Properties

Label 8036.2.a.t.1.13
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.13
Root \(1.06664\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.06664 q^{3}\) \(-0.715473 q^{5}\) \(-1.86229 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.06664 q^{3}\) \(-0.715473 q^{5}\) \(-1.86229 q^{9}\) \(-0.203291 q^{11}\) \(-4.07678 q^{13}\) \(-0.763149 q^{15}\) \(+1.49788 q^{17}\) \(-1.74419 q^{19}\) \(-4.09950 q^{23}\) \(-4.48810 q^{25}\) \(-5.18629 q^{27}\) \(-5.13540 q^{29}\) \(-3.89553 q^{31}\) \(-0.216837 q^{33}\) \(+9.19415 q^{37}\) \(-4.34844 q^{39}\) \(-1.00000 q^{41}\) \(+1.74486 q^{43}\) \(+1.33242 q^{45}\) \(+6.43307 q^{47}\) \(+1.59769 q^{51}\) \(+6.61543 q^{53}\) \(+0.145449 q^{55}\) \(-1.86042 q^{57}\) \(+12.8894 q^{59}\) \(+14.5230 q^{61}\) \(+2.91683 q^{65}\) \(-0.105967 q^{67}\) \(-4.37267 q^{69}\) \(+14.3712 q^{71}\) \(+13.2224 q^{73}\) \(-4.78716 q^{75}\) \(+6.88922 q^{79}\) \(+0.0549876 q^{81}\) \(-2.43452 q^{83}\) \(-1.07169 q^{85}\) \(-5.47760 q^{87}\) \(-4.37395 q^{89}\) \(-4.15511 q^{93}\) \(+1.24792 q^{95}\) \(+11.1054 q^{97}\) \(+0.378586 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.06664 0.615822 0.307911 0.951415i \(-0.400370\pi\)
0.307911 + 0.951415i \(0.400370\pi\)
\(4\) 0 0
\(5\) −0.715473 −0.319969 −0.159985 0.987120i \(-0.551144\pi\)
−0.159985 + 0.987120i \(0.551144\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.86229 −0.620763
\(10\) 0 0
\(11\) −0.203291 −0.0612944 −0.0306472 0.999530i \(-0.509757\pi\)
−0.0306472 + 0.999530i \(0.509757\pi\)
\(12\) 0 0
\(13\) −4.07678 −1.13070 −0.565348 0.824853i \(-0.691258\pi\)
−0.565348 + 0.824853i \(0.691258\pi\)
\(14\) 0 0
\(15\) −0.763149 −0.197044
\(16\) 0 0
\(17\) 1.49788 0.363289 0.181645 0.983364i \(-0.441858\pi\)
0.181645 + 0.983364i \(0.441858\pi\)
\(18\) 0 0
\(19\) −1.74419 −0.400145 −0.200073 0.979781i \(-0.564118\pi\)
−0.200073 + 0.979781i \(0.564118\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.09950 −0.854804 −0.427402 0.904062i \(-0.640571\pi\)
−0.427402 + 0.904062i \(0.640571\pi\)
\(24\) 0 0
\(25\) −4.48810 −0.897620
\(26\) 0 0
\(27\) −5.18629 −0.998102
\(28\) 0 0
\(29\) −5.13540 −0.953620 −0.476810 0.879006i \(-0.658207\pi\)
−0.476810 + 0.879006i \(0.658207\pi\)
\(30\) 0 0
\(31\) −3.89553 −0.699657 −0.349829 0.936814i \(-0.613760\pi\)
−0.349829 + 0.936814i \(0.613760\pi\)
\(32\) 0 0
\(33\) −0.216837 −0.0377465
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.19415 1.51151 0.755754 0.654856i \(-0.227271\pi\)
0.755754 + 0.654856i \(0.227271\pi\)
\(38\) 0 0
\(39\) −4.34844 −0.696308
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 1.74486 0.266089 0.133044 0.991110i \(-0.457525\pi\)
0.133044 + 0.991110i \(0.457525\pi\)
\(44\) 0 0
\(45\) 1.33242 0.198625
\(46\) 0 0
\(47\) 6.43307 0.938360 0.469180 0.883103i \(-0.344550\pi\)
0.469180 + 0.883103i \(0.344550\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.59769 0.223722
\(52\) 0 0
\(53\) 6.61543 0.908699 0.454349 0.890824i \(-0.349872\pi\)
0.454349 + 0.890824i \(0.349872\pi\)
\(54\) 0 0
\(55\) 0.145449 0.0196123
\(56\) 0 0
\(57\) −1.86042 −0.246418
\(58\) 0 0
\(59\) 12.8894 1.67806 0.839030 0.544085i \(-0.183123\pi\)
0.839030 + 0.544085i \(0.183123\pi\)
\(60\) 0 0
\(61\) 14.5230 1.85947 0.929737 0.368224i \(-0.120034\pi\)
0.929737 + 0.368224i \(0.120034\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.91683 0.361788
\(66\) 0 0
\(67\) −0.105967 −0.0129460 −0.00647299 0.999979i \(-0.502060\pi\)
−0.00647299 + 0.999979i \(0.502060\pi\)
\(68\) 0 0
\(69\) −4.37267 −0.526407
\(70\) 0 0
\(71\) 14.3712 1.70555 0.852775 0.522278i \(-0.174918\pi\)
0.852775 + 0.522278i \(0.174918\pi\)
\(72\) 0 0
\(73\) 13.2224 1.54756 0.773782 0.633452i \(-0.218362\pi\)
0.773782 + 0.633452i \(0.218362\pi\)
\(74\) 0 0
\(75\) −4.78716 −0.552774
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.88922 0.775098 0.387549 0.921849i \(-0.373322\pi\)
0.387549 + 0.921849i \(0.373322\pi\)
\(80\) 0 0
\(81\) 0.0549876 0.00610973
\(82\) 0 0
\(83\) −2.43452 −0.267223 −0.133612 0.991034i \(-0.542657\pi\)
−0.133612 + 0.991034i \(0.542657\pi\)
\(84\) 0 0
\(85\) −1.07169 −0.116241
\(86\) 0 0
\(87\) −5.47760 −0.587261
\(88\) 0 0
\(89\) −4.37395 −0.463638 −0.231819 0.972759i \(-0.574468\pi\)
−0.231819 + 0.972759i \(0.574468\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.15511 −0.430864
\(94\) 0 0
\(95\) 1.24792 0.128034
\(96\) 0 0
\(97\) 11.1054 1.12758 0.563789 0.825919i \(-0.309343\pi\)
0.563789 + 0.825919i \(0.309343\pi\)
\(98\) 0 0
\(99\) 0.378586 0.0380493
\(100\) 0 0
\(101\) −16.5526 −1.64705 −0.823523 0.567283i \(-0.807995\pi\)
−0.823523 + 0.567283i \(0.807995\pi\)
\(102\) 0 0
\(103\) 16.9276 1.66793 0.833964 0.551819i \(-0.186066\pi\)
0.833964 + 0.551819i \(0.186066\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0473 1.16466 0.582329 0.812953i \(-0.302142\pi\)
0.582329 + 0.812953i \(0.302142\pi\)
\(108\) 0 0
\(109\) −0.740391 −0.0709166 −0.0354583 0.999371i \(-0.511289\pi\)
−0.0354583 + 0.999371i \(0.511289\pi\)
\(110\) 0 0
\(111\) 9.80680 0.930820
\(112\) 0 0
\(113\) 15.3332 1.44242 0.721212 0.692714i \(-0.243585\pi\)
0.721212 + 0.692714i \(0.243585\pi\)
\(114\) 0 0
\(115\) 2.93308 0.273511
\(116\) 0 0
\(117\) 7.59215 0.701894
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9587 −0.996243
\(122\) 0 0
\(123\) −1.06664 −0.0961753
\(124\) 0 0
\(125\) 6.78848 0.607180
\(126\) 0 0
\(127\) −17.9159 −1.58978 −0.794889 0.606756i \(-0.792471\pi\)
−0.794889 + 0.606756i \(0.792471\pi\)
\(128\) 0 0
\(129\) 1.86113 0.163863
\(130\) 0 0
\(131\) −3.85953 −0.337208 −0.168604 0.985684i \(-0.553926\pi\)
−0.168604 + 0.985684i \(0.553926\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.71065 0.319362
\(136\) 0 0
\(137\) −9.19838 −0.785871 −0.392935 0.919566i \(-0.628540\pi\)
−0.392935 + 0.919566i \(0.628540\pi\)
\(138\) 0 0
\(139\) −5.85466 −0.496586 −0.248293 0.968685i \(-0.579870\pi\)
−0.248293 + 0.968685i \(0.579870\pi\)
\(140\) 0 0
\(141\) 6.86174 0.577863
\(142\) 0 0
\(143\) 0.828772 0.0693054
\(144\) 0 0
\(145\) 3.67424 0.305129
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −18.8299 −1.54260 −0.771301 0.636470i \(-0.780394\pi\)
−0.771301 + 0.636470i \(0.780394\pi\)
\(150\) 0 0
\(151\) −21.8901 −1.78139 −0.890696 0.454599i \(-0.849783\pi\)
−0.890696 + 0.454599i \(0.849783\pi\)
\(152\) 0 0
\(153\) −2.78949 −0.225517
\(154\) 0 0
\(155\) 2.78714 0.223869
\(156\) 0 0
\(157\) −0.114806 −0.00916251 −0.00458125 0.999990i \(-0.501458\pi\)
−0.00458125 + 0.999990i \(0.501458\pi\)
\(158\) 0 0
\(159\) 7.05625 0.559597
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.14673 0.638101 0.319051 0.947738i \(-0.396636\pi\)
0.319051 + 0.947738i \(0.396636\pi\)
\(164\) 0 0
\(165\) 0.155141 0.0120777
\(166\) 0 0
\(167\) −18.1119 −1.40154 −0.700769 0.713389i \(-0.747160\pi\)
−0.700769 + 0.713389i \(0.747160\pi\)
\(168\) 0 0
\(169\) 3.62015 0.278473
\(170\) 0 0
\(171\) 3.24819 0.248395
\(172\) 0 0
\(173\) 17.7255 1.34765 0.673824 0.738892i \(-0.264651\pi\)
0.673824 + 0.738892i \(0.264651\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.7483 1.03339
\(178\) 0 0
\(179\) 23.3759 1.74720 0.873598 0.486648i \(-0.161781\pi\)
0.873598 + 0.486648i \(0.161781\pi\)
\(180\) 0 0
\(181\) −18.2576 −1.35707 −0.678537 0.734566i \(-0.737386\pi\)
−0.678537 + 0.734566i \(0.737386\pi\)
\(182\) 0 0
\(183\) 15.4907 1.14511
\(184\) 0 0
\(185\) −6.57816 −0.483636
\(186\) 0 0
\(187\) −0.304505 −0.0222676
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.7507 0.994967 0.497484 0.867473i \(-0.334257\pi\)
0.497484 + 0.867473i \(0.334257\pi\)
\(192\) 0 0
\(193\) −12.6068 −0.907458 −0.453729 0.891140i \(-0.649907\pi\)
−0.453729 + 0.891140i \(0.649907\pi\)
\(194\) 0 0
\(195\) 3.11119 0.222797
\(196\) 0 0
\(197\) 0.817144 0.0582191 0.0291095 0.999576i \(-0.490733\pi\)
0.0291095 + 0.999576i \(0.490733\pi\)
\(198\) 0 0
\(199\) 25.7193 1.82320 0.911598 0.411083i \(-0.134849\pi\)
0.911598 + 0.411083i \(0.134849\pi\)
\(200\) 0 0
\(201\) −0.113029 −0.00797243
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.715473 0.0499708
\(206\) 0 0
\(207\) 7.63445 0.530631
\(208\) 0 0
\(209\) 0.354578 0.0245267
\(210\) 0 0
\(211\) −11.0150 −0.758306 −0.379153 0.925334i \(-0.623785\pi\)
−0.379153 + 0.925334i \(0.623785\pi\)
\(212\) 0 0
\(213\) 15.3289 1.05032
\(214\) 0 0
\(215\) −1.24840 −0.0851401
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 14.1035 0.953025
\(220\) 0 0
\(221\) −6.10653 −0.410770
\(222\) 0 0
\(223\) 25.4981 1.70748 0.853740 0.520700i \(-0.174329\pi\)
0.853740 + 0.520700i \(0.174329\pi\)
\(224\) 0 0
\(225\) 8.35814 0.557209
\(226\) 0 0
\(227\) −0.861316 −0.0571676 −0.0285838 0.999591i \(-0.509100\pi\)
−0.0285838 + 0.999591i \(0.509100\pi\)
\(228\) 0 0
\(229\) −6.01082 −0.397206 −0.198603 0.980080i \(-0.563640\pi\)
−0.198603 + 0.980080i \(0.563640\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.80151 −0.183533 −0.0917664 0.995781i \(-0.529251\pi\)
−0.0917664 + 0.995781i \(0.529251\pi\)
\(234\) 0 0
\(235\) −4.60269 −0.300246
\(236\) 0 0
\(237\) 7.34828 0.477322
\(238\) 0 0
\(239\) 19.6931 1.27384 0.636919 0.770930i \(-0.280208\pi\)
0.636919 + 0.770930i \(0.280208\pi\)
\(240\) 0 0
\(241\) 2.80922 0.180958 0.0904789 0.995898i \(-0.471160\pi\)
0.0904789 + 0.995898i \(0.471160\pi\)
\(242\) 0 0
\(243\) 15.6175 1.00186
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 7.11069 0.452443
\(248\) 0 0
\(249\) −2.59675 −0.164562
\(250\) 0 0
\(251\) −1.62156 −0.102352 −0.0511760 0.998690i \(-0.516297\pi\)
−0.0511760 + 0.998690i \(0.516297\pi\)
\(252\) 0 0
\(253\) 0.833389 0.0523947
\(254\) 0 0
\(255\) −1.14311 −0.0715840
\(256\) 0 0
\(257\) 12.7893 0.797773 0.398887 0.917000i \(-0.369397\pi\)
0.398887 + 0.917000i \(0.369397\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.56361 0.591972
\(262\) 0 0
\(263\) −24.4563 −1.50804 −0.754020 0.656852i \(-0.771888\pi\)
−0.754020 + 0.656852i \(0.771888\pi\)
\(264\) 0 0
\(265\) −4.73316 −0.290756
\(266\) 0 0
\(267\) −4.66541 −0.285518
\(268\) 0 0
\(269\) 15.5542 0.948358 0.474179 0.880429i \(-0.342745\pi\)
0.474179 + 0.880429i \(0.342745\pi\)
\(270\) 0 0
\(271\) −6.47684 −0.393440 −0.196720 0.980460i \(-0.563029\pi\)
−0.196720 + 0.980460i \(0.563029\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.912388 0.0550191
\(276\) 0 0
\(277\) −6.79599 −0.408331 −0.204166 0.978936i \(-0.565448\pi\)
−0.204166 + 0.978936i \(0.565448\pi\)
\(278\) 0 0
\(279\) 7.25459 0.434321
\(280\) 0 0
\(281\) −9.02577 −0.538432 −0.269216 0.963080i \(-0.586765\pi\)
−0.269216 + 0.963080i \(0.586765\pi\)
\(282\) 0 0
\(283\) −20.9495 −1.24532 −0.622661 0.782492i \(-0.713948\pi\)
−0.622661 + 0.782492i \(0.713948\pi\)
\(284\) 0 0
\(285\) 1.33108 0.0788463
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −14.7564 −0.868021
\(290\) 0 0
\(291\) 11.8454 0.694388
\(292\) 0 0
\(293\) −19.7143 −1.15172 −0.575861 0.817547i \(-0.695333\pi\)
−0.575861 + 0.817547i \(0.695333\pi\)
\(294\) 0 0
\(295\) −9.22203 −0.536927
\(296\) 0 0
\(297\) 1.05432 0.0611781
\(298\) 0 0
\(299\) 16.7128 0.966524
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −17.6556 −1.01429
\(304\) 0 0
\(305\) −10.3908 −0.594974
\(306\) 0 0
\(307\) 2.69256 0.153672 0.0768361 0.997044i \(-0.475518\pi\)
0.0768361 + 0.997044i \(0.475518\pi\)
\(308\) 0 0
\(309\) 18.0556 1.02715
\(310\) 0 0
\(311\) 14.2409 0.807527 0.403764 0.914863i \(-0.367702\pi\)
0.403764 + 0.914863i \(0.367702\pi\)
\(312\) 0 0
\(313\) 31.4841 1.77959 0.889794 0.456363i \(-0.150848\pi\)
0.889794 + 0.456363i \(0.150848\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.8349 −1.05787 −0.528936 0.848662i \(-0.677409\pi\)
−0.528936 + 0.848662i \(0.677409\pi\)
\(318\) 0 0
\(319\) 1.04398 0.0584516
\(320\) 0 0
\(321\) 12.8501 0.717222
\(322\) 0 0
\(323\) −2.61259 −0.145368
\(324\) 0 0
\(325\) 18.2970 1.01493
\(326\) 0 0
\(327\) −0.789727 −0.0436720
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.16405 0.448737 0.224368 0.974504i \(-0.427968\pi\)
0.224368 + 0.974504i \(0.427968\pi\)
\(332\) 0 0
\(333\) −17.1222 −0.938288
\(334\) 0 0
\(335\) 0.0758168 0.00414232
\(336\) 0 0
\(337\) 28.7590 1.56660 0.783300 0.621643i \(-0.213535\pi\)
0.783300 + 0.621643i \(0.213535\pi\)
\(338\) 0 0
\(339\) 16.3549 0.888277
\(340\) 0 0
\(341\) 0.791924 0.0428851
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 3.12853 0.168434
\(346\) 0 0
\(347\) −16.3427 −0.877320 −0.438660 0.898653i \(-0.644547\pi\)
−0.438660 + 0.898653i \(0.644547\pi\)
\(348\) 0 0
\(349\) 34.3702 1.83980 0.919898 0.392157i \(-0.128271\pi\)
0.919898 + 0.392157i \(0.128271\pi\)
\(350\) 0 0
\(351\) 21.1434 1.12855
\(352\) 0 0
\(353\) 33.6237 1.78961 0.894806 0.446456i \(-0.147314\pi\)
0.894806 + 0.446456i \(0.147314\pi\)
\(354\) 0 0
\(355\) −10.2822 −0.545723
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 28.2344 1.49015 0.745076 0.666980i \(-0.232413\pi\)
0.745076 + 0.666980i \(0.232413\pi\)
\(360\) 0 0
\(361\) −15.9578 −0.839884
\(362\) 0 0
\(363\) −11.6889 −0.613509
\(364\) 0 0
\(365\) −9.46027 −0.495173
\(366\) 0 0
\(367\) −12.7369 −0.664861 −0.332431 0.943128i \(-0.607869\pi\)
−0.332431 + 0.943128i \(0.607869\pi\)
\(368\) 0 0
\(369\) 1.86229 0.0969469
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0.0901714 0.00466890 0.00233445 0.999997i \(-0.499257\pi\)
0.00233445 + 0.999997i \(0.499257\pi\)
\(374\) 0 0
\(375\) 7.24083 0.373915
\(376\) 0 0
\(377\) 20.9359 1.07825
\(378\) 0 0
\(379\) −12.3658 −0.635186 −0.317593 0.948227i \(-0.602875\pi\)
−0.317593 + 0.948227i \(0.602875\pi\)
\(380\) 0 0
\(381\) −19.1097 −0.979020
\(382\) 0 0
\(383\) −14.1692 −0.724013 −0.362007 0.932175i \(-0.617908\pi\)
−0.362007 + 0.932175i \(0.617908\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.24943 −0.165178
\(388\) 0 0
\(389\) −18.6685 −0.946530 −0.473265 0.880920i \(-0.656925\pi\)
−0.473265 + 0.880920i \(0.656925\pi\)
\(390\) 0 0
\(391\) −6.14055 −0.310541
\(392\) 0 0
\(393\) −4.11671 −0.207660
\(394\) 0 0
\(395\) −4.92905 −0.248007
\(396\) 0 0
\(397\) −17.9221 −0.899485 −0.449743 0.893158i \(-0.648484\pi\)
−0.449743 + 0.893158i \(0.648484\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.32147 −0.115928 −0.0579642 0.998319i \(-0.518461\pi\)
−0.0579642 + 0.998319i \(0.518461\pi\)
\(402\) 0 0
\(403\) 15.8812 0.791099
\(404\) 0 0
\(405\) −0.0393421 −0.00195493
\(406\) 0 0
\(407\) −1.86908 −0.0926470
\(408\) 0 0
\(409\) 2.74754 0.135857 0.0679287 0.997690i \(-0.478361\pi\)
0.0679287 + 0.997690i \(0.478361\pi\)
\(410\) 0 0
\(411\) −9.81132 −0.483957
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.74183 0.0855033
\(416\) 0 0
\(417\) −6.24479 −0.305809
\(418\) 0 0
\(419\) −14.3395 −0.700532 −0.350266 0.936650i \(-0.613909\pi\)
−0.350266 + 0.936650i \(0.613909\pi\)
\(420\) 0 0
\(421\) 24.5005 1.19408 0.597041 0.802211i \(-0.296343\pi\)
0.597041 + 0.802211i \(0.296343\pi\)
\(422\) 0 0
\(423\) −11.9802 −0.582499
\(424\) 0 0
\(425\) −6.72263 −0.326096
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.883997 0.0426798
\(430\) 0 0
\(431\) −33.7836 −1.62730 −0.813648 0.581357i \(-0.802522\pi\)
−0.813648 + 0.581357i \(0.802522\pi\)
\(432\) 0 0
\(433\) 14.9803 0.719907 0.359953 0.932970i \(-0.382793\pi\)
0.359953 + 0.932970i \(0.382793\pi\)
\(434\) 0 0
\(435\) 3.91908 0.187905
\(436\) 0 0
\(437\) 7.15031 0.342046
\(438\) 0 0
\(439\) 10.9944 0.524733 0.262367 0.964968i \(-0.415497\pi\)
0.262367 + 0.964968i \(0.415497\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 32.5677 1.54734 0.773669 0.633590i \(-0.218419\pi\)
0.773669 + 0.633590i \(0.218419\pi\)
\(444\) 0 0
\(445\) 3.12944 0.148350
\(446\) 0 0
\(447\) −20.0846 −0.949969
\(448\) 0 0
\(449\) −40.8875 −1.92960 −0.964801 0.262982i \(-0.915294\pi\)
−0.964801 + 0.262982i \(0.915294\pi\)
\(450\) 0 0
\(451\) 0.203291 0.00957258
\(452\) 0 0
\(453\) −23.3488 −1.09702
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2.66835 −0.124820 −0.0624101 0.998051i \(-0.519879\pi\)
−0.0624101 + 0.998051i \(0.519879\pi\)
\(458\) 0 0
\(459\) −7.76844 −0.362600
\(460\) 0 0
\(461\) 5.07360 0.236301 0.118151 0.992996i \(-0.462303\pi\)
0.118151 + 0.992996i \(0.462303\pi\)
\(462\) 0 0
\(463\) −33.9827 −1.57931 −0.789655 0.613551i \(-0.789741\pi\)
−0.789655 + 0.613551i \(0.789741\pi\)
\(464\) 0 0
\(465\) 2.97287 0.137863
\(466\) 0 0
\(467\) 20.6133 0.953869 0.476935 0.878939i \(-0.341748\pi\)
0.476935 + 0.878939i \(0.341748\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.122456 −0.00564248
\(472\) 0 0
\(473\) −0.354714 −0.0163097
\(474\) 0 0
\(475\) 7.82811 0.359178
\(476\) 0 0
\(477\) −12.3198 −0.564086
\(478\) 0 0
\(479\) −0.766787 −0.0350354 −0.0175177 0.999847i \(-0.505576\pi\)
−0.0175177 + 0.999847i \(0.505576\pi\)
\(480\) 0 0
\(481\) −37.4825 −1.70906
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.94558 −0.360790
\(486\) 0 0
\(487\) −5.65740 −0.256361 −0.128181 0.991751i \(-0.540914\pi\)
−0.128181 + 0.991751i \(0.540914\pi\)
\(488\) 0 0
\(489\) 8.68960 0.392957
\(490\) 0 0
\(491\) 5.55831 0.250843 0.125422 0.992104i \(-0.459972\pi\)
0.125422 + 0.992104i \(0.459972\pi\)
\(492\) 0 0
\(493\) −7.69222 −0.346440
\(494\) 0 0
\(495\) −0.270868 −0.0121746
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 35.1207 1.57222 0.786108 0.618089i \(-0.212093\pi\)
0.786108 + 0.618089i \(0.212093\pi\)
\(500\) 0 0
\(501\) −19.3187 −0.863098
\(502\) 0 0
\(503\) −8.33640 −0.371702 −0.185851 0.982578i \(-0.559504\pi\)
−0.185851 + 0.982578i \(0.559504\pi\)
\(504\) 0 0
\(505\) 11.8429 0.527004
\(506\) 0 0
\(507\) 3.86138 0.171490
\(508\) 0 0
\(509\) 29.4727 1.30635 0.653177 0.757205i \(-0.273436\pi\)
0.653177 + 0.757205i \(0.273436\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 9.04589 0.399386
\(514\) 0 0
\(515\) −12.1112 −0.533685
\(516\) 0 0
\(517\) −1.30778 −0.0575163
\(518\) 0 0
\(519\) 18.9067 0.829911
\(520\) 0 0
\(521\) 11.8169 0.517707 0.258853 0.965917i \(-0.416655\pi\)
0.258853 + 0.965917i \(0.416655\pi\)
\(522\) 0 0
\(523\) 36.4835 1.59531 0.797656 0.603113i \(-0.206073\pi\)
0.797656 + 0.603113i \(0.206073\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.83503 −0.254178
\(528\) 0 0
\(529\) −6.19413 −0.269310
\(530\) 0 0
\(531\) −24.0038 −1.04168
\(532\) 0 0
\(533\) 4.07678 0.176585
\(534\) 0 0
\(535\) −8.61953 −0.372655
\(536\) 0 0
\(537\) 24.9335 1.07596
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 17.4703 0.751107 0.375553 0.926801i \(-0.377453\pi\)
0.375553 + 0.926801i \(0.377453\pi\)
\(542\) 0 0
\(543\) −19.4742 −0.835717
\(544\) 0 0
\(545\) 0.529730 0.0226911
\(546\) 0 0
\(547\) 22.4215 0.958673 0.479337 0.877631i \(-0.340877\pi\)
0.479337 + 0.877631i \(0.340877\pi\)
\(548\) 0 0
\(549\) −27.0459 −1.15429
\(550\) 0 0
\(551\) 8.95713 0.381587
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −7.01650 −0.297834
\(556\) 0 0
\(557\) −5.30562 −0.224806 −0.112403 0.993663i \(-0.535855\pi\)
−0.112403 + 0.993663i \(0.535855\pi\)
\(558\) 0 0
\(559\) −7.11341 −0.300865
\(560\) 0 0
\(561\) −0.324796 −0.0137129
\(562\) 0 0
\(563\) −8.36390 −0.352496 −0.176248 0.984346i \(-0.556396\pi\)
−0.176248 + 0.984346i \(0.556396\pi\)
\(564\) 0 0
\(565\) −10.9705 −0.461531
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 30.7650 1.28974 0.644868 0.764294i \(-0.276912\pi\)
0.644868 + 0.764294i \(0.276912\pi\)
\(570\) 0 0
\(571\) −10.4697 −0.438145 −0.219072 0.975709i \(-0.570303\pi\)
−0.219072 + 0.975709i \(0.570303\pi\)
\(572\) 0 0
\(573\) 14.6670 0.612723
\(574\) 0 0
\(575\) 18.3989 0.767289
\(576\) 0 0
\(577\) 19.1722 0.798150 0.399075 0.916918i \(-0.369331\pi\)
0.399075 + 0.916918i \(0.369331\pi\)
\(578\) 0 0
\(579\) −13.4469 −0.558833
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.34485 −0.0556982
\(584\) 0 0
\(585\) −5.43197 −0.224585
\(586\) 0 0
\(587\) 23.2967 0.961559 0.480779 0.876842i \(-0.340354\pi\)
0.480779 + 0.876842i \(0.340354\pi\)
\(588\) 0 0
\(589\) 6.79455 0.279964
\(590\) 0 0
\(591\) 0.871595 0.0358526
\(592\) 0 0
\(593\) −3.59717 −0.147718 −0.0738590 0.997269i \(-0.523531\pi\)
−0.0738590 + 0.997269i \(0.523531\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 27.4332 1.12276
\(598\) 0 0
\(599\) −42.0452 −1.71792 −0.858961 0.512041i \(-0.828889\pi\)
−0.858961 + 0.512041i \(0.828889\pi\)
\(600\) 0 0
\(601\) 19.9085 0.812084 0.406042 0.913854i \(-0.366909\pi\)
0.406042 + 0.913854i \(0.366909\pi\)
\(602\) 0 0
\(603\) 0.197342 0.00803639
\(604\) 0 0
\(605\) 7.84063 0.318767
\(606\) 0 0
\(607\) 37.6134 1.52668 0.763341 0.645996i \(-0.223558\pi\)
0.763341 + 0.645996i \(0.223558\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −26.2262 −1.06100
\(612\) 0 0
\(613\) 16.3767 0.661448 0.330724 0.943728i \(-0.392707\pi\)
0.330724 + 0.943728i \(0.392707\pi\)
\(614\) 0 0
\(615\) 0.763149 0.0307731
\(616\) 0 0
\(617\) 22.8650 0.920509 0.460255 0.887787i \(-0.347758\pi\)
0.460255 + 0.887787i \(0.347758\pi\)
\(618\) 0 0
\(619\) −14.3938 −0.578536 −0.289268 0.957248i \(-0.593412\pi\)
−0.289268 + 0.957248i \(0.593412\pi\)
\(620\) 0 0
\(621\) 21.2612 0.853182
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 17.5835 0.703341
\(626\) 0 0
\(627\) 0.378205 0.0151041
\(628\) 0 0
\(629\) 13.7717 0.549115
\(630\) 0 0
\(631\) −34.5118 −1.37389 −0.686946 0.726709i \(-0.741049\pi\)
−0.686946 + 0.726709i \(0.741049\pi\)
\(632\) 0 0
\(633\) −11.7490 −0.466981
\(634\) 0 0
\(635\) 12.8183 0.508680
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −26.7634 −1.05874
\(640\) 0 0
\(641\) 27.1524 1.07245 0.536227 0.844074i \(-0.319849\pi\)
0.536227 + 0.844074i \(0.319849\pi\)
\(642\) 0 0
\(643\) 29.5059 1.16360 0.581800 0.813332i \(-0.302349\pi\)
0.581800 + 0.813332i \(0.302349\pi\)
\(644\) 0 0
\(645\) −1.33159 −0.0524312
\(646\) 0 0
\(647\) −22.5174 −0.885251 −0.442625 0.896707i \(-0.645953\pi\)
−0.442625 + 0.896707i \(0.645953\pi\)
\(648\) 0 0
\(649\) −2.62030 −0.102856
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −14.7254 −0.576248 −0.288124 0.957593i \(-0.593032\pi\)
−0.288124 + 0.957593i \(0.593032\pi\)
\(654\) 0 0
\(655\) 2.76139 0.107896
\(656\) 0 0
\(657\) −24.6239 −0.960671
\(658\) 0 0
\(659\) −19.4025 −0.755816 −0.377908 0.925843i \(-0.623356\pi\)
−0.377908 + 0.925843i \(0.623356\pi\)
\(660\) 0 0
\(661\) 4.44756 0.172990 0.0864950 0.996252i \(-0.472433\pi\)
0.0864950 + 0.996252i \(0.472433\pi\)
\(662\) 0 0
\(663\) −6.51344 −0.252961
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 21.0526 0.815159
\(668\) 0 0
\(669\) 27.1972 1.05150
\(670\) 0 0
\(671\) −2.95238 −0.113975
\(672\) 0 0
\(673\) −34.2080 −1.31862 −0.659310 0.751871i \(-0.729152\pi\)
−0.659310 + 0.751871i \(0.729152\pi\)
\(674\) 0 0
\(675\) 23.2766 0.895916
\(676\) 0 0
\(677\) −7.76820 −0.298556 −0.149278 0.988795i \(-0.547695\pi\)
−0.149278 + 0.988795i \(0.547695\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.918711 −0.0352051
\(682\) 0 0
\(683\) 37.2431 1.42507 0.712534 0.701637i \(-0.247547\pi\)
0.712534 + 0.701637i \(0.247547\pi\)
\(684\) 0 0
\(685\) 6.58119 0.251454
\(686\) 0 0
\(687\) −6.41135 −0.244608
\(688\) 0 0
\(689\) −26.9696 −1.02746
\(690\) 0 0
\(691\) −1.92228 −0.0731271 −0.0365635 0.999331i \(-0.511641\pi\)
−0.0365635 + 0.999331i \(0.511641\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.18885 0.158892
\(696\) 0 0
\(697\) −1.49788 −0.0567362
\(698\) 0 0
\(699\) −2.98818 −0.113024
\(700\) 0 0
\(701\) 50.1648 1.89470 0.947350 0.320201i \(-0.103750\pi\)
0.947350 + 0.320201i \(0.103750\pi\)
\(702\) 0 0
\(703\) −16.0364 −0.604823
\(704\) 0 0
\(705\) −4.90939 −0.184898
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −41.8140 −1.57036 −0.785180 0.619268i \(-0.787429\pi\)
−0.785180 + 0.619268i \(0.787429\pi\)
\(710\) 0 0
\(711\) −12.8297 −0.481152
\(712\) 0 0
\(713\) 15.9697 0.598070
\(714\) 0 0
\(715\) −0.592964 −0.0221756
\(716\) 0 0
\(717\) 21.0053 0.784458
\(718\) 0 0
\(719\) −22.9341 −0.855298 −0.427649 0.903945i \(-0.640658\pi\)
−0.427649 + 0.903945i \(0.640658\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.99641 0.111438
\(724\) 0 0
\(725\) 23.0482 0.855989
\(726\) 0 0
\(727\) −18.6789 −0.692762 −0.346381 0.938094i \(-0.612589\pi\)
−0.346381 + 0.938094i \(0.612589\pi\)
\(728\) 0 0
\(729\) 16.4932 0.610861
\(730\) 0 0
\(731\) 2.61359 0.0966671
\(732\) 0 0
\(733\) 52.7201 1.94726 0.973631 0.228127i \(-0.0732600\pi\)
0.973631 + 0.228127i \(0.0732600\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.0215422 0.000793517 0
\(738\) 0 0
\(739\) −10.8600 −0.399490 −0.199745 0.979848i \(-0.564011\pi\)
−0.199745 + 0.979848i \(0.564011\pi\)
\(740\) 0 0
\(741\) 7.58452 0.278624
\(742\) 0 0
\(743\) −32.6159 −1.19656 −0.598281 0.801286i \(-0.704149\pi\)
−0.598281 + 0.801286i \(0.704149\pi\)
\(744\) 0 0
\(745\) 13.4723 0.493585
\(746\) 0 0
\(747\) 4.53378 0.165882
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.5099 0.456491 0.228246 0.973604i \(-0.426701\pi\)
0.228246 + 0.973604i \(0.426701\pi\)
\(752\) 0 0
\(753\) −1.72961 −0.0630307
\(754\) 0 0
\(755\) 15.6618 0.569991
\(756\) 0 0
\(757\) −45.9033 −1.66838 −0.834192 0.551474i \(-0.814066\pi\)
−0.834192 + 0.551474i \(0.814066\pi\)
\(758\) 0 0
\(759\) 0.888922 0.0322658
\(760\) 0 0
\(761\) 16.5517 0.599998 0.299999 0.953940i \(-0.403014\pi\)
0.299999 + 0.953940i \(0.403014\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.99580 0.0721583
\(766\) 0 0
\(767\) −52.5474 −1.89738
\(768\) 0 0
\(769\) 13.3183 0.480269 0.240134 0.970740i \(-0.422809\pi\)
0.240134 + 0.970740i \(0.422809\pi\)
\(770\) 0 0
\(771\) 13.6415 0.491286
\(772\) 0 0
\(773\) 16.1812 0.581998 0.290999 0.956723i \(-0.406012\pi\)
0.290999 + 0.956723i \(0.406012\pi\)
\(774\) 0 0
\(775\) 17.4835 0.628026
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.74419 0.0624922
\(780\) 0 0
\(781\) −2.92153 −0.104541
\(782\) 0 0
\(783\) 26.6337 0.951810
\(784\) 0 0
\(785\) 0.0821405 0.00293172
\(786\) 0 0
\(787\) −17.8464 −0.636156 −0.318078 0.948065i \(-0.603037\pi\)
−0.318078 + 0.948065i \(0.603037\pi\)
\(788\) 0 0
\(789\) −26.0859 −0.928684
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −59.2069 −2.10250
\(794\) 0 0
\(795\) −5.04855 −0.179054
\(796\) 0 0
\(797\) −7.13372 −0.252689 −0.126345 0.991986i \(-0.540325\pi\)
−0.126345 + 0.991986i \(0.540325\pi\)
\(798\) 0 0
\(799\) 9.63597 0.340896
\(800\) 0 0
\(801\) 8.14556 0.287809
\(802\) 0 0
\(803\) −2.68799 −0.0948571
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 16.5907 0.584020
\(808\) 0 0
\(809\) 25.3449 0.891081 0.445540 0.895262i \(-0.353012\pi\)
0.445540 + 0.895262i \(0.353012\pi\)
\(810\) 0 0
\(811\) 1.80874 0.0635136 0.0317568 0.999496i \(-0.489890\pi\)
0.0317568 + 0.999496i \(0.489890\pi\)
\(812\) 0 0
\(813\) −6.90842 −0.242289
\(814\) 0 0
\(815\) −5.82877 −0.204173
\(816\) 0 0
\(817\) −3.04337 −0.106474
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −48.5388 −1.69402 −0.847008 0.531581i \(-0.821598\pi\)
−0.847008 + 0.531581i \(0.821598\pi\)
\(822\) 0 0
\(823\) 29.2821 1.02071 0.510355 0.859964i \(-0.329514\pi\)
0.510355 + 0.859964i \(0.329514\pi\)
\(824\) 0 0
\(825\) 0.973186 0.0338820
\(826\) 0 0
\(827\) −17.6267 −0.612940 −0.306470 0.951880i \(-0.599148\pi\)
−0.306470 + 0.951880i \(0.599148\pi\)
\(828\) 0 0
\(829\) 45.7256 1.58812 0.794058 0.607843i \(-0.207965\pi\)
0.794058 + 0.607843i \(0.207965\pi\)
\(830\) 0 0
\(831\) −7.24884 −0.251459
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 12.9585 0.448449
\(836\) 0 0
\(837\) 20.2033 0.698329
\(838\) 0 0
\(839\) 24.4240 0.843210 0.421605 0.906780i \(-0.361467\pi\)
0.421605 + 0.906780i \(0.361467\pi\)
\(840\) 0 0
\(841\) −2.62763 −0.0906081
\(842\) 0 0
\(843\) −9.62720 −0.331578
\(844\) 0 0
\(845\) −2.59012 −0.0891029
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −22.3455 −0.766896
\(850\) 0 0
\(851\) −37.6914 −1.29204
\(852\) 0 0
\(853\) −1.48129 −0.0507185 −0.0253592 0.999678i \(-0.508073\pi\)
−0.0253592 + 0.999678i \(0.508073\pi\)
\(854\) 0 0
\(855\) −2.32399 −0.0794789
\(856\) 0 0
\(857\) 0.323927 0.0110652 0.00553258 0.999985i \(-0.498239\pi\)
0.00553258 + 0.999985i \(0.498239\pi\)
\(858\) 0 0
\(859\) −28.8939 −0.985847 −0.492924 0.870073i \(-0.664072\pi\)
−0.492924 + 0.870073i \(0.664072\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 30.8493 1.05012 0.525062 0.851064i \(-0.324042\pi\)
0.525062 + 0.851064i \(0.324042\pi\)
\(864\) 0 0
\(865\) −12.6821 −0.431206
\(866\) 0 0
\(867\) −15.7397 −0.534547
\(868\) 0 0
\(869\) −1.40051 −0.0475092
\(870\) 0 0
\(871\) 0.432006 0.0146380
\(872\) 0 0
\(873\) −20.6814 −0.699959
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −30.8540 −1.04187 −0.520933 0.853597i \(-0.674416\pi\)
−0.520933 + 0.853597i \(0.674416\pi\)
\(878\) 0 0
\(879\) −21.0280 −0.709257
\(880\) 0 0
\(881\) −53.8585 −1.81454 −0.907270 0.420550i \(-0.861837\pi\)
−0.907270 + 0.420550i \(0.861837\pi\)
\(882\) 0 0
\(883\) 14.1687 0.476814 0.238407 0.971165i \(-0.423375\pi\)
0.238407 + 0.971165i \(0.423375\pi\)
\(884\) 0 0
\(885\) −9.83654 −0.330652
\(886\) 0 0
\(887\) −32.6309 −1.09564 −0.547820 0.836596i \(-0.684542\pi\)
−0.547820 + 0.836596i \(0.684542\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.0111785 −0.000374493 0
\(892\) 0 0
\(893\) −11.2205 −0.375480
\(894\) 0 0
\(895\) −16.7248 −0.559049
\(896\) 0 0
\(897\) 17.8264 0.595207
\(898\) 0 0
\(899\) 20.0051 0.667207
\(900\) 0 0
\(901\) 9.90911 0.330120
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 13.0628 0.434222
\(906\) 0 0
\(907\) 48.1270 1.59803 0.799016 0.601310i \(-0.205354\pi\)
0.799016 + 0.601310i \(0.205354\pi\)
\(908\) 0 0
\(909\) 30.8257 1.02243
\(910\) 0 0
\(911\) −20.3867 −0.675441 −0.337720 0.941247i \(-0.609656\pi\)
−0.337720 + 0.941247i \(0.609656\pi\)
\(912\) 0 0
\(913\) 0.494915 0.0163793
\(914\) 0 0
\(915\) −11.0832 −0.366398
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −2.66405 −0.0878789 −0.0439395 0.999034i \(-0.513991\pi\)
−0.0439395 + 0.999034i \(0.513991\pi\)
\(920\) 0 0
\(921\) 2.87198 0.0946348
\(922\) 0 0
\(923\) −58.5883 −1.92846
\(924\) 0 0
\(925\) −41.2642 −1.35676
\(926\) 0 0
\(927\) −31.5241 −1.03539
\(928\) 0 0
\(929\) −31.5871 −1.03634 −0.518170 0.855278i \(-0.673387\pi\)
−0.518170 + 0.855278i \(0.673387\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 15.1898 0.497293
\(934\) 0 0
\(935\) 0.217865 0.00712495
\(936\) 0 0
\(937\) −7.30876 −0.238767 −0.119383 0.992848i \(-0.538092\pi\)
−0.119383 + 0.992848i \(0.538092\pi\)
\(938\) 0 0
\(939\) 33.5821 1.09591
\(940\) 0 0
\(941\) 2.93375 0.0956374 0.0478187 0.998856i \(-0.484773\pi\)
0.0478187 + 0.998856i \(0.484773\pi\)
\(942\) 0 0
\(943\) 4.09950 0.133498
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −28.7181 −0.933212 −0.466606 0.884465i \(-0.654523\pi\)
−0.466606 + 0.884465i \(0.654523\pi\)
\(948\) 0 0
\(949\) −53.9048 −1.74982
\(950\) 0 0
\(951\) −20.0899 −0.651461
\(952\) 0 0
\(953\) 39.0891 1.26622 0.633110 0.774062i \(-0.281778\pi\)
0.633110 + 0.774062i \(0.281778\pi\)
\(954\) 0 0
\(955\) −9.83827 −0.318359
\(956\) 0 0
\(957\) 1.11355 0.0359958
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −15.8249 −0.510480
\(962\) 0 0
\(963\) −22.4356 −0.722976
\(964\) 0 0
\(965\) 9.01983 0.290359
\(966\) 0 0
\(967\) 4.10133 0.131890 0.0659450 0.997823i \(-0.478994\pi\)
0.0659450 + 0.997823i \(0.478994\pi\)
\(968\) 0 0
\(969\) −2.78668 −0.0895211
\(970\) 0 0
\(971\) 32.9460 1.05729 0.528644 0.848844i \(-0.322701\pi\)
0.528644 + 0.848844i \(0.322701\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 19.5162 0.625019
\(976\) 0 0
\(977\) −28.9811 −0.927186 −0.463593 0.886048i \(-0.653440\pi\)
−0.463593 + 0.886048i \(0.653440\pi\)
\(978\) 0 0
\(979\) 0.889183 0.0284184
\(980\) 0 0
\(981\) 1.37882 0.0440224
\(982\) 0 0
\(983\) −35.2495 −1.12428 −0.562142 0.827040i \(-0.690023\pi\)
−0.562142 + 0.827040i \(0.690023\pi\)
\(984\) 0 0
\(985\) −0.584644 −0.0186283
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.15305 −0.227454
\(990\) 0 0
\(991\) 48.6066 1.54404 0.772021 0.635598i \(-0.219246\pi\)
0.772021 + 0.635598i \(0.219246\pi\)
\(992\) 0 0
\(993\) 8.70807 0.276342
\(994\) 0 0
\(995\) −18.4015 −0.583366
\(996\) 0 0
\(997\) 31.6793 1.00329 0.501647 0.865072i \(-0.332728\pi\)
0.501647 + 0.865072i \(0.332728\pi\)
\(998\) 0 0
\(999\) −47.6835 −1.50864
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 \(a_p\))