0.970022i \(0.421863\pi\)
\(180\) 0 0
\(181\) 0.0604375 0.00449228 0.00224614 0.999997i \(-0.499285\pi\)
0.00224614 + 0.999997i \(0.499285\pi\)
\(182\) 0 0
\(183\) −16.2945 −1.20452
\(184\) 0 0
\(185\) −3.62601 −0.266590
\(186\) 0 0
\(187\) −31.1679 −2.27922
\(188\) 0 0
\(189\) −5.55466 −0.404042
\(190\) 0 0
\(191\) −0.267998 −0.0193917 −0.00969583 0.999953i \(-0.503086\pi\)
−0.00969583 + 0.999953i \(0.503086\pi\)
\(192\) 0 0
\(193\) −10.4597 −0.752907 −0.376453 0.926436i \(-0.622857\pi\)
−0.376453 + 0.926436i \(0.622857\pi\)
\(194\) 0 0
\(195\) −2.38456 −0.170762
\(196\) 0 0
\(197\) 2.97933 0.212269 0.106134 0.994352i \(-0.466153\pi\)
0.106134 + 0.994352i \(0.466153\pi\)
\(198\) 0 0
\(199\) −0.134870 −0.00956065 −0.00478032 0.999989i \(-0.501522\pi\)
−0.00478032 + 0.999989i \(0.501522\pi\)
\(200\) 0 0
\(201\) −3.81301 −0.268949
\(202\) 0 0
\(203\) −4.43692 −0.311411
\(204\) 0 0
\(205\) −1.12656 −0.0786822
\(206\) 0 0
\(207\) 22.9859 1.59763
\(208\) 0 0
\(209\) −16.5264 −1.14316
\(210\) 0 0
\(211\) 16.0676 1.10614 0.553071 0.833134i \(-0.313456\pi\)
0.553071 + 0.833134i \(0.313456\pi\)
\(212\) 0 0
\(213\) 47.1096 3.22789
\(214\) 0 0
\(215\) 3.43538 0.234291
\(216\) 0 0
\(217\) −5.58340 −0.379026
\(218\) 0 0
\(219\) 20.2215 1.36644
\(220\) 0 0
\(221\) 10.0092 0.673294
\(222\) 0 0
\(223\) 12.0357 0.805972 0.402986 0.915206i \(-0.367972\pi\)
0.402986 + 0.915206i \(0.367972\pi\)
\(224\) 0 0
\(225\) −30.2058 −2.01372
\(226\) 0 0
\(227\) −14.4378 −0.958272 −0.479136 0.877741i \(-0.659050\pi\)
−0.479136 + 0.877741i \(0.659050\pi\)
\(228\) 0 0
\(229\) −5.24016 −0.346279 −0.173140 0.984897i \(-0.555391\pi\)
−0.173140 + 0.984897i \(0.555391\pi\)
\(230\) 0 0
\(231\) −9.57504 −0.629991
\(232\) 0 0
\(233\) −16.1314 −1.05681 −0.528403 0.848994i \(-0.677209\pi\)
−0.528403 + 0.848994i \(0.677209\pi\)
\(234\) 0 0
\(235\) 3.01105 0.196419
\(236\) 0 0
\(237\) −27.3019 −1.77345
\(238\) 0 0
\(239\) 5.75448 0.372227 0.186113 0.982528i \(-0.440411\pi\)
0.186113 + 0.982528i \(0.440411\pi\)
\(240\) 0 0
\(241\) −0.0221171 −0.00142469 −0.000712344 1.00000i \(-0.500227\pi\)
−0.000712344 1.00000i \(0.500227\pi\)
\(242\) 0 0
\(243\) 5.25987 0.337421
\(244\) 0 0
\(245\) −2.88900 −0.184572
\(246\) 0 0
\(247\) 5.30727 0.337694
\(248\) 0 0
\(249\) 15.6599 0.992408
\(250\) 0 0
\(251\) −23.4453 −1.47985 −0.739926 0.672688i \(-0.765139\pi\)
−0.739926 + 0.672688i \(0.765139\pi\)
\(252\) 0 0
\(253\) 20.6802 1.30015
\(254\) 0 0
\(255\) −7.26065 −0.454679
\(256\) 0 0
\(257\) 8.90928 0.555746 0.277873 0.960618i \(-0.410371\pi\)
0.277873 + 0.960618i \(0.410371\pi\)
\(258\) 0 0
\(259\) 4.67579 0.290539
\(260\) 0 0
\(261\) 49.9984 3.09482
\(262\) 0 0
\(263\) 24.7963 1.52901 0.764504 0.644619i \(-0.222984\pi\)
0.764504 + 0.644619i \(0.222984\pi\)
\(264\) 0 0
\(265\) 5.79682 0.356096
\(266\) 0 0
\(267\) −4.11312 −0.251719
\(268\) 0 0
\(269\) −12.7215 −0.775646 −0.387823 0.921734i \(-0.626773\pi\)
−0.387823 + 0.921734i \(0.626773\pi\)
\(270\) 0 0
\(271\) −14.6495 −0.889894 −0.444947 0.895557i \(-0.646777\pi\)
−0.444947 + 0.895557i \(0.646777\pi\)
\(272\) 0 0
\(273\) 3.07492 0.186103
\(274\) 0 0
\(275\) −27.1760 −1.63877
\(276\) 0 0
\(277\) 1.27406 0.0765509 0.0382755 0.999267i \(-0.487814\pi\)
0.0382755 + 0.999267i \(0.487814\pi\)
\(278\) 0 0
\(279\) 62.9178 3.76679
\(280\) 0 0
\(281\) −18.6217 −1.11088 −0.555440 0.831557i \(-0.687450\pi\)
−0.555440 + 0.831557i \(0.687450\pi\)
\(282\) 0 0
\(283\) 28.6087 1.70061 0.850305 0.526290i \(-0.176417\pi\)
0.850305 + 0.526290i \(0.176417\pi\)
\(284\) 0 0
\(285\) −3.84987 −0.228047
\(286\) 0 0
\(287\) 1.45271 0.0857509
\(288\) 0 0
\(289\) 13.4767 0.792750
\(290\) 0 0
\(291\) 27.7602 1.62733
\(292\) 0 0
\(293\) −14.2469 −0.832315 −0.416157 0.909293i \(-0.636623\pi\)
−0.416157 + 0.909293i \(0.636623\pi\)
\(294\) 0 0
\(295\) 2.51378 0.146358
\(296\) 0 0
\(297\) 56.3153 3.26775
\(298\) 0 0
\(299\) −6.64122 −0.384072
\(300\) 0 0
\(301\) −4.42996 −0.255339
\(302\) 0 0
\(303\) 44.2507 2.54214
\(304\) 0 0
\(305\) −2.31051 −0.132299
\(306\) 0 0
\(307\) −11.9222 −0.680437 −0.340219 0.940346i \(-0.610501\pi\)
−0.340219 + 0.940346i \(0.610501\pi\)
\(308\) 0 0
\(309\) 25.8884 1.47274
\(310\) 0 0
\(311\) 0.926676 0.0525469 0.0262735 0.999655i \(-0.491636\pi\)
0.0262735 + 0.999655i \(0.491636\pi\)
\(312\) 0 0
\(313\) 11.4996 0.649998 0.324999 0.945714i \(-0.394636\pi\)
0.324999 + 0.945714i \(0.394636\pi\)
\(314\) 0 0
\(315\) −1.50908 −0.0850271
\(316\) 0 0
\(317\) 8.84723 0.496910 0.248455 0.968643i \(-0.420077\pi\)
0.248455 + 0.968643i \(0.420077\pi\)
\(318\) 0 0
\(319\) 44.9832 2.51858
\(320\) 0 0
\(321\) 12.1319 0.677135
\(322\) 0 0
\(323\) 16.1599 0.899162
\(324\) 0 0
\(325\) 8.72727 0.484102
\(326\) 0 0
\(327\) −31.0480 −1.71696
\(328\) 0 0
\(329\) −3.88279 −0.214065
\(330\) 0 0
\(331\) 4.77317 0.262357 0.131179 0.991359i \(-0.458124\pi\)
0.131179 + 0.991359i \(0.458124\pi\)
\(332\) 0 0
\(333\) −52.6901 −2.88740
\(334\) 0 0
\(335\) −0.540673 −0.0295401
\(336\) 0 0
\(337\) −9.31159 −0.507235 −0.253617 0.967305i \(-0.581620\pi\)
−0.253617 + 0.967305i \(0.581620\pi\)
\(338\) 0 0
\(339\) −25.2424 −1.37098
\(340\) 0 0
\(341\) 56.6067 3.06543
\(342\) 0 0
\(343\) 7.62351 0.411631
\(344\) 0 0
\(345\) 4.81751 0.259366
\(346\) 0 0
\(347\) 16.3545 0.877957 0.438978 0.898498i \(-0.355340\pi\)
0.438978 + 0.898498i \(0.355340\pi\)
\(348\) 0 0
\(349\) −29.1583 −1.56081 −0.780405 0.625275i \(-0.784987\pi\)
−0.780405 + 0.625275i \(0.784987\pi\)
\(350\) 0 0
\(351\) −18.0851 −0.965309
\(352\) 0 0
\(353\) 15.7968 0.840778 0.420389 0.907344i \(-0.361894\pi\)
0.420389 + 0.907344i \(0.361894\pi\)
\(354\) 0 0
\(355\) 6.67999 0.354537
\(356\) 0 0
\(357\) 9.36270 0.495527
\(358\) 0 0
\(359\) −15.8941 −0.838861 −0.419430 0.907788i \(-0.637770\pi\)
−0.419430 + 0.907788i \(0.637770\pi\)
\(360\) 0 0
\(361\) −10.4314 −0.549022
\(362\) 0 0
\(363\) 63.5747 3.33681
\(364\) 0 0
\(365\) 2.86734 0.150084
\(366\) 0 0
\(367\) 27.5960 1.44050 0.720249 0.693716i \(-0.244027\pi\)
0.720249 + 0.693716i \(0.244027\pi\)
\(368\) 0 0
\(369\) −16.3702 −0.852198
\(370\) 0 0
\(371\) −7.47507 −0.388087
\(372\) 0 0
\(373\) −27.7126 −1.43491 −0.717453 0.696607i \(-0.754692\pi\)
−0.717453 + 0.696607i \(0.754692\pi\)
\(374\) 0 0
\(375\) −12.9067 −0.666500
\(376\) 0 0
\(377\) −14.4459 −0.744000
\(378\) 0 0
\(379\) −37.5567 −1.92916 −0.964578 0.263797i \(-0.915025\pi\)
−0.964578 + 0.263797i \(0.915025\pi\)
\(380\) 0 0
\(381\) −34.0818 −1.74606
\(382\) 0 0
\(383\) 16.9850 0.867894 0.433947 0.900938i \(-0.357121\pi\)
0.433947 + 0.900938i \(0.357121\pi\)
\(384\) 0 0
\(385\) −1.35771 −0.0691954
\(386\) 0 0
\(387\) 49.9200 2.53758
\(388\) 0 0
\(389\) 25.6491 1.30046 0.650230 0.759737i \(-0.274673\pi\)
0.650230 + 0.759737i \(0.274673\pi\)
\(390\) 0 0
\(391\) −20.2216 −1.02265
\(392\) 0 0
\(393\) −46.0334 −2.32208
\(394\) 0 0
\(395\) −3.87133 −0.194788
\(396\) 0 0
\(397\) −17.6198 −0.884315 −0.442157 0.896937i \(-0.645787\pi\)
−0.442157 + 0.896937i \(0.645787\pi\)
\(398\) 0 0
\(399\) 4.96445 0.248534
\(400\) 0 0
\(401\) −0.0825765 −0.00412368 −0.00206184 0.999998i \(-0.500656\pi\)
−0.00206184 + 0.999998i \(0.500656\pi\)
\(402\) 0 0
\(403\) −18.1786 −0.905542
\(404\) 0 0
\(405\) 4.98901 0.247906
\(406\) 0 0
\(407\) −47.4050 −2.34978
\(408\) 0 0
\(409\) 15.1261 0.747937 0.373968 0.927441i \(-0.377997\pi\)
0.373968 + 0.927441i \(0.377997\pi\)
\(410\) 0 0
\(411\) −70.2375 −3.46456
\(412\) 0 0
\(413\) −3.24155 −0.159506
\(414\) 0 0
\(415\) 2.22053 0.109002
\(416\) 0 0
\(417\) −5.91216 −0.289520
\(418\) 0 0
\(419\) −10.6299 −0.519303 −0.259652 0.965702i \(-0.583608\pi\)
−0.259652 + 0.965702i \(0.583608\pi\)
\(420\) 0 0
\(421\) 13.0443 0.635743 0.317871 0.948134i \(-0.397032\pi\)
0.317871 + 0.948134i \(0.397032\pi\)
\(422\) 0 0
\(423\) 43.7541 2.12740
\(424\) 0 0
\(425\) 26.5733 1.28900
\(426\) 0 0
\(427\) 2.97943 0.144185
\(428\) 0 0
\(429\) −31.1747 −1.50513
\(430\) 0 0
\(431\) −5.98042 −0.288067 −0.144033 0.989573i \(-0.546007\pi\)
−0.144033 + 0.989573i \(0.546007\pi\)
\(432\) 0 0
\(433\) −34.4280 −1.65450 −0.827251 0.561832i \(-0.810097\pi\)
−0.827251 + 0.561832i \(0.810097\pi\)
\(434\) 0 0
\(435\) 10.4790 0.502428
\(436\) 0 0
\(437\) −10.7223 −0.512915
\(438\) 0 0
\(439\) −18.6909 −0.892067 −0.446033 0.895016i \(-0.647164\pi\)
−0.446033 + 0.895016i \(0.647164\pi\)
\(440\) 0 0
\(441\) −41.9806 −1.99908
\(442\) 0 0
\(443\) 26.2653 1.24790 0.623952 0.781463i \(-0.285526\pi\)
0.623952 + 0.781463i \(0.285526\pi\)
\(444\) 0 0
\(445\) −0.583228 −0.0276477
\(446\) 0 0
\(447\) −33.9075 −1.60377
\(448\) 0 0
\(449\) 31.1457 1.46985 0.734927 0.678146i \(-0.237216\pi\)
0.734927 + 0.678146i \(0.237216\pi\)
\(450\) 0 0
\(451\) −14.7282 −0.693522
\(452\) 0 0
\(453\) −22.6021 −1.06194
\(454\) 0 0
\(455\) 0.436014 0.0204407
\(456\) 0 0
\(457\) 3.12951 0.146392 0.0731962 0.997318i \(-0.476680\pi\)
0.0731962 + 0.997318i \(0.476680\pi\)
\(458\) 0 0
\(459\) −55.0665 −2.57028
\(460\) 0 0
\(461\) 17.0168 0.792551 0.396275 0.918132i \(-0.370303\pi\)
0.396275 + 0.918132i \(0.370303\pi\)
\(462\) 0 0
\(463\) −12.4354 −0.577922 −0.288961 0.957341i \(-0.593310\pi\)
−0.288961 + 0.957341i \(0.593310\pi\)
\(464\) 0 0
\(465\) 13.1867 0.611518
\(466\) 0 0
\(467\) 19.5862 0.906341 0.453170 0.891424i \(-0.350293\pi\)
0.453170 + 0.891424i \(0.350293\pi\)
\(468\) 0 0
\(469\) 0.697205 0.0321939
\(470\) 0 0
\(471\) −60.8558 −2.80409
\(472\) 0 0
\(473\) 44.9127 2.06509
\(474\) 0 0
\(475\) 14.0902 0.646502
\(476\) 0 0
\(477\) 84.2345 3.85683
\(478\) 0 0
\(479\) −17.0728 −0.780076 −0.390038 0.920799i \(-0.627538\pi\)
−0.390038 + 0.920799i \(0.627538\pi\)
\(480\) 0 0
\(481\) 15.2236 0.694136
\(482\) 0 0
\(483\) −6.21224 −0.282667
\(484\) 0 0
\(485\) 3.93631 0.178739
\(486\) 0 0
\(487\) 5.75640 0.260848 0.130424 0.991458i \(-0.458366\pi\)
0.130424 + 0.991458i \(0.458366\pi\)
\(488\) 0 0
\(489\) −42.7846 −1.93479
\(490\) 0 0
\(491\) −7.78761 −0.351450 −0.175725 0.984439i \(-0.556227\pi\)
−0.175725 + 0.984439i \(0.556227\pi\)
\(492\) 0 0
\(493\) −43.9857 −1.98102
\(494\) 0 0
\(495\) 15.2997 0.687669
\(496\) 0 0
\(497\) −8.61394 −0.386388
\(498\) 0 0
\(499\) −26.1058 −1.16866 −0.584328 0.811518i \(-0.698642\pi\)
−0.584328 + 0.811518i \(0.698642\pi\)
\(500\) 0 0
\(501\) 44.1172 1.97101
\(502\) 0 0
\(503\) −8.78309 −0.391619 −0.195809 0.980642i \(-0.562733\pi\)
−0.195809 + 0.980642i \(0.562733\pi\)
\(504\) 0 0
\(505\) 6.27461 0.279217
\(506\) 0 0
\(507\) −29.5804 −1.31371
\(508\) 0 0
\(509\) −8.66671 −0.384145 −0.192073 0.981381i \(-0.561521\pi\)
−0.192073 + 0.981381i \(0.561521\pi\)
\(510\) 0 0
\(511\) −3.69748 −0.163567
\(512\) 0 0
\(513\) −29.1983 −1.28914
\(514\) 0 0
\(515\) 3.67089 0.161759
\(516\) 0 0
\(517\) 39.3653 1.73128
\(518\) 0 0
\(519\) 46.2341 2.02945
\(520\) 0 0
\(521\) −16.4799 −0.721999 −0.360999 0.932566i \(-0.617564\pi\)
−0.360999 + 0.932566i \(0.617564\pi\)
\(522\) 0 0
\(523\) −37.1570 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(524\) 0 0
\(525\) 8.16354 0.356286
\(526\) 0 0
\(527\) −55.3514 −2.41114
\(528\) 0 0
\(529\) −9.58277 −0.416642
\(530\) 0 0
\(531\) 36.5281 1.58518
\(532\) 0 0
\(533\) 4.72979 0.204870
\(534\) 0 0
\(535\) 1.72026 0.0743734
\(536\) 0 0
\(537\) 19.8041 0.854612
\(538\) 0 0
\(539\) −37.7696 −1.62685
\(540\) 0 0
\(541\) −12.5261 −0.538541 −0.269270 0.963065i \(-0.586782\pi\)
−0.269270 + 0.963065i \(0.586782\pi\)
\(542\) 0 0
\(543\) 0.184064 0.00789893
\(544\) 0 0
\(545\) −4.40252 −0.188583
\(546\) 0 0
\(547\) 35.4441 1.51548 0.757740 0.652557i \(-0.226304\pi\)
0.757740 + 0.652557i \(0.226304\pi\)
\(548\) 0 0
\(549\) −33.5743 −1.43292
\(550\) 0 0
\(551\) −23.3229 −0.993587
\(552\) 0 0
\(553\) 4.99213 0.212287
\(554\) 0 0
\(555\) −11.0431 −0.468754
\(556\) 0 0
\(557\) −16.0444 −0.679824 −0.339912 0.940457i \(-0.610397\pi\)
−0.339912 + 0.940457i \(0.610397\pi\)
\(558\) 0 0
\(559\) −14.4232 −0.610037
\(560\) 0 0
\(561\) −94.9227 −4.00764
\(562\) 0 0
\(563\) −39.4497 −1.66261 −0.831303 0.555820i \(-0.812404\pi\)
−0.831303 + 0.555820i \(0.812404\pi\)
\(564\) 0 0
\(565\) −3.57929 −0.150582
\(566\) 0 0
\(567\) −6.43339 −0.270177
\(568\) 0 0
\(569\) −39.3829 −1.65102 −0.825509 0.564389i \(-0.809112\pi\)
−0.825509 + 0.564389i \(0.809112\pi\)
\(570\) 0 0
\(571\) 13.0484 0.546058 0.273029 0.962006i \(-0.411975\pi\)
0.273029 + 0.962006i \(0.411975\pi\)
\(572\) 0 0
\(573\) −0.816195 −0.0340970
\(574\) 0 0
\(575\) −17.6317 −0.735291
\(576\) 0 0
\(577\) 0.582063 0.0242316 0.0121158 0.999927i \(-0.496143\pi\)
0.0121158 + 0.999927i \(0.496143\pi\)
\(578\) 0 0
\(579\) −31.8553 −1.32386
\(580\) 0 0
\(581\) −2.86340 −0.118794
\(582\) 0 0
\(583\) 75.7852 3.13870
\(584\) 0 0
\(585\) −4.91332 −0.203141
\(586\) 0 0
\(587\) 26.6837 1.10135 0.550677 0.834718i \(-0.314370\pi\)
0.550677 + 0.834718i \(0.314370\pi\)
\(588\) 0 0
\(589\) −29.3494 −1.20932
\(590\) 0 0
\(591\) 9.07363 0.373239
\(592\) 0 0
\(593\) 1.44506 0.0593417 0.0296708 0.999560i \(-0.490554\pi\)
0.0296708 + 0.999560i \(0.490554\pi\)
\(594\) 0 0
\(595\) 1.32760 0.0544264
\(596\) 0 0
\(597\) −0.410749 −0.0168108
\(598\) 0 0
\(599\) 42.0057 1.71631 0.858153 0.513394i \(-0.171612\pi\)
0.858153 + 0.513394i \(0.171612\pi\)
\(600\) 0 0
\(601\) 14.7664 0.602333 0.301167 0.953572i \(-0.402624\pi\)
0.301167 + 0.953572i \(0.402624\pi\)
\(602\) 0 0
\(603\) −7.85660 −0.319945
\(604\) 0 0
\(605\) 9.01470 0.366500
\(606\) 0 0
\(607\) −3.99527 −0.162163 −0.0810816 0.996707i \(-0.525837\pi\)
−0.0810816 + 0.996707i \(0.525837\pi\)
\(608\) 0 0
\(609\) −13.5128 −0.547565
\(610\) 0 0
\(611\) −12.6417 −0.511429
\(612\) 0 0
\(613\) 7.68638 0.310450 0.155225 0.987879i \(-0.450390\pi\)
0.155225 + 0.987879i \(0.450390\pi\)
\(614\) 0 0
\(615\) −3.43096 −0.138350
\(616\) 0 0
\(617\) 46.1071 1.85620 0.928101 0.372330i \(-0.121441\pi\)
0.928101 + 0.372330i \(0.121441\pi\)
\(618\) 0 0
\(619\) −33.9780 −1.36569 −0.682845 0.730563i \(-0.739258\pi\)
−0.682845 + 0.730563i \(0.739258\pi\)
\(620\) 0 0
\(621\) 36.5371 1.46618
\(622\) 0 0
\(623\) 0.752080 0.0301315
\(624\) 0 0
\(625\) 22.2374 0.889497
\(626\) 0 0
\(627\) −50.3316 −2.01005
\(628\) 0 0
\(629\) 46.3537 1.84824
\(630\) 0 0
\(631\) 37.3525 1.48698 0.743490 0.668747i \(-0.233169\pi\)
0.743490 + 0.668747i \(0.233169\pi\)
\(632\) 0 0
\(633\) 48.9344 1.94497
\(634\) 0 0
\(635\) −4.83269 −0.191779
\(636\) 0 0
\(637\) 12.1293 0.480581
\(638\) 0 0
\(639\) 97.0680 3.83995
\(640\) 0 0
\(641\) 31.4926 1.24388 0.621941 0.783064i \(-0.286344\pi\)
0.621941 + 0.783064i \(0.286344\pi\)
\(642\) 0 0
\(643\) 40.8967 1.61281 0.806405 0.591364i \(-0.201410\pi\)
0.806405 + 0.591364i \(0.201410\pi\)
\(644\) 0 0
\(645\) 10.4625 0.411962
\(646\) 0 0
\(647\) −29.4889 −1.15933 −0.579665 0.814855i \(-0.696817\pi\)
−0.579665 + 0.814855i \(0.696817\pi\)
\(648\) 0 0
\(649\) 32.8641 1.29003
\(650\) 0 0
\(651\) −17.0044 −0.666455
\(652\) 0 0
\(653\) 47.3354 1.85238 0.926188 0.377063i \(-0.123066\pi\)
0.926188 + 0.377063i \(0.123066\pi\)
\(654\) 0 0
\(655\) −6.52740 −0.255047
\(656\) 0 0
\(657\) 41.6658 1.62554
\(658\) 0 0
\(659\) −37.3174 −1.45368 −0.726839 0.686808i \(-0.759012\pi\)
−0.726839 + 0.686808i \(0.759012\pi\)
\(660\) 0 0
\(661\) 19.6271 0.763404 0.381702 0.924285i \(-0.375338\pi\)
0.381702 + 0.924285i \(0.375338\pi\)
\(662\) 0 0
\(663\) 30.4834 1.18388
\(664\) 0 0
\(665\) 0.703944 0.0272978
\(666\) 0 0
\(667\) 29.1849 1.13004
\(668\) 0 0
\(669\) 36.6551 1.41717
\(670\) 0 0
\(671\) −30.2066 −1.16611
\(672\) 0 0
\(673\) 11.4867 0.442779 0.221390 0.975185i \(-0.428941\pi\)
0.221390 + 0.975185i \(0.428941\pi\)
\(674\) 0 0
\(675\) −48.0137 −1.84805
\(676\) 0 0
\(677\) 11.9150 0.457929 0.228964 0.973435i \(-0.426466\pi\)
0.228964 + 0.973435i \(0.426466\pi\)
\(678\) 0 0
\(679\) −5.07592 −0.194796
\(680\) 0 0
\(681\) −43.9707 −1.68496
\(682\) 0 0
\(683\) −48.7812 −1.86656 −0.933281 0.359148i \(-0.883067\pi\)
−0.933281 + 0.359148i \(0.883067\pi\)
\(684\) 0 0
\(685\) −9.95946 −0.380532
\(686\) 0 0
\(687\) −15.9590 −0.608875
\(688\) 0 0
\(689\) −24.3376 −0.927188
\(690\) 0 0
\(691\) −26.8692 −1.02215 −0.511077 0.859535i \(-0.670753\pi\)
−0.511077 + 0.859535i \(0.670753\pi\)
\(692\) 0 0
\(693\) −19.7291 −0.749447
\(694\) 0 0
\(695\) −0.838326 −0.0317995
\(696\) 0 0
\(697\) 14.4015 0.545497
\(698\) 0 0
\(699\) −49.1287 −1.85822
\(700\) 0 0
\(701\) −34.6147 −1.30738 −0.653689 0.756763i \(-0.726780\pi\)
−0.653689 + 0.756763i \(0.726780\pi\)
\(702\) 0 0
\(703\) 24.5785 0.926995
\(704\) 0 0
\(705\) 9.17024 0.345371
\(706\) 0 0
\(707\) −8.09119 −0.304301
\(708\) 0 0
\(709\) −39.1391 −1.46990 −0.734950 0.678122i \(-0.762794\pi\)
−0.734950 + 0.678122i \(0.762794\pi\)
\(710\) 0 0
\(711\) −56.2549 −2.10972
\(712\) 0 0
\(713\) 36.7262 1.37541
\(714\) 0 0
\(715\) −4.42048 −0.165317
\(716\) 0 0
\(717\) 17.5254 0.654499
\(718\) 0 0
\(719\) −16.9750 −0.633059 −0.316529 0.948583i \(-0.602518\pi\)
−0.316529 + 0.948583i \(0.602518\pi\)
\(720\) 0 0
\(721\) −4.73366 −0.176291
\(722\) 0 0
\(723\) −0.0673582 −0.00250508
\(724\) 0 0
\(725\) −38.3521 −1.42436
\(726\) 0 0
\(727\) 32.0663 1.18927 0.594637 0.803994i \(-0.297296\pi\)
0.594637 + 0.803994i \(0.297296\pi\)
\(728\) 0 0
\(729\) −18.6392 −0.690340
\(730\) 0 0
\(731\) −43.9167 −1.62432
\(732\) 0 0
\(733\) 21.1436 0.780955 0.390477 0.920613i \(-0.372310\pi\)
0.390477 + 0.920613i \(0.372310\pi\)
\(734\) 0 0
\(735\) −8.79854 −0.324539
\(736\) 0 0
\(737\) −7.06853 −0.260373
\(738\) 0 0
\(739\) −4.13147 −0.151979 −0.0759893 0.997109i \(-0.524211\pi\)
−0.0759893 + 0.997109i \(0.524211\pi\)
\(740\) 0 0
\(741\) 16.1634 0.593779
\(742\) 0 0
\(743\) −41.6327 −1.52735 −0.763677 0.645598i \(-0.776608\pi\)
−0.763677 + 0.645598i \(0.776608\pi\)
\(744\) 0 0
\(745\) −4.80798 −0.176151
\(746\) 0 0
\(747\) 32.2669 1.18058
\(748\) 0 0
\(749\) −2.21830 −0.0810549
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −71.4031 −2.60207
\(754\) 0 0
\(755\) −3.20491 −0.116638
\(756\) 0 0
\(757\) −14.4031 −0.523490 −0.261745 0.965137i \(-0.584298\pi\)
−0.261745 + 0.965137i \(0.584298\pi\)
\(758\) 0 0
\(759\) 62.9821 2.28611
\(760\) 0 0
\(761\) −1.27444 −0.0461984 −0.0230992 0.999733i \(-0.507353\pi\)
−0.0230992 + 0.999733i \(0.507353\pi\)
\(762\) 0 0
\(763\) 5.67710 0.205525
\(764\) 0 0
\(765\) −14.9604 −0.540893
\(766\) 0 0
\(767\) −10.5539 −0.381081
\(768\) 0 0
\(769\) −29.9962 −1.08169 −0.540845 0.841122i \(-0.681895\pi\)
−0.540845 + 0.841122i \(0.681895\pi\)
\(770\) 0 0
\(771\) 27.1334 0.977187
\(772\) 0 0
\(773\) 26.7228 0.961154 0.480577 0.876953i \(-0.340427\pi\)
0.480577 + 0.876953i \(0.340427\pi\)
\(774\) 0 0
\(775\) −48.2621 −1.73363
\(776\) 0 0
\(777\) 14.2402 0.510866
\(778\) 0 0
\(779\) 7.63624 0.273597
\(780\) 0 0
\(781\) 87.3314 3.12496
\(782\) 0 0
\(783\) 79.4749 2.84020
\(784\) 0 0
\(785\) −8.62916 −0.307988
\(786\) 0 0
\(787\) −49.2183 −1.75444 −0.877222 0.480085i \(-0.840606\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(788\) 0 0
\(789\) 75.5178 2.68851
\(790\) 0 0
\(791\) 4.61554 0.164110
\(792\) 0 0
\(793\) 9.70052 0.344475
\(794\) 0 0
\(795\) 17.6544 0.626136
\(796\) 0 0
\(797\) −5.02233 −0.177900 −0.0889500 0.996036i \(-0.528351\pi\)
−0.0889500 + 0.996036i \(0.528351\pi\)
\(798\) 0 0
\(799\) −38.4923 −1.36176
\(800\) 0 0
\(801\) −8.47498 −0.299449
\(802\) 0 0
\(803\) 37.4864 1.32287
\(804\) 0 0
\(805\) −0.880877 −0.0310468
\(806\) 0 0
\(807\) −38.7438 −1.36385
\(808\) 0 0
\(809\) −32.4195 −1.13981 −0.569905 0.821710i \(-0.693020\pi\)
−0.569905 + 0.821710i \(0.693020\pi\)
\(810\) 0 0
\(811\) 29.0962 1.02171 0.510854 0.859668i \(-0.329329\pi\)
0.510854 + 0.859668i \(0.329329\pi\)
\(812\) 0 0
\(813\) −44.6154 −1.56473
\(814\) 0 0
\(815\) −6.06672 −0.212508
\(816\) 0 0
\(817\) −23.2863 −0.814684
\(818\) 0 0
\(819\) 6.33579 0.221390
\(820\) 0 0
\(821\) −19.9253 −0.695396 −0.347698 0.937607i \(-0.613037\pi\)
−0.347698 + 0.937607i \(0.613037\pi\)
\(822\) 0 0
\(823\) −48.7933 −1.70083 −0.850414 0.526114i \(-0.823649\pi\)
−0.850414 + 0.526114i \(0.823649\pi\)
\(824\) 0 0
\(825\) −82.7652 −2.88151
\(826\) 0 0
\(827\) −18.4297 −0.640862 −0.320431 0.947272i \(-0.603828\pi\)
−0.320431 + 0.947272i \(0.603828\pi\)
\(828\) 0 0
\(829\) −18.3126 −0.636024 −0.318012 0.948087i \(-0.603015\pi\)
−0.318012 + 0.948087i \(0.603015\pi\)
\(830\) 0 0
\(831\) 3.88019 0.134602
\(832\) 0 0
\(833\) 36.9321 1.27962
\(834\) 0 0
\(835\) 6.25568 0.216487
\(836\) 0 0
\(837\) 100.011 3.45688
\(838\) 0 0
\(839\) 10.3711 0.358049 0.179024 0.983845i \(-0.442706\pi\)
0.179024 + 0.983845i \(0.442706\pi\)
\(840\) 0 0
\(841\) 34.4825 1.18905
\(842\) 0 0
\(843\) −56.7129 −1.95330
\(844\) 0 0
\(845\) −4.19441 −0.144292
\(846\) 0 0
\(847\) −11.6246 −0.399425
\(848\) 0 0
\(849\) 87.1285 2.99024
\(850\) 0 0
\(851\) −30.7561 −1.05431
\(852\) 0 0
\(853\) 20.1874 0.691204 0.345602 0.938381i \(-0.387675\pi\)
0.345602 + 0.938381i \(0.387675\pi\)
\(854\) 0 0
\(855\) −7.93255 −0.271288
\(856\) 0 0
\(857\) 44.0520 1.50479 0.752394 0.658713i \(-0.228899\pi\)
0.752394 + 0.658713i \(0.228899\pi\)
\(858\) 0 0
\(859\) 11.6716 0.398229 0.199115 0.979976i \(-0.436193\pi\)
0.199115 + 0.979976i \(0.436193\pi\)
\(860\) 0 0
\(861\) 4.42427 0.150779
\(862\) 0 0
\(863\) 3.93770 0.134041 0.0670204 0.997752i \(-0.478651\pi\)
0.0670204 + 0.997752i \(0.478651\pi\)
\(864\) 0 0
\(865\) 6.55585 0.222906
\(866\) 0 0
\(867\) 41.0438 1.39392
\(868\) 0 0
\(869\) −50.6122 −1.71690
\(870\) 0 0
\(871\) 2.26998 0.0769154
\(872\) 0 0
\(873\) 57.1991 1.93590
\(874\) 0 0
\(875\) 2.35998 0.0797818
\(876\) 0 0
\(877\) 7.31165 0.246897 0.123448 0.992351i \(-0.460605\pi\)
0.123448 + 0.992351i \(0.460605\pi\)
\(878\) 0 0
\(879\) −43.3894 −1.46349
\(880\) 0 0
\(881\) 51.0114 1.71862 0.859308 0.511458i \(-0.170895\pi\)
0.859308 + 0.511458i \(0.170895\pi\)
\(882\) 0 0
\(883\) 48.4691 1.63111 0.815557 0.578677i \(-0.196431\pi\)
0.815557 + 0.578677i \(0.196431\pi\)
\(884\) 0 0
\(885\) 7.65577 0.257346
\(886\) 0 0
\(887\) 30.5216 1.02482 0.512408 0.858742i \(-0.328753\pi\)
0.512408 + 0.858742i \(0.328753\pi\)
\(888\) 0 0
\(889\) 6.23181 0.209008
\(890\) 0 0
\(891\) 65.2242 2.18509
\(892\) 0 0
\(893\) −20.4101 −0.682997
\(894\) 0 0
\(895\) 2.80817 0.0938667
\(896\) 0 0
\(897\) −20.2260 −0.675327
\(898\) 0 0
\(899\) 79.8861 2.66435
\(900\) 0 0
\(901\) −74.1046 −2.46878
\(902\) 0 0
\(903\) −13.4916 −0.448971
\(904\) 0 0
\(905\) 0.0260997 0.000867583 0
\(906\) 0 0
\(907\) −25.5773 −0.849279 −0.424639 0.905363i \(-0.639599\pi\)
−0.424639 + 0.905363i \(0.639599\pi\)
\(908\) 0 0
\(909\) 91.1773 3.02416
\(910\) 0 0
\(911\) −25.9596 −0.860079 −0.430040 0.902810i \(-0.641500\pi\)
−0.430040 + 0.902810i \(0.641500\pi\)
\(912\) 0 0
\(913\) 29.0303 0.960762
\(914\) 0 0
\(915\) −7.03670 −0.232626
\(916\) 0 0
\(917\) 8.41717 0.277959
\(918\) 0 0
\(919\) −42.5924 −1.40499 −0.702497 0.711687i \(-0.747932\pi\)
−0.702497 + 0.711687i \(0.747932\pi\)
\(920\) 0 0
\(921\) −36.3094 −1.19644
\(922\) 0 0
\(923\) −28.0455 −0.923130
\(924\) 0 0
\(925\) 40.4168 1.32890
\(926\) 0 0
\(927\) 53.3423 1.75199
\(928\) 0 0
\(929\) −10.5325 −0.345561 −0.172781 0.984960i \(-0.555275\pi\)
−0.172781 + 0.984960i \(0.555275\pi\)
\(930\) 0 0
\(931\) 19.5828 0.641799
\(932\) 0 0
\(933\) 2.82221 0.0923951
\(934\) 0 0
\(935\) −13.4597 −0.440181
\(936\) 0 0
\(937\) −42.9576 −1.40336 −0.701681 0.712491i \(-0.747567\pi\)
−0.701681 + 0.712491i \(0.747567\pi\)
\(938\) 0 0
\(939\) 35.0224 1.14291
\(940\) 0 0
\(941\) 25.3365 0.825947 0.412973 0.910743i \(-0.364490\pi\)
0.412973 + 0.910743i \(0.364490\pi\)
\(942\) 0 0
\(943\) −9.55556 −0.311172
\(944\) 0 0
\(945\) −2.39876 −0.0780316
\(946\) 0 0
\(947\) −43.0906 −1.40026 −0.700128 0.714017i \(-0.746874\pi\)
−0.700128 + 0.714017i \(0.746874\pi\)
\(948\) 0 0
\(949\) −12.0384 −0.390782
\(950\) 0 0
\(951\) 26.9444 0.873734
\(952\) 0 0
\(953\) 18.2786 0.592104 0.296052 0.955172i \(-0.404330\pi\)
0.296052 + 0.955172i \(0.404330\pi\)
\(954\) 0 0
\(955\) −0.115734 −0.00374506
\(956\) 0 0
\(957\) 136.998 4.42850
\(958\) 0 0
\(959\) 12.8429 0.414717
\(960\) 0 0
\(961\) 69.5284 2.24285
\(962\) 0 0
\(963\) 24.9974 0.805529
\(964\) 0 0
\(965\) −4.51699 −0.145407
\(966\) 0 0
\(967\) 47.7804 1.53652 0.768258 0.640141i \(-0.221124\pi\)
0.768258 + 0.640141i \(0.221124\pi\)
\(968\) 0 0
\(969\) 49.2154 1.58103
\(970\) 0 0
\(971\) −50.6508 −1.62546 −0.812731 0.582638i \(-0.802020\pi\)
−0.812731 + 0.582638i \(0.802020\pi\)
\(972\) 0 0
\(973\) 1.08103 0.0346563
\(974\) 0 0
\(975\) 26.5791 0.851213
\(976\) 0 0
\(977\) 29.6523 0.948660 0.474330 0.880347i \(-0.342690\pi\)
0.474330 + 0.880347i \(0.342690\pi\)
\(978\) 0 0
\(979\) −7.62488 −0.243692
\(980\) 0 0
\(981\) −63.9736 −2.04252
\(982\) 0 0
\(983\) −16.4889 −0.525913 −0.262956 0.964808i \(-0.584698\pi\)
−0.262956 + 0.964808i \(0.584698\pi\)
\(984\) 0 0
\(985\) 1.28661 0.0409949
\(986\) 0 0
\(987\) −11.8251 −0.376398
\(988\) 0 0
\(989\) 29.1392 0.926571
\(990\) 0 0
\(991\) −39.4035 −1.25169 −0.625847 0.779946i \(-0.715247\pi\)
−0.625847 + 0.779946i \(0.715247\pi\)
\(992\) 0 0
\(993\) 14.5368 0.461311
\(994\) 0 0
\(995\) −0.0582429 −0.00184642
\(996\) 0 0
\(997\) −22.2256 −0.703891 −0.351945 0.936021i \(-0.614480\pi\)
−0.351945 + 0.936021i \(0.614480\pi\)
\(998\) 0 0
\(999\) −83.7536 −2.64985
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 \(a_p\))