Properties

Label 8020.2.a.c.1.17
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.910150 q^{3} -1.00000 q^{5} +1.40834 q^{7} -2.17163 q^{9} +O(q^{10})\) \(q+0.910150 q^{3} -1.00000 q^{5} +1.40834 q^{7} -2.17163 q^{9} -2.72560 q^{11} +4.96710 q^{13} -0.910150 q^{15} +1.31929 q^{17} -1.68185 q^{19} +1.28180 q^{21} +4.30276 q^{23} +1.00000 q^{25} -4.70696 q^{27} -5.98564 q^{29} +0.173134 q^{31} -2.48070 q^{33} -1.40834 q^{35} -2.08751 q^{37} +4.52081 q^{39} -1.57854 q^{41} -10.3754 q^{43} +2.17163 q^{45} -2.61807 q^{47} -5.01659 q^{49} +1.20075 q^{51} +2.01074 q^{53} +2.72560 q^{55} -1.53074 q^{57} +3.37023 q^{59} +3.01769 q^{61} -3.05838 q^{63} -4.96710 q^{65} -1.07701 q^{67} +3.91616 q^{69} +0.238719 q^{71} -11.9587 q^{73} +0.910150 q^{75} -3.83856 q^{77} +4.59577 q^{79} +2.23084 q^{81} +1.18072 q^{83} -1.31929 q^{85} -5.44784 q^{87} +1.48814 q^{89} +6.99536 q^{91} +0.157578 q^{93} +1.68185 q^{95} -14.7986 q^{97} +5.91898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + O(q^{10}) \) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + 2q^{11} + 3q^{13} - 3q^{15} - 10q^{17} - 2q^{19} - 12q^{21} - 23q^{23} + 28q^{25} + 9q^{27} - 37q^{29} - 11q^{31} + 2q^{33} + 4q^{35} - 3q^{37} - 19q^{39} - 30q^{41} + 13q^{43} - 17q^{45} - 15q^{47} + 12q^{49} - 8q^{51} - 35q^{53} - 2q^{55} - 22q^{57} - q^{59} - 33q^{61} - 20q^{63} - 3q^{65} + 19q^{67} - 8q^{69} - 31q^{71} + 31q^{73} + 3q^{75} - 42q^{77} - 29q^{79} - 36q^{81} + 14q^{83} + 10q^{85} - 32q^{87} - 32q^{89} - 7q^{91} - 11q^{93} + 2q^{95} + 2q^{97} - 39q^{99} + O(q^{100}) \)

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
\(3\) 0.910150 0.525476 0.262738 0.964867i \(-0.415375\pi\)
0.262738 + 0.964867i \(0.415375\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.40834 0.532302 0.266151 0.963931i \(-0.414248\pi\)
0.266151 + 0.963931i \(0.414248\pi\)
\(8\) 0 0
\(9\) −2.17163 −0.723875
\(10\) 0 0
\(11\) −2.72560 −0.821798 −0.410899 0.911681i \(-0.634785\pi\)
−0.410899 + 0.911681i \(0.634785\pi\)
\(12\) 0 0
\(13\) 4.96710 1.37763 0.688813 0.724939i \(-0.258132\pi\)
0.688813 + 0.724939i \(0.258132\pi\)
\(14\) 0 0
\(15\) −0.910150 −0.235000
\(16\) 0 0
\(17\) 1.31929 0.319976 0.159988 0.987119i \(-0.448855\pi\)
0.159988 + 0.987119i \(0.448855\pi\)
\(18\) 0 0
\(19\) −1.68185 −0.385844 −0.192922 0.981214i \(-0.561796\pi\)
−0.192922 + 0.981214i \(0.561796\pi\)
\(20\) 0 0
\(21\) 1.28180 0.279711
\(22\) 0 0
\(23\) 4.30276 0.897188 0.448594 0.893736i \(-0.351925\pi\)
0.448594 + 0.893736i \(0.351925\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.70696 −0.905854
\(28\) 0 0
\(29\) −5.98564 −1.11151 −0.555753 0.831347i \(-0.687570\pi\)
−0.555753 + 0.831347i \(0.687570\pi\)
\(30\) 0 0
\(31\) 0.173134 0.0310957 0.0155479 0.999879i \(-0.495051\pi\)
0.0155479 + 0.999879i \(0.495051\pi\)
\(32\) 0 0
\(33\) −2.48070 −0.431835
\(34\) 0 0
\(35\) −1.40834 −0.238052
\(36\) 0 0
\(37\) −2.08751 −0.343185 −0.171592 0.985168i \(-0.554891\pi\)
−0.171592 + 0.985168i \(0.554891\pi\)
\(38\) 0 0
\(39\) 4.52081 0.723909
\(40\) 0 0
\(41\) −1.57854 −0.246526 −0.123263 0.992374i \(-0.539336\pi\)
−0.123263 + 0.992374i \(0.539336\pi\)
\(42\) 0 0
\(43\) −10.3754 −1.58223 −0.791116 0.611666i \(-0.790500\pi\)
−0.791116 + 0.611666i \(0.790500\pi\)
\(44\) 0 0
\(45\) 2.17163 0.323727
\(46\) 0 0
\(47\) −2.61807 −0.381885 −0.190942 0.981601i \(-0.561154\pi\)
−0.190942 + 0.981601i \(0.561154\pi\)
\(48\) 0 0
\(49\) −5.01659 −0.716655
\(50\) 0 0
\(51\) 1.20075 0.168139
\(52\) 0 0
\(53\) 2.01074 0.276196 0.138098 0.990419i \(-0.455901\pi\)
0.138098 + 0.990419i \(0.455901\pi\)
\(54\) 0 0
\(55\) 2.72560 0.367519
\(56\) 0 0
\(57\) −1.53074 −0.202751
\(58\) 0 0
\(59\) 3.37023 0.438767 0.219383 0.975639i \(-0.429595\pi\)
0.219383 + 0.975639i \(0.429595\pi\)
\(60\) 0 0
\(61\) 3.01769 0.386375 0.193188 0.981162i \(-0.438117\pi\)
0.193188 + 0.981162i \(0.438117\pi\)
\(62\) 0 0
\(63\) −3.05838 −0.385320
\(64\) 0 0
\(65\) −4.96710 −0.616093
\(66\) 0 0
\(67\) −1.07701 −0.131578 −0.0657891 0.997834i \(-0.520956\pi\)
−0.0657891 + 0.997834i \(0.520956\pi\)
\(68\) 0 0
\(69\) 3.91616 0.471450
\(70\) 0 0
\(71\) 0.238719 0.0283307 0.0141654 0.999900i \(-0.495491\pi\)
0.0141654 + 0.999900i \(0.495491\pi\)
\(72\) 0 0
\(73\) −11.9587 −1.39967 −0.699833 0.714307i \(-0.746742\pi\)
−0.699833 + 0.714307i \(0.746742\pi\)
\(74\) 0 0
\(75\) 0.910150 0.105095
\(76\) 0 0
\(77\) −3.83856 −0.437444
\(78\) 0 0
\(79\) 4.59577 0.517064 0.258532 0.966003i \(-0.416761\pi\)
0.258532 + 0.966003i \(0.416761\pi\)
\(80\) 0 0
\(81\) 2.23084 0.247871
\(82\) 0 0
\(83\) 1.18072 0.129601 0.0648004 0.997898i \(-0.479359\pi\)
0.0648004 + 0.997898i \(0.479359\pi\)
\(84\) 0 0
\(85\) −1.31929 −0.143097
\(86\) 0 0
\(87\) −5.44784 −0.584069
\(88\) 0 0
\(89\) 1.48814 0.157743 0.0788715 0.996885i \(-0.474868\pi\)
0.0788715 + 0.996885i \(0.474868\pi\)
\(90\) 0 0
\(91\) 6.99536 0.733313
\(92\) 0 0
\(93\) 0.157578 0.0163400
\(94\) 0 0
\(95\) 1.68185 0.172555
\(96\) 0 0
\(97\) −14.7986 −1.50257 −0.751287 0.659976i \(-0.770567\pi\)
−0.751287 + 0.659976i \(0.770567\pi\)
\(98\) 0 0
\(99\) 5.91898 0.594880
\(100\) 0 0
\(101\) 6.09561 0.606536 0.303268 0.952905i \(-0.401922\pi\)
0.303268 + 0.952905i \(0.401922\pi\)
\(102\) 0 0
\(103\) 19.0756 1.87957 0.939785 0.341766i \(-0.111025\pi\)
0.939785 + 0.341766i \(0.111025\pi\)
\(104\) 0 0
\(105\) −1.28180 −0.125091
\(106\) 0 0
\(107\) −3.44412 −0.332956 −0.166478 0.986045i \(-0.553239\pi\)
−0.166478 + 0.986045i \(0.553239\pi\)
\(108\) 0 0
\(109\) 17.5293 1.67900 0.839499 0.543361i \(-0.182848\pi\)
0.839499 + 0.543361i \(0.182848\pi\)
\(110\) 0 0
\(111\) −1.89995 −0.180335
\(112\) 0 0
\(113\) −0.663647 −0.0624306 −0.0312153 0.999513i \(-0.509938\pi\)
−0.0312153 + 0.999513i \(0.509938\pi\)
\(114\) 0 0
\(115\) −4.30276 −0.401235
\(116\) 0 0
\(117\) −10.7867 −0.997230
\(118\) 0 0
\(119\) 1.85801 0.170323
\(120\) 0 0
\(121\) −3.57112 −0.324648
\(122\) 0 0
\(123\) −1.43670 −0.129543
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −14.2684 −1.26612 −0.633058 0.774104i \(-0.718201\pi\)
−0.633058 + 0.774104i \(0.718201\pi\)
\(128\) 0 0
\(129\) −9.44317 −0.831425
\(130\) 0 0
\(131\) −5.18673 −0.453166 −0.226583 0.973992i \(-0.572756\pi\)
−0.226583 + 0.973992i \(0.572756\pi\)
\(132\) 0 0
\(133\) −2.36862 −0.205385
\(134\) 0 0
\(135\) 4.70696 0.405110
\(136\) 0 0
\(137\) −2.96049 −0.252932 −0.126466 0.991971i \(-0.540363\pi\)
−0.126466 + 0.991971i \(0.540363\pi\)
\(138\) 0 0
\(139\) −13.0029 −1.10289 −0.551444 0.834212i \(-0.685923\pi\)
−0.551444 + 0.834212i \(0.685923\pi\)
\(140\) 0 0
\(141\) −2.38284 −0.200671
\(142\) 0 0
\(143\) −13.5383 −1.13213
\(144\) 0 0
\(145\) 5.98564 0.497081
\(146\) 0 0
\(147\) −4.56585 −0.376585
\(148\) 0 0
\(149\) −8.13362 −0.666332 −0.333166 0.942868i \(-0.608117\pi\)
−0.333166 + 0.942868i \(0.608117\pi\)
\(150\) 0 0
\(151\) 5.42500 0.441481 0.220740 0.975333i \(-0.429153\pi\)
0.220740 + 0.975333i \(0.429153\pi\)
\(152\) 0 0
\(153\) −2.86501 −0.231622
\(154\) 0 0
\(155\) −0.173134 −0.0139064
\(156\) 0 0
\(157\) 12.6459 1.00925 0.504627 0.863338i \(-0.331630\pi\)
0.504627 + 0.863338i \(0.331630\pi\)
\(158\) 0 0
\(159\) 1.83007 0.145134
\(160\) 0 0
\(161\) 6.05974 0.477575
\(162\) 0 0
\(163\) 9.36001 0.733133 0.366566 0.930392i \(-0.380533\pi\)
0.366566 + 0.930392i \(0.380533\pi\)
\(164\) 0 0
\(165\) 2.48070 0.193122
\(166\) 0 0
\(167\) −6.29438 −0.487073 −0.243537 0.969892i \(-0.578308\pi\)
−0.243537 + 0.969892i \(0.578308\pi\)
\(168\) 0 0
\(169\) 11.6721 0.897855
\(170\) 0 0
\(171\) 3.65236 0.279303
\(172\) 0 0
\(173\) −16.9019 −1.28503 −0.642513 0.766275i \(-0.722108\pi\)
−0.642513 + 0.766275i \(0.722108\pi\)
\(174\) 0 0
\(175\) 1.40834 0.106460
\(176\) 0 0
\(177\) 3.06742 0.230561
\(178\) 0 0
\(179\) −3.58148 −0.267692 −0.133846 0.991002i \(-0.542733\pi\)
−0.133846 + 0.991002i \(0.542733\pi\)
\(180\) 0 0
\(181\) 13.1076 0.974280 0.487140 0.873324i \(-0.338040\pi\)
0.487140 + 0.873324i \(0.338040\pi\)
\(182\) 0 0
\(183\) 2.74655 0.203031
\(184\) 0 0
\(185\) 2.08751 0.153477
\(186\) 0 0
\(187\) −3.59586 −0.262955
\(188\) 0 0
\(189\) −6.62898 −0.482188
\(190\) 0 0
\(191\) 13.5106 0.977590 0.488795 0.872399i \(-0.337437\pi\)
0.488795 + 0.872399i \(0.337437\pi\)
\(192\) 0 0
\(193\) −24.0813 −1.73341 −0.866704 0.498824i \(-0.833766\pi\)
−0.866704 + 0.498824i \(0.833766\pi\)
\(194\) 0 0
\(195\) −4.52081 −0.323742
\(196\) 0 0
\(197\) −20.0530 −1.42872 −0.714359 0.699780i \(-0.753281\pi\)
−0.714359 + 0.699780i \(0.753281\pi\)
\(198\) 0 0
\(199\) −19.9413 −1.41360 −0.706801 0.707413i \(-0.749862\pi\)
−0.706801 + 0.707413i \(0.749862\pi\)
\(200\) 0 0
\(201\) −0.980245 −0.0691411
\(202\) 0 0
\(203\) −8.42981 −0.591656
\(204\) 0 0
\(205\) 1.57854 0.110250
\(206\) 0 0
\(207\) −9.34399 −0.649452
\(208\) 0 0
\(209\) 4.58405 0.317086
\(210\) 0 0
\(211\) −10.1730 −0.700337 −0.350169 0.936687i \(-0.613876\pi\)
−0.350169 + 0.936687i \(0.613876\pi\)
\(212\) 0 0
\(213\) 0.217270 0.0148871
\(214\) 0 0
\(215\) 10.3754 0.707596
\(216\) 0 0
\(217\) 0.243830 0.0165523
\(218\) 0 0
\(219\) −10.8843 −0.735490
\(220\) 0 0
\(221\) 6.55306 0.440807
\(222\) 0 0
\(223\) 5.14739 0.344695 0.172347 0.985036i \(-0.444865\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(224\) 0 0
\(225\) −2.17163 −0.144775
\(226\) 0 0
\(227\) −22.8204 −1.51465 −0.757323 0.653041i \(-0.773493\pi\)
−0.757323 + 0.653041i \(0.773493\pi\)
\(228\) 0 0
\(229\) −4.05583 −0.268017 −0.134008 0.990980i \(-0.542785\pi\)
−0.134008 + 0.990980i \(0.542785\pi\)
\(230\) 0 0
\(231\) −3.49367 −0.229866
\(232\) 0 0
\(233\) −25.6247 −1.67873 −0.839364 0.543570i \(-0.817072\pi\)
−0.839364 + 0.543570i \(0.817072\pi\)
\(234\) 0 0
\(235\) 2.61807 0.170784
\(236\) 0 0
\(237\) 4.18284 0.271705
\(238\) 0 0
\(239\) −23.0528 −1.49116 −0.745582 0.666414i \(-0.767828\pi\)
−0.745582 + 0.666414i \(0.767828\pi\)
\(240\) 0 0
\(241\) 1.59104 0.102488 0.0512440 0.998686i \(-0.483681\pi\)
0.0512440 + 0.998686i \(0.483681\pi\)
\(242\) 0 0
\(243\) 16.1513 1.03610
\(244\) 0 0
\(245\) 5.01659 0.320498
\(246\) 0 0
\(247\) −8.35394 −0.531548
\(248\) 0 0
\(249\) 1.07463 0.0681020
\(250\) 0 0
\(251\) −17.9822 −1.13502 −0.567512 0.823365i \(-0.692094\pi\)
−0.567512 + 0.823365i \(0.692094\pi\)
\(252\) 0 0
\(253\) −11.7276 −0.737308
\(254\) 0 0
\(255\) −1.20075 −0.0751942
\(256\) 0 0
\(257\) −27.1656 −1.69454 −0.847272 0.531159i \(-0.821757\pi\)
−0.847272 + 0.531159i \(0.821757\pi\)
\(258\) 0 0
\(259\) −2.93992 −0.182678
\(260\) 0 0
\(261\) 12.9986 0.804592
\(262\) 0 0
\(263\) −9.50076 −0.585842 −0.292921 0.956137i \(-0.594627\pi\)
−0.292921 + 0.956137i \(0.594627\pi\)
\(264\) 0 0
\(265\) −2.01074 −0.123519
\(266\) 0 0
\(267\) 1.35444 0.0828901
\(268\) 0 0
\(269\) 2.25679 0.137599 0.0687995 0.997631i \(-0.478083\pi\)
0.0687995 + 0.997631i \(0.478083\pi\)
\(270\) 0 0
\(271\) −3.67960 −0.223520 −0.111760 0.993735i \(-0.535649\pi\)
−0.111760 + 0.993735i \(0.535649\pi\)
\(272\) 0 0
\(273\) 6.36683 0.385338
\(274\) 0 0
\(275\) −2.72560 −0.164360
\(276\) 0 0
\(277\) 19.2379 1.15589 0.577947 0.816075i \(-0.303854\pi\)
0.577947 + 0.816075i \(0.303854\pi\)
\(278\) 0 0
\(279\) −0.375981 −0.0225094
\(280\) 0 0
\(281\) −19.1217 −1.14071 −0.570353 0.821400i \(-0.693193\pi\)
−0.570353 + 0.821400i \(0.693193\pi\)
\(282\) 0 0
\(283\) 19.3929 1.15279 0.576394 0.817172i \(-0.304459\pi\)
0.576394 + 0.817172i \(0.304459\pi\)
\(284\) 0 0
\(285\) 1.53074 0.0906732
\(286\) 0 0
\(287\) −2.22311 −0.131226
\(288\) 0 0
\(289\) −15.2595 −0.897616
\(290\) 0 0
\(291\) −13.4690 −0.789566
\(292\) 0 0
\(293\) 8.20722 0.479471 0.239735 0.970838i \(-0.422939\pi\)
0.239735 + 0.970838i \(0.422939\pi\)
\(294\) 0 0
\(295\) −3.37023 −0.196222
\(296\) 0 0
\(297\) 12.8293 0.744430
\(298\) 0 0
\(299\) 21.3723 1.23599
\(300\) 0 0
\(301\) −14.6121 −0.842225
\(302\) 0 0
\(303\) 5.54792 0.318720
\(304\) 0 0
\(305\) −3.01769 −0.172792
\(306\) 0 0
\(307\) 17.1911 0.981150 0.490575 0.871399i \(-0.336787\pi\)
0.490575 + 0.871399i \(0.336787\pi\)
\(308\) 0 0
\(309\) 17.3616 0.987668
\(310\) 0 0
\(311\) −4.02356 −0.228155 −0.114077 0.993472i \(-0.536391\pi\)
−0.114077 + 0.993472i \(0.536391\pi\)
\(312\) 0 0
\(313\) 29.9299 1.69174 0.845869 0.533390i \(-0.179082\pi\)
0.845869 + 0.533390i \(0.179082\pi\)
\(314\) 0 0
\(315\) 3.05838 0.172320
\(316\) 0 0
\(317\) 3.09734 0.173964 0.0869821 0.996210i \(-0.472278\pi\)
0.0869821 + 0.996210i \(0.472278\pi\)
\(318\) 0 0
\(319\) 16.3144 0.913434
\(320\) 0 0
\(321\) −3.13467 −0.174960
\(322\) 0 0
\(323\) −2.21886 −0.123461
\(324\) 0 0
\(325\) 4.96710 0.275525
\(326\) 0 0
\(327\) 15.9543 0.882273
\(328\) 0 0
\(329\) −3.68712 −0.203278
\(330\) 0 0
\(331\) −8.27948 −0.455082 −0.227541 0.973769i \(-0.573069\pi\)
−0.227541 + 0.973769i \(0.573069\pi\)
\(332\) 0 0
\(333\) 4.53329 0.248423
\(334\) 0 0
\(335\) 1.07701 0.0588436
\(336\) 0 0
\(337\) 17.2680 0.940650 0.470325 0.882493i \(-0.344137\pi\)
0.470325 + 0.882493i \(0.344137\pi\)
\(338\) 0 0
\(339\) −0.604018 −0.0328058
\(340\) 0 0
\(341\) −0.471892 −0.0255544
\(342\) 0 0
\(343\) −16.9234 −0.913778
\(344\) 0 0
\(345\) −3.91616 −0.210839
\(346\) 0 0
\(347\) −23.5763 −1.26564 −0.632820 0.774299i \(-0.718103\pi\)
−0.632820 + 0.774299i \(0.718103\pi\)
\(348\) 0 0
\(349\) −29.7277 −1.59129 −0.795644 0.605765i \(-0.792867\pi\)
−0.795644 + 0.605765i \(0.792867\pi\)
\(350\) 0 0
\(351\) −23.3799 −1.24793
\(352\) 0 0
\(353\) −32.9290 −1.75264 −0.876318 0.481734i \(-0.840007\pi\)
−0.876318 + 0.481734i \(0.840007\pi\)
\(354\) 0 0
\(355\) −0.238719 −0.0126699
\(356\) 0 0
\(357\) 1.69107 0.0895008
\(358\) 0 0
\(359\) 17.3352 0.914915 0.457458 0.889231i \(-0.348760\pi\)
0.457458 + 0.889231i \(0.348760\pi\)
\(360\) 0 0
\(361\) −16.1714 −0.851125
\(362\) 0 0
\(363\) −3.25026 −0.170594
\(364\) 0 0
\(365\) 11.9587 0.625949
\(366\) 0 0
\(367\) −30.1011 −1.57127 −0.785634 0.618692i \(-0.787663\pi\)
−0.785634 + 0.618692i \(0.787663\pi\)
\(368\) 0 0
\(369\) 3.42799 0.178454
\(370\) 0 0
\(371\) 2.83180 0.147020
\(372\) 0 0
\(373\) −13.5408 −0.701115 −0.350558 0.936541i \(-0.614008\pi\)
−0.350558 + 0.936541i \(0.614008\pi\)
\(374\) 0 0
\(375\) −0.910150 −0.0470000
\(376\) 0 0
\(377\) −29.7313 −1.53124
\(378\) 0 0
\(379\) 28.6588 1.47210 0.736052 0.676925i \(-0.236688\pi\)
0.736052 + 0.676925i \(0.236688\pi\)
\(380\) 0 0
\(381\) −12.9864 −0.665313
\(382\) 0 0
\(383\) −10.9371 −0.558861 −0.279431 0.960166i \(-0.590146\pi\)
−0.279431 + 0.960166i \(0.590146\pi\)
\(384\) 0 0
\(385\) 3.83856 0.195631
\(386\) 0 0
\(387\) 22.5315 1.14534
\(388\) 0 0
\(389\) 12.4862 0.633076 0.316538 0.948580i \(-0.397479\pi\)
0.316538 + 0.948580i \(0.397479\pi\)
\(390\) 0 0
\(391\) 5.67660 0.287078
\(392\) 0 0
\(393\) −4.72070 −0.238128
\(394\) 0 0
\(395\) −4.59577 −0.231238
\(396\) 0 0
\(397\) 21.1365 1.06081 0.530406 0.847744i \(-0.322039\pi\)
0.530406 + 0.847744i \(0.322039\pi\)
\(398\) 0 0
\(399\) −2.15580 −0.107925
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 0.859972 0.0428383
\(404\) 0 0
\(405\) −2.23084 −0.110851
\(406\) 0 0
\(407\) 5.68971 0.282029
\(408\) 0 0
\(409\) 16.1784 0.799973 0.399986 0.916521i \(-0.369015\pi\)
0.399986 + 0.916521i \(0.369015\pi\)
\(410\) 0 0
\(411\) −2.69449 −0.132910
\(412\) 0 0
\(413\) 4.74642 0.233556
\(414\) 0 0
\(415\) −1.18072 −0.0579592
\(416\) 0 0
\(417\) −11.8346 −0.579540
\(418\) 0 0
\(419\) 2.50376 0.122317 0.0611583 0.998128i \(-0.480521\pi\)
0.0611583 + 0.998128i \(0.480521\pi\)
\(420\) 0 0
\(421\) 21.1000 1.02835 0.514175 0.857685i \(-0.328098\pi\)
0.514175 + 0.857685i \(0.328098\pi\)
\(422\) 0 0
\(423\) 5.68547 0.276437
\(424\) 0 0
\(425\) 1.31929 0.0639951
\(426\) 0 0
\(427\) 4.24992 0.205668
\(428\) 0 0
\(429\) −12.3219 −0.594907
\(430\) 0 0
\(431\) −8.25772 −0.397760 −0.198880 0.980024i \(-0.563730\pi\)
−0.198880 + 0.980024i \(0.563730\pi\)
\(432\) 0 0
\(433\) 26.1255 1.25551 0.627756 0.778410i \(-0.283973\pi\)
0.627756 + 0.778410i \(0.283973\pi\)
\(434\) 0 0
\(435\) 5.44784 0.261204
\(436\) 0 0
\(437\) −7.23662 −0.346174
\(438\) 0 0
\(439\) −19.5302 −0.932124 −0.466062 0.884752i \(-0.654328\pi\)
−0.466062 + 0.884752i \(0.654328\pi\)
\(440\) 0 0
\(441\) 10.8941 0.518769
\(442\) 0 0
\(443\) −33.8710 −1.60926 −0.804629 0.593778i \(-0.797636\pi\)
−0.804629 + 0.593778i \(0.797636\pi\)
\(444\) 0 0
\(445\) −1.48814 −0.0705448
\(446\) 0 0
\(447\) −7.40282 −0.350141
\(448\) 0 0
\(449\) 10.4004 0.490827 0.245414 0.969418i \(-0.421076\pi\)
0.245414 + 0.969418i \(0.421076\pi\)
\(450\) 0 0
\(451\) 4.30245 0.202595
\(452\) 0 0
\(453\) 4.93757 0.231987
\(454\) 0 0
\(455\) −6.99536 −0.327947
\(456\) 0 0
\(457\) 9.74839 0.456011 0.228005 0.973660i \(-0.426780\pi\)
0.228005 + 0.973660i \(0.426780\pi\)
\(458\) 0 0
\(459\) −6.20986 −0.289851
\(460\) 0 0
\(461\) −2.69522 −0.125529 −0.0627644 0.998028i \(-0.519992\pi\)
−0.0627644 + 0.998028i \(0.519992\pi\)
\(462\) 0 0
\(463\) 2.80445 0.130334 0.0651669 0.997874i \(-0.479242\pi\)
0.0651669 + 0.997874i \(0.479242\pi\)
\(464\) 0 0
\(465\) −0.157578 −0.00730748
\(466\) 0 0
\(467\) 14.1427 0.654448 0.327224 0.944947i \(-0.393887\pi\)
0.327224 + 0.944947i \(0.393887\pi\)
\(468\) 0 0
\(469\) −1.51680 −0.0700393
\(470\) 0 0
\(471\) 11.5097 0.530338
\(472\) 0 0
\(473\) 28.2791 1.30028
\(474\) 0 0
\(475\) −1.68185 −0.0771687
\(476\) 0 0
\(477\) −4.36657 −0.199931
\(478\) 0 0
\(479\) −22.4348 −1.02507 −0.512536 0.858666i \(-0.671294\pi\)
−0.512536 + 0.858666i \(0.671294\pi\)
\(480\) 0 0
\(481\) −10.3689 −0.472780
\(482\) 0 0
\(483\) 5.51528 0.250954
\(484\) 0 0
\(485\) 14.7986 0.671971
\(486\) 0 0
\(487\) −9.55046 −0.432773 −0.216386 0.976308i \(-0.569427\pi\)
−0.216386 + 0.976308i \(0.569427\pi\)
\(488\) 0 0
\(489\) 8.51902 0.385243
\(490\) 0 0
\(491\) −22.4807 −1.01454 −0.507270 0.861787i \(-0.669345\pi\)
−0.507270 + 0.861787i \(0.669345\pi\)
\(492\) 0 0
\(493\) −7.89682 −0.355655
\(494\) 0 0
\(495\) −5.91898 −0.266038
\(496\) 0 0
\(497\) 0.336197 0.0150805
\(498\) 0 0
\(499\) 31.2833 1.40043 0.700217 0.713930i \(-0.253086\pi\)
0.700217 + 0.713930i \(0.253086\pi\)
\(500\) 0 0
\(501\) −5.72883 −0.255945
\(502\) 0 0
\(503\) 34.9055 1.55636 0.778180 0.628042i \(-0.216143\pi\)
0.778180 + 0.628042i \(0.216143\pi\)
\(504\) 0 0
\(505\) −6.09561 −0.271251
\(506\) 0 0
\(507\) 10.6234 0.471801
\(508\) 0 0
\(509\) −5.70394 −0.252823 −0.126411 0.991978i \(-0.540346\pi\)
−0.126411 + 0.991978i \(0.540346\pi\)
\(510\) 0 0
\(511\) −16.8420 −0.745044
\(512\) 0 0
\(513\) 7.91641 0.349518
\(514\) 0 0
\(515\) −19.0756 −0.840569
\(516\) 0 0
\(517\) 7.13580 0.313832
\(518\) 0 0
\(519\) −15.3832 −0.675249
\(520\) 0 0
\(521\) −18.4893 −0.810032 −0.405016 0.914310i \(-0.632734\pi\)
−0.405016 + 0.914310i \(0.632734\pi\)
\(522\) 0 0
\(523\) 0.185716 0.00812078 0.00406039 0.999992i \(-0.498708\pi\)
0.00406039 + 0.999992i \(0.498708\pi\)
\(524\) 0 0
\(525\) 1.28180 0.0559423
\(526\) 0 0
\(527\) 0.228414 0.00994986
\(528\) 0 0
\(529\) −4.48623 −0.195054
\(530\) 0 0
\(531\) −7.31888 −0.317612
\(532\) 0 0
\(533\) −7.84075 −0.339621
\(534\) 0 0
\(535\) 3.44412 0.148902
\(536\) 0 0
\(537\) −3.25969 −0.140666
\(538\) 0 0
\(539\) 13.6732 0.588946
\(540\) 0 0
\(541\) 32.6216 1.40251 0.701256 0.712909i \(-0.252623\pi\)
0.701256 + 0.712909i \(0.252623\pi\)
\(542\) 0 0
\(543\) 11.9299 0.511960
\(544\) 0 0
\(545\) −17.5293 −0.750871
\(546\) 0 0
\(547\) −23.7955 −1.01742 −0.508710 0.860938i \(-0.669878\pi\)
−0.508710 + 0.860938i \(0.669878\pi\)
\(548\) 0 0
\(549\) −6.55328 −0.279687
\(550\) 0 0
\(551\) 10.0670 0.428868
\(552\) 0 0
\(553\) 6.47239 0.275234
\(554\) 0 0
\(555\) 1.89995 0.0806483
\(556\) 0 0
\(557\) 23.7350 1.00568 0.502842 0.864378i \(-0.332288\pi\)
0.502842 + 0.864378i \(0.332288\pi\)
\(558\) 0 0
\(559\) −51.5356 −2.17973
\(560\) 0 0
\(561\) −3.27277 −0.138177
\(562\) 0 0
\(563\) 15.3811 0.648235 0.324117 0.946017i \(-0.394933\pi\)
0.324117 + 0.946017i \(0.394933\pi\)
\(564\) 0 0
\(565\) 0.663647 0.0279198
\(566\) 0 0
\(567\) 3.14178 0.131942
\(568\) 0 0
\(569\) −41.8330 −1.75373 −0.876865 0.480737i \(-0.840369\pi\)
−0.876865 + 0.480737i \(0.840369\pi\)
\(570\) 0 0
\(571\) 3.80060 0.159050 0.0795251 0.996833i \(-0.474660\pi\)
0.0795251 + 0.996833i \(0.474660\pi\)
\(572\) 0 0
\(573\) 12.2966 0.513700
\(574\) 0 0
\(575\) 4.30276 0.179438
\(576\) 0 0
\(577\) 27.5594 1.14731 0.573657 0.819095i \(-0.305524\pi\)
0.573657 + 0.819095i \(0.305524\pi\)
\(578\) 0 0
\(579\) −21.9176 −0.910863
\(580\) 0 0
\(581\) 1.66285 0.0689867
\(582\) 0 0
\(583\) −5.48046 −0.226977
\(584\) 0 0
\(585\) 10.7867 0.445975
\(586\) 0 0
\(587\) −31.4787 −1.29926 −0.649632 0.760249i \(-0.725077\pi\)
−0.649632 + 0.760249i \(0.725077\pi\)
\(588\) 0 0
\(589\) −0.291185 −0.0119981
\(590\) 0 0
\(591\) −18.2512 −0.750756
\(592\) 0 0
\(593\) 4.54584 0.186675 0.0933376 0.995635i \(-0.470246\pi\)
0.0933376 + 0.995635i \(0.470246\pi\)
\(594\) 0 0
\(595\) −1.85801 −0.0761710
\(596\) 0 0
\(597\) −18.1496 −0.742813
\(598\) 0 0
\(599\) 32.3791 1.32297 0.661486 0.749957i \(-0.269926\pi\)
0.661486 + 0.749957i \(0.269926\pi\)
\(600\) 0 0
\(601\) 3.98405 0.162513 0.0812563 0.996693i \(-0.474107\pi\)
0.0812563 + 0.996693i \(0.474107\pi\)
\(602\) 0 0
\(603\) 2.33887 0.0952462
\(604\) 0 0
\(605\) 3.57112 0.145187
\(606\) 0 0
\(607\) −0.788641 −0.0320100 −0.0160050 0.999872i \(-0.505095\pi\)
−0.0160050 + 0.999872i \(0.505095\pi\)
\(608\) 0 0
\(609\) −7.67239 −0.310901
\(610\) 0 0
\(611\) −13.0042 −0.526094
\(612\) 0 0
\(613\) 22.3260 0.901740 0.450870 0.892590i \(-0.351114\pi\)
0.450870 + 0.892590i \(0.351114\pi\)
\(614\) 0 0
\(615\) 1.43670 0.0579335
\(616\) 0 0
\(617\) 42.9781 1.73023 0.865116 0.501572i \(-0.167245\pi\)
0.865116 + 0.501572i \(0.167245\pi\)
\(618\) 0 0
\(619\) 31.8889 1.28172 0.640861 0.767657i \(-0.278577\pi\)
0.640861 + 0.767657i \(0.278577\pi\)
\(620\) 0 0
\(621\) −20.2529 −0.812722
\(622\) 0 0
\(623\) 2.09581 0.0839668
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.17218 0.166621
\(628\) 0 0
\(629\) −2.75404 −0.109811
\(630\) 0 0
\(631\) 46.1653 1.83781 0.918905 0.394479i \(-0.129075\pi\)
0.918905 + 0.394479i \(0.129075\pi\)
\(632\) 0 0
\(633\) −9.25895 −0.368010
\(634\) 0 0
\(635\) 14.2684 0.566224
\(636\) 0 0
\(637\) −24.9179 −0.987283
\(638\) 0 0
\(639\) −0.518408 −0.0205079
\(640\) 0 0
\(641\) −38.8169 −1.53318 −0.766588 0.642140i \(-0.778047\pi\)
−0.766588 + 0.642140i \(0.778047\pi\)
\(642\) 0 0
\(643\) −22.2086 −0.875820 −0.437910 0.899019i \(-0.644281\pi\)
−0.437910 + 0.899019i \(0.644281\pi\)
\(644\) 0 0
\(645\) 9.44317 0.371824
\(646\) 0 0
\(647\) −0.631871 −0.0248414 −0.0124207 0.999923i \(-0.503954\pi\)
−0.0124207 + 0.999923i \(0.503954\pi\)
\(648\) 0 0
\(649\) −9.18589 −0.360578
\(650\) 0 0
\(651\) 0.221922 0.00869782
\(652\) 0 0
\(653\) −16.2224 −0.634830 −0.317415 0.948287i \(-0.602815\pi\)
−0.317415 + 0.948287i \(0.602815\pi\)
\(654\) 0 0
\(655\) 5.18673 0.202662
\(656\) 0 0
\(657\) 25.9699 1.01318
\(658\) 0 0
\(659\) −45.6183 −1.77704 −0.888518 0.458841i \(-0.848265\pi\)
−0.888518 + 0.458841i \(0.848265\pi\)
\(660\) 0 0
\(661\) −29.6362 −1.15272 −0.576358 0.817197i \(-0.695527\pi\)
−0.576358 + 0.817197i \(0.695527\pi\)
\(662\) 0 0
\(663\) 5.96427 0.231633
\(664\) 0 0
\(665\) 2.36862 0.0918510
\(666\) 0 0
\(667\) −25.7548 −0.997230
\(668\) 0 0
\(669\) 4.68490 0.181129
\(670\) 0 0
\(671\) −8.22499 −0.317522
\(672\) 0 0
\(673\) 28.6613 1.10481 0.552407 0.833575i \(-0.313710\pi\)
0.552407 + 0.833575i \(0.313710\pi\)
\(674\) 0 0
\(675\) −4.70696 −0.181171
\(676\) 0 0
\(677\) −45.6801 −1.75563 −0.877815 0.479000i \(-0.840999\pi\)
−0.877815 + 0.479000i \(0.840999\pi\)
\(678\) 0 0
\(679\) −20.8415 −0.799822
\(680\) 0 0
\(681\) −20.7700 −0.795909
\(682\) 0 0
\(683\) 20.0350 0.766616 0.383308 0.923621i \(-0.374785\pi\)
0.383308 + 0.923621i \(0.374785\pi\)
\(684\) 0 0
\(685\) 2.96049 0.113115
\(686\) 0 0
\(687\) −3.69141 −0.140836
\(688\) 0 0
\(689\) 9.98754 0.380495
\(690\) 0 0
\(691\) 1.54348 0.0587166 0.0293583 0.999569i \(-0.490654\pi\)
0.0293583 + 0.999569i \(0.490654\pi\)
\(692\) 0 0
\(693\) 8.33592 0.316655
\(694\) 0 0
\(695\) 13.0029 0.493226
\(696\) 0 0
\(697\) −2.08255 −0.0788822
\(698\) 0 0
\(699\) −23.3223 −0.882130
\(700\) 0 0
\(701\) 10.4916 0.396264 0.198132 0.980175i \(-0.436513\pi\)
0.198132 + 0.980175i \(0.436513\pi\)
\(702\) 0 0
\(703\) 3.51089 0.132416
\(704\) 0 0
\(705\) 2.38284 0.0897428
\(706\) 0 0
\(707\) 8.58467 0.322860
\(708\) 0 0
\(709\) −3.08650 −0.115916 −0.0579579 0.998319i \(-0.518459\pi\)
−0.0579579 + 0.998319i \(0.518459\pi\)
\(710\) 0 0
\(711\) −9.98029 −0.374290
\(712\) 0 0
\(713\) 0.744953 0.0278987
\(714\) 0 0
\(715\) 13.5383 0.506304
\(716\) 0 0
\(717\) −20.9815 −0.783570
\(718\) 0 0
\(719\) 43.5852 1.62545 0.812727 0.582645i \(-0.197982\pi\)
0.812727 + 0.582645i \(0.197982\pi\)
\(720\) 0 0
\(721\) 26.8648 1.00050
\(722\) 0 0
\(723\) 1.44809 0.0538550
\(724\) 0 0
\(725\) −5.98564 −0.222301
\(726\) 0 0
\(727\) 14.9249 0.553532 0.276766 0.960937i \(-0.410737\pi\)
0.276766 + 0.960937i \(0.410737\pi\)
\(728\) 0 0
\(729\) 8.00757 0.296577
\(730\) 0 0
\(731\) −13.6882 −0.506276
\(732\) 0 0
\(733\) −20.0259 −0.739673 −0.369837 0.929097i \(-0.620586\pi\)
−0.369837 + 0.929097i \(0.620586\pi\)
\(734\) 0 0
\(735\) 4.56585 0.168414
\(736\) 0 0
\(737\) 2.93551 0.108131
\(738\) 0 0
\(739\) 22.2677 0.819130 0.409565 0.912281i \(-0.365680\pi\)
0.409565 + 0.912281i \(0.365680\pi\)
\(740\) 0 0
\(741\) −7.60334 −0.279316
\(742\) 0 0
\(743\) 35.6037 1.30617 0.653086 0.757284i \(-0.273474\pi\)
0.653086 + 0.757284i \(0.273474\pi\)
\(744\) 0 0
\(745\) 8.13362 0.297993
\(746\) 0 0
\(747\) −2.56408 −0.0938148
\(748\) 0 0
\(749\) −4.85049 −0.177233
\(750\) 0 0
\(751\) −3.72066 −0.135769 −0.0678844 0.997693i \(-0.521625\pi\)
−0.0678844 + 0.997693i \(0.521625\pi\)
\(752\) 0 0
\(753\) −16.3665 −0.596427
\(754\) 0 0
\(755\) −5.42500 −0.197436
\(756\) 0 0
\(757\) 4.80917 0.174792 0.0873962 0.996174i \(-0.472145\pi\)
0.0873962 + 0.996174i \(0.472145\pi\)
\(758\) 0 0
\(759\) −10.6739 −0.387437
\(760\) 0 0
\(761\) −41.8969 −1.51876 −0.759381 0.650647i \(-0.774498\pi\)
−0.759381 + 0.650647i \(0.774498\pi\)
\(762\) 0 0
\(763\) 24.6871 0.893734
\(764\) 0 0
\(765\) 2.86501 0.103585
\(766\) 0 0
\(767\) 16.7403 0.604456
\(768\) 0 0
\(769\) −12.5554 −0.452761 −0.226381 0.974039i \(-0.572689\pi\)
−0.226381 + 0.974039i \(0.572689\pi\)
\(770\) 0 0
\(771\) −24.7248 −0.890442
\(772\) 0 0
\(773\) 4.05283 0.145770 0.0728850 0.997340i \(-0.476779\pi\)
0.0728850 + 0.997340i \(0.476779\pi\)
\(774\) 0 0
\(775\) 0.173134 0.00621914
\(776\) 0 0
\(777\) −2.67577 −0.0959927
\(778\) 0 0
\(779\) 2.65487 0.0951204
\(780\) 0 0
\(781\) −0.650651 −0.0232821
\(782\) 0 0
\(783\) 28.1742 1.00686
\(784\) 0 0
\(785\) −12.6459 −0.451352
\(786\) 0 0
\(787\) −8.18545 −0.291780 −0.145890 0.989301i \(-0.546605\pi\)
−0.145890 + 0.989301i \(0.546605\pi\)
\(788\) 0 0
\(789\) −8.64712 −0.307846
\(790\) 0 0
\(791\) −0.934638 −0.0332319
\(792\) 0 0
\(793\) 14.9892 0.532280
\(794\) 0 0
\(795\) −1.83007 −0.0649060
\(796\) 0 0
\(797\) −17.0042 −0.602320 −0.301160 0.953574i \(-0.597374\pi\)
−0.301160 + 0.953574i \(0.597374\pi\)
\(798\) 0 0
\(799\) −3.45400 −0.122194
\(800\) 0 0
\(801\) −3.23169 −0.114186
\(802\) 0 0
\(803\) 32.5947 1.15024
\(804\) 0 0
\(805\) −6.05974 −0.213578
\(806\) 0 0
\(807\) 2.05402 0.0723049
\(808\) 0 0
\(809\) −13.6213 −0.478900 −0.239450 0.970909i \(-0.576967\pi\)
−0.239450 + 0.970909i \(0.576967\pi\)
\(810\) 0 0
\(811\) −9.23919 −0.324432 −0.162216 0.986755i \(-0.551864\pi\)
−0.162216 + 0.986755i \(0.551864\pi\)
\(812\) 0 0
\(813\) −3.34899 −0.117454
\(814\) 0 0
\(815\) −9.36001 −0.327867
\(816\) 0 0
\(817\) 17.4499 0.610495
\(818\) 0 0
\(819\) −15.1913 −0.530827
\(820\) 0 0
\(821\) 21.2747 0.742493 0.371246 0.928534i \(-0.378931\pi\)
0.371246 + 0.928534i \(0.378931\pi\)
\(822\) 0 0
\(823\) −12.1633 −0.423984 −0.211992 0.977271i \(-0.567995\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(824\) 0 0
\(825\) −2.48070 −0.0863670
\(826\) 0 0
\(827\) 8.71185 0.302941 0.151470 0.988462i \(-0.451599\pi\)
0.151470 + 0.988462i \(0.451599\pi\)
\(828\) 0 0
\(829\) 19.2545 0.668736 0.334368 0.942443i \(-0.391477\pi\)
0.334368 + 0.942443i \(0.391477\pi\)
\(830\) 0 0
\(831\) 17.5094 0.607394
\(832\) 0 0
\(833\) −6.61835 −0.229312
\(834\) 0 0
\(835\) 6.29438 0.217826
\(836\) 0 0
\(837\) −0.814932 −0.0281682
\(838\) 0 0
\(839\) 24.7907 0.855869 0.427934 0.903810i \(-0.359241\pi\)
0.427934 + 0.903810i \(0.359241\pi\)
\(840\) 0 0
\(841\) 6.82793 0.235446
\(842\) 0 0
\(843\) −17.4036 −0.599413
\(844\) 0 0
\(845\) −11.6721 −0.401533
\(846\) 0 0
\(847\) −5.02935 −0.172810
\(848\) 0 0
\(849\) 17.6505 0.605762
\(850\) 0 0
\(851\) −8.98206 −0.307901
\(852\) 0 0
\(853\) 0.640816 0.0219411 0.0109706 0.999940i \(-0.496508\pi\)
0.0109706 + 0.999940i \(0.496508\pi\)
\(854\) 0 0
\(855\) −3.65236 −0.124908
\(856\) 0 0
\(857\) −38.2067 −1.30512 −0.652558 0.757738i \(-0.726304\pi\)
−0.652558 + 0.757738i \(0.726304\pi\)
\(858\) 0 0
\(859\) 8.38812 0.286199 0.143099 0.989708i \(-0.454293\pi\)
0.143099 + 0.989708i \(0.454293\pi\)
\(860\) 0 0
\(861\) −2.02337 −0.0689561
\(862\) 0 0
\(863\) 1.70332 0.0579818 0.0289909 0.999580i \(-0.490771\pi\)
0.0289909 + 0.999580i \(0.490771\pi\)
\(864\) 0 0
\(865\) 16.9019 0.574681
\(866\) 0 0
\(867\) −13.8884 −0.471675
\(868\) 0 0
\(869\) −12.5262 −0.424923
\(870\) 0 0
\(871\) −5.34964 −0.181266
\(872\) 0 0
\(873\) 32.1371 1.08768
\(874\) 0 0
\(875\) −1.40834 −0.0476105
\(876\) 0 0
\(877\) 52.0454 1.75745 0.878725 0.477329i \(-0.158395\pi\)
0.878725 + 0.477329i \(0.158395\pi\)
\(878\) 0 0
\(879\) 7.46980 0.251950
\(880\) 0 0
\(881\) −7.56874 −0.254997 −0.127499 0.991839i \(-0.540695\pi\)
−0.127499 + 0.991839i \(0.540695\pi\)
\(882\) 0 0
\(883\) 59.0344 1.98666 0.993332 0.115288i \(-0.0367792\pi\)
0.993332 + 0.115288i \(0.0367792\pi\)
\(884\) 0 0
\(885\) −3.06742 −0.103110
\(886\) 0 0
\(887\) −0.169272 −0.00568361 −0.00284180 0.999996i \(-0.500905\pi\)
−0.00284180 + 0.999996i \(0.500905\pi\)
\(888\) 0 0
\(889\) −20.0947 −0.673956
\(890\) 0 0
\(891\) −6.08037 −0.203700
\(892\) 0 0
\(893\) 4.40321 0.147348
\(894\) 0 0
\(895\) 3.58148 0.119716
\(896\) 0 0
\(897\) 19.4520 0.649483
\(898\) 0 0
\(899\) −1.03632 −0.0345631
\(900\) 0 0
\(901\) 2.65275 0.0883760
\(902\) 0 0
\(903\) −13.2992 −0.442569
\(904\) 0 0
\(905\) −13.1076 −0.435711
\(906\) 0 0
\(907\) 20.2540 0.672523 0.336262 0.941769i \(-0.390837\pi\)
0.336262 + 0.941769i \(0.390837\pi\)
\(908\) 0 0
\(909\) −13.2374 −0.439056
\(910\) 0 0
\(911\) 40.6549 1.34696 0.673478 0.739207i \(-0.264800\pi\)
0.673478 + 0.739207i \(0.264800\pi\)
\(912\) 0 0
\(913\) −3.21816 −0.106506
\(914\) 0 0
\(915\) −2.74655 −0.0907981
\(916\) 0 0
\(917\) −7.30466 −0.241221
\(918\) 0 0
\(919\) 58.0652 1.91539 0.957696 0.287780i \(-0.0929173\pi\)
0.957696 + 0.287780i \(0.0929173\pi\)
\(920\) 0 0
\(921\) 15.6465 0.515571
\(922\) 0 0
\(923\) 1.18574 0.0390291
\(924\) 0 0
\(925\) −2.08751 −0.0686369
\(926\) 0 0
\(927\) −41.4250 −1.36057
\(928\) 0 0
\(929\) 37.8235 1.24095 0.620474 0.784227i \(-0.286940\pi\)
0.620474 + 0.784227i \(0.286940\pi\)
\(930\) 0 0
\(931\) 8.43716 0.276517
\(932\) 0 0
\(933\) −3.66204 −0.119890
\(934\) 0 0
\(935\) 3.59586 0.117597
\(936\) 0 0
\(937\) −18.6064 −0.607844 −0.303922 0.952697i \(-0.598296\pi\)
−0.303922 + 0.952697i \(0.598296\pi\)
\(938\) 0 0
\(939\) 27.2407 0.888967
\(940\) 0 0
\(941\) −32.9383 −1.07376 −0.536879 0.843659i \(-0.680397\pi\)
−0.536879 + 0.843659i \(0.680397\pi\)
\(942\) 0 0
\(943\) −6.79206 −0.221180
\(944\) 0 0
\(945\) 6.62898 0.215641
\(946\) 0 0
\(947\) −21.4528 −0.697123 −0.348561 0.937286i \(-0.613330\pi\)
−0.348561 + 0.937286i \(0.613330\pi\)
\(948\) 0 0
\(949\) −59.4003 −1.92822
\(950\) 0 0
\(951\) 2.81905 0.0914139
\(952\) 0 0
\(953\) 48.2736 1.56374 0.781868 0.623444i \(-0.214267\pi\)
0.781868 + 0.623444i \(0.214267\pi\)
\(954\) 0 0
\(955\) −13.5106 −0.437192
\(956\) 0 0
\(957\) 14.8486 0.479987
\(958\) 0 0
\(959\) −4.16937 −0.134636
\(960\) 0 0
\(961\) −30.9700 −0.999033
\(962\) 0 0
\(963\) 7.47935 0.241019
\(964\) 0 0
\(965\) 24.0813 0.775203
\(966\) 0 0
\(967\) −40.8247 −1.31283 −0.656416 0.754399i \(-0.727929\pi\)
−0.656416 + 0.754399i \(0.727929\pi\)
\(968\) 0 0
\(969\) −2.01949 −0.0648755
\(970\) 0 0
\(971\) 54.4176 1.74634 0.873171 0.487413i \(-0.162060\pi\)
0.873171 + 0.487413i \(0.162060\pi\)
\(972\) 0 0
\(973\) −18.3124 −0.587069
\(974\) 0 0
\(975\) 4.52081 0.144782
\(976\) 0 0
\(977\) −5.82295 −0.186293 −0.0931464 0.995652i \(-0.529692\pi\)
−0.0931464 + 0.995652i \(0.529692\pi\)
\(978\) 0 0
\(979\) −4.05608 −0.129633
\(980\) 0 0
\(981\) −38.0670 −1.21539
\(982\) 0 0
\(983\) −26.3549 −0.840590 −0.420295 0.907388i \(-0.638073\pi\)
−0.420295 + 0.907388i \(0.638073\pi\)
\(984\) 0 0
\(985\) 20.0530 0.638942
\(986\) 0 0
\(987\) −3.35584 −0.106817
\(988\) 0 0
\(989\) −44.6429 −1.41956
\(990\) 0 0
\(991\) 1.87927 0.0596969 0.0298485 0.999554i \(-0.490498\pi\)
0.0298485 + 0.999554i \(0.490498\pi\)
\(992\) 0 0
\(993\) −7.53558 −0.239134
\(994\) 0 0
\(995\) 19.9413 0.632182
\(996\) 0 0
\(997\) −50.5797 −1.60188 −0.800938 0.598748i \(-0.795665\pi\)
−0.800938 + 0.598748i \(0.795665\pi\)
\(998\) 0 0
\(999\) 9.82582 0.310875
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 \(a_p\))