Properties

Label 8036.2.a.t.1.11
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 1.11
Root \(0.476040\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.476040 q^{3}\) \(-2.17736 q^{5}\) \(-2.77339 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.476040 q^{3}\) \(-2.17736 q^{5}\) \(-2.77339 q^{9}\) \(-0.849919 q^{11}\) \(+0.662286 q^{13}\) \(-1.03651 q^{15}\) \(-5.15506 q^{17}\) \(-6.79204 q^{19}\) \(-0.144635 q^{23}\) \(-0.259093 q^{25}\) \(-2.74836 q^{27}\) \(-9.46489 q^{29}\) \(+8.50663 q^{31}\) \(-0.404596 q^{33}\) \(-7.75956 q^{37}\) \(+0.315275 q^{39}\) \(-1.00000 q^{41}\) \(-2.77075 q^{43}\) \(+6.03867 q^{45}\) \(+3.45840 q^{47}\) \(-2.45401 q^{51}\) \(+7.28924 q^{53}\) \(+1.85058 q^{55}\) \(-3.23329 q^{57}\) \(+9.84084 q^{59}\) \(+9.68365 q^{61}\) \(-1.44204 q^{65}\) \(+2.94318 q^{67}\) \(-0.0688519 q^{69}\) \(+3.88837 q^{71}\) \(-11.8207 q^{73}\) \(-0.123339 q^{75}\) \(+5.63075 q^{79}\) \(+7.01183 q^{81}\) \(+8.76939 q^{83}\) \(+11.2244 q^{85}\) \(-4.50567 q^{87}\) \(-5.94828 q^{89}\) \(+4.04950 q^{93}\) \(+14.7887 q^{95}\) \(+2.25908 q^{97}\) \(+2.35715 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.476040 0.274842 0.137421 0.990513i \(-0.456119\pi\)
0.137421 + 0.990513i \(0.456119\pi\)
\(4\) 0 0
\(5\) −2.17736 −0.973746 −0.486873 0.873473i \(-0.661863\pi\)
−0.486873 + 0.873473i \(0.661863\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.77339 −0.924462
\(10\) 0 0
\(11\) −0.849919 −0.256260 −0.128130 0.991757i \(-0.540897\pi\)
−0.128130 + 0.991757i \(0.540897\pi\)
\(12\) 0 0
\(13\) 0.662286 0.183685 0.0918426 0.995774i \(-0.470724\pi\)
0.0918426 + 0.995774i \(0.470724\pi\)
\(14\) 0 0
\(15\) −1.03651 −0.267626
\(16\) 0 0
\(17\) −5.15506 −1.25028 −0.625142 0.780511i \(-0.714959\pi\)
−0.625142 + 0.780511i \(0.714959\pi\)
\(18\) 0 0
\(19\) −6.79204 −1.55820 −0.779101 0.626899i \(-0.784324\pi\)
−0.779101 + 0.626899i \(0.784324\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.144635 −0.0301584 −0.0150792 0.999886i \(-0.504800\pi\)
−0.0150792 + 0.999886i \(0.504800\pi\)
\(24\) 0 0
\(25\) −0.259093 −0.0518187
\(26\) 0 0
\(27\) −2.74836 −0.528923
\(28\) 0 0
\(29\) −9.46489 −1.75759 −0.878793 0.477203i \(-0.841651\pi\)
−0.878793 + 0.477203i \(0.841651\pi\)
\(30\) 0 0
\(31\) 8.50663 1.52784 0.763918 0.645314i \(-0.223273\pi\)
0.763918 + 0.645314i \(0.223273\pi\)
\(32\) 0 0
\(33\) −0.404596 −0.0704310
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.75956 −1.27566 −0.637832 0.770175i \(-0.720169\pi\)
−0.637832 + 0.770175i \(0.720169\pi\)
\(38\) 0 0
\(39\) 0.315275 0.0504844
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −2.77075 −0.422536 −0.211268 0.977428i \(-0.567759\pi\)
−0.211268 + 0.977428i \(0.567759\pi\)
\(44\) 0 0
\(45\) 6.03867 0.900191
\(46\) 0 0
\(47\) 3.45840 0.504459 0.252230 0.967667i \(-0.418836\pi\)
0.252230 + 0.967667i \(0.418836\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.45401 −0.343631
\(52\) 0 0
\(53\) 7.28924 1.00125 0.500627 0.865663i \(-0.333103\pi\)
0.500627 + 0.865663i \(0.333103\pi\)
\(54\) 0 0
\(55\) 1.85058 0.249532
\(56\) 0 0
\(57\) −3.23329 −0.428259
\(58\) 0 0
\(59\) 9.84084 1.28117 0.640584 0.767888i \(-0.278692\pi\)
0.640584 + 0.767888i \(0.278692\pi\)
\(60\) 0 0
\(61\) 9.68365 1.23986 0.619932 0.784656i \(-0.287160\pi\)
0.619932 + 0.784656i \(0.287160\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.44204 −0.178863
\(66\) 0 0
\(67\) 2.94318 0.359566 0.179783 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(68\) 0 0
\(69\) −0.0688519 −0.00828879
\(70\) 0 0
\(71\) 3.88837 0.461465 0.230732 0.973017i \(-0.425888\pi\)
0.230732 + 0.973017i \(0.425888\pi\)
\(72\) 0 0
\(73\) −11.8207 −1.38350 −0.691752 0.722135i \(-0.743161\pi\)
−0.691752 + 0.722135i \(0.743161\pi\)
\(74\) 0 0
\(75\) −0.123339 −0.0142419
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.63075 0.633509 0.316754 0.948508i \(-0.397407\pi\)
0.316754 + 0.948508i \(0.397407\pi\)
\(80\) 0 0
\(81\) 7.01183 0.779092
\(82\) 0 0
\(83\) 8.76939 0.962566 0.481283 0.876565i \(-0.340171\pi\)
0.481283 + 0.876565i \(0.340171\pi\)
\(84\) 0 0
\(85\) 11.2244 1.21746
\(86\) 0 0
\(87\) −4.50567 −0.483058
\(88\) 0 0
\(89\) −5.94828 −0.630516 −0.315258 0.949006i \(-0.602091\pi\)
−0.315258 + 0.949006i \(0.602091\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.04950 0.419913
\(94\) 0 0
\(95\) 14.7887 1.51729
\(96\) 0 0
\(97\) 2.25908 0.229375 0.114687 0.993402i \(-0.463413\pi\)
0.114687 + 0.993402i \(0.463413\pi\)
\(98\) 0 0
\(99\) 2.35715 0.236903
\(100\) 0 0
\(101\) 1.07288 0.106756 0.0533778 0.998574i \(-0.483001\pi\)
0.0533778 + 0.998574i \(0.483001\pi\)
\(102\) 0 0
\(103\) 0.439620 0.0433171 0.0216585 0.999765i \(-0.493105\pi\)
0.0216585 + 0.999765i \(0.493105\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.7443 −1.81208 −0.906038 0.423196i \(-0.860908\pi\)
−0.906038 + 0.423196i \(0.860908\pi\)
\(108\) 0 0
\(109\) 7.68173 0.735777 0.367888 0.929870i \(-0.380081\pi\)
0.367888 + 0.929870i \(0.380081\pi\)
\(110\) 0 0
\(111\) −3.69387 −0.350606
\(112\) 0 0
\(113\) −6.90767 −0.649819 −0.324910 0.945745i \(-0.605334\pi\)
−0.324910 + 0.945745i \(0.605334\pi\)
\(114\) 0 0
\(115\) 0.314922 0.0293666
\(116\) 0 0
\(117\) −1.83678 −0.169810
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.2776 −0.934331
\(122\) 0 0
\(123\) −0.476040 −0.0429231
\(124\) 0 0
\(125\) 11.4510 1.02420
\(126\) 0 0
\(127\) 4.95127 0.439354 0.219677 0.975573i \(-0.429500\pi\)
0.219677 + 0.975573i \(0.429500\pi\)
\(128\) 0 0
\(129\) −1.31899 −0.116131
\(130\) 0 0
\(131\) −8.52845 −0.745135 −0.372567 0.928005i \(-0.621522\pi\)
−0.372567 + 0.928005i \(0.621522\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 5.98418 0.515037
\(136\) 0 0
\(137\) −8.32942 −0.711630 −0.355815 0.934556i \(-0.615797\pi\)
−0.355815 + 0.934556i \(0.615797\pi\)
\(138\) 0 0
\(139\) 16.0675 1.36282 0.681412 0.731900i \(-0.261366\pi\)
0.681412 + 0.731900i \(0.261366\pi\)
\(140\) 0 0
\(141\) 1.64634 0.138647
\(142\) 0 0
\(143\) −0.562890 −0.0470712
\(144\) 0 0
\(145\) 20.6085 1.71144
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.8778 1.13691 0.568456 0.822714i \(-0.307541\pi\)
0.568456 + 0.822714i \(0.307541\pi\)
\(150\) 0 0
\(151\) 1.96940 0.160267 0.0801337 0.996784i \(-0.474465\pi\)
0.0801337 + 0.996784i \(0.474465\pi\)
\(152\) 0 0
\(153\) 14.2970 1.15584
\(154\) 0 0
\(155\) −18.5220 −1.48772
\(156\) 0 0
\(157\) −0.492399 −0.0392977 −0.0196488 0.999807i \(-0.506255\pi\)
−0.0196488 + 0.999807i \(0.506255\pi\)
\(158\) 0 0
\(159\) 3.46997 0.275187
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.53172 −0.276626 −0.138313 0.990389i \(-0.544168\pi\)
−0.138313 + 0.990389i \(0.544168\pi\)
\(164\) 0 0
\(165\) 0.880951 0.0685819
\(166\) 0 0
\(167\) −10.2126 −0.790278 −0.395139 0.918621i \(-0.629304\pi\)
−0.395139 + 0.918621i \(0.629304\pi\)
\(168\) 0 0
\(169\) −12.5614 −0.966260
\(170\) 0 0
\(171\) 18.8370 1.44050
\(172\) 0 0
\(173\) 5.73071 0.435698 0.217849 0.975983i \(-0.430096\pi\)
0.217849 + 0.975983i \(0.430096\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.68464 0.352119
\(178\) 0 0
\(179\) 16.5102 1.23403 0.617016 0.786951i \(-0.288341\pi\)
0.617016 + 0.786951i \(0.288341\pi\)
\(180\) 0 0
\(181\) −12.2094 −0.907515 −0.453757 0.891125i \(-0.649917\pi\)
−0.453757 + 0.891125i \(0.649917\pi\)
\(182\) 0 0
\(183\) 4.60981 0.340767
\(184\) 0 0
\(185\) 16.8954 1.24217
\(186\) 0 0
\(187\) 4.38138 0.320398
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.93337 −0.356966 −0.178483 0.983943i \(-0.557119\pi\)
−0.178483 + 0.983943i \(0.557119\pi\)
\(192\) 0 0
\(193\) −6.12016 −0.440539 −0.220270 0.975439i \(-0.570694\pi\)
−0.220270 + 0.975439i \(0.570694\pi\)
\(194\) 0 0
\(195\) −0.686468 −0.0491590
\(196\) 0 0
\(197\) −26.6268 −1.89708 −0.948539 0.316660i \(-0.897439\pi\)
−0.948539 + 0.316660i \(0.897439\pi\)
\(198\) 0 0
\(199\) −19.5721 −1.38743 −0.693716 0.720249i \(-0.744028\pi\)
−0.693716 + 0.720249i \(0.744028\pi\)
\(200\) 0 0
\(201\) 1.40107 0.0988239
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.17736 0.152074
\(206\) 0 0
\(207\) 0.401127 0.0278803
\(208\) 0 0
\(209\) 5.77268 0.399305
\(210\) 0 0
\(211\) 20.2622 1.39490 0.697452 0.716631i \(-0.254317\pi\)
0.697452 + 0.716631i \(0.254317\pi\)
\(212\) 0 0
\(213\) 1.85102 0.126830
\(214\) 0 0
\(215\) 6.03293 0.411443
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.62711 −0.380245
\(220\) 0 0
\(221\) −3.41412 −0.229659
\(222\) 0 0
\(223\) 25.8696 1.73236 0.866180 0.499733i \(-0.166568\pi\)
0.866180 + 0.499733i \(0.166568\pi\)
\(224\) 0 0
\(225\) 0.718566 0.0479044
\(226\) 0 0
\(227\) −0.992803 −0.0658947 −0.0329473 0.999457i \(-0.510489\pi\)
−0.0329473 + 0.999457i \(0.510489\pi\)
\(228\) 0 0
\(229\) 9.34395 0.617465 0.308733 0.951149i \(-0.400095\pi\)
0.308733 + 0.951149i \(0.400095\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −25.5022 −1.67070 −0.835352 0.549715i \(-0.814736\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(234\) 0 0
\(235\) −7.53019 −0.491215
\(236\) 0 0
\(237\) 2.68046 0.174115
\(238\) 0 0
\(239\) −0.342630 −0.0221629 −0.0110815 0.999939i \(-0.503527\pi\)
−0.0110815 + 0.999939i \(0.503527\pi\)
\(240\) 0 0
\(241\) 24.2427 1.56161 0.780805 0.624774i \(-0.214809\pi\)
0.780805 + 0.624774i \(0.214809\pi\)
\(242\) 0 0
\(243\) 11.5830 0.743050
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.49828 −0.286219
\(248\) 0 0
\(249\) 4.17458 0.264553
\(250\) 0 0
\(251\) −12.3023 −0.776517 −0.388258 0.921551i \(-0.626923\pi\)
−0.388258 + 0.921551i \(0.626923\pi\)
\(252\) 0 0
\(253\) 0.122928 0.00772839
\(254\) 0 0
\(255\) 5.34328 0.334609
\(256\) 0 0
\(257\) 13.5864 0.847496 0.423748 0.905780i \(-0.360714\pi\)
0.423748 + 0.905780i \(0.360714\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 26.2498 1.62482
\(262\) 0 0
\(263\) 30.2101 1.86284 0.931419 0.363949i \(-0.118572\pi\)
0.931419 + 0.363949i \(0.118572\pi\)
\(264\) 0 0
\(265\) −15.8713 −0.974967
\(266\) 0 0
\(267\) −2.83162 −0.173292
\(268\) 0 0
\(269\) 10.7141 0.653248 0.326624 0.945154i \(-0.394089\pi\)
0.326624 + 0.945154i \(0.394089\pi\)
\(270\) 0 0
\(271\) 8.84303 0.537176 0.268588 0.963255i \(-0.413443\pi\)
0.268588 + 0.963255i \(0.413443\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.220208 0.0132791
\(276\) 0 0
\(277\) 14.2115 0.853888 0.426944 0.904278i \(-0.359590\pi\)
0.426944 + 0.904278i \(0.359590\pi\)
\(278\) 0 0
\(279\) −23.5922 −1.41243
\(280\) 0 0
\(281\) −30.8179 −1.83844 −0.919220 0.393743i \(-0.871180\pi\)
−0.919220 + 0.393743i \(0.871180\pi\)
\(282\) 0 0
\(283\) 29.1151 1.73071 0.865357 0.501156i \(-0.167092\pi\)
0.865357 + 0.501156i \(0.167092\pi\)
\(284\) 0 0
\(285\) 7.04003 0.417016
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 9.57460 0.563212
\(290\) 0 0
\(291\) 1.07541 0.0630418
\(292\) 0 0
\(293\) 10.9061 0.637142 0.318571 0.947899i \(-0.396797\pi\)
0.318571 + 0.947899i \(0.396797\pi\)
\(294\) 0 0
\(295\) −21.4271 −1.24753
\(296\) 0 0
\(297\) 2.33589 0.135542
\(298\) 0 0
\(299\) −0.0957895 −0.00553965
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0.510735 0.0293409
\(304\) 0 0
\(305\) −21.0848 −1.20731
\(306\) 0 0
\(307\) 4.34502 0.247983 0.123992 0.992283i \(-0.460430\pi\)
0.123992 + 0.992283i \(0.460430\pi\)
\(308\) 0 0
\(309\) 0.209277 0.0119054
\(310\) 0 0
\(311\) −13.0198 −0.738288 −0.369144 0.929372i \(-0.620349\pi\)
−0.369144 + 0.929372i \(0.620349\pi\)
\(312\) 0 0
\(313\) 35.0520 1.98125 0.990627 0.136595i \(-0.0436158\pi\)
0.990627 + 0.136595i \(0.0436158\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.3848 −1.36958 −0.684792 0.728738i \(-0.740107\pi\)
−0.684792 + 0.728738i \(0.740107\pi\)
\(318\) 0 0
\(319\) 8.04439 0.450399
\(320\) 0 0
\(321\) −8.92302 −0.498035
\(322\) 0 0
\(323\) 35.0134 1.94820
\(324\) 0 0
\(325\) −0.171594 −0.00951832
\(326\) 0 0
\(327\) 3.65681 0.202222
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −16.0042 −0.879671 −0.439835 0.898078i \(-0.644963\pi\)
−0.439835 + 0.898078i \(0.644963\pi\)
\(332\) 0 0
\(333\) 21.5203 1.17930
\(334\) 0 0
\(335\) −6.40836 −0.350126
\(336\) 0 0
\(337\) −2.87190 −0.156443 −0.0782213 0.996936i \(-0.524924\pi\)
−0.0782213 + 0.996936i \(0.524924\pi\)
\(338\) 0 0
\(339\) −3.28833 −0.178598
\(340\) 0 0
\(341\) −7.22994 −0.391523
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.149915 0.00807118
\(346\) 0 0
\(347\) 16.6309 0.892795 0.446397 0.894835i \(-0.352707\pi\)
0.446397 + 0.894835i \(0.352707\pi\)
\(348\) 0 0
\(349\) −13.7125 −0.734014 −0.367007 0.930218i \(-0.619618\pi\)
−0.367007 + 0.930218i \(0.619618\pi\)
\(350\) 0 0
\(351\) −1.82020 −0.0971553
\(352\) 0 0
\(353\) −23.3413 −1.24233 −0.621166 0.783679i \(-0.713341\pi\)
−0.621166 + 0.783679i \(0.713341\pi\)
\(354\) 0 0
\(355\) −8.46639 −0.449349
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.9339 −0.893737 −0.446868 0.894600i \(-0.647461\pi\)
−0.446868 + 0.894600i \(0.647461\pi\)
\(360\) 0 0
\(361\) 27.1318 1.42799
\(362\) 0 0
\(363\) −4.89257 −0.256793
\(364\) 0 0
\(365\) 25.7379 1.34718
\(366\) 0 0
\(367\) −29.4979 −1.53978 −0.769890 0.638177i \(-0.779689\pi\)
−0.769890 + 0.638177i \(0.779689\pi\)
\(368\) 0 0
\(369\) 2.77339 0.144377
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 29.5701 1.53108 0.765540 0.643389i \(-0.222472\pi\)
0.765540 + 0.643389i \(0.222472\pi\)
\(374\) 0 0
\(375\) 5.45111 0.281494
\(376\) 0 0
\(377\) −6.26847 −0.322843
\(378\) 0 0
\(379\) 35.0216 1.79894 0.899470 0.436983i \(-0.143953\pi\)
0.899470 + 0.436983i \(0.143953\pi\)
\(380\) 0 0
\(381\) 2.35700 0.120753
\(382\) 0 0
\(383\) 12.4678 0.637077 0.318538 0.947910i \(-0.396808\pi\)
0.318538 + 0.947910i \(0.396808\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.68437 0.390618
\(388\) 0 0
\(389\) −21.9851 −1.11469 −0.557345 0.830281i \(-0.688180\pi\)
−0.557345 + 0.830281i \(0.688180\pi\)
\(390\) 0 0
\(391\) 0.745599 0.0377066
\(392\) 0 0
\(393\) −4.05989 −0.204794
\(394\) 0 0
\(395\) −12.2602 −0.616877
\(396\) 0 0
\(397\) 20.1115 1.00937 0.504683 0.863304i \(-0.331609\pi\)
0.504683 + 0.863304i \(0.331609\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.2650 0.662425 0.331212 0.943556i \(-0.392542\pi\)
0.331212 + 0.943556i \(0.392542\pi\)
\(402\) 0 0
\(403\) 5.63382 0.280641
\(404\) 0 0
\(405\) −15.2673 −0.758637
\(406\) 0 0
\(407\) 6.59500 0.326902
\(408\) 0 0
\(409\) 25.6563 1.26862 0.634312 0.773077i \(-0.281283\pi\)
0.634312 + 0.773077i \(0.281283\pi\)
\(410\) 0 0
\(411\) −3.96514 −0.195586
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −19.0941 −0.937295
\(416\) 0 0
\(417\) 7.64876 0.374561
\(418\) 0 0
\(419\) 36.6937 1.79260 0.896301 0.443445i \(-0.146244\pi\)
0.896301 + 0.443445i \(0.146244\pi\)
\(420\) 0 0
\(421\) 4.48285 0.218481 0.109240 0.994015i \(-0.465158\pi\)
0.109240 + 0.994015i \(0.465158\pi\)
\(422\) 0 0
\(423\) −9.59147 −0.466353
\(424\) 0 0
\(425\) 1.33564 0.0647881
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.267958 −0.0129371
\(430\) 0 0
\(431\) 18.4278 0.887635 0.443818 0.896117i \(-0.353624\pi\)
0.443818 + 0.896117i \(0.353624\pi\)
\(432\) 0 0
\(433\) 19.7652 0.949857 0.474928 0.880024i \(-0.342474\pi\)
0.474928 + 0.880024i \(0.342474\pi\)
\(434\) 0 0
\(435\) 9.81047 0.470376
\(436\) 0 0
\(437\) 0.982364 0.0469928
\(438\) 0 0
\(439\) 14.9960 0.715719 0.357859 0.933775i \(-0.383507\pi\)
0.357859 + 0.933775i \(0.383507\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 35.5822 1.69056 0.845280 0.534323i \(-0.179433\pi\)
0.845280 + 0.534323i \(0.179433\pi\)
\(444\) 0 0
\(445\) 12.9516 0.613963
\(446\) 0 0
\(447\) 6.60638 0.312471
\(448\) 0 0
\(449\) 9.40746 0.443966 0.221983 0.975051i \(-0.428747\pi\)
0.221983 + 0.975051i \(0.428747\pi\)
\(450\) 0 0
\(451\) 0.849919 0.0400211
\(452\) 0 0
\(453\) 0.937513 0.0440482
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −30.0885 −1.40748 −0.703739 0.710458i \(-0.748488\pi\)
−0.703739 + 0.710458i \(0.748488\pi\)
\(458\) 0 0
\(459\) 14.1680 0.661304
\(460\) 0 0
\(461\) −27.7681 −1.29329 −0.646645 0.762791i \(-0.723828\pi\)
−0.646645 + 0.762791i \(0.723828\pi\)
\(462\) 0 0
\(463\) −5.94632 −0.276349 −0.138175 0.990408i \(-0.544123\pi\)
−0.138175 + 0.990408i \(0.544123\pi\)
\(464\) 0 0
\(465\) −8.81722 −0.408889
\(466\) 0 0
\(467\) 21.5875 0.998952 0.499476 0.866328i \(-0.333526\pi\)
0.499476 + 0.866328i \(0.333526\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.234402 −0.0108007
\(472\) 0 0
\(473\) 2.35491 0.108279
\(474\) 0 0
\(475\) 1.75977 0.0807439
\(476\) 0 0
\(477\) −20.2159 −0.925621
\(478\) 0 0
\(479\) −15.0166 −0.686127 −0.343063 0.939312i \(-0.611465\pi\)
−0.343063 + 0.939312i \(0.611465\pi\)
\(480\) 0 0
\(481\) −5.13905 −0.234321
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.91884 −0.223353
\(486\) 0 0
\(487\) 17.6788 0.801104 0.400552 0.916274i \(-0.368818\pi\)
0.400552 + 0.916274i \(0.368818\pi\)
\(488\) 0 0
\(489\) −1.68124 −0.0760283
\(490\) 0 0
\(491\) −10.4434 −0.471304 −0.235652 0.971837i \(-0.575723\pi\)
−0.235652 + 0.971837i \(0.575723\pi\)
\(492\) 0 0
\(493\) 48.7920 2.19748
\(494\) 0 0
\(495\) −5.13237 −0.230683
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −21.1815 −0.948213 −0.474106 0.880468i \(-0.657229\pi\)
−0.474106 + 0.880468i \(0.657229\pi\)
\(500\) 0 0
\(501\) −4.86163 −0.217202
\(502\) 0 0
\(503\) 21.2565 0.947782 0.473891 0.880584i \(-0.342849\pi\)
0.473891 + 0.880584i \(0.342849\pi\)
\(504\) 0 0
\(505\) −2.33605 −0.103953
\(506\) 0 0
\(507\) −5.97972 −0.265569
\(508\) 0 0
\(509\) 10.2697 0.455195 0.227598 0.973755i \(-0.426913\pi\)
0.227598 + 0.973755i \(0.426913\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 18.6670 0.824168
\(514\) 0 0
\(515\) −0.957213 −0.0421798
\(516\) 0 0
\(517\) −2.93936 −0.129273
\(518\) 0 0
\(519\) 2.72805 0.119748
\(520\) 0 0
\(521\) −8.72319 −0.382170 −0.191085 0.981574i \(-0.561201\pi\)
−0.191085 + 0.981574i \(0.561201\pi\)
\(522\) 0 0
\(523\) −43.6976 −1.91076 −0.955382 0.295374i \(-0.904556\pi\)
−0.955382 + 0.295374i \(0.904556\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −43.8521 −1.91023
\(528\) 0 0
\(529\) −22.9791 −0.999090
\(530\) 0 0
\(531\) −27.2924 −1.18439
\(532\) 0 0
\(533\) −0.662286 −0.0286868
\(534\) 0 0
\(535\) 40.8130 1.76450
\(536\) 0 0
\(537\) 7.85953 0.339164
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −10.2105 −0.438984 −0.219492 0.975614i \(-0.570440\pi\)
−0.219492 + 0.975614i \(0.570440\pi\)
\(542\) 0 0
\(543\) −5.81215 −0.249423
\(544\) 0 0
\(545\) −16.7259 −0.716460
\(546\) 0 0
\(547\) −24.7641 −1.05884 −0.529419 0.848361i \(-0.677590\pi\)
−0.529419 + 0.848361i \(0.677590\pi\)
\(548\) 0 0
\(549\) −26.8565 −1.14621
\(550\) 0 0
\(551\) 64.2859 2.73867
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 8.04288 0.341401
\(556\) 0 0
\(557\) −20.1450 −0.853572 −0.426786 0.904353i \(-0.640354\pi\)
−0.426786 + 0.904353i \(0.640354\pi\)
\(558\) 0 0
\(559\) −1.83503 −0.0776136
\(560\) 0 0
\(561\) 2.08571 0.0880588
\(562\) 0 0
\(563\) 16.5815 0.698828 0.349414 0.936968i \(-0.386381\pi\)
0.349414 + 0.936968i \(0.386381\pi\)
\(564\) 0 0
\(565\) 15.0405 0.632759
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15.4448 −0.647481 −0.323741 0.946146i \(-0.604941\pi\)
−0.323741 + 0.946146i \(0.604941\pi\)
\(570\) 0 0
\(571\) 28.4319 1.18984 0.594918 0.803786i \(-0.297184\pi\)
0.594918 + 0.803786i \(0.297184\pi\)
\(572\) 0 0
\(573\) −2.34848 −0.0981093
\(574\) 0 0
\(575\) 0.0374738 0.00156277
\(576\) 0 0
\(577\) −5.32206 −0.221560 −0.110780 0.993845i \(-0.535335\pi\)
−0.110780 + 0.993845i \(0.535335\pi\)
\(578\) 0 0
\(579\) −2.91344 −0.121079
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.19526 −0.256581
\(584\) 0 0
\(585\) 3.99933 0.165352
\(586\) 0 0
\(587\) −32.1095 −1.32530 −0.662650 0.748929i \(-0.730568\pi\)
−0.662650 + 0.748929i \(0.730568\pi\)
\(588\) 0 0
\(589\) −57.7774 −2.38068
\(590\) 0 0
\(591\) −12.6754 −0.521397
\(592\) 0 0
\(593\) 2.90368 0.119240 0.0596200 0.998221i \(-0.481011\pi\)
0.0596200 + 0.998221i \(0.481011\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −9.31712 −0.381324
\(598\) 0 0
\(599\) 19.0544 0.778541 0.389270 0.921124i \(-0.372727\pi\)
0.389270 + 0.921124i \(0.372727\pi\)
\(600\) 0 0
\(601\) 13.6204 0.555588 0.277794 0.960641i \(-0.410397\pi\)
0.277794 + 0.960641i \(0.410397\pi\)
\(602\) 0 0
\(603\) −8.16257 −0.332405
\(604\) 0 0
\(605\) 22.3781 0.909801
\(606\) 0 0
\(607\) −34.6925 −1.40813 −0.704063 0.710138i \(-0.748633\pi\)
−0.704063 + 0.710138i \(0.748633\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.29045 0.0926617
\(612\) 0 0
\(613\) −3.09004 −0.124805 −0.0624027 0.998051i \(-0.519876\pi\)
−0.0624027 + 0.998051i \(0.519876\pi\)
\(614\) 0 0
\(615\) 1.03651 0.0417962
\(616\) 0 0
\(617\) 32.0608 1.29072 0.645360 0.763879i \(-0.276707\pi\)
0.645360 + 0.763879i \(0.276707\pi\)
\(618\) 0 0
\(619\) 45.4105 1.82520 0.912601 0.408852i \(-0.134071\pi\)
0.912601 + 0.408852i \(0.134071\pi\)
\(620\) 0 0
\(621\) 0.397508 0.0159515
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −23.6374 −0.945496
\(626\) 0 0
\(627\) 2.74803 0.109746
\(628\) 0 0
\(629\) 40.0010 1.59494
\(630\) 0 0
\(631\) −21.8131 −0.868366 −0.434183 0.900825i \(-0.642963\pi\)
−0.434183 + 0.900825i \(0.642963\pi\)
\(632\) 0 0
\(633\) 9.64560 0.383378
\(634\) 0 0
\(635\) −10.7807 −0.427820
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −10.7839 −0.426606
\(640\) 0 0
\(641\) −5.25809 −0.207682 −0.103841 0.994594i \(-0.533113\pi\)
−0.103841 + 0.994594i \(0.533113\pi\)
\(642\) 0 0
\(643\) −22.5524 −0.889381 −0.444690 0.895684i \(-0.646686\pi\)
−0.444690 + 0.895684i \(0.646686\pi\)
\(644\) 0 0
\(645\) 2.87192 0.113082
\(646\) 0 0
\(647\) −8.47016 −0.332996 −0.166498 0.986042i \(-0.553246\pi\)
−0.166498 + 0.986042i \(0.553246\pi\)
\(648\) 0 0
\(649\) −8.36391 −0.328312
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10.8553 −0.424799 −0.212400 0.977183i \(-0.568128\pi\)
−0.212400 + 0.977183i \(0.568128\pi\)
\(654\) 0 0
\(655\) 18.5695 0.725572
\(656\) 0 0
\(657\) 32.7833 1.27900
\(658\) 0 0
\(659\) −21.6543 −0.843531 −0.421766 0.906705i \(-0.638589\pi\)
−0.421766 + 0.906705i \(0.638589\pi\)
\(660\) 0 0
\(661\) 2.39901 0.0933109 0.0466554 0.998911i \(-0.485144\pi\)
0.0466554 + 0.998911i \(0.485144\pi\)
\(662\) 0 0
\(663\) −1.62526 −0.0631199
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.36895 0.0530060
\(668\) 0 0
\(669\) 12.3150 0.476125
\(670\) 0 0
\(671\) −8.23031 −0.317728
\(672\) 0 0
\(673\) −1.83891 −0.0708846 −0.0354423 0.999372i \(-0.511284\pi\)
−0.0354423 + 0.999372i \(0.511284\pi\)
\(674\) 0 0
\(675\) 0.712083 0.0274081
\(676\) 0 0
\(677\) 22.5383 0.866219 0.433109 0.901341i \(-0.357416\pi\)
0.433109 + 0.901341i \(0.357416\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.472614 −0.0181106
\(682\) 0 0
\(683\) −29.5536 −1.13084 −0.565419 0.824803i \(-0.691286\pi\)
−0.565419 + 0.824803i \(0.691286\pi\)
\(684\) 0 0
\(685\) 18.1362 0.692947
\(686\) 0 0
\(687\) 4.44809 0.169705
\(688\) 0 0
\(689\) 4.82756 0.183916
\(690\) 0 0
\(691\) −14.0818 −0.535697 −0.267848 0.963461i \(-0.586313\pi\)
−0.267848 + 0.963461i \(0.586313\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −34.9847 −1.32704
\(696\) 0 0
\(697\) 5.15506 0.195262
\(698\) 0 0
\(699\) −12.1401 −0.459180
\(700\) 0 0
\(701\) −38.3917 −1.45003 −0.725017 0.688731i \(-0.758168\pi\)
−0.725017 + 0.688731i \(0.758168\pi\)
\(702\) 0 0
\(703\) 52.7033 1.98774
\(704\) 0 0
\(705\) −3.58467 −0.135007
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 38.3374 1.43979 0.719896 0.694081i \(-0.244189\pi\)
0.719896 + 0.694081i \(0.244189\pi\)
\(710\) 0 0
\(711\) −15.6162 −0.585655
\(712\) 0 0
\(713\) −1.23035 −0.0460771
\(714\) 0 0
\(715\) 1.22561 0.0458354
\(716\) 0 0
\(717\) −0.163106 −0.00609130
\(718\) 0 0
\(719\) 19.2051 0.716230 0.358115 0.933678i \(-0.383420\pi\)
0.358115 + 0.933678i \(0.383420\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11.5405 0.429196
\(724\) 0 0
\(725\) 2.45229 0.0910758
\(726\) 0 0
\(727\) −6.45574 −0.239430 −0.119715 0.992808i \(-0.538198\pi\)
−0.119715 + 0.992808i \(0.538198\pi\)
\(728\) 0 0
\(729\) −15.5215 −0.574870
\(730\) 0 0
\(731\) 14.2834 0.528290
\(732\) 0 0
\(733\) −44.1794 −1.63181 −0.815903 0.578189i \(-0.803759\pi\)
−0.815903 + 0.578189i \(0.803759\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.50146 −0.0921425
\(738\) 0 0
\(739\) −48.3821 −1.77976 −0.889881 0.456192i \(-0.849213\pi\)
−0.889881 + 0.456192i \(0.849213\pi\)
\(740\) 0 0
\(741\) −2.14136 −0.0786649
\(742\) 0 0
\(743\) 14.3359 0.525932 0.262966 0.964805i \(-0.415299\pi\)
0.262966 + 0.964805i \(0.415299\pi\)
\(744\) 0 0
\(745\) −30.2169 −1.10706
\(746\) 0 0
\(747\) −24.3209 −0.889855
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 43.2473 1.57812 0.789059 0.614317i \(-0.210569\pi\)
0.789059 + 0.614317i \(0.210569\pi\)
\(752\) 0 0
\(753\) −5.85641 −0.213419
\(754\) 0 0
\(755\) −4.28809 −0.156060
\(756\) 0 0
\(757\) 29.2404 1.06276 0.531380 0.847133i \(-0.321673\pi\)
0.531380 + 0.847133i \(0.321673\pi\)
\(758\) 0 0
\(759\) 0.0585185 0.00212409
\(760\) 0 0
\(761\) −19.8163 −0.718341 −0.359170 0.933272i \(-0.616940\pi\)
−0.359170 + 0.933272i \(0.616940\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −31.1297 −1.12550
\(766\) 0 0
\(767\) 6.51745 0.235332
\(768\) 0 0
\(769\) −11.3692 −0.409984 −0.204992 0.978764i \(-0.565717\pi\)
−0.204992 + 0.978764i \(0.565717\pi\)
\(770\) 0 0
\(771\) 6.46767 0.232927
\(772\) 0 0
\(773\) −28.8925 −1.03919 −0.519596 0.854412i \(-0.673917\pi\)
−0.519596 + 0.854412i \(0.673917\pi\)
\(774\) 0 0
\(775\) −2.20401 −0.0791704
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.79204 0.243350
\(780\) 0 0
\(781\) −3.30480 −0.118255
\(782\) 0 0
\(783\) 26.0130 0.929627
\(784\) 0 0
\(785\) 1.07213 0.0382660
\(786\) 0 0
\(787\) −6.69690 −0.238719 −0.119359 0.992851i \(-0.538084\pi\)
−0.119359 + 0.992851i \(0.538084\pi\)
\(788\) 0 0
\(789\) 14.3812 0.511986
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.41335 0.227745
\(794\) 0 0
\(795\) −7.55538 −0.267962
\(796\) 0 0
\(797\) 52.9987 1.87731 0.938654 0.344859i \(-0.112073\pi\)
0.938654 + 0.344859i \(0.112073\pi\)
\(798\) 0 0
\(799\) −17.8282 −0.630718
\(800\) 0 0
\(801\) 16.4969 0.582888
\(802\) 0 0
\(803\) 10.0466 0.354537
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5.10033 0.179540
\(808\) 0 0
\(809\) −3.14889 −0.110709 −0.0553545 0.998467i \(-0.517629\pi\)
−0.0553545 + 0.998467i \(0.517629\pi\)
\(810\) 0 0
\(811\) −5.67346 −0.199222 −0.0996110 0.995026i \(-0.531760\pi\)
−0.0996110 + 0.995026i \(0.531760\pi\)
\(812\) 0 0
\(813\) 4.20964 0.147638
\(814\) 0 0
\(815\) 7.68983 0.269363
\(816\) 0 0
\(817\) 18.8191 0.658396
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0738 −0.526079 −0.263039 0.964785i \(-0.584725\pi\)
−0.263039 + 0.964785i \(0.584725\pi\)
\(822\) 0 0
\(823\) 0.723286 0.0252122 0.0126061 0.999921i \(-0.495987\pi\)
0.0126061 + 0.999921i \(0.495987\pi\)
\(824\) 0 0
\(825\) 0.104828 0.00364964
\(826\) 0 0
\(827\) −52.4583 −1.82415 −0.912077 0.410019i \(-0.865522\pi\)
−0.912077 + 0.410019i \(0.865522\pi\)
\(828\) 0 0
\(829\) 11.7102 0.406713 0.203356 0.979105i \(-0.434815\pi\)
0.203356 + 0.979105i \(0.434815\pi\)
\(830\) 0 0
\(831\) 6.76526 0.234684
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 22.2366 0.769530
\(836\) 0 0
\(837\) −23.3793 −0.808107
\(838\) 0 0
\(839\) −32.7489 −1.13062 −0.565308 0.824880i \(-0.691243\pi\)
−0.565308 + 0.824880i \(0.691243\pi\)
\(840\) 0 0
\(841\) 60.5841 2.08911
\(842\) 0 0
\(843\) −14.6706 −0.505281
\(844\) 0 0
\(845\) 27.3507 0.940892
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 13.8600 0.475673
\(850\) 0 0
\(851\) 1.12230 0.0384720
\(852\) 0 0
\(853\) 50.8909 1.74247 0.871236 0.490864i \(-0.163319\pi\)
0.871236 + 0.490864i \(0.163319\pi\)
\(854\) 0 0
\(855\) −41.0149 −1.40268
\(856\) 0 0
\(857\) 23.6916 0.809290 0.404645 0.914474i \(-0.367395\pi\)
0.404645 + 0.914474i \(0.367395\pi\)
\(858\) 0 0
\(859\) −6.16836 −0.210462 −0.105231 0.994448i \(-0.533558\pi\)
−0.105231 + 0.994448i \(0.533558\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8.06291 −0.274465 −0.137232 0.990539i \(-0.543821\pi\)
−0.137232 + 0.990539i \(0.543821\pi\)
\(864\) 0 0
\(865\) −12.4778 −0.424259
\(866\) 0 0
\(867\) 4.55789 0.154794
\(868\) 0 0
\(869\) −4.78568 −0.162343
\(870\) 0 0
\(871\) 1.94923 0.0660470
\(872\) 0 0
\(873\) −6.26530 −0.212048
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 45.4028 1.53314 0.766572 0.642158i \(-0.221961\pi\)
0.766572 + 0.642158i \(0.221961\pi\)
\(878\) 0 0
\(879\) 5.19175 0.175113
\(880\) 0 0
\(881\) 11.4992 0.387418 0.193709 0.981059i \(-0.437948\pi\)
0.193709 + 0.981059i \(0.437948\pi\)
\(882\) 0 0
\(883\) 7.43213 0.250111 0.125056 0.992150i \(-0.460089\pi\)
0.125056 + 0.992150i \(0.460089\pi\)
\(884\) 0 0
\(885\) −10.2001 −0.342874
\(886\) 0 0
\(887\) −35.8611 −1.20410 −0.602050 0.798459i \(-0.705649\pi\)
−0.602050 + 0.798459i \(0.705649\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −5.95948 −0.199650
\(892\) 0 0
\(893\) −23.4896 −0.786049
\(894\) 0 0
\(895\) −35.9487 −1.20163
\(896\) 0 0
\(897\) −0.0455997 −0.00152253
\(898\) 0 0
\(899\) −80.5143 −2.68530
\(900\) 0 0
\(901\) −37.5764 −1.25185
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 26.5842 0.883689
\(906\) 0 0
\(907\) −22.5584 −0.749040 −0.374520 0.927219i \(-0.622192\pi\)
−0.374520 + 0.927219i \(0.622192\pi\)
\(908\) 0 0
\(909\) −2.97551 −0.0986916
\(910\) 0 0
\(911\) −16.4853 −0.546184 −0.273092 0.961988i \(-0.588046\pi\)
−0.273092 + 0.961988i \(0.588046\pi\)
\(912\) 0 0
\(913\) −7.45327 −0.246667
\(914\) 0 0
\(915\) −10.0372 −0.331820
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −41.4145 −1.36614 −0.683070 0.730353i \(-0.739356\pi\)
−0.683070 + 0.730353i \(0.739356\pi\)
\(920\) 0 0
\(921\) 2.06840 0.0681563
\(922\) 0 0
\(923\) 2.57521 0.0847642
\(924\) 0 0
\(925\) 2.01045 0.0661032
\(926\) 0 0
\(927\) −1.21924 −0.0400450
\(928\) 0 0
\(929\) 29.2462 0.959536 0.479768 0.877395i \(-0.340721\pi\)
0.479768 + 0.877395i \(0.340721\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −6.19797 −0.202912
\(934\) 0 0
\(935\) −9.53985 −0.311986
\(936\) 0 0
\(937\) 32.6481 1.06657 0.533283 0.845937i \(-0.320958\pi\)
0.533283 + 0.845937i \(0.320958\pi\)
\(938\) 0 0
\(939\) 16.6861 0.544532
\(940\) 0 0
\(941\) −8.83688 −0.288074 −0.144037 0.989572i \(-0.546008\pi\)
−0.144037 + 0.989572i \(0.546008\pi\)
\(942\) 0 0
\(943\) 0.144635 0.00470995
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 47.5368 1.54474 0.772369 0.635174i \(-0.219072\pi\)
0.772369 + 0.635174i \(0.219072\pi\)
\(948\) 0 0
\(949\) −7.82867 −0.254129
\(950\) 0 0
\(951\) −11.6081 −0.376419
\(952\) 0 0
\(953\) 17.7811 0.575985 0.287992 0.957633i \(-0.407012\pi\)
0.287992 + 0.957633i \(0.407012\pi\)
\(954\) 0 0
\(955\) 10.7417 0.347594
\(956\) 0 0
\(957\) 3.82945 0.123789
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 41.3627 1.33428
\(962\) 0 0
\(963\) 51.9851 1.67520
\(964\) 0 0
\(965\) 13.3258 0.428973
\(966\) 0 0
\(967\) 28.2771 0.909329 0.454665 0.890663i \(-0.349759\pi\)
0.454665 + 0.890663i \(0.349759\pi\)
\(968\) 0 0
\(969\) 16.6678 0.535446
\(970\) 0 0
\(971\) −22.4810 −0.721451 −0.360725 0.932672i \(-0.617471\pi\)
−0.360725 + 0.932672i \(0.617471\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −0.0816856 −0.00261603
\(976\) 0 0
\(977\) 29.1987 0.934150 0.467075 0.884218i \(-0.345308\pi\)
0.467075 + 0.884218i \(0.345308\pi\)
\(978\) 0 0
\(979\) 5.05555 0.161576
\(980\) 0 0
\(981\) −21.3044 −0.680198
\(982\) 0 0
\(983\) −21.7693 −0.694333 −0.347167 0.937803i \(-0.612856\pi\)
−0.347167 + 0.937803i \(0.612856\pi\)
\(984\) 0 0
\(985\) 57.9761 1.84727
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.400746 0.0127430
\(990\) 0 0
\(991\) 35.6120 1.13125 0.565626 0.824662i \(-0.308635\pi\)
0.565626 + 0.824662i \(0.308635\pi\)
\(992\) 0 0
\(993\) −7.61865 −0.241771
\(994\) 0 0
\(995\) 42.6156 1.35101
\(996\) 0 0
\(997\) 16.6525 0.527389 0.263695 0.964606i \(-0.415059\pi\)
0.263695 + 0.964606i \(0.415059\pi\)
\(998\) 0 0
\(999\) 21.3261 0.674728
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 \(a_p\))