Properties

Label 4004.2.a.j.1.5
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 1.5
Root \(0.357256\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.357256 q^{3} +3.31742 q^{5} -1.00000 q^{7} -2.87237 q^{9} +O(q^{10})\) \(q-0.357256 q^{3} +3.31742 q^{5} -1.00000 q^{7} -2.87237 q^{9} -1.00000 q^{11} -1.00000 q^{13} -1.18517 q^{15} +2.87740 q^{17} -0.480550 q^{19} +0.357256 q^{21} -8.87774 q^{23} +6.00528 q^{25} +2.09794 q^{27} +2.06825 q^{29} +8.14340 q^{31} +0.357256 q^{33} -3.31742 q^{35} +9.94343 q^{37} +0.357256 q^{39} +6.95677 q^{41} -5.10805 q^{43} -9.52885 q^{45} -3.30475 q^{47} +1.00000 q^{49} -1.02797 q^{51} -6.64805 q^{53} -3.31742 q^{55} +0.171679 q^{57} +8.21164 q^{59} +13.8367 q^{61} +2.87237 q^{63} -3.31742 q^{65} +10.8104 q^{67} +3.17163 q^{69} +8.48947 q^{71} +15.9546 q^{73} -2.14543 q^{75} +1.00000 q^{77} -1.62192 q^{79} +7.86760 q^{81} +10.8207 q^{83} +9.54555 q^{85} -0.738894 q^{87} +9.23781 q^{89} +1.00000 q^{91} -2.90928 q^{93} -1.59419 q^{95} -14.8240 q^{97} +2.87237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) −0.357256 −0.206262 −0.103131 0.994668i \(-0.532886\pi\)
−0.103131 + 0.994668i \(0.532886\pi\)
\(4\) 0 0
\(5\) 3.31742 1.48360 0.741798 0.670623i \(-0.233973\pi\)
0.741798 + 0.670623i \(0.233973\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.87237 −0.957456
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.18517 −0.306010
\(16\) 0 0
\(17\) 2.87740 0.697873 0.348936 0.937146i \(-0.386543\pi\)
0.348936 + 0.937146i \(0.386543\pi\)
\(18\) 0 0
\(19\) −0.480550 −0.110246 −0.0551228 0.998480i \(-0.517555\pi\)
−0.0551228 + 0.998480i \(0.517555\pi\)
\(20\) 0 0
\(21\) 0.357256 0.0779597
\(22\) 0 0
\(23\) −8.87774 −1.85114 −0.925569 0.378580i \(-0.876412\pi\)
−0.925569 + 0.378580i \(0.876412\pi\)
\(24\) 0 0
\(25\) 6.00528 1.20106
\(26\) 0 0
\(27\) 2.09794 0.403749
\(28\) 0 0
\(29\) 2.06825 0.384064 0.192032 0.981389i \(-0.438492\pi\)
0.192032 + 0.981389i \(0.438492\pi\)
\(30\) 0 0
\(31\) 8.14340 1.46260 0.731299 0.682057i \(-0.238915\pi\)
0.731299 + 0.682057i \(0.238915\pi\)
\(32\) 0 0
\(33\) 0.357256 0.0621904
\(34\) 0 0
\(35\) −3.31742 −0.560747
\(36\) 0 0
\(37\) 9.94343 1.63469 0.817345 0.576148i \(-0.195445\pi\)
0.817345 + 0.576148i \(0.195445\pi\)
\(38\) 0 0
\(39\) 0.357256 0.0572068
\(40\) 0 0
\(41\) 6.95677 1.08646 0.543232 0.839583i \(-0.317200\pi\)
0.543232 + 0.839583i \(0.317200\pi\)
\(42\) 0 0
\(43\) −5.10805 −0.778970 −0.389485 0.921033i \(-0.627347\pi\)
−0.389485 + 0.921033i \(0.627347\pi\)
\(44\) 0 0
\(45\) −9.52885 −1.42048
\(46\) 0 0
\(47\) −3.30475 −0.482048 −0.241024 0.970519i \(-0.577483\pi\)
−0.241024 + 0.970519i \(0.577483\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.02797 −0.143945
\(52\) 0 0
\(53\) −6.64805 −0.913180 −0.456590 0.889677i \(-0.650929\pi\)
−0.456590 + 0.889677i \(0.650929\pi\)
\(54\) 0 0
\(55\) −3.31742 −0.447321
\(56\) 0 0
\(57\) 0.171679 0.0227395
\(58\) 0 0
\(59\) 8.21164 1.06907 0.534533 0.845148i \(-0.320488\pi\)
0.534533 + 0.845148i \(0.320488\pi\)
\(60\) 0 0
\(61\) 13.8367 1.77160 0.885801 0.464065i \(-0.153610\pi\)
0.885801 + 0.464065i \(0.153610\pi\)
\(62\) 0 0
\(63\) 2.87237 0.361884
\(64\) 0 0
\(65\) −3.31742 −0.411475
\(66\) 0 0
\(67\) 10.8104 1.32070 0.660349 0.750959i \(-0.270408\pi\)
0.660349 + 0.750959i \(0.270408\pi\)
\(68\) 0 0
\(69\) 3.17163 0.381819
\(70\) 0 0
\(71\) 8.48947 1.00752 0.503758 0.863845i \(-0.331951\pi\)
0.503758 + 0.863845i \(0.331951\pi\)
\(72\) 0 0
\(73\) 15.9546 1.86735 0.933675 0.358122i \(-0.116583\pi\)
0.933675 + 0.358122i \(0.116583\pi\)
\(74\) 0 0
\(75\) −2.14543 −0.247732
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −1.62192 −0.182481 −0.0912403 0.995829i \(-0.529083\pi\)
−0.0912403 + 0.995829i \(0.529083\pi\)
\(80\) 0 0
\(81\) 7.86760 0.874178
\(82\) 0 0
\(83\) 10.8207 1.18773 0.593865 0.804564i \(-0.297601\pi\)
0.593865 + 0.804564i \(0.297601\pi\)
\(84\) 0 0
\(85\) 9.54555 1.03536
\(86\) 0 0
\(87\) −0.738894 −0.0792178
\(88\) 0 0
\(89\) 9.23781 0.979206 0.489603 0.871946i \(-0.337142\pi\)
0.489603 + 0.871946i \(0.337142\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −2.90928 −0.301678
\(94\) 0 0
\(95\) −1.59419 −0.163560
\(96\) 0 0
\(97\) −14.8240 −1.50515 −0.752574 0.658508i \(-0.771188\pi\)
−0.752574 + 0.658508i \(0.771188\pi\)
\(98\) 0 0
\(99\) 2.87237 0.288684
\(100\) 0 0
\(101\) 6.81473 0.678091 0.339045 0.940770i \(-0.389896\pi\)
0.339045 + 0.940770i \(0.389896\pi\)
\(102\) 0 0
\(103\) 5.56915 0.548745 0.274372 0.961624i \(-0.411530\pi\)
0.274372 + 0.961624i \(0.411530\pi\)
\(104\) 0 0
\(105\) 1.18517 0.115661
\(106\) 0 0
\(107\) −12.1594 −1.17550 −0.587748 0.809044i \(-0.699985\pi\)
−0.587748 + 0.809044i \(0.699985\pi\)
\(108\) 0 0
\(109\) −7.42599 −0.711281 −0.355640 0.934623i \(-0.615737\pi\)
−0.355640 + 0.934623i \(0.615737\pi\)
\(110\) 0 0
\(111\) −3.55236 −0.337175
\(112\) 0 0
\(113\) −11.9437 −1.12357 −0.561783 0.827284i \(-0.689885\pi\)
−0.561783 + 0.827284i \(0.689885\pi\)
\(114\) 0 0
\(115\) −29.4512 −2.74634
\(116\) 0 0
\(117\) 2.87237 0.265551
\(118\) 0 0
\(119\) −2.87740 −0.263771
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −2.48535 −0.224096
\(124\) 0 0
\(125\) 3.33495 0.298287
\(126\) 0 0
\(127\) −4.19697 −0.372421 −0.186210 0.982510i \(-0.559621\pi\)
−0.186210 + 0.982510i \(0.559621\pi\)
\(128\) 0 0
\(129\) 1.82488 0.160672
\(130\) 0 0
\(131\) 18.3104 1.59978 0.799892 0.600143i \(-0.204890\pi\)
0.799892 + 0.600143i \(0.204890\pi\)
\(132\) 0 0
\(133\) 0.480550 0.0416689
\(134\) 0 0
\(135\) 6.95975 0.599000
\(136\) 0 0
\(137\) 8.81368 0.753003 0.376502 0.926416i \(-0.377127\pi\)
0.376502 + 0.926416i \(0.377127\pi\)
\(138\) 0 0
\(139\) −5.52322 −0.468473 −0.234237 0.972180i \(-0.575259\pi\)
−0.234237 + 0.972180i \(0.575259\pi\)
\(140\) 0 0
\(141\) 1.18064 0.0994281
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 6.86124 0.569795
\(146\) 0 0
\(147\) −0.357256 −0.0294660
\(148\) 0 0
\(149\) −22.7718 −1.86554 −0.932770 0.360473i \(-0.882615\pi\)
−0.932770 + 0.360473i \(0.882615\pi\)
\(150\) 0 0
\(151\) 11.1108 0.904184 0.452092 0.891971i \(-0.350678\pi\)
0.452092 + 0.891971i \(0.350678\pi\)
\(152\) 0 0
\(153\) −8.26496 −0.668182
\(154\) 0 0
\(155\) 27.0151 2.16990
\(156\) 0 0
\(157\) −17.9105 −1.42941 −0.714705 0.699426i \(-0.753439\pi\)
−0.714705 + 0.699426i \(0.753439\pi\)
\(158\) 0 0
\(159\) 2.37506 0.188354
\(160\) 0 0
\(161\) 8.87774 0.699664
\(162\) 0 0
\(163\) −3.88780 −0.304516 −0.152258 0.988341i \(-0.548654\pi\)
−0.152258 + 0.988341i \(0.548654\pi\)
\(164\) 0 0
\(165\) 1.18517 0.0922654
\(166\) 0 0
\(167\) 9.13044 0.706534 0.353267 0.935522i \(-0.385071\pi\)
0.353267 + 0.935522i \(0.385071\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.38032 0.105555
\(172\) 0 0
\(173\) 22.1924 1.68726 0.843629 0.536927i \(-0.180415\pi\)
0.843629 + 0.536927i \(0.180415\pi\)
\(174\) 0 0
\(175\) −6.00528 −0.453957
\(176\) 0 0
\(177\) −2.93366 −0.220508
\(178\) 0 0
\(179\) −7.70749 −0.576085 −0.288043 0.957618i \(-0.593004\pi\)
−0.288043 + 0.957618i \(0.593004\pi\)
\(180\) 0 0
\(181\) 8.39961 0.624338 0.312169 0.950027i \(-0.398944\pi\)
0.312169 + 0.950027i \(0.398944\pi\)
\(182\) 0 0
\(183\) −4.94323 −0.365414
\(184\) 0 0
\(185\) 32.9866 2.42522
\(186\) 0 0
\(187\) −2.87740 −0.210416
\(188\) 0 0
\(189\) −2.09794 −0.152603
\(190\) 0 0
\(191\) −12.8806 −0.932005 −0.466002 0.884784i \(-0.654306\pi\)
−0.466002 + 0.884784i \(0.654306\pi\)
\(192\) 0 0
\(193\) −9.88160 −0.711293 −0.355646 0.934621i \(-0.615739\pi\)
−0.355646 + 0.934621i \(0.615739\pi\)
\(194\) 0 0
\(195\) 1.18517 0.0848718
\(196\) 0 0
\(197\) −6.78543 −0.483442 −0.241721 0.970346i \(-0.577712\pi\)
−0.241721 + 0.970346i \(0.577712\pi\)
\(198\) 0 0
\(199\) −22.4228 −1.58951 −0.794755 0.606930i \(-0.792401\pi\)
−0.794755 + 0.606930i \(0.792401\pi\)
\(200\) 0 0
\(201\) −3.86208 −0.272410
\(202\) 0 0
\(203\) −2.06825 −0.145162
\(204\) 0 0
\(205\) 23.0785 1.61187
\(206\) 0 0
\(207\) 25.5001 1.77238
\(208\) 0 0
\(209\) 0.480550 0.0332403
\(210\) 0 0
\(211\) 0.726378 0.0500059 0.0250030 0.999687i \(-0.492040\pi\)
0.0250030 + 0.999687i \(0.492040\pi\)
\(212\) 0 0
\(213\) −3.03292 −0.207812
\(214\) 0 0
\(215\) −16.9455 −1.15568
\(216\) 0 0
\(217\) −8.14340 −0.552810
\(218\) 0 0
\(219\) −5.69990 −0.385163
\(220\) 0 0
\(221\) −2.87740 −0.193555
\(222\) 0 0
\(223\) 16.9176 1.13289 0.566444 0.824100i \(-0.308319\pi\)
0.566444 + 0.824100i \(0.308319\pi\)
\(224\) 0 0
\(225\) −17.2494 −1.14996
\(226\) 0 0
\(227\) −3.43324 −0.227872 −0.113936 0.993488i \(-0.536346\pi\)
−0.113936 + 0.993488i \(0.536346\pi\)
\(228\) 0 0
\(229\) 21.7443 1.43691 0.718453 0.695576i \(-0.244851\pi\)
0.718453 + 0.695576i \(0.244851\pi\)
\(230\) 0 0
\(231\) −0.357256 −0.0235057
\(232\) 0 0
\(233\) 20.7972 1.36247 0.681236 0.732064i \(-0.261443\pi\)
0.681236 + 0.732064i \(0.261443\pi\)
\(234\) 0 0
\(235\) −10.9633 −0.715164
\(236\) 0 0
\(237\) 0.579442 0.0376388
\(238\) 0 0
\(239\) −15.5909 −1.00849 −0.504245 0.863561i \(-0.668229\pi\)
−0.504245 + 0.863561i \(0.668229\pi\)
\(240\) 0 0
\(241\) −13.2478 −0.853368 −0.426684 0.904401i \(-0.640318\pi\)
−0.426684 + 0.904401i \(0.640318\pi\)
\(242\) 0 0
\(243\) −9.10457 −0.584059
\(244\) 0 0
\(245\) 3.31742 0.211942
\(246\) 0 0
\(247\) 0.480550 0.0305766
\(248\) 0 0
\(249\) −3.86578 −0.244984
\(250\) 0 0
\(251\) −24.0058 −1.51524 −0.757618 0.652699i \(-0.773637\pi\)
−0.757618 + 0.652699i \(0.773637\pi\)
\(252\) 0 0
\(253\) 8.87774 0.558139
\(254\) 0 0
\(255\) −3.41021 −0.213556
\(256\) 0 0
\(257\) 23.3774 1.45824 0.729121 0.684385i \(-0.239929\pi\)
0.729121 + 0.684385i \(0.239929\pi\)
\(258\) 0 0
\(259\) −9.94343 −0.617855
\(260\) 0 0
\(261\) −5.94076 −0.367724
\(262\) 0 0
\(263\) −8.87124 −0.547024 −0.273512 0.961869i \(-0.588185\pi\)
−0.273512 + 0.961869i \(0.588185\pi\)
\(264\) 0 0
\(265\) −22.0544 −1.35479
\(266\) 0 0
\(267\) −3.30027 −0.201973
\(268\) 0 0
\(269\) −3.59668 −0.219293 −0.109647 0.993971i \(-0.534972\pi\)
−0.109647 + 0.993971i \(0.534972\pi\)
\(270\) 0 0
\(271\) 25.2641 1.53469 0.767343 0.641237i \(-0.221578\pi\)
0.767343 + 0.641237i \(0.221578\pi\)
\(272\) 0 0
\(273\) −0.357256 −0.0216221
\(274\) 0 0
\(275\) −6.00528 −0.362132
\(276\) 0 0
\(277\) −19.5662 −1.17562 −0.587810 0.808999i \(-0.700010\pi\)
−0.587810 + 0.808999i \(0.700010\pi\)
\(278\) 0 0
\(279\) −23.3908 −1.40037
\(280\) 0 0
\(281\) 19.0672 1.13746 0.568728 0.822526i \(-0.307436\pi\)
0.568728 + 0.822526i \(0.307436\pi\)
\(282\) 0 0
\(283\) −10.8890 −0.647281 −0.323641 0.946180i \(-0.604907\pi\)
−0.323641 + 0.946180i \(0.604907\pi\)
\(284\) 0 0
\(285\) 0.569533 0.0337362
\(286\) 0 0
\(287\) −6.95677 −0.410645
\(288\) 0 0
\(289\) −8.72056 −0.512974
\(290\) 0 0
\(291\) 5.29596 0.310455
\(292\) 0 0
\(293\) 20.6171 1.20446 0.602231 0.798322i \(-0.294279\pi\)
0.602231 + 0.798322i \(0.294279\pi\)
\(294\) 0 0
\(295\) 27.2415 1.58606
\(296\) 0 0
\(297\) −2.09794 −0.121735
\(298\) 0 0
\(299\) 8.87774 0.513413
\(300\) 0 0
\(301\) 5.10805 0.294423
\(302\) 0 0
\(303\) −2.43461 −0.139864
\(304\) 0 0
\(305\) 45.9020 2.62834
\(306\) 0 0
\(307\) 1.96417 0.112101 0.0560506 0.998428i \(-0.482149\pi\)
0.0560506 + 0.998428i \(0.482149\pi\)
\(308\) 0 0
\(309\) −1.98961 −0.113185
\(310\) 0 0
\(311\) −7.78177 −0.441264 −0.220632 0.975357i \(-0.570812\pi\)
−0.220632 + 0.975357i \(0.570812\pi\)
\(312\) 0 0
\(313\) 20.2610 1.14522 0.572609 0.819829i \(-0.305931\pi\)
0.572609 + 0.819829i \(0.305931\pi\)
\(314\) 0 0
\(315\) 9.52885 0.536890
\(316\) 0 0
\(317\) 24.6451 1.38421 0.692104 0.721798i \(-0.256684\pi\)
0.692104 + 0.721798i \(0.256684\pi\)
\(318\) 0 0
\(319\) −2.06825 −0.115800
\(320\) 0 0
\(321\) 4.34403 0.242460
\(322\) 0 0
\(323\) −1.38273 −0.0769374
\(324\) 0 0
\(325\) −6.00528 −0.333113
\(326\) 0 0
\(327\) 2.65298 0.146710
\(328\) 0 0
\(329\) 3.30475 0.182197
\(330\) 0 0
\(331\) 25.7539 1.41556 0.707781 0.706431i \(-0.249696\pi\)
0.707781 + 0.706431i \(0.249696\pi\)
\(332\) 0 0
\(333\) −28.5612 −1.56514
\(334\) 0 0
\(335\) 35.8626 1.95938
\(336\) 0 0
\(337\) 14.0916 0.767618 0.383809 0.923413i \(-0.374612\pi\)
0.383809 + 0.923413i \(0.374612\pi\)
\(338\) 0 0
\(339\) 4.26696 0.231749
\(340\) 0 0
\(341\) −8.14340 −0.440990
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 10.5216 0.566466
\(346\) 0 0
\(347\) −29.7026 −1.59452 −0.797259 0.603638i \(-0.793717\pi\)
−0.797259 + 0.603638i \(0.793717\pi\)
\(348\) 0 0
\(349\) −3.32866 −0.178179 −0.0890896 0.996024i \(-0.528396\pi\)
−0.0890896 + 0.996024i \(0.528396\pi\)
\(350\) 0 0
\(351\) −2.09794 −0.111980
\(352\) 0 0
\(353\) −14.5088 −0.772223 −0.386111 0.922452i \(-0.626182\pi\)
−0.386111 + 0.922452i \(0.626182\pi\)
\(354\) 0 0
\(355\) 28.1632 1.49475
\(356\) 0 0
\(357\) 1.02797 0.0544060
\(358\) 0 0
\(359\) 30.6298 1.61658 0.808289 0.588786i \(-0.200394\pi\)
0.808289 + 0.588786i \(0.200394\pi\)
\(360\) 0 0
\(361\) −18.7691 −0.987846
\(362\) 0 0
\(363\) −0.357256 −0.0187511
\(364\) 0 0
\(365\) 52.9283 2.77039
\(366\) 0 0
\(367\) −9.79391 −0.511238 −0.255619 0.966778i \(-0.582279\pi\)
−0.255619 + 0.966778i \(0.582279\pi\)
\(368\) 0 0
\(369\) −19.9824 −1.04024
\(370\) 0 0
\(371\) 6.64805 0.345150
\(372\) 0 0
\(373\) 8.92267 0.461998 0.230999 0.972954i \(-0.425801\pi\)
0.230999 + 0.972954i \(0.425801\pi\)
\(374\) 0 0
\(375\) −1.19143 −0.0615252
\(376\) 0 0
\(377\) −2.06825 −0.106520
\(378\) 0 0
\(379\) −25.5806 −1.31399 −0.656993 0.753897i \(-0.728172\pi\)
−0.656993 + 0.753897i \(0.728172\pi\)
\(380\) 0 0
\(381\) 1.49939 0.0768163
\(382\) 0 0
\(383\) −21.9910 −1.12369 −0.561843 0.827244i \(-0.689907\pi\)
−0.561843 + 0.827244i \(0.689907\pi\)
\(384\) 0 0
\(385\) 3.31742 0.169071
\(386\) 0 0
\(387\) 14.6722 0.745830
\(388\) 0 0
\(389\) 4.27389 0.216695 0.108347 0.994113i \(-0.465444\pi\)
0.108347 + 0.994113i \(0.465444\pi\)
\(390\) 0 0
\(391\) −25.5448 −1.29186
\(392\) 0 0
\(393\) −6.54150 −0.329975
\(394\) 0 0
\(395\) −5.38060 −0.270727
\(396\) 0 0
\(397\) 14.7076 0.738155 0.369077 0.929399i \(-0.379674\pi\)
0.369077 + 0.929399i \(0.379674\pi\)
\(398\) 0 0
\(399\) −0.171679 −0.00859472
\(400\) 0 0
\(401\) 32.2978 1.61288 0.806438 0.591318i \(-0.201392\pi\)
0.806438 + 0.591318i \(0.201392\pi\)
\(402\) 0 0
\(403\) −8.14340 −0.405652
\(404\) 0 0
\(405\) 26.1001 1.29693
\(406\) 0 0
\(407\) −9.94343 −0.492878
\(408\) 0 0
\(409\) 27.1068 1.34035 0.670173 0.742205i \(-0.266220\pi\)
0.670173 + 0.742205i \(0.266220\pi\)
\(410\) 0 0
\(411\) −3.14874 −0.155316
\(412\) 0 0
\(413\) −8.21164 −0.404069
\(414\) 0 0
\(415\) 35.8970 1.76211
\(416\) 0 0
\(417\) 1.97321 0.0966283
\(418\) 0 0
\(419\) −26.3010 −1.28489 −0.642443 0.766333i \(-0.722079\pi\)
−0.642443 + 0.766333i \(0.722079\pi\)
\(420\) 0 0
\(421\) 1.33347 0.0649892 0.0324946 0.999472i \(-0.489655\pi\)
0.0324946 + 0.999472i \(0.489655\pi\)
\(422\) 0 0
\(423\) 9.49246 0.461539
\(424\) 0 0
\(425\) 17.2796 0.838184
\(426\) 0 0
\(427\) −13.8367 −0.669603
\(428\) 0 0
\(429\) −0.357256 −0.0172485
\(430\) 0 0
\(431\) 37.8787 1.82455 0.912277 0.409574i \(-0.134323\pi\)
0.912277 + 0.409574i \(0.134323\pi\)
\(432\) 0 0
\(433\) 8.39699 0.403534 0.201767 0.979434i \(-0.435332\pi\)
0.201767 + 0.979434i \(0.435332\pi\)
\(434\) 0 0
\(435\) −2.45122 −0.117527
\(436\) 0 0
\(437\) 4.26620 0.204080
\(438\) 0 0
\(439\) 15.1229 0.721777 0.360889 0.932609i \(-0.382473\pi\)
0.360889 + 0.932609i \(0.382473\pi\)
\(440\) 0 0
\(441\) −2.87237 −0.136779
\(442\) 0 0
\(443\) −35.0430 −1.66494 −0.832471 0.554068i \(-0.813075\pi\)
−0.832471 + 0.554068i \(0.813075\pi\)
\(444\) 0 0
\(445\) 30.6457 1.45275
\(446\) 0 0
\(447\) 8.13537 0.384790
\(448\) 0 0
\(449\) −3.97901 −0.187781 −0.0938906 0.995583i \(-0.529930\pi\)
−0.0938906 + 0.995583i \(0.529930\pi\)
\(450\) 0 0
\(451\) −6.95677 −0.327581
\(452\) 0 0
\(453\) −3.96940 −0.186499
\(454\) 0 0
\(455\) 3.31742 0.155523
\(456\) 0 0
\(457\) −21.8963 −1.02426 −0.512132 0.858907i \(-0.671144\pi\)
−0.512132 + 0.858907i \(0.671144\pi\)
\(458\) 0 0
\(459\) 6.03662 0.281765
\(460\) 0 0
\(461\) −21.6825 −1.00985 −0.504926 0.863162i \(-0.668480\pi\)
−0.504926 + 0.863162i \(0.668480\pi\)
\(462\) 0 0
\(463\) −23.4072 −1.08782 −0.543912 0.839142i \(-0.683058\pi\)
−0.543912 + 0.839142i \(0.683058\pi\)
\(464\) 0 0
\(465\) −9.65131 −0.447569
\(466\) 0 0
\(467\) −2.99684 −0.138677 −0.0693385 0.997593i \(-0.522089\pi\)
−0.0693385 + 0.997593i \(0.522089\pi\)
\(468\) 0 0
\(469\) −10.8104 −0.499177
\(470\) 0 0
\(471\) 6.39863 0.294833
\(472\) 0 0
\(473\) 5.10805 0.234868
\(474\) 0 0
\(475\) −2.88584 −0.132411
\(476\) 0 0
\(477\) 19.0957 0.874330
\(478\) 0 0
\(479\) 38.2005 1.74542 0.872712 0.488235i \(-0.162359\pi\)
0.872712 + 0.488235i \(0.162359\pi\)
\(480\) 0 0
\(481\) −9.94343 −0.453382
\(482\) 0 0
\(483\) −3.17163 −0.144314
\(484\) 0 0
\(485\) −49.1774 −2.23303
\(486\) 0 0
\(487\) 8.58420 0.388987 0.194494 0.980904i \(-0.437694\pi\)
0.194494 + 0.980904i \(0.437694\pi\)
\(488\) 0 0
\(489\) 1.38894 0.0628101
\(490\) 0 0
\(491\) −13.6705 −0.616941 −0.308470 0.951234i \(-0.599817\pi\)
−0.308470 + 0.951234i \(0.599817\pi\)
\(492\) 0 0
\(493\) 5.95118 0.268028
\(494\) 0 0
\(495\) 9.52885 0.428290
\(496\) 0 0
\(497\) −8.48947 −0.380805
\(498\) 0 0
\(499\) 2.10973 0.0944443 0.0472222 0.998884i \(-0.484963\pi\)
0.0472222 + 0.998884i \(0.484963\pi\)
\(500\) 0 0
\(501\) −3.26191 −0.145731
\(502\) 0 0
\(503\) −1.80469 −0.0804671 −0.0402336 0.999190i \(-0.512810\pi\)
−0.0402336 + 0.999190i \(0.512810\pi\)
\(504\) 0 0
\(505\) 22.6073 1.00601
\(506\) 0 0
\(507\) −0.357256 −0.0158663
\(508\) 0 0
\(509\) 3.18204 0.141042 0.0705208 0.997510i \(-0.477534\pi\)
0.0705208 + 0.997510i \(0.477534\pi\)
\(510\) 0 0
\(511\) −15.9546 −0.705792
\(512\) 0 0
\(513\) −1.00816 −0.0445116
\(514\) 0 0
\(515\) 18.4752 0.814115
\(516\) 0 0
\(517\) 3.30475 0.145343
\(518\) 0 0
\(519\) −7.92838 −0.348017
\(520\) 0 0
\(521\) −13.1784 −0.577355 −0.288677 0.957426i \(-0.593215\pi\)
−0.288677 + 0.957426i \(0.593215\pi\)
\(522\) 0 0
\(523\) 11.9880 0.524199 0.262099 0.965041i \(-0.415585\pi\)
0.262099 + 0.965041i \(0.415585\pi\)
\(524\) 0 0
\(525\) 2.14543 0.0936341
\(526\) 0 0
\(527\) 23.4318 1.02071
\(528\) 0 0
\(529\) 55.8143 2.42671
\(530\) 0 0
\(531\) −23.5869 −1.02358
\(532\) 0 0
\(533\) −6.95677 −0.301331
\(534\) 0 0
\(535\) −40.3379 −1.74396
\(536\) 0 0
\(537\) 2.75355 0.118824
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −38.0987 −1.63799 −0.818995 0.573800i \(-0.805469\pi\)
−0.818995 + 0.573800i \(0.805469\pi\)
\(542\) 0 0
\(543\) −3.00082 −0.128777
\(544\) 0 0
\(545\) −24.6351 −1.05525
\(546\) 0 0
\(547\) 33.8679 1.44809 0.724044 0.689754i \(-0.242281\pi\)
0.724044 + 0.689754i \(0.242281\pi\)
\(548\) 0 0
\(549\) −39.7440 −1.69623
\(550\) 0 0
\(551\) −0.993895 −0.0423414
\(552\) 0 0
\(553\) 1.62192 0.0689712
\(554\) 0 0
\(555\) −11.7847 −0.500231
\(556\) 0 0
\(557\) 20.1538 0.853943 0.426972 0.904265i \(-0.359580\pi\)
0.426972 + 0.904265i \(0.359580\pi\)
\(558\) 0 0
\(559\) 5.10805 0.216047
\(560\) 0 0
\(561\) 1.02797 0.0434009
\(562\) 0 0
\(563\) 10.0802 0.424828 0.212414 0.977180i \(-0.431867\pi\)
0.212414 + 0.977180i \(0.431867\pi\)
\(564\) 0 0
\(565\) −39.6222 −1.66692
\(566\) 0 0
\(567\) −7.86760 −0.330408
\(568\) 0 0
\(569\) −14.3423 −0.601259 −0.300630 0.953741i \(-0.597197\pi\)
−0.300630 + 0.953741i \(0.597197\pi\)
\(570\) 0 0
\(571\) 28.3207 1.18518 0.592592 0.805502i \(-0.298104\pi\)
0.592592 + 0.805502i \(0.298104\pi\)
\(572\) 0 0
\(573\) 4.60166 0.192237
\(574\) 0 0
\(575\) −53.3133 −2.22332
\(576\) 0 0
\(577\) 7.62104 0.317268 0.158634 0.987337i \(-0.449291\pi\)
0.158634 + 0.987337i \(0.449291\pi\)
\(578\) 0 0
\(579\) 3.53026 0.146713
\(580\) 0 0
\(581\) −10.8207 −0.448920
\(582\) 0 0
\(583\) 6.64805 0.275334
\(584\) 0 0
\(585\) 9.52885 0.393970
\(586\) 0 0
\(587\) −27.5017 −1.13511 −0.567557 0.823334i \(-0.692111\pi\)
−0.567557 + 0.823334i \(0.692111\pi\)
\(588\) 0 0
\(589\) −3.91331 −0.161245
\(590\) 0 0
\(591\) 2.42414 0.0997157
\(592\) 0 0
\(593\) 34.7880 1.42857 0.714285 0.699855i \(-0.246752\pi\)
0.714285 + 0.699855i \(0.246752\pi\)
\(594\) 0 0
\(595\) −9.54555 −0.391330
\(596\) 0 0
\(597\) 8.01069 0.327856
\(598\) 0 0
\(599\) −35.6803 −1.45786 −0.728929 0.684590i \(-0.759981\pi\)
−0.728929 + 0.684590i \(0.759981\pi\)
\(600\) 0 0
\(601\) −32.2088 −1.31383 −0.656913 0.753966i \(-0.728138\pi\)
−0.656913 + 0.753966i \(0.728138\pi\)
\(602\) 0 0
\(603\) −31.0514 −1.26451
\(604\) 0 0
\(605\) 3.31742 0.134872
\(606\) 0 0
\(607\) −22.3174 −0.905836 −0.452918 0.891552i \(-0.649617\pi\)
−0.452918 + 0.891552i \(0.649617\pi\)
\(608\) 0 0
\(609\) 0.738894 0.0299415
\(610\) 0 0
\(611\) 3.30475 0.133696
\(612\) 0 0
\(613\) −12.6487 −0.510875 −0.255437 0.966826i \(-0.582219\pi\)
−0.255437 + 0.966826i \(0.582219\pi\)
\(614\) 0 0
\(615\) −8.24495 −0.332468
\(616\) 0 0
\(617\) 18.7287 0.753989 0.376994 0.926216i \(-0.376958\pi\)
0.376994 + 0.926216i \(0.376958\pi\)
\(618\) 0 0
\(619\) 19.6059 0.788028 0.394014 0.919104i \(-0.371086\pi\)
0.394014 + 0.919104i \(0.371086\pi\)
\(620\) 0 0
\(621\) −18.6250 −0.747395
\(622\) 0 0
\(623\) −9.23781 −0.370105
\(624\) 0 0
\(625\) −18.9630 −0.758520
\(626\) 0 0
\(627\) −0.171679 −0.00685622
\(628\) 0 0
\(629\) 28.6113 1.14081
\(630\) 0 0
\(631\) −34.6374 −1.37889 −0.689446 0.724337i \(-0.742146\pi\)
−0.689446 + 0.724337i \(0.742146\pi\)
\(632\) 0 0
\(633\) −0.259503 −0.0103143
\(634\) 0 0
\(635\) −13.9231 −0.552522
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −24.3849 −0.964651
\(640\) 0 0
\(641\) −36.6600 −1.44798 −0.723991 0.689809i \(-0.757694\pi\)
−0.723991 + 0.689809i \(0.757694\pi\)
\(642\) 0 0
\(643\) 24.3192 0.959056 0.479528 0.877526i \(-0.340808\pi\)
0.479528 + 0.877526i \(0.340808\pi\)
\(644\) 0 0
\(645\) 6.05391 0.238372
\(646\) 0 0
\(647\) 2.91761 0.114703 0.0573515 0.998354i \(-0.481734\pi\)
0.0573515 + 0.998354i \(0.481734\pi\)
\(648\) 0 0
\(649\) −8.21164 −0.322335
\(650\) 0 0
\(651\) 2.90928 0.114024
\(652\) 0 0
\(653\) 7.76774 0.303975 0.151988 0.988382i \(-0.451433\pi\)
0.151988 + 0.988382i \(0.451433\pi\)
\(654\) 0 0
\(655\) 60.7432 2.37343
\(656\) 0 0
\(657\) −45.8276 −1.78790
\(658\) 0 0
\(659\) 18.9750 0.739161 0.369581 0.929199i \(-0.379501\pi\)
0.369581 + 0.929199i \(0.379501\pi\)
\(660\) 0 0
\(661\) 6.42026 0.249719 0.124860 0.992174i \(-0.460152\pi\)
0.124860 + 0.992174i \(0.460152\pi\)
\(662\) 0 0
\(663\) 1.02797 0.0399231
\(664\) 0 0
\(665\) 1.59419 0.0618199
\(666\) 0 0
\(667\) −18.3614 −0.710955
\(668\) 0 0
\(669\) −6.04393 −0.233672
\(670\) 0 0
\(671\) −13.8367 −0.534158
\(672\) 0 0
\(673\) 35.6734 1.37511 0.687554 0.726133i \(-0.258684\pi\)
0.687554 + 0.726133i \(0.258684\pi\)
\(674\) 0 0
\(675\) 12.5987 0.484925
\(676\) 0 0
\(677\) −6.68403 −0.256888 −0.128444 0.991717i \(-0.540998\pi\)
−0.128444 + 0.991717i \(0.540998\pi\)
\(678\) 0 0
\(679\) 14.8240 0.568892
\(680\) 0 0
\(681\) 1.22655 0.0470014
\(682\) 0 0
\(683\) −39.3534 −1.50581 −0.752907 0.658127i \(-0.771349\pi\)
−0.752907 + 0.658127i \(0.771349\pi\)
\(684\) 0 0
\(685\) 29.2387 1.11715
\(686\) 0 0
\(687\) −7.76830 −0.296379
\(688\) 0 0
\(689\) 6.64805 0.253271
\(690\) 0 0
\(691\) −28.0281 −1.06624 −0.533119 0.846040i \(-0.678980\pi\)
−0.533119 + 0.846040i \(0.678980\pi\)
\(692\) 0 0
\(693\) −2.87237 −0.109112
\(694\) 0 0
\(695\) −18.3228 −0.695025
\(696\) 0 0
\(697\) 20.0174 0.758214
\(698\) 0 0
\(699\) −7.42995 −0.281026
\(700\) 0 0
\(701\) 31.9693 1.20746 0.603732 0.797187i \(-0.293680\pi\)
0.603732 + 0.797187i \(0.293680\pi\)
\(702\) 0 0
\(703\) −4.77831 −0.180217
\(704\) 0 0
\(705\) 3.91669 0.147511
\(706\) 0 0
\(707\) −6.81473 −0.256294
\(708\) 0 0
\(709\) 14.2914 0.536726 0.268363 0.963318i \(-0.413517\pi\)
0.268363 + 0.963318i \(0.413517\pi\)
\(710\) 0 0
\(711\) 4.65876 0.174717
\(712\) 0 0
\(713\) −72.2950 −2.70747
\(714\) 0 0
\(715\) 3.31742 0.124065
\(716\) 0 0
\(717\) 5.56994 0.208013
\(718\) 0 0
\(719\) 25.5202 0.951744 0.475872 0.879515i \(-0.342133\pi\)
0.475872 + 0.879515i \(0.342133\pi\)
\(720\) 0 0
\(721\) −5.56915 −0.207406
\(722\) 0 0
\(723\) 4.73287 0.176017
\(724\) 0 0
\(725\) 12.4204 0.461282
\(726\) 0 0
\(727\) 27.6213 1.02442 0.512208 0.858862i \(-0.328828\pi\)
0.512208 + 0.858862i \(0.328828\pi\)
\(728\) 0 0
\(729\) −20.3501 −0.753709
\(730\) 0 0
\(731\) −14.6979 −0.543622
\(732\) 0 0
\(733\) 2.95299 0.109071 0.0545356 0.998512i \(-0.482632\pi\)
0.0545356 + 0.998512i \(0.482632\pi\)
\(734\) 0 0
\(735\) −1.18517 −0.0437157
\(736\) 0 0
\(737\) −10.8104 −0.398205
\(738\) 0 0
\(739\) 14.7567 0.542835 0.271417 0.962462i \(-0.412508\pi\)
0.271417 + 0.962462i \(0.412508\pi\)
\(740\) 0 0
\(741\) −0.171679 −0.00630680
\(742\) 0 0
\(743\) −46.2320 −1.69609 −0.848044 0.529926i \(-0.822220\pi\)
−0.848044 + 0.529926i \(0.822220\pi\)
\(744\) 0 0
\(745\) −75.5437 −2.76771
\(746\) 0 0
\(747\) −31.0812 −1.13720
\(748\) 0 0
\(749\) 12.1594 0.444295
\(750\) 0 0
\(751\) 8.10505 0.295757 0.147879 0.989006i \(-0.452755\pi\)
0.147879 + 0.989006i \(0.452755\pi\)
\(752\) 0 0
\(753\) 8.57624 0.312536
\(754\) 0 0
\(755\) 36.8592 1.34144
\(756\) 0 0
\(757\) −2.55960 −0.0930303 −0.0465151 0.998918i \(-0.514812\pi\)
−0.0465151 + 0.998918i \(0.514812\pi\)
\(758\) 0 0
\(759\) −3.17163 −0.115123
\(760\) 0 0
\(761\) 3.44077 0.124728 0.0623639 0.998053i \(-0.480136\pi\)
0.0623639 + 0.998053i \(0.480136\pi\)
\(762\) 0 0
\(763\) 7.42599 0.268839
\(764\) 0 0
\(765\) −27.4183 −0.991312
\(766\) 0 0
\(767\) −8.21164 −0.296505
\(768\) 0 0
\(769\) −33.0363 −1.19132 −0.595659 0.803238i \(-0.703109\pi\)
−0.595659 + 0.803238i \(0.703109\pi\)
\(770\) 0 0
\(771\) −8.35172 −0.300780
\(772\) 0 0
\(773\) −41.4235 −1.48990 −0.744949 0.667121i \(-0.767526\pi\)
−0.744949 + 0.667121i \(0.767526\pi\)
\(774\) 0 0
\(775\) 48.9034 1.75666
\(776\) 0 0
\(777\) 3.55236 0.127440
\(778\) 0 0
\(779\) −3.34307 −0.119778
\(780\) 0 0
\(781\) −8.48947 −0.303777
\(782\) 0 0
\(783\) 4.33906 0.155065
\(784\) 0 0
\(785\) −59.4165 −2.12067
\(786\) 0 0
\(787\) 39.0531 1.39209 0.696047 0.717997i \(-0.254941\pi\)
0.696047 + 0.717997i \(0.254941\pi\)
\(788\) 0 0
\(789\) 3.16931 0.112830
\(790\) 0 0
\(791\) 11.9437 0.424668
\(792\) 0 0
\(793\) −13.8367 −0.491354
\(794\) 0 0
\(795\) 7.87907 0.279442
\(796\) 0 0
\(797\) −44.3846 −1.57218 −0.786091 0.618111i \(-0.787898\pi\)
−0.786091 + 0.618111i \(0.787898\pi\)
\(798\) 0 0
\(799\) −9.50910 −0.336408
\(800\) 0 0
\(801\) −26.5344 −0.937547
\(802\) 0 0
\(803\) −15.9546 −0.563027
\(804\) 0 0
\(805\) 29.4512 1.03802
\(806\) 0 0
\(807\) 1.28494 0.0452319
\(808\) 0 0
\(809\) −42.4134 −1.49117 −0.745587 0.666408i \(-0.767831\pi\)
−0.745587 + 0.666408i \(0.767831\pi\)
\(810\) 0 0
\(811\) 21.4979 0.754893 0.377446 0.926031i \(-0.376802\pi\)
0.377446 + 0.926031i \(0.376802\pi\)
\(812\) 0 0
\(813\) −9.02577 −0.316548
\(814\) 0 0
\(815\) −12.8975 −0.451779
\(816\) 0 0
\(817\) 2.45467 0.0858781
\(818\) 0 0
\(819\) −2.87237 −0.100369
\(820\) 0 0
\(821\) −20.9958 −0.732759 −0.366380 0.930465i \(-0.619403\pi\)
−0.366380 + 0.930465i \(0.619403\pi\)
\(822\) 0 0
\(823\) 38.0899 1.32773 0.663866 0.747852i \(-0.268915\pi\)
0.663866 + 0.747852i \(0.268915\pi\)
\(824\) 0 0
\(825\) 2.14543 0.0746941
\(826\) 0 0
\(827\) 2.36403 0.0822055 0.0411027 0.999155i \(-0.486913\pi\)
0.0411027 + 0.999155i \(0.486913\pi\)
\(828\) 0 0
\(829\) −40.0774 −1.39195 −0.695973 0.718068i \(-0.745027\pi\)
−0.695973 + 0.718068i \(0.745027\pi\)
\(830\) 0 0
\(831\) 6.99016 0.242486
\(832\) 0 0
\(833\) 2.87740 0.0996961
\(834\) 0 0
\(835\) 30.2895 1.04821
\(836\) 0 0
\(837\) 17.0844 0.590522
\(838\) 0 0
\(839\) 27.4305 0.947008 0.473504 0.880792i \(-0.342989\pi\)
0.473504 + 0.880792i \(0.342989\pi\)
\(840\) 0 0
\(841\) −24.7224 −0.852495
\(842\) 0 0
\(843\) −6.81190 −0.234614
\(844\) 0 0
\(845\) 3.31742 0.114123
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 3.89015 0.133510
\(850\) 0 0
\(851\) −88.2752 −3.02604
\(852\) 0 0
\(853\) −32.7588 −1.12164 −0.560820 0.827937i \(-0.689514\pi\)
−0.560820 + 0.827937i \(0.689514\pi\)
\(854\) 0 0
\(855\) 4.57909 0.156601
\(856\) 0 0
\(857\) −14.4748 −0.494451 −0.247225 0.968958i \(-0.579519\pi\)
−0.247225 + 0.968958i \(0.579519\pi\)
\(858\) 0 0
\(859\) −34.9700 −1.19316 −0.596580 0.802554i \(-0.703474\pi\)
−0.596580 + 0.802554i \(0.703474\pi\)
\(860\) 0 0
\(861\) 2.48535 0.0847005
\(862\) 0 0
\(863\) 3.62392 0.123360 0.0616798 0.998096i \(-0.480354\pi\)
0.0616798 + 0.998096i \(0.480354\pi\)
\(864\) 0 0
\(865\) 73.6216 2.50321
\(866\) 0 0
\(867\) 3.11547 0.105807
\(868\) 0 0
\(869\) 1.62192 0.0550200
\(870\) 0 0
\(871\) −10.8104 −0.366296
\(872\) 0 0
\(873\) 42.5799 1.44111
\(874\) 0 0
\(875\) −3.33495 −0.112742
\(876\) 0 0
\(877\) 39.0327 1.31804 0.659020 0.752125i \(-0.270971\pi\)
0.659020 + 0.752125i \(0.270971\pi\)
\(878\) 0 0
\(879\) −7.36558 −0.248435
\(880\) 0 0
\(881\) −42.9275 −1.44627 −0.723133 0.690709i \(-0.757299\pi\)
−0.723133 + 0.690709i \(0.757299\pi\)
\(882\) 0 0
\(883\) −49.6472 −1.67076 −0.835380 0.549673i \(-0.814752\pi\)
−0.835380 + 0.549673i \(0.814752\pi\)
\(884\) 0 0
\(885\) −9.73219 −0.327144
\(886\) 0 0
\(887\) −8.28643 −0.278231 −0.139116 0.990276i \(-0.544426\pi\)
−0.139116 + 0.990276i \(0.544426\pi\)
\(888\) 0 0
\(889\) 4.19697 0.140762
\(890\) 0 0
\(891\) −7.86760 −0.263575
\(892\) 0 0
\(893\) 1.58810 0.0531436
\(894\) 0 0
\(895\) −25.5690 −0.854677
\(896\) 0 0
\(897\) −3.17163 −0.105898
\(898\) 0 0
\(899\) 16.8426 0.561731
\(900\) 0 0
\(901\) −19.1291 −0.637283
\(902\) 0 0
\(903\) −1.82488 −0.0607283
\(904\) 0 0
\(905\) 27.8651 0.926266
\(906\) 0 0
\(907\) −23.4630 −0.779076 −0.389538 0.921010i \(-0.627365\pi\)
−0.389538 + 0.921010i \(0.627365\pi\)
\(908\) 0 0
\(909\) −19.5744 −0.649242
\(910\) 0 0
\(911\) 11.8253 0.391790 0.195895 0.980625i \(-0.437239\pi\)
0.195895 + 0.980625i \(0.437239\pi\)
\(912\) 0 0
\(913\) −10.8207 −0.358114
\(914\) 0 0
\(915\) −16.3988 −0.542127
\(916\) 0 0
\(917\) −18.3104 −0.604662
\(918\) 0 0
\(919\) 0.351322 0.0115890 0.00579452 0.999983i \(-0.498156\pi\)
0.00579452 + 0.999983i \(0.498156\pi\)
\(920\) 0 0
\(921\) −0.701712 −0.0231222
\(922\) 0 0
\(923\) −8.48947 −0.279434
\(924\) 0 0
\(925\) 59.7131 1.96336
\(926\) 0 0
\(927\) −15.9967 −0.525399
\(928\) 0 0
\(929\) −47.8775 −1.57081 −0.785404 0.618983i \(-0.787545\pi\)
−0.785404 + 0.618983i \(0.787545\pi\)
\(930\) 0 0
\(931\) −0.480550 −0.0157494
\(932\) 0 0
\(933\) 2.78009 0.0910160
\(934\) 0 0
\(935\) −9.54555 −0.312173
\(936\) 0 0
\(937\) −29.7007 −0.970281 −0.485141 0.874436i \(-0.661232\pi\)
−0.485141 + 0.874436i \(0.661232\pi\)
\(938\) 0 0
\(939\) −7.23836 −0.236215
\(940\) 0 0
\(941\) 54.8926 1.78945 0.894724 0.446619i \(-0.147372\pi\)
0.894724 + 0.446619i \(0.147372\pi\)
\(942\) 0 0
\(943\) −61.7604 −2.01119
\(944\) 0 0
\(945\) −6.95975 −0.226401
\(946\) 0 0
\(947\) 0.691988 0.0224866 0.0112433 0.999937i \(-0.496421\pi\)
0.0112433 + 0.999937i \(0.496421\pi\)
\(948\) 0 0
\(949\) −15.9546 −0.517910
\(950\) 0 0
\(951\) −8.80462 −0.285510
\(952\) 0 0
\(953\) −11.3735 −0.368425 −0.184212 0.982886i \(-0.558973\pi\)
−0.184212 + 0.982886i \(0.558973\pi\)
\(954\) 0 0
\(955\) −42.7302 −1.38272
\(956\) 0 0
\(957\) 0.738894 0.0238851
\(958\) 0 0
\(959\) −8.81368 −0.284609
\(960\) 0 0
\(961\) 35.3149 1.13919
\(962\) 0 0
\(963\) 34.9263 1.12548
\(964\) 0 0
\(965\) −32.7814 −1.05527
\(966\) 0 0
\(967\) 4.60866 0.148205 0.0741023 0.997251i \(-0.476391\pi\)
0.0741023 + 0.997251i \(0.476391\pi\)
\(968\) 0 0
\(969\) 0.493991 0.0158693
\(970\) 0 0
\(971\) 11.8954 0.381740 0.190870 0.981615i \(-0.438869\pi\)
0.190870 + 0.981615i \(0.438869\pi\)
\(972\) 0 0
\(973\) 5.52322 0.177066
\(974\) 0 0
\(975\) 2.14543 0.0687086
\(976\) 0 0
\(977\) 7.89304 0.252521 0.126260 0.991997i \(-0.459703\pi\)
0.126260 + 0.991997i \(0.459703\pi\)
\(978\) 0 0
\(979\) −9.23781 −0.295242
\(980\) 0 0
\(981\) 21.3302 0.681020
\(982\) 0 0
\(983\) −29.6468 −0.945585 −0.472792 0.881174i \(-0.656754\pi\)
−0.472792 + 0.881174i \(0.656754\pi\)
\(984\) 0 0
\(985\) −22.5101 −0.717232
\(986\) 0 0
\(987\) −1.18064 −0.0375803
\(988\) 0 0
\(989\) 45.3479 1.44198
\(990\) 0 0
\(991\) 56.9475 1.80900 0.904498 0.426477i \(-0.140246\pi\)
0.904498 + 0.426477i \(0.140246\pi\)
\(992\) 0 0
\(993\) −9.20075 −0.291977
\(994\) 0 0
\(995\) −74.3859 −2.35819
\(996\) 0 0
\(997\) 31.2545 0.989839 0.494920 0.868939i \(-0.335198\pi\)
0.494920 + 0.868939i \(0.335198\pi\)
\(998\) 0 0
\(999\) 20.8607 0.660004
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 \(a_p\))