Properties

Label 8036.2.a.t.1.4
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 1.4
Root \(-2.15199\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.15199 q^{3}\) \(-0.0591445 q^{5}\) \(+1.63107 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.15199 q^{3}\) \(-0.0591445 q^{5}\) \(+1.63107 q^{9}\) \(-5.19280 q^{11}\) \(+1.33719 q^{13}\) \(+0.127279 q^{15}\) \(-5.25954 q^{17}\) \(-6.42758 q^{19}\) \(-5.30631 q^{23}\) \(-4.99650 q^{25}\) \(+2.94592 q^{27}\) \(-2.05926 q^{29}\) \(-4.21473 q^{31}\) \(+11.1749 q^{33}\) \(-6.95811 q^{37}\) \(-2.87762 q^{39}\) \(-1.00000 q^{41}\) \(-4.70691 q^{43}\) \(-0.0964691 q^{45}\) \(+4.09351 q^{47}\) \(+11.3185 q^{51}\) \(+2.41022 q^{53}\) \(+0.307126 q^{55}\) \(+13.8321 q^{57}\) \(-4.59309 q^{59}\) \(-4.59729 q^{61}\) \(-0.0790874 q^{65}\) \(-9.74977 q^{67}\) \(+11.4191 q^{69}\) \(+2.36099 q^{71}\) \(+16.0737 q^{73}\) \(+10.7524 q^{75}\) \(-17.6984 q^{79}\) \(-11.2328 q^{81}\) \(+12.5923 q^{83}\) \(+0.311073 q^{85}\) \(+4.43152 q^{87}\) \(+0.670024 q^{89}\) \(+9.07008 q^{93}\) \(+0.380156 q^{95}\) \(-3.02595 q^{97}\) \(-8.46985 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.15199 −1.24245 −0.621227 0.783631i \(-0.713365\pi\)
−0.621227 + 0.783631i \(0.713365\pi\)
\(4\) 0 0
\(5\) −0.0591445 −0.0264502 −0.0132251 0.999913i \(-0.504210\pi\)
−0.0132251 + 0.999913i \(0.504210\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.63107 0.543691
\(10\) 0 0
\(11\) −5.19280 −1.56569 −0.782844 0.622218i \(-0.786232\pi\)
−0.782844 + 0.622218i \(0.786232\pi\)
\(12\) 0 0
\(13\) 1.33719 0.370870 0.185435 0.982657i \(-0.440631\pi\)
0.185435 + 0.982657i \(0.440631\pi\)
\(14\) 0 0
\(15\) 0.127279 0.0328632
\(16\) 0 0
\(17\) −5.25954 −1.27563 −0.637813 0.770191i \(-0.720161\pi\)
−0.637813 + 0.770191i \(0.720161\pi\)
\(18\) 0 0
\(19\) −6.42758 −1.47459 −0.737295 0.675571i \(-0.763897\pi\)
−0.737295 + 0.675571i \(0.763897\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.30631 −1.10644 −0.553221 0.833035i \(-0.686601\pi\)
−0.553221 + 0.833035i \(0.686601\pi\)
\(24\) 0 0
\(25\) −4.99650 −0.999300
\(26\) 0 0
\(27\) 2.94592 0.566942
\(28\) 0 0
\(29\) −2.05926 −0.382395 −0.191198 0.981552i \(-0.561237\pi\)
−0.191198 + 0.981552i \(0.561237\pi\)
\(30\) 0 0
\(31\) −4.21473 −0.756989 −0.378494 0.925604i \(-0.623558\pi\)
−0.378494 + 0.925604i \(0.623558\pi\)
\(32\) 0 0
\(33\) 11.1749 1.94530
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.95811 −1.14391 −0.571953 0.820287i \(-0.693814\pi\)
−0.571953 + 0.820287i \(0.693814\pi\)
\(38\) 0 0
\(39\) −2.87762 −0.460789
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.70691 −0.717797 −0.358898 0.933377i \(-0.616848\pi\)
−0.358898 + 0.933377i \(0.616848\pi\)
\(44\) 0 0
\(45\) −0.0964691 −0.0143808
\(46\) 0 0
\(47\) 4.09351 0.597100 0.298550 0.954394i \(-0.403497\pi\)
0.298550 + 0.954394i \(0.403497\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 11.3185 1.58491
\(52\) 0 0
\(53\) 2.41022 0.331070 0.165535 0.986204i \(-0.447065\pi\)
0.165535 + 0.986204i \(0.447065\pi\)
\(54\) 0 0
\(55\) 0.307126 0.0414128
\(56\) 0 0
\(57\) 13.8321 1.83211
\(58\) 0 0
\(59\) −4.59309 −0.597969 −0.298984 0.954258i \(-0.596648\pi\)
−0.298984 + 0.954258i \(0.596648\pi\)
\(60\) 0 0
\(61\) −4.59729 −0.588622 −0.294311 0.955710i \(-0.595090\pi\)
−0.294311 + 0.955710i \(0.595090\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.0790874 −0.00980959
\(66\) 0 0
\(67\) −9.74977 −1.19112 −0.595562 0.803309i \(-0.703071\pi\)
−0.595562 + 0.803309i \(0.703071\pi\)
\(68\) 0 0
\(69\) 11.4191 1.37470
\(70\) 0 0
\(71\) 2.36099 0.280198 0.140099 0.990137i \(-0.455258\pi\)
0.140099 + 0.990137i \(0.455258\pi\)
\(72\) 0 0
\(73\) 16.0737 1.88129 0.940643 0.339397i \(-0.110223\pi\)
0.940643 + 0.339397i \(0.110223\pi\)
\(74\) 0 0
\(75\) 10.7524 1.24158
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −17.6984 −1.99122 −0.995611 0.0935911i \(-0.970165\pi\)
−0.995611 + 0.0935911i \(0.970165\pi\)
\(80\) 0 0
\(81\) −11.2328 −1.24809
\(82\) 0 0
\(83\) 12.5923 1.38218 0.691092 0.722766i \(-0.257130\pi\)
0.691092 + 0.722766i \(0.257130\pi\)
\(84\) 0 0
\(85\) 0.311073 0.0337406
\(86\) 0 0
\(87\) 4.43152 0.475109
\(88\) 0 0
\(89\) 0.670024 0.0710224 0.0355112 0.999369i \(-0.488694\pi\)
0.0355112 + 0.999369i \(0.488694\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 9.07008 0.940524
\(94\) 0 0
\(95\) 0.380156 0.0390032
\(96\) 0 0
\(97\) −3.02595 −0.307239 −0.153619 0.988130i \(-0.549093\pi\)
−0.153619 + 0.988130i \(0.549093\pi\)
\(98\) 0 0
\(99\) −8.46985 −0.851252
\(100\) 0 0
\(101\) 3.46622 0.344902 0.172451 0.985018i \(-0.444831\pi\)
0.172451 + 0.985018i \(0.444831\pi\)
\(102\) 0 0
\(103\) −16.6119 −1.63682 −0.818411 0.574634i \(-0.805144\pi\)
−0.818411 + 0.574634i \(0.805144\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.78404 0.462491 0.231246 0.972895i \(-0.425720\pi\)
0.231246 + 0.972895i \(0.425720\pi\)
\(108\) 0 0
\(109\) 10.1783 0.974905 0.487452 0.873150i \(-0.337926\pi\)
0.487452 + 0.873150i \(0.337926\pi\)
\(110\) 0 0
\(111\) 14.9738 1.42125
\(112\) 0 0
\(113\) −8.11250 −0.763160 −0.381580 0.924336i \(-0.624620\pi\)
−0.381580 + 0.924336i \(0.624620\pi\)
\(114\) 0 0
\(115\) 0.313839 0.0292656
\(116\) 0 0
\(117\) 2.18106 0.201639
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 15.9652 1.45138
\(122\) 0 0
\(123\) 2.15199 0.194039
\(124\) 0 0
\(125\) 0.591238 0.0528820
\(126\) 0 0
\(127\) 12.3020 1.09163 0.545815 0.837906i \(-0.316220\pi\)
0.545815 + 0.837906i \(0.316220\pi\)
\(128\) 0 0
\(129\) 10.1292 0.891829
\(130\) 0 0
\(131\) −13.7437 −1.20079 −0.600397 0.799702i \(-0.704991\pi\)
−0.600397 + 0.799702i \(0.704991\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.174235 −0.0149958
\(136\) 0 0
\(137\) −16.3423 −1.39622 −0.698110 0.715990i \(-0.745975\pi\)
−0.698110 + 0.715990i \(0.745975\pi\)
\(138\) 0 0
\(139\) 3.15630 0.267714 0.133857 0.991001i \(-0.457264\pi\)
0.133857 + 0.991001i \(0.457264\pi\)
\(140\) 0 0
\(141\) −8.80921 −0.741869
\(142\) 0 0
\(143\) −6.94376 −0.580667
\(144\) 0 0
\(145\) 0.121794 0.0101144
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.60110 0.295014 0.147507 0.989061i \(-0.452875\pi\)
0.147507 + 0.989061i \(0.452875\pi\)
\(150\) 0 0
\(151\) −20.3106 −1.65286 −0.826428 0.563042i \(-0.809631\pi\)
−0.826428 + 0.563042i \(0.809631\pi\)
\(152\) 0 0
\(153\) −8.57871 −0.693547
\(154\) 0 0
\(155\) 0.249278 0.0200225
\(156\) 0 0
\(157\) −2.62122 −0.209196 −0.104598 0.994515i \(-0.533356\pi\)
−0.104598 + 0.994515i \(0.533356\pi\)
\(158\) 0 0
\(159\) −5.18678 −0.411339
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 17.2802 1.35349 0.676743 0.736219i \(-0.263391\pi\)
0.676743 + 0.736219i \(0.263391\pi\)
\(164\) 0 0
\(165\) −0.660932 −0.0514535
\(166\) 0 0
\(167\) −21.7931 −1.68640 −0.843199 0.537602i \(-0.819330\pi\)
−0.843199 + 0.537602i \(0.819330\pi\)
\(168\) 0 0
\(169\) −11.2119 −0.862456
\(170\) 0 0
\(171\) −10.4839 −0.801722
\(172\) 0 0
\(173\) 7.43619 0.565363 0.282682 0.959214i \(-0.408776\pi\)
0.282682 + 0.959214i \(0.408776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.88429 0.742949
\(178\) 0 0
\(179\) −15.6673 −1.17103 −0.585515 0.810662i \(-0.699108\pi\)
−0.585515 + 0.810662i \(0.699108\pi\)
\(180\) 0 0
\(181\) 17.9491 1.33415 0.667075 0.744991i \(-0.267546\pi\)
0.667075 + 0.744991i \(0.267546\pi\)
\(182\) 0 0
\(183\) 9.89333 0.731336
\(184\) 0 0
\(185\) 0.411534 0.0302566
\(186\) 0 0
\(187\) 27.3118 1.99723
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.9792 0.794425 0.397213 0.917727i \(-0.369978\pi\)
0.397213 + 0.917727i \(0.369978\pi\)
\(192\) 0 0
\(193\) −8.35472 −0.601386 −0.300693 0.953721i \(-0.597218\pi\)
−0.300693 + 0.953721i \(0.597218\pi\)
\(194\) 0 0
\(195\) 0.170196 0.0121880
\(196\) 0 0
\(197\) −8.62720 −0.614663 −0.307331 0.951603i \(-0.599436\pi\)
−0.307331 + 0.951603i \(0.599436\pi\)
\(198\) 0 0
\(199\) 15.1574 1.07448 0.537240 0.843430i \(-0.319467\pi\)
0.537240 + 0.843430i \(0.319467\pi\)
\(200\) 0 0
\(201\) 20.9814 1.47992
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.0591445 0.00413083
\(206\) 0 0
\(207\) −8.65498 −0.601563
\(208\) 0 0
\(209\) 33.3772 2.30875
\(210\) 0 0
\(211\) −21.4024 −1.47340 −0.736701 0.676218i \(-0.763618\pi\)
−0.736701 + 0.676218i \(0.763618\pi\)
\(212\) 0 0
\(213\) −5.08084 −0.348133
\(214\) 0 0
\(215\) 0.278388 0.0189859
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −34.5905 −2.33741
\(220\) 0 0
\(221\) −7.03301 −0.473091
\(222\) 0 0
\(223\) −13.4975 −0.903859 −0.451929 0.892054i \(-0.649264\pi\)
−0.451929 + 0.892054i \(0.649264\pi\)
\(224\) 0 0
\(225\) −8.14967 −0.543311
\(226\) 0 0
\(227\) 5.90820 0.392141 0.196071 0.980590i \(-0.437182\pi\)
0.196071 + 0.980590i \(0.437182\pi\)
\(228\) 0 0
\(229\) 26.5285 1.75305 0.876525 0.481356i \(-0.159855\pi\)
0.876525 + 0.481356i \(0.159855\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.34879 −0.415923 −0.207962 0.978137i \(-0.566683\pi\)
−0.207962 + 0.978137i \(0.566683\pi\)
\(234\) 0 0
\(235\) −0.242109 −0.0157934
\(236\) 0 0
\(237\) 38.0868 2.47400
\(238\) 0 0
\(239\) −26.2653 −1.69896 −0.849482 0.527618i \(-0.823085\pi\)
−0.849482 + 0.527618i \(0.823085\pi\)
\(240\) 0 0
\(241\) 17.5763 1.13219 0.566096 0.824340i \(-0.308453\pi\)
0.566096 + 0.824340i \(0.308453\pi\)
\(242\) 0 0
\(243\) 15.3352 0.983753
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.59490 −0.546881
\(248\) 0 0
\(249\) −27.0985 −1.71730
\(250\) 0 0
\(251\) −28.5313 −1.80088 −0.900439 0.434983i \(-0.856754\pi\)
−0.900439 + 0.434983i \(0.856754\pi\)
\(252\) 0 0
\(253\) 27.5546 1.73234
\(254\) 0 0
\(255\) −0.669427 −0.0419212
\(256\) 0 0
\(257\) −20.5221 −1.28013 −0.640066 0.768320i \(-0.721093\pi\)
−0.640066 + 0.768320i \(0.721093\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.35881 −0.207905
\(262\) 0 0
\(263\) 7.82507 0.482514 0.241257 0.970461i \(-0.422440\pi\)
0.241257 + 0.970461i \(0.422440\pi\)
\(264\) 0 0
\(265\) −0.142551 −0.00875687
\(266\) 0 0
\(267\) −1.44189 −0.0882421
\(268\) 0 0
\(269\) −23.4164 −1.42773 −0.713863 0.700286i \(-0.753056\pi\)
−0.713863 + 0.700286i \(0.753056\pi\)
\(270\) 0 0
\(271\) −2.96639 −0.180195 −0.0900976 0.995933i \(-0.528718\pi\)
−0.0900976 + 0.995933i \(0.528718\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 25.9458 1.56459
\(276\) 0 0
\(277\) −14.9330 −0.897236 −0.448618 0.893723i \(-0.648084\pi\)
−0.448618 + 0.893723i \(0.648084\pi\)
\(278\) 0 0
\(279\) −6.87455 −0.411568
\(280\) 0 0
\(281\) −3.65734 −0.218178 −0.109089 0.994032i \(-0.534793\pi\)
−0.109089 + 0.994032i \(0.534793\pi\)
\(282\) 0 0
\(283\) 19.6498 1.16806 0.584029 0.811733i \(-0.301475\pi\)
0.584029 + 0.811733i \(0.301475\pi\)
\(284\) 0 0
\(285\) −0.818094 −0.0484597
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 10.6628 0.627223
\(290\) 0 0
\(291\) 6.51183 0.381730
\(292\) 0 0
\(293\) −12.9213 −0.754872 −0.377436 0.926036i \(-0.623194\pi\)
−0.377436 + 0.926036i \(0.623194\pi\)
\(294\) 0 0
\(295\) 0.271656 0.0158164
\(296\) 0 0
\(297\) −15.2976 −0.887655
\(298\) 0 0
\(299\) −7.09554 −0.410346
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.45929 −0.428525
\(304\) 0 0
\(305\) 0.271904 0.0155692
\(306\) 0 0
\(307\) 6.33218 0.361397 0.180698 0.983539i \(-0.442164\pi\)
0.180698 + 0.983539i \(0.442164\pi\)
\(308\) 0 0
\(309\) 35.7487 2.03367
\(310\) 0 0
\(311\) 9.54819 0.541428 0.270714 0.962660i \(-0.412740\pi\)
0.270714 + 0.962660i \(0.412740\pi\)
\(312\) 0 0
\(313\) 15.6169 0.882721 0.441360 0.897330i \(-0.354496\pi\)
0.441360 + 0.897330i \(0.354496\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.6886 1.44282 0.721408 0.692510i \(-0.243495\pi\)
0.721408 + 0.692510i \(0.243495\pi\)
\(318\) 0 0
\(319\) 10.6933 0.598712
\(320\) 0 0
\(321\) −10.2952 −0.574624
\(322\) 0 0
\(323\) 33.8062 1.88102
\(324\) 0 0
\(325\) −6.68127 −0.370610
\(326\) 0 0
\(327\) −21.9036 −1.21127
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.1815 0.559625 0.279812 0.960055i \(-0.409728\pi\)
0.279812 + 0.960055i \(0.409728\pi\)
\(332\) 0 0
\(333\) −11.3492 −0.621932
\(334\) 0 0
\(335\) 0.576646 0.0315055
\(336\) 0 0
\(337\) 26.1130 1.42246 0.711232 0.702958i \(-0.248138\pi\)
0.711232 + 0.702958i \(0.248138\pi\)
\(338\) 0 0
\(339\) 17.4580 0.948191
\(340\) 0 0
\(341\) 21.8863 1.18521
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.675379 −0.0363612
\(346\) 0 0
\(347\) −29.2380 −1.56958 −0.784788 0.619764i \(-0.787228\pi\)
−0.784788 + 0.619764i \(0.787228\pi\)
\(348\) 0 0
\(349\) 30.6815 1.64234 0.821172 0.570681i \(-0.193321\pi\)
0.821172 + 0.570681i \(0.193321\pi\)
\(350\) 0 0
\(351\) 3.93925 0.210262
\(352\) 0 0
\(353\) −7.83832 −0.417191 −0.208596 0.978002i \(-0.566889\pi\)
−0.208596 + 0.978002i \(0.566889\pi\)
\(354\) 0 0
\(355\) −0.139640 −0.00741131
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.2494 1.33261 0.666305 0.745679i \(-0.267875\pi\)
0.666305 + 0.745679i \(0.267875\pi\)
\(360\) 0 0
\(361\) 22.3138 1.17441
\(362\) 0 0
\(363\) −34.3570 −1.80327
\(364\) 0 0
\(365\) −0.950672 −0.0497605
\(366\) 0 0
\(367\) 34.5939 1.80579 0.902893 0.429866i \(-0.141439\pi\)
0.902893 + 0.429866i \(0.141439\pi\)
\(368\) 0 0
\(369\) −1.63107 −0.0849103
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.08439 −0.263260 −0.131630 0.991299i \(-0.542021\pi\)
−0.131630 + 0.991299i \(0.542021\pi\)
\(374\) 0 0
\(375\) −1.27234 −0.0657034
\(376\) 0 0
\(377\) −2.75362 −0.141819
\(378\) 0 0
\(379\) −31.8842 −1.63778 −0.818891 0.573950i \(-0.805411\pi\)
−0.818891 + 0.573950i \(0.805411\pi\)
\(380\) 0 0
\(381\) −26.4739 −1.35630
\(382\) 0 0
\(383\) −3.82339 −0.195366 −0.0976831 0.995218i \(-0.531143\pi\)
−0.0976831 + 0.995218i \(0.531143\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7.67732 −0.390260
\(388\) 0 0
\(389\) 6.74436 0.341953 0.170976 0.985275i \(-0.445308\pi\)
0.170976 + 0.985275i \(0.445308\pi\)
\(390\) 0 0
\(391\) 27.9088 1.41141
\(392\) 0 0
\(393\) 29.5764 1.49193
\(394\) 0 0
\(395\) 1.04676 0.0526683
\(396\) 0 0
\(397\) −8.07782 −0.405414 −0.202707 0.979239i \(-0.564974\pi\)
−0.202707 + 0.979239i \(0.564974\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −37.6125 −1.87828 −0.939138 0.343539i \(-0.888374\pi\)
−0.939138 + 0.343539i \(0.888374\pi\)
\(402\) 0 0
\(403\) −5.63590 −0.280744
\(404\) 0 0
\(405\) 0.664360 0.0330123
\(406\) 0 0
\(407\) 36.1321 1.79100
\(408\) 0 0
\(409\) −4.69310 −0.232059 −0.116029 0.993246i \(-0.537017\pi\)
−0.116029 + 0.993246i \(0.537017\pi\)
\(410\) 0 0
\(411\) 35.1686 1.73474
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.744766 −0.0365591
\(416\) 0 0
\(417\) −6.79234 −0.332622
\(418\) 0 0
\(419\) −10.3430 −0.505287 −0.252643 0.967559i \(-0.581300\pi\)
−0.252643 + 0.967559i \(0.581300\pi\)
\(420\) 0 0
\(421\) 30.5165 1.48728 0.743641 0.668579i \(-0.233097\pi\)
0.743641 + 0.668579i \(0.233097\pi\)
\(422\) 0 0
\(423\) 6.67682 0.324638
\(424\) 0 0
\(425\) 26.2793 1.27473
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 14.9429 0.721451
\(430\) 0 0
\(431\) −19.6284 −0.945467 −0.472733 0.881205i \(-0.656733\pi\)
−0.472733 + 0.881205i \(0.656733\pi\)
\(432\) 0 0
\(433\) −11.7482 −0.564583 −0.282291 0.959329i \(-0.591095\pi\)
−0.282291 + 0.959329i \(0.591095\pi\)
\(434\) 0 0
\(435\) −0.262100 −0.0125667
\(436\) 0 0
\(437\) 34.1067 1.63155
\(438\) 0 0
\(439\) −11.6849 −0.557688 −0.278844 0.960336i \(-0.589951\pi\)
−0.278844 + 0.960336i \(0.589951\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.09105 0.0993490 0.0496745 0.998765i \(-0.484182\pi\)
0.0496745 + 0.998765i \(0.484182\pi\)
\(444\) 0 0
\(445\) −0.0396282 −0.00187856
\(446\) 0 0
\(447\) −7.74955 −0.366541
\(448\) 0 0
\(449\) 11.2663 0.531691 0.265845 0.964016i \(-0.414349\pi\)
0.265845 + 0.964016i \(0.414349\pi\)
\(450\) 0 0
\(451\) 5.19280 0.244519
\(452\) 0 0
\(453\) 43.7084 2.05360
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.8612 0.835513 0.417757 0.908559i \(-0.362817\pi\)
0.417757 + 0.908559i \(0.362817\pi\)
\(458\) 0 0
\(459\) −15.4942 −0.723207
\(460\) 0 0
\(461\) 3.76709 0.175451 0.0877254 0.996145i \(-0.472040\pi\)
0.0877254 + 0.996145i \(0.472040\pi\)
\(462\) 0 0
\(463\) 25.5750 1.18857 0.594286 0.804254i \(-0.297435\pi\)
0.594286 + 0.804254i \(0.297435\pi\)
\(464\) 0 0
\(465\) −0.536445 −0.0248771
\(466\) 0 0
\(467\) 0.506752 0.0234497 0.0117249 0.999931i \(-0.496268\pi\)
0.0117249 + 0.999931i \(0.496268\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 5.64085 0.259917
\(472\) 0 0
\(473\) 24.4420 1.12385
\(474\) 0 0
\(475\) 32.1154 1.47356
\(476\) 0 0
\(477\) 3.93125 0.180000
\(478\) 0 0
\(479\) −0.838081 −0.0382929 −0.0191465 0.999817i \(-0.506095\pi\)
−0.0191465 + 0.999817i \(0.506095\pi\)
\(480\) 0 0
\(481\) −9.30431 −0.424240
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.178968 0.00812654
\(486\) 0 0
\(487\) 10.3497 0.468992 0.234496 0.972117i \(-0.424656\pi\)
0.234496 + 0.972117i \(0.424656\pi\)
\(488\) 0 0
\(489\) −37.1868 −1.68164
\(490\) 0 0
\(491\) 15.1429 0.683391 0.341695 0.939811i \(-0.388999\pi\)
0.341695 + 0.939811i \(0.388999\pi\)
\(492\) 0 0
\(493\) 10.8308 0.487794
\(494\) 0 0
\(495\) 0.500945 0.0225158
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −7.63088 −0.341605 −0.170803 0.985305i \(-0.554636\pi\)
−0.170803 + 0.985305i \(0.554636\pi\)
\(500\) 0 0
\(501\) 46.8985 2.09527
\(502\) 0 0
\(503\) −36.2600 −1.61675 −0.808377 0.588665i \(-0.799654\pi\)
−0.808377 + 0.588665i \(0.799654\pi\)
\(504\) 0 0
\(505\) −0.205008 −0.00912274
\(506\) 0 0
\(507\) 24.1280 1.07156
\(508\) 0 0
\(509\) 7.10944 0.315120 0.157560 0.987509i \(-0.449637\pi\)
0.157560 + 0.987509i \(0.449637\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −18.9351 −0.836007
\(514\) 0 0
\(515\) 0.982504 0.0432943
\(516\) 0 0
\(517\) −21.2568 −0.934872
\(518\) 0 0
\(519\) −16.0026 −0.702437
\(520\) 0 0
\(521\) −12.0964 −0.529954 −0.264977 0.964255i \(-0.585364\pi\)
−0.264977 + 0.964255i \(0.585364\pi\)
\(522\) 0 0
\(523\) −14.5419 −0.635875 −0.317938 0.948112i \(-0.602990\pi\)
−0.317938 + 0.948112i \(0.602990\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.1676 0.965635
\(528\) 0 0
\(529\) 5.15690 0.224213
\(530\) 0 0
\(531\) −7.49166 −0.325111
\(532\) 0 0
\(533\) −1.33719 −0.0579201
\(534\) 0 0
\(535\) −0.282950 −0.0122330
\(536\) 0 0
\(537\) 33.7159 1.45495
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 10.8069 0.464624 0.232312 0.972641i \(-0.425371\pi\)
0.232312 + 0.972641i \(0.425371\pi\)
\(542\) 0 0
\(543\) −38.6264 −1.65762
\(544\) 0 0
\(545\) −0.601991 −0.0257865
\(546\) 0 0
\(547\) 11.6640 0.498716 0.249358 0.968411i \(-0.419780\pi\)
0.249358 + 0.968411i \(0.419780\pi\)
\(548\) 0 0
\(549\) −7.49852 −0.320029
\(550\) 0 0
\(551\) 13.2361 0.563876
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.885618 −0.0375924
\(556\) 0 0
\(557\) 13.7853 0.584100 0.292050 0.956403i \(-0.405663\pi\)
0.292050 + 0.956403i \(0.405663\pi\)
\(558\) 0 0
\(559\) −6.29403 −0.266209
\(560\) 0 0
\(561\) −58.7747 −2.48147
\(562\) 0 0
\(563\) 28.4480 1.19894 0.599470 0.800397i \(-0.295378\pi\)
0.599470 + 0.800397i \(0.295378\pi\)
\(564\) 0 0
\(565\) 0.479810 0.0201858
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.8115 0.914385 0.457193 0.889368i \(-0.348855\pi\)
0.457193 + 0.889368i \(0.348855\pi\)
\(570\) 0 0
\(571\) 22.5978 0.945687 0.472843 0.881147i \(-0.343228\pi\)
0.472843 + 0.881147i \(0.343228\pi\)
\(572\) 0 0
\(573\) −23.6271 −0.987037
\(574\) 0 0
\(575\) 26.5130 1.10567
\(576\) 0 0
\(577\) −34.7359 −1.44607 −0.723036 0.690810i \(-0.757254\pi\)
−0.723036 + 0.690810i \(0.757254\pi\)
\(578\) 0 0
\(579\) 17.9793 0.747195
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −12.5158 −0.518352
\(584\) 0 0
\(585\) −0.128998 −0.00533339
\(586\) 0 0
\(587\) −45.3646 −1.87240 −0.936198 0.351473i \(-0.885681\pi\)
−0.936198 + 0.351473i \(0.885681\pi\)
\(588\) 0 0
\(589\) 27.0906 1.11625
\(590\) 0 0
\(591\) 18.5657 0.763690
\(592\) 0 0
\(593\) −16.5862 −0.681112 −0.340556 0.940224i \(-0.610615\pi\)
−0.340556 + 0.940224i \(0.610615\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −32.6186 −1.33499
\(598\) 0 0
\(599\) 17.7376 0.724738 0.362369 0.932035i \(-0.381968\pi\)
0.362369 + 0.932035i \(0.381968\pi\)
\(600\) 0 0
\(601\) −9.18453 −0.374645 −0.187322 0.982298i \(-0.559981\pi\)
−0.187322 + 0.982298i \(0.559981\pi\)
\(602\) 0 0
\(603\) −15.9026 −0.647604
\(604\) 0 0
\(605\) −0.944253 −0.0383894
\(606\) 0 0
\(607\) 27.8378 1.12990 0.564951 0.825124i \(-0.308895\pi\)
0.564951 + 0.825124i \(0.308895\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.47380 0.221446
\(612\) 0 0
\(613\) 25.9148 1.04669 0.523345 0.852121i \(-0.324684\pi\)
0.523345 + 0.852121i \(0.324684\pi\)
\(614\) 0 0
\(615\) −0.127279 −0.00513237
\(616\) 0 0
\(617\) −45.0746 −1.81463 −0.907317 0.420448i \(-0.861873\pi\)
−0.907317 + 0.420448i \(0.861873\pi\)
\(618\) 0 0
\(619\) 9.98422 0.401300 0.200650 0.979663i \(-0.435695\pi\)
0.200650 + 0.979663i \(0.435695\pi\)
\(620\) 0 0
\(621\) −15.6319 −0.627288
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.9475 0.997902
\(626\) 0 0
\(627\) −71.8274 −2.86851
\(628\) 0 0
\(629\) 36.5965 1.45920
\(630\) 0 0
\(631\) −15.2360 −0.606536 −0.303268 0.952905i \(-0.598078\pi\)
−0.303268 + 0.952905i \(0.598078\pi\)
\(632\) 0 0
\(633\) 46.0578 1.83063
\(634\) 0 0
\(635\) −0.727598 −0.0288738
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3.85095 0.152341
\(640\) 0 0
\(641\) −18.6951 −0.738413 −0.369207 0.929347i \(-0.620371\pi\)
−0.369207 + 0.929347i \(0.620371\pi\)
\(642\) 0 0
\(643\) −33.6654 −1.32764 −0.663818 0.747895i \(-0.731065\pi\)
−0.663818 + 0.747895i \(0.731065\pi\)
\(644\) 0 0
\(645\) −0.599089 −0.0235891
\(646\) 0 0
\(647\) 17.7667 0.698482 0.349241 0.937033i \(-0.386439\pi\)
0.349241 + 0.937033i \(0.386439\pi\)
\(648\) 0 0
\(649\) 23.8510 0.936233
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −14.5760 −0.570403 −0.285201 0.958468i \(-0.592060\pi\)
−0.285201 + 0.958468i \(0.592060\pi\)
\(654\) 0 0
\(655\) 0.812865 0.0317613
\(656\) 0 0
\(657\) 26.2174 1.02284
\(658\) 0 0
\(659\) −7.13592 −0.277976 −0.138988 0.990294i \(-0.544385\pi\)
−0.138988 + 0.990294i \(0.544385\pi\)
\(660\) 0 0
\(661\) −16.9329 −0.658614 −0.329307 0.944223i \(-0.606815\pi\)
−0.329307 + 0.944223i \(0.606815\pi\)
\(662\) 0 0
\(663\) 15.1350 0.587794
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.9271 0.423098
\(668\) 0 0
\(669\) 29.0465 1.12300
\(670\) 0 0
\(671\) 23.8728 0.921599
\(672\) 0 0
\(673\) 10.7074 0.412738 0.206369 0.978474i \(-0.433835\pi\)
0.206369 + 0.978474i \(0.433835\pi\)
\(674\) 0 0
\(675\) −14.7193 −0.566546
\(676\) 0 0
\(677\) 37.3668 1.43612 0.718062 0.695979i \(-0.245029\pi\)
0.718062 + 0.695979i \(0.245029\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −12.7144 −0.487217
\(682\) 0 0
\(683\) −49.6732 −1.90069 −0.950346 0.311196i \(-0.899270\pi\)
−0.950346 + 0.311196i \(0.899270\pi\)
\(684\) 0 0
\(685\) 0.966560 0.0369303
\(686\) 0 0
\(687\) −57.0891 −2.17808
\(688\) 0 0
\(689\) 3.22293 0.122784
\(690\) 0 0
\(691\) −11.4435 −0.435330 −0.217665 0.976024i \(-0.569844\pi\)
−0.217665 + 0.976024i \(0.569844\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.186678 −0.00708110
\(696\) 0 0
\(697\) 5.25954 0.199219
\(698\) 0 0
\(699\) 13.6626 0.516766
\(700\) 0 0
\(701\) −8.67998 −0.327838 −0.163919 0.986474i \(-0.552414\pi\)
−0.163919 + 0.986474i \(0.552414\pi\)
\(702\) 0 0
\(703\) 44.7238 1.68679
\(704\) 0 0
\(705\) 0.521016 0.0196226
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 32.8906 1.23523 0.617615 0.786480i \(-0.288099\pi\)
0.617615 + 0.786480i \(0.288099\pi\)
\(710\) 0 0
\(711\) −28.8673 −1.08261
\(712\) 0 0
\(713\) 22.3647 0.837564
\(714\) 0 0
\(715\) 0.410685 0.0153588
\(716\) 0 0
\(717\) 56.5228 2.11088
\(718\) 0 0
\(719\) −18.6116 −0.694094 −0.347047 0.937848i \(-0.612816\pi\)
−0.347047 + 0.937848i \(0.612816\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −37.8241 −1.40670
\(724\) 0 0
\(725\) 10.2891 0.382128
\(726\) 0 0
\(727\) 11.7494 0.435760 0.217880 0.975976i \(-0.430086\pi\)
0.217880 + 0.975976i \(0.430086\pi\)
\(728\) 0 0
\(729\) 0.697225 0.0258231
\(730\) 0 0
\(731\) 24.7562 0.915641
\(732\) 0 0
\(733\) −34.0967 −1.25939 −0.629695 0.776843i \(-0.716820\pi\)
−0.629695 + 0.776843i \(0.716820\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 50.6286 1.86493
\(738\) 0 0
\(739\) 29.0138 1.06729 0.533644 0.845709i \(-0.320822\pi\)
0.533644 + 0.845709i \(0.320822\pi\)
\(740\) 0 0
\(741\) 18.4962 0.679474
\(742\) 0 0
\(743\) 54.4385 1.99715 0.998577 0.0533240i \(-0.0169816\pi\)
0.998577 + 0.0533240i \(0.0169816\pi\)
\(744\) 0 0
\(745\) −0.212985 −0.00780318
\(746\) 0 0
\(747\) 20.5390 0.751482
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 36.4957 1.33175 0.665873 0.746065i \(-0.268059\pi\)
0.665873 + 0.746065i \(0.268059\pi\)
\(752\) 0 0
\(753\) 61.3991 2.23751
\(754\) 0 0
\(755\) 1.20126 0.0437184
\(756\) 0 0
\(757\) −18.4567 −0.670820 −0.335410 0.942072i \(-0.608875\pi\)
−0.335410 + 0.942072i \(0.608875\pi\)
\(758\) 0 0
\(759\) −59.2973 −2.15236
\(760\) 0 0
\(761\) −4.88895 −0.177224 −0.0886121 0.996066i \(-0.528243\pi\)
−0.0886121 + 0.996066i \(0.528243\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.507383 0.0183445
\(766\) 0 0
\(767\) −6.14183 −0.221769
\(768\) 0 0
\(769\) 5.71646 0.206141 0.103070 0.994674i \(-0.467133\pi\)
0.103070 + 0.994674i \(0.467133\pi\)
\(770\) 0 0
\(771\) 44.1633 1.59050
\(772\) 0 0
\(773\) −26.7111 −0.960731 −0.480365 0.877068i \(-0.659496\pi\)
−0.480365 + 0.877068i \(0.659496\pi\)
\(774\) 0 0
\(775\) 21.0589 0.756459
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.42758 0.230292
\(780\) 0 0
\(781\) −12.2602 −0.438703
\(782\) 0 0
\(783\) −6.06642 −0.216796
\(784\) 0 0
\(785\) 0.155031 0.00553329
\(786\) 0 0
\(787\) 10.9270 0.389504 0.194752 0.980853i \(-0.437610\pi\)
0.194752 + 0.980853i \(0.437610\pi\)
\(788\) 0 0
\(789\) −16.8395 −0.599502
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6.14745 −0.218302
\(794\) 0 0
\(795\) 0.306770 0.0108800
\(796\) 0 0
\(797\) 35.4254 1.25483 0.627416 0.778684i \(-0.284112\pi\)
0.627416 + 0.778684i \(0.284112\pi\)
\(798\) 0 0
\(799\) −21.5300 −0.761676
\(800\) 0 0
\(801\) 1.09286 0.0386143
\(802\) 0 0
\(803\) −83.4676 −2.94551
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 50.3920 1.77388
\(808\) 0 0
\(809\) 20.9058 0.735008 0.367504 0.930022i \(-0.380212\pi\)
0.367504 + 0.930022i \(0.380212\pi\)
\(810\) 0 0
\(811\) 47.1023 1.65398 0.826992 0.562214i \(-0.190050\pi\)
0.826992 + 0.562214i \(0.190050\pi\)
\(812\) 0 0
\(813\) 6.38364 0.223884
\(814\) 0 0
\(815\) −1.02203 −0.0358000
\(816\) 0 0
\(817\) 30.2541 1.05846
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −54.8833 −1.91544 −0.957721 0.287700i \(-0.907109\pi\)
−0.957721 + 0.287700i \(0.907109\pi\)
\(822\) 0 0
\(823\) 13.0764 0.455815 0.227907 0.973683i \(-0.426812\pi\)
0.227907 + 0.973683i \(0.426812\pi\)
\(824\) 0 0
\(825\) −55.8353 −1.94393
\(826\) 0 0
\(827\) −37.0855 −1.28959 −0.644794 0.764356i \(-0.723057\pi\)
−0.644794 + 0.764356i \(0.723057\pi\)
\(828\) 0 0
\(829\) 34.3370 1.19257 0.596287 0.802771i \(-0.296642\pi\)
0.596287 + 0.802771i \(0.296642\pi\)
\(830\) 0 0
\(831\) 32.1357 1.11477
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.28894 0.0446056
\(836\) 0 0
\(837\) −12.4163 −0.429169
\(838\) 0 0
\(839\) −32.9880 −1.13887 −0.569436 0.822036i \(-0.692838\pi\)
−0.569436 + 0.822036i \(0.692838\pi\)
\(840\) 0 0
\(841\) −24.7594 −0.853774
\(842\) 0 0
\(843\) 7.87056 0.271077
\(844\) 0 0
\(845\) 0.663124 0.0228121
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −42.2862 −1.45126
\(850\) 0 0
\(851\) 36.9218 1.26566
\(852\) 0 0
\(853\) 11.8738 0.406551 0.203275 0.979122i \(-0.434841\pi\)
0.203275 + 0.979122i \(0.434841\pi\)
\(854\) 0 0
\(855\) 0.620063 0.0212057
\(856\) 0 0
\(857\) −17.6802 −0.603944 −0.301972 0.953317i \(-0.597645\pi\)
−0.301972 + 0.953317i \(0.597645\pi\)
\(858\) 0 0
\(859\) 14.0627 0.479812 0.239906 0.970796i \(-0.422883\pi\)
0.239906 + 0.970796i \(0.422883\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −31.8983 −1.08583 −0.542916 0.839787i \(-0.682680\pi\)
−0.542916 + 0.839787i \(0.682680\pi\)
\(864\) 0 0
\(865\) −0.439810 −0.0149540
\(866\) 0 0
\(867\) −22.9463 −0.779296
\(868\) 0 0
\(869\) 91.9041 3.11763
\(870\) 0 0
\(871\) −13.0373 −0.441752
\(872\) 0 0
\(873\) −4.93555 −0.167043
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −27.3189 −0.922494 −0.461247 0.887272i \(-0.652598\pi\)
−0.461247 + 0.887272i \(0.652598\pi\)
\(878\) 0 0
\(879\) 27.8066 0.937893
\(880\) 0 0
\(881\) 6.22926 0.209869 0.104935 0.994479i \(-0.466537\pi\)
0.104935 + 0.994479i \(0.466537\pi\)
\(882\) 0 0
\(883\) −31.9879 −1.07648 −0.538239 0.842792i \(-0.680910\pi\)
−0.538239 + 0.842792i \(0.680910\pi\)
\(884\) 0 0
\(885\) −0.584601 −0.0196512
\(886\) 0 0
\(887\) −22.5876 −0.758418 −0.379209 0.925311i \(-0.623804\pi\)
−0.379209 + 0.925311i \(0.623804\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 58.3298 1.95412
\(892\) 0 0
\(893\) −26.3114 −0.880477
\(894\) 0 0
\(895\) 0.926635 0.0309740
\(896\) 0 0
\(897\) 15.2696 0.509836
\(898\) 0 0
\(899\) 8.67924 0.289469
\(900\) 0 0
\(901\) −12.6767 −0.422321
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.06159 −0.0352886
\(906\) 0 0
\(907\) 27.2201 0.903829 0.451915 0.892061i \(-0.350741\pi\)
0.451915 + 0.892061i \(0.350741\pi\)
\(908\) 0 0
\(909\) 5.65367 0.187520
\(910\) 0 0
\(911\) 26.8820 0.890641 0.445321 0.895371i \(-0.353090\pi\)
0.445321 + 0.895371i \(0.353090\pi\)
\(912\) 0 0
\(913\) −65.3893 −2.16407
\(914\) 0 0
\(915\) −0.585136 −0.0193440
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 2.23690 0.0737884 0.0368942 0.999319i \(-0.488254\pi\)
0.0368942 + 0.999319i \(0.488254\pi\)
\(920\) 0 0
\(921\) −13.6268 −0.449019
\(922\) 0 0
\(923\) 3.15709 0.103917
\(924\) 0 0
\(925\) 34.7662 1.14311
\(926\) 0 0
\(927\) −27.0953 −0.889926
\(928\) 0 0
\(929\) 8.47724 0.278129 0.139065 0.990283i \(-0.455590\pi\)
0.139065 + 0.990283i \(0.455590\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −20.5476 −0.672700
\(934\) 0 0
\(935\) −1.61534 −0.0528273
\(936\) 0 0
\(937\) 1.35443 0.0442473 0.0221236 0.999755i \(-0.492957\pi\)
0.0221236 + 0.999755i \(0.492957\pi\)
\(938\) 0 0
\(939\) −33.6075 −1.09674
\(940\) 0 0
\(941\) 54.7641 1.78526 0.892630 0.450790i \(-0.148858\pi\)
0.892630 + 0.450790i \(0.148858\pi\)
\(942\) 0 0
\(943\) 5.30631 0.172797
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.23227 −0.137530 −0.0687651 0.997633i \(-0.521906\pi\)
−0.0687651 + 0.997633i \(0.521906\pi\)
\(948\) 0 0
\(949\) 21.4936 0.697712
\(950\) 0 0
\(951\) −55.2817 −1.79263
\(952\) 0 0
\(953\) 9.89170 0.320424 0.160212 0.987083i \(-0.448782\pi\)
0.160212 + 0.987083i \(0.448782\pi\)
\(954\) 0 0
\(955\) −0.649358 −0.0210127
\(956\) 0 0
\(957\) −23.0120 −0.743872
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −13.2360 −0.426968
\(962\) 0 0
\(963\) 7.80313 0.251452
\(964\) 0 0
\(965\) 0.494136 0.0159068
\(966\) 0 0
\(967\) 2.64614 0.0850942 0.0425471 0.999094i \(-0.486453\pi\)
0.0425471 + 0.999094i \(0.486453\pi\)
\(968\) 0 0
\(969\) −72.7506 −2.33709
\(970\) 0 0
\(971\) −7.20724 −0.231291 −0.115646 0.993291i \(-0.536894\pi\)
−0.115646 + 0.993291i \(0.536894\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 14.3781 0.460466
\(976\) 0 0
\(977\) −27.0409 −0.865115 −0.432557 0.901606i \(-0.642389\pi\)
−0.432557 + 0.901606i \(0.642389\pi\)
\(978\) 0 0
\(979\) −3.47930 −0.111199
\(980\) 0 0
\(981\) 16.6016 0.530048
\(982\) 0 0
\(983\) −50.7546 −1.61882 −0.809410 0.587244i \(-0.800213\pi\)
−0.809410 + 0.587244i \(0.800213\pi\)
\(984\) 0 0
\(985\) 0.510252 0.0162580
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 24.9763 0.794200
\(990\) 0 0
\(991\) −37.2471 −1.18319 −0.591596 0.806234i \(-0.701502\pi\)
−0.591596 + 0.806234i \(0.701502\pi\)
\(992\) 0 0
\(993\) −21.9105 −0.695308
\(994\) 0 0
\(995\) −0.896477 −0.0284202
\(996\) 0 0
\(997\) 39.2070 1.24170 0.620849 0.783930i \(-0.286788\pi\)
0.620849 + 0.783930i \(0.286788\pi\)
\(998\) 0 0
\(999\) −20.4980 −0.648528
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 \(a_p\))