Properties

Label 8036.2.a.t.1.18
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 1.18
Root \(2.83122\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.83122 q^{3}\) \(-2.22134 q^{5}\) \(+5.01578 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.83122 q^{3}\) \(-2.22134 q^{5}\) \(+5.01578 q^{9}\) \(-1.51529 q^{11}\) \(+6.85001 q^{13}\) \(-6.28908 q^{15}\) \(+1.59524 q^{17}\) \(-2.36268 q^{19}\) \(+4.25612 q^{23}\) \(-0.0656660 q^{25}\) \(+5.70711 q^{27}\) \(+1.45086 q^{29}\) \(+2.09156 q^{31}\) \(-4.29011 q^{33}\) \(+7.96332 q^{37}\) \(+19.3939 q^{39}\) \(-1.00000 q^{41}\) \(+3.59001 q^{43}\) \(-11.1417 q^{45}\) \(-6.92760 q^{47}\) \(+4.51646 q^{51}\) \(-7.14984 q^{53}\) \(+3.36596 q^{55}\) \(-6.68926 q^{57}\) \(-3.14694 q^{59}\) \(+3.64717 q^{61}\) \(-15.2162 q^{65}\) \(+8.76983 q^{67}\) \(+12.0500 q^{69}\) \(-0.569520 q^{71}\) \(+3.79458 q^{73}\) \(-0.185915 q^{75}\) \(-11.7557 q^{79}\) \(+1.11072 q^{81}\) \(-5.82845 q^{83}\) \(-3.54356 q^{85}\) \(+4.10769 q^{87}\) \(+10.9595 q^{89}\) \(+5.92165 q^{93}\) \(+5.24831 q^{95}\) \(+14.3858 q^{97}\) \(-7.60035 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.83122 1.63460 0.817302 0.576210i \(-0.195469\pi\)
0.817302 + 0.576210i \(0.195469\pi\)
\(4\) 0 0
\(5\) −2.22134 −0.993412 −0.496706 0.867919i \(-0.665457\pi\)
−0.496706 + 0.867919i \(0.665457\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 5.01578 1.67193
\(10\) 0 0
\(11\) −1.51529 −0.456876 −0.228438 0.973558i \(-0.573362\pi\)
−0.228438 + 0.973558i \(0.573362\pi\)
\(12\) 0 0
\(13\) 6.85001 1.89985 0.949925 0.312477i \(-0.101159\pi\)
0.949925 + 0.312477i \(0.101159\pi\)
\(14\) 0 0
\(15\) −6.28908 −1.62383
\(16\) 0 0
\(17\) 1.59524 0.386902 0.193451 0.981110i \(-0.438032\pi\)
0.193451 + 0.981110i \(0.438032\pi\)
\(18\) 0 0
\(19\) −2.36268 −0.542036 −0.271018 0.962574i \(-0.587360\pi\)
−0.271018 + 0.962574i \(0.587360\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.25612 0.887463 0.443732 0.896160i \(-0.353654\pi\)
0.443732 + 0.896160i \(0.353654\pi\)
\(24\) 0 0
\(25\) −0.0656660 −0.0131332
\(26\) 0 0
\(27\) 5.70711 1.09833
\(28\) 0 0
\(29\) 1.45086 0.269417 0.134709 0.990885i \(-0.456990\pi\)
0.134709 + 0.990885i \(0.456990\pi\)
\(30\) 0 0
\(31\) 2.09156 0.375655 0.187827 0.982202i \(-0.439855\pi\)
0.187827 + 0.982202i \(0.439855\pi\)
\(32\) 0 0
\(33\) −4.29011 −0.746811
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.96332 1.30916 0.654581 0.755992i \(-0.272845\pi\)
0.654581 + 0.755992i \(0.272845\pi\)
\(38\) 0 0
\(39\) 19.3939 3.10550
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 3.59001 0.547472 0.273736 0.961805i \(-0.411741\pi\)
0.273736 + 0.961805i \(0.411741\pi\)
\(44\) 0 0
\(45\) −11.1417 −1.66091
\(46\) 0 0
\(47\) −6.92760 −1.01049 −0.505247 0.862974i \(-0.668599\pi\)
−0.505247 + 0.862974i \(0.668599\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.51646 0.632431
\(52\) 0 0
\(53\) −7.14984 −0.982106 −0.491053 0.871130i \(-0.663388\pi\)
−0.491053 + 0.871130i \(0.663388\pi\)
\(54\) 0 0
\(55\) 3.36596 0.453866
\(56\) 0 0
\(57\) −6.68926 −0.886014
\(58\) 0 0
\(59\) −3.14694 −0.409697 −0.204848 0.978794i \(-0.565670\pi\)
−0.204848 + 0.978794i \(0.565670\pi\)
\(60\) 0 0
\(61\) 3.64717 0.466972 0.233486 0.972360i \(-0.424987\pi\)
0.233486 + 0.972360i \(0.424987\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −15.2162 −1.88733
\(66\) 0 0
\(67\) 8.76983 1.07141 0.535703 0.844407i \(-0.320047\pi\)
0.535703 + 0.844407i \(0.320047\pi\)
\(68\) 0 0
\(69\) 12.0500 1.45065
\(70\) 0 0
\(71\) −0.569520 −0.0675896 −0.0337948 0.999429i \(-0.510759\pi\)
−0.0337948 + 0.999429i \(0.510759\pi\)
\(72\) 0 0
\(73\) 3.79458 0.444122 0.222061 0.975033i \(-0.428722\pi\)
0.222061 + 0.975033i \(0.428722\pi\)
\(74\) 0 0
\(75\) −0.185915 −0.0214676
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.7557 −1.32262 −0.661308 0.750115i \(-0.729998\pi\)
−0.661308 + 0.750115i \(0.729998\pi\)
\(80\) 0 0
\(81\) 1.11072 0.123413
\(82\) 0 0
\(83\) −5.82845 −0.639755 −0.319878 0.947459i \(-0.603642\pi\)
−0.319878 + 0.947459i \(0.603642\pi\)
\(84\) 0 0
\(85\) −3.54356 −0.384353
\(86\) 0 0
\(87\) 4.10769 0.440390
\(88\) 0 0
\(89\) 10.9595 1.16170 0.580850 0.814011i \(-0.302720\pi\)
0.580850 + 0.814011i \(0.302720\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.92165 0.614046
\(94\) 0 0
\(95\) 5.24831 0.538465
\(96\) 0 0
\(97\) 14.3858 1.46065 0.730327 0.683098i \(-0.239368\pi\)
0.730327 + 0.683098i \(0.239368\pi\)
\(98\) 0 0
\(99\) −7.60035 −0.763864
\(100\) 0 0
\(101\) 10.9232 1.08690 0.543448 0.839443i \(-0.317118\pi\)
0.543448 + 0.839443i \(0.317118\pi\)
\(102\) 0 0
\(103\) −10.3706 −1.02184 −0.510922 0.859627i \(-0.670696\pi\)
−0.510922 + 0.859627i \(0.670696\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.1998 −1.08272 −0.541361 0.840790i \(-0.682091\pi\)
−0.541361 + 0.840790i \(0.682091\pi\)
\(108\) 0 0
\(109\) 11.8977 1.13959 0.569797 0.821785i \(-0.307022\pi\)
0.569797 + 0.821785i \(0.307022\pi\)
\(110\) 0 0
\(111\) 22.5459 2.13996
\(112\) 0 0
\(113\) 11.9048 1.11991 0.559955 0.828523i \(-0.310818\pi\)
0.559955 + 0.828523i \(0.310818\pi\)
\(114\) 0 0
\(115\) −9.45428 −0.881616
\(116\) 0 0
\(117\) 34.3581 3.17641
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.70390 −0.791264
\(122\) 0 0
\(123\) −2.83122 −0.255282
\(124\) 0 0
\(125\) 11.2525 1.00646
\(126\) 0 0
\(127\) 11.2729 1.00030 0.500152 0.865938i \(-0.333277\pi\)
0.500152 + 0.865938i \(0.333277\pi\)
\(128\) 0 0
\(129\) 10.1641 0.894899
\(130\) 0 0
\(131\) −1.74407 −0.152380 −0.0761900 0.997093i \(-0.524276\pi\)
−0.0761900 + 0.997093i \(0.524276\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −12.6774 −1.09110
\(136\) 0 0
\(137\) 19.1965 1.64007 0.820035 0.572313i \(-0.193954\pi\)
0.820035 + 0.572313i \(0.193954\pi\)
\(138\) 0 0
\(139\) 2.65539 0.225227 0.112614 0.993639i \(-0.464078\pi\)
0.112614 + 0.993639i \(0.464078\pi\)
\(140\) 0 0
\(141\) −19.6135 −1.65176
\(142\) 0 0
\(143\) −10.3797 −0.867997
\(144\) 0 0
\(145\) −3.22284 −0.267642
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.6148 −1.27922 −0.639608 0.768701i \(-0.720903\pi\)
−0.639608 + 0.768701i \(0.720903\pi\)
\(150\) 0 0
\(151\) 17.8020 1.44871 0.724353 0.689429i \(-0.242139\pi\)
0.724353 + 0.689429i \(0.242139\pi\)
\(152\) 0 0
\(153\) 8.00136 0.646871
\(154\) 0 0
\(155\) −4.64605 −0.373180
\(156\) 0 0
\(157\) 6.72031 0.536339 0.268169 0.963372i \(-0.413581\pi\)
0.268169 + 0.963372i \(0.413581\pi\)
\(158\) 0 0
\(159\) −20.2427 −1.60535
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.87978 0.225562 0.112781 0.993620i \(-0.464024\pi\)
0.112781 + 0.993620i \(0.464024\pi\)
\(164\) 0 0
\(165\) 9.52977 0.741891
\(166\) 0 0
\(167\) −0.494722 −0.0382827 −0.0191414 0.999817i \(-0.506093\pi\)
−0.0191414 + 0.999817i \(0.506093\pi\)
\(168\) 0 0
\(169\) 33.9226 2.60943
\(170\) 0 0
\(171\) −11.8507 −0.906245
\(172\) 0 0
\(173\) −1.30778 −0.0994283 −0.0497142 0.998763i \(-0.515831\pi\)
−0.0497142 + 0.998763i \(0.515831\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.90967 −0.669692
\(178\) 0 0
\(179\) 9.65003 0.721277 0.360639 0.932706i \(-0.382559\pi\)
0.360639 + 0.932706i \(0.382559\pi\)
\(180\) 0 0
\(181\) 5.06514 0.376489 0.188244 0.982122i \(-0.439720\pi\)
0.188244 + 0.982122i \(0.439720\pi\)
\(182\) 0 0
\(183\) 10.3259 0.763315
\(184\) 0 0
\(185\) −17.6892 −1.30054
\(186\) 0 0
\(187\) −2.41724 −0.176766
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.83889 −0.277773 −0.138886 0.990308i \(-0.544352\pi\)
−0.138886 + 0.990308i \(0.544352\pi\)
\(192\) 0 0
\(193\) 4.78954 0.344759 0.172379 0.985031i \(-0.444854\pi\)
0.172379 + 0.985031i \(0.444854\pi\)
\(194\) 0 0
\(195\) −43.0803 −3.08504
\(196\) 0 0
\(197\) −3.95862 −0.282040 −0.141020 0.990007i \(-0.545038\pi\)
−0.141020 + 0.990007i \(0.545038\pi\)
\(198\) 0 0
\(199\) −1.69274 −0.119995 −0.0599975 0.998199i \(-0.519109\pi\)
−0.0599975 + 0.998199i \(0.519109\pi\)
\(200\) 0 0
\(201\) 24.8293 1.75132
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.22134 0.155145
\(206\) 0 0
\(207\) 21.3478 1.48377
\(208\) 0 0
\(209\) 3.58014 0.247643
\(210\) 0 0
\(211\) −11.7471 −0.808701 −0.404350 0.914604i \(-0.632502\pi\)
−0.404350 + 0.914604i \(0.632502\pi\)
\(212\) 0 0
\(213\) −1.61243 −0.110482
\(214\) 0 0
\(215\) −7.97462 −0.543865
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.7433 0.725964
\(220\) 0 0
\(221\) 10.9274 0.735055
\(222\) 0 0
\(223\) 8.88732 0.595139 0.297569 0.954700i \(-0.403824\pi\)
0.297569 + 0.954700i \(0.403824\pi\)
\(224\) 0 0
\(225\) −0.329366 −0.0219578
\(226\) 0 0
\(227\) 21.1796 1.40574 0.702869 0.711320i \(-0.251902\pi\)
0.702869 + 0.711320i \(0.251902\pi\)
\(228\) 0 0
\(229\) 2.00178 0.132281 0.0661407 0.997810i \(-0.478931\pi\)
0.0661407 + 0.997810i \(0.478931\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.98056 0.391800 0.195900 0.980624i \(-0.437237\pi\)
0.195900 + 0.980624i \(0.437237\pi\)
\(234\) 0 0
\(235\) 15.3885 1.00384
\(236\) 0 0
\(237\) −33.2828 −2.16195
\(238\) 0 0
\(239\) −23.4140 −1.51452 −0.757262 0.653111i \(-0.773464\pi\)
−0.757262 + 0.653111i \(0.773464\pi\)
\(240\) 0 0
\(241\) 3.59352 0.231479 0.115739 0.993280i \(-0.463076\pi\)
0.115739 + 0.993280i \(0.463076\pi\)
\(242\) 0 0
\(243\) −13.9767 −0.896603
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −16.1844 −1.02979
\(248\) 0 0
\(249\) −16.5016 −1.04575
\(250\) 0 0
\(251\) 24.0715 1.51938 0.759690 0.650285i \(-0.225351\pi\)
0.759690 + 0.650285i \(0.225351\pi\)
\(252\) 0 0
\(253\) −6.44925 −0.405461
\(254\) 0 0
\(255\) −10.0326 −0.628264
\(256\) 0 0
\(257\) 12.0453 0.751367 0.375684 0.926748i \(-0.377408\pi\)
0.375684 + 0.926748i \(0.377408\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 7.27718 0.450446
\(262\) 0 0
\(263\) −22.8321 −1.40789 −0.703944 0.710256i \(-0.748579\pi\)
−0.703944 + 0.710256i \(0.748579\pi\)
\(264\) 0 0
\(265\) 15.8822 0.975635
\(266\) 0 0
\(267\) 31.0286 1.89892
\(268\) 0 0
\(269\) −11.3375 −0.691260 −0.345630 0.938371i \(-0.612335\pi\)
−0.345630 + 0.938371i \(0.612335\pi\)
\(270\) 0 0
\(271\) −20.4018 −1.23932 −0.619661 0.784870i \(-0.712730\pi\)
−0.619661 + 0.784870i \(0.712730\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.0995029 0.00600025
\(276\) 0 0
\(277\) −31.9214 −1.91797 −0.958987 0.283451i \(-0.908521\pi\)
−0.958987 + 0.283451i \(0.908521\pi\)
\(278\) 0 0
\(279\) 10.4908 0.628067
\(280\) 0 0
\(281\) 23.4883 1.40120 0.700598 0.713556i \(-0.252917\pi\)
0.700598 + 0.713556i \(0.252917\pi\)
\(282\) 0 0
\(283\) 21.4651 1.27597 0.637985 0.770049i \(-0.279768\pi\)
0.637985 + 0.770049i \(0.279768\pi\)
\(284\) 0 0
\(285\) 14.8591 0.880176
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −14.4552 −0.850307
\(290\) 0 0
\(291\) 40.7292 2.38759
\(292\) 0 0
\(293\) −15.4975 −0.905372 −0.452686 0.891670i \(-0.649534\pi\)
−0.452686 + 0.891670i \(0.649534\pi\)
\(294\) 0 0
\(295\) 6.99041 0.406998
\(296\) 0 0
\(297\) −8.64791 −0.501803
\(298\) 0 0
\(299\) 29.1545 1.68605
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 30.9258 1.77664
\(304\) 0 0
\(305\) −8.10159 −0.463896
\(306\) 0 0
\(307\) 0.628626 0.0358776 0.0179388 0.999839i \(-0.494290\pi\)
0.0179388 + 0.999839i \(0.494290\pi\)
\(308\) 0 0
\(309\) −29.3614 −1.67031
\(310\) 0 0
\(311\) 25.0846 1.42242 0.711209 0.702981i \(-0.248148\pi\)
0.711209 + 0.702981i \(0.248148\pi\)
\(312\) 0 0
\(313\) 6.85414 0.387419 0.193709 0.981059i \(-0.437948\pi\)
0.193709 + 0.981059i \(0.437948\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −20.8442 −1.17072 −0.585362 0.810772i \(-0.699048\pi\)
−0.585362 + 0.810772i \(0.699048\pi\)
\(318\) 0 0
\(319\) −2.19847 −0.123090
\(320\) 0 0
\(321\) −31.7089 −1.76982
\(322\) 0 0
\(323\) −3.76903 −0.209715
\(324\) 0 0
\(325\) −0.449813 −0.0249511
\(326\) 0 0
\(327\) 33.6850 1.86278
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.72356 −0.424525 −0.212263 0.977213i \(-0.568083\pi\)
−0.212263 + 0.977213i \(0.568083\pi\)
\(332\) 0 0
\(333\) 39.9422 2.18882
\(334\) 0 0
\(335\) −19.4807 −1.06435
\(336\) 0 0
\(337\) 19.0522 1.03784 0.518918 0.854824i \(-0.326335\pi\)
0.518918 + 0.854824i \(0.326335\pi\)
\(338\) 0 0
\(339\) 33.7051 1.83061
\(340\) 0 0
\(341\) −3.16931 −0.171628
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −26.7671 −1.44109
\(346\) 0 0
\(347\) 10.6948 0.574128 0.287064 0.957911i \(-0.407321\pi\)
0.287064 + 0.957911i \(0.407321\pi\)
\(348\) 0 0
\(349\) 28.9559 1.54998 0.774988 0.631976i \(-0.217756\pi\)
0.774988 + 0.631976i \(0.217756\pi\)
\(350\) 0 0
\(351\) 39.0938 2.08667
\(352\) 0 0
\(353\) 12.2613 0.652605 0.326302 0.945265i \(-0.394197\pi\)
0.326302 + 0.945265i \(0.394197\pi\)
\(354\) 0 0
\(355\) 1.26510 0.0671443
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 34.9616 1.84520 0.922600 0.385757i \(-0.126060\pi\)
0.922600 + 0.385757i \(0.126060\pi\)
\(360\) 0 0
\(361\) −13.4177 −0.706197
\(362\) 0 0
\(363\) −24.6426 −1.29340
\(364\) 0 0
\(365\) −8.42904 −0.441196
\(366\) 0 0
\(367\) −16.0566 −0.838147 −0.419074 0.907952i \(-0.637645\pi\)
−0.419074 + 0.907952i \(0.637645\pi\)
\(368\) 0 0
\(369\) −5.01578 −0.261111
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 36.0911 1.86872 0.934362 0.356325i \(-0.115971\pi\)
0.934362 + 0.356325i \(0.115971\pi\)
\(374\) 0 0
\(375\) 31.8584 1.64516
\(376\) 0 0
\(377\) 9.93838 0.511853
\(378\) 0 0
\(379\) −24.3348 −1.24999 −0.624996 0.780628i \(-0.714900\pi\)
−0.624996 + 0.780628i \(0.714900\pi\)
\(380\) 0 0
\(381\) 31.9159 1.63510
\(382\) 0 0
\(383\) 7.18694 0.367235 0.183618 0.982998i \(-0.441219\pi\)
0.183618 + 0.982998i \(0.441219\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 18.0067 0.915332
\(388\) 0 0
\(389\) −30.8869 −1.56603 −0.783013 0.622005i \(-0.786318\pi\)
−0.783013 + 0.622005i \(0.786318\pi\)
\(390\) 0 0
\(391\) 6.78952 0.343361
\(392\) 0 0
\(393\) −4.93784 −0.249081
\(394\) 0 0
\(395\) 26.1133 1.31390
\(396\) 0 0
\(397\) −20.4967 −1.02870 −0.514349 0.857581i \(-0.671966\pi\)
−0.514349 + 0.857581i \(0.671966\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.81685 −0.190605 −0.0953023 0.995448i \(-0.530382\pi\)
−0.0953023 + 0.995448i \(0.530382\pi\)
\(402\) 0 0
\(403\) 14.3272 0.713687
\(404\) 0 0
\(405\) −2.46727 −0.122600
\(406\) 0 0
\(407\) −12.0667 −0.598125
\(408\) 0 0
\(409\) −7.48011 −0.369867 −0.184934 0.982751i \(-0.559207\pi\)
−0.184934 + 0.982751i \(0.559207\pi\)
\(410\) 0 0
\(411\) 54.3495 2.68086
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.9469 0.635540
\(416\) 0 0
\(417\) 7.51798 0.368157
\(418\) 0 0
\(419\) −12.6338 −0.617202 −0.308601 0.951192i \(-0.599861\pi\)
−0.308601 + 0.951192i \(0.599861\pi\)
\(420\) 0 0
\(421\) −22.5003 −1.09660 −0.548299 0.836282i \(-0.684724\pi\)
−0.548299 + 0.836282i \(0.684724\pi\)
\(422\) 0 0
\(423\) −34.7473 −1.68947
\(424\) 0 0
\(425\) −0.104753 −0.00508126
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −29.3873 −1.41883
\(430\) 0 0
\(431\) 5.30910 0.255730 0.127865 0.991792i \(-0.459188\pi\)
0.127865 + 0.991792i \(0.459188\pi\)
\(432\) 0 0
\(433\) −17.2278 −0.827916 −0.413958 0.910296i \(-0.635854\pi\)
−0.413958 + 0.910296i \(0.635854\pi\)
\(434\) 0 0
\(435\) −9.12456 −0.437489
\(436\) 0 0
\(437\) −10.0559 −0.481037
\(438\) 0 0
\(439\) −21.7108 −1.03620 −0.518100 0.855320i \(-0.673361\pi\)
−0.518100 + 0.855320i \(0.673361\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.3891 0.921206 0.460603 0.887606i \(-0.347633\pi\)
0.460603 + 0.887606i \(0.347633\pi\)
\(444\) 0 0
\(445\) −24.3446 −1.15405
\(446\) 0 0
\(447\) −44.2089 −2.09101
\(448\) 0 0
\(449\) −27.0936 −1.27863 −0.639314 0.768946i \(-0.720782\pi\)
−0.639314 + 0.768946i \(0.720782\pi\)
\(450\) 0 0
\(451\) 1.51529 0.0713521
\(452\) 0 0
\(453\) 50.4013 2.36806
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 31.1428 1.45680 0.728400 0.685152i \(-0.240264\pi\)
0.728400 + 0.685152i \(0.240264\pi\)
\(458\) 0 0
\(459\) 9.10419 0.424947
\(460\) 0 0
\(461\) 25.5523 1.19009 0.595045 0.803692i \(-0.297134\pi\)
0.595045 + 0.803692i \(0.297134\pi\)
\(462\) 0 0
\(463\) −18.7078 −0.869424 −0.434712 0.900570i \(-0.643150\pi\)
−0.434712 + 0.900570i \(0.643150\pi\)
\(464\) 0 0
\(465\) −13.1540 −0.610000
\(466\) 0 0
\(467\) 25.3853 1.17469 0.587346 0.809336i \(-0.300173\pi\)
0.587346 + 0.809336i \(0.300173\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 19.0266 0.876701
\(472\) 0 0
\(473\) −5.43990 −0.250127
\(474\) 0 0
\(475\) 0.155148 0.00711867
\(476\) 0 0
\(477\) −35.8620 −1.64201
\(478\) 0 0
\(479\) −16.4336 −0.750871 −0.375436 0.926848i \(-0.622507\pi\)
−0.375436 + 0.926848i \(0.622507\pi\)
\(480\) 0 0
\(481\) 54.5488 2.48721
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −31.9556 −1.45103
\(486\) 0 0
\(487\) 10.1082 0.458047 0.229023 0.973421i \(-0.426447\pi\)
0.229023 + 0.973421i \(0.426447\pi\)
\(488\) 0 0
\(489\) 8.15328 0.368704
\(490\) 0 0
\(491\) −24.3172 −1.09742 −0.548710 0.836013i \(-0.684881\pi\)
−0.548710 + 0.836013i \(0.684881\pi\)
\(492\) 0 0
\(493\) 2.31446 0.104238
\(494\) 0 0
\(495\) 16.8829 0.758831
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −23.6831 −1.06020 −0.530101 0.847934i \(-0.677846\pi\)
−0.530101 + 0.847934i \(0.677846\pi\)
\(500\) 0 0
\(501\) −1.40066 −0.0625770
\(502\) 0 0
\(503\) −10.4533 −0.466090 −0.233045 0.972466i \(-0.574869\pi\)
−0.233045 + 0.972466i \(0.574869\pi\)
\(504\) 0 0
\(505\) −24.2640 −1.07974
\(506\) 0 0
\(507\) 96.0422 4.26539
\(508\) 0 0
\(509\) 17.6473 0.782201 0.391101 0.920348i \(-0.372094\pi\)
0.391101 + 0.920348i \(0.372094\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −13.4841 −0.595336
\(514\) 0 0
\(515\) 23.0366 1.01511
\(516\) 0 0
\(517\) 10.4973 0.461671
\(518\) 0 0
\(519\) −3.70259 −0.162526
\(520\) 0 0
\(521\) −17.3323 −0.759342 −0.379671 0.925122i \(-0.623963\pi\)
−0.379671 + 0.925122i \(0.623963\pi\)
\(522\) 0 0
\(523\) 19.9734 0.873377 0.436688 0.899613i \(-0.356151\pi\)
0.436688 + 0.899613i \(0.356151\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.33653 0.145341
\(528\) 0 0
\(529\) −4.88541 −0.212409
\(530\) 0 0
\(531\) −15.7844 −0.684983
\(532\) 0 0
\(533\) −6.85001 −0.296707
\(534\) 0 0
\(535\) 24.8784 1.07559
\(536\) 0 0
\(537\) 27.3213 1.17900
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.96600 −0.127518 −0.0637591 0.997965i \(-0.520309\pi\)
−0.0637591 + 0.997965i \(0.520309\pi\)
\(542\) 0 0
\(543\) 14.3405 0.615410
\(544\) 0 0
\(545\) −26.4288 −1.13209
\(546\) 0 0
\(547\) 12.9778 0.554890 0.277445 0.960741i \(-0.410512\pi\)
0.277445 + 0.960741i \(0.410512\pi\)
\(548\) 0 0
\(549\) 18.2934 0.780744
\(550\) 0 0
\(551\) −3.42791 −0.146034
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −50.0819 −2.12586
\(556\) 0 0
\(557\) −41.4658 −1.75696 −0.878482 0.477775i \(-0.841443\pi\)
−0.878482 + 0.477775i \(0.841443\pi\)
\(558\) 0 0
\(559\) 24.5916 1.04011
\(560\) 0 0
\(561\) −6.84373 −0.288943
\(562\) 0 0
\(563\) −34.1455 −1.43906 −0.719531 0.694461i \(-0.755643\pi\)
−0.719531 + 0.694461i \(0.755643\pi\)
\(564\) 0 0
\(565\) −26.4446 −1.11253
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.6113 −0.696380 −0.348190 0.937424i \(-0.613204\pi\)
−0.348190 + 0.937424i \(0.613204\pi\)
\(570\) 0 0
\(571\) −37.7089 −1.57807 −0.789034 0.614350i \(-0.789418\pi\)
−0.789034 + 0.614350i \(0.789418\pi\)
\(572\) 0 0
\(573\) −10.8687 −0.454048
\(574\) 0 0
\(575\) −0.279483 −0.0116552
\(576\) 0 0
\(577\) 42.6424 1.77522 0.887612 0.460591i \(-0.152363\pi\)
0.887612 + 0.460591i \(0.152363\pi\)
\(578\) 0 0
\(579\) 13.5602 0.563544
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.8341 0.448701
\(584\) 0 0
\(585\) −76.3210 −3.15548
\(586\) 0 0
\(587\) 19.7575 0.815478 0.407739 0.913098i \(-0.366317\pi\)
0.407739 + 0.913098i \(0.366317\pi\)
\(588\) 0 0
\(589\) −4.94168 −0.203618
\(590\) 0 0
\(591\) −11.2077 −0.461023
\(592\) 0 0
\(593\) −9.99169 −0.410310 −0.205155 0.978730i \(-0.565770\pi\)
−0.205155 + 0.978730i \(0.565770\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.79250 −0.196144
\(598\) 0 0
\(599\) −26.8488 −1.09701 −0.548507 0.836146i \(-0.684804\pi\)
−0.548507 + 0.836146i \(0.684804\pi\)
\(600\) 0 0
\(601\) 31.4747 1.28388 0.641940 0.766755i \(-0.278130\pi\)
0.641940 + 0.766755i \(0.278130\pi\)
\(602\) 0 0
\(603\) 43.9875 1.79131
\(604\) 0 0
\(605\) 19.3343 0.786051
\(606\) 0 0
\(607\) 17.2489 0.700110 0.350055 0.936729i \(-0.386163\pi\)
0.350055 + 0.936729i \(0.386163\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −47.4542 −1.91979
\(612\) 0 0
\(613\) 43.6203 1.76181 0.880904 0.473295i \(-0.156935\pi\)
0.880904 + 0.473295i \(0.156935\pi\)
\(614\) 0 0
\(615\) 6.28908 0.253600
\(616\) 0 0
\(617\) −26.1497 −1.05275 −0.526373 0.850254i \(-0.676448\pi\)
−0.526373 + 0.850254i \(0.676448\pi\)
\(618\) 0 0
\(619\) 36.2135 1.45554 0.727772 0.685819i \(-0.240556\pi\)
0.727772 + 0.685819i \(0.240556\pi\)
\(620\) 0 0
\(621\) 24.2902 0.974731
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −24.6674 −0.986694
\(626\) 0 0
\(627\) 10.1361 0.404799
\(628\) 0 0
\(629\) 12.7034 0.506517
\(630\) 0 0
\(631\) 27.3123 1.08728 0.543642 0.839317i \(-0.317045\pi\)
0.543642 + 0.839317i \(0.317045\pi\)
\(632\) 0 0
\(633\) −33.2584 −1.32190
\(634\) 0 0
\(635\) −25.0408 −0.993714
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.85659 −0.113005
\(640\) 0 0
\(641\) −32.2351 −1.27321 −0.636605 0.771190i \(-0.719662\pi\)
−0.636605 + 0.771190i \(0.719662\pi\)
\(642\) 0 0
\(643\) −11.7587 −0.463717 −0.231859 0.972749i \(-0.574481\pi\)
−0.231859 + 0.972749i \(0.574481\pi\)
\(644\) 0 0
\(645\) −22.5779 −0.889003
\(646\) 0 0
\(647\) 3.88143 0.152595 0.0762974 0.997085i \(-0.475690\pi\)
0.0762974 + 0.997085i \(0.475690\pi\)
\(648\) 0 0
\(649\) 4.76852 0.187181
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28.5009 −1.11533 −0.557664 0.830067i \(-0.688302\pi\)
−0.557664 + 0.830067i \(0.688302\pi\)
\(654\) 0 0
\(655\) 3.87416 0.151376
\(656\) 0 0
\(657\) 19.0328 0.742540
\(658\) 0 0
\(659\) −15.3075 −0.596295 −0.298148 0.954520i \(-0.596369\pi\)
−0.298148 + 0.954520i \(0.596369\pi\)
\(660\) 0 0
\(661\) 35.1796 1.36833 0.684164 0.729328i \(-0.260167\pi\)
0.684164 + 0.729328i \(0.260167\pi\)
\(662\) 0 0
\(663\) 30.9378 1.20152
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.17503 0.239098
\(668\) 0 0
\(669\) 25.1619 0.972816
\(670\) 0 0
\(671\) −5.52651 −0.213349
\(672\) 0 0
\(673\) 19.5437 0.753355 0.376678 0.926344i \(-0.377066\pi\)
0.376678 + 0.926344i \(0.377066\pi\)
\(674\) 0 0
\(675\) −0.374763 −0.0144246
\(676\) 0 0
\(677\) −19.0337 −0.731525 −0.365762 0.930708i \(-0.619192\pi\)
−0.365762 + 0.930708i \(0.619192\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 59.9639 2.29782
\(682\) 0 0
\(683\) 7.28626 0.278801 0.139401 0.990236i \(-0.455482\pi\)
0.139401 + 0.990236i \(0.455482\pi\)
\(684\) 0 0
\(685\) −42.6419 −1.62927
\(686\) 0 0
\(687\) 5.66747 0.216227
\(688\) 0 0
\(689\) −48.9765 −1.86585
\(690\) 0 0
\(691\) −2.57078 −0.0977972 −0.0488986 0.998804i \(-0.515571\pi\)
−0.0488986 + 0.998804i \(0.515571\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5.89852 −0.223743
\(696\) 0 0
\(697\) −1.59524 −0.0604239
\(698\) 0 0
\(699\) 16.9323 0.640437
\(700\) 0 0
\(701\) −35.9963 −1.35956 −0.679781 0.733415i \(-0.737925\pi\)
−0.679781 + 0.733415i \(0.737925\pi\)
\(702\) 0 0
\(703\) −18.8148 −0.709612
\(704\) 0 0
\(705\) 43.5683 1.64088
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −23.7405 −0.891593 −0.445796 0.895134i \(-0.647079\pi\)
−0.445796 + 0.895134i \(0.647079\pi\)
\(710\) 0 0
\(711\) −58.9638 −2.21132
\(712\) 0 0
\(713\) 8.90192 0.333380
\(714\) 0 0
\(715\) 23.0569 0.862278
\(716\) 0 0
\(717\) −66.2900 −2.47565
\(718\) 0 0
\(719\) −44.4669 −1.65833 −0.829167 0.559001i \(-0.811185\pi\)
−0.829167 + 0.559001i \(0.811185\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 10.1740 0.378376
\(724\) 0 0
\(725\) −0.0952720 −0.00353831
\(726\) 0 0
\(727\) −7.42795 −0.275487 −0.137744 0.990468i \(-0.543985\pi\)
−0.137744 + 0.990468i \(0.543985\pi\)
\(728\) 0 0
\(729\) −42.9031 −1.58900
\(730\) 0 0
\(731\) 5.72692 0.211818
\(732\) 0 0
\(733\) −33.4940 −1.23713 −0.618564 0.785734i \(-0.712285\pi\)
−0.618564 + 0.785734i \(0.712285\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.2888 −0.489500
\(738\) 0 0
\(739\) −49.0508 −1.80436 −0.902181 0.431358i \(-0.858035\pi\)
−0.902181 + 0.431358i \(0.858035\pi\)
\(740\) 0 0
\(741\) −45.8215 −1.68329
\(742\) 0 0
\(743\) 21.9291 0.804502 0.402251 0.915529i \(-0.368228\pi\)
0.402251 + 0.915529i \(0.368228\pi\)
\(744\) 0 0
\(745\) 34.6858 1.27079
\(746\) 0 0
\(747\) −29.2342 −1.06962
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −39.3023 −1.43416 −0.717081 0.696990i \(-0.754522\pi\)
−0.717081 + 0.696990i \(0.754522\pi\)
\(752\) 0 0
\(753\) 68.1516 2.48358
\(754\) 0 0
\(755\) −39.5442 −1.43916
\(756\) 0 0
\(757\) −2.22997 −0.0810495 −0.0405247 0.999179i \(-0.512903\pi\)
−0.0405247 + 0.999179i \(0.512903\pi\)
\(758\) 0 0
\(759\) −18.2592 −0.662768
\(760\) 0 0
\(761\) −24.2431 −0.878812 −0.439406 0.898289i \(-0.644811\pi\)
−0.439406 + 0.898289i \(0.644811\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −17.7737 −0.642609
\(766\) 0 0
\(767\) −21.5566 −0.778363
\(768\) 0 0
\(769\) −33.3488 −1.20259 −0.601295 0.799027i \(-0.705348\pi\)
−0.601295 + 0.799027i \(0.705348\pi\)
\(770\) 0 0
\(771\) 34.1029 1.22819
\(772\) 0 0
\(773\) −35.1822 −1.26542 −0.632709 0.774390i \(-0.718057\pi\)
−0.632709 + 0.774390i \(0.718057\pi\)
\(774\) 0 0
\(775\) −0.137344 −0.00493355
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.36268 0.0846518
\(780\) 0 0
\(781\) 0.862987 0.0308801
\(782\) 0 0
\(783\) 8.28020 0.295910
\(784\) 0 0
\(785\) −14.9281 −0.532805
\(786\) 0 0
\(787\) 44.3690 1.58158 0.790792 0.612086i \(-0.209669\pi\)
0.790792 + 0.612086i \(0.209669\pi\)
\(788\) 0 0
\(789\) −64.6426 −2.30134
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 24.9832 0.887178
\(794\) 0 0
\(795\) 44.9659 1.59478
\(796\) 0 0
\(797\) 50.2614 1.78035 0.890176 0.455617i \(-0.150581\pi\)
0.890176 + 0.455617i \(0.150581\pi\)
\(798\) 0 0
\(799\) −11.0512 −0.390962
\(800\) 0 0
\(801\) 54.9702 1.94228
\(802\) 0 0
\(803\) −5.74988 −0.202909
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −32.0989 −1.12994
\(808\) 0 0
\(809\) 5.78059 0.203235 0.101617 0.994824i \(-0.467598\pi\)
0.101617 + 0.994824i \(0.467598\pi\)
\(810\) 0 0
\(811\) −19.4569 −0.683224 −0.341612 0.939841i \(-0.610973\pi\)
−0.341612 + 0.939841i \(0.610973\pi\)
\(812\) 0 0
\(813\) −57.7619 −2.02580
\(814\) 0 0
\(815\) −6.39696 −0.224076
\(816\) 0 0
\(817\) −8.48205 −0.296749
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.99034 0.174164 0.0870821 0.996201i \(-0.472246\pi\)
0.0870821 + 0.996201i \(0.472246\pi\)
\(822\) 0 0
\(823\) −4.25875 −0.148451 −0.0742254 0.997241i \(-0.523648\pi\)
−0.0742254 + 0.997241i \(0.523648\pi\)
\(824\) 0 0
\(825\) 0.281714 0.00980803
\(826\) 0 0
\(827\) −5.79439 −0.201491 −0.100745 0.994912i \(-0.532123\pi\)
−0.100745 + 0.994912i \(0.532123\pi\)
\(828\) 0 0
\(829\) −34.1613 −1.18647 −0.593235 0.805030i \(-0.702149\pi\)
−0.593235 + 0.805030i \(0.702149\pi\)
\(830\) 0 0
\(831\) −90.3765 −3.13512
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.09894 0.0380305
\(836\) 0 0
\(837\) 11.9367 0.412594
\(838\) 0 0
\(839\) −38.2196 −1.31949 −0.659743 0.751491i \(-0.729335\pi\)
−0.659743 + 0.751491i \(0.729335\pi\)
\(840\) 0 0
\(841\) −26.8950 −0.927414
\(842\) 0 0
\(843\) 66.5005 2.29040
\(844\) 0 0
\(845\) −75.3535 −2.59224
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 60.7724 2.08570
\(850\) 0 0
\(851\) 33.8929 1.16183
\(852\) 0 0
\(853\) −23.6391 −0.809387 −0.404694 0.914452i \(-0.632622\pi\)
−0.404694 + 0.914452i \(0.632622\pi\)
\(854\) 0 0
\(855\) 26.3244 0.900274
\(856\) 0 0
\(857\) −35.6249 −1.21692 −0.608461 0.793584i \(-0.708213\pi\)
−0.608461 + 0.793584i \(0.708213\pi\)
\(858\) 0 0
\(859\) −6.02525 −0.205579 −0.102790 0.994703i \(-0.532777\pi\)
−0.102790 + 0.994703i \(0.532777\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.8161 −0.640509 −0.320254 0.947332i \(-0.603768\pi\)
−0.320254 + 0.947332i \(0.603768\pi\)
\(864\) 0 0
\(865\) 2.90501 0.0987733
\(866\) 0 0
\(867\) −40.9258 −1.38991
\(868\) 0 0
\(869\) 17.8132 0.604272
\(870\) 0 0
\(871\) 60.0734 2.03551
\(872\) 0 0
\(873\) 72.1559 2.44211
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5.20990 0.175926 0.0879630 0.996124i \(-0.471964\pi\)
0.0879630 + 0.996124i \(0.471964\pi\)
\(878\) 0 0
\(879\) −43.8767 −1.47992
\(880\) 0 0
\(881\) −2.58235 −0.0870016 −0.0435008 0.999053i \(-0.513851\pi\)
−0.0435008 + 0.999053i \(0.513851\pi\)
\(882\) 0 0
\(883\) −37.6520 −1.26709 −0.633546 0.773705i \(-0.718401\pi\)
−0.633546 + 0.773705i \(0.718401\pi\)
\(884\) 0 0
\(885\) 19.7914 0.665279
\(886\) 0 0
\(887\) 31.4224 1.05506 0.527530 0.849536i \(-0.323118\pi\)
0.527530 + 0.849536i \(0.323118\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.68305 −0.0563844
\(892\) 0 0
\(893\) 16.3677 0.547725
\(894\) 0 0
\(895\) −21.4360 −0.716525
\(896\) 0 0
\(897\) 82.5426 2.75602
\(898\) 0 0
\(899\) 3.03455 0.101208
\(900\) 0 0
\(901\) −11.4057 −0.379978
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11.2514 −0.374008
\(906\) 0 0
\(907\) 25.3863 0.842939 0.421469 0.906843i \(-0.361514\pi\)
0.421469 + 0.906843i \(0.361514\pi\)
\(908\) 0 0
\(909\) 54.7882 1.81721
\(910\) 0 0
\(911\) 43.5586 1.44316 0.721580 0.692331i \(-0.243416\pi\)
0.721580 + 0.692331i \(0.243416\pi\)
\(912\) 0 0
\(913\) 8.83177 0.292289
\(914\) 0 0
\(915\) −22.9374 −0.758286
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −33.4412 −1.10312 −0.551562 0.834134i \(-0.685968\pi\)
−0.551562 + 0.834134i \(0.685968\pi\)
\(920\) 0 0
\(921\) 1.77978 0.0586456
\(922\) 0 0
\(923\) −3.90122 −0.128410
\(924\) 0 0
\(925\) −0.522919 −0.0171935
\(926\) 0 0
\(927\) −52.0166 −1.70845
\(928\) 0 0
\(929\) 15.5772 0.511072 0.255536 0.966800i \(-0.417748\pi\)
0.255536 + 0.966800i \(0.417748\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 71.0200 2.32509
\(934\) 0 0
\(935\) 5.36951 0.175602
\(936\) 0 0
\(937\) 10.3002 0.336493 0.168246 0.985745i \(-0.446190\pi\)
0.168246 + 0.985745i \(0.446190\pi\)
\(938\) 0 0
\(939\) 19.4055 0.633276
\(940\) 0 0
\(941\) 2.78075 0.0906499 0.0453250 0.998972i \(-0.485568\pi\)
0.0453250 + 0.998972i \(0.485568\pi\)
\(942\) 0 0
\(943\) −4.25612 −0.138598
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.1990 −0.721372 −0.360686 0.932687i \(-0.617457\pi\)
−0.360686 + 0.932687i \(0.617457\pi\)
\(948\) 0 0
\(949\) 25.9929 0.843766
\(950\) 0 0
\(951\) −59.0143 −1.91367
\(952\) 0 0
\(953\) −35.3033 −1.14359 −0.571793 0.820398i \(-0.693752\pi\)
−0.571793 + 0.820398i \(0.693752\pi\)
\(954\) 0 0
\(955\) 8.52747 0.275943
\(956\) 0 0
\(957\) −6.22433 −0.201204
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −26.6254 −0.858884
\(962\) 0 0
\(963\) −56.1755 −1.81023
\(964\) 0 0
\(965\) −10.6392 −0.342488
\(966\) 0 0
\(967\) 20.0664 0.645292 0.322646 0.946520i \(-0.395428\pi\)
0.322646 + 0.946520i \(0.395428\pi\)
\(968\) 0 0
\(969\) −10.6709 −0.342800
\(970\) 0 0
\(971\) 3.45335 0.110823 0.0554116 0.998464i \(-0.482353\pi\)
0.0554116 + 0.998464i \(0.482353\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −1.27352 −0.0407852
\(976\) 0 0
\(977\) 18.2468 0.583768 0.291884 0.956454i \(-0.405718\pi\)
0.291884 + 0.956454i \(0.405718\pi\)
\(978\) 0 0
\(979\) −16.6067 −0.530753
\(980\) 0 0
\(981\) 59.6763 1.90532
\(982\) 0 0
\(983\) 12.6446 0.403299 0.201649 0.979458i \(-0.435370\pi\)
0.201649 + 0.979458i \(0.435370\pi\)
\(984\) 0 0
\(985\) 8.79342 0.280182
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 15.2795 0.485861
\(990\) 0 0
\(991\) −38.9308 −1.23668 −0.618339 0.785911i \(-0.712194\pi\)
−0.618339 + 0.785911i \(0.712194\pi\)
\(992\) 0 0
\(993\) −21.8671 −0.693930
\(994\) 0 0
\(995\) 3.76014 0.119204
\(996\) 0 0
\(997\) 30.7957 0.975308 0.487654 0.873037i \(-0.337853\pi\)
0.487654 + 0.873037i \(0.337853\pi\)
\(998\) 0 0
\(999\) 45.4475 1.43790
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 \(a_p\))