Properties

Label 8036.2.a.t.1.8
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 1.8
Root \(-0.146508\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.146508 q^{3}\) \(+3.56882 q^{5}\) \(-2.97854 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.146508 q^{3}\) \(+3.56882 q^{5}\) \(-2.97854 q^{9}\) \(-5.58095 q^{11}\) \(-6.25954 q^{13}\) \(-0.522862 q^{15}\) \(-6.24549 q^{17}\) \(+7.23364 q^{19}\) \(+5.27797 q^{23}\) \(+7.73647 q^{25}\) \(+0.875905 q^{27}\) \(-4.42408 q^{29}\) \(+1.06333 q^{31}\) \(+0.817655 q^{33}\) \(+2.40613 q^{37}\) \(+0.917075 q^{39}\) \(-1.00000 q^{41}\) \(+12.2876 q^{43}\) \(-10.6299 q^{45}\) \(-4.35831 q^{47}\) \(+0.915016 q^{51}\) \(+9.39440 q^{53}\) \(-19.9174 q^{55}\) \(-1.05979 q^{57}\) \(-13.2911 q^{59}\) \(+14.3104 q^{61}\) \(-22.3392 q^{65}\) \(-4.58700 q^{67}\) \(-0.773267 q^{69}\) \(-0.0228021 q^{71}\) \(+12.7838 q^{73}\) \(-1.13346 q^{75}\) \(+1.46033 q^{79}\) \(+8.80728 q^{81}\) \(+4.21437 q^{83}\) \(-22.2890 q^{85}\) \(+0.648164 q^{87}\) \(-3.56397 q^{89}\) \(-0.155787 q^{93}\) \(+25.8156 q^{95}\) \(+10.0736 q^{97}\) \(+16.6230 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.146508 −0.0845866 −0.0422933 0.999105i \(-0.513466\pi\)
−0.0422933 + 0.999105i \(0.513466\pi\)
\(4\) 0 0
\(5\) 3.56882 1.59602 0.798012 0.602641i \(-0.205885\pi\)
0.798012 + 0.602641i \(0.205885\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.97854 −0.992845
\(10\) 0 0
\(11\) −5.58095 −1.68272 −0.841359 0.540476i \(-0.818244\pi\)
−0.841359 + 0.540476i \(0.818244\pi\)
\(12\) 0 0
\(13\) −6.25954 −1.73608 −0.868042 0.496490i \(-0.834622\pi\)
−0.868042 + 0.496490i \(0.834622\pi\)
\(14\) 0 0
\(15\) −0.522862 −0.135002
\(16\) 0 0
\(17\) −6.24549 −1.51475 −0.757377 0.652978i \(-0.773519\pi\)
−0.757377 + 0.652978i \(0.773519\pi\)
\(18\) 0 0
\(19\) 7.23364 1.65951 0.829756 0.558127i \(-0.188480\pi\)
0.829756 + 0.558127i \(0.188480\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.27797 1.10053 0.550266 0.834989i \(-0.314526\pi\)
0.550266 + 0.834989i \(0.314526\pi\)
\(24\) 0 0
\(25\) 7.73647 1.54729
\(26\) 0 0
\(27\) 0.875905 0.168568
\(28\) 0 0
\(29\) −4.42408 −0.821531 −0.410765 0.911741i \(-0.634738\pi\)
−0.410765 + 0.911741i \(0.634738\pi\)
\(30\) 0 0
\(31\) 1.06333 0.190981 0.0954903 0.995430i \(-0.469558\pi\)
0.0954903 + 0.995430i \(0.469558\pi\)
\(32\) 0 0
\(33\) 0.817655 0.142336
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.40613 0.395566 0.197783 0.980246i \(-0.436626\pi\)
0.197783 + 0.980246i \(0.436626\pi\)
\(38\) 0 0
\(39\) 0.917075 0.146850
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 12.2876 1.87384 0.936920 0.349543i \(-0.113663\pi\)
0.936920 + 0.349543i \(0.113663\pi\)
\(44\) 0 0
\(45\) −10.6299 −1.58460
\(46\) 0 0
\(47\) −4.35831 −0.635725 −0.317862 0.948137i \(-0.602965\pi\)
−0.317862 + 0.948137i \(0.602965\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.915016 0.128128
\(52\) 0 0
\(53\) 9.39440 1.29042 0.645210 0.764005i \(-0.276770\pi\)
0.645210 + 0.764005i \(0.276770\pi\)
\(54\) 0 0
\(55\) −19.9174 −2.68566
\(56\) 0 0
\(57\) −1.05979 −0.140372
\(58\) 0 0
\(59\) −13.2911 −1.73035 −0.865177 0.501466i \(-0.832794\pi\)
−0.865177 + 0.501466i \(0.832794\pi\)
\(60\) 0 0
\(61\) 14.3104 1.83226 0.916130 0.400881i \(-0.131296\pi\)
0.916130 + 0.400881i \(0.131296\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −22.3392 −2.77083
\(66\) 0 0
\(67\) −4.58700 −0.560392 −0.280196 0.959943i \(-0.590399\pi\)
−0.280196 + 0.959943i \(0.590399\pi\)
\(68\) 0 0
\(69\) −0.773267 −0.0930904
\(70\) 0 0
\(71\) −0.0228021 −0.00270612 −0.00135306 0.999999i \(-0.500431\pi\)
−0.00135306 + 0.999999i \(0.500431\pi\)
\(72\) 0 0
\(73\) 12.7838 1.49623 0.748115 0.663569i \(-0.230959\pi\)
0.748115 + 0.663569i \(0.230959\pi\)
\(74\) 0 0
\(75\) −1.13346 −0.130880
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.46033 0.164300 0.0821499 0.996620i \(-0.473821\pi\)
0.0821499 + 0.996620i \(0.473821\pi\)
\(80\) 0 0
\(81\) 8.80728 0.978586
\(82\) 0 0
\(83\) 4.21437 0.462588 0.231294 0.972884i \(-0.425704\pi\)
0.231294 + 0.972884i \(0.425704\pi\)
\(84\) 0 0
\(85\) −22.2890 −2.41758
\(86\) 0 0
\(87\) 0.648164 0.0694905
\(88\) 0 0
\(89\) −3.56397 −0.377780 −0.188890 0.981998i \(-0.560489\pi\)
−0.188890 + 0.981998i \(0.560489\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.155787 −0.0161544
\(94\) 0 0
\(95\) 25.8156 2.64862
\(96\) 0 0
\(97\) 10.0736 1.02282 0.511409 0.859337i \(-0.329124\pi\)
0.511409 + 0.859337i \(0.329124\pi\)
\(98\) 0 0
\(99\) 16.6230 1.67068
\(100\) 0 0
\(101\) 6.78163 0.674797 0.337398 0.941362i \(-0.390453\pi\)
0.337398 + 0.941362i \(0.390453\pi\)
\(102\) 0 0
\(103\) 14.8830 1.46647 0.733235 0.679976i \(-0.238010\pi\)
0.733235 + 0.679976i \(0.238010\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.23983 0.313207 0.156603 0.987662i \(-0.449946\pi\)
0.156603 + 0.987662i \(0.449946\pi\)
\(108\) 0 0
\(109\) −12.0580 −1.15495 −0.577473 0.816410i \(-0.695961\pi\)
−0.577473 + 0.816410i \(0.695961\pi\)
\(110\) 0 0
\(111\) −0.352519 −0.0334596
\(112\) 0 0
\(113\) 2.15189 0.202433 0.101216 0.994864i \(-0.467727\pi\)
0.101216 + 0.994864i \(0.467727\pi\)
\(114\) 0 0
\(115\) 18.8361 1.75648
\(116\) 0 0
\(117\) 18.6443 1.72366
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 20.1470 1.83154
\(122\) 0 0
\(123\) 0.146508 0.0132102
\(124\) 0 0
\(125\) 9.76596 0.873494
\(126\) 0 0
\(127\) 10.4780 0.929769 0.464885 0.885371i \(-0.346096\pi\)
0.464885 + 0.885371i \(0.346096\pi\)
\(128\) 0 0
\(129\) −1.80024 −0.158502
\(130\) 0 0
\(131\) −15.1943 −1.32753 −0.663765 0.747941i \(-0.731043\pi\)
−0.663765 + 0.747941i \(0.731043\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.12595 0.269039
\(136\) 0 0
\(137\) 12.2648 1.04785 0.523927 0.851763i \(-0.324467\pi\)
0.523927 + 0.851763i \(0.324467\pi\)
\(138\) 0 0
\(139\) 5.87366 0.498197 0.249099 0.968478i \(-0.419866\pi\)
0.249099 + 0.968478i \(0.419866\pi\)
\(140\) 0 0
\(141\) 0.638529 0.0537738
\(142\) 0 0
\(143\) 34.9342 2.92134
\(144\) 0 0
\(145\) −15.7887 −1.31118
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.43183 −0.281147 −0.140573 0.990070i \(-0.544895\pi\)
−0.140573 + 0.990070i \(0.544895\pi\)
\(150\) 0 0
\(151\) −1.00796 −0.0820267 −0.0410134 0.999159i \(-0.513059\pi\)
−0.0410134 + 0.999159i \(0.513059\pi\)
\(152\) 0 0
\(153\) 18.6024 1.50392
\(154\) 0 0
\(155\) 3.79485 0.304810
\(156\) 0 0
\(157\) 10.1710 0.811731 0.405866 0.913933i \(-0.366970\pi\)
0.405866 + 0.913933i \(0.366970\pi\)
\(158\) 0 0
\(159\) −1.37636 −0.109152
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.8358 1.00538 0.502690 0.864467i \(-0.332344\pi\)
0.502690 + 0.864467i \(0.332344\pi\)
\(164\) 0 0
\(165\) 2.91806 0.227171
\(166\) 0 0
\(167\) −19.6228 −1.51846 −0.759230 0.650822i \(-0.774424\pi\)
−0.759230 + 0.650822i \(0.774424\pi\)
\(168\) 0 0
\(169\) 26.1819 2.01399
\(170\) 0 0
\(171\) −21.5457 −1.64764
\(172\) 0 0
\(173\) −2.34884 −0.178579 −0.0892895 0.996006i \(-0.528460\pi\)
−0.0892895 + 0.996006i \(0.528460\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.94726 0.146365
\(178\) 0 0
\(179\) −1.34712 −0.100689 −0.0503443 0.998732i \(-0.516032\pi\)
−0.0503443 + 0.998732i \(0.516032\pi\)
\(180\) 0 0
\(181\) 25.3273 1.88256 0.941281 0.337623i \(-0.109623\pi\)
0.941281 + 0.337623i \(0.109623\pi\)
\(182\) 0 0
\(183\) −2.09660 −0.154985
\(184\) 0 0
\(185\) 8.58705 0.631333
\(186\) 0 0
\(187\) 34.8557 2.54890
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.7103 −0.992042 −0.496021 0.868311i \(-0.665206\pi\)
−0.496021 + 0.868311i \(0.665206\pi\)
\(192\) 0 0
\(193\) −14.2959 −1.02904 −0.514520 0.857478i \(-0.672030\pi\)
−0.514520 + 0.857478i \(0.672030\pi\)
\(194\) 0 0
\(195\) 3.27288 0.234375
\(196\) 0 0
\(197\) −8.46578 −0.603162 −0.301581 0.953441i \(-0.597514\pi\)
−0.301581 + 0.953441i \(0.597514\pi\)
\(198\) 0 0
\(199\) −2.27139 −0.161014 −0.0805072 0.996754i \(-0.525654\pi\)
−0.0805072 + 0.996754i \(0.525654\pi\)
\(200\) 0 0
\(201\) 0.672034 0.0474017
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.56882 −0.249257
\(206\) 0 0
\(207\) −15.7206 −1.09266
\(208\) 0 0
\(209\) −40.3706 −2.79249
\(210\) 0 0
\(211\) −3.57292 −0.245970 −0.122985 0.992409i \(-0.539247\pi\)
−0.122985 + 0.992409i \(0.539247\pi\)
\(212\) 0 0
\(213\) 0.00334070 0.000228901 0
\(214\) 0 0
\(215\) 43.8522 2.99070
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.87293 −0.126561
\(220\) 0 0
\(221\) 39.0939 2.62974
\(222\) 0 0
\(223\) 5.99708 0.401594 0.200797 0.979633i \(-0.435647\pi\)
0.200797 + 0.979633i \(0.435647\pi\)
\(224\) 0 0
\(225\) −23.0433 −1.53622
\(226\) 0 0
\(227\) 8.33020 0.552894 0.276447 0.961029i \(-0.410843\pi\)
0.276447 + 0.961029i \(0.410843\pi\)
\(228\) 0 0
\(229\) 21.5041 1.42103 0.710515 0.703682i \(-0.248462\pi\)
0.710515 + 0.703682i \(0.248462\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.16205 0.403689 0.201845 0.979418i \(-0.435306\pi\)
0.201845 + 0.979418i \(0.435306\pi\)
\(234\) 0 0
\(235\) −15.5540 −1.01463
\(236\) 0 0
\(237\) −0.213950 −0.0138976
\(238\) 0 0
\(239\) −3.12242 −0.201973 −0.100986 0.994888i \(-0.532200\pi\)
−0.100986 + 0.994888i \(0.532200\pi\)
\(240\) 0 0
\(241\) 29.8712 1.92417 0.962086 0.272746i \(-0.0879319\pi\)
0.962086 + 0.272746i \(0.0879319\pi\)
\(242\) 0 0
\(243\) −3.91806 −0.251343
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −45.2793 −2.88105
\(248\) 0 0
\(249\) −0.617441 −0.0391287
\(250\) 0 0
\(251\) 6.93673 0.437843 0.218921 0.975743i \(-0.429746\pi\)
0.218921 + 0.975743i \(0.429746\pi\)
\(252\) 0 0
\(253\) −29.4561 −1.85189
\(254\) 0 0
\(255\) 3.26553 0.204495
\(256\) 0 0
\(257\) 10.8457 0.676535 0.338267 0.941050i \(-0.390159\pi\)
0.338267 + 0.941050i \(0.390159\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 13.1773 0.815653
\(262\) 0 0
\(263\) −21.5532 −1.32903 −0.664515 0.747275i \(-0.731362\pi\)
−0.664515 + 0.747275i \(0.731362\pi\)
\(264\) 0 0
\(265\) 33.5269 2.05954
\(266\) 0 0
\(267\) 0.522151 0.0319551
\(268\) 0 0
\(269\) −8.56276 −0.522081 −0.261040 0.965328i \(-0.584066\pi\)
−0.261040 + 0.965328i \(0.584066\pi\)
\(270\) 0 0
\(271\) −13.5941 −0.825784 −0.412892 0.910780i \(-0.635481\pi\)
−0.412892 + 0.910780i \(0.635481\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −43.1768 −2.60366
\(276\) 0 0
\(277\) −0.322861 −0.0193988 −0.00969941 0.999953i \(-0.503087\pi\)
−0.00969941 + 0.999953i \(0.503087\pi\)
\(278\) 0 0
\(279\) −3.16718 −0.189614
\(280\) 0 0
\(281\) −2.28975 −0.136595 −0.0682975 0.997665i \(-0.521757\pi\)
−0.0682975 + 0.997665i \(0.521757\pi\)
\(282\) 0 0
\(283\) 15.2741 0.907950 0.453975 0.891014i \(-0.350005\pi\)
0.453975 + 0.891014i \(0.350005\pi\)
\(284\) 0 0
\(285\) −3.78220 −0.224038
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 22.0061 1.29448
\(290\) 0 0
\(291\) −1.47587 −0.0865168
\(292\) 0 0
\(293\) 18.3619 1.07272 0.536358 0.843991i \(-0.319800\pi\)
0.536358 + 0.843991i \(0.319800\pi\)
\(294\) 0 0
\(295\) −47.4336 −2.76169
\(296\) 0 0
\(297\) −4.88838 −0.283653
\(298\) 0 0
\(299\) −33.0377 −1.91062
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −0.993565 −0.0570788
\(304\) 0 0
\(305\) 51.0713 2.92433
\(306\) 0 0
\(307\) −27.4007 −1.56384 −0.781920 0.623379i \(-0.785759\pi\)
−0.781920 + 0.623379i \(0.785759\pi\)
\(308\) 0 0
\(309\) −2.18049 −0.124044
\(310\) 0 0
\(311\) 9.83010 0.557414 0.278707 0.960376i \(-0.410094\pi\)
0.278707 + 0.960376i \(0.410094\pi\)
\(312\) 0 0
\(313\) 0.0229956 0.00129979 0.000649895 1.00000i \(-0.499793\pi\)
0.000649895 1.00000i \(0.499793\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.32439 −0.467544 −0.233772 0.972291i \(-0.575107\pi\)
−0.233772 + 0.972291i \(0.575107\pi\)
\(318\) 0 0
\(319\) 24.6905 1.38240
\(320\) 0 0
\(321\) −0.474663 −0.0264931
\(322\) 0 0
\(323\) −45.1776 −2.51375
\(324\) 0 0
\(325\) −48.4267 −2.68623
\(326\) 0 0
\(327\) 1.76660 0.0976930
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −18.9999 −1.04433 −0.522166 0.852844i \(-0.674876\pi\)
−0.522166 + 0.852844i \(0.674876\pi\)
\(332\) 0 0
\(333\) −7.16675 −0.392736
\(334\) 0 0
\(335\) −16.3702 −0.894399
\(336\) 0 0
\(337\) −15.8051 −0.860956 −0.430478 0.902601i \(-0.641655\pi\)
−0.430478 + 0.902601i \(0.641655\pi\)
\(338\) 0 0
\(339\) −0.315270 −0.0171231
\(340\) 0 0
\(341\) −5.93441 −0.321367
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.75965 −0.148575
\(346\) 0 0
\(347\) 16.6774 0.895289 0.447645 0.894212i \(-0.352263\pi\)
0.447645 + 0.894212i \(0.352263\pi\)
\(348\) 0 0
\(349\) 4.89892 0.262233 0.131116 0.991367i \(-0.458144\pi\)
0.131116 + 0.991367i \(0.458144\pi\)
\(350\) 0 0
\(351\) −5.48277 −0.292648
\(352\) 0 0
\(353\) −6.05193 −0.322112 −0.161056 0.986945i \(-0.551490\pi\)
−0.161056 + 0.986945i \(0.551490\pi\)
\(354\) 0 0
\(355\) −0.0813767 −0.00431903
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.5703 0.980103 0.490052 0.871693i \(-0.336978\pi\)
0.490052 + 0.871693i \(0.336978\pi\)
\(360\) 0 0
\(361\) 33.3256 1.75398
\(362\) 0 0
\(363\) −2.95170 −0.154924
\(364\) 0 0
\(365\) 45.6230 2.38802
\(366\) 0 0
\(367\) −26.4297 −1.37962 −0.689810 0.723990i \(-0.742306\pi\)
−0.689810 + 0.723990i \(0.742306\pi\)
\(368\) 0 0
\(369\) 2.97854 0.155056
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −30.4746 −1.57792 −0.788958 0.614447i \(-0.789379\pi\)
−0.788958 + 0.614447i \(0.789379\pi\)
\(374\) 0 0
\(375\) −1.43080 −0.0738860
\(376\) 0 0
\(377\) 27.6927 1.42625
\(378\) 0 0
\(379\) −33.0447 −1.69739 −0.848697 0.528880i \(-0.822612\pi\)
−0.848697 + 0.528880i \(0.822612\pi\)
\(380\) 0 0
\(381\) −1.53511 −0.0786461
\(382\) 0 0
\(383\) −5.81336 −0.297049 −0.148524 0.988909i \(-0.547452\pi\)
−0.148524 + 0.988909i \(0.547452\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −36.5990 −1.86043
\(388\) 0 0
\(389\) 9.76527 0.495119 0.247559 0.968873i \(-0.420371\pi\)
0.247559 + 0.968873i \(0.420371\pi\)
\(390\) 0 0
\(391\) −32.9635 −1.66704
\(392\) 0 0
\(393\) 2.22609 0.112291
\(394\) 0 0
\(395\) 5.21165 0.262227
\(396\) 0 0
\(397\) −4.72934 −0.237359 −0.118679 0.992933i \(-0.537866\pi\)
−0.118679 + 0.992933i \(0.537866\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −23.6521 −1.18113 −0.590566 0.806989i \(-0.701095\pi\)
−0.590566 + 0.806989i \(0.701095\pi\)
\(402\) 0 0
\(403\) −6.65599 −0.331558
\(404\) 0 0
\(405\) 31.4316 1.56185
\(406\) 0 0
\(407\) −13.4285 −0.665626
\(408\) 0 0
\(409\) −22.6946 −1.12217 −0.561087 0.827757i \(-0.689617\pi\)
−0.561087 + 0.827757i \(0.689617\pi\)
\(410\) 0 0
\(411\) −1.79690 −0.0886344
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 15.0403 0.738301
\(416\) 0 0
\(417\) −0.860540 −0.0421408
\(418\) 0 0
\(419\) 16.3286 0.797706 0.398853 0.917015i \(-0.369408\pi\)
0.398853 + 0.917015i \(0.369408\pi\)
\(420\) 0 0
\(421\) 13.9893 0.681794 0.340897 0.940101i \(-0.389269\pi\)
0.340897 + 0.940101i \(0.389269\pi\)
\(422\) 0 0
\(423\) 12.9814 0.631176
\(424\) 0 0
\(425\) −48.3180 −2.34377
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −5.11815 −0.247106
\(430\) 0 0
\(431\) 13.1555 0.633680 0.316840 0.948479i \(-0.397378\pi\)
0.316840 + 0.948479i \(0.397378\pi\)
\(432\) 0 0
\(433\) −23.1641 −1.11319 −0.556597 0.830782i \(-0.687893\pi\)
−0.556597 + 0.830782i \(0.687893\pi\)
\(434\) 0 0
\(435\) 2.31318 0.110909
\(436\) 0 0
\(437\) 38.1789 1.82635
\(438\) 0 0
\(439\) −3.29543 −0.157282 −0.0786412 0.996903i \(-0.525058\pi\)
−0.0786412 + 0.996903i \(0.525058\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.60201 −0.456205 −0.228103 0.973637i \(-0.573252\pi\)
−0.228103 + 0.973637i \(0.573252\pi\)
\(444\) 0 0
\(445\) −12.7192 −0.602946
\(446\) 0 0
\(447\) 0.502792 0.0237813
\(448\) 0 0
\(449\) 5.38167 0.253977 0.126988 0.991904i \(-0.459469\pi\)
0.126988 + 0.991904i \(0.459469\pi\)
\(450\) 0 0
\(451\) 5.58095 0.262796
\(452\) 0 0
\(453\) 0.147675 0.00693837
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17.5108 −0.819122 −0.409561 0.912283i \(-0.634318\pi\)
−0.409561 + 0.912283i \(0.634318\pi\)
\(458\) 0 0
\(459\) −5.47046 −0.255339
\(460\) 0 0
\(461\) 16.5516 0.770887 0.385443 0.922731i \(-0.374048\pi\)
0.385443 + 0.922731i \(0.374048\pi\)
\(462\) 0 0
\(463\) 20.4013 0.948131 0.474066 0.880490i \(-0.342786\pi\)
0.474066 + 0.880490i \(0.342786\pi\)
\(464\) 0 0
\(465\) −0.555977 −0.0257828
\(466\) 0 0
\(467\) −22.4563 −1.03915 −0.519576 0.854424i \(-0.673910\pi\)
−0.519576 + 0.854424i \(0.673910\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.49013 −0.0686616
\(472\) 0 0
\(473\) −68.5764 −3.15315
\(474\) 0 0
\(475\) 55.9628 2.56775
\(476\) 0 0
\(477\) −27.9815 −1.28119
\(478\) 0 0
\(479\) 24.7303 1.12996 0.564978 0.825106i \(-0.308885\pi\)
0.564978 + 0.825106i \(0.308885\pi\)
\(480\) 0 0
\(481\) −15.0613 −0.686736
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 35.9508 1.63244
\(486\) 0 0
\(487\) 42.3397 1.91859 0.959297 0.282400i \(-0.0911304\pi\)
0.959297 + 0.282400i \(0.0911304\pi\)
\(488\) 0 0
\(489\) −1.88056 −0.0850417
\(490\) 0 0
\(491\) −36.9495 −1.66751 −0.833754 0.552136i \(-0.813813\pi\)
−0.833754 + 0.552136i \(0.813813\pi\)
\(492\) 0 0
\(493\) 27.6305 1.24442
\(494\) 0 0
\(495\) 59.3246 2.66644
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −6.34747 −0.284152 −0.142076 0.989856i \(-0.545378\pi\)
−0.142076 + 0.989856i \(0.545378\pi\)
\(500\) 0 0
\(501\) 2.87491 0.128442
\(502\) 0 0
\(503\) −9.57194 −0.426792 −0.213396 0.976966i \(-0.568452\pi\)
−0.213396 + 0.976966i \(0.568452\pi\)
\(504\) 0 0
\(505\) 24.2024 1.07699
\(506\) 0 0
\(507\) −3.83586 −0.170357
\(508\) 0 0
\(509\) 12.4150 0.550284 0.275142 0.961404i \(-0.411275\pi\)
0.275142 + 0.961404i \(0.411275\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 6.33599 0.279741
\(514\) 0 0
\(515\) 53.1149 2.34052
\(516\) 0 0
\(517\) 24.3235 1.06975
\(518\) 0 0
\(519\) 0.344125 0.0151054
\(520\) 0 0
\(521\) 21.3737 0.936397 0.468199 0.883623i \(-0.344903\pi\)
0.468199 + 0.883623i \(0.344903\pi\)
\(522\) 0 0
\(523\) 19.4095 0.848718 0.424359 0.905494i \(-0.360499\pi\)
0.424359 + 0.905494i \(0.360499\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.64104 −0.289288
\(528\) 0 0
\(529\) 4.85697 0.211173
\(530\) 0 0
\(531\) 39.5880 1.71797
\(532\) 0 0
\(533\) 6.25954 0.271131
\(534\) 0 0
\(535\) 11.5624 0.499885
\(536\) 0 0
\(537\) 0.197365 0.00851692
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 18.6391 0.801359 0.400680 0.916218i \(-0.368774\pi\)
0.400680 + 0.916218i \(0.368774\pi\)
\(542\) 0 0
\(543\) −3.71066 −0.159240
\(544\) 0 0
\(545\) −43.0328 −1.84332
\(546\) 0 0
\(547\) −25.5848 −1.09393 −0.546963 0.837157i \(-0.684216\pi\)
−0.546963 + 0.837157i \(0.684216\pi\)
\(548\) 0 0
\(549\) −42.6241 −1.81915
\(550\) 0 0
\(551\) −32.0022 −1.36334
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.25808 −0.0534023
\(556\) 0 0
\(557\) 43.8379 1.85747 0.928735 0.370743i \(-0.120897\pi\)
0.928735 + 0.370743i \(0.120897\pi\)
\(558\) 0 0
\(559\) −76.9147 −3.25315
\(560\) 0 0
\(561\) −5.10666 −0.215603
\(562\) 0 0
\(563\) 0.377258 0.0158995 0.00794977 0.999968i \(-0.497469\pi\)
0.00794977 + 0.999968i \(0.497469\pi\)
\(564\) 0 0
\(565\) 7.67971 0.323088
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.1648 1.34842 0.674210 0.738539i \(-0.264484\pi\)
0.674210 + 0.738539i \(0.264484\pi\)
\(570\) 0 0
\(571\) 23.9046 1.00038 0.500189 0.865917i \(-0.333264\pi\)
0.500189 + 0.865917i \(0.333264\pi\)
\(572\) 0 0
\(573\) 2.00867 0.0839135
\(574\) 0 0
\(575\) 40.8329 1.70285
\(576\) 0 0
\(577\) 28.0194 1.16646 0.583231 0.812306i \(-0.301788\pi\)
0.583231 + 0.812306i \(0.301788\pi\)
\(578\) 0 0
\(579\) 2.09447 0.0870430
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −52.4296 −2.17141
\(584\) 0 0
\(585\) 66.5380 2.75101
\(586\) 0 0
\(587\) 30.3058 1.25085 0.625427 0.780282i \(-0.284925\pi\)
0.625427 + 0.780282i \(0.284925\pi\)
\(588\) 0 0
\(589\) 7.69178 0.316934
\(590\) 0 0
\(591\) 1.24031 0.0510194
\(592\) 0 0
\(593\) 31.3996 1.28943 0.644713 0.764425i \(-0.276977\pi\)
0.644713 + 0.764425i \(0.276977\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.332777 0.0136197
\(598\) 0 0
\(599\) 17.7301 0.724431 0.362215 0.932094i \(-0.382020\pi\)
0.362215 + 0.932094i \(0.382020\pi\)
\(600\) 0 0
\(601\) −21.8509 −0.891319 −0.445659 0.895203i \(-0.647031\pi\)
−0.445659 + 0.895203i \(0.647031\pi\)
\(602\) 0 0
\(603\) 13.6626 0.556382
\(604\) 0 0
\(605\) 71.9008 2.92318
\(606\) 0 0
\(607\) −0.438480 −0.0177974 −0.00889868 0.999960i \(-0.502833\pi\)
−0.00889868 + 0.999960i \(0.502833\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 27.2810 1.10367
\(612\) 0 0
\(613\) −8.33445 −0.336625 −0.168313 0.985734i \(-0.553832\pi\)
−0.168313 + 0.985734i \(0.553832\pi\)
\(614\) 0 0
\(615\) 0.522862 0.0210838
\(616\) 0 0
\(617\) 41.6709 1.67761 0.838803 0.544434i \(-0.183256\pi\)
0.838803 + 0.544434i \(0.183256\pi\)
\(618\) 0 0
\(619\) 22.0300 0.885461 0.442731 0.896655i \(-0.354010\pi\)
0.442731 + 0.896655i \(0.354010\pi\)
\(620\) 0 0
\(621\) 4.62300 0.185515
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.82939 −0.153176
\(626\) 0 0
\(627\) 5.91463 0.236207
\(628\) 0 0
\(629\) −15.0275 −0.599185
\(630\) 0 0
\(631\) 7.37811 0.293718 0.146859 0.989157i \(-0.453084\pi\)
0.146859 + 0.989157i \(0.453084\pi\)
\(632\) 0 0
\(633\) 0.523463 0.0208058
\(634\) 0 0
\(635\) 37.3940 1.48393
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.0679170 0.00268675
\(640\) 0 0
\(641\) −40.7267 −1.60861 −0.804304 0.594219i \(-0.797461\pi\)
−0.804304 + 0.594219i \(0.797461\pi\)
\(642\) 0 0
\(643\) −6.53076 −0.257548 −0.128774 0.991674i \(-0.541104\pi\)
−0.128774 + 0.991674i \(0.541104\pi\)
\(644\) 0 0
\(645\) −6.42472 −0.252973
\(646\) 0 0
\(647\) −16.7724 −0.659391 −0.329695 0.944087i \(-0.606946\pi\)
−0.329695 + 0.944087i \(0.606946\pi\)
\(648\) 0 0
\(649\) 74.1770 2.91170
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 29.4507 1.15249 0.576247 0.817275i \(-0.304516\pi\)
0.576247 + 0.817275i \(0.304516\pi\)
\(654\) 0 0
\(655\) −54.2256 −2.11877
\(656\) 0 0
\(657\) −38.0770 −1.48552
\(658\) 0 0
\(659\) 9.00387 0.350741 0.175370 0.984503i \(-0.443888\pi\)
0.175370 + 0.984503i \(0.443888\pi\)
\(660\) 0 0
\(661\) 10.7229 0.417074 0.208537 0.978014i \(-0.433130\pi\)
0.208537 + 0.978014i \(0.433130\pi\)
\(662\) 0 0
\(663\) −5.72758 −0.222441
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −23.3502 −0.904121
\(668\) 0 0
\(669\) −0.878622 −0.0339695
\(670\) 0 0
\(671\) −79.8656 −3.08318
\(672\) 0 0
\(673\) −19.7406 −0.760944 −0.380472 0.924792i \(-0.624238\pi\)
−0.380472 + 0.924792i \(0.624238\pi\)
\(674\) 0 0
\(675\) 6.77642 0.260824
\(676\) 0 0
\(677\) 2.56119 0.0984345 0.0492173 0.998788i \(-0.484327\pi\)
0.0492173 + 0.998788i \(0.484327\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.22044 −0.0467675
\(682\) 0 0
\(683\) −39.3304 −1.50494 −0.752469 0.658628i \(-0.771137\pi\)
−0.752469 + 0.658628i \(0.771137\pi\)
\(684\) 0 0
\(685\) 43.7709 1.67240
\(686\) 0 0
\(687\) −3.15053 −0.120200
\(688\) 0 0
\(689\) −58.8046 −2.24028
\(690\) 0 0
\(691\) 28.4369 1.08179 0.540895 0.841090i \(-0.318085\pi\)
0.540895 + 0.841090i \(0.318085\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.9620 0.795135
\(696\) 0 0
\(697\) 6.24549 0.236565
\(698\) 0 0
\(699\) −0.902792 −0.0341467
\(700\) 0 0
\(701\) −1.90674 −0.0720165 −0.0360083 0.999351i \(-0.511464\pi\)
−0.0360083 + 0.999351i \(0.511464\pi\)
\(702\) 0 0
\(703\) 17.4051 0.656446
\(704\) 0 0
\(705\) 2.27879 0.0858243
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.66673 −0.0625954 −0.0312977 0.999510i \(-0.509964\pi\)
−0.0312977 + 0.999510i \(0.509964\pi\)
\(710\) 0 0
\(711\) −4.34964 −0.163124
\(712\) 0 0
\(713\) 5.61225 0.210180
\(714\) 0 0
\(715\) 124.674 4.66253
\(716\) 0 0
\(717\) 0.457461 0.0170842
\(718\) 0 0
\(719\) 5.77861 0.215506 0.107753 0.994178i \(-0.465634\pi\)
0.107753 + 0.994178i \(0.465634\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4.37638 −0.162759
\(724\) 0 0
\(725\) −34.2267 −1.27115
\(726\) 0 0
\(727\) 35.6801 1.32330 0.661651 0.749812i \(-0.269856\pi\)
0.661651 + 0.749812i \(0.269856\pi\)
\(728\) 0 0
\(729\) −25.8478 −0.957326
\(730\) 0 0
\(731\) −76.7420 −2.83841
\(732\) 0 0
\(733\) −3.72876 −0.137725 −0.0688624 0.997626i \(-0.521937\pi\)
−0.0688624 + 0.997626i \(0.521937\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.5998 0.942981
\(738\) 0 0
\(739\) −47.8076 −1.75863 −0.879316 0.476239i \(-0.842000\pi\)
−0.879316 + 0.476239i \(0.842000\pi\)
\(740\) 0 0
\(741\) 6.63379 0.243698
\(742\) 0 0
\(743\) −23.1744 −0.850186 −0.425093 0.905150i \(-0.639759\pi\)
−0.425093 + 0.905150i \(0.639759\pi\)
\(744\) 0 0
\(745\) −12.2476 −0.448717
\(746\) 0 0
\(747\) −12.5527 −0.459278
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 36.3210 1.32537 0.662685 0.748898i \(-0.269417\pi\)
0.662685 + 0.748898i \(0.269417\pi\)
\(752\) 0 0
\(753\) −1.01629 −0.0370356
\(754\) 0 0
\(755\) −3.59723 −0.130917
\(756\) 0 0
\(757\) −21.0931 −0.766643 −0.383321 0.923615i \(-0.625220\pi\)
−0.383321 + 0.923615i \(0.625220\pi\)
\(758\) 0 0
\(759\) 4.31556 0.156645
\(760\) 0 0
\(761\) −26.6886 −0.967459 −0.483730 0.875217i \(-0.660718\pi\)
−0.483730 + 0.875217i \(0.660718\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 66.3886 2.40029
\(766\) 0 0
\(767\) 83.1962 3.00404
\(768\) 0 0
\(769\) 35.4811 1.27948 0.639740 0.768591i \(-0.279042\pi\)
0.639740 + 0.768591i \(0.279042\pi\)
\(770\) 0 0
\(771\) −1.58898 −0.0572258
\(772\) 0 0
\(773\) −5.67891 −0.204256 −0.102128 0.994771i \(-0.532565\pi\)
−0.102128 + 0.994771i \(0.532565\pi\)
\(774\) 0 0
\(775\) 8.22646 0.295503
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.23364 −0.259172
\(780\) 0 0
\(781\) 0.127257 0.00455363
\(782\) 0 0
\(783\) −3.87507 −0.138484
\(784\) 0 0
\(785\) 36.2983 1.29554
\(786\) 0 0
\(787\) −22.3367 −0.796216 −0.398108 0.917338i \(-0.630333\pi\)
−0.398108 + 0.917338i \(0.630333\pi\)
\(788\) 0 0
\(789\) 3.15773 0.112418
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −89.5766 −3.18096
\(794\) 0 0
\(795\) −4.91197 −0.174210
\(796\) 0 0
\(797\) −10.6460 −0.377101 −0.188550 0.982064i \(-0.560379\pi\)
−0.188550 + 0.982064i \(0.560379\pi\)
\(798\) 0 0
\(799\) 27.2198 0.962966
\(800\) 0 0
\(801\) 10.6154 0.375077
\(802\) 0 0
\(803\) −71.3456 −2.51773
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.25452 0.0441611
\(808\) 0 0
\(809\) −29.8892 −1.05085 −0.525425 0.850840i \(-0.676094\pi\)
−0.525425 + 0.850840i \(0.676094\pi\)
\(810\) 0 0
\(811\) −30.5838 −1.07394 −0.536971 0.843601i \(-0.680432\pi\)
−0.536971 + 0.843601i \(0.680432\pi\)
\(812\) 0 0
\(813\) 1.99165 0.0698503
\(814\) 0 0
\(815\) 45.8088 1.60461
\(816\) 0 0
\(817\) 88.8841 3.10966
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 51.0330 1.78106 0.890532 0.454921i \(-0.150332\pi\)
0.890532 + 0.454921i \(0.150332\pi\)
\(822\) 0 0
\(823\) −7.29326 −0.254227 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(824\) 0 0
\(825\) 6.32576 0.220235
\(826\) 0 0
\(827\) 20.8265 0.724209 0.362105 0.932137i \(-0.382058\pi\)
0.362105 + 0.932137i \(0.382058\pi\)
\(828\) 0 0
\(829\) −4.70821 −0.163523 −0.0817614 0.996652i \(-0.526055\pi\)
−0.0817614 + 0.996652i \(0.526055\pi\)
\(830\) 0 0
\(831\) 0.0473018 0.00164088
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −70.0304 −2.42350
\(836\) 0 0
\(837\) 0.931381 0.0321932
\(838\) 0 0
\(839\) 41.1009 1.41896 0.709480 0.704725i \(-0.248930\pi\)
0.709480 + 0.704725i \(0.248930\pi\)
\(840\) 0 0
\(841\) −9.42754 −0.325088
\(842\) 0 0
\(843\) 0.335467 0.0115541
\(844\) 0 0
\(845\) 93.4383 3.21438
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −2.23778 −0.0768005
\(850\) 0 0
\(851\) 12.6995 0.435333
\(852\) 0 0
\(853\) 33.8597 1.15934 0.579668 0.814853i \(-0.303182\pi\)
0.579668 + 0.814853i \(0.303182\pi\)
\(854\) 0 0
\(855\) −76.8926 −2.62967
\(856\) 0 0
\(857\) 18.6073 0.635613 0.317806 0.948156i \(-0.397054\pi\)
0.317806 + 0.948156i \(0.397054\pi\)
\(858\) 0 0
\(859\) −19.1801 −0.654415 −0.327207 0.944953i \(-0.606108\pi\)
−0.327207 + 0.944953i \(0.606108\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32.3298 −1.10052 −0.550259 0.834994i \(-0.685471\pi\)
−0.550259 + 0.834994i \(0.685471\pi\)
\(864\) 0 0
\(865\) −8.38258 −0.285016
\(866\) 0 0
\(867\) −3.22408 −0.109495
\(868\) 0 0
\(869\) −8.15002 −0.276470
\(870\) 0 0
\(871\) 28.7125 0.972887
\(872\) 0 0
\(873\) −30.0046 −1.01550
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −11.3251 −0.382422 −0.191211 0.981549i \(-0.561241\pi\)
−0.191211 + 0.981549i \(0.561241\pi\)
\(878\) 0 0
\(879\) −2.69018 −0.0907375
\(880\) 0 0
\(881\) −5.02177 −0.169188 −0.0845939 0.996416i \(-0.526959\pi\)
−0.0845939 + 0.996416i \(0.526959\pi\)
\(882\) 0 0
\(883\) −0.651629 −0.0219291 −0.0109645 0.999940i \(-0.503490\pi\)
−0.0109645 + 0.999940i \(0.503490\pi\)
\(884\) 0 0
\(885\) 6.94941 0.233602
\(886\) 0 0
\(887\) 15.4506 0.518779 0.259389 0.965773i \(-0.416479\pi\)
0.259389 + 0.965773i \(0.416479\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −49.1529 −1.64669
\(892\) 0 0
\(893\) −31.5264 −1.05499
\(894\) 0 0
\(895\) −4.80764 −0.160702
\(896\) 0 0
\(897\) 4.84030 0.161613
\(898\) 0 0
\(899\) −4.70428 −0.156896
\(900\) 0 0
\(901\) −58.6726 −1.95467
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 90.3885 3.00462
\(906\) 0 0
\(907\) 12.7773 0.424263 0.212132 0.977241i \(-0.431959\pi\)
0.212132 + 0.977241i \(0.431959\pi\)
\(908\) 0 0
\(909\) −20.1993 −0.669969
\(910\) 0 0
\(911\) −18.8263 −0.623744 −0.311872 0.950124i \(-0.600956\pi\)
−0.311872 + 0.950124i \(0.600956\pi\)
\(912\) 0 0
\(913\) −23.5202 −0.778405
\(914\) 0 0
\(915\) −7.48237 −0.247359
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 47.2712 1.55933 0.779667 0.626194i \(-0.215388\pi\)
0.779667 + 0.626194i \(0.215388\pi\)
\(920\) 0 0
\(921\) 4.01443 0.132280
\(922\) 0 0
\(923\) 0.142731 0.00469804
\(924\) 0 0
\(925\) 18.6150 0.612056
\(926\) 0 0
\(927\) −44.3297 −1.45598
\(928\) 0 0
\(929\) 25.1270 0.824390 0.412195 0.911096i \(-0.364762\pi\)
0.412195 + 0.911096i \(0.364762\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −1.44019 −0.0471498
\(934\) 0 0
\(935\) 124.394 4.06811
\(936\) 0 0
\(937\) −28.3047 −0.924674 −0.462337 0.886704i \(-0.652989\pi\)
−0.462337 + 0.886704i \(0.652989\pi\)
\(938\) 0 0
\(939\) −0.00336905 −0.000109945 0
\(940\) 0 0
\(941\) 2.63050 0.0857519 0.0428759 0.999080i \(-0.486348\pi\)
0.0428759 + 0.999080i \(0.486348\pi\)
\(942\) 0 0
\(943\) −5.27797 −0.171874
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −37.3928 −1.21510 −0.607552 0.794280i \(-0.707848\pi\)
−0.607552 + 0.794280i \(0.707848\pi\)
\(948\) 0 0
\(949\) −80.0207 −2.59758
\(950\) 0 0
\(951\) 1.21959 0.0395480
\(952\) 0 0
\(953\) 15.4868 0.501667 0.250833 0.968030i \(-0.419295\pi\)
0.250833 + 0.968030i \(0.419295\pi\)
\(954\) 0 0
\(955\) −48.9295 −1.58332
\(956\) 0 0
\(957\) −3.61737 −0.116933
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.8693 −0.963526
\(962\) 0 0
\(963\) −9.64996 −0.310966
\(964\) 0 0
\(965\) −51.0194 −1.64237
\(966\) 0 0
\(967\) 37.4311 1.20370 0.601852 0.798608i \(-0.294430\pi\)
0.601852 + 0.798608i \(0.294430\pi\)
\(968\) 0 0
\(969\) 6.61890 0.212630
\(970\) 0 0
\(971\) 24.2651 0.778704 0.389352 0.921089i \(-0.372699\pi\)
0.389352 + 0.921089i \(0.372699\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 7.09492 0.227219
\(976\) 0 0
\(977\) −16.1282 −0.515986 −0.257993 0.966147i \(-0.583061\pi\)
−0.257993 + 0.966147i \(0.583061\pi\)
\(978\) 0 0
\(979\) 19.8903 0.635697
\(980\) 0 0
\(981\) 35.9152 1.14668
\(982\) 0 0
\(983\) 12.9169 0.411986 0.205993 0.978553i \(-0.433958\pi\)
0.205993 + 0.978553i \(0.433958\pi\)
\(984\) 0 0
\(985\) −30.2128 −0.962661
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 64.8536 2.06222
\(990\) 0 0
\(991\) −19.8559 −0.630743 −0.315372 0.948968i \(-0.602129\pi\)
−0.315372 + 0.948968i \(0.602129\pi\)
\(992\) 0 0
\(993\) 2.78365 0.0883365
\(994\) 0 0
\(995\) −8.10617 −0.256983
\(996\) 0 0
\(997\) −38.6874 −1.22524 −0.612621 0.790377i \(-0.709885\pi\)
−0.612621 + 0.790377i \(0.709885\pi\)
\(998\) 0 0
\(999\) 2.10754 0.0666798
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 \(a_p\))