Properties

Label 6004.2.a.d.1.3
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.76571\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.76571 q^{5}\) \(+2.40269 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.76571 q^{5}\) \(+2.40269 q^{7}\) \(-3.00000 q^{9}\) \(+4.64261 q^{11}\) \(+3.69939 q^{13}\) \(+1.00852 q^{17}\) \(+1.00000 q^{19}\) \(-2.66776 q^{23}\) \(-1.88227 q^{25}\) \(-0.522363 q^{29}\) \(+7.54466 q^{31}\) \(-4.24245 q^{35}\) \(-4.36796 q^{37}\) \(+9.51751 q^{41}\) \(-0.856909 q^{43}\) \(+5.29713 q^{45}\) \(+9.01404 q^{47}\) \(-1.22708 q^{49}\) \(-12.1682 q^{53}\) \(-8.19750 q^{55}\) \(+12.6765 q^{59}\) \(-2.58820 q^{61}\) \(-7.20807 q^{63}\) \(-6.53204 q^{65}\) \(+6.77423 q^{67}\) \(-2.48726 q^{71}\) \(-5.73865 q^{73}\) \(+11.1548 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(+5.22392 q^{83}\) \(-1.78076 q^{85}\) \(-10.0219 q^{89}\) \(+8.88848 q^{91}\) \(-1.76571 q^{95}\) \(-4.55616 q^{97}\) \(-13.9278 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −1.76571 −0.789649 −0.394824 0.918757i \(-0.629195\pi\)
−0.394824 + 0.918757i \(0.629195\pi\)
\(6\) 0 0
\(7\) 2.40269 0.908132 0.454066 0.890968i \(-0.349973\pi\)
0.454066 + 0.890968i \(0.349973\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 4.64261 1.39980 0.699900 0.714241i \(-0.253228\pi\)
0.699900 + 0.714241i \(0.253228\pi\)
\(12\) 0 0
\(13\) 3.69939 1.02603 0.513013 0.858381i \(-0.328529\pi\)
0.513013 + 0.858381i \(0.328529\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00852 0.244603 0.122302 0.992493i \(-0.460972\pi\)
0.122302 + 0.992493i \(0.460972\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.66776 −0.556267 −0.278134 0.960542i \(-0.589716\pi\)
−0.278134 + 0.960542i \(0.589716\pi\)
\(24\) 0 0
\(25\) −1.88227 −0.376455
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.522363 −0.0970004 −0.0485002 0.998823i \(-0.515444\pi\)
−0.0485002 + 0.998823i \(0.515444\pi\)
\(30\) 0 0
\(31\) 7.54466 1.35506 0.677531 0.735494i \(-0.263050\pi\)
0.677531 + 0.735494i \(0.263050\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.24245 −0.717105
\(36\) 0 0
\(37\) −4.36796 −0.718088 −0.359044 0.933321i \(-0.616897\pi\)
−0.359044 + 0.933321i \(0.616897\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.51751 1.48639 0.743193 0.669077i \(-0.233311\pi\)
0.743193 + 0.669077i \(0.233311\pi\)
\(42\) 0 0
\(43\) −0.856909 −0.130677 −0.0653387 0.997863i \(-0.520813\pi\)
−0.0653387 + 0.997863i \(0.520813\pi\)
\(44\) 0 0
\(45\) 5.29713 0.789649
\(46\) 0 0
\(47\) 9.01404 1.31483 0.657416 0.753528i \(-0.271649\pi\)
0.657416 + 0.753528i \(0.271649\pi\)
\(48\) 0 0
\(49\) −1.22708 −0.175297
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.1682 −1.67144 −0.835718 0.549159i \(-0.814948\pi\)
−0.835718 + 0.549159i \(0.814948\pi\)
\(54\) 0 0
\(55\) −8.19750 −1.10535
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.6765 1.65035 0.825173 0.564881i \(-0.191078\pi\)
0.825173 + 0.564881i \(0.191078\pi\)
\(60\) 0 0
\(61\) −2.58820 −0.331384 −0.165692 0.986178i \(-0.552986\pi\)
−0.165692 + 0.986178i \(0.552986\pi\)
\(62\) 0 0
\(63\) −7.20807 −0.908132
\(64\) 0 0
\(65\) −6.53204 −0.810200
\(66\) 0 0
\(67\) 6.77423 0.827604 0.413802 0.910367i \(-0.364201\pi\)
0.413802 + 0.910367i \(0.364201\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.48726 −0.295183 −0.147592 0.989048i \(-0.547152\pi\)
−0.147592 + 0.989048i \(0.547152\pi\)
\(72\) 0 0
\(73\) −5.73865 −0.671659 −0.335829 0.941923i \(-0.609017\pi\)
−0.335829 + 0.941923i \(0.609017\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 11.1548 1.27120
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 5.22392 0.573400 0.286700 0.958020i \(-0.407442\pi\)
0.286700 + 0.958020i \(0.407442\pi\)
\(84\) 0 0
\(85\) −1.78076 −0.193151
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.0219 −1.06232 −0.531159 0.847272i \(-0.678243\pi\)
−0.531159 + 0.847272i \(0.678243\pi\)
\(90\) 0 0
\(91\) 8.88848 0.931766
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.76571 −0.181158
\(96\) 0 0
\(97\) −4.55616 −0.462608 −0.231304 0.972882i \(-0.574299\pi\)
−0.231304 + 0.972882i \(0.574299\pi\)
\(98\) 0 0
\(99\) −13.9278 −1.39980
\(100\) 0 0
\(101\) 14.0015 1.39320 0.696598 0.717461i \(-0.254696\pi\)
0.696598 + 0.717461i \(0.254696\pi\)
\(102\) 0 0
\(103\) 4.82282 0.475206 0.237603 0.971362i \(-0.423638\pi\)
0.237603 + 0.971362i \(0.423638\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.03720 −0.680312 −0.340156 0.940369i \(-0.610480\pi\)
−0.340156 + 0.940369i \(0.610480\pi\)
\(108\) 0 0
\(109\) −3.29838 −0.315928 −0.157964 0.987445i \(-0.550493\pi\)
−0.157964 + 0.987445i \(0.550493\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.4066 −1.26119 −0.630595 0.776112i \(-0.717189\pi\)
−0.630595 + 0.776112i \(0.717189\pi\)
\(114\) 0 0
\(115\) 4.71049 0.439256
\(116\) 0 0
\(117\) −11.0982 −1.02603
\(118\) 0 0
\(119\) 2.42317 0.222132
\(120\) 0 0
\(121\) 10.5538 0.959439
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1521 1.08692
\(126\) 0 0
\(127\) −4.60770 −0.408867 −0.204434 0.978880i \(-0.565535\pi\)
−0.204434 + 0.978880i \(0.565535\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.88355 0.251937 0.125968 0.992034i \(-0.459796\pi\)
0.125968 + 0.992034i \(0.459796\pi\)
\(132\) 0 0
\(133\) 2.40269 0.208340
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.1456 −1.29397 −0.646987 0.762501i \(-0.723971\pi\)
−0.646987 + 0.762501i \(0.723971\pi\)
\(138\) 0 0
\(139\) 3.53468 0.299807 0.149904 0.988701i \(-0.452104\pi\)
0.149904 + 0.988701i \(0.452104\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 17.1748 1.43623
\(144\) 0 0
\(145\) 0.922341 0.0765962
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 19.9674 1.63579 0.817897 0.575365i \(-0.195140\pi\)
0.817897 + 0.575365i \(0.195140\pi\)
\(150\) 0 0
\(151\) −2.87784 −0.234196 −0.117098 0.993120i \(-0.537359\pi\)
−0.117098 + 0.993120i \(0.537359\pi\)
\(152\) 0 0
\(153\) −3.02557 −0.244603
\(154\) 0 0
\(155\) −13.3217 −1.07002
\(156\) 0 0
\(157\) −17.4176 −1.39007 −0.695037 0.718974i \(-0.744612\pi\)
−0.695037 + 0.718974i \(0.744612\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.40981 −0.505164
\(162\) 0 0
\(163\) −6.34773 −0.497193 −0.248596 0.968607i \(-0.579969\pi\)
−0.248596 + 0.968607i \(0.579969\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.3947 1.73296 0.866478 0.499215i \(-0.166378\pi\)
0.866478 + 0.499215i \(0.166378\pi\)
\(168\) 0 0
\(169\) 0.685473 0.0527287
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) −13.4210 −1.02038 −0.510190 0.860062i \(-0.670425\pi\)
−0.510190 + 0.860062i \(0.670425\pi\)
\(174\) 0 0
\(175\) −4.52252 −0.341870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.42358 0.181147 0.0905736 0.995890i \(-0.471130\pi\)
0.0905736 + 0.995890i \(0.471130\pi\)
\(180\) 0 0
\(181\) 0.605206 0.0449846 0.0224923 0.999747i \(-0.492840\pi\)
0.0224923 + 0.999747i \(0.492840\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.71254 0.567037
\(186\) 0 0
\(187\) 4.68219 0.342395
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.6573 1.92886 0.964428 0.264345i \(-0.0851558\pi\)
0.964428 + 0.264345i \(0.0851558\pi\)
\(192\) 0 0
\(193\) 6.15357 0.442943 0.221472 0.975167i \(-0.428914\pi\)
0.221472 + 0.975167i \(0.428914\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.0310 1.78339 0.891693 0.452641i \(-0.149518\pi\)
0.891693 + 0.452641i \(0.149518\pi\)
\(198\) 0 0
\(199\) 5.76232 0.408480 0.204240 0.978921i \(-0.434528\pi\)
0.204240 + 0.978921i \(0.434528\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.25508 −0.0880891
\(204\) 0 0
\(205\) −16.8051 −1.17372
\(206\) 0 0
\(207\) 8.00329 0.556267
\(208\) 0 0
\(209\) 4.64261 0.321136
\(210\) 0 0
\(211\) 20.2654 1.39513 0.697563 0.716523i \(-0.254268\pi\)
0.697563 + 0.716523i \(0.254268\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.51305 0.103189
\(216\) 0 0
\(217\) 18.1275 1.23057
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.73093 0.250969
\(222\) 0 0
\(223\) 19.8018 1.32603 0.663015 0.748606i \(-0.269277\pi\)
0.663015 + 0.748606i \(0.269277\pi\)
\(224\) 0 0
\(225\) 5.64682 0.376455
\(226\) 0 0
\(227\) 18.6869 1.24029 0.620147 0.784486i \(-0.287073\pi\)
0.620147 + 0.784486i \(0.287073\pi\)
\(228\) 0 0
\(229\) 7.50642 0.496038 0.248019 0.968755i \(-0.420220\pi\)
0.248019 + 0.968755i \(0.420220\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.93127 0.257546 0.128773 0.991674i \(-0.458896\pi\)
0.128773 + 0.991674i \(0.458896\pi\)
\(234\) 0 0
\(235\) −15.9162 −1.03826
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.20977 0.401676 0.200838 0.979624i \(-0.435633\pi\)
0.200838 + 0.979624i \(0.435633\pi\)
\(240\) 0 0
\(241\) 3.97170 0.255840 0.127920 0.991785i \(-0.459170\pi\)
0.127920 + 0.991785i \(0.459170\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.16667 0.138423
\(246\) 0 0
\(247\) 3.69939 0.235386
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0936 1.52078 0.760389 0.649468i \(-0.225008\pi\)
0.760389 + 0.649468i \(0.225008\pi\)
\(252\) 0 0
\(253\) −12.3854 −0.778662
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.9229 1.18038 0.590190 0.807265i \(-0.299053\pi\)
0.590190 + 0.807265i \(0.299053\pi\)
\(258\) 0 0
\(259\) −10.4948 −0.652118
\(260\) 0 0
\(261\) 1.56709 0.0970004
\(262\) 0 0
\(263\) 7.10061 0.437842 0.218921 0.975743i \(-0.429746\pi\)
0.218921 + 0.975743i \(0.429746\pi\)
\(264\) 0 0
\(265\) 21.4856 1.31985
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −19.1418 −1.16710 −0.583550 0.812078i \(-0.698337\pi\)
−0.583550 + 0.812078i \(0.698337\pi\)
\(270\) 0 0
\(271\) −13.4138 −0.814829 −0.407415 0.913243i \(-0.633570\pi\)
−0.407415 + 0.913243i \(0.633570\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.73866 −0.526961
\(276\) 0 0
\(277\) 13.6792 0.821901 0.410950 0.911658i \(-0.365197\pi\)
0.410950 + 0.911658i \(0.365197\pi\)
\(278\) 0 0
\(279\) −22.6340 −1.35506
\(280\) 0 0
\(281\) −6.24356 −0.372459 −0.186230 0.982506i \(-0.559627\pi\)
−0.186230 + 0.982506i \(0.559627\pi\)
\(282\) 0 0
\(283\) 6.82226 0.405542 0.202771 0.979226i \(-0.435005\pi\)
0.202771 + 0.979226i \(0.435005\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 22.8676 1.34983
\(288\) 0 0
\(289\) −15.9829 −0.940169
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.96757 −0.114947 −0.0574735 0.998347i \(-0.518304\pi\)
−0.0574735 + 0.998347i \(0.518304\pi\)
\(294\) 0 0
\(295\) −22.3831 −1.30319
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.86909 −0.570744
\(300\) 0 0
\(301\) −2.05889 −0.118672
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.57000 0.261677
\(306\) 0 0
\(307\) 16.9276 0.966107 0.483053 0.875591i \(-0.339528\pi\)
0.483053 + 0.875591i \(0.339528\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 23.9384 1.35742 0.678712 0.734404i \(-0.262538\pi\)
0.678712 + 0.734404i \(0.262538\pi\)
\(312\) 0 0
\(313\) 28.5184 1.61195 0.805977 0.591947i \(-0.201640\pi\)
0.805977 + 0.591947i \(0.201640\pi\)
\(314\) 0 0
\(315\) 12.7274 0.717105
\(316\) 0 0
\(317\) −35.4326 −1.99009 −0.995045 0.0994238i \(-0.968300\pi\)
−0.995045 + 0.0994238i \(0.968300\pi\)
\(318\) 0 0
\(319\) −2.42513 −0.135781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.00852 0.0561158
\(324\) 0 0
\(325\) −6.96326 −0.386252
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 21.6579 1.19404
\(330\) 0 0
\(331\) −19.7650 −1.08638 −0.543192 0.839609i \(-0.682784\pi\)
−0.543192 + 0.839609i \(0.682784\pi\)
\(332\) 0 0
\(333\) 13.1039 0.718088
\(334\) 0 0
\(335\) −11.9613 −0.653517
\(336\) 0 0
\(337\) −0.499954 −0.0272342 −0.0136171 0.999907i \(-0.504335\pi\)
−0.0136171 + 0.999907i \(0.504335\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 35.0269 1.89681
\(342\) 0 0
\(343\) −19.7671 −1.06732
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 34.7187 1.86380 0.931899 0.362717i \(-0.118151\pi\)
0.931899 + 0.362717i \(0.118151\pi\)
\(348\) 0 0
\(349\) 8.02757 0.429706 0.214853 0.976646i \(-0.431073\pi\)
0.214853 + 0.976646i \(0.431073\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 35.2459 1.87595 0.937975 0.346703i \(-0.112699\pi\)
0.937975 + 0.346703i \(0.112699\pi\)
\(354\) 0 0
\(355\) 4.39177 0.233091
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −29.1604 −1.53902 −0.769512 0.638632i \(-0.779501\pi\)
−0.769512 + 0.638632i \(0.779501\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10.1328 0.530374
\(366\) 0 0
\(367\) −16.8177 −0.877878 −0.438939 0.898517i \(-0.644646\pi\)
−0.438939 + 0.898517i \(0.644646\pi\)
\(368\) 0 0
\(369\) −28.5525 −1.48639
\(370\) 0 0
\(371\) −29.2365 −1.51788
\(372\) 0 0
\(373\) −28.2832 −1.46445 −0.732223 0.681065i \(-0.761517\pi\)
−0.732223 + 0.681065i \(0.761517\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.93242 −0.0995249
\(378\) 0 0
\(379\) 31.9641 1.64188 0.820942 0.571011i \(-0.193449\pi\)
0.820942 + 0.571011i \(0.193449\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.3392 1.03928 0.519642 0.854384i \(-0.326065\pi\)
0.519642 + 0.854384i \(0.326065\pi\)
\(384\) 0 0
\(385\) −19.6960 −1.00380
\(386\) 0 0
\(387\) 2.57073 0.130677
\(388\) 0 0
\(389\) 20.4904 1.03890 0.519451 0.854500i \(-0.326136\pi\)
0.519451 + 0.854500i \(0.326136\pi\)
\(390\) 0 0
\(391\) −2.69051 −0.136065
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.76571 −0.0888424
\(396\) 0 0
\(397\) 8.73469 0.438381 0.219191 0.975682i \(-0.429658\pi\)
0.219191 + 0.975682i \(0.429658\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.66736 0.332952 0.166476 0.986045i \(-0.446761\pi\)
0.166476 + 0.986045i \(0.446761\pi\)
\(402\) 0 0
\(403\) 27.9106 1.39033
\(404\) 0 0
\(405\) −15.8914 −0.789649
\(406\) 0 0
\(407\) −20.2787 −1.00518
\(408\) 0 0
\(409\) 29.9584 1.48135 0.740674 0.671864i \(-0.234506\pi\)
0.740674 + 0.671864i \(0.234506\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 30.4578 1.49873
\(414\) 0 0
\(415\) −9.22392 −0.452784
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.94327 0.143788 0.0718941 0.997412i \(-0.477096\pi\)
0.0718941 + 0.997412i \(0.477096\pi\)
\(420\) 0 0
\(421\) 10.6518 0.519138 0.259569 0.965725i \(-0.416420\pi\)
0.259569 + 0.965725i \(0.416420\pi\)
\(422\) 0 0
\(423\) −27.0421 −1.31483
\(424\) 0 0
\(425\) −1.89832 −0.0920820
\(426\) 0 0
\(427\) −6.21863 −0.300941
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.628500 −0.0302738 −0.0151369 0.999885i \(-0.504818\pi\)
−0.0151369 + 0.999885i \(0.504818\pi\)
\(432\) 0 0
\(433\) −39.9076 −1.91784 −0.958919 0.283680i \(-0.908445\pi\)
−0.958919 + 0.283680i \(0.908445\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.66776 −0.127616
\(438\) 0 0
\(439\) 26.7748 1.27789 0.638947 0.769251i \(-0.279370\pi\)
0.638947 + 0.769251i \(0.279370\pi\)
\(440\) 0 0
\(441\) 3.68124 0.175297
\(442\) 0 0
\(443\) −36.5112 −1.73470 −0.867350 0.497698i \(-0.834179\pi\)
−0.867350 + 0.497698i \(0.834179\pi\)
\(444\) 0 0
\(445\) 17.6957 0.838858
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.42675 −0.256104 −0.128052 0.991767i \(-0.540873\pi\)
−0.128052 + 0.991767i \(0.540873\pi\)
\(450\) 0 0
\(451\) 44.1861 2.08064
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.6945 −0.735768
\(456\) 0 0
\(457\) 11.1565 0.521879 0.260940 0.965355i \(-0.415968\pi\)
0.260940 + 0.965355i \(0.415968\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.1546 −0.985269 −0.492635 0.870236i \(-0.663966\pi\)
−0.492635 + 0.870236i \(0.663966\pi\)
\(462\) 0 0
\(463\) −26.5609 −1.23439 −0.617196 0.786810i \(-0.711731\pi\)
−0.617196 + 0.786810i \(0.711731\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −31.9021 −1.47625 −0.738126 0.674663i \(-0.764289\pi\)
−0.738126 + 0.674663i \(0.764289\pi\)
\(468\) 0 0
\(469\) 16.2764 0.751574
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.97829 −0.182922
\(474\) 0 0
\(475\) −1.88227 −0.0863646
\(476\) 0 0
\(477\) 36.5047 1.67144
\(478\) 0 0
\(479\) −8.39959 −0.383787 −0.191893 0.981416i \(-0.561463\pi\)
−0.191893 + 0.981416i \(0.561463\pi\)
\(480\) 0 0
\(481\) −16.1588 −0.736777
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.04484 0.365298
\(486\) 0 0
\(487\) 15.4283 0.699122 0.349561 0.936914i \(-0.386331\pi\)
0.349561 + 0.936914i \(0.386331\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.02221 −0.181520 −0.0907600 0.995873i \(-0.528930\pi\)
−0.0907600 + 0.995873i \(0.528930\pi\)
\(492\) 0 0
\(493\) −0.526816 −0.0237266
\(494\) 0 0
\(495\) 24.5925 1.10535
\(496\) 0 0
\(497\) −5.97611 −0.268065
\(498\) 0 0
\(499\) −8.28394 −0.370840 −0.185420 0.982659i \(-0.559365\pi\)
−0.185420 + 0.982659i \(0.559365\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17.4311 −0.777214 −0.388607 0.921404i \(-0.627044\pi\)
−0.388607 + 0.921404i \(0.627044\pi\)
\(504\) 0 0
\(505\) −24.7225 −1.10014
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −33.3089 −1.47639 −0.738196 0.674586i \(-0.764322\pi\)
−0.738196 + 0.674586i \(0.764322\pi\)
\(510\) 0 0
\(511\) −13.7882 −0.609954
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.51569 −0.375246
\(516\) 0 0
\(517\) 41.8487 1.84050
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.7064 1.17003 0.585015 0.811022i \(-0.301089\pi\)
0.585015 + 0.811022i \(0.301089\pi\)
\(522\) 0 0
\(523\) −28.0788 −1.22780 −0.613900 0.789384i \(-0.710400\pi\)
−0.613900 + 0.789384i \(0.710400\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.60898 0.331452
\(528\) 0 0
\(529\) −15.8830 −0.690567
\(530\) 0 0
\(531\) −38.0296 −1.65035
\(532\) 0 0
\(533\) 35.2090 1.52507
\(534\) 0 0
\(535\) 12.4256 0.537207
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.69685 −0.245381
\(540\) 0 0
\(541\) −30.1900 −1.29797 −0.648985 0.760801i \(-0.724806\pi\)
−0.648985 + 0.760801i \(0.724806\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.82398 0.249472
\(546\) 0 0
\(547\) 5.29157 0.226251 0.113126 0.993581i \(-0.463914\pi\)
0.113126 + 0.993581i \(0.463914\pi\)
\(548\) 0 0
\(549\) 7.76459 0.331384
\(550\) 0 0
\(551\) −0.522363 −0.0222534
\(552\) 0 0
\(553\) 2.40269 0.102173
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −44.8096 −1.89864 −0.949322 0.314305i \(-0.898228\pi\)
−0.949322 + 0.314305i \(0.898228\pi\)
\(558\) 0 0
\(559\) −3.17004 −0.134078
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 30.3002 1.27700 0.638502 0.769620i \(-0.279555\pi\)
0.638502 + 0.769620i \(0.279555\pi\)
\(564\) 0 0
\(565\) 23.6722 0.995897
\(566\) 0 0
\(567\) 21.6242 0.908132
\(568\) 0 0
\(569\) 34.9579 1.46551 0.732756 0.680492i \(-0.238234\pi\)
0.732756 + 0.680492i \(0.238234\pi\)
\(570\) 0 0
\(571\) 3.85564 0.161353 0.0806767 0.996740i \(-0.474292\pi\)
0.0806767 + 0.996740i \(0.474292\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.02146 0.209409
\(576\) 0 0
\(577\) −10.4508 −0.435073 −0.217536 0.976052i \(-0.569802\pi\)
−0.217536 + 0.976052i \(0.569802\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.5515 0.520722
\(582\) 0 0
\(583\) −56.4924 −2.33968
\(584\) 0 0
\(585\) 19.5961 0.810200
\(586\) 0 0
\(587\) −14.6951 −0.606533 −0.303266 0.952906i \(-0.598077\pi\)
−0.303266 + 0.952906i \(0.598077\pi\)
\(588\) 0 0
\(589\) 7.54466 0.310872
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 42.3595 1.73950 0.869749 0.493495i \(-0.164281\pi\)
0.869749 + 0.493495i \(0.164281\pi\)
\(594\) 0 0
\(595\) −4.27862 −0.175406
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.4475 0.672025 0.336012 0.941858i \(-0.390922\pi\)
0.336012 + 0.941858i \(0.390922\pi\)
\(600\) 0 0
\(601\) −37.1503 −1.51539 −0.757697 0.652607i \(-0.773675\pi\)
−0.757697 + 0.652607i \(0.773675\pi\)
\(602\) 0 0
\(603\) −20.3227 −0.827604
\(604\) 0 0
\(605\) −18.6350 −0.757620
\(606\) 0 0
\(607\) 36.4957 1.48132 0.740658 0.671882i \(-0.234514\pi\)
0.740658 + 0.671882i \(0.234514\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 33.3464 1.34905
\(612\) 0 0
\(613\) −11.2547 −0.454572 −0.227286 0.973828i \(-0.572985\pi\)
−0.227286 + 0.973828i \(0.572985\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.33341 0.174457 0.0872284 0.996188i \(-0.472199\pi\)
0.0872284 + 0.996188i \(0.472199\pi\)
\(618\) 0 0
\(619\) 47.8805 1.92448 0.962240 0.272201i \(-0.0877516\pi\)
0.962240 + 0.272201i \(0.0877516\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.0795 −0.964724
\(624\) 0 0
\(625\) −12.0457 −0.481827
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.40519 −0.175647
\(630\) 0 0
\(631\) −46.8786 −1.86621 −0.933103 0.359608i \(-0.882910\pi\)
−0.933103 + 0.359608i \(0.882910\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8.13586 0.322862
\(636\) 0 0
\(637\) −4.53944 −0.179859
\(638\) 0 0
\(639\) 7.46177 0.295183
\(640\) 0 0
\(641\) −14.6688 −0.579382 −0.289691 0.957120i \(-0.593552\pi\)
−0.289691 + 0.957120i \(0.593552\pi\)
\(642\) 0 0
\(643\) −22.3936 −0.883118 −0.441559 0.897232i \(-0.645574\pi\)
−0.441559 + 0.897232i \(0.645574\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.4630 −0.922425 −0.461213 0.887290i \(-0.652585\pi\)
−0.461213 + 0.887290i \(0.652585\pi\)
\(648\) 0 0
\(649\) 58.8522 2.31015
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.9099 1.52266 0.761331 0.648364i \(-0.224546\pi\)
0.761331 + 0.648364i \(0.224546\pi\)
\(654\) 0 0
\(655\) −5.09150 −0.198942
\(656\) 0 0
\(657\) 17.2160 0.671659
\(658\) 0 0
\(659\) 9.66770 0.376600 0.188300 0.982112i \(-0.439702\pi\)
0.188300 + 0.982112i \(0.439702\pi\)
\(660\) 0 0
\(661\) 27.8753 1.08422 0.542112 0.840306i \(-0.317625\pi\)
0.542112 + 0.840306i \(0.317625\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.24245 −0.164515
\(666\) 0 0
\(667\) 1.39354 0.0539581
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0160 −0.463872
\(672\) 0 0
\(673\) −20.9874 −0.809004 −0.404502 0.914537i \(-0.632555\pi\)
−0.404502 + 0.914537i \(0.632555\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.2154 1.31501 0.657503 0.753452i \(-0.271613\pi\)
0.657503 + 0.753452i \(0.271613\pi\)
\(678\) 0 0
\(679\) −10.9470 −0.420109
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.276336 0.0105737 0.00528686 0.999986i \(-0.498317\pi\)
0.00528686 + 0.999986i \(0.498317\pi\)
\(684\) 0 0
\(685\) 26.7427 1.02179
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −45.0150 −1.71494
\(690\) 0 0
\(691\) −36.5978 −1.39225 −0.696124 0.717922i \(-0.745094\pi\)
−0.696124 + 0.717922i \(0.745094\pi\)
\(692\) 0 0
\(693\) −33.4643 −1.27120
\(694\) 0 0
\(695\) −6.24121 −0.236743
\(696\) 0 0
\(697\) 9.59865 0.363575
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.0319 1.13429 0.567144 0.823619i \(-0.308048\pi\)
0.567144 + 0.823619i \(0.308048\pi\)
\(702\) 0 0
\(703\) −4.36796 −0.164741
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 33.6412 1.26521
\(708\) 0 0
\(709\) 41.5061 1.55879 0.779397 0.626530i \(-0.215525\pi\)
0.779397 + 0.626530i \(0.215525\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −20.1274 −0.753776
\(714\) 0 0
\(715\) −30.3257 −1.13412
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.745956 −0.0278195 −0.0139097 0.999903i \(-0.504428\pi\)
−0.0139097 + 0.999903i \(0.504428\pi\)
\(720\) 0 0
\(721\) 11.5877 0.431550
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.983230 0.0365162
\(726\) 0 0
\(727\) 35.9346 1.33274 0.666370 0.745622i \(-0.267847\pi\)
0.666370 + 0.745622i \(0.267847\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −0.864214 −0.0319641
\(732\) 0 0
\(733\) 34.6131 1.27846 0.639232 0.769014i \(-0.279252\pi\)
0.639232 + 0.769014i \(0.279252\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.4501 1.15848
\(738\) 0 0
\(739\) −36.9541 −1.35938 −0.679689 0.733500i \(-0.737885\pi\)
−0.679689 + 0.733500i \(0.737885\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −49.0959 −1.80115 −0.900576 0.434698i \(-0.856855\pi\)
−0.900576 + 0.434698i \(0.856855\pi\)
\(744\) 0 0
\(745\) −35.2566 −1.29170
\(746\) 0 0
\(747\) −15.6718 −0.573400
\(748\) 0 0
\(749\) −16.9082 −0.617812
\(750\) 0 0
\(751\) 2.21555 0.0808465 0.0404233 0.999183i \(-0.487129\pi\)
0.0404233 + 0.999183i \(0.487129\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.08143 0.184932
\(756\) 0 0
\(757\) 27.4263 0.996827 0.498413 0.866939i \(-0.333916\pi\)
0.498413 + 0.866939i \(0.333916\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.1771 −0.767669 −0.383834 0.923402i \(-0.625397\pi\)
−0.383834 + 0.923402i \(0.625397\pi\)
\(762\) 0 0
\(763\) −7.92499 −0.286904
\(764\) 0 0
\(765\) 5.34228 0.193151
\(766\) 0 0
\(767\) 46.8955 1.69330
\(768\) 0 0
\(769\) −11.7155 −0.422471 −0.211235 0.977435i \(-0.567749\pi\)
−0.211235 + 0.977435i \(0.567749\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.7546 0.494720 0.247360 0.968924i \(-0.420437\pi\)
0.247360 + 0.968924i \(0.420437\pi\)
\(774\) 0 0
\(775\) −14.2011 −0.510119
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.51751 0.341000
\(780\) 0 0
\(781\) −11.5474 −0.413197
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 30.7544 1.09767
\(786\) 0 0
\(787\) −46.5685 −1.65999 −0.829994 0.557772i \(-0.811656\pi\)
−0.829994 + 0.557772i \(0.811656\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −32.2120 −1.14533
\(792\) 0 0
\(793\) −9.57474 −0.340009
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 39.1260 1.38591 0.692957 0.720979i \(-0.256308\pi\)
0.692957 + 0.720979i \(0.256308\pi\)
\(798\) 0 0
\(799\) 9.09088 0.321612
\(800\) 0 0
\(801\) 30.0656 1.06232
\(802\) 0 0
\(803\) −26.6423 −0.940187
\(804\) 0 0
\(805\) 11.3179 0.398902
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −13.2904 −0.467264 −0.233632 0.972325i \(-0.575061\pi\)
−0.233632 + 0.972325i \(0.575061\pi\)
\(810\) 0 0
\(811\) −38.3097 −1.34523 −0.672617 0.739991i \(-0.734830\pi\)
−0.672617 + 0.739991i \(0.734830\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 11.2082 0.392608
\(816\) 0 0
\(817\) −0.856909 −0.0299794
\(818\) 0 0
\(819\) −26.6655 −0.931766
\(820\) 0 0
\(821\) −29.6151 −1.03357 −0.516787 0.856114i \(-0.672872\pi\)
−0.516787 + 0.856114i \(0.672872\pi\)
\(822\) 0 0
\(823\) 6.59329 0.229827 0.114914 0.993375i \(-0.463341\pi\)
0.114914 + 0.993375i \(0.463341\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −48.8894 −1.70005 −0.850025 0.526742i \(-0.823413\pi\)
−0.850025 + 0.526742i \(0.823413\pi\)
\(828\) 0 0
\(829\) −50.8481 −1.76603 −0.883013 0.469349i \(-0.844489\pi\)
−0.883013 + 0.469349i \(0.844489\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.23754 −0.0428782
\(834\) 0 0
\(835\) −39.5426 −1.36843
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −39.9160 −1.37805 −0.689027 0.724735i \(-0.741962\pi\)
−0.689027 + 0.724735i \(0.741962\pi\)
\(840\) 0 0
\(841\) −28.7271 −0.990591
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.21034 −0.0416371
\(846\) 0 0
\(847\) 25.3576 0.871296
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 11.6527 0.399449
\(852\) 0 0
\(853\) −17.9827 −0.615717 −0.307859 0.951432i \(-0.599612\pi\)
−0.307859 + 0.951432i \(0.599612\pi\)
\(854\) 0 0
\(855\) 5.29713 0.181158
\(856\) 0 0
\(857\) 32.4455 1.10832 0.554158 0.832411i \(-0.313040\pi\)
0.554158 + 0.832411i \(0.313040\pi\)
\(858\) 0 0
\(859\) −53.1071 −1.81199 −0.905996 0.423287i \(-0.860876\pi\)
−0.905996 + 0.423287i \(0.860876\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26.9923 0.918829 0.459414 0.888222i \(-0.348059\pi\)
0.459414 + 0.888222i \(0.348059\pi\)
\(864\) 0 0
\(865\) 23.6976 0.805742
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.64261 0.157490
\(870\) 0 0
\(871\) 25.0605 0.849143
\(872\) 0 0
\(873\) 13.6685 0.462608
\(874\) 0 0
\(875\) 29.1977 0.987063
\(876\) 0 0
\(877\) −17.5137 −0.591395 −0.295697 0.955282i \(-0.595552\pi\)
−0.295697 + 0.955282i \(0.595552\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 8.96224 0.301946 0.150973 0.988538i \(-0.451759\pi\)
0.150973 + 0.988538i \(0.451759\pi\)
\(882\) 0 0
\(883\) −53.0134 −1.78404 −0.892021 0.451995i \(-0.850713\pi\)
−0.892021 + 0.451995i \(0.850713\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.75659 0.260441 0.130220 0.991485i \(-0.458432\pi\)
0.130220 + 0.991485i \(0.458432\pi\)
\(888\) 0 0
\(889\) −11.0709 −0.371305
\(890\) 0 0
\(891\) 41.7835 1.39980
\(892\) 0 0
\(893\) 9.01404 0.301643
\(894\) 0 0
\(895\) −4.27934 −0.143043
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.94105 −0.131441
\(900\) 0 0
\(901\) −12.2720 −0.408839
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.06862 −0.0355220
\(906\) 0 0
\(907\) 21.9437 0.728629 0.364314 0.931276i \(-0.381303\pi\)
0.364314 + 0.931276i \(0.381303\pi\)
\(908\) 0 0
\(909\) −42.0044 −1.39320
\(910\) 0 0
\(911\) −37.1133 −1.22962 −0.614809 0.788676i \(-0.710767\pi\)
−0.614809 + 0.788676i \(0.710767\pi\)
\(912\) 0 0
\(913\) 24.2526 0.802645
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 6.92827 0.228792
\(918\) 0 0
\(919\) −4.63759 −0.152980 −0.0764900 0.997070i \(-0.524371\pi\)
−0.0764900 + 0.997070i \(0.524371\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −9.20133 −0.302866
\(924\) 0 0
\(925\) 8.22169 0.270328
\(926\) 0 0
\(927\) −14.4685 −0.475206
\(928\) 0 0
\(929\) −6.33317 −0.207785 −0.103892 0.994589i \(-0.533130\pi\)
−0.103892 + 0.994589i \(0.533130\pi\)
\(930\) 0 0
\(931\) −1.22708 −0.0402159
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.26738 −0.270372
\(936\) 0 0
\(937\) 8.80575 0.287671 0.143836 0.989602i \(-0.454056\pi\)
0.143836 + 0.989602i \(0.454056\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 41.7928 1.36240 0.681202 0.732095i \(-0.261457\pi\)
0.681202 + 0.732095i \(0.261457\pi\)
\(942\) 0 0
\(943\) −25.3905 −0.826827
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7.25168 −0.235648 −0.117824 0.993034i \(-0.537592\pi\)
−0.117824 + 0.993034i \(0.537592\pi\)
\(948\) 0 0
\(949\) −21.2295 −0.689139
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 39.2211 1.27050 0.635248 0.772308i \(-0.280898\pi\)
0.635248 + 0.772308i \(0.280898\pi\)
\(954\) 0 0
\(955\) −47.0691 −1.52312
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −36.3902 −1.17510
\(960\) 0 0
\(961\) 25.9220 0.836192
\(962\) 0 0
\(963\) 21.1116 0.680312
\(964\) 0 0
\(965\) −10.8654 −0.349770
\(966\) 0 0
\(967\) 15.2063 0.489003 0.244502 0.969649i \(-0.421376\pi\)
0.244502 + 0.969649i \(0.421376\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −25.5272 −0.819206 −0.409603 0.912264i \(-0.634333\pi\)
−0.409603 + 0.912264i \(0.634333\pi\)
\(972\) 0 0
\(973\) 8.49274 0.272265
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 23.1833 0.741701 0.370850 0.928693i \(-0.379066\pi\)
0.370850 + 0.928693i \(0.379066\pi\)
\(978\) 0 0
\(979\) −46.5277 −1.48703
\(980\) 0 0
\(981\) 9.89515 0.315928
\(982\) 0 0
\(983\) −20.0431 −0.639277 −0.319638 0.947540i \(-0.603561\pi\)
−0.319638 + 0.947540i \(0.603561\pi\)
\(984\) 0 0
\(985\) −44.1975 −1.40825
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.28603 0.0726915
\(990\) 0 0
\(991\) 5.32064 0.169016 0.0845079 0.996423i \(-0.473068\pi\)
0.0845079 + 0.996423i \(0.473068\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −10.1746 −0.322556
\(996\) 0 0
\(997\) −11.5793 −0.366721 −0.183360 0.983046i \(-0.558698\pi\)
−0.183360 + 0.983046i \(0.558698\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))