Properties

Label 8036.2.a.q.1.3
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.29181\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.29181 q^{3} -3.92303 q^{5} +2.25239 q^{9} +O(q^{10})\) \(q-2.29181 q^{3} -3.92303 q^{5} +2.25239 q^{9} +3.51299 q^{11} -3.61465 q^{13} +8.99083 q^{15} -6.69217 q^{17} +0.207273 q^{19} -2.79062 q^{23} +10.3902 q^{25} +1.71338 q^{27} -2.98592 q^{29} +4.29712 q^{31} -8.05111 q^{33} -10.2843 q^{37} +8.28409 q^{39} -1.00000 q^{41} +9.05260 q^{43} -8.83619 q^{45} -10.5241 q^{47} +15.3372 q^{51} -12.7027 q^{53} -13.7816 q^{55} -0.475030 q^{57} +8.12129 q^{59} +3.81249 q^{61} +14.1804 q^{65} -4.59244 q^{67} +6.39557 q^{69} -5.96512 q^{71} -14.0691 q^{73} -23.8122 q^{75} -12.3409 q^{79} -10.6839 q^{81} -5.55113 q^{83} +26.2536 q^{85} +6.84316 q^{87} +2.33061 q^{89} -9.84818 q^{93} -0.813137 q^{95} -8.84605 q^{97} +7.91263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −2.29181 −1.32318 −0.661588 0.749867i \(-0.730117\pi\)
−0.661588 + 0.749867i \(0.730117\pi\)
\(4\) 0 0
\(5\) −3.92303 −1.75443 −0.877216 0.480096i \(-0.840602\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.25239 0.750797
\(10\) 0 0
\(11\) 3.51299 1.05921 0.529604 0.848245i \(-0.322341\pi\)
0.529604 + 0.848245i \(0.322341\pi\)
\(12\) 0 0
\(13\) −3.61465 −1.00252 −0.501262 0.865296i \(-0.667131\pi\)
−0.501262 + 0.865296i \(0.667131\pi\)
\(14\) 0 0
\(15\) 8.99083 2.32142
\(16\) 0 0
\(17\) −6.69217 −1.62309 −0.811545 0.584290i \(-0.801373\pi\)
−0.811545 + 0.584290i \(0.801373\pi\)
\(18\) 0 0
\(19\) 0.207273 0.0475517 0.0237758 0.999717i \(-0.492431\pi\)
0.0237758 + 0.999717i \(0.492431\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.79062 −0.581884 −0.290942 0.956741i \(-0.593969\pi\)
−0.290942 + 0.956741i \(0.593969\pi\)
\(24\) 0 0
\(25\) 10.3902 2.07803
\(26\) 0 0
\(27\) 1.71338 0.329740
\(28\) 0 0
\(29\) −2.98592 −0.554472 −0.277236 0.960802i \(-0.589418\pi\)
−0.277236 + 0.960802i \(0.589418\pi\)
\(30\) 0 0
\(31\) 4.29712 0.771786 0.385893 0.922544i \(-0.373893\pi\)
0.385893 + 0.922544i \(0.373893\pi\)
\(32\) 0 0
\(33\) −8.05111 −1.40152
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.2843 −1.69073 −0.845367 0.534186i \(-0.820618\pi\)
−0.845367 + 0.534186i \(0.820618\pi\)
\(38\) 0 0
\(39\) 8.28409 1.32652
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 9.05260 1.38051 0.690254 0.723567i \(-0.257499\pi\)
0.690254 + 0.723567i \(0.257499\pi\)
\(44\) 0 0
\(45\) −8.83619 −1.31722
\(46\) 0 0
\(47\) −10.5241 −1.53510 −0.767552 0.640987i \(-0.778525\pi\)
−0.767552 + 0.640987i \(0.778525\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 15.3372 2.14764
\(52\) 0 0
\(53\) −12.7027 −1.74485 −0.872423 0.488751i \(-0.837453\pi\)
−0.872423 + 0.488751i \(0.837453\pi\)
\(54\) 0 0
\(55\) −13.7816 −1.85831
\(56\) 0 0
\(57\) −0.475030 −0.0629192
\(58\) 0 0
\(59\) 8.12129 1.05730 0.528651 0.848839i \(-0.322698\pi\)
0.528651 + 0.848839i \(0.322698\pi\)
\(60\) 0 0
\(61\) 3.81249 0.488139 0.244069 0.969758i \(-0.421518\pi\)
0.244069 + 0.969758i \(0.421518\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14.1804 1.75886
\(66\) 0 0
\(67\) −4.59244 −0.561056 −0.280528 0.959846i \(-0.590510\pi\)
−0.280528 + 0.959846i \(0.590510\pi\)
\(68\) 0 0
\(69\) 6.39557 0.769936
\(70\) 0 0
\(71\) −5.96512 −0.707930 −0.353965 0.935259i \(-0.615167\pi\)
−0.353965 + 0.935259i \(0.615167\pi\)
\(72\) 0 0
\(73\) −14.0691 −1.64667 −0.823334 0.567557i \(-0.807889\pi\)
−0.823334 + 0.567557i \(0.807889\pi\)
\(74\) 0 0
\(75\) −23.8122 −2.74960
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.3409 −1.38846 −0.694232 0.719751i \(-0.744256\pi\)
−0.694232 + 0.719751i \(0.744256\pi\)
\(80\) 0 0
\(81\) −10.6839 −1.18710
\(82\) 0 0
\(83\) −5.55113 −0.609316 −0.304658 0.952462i \(-0.598542\pi\)
−0.304658 + 0.952462i \(0.598542\pi\)
\(84\) 0 0
\(85\) 26.2536 2.84760
\(86\) 0 0
\(87\) 6.84316 0.733664
\(88\) 0 0
\(89\) 2.33061 0.247044 0.123522 0.992342i \(-0.460581\pi\)
0.123522 + 0.992342i \(0.460581\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −9.84818 −1.02121
\(94\) 0 0
\(95\) −0.813137 −0.0834261
\(96\) 0 0
\(97\) −8.84605 −0.898180 −0.449090 0.893487i \(-0.648252\pi\)
−0.449090 + 0.893487i \(0.648252\pi\)
\(98\) 0 0
\(99\) 7.91263 0.795250
\(100\) 0 0
\(101\) −14.2551 −1.41844 −0.709218 0.704989i \(-0.750952\pi\)
−0.709218 + 0.704989i \(0.750952\pi\)
\(102\) 0 0
\(103\) 7.17800 0.707269 0.353635 0.935384i \(-0.384946\pi\)
0.353635 + 0.935384i \(0.384946\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.89601 0.279968 0.139984 0.990154i \(-0.455295\pi\)
0.139984 + 0.990154i \(0.455295\pi\)
\(108\) 0 0
\(109\) −8.89008 −0.851516 −0.425758 0.904837i \(-0.639992\pi\)
−0.425758 + 0.904837i \(0.639992\pi\)
\(110\) 0 0
\(111\) 23.5697 2.23714
\(112\) 0 0
\(113\) −7.70003 −0.724358 −0.362179 0.932109i \(-0.617967\pi\)
−0.362179 + 0.932109i \(0.617967\pi\)
\(114\) 0 0
\(115\) 10.9477 1.02088
\(116\) 0 0
\(117\) −8.14160 −0.752691
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.34112 0.121920
\(122\) 0 0
\(123\) 2.29181 0.206645
\(124\) 0 0
\(125\) −21.1457 −1.89133
\(126\) 0 0
\(127\) −12.7037 −1.12727 −0.563634 0.826024i \(-0.690597\pi\)
−0.563634 + 0.826024i \(0.690597\pi\)
\(128\) 0 0
\(129\) −20.7468 −1.82666
\(130\) 0 0
\(131\) 8.65299 0.756016 0.378008 0.925802i \(-0.376609\pi\)
0.378008 + 0.925802i \(0.376609\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −6.72163 −0.578506
\(136\) 0 0
\(137\) −9.33286 −0.797360 −0.398680 0.917090i \(-0.630532\pi\)
−0.398680 + 0.917090i \(0.630532\pi\)
\(138\) 0 0
\(139\) 16.9955 1.44154 0.720768 0.693176i \(-0.243789\pi\)
0.720768 + 0.693176i \(0.243789\pi\)
\(140\) 0 0
\(141\) 24.1193 2.03121
\(142\) 0 0
\(143\) −12.6982 −1.06188
\(144\) 0 0
\(145\) 11.7139 0.972783
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.42691 −0.526513 −0.263257 0.964726i \(-0.584797\pi\)
−0.263257 + 0.964726i \(0.584797\pi\)
\(150\) 0 0
\(151\) −17.6654 −1.43759 −0.718795 0.695223i \(-0.755306\pi\)
−0.718795 + 0.695223i \(0.755306\pi\)
\(152\) 0 0
\(153\) −15.0734 −1.21861
\(154\) 0 0
\(155\) −16.8577 −1.35405
\(156\) 0 0
\(157\) −10.2986 −0.821922 −0.410961 0.911653i \(-0.634807\pi\)
−0.410961 + 0.911653i \(0.634807\pi\)
\(158\) 0 0
\(159\) 29.1121 2.30874
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 16.7557 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(164\) 0 0
\(165\) 31.5847 2.45887
\(166\) 0 0
\(167\) 5.13882 0.397654 0.198827 0.980035i \(-0.436287\pi\)
0.198827 + 0.980035i \(0.436287\pi\)
\(168\) 0 0
\(169\) 0.0656916 0.00505320
\(170\) 0 0
\(171\) 0.466859 0.0357016
\(172\) 0 0
\(173\) −9.42638 −0.716675 −0.358337 0.933592i \(-0.616656\pi\)
−0.358337 + 0.933592i \(0.616656\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.6125 −1.39900
\(178\) 0 0
\(179\) 11.7752 0.880118 0.440059 0.897969i \(-0.354957\pi\)
0.440059 + 0.897969i \(0.354957\pi\)
\(180\) 0 0
\(181\) 1.02450 0.0761506 0.0380753 0.999275i \(-0.487877\pi\)
0.0380753 + 0.999275i \(0.487877\pi\)
\(182\) 0 0
\(183\) −8.73749 −0.645894
\(184\) 0 0
\(185\) 40.3457 2.96628
\(186\) 0 0
\(187\) −23.5096 −1.71919
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.4394 −0.755368 −0.377684 0.925934i \(-0.623279\pi\)
−0.377684 + 0.925934i \(0.623279\pi\)
\(192\) 0 0
\(193\) 6.51882 0.469235 0.234617 0.972088i \(-0.424616\pi\)
0.234617 + 0.972088i \(0.424616\pi\)
\(194\) 0 0
\(195\) −32.4987 −2.32728
\(196\) 0 0
\(197\) −9.53401 −0.679270 −0.339635 0.940557i \(-0.610304\pi\)
−0.339635 + 0.940557i \(0.610304\pi\)
\(198\) 0 0
\(199\) −2.16515 −0.153483 −0.0767416 0.997051i \(-0.524452\pi\)
−0.0767416 + 0.997051i \(0.524452\pi\)
\(200\) 0 0
\(201\) 10.5250 0.742377
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.92303 0.273996
\(206\) 0 0
\(207\) −6.28556 −0.436877
\(208\) 0 0
\(209\) 0.728148 0.0503671
\(210\) 0 0
\(211\) −17.2319 −1.18629 −0.593145 0.805096i \(-0.702114\pi\)
−0.593145 + 0.805096i \(0.702114\pi\)
\(212\) 0 0
\(213\) 13.6709 0.936717
\(214\) 0 0
\(215\) −35.5136 −2.42201
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 32.2438 2.17883
\(220\) 0 0
\(221\) 24.1899 1.62719
\(222\) 0 0
\(223\) 15.7640 1.05563 0.527817 0.849358i \(-0.323011\pi\)
0.527817 + 0.849358i \(0.323011\pi\)
\(224\) 0 0
\(225\) 23.4027 1.56018
\(226\) 0 0
\(227\) −11.4073 −0.757128 −0.378564 0.925575i \(-0.623582\pi\)
−0.378564 + 0.925575i \(0.623582\pi\)
\(228\) 0 0
\(229\) 25.6334 1.69390 0.846950 0.531672i \(-0.178436\pi\)
0.846950 + 0.531672i \(0.178436\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.20135 0.602800 0.301400 0.953498i \(-0.402546\pi\)
0.301400 + 0.953498i \(0.402546\pi\)
\(234\) 0 0
\(235\) 41.2865 2.69324
\(236\) 0 0
\(237\) 28.2831 1.83718
\(238\) 0 0
\(239\) −9.29402 −0.601180 −0.300590 0.953753i \(-0.597184\pi\)
−0.300590 + 0.953753i \(0.597184\pi\)
\(240\) 0 0
\(241\) −7.18759 −0.462993 −0.231497 0.972836i \(-0.574362\pi\)
−0.231497 + 0.972836i \(0.574362\pi\)
\(242\) 0 0
\(243\) 19.3453 1.24100
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.749219 −0.0476716
\(248\) 0 0
\(249\) 12.7221 0.806233
\(250\) 0 0
\(251\) 0.0203374 0.00128368 0.000641841 1.00000i \(-0.499796\pi\)
0.000641841 1.00000i \(0.499796\pi\)
\(252\) 0 0
\(253\) −9.80343 −0.616336
\(254\) 0 0
\(255\) −60.1682 −3.76788
\(256\) 0 0
\(257\) −24.2640 −1.51355 −0.756774 0.653676i \(-0.773226\pi\)
−0.756774 + 0.653676i \(0.773226\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.72546 −0.416296
\(262\) 0 0
\(263\) −17.4952 −1.07880 −0.539399 0.842051i \(-0.681348\pi\)
−0.539399 + 0.842051i \(0.681348\pi\)
\(264\) 0 0
\(265\) 49.8329 3.06121
\(266\) 0 0
\(267\) −5.34132 −0.326884
\(268\) 0 0
\(269\) −20.0679 −1.22356 −0.611781 0.791027i \(-0.709547\pi\)
−0.611781 + 0.791027i \(0.709547\pi\)
\(270\) 0 0
\(271\) −15.3783 −0.934166 −0.467083 0.884213i \(-0.654695\pi\)
−0.467083 + 0.884213i \(0.654695\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 36.5005 2.20106
\(276\) 0 0
\(277\) 23.3897 1.40535 0.702676 0.711510i \(-0.251988\pi\)
0.702676 + 0.711510i \(0.251988\pi\)
\(278\) 0 0
\(279\) 9.67879 0.579454
\(280\) 0 0
\(281\) 28.0532 1.67351 0.836757 0.547574i \(-0.184449\pi\)
0.836757 + 0.547574i \(0.184449\pi\)
\(282\) 0 0
\(283\) −20.9132 −1.24316 −0.621580 0.783351i \(-0.713509\pi\)
−0.621580 + 0.783351i \(0.713509\pi\)
\(284\) 0 0
\(285\) 1.86356 0.110388
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 27.7852 1.63442
\(290\) 0 0
\(291\) 20.2735 1.18845
\(292\) 0 0
\(293\) −14.9884 −0.875631 −0.437816 0.899065i \(-0.644248\pi\)
−0.437816 + 0.899065i \(0.644248\pi\)
\(294\) 0 0
\(295\) −31.8601 −1.85496
\(296\) 0 0
\(297\) 6.01909 0.349263
\(298\) 0 0
\(299\) 10.0871 0.583353
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 32.6700 1.87684
\(304\) 0 0
\(305\) −14.9565 −0.856406
\(306\) 0 0
\(307\) 8.70770 0.496975 0.248487 0.968635i \(-0.420067\pi\)
0.248487 + 0.968635i \(0.420067\pi\)
\(308\) 0 0
\(309\) −16.4506 −0.935842
\(310\) 0 0
\(311\) −23.4751 −1.33115 −0.665577 0.746329i \(-0.731814\pi\)
−0.665577 + 0.746329i \(0.731814\pi\)
\(312\) 0 0
\(313\) −4.07857 −0.230535 −0.115267 0.993335i \(-0.536772\pi\)
−0.115267 + 0.993335i \(0.536772\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.5518 −0.817313 −0.408656 0.912688i \(-0.634003\pi\)
−0.408656 + 0.912688i \(0.634003\pi\)
\(318\) 0 0
\(319\) −10.4895 −0.587301
\(320\) 0 0
\(321\) −6.63710 −0.370447
\(322\) 0 0
\(323\) −1.38711 −0.0771806
\(324\) 0 0
\(325\) −37.5568 −2.08327
\(326\) 0 0
\(327\) 20.3744 1.12671
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.48686 −0.136690 −0.0683451 0.997662i \(-0.521772\pi\)
−0.0683451 + 0.997662i \(0.521772\pi\)
\(332\) 0 0
\(333\) −23.1643 −1.26940
\(334\) 0 0
\(335\) 18.0163 0.984335
\(336\) 0 0
\(337\) 26.4341 1.43996 0.719980 0.693995i \(-0.244151\pi\)
0.719980 + 0.693995i \(0.244151\pi\)
\(338\) 0 0
\(339\) 17.6470 0.958453
\(340\) 0 0
\(341\) 15.0958 0.817481
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −25.0900 −1.35080
\(346\) 0 0
\(347\) 20.5078 1.10092 0.550458 0.834863i \(-0.314453\pi\)
0.550458 + 0.834863i \(0.314453\pi\)
\(348\) 0 0
\(349\) 26.6513 1.42661 0.713305 0.700854i \(-0.247198\pi\)
0.713305 + 0.700854i \(0.247198\pi\)
\(350\) 0 0
\(351\) −6.19326 −0.330572
\(352\) 0 0
\(353\) 22.3623 1.19022 0.595112 0.803643i \(-0.297108\pi\)
0.595112 + 0.803643i \(0.297108\pi\)
\(354\) 0 0
\(355\) 23.4014 1.24201
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 21.0421 1.11056 0.555280 0.831663i \(-0.312611\pi\)
0.555280 + 0.831663i \(0.312611\pi\)
\(360\) 0 0
\(361\) −18.9570 −0.997739
\(362\) 0 0
\(363\) −3.07360 −0.161322
\(364\) 0 0
\(365\) 55.1936 2.88897
\(366\) 0 0
\(367\) 28.6152 1.49370 0.746851 0.664992i \(-0.231565\pi\)
0.746851 + 0.664992i \(0.231565\pi\)
\(368\) 0 0
\(369\) −2.25239 −0.117255
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.60470 0.290200 0.145100 0.989417i \(-0.453650\pi\)
0.145100 + 0.989417i \(0.453650\pi\)
\(374\) 0 0
\(375\) 48.4619 2.50256
\(376\) 0 0
\(377\) 10.7931 0.555871
\(378\) 0 0
\(379\) −4.80556 −0.246845 −0.123423 0.992354i \(-0.539387\pi\)
−0.123423 + 0.992354i \(0.539387\pi\)
\(380\) 0 0
\(381\) 29.1144 1.49158
\(382\) 0 0
\(383\) −18.9428 −0.967932 −0.483966 0.875087i \(-0.660804\pi\)
−0.483966 + 0.875087i \(0.660804\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 20.3900 1.03648
\(388\) 0 0
\(389\) 34.3667 1.74246 0.871230 0.490874i \(-0.163323\pi\)
0.871230 + 0.490874i \(0.163323\pi\)
\(390\) 0 0
\(391\) 18.6753 0.944451
\(392\) 0 0
\(393\) −19.8310 −1.00034
\(394\) 0 0
\(395\) 48.4138 2.43596
\(396\) 0 0
\(397\) 23.8310 1.19604 0.598021 0.801480i \(-0.295954\pi\)
0.598021 + 0.801480i \(0.295954\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.9755 −0.548092 −0.274046 0.961717i \(-0.588362\pi\)
−0.274046 + 0.961717i \(0.588362\pi\)
\(402\) 0 0
\(403\) −15.5326 −0.773733
\(404\) 0 0
\(405\) 41.9133 2.08269
\(406\) 0 0
\(407\) −36.1288 −1.79084
\(408\) 0 0
\(409\) 2.47978 0.122617 0.0613086 0.998119i \(-0.480473\pi\)
0.0613086 + 0.998119i \(0.480473\pi\)
\(410\) 0 0
\(411\) 21.3891 1.05505
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 21.7773 1.06900
\(416\) 0 0
\(417\) −38.9504 −1.90741
\(418\) 0 0
\(419\) 11.6480 0.569044 0.284522 0.958670i \(-0.408165\pi\)
0.284522 + 0.958670i \(0.408165\pi\)
\(420\) 0 0
\(421\) 26.6347 1.29809 0.649047 0.760748i \(-0.275168\pi\)
0.649047 + 0.760748i \(0.275168\pi\)
\(422\) 0 0
\(423\) −23.7045 −1.15255
\(424\) 0 0
\(425\) −69.5327 −3.37283
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 29.1019 1.40506
\(430\) 0 0
\(431\) 23.5198 1.13291 0.566455 0.824093i \(-0.308315\pi\)
0.566455 + 0.824093i \(0.308315\pi\)
\(432\) 0 0
\(433\) −11.5571 −0.555401 −0.277700 0.960668i \(-0.589572\pi\)
−0.277700 + 0.960668i \(0.589572\pi\)
\(434\) 0 0
\(435\) −26.8459 −1.28716
\(436\) 0 0
\(437\) −0.578420 −0.0276696
\(438\) 0 0
\(439\) 10.0382 0.479097 0.239549 0.970884i \(-0.423001\pi\)
0.239549 + 0.970884i \(0.423001\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.598679 −0.0284441 −0.0142221 0.999899i \(-0.504527\pi\)
−0.0142221 + 0.999899i \(0.504527\pi\)
\(444\) 0 0
\(445\) −9.14306 −0.433423
\(446\) 0 0
\(447\) 14.7293 0.696670
\(448\) 0 0
\(449\) −39.3899 −1.85892 −0.929462 0.368918i \(-0.879728\pi\)
−0.929462 + 0.368918i \(0.879728\pi\)
\(450\) 0 0
\(451\) −3.51299 −0.165420
\(452\) 0 0
\(453\) 40.4857 1.90218
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.52559 −0.164920 −0.0824601 0.996594i \(-0.526278\pi\)
−0.0824601 + 0.996594i \(0.526278\pi\)
\(458\) 0 0
\(459\) −11.4662 −0.535197
\(460\) 0 0
\(461\) 2.35194 0.109541 0.0547705 0.998499i \(-0.482557\pi\)
0.0547705 + 0.998499i \(0.482557\pi\)
\(462\) 0 0
\(463\) 17.5635 0.816244 0.408122 0.912927i \(-0.366184\pi\)
0.408122 + 0.912927i \(0.366184\pi\)
\(464\) 0 0
\(465\) 38.6347 1.79164
\(466\) 0 0
\(467\) −2.67640 −0.123849 −0.0619245 0.998081i \(-0.519724\pi\)
−0.0619245 + 0.998081i \(0.519724\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 23.6025 1.08755
\(472\) 0 0
\(473\) 31.8017 1.46225
\(474\) 0 0
\(475\) 2.15360 0.0988138
\(476\) 0 0
\(477\) −28.6114 −1.31003
\(478\) 0 0
\(479\) 21.0385 0.961275 0.480637 0.876919i \(-0.340405\pi\)
0.480637 + 0.876919i \(0.340405\pi\)
\(480\) 0 0
\(481\) 37.1743 1.69500
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 34.7033 1.57580
\(486\) 0 0
\(487\) 41.1246 1.86354 0.931768 0.363055i \(-0.118266\pi\)
0.931768 + 0.363055i \(0.118266\pi\)
\(488\) 0 0
\(489\) −38.4009 −1.73655
\(490\) 0 0
\(491\) 30.4118 1.37246 0.686232 0.727383i \(-0.259264\pi\)
0.686232 + 0.727383i \(0.259264\pi\)
\(492\) 0 0
\(493\) 19.9823 0.899958
\(494\) 0 0
\(495\) −31.0415 −1.39521
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −0.935665 −0.0418861 −0.0209431 0.999781i \(-0.506667\pi\)
−0.0209431 + 0.999781i \(0.506667\pi\)
\(500\) 0 0
\(501\) −11.7772 −0.526166
\(502\) 0 0
\(503\) 7.91977 0.353125 0.176563 0.984289i \(-0.443502\pi\)
0.176563 + 0.984289i \(0.443502\pi\)
\(504\) 0 0
\(505\) 55.9232 2.48855
\(506\) 0 0
\(507\) −0.150553 −0.00668628
\(508\) 0 0
\(509\) −2.31671 −0.102686 −0.0513432 0.998681i \(-0.516350\pi\)
−0.0513432 + 0.998681i \(0.516350\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.355137 0.0156797
\(514\) 0 0
\(515\) −28.1595 −1.24086
\(516\) 0 0
\(517\) −36.9713 −1.62599
\(518\) 0 0
\(519\) 21.6035 0.948287
\(520\) 0 0
\(521\) 22.6118 0.990641 0.495321 0.868710i \(-0.335051\pi\)
0.495321 + 0.868710i \(0.335051\pi\)
\(522\) 0 0
\(523\) −8.34659 −0.364971 −0.182485 0.983209i \(-0.558414\pi\)
−0.182485 + 0.983209i \(0.558414\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −28.7571 −1.25268
\(528\) 0 0
\(529\) −15.2124 −0.661411
\(530\) 0 0
\(531\) 18.2923 0.793819
\(532\) 0 0
\(533\) 3.61465 0.156568
\(534\) 0 0
\(535\) −11.3611 −0.491184
\(536\) 0 0
\(537\) −26.9865 −1.16455
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −7.42880 −0.319389 −0.159695 0.987166i \(-0.551051\pi\)
−0.159695 + 0.987166i \(0.551051\pi\)
\(542\) 0 0
\(543\) −2.34796 −0.100761
\(544\) 0 0
\(545\) 34.8761 1.49393
\(546\) 0 0
\(547\) −22.4612 −0.960373 −0.480187 0.877166i \(-0.659431\pi\)
−0.480187 + 0.877166i \(0.659431\pi\)
\(548\) 0 0
\(549\) 8.58721 0.366493
\(550\) 0 0
\(551\) −0.618901 −0.0263661
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −92.4647 −3.92491
\(556\) 0 0
\(557\) 28.2545 1.19718 0.598590 0.801056i \(-0.295728\pi\)
0.598590 + 0.801056i \(0.295728\pi\)
\(558\) 0 0
\(559\) −32.7220 −1.38399
\(560\) 0 0
\(561\) 53.8794 2.27479
\(562\) 0 0
\(563\) 32.4582 1.36795 0.683975 0.729505i \(-0.260250\pi\)
0.683975 + 0.729505i \(0.260250\pi\)
\(564\) 0 0
\(565\) 30.2074 1.27084
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.45265 −0.186665 −0.0933325 0.995635i \(-0.529752\pi\)
−0.0933325 + 0.995635i \(0.529752\pi\)
\(570\) 0 0
\(571\) −42.7962 −1.79097 −0.895483 0.445095i \(-0.853170\pi\)
−0.895483 + 0.445095i \(0.853170\pi\)
\(572\) 0 0
\(573\) 23.9251 0.999486
\(574\) 0 0
\(575\) −28.9949 −1.20917
\(576\) 0 0
\(577\) −26.5876 −1.10686 −0.553429 0.832896i \(-0.686681\pi\)
−0.553429 + 0.832896i \(0.686681\pi\)
\(578\) 0 0
\(579\) −14.9399 −0.620881
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −44.6244 −1.84815
\(584\) 0 0
\(585\) 31.9397 1.32055
\(586\) 0 0
\(587\) 10.9973 0.453907 0.226954 0.973906i \(-0.427123\pi\)
0.226954 + 0.973906i \(0.427123\pi\)
\(588\) 0 0
\(589\) 0.890677 0.0366997
\(590\) 0 0
\(591\) 21.8501 0.898795
\(592\) 0 0
\(593\) −24.7312 −1.01559 −0.507795 0.861478i \(-0.669539\pi\)
−0.507795 + 0.861478i \(0.669539\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.96211 0.203086
\(598\) 0 0
\(599\) 35.6600 1.45703 0.728514 0.685031i \(-0.240211\pi\)
0.728514 + 0.685031i \(0.240211\pi\)
\(600\) 0 0
\(601\) −2.34760 −0.0957608 −0.0478804 0.998853i \(-0.515247\pi\)
−0.0478804 + 0.998853i \(0.515247\pi\)
\(602\) 0 0
\(603\) −10.3440 −0.421239
\(604\) 0 0
\(605\) −5.26127 −0.213901
\(606\) 0 0
\(607\) −18.4585 −0.749208 −0.374604 0.927185i \(-0.622221\pi\)
−0.374604 + 0.927185i \(0.622221\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 38.0411 1.53898
\(612\) 0 0
\(613\) 23.1740 0.935989 0.467994 0.883731i \(-0.344977\pi\)
0.467994 + 0.883731i \(0.344977\pi\)
\(614\) 0 0
\(615\) −8.99083 −0.362545
\(616\) 0 0
\(617\) 4.14273 0.166780 0.0833900 0.996517i \(-0.473425\pi\)
0.0833900 + 0.996517i \(0.473425\pi\)
\(618\) 0 0
\(619\) −4.13693 −0.166277 −0.0831387 0.996538i \(-0.526494\pi\)
−0.0831387 + 0.996538i \(0.526494\pi\)
\(620\) 0 0
\(621\) −4.78139 −0.191870
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 31.0045 1.24018
\(626\) 0 0
\(627\) −1.66878 −0.0666445
\(628\) 0 0
\(629\) 68.8245 2.74421
\(630\) 0 0
\(631\) −39.4573 −1.57077 −0.785384 0.619009i \(-0.787535\pi\)
−0.785384 + 0.619009i \(0.787535\pi\)
\(632\) 0 0
\(633\) 39.4921 1.56967
\(634\) 0 0
\(635\) 49.8369 1.97772
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −13.4358 −0.531512
\(640\) 0 0
\(641\) 17.7249 0.700090 0.350045 0.936733i \(-0.386166\pi\)
0.350045 + 0.936733i \(0.386166\pi\)
\(642\) 0 0
\(643\) 16.7180 0.659294 0.329647 0.944104i \(-0.393070\pi\)
0.329647 + 0.944104i \(0.393070\pi\)
\(644\) 0 0
\(645\) 81.3904 3.20475
\(646\) 0 0
\(647\) −26.8476 −1.05549 −0.527744 0.849403i \(-0.676962\pi\)
−0.527744 + 0.849403i \(0.676962\pi\)
\(648\) 0 0
\(649\) 28.5300 1.11990
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 41.1261 1.60939 0.804694 0.593690i \(-0.202329\pi\)
0.804694 + 0.593690i \(0.202329\pi\)
\(654\) 0 0
\(655\) −33.9459 −1.32638
\(656\) 0 0
\(657\) −31.6892 −1.23631
\(658\) 0 0
\(659\) −39.6004 −1.54261 −0.771305 0.636465i \(-0.780396\pi\)
−0.771305 + 0.636465i \(0.780396\pi\)
\(660\) 0 0
\(661\) −50.5727 −1.96705 −0.983526 0.180769i \(-0.942141\pi\)
−0.983526 + 0.180769i \(0.942141\pi\)
\(662\) 0 0
\(663\) −55.4385 −2.15305
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.33257 0.322638
\(668\) 0 0
\(669\) −36.1280 −1.39679
\(670\) 0 0
\(671\) 13.3932 0.517040
\(672\) 0 0
\(673\) −22.3840 −0.862842 −0.431421 0.902151i \(-0.641988\pi\)
−0.431421 + 0.902151i \(0.641988\pi\)
\(674\) 0 0
\(675\) 17.8023 0.685209
\(676\) 0 0
\(677\) 13.9764 0.537157 0.268579 0.963258i \(-0.413446\pi\)
0.268579 + 0.963258i \(0.413446\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 26.1433 1.00181
\(682\) 0 0
\(683\) −7.52159 −0.287805 −0.143903 0.989592i \(-0.545965\pi\)
−0.143903 + 0.989592i \(0.545965\pi\)
\(684\) 0 0
\(685\) 36.6131 1.39891
\(686\) 0 0
\(687\) −58.7468 −2.24133
\(688\) 0 0
\(689\) 45.9157 1.74925
\(690\) 0 0
\(691\) −24.4747 −0.931062 −0.465531 0.885032i \(-0.654137\pi\)
−0.465531 + 0.885032i \(0.654137\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −66.6737 −2.52908
\(696\) 0 0
\(697\) 6.69217 0.253484
\(698\) 0 0
\(699\) −21.0877 −0.797612
\(700\) 0 0
\(701\) −25.1812 −0.951081 −0.475541 0.879694i \(-0.657748\pi\)
−0.475541 + 0.879694i \(0.657748\pi\)
\(702\) 0 0
\(703\) −2.13166 −0.0803972
\(704\) 0 0
\(705\) −94.6208 −3.56363
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 35.9165 1.34887 0.674436 0.738333i \(-0.264387\pi\)
0.674436 + 0.738333i \(0.264387\pi\)
\(710\) 0 0
\(711\) −27.7966 −1.04245
\(712\) 0 0
\(713\) −11.9916 −0.449090
\(714\) 0 0
\(715\) 49.8156 1.86300
\(716\) 0 0
\(717\) 21.3001 0.795468
\(718\) 0 0
\(719\) −34.1055 −1.27192 −0.635961 0.771721i \(-0.719396\pi\)
−0.635961 + 0.771721i \(0.719396\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 16.4726 0.612622
\(724\) 0 0
\(725\) −31.0242 −1.15221
\(726\) 0 0
\(727\) −2.46037 −0.0912502 −0.0456251 0.998959i \(-0.514528\pi\)
−0.0456251 + 0.998959i \(0.514528\pi\)
\(728\) 0 0
\(729\) −12.2841 −0.454968
\(730\) 0 0
\(731\) −60.5816 −2.24069
\(732\) 0 0
\(733\) −20.4141 −0.754014 −0.377007 0.926210i \(-0.623047\pi\)
−0.377007 + 0.926210i \(0.623047\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.1332 −0.594275
\(738\) 0 0
\(739\) −42.0718 −1.54764 −0.773819 0.633407i \(-0.781656\pi\)
−0.773819 + 0.633407i \(0.781656\pi\)
\(740\) 0 0
\(741\) 1.71707 0.0630780
\(742\) 0 0
\(743\) −35.6041 −1.30619 −0.653094 0.757276i \(-0.726530\pi\)
−0.653094 + 0.757276i \(0.726530\pi\)
\(744\) 0 0
\(745\) 25.2130 0.923731
\(746\) 0 0
\(747\) −12.5033 −0.457473
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 17.5931 0.641982 0.320991 0.947082i \(-0.395984\pi\)
0.320991 + 0.947082i \(0.395984\pi\)
\(752\) 0 0
\(753\) −0.0466094 −0.00169854
\(754\) 0 0
\(755\) 69.3018 2.52215
\(756\) 0 0
\(757\) −28.0048 −1.01785 −0.508925 0.860811i \(-0.669957\pi\)
−0.508925 + 0.860811i \(0.669957\pi\)
\(758\) 0 0
\(759\) 22.4676 0.815522
\(760\) 0 0
\(761\) −39.1619 −1.41962 −0.709809 0.704394i \(-0.751219\pi\)
−0.709809 + 0.704394i \(0.751219\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 59.1333 2.13797
\(766\) 0 0
\(767\) −29.3556 −1.05997
\(768\) 0 0
\(769\) 34.4203 1.24123 0.620614 0.784116i \(-0.286883\pi\)
0.620614 + 0.784116i \(0.286883\pi\)
\(770\) 0 0
\(771\) 55.6085 2.00269
\(772\) 0 0
\(773\) −40.5515 −1.45853 −0.729267 0.684229i \(-0.760139\pi\)
−0.729267 + 0.684229i \(0.760139\pi\)
\(774\) 0 0
\(775\) 44.6477 1.60379
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.207273 −0.00742632
\(780\) 0 0
\(781\) −20.9554 −0.749845
\(782\) 0 0
\(783\) −5.11601 −0.182831
\(784\) 0 0
\(785\) 40.4019 1.44201
\(786\) 0 0
\(787\) −11.9816 −0.427099 −0.213550 0.976932i \(-0.568502\pi\)
−0.213550 + 0.976932i \(0.568502\pi\)
\(788\) 0 0
\(789\) 40.0956 1.42744
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −13.7808 −0.489371
\(794\) 0 0
\(795\) −114.208 −4.05053
\(796\) 0 0
\(797\) −31.1246 −1.10249 −0.551245 0.834344i \(-0.685847\pi\)
−0.551245 + 0.834344i \(0.685847\pi\)
\(798\) 0 0
\(799\) 70.4294 2.49161
\(800\) 0 0
\(801\) 5.24945 0.185480
\(802\) 0 0
\(803\) −49.4248 −1.74416
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 45.9918 1.61899
\(808\) 0 0
\(809\) 15.4645 0.543702 0.271851 0.962339i \(-0.412364\pi\)
0.271851 + 0.962339i \(0.412364\pi\)
\(810\) 0 0
\(811\) 5.57856 0.195890 0.0979449 0.995192i \(-0.468773\pi\)
0.0979449 + 0.995192i \(0.468773\pi\)
\(812\) 0 0
\(813\) 35.2442 1.23607
\(814\) 0 0
\(815\) −65.7332 −2.30253
\(816\) 0 0
\(817\) 1.87636 0.0656455
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −31.3680 −1.09475 −0.547375 0.836887i \(-0.684373\pi\)
−0.547375 + 0.836887i \(0.684373\pi\)
\(822\) 0 0
\(823\) −32.8396 −1.14472 −0.572358 0.820004i \(-0.693971\pi\)
−0.572358 + 0.820004i \(0.693971\pi\)
\(824\) 0 0
\(825\) −83.6523 −2.91240
\(826\) 0 0
\(827\) 21.9905 0.764686 0.382343 0.924020i \(-0.375117\pi\)
0.382343 + 0.924020i \(0.375117\pi\)
\(828\) 0 0
\(829\) −4.41854 −0.153462 −0.0767312 0.997052i \(-0.524448\pi\)
−0.0767312 + 0.997052i \(0.524448\pi\)
\(830\) 0 0
\(831\) −53.6048 −1.85953
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −20.1597 −0.697656
\(836\) 0 0
\(837\) 7.36259 0.254488
\(838\) 0 0
\(839\) −37.5622 −1.29679 −0.648396 0.761303i \(-0.724560\pi\)
−0.648396 + 0.761303i \(0.724560\pi\)
\(840\) 0 0
\(841\) −20.0843 −0.692561
\(842\) 0 0
\(843\) −64.2926 −2.21435
\(844\) 0 0
\(845\) −0.257710 −0.00886549
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 47.9291 1.64492
\(850\) 0 0
\(851\) 28.6996 0.983811
\(852\) 0 0
\(853\) −1.71726 −0.0587978 −0.0293989 0.999568i \(-0.509359\pi\)
−0.0293989 + 0.999568i \(0.509359\pi\)
\(854\) 0 0
\(855\) −1.83150 −0.0626361
\(856\) 0 0
\(857\) −15.7794 −0.539013 −0.269507 0.962999i \(-0.586861\pi\)
−0.269507 + 0.962999i \(0.586861\pi\)
\(858\) 0 0
\(859\) 33.0402 1.12732 0.563658 0.826008i \(-0.309394\pi\)
0.563658 + 0.826008i \(0.309394\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 40.7791 1.38814 0.694068 0.719910i \(-0.255817\pi\)
0.694068 + 0.719910i \(0.255817\pi\)
\(864\) 0 0
\(865\) 36.9800 1.25736
\(866\) 0 0
\(867\) −63.6783 −2.16263
\(868\) 0 0
\(869\) −43.3536 −1.47067
\(870\) 0 0
\(871\) 16.6001 0.562472
\(872\) 0 0
\(873\) −19.9248 −0.674351
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.6960 0.496248 0.248124 0.968728i \(-0.420186\pi\)
0.248124 + 0.968728i \(0.420186\pi\)
\(878\) 0 0
\(879\) 34.3505 1.15861
\(880\) 0 0
\(881\) −16.2764 −0.548366 −0.274183 0.961678i \(-0.588407\pi\)
−0.274183 + 0.961678i \(0.588407\pi\)
\(882\) 0 0
\(883\) 31.9882 1.07649 0.538245 0.842789i \(-0.319088\pi\)
0.538245 + 0.842789i \(0.319088\pi\)
\(884\) 0 0
\(885\) 73.0172 2.45445
\(886\) 0 0
\(887\) 47.4765 1.59411 0.797053 0.603909i \(-0.206391\pi\)
0.797053 + 0.603909i \(0.206391\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −37.5325 −1.25739
\(892\) 0 0
\(893\) −2.18137 −0.0729968
\(894\) 0 0
\(895\) −46.1944 −1.54411
\(896\) 0 0
\(897\) −23.1177 −0.771879
\(898\) 0 0
\(899\) −12.8309 −0.427933
\(900\) 0 0
\(901\) 85.0085 2.83204
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.01915 −0.133601
\(906\) 0 0
\(907\) 47.4456 1.57540 0.787702 0.616056i \(-0.211271\pi\)
0.787702 + 0.616056i \(0.211271\pi\)
\(908\) 0 0
\(909\) −32.1081 −1.06496
\(910\) 0 0
\(911\) −12.3231 −0.408281 −0.204141 0.978942i \(-0.565440\pi\)
−0.204141 + 0.978942i \(0.565440\pi\)
\(912\) 0 0
\(913\) −19.5011 −0.645392
\(914\) 0 0
\(915\) 34.2774 1.13318
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 2.56281 0.0845394 0.0422697 0.999106i \(-0.486541\pi\)
0.0422697 + 0.999106i \(0.486541\pi\)
\(920\) 0 0
\(921\) −19.9564 −0.657585
\(922\) 0 0
\(923\) 21.5618 0.709716
\(924\) 0 0
\(925\) −106.856 −3.51340
\(926\) 0 0
\(927\) 16.1677 0.531016
\(928\) 0 0
\(929\) −19.7784 −0.648908 −0.324454 0.945901i \(-0.605181\pi\)
−0.324454 + 0.945901i \(0.605181\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 53.8006 1.76135
\(934\) 0 0
\(935\) 92.2287 3.01620
\(936\) 0 0
\(937\) 39.7513 1.29862 0.649309 0.760525i \(-0.275058\pi\)
0.649309 + 0.760525i \(0.275058\pi\)
\(938\) 0 0
\(939\) 9.34731 0.305038
\(940\) 0 0
\(941\) −46.3470 −1.51087 −0.755435 0.655223i \(-0.772575\pi\)
−0.755435 + 0.655223i \(0.772575\pi\)
\(942\) 0 0
\(943\) 2.79062 0.0908750
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 39.3711 1.27939 0.639695 0.768629i \(-0.279061\pi\)
0.639695 + 0.768629i \(0.279061\pi\)
\(948\) 0 0
\(949\) 50.8550 1.65082
\(950\) 0 0
\(951\) 33.3500 1.08145
\(952\) 0 0
\(953\) −30.3627 −0.983546 −0.491773 0.870724i \(-0.663651\pi\)
−0.491773 + 0.870724i \(0.663651\pi\)
\(954\) 0 0
\(955\) 40.9541 1.32524
\(956\) 0 0
\(957\) 24.0400 0.777103
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −12.5348 −0.404347
\(962\) 0 0
\(963\) 6.52294 0.210199
\(964\) 0 0
\(965\) −25.5735 −0.823240
\(966\) 0 0
\(967\) 46.3933 1.49191 0.745955 0.665997i \(-0.231994\pi\)
0.745955 + 0.665997i \(0.231994\pi\)
\(968\) 0 0
\(969\) 3.17898 0.102124
\(970\) 0 0
\(971\) −3.60175 −0.115586 −0.0577929 0.998329i \(-0.518406\pi\)
−0.0577929 + 0.998329i \(0.518406\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 86.0729 2.75654
\(976\) 0 0
\(977\) −11.6914 −0.374040 −0.187020 0.982356i \(-0.559883\pi\)
−0.187020 + 0.982356i \(0.559883\pi\)
\(978\) 0 0
\(979\) 8.18743 0.261671
\(980\) 0 0
\(981\) −20.0239 −0.639315
\(982\) 0 0
\(983\) 31.6688 1.01008 0.505038 0.863097i \(-0.331478\pi\)
0.505038 + 0.863097i \(0.331478\pi\)
\(984\) 0 0
\(985\) 37.4022 1.19173
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25.2624 −0.803296
\(990\) 0 0
\(991\) −3.13395 −0.0995532 −0.0497766 0.998760i \(-0.515851\pi\)
−0.0497766 + 0.998760i \(0.515851\pi\)
\(992\) 0 0
\(993\) 5.69941 0.180865
\(994\) 0 0
\(995\) 8.49394 0.269276
\(996\) 0 0
\(997\) 44.9917 1.42490 0.712451 0.701722i \(-0.247585\pi\)
0.712451 + 0.701722i \(0.247585\pi\)
\(998\) 0 0
\(999\) −17.6210 −0.557502
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 \(a_p\))