Properties

Label 4004.2.a.j.1.3
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 1.3
Root \(2.16679\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.16679 q^{3} -1.26627 q^{5} -1.00000 q^{7} +1.69497 q^{9} +O(q^{10})\) \(q-2.16679 q^{3} -1.26627 q^{5} -1.00000 q^{7} +1.69497 q^{9} -1.00000 q^{11} -1.00000 q^{13} +2.74374 q^{15} -4.02352 q^{17} -5.92833 q^{19} +2.16679 q^{21} +4.27435 q^{23} -3.39656 q^{25} +2.82773 q^{27} -9.21632 q^{29} -0.386596 q^{31} +2.16679 q^{33} +1.26627 q^{35} +11.2499 q^{37} +2.16679 q^{39} -7.02502 q^{41} -3.45783 q^{43} -2.14628 q^{45} -9.82960 q^{47} +1.00000 q^{49} +8.71811 q^{51} +1.42216 q^{53} +1.26627 q^{55} +12.8454 q^{57} -11.6029 q^{59} +10.3432 q^{61} -1.69497 q^{63} +1.26627 q^{65} -10.6126 q^{67} -9.26160 q^{69} -0.110620 q^{71} -3.03553 q^{73} +7.35962 q^{75} +1.00000 q^{77} -0.962094 q^{79} -11.2120 q^{81} +4.40921 q^{83} +5.09487 q^{85} +19.9698 q^{87} -8.23230 q^{89} +1.00000 q^{91} +0.837670 q^{93} +7.50687 q^{95} +3.14917 q^{97} -1.69497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) −2.16679 −1.25099 −0.625497 0.780226i \(-0.715104\pi\)
−0.625497 + 0.780226i \(0.715104\pi\)
\(4\) 0 0
\(5\) −1.26627 −0.566293 −0.283147 0.959077i \(-0.591378\pi\)
−0.283147 + 0.959077i \(0.591378\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 1.69497 0.564988
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.74374 0.708430
\(16\) 0 0
\(17\) −4.02352 −0.975847 −0.487924 0.872886i \(-0.662246\pi\)
−0.487924 + 0.872886i \(0.662246\pi\)
\(18\) 0 0
\(19\) −5.92833 −1.36005 −0.680026 0.733188i \(-0.738032\pi\)
−0.680026 + 0.733188i \(0.738032\pi\)
\(20\) 0 0
\(21\) 2.16679 0.472832
\(22\) 0 0
\(23\) 4.27435 0.891263 0.445631 0.895217i \(-0.352979\pi\)
0.445631 + 0.895217i \(0.352979\pi\)
\(24\) 0 0
\(25\) −3.39656 −0.679312
\(26\) 0 0
\(27\) 2.82773 0.544197
\(28\) 0 0
\(29\) −9.21632 −1.71143 −0.855714 0.517449i \(-0.826882\pi\)
−0.855714 + 0.517449i \(0.826882\pi\)
\(30\) 0 0
\(31\) −0.386596 −0.0694346 −0.0347173 0.999397i \(-0.511053\pi\)
−0.0347173 + 0.999397i \(0.511053\pi\)
\(32\) 0 0
\(33\) 2.16679 0.377189
\(34\) 0 0
\(35\) 1.26627 0.214039
\(36\) 0 0
\(37\) 11.2499 1.84947 0.924737 0.380606i \(-0.124285\pi\)
0.924737 + 0.380606i \(0.124285\pi\)
\(38\) 0 0
\(39\) 2.16679 0.346964
\(40\) 0 0
\(41\) −7.02502 −1.09712 −0.548562 0.836110i \(-0.684825\pi\)
−0.548562 + 0.836110i \(0.684825\pi\)
\(42\) 0 0
\(43\) −3.45783 −0.527314 −0.263657 0.964616i \(-0.584929\pi\)
−0.263657 + 0.964616i \(0.584929\pi\)
\(44\) 0 0
\(45\) −2.14628 −0.319949
\(46\) 0 0
\(47\) −9.82960 −1.43379 −0.716897 0.697179i \(-0.754438\pi\)
−0.716897 + 0.697179i \(0.754438\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 8.71811 1.22078
\(52\) 0 0
\(53\) 1.42216 0.195349 0.0976743 0.995218i \(-0.468860\pi\)
0.0976743 + 0.995218i \(0.468860\pi\)
\(54\) 0 0
\(55\) 1.26627 0.170744
\(56\) 0 0
\(57\) 12.8454 1.70142
\(58\) 0 0
\(59\) −11.6029 −1.51057 −0.755286 0.655396i \(-0.772502\pi\)
−0.755286 + 0.655396i \(0.772502\pi\)
\(60\) 0 0
\(61\) 10.3432 1.32431 0.662153 0.749369i \(-0.269643\pi\)
0.662153 + 0.749369i \(0.269643\pi\)
\(62\) 0 0
\(63\) −1.69497 −0.213546
\(64\) 0 0
\(65\) 1.26627 0.157062
\(66\) 0 0
\(67\) −10.6126 −1.29654 −0.648270 0.761411i \(-0.724507\pi\)
−0.648270 + 0.761411i \(0.724507\pi\)
\(68\) 0 0
\(69\) −9.26160 −1.11497
\(70\) 0 0
\(71\) −0.110620 −0.0131282 −0.00656408 0.999978i \(-0.502089\pi\)
−0.00656408 + 0.999978i \(0.502089\pi\)
\(72\) 0 0
\(73\) −3.03553 −0.355282 −0.177641 0.984095i \(-0.556847\pi\)
−0.177641 + 0.984095i \(0.556847\pi\)
\(74\) 0 0
\(75\) 7.35962 0.849816
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −0.962094 −0.108244 −0.0541220 0.998534i \(-0.517236\pi\)
−0.0541220 + 0.998534i \(0.517236\pi\)
\(80\) 0 0
\(81\) −11.2120 −1.24578
\(82\) 0 0
\(83\) 4.40921 0.483974 0.241987 0.970279i \(-0.422201\pi\)
0.241987 + 0.970279i \(0.422201\pi\)
\(84\) 0 0
\(85\) 5.09487 0.552616
\(86\) 0 0
\(87\) 19.9698 2.14099
\(88\) 0 0
\(89\) −8.23230 −0.872622 −0.436311 0.899796i \(-0.643715\pi\)
−0.436311 + 0.899796i \(0.643715\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0.837670 0.0868624
\(94\) 0 0
\(95\) 7.50687 0.770189
\(96\) 0 0
\(97\) 3.14917 0.319750 0.159875 0.987137i \(-0.448891\pi\)
0.159875 + 0.987137i \(0.448891\pi\)
\(98\) 0 0
\(99\) −1.69497 −0.170350
\(100\) 0 0
\(101\) 3.12028 0.310479 0.155240 0.987877i \(-0.450385\pi\)
0.155240 + 0.987877i \(0.450385\pi\)
\(102\) 0 0
\(103\) −18.0568 −1.77919 −0.889595 0.456751i \(-0.849013\pi\)
−0.889595 + 0.456751i \(0.849013\pi\)
\(104\) 0 0
\(105\) −2.74374 −0.267761
\(106\) 0 0
\(107\) 5.41959 0.523931 0.261966 0.965077i \(-0.415629\pi\)
0.261966 + 0.965077i \(0.415629\pi\)
\(108\) 0 0
\(109\) 15.3316 1.46850 0.734249 0.678880i \(-0.237535\pi\)
0.734249 + 0.678880i \(0.237535\pi\)
\(110\) 0 0
\(111\) −24.3762 −2.31368
\(112\) 0 0
\(113\) −6.18191 −0.581545 −0.290773 0.956792i \(-0.593912\pi\)
−0.290773 + 0.956792i \(0.593912\pi\)
\(114\) 0 0
\(115\) −5.41248 −0.504716
\(116\) 0 0
\(117\) −1.69497 −0.156700
\(118\) 0 0
\(119\) 4.02352 0.368836
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 15.2217 1.37250
\(124\) 0 0
\(125\) 10.6323 0.950983
\(126\) 0 0
\(127\) −16.3527 −1.45107 −0.725535 0.688185i \(-0.758408\pi\)
−0.725535 + 0.688185i \(0.758408\pi\)
\(128\) 0 0
\(129\) 7.49239 0.659668
\(130\) 0 0
\(131\) 9.18222 0.802254 0.401127 0.916022i \(-0.368619\pi\)
0.401127 + 0.916022i \(0.368619\pi\)
\(132\) 0 0
\(133\) 5.92833 0.514052
\(134\) 0 0
\(135\) −3.58067 −0.308175
\(136\) 0 0
\(137\) 9.38223 0.801578 0.400789 0.916170i \(-0.368736\pi\)
0.400789 + 0.916170i \(0.368736\pi\)
\(138\) 0 0
\(139\) −2.32989 −0.197619 −0.0988094 0.995106i \(-0.531503\pi\)
−0.0988094 + 0.995106i \(0.531503\pi\)
\(140\) 0 0
\(141\) 21.2987 1.79367
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 11.6704 0.969170
\(146\) 0 0
\(147\) −2.16679 −0.178714
\(148\) 0 0
\(149\) 11.4946 0.941676 0.470838 0.882220i \(-0.343952\pi\)
0.470838 + 0.882220i \(0.343952\pi\)
\(150\) 0 0
\(151\) 7.72516 0.628665 0.314332 0.949313i \(-0.398219\pi\)
0.314332 + 0.949313i \(0.398219\pi\)
\(152\) 0 0
\(153\) −6.81973 −0.551342
\(154\) 0 0
\(155\) 0.489535 0.0393204
\(156\) 0 0
\(157\) 8.74921 0.698263 0.349131 0.937074i \(-0.386477\pi\)
0.349131 + 0.937074i \(0.386477\pi\)
\(158\) 0 0
\(159\) −3.08151 −0.244380
\(160\) 0 0
\(161\) −4.27435 −0.336866
\(162\) 0 0
\(163\) −22.5300 −1.76468 −0.882342 0.470609i \(-0.844034\pi\)
−0.882342 + 0.470609i \(0.844034\pi\)
\(164\) 0 0
\(165\) −2.74374 −0.213600
\(166\) 0 0
\(167\) 2.10426 0.162832 0.0814162 0.996680i \(-0.474056\pi\)
0.0814162 + 0.996680i \(0.474056\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −10.0483 −0.768414
\(172\) 0 0
\(173\) 19.3806 1.47348 0.736741 0.676176i \(-0.236364\pi\)
0.736741 + 0.676176i \(0.236364\pi\)
\(174\) 0 0
\(175\) 3.39656 0.256756
\(176\) 0 0
\(177\) 25.1410 1.88972
\(178\) 0 0
\(179\) 2.59082 0.193647 0.0968233 0.995302i \(-0.469132\pi\)
0.0968233 + 0.995302i \(0.469132\pi\)
\(180\) 0 0
\(181\) −5.89964 −0.438517 −0.219258 0.975667i \(-0.570364\pi\)
−0.219258 + 0.975667i \(0.570364\pi\)
\(182\) 0 0
\(183\) −22.4114 −1.65670
\(184\) 0 0
\(185\) −14.2454 −1.04735
\(186\) 0 0
\(187\) 4.02352 0.294229
\(188\) 0 0
\(189\) −2.82773 −0.205687
\(190\) 0 0
\(191\) 8.43059 0.610016 0.305008 0.952350i \(-0.401341\pi\)
0.305008 + 0.952350i \(0.401341\pi\)
\(192\) 0 0
\(193\) 12.1056 0.871380 0.435690 0.900097i \(-0.356504\pi\)
0.435690 + 0.900097i \(0.356504\pi\)
\(194\) 0 0
\(195\) −2.74374 −0.196483
\(196\) 0 0
\(197\) 17.0909 1.21768 0.608838 0.793295i \(-0.291636\pi\)
0.608838 + 0.793295i \(0.291636\pi\)
\(198\) 0 0
\(199\) 10.3031 0.730368 0.365184 0.930935i \(-0.381006\pi\)
0.365184 + 0.930935i \(0.381006\pi\)
\(200\) 0 0
\(201\) 22.9953 1.62196
\(202\) 0 0
\(203\) 9.21632 0.646859
\(204\) 0 0
\(205\) 8.89558 0.621294
\(206\) 0 0
\(207\) 7.24487 0.503553
\(208\) 0 0
\(209\) 5.92833 0.410071
\(210\) 0 0
\(211\) 20.4847 1.41023 0.705114 0.709094i \(-0.250896\pi\)
0.705114 + 0.709094i \(0.250896\pi\)
\(212\) 0 0
\(213\) 0.239690 0.0164233
\(214\) 0 0
\(215\) 4.37855 0.298615
\(216\) 0 0
\(217\) 0.386596 0.0262438
\(218\) 0 0
\(219\) 6.57735 0.444456
\(220\) 0 0
\(221\) 4.02352 0.270651
\(222\) 0 0
\(223\) −6.52746 −0.437111 −0.218555 0.975825i \(-0.570134\pi\)
−0.218555 + 0.975825i \(0.570134\pi\)
\(224\) 0 0
\(225\) −5.75705 −0.383803
\(226\) 0 0
\(227\) 1.19558 0.0793538 0.0396769 0.999213i \(-0.487367\pi\)
0.0396769 + 0.999213i \(0.487367\pi\)
\(228\) 0 0
\(229\) 19.3904 1.28135 0.640676 0.767812i \(-0.278654\pi\)
0.640676 + 0.767812i \(0.278654\pi\)
\(230\) 0 0
\(231\) −2.16679 −0.142564
\(232\) 0 0
\(233\) 24.1465 1.58189 0.790945 0.611888i \(-0.209589\pi\)
0.790945 + 0.611888i \(0.209589\pi\)
\(234\) 0 0
\(235\) 12.4469 0.811949
\(236\) 0 0
\(237\) 2.08465 0.135413
\(238\) 0 0
\(239\) −17.5581 −1.13574 −0.567868 0.823119i \(-0.692232\pi\)
−0.567868 + 0.823119i \(0.692232\pi\)
\(240\) 0 0
\(241\) −14.2266 −0.916418 −0.458209 0.888844i \(-0.651509\pi\)
−0.458209 + 0.888844i \(0.651509\pi\)
\(242\) 0 0
\(243\) 15.8108 1.01426
\(244\) 0 0
\(245\) −1.26627 −0.0808991
\(246\) 0 0
\(247\) 5.92833 0.377211
\(248\) 0 0
\(249\) −9.55383 −0.605449
\(250\) 0 0
\(251\) −14.1949 −0.895977 −0.447989 0.894039i \(-0.647859\pi\)
−0.447989 + 0.894039i \(0.647859\pi\)
\(252\) 0 0
\(253\) −4.27435 −0.268726
\(254\) 0 0
\(255\) −11.0395 −0.691320
\(256\) 0 0
\(257\) −4.71880 −0.294351 −0.147175 0.989110i \(-0.547018\pi\)
−0.147175 + 0.989110i \(0.547018\pi\)
\(258\) 0 0
\(259\) −11.2499 −0.699036
\(260\) 0 0
\(261\) −15.6213 −0.966937
\(262\) 0 0
\(263\) 13.7067 0.845189 0.422595 0.906319i \(-0.361119\pi\)
0.422595 + 0.906319i \(0.361119\pi\)
\(264\) 0 0
\(265\) −1.80084 −0.110625
\(266\) 0 0
\(267\) 17.8376 1.09165
\(268\) 0 0
\(269\) −8.63780 −0.526656 −0.263328 0.964706i \(-0.584820\pi\)
−0.263328 + 0.964706i \(0.584820\pi\)
\(270\) 0 0
\(271\) 30.2050 1.83482 0.917411 0.397941i \(-0.130275\pi\)
0.917411 + 0.397941i \(0.130275\pi\)
\(272\) 0 0
\(273\) −2.16679 −0.131140
\(274\) 0 0
\(275\) 3.39656 0.204820
\(276\) 0 0
\(277\) 13.4586 0.808649 0.404325 0.914616i \(-0.367507\pi\)
0.404325 + 0.914616i \(0.367507\pi\)
\(278\) 0 0
\(279\) −0.655266 −0.0392298
\(280\) 0 0
\(281\) −2.55064 −0.152158 −0.0760791 0.997102i \(-0.524240\pi\)
−0.0760791 + 0.997102i \(0.524240\pi\)
\(282\) 0 0
\(283\) −9.56393 −0.568517 −0.284258 0.958748i \(-0.591747\pi\)
−0.284258 + 0.958748i \(0.591747\pi\)
\(284\) 0 0
\(285\) −16.2658 −0.963503
\(286\) 0 0
\(287\) 7.02502 0.414674
\(288\) 0 0
\(289\) −0.811283 −0.0477225
\(290\) 0 0
\(291\) −6.82358 −0.400005
\(292\) 0 0
\(293\) −26.4263 −1.54384 −0.771920 0.635720i \(-0.780703\pi\)
−0.771920 + 0.635720i \(0.780703\pi\)
\(294\) 0 0
\(295\) 14.6924 0.855427
\(296\) 0 0
\(297\) −2.82773 −0.164082
\(298\) 0 0
\(299\) −4.27435 −0.247192
\(300\) 0 0
\(301\) 3.45783 0.199306
\(302\) 0 0
\(303\) −6.76098 −0.388408
\(304\) 0 0
\(305\) −13.0972 −0.749945
\(306\) 0 0
\(307\) −15.8370 −0.903865 −0.451932 0.892052i \(-0.649265\pi\)
−0.451932 + 0.892052i \(0.649265\pi\)
\(308\) 0 0
\(309\) 39.1252 2.22576
\(310\) 0 0
\(311\) 23.3430 1.32366 0.661830 0.749654i \(-0.269780\pi\)
0.661830 + 0.749654i \(0.269780\pi\)
\(312\) 0 0
\(313\) 26.1084 1.47573 0.737866 0.674947i \(-0.235834\pi\)
0.737866 + 0.674947i \(0.235834\pi\)
\(314\) 0 0
\(315\) 2.14628 0.120929
\(316\) 0 0
\(317\) −0.616309 −0.0346154 −0.0173077 0.999850i \(-0.505509\pi\)
−0.0173077 + 0.999850i \(0.505509\pi\)
\(318\) 0 0
\(319\) 9.21632 0.516015
\(320\) 0 0
\(321\) −11.7431 −0.655435
\(322\) 0 0
\(323\) 23.8528 1.32720
\(324\) 0 0
\(325\) 3.39656 0.188407
\(326\) 0 0
\(327\) −33.2202 −1.83708
\(328\) 0 0
\(329\) 9.82960 0.541924
\(330\) 0 0
\(331\) 17.6186 0.968407 0.484203 0.874955i \(-0.339109\pi\)
0.484203 + 0.874955i \(0.339109\pi\)
\(332\) 0 0
\(333\) 19.0682 1.04493
\(334\) 0 0
\(335\) 13.4385 0.734222
\(336\) 0 0
\(337\) −4.47690 −0.243872 −0.121936 0.992538i \(-0.538910\pi\)
−0.121936 + 0.992538i \(0.538910\pi\)
\(338\) 0 0
\(339\) 13.3949 0.727510
\(340\) 0 0
\(341\) 0.386596 0.0209353
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 11.7277 0.631398
\(346\) 0 0
\(347\) −19.2072 −1.03110 −0.515549 0.856860i \(-0.672412\pi\)
−0.515549 + 0.856860i \(0.672412\pi\)
\(348\) 0 0
\(349\) 24.7928 1.32713 0.663564 0.748119i \(-0.269043\pi\)
0.663564 + 0.748119i \(0.269043\pi\)
\(350\) 0 0
\(351\) −2.82773 −0.150933
\(352\) 0 0
\(353\) −27.9445 −1.48733 −0.743667 0.668550i \(-0.766915\pi\)
−0.743667 + 0.668550i \(0.766915\pi\)
\(354\) 0 0
\(355\) 0.140075 0.00743439
\(356\) 0 0
\(357\) −8.71811 −0.461411
\(358\) 0 0
\(359\) −1.25709 −0.0663468 −0.0331734 0.999450i \(-0.510561\pi\)
−0.0331734 + 0.999450i \(0.510561\pi\)
\(360\) 0 0
\(361\) 16.1451 0.849744
\(362\) 0 0
\(363\) −2.16679 −0.113727
\(364\) 0 0
\(365\) 3.84380 0.201194
\(366\) 0 0
\(367\) 0.580457 0.0302996 0.0151498 0.999885i \(-0.495177\pi\)
0.0151498 + 0.999885i \(0.495177\pi\)
\(368\) 0 0
\(369\) −11.9072 −0.619862
\(370\) 0 0
\(371\) −1.42216 −0.0738348
\(372\) 0 0
\(373\) 11.3570 0.588045 0.294023 0.955798i \(-0.405006\pi\)
0.294023 + 0.955798i \(0.405006\pi\)
\(374\) 0 0
\(375\) −23.0380 −1.18968
\(376\) 0 0
\(377\) 9.21632 0.474665
\(378\) 0 0
\(379\) 28.8713 1.48302 0.741509 0.670943i \(-0.234111\pi\)
0.741509 + 0.670943i \(0.234111\pi\)
\(380\) 0 0
\(381\) 35.4329 1.81528
\(382\) 0 0
\(383\) −36.9921 −1.89021 −0.945103 0.326772i \(-0.894039\pi\)
−0.945103 + 0.326772i \(0.894039\pi\)
\(384\) 0 0
\(385\) −1.26627 −0.0645351
\(386\) 0 0
\(387\) −5.86091 −0.297927
\(388\) 0 0
\(389\) −17.3019 −0.877241 −0.438620 0.898672i \(-0.644533\pi\)
−0.438620 + 0.898672i \(0.644533\pi\)
\(390\) 0 0
\(391\) −17.1979 −0.869736
\(392\) 0 0
\(393\) −19.8959 −1.00362
\(394\) 0 0
\(395\) 1.21827 0.0612979
\(396\) 0 0
\(397\) −37.6443 −1.88932 −0.944658 0.328057i \(-0.893606\pi\)
−0.944658 + 0.328057i \(0.893606\pi\)
\(398\) 0 0
\(399\) −12.8454 −0.643076
\(400\) 0 0
\(401\) 14.3907 0.718637 0.359319 0.933215i \(-0.383009\pi\)
0.359319 + 0.933215i \(0.383009\pi\)
\(402\) 0 0
\(403\) 0.386596 0.0192577
\(404\) 0 0
\(405\) 14.1974 0.705475
\(406\) 0 0
\(407\) −11.2499 −0.557637
\(408\) 0 0
\(409\) 15.4941 0.766134 0.383067 0.923720i \(-0.374868\pi\)
0.383067 + 0.923720i \(0.374868\pi\)
\(410\) 0 0
\(411\) −20.3293 −1.00277
\(412\) 0 0
\(413\) 11.6029 0.570942
\(414\) 0 0
\(415\) −5.58326 −0.274071
\(416\) 0 0
\(417\) 5.04838 0.247220
\(418\) 0 0
\(419\) −5.97766 −0.292028 −0.146014 0.989283i \(-0.546644\pi\)
−0.146014 + 0.989283i \(0.546644\pi\)
\(420\) 0 0
\(421\) 8.40791 0.409776 0.204888 0.978785i \(-0.434317\pi\)
0.204888 + 0.978785i \(0.434317\pi\)
\(422\) 0 0
\(423\) −16.6608 −0.810077
\(424\) 0 0
\(425\) 13.6661 0.662904
\(426\) 0 0
\(427\) −10.3432 −0.500540
\(428\) 0 0
\(429\) −2.16679 −0.104613
\(430\) 0 0
\(431\) −0.683402 −0.0329183 −0.0164592 0.999865i \(-0.505239\pi\)
−0.0164592 + 0.999865i \(0.505239\pi\)
\(432\) 0 0
\(433\) −25.1528 −1.20877 −0.604384 0.796693i \(-0.706581\pi\)
−0.604384 + 0.796693i \(0.706581\pi\)
\(434\) 0 0
\(435\) −25.2872 −1.21243
\(436\) 0 0
\(437\) −25.3398 −1.21216
\(438\) 0 0
\(439\) 29.8307 1.42374 0.711872 0.702309i \(-0.247848\pi\)
0.711872 + 0.702309i \(0.247848\pi\)
\(440\) 0 0
\(441\) 1.69497 0.0807126
\(442\) 0 0
\(443\) −19.1914 −0.911811 −0.455905 0.890028i \(-0.650684\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(444\) 0 0
\(445\) 10.4243 0.494160
\(446\) 0 0
\(447\) −24.9064 −1.17803
\(448\) 0 0
\(449\) −13.8690 −0.654518 −0.327259 0.944935i \(-0.606125\pi\)
−0.327259 + 0.944935i \(0.606125\pi\)
\(450\) 0 0
\(451\) 7.02502 0.330795
\(452\) 0 0
\(453\) −16.7388 −0.786457
\(454\) 0 0
\(455\) −1.26627 −0.0593637
\(456\) 0 0
\(457\) 8.93340 0.417887 0.208943 0.977928i \(-0.432998\pi\)
0.208943 + 0.977928i \(0.432998\pi\)
\(458\) 0 0
\(459\) −11.3774 −0.531053
\(460\) 0 0
\(461\) −5.08117 −0.236653 −0.118327 0.992975i \(-0.537753\pi\)
−0.118327 + 0.992975i \(0.537753\pi\)
\(462\) 0 0
\(463\) 5.00344 0.232530 0.116265 0.993218i \(-0.462908\pi\)
0.116265 + 0.993218i \(0.462908\pi\)
\(464\) 0 0
\(465\) −1.06072 −0.0491896
\(466\) 0 0
\(467\) 14.0959 0.652282 0.326141 0.945321i \(-0.394252\pi\)
0.326141 + 0.945321i \(0.394252\pi\)
\(468\) 0 0
\(469\) 10.6126 0.490046
\(470\) 0 0
\(471\) −18.9577 −0.873523
\(472\) 0 0
\(473\) 3.45783 0.158991
\(474\) 0 0
\(475\) 20.1359 0.923900
\(476\) 0 0
\(477\) 2.41051 0.110370
\(478\) 0 0
\(479\) −19.5024 −0.891087 −0.445543 0.895260i \(-0.646989\pi\)
−0.445543 + 0.895260i \(0.646989\pi\)
\(480\) 0 0
\(481\) −11.2499 −0.512952
\(482\) 0 0
\(483\) 9.26160 0.421417
\(484\) 0 0
\(485\) −3.98770 −0.181072
\(486\) 0 0
\(487\) −22.4696 −1.01819 −0.509096 0.860710i \(-0.670020\pi\)
−0.509096 + 0.860710i \(0.670020\pi\)
\(488\) 0 0
\(489\) 48.8176 2.20761
\(490\) 0 0
\(491\) 3.66861 0.165562 0.0827810 0.996568i \(-0.473620\pi\)
0.0827810 + 0.996568i \(0.473620\pi\)
\(492\) 0 0
\(493\) 37.0821 1.67009
\(494\) 0 0
\(495\) 2.14628 0.0964683
\(496\) 0 0
\(497\) 0.110620 0.00496198
\(498\) 0 0
\(499\) 18.5223 0.829173 0.414586 0.910010i \(-0.363926\pi\)
0.414586 + 0.910010i \(0.363926\pi\)
\(500\) 0 0
\(501\) −4.55948 −0.203703
\(502\) 0 0
\(503\) −7.36591 −0.328430 −0.164215 0.986425i \(-0.552509\pi\)
−0.164215 + 0.986425i \(0.552509\pi\)
\(504\) 0 0
\(505\) −3.95112 −0.175822
\(506\) 0 0
\(507\) −2.16679 −0.0962304
\(508\) 0 0
\(509\) 25.7009 1.13917 0.569587 0.821931i \(-0.307103\pi\)
0.569587 + 0.821931i \(0.307103\pi\)
\(510\) 0 0
\(511\) 3.03553 0.134284
\(512\) 0 0
\(513\) −16.7637 −0.740137
\(514\) 0 0
\(515\) 22.8648 1.00754
\(516\) 0 0
\(517\) 9.82960 0.432305
\(518\) 0 0
\(519\) −41.9937 −1.84332
\(520\) 0 0
\(521\) −20.4838 −0.897410 −0.448705 0.893680i \(-0.648115\pi\)
−0.448705 + 0.893680i \(0.648115\pi\)
\(522\) 0 0
\(523\) 24.4451 1.06891 0.534455 0.845197i \(-0.320517\pi\)
0.534455 + 0.845197i \(0.320517\pi\)
\(524\) 0 0
\(525\) −7.35962 −0.321200
\(526\) 0 0
\(527\) 1.55548 0.0677576
\(528\) 0 0
\(529\) −4.72996 −0.205650
\(530\) 0 0
\(531\) −19.6665 −0.853455
\(532\) 0 0
\(533\) 7.02502 0.304287
\(534\) 0 0
\(535\) −6.86266 −0.296699
\(536\) 0 0
\(537\) −5.61375 −0.242251
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 10.6128 0.456280 0.228140 0.973628i \(-0.426736\pi\)
0.228140 + 0.973628i \(0.426736\pi\)
\(542\) 0 0
\(543\) 12.7833 0.548582
\(544\) 0 0
\(545\) −19.4139 −0.831601
\(546\) 0 0
\(547\) 10.8945 0.465815 0.232907 0.972499i \(-0.425176\pi\)
0.232907 + 0.972499i \(0.425176\pi\)
\(548\) 0 0
\(549\) 17.5313 0.748217
\(550\) 0 0
\(551\) 54.6374 2.32763
\(552\) 0 0
\(553\) 0.962094 0.0409124
\(554\) 0 0
\(555\) 30.8668 1.31022
\(556\) 0 0
\(557\) −8.34509 −0.353593 −0.176796 0.984247i \(-0.556573\pi\)
−0.176796 + 0.984247i \(0.556573\pi\)
\(558\) 0 0
\(559\) 3.45783 0.146251
\(560\) 0 0
\(561\) −8.71811 −0.368079
\(562\) 0 0
\(563\) 29.1620 1.22903 0.614517 0.788904i \(-0.289351\pi\)
0.614517 + 0.788904i \(0.289351\pi\)
\(564\) 0 0
\(565\) 7.82797 0.329325
\(566\) 0 0
\(567\) 11.2120 0.470859
\(568\) 0 0
\(569\) −14.2396 −0.596957 −0.298478 0.954416i \(-0.596479\pi\)
−0.298478 + 0.954416i \(0.596479\pi\)
\(570\) 0 0
\(571\) −24.7058 −1.03390 −0.516952 0.856014i \(-0.672934\pi\)
−0.516952 + 0.856014i \(0.672934\pi\)
\(572\) 0 0
\(573\) −18.2673 −0.763127
\(574\) 0 0
\(575\) −14.5181 −0.605445
\(576\) 0 0
\(577\) 19.7337 0.821523 0.410761 0.911743i \(-0.365263\pi\)
0.410761 + 0.911743i \(0.365263\pi\)
\(578\) 0 0
\(579\) −26.2303 −1.09009
\(580\) 0 0
\(581\) −4.40921 −0.182925
\(582\) 0 0
\(583\) −1.42216 −0.0588998
\(584\) 0 0
\(585\) 2.14628 0.0887379
\(586\) 0 0
\(587\) −2.03951 −0.0841796 −0.0420898 0.999114i \(-0.513402\pi\)
−0.0420898 + 0.999114i \(0.513402\pi\)
\(588\) 0 0
\(589\) 2.29187 0.0944348
\(590\) 0 0
\(591\) −37.0323 −1.52331
\(592\) 0 0
\(593\) 16.0760 0.660160 0.330080 0.943953i \(-0.392924\pi\)
0.330080 + 0.943953i \(0.392924\pi\)
\(594\) 0 0
\(595\) −5.09487 −0.208869
\(596\) 0 0
\(597\) −22.3246 −0.913686
\(598\) 0 0
\(599\) −30.1955 −1.23376 −0.616878 0.787059i \(-0.711603\pi\)
−0.616878 + 0.787059i \(0.711603\pi\)
\(600\) 0 0
\(601\) −1.64091 −0.0669343 −0.0334671 0.999440i \(-0.510655\pi\)
−0.0334671 + 0.999440i \(0.510655\pi\)
\(602\) 0 0
\(603\) −17.9880 −0.732530
\(604\) 0 0
\(605\) −1.26627 −0.0514812
\(606\) 0 0
\(607\) 29.7180 1.20622 0.603109 0.797659i \(-0.293928\pi\)
0.603109 + 0.797659i \(0.293928\pi\)
\(608\) 0 0
\(609\) −19.9698 −0.809217
\(610\) 0 0
\(611\) 9.82960 0.397663
\(612\) 0 0
\(613\) 1.65761 0.0669504 0.0334752 0.999440i \(-0.489343\pi\)
0.0334752 + 0.999440i \(0.489343\pi\)
\(614\) 0 0
\(615\) −19.2748 −0.777236
\(616\) 0 0
\(617\) −44.4303 −1.78869 −0.894347 0.447373i \(-0.852360\pi\)
−0.894347 + 0.447373i \(0.852360\pi\)
\(618\) 0 0
\(619\) −9.75763 −0.392192 −0.196096 0.980585i \(-0.562826\pi\)
−0.196096 + 0.980585i \(0.562826\pi\)
\(620\) 0 0
\(621\) 12.0867 0.485023
\(622\) 0 0
\(623\) 8.23230 0.329820
\(624\) 0 0
\(625\) 3.51941 0.140776
\(626\) 0 0
\(627\) −12.8454 −0.512997
\(628\) 0 0
\(629\) −45.2643 −1.80480
\(630\) 0 0
\(631\) 6.50867 0.259106 0.129553 0.991572i \(-0.458646\pi\)
0.129553 + 0.991572i \(0.458646\pi\)
\(632\) 0 0
\(633\) −44.3861 −1.76419
\(634\) 0 0
\(635\) 20.7070 0.821732
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −0.187497 −0.00741726
\(640\) 0 0
\(641\) 14.3554 0.567005 0.283503 0.958971i \(-0.408504\pi\)
0.283503 + 0.958971i \(0.408504\pi\)
\(642\) 0 0
\(643\) −34.7551 −1.37061 −0.685304 0.728257i \(-0.740331\pi\)
−0.685304 + 0.728257i \(0.740331\pi\)
\(644\) 0 0
\(645\) −9.48739 −0.373566
\(646\) 0 0
\(647\) −19.7842 −0.777797 −0.388899 0.921281i \(-0.627144\pi\)
−0.388899 + 0.921281i \(0.627144\pi\)
\(648\) 0 0
\(649\) 11.6029 0.455454
\(650\) 0 0
\(651\) −0.837670 −0.0328309
\(652\) 0 0
\(653\) 3.07113 0.120183 0.0600913 0.998193i \(-0.480861\pi\)
0.0600913 + 0.998193i \(0.480861\pi\)
\(654\) 0 0
\(655\) −11.6272 −0.454311
\(656\) 0 0
\(657\) −5.14512 −0.200730
\(658\) 0 0
\(659\) 44.4879 1.73300 0.866501 0.499176i \(-0.166364\pi\)
0.866501 + 0.499176i \(0.166364\pi\)
\(660\) 0 0
\(661\) −27.1088 −1.05441 −0.527206 0.849738i \(-0.676760\pi\)
−0.527206 + 0.849738i \(0.676760\pi\)
\(662\) 0 0
\(663\) −8.71811 −0.338583
\(664\) 0 0
\(665\) −7.50687 −0.291104
\(666\) 0 0
\(667\) −39.3938 −1.52533
\(668\) 0 0
\(669\) 14.1436 0.546824
\(670\) 0 0
\(671\) −10.3432 −0.399293
\(672\) 0 0
\(673\) 12.1972 0.470168 0.235084 0.971975i \(-0.424463\pi\)
0.235084 + 0.971975i \(0.424463\pi\)
\(674\) 0 0
\(675\) −9.60456 −0.369680
\(676\) 0 0
\(677\) −33.3082 −1.28014 −0.640070 0.768317i \(-0.721095\pi\)
−0.640070 + 0.768317i \(0.721095\pi\)
\(678\) 0 0
\(679\) −3.14917 −0.120854
\(680\) 0 0
\(681\) −2.59058 −0.0992712
\(682\) 0 0
\(683\) −30.6220 −1.17172 −0.585859 0.810413i \(-0.699243\pi\)
−0.585859 + 0.810413i \(0.699243\pi\)
\(684\) 0 0
\(685\) −11.8804 −0.453928
\(686\) 0 0
\(687\) −42.0148 −1.60296
\(688\) 0 0
\(689\) −1.42216 −0.0541799
\(690\) 0 0
\(691\) 18.7175 0.712048 0.356024 0.934477i \(-0.384132\pi\)
0.356024 + 0.934477i \(0.384132\pi\)
\(692\) 0 0
\(693\) 1.69497 0.0643864
\(694\) 0 0
\(695\) 2.95027 0.111910
\(696\) 0 0
\(697\) 28.2653 1.07063
\(698\) 0 0
\(699\) −52.3203 −1.97894
\(700\) 0 0
\(701\) 8.28526 0.312930 0.156465 0.987684i \(-0.449990\pi\)
0.156465 + 0.987684i \(0.449990\pi\)
\(702\) 0 0
\(703\) −66.6932 −2.51538
\(704\) 0 0
\(705\) −26.9699 −1.01574
\(706\) 0 0
\(707\) −3.12028 −0.117350
\(708\) 0 0
\(709\) −34.1126 −1.28112 −0.640562 0.767906i \(-0.721299\pi\)
−0.640562 + 0.767906i \(0.721299\pi\)
\(710\) 0 0
\(711\) −1.63072 −0.0611566
\(712\) 0 0
\(713\) −1.65244 −0.0618845
\(714\) 0 0
\(715\) −1.26627 −0.0473558
\(716\) 0 0
\(717\) 38.0446 1.42080
\(718\) 0 0
\(719\) −43.8645 −1.63587 −0.817934 0.575312i \(-0.804881\pi\)
−0.817934 + 0.575312i \(0.804881\pi\)
\(720\) 0 0
\(721\) 18.0568 0.672470
\(722\) 0 0
\(723\) 30.8261 1.14643
\(724\) 0 0
\(725\) 31.3038 1.16259
\(726\) 0 0
\(727\) −49.5628 −1.83818 −0.919091 0.394046i \(-0.871075\pi\)
−0.919091 + 0.394046i \(0.871075\pi\)
\(728\) 0 0
\(729\) −0.622653 −0.0230612
\(730\) 0 0
\(731\) 13.9127 0.514578
\(732\) 0 0
\(733\) 6.94857 0.256651 0.128326 0.991732i \(-0.459040\pi\)
0.128326 + 0.991732i \(0.459040\pi\)
\(734\) 0 0
\(735\) 2.74374 0.101204
\(736\) 0 0
\(737\) 10.6126 0.390921
\(738\) 0 0
\(739\) 21.1168 0.776794 0.388397 0.921492i \(-0.373029\pi\)
0.388397 + 0.921492i \(0.373029\pi\)
\(740\) 0 0
\(741\) −12.8454 −0.471889
\(742\) 0 0
\(743\) −16.2453 −0.595984 −0.297992 0.954568i \(-0.596317\pi\)
−0.297992 + 0.954568i \(0.596317\pi\)
\(744\) 0 0
\(745\) −14.5553 −0.533265
\(746\) 0 0
\(747\) 7.47347 0.273440
\(748\) 0 0
\(749\) −5.41959 −0.198027
\(750\) 0 0
\(751\) 29.3475 1.07091 0.535453 0.844565i \(-0.320141\pi\)
0.535453 + 0.844565i \(0.320141\pi\)
\(752\) 0 0
\(753\) 30.7574 1.12086
\(754\) 0 0
\(755\) −9.78215 −0.356009
\(756\) 0 0
\(757\) 35.9554 1.30682 0.653410 0.757004i \(-0.273338\pi\)
0.653410 + 0.757004i \(0.273338\pi\)
\(758\) 0 0
\(759\) 9.26160 0.336175
\(760\) 0 0
\(761\) 40.5514 1.46999 0.734994 0.678074i \(-0.237185\pi\)
0.734994 + 0.678074i \(0.237185\pi\)
\(762\) 0 0
\(763\) −15.3316 −0.555040
\(764\) 0 0
\(765\) 8.63562 0.312222
\(766\) 0 0
\(767\) 11.6029 0.418957
\(768\) 0 0
\(769\) 29.6679 1.06985 0.534926 0.844899i \(-0.320340\pi\)
0.534926 + 0.844899i \(0.320340\pi\)
\(770\) 0 0
\(771\) 10.2246 0.368232
\(772\) 0 0
\(773\) 19.3481 0.695904 0.347952 0.937512i \(-0.386877\pi\)
0.347952 + 0.937512i \(0.386877\pi\)
\(774\) 0 0
\(775\) 1.31309 0.0471678
\(776\) 0 0
\(777\) 24.3762 0.874490
\(778\) 0 0
\(779\) 41.6467 1.49215
\(780\) 0 0
\(781\) 0.110620 0.00395829
\(782\) 0 0
\(783\) −26.0613 −0.931354
\(784\) 0 0
\(785\) −11.0789 −0.395422
\(786\) 0 0
\(787\) −37.8709 −1.34995 −0.674975 0.737840i \(-0.735846\pi\)
−0.674975 + 0.737840i \(0.735846\pi\)
\(788\) 0 0
\(789\) −29.6994 −1.05733
\(790\) 0 0
\(791\) 6.18191 0.219803
\(792\) 0 0
\(793\) −10.3432 −0.367296
\(794\) 0 0
\(795\) 3.90203 0.138391
\(796\) 0 0
\(797\) −52.2540 −1.85093 −0.925465 0.378833i \(-0.876325\pi\)
−0.925465 + 0.378833i \(0.876325\pi\)
\(798\) 0 0
\(799\) 39.5496 1.39916
\(800\) 0 0
\(801\) −13.9535 −0.493021
\(802\) 0 0
\(803\) 3.03553 0.107122
\(804\) 0 0
\(805\) 5.41248 0.190765
\(806\) 0 0
\(807\) 18.7163 0.658844
\(808\) 0 0
\(809\) −19.4286 −0.683073 −0.341537 0.939868i \(-0.610947\pi\)
−0.341537 + 0.939868i \(0.610947\pi\)
\(810\) 0 0
\(811\) 4.28637 0.150515 0.0752573 0.997164i \(-0.476022\pi\)
0.0752573 + 0.997164i \(0.476022\pi\)
\(812\) 0 0
\(813\) −65.4478 −2.29535
\(814\) 0 0
\(815\) 28.5290 0.999329
\(816\) 0 0
\(817\) 20.4992 0.717176
\(818\) 0 0
\(819\) 1.69497 0.0592269
\(820\) 0 0
\(821\) 23.8955 0.833960 0.416980 0.908916i \(-0.363088\pi\)
0.416980 + 0.908916i \(0.363088\pi\)
\(822\) 0 0
\(823\) 3.73641 0.130243 0.0651215 0.997877i \(-0.479256\pi\)
0.0651215 + 0.997877i \(0.479256\pi\)
\(824\) 0 0
\(825\) −7.35962 −0.256229
\(826\) 0 0
\(827\) −37.5279 −1.30497 −0.652487 0.757800i \(-0.726274\pi\)
−0.652487 + 0.757800i \(0.726274\pi\)
\(828\) 0 0
\(829\) 6.15568 0.213796 0.106898 0.994270i \(-0.465908\pi\)
0.106898 + 0.994270i \(0.465908\pi\)
\(830\) 0 0
\(831\) −29.1619 −1.01162
\(832\) 0 0
\(833\) −4.02352 −0.139407
\(834\) 0 0
\(835\) −2.66456 −0.0922110
\(836\) 0 0
\(837\) −1.09319 −0.0377861
\(838\) 0 0
\(839\) −36.8832 −1.27335 −0.636675 0.771132i \(-0.719691\pi\)
−0.636675 + 0.771132i \(0.719691\pi\)
\(840\) 0 0
\(841\) 55.9406 1.92899
\(842\) 0 0
\(843\) 5.52669 0.190349
\(844\) 0 0
\(845\) −1.26627 −0.0435610
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 20.7230 0.711212
\(850\) 0 0
\(851\) 48.0860 1.64837
\(852\) 0 0
\(853\) −31.9892 −1.09529 −0.547645 0.836711i \(-0.684476\pi\)
−0.547645 + 0.836711i \(0.684476\pi\)
\(854\) 0 0
\(855\) 12.7239 0.435148
\(856\) 0 0
\(857\) 14.3815 0.491263 0.245631 0.969363i \(-0.421005\pi\)
0.245631 + 0.969363i \(0.421005\pi\)
\(858\) 0 0
\(859\) −40.2207 −1.37231 −0.686156 0.727455i \(-0.740703\pi\)
−0.686156 + 0.727455i \(0.740703\pi\)
\(860\) 0 0
\(861\) −15.2217 −0.518755
\(862\) 0 0
\(863\) −16.6596 −0.567101 −0.283550 0.958957i \(-0.591512\pi\)
−0.283550 + 0.958957i \(0.591512\pi\)
\(864\) 0 0
\(865\) −24.5411 −0.834423
\(866\) 0 0
\(867\) 1.75788 0.0597006
\(868\) 0 0
\(869\) 0.962094 0.0326368
\(870\) 0 0
\(871\) 10.6126 0.359595
\(872\) 0 0
\(873\) 5.33773 0.180655
\(874\) 0 0
\(875\) −10.6323 −0.359438
\(876\) 0 0
\(877\) −33.1133 −1.11816 −0.559079 0.829115i \(-0.688845\pi\)
−0.559079 + 0.829115i \(0.688845\pi\)
\(878\) 0 0
\(879\) 57.2601 1.93134
\(880\) 0 0
\(881\) 52.5883 1.77175 0.885873 0.463928i \(-0.153560\pi\)
0.885873 + 0.463928i \(0.153560\pi\)
\(882\) 0 0
\(883\) −8.94639 −0.301070 −0.150535 0.988605i \(-0.548100\pi\)
−0.150535 + 0.988605i \(0.548100\pi\)
\(884\) 0 0
\(885\) −31.8354 −1.07013
\(886\) 0 0
\(887\) −2.42416 −0.0813954 −0.0406977 0.999172i \(-0.512958\pi\)
−0.0406977 + 0.999172i \(0.512958\pi\)
\(888\) 0 0
\(889\) 16.3527 0.548453
\(890\) 0 0
\(891\) 11.2120 0.375616
\(892\) 0 0
\(893\) 58.2732 1.95004
\(894\) 0 0
\(895\) −3.28067 −0.109661
\(896\) 0 0
\(897\) 9.26160 0.309236
\(898\) 0 0
\(899\) 3.56299 0.118832
\(900\) 0 0
\(901\) −5.72209 −0.190630
\(902\) 0 0
\(903\) −7.49239 −0.249331
\(904\) 0 0
\(905\) 7.47054 0.248329
\(906\) 0 0
\(907\) 19.0627 0.632967 0.316484 0.948598i \(-0.397498\pi\)
0.316484 + 0.948598i \(0.397498\pi\)
\(908\) 0 0
\(909\) 5.28876 0.175417
\(910\) 0 0
\(911\) −23.0989 −0.765302 −0.382651 0.923893i \(-0.624989\pi\)
−0.382651 + 0.923893i \(0.624989\pi\)
\(912\) 0 0
\(913\) −4.40921 −0.145924
\(914\) 0 0
\(915\) 28.3789 0.938178
\(916\) 0 0
\(917\) −9.18222 −0.303224
\(918\) 0 0
\(919\) 36.8042 1.21406 0.607030 0.794679i \(-0.292361\pi\)
0.607030 + 0.794679i \(0.292361\pi\)
\(920\) 0 0
\(921\) 34.3154 1.13073
\(922\) 0 0
\(923\) 0.110620 0.00364110
\(924\) 0 0
\(925\) −38.2110 −1.25637
\(926\) 0 0
\(927\) −30.6056 −1.00522
\(928\) 0 0
\(929\) 22.0856 0.724604 0.362302 0.932061i \(-0.381991\pi\)
0.362302 + 0.932061i \(0.381991\pi\)
\(930\) 0 0
\(931\) −5.92833 −0.194293
\(932\) 0 0
\(933\) −50.5793 −1.65589
\(934\) 0 0
\(935\) −5.09487 −0.166620
\(936\) 0 0
\(937\) −43.3523 −1.41626 −0.708129 0.706083i \(-0.750461\pi\)
−0.708129 + 0.706083i \(0.750461\pi\)
\(938\) 0 0
\(939\) −56.5713 −1.84613
\(940\) 0 0
\(941\) −51.0017 −1.66261 −0.831304 0.555818i \(-0.812405\pi\)
−0.831304 + 0.555818i \(0.812405\pi\)
\(942\) 0 0
\(943\) −30.0274 −0.977826
\(944\) 0 0
\(945\) 3.58067 0.116479
\(946\) 0 0
\(947\) −8.04943 −0.261571 −0.130786 0.991411i \(-0.541750\pi\)
−0.130786 + 0.991411i \(0.541750\pi\)
\(948\) 0 0
\(949\) 3.03553 0.0985375
\(950\) 0 0
\(951\) 1.33541 0.0433036
\(952\) 0 0
\(953\) −39.4760 −1.27875 −0.639377 0.768894i \(-0.720807\pi\)
−0.639377 + 0.768894i \(0.720807\pi\)
\(954\) 0 0
\(955\) −10.6754 −0.345448
\(956\) 0 0
\(957\) −19.9698 −0.645532
\(958\) 0 0
\(959\) −9.38223 −0.302968
\(960\) 0 0
\(961\) −30.8505 −0.995179
\(962\) 0 0
\(963\) 9.18601 0.296015
\(964\) 0 0
\(965\) −15.3290 −0.493457
\(966\) 0 0
\(967\) 26.8622 0.863829 0.431914 0.901915i \(-0.357838\pi\)
0.431914 + 0.901915i \(0.357838\pi\)
\(968\) 0 0
\(969\) −51.6839 −1.66032
\(970\) 0 0
\(971\) −45.4602 −1.45889 −0.729443 0.684041i \(-0.760221\pi\)
−0.729443 + 0.684041i \(0.760221\pi\)
\(972\) 0 0
\(973\) 2.32989 0.0746929
\(974\) 0 0
\(975\) −7.35962 −0.235696
\(976\) 0 0
\(977\) 11.8298 0.378468 0.189234 0.981932i \(-0.439400\pi\)
0.189234 + 0.981932i \(0.439400\pi\)
\(978\) 0 0
\(979\) 8.23230 0.263105
\(980\) 0 0
\(981\) 25.9865 0.829684
\(982\) 0 0
\(983\) 11.8826 0.378995 0.189497 0.981881i \(-0.439314\pi\)
0.189497 + 0.981881i \(0.439314\pi\)
\(984\) 0 0
\(985\) −21.6417 −0.689562
\(986\) 0 0
\(987\) −21.2987 −0.677944
\(988\) 0 0
\(989\) −14.7800 −0.469976
\(990\) 0 0
\(991\) 40.0821 1.27325 0.636625 0.771173i \(-0.280330\pi\)
0.636625 + 0.771173i \(0.280330\pi\)
\(992\) 0 0
\(993\) −38.1758 −1.21147
\(994\) 0 0
\(995\) −13.0465 −0.413602
\(996\) 0 0
\(997\) 14.1962 0.449599 0.224800 0.974405i \(-0.427827\pi\)
0.224800 + 0.974405i \(0.427827\pi\)
\(998\) 0 0
\(999\) 31.8117 1.00648
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 \(a_p\))