Properties

Label 8036.2.a.t.1.2
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
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: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.45978\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.45978 q^{3}\) \(-2.10149 q^{5}\) \(+3.05053 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.45978 q^{3}\) \(-2.10149 q^{5}\) \(+3.05053 q^{9}\) \(-2.99553 q^{11}\) \(+0.922682 q^{13}\) \(+5.16921 q^{15}\) \(+6.22399 q^{17}\) \(+6.64918 q^{19}\) \(-6.34110 q^{23}\) \(-0.583733 q^{25}\) \(-0.124300 q^{27}\) \(-1.64093 q^{29}\) \(+3.00257 q^{31}\) \(+7.36835 q^{33}\) \(+9.04669 q^{37}\) \(-2.26960 q^{39}\) \(-1.00000 q^{41}\) \(+7.65476 q^{43}\) \(-6.41067 q^{45}\) \(-6.66681 q^{47}\) \(-15.3097 q^{51}\) \(-7.74187 q^{53}\) \(+6.29508 q^{55}\) \(-16.3555 q^{57}\) \(-13.3223 q^{59}\) \(+9.83873 q^{61}\) \(-1.93901 q^{65}\) \(-8.26139 q^{67}\) \(+15.5977 q^{69}\) \(-3.01924 q^{71}\) \(-16.5270 q^{73}\) \(+1.43586 q^{75}\) \(+0.193471 q^{79}\) \(-8.84585 q^{81}\) \(+1.85504 q^{83}\) \(-13.0797 q^{85}\) \(+4.03632 q^{87}\) \(+1.02262 q^{89}\) \(-7.38568 q^{93}\) \(-13.9732 q^{95}\) \(+17.5072 q^{97}\) \(-9.13796 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.45978 −1.42016 −0.710078 0.704123i \(-0.751340\pi\)
−0.710078 + 0.704123i \(0.751340\pi\)
\(4\) 0 0
\(5\) −2.10149 −0.939816 −0.469908 0.882716i \(-0.655713\pi\)
−0.469908 + 0.882716i \(0.655713\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.05053 1.01684
\(10\) 0 0
\(11\) −2.99553 −0.903186 −0.451593 0.892224i \(-0.649144\pi\)
−0.451593 + 0.892224i \(0.649144\pi\)
\(12\) 0 0
\(13\) 0.922682 0.255906 0.127953 0.991780i \(-0.459159\pi\)
0.127953 + 0.991780i \(0.459159\pi\)
\(14\) 0 0
\(15\) 5.16921 1.33469
\(16\) 0 0
\(17\) 6.22399 1.50954 0.754770 0.655990i \(-0.227749\pi\)
0.754770 + 0.655990i \(0.227749\pi\)
\(18\) 0 0
\(19\) 6.64918 1.52543 0.762713 0.646737i \(-0.223867\pi\)
0.762713 + 0.646737i \(0.223867\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.34110 −1.32221 −0.661106 0.750293i \(-0.729912\pi\)
−0.661106 + 0.750293i \(0.729912\pi\)
\(24\) 0 0
\(25\) −0.583733 −0.116747
\(26\) 0 0
\(27\) −0.124300 −0.0239215
\(28\) 0 0
\(29\) −1.64093 −0.304712 −0.152356 0.988326i \(-0.548686\pi\)
−0.152356 + 0.988326i \(0.548686\pi\)
\(30\) 0 0
\(31\) 3.00257 0.539278 0.269639 0.962961i \(-0.413096\pi\)
0.269639 + 0.962961i \(0.413096\pi\)
\(32\) 0 0
\(33\) 7.36835 1.28267
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.04669 1.48727 0.743634 0.668587i \(-0.233101\pi\)
0.743634 + 0.668587i \(0.233101\pi\)
\(38\) 0 0
\(39\) −2.26960 −0.363426
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 7.65476 1.16734 0.583670 0.811991i \(-0.301616\pi\)
0.583670 + 0.811991i \(0.301616\pi\)
\(44\) 0 0
\(45\) −6.41067 −0.955646
\(46\) 0 0
\(47\) −6.66681 −0.972454 −0.486227 0.873833i \(-0.661627\pi\)
−0.486227 + 0.873833i \(0.661627\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −15.3097 −2.14378
\(52\) 0 0
\(53\) −7.74187 −1.06343 −0.531714 0.846924i \(-0.678452\pi\)
−0.531714 + 0.846924i \(0.678452\pi\)
\(54\) 0 0
\(55\) 6.29508 0.848829
\(56\) 0 0
\(57\) −16.3555 −2.16634
\(58\) 0 0
\(59\) −13.3223 −1.73442 −0.867209 0.497944i \(-0.834089\pi\)
−0.867209 + 0.497944i \(0.834089\pi\)
\(60\) 0 0
\(61\) 9.83873 1.25972 0.629860 0.776708i \(-0.283112\pi\)
0.629860 + 0.776708i \(0.283112\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.93901 −0.240504
\(66\) 0 0
\(67\) −8.26139 −1.00929 −0.504644 0.863327i \(-0.668376\pi\)
−0.504644 + 0.863327i \(0.668376\pi\)
\(68\) 0 0
\(69\) 15.5977 1.87775
\(70\) 0 0
\(71\) −3.01924 −0.358317 −0.179159 0.983820i \(-0.557338\pi\)
−0.179159 + 0.983820i \(0.557338\pi\)
\(72\) 0 0
\(73\) −16.5270 −1.93434 −0.967170 0.254130i \(-0.918211\pi\)
−0.967170 + 0.254130i \(0.918211\pi\)
\(74\) 0 0
\(75\) 1.43586 0.165799
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.193471 0.0217672 0.0108836 0.999941i \(-0.496536\pi\)
0.0108836 + 0.999941i \(0.496536\pi\)
\(80\) 0 0
\(81\) −8.84585 −0.982872
\(82\) 0 0
\(83\) 1.85504 0.203618 0.101809 0.994804i \(-0.467537\pi\)
0.101809 + 0.994804i \(0.467537\pi\)
\(84\) 0 0
\(85\) −13.0797 −1.41869
\(86\) 0 0
\(87\) 4.03632 0.432739
\(88\) 0 0
\(89\) 1.02262 0.108397 0.0541986 0.998530i \(-0.482740\pi\)
0.0541986 + 0.998530i \(0.482740\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.38568 −0.765859
\(94\) 0 0
\(95\) −13.9732 −1.43362
\(96\) 0 0
\(97\) 17.5072 1.77759 0.888794 0.458306i \(-0.151544\pi\)
0.888794 + 0.458306i \(0.151544\pi\)
\(98\) 0 0
\(99\) −9.13796 −0.918400
\(100\) 0 0
\(101\) 12.3992 1.23376 0.616882 0.787055i \(-0.288395\pi\)
0.616882 + 0.787055i \(0.288395\pi\)
\(102\) 0 0
\(103\) 12.7268 1.25401 0.627003 0.779017i \(-0.284281\pi\)
0.627003 + 0.779017i \(0.284281\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.91995 −0.475630 −0.237815 0.971311i \(-0.576431\pi\)
−0.237815 + 0.971311i \(0.576431\pi\)
\(108\) 0 0
\(109\) −9.01906 −0.863870 −0.431935 0.901905i \(-0.642169\pi\)
−0.431935 + 0.901905i \(0.642169\pi\)
\(110\) 0 0
\(111\) −22.2529 −2.11215
\(112\) 0 0
\(113\) 0.0393302 0.00369988 0.00184994 0.999998i \(-0.499411\pi\)
0.00184994 + 0.999998i \(0.499411\pi\)
\(114\) 0 0
\(115\) 13.3258 1.24263
\(116\) 0 0
\(117\) 2.81467 0.260216
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.02680 −0.184255
\(122\) 0 0
\(123\) 2.45978 0.221791
\(124\) 0 0
\(125\) 11.7342 1.04954
\(126\) 0 0
\(127\) −4.19318 −0.372085 −0.186042 0.982542i \(-0.559566\pi\)
−0.186042 + 0.982542i \(0.559566\pi\)
\(128\) 0 0
\(129\) −18.8291 −1.65781
\(130\) 0 0
\(131\) −21.2344 −1.85525 −0.927627 0.373507i \(-0.878155\pi\)
−0.927627 + 0.373507i \(0.878155\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.261215 0.0224818
\(136\) 0 0
\(137\) 0.642660 0.0549061 0.0274531 0.999623i \(-0.491260\pi\)
0.0274531 + 0.999623i \(0.491260\pi\)
\(138\) 0 0
\(139\) 1.63836 0.138964 0.0694818 0.997583i \(-0.477865\pi\)
0.0694818 + 0.997583i \(0.477865\pi\)
\(140\) 0 0
\(141\) 16.3989 1.38104
\(142\) 0 0
\(143\) −2.76392 −0.231131
\(144\) 0 0
\(145\) 3.44839 0.286373
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.58039 0.702933 0.351467 0.936200i \(-0.385683\pi\)
0.351467 + 0.936200i \(0.385683\pi\)
\(150\) 0 0
\(151\) 6.84431 0.556982 0.278491 0.960439i \(-0.410166\pi\)
0.278491 + 0.960439i \(0.410166\pi\)
\(152\) 0 0
\(153\) 18.9865 1.53497
\(154\) 0 0
\(155\) −6.30988 −0.506822
\(156\) 0 0
\(157\) 9.23915 0.737364 0.368682 0.929556i \(-0.379809\pi\)
0.368682 + 0.929556i \(0.379809\pi\)
\(158\) 0 0
\(159\) 19.0433 1.51023
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.7674 0.921697 0.460848 0.887479i \(-0.347545\pi\)
0.460848 + 0.887479i \(0.347545\pi\)
\(164\) 0 0
\(165\) −15.4845 −1.20547
\(166\) 0 0
\(167\) −4.24447 −0.328447 −0.164224 0.986423i \(-0.552512\pi\)
−0.164224 + 0.986423i \(0.552512\pi\)
\(168\) 0 0
\(169\) −12.1487 −0.934512
\(170\) 0 0
\(171\) 20.2835 1.55112
\(172\) 0 0
\(173\) −23.5768 −1.79251 −0.896256 0.443537i \(-0.853724\pi\)
−0.896256 + 0.443537i \(0.853724\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 32.7700 2.46315
\(178\) 0 0
\(179\) −3.94971 −0.295215 −0.147608 0.989046i \(-0.547157\pi\)
−0.147608 + 0.989046i \(0.547157\pi\)
\(180\) 0 0
\(181\) 12.1826 0.905523 0.452762 0.891632i \(-0.350439\pi\)
0.452762 + 0.891632i \(0.350439\pi\)
\(182\) 0 0
\(183\) −24.2012 −1.78900
\(184\) 0 0
\(185\) −19.0115 −1.39776
\(186\) 0 0
\(187\) −18.6442 −1.36340
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.7774 −0.779823 −0.389911 0.920852i \(-0.627494\pi\)
−0.389911 + 0.920852i \(0.627494\pi\)
\(192\) 0 0
\(193\) −23.7731 −1.71122 −0.855612 0.517618i \(-0.826819\pi\)
−0.855612 + 0.517618i \(0.826819\pi\)
\(194\) 0 0
\(195\) 4.76954 0.341554
\(196\) 0 0
\(197\) 11.3119 0.805940 0.402970 0.915213i \(-0.367978\pi\)
0.402970 + 0.915213i \(0.367978\pi\)
\(198\) 0 0
\(199\) −2.50514 −0.177585 −0.0887924 0.996050i \(-0.528301\pi\)
−0.0887924 + 0.996050i \(0.528301\pi\)
\(200\) 0 0
\(201\) 20.3212 1.43335
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.10149 0.146775
\(206\) 0 0
\(207\) −19.3437 −1.34448
\(208\) 0 0
\(209\) −19.9178 −1.37774
\(210\) 0 0
\(211\) 17.0504 1.17380 0.586898 0.809661i \(-0.300349\pi\)
0.586898 + 0.809661i \(0.300349\pi\)
\(212\) 0 0
\(213\) 7.42667 0.508867
\(214\) 0 0
\(215\) −16.0864 −1.09708
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 40.6529 2.74707
\(220\) 0 0
\(221\) 5.74276 0.386300
\(222\) 0 0
\(223\) −28.1839 −1.88734 −0.943668 0.330894i \(-0.892650\pi\)
−0.943668 + 0.330894i \(0.892650\pi\)
\(224\) 0 0
\(225\) −1.78070 −0.118713
\(226\) 0 0
\(227\) 11.8695 0.787810 0.393905 0.919151i \(-0.371124\pi\)
0.393905 + 0.919151i \(0.371124\pi\)
\(228\) 0 0
\(229\) −19.8424 −1.31122 −0.655611 0.755099i \(-0.727589\pi\)
−0.655611 + 0.755099i \(0.727589\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.4298 0.748792 0.374396 0.927269i \(-0.377850\pi\)
0.374396 + 0.927269i \(0.377850\pi\)
\(234\) 0 0
\(235\) 14.0102 0.913927
\(236\) 0 0
\(237\) −0.475897 −0.0309128
\(238\) 0 0
\(239\) 4.81103 0.311199 0.155600 0.987820i \(-0.450269\pi\)
0.155600 + 0.987820i \(0.450269\pi\)
\(240\) 0 0
\(241\) −10.1967 −0.656825 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(242\) 0 0
\(243\) 22.1318 1.41975
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.13507 0.390365
\(248\) 0 0
\(249\) −4.56301 −0.289169
\(250\) 0 0
\(251\) −3.18649 −0.201129 −0.100565 0.994931i \(-0.532065\pi\)
−0.100565 + 0.994931i \(0.532065\pi\)
\(252\) 0 0
\(253\) 18.9950 1.19420
\(254\) 0 0
\(255\) 32.1731 2.01476
\(256\) 0 0
\(257\) 23.6691 1.47643 0.738217 0.674563i \(-0.235668\pi\)
0.738217 + 0.674563i \(0.235668\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5.00570 −0.309845
\(262\) 0 0
\(263\) −17.5035 −1.07931 −0.539655 0.841887i \(-0.681445\pi\)
−0.539655 + 0.841887i \(0.681445\pi\)
\(264\) 0 0
\(265\) 16.2695 0.999426
\(266\) 0 0
\(267\) −2.51541 −0.153941
\(268\) 0 0
\(269\) 24.3533 1.48485 0.742425 0.669929i \(-0.233676\pi\)
0.742425 + 0.669929i \(0.233676\pi\)
\(270\) 0 0
\(271\) 6.21685 0.377647 0.188823 0.982011i \(-0.439533\pi\)
0.188823 + 0.982011i \(0.439533\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.74859 0.105444
\(276\) 0 0
\(277\) −2.77913 −0.166982 −0.0834908 0.996509i \(-0.526607\pi\)
−0.0834908 + 0.996509i \(0.526607\pi\)
\(278\) 0 0
\(279\) 9.15945 0.548362
\(280\) 0 0
\(281\) 21.2802 1.26947 0.634736 0.772729i \(-0.281109\pi\)
0.634736 + 0.772729i \(0.281109\pi\)
\(282\) 0 0
\(283\) −16.5832 −0.985771 −0.492886 0.870094i \(-0.664058\pi\)
−0.492886 + 0.870094i \(0.664058\pi\)
\(284\) 0 0
\(285\) 34.3710 2.03596
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 21.7381 1.27871
\(290\) 0 0
\(291\) −43.0640 −2.52445
\(292\) 0 0
\(293\) −7.44832 −0.435135 −0.217568 0.976045i \(-0.569812\pi\)
−0.217568 + 0.976045i \(0.569812\pi\)
\(294\) 0 0
\(295\) 27.9968 1.63003
\(296\) 0 0
\(297\) 0.372344 0.0216056
\(298\) 0 0
\(299\) −5.85082 −0.338362
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −30.4993 −1.75214
\(304\) 0 0
\(305\) −20.6760 −1.18391
\(306\) 0 0
\(307\) 16.2722 0.928703 0.464351 0.885651i \(-0.346287\pi\)
0.464351 + 0.885651i \(0.346287\pi\)
\(308\) 0 0
\(309\) −31.3051 −1.78088
\(310\) 0 0
\(311\) 17.1922 0.974882 0.487441 0.873156i \(-0.337930\pi\)
0.487441 + 0.873156i \(0.337930\pi\)
\(312\) 0 0
\(313\) 25.4997 1.44133 0.720665 0.693283i \(-0.243837\pi\)
0.720665 + 0.693283i \(0.243837\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.5574 0.592964 0.296482 0.955038i \(-0.404186\pi\)
0.296482 + 0.955038i \(0.404186\pi\)
\(318\) 0 0
\(319\) 4.91544 0.275212
\(320\) 0 0
\(321\) 12.1020 0.675469
\(322\) 0 0
\(323\) 41.3844 2.30269
\(324\) 0 0
\(325\) −0.538600 −0.0298762
\(326\) 0 0
\(327\) 22.1849 1.22683
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.40506 0.461984 0.230992 0.972956i \(-0.425803\pi\)
0.230992 + 0.972956i \(0.425803\pi\)
\(332\) 0 0
\(333\) 27.5972 1.51232
\(334\) 0 0
\(335\) 17.3612 0.948545
\(336\) 0 0
\(337\) 12.1490 0.661798 0.330899 0.943666i \(-0.392648\pi\)
0.330899 + 0.943666i \(0.392648\pi\)
\(338\) 0 0
\(339\) −0.0967438 −0.00525440
\(340\) 0 0
\(341\) −8.99430 −0.487069
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −32.7785 −1.76474
\(346\) 0 0
\(347\) 5.65522 0.303588 0.151794 0.988412i \(-0.451495\pi\)
0.151794 + 0.988412i \(0.451495\pi\)
\(348\) 0 0
\(349\) 13.5239 0.723917 0.361959 0.932194i \(-0.382108\pi\)
0.361959 + 0.932194i \(0.382108\pi\)
\(350\) 0 0
\(351\) −0.114689 −0.00612166
\(352\) 0 0
\(353\) 25.9341 1.38033 0.690165 0.723652i \(-0.257538\pi\)
0.690165 + 0.723652i \(0.257538\pi\)
\(354\) 0 0
\(355\) 6.34490 0.336752
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.31446 0.333265 0.166632 0.986019i \(-0.446711\pi\)
0.166632 + 0.986019i \(0.446711\pi\)
\(360\) 0 0
\(361\) 25.2115 1.32692
\(362\) 0 0
\(363\) 4.98549 0.261670
\(364\) 0 0
\(365\) 34.7314 1.81792
\(366\) 0 0
\(367\) 4.45266 0.232427 0.116213 0.993224i \(-0.462924\pi\)
0.116213 + 0.993224i \(0.462924\pi\)
\(368\) 0 0
\(369\) −3.05053 −0.158804
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −36.9550 −1.91346 −0.956728 0.290983i \(-0.906018\pi\)
−0.956728 + 0.290983i \(0.906018\pi\)
\(374\) 0 0
\(375\) −28.8635 −1.49051
\(376\) 0 0
\(377\) −1.51405 −0.0779777
\(378\) 0 0
\(379\) 17.6482 0.906527 0.453263 0.891377i \(-0.350260\pi\)
0.453263 + 0.891377i \(0.350260\pi\)
\(380\) 0 0
\(381\) 10.3143 0.528418
\(382\) 0 0
\(383\) −36.4077 −1.86035 −0.930174 0.367119i \(-0.880344\pi\)
−0.930174 + 0.367119i \(0.880344\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 23.3511 1.18700
\(388\) 0 0
\(389\) 20.9868 1.06407 0.532035 0.846722i \(-0.321427\pi\)
0.532035 + 0.846722i \(0.321427\pi\)
\(390\) 0 0
\(391\) −39.4670 −1.99593
\(392\) 0 0
\(393\) 52.2319 2.63475
\(394\) 0 0
\(395\) −0.406578 −0.0204572
\(396\) 0 0
\(397\) 25.5486 1.28225 0.641123 0.767438i \(-0.278469\pi\)
0.641123 + 0.767438i \(0.278469\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 29.6613 1.48121 0.740607 0.671938i \(-0.234538\pi\)
0.740607 + 0.671938i \(0.234538\pi\)
\(402\) 0 0
\(403\) 2.77042 0.138004
\(404\) 0 0
\(405\) 18.5895 0.923718
\(406\) 0 0
\(407\) −27.0996 −1.34328
\(408\) 0 0
\(409\) −4.74246 −0.234499 −0.117250 0.993102i \(-0.537408\pi\)
−0.117250 + 0.993102i \(0.537408\pi\)
\(410\) 0 0
\(411\) −1.58080 −0.0779753
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3.89836 −0.191363
\(416\) 0 0
\(417\) −4.03000 −0.197350
\(418\) 0 0
\(419\) 14.3836 0.702685 0.351342 0.936247i \(-0.385725\pi\)
0.351342 + 0.936247i \(0.385725\pi\)
\(420\) 0 0
\(421\) −9.89043 −0.482030 −0.241015 0.970521i \(-0.577480\pi\)
−0.241015 + 0.970521i \(0.577480\pi\)
\(422\) 0 0
\(423\) −20.3373 −0.988834
\(424\) 0 0
\(425\) −3.63315 −0.176234
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 6.79865 0.328242
\(430\) 0 0
\(431\) 13.1907 0.635375 0.317688 0.948195i \(-0.397094\pi\)
0.317688 + 0.948195i \(0.397094\pi\)
\(432\) 0 0
\(433\) −18.8403 −0.905406 −0.452703 0.891661i \(-0.649540\pi\)
−0.452703 + 0.891661i \(0.649540\pi\)
\(434\) 0 0
\(435\) −8.48230 −0.406695
\(436\) 0 0
\(437\) −42.1631 −2.01693
\(438\) 0 0
\(439\) −16.2902 −0.777487 −0.388743 0.921346i \(-0.627091\pi\)
−0.388743 + 0.921346i \(0.627091\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 29.7111 1.41162 0.705809 0.708402i \(-0.250584\pi\)
0.705809 + 0.708402i \(0.250584\pi\)
\(444\) 0 0
\(445\) −2.14902 −0.101873
\(446\) 0 0
\(447\) −21.1059 −0.998275
\(448\) 0 0
\(449\) 2.26145 0.106724 0.0533622 0.998575i \(-0.483006\pi\)
0.0533622 + 0.998575i \(0.483006\pi\)
\(450\) 0 0
\(451\) 2.99553 0.141054
\(452\) 0 0
\(453\) −16.8355 −0.791002
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.65074 −0.264330 −0.132165 0.991228i \(-0.542193\pi\)
−0.132165 + 0.991228i \(0.542193\pi\)
\(458\) 0 0
\(459\) −0.773642 −0.0361105
\(460\) 0 0
\(461\) −15.1407 −0.705171 −0.352585 0.935780i \(-0.614697\pi\)
−0.352585 + 0.935780i \(0.614697\pi\)
\(462\) 0 0
\(463\) −34.3527 −1.59650 −0.798252 0.602324i \(-0.794242\pi\)
−0.798252 + 0.602324i \(0.794242\pi\)
\(464\) 0 0
\(465\) 15.5209 0.719766
\(466\) 0 0
\(467\) 30.7199 1.42155 0.710773 0.703421i \(-0.248345\pi\)
0.710773 + 0.703421i \(0.248345\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −22.7263 −1.04717
\(472\) 0 0
\(473\) −22.9301 −1.05433
\(474\) 0 0
\(475\) −3.88135 −0.178088
\(476\) 0 0
\(477\) −23.6168 −1.08134
\(478\) 0 0
\(479\) −9.91797 −0.453163 −0.226582 0.973992i \(-0.572755\pi\)
−0.226582 + 0.973992i \(0.572755\pi\)
\(480\) 0 0
\(481\) 8.34722 0.380600
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −36.7913 −1.67061
\(486\) 0 0
\(487\) 6.95675 0.315240 0.157620 0.987500i \(-0.449618\pi\)
0.157620 + 0.987500i \(0.449618\pi\)
\(488\) 0 0
\(489\) −28.9453 −1.30895
\(490\) 0 0
\(491\) −6.26318 −0.282653 −0.141327 0.989963i \(-0.545137\pi\)
−0.141327 + 0.989963i \(0.545137\pi\)
\(492\) 0 0
\(493\) −10.2131 −0.459975
\(494\) 0 0
\(495\) 19.2034 0.863126
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −11.9396 −0.534491 −0.267246 0.963628i \(-0.586113\pi\)
−0.267246 + 0.963628i \(0.586113\pi\)
\(500\) 0 0
\(501\) 10.4405 0.466447
\(502\) 0 0
\(503\) −12.4862 −0.556731 −0.278366 0.960475i \(-0.589793\pi\)
−0.278366 + 0.960475i \(0.589793\pi\)
\(504\) 0 0
\(505\) −26.0568 −1.15951
\(506\) 0 0
\(507\) 29.8831 1.32715
\(508\) 0 0
\(509\) 35.0082 1.55171 0.775856 0.630910i \(-0.217318\pi\)
0.775856 + 0.630910i \(0.217318\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.826492 −0.0364905
\(514\) 0 0
\(515\) −26.7452 −1.17853
\(516\) 0 0
\(517\) 19.9706 0.878307
\(518\) 0 0
\(519\) 57.9939 2.54565
\(520\) 0 0
\(521\) 30.3464 1.32950 0.664749 0.747067i \(-0.268538\pi\)
0.664749 + 0.747067i \(0.268538\pi\)
\(522\) 0 0
\(523\) −35.2273 −1.54038 −0.770191 0.637813i \(-0.779839\pi\)
−0.770191 + 0.637813i \(0.779839\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.6880 0.814062
\(528\) 0 0
\(529\) 17.2096 0.748243
\(530\) 0 0
\(531\) −40.6402 −1.76363
\(532\) 0 0
\(533\) −0.922682 −0.0399658
\(534\) 0 0
\(535\) 10.3392 0.447004
\(536\) 0 0
\(537\) 9.71544 0.419252
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 34.5207 1.48416 0.742079 0.670312i \(-0.233840\pi\)
0.742079 + 0.670312i \(0.233840\pi\)
\(542\) 0 0
\(543\) −29.9665 −1.28598
\(544\) 0 0
\(545\) 18.9535 0.811878
\(546\) 0 0
\(547\) 1.86234 0.0796281 0.0398141 0.999207i \(-0.487323\pi\)
0.0398141 + 0.999207i \(0.487323\pi\)
\(548\) 0 0
\(549\) 30.0134 1.28094
\(550\) 0 0
\(551\) −10.9108 −0.464816
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 46.7643 1.98503
\(556\) 0 0
\(557\) 7.47891 0.316892 0.158446 0.987368i \(-0.449352\pi\)
0.158446 + 0.987368i \(0.449352\pi\)
\(558\) 0 0
\(559\) 7.06291 0.298729
\(560\) 0 0
\(561\) 45.8606 1.93623
\(562\) 0 0
\(563\) 32.4596 1.36801 0.684005 0.729477i \(-0.260237\pi\)
0.684005 + 0.729477i \(0.260237\pi\)
\(564\) 0 0
\(565\) −0.0826521 −0.00347720
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −35.6801 −1.49579 −0.747894 0.663819i \(-0.768935\pi\)
−0.747894 + 0.663819i \(0.768935\pi\)
\(570\) 0 0
\(571\) 9.06761 0.379468 0.189734 0.981836i \(-0.439237\pi\)
0.189734 + 0.981836i \(0.439237\pi\)
\(572\) 0 0
\(573\) 26.5100 1.10747
\(574\) 0 0
\(575\) 3.70151 0.154364
\(576\) 0 0
\(577\) −13.1045 −0.545548 −0.272774 0.962078i \(-0.587941\pi\)
−0.272774 + 0.962078i \(0.587941\pi\)
\(578\) 0 0
\(579\) 58.4766 2.43021
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 23.1910 0.960474
\(584\) 0 0
\(585\) −5.91501 −0.244555
\(586\) 0 0
\(587\) −34.7207 −1.43308 −0.716538 0.697548i \(-0.754274\pi\)
−0.716538 + 0.697548i \(0.754274\pi\)
\(588\) 0 0
\(589\) 19.9646 0.822629
\(590\) 0 0
\(591\) −27.8248 −1.14456
\(592\) 0 0
\(593\) 0.944182 0.0387729 0.0193864 0.999812i \(-0.493829\pi\)
0.0193864 + 0.999812i \(0.493829\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.16211 0.252198
\(598\) 0 0
\(599\) −9.72293 −0.397268 −0.198634 0.980074i \(-0.563651\pi\)
−0.198634 + 0.980074i \(0.563651\pi\)
\(600\) 0 0
\(601\) 2.61321 0.106595 0.0532976 0.998579i \(-0.483027\pi\)
0.0532976 + 0.998579i \(0.483027\pi\)
\(602\) 0 0
\(603\) −25.2016 −1.02629
\(604\) 0 0
\(605\) 4.25930 0.173165
\(606\) 0 0
\(607\) −6.08841 −0.247121 −0.123560 0.992337i \(-0.539431\pi\)
−0.123560 + 0.992337i \(0.539431\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.15134 −0.248857
\(612\) 0 0
\(613\) −2.42610 −0.0979894 −0.0489947 0.998799i \(-0.515602\pi\)
−0.0489947 + 0.998799i \(0.515602\pi\)
\(614\) 0 0
\(615\) −5.16921 −0.208443
\(616\) 0 0
\(617\) 2.75936 0.111087 0.0555437 0.998456i \(-0.482311\pi\)
0.0555437 + 0.998456i \(0.482311\pi\)
\(618\) 0 0
\(619\) 35.0572 1.40907 0.704534 0.709670i \(-0.251156\pi\)
0.704534 + 0.709670i \(0.251156\pi\)
\(620\) 0 0
\(621\) 0.788199 0.0316293
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −21.7406 −0.869624
\(626\) 0 0
\(627\) 48.9935 1.95661
\(628\) 0 0
\(629\) 56.3065 2.24509
\(630\) 0 0
\(631\) −25.2717 −1.00605 −0.503026 0.864271i \(-0.667780\pi\)
−0.503026 + 0.864271i \(0.667780\pi\)
\(632\) 0 0
\(633\) −41.9402 −1.66697
\(634\) 0 0
\(635\) 8.81193 0.349691
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −9.21028 −0.364353
\(640\) 0 0
\(641\) 4.47393 0.176710 0.0883548 0.996089i \(-0.471839\pi\)
0.0883548 + 0.996089i \(0.471839\pi\)
\(642\) 0 0
\(643\) 31.3398 1.23592 0.617961 0.786209i \(-0.287959\pi\)
0.617961 + 0.786209i \(0.287959\pi\)
\(644\) 0 0
\(645\) 39.5691 1.55803
\(646\) 0 0
\(647\) 28.1114 1.10518 0.552588 0.833455i \(-0.313640\pi\)
0.552588 + 0.833455i \(0.313640\pi\)
\(648\) 0 0
\(649\) 39.9074 1.56650
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.97196 0.194568 0.0972839 0.995257i \(-0.468985\pi\)
0.0972839 + 0.995257i \(0.468985\pi\)
\(654\) 0 0
\(655\) 44.6238 1.74360
\(656\) 0 0
\(657\) −50.4162 −1.96692
\(658\) 0 0
\(659\) −22.9246 −0.893014 −0.446507 0.894780i \(-0.647332\pi\)
−0.446507 + 0.894780i \(0.647332\pi\)
\(660\) 0 0
\(661\) 45.1921 1.75777 0.878884 0.477036i \(-0.158289\pi\)
0.878884 + 0.477036i \(0.158289\pi\)
\(662\) 0 0
\(663\) −14.1260 −0.548607
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.4053 0.402894
\(668\) 0 0
\(669\) 69.3264 2.68031
\(670\) 0 0
\(671\) −29.4722 −1.13776
\(672\) 0 0
\(673\) 47.6558 1.83700 0.918498 0.395426i \(-0.129403\pi\)
0.918498 + 0.395426i \(0.129403\pi\)
\(674\) 0 0
\(675\) 0.0725580 0.00279276
\(676\) 0 0
\(677\) 10.8310 0.416270 0.208135 0.978100i \(-0.433261\pi\)
0.208135 + 0.978100i \(0.433261\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −29.1965 −1.11881
\(682\) 0 0
\(683\) −14.1592 −0.541787 −0.270893 0.962609i \(-0.587319\pi\)
−0.270893 + 0.962609i \(0.587319\pi\)
\(684\) 0 0
\(685\) −1.35054 −0.0516016
\(686\) 0 0
\(687\) 48.8080 1.86214
\(688\) 0 0
\(689\) −7.14329 −0.272138
\(690\) 0 0
\(691\) 2.50530 0.0953061 0.0476530 0.998864i \(-0.484826\pi\)
0.0476530 + 0.998864i \(0.484826\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.44299 −0.130600
\(696\) 0 0
\(697\) −6.22399 −0.235750
\(698\) 0 0
\(699\) −28.1149 −1.06340
\(700\) 0 0
\(701\) −11.8134 −0.446185 −0.223092 0.974797i \(-0.571615\pi\)
−0.223092 + 0.974797i \(0.571615\pi\)
\(702\) 0 0
\(703\) 60.1531 2.26872
\(704\) 0 0
\(705\) −34.4622 −1.29792
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 26.5103 0.995614 0.497807 0.867288i \(-0.334139\pi\)
0.497807 + 0.867288i \(0.334139\pi\)
\(710\) 0 0
\(711\) 0.590190 0.0221339
\(712\) 0 0
\(713\) −19.0396 −0.713040
\(714\) 0 0
\(715\) 5.80836 0.217220
\(716\) 0 0
\(717\) −11.8341 −0.441952
\(718\) 0 0
\(719\) −17.0081 −0.634294 −0.317147 0.948376i \(-0.602725\pi\)
−0.317147 + 0.948376i \(0.602725\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 25.0816 0.932794
\(724\) 0 0
\(725\) 0.957864 0.0355742
\(726\) 0 0
\(727\) −2.07621 −0.0770025 −0.0385013 0.999259i \(-0.512258\pi\)
−0.0385013 + 0.999259i \(0.512258\pi\)
\(728\) 0 0
\(729\) −27.9018 −1.03340
\(730\) 0 0
\(731\) 47.6432 1.76215
\(732\) 0 0
\(733\) −31.9911 −1.18162 −0.590808 0.806812i \(-0.701191\pi\)
−0.590808 + 0.806812i \(0.701191\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.7472 0.911576
\(738\) 0 0
\(739\) 10.3436 0.380494 0.190247 0.981736i \(-0.439071\pi\)
0.190247 + 0.981736i \(0.439071\pi\)
\(740\) 0 0
\(741\) −15.0910 −0.554380
\(742\) 0 0
\(743\) 24.2982 0.891415 0.445707 0.895179i \(-0.352952\pi\)
0.445707 + 0.895179i \(0.352952\pi\)
\(744\) 0 0
\(745\) −18.0316 −0.660628
\(746\) 0 0
\(747\) 5.65887 0.207047
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 37.0572 1.35224 0.676118 0.736793i \(-0.263661\pi\)
0.676118 + 0.736793i \(0.263661\pi\)
\(752\) 0 0
\(753\) 7.83807 0.285635
\(754\) 0 0
\(755\) −14.3833 −0.523460
\(756\) 0 0
\(757\) 18.8750 0.686023 0.343011 0.939331i \(-0.388553\pi\)
0.343011 + 0.939331i \(0.388553\pi\)
\(758\) 0 0
\(759\) −46.7235 −1.69596
\(760\) 0 0
\(761\) 23.3925 0.847978 0.423989 0.905667i \(-0.360630\pi\)
0.423989 + 0.905667i \(0.360630\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −39.8999 −1.44259
\(766\) 0 0
\(767\) −12.2923 −0.443848
\(768\) 0 0
\(769\) 1.63351 0.0589060 0.0294530 0.999566i \(-0.490623\pi\)
0.0294530 + 0.999566i \(0.490623\pi\)
\(770\) 0 0
\(771\) −58.2207 −2.09677
\(772\) 0 0
\(773\) 5.51626 0.198406 0.0992031 0.995067i \(-0.468371\pi\)
0.0992031 + 0.995067i \(0.468371\pi\)
\(774\) 0 0
\(775\) −1.75270 −0.0629589
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.64918 −0.238231
\(780\) 0 0
\(781\) 9.04421 0.323627
\(782\) 0 0
\(783\) 0.203967 0.00728919
\(784\) 0 0
\(785\) −19.4160 −0.692986
\(786\) 0 0
\(787\) 52.7979 1.88204 0.941022 0.338347i \(-0.109868\pi\)
0.941022 + 0.338347i \(0.109868\pi\)
\(788\) 0 0
\(789\) 43.0547 1.53279
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 9.07802 0.322370
\(794\) 0 0
\(795\) −40.0194 −1.41934
\(796\) 0 0
\(797\) −38.4437 −1.36174 −0.680872 0.732402i \(-0.738399\pi\)
−0.680872 + 0.732402i \(0.738399\pi\)
\(798\) 0 0
\(799\) −41.4942 −1.46796
\(800\) 0 0
\(801\) 3.11953 0.110223
\(802\) 0 0
\(803\) 49.5072 1.74707
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −59.9039 −2.10872
\(808\) 0 0
\(809\) 8.92193 0.313678 0.156839 0.987624i \(-0.449870\pi\)
0.156839 + 0.987624i \(0.449870\pi\)
\(810\) 0 0
\(811\) 15.1790 0.533006 0.266503 0.963834i \(-0.414132\pi\)
0.266503 + 0.963834i \(0.414132\pi\)
\(812\) 0 0
\(813\) −15.2921 −0.536318
\(814\) 0 0
\(815\) −24.7292 −0.866225
\(816\) 0 0
\(817\) 50.8979 1.78069
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 32.8558 1.14668 0.573338 0.819319i \(-0.305648\pi\)
0.573338 + 0.819319i \(0.305648\pi\)
\(822\) 0 0
\(823\) −24.8271 −0.865418 −0.432709 0.901534i \(-0.642442\pi\)
−0.432709 + 0.901534i \(0.642442\pi\)
\(824\) 0 0
\(825\) −4.30116 −0.149747
\(826\) 0 0
\(827\) 46.9638 1.63309 0.816546 0.577281i \(-0.195886\pi\)
0.816546 + 0.577281i \(0.195886\pi\)
\(828\) 0 0
\(829\) 21.7377 0.754982 0.377491 0.926013i \(-0.376787\pi\)
0.377491 + 0.926013i \(0.376787\pi\)
\(830\) 0 0
\(831\) 6.83605 0.237140
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 8.91973 0.308680
\(836\) 0 0
\(837\) −0.373220 −0.0129004
\(838\) 0 0
\(839\) −49.7400 −1.71722 −0.858608 0.512632i \(-0.828670\pi\)
−0.858608 + 0.512632i \(0.828670\pi\)
\(840\) 0 0
\(841\) −26.3074 −0.907150
\(842\) 0 0
\(843\) −52.3448 −1.80285
\(844\) 0 0
\(845\) 25.5303 0.878269
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 40.7912 1.39995
\(850\) 0 0
\(851\) −57.3660 −1.96648
\(852\) 0 0
\(853\) 17.1076 0.585753 0.292876 0.956150i \(-0.405388\pi\)
0.292876 + 0.956150i \(0.405388\pi\)
\(854\) 0 0
\(855\) −42.6257 −1.45777
\(856\) 0 0
\(857\) −24.6162 −0.840873 −0.420437 0.907322i \(-0.638123\pi\)
−0.420437 + 0.907322i \(0.638123\pi\)
\(858\) 0 0
\(859\) −32.5001 −1.10889 −0.554445 0.832220i \(-0.687069\pi\)
−0.554445 + 0.832220i \(0.687069\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −24.6514 −0.839143 −0.419572 0.907722i \(-0.637820\pi\)
−0.419572 + 0.907722i \(0.637820\pi\)
\(864\) 0 0
\(865\) 49.5465 1.68463
\(866\) 0 0
\(867\) −53.4709 −1.81597
\(868\) 0 0
\(869\) −0.579548 −0.0196598
\(870\) 0 0
\(871\) −7.62263 −0.258283
\(872\) 0 0
\(873\) 53.4063 1.80753
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 55.9313 1.88867 0.944333 0.328991i \(-0.106709\pi\)
0.944333 + 0.328991i \(0.106709\pi\)
\(878\) 0 0
\(879\) 18.3212 0.617960
\(880\) 0 0
\(881\) −4.22704 −0.142413 −0.0712064 0.997462i \(-0.522685\pi\)
−0.0712064 + 0.997462i \(0.522685\pi\)
\(882\) 0 0
\(883\) −9.46057 −0.318374 −0.159187 0.987248i \(-0.550887\pi\)
−0.159187 + 0.987248i \(0.550887\pi\)
\(884\) 0 0
\(885\) −68.8659 −2.31490
\(886\) 0 0
\(887\) −18.4890 −0.620800 −0.310400 0.950606i \(-0.600463\pi\)
−0.310400 + 0.950606i \(0.600463\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 26.4980 0.887717
\(892\) 0 0
\(893\) −44.3288 −1.48341
\(894\) 0 0
\(895\) 8.30029 0.277448
\(896\) 0 0
\(897\) 14.3917 0.480527
\(898\) 0 0
\(899\) −4.92700 −0.164325
\(900\) 0 0
\(901\) −48.1854 −1.60529
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −25.6016 −0.851025
\(906\) 0 0
\(907\) −56.4241 −1.87353 −0.936766 0.349955i \(-0.886197\pi\)
−0.936766 + 0.349955i \(0.886197\pi\)
\(908\) 0 0
\(909\) 37.8241 1.25455
\(910\) 0 0
\(911\) 11.9011 0.394300 0.197150 0.980373i \(-0.436831\pi\)
0.197150 + 0.980373i \(0.436831\pi\)
\(912\) 0 0
\(913\) −5.55684 −0.183905
\(914\) 0 0
\(915\) 50.8585 1.68133
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 9.13243 0.301251 0.150626 0.988591i \(-0.451871\pi\)
0.150626 + 0.988591i \(0.451871\pi\)
\(920\) 0 0
\(921\) −40.0261 −1.31890
\(922\) 0 0
\(923\) −2.78579 −0.0916955
\(924\) 0 0
\(925\) −5.28086 −0.173634
\(926\) 0 0
\(927\) 38.8234 1.27513
\(928\) 0 0
\(929\) 3.42592 0.112401 0.0562003 0.998420i \(-0.482101\pi\)
0.0562003 + 0.998420i \(0.482101\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −42.2892 −1.38449
\(934\) 0 0
\(935\) 39.1805 1.28134
\(936\) 0 0
\(937\) 40.9422 1.33752 0.668761 0.743477i \(-0.266825\pi\)
0.668761 + 0.743477i \(0.266825\pi\)
\(938\) 0 0
\(939\) −62.7238 −2.04691
\(940\) 0 0
\(941\) −1.97770 −0.0644712 −0.0322356 0.999480i \(-0.510263\pi\)
−0.0322356 + 0.999480i \(0.510263\pi\)
\(942\) 0 0
\(943\) 6.34110 0.206495
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 25.4560 0.827207 0.413604 0.910457i \(-0.364270\pi\)
0.413604 + 0.910457i \(0.364270\pi\)
\(948\) 0 0
\(949\) −15.2492 −0.495009
\(950\) 0 0
\(951\) −25.9690 −0.842102
\(952\) 0 0
\(953\) −40.4963 −1.31180 −0.655902 0.754846i \(-0.727711\pi\)
−0.655902 + 0.754846i \(0.727711\pi\)
\(954\) 0 0
\(955\) 22.6485 0.732889
\(956\) 0 0
\(957\) −12.0909 −0.390844
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −21.9846 −0.709179
\(962\) 0 0
\(963\) −15.0085 −0.483641
\(964\) 0 0
\(965\) 49.9589 1.60823
\(966\) 0 0
\(967\) 23.0567 0.741454 0.370727 0.928742i \(-0.379109\pi\)
0.370727 + 0.928742i \(0.379109\pi\)
\(968\) 0 0
\(969\) −101.797 −3.27018
\(970\) 0 0
\(971\) 3.38223 0.108541 0.0542705 0.998526i \(-0.482717\pi\)
0.0542705 + 0.998526i \(0.482717\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 1.32484 0.0424288
\(976\) 0 0
\(977\) 18.6374 0.596263 0.298132 0.954525i \(-0.403637\pi\)
0.298132 + 0.954525i \(0.403637\pi\)
\(978\) 0 0
\(979\) −3.06328 −0.0979028
\(980\) 0 0
\(981\) −27.5129 −0.878421
\(982\) 0 0
\(983\) 53.6211 1.71025 0.855123 0.518425i \(-0.173481\pi\)
0.855123 + 0.518425i \(0.173481\pi\)
\(984\) 0 0
\(985\) −23.7719 −0.757435
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −48.5396 −1.54347
\(990\) 0 0
\(991\) 46.1420 1.46575 0.732875 0.680363i \(-0.238178\pi\)
0.732875 + 0.680363i \(0.238178\pi\)
\(992\) 0 0
\(993\) −20.6746 −0.656089
\(994\) 0 0
\(995\) 5.26454 0.166897
\(996\) 0 0
\(997\) −10.7038 −0.338993 −0.169496 0.985531i \(-0.554214\pi\)
−0.169496 + 0.985531i \(0.554214\pi\)
\(998\) 0 0
\(999\) −1.12450 −0.0355777
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 \(a_p\))