Properties

Label 4004.2.a.j.1.10
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-3.30965\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.30965 q^{3} -1.14150 q^{5} -1.00000 q^{7} +7.95375 q^{9} +O(q^{10})\) \(q+3.30965 q^{3} -1.14150 q^{5} -1.00000 q^{7} +7.95375 q^{9} -1.00000 q^{11} -1.00000 q^{13} -3.77797 q^{15} +6.91321 q^{17} -0.199068 q^{19} -3.30965 q^{21} +3.36118 q^{23} -3.69697 q^{25} +16.3952 q^{27} +2.35214 q^{29} -2.74433 q^{31} -3.30965 q^{33} +1.14150 q^{35} +5.34222 q^{37} -3.30965 q^{39} +8.92324 q^{41} -1.44857 q^{43} -9.07924 q^{45} -0.453744 q^{47} +1.00000 q^{49} +22.8803 q^{51} -4.92113 q^{53} +1.14150 q^{55} -0.658844 q^{57} -2.39219 q^{59} +11.1897 q^{61} -7.95375 q^{63} +1.14150 q^{65} -1.28547 q^{67} +11.1243 q^{69} -7.69296 q^{71} +9.77768 q^{73} -12.2357 q^{75} +1.00000 q^{77} +8.24589 q^{79} +30.4009 q^{81} +1.96589 q^{83} -7.89145 q^{85} +7.78475 q^{87} +12.2387 q^{89} +1.00000 q^{91} -9.08275 q^{93} +0.227237 q^{95} -16.8905 q^{97} -7.95375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 3.30965 1.91082 0.955412 0.295275i \(-0.0954112\pi\)
0.955412 + 0.295275i \(0.0954112\pi\)
\(4\) 0 0
\(5\) −1.14150 −0.510496 −0.255248 0.966876i \(-0.582157\pi\)
−0.255248 + 0.966876i \(0.582157\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 7.95375 2.65125
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.77797 −0.975468
\(16\) 0 0
\(17\) 6.91321 1.67670 0.838350 0.545133i \(-0.183521\pi\)
0.838350 + 0.545133i \(0.183521\pi\)
\(18\) 0 0
\(19\) −0.199068 −0.0456693 −0.0228346 0.999739i \(-0.507269\pi\)
−0.0228346 + 0.999739i \(0.507269\pi\)
\(20\) 0 0
\(21\) −3.30965 −0.722224
\(22\) 0 0
\(23\) 3.36118 0.700855 0.350427 0.936590i \(-0.386036\pi\)
0.350427 + 0.936590i \(0.386036\pi\)
\(24\) 0 0
\(25\) −3.69697 −0.739394
\(26\) 0 0
\(27\) 16.3952 3.15525
\(28\) 0 0
\(29\) 2.35214 0.436781 0.218391 0.975861i \(-0.429919\pi\)
0.218391 + 0.975861i \(0.429919\pi\)
\(30\) 0 0
\(31\) −2.74433 −0.492896 −0.246448 0.969156i \(-0.579263\pi\)
−0.246448 + 0.969156i \(0.579263\pi\)
\(32\) 0 0
\(33\) −3.30965 −0.576135
\(34\) 0 0
\(35\) 1.14150 0.192949
\(36\) 0 0
\(37\) 5.34222 0.878256 0.439128 0.898424i \(-0.355287\pi\)
0.439128 + 0.898424i \(0.355287\pi\)
\(38\) 0 0
\(39\) −3.30965 −0.529967
\(40\) 0 0
\(41\) 8.92324 1.39358 0.696788 0.717277i \(-0.254612\pi\)
0.696788 + 0.717277i \(0.254612\pi\)
\(42\) 0 0
\(43\) −1.44857 −0.220904 −0.110452 0.993881i \(-0.535230\pi\)
−0.110452 + 0.993881i \(0.535230\pi\)
\(44\) 0 0
\(45\) −9.07924 −1.35345
\(46\) 0 0
\(47\) −0.453744 −0.0661853 −0.0330927 0.999452i \(-0.510536\pi\)
−0.0330927 + 0.999452i \(0.510536\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 22.8803 3.20388
\(52\) 0 0
\(53\) −4.92113 −0.675969 −0.337985 0.941152i \(-0.609745\pi\)
−0.337985 + 0.941152i \(0.609745\pi\)
\(54\) 0 0
\(55\) 1.14150 0.153920
\(56\) 0 0
\(57\) −0.658844 −0.0872660
\(58\) 0 0
\(59\) −2.39219 −0.311436 −0.155718 0.987802i \(-0.549769\pi\)
−0.155718 + 0.987802i \(0.549769\pi\)
\(60\) 0 0
\(61\) 11.1897 1.43269 0.716345 0.697746i \(-0.245814\pi\)
0.716345 + 0.697746i \(0.245814\pi\)
\(62\) 0 0
\(63\) −7.95375 −1.00208
\(64\) 0 0
\(65\) 1.14150 0.141586
\(66\) 0 0
\(67\) −1.28547 −0.157045 −0.0785224 0.996912i \(-0.525020\pi\)
−0.0785224 + 0.996912i \(0.525020\pi\)
\(68\) 0 0
\(69\) 11.1243 1.33921
\(70\) 0 0
\(71\) −7.69296 −0.912986 −0.456493 0.889727i \(-0.650895\pi\)
−0.456493 + 0.889727i \(0.650895\pi\)
\(72\) 0 0
\(73\) 9.77768 1.14439 0.572196 0.820117i \(-0.306092\pi\)
0.572196 + 0.820117i \(0.306092\pi\)
\(74\) 0 0
\(75\) −12.2357 −1.41285
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 8.24589 0.927735 0.463868 0.885905i \(-0.346461\pi\)
0.463868 + 0.885905i \(0.346461\pi\)
\(80\) 0 0
\(81\) 30.4009 3.37788
\(82\) 0 0
\(83\) 1.96589 0.215784 0.107892 0.994163i \(-0.465590\pi\)
0.107892 + 0.994163i \(0.465590\pi\)
\(84\) 0 0
\(85\) −7.89145 −0.855948
\(86\) 0 0
\(87\) 7.78475 0.834612
\(88\) 0 0
\(89\) 12.2387 1.29730 0.648648 0.761089i \(-0.275335\pi\)
0.648648 + 0.761089i \(0.275335\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −9.08275 −0.941838
\(94\) 0 0
\(95\) 0.227237 0.0233140
\(96\) 0 0
\(97\) −16.8905 −1.71497 −0.857487 0.514506i \(-0.827975\pi\)
−0.857487 + 0.514506i \(0.827975\pi\)
\(98\) 0 0
\(99\) −7.95375 −0.799382
\(100\) 0 0
\(101\) 10.1919 1.01414 0.507068 0.861906i \(-0.330729\pi\)
0.507068 + 0.861906i \(0.330729\pi\)
\(102\) 0 0
\(103\) −10.9864 −1.08252 −0.541262 0.840854i \(-0.682053\pi\)
−0.541262 + 0.840854i \(0.682053\pi\)
\(104\) 0 0
\(105\) 3.77797 0.368692
\(106\) 0 0
\(107\) −4.39508 −0.424888 −0.212444 0.977173i \(-0.568142\pi\)
−0.212444 + 0.977173i \(0.568142\pi\)
\(108\) 0 0
\(109\) −6.90361 −0.661246 −0.330623 0.943763i \(-0.607259\pi\)
−0.330623 + 0.943763i \(0.607259\pi\)
\(110\) 0 0
\(111\) 17.6809 1.67819
\(112\) 0 0
\(113\) 17.2217 1.62008 0.810041 0.586373i \(-0.199445\pi\)
0.810041 + 0.586373i \(0.199445\pi\)
\(114\) 0 0
\(115\) −3.83680 −0.357784
\(116\) 0 0
\(117\) −7.95375 −0.735325
\(118\) 0 0
\(119\) −6.91321 −0.633733
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 29.5328 2.66288
\(124\) 0 0
\(125\) 9.92762 0.887954
\(126\) 0 0
\(127\) −11.3993 −1.01153 −0.505763 0.862673i \(-0.668789\pi\)
−0.505763 + 0.862673i \(0.668789\pi\)
\(128\) 0 0
\(129\) −4.79424 −0.422109
\(130\) 0 0
\(131\) −10.5176 −0.918928 −0.459464 0.888196i \(-0.651959\pi\)
−0.459464 + 0.888196i \(0.651959\pi\)
\(132\) 0 0
\(133\) 0.199068 0.0172614
\(134\) 0 0
\(135\) −18.7152 −1.61074
\(136\) 0 0
\(137\) −8.53891 −0.729528 −0.364764 0.931100i \(-0.618850\pi\)
−0.364764 + 0.931100i \(0.618850\pi\)
\(138\) 0 0
\(139\) 13.9829 1.18601 0.593007 0.805197i \(-0.297941\pi\)
0.593007 + 0.805197i \(0.297941\pi\)
\(140\) 0 0
\(141\) −1.50173 −0.126469
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −2.68498 −0.222975
\(146\) 0 0
\(147\) 3.30965 0.272975
\(148\) 0 0
\(149\) −8.17868 −0.670024 −0.335012 0.942214i \(-0.608740\pi\)
−0.335012 + 0.942214i \(0.608740\pi\)
\(150\) 0 0
\(151\) 3.84020 0.312511 0.156256 0.987717i \(-0.450058\pi\)
0.156256 + 0.987717i \(0.450058\pi\)
\(152\) 0 0
\(153\) 54.9860 4.44535
\(154\) 0 0
\(155\) 3.13266 0.251621
\(156\) 0 0
\(157\) −7.86871 −0.627991 −0.313996 0.949424i \(-0.601668\pi\)
−0.313996 + 0.949424i \(0.601668\pi\)
\(158\) 0 0
\(159\) −16.2872 −1.29166
\(160\) 0 0
\(161\) −3.36118 −0.264898
\(162\) 0 0
\(163\) 0.588165 0.0460686 0.0230343 0.999735i \(-0.492667\pi\)
0.0230343 + 0.999735i \(0.492667\pi\)
\(164\) 0 0
\(165\) 3.77797 0.294115
\(166\) 0 0
\(167\) −6.39033 −0.494499 −0.247249 0.968952i \(-0.579527\pi\)
−0.247249 + 0.968952i \(0.579527\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −1.58334 −0.121081
\(172\) 0 0
\(173\) −5.58075 −0.424297 −0.212148 0.977237i \(-0.568046\pi\)
−0.212148 + 0.977237i \(0.568046\pi\)
\(174\) 0 0
\(175\) 3.69697 0.279465
\(176\) 0 0
\(177\) −7.91730 −0.595101
\(178\) 0 0
\(179\) 11.0557 0.826341 0.413171 0.910654i \(-0.364421\pi\)
0.413171 + 0.910654i \(0.364421\pi\)
\(180\) 0 0
\(181\) −6.56448 −0.487934 −0.243967 0.969784i \(-0.578449\pi\)
−0.243967 + 0.969784i \(0.578449\pi\)
\(182\) 0 0
\(183\) 37.0338 2.73762
\(184\) 0 0
\(185\) −6.09817 −0.448346
\(186\) 0 0
\(187\) −6.91321 −0.505544
\(188\) 0 0
\(189\) −16.3952 −1.19257
\(190\) 0 0
\(191\) 0.929315 0.0672428 0.0336214 0.999435i \(-0.489296\pi\)
0.0336214 + 0.999435i \(0.489296\pi\)
\(192\) 0 0
\(193\) 6.56361 0.472459 0.236229 0.971697i \(-0.424088\pi\)
0.236229 + 0.971697i \(0.424088\pi\)
\(194\) 0 0
\(195\) 3.77797 0.270546
\(196\) 0 0
\(197\) 15.8890 1.13204 0.566021 0.824391i \(-0.308482\pi\)
0.566021 + 0.824391i \(0.308482\pi\)
\(198\) 0 0
\(199\) −17.6387 −1.25037 −0.625187 0.780475i \(-0.714977\pi\)
−0.625187 + 0.780475i \(0.714977\pi\)
\(200\) 0 0
\(201\) −4.25444 −0.300085
\(202\) 0 0
\(203\) −2.35214 −0.165088
\(204\) 0 0
\(205\) −10.1859 −0.711415
\(206\) 0 0
\(207\) 26.7340 1.85814
\(208\) 0 0
\(209\) 0.199068 0.0137698
\(210\) 0 0
\(211\) 18.0928 1.24556 0.622781 0.782396i \(-0.286003\pi\)
0.622781 + 0.782396i \(0.286003\pi\)
\(212\) 0 0
\(213\) −25.4610 −1.74456
\(214\) 0 0
\(215\) 1.65354 0.112771
\(216\) 0 0
\(217\) 2.74433 0.186297
\(218\) 0 0
\(219\) 32.3607 2.18673
\(220\) 0 0
\(221\) −6.91321 −0.465033
\(222\) 0 0
\(223\) 10.0985 0.676244 0.338122 0.941102i \(-0.390208\pi\)
0.338122 + 0.941102i \(0.390208\pi\)
\(224\) 0 0
\(225\) −29.4048 −1.96032
\(226\) 0 0
\(227\) 22.6097 1.50066 0.750330 0.661064i \(-0.229895\pi\)
0.750330 + 0.661064i \(0.229895\pi\)
\(228\) 0 0
\(229\) −5.52564 −0.365145 −0.182572 0.983192i \(-0.558442\pi\)
−0.182572 + 0.983192i \(0.558442\pi\)
\(230\) 0 0
\(231\) 3.30965 0.217759
\(232\) 0 0
\(233\) −19.0740 −1.24958 −0.624790 0.780793i \(-0.714815\pi\)
−0.624790 + 0.780793i \(0.714815\pi\)
\(234\) 0 0
\(235\) 0.517950 0.0337874
\(236\) 0 0
\(237\) 27.2910 1.77274
\(238\) 0 0
\(239\) −23.5139 −1.52099 −0.760493 0.649346i \(-0.775043\pi\)
−0.760493 + 0.649346i \(0.775043\pi\)
\(240\) 0 0
\(241\) 29.8277 1.92137 0.960684 0.277643i \(-0.0895533\pi\)
0.960684 + 0.277643i \(0.0895533\pi\)
\(242\) 0 0
\(243\) 51.4308 3.29929
\(244\) 0 0
\(245\) −1.14150 −0.0729280
\(246\) 0 0
\(247\) 0.199068 0.0126664
\(248\) 0 0
\(249\) 6.50640 0.412326
\(250\) 0 0
\(251\) 4.14866 0.261861 0.130930 0.991392i \(-0.458204\pi\)
0.130930 + 0.991392i \(0.458204\pi\)
\(252\) 0 0
\(253\) −3.36118 −0.211316
\(254\) 0 0
\(255\) −26.1179 −1.63557
\(256\) 0 0
\(257\) −25.8842 −1.61461 −0.807305 0.590134i \(-0.799075\pi\)
−0.807305 + 0.590134i \(0.799075\pi\)
\(258\) 0 0
\(259\) −5.34222 −0.331950
\(260\) 0 0
\(261\) 18.7083 1.15802
\(262\) 0 0
\(263\) 18.8923 1.16495 0.582475 0.812849i \(-0.302085\pi\)
0.582475 + 0.812849i \(0.302085\pi\)
\(264\) 0 0
\(265\) 5.61749 0.345079
\(266\) 0 0
\(267\) 40.5056 2.47890
\(268\) 0 0
\(269\) −30.6215 −1.86702 −0.933512 0.358547i \(-0.883272\pi\)
−0.933512 + 0.358547i \(0.883272\pi\)
\(270\) 0 0
\(271\) −17.4908 −1.06249 −0.531245 0.847218i \(-0.678275\pi\)
−0.531245 + 0.847218i \(0.678275\pi\)
\(272\) 0 0
\(273\) 3.30965 0.200309
\(274\) 0 0
\(275\) 3.69697 0.222936
\(276\) 0 0
\(277\) 19.1708 1.15186 0.575931 0.817498i \(-0.304640\pi\)
0.575931 + 0.817498i \(0.304640\pi\)
\(278\) 0 0
\(279\) −21.8277 −1.30679
\(280\) 0 0
\(281\) −28.3917 −1.69371 −0.846855 0.531824i \(-0.821507\pi\)
−0.846855 + 0.531824i \(0.821507\pi\)
\(282\) 0 0
\(283\) 9.67320 0.575012 0.287506 0.957779i \(-0.407174\pi\)
0.287506 + 0.957779i \(0.407174\pi\)
\(284\) 0 0
\(285\) 0.752073 0.0445490
\(286\) 0 0
\(287\) −8.92324 −0.526722
\(288\) 0 0
\(289\) 30.7925 1.81132
\(290\) 0 0
\(291\) −55.9017 −3.27701
\(292\) 0 0
\(293\) −6.32869 −0.369726 −0.184863 0.982764i \(-0.559184\pi\)
−0.184863 + 0.982764i \(0.559184\pi\)
\(294\) 0 0
\(295\) 2.73069 0.158987
\(296\) 0 0
\(297\) −16.3952 −0.951344
\(298\) 0 0
\(299\) −3.36118 −0.194382
\(300\) 0 0
\(301\) 1.44857 0.0834940
\(302\) 0 0
\(303\) 33.7317 1.93784
\(304\) 0 0
\(305\) −12.7730 −0.731382
\(306\) 0 0
\(307\) −32.1071 −1.83245 −0.916225 0.400664i \(-0.868780\pi\)
−0.916225 + 0.400664i \(0.868780\pi\)
\(308\) 0 0
\(309\) −36.3611 −2.06851
\(310\) 0 0
\(311\) −31.4868 −1.78545 −0.892725 0.450602i \(-0.851209\pi\)
−0.892725 + 0.450602i \(0.851209\pi\)
\(312\) 0 0
\(313\) 2.67474 0.151185 0.0755926 0.997139i \(-0.475915\pi\)
0.0755926 + 0.997139i \(0.475915\pi\)
\(314\) 0 0
\(315\) 9.07924 0.511557
\(316\) 0 0
\(317\) −16.9546 −0.952266 −0.476133 0.879373i \(-0.657962\pi\)
−0.476133 + 0.879373i \(0.657962\pi\)
\(318\) 0 0
\(319\) −2.35214 −0.131694
\(320\) 0 0
\(321\) −14.5461 −0.811887
\(322\) 0 0
\(323\) −1.37620 −0.0765737
\(324\) 0 0
\(325\) 3.69697 0.205071
\(326\) 0 0
\(327\) −22.8485 −1.26353
\(328\) 0 0
\(329\) 0.453744 0.0250157
\(330\) 0 0
\(331\) −3.99776 −0.219737 −0.109868 0.993946i \(-0.535043\pi\)
−0.109868 + 0.993946i \(0.535043\pi\)
\(332\) 0 0
\(333\) 42.4907 2.32848
\(334\) 0 0
\(335\) 1.46737 0.0801707
\(336\) 0 0
\(337\) −22.4860 −1.22489 −0.612446 0.790513i \(-0.709814\pi\)
−0.612446 + 0.790513i \(0.709814\pi\)
\(338\) 0 0
\(339\) 56.9978 3.09569
\(340\) 0 0
\(341\) 2.74433 0.148614
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −12.6985 −0.683662
\(346\) 0 0
\(347\) −5.98003 −0.321025 −0.160512 0.987034i \(-0.551315\pi\)
−0.160512 + 0.987034i \(0.551315\pi\)
\(348\) 0 0
\(349\) −2.02939 −0.108631 −0.0543153 0.998524i \(-0.517298\pi\)
−0.0543153 + 0.998524i \(0.517298\pi\)
\(350\) 0 0
\(351\) −16.3952 −0.875110
\(352\) 0 0
\(353\) −7.77371 −0.413753 −0.206876 0.978367i \(-0.566330\pi\)
−0.206876 + 0.978367i \(0.566330\pi\)
\(354\) 0 0
\(355\) 8.78154 0.466076
\(356\) 0 0
\(357\) −22.8803 −1.21095
\(358\) 0 0
\(359\) −9.20224 −0.485675 −0.242838 0.970067i \(-0.578078\pi\)
−0.242838 + 0.970067i \(0.578078\pi\)
\(360\) 0 0
\(361\) −18.9604 −0.997914
\(362\) 0 0
\(363\) 3.30965 0.173711
\(364\) 0 0
\(365\) −11.1613 −0.584207
\(366\) 0 0
\(367\) 22.2160 1.15966 0.579832 0.814736i \(-0.303118\pi\)
0.579832 + 0.814736i \(0.303118\pi\)
\(368\) 0 0
\(369\) 70.9732 3.69472
\(370\) 0 0
\(371\) 4.92113 0.255492
\(372\) 0 0
\(373\) 4.62781 0.239619 0.119809 0.992797i \(-0.461772\pi\)
0.119809 + 0.992797i \(0.461772\pi\)
\(374\) 0 0
\(375\) 32.8569 1.69672
\(376\) 0 0
\(377\) −2.35214 −0.121141
\(378\) 0 0
\(379\) 28.1619 1.44658 0.723290 0.690545i \(-0.242629\pi\)
0.723290 + 0.690545i \(0.242629\pi\)
\(380\) 0 0
\(381\) −37.7277 −1.93285
\(382\) 0 0
\(383\) −35.9109 −1.83496 −0.917481 0.397780i \(-0.869781\pi\)
−0.917481 + 0.397780i \(0.869781\pi\)
\(384\) 0 0
\(385\) −1.14150 −0.0581764
\(386\) 0 0
\(387\) −11.5215 −0.585673
\(388\) 0 0
\(389\) −8.07346 −0.409340 −0.204670 0.978831i \(-0.565612\pi\)
−0.204670 + 0.978831i \(0.565612\pi\)
\(390\) 0 0
\(391\) 23.2365 1.17512
\(392\) 0 0
\(393\) −34.8096 −1.75591
\(394\) 0 0
\(395\) −9.41272 −0.473605
\(396\) 0 0
\(397\) 22.8197 1.14529 0.572643 0.819805i \(-0.305918\pi\)
0.572643 + 0.819805i \(0.305918\pi\)
\(398\) 0 0
\(399\) 0.658844 0.0329835
\(400\) 0 0
\(401\) −38.7648 −1.93582 −0.967911 0.251294i \(-0.919144\pi\)
−0.967911 + 0.251294i \(0.919144\pi\)
\(402\) 0 0
\(403\) 2.74433 0.136705
\(404\) 0 0
\(405\) −34.7028 −1.72440
\(406\) 0 0
\(407\) −5.34222 −0.264804
\(408\) 0 0
\(409\) −6.66784 −0.329703 −0.164852 0.986318i \(-0.552715\pi\)
−0.164852 + 0.986318i \(0.552715\pi\)
\(410\) 0 0
\(411\) −28.2608 −1.39400
\(412\) 0 0
\(413\) 2.39219 0.117712
\(414\) 0 0
\(415\) −2.24407 −0.110157
\(416\) 0 0
\(417\) 46.2784 2.26626
\(418\) 0 0
\(419\) −5.45987 −0.266732 −0.133366 0.991067i \(-0.542579\pi\)
−0.133366 + 0.991067i \(0.542579\pi\)
\(420\) 0 0
\(421\) −5.23681 −0.255227 −0.127613 0.991824i \(-0.540732\pi\)
−0.127613 + 0.991824i \(0.540732\pi\)
\(422\) 0 0
\(423\) −3.60897 −0.175474
\(424\) 0 0
\(425\) −25.5579 −1.23974
\(426\) 0 0
\(427\) −11.1897 −0.541506
\(428\) 0 0
\(429\) 3.30965 0.159791
\(430\) 0 0
\(431\) −31.2354 −1.50456 −0.752278 0.658846i \(-0.771045\pi\)
−0.752278 + 0.658846i \(0.771045\pi\)
\(432\) 0 0
\(433\) −27.6063 −1.32667 −0.663337 0.748321i \(-0.730860\pi\)
−0.663337 + 0.748321i \(0.730860\pi\)
\(434\) 0 0
\(435\) −8.88632 −0.426066
\(436\) 0 0
\(437\) −0.669103 −0.0320075
\(438\) 0 0
\(439\) −26.8992 −1.28383 −0.641913 0.766777i \(-0.721859\pi\)
−0.641913 + 0.766777i \(0.721859\pi\)
\(440\) 0 0
\(441\) 7.95375 0.378750
\(442\) 0 0
\(443\) 10.6967 0.508217 0.254108 0.967176i \(-0.418218\pi\)
0.254108 + 0.967176i \(0.418218\pi\)
\(444\) 0 0
\(445\) −13.9705 −0.662264
\(446\) 0 0
\(447\) −27.0685 −1.28030
\(448\) 0 0
\(449\) −10.8786 −0.513394 −0.256697 0.966492i \(-0.582634\pi\)
−0.256697 + 0.966492i \(0.582634\pi\)
\(450\) 0 0
\(451\) −8.92324 −0.420179
\(452\) 0 0
\(453\) 12.7097 0.597155
\(454\) 0 0
\(455\) −1.14150 −0.0535145
\(456\) 0 0
\(457\) −20.0857 −0.939569 −0.469785 0.882781i \(-0.655668\pi\)
−0.469785 + 0.882781i \(0.655668\pi\)
\(458\) 0 0
\(459\) 113.343 5.29041
\(460\) 0 0
\(461\) 6.97216 0.324726 0.162363 0.986731i \(-0.448088\pi\)
0.162363 + 0.986731i \(0.448088\pi\)
\(462\) 0 0
\(463\) 15.9518 0.741342 0.370671 0.928764i \(-0.379128\pi\)
0.370671 + 0.928764i \(0.379128\pi\)
\(464\) 0 0
\(465\) 10.3680 0.480804
\(466\) 0 0
\(467\) 13.2261 0.612032 0.306016 0.952026i \(-0.401004\pi\)
0.306016 + 0.952026i \(0.401004\pi\)
\(468\) 0 0
\(469\) 1.28547 0.0593574
\(470\) 0 0
\(471\) −26.0426 −1.19998
\(472\) 0 0
\(473\) 1.44857 0.0666051
\(474\) 0 0
\(475\) 0.735948 0.0337676
\(476\) 0 0
\(477\) −39.1415 −1.79216
\(478\) 0 0
\(479\) −5.70067 −0.260470 −0.130235 0.991483i \(-0.541573\pi\)
−0.130235 + 0.991483i \(0.541573\pi\)
\(480\) 0 0
\(481\) −5.34222 −0.243584
\(482\) 0 0
\(483\) −11.1243 −0.506174
\(484\) 0 0
\(485\) 19.2806 0.875487
\(486\) 0 0
\(487\) 30.8527 1.39807 0.699034 0.715088i \(-0.253614\pi\)
0.699034 + 0.715088i \(0.253614\pi\)
\(488\) 0 0
\(489\) 1.94662 0.0880291
\(490\) 0 0
\(491\) 11.8240 0.533608 0.266804 0.963751i \(-0.414032\pi\)
0.266804 + 0.963751i \(0.414032\pi\)
\(492\) 0 0
\(493\) 16.2608 0.732351
\(494\) 0 0
\(495\) 9.07924 0.408082
\(496\) 0 0
\(497\) 7.69296 0.345076
\(498\) 0 0
\(499\) −12.7360 −0.570142 −0.285071 0.958506i \(-0.592017\pi\)
−0.285071 + 0.958506i \(0.592017\pi\)
\(500\) 0 0
\(501\) −21.1497 −0.944901
\(502\) 0 0
\(503\) −2.04582 −0.0912184 −0.0456092 0.998959i \(-0.514523\pi\)
−0.0456092 + 0.998959i \(0.514523\pi\)
\(504\) 0 0
\(505\) −11.6341 −0.517712
\(506\) 0 0
\(507\) 3.30965 0.146987
\(508\) 0 0
\(509\) 26.7165 1.18419 0.592094 0.805869i \(-0.298302\pi\)
0.592094 + 0.805869i \(0.298302\pi\)
\(510\) 0 0
\(511\) −9.77768 −0.432539
\(512\) 0 0
\(513\) −3.26375 −0.144098
\(514\) 0 0
\(515\) 12.5410 0.552624
\(516\) 0 0
\(517\) 0.453744 0.0199556
\(518\) 0 0
\(519\) −18.4703 −0.810757
\(520\) 0 0
\(521\) 22.7809 0.998049 0.499024 0.866588i \(-0.333692\pi\)
0.499024 + 0.866588i \(0.333692\pi\)
\(522\) 0 0
\(523\) −30.6445 −1.33999 −0.669994 0.742366i \(-0.733703\pi\)
−0.669994 + 0.742366i \(0.733703\pi\)
\(524\) 0 0
\(525\) 12.2357 0.534008
\(526\) 0 0
\(527\) −18.9721 −0.826438
\(528\) 0 0
\(529\) −11.7025 −0.508803
\(530\) 0 0
\(531\) −19.0269 −0.825696
\(532\) 0 0
\(533\) −8.92324 −0.386508
\(534\) 0 0
\(535\) 5.01700 0.216904
\(536\) 0 0
\(537\) 36.5904 1.57899
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −24.3642 −1.04750 −0.523750 0.851872i \(-0.675467\pi\)
−0.523750 + 0.851872i \(0.675467\pi\)
\(542\) 0 0
\(543\) −21.7261 −0.932357
\(544\) 0 0
\(545\) 7.88050 0.337564
\(546\) 0 0
\(547\) −29.1847 −1.24785 −0.623924 0.781485i \(-0.714462\pi\)
−0.623924 + 0.781485i \(0.714462\pi\)
\(548\) 0 0
\(549\) 88.9999 3.79842
\(550\) 0 0
\(551\) −0.468235 −0.0199475
\(552\) 0 0
\(553\) −8.24589 −0.350651
\(554\) 0 0
\(555\) −20.1828 −0.856711
\(556\) 0 0
\(557\) 23.7830 1.00772 0.503860 0.863785i \(-0.331913\pi\)
0.503860 + 0.863785i \(0.331913\pi\)
\(558\) 0 0
\(559\) 1.44857 0.0612678
\(560\) 0 0
\(561\) −22.8803 −0.966006
\(562\) 0 0
\(563\) 13.2314 0.557638 0.278819 0.960344i \(-0.410057\pi\)
0.278819 + 0.960344i \(0.410057\pi\)
\(564\) 0 0
\(565\) −19.6586 −0.827045
\(566\) 0 0
\(567\) −30.4009 −1.27672
\(568\) 0 0
\(569\) 23.5809 0.988562 0.494281 0.869302i \(-0.335431\pi\)
0.494281 + 0.869302i \(0.335431\pi\)
\(570\) 0 0
\(571\) −8.71844 −0.364856 −0.182428 0.983219i \(-0.558396\pi\)
−0.182428 + 0.983219i \(0.558396\pi\)
\(572\) 0 0
\(573\) 3.07570 0.128489
\(574\) 0 0
\(575\) −12.4262 −0.518208
\(576\) 0 0
\(577\) 12.0480 0.501566 0.250783 0.968043i \(-0.419312\pi\)
0.250783 + 0.968043i \(0.419312\pi\)
\(578\) 0 0
\(579\) 21.7232 0.902786
\(580\) 0 0
\(581\) −1.96589 −0.0815588
\(582\) 0 0
\(583\) 4.92113 0.203812
\(584\) 0 0
\(585\) 9.07924 0.375380
\(586\) 0 0
\(587\) 4.65236 0.192023 0.0960116 0.995380i \(-0.469391\pi\)
0.0960116 + 0.995380i \(0.469391\pi\)
\(588\) 0 0
\(589\) 0.546307 0.0225102
\(590\) 0 0
\(591\) 52.5868 2.16313
\(592\) 0 0
\(593\) 11.0592 0.454146 0.227073 0.973878i \(-0.427084\pi\)
0.227073 + 0.973878i \(0.427084\pi\)
\(594\) 0 0
\(595\) 7.89145 0.323518
\(596\) 0 0
\(597\) −58.3779 −2.38925
\(598\) 0 0
\(599\) −12.2328 −0.499817 −0.249909 0.968269i \(-0.580401\pi\)
−0.249909 + 0.968269i \(0.580401\pi\)
\(600\) 0 0
\(601\) 36.4471 1.48671 0.743353 0.668899i \(-0.233234\pi\)
0.743353 + 0.668899i \(0.233234\pi\)
\(602\) 0 0
\(603\) −10.2243 −0.416365
\(604\) 0 0
\(605\) −1.14150 −0.0464087
\(606\) 0 0
\(607\) −1.43071 −0.0580705 −0.0290353 0.999578i \(-0.509244\pi\)
−0.0290353 + 0.999578i \(0.509244\pi\)
\(608\) 0 0
\(609\) −7.78475 −0.315454
\(610\) 0 0
\(611\) 0.453744 0.0183565
\(612\) 0 0
\(613\) 8.88419 0.358829 0.179414 0.983774i \(-0.442580\pi\)
0.179414 + 0.983774i \(0.442580\pi\)
\(614\) 0 0
\(615\) −33.7118 −1.35939
\(616\) 0 0
\(617\) 16.6517 0.670371 0.335185 0.942152i \(-0.391201\pi\)
0.335185 + 0.942152i \(0.391201\pi\)
\(618\) 0 0
\(619\) 29.8958 1.20161 0.600807 0.799394i \(-0.294846\pi\)
0.600807 + 0.799394i \(0.294846\pi\)
\(620\) 0 0
\(621\) 55.1071 2.21137
\(622\) 0 0
\(623\) −12.2387 −0.490332
\(624\) 0 0
\(625\) 7.15243 0.286097
\(626\) 0 0
\(627\) 0.658844 0.0263117
\(628\) 0 0
\(629\) 36.9319 1.47257
\(630\) 0 0
\(631\) 28.9066 1.15075 0.575377 0.817888i \(-0.304855\pi\)
0.575377 + 0.817888i \(0.304855\pi\)
\(632\) 0 0
\(633\) 59.8809 2.38005
\(634\) 0 0
\(635\) 13.0124 0.516380
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −61.1879 −2.42056
\(640\) 0 0
\(641\) 25.4893 1.00677 0.503383 0.864063i \(-0.332088\pi\)
0.503383 + 0.864063i \(0.332088\pi\)
\(642\) 0 0
\(643\) −20.9872 −0.827656 −0.413828 0.910355i \(-0.635809\pi\)
−0.413828 + 0.910355i \(0.635809\pi\)
\(644\) 0 0
\(645\) 5.47264 0.215485
\(646\) 0 0
\(647\) −21.9394 −0.862526 −0.431263 0.902226i \(-0.641932\pi\)
−0.431263 + 0.902226i \(0.641932\pi\)
\(648\) 0 0
\(649\) 2.39219 0.0939016
\(650\) 0 0
\(651\) 9.08275 0.355981
\(652\) 0 0
\(653\) −31.4093 −1.22914 −0.614570 0.788862i \(-0.710671\pi\)
−0.614570 + 0.788862i \(0.710671\pi\)
\(654\) 0 0
\(655\) 12.0059 0.469109
\(656\) 0 0
\(657\) 77.7693 3.03407
\(658\) 0 0
\(659\) −23.5256 −0.916429 −0.458214 0.888842i \(-0.651511\pi\)
−0.458214 + 0.888842i \(0.651511\pi\)
\(660\) 0 0
\(661\) 21.9217 0.852657 0.426328 0.904569i \(-0.359807\pi\)
0.426328 + 0.904569i \(0.359807\pi\)
\(662\) 0 0
\(663\) −22.8803 −0.888596
\(664\) 0 0
\(665\) −0.227237 −0.00881186
\(666\) 0 0
\(667\) 7.90596 0.306120
\(668\) 0 0
\(669\) 33.4224 1.29218
\(670\) 0 0
\(671\) −11.1897 −0.431972
\(672\) 0 0
\(673\) −25.7204 −0.991448 −0.495724 0.868480i \(-0.665097\pi\)
−0.495724 + 0.868480i \(0.665097\pi\)
\(674\) 0 0
\(675\) −60.6124 −2.33297
\(676\) 0 0
\(677\) 30.9388 1.18907 0.594537 0.804068i \(-0.297335\pi\)
0.594537 + 0.804068i \(0.297335\pi\)
\(678\) 0 0
\(679\) 16.8905 0.648199
\(680\) 0 0
\(681\) 74.8301 2.86750
\(682\) 0 0
\(683\) −13.5224 −0.517419 −0.258709 0.965955i \(-0.583297\pi\)
−0.258709 + 0.965955i \(0.583297\pi\)
\(684\) 0 0
\(685\) 9.74720 0.372421
\(686\) 0 0
\(687\) −18.2879 −0.697727
\(688\) 0 0
\(689\) 4.92113 0.187480
\(690\) 0 0
\(691\) −4.01419 −0.152707 −0.0763536 0.997081i \(-0.524328\pi\)
−0.0763536 + 0.997081i \(0.524328\pi\)
\(692\) 0 0
\(693\) 7.95375 0.302138
\(694\) 0 0
\(695\) −15.9615 −0.605455
\(696\) 0 0
\(697\) 61.6882 2.33661
\(698\) 0 0
\(699\) −63.1282 −2.38773
\(700\) 0 0
\(701\) −15.8250 −0.597701 −0.298851 0.954300i \(-0.596603\pi\)
−0.298851 + 0.954300i \(0.596603\pi\)
\(702\) 0 0
\(703\) −1.06347 −0.0401093
\(704\) 0 0
\(705\) 1.71423 0.0645617
\(706\) 0 0
\(707\) −10.1919 −0.383307
\(708\) 0 0
\(709\) 52.4075 1.96820 0.984102 0.177602i \(-0.0568338\pi\)
0.984102 + 0.177602i \(0.0568338\pi\)
\(710\) 0 0
\(711\) 65.5858 2.45966
\(712\) 0 0
\(713\) −9.22418 −0.345448
\(714\) 0 0
\(715\) −1.14150 −0.0426898
\(716\) 0 0
\(717\) −77.8226 −2.90634
\(718\) 0 0
\(719\) 6.63927 0.247603 0.123802 0.992307i \(-0.460491\pi\)
0.123802 + 0.992307i \(0.460491\pi\)
\(720\) 0 0
\(721\) 10.9864 0.409155
\(722\) 0 0
\(723\) 98.7190 3.67140
\(724\) 0 0
\(725\) −8.69578 −0.322953
\(726\) 0 0
\(727\) 48.7650 1.80860 0.904298 0.426902i \(-0.140395\pi\)
0.904298 + 0.426902i \(0.140395\pi\)
\(728\) 0 0
\(729\) 79.0150 2.92648
\(730\) 0 0
\(731\) −10.0142 −0.370390
\(732\) 0 0
\(733\) −1.67262 −0.0617797 −0.0308899 0.999523i \(-0.509834\pi\)
−0.0308899 + 0.999523i \(0.509834\pi\)
\(734\) 0 0
\(735\) −3.77797 −0.139353
\(736\) 0 0
\(737\) 1.28547 0.0473508
\(738\) 0 0
\(739\) 9.23012 0.339536 0.169768 0.985484i \(-0.445698\pi\)
0.169768 + 0.985484i \(0.445698\pi\)
\(740\) 0 0
\(741\) 0.658844 0.0242032
\(742\) 0 0
\(743\) 34.5606 1.26790 0.633952 0.773372i \(-0.281432\pi\)
0.633952 + 0.773372i \(0.281432\pi\)
\(744\) 0 0
\(745\) 9.33600 0.342044
\(746\) 0 0
\(747\) 15.6362 0.572099
\(748\) 0 0
\(749\) 4.39508 0.160593
\(750\) 0 0
\(751\) −48.8694 −1.78327 −0.891635 0.452756i \(-0.850441\pi\)
−0.891635 + 0.452756i \(0.850441\pi\)
\(752\) 0 0
\(753\) 13.7306 0.500370
\(754\) 0 0
\(755\) −4.38361 −0.159536
\(756\) 0 0
\(757\) 27.1472 0.986682 0.493341 0.869836i \(-0.335775\pi\)
0.493341 + 0.869836i \(0.335775\pi\)
\(758\) 0 0
\(759\) −11.1243 −0.403787
\(760\) 0 0
\(761\) 34.4352 1.24827 0.624137 0.781315i \(-0.285451\pi\)
0.624137 + 0.781315i \(0.285451\pi\)
\(762\) 0 0
\(763\) 6.90361 0.249928
\(764\) 0 0
\(765\) −62.7667 −2.26933
\(766\) 0 0
\(767\) 2.39219 0.0863769
\(768\) 0 0
\(769\) 8.46306 0.305186 0.152593 0.988289i \(-0.451238\pi\)
0.152593 + 0.988289i \(0.451238\pi\)
\(770\) 0 0
\(771\) −85.6675 −3.08524
\(772\) 0 0
\(773\) −48.0135 −1.72693 −0.863463 0.504412i \(-0.831709\pi\)
−0.863463 + 0.504412i \(0.831709\pi\)
\(774\) 0 0
\(775\) 10.1457 0.364444
\(776\) 0 0
\(777\) −17.6809 −0.634298
\(778\) 0 0
\(779\) −1.77633 −0.0636436
\(780\) 0 0
\(781\) 7.69296 0.275276
\(782\) 0 0
\(783\) 38.5637 1.37815
\(784\) 0 0
\(785\) 8.98216 0.320587
\(786\) 0 0
\(787\) −44.0064 −1.56866 −0.784329 0.620345i \(-0.786993\pi\)
−0.784329 + 0.620345i \(0.786993\pi\)
\(788\) 0 0
\(789\) 62.5268 2.22601
\(790\) 0 0
\(791\) −17.2217 −0.612333
\(792\) 0 0
\(793\) −11.1897 −0.397357
\(794\) 0 0
\(795\) 18.5919 0.659386
\(796\) 0 0
\(797\) −41.3799 −1.46575 −0.732875 0.680363i \(-0.761822\pi\)
−0.732875 + 0.680363i \(0.761822\pi\)
\(798\) 0 0
\(799\) −3.13683 −0.110973
\(800\) 0 0
\(801\) 97.3433 3.43946
\(802\) 0 0
\(803\) −9.77768 −0.345047
\(804\) 0 0
\(805\) 3.83680 0.135229
\(806\) 0 0
\(807\) −101.346 −3.56755
\(808\) 0 0
\(809\) 15.7985 0.555447 0.277724 0.960661i \(-0.410420\pi\)
0.277724 + 0.960661i \(0.410420\pi\)
\(810\) 0 0
\(811\) 11.1077 0.390043 0.195022 0.980799i \(-0.437522\pi\)
0.195022 + 0.980799i \(0.437522\pi\)
\(812\) 0 0
\(813\) −57.8883 −2.03023
\(814\) 0 0
\(815\) −0.671392 −0.0235179
\(816\) 0 0
\(817\) 0.288363 0.0100885
\(818\) 0 0
\(819\) 7.95375 0.277927
\(820\) 0 0
\(821\) −2.45550 −0.0856975 −0.0428488 0.999082i \(-0.513643\pi\)
−0.0428488 + 0.999082i \(0.513643\pi\)
\(822\) 0 0
\(823\) 26.7115 0.931103 0.465552 0.885021i \(-0.345856\pi\)
0.465552 + 0.885021i \(0.345856\pi\)
\(824\) 0 0
\(825\) 12.2357 0.425991
\(826\) 0 0
\(827\) 37.7003 1.31097 0.655484 0.755209i \(-0.272465\pi\)
0.655484 + 0.755209i \(0.272465\pi\)
\(828\) 0 0
\(829\) 28.5698 0.992270 0.496135 0.868245i \(-0.334752\pi\)
0.496135 + 0.868245i \(0.334752\pi\)
\(830\) 0 0
\(831\) 63.4486 2.20101
\(832\) 0 0
\(833\) 6.91321 0.239528
\(834\) 0 0
\(835\) 7.29459 0.252440
\(836\) 0 0
\(837\) −44.9937 −1.55521
\(838\) 0 0
\(839\) 10.8409 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(840\) 0 0
\(841\) −23.4674 −0.809222
\(842\) 0 0
\(843\) −93.9666 −3.23638
\(844\) 0 0
\(845\) −1.14150 −0.0392689
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 32.0149 1.09875
\(850\) 0 0
\(851\) 17.9562 0.615530
\(852\) 0 0
\(853\) −41.0852 −1.40673 −0.703365 0.710829i \(-0.748320\pi\)
−0.703365 + 0.710829i \(0.748320\pi\)
\(854\) 0 0
\(855\) 1.80739 0.0618113
\(856\) 0 0
\(857\) −16.3782 −0.559468 −0.279734 0.960078i \(-0.590246\pi\)
−0.279734 + 0.960078i \(0.590246\pi\)
\(858\) 0 0
\(859\) −37.9594 −1.29516 −0.647579 0.761998i \(-0.724218\pi\)
−0.647579 + 0.761998i \(0.724218\pi\)
\(860\) 0 0
\(861\) −29.5328 −1.00647
\(862\) 0 0
\(863\) −49.3301 −1.67922 −0.839609 0.543191i \(-0.817216\pi\)
−0.839609 + 0.543191i \(0.817216\pi\)
\(864\) 0 0
\(865\) 6.37045 0.216602
\(866\) 0 0
\(867\) 101.912 3.46112
\(868\) 0 0
\(869\) −8.24589 −0.279723
\(870\) 0 0
\(871\) 1.28547 0.0435564
\(872\) 0 0
\(873\) −134.343 −4.54683
\(874\) 0 0
\(875\) −9.92762 −0.335615
\(876\) 0 0
\(877\) 15.0611 0.508576 0.254288 0.967129i \(-0.418159\pi\)
0.254288 + 0.967129i \(0.418159\pi\)
\(878\) 0 0
\(879\) −20.9457 −0.706482
\(880\) 0 0
\(881\) −54.7673 −1.84516 −0.922578 0.385809i \(-0.873922\pi\)
−0.922578 + 0.385809i \(0.873922\pi\)
\(882\) 0 0
\(883\) 18.7629 0.631422 0.315711 0.948855i \(-0.397757\pi\)
0.315711 + 0.948855i \(0.397757\pi\)
\(884\) 0 0
\(885\) 9.03763 0.303796
\(886\) 0 0
\(887\) 33.3836 1.12091 0.560456 0.828184i \(-0.310626\pi\)
0.560456 + 0.828184i \(0.310626\pi\)
\(888\) 0 0
\(889\) 11.3993 0.382321
\(890\) 0 0
\(891\) −30.4009 −1.01847
\(892\) 0 0
\(893\) 0.0903258 0.00302264
\(894\) 0 0
\(895\) −12.6201 −0.421844
\(896\) 0 0
\(897\) −11.1243 −0.371430
\(898\) 0 0
\(899\) −6.45504 −0.215288
\(900\) 0 0
\(901\) −34.0208 −1.13340
\(902\) 0 0
\(903\) 4.79424 0.159542
\(904\) 0 0
\(905\) 7.49338 0.249088
\(906\) 0 0
\(907\) −15.8818 −0.527347 −0.263673 0.964612i \(-0.584934\pi\)
−0.263673 + 0.964612i \(0.584934\pi\)
\(908\) 0 0
\(909\) 81.0641 2.68873
\(910\) 0 0
\(911\) −1.31682 −0.0436282 −0.0218141 0.999762i \(-0.506944\pi\)
−0.0218141 + 0.999762i \(0.506944\pi\)
\(912\) 0 0
\(913\) −1.96589 −0.0650614
\(914\) 0 0
\(915\) −42.2743 −1.39754
\(916\) 0 0
\(917\) 10.5176 0.347322
\(918\) 0 0
\(919\) −19.8174 −0.653715 −0.326858 0.945074i \(-0.605990\pi\)
−0.326858 + 0.945074i \(0.605990\pi\)
\(920\) 0 0
\(921\) −106.263 −3.50149
\(922\) 0 0
\(923\) 7.69296 0.253217
\(924\) 0 0
\(925\) −19.7500 −0.649377
\(926\) 0 0
\(927\) −87.3832 −2.87004
\(928\) 0 0
\(929\) −37.1278 −1.21812 −0.609062 0.793122i \(-0.708454\pi\)
−0.609062 + 0.793122i \(0.708454\pi\)
\(930\) 0 0
\(931\) −0.199068 −0.00652419
\(932\) 0 0
\(933\) −104.210 −3.41168
\(934\) 0 0
\(935\) 7.89145 0.258078
\(936\) 0 0
\(937\) −13.8888 −0.453727 −0.226864 0.973927i \(-0.572847\pi\)
−0.226864 + 0.973927i \(0.572847\pi\)
\(938\) 0 0
\(939\) 8.85244 0.288889
\(940\) 0 0
\(941\) −16.2735 −0.530502 −0.265251 0.964179i \(-0.585455\pi\)
−0.265251 + 0.964179i \(0.585455\pi\)
\(942\) 0 0
\(943\) 29.9926 0.976694
\(944\) 0 0
\(945\) 18.7152 0.608804
\(946\) 0 0
\(947\) −53.2212 −1.72946 −0.864729 0.502239i \(-0.832510\pi\)
−0.864729 + 0.502239i \(0.832510\pi\)
\(948\) 0 0
\(949\) −9.77768 −0.317397
\(950\) 0 0
\(951\) −56.1138 −1.81961
\(952\) 0 0
\(953\) −22.2777 −0.721644 −0.360822 0.932635i \(-0.617504\pi\)
−0.360822 + 0.932635i \(0.617504\pi\)
\(954\) 0 0
\(955\) −1.06082 −0.0343272
\(956\) 0 0
\(957\) −7.78475 −0.251645
\(958\) 0 0
\(959\) 8.53891 0.275736
\(960\) 0 0
\(961\) −23.4687 −0.757054
\(962\) 0 0
\(963\) −34.9574 −1.12648
\(964\) 0 0
\(965\) −7.49238 −0.241188
\(966\) 0 0
\(967\) −39.0297 −1.25511 −0.627555 0.778572i \(-0.715944\pi\)
−0.627555 + 0.778572i \(0.715944\pi\)
\(968\) 0 0
\(969\) −4.55473 −0.146319
\(970\) 0 0
\(971\) −46.2376 −1.48383 −0.741917 0.670491i \(-0.766083\pi\)
−0.741917 + 0.670491i \(0.766083\pi\)
\(972\) 0 0
\(973\) −13.9829 −0.448271
\(974\) 0 0
\(975\) 12.2357 0.391855
\(976\) 0 0
\(977\) −41.4591 −1.32639 −0.663196 0.748445i \(-0.730801\pi\)
−0.663196 + 0.748445i \(0.730801\pi\)
\(978\) 0 0
\(979\) −12.2387 −0.391149
\(980\) 0 0
\(981\) −54.9096 −1.75313
\(982\) 0 0
\(983\) 32.9200 1.04998 0.524992 0.851107i \(-0.324068\pi\)
0.524992 + 0.851107i \(0.324068\pi\)
\(984\) 0 0
\(985\) −18.1373 −0.577903
\(986\) 0 0
\(987\) 1.50173 0.0478006
\(988\) 0 0
\(989\) −4.86889 −0.154822
\(990\) 0 0
\(991\) −1.21876 −0.0387150 −0.0193575 0.999813i \(-0.506162\pi\)
−0.0193575 + 0.999813i \(0.506162\pi\)
\(992\) 0 0
\(993\) −13.2312 −0.419878
\(994\) 0 0
\(995\) 20.1346 0.638311
\(996\) 0 0
\(997\) 50.8135 1.60928 0.804640 0.593763i \(-0.202358\pi\)
0.804640 + 0.593763i \(0.202358\pi\)
\(998\) 0 0
\(999\) 87.5867 2.77112
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 \(a_p\))