Properties

Label 8048.2.a.v.1.11
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.823496 q^{3} -2.12271 q^{5} -4.15456 q^{7} -2.32185 q^{9} +O(q^{10})\) \(q-0.823496 q^{3} -2.12271 q^{5} -4.15456 q^{7} -2.32185 q^{9} -0.347254 q^{11} +3.83770 q^{13} +1.74804 q^{15} -6.72831 q^{17} +6.76295 q^{19} +3.42126 q^{21} -0.816344 q^{23} -0.494108 q^{25} +4.38253 q^{27} +1.71507 q^{29} -2.32959 q^{31} +0.285962 q^{33} +8.81891 q^{35} +5.48996 q^{37} -3.16033 q^{39} -1.70345 q^{41} +5.51038 q^{43} +4.92862 q^{45} +6.07376 q^{47} +10.2603 q^{49} +5.54074 q^{51} +3.81786 q^{53} +0.737119 q^{55} -5.56926 q^{57} +8.10272 q^{59} -15.2931 q^{61} +9.64627 q^{63} -8.14632 q^{65} +7.22250 q^{67} +0.672256 q^{69} +8.48015 q^{71} -4.46685 q^{73} +0.406896 q^{75} +1.44269 q^{77} -11.7094 q^{79} +3.35657 q^{81} +1.00287 q^{83} +14.2822 q^{85} -1.41235 q^{87} -8.30368 q^{89} -15.9439 q^{91} +1.91841 q^{93} -14.3558 q^{95} +15.0445 q^{97} +0.806273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) −0.823496 −0.475446 −0.237723 0.971333i \(-0.576401\pi\)
−0.237723 + 0.971333i \(0.576401\pi\)
\(4\) 0 0
\(5\) −2.12271 −0.949304 −0.474652 0.880174i \(-0.657426\pi\)
−0.474652 + 0.880174i \(0.657426\pi\)
\(6\) 0 0
\(7\) −4.15456 −1.57027 −0.785137 0.619322i \(-0.787408\pi\)
−0.785137 + 0.619322i \(0.787408\pi\)
\(8\) 0 0
\(9\) −2.32185 −0.773951
\(10\) 0 0
\(11\) −0.347254 −0.104701 −0.0523505 0.998629i \(-0.516671\pi\)
−0.0523505 + 0.998629i \(0.516671\pi\)
\(12\) 0 0
\(13\) 3.83770 1.06439 0.532193 0.846623i \(-0.321368\pi\)
0.532193 + 0.846623i \(0.321368\pi\)
\(14\) 0 0
\(15\) 1.74804 0.451343
\(16\) 0 0
\(17\) −6.72831 −1.63185 −0.815927 0.578154i \(-0.803773\pi\)
−0.815927 + 0.578154i \(0.803773\pi\)
\(18\) 0 0
\(19\) 6.76295 1.55153 0.775763 0.631024i \(-0.217365\pi\)
0.775763 + 0.631024i \(0.217365\pi\)
\(20\) 0 0
\(21\) 3.42126 0.746580
\(22\) 0 0
\(23\) −0.816344 −0.170219 −0.0851097 0.996372i \(-0.527124\pi\)
−0.0851097 + 0.996372i \(0.527124\pi\)
\(24\) 0 0
\(25\) −0.494108 −0.0988217
\(26\) 0 0
\(27\) 4.38253 0.843418
\(28\) 0 0
\(29\) 1.71507 0.318480 0.159240 0.987240i \(-0.449096\pi\)
0.159240 + 0.987240i \(0.449096\pi\)
\(30\) 0 0
\(31\) −2.32959 −0.418406 −0.209203 0.977872i \(-0.567087\pi\)
−0.209203 + 0.977872i \(0.567087\pi\)
\(32\) 0 0
\(33\) 0.285962 0.0497797
\(34\) 0 0
\(35\) 8.81891 1.49067
\(36\) 0 0
\(37\) 5.48996 0.902544 0.451272 0.892386i \(-0.350970\pi\)
0.451272 + 0.892386i \(0.350970\pi\)
\(38\) 0 0
\(39\) −3.16033 −0.506058
\(40\) 0 0
\(41\) −1.70345 −0.266035 −0.133017 0.991114i \(-0.542467\pi\)
−0.133017 + 0.991114i \(0.542467\pi\)
\(42\) 0 0
\(43\) 5.51038 0.840325 0.420163 0.907449i \(-0.361973\pi\)
0.420163 + 0.907449i \(0.361973\pi\)
\(44\) 0 0
\(45\) 4.92862 0.734715
\(46\) 0 0
\(47\) 6.07376 0.885949 0.442974 0.896534i \(-0.353923\pi\)
0.442974 + 0.896534i \(0.353923\pi\)
\(48\) 0 0
\(49\) 10.2603 1.46576
\(50\) 0 0
\(51\) 5.54074 0.775858
\(52\) 0 0
\(53\) 3.81786 0.524424 0.262212 0.965010i \(-0.415548\pi\)
0.262212 + 0.965010i \(0.415548\pi\)
\(54\) 0 0
\(55\) 0.737119 0.0993931
\(56\) 0 0
\(57\) −5.56926 −0.737667
\(58\) 0 0
\(59\) 8.10272 1.05488 0.527442 0.849591i \(-0.323151\pi\)
0.527442 + 0.849591i \(0.323151\pi\)
\(60\) 0 0
\(61\) −15.2931 −1.95808 −0.979039 0.203674i \(-0.934712\pi\)
−0.979039 + 0.203674i \(0.934712\pi\)
\(62\) 0 0
\(63\) 9.64627 1.21532
\(64\) 0 0
\(65\) −8.14632 −1.01043
\(66\) 0 0
\(67\) 7.22250 0.882368 0.441184 0.897417i \(-0.354559\pi\)
0.441184 + 0.897417i \(0.354559\pi\)
\(68\) 0 0
\(69\) 0.672256 0.0809301
\(70\) 0 0
\(71\) 8.48015 1.00641 0.503204 0.864167i \(-0.332154\pi\)
0.503204 + 0.864167i \(0.332154\pi\)
\(72\) 0 0
\(73\) −4.46685 −0.522806 −0.261403 0.965230i \(-0.584185\pi\)
−0.261403 + 0.965230i \(0.584185\pi\)
\(74\) 0 0
\(75\) 0.406896 0.0469843
\(76\) 0 0
\(77\) 1.44269 0.164409
\(78\) 0 0
\(79\) −11.7094 −1.31741 −0.658703 0.752403i \(-0.728895\pi\)
−0.658703 + 0.752403i \(0.728895\pi\)
\(80\) 0 0
\(81\) 3.35657 0.372952
\(82\) 0 0
\(83\) 1.00287 0.110079 0.0550394 0.998484i \(-0.482472\pi\)
0.0550394 + 0.998484i \(0.482472\pi\)
\(84\) 0 0
\(85\) 14.2822 1.54913
\(86\) 0 0
\(87\) −1.41235 −0.151420
\(88\) 0 0
\(89\) −8.30368 −0.880188 −0.440094 0.897952i \(-0.645055\pi\)
−0.440094 + 0.897952i \(0.645055\pi\)
\(90\) 0 0
\(91\) −15.9439 −1.67138
\(92\) 0 0
\(93\) 1.91841 0.198929
\(94\) 0 0
\(95\) −14.3558 −1.47287
\(96\) 0 0
\(97\) 15.0445 1.52753 0.763767 0.645492i \(-0.223348\pi\)
0.763767 + 0.645492i \(0.223348\pi\)
\(98\) 0 0
\(99\) 0.806273 0.0810335
\(100\) 0 0
\(101\) 13.6568 1.35890 0.679452 0.733720i \(-0.262218\pi\)
0.679452 + 0.733720i \(0.262218\pi\)
\(102\) 0 0
\(103\) −11.5941 −1.14240 −0.571202 0.820809i \(-0.693523\pi\)
−0.571202 + 0.820809i \(0.693523\pi\)
\(104\) 0 0
\(105\) −7.26234 −0.708732
\(106\) 0 0
\(107\) 0.824365 0.0796943 0.0398472 0.999206i \(-0.487313\pi\)
0.0398472 + 0.999206i \(0.487313\pi\)
\(108\) 0 0
\(109\) −7.67512 −0.735144 −0.367572 0.929995i \(-0.619811\pi\)
−0.367572 + 0.929995i \(0.619811\pi\)
\(110\) 0 0
\(111\) −4.52096 −0.429111
\(112\) 0 0
\(113\) 1.59341 0.149895 0.0749475 0.997187i \(-0.476121\pi\)
0.0749475 + 0.997187i \(0.476121\pi\)
\(114\) 0 0
\(115\) 1.73286 0.161590
\(116\) 0 0
\(117\) −8.91058 −0.823783
\(118\) 0 0
\(119\) 27.9531 2.56246
\(120\) 0 0
\(121\) −10.8794 −0.989038
\(122\) 0 0
\(123\) 1.40279 0.126485
\(124\) 0 0
\(125\) 11.6624 1.04312
\(126\) 0 0
\(127\) 15.7093 1.39397 0.696987 0.717083i \(-0.254523\pi\)
0.696987 + 0.717083i \(0.254523\pi\)
\(128\) 0 0
\(129\) −4.53778 −0.399529
\(130\) 0 0
\(131\) 19.7398 1.72468 0.862339 0.506332i \(-0.168999\pi\)
0.862339 + 0.506332i \(0.168999\pi\)
\(132\) 0 0
\(133\) −28.0971 −2.43632
\(134\) 0 0
\(135\) −9.30283 −0.800660
\(136\) 0 0
\(137\) −0.120001 −0.0102524 −0.00512618 0.999987i \(-0.501632\pi\)
−0.00512618 + 0.999987i \(0.501632\pi\)
\(138\) 0 0
\(139\) −2.83196 −0.240204 −0.120102 0.992762i \(-0.538322\pi\)
−0.120102 + 0.992762i \(0.538322\pi\)
\(140\) 0 0
\(141\) −5.00172 −0.421220
\(142\) 0 0
\(143\) −1.33266 −0.111442
\(144\) 0 0
\(145\) −3.64059 −0.302335
\(146\) 0 0
\(147\) −8.44934 −0.696890
\(148\) 0 0
\(149\) −8.31380 −0.681093 −0.340546 0.940228i \(-0.610612\pi\)
−0.340546 + 0.940228i \(0.610612\pi\)
\(150\) 0 0
\(151\) −5.69855 −0.463742 −0.231871 0.972747i \(-0.574485\pi\)
−0.231871 + 0.972747i \(0.574485\pi\)
\(152\) 0 0
\(153\) 15.6222 1.26298
\(154\) 0 0
\(155\) 4.94503 0.397195
\(156\) 0 0
\(157\) −2.49199 −0.198883 −0.0994413 0.995043i \(-0.531706\pi\)
−0.0994413 + 0.995043i \(0.531706\pi\)
\(158\) 0 0
\(159\) −3.14400 −0.249335
\(160\) 0 0
\(161\) 3.39155 0.267291
\(162\) 0 0
\(163\) −8.83664 −0.692139 −0.346070 0.938209i \(-0.612484\pi\)
−0.346070 + 0.938209i \(0.612484\pi\)
\(164\) 0 0
\(165\) −0.607015 −0.0472560
\(166\) 0 0
\(167\) −0.457582 −0.0354088 −0.0177044 0.999843i \(-0.505636\pi\)
−0.0177044 + 0.999843i \(0.505636\pi\)
\(168\) 0 0
\(169\) 1.72794 0.132918
\(170\) 0 0
\(171\) −15.7026 −1.20081
\(172\) 0 0
\(173\) 16.9072 1.28543 0.642717 0.766104i \(-0.277807\pi\)
0.642717 + 0.766104i \(0.277807\pi\)
\(174\) 0 0
\(175\) 2.05280 0.155177
\(176\) 0 0
\(177\) −6.67256 −0.501540
\(178\) 0 0
\(179\) 3.81648 0.285257 0.142628 0.989776i \(-0.454445\pi\)
0.142628 + 0.989776i \(0.454445\pi\)
\(180\) 0 0
\(181\) 14.4118 1.07122 0.535611 0.844465i \(-0.320081\pi\)
0.535611 + 0.844465i \(0.320081\pi\)
\(182\) 0 0
\(183\) 12.5938 0.930960
\(184\) 0 0
\(185\) −11.6536 −0.856789
\(186\) 0 0
\(187\) 2.33643 0.170857
\(188\) 0 0
\(189\) −18.2074 −1.32440
\(190\) 0 0
\(191\) 18.5386 1.34140 0.670701 0.741728i \(-0.265993\pi\)
0.670701 + 0.741728i \(0.265993\pi\)
\(192\) 0 0
\(193\) −24.7549 −1.78190 −0.890949 0.454103i \(-0.849960\pi\)
−0.890949 + 0.454103i \(0.849960\pi\)
\(194\) 0 0
\(195\) 6.70846 0.480403
\(196\) 0 0
\(197\) −21.0824 −1.50206 −0.751030 0.660268i \(-0.770443\pi\)
−0.751030 + 0.660268i \(0.770443\pi\)
\(198\) 0 0
\(199\) −24.5709 −1.74179 −0.870893 0.491472i \(-0.836459\pi\)
−0.870893 + 0.491472i \(0.836459\pi\)
\(200\) 0 0
\(201\) −5.94770 −0.419518
\(202\) 0 0
\(203\) −7.12535 −0.500102
\(204\) 0 0
\(205\) 3.61594 0.252548
\(206\) 0 0
\(207\) 1.89543 0.131742
\(208\) 0 0
\(209\) −2.34846 −0.162447
\(210\) 0 0
\(211\) 4.17275 0.287264 0.143632 0.989631i \(-0.454122\pi\)
0.143632 + 0.989631i \(0.454122\pi\)
\(212\) 0 0
\(213\) −6.98337 −0.478493
\(214\) 0 0
\(215\) −11.6969 −0.797724
\(216\) 0 0
\(217\) 9.67840 0.657013
\(218\) 0 0
\(219\) 3.67844 0.248566
\(220\) 0 0
\(221\) −25.8212 −1.73692
\(222\) 0 0
\(223\) −12.7125 −0.851293 −0.425646 0.904890i \(-0.639953\pi\)
−0.425646 + 0.904890i \(0.639953\pi\)
\(224\) 0 0
\(225\) 1.14725 0.0764832
\(226\) 0 0
\(227\) 1.68166 0.111616 0.0558079 0.998442i \(-0.482227\pi\)
0.0558079 + 0.998442i \(0.482227\pi\)
\(228\) 0 0
\(229\) −20.5569 −1.35844 −0.679218 0.733937i \(-0.737681\pi\)
−0.679218 + 0.733937i \(0.737681\pi\)
\(230\) 0 0
\(231\) −1.18805 −0.0781677
\(232\) 0 0
\(233\) −21.2247 −1.39047 −0.695237 0.718780i \(-0.744701\pi\)
−0.695237 + 0.718780i \(0.744701\pi\)
\(234\) 0 0
\(235\) −12.8928 −0.841035
\(236\) 0 0
\(237\) 9.64262 0.626355
\(238\) 0 0
\(239\) 25.0093 1.61772 0.808859 0.588003i \(-0.200086\pi\)
0.808859 + 0.588003i \(0.200086\pi\)
\(240\) 0 0
\(241\) 0.373029 0.0240289 0.0120145 0.999928i \(-0.496176\pi\)
0.0120145 + 0.999928i \(0.496176\pi\)
\(242\) 0 0
\(243\) −15.9117 −1.02074
\(244\) 0 0
\(245\) −21.7797 −1.39145
\(246\) 0 0
\(247\) 25.9542 1.65142
\(248\) 0 0
\(249\) −0.825856 −0.0523365
\(250\) 0 0
\(251\) 3.81990 0.241110 0.120555 0.992707i \(-0.461533\pi\)
0.120555 + 0.992707i \(0.461533\pi\)
\(252\) 0 0
\(253\) 0.283479 0.0178222
\(254\) 0 0
\(255\) −11.7614 −0.736526
\(256\) 0 0
\(257\) −21.7329 −1.35566 −0.677831 0.735218i \(-0.737080\pi\)
−0.677831 + 0.735218i \(0.737080\pi\)
\(258\) 0 0
\(259\) −22.8084 −1.41724
\(260\) 0 0
\(261\) −3.98214 −0.246488
\(262\) 0 0
\(263\) 3.00331 0.185192 0.0925961 0.995704i \(-0.470483\pi\)
0.0925961 + 0.995704i \(0.470483\pi\)
\(264\) 0 0
\(265\) −8.10421 −0.497838
\(266\) 0 0
\(267\) 6.83805 0.418482
\(268\) 0 0
\(269\) 7.97821 0.486440 0.243220 0.969971i \(-0.421796\pi\)
0.243220 + 0.969971i \(0.421796\pi\)
\(270\) 0 0
\(271\) −19.9565 −1.21227 −0.606137 0.795360i \(-0.707282\pi\)
−0.606137 + 0.795360i \(0.707282\pi\)
\(272\) 0 0
\(273\) 13.1298 0.794650
\(274\) 0 0
\(275\) 0.171581 0.0103467
\(276\) 0 0
\(277\) −25.8065 −1.55056 −0.775281 0.631616i \(-0.782392\pi\)
−0.775281 + 0.631616i \(0.782392\pi\)
\(278\) 0 0
\(279\) 5.40896 0.323826
\(280\) 0 0
\(281\) −2.93470 −0.175070 −0.0875348 0.996161i \(-0.527899\pi\)
−0.0875348 + 0.996161i \(0.527899\pi\)
\(282\) 0 0
\(283\) 21.3900 1.27151 0.635753 0.771893i \(-0.280690\pi\)
0.635753 + 0.771893i \(0.280690\pi\)
\(284\) 0 0
\(285\) 11.8219 0.700270
\(286\) 0 0
\(287\) 7.07710 0.417748
\(288\) 0 0
\(289\) 28.2702 1.66295
\(290\) 0 0
\(291\) −12.3891 −0.726260
\(292\) 0 0
\(293\) −25.3928 −1.48346 −0.741731 0.670697i \(-0.765995\pi\)
−0.741731 + 0.670697i \(0.765995\pi\)
\(294\) 0 0
\(295\) −17.1997 −1.00141
\(296\) 0 0
\(297\) −1.52185 −0.0883067
\(298\) 0 0
\(299\) −3.13288 −0.181179
\(300\) 0 0
\(301\) −22.8932 −1.31954
\(302\) 0 0
\(303\) −11.2463 −0.646085
\(304\) 0 0
\(305\) 32.4627 1.85881
\(306\) 0 0
\(307\) −10.6838 −0.609757 −0.304879 0.952391i \(-0.598616\pi\)
−0.304879 + 0.952391i \(0.598616\pi\)
\(308\) 0 0
\(309\) 9.54773 0.543151
\(310\) 0 0
\(311\) −19.3607 −1.09785 −0.548923 0.835873i \(-0.684962\pi\)
−0.548923 + 0.835873i \(0.684962\pi\)
\(312\) 0 0
\(313\) 7.47721 0.422637 0.211318 0.977417i \(-0.432224\pi\)
0.211318 + 0.977417i \(0.432224\pi\)
\(314\) 0 0
\(315\) −20.4762 −1.15370
\(316\) 0 0
\(317\) −27.9433 −1.56945 −0.784726 0.619843i \(-0.787196\pi\)
−0.784726 + 0.619843i \(0.787196\pi\)
\(318\) 0 0
\(319\) −0.595565 −0.0333452
\(320\) 0 0
\(321\) −0.678861 −0.0378903
\(322\) 0 0
\(323\) −45.5032 −2.53187
\(324\) 0 0
\(325\) −1.89624 −0.105184
\(326\) 0 0
\(327\) 6.32044 0.349521
\(328\) 0 0
\(329\) −25.2338 −1.39118
\(330\) 0 0
\(331\) 8.06821 0.443469 0.221735 0.975107i \(-0.428828\pi\)
0.221735 + 0.975107i \(0.428828\pi\)
\(332\) 0 0
\(333\) −12.7469 −0.698525
\(334\) 0 0
\(335\) −15.3313 −0.837636
\(336\) 0 0
\(337\) 10.1703 0.554013 0.277007 0.960868i \(-0.410658\pi\)
0.277007 + 0.960868i \(0.410658\pi\)
\(338\) 0 0
\(339\) −1.31216 −0.0712669
\(340\) 0 0
\(341\) 0.808959 0.0438076
\(342\) 0 0
\(343\) −13.5452 −0.731374
\(344\) 0 0
\(345\) −1.42700 −0.0768273
\(346\) 0 0
\(347\) 34.9374 1.87554 0.937768 0.347263i \(-0.112889\pi\)
0.937768 + 0.347263i \(0.112889\pi\)
\(348\) 0 0
\(349\) 1.37287 0.0734880 0.0367440 0.999325i \(-0.488301\pi\)
0.0367440 + 0.999325i \(0.488301\pi\)
\(350\) 0 0
\(351\) 16.8188 0.897722
\(352\) 0 0
\(353\) 31.0396 1.65207 0.826035 0.563619i \(-0.190591\pi\)
0.826035 + 0.563619i \(0.190591\pi\)
\(354\) 0 0
\(355\) −18.0009 −0.955388
\(356\) 0 0
\(357\) −23.0193 −1.21831
\(358\) 0 0
\(359\) 11.8881 0.627431 0.313715 0.949517i \(-0.398426\pi\)
0.313715 + 0.949517i \(0.398426\pi\)
\(360\) 0 0
\(361\) 26.7375 1.40724
\(362\) 0 0
\(363\) 8.95916 0.470234
\(364\) 0 0
\(365\) 9.48183 0.496302
\(366\) 0 0
\(367\) −9.16528 −0.478424 −0.239212 0.970967i \(-0.576889\pi\)
−0.239212 + 0.970967i \(0.576889\pi\)
\(368\) 0 0
\(369\) 3.95517 0.205898
\(370\) 0 0
\(371\) −15.8615 −0.823489
\(372\) 0 0
\(373\) −14.7199 −0.762166 −0.381083 0.924541i \(-0.624449\pi\)
−0.381083 + 0.924541i \(0.624449\pi\)
\(374\) 0 0
\(375\) −9.60393 −0.495945
\(376\) 0 0
\(377\) 6.58192 0.338986
\(378\) 0 0
\(379\) −7.82369 −0.401876 −0.200938 0.979604i \(-0.564399\pi\)
−0.200938 + 0.979604i \(0.564399\pi\)
\(380\) 0 0
\(381\) −12.9365 −0.662759
\(382\) 0 0
\(383\) −4.55131 −0.232561 −0.116280 0.993216i \(-0.537097\pi\)
−0.116280 + 0.993216i \(0.537097\pi\)
\(384\) 0 0
\(385\) −3.06240 −0.156075
\(386\) 0 0
\(387\) −12.7943 −0.650371
\(388\) 0 0
\(389\) 28.8205 1.46126 0.730628 0.682776i \(-0.239228\pi\)
0.730628 + 0.682776i \(0.239228\pi\)
\(390\) 0 0
\(391\) 5.49261 0.277773
\(392\) 0 0
\(393\) −16.2557 −0.819991
\(394\) 0 0
\(395\) 24.8556 1.25062
\(396\) 0 0
\(397\) −10.9789 −0.551013 −0.275506 0.961299i \(-0.588846\pi\)
−0.275506 + 0.961299i \(0.588846\pi\)
\(398\) 0 0
\(399\) 23.1378 1.15834
\(400\) 0 0
\(401\) 8.07798 0.403395 0.201697 0.979448i \(-0.435354\pi\)
0.201697 + 0.979448i \(0.435354\pi\)
\(402\) 0 0
\(403\) −8.94026 −0.445346
\(404\) 0 0
\(405\) −7.12502 −0.354045
\(406\) 0 0
\(407\) −1.90641 −0.0944973
\(408\) 0 0
\(409\) 12.3101 0.608695 0.304348 0.952561i \(-0.401562\pi\)
0.304348 + 0.952561i \(0.401562\pi\)
\(410\) 0 0
\(411\) 0.0988202 0.00487444
\(412\) 0 0
\(413\) −33.6632 −1.65646
\(414\) 0 0
\(415\) −2.12879 −0.104498
\(416\) 0 0
\(417\) 2.33211 0.114204
\(418\) 0 0
\(419\) −4.56527 −0.223028 −0.111514 0.993763i \(-0.535570\pi\)
−0.111514 + 0.993763i \(0.535570\pi\)
\(420\) 0 0
\(421\) −6.55210 −0.319330 −0.159665 0.987171i \(-0.551041\pi\)
−0.159665 + 0.987171i \(0.551041\pi\)
\(422\) 0 0
\(423\) −14.1024 −0.685681
\(424\) 0 0
\(425\) 3.32451 0.161263
\(426\) 0 0
\(427\) 63.5359 3.07472
\(428\) 0 0
\(429\) 1.09744 0.0529848
\(430\) 0 0
\(431\) 28.2823 1.36231 0.681155 0.732140i \(-0.261478\pi\)
0.681155 + 0.732140i \(0.261478\pi\)
\(432\) 0 0
\(433\) 4.34310 0.208716 0.104358 0.994540i \(-0.466721\pi\)
0.104358 + 0.994540i \(0.466721\pi\)
\(434\) 0 0
\(435\) 2.99801 0.143744
\(436\) 0 0
\(437\) −5.52089 −0.264100
\(438\) 0 0
\(439\) −35.3827 −1.68872 −0.844362 0.535773i \(-0.820020\pi\)
−0.844362 + 0.535773i \(0.820020\pi\)
\(440\) 0 0
\(441\) −23.8230 −1.13443
\(442\) 0 0
\(443\) −34.2931 −1.62932 −0.814658 0.579942i \(-0.803075\pi\)
−0.814658 + 0.579942i \(0.803075\pi\)
\(444\) 0 0
\(445\) 17.6263 0.835566
\(446\) 0 0
\(447\) 6.84638 0.323823
\(448\) 0 0
\(449\) 31.0109 1.46350 0.731748 0.681575i \(-0.238705\pi\)
0.731748 + 0.681575i \(0.238705\pi\)
\(450\) 0 0
\(451\) 0.591531 0.0278541
\(452\) 0 0
\(453\) 4.69273 0.220484
\(454\) 0 0
\(455\) 33.8443 1.58665
\(456\) 0 0
\(457\) 19.3168 0.903600 0.451800 0.892119i \(-0.350782\pi\)
0.451800 + 0.892119i \(0.350782\pi\)
\(458\) 0 0
\(459\) −29.4870 −1.37634
\(460\) 0 0
\(461\) 39.8254 1.85485 0.927427 0.374004i \(-0.122015\pi\)
0.927427 + 0.374004i \(0.122015\pi\)
\(462\) 0 0
\(463\) −41.4088 −1.92443 −0.962216 0.272287i \(-0.912220\pi\)
−0.962216 + 0.272287i \(0.912220\pi\)
\(464\) 0 0
\(465\) −4.07222 −0.188845
\(466\) 0 0
\(467\) 28.5289 1.32016 0.660080 0.751195i \(-0.270522\pi\)
0.660080 + 0.751195i \(0.270522\pi\)
\(468\) 0 0
\(469\) −30.0063 −1.38556
\(470\) 0 0
\(471\) 2.05215 0.0945579
\(472\) 0 0
\(473\) −1.91350 −0.0879829
\(474\) 0 0
\(475\) −3.34163 −0.153324
\(476\) 0 0
\(477\) −8.86452 −0.405879
\(478\) 0 0
\(479\) −26.6159 −1.21611 −0.608056 0.793894i \(-0.708050\pi\)
−0.608056 + 0.793894i \(0.708050\pi\)
\(480\) 0 0
\(481\) 21.0688 0.960656
\(482\) 0 0
\(483\) −2.79292 −0.127082
\(484\) 0 0
\(485\) −31.9350 −1.45009
\(486\) 0 0
\(487\) −37.0051 −1.67686 −0.838430 0.545010i \(-0.816526\pi\)
−0.838430 + 0.545010i \(0.816526\pi\)
\(488\) 0 0
\(489\) 7.27694 0.329075
\(490\) 0 0
\(491\) −17.0755 −0.770605 −0.385302 0.922790i \(-0.625903\pi\)
−0.385302 + 0.922790i \(0.625903\pi\)
\(492\) 0 0
\(493\) −11.5395 −0.519714
\(494\) 0 0
\(495\) −1.71148 −0.0769255
\(496\) 0 0
\(497\) −35.2313 −1.58034
\(498\) 0 0
\(499\) −29.3453 −1.31367 −0.656837 0.754033i \(-0.728106\pi\)
−0.656837 + 0.754033i \(0.728106\pi\)
\(500\) 0 0
\(501\) 0.376817 0.0168350
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −28.9894 −1.29001
\(506\) 0 0
\(507\) −1.42295 −0.0631955
\(508\) 0 0
\(509\) −10.3858 −0.460343 −0.230171 0.973150i \(-0.573929\pi\)
−0.230171 + 0.973150i \(0.573929\pi\)
\(510\) 0 0
\(511\) 18.5578 0.820949
\(512\) 0 0
\(513\) 29.6388 1.30859
\(514\) 0 0
\(515\) 24.6110 1.08449
\(516\) 0 0
\(517\) −2.10914 −0.0927598
\(518\) 0 0
\(519\) −13.9230 −0.611154
\(520\) 0 0
\(521\) −26.5151 −1.16165 −0.580823 0.814030i \(-0.697269\pi\)
−0.580823 + 0.814030i \(0.697269\pi\)
\(522\) 0 0
\(523\) 37.8472 1.65494 0.827472 0.561507i \(-0.189778\pi\)
0.827472 + 0.561507i \(0.189778\pi\)
\(524\) 0 0
\(525\) −1.69047 −0.0737783
\(526\) 0 0
\(527\) 15.6742 0.682778
\(528\) 0 0
\(529\) −22.3336 −0.971025
\(530\) 0 0
\(531\) −18.8133 −0.816429
\(532\) 0 0
\(533\) −6.53735 −0.283164
\(534\) 0 0
\(535\) −1.74989 −0.0756542
\(536\) 0 0
\(537\) −3.14285 −0.135624
\(538\) 0 0
\(539\) −3.56294 −0.153467
\(540\) 0 0
\(541\) 44.7987 1.92605 0.963024 0.269417i \(-0.0868308\pi\)
0.963024 + 0.269417i \(0.0868308\pi\)
\(542\) 0 0
\(543\) −11.8681 −0.509308
\(544\) 0 0
\(545\) 16.2921 0.697875
\(546\) 0 0
\(547\) 18.3039 0.782618 0.391309 0.920259i \(-0.372022\pi\)
0.391309 + 0.920259i \(0.372022\pi\)
\(548\) 0 0
\(549\) 35.5083 1.51546
\(550\) 0 0
\(551\) 11.5989 0.494131
\(552\) 0 0
\(553\) 48.6472 2.06869
\(554\) 0 0
\(555\) 9.59669 0.407357
\(556\) 0 0
\(557\) −27.3695 −1.15968 −0.579841 0.814730i \(-0.696885\pi\)
−0.579841 + 0.814730i \(0.696885\pi\)
\(558\) 0 0
\(559\) 21.1472 0.894431
\(560\) 0 0
\(561\) −1.92404 −0.0812332
\(562\) 0 0
\(563\) 3.85582 0.162504 0.0812518 0.996694i \(-0.474108\pi\)
0.0812518 + 0.996694i \(0.474108\pi\)
\(564\) 0 0
\(565\) −3.38234 −0.142296
\(566\) 0 0
\(567\) −13.9451 −0.585637
\(568\) 0 0
\(569\) 7.22012 0.302683 0.151342 0.988482i \(-0.451641\pi\)
0.151342 + 0.988482i \(0.451641\pi\)
\(570\) 0 0
\(571\) 2.96941 0.124266 0.0621330 0.998068i \(-0.480210\pi\)
0.0621330 + 0.998068i \(0.480210\pi\)
\(572\) 0 0
\(573\) −15.2664 −0.637764
\(574\) 0 0
\(575\) 0.403362 0.0168214
\(576\) 0 0
\(577\) −18.8412 −0.784370 −0.392185 0.919886i \(-0.628281\pi\)
−0.392185 + 0.919886i \(0.628281\pi\)
\(578\) 0 0
\(579\) 20.3856 0.847196
\(580\) 0 0
\(581\) −4.16646 −0.172854
\(582\) 0 0
\(583\) −1.32577 −0.0549077
\(584\) 0 0
\(585\) 18.9146 0.782021
\(586\) 0 0
\(587\) 8.88738 0.366821 0.183411 0.983036i \(-0.441286\pi\)
0.183411 + 0.983036i \(0.441286\pi\)
\(588\) 0 0
\(589\) −15.7549 −0.649169
\(590\) 0 0
\(591\) 17.3613 0.714148
\(592\) 0 0
\(593\) 9.62411 0.395215 0.197607 0.980281i \(-0.436683\pi\)
0.197607 + 0.980281i \(0.436683\pi\)
\(594\) 0 0
\(595\) −59.3364 −2.43255
\(596\) 0 0
\(597\) 20.2341 0.828125
\(598\) 0 0
\(599\) −27.0832 −1.10659 −0.553294 0.832986i \(-0.686629\pi\)
−0.553294 + 0.832986i \(0.686629\pi\)
\(600\) 0 0
\(601\) 24.6676 1.00621 0.503107 0.864224i \(-0.332190\pi\)
0.503107 + 0.864224i \(0.332190\pi\)
\(602\) 0 0
\(603\) −16.7696 −0.682910
\(604\) 0 0
\(605\) 23.0938 0.938898
\(606\) 0 0
\(607\) 6.40644 0.260030 0.130015 0.991512i \(-0.458498\pi\)
0.130015 + 0.991512i \(0.458498\pi\)
\(608\) 0 0
\(609\) 5.86770 0.237771
\(610\) 0 0
\(611\) 23.3093 0.942992
\(612\) 0 0
\(613\) 0.516185 0.0208485 0.0104243 0.999946i \(-0.496682\pi\)
0.0104243 + 0.999946i \(0.496682\pi\)
\(614\) 0 0
\(615\) −2.97771 −0.120073
\(616\) 0 0
\(617\) 18.1430 0.730409 0.365204 0.930927i \(-0.380999\pi\)
0.365204 + 0.930927i \(0.380999\pi\)
\(618\) 0 0
\(619\) −0.354113 −0.0142330 −0.00711650 0.999975i \(-0.502265\pi\)
−0.00711650 + 0.999975i \(0.502265\pi\)
\(620\) 0 0
\(621\) −3.57765 −0.143566
\(622\) 0 0
\(623\) 34.4981 1.38214
\(624\) 0 0
\(625\) −22.2853 −0.891413
\(626\) 0 0
\(627\) 1.93395 0.0772345
\(628\) 0 0
\(629\) −36.9382 −1.47282
\(630\) 0 0
\(631\) 42.9039 1.70798 0.853989 0.520291i \(-0.174176\pi\)
0.853989 + 0.520291i \(0.174176\pi\)
\(632\) 0 0
\(633\) −3.43625 −0.136579
\(634\) 0 0
\(635\) −33.3463 −1.32331
\(636\) 0 0
\(637\) 39.3761 1.56014
\(638\) 0 0
\(639\) −19.6897 −0.778912
\(640\) 0 0
\(641\) 29.2037 1.15348 0.576739 0.816928i \(-0.304325\pi\)
0.576739 + 0.816928i \(0.304325\pi\)
\(642\) 0 0
\(643\) −25.9413 −1.02303 −0.511513 0.859275i \(-0.670915\pi\)
−0.511513 + 0.859275i \(0.670915\pi\)
\(644\) 0 0
\(645\) 9.63238 0.379274
\(646\) 0 0
\(647\) −38.2575 −1.50406 −0.752029 0.659130i \(-0.770925\pi\)
−0.752029 + 0.659130i \(0.770925\pi\)
\(648\) 0 0
\(649\) −2.81370 −0.110447
\(650\) 0 0
\(651\) −7.97012 −0.312374
\(652\) 0 0
\(653\) −15.4300 −0.603824 −0.301912 0.953336i \(-0.597625\pi\)
−0.301912 + 0.953336i \(0.597625\pi\)
\(654\) 0 0
\(655\) −41.9019 −1.63724
\(656\) 0 0
\(657\) 10.3714 0.404626
\(658\) 0 0
\(659\) 42.7609 1.66573 0.832864 0.553478i \(-0.186700\pi\)
0.832864 + 0.553478i \(0.186700\pi\)
\(660\) 0 0
\(661\) 22.3138 0.867906 0.433953 0.900936i \(-0.357118\pi\)
0.433953 + 0.900936i \(0.357118\pi\)
\(662\) 0 0
\(663\) 21.2637 0.825813
\(664\) 0 0
\(665\) 59.6418 2.31281
\(666\) 0 0
\(667\) −1.40009 −0.0542115
\(668\) 0 0
\(669\) 10.4687 0.404743
\(670\) 0 0
\(671\) 5.31058 0.205013
\(672\) 0 0
\(673\) −26.9712 −1.03966 −0.519832 0.854268i \(-0.674006\pi\)
−0.519832 + 0.854268i \(0.674006\pi\)
\(674\) 0 0
\(675\) −2.16544 −0.0833479
\(676\) 0 0
\(677\) −4.23350 −0.162706 −0.0813532 0.996685i \(-0.525924\pi\)
−0.0813532 + 0.996685i \(0.525924\pi\)
\(678\) 0 0
\(679\) −62.5031 −2.39865
\(680\) 0 0
\(681\) −1.38484 −0.0530673
\(682\) 0 0
\(683\) −25.7643 −0.985842 −0.492921 0.870074i \(-0.664071\pi\)
−0.492921 + 0.870074i \(0.664071\pi\)
\(684\) 0 0
\(685\) 0.254727 0.00973261
\(686\) 0 0
\(687\) 16.9285 0.645863
\(688\) 0 0
\(689\) 14.6518 0.558190
\(690\) 0 0
\(691\) 6.35519 0.241763 0.120881 0.992667i \(-0.461428\pi\)
0.120881 + 0.992667i \(0.461428\pi\)
\(692\) 0 0
\(693\) −3.34971 −0.127245
\(694\) 0 0
\(695\) 6.01144 0.228027
\(696\) 0 0
\(697\) 11.4614 0.434130
\(698\) 0 0
\(699\) 17.4784 0.661095
\(700\) 0 0
\(701\) −4.91157 −0.185507 −0.0927537 0.995689i \(-0.529567\pi\)
−0.0927537 + 0.995689i \(0.529567\pi\)
\(702\) 0 0
\(703\) 37.1283 1.40032
\(704\) 0 0
\(705\) 10.6172 0.399866
\(706\) 0 0
\(707\) −56.7380 −2.13385
\(708\) 0 0
\(709\) 47.9150 1.79948 0.899742 0.436421i \(-0.143754\pi\)
0.899742 + 0.436421i \(0.143754\pi\)
\(710\) 0 0
\(711\) 27.1874 1.01961
\(712\) 0 0
\(713\) 1.90174 0.0712209
\(714\) 0 0
\(715\) 2.82884 0.105793
\(716\) 0 0
\(717\) −20.5951 −0.769137
\(718\) 0 0
\(719\) 0.628068 0.0234230 0.0117115 0.999931i \(-0.496272\pi\)
0.0117115 + 0.999931i \(0.496272\pi\)
\(720\) 0 0
\(721\) 48.1685 1.79389
\(722\) 0 0
\(723\) −0.307188 −0.0114244
\(724\) 0 0
\(725\) −0.847430 −0.0314728
\(726\) 0 0
\(727\) 7.77808 0.288473 0.144236 0.989543i \(-0.453927\pi\)
0.144236 + 0.989543i \(0.453927\pi\)
\(728\) 0 0
\(729\) 3.03352 0.112352
\(730\) 0 0
\(731\) −37.0755 −1.37129
\(732\) 0 0
\(733\) −24.2134 −0.894341 −0.447170 0.894449i \(-0.647568\pi\)
−0.447170 + 0.894449i \(0.647568\pi\)
\(734\) 0 0
\(735\) 17.9355 0.661561
\(736\) 0 0
\(737\) −2.50804 −0.0923849
\(738\) 0 0
\(739\) 20.5972 0.757679 0.378840 0.925462i \(-0.376323\pi\)
0.378840 + 0.925462i \(0.376323\pi\)
\(740\) 0 0
\(741\) −21.3732 −0.785163
\(742\) 0 0
\(743\) −50.6514 −1.85822 −0.929109 0.369805i \(-0.879424\pi\)
−0.929109 + 0.369805i \(0.879424\pi\)
\(744\) 0 0
\(745\) 17.6478 0.646564
\(746\) 0 0
\(747\) −2.32851 −0.0851957
\(748\) 0 0
\(749\) −3.42487 −0.125142
\(750\) 0 0
\(751\) 9.54226 0.348202 0.174101 0.984728i \(-0.444298\pi\)
0.174101 + 0.984728i \(0.444298\pi\)
\(752\) 0 0
\(753\) −3.14568 −0.114635
\(754\) 0 0
\(755\) 12.0964 0.440232
\(756\) 0 0
\(757\) −25.0891 −0.911877 −0.455939 0.890011i \(-0.650696\pi\)
−0.455939 + 0.890011i \(0.650696\pi\)
\(758\) 0 0
\(759\) −0.233444 −0.00847347
\(760\) 0 0
\(761\) −16.1210 −0.584387 −0.292193 0.956359i \(-0.594385\pi\)
−0.292193 + 0.956359i \(0.594385\pi\)
\(762\) 0 0
\(763\) 31.8867 1.15438
\(764\) 0 0
\(765\) −33.1613 −1.19895
\(766\) 0 0
\(767\) 31.0958 1.12280
\(768\) 0 0
\(769\) −3.70242 −0.133513 −0.0667563 0.997769i \(-0.521265\pi\)
−0.0667563 + 0.997769i \(0.521265\pi\)
\(770\) 0 0
\(771\) 17.8970 0.644543
\(772\) 0 0
\(773\) −15.6202 −0.561820 −0.280910 0.959734i \(-0.590636\pi\)
−0.280910 + 0.959734i \(0.590636\pi\)
\(774\) 0 0
\(775\) 1.15107 0.0413476
\(776\) 0 0
\(777\) 18.7826 0.673822
\(778\) 0 0
\(779\) −11.5204 −0.412760
\(780\) 0 0
\(781\) −2.94477 −0.105372
\(782\) 0 0
\(783\) 7.51634 0.268612
\(784\) 0 0
\(785\) 5.28977 0.188800
\(786\) 0 0
\(787\) −22.9804 −0.819162 −0.409581 0.912274i \(-0.634325\pi\)
−0.409581 + 0.912274i \(0.634325\pi\)
\(788\) 0 0
\(789\) −2.47322 −0.0880488
\(790\) 0 0
\(791\) −6.61989 −0.235376
\(792\) 0 0
\(793\) −58.6902 −2.08415
\(794\) 0 0
\(795\) 6.67379 0.236695
\(796\) 0 0
\(797\) −29.0389 −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(798\) 0 0
\(799\) −40.8661 −1.44574
\(800\) 0 0
\(801\) 19.2799 0.681223
\(802\) 0 0
\(803\) 1.55113 0.0547383
\(804\) 0 0
\(805\) −7.19926 −0.253741
\(806\) 0 0
\(807\) −6.57002 −0.231276
\(808\) 0 0
\(809\) 54.4110 1.91299 0.956495 0.291749i \(-0.0942373\pi\)
0.956495 + 0.291749i \(0.0942373\pi\)
\(810\) 0 0
\(811\) −2.15103 −0.0755329 −0.0377665 0.999287i \(-0.512024\pi\)
−0.0377665 + 0.999287i \(0.512024\pi\)
\(812\) 0 0
\(813\) 16.4341 0.576370
\(814\) 0 0
\(815\) 18.7576 0.657051
\(816\) 0 0
\(817\) 37.2664 1.30379
\(818\) 0 0
\(819\) 37.0195 1.29357
\(820\) 0 0
\(821\) 1.22999 0.0429270 0.0214635 0.999770i \(-0.493167\pi\)
0.0214635 + 0.999770i \(0.493167\pi\)
\(822\) 0 0
\(823\) −6.62689 −0.230999 −0.115499 0.993308i \(-0.536847\pi\)
−0.115499 + 0.993308i \(0.536847\pi\)
\(824\) 0 0
\(825\) −0.141296 −0.00491931
\(826\) 0 0
\(827\) −44.2468 −1.53861 −0.769306 0.638880i \(-0.779398\pi\)
−0.769306 + 0.638880i \(0.779398\pi\)
\(828\) 0 0
\(829\) 53.0928 1.84399 0.921995 0.387202i \(-0.126558\pi\)
0.921995 + 0.387202i \(0.126558\pi\)
\(830\) 0 0
\(831\) 21.2516 0.737208
\(832\) 0 0
\(833\) −69.0347 −2.39191
\(834\) 0 0
\(835\) 0.971314 0.0336137
\(836\) 0 0
\(837\) −10.2095 −0.352891
\(838\) 0 0
\(839\) −6.79163 −0.234473 −0.117237 0.993104i \(-0.537404\pi\)
−0.117237 + 0.993104i \(0.537404\pi\)
\(840\) 0 0
\(841\) −26.0585 −0.898570
\(842\) 0 0
\(843\) 2.41671 0.0832361
\(844\) 0 0
\(845\) −3.66791 −0.126180
\(846\) 0 0
\(847\) 45.1991 1.55306
\(848\) 0 0
\(849\) −17.6146 −0.604532
\(850\) 0 0
\(851\) −4.48170 −0.153631
\(852\) 0 0
\(853\) 24.2136 0.829057 0.414528 0.910036i \(-0.363947\pi\)
0.414528 + 0.910036i \(0.363947\pi\)
\(854\) 0 0
\(855\) 33.3320 1.13993
\(856\) 0 0
\(857\) −12.5641 −0.429183 −0.214591 0.976704i \(-0.568842\pi\)
−0.214591 + 0.976704i \(0.568842\pi\)
\(858\) 0 0
\(859\) 25.0971 0.856301 0.428151 0.903707i \(-0.359165\pi\)
0.428151 + 0.903707i \(0.359165\pi\)
\(860\) 0 0
\(861\) −5.82796 −0.198616
\(862\) 0 0
\(863\) −9.28070 −0.315919 −0.157959 0.987446i \(-0.550491\pi\)
−0.157959 + 0.987446i \(0.550491\pi\)
\(864\) 0 0
\(865\) −35.8891 −1.22027
\(866\) 0 0
\(867\) −23.2804 −0.790643
\(868\) 0 0
\(869\) 4.06612 0.137934
\(870\) 0 0
\(871\) 27.7178 0.939181
\(872\) 0 0
\(873\) −34.9311 −1.18224
\(874\) 0 0
\(875\) −48.4521 −1.63798
\(876\) 0 0
\(877\) −41.0652 −1.38667 −0.693336 0.720614i \(-0.743860\pi\)
−0.693336 + 0.720614i \(0.743860\pi\)
\(878\) 0 0
\(879\) 20.9109 0.705306
\(880\) 0 0
\(881\) 51.4251 1.73256 0.866278 0.499563i \(-0.166506\pi\)
0.866278 + 0.499563i \(0.166506\pi\)
\(882\) 0 0
\(883\) −0.524245 −0.0176422 −0.00882112 0.999961i \(-0.502808\pi\)
−0.00882112 + 0.999961i \(0.502808\pi\)
\(884\) 0 0
\(885\) 14.1639 0.476114
\(886\) 0 0
\(887\) −35.0210 −1.17589 −0.587945 0.808901i \(-0.700063\pi\)
−0.587945 + 0.808901i \(0.700063\pi\)
\(888\) 0 0
\(889\) −65.2651 −2.18892
\(890\) 0 0
\(891\) −1.16558 −0.0390485
\(892\) 0 0
\(893\) 41.0765 1.37457
\(894\) 0 0
\(895\) −8.10127 −0.270796
\(896\) 0 0
\(897\) 2.57992 0.0861409
\(898\) 0 0
\(899\) −3.99540 −0.133254
\(900\) 0 0
\(901\) −25.6878 −0.855784
\(902\) 0 0
\(903\) 18.8524 0.627370
\(904\) 0 0
\(905\) −30.5921 −1.01692
\(906\) 0 0
\(907\) 23.0731 0.766128 0.383064 0.923722i \(-0.374869\pi\)
0.383064 + 0.923722i \(0.374869\pi\)
\(908\) 0 0
\(909\) −31.7091 −1.05172
\(910\) 0 0
\(911\) −29.7313 −0.985040 −0.492520 0.870301i \(-0.663924\pi\)
−0.492520 + 0.870301i \(0.663924\pi\)
\(912\) 0 0
\(913\) −0.348249 −0.0115254
\(914\) 0 0
\(915\) −26.7329 −0.883764
\(916\) 0 0
\(917\) −82.0103 −2.70822
\(918\) 0 0
\(919\) 19.8975 0.656357 0.328179 0.944616i \(-0.393565\pi\)
0.328179 + 0.944616i \(0.393565\pi\)
\(920\) 0 0
\(921\) 8.79808 0.289907
\(922\) 0 0
\(923\) 32.5443 1.07121
\(924\) 0 0
\(925\) −2.71264 −0.0891909
\(926\) 0 0
\(927\) 26.9199 0.884165
\(928\) 0 0
\(929\) −25.4312 −0.834372 −0.417186 0.908821i \(-0.636984\pi\)
−0.417186 + 0.908821i \(0.636984\pi\)
\(930\) 0 0
\(931\) 69.3901 2.27417
\(932\) 0 0
\(933\) 15.9435 0.521967
\(934\) 0 0
\(935\) −4.95957 −0.162195
\(936\) 0 0
\(937\) 57.2627 1.87069 0.935345 0.353737i \(-0.115089\pi\)
0.935345 + 0.353737i \(0.115089\pi\)
\(938\) 0 0
\(939\) −6.15745 −0.200941
\(940\) 0 0
\(941\) 41.1114 1.34019 0.670096 0.742274i \(-0.266253\pi\)
0.670096 + 0.742274i \(0.266253\pi\)
\(942\) 0 0
\(943\) 1.39060 0.0452843
\(944\) 0 0
\(945\) 38.6491 1.25726
\(946\) 0 0
\(947\) −45.6839 −1.48453 −0.742263 0.670109i \(-0.766247\pi\)
−0.742263 + 0.670109i \(0.766247\pi\)
\(948\) 0 0
\(949\) −17.1424 −0.556467
\(950\) 0 0
\(951\) 23.0112 0.746189
\(952\) 0 0
\(953\) −49.4998 −1.60346 −0.801728 0.597689i \(-0.796086\pi\)
−0.801728 + 0.597689i \(0.796086\pi\)
\(954\) 0 0
\(955\) −39.3519 −1.27340
\(956\) 0 0
\(957\) 0.490445 0.0158538
\(958\) 0 0
\(959\) 0.498550 0.0160990
\(960\) 0 0
\(961\) −25.5730 −0.824936
\(962\) 0 0
\(963\) −1.91405 −0.0616795
\(964\) 0 0
\(965\) 52.5475 1.69156
\(966\) 0 0
\(967\) −3.74494 −0.120429 −0.0602146 0.998185i \(-0.519178\pi\)
−0.0602146 + 0.998185i \(0.519178\pi\)
\(968\) 0 0
\(969\) 37.4717 1.20377
\(970\) 0 0
\(971\) −41.5625 −1.33380 −0.666901 0.745146i \(-0.732380\pi\)
−0.666901 + 0.745146i \(0.732380\pi\)
\(972\) 0 0
\(973\) 11.7656 0.377186
\(974\) 0 0
\(975\) 1.56155 0.0500095
\(976\) 0 0
\(977\) 31.4357 1.00572 0.502859 0.864368i \(-0.332281\pi\)
0.502859 + 0.864368i \(0.332281\pi\)
\(978\) 0 0
\(979\) 2.88349 0.0921566
\(980\) 0 0
\(981\) 17.8205 0.568965
\(982\) 0 0
\(983\) 35.3372 1.12708 0.563540 0.826089i \(-0.309439\pi\)
0.563540 + 0.826089i \(0.309439\pi\)
\(984\) 0 0
\(985\) 44.7518 1.42591
\(986\) 0 0
\(987\) 20.7799 0.661432
\(988\) 0 0
\(989\) −4.49836 −0.143040
\(990\) 0 0
\(991\) −17.2922 −0.549304 −0.274652 0.961544i \(-0.588563\pi\)
−0.274652 + 0.961544i \(0.588563\pi\)
\(992\) 0 0
\(993\) −6.64414 −0.210846
\(994\) 0 0
\(995\) 52.1569 1.65349
\(996\) 0 0
\(997\) 10.2403 0.324312 0.162156 0.986765i \(-0.448155\pi\)
0.162156 + 0.986765i \(0.448155\pi\)
\(998\) 0 0
\(999\) 24.0599 0.761222
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 \(a_p\))